LMFDB - Embedded newform 810.3.j.f.539.4

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:	8.0.81622204416.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 14x^{6} + 165x^{4} - 434x^{2} + 961 $ x^8 - 14x^6 + 165x^4 - 434*x^2 + 961
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 270)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			539.4
Root			$1.43806 + 0.830265i$ of defining polynomial
Character	$\chi$	$=$	810.539
Dual form			810.3.j.f.269.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(4.24083 - 2.64865i) q^{5} +(-11.8534 + 6.84358i) q^{7} -2.82843 q^{8} +O(q^{10})$	\(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(4.24083 - 2.64865i) q^{5} +(-11.8534 + 6.84358i) q^{7} -2.82843 q^{8} +(6.24264 + 3.32106i) q^{10} +(10.6621 - 6.15576i) q^{11} +(-14.7295 - 8.50411i) q^{13} +(-16.7633 - 9.67828i) q^{14} +(-2.00000 - 3.46410i) q^{16} -6.89949 q^{17} -7.24264 q^{19} +(0.346763 + 9.99399i) q^{20} +(15.0785 + 8.70556i) q^{22} +(17.3995 - 30.1368i) q^{23} +(10.9693 - 22.4650i) q^{25} -24.0532i q^{26} -27.3743i q^{28} +(-18.3035 + 10.5675i) q^{29} +(19.1066 - 33.0936i) q^{31} +(2.82843 - 4.89898i) q^{32} +(-4.87868 - 8.45012i) q^{34} +(-32.1421 + 60.4180i) q^{35} +21.5380i q^{37} +(-5.12132 - 8.87039i) q^{38} +(-11.9949 + 7.49151i) q^{40} +(-31.4928 - 18.1824i) q^{41} +(-5.40331 + 3.11960i) q^{43} +24.6230i q^{44} +49.2132 q^{46} +(-20.1005 - 34.8151i) q^{47} +(69.1690 - 119.804i) q^{49} +(35.2703 - 2.45051i) q^{50} +(29.4591 - 17.0082i) q^{52} -38.2721 q^{53} +(28.9117 - 54.3457i) q^{55} +(33.5265 - 19.3566i) q^{56} +(-25.8851 - 14.9448i) q^{58} +(36.0537 + 20.8156i) q^{59} +(7.52944 + 13.0414i) q^{61} +54.0416 q^{62} +8.00000 q^{64} +(-84.9899 + 2.94891i) q^{65} +(-111.386 - 64.3089i) q^{67} +(6.89949 - 11.9503i) q^{68} +(-96.7246 + 3.35607i) q^{70} -104.967i q^{71} -2.11232i q^{73} +(-26.3786 + 15.2297i) q^{74} +(7.24264 - 12.5446i) q^{76} +(-84.2548 + 145.934i) q^{77} +(22.0477 + 38.1878i) q^{79} +(-17.6569 - 9.39338i) q^{80} -51.4275i q^{82} +(-27.5122 - 47.6525i) q^{83} +(-29.2596 + 18.2743i) q^{85} +(-7.64144 - 4.41179i) q^{86} +(-30.1569 + 17.4111i) q^{88} +68.1020i q^{89} +232.794 q^{91} +(34.7990 + 60.2736i) q^{92} +(28.4264 - 49.2360i) q^{94} +(-30.7148 + 19.1832i) q^{95} +(-87.6794 + 50.6217i) q^{97} +195.640 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} + 12 q^{5}+O(q^{10}) $ 8 * q - 8 * q^4 + 12 * q^5	$ 8 q - 8 q^{4} + 12 q^{5} + 16 q^{10} - 16 q^{16} + 24 q^{17} - 24 q^{19} + 24 q^{20} + 60 q^{23} + 12 q^{25} + 68 q^{31} - 56 q^{34} - 144 q^{35} - 24 q^{38} - 16 q^{40} + 224 q^{46} - 240 q^{47} + 180 q^{49} + 96 q^{50} - 408 q^{53} - 176 q^{55} + 196 q^{61} + 240 q^{62} + 64 q^{64} - 24 q^{65} - 24 q^{68} - 80 q^{70} + 24 q^{76} - 312 q^{77} - 180 q^{79} - 96 q^{80} + 108 q^{83} - 20 q^{85} + 912 q^{91} + 120 q^{92} - 112 q^{94} - 60 q^{95} + 1056 q^{98}+O(q^{100}) $ 8 * q - 8 * q^4 + 12 * q^5 + 16 * q^10 - 16 * q^16 + 24 * q^17 - 24 * q^19 + 24 * q^20 + 60 * q^23 + 12 * q^25 + 68 * q^31 - 56 * q^34 - 144 * q^35 - 24 * q^38 - 16 * q^40 + 224 * q^46 - 240 * q^47 + 180 * q^49 + 96 * q^50 - 408 * q^53 - 176 * q^55 + 196 * q^61 + 240 * q^62 + 64 * q^64 - 24 * q^65 - 24 * q^68 - 80 * q^70 + 24 * q^76 - 312 * q^77 - 180 * q^79 - 96 * q^80 + 108 * q^83 - 20 * q^85 + 912 * q^91 + 120 * q^92 - 112 * q^94 - 60 * q^95 + 1056 * q^98

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
$5$	4.24083	−	2.64865i	0.848166	−	0.529730i
$5$	4.24083	−	2.64865i	0.848166	−	0.529730i
$6$		0			0
$7$	−11.8534	+	6.84358i	−1.69335	+	0.977654i	−0.741562	+	0.670885i	$0.765915\pi$
$7$	−11.8534	+	6.84358i	−1.69335	+	0.977654i	−0.951784	+	0.306769i	$0.900752\pi$
$8$	−2.82843			−0.353553
$9$		0			0
$10$	6.24264	+	3.32106i	0.624264	+	0.332106i
$11$	10.6621	−	6.15576i	0.969281	−	0.559615i	0.0702641	−	0.997528i	$-0.477616\pi$
$11$	10.6621	−	6.15576i	0.969281	−	0.559615i	0.899017	+	0.437914i	$0.144282\pi$
$12$		0			0
$13$	−14.7295	−	8.50411i	−1.13304	−	0.654162i	−0.188344	−	0.982103i	$-0.560312\pi$
$13$	−14.7295	−	8.50411i	−1.13304	−	0.654162i	−0.944698	+	0.327941i	$0.893645\pi$
$14$	−16.7633	−	9.67828i	−1.19738	−	0.691306i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−6.89949			−0.405853			−0.202926	−	0.979194i	$-0.565045\pi$
$17$	−6.89949			−0.405853			−0.202926	+	0.979194i	$0.565045\pi$
$18$		0			0
$19$	−7.24264			−0.381192			−0.190596	−	0.981669i	$-0.561042\pi$
$19$	−7.24264			−0.381192			−0.190596	+	0.981669i	$0.561042\pi$
$20$	0.346763	+	9.99399i	0.0173381	+	0.499699i
$21$		0			0
$22$	15.0785	+	8.70556i	0.685385	+	0.395707i
$23$	17.3995	−	30.1368i	0.756500	−	1.31030i	−0.188125	−	0.982145i	$-0.560241\pi$
$23$	17.3995	−	30.1368i	0.756500	−	1.31030i	0.944625	−	0.328151i	$-0.106426\pi$
$24$		0			0
$25$	10.9693	−	22.4650i	0.438773	−	0.898598i
$26$		−	24.0532i		−	0.925125i
$27$		0			0
$28$		−	27.3743i		−	0.977654i
$29$	−18.3035	+	10.5675i	−0.631156	+	0.364398i	−0.781200	−	0.624281i	$-0.785392\pi$
$29$	−18.3035	+	10.5675i	−0.631156	+	0.364398i	0.150044	+	0.988679i	$0.452059\pi$
$30$		0			0
$31$	19.1066	−	33.0936i	0.616342	−	1.06754i	−0.373805	−	0.927507i	$-0.621947\pi$
$31$	19.1066	−	33.0936i	0.616342	−	1.06754i	0.990147	−	0.140029i	$-0.0447194\pi$
$32$	2.82843	−	4.89898i	0.0883883	−	0.153093i
$33$		0			0
$34$	−4.87868	−	8.45012i	−0.143491	−	0.248533i
$35$	−32.1421	+	60.4180i	−0.918347	+	1.72623i
$36$		0			0
$37$			21.5380i			0.582108i	0.956707	+	0.291054i	$0.0940060\pi$
$37$			21.5380i			0.582108i	−0.956707	+	0.291054i	$0.905994\pi$
$38$	−5.12132	−	8.87039i	−0.134772	−	0.233431i
$39$		0			0
$40$	−11.9949	+	7.49151i	−0.299872	+	0.187288i
$41$	−31.4928	−	18.1824i	−0.768117	−	0.443473i	0.0640853	−	0.997944i	$-0.479587\pi$
$41$	−31.4928	−	18.1824i	−0.768117	−	0.443473i	−0.832203	+	0.554472i	$0.812920\pi$
$42$		0			0
$43$	−5.40331	+	3.11960i	−0.125658	+	0.0725489i	−0.561512	−	0.827469i	$-0.689780\pi$
$43$	−5.40331	+	3.11960i	−0.125658	+	0.0725489i	0.435853	+	0.900018i	$0.356447\pi$
$44$			24.6230i			0.559615i
$45$		0			0
$46$	49.2132			1.06985
$47$	−20.1005	−	34.8151i	−0.427670	−	0.740747i	0.568995	−	0.822341i	$-0.307332\pi$
$47$	−20.1005	−	34.8151i	−0.427670	−	0.740747i	−0.996666	+	0.0815940i	$0.973999\pi$
$48$		0			0
$49$	69.1690	−	119.804i	1.41161	−	2.44499i
$50$	35.2703	−	2.45051i	0.705406	−	0.0490102i
$51$		0			0
$52$	29.4591	−	17.0082i	0.566521	−	0.327081i
$53$	−38.2721			−0.722115			−0.361057	−	0.932544i	$-0.617584\pi$
$53$	−38.2721			−0.722115			−0.361057	+	0.932544i	$0.617584\pi$
$54$		0			0
$55$	28.9117	−	54.3457i	0.525667	−	0.988103i
$56$	33.5265	−	19.3566i	0.598688	−	0.345653i
$57$		0			0
$58$	−25.8851	−	14.9448i	−0.446295	−	0.257668i
$59$	36.0537	+	20.8156i	0.611080	+	0.352807i	0.773388	−	0.633933i	$-0.218560\pi$
$59$	36.0537	+	20.8156i	0.611080	+	0.352807i	−0.162308	+	0.986740i	$0.551894\pi$
$60$		0			0
$61$	7.52944	+	13.0414i	0.123433	+	0.213793i	0.921119	−	0.389280i	$-0.127276\pi$
$61$	7.52944	+	13.0414i	0.123433	+	0.213793i	−0.797686	+	0.603073i	$0.793943\pi$
$62$	54.0416			0.871639
$63$		0			0
$64$	8.00000			0.125000
$65$	−84.9899	+	2.94891i	−1.30754	+	0.0453678i
$66$		0			0
$67$	−111.386	−	64.3089i	−1.66248	−	0.959834i	−0.971525	−	0.236937i	$-0.923856\pi$
$67$	−111.386	−	64.3089i	−1.66248	−	0.959834i	−0.690956	−	0.722897i	$-0.742810\pi$
$68$	6.89949	−	11.9503i	0.101463	−	0.175739i
$69$		0			0
$70$	−96.7246	+	3.35607i	−1.38178	+	0.0479438i
