LMFDB - Embedded newform 162.5.f.a.17.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,5,Mod(17,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([11]))

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

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

chi := DirichletCharacter("162.17");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	162.f (of order $18$, degree $6$, 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:	$16.7459340196$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			17.5
Character	$\chi$	$=$	162.17
Dual form			162.5.f.a.143.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.967379 + 2.65785i) q^{2} +(-6.12836 - 5.14230i) q^{4} +(-31.9962 - 5.64180i) q^{5} +(29.5375 - 24.7849i) q^{7} +(19.5959 - 11.3137i) q^{8} +O(q^{10})$	\(q+(-0.967379 + 2.65785i) q^{2} +(-6.12836 - 5.14230i) q^{4} +(-31.9962 - 5.64180i) q^{5} +(29.5375 - 24.7849i) q^{7} +(19.5959 - 11.3137i) q^{8} +(45.9475 - 79.5835i) q^{10} +(100.119 - 17.6536i) q^{11} +(-92.7403 + 33.7547i) q^{13} +(37.3007 + 102.483i) q^{14} +(11.1135 + 63.0277i) q^{16} +(-11.2824 - 6.51388i) q^{17} +(251.659 + 435.887i) q^{19} +(167.072 + 199.109i) q^{20} +(-49.9319 + 283.178i) q^{22} +(-639.359 + 761.959i) q^{23} +(404.620 + 147.270i) q^{25} -279.144i q^{26} -308.468 q^{28} +(294.140 - 808.143i) q^{29} +(1260.51 + 1057.69i) q^{31} +(-178.269 - 31.4337i) q^{32} +(28.2272 - 23.6855i) q^{34} +(-1084.92 + 626.379i) q^{35} +(-127.234 + 220.376i) q^{37} +(-1401.97 + 247.206i) q^{38} +(-690.825 + 251.440i) q^{40} +(-234.109 - 643.209i) q^{41} +(226.317 + 1283.51i) q^{43} +(-704.342 - 406.652i) q^{44} +(-1406.67 - 2436.43i) q^{46} +(1990.75 + 2372.48i) q^{47} +(-158.756 + 900.352i) q^{49} +(-782.842 + 932.955i) q^{50} +(741.923 + 270.038i) q^{52} +3437.21i q^{53} -3303.01 q^{55} +(298.406 - 819.862i) q^{56} +(1863.38 + 1563.56i) q^{58} +(-198.971 - 35.0840i) q^{59} +(-2407.40 + 2020.05i) q^{61} +(-4030.58 + 2327.05i) q^{62} +(256.000 - 443.405i) q^{64} +(3157.78 - 556.801i) q^{65} +(4391.05 - 1598.21i) q^{67} +(35.6460 + 97.9367i) q^{68} +(-615.294 - 3489.51i) q^{70} +(1071.36 + 618.551i) q^{71} +(-2791.61 - 4835.21i) q^{73} +(-462.644 - 551.357i) q^{74} +(699.203 - 3965.38i) q^{76} +(2519.71 - 3002.88i) q^{77} +(7740.77 + 2817.41i) q^{79} -2079.35i q^{80} +1936.03 q^{82} +(4356.02 - 11968.1i) q^{83} +(324.243 + 272.072i) q^{85} +(-3630.30 - 640.120i) q^{86} +(1762.19 - 1478.65i) q^{88} +(6291.23 - 3632.24i) q^{89} +(-1902.71 + 3295.59i) q^{91} +(7836.44 - 1381.78i) q^{92} +(-8231.50 + 2996.02i) q^{94} +(-5592.97 - 15366.5i) q^{95} +(-1520.39 - 8622.59i) q^{97} +(-2239.43 - 1292.93i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 18 q^{5}+O(q^{10}) $ 72 * q + 18 * q^5	$ 72 q + 18 q^{5} - 720 q^{11} + 288 q^{14} - 288 q^{20} - 1008 q^{22} - 4716 q^{23} - 882 q^{25} + 6084 q^{29} + 3330 q^{31} + 288 q^{34} - 5346 q^{35} - 576 q^{38} + 13356 q^{41} + 1260 q^{43} - 16578 q^{47} - 5904 q^{49} - 15552 q^{50} + 2304 q^{56} + 40104 q^{59} + 8352 q^{61} + 18432 q^{64} + 19674 q^{65} - 24192 q^{67} - 10224 q^{68} + 14400 q^{70} - 39528 q^{71} - 12222 q^{73} - 33120 q^{74} + 9792 q^{76} - 28206 q^{77} + 11304 q^{79} + 30078 q^{83} - 52200 q^{85} + 46224 q^{86} - 16128 q^{88} + 102222 q^{89} + 12078 q^{91} + 27504 q^{92} + 4032 q^{94} - 46728 q^{95} + 49680 q^{97} - 82944 q^{98}+O(q^{100}) $ 72 * q + 18 * q^5 - 720 * q^11 + 288 * q^14 - 288 * q^20 - 1008 * q^22 - 4716 * q^23 - 882 * q^25 + 6084 * q^29 + 3330 * q^31 + 288 * q^34 - 5346 * q^35 - 576 * q^38 + 13356 * q^41 + 1260 * q^43 - 16578 * q^47 - 5904 * q^49 - 15552 * q^50 + 2304 * q^56 + 40104 * q^59 + 8352 * q^61 + 18432 * q^64 + 19674 * q^65 - 24192 * q^67 - 10224 * q^68 + 14400 * q^70 - 39528 * q^71 - 12222 * q^73 - 33120 * q^74 + 9792 * q^76 - 28206 * q^77 + 11304 * q^79 + 30078 * q^83 - 52200 * q^85 + 46224 * q^86 - 16128 * q^88 + 102222 * q^89 + 12078 * q^91 + 27504 * q^92 + 4032 * q^94 - 46728 * q^95 + 49680 * q^97 - 82944 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{11}{18}\right)$

Coefficient data

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

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

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

$2$	−0.967379	+	2.65785i	−0.241845	+	0.664463i
$2$	−0.967379	+	2.65785i	−0.241845	+	0.664463i
$3$		0			0
$3$		0			0
$4$	−6.12836	−	5.14230i	−0.383022	−	0.321394i
$5$	−31.9962	−	5.64180i	−1.27985	−	0.225672i	−0.507933	−	0.861397i	$-0.669590\pi$
$5$	−31.9962	−	5.64180i	−1.27985	−	0.225672i	−0.771916	+	0.635725i	$0.780701\pi$
$6$		0			0
$7$	29.5375	−	24.7849i	0.602807	−	0.505815i	−0.289540	−	0.957166i	$-0.593502\pi$
$7$	29.5375	−	24.7849i	0.602807	−	0.505815i	0.892346	+	0.451351i	$0.149058\pi$
$8$	19.5959	−	11.3137i	0.306186	−	0.176777i
$9$		0			0
$10$	45.9475	−	79.5835i	0.459475	−	0.795835i
$11$	100.119	−	17.6536i	0.827426	−	0.145898i	0.256131	−	0.966642i	$-0.417552\pi$
$11$	100.119	−	17.6536i	0.827426	−	0.145898i	0.571295	+	0.820745i	$0.306441\pi$
$12$		0			0
$13$	−92.7403	+	33.7547i	−0.548759	+	0.199732i	−0.601495	−	0.798876i	$-0.705428\pi$
$13$	−92.7403	+	33.7547i	−0.548759	+	0.199732i	0.0527358	+	0.998608i	$0.483206\pi$
$14$	37.3007	+	102.483i	0.190310	+	0.522871i
$15$		0			0
$16$	11.1135	+	63.0277i	0.0434120	+	0.246202i
$17$	−11.2824	−	6.51388i	−0.0390393	−	0.0225394i	0.480353	−	0.877075i	$-0.340508\pi$
$17$	−11.2824	−	6.51388i	−0.0390393	−	0.0225394i	−0.519393	+	0.854536i	$0.673842\pi$
$18$		0			0
$19$	251.659	+	435.887i	0.697118	+	1.20744i	0.969462	+	0.245243i	$0.0788678\pi$
$19$	251.659	+	435.887i	0.697118	+	1.20744i	−0.272344	+	0.962200i	$0.587799\pi$
$20$	167.072	+	199.109i	0.417681	+	0.497773i
$21$		0			0
$22$	−49.9319	+	283.178i	−0.103165	+	0.585079i
$23$	−639.359	+	761.959i	−1.20862	+	1.44038i	−0.343247	+	0.939245i	$0.611527\pi$
$23$	−639.359	+	761.959i	−1.20862	+	1.44038i	−0.865372	+	0.501130i	$0.832918\pi$
$24$		0			0
$25$	404.620	+	147.270i	0.647392	+	0.235632i
$26$		−	279.144i		−	0.412934i
$27$		0			0
$28$	−308.468			−0.393454
$29$	294.140	−	808.143i	0.349750	−	0.960931i	−0.632698	−	0.774398i	$-0.718053\pi$
$29$	294.140	−	808.143i	0.349750	−	0.960931i	0.982449	−	0.186533i	$-0.0597251\pi$
$30$		0			0
$31$	1260.51	+	1057.69i	1.31166	+	1.10062i	0.988002	+	0.154442i	$0.0493579\pi$
$31$	1260.51	+	1057.69i	1.31166	+	1.10062i	0.323660	+	0.946173i	$0.395087\pi$
$32$	−178.269	−	31.4337i	−0.174091	−	0.0306970i
$33$		0			0
$34$	28.2272	−	23.6855i	0.0244180	−	0.0204892i
$35$	−1084.92	+	626.379i	−0.885650	+	0.511330i
$36$		0			0
$37$	−127.234	+	220.376i	−0.0929396	+	0.160976i	−0.908747	−	0.417348i	$-0.862960\pi$
$37$	−127.234	+	220.376i	−0.0929396	+	0.160976i	0.815807	+	0.578324i	$0.196293\pi$
$38$	−1401.97	+	247.206i	−0.970896	+	0.171195i
$39$		0			0
$40$	−690.825	+	251.440i	−0.431766	+	0.157150i
$41$	−234.109	−	643.209i	−0.139268	−	0.382635i	0.850377	−	0.526174i	$-0.176374\pi$
$41$	−234.109	−	643.209i	−0.139268	−	0.382635i	−0.989645	+	0.143539i	$0.954152\pi$
$42$		0			0
$43$	226.317	+	1283.51i	0.122399	+	0.694162i	0.982818	+	0.184575i	$0.0590908\pi$
$43$	226.317	+	1283.51i	0.122399	+	0.694162i	−0.860419	+	0.509587i	$0.829798\pi$
$44$	−704.342	−	406.652i	−0.363813	−	0.210048i
$45$		0			0
$46$	−1406.67	−	2436.43i	−0.664778	−	1.15143i
$47$	1990.75	+	2372.48i	0.901198	+	1.07401i	0.996907	+	0.0785960i	$0.0250437\pi$
$47$	1990.75	+	2372.48i	0.901198	+	1.07401i	−0.0957090	+	0.995409i	$0.530512\pi$
$48$		0			0
$49$	−158.756	+	900.352i	−0.0661209	+	0.374990i
$50$	−782.842	+	932.955i	−0.313137	+	0.373182i
$51$		0			0
$52$	741.923	+	270.038i	0.274380	+	0.0998660i
$53$			3437.21i			1.22364i	0.790996	+	0.611821i	$0.209563\pi$
$53$			3437.21i			1.22364i	−0.790996	+	0.611821i	$0.790437\pi$
$54$		0			0
$55$	−3303.01			−1.09191
$56$	298.406	−	819.862i	0.0951548	−	0.261436i
$57$		0			0
