LMFDB - Embedded newform 108.3.d.c.55.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,3,Mod(55,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("108.55");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	108.d (of order $2$, degree $1$, 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:	$2.94278685509$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{13})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 4x^{2} + 3x + 9 $ x^4 - x^3 + 4x^2 + 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			55.2
Root			$1.15139 - 1.99426i$ of defining polynomial
Character	$\chi$	$=$	108.55
Dual form			108.3.d.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)

$f(q)$	$=$	$q+(-1.80278 + 0.866025i) q^{2} +(2.50000 - 3.12250i) q^{4} -3.60555 q^{5} +6.24500i q^{7} +(-1.80278 + 7.79423i) q^{8} +O(q^{10})$	\(q+(-1.80278 + 0.866025i) q^{2} +(2.50000 - 3.12250i) q^{4} -3.60555 q^{5} +6.24500i q^{7} +(-1.80278 + 7.79423i) q^{8} +(6.50000 - 3.12250i) q^{10} +12.1244i q^{11} -16.0000 q^{13} +(-5.40833 - 11.2583i) q^{14} +(-3.50000 - 15.6125i) q^{16} -14.4222 q^{17} +37.4700i q^{19} +(-9.01388 + 11.2583i) q^{20} +(-10.5000 - 21.8575i) q^{22} -17.3205i q^{23} -12.0000 q^{25} +(28.8444 - 13.8564i) q^{26} +(19.5000 + 15.6125i) q^{28} +50.4777 q^{29} -6.24500i q^{31} +(19.8305 + 25.1147i) q^{32} +(26.0000 - 12.4900i) q^{34} -22.5167i q^{35} +26.0000 q^{37} +(-32.4500 - 67.5500i) q^{38} +(6.50000 - 28.1025i) q^{40} +7.21110 q^{41} -12.4900i q^{43} +(37.8583 + 30.3109i) q^{44} +(15.0000 + 31.2250i) q^{46} -3.46410i q^{47} +10.0000 q^{49} +(21.6333 - 10.3923i) q^{50} +(-40.0000 + 49.9600i) q^{52} -68.5055 q^{53} -43.7150i q^{55} +(-48.6749 - 11.2583i) q^{56} +(-91.0000 + 43.7150i) q^{58} +76.2102i q^{59} +8.00000 q^{61} +(5.40833 + 11.2583i) q^{62} +(-57.5000 - 28.1025i) q^{64} +57.6888 q^{65} -62.4500i q^{67} +(-36.0555 + 45.0333i) q^{68} +(19.5000 + 40.5925i) q^{70} -62.3538i q^{71} -19.0000 q^{73} +(-46.8722 + 22.5167i) q^{74} +(117.000 + 93.6750i) q^{76} -75.7166 q^{77} -49.9600i q^{79} +(12.6194 + 56.2917i) q^{80} +(-13.0000 + 6.24500i) q^{82} +116.047i q^{83} +52.0000 q^{85} +(10.8167 + 22.5167i) q^{86} +(-94.5000 - 21.8575i) q^{88} -79.3221 q^{89} -99.9200i q^{91} +(-54.0833 - 43.3013i) q^{92} +(3.00000 + 6.24500i) q^{94} -135.100i q^{95} +119.000 q^{97} +(-18.0278 + 8.66025i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 10 q^{4}+O(q^{10}) $ 4 * q + 10 * q^4	$ 4 q + 10 q^{4} + 26 q^{10} - 64 q^{13} - 14 q^{16} - 42 q^{22} - 48 q^{25} + 78 q^{28} + 104 q^{34} + 104 q^{37} + 26 q^{40} + 60 q^{46} + 40 q^{49} - 160 q^{52} - 364 q^{58} + 32 q^{61} - 230 q^{64} + 78 q^{70} - 76 q^{73} + 468 q^{76} - 52 q^{82} + 208 q^{85} - 378 q^{88} + 12 q^{94} + 476 q^{97}+O(q^{100}) $ 4 * q + 10 * q^4 + 26 * q^10 - 64 * q^13 - 14 * q^16 - 42 * q^22 - 48 * q^25 + 78 * q^28 + 104 * q^34 + 104 * q^37 + 26 * q^40 + 60 * q^46 + 40 * q^49 - 160 * q^52 - 364 * q^58 + 32 * q^61 - 230 * q^64 + 78 * q^70 - 76 * q^73 + 468 * q^76 - 52 * q^82 + 208 * q^85 - 378 * q^88 + 12 * q^94 + 476 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$1$	$-1$

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 $

$2$	−1.80278	+	0.866025i	−0.901388	+	0.433013i
$2$	−1.80278	+	0.866025i	−0.901388	+	0.433013i
$3$		0			0
$3$		0			0
$4$	2.50000	−	3.12250i	0.625000	−	0.780625i
$5$	−3.60555			−0.721110			−0.360555	−	0.932738i	$-0.617413\pi$
$5$	−3.60555			−0.721110			−0.360555	+	0.932738i	$0.617413\pi$
$6$		0			0
$7$			6.24500i			0.892143i	0.894997	+	0.446071i	$0.147177\pi$
$7$			6.24500i			0.892143i	−0.894997	+	0.446071i	$0.852823\pi$
$8$	−1.80278	+	7.79423i	−0.225347	+	0.974279i
$9$		0			0
$10$	6.50000	−	3.12250i	0.650000	−	0.312250i
$11$			12.1244i			1.10221i	0.834435	+	0.551107i	$0.185794\pi$
$11$			12.1244i			1.10221i	−0.834435	+	0.551107i	$0.814206\pi$
$12$		0			0
$13$	−16.0000			−1.23077			−0.615385	−	0.788227i	$-0.710999\pi$
$13$	−16.0000			−1.23077			−0.615385	+	0.788227i	$0.710999\pi$
$14$	−5.40833	−	11.2583i	−0.386309	−	0.804166i
$15$		0			0
$16$	−3.50000	−	15.6125i	−0.218750	−	0.975781i
$17$	−14.4222			−0.848365			−0.424183	−	0.905577i	$-0.639438\pi$
$17$	−14.4222			−0.848365			−0.424183	+	0.905577i	$0.639438\pi$
$18$		0			0
$19$			37.4700i			1.97210i	0.166436	+	0.986052i	$0.446774\pi$
$19$			37.4700i			1.97210i	−0.166436	+	0.986052i	$0.553226\pi$
$20$	−9.01388	+	11.2583i	−0.450694	+	0.562917i
$21$		0			0
$22$	−10.5000	−	21.8575i	−0.477273	−	0.993522i
$23$		−	17.3205i		−	0.753066i	−0.926403	−	0.376533i	$-0.877116\pi$
$23$		−	17.3205i		−	0.753066i	0.926403	−	0.376533i	$-0.122884\pi$
$24$		0			0
$25$	−12.0000			−0.480000
$26$	28.8444	−	13.8564i	1.10940	−	0.532939i
$27$		0			0
$28$	19.5000	+	15.6125i	0.696429	+	0.557589i
$29$	50.4777			1.74061			0.870305	−	0.492512i	$-0.163921\pi$
$29$	50.4777			1.74061			0.870305	+	0.492512i	$0.163921\pi$
$30$		0			0
$31$		−	6.24500i		−	0.201452i	−0.994914	−	0.100726i	$-0.967884\pi$
$31$		−	6.24500i		−	0.201452i	0.994914	−	0.100726i	$-0.0321165\pi$
$32$	19.8305	+	25.1147i	0.619704	+	0.784836i
$33$		0			0
$34$	26.0000	−	12.4900i	0.764706	−	0.367353i
$35$		−	22.5167i		−	0.643333i
$36$		0			0
$37$	26.0000			0.702703			0.351351	−	0.936244i	$-0.385722\pi$
$37$	26.0000			0.702703			0.351351	+	0.936244i	$0.385722\pi$
$38$	−32.4500	−	67.5500i	−0.853946	−	1.77763i
$39$		0			0
$40$	6.50000	−	28.1025i	0.162500	−	0.702562i
$41$	7.21110			0.175881			0.0879403	−	0.996126i	$-0.471972\pi$
$41$	7.21110			0.175881			0.0879403	+	0.996126i	$0.471972\pi$
$42$		0			0
$43$		−	12.4900i		−	0.290465i	−0.989398	−	0.145233i	$-0.953607\pi$
$43$		−	12.4900i		−	0.290465i	0.989398	−	0.145233i	$-0.0463930\pi$
$44$	37.8583	+	30.3109i	0.860416	+	0.688884i
$45$		0			0
$46$	15.0000	+	31.2250i	0.326087	+	0.678804i
$47$		−	3.46410i		−	0.0737043i	−0.999321	−	0.0368521i	$-0.988267\pi$
$47$		−	3.46410i		−	0.0737043i	0.999321	−	0.0368521i	$-0.0117331\pi$
$48$		0			0
$49$	10.0000			0.204082
$50$	21.6333	−	10.3923i	0.432666	−	0.207846i
$51$		0			0
$52$	−40.0000	+	49.9600i	−0.769231	+	0.960769i
$53$	−68.5055			−1.29256			−0.646278	−	0.763102i	$-0.723675\pi$
$53$	−68.5055			−1.29256			−0.646278	+	0.763102i	$0.723675\pi$
$54$		0			0
$55$		−	43.7150i		−	0.794818i
$56$	−48.6749	−	11.2583i	−0.869195	−	0.201042i
$57$		0			0
$58$	−91.0000	+	43.7150i	−1.56897	+	0.753707i
$59$			76.2102i			1.29170i	0.763465	+	0.645849i	$0.223497\pi$
$59$			76.2102i			1.29170i	−0.763465	+	0.645849i	$0.776503\pi$
$60$		0			0
$61$	8.00000			0.131148			0.0655738	−	0.997848i	$-0.479112\pi$
$61$	8.00000			0.131148			0.0655738	+	0.997848i	$0.479112\pi$
$62$	5.40833	+	11.2583i	0.0872311	+	0.181586i
$63$		0			0
$64$	−57.5000	−	28.1025i	−0.898438	−	0.439101i
