LMFDB - Embedded newform 126.4.g.b.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,4,Mod(37,126)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
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.b.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-3.00000 - 5.19615i) q^{5} +(-3.50000 + 18.1865i) q^{7} +8.00000 q^{8} +O(q^{10})$	\(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-3.00000 - 5.19615i) q^{5} +(-3.50000 + 18.1865i) q^{7} +8.00000 q^{8} +(-6.00000 + 10.3923i) q^{10} +(-15.0000 + 25.9808i) q^{11} +53.0000 q^{13} +(35.0000 - 12.1244i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(-42.0000 + 72.7461i) q^{17} +(48.5000 + 84.0045i) q^{19} +24.0000 q^{20} +60.0000 q^{22} +(42.0000 + 72.7461i) q^{23} +(44.5000 - 77.0763i) q^{25} +(-53.0000 - 91.7987i) q^{26} +(-56.0000 - 48.4974i) q^{28} +180.000 q^{29} +(-89.5000 + 155.019i) q^{31} +(-16.0000 + 27.7128i) q^{32} +168.000 q^{34} +(105.000 - 36.3731i) q^{35} +(72.5000 + 125.574i) q^{37} +(97.0000 - 168.009i) q^{38} +(-24.0000 - 41.5692i) q^{40} -126.000 q^{41} -325.000 q^{43} +(-60.0000 - 103.923i) q^{44} +(84.0000 - 145.492i) q^{46} +(-183.000 - 316.965i) q^{47} +(-318.500 - 127.306i) q^{49} -178.000 q^{50} +(-106.000 + 183.597i) q^{52} +(-384.000 + 665.108i) q^{53} +180.000 q^{55} +(-28.0000 + 145.492i) q^{56} +(-180.000 - 311.769i) q^{58} +(-132.000 + 228.631i) q^{59} +(-409.000 - 708.409i) q^{61} +358.000 q^{62} +64.0000 q^{64} +(-159.000 - 275.396i) q^{65} +(261.500 - 452.931i) q^{67} +(-168.000 - 290.985i) q^{68} +(-168.000 - 145.492i) q^{70} +342.000 q^{71} +(21.5000 - 37.2391i) q^{73} +(145.000 - 251.147i) q^{74} -388.000 q^{76} +(-420.000 - 363.731i) q^{77} +(585.500 + 1014.12i) q^{79} +(-48.0000 + 83.1384i) q^{80} +(126.000 + 218.238i) q^{82} +810.000 q^{83} +504.000 q^{85} +(325.000 + 562.917i) q^{86} +(-120.000 + 207.846i) q^{88} +(-300.000 - 519.615i) q^{89} +(-185.500 + 963.886i) q^{91} -336.000 q^{92} +(-366.000 + 633.931i) q^{94} +(291.000 - 504.027i) q^{95} +386.000 q^{97} +(98.0000 + 678.964i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 4 q^{4} - 6 q^{5} - 7 q^{7} + 16 q^{8}+O(q^{10}) $ 2 * q - 2 * q^2 - 4 * q^4 - 6 * q^5 - 7 * q^7 + 16 * q^8	$ 2 q - 2 q^{2} - 4 q^{4} - 6 q^{5} - 7 q^{7} + 16 q^{8} - 12 q^{10} - 30 q^{11} + 106 q^{13} + 70 q^{14} - 16 q^{16} - 84 q^{17} + 97 q^{19} + 48 q^{20} + 120 q^{22} + 84 q^{23} + 89 q^{25} - 106 q^{26} - 112 q^{28} + 360 q^{29} - 179 q^{31} - 32 q^{32} + 336 q^{34} + 210 q^{35} + 145 q^{37} + 194 q^{38} - 48 q^{40} - 252 q^{41} - 650 q^{43} - 120 q^{44} + 168 q^{46} - 366 q^{47} - 637 q^{49} - 356 q^{50} - 212 q^{52} - 768 q^{53} + 360 q^{55} - 56 q^{56} - 360 q^{58} - 264 q^{59} - 818 q^{61} + 716 q^{62} + 128 q^{64} - 318 q^{65} + 523 q^{67} - 336 q^{68} - 336 q^{70} + 684 q^{71} + 43 q^{73} + 290 q^{74} - 776 q^{76} - 840 q^{77} + 1171 q^{79} - 96 q^{80} + 252 q^{82} + 1620 q^{83} + 1008 q^{85} + 650 q^{86} - 240 q^{88} - 600 q^{89} - 371 q^{91} - 672 q^{92} - 732 q^{94} + 582 q^{95} + 772 q^{97} + 196 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 - 4 * q^4 - 6 * q^5 - 7 * q^7 + 16 * q^8 - 12 * q^10 - 30 * q^11 + 106 * q^13 + 70 * q^14 - 16 * q^16 - 84 * q^17 + 97 * q^19 + 48 * q^20 + 120 * q^22 + 84 * q^23 + 89 * q^25 - 106 * q^26 - 112 * q^28 + 360 * q^29 - 179 * q^31 - 32 * q^32 + 336 * q^34 + 210 * q^35 + 145 * q^37 + 194 * q^38 - 48 * q^40 - 252 * q^41 - 650 * q^43 - 120 * q^44 + 168 * q^46 - 366 * q^47 - 637 * q^49 - 356 * q^50 - 212 * q^52 - 768 * q^53 + 360 * q^55 - 56 * q^56 - 360 * q^58 - 264 * q^59 - 818 * q^61 + 716 * q^62 + 128 * q^64 - 318 * q^65 + 523 * q^67 - 336 * q^68 - 336 * q^70 + 684 * q^71 + 43 * q^73 + 290 * q^74 - 776 * q^76 - 840 * q^77 + 1171 * q^79 - 96 * q^80 + 252 * q^82 + 1620 * q^83 + 1008 * q^85 + 650 * q^86 - 240 * q^88 - 600 * q^89 - 371 * q^91 - 672 * q^92 - 732 * q^94 + 582 * q^95 + 772 * q^97 + 196 * q^98

Display 100 coefficients 10 coefficients

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
$5$	−3.00000	−	5.19615i	−0.268328	−	0.464758i	0.700102	−	0.714043i	$-0.253138\pi$
$5$	−3.00000	−	5.19615i	−0.268328	−	0.464758i	−0.968430	+	0.249285i	$0.919804\pi$
$6$		0			0
$7$	−3.50000	+	18.1865i	−0.188982	+	0.981981i
$7$	−3.50000	+	18.1865i	−0.188982	+	0.981981i
$8$	8.00000			0.353553
$9$		0			0
$10$	−6.00000	+	10.3923i	−0.189737	+	0.328634i
$11$	−15.0000	+	25.9808i	−0.411152	+	0.712136i	−0.995016	−	0.0997155i	$-0.968207\pi$
$11$	−15.0000	+	25.9808i	−0.411152	+	0.712136i	0.583864	+	0.811851i	$0.301540\pi$
$12$		0			0
$13$	53.0000			1.13074			0.565368	−	0.824839i	$-0.308734\pi$
$13$	53.0000			1.13074			0.565368	+	0.824839i	$0.308734\pi$
$14$	35.0000	−	12.1244i	0.668153	−	0.231455i
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−42.0000	+	72.7461i	−0.599206	+	1.03785i	0.393733	+	0.919225i	$0.371183\pi$
$17$	−42.0000	+	72.7461i	−0.599206	+	1.03785i	−0.992939	+	0.118630i	$0.962150\pi$
$18$		0			0
$19$	48.5000	+	84.0045i	0.585614	+	1.01431i	0.994799	+	0.101861i	$0.0324798\pi$
$19$	48.5000	+	84.0045i	0.585614	+	1.01431i	−0.409185	+	0.912452i	$0.634187\pi$
$20$	24.0000			0.268328
$21$		0			0
$22$	60.0000			0.581456
$23$	42.0000	+	72.7461i	0.380765	+	0.659505i	0.991172	−	0.132583i	$-0.0423272\pi$
$23$	42.0000	+	72.7461i	0.380765	+	0.659505i	−0.610406	+	0.792088i	$0.708994\pi$
$24$		0			0
$25$	44.5000	−	77.0763i	0.356000	−	0.616610i
$26$	−53.0000	−	91.7987i	−0.399775	−	0.692431i
$27$		0			0
$28$	−56.0000	−	48.4974i	−0.377964	−	0.327327i
$29$	180.000			1.15259			0.576296	−	0.817241i	$-0.304498\pi$
$29$	180.000			1.15259			0.576296	+	0.817241i	$0.304498\pi$
$30$		0			0
$31$	−89.5000	+	155.019i	−0.518538	+	0.898134i	0.481230	+	0.876594i	$0.340190\pi$
$31$	−89.5000	+	155.019i	−0.518538	+	0.898134i	−0.999768	+	0.0215397i	$0.993143\pi$
$32$	−16.0000	+	27.7128i	−0.0883883	+	0.153093i
$33$		0			0
$34$	168.000			0.847405
$35$	105.000	−	36.3731i	0.507093	−	0.175662i
$36$		0			0
$37$	72.5000	+	125.574i	0.322133	+	0.557951i	0.980928	−	0.194372i	$-0.0622668\pi$
$37$	72.5000	+	125.574i	0.322133	+	0.557951i	−0.658795	+	0.752323i	$0.728933\pi$
$38$	97.0000	−	168.009i	0.414092	−	0.717228i
$39$		0			0
$40$	−24.0000	−	41.5692i	−0.0948683	−	0.164317i
$41$	−126.000			−0.479949			−0.239974	−	0.970779i	$-0.577139\pi$
$41$	−126.000			−0.479949			−0.239974	+	0.970779i	$0.577139\pi$
$42$		0			0
$43$	−325.000			−1.15261			−0.576303	−	0.817236i	$-0.695505\pi$
$43$	−325.000			−1.15261			−0.576303	+	0.817236i	$0.695505\pi$
$44$	−60.0000	−	103.923i	−0.205576	−	0.356068i
$45$		0			0
$46$	84.0000	−	145.492i	0.269242	−	0.466341i
$47$	−183.000	−	316.965i	−0.567942	−	0.983705i	−0.996769	−	0.0803184i	$-0.974406\pi$
$47$	−183.000	−	316.965i	−0.567942	−	0.983705i	0.428827	−	0.903387i	$-0.358927\pi$
$48$		0			0
$49$	−318.500	−	127.306i	−0.928571	−	0.371154i
$50$	−178.000			−0.503460
$51$		0			0
$52$	−106.000	+	183.597i	−0.282684	+	0.489623i
$53$	−384.000	+	665.108i	−0.995216	+	1.72376i	−0.413000	+	0.910731i	$0.635519\pi$
$53$	−384.000	+	665.108i	−0.995216	+	1.72376i	−0.582217	+	0.813034i	$0.697814\pi$
$54$		0			0
$55$	180.000			0.441294
$56$	−28.0000	+	145.492i	−0.0668153	+	0.347183i
$57$		0			0
$58$	−180.000	−	311.769i	−0.407503	−	0.705815i
$59$	−132.000	+	228.631i	−0.291270	+	0.504495i	−0.974110	−	0.226073i	$-0.927411\pi$
$59$	−132.000	+	228.631i	−0.291270	+	0.504495i	0.682840	+	0.730568i	$0.260745\pi$
$60$		0			0
$61$	−409.000	−	708.409i	−0.858477	−	1.48693i	−0.873382	−	0.487036i	$-0.838078\pi$
