LMFDB - Embedded newform 810.4.e.w.271.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,4,Mod(271,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("810.271");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	810.e (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:	$47.7915471046$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 10)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			271.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	810.271
Dual form			810.4.e.w.541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(2.50000 - 4.33013i) q^{5} +(2.00000 + 3.46410i) q^{7} -8.00000 q^{8} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(2.50000 - 4.33013i) q^{5} +(2.00000 + 3.46410i) q^{7} -8.00000 q^{8} +10.0000 q^{10} +(6.00000 + 10.3923i) q^{11} +(29.0000 - 50.2295i) q^{13} +(-4.00000 + 6.92820i) q^{14} +(-8.00000 - 13.8564i) q^{16} -66.0000 q^{17} -100.000 q^{19} +(10.0000 + 17.3205i) q^{20} +(-12.0000 + 20.7846i) q^{22} +(66.0000 - 114.315i) q^{23} +(-12.5000 - 21.6506i) q^{25} +116.000 q^{26} -16.0000 q^{28} +(-45.0000 - 77.9423i) q^{29} +(-76.0000 + 131.636i) q^{31} +(16.0000 - 27.7128i) q^{32} +(-66.0000 - 114.315i) q^{34} +20.0000 q^{35} -34.0000 q^{37} +(-100.000 - 173.205i) q^{38} +(-20.0000 + 34.6410i) q^{40} +(-219.000 + 379.319i) q^{41} +(-16.0000 - 27.7128i) q^{43} -48.0000 q^{44} +264.000 q^{46} +(-102.000 - 176.669i) q^{47} +(163.500 - 283.190i) q^{49} +(25.0000 - 43.3013i) q^{50} +(116.000 + 200.918i) q^{52} -222.000 q^{53} +60.0000 q^{55} +(-16.0000 - 27.7128i) q^{56} +(90.0000 - 155.885i) q^{58} +(210.000 - 363.731i) q^{59} +(-451.000 - 781.155i) q^{61} -304.000 q^{62} +64.0000 q^{64} +(-145.000 - 251.147i) q^{65} +(512.000 - 886.810i) q^{67} +(132.000 - 228.631i) q^{68} +(20.0000 + 34.6410i) q^{70} -432.000 q^{71} +362.000 q^{73} +(-34.0000 - 58.8897i) q^{74} +(200.000 - 346.410i) q^{76} +(-24.0000 + 41.5692i) q^{77} +(80.0000 + 138.564i) q^{79} -80.0000 q^{80} -876.000 q^{82} +(36.0000 + 62.3538i) q^{83} +(-165.000 + 285.788i) q^{85} +(32.0000 - 55.4256i) q^{86} +(-48.0000 - 83.1384i) q^{88} -810.000 q^{89} +232.000 q^{91} +(264.000 + 457.261i) q^{92} +(204.000 - 353.338i) q^{94} +(-250.000 + 433.013i) q^{95} +(-553.000 - 957.824i) q^{97} +654.000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 4 q^{4} + 5 q^{5} + 4 q^{7} - 16 q^{8}+O(q^{10}) $ 2 * q + 2 * q^2 - 4 * q^4 + 5 * q^5 + 4 * q^7 - 16 * q^8	$ 2 q + 2 q^{2} - 4 q^{4} + 5 q^{5} + 4 q^{7} - 16 q^{8} + 20 q^{10} + 12 q^{11} + 58 q^{13} - 8 q^{14} - 16 q^{16} - 132 q^{17} - 200 q^{19} + 20 q^{20} - 24 q^{22} + 132 q^{23} - 25 q^{25} + 232 q^{26} - 32 q^{28} - 90 q^{29} - 152 q^{31} + 32 q^{32} - 132 q^{34} + 40 q^{35} - 68 q^{37} - 200 q^{38} - 40 q^{40} - 438 q^{41} - 32 q^{43} - 96 q^{44} + 528 q^{46} - 204 q^{47} + 327 q^{49} + 50 q^{50} + 232 q^{52} - 444 q^{53} + 120 q^{55} - 32 q^{56} + 180 q^{58} + 420 q^{59} - 902 q^{61} - 608 q^{62} + 128 q^{64} - 290 q^{65} + 1024 q^{67} + 264 q^{68} + 40 q^{70} - 864 q^{71} + 724 q^{73} - 68 q^{74} + 400 q^{76} - 48 q^{77} + 160 q^{79} - 160 q^{80} - 1752 q^{82} + 72 q^{83} - 330 q^{85} + 64 q^{86} - 96 q^{88} - 1620 q^{89} + 464 q^{91} + 528 q^{92} + 408 q^{94} - 500 q^{95} - 1106 q^{97} + 1308 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 - 4 * q^4 + 5 * q^5 + 4 * q^7 - 16 * q^8 + 20 * q^10 + 12 * q^11 + 58 * q^13 - 8 * q^14 - 16 * q^16 - 132 * q^17 - 200 * q^19 + 20 * q^20 - 24 * q^22 + 132 * q^23 - 25 * q^25 + 232 * q^26 - 32 * q^28 - 90 * q^29 - 152 * q^31 + 32 * q^32 - 132 * q^34 + 40 * q^35 - 68 * q^37 - 200 * q^38 - 40 * q^40 - 438 * q^41 - 32 * q^43 - 96 * q^44 + 528 * q^46 - 204 * q^47 + 327 * q^49 + 50 * q^50 + 232 * q^52 - 444 * q^53 + 120 * q^55 - 32 * q^56 + 180 * q^58 + 420 * q^59 - 902 * q^61 - 608 * q^62 + 128 * q^64 - 290 * q^65 + 1024 * q^67 + 264 * q^68 + 40 * q^70 - 864 * q^71 + 724 * q^73 - 68 * q^74 + 400 * q^76 - 48 * q^77 + 160 * q^79 - 160 * q^80 - 1752 * q^82 + 72 * q^83 - 330 * q^85 + 64 * q^86 - 96 * q^88 - 1620 * q^89 + 464 * q^91 + 528 * q^92 + 408 * q^94 - 500 * q^95 - 1106 * q^97 + 1308 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$6$		0			0
$7$	2.00000	+	3.46410i	0.107990	+	0.187044i	0.914956	−	0.403554i	$-0.132225\pi$
$7$	2.00000	+	3.46410i	0.107990	+	0.187044i	−0.806966	+	0.590598i	$0.798892\pi$
$8$	−8.00000			−0.353553
$9$		0			0
$10$	10.0000			0.316228
$11$	6.00000	+	10.3923i	0.164461	+	0.284854i	0.936464	−	0.350765i	$-0.114078\pi$
$11$	6.00000	+	10.3923i	0.164461	+	0.284854i	−0.772003	+	0.635619i	$0.780745\pi$
$12$		0			0
$13$	29.0000	−	50.2295i	0.618704	−	1.07163i	−0.371018	−	0.928626i	$-0.620991\pi$
$13$	29.0000	−	50.2295i	0.618704	−	1.07163i	0.989722	−	0.143001i	$-0.0456753\pi$
$14$	−4.00000	+	6.92820i	−0.0763604	+	0.132260i
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−66.0000			−0.941609			−0.470804	−	0.882238i	$-0.656036\pi$
$17$	−66.0000			−0.941609			−0.470804	+	0.882238i	$0.656036\pi$
$18$		0			0
$19$	−100.000			−1.20745			−0.603726	−	0.797192i	$-0.706318\pi$
$19$	−100.000			−1.20745			−0.603726	+	0.797192i	$0.706318\pi$
$20$	10.0000	+	17.3205i	0.111803	+	0.193649i
$21$		0			0
$22$	−12.0000	+	20.7846i	−0.116291	+	0.201422i
$23$	66.0000	−	114.315i	0.598346	−	1.03637i	−0.394720	−	0.918802i	$-0.629158\pi$
$23$	66.0000	−	114.315i	0.598346	−	1.03637i	0.993065	−	0.117564i	$-0.0375084\pi$
$24$		0			0
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	116.000			0.874980
$27$		0			0
$28$	−16.0000			−0.107990
$29$	−45.0000	−	77.9423i	−0.288148	−	0.499087i	0.685220	−	0.728336i	$-0.259706\pi$
$29$	−45.0000	−	77.9423i	−0.288148	−	0.499087i	−0.973368	+	0.229250i	$0.926373\pi$
$30$		0			0
$31$	−76.0000	+	131.636i	−0.440323	+	0.762661i	−0.997713	−	0.0675892i	$-0.978469\pi$
$31$	−76.0000	+	131.636i	−0.440323	+	0.762661i	0.557391	+	0.830250i	$0.311803\pi$
$32$	16.0000	−	27.7128i	0.0883883	−	0.153093i
$33$		0			0
$34$	−66.0000	−	114.315i	−0.332909	−	0.576615i
$35$	20.0000			0.0965891
$36$		0			0
$37$	−34.0000			−0.151069			−0.0755347	−	0.997143i	$-0.524066\pi$
$37$	−34.0000			−0.151069			−0.0755347	+	0.997143i	$0.524066\pi$
$38$	−100.000	−	173.205i	−0.426898	−	0.739410i
$39$		0			0
$40$	−20.0000	+	34.6410i	−0.0790569	+	0.136931i
$41$	−219.000	+	379.319i	−0.834196	+	1.44487i	0.0604866	+	0.998169i	$0.480735\pi$
$41$	−219.000	+	379.319i	−0.834196	+	1.44487i	−0.894683	+	0.446702i	$0.852599\pi$
$42$		0			0
$43$	−16.0000	−	27.7128i	−0.0567437	−	0.0982829i	0.836258	−	0.548336i	$-0.184738\pi$
$43$	−16.0000	−	27.7128i	−0.0567437	−	0.0982829i	−0.893002	+	0.450053i	$0.851405\pi$
$44$	−48.0000			−0.164461
$45$		0			0
$46$	264.000			0.846189
$47$	−102.000	−	176.669i	−0.316558	−	0.548295i	0.663209	−	0.748434i	$-0.269194\pi$
$47$	−102.000	−	176.669i	−0.316558	−	0.548295i	−0.979767	+	0.200139i	$0.935861\pi$
$48$		0			0
$49$	163.500	−	283.190i	0.476676	−	0.825628i
$50$	25.0000	−	43.3013i	0.0707107	−	0.122474i
$51$		0			0
$52$	116.000	+	200.918i	0.309352	+	0.535813i
$53$	−222.000			−0.575359			−0.287680	−	0.957727i	$-0.592884\pi$
$53$	−222.000			−0.575359			−0.287680	+	0.957727i	$0.592884\pi$
$54$		0			0
$55$	60.0000			0.147098
$56$	−16.0000	−	27.7128i	−0.0381802	−	0.0661300i
$57$		0			0
$58$	90.0000	−	155.885i	0.203751	−	0.352908i
$59$	210.000	−	363.731i	0.463384	−	0.802605i	−0.535743	−	0.844381i	$-0.679968\pi$
$59$	210.000	−	363.731i	0.463384	−	0.802605i	0.999127	+	0.0417762i	$0.0133016\pi$
$60$		0			0
$61$	−451.000	−	781.155i	−0.946633	−	1.63962i	−0.752447	−	0.658652i	$-0.771127\pi$
