LMFDB - Embedded newform 216.4.i.b.145.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,4,Mod(73,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("216.73");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	216.i (of order $3$, 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:	$12.7444125612$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 20x^{8} + 11x^{7} + 284x^{6} + 98x^{5} + 1567x^{4} + 780x^{3} + 6513x^{2} + 972x + 144 $ x^10 - x^9 + 20x^8 + 11x^7 + 284x^6 + 98x^5 + 1567x^4 + 780x^3 + 6513x^2 + 972x + 144
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{10} $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			145.2
Root			$1.25497 - 2.17367i$ of defining polynomial
Character	$\chi$	$=$	216.145
Dual form			216.4.i.b.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.15936 + 5.47217i) q^{5} +(14.7898 + 25.6167i) q^{7} +O(q^{10})$	$q+(-3.15936 + 5.47217i) q^{5} +(14.7898 + 25.6167i) q^{7} +(-24.5762 - 42.5672i) q^{11} +(-9.13278 + 15.8184i) q^{13} -63.7873 q^{17} -52.0413 q^{19} +(-74.6939 + 129.374i) q^{23} +(42.5369 + 73.6761i) q^{25} +(59.7077 + 103.417i) q^{29} +(-151.846 + 263.005i) q^{31} -186.905 q^{35} +170.764 q^{37} +(21.8453 - 37.8371i) q^{41} +(-223.434 - 386.999i) q^{43} +(-111.000 - 192.257i) q^{47} +(-265.976 + 460.685i) q^{49} +67.3089 q^{53} +310.579 q^{55} +(-233.898 + 405.123i) q^{59} +(237.504 + 411.369i) q^{61} +(-57.7074 - 99.9522i) q^{65} +(120.490 - 208.695i) q^{67} -550.486 q^{71} +552.924 q^{73} +(726.953 - 1259.12i) q^{77} +(-456.657 - 790.953i) q^{79} +(333.953 + 578.423i) q^{83} +(201.527 - 349.055i) q^{85} +1430.73 q^{89} -540.288 q^{91} +(164.417 - 284.779i) q^{95} +(-832.861 - 1442.56i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{5} - 3 q^{7}+O(q^{10}) $ 10 * q + 5 * q^5 - 3 * q^7	$ 10 q + 5 q^{5} - 3 q^{7} - 25 q^{11} - 29 q^{13} - 56 q^{17} + 128 q^{19} + 89 q^{23} - 322 q^{25} + 129 q^{29} - 241 q^{31} + 486 q^{35} + 732 q^{37} + 171 q^{41} - 803 q^{43} - 477 q^{47} - 1072 q^{49} - 748 q^{53} + 2938 q^{55} - 607 q^{59} - 1349 q^{61} + 527 q^{65} - 1549 q^{67} + 1624 q^{71} + 3856 q^{73} + 903 q^{77} - 1727 q^{79} - 1025 q^{83} - 2902 q^{85} - 4620 q^{89} + 5970 q^{91} - 2012 q^{95} - 2875 q^{97}+O(q^{100}) $ 10 * q + 5 * q^5 - 3 * q^7 - 25 * q^11 - 29 * q^13 - 56 * q^17 + 128 * q^19 + 89 * q^23 - 322 * q^25 + 129 * q^29 - 241 * q^31 + 486 * q^35 + 732 * q^37 + 171 * q^41 - 803 * q^43 - 477 * q^47 - 1072 * q^49 - 748 * q^53 + 2938 * q^55 - 607 * q^59 - 1349 * q^61 + 527 * q^65 - 1549 * q^67 + 1624 * q^71 + 3856 * q^73 + 903 * q^77 - 1727 * q^79 - 1025 * q^83 - 2902 * q^85 - 4620 * q^89 + 5970 * q^91 - 2012 * q^95 - 2875 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−3.15936	+	5.47217i	−0.282581	+	0.489445i	−0.972020	−	0.234899i	$-0.924524\pi$
$5$	−3.15936	+	5.47217i	−0.282581	+	0.489445i	0.689438	+	0.724344i	$0.257857\pi$
$6$		0			0
$7$	14.7898	+	25.6167i	0.798574	+	1.38317i	0.920545	+	0.390637i	$0.127745\pi$
$7$	14.7898	+	25.6167i	0.798574	+	1.38317i	−0.121971	+	0.992534i	$0.538921\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−24.5762	−	42.5672i	−0.673636	−	1.16677i	−0.976866	−	0.213854i	$-0.931398\pi$
$11$	−24.5762	−	42.5672i	−0.673636	−	1.16677i	0.303230	−	0.952917i	$-0.401935\pi$
$12$		0			0
$13$	−9.13278	+	15.8184i	−0.194844	+	0.337481i	−0.946850	−	0.321677i	$-0.895754\pi$
$13$	−9.13278	+	15.8184i	−0.194844	+	0.337481i	0.752005	+	0.659157i	$0.229087\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−63.7873			−0.910041			−0.455021	−	0.890481i	$-0.650368\pi$
$17$	−63.7873			−0.910041			−0.455021	+	0.890481i	$0.650368\pi$
$18$		0			0
$19$	−52.0413			−0.628374			−0.314187	−	0.949361i	$-0.601732\pi$
$19$	−52.0413			−0.628374			−0.314187	+	0.949361i	$0.601732\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−74.6939	+	129.374i	−0.677164	+	1.17288i	0.298668	+	0.954357i	$0.403458\pi$
$23$	−74.6939	+	129.374i	−0.677164	+	1.17288i	−0.975831	+	0.218525i	$0.929876\pi$
$24$		0			0
$25$	42.5369	+	73.6761i	0.340295	+	0.589409i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	59.7077	+	103.417i	0.382326	+	0.662207i	0.991394	−	0.130910i	$-0.0417899\pi$
$29$	59.7077	+	103.417i	0.382326	+	0.662207i	−0.609069	+	0.793118i	$0.708457\pi$
$30$		0			0
$31$	−151.846	+	263.005i	−0.879755	+	1.52378i	−0.0281446	+	0.999604i	$0.508960\pi$
$31$	−151.846	+	263.005i	−0.879755	+	1.52378i	−0.851610	+	0.524176i	$0.824373\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−186.905			−0.902649
$36$		0			0
$37$	170.764			0.758743			0.379371	−	0.925244i	$-0.376140\pi$
$37$	170.764			0.758743			0.379371	+	0.925244i	$0.376140\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	21.8453	−	37.8371i	0.0832112	−	0.144126i	−0.821416	−	0.570329i	$-0.806816\pi$
$41$	21.8453	−	37.8371i	0.0832112	−	0.144126i	0.904628	+	0.426203i	$0.140149\pi$
$42$		0			0
$43$	−223.434	−	386.999i	−0.792403	−	1.37248i	−0.924475	−	0.381242i	$-0.875496\pi$
$43$	−223.434	−	386.999i	−0.792403	−	1.37248i	0.132072	−	0.991240i	$-0.457837\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−111.000	−	192.257i	−0.344488	−	0.596671i	0.640772	−	0.767731i	$-0.278614\pi$
$47$	−111.000	−	192.257i	−0.344488	−	0.596671i	−0.985261	+	0.171060i	$0.945281\pi$
$48$		0			0
$49$	−265.976	+	460.685i	−0.775441	+	1.34310i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	67.3089			0.174445			0.0872226	−	0.996189i	$-0.472201\pi$
$53$	67.3089			0.174445			0.0872226	+	0.996189i	$0.472201\pi$
$54$		0			0
$55$	310.579			0.761428
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−233.898	+	405.123i	−0.516117	+	0.893941i	0.483708	+	0.875230i	$0.339290\pi$
$59$	−233.898	+	405.123i	−0.516117	+	0.893941i	−0.999825	+	0.0187118i	$0.994044\pi$
$60$		0			0
$61$	237.504	+	411.369i	0.498512	+	0.863449i	0.999999	−	0.00171696i	$-0.000546525\pi$
$61$	237.504	+	411.369i	0.498512	+	0.863449i	−0.501486	+	0.865166i	$0.667213\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−57.7074	−	99.9522i	−0.110119	−	0.190731i
