LMFDB - Embedded newform 405.4.e.n.136.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,4,Mod(136,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("405.136");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	405.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:	$23.8957735523$
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:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			136.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	405.136
Dual form			405.4.e.n.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.50000 - 4.33013i) q^{2} +(-8.50000 - 14.7224i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(15.0000 - 25.9808i) q^{7} -45.0000 q^{8} +O(q^{10})$	\(q+(2.50000 - 4.33013i) q^{2} +(-8.50000 - 14.7224i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(15.0000 - 25.9808i) q^{7} -45.0000 q^{8} -25.0000 q^{10} +(25.0000 - 43.3013i) q^{11} +(10.0000 + 17.3205i) q^{13} +(-75.0000 - 129.904i) q^{14} +(-44.5000 + 77.0763i) q^{16} +10.0000 q^{17} -44.0000 q^{19} +(-42.5000 + 73.6122i) q^{20} +(-125.000 - 216.506i) q^{22} +(60.0000 + 103.923i) q^{23} +(-12.5000 + 21.6506i) q^{25} +100.000 q^{26} -510.000 q^{28} +(-25.0000 + 43.3013i) q^{29} +(-54.0000 - 93.5307i) q^{31} +(42.5000 + 73.6122i) q^{32} +(25.0000 - 43.3013i) q^{34} -150.000 q^{35} -40.0000 q^{37} +(-110.000 + 190.526i) q^{38} +(112.500 + 194.856i) q^{40} +(200.000 + 346.410i) q^{41} +(-140.000 + 242.487i) q^{43} -850.000 q^{44} +600.000 q^{46} +(-140.000 + 242.487i) q^{47} +(-278.500 - 482.376i) q^{49} +(62.5000 + 108.253i) q^{50} +(170.000 - 294.449i) q^{52} +610.000 q^{53} -250.000 q^{55} +(-675.000 + 1169.13i) q^{56} +(125.000 + 216.506i) q^{58} +(25.0000 + 43.3013i) q^{59} +(259.000 - 448.601i) q^{61} -540.000 q^{62} -287.000 q^{64} +(50.0000 - 86.6025i) q^{65} +(90.0000 + 155.885i) q^{67} +(-85.0000 - 147.224i) q^{68} +(-375.000 + 649.519i) q^{70} -700.000 q^{71} -410.000 q^{73} +(-100.000 + 173.205i) q^{74} +(374.000 + 647.787i) q^{76} +(-750.000 - 1299.04i) q^{77} +(258.000 - 446.869i) q^{79} +445.000 q^{80} +2000.00 q^{82} +(330.000 - 571.577i) q^{83} +(-25.0000 - 43.3013i) q^{85} +(700.000 + 1212.44i) q^{86} +(-1125.00 + 1948.56i) q^{88} +1500.00 q^{89} +600.000 q^{91} +(1020.00 - 1766.69i) q^{92} +(700.000 + 1212.44i) q^{94} +(110.000 + 190.526i) q^{95} +(815.000 - 1411.62i) q^{97} -2785.00 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 5 q^{2} - 17 q^{4} - 5 q^{5} + 30 q^{7} - 90 q^{8}+O(q^{10}) $ 2 * q + 5 * q^2 - 17 * q^4 - 5 * q^5 + 30 * q^7 - 90 * q^8	$ 2 q + 5 q^{2} - 17 q^{4} - 5 q^{5} + 30 q^{7} - 90 q^{8} - 50 q^{10} + 50 q^{11} + 20 q^{13} - 150 q^{14} - 89 q^{16} + 20 q^{17} - 88 q^{19} - 85 q^{20} - 250 q^{22} + 120 q^{23} - 25 q^{25} + 200 q^{26} - 1020 q^{28} - 50 q^{29} - 108 q^{31} + 85 q^{32} + 50 q^{34} - 300 q^{35} - 80 q^{37} - 220 q^{38} + 225 q^{40} + 400 q^{41} - 280 q^{43} - 1700 q^{44} + 1200 q^{46} - 280 q^{47} - 557 q^{49} + 125 q^{50} + 340 q^{52} + 1220 q^{53} - 500 q^{55} - 1350 q^{56} + 250 q^{58} + 50 q^{59} + 518 q^{61} - 1080 q^{62} - 574 q^{64} + 100 q^{65} + 180 q^{67} - 170 q^{68} - 750 q^{70} - 1400 q^{71} - 820 q^{73} - 200 q^{74} + 748 q^{76} - 1500 q^{77} + 516 q^{79} + 890 q^{80} + 4000 q^{82} + 660 q^{83} - 50 q^{85} + 1400 q^{86} - 2250 q^{88} + 3000 q^{89} + 1200 q^{91} + 2040 q^{92} + 1400 q^{94} + 220 q^{95} + 1630 q^{97} - 5570 q^{98}+O(q^{100}) $ 2 * q + 5 * q^2 - 17 * q^4 - 5 * q^5 + 30 * q^7 - 90 * q^8 - 50 * q^10 + 50 * q^11 + 20 * q^13 - 150 * q^14 - 89 * q^16 + 20 * q^17 - 88 * q^19 - 85 * q^20 - 250 * q^22 + 120 * q^23 - 25 * q^25 + 200 * q^26 - 1020 * q^28 - 50 * q^29 - 108 * q^31 + 85 * q^32 + 50 * q^34 - 300 * q^35 - 80 * q^37 - 220 * q^38 + 225 * q^40 + 400 * q^41 - 280 * q^43 - 1700 * q^44 + 1200 * q^46 - 280 * q^47 - 557 * q^49 + 125 * q^50 + 340 * q^52 + 1220 * q^53 - 500 * q^55 - 1350 * q^56 + 250 * q^58 + 50 * q^59 + 518 * q^61 - 1080 * q^62 - 574 * q^64 + 100 * q^65 + 180 * q^67 - 170 * q^68 - 750 * q^70 - 1400 * q^71 - 820 * q^73 - 200 * q^74 + 748 * q^76 - 1500 * q^77 + 516 * q^79 + 890 * q^80 + 4000 * q^82 + 660 * q^83 - 50 * q^85 + 1400 * q^86 - 2250 * q^88 + 3000 * q^89 + 1200 * q^91 + 2040 * q^92 + 1400 * q^94 + 220 * q^95 + 1630 * q^97 - 5570 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	2.50000	−	4.33013i	0.883883	−	1.53093i	0.0368954	−	0.999319i	$-0.488253\pi$
$2$	2.50000	−	4.33013i	0.883883	−	1.53093i	0.846988	−	0.531612i	$-0.178414\pi$
$3$		0			0
$3$		0			0
$4$	−8.50000	−	14.7224i	−1.06250	−	1.84030i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$6$		0			0
$7$	15.0000	−	25.9808i	0.809924	−	1.40283i	−0.102992	−	0.994682i	$-0.532842\pi$
$7$	15.0000	−	25.9808i	0.809924	−	1.40283i	0.912916	−	0.408147i	$-0.133825\pi$
$8$	−45.0000			−1.98874
$9$		0			0
$10$	−25.0000			−0.790569
$11$	25.0000	−	43.3013i	0.685253	−	1.18689i	−0.288104	−	0.957599i	$-0.593025\pi$
$11$	25.0000	−	43.3013i	0.685253	−	1.18689i	0.973357	−	0.229294i	$-0.0736417\pi$
$12$		0			0
$13$	10.0000	+	17.3205i	0.213346	+	0.369527i	0.952760	−	0.303725i	$-0.0982304\pi$
$13$	10.0000	+	17.3205i	0.213346	+	0.369527i	−0.739413	+	0.673252i	$0.764897\pi$
$14$	−75.0000	−	129.904i	−1.43176	−	2.47988i
$15$		0			0
$16$	−44.5000	+	77.0763i	−0.695312	+	1.20432i
$17$	10.0000			0.142668			0.0713340	−	0.997452i	$-0.477274\pi$
$17$	10.0000			0.142668			0.0713340	+	0.997452i	$0.477274\pi$
$18$		0			0
$19$	−44.0000			−0.531279			−0.265639	−	0.964072i	$-0.585583\pi$
$19$	−44.0000			−0.531279			−0.265639	+	0.964072i	$0.585583\pi$
$20$	−42.5000	+	73.6122i	−0.475164	+	0.823009i
$21$		0			0
$22$	−125.000	−	216.506i	−1.21137	−	2.09815i
$23$	60.0000	+	103.923i	0.543951	+	0.942150i	0.998672	+	0.0515165i	$0.0164055\pi$
$23$	60.0000	+	103.923i	0.543951	+	0.942150i	−0.454721	+	0.890634i	$0.650261\pi$
$24$		0			0
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	100.000			0.754293
$27$		0			0
$28$	−510.000			−3.44218
$29$	−25.0000	+	43.3013i	−0.160082	+	0.277270i	−0.934898	−	0.354917i	$-0.884509\pi$
$29$	−25.0000	+	43.3013i	−0.160082	+	0.277270i	0.774816	+	0.632187i	$0.217843\pi$
$30$		0			0
$31$	−54.0000	−	93.5307i	−0.312861	−	0.541891i	0.666120	−	0.745845i	$-0.267954\pi$
$31$	−54.0000	−	93.5307i	−0.312861	−	0.541891i	−0.978980	+	0.203954i	$0.934621\pi$
$32$	42.5000	+	73.6122i	0.234782	+	0.406654i
$33$		0			0
$34$	25.0000	−	43.3013i	0.126102	−	0.218415i
$35$	−150.000			−0.724418
$36$		0			0
$37$	−40.0000			−0.177729			−0.0888643	−	0.996044i	$-0.528324\pi$
$37$	−40.0000			−0.177729			−0.0888643	+	0.996044i	$0.528324\pi$
$38$	−110.000	+	190.526i	−0.469588	+	0.813351i
$39$		0			0
$40$	112.500	+	194.856i	0.444695	+	0.770235i
$41$	200.000	+	346.410i	0.761823	+	1.31952i	0.941910	+	0.335866i	$0.109029\pi$
$41$	200.000	+	346.410i	0.761823	+	1.31952i	−0.180087	+	0.983651i	$0.557638\pi$
$42$		0			0
$43$	−140.000	+	242.487i	−0.496507	+	0.859975i	−0.999992	−	0.00402871i	$-0.998718\pi$
$43$	−140.000	+	242.487i	−0.496507	+	0.859975i	0.503485	+	0.864004i	$0.332051\pi$
$44$	−850.000			−2.91233
$45$		0			0
$46$	600.000			1.92316
$47$	−140.000	+	242.487i	−0.434491	+	0.752561i	−0.997254	−	0.0740573i	$-0.976405\pi$
$47$	−140.000	+	242.487i	−0.434491	+	0.752561i	0.562763	+	0.826619i	$0.309739\pi$
$48$		0			0
$49$	−278.500	−	482.376i	−0.811953	−	1.40634i
$50$	62.5000	+	108.253i	0.176777	+	0.306186i
$51$		0			0
$52$	170.000	−	294.449i	0.453361	−	0.785244i
$53$	610.000			1.58094			0.790471	−	0.612499i	$-0.209836\pi$