$61$	−451.000	−	781.155i	−0.946633	−	1.63962i	−0.194186	−	0.980965i	$-0.562206\pi$
$62$	−304.000			−0.622710
$63$		0			0
$64$	64.0000			0.125000
$65$	−145.000	−	251.147i	−0.276693	−	0.479246i
$66$		0			0
$67$	512.000	−	886.810i	0.933593	−	1.61703i	0.156470	−	0.987683i	$-0.449989\pi$
$67$	512.000	−	886.810i	0.933593	−	1.61703i	0.777123	−	0.629348i	$-0.216678\pi$
$68$	132.000	−	228.631i	0.235402	−	0.407729i
$69$		0			0
$70$	20.0000	+	34.6410i	0.0341494	+	0.0591485i
$71$	−432.000			−0.722098			−0.361049	−	0.932547i	$-0.617581\pi$
$71$	−432.000			−0.722098			−0.361049	+	0.932547i	$0.617581\pi$
$72$		0			0
$73$	362.000			0.580396			0.290198	−	0.956967i	$-0.406279\pi$
$73$	362.000			0.580396			0.290198	+	0.956967i	$0.406279\pi$
$74$	−34.0000	−	58.8897i	−0.0534111	−	0.0925107i
$75$		0			0
$76$	200.000	−	346.410i	0.301863	−	0.522842i
$77$	−24.0000	+	41.5692i	−0.0355202	+	0.0615228i
$78$		0			0
$79$	80.0000	+	138.564i	0.113933	+	0.197338i	0.917353	−	0.398075i	$-0.130322\pi$
$79$	80.0000	+	138.564i	0.113933	+	0.197338i	−0.803420	+	0.595413i	$0.796988\pi$
$80$	−80.0000			−0.111803
$81$		0			0
$82$	−876.000			−1.17973
$83$	36.0000	+	62.3538i	0.0476086	+	0.0824605i	0.888848	−	0.458203i	$-0.151507\pi$
$83$	36.0000	+	62.3538i	0.0476086	+	0.0824605i	−0.841239	+	0.540663i	$0.818173\pi$
$84$		0			0
$85$	−165.000	+	285.788i	−0.210550	+	0.364684i
$86$	32.0000	−	55.4256i	0.0401238	−	0.0694965i
$87$		0			0
$88$	−48.0000	−	83.1384i	−0.0581456	−	0.100711i
$89$	−810.000			−0.964717			−0.482359	−	0.875974i	$-0.660220\pi$
$89$	−810.000			−0.964717			−0.482359	+	0.875974i	$0.660220\pi$
$90$		0			0
$91$	232.000			0.267255
$92$	264.000	+	457.261i	0.299173	+	0.518183i
$93$		0			0
$94$	204.000	−	353.338i	0.223840	−	0.387703i
$95$	−250.000	+	433.013i	−0.269994	+	0.467644i
$96$		0			0
$97$	−553.000	−	957.824i	−0.578852	−	1.00260i	−0.995611	−	0.0935842i	$-0.970168\pi$
$97$	−553.000	−	957.824i	−0.578852	−	1.00260i	0.416759	−	0.909017i	$-0.363166\pi$
$98$	654.000			0.674122
$99$		0			0
$100$	100.000			0.100000
$101$	−129.000	−	223.435i	−0.127089	−	0.220124i	0.795459	−	0.606008i	$-0.207230\pi$
$101$	−129.000	−	223.435i	−0.127089	−	0.220124i	−0.922548	+	0.385883i	$0.873897\pi$
$102$		0			0
$103$	494.000	−	855.633i	0.472575	−	0.818525i	−0.526932	−	0.849907i	$-0.676658\pi$
$103$	494.000	−	855.633i	0.472575	−	0.818525i	0.999507	+	0.0313828i	$0.00999110\pi$
$104$	−232.000	+	401.836i	−0.218745	+	0.378877i
$105$		0			0
$106$	−222.000	−	384.515i	−0.203420	−	0.352334i
$107$	24.0000			0.0216838			0.0108419	−	0.999941i	$-0.496549\pi$
$107$	24.0000			0.0216838			0.0108419	+	0.999941i	$0.496549\pi$
$108$		0			0
$109$	950.000			0.834803			0.417401	−	0.908722i	$-0.362941\pi$
$109$	950.000			0.834803			0.417401	+	0.908722i	$0.362941\pi$
$110$	60.0000	+	103.923i	0.0520071	+	0.0900789i
$111$		0			0
$112$	32.0000	−	55.4256i	0.0269975	−	0.0467610i
$113$	−519.000	+	898.934i	−0.432066	+	0.748360i	−0.997051	−	0.0767413i	$-0.975548\pi$
$113$	−519.000	+	898.934i	−0.432066	+	0.748360i	0.564985	+	0.825101i	$0.308882\pi$
$114$		0			0
$115$	−330.000	−	571.577i	−0.267588	−	0.463477i
$116$	360.000			0.288148
$117$		0			0
$118$	840.000			0.655324
$119$	−132.000	−	228.631i	−0.101684	−	0.176122i
$120$		0			0
$121$	593.500	−	1027.97i	0.445905	−	0.772331i
$122$	902.000	−	1562.31i	0.669371	−	1.15938i
$123$		0			0
$124$	−304.000	−	526.543i	−0.220161	−	0.381331i
$125$	−125.000			−0.0894427
$126$		0			0
$127$	−124.000			−0.0866395			−0.0433198	−	0.999061i	$-0.513793\pi$
$127$	−124.000			−0.0866395			−0.0433198	+	0.999061i	$0.513793\pi$
$128$	64.0000	+	110.851i	0.0441942	+	0.0765466i
$129$		0			0
$130$	290.000	−	502.295i	0.195651	−	0.338878i
$131$	66.0000	−	114.315i	0.0440187	−	0.0762426i	−0.843177	−	0.537637i	$-0.819317\pi$
$131$	66.0000	−	114.315i	0.0440187	−	0.0762426i	0.887195	+	0.461394i	$0.152651\pi$
$132$		0			0
$133$	−200.000	−	346.410i	−0.130392	−	0.225846i
$134$	2048.00			1.32030
$135$		0			0
$136$	528.000			0.332909
$137$	−627.000	−	1086.00i	−0.391009	−	0.677247i	0.601574	−	0.798817i	$-0.294541\pi$
$137$	−627.000	−	1086.00i	−0.391009	−	0.677247i	−0.992583	+	0.121570i	$0.961207\pi$
$138$		0			0
$139$	1430.00	−	2476.83i	0.872597	−	1.51138i	0.0132968	−	0.999912i	$-0.495767\pi$
$139$	1430.00	−	2476.83i	0.872597	−	1.51138i	0.859300	−	0.511471i	$-0.170899\pi$
$140$	−40.0000	+	69.2820i	−0.0241473	+	0.0418243i
$141$		0			0
$142$	−432.000	−	748.246i	−0.255300	−	0.442193i
$143$	696.000			0.407010
$144$		0			0
$145$	−450.000			−0.257727
$146$	362.000	+	627.002i	0.205201	+	0.355418i
$147$		0			0
$148$	68.0000	−	117.779i	0.0377673	−	0.0654149i
$149$	375.000	−	649.519i	0.206183	−	0.357119i	−0.744326	−	0.667816i	$-0.767229\pi$
$149$	375.000	−	649.519i	0.206183	−	0.357119i	0.950509	+	0.310697i	$0.100563\pi$
$150$		0			0
$151$	224.000	+	387.979i	0.120721	+	0.209095i	0.920052	−	0.391796i	$-0.128146\pi$
$151$	224.000	+	387.979i	0.120721	+	0.209095i	−0.799331	+	0.600891i	$0.794813\pi$
$152$	800.000			0.426898
$153$		0			0
$154$	−96.0000			−0.0502331
$155$	380.000	+	658.179i	0.196918	+	0.341072i
$156$		0			0
$157$	−1123.00	+	1945.09i	−0.570861	+	0.988760i	0.425617	+	0.904903i	$0.360057\pi$
$157$	−1123.00	+	1945.09i	−0.570861	+	0.988760i	−0.996478	+	0.0838566i	$0.973276\pi$
$158$	−160.000	+	277.128i	−0.0805628	+	0.139539i
$159$		0			0
$160$	−80.0000	−	138.564i	−0.0395285	−	0.0684653i
$161$	528.000			0.258461
$162$		0			0
$163$	−568.000			−0.272940			−0.136470	−	0.990644i	$-0.543576\pi$
$163$	−568.000			−0.272940			−0.136470	+	0.990644i	$0.543576\pi$
$164$	−876.000	−	1517.28i	−0.417098	−	0.722435i
$165$		0			0
$166$	−72.0000	+	124.708i	−0.0336644	+	0.0583084i
$167$	−762.000	+	1319.82i	−0.353086	+	0.611563i	−0.986788	−	0.162014i	$-0.948201\pi$
$167$	−762.000	+	1319.82i	−0.353086	+	0.611563i	0.633703	+	0.773577i	$0.281534\pi$
$168$		0			0
$169$	−583.500	−	1010.65i	−0.265589	−	0.460014i
$170$	−660.000			−0.297763
$171$		0			0
$172$	128.000			0.0567437
$173$	1851.00	+	3206.03i	0.813462	+	1.40896i	0.910427	+	0.413670i	$0.135753\pi$
$173$	1851.00	+	3206.03i	0.813462	+	1.40896i	−0.0969650	+	0.995288i	$0.530914\pi$
$174$		0			0
$175$	50.0000	−	86.6025i	0.0215980	−	0.0374088i
$176$	96.0000	−	166.277i	0.0411152	−	0.0712136i
$177$		0			0
$178$	−810.000	−	1402.96i	−0.341079	−	0.590766i
$179$	−3180.00			−1.32785			−0.663923	−	0.747801i	$-0.731110\pi$
$179$	−3180.00			−1.32785			−0.663923	+	0.747801i	$0.731110\pi$
$180$		0			0
$181$	−2098.00			−0.861564			−0.430782	−	0.902456i	$-0.641762\pi$
$181$	−2098.00			−0.861564			−0.430782	+	0.902456i	$0.641762\pi$
$182$	232.000	+	401.836i	0.0944889	+	0.163660i
$183$		0			0
$184$	−528.000	+	914.523i	−0.211547	+	0.366410i
$185$	−85.0000	+	147.224i	−0.0337801	+	0.0585089i
$186$		0			0
$187$	−396.000	−	685.892i	−0.154858	−	0.268221i
$188$	816.000			0.316558
$189$		0			0
$190$	−1000.00			−0.381830
$191$	2196.00	+	3803.58i	0.831921	+	1.44093i	0.896513	+	0.443018i	$0.146092\pi$
$191$	2196.00	+	3803.58i	0.831921	+	1.44093i	−0.0645912	+	0.997912i	$0.520574\pi$
$192$		0			0
$193$	1079.00	−	1868.88i	0.402425	−	0.697021i	−0.591593	−	0.806237i	$-0.701501\pi$
$193$	1079.00	−	1868.88i	0.402425	−	0.697021i	0.994018	+	0.109216i	$0.0348339\pi$
$194$	1106.00	−	1915.65i	0.409310	−	0.708946i
$195$		0			0
$196$	654.000	+	1132.76i	0.238338	+	0.412814i
$197$	1074.00			0.388423			0.194212	−	0.980960i	$-0.437785\pi$
$197$	1074.00			0.388423			0.194212	+	0.980960i	$0.437785\pi$
$198$		0			0
$199$	2840.00			1.01167			0.505835	−	0.862630i	$-0.331185\pi$
$199$	2840.00			1.01167			0.505835	+	0.862630i	$0.331185\pi$