$61$	−409.000	−	708.409i	−0.858477	−	1.48693i	0.0149048	−	0.999889i	$-0.495255\pi$
$62$	358.000			0.733323
$63$		0			0
$64$	64.0000			0.125000
$65$	−159.000	−	275.396i	−0.303408	−	0.525518i
$66$		0			0
$67$	261.500	−	452.931i	0.476826	−	0.825886i	−0.522822	−	0.852442i	$-0.675121\pi$
$67$	261.500	−	452.931i	0.476826	−	0.825886i	0.999647	+	0.0265560i	$0.00845402\pi$
$68$	−168.000	−	290.985i	−0.299603	−	0.518927i
$69$		0			0
$70$	−168.000	−	145.492i	−0.286855	−	0.248424i
$71$	342.000			0.571661			0.285831	−	0.958280i	$-0.407731\pi$
$71$	342.000			0.571661			0.285831	+	0.958280i	$0.407731\pi$
$72$		0			0
$73$	21.5000	−	37.2391i	0.0344710	−	0.0597056i	−0.848275	−	0.529556i	$-0.822359\pi$
$73$	21.5000	−	37.2391i	0.0344710	−	0.0597056i	0.882746	+	0.469850i	$0.155692\pi$
$74$	145.000	−	251.147i	0.227783	−	0.394531i
$75$		0			0
$76$	−388.000			−0.585614
$77$	−420.000	−	363.731i	−0.621603	−	0.538324i
$78$		0			0
$79$	585.500	+	1014.12i	0.833847	+	1.44427i	0.894966	+	0.446135i	$0.147200\pi$
$79$	585.500	+	1014.12i	0.833847	+	1.44427i	−0.0611191	+	0.998130i	$0.519467\pi$
$80$	−48.0000	+	83.1384i	−0.0670820	+	0.116190i
$81$		0			0
$82$	126.000	+	218.238i	0.169687	+	0.293907i
$83$	810.000			1.07119			0.535597	−	0.844474i	$-0.320087\pi$
$83$	810.000			1.07119			0.535597	+	0.844474i	$0.320087\pi$
$84$		0			0
$85$	504.000			0.643135
$86$	325.000	+	562.917i	0.407508	+	0.705824i
$87$		0			0
$88$	−120.000	+	207.846i	−0.145364	+	0.251778i
$89$	−300.000	−	519.615i	−0.357303	−	0.618866i	0.630207	−	0.776428i	$-0.282970\pi$
$89$	−300.000	−	519.615i	−0.357303	−	0.618866i	−0.987509	+	0.157561i	$0.949637\pi$
$90$		0			0
$91$	−185.500	+	963.886i	−0.213689	+	1.11036i
$92$	−336.000			−0.380765
$93$		0			0
$94$	−366.000	+	633.931i	−0.401596	+	0.695585i
$95$	291.000	−	504.027i	0.314273	−	0.544337i
$96$		0			0
$97$	386.000			0.404045			0.202022	−	0.979381i	$-0.435249\pi$
$97$	386.000			0.404045			0.202022	+	0.979381i	$0.435249\pi$
$98$	98.0000	+	678.964i	0.101015	+	0.699854i
$99$		0			0
$100$	178.000	+	308.305i	0.178000	+	0.308305i
$101$	309.000	−	535.204i	0.304422	−	0.527275i	−0.672710	−	0.739906i	$-0.734870\pi$
$101$	309.000	−	535.204i	0.304422	−	0.527275i	0.977133	+	0.212631i	$0.0682033\pi$
$102$		0			0
$103$	−737.500	−	1277.39i	−0.705515	−	1.22199i	−0.966505	−	0.256646i	$-0.917382\pi$
$103$	−737.500	−	1277.39i	−0.705515	−	1.22199i	0.260991	−	0.965341i	$-0.415951\pi$
$104$	424.000			0.399775
$105$		0			0
$106$	1536.00			1.40745
$107$	942.000	+	1631.59i	0.851090	+	1.47413i	0.880226	+	0.474555i	$0.157391\pi$
$107$	942.000	+	1631.59i	0.851090	+	1.47413i	−0.0291364	+	0.999575i	$0.509276\pi$
$108$		0			0
$109$	−206.500	+	357.668i	−0.181460	+	0.314298i	−0.942378	−	0.334550i	$-0.891416\pi$
$109$	−206.500	+	357.668i	−0.181460	+	0.314298i	0.760918	+	0.648848i	$0.224749\pi$
$110$	−180.000	−	311.769i	−0.156021	−	0.270237i
$111$		0			0
$112$	280.000	−	96.9948i	0.236228	−	0.0818317i
$113$	882.000			0.734262			0.367131	−	0.930169i	$-0.380340\pi$
$113$	882.000			0.734262			0.367131	+	0.930169i	$0.380340\pi$
$114$		0			0
$115$	252.000	−	436.477i	0.204340	−	0.353928i
$116$	−360.000	+	623.538i	−0.288148	+	0.499087i
$117$		0			0
$118$	528.000			0.411918
$119$	−1176.00	−	1018.45i	−0.905914	−	0.784544i
$120$		0			0
$121$	215.500	+	373.257i	0.161908	+	0.280433i
$122$	−818.000	+	1416.82i	−0.607035	+	1.05142i
$123$		0			0
$124$	−358.000	−	620.074i	−0.259269	−	0.449067i
$125$	−1284.00			−0.918756
$126$		0			0
$127$	2483.00			1.73489			0.867443	−	0.497536i	$-0.165762\pi$
$127$	2483.00			1.73489			0.867443	+	0.497536i	$0.165762\pi$
$128$	−64.0000	−	110.851i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−318.000	+	550.792i	−0.214542	+	0.371597i
$131$	1059.00	+	1834.24i	0.706300	+	1.22335i	0.966220	+	0.257717i	$0.0829702\pi$
$131$	1059.00	+	1834.24i	0.706300	+	1.22335i	−0.259921	+	0.965630i	$0.583696\pi$
$132$		0			0
$133$	−1697.50	+	588.031i	−1.10671	+	0.383374i
$134$	−1046.00			−0.674333
$135$		0			0
$136$	−336.000	+	581.969i	−0.211851	+	0.366937i
$137$	1506.00	−	2608.47i	0.939170	−	1.62669i	0.172146	−	0.985071i	$-0.444930\pi$
$137$	1506.00	−	2608.47i	0.939170	−	1.62669i	0.767024	−	0.641618i	$-0.221737\pi$
$138$		0			0
$139$	−37.0000			−0.0225777			−0.0112888	−	0.999936i	$-0.503593\pi$
$139$	−37.0000			−0.0225777			−0.0112888	+	0.999936i	$0.503593\pi$
$140$	−84.0000	+	436.477i	−0.0507093	+	0.263493i
$141$		0			0
$142$	−342.000	−	592.361i	−0.202113	−	0.350069i
$143$	−795.000	+	1376.98i	−0.464904	+	0.805237i
$144$		0			0
$145$	−540.000	−	935.307i	−0.309273	−	0.535676i
$146$	−86.0000			−0.0487494
$147$		0			0
$148$	−580.000			−0.322133
$149$	−822.000	−	1423.75i	−0.451952	−	0.782804i	0.546555	−	0.837423i	$-0.315939\pi$
$149$	−822.000	−	1423.75i	−0.451952	−	0.782804i	−0.998507	+	0.0546191i	$0.982606\pi$
$150$		0			0
$151$	−544.000	+	942.236i	−0.293179	+	0.507802i	−0.974560	−	0.224128i	$-0.928047\pi$
$151$	−544.000	+	942.236i	−0.293179	+	0.507802i	0.681380	+	0.731930i	$0.261380\pi$
$152$	388.000	+	672.036i	0.207046	+	0.358614i
$153$		0			0
$154$	−210.000	+	1091.19i	−0.109885	+	0.570979i
$155$	1074.00			0.556553
$156$		0			0
$157$	−253.000	+	438.209i	−0.128609	+	0.222757i	−0.923138	−	0.384469i	$-0.874385\pi$
$157$	−253.000	+	438.209i	−0.128609	+	0.222757i	0.794529	+	0.607226i	$0.207718\pi$
$158$	1171.00	−	2028.23i	0.589619	−	1.02125i
$159$		0			0
$160$	192.000			0.0948683
$161$	−1470.00	+	509.223i	−0.719579	+	0.249270i
$162$		0			0
$163$	−922.000	−	1596.95i	−0.443047	−	0.767379i	0.554867	−	0.831939i	$-0.312769\pi$
$163$	−922.000	−	1596.95i	−0.443047	−	0.767379i	−0.997914	+	0.0645596i	$0.979436\pi$
$164$	252.000	−	436.477i	0.119987	−	0.207824i
$165$		0			0
$166$	−810.000	−	1402.96i	−0.378724	−	0.655969i
$167$	−162.000			−0.0750655			−0.0375327	−	0.999295i	$-0.511950\pi$
$167$	−162.000			−0.0750655			−0.0375327	+	0.999295i	$0.511950\pi$
$168$		0			0
$169$	612.000			0.278562
$170$	−504.000	−	872.954i	−0.227383	−	0.393838i
$171$		0			0
$172$	650.000	−	1125.83i	0.288151	−	0.499093i
$173$	−1362.00	−	2359.05i	−0.598560	−	1.03674i	−0.993034	−	0.117830i	$-0.962406\pi$
$173$	−1362.00	−	2359.05i	−0.598560	−	1.03674i	0.394473	−	0.918907i	$-0.370927\pi$
$174$		0			0
$175$	1246.00	+	1079.07i	0.538221	+	0.466113i
$176$	480.000			0.205576
$177$		0			0
$178$	−600.000	+	1039.23i	−0.252651	+	0.437605i
$179$	−627.000	+	1086.00i	−0.261811	+	0.453470i	−0.966723	−	0.255825i	$-0.917653\pi$
$179$	−627.000	+	1086.00i	−0.261811	+	0.453470i	0.704912	+	0.709295i	$0.250986\pi$
$180$		0			0
$181$	−1807.00			−0.742062			−0.371031	−	0.928620i	$-0.620996\pi$
$181$	−1807.00			−0.742062			−0.371031	+	0.928620i	$0.620996\pi$
$182$	1855.00	−	642.591i	0.755504	−	0.261714i
$183$		0			0
$184$	336.000	+	581.969i	0.134621	+	0.233170i
$185$	435.000	−	753.442i	0.172875	−	0.299428i
$186$		0			0
$187$	−1260.00	−	2182.38i	−0.492729	−	0.853432i
$188$	1464.00			0.567942
$189$		0			0
$190$	−1164.00			−0.444450
$191$	357.000	+	618.342i	0.135244	+	0.234250i	0.925691	−	0.378281i	$-0.123485\pi$
$191$	357.000	+	618.342i	0.135244	+	0.234250i	−0.790447	+	0.612531i	$0.790151\pi$
$192$		0			0
$193$	1854.50	−	3212.09i	0.691657	−	1.19799i	−0.279637	−	0.960106i	$-0.590214\pi$
$193$	1854.50	−	3212.09i	0.691657	−	1.19799i	0.971295	−	0.237880i	$-0.0764524\pi$
$194$	−386.000	−	668.572i	−0.142851	−	0.247426i
$195$		0			0
$196$	1078.00	−	848.705i	0.392857	−	0.309295i
$197$	1044.00			0.377573			0.188787	−	0.982018i	$-0.439545\pi$
