LMFDB - Embedded newform 810.3.j.b.269.2

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			269.2
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	810.269
Dual form			810.3.j.b.539.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(3.08725 + 3.93305i) q^{5} +(9.52628 + 5.50000i) q^{7} +2.82843 q^{8} +O(q^{10})$	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(3.08725 + 3.93305i) q^{5} +(9.52628 + 5.50000i) q^{7} +2.82843 q^{8} +(-7.00000 + 1.00000i) q^{10} +(6.12372 + 3.53553i) q^{11} +(-12.9904 + 7.50000i) q^{13} +(-13.4722 + 7.77817i) q^{14} +(-2.00000 + 3.46410i) q^{16} +22.6274 q^{17} -3.00000 q^{19} +(3.72500 - 9.28032i) q^{20} +(-8.66025 + 5.00000i) q^{22} +(9.19239 + 15.9217i) q^{23} +(-5.93782 + 24.2846i) q^{25} -21.2132i q^{26} -22.0000i q^{28} +(-11.0227 - 6.36396i) q^{29} +(4.00000 + 6.92820i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(-16.0000 + 27.7128i) q^{34} +(7.77817 + 54.4472i) q^{35} -65.0000i q^{37} +(2.12132 - 3.67423i) q^{38} +(8.73205 + 11.1244i) q^{40} +(67.3610 - 38.8909i) q^{41} +(-27.7128 - 16.0000i) q^{43} -14.1421i q^{44} -26.0000 q^{46} +(28.2843 - 48.9898i) q^{47} +(36.0000 + 62.3538i) q^{49} +(-25.5438 - 24.4441i) q^{50} +(25.9808 + 15.0000i) q^{52} +12.7279 q^{53} +(5.00000 + 35.0000i) q^{55} +(26.9444 + 15.5563i) q^{56} +(15.5885 - 9.00000i) q^{58} +(-68.5857 + 39.5980i) q^{59} +(-47.5000 + 82.2724i) q^{61} -11.3137 q^{62} +8.00000 q^{64} +(-69.6024 - 27.9375i) q^{65} +(-16.4545 + 9.50000i) q^{67} +(-22.6274 - 39.1918i) q^{68} +(-72.1840 - 28.9737i) q^{70} +4.24264i q^{71} +119.000i q^{73} +(79.6084 + 45.9619i) q^{74} +(3.00000 + 5.19615i) q^{76} +(38.8909 + 67.3610i) q^{77} +(-49.5000 + 85.7365i) q^{79} +(-19.7990 + 2.82843i) q^{80} +110.000i q^{82} +(-54.4472 + 94.3054i) q^{83} +(69.8564 + 88.9948i) q^{85} +(39.1918 - 22.6274i) q^{86} +(17.3205 + 10.0000i) q^{88} -90.5097i q^{89} -165.000 q^{91} +(18.3848 - 31.8434i) q^{92} +(40.0000 + 69.2820i) q^{94} +(-9.26174 - 11.7992i) q^{95} +(-82.2724 - 47.5000i) q^{97} -101.823 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

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

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
$5$	3.08725	+	3.93305i	0.617449	+	0.786611i
$5$	3.08725	+	3.93305i	0.617449	+	0.786611i
$6$		0			0
$7$	9.52628	+	5.50000i	1.36090	+	0.785714i	0.989743	−	0.142857i	$-0.0456289\pi$
$7$	9.52628	+	5.50000i	1.36090	+	0.785714i	0.371154	+	0.928571i	$0.378962\pi$
$8$	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	$-0.229176\pi$
$11$	6.12372	+	3.53553i	0.556702	+	0.321412i	−0.195119	+	0.980780i	$0.562509\pi$
$12$		0			0
$13$	−12.9904	+	7.50000i	−0.999260	+	0.576923i	−0.908029	−	0.418907i	$-0.862413\pi$
$13$	−12.9904	+	7.50000i	−0.999260	+	0.576923i	−0.0912308	+	0.995830i	$0.529080\pi$
$14$	−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	$0.525156\pi$
$20$	3.72500	−	9.28032i	0.186250	−	0.464016i
$21$		0			0
$22$	−8.66025	+	5.00000i	−0.393648	+	0.227273i
$23$	9.19239	+	15.9217i	0.399669	+	0.692247i	0.993685	−	0.112206i	$-0.0357917\pi$
$23$	9.19239	+	15.9217i	0.399669	+	0.692247i	−0.594016	+	0.804453i	$0.702458\pi$
$24$		0			0
$25$	−5.93782	+	24.2846i	−0.237513	+	0.971384i
$26$		−	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	$-0.403759\pi$
$29$	−11.0227	−	6.36396i	−0.380093	−	0.219447i	−0.677859	+	0.735192i	$0.737092\pi$
$30$		0			0
$31$	4.00000	+	6.92820i	0.129032	+	0.223490i	0.923302	−	0.384075i	$-0.125480\pi$
$31$	4.00000	+	6.92820i	0.129032	+	0.223490i	−0.794270	+	0.607565i	$0.792146\pi$
$32$	−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
$40$	8.73205	+	11.1244i	0.218301	+	0.278109i
$41$	67.3610	−	38.8909i	1.64295	−	0.948558i	0.663173	−	0.748466i	$-0.269209\pi$
$41$	67.3610	−	38.8909i	1.64295	−	0.948558i	0.979777	−	0.200092i	$-0.0641241\pi$
$42$		0			0
$43$	−27.7128	−	16.0000i	−0.644484	−	0.372093i	0.141856	−	0.989887i	$-0.454693\pi$
$43$	−27.7128	−	16.0000i	−0.644484	−	0.372093i	−0.786340	+	0.617794i	$0.788026\pi$
$44$		−	14.1421i		−	0.321412i
$45$		0			0
$46$	−26.0000			−0.565217
$47$	28.2843	−	48.9898i	0.601793	−	1.04234i	−0.390757	−	0.920494i	$-0.627787\pi$
$47$	28.2843	−	48.9898i	0.601793	−	1.04234i	0.992550	−	0.121842i	$-0.0388801\pi$
$48$		0			0
$49$	36.0000	+	62.3538i	0.734694	+	1.27253i
$50$	−25.5438	−	24.4441i	−0.510876	−	0.488883i
$51$		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	$-0.900867\pi$
