LMFDB - Embedded newform 216.2.q.b.25.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(25,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("216.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.q (of order $9$, degree $6$, 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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.2
Character	$\chi$	$=$	216.25
Dual form			216.2.q.b.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28382 - 1.16267i) q^{3} +(-1.03831 + 0.871247i) q^{5} +(-4.32665 + 1.57477i) q^{7} +(0.296376 + 2.98532i) q^{9} +O(q^{10})$	\(q+(-1.28382 - 1.16267i) q^{3} +(-1.03831 + 0.871247i) q^{5} +(-4.32665 + 1.57477i) q^{7} +(0.296376 + 2.98532i) q^{9} +(0.700045 + 0.587408i) q^{11} +(0.939486 + 5.32809i) q^{13} +(2.34598 + 0.0886962i) q^{15} +(-3.81411 - 6.60622i) q^{17} +(-0.825544 + 1.42988i) q^{19} +(7.38557 + 3.00876i) q^{21} +(-5.39555 - 1.96382i) q^{23} +(-0.549221 + 3.11479i) q^{25} +(3.09047 - 4.17720i) q^{27} +(-0.698436 + 3.96103i) q^{29} +(-2.21601 - 0.806561i) q^{31} +(-0.215767 - 1.56805i) q^{33} +(3.12039 - 5.40468i) q^{35} +(-2.81745 - 4.87996i) q^{37} +(4.98870 - 7.93261i) q^{39} +(-0.570634 - 3.23623i) q^{41} +(3.36619 + 2.82457i) q^{43} +(-2.90868 - 2.84148i) q^{45} +(4.81274 - 1.75170i) q^{47} +(10.8777 - 9.12744i) q^{49} +(-2.78427 + 12.9158i) q^{51} +2.84711 q^{53} -1.23864 q^{55} +(2.72234 - 0.875871i) q^{57} +(-0.651937 + 0.547040i) q^{59} +(-3.48246 + 1.26751i) q^{61} +(-5.98352 - 12.4497i) q^{63} +(-5.61756 - 4.71369i) q^{65} +(1.36547 + 7.74398i) q^{67} +(4.64362 + 8.79446i) q^{69} +(6.18977 + 10.7210i) q^{71} +(-2.00184 + 3.46728i) q^{73} +(4.32659 - 3.36026i) q^{75} +(-3.95388 - 1.43910i) q^{77} +(-2.30759 + 13.0870i) q^{79} +(-8.82432 + 1.76956i) q^{81} +(-0.992328 + 5.62777i) q^{83} +(9.71588 + 3.53629i) q^{85} +(5.50205 - 4.27318i) q^{87} +(4.63153 - 8.02205i) q^{89} +(-12.4553 - 21.5733i) q^{91} +(1.90718 + 3.61197i) q^{93} +(-0.388610 - 2.20392i) q^{95} +(-8.62632 - 7.23834i) q^{97} +(-1.54613 + 2.26396i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{7} - 6 q^{9}+O(q^{10}) $ 30 * q + 3 * q^7 - 6 * q^9	$ 30 q + 3 q^{7} - 6 q^{9} - 3 q^{11} - 12 q^{13} + 15 q^{15} + 6 q^{17} - 9 q^{19} + 30 q^{21} - 12 q^{23} + 24 q^{25} - 15 q^{27} - 9 q^{29} + 27 q^{31} - 30 q^{33} - 18 q^{35} - 15 q^{37} - 21 q^{39} - 15 q^{41} - 30 q^{43} + 15 q^{45} - 18 q^{47} + 15 q^{49} - 6 q^{51} - 18 q^{53} + 54 q^{55} - 72 q^{57} - 12 q^{59} + 6 q^{61} - 54 q^{63} - 54 q^{65} - 45 q^{67} + 9 q^{69} - 36 q^{73} + 69 q^{75} + 12 q^{77} + 45 q^{79} - 30 q^{81} - 3 q^{83} + 57 q^{85} - 60 q^{87} + 36 q^{89} - 39 q^{91} + 30 q^{93} + 51 q^{95} - 84 q^{97} + 162 q^{99}+O(q^{100}) $ 30 * q + 3 * q^7 - 6 * q^9 - 3 * q^11 - 12 * q^13 + 15 * q^15 + 6 * q^17 - 9 * q^19 + 30 * q^21 - 12 * q^23 + 24 * q^25 - 15 * q^27 - 9 * q^29 + 27 * q^31 - 30 * q^33 - 18 * q^35 - 15 * q^37 - 21 * q^39 - 15 * q^41 - 30 * q^43 + 15 * q^45 - 18 * q^47 + 15 * q^49 - 6 * q^51 - 18 * q^53 + 54 * q^55 - 72 * q^57 - 12 * q^59 + 6 * q^61 - 54 * q^63 - 54 * q^65 - 45 * q^67 + 9 * q^69 - 36 * q^73 + 69 * q^75 + 12 * q^77 + 45 * q^79 - 30 * q^81 - 3 * q^83 + 57 * q^85 - 60 * q^87 + 36 * q^89 - 39 * q^91 + 30 * q^93 + 51 * q^95 - 84 * q^97 + 162 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{9}\right)$

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			0
$2$		0			0
$3$	−1.28382	−	1.16267i	−0.741213	−	0.671270i
$3$	−1.28382	−	1.16267i	−0.741213	−	0.671270i
$4$		0			0
$5$	−1.03831	+	0.871247i	−0.464347	+	0.389633i	−0.844727	−	0.535197i	$-0.820237\pi$
$5$	−1.03831	+	0.871247i	−0.464347	+	0.389633i	0.380381	+	0.924830i	$0.375793\pi$
$6$		0			0
$7$	−4.32665	+	1.57477i	−1.63532	+	0.595207i	−0.986212	−	0.165489i	$-0.947080\pi$
$7$	−4.32665	+	1.57477i	−1.63532	+	0.595207i	−0.649107	+	0.760697i	$0.724857\pi$
$8$		0			0
$9$	0.296376	+	2.98532i	0.0987920	+	0.995108i
$10$		0			0
$11$	0.700045	+	0.587408i	0.211072	+	0.177110i	0.742194	−	0.670185i	$-0.233785\pi$
$11$	0.700045	+	0.587408i	0.211072	+	0.177110i	−0.531123	+	0.847295i	$0.678230\pi$
$12$		0			0
$13$	0.939486	+	5.32809i	0.260566	+	1.47775i	0.781369	+	0.624069i	$0.214521\pi$
$13$	0.939486	+	5.32809i	0.260566	+	1.47775i	−0.520803	+	0.853677i	$0.674367\pi$
$14$		0			0
$15$	2.34598	+	0.0886962i	0.605729	+	0.0229013i
$16$		0			0
$17$	−3.81411	−	6.60622i	−0.925056	−	1.60224i	−0.791470	−	0.611208i	$-0.790684\pi$
$17$	−3.81411	−	6.60622i	−0.925056	−	1.60224i	−0.133586	−	0.991037i	$-0.542649\pi$
$18$		0			0
$19$	−0.825544	+	1.42988i	−0.189393	+	0.328038i	−0.945048	−	0.326932i	$-0.893985\pi$
$19$	−0.825544	+	1.42988i	−0.189393	+	0.328038i	0.755655	+	0.654970i	$0.227319\pi$
$20$		0			0
$21$	7.38557	+	3.00876i	1.61166	+	0.656566i
$22$		0			0
$23$	−5.39555	−	1.96382i	−1.12505	−	0.409485i	−0.288558	−	0.957462i	$-0.593176\pi$
$23$	−5.39555	−	1.96382i	−1.12505	−	0.409485i	−0.836493	+	0.547977i	$0.815398\pi$
$24$		0			0
$25$	−0.549221	+	3.11479i	−0.109844	+	0.622958i
$26$		0			0
$27$	3.09047	−	4.17720i	0.594761	−	0.803903i
$28$		0			0
$29$	−0.698436	+	3.96103i	−0.129696	+	0.735544i	0.848711	+	0.528857i	$0.177379\pi$
$29$	−0.698436	+	3.96103i	−0.129696	+	0.735544i	−0.978407	+	0.206687i	$0.933732\pi$
$30$		0			0
$31$	−2.21601	−	0.806561i	−0.398007	−	0.144863i	0.135259	−	0.990810i	$-0.456813\pi$
$31$	−2.21601	−	0.806561i	−0.398007	−	0.144863i	−0.533266	+	0.845948i	$0.679036\pi$
$32$		0			0
$33$	−0.215767	−	1.56805i	−0.0375601	−	0.272962i
$34$		0			0
$35$	3.12039	−	5.40468i	0.527443	−	0.913557i
$36$		0			0
$37$	−2.81745	−	4.87996i	−0.463186	−	0.802261i	0.535932	−	0.844261i	$-0.319960\pi$
$37$	−2.81745	−	4.87996i	−0.463186	−	0.802261i	−0.999118	+	0.0420003i	$0.986627\pi$
$38$		0			0
$39$	4.98870	−	7.93261i	0.798832	−	1.27023i
$40$		0			0
$41$	−0.570634	−	3.23623i	−0.0891181	−	0.505414i	−0.996392	−	0.0848732i	$-0.972951\pi$
$41$	−0.570634	−	3.23623i	−0.0891181	−	0.505414i	0.907274	−	0.420541i	$-0.138160\pi$
$42$		0			0
$43$	3.36619	+	2.82457i	0.513339	+	0.430743i	0.862302	−	0.506394i	$-0.169022\pi$
$43$	3.36619	+	2.82457i	0.513339	+	0.430743i	−0.348963	+	0.937136i	$0.613466\pi$
$44$		0			0
$45$	−2.90868	−	2.84148i	−0.433601	−	0.423583i
$46$		0			0
$47$	4.81274	−	1.75170i	0.702011	−	0.255511i	0.0337416	−	0.999431i	$-0.489258\pi$
$47$	4.81274	−	1.75170i	0.702011	−	0.255511i	0.668269	+	0.743920i	$0.267035\pi$
$48$		0			0
$49$	10.8777	−	9.12744i	1.55395	−	1.30392i
$50$		0			0
$51$	−2.78427	+	12.9158i	−0.389876	+	1.80857i
$52$		0			0
$53$	2.84711			0.391081			0.195540	−	0.980696i	$-0.437354\pi$
$53$	2.84711			0.391081			0.195540	+	0.980696i	$0.437354\pi$
$54$		0			0
$55$	−1.23864			−0.167018
$56$		0			0
$57$	2.72234	−	0.875871i	0.360582	−	0.116012i
$58$		0			0
$59$	−0.651937	+	0.547040i	−0.0848749	+	0.0712185i	−0.684238	−	0.729259i	$-0.739865\pi$
$59$	−0.651937	+	0.547040i	−0.0848749	+	0.0712185i	0.599363	+	0.800477i	$0.295421\pi$
$60$		0			0
$61$	−3.48246	+	1.26751i	−0.445883	+	0.162288i	−0.555196	−	0.831719i	$-0.687357\pi$
$61$	−3.48246	+	1.26751i	−0.445883	+	0.162288i	0.109314	+	0.994007i	$0.465135\pi$