$197$	1044.00			0.377573			0.188787	+	0.982018i	$0.439545\pi$
$198$		0			0
$199$	68.0000	−	117.779i	0.0242231	−	0.0419556i	−0.853660	−	0.520831i	$-0.825622\pi$
$199$	68.0000	−	117.779i	0.0242231	−	0.0419556i	0.877883	+	0.478875i	$0.158955\pi$
$200$	356.000	−	616.610i	0.125865	−	0.218005i
$201$		0			0
$202$	−1236.00			−0.430518
$203$	−630.000	+	3273.58i	−0.217819	+	1.13182i
$204$		0			0
$205$	378.000	+	654.715i	0.128784	+	0.223060i
$206$	−1475.00	+	2554.77i	−0.498874	+	0.864076i
$207$		0			0
$208$	−424.000	−	734.390i	−0.141342	−	0.244811i
$209$	−2910.00			−0.963105
$210$		0			0
$211$	1484.00			0.484184			0.242092	−	0.970253i	$-0.422166\pi$
$211$	1484.00			0.484184			0.242092	+	0.970253i	$0.422166\pi$
$212$	−1536.00	−	2660.43i	−0.497608	−	0.861882i
$213$		0			0
$214$	1884.00	−	3263.18i	0.601811	−	1.04237i
$215$	975.000	+	1688.75i	0.309277	+	0.535683i
$216$		0			0
$217$	−2506.00	−	2170.26i	−0.783956	−	0.678925i
$218$	826.000			0.256623
$219$		0			0
$220$	−360.000	+	623.538i	−0.110324	+	0.191086i
$221$	−2226.00	+	3855.55i	−0.677543	+	1.17354i
$222$		0			0
$223$	−2032.00			−0.610192			−0.305096	−	0.952322i	$-0.598689\pi$
$223$	−2032.00			−0.610192			−0.305096	+	0.952322i	$0.598689\pi$
$224$	−448.000	−	387.979i	−0.133631	−	0.115728i
$225$		0			0
$226$	−882.000	−	1527.67i	−0.259601	−	0.449642i
$227$	3099.00	−	5367.63i	0.906114	−	1.56944i	0.0866989	−	0.996235i	$-0.472368\pi$
$227$	3099.00	−	5367.63i	0.906114	−	1.56944i	0.819415	−	0.573201i	$-0.194298\pi$
$228$		0			0
$229$	2295.50	+	3975.92i	0.662406	+	1.14732i	0.979982	+	0.199088i	$0.0637978\pi$
$229$	2295.50	+	3975.92i	0.662406	+	1.14732i	−0.317576	+	0.948233i	$0.602869\pi$
$230$	−1008.00			−0.288981
$231$		0			0
$232$	1440.00			0.407503
$233$	2265.00	+	3923.10i	0.636846	+	1.10305i	0.986121	+	0.166029i	$0.0530946\pi$
$233$	2265.00	+	3923.10i	0.636846	+	1.10305i	−0.349275	+	0.937020i	$0.613572\pi$
$234$		0			0
$235$	−1098.00	+	1901.79i	−0.304790	+	0.527912i
$236$	−528.000	−	914.523i	−0.145635	−	0.252247i
$237$		0			0
$238$	−588.000	+	3055.34i	−0.160144	+	0.832135i
$239$	−1530.00			−0.414090			−0.207045	−	0.978331i	$-0.566385\pi$
$239$	−1530.00			−0.414090			−0.207045	+	0.978331i	$0.566385\pi$
$240$		0			0
$241$	−2767.00	+	4792.58i	−0.739577	+	1.28099i	0.213108	+	0.977029i	$0.431641\pi$
$241$	−2767.00	+	4792.58i	−0.739577	+	1.28099i	−0.952686	+	0.303957i	$0.901692\pi$
$242$	431.000	−	746.514i	0.114486	−	0.198296i
$243$		0			0
$244$	3272.00			0.858477
$245$	294.000	+	2036.89i	0.0766652	+	0.531152i
$246$		0			0
$247$	2570.50	+	4452.24i	0.662174	+	1.14692i
$248$	−716.000	+	1240.15i	−0.183331	+	0.317538i
$249$		0			0
$250$	1284.00	+	2223.95i	0.324829	+	0.562621i
$251$	468.000			0.117689			0.0588444	−	0.998267i	$-0.481258\pi$
$251$	468.000			0.117689			0.0588444	+	0.998267i	$0.481258\pi$
$252$		0			0
$253$	−2520.00			−0.626210
$254$	−2483.00	−	4300.68i	−0.613375	−	1.06240i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−1245.00	−	2156.40i	−0.302183	−	0.523396i	0.674447	−	0.738323i	$-0.264382\pi$
$257$	−1245.00	−	2156.40i	−0.302183	−	0.523396i	−0.976630	+	0.214927i	$0.931049\pi$
$258$		0			0
$259$	−2537.50	+	879.016i	−0.608774	+	0.210886i
$260$	1272.00			0.303408
$261$		0			0
$262$	2118.00	−	3668.48i	0.499429	−	0.865037i
$263$	786.000	−	1361.39i	0.184285	−	0.319190i	−0.759051	−	0.651032i	$-0.774337\pi$
$263$	786.000	−	1361.39i	0.184285	−	0.319190i	0.943335	+	0.331841i	$0.107670\pi$
$264$		0			0
$265$	4608.00			1.06818
$266$	2716.00	+	2352.12i	0.626048	+	0.542173i
$267$		0			0
$268$	1046.00	+	1811.73i	0.238413	+	0.412943i
$269$	903.000	−	1564.04i	0.204672	−	0.354503i	−0.745356	−	0.666667i	$-0.767720\pi$
$269$	903.000	−	1564.04i	0.204672	−	0.354503i	0.950028	+	0.312164i	$0.101054\pi$
$270$		0			0
$271$	3056.00	+	5293.15i	0.685014	+	1.18648i	0.973432	+	0.228975i	$0.0735372\pi$
$271$	3056.00	+	5293.15i	0.685014	+	1.18648i	−0.288418	+	0.957504i	$0.593129\pi$
$272$	1344.00			0.299603
$273$		0			0
$274$	−6024.00			−1.32819
$275$	1335.00	+	2312.29i	0.292740	+	0.507041i
$276$		0			0
$277$	2115.50	−	3664.15i	0.458874	−	0.794793i	−0.540028	−	0.841647i	$-0.681586\pi$
$277$	2115.50	−	3664.15i	0.458874	−	0.794793i	0.998902	+	0.0468542i	$0.0149196\pi$
$278$	37.0000	+	64.0859i	0.00798242	+	0.0138260i
$279$		0			0
$280$	840.000	−	290.985i	0.179284	−	0.0621059i
$281$	3816.00			0.810119			0.405060	−	0.914290i	$-0.367251\pi$
$281$	3816.00			0.810119			0.405060	+	0.914290i	$0.367251\pi$
$282$		0			0
$283$	1998.50	−	3461.50i	0.419783	−	0.727085i	−0.576135	−	0.817355i	$-0.695440\pi$
$283$	1998.50	−	3461.50i	0.419783	−	0.727085i	0.995917	+	0.0902699i	$0.0287730\pi$
$284$	−684.000	+	1184.72i	−0.142915	+	0.247536i
$285$		0			0
$286$	3180.00			0.657473
$287$	441.000	−	2291.50i	0.0907018	−	0.471300i
$288$		0			0
$289$	−1071.50	−	1855.89i	−0.218095	−	0.377751i
$290$	−1080.00	+	1870.61i	−0.218689	+	0.378780i
$291$		0			0
$292$	86.0000	+	148.956i	0.0172355	+	0.0298528i
$293$	−4608.00			−0.918779			−0.459389	−	0.888235i	$-0.651932\pi$
$293$	−4608.00			−0.918779			−0.459389	+	0.888235i	$0.651932\pi$
$294$		0			0
$295$	1584.00			0.312624
$296$	580.000	+	1004.59i	0.113891	+	0.197265i
$297$		0			0
$298$	−1644.00	+	2847.49i	−0.319578	+	0.553526i
$299$	2226.00	+	3855.55i	0.430545	+	0.745726i
$300$		0			0
$301$	1137.50	−	5910.62i	0.217822	−	1.13184i
$302$	2176.00			0.414618
$303$		0			0
$304$	776.000	−	1344.07i	0.146403	−	0.253578i
$305$	−2454.00	+	4250.45i	−0.460707	+	0.797968i
$306$		0			0
$307$	−631.000			−0.117306			−0.0586532	−	0.998278i	$-0.518681\pi$
$307$	−631.000			−0.117306			−0.0586532	+	0.998278i	$0.518681\pi$
$308$	2100.00	−	727.461i	0.388502	−	0.134581i
$309$		0			0
$310$	−1074.00	−	1860.22i	−0.196771	−	0.340818i
$311$	1947.00	−	3372.30i	0.354998	−	0.614874i	−0.632120	−	0.774871i	$-0.717815\pi$
$311$	1947.00	−	3372.30i	0.354998	−	0.614874i	0.987118	+	0.159997i	$0.0511484\pi$
$312$		0			0
$313$	1092.50	+	1892.27i	0.197290	+	0.341716i	0.947649	−	0.319314i	$-0.103453\pi$
$313$	1092.50	+	1892.27i	0.197290	+	0.341716i	−0.750359	+	0.661031i	$0.770119\pi$
$314$	1012.00			0.181880
$315$		0			0
$316$	−4684.00			−0.833847
$317$	1752.00	+	3034.55i	0.310417	+	0.537658i	0.978453	−	0.206471i	$-0.0661981\pi$
$317$	1752.00	+	3034.55i	0.310417	+	0.537658i	−0.668036	+	0.744129i	$0.732865\pi$
$318$		0			0
$319$	−2700.00	+	4676.54i	−0.473890	+	0.820802i
$320$	−192.000	−	332.554i	−0.0335410	−	0.0580948i
$321$		0			0
$322$	2352.00	+	2036.89i	0.407055	+	0.352520i
$323$	−8148.00			−1.40361
$324$		0			0
$325$	2358.50	−	4085.04i	0.402542	−	0.697223i
$326$	−1844.00	+	3193.90i	−0.313281	+	0.542619i
$327$		0			0
$328$	−1008.00			−0.169687
$329$	6405.00	−	2218.76i	1.07331	−	0.371806i
$330$		0			0
$331$	−1472.50	−	2550.44i	−0.244519	−	0.423520i	0.717477	−	0.696582i	$-0.245297\pi$
$331$	−1472.50	−	2550.44i	−0.244519	−	0.423520i	−0.961996	+	0.273062i	$0.911964\pi$
$332$	−1620.00	+	2805.92i	−0.267798	+	0.463840i
$333$		0			0
$334$	162.000	+	280.592i	0.0265397	+	0.0459680i
$335$	−3138.00			−0.511783
$336$		0			0
$337$	4277.00			0.691344			0.345672	−	0.938355i	$-0.387651\pi$
$337$	4277.00			0.691344			0.345672	+	0.938355i	$0.387651\pi$
$338$	−612.000	−	1060.02i	−0.0984864	−	0.170583i
$339$		0			0
$340$	−1008.00	+	1745.91i	−0.160784	+	0.278486i
$341$	−2685.00	−	4650.56i	−0.426396	−	0.738539i
$342$		0			0
$343$	3430.00	−	5346.84i	0.539949	−	0.841698i
$344$	−2600.00			−0.407508
$345$		0			0
$346$	−2724.00	+	4718.11i	−0.423246	+	0.733084i
