LMFDB - Embedded newform 405.4.e.e.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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 135)
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.e.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.73205i) q^{2} +(2.00000 + 3.46410i) q^{4} +(2.50000 + 4.33013i) q^{5} -24.0000 q^{8} +O(q^{10})$	\(q+(-1.00000 + 1.73205i) q^{2} +(2.00000 + 3.46410i) q^{4} +(2.50000 + 4.33013i) q^{5} -24.0000 q^{8} -10.0000 q^{10} +(5.00000 - 8.66025i) q^{11} +(40.0000 + 69.2820i) q^{13} +(8.00000 - 13.8564i) q^{16} -7.00000 q^{17} -113.000 q^{19} +(-10.0000 + 17.3205i) q^{20} +(10.0000 + 17.3205i) q^{22} +(-40.5000 - 70.1481i) q^{23} +(-12.5000 + 21.6506i) q^{25} -160.000 q^{26} +(-110.000 + 190.526i) q^{29} +(94.5000 + 163.679i) q^{31} +(-80.0000 - 138.564i) q^{32} +(7.00000 - 12.1244i) q^{34} +170.000 q^{37} +(113.000 - 195.722i) q^{38} +(-60.0000 - 103.923i) q^{40} +(-65.0000 - 112.583i) q^{41} +(-5.00000 + 8.66025i) q^{43} +40.0000 q^{44} +162.000 q^{46} +(80.0000 - 138.564i) q^{47} +(171.500 + 297.047i) q^{49} +(-25.0000 - 43.3013i) q^{50} +(-160.000 + 277.128i) q^{52} -631.000 q^{53} +50.0000 q^{55} +(-220.000 - 381.051i) q^{58} +(-280.000 - 484.974i) q^{59} +(-114.500 + 198.320i) q^{61} -378.000 q^{62} +448.000 q^{64} +(-200.000 + 346.410i) q^{65} +(-375.000 - 649.519i) q^{67} +(-14.0000 - 24.2487i) q^{68} -890.000 q^{71} -890.000 q^{73} +(-170.000 + 294.449i) q^{74} +(-226.000 - 391.443i) q^{76} +(13.5000 - 23.3827i) q^{79} +80.0000 q^{80} +260.000 q^{82} +(214.500 - 371.525i) q^{83} +(-17.5000 - 30.3109i) q^{85} +(-10.0000 - 17.3205i) q^{86} +(-120.000 + 207.846i) q^{88} +750.000 q^{89} +(162.000 - 280.592i) q^{92} +(160.000 + 277.128i) q^{94} +(-282.500 - 489.304i) q^{95} +(740.000 - 1281.72i) q^{97} -686.000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 4 q^{4} + 5 q^{5} - 48 q^{8}+O(q^{10}) $ 2 * q - 2 * q^2 + 4 * q^4 + 5 * q^5 - 48 * q^8	$ 2 q - 2 q^{2} + 4 q^{4} + 5 q^{5} - 48 q^{8} - 20 q^{10} + 10 q^{11} + 80 q^{13} + 16 q^{16} - 14 q^{17} - 226 q^{19} - 20 q^{20} + 20 q^{22} - 81 q^{23} - 25 q^{25} - 320 q^{26} - 220 q^{29} + 189 q^{31} - 160 q^{32} + 14 q^{34} + 340 q^{37} + 226 q^{38} - 120 q^{40} - 130 q^{41} - 10 q^{43} + 80 q^{44} + 324 q^{46} + 160 q^{47} + 343 q^{49} - 50 q^{50} - 320 q^{52} - 1262 q^{53} + 100 q^{55} - 440 q^{58} - 560 q^{59} - 229 q^{61} - 756 q^{62} + 896 q^{64} - 400 q^{65} - 750 q^{67} - 28 q^{68} - 1780 q^{71} - 1780 q^{73} - 340 q^{74} - 452 q^{76} + 27 q^{79} + 160 q^{80} + 520 q^{82} + 429 q^{83} - 35 q^{85} - 20 q^{86} - 240 q^{88} + 1500 q^{89} + 324 q^{92} + 320 q^{94} - 565 q^{95} + 1480 q^{97} - 1372 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + 4 * q^4 + 5 * q^5 - 48 * q^8 - 20 * q^10 + 10 * q^11 + 80 * q^13 + 16 * q^16 - 14 * q^17 - 226 * q^19 - 20 * q^20 + 20 * q^22 - 81 * q^23 - 25 * q^25 - 320 * q^26 - 220 * q^29 + 189 * q^31 - 160 * q^32 + 14 * q^34 + 340 * q^37 + 226 * q^38 - 120 * q^40 - 130 * q^41 - 10 * q^43 + 80 * q^44 + 324 * q^46 + 160 * q^47 + 343 * q^49 - 50 * q^50 - 320 * q^52 - 1262 * q^53 + 100 * q^55 - 440 * q^58 - 560 * q^59 - 229 * q^61 - 756 * q^62 + 896 * q^64 - 400 * q^65 - 750 * q^67 - 28 * q^68 - 1780 * q^71 - 1780 * q^73 - 340 * q^74 - 452 * q^76 + 27 * q^79 + 160 * q^80 + 520 * q^82 + 429 * q^83 - 35 * q^85 - 20 * q^86 - 240 * q^88 + 1500 * q^89 + 324 * q^92 + 320 * q^94 - 565 * q^95 + 1480 * q^97 - 1372 * 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 $

$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i	−0.986869	−	0.161521i	$-0.948360\pi$
$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i	0.633316	+	0.773893i	$0.281693\pi$
$3$		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
$7$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$7$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$8$	−24.0000			−1.06066
$9$		0			0
$10$	−10.0000			−0.316228
$11$	5.00000	−	8.66025i	0.137051	−	0.237379i	−0.789328	−	0.613971i	$-0.789571\pi$
$11$	5.00000	−	8.66025i	0.137051	−	0.237379i	0.926379	+	0.376593i	$0.122904\pi$
$12$		0			0
$13$	40.0000	+	69.2820i	0.853385	+	1.47811i	0.878135	+	0.478412i	$0.158788\pi$
$13$	40.0000	+	69.2820i	0.853385	+	1.47811i	−0.0247504	+	0.999694i	$0.507879\pi$
$14$		0			0
$15$		0			0
$16$	8.00000	−	13.8564i	0.125000	−	0.216506i
$17$	−7.00000			−0.0998676			−0.0499338	−	0.998753i	$-0.515901\pi$
$17$	−7.00000			−0.0998676			−0.0499338	+	0.998753i	$0.515901\pi$
$18$		0			0
$19$	−113.000			−1.36442			−0.682210	−	0.731156i	$-0.738981\pi$
$19$	−113.000			−1.36442			−0.682210	+	0.731156i	$0.738981\pi$
$20$	−10.0000	+	17.3205i	−0.111803	+	0.193649i
$21$		0			0
$22$	10.0000	+	17.3205i	0.0969094	+	0.167852i
$23$	−40.5000	−	70.1481i	−0.367167	−	0.635951i	0.621955	−	0.783053i	$-0.286339\pi$
$23$	−40.5000	−	70.1481i	−0.367167	−	0.635951i	−0.989121	+	0.147102i	$0.953005\pi$
$24$		0			0
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	−160.000			−1.20687
$27$		0			0
$28$		0			0
$29$	−110.000	+	190.526i	−0.704362	+	1.21999i	0.262560	+	0.964916i	$0.415433\pi$
$29$	−110.000	+	190.526i	−0.704362	+	1.21999i	−0.966921	+	0.255074i	$0.917900\pi$
$30$		0			0
$31$	94.5000	+	163.679i	0.547506	+	0.948309i	0.998445	+	0.0557538i	$0.0177562\pi$
$31$	94.5000	+	163.679i	0.547506	+	0.948309i	−0.450938	+	0.892555i	$0.648910\pi$
$32$	−80.0000	−	138.564i	−0.441942	−	0.765466i
$33$		0			0
$34$	7.00000	−	12.1244i	0.0353085	−	0.0611562i
$35$		0			0
$36$		0			0
$37$	170.000			0.755347			0.377673	−	0.925939i	$-0.376724\pi$
$37$	170.000			0.755347			0.377673	+	0.925939i	$0.376724\pi$
$38$	113.000	−	195.722i	0.482395	−	0.835533i
$39$		0			0
$40$	−60.0000	−	103.923i	−0.237171	−	0.410792i
$41$	−65.0000	−	112.583i	−0.247593	−	0.428843i	0.715265	−	0.698854i	$-0.246306\pi$
$41$	−65.0000	−	112.583i	−0.247593	−	0.428843i	−0.962857	+	0.270011i	$0.912973\pi$
$42$		0			0
$43$	−5.00000	+	8.66025i	−0.0177324	+	0.0307134i	−0.874755	−	0.484565i	$-0.838978\pi$
$43$	−5.00000	+	8.66025i	−0.0177324	+	0.0307134i	0.857023	+	0.515278i	$0.172311\pi$
$44$	40.0000			0.137051
$45$		0			0
$46$	162.000			0.519252
$47$	80.0000	−	138.564i	0.248281	−	0.430035i	−0.714768	−	0.699362i	$-0.753468\pi$
$47$	80.0000	−	138.564i	0.248281	−	0.430035i	0.963049	+	0.269327i	$0.0868011\pi$
$48$		0			0
$49$	171.500	+	297.047i	0.500000	+	0.866025i
$50$	−25.0000	−	43.3013i	−0.0707107	−	0.122474i
$51$		0			0
$52$	−160.000	+	277.128i	−0.426692	+	0.739053i
$53$	−631.000			−1.63537			−0.817684	−	0.575667i	$-0.804742\pi$
$53$	−631.000			−1.63537			−0.817684	+	0.575667i	$0.804742\pi$
$54$		0			0
$55$	50.0000			0.122582
$56$		0			0
$57$		0			0
$58$	−220.000	−	381.051i	−0.498059	−	0.862663i
$59$	−280.000	−	484.974i	−0.617846	−	1.07014i	−0.989878	−	0.141920i	$-0.954672\pi$
$59$	−280.000	−	484.974i	−0.617846	−	1.07014i	0.372032	−	0.928220i	$-0.378661\pi$
$60$		0			0
$61$	−114.500	+	198.320i	−0.240332	+	0.416266i	−0.960809	−	0.277212i	$-0.910589\pi$
