LMFDB - Embedded newform 810.4.e.k.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.k.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(2.50000 + 4.33013i) q^{5} +(11.0000 - 19.0526i) q^{7} +8.00000 q^{8} -10.0000 q^{10} +(6.00000 - 10.3923i) q^{11} +(-19.0000 - 32.9090i) q^{13} +(22.0000 + 38.1051i) q^{14} +(-8.00000 + 13.8564i) q^{16} -105.000 q^{17} -157.000 q^{19} +(10.0000 - 17.3205i) q^{20} +(12.0000 + 20.7846i) q^{22} +(58.5000 + 101.325i) q^{23} +(-12.5000 + 21.6506i) q^{25} +76.0000 q^{26} -88.0000 q^{28} +(-33.0000 + 57.1577i) q^{29} +(12.5000 + 21.6506i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(105.000 - 181.865i) q^{34} +110.000 q^{35} +314.000 q^{37} +(157.000 - 271.932i) q^{38} +(20.0000 + 34.6410i) q^{40} +(252.000 + 436.477i) q^{41} +(-190.000 + 329.090i) q^{43} -48.0000 q^{44} -234.000 q^{46} +(126.000 - 218.238i) q^{47} +(-70.5000 - 122.110i) q^{49} +(-25.0000 - 43.3013i) q^{50} +(-76.0000 + 131.636i) q^{52} +3.00000 q^{53} +60.0000 q^{55} +(88.0000 - 152.420i) q^{56} +(-66.0000 - 114.315i) q^{58} +(159.000 + 275.396i) q^{59} +(-146.500 + 253.745i) q^{61} -50.0000 q^{62} +64.0000 q^{64} +(95.0000 - 164.545i) q^{65} +(161.000 + 278.860i) q^{67} +(210.000 + 363.731i) q^{68} +(-110.000 + 190.526i) q^{70} -120.000 q^{71} +44.0000 q^{73} +(-314.000 + 543.864i) q^{74} +(314.000 + 543.864i) q^{76} +(-132.000 - 228.631i) q^{77} +(-458.500 + 794.145i) q^{79} -80.0000 q^{80} -1008.00 q^{82} +(-154.500 + 267.602i) q^{83} +(-262.500 - 454.663i) q^{85} +(-380.000 - 658.179i) q^{86} +(48.0000 - 83.1384i) q^{88} +1272.00 q^{89} -836.000 q^{91} +(234.000 - 405.300i) q^{92} +(252.000 + 436.477i) q^{94} +(-392.500 - 679.830i) q^{95} +(-664.000 + 1150.08i) q^{97} +282.000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 4 q^{4} + 5 q^{5} + 22 q^{7} + 16 q^{8} - 20 q^{10} + 12 q^{11} - 38 q^{13} + 44 q^{14} - 16 q^{16} - 210 q^{17} - 314 q^{19} + 20 q^{20} + 24 q^{22} + 117 q^{23} - 25 q^{25} + 152 q^{26}+ \cdots + 564 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 - 4 * q^4 + 5 * q^5 + 22 * q^7 + 16 * q^8 - 20 * q^10 + 12 * q^11 - 38 * q^13 + 44 * q^14 - 16 * q^16 - 210 * q^17 - 314 * q^19 + 20 * q^20 + 24 * q^22 + 117 * q^23 - 25 * q^25 + 152 * q^26 - 176 * q^28 - 66 * q^29 + 25 * q^31 - 32 * q^32 + 210 * q^34 + 220 * q^35 + 628 * q^37 + 314 * q^38 + 40 * q^40 + 504 * q^41 - 380 * q^43 - 96 * q^44 - 468 * q^46 + 252 * q^47 - 141 * q^49 - 50 * q^50 - 152 * q^52 + 6 * q^53 + 120 * q^55 + 176 * q^56 - 132 * q^58 + 318 * q^59 - 293 * q^61 - 100 * q^62 + 128 * q^64 + 190 * q^65 + 322 * q^67 + 420 * q^68 - 220 * q^70 - 240 * q^71 + 88 * q^73 - 628 * q^74 + 628 * q^76 - 264 * q^77 - 917 * q^79 - 160 * q^80 - 2016 * q^82 - 309 * q^83 - 525 * q^85 - 760 * q^86 + 96 * q^88 + 2544 * q^89 - 1672 * q^91 + 468 * q^92 + 504 * q^94 - 785 * q^95 - 1328 * q^97 + 564 * q^98

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
$7$	11.0000	−	19.0526i	0.593944	−	1.02874i	−0.399751	−	0.916624i	$-0.630903\pi$
$7$	11.0000	−	19.0526i	0.593944	−	1.02874i	0.993695	−	0.112118i	$-0.0357633\pi$
$8$	8.00000			0.353553
$9$		0			0
$10$	−10.0000			−0.316228
$11$	6.00000	−	10.3923i	0.164461	−	0.284854i	−0.772003	−	0.635619i	$-0.780745\pi$
$11$	6.00000	−	10.3923i	0.164461	−	0.284854i	0.936464	+	0.350765i	$0.114078\pi$
$12$		0			0
$13$	−19.0000	−	32.9090i	−0.405358	−	0.702100i	0.589005	−	0.808129i	$-0.299520\pi$
$13$	−19.0000	−	32.9090i	−0.405358	−	0.702100i	−0.994363	+	0.106029i	$0.966186\pi$
$14$	22.0000	+	38.1051i	0.419982	+	0.727430i
$15$		0			0
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−105.000			−1.49801			−0.749007	−	0.662562i	$-0.769469\pi$
$17$	−105.000			−1.49801			−0.749007	+	0.662562i	$0.769469\pi$
$18$		0			0
$19$	−157.000			−1.89570			−0.947849	−	0.318719i	$-0.896747\pi$
$19$	−157.000			−1.89570			−0.947849	+	0.318719i	$0.896747\pi$
$20$	10.0000	−	17.3205i	0.111803	−	0.193649i
$21$		0			0
$22$	12.0000	+	20.7846i	0.116291	+	0.201422i
$23$	58.5000	+	101.325i	0.530352	+	0.918596i	0.999373	+	0.0354094i	$0.0112735\pi$
$23$	58.5000	+	101.325i	0.530352	+	0.918596i	−0.469021	+	0.883187i	$0.655393\pi$
$24$		0			0
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	76.0000			0.573263
$27$		0			0
$28$	−88.0000			−0.593944
$29$	−33.0000	+	57.1577i	−0.211308	+	0.365997i	−0.952124	−	0.305711i	$-0.901106\pi$
$29$	−33.0000	+	57.1577i	−0.211308	+	0.365997i	0.740816	+	0.671708i	$0.234439\pi$
$30$		0			0
$31$	12.5000	+	21.6506i	0.0724215	+	0.125438i	0.899962	−	0.435968i	$-0.143594\pi$
$31$	12.5000	+	21.6506i	0.0724215	+	0.125438i	−0.827541	+	0.561406i	$0.810261\pi$
$32$	−16.0000	−	27.7128i	−0.0883883	−	0.153093i
$33$		0			0
$34$	105.000	−	181.865i	0.529628	−	0.917343i
$35$	110.000			0.531240
$36$		0			0
$37$	314.000			1.39517			0.697585	−	0.716502i	$-0.254258\pi$
$37$	314.000			1.39517			0.697585	+	0.716502i	$0.254258\pi$
$38$	157.000	−	271.932i	0.670231	−	1.16087i
$39$		0			0
$40$	20.0000	+	34.6410i	0.0790569	+	0.136931i
$41$	252.000	+	436.477i	0.959897	+	1.66259i	0.722741	+	0.691119i	$0.242882\pi$
$41$	252.000	+	436.477i	0.959897	+	1.66259i	0.237157	+	0.971471i	$0.423785\pi$
$42$		0			0
$43$	−190.000	+	329.090i	−0.673831	+	1.16711i	0.302978	+	0.952997i	$0.402019\pi$
$43$	−190.000	+	329.090i	−0.673831	+	1.16711i	−0.976809	+	0.214112i	$0.931314\pi$
$44$	−48.0000			−0.164461
$45$		0			0
$46$	−234.000			−0.750031
$47$	126.000	−	218.238i	0.391042	−	0.677305i	−0.601545	−	0.798839i	$-0.705448\pi$
$47$	126.000	−	218.238i	0.391042	−	0.677305i	0.992587	+	0.121534i	$0.0387813\pi$
$48$		0			0
$49$	−70.5000	−	122.110i	−0.205539	−	0.356005i
$50$	−25.0000	−	43.3013i	−0.0707107	−	0.122474i
$51$		0			0
$52$	−76.0000	+	131.636i	−0.202679	+	0.351050i
$53$	3.00000			0.00777513			0.00388756	−	0.999992i	$-0.498763\pi$
$53$	3.00000			0.00777513			0.00388756	+	0.999992i	$0.498763\pi$
$54$		0			0
$55$	60.0000			0.147098
$56$	88.0000	−	152.420i	0.209991	−	0.363715i
$57$		0			0
$58$	−66.0000	−	114.315i	−0.149418	−	0.258799i
$59$	159.000	+	275.396i	0.350848	+	0.607687i	0.986398	−	0.164373i	$-0.0525600\pi$
$59$	159.000	+	275.396i	0.350848	+	0.607687i	−0.635550	+	0.772060i	$0.719227\pi$
$60$		0			0
$61$	−146.500	+	253.745i	−0.307498	+	0.532603i	−0.977814	−	0.209473i	$-0.932825\pi$
$61$	−146.500	+	253.745i	−0.307498	+	0.532603i	0.670316	+	0.742076i	$0.266159\pi$
$62$	−50.0000			−0.102419
$63$		0			0
$64$	64.0000			0.125000
$65$	95.0000	−	164.545i	0.181282	−	0.313989i
$66$		0			0
$67$	161.000	+	278.860i	0.293571	+	0.508480i	0.974652	−	0.223728i	$-0.0718228\pi$
$67$	161.000	+	278.860i	0.293571	+	0.508480i	−0.681080	+	0.732209i	$0.738490\pi$
$68$	210.000	+	363.731i	0.374504	+	0.648659i
$69$		0			0
$70$	−110.000	+	190.526i	−0.187822	+	0.325317i
$71$	−120.000			−0.200583			−0.100291	−	0.994958i	$-0.531978\pi$
$71$	−120.000			−0.200583			−0.100291	+	0.994958i	$0.531978\pi$
$72$		0			0
$73$	44.0000			0.0705453			0.0352727	−	0.999378i	$-0.488770\pi$
$73$	44.0000			0.0705453			0.0352727	+	0.999378i	$0.488770\pi$
