LMFDB - Embedded newform 162.4.c.f.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,4,Mod(55,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("162.55");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	162.c (of order $3$, degree $2$, not 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:	$9.55830942093$
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:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 6)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			109.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	162.109
Dual form			162.4.c.f.55.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-3.00000 + 5.19615i) q^{5} +(8.00000 + 13.8564i) q^{7} -8.00000 q^{8} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-3.00000 + 5.19615i) q^{5} +(8.00000 + 13.8564i) q^{7} -8.00000 q^{8} -12.0000 q^{10} +(-6.00000 - 10.3923i) q^{11} +(-19.0000 + 32.9090i) q^{13} +(-16.0000 + 27.7128i) q^{14} +(-8.00000 - 13.8564i) q^{16} -126.000 q^{17} +20.0000 q^{19} +(-12.0000 - 20.7846i) q^{20} +(12.0000 - 20.7846i) q^{22} +(-84.0000 + 145.492i) q^{23} +(44.5000 + 77.0763i) q^{25} -76.0000 q^{26} -64.0000 q^{28} +(-15.0000 - 25.9808i) q^{29} +(44.0000 - 76.2102i) q^{31} +(16.0000 - 27.7128i) q^{32} +(-126.000 - 218.238i) q^{34} -96.0000 q^{35} +254.000 q^{37} +(20.0000 + 34.6410i) q^{38} +(24.0000 - 41.5692i) q^{40} +(-21.0000 + 36.3731i) q^{41} +(26.0000 + 45.0333i) q^{43} +48.0000 q^{44} -336.000 q^{46} +(48.0000 + 83.1384i) q^{47} +(43.5000 - 75.3442i) q^{49} +(-89.0000 + 154.153i) q^{50} +(-76.0000 - 131.636i) q^{52} +198.000 q^{53} +72.0000 q^{55} +(-64.0000 - 110.851i) q^{56} +(30.0000 - 51.9615i) q^{58} +(330.000 - 571.577i) q^{59} +(269.000 + 465.922i) q^{61} +176.000 q^{62} +64.0000 q^{64} +(-114.000 - 197.454i) q^{65} +(-442.000 + 765.566i) q^{67} +(252.000 - 436.477i) q^{68} +(-96.0000 - 166.277i) q^{70} +792.000 q^{71} +218.000 q^{73} +(254.000 + 439.941i) q^{74} +(-40.0000 + 69.2820i) q^{76} +(96.0000 - 166.277i) q^{77} +(260.000 + 450.333i) q^{79} +96.0000 q^{80} -84.0000 q^{82} +(246.000 + 426.084i) q^{83} +(378.000 - 654.715i) q^{85} +(-52.0000 + 90.0666i) q^{86} +(48.0000 + 83.1384i) q^{88} +810.000 q^{89} -608.000 q^{91} +(-336.000 - 581.969i) q^{92} +(-96.0000 + 166.277i) q^{94} +(-60.0000 + 103.923i) q^{95} +(-577.000 - 999.393i) q^{97} +174.000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 4 q^{4} - 6 q^{5} + 16 q^{7} - 16 q^{8}+O(q^{10}) $ 2 * q + 2 * q^2 - 4 * q^4 - 6 * q^5 + 16 * q^7 - 16 * q^8	$ 2 q + 2 q^{2} - 4 q^{4} - 6 q^{5} + 16 q^{7} - 16 q^{8} - 24 q^{10} - 12 q^{11} - 38 q^{13} - 32 q^{14} - 16 q^{16} - 252 q^{17} + 40 q^{19} - 24 q^{20} + 24 q^{22} - 168 q^{23} + 89 q^{25} - 152 q^{26} - 128 q^{28} - 30 q^{29} + 88 q^{31} + 32 q^{32} - 252 q^{34} - 192 q^{35} + 508 q^{37} + 40 q^{38} + 48 q^{40} - 42 q^{41} + 52 q^{43} + 96 q^{44} - 672 q^{46} + 96 q^{47} + 87 q^{49} - 178 q^{50} - 152 q^{52} + 396 q^{53} + 144 q^{55} - 128 q^{56} + 60 q^{58} + 660 q^{59} + 538 q^{61} + 352 q^{62} + 128 q^{64} - 228 q^{65} - 884 q^{67} + 504 q^{68} - 192 q^{70} + 1584 q^{71} + 436 q^{73} + 508 q^{74} - 80 q^{76} + 192 q^{77} + 520 q^{79} + 192 q^{80} - 168 q^{82} + 492 q^{83} + 756 q^{85} - 104 q^{86} + 96 q^{88} + 1620 q^{89} - 1216 q^{91} - 672 q^{92} - 192 q^{94} - 120 q^{95} - 1154 q^{97} + 348 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 - 4 * q^4 - 6 * q^5 + 16 * q^7 - 16 * q^8 - 24 * q^10 - 12 * q^11 - 38 * q^13 - 32 * q^14 - 16 * q^16 - 252 * q^17 + 40 * q^19 - 24 * q^20 + 24 * q^22 - 168 * q^23 + 89 * q^25 - 152 * q^26 - 128 * q^28 - 30 * q^29 + 88 * q^31 + 32 * q^32 - 252 * q^34 - 192 * q^35 + 508 * q^37 + 40 * q^38 + 48 * q^40 - 42 * q^41 + 52 * q^43 + 96 * q^44 - 672 * q^46 + 96 * q^47 + 87 * q^49 - 178 * q^50 - 152 * q^52 + 396 * q^53 + 144 * q^55 - 128 * q^56 + 60 * q^58 + 660 * q^59 + 538 * q^61 + 352 * q^62 + 128 * q^64 - 228 * q^65 - 884 * q^67 + 504 * q^68 - 192 * q^70 + 1584 * q^71 + 436 * q^73 + 508 * q^74 - 80 * q^76 + 192 * q^77 + 520 * q^79 + 192 * q^80 - 168 * q^82 + 492 * q^83 + 756 * q^85 - 104 * q^86 + 96 * q^88 + 1620 * q^89 - 1216 * q^91 - 672 * q^92 - 192 * q^94 - 120 * q^95 - 1154 * q^97 + 348 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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	−0.968430	−	0.249285i	$-0.919804\pi$
$5$	−3.00000	+	5.19615i	−0.268328	+	0.464758i	0.700102	+	0.714043i	$0.253138\pi$
$6$		0			0
$7$	8.00000	+	13.8564i	0.431959	+	0.748176i	0.997042	−	0.0768587i	$-0.0244890\pi$
$7$	8.00000	+	13.8564i	0.431959	+	0.748176i	−0.565083	+	0.825034i	$0.691156\pi$
$8$	−8.00000			−0.353553
$9$		0			0
$10$	−12.0000			−0.379473
$11$	−6.00000	−	10.3923i	−0.164461	−	0.284854i	0.772003	−	0.635619i	$-0.219255\pi$
$11$	−6.00000	−	10.3923i	−0.164461	−	0.284854i	−0.936464	+	0.350765i	$0.885922\pi$
$12$		0			0
$13$	−19.0000	+	32.9090i	−0.405358	+	0.702100i	−0.994363	−	0.106029i	$-0.966186\pi$
$13$	−19.0000	+	32.9090i	−0.405358	+	0.702100i	0.589005	+	0.808129i	$0.299520\pi$
$14$	−16.0000	+	27.7128i	−0.305441	+	0.529040i
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−126.000			−1.79762			−0.898808	−	0.438342i	$-0.855566\pi$
$17$	−126.000			−1.79762			−0.898808	+	0.438342i	$0.855566\pi$
$18$		0			0
$19$	20.0000			0.241490			0.120745	−	0.992684i	$-0.461472\pi$
$19$	20.0000			0.241490			0.120745	+	0.992684i	$0.461472\pi$
$20$	−12.0000	−	20.7846i	−0.134164	−	0.232379i
$21$		0			0
$22$	12.0000	−	20.7846i	0.116291	−	0.201422i
$23$	−84.0000	+	145.492i	−0.761531	+	1.31901i	0.180530	+	0.983569i	$0.442219\pi$
$23$	−84.0000	+	145.492i	−0.761531	+	1.31901i	−0.942061	+	0.335441i	$0.891115\pi$
$24$		0			0
$25$	44.5000	+	77.0763i	0.356000	+	0.616610i
$26$	−76.0000			−0.573263
$27$		0			0
$28$	−64.0000			−0.431959
$29$	−15.0000	−	25.9808i	−0.0960493	−	0.166362i	0.813997	−	0.580869i	$-0.197287\pi$
$29$	−15.0000	−	25.9808i	−0.0960493	−	0.166362i	−0.910046	+	0.414507i	$0.863954\pi$
$30$		0			0
$31$	44.0000	−	76.2102i	0.254924	−	0.441541i	−0.709951	−	0.704251i	$-0.751283\pi$
$31$	44.0000	−	76.2102i	0.254924	−	0.441541i	0.964875	+	0.262710i	$0.0846163\pi$
$32$	16.0000	−	27.7128i	0.0883883	−	0.153093i
$33$		0			0
$34$	−126.000	−	218.238i	−0.635554	−	1.10081i
$35$	−96.0000			−0.463627
$36$		0			0
$37$	254.000			1.12858			0.564288	−	0.825578i	$-0.309151\pi$
$37$	254.000			1.12858			0.564288	+	0.825578i	$0.309151\pi$
$38$	20.0000	+	34.6410i	0.0853797	+	0.147882i
$39$		0			0
$40$	24.0000	−	41.5692i	0.0948683	−	0.164317i
$41$	−21.0000	+	36.3731i	−0.0799914	+	0.138549i	−0.903246	−	0.429123i	$-0.858823\pi$
$41$	−21.0000	+	36.3731i	−0.0799914	+	0.138549i	0.823255	+	0.567672i	$0.192156\pi$
$42$		0			0
$43$	26.0000	+	45.0333i	0.0922084	+	0.159710i	0.908440	−	0.418015i	$-0.137274\pi$
$43$	26.0000	+	45.0333i	0.0922084	+	0.159710i	−0.816232	+	0.577725i	$0.803941\pi$
$44$	48.0000			0.164461
$45$		0			0
$46$	−336.000			−1.07697
$47$	48.0000	+	83.1384i	0.148969	+	0.258021i	0.930846	−	0.365410i	$-0.119071\pi$
$47$	48.0000	+	83.1384i	0.148969	+	0.258021i	−0.781878	+	0.623431i	$0.785738\pi$
$48$		0			0
$49$	43.5000	−	75.3442i	0.126822	−	0.219662i
$50$	−89.0000	+	154.153i	−0.251730	+	0.436009i
$51$		0			0
$52$	−76.0000	−	131.636i	−0.202679	−	0.351050i
$53$	198.000			0.513158			0.256579	−	0.966523i	$-0.417405\pi$
$53$	198.000			0.513158			0.256579	+	0.966523i	$0.417405\pi$
$54$		0			0
$55$	72.0000			0.176518
$56$	−64.0000	−	110.851i	−0.152721	−	0.264520i
$57$		0			0
$58$	30.0000	−	51.9615i	0.0679171	−	0.117636i
$59$	330.000	−	571.577i	0.728175	−	1.26124i	−0.229478	−	0.973314i	$-0.573702\pi$
$59$	330.000	−	571.577i	0.728175	−	1.26124i	0.957654	−	0.287923i	$-0.0929647\pi$