$58$	1863.38	+	1563.56i	0.553918	+	0.464792i
$59$	−198.971	−	35.0840i	−0.0571593	−	0.0100787i	0.144995	−	0.989432i	$-0.453683\pi$
$59$	−198.971	−	35.0840i	−0.0571593	−	0.0100787i	−0.202155	+	0.979354i	$0.564794\pi$
$60$		0			0
$61$	−2407.40	+	2020.05i	−0.646976	+	0.542878i	−0.906152	−	0.422953i	$-0.860994\pi$
$61$	−2407.40	+	2020.05i	−0.646976	+	0.542878i	0.259176	+	0.965830i	$0.416549\pi$
$62$	−4030.58	+	2327.05i	−1.04854	+	0.605373i
$63$		0			0
$64$	256.000	−	443.405i	0.0625000	−	0.108253i
$65$	3157.78	−	556.801i	0.747403	−	0.131787i
$66$		0			0
$67$	4391.05	−	1598.21i	0.978180	−	0.356028i	0.197048	−	0.980394i	$-0.436865\pi$
$67$	4391.05	−	1598.21i	0.978180	−	0.356028i	0.781132	+	0.624366i	$0.214642\pi$
$68$	35.6460	+	97.9367i	0.00770892	+	0.0211801i
$69$		0			0
$70$	−615.294	−	3489.51i	−0.125570	−	0.712144i
$71$	1071.36	+	618.551i	0.212530	+	0.122704i	0.602487	−	0.798129i	$-0.294177\pi$
$71$	1071.36	+	618.551i	0.212530	+	0.122704i	−0.389957	+	0.920833i	$0.627510\pi$
$72$		0			0
$73$	−2791.61	−	4835.21i	−0.523853	−	0.907340i	−0.999614	−	0.0277654i	$-0.991161\pi$
$73$	−2791.61	−	4835.21i	−0.523853	−	0.907340i	0.475762	−	0.879574i	$-0.342172\pi$
$74$	−462.644	−	551.357i	−0.0844857	−	0.100686i
$75$		0			0
$76$	699.203	−	3965.38i	0.121053	−	0.686527i
$77$	2519.71	−	3002.88i	0.424981	−	0.506473i
$78$		0			0
$79$	7740.77	+	2817.41i	1.24031	+	0.451435i	0.877116	−	0.480279i	$-0.159464\pi$
$79$	7740.77	+	2817.41i	1.24031	+	0.451435i	0.363193	+	0.931714i	$0.381687\pi$
$80$		−	2079.35i		−	0.324898i
$81$		0			0
$82$	1936.03			0.287928
$83$	4356.02	−	11968.1i	0.632315	−	1.73727i	−0.0423051	−	0.999105i	$-0.513470\pi$
$83$	4356.02	−	11968.1i	0.632315	−	1.73727i	0.674620	−	0.738165i	$-0.264308\pi$
$84$		0			0
$85$	324.243	+	272.072i	0.0448779	+	0.0376571i
$86$	−3630.30	−	640.120i	−0.490847	−	0.0865495i
$87$		0			0
$88$	1762.19	−	1478.65i	0.227555	−	0.190942i
$89$	6291.23	−	3632.24i	0.794246	−	0.458558i	−0.0472090	−	0.998885i	$-0.515033\pi$
$89$	6291.23	−	3632.24i	0.794246	−	0.458558i	0.841455	+	0.540327i	$0.181699\pi$
$90$		0			0
$91$	−1902.71	+	3295.59i	−0.229768	+	0.397971i
$92$	7836.44	−	1381.78i	0.925856	−	0.163253i
$93$		0			0
$94$	−8231.50	+	2996.02i	−0.931587	+	0.339070i
$95$	−5592.97	−	15366.5i	−0.619719	−	1.70266i
$96$		0			0
$97$	−1520.39	−	8622.59i	−0.161589	−	0.916419i	−0.952512	−	0.304502i	$-0.901510\pi$
$97$	−1520.39	−	8622.59i	−0.161589	−	0.916419i	0.790922	−	0.611917i	$-0.209601\pi$
$98$	−2239.43	−	1292.93i	−0.233176	−	0.134624i
$99$		0			0
$100$	−1722.35	−	2983.20i	−0.172235	−	0.298320i
$101$	10645.0	+	12686.2i	1.04353	+	1.24363i	0.969169	+	0.246395i	$0.0792461\pi$
$101$	10645.0	+	12686.2i	1.04353	+	1.24363i	0.0743573	+	0.997232i	$0.476309\pi$
$102$		0			0
$103$	−3440.16	+	19510.1i	−0.324269	+	1.83902i	0.190498	+	0.981688i	$0.438990\pi$
$103$	−3440.16	+	19510.1i	−0.324269	+	1.83902i	−0.514766	+	0.857331i	$0.672121\pi$
$104$	−1435.44	+	1710.69i	−0.132715	+	0.158163i
$105$		0			0
$106$	−9135.60	−	3325.08i	−0.813065	−	0.295931i
$107$			5886.64i			0.514162i	0.966390	+	0.257081i	$0.0827608\pi$
$107$			5886.64i			0.514162i	−0.966390	+	0.257081i	$0.917239\pi$
$108$		0			0
$109$	−2105.48			−0.177214			−0.0886069	−	0.996067i	$-0.528241\pi$
$109$	−2105.48			−0.177214			−0.0886069	+	0.996067i	$0.528241\pi$
$110$	3195.27	−	8778.92i	0.264072	−	0.725531i
$111$		0			0
$112$	1890.40	+	1586.24i	0.150702	+	0.126454i
$113$	1374.39	+	242.343i	0.107635	+	0.0189790i	0.227206	−	0.973847i	$-0.427041\pi$
$113$	1374.39	+	242.343i	0.107635	+	0.0189790i	−0.119571	+	0.992826i	$0.538152\pi$
$114$		0			0
$115$	24755.9	−	20772.7i	1.87190	−	1.57071i
$116$	−5958.31	+	3440.03i	−0.442799	+	0.255650i
$117$		0			0
$118$	285.729	−	494.897i	0.0205206	−	0.0355427i
$119$	−494.699	+	87.2288i	−0.0349339	+	0.00615979i
$120$		0			0
$121$	−4045.96	+	1472.61i	−0.276345	+	0.100581i
$122$	−3040.12	−	8352.66i	−0.204254	−	0.561184i
$123$		0			0
$124$	−2285.87	−	12963.8i	−0.148665	−	0.843120i
$125$	5470.17	+	3158.21i	0.350091	+	0.202125i
$126$		0			0
$127$	−14460.9	−	25047.0i	−0.896578	−	1.55292i	−0.831840	−	0.555016i	$-0.812712\pi$
$127$	−14460.9	−	25047.0i	−0.896578	−	1.55292i	−0.0647382	−	0.997902i	$-0.520621\pi$
$128$	930.856	+	1109.35i	0.0568149	+	0.0677094i
$129$		0			0
$130$	−1574.87	+	8931.54i	−0.0931877	+	0.528494i
$131$	−6549.68	+	7805.61i	−0.381661	+	0.454846i	−0.922338	−	0.386385i	$-0.873724\pi$
$131$	−6549.68	+	7805.61i	−0.381661	+	0.454846i	0.540677	+	0.841230i	$0.318168\pi$
$132$		0			0
$133$	18236.8	+	6637.66i	1.03097	+	0.375242i
$134$			13216.8i			0.736068i
$135$		0			0
$136$	−294.784			−0.0159377
$137$	−9936.57	+	27300.5i	−0.529414	+	1.45455i	0.330349	+	0.943859i	$0.392834\pi$
$137$	−9936.57	+	27300.5i	−0.529414	+	1.45455i	−0.859763	+	0.510694i	$0.829389\pi$
$138$		0			0
$139$	−16498.3	−	13843.7i	−0.853906	−	0.716512i	0.106740	−	0.994287i	$-0.465959\pi$
$139$	−16498.3	−	13843.7i	−0.853906	−	0.716512i	−0.960646	+	0.277775i	$0.910403\pi$
$140$	9869.81	+	1740.31i	0.503562	+	0.0887915i
$141$		0			0
$142$	−2680.43	+	2249.15i	−0.132932	+	0.111543i
$143$	−8689.14	+	5016.68i	−0.424917	+	0.245326i
$144$		0			0
$145$	−13970.7	+	24198.0i	−0.664483	+	1.15092i
$146$	15551.8	−	2742.21i	0.729585	−	0.128645i
$147$		0			0
$148$	1912.98	−	696.267i	0.0873346	−	0.0317872i
$149$	−11854.8	−	32570.9i	−0.533977	−	1.46709i	−0.854299	−	0.519782i	$-0.826013\pi$
$149$	−11854.8	−	32570.9i	−0.533977	−	1.46709i	0.320321	−	0.947309i	$-0.396209\pi$
$150$		0			0
$151$	1792.71	+	10167.0i	0.0786242	+	0.445900i	0.998551	+	0.0538101i	$0.0171366\pi$
$151$	1792.71	+	10167.0i	0.0786242	+	0.445900i	−0.919927	+	0.392090i	$0.871752\pi$
$152$	9863.00	+	5694.40i	0.426896	+	0.246468i
$153$		0			0
$154$	5543.68	+	9601.94i	0.233753	+	0.404872i
$155$	−34364.2	−	40953.6i	−1.43035	−	1.70463i
$156$		0			0
$157$	−500.106	+	2836.24i	−0.0202891	+	0.115065i	−0.993270	−	0.115819i	$-0.963051\pi$
$157$	−500.106	+	2836.24i	−0.0202891	+	0.115065i	0.972981	+	0.230884i	$0.0741619\pi$
$158$	−14976.5	+	17848.3i	−0.599924	+	0.714962i
$159$		0			0
$160$	5526.60	+	2011.52i	0.215883	+	0.0785749i
$161$			38352.9i			1.47961i
$162$		0			0
$163$	−12175.7			−0.458267			−0.229133	−	0.973395i	$-0.573589\pi$
$163$	−12175.7			−0.458267			−0.229133	+	0.973395i	$0.573589\pi$
$164$	−1872.87	+	5145.67i	−0.0696339	+	0.191317i
$165$		0			0
$166$	27595.4	+	23155.3i	1.00143	+	0.840299i
$167$	−6591.63	−	1162.28i	−0.236353	−	0.0416753i	0.0542171	−	0.998529i	$-0.482734\pi$
$167$	−6591.63	−	1162.28i	−0.236353	−	0.0416753i	−0.290570	+	0.956854i	$0.593845\pi$
$168$		0			0
$169$	−14417.6	+	12097.8i	−0.504801	+	0.423578i
$170$	−1036.79	+	598.593i	−0.0358752	+	0.0207126i
$171$		0			0
$172$	5213.22	−	9029.57i	0.176218	−	0.305218i
$173$	−4022.97	+	709.359i	−0.134417	+	0.0237014i	−0.240452	−	0.970661i	$-0.577296\pi$
$173$	−4022.97	+	709.359i	−0.134417	+	0.0237014i	0.106035	+	0.994362i	$0.466185\pi$
$174$		0			0
$175$	15601.6	−	5678.50i	0.509438	−	0.185420i
$176$	2225.33	+	6114.05i	0.0718405	+	0.197380i
$177$		0			0
$178$	3567.96	+	20234.9i	0.112611	+	0.638647i
$179$	25591.0	+	14775.0i	0.798696	+	0.461127i	0.843015	−	0.537890i	$-0.180778\pi$
$179$	25591.0	+	14775.0i	0.798696	+	0.461127i	−0.0443190	+	0.999017i	$0.514112\pi$
$180$		0			0
$181$	9832.69	+	17030.7i	0.300134	+	0.519847i	0.976166	−	0.217025i	$-0.0696353\pi$
$181$	9832.69	+	17030.7i	0.300134	+	0.519847i	−0.676032	+	0.736872i	$0.736302\pi$
$182$	−6918.56	−	8245.22i	−0.208868	−	0.248920i
$183$		0			0
$184$	−3908.25	+	22164.8i	−0.115438	+	0.654679i
$185$	5314.33	−	6333.38i	0.155276	−	0.185051i
$186$		0			0
$187$	−1244.57	−	452.986i	−0.0355906	−	0.0129539i
$188$		−	24776.4i		−	0.701007i
$189$		0			0
$190$	46252.5			1.28123
$191$	−13377.1	+	36753.3i	−0.366687	+	1.00747i	0.609925	+	0.792459i	$0.291199\pi$
$191$	−13377.1	+	36753.3i	−0.366687	+	1.00747i	−0.976613	+	0.215006i	$0.931023\pi$
