LMFDB - Embedded newform 117.4.g.c.100.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,4,Mod(55,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("117.55");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	117.g (of order $3$, degree $2$, 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:	$6.90322347067$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	117.100
Dual form			117.4.g.c.55.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 - 3.46410i) q^{2} +(-4.00000 - 6.92820i) q^{4} -17.0000 q^{5} +(-10.0000 - 17.3205i) q^{7} +O(q^{10})$	\(q+(2.00000 - 3.46410i) q^{2} +(-4.00000 - 6.92820i) q^{4} -17.0000 q^{5} +(-10.0000 - 17.3205i) q^{7} +(-34.0000 + 58.8897i) q^{10} +(-16.0000 + 27.7128i) q^{11} +(-45.5000 - 11.2583i) q^{13} -80.0000 q^{14} +(32.0000 - 55.4256i) q^{16} +(-6.50000 - 11.2583i) q^{17} +(-15.0000 - 25.9808i) q^{19} +(68.0000 + 117.779i) q^{20} +(64.0000 + 110.851i) q^{22} +(39.0000 - 67.5500i) q^{23} +164.000 q^{25} +(-130.000 + 135.100i) q^{26} +(-80.0000 + 138.564i) q^{28} +(98.5000 - 170.607i) q^{29} -74.0000 q^{31} +(-128.000 - 221.703i) q^{32} -52.0000 q^{34} +(170.000 + 294.449i) q^{35} +(113.500 - 196.588i) q^{37} -120.000 q^{38} +(-82.5000 + 142.894i) q^{41} +(78.0000 + 135.100i) q^{43} +256.000 q^{44} +(-156.000 - 270.200i) q^{46} +162.000 q^{47} +(-28.5000 + 49.3634i) q^{49} +(328.000 - 568.113i) q^{50} +(104.000 + 360.267i) q^{52} -93.0000 q^{53} +(272.000 - 471.118i) q^{55} +(-394.000 - 682.428i) q^{58} +(-432.000 - 748.246i) q^{59} +(-72.5000 - 125.574i) q^{61} +(-148.000 + 256.344i) q^{62} -512.000 q^{64} +(773.500 + 191.392i) q^{65} +(-431.000 + 746.514i) q^{67} +(-52.0000 + 90.0666i) q^{68} +1360.00 q^{70} +(327.000 + 566.381i) q^{71} +215.000 q^{73} +(-454.000 - 786.351i) q^{74} +(-120.000 + 207.846i) q^{76} +640.000 q^{77} -76.0000 q^{79} +(-544.000 + 942.236i) q^{80} +(330.000 + 571.577i) q^{82} -628.000 q^{83} +(110.500 + 191.392i) q^{85} +624.000 q^{86} +(-133.000 + 230.363i) q^{89} +(260.000 + 900.666i) q^{91} -624.000 q^{92} +(324.000 - 561.184i) q^{94} +(255.000 + 441.673i) q^{95} +(-119.000 - 206.114i) q^{97} +(114.000 + 197.454i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} - 8 q^{4} - 34 q^{5} - 20 q^{7}+O(q^{10}) $ 2 * q + 4 * q^2 - 8 * q^4 - 34 * q^5 - 20 * q^7	$ 2 q + 4 q^{2} - 8 q^{4} - 34 q^{5} - 20 q^{7} - 68 q^{10} - 32 q^{11} - 91 q^{13} - 160 q^{14} + 64 q^{16} - 13 q^{17} - 30 q^{19} + 136 q^{20} + 128 q^{22} + 78 q^{23} + 328 q^{25} - 260 q^{26} - 160 q^{28} + 197 q^{29} - 148 q^{31} - 256 q^{32} - 104 q^{34} + 340 q^{35} + 227 q^{37} - 240 q^{38} - 165 q^{41} + 156 q^{43} + 512 q^{44} - 312 q^{46} + 324 q^{47} - 57 q^{49} + 656 q^{50} + 208 q^{52} - 186 q^{53} + 544 q^{55} - 788 q^{58} - 864 q^{59} - 145 q^{61} - 296 q^{62} - 1024 q^{64} + 1547 q^{65} - 862 q^{67} - 104 q^{68} + 2720 q^{70} + 654 q^{71} + 430 q^{73} - 908 q^{74} - 240 q^{76} + 1280 q^{77} - 152 q^{79} - 1088 q^{80} + 660 q^{82} - 1256 q^{83} + 221 q^{85} + 1248 q^{86} - 266 q^{89} + 520 q^{91} - 1248 q^{92} + 648 q^{94} + 510 q^{95} - 238 q^{97} + 228 q^{98}+O(q^{100}) $ 2 * q + 4 * q^2 - 8 * q^4 - 34 * q^5 - 20 * q^7 - 68 * q^10 - 32 * q^11 - 91 * q^13 - 160 * q^14 + 64 * q^16 - 13 * q^17 - 30 * q^19 + 136 * q^20 + 128 * q^22 + 78 * q^23 + 328 * q^25 - 260 * q^26 - 160 * q^28 + 197 * q^29 - 148 * q^31 - 256 * q^32 - 104 * q^34 + 340 * q^35 + 227 * q^37 - 240 * q^38 - 165 * q^41 + 156 * q^43 + 512 * q^44 - 312 * q^46 + 324 * q^47 - 57 * q^49 + 656 * q^50 + 208 * q^52 - 186 * q^53 + 544 * q^55 - 788 * q^58 - 864 * q^59 - 145 * q^61 - 296 * q^62 - 1024 * q^64 + 1547 * q^65 - 862 * q^67 - 104 * q^68 + 2720 * q^70 + 654 * q^71 + 430 * q^73 - 908 * q^74 - 240 * q^76 + 1280 * q^77 - 152 * q^79 - 1088 * q^80 + 660 * q^82 - 1256 * q^83 + 221 * q^85 + 1248 * q^86 - 266 * q^89 + 520 * q^91 - 1248 * q^92 + 648 * q^94 + 510 * q^95 - 238 * q^97 + 228 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	2.00000	−	3.46410i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$2$	2.00000	−	3.46410i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$3$		0			0
$3$		0			0
$4$	−4.00000	−	6.92820i	−0.500000	−	0.866025i
$5$	−17.0000			−1.52053			−0.760263	−	0.649615i	$-0.774930\pi$
$5$	−17.0000			−1.52053			−0.760263	+	0.649615i	$0.774930\pi$
$6$		0			0
$7$	−10.0000	−	17.3205i	−0.539949	−	0.935220i	−0.998906	−	0.0467610i	$-0.985110\pi$
$7$	−10.0000	−	17.3205i	−0.539949	−	0.935220i	0.458957	−	0.888459i	$-0.348223\pi$
$8$		0			0
$9$		0			0
$10$	−34.0000	+	58.8897i	−1.07517	+	1.86226i
$11$	−16.0000	+	27.7128i	−0.438562	+	0.759612i	−0.997579	−	0.0695447i	$-0.977845\pi$
$11$	−16.0000	+	27.7128i	−0.438562	+	0.759612i	0.559017	+	0.829156i	$0.311179\pi$
$12$		0			0
$13$	−45.5000	−	11.2583i	−0.970725	−	0.240192i
$13$	−45.5000	−	11.2583i	−0.970725	−	0.240192i
$14$	−80.0000			−1.52721
$15$		0			0
$16$	32.0000	−	55.4256i	0.500000	−	0.866025i
$17$	−6.50000	−	11.2583i	−0.0927342	−	0.160620i	0.815927	−	0.578156i	$-0.196227\pi$
$17$	−6.50000	−	11.2583i	−0.0927342	−	0.160620i	−0.908661	+	0.417535i	$0.862894\pi$
$18$		0			0
$19$	−15.0000	−	25.9808i	−0.181118	−	0.313705i	0.761144	−	0.648583i	$-0.224638\pi$
$19$	−15.0000	−	25.9808i	−0.181118	−	0.313705i	−0.942261	+	0.334878i	$0.891305\pi$
$20$	68.0000	+	117.779i	0.760263	+	1.31681i
$21$		0			0
$22$	64.0000	+	110.851i	0.620220	+	1.07425i
$23$	39.0000	−	67.5500i	0.353568	−	0.612398i	−0.633304	−	0.773903i	$-0.718302\pi$
$23$	39.0000	−	67.5500i	0.353568	−	0.612398i	0.986872	+	0.161506i	$0.0516350\pi$
$24$		0			0
$25$	164.000			1.31200
$26$	−130.000	+	135.100i	−0.980581	+	1.01905i
$27$		0			0
$28$	−80.0000	+	138.564i	−0.539949	+	0.935220i
$29$	98.5000	−	170.607i	0.630724	−	1.09245i	−0.356680	−	0.934227i	$-0.616091\pi$
$29$	98.5000	−	170.607i	0.630724	−	1.09245i	0.987404	−	0.158219i	$-0.0505752\pi$