$60$		0			0
$61$	269.000	+	465.922i	0.564622	+	0.977953i	0.997085	+	0.0763018i	$0.0243112\pi$
$61$	269.000	+	465.922i	0.564622	+	0.977953i	−0.432463	+	0.901652i	$0.642355\pi$
$62$	176.000			0.360516
$63$		0			0
$64$	64.0000			0.125000
$65$	−114.000	−	197.454i	−0.217538	−	0.376787i
$66$		0			0
$67$	−442.000	+	765.566i	−0.805954	+	1.39595i	0.109692	+	0.993966i	$0.465014\pi$
$67$	−442.000	+	765.566i	−0.805954	+	1.39595i	−0.915645	+	0.401987i	$0.868320\pi$
$68$	252.000	−	436.477i	0.449404	−	0.778391i
$69$		0			0
$70$	−96.0000	−	166.277i	−0.163917	−	0.283913i
$71$	792.000			1.32385			0.661923	−	0.749572i	$-0.269740\pi$
$71$	792.000			1.32385			0.661923	+	0.749572i	$0.269740\pi$
$72$		0			0
$73$	218.000			0.349520			0.174760	−	0.984611i	$-0.444085\pi$
$73$	218.000			0.349520			0.174760	+	0.984611i	$0.444085\pi$
$74$	254.000	+	439.941i	0.399012	+	0.691109i
$75$		0			0
$76$	−40.0000	+	69.2820i	−0.0603726	+	0.104568i
$77$	96.0000	−	166.277i	0.142081	−	0.246091i
$78$		0			0
$79$	260.000	+	450.333i	0.370282	+	0.641347i	0.989609	−	0.143786i	$-0.0459277\pi$
$79$	260.000	+	450.333i	0.370282	+	0.641347i	−0.619327	+	0.785133i	$0.712594\pi$
$80$	96.0000			0.134164
$81$		0			0
$82$	−84.0000			−0.113125
$83$	246.000	+	426.084i	0.325325	+	0.563480i	0.981578	−	0.191061i	$-0.0611928\pi$
$83$	246.000	+	426.084i	0.325325	+	0.563480i	−0.656253	+	0.754541i	$0.727859\pi$
$84$		0			0
$85$	378.000	−	654.715i	0.482351	−	0.835457i
$86$	−52.0000	+	90.0666i	−0.0652012	+	0.112932i
$87$		0			0
$88$	48.0000	+	83.1384i	0.0581456	+	0.100711i
$89$	810.000			0.964717			0.482359	−	0.875974i	$-0.339780\pi$
$89$	810.000			0.964717			0.482359	+	0.875974i	$0.339780\pi$
$90$		0			0
$91$	−608.000			−0.700393
$92$	−336.000	−	581.969i	−0.380765	−	0.659505i
$93$		0			0
$94$	−96.0000	+	166.277i	−0.105337	+	0.182448i
$95$	−60.0000	+	103.923i	−0.0647986	+	0.112235i
$96$		0			0
$97$	−577.000	−	999.393i	−0.603974	−	1.04611i	−0.992213	−	0.124555i	$-0.960250\pi$
$97$	−577.000	−	999.393i	−0.603974	−	1.04611i	0.388239	−	0.921559i	$-0.373084\pi$
$98$	174.000			0.179354
$99$		0			0
$100$	−356.000			−0.356000
$101$	309.000	+	535.204i	0.304422	+	0.527275i	0.977133	−	0.212631i	$-0.0682033\pi$
$101$	309.000	+	535.204i	0.304422	+	0.527275i	−0.672710	+	0.739906i	$0.734870\pi$
$102$		0			0
$103$	−64.0000	+	110.851i	−0.0612243	+	0.106044i	−0.895013	−	0.446040i	$-0.852834\pi$
$103$	−64.0000	+	110.851i	−0.0612243	+	0.106044i	0.833789	+	0.552084i	$0.186167\pi$
$104$	152.000	−	263.272i	0.143316	−	0.248230i
$105$		0			0
$106$	198.000	+	342.946i	0.181429	+	0.314244i
$107$	−1476.00			−1.33355			−0.666777	−	0.745257i	$-0.732327\pi$
$107$	−1476.00			−1.33355			−0.666777	+	0.745257i	$0.732327\pi$
$108$		0			0
$109$	1190.00			1.04570			0.522850	−	0.852425i	$-0.324869\pi$
$109$	1190.00			1.04570			0.522850	+	0.852425i	$0.324869\pi$
$110$	72.0000	+	124.708i	0.0624085	+	0.108095i
$111$		0			0
$112$	128.000	−	221.703i	0.107990	−	0.187044i
$113$	231.000	−	400.104i	0.192307	−	0.333085i	−0.753708	−	0.657210i	$-0.771737\pi$
$113$	231.000	−	400.104i	0.192307	−	0.333085i	0.946014	+	0.324125i	$0.105070\pi$
$114$		0			0
$115$	−504.000	−	872.954i	−0.408680	−	0.707855i
$116$	120.000			0.0960493
$117$		0			0
$118$	1320.00			1.02980
$119$	−1008.00	−	1745.91i	−0.776498	−	1.34493i
$120$		0			0
$121$	593.500	−	1027.97i	0.445905	−	0.772331i
$122$	−538.000	+	931.843i	−0.399248	+	0.691517i
$123$		0			0
$124$	176.000	+	304.841i	0.127462	+	0.220770i
$125$	−1284.00			−0.918756
$126$		0			0
$127$	−2536.00			−1.77192			−0.885959	−	0.463763i	$-0.846499\pi$
$127$	−2536.00			−1.77192			−0.885959	+	0.463763i	$0.846499\pi$
$128$	64.0000	+	110.851i	0.0441942	+	0.0765466i
$129$		0			0
$130$	228.000	−	394.908i	0.153822	−	0.266428i
$131$	−1146.00	+	1984.93i	−0.764324	+	1.32385i	0.176279	+	0.984340i	$0.443594\pi$
$131$	−1146.00	+	1984.93i	−0.764324	+	1.32385i	−0.940603	+	0.339508i	$0.889739\pi$
$132$		0			0
$133$	160.000	+	277.128i	0.104314	+	0.180677i
$134$	−1768.00			−1.13979
$135$		0			0
$136$	1008.00			0.635554
$137$	363.000	+	628.734i	0.226374	+	0.392091i	0.956731	−	0.290975i	$-0.0939796\pi$
$137$	363.000	+	628.734i	0.226374	+	0.392091i	−0.730357	+	0.683066i	$0.760646\pi$
$138$		0			0
$139$	−190.000	+	329.090i	−0.115939	+	0.200813i	−0.918155	−	0.396222i	$-0.870321\pi$
$139$	−190.000	+	329.090i	−0.115939	+	0.200813i	0.802215	+	0.597035i	$0.203655\pi$
$140$	192.000	−	332.554i	0.115907	−	0.200757i
$141$		0			0
$142$	792.000	+	1371.78i	0.468050	+	0.810687i
$143$	456.000			0.266662
$144$		0			0
$145$	180.000			0.103091
$146$	218.000	+	377.587i	0.123574	+	0.214036i
$147$		0			0
$148$	−508.000	+	879.882i	−0.282144	+	0.488688i
$149$	−795.000	+	1376.98i	−0.437107	+	0.757091i	−0.997465	−	0.0711590i	$-0.977330\pi$
$149$	−795.000	+	1376.98i	−0.437107	+	0.757091i	0.560358	+	0.828251i	$0.310664\pi$
$150$		0			0
$151$	−1216.00	−	2106.17i	−0.655342	−	1.13509i	−0.981808	−	0.189877i	$-0.939191\pi$
$151$	−1216.00	−	2106.17i	−0.655342	−	1.13509i	0.326466	−	0.945209i	$-0.394142\pi$
$152$	−160.000			−0.0853797
$153$		0			0
$154$	384.000			0.200932
$155$	264.000	+	457.261i	0.136806	+	0.236956i
$156$		0			0
$157$	−307.000	+	531.740i	−0.156059	+	0.270302i	−0.933444	−	0.358723i	$-0.883212\pi$
$157$	−307.000	+	531.740i	−0.156059	+	0.270302i	0.777385	+	0.629025i	$0.216546\pi$
$158$	−520.000	+	900.666i	−0.261829	+	0.453501i
$159$		0			0
$160$	96.0000	+	166.277i	0.0474342	+	0.0821584i
$161$	−2688.00			−1.31580
$162$		0			0
$163$	−1852.00			−0.889938			−0.444969	−	0.895546i	$-0.646785\pi$
$163$	−1852.00			−0.889938			−0.444969	+	0.895546i	$0.646785\pi$
$164$	−84.0000	−	145.492i	−0.0399957	−	0.0692746i
$165$		0			0
$166$	−492.000	+	852.169i	−0.230040	+	0.398441i
$167$	1068.00	−	1849.83i	0.494876	−	0.857151i	−0.505106	−	0.863057i	$-0.668547\pi$
$167$	1068.00	−	1849.83i	0.494876	−	0.857151i	0.999983	+	0.00590641i	$0.00188008\pi$
$168$		0			0
$169$	376.500	+	652.117i	0.171370	+	0.296822i
$170$	1512.00			0.682148
$171$		0			0
$172$	−208.000			−0.0922084
$173$	−879.000	−	1522.47i	−0.386296	−	0.669084i	0.605652	−	0.795729i	$-0.292912\pi$
$173$	−879.000	−	1522.47i	−0.386296	−	0.669084i	−0.991948	+	0.126646i	$0.959579\pi$
$174$		0			0
$175$	−712.000	+	1233.22i	−0.307555	+	0.532701i
$176$	−96.0000	+	166.277i	−0.0411152	+	0.0712136i
$177$		0			0
$178$	810.000	+	1402.96i	0.341079	+	0.590766i
$179$	−540.000			−0.225483			−0.112742	−	0.993624i	$-0.535963\pi$
$179$	−540.000			−0.225483			−0.112742	+	0.993624i	$0.535963\pi$
$180$		0			0
$181$	1982.00			0.813928			0.406964	−	0.913444i	$-0.366588\pi$
$181$	1982.00			0.813928			0.406964	+	0.913444i	$0.366588\pi$
$182$	−608.000	−	1053.09i	−0.247626	−	0.428901i
$183$		0			0
$184$	672.000	−	1163.94i	0.269242	−	0.466341i
$185$	−762.000	+	1319.82i	−0.302829	+	0.524515i
$186$		0			0
$187$	756.000	+	1309.43i	0.295637	+	0.512059i
$188$	−384.000			−0.148969
$189$		0			0
$190$	−240.000			−0.0916391
$191$	1344.00	+	2327.88i	0.509154	+	0.881881i	0.999944	+	0.0106027i	$0.00337499\pi$
$191$	1344.00	+	2327.88i	0.509154	+	0.881881i	−0.490790	+	0.871278i	$0.663292\pi$
$192$		0			0
$193$	1151.00	−	1993.59i	0.429279	−	0.743533i	−0.567531	−	0.823352i	$-0.692101\pi$
$193$	1151.00	−	1993.59i	0.429279	−	0.743533i	0.996809	+	0.0798198i	$0.0254345\pi$
$194$	1154.00	−	1998.79i	0.427074	−	0.739714i
$195$		0			0
$196$	174.000	+	301.377i	0.0634111	+	0.109831i
$197$	4374.00			1.58190			0.790951	−	0.611880i	$-0.209586\pi$
$197$	4374.00			1.58190			0.790951	+	0.611880i	$0.209586\pi$
$198$		0			0
$199$	−1600.00			−0.569955			−0.284977	−	0.958534i	$-0.591986\pi$
$199$	−1600.00			−0.569955			−0.284977	+	0.958534i	$0.591986\pi$