$192$		0			0
$193$	529.356	+	444.183i	0.0142113	+	0.0119247i	0.649866	−	0.760049i	$-0.274825\pi$
$193$	529.356	+	444.183i	0.0142113	+	0.0119247i	−0.635654	+	0.771974i	$0.719270\pi$
$194$	24388.4	+	4300.33i	0.648006	+	0.114261i
$195$		0			0
$196$	5602.80	−	4701.30i	0.145845	−	0.122379i
$197$	−10816.0	+	6244.64i	−0.278699	+	0.160907i	−0.632834	−	0.774287i	$-0.718109\pi$
$197$	−10816.0	+	6244.64i	−0.278699	+	0.160907i	0.354135	+	0.935194i	$0.384775\pi$
$198$		0			0
$199$	−20203.1	+	34992.8i	−0.510166	+	0.883634i	0.489764	+	0.871855i	$0.337083\pi$
$199$	−20203.1	+	34992.8i	−0.510166	+	0.883634i	−0.999931	+	0.0117791i	$0.996251\pi$
$200$	9595.07	−	1691.87i	0.239877	−	0.0422967i
$201$		0			0
$202$	−44015.9	+	16020.5i	−1.07872	+	0.392620i
$203$	−11341.6	−	31160.8i	−0.275221	−	0.756165i
$204$		0			0
$205$	3861.75	+	21901.1i	0.0918917	+	0.521144i
$206$	−48527.1	−	28017.2i	−1.14354	−	0.660221i
$207$		0			0
$208$	−3158.15	−	5470.08i	−0.0729972	−	0.126435i
$209$	32890.8	+	39197.7i	0.752976	+	0.897362i
$210$		0			0
$211$	10855.3	−	61563.7i	0.243825	−	1.38280i	−0.579381	−	0.815057i	$-0.696705\pi$
$211$	10855.3	−	61563.7i	0.243825	−	1.38280i	0.823206	−	0.567743i	$-0.192183\pi$
$212$	17675.2	−	21064.4i	0.393271	−	0.468682i
$213$		0			0
$214$	−15645.8	−	5694.62i	−0.341642	−	0.124347i
$215$		−	42344.2i		−	0.916045i
$216$		0			0
$217$	63447.1			1.34739
$218$	2036.79	−	5596.04i	0.0428582	−	0.117752i
$219$		0			0
$220$	20242.0	+	16985.1i	0.418224	+	0.350932i
$221$	1266.20	+	223.266i	0.0259250	+	0.00457128i
$222$		0			0
$223$	14844.5	−	12456.0i	0.298509	−	0.250479i	−0.481215	−	0.876603i	$-0.659804\pi$
$223$	14844.5	−	12456.0i	0.298509	−	0.250479i	0.779723	+	0.626124i	$0.215360\pi$
$224$	−6044.71	+	3489.92i	−0.120470	+	0.0695535i
$225$		0			0
$226$	−1973.67	+	3418.50i	−0.0386418	+	0.0669296i
$227$	−28246.3	+	4980.58i	−0.548162	+	0.0966558i	−0.440869	−	0.897572i	$-0.645330\pi$
$227$	−28246.3	+	4980.58i	−0.548162	+	0.0966558i	−0.107294	+	0.994227i	$0.534218\pi$
$228$		0			0
$229$	34131.4	−	12422.8i	0.650853	−	0.236891i	0.00457066	−	0.999990i	$-0.498545\pi$
$229$	34131.4	−	12422.8i	0.650853	−	0.236891i	0.646282	+	0.763098i	$0.276323\pi$
$230$	31262.3	+	85892.5i	0.590970	+	1.62368i
$231$		0			0
$232$	−3379.15	−	19164.1i	−0.0627815	−	0.356052i
$233$	−3648.88	−	2106.68i	−0.0672121	−	0.0388049i	0.466017	−	0.884776i	$-0.345688\pi$
$233$	−3648.88	−	2106.68i	−0.0672121	−	0.0388049i	−0.533229	+	0.845971i	$0.679022\pi$
$234$		0			0
$235$	−50311.3	−	87141.7i	−0.911024	−	1.57794i
$236$	1038.96	+	1238.18i	0.0186540	+	0.0222310i
$237$		0			0
$238$	246.720	−	1399.22i	0.00435563	−	0.0247020i
$239$	−47471.3	+	56574.1i	−0.831065	+	0.990425i	0.168923	+	0.985629i	$0.445971\pi$
$239$	−47471.3	+	56574.1i	−0.831065	+	0.990425i	−0.999988	+	0.00479587i	$0.998473\pi$
$240$		0			0
$241$	−56996.6	−	20745.1i	−0.981329	−	0.357175i	−0.198972	−	0.980005i	$-0.563760\pi$
$241$	−56996.6	−	20745.1i	−0.981329	−	0.357175i	−0.782357	+	0.622831i	$0.785983\pi$
$242$		−	12178.1i		−	0.207946i
$243$		0			0
$244$	25141.1			0.422284
$245$	10159.2	−	27912.2i	0.169250	−	0.465009i
$246$		0			0
$247$	−38052.2	−	31929.6i	−0.623715	−	0.523359i
$248$	36667.2	+	6465.42i	0.596176	+	0.105122i
$249$		0			0
$250$	−13685.8	+	11483.7i	−0.218972	+	0.183740i
$251$	41853.1	−	24163.9i	0.664325	−	0.383548i	−0.129598	−	0.991567i	$-0.541369\pi$
$251$	41853.1	−	24163.9i	0.664325	−	0.383548i	0.793923	+	0.608019i	$0.208035\pi$
$252$		0			0
$253$	−50560.4	+	87573.2i	−0.789895	+	1.36814i
$254$	80560.4	−	14205.0i	1.24869	−	0.220178i
$255$		0			0
$256$	−3848.98	+	1400.91i	−0.0587308	+	0.0213763i
$257$	9028.66	+	24806.0i	0.136696	+	0.375570i	0.989086	−	0.147336i	$-0.0470699\pi$
$257$	9028.66	+	24806.0i	0.136696	+	0.375570i	−0.852390	+	0.522907i	$0.824848\pi$
$258$		0			0
$259$	1703.82	+	9662.86i	0.0253995	+	0.144048i
$260$	−22215.2	−	12826.0i	−0.328628	−	0.189733i
$261$		0			0
$262$	−14410.1	−	24959.1i	−0.209926	−	0.363602i
$263$	−337.403	−	402.102i	−0.00487796	−	0.00581332i	0.763600	−	0.645690i	$-0.223430\pi$
$263$	−337.403	−	402.102i	−0.00487796	−	0.00581332i	−0.768478	+	0.639876i	$0.778986\pi$
$264$		0			0
$265$	19392.0	−	109978.i	0.276142	−	1.56608i
$266$	−35283.8	+	42049.7i	−0.498669	+	0.594291i
$267$		0			0
$268$	−35128.4	−	12785.7i	−0.489090	−	0.178014i
$269$		−	106527.i		−	1.47217i	−0.676892	−	0.736083i	$-0.736674\pi$
$269$		−	106527.i		−	1.47217i	0.676892	−	0.736083i	$-0.263326\pi$
$270$		0			0
$271$	96344.4			1.31186			0.655931	−	0.754821i	$-0.272276\pi$
$271$	96344.4			1.31186			0.655931	+	0.754821i	$0.272276\pi$
$272$	285.168	−	783.493i	0.00385446	−	0.0105900i
$273$		0			0
$274$	−62948.3	−	52819.9i	−0.838461	−	0.703552i
$275$	43109.8	+	7601.43i	0.570048	+	0.100515i
$276$		0			0
$277$	−81279.9	+	68201.9i	−1.05931	+	0.888868i	−0.994042	−	0.109000i	$-0.965235\pi$
$277$	−81279.9	+	68201.9i	−1.05931	+	0.888868i	−0.0652697	+	0.997868i	$0.520791\pi$
$278$	52754.7	−	30457.9i	0.682609	−	0.394104i
$279$		0			0
$280$	−14173.3	+	24549.0i	−0.180782	+	0.313124i
$281$	−138492.	+	24419.8i	−1.75392	+	0.309264i	−0.955972	−	0.293457i	$-0.905194\pi$
$281$	−138492.	+	24419.8i	−1.75392	+	0.309264i	−0.797952	+	0.602721i	$0.794083\pi$
$282$		0			0
$283$	−19333.5	+	7036.81i	−0.241400	+	0.0878623i	−0.459887	−	0.887977i	$-0.652110\pi$
$283$	−19333.5	+	7036.81i	−0.241400	+	0.0878623i	0.218487	+	0.975840i	$0.429888\pi$
$284$	−3384.91	−	9299.97i	−0.0419673	−	0.115304i
$285$		0			0
$286$	−4927.89	−	27947.5i	−0.0602461	−	0.341673i
$287$	−22856.9	−	13196.4i	−0.277494	−	0.160211i
$288$		0			0
$289$	−41675.6	−	72184.3i	−0.498984	−	0.864266i
$290$	−50799.8	−	60540.9i	−0.604041	−	0.719868i
$291$		0			0
$292$	−7756.13	+	43987.2i	−0.0909661	+	0.515894i
$293$	57928.8	−	69036.9i	0.674776	−	0.804166i	−0.314650	−	0.949208i	$-0.601887\pi$
$293$	57928.8	−	69036.9i	0.674776	−	0.804166i	0.989426	+	0.145041i	$0.0463315\pi$
$294$		0			0
$295$	6168.40	+	2245.11i	0.0708807	+	0.0257985i
$296$			5757.97i			0.0657182i
$297$		0			0
$298$	98036.7			1.10397
$299$	33574.7	−	92245.7i	0.375552	−	1.03182i
$300$		0			0
$301$	38496.4	+	32302.3i	0.424901	+	0.356534i
$302$	−28756.5	−	5070.55i	−0.315299	−	0.0555957i
$303$		0			0
$304$	−24676.1	+	20705.7i	−0.267012	+	0.224049i
$305$	88424.3	−	51051.8i	0.950544	−	0.548797i
$306$		0			0
$307$	21232.7	−	36776.2i	0.225283	−	0.390202i	−0.731121	−	0.682248i	$-0.761003\pi$
$307$	21232.7	−	36776.2i	0.225283	−	0.390202i	0.956404	+	0.292045i	$0.0943358\pi$
$308$	−30883.4	+	5445.57i	−0.325554	+	0.0574040i
$309$		0			0
$310$	142092.	−	51717.2i	1.47858	−	0.538161i
$311$	22213.0	+	61029.8i	0.229661	+	0.630988i	0.999978	−	0.00667342i	$-0.00212423\pi$
$311$	22213.0	+	61029.8i	0.229661	+	0.630988i	−0.770317	+	0.637661i	$0.779902\pi$
$312$		0			0
$313$	29192.4	+	165558.i	0.297976	+	1.68991i	0.654854	+	0.755755i	$0.272730\pi$
$313$	29192.4	+	165558.i	0.297976	+	1.68991i	−0.356878	+	0.934151i	$0.616159\pi$
$314$	−7054.52	−	4072.93i	−0.0715498	−	0.0413093i
$315$		0			0
$316$	−32950.2	−	57071.4i	−0.329977	−	0.571537i
$317$	28625.5	+	34114.6i	0.284862	+	0.339486i	0.889433	−	0.457066i	$-0.151100\pi$
$317$	28625.5	+	34114.6i	0.284862	+	0.339486i	−0.604571	+	0.796552i	$0.706655\pi$
$318$		0			0
$319$	15182.2	−	86102.8i	0.149195	−	0.846127i
$320$	−10692.6	+	12743.0i	−0.104420	+	0.124443i
$321$		0			0
$322$	−101936.	−	37101.7i	−0.983143	−	0.357835i
$323$		−	6557.12i		−	0.0628504i
$324$		0			0
$325$	−42495.7			−0.402326
$326$	11778.5	−	32361.2i	0.110829	−	0.304501i
$327$		0			0
$328$	−11864.7	−	9955.63i	−0.110283	−	0.0925382i
$329$	117603.	+	20736.7i	1.08650	+	0.191579i
$330$		0			0
$331$	30430.4	−	25534.1i	0.277748	−	0.233059i	−0.493263	−	0.869880i	$-0.664196\pi$
$331$	30430.4	−	25534.1i	0.277748	−	0.233059i	0.771011	+	0.636822i	$0.219751\pi$
$332$	−88238.5	+	50944.5i	−0.800538	+	0.462191i
$333$		0			0