$62$		0			0
$63$	−5.98352	−	12.4497i	−0.753852	−	1.56852i
$64$		0			0
$65$	−5.61756	−	4.71369i	−0.696772	−	0.584661i
$66$		0			0
$67$	1.36547	+	7.74398i	0.166819	+	0.946078i	0.947169	+	0.320735i	$0.103930\pi$
$67$	1.36547	+	7.74398i	0.166819	+	0.946078i	−0.780350	+	0.625343i	$0.784959\pi$
$68$		0			0
$69$	4.64362	+	8.79446i	0.559027	+	1.05873i
$70$		0			0
$71$	6.18977	+	10.7210i	0.734590	+	1.27235i	0.954903	+	0.296918i	$0.0959588\pi$
$71$	6.18977	+	10.7210i	0.734590	+	1.27235i	−0.220313	+	0.975429i	$0.570708\pi$
$72$		0			0
$73$	−2.00184	+	3.46728i	−0.234297	+	0.405814i	−0.959068	−	0.283175i	$-0.908612\pi$
$73$	−2.00184	+	3.46728i	−0.234297	+	0.405814i	0.724771	+	0.688990i	$0.241946\pi$
$74$		0			0
$75$	4.32659	−	3.36026i	0.499591	−	0.388009i
$76$		0			0
$77$	−3.95388	−	1.43910i	−0.450587	−	0.164000i
$78$		0			0
$79$	−2.30759	+	13.0870i	−0.259624	+	1.47240i	0.524293	+	0.851538i	$0.324330\pi$
$79$	−2.30759	+	13.0870i	−0.259624	+	1.47240i	−0.783917	+	0.620865i	$0.786781\pi$
$80$		0			0
$81$	−8.82432	+	1.76956i	−0.980480	+	0.196617i
$82$		0			0
$83$	−0.992328	+	5.62777i	−0.108922	+	0.617728i	0.880659	+	0.473751i	$0.157100\pi$
$83$	−0.992328	+	5.62777i	−0.108922	+	0.617728i	−0.989581	+	0.143977i	$0.954011\pi$
$84$		0			0
$85$	9.71588	+	3.53629i	1.05383	+	0.383565i
$86$		0			0
$87$	5.50205	−	4.27318i	0.589882	−	0.458133i
$88$		0			0
$89$	4.63153	−	8.02205i	0.490942	−	0.850336i	−0.509004	−	0.860764i	$-0.669986\pi$
$89$	4.63153	−	8.02205i	0.490942	−	0.850336i	0.999946	+	0.0104282i	$0.00331947\pi$
$90$		0			0
$91$	−12.4553	−	21.5733i	−1.30567	−	2.26149i
$92$		0			0
$93$	1.90718	+	3.61197i	0.197766	+	0.374544i
$94$		0			0
$95$	−0.388610	−	2.20392i	−0.0398705	−	0.226117i
$96$		0			0
$97$	−8.62632	−	7.23834i	−0.875870	−	0.734942i	0.0894560	−	0.995991i	$-0.471487\pi$
$97$	−8.62632	−	7.23834i	−0.875870	−	0.734942i	−0.965326	+	0.261049i	$0.915932\pi$
$98$		0			0
$99$	−1.54613	+	2.26396i	−0.155392	+	0.227536i
$100$		0			0
$101$	1.21621	−	0.442666i	0.121018	−	0.0440469i	−0.280801	−	0.959766i	$-0.590600\pi$
$101$	1.21621	−	0.442666i	0.121018	−	0.0440469i	0.401819	+	0.915719i	$0.368378\pi$
$102$		0			0
$103$	−7.84211	+	6.58031i	−0.772706	+	0.648378i	−0.941400	−	0.337291i	$-0.890489\pi$
$103$	−7.84211	+	6.58031i	−0.772706	+	0.648378i	0.168694	+	0.985668i	$0.446045\pi$
$104$		0			0
$105$	−10.2899	+	3.31062i	−1.00419	+	0.323084i
$106$		0			0
$107$	−5.32280			−0.514574			−0.257287	−	0.966335i	$-0.582829\pi$
$107$	−5.32280			−0.514574			−0.257287	+	0.966335i	$0.582829\pi$
$108$		0			0
$109$	10.3524			0.991579			0.495789	−	0.868443i	$-0.334879\pi$
$109$	10.3524			0.991579			0.495789	+	0.868443i	$0.334879\pi$
$110$		0			0
$111$	−2.05672	+	9.54076i	−0.195215	+	0.905569i
$112$		0			0
$113$	−13.8713	+	11.6394i	−1.30491	+	1.09495i	−0.315631	+	0.948882i	$0.602216\pi$
$113$	−13.8713	+	11.6394i	−1.30491	+	1.09495i	−0.989275	+	0.146064i	$0.953340\pi$
$114$		0			0
$115$	7.31324	−	2.66180i	0.681963	−	0.248214i
$116$		0			0
$117$	−15.6276	+	4.38379i	−1.44477	+	0.405281i
$118$		0			0
$119$	26.9056	+	22.5765i	2.46643	+	2.06958i
$120$		0			0
$121$	−1.76511	−	10.0105i	−0.160465	−	0.910042i
$122$		0			0
$123$	−3.03009	+	4.81819i	−0.273214	+	0.434441i
$124$		0			0
$125$	−5.53203	−	9.58176i	−0.494800	−	0.857019i
$126$		0			0
$127$	4.11054	−	7.11967i	0.364752	−	0.631768i	−0.623985	−	0.781437i	$-0.714487\pi$
$127$	4.11054	−	7.11967i	0.364752	−	0.631768i	0.988736	+	0.149668i	$0.0478206\pi$
$128$		0			0
$129$	−1.03752	−	7.54001i	−0.0913485	−	0.663861i
$130$		0			0
$131$	−2.97239	−	1.08186i	−0.259699	−	0.0945226i	0.208890	−	0.977939i	$-0.433015\pi$
$131$	−2.97239	−	1.08186i	−0.259699	−	0.0945226i	−0.468588	+	0.883417i	$0.655237\pi$
$132$		0			0
$133$	1.32010	−	7.48664i	0.114467	−	0.649174i
$134$		0			0
$135$	0.430504	+	7.02979i	0.0370519	+	0.605028i
$136$		0			0
$137$	−2.13867	+	12.1290i	−0.182719	+	1.03625i	0.746133	+	0.665797i	$0.231909\pi$
$137$	−2.13867	+	12.1290i	−0.182719	+	1.03625i	−0.928851	+	0.370453i	$0.879203\pi$
$138$		0			0
$139$	13.4942	+	4.91150i	1.14457	+	0.416588i	0.843560	−	0.537035i	$-0.180456\pi$
$139$	13.4942	+	4.91150i	1.14457	+	0.416588i	0.301005	+	0.953622i	$0.402678\pi$
$140$		0			0
$141$	−8.21534	−	3.34680i	−0.691856	−	0.281851i
$142$		0			0
$143$	−2.47208	+	4.28176i	−0.206726	+	0.358059i
$144$		0			0
$145$	−2.72584	−	4.72129i	−0.226369	−	0.392082i
$146$		0			0
$147$	−24.5772	−	0.929208i	−2.02709	−	0.0766398i
$148$		0			0
$149$	3.86015	+	21.8920i	0.316236	+	1.79346i	0.565204	+	0.824951i	$0.308797\pi$
$149$	3.86015	+	21.8920i	0.316236	+	1.79346i	−0.248968	+	0.968512i	$0.580091\pi$
$150$		0			0
$151$	−3.00675	−	2.52297i	−0.244686	−	0.205316i	0.512194	−	0.858870i	$-0.328833\pi$
$151$	−3.00675	−	2.52297i	−0.244686	−	0.205316i	−0.756880	+	0.653554i	$0.773277\pi$
$152$		0			0
$153$	18.5913	−	13.3443i	1.50302	−	1.07882i
$154$		0			0
$155$	3.00362	−	1.09323i	0.241257	−	0.0878102i
$156$		0			0
$157$	1.79923	−	1.50973i	0.143594	−	0.120490i	−0.568161	−	0.822917i	$-0.692345\pi$
$157$	1.79923	−	1.50973i	0.143594	−	0.120490i	0.711755	+	0.702428i	$0.247901\pi$
$158$		0			0
$159$	−3.65517	−	3.31026i	−0.289874	−	0.262521i
$160$		0			0
$161$	26.4372			2.08355
$162$		0			0
$163$	21.0781			1.65097			0.825483	−	0.564427i	$-0.190903\pi$
$163$	21.0781			1.65097			0.825483	+	0.564427i	$0.190903\pi$
$164$		0			0
$165$	1.59019	+	1.44014i	0.123796	+	0.112115i
$166$		0			0
$167$	−5.64284	+	4.73491i	−0.436656	+	0.366398i	−0.834456	−	0.551074i	$-0.814218\pi$
$167$	−5.64284	+	4.73491i	−0.436656	+	0.366398i	0.397800	+	0.917472i	$0.369774\pi$
$168$		0			0
$169$	−15.2899	+	5.56506i	−1.17614	+	0.428082i
$170$		0			0
$171$	−4.51334	−	2.04073i	−0.345143	−	0.156059i
$172$		0			0
$173$	−1.34147	−	1.12562i	−0.101990	−	0.0855795i	0.590367	−	0.807135i	$-0.298983\pi$
$173$	−1.34147	−	1.12562i	−0.101990	−	0.0855795i	−0.692357	+	0.721555i	$0.743427\pi$
$174$		0			0
$175$	−2.52879	−	14.3415i	−0.191159	−	1.08411i
$176$		0			0
$177$	1.47300	+	0.0556908i	0.110717	+	0.00418597i
$178$		0			0
$179$	−7.99947	−	13.8555i	−0.597909	−	1.03561i	−0.993129	−	0.117022i	$-0.962665\pi$
$179$	−7.99947	−	13.8555i	−0.597909	−	1.03561i	0.395221	−	0.918586i	$-0.370668\pi$
$180$		0			0
$181$	−8.14033	+	14.0995i	−0.605066	+	1.04801i	0.386975	+	0.922090i	$0.373520\pi$
$181$	−8.14033	+	14.0995i	−0.605066	+	1.04801i	−0.992041	+	0.125915i	$0.959813\pi$
$182$		0			0
$183$	5.94454	+	2.42171i	0.439433	+	0.179018i
$184$		0			0
$185$	7.17704	+	2.61223i	0.527666	+	0.192055i
$186$		0			0
$187$	1.21050	−	6.86509i	0.0885206	−	0.502025i
$188$		0			0
$189$	−6.79323	+	22.9401i	−0.494135	+	1.66864i
$190$		0			0
$191$	3.50573	−	19.8820i	0.253666	−	1.43861i	−0.545808	−	0.837910i	$-0.683777\pi$
$191$	3.50573	−	19.8820i	0.253666	−	1.43861i	0.799474	−	0.600701i	$-0.205112\pi$
$192$		0			0
$193$	9.45301	+	3.44062i	0.680443	+	0.247661i	0.659038	−	0.752110i	$-0.270964\pi$
$193$	9.45301	+	3.44062i	0.680443	+	0.247661i	0.0214052	+	0.999771i	$0.493186\pi$
$194$		0			0
$195$	1.73143	+	12.5829i	0.123990	+	0.901081i