$59$	−68.5857	+	39.5980i	−1.16247	+	0.671152i	−0.210575	+	0.977578i	$0.567534\pi$
$60$		0			0
$61$	−47.5000	+	82.2724i	−0.778689	+	1.34873i	0.154009	+	0.988069i	$0.450781\pi$
$61$	−47.5000	+	82.2724i	−0.778689	+	1.34873i	−0.932698	+	0.360659i	$0.882552\pi$
$62$	−11.3137			−0.182479
$63$		0			0
$64$	8.00000			0.125000
$65$	−69.6024	−	27.9375i	−1.07081	−	0.429808i
$66$		0			0
$67$	−16.4545	+	9.50000i	−0.245589	+	0.141791i	−0.617743	−	0.786380i	$-0.711953\pi$
$67$	−16.4545	+	9.50000i	−0.245589	+	0.141791i	0.372154	+	0.928171i	$0.378619\pi$
$68$	−22.6274	−	39.1918i	−0.332756	−	0.576351i
$69$		0			0
$70$	−72.1840	−	28.9737i	−1.03120	−	0.413910i
$71$			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	0.361650	+	0.932314i	$0.382213\pi$
$79$	−49.5000	+	85.7365i	−0.626582	+	1.08527i	−0.988233	+	0.152959i	$0.951120\pi$
$80$	−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	0.325654	+	0.945489i	$0.394416\pi$
$83$	−54.4472	+	94.3054i	−0.655991	+	1.13621i	−0.981644	+	0.190720i	$0.938918\pi$
$84$		0			0
$85$	69.8564	+	88.9948i	0.821840	+	1.04700i
$86$	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
$95$	−9.26174	−	11.7992i	−0.0974920	−	0.124202i
$96$		0			0
$97$	−82.2724	−	47.5000i	−0.848169	−	0.489691i	0.0118635	−	0.999930i	$-0.496224\pi$
$97$	−82.2724	−	47.5000i	−0.848169	−	0.489691i	−0.860033	+	0.510239i	$0.829557\pi$
$98$	−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	$-0.522565\pi$
$101$	−97.9796	−	56.5685i	−0.970095	−	0.560085i	−0.899265	+	0.437404i	$0.855898\pi$
$102$		0			0
$103$	99.5929	−	57.5000i	0.966922	−	0.558252i	0.0686252	−	0.997643i	$-0.478139\pi$
$103$	99.5929	−	57.5000i	0.966922	−	0.558252i	0.898296	+	0.439390i	$0.144805\pi$
$104$	−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	$0.488316\pi$
$110$	−46.4016	−	18.6250i	−0.421833	−	0.169318i
$111$		0			0
$112$	−38.1051	+	22.0000i	−0.340224	+	0.196429i
$113$	74.2462	+	128.598i	0.657046	+	1.13804i	0.981377	+	0.192093i	$0.0615277\pi$
$113$	74.2462	+	128.598i	0.657046	+	1.13804i	−0.324331	+	0.945944i	$0.605139\pi$
$114$		0			0
$115$	−34.2417	+	85.3083i	−0.297754	+	0.741811i
$116$			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
$130$	83.4327	−	65.4904i	0.641790	−	0.503772i
$131$	−58.7878	+	33.9411i	−0.448761	+	0.259093i	−0.707307	−	0.706907i	$-0.750090\pi$
$131$	−58.7878	+	33.9411i	−0.448761	+	0.259093i	0.258546	+	0.965999i	$0.416757\pi$
$132$		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	−0.981546	−	0.191227i	$-0.938753\pi$
$137$	−44.5477	+	77.1589i	−0.325166	+	0.563204i	0.656380	+	0.754430i	$0.272087\pi$
$138$		0			0
$139$	−41.5000	−	71.8801i	−0.298561	−	0.517123i	0.677246	−	0.735757i	$-0.263173\pi$
$139$	−41.5000	−	71.8801i	−0.298561	−	0.517123i	−0.975807	+	0.218634i	$0.929840\pi$
$140$	86.5272	−	67.9194i	0.618051	−	0.485139i
$141$		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	$-0.752289\pi$
$149$	−68.5857	+	39.5980i	−0.460307	+	0.265758i	0.251866	+	0.967762i	$0.418956\pi$
$150$		0			0
$151$	77.5000	−	134.234i	0.513245	−	0.888966i	−0.486637	−	0.873604i	$-0.661777\pi$
$151$	77.5000	−	134.234i	0.513245	−	0.888966i	0.999882	−	0.0153622i	$-0.00489013\pi$
$152$	−8.48528			−0.0558242
$153$		0			0
$154$	−110.000			−0.714286
$155$	−14.9000	+	37.1213i	−0.0961291	+	0.239492i
$156$		0			0
$157$	−8.66025	+	5.00000i	−0.0551609	+	0.0318471i	−0.527327	−	0.849663i	$-0.676806\pi$
$157$	−8.66025	+	5.00000i	−0.0551609	+	0.0318471i	0.472166	+	0.881510i	$0.343472\pi$
$158$	−70.0036	−	121.250i	−0.443061	−	0.767403i
$159$		0			0
$160$	10.5359	−	26.2487i	0.0658494	−	0.164054i
$161$			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	0.994493	−	0.104807i	$-0.0334226\pi$
$167$	67.8823	+	117.576i	0.406481	+	0.704045i	−0.588012	+	0.808852i	$0.700089\pi$
$168$		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	−0.987908	−	0.155041i	$-0.950449\pi$
$173$	−62.2254	+	107.778i	−0.359684	+	0.622992i	0.628224	+	0.778033i	$0.283782\pi$
$174$		0			0
$175$	−190.131	+	198.684i	−1.08646	+	1.13534i
$176$	−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
$185$	255.648	−	200.671i	1.38188	−	1.08471i
$186$		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	$-0.217676\pi$
$191$	117.576	+	67.8823i	0.615579	+	0.355404i	−0.159567	+	0.987187i	$0.551010\pi$
$192$		0			0
$193$	−63.2199	+	36.5000i	−0.327564	+	0.189119i	−0.654759	−	0.755838i	$-0.727230\pi$
