LMFDB - Embedded newform 810.4.e.q.541.1

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 270)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			541.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	810.541
Dual form			810.4.e.q.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(2.00000 - 3.46410i) q^{7} -8.00000 q^{8} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(2.00000 - 3.46410i) q^{7} -8.00000 q^{8} -10.0000 q^{10} +(21.0000 - 36.3731i) q^{11} +(-10.0000 - 17.3205i) q^{13} +(-4.00000 - 6.92820i) q^{14} +(-8.00000 + 13.8564i) q^{16} -93.0000 q^{17} +59.0000 q^{19} +(-10.0000 + 17.3205i) q^{20} +(-42.0000 - 72.7461i) q^{22} +(4.50000 + 7.79423i) q^{23} +(-12.5000 + 21.6506i) q^{25} -40.0000 q^{26} -16.0000 q^{28} +(60.0000 - 103.923i) q^{29} +(-23.5000 - 40.7032i) q^{31} +(16.0000 + 27.7128i) q^{32} +(-93.0000 + 161.081i) q^{34} -20.0000 q^{35} -262.000 q^{37} +(59.0000 - 102.191i) q^{38} +(20.0000 + 34.6410i) q^{40} +(63.0000 + 109.119i) q^{41} +(89.0000 - 154.153i) q^{43} -168.000 q^{44} +18.0000 q^{46} +(72.0000 - 124.708i) q^{47} +(163.500 + 283.190i) q^{49} +(25.0000 + 43.3013i) q^{50} +(-40.0000 + 69.2820i) q^{52} -741.000 q^{53} -210.000 q^{55} +(-16.0000 + 27.7128i) q^{56} +(-120.000 - 207.846i) q^{58} +(-222.000 - 384.515i) q^{59} +(-110.500 + 191.392i) q^{61} -94.0000 q^{62} +64.0000 q^{64} +(-50.0000 + 86.6025i) q^{65} +(269.000 + 465.922i) q^{67} +(186.000 + 322.161i) q^{68} +(-20.0000 + 34.6410i) q^{70} -690.000 q^{71} -1126.00 q^{73} +(-262.000 + 453.797i) q^{74} +(-118.000 - 204.382i) q^{76} +(-84.0000 - 145.492i) q^{77} +(-332.500 + 575.907i) q^{79} +80.0000 q^{80} +252.000 q^{82} +(37.5000 - 64.9519i) q^{83} +(232.500 + 402.702i) q^{85} +(-178.000 - 308.305i) q^{86} +(-168.000 + 290.985i) q^{88} +1086.00 q^{89} -80.0000 q^{91} +(18.0000 - 31.1769i) q^{92} +(-144.000 - 249.415i) q^{94} +(-147.500 - 255.477i) q^{95} +(-772.000 + 1337.14i) q^{97} +654.000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 42 q^{11} - 20 q^{13} - 8 q^{14} - 16 q^{16} - 186 q^{17} + 118 q^{19} - 20 q^{20} - 84 q^{22} + 9 q^{23} - 25 q^{25} - 80 q^{26} - 32 q^{28} + 120 q^{29} - 47 q^{31} + 32 q^{32} - 186 q^{34} - 40 q^{35} - 524 q^{37} + 118 q^{38} + 40 q^{40} + 126 q^{41} + 178 q^{43} - 336 q^{44} + 36 q^{46} + 144 q^{47} + 327 q^{49} + 50 q^{50} - 80 q^{52} - 1482 q^{53} - 420 q^{55} - 32 q^{56} - 240 q^{58} - 444 q^{59} - 221 q^{61} - 188 q^{62} + 128 q^{64} - 100 q^{65} + 538 q^{67} + 372 q^{68} - 40 q^{70} - 1380 q^{71} - 2252 q^{73} - 524 q^{74} - 236 q^{76} - 168 q^{77} - 665 q^{79} + 160 q^{80} + 504 q^{82} + 75 q^{83} + 465 q^{85} - 356 q^{86} - 336 q^{88} + 2172 q^{89} - 160 q^{91} + 36 q^{92} - 288 q^{94} - 295 q^{95} - 1544 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 + 42 * q^11 - 20 * q^13 - 8 * q^14 - 16 * q^16 - 186 * q^17 + 118 * q^19 - 20 * q^20 - 84 * q^22 + 9 * q^23 - 25 * q^25 - 80 * q^26 - 32 * q^28 + 120 * q^29 - 47 * q^31 + 32 * q^32 - 186 * q^34 - 40 * q^35 - 524 * q^37 + 118 * q^38 + 40 * q^40 + 126 * q^41 + 178 * q^43 - 336 * q^44 + 36 * q^46 + 144 * q^47 + 327 * q^49 + 50 * q^50 - 80 * q^52 - 1482 * q^53 - 420 * q^55 - 32 * q^56 - 240 * q^58 - 444 * q^59 - 221 * q^61 - 188 * q^62 + 128 * q^64 - 100 * q^65 + 538 * q^67 + 372 * q^68 - 40 * q^70 - 1380 * q^71 - 2252 * q^73 - 524 * q^74 - 236 * q^76 - 168 * q^77 - 665 * q^79 + 160 * q^80 + 504 * q^82 + 75 * q^83 + 465 * q^85 - 356 * q^86 - 336 * q^88 + 2172 * q^89 - 160 * q^91 + 36 * q^92 - 288 * q^94 - 295 * q^95 - 1544 * q^97 + 1308 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$487$	$731$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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
$5$	−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	−0.806966	−	0.590598i	$-0.798892\pi$
$7$	2.00000	−	3.46410i	0.107990	−	0.187044i	0.914956	+	0.403554i	$0.132225\pi$
$8$	−8.00000			−0.353553
$9$		0			0
$10$	−10.0000			−0.316228
$11$	21.0000	−	36.3731i	0.575613	−	0.996990i	−0.420362	−	0.907356i	$-0.638097\pi$
$11$	21.0000	−	36.3731i	0.575613	−	0.996990i	0.995975	−	0.0896338i	$-0.0285697\pi$
$12$		0			0
$13$	−10.0000	−	17.3205i	−0.213346	−	0.369527i	0.739413	−	0.673252i	$-0.235103\pi$
$13$	−10.0000	−	17.3205i	−0.213346	−	0.369527i	−0.952760	+	0.303725i	$0.901770\pi$
$14$	−4.00000	−	6.92820i	−0.0763604	−	0.132260i
$15$		0			0
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−93.0000			−1.32681			−0.663406	−	0.748259i	$-0.730890\pi$
$17$	−93.0000			−1.32681			−0.663406	+	0.748259i	$0.730890\pi$
$18$		0			0
$19$	59.0000			0.712396			0.356198	−	0.934410i	$-0.384073\pi$
$19$	59.0000			0.712396			0.356198	+	0.934410i	$0.384073\pi$
$20$	−10.0000	+	17.3205i	−0.111803	+	0.193649i
$21$		0			0
$22$	−42.0000	−	72.7461i	−0.407020	−	0.704979i
$23$	4.50000	+	7.79423i	0.0407963	+	0.0706613i	0.885703	−	0.464253i	$-0.153677\pi$
$23$	4.50000	+	7.79423i	0.0407963	+	0.0706613i	−0.844906	+	0.534914i	$0.820344\pi$
$24$		0			0
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	−40.0000			−0.301717
$27$		0			0
$28$	−16.0000			−0.107990
$29$	60.0000	−	103.923i	0.384197	−	0.665449i	−0.607460	−	0.794350i	$-0.707812\pi$
$29$	60.0000	−	103.923i	0.384197	−	0.665449i	0.991657	+	0.128901i	$0.0411449\pi$
$30$		0			0
$31$	−23.5000	−	40.7032i	−0.136152	−	0.235823i	0.789885	−	0.613255i	$-0.210140\pi$
$31$	−23.5000	−	40.7032i	−0.136152	−	0.235823i	−0.926037	+	0.377433i	$0.876807\pi$
$32$	16.0000	+	27.7128i	0.0883883	+	0.153093i
$33$		0			0
$34$	−93.0000	+	161.081i	−0.469099	+	0.812503i
$35$	−20.0000			−0.0965891
$36$		0			0
$37$	−262.000			−1.16412			−0.582061	−	0.813145i	$-0.697754\pi$
$37$	−262.000			−1.16412			−0.582061	+	0.813145i	$0.697754\pi$
$38$	59.0000	−	102.191i	0.251870	−	0.436252i
$39$		0			0
$40$	20.0000	+	34.6410i	0.0790569	+	0.136931i
$41$	63.0000	+	109.119i	0.239974	+	0.415648i	0.960707	−	0.277566i	$-0.0895276\pi$
$41$	63.0000	+	109.119i	0.239974	+	0.415648i	−0.720732	+	0.693213i	$0.756194\pi$
$42$		0			0
$43$	89.0000	−	154.153i	0.315637	−	0.546699i	−0.663936	−	0.747789i	$-0.731115\pi$
$43$	89.0000	−	154.153i	0.315637	−	0.546699i	0.979573	+	0.201091i	$0.0644486\pi$
$44$	−168.000			−0.575613
$45$		0			0
$46$	18.0000			0.0576947
$47$	72.0000	−	124.708i	0.223453	−	0.387032i	−0.732401	−	0.680873i	$-0.761600\pi$
$47$	72.0000	−	124.708i	0.223453	−	0.387032i	0.955854	+	0.293842i	$0.0949338\pi$
$48$		0			0
$49$	163.500	+	283.190i	0.476676	+	0.825628i
$50$	25.0000	+	43.3013i	0.0707107	+	0.122474i
$51$		0			0
$52$	−40.0000	+	69.2820i	−0.106673	+	0.184763i
$53$	−741.000			−1.92046			−0.960228	−	0.279217i	$-0.909925\pi$
$53$	−741.000			−1.92046			−0.960228	+	0.279217i	$0.909925\pi$
$54$		0			0
$55$	−210.000			−0.514844
$56$	−16.0000	+	27.7128i	−0.0381802	+	0.0661300i
$57$		0			0
$58$	−120.000	−	207.846i	−0.271668	−	0.470544i
$59$	−222.000	−	384.515i	−0.489863	−	0.848468i	0.510069	−	0.860134i	$-0.329620\pi$
$59$	−222.000	−	384.515i	−0.489863	−	0.848468i	−0.999932	+	0.0116655i	$0.996287\pi$
$60$		0			0
$61$	−110.500	+	191.392i	−0.231936	+	0.401724i	−0.958378	−	0.285503i	$-0.907839\pi$
$61$	−110.500	+	191.392i	−0.231936	+	0.401724i	0.726442	+	0.687228i	$0.241173\pi$
$62$	−94.0000			−0.192549
$63$		0			0
$64$	64.0000			0.125000
$65$	−50.0000	+	86.6025i	−0.0954113	+	0.165257i
$66$		0			0