$53$	610.000			1.58094			0.790471	+	0.612499i	$0.209836\pi$
$54$		0			0
$55$	−250.000			−0.612909
$56$	−675.000	+	1169.13i	−1.61073	+	2.78986i
$57$		0			0
$58$	125.000	+	216.506i	0.282988	+	0.490150i
$59$	25.0000	+	43.3013i	0.0551648	+	0.0955482i	0.892289	−	0.451465i	$-0.149098\pi$
$59$	25.0000	+	43.3013i	0.0551648	+	0.0955482i	−0.837124	+	0.547013i	$0.815765\pi$
$60$		0			0
$61$	259.000	−	448.601i	0.543632	−	0.941598i	−0.455060	−	0.890461i	$-0.650382\pi$
$61$	259.000	−	448.601i	0.543632	−	0.941598i	0.998692	−	0.0511373i	$-0.0162846\pi$
$62$	−540.000			−1.10613
$63$		0			0
$64$	−287.000			−0.560547
$65$	50.0000	−	86.6025i	0.0954113	−	0.165257i
$66$		0			0
$67$	90.0000	+	155.885i	0.164108	+	0.284244i	0.936338	−	0.351099i	$-0.114192\pi$
$67$	90.0000	+	155.885i	0.164108	+	0.284244i	−0.772230	+	0.635343i	$0.780859\pi$
$68$	−85.0000	−	147.224i	−0.151585	−	0.262553i
$69$		0			0
$70$	−375.000	+	649.519i	−0.640301	+	1.10903i
$71$	−700.000			−1.17007			−0.585033	−	0.811009i	$-0.698919\pi$
$71$	−700.000			−1.17007			−0.585033	+	0.811009i	$0.698919\pi$
$72$		0			0
$73$	−410.000			−0.657354			−0.328677	−	0.944442i	$-0.606603\pi$
$73$	−410.000			−0.657354			−0.328677	+	0.944442i	$0.606603\pi$
$74$	−100.000	+	173.205i	−0.157091	+	0.272090i
$75$		0			0
$76$	374.000	+	647.787i	0.564483	+	0.977714i
$77$	−750.000	−	1299.04i	−1.11001	−	1.92259i
$78$		0			0
$79$	258.000	−	446.869i	0.367434	−	0.636414i	−0.621730	−	0.783232i	$-0.713570\pi$
$79$	258.000	−	446.869i	0.367434	−	0.636414i	0.989164	+	0.146818i	$0.0469031\pi$
$80$	445.000			0.621906
$81$		0			0
$82$	2000.00			2.69345
$83$	330.000	−	571.577i	0.436412	−	0.755888i	−0.560998	−	0.827817i	$-0.689582\pi$
$83$	330.000	−	571.577i	0.436412	−	0.755888i	0.997410	+	0.0719295i	$0.0229156\pi$
$84$		0			0
$85$	−25.0000	−	43.3013i	−0.0319015	−	0.0552551i
$86$	700.000	+	1212.44i	0.877709	+	1.52024i
$87$		0			0
$88$	−1125.00	+	1948.56i	−1.36279	+	2.36042i
$89$	1500.00			1.78651			0.893257	−	0.449547i	$-0.148415\pi$
$89$	1500.00			1.78651			0.893257	+	0.449547i	$0.148415\pi$
$90$		0			0
$91$	600.000			0.691177
$92$	1020.00	−	1766.69i	1.15590	−	2.00207i
$93$		0			0
$94$	700.000	+	1212.44i	0.768080	+	1.33035i
$95$	110.000	+	190.526i	0.118797	+	0.205763i
$96$		0			0
$97$	815.000	−	1411.62i	0.853100	−	1.47761i	−0.0252963	−	0.999680i	$-0.508053\pi$
$97$	815.000	−	1411.62i	0.853100	−	1.47761i	0.878396	−	0.477933i	$-0.158614\pi$
$98$	−2785.00			−2.87069
$99$		0			0
$100$	425.000			0.425000
$101$	−225.000	+	389.711i	−0.221667	+	0.383938i	−0.955314	−	0.295592i	$-0.904483\pi$
$101$	−225.000	+	389.711i	−0.221667	+	0.383938i	0.733647	+	0.679530i	$0.237816\pi$
$102$		0			0
$103$	−385.000	−	666.840i	−0.368303	−	0.637919i	0.620998	−	0.783812i	$-0.286728\pi$
$103$	−385.000	−	666.840i	−0.368303	−	0.637919i	−0.989300	+	0.145893i	$0.953394\pi$
$104$	−450.000	−	779.423i	−0.424290	−	0.734891i
$105$		0			0
$106$	1525.00	−	2641.38i	1.39737	−	2.42031i
$107$	−660.000			−0.596305			−0.298152	−	0.954518i	$-0.596370\pi$
$107$	−660.000			−0.596305			−0.298152	+	0.954518i	$0.596370\pi$
$108$		0			0
$109$	1754.00			1.54131			0.770655	−	0.637253i	$-0.219929\pi$
$109$	1754.00			1.54131			0.770655	+	0.637253i	$0.219929\pi$
$110$	−625.000	+	1082.53i	−0.541740	+	0.938321i
$111$		0			0
$112$	1335.00	+	2312.29i	1.12630	+	1.95081i
$113$	−155.000	−	268.468i	−0.129037	−	0.223499i	0.794267	−	0.607569i	$-0.207855\pi$
$113$	−155.000	−	268.468i	−0.129037	−	0.223499i	−0.923304	+	0.384071i	$0.874522\pi$
$114$		0			0
$115$	300.000	−	519.615i	0.243262	−	0.421342i
$116$	850.000			0.680349
$117$		0			0
$118$	250.000			0.195037
$119$	150.000	−	259.808i	0.115550	−	0.200139i
$120$		0			0
$121$	−584.500	−	1012.38i	−0.439144	−	0.760619i
$122$	−1295.00	−	2243.01i	−0.961015	−	1.66453i
$123$		0			0
$124$	−918.000	+	1590.02i	−0.664829	+	1.15152i
$125$	125.000			0.0894427
$126$		0			0
$127$	−1070.00			−0.747615			−0.373808	−	0.927506i	$-0.621948\pi$
$127$	−1070.00			−0.747615			−0.373808	+	0.927506i	$0.621948\pi$
$128$	−1057.50	+	1831.64i	−0.730240	+	1.26481i
$129$		0			0
$130$	−250.000	−	433.013i	−0.168665	−	0.292136i
$131$	975.000	+	1688.75i	0.650276	+	1.12631i	0.983056	+	0.183306i	$0.0586800\pi$
$131$	975.000	+	1688.75i	0.650276	+	1.12631i	−0.332780	+	0.943005i	$0.607987\pi$
$132$		0			0
$133$	−660.000	+	1143.15i	−0.430295	+	0.745293i
$134$	900.000			0.580210
$135$		0			0
$136$	−450.000			−0.283729
$137$	525.000	−	909.327i	0.327400	−	0.567073i	−0.654595	−	0.755980i	$-0.727161\pi$
$137$	525.000	−	909.327i	0.327400	−	0.567073i	0.981995	+	0.188906i	$0.0604943\pi$
$138$		0			0
$139$	−838.000	−	1451.46i	−0.511354	−	0.885691i	−0.999913	−	0.0131607i	$-0.995811\pi$
$139$	−838.000	−	1451.46i	−0.511354	−	0.885691i	0.488559	−	0.872531i	$-0.337523\pi$
$140$	1275.00	+	2208.36i	0.769694	+	1.33315i
$141$		0			0
$142$	−1750.00	+	3031.09i	−1.03420	+	1.79129i
$143$	1000.00			0.584785
$144$		0			0
$145$	250.000			0.143182
$146$	−1025.00	+	1775.35i	−0.581025	+	1.00636i
$147$		0			0
$148$	340.000	+	588.897i	0.188837	+	0.327075i
$149$	1025.00	+	1775.35i	0.563566	+	0.976124i	0.997182	+	0.0750264i	$0.0239041\pi$
$149$	1025.00	+	1775.35i	0.563566	+	0.976124i	−0.433616	+	0.901098i	$0.642763\pi$
$150$		0			0
$151$	−224.000	+	387.979i	−0.120721	+	0.209095i	−0.920052	−	0.391796i	$-0.871854\pi$
$151$	−224.000	+	387.979i	−0.120721	+	0.209095i	0.799331	+	0.600891i	$0.205187\pi$
$152$	1980.00			1.05657
$153$		0			0
$154$	−7500.00			−3.92446
$155$	−270.000	+	467.654i	−0.139916	+	0.242341i
$156$		0			0
$157$	50.0000	+	86.6025i	0.0254168	+	0.0440232i	0.878454	−	0.477827i	$-0.158575\pi$
$157$	50.0000	+	86.6025i	0.0254168	+	0.0440232i	−0.853037	+	0.521850i	$0.825242\pi$
$158$	−1290.00	−	2234.35i	−0.649537	−	1.12503i
$159$		0			0
$160$	212.500	−	368.061i	0.104998	−	0.181861i
$161$	3600.00			1.76223
$162$		0			0
$163$	−1900.00			−0.913003			−0.456501	−	0.889723i	$-0.650898\pi$
$163$	−1900.00			−0.913003			−0.456501	+	0.889723i	$0.650898\pi$
$164$	3400.00	−	5888.97i	1.61887	−	2.80397i
$165$		0			0
$166$	−1650.00	−	2857.88i	−0.771475	−	1.33623i
$167$	960.000	+	1662.77i	0.444833	+	0.770473i	0.998041	−	0.0625706i	$-0.0199299\pi$
$167$	960.000	+	1662.77i	0.444833	+	0.770473i	−0.553208	+	0.833043i	$0.686597\pi$
$168$		0			0
$169$	898.500	−	1556.25i	0.408967	−	0.708351i
$170$	−250.000			−0.112789
$171$		0			0
$172$	4760.00			2.11015
$173$	1275.00	−	2208.36i	0.560326	−	0.970514i	−0.437141	−	0.899393i	$-0.644009\pi$
$173$	1275.00	−	2208.36i	0.560326	−	0.970514i	0.997468	−	0.0711209i	$-0.0226576\pi$
$174$		0			0
$175$	375.000	+	649.519i	0.161985	+	0.280566i
$176$	2225.00	+	3853.81i	0.952930	+	1.65052i
$177$		0			0
$178$	3750.00	−	6495.19i	1.57907	−	2.73503i
$179$	−3650.00			−1.52410			−0.762050	−	0.647518i	$-0.775807\pi$
$179$	−3650.00			−1.52410			−0.762050	+	0.647518i	$0.775807\pi$
$180$		0			0
$181$	−4342.00			−1.78308			−0.891542	−	0.452937i	$-0.850376\pi$
$181$	−4342.00			−1.78308			−0.891542	+	0.452937i	$0.850376\pi$
$182$	1500.00	−	2598.08i	0.610920	−	1.05814i
$183$		0			0
$184$	−2700.00	−	4676.54i	−1.08178	−	1.87369i
$185$	100.000	+	173.205i	0.0397413	+	0.0688340i
$186$		0			0
$187$	250.000	−	433.013i	0.0977637	−	0.169332i
$188$	4760.00			1.84659
$189$		0			0
$190$	1100.00			0.420013
$191$	−1750.00	+	3031.09i	−0.662961	+	1.14828i	0.316873	+	0.948468i	$0.397367\pi$
$191$	−1750.00	+	3031.09i	−0.662961	+	1.14828i	−0.979834	+	0.199814i	$0.935966\pi$