$71$		−	104.967i		−	1.47841i	−0.673478	−	0.739207i	$-0.735200\pi$
$71$		−	104.967i		−	1.47841i	0.673478	−	0.739207i	$-0.264800\pi$
$72$		0			0
$73$		−	2.11232i		−	0.0289359i	−0.999895	−	0.0144680i	$-0.995395\pi$
$73$		−	2.11232i		−	0.0289359i	0.999895	−	0.0144680i	$-0.00460546\pi$
$74$	−26.3786	+	15.2297i	−0.356467	+	0.205806i
$75$		0			0
$76$	7.24264	−	12.5446i	0.0952979	−	0.165061i
$77$	−84.2548	+	145.934i	−1.09422	+	1.89524i
$78$		0			0
$79$	22.0477	+	38.1878i	0.279085	+	0.483390i	0.971158	−	0.238438i	$-0.0766355\pi$
$79$	22.0477	+	38.1878i	0.279085	+	0.483390i	−0.692072	+	0.721828i	$0.743302\pi$
$80$	−17.6569	−	9.39338i	−0.220711	−	0.117417i
$81$		0			0
$82$		−	51.4275i		−	0.627165i
$83$	−27.5122	−	47.6525i	−0.331472	−	0.574127i	0.651329	−	0.758796i	$-0.274212\pi$
$83$	−27.5122	−	47.6525i	−0.331472	−	0.574127i	−0.982801	+	0.184669i	$0.940879\pi$
$84$		0			0
$85$	−29.2596	+	18.2743i	−0.344231	+	0.214992i
$86$	−7.64144	−	4.41179i	−0.0888539	−	0.0512998i
$87$		0			0
$88$	−30.1569	+	17.4111i	−0.342693	+	0.197854i
$89$			68.1020i			0.765191i	0.923916	+	0.382595i	$0.124970\pi$
$89$			68.1020i			0.765191i	−0.923916	+	0.382595i	$0.875030\pi$
$90$		0			0
$91$	232.794			2.55818
$92$	34.7990	+	60.2736i	0.378250	+	0.655148i
$93$		0			0
$94$	28.4264	−	49.2360i	0.302409	−	0.523787i
$95$	−30.7148	+	19.1832i	−0.323314	+	0.201929i
$96$		0			0
$97$	−87.6794	+	50.6217i	−0.903911	+	0.521873i	−0.878467	−	0.477803i	$-0.841433\pi$
$97$	−87.6794	+	50.6217i	−0.903911	+	0.521873i	−0.0254441	+	0.999676i	$0.508100\pi$
$98$	195.640			1.99632
$99$		0			0
$100$	27.9411	+	41.4644i	0.279411	+	0.414644i
$101$	−13.1893	+	7.61484i	−0.130587	+	0.0753944i	−0.563870	−	0.825863i	$-0.690688\pi$
$101$	−13.1893	+	7.61484i	−0.130587	+	0.0753944i	0.433283	+	0.901258i	$0.357355\pi$
$102$		0			0
$103$	66.7640	+	38.5462i	0.648194	+	0.374235i	0.787764	−	0.615977i	$-0.211239\pi$
$103$	66.7640	+	38.5462i	0.648194	+	0.374235i	−0.139570	+	0.990212i	$0.544572\pi$
$104$	41.6614	+	24.0532i	0.400591	+	0.231281i
$105$		0			0
$106$	−27.0624	−	46.8735i	−0.255306	−	0.442203i
$107$	78.4264			0.732957			0.366479	−	0.930427i	$-0.380563\pi$
$107$	78.4264			0.732957			0.366479	+	0.930427i	$0.380563\pi$
$108$		0			0
$109$	−146.279			−1.34201			−0.671006	−	0.741452i	$-0.734137\pi$
$109$	−146.279			−1.34201			−0.671006	+	0.741452i	$0.734137\pi$
$110$	87.0033	−	3.01876i	0.790939	−	0.0274433i
$111$		0			0
$112$	47.4137	+	27.3743i	0.423336	+	0.244413i
$113$	27.2132	−	47.1347i	0.240825	−	0.417121i	−0.720125	−	0.693845i	$-0.755915\pi$
$113$	27.2132	−	47.1347i	0.240825	−	0.417121i	0.960949	+	0.276724i	$0.0892487\pi$
$114$		0			0
$115$	−6.03350	−	173.890i	−0.0524652	−	1.51209i
$116$		−	42.2702i		−	0.364398i
$117$		0			0
$118$			58.8755i			0.498945i
$119$	81.7826	−	47.2172i	0.687249	−	0.396783i
$120$		0			0
$121$	15.2868	−	26.4775i	0.126337	−	0.218822i
$122$	−10.6482	+	18.4433i	−0.0872806	+	0.151174i
$123$		0			0
$124$	38.2132	+	66.1872i	0.308171	+	0.533768i
$125$	−12.9828	−	124.324i	−0.103862	−	0.994592i
$126$		0			0
$127$		−	159.215i		−	1.25366i	−0.779154	−	0.626832i	$-0.784351\pi$
$127$		−	159.215i		−	1.25366i	0.779154	−	0.626832i	$-0.215649\pi$
$128$	5.65685	+	9.79796i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−63.7086	−	102.006i	−0.490066	−	0.784660i
$131$	95.5252	+	55.1515i	0.729200	+	0.421004i	0.818130	−	0.575034i	$-0.195011\pi$
$131$	95.5252	+	55.1515i	0.729200	+	0.421004i	−0.0889293	+	0.996038i	$0.528345\pi$
$132$		0			0
$133$	85.8501	−	49.5656i	0.645489	−	0.372673i
$134$		−	181.893i		−	1.35741i
$135$		0			0
$136$	19.5147			0.143491
$137$	108.959	+	188.723i	0.795324	+	1.37754i	0.922633	+	0.385679i	$0.126033\pi$
$137$	108.959	+	188.723i	0.795324	+	1.37754i	−0.127309	+	0.991863i	$0.540634\pi$
$138$		0			0
$139$	53.1249	−	92.0150i	0.382193	−	0.661979i	−0.609182	−	0.793030i	$-0.708502\pi$
$139$	53.1249	−	92.0150i	0.382193	−	0.661979i	0.991376	+	0.131052i	$0.0418355\pi$
$140$	−72.5049	−	116.090i	−0.517892	−	0.829213i
$141$		0			0
$142$	128.558	−	74.2232i	0.905340	−	0.522698i
$143$	−209.397			−1.46431
$144$		0			0
$145$	−49.6325	+	93.2948i	−0.342293	+	0.643413i
$146$	2.58706	−	1.49364i	0.0177196	−	0.0102304i
$147$		0			0
$148$	−37.3049	−	21.5380i	−0.252060	−	0.145527i
$149$	12.2622	+	7.07960i	0.0822968	+	0.0475141i	0.540584	−	0.841290i	$-0.318203\pi$
$149$	12.2622	+	7.07960i	0.0822968	+	0.0475141i	−0.458287	+	0.888804i	$0.651537\pi$
$150$		0			0
$151$	−36.6690	−	63.5127i	−0.242841	−	0.420614i	0.718681	−	0.695340i	$-0.244746\pi$
$151$	−36.6690	−	63.5127i	−0.242841	−	0.420614i	−0.961522	+	0.274726i	$0.911413\pi$
$152$	20.4853			0.134772
$153$		0			0
$154$	−238.309			−1.54746
$155$	−6.62546	−	190.951i	−0.0427449	−	1.23194i
$156$		0			0
$157$	60.7475	+	35.0726i	0.386927	+	0.223392i	0.680828	−	0.732444i	$-0.261620\pi$
$157$	60.7475	+	35.0726i	0.386927	+	0.223392i	−0.293901	+	0.955836i	$0.594954\pi$
$158$	−31.1802	+	54.0057i	−0.197343	+	0.341808i
$159$		0			0
$160$	−0.980793	−	28.2673i	−0.00612996	−	0.176670i
$161$			476.299i			2.95838i
$162$		0			0
$163$		−	9.05959i		−	0.0555803i	−0.999614	−	0.0277902i	$-0.991153\pi$
$163$		−	9.05959i		−	0.0555803i	0.999614	−	0.0277902i	$-0.00884702\pi$
$164$	62.9856	−	36.3648i	0.384059	−	0.221736i
$165$		0			0
$166$	38.9081	−	67.3908i	0.234386	−	0.405969i
$167$	−31.9264	+	55.2982i	−0.191176	+	0.331127i	−0.945640	−	0.325215i	$-0.894563\pi$
$167$	−31.9264	+	55.2982i	−0.191176	+	0.331127i	0.754464	+	0.656341i	$0.227897\pi$
$168$		0			0
$169$	60.1396	+	104.165i	0.355856	+	0.616360i
$170$	−43.0711	−	22.9136i	−0.253359	−	0.134786i
$171$		0			0
$172$		−	12.4784i		−	0.0725489i
$173$	13.9939	+	24.2382i	0.0808896	+	0.140105i	0.903632	−	0.428309i	$-0.140891\pi$
$173$	13.9939	+	24.2382i	0.0808896	+	0.140105i	−0.822743	+	0.568414i	$0.807557\pi$
$174$		0			0
$175$	23.7167	+	341.356i	0.135524	+	1.95060i
$176$	−42.6484	−	24.6230i	−0.242320	−	0.139904i
$177$		0			0
$178$	−83.4075	+	48.1554i	−0.468582	+	0.270536i
$179$			21.0660i			0.117687i	0.998267	+	0.0588435i	$0.0187413\pi$
$179$			21.0660i			0.117687i	−0.998267	+	0.0588435i	$0.981259\pi$
$180$		0			0
$181$	53.6030			0.296149			0.148075	−	0.988976i	$-0.452692\pi$
$181$	53.6030			0.296149			0.148075	+	0.988976i	$0.452692\pi$
$182$	164.610	+	285.113i	0.904452	+	1.56656i
$183$		0			0
$184$	−49.2132	+	85.2398i	−0.267463	+	0.463260i
$185$	57.0466	+	91.3391i	0.308360	+	0.493725i
$186$		0			0
$187$	−73.5630	+	42.4716i	−0.393385	+	0.227121i
$188$	80.4020			0.427670
$189$		0			0
$190$	−45.2132	−	24.0532i	−0.237964	−	0.126596i
$191$	−193.144	+	111.512i	−1.01123	+	0.583831i	−0.911550	−	0.411189i	$-0.865114\pi$
$191$	−193.144	+	111.512i	−1.01123	+	0.583831i	−0.0996752	+	0.995020i	$0.531780\pi$
$192$		0			0
$193$	−152.614	−	88.1118i	−0.790746	−	0.456538i	0.0494788	−	0.998775i	$-0.484244\pi$
$193$	−152.614	−	88.1118i	−0.790746	−	0.456538i	−0.840225	+	0.542237i	$0.817577\pi$
$194$	−123.997	−	71.5899i	−0.639162	−	0.369020i
$195$		0			0
$196$	138.338	+	239.609i	0.705807	+	1.22249i
$197$	−277.586			−1.40906			−0.704532	−	0.709672i	$-0.748843\pi$
$197$	−277.586			−1.40906			−0.704532	+	0.709672i	$0.748843\pi$
$198$		0			0
$199$	71.5736			0.359666			0.179833	−	0.983697i	$-0.442444\pi$
$199$	71.5736			0.359666			0.179833	+	0.983697i	$0.442444\pi$
$200$	−31.0259	+	63.5405i	−0.155130	+	0.317702i
$201$		0			0
$202$	−18.6525	−	10.7690i	−0.0923389	−	0.0533119i
$203$	144.640	−	250.523i	0.712510	−	1.23410i