$193$	−63.2199	+	36.5000i	−0.327564	+	0.189119i	0.327195	+	0.944957i	$0.393897\pi$
$194$	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	$0.399991\pi$
$200$	−16.7947	+	68.6872i	−0.0839735	+	0.343436i
$201$		0			0
$202$	138.564	−	80.0000i	0.685961	−	0.396040i
$203$	−70.0036	−	121.250i	−0.344845	−	0.597289i
$204$		0			0
$205$	360.920	+	144.869i	1.76058	+	0.706676i
$206$			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	−0.989763	−	0.142723i	$-0.954414\pi$
$211$	−130.500	−	226.033i	−0.618483	−	1.07124i	0.371279	−	0.928521i	$-0.378919\pi$
$212$	−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
$220$	55.6218	−	43.6603i	0.252826	−	0.198456i
$221$	−293.939	+	169.706i	−1.33004	+	0.767899i
$222$		0			0
$223$	−48.4974	−	28.0000i	−0.217477	−	0.125561i	0.387304	−	0.921952i	$-0.373406\pi$
$223$	−48.4974	−	28.0000i	−0.217477	−	0.125561i	−0.604782	+	0.796391i	$0.706740\pi$
$224$		−	62.2254i		−	0.277792i
$225$		0			0
$226$	−210.000			−0.929204
$227$	211.425	−	366.199i	0.931387	−	1.61321i	0.150435	−	0.988620i	$-0.451933\pi$
$227$	211.425	−	366.199i	0.931387	−	1.61321i	0.780953	−	0.624590i	$-0.214734\pi$
$228$		0			0
$229$	−20.0000	−	34.6410i	−0.0873362	−	0.151271i	0.819048	−	0.573725i	$-0.194502\pi$
$229$	−20.0000	−	34.6410i	−0.0873362	−	0.151271i	−0.906384	+	0.422454i	$0.861169\pi$
$230$	−80.2684	−	102.259i	−0.348993	−	0.444606i
$231$		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	$-0.826848\pi$
$239$	−199.633	+	115.258i	−0.835286	+	0.482253i	0.0203729	+	0.999792i	$0.493515\pi$
$240$		0			0
$241$	104.500	−	180.999i	0.433610	−	0.751034i	−0.563571	−	0.826068i	$-0.690573\pi$
$241$	104.500	−	180.999i	0.433610	−	0.751034i	0.997181	+	0.0750331i	$0.0239062\pi$
$242$	100.409			0.414914
$243$		0			0
$244$	190.000			0.778689
$245$	−134.100	+	334.092i	−0.547347	+	1.36364i
$246$		0			0
$247$	38.9711	−	22.5000i	0.157778	−	0.0910931i
$248$	11.3137	+	19.5959i	0.0456198	+	0.0790158i
$249$		0			0
$250$	17.2801	−	175.930i	0.0691206	−	0.703720i
$251$		−	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	0.873423	+	0.486962i	$0.161895\pi$
$257$	220.617	+	382.120i	0.858433	+	1.48685i	−0.0149899	+	0.999888i	$0.504772\pi$
$258$		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	−0.623228	−	0.782040i	$-0.714179\pi$
$263$	96.1665	−	166.565i	0.365652	−	0.633328i	0.988881	+	0.148712i	$0.0475126\pi$
$264$		0			0
$265$	39.2942	+	50.0596i	0.148280	+	0.188904i
$266$	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
$275$	−122.221	+	127.719i	−0.444439	+	0.464432i
$276$		0			0
$277$	−159.349	−	92.0000i	−0.575266	−	0.332130i	0.183984	−	0.982929i	$-0.441101\pi$
$277$	−159.349	−	92.0000i	−0.575266	−	0.332130i	−0.759250	+	0.650799i	$0.774434\pi$
$278$	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	$-0.451362\pi$
$281$	−176.363	−	101.823i	−0.627627	−	0.362361i	−0.779833	+	0.625988i	$0.784696\pi$
$282$		0			0
$283$	471.118	−	272.000i	1.66473	−	0.961131i	0.694317	−	0.719669i	$-0.255707\pi$
$283$	471.118	−	272.000i	1.66473	−	0.961131i	0.970410	−	0.241461i	$-0.0776267\pi$
$284$	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
$290$	83.5229	+	33.5250i	0.288010	+	0.115604i
$291$		0			0
$292$	206.114	−	119.000i	0.705870	−	0.407534i
$293$	40.3051	+	69.8105i	0.137560	+	0.238261i	0.926572	−	0.376116i	$-0.122741\pi$
$293$	40.3051	+	69.8105i	0.137560	+	0.238261i	−0.789012	+	0.614377i	$0.789407\pi$
$294$		0			0
$295$	−367.482	−	147.503i	−1.24570	−	0.500009i
$296$		−	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
$310$	−34.9282	−	44.4974i	−0.112672	−	0.143540i
$311$	264.545	−	152.735i	0.850627	−	0.491110i	−0.0102356	−	0.999948i	$-0.503258\pi$
$311$	264.545	−	152.735i	0.850627	−	0.491110i	0.860862	+	0.508838i	$0.169925\pi$
$312$		0			0
$313$	−165.411	−	95.5000i	−0.528469	−	0.305112i	0.211924	−	0.977286i	$-0.432027\pi$
$313$	−165.411	−	95.5000i	−0.528469	−	0.305112i	−0.740393	+	0.672174i	$0.765361\pi$
$314$		−	14.1421i		−	0.0450386i
$315$		0			0
$316$	198.000			0.626582
$317$	124.451	−	215.555i	0.392589	−	0.679985i	−0.600201	−	0.799849i	$-0.704913\pi$
$317$	124.451	−	215.555i	0.392589	−	0.679985i	0.992790	+	0.119865i	$0.0382461\pi$
$318$		0			0
$319$	−45.0000	−	77.9423i	−0.141066	−	0.244333i
$320$	24.6980	+	31.4644i	0.0771812	+	0.0983263i
$321$		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	−0.959898	−	0.280349i	$-0.909550\pi$
$331$	−78.5000	+	135.966i	−0.237160	+	0.410773i	0.722738	+	0.691122i	$0.242883\pi$
