LMFDB - Embedded newform 810.3.j.b.539.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,3,Mod(269,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([1, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("810.269");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	810.j (of order $6$, 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:	$22.0709014132$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 270)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			539.1
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	810.539
Dual form			810.3.j.b.269.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.86250 - 4.64016i) q^{5} +(-9.52628 + 5.50000i) q^{7} +2.82843 q^{8} +O(q^{10})$	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.86250 - 4.64016i) q^{5} +(-9.52628 + 5.50000i) q^{7} +2.82843 q^{8} +(-7.00000 + 1.00000i) q^{10} +(-6.12372 + 3.53553i) q^{11} +(12.9904 + 7.50000i) q^{13} +(13.4722 + 7.77817i) q^{14} +(-2.00000 - 3.46410i) q^{16} +22.6274 q^{17} -3.00000 q^{19} +(6.17449 + 7.86611i) q^{20} +(8.66025 + 5.00000i) q^{22} +(9.19239 - 15.9217i) q^{23} +(-18.0622 - 17.2846i) q^{25} -21.2132i q^{26} -22.0000i q^{28} +(11.0227 - 6.36396i) q^{29} +(4.00000 - 6.92820i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(-16.0000 - 27.7128i) q^{34} +(7.77817 + 54.4472i) q^{35} -65.0000i q^{37} +(2.12132 + 3.67423i) q^{38} +(5.26795 - 13.1244i) q^{40} +(-67.3610 - 38.8909i) q^{41} +(27.7128 - 16.0000i) q^{43} -14.1421i q^{44} -26.0000 q^{46} +(28.2843 + 48.9898i) q^{47} +(36.0000 - 62.3538i) q^{49} +(-8.39735 + 34.3436i) q^{50} +(-25.9808 + 15.0000i) q^{52} +12.7279 q^{53} +(5.00000 + 35.0000i) q^{55} +(-26.9444 + 15.5563i) q^{56} +(-15.5885 - 9.00000i) q^{58} +(68.5857 + 39.5980i) q^{59} +(-47.5000 - 82.2724i) q^{61} -11.3137 q^{62} +8.00000 q^{64} +(58.9958 - 46.3087i) q^{65} +(16.4545 + 9.50000i) q^{67} +(-22.6274 + 39.1918i) q^{68} +(61.1840 - 48.0263i) q^{70} +4.24264i q^{71} +119.000i q^{73} +(-79.6084 + 45.9619i) q^{74} +(3.00000 - 5.19615i) q^{76} +(38.8909 - 67.3610i) q^{77} +(-49.5000 - 85.7365i) q^{79} +(-19.7990 + 2.82843i) q^{80} +110.000i q^{82} +(-54.4472 - 94.3054i) q^{83} +(42.1436 - 104.995i) q^{85} +(-39.1918 - 22.6274i) q^{86} +(-17.3205 + 10.0000i) q^{88} -90.5097i q^{89} -165.000 q^{91} +(18.3848 + 31.8434i) q^{92} +(40.0000 - 69.2820i) q^{94} +(-5.58750 + 13.9205i) q^{95} +(82.2724 - 47.5000i) q^{97} -101.823 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4}+O(q^{10}) $ 8 * q - 8 * q^4	$ 8 q - 8 q^{4} - 56 q^{10} - 16 q^{16} - 24 q^{19} - 96 q^{25} + 32 q^{31} - 128 q^{34} + 56 q^{40} - 208 q^{46} + 288 q^{49} + 40 q^{55} - 380 q^{61} + 64 q^{64} - 44 q^{70} + 24 q^{76} - 396 q^{79} + 448 q^{85} - 1320 q^{91} + 320 q^{94}+O(q^{100}) $ 8 * q - 8 * q^4 - 56 * q^10 - 16 * q^16 - 24 * q^19 - 96 * q^25 + 32 * q^31 - 128 * q^34 + 56 * q^40 - 208 * q^46 + 288 * q^49 + 40 * q^55 - 380 * q^61 + 64 * q^64 - 44 * q^70 + 24 * q^76 - 396 * q^79 + 448 * q^85 - 1320 * q^91 + 320 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$487$	$731$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$	1.86250	−	4.64016i	0.372500	−	0.928032i
$5$	1.86250	−	4.64016i	0.372500	−	0.928032i
$6$		0			0
$7$	−9.52628	+	5.50000i	−1.36090	+	0.785714i	−0.989743	−	0.142857i	$-0.954371\pi$
$7$	−9.52628	+	5.50000i	−1.36090	+	0.785714i	−0.371154	+	0.928571i	$0.621038\pi$
$8$	2.82843			0.353553
$9$		0			0
$10$	−7.00000	+	1.00000i	−0.700000	+	0.100000i
$11$	−6.12372	+	3.53553i	−0.556702	+	0.321412i	−0.751821	−	0.659367i	$-0.770824\pi$
$11$	−6.12372	+	3.53553i	−0.556702	+	0.321412i	0.195119	+	0.980780i	$0.437491\pi$
$12$		0			0
$13$	12.9904	+	7.50000i	0.999260	+	0.576923i	0.908029	−	0.418907i	$-0.137587\pi$
$13$	12.9904	+	7.50000i	0.999260	+	0.576923i	0.0912308	+	0.995830i	$0.470920\pi$
$14$	13.4722	+	7.77817i	0.962300	+	0.555584i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	22.6274			1.33102			0.665512	−	0.746387i	$-0.268213\pi$
$17$	22.6274			1.33102			0.665512	+	0.746387i	$0.268213\pi$
$18$		0			0
$19$	−3.00000			−0.157895			−0.0789474	−	0.996879i	$-0.525156\pi$
$19$	−3.00000			−0.157895			−0.0789474	+	0.996879i	$0.525156\pi$
$20$	6.17449	+	7.86611i	0.308725	+	0.393305i
$21$		0			0
$22$	8.66025	+	5.00000i	0.393648	+	0.227273i
$23$	9.19239	−	15.9217i	0.399669	−	0.692247i	−0.594016	−	0.804453i	$-0.702458\pi$
$23$	9.19239	−	15.9217i	0.399669	−	0.692247i	0.993685	+	0.112206i	$0.0357917\pi$
$24$		0			0
$25$	−18.0622	−	17.2846i	−0.722487	−	0.691384i
$26$		−	21.2132i		−	0.815892i
$27$		0			0
$28$		−	22.0000i		−	0.785714i
$29$	11.0227	−	6.36396i	0.380093	−	0.219447i	−0.297766	−	0.954639i	$-0.596241\pi$
$29$	11.0227	−	6.36396i	0.380093	−	0.219447i	0.677859	+	0.735192i	$0.262908\pi$
$30$		0			0
$31$	4.00000	−	6.92820i	0.129032	−	0.223490i	−0.794270	−	0.607565i	$-0.792146\pi$
$31$	4.00000	−	6.92820i	0.129032	−	0.223490i	0.923302	+	0.384075i	$0.125480\pi$
$32$	−2.82843	+	4.89898i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−16.0000	−	27.7128i	−0.470588	−	0.815083i
$35$	7.77817	+	54.4472i	0.222234	+	1.55563i
$36$		0			0
$37$		−	65.0000i		−	1.75676i	−0.477966	−	0.878378i	$-0.658626\pi$
$37$		−	65.0000i		−	1.75676i	0.477966	−	0.878378i	$-0.341374\pi$
$38$	2.12132	+	3.67423i	0.0558242	+	0.0966904i
$39$		0			0
$40$	5.26795	−	13.1244i	0.131699	−	0.328109i
$41$	−67.3610	−	38.8909i	−1.64295	−	0.948558i	−0.979777	−	0.200092i	$-0.935876\pi$
$41$	−67.3610	−	38.8909i	−1.64295	−	0.948558i	−0.663173	−	0.748466i	$-0.730791\pi$
$42$		0			0
$43$	27.7128	−	16.0000i	0.644484	−	0.372093i	−0.141856	−	0.989887i	$-0.545307\pi$
$43$	27.7128	−	16.0000i	0.644484	−	0.372093i	0.786340	+	0.617794i	$0.211974\pi$
$44$		−	14.1421i		−	0.321412i
$45$		0			0
$46$	−26.0000			−0.565217
$47$	28.2843	+	48.9898i	0.601793	+	1.04234i	0.992550	+	0.121842i	$0.0388801\pi$
$47$	28.2843	+	48.9898i	0.601793	+	1.04234i	−0.390757	+	0.920494i	$0.627787\pi$
$48$		0			0
$49$	36.0000	−	62.3538i	0.734694	−	1.27253i
$50$	−8.39735	+	34.3436i	−0.167947	+	0.686872i
$51$		0			0
$52$	−25.9808	+	15.0000i	−0.499630	+	0.288462i
$53$	12.7279			0.240149			0.120075	−	0.992765i	$-0.461687\pi$
$53$	12.7279			0.240149			0.120075	+	0.992765i	$0.461687\pi$
$54$		0			0
$55$	5.00000	+	35.0000i	0.0909091	+	0.636364i
$56$	−26.9444	+	15.5563i	−0.481150	+	0.277792i
$57$		0			0
$58$	−15.5885	−	9.00000i	−0.268767	−	0.155172i
$59$	68.5857	+	39.5980i	1.16247	+	0.671152i	0.951895	−	0.306425i	$-0.0991330\pi$
$59$	68.5857	+	39.5980i	1.16247	+	0.671152i	0.210575	+	0.977578i	$0.432466\pi$
$60$		0			0
$61$	−47.5000	−	82.2724i	−0.778689	−	1.34873i	−0.932698	−	0.360659i	$-0.882552\pi$
$61$	−47.5000	−	82.2724i	−0.778689	−	1.34873i	0.154009	−	0.988069i	$-0.450781\pi$
$62$	−11.3137			−0.182479
$63$		0			0
$64$	8.00000			0.125000
$65$	58.9958	−	46.3087i	0.907628	−	0.712441i
$66$		0			0
$67$	16.4545	+	9.50000i	0.245589	+	0.141791i	0.617743	−	0.786380i	$-0.288047\pi$
$67$	16.4545	+	9.50000i	0.245589	+	0.141791i	−0.372154	+	0.928171i	$0.621381\pi$
$68$	−22.6274	+	39.1918i	−0.332756	+	0.576351i
$69$		0			0
$70$	61.1840	−	48.0263i	0.874057	−	0.686090i
$71$			4.24264i			0.0597555i	0.999554	+	0.0298778i	$0.00951180\pi$
$71$			4.24264i			0.0597555i	−0.999554	+	0.0298778i	$0.990488\pi$
$72$		0			0
$73$			119.000i			1.63014i	0.579365	+	0.815068i	$0.303301\pi$