$200$	−356.000	−	616.610i	−0.125865	−	0.218005i
$201$		0			0
$202$	−618.000	+	1070.41i	−0.215259	+	0.372840i
$203$	240.000	−	415.692i	0.0829788	−	0.143724i
$204$		0			0
$205$	−126.000	−	218.238i	−0.0429279	−	0.0743533i
$206$	−256.000			−0.0865843
$207$		0			0
$208$	608.000			0.202679
$209$	−120.000	−	207.846i	−0.0397157	−	0.0687895i
$210$		0			0
$211$	−1666.00	+	2885.60i	−0.543565	+	0.941482i	0.455131	+	0.890425i	$0.349592\pi$
$211$	−1666.00	+	2885.60i	−0.543565	+	0.941482i	−0.998696	+	0.0510573i	$0.983741\pi$
$212$	−396.000	+	685.892i	−0.128290	+	0.222204i
$213$		0			0
$214$	−1476.00	−	2556.51i	−0.471483	−	0.816632i
$215$	−312.000			−0.0989685
$216$		0			0
$217$	1408.00			0.440467
$218$	1190.00	+	2061.14i	0.369711	+	0.640358i
$219$		0			0
$220$	−144.000	+	249.415i	−0.0441294	+	0.0764344i
$221$	2394.00	−	4146.53i	0.728678	−	1.26211i
$222$		0			0
$223$	−1324.00	−	2293.24i	−0.397586	−	0.688639i	0.595842	−	0.803102i	$-0.296819\pi$
$223$	−1324.00	−	2293.24i	−0.397586	−	0.688639i	−0.993427	+	0.114463i	$0.963485\pi$
$224$	512.000			0.152721
$225$		0			0
$226$	924.000			0.271963
$227$	−1122.00	−	1943.36i	−0.328061	−	0.568218i	0.654066	−	0.756437i	$-0.273062\pi$
$227$	−1122.00	−	1943.36i	−0.328061	−	0.568218i	−0.982127	+	0.188220i	$0.939728\pi$
$228$		0			0
$229$	2825.00	−	4893.04i	0.815202	−	1.41197i	−0.0939808	−	0.995574i	$-0.529959\pi$
$229$	2825.00	−	4893.04i	0.815202	−	1.41197i	0.909183	−	0.416397i	$-0.136707\pi$
$230$	1008.00	−	1745.91i	0.288981	−	0.500529i
$231$		0			0
$232$	120.000	+	207.846i	0.0339586	+	0.0588180i
$233$	4698.00			1.32093			0.660464	−	0.750858i	$-0.270360\pi$
$233$	4698.00			1.32093			0.660464	+	0.750858i	$0.270360\pi$
$234$		0			0
$235$	−576.000			−0.159890
$236$	1320.00	+	2286.31i	0.364088	+	0.630618i
$237$		0			0
$238$	2016.00	−	3491.81i	0.549067	−	0.951011i
$239$	600.000	−	1039.23i	0.162388	−	0.281265i	−0.773337	−	0.633996i	$-0.781414\pi$
$239$	600.000	−	1039.23i	0.162388	−	0.281265i	0.935725	+	0.352731i	$0.114747\pi$
$240$		0			0
$241$	359.000	+	621.806i	0.0959553	+	0.166199i	0.910007	−	0.414593i	$-0.136076\pi$
$241$	359.000	+	621.806i	0.0959553	+	0.166199i	−0.814052	+	0.580793i	$0.802743\pi$
$242$	2374.00			0.630605
$243$		0			0
$244$	−2152.00			−0.564622
$245$	261.000	+	452.065i	0.0680599	+	0.117883i
$246$		0			0
$247$	−380.000	+	658.179i	−0.0978900	+	0.169550i
$248$	−352.000	+	609.682i	−0.0901291	+	0.156108i
$249$		0			0
$250$	−1284.00	−	2223.95i	−0.324829	−	0.562621i
$251$	6012.00			1.51185			0.755924	−	0.654659i	$-0.227188\pi$
$251$	6012.00			1.51185			0.755924	+	0.654659i	$0.227188\pi$
$252$		0			0
$253$	2016.00			0.500968
$254$	−2536.00	−	4392.48i	−0.626468	−	1.08507i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	1023.00	−	1771.89i	0.248300	−	0.430067i	−0.714755	−	0.699375i	$-0.753462\pi$
$257$	1023.00	−	1771.89i	0.248300	−	0.430067i	0.963054	+	0.269308i	$0.0867949\pi$
$258$		0			0
$259$	2032.00	+	3519.53i	0.487499	+	0.844374i
$260$	912.000			0.217538
$261$		0			0
$262$	−4584.00			−1.08092
$263$	3036.00	+	5258.51i	0.711817	+	1.23290i	0.964175	+	0.265269i	$0.0854606\pi$
$263$	3036.00	+	5258.51i	0.711817	+	1.23290i	−0.252358	+	0.967634i	$0.581206\pi$
$264$		0			0
$265$	−594.000	+	1028.84i	−0.137695	+	0.238494i
$266$	−320.000	+	554.256i	−0.0737611	+	0.127758i
$267$		0			0
$268$	−1768.00	−	3062.27i	−0.402977	−	0.697976i
$269$	−6930.00			−1.57074			−0.785371	−	0.619025i	$-0.787528\pi$
$269$	−6930.00			−1.57074			−0.785371	+	0.619025i	$0.787528\pi$
$270$		0			0
$271$	1352.00			0.303056			0.151528	−	0.988453i	$-0.451581\pi$
$271$	1352.00			0.303056			0.151528	+	0.988453i	$0.451581\pi$
$272$	1008.00	+	1745.91i	0.224702	+	0.389195i
$273$		0			0
$274$	−726.000	+	1257.47i	−0.160070	+	0.277250i
$275$	534.000	−	924.915i	0.117096	−	0.202816i
$276$		0			0
$277$	593.000	+	1027.11i	0.128628	+	0.222790i	0.923145	−	0.384451i	$-0.125609\pi$
$277$	593.000	+	1027.11i	0.128628	+	0.222790i	−0.794517	+	0.607241i	$0.792276\pi$
$278$	−760.000			−0.163963
$279$		0			0
$280$	768.000			0.163917
$281$	−1221.00	−	2114.83i	−0.259213	−	0.448969i	0.706819	−	0.707395i	$-0.250130\pi$
$281$	−1221.00	−	2114.83i	−0.259213	−	0.448969i	−0.966031	+	0.258425i	$0.916796\pi$
$282$		0			0
$283$	−1414.00	+	2449.12i	−0.297009	+	0.514435i	−0.975450	−	0.220220i	$-0.929323\pi$
$283$	−1414.00	+	2449.12i	−0.297009	+	0.514435i	0.678441	+	0.734655i	$0.262656\pi$
$284$	−1584.00	+	2743.57i	−0.330962	+	0.573242i
$285$		0			0
$286$	456.000	+	789.815i	0.0942792	+	0.163296i
$287$	−672.000			−0.138212
$288$		0			0
$289$	10963.0			2.23143
$290$	180.000	+	311.769i	0.0364482	+	0.0631301i
$291$		0			0
$292$	−436.000	+	755.174i	−0.0873800	+	0.151347i
$293$	−2379.00	+	4120.55i	−0.474344	+	0.821587i	−0.999568	−	0.0293763i	$-0.990648\pi$
$293$	−2379.00	+	4120.55i	−0.474344	+	0.821587i	0.525225	+	0.850963i	$0.323981\pi$
$294$		0			0
$295$	1980.00	+	3429.46i	0.390780	+	0.676851i
$296$	−2032.00			−0.399012
$297$		0			0
$298$	−3180.00			−0.618163
$299$	−3192.00	−	5528.71i	−0.617385	−	1.06934i
$300$		0			0
$301$	−416.000	+	720.533i	−0.0796606	+	0.137976i
$302$	2432.00	−	4212.35i	0.463397	−	0.802627i
$303$		0			0
$304$	−160.000	−	277.128i	−0.0301863	−	0.0522842i
$305$	−3228.00			−0.606016
$306$		0			0
$307$	−8476.00			−1.57574			−0.787868	−	0.615844i	$-0.788815\pi$
$307$	−8476.00			−1.57574			−0.787868	+	0.615844i	$0.788815\pi$
$308$	384.000	+	665.108i	0.0710404	+	0.123046i
$309$		0			0
$310$	−528.000	+	914.523i	−0.0967367	+	0.167553i
$311$	−2316.00	+	4011.43i	−0.422278	+	0.731406i	−0.996162	−	0.0875302i	$-0.972103\pi$
$311$	−2316.00	+	4011.43i	−0.422278	+	0.731406i	0.573884	+	0.818936i	$0.305436\pi$
$312$		0			0
$313$	2411.00	+	4175.97i	0.435392	+	0.754122i	0.997328	−	0.0730597i	$-0.0232764\pi$
$313$	2411.00	+	4175.97i	0.435392	+	0.754122i	−0.561935	+	0.827181i	$0.689943\pi$
$314$	−1228.00			−0.220701
$315$		0			0
$316$	−2080.00			−0.370282
$317$	1713.00	+	2967.00i	0.303507	+	0.525689i	0.976928	−	0.213570i	$-0.0685091\pi$
$317$	1713.00	+	2967.00i	0.303507	+	0.525689i	−0.673421	+	0.739259i	$0.735176\pi$
$318$		0			0
$319$	−180.000	+	311.769i	−0.0315927	+	0.0547201i
$320$	−192.000	+	332.554i	−0.0335410	+	0.0580948i
$321$		0			0
$322$	−2688.00	−	4655.75i	−0.465206	−	0.805761i
$323$	−2520.00			−0.434107
$324$		0			0
$325$	−3382.00			−0.577230
$326$	−1852.00	−	3207.76i	−0.314640	−	0.544973i
$327$		0			0
$328$	168.000	−	290.985i	0.0282812	−	0.0489846i
$329$	−768.000	+	1330.22i	−0.128697	+	0.222909i
$330$		0			0
$331$	1394.00	+	2414.48i	0.231484	+	0.400942i	0.958245	−	0.285948i	$-0.0923086\pi$
$331$	1394.00	+	2414.48i	0.231484	+	0.400942i	−0.726761	+	0.686890i	$0.758975\pi$
$332$	−1968.00			−0.325325
$333$		0			0
$334$	4272.00			0.699861
$335$	−2652.00	−	4593.40i	−0.432520	−	0.749147i
$336$		0			0
$337$	−217.000	+	375.855i	−0.0350764	+	0.0607541i	−0.883031	−	0.469315i	$-0.844501\pi$
$337$	−217.000	+	375.855i	−0.0350764	+	0.0607541i	0.847954	+	0.530069i	$0.177834\pi$
$338$	−753.000	+	1304.23i	−0.121177	+	0.209885i
$339$		0			0
$340$	1512.00	+	2618.86i	0.241176	+	0.417728i
$341$	−1056.00			−0.167700
$342$		0			0
$343$	6880.00			1.08305
$344$	−208.000	−	360.267i	−0.0326006	−	0.0564659i
$345$		0			0
$346$	1758.00	−	3044.95i	0.273152	−	0.473114i
$347$	−3342.00	+	5788.51i	−0.517026	+	0.895515i	0.482779	+	0.875742i	$0.339628\pi$
$347$	−3342.00	+	5788.51i	−0.517026	+	0.895515i	−0.999805	+	0.0197726i	$0.993706\pi$
$348$		0			0
$349$	−1315.00	−	2277.65i	−0.201692	−	0.349340i	0.747382	−	0.664395i	$-0.231311\pi$
$349$	−1315.00	−	2277.65i	−0.201692	−	0.349340i	−0.949074	+	0.315055i	$0.897977\pi$
$350$	−2848.00			−0.434949
$351$		0			0