$204$		0			0
$205$	−181.714	+	6.30497i	−0.886412	+	0.0307560i
$206$			109.025i			0.529248i
$207$		0			0
$208$			68.0328i			0.327081i
$209$	−77.2217	+	44.5840i	−0.369482	+	0.213320i
$210$		0			0
$211$	−159.746	+	276.689i	−0.757091	+	1.31132i	0.187237	+	0.982315i	$0.440047\pi$
$211$	−159.746	+	276.689i	−0.757091	+	1.31132i	−0.944328	+	0.329005i	$0.893287\pi$
$212$	38.2721	−	66.2892i	0.180529	−	0.312685i
$213$		0			0
$214$	55.4558	+	96.0523i	0.259139	+	0.448843i
$215$	−14.6518	+	27.5412i	−0.0681479	+	0.128099i
$216$		0			0
$217$			523.030i			2.41028i
$218$	−103.435	−	179.155i	−0.474473	−	0.821811i
$219$		0			0
$220$	65.2178	+	104.422i	0.296445	+	0.474646i
$221$	101.626	+	58.6740i	0.459848	+	0.265493i
$222$		0			0
$223$	−140.676	+	81.2193i	−0.630834	+	0.364212i	−0.781075	−	0.624437i	$-0.785328\pi$
$223$	−140.676	+	81.2193i	−0.630834	+	0.364212i	0.150241	+	0.988649i	$0.451995\pi$
$224$			77.4262i			0.345653i
$225$		0			0
$226$	76.9706			0.340578
$227$	120.549	+	208.797i	0.531052	+	0.919809i	0.999343	+	0.0362347i	$0.0115364\pi$
$227$	120.549	+	208.797i	0.531052	+	0.919809i	−0.468291	+	0.883574i	$0.655130\pi$
$228$		0			0
$229$	−51.1102	+	88.5254i	−0.223189	+	0.386574i	−0.955774	−	0.294101i	$-0.904980\pi$
$229$	−51.1102	+	88.5254i	−0.223189	+	0.386574i	0.732586	+	0.680675i	$0.238313\pi$
$230$	208.705	−	130.349i	0.907413	−	0.566733i
$231$		0			0
$232$	51.7702	−	29.8895i	0.223147	−	0.128834i
$233$	−241.966			−1.03848			−0.519239	−	0.854629i	$-0.673785\pi$
$233$	−241.966			−1.03848			−0.519239	+	0.854629i	$0.673785\pi$
$234$		0			0
$235$	−177.456	−	94.4058i	−0.755131	−	0.401727i
$236$	−72.1075	+	41.6313i	−0.305540	+	0.176404i
$237$		0			0
$238$	115.658	+	66.7752i	0.485958	+	0.280568i
$239$	−325.157	−	187.729i	−1.36049	−	0.785478i	−0.370799	−	0.928713i	$-0.620916\pi$
$239$	−325.157	−	187.729i	−1.36049	−	0.785478i	−0.989689	+	0.143235i	$0.954250\pi$
$240$		0			0
$241$	159.140	+	275.638i	0.660330	+	1.14373i	0.980529	+	0.196375i	$0.0629171\pi$
$241$	159.140	+	275.638i	0.660330	+	1.14373i	−0.320198	+	0.947350i	$0.603750\pi$
$242$	43.2376			0.178668
$243$		0			0
$244$	−30.1177			−0.123433
$245$	−23.9853	−	691.274i	−0.0978990	−	2.82153i
$246$		0			0
$247$	106.681	+	61.5922i	0.431906	+	0.249361i
$248$	−54.0416	+	93.6028i	−0.217910	+	0.377431i
$249$		0			0
$250$	143.085	−	103.811i	0.572340	−	0.415244i
$251$		−	85.5417i		−	0.340804i	−0.985375	−	0.170402i	$-0.945493\pi$
$251$		−	85.5417i		−	0.340804i	0.985375	−	0.170402i	$-0.0545066\pi$
$252$		0			0
$253$		−	428.429i		−	1.69339i
$254$	194.998	−	112.582i	0.767709	−	0.443237i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−107.114	+	185.526i	−0.416785	+	0.721893i	−0.995614	−	0.0935562i	$-0.970177\pi$
$257$	−107.114	+	185.526i	−0.416785	+	0.721893i	0.578829	+	0.815449i	$0.303510\pi$
$258$		0			0
$259$	−147.397	−	255.299i	−0.569100	−	0.985711i
$260$	79.8823	−	150.156i	0.307239	−	0.577522i
$261$		0			0
$262$			155.992i			0.595389i
$263$	−53.4386	−	92.5584i	−0.203189	−	0.351933i	0.746365	−	0.665536i	$-0.231797\pi$
$263$	−53.4386	−	92.5584i	−0.203189	−	0.351933i	−0.949554	+	0.313603i	$0.898464\pi$
$264$		0			0
$265$	−162.305	+	101.369i	−0.612473	+	0.382526i
$266$	121.410	+	70.0963i	0.456430	+	0.263520i
$267$		0			0
$268$	222.772	−	128.618i	0.831241	−	0.479917i
$269$		−	365.927i		−	1.36032i	−0.733062	−	0.680161i	$-0.761910\pi$
$269$		−	365.927i		−	1.36032i	0.733062	−	0.680161i	$-0.238090\pi$
$270$		0			0
$271$	−92.8894			−0.342765			−0.171383	−	0.985205i	$-0.554823\pi$
$271$	−92.8894			−0.342765			−0.171383	+	0.985205i	$0.554823\pi$
$272$	13.7990	+	23.9006i	0.0507316	+	0.0878697i
$273$		0			0
$274$	−154.092	+	266.895i	−0.562379	+	0.974069i
$275$	−21.3331	−	307.048i	−0.0775747	−	1.11654i
$276$		0			0
$277$	195.841	−	113.069i	0.707006	−	0.408190i	−0.102946	−	0.994687i	$-0.532827\pi$
$277$	195.841	−	113.069i	0.707006	−	0.408190i	0.809951	+	0.586497i	$0.199493\pi$
$278$	150.260			0.540503
$279$		0			0
$280$	90.9117	−	170.888i	0.324685	−	0.610314i
$281$	54.9106	−	31.7026i	0.195411	−	0.112821i	−0.399102	−	0.916907i	$-0.630678\pi$
$281$	54.9106	−	31.7026i	0.195411	−	0.112821i	0.594513	+	0.804086i	$0.297345\pi$
$282$		0			0
$283$	314.459	+	181.553i	1.11116	+	0.641531i	0.939131	−	0.343560i	$-0.111633\pi$
$283$	314.459	+	181.553i	1.11116	+	0.641531i	0.172033	+	0.985091i	$0.444966\pi$
$284$	181.809	+	104.967i	0.640172	+	0.369604i
$285$		0			0
$286$	−148.066	−	256.458i	−0.517713	−	0.896706i
$287$	497.730			1.73425
$288$		0			0
$289$	−241.397			−0.835284
$290$	−149.358	+	5.18229i	−0.515027	+	0.0178700i
$291$		0			0
$292$	3.65865	+	2.11232i	0.0125296	+	0.00723398i
$293$	−113.717	+	196.963i	−0.388112	+	0.672229i	−0.992196	−	0.124691i	$-0.960206\pi$
$293$	−113.717	+	196.963i	−0.388112	+	0.672229i	0.604084	+	0.796921i	$0.293539\pi$
$294$		0			0
$295$	208.031	−	7.21808i	0.705190	−	0.0244681i
$296$		−	60.9187i		−	0.205806i
$297$		0			0
$298$			20.0241i			0.0671950i
$299$	−512.573	+	295.934i	−1.71429	+	0.989747i
$300$		0			0
$301$	42.6985	−	73.9559i	0.141855	−	0.245701i
$302$	51.8579	−	89.8205i	0.171715	−	0.297419i
$303$		0			0
$304$	14.4853	+	25.0892i	0.0476490	+	0.0825304i
$305$	66.4731	+	35.3634i	0.217945	+	0.115946i
$306$		0			0
$307$		−	340.164i		−	1.10803i	−0.832508	−	0.554013i	$-0.813096\pi$
$307$		−	340.164i		−	1.10803i	0.832508	−	0.554013i	$-0.186904\pi$
$308$	−168.510	−	291.867i	−0.547109	−	0.947621i
$309$		0			0
$310$	229.181	−	143.137i	0.739295	−	0.461733i
$311$	−334.951	−	193.384i	−1.07701	−	0.621815i	−0.146925	−	0.989148i	$-0.546938\pi$
$311$	−334.951	−	193.384i	−1.07701	−	0.621815i	−0.930089	+	0.367333i	$0.880271\pi$
$312$		0			0
$313$	325.974	−	188.201i	1.04145	−	0.601282i	0.121207	−	0.992627i	$-0.461323\pi$
$313$	325.974	−	188.201i	1.04145	−	0.601282i	0.920244	+	0.391345i	$0.127990\pi$
$314$			99.2002i			0.315924i
$315$		0			0
$316$	−88.1909			−0.279085
$317$	177.700	+	307.785i	0.560566	+	0.970929i	0.997447	+	0.0714099i	$0.0227499\pi$
$317$	177.700	+	307.785i	0.560566	+	0.970929i	−0.436881	+	0.899519i	$0.643917\pi$
$318$		0			0
$319$	−130.103	+	225.344i	−0.407845	+	0.706408i
$320$	33.9267	−	21.1892i	0.106021	−	0.0662162i
$321$		0			0
$322$	−583.345	+	336.794i	−1.81163	+	1.04594i
$323$	49.9706			0.154708
$324$		0			0
$325$	−352.617	+	237.614i	−1.08498	+	0.731121i
$326$	11.0957	−	6.40610i	0.0340359	−	0.0196506i
$327$		0			0
$328$	89.0751	+	51.4275i	0.271570	+	0.156791i
$329$	476.519	+	275.119i	1.44839	+	0.836227i
$330$		0			0
$331$	222.095	+	384.681i	0.670983	+	1.16218i	0.977626	+	0.210352i	$0.0674611\pi$
$331$	222.095	+	384.681i	0.670983	+	1.16218i	−0.306642	+	0.951825i	$0.599206\pi$
$332$	110.049			0.331472
$333$		0			0
$334$	−90.3015			−0.270364
$335$	−642.702	+	22.2999i	−1.91851	+	0.0665669i
$336$		0			0
$337$	352.547	+	203.543i	1.04613	+	0.603985i	0.921564	−	0.388226i	$-0.126912\pi$
$337$	352.547	+	203.543i	1.04613	+	0.603985i	0.124569	+	0.992211i	$0.460245\pi$
$338$	−85.0503	+	147.311i	−0.251628	+	0.435832i
$339$		0			0
$340$	−2.39249	−	68.9535i	−0.00703673	−	0.202804i
$341$		−	470.463i		−	1.37966i
$342$		0			0
$343$			1222.78i			3.56497i
$344$	15.2829	−	8.82357i	0.0444270	−	0.0256499i
$345$		0			0
$346$	−19.7904	+	34.2779i	−0.0571976	+	0.0990691i
$347$	−244.706	+	423.843i	−0.705204	+	1.22145i	0.261414	+	0.965227i	$0.415811\pi$
$347$	−244.706	+	423.843i	−0.705204	+	1.22145i	−0.966618	+	0.256222i	$0.917522\pi$
$348$		0			0
