LMFDB - Embedded newform 117.4.g.c.55.1

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			55.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	117.55
Dual form			117.4.g.c.100.1

$q$-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 $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	2.00000	+	3.46410i	0.707107	+	1.22474i	0.965926	+	0.258819i	$0.0833333\pi$
$2$	2.00000	+	3.46410i	0.707107	+	1.22474i	−0.258819	+	0.965926i	$0.583333\pi$
$3$		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	0.458957	+	0.888459i	$0.348223\pi$
$7$	−10.0000	+	17.3205i	−0.539949	+	0.935220i	−0.998906	+	0.0467610i	$0.985110\pi$
$8$		0			0
$9$		0			0
$10$	−34.0000	−	58.8897i	−1.07517	−	1.86226i
$11$	−16.0000	−	27.7128i	−0.438562	−	0.759612i	0.559017	−	0.829156i	$-0.311179\pi$
$11$	−16.0000	−	27.7128i	−0.438562	−	0.759612i	−0.997579	+	0.0695447i	$0.977845\pi$
$12$		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	−0.908661	−	0.417535i	$-0.862894\pi$
$17$	−6.50000	+	11.2583i	−0.0927342	+	0.160620i	0.815927	+	0.578156i	$0.196227\pi$
$18$		0			0
$19$	−15.0000	+	25.9808i	−0.181118	+	0.313705i	−0.942261	−	0.334878i	$-0.891305\pi$
$19$	−15.0000	+	25.9808i	−0.181118	+	0.313705i	0.761144	+	0.648583i	$0.224638\pi$
$20$	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	0.986872	−	0.161506i	$-0.0516350\pi$
$23$	39.0000	+	67.5500i	0.353568	+	0.612398i	−0.633304	+	0.773903i	$0.718302\pi$
$24$		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	0.987404	+	0.158219i	$0.0505752\pi$
$29$	98.5000	+	170.607i	0.630724	+	1.09245i	−0.356680	+	0.934227i	$0.616091\pi$
$30$		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	0.999988	+	0.00497814i	$0.00158460\pi$
$37$	113.500	+	196.588i	0.504305	+	0.873482i	−0.495683	+	0.868504i	$0.665082\pi$
$38$	−120.000			−0.512278
$39$		0			0
$40$		0			0
$41$	−82.5000	−	142.894i	−0.314252	−	0.544301i	0.665026	−	0.746820i	$-0.268420\pi$
$41$	−82.5000	−	142.894i	−0.314252	−	0.544301i	−0.979278	+	0.202520i	$0.935087\pi$
$42$		0			0
$43$	78.0000	−	135.100i	0.276625	−	0.479129i	−0.693919	−	0.720053i	$-0.744117\pi$
$43$	78.0000	−	135.100i	0.276625	−	0.479129i	0.970544	+	0.240924i	$0.0774506\pi$
$44$	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	−0.214919	+	0.976632i	$0.568949\pi$
$59$	−432.000	+	748.246i	−0.953248	+	1.65107i	−0.738328	+	0.674442i	$0.764384\pi$
$60$		0			0
$61$	−72.5000	+	125.574i	−0.152175	+	0.263575i	−0.932027	−	0.362389i	$-0.881961\pi$
$61$	−72.5000	+	125.574i	−0.152175	+	0.263575i	0.779852	+	0.625964i	$0.215294\pi$
$62$	−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	−0.928462	−	0.371427i	$-0.878869\pi$
$67$	−431.000	−	746.514i	−0.785896	−	1.36121i	0.142566	−	0.989785i	$-0.454465\pi$
$68$	−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	−0.451917	−	0.892060i	$-0.649260\pi$
$71$	327.000	−	566.381i	0.546588	−	0.946718i	0.998505	−	0.0546585i	$-0.0174070\pi$
$72$		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	0.775889	−	0.630869i	$-0.217302\pi$
$89$	−133.000	−	230.363i	−0.158404	−	0.274364i	−0.934293	+	0.356505i	$0.883968\pi$
$90$		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	−0.921562	−	0.388231i	$-0.873086\pi$
$97$	−119.000	+	206.114i	−0.124563	+	0.215750i	0.796999	+	0.603981i	$0.206420\pi$
$98$	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	0.590704	−	0.806888i	$-0.298850\pi$
$101$	−409.500	−	709.275i	−0.403433	−	0.698767i	−0.994138	+	0.108121i	$0.965517\pi$
$102$		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	0.959508	−	0.281681i	$-0.0908919\pi$
$107$	261.000	+	452.065i	0.235811	+	0.408437i	−0.723697	+	0.690118i	$0.757559\pi$
$108$		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	−0.789909	−	0.613224i	$-0.789872\pi$
