LMFDB - Embedded newform 162.4.c.a.55.1

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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			55.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	162.55
Dual form			162.4.c.a.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-6.00000 - 10.3923i) q^{5} +(3.50000 - 6.06218i) q^{7} +8.00000 q^{8} +O(q^{10})$	\(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-6.00000 - 10.3923i) q^{5} +(3.50000 - 6.06218i) q^{7} +8.00000 q^{8} +24.0000 q^{10} +(-30.0000 + 51.9615i) q^{11} +(39.5000 + 68.4160i) q^{13} +(7.00000 + 12.1244i) q^{14} +(-8.00000 + 13.8564i) q^{16} -108.000 q^{17} +11.0000 q^{19} +(-24.0000 + 41.5692i) q^{20} +(-60.0000 - 103.923i) q^{22} +(66.0000 + 114.315i) q^{23} +(-9.50000 + 16.4545i) q^{25} -158.000 q^{26} -28.0000 q^{28} +(-48.0000 + 83.1384i) q^{29} +(-10.0000 - 17.3205i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(108.000 - 187.061i) q^{34} -84.0000 q^{35} -169.000 q^{37} +(-11.0000 + 19.0526i) q^{38} +(-48.0000 - 83.1384i) q^{40} +(-96.0000 - 166.277i) q^{41} +(-244.000 + 422.620i) q^{43} +240.000 q^{44} -264.000 q^{46} +(-102.000 + 176.669i) q^{47} +(147.000 + 254.611i) q^{49} +(-19.0000 - 32.9090i) q^{50} +(158.000 - 273.664i) q^{52} +360.000 q^{53} +720.000 q^{55} +(28.0000 - 48.4974i) q^{56} +(-96.0000 - 166.277i) q^{58} +(-78.0000 - 135.100i) q^{59} +(-41.5000 + 71.8801i) q^{61} +40.0000 q^{62} +64.0000 q^{64} +(474.000 - 820.992i) q^{65} +(-23.5000 - 40.7032i) q^{67} +(216.000 + 374.123i) q^{68} +(84.0000 - 145.492i) q^{70} +216.000 q^{71} -511.000 q^{73} +(169.000 - 292.717i) q^{74} +(-22.0000 - 38.1051i) q^{76} +(210.000 + 363.731i) q^{77} +(264.500 - 458.127i) q^{79} +192.000 q^{80} +384.000 q^{82} +(564.000 - 976.877i) q^{83} +(648.000 + 1122.37i) q^{85} +(-488.000 - 845.241i) q^{86} +(-240.000 + 415.692i) q^{88} +36.0000 q^{89} +553.000 q^{91} +(264.000 - 457.261i) q^{92} +(-204.000 - 353.338i) q^{94} +(-66.0000 - 114.315i) q^{95} +(-302.500 + 523.945i) q^{97} -588.000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 4 q^{4} - 12 q^{5} + 7 q^{7} + 16 q^{8}+O(q^{10}) $ 2 * q - 2 * q^2 - 4 * q^4 - 12 * q^5 + 7 * q^7 + 16 * q^8	$ 2 q - 2 q^{2} - 4 q^{4} - 12 q^{5} + 7 q^{7} + 16 q^{8} + 48 q^{10} - 60 q^{11} + 79 q^{13} + 14 q^{14} - 16 q^{16} - 216 q^{17} + 22 q^{19} - 48 q^{20} - 120 q^{22} + 132 q^{23} - 19 q^{25} - 316 q^{26} - 56 q^{28} - 96 q^{29} - 20 q^{31} - 32 q^{32} + 216 q^{34} - 168 q^{35} - 338 q^{37} - 22 q^{38} - 96 q^{40} - 192 q^{41} - 488 q^{43} + 480 q^{44} - 528 q^{46} - 204 q^{47} + 294 q^{49} - 38 q^{50} + 316 q^{52} + 720 q^{53} + 1440 q^{55} + 56 q^{56} - 192 q^{58} - 156 q^{59} - 83 q^{61} + 80 q^{62} + 128 q^{64} + 948 q^{65} - 47 q^{67} + 432 q^{68} + 168 q^{70} + 432 q^{71} - 1022 q^{73} + 338 q^{74} - 44 q^{76} + 420 q^{77} + 529 q^{79} + 384 q^{80} + 768 q^{82} + 1128 q^{83} + 1296 q^{85} - 976 q^{86} - 480 q^{88} + 72 q^{89} + 1106 q^{91} + 528 q^{92} - 408 q^{94} - 132 q^{95} - 605 q^{97} - 1176 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 - 4 * q^4 - 12 * q^5 + 7 * q^7 + 16 * q^8 + 48 * q^10 - 60 * q^11 + 79 * q^13 + 14 * q^14 - 16 * q^16 - 216 * q^17 + 22 * q^19 - 48 * q^20 - 120 * q^22 + 132 * q^23 - 19 * q^25 - 316 * q^26 - 56 * q^28 - 96 * q^29 - 20 * q^31 - 32 * q^32 + 216 * q^34 - 168 * q^35 - 338 * q^37 - 22 * q^38 - 96 * q^40 - 192 * q^41 - 488 * q^43 + 480 * q^44 - 528 * q^46 - 204 * q^47 + 294 * q^49 - 38 * q^50 + 316 * q^52 + 720 * q^53 + 1440 * q^55 + 56 * q^56 - 192 * q^58 - 156 * q^59 - 83 * q^61 + 80 * q^62 + 128 * q^64 + 948 * q^65 - 47 * q^67 + 432 * q^68 + 168 * q^70 + 432 * q^71 - 1022 * q^73 + 338 * q^74 - 44 * q^76 + 420 * q^77 + 529 * q^79 + 384 * q^80 + 768 * q^82 + 1128 * q^83 + 1296 * q^85 - 976 * q^86 - 480 * q^88 + 72 * q^89 + 1106 * q^91 + 528 * q^92 - 408 * q^94 - 132 * q^95 - 605 * q^97 - 1176 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$83$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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
$5$	−6.00000	−	10.3923i	−0.536656	−	0.929516i	−0.999081	−	0.0428575i	$-0.986354\pi$
$5$	−6.00000	−	10.3923i	−0.536656	−	0.929516i	0.462425	−	0.886658i	$-0.346979\pi$
$6$		0			0
$7$	3.50000	−	6.06218i	0.188982	−	0.327327i	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	3.50000	−	6.06218i	0.188982	−	0.327327i	0.944911	+	0.327327i	$0.106148\pi$
$8$	8.00000			0.353553
$9$		0			0
$10$	24.0000			0.758947
$11$	−30.0000	+	51.9615i	−0.822304	+	1.42427i	0.0816590	+	0.996660i	$0.473978\pi$
$11$	−30.0000	+	51.9615i	−0.822304	+	1.42427i	−0.903963	+	0.427611i	$0.859355\pi$
$12$		0			0
$13$	39.5000	+	68.4160i	0.842718	+	1.45963i	0.887589	+	0.460637i	$0.152379\pi$
$13$	39.5000	+	68.4160i	0.842718	+	1.45963i	−0.0448711	+	0.998993i	$0.514288\pi$
$14$	7.00000	+	12.1244i	0.133631	+	0.231455i
$15$		0			0
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−108.000			−1.54081			−0.770407	−	0.637552i	$-0.779947\pi$
$17$	−108.000			−1.54081			−0.770407	+	0.637552i	$0.779947\pi$
$18$		0			0
$19$	11.0000			0.132820			0.0664098	−	0.997792i	$-0.478846\pi$
$19$	11.0000			0.132820			0.0664098	+	0.997792i	$0.478846\pi$
$20$	−24.0000	+	41.5692i	−0.268328	+	0.464758i
$21$		0			0
$22$	−60.0000	−	103.923i	−0.581456	−	1.00711i
$23$	66.0000	+	114.315i	0.598346	+	1.03637i	0.993065	+	0.117564i	$0.0375084\pi$
$23$	66.0000	+	114.315i	0.598346	+	1.03637i	−0.394720	+	0.918802i	$0.629158\pi$
$24$		0			0
$25$	−9.50000	+	16.4545i	−0.0760000	+	0.131636i
$26$	−158.000			−1.19178
$27$		0			0
$28$	−28.0000			−0.188982
$29$	−48.0000	+	83.1384i	−0.307358	+	0.532359i	−0.977783	−	0.209617i	$-0.932778\pi$
$29$	−48.0000	+	83.1384i	−0.307358	+	0.532359i	0.670426	+	0.741977i	$0.266112\pi$
$30$		0			0
$31$	−10.0000	−	17.3205i	−0.0579372	−	0.100350i	0.835602	−	0.549335i	$-0.185119\pi$
$31$	−10.0000	−	17.3205i	−0.0579372	−	0.100350i	−0.893539	+	0.448985i	$0.851786\pi$
$32$	−16.0000	−	27.7128i	−0.0883883	−	0.153093i
$33$		0			0
$34$	108.000	−	187.061i	0.544760	−	0.943552i
$35$	−84.0000			−0.405674
$36$		0			0
$37$	−169.000			−0.750903			−0.375452	−	0.926842i	$-0.622512\pi$
$37$	−169.000			−0.750903			−0.375452	+	0.926842i	$0.622512\pi$
$38$	−11.0000	+	19.0526i	−0.0469588	+	0.0813351i
$39$		0			0
$40$	−48.0000	−	83.1384i	−0.189737	−	0.328634i
$41$	−96.0000	−	166.277i	−0.365675	−	0.633368i	0.623209	−	0.782055i	$-0.285829\pi$
$41$	−96.0000	−	166.277i	−0.365675	−	0.633368i	−0.988884	+	0.148687i	$0.952495\pi$
$42$		0			0
$43$	−244.000	+	422.620i	−0.865341	+	1.49881i	0.00136774	+	0.999999i	$0.499565\pi$
$43$	−244.000	+	422.620i	−0.865341	+	1.49881i	−0.866708	+	0.498815i	$0.833769\pi$
$44$	240.000			0.822304
$45$		0			0
$46$	−264.000			−0.846189
$47$	−102.000	+	176.669i	−0.316558	+	0.548295i	−0.979767	−	0.200139i	$-0.935861\pi$
$47$	−102.000	+	176.669i	−0.316558	+	0.548295i	0.663209	+	0.748434i	$0.269194\pi$
$48$		0			0
$49$	147.000	+	254.611i	0.428571	+	0.742307i
$50$	−19.0000	−	32.9090i	−0.0537401	−	0.0930806i
$51$		0			0
$52$	158.000	−	273.664i	0.421359	−	0.729815i
$53$	360.000			0.933015			0.466508	−	0.884517i	$-0.345512\pi$
$53$	360.000			0.933015			0.466508	+	0.884517i	$0.345512\pi$
$54$		0			0
$55$	720.000			1.76518
$56$	28.0000	−	48.4974i	0.0668153	−	0.115728i
$57$		0			0
$58$	−96.0000	−	166.277i	−0.217335	−	0.376435i
$59$	−78.0000	−	135.100i	−0.172114	−	0.298110i	0.767045	−	0.641594i	$-0.221726\pi$