$61$	−114.500	+	198.320i	−0.240332	+	0.416266i	0.720477	+	0.693479i	$0.243923\pi$
$62$	−378.000			−0.774291
$63$		0			0
$64$	448.000			0.875000
$65$	−200.000	+	346.410i	−0.381645	+	0.661029i
$66$		0			0
$67$	−375.000	−	649.519i	−0.683784	−	1.18435i	−0.973817	−	0.227332i	$-0.927000\pi$
$67$	−375.000	−	649.519i	−0.683784	−	1.18435i	0.290033	−	0.957017i	$-0.406334\pi$
$68$	−14.0000	−	24.2487i	−0.0249669	−	0.0432439i
$69$		0			0
$70$		0			0
$71$	−890.000			−1.48766			−0.743828	−	0.668371i	$-0.766992\pi$
$71$	−890.000			−1.48766			−0.743828	+	0.668371i	$0.766992\pi$
$72$		0			0
$73$	−890.000			−1.42694			−0.713470	−	0.700686i	$-0.752878\pi$
$73$	−890.000			−1.42694			−0.713470	+	0.700686i	$0.752878\pi$
$74$	−170.000	+	294.449i	−0.267055	+	0.462553i
$75$		0			0
$76$	−226.000	−	391.443i	−0.341105	−	0.590811i
$77$		0			0
$78$		0			0
$79$	13.5000	−	23.3827i	0.0192262	−	0.0333007i	−0.856252	−	0.516558i	$-0.827213\pi$
$79$	13.5000	−	23.3827i	0.0192262	−	0.0333007i	0.875478	+	0.483257i	$0.160546\pi$
$80$	80.0000			0.111803
$81$		0			0
$82$	260.000			0.350149
$83$	214.500	−	371.525i	0.283668	−	0.491327i	−0.688617	−	0.725125i	$-0.741782\pi$
$83$	214.500	−	371.525i	0.283668	−	0.491327i	0.972285	+	0.233798i	$0.0751153\pi$
$84$		0			0
$85$	−17.5000	−	30.3109i	−0.0223311	−	0.0386786i
$86$	−10.0000	−	17.3205i	−0.0125387	−	0.0217177i
$87$		0			0
$88$	−120.000	+	207.846i	−0.145364	+	0.251778i
$89$	750.000			0.893257			0.446628	−	0.894720i	$-0.352625\pi$
$89$	750.000			0.893257			0.446628	+	0.894720i	$0.352625\pi$
$90$		0			0
$91$		0			0
$92$	162.000	−	280.592i	0.183583	−	0.317976i
$93$		0			0
$94$	160.000	+	277.128i	0.175561	+	0.304081i
$95$	−282.500	−	489.304i	−0.305094	−	0.528438i
$96$		0			0
$97$	740.000	−	1281.72i	0.774594	−	1.34164i	−0.160428	−	0.987047i	$-0.551288\pi$
$97$	740.000	−	1281.72i	0.774594	−	1.34164i	0.935022	−	0.354589i	$-0.115379\pi$
$98$	−686.000			−0.707107
$99$		0			0
$100$	−100.000			−0.100000
$101$	−750.000	+	1299.04i	−0.738889	+	1.27979i	0.214107	+	0.976810i	$0.431316\pi$
$101$	−750.000	+	1299.04i	−0.738889	+	1.27979i	−0.952996	+	0.302983i	$0.902017\pi$
$102$		0			0
$103$	230.000	+	398.372i	0.220025	+	0.381094i	0.954815	−	0.297200i	$-0.0960528\pi$
$103$	230.000	+	398.372i	0.220025	+	0.381094i	−0.734790	+	0.678294i	$0.762719\pi$
$104$	−960.000	−	1662.77i	−0.905151	−	1.56777i
$105$		0			0
$106$	631.000	−	1092.92i	0.578190	−	1.00145i
$107$	420.000			0.379467			0.189733	−	0.981836i	$-0.439238\pi$
$107$	420.000			0.379467			0.189733	+	0.981836i	$0.439238\pi$
$108$		0			0
$109$	−607.000			−0.533395			−0.266698	−	0.963780i	$-0.585932\pi$
$109$	−607.000			−0.533395			−0.266698	+	0.963780i	$0.585932\pi$
$110$	−50.0000	+	86.6025i	−0.0433392	+	0.0750657i
$111$		0			0
$112$		0			0
$113$	1085.00	+	1879.28i	0.903259	+	1.56449i	0.823238	+	0.567696i	$0.192165\pi$
$113$	1085.00	+	1879.28i	0.903259	+	1.56449i	0.0800206	+	0.996793i	$0.474501\pi$
$114$		0			0
$115$	202.500	−	350.740i	0.164202	−	0.284406i
$116$	−880.000			−0.704362
$117$		0			0
$118$	1120.00			0.873766
$119$		0			0
$120$		0			0
$121$	615.500	+	1066.08i	0.462434	+	0.800960i
$122$	−229.000	−	396.640i	−0.169940	−	0.294345i
$123$		0			0
$124$	−378.000	+	654.715i	−0.273753	+	0.474155i
$125$	−125.000			−0.0894427
$126$		0			0
$127$	−1610.00			−1.12492			−0.562458	−	0.826826i	$-0.690144\pi$
$127$	−1610.00			−1.12492			−0.562458	+	0.826826i	$0.690144\pi$
$128$	192.000	−	332.554i	0.132583	−	0.229640i
$129$		0			0
$130$	−400.000	−	692.820i	−0.269864	−	0.467418i
$131$	1185.00	+	2052.48i	0.790335	+	1.36890i	0.925759	+	0.378113i	$0.123427\pi$
$131$	1185.00	+	2052.48i	0.790335	+	1.36890i	−0.135424	+	0.990788i	$0.543240\pi$
$132$		0			0
$133$		0			0
$134$	1500.00			0.967017
$135$		0			0
$136$	168.000			0.105926
$137$	898.500	−	1556.25i	0.560321	−	0.970505i	−0.437147	−	0.899390i	$-0.644011\pi$
$137$	898.500	−	1556.25i	0.560321	−	0.970505i	0.997468	−	0.0711150i	$-0.0226557\pi$
$138$		0			0
$139$	62.0000	+	107.387i	0.0378329	+	0.0655285i	0.884322	−	0.466878i	$-0.154621\pi$
$139$	62.0000	+	107.387i	0.0378329	+	0.0655285i	−0.846489	+	0.532406i	$0.821288\pi$
$140$		0			0
$141$		0			0
$142$	890.000	−	1541.53i	0.525966	−	0.910999i
$143$	800.000			0.467828
$144$		0			0
$145$	−1100.00			−0.630000
$146$	890.000	−	1541.53i	0.504499	−	0.873819i
$147$		0			0
$148$	340.000	+	588.897i	0.188837	+	0.327075i
$149$	−35.0000	−	60.6218i	−0.0192437	−	0.0333311i	0.856243	−	0.516573i	$-0.172793\pi$
$149$	−35.0000	−	60.6218i	−0.0192437	−	0.0333311i	−0.875487	+	0.483242i	$0.839459\pi$
$150$		0			0
$151$	−1124.00	+	1946.83i	−0.605760	+	1.04921i	0.386170	+	0.922427i	$0.373798\pi$
$151$	−1124.00	+	1946.83i	−0.605760	+	1.04921i	−0.991931	+	0.126780i	$0.959536\pi$
$152$	2712.00			1.44719
$153$		0			0
$154$		0			0
$155$	−472.500	+	818.394i	−0.244852	+	0.424097i
$156$		0			0
$157$	−505.000	−	874.686i	−0.256709	−	0.444634i	0.708649	−	0.705561i	$-0.249305\pi$
$157$	−505.000	−	874.686i	−0.256709	−	0.444634i	−0.965358	+	0.260927i	$0.915972\pi$
$158$	27.0000	+	46.7654i	0.0135950	+	0.0235472i
$159$		0			0
$160$	400.000	−	692.820i	0.197642	−	0.342327i
$161$		0			0
$162$		0			0
$163$	590.000			0.283511			0.141756	−	0.989902i	$-0.454725\pi$
$163$	590.000			0.283511			0.141756	+	0.989902i	$0.454725\pi$
$164$	260.000	−	450.333i	0.123796	−	0.214421i
$165$		0			0
$166$	429.000	+	743.050i	0.200583	+	0.347421i
$167$	1201.50	+	2081.06i	0.556736	+	0.964295i	0.997766	+	0.0668024i	$0.0212797\pi$
$167$	1201.50	+	2081.06i	0.556736	+	0.964295i	−0.441031	+	0.897492i	$0.645387\pi$
$168$		0			0
$169$	−2101.50	+	3639.90i	−0.956532	+	1.65676i
$170$	70.0000			0.0315809
$171$		0			0
$172$	−40.0000			−0.0177324
$173$	400.500	−	693.686i	0.176008	−	0.304855i	−0.764501	−	0.644622i	$-0.777015\pi$
$173$	400.500	−	693.686i	0.176008	−	0.304855i	0.940510	+	0.339767i	$0.110348\pi$
$174$		0			0
$175$		0			0
$176$	−80.0000	−	138.564i	−0.0342627	−	0.0593447i
$177$		0			0
$178$	−750.000	+	1299.04i	−0.315814	+	0.547006i
$179$	2360.00			0.985445			0.492723	−	0.870186i	$-0.336002\pi$
$179$	2360.00			0.985445			0.492723	+	0.870186i	$0.336002\pi$
$180$		0			0
$181$	1241.00			0.509629			0.254814	−	0.966990i	$-0.417986\pi$
$181$	1241.00			0.509629			0.254814	+	0.966990i	$0.417986\pi$
$182$		0			0
$183$		0			0
$184$	972.000	+	1683.55i	0.389439	+	0.674528i
$185$	425.000	+	736.122i	0.168901	+	0.292545i
$186$		0			0
$187$	−35.0000	+	60.6218i	−0.0136869	+	0.0237064i
$188$	640.000			0.248281
$189$		0			0
$190$	1130.00			0.431467
$191$	−2495.00	+	4321.47i	−0.945193	+	1.63712i	−0.189829	+	0.981817i	$0.560793\pi$
$191$	−2495.00	+	4321.47i	−0.945193	+	1.63712i	−0.755364	+	0.655305i	$0.772540\pi$
$192$		0			0
$193$	1130.00	+	1957.22i	0.421447	+	0.729967i	0.996081	−	0.0884432i	$-0.0281892\pi$
$193$	1130.00	+	1957.22i	0.421447	+	0.729967i	−0.574635	+	0.818410i	$0.694856\pi$
$194$	1480.00	+	2563.44i	0.547721	+	0.948680i
$195$		0			0
$196$	−686.000	+	1188.19i	−0.250000	+	0.433013i
$197$	2247.00			0.812650			0.406325	−	0.913729i	$-0.366810\pi$