$334$	9465.79	−	16395.2i	0.0848523	−	0.146969i
$335$	−149514.	+	26363.3i	−1.33227	+	0.234915i
$336$		0			0
$337$	−23727.8	+	8636.22i	−0.208929	+	0.0760438i	−0.444364	−	0.895846i	$-0.646570\pi$
$337$	−23727.8	+	8636.22i	−0.208929	+	0.0760438i	0.235436	+	0.971890i	$0.424348\pi$
$338$	−18206.9	−	50023.0i	−0.159369	−	0.437861i
$339$		0			0
$340$	−588.000	−	3334.71i	−0.00508650	−	0.0288470i
$341$	144872.	+	83642.0i	1.24588	+	0.719310i
$342$		0			0
$343$	63915.4	+	110705.i	0.543272	+	0.940974i
$344$	18956.1	+	22591.0i	0.160189	+	0.190905i
$345$		0			0
$346$	2006.37	−	11378.7i	0.0167594	−	0.0950474i
$347$	65942.9	−	78587.7i	0.547658	−	0.652673i	−0.419229	−	0.907881i	$-0.637699\pi$
$347$	65942.9	−	78587.7i	0.547658	−	0.652673i	0.966886	+	0.255208i	$0.0821439\pi$
$348$		0			0
$349$	197406.	+	71850.0i	1.62073	+	0.589897i	0.983521	−	0.180796i	$-0.0578673\pi$
$349$	197406.	+	71850.0i	1.62073	+	0.589897i	0.637207	+	0.770693i	$0.280090\pi$
$350$			46959.9i			0.383346i
$351$		0			0
$352$	−18403.0			−0.148526
$353$	−16355.0	+	44935.0i	−0.131250	+	0.360608i	−0.987858	−	0.155361i	$-0.950346\pi$
$353$	−16355.0	+	44935.0i	−0.131250	+	0.360608i	0.856607	+	0.515969i	$0.172568\pi$
$354$		0			0
$355$	−30789.8	−	25835.7i	−0.244315	−	0.205005i
$356$	−57232.9	−	10091.7i	−0.451592	−	0.0796278i
$357$		0			0
$358$	−64025.9	+	53724.1i	−0.499563	+	0.419183i
$359$	15360.3	−	8868.27i	0.119182	−	0.0688097i	−0.439224	−	0.898378i	$-0.644747\pi$
$359$	15360.3	−	8868.27i	0.119182	−	0.0688097i	0.558406	+	0.829568i	$0.311413\pi$
$360$		0			0
$361$	−61504.5	+	106529.i	−0.471946	+	0.817434i
$362$	−54777.1	+	9658.68i	−0.418005	+	0.0737056i
$363$		0			0
$364$	28607.4	−	10412.3i	0.215912	−	0.0785854i
$365$	62041.7	+	170458.i	0.465691	+	1.27948i
$366$		0			0
$367$	−26366.9	−	149534.i	−0.195761	−	1.11022i	−0.911330	−	0.411676i	$-0.864944\pi$
$367$	−26366.9	−	149534.i	−0.195761	−	1.11022i	0.715569	−	0.698542i	$-0.246168\pi$
$368$	−55130.0	−	31829.3i	−0.407092	−	0.235035i
$369$		0			0
$370$	11692.2	+	20251.5i	0.0854069	+	0.147929i
$371$	85191.0	+	101527.i	0.618936	+	0.737620i
$372$		0			0
$373$	−27219.5	+	154370.i	−0.195642	+	1.10954i	0.715859	+	0.698245i	$0.246035\pi$
$373$	−27219.5	+	154370.i	−0.195642	+	1.10954i	−0.911501	+	0.411298i	$0.865076\pi$
$374$	2407.94	−	2869.67i	0.0172148	−	0.0205158i
$375$		0			0
$376$	65852.0	+	23968.2i	0.465793	+	0.169535i
$377$			84876.1i			0.597176i
$378$		0			0
$379$	234386.			1.63175			0.815875	−	0.578228i	$-0.196256\pi$
$379$	234386.			1.63175			0.815875	+	0.578228i	$0.196256\pi$
$380$	−44743.7	+	122932.i	−0.309860	+	0.851332i
$381$		0			0
$382$	−84744.2	−	71108.8i	−0.580742	−	0.487300i
$383$	−21920.4	−	3865.15i	−0.149434	−	0.0263493i	0.0984306	−	0.995144i	$-0.468618\pi$
$383$	−21920.4	−	3865.15i	−0.149434	−	0.0263493i	−0.247865	+	0.968795i	$0.579729\pi$
$384$		0			0
$385$	−97562.9	+	81865.0i	−0.658208	+	0.552302i
$386$	−1692.66	+	977.258i	−0.0113604	+	0.00655895i
$387$		0			0
$388$	−35022.4	+	60660.6i	−0.232639	+	0.402943i
$389$	56135.7	−	9898.24i	0.370971	−	0.0654122i	0.0149452	−	0.999888i	$-0.495243\pi$
$389$	56135.7	−	9898.24i	0.370971	−	0.0654122i	0.356026	+	0.934476i	$0.384131\pi$
$390$		0			0
$391$	12176.8	−	4431.99i	0.0796488	−	0.0289898i
$392$	7075.34	+	19439.4i	0.0460443	+	0.126506i
$393$		0			0
$394$	−6134.13	−	34788.4i	−0.0395149	−	0.224100i
$395$	−231780.	−	133818.i	−1.48553	−	0.857672i
$396$		0			0
$397$	−42155.7	−	73015.9i	−0.267470	−	0.463272i	0.700737	−	0.713419i	$-0.252854\pi$
$397$	−42155.7	−	73015.9i	−0.267470	−	0.463272i	−0.968208	+	0.250147i	$0.919521\pi$
$398$	−73461.6	−	87548.1i	−0.463761	−	0.552689i
$399$		0			0
$400$	−4785.33	+	27139.0i	−0.0299083	+	0.169619i
$401$	−41496.1	+	49453.2i	−0.258059	+	0.307543i	−0.879482	−	0.475933i	$-0.842111\pi$
$401$	−41496.1	+	49453.2i	−0.258059	+	0.307543i	0.621423	+	0.783475i	$0.286555\pi$
$402$		0			0
$403$	−152602.	−	55542.6i	−0.939615	−	0.341992i
$404$		−	132486.i		−	0.811720i
$405$		0			0
$406$	93792.4			0.569004
$407$	−8848.08	+	24309.9i	−0.0534146	+	0.146755i
$408$		0			0
$409$	96204.7	+	80725.3i	0.575108	+	0.482573i	0.883337	−	0.468739i	$-0.155292\pi$
$409$	96204.7	+	80725.3i	0.575108	+	0.482573i	−0.308228	+	0.951312i	$0.599736\pi$
$410$	−61945.5	−	10922.7i	−0.368504	−	0.0649772i
$411$		0			0
$412$	121410.	−	101875.i	0.715251	−	0.600167i
$413$	−6746.68	+	3895.20i	−0.0395540	+	0.0228365i
$414$		0			0
$415$	−206897.	+	358357.i	−1.20132	+	2.08075i
$416$	17593.8	−	3102.26i	0.101665	−	0.0179263i
$417$		0			0
$418$	−135999.	+	49499.8i	−0.778368	+	0.283303i
$419$	−56737.6	−	155885.i	−0.323179	−	0.887926i	−0.989792	−	0.142522i	$-0.954479\pi$
$419$	−56737.6	−	155885.i	−0.323179	−	0.887926i	0.666613	−	0.745404i	$-0.267743\pi$
$420$		0			0
$421$	−24570.1	−	139344.i	−0.138625	−	0.786183i	−0.972266	−	0.233876i	$-0.924859\pi$
$421$	−24570.1	−	139344.i	−0.138625	−	0.786183i	0.833641	−	0.552307i	$-0.186252\pi$
$422$	153126.	+	88407.3i	0.859852	+	0.496436i
$423$		0			0
$424$	38887.6	+	67355.3i	0.216311	+	0.374662i
$425$	−3605.78	−	4297.20i	−0.0199628	−	0.0237907i
$426$		0			0
$427$	−21041.9	+	119334.i	−0.115406	+	0.654500i
$428$	30270.9	−	36075.5i	0.165249	−	0.196936i
$429$		0			0
$430$	112545.	+	40962.9i	0.608678	+	0.221541i
$431$			13812.9i			0.0743582i	0.999309	+	0.0371791i	$0.0118372\pi$
$431$			13812.9i			0.0743582i	−0.999309	+	0.0371791i	$0.988163\pi$
$432$		0			0
$433$	317194.			1.69180			0.845902	−	0.533339i	$-0.179063\pi$
$433$	317194.			1.69180			0.845902	+	0.533339i	$0.179063\pi$
$434$	−61377.4	+	168633.i	−0.325858	+	0.895288i
$435$		0			0
$436$	12903.1	+	10827.0i	0.0678768	+	0.0569554i
$437$	−493029.	−	86934.3i	−2.58172	−	0.455227i
$438$		0			0
$439$	127993.	−	107399.i	0.664138	−	0.557278i	−0.247186	−	0.968968i	$-0.579506\pi$
$439$	127993.	−	107399.i	0.664138	−	0.557278i	0.911324	+	0.411690i	$0.135061\pi$
$440$	−64725.6	+	37369.3i	−0.334326	+	0.193023i
$441$		0			0
$442$	−1818.31	+	3149.40i	−0.00930728	+	0.0161207i
$443$	43818.4	−	7726.37i	0.223280	−	0.0393702i	−0.0608889	−	0.998145i	$-0.519394\pi$
$443$	43818.4	−	7726.37i	0.223280	−	0.0393702i	0.284169	+	0.958774i	$0.408282\pi$
$444$		0			0
$445$	−221788.	+	80724.1i	−1.12000	+	0.407646i
$446$	18746.0	+	51504.3i	0.0942410	+	0.258925i
$447$		0			0
$448$	−3428.15	−	19442.0i	−0.0170806	−	0.0968692i
$449$	191972.	+	110835.i	0.952237	+	0.549774i	0.893775	−	0.448516i	$-0.148047\pi$
$449$	191972.	+	110835.i	0.952237	+	0.549774i	0.0584616	+	0.998290i	$0.481380\pi$
$450$		0			0
$451$	−34793.6	−	60264.3i	−0.171059	−	0.296283i
$452$	−7176.57	−	8552.70i	−0.0351269	−	0.0418626i
$453$		0			0
$454$	14087.2	−	79892.5i	0.0683460	−	0.387609i
$455$	79472.7	−	94711.8i	0.383880	−	0.457490i
$456$		0			0
$457$	92665.8	+	33727.6i	0.443698	+	0.161493i	0.554201	−	0.832383i	$-0.313024\pi$
$457$	92665.8	+	33727.6i	0.443698	+	0.161493i	−0.110503	+	0.993876i	$0.535246\pi$
$458$			102734.i			0.489759i
$459$		0			0
$460$	−258532.			−1.22180
$461$	17286.8	−	47495.1i	0.0813416	−	0.223484i	−0.892354	−	0.451336i	$-0.850948\pi$
$461$	17286.8	−	47495.1i	0.0813416	−	0.223484i	0.973696	+	0.227851i	$0.0731700\pi$
$462$		0			0
$463$	−56660.6	−	47543.9i	−0.264313	−	0.221785i	0.500993	−	0.865451i	$-0.332968\pi$
$463$	−56660.6	−	47543.9i	−0.264313	−	0.221785i	−0.765306	+	0.643666i	$0.777413\pi$
$464$	54204.3	+	9557.68i	0.251766	+	0.0443932i
$465$		0			0
$466$	9129.09	−	7660.21i	0.0420393	−	0.0352752i
$467$	−285867.	+	165046.i	−1.31078	+	0.756781i	−0.982226	−	0.187703i	$-0.939896\pi$
$467$	−285867.	+	165046.i	−1.31078	+	0.756781i	−0.328557	+	0.944484i	$0.606562\pi$
$468$		0			0
$469$	90089.2	−	156039.i	0.409569	−	0.709394i
$470$	280280.	−	49420.9i	1.26881	−	0.223725i
$471$		0			0
$472$	−4295.96	+	1563.60i	−0.0192831	+	0.00701846i
$473$	45317.0	+	124507.i	0.202553	+	0.556510i
$474$		0			0
$475$	37633.6	+	213431.i	0.166797	+	0.945952i