$352$	−384.000			−0.0581456
$353$	3711.00	+	6427.64i	0.559537	+	0.969147i	0.997535	+	0.0701707i	$0.0223544\pi$
$353$	3711.00	+	6427.64i	0.559537	+	0.969147i	−0.437998	+	0.898976i	$0.644312\pi$
$354$		0			0
$355$	−2376.00	+	4115.35i	−0.355225	+	0.615268i
$356$	−1620.00	+	2805.92i	−0.241179	+	0.417735i
$357$		0			0
$358$	−540.000	−	935.307i	−0.0797204	−	0.138080i
$359$	−10440.0			−1.53482			−0.767412	−	0.641154i	$-0.778456\pi$
$359$	−10440.0			−1.53482			−0.767412	+	0.641154i	$0.778456\pi$
$360$		0			0
$361$	−6459.00			−0.941682
$362$	1982.00	+	3432.92i	0.287767	+	0.498427i
$363$		0			0
$364$	1216.00	−	2106.17i	0.175098	−	0.303279i
$365$	−654.000	+	1132.76i	−0.0937861	+	0.162442i
$366$		0			0
$367$	−5212.00	−	9027.45i	−0.741319	−	1.28400i	−0.951895	−	0.306425i	$-0.900867\pi$
$367$	−5212.00	−	9027.45i	−0.741319	−	1.28400i	0.210575	−	0.977578i	$-0.432466\pi$
$368$	2688.00			0.380765
$369$		0			0
$370$	−3048.00			−0.428265
$371$	1584.00	+	2743.57i	0.221664	+	0.383933i
$372$		0			0
$373$	−1639.00	+	2838.83i	−0.227518	+	0.394073i	−0.957072	−	0.289851i	$-0.906394\pi$
$373$	−1639.00	+	2838.83i	−0.227518	+	0.394073i	0.729554	+	0.683923i	$0.239728\pi$
$374$	−1512.00	+	2618.86i	−0.209047	+	0.362080i
$375$		0			0
$376$	−384.000	−	665.108i	−0.0526683	−	0.0912242i
$377$	1140.00			0.155737
$378$		0			0
$379$	6140.00			0.832165			0.416083	−	0.909327i	$-0.363403\pi$
$379$	6140.00			0.832165			0.416083	+	0.909327i	$0.363403\pi$
$380$	−240.000	−	415.692i	−0.0323993	−	0.0561173i
$381$		0			0
$382$	−2688.00	+	4655.75i	−0.360026	+	0.623584i
$383$	1536.00	−	2660.43i	0.204924	−	0.354939i	−0.745184	−	0.666858i	$-0.767639\pi$
$383$	1536.00	−	2660.43i	0.204924	−	0.354939i	0.950109	+	0.311919i	$0.100972\pi$
$384$		0			0
$385$	576.000	+	997.661i	0.0762485	+	0.132066i
$386$	4604.00			0.607092
$387$		0			0
$388$	4616.00			0.603974
$389$	−3075.00	−	5326.06i	−0.400794	−	0.694195i	0.593028	−	0.805182i	$-0.297932\pi$
$389$	−3075.00	−	5326.06i	−0.400794	−	0.694195i	−0.993822	+	0.110987i	$0.964599\pi$
$390$		0			0
$391$	10584.0	−	18332.0i	1.36894	−	2.37108i
$392$	−348.000	+	602.754i	−0.0448384	+	0.0776624i
$393$		0			0
$394$	4374.00	+	7575.99i	0.559287	+	0.968713i
$395$	−3120.00			−0.397428
$396$		0			0
$397$	−106.000			−0.0134005			−0.00670024	−	0.999978i	$-0.502133\pi$
$397$	−106.000			−0.0134005			−0.00670024	+	0.999978i	$0.502133\pi$
$398$	−1600.00	−	2771.28i	−0.201509	−	0.349025i
$399$		0			0
$400$	712.000	−	1233.22i	0.0890000	−	0.154153i
$401$	879.000	−	1522.47i	0.109464	−	0.189598i	−0.806089	−	0.591794i	$-0.798420\pi$
$401$	879.000	−	1522.47i	0.109464	−	0.189598i	0.915553	+	0.402197i	$0.131753\pi$
$402$		0			0
$403$	1672.00	+	2895.99i	0.206671	+	0.357964i
$404$	−2472.00			−0.304422
$405$		0			0
$406$	960.000			0.117350
$407$	−1524.00	−	2639.65i	−0.185607	−	0.321480i
$408$		0			0
$409$	1835.00	−	3178.31i	0.221846	−	0.384248i	−0.733523	−	0.679665i	$-0.762125\pi$
$409$	1835.00	−	3178.31i	0.221846	−	0.384248i	0.955368	+	0.295417i	$0.0954585\pi$
$410$	252.000	−	436.477i	0.0303546	−	0.0525757i
$411$		0			0
$412$	−256.000	−	443.405i	−0.0306122	−	0.0530218i
$413$	10560.0			1.25817
$414$		0			0
$415$	−2952.00			−0.349176
$416$	608.000	+	1053.09i	0.0716578	+	0.124115i
$417$		0			0
$418$	240.000	−	415.692i	0.0280832	−	0.0486416i
$419$	4830.00	−	8365.81i	0.563153	−	0.975409i	−0.434066	−	0.900881i	$-0.642922\pi$
$419$	4830.00	−	8365.81i	0.563153	−	0.975409i	0.997219	−	0.0745280i	$-0.0237450\pi$
$420$		0			0
$421$	−4231.00	−	7328.31i	−0.489801	−	0.848361i	0.510130	−	0.860097i	$-0.329597\pi$
$421$	−4231.00	−	7328.31i	−0.489801	−	0.848361i	−0.999931	+	0.0117367i	$0.996264\pi$
$422$	−6664.00			−0.768717
$423$		0			0
$424$	−1584.00			−0.181429
$425$	−5607.00	−	9711.61i	−0.639952	−	1.10843i
$426$		0			0
$427$	−4304.00	+	7454.75i	−0.487787	+	0.844872i
$428$	2952.00	−	5113.01i	0.333389	−	0.577446i
$429$		0			0
$430$	−312.000	−	540.400i	−0.0349906	−	0.0606056i
$431$	9792.00			1.09435			0.547174	−	0.837019i	$-0.315704\pi$
$431$	9792.00			1.09435			0.547174	+	0.837019i	$0.315704\pi$
$432$		0			0
$433$	−7342.00			−0.814859			−0.407430	−	0.913237i	$-0.633575\pi$
$433$	−7342.00			−0.814859			−0.407430	+	0.913237i	$0.633575\pi$
$434$	1408.00	+	2438.73i	0.155728	+	0.269730i
$435$		0			0
$436$	−2380.00	+	4122.28i	−0.261425	+	0.452801i
$437$	−1680.00	+	2909.85i	−0.183902	+	0.318528i
$438$		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	$-0.362982\pi$
$440$	−576.000			−0.0624085
$441$		0			0
$442$	9576.00			1.03051
$443$	8706.00	+	15079.2i	0.933712	+	1.61724i	0.776914	+	0.629606i	$0.216784\pi$
$443$	8706.00	+	15079.2i	0.933712	+	1.61724i	0.156798	+	0.987631i	$0.449883\pi$
$444$		0			0
$445$	−2430.00	+	4208.88i	−0.258861	+	0.448360i
$446$	2648.00	−	4586.47i	0.281136	−	0.486941i
$447$		0			0
$448$	512.000	+	886.810i	0.0539949	+	0.0935220i
$449$	−1710.00			−0.179732			−0.0898662	−	0.995954i	$-0.528644\pi$
$449$	−1710.00			−0.179732			−0.0898662	+	0.995954i	$0.528644\pi$
$450$		0			0
$451$	504.000			0.0526218
$452$	924.000	+	1600.41i	0.0961533	+	0.166542i
$453$		0			0
$454$	2244.00	−	3886.72i	0.231974	−	0.401791i
$455$	1824.00	−	3159.26i	0.187935	−	0.325513i
$456$		0			0
$457$	323.000	+	559.452i	0.0330619	+	0.0572649i	0.882083	−	0.471094i	$-0.156141\pi$
$457$	323.000	+	559.452i	0.0330619	+	0.0572649i	−0.849021	+	0.528359i	$0.822807\pi$
$458$	11300.0			1.15287
$459$		0			0
$460$	4032.00			0.408680
$461$	3009.00	+	5211.74i	0.303998	+	0.526540i	0.977038	−	0.213066i	$-0.0683450\pi$
$461$	3009.00	+	5211.74i	0.303998	+	0.526540i	−0.673040	+	0.739606i	$0.735012\pi$
$462$		0			0
$463$	3356.00	−	5812.76i	0.336861	−	0.583460i	−0.646980	−	0.762507i	$-0.723968\pi$
$463$	3356.00	−	5812.76i	0.336861	−	0.583460i	0.983840	+	0.179047i	$0.0573015\pi$
$464$	−240.000	+	415.692i	−0.0240123	+	0.0415906i
$465$		0			0
$466$	4698.00	+	8137.17i	0.467019	+	0.808900i
$467$	5364.00			0.531512			0.265756	−	0.964040i	$-0.414378\pi$
$467$	5364.00			0.531512			0.265756	+	0.964040i	$0.414378\pi$
$468$		0			0
$469$	−14144.0			−1.39256
$470$	−576.000	−	997.661i	−0.0565296	−	0.0979121i
$471$		0			0
$472$	−2640.00	+	4572.61i	−0.257449	+	0.445914i
$473$	312.000	−	540.400i	0.0303293	−	0.0525319i
$474$		0			0
$475$	890.000	+	1541.53i	0.0859705	+	0.148905i
$476$	8064.00			0.776498
$477$		0			0
$478$	2400.00			0.229652
$479$	−4920.00	−	8521.69i	−0.469312	−	0.812873i	0.530072	−	0.847952i	$-0.322165\pi$
$479$	−4920.00	−	8521.69i	−0.469312	−	0.812873i	−0.999385	+	0.0350799i	$0.988831\pi$
$480$		0			0
$481$	−4826.00	+	8358.88i	−0.457477	+	0.792374i
$482$	−718.000	+	1243.61i	−0.0678506	+	0.117521i
$483$		0			0
$484$	2374.00	+	4111.89i	0.222953	+	0.386165i
$485$	6924.00			0.648253
$486$		0			0
$487$	1424.00			0.132500			0.0662501	−	0.997803i	$-0.478896\pi$
$487$	1424.00			0.132500			0.0662501	+	0.997803i	$0.478896\pi$
$488$	−2152.00	−	3727.37i	−0.199624	−	0.345759i
$489$		0			0
$490$	−522.000	+	904.131i	−0.0481256	+	0.0833560i
$491$	2274.00	−	3938.68i	0.209011	−	0.362017i	−0.742393	−	0.669965i	$-0.766309\pi$
$491$	2274.00	−	3938.68i	0.209011	−	0.362017i	0.951403	+	0.307948i	$0.0996424\pi$
$492$		0			0
$493$	1890.00	+	3273.58i	0.172660	+	0.299056i
$494$	−1520.00			−0.138437
$495$		0			0
$496$	−1408.00			−0.127462
$497$	6336.00	+	10974.3i	0.571848	+	0.990470i
$498$		0			0
$499$	−3250.00	+	5629.17i	−0.291563	+	0.505002i	−0.974180	−	0.225775i	$-0.927509\pi$
$499$	−3250.00	+	5629.17i	−0.291563	+	0.505002i	0.682616	+	0.730777i	$0.260842\pi$
$500$	2568.00	−	4447.91i	0.229689	−	0.397833i
$501$		0			0
$502$	6012.00	+	10413.1i	0.534519	+	0.925815i
$503$	12168.0			1.07862			0.539308	−	0.842108i	$-0.318686\pi$