$65$	57.6888			0.887520
$66$		0			0
$67$		−	62.4500i		−	0.932089i	−0.884761	−	0.466045i	$-0.845679\pi$
$67$		−	62.4500i		−	0.932089i	0.884761	−	0.466045i	$-0.154321\pi$
$68$	−36.0555	+	45.0333i	−0.530228	+	0.662255i
$69$		0			0
$70$	19.5000	+	40.5925i	0.278571	+	0.579893i
$71$		−	62.3538i		−	0.878223i	−0.898433	−	0.439111i	$-0.855293\pi$
$71$		−	62.3538i		−	0.878223i	0.898433	−	0.439111i	$-0.144707\pi$
$72$		0			0
$73$	−19.0000			−0.260274			−0.130137	−	0.991496i	$-0.541542\pi$
$73$	−19.0000			−0.260274			−0.130137	+	0.991496i	$0.541542\pi$
$74$	−46.8722	+	22.5167i	−0.633408	+	0.304279i
$75$		0			0
$76$	117.000	+	93.6750i	1.53947	+	1.23257i
$77$	−75.7166			−0.983332
$78$		0			0
$79$		−	49.9600i		−	0.632405i	−0.948692	−	0.316202i	$-0.897592\pi$
$79$		−	49.9600i		−	0.632405i	0.948692	−	0.316202i	$-0.102408\pi$
$80$	12.6194	+	56.2917i	0.157743	+	0.703646i
$81$		0			0
$82$	−13.0000	+	6.24500i	−0.158537	+	0.0761585i
$83$			116.047i			1.39816i	0.715043	+	0.699081i	$0.246407\pi$
$83$			116.047i			1.39816i	−0.715043	+	0.699081i	$0.753593\pi$
$84$		0			0
$85$	52.0000			0.611765
$86$	10.8167	+	22.5167i	0.125775	+	0.261822i
$87$		0			0
$88$	−94.5000	−	21.8575i	−1.07386	−	0.248381i
$89$	−79.3221			−0.891260			−0.445630	−	0.895217i	$-0.647020\pi$
$89$	−79.3221			−0.891260			−0.445630	+	0.895217i	$0.647020\pi$
$90$		0			0
$91$		−	99.9200i		−	1.09802i
$92$	−54.0833	−	43.3013i	−0.587862	−	0.470666i
$93$		0			0
$94$	3.00000	+	6.24500i	0.0319149	+	0.0664361i
$95$		−	135.100i		−	1.42210i
$96$		0			0
$97$	119.000			1.22680			0.613402	−	0.789771i	$-0.289801\pi$
$97$	119.000			1.22680			0.613402	+	0.789771i	$0.289801\pi$
$98$	−18.0278	+	8.66025i	−0.183957	+	0.0883699i
$99$		0			0
$100$	−30.0000	+	37.4700i	−0.300000	+	0.374700i
$101$	61.2944			0.606875			0.303437	−	0.952851i	$-0.401866\pi$
$101$	61.2944			0.606875			0.303437	+	0.952851i	$0.401866\pi$
$102$		0			0
$103$			124.900i			1.21262i	0.795228	+	0.606310i	$0.207351\pi$
$103$			124.900i			1.21262i	−0.795228	+	0.606310i	$0.792649\pi$
$104$	28.8444	−	124.708i	0.277350	−	1.19911i
$105$		0			0
$106$	123.500	−	59.3275i	1.16509	−	0.559693i
$107$			129.904i			1.21405i	0.794681	+	0.607027i	$0.207638\pi$
$107$			129.904i			1.21405i	−0.794681	+	0.607027i	$0.792362\pi$
$108$		0			0
$109$	−46.0000			−0.422018			−0.211009	−	0.977484i	$-0.567675\pi$
$109$	−46.0000			−0.422018			−0.211009	+	0.977484i	$0.567675\pi$
$110$	37.8583	+	78.8083i	0.344166	+	0.716439i
$111$		0			0
$112$	97.5000	−	21.8575i	0.870536	−	0.195156i
$113$	93.7443			0.829596			0.414798	−	0.909914i	$-0.363852\pi$
$113$	93.7443			0.829596			0.414798	+	0.909914i	$0.363852\pi$
$114$		0			0
$115$			62.4500i			0.543043i
$116$	126.194	−	157.617i	1.08788	−	1.35876i
$117$		0			0
$118$	−66.0000	−	137.390i	−0.559322	−	1.16432i
$119$		−	90.0666i		−	0.756863i
$120$		0			0
$121$	−26.0000			−0.214876
$122$	−14.4222	+	6.92820i	−0.118215	+	0.0567886i
$123$		0			0
$124$	−19.5000	−	15.6125i	−0.157258	−	0.125907i
$125$	133.405			1.06724
$126$		0			0
$127$			18.7350i			0.147520i	0.997276	+	0.0737598i	$0.0234998\pi$
$127$			18.7350i			0.147520i	−0.997276	+	0.0737598i	$0.976500\pi$
$128$	127.997	+	0.866025i	0.999977	+	0.00676582i
$129$		0			0
$130$	−104.000	+	49.9600i	−0.800000	+	0.384308i
$131$		−	43.3013i		−	0.330544i	−0.986248	−	0.165272i	$-0.947150\pi$
$131$		−	43.3013i		−	0.330544i	0.986248	−	0.165272i	$-0.0528502\pi$
$132$		0			0
$133$	−234.000			−1.75940
$134$	54.0833	+	112.583i	0.403606	+	0.840174i
$135$		0			0
$136$	26.0000	−	112.410i	0.191176	−	0.826544i
$137$	−79.3221			−0.578994			−0.289497	−	0.957179i	$-0.593488\pi$
$137$	−79.3221			−0.578994			−0.289497	+	0.957179i	$0.593488\pi$
$138$		0			0
$139$			124.900i			0.898561i	0.893391	+	0.449280i	$0.148320\pi$
$139$			124.900i			0.898561i	−0.893391	+	0.449280i	$0.851680\pi$
$140$	−70.3082	−	56.2917i	−0.502202	−	0.402083i
$141$		0			0
$142$	54.0000	+	112.410i	0.380282	+	0.791619i
$143$		−	193.990i		−	1.35657i
$144$		0			0
$145$	−182.000			−1.25517
$146$	34.2527	−	16.4545i	0.234608	−	0.112702i
$147$		0			0
$148$	65.0000	−	81.1850i	0.439189	−	0.548547i
$149$	−3.60555			−0.0241983			−0.0120992	−	0.999927i	$-0.503851\pi$
$149$	−3.60555			−0.0241983			−0.0120992	+	0.999927i	$0.503851\pi$
$150$		0			0
$151$			193.595i			1.28209i	0.767505	+	0.641043i	$0.221498\pi$
$151$			193.595i			1.28209i	−0.767505	+	0.641043i	$0.778502\pi$
$152$	−292.050	−	67.5500i	−1.92138	−	0.444408i
$153$		0			0
$154$	136.500	−	65.5725i	0.886364	−	0.425795i
$155$			22.5167i			0.145269i
$156$		0			0
$157$	92.0000			0.585987			0.292994	−	0.956114i	$-0.405349\pi$
$157$	92.0000			0.585987			0.292994	+	0.956114i	$0.405349\pi$
$158$	43.2666	+	90.0666i	0.273839	+	0.570042i
$159$		0			0
$160$	−71.5000	−	90.5525i	−0.446875	−	0.565953i
$161$	108.167			0.671842
$162$		0			0
$163$			149.880i			0.919509i	0.888046	+	0.459754i	$0.152063\pi$
$163$			149.880i			0.919509i	−0.888046	+	0.459754i	$0.847937\pi$
$164$	18.0278	−	22.5167i	0.109925	−	0.137297i
$165$		0			0
$166$	−100.500	−	209.207i	−0.605422	−	1.26029i
$167$			169.741i			1.01641i	0.861235	+	0.508207i	$0.169691\pi$
$167$			169.741i			1.01641i	−0.861235	+	0.508207i	$0.830309\pi$
$168$		0			0
$169$	87.0000			0.514793
$170$	−93.7443	+	45.0333i	−0.551437	+	0.264902i
$171$		0			0
$172$	−39.0000	−	31.2250i	−0.226744	−	0.181541i
$173$	−176.672			−1.02123			−0.510613	−	0.859811i	$-0.670581\pi$
$173$	−176.672			−1.02123			−0.510613	+	0.859811i	$0.670581\pi$
$174$		0			0
$175$		−	74.9400i		−	0.428228i
$176$	189.291	−	42.4352i	1.07552	−	0.241109i
$177$		0			0
$178$	143.000	−	68.6950i	0.803371	−	0.385927i
$179$			265.004i			1.48047i	0.672349	+	0.740234i	$0.265285\pi$
$179$			265.004i			1.48047i	−0.672349	+	0.740234i	$0.734715\pi$
$180$		0			0
$181$	272.000			1.50276			0.751381	−	0.659868i	$-0.229388\pi$
$181$	272.000			1.50276			0.751381	+	0.659868i	$0.229388\pi$
$182$	86.5332	+	180.133i	0.475457	+	0.989743i
$183$		0			0
$184$	135.000	+	31.2250i	0.733696	+	0.169701i
$185$	−93.7443			−0.506726
$186$		0			0
$187$		−	174.860i		−	0.935080i
$188$	−10.8167	−	8.66025i	−0.0575354	−	0.0460652i
$189$		0			0
$190$	117.000	+	243.555i	0.615789	+	1.28187i
$191$		−	263.272i		−	1.37839i	−0.724578	−	0.689193i	$-0.757965\pi$
$191$		−	263.272i		−	1.37839i	0.724578	−	0.689193i	$-0.242035\pi$
$192$		0			0
$193$	−187.000			−0.968912			−0.484456	−	0.874816i	$-0.660982\pi$
$193$	−187.000			−0.968912			−0.484456	+	0.874816i	$0.660982\pi$
$194$	−214.530	+	103.057i	−1.10583	+	0.531222i
$195$		0			0
$196$	25.0000	−	31.2250i	0.127551	−	0.159311i
$197$	18.0278			0.0915115			0.0457557	−	0.998953i	$-0.485430\pi$
$197$	18.0278			0.0915115			0.0457557	+	0.998953i	$0.485430\pi$