$476$	3480.25	+	2009.32i	0.0153602	+	0.00886821i
$477$		0			0
$478$	−104443.	−	180900.i	−0.457112	−	0.791741i
$479$	24520.3	+	29222.2i	0.106870	+	0.127363i	0.816828	−	0.576881i	$-0.195731\pi$
$479$	24520.3	+	29222.2i	0.106870	+	0.127363i	−0.709958	+	0.704244i	$0.751286\pi$
$480$		0			0
$481$	4361.01	−	24732.5i	0.0188494	−	0.106900i
$482$	110275.	−	131420.i	0.474659	−	0.565676i
$483$		0			0
$484$	32367.7	+	11780.9i	0.138172	+	0.0502906i
$485$			284468.i			1.20934i
$486$		0			0
$487$	−64190.1			−0.270651			−0.135326	−	0.990801i	$-0.543208\pi$
$487$	−64190.1			−0.270651			−0.135326	+	0.990801i	$0.543208\pi$
$488$	−24321.0	+	66821.3i	−0.102127	+	0.280592i
$489$		0			0
$490$	64358.7	+	54003.3i	0.268049	+	0.224920i
$491$	−48070.9	−	8476.19i	−0.199397	−	0.0351591i	0.0730575	−	0.997328i	$-0.476724\pi$
$491$	−48070.9	−	8476.19i	−0.199397	−	0.0351591i	−0.272455	+	0.962169i	$0.587835\pi$
$492$		0			0
$493$	−8582.74	+	7201.77i	−0.0353128	+	0.0296310i
$494$	121675.	−	70249.2i	0.498595	−	0.287864i
$495$		0			0
$496$	−52655.2	+	91201.5i	−0.214032	+	0.370714i
$497$	46976.1	−	8283.16i	0.190180	−	0.0335338i
$498$		0			0
$499$	40968.4	−	14911.3i	0.164531	−	0.0598844i	−0.258441	−	0.966027i	$-0.583209\pi$
$499$	40968.4	−	14911.3i	0.164531	−	0.0598844i	0.422973	+	0.906142i	$0.360987\pi$
$500$	−17282.7	−	47483.9i	−0.0691309	−	0.189936i
$501$		0			0
$502$	23736.3	+	134615.i	0.0941901	+	0.534178i
$503$	−73148.2	−	42232.1i	−0.289113	−	0.166919i	0.348429	−	0.937335i	$-0.386715\pi$
$503$	−73148.2	−	42232.1i	−0.289113	−	0.166919i	−0.637542	+	0.770416i	$0.720049\pi$
$504$		0			0
$505$	−269027.	−	465969.i	−1.05490	−	1.82715i
$506$	−183846.	−	219099.i	−0.718046	−	0.855734i
$507$		0			0
$508$	−40177.8	+	227859.i	−0.155689	+	0.882957i
$509$	159394.	−	189958.i	0.615227	−	0.733199i	−0.365015	−	0.931002i	$-0.618936\pi$
$509$	159394.	−	189958.i	0.615227	−	0.733199i	0.980242	+	0.197802i	$0.0633804\pi$
$510$		0			0
$511$	−202298.	−	73630.3i	−0.774728	−	0.281978i
$512$		−	11585.2i		−	0.0441942i
$513$		0			0
$514$	−74664.9			−0.282612
$515$	220145.	−	604842.i	0.830029	−	2.28049i
$516$		0			0
$517$	241193.	+	202385.i	0.902369	+	0.757178i
$518$	−27330.7	−	4819.14i	−0.101857	−	0.0179602i
$519$		0			0
$520$	55580.1	−	46637.2i	0.205548	−	0.172475i
$521$	161018.	−	92963.9i	0.593198	−	0.342483i	−0.173163	−	0.984893i	$-0.555399\pi$
$521$	161018.	−	92963.9i	0.593198	−	0.342483i	0.766361	+	0.642410i	$0.222065\pi$
$522$		0			0
$523$	115621.	−	200262.i	0.422701	−	0.732140i	−0.573501	−	0.819205i	$-0.694415\pi$
$523$	115621.	−	200262.i	0.422701	−	0.732140i	0.996203	+	0.0870645i	$0.0277486\pi$
$524$	80277.6	−	14155.1i	0.292369	−	0.0515526i
$525$		0			0
$526$	1395.12	−	507.783i	0.00504244	−	0.00183530i
$527$	−7331.83	−	20144.1i	−0.0263992	−	0.0725313i
$528$		0			0
$529$	−123207.	−	698741.i	−0.440275	−	2.49692i
$530$	273545.	+	157931.i	0.973816	+	0.562233i
$531$		0			0
$532$	−77628.9	−	134457.i	−0.274284	−	0.475074i
$533$	43422.7	+	51749.2i	0.152849	+	0.182158i
$534$		0			0
$535$	33211.3	−	188350.i	0.116032	−	0.658050i
$536$	67964.9	−	80997.5i	0.236568	−	0.281930i
$537$		0			0
$538$	283134.	+	103052.i	0.978199	+	0.356035i
$539$			92944.6i			0.319924i
$540$		0			0
$541$	−534985.			−1.82788			−0.913938	−	0.405854i	$-0.866974\pi$
$541$	−534985.			−1.82788			−0.913938	+	0.405854i	$0.866974\pi$
$542$	−93201.6	+	256069.i	−0.317267	+	0.871683i
$543$		0			0
$544$	1806.54	+	1515.87i	0.00610451	+	0.00512229i
$545$	67367.3	+	11878.7i	0.226807	+	0.0399921i
$546$		0			0
$547$	368588.	−	309282.i	1.23188	−	1.03367i	0.233760	−	0.972294i	$-0.424897\pi$
$547$	368588.	−	309282.i	1.23188	−	1.03367i	0.998115	−	0.0613717i	$-0.0195475\pi$
$548$	201282.	−	116210.i	0.670262	−	0.386976i
$549$		0			0
$550$	−61907.0	+	107226.i	−0.204651	+	0.354467i
$551$	426282.	−	75165.1i	1.40409	−	0.247578i
$552$		0			0
$553$	298472.	−	108635.i	0.976009	−	0.355238i
$554$	−102642.	−	282007.i	−0.334431	−	0.918841i
$555$		0			0
$556$	29918.9	+	169679.i	0.0967824	+	0.548880i
$557$	−189146.	−	109204.i	−0.609659	−	0.351987i	0.163173	−	0.986598i	$-0.447827\pi$
$557$	−189146.	−	109204.i	−0.609659	−	0.351987i	−0.772832	+	0.634610i	$0.781161\pi$
$558$		0			0
$559$	−64313.1	−	111393.i	−0.205814	−	0.356481i
$560$	−51536.5	−	61418.8i	−0.164338	−	0.195851i
$561$		0			0
$562$	69069.7	−	391713.i	0.218683	−	1.24021i
$563$	−236484.	+	281830.i	−0.746079	+	0.889142i	−0.996883	−	0.0788959i	$-0.974861\pi$
$563$	−236484.	+	281830.i	−0.746079	+	0.889142i	0.250804	+	0.968038i	$0.419305\pi$
$564$		0			0
$565$	−42608.1	−	15508.1i	−0.133474	−	0.0485804i
$566$		−	58192.8i		−	0.181650i
$567$		0			0
$568$	27992.4			0.0867649
$569$	26288.9	−	72228.1i	0.0811984	−	0.223091i	−0.892449	−	0.451147i	$-0.851015\pi$
$569$	26288.9	−	72228.1i	0.0811984	−	0.223091i	0.973648	+	0.228057i	$0.0732371\pi$
$570$		0			0
$571$	137541.	+	115411.i	0.421853	+	0.353977i	0.828867	−	0.559445i	$-0.188986\pi$
$571$	137541.	+	115411.i	0.421853	+	0.353977i	−0.407015	+	0.913422i	$0.633430\pi$
$572$	79047.4	+	13938.2i	0.241599	+	0.0426005i
$573$		0			0
$574$	57185.5	−	47984.3i	0.173565	−	0.145638i
$575$	−370911.	+	214146.i	−1.12185	+	0.647699i
$576$		0			0
$577$	90822.6	−	157309.i	0.272799	−	0.472501i	−0.696779	−	0.717286i	$-0.745384\pi$
$577$	90822.6	−	157309.i	0.272799	−	0.472501i	0.969577	+	0.244785i	$0.0787173\pi$
$578$	232171.	−	40938.1i	0.694949	−	0.122538i
$579$		0			0
$580$	210051.	−	76452.4i	0.624409	−	0.227266i
$581$	−167961.	−	461470.i	−0.497574	−	1.36707i
$582$		0			0
$583$	60679.1	+	344129.i	0.178526	+	1.01247i
$584$	−109408.	−	63167.0i	−0.320793	−	0.185210i
$585$		0			0
$586$	127451.	+	220751.i	0.371148	+	0.642847i
$587$	−2546.70	−	3035.04i	−0.00739097	−	0.00880822i	0.762336	−	0.647181i	$-0.224052\pi$
$587$	−2546.70	−	3035.04i	−0.00739097	−	0.00880822i	−0.769727	+	0.638373i	$0.779608\pi$
$588$		0			0
$589$	−143815.	+	815617.i	−0.414548	+	2.35102i
$590$	−11934.4	+	14222.8i	−0.0342843	+	0.0408584i
$591$		0			0
$592$	−15303.8	−	5570.14i	−0.0436673	−	0.0158936i
$593$		−	333506.i		−	0.948407i	−0.880415	−	0.474204i	$-0.842736\pi$
$593$		−	333506.i		−	0.948407i	0.880415	−	0.474204i	$-0.157264\pi$
$594$		0			0
$595$	16320.6			0.0461002
$596$	−94838.7	+	260567.i	−0.266989	+	0.733546i
$597$		0			0
$598$	212696.	+	178473.i	0.594781	+	0.499080i
$599$	396385.	+	69893.4i	1.10475	+	0.194797i	0.696136	−	0.717910i	$-0.254901\pi$
$599$	396385.	+	69893.4i	1.10475	+	0.194797i	0.408614	+	0.912707i	$0.366012\pi$
$600$		0			0
$601$	−314943.	+	264268.i	−0.871932	+	0.731637i	−0.964504	−	0.264068i	$-0.914936\pi$
$601$	−314943.	+	264268.i	−0.871932	+	0.731637i	0.0925723	+	0.995706i	$0.470491\pi$
$602$	−123095.	+	71069.2i	−0.339664	+	0.196105i
$603$		0			0
$604$	41295.2	−	71525.4i	0.113195	−	0.196059i
$605$	137764.	−	24291.4i	0.376378	−	0.0663655i
$606$		0			0
$607$	−667258.	+	242862.i	−1.81099	+	0.659147i	−0.814067	+	0.580771i	$0.802751\pi$
$607$	−667258.	+	242862.i	−1.81099	+	0.659147i	−0.996924	+	0.0783759i	$0.975027\pi$
$608$	−31161.6	−	85615.8i	−0.0842971	−	0.231604i
$609$		0			0
$610$	50148.3	+	284405.i	0.134771	+	0.764325i
$611$	−264705.	−	152827.i	−0.709054	−	0.409372i
$612$		0			0
$613$	−47303.6	−	81932.2i	−0.125885	−	0.218039i	0.796194	−	0.605042i	$-0.206844\pi$
$613$	−47303.6	−	81932.2i	−0.125885	−	0.218039i	−0.922078	+	0.387003i	$0.873510\pi$
$614$	77205.6	+	92010.0i	0.204791	+	0.244061i
$615$		0			0
$616$	15402.4	−	87351.4i	0.0405908	−	0.230202i
$617$	−271921.	+	324063.i	−0.714288	+	0.851255i	−0.994062	−	0.108811i	$-0.965296\pi$
$617$	−271921.	+	324063.i	−0.714288	+	0.851255i	0.279775	+	0.960066i	$0.409740\pi$
$618$		0			0
$619$	−61311.8	−	22315.7i	−0.160016	−	0.0582410i	0.260770	−	0.965401i	$-0.416023\pi$
$619$	−61311.8	−	22315.7i	−0.160016	−	0.0582410i	−0.420786	+	0.907160i	$0.638246\pi$
$620$			427690.i			1.11262i
$621$		0			0
$622$	−183696.			−0.474810