$349$	−40.8970	−	70.8356i	−0.117183	−	0.202967i	0.801467	−	0.598039i	$-0.204053\pi$
$349$	−40.8970	−	70.8356i	−0.117183	−	0.202967i	−0.918650	+	0.395071i	$0.870720\pi$
$350$	−401.304	+	270.422i	−1.14658	+	0.772634i
$351$		0			0
$352$		−	69.6445i		−	0.197854i
$353$	−125.693	−	217.707i	−0.356072	−	0.616735i	0.631229	−	0.775597i	$-0.282551\pi$
$353$	−125.693	−	217.707i	−0.356072	−	0.616735i	−0.987301	+	0.158862i	$0.949218\pi$
$354$		0			0
$355$	−278.022	−	445.149i	−0.783160	−	1.25394i
$356$	−117.956	−	68.1020i	−0.331337	−	0.191298i
$357$		0			0
$358$	−25.8004	+	14.8959i	−0.0720682	+	0.0416086i
$359$			518.500i			1.44429i	0.691742	+	0.722145i	$0.256844\pi$
$359$			518.500i			1.44429i	−0.691742	+	0.722145i	$0.743156\pi$
$360$		0			0
$361$	−308.544			−0.854693
$362$	37.9031	+	65.6500i	0.104705	+	0.181354i
$363$		0			0
$364$	−232.794	+	403.211i	−0.639544	+	1.10772i
$365$	−5.59480	−	8.95801i	−0.0153282	−	0.0245425i
$366$		0			0
$367$	296.166	−	170.992i	0.806992	−	0.465917i	−0.0389180	−	0.999242i	$-0.512391\pi$
$367$	296.166	−	170.992i	0.806992	−	0.465917i	0.845910	+	0.533325i	$0.179058\pi$
$368$	−139.196			−0.378250
$369$		0			0
$370$	−71.5290	+	134.454i	−0.193322	+	0.363389i
$371$	453.655	−	261.918i	1.22279	−	0.705978i
$372$		0			0
$373$	−95.5252	−	55.1515i	−0.256100	−	0.147859i	0.366454	−	0.930436i	$-0.380572\pi$
$373$	−95.5252	−	55.1515i	−0.256100	−	0.147859i	−0.622554	+	0.782577i	$0.713905\pi$
$374$	−104.034	−	60.0640i	−0.278165	−	0.160599i
$375$		0			0
$376$	56.8528	+	98.4720i	0.151204	+	0.261894i
$377$	359.470			0.953502
$378$		0			0
$379$	324.345			0.855792			0.427896	−	0.903828i	$-0.359255\pi$
$379$	324.345			0.855792			0.427896	+	0.903828i	$0.359255\pi$
$380$	−2.51148	−	72.3828i	−0.00660915	−	0.190481i
$381$		0			0
$382$	−273.147	−	157.701i	−0.715044	−	0.412831i
$383$	286.240	−	495.782i	0.747363	−	1.29447i	−0.201719	−	0.979443i	$-0.564653\pi$
$383$	286.240	−	495.782i	0.747363	−	1.29447i	0.949082	−	0.315028i	$-0.102014\pi$
$384$		0			0
$385$	29.2164	+	842.042i	0.0758869	+	2.18712i
$386$		−	249.218i		−	0.645642i
$387$		0			0
$388$		−	202.487i		−	0.521873i
$389$	624.981	−	360.833i	1.60664	−	0.927592i	0.616520	−	0.787339i	$-0.288542\pi$
$389$	624.981	−	360.833i	1.60664	−	0.927592i	0.990116	−	0.140253i	$-0.0447915\pi$
$390$		0			0
$391$	−120.048	+	207.929i	−0.307027	+	0.531787i
$392$	−195.640	+	338.858i	−0.499081	+	0.864433i
$393$		0			0
$394$	−196.283	−	339.972i	−0.498180	−	0.862873i
$395$	194.647	+	103.551i	0.492777	+	0.262155i
$396$		0			0
$397$		−	379.321i		−	0.955468i	−0.878505	−	0.477734i	$-0.841458\pi$
$397$		−	379.321i		−	0.955468i	0.878505	−	0.477734i	$-0.158542\pi$
$398$	50.6102	+	87.6594i	0.127161	+	0.220250i
$399$		0			0
$400$	−99.7595	+	6.93108i	−0.249399	+	0.0173277i
$401$	303.952	+	175.487i	0.757985	+	0.437623i	0.828572	−	0.559883i	$-0.189154\pi$
$401$	303.952	+	175.487i	0.757985	+	0.437623i	−0.0705866	+	0.997506i	$0.522487\pi$
$402$		0			0
$403$	−562.863	+	324.969i	−1.39668	+	0.806375i
$404$		−	30.4593i		−	0.0753944i
$405$		0			0
$406$	409.103			1.00764
$407$	132.583	+	229.640i	0.325756	+	0.564227i
$408$		0			0
$409$	266.713	−	461.961i	0.652111	−	1.12949i	−0.330499	−	0.943806i	$-0.607217\pi$
$409$	266.713	−	461.961i	0.652111	−	1.12949i	0.982610	−	0.185682i	$-0.0594495\pi$
$410$	−136.214	−	218.096i	−0.332228	−	0.531940i
$411$		0			0
$412$	−133.528	+	77.0924i	−0.324097	+	0.187118i
$413$	−569.813			−1.37969
$414$		0			0
$415$	−242.889	−	129.216i	−0.585276	−	0.311364i
$416$	−83.3229	+	48.1065i	−0.200295	+	0.115641i
$417$		0			0
$418$	−109.208	−	63.0513i	−0.261263	−	0.150840i
$419$	207.634	+	119.878i	0.495547	+	0.286104i	0.726873	−	0.686772i	$-0.240973\pi$
$419$	207.634	+	119.878i	0.495547	+	0.286104i	−0.231326	+	0.972876i	$0.574306\pi$
$420$		0			0
$421$	−212.471	−	368.010i	−0.504681	−	0.874133i	−0.999985	−	0.00541323i	$-0.998277\pi$
$421$	−212.471	−	368.010i	−0.504681	−	0.874133i	0.495305	−	0.868719i	$-0.335056\pi$
$422$	−451.831			−1.07069
$423$		0			0
$424$	108.250			0.255306
$425$	−75.6827	+	154.997i	−0.178077	+	0.364698i
$426$		0			0
$427$	−178.499	−	103.057i	−0.418031	−	0.241350i
$428$	−78.4264	+	135.839i	−0.183239	+	0.317380i
$429$		0			0
$430$	−44.0913	+	1.52984i	−0.102538	+	0.00355777i
$431$		−	544.039i		−	1.26227i	−0.775673	−	0.631135i	$-0.782589\pi$
$431$		−	544.039i		−	1.26227i	0.775673	−	0.631135i	$-0.217411\pi$
$432$		0			0
$433$		−	602.735i		−	1.39200i	−0.718043	−	0.695999i	$-0.754962\pi$
$433$		−	602.735i		−	1.39200i	0.718043	−	0.695999i	$-0.245038\pi$
$434$	−640.578	+	369.838i	−1.47599	+	0.852161i
$435$		0			0
$436$	146.279	−	253.363i	0.335503	−	0.581108i
$437$	−126.018	+	218.270i	−0.288371	+	0.499474i
$438$		0			0
$439$	−201.143	−	348.390i	−0.458185	−	0.793600i	0.540680	−	0.841228i	$-0.318167\pi$
$439$	−201.143	−	348.390i	−0.458185	−	0.793600i	−0.998865	+	0.0476287i	$0.984834\pi$
$440$	−81.7746	+	153.713i	−0.185851	+	0.349347i
$441$		0			0
$442$			165.955i			0.375464i
$443$	219.257	+	379.765i	0.494938	+	0.857257i	0.999983	−	0.00583572i	$-0.00185758\pi$
$443$	219.257	+	379.765i	0.494938	+	0.857257i	−0.505045	+	0.863093i	$0.668524\pi$
$444$		0			0
$445$	180.378	+	288.809i	0.405344	+	0.649009i
$446$	−198.946	−	114.861i	−0.446067	−	0.257537i
$447$		0			0
$448$	−94.8274	+	54.7486i	−0.211668	+	0.122207i
$449$			670.866i			1.49413i	0.664749	+	0.747067i	$0.268538\pi$
$449$			670.866i			1.49413i	−0.664749	+	0.747067i	$0.731462\pi$
$450$		0			0
$451$	−447.706			−0.992695
$452$	54.4264	+	94.2693i	0.120412	+	0.208560i
$453$		0			0
$454$	−170.482	+	295.283i	−0.375510	+	0.650403i
$455$	987.240	−	616.589i	2.16976	−	1.35514i
$456$		0			0
$457$	601.913	−	347.514i	1.31710	−	0.760425i	0.333835	−	0.942632i	$-0.391657\pi$
$457$	601.913	−	347.514i	1.31710	−	0.760425i	0.983260	+	0.182206i	$0.0583238\pi$
$458$	−144.561			−0.315636
$459$		0			0
$460$	307.220	+	163.440i	0.667870	+	0.355304i
$461$	11.3352	−	6.54436i	0.0245882	−	0.0141960i	−0.487656	−	0.873036i	$-0.662148\pi$
$461$	11.3352	−	6.54436i	0.0245882	−	0.0141960i	0.512244	+	0.858840i	$0.328814\pi$
$462$		0			0
$463$	−202.894	−	117.141i	−0.438215	−	0.253004i	0.264625	−	0.964351i	$-0.414752\pi$
$463$	−202.894	−	117.141i	−0.438215	−	0.253004i	−0.702840	+	0.711348i	$0.748085\pi$
$464$	73.2141	+	42.2702i	0.157789	+	0.0910995i
$465$		0			0
$466$	−171.095	−	296.346i	−0.367158	−	0.635936i
$467$	742.882			1.59075			0.795377	−	0.606115i	$-0.207273\pi$
$467$	742.882			1.59075			0.795377	+	0.606115i	$0.207273\pi$
$468$		0			0
$469$	1760.41			3.75354
$470$	−9.85722	−	284.093i	−0.0209728	−	0.604453i
$471$		0			0
$472$	−101.975	−	58.8755i	−0.216049	−	0.124736i
$473$	−38.4071	+	66.5230i	−0.0811989	+	0.140641i
$474$		0			0
$475$	−79.4468	+	162.706i	−0.167256	+	0.342538i
$476$			188.869i			0.396783i
$477$		0			0
$478$		−	530.978i		−	1.11083i
$479$	387.469	−	223.705i	0.808913	−	0.467026i	−0.0376655	−	0.999290i	$-0.511992\pi$
$479$	387.469	−	223.705i	0.808913	−	0.467026i	0.846578	+	0.532264i	$0.178659\pi$
$480$		0			0
$481$	183.161	−	317.245i	0.380793	−	0.659553i
$482$	−225.057	+	389.811i	−0.466924	+	0.808736i
$483$		0			0
$484$	30.5736	+	52.9550i	0.0631686	+	0.109411i
$485$	−237.754	+	446.910i	−0.490215	+	0.921464i
$486$		0			0
$487$		−	50.3166i		−	0.103319i	−0.998665	−	0.0516597i	$-0.983549\pi$
$487$		−	50.3166i		−	0.103319i	0.998665	−	0.0516597i	$-0.0164511\pi$
$488$	−21.2965	−	36.8866i	−0.0436403	−	0.0755872i
$489$		0			0
$490$	829.675	−	518.181i	1.69321	−	1.05751i