$74$	−314.000	+	543.864i	−0.493267	+	0.854364i
$75$		0			0
$76$	314.000	+	543.864i	0.473925	+	0.820862i
$77$	−132.000	−	228.631i	−0.195361	−	0.338375i
$78$		0			0
$79$	−458.500	+	794.145i	−0.652978	+	1.13099i	0.329418	+	0.944184i	$0.393147\pi$
$79$	−458.500	+	794.145i	−0.652978	+	1.13099i	−0.982397	+	0.186807i	$0.940186\pi$
$80$	−80.0000			−0.111803
$81$		0			0
$82$	−1008.00			−1.35750
$83$	−154.500	+	267.602i	−0.204320	+	0.353893i	−0.949916	−	0.312506i	$-0.898832\pi$
$83$	−154.500	+	267.602i	−0.204320	+	0.353893i	0.745596	+	0.666399i	$0.232165\pi$
$84$		0			0
$85$	−262.500	−	454.663i	−0.334966	−	0.580178i
$86$	−380.000	−	658.179i	−0.476470	−	0.825271i
$87$		0			0
$88$	48.0000	−	83.1384i	0.0581456	−	0.100711i
$89$	1272.00			1.51496			0.757482	−	0.652856i	$-0.226430\pi$
$89$	1272.00			1.51496			0.757482	+	0.652856i	$0.226430\pi$
$90$		0			0
$91$	−836.000			−0.963040
$92$	234.000	−	405.300i	0.265176	−	0.459298i
$93$		0			0
$94$	252.000	+	436.477i	0.276509	+	0.478927i
$95$	−392.500	−	679.830i	−0.423891	−	0.734201i
$96$		0			0
$97$	−664.000	+	1150.08i	−0.695041	+	1.20385i	0.275126	+	0.961408i	$0.411281\pi$
$97$	−664.000	+	1150.08i	−0.695041	+	1.20385i	−0.970167	+	0.242438i	$0.922053\pi$
$98$	282.000			0.290677
$99$		0			0
$100$	100.000			0.100000
$101$	246.000	−	426.084i	0.242356	−	0.419772i	−0.719029	−	0.694980i	$-0.755413\pi$
$101$	246.000	−	426.084i	0.242356	−	0.419772i	0.961385	+	0.275208i	$0.0887466\pi$
$102$		0			0
$103$	−274.000	−	474.582i	−0.262117	−	0.453999i	0.704687	−	0.709518i	$-0.251087\pi$
$103$	−274.000	−	474.582i	−0.262117	−	0.453999i	−0.966804	+	0.255518i	$0.917754\pi$
$104$	−152.000	−	263.272i	−0.143316	−	0.248230i
$105$		0			0
$106$	−3.00000	+	5.19615i	−0.00274892	+	0.00476127i
$107$	732.000			0.661356			0.330678	−	0.943744i	$-0.392723\pi$
$107$	732.000			0.661356			0.330678	+	0.943744i	$0.392723\pi$
$108$		0			0
$109$	−907.000			−0.797017			−0.398508	−	0.917165i	$-0.630472\pi$
$109$	−907.000			−0.797017			−0.398508	+	0.917165i	$0.630472\pi$
$110$	−60.0000	+	103.923i	−0.0520071	+	0.0900789i
$111$		0			0
$112$	176.000	+	304.841i	0.148486	+	0.257185i
$113$	771.000	+	1335.41i	0.641855	+	1.11172i	0.985018	+	0.172449i	$0.0551681\pi$
$113$	771.000	+	1335.41i	0.641855	+	1.11172i	−0.343164	+	0.939276i	$0.611499\pi$
$114$		0			0
$115$	−292.500	+	506.625i	−0.237181	+	0.410809i
$116$	264.000			0.211308
$117$		0			0
$118$	−636.000			−0.496174
$119$	−1155.00	+	2000.52i	−0.889737	+	1.54107i
$120$		0			0
$121$	593.500	+	1027.97i	0.445905	+	0.772331i
$122$	−293.000	−	507.491i	−0.217434	−	0.376607i
$123$		0			0
$124$	50.0000	−	86.6025i	0.0362107	−	0.0627189i
$125$	−125.000			−0.0894427
$126$		0			0
$127$	−2554.00			−1.78449			−0.892247	−	0.451547i	$-0.850872\pi$
$127$	−2554.00			−1.78449			−0.892247	+	0.451547i	$0.850872\pi$
$128$	−64.0000	+	110.851i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	190.000	+	329.090i	0.128185	+	0.222024i
$131$	75.0000	+	129.904i	0.0500212	+	0.0866393i	0.889952	−	0.456054i	$-0.150738\pi$
$131$	75.0000	+	129.904i	0.0500212	+	0.0866393i	−0.839931	+	0.542694i	$0.817404\pi$
$132$		0			0
$133$	−1727.00	+	2991.25i	−1.12594	+	1.95018i
$134$	−644.000			−0.415173
$135$		0			0
$136$	−840.000			−0.529628
$137$	−826.500	+	1431.54i	−0.515421	+	0.892735i	0.484419	+	0.874836i	$0.339031\pi$
$137$	−826.500	+	1431.54i	−0.515421	+	0.892735i	−0.999840	+	0.0178990i	$0.994302\pi$
$138$		0			0
$139$	−562.000	−	973.413i	−0.342937	−	0.593984i	0.642040	−	0.766671i	$-0.278088\pi$
$139$	−562.000	−	973.413i	−0.342937	−	0.593984i	−0.984977	+	0.172687i	$0.944755\pi$
$140$	−220.000	−	381.051i	−0.132810	−	0.230034i
$141$		0			0
$142$	120.000	−	207.846i	0.0709167	−	0.122831i
$143$	−456.000			−0.266662
$144$		0			0
$145$	−330.000			−0.189000
$146$	−44.0000	+	76.2102i	−0.0249415	+	0.0432000i
$147$		0			0
$148$	−628.000	−	1087.73i	−0.348792	−	0.604126i
$149$	−804.000	−	1392.57i	−0.442055	−	0.765662i	0.555787	−	0.831325i	$-0.312417\pi$
$149$	−804.000	−	1392.57i	−0.442055	−	0.765662i	−0.997842	+	0.0656627i	$0.979084\pi$
$150$		0			0
$151$	1244.00	−	2154.67i	0.670432	−	1.16122i	−0.307349	−	0.951597i	$-0.599442\pi$
$151$	1244.00	−	2154.67i	0.670432	−	1.16122i	0.977782	−	0.209626i	$-0.0672247\pi$
$152$	−1256.00			−0.670231
$153$		0			0
$154$	528.000			0.276282
$155$	−62.5000	+	108.253i	−0.0323879	+	0.0560974i
$156$		0			0
$157$	1484.00	+	2570.36i	0.754370	+	1.30661i	0.945687	+	0.325079i	$0.105391\pi$
$157$	1484.00	+	2570.36i	0.754370	+	1.30661i	−0.191317	+	0.981528i	$0.561276\pi$
$158$	−917.000	−	1588.29i	−0.461725	−	0.799732i
$159$		0			0
$160$	80.0000	−	138.564i	0.0395285	−	0.0684653i
$161$	2574.00			1.26000
$162$		0			0
$163$	3170.00			1.52327			0.761637	−	0.648004i	$-0.224396\pi$
$163$	3170.00			1.52327			0.761637	+	0.648004i	$0.224396\pi$
$164$	1008.00	−	1745.91i	0.479949	−	0.831295i
$165$		0			0
$166$	−309.000	−	535.204i	−0.144476	−	0.250240i
$167$	−163.500	−	283.190i	−0.0757605	−	0.131221i	0.825656	−	0.564174i	$-0.190805\pi$
$167$	−163.500	−	283.190i	−0.0757605	−	0.131221i	−0.901417	+	0.432952i	$0.857472\pi$
$168$		0			0
$169$	376.500	−	652.117i	0.171370	−	0.296822i
$170$	1050.00			0.473714
$171$		0			0
$172$	1520.00			0.673831
$173$	−652.500	+	1130.16i	−0.286755	+	0.496675i	−0.973033	−	0.230665i	$-0.925910\pi$
$173$	−652.500	+	1130.16i	−0.286755	+	0.496675i	0.686278	+	0.727339i	$0.259243\pi$
$174$		0			0
$175$	275.000	+	476.314i	0.118789	+	0.205748i
$176$	96.0000	+	166.277i	0.0411152	+	0.0712136i
$177$		0			0
$178$	−1272.00	+	2203.17i	−0.535620	+	0.927722i
$179$	−4044.00			−1.68862			−0.844309	−	0.535856i	$-0.819989\pi$
$179$	−4044.00			−1.68862			−0.844309	+	0.535856i	$0.819989\pi$
$180$		0			0
$181$	−1051.00			−0.431603			−0.215802	−	0.976437i	$-0.569236\pi$
$181$	−1051.00			−0.431603			−0.215802	+	0.976437i	$0.569236\pi$
$182$	836.000	−	1447.99i	0.340486	−	0.589739i
$183$		0			0
$184$	468.000	+	810.600i	0.187508	+	0.324773i
$185$	785.000	+	1359.66i	0.311969	+	0.540347i
$186$		0			0
$187$	−630.000	+	1091.19i	−0.246365	+	0.426716i
$188$	−1008.00			−0.391042
$189$		0			0
$190$	1570.00			0.599472
$191$	1299.00	−	2249.93i	0.492106	−	0.852353i	−0.507852	−	0.861444i	$-0.669560\pi$
$191$	1299.00	−	2249.93i	0.492106	−	0.852353i	0.999959	+	0.00909077i	$0.00289372\pi$
$192$		0			0
$193$	−2185.00	−	3784.53i	−0.814921	−	1.41148i	−0.909385	−	0.415956i	$-0.863447\pi$
$193$	−2185.00	−	3784.53i	−0.814921	−	1.41148i	0.0944637	−	0.995528i	$-0.469886\pi$
$194$	−1328.00	−	2300.16i	−0.491468	−	0.851248i
$195$		0			0
$196$	−282.000	+	488.438i	−0.102770	+	0.178002i
$197$	−2943.00			−1.06437			−0.532183	−	0.846629i	$-0.678628\pi$
$197$	−2943.00			−1.06437			−0.532183	+	0.846629i	$0.678628\pi$
$198$		0			0
$199$	−4768.00			−1.69847			−0.849233	−	0.528019i	$-0.822935\pi$
$199$	−4768.00			−1.69847			−0.849233	+	0.528019i	$0.822935\pi$
$200$	−100.000	+	173.205i	−0.0353553	+	0.0612372i
$201$		0			0
$202$	492.000	+	852.169i	0.171371	+	0.296824i
$203$	726.000	+	1257.47i	0.251011	+	0.434764i
$204$		0			0