$347$	3594.00	−	6224.99i	0.556012	−	0.963040i	−0.441812	−	0.897107i	$-0.645664\pi$
$347$	3594.00	−	6224.99i	0.556012	−	0.963040i	0.997824	−	0.0659329i	$-0.0210023\pi$
$348$		0			0
$349$	−9406.00			−1.44267			−0.721335	−	0.692587i	$-0.756471\pi$
$349$	−9406.00			−1.44267			−0.721335	+	0.692587i	$0.756471\pi$
$350$	623.000	−	3237.20i	0.0951450	−	0.494388i
$351$		0			0
$352$	−480.000	−	831.384i	−0.0726821	−	0.125889i
$353$	1695.00	−	2935.83i	0.255569	−	0.442658i	−0.709481	−	0.704724i	$-0.751071\pi$
$353$	1695.00	−	2935.83i	0.255569	−	0.442658i	0.965050	+	0.262066i	$0.0844040\pi$
$354$		0			0
$355$	−1026.00	−	1777.08i	−0.153393	−	0.265684i
$356$	2400.00			0.357303
$357$		0			0
$358$	2508.00			0.370257
$359$	−2406.00	−	4167.31i	−0.353715	−	0.612653i	0.633182	−	0.774003i	$-0.281749\pi$
$359$	−2406.00	−	4167.31i	−0.353715	−	0.612653i	−0.986897	+	0.161350i	$0.948415\pi$
$360$		0			0
$361$	−1275.00	+	2208.36i	−0.185887	+	0.321966i
$362$	1807.00	+	3129.82i	0.262359	+	0.454418i
$363$		0			0
$364$	−2968.00	−	2570.36i	−0.427378	−	0.370120i
$365$	−258.000			−0.0369982
$366$		0			0
$367$	3549.50	−	6147.91i	0.504857	−	0.874437i	−0.495128	−	0.868820i	$-0.664879\pi$
$367$	3549.50	−	6147.91i	0.504857	−	0.874437i	0.999984	−	0.00561709i	$-0.00178798\pi$
$368$	672.000	−	1163.94i	0.0951914	−	0.164876i
$369$		0			0
$370$	−1740.00			−0.244482
$371$	−10752.0	−	9311.51i	−1.50463	−	1.30304i
$372$		0			0
$373$	−1481.50	−	2566.03i	−0.205655	−	0.356204i	0.744687	−	0.667414i	$-0.232599\pi$
$373$	−1481.50	−	2566.03i	−0.205655	−	0.356204i	−0.950341	+	0.311210i	$0.899266\pi$
$374$	−2520.00	+	4364.77i	−0.348412	+	0.603467i
$375$		0			0
$376$	−1464.00	−	2535.72i	−0.200798	−	0.347792i
$377$	9540.00			1.30328
$378$		0			0
$379$	−11899.0			−1.61269			−0.806346	−	0.591444i	$-0.798558\pi$
$379$	−11899.0			−1.61269			−0.806346	+	0.591444i	$0.798558\pi$
$380$	1164.00	+	2016.11i	0.157137	+	0.272169i
$381$		0			0
$382$	714.000	−	1236.68i	0.0956320	−	0.165639i
$383$	1284.00	+	2223.95i	0.171304	+	0.296707i	0.938876	−	0.344256i	$-0.111869\pi$
$383$	1284.00	+	2223.95i	0.171304	+	0.296707i	−0.767572	+	0.640963i	$0.778535\pi$
$384$		0			0
$385$	−630.000	+	3273.58i	−0.0833968	+	0.433343i
$386$	−7418.00			−0.978151
$387$		0			0
$388$	−772.000	+	1337.14i	−0.101011	+	0.174957i
$389$	−5073.00	+	8786.69i	−0.661212	+	1.14525i	0.319086	+	0.947726i	$0.396624\pi$
$389$	−5073.00	+	8786.69i	−0.661212	+	1.14525i	−0.980298	+	0.197526i	$0.936709\pi$
$390$		0			0
$391$	−7056.00			−0.912627
$392$	−2548.00	−	1018.45i	−0.328300	−	0.131223i
$393$		0			0
$394$	−1044.00	−	1808.26i	−0.133492	−	0.231215i
$395$	3513.00	−	6084.69i	0.447489	−	0.775074i
$396$		0			0
$397$	3114.50	+	5394.47i	0.393734	+	0.681967i	0.992939	−	0.118629i	$-0.0378499\pi$
$397$	3114.50	+	5394.47i	0.393734	+	0.681967i	−0.599205	+	0.800596i	$0.704517\pi$
$398$	−272.000			−0.0342566
$399$		0			0
$400$	−1424.00			−0.178000
$401$	−1236.00	−	2140.81i	−0.153922	−	0.266601i	0.778744	−	0.627342i	$-0.215857\pi$
$401$	−1236.00	−	2140.81i	−0.153922	−	0.266601i	−0.932666	+	0.360741i	$0.882524\pi$
$402$		0			0
$403$	−4743.50	+	8215.98i	−0.586329	+	1.01555i
$404$	1236.00	+	2140.81i	0.152211	+	0.263637i
$405$		0			0
$406$	6300.00	−	2182.38i	0.770108	−	0.266773i
$407$	−4350.00			−0.529783
$408$		0			0
$409$	3537.50	−	6127.13i	0.427673	−	0.740751i	−0.568993	−	0.822342i	$-0.692667\pi$
$409$	3537.50	−	6127.13i	0.427673	−	0.740751i	0.996666	+	0.0815915i	$0.0260003\pi$
$410$	756.000	−	1309.43i	0.0910639	−	0.157727i
$411$		0			0
$412$	5900.00			0.705515
$413$	−3696.00	−	3200.83i	−0.440359	−	0.381362i
$414$		0			0
$415$	−2430.00	−	4208.88i	−0.287431	−	0.497846i
$416$	−848.000	+	1468.78i	−0.0999438	+	0.173108i
$417$		0			0
$418$	2910.00	+	5040.27i	0.340509	+	0.589779i
$419$	4158.00			0.484801			0.242400	−	0.970176i	$-0.422065\pi$
$419$	4158.00			0.484801			0.242400	+	0.970176i	$0.422065\pi$
$420$		0			0
$421$	−6595.00			−0.763469			−0.381735	−	0.924272i	$-0.624673\pi$
$421$	−6595.00			−0.763469			−0.381735	+	0.924272i	$0.624673\pi$
$422$	−1484.00	−	2570.36i	−0.171185	−	0.296501i
$423$		0			0
$424$	−3072.00	+	5320.86i	−0.351862	+	0.609443i
$425$	3738.00	+	6474.41i	0.426634	+	0.738953i
$426$		0			0
$427$	14315.0	−	4958.86i	1.62237	−	0.562005i
$428$	−7536.00			−0.851090
$429$		0			0
$430$	1950.00	−	3377.50i	0.218692	−	0.378785i
$431$	759.000	−	1314.63i	0.0848254	−	0.146922i	−0.820491	−	0.571659i	$-0.806300\pi$
$431$	759.000	−	1314.63i	0.0848254	−	0.146922i	0.905317	+	0.424737i	$0.139633\pi$
$432$		0			0
$433$	8567.00			0.950817			0.475408	−	0.879765i	$-0.342300\pi$
$433$	8567.00			0.950817			0.475408	+	0.879765i	$0.342300\pi$
$434$	−1253.00	+	6510.78i	−0.138585	+	0.720109i
$435$		0			0
$436$	−826.000	−	1430.67i	−0.0907299	−	0.157149i
$437$	−4074.00	+	7056.37i	−0.445963	+	0.772431i
$438$		0			0
$439$	−5320.00	−	9214.51i	−0.578382	−	1.00179i	−0.995665	−	0.0930106i	$-0.970351\pi$
$439$	−5320.00	−	9214.51i	−0.578382	−	1.00179i	0.417283	−	0.908777i	$-0.362982\pi$
$440$	1440.00			0.156021
$441$		0			0
$442$	8904.00			0.958190
$443$	3516.00	+	6089.89i	0.377088	+	0.653136i	0.990637	−	0.136520i	$-0.0435919\pi$
$443$	3516.00	+	6089.89i	0.377088	+	0.653136i	−0.613549	+	0.789657i	$0.710259\pi$
$444$		0			0
$445$	−1800.00	+	3117.69i	−0.191749	+	0.332119i
$446$	2032.00	+	3519.53i	0.215735	+	0.373665i
$447$		0			0
$448$	−224.000	+	1163.94i	−0.0236228	+	0.122748i
$449$	14814.0			1.55705			0.778525	−	0.627613i	$-0.215968\pi$
$449$	14814.0			1.55705			0.778525	+	0.627613i	$0.215968\pi$
$450$		0			0
$451$	1890.00	−	3273.58i	0.197332	−	0.341789i
$452$	−1764.00	+	3055.34i	−0.183565	+	0.317945i
$453$		0			0
$454$	−12396.0			−1.28144
$455$	5565.00	−	1927.77i	0.573387	−	0.198627i
$456$		0			0
$457$	5625.50	+	9743.65i	0.575820	+	0.997350i	0.995952	+	0.0898866i	$0.0286505\pi$
$457$	5625.50	+	9743.65i	0.575820	+	0.997350i	−0.420132	+	0.907463i	$0.638016\pi$
$458$	4591.00	−	7951.85i	0.468392	−	0.811278i
$459$		0			0
$460$	1008.00	+	1745.91i	0.102170	+	0.176964i
$461$	3852.00			0.389166			0.194583	−	0.980886i	$-0.437665\pi$
$461$	3852.00			0.389166			0.194583	+	0.980886i	$0.437665\pi$
$462$		0			0
$463$	−475.000			−0.0476784			−0.0238392	−	0.999716i	$-0.507589\pi$
$463$	−475.000			−0.0476784			−0.0238392	+	0.999716i	$0.507589\pi$
$464$	−1440.00	−	2494.15i	−0.144074	−	0.249543i
$465$		0			0
$466$	4530.00	−	7846.19i	0.450318	−	0.779974i
$467$	2967.00	+	5138.99i	0.293997	+	0.509217i	0.974751	−	0.223295i	$-0.0716812\pi$
$467$	2967.00	+	5138.99i	0.293997	+	0.509217i	−0.680754	+	0.732512i	$0.738348\pi$
$468$		0			0
$469$	7322.00	+	6341.04i	0.720892	+	0.624311i
$470$	4392.00			0.431038
$471$		0			0
$472$	−1056.00	+	1829.05i	−0.102980	+	0.178366i
$473$	4875.00	−	8443.75i	0.473896	−	0.820812i
$474$		0			0
$475$	8633.00			0.833914
$476$	5880.00	−	2036.89i	0.566196	−	0.196136i
$477$		0			0
$478$	1530.00	+	2650.04i	0.146403	+	0.253577i
$479$	−6684.00	+	11577.0i	−0.637578	+	1.10432i	0.348385	+	0.937352i	$0.386730\pi$
$479$	−6684.00	+	11577.0i	−0.637578	+	1.10432i	−0.985963	+	0.166966i	$0.946603\pi$
$480$		0			0
$481$	3842.50	+	6655.41i	0.364247	+	0.630895i
$482$	11068.0			1.04592
$483$		0			0
$484$	−1724.00			−0.161908
$485$	−1158.00	−	2005.71i	−0.108417	−	0.187783i
$486$		0			0
$487$	−3326.50	+	5761.67i	−0.309524	+	0.536111i	−0.978258	−	0.207390i	$-0.933503\pi$
$487$	−3326.50	+	5761.67i	−0.309524	+	0.536111i	0.668734	+	0.743501i	$0.266836\pi$
$488$	−3272.00	−	5667.27i	−0.303517	−	0.525708i