$66$		0			0
$67$	120.490	−	208.695i	0.219704	−	0.380539i	−0.735013	−	0.678053i	$-0.762824\pi$
$67$	120.490	−	208.695i	0.219704	−	0.380539i	0.954718	+	0.297514i	$0.0961574\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−550.486			−0.920150			−0.460075	−	0.887880i	$-0.652177\pi$
$71$	−550.486			−0.920150			−0.460075	+	0.887880i	$0.652177\pi$
$72$		0			0
$73$	552.924			0.886505			0.443252	−	0.896397i	$-0.353825\pi$
$73$	552.924			0.886505			0.443252	+	0.896397i	$0.353825\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	726.953	−	1259.12i	1.07590	−	1.86351i
$78$		0			0
$79$	−456.657	−	790.953i	−0.650354	−	1.12645i	−0.983037	−	0.183407i	$-0.941287\pi$
$79$	−456.657	−	790.953i	−0.650354	−	1.12645i	0.332683	−	0.943039i	$-0.392046\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	333.953	+	578.423i	0.441639	+	0.764941i	0.997811	−	0.0661257i	$-0.0210638\pi$
$83$	333.953	+	578.423i	0.441639	+	0.764941i	−0.556172	+	0.831067i	$0.687730\pi$
$84$		0			0
$85$	201.527	−	349.055i	0.257161	−	0.445416i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1430.73			1.70402			0.852008	−	0.523529i	$-0.175385\pi$
$89$	1430.73			1.70402			0.852008	+	0.523529i	$0.175385\pi$
$90$		0			0
$91$	−540.288			−0.622391
$92$		0			0
$93$		0			0
$94$		0			0
$95$	164.417	−	284.779i	0.177567	−	0.307555i
$96$		0			0
$97$	−832.861	−	1442.56i	−0.871796	−	1.50999i	−0.860137	−	0.510063i	$-0.829622\pi$
$97$	−832.861	−	1442.56i	−0.871796	−	1.50999i	−0.0116584	−	0.999932i	$-0.503711\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	342.343	+	592.955i	0.337271	+	0.584171i	0.983918	−	0.178618i	$-0.0571627\pi$
$101$	342.343	+	592.955i	0.337271	+	0.584171i	−0.646647	+	0.762789i	$0.723829\pi$
$102$		0			0
$103$	150.346	−	260.407i	0.143825	−	0.249113i	−0.785109	−	0.619358i	$-0.787393\pi$
$103$	150.346	−	260.407i	0.143825	−	0.249113i	0.928934	+	0.370245i	$0.120726\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1950.79			1.76252			0.881261	−	0.472631i	$-0.156696\pi$
$107$	1950.79			1.76252			0.881261	+	0.472631i	$0.156696\pi$
$108$		0			0
$109$	1637.17			1.43865			0.719323	−	0.694676i	$-0.244452\pi$
$109$	1637.17			1.43865			0.719323	+	0.694676i	$0.244452\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−690.570	+	1196.10i	−0.574897	+	0.995751i	0.421156	+	0.906988i	$0.361625\pi$
$113$	−690.570	+	1196.10i	−0.574897	+	0.995751i	−0.996053	+	0.0887628i	$0.971709\pi$
$114$		0			0
$115$	−471.970	−	817.475i	−0.382708	−	0.662869i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−943.402	−	1634.02i	−0.726735	−	1.25874i
$120$		0			0
$121$	−542.475	+	939.594i	−0.407570	+	0.705931i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1327.40			−0.949808
$126$		0			0
$127$	1571.28			1.09786			0.548931	−	0.835868i	$-0.315035\pi$
$127$	1571.28			1.09786			0.548931	+	0.835868i	$0.315035\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−72.1901	+	125.037i	−0.0481472	+	0.0833934i	−0.889095	−	0.457723i	$-0.848665\pi$
$131$	−72.1901	+	125.037i	−0.0481472	+	0.0833934i	0.840947	+	0.541117i	$0.181998\pi$
$132$		0			0
$133$	−769.681	−	1333.13i	−0.501803	−	0.869148i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	761.191	+	1318.42i	0.474693	+	0.822193i	0.999580	−	0.0289792i	$-0.00922566\pi$
$137$	761.191	+	1318.42i	0.474693	+	0.822193i	−0.524887	+	0.851172i	$0.675892\pi$
$138$		0			0
$139$	−788.882	+	1366.38i	−0.481382	+	0.833778i	−0.999772	−	0.0213665i	$-0.993198\pi$
$139$	−788.882	+	1366.38i	−0.481382	+	0.833778i	0.518390	+	0.855144i	$0.326532\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	897.795			0.525017
$144$		0			0
$145$	−754.552			−0.432152
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1167.63	−	2022.39i	0.641984	−	1.11195i	−0.343005	−	0.939334i	$-0.611445\pi$
$149$	1167.63	−	2022.39i	0.641984	−	1.11195i	0.984989	−	0.172616i	$-0.0552219\pi$
$150$		0			0
$151$	862.918	+	1494.62i	0.465055	+	0.805498i	0.999204	−	0.0398919i	$-0.0127014\pi$
$151$	862.918	+	1494.62i	0.465055	+	0.805498i	−0.534149	+	0.845390i	$0.679368\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−959.473	−	1661.86i	−0.497205	−	0.861184i
$156$		0			0
$157$	18.4834	−	32.0143i	0.00939579	−	0.0162740i	−0.861289	−	0.508115i	$-0.830343\pi$
$157$	18.4834	−	32.0143i	0.00939579	−	0.0162740i	0.870685	+	0.491841i	$0.163676\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−4418.83			−2.16306
$162$		0			0
$163$	1112.17			0.534430			0.267215	−	0.963637i	$-0.413897\pi$
$163$	1112.17			0.534430			0.267215	+	0.963637i	$0.413897\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−828.243	+	1434.56i	−0.383781	+	0.664728i	−0.991599	−	0.129348i	$-0.958711\pi$
$167$	−828.243	+	1434.56i	−0.383781	+	0.664728i	0.607819	+	0.794076i	$0.292045\pi$
$168$		0			0
$169$	931.685	+	1613.73i	0.424071	+	0.734513i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−317.108	−	549.248i	−0.139360	−	0.241379i	0.787894	−	0.615810i	$-0.211171\pi$
$173$	−317.108	−	549.248i	−0.139360	−	0.241379i	−0.927255	+	0.374431i	$0.877838\pi$
$174$		0			0
$175$	−1258.23	+	2179.31i	−0.543502	+	0.941374i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	374.805			0.156504			0.0782521	−	0.996934i	$-0.475066\pi$
$179$	374.805			0.156504			0.0782521	+	0.996934i	$0.475066\pi$
$180$		0			0
$181$	−859.130			−0.352810			−0.176405	−	0.984318i	$-0.556447\pi$
$181$	−859.130			−0.352810			−0.176405	+	0.984318i	$0.556447\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−539.505	+	934.451i	−0.214407	+	0.371363i
$186$		0			0
$187$	1567.65	+	2715.25i	0.613036	+	1.06181i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1538.37	+	2664.54i	0.582789	+	1.00942i	0.995147	+	0.0983978i	$0.0313718\pi$
$191$	1538.37	+	2664.54i	0.582789	+	1.00942i	−0.412359	+	0.911022i	$0.635295\pi$
$192$		0			0
$193$	−68.3081	+	118.313i	−0.0254763	+	0.0441262i	−0.878482	−	0.477775i	$-0.841444\pi$