$30$		0			0
$31$	−74.0000			−0.428735			−0.214368	−	0.976753i	$-0.568769\pi$
$31$	−74.0000			−0.428735			−0.214368	+	0.976753i	$0.568769\pi$
$32$	−128.000	−	221.703i	−0.707107	−	1.22474i
$33$		0			0
$34$	−52.0000			−0.262292
$35$	170.000	+	294.449i	0.821007	+	1.42203i
$36$		0			0
$37$	113.500	−	196.588i	0.504305	−	0.873482i	−0.495683	−	0.868504i	$-0.665082\pi$
$37$	113.500	−	196.588i	0.504305	−	0.873482i	0.999988	−	0.00497814i	$-0.00158460\pi$
$38$	−120.000			−0.512278
$39$		0			0
$40$		0			0
$41$	−82.5000	+	142.894i	−0.314252	+	0.544301i	−0.979278	−	0.202520i	$-0.935087\pi$
$41$	−82.5000	+	142.894i	−0.314252	+	0.544301i	0.665026	+	0.746820i	$0.268420\pi$
$42$		0			0
$43$	78.0000	+	135.100i	0.276625	+	0.479129i	0.970544	−	0.240924i	$-0.0774506\pi$
$43$	78.0000	+	135.100i	0.276625	+	0.479129i	−0.693919	+	0.720053i	$0.744117\pi$
$44$	256.000			0.877124
$45$		0			0
$46$	−156.000	−	270.200i	−0.500021	−	0.866061i
$47$	162.000			0.502769			0.251384	−	0.967887i	$-0.419114\pi$
$47$	162.000			0.502769			0.251384	+	0.967887i	$0.419114\pi$
$48$		0			0
$49$	−28.5000	+	49.3634i	−0.0830904	+	0.143917i
$50$	328.000	−	568.113i	0.927724	−	1.60687i
$51$		0			0
$52$	104.000	+	360.267i	0.277350	+	0.960769i
$53$	−93.0000			−0.241029			−0.120514	−	0.992712i	$-0.538454\pi$
$53$	−93.0000			−0.241029			−0.120514	+	0.992712i	$0.538454\pi$
$54$		0			0
$55$	272.000	−	471.118i	0.666845	−	1.15501i
$56$		0			0
$57$		0			0
$58$	−394.000	−	682.428i	−0.891978	−	1.54495i
$59$	−432.000	−	748.246i	−0.953248	−	1.65107i	−0.738328	−	0.674442i	$-0.764384\pi$
$59$	−432.000	−	748.246i	−0.953248	−	1.65107i	−0.214919	−	0.976632i	$-0.568949\pi$
$60$		0			0
$61$	−72.5000	−	125.574i	−0.152175	−	0.263575i	0.779852	−	0.625964i	$-0.215294\pi$
$61$	−72.5000	−	125.574i	−0.152175	−	0.263575i	−0.932027	+	0.362389i	$0.881961\pi$
$62$	−148.000	+	256.344i	−0.303162	+	0.525091i
$63$		0			0
$64$	−512.000			−1.00000
$65$	773.500	+	191.392i	1.47601	+	0.365219i
$66$		0			0
$67$	−431.000	+	746.514i	−0.785896	+	1.36121i	0.142566	+	0.989785i	$0.454465\pi$
$67$	−431.000	+	746.514i	−0.785896	+	1.36121i	−0.928462	+	0.371427i	$0.878869\pi$
$68$	−52.0000	+	90.0666i	−0.0927342	+	0.160620i
$69$		0			0
$70$	1360.00			2.32216
$71$	327.000	+	566.381i	0.546588	+	0.946718i	0.998505	+	0.0546585i	$0.0174070\pi$
$71$	327.000	+	566.381i	0.546588	+	0.946718i	−0.451917	+	0.892060i	$0.649260\pi$
$72$		0			0
$73$	215.000			0.344710			0.172355	−	0.985035i	$-0.444862\pi$
$73$	215.000			0.344710			0.172355	+	0.985035i	$0.444862\pi$
$74$	−454.000	−	786.351i	−0.713195	−	1.23529i
$75$		0			0
$76$	−120.000	+	207.846i	−0.181118	+	0.313705i
$77$	640.000			0.947205
$78$		0			0
$79$	−76.0000			−0.108236			−0.0541182	−	0.998535i	$-0.517235\pi$
$79$	−76.0000			−0.108236			−0.0541182	+	0.998535i	$0.517235\pi$
$80$	−544.000	+	942.236i	−0.760263	+	1.31681i
$81$		0			0
$82$	330.000	+	571.577i	0.444420	+	0.769757i
$83$	−628.000			−0.830505			−0.415253	−	0.909706i	$-0.636307\pi$
$83$	−628.000			−0.830505			−0.415253	+	0.909706i	$0.636307\pi$
$84$		0			0
$85$	110.500	+	191.392i	0.141005	+	0.244227i
$86$	624.000			0.782415
$87$		0			0
$88$		0			0
$89$	−133.000	+	230.363i	−0.158404	+	0.274364i	−0.934293	−	0.356505i	$-0.883968\pi$
$89$	−133.000	+	230.363i	−0.158404	+	0.274364i	0.775889	+	0.630869i	$0.217302\pi$
$90$		0			0
$91$	260.000	+	900.666i	0.299510	+	1.03753i
$92$	−624.000			−0.707136
$93$		0			0
$94$	324.000	−	561.184i	0.355511	−	0.615763i
$95$	255.000	+	441.673i	0.275394	+	0.476997i
$96$		0			0
$97$	−119.000	−	206.114i	−0.124563	−	0.215750i	0.796999	−	0.603981i	$-0.206420\pi$
$97$	−119.000	−	206.114i	−0.124563	−	0.215750i	−0.921562	+	0.388231i	$0.873086\pi$
$98$	114.000	+	197.454i	0.117508	+	0.203529i
$99$		0			0
$100$	−656.000	−	1136.23i	−0.656000	−	1.13623i
$101$	−409.500	+	709.275i	−0.403433	+	0.698767i	−0.994138	−	0.108121i	$-0.965517\pi$
$101$	−409.500	+	709.275i	−0.403433	+	0.698767i	0.590704	+	0.806888i	$0.298850\pi$
$102$		0			0
$103$	1638.00			1.56696			0.783480	−	0.621417i	$-0.213443\pi$
$103$	1638.00			1.56696			0.783480	+	0.621417i	$0.213443\pi$
$104$		0			0
$105$		0			0
$106$	−186.000	+	322.161i	−0.170433	+	0.295199i
$107$	261.000	−	452.065i	0.235811	−	0.408437i	−0.723697	−	0.690118i	$-0.757559\pi$
$107$	261.000	−	452.065i	0.235811	−	0.408437i	0.959508	+	0.281681i	$0.0908919\pi$
$108$		0			0
$109$	−1634.00			−1.43586			−0.717930	−	0.696115i	$-0.754910\pi$
$109$	−1634.00			−1.43586			−0.717930	+	0.696115i	$0.754910\pi$
$110$	−1088.00	−	1884.47i	−0.943061	−	1.63343i
$111$		0			0
$112$	−1280.00			−1.07990
$113$	163.500	+	283.190i	0.136113	+	0.235755i	0.926022	−	0.377469i	$-0.123206\pi$
$113$	163.500	+	283.190i	0.136113	+	0.235755i	−0.789909	+	0.613224i	$0.789872\pi$
$114$		0			0
$115$	−663.000	+	1148.35i	−0.537609	+	0.931167i
$116$	−1576.00			−1.26145
$117$		0			0
$118$	−3456.00			−2.69619
$119$	−130.000	+	225.167i	−0.100144	+	0.173454i
$120$		0			0
$121$	153.500	+	265.870i	0.115327	+	0.199752i
$122$	−580.000			−0.430416
$123$		0			0
$124$	296.000	+	512.687i	0.214368	+	0.371296i
$125$	−663.000			−0.474404
$126$		0			0
$127$	1079.00	−	1868.88i	0.753904	−	1.30580i	−0.192014	−	0.981392i	$-0.561502\pi$
$127$	1079.00	−	1868.88i	0.753904	−	1.30580i	0.945918	−	0.324407i	$-0.105165\pi$
$128$		0			0
$129$		0			0
$130$	2210.00	−	2296.70i	1.49100	−	1.54949i
$131$	−730.000			−0.486873			−0.243437	−	0.969917i	$-0.578275\pi$
$131$	−730.000			−0.486873			−0.243437	+	0.969917i	$0.578275\pi$
$132$		0			0
$133$	−300.000	+	519.615i	−0.195589	+	0.338770i
$134$	1724.00	+	2986.06i	1.11142	+	1.92504i
$135$		0			0
$136$		0			0
$137$	835.500	+	1447.13i	0.521033	+	0.902456i	0.999701	+	0.0244601i	$0.00778666\pi$
$137$	835.500	+	1447.13i	0.521033	+	0.902456i	−0.478667	+	0.877996i	$0.658880\pi$
$138$		0			0
$139$	−456.000	−	789.815i	−0.278255	−	0.481951i	0.692696	−	0.721229i	$-0.256423\pi$