$205$	−1260.00	+	2182.38i	−0.429279	+	0.743533i
$206$	1096.00			0.370689
$207$		0			0
$208$	608.000			0.202679
$209$	−942.000	+	1631.59i	−0.311768	+	0.539998i
$210$		0			0
$211$	633.500	+	1097.25i	0.206692	+	0.358000i	0.950670	−	0.310203i	$-0.100397\pi$
$211$	633.500	+	1097.25i	0.206692	+	0.358000i	−0.743979	+	0.668203i	$0.767064\pi$
$212$	−6.00000	−	10.3923i	−0.00194378	−	0.00336673i
$213$		0			0
$214$	−732.000	+	1267.86i	−0.233825	+	0.404996i
$215$	−1900.00			−0.602693
$216$		0			0
$217$	550.000			0.172057
$218$	907.000	−	1570.97i	0.281788	−	0.488071i
$219$		0			0
$220$	−120.000	−	207.846i	−0.0367745	−	0.0636954i
$221$	1995.00	+	3455.44i	0.607232	+	1.05176i
$222$		0			0
$223$	1493.00	−	2585.95i	0.448335	−	0.776539i	−0.549943	−	0.835202i	$-0.685351\pi$
$223$	1493.00	−	2585.95i	0.448335	−	0.776539i	0.998278	+	0.0586635i	$0.0186839\pi$
$224$	−704.000			−0.209991
$225$		0			0
$226$	−3084.00			−0.907720
$227$	−2704.50	+	4684.33i	−0.790766	+	1.36965i	0.134727	+	0.990883i	$0.456984\pi$
$227$	−2704.50	+	4684.33i	−0.790766	+	1.36965i	−0.925493	+	0.378765i	$0.876349\pi$
$228$		0			0
$229$	−2165.50	−	3750.76i	−0.624892	−	1.08234i	−0.988562	−	0.150817i	$-0.951810\pi$
$229$	−2165.50	−	3750.76i	−0.624892	−	1.08234i	0.363670	−	0.931528i	$-0.381524\pi$
$230$	−585.000	−	1013.25i	−0.167712	−	0.290486i
$231$		0			0
$232$	−264.000	+	457.261i	−0.0747088	+	0.129399i
$233$	2586.00			0.727101			0.363550	−	0.931575i	$-0.381564\pi$
$233$	2586.00			0.727101			0.363550	+	0.931575i	$0.381564\pi$
$234$		0			0
$235$	1260.00			0.349759
$236$	636.000	−	1101.58i	0.175424	−	0.303843i
$237$		0			0
$238$	−2310.00	−	4001.04i	−0.629139	−	1.08970i
$239$	−255.000	−	441.673i	−0.0690150	−	0.119537i	0.829453	−	0.558577i	$-0.188652\pi$
$239$	−255.000	−	441.673i	−0.0690150	−	0.119537i	−0.898468	+	0.439039i	$0.855319\pi$
$240$		0			0
$241$	102.500	−	177.535i	0.0273967	−	0.0474525i	−0.852002	−	0.523539i	$-0.824612\pi$
$241$	102.500	−	177.535i	0.0273967	−	0.0474525i	0.879399	+	0.476086i	$0.157945\pi$
$242$	−2374.00			−0.630605
$243$		0			0
$244$	1172.00			0.307498
$245$	352.500	−	610.548i	0.0919200	−	0.159210i
$246$		0			0
$247$	2983.00	+	5166.71i	0.768436	+	1.33097i
$248$	100.000	+	173.205i	0.0256049	+	0.0443489i
$249$		0			0
$250$	125.000	−	216.506i	0.0316228	−	0.0547723i
$251$	−4680.00			−1.17689			−0.588444	−	0.808538i	$-0.700259\pi$
$251$	−4680.00			−1.17689			−0.588444	+	0.808538i	$0.700259\pi$
$252$		0			0
$253$	1404.00			0.348888
$254$	2554.00	−	4423.66i	0.630914	−	1.09278i
$255$		0			0
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	3079.50	+	5333.85i	0.747447	+	1.29462i	0.949043	+	0.315148i	$0.102054\pi$
$257$	3079.50	+	5333.85i	0.747447	+	1.29462i	−0.201595	+	0.979469i	$0.564613\pi$
$258$		0			0
$259$	3454.00	−	5982.50i	0.828653	−	1.43527i
$260$	−760.000			−0.181282
$261$		0			0
$262$	−300.000			−0.0707407
$263$	3120.00	−	5404.00i	0.731511	−	1.26701i	−0.224726	−	0.974422i	$-0.572149\pi$
$263$	3120.00	−	5404.00i	0.731511	−	1.26701i	0.956237	−	0.292593i	$-0.0945180\pi$
$264$		0			0
$265$	7.50000	+	12.9904i	0.00173857	+	0.00301129i
$266$	−3454.00	−	5982.50i	−0.796159	−	1.37899i
$267$		0			0
$268$	644.000	−	1115.44i	0.146786	−	0.254240i
$269$	−7758.00			−1.75841			−0.879207	−	0.476439i	$-0.841927\pi$
$269$	−7758.00			−1.75841			−0.879207	+	0.476439i	$0.841927\pi$
$270$		0			0
$271$	−7345.00			−1.64641			−0.823205	−	0.567745i	$-0.807816\pi$
$271$	−7345.00			−1.64641			−0.823205	+	0.567745i	$0.807816\pi$
$272$	840.000	−	1454.92i	0.187252	−	0.324330i
$273$		0			0
$274$	−1653.00	−	2863.08i	−0.364458	−	0.631259i
$275$	150.000	+	259.808i	0.0328921	+	0.0569709i
$276$		0			0
$277$	1502.00	−	2601.54i	0.325799	−	0.564301i	−0.655874	−	0.754870i	$-0.727700\pi$
$277$	1502.00	−	2601.54i	0.325799	−	0.564301i	0.981674	+	0.190569i	$0.0610333\pi$
$278$	2248.00			0.484986
$279$		0			0
$280$	880.000			0.187822
$281$	−1023.00	+	1771.89i	−0.217178	+	0.376164i	−0.953944	−	0.299984i	$-0.903019\pi$
$281$	−1023.00	+	1771.89i	−0.217178	+	0.376164i	0.736766	+	0.676148i	$0.236352\pi$
$282$		0			0
$283$	2744.00	+	4752.75i	0.576374	+	0.998309i	0.995891	+	0.0905616i	$0.0288662\pi$
$283$	2744.00	+	4752.75i	0.576374	+	0.998309i	−0.419517	+	0.907748i	$0.637800\pi$
$284$	240.000	+	415.692i	0.0501457	+	0.0868549i
$285$		0			0
$286$	456.000	−	789.815i	0.0942792	−	0.163296i
$287$	11088.0			2.28050
$288$		0			0
$289$	6112.00			1.24405
$290$	330.000	−	571.577i	0.0668216	−	0.115738i
$291$		0			0
$292$	−88.0000	−	152.420i	−0.0176363	−	0.0305470i
$293$	−166.500	−	288.386i	−0.0331981	−	0.0575007i	0.848949	−	0.528475i	$-0.177236\pi$
$293$	−166.500	−	288.386i	−0.0331981	−	0.0575007i	−0.882147	+	0.470974i	$0.843903\pi$
$294$		0			0
$295$	−795.000	+	1376.98i	−0.156904	+	0.271766i
$296$	2512.00			0.493267
$297$		0			0
$298$	3216.00			0.625161
$299$	2223.00	−	3850.35i	0.429965	−	0.744720i
$300$		0			0
$301$	4180.00	+	7239.97i	0.800436	+	1.38640i
$302$	2488.00	+	4309.34i	0.474067	+	0.821109i
$303$		0			0
$304$	1256.00	−	2175.46i	0.236962	−	0.410431i
$305$	−1465.00			−0.275035
$306$		0			0
$307$	2918.00			0.542472			0.271236	−	0.962513i	$-0.412568\pi$
$307$	2918.00			0.542472			0.271236	+	0.962513i	$0.412568\pi$
$308$	−528.000	+	914.523i	−0.0976805	+	0.169188i
$309$		0			0
$310$	−125.000	−	216.506i	−0.0229017	−	0.0396669i
$311$	2877.00	+	4983.11i	0.524565	+	0.908573i	0.999591	+	0.0286014i	$0.00910534\pi$
$311$	2877.00	+	4983.11i	0.524565	+	0.908573i	−0.475026	+	0.879972i	$0.657561\pi$
$312$		0			0
$313$	−1684.00	+	2916.77i	−0.304106	+	0.526728i	−0.977062	−	0.212955i	$-0.931691\pi$
$313$	−1684.00	+	2916.77i	−0.304106	+	0.526728i	0.672956	+	0.739683i	$0.265025\pi$
$314$	−5936.00			−1.06684
$315$		0			0
$316$	3668.00			0.652978
$317$	−1435.50	+	2486.36i	−0.254340	+	0.440529i	−0.964716	−	0.263293i	$-0.915191\pi$
$317$	−1435.50	+	2486.36i	−0.254340	+	0.440529i	0.710376	+	0.703822i	$0.248525\pi$
$318$		0			0
$319$	396.000	+	685.892i	0.0695039	+	0.120384i
$320$	160.000	+	277.128i	0.0279508	+	0.0484123i
$321$		0			0
$322$	−2574.00	+	4458.30i	−0.445476	+	0.771588i
$323$	16485.0			2.83978
$324$		0			0
$325$	950.000			0.162143
$326$	−3170.00	+	5490.60i	−0.538558	+	0.932811i
$327$		0			0
$328$	2016.00	+	3491.81i	0.339375	+	0.587815i
$329$	−2772.00	−	4801.24i	−0.464515	−	0.804563i
$330$		0			0
$331$	5270.00	−	9127.91i	0.875122	−	1.51576i	0.0184894	−	0.999829i	$-0.494114\pi$
$331$	5270.00	−	9127.91i	0.875122	−	1.51576i	0.856633	−	0.515927i	$-0.172552\pi$
$332$	1236.00			0.204320
$333$		0			0
$334$	654.000			0.107142
$335$	−805.000	+	1394.30i	−0.131289	+	0.227399i
$336$		0			0
$337$	−2503.00	−	4335.32i	−0.404591	−	0.700772i	0.589683	−	0.807635i	$-0.299253\pi$
$337$	−2503.00	−	4335.32i	−0.404591	−	0.700772i	−0.994274	+	0.106863i	$0.965919\pi$
$338$	753.000	+	1304.23i	0.121177	+	0.209885i
$339$		0			0
$340$	−1050.00	+	1818.65i	−0.167483	+	0.290089i
$341$	300.000			0.0476420
$342$		0			0
$343$	4444.00			0.699573
$344$	−1520.00	+	2632.72i	−0.238235	+	0.412635i
$345$		0			0
