LMFDB - Embedded newform 108.2.i.a.25.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,2,Mod(13,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("108.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	108.i (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:	$0.862384341830$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} + 24 x^{16} - 66 x^{15} + 153 x^{14} - 315 x^{13} + 651 x^{12} - 1350 x^{11} + \cdots + 19683 $ x^18 - 6x^17 + 24x^16 - 66x^15 + 153x^14 - 315x^13 + 651x^12 - 1350x^11 + 2700x^10 - 4941x^9 + 8100x^8 - 12150x^7 + 17577x^6 - 25515x^5 + 37179x^4 - 48114x^3 + 52488x^2 - 39366*x + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.3
Root			$-1.34999 + 1.08514i$ of defining polynomial
Character	$\chi$	$=$	108.25
Dual form			108.2.i.a.13.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30308 + 1.14105i) q^{3} +(-0.761786 + 0.639214i) q^{5} +(1.35240 - 0.492232i) q^{7} +(0.396022 + 2.97375i) q^{9} +O(q^{10})$	\(q+(1.30308 + 1.14105i) q^{3} +(-0.761786 + 0.639214i) q^{5} +(1.35240 - 0.492232i) q^{7} +(0.396022 + 2.97375i) q^{9} +(-2.56436 - 2.15175i) q^{11} +(-0.337662 - 1.91498i) q^{13} +(-1.72204 - 0.0362879i) q^{15} +(1.16107 + 2.01104i) q^{17} +(3.38586 - 5.86448i) q^{19} +(2.32394 + 0.901731i) q^{21} +(-8.41184 - 3.06166i) q^{23} +(-0.696518 + 3.95015i) q^{25} +(-2.87714 + 4.32690i) q^{27} +(0.847007 - 4.80362i) q^{29} +(-5.81772 - 2.11748i) q^{31} +(-0.886306 - 5.72995i) q^{33} +(-0.715594 + 1.23944i) q^{35} +(-0.0829061 - 0.143598i) q^{37} +(1.74508 - 2.88065i) q^{39} +(1.87304 + 10.6225i) q^{41} +(6.82940 + 5.73054i) q^{43} +(-2.20254 - 2.01221i) q^{45} +(6.14677 - 2.23724i) q^{47} +(-3.77563 + 3.16813i) q^{49} +(-0.781721 + 3.94538i) q^{51} +10.7235 q^{53} +3.32892 q^{55} +(11.1037 - 3.77845i) q^{57} +(3.02292 - 2.53653i) q^{59} +(-7.91547 + 2.88100i) q^{61} +(1.99935 + 3.82674i) q^{63} +(1.48131 + 1.24296i) q^{65} +(-0.00383180 - 0.0217312i) q^{67} +(-7.46778 - 13.5879i) q^{69} +(4.53728 + 7.85879i) q^{71} +(-2.26572 + 3.92434i) q^{73} +(-5.41493 + 4.35259i) q^{75} +(-4.52718 - 1.64776i) q^{77} +(-1.00608 + 5.70576i) q^{79} +(-8.68633 + 2.35534i) q^{81} +(0.898927 - 5.09807i) q^{83} +(-2.16997 - 0.789806i) q^{85} +(6.58487 - 5.29301i) q^{87} +(1.91749 - 3.32118i) q^{89} +(-1.39926 - 2.42360i) q^{91} +(-5.16480 - 9.39752i) q^{93} +(1.16936 + 6.63176i) q^{95} +(-5.40914 - 4.53881i) q^{97} +(5.38322 - 8.47789i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{5} + 6 q^{9}+O(q^{10}) $ 18 * q + 3 * q^5 + 6 * q^9	$ 18 q + 3 q^{5} + 6 q^{9} + 3 q^{11} - 9 q^{15} - 12 q^{17} - 30 q^{21} - 30 q^{23} + 9 q^{25} - 27 q^{27} - 24 q^{29} + 9 q^{31} - 18 q^{33} - 21 q^{35} + 3 q^{39} + 21 q^{41} - 9 q^{43} + 45 q^{45} + 45 q^{47} - 18 q^{49} + 63 q^{51} + 66 q^{53} + 54 q^{57} + 60 q^{59} - 18 q^{61} + 57 q^{63} + 33 q^{65} - 27 q^{67} - 9 q^{69} - 12 q^{71} + 9 q^{73} - 33 q^{75} - 75 q^{77} - 36 q^{79} - 54 q^{81} - 45 q^{83} - 36 q^{85} - 63 q^{87} - 48 q^{89} + 9 q^{91} - 33 q^{93} + 6 q^{95} - 27 q^{97} + 27 q^{99}+O(q^{100}) $ 18 * q + 3 * q^5 + 6 * q^9 + 3 * q^11 - 9 * q^15 - 12 * q^17 - 30 * q^21 - 30 * q^23 + 9 * q^25 - 27 * q^27 - 24 * q^29 + 9 * q^31 - 18 * q^33 - 21 * q^35 + 3 * q^39 + 21 * q^41 - 9 * q^43 + 45 * q^45 + 45 * q^47 - 18 * q^49 + 63 * q^51 + 66 * q^53 + 54 * q^57 + 60 * q^59 - 18 * q^61 + 57 * q^63 + 33 * q^65 - 27 * q^67 - 9 * q^69 - 12 * q^71 + 9 * q^73 - 33 * q^75 - 75 * q^77 - 36 * q^79 - 54 * q^81 - 45 * q^83 - 36 * q^85 - 63 * q^87 - 48 * q^89 + 9 * q^91 - 33 * q^93 + 6 * q^95 - 27 * q^97 + 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$1$

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
$3$	1.30308	+	1.14105i	0.752332	+	0.658784i
$3$	1.30308	+	1.14105i	0.752332	+	0.658784i
$4$		0			0
$5$	−0.761786	+	0.639214i	−0.340681	+	0.285865i	−0.797035	−	0.603933i	$-0.793599\pi$
$5$	−0.761786	+	0.639214i	−0.340681	+	0.285865i	0.456354	+	0.889798i	$0.349155\pi$
$6$		0			0
$7$	1.35240	−	0.492232i	0.511157	−	0.186046i	−0.0735482	−	0.997292i	$-0.523432\pi$
$7$	1.35240	−	0.492232i	0.511157	−	0.186046i	0.584706	+	0.811246i	$0.301210\pi$
$8$		0			0
$9$	0.396022	+	2.97375i	0.132007	+	0.991249i
$10$		0			0
$11$	−2.56436	−	2.15175i	−0.773183	−	0.648777i	0.168339	−	0.985729i	$-0.446160\pi$
$11$	−2.56436	−	2.15175i	−0.773183	−	0.648777i	−0.941522	+	0.336952i	$0.890604\pi$
$12$		0			0
$13$	−0.337662	−	1.91498i	−0.0936506	−	0.531119i	−0.995153	−	0.0983438i	$-0.968646\pi$
$13$	−0.337662	−	1.91498i	−0.0936506	−	0.531119i	0.901502	−	0.432775i	$-0.142466\pi$
$14$		0			0
$15$	−1.72204	−	0.0362879i	−0.444629	−	0.00936949i
$16$		0			0
$17$	1.16107	+	2.01104i	0.281602	+	0.487749i	0.971779	−	0.235891i	$-0.0758010\pi$
$17$	1.16107	+	2.01104i	0.281602	+	0.487749i	−0.690178	+	0.723640i	$0.742468\pi$
$18$		0			0
$19$	3.38586	−	5.86448i	0.776769	−	1.34540i	−0.157025	−	0.987595i	$-0.550190\pi$
$19$	3.38586	−	5.86448i	0.776769	−	1.34540i	0.933795	−	0.357809i	$-0.116476\pi$
$20$		0			0
$21$	2.32394	+	0.901731i	0.507124	+	0.196774i
$22$		0			0
$23$	−8.41184	−	3.06166i	−1.75399	−	0.638400i	−0.754157	−	0.656694i	$-0.771954\pi$
$23$	−8.41184	−	3.06166i	−1.75399	−	0.638400i	−0.999833	+	0.0182938i	$0.994177\pi$
$24$		0			0
$25$	−0.696518	+	3.95015i	−0.139304	+	0.790030i
$26$		0			0
$27$	−2.87714	+	4.32690i	−0.553705	+	0.832713i
$28$		0			0
$29$	0.847007	−	4.80362i	0.157285	−	0.892009i	−0.799381	−	0.600824i	$-0.794839\pi$