$139$	−456.000	−	789.815i	−0.278255	−	0.481951i	−0.970951	+	0.239278i	$0.923089\pi$
$140$	1360.00	−	2355.59i	0.821007	−	1.42203i
$141$		0			0
$142$	2616.00			1.54598
$143$	1040.00	−	1080.80i	0.608176	−	0.632035i
$144$		0			0
$145$	−1674.50	+	2900.32i	−0.959032	+	1.66109i
$146$	430.000	−	744.782i	0.243747	−	0.422182i
$147$		0			0
$148$	−1816.00			−1.00861
$149$	−1057.50	−	1831.64i	−0.581435	−	1.00707i	−0.995310	−	0.0967407i	$-0.969158\pi$
$149$	−1057.50	−	1831.64i	−0.581435	−	1.00707i	0.413875	−	0.910334i	$-0.364175\pi$
$150$		0			0
$151$	514.000			0.277011			0.138506	−	0.990362i	$-0.455770\pi$
$151$	514.000			0.277011			0.138506	+	0.990362i	$0.455770\pi$
$152$		0			0
$153$		0			0
$154$	1280.00	−	2217.03i	0.669775	−	1.16008i
$155$	1258.00			0.651903
$156$		0			0
$157$	2901.00			1.47468			0.737341	−	0.675521i	$-0.236081\pi$
$157$	2901.00			1.47468			0.737341	+	0.675521i	$0.236081\pi$
$158$	−152.000	+	263.272i	−0.0765346	+	0.132562i
$159$		0			0
$160$	2176.00	+	3768.94i	1.07517	+	1.86226i
$161$	−1560.00			−0.763635
$162$		0			0
$163$	−1180.00	−	2043.82i	−0.567023	−	0.982112i	−0.996858	−	0.0792052i	$-0.974762\pi$
$163$	−1180.00	−	2043.82i	−0.567023	−	0.982112i	0.429835	−	0.902907i	$-0.358572\pi$
$164$	1320.00			0.628504
$165$		0			0
$166$	−1256.00	+	2175.46i	−0.587256	+	1.01716i
$167$	140.000	−	242.487i	0.0648714	−	0.112361i	−0.831766	−	0.555127i	$-0.812670\pi$
$167$	140.000	−	242.487i	0.0648714	−	0.112361i	0.896637	+	0.442767i	$0.146003\pi$
$168$		0			0
$169$	1943.50	+	1024.51i	0.884615	+	0.466321i
$170$	884.000			0.398822
$171$		0			0
$172$	624.000	−	1080.80i	0.276625	−	0.479129i
$173$	663.000	+	1148.35i	0.291370	+	0.504667i	0.974134	−	0.225972i	$-0.0725557\pi$
$173$	663.000	+	1148.35i	0.291370	+	0.504667i	−0.682764	+	0.730639i	$0.739222\pi$
$174$		0			0
$175$	−1640.00	−	2840.56i	−0.708413	−	1.22701i
$176$	1024.00	+	1773.62i	0.438562	+	0.759612i
$177$		0			0
$178$	532.000	+	921.451i	0.224017	+	0.388009i
$179$	2132.00	−	3692.73i	0.890241	−	1.54194i	0.0506550	−	0.998716i	$-0.483869\pi$
$179$	2132.00	−	3692.73i	0.890241	−	1.54194i	0.839586	−	0.543227i	$-0.182798\pi$
$180$		0			0
$181$	−403.000			−0.165496			−0.0827479	−	0.996571i	$-0.526370\pi$
$181$	−403.000			−0.165496			−0.0827479	+	0.996571i	$0.526370\pi$
$182$	3640.00	+	900.666i	1.48250	+	0.366823i
$183$		0			0
$184$		0			0
$185$	−1929.50	+	3341.99i	−0.766809	+	1.32815i
$186$		0			0
$187$	416.000			0.162679
$188$	−648.000	−	1122.37i	−0.251384	−	0.435410i
$189$		0			0
$190$	2040.00			0.778932
$191$	−623.000	−	1079.07i	−0.236014	−	0.408788i	0.723553	−	0.690269i	$-0.242508\pi$
$191$	−623.000	−	1079.07i	−0.236014	−	0.408788i	−0.959567	+	0.281481i	$0.909174\pi$
$192$		0			0
$193$	−133.500	+	231.229i	−0.0497904	+	0.0862394i	−0.889846	−	0.456260i	$-0.849189\pi$
$193$	−133.500	+	231.229i	−0.0497904	+	0.0862394i	0.840056	+	0.542500i	$0.182522\pi$
$194$	−952.000			−0.352318
$195$		0			0
$196$	456.000			0.166181
$197$	639.000	−	1106.78i	0.231101	−	0.400278i	−0.727032	−	0.686604i	$-0.759101\pi$
$197$	639.000	−	1106.78i	0.231101	−	0.400278i	0.958132	+	0.286326i	$0.0924339\pi$
$198$		0			0
$199$	−2119.00	−	3670.22i	−0.754834	−	1.30741i	−0.945457	−	0.325747i	$-0.894384\pi$
$199$	−2119.00	−	3670.22i	−0.754834	−	1.30741i	0.190623	−	0.981663i	$-0.438949\pi$
$200$		0			0
$201$		0			0
$202$	1638.00	+	2837.10i	0.570541	+	0.988206i
$203$	−3940.00			−1.36224
$204$		0			0
$205$	1402.50	−	2429.20i	0.477829	−	0.827623i
$206$	3276.00	−	5674.20i	1.10801	−	1.91913i
$207$		0			0
$208$	−2080.00	+	2161.60i	−0.693375	+	0.720577i
$209$	960.000			0.317725
$210$		0			0
$211$	−1535.00	+	2658.70i	−0.500823	+	0.867452i	0.499176	+	0.866501i	$0.333636\pi$
$211$	−1535.00	+	2658.70i	−0.500823	+	0.867452i	−1.00000		0.000951154i	$0.999697\pi$
$212$	372.000	+	644.323i	0.120514	+	0.208737i
$213$		0			0
$214$	−1044.00	−	1808.26i	−0.333488	−	0.577618i
$215$	−1326.00	−	2296.70i	−0.420616	−	0.728528i
$216$		0			0
$217$	740.000	+	1281.72i	0.231495	+	0.400962i
$218$	−3268.00	+	5660.34i	−1.01531	+	1.75856i
$219$		0			0
$220$	−4352.00			−1.33369
$221$	169.000	+	585.433i	0.0514397	+	0.178192i
$222$		0			0
$223$	2689.00	−	4657.48i	0.807483	−	1.39860i	−0.107119	−	0.994246i	$-0.534162\pi$
$223$	2689.00	−	4657.48i	0.807483	−	1.39860i	0.914602	−	0.404356i	$-0.132504\pi$
$224$	−2560.00	+	4434.05i	−0.763604	+	1.32260i
$225$		0			0
$226$	1308.00			0.384986
$227$	−1987.00	−	3441.58i	−0.580977	−	1.00628i	−0.995364	−	0.0961811i	$-0.969337\pi$
$227$	−1987.00	−	3441.58i	−0.580977	−	1.00628i	0.414387	−	0.910101i	$-0.363996\pi$
$228$		0			0
$229$	−6298.00			−1.81740			−0.908698	−	0.417455i	$-0.862922\pi$
$229$	−6298.00			−1.81740			−0.908698	+	0.417455i	$0.862922\pi$
$230$	2652.00	+	4593.40i	0.760294	+	1.31687i
$231$		0			0
$232$		0			0
$233$	−4030.00			−1.13311			−0.566554	−	0.824025i	$-0.691724\pi$
$233$	−4030.00			−1.13311			−0.566554	+	0.824025i	$0.691724\pi$
$234$		0			0
$235$	−2754.00			−0.764473
$236$	−3456.00	+	5985.97i	−0.953248	+	1.65107i
$237$		0			0
$238$	520.000	+	900.666i	0.141624	+	0.245301i
$239$	984.000			0.266317			0.133158	−	0.991095i	$-0.457488\pi$
$239$	984.000			0.266317			0.133158	+	0.991095i	$0.457488\pi$
$240$		0			0
$241$	−471.500	−	816.662i	−0.126025	−	0.218281i	0.796108	−	0.605154i	$-0.206889\pi$
$241$	−471.500	−	816.662i	−0.126025	−	0.218281i	−0.922133	+	0.386873i	$0.873555\pi$
$242$	1228.00			0.326194
$243$		0			0
$244$	−580.000	+	1004.59i	−0.152175	+	0.263575i
$245$	484.500	−	839.179i	0.126341	−	0.218829i
$246$		0			0
$247$	390.000	+	1351.00i	0.100466	+	0.348024i
$248$		0			0
$249$		0			0
$250$	−1326.00	+	2296.70i	−0.335454	+	0.581024i
$251$	−1365.00	−	2364.25i	−0.343259	−	0.594542i	0.641777	−	0.766891i	$-0.278198\pi$
$251$	−1365.00	−	2364.25i	−0.343259	−	0.594542i	−0.985036	+	0.172349i	$0.944864\pi$
$252$		0			0