$113$	163.500	−	283.190i	0.136113	−	0.235755i	0.926022	+	0.377469i	$0.123206\pi$
$114$		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	0.945918	+	0.324407i	$0.105165\pi$
$127$	1079.00	+	1868.88i	0.753904	+	1.30580i	−0.192014	+	0.981392i	$0.561502\pi$
$128$		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	−0.478667	−	0.877996i	$-0.658880\pi$
$137$	835.500	−	1447.13i	0.521033	−	0.902456i	0.999701	−	0.0244601i	$-0.00778666\pi$
$138$		0			0
$139$	−456.000	+	789.815i	−0.278255	+	0.481951i	−0.970951	−	0.239278i	$-0.923089\pi$
$139$	−456.000	+	789.815i	−0.278255	+	0.481951i	0.692696	+	0.721229i	$0.256423\pi$
$140$	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	0.413875	+	0.910334i	$0.364175\pi$
$149$	−1057.50	+	1831.64i	−0.581435	+	1.00707i	−0.995310	+	0.0967407i	$0.969158\pi$
$150$		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	0.429835	+	0.902907i	$0.358572\pi$
$163$	−1180.00	+	2043.82i	−0.567023	+	0.982112i	−0.996858	+	0.0792052i	$0.974762\pi$
$164$	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	0.896637	−	0.442767i	$-0.146003\pi$
$167$	140.000	+	242.487i	0.0648714	+	0.112361i	−0.831766	+	0.555127i	$0.812670\pi$
$168$		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	−0.682764	−	0.730639i	$-0.739222\pi$
$173$	663.000	−	1148.35i	0.291370	−	0.504667i	0.974134	+	0.225972i	$0.0725557\pi$
$174$		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	0.839586	+	0.543227i	$0.182798\pi$
$179$	2132.00	+	3692.73i	0.890241	+	1.54194i	0.0506550	+	0.998716i	$0.483869\pi$
$180$		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	−0.959567	−	0.281481i	$-0.909174\pi$
$191$	−623.000	+	1079.07i	−0.236014	+	0.408788i	0.723553	+	0.690269i	$0.242508\pi$
$192$		0			0
$193$	−133.500	−	231.229i	−0.0497904	−	0.0862394i	0.840056	−	0.542500i	$-0.182522\pi$
$193$	−133.500	−	231.229i	−0.0497904	−	0.0862394i	−0.889846	+	0.456260i	$0.849189\pi$
$194$	−952.000			−0.352318
$195$		0			0
$196$	456.000			0.166181
$197$	639.000	+	1106.78i	0.231101	+	0.400278i	0.958132	−	0.286326i	$-0.0924339\pi$
$197$	639.000	+	1106.78i	0.231101	+	0.400278i	−0.727032	+	0.686604i	$0.759101\pi$
$198$		0			0
$199$	−2119.00	+	3670.22i	−0.754834	+	1.30741i	0.190623	+	0.981663i	$0.438949\pi$
$199$	−2119.00	+	3670.22i	−0.754834	+	1.30741i	−0.945457	+	0.325747i	$0.894384\pi$
$200$		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	−1.00000		0.000951154i	$-0.999697\pi$
$211$	−1535.00	−	2658.70i	−0.500823	−	0.867452i	0.499176	−	0.866501i	$-0.333636\pi$
$212$	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	0.914602	+	0.404356i	$0.132504\pi$
$223$	2689.00	+	4657.48i	0.807483	+	1.39860i	−0.107119	+	0.994246i	$0.534162\pi$
$224$	−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	0.414387	+	0.910101i	$0.363996\pi$
$227$	−1987.00	+	3441.58i	−0.580977	+	1.00628i	−0.995364	+	0.0961811i	$0.969337\pi$
$228$		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	−0.922133	−	0.386873i	$-0.873555\pi$
$241$	−471.500	+	816.662i	−0.126025	+	0.218281i	0.796108	+	0.605154i	$0.206889\pi$
$242$	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	−0.985036	−	0.172349i	$-0.944864\pi$
$251$	−1365.00	+	2364.25i	−0.343259	+	0.594542i	0.641777	+	0.766891i	$0.278198\pi$
$252$		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	0.728680	−	0.684854i	$-0.240134\pi$
$257$	−942.500	−	1632.46i	−0.228761	−	0.396225i	−0.957441	+	0.288629i	$0.906801\pi$
$258$		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	0.999511	−	0.0312769i	$-0.00995738\pi$
$263$	2016.00	+	3491.81i	0.472669	+	0.818686i	−0.526842	+	0.849963i	$0.676624\pi$
$264$		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	−0.544633	−	0.838674i	$-0.683331\pi$