$332$	217.789			0.655991
$333$		0			0
$334$	−192.000			−0.574850
$335$	−88.1630	−	35.3875i	−0.263173	−	0.105634i
$336$		0			0
$337$	167.143	−	96.5000i	0.495973	−	0.286350i	−0.231076	−	0.972936i	$-0.574225\pi$
$337$	167.143	−	96.5000i	0.495973	−	0.286350i	0.727049	+	0.686586i	$0.240891\pi$
$338$	39.5980	+	68.5857i	0.117154	+	0.202916i
$339$		0			0
$340$	84.2872	−	209.990i	0.247903	−	0.617617i
$341$			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	0.516857	−	0.856072i	$-0.327102\pi$
$347$	−167.584	−	290.265i	−0.482952	−	0.836497i	−0.999808	+	0.0195748i	$0.993769\pi$
$348$		0			0
$349$	171.500	−	297.047i	0.491404	−	0.851137i	−0.508547	−	0.861034i	$-0.669817\pi$
$349$	171.500	−	297.047i	0.491404	−	0.851137i	0.999951	+	0.00989751i	$0.00315053\pi$
$350$	−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	−0.980592	−	0.196061i	$-0.937185\pi$
$353$	−113.137	+	195.959i	−0.320502	+	0.555125i	0.660090	+	0.751187i	$0.270518\pi$
$354$		0			0
$355$	−16.6865	+	13.0981i	−0.0470043	+	0.0368960i
$356$	−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
$365$	−468.033	+	367.382i	−1.28228	+	1.00653i
$366$		0			0
$367$	399.238	+	230.500i	1.08784	+	0.628065i	0.933001	−	0.359874i	$-0.117180\pi$
$367$	399.238	+	230.500i	1.08784	+	0.628065i	0.154840	+	0.987940i	$0.450514\pi$
$368$	−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	$-0.735035\pi$
$373$	−137.698	+	79.5000i	−0.369164	+	0.213137i	0.303929	+	0.952695i	$0.401701\pi$
$374$	−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	$0.484456\pi$
$380$	−11.1750	+	27.8410i	−0.0294079	+	0.0732657i
$381$		0			0
$382$	−166.277	+	96.0000i	−0.435280	+	0.251309i
$383$	−231.931	−	401.716i	−0.605564	−	1.04887i	−0.991962	−	0.126536i	$-0.959614\pi$
$383$	−231.931	−	401.716i	−0.605564	−	1.04887i	0.386398	−	0.922332i	$-0.373719\pi$
$384$		0			0
$385$	−144.869	+	360.920i	−0.376282	+	0.937454i
$386$		−	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	$-0.351859\pi$
$389$	−39.1918	−	22.6274i	−0.100750	−	0.0581682i	−0.549529	+	0.835475i	$0.685193\pi$
$390$		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
$400$	−72.2487	−	69.1384i	−0.180622	−	0.172846i
$401$	549.910	−	317.491i	1.37135	−	0.791748i	0.380250	−	0.924884i	$-0.375838\pi$
$401$	549.910	−	317.491i	1.37135	−	0.791748i	0.991098	+	0.133136i	$0.0425046\pi$
$402$		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	−0.765281	−	0.643696i	$-0.777400\pi$
$409$	−384.500	−	665.974i	−0.940098	−	1.62830i	−0.174817	−	0.984601i	$-0.555933\pi$
$410$	−432.636	+	339.597i	−1.05521	+	0.828286i
$411$		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	$-0.469510\pi$
$419$	421.312	−	243.245i	1.00552	−	0.580536i	0.909876	+	0.414879i	$0.136176\pi$
$420$		0			0
$421$	83.5000	−	144.626i	0.198337	−	0.343530i	−0.749652	−	0.661832i	$-0.769779\pi$
$421$	83.5000	−	144.626i	0.198337	−	0.343530i	0.947989	+	0.318302i	$0.103113\pi$
$422$	369.110			0.874668
$423$		0			0
$424$	36.0000			0.0849057
$425$	−134.358	+	549.498i	−0.316135	+	1.29294i
$426$		0			0
$427$	−904.997	+	522.500i	−2.11943	+	1.22365i
$428$	−173.948	−	301.287i	−0.406421	−	0.703942i
$429$		0			0
$430$	209.990	+	84.2872i	0.488348	+	0.196017i
$431$		−	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	0.215335	+	0.976540i	$0.430916\pi$
$439$	−324.000	+	561.184i	−0.738041	+	1.27832i	−0.953376	+	0.301784i	$0.902418\pi$
$440$	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	−0.501990	−	0.864873i	$-0.667399\pi$
$443$	220.617	−	382.120i	0.498007	−	0.862574i	0.999997	+	0.00229923i	$0.000731869\pi$
$444$		0			0
$445$	355.979	−	279.426i	0.799954	−	0.627923i
$446$	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
$455$	−509.396	−	648.954i	−1.11955	−	1.42627i
$456$		0			0
$457$	318.697	+	184.000i	0.697368	+	0.402626i	0.806367	−	0.591416i	$-0.201431\pi$
$457$	318.697	+	184.000i	0.697368	+	0.402626i	−0.108998	+	0.994042i	$0.534764\pi$
$458$	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	$-0.174491\pi$
$461$	382.120	+	220.617i	0.828895	+	0.478563i	−0.0245795	+	0.999698i	$0.507825\pi$
$462$		0			0
$463$	59.7558	−	34.5000i	0.129062	−	0.0745140i	−0.434079	−	0.900875i	$-0.642926\pi$
$463$	59.7558	−	34.5000i	0.129062	−	0.0745140i	0.563141	+	0.826361i	$0.309593\pi$
$464$	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
$470$	−149.000	+	371.213i	−0.317021	+	0.789815i
$471$		0			0