$196$		0			0
$197$	2.36612	−	4.09824i	0.168579	−	0.291987i	−0.769341	−	0.638838i	$-0.779415\pi$
$197$	2.36612	−	4.09824i	0.168579	−	0.291987i	0.937920	+	0.346850i	$0.112749\pi$
$198$		0			0
$199$	−8.37081	−	14.4987i	−0.593391	−	1.02778i	−0.993772	−	0.111435i	$-0.964455\pi$
$199$	−8.37081	−	14.4987i	−0.593391	−	1.02778i	0.400381	−	0.916349i	$-0.368878\pi$
$200$		0			0
$201$	7.25071	−	11.5295i	0.511426	−	0.813226i
$202$		0			0
$203$	−3.21582	−	18.2378i	−0.225707	−	1.28005i
$204$		0			0
$205$	3.41205	+	2.86305i	0.238308	+	0.199964i
$206$		0			0
$207$	4.26353	−	16.6895i	0.296336	−	1.16000i
$208$		0			0
$209$	−1.41784	+	0.516052i	−0.0980742	+	0.0356961i
$210$		0			0
$211$	−4.04940	+	3.39785i	−0.278772	+	0.233917i	−0.771443	−	0.636298i	$-0.780465\pi$
$211$	−4.04940	+	3.39785i	−0.278772	+	0.233917i	0.492671	+	0.870215i	$0.336020\pi$
$212$		0			0
$213$	4.51849	−	20.9605i	0.309602	−	1.43619i
$214$		0			0
$215$	−5.95605			−0.406199
$216$		0			0
$217$	10.8580			0.737091
$218$		0			0
$219$	6.60131	−	2.12387i	0.446075	−	0.143518i
$220$		0			0
$221$	31.6152	−	26.5283i	2.12667	−	1.78449i
$222$		0			0
$223$	0.590477	−	0.214916i	0.0395412	−	0.0143918i	−0.322174	−	0.946681i	$-0.604414\pi$
$223$	0.590477	−	0.214916i	0.0395412	−	0.0143918i	0.361715	+	0.932289i	$0.382191\pi$
$224$		0			0
$225$	−9.46143	−	0.716455i	−0.630762	−	0.0477637i
$226$		0			0
$227$	−11.0455	−	9.26824i	−0.733113	−	0.615155i	0.197865	−	0.980229i	$-0.436599\pi$
$227$	−11.0455	−	9.26824i	−0.733113	−	0.615155i	−0.930978	+	0.365074i	$0.881044\pi$
$228$		0			0
$229$	−0.442858	−	2.51158i	−0.0292649	−	0.165970i	0.966673	−	0.256015i	$-0.0824098\pi$
$229$	−0.442858	−	2.51158i	−0.0292649	−	0.165970i	−0.995938	+	0.0900458i	$0.971299\pi$
$230$		0			0
$231$	3.40286	+	6.44461i	0.223892	+	0.424024i
$232$		0			0
$233$	9.74903	+	16.8858i	0.638680	+	1.10623i	0.985723	+	0.168377i	$0.0538526\pi$
$233$	9.74903	+	16.8858i	0.638680	+	1.10623i	−0.347043	+	0.937849i	$0.612814\pi$
$234$		0			0
$235$	−3.47097	+	6.01189i	−0.226421	+	0.392173i
$236$		0			0
$237$	18.1785	−	14.1184i	1.18082	−	0.917086i
$238$		0			0
$239$	2.94610	+	1.07229i	0.190567	+	0.0693609i	0.435541	−	0.900169i	$-0.356557\pi$
$239$	2.94610	+	1.07229i	0.190567	+	0.0693609i	−0.244974	+	0.969530i	$0.578779\pi$
$240$		0			0
$241$	0.325677	−	1.84701i	0.0209787	−	0.118976i	−0.972520	−	0.232819i	$-0.925205\pi$
$241$	0.325677	−	1.84701i	0.0209787	−	0.118976i	0.993499	+	0.113843i	$0.0363161\pi$
$242$		0			0
$243$	13.3862	+	7.98803i	0.858728	+	0.512432i
$244$		0			0
$245$	−3.34215	+	18.9542i	−0.213522	+	1.21094i
$246$		0			0
$247$	−8.39413	−	3.05521i	−0.534106	−	0.194399i
$248$		0			0
$249$	7.81724	−	6.07128i	0.495397	−	0.384752i
$250$		0			0
$251$	−9.60342	+	16.6336i	−0.606162	+	1.04990i	0.385704	+	0.922622i	$0.373959\pi$
$251$	−9.60342	+	16.6336i	−0.606162	+	1.04990i	−0.991867	+	0.127282i	$0.959375\pi$
$252$		0			0
$253$	−2.62357	−	4.54415i	−0.164942	−	0.285689i
$254$		0			0
$255$	−8.36186	−	15.8364i	−0.523640	−	0.991711i
$256$		0			0
$257$	−0.432375	−	2.45212i	−0.0269708	−	0.152959i	0.968348	−	0.249603i	$-0.0803002\pi$
$257$	−0.432375	−	2.45212i	−0.0269708	−	0.152959i	−0.995319	+	0.0966442i	$0.969189\pi$
$258$		0			0
$259$	19.8749	+	16.6770i	1.23497	+	1.03626i
$260$		0			0
$261$	−12.0320	−	0.911105i	−0.744759	−	0.0563960i
$262$		0			0
$263$	−22.5958	+	8.22418i	−1.39331	+	0.507125i	−0.926187	−	0.377065i	$-0.876933\pi$
$263$	−22.5958	+	8.22418i	−1.39331	+	0.507125i	−0.467127	+	0.884190i	$0.654711\pi$
$264$		0			0
$265$	−2.95619	+	2.48054i	−0.181597	+	0.152378i
$266$		0			0
$267$	−15.2731	+	4.91389i	−0.934698	+	0.300725i
$268$		0			0
$269$	−32.4941			−1.98120			−0.990599	−	0.136799i	$-0.956319\pi$
$269$	−32.4941			−1.98120			−0.990599	+	0.136799i	$0.956319\pi$
$270$		0			0
$271$	5.10128			0.309880			0.154940	−	0.987924i	$-0.450481\pi$
$271$	5.10128			0.309880			0.154940	+	0.987924i	$0.450481\pi$
$272$		0			0
$273$	−9.09232	+	42.1777i	−0.550292	+	2.55271i
$274$		0			0
$275$	−2.21413	+	1.85788i	−0.133517	+	0.112034i
$276$		0			0
$277$	9.29788	−	3.38415i	0.558655	−	0.203334i	−0.0472327	−	0.998884i	$-0.515040\pi$
$277$	9.29788	−	3.38415i	0.558655	−	0.203334i	0.605888	+	0.795550i	$0.292818\pi$
$278$		0			0
$279$	1.75108	−	6.85455i	0.104834	−	0.410371i
$280$		0			0
$281$	−8.26309	−	6.93355i	−0.492934	−	0.413621i	0.362142	−	0.932123i	$-0.382045\pi$
$281$	−8.26309	−	6.93355i	−0.492934	−	0.413621i	−0.855077	+	0.518502i	$0.826490\pi$
$282$		0			0
$283$	−1.97959	−	11.2268i	−0.117675	−	0.667366i	−0.985391	−	0.170307i	$-0.945524\pi$
$283$	−1.97959	−	11.2268i	−0.117675	−	0.667366i	0.867716	−	0.497060i	$-0.165587\pi$
$284$		0			0
$285$	−2.06353	+	3.28125i	−0.122233	+	0.194365i
$286$		0			0
$287$	7.56525	+	13.1034i	0.446563	+	0.773469i
$288$		0			0
$289$	−20.5948	+	35.6712i	−1.21146	+	2.09831i
$290$		0			0
$291$	2.65879	+	19.3223i	0.155861	+	1.13269i
$292$		0			0
$293$	10.6325	+	3.86993i	0.621159	+	0.226084i	0.633379	−	0.773842i	$-0.281667\pi$
$293$	10.6325	+	3.86993i	0.621159	+	0.226084i	−0.0122195	+	0.999925i	$0.503890\pi$
$294$		0			0
$295$	0.200307	−	1.13600i	0.0116623	−	0.0661402i
$296$		0			0
$297$	4.61719	−	1.10887i	0.267916	−	0.0643429i
$298$		0			0
$299$	5.39437	−	30.5930i	0.311964	−	1.76924i
$300$		0			0
$301$	−19.0124	−	6.91993i	−1.09585	−	0.398858i
$302$		0			0
$303$	−2.07607	−	0.845759i	−0.119267	−	0.0485876i
$304$		0			0
$305$	2.51156	−	4.35015i	0.143811	−	0.249089i
$306$		0			0
$307$	6.43732	+	11.1498i	0.367397	+	0.636351i	0.989158	−	0.146857i	$-0.0469156\pi$
$307$	6.43732	+	11.1498i	0.367397	+	0.636351i	−0.621760	+	0.783207i	$0.713582\pi$
$308$		0			0
$309$	17.7186	+	0.669901i	1.00798	+	0.0381093i
$310$		0			0
$311$	0.334051	+	1.89450i	0.0189423	+	0.107427i	0.992813	−	0.119676i	$-0.0381856\pi$
$311$	0.334051	+	1.89450i	0.0189423	+	0.107427i	−0.973871	+	0.227103i	$0.927075\pi$
$312$		0			0
$313$	−1.59294	−	1.33663i	−0.0900381	−	0.0755509i	0.596658	−	0.802496i	$-0.296495\pi$
$313$	−1.59294	−	1.33663i	−0.0900381	−	0.0755509i	−0.686696	+	0.726945i	$0.740940\pi$
$314$		0			0
$315$	17.0595	+	7.71357i	0.961195	+	0.434610i
$316$		0			0
$317$	2.18381	−	0.794842i	0.122655	−	0.0446428i	−0.279963	−	0.960011i	$-0.590322\pi$
$317$	2.18381	−	0.794842i	0.122655	−	0.0446428i	0.402619	+	0.915368i	$0.368100\pi$
$318$		0			0
$319$	−2.81568	+	2.36263i	−0.157648	+	0.132282i
$320$		0			0
$321$	6.83350	+	6.18868i	0.381409	+	0.345419i
$322$		0			0
$323$	12.5948			0.700796
$324$		0			0
$325$	−17.1119			−0.949195
$326$		0			0
$327$	−13.2906	−	12.0365i	−0.734970	−	0.665617i
$328$		0			0
$329$	−18.0645	+	15.1579i	−0.995929	+	0.835684i
$330$		0			0
$331$	2.42293	−	0.881873i	0.133176	−	0.0484721i	−0.274572	−	0.961566i	$-0.588536\pi$
$331$	2.42293	−	0.881873i	0.133176	−	0.0484721i	0.407748	+	0.913094i	$0.366314\pi$
$332$		0			0
$333$	13.7332	−	9.85730i	0.752577	−	0.540177i
$334$		0			0
$335$	−8.16471	−	6.85100i	−0.446086	−	0.374310i
$336$		0			0
$337$	2.64059	+	14.9755i	0.143842	+	0.815769i	0.968290	+	0.249831i	$0.0803749\pi$
$337$	2.64059	+	14.9755i	0.143842	+	0.815769i	−0.824447	+	0.565938i	$0.808514\pi$