$198$		0			0
$199$			93.6750i			0.470728i	0.971907	+	0.235364i	$0.0756283\pi$
$199$			93.6750i			0.470728i	−0.971907	+	0.235364i	$0.924372\pi$
$200$	21.6333	−	93.5307i	0.108167	−	0.467654i
$201$		0			0
$202$	−110.500	+	53.0825i	−0.547030	+	0.262785i
$203$			315.233i			1.55287i
$204$		0			0
$205$	−26.0000			−0.126829
$206$	−108.167	−	225.167i	−0.525080	−	1.09304i
$207$		0			0
$208$	56.0000	+	249.800i	0.269231	+	1.20096i
$209$	−454.299			−2.17368
$210$		0			0
$211$		−	62.4500i		−	0.295971i	−0.988989	−	0.147986i	$-0.952721\pi$
$211$		−	62.4500i		−	0.295971i	0.988989	−	0.147986i	$-0.0472790\pi$
$212$	−171.264	+	213.908i	−0.807848	+	1.00900i
$213$		0			0
$214$	−112.500	−	234.187i	−0.525701	−	1.09433i
$215$			45.0333i			0.209457i
$216$		0			0
$217$	39.0000			0.179724
$218$	82.9277	−	39.8372i	0.380402	−	0.182739i
$219$		0			0
$220$	−136.500	−	109.287i	−0.620455	−	0.496761i
$221$	230.755			1.04414
$222$		0			0
$223$		−	199.840i		−	0.896143i	−0.893998	−	0.448072i	$-0.852111\pi$
$223$		−	199.840i		−	0.896143i	0.893998	−	0.448072i	$-0.147889\pi$
$224$	−156.841	+	123.842i	−0.700185	+	0.552864i
$225$		0			0
$226$	−169.000	+	81.1850i	−0.747788	+	0.359226i
$227$		−	76.2102i		−	0.335728i	−0.985810	−	0.167864i	$-0.946313\pi$
$227$		−	76.2102i		−	0.335728i	0.985810	−	0.167864i	$-0.0536869\pi$
$228$		0			0
$229$	−214.000			−0.934498			−0.467249	−	0.884126i	$-0.654755\pi$
$229$	−214.000			−0.934498			−0.467249	+	0.884126i	$0.654755\pi$
$230$	−54.0833	−	112.583i	−0.235145	−	0.489493i
$231$		0			0
$232$	−91.0000	+	393.435i	−0.392241	+	1.69584i
$233$	310.077			1.33080			0.665402	−	0.746485i	$-0.268260\pi$
$233$	310.077			1.33080			0.665402	+	0.746485i	$0.268260\pi$
$234$		0			0
$235$			12.4900i			0.0531489i
$236$	237.966	+	190.526i	1.00833	+	0.807312i
$237$		0			0
$238$	78.0000	+	162.370i	0.327731	+	0.682227i
$239$		−	412.228i		−	1.72480i	−0.506224	−	0.862402i	$-0.668959\pi$
$239$		−	412.228i		−	1.72480i	0.506224	−	0.862402i	$-0.331041\pi$
$240$		0			0
$241$	206.000			0.854772			0.427386	−	0.904069i	$-0.359435\pi$
$241$	206.000			0.854772			0.427386	+	0.904069i	$0.359435\pi$
$242$	46.8722	−	22.5167i	0.193687	−	0.0930441i
$243$		0			0
$244$	20.0000	−	24.9800i	0.0819672	−	0.102377i
$245$	−36.0555			−0.147165
$246$		0			0
$247$		−	599.520i		−	2.42721i
$248$	48.6749	+	11.2583i	0.196270	+	0.0453965i
$249$		0			0
$250$	−240.500	+	115.532i	−0.962000	+	0.462130i
$251$			83.1384i			0.331229i	0.986191	+	0.165614i	$0.0529607\pi$
$251$			83.1384i			0.331229i	−0.986191	+	0.165614i	$0.947039\pi$
$252$		0			0
$253$	210.000			0.830040
$254$	−16.2250	−	33.7750i	−0.0638779	−	0.132972i
$255$		0			0
$256$	−231.500	+	109.287i	−0.904297	+	0.426904i
$257$	28.8444			0.112235			0.0561175	−	0.998424i	$-0.482128\pi$
$257$	28.8444			0.112235			0.0561175	+	0.998424i	$0.482128\pi$
$258$		0			0
$259$			162.370i			0.626911i
$260$	144.222	−	180.133i	0.554700	−	0.692820i
$261$		0			0
$262$	37.5000	+	78.0625i	0.143130	+	0.297948i
$263$		−	45.0333i		−	0.171229i	−0.996328	−	0.0856147i	$-0.972715\pi$
$263$		−	45.0333i		−	0.171229i	0.996328	−	0.0856147i	$-0.0272854\pi$
$264$		0			0
$265$	247.000			0.932075
$266$	421.849	−	202.650i	1.58590	−	0.761842i
$267$		0			0
$268$	−195.000	−	156.125i	−0.727612	−	0.582556i
$269$	50.4777			0.187650			0.0938248	−	0.995589i	$-0.470091\pi$
$269$	50.4777			0.187650			0.0938248	+	0.995589i	$0.470091\pi$
$270$		0			0
$271$		−	18.7350i		−	0.0691328i	−0.999402	−	0.0345664i	$-0.988995\pi$
$271$		−	18.7350i		−	0.0691328i	0.999402	−	0.0345664i	$-0.0110050\pi$
$272$	50.4777	+	225.167i	0.185580	+	0.827818i
$273$		0			0
$274$	143.000	−	68.6950i	0.521898	−	0.250712i
$275$		−	145.492i		−	0.529063i
$276$		0			0
$277$	−160.000			−0.577617			−0.288809	−	0.957387i	$-0.593259\pi$
$277$	−160.000			−0.577617			−0.288809	+	0.957387i	$0.593259\pi$
$278$	−108.167	−	225.167i	−0.389088	−	0.809952i
$279$		0			0
$280$	175.500	+	40.5925i	0.626786	+	0.144973i
$281$	504.777			1.79636			0.898180	−	0.439628i	$-0.144890\pi$
$281$	504.777			1.79636			0.898180	+	0.439628i	$0.144890\pi$
$282$		0			0
$283$			12.4900i			0.0441343i	0.999756	+	0.0220671i	$0.00702476\pi$
$283$			12.4900i			0.0441343i	−0.999756	+	0.0220671i	$0.992975\pi$
$284$	−194.700	−	155.885i	−0.685563	−	0.548889i
$285$		0			0
$286$	168.000	+	349.720i	0.587413	+	1.22280i
$287$			45.0333i			0.156911i
$288$		0			0
$289$	−81.0000			−0.280277
$290$	328.105	−	157.617i	1.13140	−	0.543506i
$291$		0			0
$292$	−47.5000	+	59.3275i	−0.162671	+	0.203176i
$293$	−165.855			−0.566059			−0.283030	−	0.959111i	$-0.591339\pi$
$293$	−165.855			−0.566059			−0.283030	+	0.959111i	$0.591339\pi$
$294$		0			0
$295$		−	274.780i		−	0.931457i
$296$	−46.8722	+	202.650i	−0.158352	+	0.684628i
$297$		0			0
$298$	6.50000	−	3.12250i	0.0218121	−	0.0104782i
$299$			277.128i			0.926850i
$300$		0			0
$301$	78.0000			0.259136
$302$	−167.658	−	349.008i	−0.555159	−	1.15566i
$303$		0			0
$304$	585.000	−	131.145i	1.92434	−	0.431398i
$305$	−28.8444			−0.0945718
$306$		0			0
$307$		−	524.580i		−	1.70873i	−0.519674	−	0.854365i	$-0.673947\pi$
$307$		−	524.580i		−	1.70873i	0.519674	−	0.854365i	$-0.326053\pi$
$308$	−189.291	+	236.425i	−0.614583	+	0.767613i
$309$		0			0
$310$	−19.5000	−	40.5925i	−0.0629032	−	0.130944i
$311$			24.2487i			0.0779701i	0.999240	+	0.0389851i	$0.0124125\pi$
$311$			24.2487i			0.0779701i	−0.999240	+	0.0389851i	$0.987588\pi$
$312$		0			0
$313$	233.000			0.744409			0.372204	−	0.928151i	$-0.378602\pi$
$313$	233.000			0.744409			0.372204	+	0.928151i	$0.378602\pi$
$314$	−165.855	+	79.6743i	−0.528202	+	0.253740i
$315$		0			0
$316$	−156.000	−	124.900i	−0.493671	−	0.395253i
$317$	−501.172			−1.58098			−0.790492	−	0.612473i	$-0.790175\pi$
$317$	−501.172			−1.58098			−0.790492	+	0.612473i	$0.790175\pi$
$318$		0			0
$319$			612.010i			1.91853i
$320$	207.319	+	101.325i	0.647872	+	0.316641i
$321$		0			0
$322$	−195.000	+	93.6750i	−0.605590	+	0.290916i
$323$		−	540.400i		−	1.67306i
$324$		0			0
$325$	192.000			0.590769
$326$	−129.800	−	270.200i	−0.398159	−	0.828834i
$327$		0			0
$328$	−13.0000	+	56.2050i	−0.0396341	+	0.171357i
$329$	21.6333			0.0657547
$330$		0			0
$331$			137.390i			0.415075i	0.978227	+	0.207538i	$0.0665450\pi$
$331$			137.390i			0.415075i	−0.978227	+	0.207538i	$0.933455\pi$
$332$	362.358	+	290.119i	1.09144	+	0.873851i
$333$		0			0
$334$	−147.000	−	306.005i	−0.440120	−	0.916182i
$335$			225.167i			0.672139i
$336$		0			0
$337$	50.0000			0.148368			0.0741840	−	0.997245i	$-0.476365\pi$
$337$	50.0000			0.148368			0.0741840	+	0.997245i	$0.476365\pi$
$338$	−156.841	+	75.3442i	−0.464028	+	0.222912i
$339$		0			0
$340$	130.000	−	162.370i	0.382353	−	0.477559i
$341$	75.7166			0.222043
$342$		0			0