$192$		0			0
$193$	−1675.00	−	2901.19i	−0.624711	−	1.08203i	−0.988597	−	0.150587i	$-0.951884\pi$
$193$	−1675.00	−	2901.19i	−0.624711	−	1.08203i	0.363886	−	0.931443i	$-0.381450\pi$
$194$	−4075.00	−	7058.11i	−1.50808	−	2.61208i
$195$		0			0
$196$	−4734.50	+	8200.39i	−1.72540	+	2.98848i
$197$	−90.0000			−0.0325494			−0.0162747	−	0.999868i	$-0.505181\pi$
$197$	−90.0000			−0.0325494			−0.0162747	+	0.999868i	$0.505181\pi$
$198$		0			0
$199$	3664.00			1.30520			0.652598	−	0.757704i	$-0.273679\pi$
$199$	3664.00			1.30520			0.652598	+	0.757704i	$0.273679\pi$
$200$	562.500	−	974.279i	0.198874	−	0.344459i
$201$		0			0
$202$	1125.00	+	1948.56i	0.391855	+	0.678713i
$203$	750.000	+	1299.04i	0.259309	+	0.449136i
$204$		0			0
$205$	1000.00	−	1732.05i	0.340698	−	0.590106i
$206$	−3850.00			−1.30215
$207$		0			0
$208$	−1780.00			−0.593369
$209$	−1100.00	+	1905.26i	−0.364060	+	0.630571i
$210$		0			0
$211$	134.000	+	232.095i	0.0437201	+	0.0757254i	0.887057	−	0.461659i	$-0.152746\pi$
$211$	134.000	+	232.095i	0.0437201	+	0.0757254i	−0.843337	+	0.537385i	$0.819412\pi$
$212$	−5185.00	−	8980.68i	−1.67975	−	2.90941i
$213$		0			0
$214$	−1650.00	+	2857.88i	−0.527064	+	0.912901i
$215$	1400.00			0.444089
$216$		0			0
$217$	−3240.00			−1.01357
$218$	4385.00	−	7595.04i	1.36234	−	2.35964i
$219$		0			0
$220$	2125.00	+	3680.61i	0.651216	+	1.12794i
$221$	100.000	+	173.205i	0.0304377	+	0.0527196i
$222$		0			0
$223$	1835.00	−	3178.31i	0.551034	−	0.954420i	−0.447166	−	0.894451i	$-0.647567\pi$
$223$	1835.00	−	3178.31i	0.551034	−	0.954420i	0.998200	−	0.0599686i	$-0.0191001\pi$
$224$	2550.00			0.760621
$225$		0			0
$226$	−1550.00			−0.456214
$227$	1880.00	−	3256.26i	0.549692	−	0.952094i	−0.448604	−	0.893731i	$-0.648079\pi$
$227$	1880.00	−	3256.26i	0.549692	−	0.952094i	0.998295	−	0.0583630i	$-0.0185881\pi$
$228$		0			0
$229$	717.000	+	1241.88i	0.206903	+	0.358366i	0.950737	−	0.309998i	$-0.100328\pi$
$229$	717.000	+	1241.88i	0.206903	+	0.358366i	−0.743835	+	0.668364i	$0.766995\pi$
$230$	−1500.00	−	2598.08i	−0.430031	−	0.744835i
$231$		0			0
$232$	1125.00	−	1948.56i	0.318362	−	0.551418i
$233$	3450.00			0.970030			0.485015	−	0.874506i	$-0.338814\pi$
$233$	3450.00			0.970030			0.485015	+	0.874506i	$0.338814\pi$
$234$		0			0
$235$	1400.00			0.388621
$236$	425.000	−	736.122i	0.117225	−	0.203040i
$237$		0			0
$238$	−750.000	−	1299.04i	−0.204266	−	0.353799i
$239$	−2450.00	−	4243.52i	−0.663085	−	1.14850i	−0.979801	−	0.199976i	$-0.935913\pi$
$239$	−2450.00	−	4243.52i	−0.663085	−	1.14850i	0.316716	−	0.948521i	$-0.397420\pi$
$240$		0			0
$241$	−2411.00	+	4175.97i	−0.644424	+	1.11617i	0.340010	+	0.940422i	$0.389569\pi$
$241$	−2411.00	+	4175.97i	−0.644424	+	1.11617i	−0.984434	+	0.175753i	$0.943764\pi$
$242$	−5845.00			−1.55261
$243$		0			0
$244$	−8806.00			−2.31044
$245$	−1392.50	+	2411.88i	−0.363117	+	0.628936i
$246$		0			0
$247$	−440.000	−	762.102i	−0.113346	−	0.196322i
$248$	2430.00	+	4208.88i	0.622198	+	1.07768i
$249$		0			0
$250$	312.500	−	541.266i	0.0790569	−	0.136931i
$251$	4650.00			1.16934			0.584672	−	0.811270i	$-0.301223\pi$
$251$	4650.00			1.16934			0.584672	+	0.811270i	$0.301223\pi$
$252$		0			0
$253$	6000.00			1.49098
$254$	−2675.00	+	4633.24i	−0.660805	+	1.14455i
$255$		0			0
$256$	4139.50	+	7169.82i	1.01062	+	1.75045i
$257$	2565.00	+	4442.71i	0.622569	+	1.07832i	0.989006	+	0.147878i	$0.0472444\pi$
$257$	2565.00	+	4442.71i	0.622569	+	1.07832i	−0.366436	+	0.930443i	$0.619422\pi$
$258$		0			0
$259$	−600.000	+	1039.23i	−0.143947	+	0.249323i
$260$	−1700.00			−0.405498
$261$		0			0
$262$	9750.00			2.29907
$263$	−640.000	+	1108.51i	−0.150054	+	0.259900i	−0.931247	−	0.364389i	$-0.881278\pi$
$263$	−640.000	+	1108.51i	−0.150054	+	0.259900i	0.781193	+	0.624289i	$0.214611\pi$
$264$		0			0
$265$	−1525.00	−	2641.38i	−0.353509	−	0.612296i
$266$	3300.00	+	5715.77i	0.760662	+	1.31750i
$267$		0			0
$268$	1530.00	−	2650.04i	0.348730	−	0.604018i
$269$	−3350.00			−0.759305			−0.379653	−	0.925129i	$-0.623956\pi$
$269$	−3350.00			−0.759305			−0.379653	+	0.925129i	$0.623956\pi$
$270$		0			0
$271$	5512.00			1.23554			0.617768	−	0.786361i	$-0.288037\pi$
$271$	5512.00			1.23554			0.617768	+	0.786361i	$0.288037\pi$
$272$	−445.000	+	770.763i	−0.0991989	+	0.171817i
$273$		0			0
$274$	−2625.00	−	4546.63i	−0.578767	−	1.00245i
$275$	625.000	+	1082.53i	0.137051	+	0.237379i
$276$		0			0
$277$	−2460.00	+	4260.84i	−0.533600	+	0.924222i	0.465630	+	0.884979i	$0.345828\pi$
$277$	−2460.00	+	4260.84i	−0.533600	+	0.924222i	−0.999230	+	0.0392421i	$0.987506\pi$
$278$	−8380.00			−1.80791
$279$		0			0
$280$	6750.00			1.44068
$281$	2250.00	−	3897.11i	0.477665	−	0.827339i	−0.522008	−	0.852941i	$-0.674817\pi$
$281$	2250.00	−	3897.11i	0.477665	−	0.827339i	0.999672	+	0.0256015i	$0.00815010\pi$
$282$		0			0
$283$	3450.00	+	5975.58i	0.724669	+	1.25516i	0.959110	+	0.283033i	$0.0913405\pi$
$283$	3450.00	+	5975.58i	0.724669	+	1.25516i	−0.234442	+	0.972130i	$0.575326\pi$
$284$	5950.00	+	10305.7i	1.24320	+	2.15328i
$285$		0			0
$286$	2500.00	−	4330.13i	0.516881	−	0.895265i
$287$	12000.0			2.46808
$288$		0			0
$289$	−4813.00			−0.979646
$290$	625.000	−	1082.53i	0.126556	−	0.219202i
$291$		0			0
$292$	3485.00	+	6036.20i	0.698439	+	1.20973i
$293$	765.000	+	1325.02i	0.152532	+	0.264193i	0.932158	−	0.362053i	$-0.117924\pi$
$293$	765.000	+	1325.02i	0.152532	+	0.264193i	−0.779626	+	0.626246i	$0.784591\pi$
$294$		0			0
$295$	125.000	−	216.506i	0.0246704	−	0.0427305i
$296$	1800.00			0.353456
$297$		0			0
$298$	10250.0			1.99251
$299$	−1200.00	+	2078.46i	−0.232100	+	0.402008i
$300$		0			0
$301$	4200.00	+	7274.61i	0.804266	+	1.39303i
$302$	1120.00	+	1939.90i	0.213406	+	0.369631i
$303$		0			0
$304$	1958.00	−	3391.36i	0.369405	−	0.639828i
$305$	−2590.00			−0.486239
$306$		0			0
$307$	3040.00			0.565153			0.282576	−	0.959245i	$-0.408811\pi$
$307$	3040.00			0.565153			0.282576	+	0.959245i	$0.408811\pi$
$308$	−12750.0	+	22083.6i	−2.35876	+	4.08550i
$309$		0			0
$310$	1350.00	+	2338.27i	0.247338	+	0.428402i
$311$	−2850.00	−	4936.34i	−0.519642	−	0.900046i	−0.999739	−	0.0228312i	$-0.992732\pi$
$311$	−2850.00	−	4936.34i	−0.519642	−	0.900046i	0.480097	−	0.877215i	$-0.340601\pi$
$312$		0			0
$313$	−1555.00	+	2693.34i	−0.280811	+	0.486379i	−0.971585	−	0.236692i	$-0.923937\pi$
$313$	−1555.00	+	2693.34i	−0.280811	+	0.486379i	0.690774	+	0.723071i	$0.257270\pi$
$314$	500.000			0.0898619
$315$		0			0
$316$	−8772.00			−1.56159
$317$	−475.000	+	822.724i	−0.0841598	+	0.145769i	−0.905033	−	0.425342i	$-0.860154\pi$
$317$	−475.000	+	822.724i	−0.0841598	+	0.145769i	0.820873	+	0.571111i	$0.193487\pi$
$318$		0			0
$319$	1250.00	+	2165.06i	0.219394	+	0.380001i
$320$	717.500	+	1242.75i	0.125342	+	0.217099i
$321$		0			0
$322$	9000.00	−	15588.5i	1.55761	−	2.69786i
$323$	−440.000			−0.0757965
$324$		0			0
$325$	−500.000			−0.0853385
$326$	−4750.00	+	8227.24i	−0.806988	+	1.39774i
$327$		0			0
$328$	−9000.00	−	15588.5i	−1.51507	−	2.62417i
$329$	4200.00	+	7274.61i	0.703810	+	1.21903i
$330$		0			0
$331$	−1146.00	+	1984.93i	−0.190302	+	0.329612i	−0.945350	−	0.326057i	$-0.894280\pi$
$331$	−1146.00	+	1984.93i	−0.190302	+	0.329612i	0.755049	+	0.655669i	$0.227613\pi$
$332$	−11220.0			−1.85475
$333$		0			0
$334$	9600.00			1.57272
$335$	450.000	−	779.423i	0.0733914	−	0.127118i
$336$		0			0
$337$	3865.00	+	6694.38i	0.624748	+	1.08209i	0.988590	+	0.150634i	$0.0481315\pi$
$337$	3865.00	+	6694.38i	0.624748	+	1.08209i	−0.363842	+	0.931461i	$0.618535\pi$