$623$	95802.4	−	263215.i	0.246831	−	0.678164i
$624$		0			0
$625$	−363363.	−	304898.i	−0.930209	−	0.780538i
$626$	−468270.	−	82568.6i	−1.19494	−	0.210701i
$627$		0			0
$628$	17649.6	−	14809.8i	0.0447524	−	0.0375517i
$629$	2871.01	−	1657.58i	0.00725660	−	0.00418960i
$630$		0			0
$631$	27114.3	−	46963.3i	0.0680987	−	0.117950i	−0.829966	−	0.557815i	$-0.811640\pi$
$631$	27114.3	−	46963.3i	0.0680987	−	0.117950i	0.898064	+	0.439864i	$0.144973\pi$
$632$	183563.	−	32367.1i	0.459569	−	0.0810344i
$633$		0			0
$634$	−118363.	+	43080.7i	−0.294468	+	0.107178i
$635$	321384.	+	882995.i	0.797034	+	2.18983i
$636$		0			0
$637$	−15668.0	−	88857.7i	−0.0386131	−	0.218986i
$638$	214161.	+	123646.i	0.526138	+	0.303766i
$639$		0			0
$640$	−23525.1	−	40746.7i	−0.0574344	−	0.0994793i
$641$	292070.	+	348076.i	0.710839	+	0.847145i	0.993707	−	0.112014i	$-0.0357302\pi$
$641$	292070.	+	348076.i	0.710839	+	0.847145i	−0.282868	+	0.959159i	$0.591286\pi$
$642$		0			0
$643$	−41453.9	+	235097.i	−0.100264	+	0.568623i	0.892743	+	0.450566i	$0.148778\pi$
$643$	−41453.9	+	235097.i	−0.100264	+	0.568623i	−0.993007	+	0.118057i	$0.962333\pi$
$644$	197222.	−	235040.i	0.475536	−	0.566722i
$645$		0			0
$646$	17427.8	+	6343.22i	0.0417617	+	0.0152000i
$647$		−	137126.i		−	0.327575i	−0.986496	−	0.163788i	$-0.947629\pi$
$647$		−	137126.i		−	0.327575i	0.986496	−	0.163788i	$-0.0523712\pi$
$648$		0			0
$649$	−20540.1			−0.0487655
$650$	41109.4	−	112947.i	0.0973004	−	0.267331i
$651$		0			0
$652$	74616.9	+	62611.0i	0.175526	+	0.147284i
$653$	−571234.	−	100724.i	−1.33964	−	0.236214i	−0.542523	−	0.840041i	$-0.682531\pi$
$653$	−571234.	−	100724.i	−1.33964	−	0.236214i	−0.797115	+	0.603827i	$0.793642\pi$
$654$		0			0
$655$	253603.	−	212798.i	0.591114	−	0.496004i
$656$	37938.2	−	21903.6i	0.0881596	−	0.0508989i
$657$		0			0
$658$	−168882.	+	292512.i	−0.390060	+	0.675604i
$659$	−341080.	+	60141.6i	−0.785390	+	0.138486i	−0.551941	−	0.833883i	$-0.686113\pi$
$659$	−341080.	+	60141.6i	−0.785390	+	0.138486i	−0.233450	+	0.972369i	$0.575001\pi$
$660$		0			0
$661$	589472.	−	214550.i	1.34915	−	0.491051i	0.436468	−	0.899720i	$-0.356229\pi$
$661$	589472.	−	214550.i	1.34915	−	0.491051i	0.912683	+	0.408669i	$0.134007\pi$
$662$	38428.2	+	105581.i	0.0876868	+	0.240918i
$663$		0			0
$664$	−50043.0	−	283808.i	−0.113503	−	0.643707i
$665$	−546061.	−	315269.i	−1.23480	−	0.712914i
$666$		0			0
$667$	427711.	+	740816.i	0.961387	+	1.66517i
$668$	34419.1	+	41019.1i	0.0771341	+	0.0919248i
$669$		0			0
$670$	74566.7	−	422889.i	0.166110	−	0.942056i
$671$	−205364.	+	244744.i	−0.456121	+	0.543583i
$672$		0			0
$673$	−196977.	−	71693.6i	−0.434895	−	0.158289i	0.115289	−	0.993332i	$-0.463220\pi$
$673$	−196977.	−	71693.6i	−0.434895	−	0.158289i	−0.550185	+	0.835043i	$0.685443\pi$
$674$		−	71419.5i		−	0.157216i
$675$		0			0
$676$	150567.			0.329485
$677$	79188.0	−	217567.i	0.172776	−	0.474697i	−0.822836	−	0.568279i	$-0.807609\pi$
$677$	79188.0	−	217567.i	0.172776	−	0.474697i	0.995612	+	0.0935819i	$0.0298317\pi$
$678$		0			0
$679$	−258619.	−	217007.i	−0.560946	−	0.470689i
$680$	9431.99	+	1663.11i	0.0203979	+	0.00359670i
$681$		0			0
$682$	−362455.	+	304135.i	−0.779264	+	0.653880i
$683$	−358949.	+	207239.i	−0.769470	+	0.444254i	−0.832685	−	0.553746i	$-0.813198\pi$
$683$	−358949.	+	207239.i	−0.769470	+	0.444254i	0.0632156	+	0.998000i	$0.479864\pi$
$684$		0			0
$685$	471957.	−	817453.i	1.00582	−	1.74213i
$686$	−356067.	+	62784.2i	−0.756630	+	0.133414i
$687$		0			0
$688$	−78381.2	+	28528.4i	−0.165590	+	0.0602700i
$689$	−116022.	−	318768.i	−0.244401	−	0.671485i
$690$		0			0
$691$	−19399.8	−	110022.i	−0.0406295	−	0.230421i	0.957731	−	0.287666i	$-0.0928794\pi$
$691$	−19399.8	−	110022.i	−0.0406295	−	0.230421i	−0.998360	+	0.0572452i	$0.981768\pi$
$692$	28302.0	+	16340.1i	0.0591023	+	0.0341227i
$693$		0			0
$694$	145083.	+	251291.i	0.301229	+	0.521744i
$695$	449780.	+	536027.i	0.931174	+	1.10973i
$696$		0			0
$697$	−1548.48	+	8781.88i	−0.00318743	+	0.0180768i
$698$	−381933.	+	455170.i	−0.783929	+	0.934250i
$699$		0			0
$700$	−124812.	−	45428.0i	−0.254719	−	0.0927102i
$701$			201514.i			0.410081i	0.978753	+	0.205041i	$0.0657327\pi$
$701$			201514.i			0.410081i	−0.978753	+	0.205041i	$0.934267\pi$
$702$		0			0
$703$	−128079.			−0.259159
$704$	17802.7	−	48912.4i	0.0359203	−	0.0986901i
$705$		0			0
$706$	−103609.	−	86938.3i	−0.207868	−	0.174422i
$707$	628855.	+	110884.i	1.25809	+	0.221835i
$708$		0			0
$709$	−203431.	+	170699.i	−0.404693	+	0.339578i	−0.822304	−	0.569048i	$-0.807312\pi$
$709$	−203431.	+	170699.i	−0.404693	+	0.339578i	0.417611	+	0.908626i	$0.362867\pi$
$710$	98452.9	−	56841.8i	0.195304	−	0.112759i
$711$		0			0
$712$	82188.2	−	142354.i	0.162125	−	0.280808i
$713$	−1.61183e6	+	284210.i	−3.17060	+	0.559062i
$714$		0			0
$715$	306323.	−	111492.i	0.599193	−	0.218089i
$716$	−80853.5	−	222143.i	−0.157715	−	0.433318i
$717$		0			0
$718$	8711.32	+	49404.4i	0.0168980	+	0.0958333i
$719$	687541.	+	396952.i	1.32997	+	0.767857i	0.985294	−	0.170866i	$-0.0546565\pi$
$719$	687541.	+	396952.i	1.32997	+	0.767857i	0.344673	+	0.938723i	$0.387990\pi$
$720$		0			0
$721$	381944.	+	661546.i	0.734732	+	1.27259i
$722$	−223640.	−	266524.i	−0.429017	−	0.511283i
$723$		0			0
$724$	27318.9	−	154933.i	0.0521177	−	0.295574i
$725$	238030.	−	283673.i	0.452851	−	0.539687i
$726$		0			0
$727$	47081.8	+	17136.4i	0.0890808	+	0.0324228i	0.386176	−	0.922425i	$-0.373796\pi$
$727$	47081.8	+	17136.4i	0.0890808	+	0.0324228i	−0.297095	+	0.954848i	$0.596018\pi$
$728$			86106.9i			0.162471i
$729$		0			0
$730$	−513071.			−0.962790
$731$	5807.21	−	15955.2i	0.0108676	−	0.0298584i
$732$		0			0
$733$	270681.	+	227128.i	0.503790	+	0.422730i	0.858938	−	0.512080i	$-0.171125\pi$
$733$	270681.	+	227128.i	0.503790	+	0.422730i	−0.355148	+	0.934810i	$0.615569\pi$
$734$	422947.	+	74576.9i	0.785043	+	0.138424i
$735$		0			0
$736$	137929.	−	115736.i	0.254625	−	0.213656i
$737$	411411.	−	237528.i	0.757428	−	0.437301i
$738$		0			0
$739$	−199391.	+	345355.i	−0.365104	+	0.632379i	−0.988793	−	0.149294i	$-0.952300\pi$
$739$	−199391.	+	345355.i	−0.365104	+	0.632379i	0.623689	+	0.781673i	$0.285633\pi$
$740$	−65136.3	+	11485.3i	−0.118949	+	0.0209738i
$741$		0			0
$742$	−352255.	+	128210.i	−0.639807	+	0.232871i
$743$	221179.	+	607685.i	0.400652	+	1.10078i	0.961964	+	0.273177i	$0.0880745\pi$
$743$	221179.	+	607685.i	0.400652	+	1.10078i	−0.561312	+	0.827604i	$0.689703\pi$
$744$		0			0
$745$	195552.	+	1.10903e6i	0.352329	+	1.99816i
$746$	−383960.	−	221679.i	−0.689935	−	0.398334i
$747$		0			0
$748$	5297.77	+	9176.00i	0.00946868	+	0.0164002i
$749$	145900.	+	173877.i	0.260071	+	0.309941i
$750$		0			0
$751$	−137640.	+	780594.i	−0.244042	+	1.38403i	0.578666	+	0.815565i	$0.303574\pi$
$751$	−137640.	+	780594.i	−0.244042	+	1.38403i	−0.822708	+	0.568465i	$0.807538\pi$
$752$	−127408.	+	151839.i	−0.225299	+	0.268501i
$753$		0			0
$754$	−225588.	−	82107.3i	−0.396802	−	0.144424i
$755$		−	335418.i		−	0.588427i
$756$		0			0
$757$	424123.			0.740117			0.370058	−	0.929008i	$-0.379338\pi$
$757$	424123.			0.740117			0.370058	+	0.929008i	$0.379338\pi$
$758$	−226740.	+	622964.i	−0.394630	+	1.08424i
$759$		0			0
$760$	−283452.	−	237844.i	−0.490741	−	0.411780i
$761$	357956.	+	63117.2i	0.618102	+	0.108988i	0.473927	−	0.880564i	$-0.342836\pi$
$761$	357956.	+	63117.2i	0.618102	+	0.108988i	0.144175	+	0.989552i	$0.453947\pi$
$762$		0			0
$763$	−62190.6	+	52184.1i	−0.106826	+	0.0896373i
$764$	270976.	−	156448.i	0.464242	−	0.268030i
$765$		0			0
$766$	31478.3	−	54522.0i	0.0536480	−	0.0929211i
$767$	19636.9	−	3462.52i	0.0333797	−	0.00588575i
$768$		0			0
$769$	627699.	−	228464.i	1.06145	−	0.386335i	0.248476	−	0.968638i	$-0.420070\pi$
$769$	627699.	−	228464.i	1.06145	−	0.386335i	0.812972	+	0.582303i	$0.197848\pi$
$770$	−123205.	−	338502.i	−0.207800	−	0.570926i
$771$		0			0
$772$	−959.963	−	5444.22i	−0.00161072	−	0.00913484i
