LMFDB - Embedded newform 513.2.g.c.505.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [513,2,Mod(64,513)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("513.64"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(513, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 513 = 3^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	513.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,-1,0,-17,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.09632562369$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 171)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			505.8
Character	$\chi$	$=$	513.505
Dual form			513.2.g.c.64.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0732670 + 0.126902i) q^{2} +(0.989264 - 1.71346i) q^{4} -2.57004 q^{5} +(-1.73898 + 3.01201i) q^{7} +0.582990 q^{8} +(-0.188299 - 0.326143i) q^{10} +(-2.07935 + 3.60154i) q^{11} +(-2.29925 + 3.98242i) q^{13} -0.509640 q^{14} +(-1.93581 - 3.35293i) q^{16} +(1.50797 - 2.61188i) q^{17} +(3.65690 + 2.37215i) q^{19} +(-2.54244 + 4.40364i) q^{20} -0.609391 q^{22} +(-2.45941 + 4.25982i) q^{23} +1.60509 q^{25} -0.673837 q^{26} +(3.44063 + 5.95934i) q^{28} +3.71403 q^{29} +(3.31980 + 5.75007i) q^{31} +(0.866652 - 1.50109i) q^{32} +0.441938 q^{34} +(4.46925 - 7.74097i) q^{35} -5.28491 q^{37} +(-0.0331004 + 0.637869i) q^{38} -1.49831 q^{40} -2.53193 q^{41} +(-2.39036 - 4.14022i) q^{43} +(4.11405 + 7.12574i) q^{44} -0.720775 q^{46} -9.71255 q^{47} +(-2.54812 - 4.41348i) q^{49} +(0.117600 + 0.203689i) q^{50} +(4.54913 + 7.87933i) q^{52} +(-5.35547 - 9.27595i) q^{53} +(5.34400 - 9.25609i) q^{55} +(-1.01381 + 1.75597i) q^{56} +(0.272116 + 0.471318i) q^{58} +8.96213 q^{59} +0.944170 q^{61} +(-0.486464 + 0.842580i) q^{62} -7.48927 q^{64} +(5.90916 - 10.2350i) q^{65} +(-0.688581 + 1.19266i) q^{67} +(-2.98356 - 5.16768i) q^{68} +1.30979 q^{70} +(-4.45338 + 7.71347i) q^{71} +(-2.14771 + 3.71994i) q^{73} +(-0.387210 - 0.670667i) q^{74} +(7.68221 - 3.91926i) q^{76} +(-7.23190 - 12.5260i) q^{77} +(-1.69260 - 2.93168i) q^{79} +(4.97511 + 8.61715i) q^{80} +(-0.185507 - 0.321308i) q^{82} +(-4.52640 + 7.83996i) q^{83} +(-3.87554 + 6.71263i) q^{85} +(0.350269 - 0.606683i) q^{86} +(-1.21224 + 2.09966i) q^{88} +(3.96515 + 6.86783i) q^{89} +(-7.99672 - 13.8507i) q^{91} +(4.86601 + 8.42818i) q^{92} +(-0.711609 - 1.23254i) q^{94} +(-9.39837 - 6.09650i) q^{95} +(-0.930336 - 1.61139i) q^{97} +(0.373387 - 0.646725i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - q^{2} - 17 q^{4} + 6 q^{5} + q^{7} + 36 q^{8} - 8 q^{10} - 7 q^{11} - 4 q^{13} + 2 q^{14} - 11 q^{16} + 7 q^{17} + 7 q^{19} + 3 q^{20} + 16 q^{22} - 5 q^{23} + 18 q^{25} + 4 q^{26} - 10 q^{28}+ \cdots - 18 q^{98}+O(q^{100}) $ 32 * q - q^2 - 17 * q^4 + 6 * q^5 + q^7 + 36 * q^8 - 8 * q^10 - 7 * q^11 - 4 * q^13 + 2 * q^14 - 11 * q^16 + 7 * q^17 + 7 * q^19 + 3 * q^20 + 16 * q^22 - 5 * q^23 + 18 * q^25 + 4 * q^26 - 10 * q^28 + 20 * q^29 - 10 * q^31 - 17 * q^32 + 26 * q^34 + 3 * q^35 + 2 * q^37 - 38 * q^38 - 24 * q^40 + 12 * q^41 + 7 * q^43 - 20 * q^44 - 18 * q^47 - 13 * q^49 - q^50 + 19 * q^52 - 16 * q^53 + 15 * q^55 + 6 * q^56 + 74 * q^59 + 24 * q^61 - 54 * q^62 - 64 * q^64 - 54 * q^65 - 11 * q^67 + 2 * q^68 - 48 * q^70 - 9 * q^71 - 10 * q^73 - 6 * q^74 + 29 * q^76 - 46 * q^77 - 8 * q^79 + 24 * q^80 + 7 * q^82 - 3 * q^83 - 27 * q^85 - 17 * q^86 + 9 * q^88 - 30 * q^89 - q^91 + 17 * q^92 - 18 * q^94 + 6 * q^95 - 18 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/513\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.0732670	+	0.126902i	0.0518076	+	0.0897334i	0.890766	−	0.454462i	$-0.150168\pi$
$2$	0.0732670	+	0.126902i	0.0518076	+	0.0897334i	−0.838959	+	0.544195i	$0.816835\pi$
$3$		0			0
$3$		0			0
$4$	0.989264	−	1.71346i	0.494632	−	0.856728i
$5$	−2.57004			−1.14936			−0.574678	−	0.818380i	$-0.694873\pi$
$5$	−2.57004			−1.14936			−0.574678	+	0.818380i	$0.694873\pi$
$6$		0			0
$7$	−1.73898	+	3.01201i	−0.657274	+	1.13843i	0.324045	+	0.946042i	$0.394957\pi$
$7$	−1.73898	+	3.01201i	−0.657274	+	1.13843i	−0.981319	+	0.192390i	$0.938376\pi$
$8$	0.582990			0.206118
$9$		0			0
$10$	−0.188299	−	0.326143i	−0.0595454	−	0.103136i
$11$	−2.07935	+	3.60154i	−0.626947	+	1.08590i	0.361214	+	0.932483i	$0.382363\pi$
$11$	−2.07935	+	3.60154i	−0.626947	+	1.08590i	−0.988161	+	0.153421i	$0.950971\pi$
$12$		0			0
$13$	−2.29925	+	3.98242i	−0.637698	+	1.10452i	0.348239	+	0.937406i	$0.386780\pi$
$13$	−2.29925	+	3.98242i	−0.637698	+	1.10452i	−0.985937	+	0.167119i	$0.946554\pi$
$14$	−0.509640			−0.136207
$15$		0			0
$16$	−1.93581	−	3.35293i	−0.483953	−	0.838232i
$17$	1.50797	−	2.61188i	0.365736	−	0.633474i	−0.623158	−	0.782096i	$-0.714150\pi$
$17$	1.50797	−	2.61188i	0.365736	−	0.633474i	0.988894	+	0.148622i	$0.0474838\pi$
$18$		0			0
$19$	3.65690	+	2.37215i	0.838951	+	0.544208i
$19$	3.65690	+	2.37215i	0.838951	+	0.544208i
$20$	−2.54244	+	4.40364i	−0.568508	+	0.984685i
$21$		0			0
$22$	−0.609391			−0.129923
$23$	−2.45941	+	4.25982i	−0.512822	+	0.888234i	0.487067	+	0.873365i	$0.338067\pi$
$23$	−2.45941	+	4.25982i	−0.512822	+	0.888234i	−0.999889	+	0.0148698i	$0.995267\pi$
$24$		0			0
$25$	1.60509			0.321018
$26$	−0.673837			−0.132150
$27$		0			0
$28$	3.44063	+	5.95934i	0.650217	+	1.12621i
$29$	3.71403			0.689678			0.344839	−	0.938662i	$-0.387934\pi$
$29$	3.71403			0.689678			0.344839	+	0.938662i	$0.387934\pi$
$30$		0			0
$31$	3.31980	+	5.75007i	0.596254	+	1.03274i	0.993369	+	0.114973i	$0.0366782\pi$
$31$	3.31980	+	5.75007i	0.596254	+	1.03274i	−0.397115	+	0.917769i	$0.629988\pi$
$32$	0.866652	−	1.50109i	0.153204	−	0.265357i
$33$		0			0
$34$	0.441938			0.0757917
$35$	4.46925	−	7.74097i	0.755441	−	1.30846i
$36$		0			0
$37$	−5.28491			−0.868834			−0.434417	−	0.900712i	$-0.643046\pi$
$37$	−5.28491			−0.868834			−0.434417	+	0.900712i	$0.643046\pi$
$38$	−0.0331004	+	0.637869i	−0.00536959	+	0.103476i
$39$		0			0
$40$	−1.49831			−0.236903
$41$	−2.53193			−0.395422			−0.197711	−	0.980260i	$-0.563351\pi$
$41$	−2.53193			−0.395422			−0.197711	+	0.980260i	$0.563351\pi$
$42$		0			0
$43$	−2.39036	−	4.14022i	−0.364526	−	0.631378i	0.624174	−	0.781285i	$-0.285436\pi$
$43$	−2.39036	−	4.14022i	−0.364526	−	0.631378i	−0.988700	+	0.149908i	$0.952102\pi$
$44$	4.11405	+	7.12574i	0.620216	+	1.07425i
$45$		0			0
$46$	−0.720775			−0.106272
$47$	−9.71255			−1.41672			−0.708360	−	0.705851i	$-0.750565\pi$
$47$	−9.71255			−1.41672			−0.708360	+	0.705851i	$0.750565\pi$
$48$		0			0
$49$	−2.54812	−	4.41348i	−0.364017	−	0.630497i
$50$	0.117600	+	0.203689i	0.0166312	+	0.0288060i
$51$		0			0
$52$	4.54913	+	7.87933i	0.630851	+	1.09267i
$53$	−5.35547	−	9.27595i	−0.735631	−	1.27415i	−0.954446	−	0.298384i	$-0.903553\pi$
$53$	−5.35547	−	9.27595i	−0.735631	−	1.27415i	0.218815	−	0.975766i	$-0.429781\pi$
$54$		0			0
$55$	5.34400	−	9.25609i	0.720585	−	1.24809i
$56$	−1.01381	+	1.75597i	−0.135476	+	0.234651i
$57$		0			0
$58$	0.272116	+	0.471318i	0.0357305	+	0.0618871i
$59$	8.96213			1.16677			0.583385	−	0.812196i	$-0.301728\pi$
$59$	8.96213			1.16677			0.583385	+	0.812196i	$0.301728\pi$
$60$		0			0
$61$	0.944170			0.120889			0.0604443	−	0.998172i	$-0.480748\pi$
$61$	0.944170			0.120889			0.0604443	+	0.998172i	$0.480748\pi$
$62$	−0.486464	+	0.842580i	−0.0617810	+	0.107008i
$63$		0			0
$64$	−7.48927			−0.936158