$59$	−78.0000	−	135.100i	−0.172114	−	0.298110i	−0.939159	+	0.343483i	$0.888393\pi$
$60$		0			0
$61$	−41.5000	+	71.8801i	−0.0871071	+	0.150874i	−0.906287	−	0.422663i	$-0.861096\pi$
$61$	−41.5000	+	71.8801i	−0.0871071	+	0.150874i	0.819180	+	0.573536i	$0.194429\pi$
$62$	40.0000			0.0819356
$63$		0			0
$64$	64.0000			0.125000
$65$	474.000	−	820.992i	0.904499	−	1.56664i
$66$		0			0
$67$	−23.5000	−	40.7032i	−0.0428505	−	0.0742192i	0.843805	−	0.536650i	$-0.180311\pi$
$67$	−23.5000	−	40.7032i	−0.0428505	−	0.0742192i	−0.886655	+	0.462431i	$0.846977\pi$
$68$	216.000	+	374.123i	0.385204	+	0.667192i
$69$		0			0
$70$	84.0000	−	145.492i	0.143427	−	0.248424i
$71$	216.000			0.361049			0.180525	−	0.983570i	$-0.442220\pi$
$71$	216.000			0.361049			0.180525	+	0.983570i	$0.442220\pi$
$72$		0			0
$73$	−511.000			−0.819288			−0.409644	−	0.912245i	$-0.634347\pi$
$73$	−511.000			−0.819288			−0.409644	+	0.912245i	$0.634347\pi$
$74$	169.000	−	292.717i	0.265484	−	0.459833i
$75$		0			0
$76$	−22.0000	−	38.1051i	−0.0332049	−	0.0575126i
$77$	210.000	+	363.731i	0.310802	+	0.538324i
$78$		0			0
$79$	264.500	−	458.127i	0.376691	−	0.652448i	−0.613888	−	0.789393i	$-0.710395\pi$
$79$	264.500	−	458.127i	0.376691	−	0.652448i	0.990579	+	0.136946i	$0.0437286\pi$
$80$	192.000			0.268328
$81$		0			0
$82$	384.000			0.517143
$83$	564.000	−	976.877i	0.745868	−	1.29188i	−0.203920	−	0.978988i	$-0.565368\pi$
$83$	564.000	−	976.877i	0.745868	−	1.29188i	0.949788	−	0.312894i	$-0.101298\pi$
$84$		0			0
$85$	648.000	+	1122.37i	0.826888	+	1.43221i
$86$	−488.000	−	845.241i	−0.611888	−	1.05982i
$87$		0			0
$88$	−240.000	+	415.692i	−0.290728	+	0.503556i
$89$	36.0000			0.0428763			0.0214382	−	0.999770i	$-0.493175\pi$
$89$	36.0000			0.0428763			0.0214382	+	0.999770i	$0.493175\pi$
$90$		0			0
$91$	553.000			0.637035
$92$	264.000	−	457.261i	0.299173	−	0.518183i
$93$		0			0
$94$	−204.000	−	353.338i	−0.223840	−	0.387703i
$95$	−66.0000	−	114.315i	−0.0712785	−	0.123458i
$96$		0			0
$97$	−302.500	+	523.945i	−0.316641	+	0.548439i	−0.979785	−	0.200053i	$-0.935889\pi$
$97$	−302.500	+	523.945i	−0.316641	+	0.548439i	0.663144	+	0.748492i	$0.269222\pi$
$98$	−588.000			−0.606092
$99$		0			0
$100$	76.0000			0.0760000
$101$	−624.000	+	1080.80i	−0.614756	+	1.06479i	0.375672	+	0.926753i	$0.377412\pi$
$101$	−624.000	+	1080.80i	−0.614756	+	1.06479i	−0.990427	+	0.138035i	$0.955921\pi$
$102$		0			0
$103$	−482.500	−	835.715i	−0.461574	−	0.799470i	0.537465	−	0.843286i	$-0.319382\pi$
$103$	−482.500	−	835.715i	−0.461574	−	0.799470i	−0.999040	+	0.0438159i	$0.986049\pi$
$104$	316.000	+	547.328i	0.297946	+	0.516057i
$105$		0			0
$106$	−360.000	+	623.538i	−0.329871	+	0.571353i
$107$	1332.00			1.20345			0.601726	−	0.798703i	$-0.294480\pi$
$107$	1332.00			1.20345			0.601726	+	0.798703i	$0.294480\pi$
$108$		0			0
$109$	−1942.00			−1.70651			−0.853256	−	0.521492i	$-0.825376\pi$
$109$	−1942.00			−1.70651			−0.853256	+	0.521492i	$0.825376\pi$
$110$	−720.000	+	1247.08i	−0.624085	+	1.08095i
$111$		0			0
$112$	56.0000	+	96.9948i	0.0472456	+	0.0818317i
$113$	−258.000	−	446.869i	−0.214784	−	0.372017i	0.738422	−	0.674339i	$-0.235571\pi$
$113$	−258.000	−	446.869i	−0.214784	−	0.372017i	−0.953206	+	0.302322i	$0.902238\pi$
$114$		0			0
$115$	792.000	−	1371.78i	0.642212	−	1.11234i
$116$	384.000			0.307358
$117$		0			0
$118$	312.000			0.243406
$119$	−378.000	+	654.715i	−0.291187	+	0.504350i
$120$		0			0
$121$	−1134.50	−	1965.01i	−0.852367	−	1.47634i
$122$	−83.0000	−	143.760i	−0.0615940	−	0.106684i
$123$		0			0
$124$	−40.0000	+	69.2820i	−0.0289686	+	0.0501751i
$125$	−1272.00			−0.910169
$126$		0			0
$127$	−52.0000			−0.0363327			−0.0181664	−	0.999835i	$-0.505783\pi$
$127$	−52.0000			−0.0363327			−0.0181664	+	0.999835i	$0.505783\pi$
$128$	−64.0000	+	110.851i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	948.000	+	1641.98i	0.639578	+	1.10778i
$131$	−24.0000	−	41.5692i	−0.0160068	−	0.0277246i	0.857911	−	0.513798i	$-0.171762\pi$
$131$	−24.0000	−	41.5692i	−0.0160068	−	0.0277246i	−0.873918	+	0.486074i	$0.838429\pi$
$132$		0			0
$133$	38.5000	−	66.6840i	0.0251006	−	0.0434754i
$134$	94.0000			0.0605997
$135$		0			0
$136$	−864.000			−0.544760
$137$	−1182.00	+	2047.28i	−0.737117	+	1.27672i	0.216671	+	0.976245i	$0.430480\pi$
$137$	−1182.00	+	2047.28i	−0.737117	+	1.27672i	−0.953788	+	0.300480i	$0.902853\pi$
$138$		0			0
$139$	−86.5000	−	149.822i	−0.0527830	−	0.0914228i	0.838427	−	0.545014i	$-0.183476\pi$
$139$	−86.5000	−	149.822i	−0.0527830	−	0.0914228i	−0.891210	+	0.453592i	$0.850142\pi$
$140$	168.000	+	290.985i	0.101419	+	0.175662i
$141$		0			0
$142$	−216.000	+	374.123i	−0.127650	+	0.221096i
$143$	−4740.00			−2.77188
$144$		0			0
$145$	1152.00			0.659782
$146$	511.000	−	885.078i	0.289662	−	0.501709i
$147$		0			0
$148$	338.000	+	585.433i	0.187726	+	0.325151i
$149$	804.000	+	1392.57i	0.442055	+	0.765662i	0.997842	−	0.0656627i	$-0.0209161\pi$
$149$	804.000	+	1392.57i	0.442055	+	0.765662i	−0.555787	+	0.831325i	$0.687583\pi$
$150$		0			0
$151$	498.500	−	863.427i	0.268658	−	0.465329i	−0.699858	−	0.714282i	$-0.746753\pi$
$151$	498.500	−	863.427i	0.268658	−	0.465329i	0.968516	+	0.248953i	$0.0800865\pi$
$152$	88.0000			0.0469588
$153$		0			0
$154$	−840.000			−0.439540
$155$	−120.000	+	207.846i	−0.0621847	+	0.107707i
$156$		0			0
$157$	−307.000	−	531.740i	−0.156059	−	0.270302i	0.777385	−	0.629025i	$-0.216546\pi$
$157$	−307.000	−	531.740i	−0.156059	−	0.270302i	−0.933444	+	0.358723i	$0.883212\pi$
$158$	529.000	+	916.255i	0.266361	+	0.461350i
$159$		0			0
$160$	−192.000	+	332.554i	−0.0948683	+	0.164317i
$161$	924.000			0.452307
$162$		0			0
$163$	2693.00			1.29406			0.647031	−	0.762464i	$-0.276011\pi$
$163$	2693.00			1.29406			0.647031	+	0.762464i	$0.276011\pi$
$164$	−384.000	+	665.108i	−0.182838	+	0.316684i
$165$		0			0
$166$	1128.00	+	1953.75i	0.527408	+	0.913498i
$167$	−582.000	−	1008.05i	−0.269680	−	0.467099i	0.699099	−	0.715025i	$-0.253584\pi$
$167$	−582.000	−	1008.05i	−0.269680	−	0.467099i	−0.968779	+	0.247926i	$0.920251\pi$
$168$		0			0
$169$	−2022.00	+	3502.21i	−0.920346	+	1.59409i
$170$	−2592.00			−1.16940
$171$		0			0
$172$	1952.00			0.865341
$173$	1824.00	−	3159.26i	0.801596	−	1.38841i	−0.116969	−	0.993136i	$-0.537318\pi$
$173$	1824.00	−	3159.26i	0.801596	−	1.38841i	0.918565	−	0.395270i	$-0.129349\pi$
$174$		0			0
$175$	66.5000	+	115.181i	0.0287253	+	0.0497537i
$176$	−480.000	−	831.384i	−0.205576	−	0.356068i
$177$		0			0
$178$	−36.0000	+	62.3538i	−0.0151591	+	0.0262563i
$179$	1800.00			0.751611			0.375805	−	0.926699i	$-0.377366\pi$
$179$	1800.00			0.751611			0.375805	+	0.926699i	$0.377366\pi$
$180$		0			0
$181$	−547.000			−0.224631			−0.112315	−	0.993673i	$-0.535827\pi$
$181$	−547.000			−0.224631			−0.112315	+	0.993673i	$0.535827\pi$
$182$	−553.000	+	957.824i	−0.225226	+	0.390102i
$183$		0			0
$184$	528.000	+	914.523i	0.211547	+	0.366410i
$185$	1014.00	+	1756.30i	0.402977	+	0.697977i
$186$		0			0
$187$	3240.00	−	5611.84i	1.26702	−	2.19454i
$188$	816.000			0.316558
$189$		0			0
$190$	264.000			0.100803
$191$	−1578.00	+	2733.18i	−0.597801	+	1.03542i	0.395344	+	0.918533i	$0.370626\pi$
$191$	−1578.00	+	2733.18i	−0.597801	+	1.03542i	−0.993145	+	0.116889i	$0.962708\pi$
$192$		0			0
$193$	−563.500	−	976.011i	−0.210164	−	0.364014i	0.741602	−	0.670840i	$-0.234066\pi$
$193$	−563.500	−	976.011i	−0.210164	−	0.364014i	−0.951766	+	0.306826i	$0.900733\pi$
$194$	−605.000	−	1047.89i	−0.223899	−	0.387805i
$195$		0			0