$338$	−4492.50	−	7781.24i	−0.722958	−	1.25220i
$339$		0			0
$340$	−425.000	+	736.122i	−0.0677908	+	0.117417i
$341$	−5400.00			−0.857555
$342$		0			0
$343$	−6420.00			−1.01063
$344$	6300.00	−	10911.9i	0.987422	−	1.71027i
$345$		0			0
$346$	−6375.00	−	11041.8i	−0.990526	−	1.71564i
$347$	−560.000	−	969.948i	−0.0866351	−	0.150056i	0.819452	−	0.573148i	$-0.194278\pi$
$347$	−560.000	−	969.948i	−0.0866351	−	0.150056i	−0.906087	+	0.423092i	$0.860945\pi$
$348$		0			0
$349$	−593.000	+	1027.11i	−0.0909529	+	0.157535i	−0.907912	−	0.419160i	$-0.862325\pi$
$349$	−593.000	+	1027.11i	−0.0909529	+	0.157535i	0.816959	+	0.576695i	$0.195658\pi$
$350$	3750.00			0.572703
$351$		0			0
$352$	4250.00			0.643539
$353$	1815.00	−	3143.67i	0.273662	−	0.473997i	−0.696135	−	0.717911i	$-0.745098\pi$
$353$	1815.00	−	3143.67i	0.273662	−	0.473997i	0.969797	+	0.243915i	$0.0784317\pi$
$354$		0			0
$355$	1750.00	+	3031.09i	0.261635	+	0.453165i
$356$	−12750.0	−	22083.6i	−1.89817	−	3.28773i
$357$		0			0
$358$	−9125.00	+	15805.0i	−1.34713	+	2.33329i
$359$	1800.00			0.264625			0.132312	−	0.991208i	$-0.457760\pi$
$359$	1800.00			0.264625			0.132312	+	0.991208i	$0.457760\pi$
$360$		0			0
$361$	−4923.00			−0.717743
$362$	−10855.0	+	18801.4i	−1.57604	+	2.72978i
$363$		0			0
$364$	−5100.00	−	8833.46i	−0.734375	−	1.27198i
$365$	1025.00	+	1775.35i	0.146989	+	0.254592i
$366$		0			0
$367$	−4245.00	+	7352.56i	−0.603780	+	1.04578i	0.388463	+	0.921464i	$0.373006\pi$
$367$	−4245.00	+	7352.56i	−0.603780	+	1.04578i	−0.992243	+	0.124313i	$0.960327\pi$
$368$	−10680.0			−1.51286
$369$		0			0
$370$	1000.00			0.140507
$371$	9150.00	−	15848.3i	1.28044	−	2.21779i
$372$		0			0
$373$	−50.0000	−	86.6025i	−0.00694076	−	0.0120217i	0.862534	−	0.505999i	$-0.168876\pi$
$373$	−50.0000	−	86.6025i	−0.00694076	−	0.0120217i	−0.869475	+	0.493977i	$0.835543\pi$
$374$	−1250.00	−	2165.06i	−0.172823	−	0.299339i
$375$		0			0
$376$	6300.00	−	10911.9i	0.864090	−	1.49665i
$377$	−1000.00			−0.136612
$378$		0			0
$379$	−8084.00			−1.09564			−0.547820	−	0.836597i	$-0.684542\pi$
$379$	−8084.00			−1.09564			−0.547820	+	0.836597i	$0.684542\pi$
$380$	1870.00	−	3238.94i	0.252445	−	0.437247i
$381$		0			0
$382$	8750.00	+	15155.4i	1.17196	+	2.02990i
$383$	−4740.00	−	8209.92i	−0.632383	−	1.09532i	−0.987063	−	0.160332i	$-0.948744\pi$
$383$	−4740.00	−	8209.92i	−0.632383	−	1.09532i	0.354680	−	0.934988i	$-0.384590\pi$
$384$		0			0
$385$	−3750.00	+	6495.19i	−0.496410	+	0.859807i
$386$	−16750.0			−2.20869
$387$		0			0
$388$	−27710.0			−3.62568
$389$	−5475.00	+	9482.98i	−0.713608	+	1.23601i	0.249886	+	0.968275i	$0.419607\pi$
$389$	−5475.00	+	9482.98i	−0.713608	+	1.23601i	−0.963494	+	0.267730i	$0.913726\pi$
$390$		0			0
$391$	600.000	+	1039.23i	0.0776044	+	0.134415i
$392$	12532.5	+	21706.9i	1.61476	+	2.79685i
$393$		0			0
$394$	−225.000	+	389.711i	−0.0287699	+	0.0498309i
$395$	−2580.00			−0.328643
$396$		0			0
$397$	13840.0			1.74965			0.874823	−	0.484442i	$-0.160977\pi$
$397$	13840.0			1.74965			0.874823	+	0.484442i	$0.160977\pi$
$398$	9160.00	−	15865.6i	1.15364	−	1.99817i
$399$		0			0
$400$	−1112.50	−	1926.91i	−0.139063	−	0.240863i
$401$	4650.00	+	8054.04i	0.579077	+	1.00299i	0.995585	+	0.0938591i	$0.0299203\pi$
$401$	4650.00	+	8054.04i	0.579077	+	1.00299i	−0.416508	+	0.909132i	$0.636746\pi$
$402$		0			0
$403$	1080.00	−	1870.61i	0.133495	−	0.231221i
$404$	7650.00			0.942083
$405$		0			0
$406$	7500.00			0.916795
$407$	−1000.00	+	1732.05i	−0.121789	+	0.210945i
$408$		0			0
$409$	1427.00	+	2471.64i	0.172520	+	0.298813i	0.939300	−	0.343096i	$-0.111476\pi$
$409$	1427.00	+	2471.64i	0.172520	+	0.298813i	−0.766780	+	0.641910i	$0.778142\pi$
$410$	−5000.00	−	8660.25i	−0.602274	−	1.04317i
$411$		0			0
$412$	−6545.00	+	11336.3i	−0.782643	+	1.35558i
$413$	1500.00			0.178717
$414$		0			0
$415$	−3300.00			−0.390339
$416$	−850.000	+	1472.24i	−0.100180	+	0.173516i
$417$		0			0
$418$	5500.00	+	9526.28i	0.643574	+	1.11470i
$419$	575.000	+	995.929i	0.0670420	+	0.116120i	0.897598	−	0.440815i	$-0.145311\pi$
$419$	575.000	+	995.929i	0.0670420	+	0.116120i	−0.830556	+	0.556935i	$0.811977\pi$
$420$		0			0
$421$	5581.00	−	9666.58i	0.646084	−	1.11905i	−0.337966	−	0.941158i	$-0.609739\pi$
$421$	5581.00	−	9666.58i	0.646084	−	1.11905i	0.984050	−	0.177892i	$-0.0569277\pi$
$422$	1340.00			0.154574
$423$		0			0
$424$	−27450.0			−3.14408
$425$	−125.000	+	216.506i	−0.0142668	+	0.0247108i
$426$		0			0
$427$	−7770.00	−	13458.0i	−0.880601	−	1.52525i
$428$	5610.00	+	9716.81i	0.633574	+	1.09738i
$429$		0			0
$430$	3500.00	−	6062.18i	0.392523	−	0.679870i
$431$	1200.00			0.134111			0.0670556	−	0.997749i	$-0.478639\pi$
$431$	1200.00			0.134111			0.0670556	+	0.997749i	$0.478639\pi$
$432$		0			0
$433$	1510.00			0.167589			0.0837944	−	0.996483i	$-0.473296\pi$
$433$	1510.00			0.167589			0.0837944	+	0.996483i	$0.473296\pi$
$434$	−8100.00	+	14029.6i	−0.895881	+	1.55171i
$435$		0			0
$436$	−14909.0	−	25823.1i	−1.63764	−	2.83648i
$437$	−2640.00	−	4572.61i	−0.288989	−	0.500544i
$438$		0			0
$439$	−212.000	+	367.195i	−0.0230483	+	0.0399208i	−0.877320	−	0.479907i	$-0.840670\pi$
$439$	−212.000	+	367.195i	−0.0230483	+	0.0399208i	0.854271	+	0.519828i	$0.174004\pi$
$440$	11250.0			1.21892
$441$		0			0
$442$	1000.00			0.107613
$443$	6180.00	−	10704.1i	0.662801	−	1.14800i	−0.317076	−	0.948400i	$-0.602701\pi$
$443$	6180.00	−	10704.1i	0.662801	−	1.14800i	0.979877	−	0.199604i	$-0.0639656\pi$
$444$		0			0
$445$	−3750.00	−	6495.19i	−0.399477	−	0.691914i
$446$	−9175.00	−	15891.6i	−0.974101	−	1.68719i
$447$		0			0
$448$	−4305.00	+	7456.48i	−0.454000	+	0.786352i
$449$	1300.00			0.136639			0.0683194	−	0.997664i	$-0.478236\pi$
$449$	1300.00			0.136639			0.0683194	+	0.997664i	$0.478236\pi$
$450$		0			0
$451$	20000.0			2.08817
$452$	−2635.00	+	4563.95i	−0.274203	+	0.474934i
$453$		0			0
$454$	−9400.00	−	16281.3i	−0.971727	−	1.68308i
$455$	−1500.00	−	2598.08i	−0.154552	−	0.267692i
$456$		0			0
$457$	3595.00	−	6226.72i	0.367980	−	0.637361i	−0.621269	−	0.783597i	$-0.713383\pi$
$457$	3595.00	−	6226.72i	0.367980	−	0.637361i	0.989250	+	0.146236i	$0.0467160\pi$
$458$	7170.00			0.731511
$459$		0			0
$460$	−10200.0			−1.03386
$461$	−75.0000	+	129.904i	−0.00757722	+	0.0131241i	−0.869789	−	0.493424i	$-0.835745\pi$
$461$	−75.0000	+	129.904i	−0.00757722	+	0.0131241i	0.862212	+	0.506548i	$0.169079\pi$
$462$		0			0
$463$	−1335.00	−	2312.29i	−0.134002	−	0.232097i	0.791214	−	0.611539i	$-0.209449\pi$
$463$	−1335.00	−	2312.29i	−0.134002	−	0.232097i	−0.925216	+	0.379442i	$0.876116\pi$
$464$	−2225.00	−	3853.81i	−0.222614	−	0.385579i
$465$		0			0
$466$	8625.00	−	14938.9i	0.857394	−	1.48505i
$467$	−1180.00			−0.116925			−0.0584624	−	0.998290i	$-0.518620\pi$
$467$	−1180.00			−0.116925			−0.0584624	+	0.998290i	$0.518620\pi$
$468$		0			0
$469$	5400.00			0.531661
$470$	3500.00	−	6062.18i	0.343496	−	0.594952i
$471$		0			0
$472$	−1125.00	−	1948.56i	−0.109708	−	0.190020i
$473$	7000.00	+	12124.4i	0.680466	+	1.17860i
$474$		0			0
$475$	550.000	−	952.628i	0.0531279	−	0.0920201i
$476$	−5100.00			−0.491088
$477$		0			0
$478$	−24500.0			−2.34436
$479$	−7050.00	+	12211.0i	−0.672490	+	1.16479i	0.304706	+	0.952447i	$0.401442\pi$
$479$	−7050.00	+	12211.0i	−0.672490	+	1.16479i	−0.977196	+	0.212340i	$0.931891\pi$
$480$		0			0
$481$	−400.000	−	692.820i	−0.0379177	−	0.0656754i
$482$	12055.0	+	20879.9i	1.13919	+	1.97314i
$483$		0			0
$484$	−9936.50	+	17210.5i	−0.933180	+	1.61632i
$485$	−8150.00			−0.763036