$343$			368.455i			1.07421i
$344$	97.3499	+	22.5167i	0.282994	+	0.0654554i
$345$		0			0
$346$	318.500	−	153.002i	0.920520	−	0.442204i
$347$			195.722i			0.564040i	0.959409	+	0.282020i	$0.0910044\pi$
$347$			195.722i			0.564040i	−0.959409	+	0.282020i	$0.908996\pi$
$348$		0			0
$349$	−538.000			−1.54155			−0.770774	−	0.637109i	$-0.780130\pi$
$349$	−538.000			−1.54155			−0.770774	+	0.637109i	$0.780130\pi$
$350$	64.8999	+	135.100i	0.185428	+	0.386000i
$351$		0			0
$352$	−304.500	+	240.432i	−0.865057	+	0.683047i
$353$	223.544			0.633270			0.316635	−	0.948548i	$-0.397447\pi$
$353$	223.544			0.633270			0.316635	+	0.948548i	$0.397447\pi$
$354$		0			0
$355$			224.820i			0.633296i
$356$	−198.305	+	247.683i	−0.557037	+	0.695740i
$357$		0			0
$358$	−229.500	−	477.742i	−0.641061	−	1.33448i
$359$			446.869i			1.24476i	0.782715	+	0.622380i	$0.213834\pi$
$359$			446.869i			1.24476i	−0.782715	+	0.622380i	$0.786166\pi$
$360$		0			0
$361$	−1043.00			−2.88920
$362$	−490.355	+	235.559i	−1.35457	+	0.650715i
$363$		0			0
$364$	−312.000	−	249.800i	−0.857143	−	0.686264i
$365$	68.5055			0.187686
$366$		0			0
$367$			268.535i			0.731703i	0.930673	+	0.365851i	$0.119222\pi$
$367$			268.535i			0.731703i	−0.930673	+	0.365851i	$0.880778\pi$
$368$	−270.416	+	60.6218i	−0.734827	+	0.164733i
$369$		0			0
$370$	169.000	−	81.1850i	0.456757	−	0.219419i
$371$		−	427.817i		−	1.15314i
$372$		0			0
$373$	212.000			0.568365			0.284182	−	0.958770i	$-0.408278\pi$
$373$	212.000			0.568365			0.284182	+	0.958770i	$0.408278\pi$
$374$	151.433	+	315.233i	0.404901	+	0.842870i
$375$		0			0
$376$	27.0000	+	6.24500i	0.0718085	+	0.0166090i
$377$	−807.643			−2.14229
$378$		0			0
$379$			224.820i			0.593192i	0.955003	+	0.296596i	$0.0958515\pi$
$379$			224.820i			0.593192i	−0.955003	+	0.296596i	$0.904148\pi$
$380$	−421.849	−	337.750i	−1.11013	−	0.888816i
$381$		0			0
$382$	228.000	+	474.620i	0.596859	+	1.24246i
$383$			242.487i			0.633126i	0.948572	+	0.316563i	$0.102529\pi$
$383$			242.487i			0.633126i	−0.948572	+	0.316563i	$0.897471\pi$
$384$		0			0
$385$	273.000			0.709091
$386$	337.119	−	161.947i	0.873365	−	0.419551i
$387$		0			0
$388$	297.500	−	371.577i	0.766753	−	0.957674i
$389$	515.594			1.32543			0.662717	−	0.748870i	$-0.269403\pi$
$389$	515.594			1.32543			0.662717	+	0.748870i	$0.269403\pi$
$390$		0			0
$391$			249.800i			0.638874i
$392$	−18.0278	+	77.9423i	−0.0459892	+	0.198832i
$393$		0			0
$394$	−32.5000	+	15.6125i	−0.0824873	+	0.0396256i
$395$			180.133i			0.456034i
$396$		0			0
$397$	80.0000			0.201511			0.100756	−	0.994911i	$-0.467874\pi$
$397$	80.0000			0.201511			0.100756	+	0.994911i	$0.467874\pi$
$398$	−81.1249	−	168.875i	−0.203831	−	0.424309i
$399$		0			0
$400$	42.0000	+	187.350i	0.105000	+	0.468375i
$401$	−620.155			−1.54652			−0.773260	−	0.634089i	$-0.781375\pi$
$401$	−620.155			−1.54652			−0.773260	+	0.634089i	$0.781375\pi$
$402$		0			0
$403$			99.9200i			0.247940i
$404$	153.236	−	191.392i	0.379297	−	0.473742i
$405$		0			0
$406$	−273.000	−	568.295i	−0.672414	−	1.39974i
$407$			315.233i			0.774529i
$408$		0			0
$409$	−349.000			−0.853301			−0.426650	−	0.904417i	$-0.640307\pi$
$409$	−349.000			−0.853301			−0.426650	+	0.904417i	$0.640307\pi$
$410$	46.8722	−	22.5167i	0.114322	−	0.0549187i
$411$		0			0
$412$	390.000	+	312.250i	0.946602	+	0.757888i
$413$	−475.933			−1.15238
$414$		0			0
$415$		−	418.415i		−	1.00823i
$416$	−317.289	−	401.836i	−0.762713	−	0.965951i
$417$		0			0
$418$	819.000	−	393.435i	1.95933	−	0.941232i
$419$		−	297.913i		−	0.711009i	−0.934675	−	0.355504i	$-0.884309\pi$
$419$		−	297.913i		−	0.711009i	0.934675	−	0.355504i	$-0.115691\pi$
$420$		0			0
$421$	−208.000			−0.494062			−0.247031	−	0.969008i	$-0.579455\pi$
$421$	−208.000			−0.494062			−0.247031	+	0.969008i	$0.579455\pi$
$422$	54.0833	+	112.583i	0.128159	+	0.266785i
$423$		0			0
$424$	123.500	−	533.947i	0.291274	−	1.25931i
$425$	173.066			0.407215
$426$		0			0
$427$			49.9600i			0.117002i
$428$	405.625	+	324.760i	0.947721	+	0.758784i
$429$		0			0
$430$	−39.0000	−	81.1850i	−0.0906977	−	0.188802i
$431$		−	550.792i		−	1.27794i	−0.769232	−	0.638970i	$-0.779361\pi$
$431$		−	550.792i		−	1.27794i	0.769232	−	0.638970i	$-0.220639\pi$
$432$		0			0
$433$	125.000			0.288684			0.144342	−	0.989528i	$-0.453894\pi$
$433$	125.000			0.288684			0.144342	+	0.989528i	$0.453894\pi$
$434$	−70.3082	+	33.7750i	−0.162001	+	0.0778226i
$435$		0			0
$436$	−115.000	+	143.635i	−0.263761	+	0.329438i
$437$	648.999			1.48512
$438$		0			0
$439$			568.295i			1.29452i	0.762269	+	0.647261i	$0.224085\pi$
$439$			568.295i			1.29452i	−0.762269	+	0.647261i	$0.775915\pi$
$440$	340.725	+	78.8083i	0.774374	+	0.179110i
$441$		0			0
$442$	−416.000	+	199.840i	−0.941176	+	0.452127i
$443$			381.051i			0.860161i	0.902791	+	0.430080i	$0.141515\pi$
$443$			381.051i			0.860161i	−0.902791	+	0.430080i	$0.858485\pi$
$444$		0			0
$445$	286.000			0.642697
$446$	173.066	+	360.267i	0.388041	+	0.807773i
$447$		0			0
$448$	175.500	−	359.087i	0.391741	−	0.801534i
$449$	483.144			1.07604			0.538022	−	0.842931i	$-0.319172\pi$
$449$	483.144			1.07604			0.538022	+	0.842931i	$0.319172\pi$
$450$		0			0
$451$			87.4300i			0.193858i
$452$	234.361	−	292.717i	0.518497	−	0.647603i
$453$		0			0
$454$	66.0000	+	137.390i	0.145374	+	0.302621i
$455$			360.267i			0.791795i
$456$		0			0
$457$	827.000			1.80963			0.904814	−	0.425807i	$-0.140010\pi$
$457$	827.000			1.80963			0.904814	+	0.425807i	$0.140010\pi$
$458$	385.794	−	185.329i	0.842345	−	0.404649i
$459$		0			0
$460$	195.000	+	156.125i	0.423913	+	0.339402i
$461$	645.394			1.39999			0.699993	−	0.714150i	$-0.253186\pi$
$461$	645.394			1.39999			0.699993	+	0.714150i	$0.253186\pi$
$462$		0			0
$463$			106.165i			0.229298i	0.993406	+	0.114649i	$0.0365743\pi$
$463$			106.165i			0.229298i	−0.993406	+	0.114649i	$0.963426\pi$
$464$	−176.672	−	788.083i	−0.380759	−	1.69845i
$465$		0			0
$466$	−559.000	+	268.535i	−1.19957	+	0.576255i
$467$		−	743.050i		−	1.59111i	−0.605879	−	0.795557i	$-0.707179\pi$
$467$		−	743.050i		−	1.59111i	0.605879	−	0.795557i	$-0.292821\pi$
$468$		0			0
$469$	390.000			0.831557
$470$	−10.8167	−	22.5167i	−0.0230142	−	0.0479078i
$471$		0			0
$472$	−594.000	−	137.390i	−1.25847	−	0.291080i
$473$	151.433			0.320155
$474$		0			0
$475$		−	449.640i		−	0.946610i
$476$	−281.233	−	225.167i	−0.590826	−	0.473039i
$477$		0			0
$478$	357.000	+	743.155i	0.746862	+	1.55472i
$479$		−	336.018i		−	0.701499i	−0.936469	−	0.350749i	$-0.885927\pi$
$479$		−	336.018i		−	0.701499i	0.936469	−	0.350749i	$-0.114073\pi$
$480$		0			0
$481$	−416.000			−0.864865
$482$	−371.372	+	178.401i	−0.770481	+	0.370127i
$483$		0			0
$484$	−65.0000	+	81.1850i	−0.134298	+	0.167738i
$485$	−429.061			−0.884661
$486$		0			0