$196$	588.000	−	1018.45i	0.214286	−	0.371154i
$197$	1116.00			0.403613			0.201806	−	0.979425i	$-0.435319\pi$
$197$	1116.00			0.403613			0.201806	+	0.979425i	$0.435319\pi$
$198$		0			0
$199$	−3283.00			−1.16948			−0.584738	−	0.811222i	$-0.698803\pi$
$199$	−3283.00			−1.16948			−0.584738	+	0.811222i	$0.698803\pi$
$200$	−76.0000	+	131.636i	−0.0268701	+	0.0465403i
$201$		0			0
$202$	−1248.00	−	2161.60i	−0.434698	−	0.752919i
$203$	336.000	+	581.969i	0.116170	+	0.201213i
$204$		0			0
$205$	−1152.00	+	1995.32i	−0.392484	+	0.679802i
$206$	1930.00			0.652764
$207$		0			0
$208$	−1264.00			−0.421359
$209$	−330.000	+	571.577i	−0.109218	+	0.189171i
$210$		0			0
$211$	147.500	+	255.477i	0.0481247	+	0.0833545i	0.889084	−	0.457743i	$-0.151342\pi$
$211$	147.500	+	255.477i	0.0481247	+	0.0833545i	−0.840960	+	0.541098i	$0.818009\pi$
$212$	−720.000	−	1247.08i	−0.233254	−	0.404007i
$213$		0			0
$214$	−1332.00	+	2307.09i	−0.425484	+	0.736960i
$215$	5856.00			1.85756
$216$		0			0
$217$	−140.000			−0.0437964
$218$	1942.00	−	3363.64i	0.603343	−	1.04502i
$219$		0			0
$220$	−1440.00	−	2494.15i	−0.441294	−	0.764344i
$221$	−4266.00	−	7388.93i	−1.29847	−	2.24902i
$222$		0			0
$223$	1322.00	−	2289.77i	0.396985	−	0.687598i	−0.596367	−	0.802712i	$-0.703390\pi$
$223$	1322.00	−	2289.77i	0.396985	−	0.687598i	0.993352	+	0.115113i	$0.0367231\pi$
$224$	−224.000			−0.0668153
$225$		0			0
$226$	1032.00			0.303751
$227$	3012.00	−	5216.94i	0.880676	−	1.52538i	0.0300853	−	0.999547i	$-0.490422\pi$
$227$	3012.00	−	5216.94i	0.880676	−	1.52538i	0.850591	−	0.525828i	$-0.176245\pi$
$228$		0			0
$229$	2231.00	+	3864.21i	0.643793	+	1.11508i	0.984579	+	0.174941i	$0.0559736\pi$
$229$	2231.00	+	3864.21i	0.643793	+	1.11508i	−0.340786	+	0.940141i	$0.610693\pi$
$230$	1584.00	+	2743.57i	0.454112	+	0.786546i
$231$		0			0
$232$	−384.000	+	665.108i	−0.108667	+	0.188217i
$233$	−1008.00			−0.283417			−0.141709	−	0.989908i	$-0.545260\pi$
$233$	−1008.00			−0.283417			−0.141709	+	0.989908i	$0.545260\pi$
$234$		0			0
$235$	2448.00			0.679532
$236$	−312.000	+	540.400i	−0.0860571	+	0.149055i
$237$		0			0
$238$	−756.000	−	1309.43i	−0.205900	−	0.356629i
$239$	2532.00	+	4385.55i	0.685278	+	1.18694i	0.973349	+	0.229327i	$0.0736527\pi$
$239$	2532.00	+	4385.55i	0.685278	+	1.18694i	−0.288071	+	0.957609i	$0.593014\pi$
$240$		0			0
$241$	−3128.50	+	5418.72i	−0.836201	+	1.44834i	0.0568481	+	0.998383i	$0.481895\pi$
$241$	−3128.50	+	5418.72i	−0.836201	+	1.44834i	−0.893049	+	0.449959i	$0.851438\pi$
$242$	4538.00			1.20543
$243$		0			0
$244$	332.000			0.0871071
$245$	1764.00	−	3055.34i	0.459991	−	0.796728i
$246$		0			0
$247$	434.500	+	752.576i	0.111929	+	0.193867i
$248$	−80.0000	−	138.564i	−0.0204839	−	0.0354791i
$249$		0			0
$250$	1272.00	−	2203.17i	0.321793	−	0.557362i
$251$	−2160.00			−0.543179			−0.271590	−	0.962413i	$-0.587549\pi$
$251$	−2160.00			−0.543179			−0.271590	+	0.962413i	$0.587549\pi$
$252$		0			0
$253$	−7920.00			−1.96809
$254$	52.0000	−	90.0666i	0.0128456	−	0.0222491i
$255$		0			0
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	84.0000	+	145.492i	0.0203882	+	0.0353135i	0.876040	−	0.482239i	$-0.160176\pi$
$257$	84.0000	+	145.492i	0.0203882	+	0.0353135i	−0.855651	+	0.517553i	$0.826843\pi$
$258$		0			0
$259$	−591.500	+	1024.51i	−0.141907	+	0.245791i
$260$	−3792.00			−0.904499
$261$		0			0
$262$	96.0000			0.0226370
$263$	1212.00	−	2099.25i	0.284164	−	0.492186i	−0.688242	−	0.725481i	$-0.741617\pi$
$263$	1212.00	−	2099.25i	0.284164	−	0.492186i	0.972406	+	0.233295i	$0.0749507\pi$
$264$		0			0
$265$	−2160.00	−	3741.23i	−0.500708	−	0.867253i
$266$	77.0000	+	133.368i	0.0177488	+	0.0307418i
$267$		0			0
$268$	−94.0000	+	162.813i	−0.0214252	+	0.0371096i
$269$	−396.000			−0.0897567			−0.0448783	−	0.998992i	$-0.514290\pi$
$269$	−396.000			−0.0897567			−0.0448783	+	0.998992i	$0.514290\pi$
$270$		0			0
$271$	1811.00			0.405942			0.202971	−	0.979185i	$-0.434940\pi$
$271$	1811.00			0.405942			0.202971	+	0.979185i	$0.434940\pi$
$272$	864.000	−	1496.49i	0.192602	−	0.333596i
$273$		0			0
$274$	−2364.00	−	4094.57i	−0.521221	−	0.902781i
$275$	−570.000	−	987.269i	−0.124990	−	0.216489i
$276$		0			0
$277$	1511.00	−	2617.13i	0.327752	−	0.567682i	−0.654314	−	0.756223i	$-0.727042\pi$
$277$	1511.00	−	2617.13i	0.327752	−	0.567682i	0.982065	+	0.188541i	$0.0603758\pi$
$278$	346.000			0.0746464
$279$		0			0
$280$	−672.000			−0.143427
$281$	1536.00	−	2660.43i	0.326086	−	0.564797i	−0.655646	−	0.755069i	$-0.727604\pi$
$281$	1536.00	−	2660.43i	0.326086	−	0.564797i	0.981731	+	0.190272i	$0.0609369\pi$
$282$		0			0
$283$	4040.00	+	6997.49i	0.848597	+	1.46981i	0.882460	+	0.470387i	$0.155886\pi$
$283$	4040.00	+	6997.49i	0.848597	+	1.46981i	−0.0338626	+	0.999426i	$0.510781\pi$
$284$	−432.000	−	748.246i	−0.0902623	−	0.156339i
$285$		0			0
$286$	4740.00	−	8209.92i	0.980007	−	1.69742i
$287$	−1344.00			−0.276424
$288$		0			0
$289$	6751.00			1.37411
$290$	−1152.00	+	1995.32i	−0.233268	+	0.404032i
$291$		0			0
$292$	1022.00	+	1770.16i	0.204822	+	0.354762i
$293$	2334.00	+	4042.61i	0.465371	+	0.806046i	0.999218	−	0.0395346i	$-0.0125875\pi$
$293$	2334.00	+	4042.61i	0.465371	+	0.806046i	−0.533847	+	0.845581i	$0.679254\pi$
$294$		0			0
$295$	−936.000	+	1621.20i	−0.184732	+	0.319966i
$296$	−1352.00			−0.265484
$297$		0			0
$298$	−3216.00			−0.625161
$299$	−5214.00	+	9030.91i	−1.00847	+	1.74673i
$300$		0			0
$301$	1708.00	+	2958.34i	0.327068	+	0.566498i
$302$	997.000	+	1726.85i	0.189970	+	0.329037i
$303$		0			0
$304$	−88.0000	+	152.420i	−0.0166025	+	0.0287563i
$305$	996.000			0.186986
$306$		0			0
$307$	6752.00			1.25523			0.627617	−	0.778522i	$-0.284030\pi$
$307$	6752.00			1.25523			0.627617	+	0.778522i	$0.284030\pi$
$308$	840.000	−	1454.92i	0.155401	−	0.269162i
$309$		0			0
$310$	−240.000	−	415.692i	−0.0439712	−	0.0761604i
$311$	−906.000	−	1569.24i	−0.165191	−	0.286120i	0.771532	−	0.636191i	$-0.219491\pi$
$311$	−906.000	−	1569.24i	−0.165191	−	0.286120i	−0.936723	+	0.350071i	$0.886158\pi$
$312$		0			0
$313$	−3101.50	+	5371.96i	−0.560087	+	0.970099i	0.437402	+	0.899266i	$0.355899\pi$
$313$	−3101.50	+	5371.96i	−0.560087	+	0.970099i	−0.997488	+	0.0708323i	$0.977434\pi$
$314$	1228.00			0.220701
$315$		0			0
$316$	−2116.00			−0.376691
$317$	−5484.00	+	9498.57i	−0.971647	+	1.68294i	−0.281064	+	0.959689i	$0.590687\pi$
$317$	−5484.00	+	9498.57i	−0.971647	+	1.68294i	−0.690583	+	0.723253i	$0.742646\pi$
$318$		0			0
$319$	−2880.00	−	4988.31i	−0.505483	−	0.875522i
$320$	−384.000	−	665.108i	−0.0670820	−	0.116190i
$321$		0			0
$322$	−924.000	+	1600.41i	−0.159915	+	0.276980i
$323$	−1188.00			−0.204650
$324$		0			0
$325$	−1501.00			−0.256186
$326$	−2693.00	+	4664.41i	−0.457520	+	0.792448i
$327$		0			0
$328$	−768.000	−	1330.22i	−0.129286	−	0.223929i
$329$	714.000	+	1236.68i	0.119648	+	0.207236i
$330$		0			0
$331$	−4082.50	+	7071.10i	−0.677929	+	1.17421i	0.297675	+	0.954667i	$0.403789\pi$
$331$	−4082.50	+	7071.10i	−0.677929	+	1.17421i	−0.975603	+	0.219540i	$0.929544\pi$
$332$	−4512.00			−0.745868
$333$		0			0
$334$	2328.00			0.381385
$335$	−282.000	+	488.438i	−0.0459920	+	0.0796604i
$336$		0			0
$337$	3261.50	+	5649.08i	0.527197	+	0.913131i	0.999498	+	0.0316939i	$0.0100902\pi$
$337$	3261.50	+	5649.08i	0.527197	+	0.913131i	−0.472301	+	0.881437i	$0.656577\pi$
$338$	−4044.00	−	7004.41i	−0.650783	−	1.12719i
$339$		0			0
$340$	2592.00	−	4489.48i	0.413444	−	0.716106i
$341$	1200.00			0.190568
$342$		0			0
$343$	4459.00			0.701934