$472$	−193.990	+	112.000i	−0.410995	+	0.237288i
$473$	−113.137	−	195.959i	−0.239190	−	0.414290i
$474$		0			0
$475$	17.8135	−	72.8538i	0.0375020	−	0.153376i
$476$		−	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	$-0.528039\pi$
$479$	−476.426	−	275.065i	−0.994626	−	0.574247i	−0.906654	+	0.421875i	$0.861372\pi$
$480$		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
$490$	−314.354	−	400.477i	−0.641538	−	0.817300i
$491$	−25.7196	+	14.8492i	−0.0523822	+	0.0302429i	−0.525962	−	0.850508i	$-0.676295\pi$
$491$	−25.7196	+	14.8492i	−0.0523822	+	0.0302429i	0.473580	+	0.880751i	$0.342961\pi$
$492$		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	0.999588	−	0.0286877i	$-0.00913284\pi$
$499$	237.000	+	410.496i	0.474950	+	0.822637i	−0.524639	+	0.851325i	$0.675800\pi$
$500$	203.251	+	145.565i	0.406501	+	0.291130i
$501$		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	$-0.850501\pi$
$509$	−481.325	+	277.893i	−0.945628	+	0.545959i	−0.0539080	+	0.998546i	$0.517168\pi$
$510$		0			0
$511$	−654.500	+	1133.63i	−1.28082	+	2.21845i
$512$	22.6274			0.0441942
$513$		0			0
$514$	−624.000			−1.21401
$515$	533.618	+	214.188i	1.03615	+	0.415898i
$516$		0			0
$517$	346.410	−	200.000i	0.670039	−	0.386847i
$518$	505.581	+	875.693i	0.976026	+	1.69053i
$519$		0			0
$520$	−196.865	−	79.0192i	−0.378587	−	0.151960i
$521$		−	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
$535$	537.021	+	684.148i	1.00378	+	1.27878i
$536$	−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
$545$	24.6980	+	31.4644i	0.0453174	+	0.0577329i
$546$		0			0
$547$	217.372	+	125.500i	0.397390	+	0.229433i	0.685357	−	0.728207i	$-0.259646\pi$
$547$	217.372	+	125.500i	0.397390	+	0.229433i	−0.287967	+	0.957640i	$0.592979\pi$
$548$	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
$560$	−204.167	−	81.9501i	−0.364584	−	0.146339i
$561$		0			0
$562$	249.415	−	144.000i	0.443799	−	0.256228i
$563$	−164.049	−	284.141i	−0.291383	−	0.504691i	0.682754	−	0.730649i	$-0.260782\pi$
$563$	−164.049	−	284.141i	−0.291383	−	0.504691i	−0.974137	+	0.225958i	$0.927449\pi$
$564$		0			0
$565$	−276.567	+	689.029i	−0.489500	+	1.21952i
$566$			769.332i			1.35924i
$567$		0			0
$568$			12.0000i			0.0211268i
$569$	−862.220	−	497.803i	−1.51533	−	0.874874i	−0.999838	−	0.0179766i	$-0.994278\pi$
$569$	−862.220	−	497.803i	−1.51533	−	0.874874i	−0.515487	−	0.856897i	$-0.672389\pi$
$570$		0			0
$571$	17.5000	+	30.3109i	0.0306480	+	0.0530839i	0.880943	−	0.473223i	$-0.156910\pi$
$571$	17.5000	+	30.3109i	0.0306480	+	0.0530839i	−0.850295	+	0.526307i	$0.823576\pi$
$572$	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
$580$	−100.119	+	78.5885i	−0.172619	+	0.135497i
$581$	−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	−0.592728	−	0.805403i	$-0.701949\pi$
$587$	235.467	−	407.840i	0.401136	−	0.694787i	0.993863	+	0.110616i	$0.0352823\pi$
$588$		0			0
$589$	−12.0000	−	20.7846i	−0.0203735	−	0.0352880i
$590$	440.502	−	345.772i	0.746614	−	0.586054i
$591$		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	$-0.473544\pi$
$599$	591.552	−	341.533i	0.987566	−	0.570171i	0.904546	+	0.426377i	$0.140210\pi$
$600$		0			0
$601$	−304.000	+	526.543i	−0.505824	+	0.876112i	0.494154	+	0.869375i	$0.335478\pi$
$601$	−304.000	+	526.543i	−0.505824	+	0.876112i	−0.999977	+	0.00673765i	$0.997855\pi$
$602$	497.803			0.826916
$603$		0			0
$604$	−310.000			−0.513245
$605$	132.238	−	329.451i	0.218575	−	0.544548i
$606$		0			0
$607$	−364.597	+	210.500i	−0.600654	+	0.346787i	−0.769299	−	0.638889i	$-0.779394\pi$
$607$	−364.597	+	210.500i	−0.600654	+	0.346787i	0.168645	+	0.985677i	$0.446061\pi$
$608$	8.48528	+	14.6969i	0.0139561	+	0.0241726i
$609$		0			0
$610$	250.228	−	623.407i	0.410209	−	1.02198i
$611$			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	0.903838	−	0.427875i	$-0.140737\pi$
$617$	50.2046	+	86.9569i	0.0813689	+	0.140935i	−0.822469	+	0.568810i	$0.807404\pi$
$618$		0			0
$619$	470.500	−	814.930i	0.760097	−	1.31653i	−0.182703	−	0.983168i	$-0.558485\pi$
$619$	470.500	−	814.930i	0.760097	−	1.31653i	0.942800	−	0.333358i	$-0.108182\pi$
$620$	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
$625$	−554.485	−	288.395i	−0.887175	−	0.461433i
$626$	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
$635$	409.038	−	321.074i	0.644154	−	0.505628i
$636$		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	$-0.313657\pi$
