LMFDB - Embedded newform 126.4.g.c.109.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [126,4,Mod(37,126)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("126.37"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(126, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	126.g (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,-2,0,-4,7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.43424066072$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			109.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	126.109
Dual form			126.4.g.c.37.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(3.50000 + 6.06218i) q^{5} +(-10.0000 - 15.5885i) q^{7} +8.00000 q^{8} +(7.00000 - 12.1244i) q^{10} +(17.5000 - 30.3109i) q^{11} +66.0000 q^{13} +(-17.0000 + 32.9090i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(29.5000 - 51.0955i) q^{17} +(-68.5000 - 118.645i) q^{19} -28.0000 q^{20} -70.0000 q^{22} +(-3.50000 - 6.06218i) q^{23} +(38.0000 - 65.8179i) q^{25} +(-66.0000 - 114.315i) q^{26} +(74.0000 - 3.46410i) q^{28} -106.000 q^{29} +(-37.5000 + 64.9519i) q^{31} +(-16.0000 + 27.7128i) q^{32} -118.000 q^{34} +(59.5000 - 115.181i) q^{35} +(-5.50000 - 9.52628i) q^{37} +(-137.000 + 237.291i) q^{38} +(28.0000 + 48.4974i) q^{40} +498.000 q^{41} +260.000 q^{43} +(70.0000 + 121.244i) q^{44} +(-7.00000 + 12.1244i) q^{46} +(-85.5000 - 148.090i) q^{47} +(-143.000 + 311.769i) q^{49} -152.000 q^{50} +(-132.000 + 228.631i) q^{52} +(-208.500 + 361.133i) q^{53} +245.000 q^{55} +(-80.0000 - 124.708i) q^{56} +(106.000 + 183.597i) q^{58} +(-8.50000 + 14.7224i) q^{59} +(-25.5000 - 44.1673i) q^{61} +150.000 q^{62} +64.0000 q^{64} +(231.000 + 400.104i) q^{65} +(-219.500 + 380.185i) q^{67} +(118.000 + 204.382i) q^{68} +(-259.000 + 12.1244i) q^{70} +784.000 q^{71} +(-147.500 + 255.477i) q^{73} +(-11.0000 + 19.0526i) q^{74} +548.000 q^{76} +(-647.500 + 30.3109i) q^{77} +(247.500 + 428.683i) q^{79} +(56.0000 - 96.9948i) q^{80} +(-498.000 - 862.561i) q^{82} -932.000 q^{83} +413.000 q^{85} +(-260.000 - 450.333i) q^{86} +(140.000 - 242.487i) q^{88} +(-436.500 - 756.040i) q^{89} +(-660.000 - 1028.84i) q^{91} +28.0000 q^{92} +(-171.000 + 296.181i) q^{94} +(479.500 - 830.518i) q^{95} -290.000 q^{97} +(683.000 - 64.0859i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 4 q^{4} + 7 q^{5} - 20 q^{7} + 16 q^{8} + 14 q^{10} + 35 q^{11} + 132 q^{13} - 34 q^{14} - 16 q^{16} + 59 q^{17} - 137 q^{19} - 56 q^{20} - 140 q^{22} - 7 q^{23} + 76 q^{25} - 132 q^{26}+ \cdots + 1366 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 - 4 * q^4 + 7 * q^5 - 20 * q^7 + 16 * q^8 + 14 * q^10 + 35 * q^11 + 132 * q^13 - 34 * q^14 - 16 * q^16 + 59 * q^17 - 137 * q^19 - 56 * q^20 - 140 * q^22 - 7 * q^23 + 76 * q^25 - 132 * q^26 + 148 * q^28 - 212 * q^29 - 75 * q^31 - 32 * q^32 - 236 * q^34 + 119 * q^35 - 11 * q^37 - 274 * q^38 + 56 * q^40 + 996 * q^41 + 520 * q^43 + 140 * q^44 - 14 * q^46 - 171 * q^47 - 286 * q^49 - 304 * q^50 - 264 * q^52 - 417 * q^53 + 490 * q^55 - 160 * q^56 + 212 * q^58 - 17 * q^59 - 51 * q^61 + 300 * q^62 + 128 * q^64 + 462 * q^65 - 439 * q^67 + 236 * q^68 - 518 * q^70 + 1568 * q^71 - 295 * q^73 - 22 * q^74 + 1096 * q^76 - 1295 * q^77 + 495 * q^79 + 112 * q^80 - 996 * q^82 - 1864 * q^83 + 826 * q^85 - 520 * q^86 + 280 * q^88 - 873 * q^89 - 1320 * q^91 + 56 * q^92 - 342 * q^94 + 959 * q^95 - 580 * q^97 + 1366 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	3.50000	+	6.06218i	0.313050	+	0.542218i	0.979021	−	0.203760i	$-0.0653161\pi$
$5$	3.50000	+	6.06218i	0.313050	+	0.542218i	−0.665971	+	0.745977i	$0.731983\pi$
$6$		0			0
$7$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$7$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$8$	8.00000			0.353553
$9$		0			0
$10$	7.00000	−	12.1244i	0.221359	−	0.383406i
$11$	17.5000	−	30.3109i	0.479677	−	0.830825i	−0.520051	−	0.854135i	$-0.674087\pi$
$11$	17.5000	−	30.3109i	0.479677	−	0.830825i	0.999728	+	0.0233099i	$0.00742046\pi$
$12$		0			0
$13$	66.0000			1.40809			0.704043	−	0.710158i	$-0.251376\pi$
$13$	66.0000			1.40809			0.704043	+	0.710158i	$0.251376\pi$
$14$	−17.0000	+	32.9090i	−0.324532	+	0.628235i
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	29.5000	−	51.0955i	0.420871	−	0.728969i	−0.575154	−	0.818045i	$-0.695058\pi$
$17$	29.5000	−	51.0955i	0.420871	−	0.728969i	0.996025	+	0.0890757i	$0.0283913\pi$
$18$		0			0
$19$	−68.5000	−	118.645i	−0.827104	−	1.43259i	−0.900301	−	0.435269i	$-0.856653\pi$
$19$	−68.5000	−	118.645i	−0.827104	−	1.43259i	0.0731965	−	0.997318i	$-0.476680\pi$
$20$	−28.0000			−0.313050
$21$		0			0
$22$	−70.0000			−0.678366
$23$	−3.50000	−	6.06218i	−0.0317305	−	0.0549588i	0.849724	−	0.527228i	$-0.176768\pi$
$23$	−3.50000	−	6.06218i	−0.0317305	−	0.0549588i	−0.881455	+	0.472269i	$0.843435\pi$
$24$		0			0
$25$	38.0000	−	65.8179i	0.304000	−	0.526543i
$26$	−66.0000	−	114.315i	−0.497833	−	0.862273i
$27$		0			0
$28$	74.0000	−	3.46410i	0.499453	−	0.0233805i
$29$	−106.000			−0.678748			−0.339374	−	0.940651i	$-0.610215\pi$
$29$	−106.000			−0.678748			−0.339374	+	0.940651i	$0.610215\pi$
$30$		0			0
$31$	−37.5000	+	64.9519i	−0.217264	+	0.376313i	−0.953971	−	0.299900i	$-0.903047\pi$
$31$	−37.5000	+	64.9519i	−0.217264	+	0.376313i	0.736706	+	0.676213i	$0.236380\pi$
$32$	−16.0000	+	27.7128i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−118.000			−0.595201
$35$	59.5000	−	115.181i	0.287352	−	0.556263i
$36$		0			0
$37$	−5.50000	−	9.52628i	−0.0244377	−	0.0423273i	0.853548	−	0.521014i	$-0.174446\pi$
$37$	−5.50000	−	9.52628i	−0.0244377	−	0.0423273i	−0.877986	+	0.478687i	$0.841113\pi$
$38$	−137.000	+	237.291i	−0.584851	+	1.01299i
$39$		0			0
$40$	28.0000	+	48.4974i	0.110680	+	0.191703i
$41$	498.000			1.89694			0.948470	−	0.316867i	$-0.102631\pi$
$41$	498.000			1.89694			0.948470	+	0.316867i	$0.102631\pi$
$42$		0			0
$43$	260.000			0.922084			0.461042	−	0.887378i	$-0.347476\pi$
$43$	260.000			0.922084			0.461042	+	0.887378i	$0.347476\pi$
$44$	70.0000	+	121.244i	0.239839	+	0.415413i
$45$		0			0
$46$	−7.00000	+	12.1244i	−0.0224368	+	0.0388617i
$47$	−85.5000	−	148.090i	−0.265350	−	0.459600i	0.702305	−	0.711876i	$-0.252154\pi$
$47$	−85.5000	−	148.090i	−0.265350	−	0.459600i	−0.967655	+	0.252276i	$0.918821\pi$
$48$		0			0
$49$	−143.000	+	311.769i	−0.416910	+	0.908948i
$50$	−152.000			−0.429921
$51$		0			0
$52$	−132.000	+	228.631i	−0.352021	+	0.609719i
$53$	−208.500	+	361.133i	−0.540371	+	0.935951i	0.458511	+	0.888689i	$0.348383\pi$
$53$	−208.500	+	361.133i	−0.540371	+	0.935951i	−0.998883	+	0.0472619i	$0.984950\pi$
$54$		0			0
$55$	245.000			0.600651
$56$	−80.0000	−	124.708i	−0.190901	−	0.297585i
$57$		0			0
$58$	106.000	+	183.597i	0.239974	+	0.415647i
$59$	−8.50000	+	14.7224i	−0.0187560	+	0.0324864i	−0.875251	−	0.483669i	$-0.839304\pi$
$59$	−8.50000	+	14.7224i	−0.0187560	+	0.0324864i	0.856495	+	0.516155i	$0.172637\pi$
$60$		0			0
$61$	−25.5000	−	44.1673i	−0.0535236	−	0.0927056i	0.838022	−	0.545636i	$-0.183712\pi$
$61$	−25.5000	−	44.1673i	−0.0535236	−	0.0927056i	−0.891546	+	0.452930i	$0.850379\pi$
$62$	150.000			0.307258
$63$		0			0
$64$	64.0000			0.125000
$65$	231.000	+	400.104i	0.440800	+	0.763489i
$66$		0			0
$67$	−219.500	+	380.185i	−0.400242	+	0.693239i	−0.993755	−	0.111585i	$-0.964407\pi$
$67$	−219.500	+	380.185i	−0.400242	+	0.693239i	0.593513	+	0.804824i	$0.297740\pi$
$68$	118.000	+	204.382i	0.210435	+	0.364485i
$69$		0			0