$344$	−1952.00	+	3380.96i	−0.305944	+	0.529911i
$345$		0			0
$346$	3648.00	+	6318.52i	0.566814	+	0.981751i
$347$	−3084.00	−	5341.64i	−0.477112	−	0.826382i	0.522544	−	0.852612i	$-0.324983\pi$
$347$	−3084.00	−	5341.64i	−0.477112	−	0.826382i	−0.999656	+	0.0262304i	$0.991650\pi$
$348$		0			0
$349$	3000.50	−	5197.02i	0.460209	−	0.797106i	−0.538762	−	0.842458i	$-0.681108\pi$
$349$	3000.50	−	5197.02i	0.460209	−	0.797106i	0.998971	+	0.0453522i	$0.0144410\pi$
$350$	−266.000			−0.0406237
$351$		0			0
$352$	1920.00			0.290728
$353$	276.000	−	478.046i	0.0416147	−	0.0720788i	−0.844468	−	0.535606i	$-0.820083\pi$
$353$	276.000	−	478.046i	0.0416147	−	0.0720788i	0.886083	+	0.463527i	$0.153416\pi$
$354$		0			0
$355$	−1296.00	−	2244.74i	−0.193759	−	0.335601i
$356$	−72.0000	−	124.708i	−0.0107191	−	0.0185660i
$357$		0			0
$358$	−1800.00	+	3117.69i	−0.265735	+	0.460266i
$359$	−5004.00			−0.735657			−0.367829	−	0.929894i	$-0.619899\pi$
$359$	−5004.00			−0.735657			−0.367829	+	0.929894i	$0.619899\pi$
$360$		0			0
$361$	−6738.00			−0.982359
$362$	547.000	−	947.432i	0.0794190	−	0.137558i
$363$		0			0
$364$	−1106.00	−	1915.65i	−0.159259	−	0.275844i
$365$	3066.00	+	5310.47i	0.439676	+	0.761541i
$366$		0			0
$367$	2145.50	−	3716.12i	0.305161	−	0.528555i	−0.672136	−	0.740428i	$-0.734623\pi$
$367$	2145.50	−	3716.12i	0.305161	−	0.528555i	0.977297	+	0.211873i	$0.0679563\pi$
$368$	−2112.00			−0.299173
$369$		0			0
$370$	−4056.00			−0.569896
$371$	1260.00	−	2182.38i	0.176323	−	0.305401i
$372$		0			0
$373$	1416.50	+	2453.45i	0.196632	+	0.340576i	0.947434	−	0.319951i	$-0.103666\pi$
$373$	1416.50	+	2453.45i	0.196632	+	0.340576i	−0.750803	+	0.660527i	$0.770333\pi$
$374$	6480.00	+	11223.7i	0.895917	+	1.55177i
$375$		0			0
$376$	−816.000	+	1413.35i	−0.111920	+	0.193851i
$377$	−7584.00			−1.03606
$378$		0			0
$379$	−5137.00			−0.696227			−0.348113	−	0.937452i	$-0.613178\pi$
$379$	−5137.00			−0.696227			−0.348113	+	0.937452i	$0.613178\pi$
$380$	−264.000	+	457.261i	−0.0356392	+	0.0617290i
$381$		0			0
$382$	−3156.00	−	5466.35i	−0.422709	−	0.732154i
$383$	−2544.00	−	4406.34i	−0.339406	−	0.587868i	0.644915	−	0.764254i	$-0.276893\pi$
$383$	−2544.00	−	4406.34i	−0.339406	−	0.587868i	−0.984321	+	0.176386i	$0.943559\pi$
$384$		0			0
$385$	2520.00	−	4364.77i	0.333587	−	0.577790i
$386$	2254.00			0.297217
$387$		0			0
$388$	2420.00			0.316641
$389$	−3990.00	+	6910.88i	−0.520054	+	0.900760i	0.479674	+	0.877447i	$0.340755\pi$
$389$	−3990.00	+	6910.88i	−0.520054	+	0.900760i	−0.999728	+	0.0233134i	$0.992578\pi$
$390$		0			0
$391$	−7128.00	−	12346.1i	−0.921940	−	1.59685i
$392$	1176.00	+	2036.89i	0.151523	+	0.262445i
$393$		0			0
$394$	−1116.00	+	1932.97i	−0.142699	+	0.247161i
$395$	−6348.00			−0.808614
$396$		0			0
$397$	−1834.00			−0.231853			−0.115927	−	0.993258i	$-0.536984\pi$
$397$	−1834.00			−0.231853			−0.115927	+	0.993258i	$0.536984\pi$
$398$	3283.00	−	5686.32i	0.413472	−	0.716155i
$399$		0			0
$400$	−152.000	−	263.272i	−0.0190000	−	0.0329090i
$401$	732.000	+	1267.86i	0.0911579	+	0.157890i	0.907999	−	0.418973i	$-0.137610\pi$
$401$	732.000	+	1267.86i	0.0911579	+	0.157890i	−0.816841	+	0.576863i	$0.804277\pi$
$402$		0			0
$403$	790.000	−	1368.32i	0.0976494	−	0.169134i
$404$	4992.00			0.614756
$405$		0			0
$406$	−1344.00			−0.164290
$407$	5070.00	−	8781.50i	0.617471	−	1.06949i
$408$		0			0
$409$	75.5000	+	130.770i	0.00912771	+	0.0158097i	0.870553	−	0.492074i	$-0.163761\pi$
$409$	75.5000	+	130.770i	0.00912771	+	0.0158097i	−0.861425	+	0.507884i	$0.830428\pi$
$410$	−2304.00	−	3990.65i	−0.277528	−	0.480692i
$411$		0			0
$412$	−1930.00	+	3342.86i	−0.230787	+	0.399735i
$413$	−1092.00			−0.130106
$414$		0			0
$415$	−13536.0			−1.60110
$416$	1264.00	−	2189.31i	0.148973	−	0.258029i
$417$		0			0
$418$	−660.000	−	1143.15i	−0.0772288	−	0.133764i
$419$	5754.00	+	9966.22i	0.670886	+	1.16201i	0.977653	+	0.210224i	$0.0674194\pi$
$419$	5754.00	+	9966.22i	0.670886	+	1.16201i	−0.306767	+	0.951785i	$0.599247\pi$
$420$		0			0
$421$	3135.50	−	5430.85i	0.362981	−	0.628701i	−0.625469	−	0.780249i	$-0.715092\pi$
$421$	3135.50	−	5430.85i	0.362981	−	0.628701i	0.988450	+	0.151548i	$0.0484257\pi$
$422$	−590.000			−0.0680587
$423$		0			0
$424$	2880.00			0.329871
$425$	1026.00	−	1777.08i	0.117102	−	0.202826i
$426$		0			0
$427$	290.500	+	503.161i	0.0329234	+	0.0570250i
$428$	−2664.00	−	4614.18i	−0.300863	−	0.521110i
$429$		0			0
$430$	−5856.00	+	10142.9i	−0.656747	+	1.13752i
$431$	9468.00			1.05814			0.529069	−	0.848579i	$-0.322541\pi$
$431$	9468.00			1.05814			0.529069	+	0.848579i	$0.322541\pi$
$432$		0			0
$433$	3026.00			0.335844			0.167922	−	0.985800i	$-0.446294\pi$
$433$	3026.00			0.335844			0.167922	+	0.985800i	$0.446294\pi$
$434$	140.000	−	242.487i	0.0154844	−	0.0268197i
$435$		0			0
$436$	3884.00	+	6727.29i	0.426628	+	0.738942i
$437$	726.000	+	1257.47i	0.0794721	+	0.137650i
$438$		0			0
$439$	−5590.00	+	9682.16i	−0.607736	+	1.05263i	0.383877	+	0.923384i	$0.374589\pi$
$439$	−5590.00	+	9682.16i	−0.607736	+	1.05263i	−0.991613	+	0.129245i	$0.958745\pi$
$440$	5760.00			0.624085
$441$		0			0
$442$	17064.0			1.83632
$443$	420.000	−	727.461i	0.0450447	−	0.0780197i	−0.842624	−	0.538502i	$-0.818990\pi$
$443$	420.000	−	727.461i	0.0450447	−	0.0780197i	0.887669	+	0.460483i	$0.152324\pi$
$444$		0			0
$445$	−216.000	−	374.123i	−0.0230098	−	0.0398542i
$446$	2644.00	+	4579.54i	0.280711	+	0.486205i
$447$		0			0
$448$	224.000	−	387.979i	0.0236228	−	0.0409159i
$449$	12780.0			1.34326			0.671632	−	0.740885i	$-0.265594\pi$
$449$	12780.0			1.34326			0.671632	+	0.740885i	$0.265594\pi$
$450$		0			0
$451$	11520.0			1.20278
$452$	−1032.00	+	1787.48i	−0.107392	+	0.186008i
$453$		0			0
$454$	6024.00	+	10433.9i	0.622732	+	1.07860i
$455$	−3318.00	−	5746.94i	−0.341869	−	0.592134i
$456$		0			0
$457$	7829.00	−	13560.2i	0.801368	−	1.38801i	−0.117348	−	0.993091i	$-0.537439\pi$
$457$	7829.00	−	13560.2i	0.801368	−	1.38801i	0.918716	−	0.394919i	$-0.129227\pi$
$458$	−8924.00			−0.910461
$459$		0			0
$460$	−6336.00			−0.642212
$461$	7782.00	−	13478.8i	0.786212	−	1.36176i	−0.142060	−	0.989858i	$-0.545373\pi$
$461$	7782.00	−	13478.8i	0.786212	−	1.36176i	0.928272	−	0.371902i	$-0.121294\pi$
$462$		0			0
$463$	2091.50	+	3622.58i	0.209936	+	0.363619i	0.951694	−	0.307048i	$-0.0993412\pi$
$463$	2091.50	+	3622.58i	0.209936	+	0.363619i	−0.741758	+	0.670667i	$0.766008\pi$
$464$	−768.000	−	1330.22i	−0.0768395	−	0.133090i
$465$		0			0
$466$	1008.00	−	1745.91i	0.100203	−	0.173557i
$467$	13932.0			1.38051			0.690253	−	0.723568i	$-0.257499\pi$
$467$	13932.0			1.38051			0.690253	+	0.723568i	$0.257499\pi$
$468$		0			0
$469$	−329.000			−0.0323919
$470$	−2448.00	+	4240.06i	−0.240251	+	0.416126i
$471$		0			0
$472$	−624.000	−	1080.80i	−0.0608515	−	0.105398i
$473$	−14640.0	−	25357.2i	−1.42315	−	2.46496i
$474$		0			0
$475$	−104.500	+	180.999i	−0.0100943	+	0.0174838i
$476$	3024.00			0.291187
$477$		0			0
$478$	−10128.0			−0.969130
$479$	1356.00	−	2348.66i	0.129347	−	0.224036i	−0.794077	−	0.607817i	$-0.792045\pi$
$479$	1356.00	−	2348.66i	0.129347	−	0.224036i	0.923424	+	0.383782i	$0.125379\pi$
$480$		0			0
$481$	−6675.50	−	11562.3i	−0.632800	−	1.09604i
$482$	−6257.00	−	10837.4i	−0.591283	−	1.02413i
$483$		0			0
$484$	−4538.00	+	7860.05i	−0.426183	+	0.738171i
$485$	7260.00			0.679711
$486$		0			0
$487$	−9439.00			−0.878279			−0.439140	−	0.898419i	$-0.644717\pi$
$487$	−9439.00			−0.878279			−0.439140	+	0.898419i	$0.644717\pi$