$487$		−	599.520i		−	1.23105i	−0.788119	−	0.615523i	$-0.788945\pi$
$487$		−	599.520i		−	1.23105i	0.788119	−	0.615523i	$-0.211055\pi$
$488$	−14.4222	+	62.3538i	−0.0295537	+	0.127774i
$489$		0			0
$490$	65.0000	−	31.2250i	0.132653	−	0.0637245i
$491$		−	490.170i		−	0.998310i	−0.866513	−	0.499155i	$-0.833644\pi$
$491$		−	490.170i		−	0.998310i	0.866513	−	0.499155i	$-0.166356\pi$
$492$		0			0
$493$	−728.000			−1.47667
$494$	519.199	+	1080.80i	1.05101	+	2.18785i
$495$		0			0
$496$	−97.5000	+	21.8575i	−0.196573	+	0.0440675i
$497$	389.400			0.783500
$498$		0			0
$499$		−	661.970i		−	1.32659i	−0.748357	−	0.663296i	$-0.769157\pi$
$499$		−	661.970i		−	1.32659i	0.748357	−	0.663296i	$-0.230843\pi$
$500$	333.513	−	416.558i	0.667027	−	0.833116i
$501$		0			0
$502$	−72.0000	−	149.880i	−0.143426	−	0.298566i
$503$			322.161i			0.640480i	0.947336	+	0.320240i	$0.103764\pi$
$503$			322.161i			0.640480i	−0.947336	+	0.320240i	$0.896236\pi$
$504$		0			0
$505$	−221.000			−0.437624
$506$	−378.583	+	181.865i	−0.748188	+	0.359418i
$507$		0			0
$508$	58.5000	+	46.8375i	0.115157	+	0.0921998i
$509$	−544.438			−1.06962			−0.534812	−	0.844971i	$-0.679617\pi$
$509$	−544.438			−1.06962			−0.534812	+	0.844971i	$0.679617\pi$
$510$		0			0
$511$		−	118.655i		−	0.232201i
$512$	322.697	−	397.506i	0.630267	−	0.776378i
$513$		0			0
$514$	−52.0000	+	24.9800i	−0.101167	+	0.0485992i
$515$		−	450.333i		−	0.874433i
$516$		0			0
$517$	42.0000			0.0812379
$518$	−140.616	−	292.717i	−0.271460	−	0.565090i
$519$		0			0
$520$	−104.000	+	449.640i	−0.200000	+	0.864692i
$521$	−230.755			−0.442908			−0.221454	−	0.975171i	$-0.571080\pi$
$521$	−230.755			−0.442908			−0.221454	+	0.975171i	$0.571080\pi$
$522$		0			0
$523$			674.460i			1.28960i	0.764352	+	0.644799i	$0.223059\pi$
$523$			674.460i			1.28960i	−0.764352	+	0.644799i	$0.776941\pi$
$524$	−135.208	−	108.253i	−0.258031	−	0.206590i
$525$		0			0
$526$	39.0000	+	81.1850i	0.0741445	+	0.154344i
$527$			90.0666i			0.170904i
$528$		0			0
$529$	229.000			0.432892
$530$	−445.286	+	213.908i	−0.840161	+	0.403601i
$531$		0			0
$532$	−585.000	+	730.665i	−1.09962	+	1.37343i
$533$	−115.378			−0.216468
$534$		0			0
$535$		−	468.375i		−	0.875467i
$536$	486.749	+	112.583i	0.908115	+	0.210043i
$537$		0			0
$538$	−91.0000	+	43.7150i	−0.169145	+	0.0812546i
$539$			121.244i			0.224942i
$540$		0			0
$541$	260.000			0.480591			0.240296	−	0.970700i	$-0.422756\pi$
$541$	260.000			0.480591			0.240296	+	0.970700i	$0.422756\pi$
$542$	16.2250	+	33.7750i	0.0299354	+	0.0623155i
$543$		0			0
$544$	−286.000	−	362.210i	−0.525735	−	0.665827i
$545$	165.855			0.304322
$546$		0			0
$547$		−	874.300i		−	1.59835i	−0.601096	−	0.799177i	$-0.705269\pi$
$547$		−	874.300i		−	1.59835i	0.601096	−	0.799177i	$-0.294731\pi$
$548$	−198.305	+	247.683i	−0.361871	+	0.451977i
$549$		0			0
$550$	126.000	+	262.290i	0.229091	+	0.476891i
$551$			1891.40i			3.43267i
$552$		0			0
$553$	312.000			0.564195
$554$	288.444	−	138.564i	0.520657	−	0.250116i
$555$		0			0
$556$	390.000	+	312.250i	0.701439	+	0.561601i
$557$	472.327			0.847984			0.423992	−	0.905666i	$-0.360628\pi$
$557$	472.327			0.847984			0.423992	+	0.905666i	$0.360628\pi$
$558$		0			0
$559$			199.840i			0.357495i
$560$	−351.541	+	78.8083i	−0.627752	+	0.140729i
$561$		0			0
$562$	−910.000	+	437.150i	−1.61922	+	0.777847i
$563$		−	698.016i		−	1.23982i	−0.784674	−	0.619908i	$-0.787170\pi$
$563$		−	698.016i		−	1.23982i	0.784674	−	0.619908i	$-0.212830\pi$
$564$		0			0
$565$	−338.000			−0.598230
$566$	−10.8167	−	22.5167i	−0.0191107	−	0.0397821i
$567$		0			0
$568$	486.000	+	112.410i	0.855634	+	0.197905i
$569$	−274.022			−0.481585			−0.240793	−	0.970577i	$-0.577407\pi$
$569$	−274.022			−0.481585			−0.240793	+	0.970577i	$0.577407\pi$
$570$		0			0
$571$		−	249.800i		−	0.437478i	−0.975783	−	0.218739i	$-0.929806\pi$
$571$		−	249.800i		−	0.437478i	0.975783	−	0.218739i	$-0.0701943\pi$
$572$	−605.733	−	484.974i	−1.05897	−	0.847857i
$573$		0			0
$574$	−39.0000	−	81.1850i	−0.0679443	−	0.141437i
$575$			207.846i			0.361471i
$576$		0			0
$577$	494.000			0.856153			0.428076	−	0.903743i	$-0.359191\pi$
$577$	494.000			0.856153			0.428076	+	0.903743i	$0.359191\pi$
$578$	146.025	−	70.1481i	0.252638	−	0.121363i
$579$		0			0
$580$	−455.000	+	568.295i	−0.784483	+	0.979819i
$581$	−724.716			−1.24736
$582$		0			0
$583$		−	830.585i		−	1.42467i
$584$	34.2527	−	148.090i	0.0586519	−	0.253579i
$585$		0			0
$586$	299.000	−	143.635i	0.510239	−	0.245111i
$587$		−	237.291i		−	0.404244i	−0.979360	−	0.202122i	$-0.935216\pi$
$587$		−	237.291i		−	0.404244i	0.979360	−	0.202122i	$-0.0647837\pi$
$588$		0			0
$589$	234.000			0.397284
$590$	237.966	+	495.367i	0.403333	+	0.839604i
$591$		0			0
$592$	−91.0000	−	405.925i	−0.153716	−	0.685684i
$593$	−468.722			−0.790424			−0.395212	−	0.918590i	$-0.629329\pi$
$593$	−468.722			−0.790424			−0.395212	+	0.918590i	$0.629329\pi$
$594$		0			0
$595$			324.740i			0.545781i
$596$	−9.01388	+	11.2583i	−0.0151240	+	0.0188898i
$597$		0			0
$598$	−240.000	−	499.600i	−0.401338	−	0.835451i
$599$			564.649i			0.942652i	0.881959	+	0.471326i	$0.156224\pi$
$599$			564.649i			0.942652i	−0.881959	+	0.471326i	$0.843776\pi$
$600$		0			0
$601$	647.000			1.07654			0.538270	−	0.842773i	$-0.319078\pi$
$601$	647.000			1.07654			0.538270	+	0.842773i	$0.319078\pi$
$602$	−140.616	+	67.5500i	−0.233582	+	0.112209i
$603$		0			0
$604$	604.500	+	483.987i	1.00083	+	0.801304i
$605$	93.7443			0.154949
$606$		0			0
$607$		−	399.680i		−	0.658451i	−0.944251	−	0.329226i	$-0.893212\pi$
$607$		−	399.680i		−	0.658451i	0.944251	−	0.329226i	$-0.106788\pi$
$608$	−941.049	+	743.050i	−1.54778	+	1.22212i
$609$		0			0
$610$	52.0000	−	24.9800i	0.0852459	−	0.0409508i
$611$			55.4256i			0.0907130i
$612$		0			0
$613$	866.000			1.41272			0.706362	−	0.707851i	$-0.250335\pi$
$613$	866.000			1.41272			0.706362	+	0.707851i	$0.250335\pi$
$614$	454.299	+	945.700i	0.739901	+	1.54023i
$615$		0			0
$616$	136.500	−	590.152i	0.221591	−	0.958039i
$617$	223.544			0.362308			0.181154	−	0.983455i	$-0.442017\pi$
$617$	223.544			0.362308			0.181154	+	0.983455i	$0.442017\pi$
$618$		0			0
$619$			999.200i			1.61422i	0.590404	+	0.807108i	$0.298968\pi$
$619$			999.200i			1.61422i	−0.590404	+	0.807108i	$0.701032\pi$
$620$	70.3082	+	56.2917i	0.113400	+	0.0907930i
$621$		0			0
$622$	−21.0000	−	43.7150i	−0.0337621	−	0.0702813i
$623$		−	495.367i		−	0.795131i
$624$		0			0
$625$	−181.000			−0.289600
$626$	−420.047	+	201.784i	−0.671001	+	0.322339i
$627$		0			0
$628$	230.000	−	287.270i	0.366242	−	0.457436i
$629$	−374.977			−0.596148
$630$		0			0
$631$		−	93.6750i		−	0.148455i	−0.997241	−	0.0742274i	$-0.976351\pi$
$631$		−	93.6750i		−	0.148455i	0.997241	−	0.0742274i	$-0.0236491\pi$