$70$	−259.000	+	12.1244i	−0.442235	+	0.0207020i
$71$	784.000			1.31047			0.655237	−	0.755423i	$-0.272569\pi$
$71$	784.000			1.31047			0.655237	+	0.755423i	$0.272569\pi$
$72$		0			0
$73$	−147.500	+	255.477i	−0.236487	+	0.409608i	−0.959704	−	0.281013i	$-0.909329\pi$
$73$	−147.500	+	255.477i	−0.236487	+	0.409608i	0.723217	+	0.690621i	$0.242663\pi$
$74$	−11.0000	+	19.0526i	−0.0172801	+	0.0299299i
$75$		0			0
$76$	548.000			0.827104
$77$	−647.500	+	30.3109i	−0.958305	+	0.0448603i
$78$		0			0
$79$	247.500	+	428.683i	0.352480	+	0.610513i	0.986683	−	0.162653i	$-0.0520051\pi$
$79$	247.500	+	428.683i	0.352480	+	0.610513i	−0.634203	+	0.773166i	$0.718672\pi$
$80$	56.0000	−	96.9948i	0.0782624	−	0.135554i
$81$		0			0
$82$	−498.000	−	862.561i	−0.670670	−	1.16163i
$83$	−932.000			−1.23253			−0.616267	−	0.787537i	$-0.711356\pi$
$83$	−932.000			−1.23253			−0.616267	+	0.787537i	$0.711356\pi$
$84$		0			0
$85$	413.000			0.527013
$86$	−260.000	−	450.333i	−0.326006	−	0.564659i
$87$		0			0
$88$	140.000	−	242.487i	0.169591	−	0.293741i
$89$	−436.500	−	756.040i	−0.519875	−	0.900451i	−0.999733	−	0.0231042i	$-0.992645\pi$
$89$	−436.500	−	756.040i	−0.519875	−	0.900451i	0.479858	−	0.877346i	$-0.340688\pi$
$90$		0			0
$91$	−660.000	−	1028.84i	−0.760294	−	1.18518i
$92$	28.0000			0.0317305
$93$		0			0
$94$	−171.000	+	296.181i	−0.187631	+	0.324986i
$95$	479.500	−	830.518i	0.517849	−	0.896941i
$96$		0			0
$97$	−290.000			−0.303557			−0.151779	−	0.988415i	$-0.548500\pi$
$97$	−290.000			−0.303557			−0.151779	+	0.988415i	$0.548500\pi$
$98$	683.000	−	64.0859i	0.704014	−	0.0660577i
$99$		0			0
$100$	152.000	+	263.272i	0.152000	+	0.263272i
$101$	−542.500	+	939.638i	−0.534463	+	0.925717i	0.464726	+	0.885454i	$0.346153\pi$
$101$	−542.500	+	939.638i	−0.534463	+	0.925717i	−0.999189	+	0.0402627i	$0.987181\pi$
$102$		0			0
$103$	−776.500	−	1344.94i	−0.742823	−	1.28661i	−0.951205	−	0.308560i	$-0.900153\pi$
$103$	−776.500	−	1344.94i	−0.742823	−	1.28661i	0.208381	−	0.978048i	$-0.433181\pi$
$104$	528.000			0.497833
$105$		0			0
$106$	834.000			0.764200
$107$	64.5000	+	111.717i	0.0582752	+	0.100936i	0.893691	−	0.448682i	$-0.148107\pi$
$107$	64.5000	+	111.717i	0.0582752	+	0.100936i	−0.835416	+	0.549618i	$0.814773\pi$
$108$		0			0
$109$	482.500	−	835.715i	0.423992	−	0.734376i	−0.572334	−	0.820021i	$-0.693962\pi$
$109$	482.500	−	835.715i	0.423992	−	0.734376i	0.996326	+	0.0856452i	$0.0272952\pi$
$110$	−245.000	−	424.352i	−0.212362	−	0.367822i
$111$		0			0
$112$	−136.000	+	263.272i	−0.114739	+	0.222115i
$113$	50.0000			0.0416248			0.0208124	−	0.999783i	$-0.493375\pi$
$113$	50.0000			0.0416248			0.0208124	+	0.999783i	$0.493375\pi$
$114$		0			0
$115$	24.5000	−	42.4352i	0.0198664	−	0.0344096i
$116$	212.000	−	367.195i	0.169687	−	0.293907i
$117$		0			0
$118$	34.0000			0.0265250
$119$	−1091.50	+	51.0955i	−0.840821	+	0.0393606i
$120$		0			0
$121$	53.0000	+	91.7987i	0.0398197	+	0.0689697i
$122$	−51.0000	+	88.3346i	−0.0378469	+	0.0655528i
$123$		0			0
$124$	−150.000	−	259.808i	−0.108632	−	0.188157i
$125$	1407.00			1.00677
$126$		0			0
$127$	936.000			0.653989			0.326994	−	0.945026i	$-0.393964\pi$
$127$	936.000			0.653989			0.326994	+	0.945026i	$0.393964\pi$
$128$	−64.0000	−	110.851i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	462.000	−	800.207i	0.311693	−	0.539868i
$131$	−377.500	−	653.849i	−0.251773	−	0.436084i	0.712241	−	0.701935i	$-0.247680\pi$
$131$	−377.500	−	653.849i	−0.251773	−	0.436084i	−0.964014	+	0.265851i	$0.914347\pi$
$132$		0			0
$133$	−1164.50	+	2254.26i	−0.759210	+	1.46970i
$134$	878.000			0.566027
$135$		0			0
$136$	236.000	−	408.764i	0.148800	−	0.257730i
$137$	−1178.50	+	2041.22i	−0.734935	+	1.27294i	0.219817	+	0.975541i	$0.429454\pi$
$137$	−1178.50	+	2041.22i	−0.734935	+	1.27294i	−0.954752	+	0.297403i	$0.903879\pi$
$138$		0			0
$139$	28.0000			0.0170858			0.00854291	−	0.999964i	$-0.497281\pi$
$139$	28.0000			0.0170858			0.00854291	+	0.999964i	$0.497281\pi$
$140$	280.000	+	436.477i	0.169031	+	0.263493i
$141$		0			0
$142$	−784.000	−	1357.93i	−0.463323	−	0.802498i
$143$	1155.00	−	2000.52i	0.675426	−	1.16987i
$144$		0			0
$145$	−371.000	−	642.591i	−0.212482	−	0.368029i
$146$	590.000			0.334443
$147$		0			0
$148$	44.0000			0.0244377
$149$	1147.50	+	1987.53i	0.630919	+	1.09278i	0.987364	+	0.158467i	$0.0506551\pi$
$149$	1147.50	+	1987.53i	0.630919	+	1.09278i	−0.356446	+	0.934316i	$0.616012\pi$
$150$		0			0
$151$	554.500	−	960.422i	0.298838	−	0.517603i	−0.677032	−	0.735953i	$-0.736734\pi$
$151$	554.500	−	960.422i	0.298838	−	0.517603i	0.975870	+	0.218350i	$0.0700676\pi$
$152$	−548.000	−	949.164i	−0.292425	−	0.506496i
$153$		0			0
$154$	700.000	+	1091.19i	0.366283	+	0.570979i
$155$	−525.000			−0.272058
$156$		0			0
$157$	−779.500	+	1350.13i	−0.396248	+	0.686321i	−0.993260	−	0.115911i	$-0.963021\pi$
$157$	−779.500	+	1350.13i	−0.396248	+	0.686321i	0.597012	+	0.802232i	$0.296354\pi$
$158$	495.000	−	857.365i	0.249241	−	0.431698i
$159$		0			0
$160$	−224.000			−0.110680
$161$	−59.5000	+	115.181i	−0.0291258	+	0.0563824i
$162$		0			0
$163$	1125.50	+	1949.42i	0.540834	+	0.936752i	0.998856	+	0.0478115i	$0.0152247\pi$
$163$	1125.50	+	1949.42i	0.540834	+	0.936752i	−0.458022	+	0.888941i	$0.651442\pi$
$164$	−996.000	+	1725.12i	−0.474235	+	0.821399i
$165$		0			0
$166$	932.000	+	1614.27i	0.435766	+	0.754770i
$167$	−2788.00			−1.29187			−0.645934	−	0.763393i	$-0.723532\pi$
$167$	−2788.00			−1.29187			−0.645934	+	0.763393i	$0.723532\pi$
$168$		0			0
$169$	2159.00			0.982704
$170$	−413.000	−	715.337i	−0.186327	−	0.322728i
$171$		0			0
$172$	−520.000	+	900.666i	−0.230521	+	0.399274i
$173$	789.500	+	1367.45i	0.346963	+	0.600957i	0.985708	−	0.168461i	$-0.0538797\pi$
$173$	789.500	+	1367.45i	0.346963	+	0.600957i	−0.638746	+	0.769418i	$0.720546\pi$
$174$		0			0
$175$	−1406.00	+	65.8179i	−0.607335	+	0.0284307i
$176$	−560.000			−0.239839
$177$		0			0
$178$	−873.000	+	1512.08i	−0.367607	+	0.636715i
$179$	1225.50	−	2122.63i	0.511722	−	0.886328i	−0.488186	−	0.872740i	$-0.662341\pi$
$179$	1225.50	−	2122.63i	0.511722	−	0.886328i	0.999908	−	0.0135883i	$-0.00432541\pi$
$180$		0			0
$181$	−1170.00			−0.480472			−0.240236	−	0.970715i	$-0.577225\pi$
$181$	−1170.00			−0.480472			−0.240236	+	0.970715i	$0.577225\pi$
$182$	−1122.00	+	2171.99i	−0.456968	+	0.884608i
$183$		0			0
$184$	−28.0000	−	48.4974i	−0.0112184	−	0.0194309i
$185$	38.5000	−	66.6840i	0.0153004	−	0.0265011i
$186$		0			0
$187$	−1032.50	−	1788.34i	−0.403764	−	0.699340i
$188$	684.000			0.265350
$189$		0			0
$190$	−1918.00			−0.732349
$191$	−637.500	−	1104.18i	−0.241507	−	0.418303i	0.719637	−	0.694351i	$-0.244308\pi$
$191$	−637.500	−	1104.18i	−0.241507	−	0.418303i	−0.961144	+	0.276048i	$0.910975\pi$
$192$		0			0
$193$	−17.5000	+	30.3109i	−0.00652683	+	0.0113048i	−0.869270	−	0.494337i	$-0.835411\pi$
$193$	−17.5000	+	30.3109i	−0.00652683	+	0.0113048i	0.862744	+	0.505642i	$0.168744\pi$
$194$	290.000	+	502.295i	0.107324	+	0.185890i
$195$		0			0
$196$	−794.000	−	1118.90i	−0.289359	−	0.407764i
$197$	2734.00			0.988779			0.494389	−	0.869241i	$-0.335392\pi$
$197$	2734.00			0.988779			0.494389	+	0.869241i	$0.335392\pi$
$198$		0			0
$199$	−1121.50	+	1942.49i	−0.399503	+	0.691959i	−0.993665	−	0.112387i	$-0.964151\pi$
$199$	−1121.50	+	1942.49i	−0.399503	+	0.691959i	0.594162	+	0.804345i	$0.297484\pi$
$200$	304.000	−	526.543i	0.107480	−	0.186161i
$201$		0			0
$202$	2170.00			0.755845
$203$	1060.00	+	1652.38i	0.366490	+	0.571301i