$491$	−684.707	−	395.316i	−1.39452	−	0.805124i	−0.400704	−	0.916208i	$-0.631234\pi$
$491$	−684.707	−	395.316i	−1.39452	−	0.805124i	−0.993811	+	0.111084i	$0.964568\pi$
$492$		0			0
$493$	126.285	−	72.9107i	0.256156	−	0.147892i
$494$			174.209i			0.352650i
$495$		0			0
$496$	−152.853			−0.308171
$497$	718.352	+	1244.22i	1.44538	+	2.50347i
$498$		0			0
$499$	300.195	−	519.953i	0.601593	−	1.04199i	−0.390987	−	0.920396i	$-0.627866\pi$
$499$	300.195	−	519.953i	0.601593	−	1.04199i	0.992580	−	0.121593i	$-0.0388004\pi$
$500$	228.318	+	101.837i	0.456636	+	0.203674i
$501$		0			0
$502$	104.767	−	60.4871i	0.208699	−	0.120492i
$503$	433.368			0.861566			0.430783	−	0.902456i	$-0.358237\pi$
$503$	433.368			0.861566			0.430783	+	0.902456i	$0.358237\pi$
$504$		0			0
$505$	−35.7645	+	67.2270i	−0.0708208	+	0.133123i
$506$	524.716	−	302.945i	1.03699	−	0.598705i
$507$		0			0
$508$	275.769	+	159.215i	0.542852	+	0.313416i
$509$	−832.870	−	480.857i	−1.63629	−	0.944710i	−0.982096	−	0.188380i	$-0.939676\pi$
$509$	−832.870	−	480.857i	−1.63629	−	0.944710i	−0.654190	−	0.756331i	$-0.726990\pi$
$510$		0			0
$511$	14.4558	+	25.0383i	0.0282893	+	0.0489985i
$512$	−22.6274			−0.0441942
$513$		0			0
$514$	−302.963			−0.589423
$515$	385.230	−	13.3664i	0.748020	−	0.0259542i
$516$		0			0
$517$	−428.627	−	247.468i	−0.829065	−	0.478661i
$518$	208.451	−	361.047i	0.402415	−	0.697003i
$519$		0			0
$520$	240.388	−	8.34077i	0.462284	−	0.0160399i
$521$			5.90542i			0.0113348i	0.999984	+	0.00566739i	$0.00180400\pi$
$521$			5.90542i			0.0113348i	−0.999984	+	0.00566739i	$0.998196\pi$
$522$		0			0
$523$		−	165.846i		−	0.317104i	−0.987351	−	0.158552i	$-0.949317\pi$
$523$		−	165.846i		−	0.317104i	0.987351	−	0.158552i	$-0.0506826\pi$
$524$	−191.050	+	110.303i	−0.364600	+	0.210502i
$525$		0			0
$526$	75.5736	−	130.897i	0.143676	−	0.248854i
$527$	−131.826	+	228.329i	−0.250144	+	0.433262i
$528$		0			0
$529$	−340.985	−	590.603i	−0.644584	−	1.11645i
$530$	−238.919	−	127.104i	−0.450790	−	0.239819i
$531$		0			0
$532$			198.262i			0.372673i
$533$	309.250	+	535.636i	0.580206	+	1.00495i
$534$		0			0
$535$	332.593	−	207.724i	0.621670	−	0.388269i
$536$	315.048	+	181.893i	0.587776	+	0.339353i
$537$		0			0
$538$	448.167	−	258.749i	0.833024	−	0.480947i
$539$		−	1703.15i		−	3.15984i
$540$		0			0
$541$	216.985			0.401081			0.200541	−	0.979685i	$-0.435730\pi$
$541$	216.985			0.401081			0.200541	+	0.979685i	$0.435730\pi$
$542$	−65.6827	−	113.766i	−0.121186	−	0.209900i
$543$		0			0
$544$	−19.5147	+	33.8005i	−0.0358726	+	0.0621332i
$545$	−620.346	+	387.442i	−1.13825	+	0.710903i
$546$		0			0
$547$	−87.1611	+	50.3225i	−0.159344	+	0.0919973i	−0.577552	−	0.816354i	$-0.695992\pi$
$547$	−87.1611	+	50.3225i	−0.159344	+	0.0919973i	0.418208	+	0.908351i	$0.362658\pi$
$548$	−435.838			−0.795324
$549$		0			0
$550$	360.971	−	243.243i	0.656310	−	0.442260i
$551$	132.566	−	76.5369i	0.240591	−	0.138906i
$552$		0			0
$553$	−522.682	−	301.771i	−0.945175	−	0.545697i
$554$	276.960	+	159.903i	0.499928	+	0.288634i
$555$		0			0
$556$	106.250	+	184.030i	0.191097	+	0.330989i
$557$	−116.662			−0.209447			−0.104723	−	0.994501i	$-0.533396\pi$
$557$	−116.662			−0.209447			−0.104723	+	0.994501i	$0.533396\pi$
$558$		0			0
$559$	106.118			0.189835
$560$	273.578	−	9.49239i	0.488533	−	0.0169507i
$561$		0			0
$562$	77.6553	+	44.8343i	0.138177	+	0.0797763i
$563$	266.953	−	462.377i	0.474162	−	0.821273i	−0.525400	−	0.850855i	$-0.676084\pi$
$563$	266.953	−	462.377i	0.474162	−	0.821273i	0.999562	+	0.0295822i	$0.00941769\pi$
$564$		0			0
$565$	−9.43653	−	271.968i	−0.0167018	−	0.481360i
$566$			513.510i			0.907262i
$567$		0			0
$568$			296.893i			0.522698i
$569$	−97.5590	+	56.3257i	−0.171457	+	0.0989907i	−0.583273	−	0.812276i	$-0.698228\pi$
$569$	−97.5590	+	56.3257i	−0.171457	+	0.0989907i	0.411816	+	0.911267i	$0.364895\pi$
$570$		0			0
$571$	430.768	−	746.111i	0.754409	−	1.30668i	−0.191258	−	0.981540i	$-0.561257\pi$
$571$	430.768	−	746.111i	0.754409	−	1.30668i	0.945668	−	0.325135i	$-0.105410\pi$
$572$	209.397	−	362.686i	0.366079	−	0.634067i
$573$		0			0
$574$	351.948	+	609.592i	0.613150	+	1.06201i
$575$	−486.161	−	721.459i	−0.845498	−	1.25471i
$576$		0			0
$577$		−	37.3256i		−	0.0646891i	−0.999477	−	0.0323446i	$-0.989703\pi$
$577$		−	37.3256i		−	0.0646891i	0.999477	−	0.0323446i	$-0.0102974\pi$
$578$	−170.693	−	295.650i	−0.295317	−	0.511505i
$579$		0			0
$580$	−111.959	−	179.261i	−0.193033	−	0.309070i
$581$	652.227	+	376.564i	1.12259	+	0.648130i
$582$		0			0
$583$	−408.060	+	235.594i	−0.699932	+	0.404106i
$584$			5.97455i			0.0102304i
$585$		0			0
$586$	−321.640			−0.548873
$587$	−269.051	−	466.011i	−0.458350	−	0.793885i	0.540524	−	0.841328i	$-0.318226\pi$
$587$	−269.051	−	466.011i	−0.458350	−	0.793885i	−0.998874	+	0.0474434i	$0.984893\pi$
$588$		0			0
$589$	−138.382	+	239.685i	−0.234944	+	0.406936i
$590$	155.941	+	249.681i	0.264306	+	0.423188i
$591$		0			0
$592$	74.6098	−	43.0760i	0.126030	−	0.0727635i
$593$	884.169			1.49101			0.745505	−	0.666500i	$-0.232208\pi$
$593$	884.169			1.49101			0.745505	+	0.666500i	$0.232208\pi$
$594$		0			0
$595$	221.765	−	416.854i	0.372713	−	0.700595i
$596$	−24.5244	+	14.1592i	−0.0411484	+	0.0237570i
$597$		0			0
$598$	−724.888	−	418.514i	−1.21219	−	0.699857i
$599$	38.7750	+	22.3868i	0.0647330	+	0.0373736i	0.532017	−	0.846734i	$-0.321434\pi$
$599$	38.7750	+	22.3868i	0.0647330	+	0.0373736i	−0.467284	+	0.884107i	$0.654768\pi$
$600$		0			0
$601$	−197.287	−	341.711i	−0.328264	−	0.568570i	0.653903	−	0.756578i	$-0.273130\pi$
$601$	−197.287	−	341.711i	−0.328264	−	0.568570i	−0.982168	+	0.188008i	$0.939797\pi$
$602$	120.770			0.200614
$603$		0			0
$604$	146.676			0.242841
$605$	−5.30089	−	152.776i	−0.00876181	−	0.252522i
$606$		0			0
$607$	186.345	+	107.586i	0.306993	+	0.177243i	0.645580	−	0.763692i	$-0.276616\pi$
$607$	186.345	+	107.586i	0.306993	+	0.177243i	−0.338587	+	0.940935i	$0.609949\pi$
$608$	−20.4853	+	35.4815i	−0.0336929	+	0.0583578i
$609$		0			0
$610$	3.69241	+	106.418i	0.00605313	+	0.174456i
$611$			683.747i			1.11906i
$612$		0			0
$613$		−	333.937i		−	0.544758i	−0.962190	−	0.272379i	$-0.912189\pi$
$613$		−	333.937i		−	0.544758i	0.962190	−	0.272379i	$-0.0878105\pi$
$614$	416.614	−	240.532i	0.678525	−	0.391747i
$615$		0			0
$616$	238.309	−	412.763i	0.386865	−	0.670069i
$617$	−32.7117	+	56.6584i	−0.0530174	+	0.0918288i	−0.891316	−	0.453382i	$-0.850217\pi$
$617$	−32.7117	+	56.6584i	−0.0530174	+	0.0918288i	0.838299	+	0.545211i	$0.183551\pi$
$618$		0			0
$619$	9.96342	+	17.2571i	0.0160960	+	0.0278791i	0.873961	−	0.485996i	$-0.161543\pi$
$619$	9.96342	+	17.2571i	0.0160960	+	0.0278791i	−0.857865	+	0.513875i	$0.828210\pi$
$620$	337.362	+	179.475i	0.544133	+	0.289477i
$621$		0			0
$622$		−	546.973i		−	0.879379i
$623$	−466.061	−	807.241i	−0.748091	−	1.29573i
$624$		0			0
$625$	−384.348	−	492.850i	−0.614957	−	0.788560i
$626$	460.997	+	266.157i	0.736417	+	0.425171i
$627$		0			0
$628$	−121.495	+	70.1452i	−0.193463	+	0.111696i
$629$		−	148.601i		−	0.236250i
$630$		0			0
$631$	−210.625			−0.333796			−0.166898	−	0.985974i	$-0.553375\pi$
$631$	−210.625			−0.333796			−0.166898	+	0.985974i	$0.553375\pi$
$632$	−62.3604	−	108.011i	−0.0986715	−	0.170904i
$633$		0			0
$634$	−251.305	+	435.273i	−0.396380	+	0.686551i
$635$	−421.706	−	675.206i	−0.664103	−	1.06332i
$636$		0			0
$637$	−2037.66	+	1176.44i	−3.19883	+	1.84685i
$638$	−367.986			−0.576780
$639$		0			0