$73$			119.000i			1.63014i	−0.579365	+	0.815068i	$0.696699\pi$
$74$	−79.6084	+	45.9619i	−1.07579	+	0.621107i
$75$		0			0
$76$	3.00000	−	5.19615i	0.0394737	−	0.0683704i
$77$	38.8909	−	67.3610i	0.505076	−	0.874818i
$78$		0			0
$79$	−49.5000	−	85.7365i	−0.626582	−	1.08527i	−0.988233	−	0.152959i	$-0.951120\pi$
$79$	−49.5000	−	85.7365i	−0.626582	−	1.08527i	0.361650	−	0.932314i	$-0.382213\pi$
$80$	−19.7990	+	2.82843i	−0.247487	+	0.0353553i
$81$		0			0
$82$			110.000i			1.34146i
$83$	−54.4472	−	94.3054i	−0.655991	−	1.13621i	−0.981644	−	0.190720i	$-0.938918\pi$
$83$	−54.4472	−	94.3054i	−0.655991	−	1.13621i	0.325654	−	0.945489i	$-0.394416\pi$
$84$		0			0
$85$	42.1436	−	104.995i	0.495807	−	1.23523i
$86$	−39.1918	−	22.6274i	−0.455719	−	0.263109i
$87$		0			0
$88$	−17.3205	+	10.0000i	−0.196824	+	0.113636i
$89$		−	90.5097i		−	1.01696i	−0.861073	−	0.508481i	$-0.830207\pi$
$89$		−	90.5097i		−	1.01696i	0.861073	−	0.508481i	$-0.169793\pi$
$90$		0			0
$91$	−165.000			−1.81319
$92$	18.3848	+	31.8434i	0.199835	+	0.346124i
$93$		0			0
$94$	40.0000	−	69.2820i	0.425532	−	0.737043i
$95$	−5.58750	+	13.9205i	−0.0588158	+	0.146531i
$96$		0			0
$97$	82.2724	−	47.5000i	0.848169	−	0.489691i	−0.0118635	−	0.999930i	$-0.503776\pi$
$97$	82.2724	−	47.5000i	0.848169	−	0.489691i	0.860033	+	0.510239i	$0.170443\pi$
$98$	−101.823			−1.03901
$99$		0			0
$100$	48.0000	−	14.0000i	0.480000	−	0.140000i
$101$	97.9796	−	56.5685i	0.970095	−	0.560085i	0.0708298	−	0.997488i	$-0.477435\pi$
$101$	97.9796	−	56.5685i	0.970095	−	0.560085i	0.899265	+	0.437404i	$0.144102\pi$
$102$		0			0
$103$	−99.5929	−	57.5000i	−0.966922	−	0.558252i	−0.0686252	−	0.997643i	$-0.521861\pi$
$103$	−99.5929	−	57.5000i	−0.966922	−	0.558252i	−0.898296	+	0.439390i	$0.855195\pi$
$104$	36.7423	+	21.2132i	0.353292	+	0.203973i
$105$		0			0
$106$	−9.00000	−	15.5885i	−0.0849057	−	0.147061i
$107$	173.948			1.62568			0.812842	−	0.582484i	$-0.197919\pi$
$107$	173.948			1.62568			0.812842	+	0.582484i	$0.197919\pi$
$108$		0			0
$109$	8.00000			0.0733945			0.0366972	−	0.999326i	$-0.488316\pi$
$109$	8.00000			0.0733945			0.0366972	+	0.999326i	$0.488316\pi$
$110$	39.3305	−	30.8725i	0.357550	−	0.280659i
$111$		0			0
$112$	38.1051	+	22.0000i	0.340224	+	0.196429i
$113$	74.2462	−	128.598i	0.657046	−	1.13804i	−0.324331	−	0.945944i	$-0.605139\pi$
$113$	74.2462	−	128.598i	0.657046	−	1.13804i	0.981377	−	0.192093i	$-0.0615277\pi$
$114$		0			0
$115$	−56.7583	−	72.3083i	−0.493551	−	0.628768i
$116$			25.4558i			0.219447i
$117$		0			0
$118$		−	112.000i		−	0.949153i
$119$	−215.555	+	124.451i	−1.81139	+	1.04580i
$120$		0			0
$121$	−35.5000	+	61.4878i	−0.293388	+	0.508164i
$122$	−67.1751	+	116.351i	−0.550616	+	0.953695i
$123$		0			0
$124$	8.00000	+	13.8564i	0.0645161	+	0.111745i
$125$	−113.844	+	51.6188i	−0.910754	+	0.412950i
$126$		0			0
$127$		−	104.000i		−	0.818898i	−0.912333	−	0.409449i	$-0.865721\pi$
$127$		−	104.000i		−	0.818898i	0.912333	−	0.409449i	$-0.134279\pi$
$128$	−5.65685	−	9.79796i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−98.4327	−	39.5096i	−0.757174	−	0.303920i
$131$	58.7878	+	33.9411i	0.448761	+	0.259093i	0.707307	−	0.706907i	$-0.249910\pi$
$131$	58.7878	+	33.9411i	0.448761	+	0.259093i	−0.258546	+	0.965999i	$0.583243\pi$
$132$		0			0
$133$	28.5788	−	16.5000i	0.214878	−	0.124060i
$134$		−	26.8701i		−	0.200523i
$135$		0			0
$136$	64.0000			0.470588
$137$	−44.5477	−	77.1589i	−0.325166	−	0.563204i	0.656380	−	0.754430i	$-0.272087\pi$
$137$	−44.5477	−	77.1589i	−0.325166	−	0.563204i	−0.981546	+	0.191227i	$0.938753\pi$
$138$		0			0
$139$	−41.5000	+	71.8801i	−0.298561	+	0.517123i	−0.975807	−	0.218634i	$-0.929840\pi$
$139$	−41.5000	+	71.8801i	−0.298561	+	0.517123i	0.677246	+	0.735757i	$0.263173\pi$
$140$	−102.084	−	40.9750i	−0.729168	−	0.292679i
$141$		0			0
$142$	5.19615	−	3.00000i	0.0365926	−	0.0211268i
$143$	−106.066			−0.741720
$144$		0			0
$145$	−9.00000	−	63.0000i	−0.0620690	−	0.434483i
$146$	145.745	−	84.1457i	0.998251	−	0.576340i
$147$		0			0
$148$	112.583	+	65.0000i	0.760698	+	0.439189i
$149$	68.5857	+	39.5980i	0.460307	+	0.265758i	0.712173	−	0.702004i	$-0.247711\pi$
$149$	68.5857	+	39.5980i	0.460307	+	0.265758i	−0.251866	+	0.967762i	$0.581044\pi$
$150$		0			0
$151$	77.5000	+	134.234i	0.513245	+	0.888966i	0.999882	+	0.0153622i	$0.00489013\pi$
$151$	77.5000	+	134.234i	0.513245	+	0.888966i	−0.486637	+	0.873604i	$0.661777\pi$
$152$	−8.48528			−0.0558242
$153$		0			0
$154$	−110.000			−0.714286
$155$	−24.6980	−	31.4644i	−0.159342	−	0.202996i
$156$		0			0
$157$	8.66025	+	5.00000i	0.0551609	+	0.0318471i	0.527327	−	0.849663i	$-0.323194\pi$
$157$	8.66025	+	5.00000i	0.0551609	+	0.0318471i	−0.472166	+	0.881510i	$0.656528\pi$
$158$	−70.0036	+	121.250i	−0.443061	+	0.767403i
$159$		0			0
$160$	17.4641	+	22.2487i	0.109151	+	0.139054i
$161$			202.233i			1.25610i
$162$		0			0
$163$		−	53.0000i		−	0.325153i	−0.986696	−	0.162577i	$-0.948020\pi$
$163$		−	53.0000i		−	0.325153i	0.986696	−	0.162577i	$-0.0519805\pi$
$164$	134.722	−	77.7817i	0.821475	−	0.474279i
$165$		0			0
$166$	−77.0000	+	133.368i	−0.463855	+	0.803421i
$167$	67.8823	−	117.576i	0.406481	−	0.704045i	−0.588012	−	0.808852i	$-0.700089\pi$
$167$	67.8823	−	117.576i	0.406481	−	0.704045i	0.994493	+	0.104807i	$0.0334226\pi$
$168$		0			0
$169$	28.0000	+	48.4974i	0.165680	+	0.286967i
$170$	−158.392	+	22.6274i	−0.931717	+	0.133102i
$171$		0			0
$172$			64.0000i			0.372093i
$173$	−62.2254	−	107.778i	−0.359684	−	0.622992i	0.628224	−	0.778033i	$-0.283782\pi$
$173$	−62.2254	−	107.778i	−0.359684	−	0.622992i	−0.987908	+	0.155041i	$0.950449\pi$
$174$		0			0
$175$	267.131	+	65.3160i	1.52646	+	0.373235i
$176$	24.4949	+	14.1421i	0.139176	+	0.0803530i
$177$		0			0
$178$	−110.851	+	64.0000i	−0.622760	+	0.359551i
$179$		−	287.085i		−	1.60383i	−0.597439	−	0.801914i	$-0.703815\pi$
$179$		−	287.085i		−	1.60383i	0.597439	−	0.801914i	$-0.296185\pi$
$180$		0			0
$181$	113.000			0.624309			0.312155	−	0.950031i	$-0.398949\pi$
$181$	113.000			0.624309			0.312155	+	0.950031i	$0.398949\pi$
$182$	116.673	+	202.083i	0.641058	+	1.11035i
$183$		0			0
$184$	26.0000	−	45.0333i	0.141304	−	0.244746i
$185$	−301.610	−	121.063i	−1.63033	−	0.654392i
$186$		0			0
$187$	−138.564	+	80.0000i	−0.740984	+	0.427807i
$188$	−113.137			−0.601793
$189$		0			0
$190$	21.0000	−	3.00000i	0.110526	−	0.0157895i
$191$	−117.576	+	67.8823i	−0.615579	+	0.355404i	−0.775146	−	0.631783i	$-0.782324\pi$
$191$	−117.576	+	67.8823i	−0.615579	+	0.355404i	0.159567	+	0.987187i	$0.448990\pi$
$192$		0			0
$193$	63.2199	+	36.5000i	0.327564	+	0.189119i	0.654759	−	0.755838i	$-0.272770\pi$
$193$	63.2199	+	36.5000i	0.327564	+	0.189119i	−0.327195	+	0.944957i	$0.606103\pi$
$194$	−116.351	−	67.1751i	−0.599746	−	0.346264i
$195$		0			0
$196$	72.0000	+	124.708i	0.367347	+	0.636264i
$197$	214.960			1.09117			0.545585	−	0.838056i	$-0.316308\pi$
$197$	214.960			1.09117			0.545585	+	0.838056i	$0.316308\pi$
$198$		0			0
$199$	123.000			0.618090			0.309045	−	0.951047i	$-0.399991\pi$
$199$	123.000			0.618090			0.309045	+	0.951047i	$0.399991\pi$
$200$	−51.0876	−	48.8883i	−0.255438	−	0.244441i
$201$		0			0
$202$	−138.564	−	80.0000i	−0.685961	−	0.396040i
$203$	−70.0036	+	121.250i	−0.344845	+	0.597289i
$204$		0			0
$205$	−305.920	+	240.131i	−1.49229	+	1.17137i
$206$			162.635i			0.789488i
$207$		0			0
$208$		−	60.0000i		−	0.288462i
$209$	18.3712	−	10.6066i	0.0879003	−	0.0507493i