$269$	2003.00	−	3469.30i	0.453997	−	0.786345i	0.998630	+	0.0523292i	$0.0166645\pi$
$270$		0			0
$271$	2148.00	+	3720.45i	0.481482	+	0.833952i	0.999774	−	0.0212520i	$-0.00676523\pi$
$271$	2148.00	+	3720.45i	0.481482	+	0.833952i	−0.518292	+	0.855204i	$0.673432\pi$
$272$	−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	−0.390478	−	0.920612i	$-0.627690\pi$
$277$	2775.50	−	4807.31i	0.602035	−	1.04275i	0.992513	−	0.122142i	$-0.0389765\pi$
$278$	−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	0.654374	−	0.756171i	$-0.272932\pi$
$283$	−1560.00	−	2702.00i	−0.327676	−	0.567552i	−0.982050	+	0.188619i	$0.939599\pi$
$284$	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	−0.0723887	−	0.997376i	$-0.523062\pi$
$293$	4150.50	−	7188.88i	0.827559	−	1.43337i	0.899948	−	0.435998i	$-0.143604\pi$
$294$		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	−0.973715	−	0.227769i	$-0.926857\pi$
$331$	−1744.00	+	3020.70i	−0.289604	+	0.501609i	0.684111	+	0.729378i	$0.260190\pi$
$332$	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	−0.438298	−	0.898830i	$-0.644419\pi$
$347$	3615.00	−	6261.36i	0.559260	−	0.968667i	0.997558	−	0.0698377i	$-0.0222481\pi$
$348$		0			0
$349$	2629.00	+	4553.56i	0.403230	+	0.698414i	0.994114	−	0.108342i	$-0.0345543\pi$
$349$	2629.00	+	4553.56i	0.403230	+	0.698414i	−0.590884	+	0.806757i	$0.701221\pi$
$350$	−13120.0			−2.00370
$351$		0			0
$352$	8192.00			1.24044
$353$	1581.50	+	2739.24i	0.238455	+	0.413017i	0.960271	−	0.279068i	$-0.0900256\pi$
$353$	1581.50	+	2739.24i	0.238455	+	0.413017i	−0.721816	+	0.692085i	$0.756692\pi$
$354$		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	−0.999429	−	0.0337755i	$-0.989247\pi$
$367$	−3719.00	−	6441.50i	−0.528965	−	0.916195i	0.470464	−	0.882419i	$-0.344086\pi$
$368$	−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	−0.305242	−	0.952275i	$-0.598737\pi$
$373$	4841.50	−	8385.72i	0.672073	−	1.16407i	0.977315	−	0.211790i	$-0.0679294\pi$
$374$	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	0.899763	−	0.436378i	$-0.143739\pi$
$379$	531.000	+	919.719i	0.0719674	+	0.124651i	−0.827796	+	0.561029i	$0.810406\pi$
$380$	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	−0.959450	−	0.281880i	$-0.909042\pi$
$383$	−1766.00	+	3058.80i	−0.235609	+	0.408087i	0.723840	+	0.689968i	$0.242375\pi$
$384$		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	−0.612452	−	0.790508i	$-0.709817\pi$
$397$	2993.00	−	5184.03i	0.378374	−	0.655362i	0.990826	+	0.135145i	$0.0431501\pi$
$398$	−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	0.989495	−	0.144565i	$-0.0461782\pi$
$401$	2967.50	+	5139.86i	0.369551	+	0.640081i	−0.619945	+	0.784646i	$0.712845\pi$
$402$		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	0.101023	−	0.994884i	$-0.467788\pi$
$409$	7544.50	−	13067.5i	0.912106	−	1.57981i	0.811083	−	0.584931i	$-0.198878\pi$
$410$	−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	−0.987464	−	0.157843i	$-0.949546\pi$
$419$	−5407.00	−	9365.20i	−0.630428	−	1.09193i	0.357037	−	0.934090i	$-0.383787\pi$
$420$		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	0.916029	−	0.401112i	$-0.131376\pi$
$431$	990.000	+	1714.73i	0.110642	+	0.191637i	−0.805387	+	0.592749i	$0.798043\pi$
$432$		0			0
$433$	3464.50	−	6000.69i	0.384511	−	0.665993i	−0.607190	−	0.794556i	$-0.707703\pi$
$433$	3464.50	−	6000.69i	0.384511	−	0.665993i	0.991701	+	0.128564i	$0.0410368\pi$
$434$	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	0.963179	−	0.268862i	$-0.0866476\pi$
$439$	2288.00	+	3962.93i	0.248748	+	0.430844i	−0.714431	+	0.699706i	$0.753314\pi$
$440$		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	−0.811216	−	0.584747i	$-0.801194\pi$