$193$	−68.3081	+	118.313i	−0.0254763	+	0.0441262i	0.853006	+	0.521901i	$0.174777\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−3635.05			−1.31465			−0.657326	−	0.753606i	$-0.728313\pi$
$197$	−3635.05			−1.31465			−0.657326	+	0.753606i	$0.728313\pi$
$198$		0			0
$199$	−1611.10			−0.573909			−0.286955	−	0.957944i	$-0.592643\pi$
$199$	−1611.10			−0.573909			−0.286955	+	0.957944i	$0.592643\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1766.13	+	3059.03i	−0.610631	+	1.05764i
$204$		0			0
$205$	138.034	+	239.082i	0.0470279	+	0.0814547i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1278.98	+	2215.25i	0.423295	+	0.733168i
$210$		0			0
$211$	1646.97	−	2852.63i	0.537355	−	0.930726i	−0.461691	−	0.887041i	$-0.652757\pi$
$211$	1646.97	−	2852.63i	0.537355	−	0.930726i	0.999045	−	0.0436847i	$-0.0139097\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	2823.63			0.895674
$216$		0			0
$217$	−8983.10			−2.81020
$218$		0			0
$219$		0			0
$220$		0			0
$221$	582.556	−	1009.02i	0.177316	−	0.307121i
$222$		0			0
$223$	−519.225	−	899.324i	−0.155919	−	0.270059i	0.777474	−	0.628914i	$-0.216500\pi$
$223$	−519.225	−	899.324i	−0.155919	−	0.270059i	−0.933393	+	0.358855i	$0.883167\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−2314.33	−	4008.54i	−0.676686	−	1.17205i	−0.975973	−	0.217891i	$-0.930082\pi$
$227$	−2314.33	−	4008.54i	−0.676686	−	1.17205i	0.299287	−	0.954163i	$-0.403251\pi$
$228$		0			0
$229$	172.157	−	298.184i	0.0496787	−	0.0860460i	−0.840117	−	0.542406i	$-0.817514\pi$
$229$	172.157	−	298.184i	0.0496787	−	0.0860460i	0.889795	+	0.456360i	$0.150847\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−401.177			−0.112798			−0.0563991	−	0.998408i	$-0.517962\pi$
$233$	−401.177			−0.112798			−0.0563991	+	0.998408i	$0.517962\pi$
$234$		0			0
$235$	1402.75			0.389384
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1138.16	−	1971.35i	0.308039	−	0.533539i	−0.669894	−	0.742457i	$-0.733661\pi$
$239$	1138.16	−	1971.35i	0.308039	−	0.533539i	0.977933	+	0.208917i	$0.0669939\pi$
$240$		0			0
$241$	−107.828	−	186.764i	−0.0288208	−	0.0499191i	0.851255	−	0.524752i	$-0.175842\pi$
$241$	−107.828	−	186.764i	−0.0288208	−	0.0499191i	−0.880076	+	0.474833i	$0.842509\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1680.63	−	2910.93i	−0.438251	−	0.759072i
$246$		0			0
$247$	475.282	−	823.213i	0.122435	−	0.212064i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	335.402			0.0843443			0.0421721	−	0.999110i	$-0.486572\pi$
$251$	335.402			0.0843443			0.0421721	+	0.999110i	$0.486572\pi$
$252$		0			0
$253$	7342.76			1.82465
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−2253.80	+	3903.69i	−0.547035	+	0.947493i	0.451441	+	0.892301i	$0.350910\pi$
$257$	−2253.80	+	3903.69i	−0.547035	+	0.947493i	−0.998476	+	0.0551917i	$0.982423\pi$
$258$		0			0
$259$	2525.57	+	4374.42i	0.605912	+	1.04947i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	1077.54	+	1866.35i	0.252638	+	0.437582i	0.964251	−	0.264990i	$-0.0853685\pi$
$263$	1077.54	+	1866.35i	0.252638	+	0.437582i	−0.711613	+	0.702571i	$0.752035\pi$
$264$		0			0
$265$	−212.653	+	368.326i	−0.0492950	+	0.0853814i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	4048.11			0.917537			0.458768	−	0.888556i	$-0.348291\pi$
$269$	4048.11			0.917537			0.458768	+	0.888556i	$0.348291\pi$
$270$		0			0
$271$	−290.780			−0.0651794			−0.0325897	−	0.999469i	$-0.510375\pi$
$271$	−290.780			−0.0651794			−0.0325897	+	0.999469i	$0.510375\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2090.79	−	3621.35i	0.458470	−	0.794094i
$276$		0			0
$277$	1075.95	+	1863.60i	0.233385	+	0.404235i	0.958802	−	0.284075i	$-0.0916864\pi$
$277$	1075.95	+	1863.60i	0.233385	+	0.404235i	−0.725417	+	0.688310i	$0.758353\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	2135.57	+	3698.91i	0.453371	+	0.785261i	0.998593	−	0.0530302i	$-0.0168880\pi$
$281$	2135.57	+	3698.91i	0.453371	+	0.785261i	−0.545222	+	0.838292i	$0.683555\pi$
$282$		0			0
$283$	82.4026	−	142.725i	0.0173086	−	0.0299793i	−0.857241	−	0.514915i	$-0.827824\pi$
$283$	82.4026	−	142.725i	0.0173086	−	0.0299793i	0.874550	+	0.484935i	$0.161157\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1292.35			0.265801
$288$		0			0
$289$	−844.176			−0.171825
$290$		0			0
$291$		0			0
$292$		0			0
$293$	2744.86	−	4754.24i	0.547292	−	0.947937i	−0.451167	−	0.892439i	$-0.648992\pi$
$293$	2744.86	−	4754.24i	0.547292	−	0.947937i	0.998459	−	0.0554975i	$-0.0176745\pi$
$294$		0			0
$295$	−1477.93	−	2559.86i	−0.291690	−	0.505223i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1364.33	−	2363.08i	−0.263883	−	0.457059i
$300$		0			0
$301$	6609.08	−	11447.3i	1.26559	−	2.19206i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−3001.44			−0.563481
$306$		0			0
$307$	−6126.58			−1.13897			−0.569483	−	0.822003i	$-0.692857\pi$
$307$	−6126.58			−1.13897			−0.569483	+	0.822003i	$0.692857\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−73.0772	+	126.573i	−0.0133242	+	0.0230782i	−0.872611	−	0.488417i	$-0.837575\pi$
$311$	−73.0772	+	126.573i	−0.0133242	+	0.0230782i	0.859286	+	0.511495i	$0.170908\pi$
$312$		0			0
$313$	−2123.90	−	3678.71i	−0.383546	−	0.664322i	0.608020	−	0.793922i	$-0.291964\pi$
$313$	−2123.90	−	3678.71i	−0.383546	−	0.664322i	−0.991566	+	0.129600i	$0.958631\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1793.68	−	3106.75i	−0.317802	−	0.550450i	0.662227	−	0.749303i	$-0.269612\pi$
$317$	−1793.68	−	3106.75i	−0.317802	−	0.550450i	−0.980029	+	0.198854i	$0.936278\pi$
$318$		0			0
$319$	2934.77	−	5083.17i	0.515096	−	0.892173i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	3319.58			0.571846
$324$		0			0
$325$	−1553.92			−0.265219
$326$		0			0
$327$		0			0
$328$		0			0
$329$	3283.32	−	5686.88i	0.550199	−	0.952973i
$330$		0			0
$331$	−1246.46	−	2158.94i	−0.206984	−	0.358507i	0.743779	−	0.668426i	$-0.233032\pi$
$331$	−1246.46	−	2158.94i	−0.206984	−	0.358507i	−0.950763	+	0.309919i	$0.899698\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	761.341	+	1318.68i	0.124169	+	0.215067i