$200$	100.000	+	173.205i	0.0353553	+	0.0612372i
$201$		0			0
$202$	258.000	−	446.869i	0.0898654	−	0.155651i
$203$	180.000	−	311.769i	0.0622341	−	0.107793i
$204$		0			0
$205$	1095.00	+	1896.60i	0.373064	+	0.646166i
$206$	1976.00			0.668323
$207$		0			0
$208$	−928.000			−0.309352
$209$	−600.000	−	1039.23i	−0.198578	−	0.343948i
$210$		0			0
$211$	1334.00	−	2310.56i	0.435243	−	0.753864i	−0.562072	−	0.827088i	$-0.689996\pi$
$211$	1334.00	−	2310.56i	0.435243	−	0.753864i	0.997315	+	0.0732246i	$0.0233290\pi$
$212$	444.000	−	769.031i	0.143840	−	0.249138i
$213$		0			0
$214$	24.0000	+	41.5692i	0.00766638	+	0.0132786i
$215$	−160.000			−0.0507531
$216$		0			0
$217$	−608.000			−0.190202
$218$	950.000	+	1645.45i	0.295147	+	0.511210i
$219$		0			0
$220$	−120.000	+	207.846i	−0.0367745	+	0.0636954i
$221$	−1914.00	+	3315.15i	−0.582577	+	1.00905i
$222$		0			0
$223$	−886.000	−	1534.60i	−0.266058	−	0.460826i	0.701782	−	0.712392i	$-0.252388\pi$
$223$	−886.000	−	1534.60i	−0.266058	−	0.460826i	−0.967840	+	0.251565i	$0.919055\pi$
$224$	128.000			0.0381802
$225$		0			0
$226$	−2076.00			−0.611033
$227$	−1392.00	−	2411.01i	−0.407006	−	0.704954i	0.587547	−	0.809190i	$-0.300094\pi$
$227$	−1392.00	−	2411.01i	−0.407006	−	0.704954i	−0.994553	+	0.104236i	$0.966760\pi$
$228$		0			0
$229$	−175.000	+	303.109i	−0.0504992	+	0.0874672i	−0.890170	−	0.455628i	$-0.849415\pi$
$229$	−175.000	+	303.109i	−0.0504992	+	0.0874672i	0.839671	+	0.543096i	$0.182748\pi$
$230$	660.000	−	1143.15i	0.189214	−	0.327727i
$231$		0			0
$232$	360.000	+	623.538i	0.101876	+	0.176454i
$233$	−1962.00			−0.551652			−0.275826	−	0.961208i	$-0.588951\pi$
$233$	−1962.00			−0.551652			−0.275826	+	0.961208i	$0.588951\pi$
$234$		0			0
$235$	−1020.00			−0.283138
$236$	840.000	+	1454.92i	0.231692	+	0.401303i
$237$		0			0
$238$	264.000	−	457.261i	0.0719016	−	0.124537i
$239$	−2160.00	+	3741.23i	−0.584597	+	1.01255i	0.410328	+	0.911938i	$0.365414\pi$
$239$	−2160.00	+	3741.23i	−0.584597	+	1.01255i	−0.994925	+	0.100614i	$0.967919\pi$
$240$		0			0
$241$	239.000	+	413.960i	0.0638811	+	0.110645i	0.896197	−	0.443656i	$-0.146319\pi$
$241$	239.000	+	413.960i	0.0638811	+	0.110645i	−0.832316	+	0.554301i	$0.812985\pi$
$242$	2374.00			0.630605
$243$		0			0
$244$	3608.00			0.946633
$245$	−817.500	−	1415.95i	−0.213176	−	0.369232i
$246$		0			0
$247$	−2900.00	+	5022.95i	−0.747055	+	1.29394i
$248$	608.000	−	1053.09i	0.155678	−	0.269641i
$249$		0			0
$250$	−125.000	−	216.506i	−0.0316228	−	0.0547723i
$251$	−2652.00			−0.666903			−0.333452	−	0.942767i	$-0.608213\pi$
$251$	−2652.00			−0.666903			−0.333452	+	0.942767i	$0.608213\pi$
$252$		0			0
$253$	1584.00			0.393617
$254$	−124.000	−	214.774i	−0.0306317	−	0.0530557i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−1167.00	+	2021.30i	−0.283251	+	0.490605i	−0.972183	−	0.234221i	$-0.924746\pi$
$257$	−1167.00	+	2021.30i	−0.283251	+	0.490605i	0.688933	+	0.724825i	$0.258080\pi$
$258$		0			0
$259$	−68.0000	−	117.779i	−0.0163140	−	0.0282566i
$260$	1160.00			0.276693
$261$		0			0
$262$	264.000			0.0622518
$263$	−1974.00	−	3419.07i	−0.462822	−	0.801630i	0.536279	−	0.844041i	$-0.319830\pi$
$263$	−1974.00	−	3419.07i	−0.462822	−	0.801630i	−0.999100	+	0.0424106i	$0.986496\pi$
$264$		0			0
$265$	−555.000	+	961.288i	−0.128654	+	0.222836i
$266$	400.000	−	692.820i	0.0922014	−	0.159698i
$267$		0			0
$268$	2048.00	+	3547.24i	0.466797	+	0.808516i
$269$	−1590.00			−0.360387			−0.180193	−	0.983631i	$-0.557672\pi$
$269$	−1590.00			−0.360387			−0.180193	+	0.983631i	$0.557672\pi$
$270$		0			0
$271$	4952.00			1.11001			0.555005	−	0.831847i	$-0.312716\pi$
$271$	4952.00			1.11001			0.555005	+	0.831847i	$0.312716\pi$
$272$	528.000	+	914.523i	0.117701	+	0.203864i
$273$		0			0
$274$	1254.00	−	2171.99i	0.276485	−	0.478886i
$275$	150.000	−	259.808i	0.0328921	−	0.0569709i
$276$		0			0
$277$	−823.000	−	1425.48i	−0.178517	−	0.309201i	0.762856	−	0.646569i	$-0.223797\pi$
$277$	−823.000	−	1425.48i	−0.178517	−	0.309201i	−0.941373	+	0.337368i	$0.890463\pi$
$278$	5720.00			1.23404
$279$		0			0
$280$	−160.000			−0.0341494
$281$	−579.000	−	1002.86i	−0.122919	−	0.212902i	0.797999	−	0.602659i	$-0.205892\pi$
$281$	−579.000	−	1002.86i	−0.122919	−	0.212902i	−0.920918	+	0.389757i	$0.872559\pi$
$282$		0			0
$283$	−3496.00	+	6055.25i	−0.734331	+	1.27190i	0.220685	+	0.975345i	$0.429171\pi$
$283$	−3496.00	+	6055.25i	−0.734331	+	1.27190i	−0.955016	+	0.296553i	$0.904163\pi$
$284$	864.000	−	1496.49i	0.180525	−	0.312678i
$285$		0			0
$286$	696.000	+	1205.51i	0.143900	+	0.249242i
$287$	−1752.00			−0.360339
$288$		0			0
$289$	−557.000			−0.113373
$290$	−450.000	−	779.423i	−0.0911204	−	0.157825i
$291$		0			0
$292$	−724.000	+	1254.00i	−0.145099	+	0.251319i
$293$	−129.000	+	223.435i	−0.0257210	+	0.0445501i	−0.878599	−	0.477560i	$-0.841521\pi$
$293$	−129.000	+	223.435i	−0.0257210	+	0.0445501i	0.852878	+	0.522110i	$0.174855\pi$
$294$		0			0
$295$	−1050.00	−	1818.65i	−0.207232	−	0.358936i
$296$	272.000			0.0534111
$297$		0			0
$298$	1500.00			0.291586
$299$	−3828.00	−	6630.29i	−0.740398	−	1.28241i
$300$		0			0
$301$	64.0000	−	110.851i	0.0122555	−	0.0212271i
$302$	−448.000	+	775.959i	−0.0853626	+	0.147852i
$303$		0			0
$304$	800.000	+	1385.64i	0.150931	+	0.261421i
$305$	−4510.00			−0.846695
$306$		0			0
$307$	−8944.00			−1.66274			−0.831370	−	0.555720i	$-0.812443\pi$
$307$	−8944.00			−1.66274			−0.831370	+	0.555720i	$0.812443\pi$
$308$	−96.0000	−	166.277i	−0.0177601	−	0.0307614i
$309$		0			0
$310$	−760.000	+	1316.36i	−0.139242	+	0.241175i
$311$	696.000	−	1205.51i	0.126902	−	0.219801i	−0.795573	−	0.605858i	$-0.792830\pi$
$311$	696.000	−	1205.51i	0.126902	−	0.219801i	0.922475	+	0.386057i	$0.126163\pi$
$312$		0			0
$313$	2939.00	+	5090.50i	0.530742	+	0.919271i	0.999357	+	0.0358688i	$0.0114198\pi$
$313$	2939.00	+	5090.50i	0.530742	+	0.919271i	−0.468615	+	0.883403i	$0.655247\pi$
$314$	−4492.00			−0.807319
$315$		0			0
$316$	−640.000			−0.113933
$317$	5163.00	+	8942.58i	0.914773	+	1.58443i	0.807234	+	0.590232i	$0.200964\pi$
$317$	5163.00	+	8942.58i	0.914773	+	1.58443i	0.107539	+	0.994201i	$0.465703\pi$
$318$		0			0
$319$	540.000	−	935.307i	0.0947780	−	0.164160i
$320$	160.000	−	277.128i	0.0279508	−	0.0484123i
$321$		0			0
$322$	528.000	+	914.523i	0.0913798	+	0.158274i
$323$	6600.00			1.13695
$324$		0			0
$325$	−1450.00			−0.247482
$326$	−568.000	−	983.805i	−0.0964988	−	0.167141i
$327$		0			0
$328$	1752.00	−	3034.55i	0.294933	−	0.510839i
$329$	408.000	−	706.677i	0.0683701	−	0.118421i
$330$		0			0
$331$	2114.00	+	3661.56i	0.351045	+	0.608028i	0.986433	−	0.164165i	$-0.0524930\pi$
$331$	2114.00	+	3661.56i	0.351045	+	0.608028i	−0.635388	+	0.772193i	$0.719160\pi$
$332$	−288.000			−0.0476086
$333$		0			0
$334$	−3048.00			−0.499339
$335$	−2560.00	−	4434.05i	−0.417516	−	0.723158i
$336$		0			0
$337$	−553.000	+	957.824i	−0.0893882	+	0.154825i	−0.907253	−	0.420586i	$-0.861825\pi$
$337$	−553.000	+	957.824i	−0.0893882	+	0.154825i	0.817864	+	0.575411i	$0.195158\pi$
$338$	1167.00	−	2021.30i	0.187800	−	0.325279i
$339$		0			0
$340$	−660.000	−	1143.15i	−0.105275	−	0.182342i
$341$	−1824.00			−0.289663
$342$		0			0
$343$	2680.00			0.421885
$344$	128.000	+	221.703i	0.0200619	+	0.0347482i
$345$		0			0
$346$	−3702.00	+	6412.05i	−0.575204	+	0.996283i
$347$	4668.00	−	8085.21i	0.722165	−	1.25083i	−0.237965	−	0.971274i	$-0.576480\pi$
$347$	4668.00	−	8085.21i	0.722165	−	1.25083i	0.960130	−	0.279553i	$-0.0901864\pi$
$348$		0			0
$349$	5885.00	+	10193.1i	0.902627	+	1.56340i	0.824071	+	0.566486i	$0.191698\pi$
$349$	5885.00	+	10193.1i	0.902627	+	1.56340i	0.0785557	+	0.996910i	$0.474969\pi$