$210$		0			0
$211$	−130.500	+	226.033i	−0.618483	+	1.07124i	0.371279	+	0.928521i	$0.378919\pi$
$211$	−130.500	+	226.033i	−0.618483	+	1.07124i	−0.989763	+	0.142723i	$0.954414\pi$
$212$	−12.7279	+	22.0454i	−0.0600374	+	0.103988i
$213$		0			0
$214$	−123.000	−	213.042i	−0.574766	−	0.995525i
$215$	−22.6274	−	158.392i	−0.105244	−	0.736707i
$216$		0			0
$217$			88.0000i			0.405530i
$218$	−5.65685	−	9.79796i	−0.0259489	−	0.0449448i
$219$		0			0
$220$	−65.6218	−	26.3397i	−0.298281	−	0.119726i
$221$	293.939	+	169.706i	1.33004	+	0.767899i
$222$		0			0
$223$	48.4974	−	28.0000i	0.217477	−	0.125561i	−0.387304	−	0.921952i	$-0.626594\pi$
$223$	48.4974	−	28.0000i	0.217477	−	0.125561i	0.604782	+	0.796391i	$0.293260\pi$
$224$		−	62.2254i		−	0.277792i
$225$		0			0
$226$	−210.000			−0.929204
$227$	211.425	+	366.199i	0.931387	+	1.61321i	0.780953	+	0.624590i	$0.214734\pi$
$227$	211.425	+	366.199i	0.931387	+	1.61321i	0.150435	+	0.988620i	$0.451933\pi$
$228$		0			0
$229$	−20.0000	+	34.6410i	−0.0873362	+	0.151271i	−0.906384	−	0.422454i	$-0.861169\pi$
$229$	−20.0000	+	34.6410i	−0.0873362	+	0.151271i	0.819048	+	0.573725i	$0.194502\pi$
$230$	−48.4250	+	120.644i	−0.210544	+	0.524540i
$231$		0			0
$232$	31.1769	−	18.0000i	0.134383	−	0.0775862i
$233$	90.5097			0.388454			0.194227	−	0.980957i	$-0.437780\pi$
$233$	90.5097			0.388454			0.194227	+	0.980957i	$0.437780\pi$
$234$		0			0
$235$	280.000	−	40.0000i	1.19149	−	0.170213i
$236$	−137.171	+	79.1960i	−0.581235	+	0.335576i
$237$		0			0
$238$	304.841	+	176.000i	1.28084	+	0.739496i
$239$	199.633	+	115.258i	0.835286	+	0.482253i	0.855659	−	0.517540i	$-0.173152\pi$
$239$	199.633	+	115.258i	0.835286	+	0.482253i	−0.0203729	+	0.999792i	$0.506485\pi$
$240$		0			0
$241$	104.500	+	180.999i	0.433610	+	0.751034i	0.997181	−	0.0750331i	$-0.0239062\pi$
$241$	104.500	+	180.999i	0.433610	+	0.751034i	−0.563571	+	0.826068i	$0.690573\pi$
$242$	100.409			0.414914
$243$		0			0
$244$	190.000			0.778689
$245$	−222.282	−	283.180i	−0.907272	−	1.15584i
$246$		0			0
$247$	−38.9711	−	22.5000i	−0.157778	−	0.0910931i
$248$	11.3137	−	19.5959i	0.0456198	−	0.0790158i
$249$		0			0
$250$	143.720	+	102.930i	0.574879	+	0.411720i
$251$		−	207.889i		−	0.828245i	−0.910221	−	0.414122i	$-0.864089\pi$
$251$		−	207.889i		−	0.828245i	0.910221	−	0.414122i	$-0.135911\pi$
$252$		0			0
$253$			130.000i			0.513834i
$254$	−127.373	+	73.5391i	−0.501470	+	0.289524i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	220.617	−	382.120i	0.858433	−	1.48685i	−0.0149899	−	0.999888i	$-0.504772\pi$
$257$	220.617	−	382.120i	0.858433	−	1.48685i	0.873423	−	0.486962i	$-0.161895\pi$
$258$		0			0
$259$	357.500	+	619.208i	1.38031	+	2.39077i
$260$	21.2132	+	148.492i	0.0815892	+	0.571125i
$261$		0			0
$262$		−	96.0000i		−	0.366412i
$263$	96.1665	+	166.565i	0.365652	+	0.633328i	0.988881	−	0.148712i	$-0.0475126\pi$
$263$	96.1665	+	166.565i	0.365652	+	0.633328i	−0.623228	+	0.782040i	$0.714179\pi$
$264$		0			0
$265$	23.7058	−	59.0596i	0.0894557	−	0.222866i
$266$	−40.4166	−	23.3345i	−0.151942	−	0.0877238i
$267$		0			0
$268$	−32.9090	+	19.0000i	−0.122795	+	0.0708955i
$269$			407.294i			1.51410i	0.653356	+	0.757051i	$0.273361\pi$
$269$			407.294i			1.51410i	−0.653356	+	0.757051i	$0.726639\pi$
$270$		0			0
$271$	−101.000			−0.372694			−0.186347	−	0.982484i	$-0.559665\pi$
$271$	−101.000			−0.372694			−0.186347	+	0.982484i	$0.559665\pi$
$272$	−45.2548	−	78.3837i	−0.166378	−	0.288175i
$273$		0			0
$274$	−63.0000	+	109.119i	−0.229927	+	0.398245i
$275$	171.718	+	41.9867i	0.624430	+	0.152679i
$276$		0			0
$277$	159.349	−	92.0000i	0.575266	−	0.332130i	−0.183984	−	0.982929i	$-0.558899\pi$
$277$	159.349	−	92.0000i	0.575266	−	0.332130i	0.759250	+	0.650799i	$0.225566\pi$
$278$	117.380			0.422229
$279$		0			0
$280$	22.0000	+	154.000i	0.0785714	+	0.550000i
$281$	176.363	−	101.823i	0.627627	−	0.362361i	−0.152205	−	0.988349i	$-0.548638\pi$
$281$	176.363	−	101.823i	0.627627	−	0.362361i	0.779833	+	0.625988i	$0.215304\pi$
$282$		0			0
$283$	−471.118	−	272.000i	−1.66473	−	0.961131i	−0.970410	−	0.241461i	$-0.922373\pi$
$283$	−471.118	−	272.000i	−1.66473	−	0.961131i	−0.694317	−	0.719669i	$-0.744293\pi$
$284$	−7.34847	−	4.24264i	−0.0258749	−	0.0149389i
$285$		0			0
$286$	75.0000	+	129.904i	0.262238	+	0.454209i
$287$	855.599			2.98118
$288$		0			0
$289$	223.000			0.771626
$290$	−70.7950	+	55.5704i	−0.244121	+	0.191622i
$291$		0			0
$292$	−206.114	−	119.000i	−0.705870	−	0.407534i
$293$	40.3051	−	69.8105i	0.137560	−	0.238261i	−0.789012	−	0.614377i	$-0.789407\pi$
$293$	40.3051	−	69.8105i	0.137560	−	0.238261i	0.926572	+	0.376116i	$0.122741\pi$
$294$		0			0
$295$	311.482	−	244.497i	1.05587	−	0.828805i
$296$		−	183.848i		−	0.621107i
$297$		0			0
$298$		−	112.000i		−	0.375839i
$299$	238.825	−	137.886i	0.798747	−	0.461157i
$300$		0			0
$301$	−176.000	+	304.841i	−0.584718	+	1.01276i
$302$	109.602	−	189.835i	0.362919	−	0.628594i
$303$		0			0
$304$	6.00000	+	10.3923i	0.0197368	+	0.0341852i
$305$	−470.226	+	67.1751i	−1.54172	+	0.220246i
$306$		0			0
$307$			282.000i			0.918567i	0.888290	+	0.459283i	$0.151894\pi$
$307$			282.000i			0.918567i	−0.888290	+	0.459283i	$0.848106\pi$
$308$	77.7817	+	134.722i	0.252538	+	0.437409i
$309$		0			0
$310$	−21.0718	+	52.4974i	−0.0679735	+	0.169347i
$311$	−264.545	−	152.735i	−0.850627	−	0.491110i	0.0102356	−	0.999948i	$-0.496742\pi$
$311$	−264.545	−	152.735i	−0.850627	−	0.491110i	−0.860862	+	0.508838i	$0.830075\pi$
$312$		0			0
$313$	165.411	−	95.5000i	0.528469	−	0.305112i	−0.211924	−	0.977286i	$-0.567973\pi$
$313$	165.411	−	95.5000i	0.528469	−	0.305112i	0.740393	+	0.672174i	$0.234639\pi$
$314$		−	14.1421i		−	0.0450386i
$315$		0			0
$316$	198.000			0.626582
$317$	124.451	+	215.555i	0.392589	+	0.679985i	0.992790	−	0.119865i	$-0.0382461\pi$
$317$	124.451	+	215.555i	0.392589	+	0.679985i	−0.600201	+	0.799849i	$0.704913\pi$
$318$		0			0
$319$	−45.0000	+	77.9423i	−0.141066	+	0.244333i
$320$	14.9000	−	37.1213i	0.0465625	−	0.116004i
$321$		0			0
$322$	247.683	−	143.000i	0.769203	−	0.444099i
$323$	−67.8823			−0.210162
$324$		0			0
$325$	−105.000	−	360.000i	−0.323077	−	1.10769i
$326$	−64.9115	+	37.4767i	−0.199115	+	0.114959i
$327$		0			0
$328$	−190.526	−	110.000i	−0.580871	−	0.335366i
$329$	−538.888	−	311.127i	−1.63796	−	0.945675i
$330$		0			0
$331$	−78.5000	−	135.966i	−0.237160	−	0.410773i	0.722738	−	0.691122i	$-0.242883\pi$
$331$	−78.5000	−	135.966i	−0.237160	−	0.410773i	−0.959898	+	0.280349i	$0.909550\pi$
$332$	217.789			0.655991
$333$		0			0
$334$	−192.000			−0.574850
$335$	74.7280	−	58.6577i	0.223069	−	0.175098i
$336$		0			0
$337$	−167.143	−	96.5000i	−0.495973	−	0.286350i	0.231076	−	0.972936i	$-0.425775\pi$
$337$	−167.143	−	96.5000i	−0.495973	−	0.286350i	−0.727049	+	0.686586i	$0.759109\pi$
$338$	39.5980	−	68.5857i	0.117154	−	0.202916i
$339$		0			0
$340$	139.713	+	177.990i	0.410920	+	0.523499i
$341$			56.5685i			0.165890i
$342$		0			0
$343$			253.000i			0.737609i
$344$	78.3837	−	45.2548i	0.227860	−	0.131555i
$345$		0			0
$346$	−88.0000	+	152.420i	−0.254335	+	0.440522i
$347$	−167.584	+	290.265i	−0.482952	+	0.836497i	−0.999808	−	0.0195748i	$-0.993769\pi$
$347$	−167.584	+	290.265i	−0.482952	+	0.836497i	0.516857	+	0.856072i	$0.327102\pi$
$348$		0			0
$349$	171.500	+	297.047i	0.491404	+	0.851137i	0.999951	−	0.00989751i	$-0.00315053\pi$