$67$	269.000	+	465.922i	0.490501	+	0.849573i	0.999940	−	0.0109338i	$-0.00348039\pi$
$67$	269.000	+	465.922i	0.490501	+	0.849573i	−0.509439	+	0.860507i	$0.670147\pi$
$68$	186.000	+	322.161i	0.331703	+	0.574527i
$69$		0			0
$70$	−20.0000	+	34.6410i	−0.0341494	+	0.0591485i
$71$	−690.000			−1.15335			−0.576676	−	0.816973i	$-0.695650\pi$
$71$	−690.000			−1.15335			−0.576676	+	0.816973i	$0.695650\pi$
$72$		0			0
$73$	−1126.00			−1.80532			−0.902660	−	0.430355i	$-0.858388\pi$
$73$	−1126.00			−1.80532			−0.902660	+	0.430355i	$0.858388\pi$
$74$	−262.000	+	453.797i	−0.411579	+	0.712877i
$75$		0			0
$76$	−118.000	−	204.382i	−0.178099	−	0.308477i
$77$	−84.0000	−	145.492i	−0.124321	−	0.215330i
$78$		0			0
$79$	−332.500	+	575.907i	−0.473534	+	0.820185i	−0.999541	−	0.0302955i	$-0.990355\pi$
$79$	−332.500	+	575.907i	−0.473534	+	0.820185i	0.526007	+	0.850480i	$0.323689\pi$
$80$	80.0000			0.111803
$81$		0			0
$82$	252.000			0.339375
$83$	37.5000	−	64.9519i	0.0495923	−	0.0858964i	−0.840164	−	0.542333i	$-0.817541\pi$
$83$	37.5000	−	64.9519i	0.0495923	−	0.0858964i	0.889756	+	0.456437i	$0.150874\pi$
$84$		0			0
$85$	232.500	+	402.702i	0.296684	+	0.513872i
$86$	−178.000	−	308.305i	−0.223189	−	0.386574i
$87$		0			0
$88$	−168.000	+	290.985i	−0.203510	+	0.352489i
$89$	1086.00			1.29344			0.646718	−	0.762729i	$-0.276141\pi$
$89$	1086.00			1.29344			0.646718	+	0.762729i	$0.276141\pi$
$90$		0			0
$91$	−80.0000			−0.0921569
$92$	18.0000	−	31.1769i	0.0203981	−	0.0353306i
$93$		0			0
$94$	−144.000	−	249.415i	−0.158005	−	0.273673i
$95$	−147.500	−	255.477i	−0.159297	−	0.275910i
$96$		0			0
$97$	−772.000	+	1337.14i	−0.808090	+	1.39965i	0.106095	+	0.994356i	$0.466165\pi$
$97$	−772.000	+	1337.14i	−0.808090	+	1.39965i	−0.914185	+	0.405297i	$0.867168\pi$
$98$	654.000			0.674122
$99$		0			0
$100$	100.000			0.100000
$101$	−66.0000	+	114.315i	−0.0650222	+	0.112622i	−0.896704	−	0.442631i	$-0.854045\pi$
$101$	−66.0000	+	114.315i	−0.0650222	+	0.112622i	0.831682	+	0.555253i	$0.187378\pi$
$102$		0			0
$103$	446.000	+	772.495i	0.426657	+	0.738992i	0.996574	−	0.0827108i	$-0.0263578\pi$
$103$	446.000	+	772.495i	0.426657	+	0.738992i	−0.569916	+	0.821703i	$0.693024\pi$
$104$	80.0000	+	138.564i	0.0754293	+	0.130647i
$105$		0			0
$106$	−741.000	+	1283.45i	−0.678984	+	1.17603i
$107$	1140.00			1.02998			0.514990	−	0.857196i	$-0.327795\pi$
$107$	1140.00			1.02998			0.514990	+	0.857196i	$0.327795\pi$
$108$		0			0
$109$	−1735.00			−1.52461			−0.762307	−	0.647216i	$-0.775933\pi$
$109$	−1735.00			−1.52461			−0.762307	+	0.647216i	$0.775933\pi$
$110$	−210.000	+	363.731i	−0.182025	+	0.315276i
$111$		0			0
$112$	32.0000	+	55.4256i	0.0269975	+	0.0467610i
$113$	−717.000	−	1241.88i	−0.596900	−	1.03386i	−0.993276	−	0.115773i	$-0.963066\pi$
$113$	−717.000	−	1241.88i	−0.596900	−	1.03386i	0.396376	−	0.918088i	$-0.370268\pi$
$114$		0			0
$115$	22.5000	−	38.9711i	0.0182447	−	0.0316007i
$116$	−480.000			−0.384197
$117$		0			0
$118$	−888.000			−0.692771
$119$	−186.000	+	322.161i	−0.143282	+	0.248172i
$120$		0			0
$121$	−216.500	−	374.989i	−0.162660	−	0.281735i
$122$	221.000	+	382.783i	0.164003	+	0.284062i
$123$		0			0
$124$	−94.0000	+	162.813i	−0.0680762	+	0.117911i
$125$	125.000			0.0894427
$126$		0			0
$127$	686.000			0.479312			0.239656	−	0.970858i	$-0.422965\pi$
$127$	686.000			0.479312			0.239656	+	0.970858i	$0.422965\pi$
$128$	64.0000	−	110.851i	0.0441942	−	0.0765466i
$129$		0			0
$130$	100.000	+	173.205i	0.0674660	+	0.116855i
$131$	−57.0000	−	98.7269i	−0.0380161	−	0.0658459i	0.846391	−	0.532561i	$-0.178770\pi$
$131$	−57.0000	−	98.7269i	−0.0380161	−	0.0658459i	−0.884407	+	0.466716i	$0.845437\pi$
$132$		0			0
$133$	118.000	−	204.382i	0.0769316	−	0.133249i
$134$	1076.00			0.693673
$135$		0			0
$136$	744.000			0.469099
$137$	79.5000	−	137.698i	0.0495777	−	0.0858711i	−0.840172	−	0.542321i	$-0.817546\pi$
$137$	79.5000	−	137.698i	0.0495777	−	0.0858711i	0.889749	+	0.456450i	$0.150879\pi$
$138$		0			0
$139$	−1138.00	−	1971.07i	−0.694417	−	1.20276i	−0.970377	−	0.241596i	$-0.922329\pi$
$139$	−1138.00	−	1971.07i	−0.694417	−	1.20276i	0.275960	−	0.961169i	$-0.411004\pi$
$140$	40.0000	+	69.2820i	0.0241473	+	0.0418243i
$141$		0			0
$142$	−690.000	+	1195.12i	−0.407771	+	0.706280i
$143$	−840.000			−0.491219
$144$		0			0
$145$	−600.000			−0.343636
$146$	−1126.00	+	1950.29i	−0.638277	+	1.10553i
$147$		0			0
$148$	524.000	+	907.595i	0.291031	+	0.504080i
$149$	−699.000	−	1210.70i	−0.384324	−	0.665669i	0.607351	−	0.794434i	$-0.292232\pi$
$149$	−699.000	−	1210.70i	−0.384324	−	0.665669i	−0.991675	+	0.128765i	$0.958899\pi$
$150$		0			0
$151$	−1312.00	+	2272.45i	−0.707080	+	1.22470i	0.258856	+	0.965916i	$0.416655\pi$
$151$	−1312.00	+	2272.45i	−0.707080	+	1.22470i	−0.965936	+	0.258782i	$0.916679\pi$
$152$	−472.000			−0.251870
$153$		0			0
$154$	−336.000			−0.175816
$155$	−117.500	+	203.516i	−0.0608892	+	0.105463i
$156$		0			0
$157$	197.000	+	341.214i	0.100142	+	0.173451i	0.911743	−	0.410761i	$-0.134737\pi$
$157$	197.000	+	341.214i	0.100142	+	0.173451i	−0.811601	+	0.584212i	$0.801404\pi$
$158$	665.000	+	1151.81i	0.334839	+	0.579958i
$159$		0			0
$160$	80.0000	−	138.564i	0.0395285	−	0.0684653i
$161$	36.0000			0.0176223
$162$		0			0
$163$	−3346.00			−1.60785			−0.803923	−	0.594733i	$-0.797258\pi$
$163$	−3346.00			−1.60785			−0.803923	+	0.594733i	$0.797258\pi$
$164$	252.000	−	436.477i	0.119987	−	0.207824i
$165$		0			0
$166$	−75.0000	−	129.904i	−0.0350670	−	0.0607379i
$167$	−745.500	−	1291.24i	−0.345440	−	0.598320i	0.639993	−	0.768380i	$-0.278937\pi$
$167$	−745.500	−	1291.24i	−0.345440	−	0.598320i	−0.985434	+	0.170060i	$0.945604\pi$
$168$		0			0
$169$	898.500	−	1556.25i	0.408967	−	0.708351i
$170$	930.000			0.419575
$171$		0			0
$172$	−712.000			−0.315637
$173$	1201.50	−	2081.06i	0.528025	−	0.914566i	−0.471441	−	0.881898i	$-0.656266\pi$
$173$	1201.50	−	2081.06i	0.528025	−	0.914566i	0.999466	−	0.0326688i	$-0.0104007\pi$
$174$		0			0
$175$	50.0000	+	86.6025i	0.0215980	+	0.0374088i
$176$	336.000	+	581.969i	0.143903	+	0.249248i
$177$		0			0
$178$	1086.00	−	1881.01i	0.457299	−	0.792064i
$179$	2640.00			1.10236			0.551181	−	0.834386i	$-0.314177\pi$
$179$	2640.00			1.10236			0.551181	+	0.834386i	$0.314177\pi$
$180$		0			0
$181$	1073.00			0.440638			0.220319	−	0.975428i	$-0.429290\pi$
$181$	1073.00			0.440638			0.220319	+	0.975428i	$0.429290\pi$
$182$	−80.0000	+	138.564i	−0.0325824	+	0.0564344i
$183$		0			0
$184$	−36.0000	−	62.3538i	−0.0144237	−	0.0249825i
$185$	655.000	+	1134.49i	0.260306	+	0.450863i
$186$		0			0
$187$	−1953.00	+	3382.70i	−0.763730	+	1.32282i
$188$	−576.000			−0.223453
$189$		0			0
$190$	−590.000			−0.225279
$191$	735.000	−	1273.06i	0.278444	−	0.482279i	−0.692555	−	0.721366i	$-0.743515\pi$
$191$	735.000	−	1273.06i	0.278444	−	0.482279i	0.970998	+	0.239087i	$0.0768481\pi$
$192$		0			0
$193$	2360.00	+	4087.64i	0.880189	+	1.52453i	0.851130	+	0.524955i	$0.175918\pi$
$193$	2360.00	+	4087.64i	0.880189	+	1.52453i	0.0290591	+	0.999578i	$0.490749\pi$
$194$	1544.00	+	2674.29i	0.571406	+	0.989704i
$195$		0			0
$196$	654.000	−	1132.76i	0.238338	−	0.412814i
$197$	765.000			0.276670			0.138335	−	0.990385i	$-0.455825\pi$
$197$	765.000			0.276670			0.138335	+	0.990385i	$0.455825\pi$
$198$		0			0
$199$	668.000			0.237956			0.118978	−	0.992897i	$-0.462038\pi$
$199$	668.000			0.237956			0.118978	+	0.992897i	$0.462038\pi$
$200$	100.000	−	173.205i	0.0353553	−	0.0612372i