$29$	0.847007	−	4.80362i	0.157285	−	0.892009i	0.956667	−	0.291185i	$-0.0940496\pi$
$30$		0			0
$31$	−5.81772	−	2.11748i	−1.04489	−	0.380310i	−0.238160	−	0.971226i	$-0.576544\pi$
$31$	−5.81772	−	2.11748i	−1.04489	−	0.380310i	−0.806733	+	0.590916i	$0.798766\pi$
$32$		0			0
$33$	−0.886306	−	5.72995i	−0.154286	−	0.997456i
$34$		0			0
$35$	−0.715594	+	1.23944i	−0.120957	+	0.209504i
$36$		0			0
$37$	−0.0829061	−	0.143598i	−0.0136297	−	0.0236073i	0.859130	−	0.511757i	$-0.171005\pi$
$37$	−0.0829061	−	0.143598i	−0.0136297	−	0.0236073i	−0.872760	+	0.488150i	$0.837672\pi$
$38$		0			0
$39$	1.74508	−	2.88065i	0.279436	−	0.461273i
$40$		0			0
$41$	1.87304	+	10.6225i	0.292519	+	1.65896i	0.677117	+	0.735876i	$0.263229\pi$
$41$	1.87304	+	10.6225i	0.292519	+	1.65896i	−0.384597	+	0.923084i	$0.625660\pi$
$42$		0			0
$43$	6.82940	+	5.73054i	1.04147	+	0.873900i	0.992171	−	0.124884i	$-0.0398560\pi$
$43$	6.82940	+	5.73054i	1.04147	+	0.873900i	0.0493017	+	0.998784i	$0.484300\pi$
$44$		0			0
$45$	−2.20254	−	2.01221i	−0.328336	−	0.299963i
$46$		0			0
$47$	6.14677	−	2.23724i	0.896599	−	0.326335i	0.147710	−	0.989031i	$-0.452810\pi$
$47$	6.14677	−	2.23724i	0.896599	−	0.326335i	0.748889	+	0.662695i	$0.230588\pi$
$48$		0			0
$49$	−3.77563	+	3.16813i	−0.539376	+	0.452590i
$50$		0			0
$51$	−0.781721	+	3.94538i	−0.109463	+	0.552464i
$52$		0			0
$53$	10.7235			1.47299			0.736495	−	0.676443i	$-0.236479\pi$
$53$	10.7235			1.47299			0.736495	+	0.676443i	$0.236479\pi$
$54$		0			0
$55$	3.32892			0.448871
$56$		0			0
$57$	11.1037	−	3.77845i	1.47072	−	0.500468i
$58$		0			0
$59$	3.02292	−	2.53653i	0.393551	−	0.330229i	−0.424444	−	0.905454i	$-0.639530\pi$
$59$	3.02292	−	2.53653i	0.393551	−	0.330229i	0.817995	+	0.575226i	$0.195086\pi$
$60$		0			0
$61$	−7.91547	+	2.88100i	−1.01347	+	0.368874i	−0.794765	−	0.606917i	$-0.792406\pi$
$61$	−7.91547	+	2.88100i	−1.01347	+	0.368874i	−0.218707	+	0.975791i	$0.570184\pi$
$62$		0			0
$63$	1.99935	+	3.82674i	0.251894	+	0.482125i
$64$		0			0
$65$	1.48131	+	1.24296i	0.183733	+	0.154171i
$66$		0			0
$67$	−0.00383180	−	0.0217312i	−0.000468128	−	0.00265489i	0.984573	−	0.174975i	$-0.0559846\pi$
$67$	−0.00383180	−	0.0217312i	−0.000468128	−	0.00265489i	−0.985041	+	0.172321i	$0.944874\pi$
$68$		0			0
$69$	−7.46778	−	13.5879i	−0.899015	−	1.63579i
$70$		0			0
$71$	4.53728	+	7.85879i	0.538476	+	0.932667i	0.998986	+	0.0450131i	$0.0143329\pi$
$71$	4.53728	+	7.85879i	0.538476	+	0.932667i	−0.460511	+	0.887654i	$0.652334\pi$
$72$		0			0
$73$	−2.26572	+	3.92434i	−0.265182	+	0.459309i	−0.967611	−	0.252445i	$-0.918765\pi$
$73$	−2.26572	+	3.92434i	−0.265182	+	0.459309i	0.702429	+	0.711754i	$0.252099\pi$
$74$		0			0
$75$	−5.41493	+	4.35259i	−0.625262	+	0.502594i
$76$		0			0
$77$	−4.52718	−	1.64776i	−0.515920	−	0.187780i
$78$		0			0
$79$	−1.00608	+	5.70576i	−0.113193	+	0.641949i	0.874436	+	0.485140i	$0.161232\pi$
$79$	−1.00608	+	5.70576i	−0.113193	+	0.641949i	−0.987629	+	0.156808i	$0.949880\pi$
$80$		0			0
$81$	−8.68633	+	2.35534i	−0.965148	+	0.261704i
$82$		0			0
$83$	0.898927	−	5.09807i	0.0986700	−	0.559586i	−0.894891	−	0.446285i	$-0.852747\pi$
$83$	0.898927	−	5.09807i	0.0986700	−	0.559586i	0.993561	−	0.113300i	$-0.0361422\pi$
$84$		0			0
$85$	−2.16997	−	0.789806i	−0.235367	−	0.0856664i
$86$		0			0
$87$	6.58487	−	5.29301i	0.705972	−	0.567470i
$88$		0			0
$89$	1.91749	−	3.32118i	0.203253	−	0.352045i	−0.746322	−	0.665585i	$-0.768182\pi$
$89$	1.91749	−	3.32118i	0.203253	−	0.352045i	0.949575	+	0.313541i	$0.101515\pi$
$90$		0			0
$91$	−1.39926	−	2.42360i	−0.146683	−	0.254062i
$92$		0			0
$93$	−5.16480	−	9.39752i	−0.535564	−	0.974478i
$94$		0			0
$95$	1.16936	+	6.63176i	0.119974	+	0.680405i
$96$		0			0
$97$	−5.40914	−	4.53881i	−0.549215	−	0.460846i	0.325460	−	0.945556i	$-0.394481\pi$
$97$	−5.40914	−	4.53881i	−0.549215	−	0.460846i	−0.874675	+	0.484710i	$0.838925\pi$
$98$		0			0
$99$	5.38322	−	8.47789i	0.541034	−	0.852060i
$100$		0			0
$101$	−8.98129	+	3.26892i	−0.893672	+	0.325270i	−0.747714	−	0.664021i	$-0.768849\pi$
$101$	−8.98129	+	3.26892i	−0.893672	+	0.325270i	−0.145958	+	0.989291i	$0.546626\pi$
$102$		0			0
$103$	−4.54565	+	3.81425i	−0.447896	+	0.375829i	−0.838654	−	0.544664i	$-0.816657\pi$
$103$	−4.54565	+	3.81425i	−0.447896	+	0.375829i	0.390759	+	0.920493i	$0.372213\pi$
$104$		0			0
$105$	−2.34674	+	0.798566i	−0.229018	+	0.0779321i
$106$		0			0
$107$	−6.76312			−0.653815			−0.326908	−	0.945056i	$-0.606007\pi$
$107$	−6.76312			−0.653815			−0.326908	+	0.945056i	$0.606007\pi$
$108$		0			0
$109$	−1.73410			−0.166097			−0.0830484	−	0.996546i	$-0.526466\pi$
$109$	−1.73410			−0.166097			−0.0830484	+	0.996546i	$0.526466\pi$
$110$		0			0
$111$	0.0558185	−	0.281718i	0.00529806	−	0.0267395i
$112$		0			0
$113$	13.3733	−	11.2215i	1.25805	−	1.05563i	0.262168	−	0.965022i	$-0.415563\pi$
$113$	13.3733	−	11.2215i	1.25805	−	1.05563i	0.995886	−	0.0906103i	$-0.0288818\pi$
$114$		0			0
$115$	8.36507	−	3.04464i	0.780047	−	0.283914i
$116$		0			0
$117$	5.56093	−	1.76249i	0.514108	−	0.162943i
$118$		0			0
$119$	2.56013	+	2.14820i	0.234686	+	0.196925i
$120$		0			0
$121$	0.0357637	+	0.202826i	0.00325125	+	0.0184387i
$122$		0			0
$123$	−9.68009	+	15.9792i	−0.872825	+	1.44080i
$124$		0			0
$125$	−4.48049	−	7.76044i	−0.400748	−	0.694115i
$126$		0			0
$127$	1.47934	−	2.56230i	0.131270	−	0.227367i	−0.792896	−	0.609357i	$-0.791428\pi$