$486$		0			0
$487$	−9850.00			−0.916522			−0.458261	−	0.888818i	$-0.651527\pi$
$487$	−9850.00			−0.916522			−0.458261	+	0.888818i	$0.651527\pi$
$488$	−11655.0	+	20187.1i	−1.08114	+	1.87259i
$489$		0			0
$490$	6962.50	+	12059.4i	0.641905	+	1.11181i
$491$	−1225.00	−	2121.76i	−0.112594	−	0.195018i	0.804222	−	0.594330i	$-0.202582\pi$
$491$	−1225.00	−	2121.76i	−0.112594	−	0.195018i	−0.916815	+	0.399312i	$0.869249\pi$
$492$		0			0
$493$	−250.000	+	433.013i	−0.0228386	+	0.0395576i
$494$	−4400.00			−0.400740
$495$		0			0
$496$	9612.00			0.870144
$497$	−10500.0	+	18186.5i	−0.947665	+	1.64140i
$498$		0			0
$499$	8518.00	+	14753.6i	0.764164	+	1.32357i	0.940687	+	0.339275i	$0.110182\pi$
$499$	8518.00	+	14753.6i	0.764164	+	1.32357i	−0.176523	+	0.984297i	$0.556485\pi$
$500$	−1062.50	−	1840.30i	−0.0950329	−	0.164602i
$501$		0			0
$502$	11625.0	−	20135.1i	1.03356	−	1.79019i
$503$	20600.0			1.82606			0.913030	−	0.407891i	$-0.133736\pi$
$503$	20600.0			1.82606			0.913030	+	0.407891i	$0.133736\pi$
$504$		0			0
$505$	2250.00			0.198265
$506$	15000.0	−	25980.8i	1.31785	−	2.28258i
$507$		0			0
$508$	9095.00	+	15753.0i	0.794341	+	1.37584i
$509$	2875.00	+	4979.65i	0.250358	+	0.433632i	0.963624	−	0.267260i	$-0.0861184\pi$
$509$	2875.00	+	4979.65i	0.250358	+	0.433632i	−0.713267	+	0.700893i	$0.752785\pi$
$510$		0			0
$511$	−6150.00	+	10652.1i	−0.532407	+	0.922156i
$512$	24475.0			2.11260
$513$		0			0
$514$	25650.0			2.20111
$515$	−1925.00	+	3334.20i	−0.164710	+	0.285286i
$516$		0			0
$517$	7000.00	+	12124.4i	0.595473	+	1.03139i
$518$	3000.00	+	5196.15i	0.254464	+	0.440745i
$519$		0			0
$520$	−2250.00	+	3897.11i	−0.189748	+	0.328653i
$521$	15500.0			1.30339			0.651696	−	0.758480i	$-0.274058\pi$
$521$	15500.0			1.30339			0.651696	+	0.758480i	$0.274058\pi$
$522$		0			0
$523$	−13940.0			−1.16549			−0.582747	−	0.812653i	$-0.698022\pi$
$523$	−13940.0			−1.16549			−0.582747	+	0.812653i	$0.698022\pi$
$524$	16575.0	−	28708.7i	1.38184	−	2.39341i
$525$		0			0
$526$	3200.00	+	5542.56i	0.265260	+	0.459443i
$527$	−540.000	−	935.307i	−0.0446352	−	0.0773105i
$528$		0			0
$529$	−1116.50	+	1933.83i	−0.0917646	+	0.158941i
$530$	−15250.0			−1.24984
$531$		0			0
$532$	22440.0			1.82875
$533$	−4000.00	+	6928.20i	−0.325064	+	0.563028i
$534$		0			0
$535$	1650.00	+	2857.88i	0.133338	+	0.230948i
$536$	−4050.00	−	7014.81i	−0.326368	−	0.565286i
$537$		0			0
$538$	−8375.00	+	14505.9i	−0.671137	+	1.16244i
$539$	−27850.0			−2.22557
$540$		0			0
$541$	−20478.0			−1.62739			−0.813695	−	0.581292i	$-0.802547\pi$
$541$	−20478.0			−1.62739			−0.813695	+	0.581292i	$0.802547\pi$
$542$	13780.0	−	23867.7i	1.09207	−	1.89152i
$543$		0			0
$544$	425.000	+	736.122i	0.0334958	+	0.0580165i
$545$	−4385.00	−	7595.04i	−0.344647	−	0.596947i
$546$		0			0
$547$	−6020.00	+	10426.9i	−0.470561	+	0.815035i	−0.999433	−	0.0336665i	$-0.989282\pi$
$547$	−6020.00	+	10426.9i	−0.470561	+	0.815035i	0.528873	+	0.848701i	$0.322615\pi$
$548$	−17850.0			−1.39145
$549$		0			0
$550$	6250.00			0.484547
$551$	1100.00	−	1905.26i	0.0850482	−	0.147308i
$552$		0			0
$553$	−7740.00	−	13406.1i	−0.595187	−	1.03089i
$554$	12300.0	+	21304.2i	0.943280	+	1.63381i
$555$		0			0
$556$	−14246.0	+	24674.8i	−1.08663	+	1.88209i
$557$	−23550.0			−1.79146			−0.895732	−	0.444594i	$-0.853348\pi$
$557$	−23550.0			−1.79146			−0.895732	+	0.444594i	$0.853348\pi$
$558$		0			0
$559$	−5600.00			−0.423712
$560$	6675.00	−	11561.4i	0.503697	−	0.872429i
$561$		0			0
$562$	−11250.0	−	19485.6i	−0.844400	−	1.46254i
$563$	−3060.00	−	5300.08i	−0.229065	−	0.396752i	0.728466	−	0.685082i	$-0.240234\pi$
$563$	−3060.00	−	5300.08i	−0.229065	−	0.396752i	−0.957531	+	0.288329i	$0.906900\pi$
$564$		0			0
$565$	−775.000	+	1342.34i	−0.0577071	+	0.0999516i
$566$	34500.0			2.56209
$567$		0			0
$568$	31500.0			2.32696
$569$	−5850.00	+	10132.5i	−0.431010	+	0.746531i	−0.996961	−	0.0779078i	$-0.975176\pi$
$569$	−5850.00	+	10132.5i	−0.431010	+	0.746531i	0.565950	+	0.824439i	$0.308509\pi$
$570$		0			0
$571$	4094.00	+	7091.02i	0.300050	+	0.519702i	0.976147	−	0.217111i	$-0.0696633\pi$
$571$	4094.00	+	7091.02i	0.300050	+	0.519702i	−0.676097	+	0.736813i	$0.736330\pi$
$572$	−8500.00	−	14722.4i	−0.621334	−	1.07618i
$573$		0			0
$574$	30000.0	−	51961.5i	2.18149	−	3.77845i
$575$	−3000.00			−0.217580
$576$		0			0
$577$	11690.0			0.843433			0.421717	−	0.906728i	$-0.361428\pi$
$577$	11690.0			0.843433			0.421717	+	0.906728i	$0.361428\pi$
$578$	−12032.5	+	20840.9i	−0.865893	+	1.49977i
$579$		0			0
$580$	−2125.00	−	3680.61i	−0.152131	−	0.263498i
$581$	−9900.00	−	17147.3i	−0.706921	−	1.22442i
$582$		0			0
$583$	15250.0	−	26413.8i	1.08335	−	1.87641i
$584$	18450.0			1.30731
$585$		0			0
$586$	7650.00			0.539281
$587$	10530.0	−	18238.5i	0.740408	−	1.28242i	−0.211901	−	0.977291i	$-0.567966\pi$
$587$	10530.0	−	18238.5i	0.740408	−	1.28242i	0.952310	−	0.305134i	$-0.0987011\pi$
$588$		0			0
$589$	2376.00	+	4115.35i	0.166216	+	0.287895i
$590$	−625.000	−	1082.53i	−0.0436116	−	0.0755375i
$591$		0			0
$592$	1780.00	−	3083.05i	0.123577	−	0.214042i
$593$	22910.0			1.58651			0.793255	−	0.608889i	$-0.208385\pi$
$593$	22910.0			1.58651			0.793255	+	0.608889i	$0.208385\pi$
$594$		0			0
$595$	−1500.00			−0.103351
$596$	17425.0	−	30181.0i	1.19758	−	2.07426i
$597$		0			0
$598$	6000.00	+	10392.3i	0.410298	+	0.710657i
$599$	−700.000	−	1212.44i	−0.0477483	−	0.0827025i	0.841163	−	0.540781i	$-0.181871\pi$
$599$	−700.000	−	1212.44i	−0.0477483	−	0.0827025i	−0.888912	+	0.458078i	$0.848538\pi$
$600$		0			0
$601$	5501.00	−	9528.01i	0.373362	−	0.646682i	−0.616719	−	0.787184i	$-0.711538\pi$
$601$	5501.00	−	9528.01i	0.373362	−	0.646682i	0.990080	+	0.140502i	$0.0448717\pi$
$602$	42000.0			2.84351
$603$		0			0
$604$	7616.00			0.513064
$605$	−2922.50	+	5061.92i	−0.196391	+	0.340159i
$606$		0			0
$607$	−2315.00	−	4009.70i	−0.154799	−	0.268120i	0.778187	−	0.628033i	$-0.216140\pi$
$607$	−2315.00	−	4009.70i	−0.154799	−	0.268120i	−0.932986	+	0.359913i	$0.882806\pi$
$608$	−1870.00	−	3238.94i	−0.124734	−	0.216046i
$609$		0			0
$610$	−6475.00	+	11215.0i	−0.429779	+	0.744399i
$611$	−5600.00			−0.370788
$612$		0			0
$613$	24040.0			1.58396			0.791979	−	0.610548i	$-0.209051\pi$
$613$	24040.0			1.58396			0.791979	+	0.610548i	$0.209051\pi$
$614$	7600.00	−	13163.6i	0.499529	−	0.865210i
$615$		0			0
$616$	33750.0	+	58456.7i	2.20751	+	3.82352i
$617$	−945.000	−	1636.79i	−0.0616601	−	0.106798i	0.833547	−	0.552448i	$-0.186306\pi$
$617$	−945.000	−	1636.79i	−0.0616601	−	0.106798i	−0.895208	+	0.445649i	$0.852973\pi$
$618$		0			0
$619$	−9622.00	+	16665.8i	−0.624783	+	1.08216i	0.363799	+	0.931477i	$0.381479\pi$
$619$	−9622.00	+	16665.8i	−0.624783	+	1.08216i	−0.988583	+	0.150679i	$0.951854\pi$
$620$	9180.00			0.594641
$621$		0			0
$622$	−28500.0			−1.83721
$623$	22500.0	−	38971.1i	1.44694	−	2.50617i
$624$		0			0
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	7775.00	+	13466.7i	0.496408	+	0.859804i
$627$		0			0
$628$	850.000	−	1472.24i	0.0540107	−	0.0935492i
$629$	−400.000			−0.0253562
$630$		0			0
$631$	15892.0			1.00262			0.501308	−	0.865269i	$-0.332852\pi$
$631$	15892.0			1.00262			0.501308	+	0.865269i	$0.332852\pi$
$632$	−11610.0	+	20109.1i	−0.730729	+	1.26566i
$633$		0			0
$634$	2375.00	+	4113.62i	0.148775	+	0.257686i
$635$	2675.00	+	4633.24i	0.167172	+	0.289550i
$636$		0			0
$637$	5570.00	−	9647.52i	0.346454	−	0.600077i
$638$	12500.0			0.775674
$639$		0			0
$640$	10575.0			0.653146