$201$		0			0
$202$	132.000	+	228.631i	0.0459777	+	0.0796356i
$203$	−240.000	−	415.692i	−0.0829788	−	0.143724i
$204$		0			0
$205$	315.000	−	545.596i	0.107320	−	0.185883i
$206$	1784.00			0.603384
$207$		0			0
$208$	320.000			0.106673
$209$	1239.00	−	2146.01i	0.410064	−	0.710252i
$210$		0			0
$211$	−2300.50	−	3984.58i	−0.750583	−	1.30005i	−0.947541	−	0.319635i	$-0.896440\pi$
$211$	−2300.50	−	3984.58i	−0.750583	−	1.30005i	0.196958	−	0.980412i	$-0.436894\pi$
$212$	1482.00	+	2566.90i	0.480114	+	0.831582i
$213$		0			0
$214$	1140.00	−	1974.54i	0.364153	−	0.630732i
$215$	−890.000			−0.282314
$216$		0			0
$217$	−188.000			−0.0588123
$218$	−1735.00	+	3005.11i	−0.539032	+	0.933631i
$219$		0			0
$220$	420.000	+	727.461i	0.128711	+	0.222934i
$221$	930.000	+	1610.81i	0.283070	+	0.490292i
$222$		0			0
$223$	1079.00	−	1868.88i	0.324014	−	0.561209i	−0.657298	−	0.753631i	$-0.728301\pi$
$223$	1079.00	−	1868.88i	0.324014	−	0.561209i	0.981312	+	0.192421i	$0.0616341\pi$
$224$	128.000			0.0381802
$225$		0			0
$226$	−2868.00			−0.844144
$227$	1561.50	−	2704.60i	0.456566	−	0.790795i	−0.542211	−	0.840242i	$-0.682413\pi$
$227$	1561.50	−	2704.60i	0.456566	−	0.790795i	0.998777	+	0.0494474i	$0.0157460\pi$
$228$		0			0
$229$	−1013.50	−	1755.43i	−0.292463	−	0.506560i	0.681929	−	0.731419i	$-0.261141\pi$
$229$	−1013.50	−	1755.43i	−0.292463	−	0.506560i	−0.974391	+	0.224858i	$0.927808\pi$
$230$	−45.0000	−	77.9423i	−0.0129009	−	0.0223451i
$231$		0			0
$232$	−480.000	+	831.384i	−0.135834	+	0.235272i
$233$	438.000			0.123152			0.0615758	−	0.998102i	$-0.480387\pi$
$233$	438.000			0.123152			0.0615758	+	0.998102i	$0.480387\pi$
$234$		0			0
$235$	−720.000			−0.199862
$236$	−888.000	+	1538.06i	−0.244932	+	0.424234i
$237$		0			0
$238$	372.000	+	644.323i	0.101316	+	0.175484i
$239$	3207.00	+	5554.69i	0.867965	+	1.50336i	0.864073	+	0.503367i	$0.167905\pi$
$239$	3207.00	+	5554.69i	0.867965	+	1.50336i	0.00389189	+	0.999992i	$0.498761\pi$
$240$		0			0
$241$	−1715.50	+	2971.33i	−0.458527	+	0.794193i	−0.998883	−	0.0472439i	$-0.984956\pi$
$241$	−1715.50	+	2971.33i	−0.458527	+	0.794193i	0.540356	+	0.841436i	$0.318290\pi$
$242$	−866.000			−0.230035
$243$		0			0
$244$	884.000			0.231936
$245$	817.500	−	1415.95i	0.213176	−	0.369232i
$246$		0			0
$247$	−590.000	−	1021.91i	−0.151987	−	0.263249i
$248$	188.000	+	325.626i	0.0481371	+	0.0833760i
$249$		0			0
$250$	125.000	−	216.506i	0.0316228	−	0.0547723i
$251$	−7308.00			−1.83776			−0.918878	−	0.394541i	$-0.870904\pi$
$251$	−7308.00			−1.83776			−0.918878	+	0.394541i	$0.870904\pi$
$252$		0			0
$253$	378.000			0.0939314
$254$	686.000	−	1188.19i	0.169462	−	0.293518i
$255$		0			0
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−1864.50	−	3229.41i	−0.452546	−	0.783833i	0.545997	−	0.837787i	$-0.316151\pi$
$257$	−1864.50	−	3229.41i	−0.452546	−	0.783833i	−0.998543	+	0.0539542i	$0.982817\pi$
$258$		0			0
$259$	−524.000	+	907.595i	−0.125713	+	0.217742i
$260$	400.000			0.0954113
$261$		0			0
$262$	−228.000			−0.0537629
$263$	−978.000	+	1693.95i	−0.229301	+	0.397160i	−0.957601	−	0.288098i	$-0.906977\pi$
$263$	−978.000	+	1693.95i	−0.229301	+	0.397160i	0.728300	+	0.685258i	$0.240311\pi$
$264$		0			0
$265$	1852.50	+	3208.62i	0.429427	+	0.743789i
$266$	−236.000	−	408.764i	−0.0543988	−	0.0942215i
$267$		0			0
$268$	1076.00	−	1863.69i	0.245251	−	0.424787i
$269$	−990.000			−0.224392			−0.112196	−	0.993686i	$-0.535788\pi$
$269$	−990.000			−0.224392			−0.112196	+	0.993686i	$0.535788\pi$
$270$		0			0
$271$	8495.00			1.90419			0.952093	−	0.305808i	$-0.0989266\pi$
$271$	8495.00			1.90419			0.952093	+	0.305808i	$0.0989266\pi$
$272$	744.000	−	1288.65i	0.165852	−	0.287263i
$273$		0			0
$274$	−159.000	−	275.396i	−0.0350567	−	0.0607200i
$275$	525.000	+	909.327i	0.115123	+	0.199398i
$276$		0			0
$277$	683.000	−	1182.99i	0.148150	−	0.256603i	−0.782394	−	0.622784i	$-0.786002\pi$
$277$	683.000	−	1182.99i	0.148150	−	0.256603i	0.930544	+	0.366181i	$0.119335\pi$
$278$	−4552.00			−0.982053
$279$		0			0
$280$	160.000			0.0341494
$281$	2760.00	−	4780.46i	0.585935	−	1.01487i	−0.408823	−	0.912614i	$-0.634061\pi$
$281$	2760.00	−	4780.46i	0.585935	−	1.01487i	0.994758	−	0.102256i	$-0.0326060\pi$
$282$		0			0
$283$	−2719.00	−	4709.45i	−0.571123	−	0.989214i	−0.996451	−	0.0841746i	$-0.973175\pi$
$283$	−2719.00	−	4709.45i	−0.571123	−	0.989214i	0.425328	−	0.905039i	$-0.360159\pi$
$284$	1380.00	+	2390.23i	0.288338	+	0.499416i
$285$		0			0
$286$	−840.000	+	1454.92i	−0.173672	+	0.300809i
$287$	504.000			0.103659
$288$		0			0
$289$	3736.00			0.760432
$290$	−600.000	+	1039.23i	−0.121494	+	0.210434i
$291$		0			0
$292$	2252.00	+	3900.58i	0.451330	+	0.781726i
$293$	−4126.50	−	7147.31i	−0.822774	−	1.42509i	−0.903609	−	0.428358i	$-0.859092\pi$
$293$	−4126.50	−	7147.31i	−0.822774	−	1.42509i	0.0808352	−	0.996727i	$-0.474241\pi$
$294$		0			0
$295$	−1110.00	+	1922.58i	−0.219074	+	0.379447i
$296$	2096.00			0.411579
$297$		0			0
$298$	−2796.00			−0.543517
$299$	90.0000	−	155.885i	0.0174075	−	0.0301506i
$300$		0			0
$301$	−356.000	−	616.610i	−0.0681711	−	0.118076i
$302$	2624.00	+	4544.90i	0.499981	+	0.865992i
$303$		0			0
$304$	−472.000	+	817.528i	−0.0890495	+	0.154238i
$305$	1105.00			0.207450
$306$		0			0
$307$	9290.00			1.72706			0.863531	−	0.504295i	$-0.168248\pi$
$307$	9290.00			1.72706			0.863531	+	0.504295i	$0.168248\pi$
$308$	−336.000	+	581.969i	−0.0621603	+	0.107665i
$309$		0			0
$310$	235.000	+	407.032i	0.0430552	+	0.0745737i
$311$	−4056.00	−	7025.20i	−0.739533	−	1.28091i	−0.952706	−	0.303894i	$-0.901713\pi$
$311$	−4056.00	−	7025.20i	−0.739533	−	1.28091i	0.213173	−	0.977014i	$-0.431620\pi$
$312$		0			0
$313$	3950.00	−	6841.60i	0.713314	−	1.23550i	−0.250293	−	0.968170i	$-0.580527\pi$
$313$	3950.00	−	6841.60i	0.713314	−	1.23550i	0.963606	−	0.267325i	$-0.0861399\pi$
$314$	788.000			0.141622
$315$		0			0
$316$	2660.00			0.473534
$317$	−2209.50	+	3826.97i	−0.391476	+	0.678056i	−0.992644	−	0.121066i	$-0.961369\pi$
$317$	−2209.50	+	3826.97i	−0.391476	+	0.678056i	0.601168	+	0.799122i	$0.294702\pi$
$318$		0			0
$319$	−2520.00	−	4364.77i	−0.442298	−	0.766082i
$320$	−160.000	−	277.128i	−0.0279508	−	0.0484123i
$321$		0			0
$322$	36.0000	−	62.3538i	0.00623044	−	0.0107914i
$323$	−5487.00			−0.945216
$324$		0			0
$325$	500.000			0.0853385
$326$	−3346.00	+	5795.44i	−0.568460	+	0.984601i
$327$		0			0
$328$	−504.000	−	872.954i	−0.0848437	−	0.146954i
$329$	−288.000	−	498.831i	−0.0482613	−	0.0835910i
$330$		0			0
$331$	4100.00	−	7101.41i	0.680835	−	1.17924i	−0.293891	−	0.955839i	$-0.594950\pi$
$331$	4100.00	−	7101.41i	0.680835	−	1.17924i	0.974726	−	0.223402i	$-0.0717163\pi$
$332$	−300.000			−0.0495923
$333$		0			0
$334$	−2982.00			−0.488526
$335$	1345.00	−	2329.61i	0.219359	−	0.379941i
$336$		0			0
$337$	4778.00	+	8275.74i	0.772327	+	1.33771i	0.936285	+	0.351242i	$0.114241\pi$
$337$	4778.00	+	8275.74i	0.772327	+	1.33771i	−0.163957	+	0.986467i	$0.552426\pi$
$338$	−1797.00	−	3112.50i	−0.289183	−	0.500880i
$339$		0			0
$340$	930.000	−	1610.81i	0.148342	−	0.256936i
$341$	−1974.00			−0.313484
$342$		0			0
$343$	2680.00			0.421885
$344$	−712.000	+	1233.22i	−0.111594	+	0.193287i
$345$		0			0
$346$	−2403.00	−	4162.12i	−0.373370	−	0.646696i
$347$	−5058.00	−	8760.71i	−0.782500	−	1.35533i	−0.930481	−	0.366340i	$-0.880611\pi$
$347$	−5058.00	−	8760.71i	−0.782500	−	1.35533i	0.147980	−	0.988990i	$-0.452723\pi$