$773$	567262.	+	327509.i	0.949347	+	0.548106i	0.892878	−	0.450299i	$-0.148682\pi$
$773$	567262.	+	327509.i	0.949347	+	0.548106i	0.0564691	+	0.998404i	$0.482016\pi$
$774$		0			0
$775$	354261.	+	613598.i	0.589820	+	1.02160i
$776$	−127347.	−	151766.i	−0.211478	−	0.252030i
$777$		0			0
$778$	−27996.5	+	158776.i	−0.0462534	+	0.262316i
$779$	221451.	−	263915.i	0.364924	−	0.434899i
$780$		0			0
$781$	118183.	+	43015.1i	0.193755	+	0.0705210i
$782$			36651.5i			0.0599347i
$783$		0			0
$784$	−58511.5			−0.0951938
$785$	32003.0	−	87927.5i	0.0519340	−	0.142687i
$786$		0			0
$787$	3488.46	+	2927.16i	0.00563228	+	0.00472604i	0.645599	−	0.763676i	$-0.276608\pi$
$787$	3488.46	+	2927.16i	0.00563228	+	0.00472604i	−0.639967	+	0.768402i	$0.721052\pi$
$788$	98396.4	+	17349.9i	0.158463	+	0.0279412i
$789$		0			0
$790$	579888.	−	486584.i	0.929159	−	0.779657i
$791$	46602.6	−	26906.0i	0.0744830	−	0.0430028i
$792$		0			0
$793$	155077.	−	268601.i	0.246604	−	0.427131i
$794$	234846.	−	41409.7i	0.372514	−	0.0656842i
$795$		0			0
$796$	303755.	−	110558.i	0.479400	−	0.174487i
$797$	−312731.	−	859221.i	−0.492328	−	1.35266i	−0.898544	−	0.438883i	$-0.855374\pi$
$797$	−312731.	−	859221.i	−0.492328	−	1.35266i	0.406217	−	0.913777i	$-0.366848\pi$
$798$		0			0
$799$	−7006.29	−	39734.6i	−0.0109747	−	0.0622409i
$800$	−67502.1	−	38972.4i	−0.105472	−	0.0608943i
$801$		0			0
$802$	−91296.7	−	158131.i	−0.141941	−	0.245848i
$803$	−364851.	−	434813.i	−0.565828	−	0.674328i
$804$		0			0
$805$	216379.	−	1.22715e6i	0.333905	−	1.89367i
$806$	295248.	−	351863.i	0.454482	−	0.541631i
$807$		0			0
$808$	352127.	+	128164.i	0.539358	+	0.196310i
$809$		−	581200.i		−	0.888031i	−0.896019	−	0.444016i	$-0.853553\pi$
$809$		−	581200.i		−	0.888031i	0.896019	−	0.444016i	$-0.146447\pi$
$810$		0			0
$811$	−430456.			−0.654465			−0.327233	−	0.944944i	$-0.606116\pi$
$811$	−430456.			−0.654465			−0.327233	+	0.944944i	$0.606116\pi$
$812$	−90732.8	+	249286.i	−0.137611	+	0.378082i
$813$		0			0
$814$	−56052.7	−	47033.8i	−0.0845955	−	0.0709841i
$815$	389576.	+	68692.7i	0.586512	+	0.103418i
$816$		0			0
$817$	−502509.	+	421655.i	−0.752834	+	0.631703i
$818$	−307622.	+	177606.i	−0.459739	+	0.265430i
$819$		0			0
$820$	88955.7	−	154076.i	0.132296	−	0.229143i
$821$	−355921.	+	62758.5i	−0.528041	+	0.0931079i	−0.431312	−	0.902203i	$-0.641949\pi$
$821$	−355921.	+	62758.5i	−0.528041	+	0.0931079i	−0.0967292	+	0.995311i	$0.530838\pi$
$822$		0			0
$823$	−1.14624e6	+	417197.i	−1.69229	+	0.615944i	−0.994911	−	0.100757i	$-0.967874\pi$
$823$	−1.14624e6	+	417197.i	−1.69229	+	0.615944i	−0.697381	+	0.716701i	$0.745651\pi$
$824$	153319.	+	421240.i	0.225809	+	0.620405i
$825$		0			0
$826$	−3826.26	−	21699.8i	−0.00560809	−	0.0318050i
$827$	322272.	+	186064.i	0.471207	+	0.272052i	0.716745	−	0.697335i	$-0.245631\pi$
$827$	322272.	+	186064.i	0.471207	+	0.272052i	−0.245538	+	0.969387i	$0.578964\pi$
$828$		0			0
$829$	−168515.	−	291877.i	−0.245206	−	0.424709i	0.716984	−	0.697090i	$-0.245522\pi$
$829$	−168515.	−	291877.i	−0.245206	−	0.424709i	−0.962189	+	0.272381i	$0.912189\pi$
$830$	−752311.	−	896569.i	−1.09205	−	1.30145i
$831$		0			0
$832$	−8774.51	+	49762.7i	−0.0126758	+	0.0718882i
$833$	7655.93	−	9123.98i	0.0110334	−	0.0131491i
$834$		0			0
$835$	204350.	+	74377.3i	0.293091	+	0.106676i
$836$		−	409352.i		−	0.585712i
$837$		0			0
$838$	469206.			0.668153
$839$	351374.	−	965391.i	0.499166	−	1.37145i	−0.392916	−	0.919575i	$-0.628534\pi$
$839$	351374.	−	965391.i	0.499166	−	1.37145i	0.892082	−	0.451874i	$-0.149244\pi$
$840$		0			0
$841$	−24768.3	−	20783.0i	−0.0350190	−	0.0293844i
$842$	394124.	+	69494.7i	0.555915	+	0.0980228i
$843$		0			0
$844$	−383104.	+	321463.i	−0.537814	+	0.451279i
$845$	529562.	−	305743.i	0.741658	−	0.428196i
$846$		0			0
$847$	−83009.2	+	143776.i	−0.115707	+	0.200410i
$848$	−216639.	+	38199.4i	−0.301263	+	0.0531208i
$849$		0			0
$850$	14909.5	−	5426.60i	0.0206359	−	0.00751087i
$851$	−86569.2	−	237847.i	−0.119537	−	0.328427i
$852$		0			0
$853$	−199088.	−	1.12909e6i	−0.273620	−	1.55178i	−0.743312	−	0.668945i	$-0.766746\pi$
$853$	−199088.	−	1.12909e6i	−0.273620	−	1.55178i	0.469692	−	0.882830i	$-0.344365\pi$
$854$	−296818.	−	171368.i	−0.406981	−	0.234971i
$855$		0			0
$856$	66599.8	+	115354.i	0.0908919	+	0.157429i
$857$	−169074.	−	201495.i	−0.230206	−	0.274348i	0.638560	−	0.769572i	$-0.279531\pi$
$857$	−169074.	−	201495.i	−0.230206	−	0.274348i	−0.868765	+	0.495224i	$0.835086\pi$
$858$		0			0
$859$	238467.	−	1.35241e6i	0.323178	−	1.83283i	−0.199006	−	0.979998i	$-0.563771\pi$
$859$	238467.	−	1.35241e6i	0.323178	−	1.83283i	0.522184	−	0.852833i	$-0.325117\pi$
$860$	−217746.	+	259500.i	−0.294411	+	0.350865i
$861$		0			0
$862$	−36712.5	−	13362.3i	−0.0494083	−	0.0179831i
$863$			158217.i			0.212438i	0.994343	+	0.106219i	$0.0338745\pi$
$863$			158217.i			0.212438i	−0.994343	+	0.106219i	$0.966126\pi$
$864$		0			0
$865$	132722.			0.177383
$866$	−306847.	+	843056.i	−0.409154	+	1.12414i
$867$		0			0
$868$	−388826.	−	326264.i	−0.516079	−	0.433042i
$869$	824732.	+	145422.i	1.09213	+	0.192572i
$870$		0			0
$871$	−353280.	+	296437.i	−0.465675	+	0.390748i
$872$	−41258.7	+	23820.7i	−0.0542604	+	0.0313273i
$873$		0			0
$874$	708004.	−	1.22630e6i	0.926857	−	1.60536i
$875$	239851.	−	42292.3i	0.313275	−	0.0552389i
$876$		0			0
$877$	−256411.	+	93326.1i	−0.333379	+	0.121340i	−0.503286	−	0.864120i	$-0.667876\pi$
$877$	−256411.	+	93326.1i	−0.333379	+	0.121340i	0.169907	+	0.985460i	$0.445653\pi$
$878$	161633.	+	444083.i	0.209672	+	0.576070i
$879$		0			0
$880$	−36708.0	−	208181.i	−0.0474018	−	0.268829i
$881$	−160292.	−	92544.6i	−0.206519	−	0.119234i	0.393174	−	0.919464i	$-0.371377\pi$
$881$	−160292.	−	92544.6i	−0.206519	−	0.119234i	−0.599693	+	0.800230i	$0.704710\pi$
$882$		0			0
$883$	567052.	+	982162.i	0.727279	+	1.25968i	0.958029	+	0.286672i	$0.0925489\pi$
$883$	567052.	+	982162.i	0.727279	+	1.25968i	−0.230750	+	0.973013i	$0.574118\pi$
$884$	−6611.65	−	7879.46i	−0.00846068	−	0.0100830i
$885$		0			0
$886$	−21853.5	+	123937.i	−0.0278390	+	0.157883i
$887$	−650542.	+	775285.i	−0.826852	+	0.985404i	0.173148	+	0.984896i	$0.444606\pi$
$887$	−650542.	+	775285.i	−0.826852	+	0.985404i	−1.00000		0.000508279i	$0.999838\pi$
$888$		0			0
$889$	−1.04793e6	−	381415.i	−1.32595	−	0.482607i
$890$		−	667570.i		−	0.842785i
$891$		0			0
$892$	−155025.			−0.194838
$893$	−533142.	+	1.46480e6i	−0.668560	+	1.83685i
$894$		0			0
$895$	−735458.	−	617123.i	−0.918147	−	0.770416i
$896$	54990.4	+	9696.29i	0.0684969	+	0.0120778i
$897$		0			0
$898$	−480293.	+	403013.i	−0.595598	+	0.499766i
$899$	1.22553e6	−	707561.i	1.51637	−	0.875477i
$900$		0			0
$901$	22389.6	−	38779.9i	0.0275801	−	0.0477702i
$902$	193832.	−	34177.9i	0.238239	−	0.0420080i
$903$		0			0
$904$	29674.3	−	10800.6i	0.0363114	−	0.0132163i
$905$	−218525.	−	600393.i	−0.266811	−	0.733058i
$906$		0			0
$907$	−204654.	−	1.16065e6i	−0.248774	−	1.41087i	−0.811562	−	0.584266i	$-0.801383\pi$
$907$	−204654.	−	1.16065e6i	−0.248774	−	1.41087i	0.562788	−	0.826601i	$-0.309729\pi$
$908$	198715.	+	114728.i	0.241023	+	0.139155i
$909$		0			0
$910$	174850.	+	302849.i	0.211146	+	0.365715i
$911$	431434.	+	514163.i	0.519850	+	0.619533i	0.960545	−	0.278124i	$-0.0897126\pi$
$911$	431434.	+	514163.i	0.519850	+	0.619533i	−0.440696	+	0.897657i	$0.645268\pi$
$912$		0			0
$913$	224839.	−	1.27512e6i	0.269730	−	1.52972i
$914$	−179286.	+	213665.i	−0.214612	+	0.255764i
$915$		0			0
$916$	−273051.	−	99382.4i	−0.325426	−	0.118446i
$917$			392892.i			0.467234i
$918$		0			0
$919$	−553029.			−0.654812			−0.327406	−	0.944884i	$-0.606174\pi$
$919$	−553029.			−0.654812			−0.327406	+	0.944884i	$0.606174\pi$
$920$	250099.	−	687140.i	0.295485	−	0.811839i
$921$		0			0
$922$	109512.	+	91891.5i	0.128825	+	0.108097i
$923$	−120238.	−	21201.1i	−0.141136	−	0.0248860i
$924$		0			0
$925$	−83936.3	+	70430.9i	−0.0980994	+	0.0823152i