$197$	2247.00			0.812650			0.406325	+	0.913729i	$0.366810\pi$
$198$		0			0
$199$	4564.00			1.62580			0.812898	−	0.582406i	$-0.197889\pi$
$199$	4564.00			1.62580			0.812898	+	0.582406i	$0.197889\pi$
$200$	300.000	−	519.615i	0.106066	−	0.183712i
$201$		0			0
$202$	−1500.00	−	2598.08i	−0.522473	−	0.904951i
$203$		0			0
$204$		0			0
$205$	325.000	−	562.917i	0.110727	−	0.191784i
$206$	−920.000			−0.311162
$207$		0			0
$208$	1280.00			0.426692
$209$	−565.000	+	978.609i	−0.186995	+	0.323884i
$210$		0			0
$211$	−2474.50	−	4285.96i	−0.807354	−	1.39838i	−0.914691	−	0.404155i	$-0.867566\pi$
$211$	−2474.50	−	4285.96i	−0.807354	−	1.39838i	0.107337	−	0.994223i	$-0.465768\pi$
$212$	−1262.00	−	2185.85i	−0.408842	−	0.708135i
$213$		0			0
$214$	−420.000	+	727.461i	−0.134162	+	0.232375i
$215$	−50.0000			−0.0158603
$216$		0			0
$217$		0			0
$218$	607.000	−	1051.35i	0.188584	−	0.326636i
$219$		0			0
$220$	100.000	+	173.205i	0.0306454	+	0.0530795i
$221$	−280.000	−	484.974i	−0.0852255	−	0.147615i
$222$		0			0
$223$	−1945.00	+	3368.84i	−0.584067	+	1.01163i	0.410925	+	0.911669i	$0.365206\pi$
$223$	−1945.00	+	3368.84i	−0.584067	+	1.01163i	−0.994991	+	0.0999635i	$0.968127\pi$
$224$		0			0
$225$		0			0
$226$	−4340.00			−1.27740
$227$	1226.50	−	2124.36i	0.358615	−	0.621140i	−0.629114	−	0.777313i	$-0.716582\pi$
$227$	1226.50	−	2124.36i	0.358615	−	0.621140i	0.987730	+	0.156173i	$0.0499157\pi$
$228$		0			0
$229$	3106.50	+	5380.62i	0.896434	+	1.55267i	0.832020	+	0.554745i	$0.187184\pi$
$229$	3106.50	+	5380.62i	0.896434	+	1.55267i	0.0644134	+	0.997923i	$0.479482\pi$
$230$	405.000	+	701.481i	0.116108	+	0.201105i
$231$		0			0
$232$	2640.00	−	4572.61i	0.747088	−	1.29399i
$233$	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
$235$	800.000			0.222069
$236$	1120.00	−	1939.90i	0.308923	−	0.535070i
$237$		0			0
$238$		0			0
$239$	3245.00	+	5620.50i	0.878249	+	1.52117i	0.853261	+	0.521485i	$0.174622\pi$
$239$	3245.00	+	5620.50i	0.878249	+	1.52117i	0.0249888	+	0.999688i	$0.492045\pi$
$240$		0			0
$241$	1700.50	−	2945.35i	0.454518	−	0.787248i	−0.544142	−	0.838993i	$-0.683145\pi$
$241$	1700.50	−	2945.35i	0.454518	−	0.787248i	0.998660	+	0.0517447i	$0.0164782\pi$
$242$	−2462.00			−0.653981
$243$		0			0
$244$	−916.000			−0.240332
$245$	−857.500	+	1485.23i	−0.223607	+	0.387298i
$246$		0			0
$247$	−4520.00	−	7828.87i	−1.16438	−	2.01676i
$248$	−2268.00	−	3928.29i	−0.580718	−	1.00583i
$249$		0			0
$250$	125.000	−	216.506i	0.0316228	−	0.0547723i
$251$	4980.00			1.25233			0.626165	−	0.779691i	$-0.284624\pi$
$251$	4980.00			1.25233			0.626165	+	0.779691i	$0.284624\pi$
$252$		0			0
$253$	−810.000			−0.201282
$254$	1610.00	−	2788.60i	0.397718	−	0.688868i
$255$		0			0
$256$	2176.00	+	3768.94i	0.531250	+	0.920152i
$257$	1678.50	+	2907.25i	0.407401	+	0.705639i	0.994598	−	0.103806i	$-0.0331020\pi$
$257$	1678.50	+	2907.25i	0.407401	+	0.705639i	−0.587197	+	0.809444i	$0.699769\pi$
$258$		0			0
$259$		0			0
$260$	−1600.00			−0.381645
$261$		0			0
$262$	−4740.00			−1.11770
$263$	−2270.00	+	3931.76i	−0.532221	+	0.921834i	0.467071	+	0.884220i	$0.345309\pi$
$263$	−2270.00	+	3931.76i	−0.532221	+	0.921834i	−0.999292	+	0.0376145i	$0.988024\pi$
$264$		0			0
$265$	−1577.50	−	2732.31i	−0.365679	−	0.633375i
$266$		0			0
$267$		0			0
$268$	1500.00	−	2598.08i	0.341892	−	0.592174i
$269$	−8410.00			−1.90620			−0.953098	−	0.302662i	$-0.902125\pi$
$269$	−8410.00			−1.90620			−0.953098	+	0.302662i	$0.902125\pi$
$270$		0			0
$271$	259.000			0.0580558			0.0290279	−	0.999579i	$-0.490759\pi$
$271$	259.000			0.0580558			0.0290279	+	0.999579i	$0.490759\pi$
$272$	−56.0000	+	96.9948i	−0.0124835	+	0.0216220i
$273$		0			0
$274$	1797.00	+	3112.50i	0.396207	+	0.686251i
$275$	125.000	+	216.506i	0.0274101	+	0.0474757i
$276$		0			0
$277$	2085.00	−	3611.33i	0.452258	−	0.783334i	−0.546268	−	0.837611i	$-0.683952\pi$
$277$	2085.00	−	3611.33i	0.452258	−	0.783334i	0.998526	+	0.0542765i	$0.0172852\pi$
$278$	−248.000			−0.0535038
$279$		0			0
$280$		0			0
$281$	−870.000	+	1506.88i	−0.184697	+	0.319905i	−0.943474	−	0.331445i	$-0.892464\pi$
$281$	−870.000	+	1506.88i	−0.184697	+	0.319905i	0.758777	+	0.651350i	$0.225797\pi$
$282$		0			0
$283$	2535.00	+	4390.75i	0.532474	+	0.922272i	0.999281	+	0.0379127i	$0.0120709\pi$
$283$	2535.00	+	4390.75i	0.532474	+	0.922272i	−0.466807	+	0.884359i	$0.654596\pi$
$284$	−1780.00	−	3083.05i	−0.371914	−	0.644174i
$285$		0			0
$286$	−800.000	+	1385.64i	−0.165402	+	0.286485i
$287$		0			0
$288$		0			0
$289$	−4864.00			−0.990026
$290$	1100.00	−	1905.26i	0.222739	−	0.385795i
$291$		0			0
$292$	−1780.00	−	3083.05i	−0.356735	−	0.617883i
$293$	−79.5000	−	137.698i	−0.0158513	−	0.0274553i	0.857991	−	0.513665i	$-0.171713\pi$
$293$	−79.5000	−	137.698i	−0.0158513	−	0.0274553i	−0.873842	+	0.486210i	$0.838379\pi$
$294$		0			0
$295$	1400.00	−	2424.87i	0.276309	−	0.478581i
$296$	−4080.00			−0.801166
$297$		0			0
$298$	140.000			0.0272147
$299$	3240.00	−	5611.84i	0.626669	−	1.08542i
$300$		0			0
$301$		0			0
$302$	−2248.00	−	3893.65i	−0.428337	−	0.741902i
$303$		0			0
$304$	−904.000	+	1565.77i	−0.170552	+	0.295406i
$305$	−1145.00			−0.214959
$306$		0			0
$307$	6490.00			1.20653			0.603264	−	0.797542i	$-0.293867\pi$
$307$	6490.00			1.20653			0.603264	+	0.797542i	$0.293867\pi$
$308$		0			0
$309$		0			0
$310$	−945.000	−	1636.79i	−0.173137	−	0.299882i
$311$	−4110.00	−	7118.73i	−0.749379	−	1.29796i	−0.948121	−	0.317910i	$-0.897019\pi$
$311$	−4110.00	−	7118.73i	−0.749379	−	1.29796i	0.198742	−	0.980052i	$-0.436314\pi$
$312$		0			0
$313$	2330.00	−	4035.68i	0.420765	−	0.728786i	−0.575250	−	0.817978i	$-0.695095\pi$
$313$	2330.00	−	4035.68i	0.420765	−	0.728786i	0.996014	+	0.0891919i	$0.0284284\pi$
$314$	2020.00			0.363042
$315$		0			0
$316$	108.000			0.0192262
$317$	−3408.50	+	5903.70i	−0.603913	+	1.04601i	0.388309	+	0.921529i	$0.373059\pi$
$317$	−3408.50	+	5903.70i	−0.603913	+	1.04601i	−0.992222	+	0.124479i	$0.960274\pi$
$318$		0			0
$319$	1100.00	+	1905.26i	0.193066	+	0.334401i
$320$	1120.00	+	1939.90i	0.195656	+	0.338886i
$321$		0			0
$322$		0			0
$323$	791.000			0.136261
$324$		0			0
$325$	−2000.00			−0.341354
$326$	−590.000	+	1021.91i	−0.100236	+	0.173615i
$327$		0			0
$328$	1560.00	+	2702.00i	0.262612	+	0.454857i
$329$		0			0
$330$		0			0
$331$	−96.0000	+	166.277i	−0.0159415	+	0.0276115i	−0.873886	−	0.486131i	$-0.838408\pi$
$331$	−96.0000	+	166.277i	−0.0159415	+	0.0276115i	0.857945	+	0.513742i	$0.171741\pi$
$332$	1716.00			0.283668
$333$		0			0
$334$	−4806.00			−0.787343
$335$	1875.00	−	3247.60i	0.305798	−	0.529657i
$336$		0			0
$337$	−2420.00	−	4191.56i	−0.391174	−	0.677534i	0.601430	−	0.798925i	$-0.294598\pi$
$337$	−2420.00	−	4191.56i	−0.391174	−	0.677534i	−0.992605	+	0.121391i	$0.961264\pi$
$338$	−4203.00	−	7279.81i	−0.676370	−	1.17151i
$339$		0			0
$340$	70.0000	−	121.244i	0.0111655	−	0.0193393i
$341$	1890.00			0.300144
$342$		0			0
$343$		0			0
$344$	120.000	−	207.846i	0.0188080	−	0.0325765i
$345$		0			0
$346$	801.000	+	1387.37i	0.124457	+	0.215565i