$449$	959.000	−	1661.04i	0.100797	−	0.174586i	0.912013	+	0.410160i	$0.134527\pi$
$450$		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	0.992530	+	0.122002i	$0.0389314\pi$
$457$	5880.50	+	10185.3i	0.601922	+	1.04256i	−0.390608	+	0.920557i	$0.627735\pi$
$458$	−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	−0.842371	−	0.538898i	$-0.818841\pi$
$461$	450.500	−	780.289i	0.0455138	−	0.0788323i	0.887885	+	0.460066i	$0.152174\pi$
$462$		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	0.933408	−	0.358816i	$-0.116819\pi$
$479$	1635.00	+	2831.90i	0.155960	+	0.270131i	−0.777448	+	0.628947i	$0.783486\pi$
$480$		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	−0.138046	+	0.990426i	$0.544082\pi$
$487$	−9960.00	+	17251.2i	−0.926757	+	1.60519i	−0.788711	+	0.614765i	$0.789251\pi$
$488$		0			0
$489$		0			0
$490$	−1938.00	+	3356.71i	−0.178673	+	0.309471i
$491$	3276.00	+	5674.20i	0.301108	+	0.521534i	0.976387	−	0.216028i	$-0.0693103\pi$
$491$	3276.00	+	5674.20i	0.301108	+	0.521534i	−0.675280	+	0.737562i	$0.735977\pi$
$492$		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	−0.331661	−	0.943399i	$-0.607609\pi$
$503$	7346.00	−	12723.6i	0.651177	−	1.12787i	0.982838	−	0.184473i	$-0.0590577\pi$
$504$		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	0.986543	−	0.163500i	$-0.0522784\pi$
$509$	4038.50	+	6994.89i	0.351677	+	0.609122i	−0.634867	+	0.772622i	$0.718945\pi$
$510$		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	0.803255	−	0.595636i	$-0.203100\pi$
$523$	−1366.00	−	2365.98i	−0.114208	−	0.197815i	−0.917463	+	0.397821i	$0.869767\pi$
$524$	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	0.872512	−	0.488593i	$-0.162490\pi$
$557$	172.500	+	298.779i	0.0131222	+	0.0227283i	−0.859390	+	0.511321i	$0.829156\pi$
$558$		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	−0.980724	−	0.195400i	$-0.937399\pi$
$563$	−4290.00	+	7430.50i	−0.321140	+	0.556231i	0.659583	+	0.751631i	$0.270733\pi$
$564$		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	−0.958951	−	0.283570i	$-0.908481\pi$
$569$	−9841.00	−	17045.1i	−0.725055	−	1.25583i	0.233897	−	0.972261i	$-0.424852\pi$
$570$		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	0.889714	−	0.456518i	$-0.150904\pi$
$587$	704.000	+	1219.36i	0.0495012	+	0.0857386i	−0.840213	+	0.542256i	$0.817570\pi$
$588$		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	0.999368	−	0.0355563i	$-0.0113203\pi$
$601$	6908.50	+	11965.9i	0.468891	+	0.812143i	−0.530477	+	0.847700i	$0.677987\pi$
$602$	−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	−0.970512	−	0.241053i	$-0.922507\pi$
$607$	−4135.00	+	7162.03i	−0.276498	+	0.478909i	0.694014	+	0.719962i	$0.255841\pi$
$608$	−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	−0.955262	−	0.295760i	$-0.904427\pi$
$613$	−11136.5	−	19289.0i	−0.733767	−	1.27092i	0.221496	−	0.975161i	$-0.428906\pi$
$614$	17356.0	+	30061.5i	1.14077	+	1.97587i
$615$		0			0
$616$		0			0
$617$	−9494.50	+	16445.0i	−0.619504	+	1.07301i	0.370072	+	0.929003i	$0.379333\pi$
$617$	−9494.50	+	16445.0i	−0.619504	+	1.07301i	−0.989576	+	0.144010i	$0.954000\pi$
$618$		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	−0.216097	−	0.976372i	$-0.569333\pi$
$631$	11690.0	−	20247.7i	0.737514	−	1.27741i	0.953611	−	0.301040i	$-0.0973339\pi$
$632$		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	−0.750786	−	0.660546i	$-0.770325\pi$
$641$	3191.50	−	5527.84i	0.196656	−	0.340619i	0.947442	+	0.319927i	$0.103658\pi$
$642$		0			0
$643$	8552.00	−	14812.5i	0.524507	−	0.908473i	−0.475086	−	0.879939i	$-0.657583\pi$
$643$	8552.00	−	14812.5i	0.524507	−	0.908473i	0.999593	−	0.0285332i	$-0.00908365\pi$