$350$	200.000			0.0305441
$351$		0			0
$352$	384.000			0.0581456
$353$	4161.00	+	7207.06i	0.627387	+	1.08667i	0.988074	+	0.153980i	$0.0492090\pi$
$353$	4161.00	+	7207.06i	0.627387	+	1.08667i	−0.360687	+	0.932687i	$0.617458\pi$
$354$		0			0
$355$	−1080.00	+	1870.61i	−0.161466	+	0.279667i
$356$	1620.00	−	2805.92i	0.241179	−	0.417735i
$357$		0			0
$358$	−3180.00	−	5507.92i	−0.469464	−	0.813136i
$359$	−10680.0			−1.57011			−0.785054	−	0.619427i	$-0.787365\pi$
$359$	−10680.0			−1.57011			−0.785054	+	0.619427i	$0.787365\pi$
$360$		0			0
$361$	3141.00			0.457938
$362$	−2098.00	−	3633.84i	−0.304609	−	0.527598i
$363$		0			0
$364$	−464.000	+	803.672i	−0.0668138	+	0.115725i
$365$	905.000	−	1567.51i	0.129780	−	0.224786i
$366$		0			0
$367$	2942.00	+	5095.69i	0.418450	+	0.724777i	0.995784	−	0.0917316i	$-0.0292402\pi$
$367$	2942.00	+	5095.69i	0.418450	+	0.724777i	−0.577334	+	0.816508i	$0.695907\pi$
$368$	−2112.00			−0.299173
$369$		0			0
$370$	−340.000			−0.0477723
$371$	−444.000	−	769.031i	−0.0621330	−	0.107617i
$372$		0			0
$373$	1049.00	−	1816.92i	0.145617	−	0.252216i	−0.783986	−	0.620779i	$-0.786817\pi$
$373$	1049.00	−	1816.92i	0.145617	−	0.252216i	0.929603	+	0.368562i	$0.120150\pi$
$374$	792.000	−	1371.78i	0.109501	−	0.189661i
$375$		0			0
$376$	816.000	+	1413.35i	0.111920	+	0.193851i
$377$	−5220.00			−0.713113
$378$		0			0
$379$	3860.00			0.523153			0.261576	−	0.965183i	$-0.415758\pi$
$379$	3860.00			0.523153			0.261576	+	0.965183i	$0.415758\pi$
$380$	−1000.00	−	1732.05i	−0.134997	−	0.233822i
$381$		0			0
$382$	−4392.00	+	7607.17i	−0.588257	+	1.01889i
$383$	−4794.00	+	8303.45i	−0.639587	+	1.10780i	0.345936	+	0.938258i	$0.387561\pi$
$383$	−4794.00	+	8303.45i	−0.639587	+	1.10780i	−0.985523	+	0.169540i	$0.945772\pi$
$384$		0			0
$385$	120.000	+	207.846i	0.0158851	+	0.0275138i
$386$	4316.00			0.569116
$387$		0			0
$388$	4424.00			0.578852
$389$	−6705.00	−	11613.4i	−0.873925	−	1.51368i	−0.857903	−	0.513812i	$-0.828233\pi$
$389$	−6705.00	−	11613.4i	−0.873925	−	1.51368i	−0.0160224	−	0.999872i	$-0.505100\pi$
$390$		0			0
$391$	−4356.00	+	7544.81i	−0.563408	+	0.975851i
$392$	−1308.00	+	2265.52i	−0.168531	+	0.291903i
$393$		0			0
$394$	1074.00	+	1860.22i	0.137328	+	0.237860i
$395$	800.000			0.101905
$396$		0			0
$397$	−13114.0			−1.65787			−0.828933	−	0.559348i	$-0.811052\pi$
$397$	−13114.0			−1.65787			−0.828933	+	0.559348i	$0.811052\pi$
$398$	2840.00	+	4919.02i	0.357679	+	0.619519i
$399$		0			0
$400$	−200.000	+	346.410i	−0.0250000	+	0.0433013i
$401$	−2919.00	+	5055.86i	−0.363511	+	0.629619i	−0.988536	−	0.150985i	$-0.951755\pi$
$401$	−2919.00	+	5055.86i	−0.363511	+	0.629619i	0.625025	+	0.780605i	$0.285089\pi$
$402$		0			0
$403$	4408.00	+	7634.88i	0.544859	+	0.943723i
$404$	1032.00			0.127089
$405$		0			0
$406$	720.000			0.0880123
$407$	−204.000	−	353.338i	−0.0248450	−	0.0430328i
$408$		0			0
$409$	−4765.00	+	8253.22i	−0.576074	+	0.997789i	0.419851	+	0.907593i	$0.362082\pi$
$409$	−4765.00	+	8253.22i	−0.576074	+	0.997789i	−0.995924	+	0.0901954i	$0.971251\pi$
$410$	−2190.00	+	3793.19i	−0.263796	+	0.456908i
$411$		0			0
$412$	1976.00	+	3422.53i	0.236288	+	0.409262i
$413$	1680.00			0.200163
$414$		0			0
$415$	360.000			0.0425824
$416$	−928.000	−	1607.34i	−0.109372	−	0.189439i
$417$		0			0
$418$	1200.00	−	2078.46i	0.140416	−	0.243208i
$419$	3630.00	−	6287.34i	0.423239	−	0.733071i	−0.573015	−	0.819545i	$-0.694226\pi$
$419$	3630.00	−	6287.34i	0.423239	−	0.733071i	0.996254	+	0.0864734i	$0.0275598\pi$
$420$		0			0
$421$	−6031.00	−	10446.0i	−0.698178	−	1.20928i	−0.969098	−	0.246678i	$-0.920661\pi$
$421$	−6031.00	−	10446.0i	−0.698178	−	1.20928i	0.270920	−	0.962602i	$-0.412672\pi$
$422$	5336.00			0.615527
$423$		0			0
$424$	1776.00			0.203420
$425$	825.000	+	1428.94i	0.0941609	+	0.163091i
$426$		0			0
$427$	1804.00	−	3124.62i	0.204454	−	0.354124i
$428$	−48.0000	+	83.1384i	−0.00542095	+	0.00938936i
$429$		0			0
$430$	−160.000	−	277.128i	−0.0179439	−	0.0310798i
$431$	13608.0			1.52082			0.760411	−	0.649442i	$-0.224998\pi$
$431$	13608.0			1.52082			0.760411	+	0.649442i	$0.224998\pi$
$432$		0			0
$433$	−3838.00			−0.425964			−0.212982	−	0.977056i	$-0.568318\pi$
$433$	−3838.00			−0.425964			−0.212982	+	0.977056i	$0.568318\pi$
$434$	−608.000	−	1053.09i	−0.0672464	−	0.116474i
$435$		0			0
$436$	−1900.00	+	3290.90i	−0.208701	+	0.361480i
$437$	−6600.00	+	11431.5i	−0.722473	+	1.25136i
$438$		0			0
$439$	−3700.00	−	6408.59i	−0.402258	−	0.696732i	0.591740	−	0.806129i	$-0.298441\pi$
$439$	−3700.00	−	6408.59i	−0.402258	−	0.696732i	−0.993998	+	0.109397i	$0.965108\pi$
$440$	−480.000			−0.0520071
$441$		0			0
$442$	−7656.00			−0.823889
$443$	4176.00	+	7233.04i	0.447873	+	0.775739i	0.998247	−	0.0591792i	$-0.0188483\pi$
$443$	4176.00	+	7233.04i	0.447873	+	0.775739i	−0.550374	+	0.834918i	$0.685515\pi$
$444$		0			0
$445$	−2025.00	+	3507.40i	−0.215717	+	0.373633i
$446$	1772.00	−	3069.19i	0.188131	−	0.325853i
$447$		0			0
$448$	128.000	+	221.703i	0.0134987	+	0.0233805i
$449$	−10770.0			−1.13200			−0.566000	−	0.824405i	$-0.691510\pi$
$449$	−10770.0			−1.13200			−0.566000	+	0.824405i	$0.691510\pi$
$450$		0			0
$451$	−5256.00			−0.548770
$452$	−2076.00	−	3595.74i	−0.216033	−	0.374180i
$453$		0			0
$454$	2784.00	−	4822.03i	0.287796	−	0.498478i
$455$	580.000	−	1004.59i	0.0597600	−	0.103507i
$456$		0			0
$457$	3347.00	+	5797.17i	0.342595	+	0.593392i	0.984914	−	0.173045i	$-0.0553607\pi$
$457$	3347.00	+	5797.17i	0.342595	+	0.593392i	−0.642319	+	0.766438i	$0.722027\pi$
$458$	−700.000			−0.0714167
$459$		0			0
$460$	2640.00			0.267588
$461$	−1509.00	−	2613.66i	−0.152454	−	0.264057i	0.779675	−	0.626184i	$-0.215384\pi$
$461$	−1509.00	−	2613.66i	−0.152454	−	0.264057i	−0.932129	+	0.362127i	$0.882051\pi$
$462$		0			0
$463$	−7246.00	+	12550.4i	−0.727322	+	1.25976i	0.230689	+	0.973028i	$0.425902\pi$
$463$	−7246.00	+	12550.4i	−0.727322	+	1.25976i	−0.958011	+	0.286731i	$0.907431\pi$
$464$	−720.000	+	1247.08i	−0.0720370	+	0.124772i
$465$		0			0
$466$	−1962.00	−	3398.28i	−0.195038	−	0.337816i
$467$	−7776.00			−0.770515			−0.385257	−	0.922809i	$-0.625887\pi$
$467$	−7776.00			−0.770515			−0.385257	+	0.922809i	$0.625887\pi$
$468$		0			0
$469$	4096.00			0.403274
$470$	−1020.00	−	1766.69i	−0.100104	−	0.173386i
$471$		0			0
$472$	−1680.00	+	2909.85i	−0.163831	+	0.283764i
$473$	192.000	−	332.554i	0.0186642	−	0.0323274i
$474$		0			0
$475$	1250.00	+	2165.06i	0.120745	+	0.209137i
$476$	1056.00			0.101684
$477$		0			0
$478$	−8640.00			−0.826746
$479$	−6840.00	−	11847.2i	−0.652458	−	1.13009i	−0.982525	−	0.186133i	$-0.940404\pi$
$479$	−6840.00	−	11847.2i	−0.652458	−	1.13009i	0.330066	−	0.943958i	$-0.392929\pi$
$480$		0			0
$481$	−986.000	+	1707.80i	−0.0934672	+	0.161890i
$482$	−478.000	+	827.920i	−0.0451708	+	0.0782380i
$483$		0			0
$484$	2374.00	+	4111.89i	0.222953	+	0.386165i
$485$	−5530.00			−0.517741
$486$		0			0
$487$	7916.00			0.736567			0.368284	−	0.929714i	$-0.379946\pi$
$487$	7916.00			0.736567			0.368284	+	0.929714i	$0.379946\pi$
$488$	3608.00	+	6249.24i	0.334685	+	0.579692i
$489$		0			0
$490$	1635.00	−	2831.90i	0.150738	−	0.261086i
$491$	6966.00	−	12065.5i	0.640267	−	1.10898i	−0.345106	−	0.938564i	$-0.612157\pi$
$491$	6966.00	−	12065.5i	0.640267	−	1.10898i	0.985373	−	0.170411i	$-0.0545097\pi$
$492$		0			0
$493$	2970.00	+	5144.19i	0.271323	+	0.469945i
$494$	−11600.0			−1.05650
$495$		0			0
$496$	2432.00			0.220161
$497$	−864.000	−	1496.49i	−0.0779793	−	0.135064i
$498$		0			0
$499$	4130.00	−	7153.37i	0.370509	−	0.641741i	−0.619135	−	0.785285i	$-0.712516\pi$