$503$	12168.0			1.07862			0.539308	+	0.842108i	$0.318686\pi$
$504$		0			0
$505$	−3708.00			−0.326740
$506$	2016.00	+	3491.81i	0.177119	+	0.306779i
$507$		0			0
$508$	5072.00	−	8784.96i	0.442980	−	0.767263i
$509$	10545.0	−	18264.5i	0.918269	−	1.59049i	0.116226	−	0.993223i	$-0.462920\pi$
$509$	10545.0	−	18264.5i	0.918269	−	1.59049i	0.802043	−	0.597266i	$-0.203746\pi$
$510$		0			0
$511$	1744.00	+	3020.70i	0.150979	+	0.261502i
$512$	−512.000			−0.0441942
$513$		0			0
$514$	4092.00			0.351149
$515$	−384.000	−	665.108i	−0.0328564	−	0.0569090i
$516$		0			0
$517$	576.000	−	997.661i	0.0489989	−	0.0848687i
$518$	−4064.00	+	7039.05i	−0.344714	+	0.597062i
$519$		0			0
$520$	912.000	+	1579.63i	0.0769112	+	0.133214i
$521$	−5238.00			−0.440462			−0.220231	−	0.975448i	$-0.570681\pi$
$521$	−5238.00			−0.440462			−0.220231	+	0.975448i	$0.570681\pi$
$522$		0			0
$523$	8588.00			0.718025			0.359012	−	0.933333i	$-0.383114\pi$
$523$	8588.00			0.718025			0.359012	+	0.933333i	$0.383114\pi$
$524$	−4584.00	−	7939.72i	−0.382162	−	0.661924i
$525$		0			0
$526$	−6072.00	+	10517.0i	−0.503330	+	0.871794i
$527$	−5544.00	+	9602.49i	−0.458255	+	0.793721i
$528$		0			0
$529$	−8028.50	−	13905.8i	−0.659859	−	1.14291i
$530$	−2376.00			−0.194730
$531$		0			0
$532$	−1280.00			−0.104314
$533$	−798.000	−	1382.18i	−0.0648503	−	0.112324i
$534$		0			0
$535$	4428.00	−	7669.52i	0.357830	−	0.619780i
$536$	3536.00	−	6124.53i	0.284948	−	0.493544i
$537$		0			0
$538$	−6930.00	−	12003.1i	−0.555341	−	0.961879i
$539$	−1044.00			−0.0834291
$540$		0			0
$541$	3062.00			0.243338			0.121669	−	0.992571i	$-0.461175\pi$
$541$	3062.00			0.243338			0.121669	+	0.992571i	$0.461175\pi$
$542$	1352.00	+	2341.73i	0.107146	+	0.185583i
$543$		0			0
$544$	−2016.00	+	3491.81i	−0.158888	+	0.275203i
$545$	−3570.00	+	6183.42i	−0.280591	+	0.485998i
$546$		0			0
$547$	4238.00	+	7340.43i	0.331268	+	0.573774i	0.982761	−	0.184881i	$-0.0591901\pi$
$547$	4238.00	+	7340.43i	0.331268	+	0.573774i	−0.651492	+	0.758655i	$0.725857\pi$
$548$	−2904.00			−0.226374
$549$		0			0
$550$	2136.00			0.165599
$551$	−300.000	−	519.615i	−0.0231950	−	0.0401749i
$552$		0			0
$553$	−4160.00	+	7205.33i	−0.319894	+	0.554072i
$554$	−1186.00	+	2054.21i	−0.0909536	+	0.157536i
$555$		0			0
$556$	−760.000	−	1316.36i	−0.0579697	−	0.100407i
$557$	−12546.0			−0.954383			−0.477191	−	0.878799i	$-0.658345\pi$
$557$	−12546.0			−0.954383			−0.477191	+	0.878799i	$0.658345\pi$
$558$		0			0
$559$	−1976.00			−0.149510
$560$	768.000	+	1330.22i	0.0579534	+	0.100378i
$561$		0			0
$562$	2442.00	−	4229.67i	0.183291	−	0.317469i
$563$	6.00000	−	10.3923i	0.000449147	−	0.000777946i	−0.865801	−	0.500389i	$-0.833190\pi$
$563$	6.00000	−	10.3923i	0.000449147	−	0.000777946i	0.866250	+	0.499611i	$0.166524\pi$
$564$		0			0
$565$	1386.00	+	2400.62i	0.103203	+	0.178752i
$566$	−5656.00			−0.420034
$567$		0			0
$568$	−6336.00			−0.468050
$569$	−9645.00	−	16705.6i	−0.710614	−	1.23082i	−0.964627	−	0.263619i	$-0.915084\pi$
$569$	−9645.00	−	16705.6i	−0.710614	−	1.23082i	0.254013	−	0.967201i	$-0.418249\pi$
$570$		0			0
$571$	6074.00	−	10520.5i	0.445165	−	0.771048i	−0.552899	−	0.833248i	$-0.686478\pi$
$571$	6074.00	−	10520.5i	0.445165	−	0.771048i	0.998064	+	0.0622005i	$0.0198118\pi$
$572$	−912.000	+	1579.63i	−0.0666654	+	0.115468i
$573$		0			0
$574$	−672.000	−	1163.94i	−0.0488654	−	0.0846374i
$575$	−14952.0			−1.08442
$576$		0			0
$577$	−10366.0			−0.747907			−0.373953	−	0.927447i	$-0.621998\pi$
$577$	−10366.0			−0.747907			−0.373953	+	0.927447i	$0.621998\pi$
$578$	10963.0	+	18988.5i	0.788929	+	1.36646i
$579$		0			0
$580$	−360.000	+	623.538i	−0.0257727	+	0.0446397i
$581$	−3936.00	+	6817.35i	−0.281055	+	0.486801i
$582$		0			0
$583$	−1188.00	−	2057.68i	−0.0843944	−	0.146175i
$584$	−1744.00			−0.123574
$585$		0			0
$586$	−9516.00			−0.670823
$587$	−3822.00	−	6619.90i	−0.268741	−	0.465473i	0.699796	−	0.714343i	$-0.253274\pi$
$587$	−3822.00	−	6619.90i	−0.268741	−	0.465473i	−0.968537	+	0.248870i	$0.919941\pi$
$588$		0			0
$589$	880.000	−	1524.20i	0.0615616	−	0.106628i
$590$	−3960.00	+	6858.92i	−0.276323	+	0.478606i
$591$		0			0
$592$	−2032.00	−	3519.53i	−0.141072	−	0.244344i
$593$	8658.00			0.599564			0.299782	−	0.954008i	$-0.403086\pi$
$593$	8658.00			0.599564			0.299782	+	0.954008i	$0.403086\pi$
$594$		0			0
$595$	12096.0			0.833425
$596$	−3180.00	−	5507.92i	−0.218553	−	0.378546i
$597$		0			0
$598$	6384.00	−	11057.4i	0.436557	−	0.756139i
$599$	−12900.0	+	22343.5i	−0.879933	+	1.52409i	−0.0285192	+	0.999593i	$0.509079\pi$
$599$	−12900.0	+	22343.5i	−0.879933	+	1.52409i	−0.851414	+	0.524495i	$0.824254\pi$
$600$		0			0
$601$	−8101.00	−	14031.3i	−0.549828	−	0.952330i	−0.998286	−	0.0585262i	$-0.981360\pi$
$601$	−8101.00	−	14031.3i	−0.549828	−	0.952330i	0.448458	−	0.893804i	$-0.351973\pi$
$602$	−1664.00			−0.112657
$603$		0			0
$604$	9728.00			0.655342
$605$	3561.00	+	6167.83i	0.239298	+	0.414476i
$606$		0			0
$607$	12068.0	−	20902.4i	0.806960	−	1.39770i	−0.107999	−	0.994151i	$-0.534444\pi$
$607$	12068.0	−	20902.4i	0.806960	−	1.39770i	0.914960	−	0.403546i	$-0.132222\pi$
$608$	320.000	−	554.256i	0.0213449	−	0.0369705i
$609$		0			0
$610$	−3228.00	−	5591.06i	−0.214259	−	0.371107i
$611$	−3648.00			−0.241542
$612$		0			0
$613$	−4642.00			−0.305854			−0.152927	−	0.988237i	$-0.548870\pi$
$613$	−4642.00			−0.305854			−0.152927	+	0.988237i	$0.548870\pi$
$614$	−8476.00	−	14680.9i	−0.557107	−	0.964937i
$615$		0			0
$616$	−768.000	+	1330.22i	−0.0502331	+	0.0870063i
$617$	3363.00	−	5824.89i	0.219432	−	0.380067i	−0.735203	−	0.677847i	$-0.762913\pi$
$617$	3363.00	−	5824.89i	0.219432	−	0.380067i	0.954634	+	0.297781i	$0.0962464\pi$
$618$		0			0
$619$	10610.0	+	18377.1i	0.688937	+	1.19327i	0.972182	+	0.234226i	$0.0752556\pi$
$619$	10610.0	+	18377.1i	0.688937	+	1.19327i	−0.283245	+	0.959047i	$0.591411\pi$
$620$	−2112.00			−0.136806
$621$		0			0
$622$	−9264.00			−0.597191
$623$	6480.00	+	11223.7i	0.416719	+	0.721778i
$624$		0			0
$625$	−1710.50	+	2962.67i	−0.109472	+	0.189611i
$626$	−4822.00	+	8351.95i	−0.307869	+	0.533244i
$627$		0			0
$628$	−1228.00	−	2126.96i	−0.0780295	−	0.135151i
$629$	−32004.0			−2.02875
$630$		0			0
$631$	29792.0			1.87956			0.939779	−	0.341783i	$-0.111031\pi$
$631$	29792.0			1.87956			0.939779	+	0.341783i	$0.111031\pi$
$632$	−2080.00	−	3602.67i	−0.130914	−	0.226751i
$633$		0			0
$634$	−3426.00	+	5934.01i	−0.214612	+	0.371718i
$635$	7608.00	−	13177.4i	0.475456	−	0.823513i
$636$		0			0
$637$	1653.00	+	2863.08i	0.102817	+	0.178084i
$638$	−720.000			−0.0446788
$639$		0			0
$640$	−768.000			−0.0474342
$641$	5079.00	+	8797.09i	0.312962	+	0.542066i	0.979002	−	0.203850i	$-0.0653455\pi$
$641$	5079.00	+	8797.09i	0.312962	+	0.542066i	−0.666040	+	0.745916i	$0.732012\pi$
$642$		0			0
$643$	−14914.0	+	25831.8i	−0.914698	+	1.58430i	−0.107355	+	0.994221i	$0.534238\pi$
$643$	−14914.0	+	25831.8i	−0.914698	+	1.58430i	−0.807343	+	0.590082i	$0.799095\pi$
$644$	5376.00	−	9311.51i	0.328950	−	0.569759i
$645$		0			0
$646$	−2520.00	−	4364.77i	−0.153480	−	0.265835i
$647$	1944.00			0.118124			0.0590622	−	0.998254i	$-0.481189\pi$
$647$	1944.00			0.118124			0.0590622	+	0.998254i	$0.481189\pi$
$648$		0			0
$649$	−7920.00			−0.479025
$650$	−3382.00	−	5857.80i	−0.204081	−	0.353479i
$651$		0			0
$652$	3704.00	−	6415.52i	0.222484	−	0.385354i
$653$	−13359.0	+	23138.5i	−0.800579	+	1.38664i	0.118657	+	0.992935i	$0.462141\pi$
$653$	−13359.0	+	23138.5i	−0.800579	+	1.38664i	−0.919236	+	0.393708i	$0.871192\pi$
$654$		0			0
$655$	−6876.00	−	11909.6i	−0.410179	−	0.710452i
$656$	672.000			0.0399957
$657$		0			0
$658$	−3072.00			−0.182005
$659$	−2130.00	−	3689.27i	−0.125907	−	0.218078i	0.796180	−	0.605060i	$-0.206851\pi$