$347$	−430.000	−	744.782i	−0.0665234	−	0.115222i	0.830845	−	0.556503i	$-0.187857\pi$
$347$	−430.000	−	744.782i	−0.0665234	−	0.115222i	−0.897369	+	0.441282i	$0.854524\pi$
$348$		0			0
$349$	−2688.50	+	4656.62i	−0.412356	+	0.714221i	−0.995147	−	0.0984011i	$-0.968627\pi$
$349$	−2688.50	+	4656.62i	−0.412356	+	0.714221i	0.582791	+	0.812622i	$0.301961\pi$
$350$		0			0
$351$		0			0
$352$	−1600.00			−0.242274
$353$	−4005.00	+	6936.86i	−0.603866	+	1.04593i	0.388364	+	0.921506i	$0.373040\pi$
$353$	−4005.00	+	6936.86i	−0.603866	+	1.04593i	−0.992230	+	0.124420i	$0.960293\pi$
$354$		0			0
$355$	−2225.00	−	3853.81i	−0.332650	−	0.576167i
$356$	1500.00	+	2598.08i	0.223314	+	0.386791i
$357$		0			0
$358$	−2360.00	+	4087.64i	−0.348407	+	0.603459i
$359$	−12930.0			−1.90089			−0.950445	−	0.310894i	$-0.899372\pi$
$359$	−12930.0			−1.90089			−0.950445	+	0.310894i	$0.899372\pi$
$360$		0			0
$361$	5910.00			0.861642
$362$	−1241.00	+	2149.48i	−0.180181	+	0.312083i
$363$		0			0
$364$		0			0
$365$	−2225.00	−	3853.81i	−0.319073	−	0.552651i
$366$		0			0
$367$	3000.00	−	5196.15i	0.426700	−	0.739065i	−0.569878	−	0.821729i	$-0.693010\pi$
$367$	3000.00	−	5196.15i	0.426700	−	0.739065i	0.996577	+	0.0826641i	$0.0263429\pi$
$368$	−1296.00			−0.183583
$369$		0			0
$370$	−1700.00			−0.238862
$371$		0			0
$372$		0			0
$373$	70.0000	+	121.244i	0.00971706	+	0.0168304i	0.870843	−	0.491561i	$-0.163574\pi$
$373$	70.0000	+	121.244i	0.00971706	+	0.0168304i	−0.861126	+	0.508392i	$0.830240\pi$
$374$	−70.0000	−	121.244i	−0.00967811	−	0.0167630i
$375$		0			0
$376$	−1920.00	+	3325.54i	−0.263342	+	0.456121i
$377$	−17600.0			−2.40437
$378$		0			0
$379$	6217.00			0.842601			0.421301	−	0.906921i	$-0.361574\pi$
$379$	6217.00			0.842601			0.421301	+	0.906921i	$0.361574\pi$
$380$	1130.00	−	1957.22i	0.152547	−	0.264219i
$381$		0			0
$382$	−4990.00	−	8642.93i	−0.668352	−	1.15762i
$383$	2275.50	+	3941.28i	0.303584	+	0.525823i	0.976945	−	0.213491i	$-0.0684834\pi$
$383$	2275.50	+	3941.28i	0.303584	+	0.525823i	−0.673361	+	0.739314i	$0.735150\pi$
$384$		0			0
$385$		0			0
$386$	−4520.00			−0.596015
$387$		0			0
$388$	5920.00			0.774594
$389$	−1155.00	+	2000.52i	−0.150542	+	0.260746i	−0.931427	−	0.363929i	$-0.881435\pi$
$389$	−1155.00	+	2000.52i	−0.150542	+	0.260746i	0.780885	+	0.624675i	$0.214769\pi$
$390$		0			0
$391$	283.500	+	491.036i	0.0366681	+	0.0635109i
$392$	−4116.00	−	7129.12i	−0.530330	−	0.918559i
$393$		0			0
$394$	−2247.00	+	3891.92i	−0.287315	+	0.497645i
$395$	135.000			0.0171964
$396$		0			0
$397$	−2900.00			−0.366617			−0.183308	−	0.983055i	$-0.558681\pi$
$397$	−2900.00			−0.366617			−0.183308	+	0.983055i	$0.558681\pi$
$398$	−4564.00	+	7905.08i	−0.574806	+	0.995593i
$399$		0			0
$400$	200.000	+	346.410i	0.0250000	+	0.0433013i
$401$	1125.00	+	1948.56i	0.140099	+	0.242659i	0.927534	−	0.373739i	$-0.121924\pi$
$401$	1125.00	+	1948.56i	0.140099	+	0.242659i	−0.787435	+	0.616398i	$0.788591\pi$
$402$		0			0
$403$	−7560.00	+	13094.3i	−0.934468	+	1.61855i
$404$	−6000.00			−0.738889
$405$		0			0
$406$		0			0
$407$	850.000	−	1472.24i	0.103521	−	0.179303i
$408$		0			0
$409$	5631.50	+	9754.04i	0.680831	+	1.17923i	0.974728	+	0.223396i	$0.0717144\pi$
$409$	5631.50	+	9754.04i	0.680831	+	1.17923i	−0.293897	+	0.955837i	$0.594952\pi$
$410$	650.000	+	1125.83i	0.0782956	+	0.135612i
$411$		0			0
$412$	−920.000	+	1593.49i	−0.110012	+	0.190547i
$413$		0			0
$414$		0			0
$415$	2145.00			0.253720
$416$	6400.00	−	11085.1i	0.754293	−	1.30647i
$417$		0			0
$418$	−1130.00	−	1957.22i	−0.132225	−	0.229021i
$419$	−3455.00	−	5984.24i	−0.402835	−	0.697730i	0.591232	−	0.806502i	$-0.298642\pi$
$419$	−3455.00	−	5984.24i	−0.402835	−	0.697730i	−0.994067	+	0.108771i	$0.965308\pi$
$420$		0			0
$421$	2624.50	−	4545.77i	0.303825	−	0.526240i	−0.673174	−	0.739484i	$-0.735070\pi$
$421$	2624.50	−	4545.77i	0.303825	−	0.526240i	0.976999	+	0.213244i	$0.0684029\pi$
$422$	9898.00			1.14177
$423$		0			0
$424$	15144.0			1.73457
$425$	87.5000	−	151.554i	0.00998676	−	0.0172976i
$426$		0			0
$427$		0			0
$428$	840.000	+	1454.92i	0.0948667	+	0.164314i
$429$		0			0
$430$	50.0000	−	86.6025i	0.00560747	−	0.00971243i
$431$	11880.0			1.32770			0.663851	−	0.747865i	$-0.268921\pi$
$431$	11880.0			1.32770			0.663851	+	0.747865i	$0.268921\pi$
$432$		0			0
$433$	−4280.00			−0.475020			−0.237510	−	0.971385i	$-0.576331\pi$
$433$	−4280.00			−0.475020			−0.237510	+	0.971385i	$0.576331\pi$
$434$		0			0
$435$		0			0
$436$	−1214.00	−	2102.71i	−0.133349	−	0.230967i
$437$	4576.50	+	7926.73i	0.500970	+	0.867705i
$438$		0			0
$439$	−3231.50	+	5597.12i	−0.351324	+	0.608510i	−0.986482	−	0.163872i	$-0.947602\pi$
$439$	−3231.50	+	5597.12i	−0.351324	+	0.608510i	0.635158	+	0.772382i	$0.280935\pi$
$440$	−1200.00			−0.130018
$441$		0			0
$442$	1120.00			0.120527
$443$	5860.50	−	10150.7i	0.628534	−	1.08865i	−0.359312	−	0.933218i	$-0.616988\pi$
$443$	5860.50	−	10150.7i	0.628534	−	1.08865i	0.987846	−	0.155436i	$-0.0496782\pi$
$444$		0			0
$445$	1875.00	+	3247.60i	0.199738	+	0.345957i
$446$	−3890.00	−	6737.68i	−0.412997	−	0.715332i
$447$		0			0
$448$		0			0
$449$	2180.00			0.229133			0.114566	−	0.993416i	$-0.463452\pi$
$449$	2180.00			0.229133			0.114566	+	0.993416i	$0.463452\pi$
$450$		0			0
$451$	−1300.00			−0.135731
$452$	−4340.00	+	7517.10i	−0.451629	+	0.782245i
$453$		0			0
$454$	2453.00	+	4248.72i	0.253579	+	0.439212i
$455$		0			0
$456$		0			0
$457$	8920.00	−	15449.9i	0.913042	−	1.58143i	0.103298	−	0.994650i	$-0.467060\pi$
$457$	8920.00	−	15449.9i	0.913042	−	1.58143i	0.809744	−	0.586784i	$-0.199606\pi$
$458$	−12426.0			−1.26775
$459$		0			0
$460$	1620.00			0.164202
$461$	−1125.00	+	1948.56i	−0.113658	+	0.196862i	−0.917243	−	0.398329i	$-0.869590\pi$
$461$	−1125.00	+	1948.56i	−0.113658	+	0.196862i	0.803584	+	0.595191i	$0.202924\pi$
$462$		0			0
$463$	−615.000	−	1065.21i	−0.0617310	−	0.106921i	0.833508	−	0.552507i	$-0.186329\pi$
$463$	−615.000	−	1065.21i	−0.0617310	−	0.106921i	−0.895239	+	0.445586i	$0.852995\pi$
$464$	1760.00	+	3048.41i	0.176090	+	0.304998i
$465$		0			0
$466$	−3450.00	+	5975.58i	−0.342957	+	0.594020i
$467$	−5813.00			−0.576003			−0.288002	−	0.957630i	$-0.592991\pi$
$467$	−5813.00			−0.576003			−0.288002	+	0.957630i	$0.592991\pi$
$468$		0			0
$469$		0			0
$470$	−800.000	+	1385.64i	−0.0785133	+	0.135989i
$471$		0			0
$472$	6720.00	+	11639.4i	0.655324	+	1.13505i
$473$	50.0000	+	86.6025i	0.00486047	+	0.00841858i
$474$		0			0
$475$	1412.50	−	2446.52i	0.136442	−	0.236324i
$476$		0			0
$477$		0			0
$478$	−12980.0			−1.24203
$479$	−3375.00	+	5845.67i	−0.321937	+	0.557611i	−0.980888	−	0.194575i	$-0.937667\pi$
$479$	−3375.00	+	5845.67i	−0.321937	+	0.557611i	0.658951	+	0.752186i	$0.271000\pi$
$480$		0			0
$481$	6800.00	+	11777.9i	0.644601	+	1.11648i
$482$	3401.00	+	5890.70i	0.321393	+	0.556669i
$483$		0			0
$484$	−2462.00	+	4264.31i	−0.231217	+	0.400480i
$485$	7400.00			0.692818
$486$		0			0
$487$	−6610.00			−0.615047			−0.307523	−	0.951541i	$-0.599500\pi$
$487$	−6610.00			−0.615047			−0.307523	+	0.951541i	$0.599500\pi$