$348$		0			0
$349$	3375.50	−	5846.54i	0.517726	−	0.896728i	−0.482062	−	0.876137i	$-0.660112\pi$
$349$	3375.50	−	5846.54i	0.517726	−	0.896728i	0.999788	−	0.0205906i	$-0.00655466\pi$
$350$	200.000			0.0305441
$351$		0			0
$352$	1344.00			0.203510
$353$	−2031.00	+	3517.80i	−0.306230	+	0.530406i	−0.977534	−	0.210776i	$-0.932401\pi$
$353$	−2031.00	+	3517.80i	−0.306230	+	0.530406i	0.671304	+	0.741182i	$0.265734\pi$
$354$		0			0
$355$	1725.00	+	2987.79i	0.257897	+	0.446691i
$356$	−2172.00	−	3762.01i	−0.323359	−	0.560074i
$357$		0			0
$358$	2640.00	−	4572.61i	0.389744	−	0.675056i
$359$	8778.00			1.29049			0.645244	−	0.763977i	$-0.276756\pi$
$359$	8778.00			1.29049			0.645244	+	0.763977i	$0.276756\pi$
$360$		0			0
$361$	−3378.00			−0.492492
$362$	1073.00	−	1858.49i	0.155789	−	0.269835i
$363$		0			0
$364$	160.000	+	277.128i	0.0230392	+	0.0399051i
$365$	2815.00	+	4875.72i	0.403682	+	0.699197i
$366$		0			0
$367$	−478.000	+	827.920i	−0.0679875	+	0.117758i	−0.898015	−	0.439964i	$-0.854991\pi$
$367$	−478.000	+	827.920i	−0.0679875	+	0.117758i	0.830028	+	0.557722i	$0.188324\pi$
$368$	−144.000			−0.0203981
$369$		0			0
$370$	2620.00			0.368128
$371$	−1482.00	+	2566.90i	−0.207390	+	0.359210i
$372$		0			0
$373$	−1150.00	−	1991.86i	−0.159637	−	0.276500i	0.775101	−	0.631838i	$-0.217699\pi$
$373$	−1150.00	−	1991.86i	−0.159637	−	0.276500i	−0.934738	+	0.355338i	$0.884366\pi$
$374$	3906.00	+	6765.39i	0.540039	+	0.935374i
$375$		0			0
$376$	−576.000	+	997.661i	−0.0790025	+	0.136836i
$377$	−2400.00			−0.327868
$378$		0			0
$379$	29.0000			0.00393042			0.00196521	−	0.999998i	$-0.499374\pi$
$379$	29.0000			0.00393042			0.00196521	+	0.999998i	$0.499374\pi$
$380$	−590.000	+	1021.91i	−0.0796483	+	0.137955i
$381$		0			0
$382$	−1470.00	−	2546.11i	−0.196889	−	0.341022i
$383$	−4063.50	−	7038.19i	−0.542128	−	0.938994i	−0.998782	−	0.0493491i	$-0.984285\pi$
$383$	−4063.50	−	7038.19i	−0.542128	−	0.938994i	0.456653	−	0.889645i	$-0.349048\pi$
$384$		0			0
$385$	−420.000	+	727.461i	−0.0555979	+	0.0962983i
$386$	9440.00			1.24478
$387$		0			0
$388$	6176.00			0.808090
$389$	3969.00	−	6874.51i	0.517317	−	0.896019i	−0.482481	−	0.875907i	$-0.660264\pi$
$389$	3969.00	−	6874.51i	0.517317	−	0.896019i	0.999798	−	0.0201127i	$-0.00640249\pi$
$390$		0			0
$391$	−418.500	−	724.863i	−0.0541290	−	0.0937542i
$392$	−1308.00	−	2265.52i	−0.168531	−	0.291903i
$393$		0			0
$394$	765.000	−	1325.02i	0.0978176	−	0.169425i
$395$	3325.00			0.423542
$396$		0			0
$397$	272.000			0.0343861			0.0171931	−	0.999852i	$-0.494527\pi$
$397$	272.000			0.0343861			0.0171931	+	0.999852i	$0.494527\pi$
$398$	668.000	−	1157.01i	0.0841302	−	0.145718i
$399$		0			0
$400$	−200.000	−	346.410i	−0.0250000	−	0.0433013i
$401$	−2277.00	−	3943.88i	−0.283561	−	0.491142i	0.688698	−	0.725048i	$-0.258183\pi$
$401$	−2277.00	−	3943.88i	−0.283561	−	0.491142i	−0.972259	+	0.233906i	$0.924849\pi$
$402$		0			0
$403$	−470.000	+	814.064i	−0.0580952	+	0.100624i
$404$	528.000			0.0650222
$405$		0			0
$406$	−960.000			−0.117350
$407$	−5502.00	+	9529.74i	−0.670084	+	1.16062i
$408$		0			0
$409$	−500.500	−	866.891i	−0.0605089	−	0.104804i	0.834184	−	0.551486i	$-0.185939\pi$
$409$	−500.500	−	866.891i	−0.0605089	−	0.104804i	−0.894693	+	0.446682i	$0.852606\pi$
$410$	−630.000	−	1091.19i	−0.0758865	−	0.131439i
$411$		0			0
$412$	1784.00	−	3089.98i	0.213329	−	0.369496i
$413$	−1776.00			−0.211601
$414$		0			0
$415$	−375.000			−0.0443567
$416$	320.000	−	554.256i	0.0377146	−	0.0653237i
$417$		0			0
$418$	−2478.00	−	4292.02i	−0.289959	−	0.502224i
$419$	897.000	+	1553.65i	0.104585	+	0.181147i	0.913569	−	0.406684i	$-0.133315\pi$
$419$	897.000	+	1553.65i	0.104585	+	0.181147i	−0.808983	+	0.587832i	$0.799982\pi$
$420$		0			0
$421$	8064.50	−	13968.1i	0.933586	−	1.61702i	0.156450	−	0.987686i	$-0.449995\pi$
$421$	8064.50	−	13968.1i	0.933586	−	1.61702i	0.777136	−	0.629332i	$-0.216672\pi$
$422$	−9202.00			−1.06148
$423$		0			0
$424$	5928.00			0.678984
$425$	1162.50	−	2013.51i	0.132681	−	0.229811i
$426$		0			0
$427$	442.000	+	765.566i	0.0500934	+	0.0867643i
$428$	−2280.00	−	3949.08i	−0.257495	−	0.445995i
$429$		0			0
$430$	−890.000	+	1541.53i	−0.0998130	+	0.172881i
$431$	−13356.0			−1.49266			−0.746329	−	0.665577i	$-0.768186\pi$
$431$	−13356.0			−1.49266			−0.746329	+	0.665577i	$0.768186\pi$
$432$		0			0
$433$	−11500.0			−1.27634			−0.638169	−	0.769896i	$-0.720308\pi$
$433$	−11500.0			−1.27634			−0.638169	+	0.769896i	$0.720308\pi$
$434$	−188.000	+	325.626i	−0.0207933	+	0.0360150i
$435$		0			0
$436$	3470.00	+	6010.22i	0.381153	+	0.660177i
$437$	265.500	+	459.859i	0.0290631	+	0.0503388i
$438$		0			0
$439$	5574.50	−	9655.32i	0.606051	−	1.04971i	−0.385833	−	0.922568i	$-0.626086\pi$
$439$	5574.50	−	9655.32i	0.606051	−	1.04971i	0.991884	−	0.127143i	$-0.0405806\pi$
$440$	1680.00			0.182025
$441$		0			0
$442$	3720.00			0.400322
$443$	−1924.50	+	3333.33i	−0.206401	+	0.357497i	−0.950578	−	0.310485i	$-0.899509\pi$
$443$	−1924.50	+	3333.33i	−0.206401	+	0.357497i	0.744177	+	0.667982i	$0.232842\pi$
$444$		0			0
$445$	−2715.00	−	4702.52i	−0.289221	−	0.500945i
$446$	−2158.00	−	3737.77i	−0.229113	−	0.396835i
$447$		0			0
$448$	128.000	−	221.703i	0.0134987	−	0.0233805i
$449$	18048.0			1.89697			0.948483	−	0.316828i	$-0.102618\pi$
$449$	18048.0			1.89697			0.948483	+	0.316828i	$0.102618\pi$
$450$		0			0
$451$	5292.00			0.552529
$452$	−2868.00	+	4967.52i	−0.298450	+	0.516930i
$453$		0			0
$454$	−3123.00	−	5409.19i	−0.322841	−	0.559176i
$455$	200.000	+	346.410i	0.0206069	+	0.0356922i
$456$		0			0
$457$	2132.00	−	3692.73i	0.218229	−	0.377984i	−0.736037	−	0.676941i	$-0.763305\pi$
$457$	2132.00	−	3692.73i	0.218229	−	0.377984i	0.954267	+	0.298957i	$0.0966386\pi$
$458$	−4054.00			−0.413605
$459$		0			0
$460$	−180.000			−0.0182447
$461$	5121.00	−	8869.83i	0.517373	−	0.896116i	−0.482424	−	0.875938i	$-0.660243\pi$
$461$	5121.00	−	8869.83i	0.517373	−	0.896116i	0.999796	−	0.0201776i	$-0.00642318\pi$
$462$		0			0
$463$	−1651.00	−	2859.62i	−0.165720	−	0.287036i	0.771191	−	0.636604i	$-0.219662\pi$
$463$	−1651.00	−	2859.62i	−0.165720	−	0.287036i	−0.936911	+	0.349568i	$0.886328\pi$
$464$	960.000	+	1662.77i	0.0960493	+	0.166362i
$465$		0			0
$466$	438.000	−	758.638i	0.0435407	−	0.0754147i
$467$	−1923.00			−0.190548			−0.0952739	−	0.995451i	$-0.530373\pi$
$467$	−1923.00			−0.190548			−0.0952739	+	0.995451i	$0.530373\pi$
$468$		0			0
$469$	2152.00			0.211877
$470$	−720.000	+	1247.08i	−0.0706620	+	0.122390i
$471$		0			0
$472$	1776.00	+	3076.12i	0.173193	+	0.299979i
$473$	−3738.00	−	6474.41i	−0.363369	−	0.629373i
$474$		0			0
$475$	−737.500	+	1277.39i	−0.0712396	+	0.123391i
$476$	1488.00			0.143282
$477$		0			0
$478$	12828.0			1.22749
$479$	−7623.00	+	13203.4i	−0.727148	+	1.25946i	0.230936	+	0.972969i	$0.425821\pi$
$479$	−7623.00	+	13203.4i	−0.727148	+	1.25946i	−0.958084	+	0.286488i	$0.907512\pi$
$480$		0			0
$481$	2620.00	+	4537.97i	0.248361	+	0.430174i
$482$	3431.00	+	5942.67i	0.324228	+	0.561579i
$483$		0			0
$484$	−866.000	+	1499.96i	−0.0813298	+	0.140867i
$485$	7720.00			0.722778
$486$		0			0
$487$	−8206.00			−0.763551			−0.381776	−	0.924255i	$-0.624687\pi$
$487$	−8206.00			−0.763551			−0.381776	+	0.924255i	$0.624687\pi$
$488$	884.000	−	1531.13i	0.0820016	−	0.142031i
$489$		0			0
$490$	−1635.00	−	2831.90i	−0.150738	−	0.261086i