$204$		0			0
$205$	1743.00	+	3018.96i	0.593836	+	1.02855i
$206$	−1553.00	+	2689.87i	−0.525256	+	0.909769i
$207$		0			0
$208$	−528.000	−	914.523i	−0.176011	−	0.304859i
$209$	−4795.00			−1.58697
$210$		0			0
$211$	1172.00			0.382388			0.191194	−	0.981552i	$-0.438764\pi$
$211$	1172.00			0.382388			0.191194	+	0.981552i	$0.438764\pi$
$212$	−834.000	−	1444.53i	−0.270186	−	0.467975i
$213$		0			0
$214$	129.000	−	223.435i	0.0412068	−	0.0713723i
$215$	910.000	+	1576.17i	0.288658	+	0.499970i
$216$		0			0
$217$	1387.50	−	64.9519i	0.434054	−	0.0203190i
$218$	−1930.00			−0.599615
$219$		0			0
$220$	−490.000	+	848.705i	−0.150163	+	0.260089i
$221$	1947.00	−	3372.30i	0.592622	−	1.02645i
$222$		0			0
$223$	2024.00			0.607790			0.303895	−	0.952706i	$-0.401713\pi$
$223$	2024.00			0.607790			0.303895	+	0.952706i	$0.401713\pi$
$224$	592.000	−	27.7128i	0.176583	−	0.00826625i
$225$		0			0
$226$	−50.0000	−	86.6025i	−0.0147166	−	0.0254899i
$227$	1285.50	−	2226.55i	0.375866	−	0.651019i	−0.614590	−	0.788847i	$-0.710679\pi$
$227$	1285.50	−	2226.55i	0.375866	−	0.651019i	0.990456	+	0.137827i	$0.0440119\pi$
$228$		0			0
$229$	−447.500	−	775.093i	−0.129134	−	0.223666i	0.794207	−	0.607647i	$-0.207886\pi$
$229$	−447.500	−	775.093i	−0.129134	−	0.223666i	−0.923341	+	0.383980i	$0.874553\pi$
$230$	−98.0000			−0.0280953
$231$		0			0
$232$	−848.000			−0.239974
$233$	893.500	+	1547.59i	0.251224	+	0.435132i	0.963863	−	0.266398i	$-0.0858337\pi$
$233$	893.500	+	1547.59i	0.251224	+	0.435132i	−0.712639	+	0.701531i	$0.752500\pi$
$234$		0			0
$235$	598.500	−	1036.63i	0.166135	−	0.287755i
$236$	−34.0000	−	58.8897i	−0.00937801	−	0.0162432i
$237$		0			0
$238$	1180.00	+	1839.44i	0.321378	+	0.500979i
$239$	5100.00			1.38030			0.690150	−	0.723667i	$-0.257545\pi$
$239$	5100.00			1.38030			0.690150	+	0.723667i	$0.257545\pi$
$240$		0			0
$241$	2088.50	−	3617.39i	0.558225	−	0.966873i	−0.439420	−	0.898282i	$-0.644816\pi$
$241$	2088.50	−	3617.39i	0.558225	−	0.966873i	0.997645	−	0.0685917i	$-0.0218506\pi$
$242$	106.000	−	183.597i	0.0281568	−	0.0487690i
$243$		0			0
$244$	204.000			0.0535236
$245$	−2390.50	+	224.301i	−0.623361	+	0.0584900i
$246$		0			0
$247$	−4521.00	−	7830.60i	−1.16463	−	2.01720i
$248$	−300.000	+	519.615i	−0.0768146	+	0.133047i
$249$		0			0
$250$	−1407.00	−	2437.00i	−0.355946	−	0.616517i
$251$	4680.00			1.17689			0.588444	−	0.808538i	$-0.299741\pi$
$251$	4680.00			1.17689			0.588444	+	0.808538i	$0.299741\pi$
$252$		0			0
$253$	−245.000			−0.0608815
$254$	−936.000	−	1621.20i	−0.231220	−	0.400485i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−874.500	−	1514.68i	−0.212256	−	0.367638i	0.740164	−	0.672426i	$-0.234748\pi$
$257$	−874.500	−	1514.68i	−0.212256	−	0.367638i	−0.952420	+	0.304788i	$0.901414\pi$
$258$		0			0
$259$	−93.5000	+	180.999i	−0.0224317	+	0.0434237i
$260$	−1848.00			−0.440800
$261$		0			0
$262$	−755.000	+	1307.70i	−0.178031	+	0.308358i
$263$	−2236.50	+	3873.73i	−0.524367	+	0.908230i	0.475231	+	0.879861i	$0.342365\pi$
$263$	−2236.50	+	3873.73i	−0.524367	+	0.908230i	−0.999598	+	0.0283689i	$0.990969\pi$
$264$		0			0
$265$	−2919.00			−0.676652
$266$	5069.00	−	237.291i	1.16842	−	0.0546964i
$267$		0			0
$268$	−878.000	−	1520.74i	−0.200121	−	0.346619i
$269$	987.500	−	1710.40i	0.223825	−	0.387676i	−0.732141	−	0.681153i	$-0.761479\pi$
$269$	987.500	−	1710.40i	0.223825	−	0.387676i	0.955966	+	0.293476i	$0.0948122\pi$
$270$		0			0
$271$	4219.50	+	7308.39i	0.945817	+	1.63820i	0.754107	+	0.656751i	$0.228070\pi$
$271$	4219.50	+	7308.39i	0.945817	+	1.63820i	0.191710	+	0.981452i	$0.438597\pi$
$272$	−944.000			−0.210435
$273$		0			0
$274$	4714.00			1.03935
$275$	−1330.00	−	2303.63i	−0.291644	−	0.505142i
$276$		0			0
$277$	−263.500	+	456.395i	−0.0571559	+	0.0989969i	−0.893188	−	0.449684i	$-0.851537\pi$
$277$	−263.500	+	456.395i	−0.0571559	+	0.0989969i	0.836032	+	0.548681i	$0.184870\pi$
$278$	−28.0000	−	48.4974i	−0.00604075	−	0.0104629i
$279$		0			0
$280$	476.000	−	921.451i	0.101594	−	0.196669i
$281$	202.000			0.0428837			0.0214418	−	0.999770i	$-0.493174\pi$
$281$	202.000			0.0428837			0.0214418	+	0.999770i	$0.493174\pi$
$282$		0			0
$283$	3974.50	−	6884.04i	0.834839	−	1.44598i	−0.0593220	−	0.998239i	$-0.518894\pi$
$283$	3974.50	−	6884.04i	0.834839	−	1.44598i	0.894161	−	0.447745i	$-0.147773\pi$
$284$	−1568.00	+	2715.86i	−0.327619	+	0.567452i
$285$		0			0
$286$	−4620.00			−0.955197
$287$	−4980.00	−	7763.05i	−1.02425	−	1.59665i
$288$		0			0
$289$	716.000	+	1240.15i	0.145736	+	0.252422i
$290$	−742.000	+	1285.18i	−0.150247	+	0.260236i
$291$		0			0
$292$	−590.000	−	1021.91i	−0.118244	−	0.204804i
$293$	−318.000			−0.0634053			−0.0317027	−	0.999497i	$-0.510093\pi$
$293$	−318.000			−0.0634053			−0.0317027	+	0.999497i	$0.510093\pi$
$294$		0			0
$295$	−119.000			−0.0234863
$296$	−44.0000	−	76.2102i	−0.00864003	−	0.0149650i
$297$		0			0
$298$	2295.00	−	3975.06i	0.446127	−	0.772714i
$299$	−231.000	−	400.104i	−0.0446792	−	0.0773866i
$300$		0			0
$301$	−2600.00	−	4053.00i	−0.497879	−	0.776116i
$302$	−2218.00			−0.422621
$303$		0			0
$304$	−1096.00	+	1898.33i	−0.206776	+	0.358147i
$305$	178.500	−	309.171i	0.0335111	−	0.0580429i
$306$		0			0
$307$	−8132.00			−1.51178			−0.755892	−	0.654696i	$-0.772797\pi$
$307$	−8132.00			−1.51178			−0.755892	+	0.654696i	$0.772797\pi$
$308$	1190.00	−	2303.63i	0.220151	−	0.426173i
$309$		0			0
$310$	525.000	+	909.327i	0.0961871	+	0.166601i
$311$	−464.500	+	804.538i	−0.0846925	+	0.146692i	−0.905260	−	0.424858i	$-0.860324\pi$
$311$	−464.500	+	804.538i	−0.0846925	+	0.146692i	0.820568	+	0.571549i	$0.193657\pi$
$312$		0			0
$313$	104.500	+	180.999i	0.0188712	+	0.0326859i	0.875307	−	0.483568i	$-0.160659\pi$
$313$	104.500	+	180.999i	0.0188712	+	0.0326859i	−0.856436	+	0.516254i	$0.827326\pi$
$314$	3118.00			0.560379
$315$		0			0
$316$	−1980.00			−0.352480
$317$	3565.50	+	6175.63i	0.631730	+	1.09419i	0.987198	+	0.159500i	$0.0509882\pi$
$317$	3565.50	+	6175.63i	0.631730	+	1.09419i	−0.355468	+	0.934689i	$0.615678\pi$
$318$		0			0
$319$	−1855.00	+	3212.95i	−0.325580	+	0.563921i
$320$	224.000	+	387.979i	0.0391312	+	0.0677772i
$321$		0			0
$322$	259.000	−	12.1244i	0.0448246	−	0.00209834i
$323$	−8083.00			−1.39242
$324$		0			0
$325$	2508.00	−	4343.98i	0.428058	−	0.741418i
$326$	2251.00	−	3898.85i	0.382427	−	0.662384i
$327$		0			0
$328$	3984.00			0.670670
$329$	−1453.50	+	2813.72i	−0.243569	+	0.471505i
$330$		0			0
$331$	3285.50	+	5690.65i	0.545581	+	0.944975i	0.998570	+	0.0534583i	$0.0170244\pi$
$331$	3285.50	+	5690.65i	0.545581	+	0.944975i	−0.452989	+	0.891516i	$0.649642\pi$
$332$	1864.00	−	3228.54i	0.308133	−	0.533703i
$333$		0			0
$334$	2788.00	+	4828.96i	0.456744	+	0.791104i
$335$	−3073.00			−0.501182
$336$		0			0
$337$	−11466.0			−1.85339			−0.926696	−	0.375813i	$-0.877364\pi$
$337$	−11466.0			−1.85339			−0.926696	+	0.375813i	$0.877364\pi$
$338$	−2159.00	−	3739.50i	−0.347438	−	0.601781i
$339$		0			0
$340$	−826.000	+	1430.67i	−0.131753	+	0.228203i
$341$	1312.50	+	2273.32i	0.208434	+	0.361018i
$342$		0			0
$343$	6290.00	−	888.542i	0.990169	−	0.139874i
$344$	2080.00			0.326006
$345$		0			0
$346$	1579.00	−	2734.91i	0.245340	−	0.424941i
$347$	−4888.50	+	8467.13i	−0.756278	+	1.30991i	0.188459	+	0.982081i	$0.439651\pi$
$347$	−4888.50	+	8467.13i	−0.756278	+	1.30991i	−0.944737	+	0.327831i	$0.893682\pi$
$348$		0			0
$349$	11914.0			1.82734			0.913670	−	0.406456i	$-0.133236\pi$
$349$	11914.0			1.82734			0.913670	+	0.406456i	$0.133236\pi$