$346$	−1305.00	−	2260.33i	−0.202767	−	0.351202i
$347$	18.0000	+	31.1769i	0.00278470	+	0.00482324i	0.867414	−	0.497586i	$-0.165780\pi$
$347$	18.0000	+	31.1769i	0.00278470	+	0.00482324i	−0.864630	+	0.502410i	$0.832447\pi$
$348$		0			0
$349$	3357.50	−	5815.36i	0.514965	−	0.891946i	−0.484884	−	0.874578i	$-0.661138\pi$
$349$	3357.50	−	5815.36i	0.514965	−	0.891946i	0.999849	−	0.0173674i	$-0.00552849\pi$
$350$	−1100.00			−0.167993
$351$		0			0
$352$	−384.000			−0.0581456
$353$	−6411.00	+	11104.2i	−0.966638	+	1.67427i	−0.261488	+	0.965207i	$0.584213\pi$
$353$	−6411.00	+	11104.2i	−0.966638	+	1.67427i	−0.705149	+	0.709059i	$0.749120\pi$
$354$		0			0
$355$	−300.000	−	519.615i	−0.0448517	−	0.0776854i
$356$	−2544.00	−	4406.34i	−0.378741	−	0.655998i
$357$		0			0
$358$	4044.00	−	7004.41i	0.597017	−	1.03406i
$359$	5478.00			0.805342			0.402671	−	0.915345i	$-0.368082\pi$
$359$	5478.00			0.805342			0.402671	+	0.915345i	$0.368082\pi$
$360$		0			0
$361$	17790.0			2.59367
$362$	1051.00	−	1820.39i	0.152595	−	0.264302i
$363$		0			0
$364$	1672.00	+	2895.99i	0.240760	+	0.417008i
$365$	110.000	+	190.526i	0.0157744	+	0.0273221i
$366$		0			0
$367$	1223.00	−	2118.30i	0.173951	−	0.301292i	−0.765847	−	0.643023i	$-0.777680\pi$
$367$	1223.00	−	2118.30i	0.173951	−	0.301292i	0.939798	+	0.341731i	$0.111013\pi$
$368$	−1872.00			−0.265176
$369$		0			0
$370$	−3140.00			−0.441191
$371$	33.0000	−	57.1577i	0.00461799	−	0.00799859i
$372$		0			0
$373$	−5848.00	−	10129.0i	−0.811791	−	1.40606i	−0.911610	−	0.411057i	$-0.865160\pi$
$373$	−5848.00	−	10129.0i	−0.811791	−	1.40606i	0.0998188	−	0.995006i	$-0.468174\pi$
$374$	−1260.00	−	2182.38i	−0.174206	−	0.301734i
$375$		0			0
$376$	1008.00	−	1745.91i	0.138254	−	0.239464i
$377$	2508.00			0.342622
$378$		0			0
$379$	−2095.00			−0.283939			−0.141970	−	0.989871i	$-0.545344\pi$
$379$	−2095.00			−0.283939			−0.141970	+	0.989871i	$0.545344\pi$
$380$	−1570.00	+	2719.32i	−0.211946	+	0.367100i
$381$		0			0
$382$	2598.00	+	4499.87i	0.347972	+	0.602705i
$383$	5656.50	+	9797.35i	0.754657	+	1.30710i	0.945545	+	0.325492i	$0.105530\pi$
$383$	5656.50	+	9797.35i	0.754657	+	1.30710i	−0.190888	+	0.981612i	$0.561137\pi$
$384$		0			0
$385$	660.000	−	1143.15i	0.0873681	−	0.151326i
$386$	8740.00			1.15247
$387$		0			0
$388$	5312.00			0.695041
$389$	−1062.00	+	1839.44i	−0.138420	+	0.239751i	−0.926899	−	0.375311i	$-0.877536\pi$
$389$	−1062.00	+	1839.44i	−0.138420	+	0.239751i	0.788478	+	0.615062i	$0.210869\pi$
$390$		0			0
$391$	−6142.50	−	10639.1i	−0.794475	−	1.37607i
$392$	−564.000	−	976.877i	−0.0726691	−	0.125867i
$393$		0			0
$394$	2943.00	−	5097.43i	0.376310	−	0.651788i
$395$	−4585.00			−0.584041
$396$		0			0
$397$	6410.00			0.810349			0.405175	−	0.914239i	$-0.367211\pi$
$397$	6410.00			0.810349			0.405175	+	0.914239i	$0.367211\pi$
$398$	4768.00	−	8258.42i	0.600498	−	1.04009i
$399$		0			0
$400$	−200.000	−	346.410i	−0.0250000	−	0.0433013i
$401$	4941.00	+	8558.06i	0.615316	+	1.06576i	0.990329	+	0.138739i	$0.0443050\pi$
$401$	4941.00	+	8558.06i	0.615316	+	1.06576i	−0.375013	+	0.927020i	$0.622362\pi$
$402$		0			0
$403$	475.000	−	822.724i	0.0587132	−	0.101694i
$404$	−1968.00			−0.242356
$405$		0			0
$406$	−2904.00			−0.354983
$407$	1884.00	−	3263.18i	0.229451	−	0.397420i
$408$		0			0
$409$	−2948.50	−	5106.95i	−0.356464	−	0.617414i	0.630903	−	0.775862i	$-0.282685\pi$
$409$	−2948.50	−	5106.95i	−0.356464	−	0.617414i	−0.987367	+	0.158447i	$0.949351\pi$
$410$	−2520.00	−	4364.77i	−0.303546	−	0.525757i
$411$		0			0
$412$	−1096.00	+	1898.33i	−0.131058	+	0.227000i
$413$	6996.00			0.833537
$414$		0			0
$415$	−1545.00			−0.182750
$416$	−608.000	+	1053.09i	−0.0716578	+	0.124115i
$417$		0			0
$418$	−1884.00	−	3263.18i	−0.220453	−	0.381836i
$419$	−3426.00	−	5934.01i	−0.399454	−	0.691874i	0.594205	−	0.804314i	$-0.297467\pi$
$419$	−3426.00	−	5934.01i	−0.399454	−	0.691874i	−0.993659	+	0.112440i	$0.964133\pi$
$420$		0			0
$421$	−161.500	+	279.726i	−0.0186960	+	0.0323825i	−0.875222	−	0.483721i	$-0.839285\pi$
$421$	−161.500	+	279.726i	−0.0186960	+	0.0323825i	0.856526	+	0.516104i	$0.172618\pi$
$422$	−2534.00			−0.292306
$423$		0			0
$424$	24.0000			0.00274892
$425$	1312.50	−	2273.32i	0.149801	−	0.259464i
$426$		0			0
$427$	3223.00	+	5582.40i	0.365274	+	0.632673i
$428$	−1464.00	−	2535.72i	−0.165339	−	0.286376i
$429$		0			0
$430$	1900.00	−	3290.90i	0.213084	−	0.369072i
$431$	10242.0			1.14464			0.572320	−	0.820030i	$-0.306044\pi$
$431$	10242.0			1.14464			0.572320	+	0.820030i	$0.306044\pi$
$432$		0			0
$433$	−14398.0			−1.59798			−0.798988	−	0.601347i	$-0.794631\pi$
$433$	−14398.0			−1.59798			−0.798988	+	0.601347i	$0.794631\pi$
$434$	−550.000	+	952.628i	−0.0608314	+	0.105363i
$435$		0			0
$436$	1814.00	+	3141.94i	0.199254	+	0.345118i
$437$	−9184.50	−	15908.0i	−1.00539	−	1.74138i
$438$		0			0
$439$	−2039.50	+	3532.52i	−0.221731	+	0.384050i	−0.955334	−	0.295529i	$-0.904504\pi$
$439$	−2039.50	+	3532.52i	−0.221731	+	0.384050i	0.733603	+	0.679579i	$0.237837\pi$
$440$	480.000			0.0520071
$441$		0			0
$442$	−7980.00			−0.858755
$443$	−2890.50	+	5006.49i	−0.310004	+	0.536943i	−0.978363	−	0.206896i	$-0.933664\pi$
$443$	−2890.50	+	5006.49i	−0.310004	+	0.536943i	0.668359	+	0.743839i	$0.266997\pi$
$444$		0			0
$445$	3180.00	+	5507.92i	0.338756	+	0.586743i
$446$	2986.00	+	5171.90i	0.317021	+	0.549096i
$447$		0			0
$448$	704.000	−	1219.36i	0.0742430	−	0.128593i
$449$	−15078.0			−1.58480			−0.792400	−	0.610002i	$-0.791168\pi$
$449$	−15078.0			−1.58480			−0.792400	+	0.610002i	$0.791168\pi$
$450$		0			0
$451$	6048.00			0.631462
$452$	3084.00	−	5341.64i	0.320927	−	0.555862i
$453$		0			0
$454$	−5409.00	−	9368.66i	−0.559156	−	0.968487i
$455$	−2090.00	−	3619.99i	−0.215342	−	0.372984i
$456$		0			0
$457$	−2134.00	+	3696.20i	−0.218434	+	0.378339i	−0.954329	−	0.298757i	$-0.903428\pi$
$457$	−2134.00	+	3696.20i	−0.218434	+	0.378339i	0.735895	+	0.677095i	$0.236761\pi$
$458$	8662.00			0.883731
$459$		0			0
$460$	2340.00			0.237181
$461$	2817.00	−	4879.19i	0.284600	−	0.492942i	−0.687912	−	0.725794i	$-0.741472\pi$
$461$	2817.00	−	4879.19i	0.284600	−	0.492942i	0.972512	+	0.232852i	$0.0748058\pi$
$462$		0			0
$463$	−2263.00	−	3919.63i	−0.227150	−	0.393436i	0.729812	−	0.683648i	$-0.239607\pi$
$463$	−2263.00	−	3919.63i	−0.227150	−	0.393436i	−0.956962	+	0.290212i	$0.906274\pi$
$464$	−528.000	−	914.523i	−0.0528271	−	0.0914993i
$465$		0			0
$466$	−2586.00	+	4479.08i	−0.257069	+	0.445257i
$467$	969.000			0.0960171			0.0480085	−	0.998847i	$-0.484713\pi$
$467$	969.000			0.0960171			0.0480085	+	0.998847i	$0.484713\pi$
$468$		0			0
$469$	7084.00			0.697460
$470$	−1260.00	+	2182.38i	−0.123658	+	0.214183i
$471$		0			0
$472$	1272.00	+	2203.17i	0.124044	+	0.214850i
$473$	2280.00	+	3949.08i	0.221637	+	0.383887i
$474$		0			0
$475$	1962.50	−	3399.15i	0.189570	−	0.328345i
$476$	9240.00			0.889737
$477$		0			0
$478$	1020.00			0.0976019
$479$	−4878.00	+	8448.94i	−0.465306	+	0.805933i	−0.999215	−	0.0396083i	$-0.987389\pi$
$479$	−4878.00	+	8448.94i	−0.465306	+	0.805933i	0.533909	+	0.845542i	$0.320722\pi$