$641$	−6300.00	+	10911.9i	−0.388198	+	0.672379i	−0.992207	−	0.124598i	$-0.960236\pi$
$641$	−6300.00	+	10911.9i	−0.388198	+	0.672379i	0.604009	+	0.796977i	$0.293569\pi$
$642$		0			0
$643$	−3630.00	−	6287.34i	−0.222633	−	0.385612i	0.732973	−	0.680257i	$-0.238132\pi$
$643$	−3630.00	−	6287.34i	−0.222633	−	0.385612i	−0.955607	+	0.294645i	$0.904799\pi$
$644$	−30600.0	−	53000.8i	−1.87237	−	3.24305i
$645$		0			0
$646$	−1100.00	+	1905.26i	−0.0669952	+	0.116039i
$647$	−7400.00			−0.449651			−0.224825	−	0.974399i	$-0.572181\pi$
$647$	−7400.00			−0.449651			−0.224825	+	0.974399i	$0.572181\pi$
$648$		0			0
$649$	2500.00			0.151207
$650$	−1250.00	+	2165.06i	−0.0754293	+	0.130647i
$651$		0			0
$652$	16150.0	+	27972.6i	0.970066	+	1.68020i
$653$	−2395.00	−	4148.26i	−0.143528	−	0.248597i	0.785295	−	0.619122i	$-0.212511\pi$
$653$	−2395.00	−	4148.26i	−0.143528	−	0.248597i	−0.928823	+	0.370525i	$0.879178\pi$
$654$		0			0
$655$	4875.00	−	8443.75i	0.290812	−	0.503702i
$656$	−35600.0			−2.11882
$657$		0			0
$658$	42000.0			2.48834
$659$	−725.000	+	1255.74i	−0.0428558	+	0.0742285i	−0.886658	−	0.462426i	$-0.846979\pi$
$659$	−725.000	+	1255.74i	−0.0428558	+	0.0742285i	0.843802	+	0.536655i	$0.180312\pi$
$660$		0			0
$661$	−5909.00	−	10234.7i	−0.347706	−	0.602244i	0.638136	−	0.769924i	$-0.279706\pi$
$661$	−5909.00	−	10234.7i	−0.347706	−	0.602244i	−0.985841	+	0.167680i	$0.946372\pi$
$662$	5730.00	+	9924.65i	0.336409	+	0.582678i
$663$		0			0
$664$	−14850.0	+	25721.0i	−0.867909	+	1.50326i
$665$	6600.00			0.384868
$666$		0			0
$667$	−6000.00			−0.348307
$668$	16320.0	−	28267.1i	0.945269	−	1.63725i
$669$		0			0
$670$	−2250.00	−	3897.11i	−0.129739	−	0.224714i
$671$	−12950.0	−	22430.1i	−0.745051	−	1.29047i
$672$		0			0
$673$	−2775.00	+	4806.44i	−0.158943	+	0.275297i	−0.934488	−	0.355996i	$-0.884142\pi$
$673$	−2775.00	+	4806.44i	−0.158943	+	0.275297i	0.775545	+	0.631292i	$0.217475\pi$
$674$	38650.0			2.20882
$675$		0			0
$676$	−30549.0			−1.73811
$677$	6465.00	−	11197.7i	0.367016	−	0.635691i	−0.622081	−	0.782953i	$-0.713713\pi$
$677$	6465.00	−	11197.7i	0.367016	−	0.635691i	0.989098	+	0.147262i	$0.0470459\pi$
$678$		0			0
$679$	−24450.0	−	42348.6i	−1.38189	−	2.39351i
$680$	1125.00	+	1948.56i	0.0634438	+	0.109888i
$681$		0			0
$682$	−13500.0	+	23382.7i	−0.757979	+	1.31286i
$683$	−32580.0			−1.82524			−0.912620	−	0.408809i	$-0.865944\pi$
$683$	−32580.0			−1.82524			−0.912620	+	0.408809i	$0.865944\pi$
$684$		0			0
$685$	−5250.00			−0.292835
$686$	−16050.0	+	27799.4i	−0.893283	+	1.54721i
$687$		0			0
$688$	−12460.0	−	21581.4i	−0.690455	−	1.19590i
$689$	6100.00	+	10565.5i	0.337288	+	0.584200i
$690$		0			0
$691$	−5114.00	+	8857.71i	−0.281542	+	0.487646i	−0.971765	−	0.235952i	$-0.924179\pi$
$691$	−5114.00	+	8857.71i	−0.281542	+	0.487646i	0.690223	+	0.723597i	$0.257513\pi$
$692$	−43350.0			−2.38139
$693$		0			0
$694$	−5600.00			−0.306301
$695$	−4190.00	+	7257.29i	−0.228685	+	0.396093i
$696$		0			0
$697$	2000.00	+	3464.10i	0.108688	+	0.188253i
$698$	2965.00	+	5135.53i	0.160784	+	0.278485i
$699$		0			0
$700$	6375.00	−	11041.8i	0.344218	−	0.596202i
$701$	−8350.00			−0.449893			−0.224947	−	0.974371i	$-0.572221\pi$
$701$	−8350.00			−0.449893			−0.224947	+	0.974371i	$0.572221\pi$
$702$		0			0
$703$	1760.00			0.0944234
$704$	−7175.00	+	12427.5i	−0.384116	+	0.665309i
$705$		0			0
$706$	−9075.00	−	15718.4i	−0.483771	−	0.837915i
$707$	6750.00	+	11691.3i	0.359066	+	0.621921i
$708$		0			0
$709$	7477.00	−	12950.5i	0.396057	−	0.685991i	−0.597178	−	0.802109i	$-0.703711\pi$
$709$	7477.00	−	12950.5i	0.396057	−	0.685991i	0.993236	+	0.116117i	$0.0370448\pi$
$710$	17500.0			0.925019
$711$		0			0
$712$	−67500.0			−3.55291
$713$	6480.00	−	11223.7i	0.340362	−	0.589524i
$714$		0			0
$715$	−2500.00	−	4330.13i	−0.130762	−	0.226486i
$716$	31025.0	+	53736.9i	1.61936	+	2.80481i
$717$		0			0
$718$	4500.00	−	7794.23i	0.233898	−	0.405123i
$719$	−29400.0			−1.52494			−0.762472	−	0.647021i	$-0.776015\pi$
$719$	−29400.0			−1.52494			−0.762472	+	0.647021i	$0.776015\pi$
$720$		0			0
$721$	−23100.0			−1.19319
$722$	−12307.5	+	21317.2i	−0.634401	+	1.09882i
$723$		0			0
$724$	36907.0	+	63924.8i	1.89453	+	3.28142i
$725$	−625.000	−	1082.53i	−0.0320164	−	0.0554541i
$726$		0			0
$727$	8165.00	−	14142.2i	0.416538	−	0.721465i	−0.579051	−	0.815292i	$-0.696577\pi$
$727$	8165.00	−	14142.2i	0.416538	−	0.721465i	0.995589	+	0.0938267i	$0.0299100\pi$
$728$	−27000.0			−1.37457
$729$		0			0
$730$	10250.0			0.519684
$731$	−1400.00	+	2424.87i	−0.0708357	+	0.122691i
$732$		0			0
$733$	−15400.0	−	26673.6i	−0.776005	−	1.34408i	−0.934228	−	0.356677i	$-0.883910\pi$
$733$	−15400.0	−	26673.6i	−0.776005	−	1.34408i	0.158222	−	0.987404i	$-0.449424\pi$
$734$	21225.0	+	36762.8i	1.06734	+	1.84869i
$735$		0			0
$736$	−5100.00	+	8833.46i	−0.255419	+	0.442399i
$737$	9000.00			0.449823
$738$		0			0
$739$	−9524.00			−0.474081			−0.237041	−	0.971500i	$-0.576177\pi$
$739$	−9524.00			−0.474081			−0.237041	+	0.971500i	$0.576177\pi$
$740$	1700.00	−	2944.49i	0.0844503	−	0.146272i
$741$		0			0
$742$	−45750.0	−	79241.3i	−2.26352	−	3.92054i
$743$	−14300.0	−	24768.3i	−0.706078	−	1.22296i	−0.966301	−	0.257415i	$-0.917129\pi$
$743$	−14300.0	−	24768.3i	−0.706078	−	1.22296i	0.260223	−	0.965549i	$-0.416204\pi$
$744$		0			0
$745$	5125.00	−	8876.76i	0.252034	−	0.436536i
$746$	−500.000			−0.0245393
$747$		0			0
$748$	−8500.00			−0.415496
$749$	−9900.00	+	17147.3i	−0.482961	+	0.836514i
$750$		0			0
$751$	4126.00	+	7146.44i	0.200479	+	0.347240i	0.948683	−	0.316229i	$-0.102417\pi$
$751$	4126.00	+	7146.44i	0.200479	+	0.347240i	−0.748204	+	0.663469i	$0.769083\pi$
$752$	−12460.0	−	21581.4i	−0.604215	−	1.04653i
$753$		0			0
$754$	−2500.00	+	4330.13i	−0.120749	+	0.209143i
$755$	2240.00			0.107976
$756$		0			0
$757$	−24920.0			−1.19648			−0.598238	−	0.801318i	$-0.704132\pi$
$757$	−24920.0			−1.19648			−0.598238	+	0.801318i	$0.704132\pi$
$758$	−20210.0	+	35004.7i	−0.968417	+	1.67735i
$759$		0			0
$760$	−4950.00	−	8573.65i	−0.236257	−	0.409209i
$761$	13950.0	+	24162.1i	0.664503	+	1.15095i	0.979420	+	0.201834i	$0.0646902\pi$
$761$	13950.0	+	24162.1i	0.664503	+	1.15095i	−0.314916	+	0.949119i	$0.601976\pi$
$762$		0			0
$763$	26310.0	−	45570.3i	1.24834	−	2.16219i
$764$	59500.0			2.81758
$765$		0			0
$766$	−47400.0			−2.23581
$767$	−500.000	+	866.025i	−0.0235384	+	0.0407697i
$768$		0			0
$769$	5753.00	+	9964.49i	0.269777	+	0.467267i	0.968804	−	0.247828i	$-0.0797167\pi$
$769$	5753.00	+	9964.49i	0.269777	+	0.467267i	−0.699027	+	0.715095i	$0.746383\pi$
$770$	18750.0	+	32476.0i	0.877536	+	1.51994i
$771$		0			0
$772$	−28475.0	+	49320.1i	−1.32751	+	2.29931i
$773$	12510.0			0.582087			0.291044	−	0.956710i	$-0.405998\pi$
$773$	12510.0			0.582087			0.291044	+	0.956710i	$0.405998\pi$
$774$		0			0
$775$	2700.00			0.125144
$776$	−36675.0	+	63523.0i	−1.69659	+	2.93858i
$777$		0			0
$778$	27375.0	+	47414.9i	1.26149	+	2.18497i
$779$	−8800.00	−	15242.0i	−0.404740	−	0.701031i
$780$		0			0
$781$	−17500.0	+	30310.9i	−0.801792	+	1.38874i
$782$	6000.00			0.274373
$783$		0			0
$784$	49573.0			2.25825
$785$	250.000	−	433.013i	0.0113667	−	0.0196878i
$786$		0			0
$787$	550.000	+	952.628i	0.0249115	+	0.0431481i	0.878212	−	0.478271i	$-0.158736\pi$
$787$	550.000	+	952.628i	0.0249115	+	0.0431481i	−0.853301	+	0.521419i	$0.825403\pi$
$788$	765.000	+	1325.02i	0.0345838	+	0.0599008i
$789$		0			0
$790$	−6450.00	+	11171.7i	−0.290482	+	0.503129i
$791$	−9300.00			−0.418040
$792$		0			0
$793$	10360.0			0.463927