$336$		0			0
$337$	534.073	−	925.042i	0.0863288	−	0.149526i	−0.819628	−	0.572896i	$-0.805820\pi$
$337$	534.073	−	925.042i	0.0863288	−	0.149526i	0.905957	+	0.423370i	$0.139153\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	14927.2			2.37054
$342$		0			0
$343$	−5589.14			−0.879841
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−3042.61	+	5269.96i	−0.470709	+	0.815292i	−0.999439	−	0.0334980i	$-0.989335\pi$
$347$	−3042.61	+	5269.96i	−0.470709	+	0.815292i	0.528730	+	0.848790i	$0.322669\pi$
$348$		0			0
$349$	3533.63	+	6120.43i	0.541979	+	0.938736i	0.998790	+	0.0491722i	$0.0156583\pi$
$349$	3533.63	+	6120.43i	0.541979	+	0.938736i	−0.456811	+	0.889564i	$0.651008\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	5016.09	+	8688.12i	0.756316	+	1.30998i	0.944718	+	0.327885i	$0.106336\pi$
$353$	5016.09	+	8688.12i	0.756316	+	1.30998i	−0.188402	+	0.982092i	$0.560331\pi$
$354$		0			0
$355$	1739.18	−	3012.35i	0.260017	−	0.450363i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−7628.71			−1.12153			−0.560763	−	0.827976i	$-0.689492\pi$
$359$	−7628.71			−1.12153			−0.560763	+	0.827976i	$0.689492\pi$
$360$		0			0
$361$	−4150.70			−0.605146
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−1746.88	+	3025.69i	−0.250510	+	0.433896i
$366$		0			0
$367$	673.488	+	1166.52i	0.0957924	+	0.165917i	0.909939	−	0.414742i	$-0.136128\pi$
$367$	673.488	+	1166.52i	0.0957924	+	0.165917i	−0.814147	+	0.580659i	$0.802795\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	995.486	+	1724.23i	0.139307	+	0.241287i
$372$		0			0
$373$	66.5062	−	115.192i	0.00923206	−	0.0159904i	−0.861372	−	0.507974i	$-0.830395\pi$
$373$	66.5062	−	115.192i	0.00923206	−	0.0159904i	0.870605	+	0.491983i	$0.163728\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2181.19			−0.297976
$378$		0			0
$379$	2109.40			0.285891			0.142945	−	0.989731i	$-0.454343\pi$
$379$	2109.40			0.285891			0.142945	+	0.989731i	$0.454343\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−119.054	+	206.207i	−0.0158835	+	0.0275110i	−0.873858	−	0.486181i	$-0.838389\pi$
$383$	−119.054	+	206.207i	−0.0158835	+	0.0275110i	0.857974	+	0.513692i	$0.171723\pi$
$384$		0			0
$385$	4593.41	+	7956.01i	0.608056	+	1.05318i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	4.07864	+	7.06440i	0.000531607	+	0.000920770i	0.866291	−	0.499540i	$-0.166497\pi$
$389$	4.07864	+	7.06440i	0.000531607	+	0.000920770i	−0.865759	+	0.500460i	$0.833164\pi$
$390$		0			0
$391$	4764.53	−	8252.40i	0.616247	−	1.06737i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	5770.97			0.735112
$396$		0			0
$397$	347.061			0.0438753			0.0219376	−	0.999759i	$-0.493016\pi$
$397$	347.061			0.0438753			0.0219376	+	0.999759i	$0.493016\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	3515.36	−	6088.77i	0.437777	−	0.758251i	−0.559741	−	0.828668i	$-0.689099\pi$
$401$	3515.36	−	6088.77i	0.437777	−	0.758251i	0.997518	+	0.0704161i	$0.0224327\pi$
$402$		0			0
$403$	−2773.56	−	4803.94i	−0.342831	−	0.593800i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−4196.73	−	7268.95i	−0.511116	−	0.885279i
$408$		0			0
$409$	−7499.75	+	12990.0i	−0.906697	+	1.57044i	−0.0880735	+	0.996114i	$0.528071\pi$
$409$	−7499.75	+	12990.0i	−0.906697	+	1.57044i	−0.818623	+	0.574331i	$0.805262\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−13837.2			−1.64863
$414$		0			0
$415$	−4220.30			−0.499196
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−5234.16	+	9065.83i	−0.610275	+	1.05703i	0.380918	+	0.924609i	$0.375608\pi$
$419$	−5234.16	+	9065.83i	−0.610275	+	1.05703i	−0.991194	+	0.132419i	$0.957725\pi$
$420$		0			0
$421$	1898.54	+	3288.37i	0.219784	+	0.380677i	0.954742	−	0.297436i	$-0.0961314\pi$
$421$	1898.54	+	3288.37i	0.219784	+	0.380677i	−0.734958	+	0.678113i	$0.762798\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−2713.32	−	4699.60i	−0.309683	−	0.536387i
$426$		0			0
$427$	−7025.27	+	12168.1i	−0.796198	+	1.37906i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−16434.0			−1.83665			−0.918326	−	0.395825i	$-0.870459\pi$
$431$	−16434.0			−1.83665			−0.918326	+	0.395825i	$0.870459\pi$
$432$		0			0
$433$	15688.1			1.74116			0.870581	−	0.492024i	$-0.163743\pi$
$433$	15688.1			1.74116			0.870581	+	0.492024i	$0.163743\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	3887.17	−	6732.78i	0.425512	−	0.737008i
$438$		0			0
$439$	399.898	+	692.644i	0.0434763	+	0.0753032i	0.886945	−	0.461876i	$-0.152823\pi$
$439$	399.898	+	692.644i	0.0434763	+	0.0753032i	−0.843468	+	0.537179i	$0.819490\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−981.481	−	1699.97i	−0.105263	−	0.182321i	0.808583	−	0.588383i	$-0.200235\pi$
$443$	−981.481	−	1699.97i	−0.105263	−	0.182321i	−0.913846	+	0.406062i	$0.866902\pi$
$444$		0			0
$445$	−4520.20	+	7829.21i	−0.481523	+	0.834023i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	4590.96			0.482541			0.241270	−	0.970458i	$-0.422436\pi$
$449$	4590.96			0.482541			0.241270	+	0.970458i	$0.422436\pi$
$450$		0			0
$451$	−2147.49			−0.224216
$452$		0			0
$453$		0			0
$454$		0			0
$455$	1706.96	−	2956.55i	0.175876	−	0.304626i
$456$		0			0
$457$	−797.352	−	1381.05i	−0.0816161	−	0.141363i	0.822328	−	0.569014i	$-0.192675\pi$
$457$	−797.352	−	1381.05i	−0.0816161	−	0.141363i	−0.903944	+	0.427650i	$0.859341\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−2787.12	−	4827.44i	−0.281582	−	0.487714i	0.690193	−	0.723626i	$-0.257526\pi$
$461$	−2787.12	−	4827.44i	−0.281582	−	0.487714i	−0.971774	+	0.235912i	$0.924192\pi$
$462$		0			0
$463$	−6644.81	+	11509.1i	−0.666977	+	1.15524i	0.311768	+	0.950158i	$0.399079\pi$
$463$	−6644.81	+	11509.1i	−0.666977	+	1.15524i	−0.978745	+	0.205080i	$0.934255\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−18331.8			−1.81648			−0.908238	−	0.418455i	$-0.862572\pi$
$467$	−18331.8			−1.81648			−0.908238	+	0.418455i	$0.862572\pi$
$468$		0			0
$469$	7128.09			0.701801
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−10982.3	+	19021.9i	−1.06758	+	1.84911i