$632$	389.400	+	90.0666i	0.616139	+	0.142511i
$633$		0			0
$634$	903.500	−	434.027i	1.42508	−	0.684586i
$635$		−	67.5500i		−	0.106378i
$636$		0			0
$637$	−160.000			−0.251177
$638$	−530.016	−	1103.32i	−0.830746	−	1.72934i
$639$		0			0
$640$	−461.500	−	3.12250i	−0.721094	−	0.00487890i
$641$	−858.121			−1.33872			−0.669361	−	0.742937i	$-0.733432\pi$
$641$	−858.121			−1.33872			−0.669361	+	0.742937i	$0.733432\pi$
$642$		0			0
$643$		−	24.9800i		−	0.0388491i	−0.999811	−	0.0194246i	$-0.993817\pi$
$643$		−	24.9800i		−	0.0388491i	0.999811	−	0.0194246i	$-0.00618342\pi$
$644$	270.416	−	337.750i	0.419901	−	0.524456i
$645$		0			0
$646$	468.000	+	974.220i	0.724458	+	1.50808i
$647$			540.400i			0.835239i	0.908622	+	0.417620i	$0.137136\pi$
$647$			540.400i			0.835239i	−0.908622	+	0.417620i	$0.862864\pi$
$648$		0			0
$649$	−924.000			−1.42373
$650$	−346.133	+	166.277i	−0.532512	+	0.255811i
$651$		0			0
$652$	468.000	+	374.700i	0.717791	+	0.574693i
$653$	429.061			0.657061			0.328530	−	0.944493i	$-0.393447\pi$
$653$	429.061			0.657061			0.328530	+	0.944493i	$0.393447\pi$
$654$		0			0
$655$			156.125i			0.238359i
$656$	−25.2389	−	112.583i	−0.0384739	−	0.171621i
$657$		0			0
$658$	−39.0000	+	18.7350i	−0.0592705	+	0.0284726i
$659$		−	975.145i		−	1.47973i	−0.672753	−	0.739867i	$-0.734888\pi$
$659$		−	975.145i		−	1.47973i	0.672753	−	0.739867i	$-0.265112\pi$
$660$		0			0
$661$	−970.000			−1.46747			−0.733737	−	0.679434i	$-0.762225\pi$
$661$	−970.000			−1.46747			−0.733737	+	0.679434i	$0.762225\pi$
$662$	−118.983	−	247.683i	−0.179733	−	0.374144i
$663$		0			0
$664$	−904.500	−	209.207i	−1.36220	−	0.315071i
$665$	843.699			1.26872
$666$		0			0
$667$		−	874.300i		−	1.31079i
$668$	530.016	+	424.352i	0.793437	+	0.635258i
$669$		0			0
$670$	−195.000	−	405.925i	−0.291045	−	0.605858i
$671$			96.9948i			0.144553i
$672$		0			0
$673$	−595.000			−0.884101			−0.442051	−	0.896990i	$-0.645749\pi$
$673$	−595.000			−0.884101			−0.442051	+	0.896990i	$0.645749\pi$
$674$	−90.1388	+	43.3013i	−0.133737	+	0.0642452i
$675$		0			0
$676$	217.500	−	271.657i	0.321746	−	0.401860i
$677$	−425.455			−0.628442			−0.314221	−	0.949350i	$-0.601743\pi$
$677$	−425.455			−0.628442			−0.314221	+	0.949350i	$0.601743\pi$
$678$		0			0
$679$			743.155i			1.09448i
$680$	−93.7443	+	405.300i	−0.137859	+	0.596029i
$681$		0			0
$682$	−136.500	+	65.5725i	−0.200147	+	0.0961473i
$683$			62.3538i			0.0912940i	0.998958	+	0.0456470i	$0.0145349\pi$
$683$			62.3538i			0.0912940i	−0.998958	+	0.0456470i	$0.985465\pi$
$684$		0			0
$685$	286.000			0.417518
$686$	−319.091	−	664.241i	−0.465148	−	0.968282i
$687$		0			0
$688$	−195.000	+	43.7150i	−0.283430	+	0.0635392i
$689$	1096.09			1.59084
$690$		0			0
$691$			1074.14i			1.55447i	0.629210	+	0.777236i	$0.283379\pi$
$691$			1074.14i			1.55447i	−0.629210	+	0.777236i	$0.716621\pi$
$692$	−441.680	+	551.658i	−0.638266	+	0.797194i
$693$		0			0
$694$	−169.500	−	352.842i	−0.244236	−	0.508418i
$695$		−	450.333i		−	0.647961i
$696$		0			0
$697$	−104.000			−0.149211
$698$	969.893	−	465.922i	1.38953	−	0.667510i
$699$		0			0
$700$	−234.000	−	187.350i	−0.334286	−	0.267643i
$701$	926.627			1.32186			0.660932	−	0.750446i	$-0.270161\pi$
$701$	926.627			1.32186			0.660932	+	0.750446i	$0.270161\pi$
$702$		0			0
$703$			974.220i			1.38580i
$704$	340.725	−	697.150i	0.483984	−	0.990271i
$705$		0			0
$706$	−403.000	+	193.595i	−0.570822	+	0.274214i
$707$			382.783i			0.541419i
$708$		0			0
$709$	−28.0000			−0.0394922			−0.0197461	−	0.999805i	$-0.506286\pi$
$709$	−28.0000			−0.0394922			−0.0197461	+	0.999805i	$0.506286\pi$
$710$	−194.700	−	405.300i	−0.274225	−	0.570845i
$711$		0			0
$712$	143.000	−	618.255i	0.200843	−	0.868335i
$713$	−108.167			−0.151706
$714$		0			0
$715$			699.440i			0.978237i
$716$	827.474	+	662.509i	1.15569	+	0.925293i
$717$		0			0
$718$	−387.000	−	805.605i	−0.538997	−	1.12201i
$719$		−	270.200i		−	0.375800i	−0.982188	−	0.187900i	$-0.939832\pi$
$719$		−	270.200i		−	0.375800i	0.982188	−	0.187900i	$-0.0601680\pi$
$720$		0			0
$721$	−780.000			−1.08183
$722$	1880.29	−	903.264i	2.60429	−	1.25106i
$723$		0			0
$724$	680.000	−	849.320i	0.939227	−	1.17309i
$725$	−605.733			−0.835493
$726$		0			0
$727$			6.24500i			0.00859009i	0.999991	+	0.00429505i	$0.00136716\pi$
$727$			6.24500i			0.00859009i	−0.999991	+	0.00429505i	$0.998633\pi$
$728$	778.799	+	180.133i	1.06978	+	0.247436i
$729$		0			0
$730$	−123.500	+	59.3275i	−0.169178	+	0.0812705i
$731$			180.133i			0.246420i
$732$		0			0
$733$	338.000			0.461119			0.230559	−	0.973058i	$-0.425944\pi$
$733$	338.000			0.461119			0.230559	+	0.973058i	$0.425944\pi$
$734$	−232.558	−	484.108i	−0.316837	−	0.659548i
$735$		0			0
$736$	435.000	−	343.475i	0.591033	−	0.466678i
$737$	757.166			1.02736
$738$		0			0
$739$			824.340i			1.11548i	0.830016	+	0.557740i	$0.188331\pi$
$739$			824.340i			1.11548i	−0.830016	+	0.557740i	$0.811669\pi$
$740$	−234.361	+	292.717i	−0.316704	+	0.395563i
$741$		0			0
$742$	370.500	+	771.257i	0.499326	+	1.03943i
$743$			595.825i			0.801919i	0.916096	+	0.400959i	$0.131323\pi$
$743$			595.825i			0.801919i	−0.916096	+	0.400959i	$0.868677\pi$
$744$		0			0
$745$	13.0000			0.0174497
$746$	−382.188	+	183.597i	−0.512317	+	0.246109i
$747$		0			0
$748$	−546.000	−	437.150i	−0.729947	−	0.584425i
$749$	−811.249			−1.08311
$750$		0			0
$751$		−	530.825i		−	0.706824i	−0.935468	−	0.353412i	$-0.885021\pi$
$751$		−	530.825i		−	0.706824i	0.935468	−	0.353412i	$-0.114979\pi$
$752$	−54.0833	+	12.1244i	−0.0719192	+	0.0161228i
$753$		0			0
$754$	1456.00	−	699.440i	1.93103	−	0.927639i
$755$		−	698.016i		−	0.924525i
$756$		0			0
$757$	−250.000			−0.330251			−0.165125	−	0.986273i	$-0.552803\pi$
$757$	−250.000			−0.330251			−0.165125	+	0.986273i	$0.552803\pi$
$758$	−194.700	−	405.300i	−0.256860	−	0.534696i
$759$		0			0
$760$	1053.00	+	243.555i	1.38553	+	0.320467i
$761$	−490.355			−0.644356			−0.322178	−	0.946679i	$-0.604415\pi$
$761$	−490.355			−0.644356			−0.322178	+	0.946679i	$0.604415\pi$
$762$		0			0
$763$		−	287.270i		−	0.376501i
$764$	−822.066	−	658.179i	−1.07600	−	0.861491i
$765$		0			0
$766$	−210.000	−	437.150i	−0.274151	−	0.570692i
$767$		−	1219.36i		−	1.58978i
$768$		0			0
$769$	65.0000			0.0845254			0.0422627	−	0.999107i	$-0.486543\pi$
$769$	65.0000			0.0845254			0.0422627	+	0.999107i	$0.486543\pi$
$770$	−492.158	+	236.425i	−0.639166	+	0.307045i
$771$		0			0
$772$	−467.500	+	583.907i	−0.605570	+	0.756357i
$773$	829.277			1.07280			0.536402	−	0.843963i	$-0.319783\pi$
$773$	829.277			1.07280			0.536402	+	0.843963i	$0.319783\pi$
$774$		0			0
$775$			74.9400i			0.0966967i
$776$	−214.530	+	927.513i	−0.276457	+	1.19525i
$777$		0			0
$778$	−929.500	+	446.517i	−1.19473	+	0.573930i