$338$		0			0
$339$	31.3411	+	1.18494i	1.70222	+	0.0643571i
$340$		0			0
$341$	−1.07753	−	1.86633i	−0.0583513	−	0.101067i
$342$		0			0
$343$	−16.5750	+	28.7088i	−0.894968	+	1.55013i
$344$		0			0
$345$	−12.4837	−	5.08565i	−0.672098	−	0.273802i
$346$		0			0
$347$	−30.8839	−	11.2408i	−1.65793	−	0.603439i	−0.667898	−	0.744253i	$-0.732806\pi$
$347$	−30.8839	−	11.2408i	−1.65793	−	0.603439i	−0.990036	+	0.140814i	$0.955028\pi$
$348$		0			0
$349$	−1.16230	+	6.59172i	−0.0622164	+	0.352847i	0.937768	+	0.347262i	$0.112889\pi$
$349$	−1.16230	+	6.59172i	−0.0622164	+	0.352847i	−0.999984	+	0.00558437i	$0.998222\pi$
$350$		0			0
$351$	25.1599	+	12.5419i	1.34294	+	0.669435i
$352$		0			0
$353$	4.91643	−	27.8825i	0.261675	−	1.48403i	−0.516663	−	0.856189i	$-0.672826\pi$
$353$	4.91643	−	27.8825i	0.261675	−	1.48403i	0.778338	−	0.627845i	$-0.216063\pi$
$354$		0			0
$355$	−15.7675	−	5.73891i	−0.836853	−	0.304590i
$356$		0			0
$357$	−8.29278	−	60.2665i	−0.438901	−	3.18964i
$358$		0			0
$359$	−0.531810	+	0.921122i	−0.0280679	+	0.0486150i	−0.879718	−	0.475496i	$-0.842269\pi$
$359$	−0.531810	+	0.921122i	−0.0280679	+	0.0486150i	0.851650	+	0.524110i	$0.175602\pi$
$360$		0			0
$361$	8.13696	+	14.0936i	0.428261	+	0.741770i
$362$		0			0
$363$	−9.37282	+	14.9039i	−0.491946	+	0.782250i
$364$		0			0
$365$	−0.942328	−	5.34421i	−0.0493237	−	0.279729i
$366$		0			0
$367$	−5.81851	−	4.88231i	−0.303724	−	0.254854i	0.478169	−	0.878268i	$-0.341301\pi$
$367$	−5.81851	−	4.88231i	−0.303724	−	0.254854i	−0.781892	+	0.623414i	$0.785745\pi$
$368$		0			0
$369$	9.49207	−	2.66267i	0.494137	−	0.138613i
$370$		0			0
$371$	−12.3184	+	4.48355i	−0.639542	+	0.232774i
$372$		0			0
$373$	−24.5910	+	20.6343i	−1.27327	+	1.06840i	−0.279139	+	0.960251i	$0.590049\pi$
$373$	−24.5910	+	20.6343i	−1.27327	+	1.06840i	−0.994134	+	0.108152i	$0.965507\pi$
$374$		0			0
$375$	−4.03835	+	18.7332i	−0.208539	+	0.967378i
$376$		0			0
$377$	−21.7609			−1.12074
$378$		0			0
$379$	29.4099			1.51069			0.755344	−	0.655329i	$-0.227470\pi$
$379$	29.4099			1.51069			0.755344	+	0.655329i	$0.227470\pi$
$380$		0			0
$381$	−13.5550	+	4.36113i	−0.694446	+	0.223428i
$382$		0			0
$383$	15.6512	−	13.1329i	0.799738	−	0.671060i	−0.148397	−	0.988928i	$-0.547411\pi$
$383$	15.6512	−	13.1329i	0.799738	−	0.671060i	0.948135	+	0.317868i	$0.102967\pi$
$384$		0			0
$385$	5.35917	−	1.95058i	0.273128	−	0.0994106i
$386$		0			0
$387$	−7.43460	+	10.8863i	−0.377922	+	0.553382i
$388$		0			0
$389$	−13.0322	−	10.9353i	−0.660758	−	0.554442i	0.249556	−	0.968360i	$-0.419715\pi$
$389$	−13.0322	−	10.9353i	−0.660758	−	0.554442i	−0.910314	+	0.413919i	$0.864160\pi$
$390$		0			0
$391$	7.60577	+	43.1345i	0.384640	+	2.18140i
$392$		0			0
$393$	2.55815	+	4.84483i	0.129042	+	0.244389i
$394$		0			0
$395$	−9.00601	−	15.5989i	−0.453142	−	0.784864i
$396$		0			0
$397$	4.83292	−	8.37087i	0.242557	−	0.420122i	−0.718885	−	0.695129i	$-0.755347\pi$
$397$	4.83292	−	8.37087i	0.242557	−	0.420122i	0.961442	+	0.275008i	$0.0886804\pi$
$398$		0			0
$399$	−10.3993	+	8.07664i	−0.520616	+	0.404338i
$400$		0			0
$401$	22.8544	+	8.31831i	1.14129	+	0.415396i	0.842380	−	0.538884i	$-0.181154\pi$
$401$	22.8544	+	8.31831i	1.14129	+	0.415396i	0.298912	+	0.954281i	$0.403376\pi$
$402$		0			0
$403$	2.21552	−	12.5648i	0.110363	−	0.625899i
$404$		0			0
$405$	7.62067	−	9.52551i	0.378674	−	0.473326i
$406$		0			0
$407$	0.894187	−	5.07119i	0.0443232	−	0.251369i
$408$		0			0
$409$	−15.1263	−	5.50554i	−0.747949	−	0.272231i	−0.0602066	−	0.998186i	$-0.519176\pi$
$409$	−15.1263	−	5.50554i	−0.747949	−	0.272231i	−0.687743	+	0.725955i	$0.741398\pi$
$410$		0			0
$411$	16.8477	−	13.0848i	0.831038	−	0.645428i
$412$		0			0
$413$	1.95924	−	3.39350i	0.0964078	−	0.166983i
$414$		0			0
$415$	−3.87283	−	6.70794i	−0.190110	−	0.329280i
$416$		0			0
$417$	−11.6137	−	21.9949i	−0.568723	−	1.07709i
$418$		0			0
$419$	0.225339	+	1.27796i	0.0110085	+	0.0624324i	0.989817	−	0.142345i	$-0.0454642\pi$
$419$	0.225339	+	1.27796i	0.0110085	+	0.0624324i	−0.978809	+	0.204777i	$0.934353\pi$
$420$		0			0
$421$	−22.6585	−	19.0127i	−1.10431	−	0.926624i	−0.106601	−	0.994302i	$-0.533997\pi$
$421$	−22.6585	−	19.0127i	−1.10431	−	0.926624i	−0.997707	+	0.0676775i	$0.978441\pi$
$422$		0			0
$423$	6.65576	+	13.8484i	0.323614	+	0.673334i
$424$		0			0
$425$	22.6718	−	8.25185i	1.09974	−	0.400274i
$426$		0			0
$427$	13.0713	−	10.9681i	0.632566	−	0.530785i
$428$		0			0
$429$	8.15199	−	2.62278i	0.393582	−	0.126629i
$430$		0			0
$431$	−5.16237			−0.248662			−0.124331	−	0.992241i	$-0.539679\pi$
$431$	−5.16237			−0.248662			−0.124331	+	0.992241i	$0.539679\pi$
$432$		0			0
$433$	30.9979			1.48966			0.744832	−	0.667252i	$-0.232530\pi$
$433$	30.9979			1.48966			0.744832	+	0.667252i	$0.232530\pi$
$434$		0			0
$435$	−1.98984	+	9.23054i	−0.0954057	+	0.442570i
$436$		0			0
$437$	7.26230	−	6.09379i	0.347403	−	0.291506i
$438$		0			0
$439$	27.6769	−	10.0736i	1.32095	−	0.480786i	0.417186	−	0.908821i	$-0.363016\pi$
$439$	27.6769	−	10.0736i	1.32095	−	0.480786i	0.903762	+	0.428035i	$0.140794\pi$
$440$		0			0
$441$	30.4722	+	29.7682i	1.45106	+	1.41753i
$442$		0			0
$443$	24.6585	+	20.6909i	1.17156	+	0.983055i	0.999998	−	0.00211877i	$-0.000674426\pi$
$443$	24.6585	+	20.6909i	1.17156	+	0.983055i	0.171561	+	0.985173i	$0.445119\pi$
$444$		0			0
$445$	2.18021	+	12.3646i	0.103352	+	0.586138i
$446$		0			0
$447$	20.4975	−	32.5934i	0.969501	−	1.54162i
$448$		0			0
$449$	10.8031	+	18.7115i	0.509828	+	0.883048i	0.999935	+	0.0113861i	$0.00362440\pi$
$449$	10.8031	+	18.7115i	0.509828	+	0.883048i	−0.490107	+	0.871662i	$0.663042\pi$
$450$		0			0
$451$	1.50152	−	2.60070i	0.0707036	−	0.122462i
$452$		0			0
$453$	0.926736	+	6.73491i	0.0435418	+	0.316434i
$454$		0			0
$455$	31.7282	+	11.5481i	1.48744	+	0.541384i
$456$		0			0
$457$	−0.951705	+	5.39739i	−0.0445189	+	0.252479i	−0.998943	−	0.0459761i	$-0.985360\pi$
$457$	−0.951705	+	5.39739i	−0.0445189	+	0.252479i	0.954424	+	0.298455i	$0.0964713\pi$
$458$		0			0
$459$	−39.3829	−	4.48404i	−1.83824	−	0.209297i
$460$		0			0
$461$	−3.44859	+	19.5579i	−0.160617	+	0.910903i	0.792853	+	0.609413i	$0.208595\pi$
$461$	−3.44859	+	19.5579i	−0.160617	+	0.910903i	−0.953469	+	0.301490i	$0.902516\pi$
$462$		0			0
$463$	−25.8024	−	9.39132i	−1.19914	−	0.436452i	−0.336217	−	0.941785i	$-0.609147\pi$
$463$	−25.8024	−	9.39132i	−1.19914	−	0.436452i	−0.862924	+	0.505333i	$0.831370\pi$
$464$		0			0
$465$	−5.12717	−	2.08873i	−0.237767	−	0.0968624i
$466$		0			0
$467$	−20.9145	+	36.2249i	−0.967806	+	1.67629i	−0.265925	+	0.963994i	$0.585677\pi$
$467$	−20.9145	+	36.2249i	−0.967806	+	1.67629i	−0.701880	+	0.712295i	$0.747656\pi$
$468$		0			0
$469$	−18.1029	−	31.3552i	−0.835915	−	1.44785i
$470$		0			0
$471$	−4.06520	−	0.153696i	−0.187315	−	0.00708195i
$472$		0			0
$473$	0.697312	+	3.95465i	0.0320624	+	0.181835i
$474$		0			0
$475$	−4.00038	−	3.35672i	−0.183550	−	0.154017i
$476$		0			0
$477$	0.843815	+	8.49955i	0.0386357	+	0.389168i
$478$		0			0
$479$	−4.21574	+	1.53440i	−0.192622	+	0.0701087i	−0.436530	−	0.899690i	$-0.643793\pi$