$491$	8403.00	+	14554.4i	0.772346	+	1.33774i	0.936274	+	0.351271i	$0.114250\pi$
$491$	8403.00	+	14554.4i	0.772346	+	1.33774i	−0.163928	+	0.986472i	$0.552416\pi$
$492$		0			0
$493$	−5580.00	+	9664.84i	−0.509758	+	0.882926i
$494$	−2360.00			−0.214942
$495$		0			0
$496$	752.000			0.0680762
$497$	−1380.00	+	2390.23i	−0.124550	+	0.215727i
$498$		0			0
$499$	2712.50	+	4698.19i	0.243343	+	0.421483i	0.961664	−	0.274229i	$-0.0884226\pi$
$499$	2712.50	+	4698.19i	0.243343	+	0.421483i	−0.718321	+	0.695711i	$0.755089\pi$
$500$	−250.000	−	433.013i	−0.0223607	−	0.0387298i
$501$		0			0
$502$	−7308.00	+	12657.8i	−0.649745	+	1.12539i
$503$	−19665.0			−1.74318			−0.871589	−	0.490236i	$-0.836910\pi$
$503$	−19665.0			−1.74318			−0.871589	+	0.490236i	$0.836910\pi$
$504$		0			0
$505$	660.000			0.0581577
$506$	378.000	−	654.715i	0.0332098	−	0.0575210i
$507$		0			0
$508$	−1372.00	−	2376.37i	−0.119828	−	0.207548i
$509$	7362.00	+	12751.4i	0.641090	+	1.11040i	0.985190	+	0.171468i	$0.0548509\pi$
$509$	7362.00	+	12751.4i	0.641090	+	1.11040i	−0.344100	+	0.938933i	$0.611816\pi$
$510$		0			0
$511$	−2252.00	+	3900.58i	−0.194956	+	0.337674i
$512$	−512.000			−0.0441942
$513$		0			0
$514$	−7458.00			−0.639997
$515$	2230.00	−	3862.47i	0.190807	−	0.330487i
$516$		0			0
$517$	−3024.00	−	5237.72i	−0.257244	−	0.445560i
$518$	1048.00	+	1815.19i	0.0888928	+	0.153967i
$519$		0			0
$520$	400.000	−	692.820i	0.0337330	−	0.0584273i
$521$	2058.00			0.173057			0.0865284	−	0.996249i	$-0.472423\pi$
$521$	2058.00			0.173057			0.0865284	+	0.996249i	$0.472423\pi$
$522$		0			0
$523$	11912.0			0.995938			0.497969	−	0.867195i	$-0.334079\pi$
$523$	11912.0			0.995938			0.497969	+	0.867195i	$0.334079\pi$
$524$	−228.000	+	394.908i	−0.0190081	+	0.0329229i
$525$		0			0
$526$	1956.00	+	3387.89i	0.162140	+	0.280835i
$527$	2185.50	+	3785.40i	0.180649	+	0.312893i
$528$		0			0
$529$	6043.00	−	10466.8i	0.496671	−	0.860260i
$530$	7410.00			0.607302
$531$		0			0
$532$	−944.000			−0.0769316
$533$	1260.00	−	2182.38i	0.102395	−	0.177354i
$534$		0			0
$535$	−2850.00	−	4936.34i	−0.230311	−	0.398910i
$536$	−2152.00	−	3727.37i	−0.173418	−	0.300369i
$537$		0			0
$538$	−990.000	+	1714.73i	−0.0793344	+	0.137411i
$539$	13734.0			1.09752
$540$		0			0
$541$	−5170.00			−0.410861			−0.205430	−	0.978672i	$-0.565859\pi$
$541$	−5170.00			−0.410861			−0.205430	+	0.978672i	$0.565859\pi$
$542$	8495.00	−	14713.8i	0.673232	−	1.16607i
$543$		0			0
$544$	−1488.00	−	2577.29i	−0.117275	−	0.203126i
$545$	4337.50	+	7512.77i	0.340914	+	0.590480i
$546$		0			0
$547$	2093.00	−	3625.18i	0.163602	−	0.283367i	−0.772556	−	0.634947i	$-0.781022\pi$
$547$	2093.00	−	3625.18i	0.163602	−	0.283367i	0.936158	+	0.351580i	$0.114355\pi$
$548$	−636.000			−0.0495777
$549$		0			0
$550$	2100.00			0.162808
$551$	3540.00	−	6131.46i	0.273701	−	0.474063i
$552$		0			0
$553$	1330.00	+	2303.63i	0.102274	+	0.177143i
$554$	−1366.00	−	2365.98i	−0.104758	−	0.181446i
$555$		0			0
$556$	−4552.00	+	7884.30i	−0.347208	+	0.601382i
$557$	13026.0			0.990896			0.495448	−	0.868637i	$-0.335004\pi$
$557$	13026.0			0.990896			0.495448	+	0.868637i	$0.335004\pi$
$558$		0			0
$559$	−3560.00			−0.269359
$560$	160.000	−	277.128i	0.0120736	−	0.0209121i
$561$		0			0
$562$	−5520.00	−	9560.92i	−0.414319	−	0.717621i
$563$	5334.00	+	9238.76i	0.399292	+	0.691594i	0.993639	−	0.112615i	$-0.0359227\pi$
$563$	5334.00	+	9238.76i	0.399292	+	0.691594i	−0.594347	+	0.804209i	$0.702589\pi$
$564$		0			0
$565$	−3585.00	+	6209.40i	−0.266942	+	0.462357i
$566$	−10876.0			−0.807690
$567$		0			0
$568$	5520.00			0.407771
$569$	7686.00	−	13312.5i	0.566281	−	0.980827i	−0.430648	−	0.902520i	$-0.641715\pi$
$569$	7686.00	−	13312.5i	0.566281	−	0.980827i	0.996929	−	0.0783076i	$-0.0249516\pi$
$570$		0			0
$571$	7494.50	+	12980.9i	0.549273	+	0.951369i	0.998325	+	0.0578633i	$0.0184287\pi$
$571$	7494.50	+	12980.9i	0.549273	+	0.951369i	−0.449051	+	0.893506i	$0.648238\pi$
$572$	1680.00	+	2909.85i	0.122805	+	0.212704i
$573$		0			0
$574$	504.000	−	872.954i	0.0366490	−	0.0634780i
$575$	−225.000			−0.0163185
$576$		0			0
$577$	−1066.00			−0.0769119			−0.0384559	−	0.999260i	$-0.512244\pi$
$577$	−1066.00			−0.0769119			−0.0384559	+	0.999260i	$0.512244\pi$
$578$	3736.00	−	6470.94i	0.268853	−	0.465667i
$579$		0			0
$580$	1200.00	+	2078.46i	0.0859091	+	0.148799i
$581$	−150.000	−	259.808i	−0.0107109	−	0.0185519i
$582$		0			0
$583$	−15561.0	+	26952.4i	−1.10544	+	1.91468i
$584$	9008.00			0.638277
$585$		0			0
$586$	−16506.0			−1.16358
$587$	310.500	−	537.802i	0.0218325	−	0.0378151i	−0.854903	−	0.518788i	$-0.826383\pi$
$587$	310.500	−	537.802i	0.0218325	−	0.0378151i	0.876735	+	0.480973i	$0.159717\pi$
$588$		0			0
$589$	−1386.50	−	2401.49i	−0.0969945	−	0.167999i
$590$	2220.00	+	3845.15i	0.154908	+	0.268309i
$591$		0			0
$592$	2096.00	−	3630.38i	0.145515	−	0.252040i
$593$	−20187.0			−1.39794			−0.698972	−	0.715149i	$-0.746359\pi$
$593$	−20187.0			−1.39794			−0.698972	+	0.715149i	$0.746359\pi$
$594$		0			0
$595$	1860.00			0.128156
$596$	−2796.00	+	4842.81i	−0.192162	+	0.332835i
$597$		0			0
$598$	−180.000	−	311.769i	−0.0123089	−	0.0213197i
$599$	9114.00	+	15785.9i	0.621683	+	1.07679i	0.989172	+	0.146758i	$0.0468840\pi$
$599$	9114.00	+	15785.9i	0.621683	+	1.07679i	−0.367490	+	0.930028i	$0.619783\pi$
$600$		0			0
$601$	5871.50	−	10169.7i	0.398508	−	0.690237i	−0.595034	−	0.803701i	$-0.702861\pi$
$601$	5871.50	−	10169.7i	0.398508	−	0.690237i	0.993542	+	0.113464i	$0.0361947\pi$
$602$	−1424.00			−0.0964085
$603$		0			0
$604$	10496.0			0.707080
$605$	−1082.50	+	1874.94i	−0.0727436	+	0.125996i
$606$		0			0
$607$	12209.0	+	21146.6i	0.816389	+	1.41403i	0.908326	+	0.418262i	$0.137361\pi$
$607$	12209.0	+	21146.6i	0.816389	+	1.41403i	−0.0919375	+	0.995765i	$0.529306\pi$
$608$	944.000	+	1635.06i	0.0629675	+	0.109063i
$609$		0			0
$610$	1105.00	−	1913.92i	0.0733445	−	0.127036i
$611$	−2880.00			−0.190691
$612$		0			0
$613$	2672.00			0.176054			0.0880270	−	0.996118i	$-0.471944\pi$
$613$	2672.00			0.176054			0.0880270	+	0.996118i	$0.471944\pi$
$614$	9290.00	−	16090.8i	0.610609	−	1.05761i
$615$		0			0
$616$	672.000	+	1163.94i	0.0439540	+	0.0761305i
$617$	4300.50	+	7448.68i	0.280602	+	0.486017i	0.971533	−	0.236903i	$-0.0761325\pi$
$617$	4300.50	+	7448.68i	0.280602	+	0.486017i	−0.690931	+	0.722921i	$0.742799\pi$
$618$		0			0
$619$	−10654.0	+	18453.3i	−0.691794	+	1.19822i	0.279456	+	0.960159i	$0.409846\pi$
$619$	−10654.0	+	18453.3i	−0.691794	+	1.19822i	−0.971250	+	0.238064i	$0.923487\pi$
$620$	940.000			0.0608892
$621$		0			0
$622$	−16224.0			−1.04586
$623$	2172.00	−	3762.01i	0.139678	−	0.241929i
$624$		0			0
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	−7900.00	−	13683.2i	−0.504389	−	0.873627i
$627$		0			0
$628$	788.000	−	1364.86i	0.0500711	−	0.0867256i
$629$	24366.0			1.54457
$630$		0			0
$631$	−19015.0			−1.19964			−0.599822	−	0.800134i	$-0.704762\pi$
$631$	−19015.0			−1.19964			−0.599822	+	0.800134i	$0.704762\pi$
$632$	2660.00	−	4607.26i	0.167419	−	0.289979i
$633$		0			0
$634$	4419.00	+	7653.93i	0.276815	+	0.479458i
$635$	−1715.00	−	2970.47i	−0.107177	−	0.185637i
$636$		0			0
$637$	3270.00	−	5663.81i	0.203394	−	0.352289i
$638$	−10080.0			−0.625503
$639$		0			0
$640$	−640.000			−0.0395285
$641$	2208.00	−	3824.37i	0.136054	−	0.235653i	−0.789945	−	0.613177i	$-0.789891\pi$
$641$	2208.00	−	3824.37i	0.136054	−	0.235653i	0.926000	+	0.377524i	$0.123225\pi$