$794$	34600.0	−	59929.0i	1.54648	−	2.67859i
$795$		0			0
$796$	−31144.0	−	53943.0i	−1.38677	−	2.40196i
$797$	−2245.00	−	3888.45i	−0.0997766	−	0.172818i	0.811815	−	0.583914i	$-0.198479\pi$
$797$	−2245.00	−	3888.45i	−0.0997766	−	0.172818i	−0.911592	+	0.411096i	$0.865146\pi$
$798$		0			0
$799$	−1400.00	+	2424.87i	−0.0619880	+	0.107366i
$800$	−2125.00			−0.0939126
$801$		0			0
$802$	46500.0			2.04735
$803$	−10250.0	+	17753.5i	−0.450454	+	0.780209i
$804$		0			0
$805$	−9000.00	−	15588.5i	−0.394048	−	0.682510i
$806$	−5400.00	−	9353.07i	−0.235989	−	0.408744i
$807$		0			0
$808$	10125.0	−	17537.0i	0.440837	−	0.763552i
$809$	−28600.0			−1.24292			−0.621460	−	0.783446i	$-0.713460\pi$
$809$	−28600.0			−1.24292			−0.621460	+	0.783446i	$0.713460\pi$
$810$		0			0
$811$	10068.0			0.435925			0.217963	−	0.975957i	$-0.430059\pi$
$811$	10068.0			0.435925			0.217963	+	0.975957i	$0.430059\pi$
$812$	12750.0	−	22083.6i	0.551031	−	0.954414i
$813$		0			0
$814$	5000.00	+	8660.25i	0.215295	+	0.372901i
$815$	4750.00	+	8227.24i	0.204154	+	0.353605i
$816$		0			0
$817$	6160.00	−	10669.4i	0.263784	−	0.456886i
$818$	14270.0			0.609950
$819$		0			0
$820$	−34000.0			−1.44797
$821$	−7125.00	+	12340.9i	−0.302880	+	0.524603i	−0.976787	−	0.214213i	$-0.931281\pi$
$821$	−7125.00	+	12340.9i	−0.302880	+	0.524603i	0.673907	+	0.738816i	$0.264615\pi$
$822$		0			0
$823$	−3415.00	−	5914.95i	−0.144641	−	0.250525i	0.784598	−	0.620005i	$-0.212869\pi$
$823$	−3415.00	−	5914.95i	−0.144641	−	0.250525i	−0.929239	+	0.369479i	$0.879536\pi$
$824$	17325.0	+	30007.8i	0.732457	+	1.26865i
$825$		0			0
$826$	3750.00	−	6495.19i	0.157965	−	0.273604i
$827$	8920.00			0.375065			0.187533	−	0.982258i	$-0.439951\pi$
$827$	8920.00			0.375065			0.187533	+	0.982258i	$0.439951\pi$
$828$		0			0
$829$	−3534.00			−0.148059			−0.0740295	−	0.997256i	$-0.523586\pi$
$829$	−3534.00			−0.148059			−0.0740295	+	0.997256i	$0.523586\pi$
$830$	−8250.00	+	14289.4i	−0.345014	+	0.597582i
$831$		0			0
$832$	−2870.00	−	4970.99i	−0.119591	−	0.207137i
$833$	−2785.00	−	4823.76i	−0.115840	−	0.200640i
$834$		0			0
$835$	4800.00	−	8313.84i	0.198935	−	0.344566i
$836$	37400.0			1.54726
$837$		0			0
$838$	5750.00			0.237029
$839$	−4000.00	+	6928.20i	−0.164595	+	0.285087i	−0.936511	−	0.350637i	$-0.885965\pi$
$839$	−4000.00	+	6928.20i	−0.164595	+	0.285087i	0.771916	+	0.635724i	$0.219298\pi$
$840$		0			0
$841$	10944.5	+	18956.4i	0.448747	+	0.777253i
$842$	−27905.0	−	48332.9i	−1.14213	−	1.97822i
$843$		0			0
$844$	2278.00	−	3945.61i	0.0929052	−	0.160917i
$845$	−8985.00			−0.365791
$846$		0			0
$847$	−35070.0			−1.42269
$848$	−27145.0	+	47016.5i	−1.09925	+	1.90396i
$849$		0			0
$850$	625.000	+	1082.53i	0.0252204	+	0.0436830i
$851$	−2400.00	−	4156.92i	−0.0966756	−	0.167447i
$852$		0			0
$853$	−2580.00	+	4468.69i	−0.103561	+	0.179373i	−0.913149	−	0.407625i	$-0.866357\pi$
$853$	−2580.00	+	4468.69i	−0.103561	+	0.179373i	0.809588	+	0.586998i	$0.199690\pi$
$854$	−77700.0			−3.11339
$855$		0			0
$856$	29700.0			1.18589
$857$	3835.00	−	6642.41i	0.152860	−	0.264761i	−0.779418	−	0.626505i	$-0.784485\pi$
$857$	3835.00	−	6642.41i	0.152860	−	0.264761i	0.932278	+	0.361743i	$0.117818\pi$
$858$		0			0
$859$	−12902.0	−	22346.9i	−0.512469	−	0.887622i	−0.999895	−	0.0144579i	$-0.995398\pi$
$859$	−12902.0	−	22346.9i	−0.512469	−	0.887622i	0.487427	−	0.873164i	$-0.337936\pi$
$860$	−11900.0	−	20611.4i	−0.471845	−	0.817259i
$861$		0			0
$862$	3000.00	−	5196.15i	0.118539	−	0.205315i
$863$	−400.000			−0.0157777			−0.00788885	−	0.999969i	$-0.502511\pi$
$863$	−400.000			−0.0157777			−0.00788885	+	0.999969i	$0.502511\pi$
$864$		0			0
$865$	−12750.0			−0.501171
$866$	3775.00	−	6538.49i	0.148129	−	0.256567i
$867$		0			0
$868$	27540.0	+	47700.7i	1.07692	+	1.86528i
$869$	−12900.0	−	22343.5i	−0.503570	−	0.872209i
$870$		0			0
$871$	−1800.00	+	3117.69i	−0.0700237	+	0.121285i
$872$	−78930.0			−3.06526
$873$		0			0
$874$	−26400.0			−1.02173
$875$	1875.00	−	3247.60i	0.0724418	−	0.125473i
$876$		0			0
$877$	17550.0	+	30397.5i	0.675737	+	1.17041i	0.976253	+	0.216634i	$0.0695078\pi$
$877$	17550.0	+	30397.5i	0.675737	+	1.17041i	−0.300516	+	0.953777i	$0.597159\pi$
$878$	1060.00	+	1835.97i	0.0407440	+	0.0705707i
$879$		0			0
$880$	11125.0	−	19269.1i	0.426163	−	0.738136i
$881$	18700.0			0.715118			0.357559	−	0.933891i	$-0.383609\pi$
$881$	18700.0			0.715118			0.357559	+	0.933891i	$0.383609\pi$
$882$		0			0
$883$	−2980.00			−0.113573			−0.0567865	−	0.998386i	$-0.518085\pi$
$883$	−2980.00			−0.113573			−0.0567865	+	0.998386i	$0.518085\pi$
$884$	1700.00	−	2944.49i	0.0646801	−	0.112029i
$885$		0			0
$886$	−30900.0	−	53520.4i	−1.17168	−	2.02940i
$887$	−17940.0	−	31073.0i	−0.679105	−	1.17624i	−0.975251	−	0.221102i	$-0.929035\pi$
$887$	−17940.0	−	31073.0i	−0.679105	−	1.17624i	0.296146	−	0.955143i	$-0.404299\pi$
$888$		0			0
$889$	−16050.0	+	27799.4i	−0.605511	+	1.04878i
$890$	−37500.0			−1.41236
$891$		0			0
$892$	−62390.0			−2.34190
$893$	6160.00	−	10669.4i	0.230836	−	0.399820i
$894$		0			0
$895$	9125.00	+	15805.0i	0.340799	+	0.590281i
$896$	31725.0	+	54949.3i	1.18288	+	2.04880i
$897$		0			0
$898$	3250.00	−	5629.17i	0.120773	−	0.209184i
$899$	5400.00			0.200334
$900$		0			0
$901$	6100.00			0.225550
$902$	50000.0	−	86602.5i	1.84570	−	3.19684i
$903$		0			0
$904$	6975.00	+	12081.1i	0.256621	+	0.444480i
$905$	10855.0	+	18801.4i	0.398710	+	0.690586i
$906$		0			0
$907$	−22620.0	+	39179.0i	−0.828098	+	1.43431i	0.0714307	+	0.997446i	$0.477244\pi$
$907$	−22620.0	+	39179.0i	−0.828098	+	1.43431i	−0.899529	+	0.436862i	$0.856090\pi$
$908$	−63920.0			−2.33619
$909$		0			0
$910$	−15000.0			−0.546423
$911$	16600.0	−	28752.0i	0.603713	−	1.04566i	−0.388540	−	0.921432i	$-0.627021\pi$
$911$	16600.0	−	28752.0i	0.603713	−	1.04566i	0.992253	−	0.124230i	$-0.0396460\pi$
$912$		0			0
$913$	−16500.0	−	28578.8i	−0.598105	−	1.03595i
$914$	−17975.0	−	31133.6i	−0.650503	−	1.12671i
$915$		0			0
$916$	12189.0	−	21112.0i	0.439668	−	0.761527i
$917$	58500.0			2.10670
$918$		0			0
$919$	35356.0			1.26908			0.634541	−	0.772889i	$-0.281189\pi$
$919$	35356.0			1.26908			0.634541	+	0.772889i	$0.281189\pi$
$920$	−13500.0	+	23382.7i	−0.483785	+	0.837939i
$921$		0			0
$922$	375.000	+	649.519i	0.0133948	+	0.0232004i
$923$	−7000.00	−	12124.4i	−0.249629	−	0.432371i
$924$		0			0
$925$	500.000	−	866.025i	0.0177729	−	0.0307835i
$926$	−13350.0			−0.473767
$927$		0			0
$928$	−4250.00			−0.150337
$929$	−12850.0	+	22256.9i	−0.453816	+	0.786032i	−0.998619	−	0.0525318i	$-0.983271\pi$
$929$	−12850.0	+	22256.9i	−0.453816	+	0.786032i	0.544804	+	0.838564i	$0.316604\pi$
$930$		0			0
$931$	12254.0	+	21224.6i	0.431373	+	0.747161i
$932$	−29325.0	−	50792.4i	−1.03066	−	1.78515i
$933$		0			0
$934$	−2950.00	+	5109.55i	−0.103348	+	0.179004i
$935$	−2500.00			−0.0874425
$936$		0			0
$937$	52890.0			1.84401			0.922007	−	0.387173i	$-0.126549\pi$
$937$	52890.0			1.84401			0.922007	+	0.387173i	$0.126549\pi$
$938$	13500.0	−	23382.7i	0.469926	−	0.813936i
$939$		0			0
$940$	−11900.0	−	20611.4i	−0.412910	−	0.715181i
$941$	19025.0	+	32952.3i	0.659083	+	1.14157i	0.980853	+	0.194748i	$0.0623888\pi$
$941$	19025.0	+	32952.3i	0.659083	+	1.14157i	−0.321770	+	0.946818i	$0.604278\pi$
$942$		0			0
$943$	−24000.0	+	41569.2i	−0.828788	+	1.43550i
$944$	−4450.00			−0.153427
$945$		0			0
$946$	70000.0			2.40581
$947$	−14820.0	+	25669.0i	−0.508538	+	0.880813i	0.491413	+	0.870926i	$0.336480\pi$
$947$	−14820.0	+	25669.0i	−0.508538	+	0.880813i	−0.999951	+	0.00988681i	$0.996853\pi$