$779$			270.200i			0.346855i
$780$		0			0
$781$	756.000			0.967990
$782$	−216.333	−	450.333i	−0.276641	−	0.575874i
$783$		0			0
$784$	−35.0000	−	156.125i	−0.0446429	−	0.199139i
$785$	−331.711			−0.422561
$786$		0			0
$787$			799.360i			1.01570i	0.861444	+	0.507852i	$0.169560\pi$
$787$			799.360i			1.01570i	−0.861444	+	0.507852i	$0.830440\pi$
$788$	45.0694	−	56.2917i	0.0571947	−	0.0714361i
$789$		0			0
$790$	−156.000	−	324.740i	−0.197468	−	0.411063i
$791$			585.433i			0.740118i
$792$		0			0
$793$	−128.000			−0.161412
$794$	−144.222	+	69.2820i	−0.181640	+	0.0872570i
$795$		0			0
$796$	292.500	+	234.187i	0.367462	+	0.294205i
$797$	775.194			0.972639			0.486320	−	0.873781i	$-0.338339\pi$
$797$	775.194			0.972639			0.486320	+	0.873781i	$0.338339\pi$
$798$		0			0
$799$			49.9600i			0.0625281i
$800$	−237.966	−	301.377i	−0.297458	−	0.376721i
$801$		0			0
$802$	1118.00	−	537.070i	1.39401	−	0.669663i
$803$		−	230.363i		−	0.286878i
$804$		0			0
$805$	−390.000			−0.484472
$806$	−86.5332	−	180.133i	−0.107361	−	0.223490i
$807$		0			0
$808$	−110.500	+	477.742i	−0.136757	+	0.591265i
$809$	−209.122			−0.258494			−0.129247	−	0.991612i	$-0.541256\pi$
$809$	−209.122			−0.258494			−0.129247	+	0.991612i	$0.541256\pi$
$810$		0			0
$811$		−	1461.33i		−	1.80189i	−0.433937	−	0.900943i	$-0.642876\pi$
$811$		−	1461.33i		−	1.80189i	0.433937	−	0.900943i	$-0.357124\pi$
$812$	984.315	+	788.083i	1.21221	+	0.970546i
$813$		0			0
$814$	−273.000	−	568.295i	−0.335381	−	0.698151i
$815$		−	540.400i		−	0.663067i
$816$		0			0
$817$	468.000			0.572827
$818$	629.169	−	302.243i	0.769155	−	0.369490i
$819$		0			0
$820$	−65.0000	+	81.1850i	−0.0792683	+	0.0990061i
$821$	50.4777			0.0614832			0.0307416	−	0.999527i	$-0.490213\pi$
$821$	50.4777			0.0614832			0.0307416	+	0.999527i	$0.490213\pi$
$822$		0			0
$823$			1342.67i			1.63144i	0.578447	+	0.815720i	$0.303659\pi$
$823$			1342.67i			1.63144i	−0.578447	+	0.815720i	$0.696341\pi$
$824$	−973.499	−	225.167i	−1.18143	−	0.273260i
$825$		0			0
$826$	858.000	−	412.170i	1.03874	−	0.498995i
$827$			581.969i			0.703711i	0.936054	+	0.351856i	$0.114449\pi$
$827$			581.969i			0.703711i	−0.936054	+	0.351856i	$0.885551\pi$
$828$		0			0
$829$	−1186.00			−1.43064			−0.715320	−	0.698797i	$-0.753719\pi$
$829$	−1186.00			−1.43064			−0.715320	+	0.698797i	$0.753719\pi$
$830$	362.358	+	754.308i	0.436576	+	0.908805i
$831$		0			0
$832$	920.000	+	449.640i	1.10577	+	0.540433i
$833$	−144.222			−0.173136
$834$		0			0
$835$		−	612.010i		−	0.732946i
$836$	−1135.75	+	1418.55i	−1.35855	+	1.69683i
$837$		0			0
$838$	258.000	+	537.070i	0.307876	+	0.640895i
$839$			838.313i			0.999181i	0.866262	+	0.499590i	$0.166516\pi$
$839$			838.313i			0.999181i	−0.866262	+	0.499590i	$0.833484\pi$
$840$		0			0
$841$	1707.00			2.02973
$842$	374.977	−	180.133i	0.445341	−	0.213935i
$843$		0			0
$844$	−195.000	−	156.125i	−0.231043	−	0.184982i
$845$	−313.683			−0.371222
$846$		0			0
$847$		−	162.370i		−	0.191700i
$848$	239.769	+	1069.54i	0.282747	+	1.26125i
$849$		0			0
$850$	−312.000	+	149.880i	−0.367059	+	0.176329i
$851$		−	450.333i		−	0.529181i
$852$		0			0
$853$	−1294.00			−1.51700			−0.758499	−	0.651674i	$-0.774067\pi$
$853$	−1294.00			−1.51700			−0.758499	+	0.651674i	$0.774067\pi$
$854$	−43.2666	−	90.0666i	−0.0506635	−	0.105464i
$855$		0			0
$856$	−1012.50	−	234.187i	−1.18283	−	0.273583i
$857$	−1312.42			−1.53141			−0.765706	−	0.643190i	$-0.777610\pi$
$857$	−1312.42			−1.53141			−0.765706	+	0.643190i	$0.777610\pi$
$858$		0			0
$859$		−	399.680i		−	0.465285i	−0.972562	−	0.232643i	$-0.925263\pi$
$859$		−	399.680i		−	0.465285i	0.972562	−	0.232643i	$-0.0747372\pi$
$860$	140.616	+	112.583i	0.163508	+	0.130911i
$861$		0			0
$862$	477.000	+	992.955i	0.553364	+	1.15192i
$863$			852.169i			0.987450i	0.869618	+	0.493725i	$0.164365\pi$
$863$			852.169i			0.987450i	−0.869618	+	0.493725i	$0.835635\pi$
$864$		0			0
$865$	637.000			0.736416
$866$	−225.347	+	108.253i	−0.260216	+	0.125004i
$867$		0			0
$868$	97.5000	−	121.777i	0.112327	−	0.140297i
$869$	605.733			0.697046
$870$		0			0
$871$			999.200i			1.14719i
$872$	82.9277	−	358.535i	0.0951005	−	0.411163i
$873$		0			0
$874$	−1170.00	+	562.050i	−1.33867	+	0.643078i
$875$			833.116i			0.952133i
$876$		0			0
$877$	1118.00			1.27480			0.637400	−	0.770533i	$-0.280010\pi$
$877$	1118.00			1.27480			0.637400	+	0.770533i	$0.280010\pi$
$878$	−492.158	−	1024.51i	−0.560544	−	1.16687i
$879$		0			0
$880$	−682.500	+	153.002i	−0.775568	+	0.173866i
$881$	−749.955			−0.851254			−0.425627	−	0.904899i	$-0.639946\pi$
$881$	−749.955			−0.851254			−0.425627	+	0.904899i	$0.639946\pi$
$882$		0			0
$883$		−	1311.45i		−	1.48522i	−0.669724	−	0.742610i	$-0.733588\pi$
$883$		−	1311.45i		−	1.48522i	0.669724	−	0.742610i	$-0.266412\pi$
$884$	576.888	−	720.533i	0.652588	−	0.815083i
$885$		0			0
$886$	−330.000	−	686.950i	−0.372460	−	0.775338i
$887$		−	1108.51i		−	1.24973i	−0.780732	−	0.624866i	$-0.785154\pi$
$887$		−	1108.51i		−	1.24973i	0.780732	−	0.624866i	$-0.214846\pi$
$888$		0			0
$889$	−117.000			−0.131609
$890$	−515.594	+	247.683i	−0.579319	+	0.278296i
$891$		0			0
$892$	−624.000	−	499.600i	−0.699552	−	0.560090i
$893$	129.800			0.145353
$894$		0			0
$895$		−	955.485i		−	1.06758i
$896$	−5.40833	+	799.341i	−0.00603608	+	0.892122i
$897$		0			0
$898$	−871.000	+	418.415i	−0.969933	+	0.465941i
$899$		−	315.233i		−	0.350649i
$900$		0			0
$901$	988.000			1.09656
$902$	−75.7166	−	157.617i	−0.0839430	−	0.174741i
$903$		0			0
$904$	−169.000	+	730.665i	−0.186947	+	0.808257i
$905$	−980.710			−1.08366
$906$		0			0
$907$		−	612.010i		−	0.674763i	−0.941368	−	0.337381i	$-0.890459\pi$
$907$		−	612.010i		−	0.674763i	0.941368	−	0.337381i	$-0.109541\pi$
$908$	−237.966	−	190.526i	−0.262078	−	0.209830i
$909$		0			0
$910$	−312.000	−	649.480i	−0.342857	−	0.713714i
$911$			786.351i			0.863174i	0.902071	+	0.431587i	$0.142046\pi$
$911$			786.351i			0.863174i	−0.902071	+	0.431587i	$0.857954\pi$
$912$		0			0
$913$	−1407.00			−1.54107
$914$	−1490.90	+	716.203i	−1.63118	+	0.783592i
$915$		0			0
$916$	−535.000	+	668.215i	−0.584061	+	0.729492i
$917$	270.416			0.294892
$918$		0			0
$919$		−	880.545i		−	0.958155i	−0.877773	−	0.479078i	$-0.840971\pi$
$919$		−	880.545i		−	0.958155i	0.877773	−	0.479078i	$-0.159029\pi$
$920$	−486.749	−	112.583i	−0.529075	−	0.122373i
$921$		0			0
$922$	−1163.50	+	558.927i	−1.26193	+	0.606212i
$923$			997.661i			1.08089i
$924$		0			0
$925$	−312.000			−0.337297
$926$	−91.9416	−	191.392i	−0.0992889	−	0.206686i
$927$		0			0
$928$	1001.00	+	1267.73i	1.07866	+	1.36609i
$929$	245.177			0.263915			0.131958	−	0.991255i	$-0.457874\pi$
$929$	245.177			0.263915			0.131958	+	0.991255i	$0.457874\pi$
$930$		0			0
$931$			374.700i			0.402470i