$253$	1248.00	+	2161.60i	0.310123	+	0.537149i
$254$	−4316.00	−	7475.53i	−1.06618	−	1.84668i
$255$		0			0
$256$	−2048.00	−	3547.24i	−0.500000	−	0.866025i
$257$	−942.500	+	1632.46i	−0.228761	+	0.396225i	−0.957441	−	0.288629i	$-0.906801\pi$
$257$	−942.500	+	1632.46i	−0.228761	+	0.396225i	0.728680	+	0.684854i	$0.240134\pi$
$258$		0			0
$259$	−4540.00			−1.08920
$260$	−1768.00	−	6124.53i	−0.421718	−	1.46087i
$261$		0			0
$262$	−1460.00	+	2528.79i	−0.344271	+	0.596296i
$263$	2016.00	−	3491.81i	0.472669	−	0.818686i	−0.526842	−	0.849963i	$-0.676624\pi$
$263$	2016.00	−	3491.81i	0.472669	−	0.818686i	0.999511	+	0.0312769i	$0.00995738\pi$
$264$		0			0
$265$	1581.00			0.366491
$266$	1200.00	+	2078.46i	0.276604	+	0.479093i
$267$		0			0
$268$	6896.00			1.57179
$269$	2003.00	+	3469.30i	0.453997	+	0.786345i	0.998630	−	0.0523292i	$-0.0166645\pi$
$269$	2003.00	+	3469.30i	0.453997	+	0.786345i	−0.544633	+	0.838674i	$0.683331\pi$
$270$		0			0
$271$	2148.00	−	3720.45i	0.481482	−	0.833952i	−0.518292	−	0.855204i	$-0.673432\pi$
$271$	2148.00	−	3720.45i	0.481482	−	0.833952i	0.999774	+	0.0212520i	$0.00676523\pi$
$272$	−832.000			−0.185468
$273$		0			0
$274$	6684.00			1.47371
$275$	−2624.00	+	4544.90i	−0.575393	+	0.996610i
$276$		0			0
$277$	2775.50	+	4807.31i	0.602035	+	1.04275i	0.992513	+	0.122142i	$0.0389765\pi$
$277$	2775.50	+	4807.31i	0.602035	+	1.04275i	−0.390478	+	0.920612i	$0.627690\pi$
$278$	−3648.00			−0.787023
$279$		0			0
$280$		0			0
$281$	5557.00			1.17973			0.589863	−	0.807504i	$-0.299182\pi$
$281$	5557.00			1.17973			0.589863	+	0.807504i	$0.299182\pi$
$282$		0			0
$283$	−1560.00	+	2702.00i	−0.327676	+	0.567552i	−0.982050	−	0.188619i	$-0.939599\pi$
$283$	−1560.00	+	2702.00i	−0.327676	+	0.567552i	0.654374	+	0.756171i	$0.272932\pi$
$284$	2616.00	−	4531.04i	0.546588	−	0.946718i
$285$		0			0
$286$	−1664.00	−	5764.27i	−0.344036	−	1.19178i
$287$	3300.00			0.678721
$288$		0			0
$289$	2372.00	−	4108.42i	0.482801	−	0.836235i
$290$	6698.00	+	11601.3i	1.35628	+	2.34914i
$291$		0			0
$292$	−860.000	−	1489.56i	−0.172355	−	0.298528i
$293$	4150.50	+	7188.88i	0.827559	+	1.43337i	0.899948	+	0.435998i	$0.143604\pi$
$293$	4150.50	+	7188.88i	0.827559	+	1.43337i	−0.0723887	+	0.997376i	$0.523062\pi$
$294$		0			0
$295$	7344.00	+	12720.2i	1.44944	+	2.51050i
$296$		0			0
$297$		0			0
$298$	−8460.00			−1.64455
$299$	−2535.00	+	2634.45i	−0.490310	+	0.509546i
$300$		0			0
$301$	1560.00	−	2702.00i	0.298727	−	0.517411i
$302$	1028.00	−	1780.55i	0.195877	−	0.339268i
$303$		0			0
$304$	−1920.00			−0.362235
$305$	1232.50	+	2134.75i	0.231386	+	0.400772i
$306$		0			0
$307$	8678.00			1.61329			0.806644	−	0.591037i	$-0.201281\pi$
$307$	8678.00			1.61329			0.806644	+	0.591037i	$0.201281\pi$
$308$	−2560.00	−	4434.05i	−0.473602	−	0.820303i
$309$		0			0
$310$	2516.00	−	4357.84i	0.460965	−	0.798415i
$311$	−8658.00			−1.57862			−0.789309	−	0.613996i	$-0.789561\pi$
$311$	−8658.00			−1.57862			−0.789309	+	0.613996i	$0.789561\pi$
$312$		0			0
$313$	−5250.00			−0.948075			−0.474038	−	0.880505i	$-0.657204\pi$
$313$	−5250.00			−0.948075			−0.474038	+	0.880505i	$0.657204\pi$
$314$	5802.00	−	10049.4i	1.04276	−	1.80611i
$315$		0			0
$316$	304.000	+	526.543i	0.0541182	+	0.0937354i
$317$	−6413.00			−1.13625			−0.568123	−	0.822944i	$-0.692330\pi$
$317$	−6413.00			−1.13625			−0.568123	+	0.822944i	$0.692330\pi$
$318$		0			0
$319$	3152.00	+	5459.42i	0.553223	+	0.958210i
$320$	8704.00			1.52053
$321$		0			0
$322$	−3120.00	+	5404.00i	−0.539971	+	0.935258i
$323$	−195.000	+	337.750i	−0.0335916	+	0.0581824i
$324$		0			0
$325$	−7462.00	−	1846.37i	−1.27359	−	0.315132i
$326$	−9440.00			−1.60378
$327$		0			0
$328$		0			0
$329$	−1620.00	−	2805.92i	−0.271470	−	0.470199i
$330$		0			0
$331$	−1744.00	−	3020.70i	−0.289604	−	0.501609i	0.684111	−	0.729378i	$-0.260190\pi$
$331$	−1744.00	−	3020.70i	−0.289604	−	0.501609i	−0.973715	+	0.227769i	$0.926857\pi$
$332$	2512.00	+	4350.91i	0.415253	+	0.719239i
$333$		0			0
$334$	−560.000	−	969.948i	−0.0917420	−	0.158902i
$335$	7327.00	−	12690.7i	1.19498	−	2.06976i
$336$		0			0
$337$	−1833.00			−0.296290			−0.148145	−	0.988966i	$-0.547330\pi$
$337$	−1833.00			−0.296290			−0.148145	+	0.988966i	$0.547330\pi$
$338$	7436.00	−	4683.47i	1.19664	−	0.753689i
$339$		0			0
$340$	884.000	−	1531.13i	0.141005	−	0.244227i
$341$	1184.00	−	2050.75i	0.188027	−	0.325672i
$342$		0			0
$343$	−5720.00			−0.900440
$344$		0			0
$345$		0			0
$346$	5304.00			0.824118
$347$	3615.00	+	6261.36i	0.559260	+	0.968667i	0.997558	+	0.0698377i	$0.0222481\pi$
$347$	3615.00	+	6261.36i	0.559260	+	0.968667i	−0.438298	+	0.898830i	$0.644419\pi$
$348$		0			0
$349$	2629.00	−	4553.56i	0.403230	−	0.698414i	−0.590884	−	0.806757i	$-0.701221\pi$
$349$	2629.00	−	4553.56i	0.403230	−	0.698414i	0.994114	+	0.108342i	$0.0345543\pi$
$350$	−13120.0			−2.00370
$351$		0			0
$352$	8192.00			1.24044
$353$	1581.50	−	2739.24i	0.238455	−	0.413017i	−0.721816	−	0.692085i	$-0.756692\pi$
$353$	1581.50	−	2739.24i	0.238455	−	0.413017i	0.960271	+	0.279068i	$0.0900256\pi$
$354$		0			0
$355$	−5559.00	−	9628.47i	−0.831102	−	1.43951i
$356$	2128.00			0.316808
$357$		0			0
$358$	−8528.00	−	14770.9i	−1.25899	−	2.18064i
$359$	10068.0			1.48014			0.740068	−	0.672532i	$-0.234793\pi$
$359$	10068.0			1.48014			0.740068	+	0.672532i	$0.234793\pi$
$360$		0			0
$361$	2979.50	−	5160.65i	0.434393	−	0.752390i
$362$	−806.000	+	1396.03i	−0.117023	+	0.202690i
$363$		0			0
$364$	5200.00	−	5404.00i	0.748775	−	0.778150i
$365$	−3655.00			−0.524141
$366$		0			0
$367$	−3719.00	+	6441.50i	−0.528965	+	0.916195i	0.470464	+	0.882419i	$0.344086\pi$
$367$	−3719.00	+	6441.50i	−0.528965	+	0.916195i	−0.999429	+	0.0337755i	$0.989247\pi$
$368$	−2496.00	−	4323.20i	−0.353568	−	0.612398i
$369$		0			0
$370$	7718.00	+	13368.0i	1.08443	+	1.87829i
$371$	930.000	+	1610.81i	0.130143	+	0.225415i
$372$		0			0