$499$	4130.00	−	7153.37i	0.370509	−	0.641741i	0.989644	+	0.143544i	$0.0458498\pi$
$500$	250.000	−	433.013i	0.0223607	−	0.0387298i
$501$		0			0
$502$	−2652.00	−	4593.40i	−0.235786	−	0.408393i
$503$	11148.0			0.988200			0.494100	−	0.869405i	$-0.335498\pi$
$503$	11148.0			0.988200			0.494100	+	0.869405i	$0.335498\pi$
$504$		0			0
$505$	−1290.00			−0.113672
$506$	1584.00	+	2743.57i	0.139165	+	0.241041i
$507$		0			0
$508$	248.000	−	429.549i	0.0216599	−	0.0375160i
$509$	−4845.00	+	8391.79i	−0.421907	+	0.730765i	−0.996126	−	0.0879370i	$-0.971973\pi$
$509$	−4845.00	+	8391.79i	−0.421907	+	0.730765i	0.574219	+	0.818702i	$0.305306\pi$
$510$		0			0
$511$	724.000	+	1254.00i	0.0626769	+	0.108560i
$512$	−512.000			−0.0441942
$513$		0			0
$514$	−4668.00			−0.400577
$515$	−2470.00	−	4278.17i	−0.211342	−	0.366055i
$516$		0			0
$517$	1224.00	−	2120.03i	0.104123	−	0.180346i
$518$	136.000	−	235.559i	0.0115357	−	0.0199804i
$519$		0			0
$520$	1160.00	+	2009.18i	0.0978257	+	0.169439i
$521$	16038.0			1.34863			0.674316	−	0.738443i	$-0.264438\pi$
$521$	16038.0			1.34863			0.674316	+	0.738443i	$0.264438\pi$
$522$		0			0
$523$	992.000			0.0829391			0.0414695	−	0.999140i	$-0.486796\pi$
$523$	992.000			0.0829391			0.0414695	+	0.999140i	$0.486796\pi$
$524$	264.000	+	457.261i	0.0220093	+	0.0381213i
$525$		0			0
$526$	3948.00	−	6838.14i	0.327264	−	0.566838i
$527$	5016.00	−	8687.97i	0.414612	−	0.718129i
$528$		0			0
$529$	−2628.50	−	4552.70i	−0.216035	−	0.374184i
$530$	−2220.00			−0.181945
$531$		0			0
$532$	1600.00			0.130392
$533$	12702.0	+	22000.5i	1.03224	+	1.78789i
$534$		0			0
$535$	60.0000	−	103.923i	0.00484865	−	0.00839810i
$536$	−4096.00	+	7094.48i	−0.330075	+	0.571707i
$537$		0			0
$538$	−1590.00	−	2753.96i	−0.127416	−	0.220691i
$539$	3924.00			0.313578
$540$		0			0
$541$	7142.00			0.567576			0.283788	−	0.958887i	$-0.408409\pi$
$541$	7142.00			0.567576			0.283788	+	0.958887i	$0.408409\pi$
$542$	4952.00	+	8577.12i	0.392448	+	0.679739i
$543$		0			0
$544$	−1056.00	+	1829.05i	−0.0832273	+	0.144154i
$545$	2375.00	−	4113.62i	0.186668	−	0.323318i
$546$		0			0
$547$	−3808.00	−	6595.65i	−0.297657	−	0.515557i	0.677943	−	0.735115i	$-0.262872\pi$
$547$	−3808.00	−	6595.65i	−0.297657	−	0.515557i	−0.975599	+	0.219558i	$0.929538\pi$
$548$	5016.00			0.391009
$549$		0			0
$550$	600.000			0.0465165
$551$	4500.00	+	7794.23i	0.347925	+	0.602623i
$552$		0			0
$553$	−320.000	+	554.256i	−0.0246072	+	0.0426209i
$554$	1646.00	−	2850.96i	0.126231	−	0.218638i
$555$		0			0
$556$	5720.00	+	9907.33i	0.436299	+	0.755691i
$557$	10314.0			0.784593			0.392296	−	0.919839i	$-0.371681\pi$
$557$	10314.0			0.784593			0.392296	+	0.919839i	$0.371681\pi$
$558$		0			0
$559$	−1856.00			−0.140430
$560$	−160.000	−	277.128i	−0.0120736	−	0.0209121i
$561$		0			0
$562$	1158.00	−	2005.71i	0.0869169	−	0.150544i
$563$	−3564.00	+	6173.03i	−0.266793	+	0.462100i	−0.968032	−	0.250827i	$-0.919297\pi$
$563$	−3564.00	+	6173.03i	−0.266793	+	0.462100i	0.701239	+	0.712927i	$0.252631\pi$
$564$		0			0
$565$	2595.00	+	4494.67i	0.193226	+	0.334677i
$566$	−13984.0			−1.03850
$567$		0			0
$568$	3456.00			0.255300
$569$	1005.00	+	1740.71i	0.0740453	+	0.128250i	0.900671	−	0.434502i	$-0.143076\pi$
$569$	1005.00	+	1740.71i	0.0740453	+	0.128250i	−0.826625	+	0.562753i	$0.809742\pi$
$570$		0			0
$571$	11594.0	−	20081.4i	0.849726	−	1.47177i	−0.0317260	−	0.999497i	$-0.510100\pi$
$571$	11594.0	−	20081.4i	0.849726	−	1.47177i	0.881452	−	0.472273i	$-0.156566\pi$
$572$	−1392.00	+	2411.01i	−0.101753	+	0.176241i
$573$		0			0
$574$	−1752.00	−	3034.55i	−0.127399	−	0.220662i
$575$	−3300.00			−0.239338
$576$		0			0
$577$	22466.0			1.62092			0.810461	−	0.585793i	$-0.199217\pi$
$577$	22466.0			1.62092			0.810461	+	0.585793i	$0.199217\pi$
$578$	−557.000	−	964.752i	−0.0400833	−	0.0694263i
$579$		0			0
$580$	900.000	−	1558.85i	0.0644318	−	0.111599i
$581$	−144.000	+	249.415i	−0.0102825	+	0.0178098i
$582$		0			0
$583$	−1332.00	−	2307.09i	−0.0946240	−	0.163894i
$584$	−2896.00			−0.205201
$585$		0			0
$586$	−516.000			−0.0363750
$587$	11388.0	+	19724.6i	0.800738	+	1.38692i	0.919131	+	0.393952i	$0.128892\pi$
$587$	11388.0	+	19724.6i	0.800738	+	1.38692i	−0.118393	+	0.992967i	$0.537774\pi$
$588$		0			0
$589$	7600.00	−	13163.6i	0.531668	−	0.920876i
$590$	2100.00	−	3637.31i	0.146535	−	0.253806i
$591$		0			0
$592$	272.000	+	471.118i	0.0188837	+	0.0327075i
$593$	21198.0			1.46796			0.733978	−	0.679174i	$-0.237662\pi$
$593$	21198.0			1.46796			0.733978	+	0.679174i	$0.237662\pi$
$594$		0			0
$595$	−1320.00			−0.0909491
$596$	1500.00	+	2598.08i	0.103091	+	0.178559i
$597$		0			0
$598$	7656.00	−	13260.6i	0.523540	−	0.906798i
$599$	7980.00	−	13821.8i	0.544330	−	0.942808i	−0.454318	−	0.890839i	$-0.650117\pi$
$599$	7980.00	−	13821.8i	0.544330	−	0.942808i	0.998649	−	0.0519686i	$-0.0165496\pi$
$600$		0			0
$601$	−2941.00	−	5093.96i	−0.199610	−	0.345735i	0.748792	−	0.662805i	$-0.230634\pi$
$601$	−2941.00	−	5093.96i	−0.199610	−	0.345735i	−0.948402	+	0.317070i	$0.897301\pi$
$602$	256.000			0.0173319
$603$		0			0
$604$	−1792.00			−0.120721
$605$	−2967.50	−	5139.86i	−0.199415	−	0.345397i
$606$		0			0
$607$	−4258.00	+	7375.07i	−0.284723	+	0.493155i	−0.972542	−	0.232728i	$-0.925235\pi$
$607$	−4258.00	+	7375.07i	−0.284723	+	0.493155i	0.687819	+	0.725882i	$0.258568\pi$
$608$	−1600.00	+	2771.28i	−0.106725	+	0.184852i
$609$		0			0
$610$	−4510.00	−	7811.55i	−0.299352	−	0.518492i
$611$	−11832.0			−0.783423
$612$		0			0
$613$	8462.00			0.557548			0.278774	−	0.960357i	$-0.410072\pi$
$613$	8462.00			0.557548			0.278774	+	0.960357i	$0.410072\pi$
$614$	−8944.00	−	15491.5i	−0.587867	−	1.01822i
$615$		0			0
$616$	192.000	−	332.554i	0.0125583	−	0.0217516i
$617$	−5547.00	+	9607.69i	−0.361935	+	0.626890i	−0.988279	−	0.152657i	$-0.951217\pi$
$617$	−5547.00	+	9607.69i	−0.361935	+	0.626890i	0.626344	+	0.779546i	$0.284550\pi$
$618$		0			0
$619$	−1090.00	−	1887.94i	−0.0707767	−	0.122589i	0.828465	−	0.560041i	$-0.189214\pi$
$619$	−1090.00	−	1887.94i	−0.0707767	−	0.122589i	−0.899242	+	0.437452i	$0.855881\pi$
$620$	−3040.00			−0.196918
$621$		0			0
$622$	2784.00			0.179467
$623$	−1620.00	−	2805.92i	−0.104180	−	0.180444i
$624$		0			0
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	−5878.00	+	10181.0i	−0.375291	+	0.650023i
$627$		0			0
$628$	−4492.00	−	7780.37i	−0.285430	−	0.494380i
$629$	2244.00			0.142248
$630$		0			0
$631$	−26848.0			−1.69382			−0.846911	−	0.531734i	$-0.821541\pi$
$631$	−26848.0			−1.69382			−0.846911	+	0.531734i	$0.821541\pi$
$632$	−640.000	−	1108.51i	−0.0402814	−	0.0697694i
$633$		0			0
$634$	−10326.0	+	17885.2i	−0.646842	+	1.12036i
$635$	−310.000	+	536.936i	−0.0193732	+	0.0335553i
$636$		0			0
$637$	−9483.00	−	16425.0i	−0.589843	−	1.02164i
$638$	2160.00			0.134036
$639$		0			0
$640$	640.000			0.0395285
$641$	13161.0	+	22795.5i	0.810965	+	1.40463i	0.912190	+	0.409768i	$0.134390\pi$
$641$	13161.0	+	22795.5i	0.810965	+	1.40463i	−0.101225	+	0.994864i	$0.532276\pi$
$642$		0			0
$643$	5084.00	−	8805.75i	0.311809	−	0.540070i	−0.666945	−	0.745107i	$-0.732398\pi$
$643$	5084.00	−	8805.75i	0.311809	−	0.540070i	0.978754	+	0.205038i	$0.0657317\pi$
$644$	−1056.00	+	1829.05i	−0.0646153	+	0.111917i
$645$		0			0
$646$	6600.00	+	11431.5i	0.401971	+	0.696235i
$647$	23604.0			1.43426			0.717132	−	0.696937i	$-0.245454\pi$
$647$	23604.0			1.43426			0.717132	+	0.696937i	$0.245454\pi$
$648$		0			0
$649$	5040.00			0.304834
$650$	−1450.00	−	2511.47i	−0.0874980	−	0.151551i
$651$		0			0
$652$	1136.00	−	1967.61i	0.0682350	−	0.118186i