$641$	68.5857	+	39.5980i	0.106998	+	0.0617753i	−0.445546	+	0.895259i	$0.646990\pi$
$642$		0			0
$643$	956.092	−	552.000i	1.48692	−	0.858476i	0.487035	−	0.873382i	$-0.338078\pi$
$643$	956.092	−	552.000i	1.48692	−	0.858476i	0.999889	+	0.0149066i	$0.00474509\pi$
$644$	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
$650$	515.154	+	125.960i	0.792545	+	0.193785i
$651$		0			0
$652$	−91.7987	+	53.0000i	−0.140796	+	0.0812883i
$653$	−73.5391	−	127.373i	−0.112617	−	0.195059i	0.804207	−	0.594349i	$-0.202590\pi$
$653$	−73.5391	−	127.373i	−0.112617	−	0.195059i	−0.916825	+	0.399290i	$0.869257\pi$
$654$		0			0
$655$	−314.985	−	126.431i	−0.480892	−	0.193024i
$656$			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	$-0.0607799\pi$
$659$	862.220	+	497.803i	1.30838	+	0.755392i	0.326552	+	0.945179i	$0.394113\pi$
$660$		0			0
$661$	624.500	+	1081.67i	0.944781	+	1.63641i	0.756190	+	0.654352i	$0.227059\pi$
$661$	624.500	+	1081.67i	0.944781	+	1.63641i	0.188591	+	0.982056i	$0.439608\pi$
$662$	−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
$670$	105.681	−	82.9545i	0.157733	−	0.123813i
$671$	−581.754	+	335.876i	−0.866995	+	0.500560i
$672$		0			0
$673$	735.256	+	424.500i	1.09250	+	0.630758i	0.934242	−	0.356639i	$-0.116077\pi$
$673$	735.256	+	424.500i	1.09250	+	0.630758i	0.158262	+	0.987397i	$0.449411\pi$
$674$			272.943i			0.404960i
$675$		0			0
$676$	−112.000			−0.165680
$677$	−282.843	+	489.898i	−0.417788	+	0.723631i	−0.995717	−	0.0924569i	$-0.970528\pi$
$677$	−282.843	+	489.898i	−0.417788	+	0.723631i	0.577928	+	0.816088i	$0.303861\pi$
$678$		0			0
$679$	−522.500	−	904.997i	−0.769514	−	1.33284i
$680$	197.584	+	251.715i	0.290564	+	0.370170i
$681$		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	−0.871756	−	0.489940i	$-0.837019\pi$
$691$	−8.00000	+	13.8564i	−0.0115774	+	0.0200527i	0.860179	+	0.509993i	$0.170352\pi$
$692$	248.902			0.359684
$693$		0			0
$694$	474.000			0.682997
$695$	154.588	−	385.133i	0.222428	−	0.554149i
$696$		0			0
$697$	1524.20	−	880.000i	2.18681	−	1.26255i
$698$	242.538	+	420.087i	0.347475	+	0.601845i
$699$		0			0
$700$	534.261	+	130.632i	0.763231	+	0.186617i
$701$		−	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	−0.935910	−	0.352241i	$-0.885420\pi$
$709$	−115.500	+	200.052i	−0.162906	+	0.282161i	0.773004	+	0.634401i	$0.218753\pi$
$710$	−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
$715$	−327.452	−	417.163i	−0.457975	−	0.583445i
$716$	−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
$725$	219.997	−	229.894i	0.303444	−	0.317095i
$726$		0			0
$727$	−935.307	−	540.000i	−1.28653	−	0.742779i	−0.308496	−	0.951225i	$-0.599826\pi$
$727$	−935.307	−	540.000i	−1.28653	−	0.742779i	−0.978034	+	0.208447i	$0.933159\pi$
$728$	−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	$-0.742062\pi$
$733$	−297.913	+	172.000i	−0.406429	+	0.234652i	0.282825	+	0.959172i	$0.408728\pi$
$734$	−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	$0.642551\pi$
$740$	−603.221	−	242.125i	−0.815163	−	0.327196i
$741$		0			0
$742$	−171.473	+	99.0000i	−0.231096	+	0.133423i
$743$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$743$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$744$		0			0
$745$	−367.482	−	147.503i	−0.493264	−	0.197990i
$746$		−	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	0.948657	−	0.316306i	$-0.102443\pi$
$751$	150.500	+	260.674i	0.200399	+	0.347102i	−0.748258	+	0.663408i	$0.769109\pi$
$752$	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
$760$	−26.1962	−	33.3731i	−0.0344686	−	0.0439119i
$761$	69.8105	−	40.3051i	0.0917352	−	0.0529633i	−0.453431	−	0.891292i	$-0.649800\pi$
$761$	69.8105	−	40.3051i	0.0917352	−	0.0529633i	0.545166	+	0.838328i	$0.316467\pi$
$762$		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	0.969152	−	0.246465i	$-0.0792689\pi$
$769$	208.500	+	361.133i	0.271131	+	0.469613i	−0.698020	+	0.716078i	$0.745936\pi$
$770$	−339.597	−	432.636i	−0.441035	−	0.561865i
$771$		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
$785$	−46.4016	−	18.6250i	−0.0591103	−	0.0237261i
$786$		0			0
$787$	328.224	−	189.500i	0.417057	−	0.240788i	−0.276761	−	0.960939i	$-0.589261\pi$
$787$	328.224	−	189.500i	0.417057	−	0.240788i	0.693817	+	0.720151i	$0.255928\pi$
$788$	−214.960	−	372.322i	−0.272792	−	0.472490i
$789$		0			0
$790$	260.763	−	649.656i	0.330080	−	0.822349i
$791$			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	0.997127	−	0.0757536i	$-0.0241362\pi$