$65$	5.90916	−	10.2350i	0.732941	−	1.26949i
$66$		0			0
$67$	−0.688581	+	1.19266i	−0.0841236	+	0.145706i	−0.905017	−	0.425375i	$-0.860142\pi$
$67$	−0.688581	+	1.19266i	−0.0841236	+	0.145706i	0.820894	+	0.571081i	$0.193476\pi$
$68$	−2.98356	−	5.16768i	−0.361810	−	0.626673i
$69$		0			0
$70$	1.30979			0.156550
$71$	−4.45338	+	7.71347i	−0.528519	+	0.915421i	0.470929	+	0.882171i	$0.343919\pi$
$71$	−4.45338	+	7.71347i	−0.528519	+	0.915421i	−0.999447	+	0.0332496i	$0.989414\pi$
$72$		0			0
$73$	−2.14771	+	3.71994i	−0.251370	+	0.435386i	−0.963903	−	0.266253i	$-0.914214\pi$
$73$	−2.14771	+	3.71994i	−0.251370	+	0.435386i	0.712533	+	0.701638i	$0.247548\pi$
$74$	−0.387210	−	0.670667i	−0.0450122	−	0.0779635i
$75$		0			0
$76$	7.68221	−	3.91926i	0.881210	−	0.449570i
$77$	−7.23190	−	12.5260i	−0.824152	−	1.42747i
$78$		0			0
$79$	−1.69260	−	2.93168i	−0.190433	−	0.329840i	0.754961	−	0.655770i	$-0.227656\pi$
$79$	−1.69260	−	2.93168i	−0.190433	−	0.329840i	−0.945394	+	0.325930i	$0.894323\pi$
$80$	4.97511	+	8.61715i	0.556235	+	0.963427i
$81$		0			0
$82$	−0.185507	−	0.321308i	−0.0204858	−	0.0354825i
$83$	−4.52640	+	7.83996i	−0.496837	+	0.860547i	−0.999993	−	0.00364819i	$-0.998839\pi$
$83$	−4.52640	+	7.83996i	−0.496837	+	0.860547i	0.503156	+	0.864196i	$0.332172\pi$
$84$		0			0
$85$	−3.87554	+	6.71263i	−0.420361	+	0.728087i
$86$	0.350269	−	0.606683i	0.0377705	−	0.0654204i
$87$		0			0
$88$	−1.21224	+	2.09966i	−0.129225	+	0.223824i
$89$	3.96515	+	6.86783i	0.420305	+	0.727989i	0.995969	−	0.0896971i	$-0.0285899\pi$
$89$	3.96515	+	6.86783i	0.420305	+	0.727989i	−0.575665	+	0.817686i	$0.695257\pi$
$90$		0			0
$91$	−7.99672	−	13.8507i	−0.838284	−	1.45195i
$92$	4.86601	+	8.42818i	0.507317	+	0.878698i
$93$		0			0
$94$	−0.711609	−	1.23254i	−0.0733969	−	0.127127i
$95$	−9.39837	−	6.09650i	−0.964252	−	0.625488i
$96$		0			0
$97$	−0.930336	−	1.61139i	−0.0944613	−	0.163612i	0.814922	−	0.579570i	$-0.196780\pi$
$97$	−0.930336	−	1.61139i	−0.0944613	−	0.163612i	−0.909384	+	0.415958i	$0.863446\pi$
$98$	0.373387	−	0.646725i	0.0377177	−	0.0653291i
$99$		0			0
$100$	1.58786	−	2.75025i	0.158786	−	0.275025i
$101$	9.88304			0.983400			0.491700	−	0.870765i	$-0.336376\pi$
$101$	9.88304			0.983400			0.491700	+	0.870765i	$0.336376\pi$
$102$		0			0
$103$	−9.35247	−	16.1990i	−0.921527	−	1.59613i	−0.797054	−	0.603908i	$-0.793609\pi$
$103$	−9.35247	−	16.1990i	−0.921527	−	1.59613i	−0.124473	−	0.992223i	$-0.539724\pi$
$104$	−1.34044	+	2.32171i	−0.131441	+	0.227662i
$105$		0			0
$106$	0.784759	−	1.35924i	0.0762225	−	0.132021i
$107$	15.3037			1.47947			0.739733	−	0.672901i	$-0.234952\pi$
$107$	15.3037			1.47947			0.739733	+	0.672901i	$0.234952\pi$
$108$		0			0
$109$	1.64679	−	2.85232i	0.157734	−	0.273203i	−0.776317	−	0.630342i	$-0.782915\pi$
$109$	1.64679	−	2.85232i	0.157734	−	0.273203i	0.934051	+	0.357139i	$0.116248\pi$
$110$	1.56616			0.149327
$111$		0			0
$112$	13.4654			1.27236
$113$	1.80784	+	3.13127i	0.170067	+	0.294565i	0.938443	−	0.345434i	$-0.112268\pi$
$113$	1.80784	+	3.13127i	0.170067	+	0.294565i	−0.768376	+	0.639999i	$0.778935\pi$
$114$		0			0
$115$	6.32077	−	10.9479i	0.589415	−	1.02090i
$116$	3.67415	−	6.36382i	0.341137	−	0.590866i
$117$		0			0
$118$	0.656629	+	1.13731i	0.0604476	+	0.104698i
$119$	5.24467	+	9.08403i	0.480778	+	0.832732i
$120$		0			0
$121$	−3.14738	−	5.45143i	−0.286126	−	0.495584i
$122$	0.0691765	+	0.119817i	0.00626295	+	0.0108477i
$123$		0			0
$124$	13.1366			1.17971
$125$	8.72504			0.780392
$126$		0			0
$127$	9.12699	+	15.8084i	0.809890	+	1.40277i	0.912940	+	0.408094i	$0.133806\pi$
$127$	9.12699	+	15.8084i	0.809890	+	1.40277i	−0.103050	+	0.994676i	$0.532860\pi$
$128$	−2.28202	−	3.95258i	−0.201704	−	0.349362i
$129$		0			0
$130$	1.73179			0.151888
$131$	21.4998			1.87844			0.939222	−	0.343312i	$-0.111549\pi$
$131$	21.4998			1.87844			0.939222	+	0.343312i	$0.111549\pi$
$132$		0			0
$133$	−13.5042	+	6.88949i	−1.17096	+	0.597394i
$134$	−0.201801			−0.0174330
$135$		0			0
$136$	0.879131	−	1.52270i	0.0753849	−	0.130570i
$137$	8.84164			0.755392			0.377696	−	0.925930i	$-0.376716\pi$
$137$	8.84164			0.755392			0.377696	+	0.925930i	$0.376716\pi$
$138$		0			0
$139$	6.64472	−	11.5090i	0.563598	−	0.976180i	−0.433581	−	0.901115i	$-0.642750\pi$
$139$	6.64472	−	11.5090i	0.563598	−	0.976180i	0.997179	−	0.0750651i	$-0.0239164\pi$
$140$	−8.84254	−	15.3157i	−0.747331	−	1.29441i
$141$		0			0
$142$	−1.30514			−0.109525
$143$	−9.56189	−	16.5617i	−0.799606	−	1.38496i
$144$		0			0
$145$	−9.54519			−0.792685
$146$	−0.629425			−0.0520915
$147$		0			0
$148$	−5.22817	+	9.05546i	−0.429753	+	0.744354i
$149$	−13.8148			−1.13175			−0.565875	−	0.824491i	$-0.691462\pi$
$149$	−13.8148			−1.13175			−0.565875	+	0.824491i	$0.691462\pi$
$150$		0			0
$151$	−1.82757	+	3.16545i	−0.148726	+	0.257600i	−0.930757	−	0.365639i	$-0.880850\pi$
$151$	−1.82757	+	3.16545i	−0.148726	+	0.257600i	0.782031	+	0.623239i	$0.214184\pi$
$152$	2.13194	+	1.38294i	0.172923	+	0.112171i
$153$		0			0
$154$	1.05972	−	1.83549i	0.0853947	−	0.147908i
$155$	−8.53201	−	14.7779i	−0.685308	−	1.18699i
$156$		0			0
$157$	4.54548			0.362768			0.181384	−	0.983412i	$-0.441942\pi$
$157$	4.54548			0.362768			0.181384	+	0.983412i	$0.441942\pi$
$158$	0.248024	−	0.429591i	0.0197318	−	0.0341764i
$159$		0			0
$160$	−2.22733	+	3.85785i	−0.176086	+	0.304990i
$161$	−8.55374	−	14.8155i	−0.674129	−	1.16763i
$162$		0			0
$163$	−2.30348			−0.180422			−0.0902111	−	0.995923i	$-0.528754\pi$
$163$	−2.30348			−0.180422			−0.0902111	+	0.995923i	$0.528754\pi$
$164$	−2.50475	+	4.33835i	−0.195588	+	0.338769i
$165$		0			0
$166$	−1.32654			−0.102960
$167$	−4.47102	+	7.74404i	−0.345978	+	0.599251i	−0.985531	−	0.169496i	$-0.945786\pi$
$167$	−4.47102	+	7.74404i	−0.345978	+	0.599251i	0.639553	+	0.768747i	$0.279119\pi$
$168$		0			0
$169$	−4.07311	−	7.05484i	−0.313317	−	0.542680i
$170$	−1.13580			−0.0871116
$171$		0			0
$172$	−9.45878			−0.721225
$173$	−0.647453	−	1.12142i	−0.0492249	−	0.0852600i	0.840363	−	0.542024i	$-0.182342\pi$
$173$	−0.647453	−	1.12142i	−0.0492249	−	0.0852600i	−0.889588	+	0.456764i	$0.849008\pi$
$174$		0			0
$175$	−2.79122	+	4.83454i	−0.210997	+	0.365457i
$176$	16.1009			1.21365
$177$		0			0
$178$	−0.581029	+	1.00637i	−0.0435499	+	0.0754307i
$179$	−7.43054			−0.555385			−0.277692	−	0.960670i	$-0.589570\pi$
$179$	−7.43054			−0.555385			−0.277692	+	0.960670i	$0.589570\pi$
$180$		0			0
$181$	−0.306836	−	0.531455i	−0.0228069	−	0.0395027i	0.854397	−	0.519621i	$-0.173927\pi$
$181$	−0.306836	−	0.531455i	−0.0228069	−	0.0395027i	−0.877204	+	0.480119i	$0.840594\pi$
$182$	1.17179	−	2.02960i	0.0868590	−	0.150444i
$183$		0			0
$184$	−1.43381	+	2.48343i	−0.105702	+	0.183081i
$185$	13.5824			0.998599
$186$		0			0
$187$	6.27119	+	10.8620i	0.458595	+	0.794310i
$188$	−9.60827	+	16.6420i	−0.700755	+	1.21374i
$189$		0			0
$190$	0.0850692	−	1.63935i	0.00617157	−	0.118931i
$191$	2.82733	−	4.89708i	0.204578	−	0.354340i	−0.745420	−	0.666595i	$-0.767751\pi$
$191$	2.82733	−	4.89708i	0.204578	−	0.354340i	0.949998	+	0.312255i	$0.101084\pi$
$192$		0			0
$193$	1.76494			0.127043			0.0635215	−	0.997980i	$-0.479767\pi$
$193$	1.76494			0.127043			0.0635215	+	0.997980i	$0.479767\pi$
$194$	0.136326	−	0.236123i	0.00978763	−	0.0169527i
$195$		0			0
$196$	−10.0831			−0.720219