$488$	−332.000	+	575.041i	−0.0307970	+	0.0533420i
$489$		0			0
$490$	3528.00	+	6110.68i	0.325263	+	0.563372i
$491$	5862.00	+	10153.3i	0.538795	+	0.933220i	0.998969	+	0.0453917i	$0.0144536\pi$
$491$	5862.00	+	10153.3i	0.538795	+	0.933220i	−0.460174	+	0.887829i	$0.652213\pi$
$492$		0			0
$493$	5184.00	−	8978.95i	0.473581	−	0.820267i
$494$	−1738.00			−0.158292
$495$		0			0
$496$	320.000			0.0289686
$497$	756.000	−	1309.43i	0.0682319	−	0.118181i
$498$		0			0
$499$	5984.00	+	10364.6i	0.536835	+	0.929825i	0.999072	+	0.0430690i	$0.0137135\pi$
$499$	5984.00	+	10364.6i	0.536835	+	0.929825i	−0.462237	+	0.886756i	$0.652953\pi$
$500$	2544.00	+	4406.34i	0.227542	+	0.394115i
$501$		0			0
$502$	2160.00	−	3741.23i	0.192043	−	0.332628i
$503$	8892.00			0.788220			0.394110	−	0.919063i	$-0.371053\pi$
$503$	8892.00			0.788220			0.394110	+	0.919063i	$0.371053\pi$
$504$		0			0
$505$	14976.0			1.31965
$506$	7920.00	−	13717.8i	0.695824	−	1.20520i
$507$		0			0
$508$	104.000	+	180.133i	0.00908318	+	0.0157325i
$509$	3378.00	+	5850.87i	0.294160	+	0.509499i	0.974789	−	0.223129i	$-0.0716270\pi$
$509$	3378.00	+	5850.87i	0.294160	+	0.509499i	−0.680629	+	0.732628i	$0.738294\pi$
$510$		0			0
$511$	−1788.50	+	3097.77i	−0.154831	+	0.268175i
$512$	512.000			0.0441942
$513$		0			0
$514$	−336.000			−0.0288333
$515$	−5790.00	+	10028.6i	−0.495413	+	0.858081i
$516$		0			0
$517$	−6120.00	−	10600.2i	−0.520614	−	0.901729i
$518$	−1183.00	−	2049.02i	−0.100344	−	0.173800i
$519$		0			0
$520$	3792.00	−	6567.94i	0.319789	−	0.553891i
$521$	−6228.00			−0.523711			−0.261856	−	0.965107i	$-0.584334\pi$
$521$	−6228.00			−0.523711			−0.261856	+	0.965107i	$0.584334\pi$
$522$		0			0
$523$	11639.0			0.973113			0.486556	−	0.873649i	$-0.338253\pi$
$523$	11639.0			0.973113			0.486556	+	0.873649i	$0.338253\pi$
$524$	−96.0000	+	166.277i	−0.00800340	+	0.0138623i
$525$		0			0
$526$	2424.00	+	4198.49i	0.200934	+	0.348028i
$527$	1080.00	+	1870.61i	0.0892705	+	0.154621i
$528$		0			0
$529$	−2628.50	+	4552.70i	−0.216035	+	0.374184i
$530$	8640.00			0.708109
$531$		0			0
$532$	−308.000			−0.0251006
$533$	7584.00	−	13135.9i	0.616322	−	1.06750i
$534$		0			0
$535$	−7992.00	−	13842.6i	−0.645840	−	1.11863i
$536$	−188.000	−	325.626i	−0.0151499	−	0.0262405i
$537$		0			0
$538$	396.000	−	685.892i	0.0317338	−	0.0549645i
$539$	−17640.0			−1.40966
$540$		0			0
$541$	17705.0			1.40702			0.703510	−	0.710686i	$-0.251615\pi$
$541$	17705.0			1.40702			0.703510	+	0.710686i	$0.251615\pi$
$542$	−1811.00	+	3136.74i	−0.143522	+	0.248588i
$543$		0			0
$544$	1728.00	+	2992.98i	0.136190	+	0.235888i
$545$	11652.0	+	20181.9i	0.915811	+	1.58623i
$546$		0			0
$547$	−1742.50	+	3018.10i	−0.136205	+	0.235913i	−0.926057	−	0.377384i	$-0.876824\pi$
$547$	−1742.50	+	3018.10i	−0.136205	+	0.235913i	0.789852	+	0.613297i	$0.210157\pi$
$548$	9456.00			0.737117
$549$		0			0
$550$	2280.00			0.176763
$551$	−528.000	+	914.523i	−0.0408232	+	0.0707078i
$552$		0			0
$553$	−1851.50	−	3206.89i	−0.142376	−	0.246602i
$554$	3022.00	+	5234.26i	0.231755	+	0.401412i
$555$		0			0
$556$	−346.000	+	599.290i	−0.0263915	+	0.0457114i
$557$	−19116.0			−1.45417			−0.727083	−	0.686549i	$-0.759125\pi$
$557$	−19116.0			−1.45417			−0.727083	+	0.686549i	$0.759125\pi$
$558$		0			0
$559$	−38552.0			−2.91695
$560$	672.000	−	1163.94i	0.0507093	−	0.0878310i
$561$		0			0
$562$	3072.00	+	5320.86i	0.230577	+	0.399372i
$563$	−11184.0	−	19371.3i	−0.837210	−	1.45009i	−0.892218	−	0.451605i	$-0.850852\pi$
$563$	−11184.0	−	19371.3i	−0.837210	−	1.45009i	0.0550077	−	0.998486i	$-0.482482\pi$
$564$		0			0
$565$	−3096.00	+	5362.43i	−0.230530	+	0.399290i
$566$	−16160.0			−1.20010
$567$		0			0
$568$	1728.00			0.127650
$569$	−4170.00	+	7222.65i	−0.307233	+	0.532143i	−0.977756	−	0.209746i	$-0.932736\pi$
$569$	−4170.00	+	7222.65i	−0.307233	+	0.532143i	0.670523	+	0.741889i	$0.266070\pi$
$570$		0			0
$571$	7338.50	+	12710.7i	0.537840	+	0.931566i	0.999020	+	0.0442597i	$0.0140929\pi$
$571$	7338.50	+	12710.7i	0.537840	+	0.931566i	−0.461180	+	0.887307i	$0.652574\pi$
$572$	9480.00	+	16419.8i	0.692970	+	1.20026i
$573$		0			0
$574$	1344.00	−	2327.88i	0.0977308	−	0.169275i
$575$	−2508.00			−0.181897
$576$		0			0
$577$	−10069.0			−0.726478			−0.363239	−	0.931696i	$-0.618329\pi$
$577$	−10069.0			−0.726478			−0.363239	+	0.931696i	$0.618329\pi$
$578$	−6751.00	+	11693.1i	−0.485821	+	0.841467i
$579$		0			0
$580$	−2304.00	−	3990.65i	−0.164946	−	0.285694i
$581$	−3948.00	−	6838.14i	−0.281912	−	0.488285i
$582$		0			0
$583$	−10800.0	+	18706.1i	−0.767222	+	1.32887i
$584$	−4088.00			−0.289662
$585$		0			0
$586$	−9336.00			−0.658134
$587$	−786.000	+	1361.39i	−0.0552669	+	0.0957251i	−0.892335	−	0.451373i	$-0.850934\pi$
$587$	−786.000	+	1361.39i	−0.0552669	+	0.0957251i	0.837068	+	0.547098i	$0.184268\pi$
$588$		0			0
$589$	−110.000	−	190.526i	−0.00769520	−	0.0133285i
$590$	−1872.00	−	3242.40i	−0.130625	−	0.226250i
$591$		0			0
$592$	1352.00	−	2341.73i	0.0938629	−	0.162575i
$593$	1368.00			0.0947336			0.0473668	−	0.998878i	$-0.484917\pi$
$593$	1368.00			0.0947336			0.0473668	+	0.998878i	$0.484917\pi$
$594$		0			0
$595$	9072.00			0.625068
$596$	3216.00	−	5570.28i	0.221028	−	0.382831i
$597$		0			0
$598$	−10428.0	−	18061.8i	−0.713098	−	1.23512i
$599$	11856.0	+	20535.2i	0.808720	+	1.40074i	0.913751	+	0.406275i	$0.133172\pi$
$599$	11856.0	+	20535.2i	0.808720	+	1.40074i	−0.105031	+	0.994469i	$0.533494\pi$
$600$		0			0
$601$	5507.00	−	9538.40i	0.373769	−	0.647387i	−0.616373	−	0.787454i	$-0.711399\pi$
$601$	5507.00	−	9538.40i	0.373769	−	0.647387i	0.990142	+	0.140067i	$0.0447319\pi$
$602$	−6832.00			−0.462544
$603$		0			0
$604$	−3988.00			−0.268658
$605$	−13614.0	+	23580.1i	−0.914856	+	1.58458i
$606$		0			0
$607$	3207.50	+	5555.55i	0.214478	+	0.371488i	0.953111	−	0.302621i	$-0.0978615\pi$
$607$	3207.50	+	5555.55i	0.214478	+	0.371488i	−0.738633	+	0.674108i	$0.764528\pi$
$608$	−176.000	−	304.841i	−0.0117397	−	0.0203338i
$609$		0			0
$610$	−996.000	+	1725.12i	−0.0661096	+	0.114505i
$611$	−16116.0			−1.06708
$612$		0			0
$613$	15851.0			1.04440			0.522199	−	0.852824i	$-0.325112\pi$
$613$	15851.0			1.04440			0.522199	+	0.852824i	$0.325112\pi$
$614$	−6752.00	+	11694.8i	−0.443792	+	0.768671i
$615$		0			0
$616$	1680.00	+	2909.85i	0.109885	+	0.190326i
$617$	−2886.00	−	4998.70i	−0.188308	−	0.326159i	0.756378	−	0.654134i	$-0.226967\pi$
$617$	−2886.00	−	4998.70i	−0.188308	−	0.326159i	−0.944686	+	0.327976i	$0.893634\pi$
$618$		0			0
$619$	13890.5	−	24059.1i	0.901949	−	1.56222i	0.0769875	−	0.997032i	$-0.475470\pi$
$619$	13890.5	−	24059.1i	0.901949	−	1.56222i	0.824961	−	0.565189i	$-0.191197\pi$
$620$	960.000			0.0621847
$621$		0			0
$622$	3624.00			0.233616
$623$	126.000	−	218.238i	0.00810286	−	0.0140346i
$624$		0			0
$625$	8819.50	+	15275.8i	0.564448	+	0.977653i
$626$	−6203.00	−	10743.9i	−0.396041	−	0.685963i
$627$		0			0
$628$	−1228.00	+	2126.96i	−0.0780295	+	0.135151i
$629$	18252.0			1.15700
$630$		0			0
$631$	−29869.0			−1.88442			−0.942208	−	0.335029i	$-0.891254\pi$
$631$	−29869.0			−1.88442			−0.942208	+	0.335029i	$0.891254\pi$
$632$	2116.00	−	3665.02i	0.133180	−	0.230675i
$633$		0			0
$634$	−10968.0	−	18997.1i	−0.687058	−	1.19002i
$635$	312.000	+	540.400i	0.0194982	+	0.0337718i
$636$		0			0
$637$	−11613.0	+	20114.3i	−0.722329	+	1.25111i
$638$	11520.0			0.714861
$639$		0			0
$640$	1536.00			0.0948683
$641$	−1740.00	+	3013.77i	−0.107217	+	0.185705i	−0.914642	−	0.404266i	$-0.867527\pi$