$479$	−4.21574	+	1.53440i	−0.192622	+	0.0701087i	0.243908	+	0.969798i	$0.421571\pi$
$480$		0			0
$481$	23.3539	−	19.5963i	1.06485	−	0.893513i
$482$		0			0
$483$	−33.9406	−	30.7379i	−1.54435	−	1.39862i
$484$		0			0
$485$	15.2632			0.693065
$486$		0			0
$487$	−0.660119			−0.0299129			−0.0149564	−	0.999888i	$-0.504761\pi$
$487$	−0.660119			−0.0299129			−0.0149564	+	0.999888i	$0.504761\pi$
$488$		0			0
$489$	−27.0605	−	24.5070i	−1.22372	−	1.10824i
$490$		0			0
$491$	17.5938	−	14.7630i	0.793998	−	0.666244i	−0.152733	−	0.988267i	$-0.548808\pi$
$491$	17.5938	−	14.7630i	0.793998	−	0.666244i	0.946732	+	0.322024i	$0.104363\pi$
$492$		0			0
$493$	28.8313	−	10.4938i	1.29850	−	0.472615i
$494$		0			0
$495$	−0.367104	−	3.69775i	−0.0165001	−	0.166201i
$496$		0			0
$497$	−43.6640	−	36.6385i	−1.95860	−	1.64346i
$498$		0			0
$499$	−1.06574	−	6.04411i	−0.0477091	−	0.270572i	0.951617	−	0.307288i	$-0.0994214\pi$
$499$	−1.06574	−	6.04411i	−0.0477091	−	0.270572i	−0.999326	+	0.0367161i	$0.988310\pi$
$500$		0			0
$501$	12.7495	+	0.482031i	0.569607	+	0.0215356i
$502$		0			0
$503$	−6.53069	−	11.3115i	−0.291189	−	0.504354i	0.682902	−	0.730510i	$-0.260718\pi$
$503$	−6.53069	−	11.3115i	−0.291189	−	0.504354i	−0.974091	+	0.226156i	$0.927384\pi$
$504$		0			0
$505$	−0.877138	+	1.51925i	−0.0390321	+	0.0676056i
$506$		0			0
$507$	26.0998	+	10.6326i	1.15913	+	0.472212i
$508$		0			0
$509$	−22.5291	−	8.19993i	−0.998586	−	0.363456i	−0.209547	−	0.977799i	$-0.567199\pi$
$509$	−22.5291	−	8.19993i	−0.998586	−	0.363456i	−0.789039	+	0.614343i	$0.789421\pi$
$510$		0			0
$511$	3.20106	−	18.1541i	0.141607	−	0.803091i
$512$		0			0
$513$	3.42159	+	7.86747i	0.151067	+	0.347357i
$514$		0			0
$515$	2.40948	−	13.6648i	0.106174	−	0.602144i
$516$		0			0
$517$	4.39810	+	1.60078i	0.193428	+	0.0704021i
$518$		0			0
$519$	0.413464	+	3.00478i	0.0181490	+	0.131895i
$520$		0			0
$521$	−6.28771	+	10.8906i	−0.275470	+	0.477127i	−0.970254	−	0.242091i	$-0.922167\pi$
$521$	−6.28771	+	10.8906i	−0.275470	+	0.477127i	0.694784	+	0.719219i	$0.255500\pi$
$522$		0			0
$523$	14.6661	+	25.4024i	0.641303	+	1.11077i	0.985142	+	0.171741i	$0.0549391\pi$
$523$	14.6661	+	25.4024i	0.641303	+	1.11077i	−0.343839	+	0.939028i	$0.611728\pi$
$524$		0			0
$525$	−13.4280	+	21.3520i	−0.586045	+	0.931879i
$526$		0			0
$527$	3.12377	+	17.7158i	0.136073	+	0.771711i
$528$		0			0
$529$	7.63639	+	6.40769i	0.332017	+	0.278595i
$530$		0			0
$531$	−1.82631	−	1.78411i	−0.0792551	−	0.0774239i
$532$		0			0
$533$	16.7068	−	6.08078i	0.723652	−	0.263388i
$534$		0			0
$535$	5.52672	−	4.63747i	0.238941	−	0.200495i
$536$		0			0
$537$	−5.83956	+	27.0887i	−0.251996	+	1.16896i
$538$		0			0
$539$	12.9764			0.558932
$540$		0			0
$541$	19.0813			0.820369			0.410185	−	0.912003i	$-0.365464\pi$
$541$	19.0813			0.820369			0.410185	+	0.912003i	$0.365464\pi$
$542$		0			0
$543$	26.8438	−	8.63659i	1.15198	−	0.370632i
$544$		0			0
$545$	−10.7490	+	9.01948i	−0.460436	+	0.386352i
$546$		0			0
$547$	−10.8995	+	3.96711i	−0.466031	+	0.169621i	−0.564353	−	0.825533i	$-0.690874\pi$
$547$	−10.8995	+	3.96711i	−0.466031	+	0.169621i	0.0983227	+	0.995155i	$0.468652\pi$
$548$		0			0
$549$	−4.81605	−	10.0206i	−0.205544	−	0.427669i
$550$		0			0
$551$	−5.08722	−	4.26868i	−0.216723	−	0.181852i
$552$		0			0
$553$	−10.6249	−	60.2568i	−0.451817	−	2.56238i
$554$		0			0
$555$	−6.17684	−	11.6982i	−0.262192	−	0.496560i
$556$		0			0
$557$	1.28938	+	2.23327i	0.0546329	+	0.0946269i	0.892048	−	0.451940i	$-0.149268\pi$
$557$	1.28938	+	2.23327i	0.0546329	+	0.0946269i	−0.837416	+	0.546567i	$0.815934\pi$
$558$		0			0
$559$	−11.8871	+	20.5890i	−0.502769	+	0.870822i
$560$		0			0
$561$	−9.53593	+	7.40611i	−0.402607	+	0.312686i
$562$		0			0
$563$	35.1335	+	12.7876i	1.48070	+	0.538931i	0.950983	−	0.309243i	$-0.100076\pi$
$563$	35.1335	+	12.7876i	1.48070	+	0.538931i	0.529718	+	0.848174i	$0.322298\pi$
$564$		0			0
$565$	4.26195	−	24.1707i	0.179302	−	1.01687i
$566$		0			0
$567$	35.3931	−	21.5525i	1.48637	−	0.905121i
$568$		0			0
$569$	−2.36831	+	13.4314i	−0.0992847	+	0.563072i	0.894065	+	0.447937i	$0.147841\pi$
$569$	−2.36831	+	13.4314i	−0.0992847	+	0.563072i	−0.993350	+	0.115135i	$0.963270\pi$
$570$		0			0
$571$	−26.7818	−	9.74780i	−1.12079	−	0.407933i	−0.285847	−	0.958275i	$-0.592275\pi$
$571$	−26.7818	−	9.74780i	−1.12079	−	0.407933i	−0.834939	+	0.550343i	$0.814497\pi$
$572$		0			0
$573$	−27.6170	+	21.4488i	−1.15372	+	0.896038i
$574$		0			0
$575$	9.08024	−	15.7274i	0.378672	−	0.655880i
$576$		0			0
$577$	20.2200	+	35.0221i	0.841770	+	1.45799i	0.888397	+	0.459076i	$0.151819\pi$
$577$	20.2200	+	35.0221i	0.841770	+	1.45799i	−0.0466274	+	0.998912i	$0.514847\pi$
$578$		0			0
$579$	−8.13563	−	15.4079i	−0.338105	−	0.640331i
$580$		0			0
$581$	−4.56900	−	25.9121i	−0.189554	−	1.07501i
$582$		0			0
$583$	1.99311	+	1.67242i	0.0825461	+	0.0692644i
$584$		0			0
$585$	12.4070	−	18.1672i	0.512966	−	0.751123i
$586$		0			0
$587$	−17.7921	+	6.47580i	−0.734359	+	0.267285i	−0.682009	−	0.731344i	$-0.738893\pi$
$587$	−17.7921	+	6.47580i	−0.734359	+	0.267285i	−0.0523502	+	0.998629i	$0.516671\pi$
$588$		0			0
$589$	2.98270	−	2.50278i	0.122900	−	0.103125i
$590$		0			0
$591$	−7.80259	+	2.51037i	−0.320955	+	0.103263i
$592$		0			0
$593$	14.1596			0.581465			0.290733	−	0.956804i	$-0.406101\pi$
$593$	14.1596			0.581465			0.290733	+	0.956804i	$0.406101\pi$
$594$		0			0
$595$	−47.6060			−1.95166
$596$		0			0
$597$	−6.11064	+	28.3462i	−0.250092	+	1.16013i
$598$		0			0
$599$	−2.02078	+	1.69564i	−0.0825670	+	0.0692819i	−0.683137	−	0.730290i	$-0.739385\pi$
$599$	−2.02078	+	1.69564i	−0.0825670	+	0.0692819i	0.600570	+	0.799572i	$0.294940\pi$
$600$		0			0
$601$	−33.9881	+	12.3707i	−1.38640	+	0.504610i	−0.924113	−	0.382118i	$-0.875195\pi$
$601$	−33.9881	+	12.3707i	−1.38640	+	0.504610i	−0.462291	+	0.886728i	$0.652973\pi$
$602$		0			0
$603$	−22.7136	+	6.37151i	−0.924970	+	0.259468i
$604$		0			0
$605$	10.5543	+	8.85612i	0.429094	+	0.360053i
$606$		0			0
$607$	−3.17829	−	18.0250i	−0.129003	−	0.731610i	−0.978850	−	0.204581i	$-0.934417\pi$
$607$	−3.17829	−	18.0250i	−0.129003	−	0.731610i	0.849847	−	0.527029i	$-0.176694\pi$
$608$		0			0
$609$	−17.0761	+	27.1530i	−0.691960	+	1.10030i
$610$		0			0
$611$	13.8547	+	23.9970i	0.560501	+	0.970816i
$612$		0			0
$613$	−2.07850	+	3.60007i	−0.0839498	+	0.145405i	−0.904943	−	0.425532i	$-0.860087\pi$
$613$	−2.07850	+	3.60007i	−0.0839498	+	0.145405i	0.820993	+	0.570938i	$0.193420\pi$
$614$		0			0
$615$	−1.05165	−	7.64273i	−0.0424068	−	0.308185i
$616$		0			0
$617$	18.9979	+	6.91468i	0.764827	+	0.278374i	0.694831	−	0.719173i	$-0.255479\pi$
$617$	18.9979	+	6.91468i	0.764827	+	0.278374i	0.0699961	+	0.997547i	$0.477701\pi$
$618$		0			0
$619$	−2.73073	+	15.4868i	−0.109757	+	0.622465i	0.879456	+	0.475981i	$0.157907\pi$
$619$	−2.73073	+	15.4868i	−0.109757	+	0.622465i	−0.989213	+	0.146484i	$0.953204\pi$
$620$		0			0
$621$	−24.8781	+	16.4692i	−0.998322	+	0.660886i
$622$		0			0
$623$	−7.40612	+	42.0022i	−0.296720	+	1.68278i
$624$		0			0
$625$	−0.768434	−	0.279687i	−0.0307374	−	0.0111875i
$626$		0			0