$373$	4841.50	+	8385.72i	0.672073	+	1.16407i	0.977315	+	0.211790i	$0.0679294\pi$
$373$	4841.50	+	8385.72i	0.672073	+	1.16407i	−0.305242	+	0.952275i	$0.598737\pi$
$374$	832.000	−	1441.07i	0.115031	−	0.199240i
$375$		0			0
$376$		0			0
$377$	−6402.50	+	6653.67i	−0.874657	+	0.908970i
$378$		0			0
$379$	531.000	−	919.719i	0.0719674	−	0.124651i	−0.827796	−	0.561029i	$-0.810406\pi$
$379$	531.000	−	919.719i	0.0719674	−	0.124651i	0.899763	+	0.436378i	$0.143739\pi$
$380$	2040.00	−	3533.38i	0.275394	−	0.476997i
$381$		0			0
$382$	−4984.00			−0.667549
$383$	−1766.00	−	3058.80i	−0.235609	−	0.408087i	0.723840	−	0.689968i	$-0.242375\pi$
$383$	−1766.00	−	3058.80i	−0.235609	−	0.408087i	−0.959450	+	0.281880i	$0.909042\pi$
$384$		0			0
$385$	−10880.0			−1.44025
$386$	534.000	+	924.915i	0.0704142	+	0.121961i
$387$		0			0
$388$	−952.000	+	1648.91i	−0.124563	+	0.215750i
$389$	11063.0			1.44194			0.720972	−	0.692964i	$-0.243696\pi$
$389$	11063.0			1.44194			0.720972	+	0.692964i	$0.243696\pi$
$390$		0			0
$391$	−1014.00			−0.131151
$392$		0			0
$393$		0			0
$394$	−2556.00	−	4427.12i	−0.326826	−	0.566079i
$395$	1292.00			0.164576
$396$		0			0
$397$	2993.00	+	5184.03i	0.378374	+	0.655362i	0.990826	−	0.135145i	$-0.0431501\pi$
$397$	2993.00	+	5184.03i	0.378374	+	0.655362i	−0.612452	+	0.790508i	$0.709817\pi$
$398$	−16952.0			−2.13499
$399$		0			0
$400$	5248.00	−	9089.80i	0.656000	−	1.13623i
$401$	2967.50	−	5139.86i	0.369551	−	0.640081i	−0.619945	−	0.784646i	$-0.712845\pi$
$401$	2967.50	−	5139.86i	0.369551	−	0.640081i	0.989495	+	0.144565i	$0.0461782\pi$
$402$		0			0
$403$	3367.00	+	833.116i	0.416184	+	0.102979i
$404$	6552.00			0.806867
$405$		0			0
$406$	−7880.00	+	13648.6i	−0.963246	+	1.66839i
$407$	3632.00	+	6290.81i	0.442338	+	0.766152i
$408$		0			0
$409$	7544.50	+	13067.5i	0.912106	+	1.57981i	0.811083	+	0.584931i	$0.198878\pi$
$409$	7544.50	+	13067.5i	0.912106	+	1.57981i	0.101023	+	0.994884i	$0.467788\pi$
$410$	−5610.00	−	9716.81i	−0.675752	−	1.17044i
$411$		0			0
$412$	−6552.00	−	11348.4i	−0.783480	−	1.35703i
$413$	−8640.00	+	14964.9i	−1.02941	+	1.78299i
$414$		0			0
$415$	10676.0			1.26281
$416$	3328.00	+	11528.5i	0.392232	+	1.35873i
$417$		0			0
$418$	1920.00	−	3325.54i	0.224666	−	0.389132i
$419$	−5407.00	+	9365.20i	−0.630428	+	1.09193i	0.357037	+	0.934090i	$0.383787\pi$
$419$	−5407.00	+	9365.20i	−0.630428	+	1.09193i	−0.987464	+	0.157843i	$0.949546\pi$
$420$		0			0
$421$	−6535.00			−0.756524			−0.378262	−	0.925699i	$-0.623478\pi$
$421$	−6535.00			−0.756524			−0.378262	+	0.925699i	$0.623478\pi$
$422$	6140.00	+	10634.8i	0.708271	+	1.22676i
$423$		0			0
$424$		0			0
$425$	−1066.00	−	1846.37i	−0.121667	−	0.210734i
$426$		0			0
$427$	−1450.00	+	2511.47i	−0.164334	+	0.284634i
$428$	−4176.00			−0.471623
$429$		0			0
$430$	−10608.0			−1.18968
$431$	990.000	−	1714.73i	0.110642	−	0.191637i	−0.805387	−	0.592749i	$-0.798043\pi$
$431$	990.000	−	1714.73i	0.110642	−	0.191637i	0.916029	+	0.401112i	$0.131376\pi$
$432$		0			0
$433$	3464.50	+	6000.69i	0.384511	+	0.665993i	0.991701	−	0.128564i	$-0.0410368\pi$
$433$	3464.50	+	6000.69i	0.384511	+	0.665993i	−0.607190	+	0.794556i	$0.707703\pi$
$434$	5920.00			0.654767
$435$		0			0
$436$	6536.00	+	11320.7i	0.717930	+	1.24349i
$437$	−2340.00			−0.256150
$438$		0			0
$439$	2288.00	−	3962.93i	0.248748	−	0.430844i	−0.714431	−	0.699706i	$-0.753314\pi$
$439$	2288.00	−	3962.93i	0.248748	−	0.430844i	0.963179	+	0.268862i	$0.0866476\pi$
$440$		0			0
$441$		0			0
$442$	2366.00	+	585.433i	0.254613	+	0.0630005i
$443$	8812.00			0.945081			0.472540	−	0.881309i	$-0.343337\pi$
$443$	8812.00			0.945081			0.472540	+	0.881309i	$0.343337\pi$
$444$		0			0
$445$	2261.00	−	3916.17i	0.240858	−	0.417178i
$446$	−10756.0	−	18629.9i	−1.14195	−	1.97792i
$447$		0			0
$448$	5120.00	+	8868.10i	0.539949	+	0.935220i
$449$	959.000	+	1661.04i	0.100797	+	0.174586i	0.912013	−	0.410160i	$-0.134527\pi$
$449$	959.000	+	1661.04i	0.100797	+	0.174586i	−0.811216	+	0.584747i	$0.801194\pi$
$450$		0			0
$451$	−2640.00	−	4572.61i	−0.275638	−	0.477419i
$452$	1308.00	−	2265.52i	0.136113	−	0.235755i
$453$		0			0
$454$	−15896.0			−1.64325
$455$	−4420.00	−	15311.3i	−0.455413	−	1.57760i
$456$		0			0
$457$	5880.50	−	10185.3i	0.601922	−	1.04256i	−0.390608	−	0.920557i	$-0.627735\pi$
$457$	5880.50	−	10185.3i	0.601922	−	1.04256i	0.992530	−	0.122002i	$-0.0389314\pi$
$458$	−12596.0	+	21816.9i	−1.28509	+	2.22585i
$459$		0			0
$460$	10608.0			1.07522
$461$	450.500	+	780.289i	0.0455138	+	0.0788323i	0.887885	−	0.460066i	$-0.152174\pi$
$461$	450.500	+	780.289i	0.0455138	+	0.0788323i	−0.842371	+	0.538898i	$0.818841\pi$
$462$		0			0
$463$	1372.00			0.137715			0.0688577	−	0.997626i	$-0.478065\pi$
$463$	1372.00			0.137715			0.0688577	+	0.997626i	$0.478065\pi$
$464$	−6304.00	−	10918.8i	−0.630724	−	1.09245i
$465$		0			0
$466$	−8060.00	+	13960.3i	−0.801228	+	1.38777i
$467$	6396.00			0.633772			0.316886	−	0.948464i	$-0.397363\pi$
$467$	6396.00			0.633772			0.316886	+	0.948464i	$0.397363\pi$
$468$		0			0
$469$	17240.0			1.69738
$470$	−5508.00	+	9540.14i	−0.540564	+	0.936284i
$471$		0			0
$472$		0			0
$473$	−4992.00			−0.485269
$474$		0			0
$475$	−2460.00	−	4260.84i	−0.237626	−	0.411581i
$476$	2080.00			0.200287
$477$		0			0
$478$	1968.00	−	3408.68i	0.188314	−	0.326170i
$479$	1635.00	−	2831.90i	0.155960	−	0.270131i	−0.777448	−	0.628947i	$-0.783486\pi$
$479$	1635.00	−	2831.90i	0.155960	−	0.270131i	0.933408	+	0.358816i	$0.116819\pi$
$480$		0			0
$481$	−7377.50	+	7666.92i	−0.699345	+	0.726781i
$482$	−3772.00			−0.356452
$483$		0			0
$484$	1228.00	−	2126.96i	0.115327	−	0.199752i
$485$	2023.00	+	3503.94i	0.189401	+	0.328053i
$486$		0			0
$487$	−9960.00	−	17251.2i	−0.926757	−	1.60519i	−0.788711	−	0.614765i	$-0.789251\pi$
$487$	−9960.00	−	17251.2i	−0.926757	−	1.60519i	−0.138046	−	0.990426i	$-0.544082\pi$
$488$		0			0
$489$		0			0
$490$	−1938.00	−	3356.71i	−0.178673	−	0.309471i