$488$	2748.00	−	4759.68i	0.254910	−	0.441517i
$489$		0			0
$490$	−1715.00	−	2970.47i	−0.158114	−	0.273861i
$491$	−2495.00	−	4321.47i	−0.229323	−	0.397200i	0.728284	−	0.685275i	$-0.240318\pi$
$491$	−2495.00	−	4321.47i	−0.229323	−	0.397200i	−0.957608	+	0.288075i	$0.906985\pi$
$492$		0			0
$493$	770.000	−	1333.68i	0.0703429	−	0.121837i
$494$	18080.0			1.64668
$495$		0			0
$496$	3024.00			0.273753
$497$		0			0
$498$		0			0
$499$	−741.500	−	1284.32i	−0.0665212	−	0.115218i	0.830847	−	0.556502i	$-0.187857\pi$
$499$	−741.500	−	1284.32i	−0.0665212	−	0.115218i	−0.897368	+	0.441283i	$0.854523\pi$
$500$	−250.000	−	433.013i	−0.0223607	−	0.0387298i
$501$		0			0
$502$	−4980.00	+	8625.61i	−0.442765	+	0.766892i
$503$	11641.0			1.03190			0.515951	−	0.856618i	$-0.327439\pi$
$503$	11641.0			1.03190			0.515951	+	0.856618i	$0.327439\pi$
$504$		0			0
$505$	−7500.00			−0.660882
$506$	810.000	−	1402.96i	0.0711638	−	0.123259i
$507$		0			0
$508$	−3220.00	−	5577.20i	−0.281229	−	0.487103i
$509$	1310.00	+	2268.99i	0.114076	+	0.197586i	0.917410	−	0.397943i	$-0.130276\pi$
$509$	1310.00	+	2268.99i	0.114076	+	0.197586i	−0.803334	+	0.595529i	$0.796943\pi$
$510$		0			0
$511$		0			0
$512$	−5632.00			−0.486136
$513$		0			0
$514$	−6714.00			−0.576151
$515$	−1150.00	+	1991.86i	−0.0983982	+	0.170431i
$516$		0			0
$517$	−800.000	−	1385.64i	−0.0680541	−	0.117873i
$518$		0			0
$519$		0			0
$520$	4800.00	−	8313.84i	0.404796	−	0.701127i
$521$	13690.0			1.15119			0.575595	−	0.817735i	$-0.304771\pi$
$521$	13690.0			1.15119			0.575595	+	0.817735i	$0.304771\pi$
$522$		0			0
$523$	−10220.0			−0.854473			−0.427237	−	0.904140i	$-0.640513\pi$
$523$	−10220.0			−0.854473			−0.427237	+	0.904140i	$0.640513\pi$
$524$	−4740.00	+	8209.92i	−0.395168	+	0.684450i
$525$		0			0
$526$	−4540.00	−	7863.51i	−0.376337	−	0.651835i
$527$	−661.500	−	1145.75i	−0.0546782	−	0.0947054i
$528$		0			0
$529$	2803.00	−	4854.94i	0.230377	−	0.399025i
$530$	6310.00			0.517149
$531$		0			0
$532$		0			0
$533$	5200.00	−	9006.66i	0.422583	−	0.731936i
$534$		0			0
$535$	1050.00	+	1818.65i	0.0848513	+	0.146967i
$536$	9000.00	+	15588.5i	0.725263	+	1.25619i
$537$		0			0
$538$	8410.00	−	14566.5i	0.673942	−	1.16730i
$539$	3430.00			0.274101
$540$		0			0
$541$	−2778.00			−0.220768			−0.110384	−	0.993889i	$-0.535208\pi$
$541$	−2778.00			−0.220768			−0.110384	+	0.993889i	$0.535208\pi$
$542$	−259.000	+	448.601i	−0.0205258	+	0.0355518i
$543$		0			0
$544$	560.000	+	969.948i	0.0441357	+	0.0764452i
$545$	−1517.50	−	2628.39i	−0.119271	−	0.206583i
$546$		0			0
$547$	6415.00	−	11111.1i	0.501436	−	0.868513i	−0.498562	−	0.866854i	$-0.666139\pi$
$547$	6415.00	−	11111.1i	0.501436	−	0.868513i	0.999999	−	0.00165916i	$-0.000528127\pi$
$548$	7188.00			0.560321
$549$		0			0
$550$	−500.000			−0.0387638
$551$	12430.0	−	21529.4i	0.961045	−	1.66458i
$552$		0			0
$553$		0			0
$554$	4170.00	+	7222.65i	0.319795	+	0.553901i
$555$		0			0
$556$	−248.000	+	429.549i	−0.0189164	+	0.0327642i
$557$	4950.00			0.376550			0.188275	−	0.982116i	$-0.439710\pi$
$557$	4950.00			0.376550			0.188275	+	0.982116i	$0.439710\pi$
$558$		0			0
$559$	−800.000			−0.0605302
$560$		0			0
$561$		0			0
$562$	−1740.00	−	3013.77i	−0.130600	−	0.226207i
$563$	3270.00	+	5663.81i	0.244785	+	0.423980i	0.962071	−	0.272798i	$-0.0879492\pi$
$563$	3270.00	+	5663.81i	0.244785	+	0.423980i	−0.717286	+	0.696779i	$0.754616\pi$
$564$		0			0
$565$	−5425.00	+	9396.38i	−0.403949	+	0.699661i
$566$	−10140.0			−0.753032
$567$		0			0
$568$	21360.0			1.57790
$569$	−7620.00	+	13198.2i	−0.561418	+	0.972405i	0.435955	+	0.899969i	$0.356411\pi$
$569$	−7620.00	+	13198.2i	−0.561418	+	0.972405i	−0.997373	+	0.0724364i	$0.976923\pi$
$570$		0			0
$571$	2640.50	+	4573.48i	0.193523	+	0.335191i	0.946415	−	0.322952i	$-0.104675\pi$
$571$	2640.50	+	4573.48i	0.193523	+	0.335191i	−0.752893	+	0.658144i	$0.771342\pi$
$572$	1600.00	+	2771.28i	0.116957	+	0.202575i
$573$		0			0
$574$		0			0
$575$	2025.00			0.146867
$576$		0			0
$577$	−10510.0			−0.758296			−0.379148	−	0.925336i	$-0.623783\pi$
$577$	−10510.0			−0.758296			−0.379148	+	0.925336i	$0.623783\pi$
$578$	4864.00	−	8424.70i	0.350027	−	0.606265i
$579$		0			0
$580$	−2200.00	−	3810.51i	−0.157500	−	0.272798i
$581$		0			0
$582$		0			0
$583$	−3155.00	+	5464.62i	−0.224128	+	0.388201i
$584$	21360.0			1.51350
$585$		0			0
$586$	318.000			0.0224172
$587$	2053.50	−	3556.77i	0.144390	−	0.250091i	−0.784755	−	0.619806i	$-0.787211\pi$
$587$	2053.50	−	3556.77i	0.144390	−	0.250091i	0.929145	+	0.369715i	$0.120545\pi$
$588$		0			0
$589$	−10678.5	−	18495.7i	−0.747029	−	1.29389i
$590$	2800.00	+	4849.74i	0.195380	+	0.338408i
$591$		0			0
$592$	1360.00	−	2355.59i	0.0944183	−	0.163537i
$593$	−26129.0			−1.80943			−0.904713	−	0.426022i	$-0.859915\pi$
$593$	−26129.0			−1.80943			−0.904713	+	0.426022i	$0.859915\pi$
$594$		0			0
$595$		0			0
$596$	140.000	−	242.487i	0.00962185	−	0.0166655i
$597$		0			0
$598$	6480.00	+	11223.7i	0.443122	+	0.767510i
$599$	−2180.00	−	3775.87i	−0.148702	−	0.257559i	0.782046	−	0.623221i	$-0.214176\pi$
$599$	−2180.00	−	3775.87i	−0.148702	−	0.257559i	−0.930748	+	0.365661i	$0.880843\pi$
$600$		0			0
$601$	8319.50	−	14409.8i	0.564658	−	0.978016i	−0.432423	−	0.901671i	$-0.642341\pi$
$601$	8319.50	−	14409.8i	0.564658	−	0.978016i	0.997081	−	0.0763457i	$-0.0243253\pi$
$602$		0			0
$603$		0			0
$604$	−8992.00			−0.605760
$605$	−3077.50	+	5330.39i	−0.206807	+	0.358200i
$606$		0			0
$607$	−245.000	−	424.352i	−0.0163826	−	0.0283755i	0.857718	−	0.514121i	$-0.171882\pi$
$607$	−245.000	−	424.352i	−0.0163826	−	0.0283755i	−0.874100	+	0.485745i	$0.838548\pi$
$608$	9040.00	+	15657.7i	0.602994	+	1.04442i
$609$		0			0
$610$	1145.00	−	1983.20i	0.0759995	−	0.131635i
$611$	12800.0			0.847516
$612$		0			0
$613$	18400.0			1.21235			0.606174	−	0.795332i	$-0.292704\pi$
$613$	18400.0			1.21235			0.606174	+	0.795332i	$0.292704\pi$
$614$	−6490.00	+	11241.0i	−0.426572	+	0.738844i
$615$		0			0
$616$		0			0
$617$	3913.50	+	6778.38i	0.255351	+	0.442281i	0.964991	−	0.262284i	$-0.0844756\pi$
$617$	3913.50	+	6778.38i	0.255351	+	0.442281i	−0.709640	+	0.704565i	$0.751142\pi$
$618$		0			0
$619$	9878.00	−	17109.2i	0.641406	−	1.11095i	−0.343713	−	0.939075i	$-0.611685\pi$
$619$	9878.00	−	17109.2i	0.641406	−	1.11095i	0.985119	−	0.171873i	$-0.0549819\pi$
$620$	−3780.00			−0.244852
$621$		0			0
$622$	16440.0			1.05978
$623$		0			0
$624$		0			0
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	4660.00	+	8071.36i	0.297526	+	0.515330i
$627$		0			0
$628$	2020.00	−	3498.74i	0.128355	−	0.222317i
$629$	−1190.00			−0.0754347
$630$		0			0
$631$	9829.00			0.620105			0.310053	−	0.950719i	$-0.399653\pi$
$631$	9829.00			0.620105			0.310053	+	0.950719i	$0.399653\pi$
$632$	−324.000	+	561.184i	−0.0203924	+	0.0353208i
$633$		0			0
$634$	−6817.00	−	11807.4i	−0.427031	−	0.739639i
$635$	−4025.00	−	6971.50i	−0.251539	−	0.435678i
$636$		0			0
$637$	−13720.0	+	23763.7i	−0.853385	+	1.47811i
$638$	−4400.00			−0.273037
$639$		0			0
$640$	1920.00			0.118585