$627$	2.42025	+	0.985972i	0.0966556	+	0.0393759i
$628$		0			0
$629$	−21.4921	+	37.2254i	−0.856945	+	1.48427i
$630$		0			0
$631$	−9.42016	−	16.3162i	−0.375011	−	0.649537i	0.615318	−	0.788279i	$-0.289028\pi$
$631$	−9.42016	−	16.3162i	−0.375011	−	0.649537i	−0.990329	+	0.138742i	$0.955694\pi$
$632$		0			0
$633$	9.14928	+	0.345914i	0.363651	+	0.0137488i
$634$		0			0
$635$	1.93496	+	10.9737i	0.0767867	+	0.435479i
$636$		0			0
$637$	58.8512	+	49.3820i	2.33177	+	1.95659i
$638$		0			0
$639$	−30.1711	+	21.6559i	−1.19355	+	0.856694i
$640$		0			0
$641$	10.3247	−	3.75787i	0.407800	−	0.148427i	−0.129972	−	0.991518i	$-0.541489\pi$
$641$	10.3247	−	3.75787i	0.407800	−	0.148427i	0.537771	+	0.843091i	$0.319266\pi$
$642$		0			0
$643$	0.925080	−	0.776234i	0.0364816	−	0.0306117i	−0.624365	−	0.781133i	$-0.714642\pi$
$643$	0.925080	−	0.776234i	0.0364816	−	0.0306117i	0.660846	+	0.750521i	$0.270198\pi$
$644$		0			0
$645$	7.64648	+	6.92494i	0.301080	+	0.272669i
$646$		0			0
$647$	−3.98494			−0.156664			−0.0783320	−	0.996927i	$-0.524959\pi$
$647$	−3.98494			−0.156664			−0.0783320	+	0.996927i	$0.524959\pi$
$648$		0			0
$649$	−0.777721			−0.0305282
$650$		0			0
$651$	−13.9397	−	12.6244i	−0.546341	−	0.494788i
$652$		0			0
$653$	14.9489	−	12.5437i	0.584997	−	0.490871i	−0.301587	−	0.953439i	$-0.597516\pi$
$653$	14.9489	−	12.5437i	0.584997	−	0.490871i	0.886584	+	0.462568i	$0.153072\pi$
$654$		0			0
$655$	4.02883	−	1.46637i	0.157419	−	0.0572960i
$656$		0			0
$657$	−10.9443	−	4.94851i	−0.426976	−	0.193060i
$658$		0			0
$659$	3.92635	+	3.29460i	0.152949	+	0.128339i	0.716051	−	0.698048i	$-0.245948\pi$
$659$	3.92635	+	3.29460i	0.152949	+	0.128339i	−0.563102	+	0.826387i	$0.690392\pi$
$660$		0			0
$661$	0.995380	+	5.64508i	0.0387158	+	0.219568i	0.998027	−	0.0627818i	$-0.0199972\pi$
$661$	0.995380	+	5.64508i	0.0387158	+	0.219568i	−0.959312	+	0.282350i	$0.908886\pi$
$662$		0			0
$663$	−71.4320	−	2.70069i	−2.77419	−	0.104886i
$664$		0			0
$665$	5.15204	+	8.92359i	0.199788	+	0.346042i
$666$		0			0
$667$	11.5472	−	20.0003i	0.447109	−	0.774416i
$668$		0			0
$669$	−1.00794	−	0.410619i	−0.0389693	−	0.0158755i
$670$		0			0
$671$	−3.18242	−	1.15831i	−0.122856	−	0.0447159i
$672$		0			0
$673$	4.81534	−	27.3092i	0.185618	−	1.05269i	−0.739541	−	0.673111i	$-0.764958\pi$
$673$	4.81534	−	27.3092i	0.185618	−	1.05269i	0.925159	−	0.379580i	$-0.123931\pi$
$674$		0			0
$675$	11.3137	+	11.9204i	0.435466	+	0.458815i
$676$		0			0
$677$	−4.13035	+	23.4244i	−0.158742	+	0.900273i	0.796542	+	0.604583i	$0.206660\pi$
$677$	−4.13035	+	23.4244i	−0.158742	+	0.900273i	−0.955284	+	0.295689i	$0.904451\pi$
$678$		0			0
$679$	48.7217	+	17.7333i	1.86977	+	0.680540i
$680$		0			0
$681$	3.40441	+	24.7410i	0.130457	+	0.948077i
$682$		0			0
$683$	11.2705	−	19.5211i	0.431255	−	0.746956i	−0.565727	−	0.824593i	$-0.691404\pi$
$683$	11.2705	−	19.5211i	0.431255	−	0.746956i	0.996982	+	0.0776373i	$0.0247376\pi$
$684$		0			0
$685$	−8.34674	−	14.4570i	−0.318913	−	0.552373i
$686$		0			0
$687$	−2.35159	+	3.73930i	−0.0897189	+	0.142663i
$688$		0			0
$689$	2.67482	+	15.1697i	0.101903	+	0.577918i
$690$		0			0
$691$	−26.1022	−	21.9024i	−0.992975	−	0.833205i	−0.00697948	−	0.999976i	$-0.502222\pi$
$691$	−26.1022	−	21.9024i	−0.992975	−	0.833205i	−0.985996	+	0.166770i	$0.946666\pi$
$692$		0			0
$693$	3.12433	−	12.2301i	0.118684	−	0.464584i
$694$		0			0
$695$	−18.2903	+	6.65714i	−0.693792	+	0.252520i
$696$		0			0
$697$	−19.2028	+	16.1131i	−0.727358	+	0.610325i
$698$		0			0
$699$	7.11673	−	33.0133i	0.269179	−	1.24868i
$700$		0			0
$701$	−36.0541			−1.36174			−0.680872	−	0.732402i	$-0.738399\pi$
$701$	−36.0541			−1.36174			−0.680872	+	0.732402i	$0.738399\pi$
$702$		0			0
$703$	9.30370			0.350896
$704$		0			0
$705$	11.4460	−	3.68257i	0.431080	−	0.138694i
$706$		0			0
$707$	−4.56503	+	3.83052i	−0.171686	+	0.144061i
$708$		0			0
$709$	35.3142	−	12.8533i	1.32625	−	0.482717i	0.420797	−	0.907155i	$-0.361751\pi$
$709$	35.3142	−	12.8533i	1.32625	−	0.482717i	0.905457	+	0.424438i	$0.139528\pi$
$710$		0			0
$711$	−39.7529	−	3.01024i	−1.49085	−	0.112893i
$712$		0			0
$713$	10.3727	+	8.70369i	0.388459	+	0.325956i
$714$		0			0
$715$	−1.16369	−	6.59959i	−0.0435194	−	0.246811i
$716$		0			0
$717$	−2.53553	−	4.80199i	−0.0946911	−	0.179333i
$718$		0			0
$719$	9.11357	+	15.7852i	0.339879	+	0.588687i	0.984410	−	0.175891i	$-0.0562806\pi$
$719$	9.11357	+	15.7852i	0.339879	+	0.588687i	−0.644531	+	0.764578i	$0.722947\pi$
$720$		0			0
$721$	23.5676	−	40.8202i	0.877702	−	1.52022i
$722$		0			0
$723$	−2.56558	+	1.99256i	−0.0954148	+	0.0741042i
$724$		0			0
$725$	−11.9542	−	4.35096i	−0.443967	−	0.161591i
$726$		0			0
$727$	−1.87727	+	10.6465i	−0.0696241	+	0.394858i	0.930003	+	0.367552i	$0.119804\pi$
$727$	−1.87727	+	10.6465i	−0.0696241	+	0.394858i	−0.999627	+	0.0273059i	$0.991307\pi$
$728$		0			0
$729$	−7.89802	−	25.8190i	−0.292519	−	0.956260i
$730$		0			0
$731$	5.82073	−	33.0110i	0.215288	−	1.22096i
$732$		0			0
$733$	16.5132	+	6.01031i	0.609929	+	0.221996i	0.628472	−	0.777832i	$-0.283681\pi$
$733$	16.5132	+	6.01031i	0.609929	+	0.221996i	−0.0185434	+	0.999828i	$0.505903\pi$
$734$		0			0
$735$	26.3283	−	20.4480i	0.971135	−	0.754235i
$736$		0			0
$737$	−3.59298	+	6.22323i	−0.132349	+	0.229236i
$738$		0			0
$739$	−1.87191	−	3.24224i	−0.0688593	−	0.119268i	0.829540	−	0.558447i	$-0.188603\pi$
$739$	−1.87191	−	3.24224i	−0.0688593	−	0.119268i	−0.898399	+	0.439179i	$0.855269\pi$
$740$		0			0
$741$	7.22431	+	13.6820i	0.265392	+	0.502620i
$742$		0			0
$743$	3.17293	+	17.9946i	0.116403	+	0.660157i	0.986046	+	0.166474i	$0.0532383\pi$
$743$	3.17293	+	17.9946i	0.116403	+	0.660157i	−0.869642	+	0.493682i	$0.835651\pi$
$744$		0			0
$745$	−23.0814	−	19.3676i	−0.845636	−	0.709573i
$746$		0			0
$747$	−17.0948	−	1.29449i	−0.625467	−	0.0473627i
$748$		0			0
$749$	23.0299	−	8.38219i	0.841493	−	0.306279i
$750$		0			0
$751$	−9.30946	+	7.81156i	−0.339707	+	0.285048i	−0.796641	−	0.604453i	$-0.793392\pi$
$751$	−9.30946	+	7.81156i	−0.339707	+	0.285048i	0.456934	+	0.889500i	$0.348947\pi$
$752$		0			0
$753$	31.6685	−	10.1889i	1.15406	−	0.371303i
$754$		0			0
$755$	5.32007			0.193617
$756$		0			0
$757$	−24.5310			−0.891595			−0.445798	−	0.895134i	$-0.647080\pi$
$757$	−24.5310			−0.891595			−0.445798	+	0.895134i	$0.647080\pi$
$758$		0			0
$759$	−1.91519	+	8.88422i	−0.0695169	+	0.322477i
$760$		0			0
$761$	−1.65692	+	1.39032i	−0.0600633	+	0.0503991i	−0.672325	−	0.740256i	$-0.734704\pi$
$761$	−1.65692	+	1.39032i	−0.0600633	+	0.0503991i	0.612262	+	0.790655i	$0.290260\pi$
$762$		0			0
$763$	−44.7911	+	16.3026i	−1.62155	+	0.590195i
$764$		0			0
$765$	−7.67742	+	30.0531i	−0.277578	+	1.08657i
$766$		0			0
$767$	−3.52716	−	2.95964i	−0.127358	−	0.106866i
$768$		0			0
$769$	2.99276	+	16.9728i	0.107922	+	0.612054i	0.990013	+	0.140976i	$0.0450239\pi$
$769$	2.99276	+	16.9728i	0.107922	+	0.612054i	−0.882091	+	0.471078i	$0.843865\pi$
$770$		0			0
$771$	−2.29593	+	3.65079i	−0.0826858	+	0.131480i
$772$		0			0
$773$	−11.0025	−	19.0568i	−0.395731	−	0.685427i	0.597463	−	0.801897i	$-0.296176\pi$