$197$	1.37197			0.0977491			0.0488745	−	0.998805i	$-0.484437\pi$
$197$	1.37197			0.0977491			0.0488745	+	0.998805i	$0.484437\pi$
$198$		0			0
$199$	12.3083	+	21.3186i	0.872513	+	1.51124i	0.859389	+	0.511322i	$0.170844\pi$
$199$	12.3083	+	21.3186i	0.872513	+	1.51124i	0.0131236	+	0.999914i	$0.495823\pi$
$200$	0.935751			0.0661676
$201$		0			0
$202$	0.724101	+	1.25418i	0.0509476	+	0.0882438i
$203$	−6.45863	+	11.1867i	−0.453307	+	0.785151i
$204$		0			0
$205$	6.50716			0.454480
$206$	1.37046	−	2.37370i	0.0954842	−	0.165383i
$207$		0			0
$208$	17.8037			1.23446
$209$	−16.1473	+	8.23795i	−1.11694	+	0.569831i
$210$		0			0
$211$	−7.16527			−0.493278			−0.246639	−	0.969107i	$-0.579326\pi$
$211$	−7.16527			−0.493278			−0.246639	+	0.969107i	$0.579326\pi$
$212$	−21.1919			−1.45547
$213$		0			0
$214$	1.12126	+	1.94208i	0.0766476	+	0.132758i
$215$	6.14331	+	10.6405i	0.418970	+	0.725678i
$216$		0			0
$217$	−23.0923			−1.56761
$218$	0.482621			0.0326872
$219$		0			0
$220$	−10.5733	−	18.3134i	−0.712849	−	1.23469i
$221$	6.93440	+	12.0107i	0.466459	+	0.807930i
$222$		0			0
$223$	−0.607729	−	1.05262i	−0.0406965	−	0.0704885i	0.844960	−	0.534830i	$-0.179624\pi$
$223$	−0.607729	−	1.05262i	−0.0406965	−	0.0704885i	−0.885656	+	0.464342i	$0.846291\pi$
$224$	3.01419	+	5.22073i	0.201394	+	0.348824i
$225$		0			0
$226$	−0.264910	+	0.458837i	−0.0176215	+	0.0305214i
$227$	4.45999	−	7.72493i	0.296020	−	0.512722i	−0.679202	−	0.733952i	$-0.737674\pi$
$227$	4.45999	−	7.72493i	0.296020	−	0.512722i	0.975222	+	0.221230i	$0.0710072\pi$
$228$		0			0
$229$	6.50685	+	11.2702i	0.429985	+	0.744756i	0.996871	−	0.0790402i	$-0.0251856\pi$
$229$	6.50685	+	11.2702i	0.429985	+	0.744756i	−0.566887	+	0.823796i	$0.691852\pi$
$230$	1.85242			0.122145
$231$		0			0
$232$	2.16524			0.142155
$233$	−8.92397	+	15.4568i	−0.584629	+	1.01261i	0.410293	+	0.911954i	$0.365426\pi$
$233$	−8.92397	+	15.4568i	−0.584629	+	1.01261i	−0.994922	+	0.100653i	$0.967907\pi$
$234$		0			0
$235$	24.9616			1.62832
$236$	8.86592	−	15.3562i	0.577122	−	0.999605i
$237$		0			0
$238$	−0.768522	+	1.33112i	−0.0498159	+	0.0862837i
$239$	3.30689	+	5.72770i	0.213905	+	0.370494i	0.952933	−	0.303180i	$-0.0980484\pi$
$239$	3.30689	+	5.72770i	0.213905	+	0.370494i	−0.739028	+	0.673674i	$0.764715\pi$
$240$		0			0
$241$	−7.71904			−0.497227			−0.248613	−	0.968603i	$-0.579975\pi$
$241$	−7.71904			−0.497227			−0.248613	+	0.968603i	$0.579975\pi$
$242$	0.461199	−	0.798820i	0.0296470	−	0.0513501i
$243$		0			0
$244$	0.934033	−	1.61779i	0.0597953	−	0.103569i
$245$	6.54877	+	11.3428i	0.418385	+	0.724665i
$246$		0			0
$247$	−17.8550	+	9.10915i	−1.13609	+	0.579602i
$248$	1.93541	+	3.35223i	0.122899	+	0.212867i
$249$		0			0
$250$	0.639258	+	1.10723i	0.0404302	+	0.0700272i
$251$	−9.90854	−	17.1621i	−0.625422	−	1.08326i	−0.988459	−	0.151487i	$-0.951594\pi$
$251$	−9.90854	−	17.1621i	−0.625422	−	1.08326i	0.363038	−	0.931775i	$-0.381740\pi$
$252$		0			0
$253$	−10.2279	−	17.7153i	−0.643025	−	1.11375i
$254$	−1.33742	+	2.31647i	−0.0839169	+	0.145348i
$255$		0			0
$256$	−7.15487	+	12.3926i	−0.447180	+	0.774538i
$257$	−9.54829	+	16.5381i	−0.595606	+	1.03162i	0.397855	+	0.917448i	$0.369755\pi$
$257$	−9.54829	+	16.5381i	−0.595606	+	1.03162i	−0.993461	+	0.114171i	$0.963579\pi$
$258$		0			0
$259$	9.19037	−	15.9182i	0.571062	−	0.989108i
$260$	−11.6914	−	20.2502i	−0.725072	−	1.25586i
$261$		0			0
$262$	1.57522	+	2.72837i	0.0973177	+	0.168559i
$263$	9.42257	+	16.3204i	0.581020	+	1.00636i	0.995359	+	0.0962340i	$0.0306797\pi$
$263$	9.42257	+	16.3204i	0.581020	+	1.00636i	−0.414338	+	0.910123i	$0.635987\pi$
$264$		0			0
$265$	13.7638	+	23.8395i	0.845501	+	1.46445i
$266$	−1.86370	−	1.20894i	−0.114271	−	0.0741250i
$267$		0			0
$268$	1.36238	+	2.35971i	0.0832204	+	0.144142i
$269$	−8.42218	+	14.5876i	−0.513509	+	0.889424i	0.486368	+	0.873754i	$0.338322\pi$
$269$	−8.42218	+	14.5876i	−0.513509	+	0.889424i	−0.999877	+	0.0156702i	$0.995012\pi$
$270$		0			0
$271$	10.1398	−	17.5626i	0.615946	−	1.06685i	−0.374271	−	0.927319i	$-0.622107\pi$
$271$	10.1398	−	17.5626i	0.615946	−	1.06685i	0.990218	−	0.139531i	$-0.0445596\pi$
$272$	−11.6766			−0.707998
$273$		0			0
$274$	0.647801	+	1.12202i	0.0391351	+	0.0677839i
$275$	−3.33754	+	5.78079i	−0.201261	+	0.348595i
$276$		0			0
$277$	−4.15551	+	7.19756i	−0.249681	+	0.432460i	−0.963437	−	0.267934i	$-0.913659\pi$
$277$	−4.15551	+	7.19756i	−0.249681	+	0.432460i	0.713756	+	0.700394i	$0.246992\pi$
$278$	1.94735			0.116795
$279$		0			0
$280$	2.60553	−	4.51291i	0.155710	−	0.269698i
$281$	−12.4313			−0.741592			−0.370796	−	0.928714i	$-0.620915\pi$
$281$	−12.4313			−0.741592			−0.370796	+	0.928714i	$0.620915\pi$
$282$		0			0
$283$	29.3251			1.74320			0.871598	−	0.490221i	$-0.163084\pi$
$283$	29.3251			1.74320			0.871598	+	0.490221i	$0.163084\pi$
$284$	8.81113	+	15.2613i	0.522844	+	0.905593i
$285$		0			0
$286$	1.40114	−	2.42685i	0.0828513	−	0.143503i
$287$	4.40299	−	7.62620i	0.259900	−	0.450160i
$288$		0			0
$289$	3.95205	+	6.84516i	0.232474	+	0.402656i
$290$	−0.699348	−	1.21131i	−0.0410671	−	0.0711303i
$291$		0			0
$292$	4.24930	+	7.36000i	0.248671	+	0.430712i
$293$	−1.02728	−	1.77930i	−0.0600143	−	0.103948i	0.834457	−	0.551073i	$-0.185781\pi$
$293$	−1.02728	−	1.77930i	−0.0600143	−	0.103948i	−0.894472	+	0.447125i	$0.852448\pi$
$294$		0			0
$295$	−23.0330			−1.34103
$296$	−3.08105			−0.179082
$297$		0			0
$298$	−1.01217	−	1.75313i	−0.0586333	−	0.101556i
$299$	−11.3096	−	19.5888i	−0.654051	−	1.13285i
$300$		0			0
$301$	16.6272			0.958374
$302$	−0.535603			−0.0308205
$303$		0			0
$304$	0.874557	−	16.8534i	0.0501593	−	0.966606i
$305$	−2.42655			−0.138944
$306$		0			0
$307$	−5.53654	+	9.58957i	−0.315987	+	0.547306i	−0.979647	−	0.200729i	$-0.935669\pi$
$307$	−5.53654	+	9.58957i	−0.315987	+	0.547306i	0.663660	+	0.748035i	$0.269002\pi$
$308$	−28.6170			−1.63061
$309$		0			0
$310$	1.25023	−	2.16546i	0.0710083	−	0.122990i
$311$	9.02794	+	15.6369i	0.511928	+	0.886685i	0.999904	+	0.0138280i	$0.00440174\pi$
$311$	9.02794	+	15.6369i	0.511928	+	0.886685i	−0.487977	+	0.872857i	$0.662265\pi$
$312$		0			0
$313$	11.7762			0.665631			0.332815	−	0.942992i	$-0.392001\pi$
$313$	11.7762			0.665631			0.332815	+	0.942992i	$0.392001\pi$
$314$	0.333033	+	0.576831i	0.0187942	+	0.0325525i
$315$		0			0
$316$	−6.69773			−0.376777
$317$	−5.91702			−0.332333			−0.166166	−	0.986098i	$-0.553139\pi$
$317$	−5.91702			−0.332333			−0.166166	+	0.986098i	$0.553139\pi$
$318$		0			0
$319$	−7.72276	+	13.3762i	−0.432391	+	0.748924i
$320$	19.2477			1.07598
$321$		0			0
$322$	1.25341	−	2.17098i	0.0698501	−	0.120984i
$323$	11.7103	−	5.97426i	0.651576	−	0.332417i
$324$		0			0
$325$	−3.69051	+	6.39214i	−0.204712	+	0.354572i
$326$	−0.168769	−	0.292316i	−0.00934724	−	0.0161899i
$327$		0			0
$328$	−1.47609			−0.0815035
$329$	16.8900	−	29.2543i	0.931173	−	1.61284i
$330$		0			0
$331$	5.39815	−	9.34987i	0.296709	−	0.513916i	−0.678672	−	0.734442i	$-0.737444\pi$
$331$	5.39815	−	9.34987i	0.296709	−	0.513916i	0.975381	+	0.220526i	$0.0707774\pi$
$332$	8.95561	+	15.5116i	0.491503	+	0.851308i
$333$		0			0
$334$	−1.31031			−0.0716972
$335$	1.76968	−	3.06517i	0.0966879	−	0.167468i
$336$		0			0
$337$	−29.0477			−1.58233			−0.791164	−	0.611604i	$-0.790525\pi$
$337$	−29.0477			−1.58233			−0.791164	+	0.611604i	$0.790525\pi$