$480$		0			0
$481$	−5966.00	−	10333.4i	−0.565543	−	0.979549i
$482$	205.000	+	355.070i	0.0193724	+	0.0335540i
$483$		0			0
$484$	2374.00	−	4111.89i	0.222953	−	0.386165i
$485$	−6640.00			−0.621664
$486$		0			0
$487$	8768.00			0.815844			0.407922	−	0.913017i	$-0.366254\pi$
$487$	8768.00			0.815844			0.407922	+	0.913017i	$0.366254\pi$
$488$	−1172.00	+	2029.96i	−0.108717	+	0.188304i
$489$		0			0
$490$	705.000	+	1221.10i	0.0649973	+	0.112579i
$491$	1137.00	+	1969.34i	0.104505	+	0.181008i	0.913536	−	0.406758i	$-0.133341\pi$
$491$	1137.00	+	1969.34i	0.104505	+	0.181008i	−0.809031	+	0.587766i	$0.800007\pi$
$492$		0			0
$493$	3465.00	−	6001.56i	0.316543	−	0.548269i
$494$	−11932.0			−1.08673
$495$		0			0
$496$	−400.000			−0.0362107
$497$	−1320.00	+	2286.31i	−0.119135	+	0.206348i
$498$		0			0
$499$	984.500	+	1705.20i	0.0883212	+	0.152977i	0.906802	−	0.421558i	$-0.138516\pi$
$499$	984.500	+	1705.20i	0.0883212	+	0.152977i	−0.818480	+	0.574534i	$0.805183\pi$
$500$	250.000	+	433.013i	0.0223607	+	0.0387298i
$501$		0			0
$502$	4680.00	−	8106.00i	0.416093	−	0.720694i
$503$	−10701.0			−0.948577			−0.474288	−	0.880370i	$-0.657295\pi$
$503$	−10701.0			−0.948577			−0.474288	+	0.880370i	$0.657295\pi$
$504$		0			0
$505$	2460.00			0.216769
$506$	−1404.00	+	2431.80i	−0.123351	+	0.213650i
$507$		0			0
$508$	5108.00	+	8847.32i	0.446124	+	0.772709i
$509$	−6210.00	−	10756.0i	−0.540773	−	0.936646i	−0.998860	−	0.0477388i	$-0.984799\pi$
$509$	−6210.00	−	10756.0i	−0.540773	−	0.936646i	0.458087	−	0.888907i	$-0.348535\pi$
$510$		0			0
$511$	484.000	−	838.313i	0.0419000	−	0.0725729i
$512$	512.000			0.0441942
$513$		0			0
$514$	−12318.0			−1.05705
$515$	1370.00	−	2372.91i	0.117222	−	0.203035i
$516$		0			0
$517$	−1512.00	−	2618.86i	−0.128622	−	0.222780i
$518$	6908.00	+	11965.0i	0.585946	+	1.01489i
$519$		0			0
$520$	760.000	−	1316.36i	0.0640927	−	0.111012i
$521$	−18816.0			−1.58223			−0.791117	−	0.611665i	$-0.790500\pi$
$521$	−18816.0			−1.58223			−0.791117	+	0.611665i	$0.790500\pi$
$522$		0			0
$523$	−16798.0			−1.40445			−0.702223	−	0.711957i	$-0.747809\pi$
$523$	−16798.0			−1.40445			−0.702223	+	0.711957i	$0.747809\pi$
$524$	300.000	−	519.615i	0.0250106	−	0.0433197i
$525$		0			0
$526$	6240.00	+	10808.0i	0.517257	+	0.895915i
$527$	−1312.50	−	2273.32i	−0.108488	−	0.187907i
$528$		0			0
$529$	−761.000	+	1318.09i	−0.0625462	+	0.108333i
$530$	−30.0000			−0.00245871
$531$		0			0
$532$	13816.0			1.12594
$533$	9576.00	−	16586.1i	0.778204	−	1.34789i
$534$		0			0
$535$	1830.00	+	3169.65i	0.147884	+	0.256142i
$536$	1288.00	+	2230.88i	0.103793	+	0.179775i
$537$		0			0
$538$	7758.00	−	13437.3i	0.621694	−	1.07680i
$539$	−1692.00			−0.135213
$540$		0			0
$541$	−5890.00			−0.468079			−0.234040	−	0.972227i	$-0.575195\pi$
$541$	−5890.00			−0.468079			−0.234040	+	0.972227i	$0.575195\pi$
$542$	7345.00	−	12721.9i	0.582094	−	1.00822i
$543$		0			0
$544$	1680.00	+	2909.85i	0.132407	+	0.229336i
$545$	−2267.50	−	3927.43i	−0.178218	−	0.308683i
$546$		0			0
$547$	−2758.00	+	4777.00i	−0.215582	+	0.373400i	−0.953453	−	0.301543i	$-0.902498\pi$
$547$	−2758.00	+	4777.00i	−0.215582	+	0.373400i	0.737870	+	0.674943i	$0.235832\pi$
$548$	6612.00			0.515421
$549$		0			0
$550$	−600.000			−0.0465165
$551$	5181.00	−	8973.76i	0.400577	−	0.693820i
$552$		0			0
$553$	10087.0	+	17471.2i	0.775665	+	1.34349i
$554$	3004.00	+	5203.08i	0.230375	+	0.399021i
$555$		0			0
$556$	−2248.00	+	3893.65i	−0.171468	+	0.296992i
$557$	4146.00			0.315389			0.157694	−	0.987488i	$-0.449594\pi$
$557$	4146.00			0.315389			0.157694	+	0.987488i	$0.449594\pi$
$558$		0			0
$559$	14440.0			1.09257
$560$	−880.000	+	1524.20i	−0.0664050	+	0.115017i
$561$		0			0
$562$	−2046.00	−	3543.78i	−0.153568	−	0.265988i
$563$	10722.0	+	18571.0i	0.802626	+	1.39019i	0.917882	+	0.396853i	$0.129898\pi$
$563$	10722.0	+	18571.0i	0.802626	+	1.39019i	−0.115256	+	0.993336i	$0.536769\pi$
$564$		0			0
$565$	−3855.00	+	6677.06i	−0.287046	+	0.497178i
$566$	−10976.0			−0.815116
$567$		0			0
$568$	−960.000			−0.0709167
$569$	−7389.00	+	12798.1i	−0.544399	+	0.942927i	0.454246	+	0.890877i	$0.349909\pi$
$569$	−7389.00	+	12798.1i	−0.544399	+	0.942927i	−0.998644	+	0.0520501i	$0.983424\pi$
$570$		0			0
$571$	−4565.50	−	7907.68i	−0.334606	−	0.579555i	0.648803	−	0.760957i	$-0.275270\pi$
$571$	−4565.50	−	7907.68i	−0.334606	−	0.579555i	−0.983409	+	0.181401i	$0.941937\pi$
$572$	912.000	+	1579.63i	0.0666654	+	0.115468i
$573$		0			0
$574$	−11088.0	+	19205.0i	−0.806279	+	1.39652i
$575$	−2925.00			−0.212141
$576$		0			0
$577$	−2344.00			−0.169120			−0.0845598	−	0.996418i	$-0.526948\pi$
$577$	−2344.00			−0.169120			−0.0845598	+	0.996418i	$0.526948\pi$
$578$	−6112.00	+	10586.3i	−0.439837	+	0.761820i
$579$		0			0
$580$	660.000	+	1143.15i	0.0472500	+	0.0818394i
$581$	3399.00	+	5887.24i	0.242710	+	0.420385i
$582$		0			0
$583$	18.0000	−	31.1769i	0.00127870	−	0.00221478i
$584$	352.000			0.0249415
$585$		0			0
$586$	666.000			0.0469492
$587$	13414.5	−	23234.6i	0.943229	−	1.63372i	0.183971	−	0.982932i	$-0.441105\pi$
$587$	13414.5	−	23234.6i	0.943229	−	1.63372i	0.759258	−	0.650790i	$-0.225562\pi$
$588$		0			0
$589$	−1962.50	−	3399.15i	−0.137289	−	0.237792i
$590$	−1590.00	−	2753.96i	−0.110948	−	0.192167i
$591$		0			0
$592$	−2512.00	+	4350.91i	−0.174396	+	0.302063i
$593$	8181.00			0.566532			0.283266	−	0.959041i	$-0.408582\pi$
$593$	8181.00			0.566532			0.283266	+	0.959041i	$0.408582\pi$
$594$		0			0
$595$	−11550.0			−0.795805
$596$	−3216.00	+	5570.28i	−0.221028	+	0.382831i
$597$		0			0
$598$	4446.00	+	7700.70i	0.304031	+	0.526597i
$599$	−12039.0	−	20852.2i	−0.821202	−	1.42236i	−0.904787	−	0.425864i	$-0.859970\pi$
$599$	−12039.0	−	20852.2i	−0.821202	−	1.42236i	0.0835851	−	0.996501i	$-0.473363\pi$
$600$		0			0
$601$	−11282.5	+	19541.9i	−0.765762	+	1.32634i	0.174081	+	0.984731i	$0.444304\pi$
$601$	−11282.5	+	19541.9i	−0.765762	+	1.32634i	−0.939843	+	0.341607i	$0.889029\pi$
$602$	−16720.0			−1.13199
$603$		0			0
$604$	−9952.00			−0.670432
$605$	−2967.50	+	5139.86i	−0.199415	+	0.345397i
$606$		0			0
$607$	7358.00	+	12744.4i	0.492013	+	0.852192i	0.999958	−	0.00919795i	$-0.00292784\pi$
$607$	7358.00	+	12744.4i	0.492013	+	0.852192i	−0.507945	+	0.861390i	$0.669595\pi$
$608$	2512.00	+	4350.91i	0.167558	+	0.290218i
$609$		0			0
$610$	1465.00	−	2537.45i	0.0972395	−	0.168424i
$611$	−9576.00			−0.634048
$612$		0			0
$613$	−7552.00			−0.497590			−0.248795	−	0.968556i	$-0.580034\pi$
$613$	−7552.00			−0.497590			−0.248795	+	0.968556i	$0.580034\pi$
$614$	−2918.00	+	5054.12i	−0.191793	+	0.332195i
$615$		0			0
$616$	−1056.00	−	1829.05i	−0.0690705	−	0.119634i
$617$	1990.50	+	3447.65i	0.129878	+	0.224955i	0.923629	−	0.383288i	$-0.125208\pi$
$617$	1990.50	+	3447.65i	0.129878	+	0.224955i	−0.793751	+	0.608242i	$0.791875\pi$
$618$		0			0
$619$	−6964.00	+	12062.0i	−0.452192	+	0.783219i	−0.998522	−	0.0543507i	$-0.982691\pi$
$619$	−6964.00	+	12062.0i	−0.452192	+	0.783219i	0.546330	+	0.837570i	$0.316024\pi$
$620$	500.000			0.0323879
$621$		0			0
$622$	−11508.0			−0.741847