$642$		0			0
$643$	−3790.00	−	6564.47i	−0.232446	−	0.402609i	0.726081	−	0.687609i	$-0.241340\pi$
$643$	−3790.00	−	6564.47i	−0.232446	−	0.402609i	−0.958527	+	0.285000i	$0.908006\pi$
$644$	−72.0000	−	124.708i	−0.00440559	−	0.00763070i
$645$		0			0
$646$	−5487.00	+	9503.76i	−0.334184	+	0.578824i
$647$	−14901.0			−0.905439			−0.452719	−	0.891653i	$-0.649546\pi$
$647$	−14901.0			−0.905439			−0.452719	+	0.891653i	$0.649546\pi$
$648$		0			0
$649$	−18648.0			−1.12789
$650$	500.000	−	866.025i	0.0301717	−	0.0522589i
$651$		0			0
$652$	6692.00	+	11590.9i	0.401962	+	0.696218i
$653$	−6457.50	−	11184.7i	−0.386985	−	0.670278i	0.605057	−	0.796182i	$-0.293150\pi$
$653$	−6457.50	−	11184.7i	−0.386985	−	0.670278i	−0.992042	+	0.125904i	$0.959817\pi$
$654$		0			0
$655$	−285.000	+	493.634i	−0.0170013	+	0.0294472i
$656$	−2016.00			−0.119987
$657$		0			0
$658$	−1152.00			−0.0682517
$659$	−14064.0	+	24359.6i	−0.831344	+	1.43993i	0.0656288	+	0.997844i	$0.479095\pi$
$659$	−14064.0	+	24359.6i	−0.831344	+	1.43993i	−0.896973	+	0.442086i	$0.854239\pi$
$660$		0			0
$661$	4181.00	+	7241.70i	0.246024	+	0.426127i	0.962419	−	0.271569i	$-0.0875424\pi$
$661$	4181.00	+	7241.70i	0.246024	+	0.426127i	−0.716395	+	0.697695i	$0.754209\pi$
$662$	−8200.00	−	14202.8i	−0.481423	−	0.833849i
$663$		0			0
$664$	−300.000	+	519.615i	−0.0175335	+	0.0303689i
$665$	−1180.00			−0.0688097
$666$		0			0
$667$	1080.00			0.0626953
$668$	−2982.00	+	5164.98i	−0.172720	+	0.299160i
$669$		0			0
$670$	−2690.00	−	4659.22i	−0.155110	−	0.268659i
$671$	4641.00	+	8038.45i	0.267010	+	0.462475i
$672$		0			0
$673$	−14854.0	+	25727.9i	−0.850787	+	1.47361i	0.0297122	+	0.999558i	$0.490541\pi$
$673$	−14854.0	+	25727.9i	−0.850787	+	1.47361i	−0.880499	+	0.474048i	$0.842792\pi$
$674$	19112.0			1.09224
$675$		0			0
$676$	−7188.00			−0.408967
$677$	−3381.00	+	5856.06i	−0.191939	+	0.332447i	−0.945893	−	0.324480i	$-0.894811\pi$
$677$	−3381.00	+	5856.06i	−0.191939	+	0.332447i	0.753954	+	0.656927i	$0.228144\pi$
$678$		0			0
$679$	3088.00	+	5348.57i	0.174531	+	0.302297i
$680$	−1860.00	−	3221.61i	−0.104894	−	0.181681i
$681$		0			0
$682$	−1974.00	+	3419.07i	−0.110833	+	0.191969i
$683$	−19155.0			−1.07313			−0.536563	−	0.843860i	$-0.680278\pi$
$683$	−19155.0			−1.07313			−0.536563	+	0.843860i	$0.680278\pi$
$684$		0			0
$685$	−795.000			−0.0443436
$686$	2680.00	−	4641.90i	0.149159	−	0.258350i
$687$		0			0
$688$	1424.00	+	2466.44i	0.0789091	+	0.136675i
$689$	7410.00	+	12834.5i	0.409722	+	0.709659i
$690$		0			0
$691$	11487.5	−	19896.9i	0.632424	−	1.09539i	−0.354630	−	0.935007i	$-0.615393\pi$
$691$	11487.5	−	19896.9i	0.632424	−	1.09539i	0.987055	−	0.160384i	$-0.0512733\pi$
$692$	−9612.00			−0.528025
$693$		0			0
$694$	−20232.0			−1.10662
$695$	−5690.00	+	9855.37i	−0.310553	+	0.537893i
$696$		0			0
$697$	−5859.00	−	10148.1i	−0.318401	−	0.551487i
$698$	−6751.00	−	11693.1i	−0.366088	−	0.634082i
$699$		0			0
$700$	200.000	−	346.410i	0.0107990	−	0.0187044i
$701$	−6450.00			−0.347522			−0.173761	−	0.984788i	$-0.555592\pi$
$701$	−6450.00			−0.347522			−0.173761	+	0.984788i	$0.555592\pi$
$702$		0			0
$703$	−15458.0			−0.829317
$704$	1344.00	−	2327.88i	0.0719516	−	0.124624i
$705$		0			0
$706$	4062.00	+	7035.59i	0.216537	+	0.375054i
$707$	264.000	+	457.261i	0.0140435	+	0.0243240i
$708$		0			0
$709$	−17269.0	+	29910.8i	−0.914740	+	1.58438i	−0.107459	+	0.994209i	$0.534272\pi$
$709$	−17269.0	+	29910.8i	−0.914740	+	1.58438i	−0.807281	+	0.590167i	$0.799062\pi$
$710$	6900.00			0.364722
$711$		0			0
$712$	−8688.00			−0.457299
$713$	211.500	−	366.329i	0.0111090	−	0.0192414i
$714$		0			0
$715$	2100.00	+	3637.31i	0.109840	+	0.190248i
$716$	−5280.00	−	9145.23i	−0.275591	−	0.477337i
$717$		0			0
$718$	8778.00	−	15203.9i	0.456256	−	0.790259i
$719$	27114.0			1.40637			0.703186	−	0.711006i	$-0.251760\pi$
$719$	27114.0			1.40637			0.703186	+	0.711006i	$0.251760\pi$
$720$		0			0
$721$	3568.00			0.184299
$722$	−3378.00	+	5850.87i	−0.174122	+	0.301588i
$723$		0			0
$724$	−2146.00	−	3716.98i	−0.110159	−	0.190802i
$725$	1500.00	+	2598.08i	0.0768395	+	0.133090i
$726$		0			0
$727$	−118.000	+	204.382i	−0.00601978	+	0.0104266i	−0.869020	−	0.494778i	$-0.835249\pi$
$727$	−118.000	+	204.382i	−0.00601978	+	0.0104266i	0.863000	+	0.505204i	$0.168583\pi$
$728$	640.000			0.0325824
$729$		0			0
$730$	11260.0			0.570892
$731$	−8277.00	+	14336.2i	−0.418791	+	0.725367i
$732$		0			0
$733$	−13564.0	−	23493.5i	−0.683489	−	1.18384i	−0.973909	−	0.226939i	$-0.927128\pi$
$733$	−13564.0	−	23493.5i	−0.683489	−	1.18384i	0.290420	−	0.956899i	$-0.406205\pi$
$734$	956.000	+	1655.84i	0.0480744	+	0.0832673i
$735$		0			0
$736$	−144.000	+	249.415i	−0.00721183	+	0.0124913i
$737$	22596.0			1.12935
$738$		0			0
$739$	5249.00			0.261282			0.130641	−	0.991430i	$-0.458296\pi$
$739$	5249.00			0.261282			0.130641	+	0.991430i	$0.458296\pi$
$740$	2620.00	−	4537.97i	0.130153	−	0.225431i
$741$		0			0
$742$	2964.00	+	5133.80i	0.146647	+	0.254000i
$743$	−6948.00	−	12034.3i	−0.343065	−	0.594206i	0.641935	−	0.766759i	$-0.278132\pi$
$743$	−6948.00	−	12034.3i	−0.343065	−	0.594206i	−0.985000	+	0.172553i	$0.944798\pi$
$744$		0			0
$745$	−3495.00	+	6053.52i	−0.171875	+	0.297696i
$746$	−4600.00			−0.225761
$747$		0			0
$748$	15624.0			0.763730
$749$	2280.00	−	3949.08i	0.111227	−	0.192652i
$750$		0			0
$751$	−13832.5	−	23958.6i	−0.672111	−	1.16413i	−0.977304	−	0.211840i	$-0.932055\pi$
$751$	−13832.5	−	23958.6i	−0.672111	−	1.16413i	0.305194	−	0.952290i	$-0.401279\pi$
$752$	1152.00	+	1995.32i	0.0558632	+	0.0967579i
$753$		0			0
$754$	−2400.00	+	4156.92i	−0.115919	+	0.200777i
$755$	13120.0			0.632431
$756$		0			0
$757$	−8122.00			−0.389959			−0.194980	−	0.980807i	$-0.562464\pi$
$757$	−8122.00			−0.389959			−0.194980	+	0.980807i	$0.562464\pi$
$758$	29.0000	−	50.2295i	0.00138961	−	0.00240688i
$759$		0			0
$760$	1180.00	+	2043.82i	0.0563199	+	0.0975489i
$761$	−5292.00	−	9166.01i	−0.252083	−	0.436620i	0.712016	−	0.702163i	$-0.247782\pi$
$761$	−5292.00	−	9166.01i	−0.252083	−	0.436620i	−0.964099	+	0.265543i	$0.914449\pi$
$762$		0			0
$763$	−3470.00	+	6010.22i	−0.164643	+	0.285170i
$764$	−5880.00			−0.278444
$765$		0			0
$766$	−16254.0			−0.766685
$767$	−4440.00	+	7690.31i	−0.209021	+	0.362035i
$768$		0			0
$769$	9309.50	+	16124.5i	0.436553	+	0.756132i	0.997421	−	0.0717734i	$-0.0228659\pi$
$769$	9309.50	+	16124.5i	0.436553	+	0.756132i	−0.560868	+	0.827905i	$0.689533\pi$
$770$	840.000	+	1454.92i	0.0393136	+	0.0680932i
$771$		0			0
$772$	9440.00	−	16350.6i	0.440095	−	0.762266i
$773$	22251.0			1.03533			0.517667	−	0.855582i	$-0.326801\pi$
$773$	22251.0			1.03533			0.517667	+	0.855582i	$0.326801\pi$
$774$		0			0
$775$	1175.00			0.0544610
$776$	6176.00	−	10697.1i	0.285703	−	0.494852i
$777$		0			0
$778$	−7938.00	−	13749.0i	−0.365798	−	0.633581i
$779$	3717.00	+	6438.03i	0.170957	+	0.296106i
$780$		0			0
$781$	−14490.0	+	25097.4i	−0.663883	+	1.14988i
$782$	−1674.00			−0.0765500
$783$		0			0
$784$	−5232.00			−0.238338
$785$	985.000	−	1706.07i	0.0447849	−	0.0775697i
$786$		0			0
$787$	−12427.0	−	21524.2i	−0.562865	−	0.974911i	−0.997245	−	0.0741809i	$-0.976366\pi$
$787$	−12427.0	−	21524.2i	−0.562865	−	0.974911i	0.434380	−	0.900730i	$-0.356968\pi$
$788$	−1530.00	−	2650.04i	−0.0691675	−	0.119802i
$789$		0			0
$790$	3325.00	−	5759.07i	0.149745	−	0.259365i
$791$	−5736.00			−0.257837