$797$	345.068	+	597.675i	0.432959	+	0.749907i	−0.564168	+	0.825660i	$0.690803\pi$
$798$		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
$805$	−795.391	+	624.342i	−0.988064	+	0.775580i
$806$	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
$815$	208.452	−	163.624i	0.255769	−	0.200766i
$816$		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	$-0.295963\pi$
$821$	166.565	+	96.1665i	0.202881	+	0.117133i	−0.395118	+	0.918631i	$0.629296\pi$
$822$		0			0
$823$	−293.583	+	169.500i	−0.356722	+	0.205954i	−0.667642	−	0.744482i	$-0.732696\pi$
$823$	−293.583	+	169.500i	−0.356722	+	0.205954i	0.310920	+	0.950436i	$0.399363\pi$
$824$	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	$0.374062\pi$
$830$	286.825	−	714.585i	0.345573	−	0.860945i
$831$		0			0
$832$	−103.923	+	60.0000i	−0.124908	+	0.0721154i
$833$	814.587	+	1410.91i	0.977896	+	1.69376i
$834$		0			0
$835$	−252.862	+	629.969i	−0.302828	+	0.754454i
$836$			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	$-0.279422\pi$
$839$	244.949	+	141.421i	0.291953	+	0.168559i	−0.346869	+	0.937914i	$0.612755\pi$
$840$		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
$850$	−577.990	−	553.108i	−0.679988	−	0.650715i
$851$	1034.91	−	597.505i	1.21611	−	0.702121i
$852$		0			0
$853$	830.518	+	479.500i	0.973644	+	0.562134i	0.900345	−	0.435176i	$-0.143314\pi$
$853$	830.518	+	479.500i	0.973644	+	0.562134i	0.0732988	+	0.997310i	$0.476647\pi$
$854$		−	1477.85i		−	1.73051i
$855$		0			0
$856$	492.000			0.574766
$857$	−91.2168	+	157.992i	−0.106437	+	0.184355i	−0.914325	−	0.404982i	$-0.867278\pi$
$857$	−91.2168	+	157.992i	−0.106437	+	0.184355i	0.807887	+	0.589337i	$0.200611\pi$
$858$		0			0
$859$	−573.500	−	993.331i	−0.667637	−	1.15638i	−0.978563	−	0.205947i	$-0.933973\pi$
$859$	−573.500	−	993.331i	−0.667637	−	1.15638i	0.310926	−	0.950434i	$-0.399361\pi$
$860$	−251.715	+	197.584i	−0.292692	+	0.229749i
$861$		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
$875$	−1368.41	−	134.408i	−1.56390	−	0.153609i
$876$		0			0
$877$	−567.247	+	327.500i	−0.646803	+	0.373432i	−0.787230	−	0.616659i	$-0.788486\pi$
$877$	−567.247	+	327.500i	−0.646803	+	0.373432i	0.140427	+	0.990091i	$0.455152\pi$
$878$	−458.205	−	793.635i	−0.521874	−	0.903912i
$879$		0			0
$880$	−131.244	−	52.6795i	−0.149140	−	0.0598631i
$881$			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	0.997693	−	0.0678939i	$-0.0216279\pi$
$887$	390.323	+	676.059i	0.440048	+	0.762186i	−0.557644	+	0.830080i	$0.688295\pi$
$888$		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
$895$	1129.12	−	886.303i	1.26159	−	0.990283i
$896$	−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
$905$	348.859	+	444.435i	0.385479	+	0.491088i
$906$		0			0
$907$	454.663	+	262.500i	0.501283	+	0.289416i	0.729243	−	0.684255i	$-0.239872\pi$
$907$	454.663	+	262.500i	0.501283	+	0.289416i	−0.227960	+	0.973670i	$0.573206\pi$
$908$	−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	$-0.423478\pi$
$911$	−440.908	−	254.558i	−0.483983	−	0.279427i	−0.722075	+	0.691815i	$0.756811\pi$
$912$		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	$0.256705\pi$
$920$	−96.8501	+	241.288i	−0.105272	+	0.262270i
$921$		0			0
$922$	−540.400	+	312.000i	−0.586117	+	0.338395i
$923$	−31.8198	−	55.1135i	−0.0344743	−	0.0597113i
$924$		0			0
$925$	1578.50	+	385.958i	1.70649	+	0.417252i
$926$			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	$-0.430030\pi$
$929$	−481.325	−	277.893i	−0.518111	−	0.299131i	−0.736161	+	0.676806i	$0.763364\pi$
$930$		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
$940$	−349.282	−	444.974i	−0.371577	−	0.473377i
$941$	978.571	−	564.978i	1.03993	−	0.600402i	0.120114	−	0.992760i	$-0.461674\pi$
$941$	978.571	−	564.978i	1.03993	−	0.600402i	0.919813	+	0.392358i	$0.128341\pi$
$942$		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	−0.995127	−	0.0986061i	$-0.968562\pi$
$947$	−390.323	+	676.059i	−0.412168	+	0.713896i	0.582959	+	0.812502i	$0.301895\pi$
$948$		0			0
$949$	−892.500	−	1545.86i	−0.940464	−	1.62893i
$950$	76.6313	+	73.3324i	0.0806646	+	0.0771920i
$951$		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
$965$	−338.732	−	135.963i	−0.351017	−	0.140894i
$966$		0			0
$967$	−993.331	+	573.500i	−1.02723	+	0.593071i	−0.916190	−	0.400745i	$-0.868751\pi$
$967$	−993.331	+	573.500i	−1.02723	+	0.593071i	−0.111040	+	0.993816i	$0.535418\pi$