$127$	1.47934	−	2.56230i	0.131270	−	0.227367i	0.924167	+	0.381990i	$0.124761\pi$
$128$		0			0
$129$	2.36041	+	15.2600i	0.207823	+	1.34357i
$130$		0			0
$131$	−17.7679	−	6.46697i	−1.55239	−	0.565022i	−0.583410	−	0.812178i	$-0.698282\pi$
$131$	−17.7679	−	6.46697i	−1.55239	−	0.565022i	−0.968976	+	0.247156i	$0.920504\pi$
$132$		0			0
$133$	1.69234	−	9.59772i	0.146744	−	0.832228i
$134$		0			0
$135$	−0.574055	−	5.13528i	−0.0494068	−	0.441974i
$136$		0			0
$137$	−1.12910	+	6.40346i	−0.0964658	+	0.547085i	0.897823	+	0.440358i	$0.145148\pi$
$137$	−1.12910	+	6.40346i	−0.0964658	+	0.547085i	−0.994288	+	0.106727i	$0.965963\pi$
$138$		0			0
$139$	5.77063	+	2.10034i	0.489459	+	0.178148i	0.574947	−	0.818191i	$-0.305023\pi$
$139$	5.77063	+	2.10034i	0.489459	+	0.178148i	−0.0854880	+	0.996339i	$0.527245\pi$
$140$		0			0
$141$	10.5625	+	4.09846i	0.889525	+	0.345152i
$142$		0			0
$143$	−3.25467	+	5.63725i	−0.272169	+	0.471410i
$144$		0			0
$145$	2.42530	+	4.20074i	0.201410	+	0.348853i
$146$		0			0
$147$	−8.53493	−	0.179853i	−0.703949	−	0.0148341i
$148$		0			0
$149$	2.70785	+	15.3570i	0.221835	+	1.25809i	0.868643	+	0.495438i	$0.164992\pi$
$149$	2.70785	+	15.3570i	0.221835	+	1.25809i	−0.646808	+	0.762653i	$0.723896\pi$
$150$		0			0
$151$	−3.02970	−	2.54222i	−0.246553	−	0.206883i	0.511133	−	0.859502i	$-0.329226\pi$
$151$	−3.02970	−	2.54222i	−0.246553	−	0.206883i	−0.757687	+	0.652619i	$0.773670\pi$
$152$		0			0
$153$	−5.52051	+	4.24915i	−0.446307	+	0.343524i
$154$		0			0
$155$	5.78537	−	2.10570i	0.464692	−	0.169134i
$156$		0			0
$157$	18.3183	−	15.3709i	1.46196	−	1.22673i	0.538728	−	0.842480i	$-0.318905\pi$
$157$	18.3183	−	15.3709i	1.46196	−	1.22673i	0.923230	−	0.384248i	$-0.125539\pi$
$158$		0			0
$159$	13.9736	+	12.2361i	1.10818	+	0.970382i
$160$		0			0
$161$	−12.8832			−1.01534
$162$		0			0
$163$	2.81718			0.220659			0.110329	−	0.993895i	$-0.464809\pi$
$163$	2.81718			0.220659			0.110329	+	0.993895i	$0.464809\pi$
$164$		0			0
$165$	4.33784	+	3.79845i	0.337700	+	0.295709i
$166$		0			0
$167$	12.8535	−	10.7853i	0.994631	−	0.834594i	0.00839915	−	0.999965i	$-0.497326\pi$
$167$	12.8535	−	10.7853i	0.994631	−	0.834594i	0.986232	+	0.165371i	$0.0528820\pi$
$168$		0			0
$169$	8.66288	−	3.15303i	0.666376	−	0.242541i
$170$		0			0
$171$	18.7803	+	7.74622i	1.43617	+	0.592368i
$172$		0			0
$173$	−2.67049	−	2.24080i	−0.203033	−	0.170365i	0.535602	−	0.844471i	$-0.320085\pi$
$173$	−2.67049	−	2.24080i	−0.203033	−	0.170365i	−0.738635	+	0.674106i	$0.764529\pi$
$174$		0			0
$175$	1.00242	+	5.68501i	0.0757759	+	0.429747i
$176$		0			0
$177$	6.83341	+	0.143998i	0.513631	+	0.0108235i
$178$		0			0
$179$	−6.96923	−	12.0711i	−0.520905	−	0.902234i	−0.999704	−	0.0243097i	$-0.992261\pi$
$179$	−6.96923	−	12.0711i	−0.520905	−	0.902234i	0.478799	−	0.877924i	$-0.341072\pi$
$180$		0			0
$181$	−8.57338	+	14.8495i	−0.637254	+	1.10376i	0.348779	+	0.937205i	$0.386596\pi$
$181$	−8.57338	+	14.8495i	−0.637254	+	1.10376i	−0.986033	+	0.166551i	$0.946737\pi$
$182$		0			0
$183$	−13.6018	−	5.27776i	−1.00548	−	0.390144i
$184$		0			0
$185$	0.154946	+	0.0563958i	0.0113919	+	0.00414630i
$186$		0			0
$187$	1.34985	−	7.65536i	0.0987106	−	0.559815i
$188$		0			0
$189$	−1.76119	+	7.26790i	−0.128108	+	0.528662i
$190$		0			0
$191$	−3.94408	+	22.3680i	−0.285384	+	1.61849i	0.418529	+	0.908204i	$0.362546\pi$
$191$	−3.94408	+	22.3680i	−0.285384	+	1.61849i	−0.703912	+	0.710287i	$0.748565\pi$
$192$		0			0
$193$	23.8297	+	8.67330i	1.71530	+	0.624318i	0.997416	−	0.0718466i	$-0.0228892\pi$
$193$	23.8297	+	8.67330i	1.71530	+	0.624318i	0.717883	+	0.696164i	$0.245111\pi$
$194$		0			0
$195$	0.511977	+	3.30992i	0.0366634	+	0.237028i
$196$		0			0
$197$	4.59713	−	7.96247i	0.327532	−	0.567303i	−0.654489	−	0.756071i	$-0.727116\pi$
$197$	4.59713	−	7.96247i	0.327532	−	0.567303i	0.982022	+	0.188769i	$0.0604497\pi$
$198$		0			0
$199$	−8.26695	−	14.3188i	−0.586029	−	1.01503i	−0.994746	−	0.102371i	$-0.967357\pi$
$199$	−8.26695	−	14.3188i	−0.586029	−	1.01503i	0.408718	−	0.912661i	$-0.365976\pi$
$200$		0			0
$201$	0.0198032	−	0.0326897i	0.00139681	−	0.00230575i
$202$		0			0
$203$	−1.21900	−	6.91331i	−0.0855572	−	0.485219i
$204$		0			0
$205$	−8.21692	−	6.89482i	−0.573895	−	0.481555i
$206$		0			0
$207$	5.77332	−	26.2272i	0.401274	−	1.82291i
$208$		0			0
$209$	−21.3014	+	7.75309i	−1.47345	+	0.536293i
$210$		0			0
$211$	2.60930	−	2.18947i	0.179632	−	0.150729i	−0.548538	−	0.836125i	$-0.684816\pi$
$211$	2.60930	−	2.18947i	0.179632	−	0.150729i	0.728170	+	0.685396i	$0.240371\pi$
$212$		0			0
$213$	−3.05483	+	15.4179i	−0.209314	+	1.05641i
$214$		0			0
$215$	−8.86558			−0.604627
$216$		0			0
$217$	−8.91014			−0.604860
$218$		0			0
$219$	−7.43026	+	2.52843i	−0.502091	+	0.170855i
$220$		0			0
$221$	3.45904	−	2.90248i	0.232680	−	0.195242i
$222$		0			0
$223$	−9.67690	+	3.52210i	−0.648013	+	0.235858i	−0.645053	−	0.764138i	$-0.723165\pi$
$223$	−9.67690	+	3.52210i	−0.648013	+	0.235858i	−0.00296060	+	0.999996i	$0.500942\pi$
$224$		0			0
$225$	−12.0226	−	0.506920i	−0.801506	−	0.0337947i
$226$		0			0
$227$	−0.438383	−	0.367847i	−0.0290965	−	0.0244148i	0.628123	−	0.778114i	$-0.283823\pi$
$227$	−0.438383	−	0.367847i	−0.0290965	−	0.0244148i	−0.657220	+	0.753699i	$0.728268\pi$
$228$		0			0
$229$	−1.18180	−	6.70231i	−0.0780955	−	0.442901i	−0.998634	−	0.0522497i	$-0.983361\pi$
$229$	−1.18180	−	6.70231i	−0.0780955	−	0.442901i	0.920539	−	0.390652i	$-0.127750\pi$