$644$	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	0.952493	−	0.304560i	$-0.0985093\pi$
$647$	3497.00	+	6056.98i	0.212490	+	0.368044i	−0.740003	+	0.672604i	$0.765176\pi$
$648$		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	0.776587	−	0.630010i	$-0.216949\pi$
$653$	−2625.00	−	4546.63i	−0.157311	−	0.272471i	−0.933898	+	0.357539i	$0.883616\pi$
$654$		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	−0.923007	−	0.384783i	$-0.874276\pi$
$659$	−2170.00	+	3758.55i	−0.128272	+	0.222173i	0.794735	+	0.606956i	$0.207610\pi$
$660$		0			0
$661$	2089.50	+	3619.12i	0.122953	+	0.212961i	0.920931	−	0.389726i	$-0.127430\pi$
$661$	2089.50	+	3619.12i	0.122953	+	0.212961i	−0.797978	+	0.602687i	$0.794097\pi$
$662$	−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	−0.981926	−	0.189266i	$-0.939389\pi$
$673$	−11433.5	−	19803.4i	−0.654872	−	1.13427i	0.327054	−	0.945006i	$-0.393944\pi$
$674$	−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	−0.991111	−	0.133037i	$-0.957527\pi$
$683$	−6789.00	+	11758.9i	−0.380342	+	0.658772i	0.610769	+	0.791809i	$0.290861\pi$
$684$		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	0.635590	−	0.772026i	$-0.280757\pi$
$691$	−6372.00	−	11036.6i	−0.350799	−	0.607602i	−0.986390	+	0.164424i	$0.947423\pi$
$692$	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	−0.875262	−	0.483650i	$-0.839311\pi$
$709$	−354.500	+	614.012i	−0.0187779	+	0.0325243i	0.856484	+	0.516174i	$0.172644\pi$
$710$	−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	−0.947959	−	0.318393i	$-0.896857\pi$
$719$	−3822.00	+	6619.90i	−0.198243	+	0.343367i	0.749716	+	0.661760i	$0.230190\pi$
$720$		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	0.810834	−	0.585276i	$-0.199014\pi$
$739$	−2038.00	−	3529.92i	−0.101447	−	0.175711i	−0.912281	+	0.409565i	$0.865680\pi$
$740$	30872.0			1.53362
$741$		0			0
$742$	7440.00			0.368101
$743$	−17028.0	−	29493.4i	−0.840776	−	1.45627i	−0.889239	−	0.457442i	$-0.848766\pi$
$743$	−17028.0	−	29493.4i	−0.840776	−	1.45627i	0.0484632	−	0.998825i	$-0.484568\pi$
$744$		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	0.870413	−	0.492322i	$-0.163852\pi$
$751$	182.000	+	315.233i	0.00884324	+	0.0153169i	−0.861570	+	0.507639i	$0.830518\pi$
$752$	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	0.937003	−	0.349322i	$-0.113588\pi$
$757$	3457.00	+	5987.70i	0.165980	+	0.287486i	−0.771023	+	0.636807i	$0.780255\pi$
$758$	−2124.00	+	3678.88i	−0.101777	+	0.176283i
$759$		0			0
$760$		0			0
$761$	6991.00	−	12108.8i	0.333014	−	0.576797i	−0.650087	−	0.759859i	$-0.725268\pi$
$761$	6991.00	−	12108.8i	0.333014	−	0.576797i	0.983101	+	0.183062i	$0.0586011\pi$
$762$		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	0.996287	−	0.0860907i	$-0.0274375\pi$
$769$	9033.00	+	15645.6i	0.423587	+	0.733674i	−0.572700	+	0.819765i	$0.694104\pi$
$770$	−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	−0.647834	−	0.761782i	$-0.724325\pi$
$773$	7217.00	−	12500.2i	0.335805	−	0.581632i	0.983639	+	0.180150i	$0.0576583\pi$
$774$		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
$780$		0			0
$781$	−20928.0			−0.958851
$782$	−2028.00	−	3512.60i	−0.0927380	−	0.160627i
$783$		0			0
$784$	1824.00	−	3159.26i	0.0830904	−	0.143917i
$785$	−49317.0			−2.24229
$786$		0			0
$787$	7699.00	−	13335.1i	0.348716	−	0.603994i	−0.637305	−	0.770611i	$-0.719951\pi$
$787$	7699.00	−	13335.1i	0.348716	−	0.603994i	0.986022	+	0.166617i	$0.0532843\pi$
$788$	−10224.0			−0.462202
$789$		0			0
$790$	2584.00	+	4475.62i	0.116373	+	0.201564i
$791$	3270.00	+	5663.81i	0.146988	+	0.254591i
$792$		0			0
$793$	1885.00	−	6529.83i	0.0844115	−	0.292410i
$794$	23944.0			1.07020