$640$	49.9411	+	26.5685i	0.0780330	+	0.0415132i
$641$	−1019.97	+	588.881i	−1.59122	+	0.918692i	−0.598122	+	0.801405i	$0.704086\pi$
$641$	−1019.97	+	588.881i	−1.59122	+	0.918692i	−0.993098	+	0.117287i	$0.962580\pi$
$642$		0			0
$643$	−32.5995	−	18.8213i	−0.0506990	−	0.0292711i	0.474436	−	0.880290i	$-0.342652\pi$
$643$	−32.5995	−	18.8213i	−0.0506990	−	0.0292711i	−0.525135	+	0.851019i	$0.675985\pi$
$644$	−824.974	−	476.299i	−1.28102	−	0.739595i
$645$		0			0
$646$	35.3345	+	61.2012i	0.0546974	+	0.0947387i
$647$	695.382			1.07478			0.537389	−	0.843334i	$-0.319411\pi$
$647$	695.382			1.07478			0.537389	+	0.843334i	$0.319411\pi$
$648$		0			0
$649$	512.544			0.789744
$650$	−540.355	−	263.848i	−0.831315	−	0.405919i
$651$		0			0
$652$	15.6917	+	9.05959i	0.0240670	+	0.0138951i
$653$	−462.148	+	800.464i	−0.707731	+	1.22583i	0.257966	+	0.966154i	$0.416948\pi$
$653$	−462.148	+	800.464i	−0.707731	+	1.22583i	−0.965697	+	0.259672i	$0.916386\pi$
$654$		0			0
$655$	551.183	−	19.1245i	0.841501	−	0.0291977i
$656$			145.459i			0.221736i
$657$		0			0
$658$			778.153i			1.18260i
$659$	58.6043	−	33.8352i	0.0889291	−	0.0513433i	−0.454876	−	0.890555i	$-0.650316\pi$
$659$	58.6043	−	33.8352i	0.0889291	−	0.0513433i	0.543805	+	0.839212i	$0.316983\pi$
$660$		0			0
$661$	−516.434	+	894.489i	−0.781291	+	1.35324i	0.149898	+	0.988701i	$0.452105\pi$
$661$	−516.434	+	894.489i	−0.781291	+	1.35324i	−0.931190	+	0.364535i	$0.881228\pi$
$662$	−314.090	+	544.021i	−0.474457	+	0.821783i
$663$		0			0
$664$	77.8162	+	134.782i	0.117193	+	0.202984i
$665$	232.794	−	437.586i	0.350066	−	0.658024i
$666$		0			0
$667$			735.480i			1.10267i
$668$	−63.8528	−	110.596i	−0.0955880	−	0.165563i
$669$		0			0
$670$	−481.771	−	771.377i	−0.719061	−	1.15131i
$671$	160.559	+	92.6988i	0.239283	+	0.138150i
$672$		0			0
$673$	−8.80797	+	5.08528i	−0.0130876	+	0.00755614i	−0.506530	−	0.862223i	$-0.669072\pi$
$673$	−8.80797	+	5.08528i	−0.0130876	+	0.00755614i	0.493442	+	0.869779i	$0.335739\pi$
$674$			575.707i			0.854164i
$675$		0			0
$676$	−240.558			−0.355856
$677$	288.468	+	499.641i	0.426098	+	0.738023i	0.996522	−	0.0833273i	$-0.0265547\pi$
$677$	288.468	+	499.641i	0.426098	+	0.738023i	−0.570425	+	0.821350i	$0.693221\pi$
$678$		0			0
$679$	692.867	−	1200.08i	1.02042	−	1.76742i
$680$	82.7586	−	51.6876i	0.121704	−	0.0760112i
$681$		0			0
$682$	576.197	−	332.667i	0.844863	−	0.487782i
$683$	526.009			0.770145			0.385073	−	0.922886i	$-0.374176\pi$
$683$	526.009			0.770145			0.385073	+	0.922886i	$0.374176\pi$
$684$		0			0
$685$	961.940	+	511.748i	1.40429	+	0.747078i
$686$	−1497.60	+	864.639i	−2.18309	+	1.26041i
$687$		0			0
$688$	21.6132	+	12.4784i	0.0314146	+	0.0181372i
$689$	563.730	+	325.470i	0.818186	+	0.472380i
$690$		0			0
$691$	−211.452	−	366.245i	−0.306008	−	0.530022i	0.671477	−	0.741025i	$-0.265660\pi$
$691$	−211.452	−	366.245i	−0.306008	−	0.530022i	−0.977485	+	0.211003i	$0.932327\pi$
$692$	−55.9756			−0.0808896
$693$		0			0
$694$	−692.132			−0.997308
$695$	−18.4217	−	530.929i	−0.0265061	−	0.763927i
$696$		0			0
$697$	217.284	+	125.449i	0.311742	+	0.179985i
$698$	57.8370	−	100.177i	0.0828611	−	0.143520i
$699$		0			0
$700$	−614.962	−	300.277i	−0.878518	−	0.428968i
$701$			881.146i			1.25698i	0.777816	+	0.628492i	$0.216328\pi$
$701$			881.146i			1.25698i	−0.777816	+	0.628492i	$0.783672\pi$
$702$		0			0
$703$		−	155.992i		−	0.221895i
$704$	85.2967	−	49.2461i	0.121160	−	0.0699518i
$705$		0			0
$706$	177.757	−	307.885i	0.251781	−	0.436097i
$707$	104.225	−	180.524i	0.147419	−	0.255338i
$708$		0			0
$709$	−50.7136	−	87.8386i	−0.0715284	−	0.123891i	0.828043	−	0.560665i	$-0.189454\pi$
$709$	−50.7136	−	87.8386i	−0.0715284	−	0.123891i	−0.899571	+	0.436774i	$0.856121\pi$
$710$	348.603	−	655.274i	0.490990	−	0.922921i
$711$		0			0
$712$		−	192.621i		−	0.270536i
$713$	−664.890	−	1151.62i	−0.932525	−	1.61518i
$714$		0			0
$715$	−888.017	+	554.619i	−1.24198	+	0.775691i
$716$	−36.4873	−	21.0660i	−0.0509599	−	0.0294217i
$717$		0			0
$718$	−635.030	+	366.635i	−0.884443	+	0.510634i
$719$			36.2956i			0.0504807i	0.999681	+	0.0252404i	$0.00803511\pi$
$719$			36.2956i			0.0504807i	−0.999681	+	0.0252404i	$0.991965\pi$
$720$		0			0
$721$	−1055.18			−1.46349
$722$	−218.174	−	377.888i	−0.302180	−	0.523390i
$723$		0			0
$724$	−53.6030	+	92.8432i	−0.0740373	+	0.128236i
$725$	36.6223	+	527.107i	0.0505135	+	0.727044i
$726$		0			0
$727$	457.049	−	263.878i	0.628679	−	0.362968i	−0.151561	−	0.988448i	$-0.548430\pi$
$727$	457.049	−	263.878i	0.628679	−	0.362968i	0.780240	+	0.625480i	$0.215097\pi$
$728$	−658.441			−0.904452
$729$		0			0
$730$	7.01515	−	13.1865i	0.00960980	−	0.0180637i
$731$	37.2801	−	21.5237i	0.0509988	−	0.0294442i
$732$		0			0
$733$	1130.97	+	652.966i	1.54293	+	0.890813i	0.998652	+	0.0519106i	$0.0165311\pi$
$733$	1130.97	+	652.966i	1.54293	+	0.890813i	0.544282	+	0.838902i	$0.316802\pi$
$734$	418.842	+	241.819i	0.570630	+	0.329453i
$735$		0			0
$736$	−98.4264	−	170.480i	−0.133732	−	0.231630i
$737$	−1583.48			−2.14855
$738$		0			0
$739$	754.875			1.02148			0.510741	−	0.859735i	$-0.329371\pi$
$739$	754.875			1.02148			0.510741	+	0.859735i	$0.329371\pi$
$740$	−215.251	+	7.46858i	−0.290879	+	0.0100927i
$741$		0			0
$742$	641.565	+	370.408i	0.864643	+	0.499202i
$743$	656.294	−	1136.73i	0.883302	−	1.52992i	0.0356548	−	0.999364i	$-0.488648\pi$
$743$	656.294	−	1136.73i	0.883302	−	1.52992i	0.847647	−	0.530560i	$-0.178018\pi$
$744$		0			0
$745$	70.7534	−	2.45494i	0.0949710	−	0.00329522i
$746$		−	155.992i		−	0.209105i
$747$		0			0
$748$		−	169.887i		−	0.227121i
$749$	−929.621	+	536.717i	−1.24115	+	0.716578i
$750$		0			0
$751$	−616.216	+	1067.32i	−0.820528	+	1.42120i	0.0847620	+	0.996401i	$0.472987\pi$
$751$	−616.216	+	1067.32i	−0.820528	+	1.42120i	−0.905290	+	0.424795i	$0.860346\pi$
$752$	−80.4020	+	139.260i	−0.106918	+	0.185187i
$753$		0			0
$754$	254.184	+	440.259i	0.337114	+	0.583898i
$755$	−323.730	−	172.223i	−0.428781	−	0.228110i
$756$		0			0
$757$		−	401.164i		−	0.529939i	−0.964257	−	0.264970i	$-0.914638\pi$
$757$		−	401.164i		−	0.529939i	0.964257	−	0.264970i	$-0.0853619\pi$
$758$	229.347	+	397.240i	0.302568	+	0.524064i
$759$		0			0
$760$	86.8746	−	54.2583i	0.114309	−	0.0713925i
$761$	−454.776	−	262.565i	−0.597603	−	0.345027i	0.170495	−	0.985359i	$-0.445463\pi$
$761$	−454.776	−	262.565i	−0.597603	−	0.345027i	−0.768098	+	0.640332i	$0.778797\pi$
$762$		0			0
$763$	1733.91	−	1001.07i	2.27249	−	1.31202i
$764$		−	446.047i		−	0.583831i
$765$		0			0
$766$	809.609			1.05693
$767$	−354.037	−	613.209i	−0.461586	−	0.799491i
$768$		0			0
$769$	271.375	−	470.035i	0.352894	−	0.611229i	−0.633862	−	0.773446i	$-0.718531\pi$
$769$	271.375	−	470.035i	0.352894	−	0.611229i	0.986755	+	0.162217i	$0.0518645\pi$
$770$	−1010.63	+	631.196i	−1.31250	+	0.819735i
$771$		0			0
$772$	305.228	−	176.224i	0.395373	−	0.228269i
$773$	522.640			0.676119			0.338059	−	0.941125i	$-0.390230\pi$
$773$	522.640			0.676119			0.338059	+	0.941125i	$0.390230\pi$
$774$		0			0
$775$	−533.860	−	792.243i	−0.688852	−	1.02225i
$776$	247.995	−	143.180i	0.319581	−	0.184510i
$777$		0			0
$778$	883.857	+	510.295i	1.13606	+	0.655906i
$779$	228.091	+	131.688i	0.292800	+	0.169048i
$780$		0			0
$781$	−646.154	−	1119.17i	−0.827342	−	1.43300i
$782$	−339.546			−0.434202
$783$		0			0
$784$	−553.352			−0.705807
$785$	350.515	−	12.1619i	0.446516	−	0.0154928i
$786$		0			0
$787$	−717.835	−	414.442i	−0.912116	−	0.526610i	−0.0310043	−	0.999519i	$-0.509871\pi$