$659$	−2130.00	−	3689.27i	−0.125907	−	0.218078i	−0.922087	+	0.386982i	$0.873518\pi$
$660$		0			0
$661$	−11431.0	+	19799.1i	−0.672639	+	1.16504i	0.304514	+	0.952508i	$0.401506\pi$
$661$	−11431.0	+	19799.1i	−0.672639	+	1.16504i	−0.977153	+	0.212537i	$0.931827\pi$
$662$	−2788.00	+	4828.96i	−0.163684	+	0.283509i
$663$		0			0
$664$	−1968.00	−	3408.68i	−0.115020	−	0.199220i
$665$	−1920.00			−0.111962
$666$		0			0
$667$	5040.00			0.292578
$668$	4272.00	+	7399.32i	0.247438	+	0.428575i
$669$		0			0
$670$	5304.00	−	9186.80i	0.305838	−	0.529727i
$671$	3228.00	−	5591.06i	0.185716	−	0.321670i
$672$		0			0
$673$	16271.0	+	28182.2i	0.931948	+	1.61418i	0.779988	+	0.625795i	$0.215225\pi$
$673$	16271.0	+	28182.2i	0.931948	+	1.61418i	0.151960	+	0.988387i	$0.451442\pi$
$674$	−868.000			−0.0496055
$675$		0			0
$676$	−3012.00			−0.171370
$677$	−7107.00	−	12309.7i	−0.403463	−	0.698818i	0.590679	−	0.806907i	$-0.298860\pi$
$677$	−7107.00	−	12309.7i	−0.403463	−	0.698818i	−0.994141	+	0.108089i	$0.965527\pi$
$678$		0			0
$679$	9232.00	−	15990.3i	0.521784	−	0.903757i
$680$	−3024.00	+	5237.72i	−0.170537	+	0.295379i
$681$		0			0
$682$	−1056.00	−	1829.05i	−0.0592908	−	0.102695i
$683$	−7092.00			−0.397317			−0.198659	−	0.980069i	$-0.563659\pi$
$683$	−7092.00			−0.397317			−0.198659	+	0.980069i	$0.563659\pi$
$684$		0			0
$685$	−4356.00			−0.242970
$686$	6880.00	+	11916.5i	0.382915	+	0.663228i
$687$		0			0
$688$	416.000	−	720.533i	0.0230521	−	0.0399274i
$689$	−3762.00	+	6515.98i	−0.208013	+	0.360289i
$690$		0			0
$691$	6614.00	+	11455.8i	0.364122	+	0.630678i	0.988635	−	0.150337i	$-0.0480357\pi$
$691$	6614.00	+	11455.8i	0.364122	+	0.630678i	−0.624513	+	0.781015i	$0.714702\pi$
$692$	7032.00			0.386296
$693$		0			0
$694$	−13368.0			−0.731185
$695$	−1140.00	−	1974.54i	−0.0622197	−	0.107768i
$696$		0			0
$697$	2646.00	−	4583.01i	0.143794	−	0.249058i
$698$	2630.00	−	4555.29i	0.142617	−	0.247021i
$699$		0			0
$700$	−2848.00	−	4932.88i	−0.153778	−	0.266351i
$701$	28062.0			1.51196			0.755982	−	0.654592i	$-0.227160\pi$
$701$	28062.0			1.51196			0.755982	+	0.654592i	$0.227160\pi$
$702$		0			0
$703$	5080.00			0.272540
$704$	−384.000	−	665.108i	−0.0205576	−	0.0356068i
$705$		0			0
$706$	−7422.00	+	12855.3i	−0.395652	+	0.685290i
$707$	−4944.00	+	8563.26i	−0.262996	+	0.455523i
$708$		0			0
$709$	13625.0	+	23599.2i	0.721717	+	1.25005i	0.960311	+	0.278932i	$0.0899803\pi$
$709$	13625.0	+	23599.2i	0.721717	+	1.25005i	−0.238594	+	0.971120i	$0.576686\pi$
$710$	−9504.00			−0.502364
$711$		0			0
$712$	−6480.00			−0.341079
$713$	7392.00	+	12803.3i	0.388264	+	0.672494i
$714$		0			0
$715$	−1368.00	+	2369.45i	−0.0715529	+	0.123933i
$716$	1080.00	−	1870.61i	0.0563708	−	0.0976371i
$717$		0			0
$718$	−10440.0	−	18082.6i	−0.542643	−	0.939884i
$719$	−14400.0			−0.746912			−0.373456	−	0.927648i	$-0.621827\pi$
$719$	−14400.0			−0.746912			−0.373456	+	0.927648i	$0.621827\pi$
$720$		0			0
$721$	−2048.00			−0.105786
$722$	−6459.00	−	11187.3i	−0.332935	−	0.576660i
$723$		0			0
$724$	−3964.00	+	6865.85i	−0.203482	+	0.352441i
$725$	1335.00	−	2312.29i	0.0683871	−	0.118450i
$726$		0			0
$727$	−8992.00	−	15574.6i	−0.458727	−	0.794539i	0.540167	−	0.841558i	$-0.318361\pi$
$727$	−8992.00	−	15574.6i	−0.458727	−	0.794539i	−0.998894	+	0.0470189i	$0.985028\pi$
$728$	4864.00			0.247626
$729$		0			0
$730$	−2616.00			−0.132634
$731$	−3276.00	−	5674.20i	−0.165755	−	0.287097i
$732$		0			0
$733$	−8299.00	+	14374.3i	−0.418186	+	0.724320i	−0.995757	−	0.0920207i	$-0.970667\pi$
$733$	−8299.00	+	14374.3i	−0.418186	+	0.724320i	0.577571	+	0.816341i	$0.304001\pi$
$734$	10424.0	−	18054.9i	0.524192	−	0.907927i
$735$		0			0
$736$	2688.00	+	4655.75i	0.134621	+	0.233170i
$737$	10608.0			0.530191
$738$		0			0
$739$	1460.00			0.0726752			0.0363376	−	0.999340i	$-0.488431\pi$
$739$	1460.00			0.0726752			0.0363376	+	0.999340i	$0.488431\pi$
$740$	−3048.00	−	5279.29i	−0.151414	−	0.262258i
$741$		0			0
$742$	−3168.00	+	5487.14i	−0.156740	+	0.271481i
$743$	15036.0	−	26043.1i	0.742419	−	1.28591i	−0.208972	−	0.977922i	$-0.567012\pi$
$743$	15036.0	−	26043.1i	0.742419	−	1.28591i	0.951391	−	0.307986i	$-0.0996549\pi$
$744$		0			0
$745$	−4770.00	−	8261.88i	−0.234576	−	0.406298i
$746$	−6556.00			−0.321759
$747$		0			0
$748$	−6048.00			−0.295637
$749$	−11808.0	−	20452.1i	−0.576041	−	0.997733i
$750$		0			0
$751$	9044.00	−	15664.7i	0.439441	−	0.761134i	−0.558205	−	0.829703i	$-0.688510\pi$
$751$	9044.00	−	15664.7i	0.439441	−	0.761134i	0.997646	+	0.0685686i	$0.0218432\pi$
$752$	768.000	−	1330.22i	0.0372421	−	0.0645053i
$753$		0			0
$754$	1140.00	+	1974.54i	0.0550615	+	0.0953693i
$755$	14592.0			0.703387
$756$		0			0
$757$	24734.0			1.18755			0.593773	−	0.804633i	$-0.297638\pi$
$757$	24734.0			1.18755			0.593773	+	0.804633i	$0.297638\pi$
$758$	6140.00	+	10634.8i	0.294215	+	0.509595i
$759$		0			0
$760$	480.000	−	831.384i	0.0229098	−	0.0396809i
$761$	11139.0	−	19293.3i	0.530602	−	0.919030i	−0.468760	−	0.883326i	$-0.655299\pi$
$761$	11139.0	−	19293.3i	0.530602	−	0.919030i	0.999362	−	0.0357047i	$-0.0113676\pi$
$762$		0			0
$763$	9520.00	+	16489.1i	0.451700	+	0.782367i
$764$	−10752.0			−0.509154
$765$		0			0
$766$	6144.00			0.289806
$767$	12540.0	+	21719.9i	0.590343	+	1.02250i
$768$		0			0
$769$	−8065.00	+	13969.0i	−0.378194	+	0.655052i	−0.990800	−	0.135337i	$-0.956788\pi$
$769$	−8065.00	+	13969.0i	−0.378194	+	0.655052i	0.612605	+	0.790389i	$0.290122\pi$
$770$	−1152.00	+	1995.32i	−0.0539158	+	0.0933850i
$771$		0			0
$772$	4604.00	+	7974.36i	0.214639	+	0.371766i
$773$	29718.0			1.38277			0.691386	−	0.722486i	$-0.257001\pi$
$773$	29718.0			1.38277			0.691386	+	0.722486i	$0.257001\pi$
$774$		0			0
$775$	7832.00			0.363011
$776$	4616.00	+	7995.15i	0.213537	+	0.369857i
$777$		0			0
$778$	6150.00	−	10652.1i	0.283404	−	0.490870i
$779$	−420.000	+	727.461i	−0.0193172	+	0.0334583i
$780$		0			0
$781$	−4752.00	−	8230.71i	−0.217721	−	0.377103i
$782$	42336.0			1.93597
$783$		0			0
$784$	−1392.00			−0.0634111
$785$	−1842.00	−	3190.44i	−0.0837501	−	0.145059i
$786$		0			0
$787$	−4762.00	+	8248.03i	−0.215689	+	0.373584i	−0.953485	−	0.301439i	$-0.902533\pi$
$787$	−4762.00	+	8248.03i	−0.215689	+	0.373584i	0.737797	+	0.675023i	$0.235866\pi$
$788$	−8748.00	+	15152.0i	−0.395475	+	0.684983i
$789$		0			0
$790$	−3120.00	−	5404.00i	−0.140512	−	0.243374i
$791$	7392.00			0.332275
$792$		0			0
$793$	−20444.0			−0.915495
$794$	−106.000	−	183.597i	−0.00473778	−	0.00820608i
$795$		0			0
$796$	3200.00	−	5542.56i	0.142489	−	0.246798i
$797$	16953.0	−	29363.5i	0.753458	−	1.30503i	−0.192679	−	0.981262i	$-0.561718\pi$
$797$	16953.0	−	29363.5i	0.753458	−	1.30503i	0.946137	−	0.323766i	$-0.104949\pi$
$798$		0			0
$799$	−6048.00	−	10475.4i	−0.267788	−	0.463823i
$800$	2848.00			0.125865
$801$		0			0
$802$	3516.00			0.154806
$803$	−1308.00	−	2265.52i	−0.0574823	−	0.0995623i
$804$		0			0
$805$	8064.00	−	13967.3i	0.353067	−	0.611529i
$806$	−3344.00	+	5791.98i	−0.146138	+	0.253119i
$807$		0			0
$808$	−2472.00	−	4281.63i	−0.107630	−	0.186420i
$809$	−630.000			−0.0273790			−0.0136895	−	0.999906i	$-0.504358\pi$
$809$	−630.000			−0.0273790			−0.0136895	+	0.999906i	$0.504358\pi$
$810$		0			0
$811$	−20788.0			−0.900081			−0.450040	−	0.893008i	$-0.648590\pi$
$811$	−20788.0			−0.900081			−0.450040	+	0.893008i	$0.648590\pi$
$812$	960.000	+	1662.77i	0.0414894	+	0.0718618i
$813$		0			0
$814$	3048.00	−	5279.29i	0.131244	−	0.227321i
$815$	5556.00	−	9623.27i	0.238795	−	0.413606i
$816$		0			0
$817$	520.000	+	900.666i	0.0222674	+	0.0385683i
$818$	7340.00			0.313737
$819$		0			0
$820$	1008.00			0.0429279
$821$	21549.0	+	37324.0i	0.916036	+	1.58662i	0.805378	+	0.592762i	$0.201962\pi$