$968$	−100.409	−	173.914i	−0.103728	−	0.179663i
$969$		0			0
$970$	623.407	+	250.228i	0.642688	+	0.257967i
$971$		−	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	0.519885	−	0.854237i	$-0.325975\pi$
$977$	−468.812	−	812.006i	−0.479848	−	0.831122i	−0.999733	+	0.0231149i	$0.992642\pi$
$978$		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	−0.276305	−	0.961070i	$-0.589110\pi$
$983$	682.358	−	1181.88i	0.694159	−	1.20232i	0.970463	−	0.241248i	$-0.0775568\pi$
$984$		0			0
$985$	663.636	+	845.451i	0.673742	+	0.858326i
$986$	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
$995$	379.731	+	483.766i	0.381639	+	0.486197i
$996$		0			0
$997$	−1143.15	−	660.000i	−1.14659	−	0.661986i	−0.198539	−	0.980093i	$-0.563619\pi$
$997$	−1143.15	−	660.000i	−1.14659	−	0.661986i	−0.948055	+	0.318107i	$0.896953\pi$
$998$	−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.269.2		8
3.2	odd	2	inner	810.3.j.b.269.3		8
5.4	even	2	inner	810.3.j.b.269.4		8
9.2	odd	6		270.3.b.b.269.1	✓	4
9.4	even	3	inner	810.3.j.b.539.1		8
9.5	odd	6	inner	810.3.j.b.539.4		8
9.7	even	3		270.3.b.b.269.4	yes	4
15.14	odd	2	inner	810.3.j.b.269.1		8
36.7	odd	6		2160.3.c.j.1889.2		4
36.11	even	6		2160.3.c.j.1889.3		4
45.2	even	12		1350.3.d.j.701.1		2
45.4	even	6	inner	810.3.j.b.539.3		8
45.7	odd	12		1350.3.d.j.701.2		2
45.14	odd	6	inner	810.3.j.b.539.2		8
45.29	odd	6		270.3.b.b.269.3	yes	4
45.34	even	6		270.3.b.b.269.2	yes	4
45.38	even	12		1350.3.d.b.701.2		2
45.43	odd	12		1350.3.d.b.701.1		2
180.79	odd	6		2160.3.c.j.1889.4		4
180.119	even	6		2160.3.c.j.1889.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.3.b.b.269.1	✓	4	9.2	odd	6
270.3.b.b.269.2	yes	4	45.34	even	6
270.3.b.b.269.3	yes	4	45.29	odd	6
270.3.b.b.269.4	yes	4	9.7	even	3
810.3.j.b.269.1		8	15.14	odd	2	inner
810.3.j.b.269.2		8	1.1	even	1	trivial
810.3.j.b.269.3		8	3.2	odd	2	inner
810.3.j.b.269.4		8	5.4	even	2	inner
810.3.j.b.539.1		8	9.4	even	3	inner
810.3.j.b.539.2		8	45.14	odd	6	inner
810.3.j.b.539.3		8	45.4	even	6	inner
810.3.j.b.539.4		8	9.5	odd	6	inner
1350.3.d.b.701.1		2	45.43	odd	12
1350.3.d.b.701.2		2	45.38	even	12
1350.3.d.j.701.1		2	45.2	even	12
1350.3.d.j.701.2		2	45.7	odd	12
2160.3.c.j.1889.1		4	180.119	even	6
2160.3.c.j.1889.2		4	36.7	odd	6
2160.3.c.j.1889.3		4	36.11	even	6
2160.3.c.j.1889.4		4	180.79	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)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(3.08725 + 3.93305i) q^{5} +(9.52628 + 5.50000i) q^{7} +2.82843 q^{8} +O(q^{10})\)	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(3.08725 + 3.93305i) q^{5} +(9.52628 + 5.50000i) q^{7} +2.82843 q^{8} +(-7.00000 + 1.00000i) q^{10} +(6.12372 + 3.53553i) q^{11} +(-12.9904 + 7.50000i) q^{13} +(-13.4722 + 7.77817i) q^{14} +(-2.00000 + 3.46410i) q^{16} +22.6274 q^{17} -3.00000 q^{19} +(3.72500 - 9.28032i) q^{20} +(-8.66025 + 5.00000i) q^{22} +(9.19239 + 15.9217i) q^{23} +(-5.93782 + 24.2846i) q^{25} -21.2132i q^{26} -22.0000i q^{28} +(-11.0227 - 6.36396i) q^{29} +(4.00000 + 6.92820i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(-16.0000 + 27.7128i) q^{34} +(7.77817 + 54.4472i) q^{35} -65.0000i q^{37} +(2.12132 - 3.67423i) q^{38} +(8.73205 + 11.1244i) q^{40} +(67.3610 - 38.8909i) q^{41} +(-27.7128 - 16.0000i) q^{43} -14.1421i q^{44} -26.0000 q^{46} +(28.2843 - 48.9898i) q^{47} +(36.0000 + 62.3538i) q^{49} +(-25.5438 - 24.4441i) q^{50} +(25.9808 + 15.0000i) q^{52} +12.7279 q^{53} +(5.00000 + 35.0000i) q^{55} +(26.9444 + 15.5563i) q^{56} +(15.5885 - 9.00000i) q^{58} +(-68.5857 + 39.5980i) q^{59} +(-47.5000 + 82.2724i) q^{61} -11.3137 q^{62} +8.00000 q^{64} +(-69.6024 - 27.9375i) q^{65} +(-16.4545 + 9.50000i) q^{67} +(-22.6274 - 39.1918i) q^{68} +(-72.1840 - 28.9737i) q^{70} +4.24264i q^{71} +119.000i q^{73} +(79.6084 + 45.9619i) q^{74} +(3.00000 + 5.19615i) q^{76} +(38.8909 + 67.3610i) q^{77} +(-49.5000 + 85.7365i) q^{79} +(-19.7990 + 2.82843i) q^{80} +110.000i q^{82} +(-54.4472 + 94.3054i) q^{83} +(69.8564 + 88.9948i) q^{85} +(39.1918 - 22.6274i) q^{86} +(17.3205 + 10.0000i) q^{88} -90.5097i q^{89} -165.000 q^{91} +(18.3848 - 31.8434i) q^{92} +(40.0000 + 69.2820i) q^{94} +(-9.26174 - 11.7992i) q^{95} +(-82.2724 - 47.5000i) q^{97} -101.823 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4}+O(q^{10}) \) 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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