$230$		0			0
$231$	−4.01910	−	7.31289i	−0.264437	−	0.481153i
$232$		0			0
$233$	−8.20978	−	14.2198i	−0.537840	−	0.931567i	−0.999020	−	0.0442602i	$-0.985907\pi$
$233$	−8.20978	−	14.2198i	−0.537840	−	0.931567i	0.461180	−	0.887307i	$-0.347426\pi$
$234$		0			0
$235$	−3.25245	+	5.63340i	−0.212166	+	0.367483i
$236$		0			0
$237$	−7.82155	+	6.28707i	−0.508064	+	0.408389i
$238$		0			0
$239$	12.5301	+	4.56059i	0.810506	+	0.295000i	0.713833	−	0.700316i	$-0.246958\pi$
$239$	12.5301	+	4.56059i	0.810506	+	0.295000i	0.0966732	+	0.995316i	$0.469180\pi$
$240$		0			0
$241$	3.34886	−	18.9923i	0.215719	−	1.22340i	−0.663935	−	0.747790i	$-0.731115\pi$
$241$	3.34886	−	18.9923i	0.215719	−	1.22340i	0.879654	−	0.475613i	$-0.157774\pi$
$242$		0			0
$243$	−14.0065	−	6.84232i	−0.898519	−	0.438935i
$244$		0			0
$245$	0.851108	−	4.82687i	0.0543753	−	0.308378i
$246$		0			0
$247$	−12.3736	−	4.50363i	−0.787314	−	0.286559i
$248$		0			0
$249$	6.98851	−	5.61746i	0.442879	−	0.355992i
$250$		0			0
$251$	−4.87417	+	8.44230i	−0.307655	+	0.532873i	−0.977849	−	0.209312i	$-0.932877\pi$
$251$	−4.87417	+	8.44230i	−0.307655	+	0.532873i	0.670194	+	0.742186i	$0.266211\pi$
$252$		0			0
$253$	14.9830	+	25.9514i	0.941975	+	1.63155i
$254$		0			0
$255$	−1.92644	−	3.50522i	−0.120638	−	0.219505i
$256$		0			0
$257$	0.209220	+	1.18654i	0.0130508	+	0.0740145i	0.990638	−	0.136518i	$-0.0435912\pi$
$257$	0.209220	+	1.18654i	0.0130508	+	0.0740145i	−0.977587	+	0.210533i	$0.932480\pi$
$258$		0			0
$259$	−0.182805	−	0.153392i	−0.0113589	−	0.00953129i
$260$		0			0
$261$	14.6202	+	0.616445i	0.904966	+	0.0381570i
$262$		0			0
$263$	26.9229	−	9.79914i	1.66014	−	0.604241i	0.669754	−	0.742583i	$-0.266400\pi$
$263$	26.9229	−	9.79914i	1.66014	−	0.604241i	0.990384	+	0.138342i	$0.0441774\pi$
$264$		0			0
$265$	−8.16903	+	6.85463i	−0.501820	+	0.421077i
$266$		0			0
$267$	6.28826	−	2.13982i	0.384835	−	0.130955i
$268$		0			0
$269$	3.77611			0.230233			0.115117	−	0.993352i	$-0.463276\pi$
$269$	3.77611			0.230233			0.115117	+	0.993352i	$0.463276\pi$
$270$		0			0
$271$	−25.5857			−1.55422			−0.777110	−	0.629365i	$-0.783315\pi$
$271$	−25.5857			−1.55422			−0.777110	+	0.629365i	$0.783315\pi$
$272$		0			0
$273$	0.942089	−	4.75476i	0.0570178	−	0.287771i
$274$		0			0
$275$	10.2859	−	8.63086i	0.620261	−	0.520461i
$276$		0			0
$277$	−9.50104	+	3.45810i	−0.570862	+	0.207777i	−0.611291	−	0.791406i	$-0.709350\pi$
$277$	−9.50104	+	3.45810i	−0.570862	+	0.207777i	0.0404293	+	0.999182i	$0.487127\pi$
$278$		0			0
$279$	3.99289	−	18.1390i	0.239048	−	1.08595i
$280$		0			0
$281$	14.6158	+	12.2641i	0.871905	+	0.731615i	0.964498	−	0.264089i	$-0.0850712\pi$
$281$	14.6158	+	12.2641i	0.871905	+	0.731615i	−0.0925932	+	0.995704i	$0.529516\pi$
$282$		0			0
$283$	3.09772	+	17.5681i	0.184141	+	1.04431i	0.927055	+	0.374926i	$0.122332\pi$
$283$	3.09772	+	17.5681i	0.184141	+	1.04431i	−0.742914	+	0.669387i	$0.766557\pi$
$284$		0			0
$285$	−6.04339	+	9.97600i	−0.357980	+	0.590927i
$286$		0			0
$287$	7.76183	+	13.4439i	0.458166	+	0.793568i
$288$		0			0
$289$	5.80382	−	10.0525i	0.341401	−	0.591324i
$290$		0			0
$291$	−1.86954	−	12.0865i	−0.109594	−	0.708523i
$292$		0			0
$293$	2.65793	+	0.967409i	0.155278	+	0.0565166i	0.418490	−	0.908221i	$-0.362560\pi$
$293$	2.65793	+	0.967409i	0.155278	+	0.0565166i	−0.263212	+	0.964738i	$0.584782\pi$
$294$		0			0
$295$	−0.681432	+	3.86459i	−0.0396745	+	0.225005i
$296$		0			0
$297$	16.6884	−	4.90484i	0.968360	−	0.284608i
$298$		0			0
$299$	−3.02265	+	17.1423i	−0.174804	+	0.991364i
$300$		0			0
$301$	12.0568	+	4.38831i	0.694942	+	0.252938i
$302$		0			0
$303$	−15.4333	−	5.98842i	−0.886621	−	0.344026i
$304$		0			0
$305$	4.18832	−	7.25438i	0.239822	−	0.415385i
$306$		0			0
$307$	3.85918	+	6.68429i	0.220255	+	0.381493i	0.954885	−	0.296975i	$-0.0959778\pi$
$307$	3.85918	+	6.68429i	0.220255	+	0.381493i	−0.734630	+	0.678468i	$0.762644\pi$
$308$		0			0
$309$	−10.2756	−	0.216533i	−0.584557	−	0.0123181i
$310$		0			0
$311$	1.04067	+	5.90192i	0.0590108	+	0.334667i	0.999993	−	0.00378966i	$-0.00120629\pi$
$311$	1.04067	+	5.90192i	0.0590108	+	0.334667i	−0.940982	+	0.338457i	$0.890095\pi$
$312$		0			0
$313$	3.08757	+	2.59078i	0.174520	+	0.146439i	0.725864	−	0.687839i	$-0.241440\pi$
$313$	3.08757	+	2.59078i	0.174520	+	0.146439i	−0.551344	+	0.834278i	$0.685885\pi$
$314$		0			0
$315$	−3.96918	−	1.63715i	−0.223638	−	0.0922427i
$316$		0			0
$317$	−17.3768	+	6.32464i	−0.975979	+	0.355227i	−0.780276	−	0.625436i	$-0.784921\pi$
$317$	−17.3768	+	6.32464i	−0.975979	+	0.355227i	−0.195704	+	0.980663i	$0.562699\pi$
$318$		0			0
$319$	−12.5082	+	10.4956i	−0.700325	+	0.587643i
$320$		0			0
$321$	−8.81287	−	7.71704i	−0.491886	−	0.430723i
$322$		0			0
$323$	15.7249			0.874958
$324$		0			0
$325$	7.79963			0.432646
$326$		0			0
$327$	−2.25967	−	1.97869i	−0.124960	−	0.109422i
$328$		0			0
$329$	7.21162	−	6.05127i	0.397590	−	0.333617i
$330$		0			0
$331$	2.97650	−	1.08336i	0.163603	−	0.0595466i	−0.258920	−	0.965899i	$-0.583367\pi$
$331$	2.97650	−	1.08336i	0.163603	−	0.0595466i	0.422523	+	0.906352i	$0.361144\pi$
$332$		0			0
$333$	0.394190	−	0.303409i	0.0216015	−	0.0166267i
$334$		0			0
$335$	0.0168099	+	0.0141052i	0.000918422	+	0.000770648i
$336$		0			0
$337$	0.734248	+	4.16413i	0.0399971	+	0.226835i	0.998254	−	0.0590754i	$-0.0188153\pi$
$337$	0.734248	+	4.16413i	0.0399971	+	0.226835i	−0.958256	+	0.285910i	$0.907704\pi$
$338$		0			0