$474$		0			0
$475$	−2213.68	−	3834.20i	−0.213833	−	0.370369i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	9961.77	+	17254.3i	0.950240	+	1.64586i	0.744903	+	0.667172i	$0.232496\pi$
$479$	9961.77	+	17254.3i	0.950240	+	1.64586i	0.205337	+	0.978691i	$0.434171\pi$
$480$		0			0
$481$	−1559.55	+	2701.23i	−0.147837	+	0.256061i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	10525.2			0.985413
$486$		0			0
$487$	6788.63			0.631668			0.315834	−	0.948814i	$-0.397716\pi$
$487$	6788.63			0.631668			0.315834	+	0.948814i	$0.397716\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−3035.78	+	5258.12i	−0.279028	+	0.483291i	−0.971143	−	0.238496i	$-0.923346\pi$
$491$	−3035.78	+	5258.12i	−0.279028	+	0.483291i	0.692115	+	0.721787i	$0.256679\pi$
$492$		0			0
$493$	−3808.60	−	6596.68i	−0.347932	−	0.602636i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−8141.57	−	14101.6i	−0.734808	−	1.27272i
$498$		0			0
$499$	3663.64	−	6345.60i	0.328671	−	0.569275i	−0.653577	−	0.756860i	$-0.726733\pi$
$499$	3663.64	−	6345.60i	0.328671	−	0.569275i	0.982248	+	0.187585i	$0.0600659\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	2121.18			0.188029			0.0940145	−	0.995571i	$-0.470030\pi$
$503$	2121.18			0.188029			0.0940145	+	0.995571i	$0.470030\pi$
$504$		0			0
$505$	−4326.33			−0.381226
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−5680.40	+	9838.74i	−0.494655	+	0.856767i	−0.999981	−	0.00616140i	$-0.998039\pi$
$509$	−5680.40	+	9838.74i	−0.494655	+	0.856767i	0.505326	+	0.862928i	$0.331372\pi$
$510$		0			0
$511$	8177.64	+	14164.1i	0.707940	+	1.22619i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	949.992	+	1645.43i	0.0812847	+	0.140789i
$516$		0			0
$517$	−5455.89	+	9449.87i	−0.464119	+	0.803878i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	9012.94			0.757897			0.378948	−	0.925418i	$-0.376286\pi$
$521$	9012.94			0.757897			0.378948	+	0.925418i	$0.376286\pi$
$522$		0			0
$523$	7991.81			0.668178			0.334089	−	0.942541i	$-0.391571\pi$
$523$	7991.81			0.668178			0.334089	+	0.942541i	$0.391571\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	9685.87	−	16776.4i	0.800613	−	1.38670i
$528$		0			0
$529$	−5074.87	−	8789.94i	−0.417101	−	0.722441i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	399.017	+	691.117i	0.0324265	+	0.0561643i
$534$		0			0
$535$	−6163.23	+	10675.0i	−0.498056	+	0.862658i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	26146.7			2.08946
$540$		0			0
$541$	−19447.1			−1.54546			−0.772732	−	0.634732i	$-0.781111\pi$
$541$	−19447.1			−1.54546			−0.772732	+	0.634732i	$0.781111\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−5172.40	+	8958.86i	−0.406534	+	0.704138i
$546$		0			0
$547$	−8386.46	−	14525.8i	−0.655537	−	1.13542i	−0.981759	−	0.190131i	$-0.939109\pi$
$547$	−8386.46	−	14525.8i	−0.655537	−	1.13542i	0.326221	−	0.945293i	$-0.394224\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−3107.27	−	5381.95i	−0.240243	−	0.416114i
$552$		0			0
$553$	13507.7	−	23396.1i	1.03871	−	1.79910i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−7836.27			−0.596110			−0.298055	−	0.954549i	$-0.596338\pi$
$557$	−7836.27			−0.596110			−0.298055	+	0.954549i	$0.596338\pi$
$558$		0			0
$559$	8162.29			0.617581
$560$		0			0
$561$		0			0
$562$		0			0
$563$	12388.9	−	21458.3i	0.927409	−	1.60632i	0.139768	−	0.990184i	$-0.455364\pi$
$563$	12388.9	−	21458.3i	0.927409	−	1.60632i	0.787641	−	0.616134i	$-0.211302\pi$
$564$		0			0
$565$	−4363.52	−	7557.83i	−0.324911	−	0.562762i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	5785.67	+	10021.1i	0.426270	+	0.738322i	0.996538	−	0.0831371i	$-0.0264939\pi$
$569$	5785.67	+	10021.1i	0.426270	+	0.738322i	−0.570268	+	0.821459i	$0.693161\pi$
$570$		0			0
$571$	97.6465	−	169.129i	0.00715653	−	0.0123955i	−0.862425	−	0.506185i	$-0.831055\pi$
$571$	97.6465	−	169.129i	0.00715653	−	0.0123955i	0.869581	+	0.493789i	$0.164389\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−12709.0			−0.921743
$576$		0			0
$577$	−5912.60			−0.426594			−0.213297	−	0.976987i	$-0.568420\pi$
$577$	−5912.60			−0.426594			−0.213297	+	0.976987i	$0.568420\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−9878.18	+	17109.5i	−0.705363	+	1.22172i
$582$		0			0
$583$	−1654.19	−	2865.15i	−0.117512	−	0.203538i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	574.756	+	995.507i	0.0404135	+	0.0699983i	0.885525	−	0.464592i	$-0.153799\pi$
$587$	574.756	+	995.507i	0.0404135	+	0.0699983i	−0.845111	+	0.534591i	$0.820466\pi$
$588$		0			0
$589$	7902.28	−	13687.2i	0.552815	−	0.957503i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	6387.66			0.442344			0.221172	−	0.975235i	$-0.429012\pi$
$593$	6387.66			0.442344			0.221172	+	0.975235i	$0.429012\pi$
$594$		0			0
$595$	11922.2			0.821448
$596$		0			0
$597$		0			0
$598$		0			0
$599$	8626.38	−	14941.3i	0.588421	−	1.01918i	−0.406018	−	0.913865i	$-0.633083\pi$
$599$	8626.38	−	14941.3i	0.588421	−	1.01918i	0.994439	−	0.105310i	$-0.0335836\pi$
$600$		0			0
$601$	−3790.51	−	6565.36i	−0.257268	−	0.445602i	0.708241	−	0.705971i	$-0.249489\pi$
$601$	−3790.51	−	6565.36i	−0.257268	−	0.445602i	−0.965509	+	0.260369i	$0.916156\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−3427.74	−	5937.03i	−0.230343	−	0.398966i
$606$		0			0
$607$	−7895.62	+	13675.6i	−0.527963	+	0.914458i	0.471506	+	0.881863i	$0.343711\pi$
$607$	−7895.62	+	13675.6i	−0.527963	+	0.914458i	−0.999469	+	0.0325952i	$0.989623\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	4054.94			0.268487
$612$		0			0
$613$	16043.4			1.05708			0.528538	−	0.848910i	$-0.322740\pi$
$613$	16043.4			1.05708			0.528538	+	0.848910i	$0.322740\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	12582.2	−	21793.1i	0.820975	−	1.42197i	−0.0839822	−	0.996467i	$-0.526764\pi$
$617$	12582.2	−	21793.1i	0.820975	−	1.42197i	0.904957	−	0.425503i	$-0.139903\pi$
$618$		0			0
$619$	−158.460	−	274.460i	−0.0102892	−	0.0178215i	0.860835	−	0.508884i	$-0.169942\pi$