$338$	0.596850	−	1.03377i	0.0324644	−	0.0562299i
$339$		0			0
$340$	7.66786	+	13.2811i	0.415848	+	0.720270i
$341$	−27.6121			−1.49528
$342$		0			0
$343$	−6.62120			−0.357511
$344$	−1.39355	−	2.41371i	−0.0751354	−	0.130138i
$345$		0			0
$346$	0.0948739	−	0.164326i	0.00510045	−	0.00883424i
$347$	−12.2521			−0.657729			−0.328865	−	0.944377i	$-0.606666\pi$
$347$	−12.2521			−0.657729			−0.328865	+	0.944377i	$0.606666\pi$
$348$		0			0
$349$	−3.55181	+	6.15191i	−0.190124	+	0.329304i	−0.945291	−	0.326228i	$-0.894222\pi$
$349$	−3.55181	+	6.15191i	−0.190124	+	0.329304i	0.755167	+	0.655532i	$0.227556\pi$
$350$	−0.818019			−0.0437249
$351$		0			0
$352$	3.60415	+	6.24256i	0.192102	+	0.332730i
$353$	17.7023	−	30.6613i	0.942200	−	1.63194i	0.180936	−	0.983495i	$-0.442087\pi$
$353$	17.7023	−	30.6613i	0.942200	−	1.63194i	0.761264	−	0.648443i	$-0.224579\pi$
$354$		0			0
$355$	11.4453	−	19.8239i	0.607456	−	1.05214i
$356$	15.6903			0.831584
$357$		0			0
$358$	−0.544414	−	0.942952i	−0.0287732	−	0.0498366i
$359$	−7.86541	+	13.6233i	−0.415121	+	0.719010i	−0.995441	−	0.0953781i	$-0.969594\pi$
$359$	−7.86541	+	13.6233i	−0.415121	+	0.719010i	0.580320	+	0.814388i	$0.302927\pi$
$360$		0			0
$361$	7.74584	+	17.3494i	0.407676	+	0.913127i
$362$	0.0449619	−	0.0778762i	0.00236314	−	0.00409308i
$363$		0			0
$364$	−31.6435			−1.65857
$365$	5.51969	−	9.56038i	0.288914	−	0.500413i
$366$		0			0
$367$	29.9482			1.56328			0.781641	−	0.623729i	$-0.214383\pi$
$367$	29.9482			1.56328			0.781641	+	0.623729i	$0.214383\pi$
$368$	19.0438			0.992729
$369$		0			0
$370$	0.995143	+	1.72364i	0.0517350	+	0.0896077i
$371$	37.2523			1.93404
$372$		0			0
$373$	−5.46086	−	9.45848i	−0.282753	−	0.489742i	0.689309	−	0.724467i	$-0.257914\pi$
$373$	−5.46086	−	9.45848i	−0.282753	−	0.489742i	−0.972062	+	0.234726i	$0.924581\pi$
$374$	−0.918943	+	1.59166i	−0.0475174	+	0.0823026i
$375$		0			0
$376$	−5.66232			−0.292012
$377$	−8.53948	+	14.7908i	−0.439806	+	0.761766i
$378$		0			0
$379$	−17.0217			−0.874348			−0.437174	−	0.899377i	$-0.644021\pi$
$379$	−17.0217			−0.874348			−0.437174	+	0.899377i	$0.644021\pi$
$380$	−19.7436	+	10.0726i	−1.01282	+	0.516715i
$381$		0			0
$382$	0.828600			0.0423949
$383$	9.55115			0.488041			0.244021	−	0.969770i	$-0.421534\pi$
$383$	9.55115			0.488041			0.244021	+	0.969770i	$0.421534\pi$
$384$		0			0
$385$	18.5863	+	32.1923i	0.947244	+	1.64067i
$386$	0.129312	+	0.223974i	0.00658179	+	0.0114000i
$387$		0			0
$388$	−3.68139			−0.186894
$389$	−17.7691			−0.900927			−0.450463	−	0.892795i	$-0.648741\pi$
$389$	−17.7691			−0.900927			−0.450463	+	0.892795i	$0.648741\pi$
$390$		0			0
$391$	7.41743	+	12.8474i	0.375116	+	0.649719i
$392$	−1.48553	−	2.57301i	−0.0750306	−	0.129957i
$393$		0			0
$394$	0.100520	+	0.174106i	0.00506414	+	0.00877136i
$395$	4.35006	+	7.53452i	0.218875	+	0.379103i
$396$		0			0
$397$	−4.95146	+	8.57619i	−0.248507	+	0.430426i	−0.963112	−	0.269102i	$-0.913273\pi$
$397$	−4.95146	+	8.57619i	−0.248507	+	0.430426i	0.714605	+	0.699528i	$0.246607\pi$
$398$	−1.80359	+	3.12390i	−0.0904056	+	0.156587i
$399$		0			0
$400$	−3.10716	−	5.38175i	−0.155358	−	0.269088i
$401$	−16.4249			−0.820220			−0.410110	−	0.912036i	$-0.634510\pi$
$401$	−16.4249			−0.820220			−0.410110	+	0.912036i	$0.634510\pi$
$402$		0			0
$403$	−30.5322			−1.52092
$404$	9.77694	−	16.9342i	0.486421	−	0.842506i
$405$		0			0
$406$	−1.89282			−0.0939390
$407$	10.9892	−	19.0338i	0.544713	−	0.943471i
$408$		0			0
$409$	14.0437	−	24.3245i	0.694418	−	1.20277i	−0.275958	−	0.961170i	$-0.588995\pi$
$409$	14.0437	−	24.3245i	0.694418	−	1.20277i	0.970376	−	0.241598i	$-0.0776716\pi$
$410$	0.476760	+	0.825773i	0.0235455	+	0.0407820i
$411$		0			0
$412$	−37.0083			−1.82327
$413$	−15.5850	+	26.9940i	−0.766888	+	1.32829i
$414$		0			0
$415$	11.6330	−	20.1490i	0.571043	−	0.989075i
$416$	3.98530	+	6.90275i	0.195396	+	0.338435i
$417$		0			0
$418$	−2.22848	−	1.44556i	−0.108999	−	0.0707049i
$419$	−2.35560	−	4.08002i	−0.115079	−	0.199322i	0.802733	−	0.596339i	$-0.203379\pi$
$419$	−2.35560	−	4.08002i	−0.115079	−	0.199322i	−0.917811	+	0.397017i	$0.870045\pi$
$420$		0			0
$421$	−8.34511	−	14.4542i	−0.406716	−	0.704452i	0.587804	−	0.809004i	$-0.299993\pi$
$421$	−8.34511	−	14.4542i	−0.406716	−	0.704452i	−0.994520	+	0.104551i	$0.966659\pi$
$422$	−0.524978	−	0.909289i	−0.0255555	−	0.0442635i
$423$		0			0
$424$	−3.12219	−	5.40778i	−0.151627	−	0.262625i
$425$	2.42043	−	4.19230i	0.117408	−	0.203357i
$426$		0			0
$427$	−1.64190	+	2.84385i	−0.0794569	+	0.137623i
$428$	15.1394	−	26.2222i	0.731791	−	1.26750i
$429$		0			0
$430$	−0.900204	+	1.55920i	−0.0434117	+	0.0751912i
$431$	−13.7404	−	23.7990i	−0.661850	−	1.14636i	−0.980129	−	0.198360i	$-0.936438\pi$
$431$	−13.7404	−	23.7990i	−0.661850	−	1.14636i	0.318279	−	0.947997i	$-0.396895\pi$
$432$		0			0
$433$	16.6749	+	28.8817i	0.801343	+	1.38797i	0.918732	+	0.394881i	$0.129214\pi$
$433$	16.6749	+	28.8817i	0.801343	+	1.38797i	−0.117389	+	0.993086i	$0.537452\pi$
$434$	−1.69191	−	2.93047i	−0.0812140	−	0.140667i
$435$		0			0
$436$	−3.25822	−	5.64340i	−0.156040	−	0.270270i
$437$	−19.0987	+	9.74367i	−0.913617	+	0.466103i
$438$		0			0
$439$	13.1597	+	22.7932i	0.628078	+	1.08786i	0.987937	+	0.154856i	$0.0494913\pi$
$439$	13.1597	+	22.7932i	0.628078	+	1.08786i	−0.359860	+	0.933006i	$0.617175\pi$
$440$	3.11550	−	5.39620i	0.148526	−	0.257254i
$441$		0			0
$442$	−1.01613	+	1.75998i	−0.0483322	+	0.0837138i
$443$	28.5529			1.35659			0.678293	−	0.734791i	$-0.262720\pi$
$443$	28.5529			1.35659			0.678293	+	0.734791i	$0.262720\pi$
$444$		0			0
$445$	−10.1906	−	17.6506i	−0.483079	−	0.836718i
$446$	0.0890530	−	0.154244i	0.00421678	−	0.00730368i
$447$		0			0
$448$	13.0237	−	22.5577i	0.615312	−	1.06575i
$449$	−29.8391			−1.40819			−0.704097	−	0.710104i	$-0.748648\pi$
$449$	−29.8391			−1.40819			−0.704097	+	0.710104i	$0.748648\pi$
$450$		0			0
$451$	5.26477	−	9.11885i	0.247908	−	0.429390i
$452$	7.15371			0.336482
$453$		0			0
$454$	1.30708			0.0613444
$455$	20.5519	+	35.5969i	0.963486	+	1.66881i
$456$		0			0
$457$	−2.02990	+	3.51588i	−0.0949546	+	0.164466i	−0.909590	−	0.415508i	$-0.863604\pi$
$457$	−2.02990	+	3.51588i	−0.0949546	+	0.164466i	0.814635	+	0.579974i	$0.196937\pi$
$458$	−0.953475	+	1.65147i	−0.0445530	+	0.0771680i
$459$		0			0
$460$	−12.5058	−	21.6607i	−0.583087	−	1.00994i
$461$	−8.39068	−	14.5331i	−0.390793	−	0.676873i	0.601761	−	0.798676i	$-0.294466\pi$
$461$	−8.39068	−	14.5331i	−0.390793	−	0.676873i	−0.992554	+	0.121803i	$0.961133\pi$
$462$		0			0
$463$	−0.887050	−	1.53642i	−0.0412247	−	0.0714033i	0.844677	−	0.535277i	$-0.179793\pi$
$463$	−0.887050	−	1.53642i	−0.0412247	−	0.0714033i	−0.885902	+	0.463873i	$0.846459\pi$
$464$	−7.18967	−	12.4529i	−0.333772	−	0.578110i
$465$		0			0
$466$	−2.61533			−0.121153
$467$	−13.4739			−0.623496			−0.311748	−	0.950165i	$-0.600914\pi$
$467$	−13.4739			−0.623496			−0.311748	+	0.950165i	$0.600914\pi$
$468$		0			0
$469$	−2.39486	−	4.14802i	−0.110584	−	0.191538i
$470$	1.82886	+	3.16768i	0.0843591	+	0.146114i
$471$		0			0
$472$	5.22483			0.240492
$473$	19.8816			0.914155
$474$		0			0
$475$	5.86965	+	3.80751i	0.269318	+	0.174700i
$476$	20.7534			0.951232
$477$		0			0
$478$	−0.484572	+	0.839303i	−0.0221638	+	0.0383888i
$479$	20.4128			0.932685			0.466343	−	0.884604i	$-0.345571\pi$
$479$	20.4128			0.932685			0.466343	+	0.884604i	$0.345571\pi$