$339$	30.2307	+	0.637041i	1.64191	+	0.0345993i
$340$		0			0
$341$	10.3624	+	17.9482i	0.561156	+	0.971951i
$342$		0			0
$343$	−8.58385	+	14.8677i	−0.463484	+	0.802779i
$344$		0			0
$345$	14.3744	+	5.57754i	0.773892	+	0.300285i
$346$		0			0
$347$	4.83722	+	1.76060i	0.259676	+	0.0945142i	0.468577	−	0.883422i	$-0.344767\pi$
$347$	4.83722	+	1.76060i	0.259676	+	0.0945142i	−0.208902	+	0.977937i	$0.566989\pi$
$348$		0			0
$349$	−4.41135	+	25.0180i	−0.236134	+	1.33918i	0.604079	+	0.796925i	$0.293541\pi$
$349$	−4.41135	+	25.0180i	−0.236134	+	1.33918i	−0.840212	+	0.542257i	$0.817570\pi$
$350$		0			0
$351$	9.25742	+	4.04862i	0.494124	+	0.216099i
$352$		0			0
$353$	4.54522	−	25.7772i	0.241918	−	1.37198i	−0.585626	−	0.810582i	$-0.699151\pi$
$353$	4.54522	−	25.7772i	0.241918	−	1.37198i	0.827543	−	0.561402i	$-0.189738\pi$
$354$		0			0
$355$	−8.47988	−	3.08642i	−0.450065	−	0.163810i
$356$		0			0
$357$	0.884845	+	5.72050i	0.0468309	+	0.302761i
$358$		0			0
$359$	0.586533	−	1.01590i	0.0309560	−	0.0536174i	−0.850132	−	0.526569i	$-0.823478\pi$
$359$	0.586533	−	1.01590i	0.0309560	−	0.0536174i	0.881088	+	0.472952i	$0.156811\pi$
$360$		0			0
$361$	−13.4281	−	23.2581i	−0.706741	−	1.22411i
$362$		0			0
$363$	−0.184831	+	0.305106i	−0.00970113	+	0.0160139i
$364$		0			0
$365$	−0.782501	−	4.43778i	−0.0409580	−	0.232284i
$366$		0			0
$367$	4.40016	+	3.69217i	0.229686	+	0.192730i	0.750366	−	0.661022i	$-0.229877\pi$
$367$	4.40016	+	3.69217i	0.229686	+	0.192730i	−0.520680	+	0.853752i	$0.674322\pi$
$368$		0			0
$369$	−30.8469	+	9.77670i	−1.60583	+	0.508955i
$370$		0			0
$371$	14.5024	−	5.27846i	0.752930	−	0.274044i
$372$		0			0
$373$	16.3175	−	13.6920i	0.844888	−	0.708945i	−0.113770	−	0.993507i	$-0.536293\pi$
$373$	16.3175	−	13.6920i	0.844888	−	0.708945i	0.958658	+	0.284562i	$0.0918483\pi$
$374$		0			0
$375$	3.01660	−	15.2249i	0.155777	−	0.786211i
$376$		0			0
$377$	−9.48481			−0.488493
$378$		0			0
$379$	18.1076			0.930123			0.465062	−	0.885278i	$-0.346032\pi$
$379$	18.1076			0.930123			0.465062	+	0.885278i	$0.346032\pi$
$380$		0			0
$381$	4.85140	−	1.65087i	0.248545	−	0.0845767i
$382$		0			0
$383$	−18.8004	+	15.7754i	−0.960658	+	0.806087i	−0.981060	−	0.193704i	$-0.937950\pi$
$383$	−18.8004	+	15.7754i	−0.960658	+	0.806087i	0.0204024	+	0.999792i	$0.493505\pi$
$384$		0			0
$385$	4.50201	−	1.63860i	0.229444	−	0.0835107i
$386$		0			0
$387$	−14.3366	+	22.5783i	−0.728770	+	1.14772i
$388$		0			0
$389$	−1.21272	−	1.01760i	−0.0614875	−	0.0515942i	0.611526	−	0.791224i	$-0.290556\pi$
$389$	−1.21272	−	1.01760i	−0.0614875	−	0.0515942i	−0.673013	+	0.739630i	$0.735000\pi$
$390$		0			0
$391$	−3.60965	−	20.4713i	−0.182548	−	1.03528i
$392$		0			0
$393$	−15.7738	−	28.7009i	−0.795682	−	1.44777i
$394$		0			0
$395$	−2.88079	−	4.98967i	−0.144948	−	0.251057i
$396$		0			0
$397$	5.40150	−	9.35568i	0.271094	−	0.469548i	−0.698049	−	0.716050i	$-0.745948\pi$
$397$	5.40150	−	9.35568i	0.271094	−	0.469548i	0.969142	+	0.246503i	$0.0792814\pi$
$398$		0			0
$399$	13.1567	−	10.5755i	0.658659	−	0.529439i
$400$		0			0
$401$	−2.13798	−	0.778161i	−0.106766	−	0.0388595i	0.288085	−	0.957605i	$-0.406981\pi$
$401$	−2.13798	−	0.778161i	−0.106766	−	0.0388595i	−0.394851	+	0.918745i	$0.629204\pi$
$402$		0			0
$403$	−2.09049	+	11.8558i	−0.104135	+	0.590578i
$404$		0			0
$405$	5.11156	−	7.34669i	0.253995	−	0.365060i
$406$		0			0
$407$	−0.0963853	+	0.546628i	−0.00477764	+	0.0270954i
$408$		0			0
$409$	−32.1074	−	11.6861i	−1.58761	−	0.577842i	−0.610767	−	0.791810i	$-0.709139\pi$
$409$	−32.1074	−	11.6861i	−1.58761	−	0.577842i	−0.976841	+	0.213968i	$0.931361\pi$
$410$		0			0
$411$	−8.77796	+	7.05585i	−0.432985	+	0.348039i
$412$		0			0
$413$	2.83963	−	4.91837i	0.139729	−	0.242017i
$414$		0			0
$415$	2.57397	+	4.45824i	0.126351	+	0.218846i
$416$		0			0
$417$	5.12300	+	9.32147i	0.250874	+	0.456474i
$418$		0			0
$419$	−1.82203	−	10.3333i	−0.0890121	−	0.504813i	−0.996419	−	0.0845586i	$-0.973052\pi$
$419$	−1.82203	−	10.3333i	−0.0890121	−	0.504813i	0.907406	−	0.420254i	$-0.138059\pi$
$420$		0			0
$421$	−16.0206	−	13.4429i	−0.780798	−	0.655167i	0.162652	−	0.986684i	$-0.447995\pi$
$421$	−16.0206	−	13.4429i	−0.780798	−	0.655167i	−0.943449	+	0.331516i	$0.892440\pi$
$422$		0			0
$423$	9.08725	+	17.3929i	0.441837	+	0.845674i
$424$		0			0
$425$	−8.75262	+	3.18569i	−0.424564	+	0.154529i
$426$		0			0
$427$	−9.28672	+	7.79249i	−0.449416	+	0.377105i
$428$		0			0
$429$	−10.6734	+	3.63204i	−0.515319	+	0.175357i
$430$		0			0
$431$	7.25638			0.349528			0.174764	−	0.984610i	$-0.444084\pi$
$431$	7.25638			0.349528			0.174764	+	0.984610i	$0.444084\pi$
$432$		0			0
$433$	−4.35238			−0.209162			−0.104581	−	0.994516i	$-0.533350\pi$
$433$	−4.35238			−0.209162			−0.104581	+	0.994516i	$0.533350\pi$
$434$		0			0
$435$	−1.63289	+	8.24128i	−0.0782912	+	0.395139i
$436$		0			0
$437$	−46.4363	+	38.9647i	−2.22135	+	1.86394i
$438$		0			0
$439$	9.20682	−	3.35101i	0.439417	−	0.159935i	−0.112831	−	0.993614i	$-0.535992\pi$
$439$	9.20682	−	3.35101i	0.439417	−	0.159935i	0.552249	+	0.833679i	$0.313770\pi$
$440$		0			0
$441$	−10.9164	−	9.97312i	−0.519831	−	0.474910i
$442$		0			0
$443$	−21.8385	−	18.3247i	−1.03758	−	0.870633i	−0.0458469	−	0.998948i	$-0.514599\pi$
$443$	−21.8385	−	18.3247i	−1.03758	−	0.870633i	−0.991733	+	0.128315i	$0.959043\pi$
$444$		0			0
$445$	0.662234	+	3.75571i	0.0313929	+	0.178038i
$446$		0			0
$447$	−13.9945	+	23.1011i	−0.661916	+	1.09264i