$349$	171.500	+	297.047i	0.491404	+	0.851137i	−0.508547	+	0.861034i	$0.669817\pi$
$350$	−108.894	−	373.352i	−0.311127	−	1.06672i
$351$		0			0
$352$		−	40.0000i		−	0.113636i
$353$	−113.137	−	195.959i	−0.320502	−	0.555125i	0.660090	−	0.751187i	$-0.270518\pi$
$353$	−113.137	−	195.959i	−0.320502	−	0.555125i	−0.980592	+	0.196061i	$0.937185\pi$
$354$		0			0
$355$	19.6865	+	7.90192i	0.0554550	+	0.0222589i
$356$	156.767	+	90.5097i	0.440358	+	0.254241i
$357$		0			0
$358$	−351.606	+	203.000i	−0.982141	+	0.567039i
$359$			411.536i			1.14634i	0.819436	+	0.573170i	$0.194287\pi$
$359$			411.536i			1.14634i	−0.819436	+	0.573170i	$0.805713\pi$
$360$		0			0
$361$	−352.000			−0.975069
$362$	−79.9031	−	138.396i	−0.220727	−	0.382310i
$363$		0			0
$364$	165.000	−	285.788i	0.453297	−	0.785133i
$365$	552.179	+	221.638i	1.51282	+	0.607226i
$366$		0			0
$367$	−399.238	+	230.500i	−1.08784	+	0.628065i	−0.933001	−	0.359874i	$-0.882820\pi$
$367$	−399.238	+	230.500i	−1.08784	+	0.628065i	−0.154840	+	0.987940i	$0.549486\pi$
$368$	−73.5391			−0.199835
$369$		0			0
$370$	65.0000	+	455.000i	0.175676	+	1.22973i
$371$	−121.250	+	70.0036i	−0.326819	+	0.188689i
$372$		0			0
$373$	137.698	+	79.5000i	0.369164	+	0.213137i	0.673093	−	0.739558i	$-0.264965\pi$
$373$	137.698	+	79.5000i	0.369164	+	0.213137i	−0.303929	+	0.952695i	$0.598299\pi$
$374$	195.959	+	113.137i	0.523955	+	0.302506i
$375$		0			0
$376$	80.0000	+	138.564i	0.212766	+	0.368521i
$377$	190.919			0.506416
$378$		0			0
$379$	37.0000			0.0976253			0.0488127	−	0.998808i	$-0.484456\pi$
$379$	37.0000			0.0976253			0.0488127	+	0.998808i	$0.484456\pi$
$380$	−18.5235	−	23.5983i	−0.0487460	−	0.0621008i
$381$		0			0
$382$	166.277	+	96.0000i	0.435280	+	0.251309i
$383$	−231.931	+	401.716i	−0.605564	+	1.04887i	0.386398	+	0.922332i	$0.373719\pi$
$383$	−231.931	+	401.716i	−0.605564	+	1.04887i	−0.991962	+	0.126536i	$0.959614\pi$
$384$		0			0
$385$	−240.131	−	305.920i	−0.623718	−	0.794597i
$386$		−	103.238i		−	0.267455i
$387$		0			0
$388$			190.000i			0.489691i
$389$	39.1918	−	22.6274i	0.100750	−	0.0581682i	−0.448778	−	0.893643i	$-0.648141\pi$
$389$	39.1918	−	22.6274i	0.100750	−	0.0581682i	0.549529	+	0.835475i	$0.314807\pi$
$390$		0			0
$391$	208.000	−	360.267i	0.531969	−	0.921398i
$392$	101.823	−	176.363i	0.259754	−	0.449906i
$393$		0			0
$394$	−152.000	−	263.272i	−0.385787	−	0.668202i
$395$	−490.025	+	70.0036i	−1.24057	+	0.177224i
$396$		0			0
$397$			40.0000i			0.100756i	0.998730	+	0.0503778i	$0.0160426\pi$
$397$			40.0000i			0.100756i	−0.998730	+	0.0503778i	$0.983957\pi$
$398$	−86.9741	−	150.644i	−0.218528	−	0.378502i
$399$		0			0
$400$	−23.7513	+	97.1384i	−0.0593782	+	0.242846i
$401$	−549.910	−	317.491i	−1.37135	−	0.791748i	−0.380250	−	0.924884i	$-0.624162\pi$
$401$	−549.910	−	317.491i	−1.37135	−	0.791748i	−0.991098	+	0.133136i	$0.957495\pi$
$402$		0			0
$403$	103.923	−	60.0000i	0.257874	−	0.148883i
$404$			226.274i			0.560085i
$405$		0			0
$406$	198.000			0.487685
$407$	229.810	+	398.042i	0.564643	+	0.977990i
$408$		0			0
$409$	−384.500	+	665.974i	−0.940098	+	1.62830i	−0.174817	+	0.984601i	$0.555933\pi$
$409$	−384.500	+	665.974i	−0.940098	+	1.62830i	−0.765281	+	0.643696i	$0.777400\pi$
$410$	510.418	+	204.875i	1.24492	+	0.499695i
$411$		0			0
$412$	199.186	−	115.000i	0.483461	−	0.279126i
$413$	−871.156			−2.10934
$414$		0			0
$415$	−539.000	+	77.0000i	−1.29880	+	0.185542i
$416$	−73.4847	+	42.4264i	−0.176646	+	0.101987i
$417$		0			0
$418$	−25.9808	−	15.0000i	−0.0621549	−	0.0358852i
$419$	−421.312	−	243.245i	−1.00552	−	0.580536i	−0.0956421	−	0.995416i	$-0.530490\pi$
$419$	−421.312	−	243.245i	−1.00552	−	0.580536i	−0.909876	+	0.414879i	$0.863824\pi$
$420$		0			0
$421$	83.5000	+	144.626i	0.198337	+	0.343530i	0.947989	−	0.318302i	$-0.103113\pi$
$421$	83.5000	+	144.626i	0.198337	+	0.343530i	−0.749652	+	0.661832i	$0.769779\pi$
$422$	369.110			0.874668
$423$		0			0
$424$	36.0000			0.0849057
$425$	−408.700	−	391.106i	−0.961648	−	0.920250i
$426$		0			0
$427$	904.997	+	522.500i	2.11943	+	1.22365i
$428$	−173.948	+	301.287i	−0.406421	+	0.703942i
$429$		0			0
$430$	−177.990	+	139.713i	−0.413930	+	0.324914i
$431$		−	422.850i		−	0.981090i	−0.871416	−	0.490545i	$-0.836798\pi$
$431$		−	422.850i		−	0.981090i	0.871416	−	0.490545i	$-0.163202\pi$
$432$		0			0
$433$			32.0000i			0.0739030i	0.999317	+	0.0369515i	$0.0117647\pi$
$433$			32.0000i			0.0739030i	−0.999317	+	0.0369515i	$0.988235\pi$
$434$	107.778	−	62.2254i	0.248335	−	0.143376i
$435$		0			0
$436$	−8.00000	+	13.8564i	−0.0183486	+	0.0317807i
$437$	−27.5772	+	47.7650i	−0.0631056	+	0.109302i
$438$		0			0
$439$	−324.000	−	561.184i	−0.738041	−	1.27832i	−0.953376	−	0.301784i	$-0.902418\pi$
$439$	−324.000	−	561.184i	−0.738041	−	1.27832i	0.215335	−	0.976540i	$-0.430916\pi$
$440$	14.1421	+	98.9949i	0.0321412	+	0.224989i
$441$		0			0
$442$		−	480.000i		−	1.08597i
$443$	220.617	+	382.120i	0.498007	+	0.862574i	0.999997	−	0.00229923i	$-0.000731869\pi$
$443$	220.617	+	382.120i	0.498007	+	0.862574i	−0.501990	+	0.864873i	$0.667399\pi$
$444$		0			0
$445$	−419.979	−	168.574i	−0.943774	−	0.378819i
$446$	−68.5857	−	39.5980i	−0.153780	−	0.0887847i
$447$		0			0
$448$	−76.2102	+	44.0000i	−0.170112	+	0.0982143i
$449$			101.823i			0.226778i	0.993551	+	0.113389i	$0.0361707\pi$
$449$			101.823i			0.226778i	−0.993551	+	0.113389i	$0.963829\pi$
$450$		0			0
$451$	550.000			1.21951
$452$	148.492	+	257.196i	0.328523	+	0.569019i
$453$		0			0
$454$	299.000	−	517.883i	0.658590	−	1.14071i
$455$	−307.313	+	765.626i	−0.675413	+	1.68270i
$456$		0			0
$457$	−318.697	+	184.000i	−0.697368	+	0.402626i	−0.806367	−	0.591416i	$-0.798569\pi$
$457$	−318.697	+	184.000i	−0.697368	+	0.402626i	0.108998	+	0.994042i	$0.465236\pi$
$458$	56.5685			0.123512
$459$		0			0
$460$	182.000	−	26.0000i	0.395652	−	0.0565217i
$461$	−382.120	+	220.617i	−0.828895	+	0.478563i	−0.853474	−	0.521135i	$-0.825509\pi$
$461$	−382.120	+	220.617i	−0.828895	+	0.478563i	0.0245795	+	0.999698i	$0.492175\pi$
$462$		0			0
$463$	−59.7558	−	34.5000i	−0.129062	−	0.0745140i	0.434079	−	0.900875i	$-0.357074\pi$
$463$	−59.7558	−	34.5000i	−0.129062	−	0.0745140i	−0.563141	+	0.826361i	$0.690407\pi$
$464$	−44.0908	−	25.4558i	−0.0950233	−	0.0548617i
$465$		0			0
$466$	−64.0000	−	110.851i	−0.137339	−	0.237878i
$467$	−475.176			−1.01751			−0.508753	−	0.860912i	$-0.669894\pi$
$467$	−475.176			−1.01751			−0.508753	+	0.860912i	$0.669894\pi$
$468$		0			0
$469$	−209.000			−0.445629
$470$	−246.980	−	314.644i	−0.525489	−	0.669456i
$471$		0			0
$472$	193.990	+	112.000i	0.410995	+	0.237288i
$473$	−113.137	+	195.959i	−0.239190	+	0.414290i
$474$		0			0
$475$	54.1865	+	51.8538i	0.114077	+	0.109166i
$476$		−	497.803i		−	1.04580i
$477$		0			0
$478$		−	326.000i		−	0.682008i
$479$	476.426	−	275.065i	0.994626	−	0.574247i	0.0879720	−	0.996123i	$-0.471961\pi$
$479$	476.426	−	275.065i	0.994626	−	0.574247i	0.906654	+	0.421875i	$0.138628\pi$
$480$		0			0
$481$	487.500	−	844.375i	1.01351	−	1.75546i
$482$	147.785	−	255.972i	0.306609	−	0.531062i
$483$		0			0
$484$	−71.0000	−	122.976i	−0.146694	−	0.254082i
$485$	−67.1751	−	470.226i	−0.138505	−	0.969538i
$486$		0			0
$487$		−	507.000i		−	1.04107i	−0.853841	−	0.520534i	$-0.825733\pi$
$487$		−	507.000i		−	1.04107i	0.853841	−	0.520534i	$-0.174267\pi$
$488$	−134.350	−	232.702i	−0.275308	−	0.476847i
$489$		0			0
$490$	−189.646	+	472.477i	−0.387033	+	0.964238i