$350$	1520.00	+	2369.45i	0.232135	+	0.361863i
$351$		0			0
$352$	560.000	+	969.948i	0.0847957	+	0.146871i
$353$	4561.50	−	7900.75i	0.687774	−	1.19126i	−0.284783	−	0.958592i	$-0.591921\pi$
$353$	4561.50	−	7900.75i	0.687774	−	1.19126i	0.972556	−	0.232667i	$-0.0747452\pi$
$354$		0			0
$355$	2744.00	+	4752.75i	0.410243	+	0.710562i
$356$	3492.00			0.519875
$357$		0			0
$358$	−4902.00			−0.723684
$359$	4074.50	+	7057.24i	0.599008	+	1.03751i	0.992968	+	0.118385i	$0.0377716\pi$
$359$	4074.50	+	7057.24i	0.599008	+	1.03751i	−0.393960	+	0.919128i	$0.628895\pi$
$360$		0			0
$361$	−5955.00	+	10314.4i	−0.868202	+	1.50377i
$362$	1170.00	+	2026.50i	0.169872	+	0.294228i
$363$		0			0
$364$	4884.00	−	228.631i	0.703272	−	0.0329217i
$365$	−2065.00			−0.296129
$366$		0			0
$367$	−4835.50	+	8375.33i	−0.687769	+	1.19125i	0.284790	+	0.958590i	$0.408076\pi$
$367$	−4835.50	+	8375.33i	−0.687769	+	1.19125i	−0.972558	+	0.232660i	$0.925257\pi$
$368$	−56.0000	+	96.9948i	−0.00793261	+	0.0137397i
$369$		0			0
$370$	−154.000			−0.0216381
$371$	7714.50	−	361.133i	1.07956	−	0.0505366i
$372$		0			0
$373$	2054.50	+	3558.50i	0.285196	+	0.493973i	0.972657	−	0.232248i	$-0.0746081\pi$
$373$	2054.50	+	3558.50i	0.285196	+	0.493973i	−0.687461	+	0.726221i	$0.741275\pi$
$374$	−2065.00	+	3576.68i	−0.285504	+	0.494508i
$375$		0			0
$376$	−684.000	−	1184.72i	−0.0938154	−	0.162493i
$377$	−6996.00			−0.955736
$378$		0			0
$379$	−3488.00			−0.472735			−0.236367	−	0.971664i	$-0.575957\pi$
$379$	−3488.00			−0.472735			−0.236367	+	0.971664i	$0.575957\pi$
$380$	1918.00	+	3322.07i	0.258925	+	0.448470i
$381$		0			0
$382$	−1275.00	+	2208.36i	−0.170771	+	0.295785i
$383$	4358.50	+	7549.14i	0.581485	+	1.00716i	0.995304	+	0.0968028i	$0.0308616\pi$
$383$	4358.50	+	7549.14i	0.581485	+	1.00716i	−0.413818	+	0.910360i	$0.635805\pi$
$384$		0			0
$385$	−2450.00	−	3819.17i	−0.324321	−	0.505566i
$386$	70.0000			0.00923033
$387$		0			0
$388$	580.000	−	1004.59i	0.0758893	−	0.131444i
$389$	81.5000	−	141.162i	0.0106227	−	0.0183990i	−0.860665	−	0.509171i	$-0.829952\pi$
$389$	81.5000	−	141.162i	0.0106227	−	0.0183990i	0.871288	+	0.490772i	$0.163285\pi$
$390$		0			0
$391$	−413.000			−0.0534177
$392$	−1144.00	+	2494.15i	−0.147400	+	0.321362i
$393$		0			0
$394$	−2734.00	−	4735.43i	−0.349586	−	0.605501i
$395$	−1732.50	+	3000.78i	−0.220687	+	0.382242i
$396$		0			0
$397$	−499.500	−	865.159i	−0.0631466	−	0.109373i	0.832724	−	0.553689i	$-0.186780\pi$
$397$	−499.500	−	865.159i	−0.0631466	−	0.109373i	−0.895870	+	0.444316i	$0.853447\pi$
$398$	4486.00			0.564982
$399$		0			0
$400$	−1216.00			−0.152000
$401$	−7378.50	−	12779.9i	−0.918865	−	1.59152i	−0.801143	−	0.598474i	$-0.795774\pi$
$401$	−7378.50	−	12779.9i	−0.918865	−	1.59152i	−0.117722	−	0.993047i	$-0.537559\pi$
$402$		0			0
$403$	−2475.00	+	4286.83i	−0.305927	+	0.529881i
$404$	−2170.00	−	3758.55i	−0.267232	−	0.462859i
$405$		0			0
$406$	1802.00	−	3488.35i	0.220275	−	0.426414i
$407$	−385.000			−0.0468888
$408$		0			0
$409$	66.5000	−	115.181i	0.00803964	−	0.0139251i	−0.861978	−	0.506946i	$-0.830774\pi$
$409$	66.5000	−	115.181i	0.00803964	−	0.0139251i	0.870017	+	0.493021i	$0.164108\pi$
$410$	3486.00	−	6037.93i	0.419906	−	0.727298i
$411$		0			0
$412$	6212.00			0.742823
$413$	314.500	−	14.7224i	0.0374710	−	0.00175410i
$414$		0			0
$415$	−3262.00	−	5649.95i	−0.385844	−	0.668302i
$416$	−1056.00	+	1829.05i	−0.124458	+	0.215568i
$417$		0			0
$418$	4795.00	+	8305.18i	0.561079	+	0.971818i
$419$	6420.00			0.748538			0.374269	−	0.927320i	$-0.377894\pi$
$419$	6420.00			0.748538			0.374269	+	0.927320i	$0.377894\pi$
$420$		0			0
$421$	10266.0			1.18844			0.594221	−	0.804302i	$-0.297460\pi$
$421$	10266.0			1.18844			0.594221	+	0.804302i	$0.297460\pi$
$422$	−1172.00	−	2029.96i	−0.135194	−	0.234164i
$423$		0			0
$424$	−1668.00	+	2889.06i	−0.191050	+	0.330908i
$425$	−2242.00	−	3883.26i	−0.255889	−	0.443213i
$426$		0			0
$427$	−433.500	+	839.179i	−0.0491301	+	0.0951070i
$428$	−516.000			−0.0582752
$429$		0			0
$430$	1820.00	−	3152.33i	0.204112	−	0.353532i
$431$	−7606.50	+	13174.8i	−0.850098	+	1.47241i	0.0310213	+	0.999519i	$0.490124\pi$
$431$	−7606.50	+	13174.8i	−0.850098	+	1.47241i	−0.881119	+	0.472894i	$0.843209\pi$
$432$		0			0
$433$	−1378.00			−0.152939			−0.0764693	−	0.997072i	$-0.524365\pi$
$433$	−1378.00			−0.152939			−0.0764693	+	0.997072i	$0.524365\pi$
$434$	−1500.00	−	2338.27i	−0.165904	−	0.258619i
$435$		0			0
$436$	1930.00	+	3342.86i	0.211996	+	0.367188i
$437$	−479.500	+	830.518i	−0.0524888	+	0.0909132i
$438$		0			0
$439$	1381.50	+	2392.83i	0.150195	+	0.260145i	0.931299	−	0.364256i	$-0.118677\pi$
$439$	1381.50	+	2392.83i	0.150195	+	0.260145i	−0.781104	+	0.624401i	$0.785343\pi$
$440$	1960.00			0.212362
$441$		0			0
$442$	−7788.00			−0.838094
$443$	2924.50	+	5065.38i	0.313651	+	0.543259i	0.979150	−	0.203140i	$-0.0651146\pi$
$443$	2924.50	+	5065.38i	0.313651	+	0.543259i	−0.665499	+	0.746399i	$0.731781\pi$
$444$		0			0
$445$	3055.50	−	5292.28i	0.325493	−	0.563771i
$446$	−2024.00	−	3505.67i	−0.214886	−	0.372194i
$447$		0			0
$448$	−640.000	−	997.661i	−0.0674937	−	0.105212i
$449$	−4582.00			−0.481599			−0.240799	−	0.970575i	$-0.577410\pi$
$449$	−4582.00			−0.481599			−0.240799	+	0.970575i	$0.577410\pi$
$450$		0			0
$451$	8715.00	−	15094.8i	0.909919	−	1.57603i
$452$	−100.000	+	173.205i	−0.0104062	+	0.0180241i
$453$		0			0
$454$	−5142.00			−0.531555
$455$	3927.00	−	7601.97i	0.404617	−	0.783266i
$456$		0			0
$457$	−5775.50	−	10003.5i	−0.591174	−	1.02394i	−0.994075	−	0.108700i	$-0.965331\pi$
$457$	−5775.50	−	10003.5i	−0.591174	−	1.02394i	0.402901	−	0.915244i	$-0.368002\pi$
$458$	−895.000	+	1550.19i	−0.0913114	+	0.158156i
$459$		0			0
$460$	98.0000	+	169.741i	0.00993320	+	0.0172048i
$461$	9494.00			0.959175			0.479587	−	0.877494i	$-0.340786\pi$
$461$	9494.00			0.959175			0.479587	+	0.877494i	$0.340786\pi$
$462$		0			0
$463$	−10160.0			−1.01982			−0.509908	−	0.860229i	$-0.670321\pi$
$463$	−10160.0			−1.01982			−0.509908	+	0.860229i	$0.670321\pi$
$464$	848.000	+	1468.78i	0.0848436	+	0.146953i
$465$		0			0
$466$	1787.00	−	3095.17i	0.177642	−	0.307685i
$467$	−653.500	−	1131.90i	−0.0647545	−	0.112158i	0.831831	−	0.555030i	$-0.187293\pi$
$467$	−653.500	−	1131.90i	−0.0647545	−	0.112158i	−0.896585	+	0.442872i	$0.853960\pi$
$468$		0			0
$469$	8121.50	−	380.185i	0.799608	−	0.0374314i
$470$	−2394.00			−0.234951
$471$		0			0
$472$	−68.0000	+	117.779i	−0.00663126	+	0.0114857i
$473$	4550.00	−	7880.83i	0.442303	−	0.766091i
$474$		0			0
$475$	−10412.0			−1.00576
$476$	2006.00	−	3883.26i	0.193161	−	0.373926i
$477$		0			0
$478$	−5100.00	−	8833.46i	−0.488010	−	0.845257i
$479$	9143.50	−	15837.0i	0.872186	−	1.51067i	0.0124559	−	0.999922i	$-0.496035\pi$
$479$	9143.50	−	15837.0i	0.872186	−	1.51067i	0.859730	−	0.510748i	$-0.170632\pi$
$480$		0			0
$481$	−363.000	−	628.734i	−0.0344103	−	0.0596005i
$482$	−8354.00			−0.789449
$483$		0			0
$484$	−424.000			−0.0398197
$485$	−1015.00	−	1758.03i	−0.0950284	−	0.164594i
$486$		0			0
$487$	7476.50	−	12949.7i	0.695673	−	1.20494i	−0.274281	−	0.961650i	$-0.588440\pi$
$487$	7476.50	−	12949.7i	0.695673	−	1.20494i	0.969953	−	0.243291i	$-0.0782269\pi$
$488$	−204.000	−	353.338i	−0.0189235	−	0.0327764i
$489$		0			0
$490$	2779.00	+	3916.17i	0.256209	+	0.361050i
$491$	−14352.0			−1.31914			−0.659569	−	0.751644i	$-0.729261\pi$
$491$	−14352.0			−1.31914			−0.659569	+	0.751644i	$0.729261\pi$
$492$		0			0