$653$	8211.00	−	14221.9i	0.492069	−	0.852289i	−0.507889	−	0.861423i	$-0.669574\pi$
$653$	8211.00	−	14221.9i	0.492069	−	0.852289i	0.999958	+	0.00913349i	$0.00290732\pi$
$654$		0			0
$655$	−330.000	−	571.577i	−0.0196858	−	0.0340967i
$656$	7008.00			0.417098
$657$		0			0
$658$	1632.00			0.0966899
$659$	−13050.0	−	22603.3i	−0.771405	−	1.33611i	−0.936793	−	0.349884i	$-0.886221\pi$
$659$	−13050.0	−	22603.3i	−0.771405	−	1.33611i	0.165388	−	0.986229i	$-0.447112\pi$
$660$		0			0
$661$	1529.00	−	2648.31i	0.0899716	−	0.155835i	−0.817527	−	0.575890i	$-0.804656\pi$
$661$	1529.00	−	2648.31i	0.0899716	−	0.155835i	0.907499	+	0.420055i	$0.137989\pi$
$662$	−4228.00	+	7323.11i	−0.248226	+	0.429941i
$663$		0			0
$664$	−288.000	−	498.831i	−0.0168322	−	0.0291542i
$665$	−2000.00			−0.116627
$666$		0			0
$667$	−11880.0			−0.689648
$668$	−3048.00	−	5279.29i	−0.176543	−	0.305781i
$669$		0			0
$670$	5120.00	−	8868.10i	0.295228	−	0.511350i
$671$	5412.00	−	9373.86i	0.311368	−	0.539305i
$672$		0			0
$673$	−5401.00	−	9354.81i	−0.309351	−	0.535812i	0.668870	−	0.743380i	$-0.266778\pi$
$673$	−5401.00	−	9354.81i	−0.309351	−	0.535812i	−0.978221	+	0.207568i	$0.933445\pi$
$674$	−2212.00			−0.126414
$675$		0			0
$676$	4668.00			0.265589
$677$	−5337.00	−	9243.96i	−0.302980	−	0.524777i	0.673829	−	0.738887i	$-0.264648\pi$
$677$	−5337.00	−	9243.96i	−0.302980	−	0.524777i	−0.976810	+	0.214110i	$0.931315\pi$
$678$		0			0
$679$	2212.00	−	3831.30i	0.125020	−	0.216541i
$680$	1320.00	−	2286.31i	0.0744407	−	0.128935i
$681$		0			0
$682$	−1824.00	−	3159.26i	−0.102411	−	0.177382i
$683$	28608.0			1.60272			0.801358	−	0.598185i	$-0.204111\pi$
$683$	28608.0			1.60272			0.801358	+	0.598185i	$0.204111\pi$
$684$		0			0
$685$	−6270.00			−0.349729
$686$	2680.00	+	4641.90i	0.149159	+	0.258350i
$687$		0			0
$688$	−256.000	+	443.405i	−0.0141859	+	0.0245707i
$689$	−6438.00	+	11150.9i	−0.355977	+	0.616571i
$690$		0			0
$691$	1214.00	+	2102.71i	0.0668346	+	0.115761i	0.897506	−	0.441002i	$-0.145377\pi$
$691$	1214.00	+	2102.71i	0.0668346	+	0.115761i	−0.830672	+	0.556763i	$0.812043\pi$
$692$	−14808.0			−0.813462
$693$		0			0
$694$	18672.0			1.02130
$695$	−7150.00	−	12384.2i	−0.390237	−	0.675911i
$696$		0			0
$697$	14454.0	−	25035.1i	0.785487	−	1.36050i
$698$	−11770.0	+	20386.2i	−0.638254	+	1.10549i
$699$		0			0
$700$	200.000	+	346.410i	0.0107990	+	0.0187044i
$701$	6618.00			0.356574			0.178287	−	0.983979i	$-0.442944\pi$
$701$	6618.00			0.356574			0.178287	+	0.983979i	$0.442944\pi$
$702$		0			0
$703$	3400.00			0.182409
$704$	384.000	+	665.108i	0.0205576	+	0.0356068i
$705$		0			0
$706$	−8322.00	+	14414.1i	−0.443630	+	0.768389i
$707$	516.000	−	893.738i	0.0274486	−	0.0475424i
$708$		0			0
$709$	−10255.0	−	17762.2i	−0.543208	−	0.940864i	−0.998717	−	0.0506331i	$-0.983876\pi$
$709$	−10255.0	−	17762.2i	−0.543208	−	0.940864i	0.455509	−	0.890231i	$-0.349457\pi$
$710$	−4320.00			−0.228347
$711$		0			0
$712$	6480.00			0.341079
$713$	10032.0	+	17375.9i	0.526930	+	0.912670i
$714$		0			0
$715$	1740.00	−	3013.77i	0.0910102	−	0.157634i
$716$	6360.00	−	11015.8i	0.331961	−	0.574974i
$717$		0			0
$718$	−10680.0	−	18498.3i	−0.555117	−	0.961491i
$719$	−31680.0			−1.64321			−0.821603	−	0.570061i	$-0.806920\pi$
$719$	−31680.0			−1.64321			−0.821603	+	0.570061i	$0.806920\pi$
$720$		0			0
$721$	3952.00			0.204133
$722$	3141.00	+	5440.37i	0.161906	+	0.280429i
$723$		0			0
$724$	4196.00	−	7267.69i	0.215391	−	0.373068i
$725$	−1125.00	+	1948.56i	−0.0576296	+	0.0998174i
$726$		0			0
$727$	−6598.00	−	11428.1i	−0.336597	−	0.583004i	0.647193	−	0.762326i	$-0.275943\pi$
$727$	−6598.00	−	11428.1i	−0.336597	−	0.583004i	−0.983790	+	0.179322i	$0.942609\pi$
$728$	−1856.00			−0.0944889
$729$		0			0
$730$	3620.00			0.183537
$731$	1056.00	+	1829.05i	0.0534303	+	0.0925440i
$732$		0			0
$733$	−4051.00	+	7016.54i	−0.204130	+	0.353563i	−0.949855	−	0.312690i	$-0.898770\pi$
$733$	−4051.00	+	7016.54i	−0.204130	+	0.353563i	0.745725	+	0.666253i	$0.232103\pi$
$734$	−5884.00	+	10191.4i	−0.295889	+	0.512494i
$735$		0			0
$736$	−2112.00	−	3658.09i	−0.105774	−	0.183205i
$737$	12288.0			0.614158
$738$		0			0
$739$	−12580.0			−0.626201			−0.313101	−	0.949720i	$-0.601368\pi$
$739$	−12580.0			−0.626201			−0.313101	+	0.949720i	$0.601368\pi$
$740$	−340.000	−	588.897i	−0.0168901	−	0.0292545i
$741$		0			0
$742$	888.000	−	1538.06i	0.0439346	−	0.0760970i
$743$	14946.0	−	25887.2i	0.737975	−	1.27821i	−0.215430	−	0.976519i	$-0.569115\pi$
$743$	14946.0	−	25887.2i	0.737975	−	1.27821i	0.953406	−	0.301691i	$-0.0975512\pi$
$744$		0			0
$745$	−1875.00	−	3247.60i	−0.0922076	−	0.159708i
$746$	4196.00			0.205934
$747$		0			0
$748$	3168.00			0.154858
$749$	48.0000	+	83.1384i	0.00234163	+	0.00405582i
$750$		0			0
$751$	20204.0	−	34994.4i	0.981697	−	1.70035i	0.325914	−	0.945399i	$-0.394328\pi$
$751$	20204.0	−	34994.4i	0.981697	−	1.70035i	0.655783	−	0.754950i	$-0.272339\pi$
$752$	−1632.00	+	2826.71i	−0.0791395	+	0.137074i
$753$		0			0
$754$	−5220.00	−	9041.31i	−0.252124	−	0.436691i
$755$	2240.00			0.107976
$756$		0			0
$757$	32366.0			1.55398			0.776990	−	0.629513i	$-0.216746\pi$
$757$	32366.0			1.55398			0.776990	+	0.629513i	$0.216746\pi$
$758$	3860.00	+	6685.72i	0.184962	+	0.320364i
$759$		0			0
$760$	2000.00	−	3464.10i	0.0954574	−	0.165337i
$761$	−8619.00	+	14928.5i	−0.410563	+	0.711116i	−0.994951	−	0.100358i	$-0.968001\pi$
$761$	−8619.00	+	14928.5i	−0.410563	+	0.711116i	0.584388	+	0.811474i	$0.301335\pi$
$762$		0			0
$763$	1900.00	+	3290.90i	0.0901502	+	0.156145i
$764$	−17568.0			−0.831921
$765$		0			0
$766$	−19176.0			−0.904513
$767$	−12180.0	−	21096.4i	−0.573395	−	0.993150i
$768$		0			0
$769$	−5425.00	+	9396.38i	−0.254396	+	0.440627i	−0.964731	−	0.263237i	$-0.915210\pi$
$769$	−5425.00	+	9396.38i	−0.254396	+	0.440627i	0.710335	+	0.703863i	$0.248543\pi$
$770$	−240.000	+	415.692i	−0.0112325	+	0.0194552i
$771$		0			0
$772$	4316.00	+	7475.53i	0.201213	+	0.348511i
$773$	−9102.00			−0.423514			−0.211757	−	0.977322i	$-0.567919\pi$
$773$	−9102.00			−0.423514			−0.211757	+	0.977322i	$0.567919\pi$
$774$		0			0
$775$	3800.00			0.176129
$776$	4424.00	+	7662.59i	0.204655	+	0.354473i
$777$		0			0
$778$	13410.0	−	23226.8i	0.617959	−	1.07034i
$779$	21900.0	−	37931.9i	1.00725	−	1.74461i
$780$		0			0
$781$	−2592.00	−	4489.48i	−0.118757	−	0.205693i
$782$	−17424.0			−0.796779
$783$		0			0
$784$	−5232.00			−0.238338
$785$	5615.00	+	9725.47i	0.255297	+	0.442187i
$786$		0			0
$787$	12752.0	−	22087.1i	0.577585	−	1.00041i	−0.418170	−	0.908369i	$-0.637328\pi$
$787$	12752.0	−	22087.1i	0.577585	−	1.00041i	0.995755	−	0.0920385i	$-0.0293383\pi$
$788$	−2148.00	+	3720.45i	−0.0971058	+	0.168192i
$789$		0			0
$790$	800.000	+	1385.64i	0.0360288	+	0.0624036i
$791$	−4152.00			−0.186635
$792$		0			0
$793$	−52316.0			−2.34274
$794$	−13114.0	−	22714.1i	−0.586144	−	1.01523i
$795$		0			0
$796$	−5680.00	+	9838.05i	−0.252917	+	0.438066i
$797$	7083.00	−	12268.1i	0.314796	−	0.545243i	−0.664598	−	0.747201i	$-0.731397\pi$
$797$	7083.00	−	12268.1i	0.314796	−	0.545243i	0.979394	+	0.201958i	$0.0647304\pi$
$798$		0			0
$799$	6732.00	+	11660.2i	0.298074	+	0.516279i
$800$	−800.000			−0.0353553
$801$		0			0
$802$	−11676.0			−0.514082
$803$	2172.00	+	3762.01i	0.0954523	+	0.165328i
$804$		0			0
$805$	1320.00	−	2286.31i	0.0577936	−	0.100102i
$806$	−8816.00	+	15269.8i	−0.385273	+	0.667313i
$807$		0			0
$808$	1032.00	+	1787.48i	0.0449327	+	0.0778257i
$809$	−33210.0			−1.44327			−0.721633	−	0.692276i	$-0.756608\pi$
$809$	−33210.0			−1.44327			−0.721633	+	0.692276i	$0.756608\pi$
$810$		0			0
$811$	39212.0			1.69780			0.848902	−	0.528550i	$-0.177264\pi$