$926$	181177.	−	104602.i	0.211291	−	0.121989i
$927$		0			0
$928$	−77839.0	+	134821.i	−0.0903861	+	0.156553i
$929$	246586.	−	43479.7i	0.285717	−	0.0503796i	−0.0289529	−	0.999581i	$-0.509217\pi$
$929$	246586.	−	43479.7i	0.285717	−	0.0503796i	0.314670	+	0.949201i	$0.398106\pi$
$930$		0			0
$931$	−432404.	+	157382.i	−0.498874	+	0.181575i
$932$	11528.4	+	31674.1i	0.0132721	+	0.0364647i
$933$		0			0
$934$	−162125.	−	919455.i	−0.185847	−	1.05399i
$935$	37265.8	+	21515.4i	0.0426273	+	0.0246109i
$936$		0			0
$937$	610660.	+	1.05769e6i	0.695537	+	1.20470i	0.969999	+	0.243107i	$0.0781667\pi$
$937$	610660.	+	1.05769e6i	0.695537	+	1.20470i	−0.274463	+	0.961598i	$0.588500\pi$
$938$	327578.	+	390393.i	0.372314	+	0.443707i
$939$		0			0
$940$	−139783.	+	792751.i	−0.158198	+	0.897183i
$941$	−350445.	+	417645.i	−0.395768	+	0.471658i	−0.926725	−	0.375741i	$-0.877388\pi$
$941$	−350445.	+	417645.i	−0.395768	+	0.471658i	0.530956	+	0.847399i	$0.321833\pi$
$942$		0			0
$943$	639779.	+	232860.i	0.719459	+	0.261862i
$944$		−	12930.6i		−	0.0145103i
$945$		0			0
$946$	−374761.			−0.418767
$947$	125058.	−	343594.i	0.139448	−	0.383130i	−0.850235	−	0.526403i	$-0.823540\pi$
$947$	125058.	−	343594.i	0.139448	−	0.383130i	0.989683	+	0.143273i	$0.0457627\pi$
$948$		0			0
$949$	422106.	+	354189.i	0.468694	+	0.393281i
$950$	−603673.	−	106444.i	−0.668889	−	0.117943i
$951$		0			0
$952$	−8707.20	+	7306.21i	−0.00960738	+	0.00806155i
$953$	−164411.	+	94923.0i	−0.181028	+	0.104517i	−0.587776	−	0.809024i	$-0.699996\pi$
$953$	−164411.	+	94923.0i	−0.181028	+	0.104517i	0.406747	+	0.913541i	$0.366663\pi$
$954$		0			0
$955$	635372.	−	1.10050e6i	0.696661	−	1.20665i
$956$	581842.	−	102594.i	0.636633	−	0.112256i
$957$		0			0
$958$	−101389.	+	36902.5i	−0.110474	+	0.0402091i
$959$	383139.	+	1.05267e6i	0.416600	+	1.14460i
$960$		0			0
$961$	309800.	+	1.75696e6i	0.335456	+	1.90246i
$962$	61516.6	+	35516.6i	0.0664726	+	0.0383780i
$963$		0			0
$964$	242618.	+	420227.i	0.261077	+	0.452199i
$965$	−14431.4	−	17198.7i	−0.0154972	−	0.0184689i
$966$		0			0
$967$	−101562.	+	575989.i	−0.108613	+	0.615973i	0.881103	+	0.472924i	$0.156802\pi$
$967$	−101562.	+	575989.i	−0.108613	+	0.615973i	−0.989716	+	0.143048i	$0.954310\pi$
$968$	−62623.6	+	74631.9i	−0.0668325	+	0.0796479i
$969$		0			0
$970$	−756074.	−	275188.i	−0.803564	−	0.292473i
$971$		−	476627.i		−	0.505522i	−0.967529	−	0.252761i	$-0.918661\pi$
$971$		−	476627.i		−	0.505522i	0.967529	−	0.252761i	$-0.0813386\pi$
$972$		0			0
$973$	−830435.			−0.877163
$974$	62096.2	−	170608.i	0.0654556	−	0.179838i
$975$		0			0
$976$	−154074.	−	129283.i	−0.161744	−	0.135719i
$977$	484635.	+	85454.2i	0.507722	+	0.0895250i	0.421640	−	0.906763i	$-0.361454\pi$
$977$	484635.	+	85454.2i	0.507722	+	0.0895250i	0.0860811	+	0.996288i	$0.472566\pi$
$978$		0			0
$979$	565746.	−	474718.i	0.590278	−	0.495302i
$980$	−205792.	+	118814.i	−0.214278	+	0.123713i
$981$		0			0
$982$	69031.2	−	119566.i	0.0715851	−	0.123989i
$983$	−513854.	+	90606.4i	−0.531781	+	0.0937673i	−0.433090	−	0.901351i	$-0.642577\pi$
$983$	−513854.	+	90606.4i	−0.531781	+	0.0937673i	−0.0986912	+	0.995118i	$0.531466\pi$
$984$		0			0
$985$	381303.	−	138783.i	0.393005	−	0.143042i
$986$	−10838.5	−	29778.5i	−0.0111485	−	0.0306301i
$987$		0			0
$988$	69005.9	+	391352.i	0.0706924	+	0.400916i
$989$	−1.12268e6	−	648177.i	−1.14779	−	0.662676i
$990$		0			0
$991$	229.116	+	396.841i	0.000233297	+	0.000404082i	0.866142	−	0.499798i	$-0.166592\pi$
$991$	229.116	+	396.841i	0.000233297	+	0.000404082i	−0.865909	+	0.500202i	$0.833259\pi$
$992$	−191463.	−	228176.i	−0.194563	−	0.231871i
$993$		0			0
$994$	−23428.3	+	132869.i	−0.0237120	+	0.134477i
$995$	843845.	−	1.00566e6i	0.852347	−	1.01579i
$996$		0			0
$997$	294827.	+	107308.i	0.296604	+	0.107955i	0.486036	−	0.873939i	$-0.338442\pi$
$997$	294827.	+	107308.i	0.296604	+	0.107955i	−0.189432	+	0.981894i	$0.560665\pi$
$998$			123313.i			0.123808i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.5.f.a.17.5		72
3.2	odd	2		54.5.f.a.23.10	✓	72
27.7	even	9		54.5.f.a.47.10	yes	72
27.20	odd	18	inner	162.5.f.a.143.5		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.5.f.a.23.10	✓	72	3.2	odd	2
54.5.f.a.47.10	yes	72	27.7	even	9
162.5.f.a.17.5		72	1.1	even	1	trivial
162.5.f.a.143.5		72	27.20	odd	18	inner

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	162.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.967379 + 2.65785i) q^{2} +(-6.12836 - 5.14230i) q^{4} +(-31.9962 - 5.64180i) q^{5} +(29.5375 - 24.7849i) q^{7} +(19.5959 - 11.3137i) q^{8} +O(q^{10})\)	\(q+(-0.967379 + 2.65785i) q^{2} +(-6.12836 - 5.14230i) q^{4} +(-31.9962 - 5.64180i) q^{5} +(29.5375 - 24.7849i) q^{7} +(19.5959 - 11.3137i) q^{8} +(45.9475 - 79.5835i) q^{10} +(100.119 - 17.6536i) q^{11} +(-92.7403 + 33.7547i) q^{13} +(37.3007 + 102.483i) q^{14} +(11.1135 + 63.0277i) q^{16} +(-11.2824 - 6.51388i) q^{17} +(251.659 + 435.887i) q^{19} +(167.072 + 199.109i) q^{20} +(-49.9319 + 283.178i) q^{22} +(-639.359 + 761.959i) q^{23} +(404.620 + 147.270i) q^{25} -279.144i q^{26} -308.468 q^{28} +(294.140 - 808.143i) q^{29} +(1260.51 + 1057.69i) q^{31} +(-178.269 - 31.4337i) q^{32} +(28.2272 - 23.6855i) q^{34} +(-1084.92 + 626.379i) q^{35} +(-127.234 + 220.376i) q^{37} +(-1401.97 + 247.206i) q^{38} +(-690.825 + 251.440i) q^{40} +(-234.109 - 643.209i) q^{41} +(226.317 + 1283.51i) q^{43} +(-704.342 - 406.652i) q^{44} +(-1406.67 - 2436.43i) q^{46} +(1990.75 + 2372.48i) q^{47} +(-158.756 + 900.352i) q^{49} +(-782.842 + 932.955i) q^{50} +(741.923 + 270.038i) q^{52} +3437.21i q^{53} -3303.01 q^{55} +(298.406 - 819.862i) q^{56} +(1863.38 + 1563.56i) q^{58} +(-198.971 - 35.0840i) q^{59} +(-2407.40 + 2020.05i) q^{61} +(-4030.58 + 2327.05i) q^{62} +(256.000 - 443.405i) q^{64} +(3157.78 - 556.801i) q^{65} +(4391.05 - 1598.21i) q^{67} +(35.6460 + 97.9367i) q^{68} +(-615.294 - 3489.51i) q^{70} +(1071.36 + 618.551i) q^{71} +(-2791.61 - 4835.21i) q^{73} +(-462.644 - 551.357i) q^{74} +(699.203 - 3965.38i) q^{76} +(2519.71 - 3002.88i) q^{77} +(7740.77 + 2817.41i) q^{79} -2079.35i q^{80} +1936.03 q^{82} +(4356.02 - 11968.1i) q^{83} +(324.243 + 272.072i) q^{85} +(-3630.30 - 640.120i) q^{86} +(1762.19 - 1478.65i) q^{88} +(6291.23 - 3632.24i) q^{89} +(-1902.71 + 3295.59i) q^{91} +(7836.44 - 1381.78i) q^{92} +(-8231.50 + 2996.02i) q^{94} +(-5592.97 - 15366.5i) q^{95} +(-1520.39 - 8622.59i) q^{97} +(-2239.43 - 1292.93i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 18 q^{5}+O(q^{10}) \) 72 * q + 18 * q^5	\( 72 q + 18 q^{5} - 720 q^{11} + 288 q^{14} - 288 q^{20} - 1008 q^{22} - 4716 q^{23} - 882 q^{25} + 6084 q^{29} + 3330 q^{31} + 288 q^{34} - 5346 q^{35} - 576 q^{38} + 13356 q^{41} + 1260 q^{43} - 16578 q^{47} - 5904 q^{49} - 15552 q^{50} + 2304 q^{56} + 40104 q^{59} + 8352 q^{61} + 18432 q^{64} + 19674 q^{65} - 24192 q^{67} - 10224 q^{68} + 14400 q^{70} - 39528 q^{71} - 12222 q^{73} - 33120 q^{74} + 9792 q^{76} - 28206 q^{77} + 11304 q^{79} + 30078 q^{83} - 52200 q^{85} + 46224 q^{86} - 16128 q^{88} + 102222 q^{89} + 12078 q^{91} + 27504 q^{92} + 4032 q^{94} - 46728 q^{95} + 49680 q^{97} - 82944 q^{98}+O(q^{100}) \) 72 * q + 18 * q^5 - 720 * q^11 + 288 * q^14 - 288 * q^20 - 1008 * q^22 - 4716 * q^23 - 882 * q^25 + 6084 * q^29 + 3330 * q^31 + 288 * q^34 - 5346 * q^35 - 576 * q^38 + 13356 * q^41 + 1260 * q^43 - 16578 * q^47 - 5904 * q^49 - 15552 * q^50 + 2304 * q^56 + 40104 * q^59 + 8352 * q^61 + 18432 * q^64 + 19674 * q^65 - 24192 * q^67 - 10224 * q^68 + 14400 * q^70 - 39528 * q^71 - 12222 * q^73 - 33120 * q^74 + 9792 * q^76 - 28206 * q^77 + 11304 * q^79 + 30078 * q^83 - 52200 * q^85 + 46224 * q^86 - 16128 * q^88 + 102222 * q^89 + 12078 * q^91 + 27504 * q^92 + 4032 * q^94 - 46728 * q^95 + 49680 * q^97 - 82944 * q^98

Introduction

L-functions

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