$480$		0			0
$481$	12.1513	−	21.0467i	0.554054	−	0.959649i
$482$	−0.565551	−	0.979563i	−0.0257601	−	0.0446179i
$483$		0			0
$484$	−12.4544			−0.566108
$485$	2.39100	+	4.14133i	0.108570	+	0.188048i
$486$		0			0
$487$	23.6649			1.07236			0.536180	−	0.844104i	$-0.319867\pi$
$487$	23.6649			1.07236			0.536180	+	0.844104i	$0.319867\pi$
$488$	0.550441			0.0249173
$489$		0			0
$490$	−0.959617	+	1.66211i	−0.0433511	+	0.0750863i
$491$	−4.06836			−0.183603			−0.0918013	−	0.995777i	$-0.529262\pi$
$491$	−4.06836			−0.183603			−0.0918013	+	0.995777i	$0.529262\pi$
$492$		0			0
$493$	5.60064	−	9.70060i	0.252240	−	0.436893i
$494$	−2.46416	−	1.59844i	−0.110868	−	0.0719172i
$495$		0			0
$496$	12.8530	−	22.2621i	0.577118	−	0.999598i
$497$	−15.4887	−	26.8272i	−0.694763	−	1.20336i
$498$		0			0
$499$	27.3100			1.22257			0.611283	−	0.791412i	$-0.290654\pi$
$499$	27.3100			1.22257			0.611283	+	0.791412i	$0.290654\pi$
$500$	8.63137	−	14.9500i	0.386007	−	0.668583i
$501$		0			0
$502$	1.45194	−	2.51483i	0.0648032	−	0.112242i
$503$	10.8699	+	18.8272i	0.484665	+	0.839465i	0.999845	−	0.0176172i	$-0.00560801\pi$
$503$	10.8699	+	18.8272i	0.484665	+	0.839465i	−0.515179	+	0.857082i	$0.672275\pi$
$504$		0			0
$505$	−25.3998			−1.13028
$506$	1.49874	−	2.59590i	0.0666272	−	0.115402i
$507$		0			0
$508$	36.1160			1.60239
$509$	−13.0857	+	22.6651i	−0.580012	+	1.00461i	0.415465	+	0.909609i	$0.363619\pi$
$509$	−13.0857	+	22.6651i	−0.580012	+	1.00461i	−0.995477	+	0.0950015i	$0.969714\pi$
$510$		0			0
$511$	−7.46965	−	12.9378i	−0.330438	−	0.572335i
$512$	−11.2250			−0.496077
$513$		0			0
$514$	−2.79830			−0.123428
$515$	24.0362	+	41.6319i	1.05916	+	1.83452i
$516$		0			0
$517$	20.1958	−	34.9801i	0.888209	−	1.53842i
$518$	2.69340			0.118341
$519$		0			0
$520$	3.44498	−	5.96688i	0.151072	−	0.261665i
$521$	30.4889			1.33574			0.667872	−	0.744276i	$-0.267205\pi$
$521$	30.4889			1.33574			0.667872	+	0.744276i	$0.267205\pi$
$522$		0			0
$523$	−10.8103	−	18.7241i	−0.472703	−	0.818746i	0.526809	−	0.849984i	$-0.323388\pi$
$523$	−10.8103	−	18.7241i	−0.472703	−	0.818746i	−0.999512	+	0.0312380i	$0.990055\pi$
$524$	21.2689	−	36.8389i	0.929138	−	1.60931i
$525$		0			0
$526$	−1.38073	+	2.39149i	−0.0602026	+	0.104274i
$527$	20.0246			0.872287
$528$		0			0
$529$	−0.597391	−	1.03471i	−0.0259735	−	0.0449875i
$530$	−2.01686	+	3.49330i	−0.0876068	+	0.151739i
$531$		0			0
$532$	−1.55440	+	29.9544i	−0.0673916	+	1.29869i
$533$	5.82155	−	10.0832i	0.252159	−	0.436753i
$534$		0			0
$535$	−39.3311			−1.70043
$536$	−0.401436	+	0.695307i	−0.0173394	+	0.0300327i
$537$		0			0
$538$	−2.46827			−0.106415
$539$	21.1937			0.912879
$540$		0			0
$541$	−18.3616	−	31.8032i	−0.789427	−	1.36733i	−0.926318	−	0.376742i	$-0.877044\pi$
$541$	−18.3616	−	31.8032i	−0.789427	−	1.36733i	0.136891	−	0.990586i	$-0.456289\pi$
$542$	2.97164			0.127643
$543$		0			0
$544$	−2.61377	−	4.52719i	−0.112065	−	0.194101i
$545$	−4.23231	+	7.33057i	−0.181292	+	0.314007i
$546$		0			0
$547$	17.2131			0.735980			0.367990	−	0.929830i	$-0.380046\pi$
$547$	17.2131			0.735980			0.367990	+	0.929830i	$0.380046\pi$
$548$	8.74672	−	15.1498i	0.373641	−	0.647166i
$549$		0			0
$550$	−0.978127			−0.0417075
$551$	13.5818	+	8.81022i	0.578605	+	0.375328i
$552$		0			0
$553$	11.7736			0.500666
$554$	−1.21785			−0.0517414
$555$		0			0
$556$	−13.1468	−	22.7709i	−0.557547	−	0.965699i
$557$	−8.67769	−	15.0302i	−0.367686	−	0.636850i	0.621518	−	0.783400i	$-0.286516\pi$
$557$	−8.67769	−	15.0302i	−0.367686	−	0.636850i	−0.989203	+	0.146550i	$0.953183\pi$
$558$		0			0
$559$	21.9841			0.929830
$560$	−34.6065			−1.46239
$561$		0			0
$562$	−0.910808	−	1.57757i	−0.0384201	−	0.0665456i
$563$	−8.34041	−	14.4460i	−0.351506	−	0.608827i	0.635007	−	0.772506i	$-0.280997\pi$
$563$	−8.34041	−	14.4460i	−0.351506	−	0.608827i	−0.986514	+	0.163679i	$0.947664\pi$
$564$		0			0
$565$	−4.64621	−	8.04747i	−0.195468	−	0.338560i
$566$	2.14856	+	3.72142i	0.0903108	+	0.156423i
$567$		0			0
$568$	−2.59627	+	4.49688i	−0.108937	+	0.188685i
$569$	−5.41399	+	9.37731i	−0.226966	+	0.393117i	−0.956908	−	0.290393i	$-0.906214\pi$
$569$	−5.41399	+	9.37731i	−0.226966	+	0.393117i	0.729941	+	0.683510i	$0.239547\pi$
$570$		0			0
$571$	−11.5342	−	19.9778i	−0.482691	−	0.836045i	0.517111	−	0.855918i	$-0.327007\pi$
$571$	−11.5342	−	19.9778i	−0.482691	−	0.836045i	−0.999803	+	0.0198726i	$0.993674\pi$
$572$	−37.8369			−1.58204
$573$		0			0
$574$	1.29038			0.0538592
$575$	−3.94757	+	6.83740i	−0.164625	+	0.285139i
$576$		0			0
$577$	2.29118			0.0953830			0.0476915	−	0.998862i	$-0.484814\pi$
$577$	2.29118			0.0953830			0.0476915	+	0.998862i	$0.484814\pi$
$578$	−0.579110	+	1.00305i	−0.0240878	+	0.0417213i
$579$		0			0
$580$	−9.44271	+	16.3553i	−0.392087	+	0.679115i
$581$	−15.7427	−	27.2671i	−0.653116	−	1.13123i
$582$		0			0
$583$	44.5436			1.84481
$584$	−1.25209	+	2.16869i	−0.0518119	+	0.0897409i
$585$		0			0
$586$	0.150531	−	0.260728i	0.00621840	−	0.0107706i
$587$	18.0322	+	31.2326i	0.744267	+	1.28911i	0.950536	+	0.310614i	$0.100535\pi$
$587$	18.0322	+	31.2326i	0.744267	+	1.28911i	−0.206269	+	0.978495i	$0.566132\pi$
$588$		0			0
$589$	−1.49981	+	28.9025i	−0.0617987	+	1.19091i
$590$	−1.68756	−	2.92294i	−0.0694758	−	0.120336i
$591$		0			0
$592$	10.2306	+	17.7199i	0.420475	+	0.728285i
$593$	3.95398	+	6.84849i	0.162370	+	0.281234i	0.935718	−	0.352748i	$-0.114753\pi$
$593$	3.95398	+	6.84849i	0.162370	+	0.281234i	−0.773348	+	0.633982i	$0.781419\pi$
$594$		0			0
$595$	−13.4790	−	23.3463i	−0.552585	−	0.957105i
$596$	−13.6665	+	23.6710i	−0.559800	+	0.969602i
$597$		0			0
$598$	1.65724	−	2.87043i	0.0677697	−	0.117380i
$599$	−16.0109	+	27.7317i	−0.654187	+	1.13309i	0.327910	+	0.944709i	$0.393656\pi$
$599$	−16.0109	+	27.7317i	−0.654187	+	1.13309i	−0.982097	+	0.188376i	$0.939677\pi$
$600$		0			0
$601$	−16.6013	+	28.7542i	−0.677180	+	1.17291i	0.298646	+	0.954364i	$0.403465\pi$
$601$	−16.6013	+	28.7542i	−0.677180	+	1.17291i	−0.975827	+	0.218546i	$0.929868\pi$
$602$	1.21822	+	2.11002i	0.0496511	+	0.0859982i
$603$		0			0
$604$	3.61590	+	6.26293i	0.147129	+	0.254835i
$605$	8.08889	+	14.0104i	0.328860	+	0.569603i
$606$		0			0
$607$	19.9393	+	34.5360i	0.809313	+	1.40177i	0.913340	+	0.407197i	$0.133494\pi$
$607$	19.9393	+	34.5360i	0.809313	+	1.40177i	−0.104027	+	0.994574i	$0.533173\pi$
$608$	6.73006	−	3.43350i	0.272940	−	0.139247i
$609$		0			0
$610$	−0.177786	−	0.307935i	−0.00719835	−	0.0124679i
$611$	22.3316	−	38.6794i	0.903439	−	1.56480i
$612$		0			0
$613$	−4.68793	+	8.11973i	−0.189344	+	0.327953i	−0.945032	−	0.326979i	$-0.893969\pi$
$613$	−4.68793	+	8.11973i	−0.189344	+	0.327953i	0.755688	+	0.654932i	$0.227303\pi$
$614$	−1.62258			−0.0654822
$615$		0			0
$616$	−4.21613	−	7.30254i	−0.169873	−	0.294228i
$617$	15.2062	−	26.3379i	0.612179	−	1.06033i	−0.378693	−	0.925522i	$-0.623626\pi$
$617$	15.2062	−	26.3379i	0.612179	−	1.06033i	0.990872	−	0.134803i	$-0.0430402\pi$
$618$		0			0
$619$	−11.8294	+	20.4890i	−0.475462	+	0.823524i	−0.999605	−	0.0281061i	$-0.991052\pi$
$619$	−11.8294	+	20.4890i	−0.475462	+	0.823524i	0.524143	+	0.851630i	$0.324386\pi$
$620$	−33.7617			−1.35590
$621$		0			0
$622$	−1.32290	+	2.29133i	−0.0530435	+	0.0918740i
$623$	−27.5813			−1.10502
$624$		0			0
$625$	−30.4491			−1.21797
$626$	0.862808	+	1.49443i	0.0344847	+	0.0597293i