$619$	−158.460	−	274.460i	−0.0102892	−	0.0178215i	−0.871124	+	0.491063i	$0.836609\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	21160.3	+	36650.6i	1.36078	+	2.35695i
$624$		0			0
$625$	−1123.40	+	1945.78i	−0.0718974	+	0.124530i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−10892.6			−0.690487
$630$		0			0
$631$	24816.8			1.56567			0.782837	−	0.622227i	$-0.213772\pi$
$631$	24816.8			1.56567			0.782837	+	0.622227i	$0.213772\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−4964.23	+	8598.30i	−0.310235	+	0.537343i
$636$		0			0
$637$	−4858.21	−	8414.66i	−0.302181	−	0.523393i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−9911.62	−	17167.4i	−0.610742	−	1.05784i	−0.991116	−	0.133003i	$-0.957538\pi$
$641$	−9911.62	−	17167.4i	−0.610742	−	1.05784i	0.380374	−	0.924833i	$-0.375795\pi$
$642$		0			0
$643$	−3047.77	+	5278.88i	−0.186924	+	0.323762i	−0.944223	−	0.329306i	$-0.893185\pi$
$643$	−3047.77	+	5278.88i	−0.186924	+	0.323762i	0.757299	+	0.653068i	$0.226518\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−7321.69			−0.444892			−0.222446	−	0.974945i	$-0.571404\pi$
$647$	−7321.69			−0.444892			−0.222446	+	0.974945i	$0.571404\pi$
$648$		0			0
$649$	22993.3			1.39070
$650$		0			0
$651$		0			0
$652$		0			0
$653$	3367.87	−	5833.31i	0.201830	−	0.349579i	−0.747288	−	0.664500i	$-0.768645\pi$
$653$	3367.87	−	5833.31i	0.201830	−	0.349579i	0.949118	+	0.314921i	$0.101978\pi$
$654$		0			0
$655$	−456.149	−	790.073i	−0.0272110	−	0.0471308i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−11500.6	−	19919.6i	−0.679818	−	1.17748i	−0.975035	−	0.222050i	$-0.928725\pi$
$659$	−11500.6	−	19919.6i	−0.679818	−	1.17748i	0.295217	−	0.955430i	$-0.404608\pi$
$660$		0			0
$661$	−12856.4	+	22268.0i	−0.756517	+	1.31033i	0.188099	+	0.982150i	$0.439767\pi$
$661$	−12856.4	+	22268.0i	−0.756517	+	1.31033i	−0.944617	+	0.328176i	$0.893566\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	9726.79			0.567201
$666$		0			0
$667$	−17839.2			−1.03559
$668$		0			0
$669$		0			0
$670$		0			0
$671$	11673.9	−	20219.7i	0.671631	−	1.16330i
$672$		0			0
$673$	−2310.89	−	4002.58i	−0.132360	−	0.229254i	0.792226	−	0.610228i	$-0.208922\pi$
$673$	−2310.89	−	4002.58i	−0.132360	−	0.229254i	−0.924586	+	0.380974i	$0.875589\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	9136.02	+	15824.1i	0.518650	+	0.898328i	0.999765	+	0.0216704i	$0.00689844\pi$
$677$	9136.02	+	15824.1i	0.518650	+	0.898328i	−0.481115	+	0.876657i	$0.659768\pi$
$678$		0			0
$679$	24635.7	−	42670.3i	1.39239	−	2.41169i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	30350.5			1.70034			0.850169	−	0.526510i	$-0.176500\pi$
$683$	30350.5			1.70034			0.850169	+	0.526510i	$0.176500\pi$
$684$		0			0
$685$	−9619.50			−0.536558
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−614.718	+	1064.72i	−0.0339897	+	0.0588718i
$690$		0			0
$691$	5417.32	+	9383.07i	0.298241	+	0.516568i	0.975734	−	0.218961i	$-0.0702668\pi$
$691$	5417.32	+	9383.07i	0.298241	+	0.516568i	−0.677493	+	0.735529i	$0.736933\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−4984.72	−	8633.79i	−0.272059	−	0.471220i
$696$		0			0
$697$	−1393.45	+	2413.53i	−0.0757257	+	0.131161i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	12323.5			0.663982			0.331991	−	0.943283i	$-0.392280\pi$
$701$	12323.5			0.663982			0.331991	+	0.943283i	$0.392280\pi$
$702$		0			0
$703$	−8886.81			−0.476774
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−10126.4	+	17539.4i	−0.538672	+	0.933008i
$708$		0			0
$709$	−16451.2	−	28494.4i	−0.871424	−	1.50935i	−0.860524	−	0.509409i	$-0.829864\pi$
$709$	−16451.2	−	28494.4i	−0.871424	−	1.50935i	−0.0108993	−	0.999941i	$-0.503469\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−22684.0	−	39289.8i	−1.19148	−	2.06370i
$714$		0			0
$715$	−2836.45	+	4912.88i	−0.148360	+	0.256967i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	8518.05			0.441821			0.220911	−	0.975294i	$-0.429097\pi$
$719$	8518.05			0.441821			0.220911	+	0.975294i	$0.429097\pi$
$720$		0			0
$721$	8894.34			0.459421
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−5079.56	+	8798.06i	−0.260207	+	0.450692i
$726$		0			0
$727$	−18606.1	−	32226.8i	−0.949193	−	1.64405i	−0.747129	−	0.664679i	$-0.768568\pi$
$727$	−18606.1	−	32226.8i	−0.949193	−	1.64405i	−0.202064	−	0.979372i	$-0.564765\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	14252.2	+	24685.6i	0.721120	+	1.24902i
$732$		0			0
$733$	−10477.0	+	18146.8i	−0.527938	+	0.914415i	0.471532	+	0.881849i	$0.343701\pi$
$733$	−10477.0	+	18146.8i	−0.527938	+	0.914415i	−0.999470	+	0.0325659i	$0.989632\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−11844.7			−0.592002
$738$		0			0
$739$	28544.4			1.42087			0.710435	−	0.703763i	$-0.248498\pi$
$739$	28544.4			1.42087			0.710435	+	0.703763i	$0.248498\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−7505.41	+	12999.7i	−0.370588	+	0.641877i	−0.989656	−	0.143460i	$-0.954177\pi$
$743$	−7505.41	+	12999.7i	−0.370588	+	0.641877i	0.619068	+	0.785337i	$0.287510\pi$
$744$		0			0
$745$	7377.90	+	12778.9i	0.362826	+	0.628433i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	28851.8	+	49972.7i	1.40750	+	2.43787i
$750$		0			0
$751$	−7331.27	+	12698.1i	−0.356221	+	0.616992i	−0.987326	−	0.158705i	$-0.949268\pi$
$751$	−7331.27	+	12698.1i	−0.356221	+	0.616992i	0.631105	+	0.775697i	$0.282602\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−10905.1			−0.525663
$756$		0			0
$757$	−36100.7			−1.73329			−0.866646	−	0.498924i	$-0.833729\pi$
$757$	−36100.7			−1.73329			−0.866646	+	0.498924i	$0.833729\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−8415.28	+	14575.7i	−0.400859	+	0.694308i	−0.993830	−	0.110916i	$-0.964622\pi$
$761$	−8415.28	+	14575.7i	−0.400859	+	0.694308i	0.592971	+	0.805224i	$0.297955\pi$
$762$		0			0
$763$	24213.4	+	41938.8i	1.14886	+	1.98989i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−4272.28	−	7399.80i	−0.201125	−	0.348359i
$768$		0			0