$491$	3276.00	−	5674.20i	0.301108	−	0.521534i	−0.675280	−	0.737562i	$-0.735977\pi$
$491$	3276.00	−	5674.20i	0.301108	−	0.521534i	0.976387	+	0.216028i	$0.0693103\pi$
$492$		0			0
$493$	−2561.00			−0.233959
$494$	5460.00	+	1351.00i	0.497281	+	0.123045i
$495$		0			0
$496$	−2368.00	+	4101.50i	−0.214368	+	0.371296i
$497$	6540.00	−	11327.6i	0.590260	−	1.02236i
$498$		0			0
$499$	1746.00			0.156637			0.0783183	−	0.996928i	$-0.475045\pi$
$499$	1746.00			0.156637			0.0783183	+	0.996928i	$0.475045\pi$
$500$	2652.00	+	4593.40i	0.237202	+	0.410846i
$501$		0			0
$502$	−10920.0			−0.970883
$503$	7346.00	+	12723.6i	0.651177	+	1.12787i	0.982838	+	0.184473i	$0.0590577\pi$
$503$	7346.00	+	12723.6i	0.651177	+	1.12787i	−0.331661	+	0.943399i	$0.607609\pi$
$504$		0			0
$505$	6961.50	−	12057.7i	0.613431	−	1.06249i
$506$	9984.00			0.877160
$507$		0			0
$508$	−17264.0			−1.50781
$509$	4038.50	−	6994.89i	0.351677	−	0.609122i	−0.634867	−	0.772622i	$-0.718945\pi$
$509$	4038.50	−	6994.89i	0.351677	−	0.609122i	0.986543	+	0.163500i	$0.0522784\pi$
$510$		0			0
$511$	−2150.00	−	3723.91i	−0.186126	−	0.322380i
$512$	−16384.0			−1.41421
$513$		0			0
$514$	3770.00	+	6529.83i	0.323517	+	0.560347i
$515$	−27846.0			−2.38260
$516$		0			0
$517$	−2592.00	+	4489.48i	−0.220495	+	0.381909i
$518$	−9080.00	+	15727.0i	−0.770178	+	1.33399i
$519$		0			0
$520$		0			0
$521$	−11247.0			−0.945758			−0.472879	−	0.881127i	$-0.656785\pi$
$521$	−11247.0			−0.945758			−0.472879	+	0.881127i	$0.656785\pi$
$522$		0			0
$523$	−1366.00	+	2365.98i	−0.114208	+	0.197815i	−0.917463	−	0.397821i	$-0.869767\pi$
$523$	−1366.00	+	2365.98i	−0.114208	+	0.197815i	0.803255	+	0.595636i	$0.203100\pi$
$524$	2920.00	+	5057.59i	0.243437	+	0.421645i
$525$		0			0
$526$	−8064.00	−	13967.3i	−0.668455	−	1.15780i
$527$	481.000	+	833.116i	0.0397584	+	0.0688636i
$528$		0			0
$529$	3041.50	+	5268.03i	0.249979	+	0.432977i
$530$	3162.00	−	5476.74i	0.259148	−	0.448858i
$531$		0			0
$532$	4800.00			0.391177
$533$	5362.50	−	5572.87i	0.435789	−	0.452885i
$534$		0			0
$535$	−4437.00	+	7685.11i	−0.358557	+	0.621040i
$536$		0			0
$537$		0			0
$538$	16024.0			1.28410
$539$	−912.000	−	1579.63i	−0.0728806	−	0.126233i
$540$		0			0
$541$	−18375.0			−1.46026			−0.730132	−	0.683306i	$-0.760542\pi$
$541$	−18375.0			−1.46026			−0.730132	+	0.683306i	$0.760542\pi$
$542$	−8592.00	−	14881.8i	−0.680919	−	1.17939i
$543$		0			0
$544$	−1664.00	+	2882.13i	−0.131146	+	0.227151i
$545$	27778.0			2.18326
$546$		0			0
$547$	−10346.0			−0.808708			−0.404354	−	0.914603i	$-0.632504\pi$
$547$	−10346.0			−0.808708			−0.404354	+	0.914603i	$0.632504\pi$
$548$	6684.00	−	11577.0i	0.521033	−	0.902456i
$549$		0			0
$550$	10496.0	+	18179.6i	0.813729	+	1.40942i
$551$	−5910.00			−0.456941
$552$		0			0
$553$	760.000	+	1316.36i	0.0584421	+	0.101225i
$554$	22204.0			1.70281
$555$		0			0
$556$	−3648.00	+	6318.52i	−0.278255	+	0.481951i
$557$	172.500	−	298.779i	0.0131222	−	0.0227283i	−0.859390	−	0.511321i	$-0.829156\pi$
$557$	172.500	−	298.779i	0.0131222	−	0.0227283i	0.872512	+	0.488593i	$0.162490\pi$
$558$		0			0
$559$	−2028.00	−	7025.20i	−0.153444	−	0.531546i
$560$	21760.0			1.64201
$561$		0			0
$562$	11114.0	−	19250.0i	0.834192	−	1.44486i
$563$	−4290.00	−	7430.50i	−0.321140	−	0.556231i	0.659583	−	0.751631i	$-0.270733\pi$
$563$	−4290.00	−	7430.50i	−0.321140	−	0.556231i	−0.980724	+	0.195400i	$0.937399\pi$
$564$		0			0
$565$	−2779.50	−	4814.24i	−0.206964	−	0.358472i
$566$	6240.00	+	10808.0i	0.463404	+	0.802640i
$567$		0			0
$568$		0			0
$569$	−9841.00	+	17045.1i	−0.725055	+	1.25583i	0.233897	+	0.972261i	$0.424852\pi$
$569$	−9841.00	+	17045.1i	−0.725055	+	1.25583i	−0.958951	+	0.283570i	$0.908481\pi$
$570$		0			0
$571$	26624.0			1.95128			0.975639	−	0.219382i	$-0.0704042\pi$
$571$	26624.0			1.95128			0.975639	+	0.219382i	$0.0704042\pi$
$572$	−11648.0	−	2882.13i	−0.851446	−	0.210678i
$573$		0			0
$574$	6600.00	−	11431.5i	0.479928	−	0.831260i
$575$	6396.00	−	11078.2i	0.463881	−	0.803466i
$576$		0			0
$577$	−14101.0			−1.01739			−0.508694	−	0.860948i	$-0.669871\pi$
$577$	−14101.0			−1.01739			−0.508694	+	0.860948i	$0.669871\pi$
$578$	−9488.00	−	16433.7i	−0.682783	−	1.18262i
$579$		0			0
$580$	26792.0			1.91806
$581$	6280.00	+	10877.3i	0.448431	+	0.776705i
$582$		0			0
$583$	1488.00	−	2577.29i	0.105706	−	0.183088i
$584$		0			0
$585$		0			0
$586$	33204.0			2.34069
$587$	704.000	−	1219.36i	0.0495012	−	0.0857386i	−0.840213	−	0.542256i	$-0.817570\pi$
$587$	704.000	−	1219.36i	0.0495012	−	0.0857386i	0.889714	+	0.456518i	$0.150904\pi$
$588$		0			0
$589$	1110.00	+	1922.58i	0.0776515	+	0.134496i
$590$	58752.0			4.09963
$591$		0			0
$592$	−7264.00	−	12581.6i	−0.504305	−	0.873482i
$593$	1241.00			0.0859389			0.0429694	−	0.999076i	$-0.486318\pi$
$593$	1241.00			0.0859389			0.0429694	+	0.999076i	$0.486318\pi$
$594$		0			0
$595$	2210.00	−	3827.83i	0.152271	−	0.263741i
$596$	−8460.00	+	14653.1i	−0.581435	+	1.00707i
$597$		0			0
$598$	4056.00	+	14050.4i	0.277361	+	0.960808i
$599$	−11078.0			−0.755651			−0.377825	−	0.925877i	$-0.623328\pi$
$599$	−11078.0			−0.755651			−0.377825	+	0.925877i	$0.623328\pi$
$600$		0			0
$601$	6908.50	−	11965.9i	0.468891	−	0.812143i	−0.530477	−	0.847700i	$-0.677987\pi$
$601$	6908.50	−	11965.9i	0.468891	−	0.812143i	0.999368	+	0.0355563i	$0.0113203\pi$
$602$	−6240.00	−	10808.0i	−0.422464	−	0.731729i
$603$		0			0
$604$	−2056.00	−	3561.10i	−0.138506	−	0.239899i
$605$	−2609.50	−	4519.79i	−0.175357	−	0.303728i
$606$		0			0
$607$	−4135.00	−	7162.03i	−0.276498	−	0.478909i	0.694014	−	0.719962i	$-0.255841\pi$
$607$	−4135.00	−	7162.03i	−0.276498	−	0.478909i	−0.970512	+	0.241053i	$0.922507\pi$
$608$	−3840.00	+	6651.08i	−0.256139	+	0.443646i
$609$		0			0
$610$	9860.00			0.654459
$611$	−7371.00	−	1823.85i	−0.488050	−	0.120761i
$612$		0			0
$613$	−11136.5	+	19289.0i	−0.733767	+	1.27092i	0.221496	+	0.975161i	$0.428906\pi$