$627$		0			0
$628$	4.49667	−	7.78847i	0.179437	−	0.310794i
$629$	−7.96949	+	13.8036i	−0.317764	+	0.550384i
$630$		0			0
$631$	9.85638	+	17.0717i	0.392376	+	0.679615i	0.992762	−	0.120095i	$-0.0383198\pi$
$631$	9.85638	+	17.0717i	0.392376	+	0.679615i	−0.600386	+	0.799710i	$0.704986\pi$
$632$	−0.986771	−	1.70914i	−0.0392517	−	0.0679859i
$633$		0			0
$634$	−0.433522	−	0.750883i	−0.0172174	−	0.0298214i
$635$	−23.4567	−	40.6282i	−0.930851	−	1.61228i
$636$		0			0
$637$	23.4351			0.928532
$638$	−2.26329			−0.0896047
$639$		0			0
$640$	5.86488	+	10.1583i	0.231830	+	0.401541i
$641$	−0.592690	−	1.02657i	−0.0234098	−	0.0405470i	0.854083	−	0.520136i	$-0.174119\pi$
$641$	−0.592690	−	1.02657i	−0.0234098	−	0.0405470i	−0.877493	+	0.479589i	$0.840786\pi$
$642$		0			0
$643$	−27.8563			−1.09854			−0.549272	−	0.835644i	$-0.685095\pi$
$643$	−27.8563			−1.09854			−0.549272	+	0.835644i	$0.685095\pi$
$644$	−33.8476			−1.33378
$645$		0			0
$646$	1.61612	+	1.04834i	0.0635855	+	0.0412464i
$647$	3.69287			0.145182			0.0725909	−	0.997362i	$-0.476873\pi$
$647$	3.69287			0.145182			0.0725909	+	0.997362i	$0.476873\pi$
$648$		0			0
$649$	−18.6354	+	32.2775i	−0.731504	+	1.26700i
$650$	−1.08157			−0.0424226
$651$		0			0
$652$	−2.27875	+	3.94690i	−0.0892426	+	0.154573i
$653$	−0.659445	−	1.14219i	−0.0258061	−	0.0446974i	0.852834	−	0.522182i	$-0.174882\pi$
$653$	−0.659445	−	1.14219i	−0.0258061	−	0.0446974i	−0.878640	+	0.477485i	$0.841549\pi$
$654$		0			0
$655$	−55.2552			−2.15900
$656$	4.90135	+	8.48939i	0.191366	+	0.331455i
$657$		0			0
$658$	4.94991			0.192967
$659$	4.85745			0.189219			0.0946097	−	0.995514i	$-0.469840\pi$
$659$	4.85745			0.189219			0.0946097	+	0.995514i	$0.469840\pi$
$660$		0			0
$661$	−15.1068	+	26.1657i	−0.587586	+	1.01773i	0.406962	+	0.913445i	$0.366588\pi$
$661$	−15.1068	+	26.1657i	−0.587586	+	1.01773i	−0.994548	+	0.104283i	$0.966745\pi$
$662$	1.58203			0.0614872
$663$		0			0
$664$	−2.63885	+	4.57062i	−0.102407	+	0.177374i
$665$	34.7063	−	17.7062i	1.34585	−	0.686618i
$666$		0			0
$667$	−9.13431	+	15.8211i	−0.353682	+	0.612595i
$668$	8.84604	+	15.3218i	0.342264	+	0.592818i
$669$		0			0
$670$	0.518636			0.0200367
$671$	−1.96326	+	3.40046i	−0.0757908	+	0.131273i
$672$		0			0
$673$	3.03772	−	5.26149i	0.117096	−	0.202815i	−0.801520	−	0.597968i	$-0.795975\pi$
$673$	3.03772	−	5.26149i	0.117096	−	0.202815i	0.918615	+	0.395153i	$0.129308\pi$
$674$	−2.12824	−	3.68622i	−0.0819767	−	0.141988i
$675$		0			0
$676$	−16.1175			−0.619905
$677$	−5.96003	+	10.3231i	−0.229062	+	0.396748i	−0.957531	−	0.288332i	$-0.906899\pi$
$677$	−5.96003	+	10.3231i	−0.229062	+	0.396748i	0.728468	+	0.685080i	$0.240233\pi$
$678$		0			0
$679$	6.47135			0.248348
$680$	−2.25940	+	3.91339i	−0.0866440	+	0.150072i
$681$		0			0
$682$	−2.02306	−	3.50404i	−0.0774669	−	0.134177i
$683$	0.0898958			0.00343977			0.00171988	−	0.999999i	$-0.499453\pi$
$683$	0.0898958			0.00343977			0.00171988	+	0.999999i	$0.499453\pi$
$684$		0			0
$685$	−22.7233			−0.868214
$686$	−0.485115	−	0.840245i	−0.0185218	−	0.0320807i
$687$		0			0
$688$	−9.25458	+	16.0294i	−0.352827	+	0.611115i
$689$	49.2543			1.87644
$690$		0			0
$691$	3.96889	−	6.87432i	0.150984	−	0.261512i	−0.780606	−	0.625024i	$-0.785089\pi$
$691$	3.96889	−	6.87432i	0.150984	−	0.261512i	0.931589	+	0.363512i	$0.118423\pi$
$692$	−2.56201			−0.0973929
$693$		0			0
$694$	−0.897678	−	1.55482i	−0.0340754	−	0.0590203i
$695$	−17.0772	+	29.5785i	−0.647774	+	1.12198i
$696$		0			0
$697$	−3.81808	+	6.61311i	−0.144620	+	0.250489i
$698$	−1.04092			−0.0393995
$699$		0			0
$700$	5.52251	+	9.56527i	0.208731	+	0.361533i
$701$	24.0605	−	41.6741i	0.908753	−	1.57401i	0.0929554	−	0.995670i	$-0.470369\pi$
$701$	24.0605	−	41.6741i	0.908753	−	1.57401i	0.815798	−	0.578337i	$-0.196298\pi$
$702$		0			0
$703$	−19.3264	−	12.5366i	−0.728909	−	0.472826i
$704$	15.5728	−	26.9729i	0.586922	−	1.01658i
$705$		0			0
$706$	5.18799			0.195252
$707$	−17.1864	+	29.7678i	−0.646363	+	1.11953i
$708$		0			0
$709$	22.6589			0.850974			0.425487	−	0.904964i	$-0.360103\pi$
$709$	22.6589			0.850974			0.425487	+	0.904964i	$0.360103\pi$
$710$	3.35426			0.125883
$711$		0			0
$712$	2.31164	+	4.00388i	0.0866323	+	0.150052i
$713$	−32.6590			−1.22309
$714$		0			0
$715$	24.5744	+	42.5641i	0.919031	+	1.59181i
$716$	−7.35077	+	12.7319i	−0.274711	+	0.475813i
$717$		0			0
$718$	−2.30510			−0.0860256
$719$	7.93724	−	13.7477i	0.296009	−	0.512703i	−0.679210	−	0.733944i	$-0.737677\pi$
$719$	7.93724	−	13.7477i	0.296009	−	0.512703i	0.975219	+	0.221241i	$0.0710108\pi$
$720$		0			0
$721$	65.0552			2.42278
$722$	−1.63416	+	2.25410i	−0.0608173	+	0.0838891i
$723$		0			0
$724$	−1.21417			−0.0451241
$725$	5.96135			0.221399
$726$		0			0
$727$	−9.86736	−	17.0908i	−0.365960	−	0.633862i	0.622969	−	0.782246i	$-0.285926\pi$
$727$	−9.86736	−	17.0908i	−0.365960	−	0.633862i	−0.988930	+	0.148384i	$0.952593\pi$
$728$	−4.66200	−	8.07483i	−0.172785	−	0.299273i
$729$		0			0
$730$	1.61764			0.0598717
$731$	−14.4184			−0.533282
$732$		0			0
$733$	−8.80378	−	15.2486i	−0.325175	−	0.563220i	0.656373	−	0.754437i	$-0.272090\pi$
$733$	−8.80378	−	15.2486i	−0.325175	−	0.563220i	−0.981548	+	0.191217i	$0.938757\pi$
$734$	2.19421	+	3.80049i	0.0809899	+	0.140279i
$735$		0			0
$736$	4.26291	+	7.38357i	0.157133	+	0.272162i
$737$	−2.86360	−	4.95990i	−0.105482	−	0.182700i
$738$		0			0
$739$	9.37525	−	16.2384i	0.344874	−	0.597339i	−0.640457	−	0.767994i	$-0.721255\pi$
$739$	9.37525	−	16.2384i	0.344874	−	0.597339i	0.985331	+	0.170655i	$0.0545883\pi$
$740$	13.4366	−	23.2729i	0.493939	−	0.855528i
$741$		0			0
$742$	2.72937	+	4.72740i	0.100198	+	0.173548i
$743$	−21.4141			−0.785609			−0.392804	−	0.919622i	$-0.628495\pi$
$743$	−21.4141			−0.785609			−0.392804	+	0.919622i	$0.628495\pi$
$744$		0			0
$745$	35.5045			1.30078
$746$	0.800202	−	1.38599i	0.0292975	−	0.0507447i
$747$		0			0
$748$	24.8155			0.907343
$749$	−26.6129	+	46.0949i	−0.972414	+	1.68427i
$750$		0			0
$751$	16.1013	−	27.8883i	0.587546	−	1.01766i	−0.407007	−	0.913425i	$-0.633428\pi$
$751$	16.1013	−	27.8883i	0.587546	−	1.01766i	0.994553	−	0.104234i	$-0.0332391\pi$
$752$	18.8017	+	32.5655i	0.685627	+	1.18754i
$753$		0			0
$754$	−2.50265			−0.0911411
$755$	4.69693	−	8.13532i	0.170939	−	0.296075i
$756$		0			0
$757$	13.3362	−	23.0990i	0.484713	−	0.839548i	−0.515133	−	0.857111i	$-0.672257\pi$
$757$	13.3362	−	23.0990i	0.484713	−	0.839548i	0.999846	+	0.0175627i	$0.00559065\pi$
$758$	−1.24713	−	2.16010i	−0.0452979	−	0.0784582i
$759$		0			0
$760$	−5.47915	−	3.55420i	−0.198750	−	0.128924i
$761$	−2.75558	−	4.77281i	−0.0998898	−	0.173014i	0.811749	−	0.584006i	$-0.198516\pi$
$761$	−2.75558	−	4.77281i	−0.0998898	−	0.173014i	−0.911639	+	0.410992i	$0.865182\pi$
$762$		0			0
$763$	5.72747	+	9.92027i	0.207348	+	0.359138i
$764$	−5.59395	−	9.68901i	−0.202382	−	0.350536i
$765$		0			0
$766$	0.699784	+	1.21206i	0.0252842	+	0.0437936i
$767$	−20.6062	+	35.6910i	−0.744047	+	1.28873i
$768$		0			0
$769$	−8.53835	+	14.7889i	−0.307901	+	0.533300i	−0.977903	−	0.209059i	$-0.932960\pi$
$769$	−8.53835	+	14.7889i	−0.307901	+	0.533300i	0.670002	+	0.742359i	$0.266293\pi$
$770$	−2.72352	+	4.71728i	−0.0981488	+	0.169999i
$771$		0			0
$772$	1.74599	−	3.02414i	0.0628395	−	0.108841i
$773$	24.4260	+	42.3071i	0.878542	+	1.52168i	0.852941	+	0.522008i	$0.174817\pi$