$491$	25.7196	+	14.8492i	0.0523822	+	0.0302429i	0.525962	−	0.850508i	$-0.323705\pi$
$491$	25.7196	+	14.8492i	0.0523822	+	0.0302429i	−0.473580	+	0.880751i	$0.657039\pi$
$492$		0			0
$493$	249.415	−	144.000i	0.505913	−	0.292089i
$494$			63.6396i			0.128825i
$495$		0			0
$496$	−32.0000			−0.0645161
$497$	−23.3345	−	40.4166i	−0.0469508	−	0.0813211i
$498$		0			0
$499$	237.000	−	410.496i	0.474950	−	0.822637i	−0.524639	−	0.851325i	$-0.675800\pi$
$499$	237.000	−	410.496i	0.474950	−	0.822637i	0.999588	+	0.0286877i	$0.00913284\pi$
$500$	24.4378	−	248.803i	0.0488756	−	0.497605i
$501$		0			0
$502$	−254.611	+	147.000i	−0.507194	+	0.292829i
$503$	165.463			0.328952			0.164476	−	0.986381i	$-0.447407\pi$
$503$	165.463			0.328952			0.164476	+	0.986381i	$0.447407\pi$
$504$		0			0
$505$	−80.0000	−	560.000i	−0.158416	−	1.10891i
$506$	159.217	−	91.9239i	0.314658	−	0.181668i
$507$		0			0
$508$	180.133	+	104.000i	0.354593	+	0.204724i
$509$	481.325	+	277.893i	0.945628	+	0.545959i	0.891720	−	0.452587i	$-0.149499\pi$
$509$	481.325	+	277.893i	0.945628	+	0.545959i	0.0539080	+	0.998546i	$0.482832\pi$
$510$		0			0
$511$	−654.500	−	1133.63i	−1.28082	−	2.21845i
$512$	22.6274			0.0441942
$513$		0			0
$514$	−624.000			−1.21401
$515$	−452.301	+	355.033i	−0.878255	+	0.689385i
$516$		0			0
$517$	−346.410	−	200.000i	−0.670039	−	0.386847i
$518$	505.581	−	875.693i	0.976026	−	1.69053i
$519$		0			0
$520$	166.865	−	130.981i	0.320895	−	0.251886i
$521$		−	281.428i		−	0.540170i	−0.962837	−	0.270085i	$-0.912948\pi$
$521$		−	281.428i		−	0.540170i	0.962837	−	0.270085i	$-0.0870518\pi$
$522$		0			0
$523$		−	851.000i		−	1.62715i	−0.581459	−	0.813576i	$-0.697518\pi$
$523$		−	851.000i		−	1.62715i	0.581459	−	0.813576i	$-0.302482\pi$
$524$	−117.576	+	67.8823i	−0.224381	+	0.129546i
$525$		0			0
$526$	136.000	−	235.559i	0.258555	−	0.447831i
$527$	90.5097	−	156.767i	0.171745	−	0.297471i
$528$		0			0
$529$	95.5000	+	165.411i	0.180529	+	0.312686i
$530$	−89.0955	+	12.7279i	−0.168105	+	0.0240149i
$531$		0			0
$532$			66.0000i			0.124060i
$533$	−583.363	−	1010.41i	−1.09449	−	1.89571i
$534$		0			0
$535$	323.979	−	807.148i	0.605568	−	1.50869i
$536$	46.5403	+	26.8701i	0.0868289	+	0.0501307i
$537$		0			0
$538$	498.831	−	288.000i	0.927194	−	0.535316i
$539$			509.117i			0.944558i
$540$		0			0
$541$	73.0000			0.134935			0.0674677	−	0.997721i	$-0.478508\pi$
$541$	73.0000			0.134935			0.0674677	+	0.997721i	$0.478508\pi$
$542$	71.4178	+	123.699i	0.131767	+	0.228227i
$543$		0			0
$544$	−64.0000	+	110.851i	−0.117647	+	0.203771i
$545$	14.9000	−	37.1213i	0.0273395	−	0.0681124i
$546$		0			0
$547$	−217.372	+	125.500i	−0.397390	+	0.229433i	−0.685357	−	0.728207i	$-0.740354\pi$
$547$	−217.372	+	125.500i	−0.397390	+	0.229433i	0.287967	+	0.957640i	$0.407021\pi$
$548$	178.191			0.325166
$549$		0			0
$550$	−70.0000	−	240.000i	−0.127273	−	0.436364i
$551$	−33.0681	+	19.0919i	−0.0600147	+	0.0346495i
$552$		0			0
$553$	943.102	+	544.500i	1.70543	+	0.984629i
$554$	−225.353	−	130.108i	−0.406774	−	0.234851i
$555$		0			0
$556$	−83.0000	−	143.760i	−0.149281	−	0.258562i
$557$	441.235			0.792163			0.396081	−	0.918215i	$-0.370370\pi$
$557$	441.235			0.792163			0.396081	+	0.918215i	$0.370370\pi$
$558$		0			0
$559$	480.000			0.858676
$560$	173.054	−	135.839i	0.309026	−	0.242569i
$561$		0			0
$562$	−249.415	−	144.000i	−0.443799	−	0.256228i
$563$	−164.049	+	284.141i	−0.291383	+	0.504691i	−0.974137	−	0.225958i	$-0.927449\pi$
$563$	−164.049	+	284.141i	−0.291383	+	0.504691i	0.682754	+	0.730649i	$0.260782\pi$
$564$		0			0
$565$	−458.433	−	584.029i	−0.811385	−	1.03368i
$566$			769.332i			1.35924i
$567$		0			0
$568$			12.0000i			0.0211268i
$569$	862.220	−	497.803i	1.51533	−	0.874874i	0.515487	−	0.856897i	$-0.327611\pi$
$569$	862.220	−	497.803i	1.51533	−	0.874874i	0.999838	−	0.0179766i	$-0.00572244\pi$
$570$		0			0
$571$	17.5000	−	30.3109i	0.0306480	−	0.0530839i	−0.850295	−	0.526307i	$-0.823576\pi$
$571$	17.5000	−	30.3109i	0.0306480	−	0.0530839i	0.880943	+	0.473223i	$0.156910\pi$
$572$	106.066	−	183.712i	0.185430	−	0.321174i
$573$		0			0
$574$	−605.000	−	1047.89i	−1.05401	−	1.82559i
$575$	−441.235	+	128.693i	−0.767365	+	0.223815i
$576$		0			0
$577$			337.000i			0.584055i	0.956410	+	0.292028i	$0.0943300\pi$
$577$			337.000i			0.584055i	−0.956410	+	0.292028i	$0.905670\pi$
$578$	−157.685	−	273.118i	−0.272811	−	0.472523i
$579$		0			0
$580$	118.119	+	47.4115i	0.203654	+	0.0817440i
$581$	1037.36	+	598.919i	1.78547	+	1.03084i
$582$		0			0
$583$	−77.9423	+	45.0000i	−0.133692	+	0.0771870i
$584$			336.583i			0.576340i
$585$		0			0
$586$	−114.000			−0.194539
$587$	235.467	+	407.840i	0.401136	+	0.694787i	0.993863	−	0.110616i	$-0.0352823\pi$
$587$	235.467	+	407.840i	0.401136	+	0.694787i	−0.592728	+	0.805403i	$0.701949\pi$
$588$		0			0
$589$	−12.0000	+	20.7846i	−0.0203735	+	0.0352880i
$590$	−519.698	−	208.600i	−0.880844	−	0.353560i
$591$		0			0
$592$	−225.167	+	130.000i	−0.380349	+	0.219595i
$593$	−666.095			−1.12326			−0.561631	−	0.827388i	$-0.689826\pi$
$593$	−666.095			−1.12326			−0.561631	+	0.827388i	$0.689826\pi$
$594$		0			0
$595$	176.000	+	1232.00i	0.295798	+	2.07059i
$596$	−137.171	+	79.1960i	−0.230153	+	0.132879i
$597$		0			0
$598$	−337.750	−	195.000i	−0.564799	−	0.326087i
$599$	−591.552	−	341.533i	−0.987566	−	0.570171i	−0.0830198	−	0.996548i	$-0.526456\pi$
$599$	−591.552	−	341.533i	−0.987566	−	0.570171i	−0.904546	+	0.426377i	$0.859790\pi$
$600$		0			0
$601$	−304.000	−	526.543i	−0.505824	−	0.876112i	−0.999977	−	0.00673765i	$-0.997855\pi$
$601$	−304.000	−	526.543i	−0.505824	−	0.876112i	0.494154	−	0.869375i	$-0.335478\pi$
$602$	497.803			0.826916
$603$		0			0
$604$	−310.000			−0.513245
$605$	219.194	+	279.247i	0.362305	+	0.461565i
$606$		0			0
$607$	364.597	+	210.500i	0.600654	+	0.346787i	0.769299	−	0.638889i	$-0.220606\pi$
$607$	364.597	+	210.500i	0.600654	+	0.346787i	−0.168645	+	0.985677i	$0.553939\pi$
$608$	8.48528	−	14.6969i	0.0139561	−	0.0241726i
$609$		0			0
$610$	414.772	+	528.407i	0.679955	+	0.866241i
$611$			848.528i			1.38875i
$612$		0			0
$613$			761.000i			1.24144i	0.784034	+	0.620718i	$0.213159\pi$
$613$			761.000i			1.24144i	−0.784034	+	0.620718i	$0.786841\pi$
$614$	345.378	−	199.404i	0.562505	−	0.324762i
$615$		0			0
$616$	110.000	−	190.526i	0.178571	−	0.309295i
$617$	50.2046	−	86.9569i	0.0813689	−	0.140935i	−0.822469	−	0.568810i	$-0.807404\pi$
$617$	50.2046	−	86.9569i	0.0813689	−	0.140935i	0.903838	+	0.427875i	$0.140737\pi$
$618$		0			0
$619$	470.500	+	814.930i	0.760097	+	1.31653i	0.942800	+	0.333358i	$0.108182\pi$
$619$	470.500	+	814.930i	0.760097	+	1.31653i	−0.182703	+	0.983168i	$0.558485\pi$
$620$	79.1960	−	11.3137i	0.127735	−	0.0182479i
$621$		0			0
$622$			432.000i			0.694534i
$623$	497.803	+	862.220i	0.799042	+	1.38398i
$624$		0			0
$625$	27.4845	+	624.395i	0.0439753	+	0.999033i
$626$	−233.926	−	135.057i	−0.373684	−	0.215747i
$627$		0			0
$628$	−17.3205	+	10.0000i	−0.0275804	+	0.0159236i
$629$		−	1470.78i		−	2.33829i
$630$		0			0
$631$	−805.000			−1.27575			−0.637876	−	0.770139i	$-0.720187\pi$
$631$	−805.000			−1.27575			−0.637876	+	0.770139i	$0.720187\pi$
$632$	−140.007	−	242.499i	−0.221530	−	0.383702i
$633$		0			0
$634$	176.000	−	304.841i	0.277603	−	0.480822i
$635$	−482.577	−	193.700i	−0.759963	−	0.305040i
$636$		0			0
$637$	935.307	−	540.000i	1.46830	−	0.847724i
$638$	127.279			0.199497