$641$	−3000.00	+	5196.15i	−0.184856	+	0.320180i	−0.943528	−	0.331293i	$-0.892515\pi$
$641$	−3000.00	+	5196.15i	−0.184856	+	0.320180i	0.758672	+	0.651473i	$0.225849\pi$
$642$		0			0
$643$	−4140.00	−	7170.69i	−0.253912	−	0.439789i	0.710687	−	0.703508i	$-0.248384\pi$
$643$	−4140.00	−	7170.69i	−0.253912	−	0.439789i	−0.964600	+	0.263719i	$0.915051\pi$
$644$		0			0
$645$		0			0
$646$	−791.000	+	1370.05i	−0.0481757	+	0.0834427i
$647$	16637.0			1.01092			0.505462	−	0.862849i	$-0.331322\pi$
$647$	16637.0			1.01092			0.505462	+	0.862849i	$0.331322\pi$
$648$		0			0
$649$	−5600.00			−0.338705
$650$	2000.00	−	3464.10i	0.120687	−	0.209036i
$651$		0			0
$652$	1180.00	+	2043.82i	0.0708779	+	0.122764i
$653$	9875.50	+	17104.9i	0.591820	+	1.02506i	0.993987	+	0.109496i	$0.0349235\pi$
$653$	9875.50	+	17104.9i	0.591820	+	1.02506i	−0.402168	+	0.915566i	$0.631743\pi$
$654$		0			0
$655$	−5925.00	+	10262.4i	−0.353449	+	0.612191i
$656$	−2080.00			−0.123796
$657$		0			0
$658$		0			0
$659$	7130.00	−	12349.5i	0.421465	−	0.729999i	−0.574618	−	0.818422i	$-0.694849\pi$
$659$	7130.00	−	12349.5i	0.421465	−	0.729999i	0.996083	+	0.0884231i	$0.0281827\pi$
$660$		0			0
$661$	−11159.0	−	19328.0i	−0.656634	−	1.13732i	−0.981482	−	0.191556i	$-0.938646\pi$
$661$	−11159.0	−	19328.0i	−0.656634	−	1.13732i	0.324848	−	0.945766i	$-0.394687\pi$
$662$	−192.000	−	332.554i	−0.0112723	−	0.0195243i
$663$		0			0
$664$	−5148.00	+	8916.60i	−0.300875	+	0.521131i
$665$		0			0
$666$		0			0
$667$	17820.0			1.03447
$668$	−4806.00	+	8324.24i	−0.278368	+	0.482147i
$669$		0			0
$670$	3750.00	+	6495.19i	0.216232	+	0.374524i
$671$	1145.00	+	1983.20i	0.0658752	+	0.114099i
$672$		0			0
$673$	−10020.0	+	17355.1i	−0.573912	+	0.994044i	0.422247	+	0.906481i	$0.361241\pi$
$673$	−10020.0	+	17355.1i	−0.573912	+	0.994044i	−0.996159	+	0.0875636i	$0.972092\pi$
$674$	9680.00			0.553204
$675$		0			0
$676$	−16812.0			−0.956532
$677$	−1155.00	+	2000.52i	−0.0655691	+	0.113569i	−0.896946	−	0.442140i	$-0.854220\pi$
$677$	−1155.00	+	2000.52i	−0.0655691	+	0.113569i	0.831377	+	0.555708i	$0.187553\pi$
$678$		0			0
$679$		0			0
$680$	420.000	+	727.461i	0.0236857	+	0.0410248i
$681$		0			0
$682$	−1890.00	+	3273.58i	−0.106117	+	0.183800i
$683$	26739.0			1.49801			0.749004	−	0.662566i	$-0.230532\pi$
$683$	26739.0			1.49801			0.749004	+	0.662566i	$0.230532\pi$
$684$		0			0
$685$	8985.00			0.501167
$686$		0			0
$687$		0			0
$688$	80.0000	+	138.564i	0.00443310	+	0.00767835i
$689$	−25240.0	−	43717.0i	−1.39560	−	2.41725i
$690$		0			0
$691$	−2550.50	+	4417.60i	−0.140413	+	0.243203i	−0.927652	−	0.373445i	$-0.878176\pi$
$691$	−2550.50	+	4417.60i	−0.140413	+	0.243203i	0.787239	+	0.616648i	$0.211510\pi$
$692$	3204.00			0.176008
$693$		0			0
$694$	1720.00			0.0940783
$695$	−310.000	+	536.936i	−0.0169194	+	0.0293052i
$696$		0			0
$697$	455.000	+	788.083i	0.0247265	+	0.0428275i
$698$	−5377.00	−	9313.24i	−0.291579	−	0.505030i
$699$		0			0
$700$		0			0
$701$	−26030.0			−1.40248			−0.701241	−	0.712925i	$-0.747370\pi$
$701$	−26030.0			−1.40248			−0.701241	+	0.712925i	$0.747370\pi$
$702$		0			0
$703$	−19210.0			−1.03061
$704$	2240.00	−	3879.79i	0.119919	−	0.207706i
$705$		0			0
$706$	−8010.00	−	13873.7i	−0.426998	−	0.739582i
$707$		0			0
$708$		0			0
$709$	1927.00	−	3337.66i	0.102073	−	0.176796i	−0.810465	−	0.585787i	$-0.800786\pi$
$709$	1927.00	−	3337.66i	0.102073	−	0.176796i	0.912539	+	0.408990i	$0.134119\pi$
$710$	8900.00			0.470438
$711$		0			0
$712$	−18000.0			−0.947442
$713$	7654.50	−	13258.0i	0.402052	−	0.696375i
$714$		0			0
$715$	2000.00	+	3464.10i	0.104609	+	0.181189i
$716$	4720.00	+	8175.28i	0.246361	+	0.426710i
$717$		0			0
$718$	12930.0	−	22395.4i	0.672066	−	1.16405i
$719$	870.000			0.0451259			0.0225630	−	0.999745i	$-0.492817\pi$
$719$	870.000			0.0451259			0.0225630	+	0.999745i	$0.492817\pi$
$720$		0			0
$721$		0			0
$722$	−5910.00	+	10236.4i	−0.304636	+	0.527646i
$723$		0			0
$724$	2482.00	+	4298.95i	0.127407	+	0.220676i
$725$	−2750.00	−	4763.14i	−0.140872	−	0.243998i
$726$		0			0
$727$	−17890.0	+	30986.4i	−0.912659	+	1.58077i	−0.102367	+	0.994747i	$0.532642\pi$
$727$	−17890.0	+	30986.4i	−0.912659	+	1.58077i	−0.810292	+	0.586026i	$0.800692\pi$
$728$		0			0
$729$		0			0
$730$	8900.00			0.451238
$731$	35.0000	−	60.6218i	0.00177089	−	0.00306727i
$732$		0			0
$733$	1700.00	+	2944.49i	0.0856629	+	0.148373i	0.905674	−	0.423976i	$-0.139366\pi$
$733$	1700.00	+	2944.49i	0.0856629	+	0.148373i	−0.820011	+	0.572348i	$0.806033\pi$
$734$	6000.00	+	10392.3i	0.301722	+	0.522598i
$735$		0			0
$736$	−6480.00	+	11223.7i	−0.324533	+	0.562107i
$737$	−7500.00			−0.374852
$738$		0			0
$739$	−683.000			−0.0339981			−0.0169990	−	0.999856i	$-0.505411\pi$
$739$	−683.000			−0.0339981			−0.0169990	+	0.999856i	$0.505411\pi$
$740$	−1700.00	+	2944.49i	−0.0844503	+	0.146272i
$741$		0			0
$742$		0			0
$743$	−6700.00	−	11604.7i	−0.330820	−	0.572997i	0.651853	−	0.758345i	$-0.273992\pi$
$743$	−6700.00	−	11604.7i	−0.330820	−	0.572997i	−0.982673	+	0.185349i	$0.940659\pi$
$744$		0			0
$745$	175.000	−	303.109i	0.00860605	−	0.0149061i
$746$	−280.000			−0.0137420
$747$		0			0
$748$	−280.000			−0.0136869
$749$		0			0
$750$		0			0
$751$	11609.5	+	20108.2i	0.564097	+	0.977044i	0.997133	+	0.0756678i	$0.0241088\pi$
$751$	11609.5	+	20108.2i	0.564097	+	0.977044i	−0.433036	+	0.901376i	$0.642558\pi$
$752$	−1280.00	−	2217.03i	−0.0620702	−	0.107509i
$753$		0			0
$754$	17600.0	−	30484.1i	0.850072	−	1.47237i
$755$	−11240.0			−0.541809
$756$		0			0
$757$	19630.0			0.942489			0.471245	−	0.882003i	$-0.343805\pi$
$757$	19630.0			0.942489			0.471245	+	0.882003i	$0.343805\pi$
$758$	−6217.00	+	10768.2i	−0.297904	+	0.515986i
$759$		0			0
$760$	6780.00	+	11743.3i	0.323601	+	0.560493i
$761$	1470.00	+	2546.11i	0.0700229	+	0.121283i	0.898911	−	0.438131i	$-0.144359\pi$
$761$	1470.00	+	2546.11i	0.0700229	+	0.121283i	−0.828888	+	0.559414i	$0.811026\pi$
$762$		0			0
$763$		0			0
$764$	−19960.0			−0.945193
$765$		0			0
$766$	−9102.00			−0.429332
$767$	22400.0	−	38797.9i	1.05452	−	1.82648i
$768$		0			0
$769$	6993.50	+	12113.1i	0.327948	+	0.568023i	0.982105	−	0.188337i	$-0.0603096\pi$
$769$	6993.50	+	12113.1i	0.327948	+	0.568023i	−0.654156	+	0.756359i	$0.726976\pi$
$770$		0			0
$771$		0			0
$772$	−4520.00	+	7828.87i	−0.210723	+	0.364983i
$773$	−19839.0			−0.923104			−0.461552	−	0.887113i	$-0.652707\pi$
$773$	−19839.0			−0.923104			−0.461552	+	0.887113i	$0.652707\pi$
$774$		0			0
$775$	−4725.00			−0.219003
$776$	−17760.0	+	30761.2i	−0.821581	+	1.42302i
$777$		0			0
$778$	−2310.00	−	4001.04i	−0.106449	−	0.184376i
$779$	7345.00	+	12721.9i	0.337820	+	0.585122i
$780$		0			0
$781$	−4450.00	+	7707.63i	−0.203884	+	0.353138i
$782$	−1134.00			−0.0518565
$783$		0			0
$784$	5488.00			0.250000
$785$	2525.00	−	4373.43i	0.114804	−	0.198846i
$786$		0			0
$787$	19195.0	+	33246.7i	0.869413	+	1.50587i	0.862598	+	0.505890i	$0.168836\pi$
$787$	19195.0	+	33246.7i	0.869413	+	1.50587i	0.00681497	+	0.999977i	$0.497831\pi$
$788$	4494.00	+	7783.84i	0.203163	+	0.351888i
$789$		0			0