$769$	3711.90	−	6429.19i	0.174063	−	0.301486i	−0.765774	−	0.643110i	$-0.777644\pi$
$769$	3711.90	−	6429.19i	0.174063	−	0.301486i	0.939837	+	0.341624i	$0.110977\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−13516.7			−0.628929			−0.314464	−	0.949269i	$-0.601825\pi$
$773$	−13516.7			−0.628929			−0.314464	+	0.949269i	$0.601825\pi$
$774$		0			0
$775$	−25836.3			−1.19751
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1136.86	+	1969.10i	−0.0522878	+	0.0905651i
$780$		0			0
$781$	13528.8	+	23432.6i	0.619846	+	1.07360i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	116.792	+	202.289i	0.00531015	+	0.00919746i
$786$		0			0
$787$	2191.09	−	3795.08i	0.0992426	−	0.171893i	−0.812129	−	0.583478i	$-0.801691\pi$
$787$	2191.09	−	3795.08i	0.0992426	−	0.171893i	0.911371	+	0.411585i	$0.135025\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−40853.6			−1.83639
$792$		0			0
$793$	−8676.28			−0.388529
$794$		0			0
$795$		0			0
$796$		0			0
$797$	2171.85	−	3761.75i	0.0965254	−	0.167187i	−0.813719	−	0.581259i	$-0.802560\pi$
$797$	2171.85	−	3761.75i	0.0965254	−	0.167187i	0.910244	+	0.414072i	$0.135894\pi$
$798$		0			0
$799$	7080.37	+	12263.6i	0.313499	+	0.542996i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−13588.7	−	23536.4i	−0.597181	−	1.03435i
$804$		0			0
$805$	13960.7	−	24180.6i	0.611241	−	1.05870i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	14546.1			0.632155			0.316077	−	0.948733i	$-0.397634\pi$
$809$	14546.1			0.632155			0.316077	+	0.948733i	$0.397634\pi$
$810$		0			0
$811$	−22663.2			−0.981272			−0.490636	−	0.871365i	$-0.663236\pi$
$811$	−22663.2			−0.981272			−0.490636	+	0.871365i	$0.663236\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−3513.75	+	6086.00i	−0.151020	+	0.261574i
$816$		0			0
$817$	11627.8	+	20139.9i	0.497925	+	0.862432i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−18211.0	−	31542.4i	−0.774139	−	1.34085i	−0.935277	−	0.353917i	$-0.884850\pi$
$821$	−18211.0	−	31542.4i	−0.774139	−	1.34085i	0.161138	−	0.986932i	$-0.448484\pi$
$822$		0			0
$823$	−3934.78	+	6815.24i	−0.166656	+	0.288656i	−0.937242	−	0.348679i	$-0.886630\pi$
$823$	−3934.78	+	6815.24i	−0.166656	+	0.288656i	0.770586	+	0.637336i	$0.219964\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−22101.6			−0.929322			−0.464661	−	0.885489i	$-0.653824\pi$
$827$	−22101.6			−0.929322			−0.464661	+	0.885489i	$0.653824\pi$
$828$		0			0
$829$	17056.2			0.714580			0.357290	−	0.933994i	$-0.383701\pi$
$829$	17056.2			0.714580			0.357290	+	0.933994i	$0.383701\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	16965.9	−	29385.8i	0.705684	−	1.22228i
$834$		0			0
$835$	−5233.43	−	9064.57i	−0.216899	−	0.375679i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	11472.3	+	19870.6i	0.472072	+	0.817653i	0.999489	−	0.0319535i	$-0.0101729\pi$
$839$	11472.3	+	19870.6i	0.472072	+	0.817653i	−0.527417	+	0.849606i	$0.676840\pi$
$840$		0			0
$841$	5064.48	−	8771.94i	0.207654	−	0.359668i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−11774.1			−0.479339
$846$		0			0
$847$	−32092.4			−1.30190
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−12755.1	+	22092.4i	−0.513793	+	0.889916i
$852$		0			0
$853$	15435.6	+	26735.3i	0.619584	+	1.07315i	0.989562	+	0.144110i	$0.0460320\pi$
$853$	15435.6	+	26735.3i	0.619584	+	1.07315i	−0.369978	+	0.929041i	$0.620635\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−7544.95	−	13068.2i	−0.300736	−	0.520890i	0.675567	−	0.737299i	$-0.263899\pi$
$857$	−7544.95	−	13068.2i	−0.300736	−	0.520890i	−0.976303	+	0.216409i	$0.930566\pi$
$858$		0			0
$859$	−3876.35	+	6714.03i	−0.153969	+	0.266682i	−0.932683	−	0.360697i	$-0.882539\pi$
$859$	−3876.35	+	6714.03i	−0.153969	+	0.266682i	0.778714	+	0.627379i	$0.215872\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	22050.5			0.869765			0.434883	−	0.900487i	$-0.356790\pi$
$863$	22050.5			0.869765			0.434883	+	0.900487i	$0.356790\pi$
$864$		0			0
$865$	4007.44			0.157522
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−22445.8	+	38877.2i	−0.876203	+	1.51763i
$870$		0			0
$871$	2200.82	+	3811.93i	0.0856163	+	0.148292i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−19631.9	−	34003.5i	−0.758492	−	1.31375i
$876$		0			0
$877$	−17186.7	+	29768.3i	−0.661749	+	1.14618i	0.318407	+	0.947954i	$0.396852\pi$
$877$	−17186.7	+	29768.3i	−0.661749	+	1.14618i	−0.980156	+	0.198229i	$0.936481\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	14030.0			0.536531			0.268266	−	0.963345i	$-0.413550\pi$
$881$	14030.0			0.536531			0.268266	+	0.963345i	$0.413550\pi$
$882$		0			0
$883$	−14608.8			−0.556767			−0.278383	−	0.960470i	$-0.589799\pi$
$883$	−14608.8			−0.556767			−0.278383	+	0.960470i	$0.589799\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	12326.8	−	21350.6i	0.466620	−	0.808209i	−0.532653	−	0.846334i	$-0.678805\pi$
$887$	12326.8	−	21350.6i	0.466620	−	0.808209i	0.999273	+	0.0381243i	$0.0121383\pi$
$888$		0			0
$889$	23238.9	+	40250.9i	0.876724	+	1.51853i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	5776.57	+	10005.3i	0.216467	+	0.374933i
$894$		0			0
$895$	−1184.14	+	2051.00i	−0.0442252	+	0.0766003i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−36265.6			−1.34541
$900$		0			0
$901$	−4293.46			−0.158752
$902$		0			0
$903$		0			0
$904$		0			0
$905$	2714.30	−	4701.30i	0.0996975	−	0.172681i
$906$		0			0
$907$	8151.01	+	14118.0i	0.298401	+	0.516846i	0.975770	−	0.218797i	$-0.0702133\pi$
$907$	8151.01	+	14118.0i	0.298401	+	0.516846i	−0.677369	+	0.735643i	$0.736880\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	15514.2	+	26871.4i	0.564225	+	0.977266i	0.997121	+	0.0758225i	$0.0241582\pi$
$911$	15514.2	+	26871.4i	0.564225	+	0.977266i	−0.432896	+	0.901444i	$0.642508\pi$
$912$		0			0
$913$	16414.5	−	28430.8i	0.595008	−	1.03058i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−4270.71			−0.153796
$918$		0			0
$919$	21538.9			0.773126			0.386563	−	0.922263i	$-0.373662\pi$