$795$		0			0
$796$	−16952.0	−	29361.7i	−0.754834	−	1.30741i
$797$	−18421.0	+	31906.1i	−0.818702	+	1.41803i	0.0879373	+	0.996126i	$0.471972\pi$
$797$	−18421.0	+	31906.1i	−0.818702	+	1.41803i	−0.906639	+	0.421907i	$0.861361\pi$
$798$		0			0
$799$	−1053.00	+	1823.85i	−0.0466239	+	0.0807549i
$800$	−20992.0	+	36359.2i	−0.927724	+	1.60687i
$801$		0			0
$802$	−11870.0	+	20559.4i	−0.522624	+	0.905211i
$803$	−3440.00	−	5958.25i	−0.151177	−	0.261846i
$804$		0			0
$805$	26520.0			1.16113
$806$	9620.00	+	9997.40i	0.420409	+	0.436902i
$807$		0			0
$808$		0			0
$809$	20755.5	+	35949.6i	0.902008	+	1.56232i	0.824884	+	0.565302i	$0.191240\pi$
$809$	20755.5	+	35949.6i	0.902008	+	1.56232i	0.0771242	+	0.997021i	$0.475426\pi$
$810$		0			0
$811$	23066.0			0.998714			0.499357	−	0.866396i	$-0.333570\pi$
$811$	23066.0			0.998714			0.499357	+	0.866396i	$0.333570\pi$
$812$	15760.0	−	27297.1i	0.681118	−	1.17973i
$813$		0			0
$814$	29056.0			1.25112
$815$	20060.0	−	34744.9i	0.862173	−	1.49333i
$816$		0			0
$817$	2340.00	+	4053.00i	0.100203	+	0.173558i
$818$	60356.0			2.57983
$819$		0			0
$820$	−22440.0			−0.955657
$821$	14419.0	+	24974.4i	0.612943	+	1.06165i	0.990742	+	0.135761i	$0.0433480\pi$
$821$	14419.0	+	24974.4i	0.612943	+	1.06165i	−0.377798	+	0.925888i	$0.623319\pi$
$822$		0			0
$823$	−13728.0	+	23777.6i	−0.581443	+	1.00709i	0.413865	+	0.910338i	$0.364179\pi$
$823$	−13728.0	+	23777.6i	−0.581443	+	1.00709i	−0.995309	+	0.0967514i	$0.969155\pi$
$824$		0			0
$825$		0			0
$826$	34560.0	−	59859.7i	1.45581	−	2.52153i
$827$	33572.0			1.41162			0.705812	−	0.708399i	$-0.250582\pi$
$827$	33572.0			1.41162			0.705812	+	0.708399i	$0.250582\pi$
$828$		0			0
$829$	22899.5	+	39663.1i	0.959388	+	1.66171i	0.723991	+	0.689809i	$0.242306\pi$
$829$	22899.5	+	39663.1i	0.959388	+	1.66171i	0.235396	+	0.971899i	$0.424361\pi$
$830$	21352.0	+	36982.7i	0.892938	+	1.54661i
$831$		0			0
$832$	23296.0	−	5764.27i	0.970725	−	0.240192i
$833$	741.000			0.0308213
$834$		0			0
$835$	−2380.00	−	4122.28i	−0.0986387	−	0.170847i
$836$	−3840.00	+	6651.08i	−0.158863	+	0.275158i
$837$		0			0
$838$	21628.0	−	37460.8i	0.891560	−	1.54423i
$839$	16143.0	−	27960.5i	0.664265	−	1.15054i	−0.315219	−	0.949019i	$-0.602078\pi$
$839$	16143.0	−	27960.5i	0.664265	−	1.15054i	0.979484	−	0.201522i	$-0.0645886\pi$
$840$		0			0
$841$	−7210.00	+	12488.1i	−0.295625	+	0.512038i
$842$	−13070.0	−	22637.9i	−0.534943	−	0.926548i
$843$		0			0
$844$	24560.0			1.00165
$845$	−33039.5	+	17416.6i	−1.34508	+	0.709054i
$846$		0			0
$847$	3070.00	+	5317.40i	0.124541	+	0.215712i
$848$	−2976.00	−	5154.58i	−0.120514	−	0.208737i
$849$		0			0
$850$	−8528.00			−0.344127
$851$	−8853.00	+	15333.8i	−0.356612	+	0.617670i
$852$		0			0
$853$	20937.0			0.840409			0.420205	−	0.907429i	$-0.361958\pi$
$853$	20937.0			0.840409			0.420205	+	0.907429i	$0.361958\pi$
$854$	5800.00	−	10045.9i	0.232403	−	0.402533i
$855$		0			0
$856$		0			0
$857$	7189.00			0.286548			0.143274	−	0.989683i	$-0.454237\pi$
$857$	7189.00			0.286548			0.143274	+	0.989683i	$0.454237\pi$
$858$		0			0
$859$	−32498.0			−1.29082			−0.645412	−	0.763835i	$-0.723314\pi$
$859$	−32498.0			−1.29082			−0.645412	+	0.763835i	$0.723314\pi$
$860$	−10608.0	−	18373.6i	−0.420616	−	0.728528i
$861$		0			0
$862$	−3960.00	+	6858.92i	−0.156471	+	0.271016i
$863$	−8428.00			−0.332436			−0.166218	−	0.986089i	$-0.553156\pi$
$863$	−8428.00			−0.332436			−0.166218	+	0.986089i	$0.553156\pi$
$864$		0			0
$865$	−11271.0	+	19521.9i	−0.443035	+	0.767360i
$866$	27716.0			1.08756
$867$		0			0
$868$	5920.00	+	10253.7i	0.231495	+	0.400962i
$869$	1216.00	+	2106.17i	0.0474683	+	0.0822176i
$870$		0			0
$871$	28015.0	+	29114.0i	1.08984	+	1.13260i
$872$		0			0