$641$	−1740.00	+	3013.77i	−0.107217	+	0.185705i	0.807425	+	0.589970i	$0.200861\pi$
$642$		0			0
$643$	3716.00	+	6436.30i	0.227908	+	0.394748i	0.957188	−	0.289467i	$-0.0934782\pi$
$643$	3716.00	+	6436.30i	0.227908	+	0.394748i	−0.729280	+	0.684215i	$0.760145\pi$
$644$	−1848.00	−	3200.83i	−0.113077	−	0.195855i
$645$		0			0
$646$	1188.00	−	2057.68i	0.0723549	−	0.125322i
$647$	−12960.0			−0.787496			−0.393748	−	0.919218i	$-0.628822\pi$
$647$	−12960.0			−0.787496			−0.393748	+	0.919218i	$0.628822\pi$
$648$		0			0
$649$	9360.00			0.566120
$650$	1501.00	−	2599.81i	0.0905755	−	0.156881i
$651$		0			0
$652$	−5386.00	−	9328.83i	−0.323515	−	0.560345i
$653$	−11796.0	−	20431.3i	−0.706911	−	1.22441i	−0.965997	−	0.258552i	$-0.916755\pi$
$653$	−11796.0	−	20431.3i	−0.706911	−	1.22441i	0.259086	−	0.965854i	$-0.416579\pi$
$654$		0			0
$655$	−288.000	+	498.831i	−0.0171803	+	0.0297571i
$656$	3072.00			0.182838
$657$		0			0
$658$	−2856.00			−0.169207
$659$	−16140.0	+	27955.3i	−0.954059	+	1.65248i	−0.217553	+	0.976048i	$0.569808\pi$
$659$	−16140.0	+	27955.3i	−0.954059	+	1.65248i	−0.736506	+	0.676431i	$0.763526\pi$
$660$		0			0
$661$	−11309.5	−	19588.6i	−0.665490	−	1.15266i	−0.979152	−	0.203127i	$-0.934889\pi$
$661$	−11309.5	−	19588.6i	−0.665490	−	1.15266i	0.313663	−	0.949534i	$-0.398444\pi$
$662$	−8165.00	−	14142.2i	−0.479368	−	0.830290i
$663$		0			0
$664$	4512.00	−	7815.01i	0.263704	−	0.456749i
$665$	−924.000			−0.0538815
$666$		0			0
$667$	−12672.0			−0.735625
$668$	−2328.00	+	4032.21i	−0.134840	+	0.233549i
$669$		0			0
$670$	−564.000	−	976.877i	−0.0325212	−	0.0563284i
$671$	−2490.00	−	4312.81i	−0.143257	−	0.248128i
$672$		0			0
$673$	9930.50	−	17200.1i	0.568786	−	0.985165i	−0.427901	−	0.903826i	$-0.640747\pi$
$673$	9930.50	−	17200.1i	0.568786	−	0.985165i	0.996686	−	0.0813397i	$-0.0259199\pi$
$674$	−13046.0			−0.745568
$675$		0			0
$676$	16176.0			0.920346
$677$	4146.00	−	7181.08i	0.235367	−	0.407668i	−0.724012	−	0.689787i	$-0.757704\pi$
$677$	4146.00	−	7181.08i	0.235367	−	0.407668i	0.959379	+	0.282119i	$0.0910373\pi$
$678$		0			0
$679$	2117.50	+	3667.62i	0.119679	+	0.207290i
$680$	5184.00	+	8978.95i	0.292349	+	0.506363i
$681$		0			0
$682$	−1200.00	+	2078.46i	−0.0673759	+	0.116699i
$683$	19728.0			1.10523			0.552614	−	0.833437i	$-0.313630\pi$
$683$	19728.0			1.10523			0.552614	+	0.833437i	$0.313630\pi$
$684$		0			0
$685$	28368.0			1.58231
$686$	−4459.00	+	7723.21i	−0.248171	+	0.429845i
$687$		0			0
$688$	−3904.00	−	6761.93i	−0.216335	−	0.374704i
$689$	14220.0	+	24629.8i	0.786268	+	1.36186i
$690$		0			0
$691$	−13636.0	+	23618.2i	−0.750706	+	1.30026i	0.196775	+	0.980449i	$0.436953\pi$
$691$	−13636.0	+	23618.2i	−0.750706	+	1.30026i	−0.947481	+	0.319812i	$0.896380\pi$
$692$	−14592.0			−0.801596
$693$		0			0
$694$	12336.0			0.674738
$695$	−1038.00	+	1797.87i	−0.0566526	+	0.0981252i
$696$		0			0
$697$	10368.0	+	17957.9i	0.563438	+	0.975903i
$698$	6001.00	+	10394.0i	0.325417	+	0.563639i
$699$		0			0
$700$	266.000	−	460.726i	0.0143626	−	0.0248768i
$701$	−21996.0			−1.18513			−0.592566	−	0.805522i	$-0.701885\pi$
$701$	−21996.0			−1.18513			−0.592566	+	0.805522i	$0.701885\pi$
$702$		0			0
$703$	−1859.00			−0.0997347
$704$	−1920.00	+	3325.54i	−0.102788	+	0.178034i
$705$		0			0
$706$	552.000	+	956.092i	0.0294261	+	0.0509674i
$707$	4368.00	+	7565.60i	0.232356	+	0.402452i
$708$		0			0
$709$	−1004.50	+	1739.85i	−0.0532084	+	0.0921597i	−0.891403	−	0.453212i	$-0.850278\pi$
$709$	−1004.50	+	1739.85i	−0.0532084	+	0.0921597i	0.838194	+	0.545372i	$0.183611\pi$
$710$	5184.00			0.274017
$711$		0			0
$712$	288.000			0.0151591
$713$	1320.00	−	2286.31i	0.0693329	−	0.120088i
$714$		0			0
$715$	28440.0	+	49259.5i	1.48755	+	2.57651i
$716$	−3600.00	−	6235.38i	−0.187903	−	0.325457i
$717$		0			0
$718$	5004.00	−	8667.18i	0.260094	−	0.450496i
$719$	26280.0			1.36311			0.681557	−	0.731765i	$-0.261303\pi$
$719$	26280.0			1.36311			0.681557	+	0.731765i	$0.261303\pi$
$720$		0			0
$721$	−6755.00			−0.348917
$722$	6738.00	−	11670.6i	0.347316	−	0.601570i
$723$		0			0
$724$	1094.00	+	1894.86i	0.0561577	+	0.0972680i
$725$	−912.000	−	1579.63i	−0.0467184	−	0.0809186i
$726$		0			0
$727$	−10450.0	+	18099.9i	−0.533107	+	0.923369i	0.466145	+	0.884708i	$0.345642\pi$
$727$	−10450.0	+	18099.9i	−0.533107	+	0.923369i	−0.999252	+	0.0386607i	$0.987691\pi$
$728$	4424.00			0.225226
$729$		0			0
$730$	−12264.0			−0.621796
$731$	26352.0	−	45643.0i	1.33333	−	2.30939i
$732$		0			0
$733$	8819.00	+	15275.0i	0.444389	+	0.769704i	0.998009	−	0.0630647i	$-0.0200874\pi$
$733$	8819.00	+	15275.0i	0.444389	+	0.769704i	−0.553620	+	0.832769i	$0.686754\pi$
$734$	4291.00	+	7432.23i	0.215782	+	0.373745i
$735$		0			0
$736$	2112.00	−	3658.09i	0.105774	−	0.183205i
$737$	2820.00			0.140944
$738$		0			0
$739$	30080.0			1.49731			0.748654	−	0.662961i	$-0.230700\pi$
$739$	30080.0			1.49731			0.748654	+	0.662961i	$0.230700\pi$
$740$	4056.00	−	7025.20i	0.201489	−	0.348988i
$741$		0			0
$742$	2520.00	+	4364.77i	0.124679	+	0.215951i
$743$	−7854.00	−	13603.5i	−0.387800	−	0.671689i	0.604353	−	0.796716i	$-0.293432\pi$
$743$	−7854.00	−	13603.5i	−0.387800	−	0.671689i	−0.992153	+	0.125027i	$0.960098\pi$
$744$		0			0
$745$	9648.00	−	16710.8i	0.474464	−	0.821795i
$746$	−5666.00			−0.278079
$747$		0			0
$748$	−25920.0			−1.26702
$749$	4662.00	−	8074.82i	0.227431	−	0.393922i
$750$		0			0
$751$	−10211.5	−	17686.8i	−0.496169	−	0.859390i	0.503821	−	0.863808i	$-0.331927\pi$
$751$	−10211.5	−	17686.8i	−0.496169	−	0.859390i	−0.999990	+	0.00441801i	$0.998594\pi$
$752$	−1632.00	−	2826.71i	−0.0791395	−	0.137074i
$753$		0			0
$754$	7584.00	−	13135.9i	0.366304	−	0.634457i
$755$	−11964.0			−0.576708
$756$		0			0
$757$	−4399.00			−0.211208			−0.105604	−	0.994408i	$-0.533678\pi$
$757$	−4399.00			−0.211208			−0.105604	+	0.994408i	$0.533678\pi$
$758$	5137.00	−	8897.54i	0.246153	−	0.426350i
$759$		0			0
$760$	−528.000	−	914.523i	−0.0252008	−	0.0436490i
$761$	10326.0	+	17885.2i	0.491875	+	0.851953i	0.999956	−	0.00935617i	$-0.00297820\pi$
$761$	10326.0	+	17885.2i	0.491875	+	0.851953i	−0.508081	+	0.861309i	$0.669645\pi$
$762$		0			0
$763$	−6797.00	+	11772.7i	−0.322501	+	0.558587i
$764$	12624.0			0.597801
$765$		0			0
$766$	10176.0			0.479992
$767$	6162.00	−	10672.9i	0.290087	−	0.502446i
$768$		0			0
$769$	−13703.5	−	23735.2i	−0.642602	−	1.11302i	−0.984850	−	0.173409i	$-0.944522\pi$
$769$	−13703.5	−	23735.2i	−0.642602	−	1.11302i	0.342248	−	0.939610i	$-0.388812\pi$
$770$	5040.00	+	8729.54i	0.235882	+	0.408559i
$771$		0			0
$772$	−2254.00	+	3904.04i	−0.105082	+	0.182007i
$773$	5976.00			0.278062			0.139031	−	0.990288i	$-0.455601\pi$
$773$	5976.00			0.278062			0.139031	+	0.990288i	$0.455601\pi$
$774$		0			0
$775$	380.000			0.0176129
$776$	−2420.00	+	4191.56i	−0.111950	+	0.193903i
$777$		0			0
$778$	−7980.00	−	13821.8i	−0.367734	−	0.636934i
$779$	−1056.00	−	1829.05i	−0.0485688	−	0.0841237i
$780$		0			0
$781$	−6480.00	+	11223.7i	−0.296892	+	0.514232i
$782$	28512.0			1.30382
$783$		0			0
$784$	−4704.00			−0.214286
$785$	−3684.00	+	6380.88i	−0.167500	+	0.290119i
$786$		0			0
$787$	−12065.5	−	20898.1i	−0.546491	−	0.946551i	−0.998511	−	0.0545429i	$-0.982630\pi$
$787$	−12065.5	−	20898.1i	−0.546491	−	0.946551i	0.452020	−	0.892008i	$-0.350704\pi$
$788$	−2232.00	−	3865.94i	−0.100903	−	0.174769i
$789$		0			0
$790$	6348.00	−	10995.1i	0.285888	−	0.495173i
$791$	−3612.00			−0.162361
$792$		0			0
$793$	−6557.00			−0.293627
$794$	1834.00	−	3176.58i	0.0819726	−	0.141981i
$795$		0			0