$787$	−717.835	−	414.442i	−0.912116	−	0.526610i	−0.881111	+	0.472909i	$0.843204\pi$
$788$	277.586	−	480.793i	0.352266	−	0.610143i
$789$		0			0
$790$	10.8121	+	311.614i	0.0136862	+	0.394449i
$791$			744.942i			0.941773i
$792$		0			0
$793$		−	256.125i		−	0.322982i
$794$	464.571	−	268.220i	0.585102	−	0.337809i
$795$		0			0
$796$	−71.5736	+	123.969i	−0.0899166	+	0.155740i
$797$	306.803	−	531.398i	0.384947	−	0.666748i	−0.606815	−	0.794843i	$-0.707553\pi$
$797$	306.803	−	531.398i	0.384947	−	0.666748i	0.991762	+	0.128095i	$0.0408863\pi$
$798$		0			0
$799$	138.683	+	240.207i	0.173571	+	0.300634i
$800$	−79.0294	−	117.279i	−0.0987868	−	0.146599i
$801$		0			0
$802$			496.352i			0.618892i
$803$	−13.0030	−	22.5218i	−0.0161930	−	0.0280471i
$804$		0			0
$805$	1261.55	+	2019.90i	1.56714	+	2.50920i
$806$	−796.008	−	459.576i	−0.987604	−	0.570193i
$807$		0			0
$808$	37.3049	−	21.5380i	0.0461695	−	0.0266559i
$809$			545.471i			0.674254i	0.941459	+	0.337127i	$0.109455\pi$
$809$			545.471i			0.674254i	−0.941459	+	0.337127i	$0.890545\pi$
$810$		0			0
$811$	−293.192			−0.361519			−0.180759	−	0.983527i	$-0.557856\pi$
$811$	−293.192			−0.361519			−0.180759	+	0.983527i	$0.557856\pi$
$812$	289.279	+	501.046i	0.356255	+	0.617052i
$813$		0			0
$814$	−187.500	+	324.760i	−0.230345	+	0.398968i
$815$	−23.9957	−	38.4202i	−0.0294426	−	0.0471414i
$816$		0			0
$817$	39.1342	−	22.5942i	0.0478999	−	0.0276550i
$818$	754.379			0.922224
$819$		0			0
$820$	170.794	−	321.044i	0.208285	−	0.391517i
$821$	739.318	−	426.846i	0.900509	−	0.519909i	0.0231439	−	0.999732i	$-0.492632\pi$
$821$	739.318	−	426.846i	0.900509	−	0.519909i	0.877365	+	0.479823i	$0.159299\pi$
$822$		0			0
$823$	175.349	+	101.238i	0.213060	+	0.123010i	0.602733	−	0.797943i	$-0.294079\pi$
$823$	175.349	+	101.238i	0.213060	+	0.123010i	−0.389673	+	0.920953i	$0.627412\pi$
$824$	−188.837	−	109.025i	−0.229171	−	0.132312i
$825$		0			0
$826$	−402.919	−	697.876i	−0.487795	−	0.844886i
$827$	15.3734			0.0185894			0.00929471	−	0.999957i	$-0.497041\pi$
$827$	15.3734			0.0185894			0.00929471	+	0.999957i	$0.497041\pi$
$828$		0			0
$829$	−1135.22			−1.36938			−0.684692	−	0.728833i	$-0.740063\pi$
$829$	−1135.22			−1.36938			−0.684692	+	0.728833i	$0.740063\pi$
$830$	−13.4919	−	388.847i	−0.0162553	−	0.468491i
$831$		0			0
$832$	−117.836	−	68.0328i	−0.141630	−	0.0817702i
$833$	−477.231	+	826.589i	−0.572907	+	0.992304i
$834$		0			0
$835$	11.0709	+	319.072i	0.0132586	+	0.382122i
$836$		−	178.336i		−	0.213320i
$837$		0			0
$838$			339.065i			0.404612i
$839$	215.216	−	124.255i	0.256515	−	0.148099i	−0.366229	−	0.930525i	$-0.619351\pi$
$839$	215.216	−	124.255i	0.256515	−	0.148099i	0.622744	+	0.782426i	$0.286018\pi$
$840$		0			0
$841$	−197.154	+	341.481i	−0.234428	+	0.406041i
$842$	300.479	−	520.444i	0.356863	−	0.618105i
$843$		0			0
$844$	−319.492	−	553.377i	−0.378546	−	0.655660i
$845$	530.938	+	282.457i	0.628329	+	0.334269i
$846$		0			0
$847$			418.465i			0.494056i
$848$	76.5442	+	132.578i	0.0902643	+	0.156342i
$849$		0			0
$850$	−243.347	+	16.9073i	−0.286291	+	0.0198909i
$851$	649.087	+	374.750i	0.762734	+	0.440365i
$852$		0			0
$853$	17.4261	−	10.0609i	0.0204291	−	0.0117948i	−0.489751	−	0.871863i	$-0.662912\pi$
$853$	17.4261	−	10.0609i	0.0204291	−	0.0117948i	0.510180	+	0.860068i	$0.329579\pi$
$854$		−	291.488i		−	0.341321i
$855$		0			0
$856$	−221.823			−0.259139
$857$	92.7837	+	160.706i	0.108266	+	0.187522i	0.915068	−	0.403300i	$-0.132137\pi$
$857$	92.7837	+	160.706i	0.108266	+	0.187522i	−0.806802	+	0.590822i	$0.798804\pi$
$858$		0			0
$859$	549.239	−	951.309i	0.639393	−	1.10746i	−0.346173	−	0.938171i	$-0.612519\pi$
$859$	549.239	−	951.309i	0.639393	−	1.10746i	0.985566	−	0.169291i	$-0.0541476\pi$
$860$	−33.0509	−	52.9189i	−0.0384313	−	0.0615336i
$861$		0			0
$862$	666.308	−	384.693i	0.772980	−	0.446280i
$863$	−32.5736			−0.0377446			−0.0188723	−	0.999822i	$-0.506008\pi$
$863$	−32.5736			−0.0377446			−0.0188723	+	0.999822i	$0.506008\pi$
$864$		0			0
$865$	123.544	+	65.7250i	0.142826	+	0.0759827i
$866$	738.197	−	426.198i	0.852421	−	0.492146i
$867$		0			0
$868$	−905.914	−	523.030i	−1.04368	−	0.602569i
$869$	470.150	+	271.441i	0.541024	+	0.312360i
$870$		0			0
$871$	1093.78	+	1894.48i	1.25577	+	2.17506i
$872$	413.740			0.474473
$873$		0			0
$874$	−356.434			−0.407819
$875$	1004.71	+	1384.82i	1.14824	+	1.58265i
$876$		0			0
$877$	−867.139	−	500.643i	−0.988756	−	0.570859i	−0.0838540	−	0.996478i	$-0.526723\pi$
$877$	−867.139	−	500.643i	−0.988756	−	0.570859i	−0.904902	+	0.425619i	$0.860056\pi$
$878$	284.459	−	492.698i	0.323986	−	0.561160i
$879$		0			0
$880$	−246.082	+	8.53836i	−0.279639	+	0.00970268i
$881$		−	1664.18i		−	1.88897i	−0.328559	−	0.944483i	$-0.606563\pi$
$881$		−	1664.18i		−	1.88897i	0.328559	−	0.944483i	$-0.393437\pi$
$882$		0			0
$883$			221.400i			0.250736i	0.992110	+	0.125368i	$0.0400112\pi$
$883$			221.400i			0.250736i	−0.992110	+	0.125368i	$0.959989\pi$
$884$	−203.253	+	117.348i	−0.229924	+	0.132747i
$885$		0			0
$886$	−310.077	+	537.069i	−0.349974	+	0.606172i
$887$	829.771	−	1437.21i	0.935481	−	1.62030i	0.161706	−	0.986839i	$-0.448300\pi$
$887$	829.771	−	1437.21i	0.935481	−	1.62030i	0.773775	−	0.633461i	$-0.218366\pi$
$888$		0			0
$889$	1089.60	+	1887.25i	1.22565	+	2.12289i
$890$	−226.171	+	425.136i	−0.254124	+	0.477681i
$891$		0			0
$892$		−	324.877i		−	0.364212i
$893$	145.581	+	252.153i	0.163024	+	0.282366i
$894$		0			0
$895$	55.7964	+	89.3372i	0.0623423	+	0.0998181i
$896$	−134.106	−	77.4262i	−0.149672	−	0.0864132i
$897$		0			0
$898$	−821.640	+	474.374i	−0.914966	+	0.528256i
$899$			807.640i			0.898376i
$900$		0			0
$901$	264.058			0.293072
$902$	−316.576	−	548.325i	−0.350971	−	0.607899i
$903$		0			0
$904$	−76.9706	+	133.317i	−0.0851444	+	0.147474i
$905$	227.321	−	141.976i	0.251184	−	0.156879i
$906$		0			0
$907$	145.920	−	84.2471i	0.160882	−	0.0928854i	−0.417397	−	0.908724i	$-0.637058\pi$
$907$	145.920	−	84.2471i	0.160882	−	0.0928854i	0.578280	+	0.815839i	$0.303724\pi$
$908$	−482.195			−0.531052
$909$		0			0
$910$	1453.25	+	773.123i	1.59698	+	0.849585i
$911$	−1252.73	+	723.264i	−1.37511	+	0.793923i	−0.991567	−	0.129598i	$-0.958631\pi$
$911$	−1252.73	+	723.264i	−1.37511	+	0.793923i	−0.383548	+	0.923521i	$0.625298\pi$
$912$		0			0
$913$	−586.675	−	338.717i	−0.642579	−	0.370993i
$914$	851.233	+	491.460i	0.931327	+	0.537702i
$915$		0			0
$916$	−102.220	−	177.051i	−0.111594	−	0.193287i
$917$	−1509.73			−1.64638
$918$		0			0
$919$	−1279.60			−1.39239			−0.696193	−	0.717855i	$-0.745124\pi$
$919$	−1279.60			−1.39239			−0.696193	+	0.717855i	$0.745124\pi$
$920$	17.0653	+	491.836i	0.0185492	+	0.534604i
$921$		0			0
$922$	16.0303	+	9.25512i	0.0173865	+	0.0100381i
$923$	−892.654	+	1546.12i	−0.967122	+	1.67510i
$924$		0			0
$925$	483.850	+	236.257i	0.523081	+	0.255413i
$926$		−	331.324i		−	0.357801i
$927$		0			0
$928$			119.558i			0.128834i
$929$	851.532	−	491.632i	0.916612	−	0.529206i	0.0340592	−	0.999420i	$-0.489157\pi$
$929$	851.532	−	491.632i	0.916612	−	0.529206i	0.882553	+	0.470214i	$0.155823\pi$
$930$		0			0
$931$	−500.967	+	867.700i	−0.538095	+	0.932008i
$932$	241.966	−	419.097i	0.259620	−	0.449674i
$933$		0			0
$934$	525.297	+	909.841i	0.562417	+	0.974134i
$935$	−199.476	+	374.958i	−0.213343	+	0.401024i
$936$		0			0
$937$			964.938i			1.02982i	0.857245	+	0.514908i	$0.172174\pi$
$937$			964.938i			1.02982i	−0.857245	+	0.514908i	$0.827826\pi$
$938$	1244.80	+	2156.05i	1.32708	+	2.29856i