$811$	39212.0			1.69780			0.848902	+	0.528550i	$0.177264\pi$
$812$	720.000	+	1247.08i	0.0311171	+	0.0538963i
$813$		0			0
$814$	408.000	−	706.677i	0.0175680	−	0.0304288i
$815$	−1420.00	+	2459.51i	−0.0610312	+	0.105709i
$816$		0			0
$817$	1600.00	+	2771.28i	0.0685152	+	0.118672i
$818$	−19060.0			−0.814691
$819$		0			0
$820$	−8760.00			−0.373064
$821$	3111.00	+	5388.41i	0.132247	+	0.229058i	0.924542	−	0.381079i	$-0.124448\pi$
$821$	3111.00	+	5388.41i	0.132247	+	0.229058i	−0.792296	+	0.610138i	$0.791114\pi$
$822$		0			0
$823$	−15586.0	+	26995.7i	−0.660138	+	1.14339i	0.320441	+	0.947269i	$0.396169\pi$
$823$	−15586.0	+	26995.7i	−0.660138	+	1.14339i	−0.980579	+	0.196124i	$0.937164\pi$
$824$	−3952.00	+	6845.06i	−0.167081	+	0.289392i
$825$		0			0
$826$	1680.00	+	2909.85i	0.0707684	+	0.122574i
$827$	264.000			0.0111006			0.00555029	−	0.999985i	$-0.498233\pi$
$827$	264.000			0.0111006			0.00555029	+	0.999985i	$0.498233\pi$
$828$		0			0
$829$	−29050.0			−1.21707			−0.608533	−	0.793528i	$-0.708242\pi$
$829$	−29050.0			−1.21707			−0.608533	+	0.793528i	$0.708242\pi$
$830$	360.000	+	623.538i	0.0150552	+	0.0260763i
$831$		0			0
$832$	1856.00	−	3214.69i	0.0773380	−	0.133953i
$833$	−10791.0	+	18690.6i	−0.448843	+	0.777418i
$834$		0			0
$835$	3810.00	+	6599.11i	0.157905	+	0.273499i
$836$	4800.00			0.198578
$837$		0			0
$838$	14520.0			0.598550
$839$	−10860.0	−	18810.1i	−0.446876	−	0.774012i	0.551305	−	0.834304i	$-0.314130\pi$
$839$	−10860.0	−	18810.1i	−0.446876	−	0.774012i	−0.998181	+	0.0602922i	$0.980797\pi$
$840$		0			0
$841$	8144.50	−	14106.7i	0.333942	−	0.578404i
$842$	12062.0	−	20892.0i	0.493686	−	0.855090i
$843$		0			0
$844$	5336.00	+	9242.22i	0.217622	+	0.376932i
$845$	−5835.00			−0.237550
$846$		0			0
$847$	4748.00			0.192613
$848$	1776.00	+	3076.12i	0.0719199	+	0.124569i
$849$		0			0
$850$	−1650.00	+	2857.88i	−0.0665818	+	0.115323i
$851$	−2244.00	+	3886.72i	−0.0903917	+	0.156563i
$852$		0			0
$853$	3329.00	+	5766.00i	0.133626	+	0.231447i	0.925072	−	0.379793i	$-0.124005\pi$
$853$	3329.00	+	5766.00i	0.133626	+	0.231447i	−0.791446	+	0.611239i	$0.790671\pi$
$854$	7216.00			0.289141
$855$		0			0
$856$	−192.000			−0.00766638
$857$	−6987.00	−	12101.8i	−0.278496	−	0.482370i	0.692515	−	0.721404i	$-0.256503\pi$
$857$	−6987.00	−	12101.8i	−0.278496	−	0.482370i	−0.971011	+	0.239034i	$0.923169\pi$
$858$		0			0
$859$	−11890.0	+	20594.1i	−0.472272	+	0.817999i	−0.999497	−	0.0317270i	$-0.989899\pi$
$859$	−11890.0	+	20594.1i	−0.472272	+	0.817999i	0.527225	+	0.849726i	$0.323233\pi$
$860$	320.000	−	554.256i	0.0126883	−	0.0219767i
$861$		0			0
$862$	13608.0	+	23569.7i	0.537692	+	0.931309i
$863$	12228.0			0.482324			0.241162	−	0.970485i	$-0.422471\pi$
$863$	12228.0			0.482324			0.241162	+	0.970485i	$0.422471\pi$
$864$		0			0
$865$	18510.0			0.727583
$866$	−3838.00	−	6647.61i	−0.150601	−	0.260849i
$867$		0			0
$868$	1216.00	−	2106.17i	0.0475504	−	0.0823597i
$869$	−960.000	+	1662.77i	−0.0374750	+	0.0649086i
$870$		0			0
$871$	−29696.0	−	51435.0i	−1.15524	−	2.00093i
$872$	−7600.00			−0.295147
$873$		0			0
$874$	−26400.0			−1.02173
$875$	−250.000	−	433.013i	−0.00965891	−	0.0167297i
$876$		0			0
$877$	−5803.00	+	10051.1i	−0.223436	+	0.387003i	−0.955849	−	0.293858i	$-0.905061\pi$
$877$	−5803.00	+	10051.1i	−0.223436	+	0.387003i	0.732413	+	0.680861i	$0.238394\pi$
$878$	7400.00	−	12817.2i	0.284440	−	0.492664i
$879$		0			0
$880$	−480.000	−	831.384i	−0.0183873	−	0.0318477i
$881$	32958.0			1.26037			0.630183	−	0.776446i	$-0.282980\pi$
$881$	32958.0			1.26037			0.630183	+	0.776446i	$0.282980\pi$
$882$		0			0
$883$	8072.00			0.307638			0.153819	−	0.988099i	$-0.450843\pi$
$883$	8072.00			0.307638			0.153819	+	0.988099i	$0.450843\pi$
$884$	−7656.00	−	13260.6i	−0.291289	−	0.504527i
$885$		0			0
$886$	−8352.00	+	14466.1i	−0.316694	+	0.548530i
$887$	7878.00	−	13645.1i	0.298216	−	0.516525i	−0.677512	−	0.735512i	$-0.736942\pi$
$887$	7878.00	−	13645.1i	0.298216	−	0.516525i	0.975728	+	0.218987i	$0.0702752\pi$
$888$		0			0
$889$	−248.000	−	429.549i	−0.00935619	−	0.0162054i
$890$	−8100.00			−0.305070
$891$		0			0
$892$	7088.00			0.266058
$893$	10200.0	+	17666.9i	0.382228	+	0.662039i
$894$		0			0
$895$	−7950.00	+	13769.8i	−0.296915	+	0.514272i
$896$	−256.000	+	443.405i	−0.00954504	+	0.0165325i
$897$		0			0
$898$	−10770.0	−	18654.2i	−0.400222	−	0.693205i
$899$	13680.0			0.507512
$900$		0			0
$901$	14652.0			0.541763
$902$	−5256.00	−	9103.66i	−0.194020	−	0.336052i
$903$		0			0
$904$	4152.00	−	7191.47i	0.152758	−	0.264585i
$905$	−5245.00	+	9084.61i	−0.192652	+	0.333682i
$906$		0			0
$907$	−9388.00	−	16260.5i	−0.343686	−	0.595282i	0.641428	−	0.767183i	$-0.278342\pi$
$907$	−9388.00	−	16260.5i	−0.343686	−	0.595282i	−0.985114	+	0.171901i	$0.945009\pi$
$908$	11136.0			0.407006
$909$		0			0
$910$	2320.00			0.0845135
$911$	−10284.0	−	17812.4i	−0.374011	−	0.647806i	0.616167	−	0.787615i	$-0.288684\pi$
$911$	−10284.0	−	17812.4i	−0.374011	−	0.647806i	−0.990178	+	0.139809i	$0.955351\pi$
$912$		0			0
$913$	−432.000	+	748.246i	−0.0156595	+	0.0271230i
$914$	−6694.00	+	11594.3i	−0.242251	+	0.419592i
$915$		0			0
$916$	−700.000	−	1212.44i	−0.0252496	−	0.0437336i
$917$	528.000			0.0190143
$918$		0			0
$919$	−6280.00			−0.225417			−0.112708	−	0.993628i	$-0.535953\pi$
$919$	−6280.00			−0.225417			−0.112708	+	0.993628i	$0.535953\pi$
$920$	2640.00	+	4572.61i	0.0946068	+	0.163864i
$921$		0			0
$922$	3018.00	−	5227.33i	0.107801	−	0.186717i
$923$	−12528.0	+	21699.1i	−0.446765	+	0.773820i
$924$		0			0
$925$	425.000	+	736.122i	0.0151069	+	0.0261660i
$926$	−28984.0			−1.02859
$927$		0			0
$928$	−2880.00			−0.101876
$929$	−10215.0	−	17692.9i	−0.360757	−	0.624850i	0.627329	−	0.778755i	$-0.284148\pi$
$929$	−10215.0	−	17692.9i	−0.360757	−	0.624850i	−0.988086	+	0.153905i	$0.950815\pi$
$930$		0			0
$931$	−16350.0	+	28319.0i	−0.575563	+	0.996905i
$932$	3924.00	−	6796.57i	0.137913	−	0.238872i
$933$		0			0
$934$	−7776.00	−	13468.4i	−0.272418	−	0.471842i
$935$	−3960.00			−0.138509
$936$		0			0
$937$	8906.00			0.310508			0.155254	−	0.987875i	$-0.450380\pi$
$937$	8906.00			0.310508			0.155254	+	0.987875i	$0.450380\pi$
$938$	4096.00	+	7094.48i	0.142579	+	0.246954i
$939$		0			0
$940$	2040.00	−	3533.38i	0.0707845	−	0.122602i
$941$	−8709.00	+	15084.4i	−0.301706	+	0.522570i	−0.976522	−	0.215416i	$-0.930889\pi$
$941$	−8709.00	+	15084.4i	−0.301706	+	0.522570i	0.674817	+	0.737986i	$0.264223\pi$
$942$		0			0
$943$	28908.0	+	50070.1i	0.998276	+	1.72906i
$944$	−6720.00			−0.231692
$945$		0			0
$946$	768.000			0.0263952
$947$	−1272.00	−	2203.17i	−0.0436478	−	0.0756002i	0.843376	−	0.537324i	$-0.180565\pi$
$947$	−1272.00	−	2203.17i	−0.0436478	−	0.0756002i	−0.887024	+	0.461723i	$0.847231\pi$
$948$		0			0
$949$	10498.0	−	18183.1i	0.359093	−	0.621968i
$950$	−2500.00	+	4330.13i	−0.0853797	+	0.147882i
$951$		0			0
$952$	1056.00	+	1829.05i	0.0359508	+	0.0622686i
$953$	−15402.0			−0.523525			−0.261763	−	0.965132i	$-0.584304\pi$
$953$	−15402.0			−0.523525			−0.261763	+	0.965132i	$0.584304\pi$
$954$		0			0
$955$	21960.0			0.744093
$956$	−8640.00	−	14964.9i	−0.292299	−	0.506276i
$957$		0			0
$958$	13680.0	−	23694.5i	0.461358	−	0.799095i
$959$	2508.00	−	4343.98i	0.0844500	−	0.146272i
$960$		0			0
$961$	3343.50	+	5791.11i	0.112232	+	0.194391i
$962$	−3944.00			−0.132183
$963$		0			0
$964$	−1912.00			−0.0638811
$965$	−5395.00	−	9344.41i	−0.179970	−	0.311717i
$966$		0			0
$967$	24722.0	−	42819.8i	0.822136	−	1.42398i	−0.0819518	−	0.996636i	$-0.526115\pi$
$967$	24722.0	−	42819.8i	0.822136	−	1.42398i	0.904088	−	0.427346i	$-0.140551\pi$