$623$	13992.0	−	24234.9i	0.899804	−	1.55851i
$624$		0			0
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	−3368.00	−	5833.55i	−0.215036	−	0.372453i
$627$		0			0
$628$	5936.00	−	10281.5i	0.377185	−	0.653304i
$629$	−32970.0			−2.08998
$630$		0			0
$631$	18605.0			1.17378			0.586889	−	0.809668i	$-0.300353\pi$
$631$	18605.0			1.17378			0.586889	+	0.809668i	$0.300353\pi$
$632$	−3668.00	+	6353.16i	−0.230863	+	0.399866i
$633$		0			0
$634$	−2871.00	−	4972.72i	−0.179845	−	0.311501i
$635$	−6385.00	−	11059.1i	−0.399025	−	0.691132i
$636$		0			0
$637$	−2679.00	+	4640.16i	−0.166634	+	0.288619i
$638$	−1584.00			−0.0982934
$639$		0			0
$640$	−640.000			−0.0395285
$641$	−7464.00	+	12928.0i	−0.459922	+	0.796609i	−0.998956	−	0.0456750i	$-0.985456\pi$
$641$	−7464.00	+	12928.0i	−0.459922	+	0.796609i	0.539034	+	0.842284i	$0.318789\pi$
$642$		0			0
$643$	3041.00	+	5267.17i	0.186509	+	0.323043i	0.944084	−	0.329705i	$-0.106949\pi$
$643$	3041.00	+	5267.17i	0.186509	+	0.323043i	−0.757575	+	0.652748i	$0.773616\pi$
$644$	−5148.00	−	8916.60i	−0.314999	−	0.545595i
$645$		0			0
$646$	−16485.0	+	28552.9i	−1.00401	+	1.73900i
$647$	4875.00			0.296223			0.148111	−	0.988971i	$-0.452681\pi$
$647$	4875.00			0.296223			0.148111	+	0.988971i	$0.452681\pi$
$648$		0			0
$649$	3816.00			0.230803
$650$	−950.000	+	1645.45i	−0.0573263	+	0.0992920i
$651$		0			0
$652$	−6340.00	−	10981.2i	−0.380818	−	0.659597i
$653$	2578.50	+	4466.09i	0.154525	+	0.267644i	0.932886	−	0.360172i	$-0.117282\pi$
$653$	2578.50	+	4466.09i	0.154525	+	0.267644i	−0.778361	+	0.627817i	$0.783949\pi$
$654$		0			0
$655$	−375.000	+	649.519i	−0.0223702	+	0.0387463i
$656$	−8064.00			−0.479949
$657$		0			0
$658$	11088.0			0.656923
$659$	753.000	−	1304.23i	0.0445109	−	0.0770952i	−0.842912	−	0.538052i	$-0.819160\pi$
$659$	753.000	−	1304.23i	0.0445109	−	0.0770952i	0.887423	+	0.460957i	$0.152494\pi$
$660$		0			0
$661$	1193.00	+	2066.34i	0.0702002	+	0.121590i	0.898989	−	0.437971i	$-0.144303\pi$
$661$	1193.00	+	2066.34i	0.0702002	+	0.121590i	−0.828789	+	0.559562i	$0.810970\pi$
$662$	10540.0	+	18255.8i	0.618805	+	1.07180i
$663$		0			0
$664$	−1236.00	+	2140.81i	−0.0722381	+	0.125120i
$665$	−17270.0			−1.00707
$666$		0			0
$667$	−7722.00			−0.448271
$668$	−654.000	+	1132.76i	−0.0378803	+	0.0656106i
$669$		0			0
$670$	−1610.00	−	2788.60i	−0.0928354	−	0.160796i
$671$	1758.00	+	3044.95i	0.101143	+	0.175185i
$672$		0			0
$673$	−10579.0	+	18323.4i	−0.605929	+	1.04950i	0.385974	+	0.922509i	$0.373865\pi$
$673$	−10579.0	+	18323.4i	−0.605929	+	1.04950i	−0.991904	+	0.126991i	$0.959468\pi$
$674$	10012.0			0.572178
$675$		0			0
$676$	−3012.00			−0.171370
$677$	−13413.0	+	23232.0i	−0.761453	+	1.31887i	0.180649	+	0.983548i	$0.442180\pi$
$677$	−13413.0	+	23232.0i	−0.761453	+	1.31887i	−0.942102	+	0.335327i	$0.891153\pi$
$678$		0			0
$679$	14608.0	+	25301.8i	0.825631	+	1.43004i
$680$	−2100.00	−	3637.31i	−0.118428	−	0.205124i
$681$		0			0
$682$	−300.000	+	519.615i	−0.0168440	+	0.0291746i
$683$	32493.0			1.82037			0.910183	−	0.414206i	$-0.135941\pi$
$683$	32493.0			1.82037			0.910183	+	0.414206i	$0.135941\pi$
$684$		0			0
$685$	−8265.00			−0.461006
$686$	−4444.00	+	7697.23i	−0.247336	+	0.428399i
$687$		0			0
$688$	−3040.00	−	5265.43i	−0.168458	−	0.291777i
$689$	−57.0000	−	98.7269i	−0.00315171	−	0.00545892i
$690$		0			0
$691$	3765.50	−	6522.04i	0.207303	−	0.359059i	−0.743561	−	0.668668i	$-0.766865\pi$
$691$	3765.50	−	6522.04i	0.207303	−	0.359059i	0.950864	+	0.309609i	$0.100198\pi$
$692$	5220.00			0.286755
$693$		0			0
$694$	−72.0000			−0.00393816
$695$	2810.00	−	4867.06i	0.153366	−	0.265638i
$696$		0			0
$697$	−26460.0	−	45830.1i	−1.43794	−	2.49058i
$698$	6715.00	+	11630.7i	0.364135	+	0.630701i
$699$		0			0
$700$	1100.00	−	1905.26i	0.0593944	−	0.102874i
$701$	24306.0			1.30959			0.654797	−	0.755805i	$-0.272754\pi$
$701$	24306.0			1.30959			0.654797	+	0.755805i	$0.272754\pi$
$702$		0			0
$703$	−49298.0			−2.64482
$704$	384.000	−	665.108i	0.0205576	−	0.0356068i
$705$		0			0
$706$	−12822.0	−	22208.4i	−0.683516	−	1.18388i
$707$	−5412.00	−	9373.86i	−0.287891	−	0.498643i
$708$		0			0
$709$	13727.0	−	23775.9i	0.727120	−	1.25941i	−0.230975	−	0.972960i	$-0.574192\pi$
$709$	13727.0	−	23775.9i	0.727120	−	1.25941i	0.958095	−	0.286450i	$-0.0924751\pi$
$710$	1200.00			0.0634299
$711$		0			0
$712$	10176.0			0.535620
$713$	−1462.50	+	2533.12i	−0.0768177	+	0.133052i
$714$		0			0
$715$	−1140.00	−	1974.54i	−0.0596274	−	0.103278i
$716$	8088.00	+	14008.8i	0.422155	+	0.731193i
$717$		0			0
$718$	−5478.00	+	9488.17i	−0.284731	+	0.493169i
$719$	−5334.00			−0.276668			−0.138334	−	0.990386i	$-0.544175\pi$
$719$	−5334.00			−0.276668			−0.138334	+	0.990386i	$0.544175\pi$
$720$		0			0
$721$	−12056.0			−0.622731
$722$	−17790.0	+	30813.2i	−0.917002	+	1.58829i
$723$		0			0
$724$	2102.00	+	3640.77i	0.107901	+	0.186890i
$725$	−825.000	−	1428.94i	−0.0422617	−	0.0731994i
$726$		0			0
$727$	−13024.0	+	22558.2i	−0.664420	+	1.15081i	0.315022	+	0.949084i	$0.397988\pi$
$727$	−13024.0	+	22558.2i	−0.664420	+	1.15081i	−0.979442	+	0.201725i	$0.935345\pi$
$728$	−6688.00			−0.340486
$729$		0			0
$730$	−440.000			−0.0223084
$731$	19950.0	−	34554.4i	1.00941	−	1.74835i
$732$		0			0
$733$	16568.0	+	28696.6i	0.834861	+	1.44602i	0.894144	+	0.447780i	$0.147785\pi$
$733$	16568.0	+	28696.6i	0.834861	+	1.44602i	−0.0592827	+	0.998241i	$0.518881\pi$
$734$	2446.00	+	4236.60i	0.123002	+	0.213046i
$735$		0			0
$736$	1872.00	−	3242.40i	0.0937539	−	0.162386i
$737$	3864.00			0.193124
$738$		0			0
$739$	−11599.0			−0.577370			−0.288685	−	0.957424i	$-0.593218\pi$
$739$	−11599.0			−0.577370			−0.288685	+	0.957424i	$0.593218\pi$
$740$	3140.00	−	5438.64i	0.155985	−	0.270173i
$741$		0			0
$742$	66.0000	+	114.315i	0.00326541	+	0.00565586i
$743$	−13212.0	−	22883.9i	−0.652357	−	1.12992i	−0.982549	−	0.186002i	$-0.940447\pi$
$743$	−13212.0	−	22883.9i	−0.652357	−	1.12992i	0.330192	−	0.943914i	$-0.392886\pi$
$744$		0			0
$745$	4020.00	−	6962.84i	0.197693	−	0.342415i
$746$	23392.0			1.14805
$747$		0			0
$748$	5040.00			0.246365
$749$	8052.00	−	13946.5i	0.392809	−	0.680365i
$750$		0			0
$751$	−6830.50	−	11830.8i	−0.331889	−	0.574848i	0.650993	−	0.759083i	$-0.274353\pi$
$751$	−6830.50	−	11830.8i	−0.331889	−	0.574848i	−0.982882	+	0.184235i	$0.941019\pi$
$752$	2016.00	+	3491.81i	0.0977606	+	0.169326i
$753$		0			0
$754$	−2508.00	+	4343.98i	−0.121135	+	0.209812i
$755$	12440.0			0.599653
$756$		0			0
$757$	−22846.0			−1.09690			−0.548449	−	0.836184i	$-0.684782\pi$
$757$	−22846.0			−1.09690			−0.548449	+	0.836184i	$0.684782\pi$
$758$	2095.00	−	3628.65i	0.100388	−	0.173876i
$759$		0			0
$760$	−3140.00	−	5438.64i	−0.149868	−	0.259579i
$761$	−10431.0	−	18067.0i	−0.496877	−	0.860616i	0.503116	−	0.864219i	$-0.332187\pi$
$761$	−10431.0	−	18067.0i	−0.496877	−	0.860616i	−0.999994	+	0.00360230i	$0.998853\pi$
$762$		0			0
$763$	−9977.00	+	17280.7i	−0.473384	+	0.819924i
$764$	−10392.0			−0.492106
$765$		0			0
$766$	−22626.0			−1.06725
$767$	6042.00	−	10465.1i	0.284438	−	0.492661i