$448$		0			0
$449$	−9.03115	−	15.6424i	−0.426206	−	0.738211i	0.570326	−	0.821418i	$-0.306817\pi$
$449$	−9.03115	−	15.6424i	−0.426206	−	0.738211i	−0.996532	+	0.0832075i	$0.973484\pi$
$450$		0			0
$451$	18.0539	−	31.2703i	0.850125	−	1.47246i
$452$		0			0
$453$	−1.04714	−	6.76974i	−0.0491990	−	0.318070i
$454$		0			0
$455$	2.61514	+	0.951832i	0.122599	+	0.0446226i
$456$		0			0
$457$	1.52536	−	8.65075i	0.0713534	−	0.404665i	−0.928122	−	0.372276i	$-0.878577\pi$
$457$	1.52536	−	8.65075i	0.0713534	−	0.404665i	0.999475	−	0.0323889i	$-0.0103115\pi$
$458$		0			0
$459$	−12.0421	−	0.762181i	−0.562079	−	0.0355756i
$460$		0			0
$461$	6.91883	−	39.2386i	0.322242	−	1.82753i	−0.206144	−	0.978522i	$-0.566091\pi$
$461$	6.91883	−	39.2386i	0.322242	−	1.82753i	0.528386	−	0.849004i	$-0.322797\pi$
$462$		0			0
$463$	22.3956	+	8.15134i	1.04081	+	0.378825i	0.805188	−	0.593019i	$-0.202064\pi$
$463$	22.3956	+	8.15134i	1.04081	+	0.378825i	0.235624	+	0.971844i	$0.424286\pi$
$464$		0			0
$465$	9.94149	+	3.85749i	0.461026	+	0.178887i
$466$		0			0
$467$	−5.35121	+	9.26856i	−0.247624	+	0.428898i	−0.962866	−	0.269979i	$-0.912983\pi$
$467$	−5.35121	+	9.26856i	−0.247624	+	0.428898i	0.715242	+	0.698877i	$0.246317\pi$
$468$		0			0
$469$	−0.0158789	−	0.0275030i	−0.000733219	−	0.00126997i
$470$		0			0
$471$	41.4090	+	0.872597i	1.90803	+	0.0402071i
$472$		0			0
$473$	−5.18231	−	29.3903i	−0.238283	−	1.35137i
$474$		0			0
$475$	20.8073	+	17.4594i	0.954703	+	0.801091i
$476$		0			0
$477$	4.24676	+	31.8891i	0.194446	+	1.46010i
$478$		0			0
$479$	−11.9843	+	4.36195i	−0.547579	+	0.199302i	−0.600970	−	0.799271i	$-0.705219\pi$
$479$	−11.9843	+	4.36195i	−0.547579	+	0.199302i	0.0533916	+	0.998574i	$0.482997\pi$
$480$		0			0
$481$	−0.246992	+	0.207251i	−0.0112618	+	0.00944981i
$482$		0			0
$483$	−16.7878	−	14.7003i	−0.763870	−	0.668887i
$484$		0			0
$485$	7.02187			0.318847
$486$		0			0
$487$	15.2559			0.691313			0.345656	−	0.938361i	$-0.387656\pi$
$487$	15.2559			0.691313			0.345656	+	0.938361i	$0.387656\pi$
$488$		0			0
$489$	3.67101	+	3.21454i	0.166009	+	0.145366i
$490$		0			0
$491$	−24.0693	+	20.1965i	−1.08623	+	0.911457i	−0.996423	−	0.0845017i	$-0.973070\pi$
$491$	−24.0693	+	20.1965i	−1.08623	+	0.911457i	−0.0898092	+	0.995959i	$0.528626\pi$
$492$		0			0
$493$	10.6437	−	3.87399i	0.479368	−	0.174476i
$494$		0			0
$495$	1.31833	+	9.89936i	0.0592544	+	0.444943i
$496$		0			0
$497$	10.0045	+	8.39480i	0.448765	+	0.376558i
$498$		0			0
$499$	−5.93176	−	33.6407i	−0.265542	−	1.50596i	−0.767487	−	0.641065i	$-0.778493\pi$
$499$	−5.93176	−	33.6407i	−0.265542	−	1.50596i	0.501945	−	0.864900i	$-0.332618\pi$
$500$		0			0
$501$	29.0556	+	0.612279i	1.29811	+	0.0273546i
$502$		0			0
$503$	10.1654	+	17.6069i	0.453252	+	0.785055i	0.998586	−	0.0531640i	$-0.0169306\pi$
$503$	10.1654	+	17.6069i	0.453252	+	0.785055i	−0.545334	+	0.838219i	$0.683597\pi$
$504$		0			0
$505$	4.75228	−	8.23119i	0.211474	−	0.366283i
$506$		0			0
$507$	14.8862	+	5.77612i	0.661118	+	0.256526i
$508$		0			0
$509$	7.69531	+	2.80086i	0.341088	+	0.124146i	0.506884	−	0.862014i	$-0.330797\pi$
$509$	7.69531	+	2.80086i	0.341088	+	0.124146i	−0.165796	+	0.986160i	$0.553019\pi$
$510$		0			0
$511$	−1.13246	+	6.42251i	−0.0500972	+	0.284115i
$512$		0			0
$513$	15.6335	+	31.5232i	0.690234	+	1.39178i
$514$		0			0
$515$	1.02469	−	5.81128i	0.0451530	−	0.256076i
$516$		0			0
$517$	−20.5765	−	7.48923i	−0.904953	−	0.329376i
$518$		0			0
$519$	−0.922987	−	5.96709i	−0.0405146	−	0.261926i
$520$		0			0
$521$	−16.5346	+	28.6387i	−0.724392	+	1.25468i	0.234832	+	0.972036i	$0.424546\pi$
$521$	−16.5346	+	28.6387i	−0.724392	+	1.25468i	−0.959224	+	0.282648i	$0.908787\pi$
$522$		0			0
$523$	−2.92714	−	5.06995i	−0.127995	−	0.221693i	0.794905	−	0.606734i	$-0.207521\pi$
$523$	−2.92714	−	5.06995i	−0.127995	−	0.221693i	−0.922900	+	0.385041i	$0.874187\pi$
$524$		0			0
$525$	−5.18064	+	8.55182i	−0.226101	+	0.373232i
$526$		0			0
$527$	−2.49647	−	14.1582i	−0.108748	−	0.616741i
$528$		0			0
$529$	43.7663	+	36.7243i	1.90288	+	1.59671i
$530$		0			0
$531$	8.74015	+	7.98488i	0.379290	+	0.346514i
$532$		0			0
$533$	19.7094	−	7.17365i	0.853711	−	0.310725i
$534$		0			0
$535$	5.15205	−	4.32308i	0.222742	−	0.186903i
$536$		0			0
$537$	4.69221	−	23.6818i	0.202484	−	1.02194i
$538$		0			0
$539$	16.4991			0.710666
$540$		0			0
$541$	40.9249			1.75950			0.879750	−	0.475436i	$-0.157710\pi$
$541$	40.9249			1.75950			0.879750	+	0.475436i	$0.157710\pi$
$542$		0			0
$543$	−28.1158	+	9.56745i	−1.20656	+	0.410579i
$544$		0			0
$545$	1.32101	−	1.10846i	0.0565860	−	0.0474813i
$546$		0			0
$547$	−23.9504	+	8.71722i	−1.02404	+	0.372721i	−0.798810	−	0.601583i	$-0.794537\pi$
$547$	−23.9504	+	8.71722i	−1.02404	+	0.372721i	−0.225234	+	0.974305i	$0.572315\pi$
$548$		0			0
$549$	−11.7021	−	22.3977i	−0.499431	−	0.955909i
$550$		0			0
$551$	−25.3029	−	21.2316i	−1.07794	−	0.904498i
$552$		0			0
$553$	1.44794	+	8.21167i	0.0615726	+	0.349196i
$554$		0			0
$555$	0.137557	+	0.250289i	0.00583895	+	0.0106242i
$556$		0			0
$557$	18.5450	+	32.1208i	0.785775	+	1.36100i	0.928535	+	0.371245i	$0.121069\pi$
$557$	18.5450	+	32.1208i	0.785775	+	1.36100i	−0.142760	+	0.989757i	$0.545598\pi$
$558$		0			0
$559$	8.66783	−	15.0131i	0.366610	−	0.634987i
$560$		0			0
$561$	10.4941	−	8.43529i	0.443061	−	0.356138i
$562$		0			0
$563$	−11.6768	−	4.25002i	−0.492120	−	0.179117i	0.0840264	−	0.996464i	$-0.473222\pi$