$613$	−11136.5	+	19289.0i	−0.733767	+	1.27092i	−0.955262	+	0.295760i	$0.904427\pi$
$614$	17356.0	−	30061.5i	1.14077	−	1.97587i
$615$		0			0
$616$		0			0
$617$	−9494.50	−	16445.0i	−0.619504	−	1.07301i	−0.989576	−	0.144010i	$-0.954000\pi$
$617$	−9494.50	−	16445.0i	−0.619504	−	1.07301i	0.370072	−	0.929003i	$-0.379333\pi$
$618$		0			0
$619$	72.0000			0.00467516			0.00233758	−	0.999997i	$-0.499256\pi$
$619$	72.0000			0.00467516			0.00233758	+	0.999997i	$0.499256\pi$
$620$	−5032.00	−	8715.68i	−0.325952	−	0.564565i
$621$		0			0
$622$	−17316.0	+	29992.2i	−1.11625	+	1.93340i
$623$	5320.00			0.342121
$624$		0			0
$625$	−9229.00			−0.590656
$626$	−10500.0	+	18186.5i	−0.670390	+	1.16115i
$627$		0			0
$628$	−11604.0	−	20098.7i	−0.737341	−	1.27711i
$629$	−2951.00			−0.187065
$630$		0			0
$631$	11690.0	+	20247.7i	0.737514	+	1.27741i	0.953611	+	0.301040i	$0.0973339\pi$
$631$	11690.0	+	20247.7i	0.737514	+	1.27741i	−0.216097	+	0.976372i	$0.569333\pi$
$632$		0			0
$633$		0			0
$634$	−12826.0	+	22215.3i	−0.803447	+	1.39161i
$635$	−18343.0	+	31771.0i	−1.14633	+	1.98550i
$636$		0			0
$637$	1852.50	−	1925.17i	0.115226	−	0.119746i
$638$	25216.0			1.56475
$639$		0			0
$640$		0			0
$641$	3191.50	+	5527.84i	0.196656	+	0.340619i	0.947442	−	0.319927i	$-0.103658\pi$
$641$	3191.50	+	5527.84i	0.196656	+	0.340619i	−0.750786	+	0.660546i	$0.770325\pi$
$642$		0			0
$643$	8552.00	+	14812.5i	0.524507	+	0.908473i	0.999593	+	0.0285332i	$0.00908365\pi$
$643$	8552.00	+	14812.5i	0.524507	+	0.908473i	−0.475086	+	0.879939i	$0.657583\pi$
$644$	6240.00	+	10808.0i	0.381817	+	0.661327i
$645$		0			0
$646$	780.000	+	1351.00i	0.0475057	+	0.0822823i
$647$	3497.00	−	6056.98i	0.212490	−	0.368044i	−0.740003	−	0.672604i	$-0.765176\pi$
$647$	3497.00	−	6056.98i	0.212490	−	0.368044i	0.952493	+	0.304560i	$0.0985093\pi$
$648$		0			0
$649$	27648.0			1.67223
$650$	−21320.0	+	22156.4i	−1.28652	+	1.33699i
$651$		0			0
$652$	−9440.00	+	16350.6i	−0.567023	+	0.982112i
$653$	−2625.00	+	4546.63i	−0.157311	+	0.272471i	−0.933898	−	0.357539i	$-0.883616\pi$
$653$	−2625.00	+	4546.63i	−0.157311	+	0.272471i	0.776587	+	0.630010i	$0.216949\pi$
$654$		0			0
$655$	12410.0			0.740304
$656$	5280.00	+	9145.23i	0.314252	+	0.544301i
$657$		0			0
$658$	−12960.0			−0.767832
$659$	−2170.00	−	3758.55i	−0.128272	−	0.222173i	0.794735	−	0.606956i	$-0.207610\pi$
$659$	−2170.00	−	3758.55i	−0.128272	−	0.222173i	−0.923007	+	0.384783i	$0.874276\pi$
$660$		0			0
$661$	2089.50	−	3619.12i	0.122953	−	0.212961i	−0.797978	−	0.602687i	$-0.794097\pi$
$661$	2089.50	−	3619.12i	0.122953	−	0.212961i	0.920931	+	0.389726i	$0.127430\pi$
$662$	−13952.0			−0.819124
$663$		0			0
$664$		0			0
$665$	5100.00	−	8833.46i	0.297398	−	0.515108i
$666$		0			0
$667$	−7683.00	−	13307.3i	−0.446007	−	0.772508i
$668$	−2240.00			−0.129743
$669$		0			0
$670$	−29308.0	−	50762.9i	−1.68995	−	2.92708i
$671$	4640.00			0.266953
$672$		0			0
$673$	−11433.5	+	19803.4i	−0.654872	+	1.13427i	0.327054	+	0.945006i	$0.393944\pi$
$673$	−11433.5	+	19803.4i	−0.654872	+	1.13427i	−0.981926	+	0.189266i	$0.939389\pi$
$674$	−3666.00	+	6349.70i	−0.209509	+	0.362880i
$675$		0			0
$676$	−676.000	−	17563.0i	−0.0384615	−	0.999260i
$677$	−5410.00			−0.307124			−0.153562	−	0.988139i	$-0.549075\pi$
$677$	−5410.00			−0.307124			−0.153562	+	0.988139i	$0.549075\pi$
$678$		0			0
$679$	−2380.00	+	4122.28i	−0.134515	+	0.232988i
$680$		0			0
$681$		0			0
$682$	−4736.00	−	8202.99i	−0.265910	−	0.460570i
$683$	−6789.00	−	11758.9i	−0.380342	−	0.658772i	0.610769	−	0.791809i	$-0.290861\pi$
$683$	−6789.00	−	11758.9i	−0.380342	−	0.658772i	−0.991111	+	0.133037i	$0.957527\pi$
$684$		0			0
$685$	−14203.5	−	24601.2i	−0.792245	−	1.37221i
$686$	−11440.0	+	19814.7i	−0.636707	+	1.10281i
$687$		0			0
$688$	9984.00			0.553251
$689$	4231.50	+	1047.02i	0.233973	+	0.0578933i
$690$		0			0
$691$	−6372.00	+	11036.6i	−0.350799	+	0.607602i	−0.986390	−	0.164424i	$-0.947423\pi$
$691$	−6372.00	+	11036.6i	−0.350799	+	0.607602i	0.635590	+	0.772026i	$0.280757\pi$
$692$	5304.00	−	9186.80i	0.291370	−	0.504667i
$693$		0			0
$694$	28920.0			1.58183
$695$	7752.00	+	13426.9i	0.423094	+	0.732820i
$696$		0			0
$697$	2145.00			0.116568
$698$	−10516.0	−	18214.2i	−0.570253	−	0.987707i
$699$		0			0
$700$	−13120.0	+	22724.5i	−0.708413	+	1.22701i
$701$	−16406.0			−0.883946			−0.441973	−	0.897028i	$-0.645721\pi$
$701$	−16406.0			−0.883946			−0.441973	+	0.897028i	$0.645721\pi$
$702$		0			0
$703$	−6810.00			−0.365354
$704$	8192.00	−	14189.0i	0.438562	−	0.759612i
$705$		0			0
$706$	−6326.00	−	10957.0i	−0.337227	−	0.584094i
$707$	16380.0			0.871334
$708$		0			0
$709$	−354.500	−	614.012i	−0.0187779	−	0.0325243i	0.856484	−	0.516174i	$-0.172644\pi$
$709$	−354.500	−	614.012i	−0.0187779	−	0.0325243i	−0.875262	+	0.483650i	$0.839311\pi$
$710$	−44472.0			−2.35071
$711$		0			0
$712$		0			0
$713$	−2886.00	+	4998.70i	−0.151587	+	0.262556i
$714$		0			0
$715$	−17680.0	+	18373.6i	−0.924748	+	0.961026i
$716$	−34112.0			−1.78048
$717$		0			0
$718$	20136.0	−	34876.6i	1.04661	−	1.81279i
$719$	−3822.00	−	6619.90i	−0.198243	−	0.343367i	0.749716	−	0.661760i	$-0.230190\pi$
$719$	−3822.00	−	6619.90i	−0.198243	−	0.343367i	−0.947959	+	0.318393i	$0.896857\pi$
$720$		0			0
$721$	−16380.0	−	28371.0i	−0.846079	−	1.46545i
$722$	−11918.0	−	20642.6i	−0.614324	−	1.06404i
$723$		0			0
$724$	1612.00	+	2792.07i	0.0827479	+	0.143324i
$725$	16154.0	−	27979.5i	0.827510	−	1.43329i
$726$		0			0
$727$	−15808.0			−0.806446			−0.403223	−	0.915102i	$-0.632110\pi$
$727$	−15808.0			−0.806446			−0.403223	+	0.915102i	$0.632110\pi$
$728$		0			0
$729$		0			0
$730$	−7310.00	+	12661.3i	−0.370624	+	0.641939i
$731$	1014.00	−	1756.30i	0.0513053	−	0.0888633i
$732$		0			0
$733$	−2583.00			−0.130157			−0.0650786	−	0.997880i	$-0.520730\pi$
$733$	−2583.00			−0.130157			−0.0650786	+	0.997880i	$0.520730\pi$