$773$	−11.0025	−	19.0568i	−0.395731	−	0.685427i	−0.993194	+	0.116470i	$0.962842\pi$
$774$		0			0
$775$	3.72935	−	6.45942i	0.133962	−	0.232029i
$776$		0			0
$777$	−6.12581	−	44.5183i	−0.219762	−	1.59709i
$778$		0			0
$779$	5.09851	+	1.85571i	0.182673	+	0.0664876i
$780$		0			0
$781$	−1.96448	+	11.1411i	−0.0702945	+	0.398660i
$782$		0			0
$783$	14.3875	+	15.1589i	0.514168	+	0.541736i
$784$		0			0
$785$	−0.552809	+	3.13514i	−0.0197306	+	0.111898i
$786$		0			0
$787$	46.2276	+	16.8255i	1.64784	+	0.599763i	0.988383	−	0.151982i	$-0.0485656\pi$
$787$	46.2276	+	16.8255i	1.64784	+	0.599763i	0.659453	+	0.751746i	$0.270788\pi$
$788$		0			0
$789$	38.5709	+	15.7132i	1.37316	+	0.559403i
$790$		0			0
$791$	41.6869	−	72.2039i	1.48222	−	2.56728i
$792$		0			0
$793$	−10.0251	−	17.3640i	−0.356003	−	0.616615i
$794$		0			0
$795$	6.67926	+	0.252528i	0.236889	+	0.00895625i
$796$		0			0
$797$	−4.95275	−	28.0884i	−0.175435	−	0.994943i	−0.937640	−	0.347607i	$-0.886994\pi$
$797$	−4.95275	−	28.0884i	−0.175435	−	0.994943i	0.762205	−	0.647336i	$-0.224117\pi$
$798$		0			0
$799$	−29.9284	−	25.1129i	−1.05879	−	0.888431i
$800$		0			0
$801$	25.3211	+	11.4491i	0.894677	+	0.404534i
$802$		0			0
$803$	−3.43808	+	1.25136i	−0.121327	+	0.0441595i
$804$		0			0
$805$	−27.4501	+	23.0333i	−0.967488	+	0.811819i
$806$		0			0
$807$	41.7164	+	37.7800i	1.46849	+	1.32992i
$808$		0			0
$809$	24.5773			0.864094			0.432047	−	0.901851i	$-0.357792\pi$
$809$	24.5773			0.864094			0.432047	+	0.901851i	$0.357792\pi$
$810$		0			0
$811$	2.52317			0.0886006			0.0443003	−	0.999018i	$-0.485894\pi$
$811$	2.52317			0.0886006			0.0443003	+	0.999018i	$0.485894\pi$
$812$		0			0
$813$	−6.54911	−	5.93112i	−0.229687	−	0.208014i
$814$		0			0
$815$	−21.8856	+	18.3642i	−0.766621	+	0.643271i
$816$		0			0
$817$	−6.81774	+	2.48145i	−0.238523	+	0.0868151i
$818$		0			0
$819$	60.7118	−	43.5770i	2.12144	−	1.52270i
$820$		0			0
$821$	16.0104	+	13.4343i	0.558767	+	0.468861i	0.877897	−	0.478850i	$-0.158946\pi$
$821$	16.0104	+	13.4343i	0.558767	+	0.468861i	−0.319130	+	0.947711i	$0.603391\pi$
$822$		0			0
$823$	−5.05823	−	28.6866i	−0.176319	−	0.999954i	−0.936611	−	0.350372i	$-0.886055\pi$
$823$	−5.05823	−	28.6866i	−0.176319	−	0.999954i	0.760292	−	0.649582i	$-0.225056\pi$
$824$		0			0
$825$	5.00265	+	0.189139i	0.174170	+	0.00658497i
$826$		0			0
$827$	−1.30995	−	2.26889i	−0.0455513	−	0.0788971i	0.842351	−	0.538930i	$-0.181171\pi$
$827$	−1.30995	−	2.26889i	−0.0455513	−	0.0788971i	−0.887902	+	0.460032i	$0.847838\pi$
$828$		0			0
$829$	20.9195	−	36.2336i	0.726563	−	1.25844i	−0.231764	−	0.972772i	$-0.574450\pi$
$829$	20.9195	−	36.2336i	0.726563	−	1.25844i	0.958327	−	0.285672i	$-0.0922169\pi$
$830$		0			0
$831$	−15.8714	−	6.46577i	−0.550574	−	0.224295i
$832$		0			0
$833$	−101.786	−	37.0472i	−3.52669	−	1.28361i
$834$		0			0
$835$	1.73375	−	9.83261i	0.0599990	−	0.340272i
$836$		0			0
$837$	−10.2177	+	6.76406i	−0.353174	+	0.233800i
$838$		0			0
$839$	7.53509	−	42.7336i	0.260140	−	1.47533i	−0.522385	−	0.852709i	$-0.674958\pi$
$839$	7.53509	−	42.7336i	0.260140	−	1.47533i	0.782526	−	0.622618i	$-0.213931\pi$
$840$		0			0
$841$	12.0492	+	4.38553i	0.415488	+	0.151225i
$842$		0			0
$843$	2.54683	+	18.5087i	0.0877175	+	0.637473i
$844$		0			0
$845$	11.0271	−	19.0995i	0.379344	−	0.657043i
$846$		0			0
$847$	23.4012	+	40.5321i	0.804075	+	1.39270i
$848$		0			0
$849$	−10.5117	+	16.7148i	−0.360761	+	0.573652i
$850$		0			0
$851$	5.61832	+	31.8631i	0.192593	+	1.09225i
$852$		0			0
$853$	33.5499	+	28.1517i	1.14873	+	0.963898i	0.999689	−	0.0249337i	$-0.00793747\pi$
$853$	33.5499	+	28.1517i	1.14873	+	0.963898i	0.149039	+	0.988831i	$0.452382\pi$
$854$		0			0
$855$	6.46423	−	1.81331i	0.221072	−	0.0620140i
$856$		0			0
$857$	17.6261	−	6.41536i	0.602095	−	0.219145i	−0.0229461	−	0.999737i	$-0.507305\pi$
$857$	17.6261	−	6.41536i	0.602095	−	0.219145i	0.625041	+	0.780592i	$0.285082\pi$
$858$		0			0
$859$	2.83932	−	2.38247i	0.0968762	−	0.0812888i	−0.593063	−	0.805156i	$-0.702082\pi$
$859$	2.83932	−	2.38247i	0.0968762	−	0.0812888i	0.689939	+	0.723867i	$0.257637\pi$
$860$		0			0
$861$	5.52258	−	25.6183i	0.188209	−	0.873069i
$862$		0			0
$863$	−36.9435			−1.25757			−0.628785	−	0.777579i	$-0.716447\pi$
$863$	−36.9435			−1.25757			−0.628785	+	0.777579i	$0.716447\pi$
$864$		0			0
$865$	2.37355			0.0807032
$866$		0			0
$867$	67.9140	−	21.8503i	2.30648	−	0.742076i
$868$		0			0
$869$	−9.30283	+	7.80600i	−0.315577	+	0.264800i
$870$		0			0
$871$	−39.9778	+	14.5507i	−1.35460	+	0.493032i
$872$		0			0
$873$	19.0522	−	27.8976i	0.644818	−	0.944191i
$874$		0			0
$875$	39.0242	+	32.7452i	1.31926	+	1.10699i
$876$		0			0
$877$	4.58914	+	26.0263i	0.154964	+	0.878845i	0.958819	+	0.284019i	$0.0916679\pi$
$877$	4.58914	+	26.0263i	0.154964	+	0.878845i	−0.803855	+	0.594826i	$0.797221\pi$
$878$		0			0
$879$	−9.15077	−	17.3305i	−0.308648	−	0.584542i
$880$		0			0
$881$	−26.5192	−	45.9326i	−0.893454	−	1.54751i	−0.835706	−	0.549177i	$-0.814941\pi$
$881$	−26.5192	−	45.9326i	−0.893454	−	1.54751i	−0.0577486	−	0.998331i	$-0.518392\pi$
$882$		0			0
$883$	−15.4631	+	26.7829i	−0.520375	+	0.901316i	0.479344	+	0.877627i	$0.340875\pi$
$883$	−15.4631	+	26.7829i	−0.520375	+	0.901316i	−0.999719	+	0.0236893i	$0.992459\pi$
$884$		0			0
$885$	−1.57795	+	1.22552i	−0.0530422	+	0.0411954i
$886$		0			0
$887$	−10.7667	−	3.91878i	−0.361512	−	0.131580i	0.154877	−	0.987934i	$-0.450502\pi$
$887$	−10.7667	−	3.91878i	−0.361512	−	0.131580i	−0.516389	+	0.856354i	$0.672724\pi$
$888$		0			0
$889$	−6.57302	+	37.2774i	−0.220452	+	1.25025i
$890$		0			0
$891$	−7.21688	−	3.94471i	−0.241774	−	0.132153i
$892$		0			0
$893$	−1.46841	+	8.32776i	−0.0491384	+	0.278678i
$894$		0			0
$895$	20.3775	+	7.41680i	0.681144	+	0.247916i
$896$		0			0
$897$	−42.4950	+	33.0039i	−1.41887	+	1.10197i
$898$		0			0
$899$	4.74255	−	8.21434i	0.158173	−	0.273964i
$900$		0			0
$901$	−10.8592	−	18.8087i	−0.361772	−	0.626607i
$902$		0			0
$903$	16.3628	+	30.9891i	0.544519	+	1.03125i
$904$		0			0
$905$	−3.83192	−	21.7319i	−0.127377	−	0.722392i
$906$		0			0
$907$	2.00276	+	1.68051i	0.0665004	+	0.0558005i	0.675432	−	0.737422i	$-0.263957\pi$
$907$	2.00276	+	1.68051i	0.0665004	+	0.0558005i	−0.608932	+	0.793223i	$0.708402\pi$
$908$		0			0
$909$	1.68196	+	3.49960i	0.0557870	+	0.116074i
$910$		0			0
$911$	37.9408	−	13.8093i	1.25704	−	0.457524i	0.374263	−	0.927323i	$-0.377896\pi$
$911$	37.9408	−	13.8093i	1.25704	−	0.457524i	0.882773	+	0.469799i	$0.155674\pi$
$912$		0			0
$913$	−4.00047	+	3.35679i	−0.132396	+	0.111094i
$914$		0			0
$915$	−8.28219	+	2.66467i	−0.273801	+	0.0880913i
$916$		0			0
$917$	14.5642			0.480951
$918$		0			0
$919$	−0.927946			−0.0306101			−0.0153051	−	0.999883i	$-0.504872\pi$
$919$	−0.927946			−0.0306101			−0.0153051	+	0.999883i	$0.504872\pi$
$920$		0			0
$921$	4.69920	−	21.7988i	0.154844	−	0.718294i
$922$		0			0
$923$	−51.3072	+	43.0518i	−1.68880	+	1.41707i
$924$		0			0
$925$	16.7475	−	6.09557i	0.550653	−	0.200421i
$926$		0			0
$927$	−21.9686	−	21.4610i	−0.721543	−	0.704872i
$928$		0			0
$929$	−13.5635	−	11.3811i	−0.445005	−	0.373403i	0.392574	−	0.919721i	$-0.371585\pi$