$489$		0			0
$490$	3234.00	−	2546.11i	0.298158	−	0.234738i
$491$	−15444.0			−1.41951			−0.709754	−	0.704450i	$-0.751194\pi$
$491$	−15444.0			−1.41951			−0.709754	+	0.704450i	$0.751194\pi$
$492$		0			0
$493$	−7560.00	+	13094.3i	−0.690640	+	1.19622i
$494$	5141.00	−	8904.47i	0.468228	−	0.810994i
$495$		0			0
$496$	2864.00			0.259269
$497$	−1197.00	+	6219.79i	−0.108034	+	0.561360i
$498$		0			0
$499$	−341.500	−	591.495i	−0.0306366	−	0.0530641i	0.850301	−	0.526297i	$-0.176420\pi$
$499$	−341.500	−	591.495i	−0.0306366	−	0.0530641i	−0.880937	+	0.473233i	$0.843087\pi$
$500$	2568.00	−	4447.91i	0.229689	−	0.397833i
$501$		0			0
$502$	−468.000	−	810.600i	−0.0416093	−	0.0720694i
$503$	−9882.00			−0.875977			−0.437989	−	0.898980i	$-0.644309\pi$
$503$	−9882.00			−0.875977			−0.437989	+	0.898980i	$0.644309\pi$
$504$		0			0
$505$	−3708.00			−0.326740
$506$	2520.00	+	4364.77i	0.221399	+	0.383474i
$507$		0			0
$508$	−4966.00	+	8601.36i	−0.433722	+	0.751228i
$509$	2103.00	+	3642.50i	0.183131	+	0.317193i	0.942945	−	0.332948i	$-0.108043\pi$
$509$	2103.00	+	3642.50i	0.183131	+	0.317193i	−0.759814	+	0.650141i	$0.774710\pi$
$510$		0			0
$511$	602.000	+	521.347i	0.0521153	+	0.0451332i
$512$	512.000			0.0441942
$513$		0			0
$514$	−2490.00	+	4312.81i	−0.213675	+	0.370097i
$515$	−4425.00	+	7664.32i	−0.378619	+	0.655787i
$516$		0			0
$517$	10980.0			0.934042
$518$	4060.00	+	3516.06i	0.344375	+	0.298237i
$519$		0			0
$520$	−1272.00	−	2203.17i	−0.107271	−	0.185799i
$521$	4530.00	−	7846.19i	0.380927	−	0.659785i	−0.610268	−	0.792195i	$-0.708938\pi$
$521$	4530.00	−	7846.19i	0.380927	−	0.659785i	0.991195	+	0.132410i	$0.0422716\pi$
$522$		0			0
$523$	7839.50	+	13578.4i	0.655444	+	1.13526i	0.981782	+	0.190010i	$0.0608520\pi$
$523$	7839.50	+	13578.4i	0.655444	+	1.13526i	−0.326338	+	0.945253i	$0.605815\pi$
$524$	−8472.00			−0.706300
$525$		0			0
$526$	−3144.00			−0.260618
$527$	−7518.00	−	13021.6i	−0.621422	−	1.07633i
$528$		0			0
$529$	2555.50	−	4426.26i	0.210035	−	0.363792i
$530$	−4608.00	−	7981.29i	−0.377658	−	0.654123i
$531$		0			0
$532$	1358.00	−	7056.37i	0.110671	−	0.575061i
$533$	−6678.00			−0.542695
$534$		0			0
$535$	5652.00	−	9789.55i	0.456743	−	0.791101i
$536$	2092.00	−	3623.45i	0.168583	−	0.291995i
$537$		0			0
$538$	−3612.00			−0.289451
$539$	8085.00	−	6365.29i	0.646096	−	0.508668i
$540$		0			0
$541$	3855.50	+	6677.92i	0.306397	+	0.530696i	0.977571	−	0.210604i	$-0.0675431\pi$
$541$	3855.50	+	6677.92i	0.306397	+	0.530696i	−0.671174	+	0.741300i	$0.734210\pi$
$542$	6112.00	−	10586.3i	0.484378	−	0.838967i
$543$		0			0
$544$	−1344.00	−	2327.88i	−0.105926	−	0.183469i
$545$	2478.00			0.194763
$546$		0			0
$547$	4292.00			0.335489			0.167745	−	0.985830i	$-0.446352\pi$
$547$	4292.00			0.335489			0.167745	+	0.985830i	$0.446352\pi$
$548$	6024.00	+	10433.9i	0.469585	+	0.813345i
$549$		0			0
$550$	2670.00	−	4624.58i	0.206999	−	0.358532i
$551$	8730.00	+	15120.8i	0.674974	+	1.16909i
$552$		0			0
$553$	−20492.5	+	7098.81i	−1.57582	+	0.545881i
$554$	−8462.00			−0.648946
$555$		0			0
$556$	74.0000	−	128.172i	0.00564442	−	0.00977643i
$557$	−4929.00	+	8537.28i	−0.374952	+	0.649436i	−0.990320	−	0.138804i	$-0.955674\pi$
$557$	−4929.00	+	8537.28i	−0.374952	+	0.649436i	0.615368	+	0.788240i	$0.289008\pi$
$558$		0			0
$559$	−17225.0			−1.30329
$560$	−1344.00	−	1163.94i	−0.101419	−	0.0878310i
$561$		0			0
$562$	−3816.00	−	6609.51i	−0.286420	−	0.496095i
$563$	−6945.00	+	12029.1i	−0.519888	+	0.900472i	0.479845	+	0.877353i	$0.340693\pi$
$563$	−6945.00	+	12029.1i	−0.519888	+	0.900472i	−0.999733	+	0.0231188i	$0.992640\pi$
$564$		0			0
$565$	−2646.00	−	4583.01i	−0.197023	−	0.341254i
$566$	−7994.00			−0.593662
$567$		0			0
$568$	2736.00			0.202113
$569$	9519.00	+	16487.4i	0.701331	+	1.21474i	0.967999	+	0.250952i	$0.0807437\pi$
$569$	9519.00	+	16487.4i	0.701331	+	1.21474i	−0.266669	+	0.963788i	$0.585923\pi$
$570$		0			0
$571$	4026.50	−	6974.10i	0.295103	−	0.511133i	−0.679906	−	0.733299i	$-0.737979\pi$
$571$	4026.50	−	6974.10i	0.295103	−	0.511133i	0.975009	+	0.222166i	$0.0713127\pi$
$572$	−3180.00	−	5507.92i	−0.232452	−	0.402618i
$573$		0			0
$574$	−4410.00	+	1527.67i	−0.320679	+	0.111087i
$575$	7476.00			0.542210
$576$		0			0
$577$	8568.50	−	14841.1i	0.618217	−	1.07078i	−0.371594	−	0.928395i	$-0.621189\pi$
$577$	8568.50	−	14841.1i	0.618217	−	1.07078i	0.989811	−	0.142388i	$-0.0454781\pi$
$578$	−2143.00	+	3711.78i	−0.154216	+	0.267111i
$579$		0			0
$580$	4320.00			0.309273
$581$	−2835.00	+	14731.1i	−0.202437	+	1.05189i
$582$		0			0
$583$	−11520.0	−	19953.2i	−0.818370	−	1.41746i
$584$	172.000	−	297.913i	0.0121873	−	0.0211091i
$585$		0			0
$586$	4608.00	+	7981.29i	0.324837	+	0.562635i
$587$	−18144.0			−1.27578			−0.637890	−	0.770127i	$-0.720193\pi$
$587$	−18144.0			−1.27578			−0.637890	+	0.770127i	$0.720193\pi$
$588$		0			0
$589$	−17363.0			−1.21465
$590$	−1584.00	−	2743.57i	−0.110529	−	0.191442i
$591$		0			0
$592$	1160.00	−	2009.18i	0.0805333	−	0.139488i
$593$	−12351.0	−	21392.6i	−0.855303	−	1.48143i	−0.876363	−	0.481650i	$-0.840038\pi$
$593$	−12351.0	−	21392.6i	−0.855303	−	1.48143i	0.0210603	−	0.999778i	$-0.493296\pi$
$594$		0			0
$595$	−1764.00	+	9166.01i	−0.121541	+	0.631546i
$596$	6576.00			0.451952
$597$		0			0
$598$	4452.00	−	7711.09i	0.304441	−	0.527308i
$599$	−1086.00	+	1881.01i	−0.0740781	+	0.128307i	−0.900685	−	0.434473i	$-0.856935\pi$
$599$	−1086.00	+	1881.01i	−0.0740781	+	0.128307i	0.826607	+	0.562780i	$0.190268\pi$
$600$		0			0
$601$	4175.00			0.283364			0.141682	−	0.989912i	$-0.454749\pi$
$601$	4175.00			0.283364			0.141682	+	0.989912i	$0.454749\pi$
$602$	−11375.0	+	3940.42i	−0.770117	+	0.266776i
$603$		0			0
$604$	−2176.00	−	3768.94i	−0.146590	−	0.253901i
$605$	1293.00	−	2239.54i	0.0868891	−	0.150496i
$606$		0			0
$607$	−1130.50	−	1958.08i	−0.0755940	−	0.130933i	0.825750	−	0.564036i	$-0.190752\pi$
$607$	−1130.50	−	1958.08i	−0.0755940	−	0.130933i	−0.901344	+	0.433103i	$0.857419\pi$
$608$	−3104.00			−0.207046
$609$		0			0
$610$	9816.00			0.651538
$611$	−9699.00	−	16799.2i	−0.642192	−	1.11231i
$612$		0			0
$613$	8159.00	−	14131.8i	0.537584	−	0.931123i	−0.461450	−	0.887166i	$-0.652670\pi$
$613$	8159.00	−	14131.8i	0.537584	−	0.931123i	0.999033	−	0.0439561i	$-0.0139962\pi$
$614$	631.000	+	1092.92i	0.0414741	+	0.0718352i
$615$		0			0
$616$	−3360.00	−	2909.85i	−0.219770	−	0.190326i
$617$	26550.0			1.73235			0.866177	−	0.499737i	$-0.166570\pi$
$617$	26550.0			1.73235			0.866177	+	0.499737i	$0.166570\pi$
$618$		0			0
$619$	−9962.50	+	17255.6i	−0.646893	+	1.12045i	0.336968	+	0.941516i	$0.390599\pi$
$619$	−9962.50	+	17255.6i	−0.646893	+	1.12045i	−0.983861	+	0.178935i	$0.942735\pi$
$620$	−2148.00	+	3720.45i	−0.139138	+	0.240995i
$621$		0			0
$622$	−7788.00			−0.502042
$623$	10500.0	−	3637.31i	0.675239	−	0.233909i
$624$		0			0
$625$	−1710.50	−	2962.67i	−0.109472	−	0.189611i
$626$	2185.00	−	3784.53i	0.139505	−	0.241630i
$627$		0			0
$628$	−1012.00	−	1752.84i	−0.0643045	−	0.111379i
$629$	−12180.0			−0.772096
$630$		0			0
$631$	−6832.00			−0.431026			−0.215513	−	0.976501i	$-0.569142\pi$
$631$	−6832.00			−0.431026			−0.215513	+	0.976501i	$0.569142\pi$
$632$	4684.00	+	8112.93i	0.294809	+	0.510625i
$633$		0			0
$634$	3504.00	−	6069.11i	0.219498	−	0.380181i
$635$	−7449.00	−	12902.0i	−0.465519	−	0.806303i
$636$		0			0
$637$	−16880.5	−	6747.20i	−1.04997	−	0.419677i
$638$	10800.0			0.670182
$639$		0			0
$640$	−384.000	+	665.108i	−0.0237171	+	0.0410792i
$641$	5106.00	−	8843.85i	0.314625	−	0.544947i	−0.664732	−	0.747082i	$-0.731454\pi$