$821$	21549.0	+	37324.0i	0.916036	+	1.58662i	0.110658	+	0.993859i	$0.464704\pi$
$822$		0			0
$823$	7136.00	−	12359.9i	0.302242	−	0.523499i	−0.674401	−	0.738365i	$-0.735598\pi$
$823$	7136.00	−	12359.9i	0.302242	−	0.523499i	0.976644	+	0.214866i	$0.0689315\pi$
$824$	512.000	−	886.810i	0.0216461	−	0.0374921i
$825$		0			0
$826$	10560.0	+	18290.5i	0.444830	+	0.770468i
$827$	13644.0			0.573698			0.286849	−	0.957976i	$-0.407392\pi$
$827$	13644.0			0.573698			0.286849	+	0.957976i	$0.407392\pi$
$828$		0			0
$829$	−2410.00			−0.100968			−0.0504842	−	0.998725i	$-0.516076\pi$
$829$	−2410.00			−0.100968			−0.0504842	+	0.998725i	$0.516076\pi$
$830$	−2952.00	−	5113.01i	−0.123452	−	0.213826i
$831$		0			0
$832$	−1216.00	+	2106.17i	−0.0506697	+	0.0877625i
$833$	−5481.00	+	9493.37i	−0.227978	+	0.394869i
$834$		0			0
$835$	6408.00	+	11099.0i	0.265578	+	0.459995i
$836$	960.000			0.0397157
$837$		0			0
$838$	19320.0			0.796418
$839$	−11580.0	−	20057.1i	−0.476503	−	0.825327i	0.523135	−	0.852250i	$-0.324763\pi$
$839$	−11580.0	−	20057.1i	−0.476503	−	0.825327i	−0.999638	+	0.0269227i	$0.991429\pi$
$840$		0			0
$841$	11744.5	−	20342.1i	0.481549	−	0.834067i
$842$	8462.00	−	14656.6i	0.346342	−	0.599882i
$843$		0			0
$844$	−6664.00	−	11542.4i	−0.271782	−	0.470741i
$845$	−4518.00			−0.183934
$846$		0			0
$847$	18992.0			0.770452
$848$	−1584.00	−	2743.57i	−0.0641448	−	0.111102i
$849$		0			0
$850$	11214.0	−	19423.2i	0.452514	−	0.783777i
$851$	−21336.0	+	36955.0i	−0.859446	+	1.48860i
$852$		0			0
$853$	−16039.0	−	27780.4i	−0.643804	−	1.11510i	−0.984576	−	0.174956i	$-0.944022\pi$
$853$	−16039.0	−	27780.4i	−0.643804	−	1.11510i	0.340772	−	0.940146i	$-0.389312\pi$
$854$	−17216.0			−0.689835
$855$		0			0
$856$	11808.0			0.471483
$857$	7203.00	+	12476.0i	0.287106	+	0.497282i	0.973118	−	0.230308i	$-0.0739735\pi$
$857$	7203.00	+	12476.0i	0.287106	+	0.497282i	−0.686012	+	0.727590i	$0.740640\pi$
$858$		0			0
$859$	−15310.0	+	26517.7i	−0.608115	+	1.05329i	0.383436	+	0.923567i	$0.374741\pi$
$859$	−15310.0	+	26517.7i	−0.608115	+	1.05329i	−0.991551	+	0.129718i	$0.958593\pi$
$860$	624.000	−	1080.80i	0.0247421	−	0.0428546i
$861$		0			0
$862$	9792.00	+	16960.2i	0.386910	+	0.670149i
$863$	17568.0			0.692957			0.346478	−	0.938058i	$-0.387377\pi$
$863$	17568.0			0.692957			0.346478	+	0.938058i	$0.387377\pi$
$864$		0			0
$865$	10548.0			0.414616
$866$	−7342.00	−	12716.7i	−0.288096	−	0.498997i
$867$		0			0
$868$	−2816.00	+	4877.46i	−0.110117	+	0.190728i
$869$	3120.00	−	5404.00i	0.121794	−	0.210953i
$870$		0			0
$871$	−16796.0	−	29091.5i	−0.653399	−	1.13172i
$872$	−9520.00			−0.369711
$873$		0			0
$874$	−6720.00			−0.260077
$875$	−10272.0	−	17791.6i	−0.396865	−	0.687391i
$876$		0			0
$877$	10853.0	−	18797.9i	0.417879	−	0.723787i	−0.577847	−	0.816145i	$-0.696107\pi$
$877$	10853.0	−	18797.9i	0.417879	−	0.723787i	0.995726	+	0.0923577i	$0.0294403\pi$
$878$	10640.0	−	18429.0i	0.408978	−	0.708371i
$879$		0			0
$880$	−576.000	−	997.661i	−0.0220647	−	0.0382172i
$881$	−14958.0			−0.572018			−0.286009	−	0.958227i	$-0.592329\pi$
$881$	−14958.0			−0.572018			−0.286009	+	0.958227i	$0.592329\pi$
$882$		0			0
$883$	−32812.0			−1.25052			−0.625261	−	0.780415i	$-0.715008\pi$
$883$	−32812.0			−1.25052			−0.625261	+	0.780415i	$0.715008\pi$
$884$	9576.00	+	16586.1i	0.364339	+	0.631054i
$885$		0			0
$886$	−17412.0	+	30158.5i	−0.660234	+	1.14356i
$887$	19428.0	−	33650.3i	0.735432	−	1.27381i	−0.219101	−	0.975702i	$-0.570312\pi$
$887$	19428.0	−	33650.3i	0.735432	−	1.27381i	0.954533	−	0.298104i	$-0.0963542\pi$
$888$		0			0
$889$	−20288.0	−	35139.8i	−0.765397	−	1.32571i
$890$	−9720.00			−0.366084
$891$		0			0
$892$	10592.0			0.397586
$893$	960.000	+	1662.77i	0.0359744	+	0.0623096i
$894$		0			0
$895$	1620.00	−	2805.92i	0.0605035	−	0.104795i
$896$	−1024.00	+	1773.62i	−0.0381802	+	0.0661300i
$897$		0			0
$898$	−1710.00	−	2961.81i	−0.0635450	−	0.110063i
$899$	−2640.00			−0.0979410
$900$		0			0
$901$	−24948.0			−0.922462
$902$	504.000	+	872.954i	0.0186046	+	0.0322241i
$903$		0			0
$904$	−1848.00	+	3200.83i	−0.0679907	+	0.117763i
$905$	−5946.00	+	10298.8i	−0.218400	+	0.378279i
$906$		0			0
$907$	14138.0	+	24487.7i	0.517579	+	0.896474i	0.999792	+	0.0204194i	$0.00650015\pi$
$907$	14138.0	+	24487.7i	0.517579	+	0.896474i	−0.482212	+	0.876055i	$0.660167\pi$
$908$	8976.00			0.328061
$909$		0			0
$910$	7296.00			0.265780
$911$	−4056.00	−	7025.20i	−0.147510	−	0.255494i	0.782797	−	0.622277i	$-0.213792\pi$
$911$	−4056.00	−	7025.20i	−0.147510	−	0.255494i	−0.930306	+	0.366783i	$0.880459\pi$
$912$		0			0
$913$	2952.00	−	5113.01i	0.107007	−	0.185341i
$914$	−646.000	+	1118.90i	−0.0233783	+	0.0404924i
$915$		0			0
$916$	11300.0	+	19572.2i	0.407601	+	0.705986i
$917$	−36672.0			−1.32063
$918$		0			0
$919$	−26080.0			−0.936126			−0.468063	−	0.883695i	$-0.655048\pi$
$919$	−26080.0			−0.936126			−0.468063	+	0.883695i	$0.655048\pi$
$920$	4032.00	+	6983.63i	0.144490	+	0.250265i
$921$		0			0
$922$	−6018.00	+	10423.5i	−0.214959	+	0.372320i
$923$	−15048.0	+	26063.9i	−0.536632	+	0.929473i
$924$		0			0
$925$	11303.0	+	19577.4i	0.401773	+	0.695892i
$926$	13424.0			0.476393
$927$		0			0
$928$	−960.000			−0.0339586
$929$	−24585.0	−	42582.5i	−0.868254	−	1.50386i	−0.863780	−	0.503870i	$-0.831909\pi$
$929$	−24585.0	−	42582.5i	−0.868254	−	1.50386i	−0.00447392	−	0.999990i	$-0.501424\pi$
$930$		0			0
$931$	870.000	−	1506.88i	0.0306263	−	0.0530463i
$932$	−9396.00	+	16274.3i	−0.330232	+	0.571979i
$933$		0			0
$934$	5364.00	+	9290.72i	0.187918	+	0.325484i
$935$	−9072.00			−0.317311
$936$		0			0
$937$	48314.0			1.68447			0.842236	−	0.539110i	$-0.181239\pi$
$937$	48314.0			1.68447			0.842236	+	0.539110i	$0.181239\pi$
$938$	−14144.0	−	24498.1i	−0.492343	−	0.852764i
$939$		0			0
$940$	1152.00	−	1995.32i	0.0399724	−	0.0692343i
$941$	−17391.0	+	30122.1i	−0.602477	+	1.04352i	0.389968	+	0.920828i	$0.372486\pi$
$941$	−17391.0	+	30122.1i	−0.602477	+	1.04352i	−0.992445	+	0.122692i	$0.960847\pi$
$942$		0			0
$943$	−3528.00	−	6110.68i	−0.121832	−	0.211019i
$944$	−10560.0			−0.364088
$945$		0			0
$946$	1248.00			0.0428922
$947$	12558.0	+	21751.1i	0.430919	+	0.746373i	0.996953	−	0.0780087i	$-0.0248562\pi$
$947$	12558.0	+	21751.1i	0.430919	+	0.746373i	−0.566034	+	0.824382i	$0.691523\pi$
$948$		0			0
$949$	−4142.00	+	7174.15i	−0.141681	+	0.245398i
$950$	−1780.00	+	3083.05i	−0.0607903	+	0.105292i
$951$		0			0
$952$	8064.00	+	13967.3i	0.274533	+	0.475506i
$953$	−15462.0			−0.525565			−0.262782	−	0.964855i	$-0.584640\pi$
$953$	−15462.0			−0.525565			−0.262782	+	0.964855i	$0.584640\pi$
$954$		0			0
$955$	−16128.0			−0.546481
$956$	2400.00	+	4156.92i	0.0811941	+	0.140632i
$957$		0			0
$958$	9840.00	−	17043.4i	0.331854	−	0.574788i
$959$	−5808.00	+	10059.8i	−0.195568	+	0.338734i
$960$		0			0
$961$	11023.5	+	19093.3i	0.370028	+	0.640907i
$962$	−19304.0			−0.646971
$963$		0			0
$964$	−2872.00			−0.0959553
$965$	6906.00	+	11961.5i	0.230375	+	0.399021i
$966$		0			0
$967$	368.000	−	637.395i	0.0122379	−	0.0211967i	−0.859842	−	0.510561i	$-0.829438\pi$
$967$	368.000	−	637.395i	0.0122379	−	0.0211967i	0.872080	+	0.489364i	$0.162771\pi$
$968$	−4748.00	+	8223.78i	−0.157651	+	0.273060i
$969$		0			0
$970$	6924.00	+	11992.7i	0.229192	+	0.396972i
$971$	−29268.0			−0.967307			−0.483653	−	0.875260i	$-0.660690\pi$
$971$	−29268.0			−0.967307			−0.483653	+	0.875260i	$0.660690\pi$
$972$		0			0
$973$	−6080.00			−0.200325
$974$	1424.00	+	2466.44i	0.0468459	+	0.0811395i
$975$		0			0
$976$	4304.00	−	7454.75i	0.141155	−	0.244488i
$977$	−8337.00	+	14440.1i	−0.273003	+	0.472856i	−0.969629	−	0.244579i	$-0.921350\pi$