$773$	24.4260	+	42.3071i	0.878542	+	1.52168i	0.0256018	+	0.999672i	$0.491850\pi$
$774$		0			0
$775$	5.32858	+	9.22937i	0.191408	+	0.331529i
$776$	−0.542376	−	0.939423i	−0.0194702	−	0.0337233i
$777$		0			0
$778$	−1.30189	−	2.25493i	−0.0466749	−	0.0808432i
$779$	−9.25903	−	6.00612i	−0.331739	−	0.215191i
$780$		0			0
$781$	−18.5202	−	32.0780i	−0.662706	−	1.14784i
$782$	−1.08691	+	1.88258i	−0.0388677	+	0.0673208i
$783$		0			0
$784$	−9.86538	+	17.0873i	−0.352335	+	0.610262i
$785$	−11.6820			−0.416950
$786$		0			0
$787$	−14.3827	−	24.9115i	−0.512687	−	0.888000i	−0.999892	−	0.0147124i	$-0.995317\pi$
$787$	−14.3827	−	24.9115i	−0.512687	−	0.888000i	0.487205	−	0.873288i	$-0.338017\pi$
$788$	1.35724	−	2.35081i	0.0483498	−	0.0837443i
$789$		0			0
$790$	−0.637432	+	1.10406i	−0.0226788	+	0.0392808i
$791$	−12.5752			−0.447122
$792$		0			0
$793$	−2.17088	+	3.76008i	−0.0770903	+	0.133524i
$794$	−1.45112			−0.0514982
$795$		0			0
$796$	48.7046			1.72629
$797$	−4.94044	−	8.55709i	−0.174999	−	0.303108i	0.765162	−	0.643838i	$-0.222659\pi$
$797$	−4.94044	−	8.55709i	−0.174999	−	0.303108i	−0.940161	+	0.340730i	$0.889326\pi$
$798$		0			0
$799$	−14.6462	+	25.3680i	−0.518146	+	0.897456i
$800$	1.39106	−	2.40938i	0.0491812	−	0.0851844i
$801$		0			0
$802$	−1.20340	−	2.08435i	−0.0424936	−	0.0736011i
$803$	−8.93167	−	15.4701i	−0.315192	−	0.545928i
$804$		0			0
$805$	21.9834	+	38.0764i	0.774814	+	1.34202i
$806$	−2.23701	−	3.87461i	−0.0787952	−	0.136477i
$807$		0			0
$808$	5.76171			0.202696
$809$	−21.3112			−0.749262			−0.374631	−	0.927174i	$-0.622231\pi$
$809$	−21.3112			−0.749262			−0.374631	+	0.927174i	$0.622231\pi$
$810$		0			0
$811$	−4.62375	−	8.00857i	−0.162362	−	0.281219i	0.773353	−	0.633975i	$-0.218578\pi$
$811$	−4.62375	−	8.00857i	−0.162362	−	0.281219i	−0.935715	+	0.352756i	$0.885244\pi$
$812$	12.7786	+	22.1331i	0.448440	+	0.776721i
$813$		0			0
$814$	3.22058			0.112881
$815$	5.92002			0.207369
$816$		0			0
$817$	1.07991	−	20.8107i	0.0377813	−	0.728073i
$818$	4.11577			0.143905
$819$		0			0
$820$	6.43730	−	11.1497i	0.224800	−	0.389366i
$821$	45.2624			1.57967			0.789834	−	0.613320i	$-0.210166\pi$
$821$	45.2624			1.57967			0.789834	+	0.613320i	$0.210166\pi$
$822$		0			0
$823$	−16.7529	+	29.0168i	−0.583968	+	1.01146i	0.411035	+	0.911619i	$0.365167\pi$
$823$	−16.7529	+	29.0168i	−0.583968	+	1.01146i	−0.995003	+	0.0998428i	$0.968166\pi$
$824$	−5.45240	−	9.44383i	−0.189943	−	0.328991i
$825$		0			0
$826$	−4.56747			−0.158922
$827$	7.94152	+	13.7551i	0.276154	+	0.478312i	0.970426	−	0.241401i	$-0.0776068\pi$
$827$	7.94152	+	13.7551i	0.276154	+	0.478312i	−0.694272	+	0.719713i	$0.744273\pi$
$828$		0			0
$829$	16.0447			0.557254			0.278627	−	0.960399i	$-0.410121\pi$
$829$	16.0447			0.557254			0.278627	+	0.960399i	$0.410121\pi$
$830$	3.40927			0.118337
$831$		0			0
$832$	17.2197	−	29.8254i	0.596986	−	1.03401i
$833$	−15.3700			−0.532538
$834$		0			0
$835$	11.4907	−	19.9025i	0.397652	−	0.688753i
$836$	−1.85863	+	35.8173i	−0.0642822	+	1.23877i
$837$		0			0
$838$	0.345176	−	0.597862i	0.0119239	−	0.0206528i
$839$	−27.0487	−	46.8497i	−0.933823	−	1.61743i	−0.776719	−	0.629848i	$-0.783117\pi$
$839$	−27.0487	−	46.8497i	−0.933823	−	1.61743i	−0.157105	−	0.987582i	$-0.550216\pi$
$840$		0			0
$841$	−15.2060			−0.524345
$842$	1.22284	−	2.11803i	0.0421419	−	0.0729920i
$843$		0			0
$844$	−7.08834	+	12.2774i	−0.243991	+	0.422605i
$845$	10.4681	+	18.1312i	0.360112	+	0.623732i
$846$		0			0
$847$	21.8930			0.752252
$848$	−20.7344	+	35.9130i	−0.712022	+	1.23326i
$849$		0			0
$850$	0.709350			0.0243305
$851$	12.9978	−	22.5128i	0.445558	−	0.771728i
$852$		0			0
$853$	16.4770	+	28.5390i	0.564162	+	0.977158i	0.997127	+	0.0757469i	$0.0241341\pi$
$853$	16.4770	+	28.5390i	0.564162	+	0.977158i	−0.432965	+	0.901411i	$0.642533\pi$
$854$	−0.481187			−0.0164659
$855$		0			0
$856$	8.92191			0.304945
$857$	−20.8099	−	36.0439i	−0.710854	−	1.23123i	−0.964537	−	0.263947i	$-0.914975\pi$
$857$	−20.8099	−	36.0439i	−0.710854	−	1.23123i	0.253683	−	0.967287i	$-0.418358\pi$
$858$		0			0
$859$	−13.1480	+	22.7730i	−0.448604	+	0.777005i	−0.998295	−	0.0583631i	$-0.981412\pi$
$859$	−13.1480	+	22.7730i	−0.448604	+	0.777005i	0.549692	+	0.835368i	$0.314745\pi$
$860$	24.3094			0.828944
$861$		0			0
$862$	2.01343	−	3.48736i	0.0685777	−	0.118780i
$863$	52.7542			1.79577			0.897886	−	0.440228i	$-0.145102\pi$
$863$	52.7542			1.79577			0.897886	+	0.440228i	$0.145102\pi$
$864$		0			0
$865$	1.66398	+	2.88209i	0.0565769	+	0.0979941i
$866$	−2.44344	+	4.23216i	−0.0830314	+	0.143815i
$867$		0			0
$868$	−22.8444	+	39.5676i	−0.775389	+	1.34301i
$869$	14.0781			0.477566
$870$		0			0
$871$	−3.16644	−	5.48444i	−0.107291	−	0.185833i
$872$	0.960061	−	1.66287i	0.0325118	−	0.0563120i
$873$		0			0
$874$	−2.63580	−	1.70978i	−0.0891573	−	0.0578343i
$875$	−15.1727	+	26.2799i	−0.512931	+	0.888422i
$876$		0			0
$877$	2.39397			0.0808386			0.0404193	−	0.999183i	$-0.487131\pi$
$877$	2.39397			0.0808386			0.0404193	+	0.999183i	$0.487131\pi$
$878$	−1.92834	+	3.33999i	−0.0650784	+	0.112719i
$879$		0			0
$880$	−41.3800			−1.39492
$881$	−44.3808			−1.49523			−0.747613	−	0.664135i	$-0.768800\pi$
$881$	−44.3808			−1.49523			−0.747613	+	0.664135i	$0.768800\pi$
$882$		0			0
$883$	1.13232	+	1.96123i	0.0381055	+	0.0660007i	0.884449	−	0.466637i	$-0.154534\pi$
$883$	1.13232	+	1.96123i	0.0381055	+	0.0660007i	−0.846344	+	0.532637i	$0.821201\pi$
$884$	27.4398			0.922901
$885$		0			0
$886$	2.09198	+	3.62342i	0.0702815	+	0.121731i
$887$	−17.8209	+	30.8667i	−0.598367	+	1.03640i	0.394696	+	0.918812i	$0.370850\pi$
$887$	−17.8209	+	30.8667i	−0.598367	+	1.03640i	−0.993062	+	0.117589i	$0.962483\pi$
$888$		0			0
$889$	−63.4867			−2.12928
$890$	1.49327	−	2.58641i	0.0500544	−	0.0866967i
$891$		0			0
$892$	−2.40482			−0.0805192
$893$	−35.5178	−	23.0396i	−1.18856	−	0.770990i
$894$		0			0
$895$	19.0968			0.638334
$896$	15.8736			0.530299
$897$		0			0
$898$	−2.18622	−	3.78665i	−0.0729552	−	0.126362i
$899$	12.3298	+	21.3559i	0.411223	+	0.712259i
$900$		0			0
$901$	−32.3036			−1.07619
$902$	1.54294			0.0513742
$903$		0			0
$904$	1.05395	+	1.82550i	0.0350539	+	0.0607151i
$905$	0.788579	+	1.36586i	0.0262132	+	0.0454027i
$906$		0			0
$907$	−2.81441	−	4.87470i	−0.0934509	−	0.161862i	0.815510	−	0.578743i	$-0.196456\pi$
$907$	−2.81441	−	4.87470i	−0.0934509	−	0.161862i	−0.908961	+	0.416881i	$0.863123\pi$
$908$	−8.82422	−	15.2840i	−0.292842	−	0.507217i
$909$		0			0
$910$	−3.01155	+	5.21615i	−0.0998318	+	0.172914i
$911$	−10.5622	+	18.2942i	−0.349941	+	0.606115i	−0.986239	−	0.165328i	$-0.947132\pi$
$911$	−10.5622	+	18.2942i	−0.349941	+	0.606115i	0.636298	+	0.771444i	$0.280465\pi$
$912$		0			0
$913$	−18.8239	−	32.6040i	−0.622982	−	1.07904i
$914$	−0.594898			−0.0196775
$915$		0			0
$916$	25.7480			0.850737
$917$	−37.3877	+	64.7574i	−1.23465	+	2.13848i
$918$		0			0
$919$	−60.0424			−1.98062			−0.990308	−	0.138887i	$-0.955647\pi$
$919$	−60.0424			−1.98062			−0.990308	+	0.138887i	$0.955647\pi$
$920$	3.68495	−	6.38251i	0.121489	−	0.210425i
$921$		0			0
$922$	1.22952	−	2.12959i	0.0404921	−	0.0701344i
$923$	−20.4789	−	35.4704i	−0.674070	−	1.16752i
$924$		0			0
$925$	−8.48276			−0.278911
$926$	0.129983	−	0.225137i	0.00427151	−	0.00739846i
$927$		0			0
$928$	3.21877	−	5.57507i	0.105661	−	0.183011i