$641$	5106.00	−	8843.85i	0.314625	−	0.544947i	0.979358	+	0.202134i	$0.0647878\pi$
$642$		0			0
$643$	3779.00			0.231772			0.115886	−	0.993263i	$-0.463029\pi$
$643$	3779.00			0.231772			0.115886	+	0.993263i	$0.463029\pi$
$644$	1176.00	−	6110.68i	0.0719579	−	0.373904i
$645$		0			0
$646$	8148.00	+	14112.7i	0.496252	+	0.859534i
$647$	8499.00	−	14720.7i	0.516430	−	0.894483i	−0.483388	−	0.875406i	$-0.660594\pi$
$647$	8499.00	−	14720.7i	0.516430	−	0.894483i	0.999818	−	0.0190767i	$-0.00607268\pi$
$648$		0			0
$649$	−3960.00	−	6858.92i	−0.239512	−	0.414848i
$650$	−9434.00			−0.569280
$651$		0			0
$652$	7376.00			0.443047
$653$	−10875.0	−	18836.1i	−0.651718	−	1.12881i	−0.982706	−	0.185173i	$-0.940715\pi$
$653$	−10875.0	−	18836.1i	−0.651718	−	1.12881i	0.330988	−	0.943635i	$-0.392618\pi$
$654$		0			0
$655$	6354.00	−	11005.5i	0.379040	−	0.656517i
$656$	1008.00	+	1745.91i	0.0599936	+	0.103912i
$657$		0			0
$658$	−10248.0	−	8875.03i	−0.607156	−	0.525813i
$659$	10944.0			0.646916			0.323458	−	0.946243i	$-0.395155\pi$
$659$	10944.0			0.646916			0.323458	+	0.946243i	$0.395155\pi$
$660$		0			0
$661$	−5477.50	+	9487.31i	−0.322315	+	0.558266i	−0.980965	−	0.194184i	$-0.937794\pi$
$661$	−5477.50	+	9487.31i	−0.322315	+	0.558266i	0.658650	+	0.752449i	$0.271128\pi$
$662$	−2945.00	+	5100.89i	−0.172901	+	0.299474i
$663$		0			0
$664$	6480.00			0.378724
$665$	8148.00	+	7056.37i	0.475137	+	0.411480i
$666$		0			0
$667$	7560.00	+	13094.3i	0.438867	+	0.760140i
$668$	324.000	−	561.184i	0.0187664	−	0.0325043i
$669$		0			0
$670$	3138.00	+	5435.18i	0.180943	+	0.313402i
$671$	24540.0			1.41186
$672$		0			0
$673$	25103.0			1.43782			0.718908	−	0.695106i	$-0.244642\pi$
$673$	25103.0			1.43782			0.718908	+	0.695106i	$0.244642\pi$
$674$	−4277.00	−	7407.98i	−0.244427	−	0.423360i
$675$		0			0
$676$	−1224.00	+	2120.03i	−0.0696404	+	0.120621i
$677$	−2802.00	−	4853.21i	−0.159069	−	0.275515i	0.775464	−	0.631391i	$-0.217516\pi$
$677$	−2802.00	−	4853.21i	−0.159069	−	0.275515i	−0.934533	+	0.355876i	$0.884183\pi$
$678$		0			0
$679$	−1351.00	+	7020.00i	−0.0763573	+	0.396764i
$680$	4032.00			0.227383
$681$		0			0
$682$	−5370.00	+	9301.11i	−0.301507	+	0.522226i
$683$	5484.00	−	9498.57i	0.307232	−	0.532141i	−0.670524	−	0.741888i	$-0.733931\pi$
$683$	5484.00	−	9498.57i	0.307232	−	0.532141i	0.977756	+	0.209747i	$0.0672639\pi$
$684$		0			0
$685$	−18072.0			−1.00802
$686$	−12691.0	−	594.093i	−0.706333	−	0.0330650i
$687$		0			0
$688$	2600.00	+	4503.33i	0.144076	+	0.249546i
$689$	−20352.0	+	35250.7i	−1.12533	+	1.94912i
$690$		0			0
$691$	−4202.50	−	7278.94i	−0.231361	−	0.400729i	0.726848	−	0.686799i	$-0.240985\pi$
$691$	−4202.50	−	7278.94i	−0.231361	−	0.400729i	−0.958209	+	0.286069i	$0.907651\pi$
$692$	10896.0			0.598560
$693$		0			0
$694$	−14376.0			−0.786319
$695$	111.000	+	192.258i	0.00605823	+	0.0104932i
$696$		0			0
$697$	5292.00	−	9166.01i	0.287588	−	0.498117i
$698$	9406.00	+	16291.7i	0.510061	+	0.883451i
$699$		0			0
$700$	−6230.00	+	2158.14i	−0.336388	+	0.116528i
$701$	−468.000			−0.0252156			−0.0126078	−	0.999921i	$-0.504013\pi$
$701$	−468.000			−0.0252156			−0.0126078	+	0.999921i	$0.504013\pi$
$702$		0			0
$703$	−7032.50	+	12180.6i	−0.377291	+	0.653488i
$704$	−960.000	+	1662.77i	−0.0513940	+	0.0890170i
$705$		0			0
$706$	−6780.00			−0.361429
$707$	8652.00	+	7492.85i	0.460243	+	0.398582i
$708$		0			0
$709$	12533.0	+	21707.8i	0.663874	+	1.14986i	0.979589	+	0.201010i	$0.0644222\pi$
$709$	12533.0	+	21707.8i	0.663874	+	1.14986i	−0.315715	+	0.948854i	$0.602244\pi$
$710$	−2052.00	+	3554.17i	−0.108465	+	0.187867i
$711$		0			0
$712$	−2400.00	−	4156.92i	−0.126326	−	0.218802i
$713$	−15036.0			−0.789765
$714$		0			0
$715$	9540.00			0.498987
$716$	−2508.00	−	4343.98i	−0.130906	−	0.226735i
$717$		0			0
$718$	−4812.00	+	8334.63i	−0.250115	+	0.433211i
$719$	5541.00	+	9597.29i	0.287405	+	0.497801i	0.973190	−	0.230004i	$-0.0738740\pi$
$719$	5541.00	+	9597.29i	0.287405	+	0.497801i	−0.685784	+	0.727805i	$0.740541\pi$
$720$		0			0
$721$	25812.5	−	8941.71i	1.33330	−	0.461868i
$722$	5100.00			0.262884
$723$		0			0
$724$	3614.00	−	6259.63i	0.185516	−	0.321322i
$725$	8010.00	−	13873.7i	0.410323	−	0.710700i
$726$		0			0
$727$	13481.0			0.687734			0.343867	−	0.939018i	$-0.388263\pi$
$727$	13481.0			0.687734			0.343867	+	0.939018i	$0.388263\pi$
$728$	−1484.00	+	7711.09i	−0.0755504	+	0.392571i
$729$		0			0
$730$	258.000	+	446.869i	0.0130808	+	0.0226567i
$731$	13650.0	−	23642.5i	0.690648	−	1.19624i
$732$		0			0
$733$	−12158.5	−	21059.1i	−0.612666	−	1.06117i	−0.990789	−	0.135414i	$-0.956764\pi$
$733$	−12158.5	−	21059.1i	−0.612666	−	1.06117i	0.378123	−	0.925755i	$-0.376570\pi$
$734$	−14198.0			−0.713975
$735$		0			0
$736$	−2688.00			−0.134621
$737$	7845.00	+	13587.9i	0.392095	+	0.679129i
$738$		0			0
$739$	9108.50	−	15776.4i	0.453399	−	0.785309i	−0.545196	−	0.838309i	$-0.683545\pi$
$739$	9108.50	−	15776.4i	0.453399	−	0.785309i	0.998595	+	0.0529992i	$0.0168781\pi$
$740$	1740.00	+	3013.77i	0.0864374	+	0.149714i
$741$		0			0
$742$	−5376.00	+	27934.5i	−0.265983	+	1.38209i
$743$	−19782.0			−0.976758			−0.488379	−	0.872632i	$-0.662412\pi$
$743$	−19782.0			−0.976758			−0.488379	+	0.872632i	$0.662412\pi$
$744$		0			0
$745$	−4932.00	+	8542.47i	−0.242543	+	0.420097i
$746$	−2963.00	+	5132.07i	−0.145420	+	0.251874i
$747$		0			0
$748$	10080.0			0.492729
$749$	−32970.0	+	11421.1i	−1.60841	+	0.557169i
$750$		0			0
$751$	2460.50	+	4261.71i	0.119554	+	0.207073i	0.919591	−	0.392877i	$-0.128520\pi$
$751$	2460.50	+	4261.71i	0.119554	+	0.207073i	−0.800037	+	0.599951i	$0.795187\pi$
$752$	−2928.00	+	5071.44i	−0.141986	+	0.245926i
$753$		0			0
$754$	−9540.00	−	16523.8i	−0.460778	−	0.798090i
$755$	6528.00			0.314673
$756$		0			0
$757$	18098.0			0.868934			0.434467	−	0.900688i	$-0.356937\pi$
$757$	18098.0			0.868934			0.434467	+	0.900688i	$0.356937\pi$
$758$	11899.0	+	20609.7i	0.570173	+	0.987569i
$759$		0			0
$760$	2328.00	−	4032.21i	0.111112	−	0.192452i
$761$	−12234.0	−	21189.9i	−0.582762	−	1.00937i	−0.995150	−	0.0983657i	$-0.968639\pi$
$761$	−12234.0	−	21189.9i	−0.582762	−	1.00937i	0.412388	−	0.911008i	$-0.364695\pi$
$762$		0			0
$763$	−5782.00	−	5007.36i	−0.274341	−	0.237587i
$764$	−2856.00			−0.135244
$765$		0			0
$766$	2568.00	−	4447.91i	0.121130	−	0.209803i
$767$	−6996.00	+	12117.4i	−0.329349	+	0.570450i
$768$		0			0
$769$	21719.0			1.01847			0.509237	−	0.860626i	$-0.329928\pi$
$769$	21719.0			1.01847			0.509237	+	0.860626i	$0.329928\pi$
$770$	6300.00	−	2182.38i	0.294852	−	0.102140i
$771$		0			0
$772$	7418.00	+	12848.4i	0.345829	+	0.598993i
$773$	−15153.0	+	26245.8i	−0.705065	+	1.22121i	0.261603	+	0.965176i	$0.415749\pi$
$773$	−15153.0	+	26245.8i	−0.705065	+	1.22121i	−0.966668	+	0.256033i	$0.917584\pi$
$774$		0			0
$775$	7965.50	+	13796.7i	0.369199	+	0.639471i
$776$	3088.00			0.142851
$777$		0			0
$778$	20292.0			0.935094
$779$	−6111.00	−	10584.6i	−0.281065	−	0.486818i
$780$		0			0
$781$	−5130.00	+	8885.42i	−0.235039	+	0.407100i
$782$	7056.00	+	12221.4i	0.322662	+	0.558868i
$783$		0			0
$784$	784.000	+	5431.71i	0.0357143	+	0.247436i
$785$	3036.00			0.138038
$786$		0			0
$787$	−13648.0	+	23639.0i	−0.618169	+	1.07070i	0.371651	+	0.928372i	$0.378792\pi$
$787$	−13648.0	+	23639.0i	−0.618169	+	1.07070i	−0.989820	+	0.142327i	$0.954542\pi$
$788$	−2088.00	+	3616.52i	−0.0943933	+	0.163494i
$789$		0			0
$790$	−14052.0			−0.632845
$791$	−3087.00	+	16040.5i	−0.138762	+	0.721031i
$792$		0			0