$563$	−11.6768	−	4.25002i	−0.492120	−	0.179117i	−0.576146	+	0.817346i	$0.695444\pi$
$564$		0			0
$565$	−3.01463	+	17.0968i	−0.126826	+	0.719268i
$566$		0			0
$567$	−10.5880	+	7.46104i	−0.444653	+	0.313334i
$568$		0			0
$569$	−4.64088	+	26.3198i	−0.194556	+	1.10338i	0.718494	+	0.695533i	$0.244832\pi$
$569$	−4.64088	+	26.3198i	−0.194556	+	1.10338i	−0.913050	+	0.407848i	$0.866279\pi$
$570$		0			0
$571$	−6.28728	−	2.28838i	−0.263115	−	0.0957659i	0.207094	−	0.978321i	$-0.433599\pi$
$571$	−6.28728	−	2.28838i	−0.263115	−	0.0957659i	−0.470209	+	0.882555i	$0.655821\pi$
$572$		0			0
$573$	−30.6624	+	24.6468i	−1.28094	+	1.02964i
$574$		0			0
$575$	17.9530	−	31.0955i	0.748693	−	1.29677i
$576$		0			0
$577$	−14.5989	−	25.2860i	−0.607760	−	1.05267i	−0.991609	−	0.129275i	$-0.958735\pi$
$577$	−14.5989	−	25.2860i	−0.607760	−	1.05267i	0.383849	−	0.923396i	$-0.374598\pi$
$578$		0			0
$579$	21.1553	+	38.4928i	0.879184	+	1.59971i
$580$		0			0
$581$	−1.29373	−	7.33708i	−0.0536728	−	0.304393i
$582$		0			0
$583$	−27.4990	−	23.0744i	−1.13889	−	0.955642i
$584$		0			0
$585$	−3.10963	+	4.89727i	−0.128567	+	0.202477i
$586$		0			0
$587$	7.33702	−	2.67046i	0.302831	−	0.110222i	−0.186135	−	0.982524i	$-0.559596\pi$
$587$	7.33702	−	2.67046i	0.302831	−	0.110222i	0.488967	+	0.872303i	$0.337374\pi$
$588$		0			0
$589$	−32.1159	+	26.9484i	−1.32331	+	1.11039i
$590$		0			0
$591$	15.0760	−	5.13017i	0.620143	−	0.211027i
$592$		0			0
$593$	6.64855			0.273023			0.136512	−	0.990638i	$-0.456411\pi$
$593$	6.64855			0.273023			0.136512	+	0.990638i	$0.456411\pi$
$594$		0			0
$595$	−3.32343			−0.136247
$596$		0			0
$597$	5.56593	−	28.0915i	0.227798	−	1.14971i
$598$		0			0
$599$	−11.1040	+	9.31733i	−0.453696	+	0.380696i	−0.840805	−	0.541338i	$-0.817918\pi$
$599$	−11.1040	+	9.31733i	−0.453696	+	0.380696i	0.387110	+	0.922034i	$0.373474\pi$
$600$		0			0
$601$	−3.52740	+	1.28387i	−0.143886	+	0.0523701i	−0.412959	−	0.910750i	$-0.635505\pi$
$601$	−3.52740	+	1.28387i	−0.143886	+	0.0523701i	0.269073	+	0.963120i	$0.413283\pi$
$602$		0			0
$603$	0.0631056	−	0.0200008i	0.00256986	−	0.000814497i
$604$		0			0
$605$	−0.156894	−	0.131649i	−0.00637863	−	0.00535231i
$606$		0			0
$607$	4.47607	+	25.3851i	0.181678	+	1.03035i	0.930150	+	0.367181i	$0.119677\pi$
$607$	4.47607	+	25.3851i	0.181678	+	1.03035i	−0.748472	+	0.663167i	$0.769212\pi$
$608$		0			0
$609$	6.29996	−	10.3995i	0.255287	−	0.421410i
$610$		0			0
$611$	−6.35980	−	11.0155i	−0.257290	−	0.445639i
$612$		0			0
$613$	−7.07992	+	12.2628i	−0.285955	+	0.495289i	−0.972840	−	0.231477i	$-0.925644\pi$
$613$	−7.07992	+	12.2628i	−0.285955	+	0.495289i	0.686885	+	0.726766i	$0.258978\pi$
$614$		0			0
$615$	−2.83998	−	18.3604i	−0.114519	−	0.740362i
$616$		0			0
$617$	26.1322	+	9.51134i	1.05204	+	0.382912i	0.809433	−	0.587212i	$-0.199774\pi$
$617$	26.1322	+	9.51134i	1.05204	+	0.382912i	0.242609	+	0.970124i	$0.421997\pi$
$618$		0			0
$619$	5.54233	−	31.4321i	0.222765	−	1.26336i	−0.644146	−	0.764902i	$-0.722787\pi$
$619$	5.54233	−	31.4321i	0.222765	−	1.26336i	0.866912	−	0.498462i	$-0.166102\pi$
$620$		0			0
$621$	37.4495	−	27.5884i	1.50280	−	1.10708i
$622$		0			0
$623$	0.958408	−	5.43540i	0.0383978	−	0.217765i
$624$		0			0
$625$	−10.4722	−	3.81157i	−0.418888	−	0.152463i
$626$		0			0
$627$	−36.6041	−	14.2031i	−1.46183	−	0.567216i
$628$		0			0
$629$	0.192520	−	0.333455i	0.00767628	−	0.0132957i
$630$		0			0
$631$	10.6272	+	18.4068i	0.423062	+	0.732765i	0.996237	−	0.0866680i	$-0.0276219\pi$
$631$	10.6272	+	18.4068i	0.423062	+	0.732765i	−0.573175	+	0.819433i	$0.694289\pi$
$632$		0			0
$633$	5.89841	+	0.124295i	0.234441	+	0.00494028i
$634$		0			0
$635$	0.510914	+	2.89754i	0.0202750	+	0.114985i
$636$		0			0
$637$	7.34178	+	6.16049i	0.290892	+	0.244087i
$638$		0			0
$639$	−21.5732	+	16.6050i	−0.853422	+	0.656882i
$640$		0			0
$641$	14.8823	−	5.41670i	0.587814	−	0.213947i	−0.0309539	−	0.999521i	$-0.509855\pi$
$641$	14.8823	−	5.41670i	0.587814	−	0.213947i	0.618768	+	0.785574i	$0.287632\pi$
$642$		0			0
$643$	22.4373	−	18.8271i	0.884839	−	0.742468i	−0.0823289	−	0.996605i	$-0.526236\pi$
$643$	22.4373	−	18.8271i	0.884839	−	0.742468i	0.967168	+	0.254137i	$0.0817914\pi$
$644$		0			0
$645$	−11.5525	−	10.1160i	−0.454881	−	0.398319i
$646$		0			0
$647$	−20.4322			−0.803272			−0.401636	−	0.915799i	$-0.631558\pi$
$647$	−20.4322			−0.803272			−0.401636	+	0.915799i	$0.631558\pi$
$648$		0			0
$649$	−13.2098			−0.518532
$650$		0			0
$651$	−11.6106	−	10.1669i	−0.455055	−	0.398472i
$652$		0			0
$653$	−13.7302	+	11.5210i	−0.537306	+	0.450853i	−0.870615	−	0.491964i	$-0.836279\pi$
$653$	−13.7302	+	11.5210i	−0.537306	+	0.450853i	0.333309	+	0.942817i	$0.391835\pi$
$654$		0			0
$655$	17.6691	−	6.43102i	0.690388	−	0.251281i
$656$		0			0
$657$	−12.5673	−	5.18354i	−0.490296	−	0.202229i
$658$		0			0
$659$	−9.71001	−	8.14766i	−0.378248	−	0.317388i	0.433766	−	0.901026i	$-0.357184\pi$
$659$	−9.71001	−	8.14766i	−0.378248	−	0.317388i	−0.812014	+	0.583638i	$0.801629\pi$
$660$		0			0
$661$	−3.10157	−	17.5899i	−0.120637	−	0.684167i	−0.983804	−	0.179248i	$-0.942634\pi$
$661$	−3.10157	−	17.5899i	−0.120637	−	0.684167i	0.863167	−	0.504919i	$-0.168478\pi$
$662$		0			0
$663$	7.81927	+	0.164773i	0.303675	+	0.00639923i
$664$		0			0
$665$	4.84580	+	8.39317i	0.187912	+	0.325473i
$666$		0			0
$667$	−21.8319	+	37.8140i	−0.845335	+	1.46416i
$668$		0			0
$669$	−16.6286	−	6.45223i	−0.642900	−	0.249458i
$670$		0			0