$493$	−3127.00	+	5416.12i	−0.285665	+	0.494787i
$494$	−9042.00	+	15661.2i	−0.823520	+	1.42638i
$495$		0			0
$496$	1200.00			0.108632
$497$	−7840.00	−	12221.4i	−0.707590	−	1.10302i
$498$		0			0
$499$	2765.50	+	4789.99i	0.248098	+	0.429718i	0.962998	−	0.269509i	$-0.0868612\pi$
$499$	2765.50	+	4789.99i	0.248098	+	0.429718i	−0.714900	+	0.699226i	$0.753528\pi$
$500$	−2814.00	+	4873.99i	−0.251692	+	0.435943i
$501$		0			0
$502$	−4680.00	−	8106.00i	−0.416093	−	0.720694i
$503$	−8400.00			−0.744607			−0.372304	−	0.928111i	$-0.621432\pi$
$503$	−8400.00			−0.744607			−0.372304	+	0.928111i	$0.621432\pi$
$504$		0			0
$505$	−7595.00			−0.669254
$506$	245.000	+	424.352i	0.0215249	+	0.0372821i
$507$		0			0
$508$	−1872.00	+	3242.40i	−0.163497	+	0.283185i
$509$	−1192.50	−	2065.47i	−0.103844	−	0.179863i	0.809421	−	0.587228i	$-0.199781\pi$
$509$	−1192.50	−	2065.47i	−0.103844	−	0.179863i	−0.913265	+	0.407365i	$0.866448\pi$
$510$		0			0
$511$	5457.50	−	255.477i	0.472457	−	0.0221167i
$512$	512.000			0.0441942
$513$		0			0
$514$	−1749.00	+	3029.36i	−0.150088	+	0.259960i
$515$	5435.50	−	9414.56i	0.465081	−	0.805544i
$516$		0			0
$517$	−5985.00			−0.509130
$518$	407.000	−	19.0526i	0.0345223	−	0.00161606i
$519$		0			0
$520$	1848.00	+	3200.83i	0.155846	+	0.269934i
$521$	−4576.50	+	7926.73i	−0.384837	+	0.666557i	−0.991747	−	0.128214i	$-0.959076\pi$
$521$	−4576.50	+	7926.73i	−0.384837	+	0.666557i	0.606910	+	0.794771i	$0.292409\pi$
$522$		0			0
$523$	6903.50	+	11957.2i	0.577187	+	0.999718i	0.995800	+	0.0915530i	$0.0291831\pi$
$523$	6903.50	+	11957.2i	0.577187	+	0.999718i	−0.418613	+	0.908165i	$0.637484\pi$
$524$	3020.00			0.251773
$525$		0			0
$526$	8946.00			0.741567
$527$	2212.50	+	3832.16i	0.182880	+	0.316758i
$528$		0			0
$529$	6059.00	−	10494.5i	0.497986	−	0.862538i
$530$	2919.00	+	5055.86i	0.239233	+	0.414363i
$531$		0			0
$532$	−5480.00	−	8542.47i	−0.446594	−	0.696172i
$533$	32868.0			2.67105
$534$		0			0
$535$	−451.500	+	782.021i	−0.0364861	+	0.0631957i
$536$	−1756.00	+	3041.48i	−0.141507	+	0.245097i
$537$		0			0
$538$	−3950.00			−0.316536
$539$	6947.50	+	9790.42i	0.555195	+	0.782381i
$540$		0			0
$541$	−4087.50	−	7079.76i	−0.324834	−	0.562629i	0.656645	−	0.754200i	$-0.271975\pi$
$541$	−4087.50	−	7079.76i	−0.324834	−	0.562629i	−0.981479	+	0.191571i	$0.938642\pi$
$542$	8439.00	−	14616.8i	0.668794	−	1.15838i
$543$		0			0
$544$	944.000	+	1635.06i	0.0744001	+	0.128865i
$545$	6755.00			0.530922
$546$		0			0
$547$	4656.00			0.363942			0.181971	−	0.983304i	$-0.441752\pi$
$547$	4656.00			0.363942			0.181971	+	0.983304i	$0.441752\pi$
$548$	−4714.00	−	8164.89i	−0.367467	−	0.636472i
$549$		0			0
$550$	−2660.00	+	4607.26i	−0.206223	+	0.357189i
$551$	7261.00	+	12576.4i	0.561396	+	0.972366i
$552$		0			0
$553$	4207.50	−	8144.97i	0.323546	−	0.626328i
$554$	1054.00			0.0808306
$555$		0			0
$556$	−56.0000	+	96.9948i	−0.00427146	+	0.00739838i
$557$	3501.50	−	6064.78i	0.266361	−	0.461352i	−0.701558	−	0.712612i	$-0.747512\pi$
$557$	3501.50	−	6064.78i	0.266361	−	0.461352i	0.967919	+	0.251261i	$0.0808452\pi$
$558$		0			0
$559$	17160.0			1.29837
$560$	−2072.00	+	96.9948i	−0.156354	+	0.00731925i
$561$		0			0
$562$	−202.000	−	349.874i	−0.0151617	−	0.0262608i
$563$	−9876.50	+	17106.6i	−0.739334	+	1.28056i	0.213462	+	0.976951i	$0.431526\pi$
$563$	−9876.50	+	17106.6i	−0.739334	+	1.28056i	−0.952796	+	0.303612i	$0.901807\pi$
$564$		0			0
$565$	175.000	+	303.109i	0.0130306	+	0.0225697i
$566$	−15898.0			−1.18064
$567$		0			0
$568$	6272.00			0.463323
$569$	−3448.50	−	5972.98i	−0.254075	−	0.440071i	0.710569	−	0.703628i	$-0.248438\pi$
$569$	−3448.50	−	5972.98i	−0.254075	−	0.440071i	−0.964644	+	0.263557i	$0.915104\pi$
$570$		0			0
$571$	−12457.5	+	21577.0i	−0.913013	+	1.58138i	−0.103227	+	0.994658i	$0.532917\pi$
$571$	−12457.5	+	21577.0i	−0.913013	+	1.58138i	−0.809785	+	0.586726i	$0.800416\pi$
$572$	4620.00	+	8002.07i	0.337713	+	0.584936i
$573$		0			0
$574$	−8466.00	+	16388.7i	−0.615617	+	1.19172i
$575$	−532.000			−0.0385842
$576$		0			0
$577$	−63.5000	+	109.985i	−0.00458152	+	0.00793543i	−0.868307	−	0.496027i	$-0.834792\pi$
$577$	−63.5000	+	109.985i	−0.00458152	+	0.00793543i	0.863726	+	0.503962i	$0.168125\pi$
$578$	1432.00	−	2480.30i	0.103051	−	0.178489i
$579$		0			0
$580$	2968.00			0.212482
$581$	9320.00	+	14528.4i	0.665506	+	1.03742i
$582$		0			0
$583$	7297.50	+	12639.6i	0.518407	+	0.897908i
$584$	−1180.00	+	2043.82i	−0.0836109	+	0.144818i
$585$		0			0
$586$	318.000	+	550.792i	0.0224172	+	0.0388277i
$587$	−9044.00			−0.635921			−0.317961	−	0.948104i	$-0.602998\pi$
$587$	−9044.00			−0.635921			−0.317961	+	0.948104i	$0.602998\pi$
$588$		0			0
$589$	10275.0			0.718801
$590$	119.000	+	206.114i	0.00830365	+	0.0143823i
$591$		0			0
$592$	−88.0000	+	152.420i	−0.00610942	+	0.0105818i
$593$	−5350.50	−	9267.34i	−0.370521	−	0.641760i	0.619125	−	0.785292i	$-0.287487\pi$
$593$	−5350.50	−	9267.34i	−0.370521	−	0.641760i	−0.989646	+	0.143532i	$0.954154\pi$
$594$		0			0
$595$	−4130.00	−	6438.03i	−0.284560	−	0.443586i
$596$	−9180.00			−0.630919
$597$		0			0
$598$	−462.000	+	800.207i	−0.0315930	+	0.0547206i
$599$	10399.5	−	18012.5i	0.709369	−	1.22866i	−0.255722	−	0.966750i	$-0.582313\pi$
$599$	10399.5	−	18012.5i	0.709369	−	1.22866i	0.965091	−	0.261913i	$-0.0843533\pi$
$600$		0			0
$601$	−1402.00			−0.0951560			−0.0475780	−	0.998868i	$-0.515150\pi$
$601$	−1402.00			−0.0951560			−0.0475780	+	0.998868i	$0.515150\pi$
$602$	−4420.00	+	8556.33i	−0.299245	+	0.579286i
$603$		0			0
$604$	2218.00	+	3841.69i	0.149419	+	0.258801i
$605$	−371.000	+	642.591i	−0.0249311	+	0.0431819i
$606$		0			0
$607$	−3262.50	−	5650.82i	−0.218156	−	0.377858i	0.736088	−	0.676886i	$-0.236671\pi$
$607$	−3262.50	−	5650.82i	−0.218156	−	0.377858i	−0.954244	+	0.299028i	$0.903338\pi$
$608$	4384.00			0.292425
$609$		0			0
$610$	−714.000			−0.0473918
$611$	−5643.00	−	9773.96i	−0.373636	−	0.647156i
$612$		0			0
$613$	−7525.50	+	13034.5i	−0.495844	+	0.858826i	−0.999989	−	0.00479285i	$-0.998474\pi$
$613$	−7525.50	+	13034.5i	−0.495844	+	0.858826i	0.504145	+	0.863619i	$0.331808\pi$
$614$	8132.00	+	14085.0i	0.534496	+	0.925775i
$615$		0			0
$616$	−5180.00	+	242.487i	−0.338812	+	0.0158605i
$617$	−11150.0			−0.727524			−0.363762	−	0.931492i	$-0.618508\pi$
$617$	−11150.0			−0.727524			−0.363762	+	0.931492i	$0.618508\pi$
$618$		0			0
$619$	−1707.50	+	2957.48i	−0.110873	+	0.192037i	−0.916122	−	0.400899i	$-0.868698\pi$
$619$	−1707.50	+	2957.48i	−0.110873	+	0.192037i	0.805250	+	0.592936i	$0.202031\pi$
$620$	1050.00	−	1818.65i	0.0680145	−	0.117805i
$621$		0			0
$622$	1858.00			0.119773
$623$	−7420.50	+	14364.8i	−0.477201	+	0.923775i
$624$		0			0
$625$	174.500	+	302.243i	0.0111680	+	0.0193435i
$626$	209.000	−	361.999i	0.0133440	−	0.0231124i
$627$		0			0
$628$	−3118.00	−	5400.53i	−0.198124	−	0.343160i
$629$	−649.000			−0.0411404
$630$		0			0
$631$	−21184.0			−1.33648			−0.668242	−	0.743944i	$-0.732953\pi$
$631$	−21184.0			−1.33648			−0.668242	+	0.743944i	$0.732953\pi$
$632$	1980.00	+	3429.46i	0.124621	+	0.215849i
$633$		0			0
$634$	7131.00	−	12351.3i	0.446701	−	0.773708i
$635$	3276.00	+	5674.20i	0.204731	+	0.354604i
$636$		0			0
$637$	−9438.00	+	20576.8i	−0.587044	+	1.27988i
$638$	7420.00			0.460440
$639$		0			0
$640$	448.000	−	775.959i	0.0276699	−	0.0479257i
$641$	−5352.50	+	9270.80i	−0.329814	+	0.571255i	−0.982475	−	0.186395i	$-0.940320\pi$
$641$	−5352.50	+	9270.80i	−0.329814	+	0.571255i	0.652660	+	0.757651i	$0.273653\pi$
$642$		0			0