$790$	−135.000	+	233.827i	−0.00607985	+	0.0105306i
$791$		0			0
$792$		0			0
$793$	−18320.0			−0.820381
$794$	2900.00	−	5022.95i	0.129619	−	0.224506i
$795$		0			0
$796$	9128.00	+	15810.2i	0.406449	+	0.703990i
$797$	−14013.5	−	24272.1i	−0.622815	−	1.07875i	−0.988959	−	0.148189i	$-0.952656\pi$
$797$	−14013.5	−	24272.1i	−0.622815	−	1.07875i	0.366144	−	0.930558i	$-0.380678\pi$
$798$		0			0
$799$	−560.000	+	969.948i	−0.0247952	+	0.0429466i
$800$	4000.00			0.176777
$801$		0			0
$802$	−4500.00			−0.198130
$803$	−4450.00	+	7707.63i	−0.195563	+	0.338725i
$804$		0			0
$805$		0			0
$806$	−15120.0	−	26188.6i	−0.660768	−	1.14448i
$807$		0			0
$808$	18000.0	−	31176.9i	0.783710	−	1.35743i
$809$	−8630.00			−0.375049			−0.187525	−	0.982260i	$-0.560046\pi$
$809$	−8630.00			−0.375049			−0.187525	+	0.982260i	$0.560046\pi$
$810$		0			0
$811$	−1932.00			−0.0836519			−0.0418260	−	0.999125i	$-0.513317\pi$
$811$	−1932.00			−0.0836519			−0.0418260	+	0.999125i	$0.513317\pi$
$812$		0			0
$813$		0			0
$814$	1700.00	+	2944.49i	0.0732002	+	0.126786i
$815$	1475.00	+	2554.77i	0.0633951	+	0.109804i
$816$		0			0
$817$	565.000	−	978.609i	0.0241944	−	0.0419060i
$818$	−22526.0			−0.962840
$819$		0			0
$820$	2600.00			0.110727
$821$	−9045.00	+	15666.4i	−0.384498	+	0.665970i	−0.991699	−	0.128578i	$-0.958959\pi$
$821$	−9045.00	+	15666.4i	−0.384498	+	0.665970i	0.607202	+	0.794548i	$0.292292\pi$
$822$		0			0
$823$	−6445.00	−	11163.1i	−0.272975	−	0.472807i	0.696647	−	0.717414i	$-0.254674\pi$
$823$	−6445.00	−	11163.1i	−0.272975	−	0.472807i	−0.969622	+	0.244607i	$0.921341\pi$
$824$	−5520.00	−	9560.92i	−0.233372	−	0.404212i
$825$		0			0
$826$		0			0
$827$	−14887.0			−0.625963			−0.312982	−	0.949759i	$-0.601328\pi$
$827$	−14887.0			−0.625963			−0.312982	+	0.949759i	$0.601328\pi$
$828$		0			0
$829$	12666.0			0.530649			0.265325	−	0.964159i	$-0.414521\pi$
$829$	12666.0			0.530649			0.265325	+	0.964159i	$0.414521\pi$
$830$	−2145.00	+	3715.25i	−0.0897037	+	0.155371i
$831$		0			0
$832$	17920.0	+	31038.4i	0.746712	+	1.29334i
$833$	−1200.50	−	2079.33i	−0.0499338	−	0.0864879i
$834$		0			0
$835$	−6007.50	+	10405.3i	−0.248980	+	0.431246i
$836$	−4520.00			−0.186995
$837$		0			0
$838$	13820.0			0.569694
$839$	21910.0	−	37949.2i	0.901570	−	1.56156i	0.0761135	−	0.997099i	$-0.475749\pi$
$839$	21910.0	−	37949.2i	0.901570	−	1.56156i	0.825456	−	0.564466i	$-0.190918\pi$
$840$		0			0
$841$	−12005.5	−	20794.1i	−0.492251	−	0.852603i
$842$	5249.00	+	9091.53i	0.214837	+	0.372108i
$843$		0			0
$844$	9898.00	−	17143.8i	0.403677	−	0.699189i
$845$	−21015.0			−0.855548
$846$		0			0
$847$		0			0
$848$	−5048.00	+	8743.39i	−0.204421	+	0.354068i
$849$		0			0
$850$	175.000	+	303.109i	0.00706171	+	0.0122312i
$851$	−6885.00	−	11925.2i	−0.277338	−	0.480364i
$852$		0			0
$853$	−9660.00	+	16731.6i	−0.387752	+	0.671605i	−0.992147	−	0.125079i	$-0.960081\pi$
$853$	−9660.00	+	16731.6i	−0.387752	+	0.671605i	0.604395	+	0.796685i	$0.293415\pi$
$854$		0			0
$855$		0			0
$856$	−10080.0			−0.402485
$857$	−1826.50	+	3163.59i	−0.0728029	+	0.126098i	−0.900129	−	0.435624i	$-0.856528\pi$
$857$	−1826.50	+	3163.59i	−0.0728029	+	0.126098i	0.827326	+	0.561722i	$0.189861\pi$
$858$		0			0
$859$	−12186.5	−	21107.6i	−0.484049	−	0.838397i	0.515783	−	0.856719i	$-0.327501\pi$
$859$	−12186.5	−	21107.6i	−0.484049	−	0.838397i	−0.999832	+	0.0183218i	$0.994168\pi$
$860$	−100.000	−	173.205i	−0.00396508	−	0.00686773i
$861$		0			0
$862$	−11880.0	+	20576.8i	−0.469413	+	0.813048i
$863$	17629.0			0.695363			0.347681	−	0.937613i	$-0.386969\pi$
$863$	17629.0			0.695363			0.347681	+	0.937613i	$0.386969\pi$
$864$		0			0
$865$	4005.00			0.157427
$866$	4280.00	−	7413.18i	0.167945	−	0.290889i
$867$		0			0
$868$		0			0
$869$	−135.000	−	233.827i	−0.00526992	−	0.00912777i
$870$		0			0
$871$	30000.0	−	51961.5i	1.16706	−	2.02141i
$872$	14568.0			0.565751
$873$		0			0
$874$	−18306.0			−0.708478
$875$		0			0
$876$		0			0
$877$	10605.0	+	18368.4i	0.408330	+	0.707248i	0.994703	−	0.102793i	$-0.0327779\pi$
$877$	10605.0	+	18368.4i	0.408330	+	0.707248i	−0.586373	+	0.810041i	$0.699445\pi$
$878$	−6463.00	−	11194.2i	−0.248423	−	0.430282i
$879$		0			0
$880$	400.000	−	692.820i	0.0153227	−	0.0265397i
$881$	−39340.0			−1.50442			−0.752212	−	0.658921i	$-0.771013\pi$
$881$	−39340.0			−1.50442			−0.752212	+	0.658921i	$0.771013\pi$
$882$		0			0
$883$	−4240.00			−0.161594			−0.0807969	−	0.996731i	$-0.525747\pi$
$883$	−4240.00			−0.161594			−0.0807969	+	0.996731i	$0.525747\pi$
$884$	1120.00	−	1939.90i	0.0426128	−	0.0738075i
$885$		0			0
$886$	11721.0	+	20301.4i	0.444441	+	0.769794i
$887$	−7966.50	−	13798.4i	−0.301566	−	0.522327i	0.674925	−	0.737886i	$-0.264176\pi$
$887$	−7966.50	−	13798.4i	−0.301566	−	0.522327i	−0.976491	+	0.215559i	$0.930843\pi$
$888$		0			0
$889$		0			0
$890$	−7500.00			−0.282473
$891$		0			0
$892$	−15560.0			−0.584067
$893$	−9040.00	+	15657.7i	−0.338759	+	0.586748i
$894$		0			0
$895$	5900.00	+	10219.1i	0.220352	+	0.381661i
$896$		0			0
$897$		0			0
$898$	−2180.00	+	3775.87i	−0.0810106	+	0.140315i
$899$	−41580.0			−1.54257
$900$		0			0
$901$	4417.00			0.163320
$902$	1300.00	−	2251.67i	0.0479881	−	0.0831178i
$903$		0			0
$904$	−26040.0	−	45102.6i	−0.958050	−	1.65939i
$905$	3102.50	+	5373.69i	0.113956	+	0.197378i
$906$		0			0
$907$	3390.00	−	5871.65i	0.124105	−	0.214956i	−0.797278	−	0.603613i	$-0.793727\pi$
$907$	3390.00	−	5871.65i	0.124105	−	0.214956i	0.921383	+	0.388657i	$0.127061\pi$
$908$	9812.00			0.358615
$909$		0			0
$910$		0			0
$911$	−12370.0	+	21425.5i	−0.449875	+	0.779207i	−0.998377	−	0.0569423i	$-0.981865\pi$
$911$	−12370.0	+	21425.5i	−0.449875	+	0.779207i	0.548502	+	0.836149i	$0.315198\pi$
$912$		0			0
$913$	−2145.00	−	3715.25i	−0.0777537	−	0.134673i
$914$	17840.0	+	30899.8i	0.645618	+	1.11824i
$915$		0			0
$916$	−12426.0	+	21522.5i	−0.448217	+	0.776334i
$917$		0			0
$918$		0			0
$919$	−48344.0			−1.73528			−0.867640	−	0.497194i	$-0.834364\pi$
$919$	−48344.0			−1.73528			−0.867640	+	0.497194i	$0.834364\pi$
$920$	−4860.00	+	8417.77i	−0.174162	+	0.301658i
$921$		0			0
$922$	−2250.00	−	3897.11i	−0.0803686	−	0.139202i
$923$	−35600.0	−	61661.0i	−1.26954	−	2.19891i
$924$		0			0
$925$	−2125.00	+	3680.61i	−0.0755347	+	0.130830i
$926$	2460.00			0.0873009
$927$		0			0
$928$	35200.0			1.24515
$929$	−14825.0	+	25677.7i	−0.523566	+	0.906842i	0.476058	+	0.879414i	$0.342065\pi$
$929$	−14825.0	+	25677.7i	−0.523566	+	0.906842i	−0.999624	+	0.0274285i	$0.991268\pi$
$930$		0			0
$931$	−19379.5	−	33566.3i	−0.682210	−	1.18162i
$932$	6900.00	+	11951.2i	0.242508	+	0.420035i
$933$		0			0
$934$	5813.00	−	10068.4i	0.203648	−	0.352729i
$935$	−350.000			−0.0122420
$936$		0			0
$937$	10260.0			0.357716			0.178858	−	0.983875i	$-0.442760\pi$
$937$	10260.0			0.357716			0.178858	+	0.983875i	$0.442760\pi$
$938$		0			0
$939$		0			0
$940$	1600.00	+	2771.28i	0.0555173	+	0.0961588i
$941$	−8135.00	−	14090.2i	−0.281821	−	0.488128i	0.690012	−	0.723798i	$-0.257605\pi$
$941$	−8135.00	−	14090.2i	−0.281821	−	0.488128i	−0.971833	+	0.235670i	$0.924272\pi$