$639$		0			0
$640$	−56.0000	+	8.00000i	−0.0875000	+	0.0125000i
$641$	−68.5857	+	39.5980i	−0.106998	+	0.0617753i	−0.552544	−	0.833484i	$-0.686343\pi$
$641$	−68.5857	+	39.5980i	−0.106998	+	0.0617753i	0.445546	+	0.895259i	$0.353010\pi$
$642$		0			0
$643$	−956.092	−	552.000i	−1.48692	−	0.858476i	−0.487035	−	0.873382i	$-0.661922\pi$
$643$	−956.092	−	552.000i	−1.48692	−	0.858476i	−0.999889	+	0.0149066i	$0.995255\pi$
$644$	−350.277	−	202.233i	−0.543908	−	0.314026i
$645$		0			0
$646$	48.0000	+	83.1384i	0.0743034	+	0.128697i
$647$	750.947			1.16066			0.580330	−	0.814381i	$-0.302923\pi$
$647$	750.947			1.16066			0.580330	+	0.814381i	$0.302923\pi$
$648$		0			0
$649$	−560.000			−0.862866
$650$	−366.662	+	383.157i	−0.564095	+	0.589472i
$651$		0			0
$652$	91.7987	+	53.0000i	0.140796	+	0.0812883i
$653$	−73.5391	+	127.373i	−0.112617	+	0.195059i	−0.916825	−	0.399290i	$-0.869257\pi$
$653$	−73.5391	+	127.373i	−0.112617	+	0.195059i	0.804207	+	0.594349i	$0.202590\pi$
$654$		0			0
$655$	266.985	−	209.569i	0.407610	−	0.319953i
$656$			311.127i			0.474279i
$657$		0			0
$658$			880.000i			1.33739i
$659$	−862.220	+	497.803i	−1.30838	+	0.755392i	−0.981825	−	0.189788i	$-0.939220\pi$
$659$	−862.220	+	497.803i	−1.30838	+	0.755392i	−0.326552	+	0.945179i	$0.605887\pi$
$660$		0			0
$661$	624.500	−	1081.67i	0.944781	−	1.63641i	0.188591	−	0.982056i	$-0.439608\pi$
$661$	624.500	−	1081.67i	0.944781	−	1.63641i	0.756190	−	0.654352i	$-0.227059\pi$
$662$	−111.016	+	192.285i	−0.167698	+	0.290461i
$663$		0			0
$664$	−154.000	−	266.736i	−0.231928	−	0.401711i
$665$	−23.3345	−	163.342i	−0.0350895	−	0.245627i
$666$		0			0
$667$		−	234.000i		−	0.350825i
$668$	135.765	+	235.151i	0.203240	+	0.352022i
$669$		0			0
$670$	−124.681	−	50.0455i	−0.186092	−	0.0746948i
$671$	581.754	+	335.876i	0.866995	+	0.500560i
$672$		0			0
$673$	−735.256	+	424.500i	−1.09250	+	0.630758i	−0.934242	−	0.356639i	$-0.883923\pi$
$673$	−735.256	+	424.500i	−1.09250	+	0.630758i	−0.158262	+	0.987397i	$0.550589\pi$
$674$			272.943i			0.404960i
$675$		0			0
$676$	−112.000			−0.165680
$677$	−282.843	−	489.898i	−0.417788	−	0.723631i	0.577928	−	0.816088i	$-0.303861\pi$
$677$	−282.843	−	489.898i	−0.417788	−	0.723631i	−0.995717	+	0.0924569i	$0.970528\pi$
$678$		0			0
$679$	−522.500	+	904.997i	−0.769514	+	1.33284i
$680$	119.200	−	296.970i	0.175294	−	0.436721i
$681$		0			0
$682$	69.2820	−	40.0000i	0.101587	−	0.0586510i
$683$	117.380			0.171859			0.0859295	−	0.996301i	$-0.472614\pi$
$683$	117.380			0.171859			0.0859295	+	0.996301i	$0.472614\pi$
$684$		0			0
$685$	−441.000	+	63.0000i	−0.643796	+	0.0919708i
$686$	309.860	−	178.898i	0.451692	−	0.260784i
$687$		0			0
$688$	−110.851	−	64.0000i	−0.161121	−	0.0930233i
$689$	165.341	+	95.4594i	0.239972	+	0.138548i
$690$		0			0
$691$	−8.00000	−	13.8564i	−0.0115774	−	0.0200527i	0.860179	−	0.509993i	$-0.170352\pi$
$691$	−8.00000	−	13.8564i	−0.0115774	−	0.0200527i	−0.871756	+	0.489940i	$0.837019\pi$
$692$	248.902			0.359684
$693$		0			0
$694$	474.000			0.682997
$695$	256.241	+	326.443i	0.368693	+	0.469703i
$696$		0			0
$697$	−1524.20	−	880.000i	−2.18681	−	1.26255i
$698$	242.538	−	420.087i	0.347475	−	0.601845i
$699$		0			0
$700$	−380.261	+	397.368i	−0.543231	+	0.567668i
$701$		−	1016.82i		−	1.45053i	−0.688471	−	0.725264i	$-0.741718\pi$
$701$		−	1016.82i		−	1.45053i	0.688471	−	0.725264i	$-0.258282\pi$
$702$		0			0
$703$			195.000i			0.277383i
$704$	−48.9898	+	28.2843i	−0.0695878	+	0.0401765i
$705$		0			0
$706$	−160.000	+	277.128i	−0.226629	+	0.392533i
$707$	−622.254	+	1077.78i	−0.880133	+	1.52443i
$708$		0			0
$709$	−115.500	−	200.052i	−0.162906	−	0.282161i	0.773004	−	0.634401i	$-0.218753\pi$
$709$	−115.500	−	200.052i	−0.162906	−	0.282161i	−0.935910	+	0.352241i	$0.885420\pi$
$710$	−4.24264	−	29.6985i	−0.00597555	−	0.0418289i
$711$		0			0
$712$		−	256.000i		−	0.359551i
$713$	−73.5391	−	127.373i	−0.103140	−	0.178644i
$714$		0			0
$715$	−197.548	+	492.163i	−0.276291	+	0.688340i
$716$	497.246	+	287.085i	0.694478	+	0.400957i
$717$		0			0
$718$	504.027	−	291.000i	0.701987	−	0.405292i
$719$		−	120.208i		−	0.167188i	−0.996500	−	0.0835940i	$-0.973360\pi$
$719$		−	120.208i		−	0.167188i	0.996500	−	0.0835940i	$-0.0266399\pi$
$720$		0			0
$721$	1265.00			1.75451
$722$	248.902	+	431.110i	0.344739	+	0.597106i
$723$		0			0
$724$	−113.000	+	195.722i	−0.156077	+	0.270334i
$725$	−309.093	−	75.5761i	−0.426335	−	0.104243i
$726$		0			0
$727$	935.307	−	540.000i	1.28653	−	0.742779i	0.308496	−	0.951225i	$-0.400174\pi$
$727$	935.307	−	540.000i	1.28653	−	0.742779i	0.978034	+	0.208447i	$0.0668409\pi$
$728$	−466.690			−0.641058
$729$		0			0
$730$	−119.000	−	833.000i	−0.163014	−	1.14110i
$731$	627.069	−	362.039i	0.857824	−	0.495265i
$732$		0			0
$733$	297.913	+	172.000i	0.406429	+	0.234652i	0.689254	−	0.724519i	$-0.257938\pi$
$733$	297.913	+	172.000i	0.406429	+	0.234652i	−0.282825	+	0.959172i	$0.591272\pi$
$734$	564.607	+	325.976i	0.769220	+	0.444109i
$735$		0			0
$736$	52.0000	+	90.0666i	0.0706522	+	0.122373i
$737$	−134.350			−0.182293
$738$		0			0
$739$	−640.000			−0.866035			−0.433018	−	0.901385i	$-0.642551\pi$
$739$	−640.000			−0.866035			−0.433018	+	0.901385i	$0.642551\pi$
$740$	511.297	−	401.342i	0.690942	−	0.542354i
$741$		0			0
$742$	171.473	+	99.0000i	0.231096	+	0.133423i
$743$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$743$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$744$		0			0
$745$	311.482	−	244.497i	0.418097	−	0.328184i
$746$		−	224.860i		−	0.301421i
$747$		0			0
$748$		−	320.000i		−	0.427807i
$749$	−1657.08	+	956.715i	−2.21239	+	1.27732i
$750$		0			0
$751$	150.500	−	260.674i	0.200399	−	0.347102i	−0.748258	−	0.663408i	$-0.769109\pi$
$751$	150.500	−	260.674i	0.200399	−	0.347102i	0.948657	+	0.316306i	$0.102443\pi$
$752$	113.137	−	195.959i	0.150448	−	0.260584i
$753$		0			0
$754$	−135.000	−	233.827i	−0.179045	−	0.310115i
$755$	767.211	−	109.602i	1.01617	−	0.145168i
$756$		0			0
$757$			367.000i			0.484808i	0.970175	+	0.242404i	$0.0779360\pi$
$757$			367.000i			0.484808i	−0.970175	+	0.242404i	$0.922064\pi$
$758$	−26.1630	−	45.3156i	−0.0345158	−	0.0597831i
$759$		0			0
$760$	−15.8038	+	39.3731i	−0.0207945	+	0.0518067i
$761$	−69.8105	−	40.3051i	−0.0917352	−	0.0529633i	0.453431	−	0.891292i	$-0.350200\pi$
$761$	−69.8105	−	40.3051i	−0.0917352	−	0.0529633i	−0.545166	+	0.838328i	$0.683533\pi$
$762$		0			0
$763$	−76.2102	+	44.0000i	−0.0998824	+	0.0576671i
$764$		−	271.529i		−	0.355404i
$765$		0			0
$766$	656.000			0.856397
$767$	593.970	+	1028.79i	0.774406	+	1.34131i
$768$		0			0
$769$	208.500	−	361.133i	0.271131	−	0.469613i	−0.698020	−	0.716078i	$-0.745936\pi$
$769$	208.500	−	361.133i	0.271131	−	0.469613i	0.969152	+	0.246465i	$0.0792689\pi$
$770$	−204.875	+	510.418i	−0.266072	+	0.662880i
$771$		0			0
$772$	−126.440	+	73.0000i	−0.163782	+	0.0945596i
$773$	292.742			0.378709			0.189355	−	0.981909i	$-0.439360\pi$
$773$	292.742			0.378709			0.189355	+	0.981909i	$0.439360\pi$
$774$		0			0
$775$	−192.000	+	56.0000i	−0.247742	+	0.0722581i
$776$	232.702	−	134.350i	0.299873	−	0.173132i
$777$		0			0
$778$	−55.4256	−	32.0000i	−0.0712412	−	0.0411311i
$779$	202.083	+	116.673i	0.259413	+	0.149772i
$780$		0			0
$781$	−15.0000	−	25.9808i	−0.0192061	−	0.0332660i
$782$	−588.313			−0.752318
$783$		0			0
$784$	−288.000			−0.367347
$785$	39.3305	−	30.8725i	0.0501026	−	0.0393280i