$796$	6566.00	+	11372.6i	0.292369	+	0.506398i
$797$	−456.000	−	789.815i	−0.0202664	−	0.0351025i	0.855714	−	0.517449i	$-0.173118\pi$
$797$	−456.000	−	789.815i	−0.0202664	−	0.0351025i	−0.875981	+	0.482346i	$0.839785\pi$
$798$		0			0
$799$	11016.0	−	19080.3i	0.487757	−	0.844820i
$800$	608.000			0.0268701
$801$		0			0
$802$	−2928.00			−0.128917
$803$	15330.0	−	26552.3i	0.673704	−	1.16689i
$804$		0			0
$805$	−5544.00	−	9602.49i	−0.242733	−	0.420426i
$806$	1580.00	+	2736.64i	0.0690485	+	0.119596i
$807$		0			0
$808$	−4992.00	+	8646.40i	−0.217349	+	0.376459i
$809$	−12888.0			−0.560096			−0.280048	−	0.959986i	$-0.590350\pi$
$809$	−12888.0			−0.560096			−0.280048	+	0.959986i	$0.590350\pi$
$810$		0			0
$811$	−6856.00			−0.296852			−0.148426	−	0.988924i	$-0.547421\pi$
$811$	−6856.00			−0.296852			−0.148426	+	0.988924i	$0.547421\pi$
$812$	1344.00	−	2327.88i	0.0580852	−	0.100606i
$813$		0			0
$814$	10140.0	+	17563.0i	0.436618	+	0.756244i
$815$	−16158.0	−	27986.5i	−0.694466	−	1.20285i
$816$		0			0
$817$	−2684.00	+	4648.82i	−0.114934	+	0.199072i
$818$	−302.000			−0.0129085
$819$		0			0
$820$	9216.00			0.392484
$821$	−318.000	+	550.792i	−0.0135180	+	0.0234139i	−0.872705	−	0.488247i	$-0.837636\pi$
$821$	−318.000	+	550.792i	−0.0135180	+	0.0234139i	0.859187	+	0.511661i	$0.170970\pi$
$822$		0			0
$823$	−19913.5	−	34491.2i	−0.843428	−	1.46086i	−0.886980	−	0.461808i	$-0.847201\pi$
$823$	−19913.5	−	34491.2i	−0.843428	−	1.46086i	0.0435520	−	0.999051i	$-0.486133\pi$
$824$	−3860.00	−	6685.72i	−0.163191	−	0.282655i
$825$		0			0
$826$	1092.00	−	1891.40i	0.0459994	−	0.0796734i
$827$	38124.0			1.60302			0.801512	−	0.597978i	$-0.204029\pi$
$827$	38124.0			1.60302			0.801512	+	0.597978i	$0.204029\pi$
$828$		0			0
$829$	18965.0			0.794550			0.397275	−	0.917700i	$-0.369956\pi$
$829$	18965.0			0.794550			0.397275	+	0.917700i	$0.369956\pi$
$830$	13536.0	−	23445.0i	0.566074	−	0.980469i
$831$		0			0
$832$	2528.00	+	4378.62i	0.105340	+	0.182454i
$833$	−15876.0	−	27498.0i	−0.660349	−	1.14376i
$834$		0			0
$835$	−6984.00	+	12096.6i	−0.289451	+	0.501343i
$836$	2640.00			0.109218
$837$		0			0
$838$	−23016.0			−0.948776
$839$	−13908.0	+	24089.4i	−0.572297	+	0.991248i	0.424032	+	0.905647i	$0.360614\pi$
$839$	−13908.0	+	24089.4i	−0.572297	+	0.991248i	−0.996330	+	0.0856010i	$0.972719\pi$
$840$		0			0
$841$	7586.50	+	13140.2i	0.311062	+	0.538776i
$842$	6271.00	+	10861.7i	0.256666	+	0.444559i
$843$		0			0
$844$	590.000	−	1021.91i	0.0240624	−	0.0416772i
$845$	48528.0			1.97564
$846$		0			0
$847$	−15883.0			−0.644329
$848$	−2880.00	+	4988.31i	−0.116627	+	0.202004i
$849$		0			0
$850$	2052.00	+	3554.17i	0.0828036	+	0.143420i
$851$	−11154.0	−	19319.3i	−0.449300	−	0.778210i
$852$		0			0
$853$	6168.50	−	10684.2i	0.247603	−	0.428861i	−0.715257	−	0.698861i	$-0.753690\pi$
$853$	6168.50	−	10684.2i	0.247603	−	0.428861i	0.962860	+	0.270000i	$0.0870238\pi$
$854$	−1162.00			−0.0465607
$855$		0			0
$856$	10656.0			0.425484
$857$	5676.00	−	9831.12i	0.226241	−	0.391861i	−0.730450	−	0.682966i	$-0.760690\pi$
$857$	5676.00	−	9831.12i	0.226241	−	0.391861i	0.956691	+	0.291105i	$0.0940230\pi$
$858$		0			0
$859$	1263.50	+	2188.45i	0.0501863	+	0.0869253i	0.890027	−	0.455907i	$-0.150685\pi$
$859$	1263.50	+	2188.45i	0.0501863	+	0.0869253i	−0.839841	+	0.542833i	$0.817352\pi$
$860$	−11712.0	−	20285.8i	−0.464391	−	0.804348i
$861$		0			0
$862$	−9468.00	+	16399.1i	−0.374108	+	0.647975i
$863$	−26388.0			−1.04086			−0.520428	−	0.853906i	$-0.674227\pi$
$863$	−26388.0			−1.04086			−0.520428	+	0.853906i	$0.674227\pi$
$864$		0			0
$865$	−43776.0			−1.72073
$866$	−3026.00	+	5241.19i	−0.118739	+	0.205661i
$867$		0			0
$868$	280.000	+	484.974i	0.0109491	+	0.0189644i
$869$	15870.0	+	27487.6i	0.619508	+	1.07302i
$870$		0			0
$871$	1856.50	−	3215.55i	0.0722217	−	0.125092i
$872$	−15536.0			−0.603343
$873$		0			0
$874$	−2904.00			−0.112390
$875$	−4452.00	+	7711.09i	−0.172006	+	0.297923i
$876$		0			0
$877$	−3191.50	−	5527.84i	−0.122884	−	0.212841i	0.798020	−	0.602631i	$-0.205881\pi$
$877$	−3191.50	−	5527.84i	−0.122884	−	0.212841i	−0.920904	+	0.389790i	$0.872548\pi$
$878$	−11180.0	−	19364.3i	−0.429734	−	0.744322i
$879$		0			0
$880$	−5760.00	+	9976.61i	−0.220647	+	0.382172i
$881$	28908.0			1.10549			0.552744	−	0.833351i	$-0.313581\pi$
$881$	28908.0			1.10549			0.552744	+	0.833351i	$0.313581\pi$
$882$		0			0
$883$	36893.0			1.40606			0.703028	−	0.711162i	$-0.251831\pi$
$883$	36893.0			1.40606			0.703028	+	0.711162i	$0.251831\pi$
$884$	−17064.0	+	29555.7i	−0.649236	+	1.12451i
$885$		0			0
$886$	840.000	+	1454.92i	0.0318514	+	0.0551683i
$887$	22764.0	+	39428.4i	0.861714	+	1.49253i	0.870273	+	0.492569i	$0.163942\pi$
$887$	22764.0	+	39428.4i	0.861714	+	1.49253i	−0.00855937	+	0.999963i	$0.502725\pi$
$888$		0			0
$889$	−182.000	+	315.233i	−0.00686624	+	0.0118927i
$890$	864.000			0.0325408
$891$		0			0
$892$	−10576.0			−0.396985
$893$	−1122.00	+	1943.36i	−0.0420451	+	0.0728243i
$894$		0			0
$895$	−10800.0	−	18706.1i	−0.403357	−	0.698634i
$896$	448.000	+	775.959i	0.0167038	+	0.0289319i
$897$		0			0
$898$	−12780.0	+	22135.6i	−0.474916	+	0.822578i
$899$	1920.00			0.0712298
$900$		0			0
$901$	−38880.0			−1.43760
$902$	−11520.0	+	19953.2i	−0.425248	+	0.736552i
$903$		0			0
$904$	−2064.00	−	3574.95i	−0.0759376	−	0.131528i
$905$	3282.00	+	5684.59i	0.120550	+	0.208798i
$906$		0			0
$907$	15600.5	−	27020.9i	0.571120	−	0.989209i	−0.425331	−	0.905038i	$-0.639842\pi$
$907$	15600.5	−	27020.9i	0.571120	−	0.989209i	0.996451	−	0.0841715i	$-0.0268244\pi$
$908$	−24096.0			−0.880676
$909$		0			0
$910$	13272.0			0.483475
$911$	−11928.0	+	20659.9i	−0.433801	+	0.751365i	−0.997197	−	0.0748222i	$-0.976161\pi$
$911$	−11928.0	+	20659.9i	−0.433801	+	0.751365i	0.563396	+	0.826187i	$0.309494\pi$
$912$		0			0
$913$	33840.0	+	58612.6i	1.22666	+	2.12464i
$914$	15658.0	+	27120.5i	0.566653	+	0.981471i
$915$		0			0
$916$	8924.00	−	15456.8i	0.321897	−	0.557541i
$917$	−336.000			−0.0121000
$918$		0			0
$919$	23492.0			0.843231			0.421616	−	0.906775i	$-0.361463\pi$
$919$	23492.0			0.843231			0.421616	+	0.906775i	$0.361463\pi$
$920$	6336.00	−	10974.3i	0.227056	−	0.393273i
$921$		0			0
$922$	15564.0	+	26957.6i	0.555936	+	0.962909i
$923$	8532.00	+	14777.9i	0.304262	+	0.526998i
$924$		0			0
$925$	1605.50	−	2780.81i	0.0570687	−	0.0988458i
$926$	−8366.00			−0.296894
$927$		0			0
$928$	3072.00			0.108667
$929$	7548.00	−	13073.5i	0.266568	−	0.461710i	−0.701405	−	0.712763i	$-0.747444\pi$
$929$	7548.00	−	13073.5i	0.266568	−	0.461710i	0.967973	+	0.251053i	$0.0807769\pi$
$930$		0			0
$931$	1617.00	+	2800.73i	0.0569227	+	0.0985930i
$932$	2016.00	+	3491.81i	0.0708544	+	0.122723i
$933$		0			0
$934$	−13932.0	+	24130.9i	−0.488082	+	0.845384i
$935$	−77760.0			−2.71981
$936$		0			0
$937$	−14965.0			−0.521756			−0.260878	−	0.965372i	$-0.584012\pi$
$937$	−14965.0			−0.521756			−0.260878	+	0.965372i	$0.584012\pi$
$938$	329.000	−	569.845i	0.0114523	−	0.0198359i
$939$		0			0
$940$	−4896.00	−	8480.12i	−0.169883	−	0.294246i
$941$	−9762.00	−	16908.3i	−0.338185	−	0.585754i	0.645906	−	0.763417i	$-0.276480\pi$
$941$	−9762.00	−	16908.3i	−0.338185	−	0.585754i	−0.984091	+	0.177663i	$0.943146\pi$
$942$		0			0
$943$	12672.0	−	21948.5i	0.437600	−	0.757946i
$944$	2496.00			0.0860571
$945$		0			0
$946$	58560.0			2.01263
$947$	−5538.00	+	9592.10i	−0.190033	+	0.329146i	−0.945261	−	0.326316i	$-0.894193\pi$
$947$	−5538.00	+	9592.10i	−0.190033	+	0.329146i	0.755228	+	0.655462i	$0.227526\pi$