$643$	6860.00			0.420734			0.210367	−	0.977622i	$-0.432534\pi$
$643$	6860.00			0.420734			0.210367	+	0.977622i	$0.432534\pi$
$644$	−280.000	−	436.477i	−0.0171328	−	0.0267074i
$645$		0			0
$646$	8083.00	+	14000.2i	0.492293	+	0.852677i
$647$	7231.50	−	12525.3i	0.439412	−	0.761084i	−0.558232	−	0.829685i	$-0.688520\pi$
$647$	7231.50	−	12525.3i	0.439412	−	0.761084i	0.997644	+	0.0686008i	$0.0218535\pi$
$648$		0			0
$649$	297.500	+	515.285i	0.0179937	+	0.0311660i
$650$	−10032.0			−0.605365
$651$		0			0
$652$	−9004.00			−0.540834
$653$	2989.50	+	5177.97i	0.179155	+	0.310305i	0.941591	−	0.336758i	$-0.109330\pi$
$653$	2989.50	+	5177.97i	0.179155	+	0.310305i	−0.762436	+	0.647063i	$0.775997\pi$
$654$		0			0
$655$	2642.50	−	4576.94i	0.157635	−	0.273032i
$656$	−3984.00	−	6900.49i	−0.237117	−	0.410700i
$657$		0			0
$658$	6327.00	−	296.181i	0.374851	−	0.0175476i
$659$	6940.00			0.410234			0.205117	−	0.978737i	$-0.434243\pi$
$659$	6940.00			0.410234			0.205117	+	0.978737i	$0.434243\pi$
$660$		0			0
$661$	−6699.50	+	11603.9i	−0.394221	+	0.682812i	−0.993001	−	0.118102i	$-0.962319\pi$
$661$	−6699.50	+	11603.9i	−0.394221	+	0.682812i	0.598780	+	0.800914i	$0.295652\pi$
$662$	6571.00	−	11381.3i	0.385784	−	0.668198i
$663$		0			0
$664$	−7456.00			−0.435766
$665$	−17741.5	+	830.518i	−1.03457	+	0.0484303i
$666$		0			0
$667$	371.000	+	642.591i	0.0215370	+	0.0373032i
$668$	5576.00	−	9657.92i	0.322967	−	0.559395i
$669$		0			0
$670$	3073.00	+	5322.59i	0.177195	+	0.306910i
$671$	−1785.00			−0.102696
$672$		0			0
$673$	29510.0			1.69023			0.845117	−	0.534582i	$-0.179531\pi$
$673$	29510.0			1.69023			0.845117	+	0.534582i	$0.179531\pi$
$674$	11466.0	+	19859.7i	0.655273	+	1.13497i
$675$		0			0
$676$	−4318.00	+	7479.00i	−0.245676	+	0.425523i
$677$	−13000.5	−	22517.5i	−0.738035	−	1.27831i	−0.953379	−	0.301776i	$-0.902421\pi$
$677$	−13000.5	−	22517.5i	−0.738035	−	1.27831i	0.215344	−	0.976538i	$-0.430913\pi$
$678$		0			0
$679$	2900.00	+	4520.65i	0.163905	+	0.255503i
$680$	3304.00			0.186327
$681$		0			0
$682$	2625.00	−	4546.63i	0.147385	−	0.255278i
$683$	−4402.50	+	7625.35i	−0.246643	+	0.427198i	−0.962592	−	0.270954i	$-0.912661\pi$
$683$	−4402.50	+	7625.35i	−0.246643	+	0.427198i	0.715949	+	0.698152i	$0.245994\pi$
$684$		0			0
$685$	−16499.0			−0.920284
$686$	−7829.00	−	10006.1i	−0.435733	−	0.556899i
$687$		0			0
$688$	−2080.00	−	3602.67i	−0.115261	−	0.199637i
$689$	−13761.0	+	23834.8i	−0.760889	+	1.31790i
$690$		0			0
$691$	−14342.5	−	24841.9i	−0.789601	−	1.36763i	−0.926211	−	0.377004i	$-0.876954\pi$
$691$	−14342.5	−	24841.9i	−0.789601	−	1.36763i	0.136610	−	0.990625i	$-0.456379\pi$
$692$	−6316.00			−0.346963
$693$		0			0
$694$	19554.0			1.06954
$695$	98.0000	+	169.741i	0.00534871	+	0.00926423i
$696$		0			0
$697$	14691.0	−	25445.6i	0.798366	−	1.38281i
$698$	−11914.0	−	20635.7i	−0.646062	−	1.11901i
$699$		0			0
$700$	2584.00	−	5002.16i	0.139523	−	0.270091i
$701$	3146.00			0.169505			0.0847523	−	0.996402i	$-0.472990\pi$
$701$	3146.00			0.169505			0.0847523	+	0.996402i	$0.472990\pi$
$702$		0			0
$703$	−753.500	+	1305.10i	−0.0404250	+	0.0700182i
$704$	1120.00	−	1939.90i	0.0599596	−	0.103853i
$705$		0			0
$706$	−18246.0			−0.972659
$707$	20072.5	−	939.638i	1.06776	−	0.0499840i
$708$		0			0
$709$	−629.500	−	1090.33i	−0.0333447	−	0.0577547i	0.848871	−	0.528599i	$-0.177283\pi$
$709$	−629.500	−	1090.33i	−0.0333447	−	0.0577547i	−0.882216	+	0.470845i	$0.843949\pi$
$710$	5488.00	−	9505.49i	0.290086	−	0.502443i
$711$		0			0
$712$	−3492.00	−	6048.32i	−0.183804	−	0.318357i
$713$	525.000			0.0275756
$714$		0			0
$715$	16170.0			0.845767
$716$	4902.00	+	8490.51i	0.255861	+	0.443164i
$717$		0			0
$718$	8149.00	−	14114.5i	0.423563	−	0.733632i
$719$	8212.50	+	14224.5i	0.425973	+	0.737807i	0.996511	−	0.0834645i	$-0.0265985\pi$
$719$	8212.50	+	14224.5i	0.425973	+	0.737807i	−0.570538	+	0.821271i	$0.693265\pi$
$720$		0			0
$721$	−13200.5	+	25553.8i	−0.681848	+	1.31994i
$722$	23820.0			1.22782
$723$		0			0
$724$	2340.00	−	4053.00i	0.120118	−	0.208050i
$725$	−4028.00	+	6976.70i	−0.206340	+	0.357391i
$726$		0			0
$727$	−6032.00			−0.307723			−0.153861	−	0.988092i	$-0.549171\pi$
$727$	−6032.00			−0.307723			−0.153861	+	0.988092i	$0.549171\pi$
$728$	−5280.00	−	8230.71i	−0.268805	−	0.419025i
$729$		0			0
$730$	2065.00	+	3576.68i	0.104697	+	0.181341i
$731$	7670.00	−	13284.8i	0.388078	−	0.672171i
$732$		0			0
$733$	−7621.50	−	13200.8i	−0.384047	−	0.665189i	0.607589	−	0.794251i	$-0.292137\pi$
$733$	−7621.50	−	13200.8i	−0.384047	−	0.665189i	−0.991636	+	0.129062i	$0.958803\pi$
$734$	19342.0			0.972652
$735$		0			0
$736$	224.000			0.0112184
$737$	7682.50	+	13306.5i	0.383974	+	0.665062i
$738$		0			0
$739$	5026.50	−	8706.15i	0.250207	−	0.433371i	−0.713376	−	0.700782i	$-0.752835\pi$
$739$	5026.50	−	8706.15i	0.250207	−	0.433371i	0.963583	+	0.267411i	$0.0861681\pi$
$740$	154.000	+	266.736i	0.00765021	+	0.0132505i
$741$		0			0
$742$	−8340.00	−	13000.8i	−0.412629	−	0.643226i
$743$	−24384.0			−1.20399			−0.601993	−	0.798501i	$-0.705627\pi$
$743$	−24384.0			−1.20399			−0.601993	+	0.798501i	$0.705627\pi$
$744$		0			0
$745$	−8032.50	+	13912.7i	−0.395017	+	0.684190i
$746$	4109.00	−	7117.00i	0.201664	−	0.349292i
$747$		0			0
$748$	8260.00			0.403764
$749$	1096.50	−	2122.63i	0.0534916	−	0.103550i
$750$		0			0
$751$	−5794.50	−	10036.4i	−0.281550	−	0.487660i	0.690216	−	0.723603i	$-0.257515\pi$
$751$	−5794.50	−	10036.4i	−0.281550	−	0.487660i	−0.971767	+	0.235943i	$0.924182\pi$
$752$	−1368.00	+	2369.45i	−0.0663375	+	0.114900i
$753$		0			0
$754$	6996.00	+	12117.4i	0.337904	+	0.585266i
$755$	7763.00			0.374205
$756$		0			0
$757$	14562.0			0.699161			0.349581	−	0.936906i	$-0.386324\pi$
$757$	14562.0			0.699161			0.349581	+	0.936906i	$0.386324\pi$
$758$	3488.00	+	6041.39i	0.167137	+	0.289490i
$759$		0			0
$760$	3836.00	−	6644.15i	0.183087	−	0.317116i
$761$	−11382.5	−	19715.1i	−0.542201	−	0.939120i	−0.998777	−	0.0494360i	$-0.984258\pi$
$761$	−11382.5	−	19715.1i	−0.542201	−	0.939120i	0.456576	−	0.889684i	$-0.349076\pi$
$762$		0			0
$763$	−17852.5	+	835.715i	−0.847056	+	0.0396526i
$764$	5100.00			0.241507
$765$		0			0
$766$	8717.00	−	15098.3i	0.411172	−	0.712171i
$767$	−561.000	+	971.681i	−0.0264101	+	0.0457436i
$768$		0			0
$769$	3766.00			0.176600			0.0883000	−	0.996094i	$-0.471857\pi$
$769$	3766.00			0.176600			0.0883000	+	0.996094i	$0.471857\pi$
$770$	−4165.00	+	8062.70i	−0.194930	+	0.377350i
$771$		0			0
$772$	−70.0000	−	121.244i	−0.00326341	−	0.00565240i
$773$	−13430.5	+	23262.3i	−0.624918	+	1.08239i	0.363639	+	0.931540i	$0.381534\pi$
$773$	−13430.5	+	23262.3i	−0.624918	+	1.08239i	−0.988557	+	0.150849i	$0.951799\pi$
$774$		0			0
$775$	2850.00	+	4936.34i	0.132097	+	0.228798i
$776$	−2320.00			−0.107324
$777$		0			0
$778$	−326.000			−0.0150227
$779$	−34113.0	−	59085.4i	−1.56897	−	2.71753i
$780$		0			0
$781$	13720.0	−	23763.7i	0.628605	−	1.08878i
$782$	413.000	+	715.337i	0.0188860	+	0.0327115i
$783$		0			0
$784$	5464.00	−	512.687i	0.248907	−	0.0233549i
$785$	−10913.0			−0.496180
$786$		0			0
$787$	1048.50	−	1816.06i	0.0474905	−	0.0822559i	−0.841303	−	0.540564i	$-0.818211\pi$
$787$	1048.50	−	1816.06i	0.0474905	−	0.0822559i	0.888793	+	0.458308i	$0.151544\pi$
$788$	−5468.00	+	9470.85i	−0.247195	+	0.428154i
$789$		0			0
$790$	6930.00			0.312099
$791$	−500.000	−	779.423i	−0.0224753	−	0.0350355i
$792$		0			0
$793$	−1683.00	−	2915.04i	−0.0753658	−	0.130537i
$794$	−999.000	+	1730.32i	−0.0446514	+	0.0773384i