$793$	−21677.0	−	37545.7i	−0.970710	−	1.68132i
$794$	6229.00	−	10788.9i	0.278412	−	0.482223i
$795$		0			0
$796$	272.000	+	471.118i	0.0121115	+	0.0209778i
$797$	35100.0			1.55998			0.779991	−	0.625791i	$-0.215224\pi$
$797$	35100.0			1.55998			0.779991	+	0.625791i	$0.215224\pi$
$798$		0			0
$799$	30744.0			1.36126
$800$	1424.00	+	2466.44i	0.0629325	+	0.109002i
$801$		0			0
$802$	−2472.00	+	4281.63i	−0.108840	+	0.188516i
$803$	645.000	+	1117.17i	0.0283456	+	0.0490961i
$804$		0			0
$805$	7056.00	+	6110.68i	0.308933	+	0.267544i
$806$	18974.0			0.829194
$807$		0			0
$808$	2472.00	−	4281.63i	0.107630	−	0.186420i
$809$	22197.0	−	38446.3i	0.964654	−	1.67083i	0.254112	−	0.967175i	$-0.418217\pi$
$809$	22197.0	−	38446.3i	0.964654	−	1.67083i	0.710542	−	0.703655i	$-0.248450\pi$
$810$		0			0
$811$	−8584.00			−0.371671			−0.185835	−	0.982581i	$-0.559499\pi$
$811$	−8584.00			−0.371671			−0.185835	+	0.982581i	$0.559499\pi$
$812$	−10080.0	−	8729.54i	−0.435639	−	0.377274i
$813$		0			0
$814$	4350.00	+	7534.42i	0.187306	+	0.324424i
$815$	−5532.00	+	9581.71i	−0.237764	+	0.411819i
$816$		0			0
$817$	−15762.5	−	27301.5i	−0.674982	−	1.16910i
$818$	−14150.0			−0.604820
$819$		0			0
$820$	−3024.00			−0.128784
$821$	−4917.00	−	8516.49i	−0.209019	−	0.362031i	0.742387	−	0.669971i	$-0.233694\pi$
$821$	−4917.00	−	8516.49i	−0.209019	−	0.362031i	−0.951406	+	0.307940i	$0.900360\pi$
$822$		0			0
$823$	−21928.0	+	37980.4i	−0.928751	+	1.60864i	−0.143336	+	0.989674i	$0.545783\pi$
$823$	−21928.0	+	37980.4i	−0.928751	+	1.60864i	−0.785415	+	0.618970i	$0.787550\pi$
$824$	−5900.00	−	10219.1i	−0.249437	−	0.432038i
$825$		0			0
$826$	−1848.00	+	9602.49i	−0.0778452	+	0.404496i
$827$	−13266.0			−0.557804			−0.278902	−	0.960320i	$-0.589970\pi$
$827$	−13266.0			−0.557804			−0.278902	+	0.960320i	$0.589970\pi$
$828$		0			0
$829$	−8726.50	+	15114.7i	−0.365602	+	0.633241i	−0.988873	−	0.148765i	$-0.952470\pi$
$829$	−8726.50	+	15114.7i	−0.365602	+	0.633241i	0.623271	+	0.782006i	$0.285803\pi$
$830$	−4860.00	+	8417.77i	−0.203245	+	0.352030i
$831$		0			0
$832$	3392.00			0.141342
$833$	22638.0	−	17822.8i	0.941609	−	0.741325i
$834$		0			0
$835$	486.000	+	841.777i	0.0201422	+	0.0348873i
$836$	5820.00	−	10080.5i	0.240776	−	0.417037i
$837$		0			0
$838$	−4158.00	−	7201.87i	−0.171403	−	0.296879i
$839$	35172.0			1.44729			0.723643	−	0.690175i	$-0.242466\pi$
$839$	35172.0			1.44729			0.723643	+	0.690175i	$0.242466\pi$
$840$		0			0
$841$	8011.00			0.328468
$842$	6595.00	+	11422.9i	0.269927	+	0.467528i
$843$		0			0
$844$	−2968.00	+	5140.73i	−0.121046	+	0.209658i
$845$	−1836.00	−	3180.05i	−0.0747459	−	0.129464i
$846$		0			0
$847$	−7542.50	+	2612.80i	−0.305978	+	0.105994i
$848$	12288.0			0.497608
$849$		0			0
$850$	7476.00	−	12948.8i	0.301676	−	0.522518i
$851$	−6090.00	+	10548.2i	−0.245314	+	0.424897i
$852$		0			0
$853$	3503.00			0.140610			0.0703051	−	0.997526i	$-0.477603\pi$
$853$	3503.00			0.140610			0.0703051	+	0.997526i	$0.477603\pi$
$854$	−22904.0	−	19835.4i	−0.917750	−	0.794795i
$855$		0			0
$856$	7536.00	+	13052.7i	0.300906	+	0.521184i
$857$	11424.0	−	19786.9i	0.455352	−	0.788692i	−0.543357	−	0.839502i	$-0.682847\pi$
$857$	11424.0	−	19786.9i	0.455352	−	0.788692i	0.998708	+	0.0508097i	$0.0161802\pi$
$858$		0			0
$859$	6728.00	+	11653.2i	0.267237	+	0.462868i	0.968147	−	0.250382i	$-0.0805561\pi$
$859$	6728.00	+	11653.2i	0.267237	+	0.462868i	−0.700910	+	0.713249i	$0.747223\pi$
$860$	−7800.00			−0.309277
$861$		0			0
$862$	−3036.00			−0.119961
$863$	20355.0	+	35255.9i	0.802888	+	1.39064i	0.917708	+	0.397256i	$0.130038\pi$
$863$	20355.0	+	35255.9i	0.802888	+	1.39064i	−0.114820	+	0.993386i	$0.536629\pi$
$864$		0			0
$865$	−8172.00	+	14154.3i	−0.321221	+	0.556371i
$866$	−8567.00	−	14838.5i	−0.336165	−	0.582254i
$867$		0			0
$868$	12530.0	−	4340.52i	0.489972	−	0.169731i
$869$	−35130.0			−1.37135
$870$		0			0
$871$	13859.5	−	24005.4i	0.539163	−	0.933858i
$872$	−1652.00	+	2861.35i	−0.0641557	+	0.111121i
$873$		0			0
$874$	16296.0			0.630687
$875$	4494.00	−	23351.5i	0.173628	−	0.902200i
$876$		0			0
$877$	−1453.00	−	2516.67i	−0.0559456	−	0.0969007i	0.836696	−	0.547667i	$-0.184484\pi$
$877$	−1453.00	−	2516.67i	−0.0559456	−	0.0969007i	−0.892642	+	0.450767i	$0.851151\pi$
$878$	−10640.0	+	18429.0i	−0.408978	+	0.708371i
$879$		0			0
$880$	−1440.00	−	2494.15i	−0.0551618	−	0.0955431i
$881$	19188.0			0.733780			0.366890	−	0.930264i	$-0.380423\pi$
$881$	19188.0			0.733780			0.366890	+	0.930264i	$0.380423\pi$
$882$		0			0
$883$	−17251.0			−0.657466			−0.328733	−	0.944423i	$-0.606622\pi$
$883$	−17251.0			−0.657466			−0.328733	+	0.944423i	$0.606622\pi$
$884$	−8904.00	−	15422.2i	−0.338771	−	0.586769i
$885$		0			0
$886$	7032.00	−	12179.8i	0.266642	−	0.461837i
$887$	−1047.00	−	1813.46i	−0.0396334	−	0.0686471i	0.845528	−	0.533931i	$-0.179286\pi$
$887$	−1047.00	−	1813.46i	−0.0396334	−	0.0686471i	−0.885162	+	0.465284i	$0.845952\pi$
$888$		0			0
$889$	−8690.50	+	45157.2i	−0.327863	+	1.70362i
$890$	7200.00			0.271174
$891$		0			0
$892$	4064.00	−	7039.05i	0.152548	−	0.264221i
$893$	17751.0	−	30745.6i	0.665190	−	1.15214i
$894$		0			0
$895$	7524.00			0.281005
$896$	2240.00	−	775.959i	0.0835191	−	0.0289319i
$897$		0			0
$898$	−14814.0	−	25658.6i	−0.550501	−	0.953495i
$899$	−16110.0	+	27903.3i	−0.597662	+	1.03518i
$900$		0			0
$901$	−32256.0	−	55869.0i	−1.19268	−	2.06578i
$902$	−7560.00			−0.279069
$903$		0			0
$904$	7056.00			0.259601
$905$	5421.00	+	9389.45i	0.199116	+	0.344879i
$906$		0			0
$907$	20133.5	−	34872.2i	0.737069	−	1.27664i	−0.216740	−	0.976229i	$-0.569542\pi$
$907$	20133.5	−	34872.2i	0.737069	−	1.27664i	0.953809	−	0.300412i	$-0.0971242\pi$
$908$	12396.0	+	21470.5i	0.453057	+	0.784718i
$909$		0			0
$910$	−8904.00	−	7711.09i	−0.324357	−	0.280901i
$911$	−17604.0			−0.640227			−0.320113	−	0.947379i	$-0.603721\pi$
$911$	−17604.0			−0.640227			−0.320113	+	0.947379i	$0.603721\pi$
$912$		0			0
$913$	−12150.0	+	21044.4i	−0.440423	+	0.762835i
$914$	11251.0	−	19487.3i	0.407166	−	0.705233i
$915$		0			0
$916$	−18364.0			−0.662406
$917$	−37065.0	+	12839.7i	−1.33478	+	0.462382i
$918$		0			0
$919$	−1754.50	−	3038.88i	−0.0629767	−	0.109079i	0.832818	−	0.553547i	$-0.186726\pi$
$919$	−1754.50	−	3038.88i	−0.0629767	−	0.109079i	−0.895795	+	0.444468i	$0.853393\pi$
$920$	2016.00	−	3491.81i	0.0722452	−	0.125132i
$921$		0			0
$922$	−3852.00	−	6671.86i	−0.137591	−	0.238315i
$923$	18126.0			0.646397
$924$		0			0
$925$	12905.0			0.458718
$926$	475.000	+	822.724i	0.0168569	+	0.0291970i
$927$		0			0
$928$	−2880.00	+	4988.31i	−0.101876	+	0.176454i
$929$	−17319.0	−	29997.4i	−0.611645	−	1.05940i	−0.990963	−	0.134134i	$-0.957175\pi$
$929$	−17319.0	−	29997.4i	−0.611645	−	1.05940i	0.379319	−	0.925266i	$-0.376158\pi$
$930$		0			0
$931$	−4753.00	−	32929.7i	−0.167318	−	1.15921i
$932$	−18120.0			−0.636846
$933$		0			0
$934$	5934.00	−	10278.0i	0.207887	−	0.360071i
$935$	−7560.00	+	13094.3i	−0.264426	+	0.458000i
$936$		0			0
$937$	−17353.0			−0.605014			−0.302507	−	0.953147i	$-0.597824\pi$
$937$	−17353.0			−0.605014			−0.302507	+	0.953147i	$0.597824\pi$
$938$	3661.00	−	19023.1i	0.127437	−	0.662182i
$939$		0			0
$940$	−4392.00	−	7607.17i	−0.152395	−	0.263956i
$941$	−23460.0	+	40633.9i	−0.812725	+	1.40768i	0.0982252	+	0.995164i	$0.468683\pi$
$941$	−23460.0	+	40633.9i	−0.812725	+	1.40768i	−0.910950	+	0.412517i	$0.864650\pi$
$942$		0			0
$943$	−5292.00	−	9166.01i	−0.182748	−	0.316529i
$944$	4224.00			0.145635
$945$		0			0
$946$	−19500.0			−0.670190