$939$		0			0
$940$	340.971	−	212.957i	0.362736	−	0.226550i
$941$	−891.907	−	514.943i	−0.947829	−	0.547230i	−0.0554234	−	0.998463i	$-0.517651\pi$
$941$	−891.907	−	514.943i	−0.947829	−	0.547230i	−0.892406	+	0.451233i	$0.850984\pi$
$942$		0			0
$943$	−1095.92	+	632.729i	−1.16216	+	0.670974i
$944$		−	166.525i		−	0.176404i
$945$		0			0
$946$	−108.632			−0.114833
$947$	93.4340	+	161.832i	0.0986631	+	0.170890i	0.911132	−	0.412116i	$-0.135210\pi$
$947$	93.4340	+	161.832i	0.0986631	+	0.170890i	−0.812468	+	0.583005i	$0.801877\pi$
$948$		0			0
$949$	−17.9634	+	31.1136i	−0.0189288	+	0.0327856i
$950$	−255.450	+	17.7482i	−0.268895	+	0.0186823i
$951$		0			0
$952$	−231.316	+	133.550i	−0.242979	+	0.140284i
$953$	−857.170			−0.899444			−0.449722	−	0.893169i	$-0.648477\pi$
$953$	−857.170			−0.899444			−0.449722	+	0.893169i	$0.648477\pi$
$954$		0			0
$955$	−523.736	+	984.474i	−0.548415	+	1.03086i
$956$	650.313	−	375.458i	0.680244	−	0.392739i
$957$		0			0
$958$	547.964	+	316.367i	0.571988	+	0.330237i
$959$	−2583.08	−	1491.34i	−2.69352	−	1.55510i
$960$		0			0
$961$	−249.624	−	432.362i	−0.259755	−	0.449909i
$962$	518.059			0.538523
$963$		0			0
$964$	−636.558			−0.660330
$965$	−880.588	+	30.5539i	−0.912526	+	0.0316621i
$966$		0			0
$967$	1068.71	+	617.021i	1.10518	+	0.638077i	0.937577	−	0.347777i	$-0.113063\pi$
$967$	1068.71	+	617.021i	1.10518	+	0.638077i	0.167605	+	0.985854i	$0.446397\pi$
$968$	−43.2376	+	74.8897i	−0.0446669	+	0.0773654i
$969$		0			0
$970$	−715.469	+	24.8247i	−0.737597	+	0.0255925i
$971$		−	1313.38i		−	1.35261i	−0.736624	−	0.676303i	$-0.763581\pi$
$971$		−	1313.38i		−	1.35261i	0.736624	−	0.676303i	$-0.236419\pi$
$972$		0			0
$973$			1454.26i			1.49461i
$974$	61.6250	−	35.5792i	0.0632700	−	0.0365289i
$975$		0			0
$976$	30.1177	−	52.1655i	0.0308583	−	0.0534482i
$977$	−54.7431	+	94.8178i	−0.0560318	+	0.0970499i	−0.892681	−	0.450690i	$-0.851178\pi$
$977$	−54.7431	+	94.8178i	−0.0560318	+	0.0970499i	0.836649	+	0.547739i	$0.184511\pi$
$978$		0			0
$979$	419.219	+	726.109i	0.428212	+	0.741685i
$980$	1221.31	+	649.731i	1.24623	+	0.662991i
$981$		0			0
$982$		−	1118.12i		−	1.13862i
$983$	170.997	+	296.176i	0.173955	+	0.301298i	0.939799	−	0.341728i	$-0.111012\pi$
$983$	170.997	+	296.176i	0.173955	+	0.301298i	−0.765844	+	0.643026i	$0.777679\pi$
$984$		0			0
$985$	−1177.19	+	735.227i	−1.19512	+	0.746424i
$986$	178.594	+	103.111i	0.181130	+	0.104575i
$987$		0			0
$988$	−213.362	+	123.184i	−0.215953	+	0.124681i
$989$			217.118i			0.219533i
$990$		0			0
$991$	140.258			0.141532			0.0707658	−	0.997493i	$-0.477456\pi$
$991$	140.258			0.141532			0.0707658	+	0.997493i	$0.477456\pi$
$992$	−108.083	−	187.206i	−0.108955	−	0.188715i
$993$		0			0
$994$	−1015.90	+	1759.60i	−1.02204	+	1.77022i
$995$	303.532	−	189.573i	0.305057	−	0.190526i
$996$		0			0
$997$	536.619	−	309.817i	0.538233	−	0.310749i	−0.206129	−	0.978525i	$-0.566087\pi$
$997$	536.619	−	309.817i	0.538233	−	0.310749i	0.744363	+	0.667776i	$0.232753\pi$
$998$	849.079			0.850781
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.3.j.f.539.4		8
3.2	odd	2		810.3.j.a.539.1		8
5.4	even	2		810.3.j.a.539.2		8
9.2	odd	6		810.3.j.a.269.2		8
9.4	even	3		270.3.b.a.269.1	✓	4
9.5	odd	6		270.3.b.d.269.4	yes	4
9.7	even	3	inner	810.3.j.f.269.3		8
15.14	odd	2	inner	810.3.j.f.539.3		8
36.23	even	6		2160.3.c.m.1889.4		4
36.31	odd	6		2160.3.c.g.1889.1		4
45.4	even	6		270.3.b.d.269.3	yes	4
45.13	odd	12		1350.3.d.o.701.5		8
45.14	odd	6		270.3.b.a.269.2	yes	4
45.22	odd	12		1350.3.d.o.701.4		8
45.23	even	12		1350.3.d.o.701.1		8
45.29	odd	6	inner	810.3.j.f.269.4		8
45.32	even	12		1350.3.d.o.701.8		8
45.34	even	6		810.3.j.a.269.1		8
180.59	even	6		2160.3.c.g.1889.2		4
180.139	odd	6		2160.3.c.m.1889.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.3.b.a.269.1	✓	4	9.4	even	3
270.3.b.a.269.2	yes	4	45.14	odd	6
270.3.b.d.269.3	yes	4	45.4	even	6
270.3.b.d.269.4	yes	4	9.5	odd	6
810.3.j.a.269.1		8	45.34	even	6
810.3.j.a.269.2		8	9.2	odd	6
810.3.j.a.539.1		8	3.2	odd	2
810.3.j.a.539.2		8	5.4	even	2
810.3.j.f.269.3		8	9.7	even	3	inner
810.3.j.f.269.4		8	45.29	odd	6	inner
810.3.j.f.539.3		8	15.14	odd	2	inner
810.3.j.f.539.4		8	1.1	even	1	trivial
1350.3.d.o.701.1		8	45.23	even	12
1350.3.d.o.701.4		8	45.22	odd	12
1350.3.d.o.701.5		8	45.13	odd	12
1350.3.d.o.701.8		8	45.32	even	12
2160.3.c.g.1889.1		4	36.31	odd	6
2160.3.c.g.1889.2		4	180.59	even	6
2160.3.c.m.1889.3		4	180.139	odd	6
2160.3.c.m.1889.4		4	36.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(4.24083 - 2.64865i) q^{5} +(-11.8534 + 6.84358i) q^{7} -2.82843 q^{8} +O(q^{10})\)	\(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(4.24083 - 2.64865i) q^{5} +(-11.8534 + 6.84358i) q^{7} -2.82843 q^{8} +(6.24264 + 3.32106i) q^{10} +(10.6621 - 6.15576i) q^{11} +(-14.7295 - 8.50411i) q^{13} +(-16.7633 - 9.67828i) q^{14} +(-2.00000 - 3.46410i) q^{16} -6.89949 q^{17} -7.24264 q^{19} +(0.346763 + 9.99399i) q^{20} +(15.0785 + 8.70556i) q^{22} +(17.3995 - 30.1368i) q^{23} +(10.9693 - 22.4650i) q^{25} -24.0532i q^{26} -27.3743i q^{28} +(-18.3035 + 10.5675i) q^{29} +(19.1066 - 33.0936i) q^{31} +(2.82843 - 4.89898i) q^{32} +(-4.87868 - 8.45012i) q^{34} +(-32.1421 + 60.4180i) q^{35} +21.5380i q^{37} +(-5.12132 - 8.87039i) q^{38} +(-11.9949 + 7.49151i) q^{40} +(-31.4928 - 18.1824i) q^{41} +(-5.40331 + 3.11960i) q^{43} +24.6230i q^{44} +49.2132 q^{46} +(-20.1005 - 34.8151i) q^{47} +(69.1690 - 119.804i) q^{49} +(35.2703 - 2.45051i) q^{50} +(29.4591 - 17.0082i) q^{52} -38.2721 q^{53} +(28.9117 - 54.3457i) q^{55} +(33.5265 - 19.3566i) q^{56} +(-25.8851 - 14.9448i) q^{58} +(36.0537 + 20.8156i) q^{59} +(7.52944 + 13.0414i) q^{61} +54.0416 q^{62} +8.00000 q^{64} +(-84.9899 + 2.94891i) q^{65} +(-111.386 - 64.3089i) q^{67} +(6.89949 - 11.9503i) q^{68} +(-96.7246 + 3.35607i) q^{70} -104.967i q^{71} -2.11232i q^{73} +(-26.3786 + 15.2297i) q^{74} +(7.24264 - 12.5446i) q^{76} +(-84.2548 + 145.934i) q^{77} +(22.0477 + 38.1878i) q^{79} +(-17.6569 - 9.39338i) q^{80} -51.4275i q^{82} +(-27.5122 - 47.6525i) q^{83} +(-29.2596 + 18.2743i) q^{85} +(-7.64144 - 4.41179i) q^{86} +(-30.1569 + 17.4111i) q^{88} +68.1020i q^{89} +232.794 q^{91} +(34.7990 + 60.2736i) q^{92} +(28.4264 - 49.2360i) q^{94} +(-30.7148 + 19.1832i) q^{95} +(-87.6794 + 50.6217i) q^{97} +195.640 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 12 q^{5}+O(q^{10}) \) 8 * q - 8 * q^4 + 12 * q^5	\( 8 q - 8 q^{4} + 12 q^{5} + 16 q^{10} - 16 q^{16} + 24 q^{17} - 24 q^{19} + 24 q^{20} + 60 q^{23} + 12 q^{25} + 68 q^{31} - 56 q^{34} - 144 q^{35} - 24 q^{38} - 16 q^{40} + 224 q^{46} - 240 q^{47} + 180 q^{49} + 96 q^{50} - 408 q^{53} - 176 q^{55} + 196 q^{61} + 240 q^{62} + 64 q^{64} - 24 q^{65} - 24 q^{68} - 80 q^{70} + 24 q^{76} - 312 q^{77} - 180 q^{79} - 96 q^{80} + 108 q^{83} - 20 q^{85} + 912 q^{91} + 120 q^{92} - 112 q^{94} - 60 q^{95} + 1056 q^{98}+O(q^{100}) \) 8 * q - 8 * q^4 + 12 * q^5 + 16 * q^10 - 16 * q^16 + 24 * q^17 - 24 * q^19 + 24 * q^20 + 60 * q^23 + 12 * q^25 + 68 * q^31 - 56 * q^34 - 144 * q^35 - 24 * q^38 - 16 * q^40 + 224 * q^46 - 240 * q^47 + 180 * q^49 + 96 * q^50 - 408 * q^53 - 176 * q^55 + 196 * q^61 + 240 * q^62 + 64 * q^64 - 24 * q^65 - 24 * q^68 - 80 * q^70 + 24 * q^76 - 312 * q^77 - 180 * q^79 - 96 * q^80 + 108 * q^83 - 20 * q^85 + 912 * q^91 + 120 * q^92 - 112 * q^94 - 60 * q^95 + 1056 * q^98

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