$786$		0			0
$787$	−328.224	−	189.500i	−0.417057	−	0.240788i	0.276761	−	0.960939i	$-0.410739\pi$
$787$	−328.224	−	189.500i	−0.417057	−	0.240788i	−0.693817	+	0.720151i	$0.744072\pi$
$788$	−214.960	+	372.322i	−0.272792	+	0.472490i
$789$		0			0
$790$	432.237	+	550.656i	0.547135	+	0.697032i
$791$			1633.42i			2.06500i
$792$		0			0
$793$		−	1425.00i		−	1.79697i
$794$	48.9898	−	28.2843i	0.0617000	−	0.0356225i
$795$		0			0
$796$	−123.000	+	213.042i	−0.154523	+	0.267641i
$797$	345.068	−	597.675i	0.432959	−	0.749907i	−0.564168	−	0.825660i	$-0.690803\pi$
$797$	345.068	−	597.675i	0.432959	−	0.749907i	0.997127	+	0.0757536i	$0.0241362\pi$
$798$		0			0
$799$	640.000	+	1108.51i	0.801001	+	1.38737i
$800$	135.765	−	39.5980i	0.169706	−	0.0494975i
$801$		0			0
$802$			898.000i			1.11970i
$803$	−420.729	−	728.723i	−0.523946	−	0.907501i
$804$		0			0
$805$	938.391	+	376.658i	1.16570	+	0.467899i
$806$	−146.969	−	84.8528i	−0.182344	−	0.105276i
$807$		0			0
$808$	277.128	−	160.000i	0.342980	−	0.198020i
$809$			644.881i			0.797134i	0.917139	+	0.398567i	$0.130492\pi$
$809$			644.881i			0.797134i	−0.917139	+	0.398567i	$0.869508\pi$
$810$		0			0
$811$	64.0000			0.0789149			0.0394575	−	0.999221i	$-0.487437\pi$
$811$	64.0000			0.0789149			0.0394575	+	0.999221i	$0.487437\pi$
$812$	−140.007	−	242.499i	−0.172423	−	0.298645i
$813$		0			0
$814$	325.000	−	562.917i	0.399263	−	0.691544i
$815$	−245.929	−	98.7126i	−0.301753	−	0.121120i
$816$		0			0
$817$	−83.1384	+	48.0000i	−0.101761	+	0.0587515i
$818$	1087.53			1.32950
$819$		0			0
$820$	−110.000	−	770.000i	−0.134146	−	0.939024i
$821$	−166.565	+	96.1665i	−0.202881	+	0.117133i	−0.597999	−	0.801497i	$-0.704037\pi$
$821$	−166.565	+	96.1665i	−0.202881	+	0.117133i	0.395118	+	0.918631i	$0.370704\pi$
$822$		0			0
$823$	293.583	+	169.500i	0.356722	+	0.205954i	0.667642	−	0.744482i	$-0.267304\pi$
$823$	293.583	+	169.500i	0.356722	+	0.205954i	−0.310920	+	0.950436i	$0.600637\pi$
$824$	−281.691	−	162.635i	−0.341858	−	0.197372i
$825$		0			0
$826$	616.000	+	1066.94i	0.745763	+	1.29170i
$827$	−724.077			−0.875547			−0.437773	−	0.899085i	$-0.644233\pi$
$827$	−724.077			−0.875547			−0.437773	+	0.899085i	$0.644233\pi$
$828$		0			0
$829$	639.000			0.770808			0.385404	−	0.922748i	$-0.374062\pi$
$829$	639.000			0.770808			0.385404	+	0.922748i	$0.374062\pi$
$830$	475.436	+	605.690i	0.572814	+	0.729747i
$831$		0			0
$832$	103.923	+	60.0000i	0.124908	+	0.0721154i
$833$	814.587	−	1410.91i	0.977896	−	1.69376i
$834$		0			0
$835$	−419.138	−	533.969i	−0.501962	−	0.639484i
$836$			42.4264i			0.0507493i
$837$		0			0
$838$			688.000i			0.821002i
$839$	−244.949	+	141.421i	−0.291953	+	0.168559i	−0.638822	−	0.769354i	$-0.720578\pi$
$839$	−244.949	+	141.421i	−0.291953	+	0.168559i	0.346869	+	0.937914i	$0.387245\pi$
$840$		0			0
$841$	−339.500	+	588.031i	−0.403686	+	0.699205i
$842$	118.087	−	204.532i	0.140246	−	0.242913i
$843$		0			0
$844$	−261.000	−	452.065i	−0.309242	−	0.535622i
$845$	277.186	−	39.5980i	0.328031	−	0.0468615i
$846$		0			0
$847$		−	781.000i		−	0.922078i
$848$	−25.4558	−	44.0908i	−0.0300187	−	0.0519939i
$849$		0			0
$850$	−190.010	+	777.108i	−0.223542	+	0.914244i
$851$	−1034.91	−	597.505i	−1.21611	−	0.702121i
$852$		0			0
$853$	−830.518	+	479.500i	−0.973644	+	0.562134i	−0.900345	−	0.435176i	$-0.856686\pi$
$853$	−830.518	+	479.500i	−0.973644	+	0.562134i	−0.0732988	+	0.997310i	$0.523353\pi$
$854$		−	1477.85i		−	1.73051i
$855$		0			0
$856$	492.000			0.574766
$857$	−91.2168	−	157.992i	−0.106437	−	0.184355i	0.807887	−	0.589337i	$-0.200611\pi$
$857$	−91.2168	−	157.992i	−0.106437	−	0.184355i	−0.914325	+	0.404982i	$0.867278\pi$
$858$		0			0
$859$	−573.500	+	993.331i	−0.667637	+	1.15638i	0.310926	+	0.950434i	$0.399361\pi$
$859$	−573.500	+	993.331i	−0.667637	+	1.15638i	−0.978563	+	0.205947i	$0.933973\pi$
$860$	296.970	+	119.200i	0.345314	+	0.138605i
$861$		0			0
$862$	−517.883	+	299.000i	−0.600793	+	0.346868i
$863$	746.705			0.865243			0.432622	−	0.901576i	$-0.357589\pi$
$863$	746.705			0.865243			0.432622	+	0.901576i	$0.357589\pi$
$864$		0			0
$865$	−616.000	+	88.0000i	−0.712139	+	0.101734i
$866$	39.1918	−	22.6274i	0.0452562	−	0.0261287i
$867$		0			0
$868$	−152.420	−	88.0000i	−0.175600	−	0.101382i
$869$	606.249	+	350.018i	0.697639	+	0.402782i
$870$		0			0
$871$	142.500	+	246.817i	0.163605	+	0.283372i
$872$	22.6274			0.0259489
$873$		0			0
$874$	78.0000			0.0892449
$875$	800.608	−	1117.88i	0.914981	−	1.27757i
$876$		0			0
$877$	567.247	+	327.500i	0.646803	+	0.373432i	0.787230	−	0.616659i	$-0.211514\pi$
$877$	567.247	+	327.500i	0.646803	+	0.373432i	−0.140427	+	0.990091i	$0.544848\pi$
$878$	−458.205	+	793.635i	−0.521874	+	0.903912i
$879$		0			0
$880$	111.244	−	87.3205i	0.126413	−	0.0992279i
$881$			318.198i			0.361178i	0.983559	+	0.180589i	$0.0578004\pi$
$881$			318.198i			0.361178i	−0.983559	+	0.180589i	$0.942200\pi$
$882$		0			0
$883$		−	261.000i		−	0.295583i	−0.989019	−	0.147792i	$-0.952784\pi$
$883$		−	261.000i		−	0.295583i	0.989019	−	0.147792i	$-0.0472165\pi$
$884$	−587.878	+	339.411i	−0.665020	+	0.383949i
$885$		0			0
$886$	312.000	−	540.400i	0.352144	−	0.609932i
$887$	390.323	−	676.059i	0.440048	−	0.762186i	−0.557644	−	0.830080i	$-0.688295\pi$
$887$	390.323	−	676.059i	0.440048	−	0.762186i	0.997693	+	0.0678939i	$0.0216279\pi$
$888$		0			0
$889$	572.000	+	990.733i	0.643420	+	1.11444i
$890$	90.5097	+	633.568i	0.101696	+	0.711874i
$891$		0			0
$892$			112.000i			0.125561i
$893$	−84.8528	−	146.969i	−0.0950199	−	0.164579i
$894$		0			0
$895$	−1332.12	−	534.697i	−1.48840	−	0.597427i
$896$	107.778	+	62.2254i	0.120287	+	0.0694480i
$897$		0			0
$898$	124.708	−	72.0000i	0.138873	−	0.0801782i
$899$		−	101.823i		−	0.113263i
$900$		0			0
$901$	288.000			0.319645
$902$	−388.909	−	673.610i	−0.431163	−	0.746796i
$903$		0			0
$904$	210.000	−	363.731i	0.232301	−	0.402357i
$905$	210.463	−	524.338i	0.232555	−	0.579379i
$906$		0			0
$907$	−454.663	+	262.500i	−0.501283	+	0.289416i	−0.729243	−	0.684255i	$-0.760128\pi$
$907$	−454.663	+	262.500i	−0.501283	+	0.289416i	0.227960	+	0.973670i	$0.426794\pi$
$908$	−845.700			−0.931387
$909$		0			0
$910$	1155.00	−	165.000i	1.26923	−	0.181319i
$911$	440.908	−	254.558i	0.483983	−	0.279427i	−0.238092	−	0.971243i	$-0.576522\pi$
$911$	440.908	−	254.558i	0.483983	−	0.279427i	0.722075	+	0.691815i	$0.243189\pi$
$912$		0			0
$913$	666.840	+	385.000i	0.730383	+	0.421687i
$914$	450.706	+	260.215i	0.493114	+	0.284699i
$915$		0			0
$916$	−40.0000	−	69.2820i	−0.0436681	−	0.0756354i
$917$	−746.705			−0.814291
$918$		0			0
$919$	1272.00			1.38411			0.692057	−	0.721843i	$-0.256705\pi$
$919$	1272.00			1.38411			0.692057	+	0.721843i	$0.256705\pi$
$920$	−160.537	−	204.519i	−0.174497	−	0.222303i
$921$		0			0
$922$	540.400	+	312.000i	0.586117	+	0.338395i
$923$	−31.8198	+	55.1135i	−0.0344743	+	0.0597113i
$924$		0			0
$925$	−1123.50	+	1174.04i	−1.21459	+	1.26923i
$926$			97.5807i			0.105379i
$927$		0			0
$928$			72.0000i			0.0775862i
$929$	481.325	−	277.893i	0.518111	−	0.299131i	−0.218051	−	0.975937i	$-0.569970\pi$
$929$	481.325	−	277.893i	0.518111	−	0.299131i	0.736161	+	0.676806i	$0.236636\pi$
$930$		0			0
$931$	−108.000	+	187.061i	−0.116004	+	0.200925i
$932$	−90.5097	+	156.767i	−0.0971134	+	0.168205i
$933$		0			0
$934$	336.000	+	581.969i	0.359743	+	0.623093i
$935$	113.137	+	791.960i	0.121002	+	0.847016i