$942$		0			0
$943$	−5265.00	+	9119.25i	−0.181815	+	0.314914i
$944$	−8960.00			−0.308923
$945$		0			0
$946$	−200.000			−0.00687374
$947$	−11551.5	+	20007.8i	−0.396382	+	0.686553i	−0.993276	−	0.115766i	$-0.963068\pi$
$947$	−11551.5	+	20007.8i	−0.396382	+	0.686553i	0.596895	+	0.802319i	$0.296401\pi$
$948$		0			0
$949$	−35600.0	−	61661.0i	−1.21773	−	2.10917i
$950$	2825.00	+	4893.04i	0.0964791	+	0.167107i
$951$		0			0
$952$		0			0
$953$	32090.0			1.09076			0.545381	−	0.838188i	$-0.316385\pi$
$953$	32090.0			1.09076			0.545381	+	0.838188i	$0.316385\pi$
$954$		0			0
$955$	−24950.0			−0.845406
$956$	−12980.0	+	22482.0i	−0.439125	+	0.760586i
$957$		0			0
$958$	−6750.00	−	11691.3i	−0.227644	−	0.394290i
$959$		0			0
$960$		0			0
$961$	−2965.00	+	5135.53i	−0.0995267	+	0.172385i
$962$	−27200.0			−0.911604
$963$		0			0
$964$	13604.0			0.454518
$965$	−5650.00	+	9786.09i	−0.188477	+	0.326451i
$966$		0			0
$967$	21005.0	+	36381.7i	0.698527	+	1.20988i	0.968977	+	0.247150i	$0.0794940\pi$
$967$	21005.0	+	36381.7i	0.698527	+	1.20988i	−0.270451	+	0.962734i	$0.587173\pi$
$968$	−14772.0	−	25585.9i	−0.490486	−	0.849546i
$969$		0			0
$970$	−7400.00	+	12817.2i	−0.244948	+	0.424263i
$971$	−17490.0			−0.578044			−0.289022	−	0.957322i	$-0.593330\pi$
$971$	−17490.0			−0.578044			−0.289022	+	0.957322i	$0.593330\pi$
$972$		0			0
$973$		0			0
$974$	6610.00	−	11448.9i	0.217452	−	0.376638i
$975$		0			0
$976$	1832.00	+	3173.12i	0.0600829	+	0.104067i
$977$	−11065.0	−	19165.1i	−0.362334	−	0.627582i	0.626010	−	0.779815i	$-0.284687\pi$
$977$	−11065.0	−	19165.1i	−0.362334	−	0.627582i	−0.988345	+	0.152233i	$0.951353\pi$
$978$		0			0
$979$	3750.00	−	6495.19i	0.122421	−	0.212040i
$980$	−6860.00			−0.223607
$981$		0			0
$982$	9980.00			0.324312
$983$	20479.5	−	35471.5i	0.664491	−	1.15093i	−0.314932	−	0.949114i	$-0.601982\pi$
$983$	20479.5	−	35471.5i	0.664491	−	1.15093i	0.979423	−	0.201818i	$-0.0646849\pi$
$984$		0			0
$985$	5617.50	+	9729.80i	0.181714	+	0.314738i
$986$	1540.00	+	2667.36i	0.0497400	+	0.0861521i
$987$		0			0
$988$	18080.0	−	31315.5i	0.582188	−	1.00838i
$989$	810.000			0.0260430
$990$		0			0
$991$	61169.0			1.96074			0.980372	−	0.197157i	$-0.0631707\pi$
$991$	61169.0			1.96074			0.980372	+	0.197157i	$0.0631707\pi$
$992$	15120.0	−	26188.6i	0.483932	−	0.838195i
$993$		0			0
$994$		0			0
$995$	11410.0	+	19762.7i	0.363539	+	0.629668i
$996$		0			0
$997$	−13095.0	+	22681.2i	−0.415971	+	0.720482i	−0.995530	−	0.0944478i	$-0.969891\pi$
$997$	−13095.0	+	22681.2i	−0.415971	+	0.720482i	0.579559	+	0.814930i	$0.303225\pi$
$998$	2966.00			0.0940752
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.4.e.e.136.1		2
3.2	odd	2		405.4.e.j.136.1		2
9.2	odd	6		135.4.a.a.1.1	✓	1
9.4	even	3	inner	405.4.e.e.271.1		2
9.5	odd	6		405.4.e.j.271.1		2
9.7	even	3		135.4.a.d.1.1	yes	1
36.7	odd	6		2160.4.a.d.1.1		1
36.11	even	6		2160.4.a.n.1.1		1
45.2	even	12		675.4.b.d.649.1		2
45.7	odd	12		675.4.b.c.649.2		2
45.29	odd	6		675.4.a.i.1.1		1
45.34	even	6		675.4.a.b.1.1		1
45.38	even	12		675.4.b.d.649.2		2
45.43	odd	12		675.4.b.c.649.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.4.a.a.1.1	✓	1	9.2	odd	6
135.4.a.d.1.1	yes	1	9.7	even	3
405.4.e.e.136.1		2	1.1	even	1	trivial
405.4.e.e.271.1		2	9.4	even	3	inner
405.4.e.j.136.1		2	3.2	odd	2
405.4.e.j.271.1		2	9.5	odd	6
675.4.a.b.1.1		1	45.34	even	6
675.4.a.i.1.1		1	45.29	odd	6
675.4.b.c.649.1		2	45.43	odd	12
675.4.b.c.649.2		2	45.7	odd	12
675.4.b.d.649.1		2	45.2	even	12
675.4.b.d.649.2		2	45.38	even	12
2160.4.a.d.1.1		1	36.7	odd	6
2160.4.a.n.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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	405.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{2} +(2.00000 + 3.46410i) q^{4} +(2.50000 + 4.33013i) q^{5} -24.0000 q^{8} +O(q^{10})\)	\(q+(-1.00000 + 1.73205i) q^{2} +(2.00000 + 3.46410i) q^{4} +(2.50000 + 4.33013i) q^{5} -24.0000 q^{8} -10.0000 q^{10} +(5.00000 - 8.66025i) q^{11} +(40.0000 + 69.2820i) q^{13} +(8.00000 - 13.8564i) q^{16} -7.00000 q^{17} -113.000 q^{19} +(-10.0000 + 17.3205i) q^{20} +(10.0000 + 17.3205i) q^{22} +(-40.5000 - 70.1481i) q^{23} +(-12.5000 + 21.6506i) q^{25} -160.000 q^{26} +(-110.000 + 190.526i) q^{29} +(94.5000 + 163.679i) q^{31} +(-80.0000 - 138.564i) q^{32} +(7.00000 - 12.1244i) q^{34} +170.000 q^{37} +(113.000 - 195.722i) q^{38} +(-60.0000 - 103.923i) q^{40} +(-65.0000 - 112.583i) q^{41} +(-5.00000 + 8.66025i) q^{43} +40.0000 q^{44} +162.000 q^{46} +(80.0000 - 138.564i) q^{47} +(171.500 + 297.047i) q^{49} +(-25.0000 - 43.3013i) q^{50} +(-160.000 + 277.128i) q^{52} -631.000 q^{53} +50.0000 q^{55} +(-220.000 - 381.051i) q^{58} +(-280.000 - 484.974i) q^{59} +(-114.500 + 198.320i) q^{61} -378.000 q^{62} +448.000 q^{64} +(-200.000 + 346.410i) q^{65} +(-375.000 - 649.519i) q^{67} +(-14.0000 - 24.2487i) q^{68} -890.000 q^{71} -890.000 q^{73} +(-170.000 + 294.449i) q^{74} +(-226.000 - 391.443i) q^{76} +(13.5000 - 23.3827i) q^{79} +80.0000 q^{80} +260.000 q^{82} +(214.500 - 371.525i) q^{83} +(-17.5000 - 30.3109i) q^{85} +(-10.0000 - 17.3205i) q^{86} +(-120.000 + 207.846i) q^{88} +750.000 q^{89} +(162.000 - 280.592i) q^{92} +(160.000 + 277.128i) q^{94} +(-282.500 - 489.304i) q^{95} +(740.000 - 1281.72i) q^{97} -686.000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 4 q^{4} + 5 q^{5} - 48 q^{8}+O(q^{10}) \) 2 * q - 2 * q^2 + 4 * q^4 + 5 * q^5 - 48 * q^8	\( 2 q - 2 q^{2} + 4 q^{4} + 5 q^{5} - 48 q^{8} - 20 q^{10} + 10 q^{11} + 80 q^{13} + 16 q^{16} - 14 q^{17} - 226 q^{19} - 20 q^{20} + 20 q^{22} - 81 q^{23} - 25 q^{25} - 320 q^{26} - 220 q^{29} + 189 q^{31} - 160 q^{32} + 14 q^{34} + 340 q^{37} + 226 q^{38} - 120 q^{40} - 130 q^{41} - 10 q^{43} + 80 q^{44} + 324 q^{46} + 160 q^{47} + 343 q^{49} - 50 q^{50} - 320 q^{52} - 1262 q^{53} + 100 q^{55} - 440 q^{58} - 560 q^{59} - 229 q^{61} - 756 q^{62} + 896 q^{64} - 400 q^{65} - 750 q^{67} - 28 q^{68} - 1780 q^{71} - 1780 q^{73} - 340 q^{74} - 452 q^{76} + 27 q^{79} + 160 q^{80} + 520 q^{82} + 429 q^{83} - 35 q^{85} - 20 q^{86} - 240 q^{88} + 1500 q^{89} + 324 q^{92} + 320 q^{94} - 565 q^{95} + 1480 q^{97} - 1372 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 + 4 * q^4 + 5 * q^5 - 48 * q^8 - 20 * q^10 + 10 * q^11 + 80 * q^13 + 16 * q^16 - 14 * q^17 - 226 * q^19 - 20 * q^20 + 20 * q^22 - 81 * q^23 - 25 * q^25 - 320 * q^26 - 220 * q^29 + 189 * q^31 - 160 * q^32 + 14 * q^34 + 340 * q^37 + 226 * q^38 - 120 * q^40 - 130 * q^41 - 10 * q^43 + 80 * q^44 + 324 * q^46 + 160 * q^47 + 343 * q^49 - 50 * q^50 - 320 * q^52 - 1262 * q^53 + 100 * q^55 - 440 * q^58 - 560 * q^59 - 229 * q^61 - 756 * q^62 + 896 * q^64 - 400 * q^65 - 750 * q^67 - 28 * q^68 - 1780 * q^71 - 1780 * q^73 - 340 * q^74 - 452 * q^76 + 27 * q^79 + 160 * q^80 + 520 * q^82 + 429 * q^83 - 35 * q^85 - 20 * q^86 - 240 * q^88 + 1500 * q^89 + 324 * q^92 + 320 * q^94 - 565 * q^95 + 1480 * q^97 - 1372 * q^98

Introduction

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