$948$		0			0
$949$	−4100.00	−	7101.41i	−0.140244	−	0.242910i
$950$	−2750.00	−	4763.14i	−0.0939177	−	0.162670i
$951$		0			0
$952$	−6750.00	+	11691.3i	−0.229799	+	0.398024i
$953$	−15170.0			−0.515640			−0.257820	−	0.966193i	$-0.583004\pi$
$953$	−15170.0			−0.515640			−0.257820	+	0.966193i	$0.583004\pi$
$954$		0			0
$955$	17500.0			0.592970
$956$	−41650.0	+	72139.9i	−1.40906	+	2.44056i
$957$		0			0
$958$	35250.0	+	61054.8i	1.18881	+	2.05907i
$959$	−15750.0	−	27279.8i	−0.530338	−	0.918572i
$960$		0			0
$961$	9063.50	−	15698.4i	0.304236	−	0.526953i
$962$	−4000.00			−0.134059
$963$		0			0
$964$	81974.0			2.73880
$965$	−8375.00	+	14505.9i	−0.279379	+	0.483899i
$966$		0			0
$967$	2735.00	+	4737.16i	0.0909531	+	0.157535i	0.907912	−	0.419160i	$-0.137675\pi$
$967$	2735.00	+	4737.16i	0.0909531	+	0.157535i	−0.816959	+	0.576695i	$0.804342\pi$
$968$	26302.5	+	45557.3i	0.873341	+	1.51267i
$969$		0			0
$970$	−20375.0	+	35290.5i	−0.674435	+	1.16816i
$971$	−15150.0			−0.500707			−0.250354	−	0.968154i	$-0.580547\pi$
$971$	−15150.0			−0.500707			−0.250354	+	0.968154i	$0.580547\pi$
$972$		0			0
$973$	−50280.0			−1.65663
$974$	−24625.0	+	42651.8i	−0.810098	+	1.40313i
$975$		0			0
$976$	23051.0	+	39925.5i	0.755988	+	1.30941i
$977$	15595.0	+	27011.3i	0.510674	+	0.884513i	0.999923	+	0.0123692i	$0.00393732\pi$
$977$	15595.0	+	27011.3i	0.510674	+	0.884513i	−0.489250	+	0.872144i	$0.662729\pi$
$978$		0			0
$979$	37500.0	−	64951.9i	1.22421	−	2.12040i
$980$	47345.0			1.54325
$981$		0			0
$982$	−12250.0			−0.398079
$983$	−3780.00	+	6547.15i	−0.122648	+	0.212433i	−0.920811	−	0.390009i	$-0.872472\pi$
$983$	−3780.00	+	6547.15i	−0.122648	+	0.212433i	0.798163	+	0.602442i	$0.205805\pi$
$984$		0			0
$985$	225.000	+	389.711i	0.00727827	+	0.0126063i
$986$	1250.00	+	2165.06i	0.0403733	+	0.0699287i
$987$		0			0
$988$	−7480.00	+	12955.7i	−0.240861	+	0.417183i
$989$	−33600.0			−1.08030
$990$		0			0
$991$	32672.0			1.04729			0.523643	−	0.851938i	$-0.324573\pi$
$991$	32672.0			1.04729			0.523643	+	0.851938i	$0.324573\pi$
$992$	4590.00	−	7950.11i	0.146908	−	0.254452i
$993$		0			0
$994$	52500.0	+	90932.7i	1.67525	+	2.90162i
$995$	−9160.00	−	15865.6i	−0.291851	−	0.505500i
$996$		0			0
$997$	2370.00	−	4104.96i	0.0752845	−	0.130397i	−0.825925	−	0.563779i	$-0.809347\pi$
$997$	2370.00	−	4104.96i	0.0752845	−	0.130397i	0.901210	+	0.433383i	$0.142680\pi$
$998$	85180.0			2.70173
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.4.e.n.136.1		2
3.2	odd	2		405.4.e.b.136.1		2
9.2	odd	6		45.4.a.e.1.1	yes	1
9.4	even	3	inner	405.4.e.n.271.1		2
9.5	odd	6		405.4.e.b.271.1		2
9.7	even	3		45.4.a.a.1.1	✓	1
36.7	odd	6		720.4.a.bc.1.1		1
36.11	even	6		720.4.a.o.1.1		1
45.2	even	12		225.4.b.b.199.2		2
45.7	odd	12		225.4.b.a.199.1		2
45.29	odd	6		225.4.a.a.1.1		1
45.34	even	6		225.4.a.h.1.1		1
45.38	even	12		225.4.b.b.199.1		2
45.43	odd	12		225.4.b.a.199.2		2
63.20	even	6		2205.4.a.t.1.1		1
63.34	odd	6		2205.4.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.a.a.1.1	✓	1	9.7	even	3
45.4.a.e.1.1	yes	1	9.2	odd	6
225.4.a.a.1.1		1	45.29	odd	6
225.4.a.h.1.1		1	45.34	even	6
225.4.b.a.199.1		2	45.7	odd	12
225.4.b.a.199.2		2	45.43	odd	12
225.4.b.b.199.1		2	45.38	even	12
225.4.b.b.199.2		2	45.2	even	12
405.4.e.b.136.1		2	3.2	odd	2
405.4.e.b.271.1		2	9.5	odd	6
405.4.e.n.136.1		2	1.1	even	1	trivial
405.4.e.n.271.1		2	9.4	even	3	inner
720.4.a.o.1.1		1	36.11	even	6
720.4.a.bc.1.1		1	36.7	odd	6
2205.4.a.a.1.1		1	63.34	odd	6
2205.4.a.t.1.1		1	63.20	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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	405.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.50000 - 4.33013i) q^{2} +(-8.50000 - 14.7224i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(15.0000 - 25.9808i) q^{7} -45.0000 q^{8} +O(q^{10})\)	\(q+(2.50000 - 4.33013i) q^{2} +(-8.50000 - 14.7224i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(15.0000 - 25.9808i) q^{7} -45.0000 q^{8} -25.0000 q^{10} +(25.0000 - 43.3013i) q^{11} +(10.0000 + 17.3205i) q^{13} +(-75.0000 - 129.904i) q^{14} +(-44.5000 + 77.0763i) q^{16} +10.0000 q^{17} -44.0000 q^{19} +(-42.5000 + 73.6122i) q^{20} +(-125.000 - 216.506i) q^{22} +(60.0000 + 103.923i) q^{23} +(-12.5000 + 21.6506i) q^{25} +100.000 q^{26} -510.000 q^{28} +(-25.0000 + 43.3013i) q^{29} +(-54.0000 - 93.5307i) q^{31} +(42.5000 + 73.6122i) q^{32} +(25.0000 - 43.3013i) q^{34} -150.000 q^{35} -40.0000 q^{37} +(-110.000 + 190.526i) q^{38} +(112.500 + 194.856i) q^{40} +(200.000 + 346.410i) q^{41} +(-140.000 + 242.487i) q^{43} -850.000 q^{44} +600.000 q^{46} +(-140.000 + 242.487i) q^{47} +(-278.500 - 482.376i) q^{49} +(62.5000 + 108.253i) q^{50} +(170.000 - 294.449i) q^{52} +610.000 q^{53} -250.000 q^{55} +(-675.000 + 1169.13i) q^{56} +(125.000 + 216.506i) q^{58} +(25.0000 + 43.3013i) q^{59} +(259.000 - 448.601i) q^{61} -540.000 q^{62} -287.000 q^{64} +(50.0000 - 86.6025i) q^{65} +(90.0000 + 155.885i) q^{67} +(-85.0000 - 147.224i) q^{68} +(-375.000 + 649.519i) q^{70} -700.000 q^{71} -410.000 q^{73} +(-100.000 + 173.205i) q^{74} +(374.000 + 647.787i) q^{76} +(-750.000 - 1299.04i) q^{77} +(258.000 - 446.869i) q^{79} +445.000 q^{80} +2000.00 q^{82} +(330.000 - 571.577i) q^{83} +(-25.0000 - 43.3013i) q^{85} +(700.000 + 1212.44i) q^{86} +(-1125.00 + 1948.56i) q^{88} +1500.00 q^{89} +600.000 q^{91} +(1020.00 - 1766.69i) q^{92} +(700.000 + 1212.44i) q^{94} +(110.000 + 190.526i) q^{95} +(815.000 - 1411.62i) q^{97} -2785.00 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 5 q^{2} - 17 q^{4} - 5 q^{5} + 30 q^{7} - 90 q^{8}+O(q^{10}) \) 2 * q + 5 * q^2 - 17 * q^4 - 5 * q^5 + 30 * q^7 - 90 * q^8	\( 2 q + 5 q^{2} - 17 q^{4} - 5 q^{5} + 30 q^{7} - 90 q^{8} - 50 q^{10} + 50 q^{11} + 20 q^{13} - 150 q^{14} - 89 q^{16} + 20 q^{17} - 88 q^{19} - 85 q^{20} - 250 q^{22} + 120 q^{23} - 25 q^{25} + 200 q^{26} - 1020 q^{28} - 50 q^{29} - 108 q^{31} + 85 q^{32} + 50 q^{34} - 300 q^{35} - 80 q^{37} - 220 q^{38} + 225 q^{40} + 400 q^{41} - 280 q^{43} - 1700 q^{44} + 1200 q^{46} - 280 q^{47} - 557 q^{49} + 125 q^{50} + 340 q^{52} + 1220 q^{53} - 500 q^{55} - 1350 q^{56} + 250 q^{58} + 50 q^{59} + 518 q^{61} - 1080 q^{62} - 574 q^{64} + 100 q^{65} + 180 q^{67} - 170 q^{68} - 750 q^{70} - 1400 q^{71} - 820 q^{73} - 200 q^{74} + 748 q^{76} - 1500 q^{77} + 516 q^{79} + 890 q^{80} + 4000 q^{82} + 660 q^{83} - 50 q^{85} + 1400 q^{86} - 2250 q^{88} + 3000 q^{89} + 1200 q^{91} + 2040 q^{92} + 1400 q^{94} + 220 q^{95} + 1630 q^{97} - 5570 q^{98}+O(q^{100}) \) 2 * q + 5 * q^2 - 17 * q^4 - 5 * q^5 + 30 * q^7 - 90 * q^8 - 50 * q^10 + 50 * q^11 + 20 * q^13 - 150 * q^14 - 89 * q^16 + 20 * q^17 - 88 * q^19 - 85 * q^20 - 250 * q^22 + 120 * q^23 - 25 * q^25 + 200 * q^26 - 1020 * q^28 - 50 * q^29 - 108 * q^31 + 85 * q^32 + 50 * q^34 - 300 * q^35 - 80 * q^37 - 220 * q^38 + 225 * q^40 + 400 * q^41 - 280 * q^43 - 1700 * q^44 + 1200 * q^46 - 280 * q^47 - 557 * q^49 + 125 * q^50 + 340 * q^52 + 1220 * q^53 - 500 * q^55 - 1350 * q^56 + 250 * q^58 + 50 * q^59 + 518 * q^61 - 1080 * q^62 - 574 * q^64 + 100 * q^65 + 180 * q^67 - 170 * q^68 - 750 * q^70 - 1400 * q^71 - 820 * q^73 - 200 * q^74 + 748 * q^76 - 1500 * q^77 + 516 * q^79 + 890 * q^80 + 4000 * q^82 + 660 * q^83 - 50 * q^85 + 1400 * q^86 - 2250 * q^88 + 3000 * q^89 + 1200 * q^91 + 2040 * q^92 + 1400 * q^94 + 220 * q^95 + 1630 * q^97 - 5570 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more