$795$		0			0
$796$	−4486.00	−	7769.98i	−0.199751	−	0.345979i
$797$	35334.0			1.57038			0.785191	−	0.619254i	$-0.212565\pi$
$797$	35334.0			1.57038			0.785191	+	0.619254i	$0.212565\pi$
$798$		0			0
$799$	−10089.0			−0.446712
$800$	1216.00	+	2106.17i	0.0537401	+	0.0930806i
$801$		0			0
$802$	−14757.0	+	25559.9i	−0.649735	+	1.12537i
$803$	5162.50	+	8941.71i	0.226875	+	0.392959i
$804$		0			0
$805$	−906.500	+	42.4352i	−0.0396894	+	0.00185795i
$806$	9900.00			0.432646
$807$		0			0
$808$	−4340.00	+	7517.10i	−0.188961	+	0.327290i
$809$	21267.5	−	36836.4i	0.924259	−	1.60086i	0.131510	−	0.991315i	$-0.458017\pi$
$809$	21267.5	−	36836.4i	0.924259	−	1.60086i	0.792749	−	0.609549i	$-0.208649\pi$
$810$		0			0
$811$	30676.0			1.32821			0.664106	−	0.747638i	$-0.268812\pi$
$811$	30676.0			1.32821			0.664106	+	0.747638i	$0.268812\pi$
$812$	−7844.00	+	367.195i	−0.339003	+	0.0158695i
$813$		0			0
$814$	385.000	+	666.840i	0.0165777	+	0.0287134i
$815$	−7878.50	+	13646.0i	−0.338616	+	0.586500i
$816$		0			0
$817$	−17810.0	−	30847.8i	−0.762660	−	1.32097i
$818$	−266.000			−0.0113698
$819$		0			0
$820$	−13944.0			−0.593836
$821$	18671.5	+	32340.0i	0.793715	+	1.37475i	0.923652	+	0.383232i	$0.125189\pi$
$821$	18671.5	+	32340.0i	0.793715	+	1.37475i	−0.129937	+	0.991522i	$0.541478\pi$
$822$		0			0
$823$	−1407.50	+	2437.86i	−0.0596141	+	0.103255i	−0.894292	−	0.447483i	$-0.852320\pi$
$823$	−1407.50	+	2437.86i	−0.0596141	+	0.103255i	0.834678	+	0.550738i	$0.185654\pi$
$824$	−6212.00	−	10759.5i	−0.262628	−	0.454885i
$825$		0			0
$826$	−340.000	−	530.008i	−0.0143222	−	0.0223261i
$827$	9276.00			0.390034			0.195017	−	0.980800i	$-0.437524\pi$
$827$	9276.00			0.390034			0.195017	+	0.980800i	$0.437524\pi$
$828$		0			0
$829$	−9285.50	+	16083.0i	−0.389021	+	0.673805i	−0.992318	−	0.123712i	$-0.960520\pi$
$829$	−9285.50	+	16083.0i	−0.389021	+	0.673805i	0.603297	+	0.797517i	$0.293853\pi$
$830$	−6524.00	+	11299.9i	−0.272833	+	0.472561i
$831$		0			0
$832$	4224.00			0.176011
$833$	11711.5	+	16503.8i	0.487130	+	0.686464i
$834$		0			0
$835$	−9758.00	−	16901.4i	−0.404419	−	0.700474i
$836$	9590.00	−	16610.4i	0.396743	−	0.687179i
$837$		0			0
$838$	−6420.00	−	11119.8i	−0.264648	−	0.458384i
$839$	−29048.0			−1.19529			−0.597645	−	0.801761i	$-0.703897\pi$
$839$	−29048.0			−1.19529			−0.597645	+	0.801761i	$0.703897\pi$
$840$		0			0
$841$	−13153.0			−0.539301
$842$	−10266.0	−	17781.2i	−0.420178	−	0.727769i
$843$		0			0
$844$	−2344.00	+	4059.93i	−0.0955969	+	0.165579i
$845$	7556.50	+	13088.2i	0.307635	+	0.532839i
$846$		0			0
$847$	901.000	−	1744.18i	0.0365510	−	0.0707563i
$848$	6672.00			0.270186
$849$		0			0
$850$	−4484.00	+	7766.52i	−0.180941	+	0.313399i
$851$	−38.5000	+	66.6840i	−0.00155084	+	0.00268613i
$852$		0			0
$853$	32090.0			1.28809			0.644045	−	0.764988i	$-0.277255\pi$
$853$	32090.0			1.28809			0.644045	+	0.764988i	$0.277255\pi$
$854$	1887.00	−	88.3346i	0.0756110	−	0.00353952i
$855$		0			0
$856$	516.000	+	893.738i	0.0206034	+	0.0356861i
$857$	−12268.5	+	21249.7i	−0.489013	+	0.846995i	−0.999920	−	0.0126408i	$-0.995976\pi$
$857$	−12268.5	+	21249.7i	−0.489013	+	0.846995i	0.510907	+	0.859636i	$0.329310\pi$
$858$		0			0
$859$	−10412.5	−	18035.0i	−0.413585	−	0.716351i	0.581693	−	0.813408i	$-0.302390\pi$
$859$	−10412.5	−	18035.0i	−0.413585	−	0.716351i	−0.995279	+	0.0970571i	$0.969057\pi$
$860$	−7280.00			−0.288658
$861$		0			0
$862$	30426.0			1.20222
$863$	−11423.5	−	19786.1i	−0.450591	−	0.780447i	0.547831	−	0.836589i	$-0.315454\pi$
$863$	−11423.5	−	19786.1i	−0.450591	−	0.780447i	−0.998423	+	0.0561414i	$0.982120\pi$
$864$		0			0
$865$	−5526.50	+	9572.18i	−0.217233	+	0.376259i
$866$	1378.00	+	2386.77i	0.0540720	+	0.0936554i
$867$		0			0
$868$	−2550.00	+	4936.34i	−0.0997150	+	0.193030i
$869$	17325.0			0.676307
$870$		0			0
$871$	−14487.0	+	25092.2i	−0.563574	+	0.976139i
$872$	3860.00	−	6685.72i	0.149904	−	0.259641i
$873$		0			0
$874$	1918.00			0.0742303
$875$	−14070.0	−	21933.0i	−0.543603	−	0.847394i
$876$		0			0
$877$	21368.5	+	37011.3i	0.822763	+	1.42507i	0.903617	+	0.428341i	$0.140902\pi$
$877$	21368.5	+	37011.3i	0.822763	+	1.42507i	−0.0808543	+	0.996726i	$0.525765\pi$
$878$	2763.00	−	4785.66i	0.106204	−	0.183950i
$879$		0			0
$880$	−1960.00	−	3394.82i	−0.0750813	−	0.130045i
$881$	−6162.00			−0.235645			−0.117822	−	0.993035i	$-0.537591\pi$
$881$	−6162.00			−0.235645			−0.117822	+	0.993035i	$0.537591\pi$
$882$		0			0
$883$	7748.00			0.295290			0.147645	−	0.989040i	$-0.452831\pi$
$883$	7748.00			0.295290			0.147645	+	0.989040i	$0.452831\pi$
$884$	7788.00	+	13489.2i	0.296311	+	0.513225i
$885$		0			0
$886$	5849.00	−	10130.8i	0.221784	−	0.384142i
$887$	−12961.5	−	22450.0i	−0.490648	−	0.849827i	0.509294	−	0.860592i	$-0.329906\pi$
$887$	−12961.5	−	22450.0i	−0.490648	−	0.849827i	−0.999942	+	0.0107656i	$0.996573\pi$
$888$		0			0
$889$	−9360.00	−	14590.8i	−0.353121	−	0.550461i
$890$	−12222.0			−0.460317
$891$		0			0
$892$	−4048.00	+	7011.34i	−0.151947	+	0.263181i
$893$	−11713.5	+	20288.4i	−0.438944	+	0.760274i
$894$		0			0
$895$	17157.0			0.640777
$896$	−1088.00	+	2106.17i	−0.0405664	+	0.0785294i
$897$		0			0
$898$	4582.00	+	7936.26i	0.170271	+	0.294918i
$899$	3975.00	−	6884.90i	0.147468	−	0.255422i
$900$		0			0
$901$	12301.5	+	21306.8i	0.454853	+	0.787828i
$902$	−34860.0			−1.28682
$903$		0			0
$904$	400.000			0.0147166
$905$	−4095.00	−	7092.75i	−0.150411	−	0.260520i
$906$		0			0
$907$	−15967.5	+	27656.5i	−0.584556	+	1.01248i	0.410375	+	0.911917i	$0.365398\pi$
$907$	−15967.5	+	27656.5i	−0.584556	+	1.01248i	−0.994931	+	0.100563i	$0.967935\pi$
$908$	5142.00	+	8906.21i	0.187933	+	0.325510i
$909$		0			0
$910$	−17094.0	+	800.207i	−0.622704	+	0.0291501i
$911$	−3408.00			−0.123943			−0.0619715	−	0.998078i	$-0.519739\pi$
$911$	−3408.00			−0.123943			−0.0619715	+	0.998078i	$0.519739\pi$
$912$		0			0
$913$	−16310.0	+	28249.7i	−0.591218	+	1.02402i
$914$	−11551.0	+	20006.9i	−0.418023	+	0.724037i
$915$		0			0
$916$	3580.00			0.129134
$917$	−6417.50	+	12423.1i	−0.231106	+	0.447381i
$918$		0			0
$919$	−6954.50	−	12045.5i	−0.249628	−	0.432368i	0.713795	−	0.700355i	$-0.246975\pi$
$919$	−6954.50	−	12045.5i	−0.249628	−	0.432368i	−0.963423	+	0.267987i	$0.913642\pi$
$920$	196.000	−	339.482i	0.00702384	−	0.0121656i
$921$		0			0
$922$	−9494.00	−	16444.1i	−0.339120	−	0.587372i
$923$	51744.0			1.84526
$924$		0			0
$925$	−836.000			−0.0297162
$926$	10160.0	+	17597.6i	0.360560	+	0.624508i
$927$		0			0
$928$	1696.00	−	2937.56i	0.0599935	−	0.103912i
$929$	−12268.5	−	21249.7i	−0.433279	−	0.750462i	0.563874	−	0.825861i	$-0.309310\pi$
$929$	−12268.5	−	21249.7i	−0.433279	−	0.750462i	−0.997153	+	0.0753990i	$0.975977\pi$
$930$		0			0
$931$	46785.5	−	4389.88i	1.64697	−	0.154536i
$932$	−7148.00			−0.251224
$933$		0			0
$934$	−1307.00	+	2263.79i	−0.0457884	+	0.0793078i
$935$	7227.50	−	12518.4i	0.252796	−	0.437856i
$936$		0			0
$937$	−32758.0			−1.14211			−0.571055	−	0.820912i	$-0.693466\pi$
$937$	−32758.0			−1.14211			−0.571055	+	0.820912i	$0.693466\pi$
$938$	−8780.00	−	13686.7i	−0.305626	−	0.476424i
$939$		0			0
$940$	2394.00	+	4146.53i	0.0830677	+	0.143878i
$941$	−19280.5	+	33394.8i	−0.667934	+	1.15690i	0.310546	+	0.950558i	$0.399488\pi$
$941$	−19280.5	+	33394.8i	−0.667934	+	1.15690i	−0.978481	+	0.206338i	$0.933845\pi$
$942$		0			0
$943$	−1743.00	−	3018.96i	−0.0601908	−	0.104253i
$944$	272.000			0.00937801
$945$		0			0
$946$	−18200.0			−0.625511