$968$	−4748.00	+	8223.78i	−0.157651	+	0.273060i
$969$		0			0
$970$	−5530.00	−	9578.24i	−0.183049	−	0.317050i
$971$	25188.0			0.832463			0.416231	−	0.909259i	$-0.363351\pi$
$971$	25188.0			0.832463			0.416231	+	0.909259i	$0.363351\pi$
$972$		0			0
$973$	11440.0			0.376927
$974$	7916.00	+	13710.9i	0.260416	+	0.451053i
$975$		0			0
$976$	−7216.00	+	12498.5i	−0.236658	+	0.409904i
$977$	1473.00	−	2551.31i	0.0482348	−	0.0835452i	−0.840900	−	0.541191i	$-0.817974\pi$
$977$	1473.00	−	2551.31i	0.0482348	−	0.0835452i	0.889135	+	0.457645i	$0.151307\pi$
$978$		0			0
$979$	−4860.00	−	8417.77i	−0.158658	−	0.274804i
$980$	6540.00			0.213176
$981$		0			0
$982$	27864.0			0.905475
$983$	7506.00	+	13000.8i	0.243544	+	0.421831i	0.961721	−	0.274029i	$-0.0883565\pi$
$983$	7506.00	+	13000.8i	0.243544	+	0.421831i	−0.718177	+	0.695861i	$0.755023\pi$
$984$		0			0
$985$	2685.00	−	4650.56i	0.0868540	−	0.150436i
$986$	−5940.00	+	10288.4i	−0.191854	+	0.332301i
$987$		0			0
$988$	−11600.0	−	20091.8i	−0.373527	−	0.646969i
$989$	−4224.00			−0.135809
$990$		0			0
$991$	−5128.00			−0.164376			−0.0821878	−	0.996617i	$-0.526191\pi$
$991$	−5128.00			−0.164376			−0.0821878	+	0.996617i	$0.526191\pi$
$992$	2432.00	+	4212.35i	0.0778388	+	0.134821i
$993$		0			0
$994$	1728.00	−	2992.98i	0.0551397	−	0.0955047i
$995$	7100.00	−	12297.6i	0.226216	−	0.391818i
$996$		0			0
$997$	24857.0	+	43053.6i	0.789598	+	1.36762i	0.926213	+	0.377000i	$0.123044\pi$
$997$	24857.0	+	43053.6i	0.789598	+	1.36762i	−0.136616	+	0.990624i	$0.543623\pi$
$998$	16520.0			0.523979
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.4.e.w.271.1		2
3.2	odd	2		810.4.e.c.271.1		2
9.2	odd	6		810.4.e.c.541.1		2
9.4	even	3		90.4.a.a.1.1		1
9.5	odd	6		10.4.a.a.1.1	✓	1
9.7	even	3	inner	810.4.e.w.541.1		2
36.23	even	6		80.4.a.f.1.1		1
36.31	odd	6		720.4.a.j.1.1		1
45.4	even	6		450.4.a.q.1.1		1
45.13	odd	12		450.4.c.d.199.2		2
45.14	odd	6		50.4.a.c.1.1		1
45.22	odd	12		450.4.c.d.199.1		2
45.23	even	12		50.4.b.a.49.1		2
45.32	even	12		50.4.b.a.49.2		2
63.5	even	6		490.4.e.a.361.1		2
63.23	odd	6		490.4.e.i.361.1		2
63.32	odd	6		490.4.e.i.471.1		2
63.41	even	6		490.4.a.o.1.1		1
63.59	even	6		490.4.e.a.471.1		2
72.5	odd	6		320.4.a.m.1.1		1
72.59	even	6		320.4.a.b.1.1		1
99.32	even	6		1210.4.a.b.1.1		1
117.77	odd	6		1690.4.a.a.1.1		1
144.5	odd	12		1280.4.d.j.641.2		2
144.59	even	12		1280.4.d.g.641.1		2
144.77	odd	12		1280.4.d.j.641.1		2
144.131	even	12		1280.4.d.g.641.2		2
180.23	odd	12		400.4.c.c.49.2		2
180.59	even	6		400.4.a.b.1.1		1
180.167	odd	12		400.4.c.c.49.1		2
315.104	even	6		2450.4.a.b.1.1		1
360.59	even	6		1600.4.a.bx.1.1		1
360.149	odd	6		1600.4.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.4.a.a.1.1	✓	1	9.5	odd	6
50.4.a.c.1.1		1	45.14	odd	6
50.4.b.a.49.1		2	45.23	even	12
50.4.b.a.49.2		2	45.32	even	12
80.4.a.f.1.1		1	36.23	even	6
90.4.a.a.1.1		1	9.4	even	3
320.4.a.b.1.1		1	72.59	even	6
320.4.a.m.1.1		1	72.5	odd	6
400.4.a.b.1.1		1	180.59	even	6
400.4.c.c.49.1		2	180.167	odd	12
400.4.c.c.49.2		2	180.23	odd	12
450.4.a.q.1.1		1	45.4	even	6
450.4.c.d.199.1		2	45.22	odd	12
450.4.c.d.199.2		2	45.13	odd	12
490.4.a.o.1.1		1	63.41	even	6
490.4.e.a.361.1		2	63.5	even	6
490.4.e.a.471.1		2	63.59	even	6
490.4.e.i.361.1		2	63.23	odd	6
490.4.e.i.471.1		2	63.32	odd	6
720.4.a.j.1.1		1	36.31	odd	6
810.4.e.c.271.1		2	3.2	odd	2
810.4.e.c.541.1		2	9.2	odd	6
810.4.e.w.271.1		2	1.1	even	1	trivial
810.4.e.w.541.1		2	9.7	even	3	inner
1210.4.a.b.1.1		1	99.32	even	6
1280.4.d.g.641.1		2	144.59	even	12
1280.4.d.g.641.2		2	144.131	even	12
1280.4.d.j.641.1		2	144.77	odd	12
1280.4.d.j.641.2		2	144.5	odd	12
1600.4.a.d.1.1		1	360.149	odd	6
1600.4.a.bx.1.1		1	360.59	even	6
1690.4.a.a.1.1		1	117.77	odd	6
2450.4.a.b.1.1		1	315.104	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:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	810.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(2.50000 - 4.33013i) q^{5} +(2.00000 + 3.46410i) q^{7} -8.00000 q^{8} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(2.50000 - 4.33013i) q^{5} +(2.00000 + 3.46410i) q^{7} -8.00000 q^{8} +10.0000 q^{10} +(6.00000 + 10.3923i) q^{11} +(29.0000 - 50.2295i) q^{13} +(-4.00000 + 6.92820i) q^{14} +(-8.00000 - 13.8564i) q^{16} -66.0000 q^{17} -100.000 q^{19} +(10.0000 + 17.3205i) q^{20} +(-12.0000 + 20.7846i) q^{22} +(66.0000 - 114.315i) q^{23} +(-12.5000 - 21.6506i) q^{25} +116.000 q^{26} -16.0000 q^{28} +(-45.0000 - 77.9423i) q^{29} +(-76.0000 + 131.636i) q^{31} +(16.0000 - 27.7128i) q^{32} +(-66.0000 - 114.315i) q^{34} +20.0000 q^{35} -34.0000 q^{37} +(-100.000 - 173.205i) q^{38} +(-20.0000 + 34.6410i) q^{40} +(-219.000 + 379.319i) q^{41} +(-16.0000 - 27.7128i) q^{43} -48.0000 q^{44} +264.000 q^{46} +(-102.000 - 176.669i) q^{47} +(163.500 - 283.190i) q^{49} +(25.0000 - 43.3013i) q^{50} +(116.000 + 200.918i) q^{52} -222.000 q^{53} +60.0000 q^{55} +(-16.0000 - 27.7128i) q^{56} +(90.0000 - 155.885i) q^{58} +(210.000 - 363.731i) q^{59} +(-451.000 - 781.155i) q^{61} -304.000 q^{62} +64.0000 q^{64} +(-145.000 - 251.147i) q^{65} +(512.000 - 886.810i) q^{67} +(132.000 - 228.631i) q^{68} +(20.0000 + 34.6410i) q^{70} -432.000 q^{71} +362.000 q^{73} +(-34.0000 - 58.8897i) q^{74} +(200.000 - 346.410i) q^{76} +(-24.0000 + 41.5692i) q^{77} +(80.0000 + 138.564i) q^{79} -80.0000 q^{80} -876.000 q^{82} +(36.0000 + 62.3538i) q^{83} +(-165.000 + 285.788i) q^{85} +(32.0000 - 55.4256i) q^{86} +(-48.0000 - 83.1384i) q^{88} -810.000 q^{89} +232.000 q^{91} +(264.000 + 457.261i) q^{92} +(204.000 - 353.338i) q^{94} +(-250.000 + 433.013i) q^{95} +(-553.000 - 957.824i) q^{97} +654.000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 4 q^{4} + 5 q^{5} + 4 q^{7} - 16 q^{8}+O(q^{10}) \) 2 * q + 2 * q^2 - 4 * q^4 + 5 * q^5 + 4 * q^7 - 16 * q^8	\( 2 q + 2 q^{2} - 4 q^{4} + 5 q^{5} + 4 q^{7} - 16 q^{8} + 20 q^{10} + 12 q^{11} + 58 q^{13} - 8 q^{14} - 16 q^{16} - 132 q^{17} - 200 q^{19} + 20 q^{20} - 24 q^{22} + 132 q^{23} - 25 q^{25} + 232 q^{26} - 32 q^{28} - 90 q^{29} - 152 q^{31} + 32 q^{32} - 132 q^{34} + 40 q^{35} - 68 q^{37} - 200 q^{38} - 40 q^{40} - 438 q^{41} - 32 q^{43} - 96 q^{44} + 528 q^{46} - 204 q^{47} + 327 q^{49} + 50 q^{50} + 232 q^{52} - 444 q^{53} + 120 q^{55} - 32 q^{56} + 180 q^{58} + 420 q^{59} - 902 q^{61} - 608 q^{62} + 128 q^{64} - 290 q^{65} + 1024 q^{67} + 264 q^{68} + 40 q^{70} - 864 q^{71} + 724 q^{73} - 68 q^{74} + 400 q^{76} - 48 q^{77} + 160 q^{79} - 160 q^{80} - 1752 q^{82} + 72 q^{83} - 330 q^{85} + 64 q^{86} - 96 q^{88} - 1620 q^{89} + 464 q^{91} + 528 q^{92} + 408 q^{94} - 500 q^{95} - 1106 q^{97} + 1308 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 - 4 * q^4 + 5 * q^5 + 4 * q^7 - 16 * q^8 + 20 * q^10 + 12 * q^11 + 58 * q^13 - 8 * q^14 - 16 * q^16 - 132 * q^17 - 200 * q^19 + 20 * q^20 - 24 * q^22 + 132 * q^23 - 25 * q^25 + 232 * q^26 - 32 * q^28 - 90 * q^29 - 152 * q^31 + 32 * q^32 - 132 * q^34 + 40 * q^35 - 68 * q^37 - 200 * q^38 - 40 * q^40 - 438 * q^41 - 32 * q^43 - 96 * q^44 + 528 * q^46 - 204 * q^47 + 327 * q^49 + 50 * q^50 + 232 * q^52 - 444 * q^53 + 120 * q^55 - 32 * q^56 + 180 * q^58 + 420 * q^59 - 902 * q^61 - 608 * q^62 + 128 * q^64 - 290 * q^65 + 1024 * q^67 + 264 * q^68 + 40 * q^70 - 864 * q^71 + 724 * q^73 - 68 * q^74 + 400 * q^76 - 48 * q^77 + 160 * q^79 - 160 * q^80 - 1752 * q^82 + 72 * q^83 - 330 * q^85 + 64 * q^86 - 96 * q^88 - 1620 * q^89 + 464 * q^91 + 528 * q^92 + 408 * q^94 - 500 * q^95 - 1106 * q^97 + 1308 * q^98

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