$947$	9177.00	+	15895.0i	0.314902	+	0.545427i	0.979417	−	0.201849i	$-0.0646949\pi$
$947$	9177.00	+	15895.0i	0.314902	+	0.545427i	−0.664514	+	0.747275i	$0.731362\pi$
$948$		0			0
$949$	1139.50	−	1973.67i	0.0389776	−	0.0675112i
$950$	−8633.00	−	14952.8i	−0.294833	−	0.510666i
$951$		0			0
$952$	−9408.00	−	8147.57i	−0.320289	−	0.277378i
$953$	−35568.0			−1.20898			−0.604491	−	0.796612i	$-0.706624\pi$
$953$	−35568.0			−1.20898			−0.604491	+	0.796612i	$0.706624\pi$
$954$		0			0
$955$	2142.00	−	3710.05i	0.0725796	−	0.125712i
$956$	3060.00	−	5300.08i	0.103522	−	0.179306i
$957$		0			0
$958$	26736.0			0.901671
$959$	42168.0	+	36518.6i	1.41989	+	1.22966i
$960$		0			0
$961$	−1125.00	−	1948.56i	−0.0377631	−	0.0654076i
$962$	7685.00	−	13310.8i	0.257562	−	0.446110i
$963$		0			0
$964$	−11068.0	−	19170.3i	−0.369789	−	0.640493i
$965$	−22254.0			−0.742364
$966$		0			0
$967$	−27343.0			−0.909298			−0.454649	−	0.890671i	$-0.650235\pi$
$967$	−27343.0			−0.909298			−0.454649	+	0.890671i	$0.650235\pi$
$968$	1724.00	+	2986.06i	0.0572432	+	0.0991482i
$969$		0			0
$970$	−2316.00	+	4011.43i	−0.0766621	+	0.132783i
$971$	25512.0	+	44188.1i	0.843171	+	1.46042i	0.887200	+	0.461385i	$0.152647\pi$
$971$	25512.0	+	44188.1i	0.843171	+	1.46042i	−0.0440291	+	0.999030i	$0.514019\pi$
$972$		0			0
$973$	129.500	−	672.902i	0.00426678	−	0.0221709i
$974$	13306.0			0.437733
$975$		0			0
$976$	−6544.00	+	11334.5i	−0.214619	+	0.371731i
$977$	−1113.00	+	1927.77i	−0.0364463	+	0.0631268i	−0.883673	−	0.468104i	$-0.844937\pi$
$977$	−1113.00	+	1927.77i	−0.0364463	+	0.0631268i	0.847227	+	0.531231i	$0.178270\pi$
$978$		0			0
$979$	18000.0			0.587623
$980$	−7644.00	−	3055.34i	−0.249162	−	0.0995910i
$981$		0			0
$982$	15444.0	+	26749.8i	0.501872	+	0.869267i
$983$	17652.0	−	30574.2i	0.572748	−	0.992029i	−0.423534	−	0.905880i	$-0.639211\pi$
$983$	17652.0	−	30574.2i	0.572748	−	0.992029i	0.996282	−	0.0861487i	$-0.0274560\pi$
$984$		0			0
$985$	−3132.00	−	5424.78i	−0.101314	−	0.175480i
$986$	30240.0			0.976712
$987$		0			0
$988$	−20564.0			−0.662174
$989$	−13650.0	−	23642.5i	−0.438872	−	0.760149i
$990$		0			0
$991$	1170.50	−	2027.37i	0.0375198	−	0.0649863i	−0.846656	−	0.532141i	$-0.821388\pi$
$991$	1170.50	−	2027.37i	0.0375198	−	0.0649863i	0.884176	+	0.467155i	$0.154721\pi$
$992$	−2864.00	−	4960.59i	−0.0916654	−	0.158769i
$993$		0			0
$994$	11970.0	−	4146.53i	0.381957	−	0.132314i
$995$	−816.000			−0.0259989
$996$		0			0
$997$	−14507.5	+	25127.7i	−0.460840	+	0.798198i	−0.999003	−	0.0446429i	$-0.985785\pi$
$997$	−14507.5	+	25127.7i	−0.460840	+	0.798198i	0.538163	+	0.842841i	$0.319118\pi$
$998$	−683.000	+	1182.99i	−0.0216633	+	0.0375220i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.4.g.b.109.1		2
3.2	odd	2		42.4.e.a.25.1	✓	2
7.2	even	3	inner	126.4.g.b.37.1		2
7.3	odd	6		882.4.a.l.1.1		1
7.4	even	3		882.4.a.o.1.1		1
7.5	odd	6		882.4.g.g.667.1		2
7.6	odd	2		882.4.g.g.361.1		2
12.11	even	2		336.4.q.f.193.1		2
21.2	odd	6		42.4.e.a.37.1	yes	2
21.5	even	6		294.4.e.i.79.1		2
21.11	odd	6		294.4.a.d.1.1		1
21.17	even	6		294.4.a.c.1.1		1
21.20	even	2		294.4.e.i.67.1		2
84.11	even	6		2352.4.a.f.1.1		1
84.23	even	6		336.4.q.f.289.1		2
84.59	odd	6		2352.4.a.bf.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.4.e.a.25.1	✓	2	3.2	odd	2
42.4.e.a.37.1	yes	2	21.2	odd	6
126.4.g.b.37.1		2	7.2	even	3	inner
126.4.g.b.109.1		2	1.1	even	1	trivial
294.4.a.c.1.1		1	21.17	even	6
294.4.a.d.1.1		1	21.11	odd	6
294.4.e.i.67.1		2	21.20	even	2
294.4.e.i.79.1		2	21.5	even	6
336.4.q.f.193.1		2	12.11	even	2
336.4.q.f.289.1		2	84.23	even	6
882.4.a.l.1.1		1	7.3	odd	6
882.4.a.o.1.1		1	7.4	even	3
882.4.g.g.361.1		2	7.6	odd	2
882.4.g.g.667.1		2	7.5	odd	6
2352.4.a.f.1.1		1	84.11	even	6
2352.4.a.bf.1.1		1	84.59	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-3.00000 - 5.19615i) q^{5} +(-3.50000 + 18.1865i) q^{7} +8.00000 q^{8} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-3.00000 - 5.19615i) q^{5} +(-3.50000 + 18.1865i) q^{7} +8.00000 q^{8} +(-6.00000 + 10.3923i) q^{10} +(-15.0000 + 25.9808i) q^{11} +53.0000 q^{13} +(35.0000 - 12.1244i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(-42.0000 + 72.7461i) q^{17} +(48.5000 + 84.0045i) q^{19} +24.0000 q^{20} +60.0000 q^{22} +(42.0000 + 72.7461i) q^{23} +(44.5000 - 77.0763i) q^{25} +(-53.0000 - 91.7987i) q^{26} +(-56.0000 - 48.4974i) q^{28} +180.000 q^{29} +(-89.5000 + 155.019i) q^{31} +(-16.0000 + 27.7128i) q^{32} +168.000 q^{34} +(105.000 - 36.3731i) q^{35} +(72.5000 + 125.574i) q^{37} +(97.0000 - 168.009i) q^{38} +(-24.0000 - 41.5692i) q^{40} -126.000 q^{41} -325.000 q^{43} +(-60.0000 - 103.923i) q^{44} +(84.0000 - 145.492i) q^{46} +(-183.000 - 316.965i) q^{47} +(-318.500 - 127.306i) q^{49} -178.000 q^{50} +(-106.000 + 183.597i) q^{52} +(-384.000 + 665.108i) q^{53} +180.000 q^{55} +(-28.0000 + 145.492i) q^{56} +(-180.000 - 311.769i) q^{58} +(-132.000 + 228.631i) q^{59} +(-409.000 - 708.409i) q^{61} +358.000 q^{62} +64.0000 q^{64} +(-159.000 - 275.396i) q^{65} +(261.500 - 452.931i) q^{67} +(-168.000 - 290.985i) q^{68} +(-168.000 - 145.492i) q^{70} +342.000 q^{71} +(21.5000 - 37.2391i) q^{73} +(145.000 - 251.147i) q^{74} -388.000 q^{76} +(-420.000 - 363.731i) q^{77} +(585.500 + 1014.12i) q^{79} +(-48.0000 + 83.1384i) q^{80} +(126.000 + 218.238i) q^{82} +810.000 q^{83} +504.000 q^{85} +(325.000 + 562.917i) q^{86} +(-120.000 + 207.846i) q^{88} +(-300.000 - 519.615i) q^{89} +(-185.500 + 963.886i) q^{91} -336.000 q^{92} +(-366.000 + 633.931i) q^{94} +(291.000 - 504.027i) q^{95} +386.000 q^{97} +(98.0000 + 678.964i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 4 q^{4} - 6 q^{5} - 7 q^{7} + 16 q^{8}+O(q^{10}) \) 2 * q - 2 * q^2 - 4 * q^4 - 6 * q^5 - 7 * q^7 + 16 * q^8	\( 2 q - 2 q^{2} - 4 q^{4} - 6 q^{5} - 7 q^{7} + 16 q^{8} - 12 q^{10} - 30 q^{11} + 106 q^{13} + 70 q^{14} - 16 q^{16} - 84 q^{17} + 97 q^{19} + 48 q^{20} + 120 q^{22} + 84 q^{23} + 89 q^{25} - 106 q^{26} - 112 q^{28} + 360 q^{29} - 179 q^{31} - 32 q^{32} + 336 q^{34} + 210 q^{35} + 145 q^{37} + 194 q^{38} - 48 q^{40} - 252 q^{41} - 650 q^{43} - 120 q^{44} + 168 q^{46} - 366 q^{47} - 637 q^{49} - 356 q^{50} - 212 q^{52} - 768 q^{53} + 360 q^{55} - 56 q^{56} - 360 q^{58} - 264 q^{59} - 818 q^{61} + 716 q^{62} + 128 q^{64} - 318 q^{65} + 523 q^{67} - 336 q^{68} - 336 q^{70} + 684 q^{71} + 43 q^{73} + 290 q^{74} - 776 q^{76} - 840 q^{77} + 1171 q^{79} - 96 q^{80} + 252 q^{82} + 1620 q^{83} + 1008 q^{85} + 650 q^{86} - 240 q^{88} - 600 q^{89} - 371 q^{91} - 672 q^{92} - 732 q^{94} + 582 q^{95} + 772 q^{97} + 196 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 4 * q^4 - 6 * q^5 - 7 * q^7 + 16 * q^8 - 12 * q^10 - 30 * q^11 + 106 * q^13 + 70 * q^14 - 16 * q^16 - 84 * q^17 + 97 * q^19 + 48 * q^20 + 120 * q^22 + 84 * q^23 + 89 * q^25 - 106 * q^26 - 112 * q^28 + 360 * q^29 - 179 * q^31 - 32 * q^32 + 336 * q^34 + 210 * q^35 + 145 * q^37 + 194 * q^38 - 48 * q^40 - 252 * q^41 - 650 * q^43 - 120 * q^44 + 168 * q^46 - 366 * q^47 - 637 * q^49 - 356 * q^50 - 212 * q^52 - 768 * q^53 + 360 * q^55 - 56 * q^56 - 360 * q^58 - 264 * q^59 - 818 * q^61 + 716 * q^62 + 128 * q^64 - 318 * q^65 + 523 * q^67 - 336 * q^68 - 336 * q^70 + 684 * q^71 + 43 * q^73 + 290 * q^74 - 776 * q^76 - 840 * q^77 + 1171 * q^79 - 96 * q^80 + 252 * q^82 + 1620 * q^83 + 1008 * q^85 + 650 * q^86 - 240 * q^88 - 600 * q^89 - 371 * q^91 - 672 * q^92 - 732 * q^94 + 582 * q^95 + 772 * q^97 + 196 * q^98

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