$929$	3.69816	+	6.40539i	0.121333	+	0.210154i	0.920293	−	0.391229i	$-0.127950\pi$
$929$	3.69816	+	6.40539i	0.121333	+	0.210154i	−0.798961	+	0.601383i	$0.794617\pi$
$930$		0			0
$931$	1.15118	−	22.1842i	0.0377285	−	0.727057i
$932$	17.6563	+	30.5817i	0.578352	+	1.00174i
$933$		0			0
$934$	−0.987189	−	1.70986i	−0.0323018	−	0.0559484i
$935$	−16.1172	−	27.9158i	−0.527089	−	0.912944i
$936$		0			0
$937$	16.6488	+	28.8365i	0.543891	+	0.942048i	0.998676	+	0.0514461i	$0.0163830\pi$
$937$	16.6488	+	28.8365i	0.543891	+	0.942048i	−0.454784	+	0.890602i	$0.650284\pi$
$938$	0.350929	−	0.607826i	0.0114582	−	0.0198462i
$939$		0			0
$940$	24.6936	−	42.7706i	0.805417	−	1.39502i
$941$	7.04140	−	12.1961i	0.229543	−	0.397580i	−0.728130	−	0.685439i	$-0.759610\pi$
$941$	7.04140	−	12.1961i	0.229543	−	0.397580i	0.957673	+	0.287859i	$0.0929435\pi$
$942$		0			0
$943$	6.22706	−	10.7856i	0.202781	−	0.351227i
$944$	−17.3490	−	30.0494i	−0.564663	−	0.978024i
$945$		0			0
$946$	1.45666	+	2.52301i	0.0473602	+	0.0820302i
$947$	18.4941	+	32.0327i	0.600977	+	1.04092i	0.992673	+	0.120828i	$0.0385551\pi$
$947$	18.4941	+	32.0327i	0.600977	+	1.04092i	−0.391696	+	0.920095i	$0.628112\pi$
$948$		0			0
$949$	−9.87624	−	17.1061i	−0.320596	−	0.555289i
$950$	−0.0531291	+	1.02384i	−0.00172374	+	0.0332177i
$951$		0			0
$952$	3.05759	+	5.29590i	0.0990970	+	0.171641i
$953$	−15.5969	+	27.0147i	−0.505235	+	0.875092i	0.494747	+	0.869037i	$0.335261\pi$
$953$	−15.5969	+	27.0147i	−0.505235	+	0.875092i	−0.999982	+	0.00605517i	$0.998073\pi$
$954$		0			0
$955$	−7.26634	+	12.5857i	−0.235133	+	0.407263i
$956$	13.0855			0.423217
$957$		0			0
$958$	1.49559	+	2.59043i	0.0483202	+	0.0836930i
$959$	−15.3755	+	26.6311i	−0.496500	+	0.859962i
$960$		0			0
$961$	−6.54217	+	11.3314i	−0.211038	+	0.365528i
$962$	3.56117			0.114817
$963$		0			0
$964$	−7.63617	+	13.2262i	−0.245944	+	0.425988i
$965$	−4.53596			−0.146018
$966$		0			0
$967$	−13.7317			−0.441583			−0.220792	−	0.975321i	$-0.570864\pi$
$967$	−13.7317			−0.441583			−0.220792	+	0.975321i	$0.570864\pi$
$968$	−1.83489	−	3.17813i	−0.0589757	−	0.102149i
$969$		0			0
$970$	−0.350363	+	0.606846i	−0.0112495	+	0.0194846i
$971$	10.0476	−	17.4030i	0.322444	−	0.558489i	−0.658548	−	0.752539i	$-0.728829\pi$
$971$	10.0476	−	17.4030i	0.322444	−	0.558489i	0.980992	+	0.194050i	$0.0621624\pi$
$972$		0			0
$973$	23.1101	+	40.0279i	0.740876	+	1.28323i
$974$	1.73386	+	3.00313i	0.0555564	+	0.0962265i
$975$		0			0
$976$	−1.82774	−	3.16573i	−0.0585044	−	0.101333i
$977$	−22.4381	−	38.8639i	−0.717858	−	1.24337i	−0.961847	−	0.273588i	$-0.911789\pi$
$977$	−22.4381	−	38.8639i	−0.717858	−	1.24337i	0.243989	−	0.969778i	$-0.421544\pi$
$978$		0			0
$979$	−32.9797			−1.05404
$980$	25.9138			0.827787
$981$		0			0
$982$	−0.298077	−	0.516284i	−0.00951201	−	0.0164753i
$983$	−20.4627	−	35.4425i	−0.652660	−	1.13044i	−0.982475	−	0.186395i	$-0.940320\pi$
$983$	−20.4627	−	35.4425i	−0.652660	−	1.13044i	0.329815	−	0.944046i	$-0.393014\pi$
$984$		0			0
$985$	−3.52602			−0.112348
$986$	1.64137			0.0522718
$987$		0			0
$988$	−2.05520	+	39.6051i	−0.0653845	+	1.26001i
$989$	23.5155			0.747749
$990$		0			0
$991$	−3.01999	+	5.23077i	−0.0959330	+	0.166161i	−0.909998	−	0.414613i	$-0.863917\pi$
$991$	−3.01999	+	5.23077i	−0.0959330	+	0.166161i	0.814065	+	0.580774i	$0.197250\pi$
$992$	11.5085			0.365394
$993$		0			0
$994$	2.26962	−	3.93110i	0.0719880	−	0.124687i
$995$	−31.6328	−	54.7896i	−1.00283	−	1.73695i
$996$		0			0
$997$	42.4556			1.34458			0.672291	−	0.740287i	$-0.265310\pi$
$997$	42.4556			1.34458			0.672291	+	0.740287i	$0.265310\pi$
$998$	2.00093	+	3.46570i	0.0633382	+	0.109705i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	513.2.g.c.505.8		32
3.2	odd	2		171.2.g.c.106.9	✓	32
9.4	even	3		513.2.h.c.334.9		32
9.5	odd	6		171.2.h.c.49.8	yes	32
19.7	even	3		513.2.h.c.235.9		32
57.26	odd	6		171.2.h.c.7.8	yes	32
171.121	even	3	inner	513.2.g.c.64.8		32
171.140	odd	6		171.2.g.c.121.9	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.g.c.106.9	✓	32	3.2	odd	2
171.2.g.c.121.9	yes	32	171.140	odd	6
171.2.h.c.7.8	yes	32	57.26	odd	6
171.2.h.c.49.8	yes	32	9.5	odd	6
513.2.g.c.64.8		32	171.121	even	3	inner
513.2.g.c.505.8		32	1.1	even	1	trivial
513.2.h.c.235.9		32	19.7	even	3
513.2.h.c.334.9		32	9.4	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 513 = 3^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	513.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0732670 + 0.126902i) q^{2} +(0.989264 - 1.71346i) q^{4} -2.57004 q^{5} +(-1.73898 + 3.01201i) q^{7} +0.582990 q^{8} +(-0.188299 - 0.326143i) q^{10} +(-2.07935 + 3.60154i) q^{11} +(-2.29925 + 3.98242i) q^{13} -0.509640 q^{14} +(-1.93581 - 3.35293i) q^{16} +(1.50797 - 2.61188i) q^{17} +(3.65690 + 2.37215i) q^{19} +(-2.54244 + 4.40364i) q^{20} -0.609391 q^{22} +(-2.45941 + 4.25982i) q^{23} +1.60509 q^{25} -0.673837 q^{26} +(3.44063 + 5.95934i) q^{28} +3.71403 q^{29} +(3.31980 + 5.75007i) q^{31} +(0.866652 - 1.50109i) q^{32} +0.441938 q^{34} +(4.46925 - 7.74097i) q^{35} -5.28491 q^{37} +(-0.0331004 + 0.637869i) q^{38} -1.49831 q^{40} -2.53193 q^{41} +(-2.39036 - 4.14022i) q^{43} +(4.11405 + 7.12574i) q^{44} -0.720775 q^{46} -9.71255 q^{47} +(-2.54812 - 4.41348i) q^{49} +(0.117600 + 0.203689i) q^{50} +(4.54913 + 7.87933i) q^{52} +(-5.35547 - 9.27595i) q^{53} +(5.34400 - 9.25609i) q^{55} +(-1.01381 + 1.75597i) q^{56} +(0.272116 + 0.471318i) q^{58} +8.96213 q^{59} +0.944170 q^{61} +(-0.486464 + 0.842580i) q^{62} -7.48927 q^{64} +(5.90916 - 10.2350i) q^{65} +(-0.688581 + 1.19266i) q^{67} +(-2.98356 - 5.16768i) q^{68} +1.30979 q^{70} +(-4.45338 + 7.71347i) q^{71} +(-2.14771 + 3.71994i) q^{73} +(-0.387210 - 0.670667i) q^{74} +(7.68221 - 3.91926i) q^{76} +(-7.23190 - 12.5260i) q^{77} +(-1.69260 - 2.93168i) q^{79} +(4.97511 + 8.61715i) q^{80} +(-0.185507 - 0.321308i) q^{82} +(-4.52640 + 7.83996i) q^{83} +(-3.87554 + 6.71263i) q^{85} +(0.350269 - 0.606683i) q^{86} +(-1.21224 + 2.09966i) q^{88} +(3.96515 + 6.86783i) q^{89} +(-7.99672 - 13.8507i) q^{91} +(4.86601 + 8.42818i) q^{92} +(-0.711609 - 1.23254i) q^{94} +(-9.39837 - 6.09650i) q^{95} +(-0.930336 - 1.61139i) q^{97} +(0.373387 - 0.646725i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - q^{2} - 17 q^{4} + 6 q^{5} + q^{7} + 36 q^{8} - 8 q^{10} - 7 q^{11} - 4 q^{13} + 2 q^{14} - 11 q^{16} + 7 q^{17} + 7 q^{19} + 3 q^{20} + 16 q^{22} - 5 q^{23} + 18 q^{25} + 4 q^{26} - 10 q^{28}+ \cdots - 18 q^{98}+O(q^{100}) \) 32 * q - q^2 - 17 * q^4 + 6 * q^5 + q^7 + 36 * q^8 - 8 * q^10 - 7 * q^11 - 4 * q^13 + 2 * q^14 - 11 * q^16 + 7 * q^17 + 7 * q^19 + 3 * q^20 + 16 * q^22 - 5 * q^23 + 18 * q^25 + 4 * q^26 - 10 * q^28 + 20 * q^29 - 10 * q^31 - 17 * q^32 + 26 * q^34 + 3 * q^35 + 2 * q^37 - 38 * q^38 - 24 * q^40 + 12 * q^41 + 7 * q^43 - 20 * q^44 - 18 * q^47 - 13 * q^49 - q^50 + 19 * q^52 - 16 * q^53 + 15 * q^55 + 6 * q^56 + 74 * q^59 + 24 * q^61 - 54 * q^62 - 64 * q^64 - 54 * q^65 - 11 * q^67 + 2 * q^68 - 48 * q^70 - 9 * q^71 - 10 * q^73 - 6 * q^74 + 29 * q^76 - 46 * q^77 - 8 * q^79 + 24 * q^80 + 7 * q^82 - 3 * q^83 - 27 * q^85 - 17 * q^86 + 9 * q^88 - 30 * q^89 - q^91 + 17 * q^92 - 18 * q^94 + 6 * q^95 - 18 * q^98

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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