$734$	14876.0	+	25766.0i	0.748070	+	1.29569i
$735$		0			0
$736$	−19968.0			−1.00004
$737$	−13792.0	−	23888.4i	−0.689328	−	1.19395i
$738$		0			0
$739$	−2038.00	+	3529.92i	−0.101447	+	0.175711i	−0.912281	−	0.409565i	$-0.865680\pi$
$739$	−2038.00	+	3529.92i	−0.101447	+	0.175711i	0.810834	+	0.585276i	$0.199014\pi$
$740$	30872.0			1.53362
$741$		0			0
$742$	7440.00			0.368101
$743$	−17028.0	+	29493.4i	−0.840776	+	1.45627i	0.0484632	+	0.998825i	$0.484568\pi$
$743$	−17028.0	+	29493.4i	−0.840776	+	1.45627i	−0.889239	+	0.457442i	$0.848766\pi$
$744$		0			0
$745$	17977.5	+	31137.9i	0.884087	+	1.53128i
$746$	38732.0			1.90091
$747$		0			0
$748$	−1664.00	−	2882.13i	−0.0813394	−	0.140884i
$749$	−10440.0			−0.509305
$750$		0			0
$751$	182.000	−	315.233i	0.00884324	−	0.0153169i	−0.861570	−	0.507639i	$-0.830518\pi$
$751$	182.000	−	315.233i	0.00884324	−	0.0153169i	0.870413	+	0.492322i	$0.163852\pi$
$752$	5184.00	−	8978.95i	0.251384	−	0.435410i
$753$		0			0
$754$	10244.0	+	35486.3i	0.494780	+	1.71397i
$755$	−8738.00			−0.421203
$756$		0			0
$757$	3457.00	−	5987.70i	0.165980	−	0.287486i	−0.771023	−	0.636807i	$-0.780255\pi$
$757$	3457.00	−	5987.70i	0.165980	−	0.287486i	0.937003	+	0.349322i	$0.113588\pi$
$758$	−2124.00	−	3678.88i	−0.101777	−	0.176283i
$759$		0			0
$760$		0			0
$761$	6991.00	+	12108.8i	0.333014	+	0.576797i	0.983101	−	0.183062i	$-0.0586011\pi$
$761$	6991.00	+	12108.8i	0.333014	+	0.576797i	−0.650087	+	0.759859i	$0.725268\pi$
$762$		0			0
$763$	16340.0	+	28301.7i	0.775292	+	1.34284i
$764$	−4984.00	+	8632.54i	−0.236014	+	0.408788i
$765$		0			0
$766$	−14128.0			−0.666404
$767$	11232.0	+	38908.8i	0.528767	+	1.83170i
$768$		0			0
$769$	9033.00	−	15645.6i	0.423587	−	0.733674i	−0.572700	−	0.819765i	$-0.694104\pi$
$769$	9033.00	−	15645.6i	0.423587	−	0.733674i	0.996287	+	0.0860907i	$0.0274375\pi$
$770$	−21760.0	+	37689.4i	−1.01841	+	1.76394i
$771$		0			0
$772$	2136.00			0.0995807
$773$	7217.00	+	12500.2i	0.335805	+	0.581632i	0.983639	−	0.180150i	$-0.0576583\pi$
$773$	7217.00	+	12500.2i	0.335805	+	0.581632i	−0.647834	+	0.761782i	$0.724325\pi$
$774$		0			0
$775$	−12136.0			−0.562501
$776$		0			0
$777$		0			0
$778$	22126.0	−	38323.4i	1.01961	−	1.76601i
$779$	4950.00			0.227666

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	117.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 - 3.46410i) q^{2} +(-4.00000 - 6.92820i) q^{4} -17.0000 q^{5} +(-10.0000 - 17.3205i) q^{7} +O(q^{10})\)	\(q+(2.00000 - 3.46410i) q^{2} +(-4.00000 - 6.92820i) q^{4} -17.0000 q^{5} +(-10.0000 - 17.3205i) q^{7} +(-34.0000 + 58.8897i) q^{10} +(-16.0000 + 27.7128i) q^{11} +(-45.5000 - 11.2583i) q^{13} -80.0000 q^{14} +(32.0000 - 55.4256i) q^{16} +(-6.50000 - 11.2583i) q^{17} +(-15.0000 - 25.9808i) q^{19} +(68.0000 + 117.779i) q^{20} +(64.0000 + 110.851i) q^{22} +(39.0000 - 67.5500i) q^{23} +164.000 q^{25} +(-130.000 + 135.100i) q^{26} +(-80.0000 + 138.564i) q^{28} +(98.5000 - 170.607i) q^{29} -74.0000 q^{31} +(-128.000 - 221.703i) q^{32} -52.0000 q^{34} +(170.000 + 294.449i) q^{35} +(113.500 - 196.588i) q^{37} -120.000 q^{38} +(-82.5000 + 142.894i) q^{41} +(78.0000 + 135.100i) q^{43} +256.000 q^{44} +(-156.000 - 270.200i) q^{46} +162.000 q^{47} +(-28.5000 + 49.3634i) q^{49} +(328.000 - 568.113i) q^{50} +(104.000 + 360.267i) q^{52} -93.0000 q^{53} +(272.000 - 471.118i) q^{55} +(-394.000 - 682.428i) q^{58} +(-432.000 - 748.246i) q^{59} +(-72.5000 - 125.574i) q^{61} +(-148.000 + 256.344i) q^{62} -512.000 q^{64} +(773.500 + 191.392i) q^{65} +(-431.000 + 746.514i) q^{67} +(-52.0000 + 90.0666i) q^{68} +1360.00 q^{70} +(327.000 + 566.381i) q^{71} +215.000 q^{73} +(-454.000 - 786.351i) q^{74} +(-120.000 + 207.846i) q^{76} +640.000 q^{77} -76.0000 q^{79} +(-544.000 + 942.236i) q^{80} +(330.000 + 571.577i) q^{82} -628.000 q^{83} +(110.500 + 191.392i) q^{85} +624.000 q^{86} +(-133.000 + 230.363i) q^{89} +(260.000 + 900.666i) q^{91} -624.000 q^{92} +(324.000 - 561.184i) q^{94} +(255.000 + 441.673i) q^{95} +(-119.000 - 206.114i) q^{97} +(114.000 + 197.454i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} - 8 q^{4} - 34 q^{5} - 20 q^{7}+O(q^{10}) \) 2 * q + 4 * q^2 - 8 * q^4 - 34 * q^5 - 20 * q^7	\( 2 q + 4 q^{2} - 8 q^{4} - 34 q^{5} - 20 q^{7} - 68 q^{10} - 32 q^{11} - 91 q^{13} - 160 q^{14} + 64 q^{16} - 13 q^{17} - 30 q^{19} + 136 q^{20} + 128 q^{22} + 78 q^{23} + 328 q^{25} - 260 q^{26} - 160 q^{28} + 197 q^{29} - 148 q^{31} - 256 q^{32} - 104 q^{34} + 340 q^{35} + 227 q^{37} - 240 q^{38} - 165 q^{41} + 156 q^{43} + 512 q^{44} - 312 q^{46} + 324 q^{47} - 57 q^{49} + 656 q^{50} + 208 q^{52} - 186 q^{53} + 544 q^{55} - 788 q^{58} - 864 q^{59} - 145 q^{61} - 296 q^{62} - 1024 q^{64} + 1547 q^{65} - 862 q^{67} - 104 q^{68} + 2720 q^{70} + 654 q^{71} + 430 q^{73} - 908 q^{74} - 240 q^{76} + 1280 q^{77} - 152 q^{79} - 1088 q^{80} + 660 q^{82} - 1256 q^{83} + 221 q^{85} + 1248 q^{86} - 266 q^{89} + 520 q^{91} - 1248 q^{92} + 648 q^{94} + 510 q^{95} - 238 q^{97} + 228 q^{98}+O(q^{100}) \) 2 * q + 4 * q^2 - 8 * q^4 - 34 * q^5 - 20 * q^7 - 68 * q^10 - 32 * q^11 - 91 * q^13 - 160 * q^14 + 64 * q^16 - 13 * q^17 - 30 * q^19 + 136 * q^20 + 128 * q^22 + 78 * q^23 + 328 * q^25 - 260 * q^26 - 160 * q^28 + 197 * q^29 - 148 * q^31 - 256 * q^32 - 104 * q^34 + 340 * q^35 + 227 * q^37 - 240 * q^38 - 165 * q^41 + 156 * q^43 + 512 * q^44 - 312 * q^46 + 324 * q^47 - 57 * q^49 + 656 * q^50 + 208 * q^52 - 186 * q^53 + 544 * q^55 - 788 * q^58 - 864 * q^59 - 145 * q^61 - 296 * q^62 - 1024 * q^64 + 1547 * q^65 - 862 * q^67 - 104 * q^68 + 2720 * q^70 + 654 * q^71 + 430 * q^73 - 908 * q^74 - 240 * q^76 + 1280 * q^77 - 152 * q^79 - 1088 * q^80 + 660 * q^82 - 1256 * q^83 + 221 * q^85 + 1248 * q^86 - 266 * q^89 + 520 * q^91 - 1248 * q^92 + 648 * q^94 + 510 * q^95 - 238 * q^97 + 228 * q^98

Introduction

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