$932$	775.194	−	968.216i	0.831753	−	1.03886i
$933$		0			0
$934$	643.500	+	1339.55i	0.688972	+	1.43421i
$935$			630.466i			0.674296i
$936$		0			0
$937$	−649.000			−0.692636			−0.346318	−	0.938117i	$-0.612568\pi$
$937$	−649.000			−0.692636			−0.346318	+	0.938117i	$0.612568\pi$
$938$	−703.082	+	337.750i	−0.749555	+	0.360075i
$939$		0			0
$940$	39.0000	+	31.2250i	0.0414894	+	0.0332181i
$941$	−1561.20			−1.65909			−0.829545	−	0.558440i	$-0.811400\pi$
$941$	−1561.20			−1.65909			−0.829545	+	0.558440i	$0.811400\pi$
$942$		0			0
$943$		−	124.900i		−	0.132450i
$944$	1189.83	−	266.736i	1.26042	−	0.282559i
$945$		0			0
$946$	−273.000	+	131.145i	−0.288584	+	0.138631i
$947$		−	102.191i		−	0.107910i	−0.998543	−	0.0539551i	$-0.982817\pi$
$947$		−	102.191i		−	0.107910i	0.998543	−	0.0539551i	$-0.0171828\pi$
$948$		0			0
$949$	304.000			0.320337
$950$	389.400	+	810.600i	0.409894	+	0.853263i
$951$		0			0
$952$	702.000	+	162.370i	0.737395	+	0.170557i
$953$	504.777			0.529672			0.264836	−	0.964294i	$-0.414682\pi$
$953$	504.777			0.529672			0.264836	+	0.964294i	$0.414682\pi$
$954$		0			0
$955$			949.240i			0.993968i
$956$	−1287.18	−	1030.57i	−1.34642	−	1.07800i
$957$		0			0
$958$	291.000	+	605.765i	0.303758	+	0.632322i
$959$		−	495.367i		−	0.516545i
$960$		0			0
$961$	922.000			0.959417
$962$	749.955	−	360.267i	0.779579	−	0.374497i
$963$		0			0
$964$	515.000	−	643.235i	0.534232	−	0.667256i
$965$	674.238			0.698692
$966$		0			0
$967$		−	942.995i		−	0.975175i	−0.873074	−	0.487588i	$-0.837877\pi$
$967$		−	942.995i		−	0.975175i	0.873074	−	0.487588i	$-0.162123\pi$
$968$	46.8722	−	202.650i	0.0484217	−	0.209349i
$969$		0			0
$970$	773.500	−	371.577i	0.797423	−	0.383069i
$971$			524.811i			0.540485i	0.962792	+	0.270243i	$0.0871040\pi$
$971$			524.811i			0.540485i	−0.962792	+	0.270243i	$0.912896\pi$
$972$		0			0
$973$	−780.000			−0.801644
$974$	519.199	+	1080.80i	0.533059	+	1.10965i
$975$		0			0
$976$	−28.0000	−	124.900i	−0.0286885	−	0.127971i
$977$	1305.21			1.33594			0.667968	−	0.744190i	$-0.267164\pi$
$977$	1305.21			1.33594			0.667968	+	0.744190i	$0.267164\pi$
$978$		0			0
$979$		−	961.730i		−	0.982359i
$980$	−90.1388	+	112.583i	−0.0919783	+	0.114881i
$981$		0			0
$982$	424.500	+	883.667i	0.432281	+	0.899865i
$983$		−	1707.80i		−	1.73734i	−0.495394	−	0.868668i	$-0.664976\pi$
$983$		−	1707.80i		−	1.73734i	0.495394	−	0.868668i	$-0.335024\pi$
$984$		0			0
$985$	−65.0000			−0.0659898
$986$	1312.42	−	630.466i	1.33106	−	0.639418i
$987$		0			0
$988$	−1872.00	−	1498.80i	−1.89474	−	1.51700i
$989$	−216.333			−0.218739
$990$		0			0
$991$		−	318.495i		−	0.321387i	−0.987004	−	0.160694i	$-0.948627\pi$
$991$		−	318.495i		−	0.321387i	0.987004	−	0.160694i	$-0.0513731\pi$
$992$	156.841	−	123.842i	0.158106	−	0.124840i
$993$		0			0
$994$	−702.000	+	337.230i	−0.706237	+	0.339265i
$995$		−	337.750i		−	0.339447i
$996$		0			0
$997$	1304.00			1.30792			0.653962	−	0.756527i	$-0.273106\pi$
$997$	1304.00			1.30792			0.653962	+	0.756527i	$0.273106\pi$
$998$	573.283	+	1193.38i	0.574432	+	1.19577i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.3.d.c.55.2	yes	4
3.2	odd	2	inner	108.3.d.c.55.3	yes	4
4.3	odd	2	inner	108.3.d.c.55.1	✓	4
8.3	odd	2		1728.3.g.i.703.3		4
8.5	even	2		1728.3.g.i.703.4		4
9.2	odd	6		324.3.f.l.271.1		4
9.4	even	3		324.3.f.l.55.2		4
9.5	odd	6		324.3.f.m.55.1		4
9.7	even	3		324.3.f.m.271.2		4
12.11	even	2	inner	108.3.d.c.55.4	yes	4
24.5	odd	2		1728.3.g.i.703.2		4
24.11	even	2		1728.3.g.i.703.1		4
36.7	odd	6		324.3.f.l.271.2		4
36.11	even	6		324.3.f.m.271.1		4
36.23	even	6		324.3.f.l.55.1		4
36.31	odd	6		324.3.f.m.55.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.d.c.55.1	✓	4	4.3	odd	2	inner
108.3.d.c.55.2	yes	4	1.1	even	1	trivial
108.3.d.c.55.3	yes	4	3.2	odd	2	inner
108.3.d.c.55.4	yes	4	12.11	even	2	inner
324.3.f.l.55.1		4	36.23	even	6
324.3.f.l.55.2		4	9.4	even	3
324.3.f.l.271.1		4	9.2	odd	6
324.3.f.l.271.2		4	36.7	odd	6
324.3.f.m.55.1		4	9.5	odd	6
324.3.f.m.55.2		4	36.31	odd	6
324.3.f.m.271.1		4	36.11	even	6
324.3.f.m.271.2		4	9.7	even	3
1728.3.g.i.703.1		4	24.11	even	2
1728.3.g.i.703.2		4	24.5	odd	2
1728.3.g.i.703.3		4	8.3	odd	2
1728.3.g.i.703.4		4	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	108.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.80278 + 0.866025i) q^{2} +(2.50000 - 3.12250i) q^{4} -3.60555 q^{5} +6.24500i q^{7} +(-1.80278 + 7.79423i) q^{8} +O(q^{10})\)	\(q+(-1.80278 + 0.866025i) q^{2} +(2.50000 - 3.12250i) q^{4} -3.60555 q^{5} +6.24500i q^{7} +(-1.80278 + 7.79423i) q^{8} +(6.50000 - 3.12250i) q^{10} +12.1244i q^{11} -16.0000 q^{13} +(-5.40833 - 11.2583i) q^{14} +(-3.50000 - 15.6125i) q^{16} -14.4222 q^{17} +37.4700i q^{19} +(-9.01388 + 11.2583i) q^{20} +(-10.5000 - 21.8575i) q^{22} -17.3205i q^{23} -12.0000 q^{25} +(28.8444 - 13.8564i) q^{26} +(19.5000 + 15.6125i) q^{28} +50.4777 q^{29} -6.24500i q^{31} +(19.8305 + 25.1147i) q^{32} +(26.0000 - 12.4900i) q^{34} -22.5167i q^{35} +26.0000 q^{37} +(-32.4500 - 67.5500i) q^{38} +(6.50000 - 28.1025i) q^{40} +7.21110 q^{41} -12.4900i q^{43} +(37.8583 + 30.3109i) q^{44} +(15.0000 + 31.2250i) q^{46} -3.46410i q^{47} +10.0000 q^{49} +(21.6333 - 10.3923i) q^{50} +(-40.0000 + 49.9600i) q^{52} -68.5055 q^{53} -43.7150i q^{55} +(-48.6749 - 11.2583i) q^{56} +(-91.0000 + 43.7150i) q^{58} +76.2102i q^{59} +8.00000 q^{61} +(5.40833 + 11.2583i) q^{62} +(-57.5000 - 28.1025i) q^{64} +57.6888 q^{65} -62.4500i q^{67} +(-36.0555 + 45.0333i) q^{68} +(19.5000 + 40.5925i) q^{70} -62.3538i q^{71} -19.0000 q^{73} +(-46.8722 + 22.5167i) q^{74} +(117.000 + 93.6750i) q^{76} -75.7166 q^{77} -49.9600i q^{79} +(12.6194 + 56.2917i) q^{80} +(-13.0000 + 6.24500i) q^{82} +116.047i q^{83} +52.0000 q^{85} +(10.8167 + 22.5167i) q^{86} +(-94.5000 - 21.8575i) q^{88} -79.3221 q^{89} -99.9200i q^{91} +(-54.0833 - 43.3013i) q^{92} +(3.00000 + 6.24500i) q^{94} -135.100i q^{95} +119.000 q^{97} +(-18.0278 + 8.66025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 10 q^{4}+O(q^{10}) \) 4 * q + 10 * q^4	\( 4 q + 10 q^{4} + 26 q^{10} - 64 q^{13} - 14 q^{16} - 42 q^{22} - 48 q^{25} + 78 q^{28} + 104 q^{34} + 104 q^{37} + 26 q^{40} + 60 q^{46} + 40 q^{49} - 160 q^{52} - 364 q^{58} + 32 q^{61} - 230 q^{64} + 78 q^{70} - 76 q^{73} + 468 q^{76} - 52 q^{82} + 208 q^{85} - 378 q^{88} + 12 q^{94} + 476 q^{97}+O(q^{100}) \) 4 * q + 10 * q^4 + 26 * q^10 - 64 * q^13 - 14 * q^16 - 42 * q^22 - 48 * q^25 + 78 * q^28 + 104 * q^34 + 104 * q^37 + 26 * q^40 + 60 * q^46 + 40 * q^49 - 160 * q^52 - 364 * q^58 + 32 * q^61 - 230 * q^64 + 78 * q^70 - 76 * q^73 + 468 * q^76 - 52 * q^82 + 208 * q^85 - 378 * q^88 + 12 * q^94 + 476 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more