$936$		0			0
$937$			1265.00i			1.35005i	0.737793	+	0.675027i	$0.235868\pi$
$937$			1265.00i			1.35005i	−0.737793	+	0.675027i	$0.764132\pi$
$938$	147.785	+	255.972i	0.157554	+	0.272891i
$939$		0			0
$940$	−210.718	+	524.974i	−0.224168	+	0.558483i
$941$	−978.571	−	564.978i	−1.03993	−	0.600402i	−0.120114	−	0.992760i	$-0.538326\pi$
$941$	−978.571	−	564.978i	−1.03993	−	0.600402i	−0.919813	+	0.392358i	$0.871659\pi$
$942$		0			0
$943$	−1238.42	+	715.000i	−1.31327	+	0.758218i
$944$		−	316.784i		−	0.335576i
$945$		0			0
$946$	320.000			0.338266
$947$	−390.323	−	676.059i	−0.412168	−	0.713896i	0.582959	−	0.812502i	$-0.301895\pi$
$947$	−390.323	−	676.059i	−0.412168	−	0.713896i	−0.995127	+	0.0986061i	$0.968562\pi$
$948$		0			0
$949$	−892.500	+	1545.86i	−0.940464	+	1.62893i
$950$	25.1920	−	103.031i	0.0265179	−	0.108454i
$951$		0			0
$952$	−609.682	+	352.000i	−0.640422	+	0.369748i
$953$	463.862			0.486739			0.243369	−	0.969934i	$-0.421747\pi$
$953$	463.862			0.486739			0.243369	+	0.969934i	$0.421747\pi$
$954$		0			0
$955$	96.0000	+	672.000i	0.100524	+	0.703665i
$956$	−399.267	+	230.517i	−0.417643	+	0.241126i
$957$		0			0
$958$	−673.768	−	389.000i	−0.703307	−	0.406054i
$959$	848.748	+	490.025i	0.885035	+	0.510975i
$960$		0			0
$961$	448.500	+	776.825i	0.466701	+	0.808350i
$962$	−1378.86			−1.43332
$963$		0			0
$964$	−418.000			−0.433610
$965$	287.113	−	225.369i	0.297526	−	0.233543i
$966$		0			0
$967$	993.331	+	573.500i	1.02723	+	0.593071i	0.916190	−	0.400745i	$-0.131249\pi$
$967$	993.331	+	573.500i	1.02723	+	0.593071i	0.111040	+	0.993816i	$0.464582\pi$
$968$	−100.409	+	173.914i	−0.103728	+	0.179663i
$969$		0			0
$970$	−528.407	+	414.772i	−0.544749	+	0.427600i
$971$		−	814.587i		−	0.838916i	−0.907775	−	0.419458i	$-0.862220\pi$
$971$		−	814.587i		−	0.838916i	0.907775	−	0.419458i	$-0.137780\pi$
$972$		0			0
$973$		−	913.000i		−	0.938335i
$974$	−620.946	+	358.503i	−0.637521	+	0.368073i
$975$		0			0
$976$	−190.000	+	329.090i	−0.194672	+	0.337182i
$977$	−468.812	+	812.006i	−0.479848	+	0.831122i	−0.999733	−	0.0231149i	$-0.992642\pi$
$977$	−468.812	+	812.006i	−0.479848	+	0.831122i	0.519885	+	0.854237i	$0.325975\pi$
$978$		0			0
$979$	320.000	+	554.256i	0.326864	+	0.566145i
$980$	712.764	−	101.823i	0.727310	−	0.103901i
$981$		0			0
$982$		−	42.0000i		−	0.0427699i
$983$	682.358	+	1181.88i	0.694159	+	1.20232i	0.970463	+	0.241248i	$0.0775568\pi$
$983$	682.358	+	1181.88i	0.694159	+	1.20232i	−0.276305	+	0.961070i	$0.589110\pi$
$984$		0			0
$985$	400.364	−	997.451i	0.406461	−	1.01264i
$986$	−352.727	−	203.647i	−0.357735	−	0.206538i
$987$		0			0
$988$	77.9423	−	45.0000i	0.0788890	−	0.0455466i
$989$		−	588.313i		−	0.594856i
$990$		0			0
$991$	−1115.00			−1.12513			−0.562563	−	0.826754i	$-0.690185\pi$
$991$	−1115.00			−1.12513			−0.562563	+	0.826754i	$0.690185\pi$
$992$	22.6274	+	39.1918i	0.0228099	+	0.0395079i
$993$		0			0
$994$	−33.0000	+	57.1577i	−0.0331992	+	0.0575027i
$995$	229.088	−	570.740i	0.230239	−	0.573608i
$996$		0			0
$997$	1143.15	−	660.000i	1.14659	−	0.661986i	0.198539	−	0.980093i	$-0.436381\pi$
$997$	1143.15	−	660.000i	1.14659	−	0.661986i	0.948055	+	0.318107i	$0.103047\pi$
$998$	−670.337			−0.671681
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.3.j.b.539.1		8
3.2	odd	2	inner	810.3.j.b.539.4		8
5.4	even	2	inner	810.3.j.b.539.3		8
9.2	odd	6	inner	810.3.j.b.269.3		8
9.4	even	3		270.3.b.b.269.4	yes	4
9.5	odd	6		270.3.b.b.269.1	✓	4
9.7	even	3	inner	810.3.j.b.269.2		8
15.14	odd	2	inner	810.3.j.b.539.2		8
36.23	even	6		2160.3.c.j.1889.3		4
36.31	odd	6		2160.3.c.j.1889.2		4
45.4	even	6		270.3.b.b.269.2	yes	4
45.13	odd	12		1350.3.d.b.701.1		2
45.14	odd	6		270.3.b.b.269.3	yes	4
45.22	odd	12		1350.3.d.j.701.2		2
45.23	even	12		1350.3.d.b.701.2		2
45.29	odd	6	inner	810.3.j.b.269.1		8
45.32	even	12		1350.3.d.j.701.1		2
45.34	even	6	inner	810.3.j.b.269.4		8
180.59	even	6		2160.3.c.j.1889.1		4
180.139	odd	6		2160.3.c.j.1889.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.3.b.b.269.1	✓	4	9.5	odd	6
270.3.b.b.269.2	yes	4	45.4	even	6
270.3.b.b.269.3	yes	4	45.14	odd	6
270.3.b.b.269.4	yes	4	9.4	even	3
810.3.j.b.269.1		8	45.29	odd	6	inner
810.3.j.b.269.2		8	9.7	even	3	inner
810.3.j.b.269.3		8	9.2	odd	6	inner
810.3.j.b.269.4		8	45.34	even	6	inner
810.3.j.b.539.1		8	1.1	even	1	trivial
810.3.j.b.539.2		8	15.14	odd	2	inner
810.3.j.b.539.3		8	5.4	even	2	inner
810.3.j.b.539.4		8	3.2	odd	2	inner
1350.3.d.b.701.1		2	45.13	odd	12
1350.3.d.b.701.2		2	45.23	even	12
1350.3.d.j.701.1		2	45.32	even	12
1350.3.d.j.701.2		2	45.22	odd	12
2160.3.c.j.1889.1		4	180.59	even	6
2160.3.c.j.1889.2		4	36.31	odd	6
2160.3.c.j.1889.3		4	36.23	even	6
2160.3.c.j.1889.4		4	180.139	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	810.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.86250 - 4.64016i) q^{5} +(-9.52628 + 5.50000i) q^{7} +2.82843 q^{8} +O(q^{10})\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.86250 - 4.64016i) q^{5} +(-9.52628 + 5.50000i) q^{7} +2.82843 q^{8} +(-7.00000 + 1.00000i) q^{10} +(-6.12372 + 3.53553i) q^{11} +(12.9904 + 7.50000i) q^{13} +(13.4722 + 7.77817i) q^{14} +(-2.00000 - 3.46410i) q^{16} +22.6274 q^{17} -3.00000 q^{19} +(6.17449 + 7.86611i) q^{20} +(8.66025 + 5.00000i) q^{22} +(9.19239 - 15.9217i) q^{23} +(-18.0622 - 17.2846i) q^{25} -21.2132i q^{26} -22.0000i q^{28} +(11.0227 - 6.36396i) q^{29} +(4.00000 - 6.92820i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(-16.0000 - 27.7128i) q^{34} +(7.77817 + 54.4472i) q^{35} -65.0000i q^{37} +(2.12132 + 3.67423i) q^{38} +(5.26795 - 13.1244i) q^{40} +(-67.3610 - 38.8909i) q^{41} +(27.7128 - 16.0000i) q^{43} -14.1421i q^{44} -26.0000 q^{46} +(28.2843 + 48.9898i) q^{47} +(36.0000 - 62.3538i) q^{49} +(-8.39735 + 34.3436i) q^{50} +(-25.9808 + 15.0000i) q^{52} +12.7279 q^{53} +(5.00000 + 35.0000i) q^{55} +(-26.9444 + 15.5563i) q^{56} +(-15.5885 - 9.00000i) q^{58} +(68.5857 + 39.5980i) q^{59} +(-47.5000 - 82.2724i) q^{61} -11.3137 q^{62} +8.00000 q^{64} +(58.9958 - 46.3087i) q^{65} +(16.4545 + 9.50000i) q^{67} +(-22.6274 + 39.1918i) q^{68} +(61.1840 - 48.0263i) q^{70} +4.24264i q^{71} +119.000i q^{73} +(-79.6084 + 45.9619i) q^{74} +(3.00000 - 5.19615i) q^{76} +(38.8909 - 67.3610i) q^{77} +(-49.5000 - 85.7365i) q^{79} +(-19.7990 + 2.82843i) q^{80} +110.000i q^{82} +(-54.4472 - 94.3054i) q^{83} +(42.1436 - 104.995i) q^{85} +(-39.1918 - 22.6274i) q^{86} +(-17.3205 + 10.0000i) q^{88} -90.5097i q^{89} -165.000 q^{91} +(18.3848 + 31.8434i) q^{92} +(40.0000 - 69.2820i) q^{94} +(-5.58750 + 13.9205i) q^{95} +(82.2724 - 47.5000i) q^{97} -101.823 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4}+O(q^{10}) \) 8 * q - 8 * q^4	\( 8 q - 8 q^{4} - 56 q^{10} - 16 q^{16} - 24 q^{19} - 96 q^{25} + 32 q^{31} - 128 q^{34} + 56 q^{40} - 208 q^{46} + 288 q^{49} + 40 q^{55} - 380 q^{61} + 64 q^{64} - 44 q^{70} + 24 q^{76} - 396 q^{79} + 448 q^{85} - 1320 q^{91} + 320 q^{94}+O(q^{100}) \) 8 * q - 8 * q^4 - 56 * q^10 - 16 * q^16 - 24 * q^19 - 96 * q^25 + 32 * q^31 - 128 * q^34 + 56 * q^40 - 208 * q^46 + 288 * q^49 + 40 * q^55 - 380 * q^61 + 64 * q^64 - 44 * q^70 + 24 * q^76 - 396 * q^79 + 448 * q^85 - 1320 * q^91 + 320 * q^94

Introduction

L-functions

Modular forms

Varieties

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Database

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