$919$	21538.9			0.773126			0.386563	+	0.922263i	$0.373662\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	5027.47	−	8707.83i	0.179286	−	0.310533i
$924$		0			0
$925$	7263.79	+	12581.3i	0.258197	+	0.447210i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	23463.6	+	40640.2i	0.828650	+	1.43526i	0.899097	+	0.437749i	$0.144224\pi$
$929$	23463.6	+	40640.2i	0.828650	+	1.43526i	−0.0704469	+	0.997516i	$0.522443\pi$
$930$		0			0
$931$	13841.8	−	23974.6i	0.487267	−	0.843971i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−19811.0			−0.692931
$936$		0			0
$937$	35694.0			1.24447			0.622237	−	0.782829i	$-0.286224\pi$
$937$	35694.0			1.24447			0.622237	+	0.782829i	$0.286224\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	3239.14	−	5610.36i	0.112214	−	0.194360i	−0.804449	−	0.594022i	$-0.797539\pi$
$941$	3239.14	−	5610.36i	0.112214	−	0.194360i	0.916663	+	0.399662i	$0.130873\pi$
$942$		0			0
$943$	3263.42	+	5652.41i	0.112695	+	0.195194i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−25776.7	−	44646.5i	−0.884509	−	1.53201i	−0.846275	−	0.532746i	$-0.821160\pi$
$947$	−25776.7	−	44646.5i	−0.884509	−	1.53201i	−0.0382335	−	0.999269i	$-0.512173\pi$
$948$		0			0
$949$	−5049.73	+	8746.40i	−0.172731	+	0.299178i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−14395.3			−0.489306			−0.244653	−	0.969611i	$-0.578674\pi$
$953$	−14395.3			−0.489306			−0.244653	+	0.969611i	$0.578674\pi$
$954$		0			0
$955$	−19441.1			−0.658741
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−22515.7	+	38998.4i	−0.758156	+	1.31316i
$960$		0			0
$961$	−31219.1	−	54073.0i	−1.04794	−	1.81508i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−431.619	−	747.586i	−0.0143982	−	0.0249385i
$966$		0			0
$967$	−7338.24	+	12710.2i	−0.244035	+	0.422681i	−0.961860	−	0.273543i	$-0.911805\pi$
$967$	−7338.24	+	12710.2i	−0.244035	+	0.422681i	0.717825	+	0.696224i	$0.245138\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	36879.2			1.21886			0.609429	−	0.792841i	$-0.291399\pi$
$971$	36879.2			1.21886			0.609429	+	0.792841i	$0.291399\pi$
$972$		0			0
$973$	−46669.6			−1.53768
$974$		0			0
$975$		0			0
$976$		0			0
$977$	16256.4	−	28157.0i	0.532333	−	0.922029i	−0.466954	−	0.884282i	$-0.654649\pi$
$977$	16256.4	−	28157.0i	0.532333	−	0.922029i	0.999287	−	0.0377469i	$-0.0120181\pi$
$978$		0			0
$979$	−35161.9	−	60902.2i	−1.14789	−	1.98820i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	9772.57	+	16926.6i	0.317087	+	0.549211i	0.979879	−	0.199593i	$-0.0639620\pi$
$983$	9772.57	+	16926.6i	0.317087	+	0.549211i	−0.662792	+	0.748804i	$0.730629\pi$
$984$		0			0
$985$	11484.4	−	19891.6i	0.371496	−	0.643451i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	66756.6			2.14635
$990$		0			0
$991$	−9818.92			−0.314741			−0.157370	−	0.987540i	$-0.550302\pi$
$991$	−9818.92			−0.314741			−0.157370	+	0.987540i	$0.550302\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	5090.04	−	8816.21i	0.162176	−	0.280897i
$996$		0			0
$997$	−5712.93	−	9895.08i	−0.181475	−	0.314323i	0.760908	−	0.648859i	$-0.224754\pi$
$997$	−5712.93	−	9895.08i	−0.181475	−	0.314323i	−0.942383	+	0.334536i	$0.891420\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.4.i.b.145.2		10
3.2	odd	2		72.4.i.b.49.1	yes	10
4.3	odd	2		432.4.i.f.145.2		10
9.2	odd	6		72.4.i.b.25.1	✓	10
9.4	even	3		648.4.a.k.1.4		5
9.5	odd	6		648.4.a.l.1.2		5
9.7	even	3	inner	216.4.i.b.73.2		10
12.11	even	2		144.4.i.f.49.5		10
36.7	odd	6		432.4.i.f.289.2		10
36.11	even	6		144.4.i.f.97.5		10
36.23	even	6		1296.4.a.bd.1.2		5
36.31	odd	6		1296.4.a.bc.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.4.i.b.25.1	✓	10	9.2	odd	6
72.4.i.b.49.1	yes	10	3.2	odd	2
144.4.i.f.49.5		10	12.11	even	2
144.4.i.f.97.5		10	36.11	even	6
216.4.i.b.73.2		10	9.7	even	3	inner
216.4.i.b.145.2		10	1.1	even	1	trivial
432.4.i.f.145.2		10	4.3	odd	2
432.4.i.f.289.2		10	36.7	odd	6
648.4.a.k.1.4		5	9.4	even	3
648.4.a.l.1.2		5	9.5	odd	6
1296.4.a.bc.1.4		5	36.31	odd	6
1296.4.a.bd.1.2		5	36.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	216.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.15936 + 5.47217i) q^{5} +(14.7898 + 25.6167i) q^{7} +O(q^{10})\)	\(q+(-3.15936 + 5.47217i) q^{5} +(14.7898 + 25.6167i) q^{7} +(-24.5762 - 42.5672i) q^{11} +(-9.13278 + 15.8184i) q^{13} -63.7873 q^{17} -52.0413 q^{19} +(-74.6939 + 129.374i) q^{23} +(42.5369 + 73.6761i) q^{25} +(59.7077 + 103.417i) q^{29} +(-151.846 + 263.005i) q^{31} -186.905 q^{35} +170.764 q^{37} +(21.8453 - 37.8371i) q^{41} +(-223.434 - 386.999i) q^{43} +(-111.000 - 192.257i) q^{47} +(-265.976 + 460.685i) q^{49} +67.3089 q^{53} +310.579 q^{55} +(-233.898 + 405.123i) q^{59} +(237.504 + 411.369i) q^{61} +(-57.7074 - 99.9522i) q^{65} +(120.490 - 208.695i) q^{67} -550.486 q^{71} +552.924 q^{73} +(726.953 - 1259.12i) q^{77} +(-456.657 - 790.953i) q^{79} +(333.953 + 578.423i) q^{83} +(201.527 - 349.055i) q^{85} +1430.73 q^{89} -540.288 q^{91} +(164.417 - 284.779i) q^{95} +(-832.861 - 1442.56i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{5} - 3 q^{7}+O(q^{10}) \) 10 * q + 5 * q^5 - 3 * q^7	\( 10 q + 5 q^{5} - 3 q^{7} - 25 q^{11} - 29 q^{13} - 56 q^{17} + 128 q^{19} + 89 q^{23} - 322 q^{25} + 129 q^{29} - 241 q^{31} + 486 q^{35} + 732 q^{37} + 171 q^{41} - 803 q^{43} - 477 q^{47} - 1072 q^{49} - 748 q^{53} + 2938 q^{55} - 607 q^{59} - 1349 q^{61} + 527 q^{65} - 1549 q^{67} + 1624 q^{71} + 3856 q^{73} + 903 q^{77} - 1727 q^{79} - 1025 q^{83} - 2902 q^{85} - 4620 q^{89} + 5970 q^{91} - 2012 q^{95} - 2875 q^{97}+O(q^{100}) \) 10 * q + 5 * q^5 - 3 * q^7 - 25 * q^11 - 29 * q^13 - 56 * q^17 + 128 * q^19 + 89 * q^23 - 322 * q^25 + 129 * q^29 - 241 * q^31 + 486 * q^35 + 732 * q^37 + 171 * q^41 - 803 * q^43 - 477 * q^47 - 1072 * q^49 - 748 * q^53 + 2938 * q^55 - 607 * q^59 - 1349 * q^61 + 527 * q^65 - 1549 * q^67 + 1624 * q^71 + 3856 * q^73 + 903 * q^77 - 1727 * q^79 - 1025 * q^83 - 2902 * q^85 - 4620 * q^89 + 5970 * q^91 - 2012 * q^95 - 2875 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more