$948$		0			0
$949$	−20184.5	−	34960.6i	−0.690428	−	1.19586i
$950$	−209.000	−	361.999i	−0.00713774	−	0.0123629i
$951$		0			0
$952$	−3024.00	+	5237.72i	−0.102950	+	0.178315i
$953$	−44748.0			−1.52102			−0.760509	−	0.649328i	$-0.775050\pi$
$953$	−44748.0			−1.52102			−0.760509	+	0.649328i	$0.775050\pi$
$954$		0			0
$955$	37872.0			1.28326
$956$	10128.0	−	17542.2i	0.342639	−	0.593468i
$957$		0			0
$958$	2712.00	+	4697.32i	0.0914622	+	0.158417i
$959$	8274.00	+	14331.0i	0.278604	+	0.482557i
$960$		0			0
$961$	14695.5	−	25453.4i	0.493287	−	0.854397i
$962$	26702.0			0.894914
$963$		0			0
$964$	25028.0			0.836201
$965$	−6762.00	+	11712.1i	−0.225571	+	0.390701i
$966$		0			0
$967$	−20759.5	−	35956.5i	−0.690362	−	1.19574i	−0.971719	−	0.236140i	$-0.924118\pi$
$967$	−20759.5	−	35956.5i	−0.690362	−	1.19574i	0.281357	−	0.959603i	$-0.409216\pi$
$968$	−9076.00	−	15720.1i	−0.301357	−	0.521966i
$969$		0			0
$970$	−7260.00	+	12574.7i	−0.240314	+	0.416236i
$971$	28404.0			0.938752			0.469376	−	0.882999i	$-0.344479\pi$
$971$	28404.0			0.938752			0.469376	+	0.882999i	$0.344479\pi$
$972$		0			0
$973$	−1211.00			−0.0399002
$974$	9439.00	−	16348.8i	0.310519	−	0.537834i
$975$		0			0
$976$	−664.000	−	1150.08i	−0.0217768	−	0.0377185i
$977$	−21516.0	−	37266.8i	−0.704563	−	1.22034i	−0.966849	−	0.255348i	$-0.917810\pi$
$977$	−21516.0	−	37266.8i	−0.704563	−	1.22034i	0.262286	−	0.964990i	$-0.415524\pi$
$978$		0			0
$979$	−1080.00	+	1870.61i	−0.0352574	+	0.0610675i
$980$	−14112.0			−0.459991
$981$		0			0
$982$	−23448.0			−0.761971
$983$	−9066.00	+	15702.8i	−0.294161	+	0.509502i	−0.974789	−	0.223127i	$-0.928374\pi$
$983$	−9066.00	+	15702.8i	−0.294161	+	0.509502i	0.680628	+	0.732629i	$0.261707\pi$
$984$		0			0
$985$	−6696.00	−	11597.8i	−0.216601	−	0.375164i
$986$	10368.0	+	17957.9i	0.334873	+	0.580016i
$987$		0			0
$988$	1738.00	−	3010.30i	0.0559647	−	0.0969337i
$989$	−64416.0			−2.07109
$990$		0			0
$991$	−44467.0			−1.42537			−0.712685	−	0.701485i	$-0.752521\pi$
$991$	−44467.0			−1.42537			−0.712685	+	0.701485i	$0.752521\pi$
$992$	−320.000	+	554.256i	−0.0102419	+	0.0177396i
$993$		0			0
$994$	1512.00	+	2618.86i	0.0482472	+	0.0835666i
$995$	19698.0	+	34117.9i	0.627607	+	1.08705i
$996$		0			0
$997$	−9775.00	+	16930.8i	−0.310509	+	0.537817i	−0.978473	−	0.206377i	$-0.933833\pi$
$997$	−9775.00	+	16930.8i	−0.310509	+	0.537817i	0.667964	+	0.744194i	$0.267166\pi$
$998$	−23936.0			−0.759199
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.4.c.a.55.1		2
3.2	odd	2		162.4.c.h.55.1		2
9.2	odd	6		54.4.a.a.1.1	✓	1
9.4	even	3	inner	162.4.c.a.109.1		2
9.5	odd	6		162.4.c.h.109.1		2
9.7	even	3		54.4.a.d.1.1	yes	1
36.7	odd	6		432.4.a.m.1.1		1
36.11	even	6		432.4.a.b.1.1		1
45.2	even	12		1350.4.c.a.649.1		2
45.7	odd	12		1350.4.c.t.649.2		2
45.29	odd	6		1350.4.a.v.1.1		1
45.34	even	6		1350.4.a.h.1.1		1
45.38	even	12		1350.4.c.a.649.2		2
45.43	odd	12		1350.4.c.t.649.1		2
72.11	even	6		1728.4.a.bb.1.1		1
72.29	odd	6		1728.4.a.ba.1.1		1
72.43	odd	6		1728.4.a.f.1.1		1
72.61	even	6		1728.4.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.4.a.a.1.1	✓	1	9.2	odd	6
54.4.a.d.1.1	yes	1	9.7	even	3
162.4.c.a.55.1		2	1.1	even	1	trivial
162.4.c.a.109.1		2	9.4	even	3	inner
162.4.c.h.55.1		2	3.2	odd	2
162.4.c.h.109.1		2	9.5	odd	6
432.4.a.b.1.1		1	36.11	even	6
432.4.a.m.1.1		1	36.7	odd	6
1350.4.a.h.1.1		1	45.34	even	6
1350.4.a.v.1.1		1	45.29	odd	6
1350.4.c.a.649.1		2	45.2	even	12
1350.4.c.a.649.2		2	45.38	even	12
1350.4.c.t.649.1		2	45.43	odd	12
1350.4.c.t.649.2		2	45.7	odd	12
1728.4.a.e.1.1		1	72.61	even	6
1728.4.a.f.1.1		1	72.43	odd	6
1728.4.a.ba.1.1		1	72.29	odd	6
1728.4.a.bb.1.1		1	72.11	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)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-6.00000 - 10.3923i) q^{5} +(3.50000 - 6.06218i) q^{7} +8.00000 q^{8} +O(q^{10})\)	\(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-6.00000 - 10.3923i) q^{5} +(3.50000 - 6.06218i) q^{7} +8.00000 q^{8} +24.0000 q^{10} +(-30.0000 + 51.9615i) q^{11} +(39.5000 + 68.4160i) q^{13} +(7.00000 + 12.1244i) q^{14} +(-8.00000 + 13.8564i) q^{16} -108.000 q^{17} +11.0000 q^{19} +(-24.0000 + 41.5692i) q^{20} +(-60.0000 - 103.923i) q^{22} +(66.0000 + 114.315i) q^{23} +(-9.50000 + 16.4545i) q^{25} -158.000 q^{26} -28.0000 q^{28} +(-48.0000 + 83.1384i) q^{29} +(-10.0000 - 17.3205i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(108.000 - 187.061i) q^{34} -84.0000 q^{35} -169.000 q^{37} +(-11.0000 + 19.0526i) q^{38} +(-48.0000 - 83.1384i) q^{40} +(-96.0000 - 166.277i) q^{41} +(-244.000 + 422.620i) q^{43} +240.000 q^{44} -264.000 q^{46} +(-102.000 + 176.669i) q^{47} +(147.000 + 254.611i) q^{49} +(-19.0000 - 32.9090i) q^{50} +(158.000 - 273.664i) q^{52} +360.000 q^{53} +720.000 q^{55} +(28.0000 - 48.4974i) q^{56} +(-96.0000 - 166.277i) q^{58} +(-78.0000 - 135.100i) q^{59} +(-41.5000 + 71.8801i) q^{61} +40.0000 q^{62} +64.0000 q^{64} +(474.000 - 820.992i) q^{65} +(-23.5000 - 40.7032i) q^{67} +(216.000 + 374.123i) q^{68} +(84.0000 - 145.492i) q^{70} +216.000 q^{71} -511.000 q^{73} +(169.000 - 292.717i) q^{74} +(-22.0000 - 38.1051i) q^{76} +(210.000 + 363.731i) q^{77} +(264.500 - 458.127i) q^{79} +192.000 q^{80} +384.000 q^{82} +(564.000 - 976.877i) q^{83} +(648.000 + 1122.37i) q^{85} +(-488.000 - 845.241i) q^{86} +(-240.000 + 415.692i) q^{88} +36.0000 q^{89} +553.000 q^{91} +(264.000 - 457.261i) q^{92} +(-204.000 - 353.338i) q^{94} +(-66.0000 - 114.315i) q^{95} +(-302.500 + 523.945i) q^{97} -588.000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 4 q^{4} - 12 q^{5} + 7 q^{7} + 16 q^{8}+O(q^{10}) \) 2 * q - 2 * q^2 - 4 * q^4 - 12 * q^5 + 7 * q^7 + 16 * q^8	\( 2 q - 2 q^{2} - 4 q^{4} - 12 q^{5} + 7 q^{7} + 16 q^{8} + 48 q^{10} - 60 q^{11} + 79 q^{13} + 14 q^{14} - 16 q^{16} - 216 q^{17} + 22 q^{19} - 48 q^{20} - 120 q^{22} + 132 q^{23} - 19 q^{25} - 316 q^{26} - 56 q^{28} - 96 q^{29} - 20 q^{31} - 32 q^{32} + 216 q^{34} - 168 q^{35} - 338 q^{37} - 22 q^{38} - 96 q^{40} - 192 q^{41} - 488 q^{43} + 480 q^{44} - 528 q^{46} - 204 q^{47} + 294 q^{49} - 38 q^{50} + 316 q^{52} + 720 q^{53} + 1440 q^{55} + 56 q^{56} - 192 q^{58} - 156 q^{59} - 83 q^{61} + 80 q^{62} + 128 q^{64} + 948 q^{65} - 47 q^{67} + 432 q^{68} + 168 q^{70} + 432 q^{71} - 1022 q^{73} + 338 q^{74} - 44 q^{76} + 420 q^{77} + 529 q^{79} + 384 q^{80} + 768 q^{82} + 1128 q^{83} + 1296 q^{85} - 976 q^{86} - 480 q^{88} + 72 q^{89} + 1106 q^{91} + 528 q^{92} - 408 q^{94} - 132 q^{95} - 605 q^{97} - 1176 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 4 * q^4 - 12 * q^5 + 7 * q^7 + 16 * q^8 + 48 * q^10 - 60 * q^11 + 79 * q^13 + 14 * q^14 - 16 * q^16 - 216 * q^17 + 22 * q^19 - 48 * q^20 - 120 * q^22 + 132 * q^23 - 19 * q^25 - 316 * q^26 - 56 * q^28 - 96 * q^29 - 20 * q^31 - 32 * q^32 + 216 * q^34 - 168 * q^35 - 338 * q^37 - 22 * q^38 - 96 * q^40 - 192 * q^41 - 488 * q^43 + 480 * q^44 - 528 * q^46 - 204 * q^47 + 294 * q^49 - 38 * q^50 + 316 * q^52 + 720 * q^53 + 1440 * q^55 + 56 * q^56 - 192 * q^58 - 156 * q^59 - 83 * q^61 + 80 * q^62 + 128 * q^64 + 948 * q^65 - 47 * q^67 + 432 * q^68 + 168 * q^70 + 432 * q^71 - 1022 * q^73 + 338 * q^74 - 44 * q^76 + 420 * q^77 + 529 * q^79 + 384 * q^80 + 768 * q^82 + 1128 * q^83 + 1296 * q^85 - 976 * q^86 - 480 * q^88 + 72 * q^89 + 1106 * q^91 + 528 * q^92 - 408 * q^94 - 132 * q^95 - 605 * q^97 - 1176 * q^98

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