$792$		0			0
$793$	4420.00			0.197930
$794$	272.000	−	471.118i	0.0121573	−	0.0210571i
$795$		0			0
$796$	−1336.00	−	2314.02i	−0.0594890	−	0.103038i
$797$	−1840.50	−	3187.84i	−0.0817991	−	0.141680i	0.822224	−	0.569164i	$-0.192733\pi$
$797$	−1840.50	−	3187.84i	−0.0817991	−	0.141680i	−0.904023	+	0.427484i	$0.859400\pi$
$798$		0			0
$799$	−6696.00	+	11597.8i	−0.296480	+	0.513518i
$800$	−800.000			−0.0353553
$801$		0			0
$802$	−9108.00			−0.401016
$803$	−23646.0	+	40956.1i	−1.03916	+	1.79989i
$804$		0			0
$805$	−90.0000	−	155.885i	−0.00394048	−	0.00682510i
$806$	940.000	+	1628.13i	0.0410795	+	0.0711518i
$807$		0			0
$808$	528.000	−	914.523i	0.0229888	−	0.0398178i
$809$	−5142.00			−0.223465			−0.111732	−	0.993738i	$-0.535640\pi$
$809$	−5142.00			−0.223465			−0.111732	+	0.993738i	$0.535640\pi$
$810$		0			0
$811$	−18484.0			−0.800322			−0.400161	−	0.916445i	$-0.631046\pi$
$811$	−18484.0			−0.800322			−0.400161	+	0.916445i	$0.631046\pi$
$812$	−960.000	+	1662.77i	−0.0414894	+	0.0718618i
$813$		0			0
$814$	11004.0	+	19059.5i	0.473821	+	0.820681i
$815$	8365.00	+	14488.6i	0.359525	+	0.622716i
$816$		0			0
$817$	5251.00	−	9095.00i	0.224858	−	0.389466i
$818$	−2002.00			−0.0855725
$819$		0			0
$820$	−2520.00			−0.107320
$821$	−12507.0	+	21662.8i	−0.531665	+	0.920872i	0.467651	+	0.883913i	$0.345100\pi$
$821$	−12507.0	+	21662.8i	−0.531665	+	0.920872i	−0.999317	+	0.0369585i	$0.988233\pi$
$822$		0			0
$823$	16073.0	+	27839.3i	0.680765	+	1.17912i	0.974748	+	0.223309i	$0.0716858\pi$
$823$	16073.0	+	27839.3i	0.680765	+	1.17912i	−0.293983	+	0.955811i	$0.594981\pi$
$824$	−3568.00	−	6179.96i	−0.150846	−	0.261273i
$825$		0			0
$826$	−1776.00	+	3076.12i	−0.0748123	+	0.129579i
$827$	−10977.0			−0.461557			−0.230779	−	0.973006i	$-0.574127\pi$
$827$	−10977.0			−0.461557			−0.230779	+	0.973006i	$0.574127\pi$
$828$		0			0
$829$	36602.0			1.53346			0.766731	−	0.641969i	$-0.221882\pi$
$829$	36602.0			1.53346			0.766731	+	0.641969i	$0.221882\pi$
$830$	−375.000	+	649.519i	−0.0156825	+	0.0271628i
$831$		0			0
$832$	−640.000	−	1108.51i	−0.0266683	−	0.0461908i
$833$	−15205.5	−	26336.7i	−0.632460	−	1.09545i
$834$		0			0
$835$	−3727.50	+	6456.22i	−0.154486	+	0.267577i
$836$	−9912.00			−0.410064
$837$		0			0
$838$	3588.00			0.147906
$839$	−5538.00	+	9592.10i	−0.227882	+	0.394703i	−0.957180	−	0.289493i	$-0.906513\pi$
$839$	−5538.00	+	9592.10i	−0.227882	+	0.394703i	0.729298	+	0.684196i	$0.239847\pi$
$840$		0			0
$841$	4994.50	+	8650.73i	0.204785	+	0.354698i
$842$	−16129.0	−	27936.2i	−0.660145	−	1.14340i
$843$		0			0
$844$	−9202.00	+	15938.3i	−0.375291	+	0.650024i
$845$	−8985.00			−0.365791
$846$		0			0
$847$	−1732.00			−0.0702624
$848$	5928.00	−	10267.6i	0.240057	−	0.415791i
$849$		0			0
$850$	−2325.00	−	4027.02i	−0.0938198	−	0.162501i
$851$	−1179.00	−	2042.09i	−0.0474919	−	0.0822584i
$852$		0			0
$853$	−18424.0	+	31911.3i	−0.739538	+	1.28092i	0.213166	+	0.977016i	$0.431623\pi$
$853$	−18424.0	+	31911.3i	−0.739538	+	1.28092i	−0.952704	+	0.303901i	$0.901711\pi$
$854$	1768.00			0.0708428
$855$		0			0
$856$	−9120.00			−0.364153
$857$	13480.5	−	23348.9i	0.537322	−	0.930669i	−0.461725	−	0.887023i	$-0.652769\pi$
$857$	13480.5	−	23348.9i	0.537322	−	0.930669i	0.999047	−	0.0436461i	$-0.0138974\pi$
$858$		0			0
$859$	207.500	+	359.401i	0.00824192	+	0.0142754i	0.870117	−	0.492845i	$-0.164043\pi$
$859$	207.500	+	359.401i	0.00824192	+	0.0142754i	−0.861875	+	0.507121i	$0.830710\pi$
$860$	1780.00	+	3083.05i	0.0705785	+	0.122246i
$861$		0			0
$862$	−13356.0	+	23133.3i	−0.527735	+	0.914063i
$863$	−45501.0			−1.79475			−0.897377	−	0.441265i	$-0.854530\pi$
$863$	−45501.0			−1.79475			−0.897377	+	0.441265i	$0.854530\pi$
$864$		0			0
$865$	−12015.0			−0.472280
$866$	−11500.0	+	19918.6i	−0.451254	+	0.781595i
$867$		0			0
$868$	376.000	+	651.251i	0.0147031	+	0.0254665i
$869$	13965.0	+	24188.1i	0.545144	+	0.944217i
$870$		0			0
$871$	5380.00	−	9318.43i	0.209293	−	0.362506i
$872$	13880.0			0.539032
$873$		0			0
$874$	1062.00			0.0411015
$875$	250.000	−	433.013i	0.00965891	−	0.0167297i
$876$		0			0
$877$	−17521.0	−	30347.3i	−0.674620	−	1.16848i	−0.976580	−	0.215156i	$-0.930974\pi$
$877$	−17521.0	−	30347.3i	−0.674620	−	1.16848i	0.301959	−	0.953321i	$-0.402359\pi$
$878$	−11149.0	−	19310.6i	−0.428543	−	0.742258i
$879$		0			0
$880$	1680.00	−	2909.85i	0.0643554	−	0.111467i
$881$	1080.00			0.0413009			0.0206505	−	0.999787i	$-0.493426\pi$
$881$	1080.00			0.0413009			0.0206505	+	0.999787i	$0.493426\pi$
$882$		0			0
$883$	−20164.0			−0.768485			−0.384243	−	0.923232i	$-0.625537\pi$
$883$	−20164.0			−0.768485			−0.384243	+	0.923232i	$0.625537\pi$
$884$	3720.00	−	6443.23i	0.141535	−	0.245146i
$885$		0			0
$886$	3849.00	+	6666.66i	0.145948	+	0.252789i
$887$	−10033.5	−	17378.5i	−0.379811	−	0.657851i	0.611224	−	0.791458i	$-0.290677\pi$
$887$	−10033.5	−	17378.5i	−0.379811	−	0.657851i	−0.991034	+	0.133607i	$0.957344\pi$
$888$		0			0
$889$	1372.00	−	2376.37i	0.0517609	−	0.0896524i
$890$	−10860.0			−0.409020
$891$		0			0
$892$	−8632.00			−0.324014
$893$	4248.00	−	7357.75i	0.159187	−	0.275720i
$894$		0			0
$895$	−6600.00	−	11431.5i	−0.246496	−	0.426943i
$896$	−256.000	−	443.405i	−0.00954504	−	0.0165325i
$897$		0			0
$898$	18048.0	−	31260.1i	0.670679	−	1.16165i
$899$	−5640.00			−0.209238
$900$		0			0
$901$	68913.0			2.54809
$902$	5292.00	−	9166.01i	0.195348	−	0.338353i
$903$		0			0
$904$	5736.00	+	9935.04i	0.211036	+	0.365525i
$905$	−2682.50	−	4646.23i	−0.0985296	−	0.170658i
$906$		0			0
$907$	13262.0	−	22970.5i	0.485510	−	0.840928i	−0.514351	−	0.857579i	$-0.671967\pi$
$907$	13262.0	−	22970.5i	0.485510	−	0.840928i	0.999861	+	0.0166517i	$0.00530064\pi$
$908$	−12492.0			−0.456566
$909$		0			0
$910$	800.000			0.0291426
$911$	−17784.0	+	30802.8i	−0.646773	+	1.12024i	0.337116	+	0.941463i	$0.390549\pi$
$911$	−17784.0	+	30802.8i	−0.646773	+	1.12024i	−0.983889	+	0.178781i	$0.942785\pi$
$912$		0			0
$913$	−1575.00	−	2727.98i	−0.0570919	−	0.0988860i
$914$	−4264.00	−	7385.46i	−0.154311	−	0.267275i
$915$		0			0
$916$	−4054.00	+	7021.73i	−0.146231	+	0.253280i
$917$	−456.000			−0.0164214
$918$		0			0
$919$	−23704.0			−0.850841			−0.425420	−	0.904996i	$-0.639874\pi$
$919$	−23704.0			−0.850841			−0.425420	+	0.904996i	$0.639874\pi$
$920$	−180.000	+	311.769i	−0.00645046	+	0.0111725i
$921$		0			0
$922$	−10242.0	−	17739.7i	−0.365838	−	0.633649i
$923$	6900.00	+	11951.2i	0.246063	+	0.426194i
$924$		0			0
$925$	3275.00	−	5672.47i	0.116412	−	0.201632i
$926$	−6604.00			−0.234364
$927$		0			0
$928$	3840.00			0.135834
$929$	20295.0	−	35152.0i	0.716746	−	1.24144i	−0.245536	−	0.969388i	$-0.578964\pi$
$929$	20295.0	−	35152.0i	0.716746	−	1.24144i	0.962282	−	0.272054i	$-0.0877028\pi$
$930$		0			0
$931$	9646.50	+	16708.2i	0.339582	+	0.588174i
$932$	−876.000	−	1517.28i	−0.0307879	−	0.0533262i
$933$		0			0
$934$	−1923.00	+	3330.73i	−0.0673688	+	0.116686i
$935$	19530.0			0.683101
$936$		0			0
$937$	−12964.0			−0.451991			−0.225995	−	0.974128i	$-0.572563\pi$
$937$	−12964.0			−0.451991			−0.225995	+	0.974128i	$0.572563\pi$
$938$	2152.00	−	3727.37i	0.0749097	−	0.129747i
$939$		0			0
$940$	1440.00	+	2494.15i	0.0499656	+	0.0865429i
$941$	−14961.0	−	25913.2i	−0.518294	−	0.897712i	−0.999774	−	0.0212545i	$-0.993234\pi$
$941$	−14961.0	−	25913.2i	−0.518294	−	0.897712i	0.481480	−	0.876457i	$-0.340099\pi$
$942$		0			0