$947$	19830.5	+	34347.4i	0.680470	+	1.17861i	0.974838	+	0.222916i	$0.0715575\pi$
$947$	19830.5	+	34347.4i	0.680470	+	1.17861i	−0.294368	+	0.955692i	$0.595109\pi$
$948$		0			0
$949$	−9735.00	+	16861.5i	−0.332994	+	0.576763i
$950$	10412.0	+	18034.1i	0.355589	+	0.615899i
$951$		0			0
$952$	−8732.00	+	408.764i	−0.297275	+	0.0139161i
$953$	46618.0			1.58458			0.792290	−	0.610144i	$-0.208889\pi$
$953$	46618.0			1.58458			0.792290	+	0.610144i	$0.208889\pi$
$954$		0			0
$955$	4462.50	−	7729.28i	0.151207	−	0.261899i
$956$	−10200.0	+	17666.9i	−0.345075	+	0.597687i
$957$		0			0
$958$	−36574.0			−1.23346
$959$	43604.5	−	2041.22i	1.46826	−	0.0687325i
$960$		0			0
$961$	12083.0	+	20928.4i	0.405592	+	0.702506i
$962$	−726.000	+	1257.47i	−0.0243318	+	0.0421439i
$963$		0			0
$964$	8354.00	+	14469.6i	0.279112	+	0.483437i
$965$	−245.000			−0.00817288
$966$		0			0
$967$	14816.0			0.492710			0.246355	−	0.969180i	$-0.420767\pi$
$967$	14816.0			0.492710			0.246355	+	0.969180i	$0.420767\pi$
$968$	424.000	+	734.390i	0.0140784	+	0.0243845i
$969$		0			0
$970$	−2030.00	+	3516.06i	−0.0671952	+	0.116386i
$971$	−8437.50	−	14614.2i	−0.278859	−	0.482998i	0.692242	−	0.721665i	$-0.256623\pi$
$971$	−8437.50	−	14614.2i	−0.278859	−	0.482998i	−0.971102	+	0.238667i	$0.923290\pi$
$972$		0			0
$973$	−280.000	−	436.477i	−0.00922548	−	0.0143811i
$974$	−29906.0			−0.983830
$975$		0			0
$976$	−408.000	+	706.677i	−0.0133809	+	0.0231764i
$977$	−7918.50	+	13715.2i	−0.259299	+	0.449119i	−0.966054	−	0.258339i	$-0.916825\pi$
$977$	−7918.50	+	13715.2i	−0.259299	+	0.449119i	0.706755	+	0.707458i	$0.250158\pi$
$978$		0			0
$979$	−30555.0			−0.997489
$980$	4004.00	−	8729.54i	0.130513	−	0.284546i
$981$		0			0
$982$	14352.0	+	24858.4i	0.466386	+	0.807804i
$983$	4957.50	−	8586.64i	0.160854	−	0.278608i	−0.774321	−	0.632793i	$-0.781908\pi$
$983$	4957.50	−	8586.64i	0.160854	−	0.278608i	0.935175	+	0.354185i	$0.115242\pi$
$984$		0			0
$985$	9569.00	+	16574.0i	0.309537	+	0.536133i
$986$	12508.0			0.403992
$987$		0			0
$988$	36168.0			1.16463
$989$	−910.000	−	1576.17i	−0.0292582	−	0.0506766i
$990$		0			0
$991$	21840.5	−	37828.9i	0.700087	−	1.21259i	−0.268348	−	0.963322i	$-0.586478\pi$
$991$	21840.5	−	37828.9i	0.700087	−	1.21259i	0.968435	−	0.249265i	$-0.0801889\pi$
$992$	−1200.00	−	2078.46i	−0.0384073	−	0.0665234i
$993$		0			0
$994$	−13328.0	+	25800.6i	−0.425290	+	0.823286i
$995$	−15701.0			−0.500256
$996$		0			0
$997$	23556.5	−	40801.1i	0.748287	−	1.29607i	−0.200357	−	0.979723i	$-0.564210\pi$
$997$	23556.5	−	40801.1i	0.748287	−	1.29607i	0.948643	−	0.316348i	$-0.102457\pi$
$998$	5531.00	−	9579.97i	0.175432	−	0.303856i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.4.g.c.109.1		2
3.2	odd	2		14.4.c.b.11.1	yes	2
7.2	even	3	inner	126.4.g.c.37.1		2
7.3	odd	6		882.4.a.p.1.1		1
7.4	even	3		882.4.a.k.1.1		1
7.5	odd	6		882.4.g.d.667.1		2
7.6	odd	2		882.4.g.d.361.1		2
12.11	even	2		112.4.i.b.81.1		2
15.2	even	4		350.4.j.d.249.1		4
15.8	even	4		350.4.j.d.249.2		4
15.14	odd	2		350.4.e.b.151.1		2
21.2	odd	6		14.4.c.b.9.1	✓	2
21.5	even	6		98.4.c.e.79.1		2
21.11	odd	6		98.4.a.b.1.1		1
21.17	even	6		98.4.a.c.1.1		1
21.20	even	2		98.4.c.e.67.1		2
24.5	odd	2		448.4.i.c.193.1		2
24.11	even	2		448.4.i.d.193.1		2
84.11	even	6		784.4.a.l.1.1		1
84.23	even	6		112.4.i.b.65.1		2
84.59	odd	6		784.4.a.j.1.1		1
105.2	even	12		350.4.j.d.149.2		4
105.23	even	12		350.4.j.d.149.1		4
105.44	odd	6		350.4.e.b.51.1		2
105.59	even	6		2450.4.a.bf.1.1		1
105.74	odd	6		2450.4.a.bh.1.1		1
168.107	even	6		448.4.i.d.65.1		2
168.149	odd	6		448.4.i.c.65.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.4.c.b.9.1	✓	2	21.2	odd	6
14.4.c.b.11.1	yes	2	3.2	odd	2
98.4.a.b.1.1		1	21.11	odd	6
98.4.a.c.1.1		1	21.17	even	6
98.4.c.e.67.1		2	21.20	even	2
98.4.c.e.79.1		2	21.5	even	6
112.4.i.b.65.1		2	84.23	even	6
112.4.i.b.81.1		2	12.11	even	2
126.4.g.c.37.1		2	7.2	even	3	inner
126.4.g.c.109.1		2	1.1	even	1	trivial
350.4.e.b.51.1		2	105.44	odd	6
350.4.e.b.151.1		2	15.14	odd	2
350.4.j.d.149.1		4	105.23	even	12
350.4.j.d.149.2		4	105.2	even	12
350.4.j.d.249.1		4	15.2	even	4
350.4.j.d.249.2		4	15.8	even	4
448.4.i.c.65.1		2	168.149	odd	6
448.4.i.c.193.1		2	24.5	odd	2
448.4.i.d.65.1		2	168.107	even	6
448.4.i.d.193.1		2	24.11	even	2
784.4.a.j.1.1		1	84.59	odd	6
784.4.a.l.1.1		1	84.11	even	6
882.4.a.k.1.1		1	7.4	even	3
882.4.a.p.1.1		1	7.3	odd	6
882.4.g.d.361.1		2	7.6	odd	2
882.4.g.d.667.1		2	7.5	odd	6
2450.4.a.bf.1.1		1	105.59	even	6
2450.4.a.bh.1.1		1	105.74	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	126.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(3.50000 + 6.06218i) q^{5} +(-10.0000 - 15.5885i) q^{7} +8.00000 q^{8} +(7.00000 - 12.1244i) q^{10} +(17.5000 - 30.3109i) q^{11} +66.0000 q^{13} +(-17.0000 + 32.9090i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(29.5000 - 51.0955i) q^{17} +(-68.5000 - 118.645i) q^{19} -28.0000 q^{20} -70.0000 q^{22} +(-3.50000 - 6.06218i) q^{23} +(38.0000 - 65.8179i) q^{25} +(-66.0000 - 114.315i) q^{26} +(74.0000 - 3.46410i) q^{28} -106.000 q^{29} +(-37.5000 + 64.9519i) q^{31} +(-16.0000 + 27.7128i) q^{32} -118.000 q^{34} +(59.5000 - 115.181i) q^{35} +(-5.50000 - 9.52628i) q^{37} +(-137.000 + 237.291i) q^{38} +(28.0000 + 48.4974i) q^{40} +498.000 q^{41} +260.000 q^{43} +(70.0000 + 121.244i) q^{44} +(-7.00000 + 12.1244i) q^{46} +(-85.5000 - 148.090i) q^{47} +(-143.000 + 311.769i) q^{49} -152.000 q^{50} +(-132.000 + 228.631i) q^{52} +(-208.500 + 361.133i) q^{53} +245.000 q^{55} +(-80.0000 - 124.708i) q^{56} +(106.000 + 183.597i) q^{58} +(-8.50000 + 14.7224i) q^{59} +(-25.5000 - 44.1673i) q^{61} +150.000 q^{62} +64.0000 q^{64} +(231.000 + 400.104i) q^{65} +(-219.500 + 380.185i) q^{67} +(118.000 + 204.382i) q^{68} +(-259.000 + 12.1244i) q^{70} +784.000 q^{71} +(-147.500 + 255.477i) q^{73} +(-11.0000 + 19.0526i) q^{74} +548.000 q^{76} +(-647.500 + 30.3109i) q^{77} +(247.500 + 428.683i) q^{79} +(56.0000 - 96.9948i) q^{80} +(-498.000 - 862.561i) q^{82} -932.000 q^{83} +413.000 q^{85} +(-260.000 - 450.333i) q^{86} +(140.000 - 242.487i) q^{88} +(-436.500 - 756.040i) q^{89} +(-660.000 - 1028.84i) q^{91} +28.0000 q^{92} +(-171.000 + 296.181i) q^{94} +(479.500 - 830.518i) q^{95} -290.000 q^{97} +(683.000 - 64.0859i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 4 q^{4} + 7 q^{5} - 20 q^{7} + 16 q^{8} + 14 q^{10} + 35 q^{11} + 132 q^{13} - 34 q^{14} - 16 q^{16} + 59 q^{17} - 137 q^{19} - 56 q^{20} - 140 q^{22} - 7 q^{23} + 76 q^{25} - 132 q^{26}+ \cdots + 1366 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 4 * q^4 + 7 * q^5 - 20 * q^7 + 16 * q^8 + 14 * q^10 + 35 * q^11 + 132 * q^13 - 34 * q^14 - 16 * q^16 + 59 * q^17 - 137 * q^19 - 56 * q^20 - 140 * q^22 - 7 * q^23 + 76 * q^25 - 132 * q^26 + 148 * q^28 - 212 * q^29 - 75 * q^31 - 32 * q^32 - 236 * q^34 + 119 * q^35 - 11 * q^37 - 274 * q^38 + 56 * q^40 + 996 * q^41 + 520 * q^43 + 140 * q^44 - 14 * q^46 - 171 * q^47 - 286 * q^49 - 304 * q^50 - 264 * q^52 - 417 * q^53 + 490 * q^55 - 160 * q^56 + 212 * q^58 - 17 * q^59 - 51 * q^61 + 300 * q^62 + 128 * q^64 + 462 * q^65 - 439 * q^67 + 236 * q^68 - 518 * q^70 + 1568 * q^71 - 295 * q^73 - 22 * q^74 + 1096 * q^76 - 1295 * q^77 + 495 * q^79 + 112 * q^80 - 996 * q^82 - 1864 * q^83 + 826 * q^85 - 520 * q^86 + 280 * q^88 - 873 * q^89 - 1320 * q^91 + 56 * q^92 - 342 * q^94 + 959 * q^95 - 580 * q^97 + 1366 * q^98

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