$929$	−13.5635	−	11.3811i	−0.445005	−	0.373403i	−0.837578	+	0.546317i	$0.816029\pi$
$930$		0			0
$931$	4.07119	+	23.0889i	0.133428	+	0.756708i
$932$		0			0
$933$	1.77382	−	2.82058i	0.0580724	−	0.0923417i
$934$		0			0
$935$	4.72431	+	8.18275i	0.154501	+	0.267604i
$936$		0			0
$937$	17.4968	−	30.3053i	0.571595	−	0.990032i	−0.424807	−	0.905284i	$-0.639658\pi$
$937$	17.4968	−	30.3053i	0.571595	−	0.990032i	0.996402	−	0.0847481i	$-0.0270086\pi$
$938$		0			0
$939$	0.490972	+	3.56806i	0.0160223	+	0.116439i
$940$		0			0
$941$	15.1518	+	5.51481i	0.493935	+	0.179778i	0.576964	−	0.816769i	$-0.304237\pi$
$941$	15.1518	+	5.51481i	0.493935	+	0.179778i	−0.0830292	+	0.996547i	$0.526459\pi$
$942$		0			0
$943$	−3.27648	+	18.5819i	−0.106697	+	0.605109i
$944$		0			0
$945$	−12.9330	−	29.7375i	−0.420709	−	0.967361i
$946$		0			0
$947$	−10.1675	+	57.6626i	−0.330399	+	1.87378i	0.138248	+	0.990398i	$0.455853\pi$
$947$	−10.1675	+	57.6626i	−0.330399	+	1.87378i	−0.468647	+	0.883386i	$0.655258\pi$
$948$		0			0
$949$	−20.3547	−	7.40849i	−0.660740	−	0.240490i
$950$		0			0
$951$	−3.72776	−	1.51863i	−0.120881	−	0.0492449i
$952$		0			0
$953$	−2.48854	+	4.31028i	−0.0806117	+	0.139624i	−0.903513	−	0.428561i	$-0.859021\pi$
$953$	−2.48854	+	4.31028i	−0.0806117	+	0.139624i	0.822901	+	0.568185i	$0.192354\pi$
$954$		0			0
$955$	13.6821	+	23.6981i	0.442742	+	0.766851i
$956$		0			0
$957$	6.36179	+	0.240525i	0.205647	+	0.00777507i
$958$		0			0
$959$	−9.84712	−	55.8458i	−0.317980	−	1.80335i
$960$		0			0
$961$	−19.4872	−	16.3517i	−0.628620	−	0.527475i
$962$		0			0
$963$	−1.57755	−	15.8903i	−0.0508358	−	0.512057i
$964$		0			0
$965$	−12.8128	+	4.66348i	−0.412458	+	0.150123i
$966$		0			0
$967$	26.9907	−	22.6479i	0.867963	−	0.728307i	−0.0957054	−	0.995410i	$-0.530511\pi$
$967$	26.9907	−	22.6479i	0.867963	−	0.728307i	0.963668	+	0.267102i	$0.0860662\pi$
$968$		0			0
$969$	−16.1695	−	14.6437i	−0.519439	−	0.470423i
$970$		0			0
$971$	60.2387			1.93315			0.966576	−	0.256382i	$-0.0825305\pi$
$971$	60.2387			1.93315			0.966576	+	0.256382i	$0.0825305\pi$
$972$		0			0
$973$	−66.1192			−2.11969
$974$		0			0
$975$	21.9685	+	19.8955i	0.703555	+	0.637166i
$976$		0			0
$977$	17.8891	−	15.0108i	0.572324	−	0.480237i	−0.310092	−	0.950706i	$-0.600360\pi$
$977$	17.8891	−	15.0108i	0.572324	−	0.480237i	0.882416	+	0.470470i	$0.155916\pi$
$978$		0			0
$979$	7.95450	−	2.89520i	0.254227	−	0.0925310i
$980$		0			0
$981$	3.06820	+	30.9052i	0.0979600	+	0.986728i
$982$		0			0
$983$	−10.2189	−	8.57466i	−0.325932	−	0.273489i	0.465108	−	0.885254i	$-0.346015\pi$
$983$	−10.2189	−	8.57466i	−0.325932	−	0.273489i	−0.791040	+	0.611765i	$0.790460\pi$
$984$		0			0
$985$	1.11381	+	6.31672i	0.0354889	+	0.201267i
$986$		0			0
$987$	40.8153	+	1.54314i	1.29917	+	0.0491186i
$988$		0			0
$989$	−12.6155	−	21.8507i	−0.401150	−	0.694812i
$990$		0			0
$991$	14.2786	−	24.7312i	0.453573	−	0.785612i	−0.545031	−	0.838416i	$-0.683482\pi$
$991$	14.2786	−	24.7312i	0.453573	−	0.785612i	0.998605	+	0.0528033i	$0.0168156\pi$
$992$		0			0
$993$	−4.13593	−	1.68491i	−0.131250	−	0.0534690i
$994$		0			0
$995$	21.3234	+	7.76109i	0.675998	+	0.246043i
$996$		0			0
$997$	−9.00227	+	51.0544i	−0.285105	+	1.61691i	0.419807	+	0.907613i	$0.362098\pi$
$997$	−9.00227	+	51.0544i	−0.285105	+	1.61691i	−0.704911	+	0.709295i	$0.749013\pi$
$998$		0			0
$999$	−29.0918	−	3.31232i	−0.920424	−	0.104797i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.q.b.25.2	✓	30
3.2	odd	2		648.2.q.b.73.4		30
4.3	odd	2		432.2.u.f.241.4		30
27.11	odd	18		5832.2.a.l.1.9		15
27.13	even	9	inner	216.2.q.b.121.2	yes	30
27.14	odd	18		648.2.q.b.577.4		30
27.16	even	9		5832.2.a.k.1.7		15
108.67	odd	18		432.2.u.f.337.4		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.q.b.25.2	✓	30	1.1	even	1	trivial
216.2.q.b.121.2	yes	30	27.13	even	9	inner
432.2.u.f.241.4		30	4.3	odd	2
432.2.u.f.337.4		30	108.67	odd	18
648.2.q.b.73.4		30	3.2	odd	2
648.2.q.b.577.4		30	27.14	odd	18
5832.2.a.k.1.7		15	27.16	even	9
5832.2.a.l.1.9		15	27.11	odd	18

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.q (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28382 - 1.16267i) q^{3} +(-1.03831 + 0.871247i) q^{5} +(-4.32665 + 1.57477i) q^{7} +(0.296376 + 2.98532i) q^{9} +O(q^{10})\)	\(q+(-1.28382 - 1.16267i) q^{3} +(-1.03831 + 0.871247i) q^{5} +(-4.32665 + 1.57477i) q^{7} +(0.296376 + 2.98532i) q^{9} +(0.700045 + 0.587408i) q^{11} +(0.939486 + 5.32809i) q^{13} +(2.34598 + 0.0886962i) q^{15} +(-3.81411 - 6.60622i) q^{17} +(-0.825544 + 1.42988i) q^{19} +(7.38557 + 3.00876i) q^{21} +(-5.39555 - 1.96382i) q^{23} +(-0.549221 + 3.11479i) q^{25} +(3.09047 - 4.17720i) q^{27} +(-0.698436 + 3.96103i) q^{29} +(-2.21601 - 0.806561i) q^{31} +(-0.215767 - 1.56805i) q^{33} +(3.12039 - 5.40468i) q^{35} +(-2.81745 - 4.87996i) q^{37} +(4.98870 - 7.93261i) q^{39} +(-0.570634 - 3.23623i) q^{41} +(3.36619 + 2.82457i) q^{43} +(-2.90868 - 2.84148i) q^{45} +(4.81274 - 1.75170i) q^{47} +(10.8777 - 9.12744i) q^{49} +(-2.78427 + 12.9158i) q^{51} +2.84711 q^{53} -1.23864 q^{55} +(2.72234 - 0.875871i) q^{57} +(-0.651937 + 0.547040i) q^{59} +(-3.48246 + 1.26751i) q^{61} +(-5.98352 - 12.4497i) q^{63} +(-5.61756 - 4.71369i) q^{65} +(1.36547 + 7.74398i) q^{67} +(4.64362 + 8.79446i) q^{69} +(6.18977 + 10.7210i) q^{71} +(-2.00184 + 3.46728i) q^{73} +(4.32659 - 3.36026i) q^{75} +(-3.95388 - 1.43910i) q^{77} +(-2.30759 + 13.0870i) q^{79} +(-8.82432 + 1.76956i) q^{81} +(-0.992328 + 5.62777i) q^{83} +(9.71588 + 3.53629i) q^{85} +(5.50205 - 4.27318i) q^{87} +(4.63153 - 8.02205i) q^{89} +(-12.4553 - 21.5733i) q^{91} +(1.90718 + 3.61197i) q^{93} +(-0.388610 - 2.20392i) q^{95} +(-8.62632 - 7.23834i) q^{97} +(-1.54613 + 2.26396i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{7} - 6 q^{9}+O(q^{10}) \) 30 * q + 3 * q^7 - 6 * q^9	\( 30 q + 3 q^{7} - 6 q^{9} - 3 q^{11} - 12 q^{13} + 15 q^{15} + 6 q^{17} - 9 q^{19} + 30 q^{21} - 12 q^{23} + 24 q^{25} - 15 q^{27} - 9 q^{29} + 27 q^{31} - 30 q^{33} - 18 q^{35} - 15 q^{37} - 21 q^{39} - 15 q^{41} - 30 q^{43} + 15 q^{45} - 18 q^{47} + 15 q^{49} - 6 q^{51} - 18 q^{53} + 54 q^{55} - 72 q^{57} - 12 q^{59} + 6 q^{61} - 54 q^{63} - 54 q^{65} - 45 q^{67} + 9 q^{69} - 36 q^{73} + 69 q^{75} + 12 q^{77} + 45 q^{79} - 30 q^{81} - 3 q^{83} + 57 q^{85} - 60 q^{87} + 36 q^{89} - 39 q^{91} + 30 q^{93} + 51 q^{95} - 84 q^{97} + 162 q^{99}+O(q^{100}) \) 30 * q + 3 * q^7 - 6 * q^9 - 3 * q^11 - 12 * q^13 + 15 * q^15 + 6 * q^17 - 9 * q^19 + 30 * q^21 - 12 * q^23 + 24 * q^25 - 15 * q^27 - 9 * q^29 + 27 * q^31 - 30 * q^33 - 18 * q^35 - 15 * q^37 - 21 * q^39 - 15 * q^41 - 30 * q^43 + 15 * q^45 - 18 * q^47 + 15 * q^49 - 6 * q^51 - 18 * q^53 + 54 * q^55 - 72 * q^57 - 12 * q^59 + 6 * q^61 - 54 * q^63 - 54 * q^65 - 45 * q^67 + 9 * q^69 - 36 * q^73 + 69 * q^75 + 12 * q^77 + 45 * q^79 - 30 * q^81 - 3 * q^83 + 57 * q^85 - 60 * q^87 + 36 * q^89 - 39 * q^91 + 30 * q^93 + 51 * q^95 - 84 * q^97 + 162 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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