$873$		0			0
$874$	−4680.00	−	8106.00i	−0.181125	−	0.313718i
$875$	6630.00	−	11483.5i	0.256154	−	0.443672i
$876$		0			0
$877$	3423.50	−	5929.68i	0.131817	−	0.228313i	−0.792560	−	0.609794i	$-0.791252\pi$
$877$	3423.50	−	5929.68i	0.131817	−	0.228313i	0.924377	+	0.381480i	$0.124586\pi$
$878$	−9152.00	+	15851.7i	−0.351783	+	0.609305i
$879$		0			0
$880$	−17408.0	+	30151.5i	−0.666845	+	1.15501i
$881$	14865.5	+	25747.8i	0.568481	+	0.984637i	0.996717	+	0.0809703i	$0.0258019\pi$
$881$	14865.5	+	25747.8i	0.568481	+	0.984637i	−0.428236	+	0.903667i	$0.640865\pi$
$882$		0			0
$883$	−23738.0			−0.904697			−0.452348	−	0.891841i	$-0.649414\pi$
$883$	−23738.0			−0.904697			−0.452348	+	0.891841i	$0.649414\pi$
$884$	3380.00	+	3512.60i	0.128599	+	0.133644i
$885$		0			0
$886$	17624.0	+	30525.7i	0.668273	+	1.15748i
$887$	13794.0	+	23891.9i	0.522161	+	0.904410i	0.999668	+	0.0257817i	$0.00820749\pi$
$887$	13794.0	+	23891.9i	0.522161	+	0.904410i	−0.477506	+	0.878628i	$0.658459\pi$
$888$		0			0
$889$	−43160.0			−1.62828
$890$	−9044.00	+	15664.7i	−0.340624	+	0.589978i
$891$		0			0
$892$	−43024.0			−1.61497
$893$	−2430.00	+	4208.88i	−0.0910603	+	0.157721i
$894$		0			0
$895$	−36244.0	−	62776.4i	−1.35363	−	2.34456i
$896$		0			0
$897$		0			0
$898$	7672.00			0.285098
$899$	−7289.00	−	12624.9i	−0.270414	−	0.468370i
$900$		0			0
$901$	604.500	−	1047.02i	0.0223516	−	0.0387142i
$902$	−21120.0			−0.779622
$903$		0			0
$904$		0			0
$905$	6851.00			0.251641
$906$		0			0
$907$	18564.0	+	32153.8i	0.679611	+	1.17712i	0.975098	+	0.221775i	$0.0711849\pi$
$907$	18564.0	+	32153.8i	0.679611	+	1.17712i	−0.295487	+	0.955347i	$0.595482\pi$
$908$	−15896.0	−	27532.7i	−0.580977	−	1.00628i
$909$		0			0
$910$	−61880.0	+	15311.3i	−2.25418	+	0.557764i
$911$	−20516.0			−0.746131			−0.373066	−	0.927805i	$-0.621693\pi$
$911$	−20516.0			−0.746131			−0.373066	+	0.927805i	$0.621693\pi$
$912$		0			0
$913$	10048.0	+	17403.6i	0.364228	+	0.630862i
$914$	−23522.0	+	40741.3i	−0.851246	+	1.47440i
$915$		0			0
$916$	25192.0	−	43633.8i	0.908698	−	1.57391i
$917$	7300.00	−	12644.0i	0.262887	−	0.455333i
$918$		0			0
$919$	10503.0	−	18191.7i	0.376999	−	0.652981i	−0.613625	−	0.789597i	$-0.710289\pi$
$919$	10503.0	−	18191.7i	0.376999	−	0.652981i	0.990624	+	0.136616i	$0.0436227\pi$
$920$		0			0
$921$		0			0
$922$	3604.00			0.128733
$923$	−8502.00	+	29451.8i	−0.303193	+	1.05029i
$924$		0			0
$925$	18614.0	+	32240.4i	0.661648	+	1.14601i
$926$	2744.00	+	4752.75i	0.0973795	+	0.168666i
$927$		0			0
$928$	−50432.0			−1.78396
$929$	10213.5	−	17690.3i	0.360704	−	0.624758i	−0.627373	−	0.778719i	$-0.715870\pi$
$929$	10213.5	−	17690.3i	0.360704	−	0.624758i	0.988077	+	0.153961i	$0.0492031\pi$
$930$		0			0
$931$	1710.00			0.0601965
$932$	16120.0	−	27920.7i	0.566554	−	0.981300i
$933$		0			0
$934$	12792.0	+	22156.4i	0.448145	+	0.776209i
$935$	−7072.00			−0.247357
$936$		0			0
$937$	33191.0			1.15721			0.578603	−	0.815609i	$-0.303598\pi$
$937$	33191.0			1.15721			0.578603	+	0.815609i	$0.303598\pi$
$938$	34480.0	+	59721.1i	1.20023	+	2.07885i
$939$		0			0
$940$	11016.0	−	19080.3i	0.382236	−	0.662053i
$941$	36422.0			1.26177			0.630884	−	0.775877i	$-0.282692\pi$
$941$	36422.0			1.26177			0.630884	+	0.775877i	$0.282692\pi$
$942$		0			0
$943$	6435.00	−	11145.7i	0.222219	−	0.384894i
$944$	−55296.0			−1.90650
$945$		0			0
$946$	−9984.00	−	17292.8i	−0.343137	−	0.594331i
$947$	−19815.0	−	34320.6i	−0.679938	−	1.17769i	−0.974999	−	0.222208i	$-0.928673\pi$
$947$	−19815.0	−	34320.6i	−0.679938	−	1.17769i	0.295062	−	0.955478i	$-0.404660\pi$
$948$		0			0
$949$	−9782.50	+	2420.54i	−0.334619	+	0.0827967i
$950$	−19680.0			−0.672109
$951$		0			0
$952$		0			0