$768$		0			0
$769$	11109.5	+	19242.2i	0.520961	+	0.902330i	0.999703	+	0.0243749i	$0.00775955\pi$
$769$	11109.5	+	19242.2i	0.520961	+	0.902330i	−0.478742	+	0.877956i	$0.658907\pi$
$770$	1320.00	+	2286.31i	0.0617786	+	0.107004i
$771$		0			0
$772$	−8740.00	+	15138.1i	−0.407460	+	0.705742i
$773$	17619.0			0.819808			0.409904	−	0.912129i	$-0.365562\pi$
$773$	17619.0			0.819808			0.409904	+	0.912129i	$0.365562\pi$
$774$		0			0
$775$	−625.000			−0.0289686
$776$	−5312.00	+	9200.65i	−0.245734	+	0.425624i
$777$		0			0
$778$	−2124.00	−	3678.88i	−0.0978780	−	0.169530i
$779$	−39564.0	−	68526.9i	−1.81968	−	3.15177i
$780$		0			0
$781$	−720.000	+	1247.08i	−0.0329880	+	0.0571369i
$782$	24570.0			1.12356
$783$		0			0
$784$	2256.00			0.102770
$785$	−7420.00	+	12851.8i	−0.337365	+	0.584333i
$786$		0			0
$787$	−7792.00	−	13496.1i	−0.352929	−	0.611290i	0.633833	−	0.773470i	$-0.281481\pi$
$787$	−7792.00	−	13496.1i	−0.352929	−	0.611290i	−0.986761	+	0.162180i	$0.948147\pi$
$788$	5886.00	+	10194.9i	0.266091	+	0.460884i
$789$		0			0
$790$	4585.00	−	7941.45i	0.206490	−	0.357651i
$791$	33924.0			1.52490
$792$		0			0
$793$	11134.0			0.498588
$794$	−6410.00	+	11102.4i	−0.286502	+	0.496236i
$795$		0			0
$796$	9536.00	+	16516.8i	0.424616	+	0.735457i
$797$	6511.50	+	11278.2i	0.289397	+	0.501250i	0.973666	−	0.227980i	$-0.0732120\pi$
$797$	6511.50	+	11278.2i	0.289397	+	0.501250i	−0.684269	+	0.729230i	$0.739879\pi$
$798$		0			0
$799$	−13230.0	+	22915.0i	−0.585787	+	1.01461i
$800$	800.000			0.0353553
$801$		0			0
$802$	−19764.0			−0.870188
$803$	264.000	−	457.261i	0.0116019	−	0.0200951i
$804$		0			0
$805$	6435.00	+	11145.7i	0.281744	+	0.487995i
$806$	950.000	+	1645.45i	0.0415165	+	0.0719087i
$807$		0			0
$808$	1968.00	−	3408.68i	0.0856856	−	0.148412i
$809$	−25872.0			−1.12436			−0.562182	−	0.827013i	$-0.690038\pi$
$809$	−25872.0			−1.12436			−0.562182	+	0.827013i	$0.690038\pi$
$810$		0			0
$811$	22052.0			0.954809			0.477405	−	0.878684i	$-0.341578\pi$
$811$	22052.0			0.954809			0.477405	+	0.878684i	$0.341578\pi$
$812$	2904.00	−	5029.88i	0.125505	−	0.217382i
$813$		0			0
$814$	3768.00	+	6526.37i	0.162246	+	0.281019i
$815$	7925.00	+	13726.5i	0.340614	+	0.589961i
$816$		0			0
$817$	29830.0	−	51667.1i	1.27738	−	2.21249i
$818$	11794.0			0.504117
$819$		0			0
$820$	10080.0			0.429279
$821$	−957.000	+	1657.57i	−0.0406815	+	0.0704625i	−0.885649	−	0.464355i	$-0.846286\pi$
$821$	−957.000	+	1657.57i	−0.0406815	+	0.0704625i	0.844968	+	0.534817i	$0.179620\pi$
$822$		0			0
$823$	5534.00	+	9585.17i	0.234390	+	0.405976i	0.959095	−	0.283083i	$-0.0913573\pi$
$823$	5534.00	+	9585.17i	0.234390	+	0.405976i	−0.724705	+	0.689059i	$0.758024\pi$
$824$	−2192.00	−	3796.66i	−0.0926723	−	0.160513i
$825$		0			0
$826$	−6996.00	+	12117.4i	−0.294700	+	0.510435i
$827$	−21405.0			−0.900030			−0.450015	−	0.893021i	$-0.648581\pi$
$827$	−21405.0			−0.900030			−0.450015	+	0.893021i	$0.648581\pi$
$828$		0			0
$829$	−40042.0			−1.67758			−0.838791	−	0.544453i	$-0.816737\pi$
$829$	−40042.0			−1.67758			−0.838791	+	0.544453i	$0.816737\pi$
$830$	1545.00	−	2676.02i	0.0646117	−	0.111911i
$831$		0			0
$832$	−1216.00	−	2106.17i	−0.0506697	−	0.0877625i
$833$	7402.50	+	12821.5i	0.307901	+	0.533300i
$834$		0			0
$835$	817.500	−	1415.95i	0.0338811	−	0.0586839i
$836$	7536.00			0.311768
$837$		0			0
$838$	13704.0			0.564913
$839$	−8952.00	+	15505.3i	−0.368364	+	0.638025i	−0.989310	−	0.145828i	$-0.953415\pi$
$839$	−8952.00	+	15505.3i	−0.368364	+	0.638025i	0.620946	+	0.783853i	$0.286749\pi$
$840$		0			0
$841$	10016.5	+	17349.1i	0.410697	+	0.711349i
$842$	−323.000	−	559.452i	−0.0132201	−	0.0228979i
$843$		0			0
$844$	2534.00	−	4389.02i	0.103346	−	0.179000i
$845$	3765.00			0.153278
$846$		0			0
$847$	26114.0			1.05937
$848$	−24.0000	+	41.5692i	−0.000971891	+	0.00168336i
$849$		0			0
$850$	2625.00	+	4546.63i	0.105926	+	0.183469i
$851$	18369.0	+	31816.0i	0.739931	+	1.28160i
$852$		0			0
$853$	10790.0	−	18688.8i	0.433110	−	0.750168i	−0.564030	−	0.825755i	$-0.690750\pi$
$853$	10790.0	−	18688.8i	0.433110	−	0.750168i	0.997139	+	0.0755866i	$0.0240829\pi$
$854$	−12892.0			−0.516575
$855$		0			0
$856$	5856.00			0.233825
$857$	−8575.50	+	14853.2i	−0.341813	+	0.592037i	−0.984769	−	0.173866i	$-0.944374\pi$
$857$	−8575.50	+	14853.2i	−0.341813	+	0.592037i	0.642957	+	0.765903i	$0.277708\pi$
$858$		0			0
$859$	−16712.5	−	28946.9i	−0.663822	−	1.14977i	−0.979603	−	0.200941i	$-0.935600\pi$
$859$	−16712.5	−	28946.9i	−0.663822	−	1.14977i	0.315781	−	0.948832i	$-0.397733\pi$
$860$	3800.00	+	6581.79i	0.150673	+	0.260974i
$861$		0			0
$862$	−10242.0	+	17739.7i	−0.404691	+	0.700946i
$863$	6603.00			0.260450			0.130225	−	0.991484i	$-0.458430\pi$
$863$	6603.00			0.260450			0.130225	+	0.991484i	$0.458430\pi$
$864$		0			0
$865$	−6525.00			−0.256482
$866$	14398.0	−	24938.1i	0.564970	−	0.978557i
$867$		0			0
$868$	−1100.00	−	1905.26i	−0.0430143	−	0.0745030i
$869$	5502.00	+	9529.74i	0.214779	+	0.372007i
$870$		0			0
$871$	6118.00	−	10596.7i	0.238003	−	0.412233i
$872$	−7256.00			−0.281788
$873$		0			0
$874$	36738.0			1.42183
$875$	−1375.00	+	2381.57i	−0.0531240	+	0.0920134i
$876$		0			0
$877$	21692.0	+	37571.6i	0.835219	+	1.44664i	0.893852	+	0.448362i	$0.147992\pi$
$877$	21692.0	+	37571.6i	0.835219	+	1.44664i	−0.0586336	+	0.998280i	$0.518674\pi$
$878$	−4079.00	−	7065.04i	−0.156788	−	0.271564i
$879$		0			0
$880$	−480.000	+	831.384i	−0.0183873	+	0.0318477i
$881$	12726.0			0.486663			0.243331	−	0.969943i	$-0.421760\pi$
$881$	12726.0			0.486663			0.243331	+	0.969943i	$0.421760\pi$
$882$		0			0
$883$	2786.00			0.106179			0.0530897	−	0.998590i	$-0.483093\pi$
$883$	2786.00			0.106179			0.0530897	+	0.998590i	$0.483093\pi$
$884$	7980.00	−	13821.8i	0.303616	−	0.525878i
$885$		0			0
$886$	−5781.00	−	10013.0i	−0.219206	−	0.379676i
$887$	2194.50	+	3800.99i	0.0830711	+	0.143883i	0.904568	−	0.426330i	$-0.140194\pi$
$887$	2194.50	+	3800.99i	0.0830711	+	0.143883i	−0.821497	+	0.570214i	$0.806860\pi$
$888$		0			0
$889$	−28094.0	+	48660.2i	−1.05989	+	1.83578i
$890$	−12720.0			−0.479073
$891$		0			0
$892$	−11944.0			−0.448335
$893$	−19782.0	+	34263.4i	−0.741298	+	1.28397i
$894$		0			0
$895$	−10110.0	−	17511.0i	−0.377587	−	0.653999i
$896$	1408.00	+	2438.73i	0.0524977	+	0.0909288i
$897$		0			0
$898$	15078.0	−	26115.9i	0.560311	−	0.970487i
$899$	−1650.00			−0.0612131
$900$		0			0
$901$	−315.000			−0.0116472
$902$	−6048.00	+	10475.4i	−0.223255	+	0.386690i
$903$		0			0
$904$	6168.00	+	10683.3i	0.226930	+	0.393054i
$905$	−2627.50	−	4550.96i	−0.0965095	−	0.167159i
$906$		0			0
$907$	12434.0	−	21536.3i	0.455198	−	0.788425i	−0.543502	−	0.839408i	$-0.682902\pi$
$907$	12434.0	−	21536.3i	0.455198	−	0.788425i	0.998700	+	0.0509826i	$0.0162353\pi$
$908$	21636.0			0.790766
$909$		0			0
$910$	8360.00			0.304540
$911$	63.0000	−	109.119i	0.00229120	−	0.00396847i	−0.864878	−	0.501983i	$-0.832604\pi$
$911$	63.0000	−	109.119i	0.00229120	−	0.00396847i	0.867169	+	0.498014i	$0.165937\pi$
$912$		0			0
$913$	1854.00	+	3211.22i	0.0672053	+	0.116403i