$943$	−567.000	+	982.073i	−0.0195801	+	0.0339138i
$944$	7104.00			0.244932
$945$		0			0
$946$	−14952.0			−0.513881
$947$	−2620.50	+	4538.84i	−0.0899206	+	0.155747i	−0.907477	−	0.420101i	$-0.861995\pi$
$947$	−2620.50	+	4538.84i	−0.0899206	+	0.155747i	0.817557	+	0.575848i	$0.195328\pi$
$948$		0			0
$949$	11260.0	+	19502.9i	0.385158	+	0.667113i
$950$	1475.00	+	2554.77i	0.0503740	+	0.0872504i
$951$		0			0
$952$	1488.00	−	2577.29i	0.0506579	−	0.0877421i
$953$	26214.0			0.891033			0.445517	−	0.895274i	$-0.353020\pi$
$953$	26214.0			0.891033			0.445517	+	0.895274i	$0.353020\pi$
$954$		0			0
$955$	−7350.00			−0.249048
$956$	12828.0	−	22218.7i	0.433982	−	0.751680i
$957$		0			0
$958$	15246.0	+	26406.8i	0.514171	+	0.890570i
$959$	−318.000	−	550.792i	−0.0107078	−	0.0185464i
$960$		0			0
$961$	13791.0	−	23886.7i	0.462925	−	0.801810i
$962$	10480.0			0.351236
$963$		0			0
$964$	13724.0			0.458527
$965$	11800.0	−	20438.2i	0.393633	−	0.681792i
$966$		0			0
$967$	−9139.00	−	15829.2i	−0.303920	−	0.526405i	0.673100	−	0.739551i	$-0.264962\pi$
$967$	−9139.00	−	15829.2i	−0.303920	−	0.526405i	−0.977020	+	0.213147i	$0.931629\pi$
$968$	1732.00	+	2999.91i	0.0575089	+	0.0996083i
$969$		0			0
$970$	7720.00	−	13371.4i	0.255540	−	0.442609i
$971$	−24942.0			−0.824333			−0.412166	−	0.911109i	$-0.635228\pi$
$971$	−24942.0			−0.824333			−0.412166	+	0.911109i	$0.635228\pi$
$972$		0			0
$973$	−9104.00			−0.299960
$974$	−8206.00	+	14213.2i	−0.269956	+	0.467578i
$975$		0			0
$976$	−1768.00	−	3062.27i	−0.0579839	−	0.100431i
$977$	5613.00	+	9722.00i	0.183803	+	0.318357i	0.943173	−	0.332303i	$-0.107826\pi$
$977$	5613.00	+	9722.00i	0.183803	+	0.318357i	−0.759369	+	0.650660i	$0.774492\pi$
$978$		0			0
$979$	22806.0	−	39501.2i	0.744518	−	1.28954i
$980$	−6540.00			−0.213176
$981$		0			0
$982$	33612.0			1.09226
$983$	11536.5	−	19981.8i	0.374321	−	0.648342i	−0.615904	−	0.787821i	$-0.711209\pi$
$983$	11536.5	−	19981.8i	0.374321	−	0.648342i	0.990225	+	0.139478i	$0.0445426\pi$
$984$		0			0
$985$	−1912.50	−	3312.55i	−0.0618653	−	0.107154i
$986$	11160.0	+	19329.7i	0.360453	+	0.624323i
$987$		0			0
$988$	−2360.00	+	4087.64i	−0.0759935	+	0.131625i
$989$	1602.00			0.0515072
$990$		0			0
$991$	22037.0			0.706386			0.353193	−	0.935551i	$-0.385096\pi$
$991$	22037.0			0.706386			0.353193	+	0.935551i	$0.385096\pi$
$992$	752.000	−	1302.50i	0.0240686	−	0.0416880i
$993$		0			0
$994$	2760.00	+	4780.46i	0.0880703	+	0.152542i
$995$	−1670.00	−	2892.52i	−0.0532086	−	0.0921600i
$996$		0			0
$997$	−9541.00	+	16525.5i	−0.303076	+	0.524943i	−0.976831	−	0.214012i	$-0.931347\pi$
$997$	−9541.00	+	16525.5i	−0.303076	+	0.524943i	0.673755	+	0.738955i	$0.264680\pi$
$998$	10850.0			0.344139
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.4.e.q.541.1		2
3.2	odd	2		810.4.e.h.541.1		2
9.2	odd	6		270.4.a.i.1.1	yes	1
9.4	even	3	inner	810.4.e.q.271.1		2
9.5	odd	6		810.4.e.h.271.1		2
9.7	even	3		270.4.a.e.1.1	✓	1
36.7	odd	6		2160.4.a.o.1.1		1
36.11	even	6		2160.4.a.e.1.1		1
45.2	even	12		1350.4.c.q.649.2		2
45.7	odd	12		1350.4.c.d.649.1		2
45.29	odd	6		1350.4.a.g.1.1		1
45.34	even	6		1350.4.a.u.1.1		1
45.38	even	12		1350.4.c.q.649.1		2
45.43	odd	12		1350.4.c.d.649.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.4.a.e.1.1	✓	1	9.7	even	3
270.4.a.i.1.1	yes	1	9.2	odd	6
810.4.e.h.271.1		2	9.5	odd	6
810.4.e.h.541.1		2	3.2	odd	2
810.4.e.q.271.1		2	9.4	even	3	inner
810.4.e.q.541.1		2	1.1	even	1	trivial
1350.4.a.g.1.1		1	45.29	odd	6
1350.4.a.u.1.1		1	45.34	even	6
1350.4.c.d.649.1		2	45.7	odd	12
1350.4.c.d.649.2		2	45.43	odd	12
1350.4.c.q.649.1		2	45.38	even	12
1350.4.c.q.649.2		2	45.2	even	12
2160.4.a.e.1.1		1	36.11	even	6
2160.4.a.o.1.1		1	36.7	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	810.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(2.00000 - 3.46410i) q^{7} -8.00000 q^{8} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(2.00000 - 3.46410i) q^{7} -8.00000 q^{8} -10.0000 q^{10} +(21.0000 - 36.3731i) q^{11} +(-10.0000 - 17.3205i) q^{13} +(-4.00000 - 6.92820i) q^{14} +(-8.00000 + 13.8564i) q^{16} -93.0000 q^{17} +59.0000 q^{19} +(-10.0000 + 17.3205i) q^{20} +(-42.0000 - 72.7461i) q^{22} +(4.50000 + 7.79423i) q^{23} +(-12.5000 + 21.6506i) q^{25} -40.0000 q^{26} -16.0000 q^{28} +(60.0000 - 103.923i) q^{29} +(-23.5000 - 40.7032i) q^{31} +(16.0000 + 27.7128i) q^{32} +(-93.0000 + 161.081i) q^{34} -20.0000 q^{35} -262.000 q^{37} +(59.0000 - 102.191i) q^{38} +(20.0000 + 34.6410i) q^{40} +(63.0000 + 109.119i) q^{41} +(89.0000 - 154.153i) q^{43} -168.000 q^{44} +18.0000 q^{46} +(72.0000 - 124.708i) q^{47} +(163.500 + 283.190i) q^{49} +(25.0000 + 43.3013i) q^{50} +(-40.0000 + 69.2820i) q^{52} -741.000 q^{53} -210.000 q^{55} +(-16.0000 + 27.7128i) q^{56} +(-120.000 - 207.846i) q^{58} +(-222.000 - 384.515i) q^{59} +(-110.500 + 191.392i) q^{61} -94.0000 q^{62} +64.0000 q^{64} +(-50.0000 + 86.6025i) q^{65} +(269.000 + 465.922i) q^{67} +(186.000 + 322.161i) q^{68} +(-20.0000 + 34.6410i) q^{70} -690.000 q^{71} -1126.00 q^{73} +(-262.000 + 453.797i) q^{74} +(-118.000 - 204.382i) q^{76} +(-84.0000 - 145.492i) q^{77} +(-332.500 + 575.907i) q^{79} +80.0000 q^{80} +252.000 q^{82} +(37.5000 - 64.9519i) q^{83} +(232.500 + 402.702i) q^{85} +(-178.000 - 308.305i) q^{86} +(-168.000 + 290.985i) q^{88} +1086.00 q^{89} -80.0000 q^{91} +(18.0000 - 31.1769i) q^{92} +(-144.000 - 249.415i) q^{94} +(-147.500 - 255.477i) q^{95} +(-772.000 + 1337.14i) q^{97} +654.000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 4 q^{4} - 5 q^{5} + 4 q^{7} - 16 q^{8}+O(q^{10}) \) 2 * q + 2 * q^2 - 4 * q^4 - 5 * q^5 + 4 * q^7 - 16 * q^8	\( 2 q + 2 q^{2} - 4 q^{4} - 5 q^{5} + 4 q^{7} - 16 q^{8} - 20 q^{10} + 42 q^{11} - 20 q^{13} - 8 q^{14} - 16 q^{16} - 186 q^{17} + 118 q^{19} - 20 q^{20} - 84 q^{22} + 9 q^{23} - 25 q^{25} - 80 q^{26} - 32 q^{28} + 120 q^{29} - 47 q^{31} + 32 q^{32} - 186 q^{34} - 40 q^{35} - 524 q^{37} + 118 q^{38} + 40 q^{40} + 126 q^{41} + 178 q^{43} - 336 q^{44} + 36 q^{46} + 144 q^{47} + 327 q^{49} + 50 q^{50} - 80 q^{52} - 1482 q^{53} - 420 q^{55} - 32 q^{56} - 240 q^{58} - 444 q^{59} - 221 q^{61} - 188 q^{62} + 128 q^{64} - 100 q^{65} + 538 q^{67} + 372 q^{68} - 40 q^{70} - 1380 q^{71} - 2252 q^{73} - 524 q^{74} - 236 q^{76} - 168 q^{77} - 665 q^{79} + 160 q^{80} + 504 q^{82} + 75 q^{83} + 465 q^{85} - 356 q^{86} - 336 q^{88} + 2172 q^{89} - 160 q^{91} + 36 q^{92} - 288 q^{94} - 295 q^{95} - 1544 q^{97} + 1308 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 - 4 * q^4 - 5 * q^5 + 4 * q^7 - 16 * q^8 - 20 * q^10 + 42 * q^11 - 20 * q^13 - 8 * q^14 - 16 * q^16 - 186 * q^17 + 118 * q^19 - 20 * q^20 - 84 * q^22 + 9 * q^23 - 25 * q^25 - 80 * q^26 - 32 * q^28 + 120 * q^29 - 47 * q^31 + 32 * q^32 - 186 * q^34 - 40 * q^35 - 524 * q^37 + 118 * q^38 + 40 * q^40 + 126 * q^41 + 178 * q^43 - 336 * q^44 + 36 * q^46 + 144 * q^47 + 327 * q^49 + 50 * q^50 - 80 * q^52 - 1482 * q^53 - 420 * q^55 - 32 * q^56 - 240 * q^58 - 444 * q^59 - 221 * q^61 - 188 * q^62 + 128 * q^64 - 100 * q^65 + 538 * q^67 + 372 * q^68 - 40 * q^70 - 1380 * q^71 - 2252 * q^73 - 524 * q^74 - 236 * q^76 - 168 * q^77 - 665 * q^79 + 160 * q^80 + 504 * q^82 + 75 * q^83 + 465 * q^85 - 356 * q^86 - 336 * q^88 + 2172 * q^89 - 160 * q^91 + 36 * q^92 - 288 * q^94 - 295 * q^95 - 1544 * q^97 + 1308 * q^98

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