$977$	−8337.00	+	14440.1i	−0.273003	+	0.472856i	0.696626	+	0.717434i	$0.254684\pi$
$978$		0			0
$979$	−4860.00	−	8417.77i	−0.158658	−	0.274804i
$980$	−2088.00			−0.0680599
$981$		0			0
$982$	9096.00			0.295586
$983$	15636.0	+	27082.3i	0.507336	+	0.878731i	0.999964	+	0.00849130i	$0.00270290\pi$
$983$	15636.0	+	27082.3i	0.507336	+	0.878731i	−0.492628	+	0.870240i	$0.663964\pi$
$984$		0			0
$985$	−13122.0	+	22728.0i	−0.424469	+	0.735201i
$986$	−3780.00	+	6547.15i	−0.122089	+	0.211464i
$987$		0			0
$988$	−1520.00	−	2632.72i	−0.0489450	−	0.0847752i
$989$	−8736.00			−0.280878
$990$		0			0
$991$	−15928.0			−0.510565			−0.255282	−	0.966867i	$-0.582168\pi$
$991$	−15928.0			−0.510565			−0.255282	+	0.966867i	$0.582168\pi$
$992$	−1408.00	−	2438.73i	−0.0450646	−	0.0780541i
$993$		0			0
$994$	−12672.0	+	21948.5i	−0.404358	+	0.700368i
$995$	4800.00	−	8313.84i	0.152935	−	0.264891i
$996$		0			0
$997$	−21007.0	−	36385.2i	−0.667300	−	1.15580i	−0.978656	−	0.205505i	$-0.934116\pi$
$997$	−21007.0	−	36385.2i	−0.667300	−	1.15580i	0.311356	−	0.950293i	$-0.399217\pi$
$998$	−13000.0			−0.412332
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.4.c.f.109.1		2
3.2	odd	2		162.4.c.c.109.1		2
9.2	odd	6		162.4.c.c.55.1		2
9.4	even	3		6.4.a.a.1.1	✓	1
9.5	odd	6		18.4.a.a.1.1		1
9.7	even	3	inner	162.4.c.f.55.1		2
36.23	even	6		144.4.a.c.1.1		1
36.31	odd	6		48.4.a.c.1.1		1
45.4	even	6		150.4.a.i.1.1		1
45.13	odd	12		150.4.c.d.49.2		2
45.14	odd	6		450.4.a.h.1.1		1
45.22	odd	12		150.4.c.d.49.1		2
45.23	even	12		450.4.c.e.199.1		2
45.32	even	12		450.4.c.e.199.2		2
63.4	even	3		294.4.e.h.79.1		2
63.5	even	6		882.4.g.f.361.1		2
63.13	odd	6		294.4.a.e.1.1		1
63.23	odd	6		882.4.g.i.361.1		2
63.31	odd	6		294.4.e.g.79.1		2
63.32	odd	6		882.4.g.i.667.1		2
63.40	odd	6		294.4.e.g.67.1		2
63.41	even	6		882.4.a.n.1.1		1
63.58	even	3		294.4.e.h.67.1		2
63.59	even	6		882.4.g.f.667.1		2
72.5	odd	6		576.4.a.q.1.1		1
72.13	even	6		192.4.a.i.1.1		1
72.59	even	6		576.4.a.r.1.1		1
72.67	odd	6		192.4.a.c.1.1		1
99.32	even	6		2178.4.a.e.1.1		1
99.76	odd	6		726.4.a.f.1.1		1
117.31	odd	12		1014.4.b.d.337.2		2
117.103	even	6		1014.4.a.g.1.1		1
117.112	odd	12		1014.4.b.d.337.1		2
144.13	even	12		768.4.d.n.385.1		2
144.67	odd	12		768.4.d.c.385.2		2
144.85	even	12		768.4.d.n.385.2		2
144.139	odd	12		768.4.d.c.385.1		2
153.67	even	6		1734.4.a.d.1.1		1
171.94	odd	6		2166.4.a.i.1.1		1
180.67	even	12		1200.4.f.j.49.1		2
180.103	even	12		1200.4.f.j.49.2		2
180.139	odd	6		1200.4.a.b.1.1		1
252.139	even	6		2352.4.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.4.a.a.1.1	✓	1	9.4	even	3
18.4.a.a.1.1		1	9.5	odd	6
48.4.a.c.1.1		1	36.31	odd	6
144.4.a.c.1.1		1	36.23	even	6
150.4.a.i.1.1		1	45.4	even	6
150.4.c.d.49.1		2	45.22	odd	12
150.4.c.d.49.2		2	45.13	odd	12
162.4.c.c.55.1		2	9.2	odd	6
162.4.c.c.109.1		2	3.2	odd	2
162.4.c.f.55.1		2	9.7	even	3	inner
162.4.c.f.109.1		2	1.1	even	1	trivial
192.4.a.c.1.1		1	72.67	odd	6
192.4.a.i.1.1		1	72.13	even	6
294.4.a.e.1.1		1	63.13	odd	6
294.4.e.g.67.1		2	63.40	odd	6
294.4.e.g.79.1		2	63.31	odd	6
294.4.e.h.67.1		2	63.58	even	3
294.4.e.h.79.1		2	63.4	even	3
450.4.a.h.1.1		1	45.14	odd	6
450.4.c.e.199.1		2	45.23	even	12
450.4.c.e.199.2		2	45.32	even	12
576.4.a.q.1.1		1	72.5	odd	6
576.4.a.r.1.1		1	72.59	even	6
726.4.a.f.1.1		1	99.76	odd	6
768.4.d.c.385.1		2	144.139	odd	12
768.4.d.c.385.2		2	144.67	odd	12
768.4.d.n.385.1		2	144.13	even	12
768.4.d.n.385.2		2	144.85	even	12
882.4.a.n.1.1		1	63.41	even	6
882.4.g.f.361.1		2	63.5	even	6
882.4.g.f.667.1		2	63.59	even	6
882.4.g.i.361.1		2	63.23	odd	6
882.4.g.i.667.1		2	63.32	odd	6
1014.4.a.g.1.1		1	117.103	even	6
1014.4.b.d.337.1		2	117.112	odd	12
1014.4.b.d.337.2		2	117.31	odd	12
1200.4.a.b.1.1		1	180.139	odd	6
1200.4.f.j.49.1		2	180.67	even	12
1200.4.f.j.49.2		2	180.103	even	12
1734.4.a.d.1.1		1	153.67	even	6
2166.4.a.i.1.1		1	171.94	odd	6
2178.4.a.e.1.1		1	99.32	even	6
2352.4.a.e.1.1		1	252.139	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	162.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-3.00000 + 5.19615i) q^{5} +(8.00000 + 13.8564i) q^{7} -8.00000 q^{8} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-3.00000 + 5.19615i) q^{5} +(8.00000 + 13.8564i) q^{7} -8.00000 q^{8} -12.0000 q^{10} +(-6.00000 - 10.3923i) q^{11} +(-19.0000 + 32.9090i) q^{13} +(-16.0000 + 27.7128i) q^{14} +(-8.00000 - 13.8564i) q^{16} -126.000 q^{17} +20.0000 q^{19} +(-12.0000 - 20.7846i) q^{20} +(12.0000 - 20.7846i) q^{22} +(-84.0000 + 145.492i) q^{23} +(44.5000 + 77.0763i) q^{25} -76.0000 q^{26} -64.0000 q^{28} +(-15.0000 - 25.9808i) q^{29} +(44.0000 - 76.2102i) q^{31} +(16.0000 - 27.7128i) q^{32} +(-126.000 - 218.238i) q^{34} -96.0000 q^{35} +254.000 q^{37} +(20.0000 + 34.6410i) q^{38} +(24.0000 - 41.5692i) q^{40} +(-21.0000 + 36.3731i) q^{41} +(26.0000 + 45.0333i) q^{43} +48.0000 q^{44} -336.000 q^{46} +(48.0000 + 83.1384i) q^{47} +(43.5000 - 75.3442i) q^{49} +(-89.0000 + 154.153i) q^{50} +(-76.0000 - 131.636i) q^{52} +198.000 q^{53} +72.0000 q^{55} +(-64.0000 - 110.851i) q^{56} +(30.0000 - 51.9615i) q^{58} +(330.000 - 571.577i) q^{59} +(269.000 + 465.922i) q^{61} +176.000 q^{62} +64.0000 q^{64} +(-114.000 - 197.454i) q^{65} +(-442.000 + 765.566i) q^{67} +(252.000 - 436.477i) q^{68} +(-96.0000 - 166.277i) q^{70} +792.000 q^{71} +218.000 q^{73} +(254.000 + 439.941i) q^{74} +(-40.0000 + 69.2820i) q^{76} +(96.0000 - 166.277i) q^{77} +(260.000 + 450.333i) q^{79} +96.0000 q^{80} -84.0000 q^{82} +(246.000 + 426.084i) q^{83} +(378.000 - 654.715i) q^{85} +(-52.0000 + 90.0666i) q^{86} +(48.0000 + 83.1384i) q^{88} +810.000 q^{89} -608.000 q^{91} +(-336.000 - 581.969i) q^{92} +(-96.0000 + 166.277i) q^{94} +(-60.0000 + 103.923i) q^{95} +(-577.000 - 999.393i) q^{97} +174.000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 4 q^{4} - 6 q^{5} + 16 q^{7} - 16 q^{8}+O(q^{10}) \) 2 * q + 2 * q^2 - 4 * q^4 - 6 * q^5 + 16 * q^7 - 16 * q^8	\( 2 q + 2 q^{2} - 4 q^{4} - 6 q^{5} + 16 q^{7} - 16 q^{8} - 24 q^{10} - 12 q^{11} - 38 q^{13} - 32 q^{14} - 16 q^{16} - 252 q^{17} + 40 q^{19} - 24 q^{20} + 24 q^{22} - 168 q^{23} + 89 q^{25} - 152 q^{26} - 128 q^{28} - 30 q^{29} + 88 q^{31} + 32 q^{32} - 252 q^{34} - 192 q^{35} + 508 q^{37} + 40 q^{38} + 48 q^{40} - 42 q^{41} + 52 q^{43} + 96 q^{44} - 672 q^{46} + 96 q^{47} + 87 q^{49} - 178 q^{50} - 152 q^{52} + 396 q^{53} + 144 q^{55} - 128 q^{56} + 60 q^{58} + 660 q^{59} + 538 q^{61} + 352 q^{62} + 128 q^{64} - 228 q^{65} - 884 q^{67} + 504 q^{68} - 192 q^{70} + 1584 q^{71} + 436 q^{73} + 508 q^{74} - 80 q^{76} + 192 q^{77} + 520 q^{79} + 192 q^{80} - 168 q^{82} + 492 q^{83} + 756 q^{85} - 104 q^{86} + 96 q^{88} + 1620 q^{89} - 1216 q^{91} - 672 q^{92} - 192 q^{94} - 120 q^{95} - 1154 q^{97} + 348 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 - 4 * q^4 - 6 * q^5 + 16 * q^7 - 16 * q^8 - 24 * q^10 - 12 * q^11 - 38 * q^13 - 32 * q^14 - 16 * q^16 - 252 * q^17 + 40 * q^19 - 24 * q^20 + 24 * q^22 - 168 * q^23 + 89 * q^25 - 152 * q^26 - 128 * q^28 - 30 * q^29 + 88 * q^31 + 32 * q^32 - 252 * q^34 - 192 * q^35 + 508 * q^37 + 40 * q^38 + 48 * q^40 - 42 * q^41 + 52 * q^43 + 96 * q^44 - 672 * q^46 + 96 * q^47 + 87 * q^49 - 178 * q^50 - 152 * q^52 + 396 * q^53 + 144 * q^55 - 128 * q^56 + 60 * q^58 + 660 * q^59 + 538 * q^61 + 352 * q^62 + 128 * q^64 - 228 * q^65 - 884 * q^67 + 504 * q^68 - 192 * q^70 + 1584 * q^71 + 436 * q^73 + 508 * q^74 - 80 * q^76 + 192 * q^77 + 520 * q^79 + 192 * q^80 - 168 * q^82 + 492 * q^83 + 756 * q^85 - 104 * q^86 + 96 * q^88 + 1620 * q^89 - 1216 * q^91 - 672 * q^92 - 192 * q^94 - 120 * q^95 - 1154 * q^97 + 348 * q^98

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