$914$	−4268.00	−	7392.39i	−0.154456	−	0.267526i
$915$		0			0
$916$	−8662.00	+	15003.0i	−0.312446	+	0.541172i
$917$	3300.00			0.118839
$918$		0			0
$919$	−16144.0			−0.579479			−0.289740	−	0.957106i	$-0.593569\pi$
$919$	−16144.0			−0.579479			−0.289740	+	0.957106i	$0.593569\pi$
$920$	−2340.00	+	4053.00i	−0.0838560	+	0.145243i
$921$		0			0
$922$	5634.00	+	9758.37i	0.201243	+	0.348563i
$923$	2280.00	+	3949.08i	0.0813078	+	0.140829i
$924$		0			0
$925$	−3925.00	+	6798.30i	−0.139517	+	0.241650i
$926$	9052.00			0.321239
$927$		0			0
$928$	2112.00			0.0747088
$929$	21096.0	−	36539.3i	0.745035	−	1.29044i	−0.205144	−	0.978732i	$-0.565766\pi$
$929$	21096.0	−	36539.3i	0.745035	−	1.29044i	0.950179	−	0.311706i	$-0.100900\pi$
$930$		0			0
$931$	11068.5	+	19171.2i	0.389641	+	0.674877i
$932$	−5172.00	−	8958.17i	−0.181775	−	0.314844i
$933$		0			0
$934$	−969.000	+	1678.36i	−0.0339472	+	0.0587982i
$935$	−6300.00			−0.220355
$936$		0			0
$937$	3272.00			0.114079			0.0570393	−	0.998372i	$-0.481834\pi$
$937$	3272.00			0.114079			0.0570393	+	0.998372i	$0.481834\pi$
$938$	−7084.00	+	12269.8i	−0.246589	+	0.427105i
$939$		0			0
$940$	−2520.00	−	4364.77i	−0.0874397	−	0.151450i
$941$	−10419.0	−	18046.2i	−0.360945	−	0.625176i	0.627171	−	0.778881i	$-0.284213\pi$
$941$	−10419.0	−	18046.2i	−0.360945	−	0.625176i	−0.988117	+	0.153706i	$0.950879\pi$
$942$		0			0
$943$	−29484.0	+	51067.8i	−1.01817	+	1.76352i
$944$	−5088.00			−0.175424
$945$		0			0
$946$	−9120.00			−0.313443
$947$	−6676.50	+	11564.0i	−0.229099	+	0.396812i	−0.957541	−	0.288296i	$-0.906911\pi$
$947$	−6676.50	+	11564.0i	−0.229099	+	0.396812i	0.728442	+	0.685107i	$0.240245\pi$
$948$		0			0
$949$	−836.000	−	1447.99i	−0.0285961	−	0.0495299i
$950$	3925.00	+	6798.30i	0.134046	+	0.232175i
$951$		0			0
$952$	−9240.00	+	16004.1i	−0.314569	+	0.544850i
$953$	13098.0			0.445211			0.222605	−	0.974909i	$-0.428544\pi$
$953$	13098.0			0.445211			0.222605	+	0.974909i	$0.428544\pi$
$954$		0			0
$955$	12990.0			0.440153
$956$	−1020.00	+	1766.69i	−0.0345075	+	0.0597687i
$957$		0			0
$958$	−9756.00	−	16897.9i	−0.329021	−	0.569881i
$959$	18183.0	+	31493.9i	0.612262	+	1.06047i
$960$		0			0
$961$	14583.0	−	25258.5i	0.489510	−	0.847857i
$962$	23864.0			0.799799
$963$		0			0
$964$	−820.000			−0.0273967
$965$	10925.0	−	18922.7i	0.364444	−	0.631235i
$966$		0			0
$967$	−9913.00	−	17169.8i	−0.329659	−	0.570987i	0.652785	−	0.757543i	$-0.273601\pi$
$967$	−9913.00	−	17169.8i	−0.329659	−	0.570987i	−0.982444	+	0.186557i	$0.940267\pi$
$968$	4748.00	+	8223.78i	0.157651	+	0.273060i
$969$		0			0
$970$	6640.00	−	11500.8i	0.219791	−	0.380690i
$971$	23322.0			0.770792			0.385396	−	0.922751i	$-0.374065\pi$
$971$	23322.0			0.770792			0.385396	+	0.922751i	$0.374065\pi$
$972$		0			0
$973$	−24728.0			−0.814741
$974$	−8768.00	+	15186.6i	−0.288444	+	0.499600i
$975$		0			0
$976$	−2344.00	−	4059.93i	−0.0768746	−	0.133151i
$977$	23673.0	+	41002.8i	0.775196	+	1.34268i	0.934684	+	0.355479i	$0.115682\pi$
$977$	23673.0	+	41002.8i	0.775196	+	1.34268i	−0.159488	+	0.987200i	$0.550984\pi$
$978$		0			0
$979$	7632.00	−	13219.0i	0.249152	−	0.431544i
$980$	−2820.00			−0.0919200
$981$		0			0
$982$	−4548.00			−0.147793
$983$	16516.5	−	28607.4i	0.535905	−	0.928215i	−0.463214	−	0.886246i	$-0.653304\pi$
$983$	16516.5	−	28607.4i	0.535905	−	0.928215i	0.999119	−	0.0419681i	$-0.0133628\pi$
$984$		0			0
$985$	−7357.50	−	12743.6i	−0.237999	−	0.412227i
$986$	6930.00	+	12003.1i	0.223830	+	0.387685i
$987$		0			0
$988$	11932.0	−	20666.8i	0.384218	−	0.665485i
$989$	−44460.0			−1.42947
$990$		0			0
$991$	6017.00			0.192872			0.0964361	−	0.995339i	$-0.469256\pi$
$991$	6017.00			0.192872			0.0964361	+	0.995339i	$0.469256\pi$
$992$	400.000	−	692.820i	0.0128024	−	0.0221745i
$993$		0			0
$994$	−2640.00	−	4572.61i	−0.0842412	−	0.145910i
$995$	−11920.0	−	20646.0i	−0.379788	−	0.657813i
$996$		0			0
$997$	17108.0	−	29631.9i	0.543446	−	0.941276i	−0.455257	−	0.890360i	$-0.650453\pi$
$997$	17108.0	−	29631.9i	0.543446	−	0.941276i	0.998703	−	0.0509161i	$-0.0162141\pi$
$998$	−3938.00			−0.124905
$999$		0			0

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(2.50000 + 4.33013i) q^{5} +(11.0000 - 19.0526i) q^{7} +8.00000 q^{8} -10.0000 q^{10} +(6.00000 - 10.3923i) q^{11} +(-19.0000 - 32.9090i) q^{13} +(22.0000 + 38.1051i) q^{14} +(-8.00000 + 13.8564i) q^{16} -105.000 q^{17} -157.000 q^{19} +(10.0000 - 17.3205i) q^{20} +(12.0000 + 20.7846i) q^{22} +(58.5000 + 101.325i) q^{23} +(-12.5000 + 21.6506i) q^{25} +76.0000 q^{26} -88.0000 q^{28} +(-33.0000 + 57.1577i) q^{29} +(12.5000 + 21.6506i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(105.000 - 181.865i) q^{34} +110.000 q^{35} +314.000 q^{37} +(157.000 - 271.932i) q^{38} +(20.0000 + 34.6410i) q^{40} +(252.000 + 436.477i) q^{41} +(-190.000 + 329.090i) q^{43} -48.0000 q^{44} -234.000 q^{46} +(126.000 - 218.238i) q^{47} +(-70.5000 - 122.110i) q^{49} +(-25.0000 - 43.3013i) q^{50} +(-76.0000 + 131.636i) q^{52} +3.00000 q^{53} +60.0000 q^{55} +(88.0000 - 152.420i) q^{56} +(-66.0000 - 114.315i) q^{58} +(159.000 + 275.396i) q^{59} +(-146.500 + 253.745i) q^{61} -50.0000 q^{62} +64.0000 q^{64} +(95.0000 - 164.545i) q^{65} +(161.000 + 278.860i) q^{67} +(210.000 + 363.731i) q^{68} +(-110.000 + 190.526i) q^{70} -120.000 q^{71} +44.0000 q^{73} +(-314.000 + 543.864i) q^{74} +(314.000 + 543.864i) q^{76} +(-132.000 - 228.631i) q^{77} +(-458.500 + 794.145i) q^{79} -80.0000 q^{80} -1008.00 q^{82} +(-154.500 + 267.602i) q^{83} +(-262.500 - 454.663i) q^{85} +(-380.000 - 658.179i) q^{86} +(48.0000 - 83.1384i) q^{88} +1272.00 q^{89} -836.000 q^{91} +(234.000 - 405.300i) q^{92} +(252.000 + 436.477i) q^{94} +(-392.500 - 679.830i) q^{95} +(-664.000 + 1150.08i) q^{97} +282.000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 4 q^{4} + 5 q^{5} + 22 q^{7} + 16 q^{8} - 20 q^{10} + 12 q^{11} - 38 q^{13} + 44 q^{14} - 16 q^{16} - 210 q^{17} - 314 q^{19} + 20 q^{20} + 24 q^{22} + 117 q^{23} - 25 q^{25} + 152 q^{26}+ \cdots + 564 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 4 * q^4 + 5 * q^5 + 22 * q^7 + 16 * q^8 - 20 * q^10 + 12 * q^11 - 38 * q^13 + 44 * q^14 - 16 * q^16 - 210 * q^17 - 314 * q^19 + 20 * q^20 + 24 * q^22 + 117 * q^23 - 25 * q^25 + 152 * q^26 - 176 * q^28 - 66 * q^29 + 25 * q^31 - 32 * q^32 + 210 * q^34 + 220 * q^35 + 628 * q^37 + 314 * q^38 + 40 * q^40 + 504 * q^41 - 380 * q^43 - 96 * q^44 - 468 * q^46 + 252 * q^47 - 141 * q^49 - 50 * q^50 - 152 * q^52 + 6 * q^53 + 120 * q^55 + 176 * q^56 - 132 * q^58 + 318 * q^59 - 293 * q^61 - 100 * q^62 + 128 * q^64 + 190 * q^65 + 322 * q^67 + 420 * q^68 - 220 * q^70 - 240 * q^71 + 88 * q^73 - 628 * q^74 + 628 * q^76 - 264 * q^77 - 917 * q^79 - 160 * q^80 - 2016 * q^82 - 309 * q^83 - 525 * q^85 - 760 * q^86 + 96 * q^88 + 2544 * q^89 - 1672 * q^91 + 468 * q^92 + 504 * q^94 - 785 * q^95 - 1328 * q^97 + 564 * q^98

Introduction

L-functions

Modular forms

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Database

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