$953$	28821.0	−	49919.4i	0.979647	−	1.69680i	0.315989	−	0.948763i	$-0.397664\pi$
$953$	28821.0	−	49919.4i	0.979647	−	1.69680i	0.663658	−	0.748036i	$-0.269003\pi$
$954$		0			0
$955$	10591.0	−	18344.2i	0.358866	−	0.621574i
$956$	−3936.00	+	6817.35i	−0.133158	+	0.230637i
$957$		0			0
$958$	−6540.00	+	11327.6i	−0.220561	+	0.382024i
$959$	16710.0	+	28942.6i	0.562663	+	0.974561i
$960$		0			0
$961$	−24315.0			−0.816186
$962$	11804.0	−	40890.3i	0.395609	−	1.37043i
$963$		0			0
$964$	−3772.00	−	6533.30i	−0.126025	−	0.218281i
$965$	2269.50	+	3930.89i	0.0757076	+	0.131129i
$966$		0			0
$967$	2162.00			0.0718979			0.0359489	−	0.999354i	$-0.488555\pi$
$967$	2162.00			0.0718979			0.0359489	+	0.999354i	$0.488555\pi$
$968$		0			0
$969$		0			0
$970$	16184.0			0.535708
$971$	−9879.00	+	17110.9i	−0.326501	+	0.565516i	−0.981815	−	0.189841i	$-0.939203\pi$
$971$	−9879.00	+	17110.9i	−0.326501	+	0.565516i	0.655314	+	0.755356i	$0.272536\pi$
$972$		0			0
$973$	−9120.00	−	15796.3i	−0.300487	−	0.520459i
$974$	−79680.0			−2.62126
$975$		0			0
$976$	−9280.00			−0.304350
$977$	−6244.50	−	10815.8i	−0.204482	−	0.354174i	0.745485	−	0.666522i	$-0.232218\pi$
$977$	−6244.50	−	10815.8i	−0.204482	−	0.354174i	−0.949968	+	0.312348i	$0.898884\pi$
$978$		0			0
$979$	−4256.00	+	7371.61i	−0.138940	+	0.240651i
$980$	−7752.00			−0.252682
$981$		0			0
$982$	−13104.0	+	22696.8i	−0.425830	+	0.737560i
$983$	28658.0			0.929856			0.464928	−	0.885349i	$-0.346080\pi$
$983$	28658.0			0.929856			0.464928	+	0.885349i	$0.346080\pi$
$984$		0			0
$985$	−10863.0	−	18815.3i	−0.351395	−	0.608634i
$986$	−5122.00	−	8871.56i	−0.165434	−	0.286540i
$987$		0			0
$988$	7800.00	+	8106.00i	0.251165	+	0.261018i
$989$	12168.0			0.391223
$990$		0			0
$991$	21397.0	+	37060.7i	0.685871	+	1.18796i	0.973162	+	0.230120i	$0.0739119\pi$
$991$	21397.0	+	37060.7i	0.685871	+	1.18796i	−0.287291	+	0.957843i	$0.592755\pi$
$992$	9472.00	−	16406.0i	0.303162	−	0.525091i
$993$		0			0
$994$	−26160.0	+	45310.4i	−0.834753	+	1.44584i
$995$	36023.0	−	62393.7i	1.14774	−	1.98795i
$996$		0			0
$997$	26291.5	−	45538.2i	0.835166	−	1.44655i	−0.0587298	−	0.998274i	$-0.518705\pi$
$997$	26291.5	−	45538.2i	0.835166	−	1.44655i	0.893895	−	0.448275i	$-0.147962\pi$
$998$	3492.00	+	6048.32i	0.110759	+	0.191840i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.4.g.c.55.1		2
3.2	odd	2		13.4.c.a.3.1	✓	2
12.11	even	2		208.4.i.b.81.1		2
13.3	even	3		1521.4.a.b.1.1		1
13.9	even	3	inner	117.4.g.c.100.1		2
13.10	even	6		1521.4.a.k.1.1		1
39.2	even	12		169.4.b.c.168.1		2
39.5	even	4		169.4.e.c.23.1		4
39.8	even	4		169.4.e.c.23.2		4
39.11	even	12		169.4.b.c.168.2		2
39.17	odd	6		169.4.c.d.22.1		2
39.20	even	12		169.4.e.c.147.1		4
39.23	odd	6		169.4.a.a.1.1		1
39.29	odd	6		169.4.a.d.1.1		1
39.32	even	12		169.4.e.c.147.2		4
39.35	odd	6		13.4.c.a.9.1	yes	2
39.38	odd	2		169.4.c.d.146.1		2
156.35	even	6		208.4.i.b.113.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.4.c.a.3.1	✓	2	3.2	odd	2
13.4.c.a.9.1	yes	2	39.35	odd	6
117.4.g.c.55.1		2	1.1	even	1	trivial
117.4.g.c.100.1		2	13.9	even	3	inner
169.4.a.a.1.1		1	39.23	odd	6
169.4.a.d.1.1		1	39.29	odd	6
169.4.b.c.168.1		2	39.2	even	12
169.4.b.c.168.2		2	39.11	even	12
169.4.c.d.22.1		2	39.17	odd	6
169.4.c.d.146.1		2	39.38	odd	2
169.4.e.c.23.1		4	39.5	even	4
169.4.e.c.23.2		4	39.8	even	4
169.4.e.c.147.1		4	39.20	even	12
169.4.e.c.147.2		4	39.32	even	12
208.4.i.b.81.1		2	12.11	even	2
208.4.i.b.113.1		2	156.35	even	6
1521.4.a.b.1.1		1	13.3	even	3
1521.4.a.k.1.1		1	13.10	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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
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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