$671$	26.4973	+	9.64422i	1.02292	+	0.372311i
$672$		0			0
$673$	−4.94149	+	28.0246i	−0.190480	+	1.08027i	0.728229	+	0.685334i	$0.240344\pi$
$673$	−4.94149	+	28.0246i	−0.190480	+	1.08027i	−0.918709	+	0.394934i	$0.870767\pi$
$674$		0			0
$675$	−15.0879	−	14.3789i	−0.580735	−	0.553444i
$676$		0			0
$677$	3.73652	−	21.1909i	0.143606	−	0.814431i	−0.824869	−	0.565323i	$-0.808751\pi$
$677$	3.73652	−	21.1909i	0.143606	−	0.814431i	0.968476	−	0.249108i	$-0.0801375\pi$
$678$		0			0
$679$	−9.54944	−	3.47571i	−0.366474	−	0.133386i
$680$		0			0
$681$	−0.151516	−	0.979548i	−0.00580611	−	0.0375364i
$682$		0			0
$683$	−2.31436	+	4.00859i	−0.0885566	+	0.153384i	−0.906901	−	0.421343i	$-0.861559\pi$
$683$	−2.31436	+	4.00859i	−0.0885566	+	0.153384i	0.818345	+	0.574728i	$0.194892\pi$
$684$		0			0
$685$	−3.23305	−	5.59980i	−0.123528	−	0.213958i
$686$		0			0
$687$	6.10768	−	10.0821i	0.233023	−	0.384657i
$688$		0			0
$689$	−3.62093	−	20.5353i	−0.137946	−	0.782333i
$690$		0			0
$691$	−13.4054	−	11.2485i	−0.509966	−	0.427913i	0.351151	−	0.936319i	$-0.385790\pi$
$691$	−13.4054	−	11.2485i	−0.509966	−	0.427913i	−0.861117	+	0.508406i	$0.830235\pi$
$692$		0			0
$693$	3.10715	−	14.1152i	0.118031	−	0.536194i
$694$		0			0
$695$	−5.73855	+	2.08866i	−0.217676	+	0.0792275i
$696$		0			0
$697$	−19.1876	+	16.1003i	−0.726781	+	0.609842i
$698$		0			0
$699$	5.52743	−	27.8972i	0.209067	−	1.05517i
$700$		0			0
$701$	20.6892			0.781420			0.390710	−	0.920514i	$-0.372229\pi$
$701$	20.6892			0.781420			0.390710	+	0.920514i	$0.372229\pi$
$702$		0			0
$703$	−1.12283			−0.0423484
$704$		0			0
$705$	−10.6662	+	3.62956i	−0.401711	+	0.136697i
$706$		0			0
$707$	−10.5372	+	8.84175i	−0.396292	+	0.332528i
$708$		0			0
$709$	−41.9234	+	15.2589i	−1.57447	+	0.573059i	−0.973992	−	0.226584i	$-0.927244\pi$
$709$	−41.9234	+	15.2589i	−1.57447	+	0.573059i	−0.600476	+	0.799643i	$0.705022\pi$
$710$		0			0
$711$	−17.3659	−	0.732217i	−0.651273	−	0.0274603i
$712$		0			0
$713$	42.4547	+	35.6237i	1.58994	+	1.33412i
$714$		0			0
$715$	−1.12405	−	6.37480i	−0.0420371	−	0.238404i
$716$		0			0
$717$	11.1239	+	20.2403i	0.415429	+	0.755886i
$718$		0			0
$719$	−15.0646	−	26.0926i	−0.561814	−	0.973091i	−0.997338	−	0.0729139i	$-0.976770\pi$
$719$	−15.0646	−	26.0926i	−0.561814	−	0.973091i	0.435524	−	0.900177i	$-0.356563\pi$
$720$		0			0
$721$	−4.27002	+	7.39588i	−0.159024	+	0.275437i
$722$		0			0
$723$	26.0350	−	20.9273i	0.968251	−	0.778293i
$724$		0			0
$725$	18.3851	+	6.69161i	0.682804	+	0.248520i
$726$		0			0
$727$	−3.07006	+	17.4112i	−0.113862	+	0.645745i	0.873445	+	0.486923i	$0.161881\pi$
$727$	−3.07006	+	17.4112i	−0.113862	+	0.645745i	−0.987307	+	0.158822i	$0.949230\pi$
$728$		0			0
$729$	−10.4442	−	24.8982i	−0.386821	−	0.922155i
$730$		0			0
$731$	−3.59491	+	20.3878i	−0.132963	+	0.754069i
$732$		0			0
$733$	7.47895	+	2.72211i	0.276241	+	0.100544i	0.476426	−	0.879215i	$-0.341932\pi$
$733$	7.47895	+	2.72211i	0.276241	+	0.100544i	−0.200185	+	0.979758i	$0.564154\pi$
$734$		0			0
$735$	6.61675	−	5.31863i	0.244062	−	0.196181i
$736$		0			0
$737$	−0.0369340	+	0.0639716i	−0.00136048	+	0.00235642i
$738$		0			0
$739$	6.81386	+	11.8019i	0.250652	+	0.434142i	0.963705	−	0.266968i	$-0.0860218\pi$
$739$	6.81386	+	11.8019i	0.250652	+	0.434142i	−0.713054	+	0.701109i	$0.752688\pi$
$740$		0			0
$741$	−10.9849	−	19.9875i	−0.403541	−	0.734258i
$742$		0			0
$743$	−3.87103	−	21.9537i	−0.142014	−	0.805403i	−0.969716	−	0.244235i	$-0.921463\pi$
$743$	−3.87103	−	21.9537i	−0.142014	−	0.805403i	0.827702	−	0.561168i	$-0.189648\pi$
$744$		0			0
$745$	−11.8792	−	9.96782i	−0.435220	−	0.365193i
$746$		0			0
$747$	15.5164	+	0.654231i	0.567714	+	0.0239371i
$748$		0			0
$749$	−9.14641	+	3.32902i	−0.334203	+	0.121640i
$750$		0			0
$751$	12.8736	−	10.8023i	0.469766	−	0.394180i	−0.376943	−	0.926236i	$-0.623025\pi$
$751$	12.8736	−	10.8023i	0.469766	−	0.394180i	0.846709	+	0.532056i	$0.178580\pi$
$752$		0			0
$753$	−15.9845	+	5.43932i	−0.582507	+	0.198220i
$754$		0			0
$755$	3.93300			0.143137
$756$		0			0
$757$	−41.9124			−1.52333			−0.761666	−	0.647970i	$-0.775618\pi$
$757$	−41.9124			−1.52333			−0.761666	+	0.647970i	$0.775618\pi$
$758$		0			0
$759$	−10.0877	+	50.9130i	−0.366160	+	1.84802i
$760$		0			0
$761$	5.72263	−	4.80186i	0.207445	−	0.174067i	−0.533146	−	0.846024i	$-0.678990\pi$
$761$	5.72263	−	4.80186i	0.207445	−	0.174067i	0.740591	+	0.671956i	$0.234546\pi$
$762$		0			0
$763$	−2.34519	+	0.853579i	−0.0849016	+	0.0309016i
$764$		0			0
$765$	1.48932	−	6.76573i	0.0538466	−	0.244615i
$766$		0			0
$767$	−5.87813	−	4.93234i	−0.212247	−	0.178096i
$768$		0			0
$769$	8.44440	+	47.8906i	0.304513	+	1.72698i	0.625789	+	0.779993i	$0.284777\pi$
$769$	8.44440	+	47.8906i	0.304513	+	1.72698i	−0.321276	+	0.946986i	$0.604112\pi$
$770$		0			0
$771$	−1.08127	+	1.78489i	−0.0389411	+	0.0642811i
$772$		0			0
$773$	14.2586	+	24.6966i	0.512846	+	0.888276i	0.999889	+	0.0148977i	$0.00474228\pi$
$773$	14.2586	+	24.6966i	0.512846	+	0.888276i	−0.487043	+	0.873378i	$0.661924\pi$
$774$		0			0
$775$	12.4165	−	21.5060i	0.446014	−	0.772518i
$776$		0			0
$777$	−0.0631820	−	0.408470i	−0.00226664	−	0.0146538i
$778$		0			0
$779$	68.6374	+	24.9820i	2.45919	+	0.895073i
$780$		0			0
$781$	5.27497	−	29.9158i	0.188753	−	1.07047i
$782$		0			0
$783$	18.3478	+	17.4856i	0.655698	+	0.624884i
$784$		0			0
$785$	−4.12933	+	23.4186i	−0.147382	+	0.835845i
$786$		0			0
$787$	45.9010	+	16.7066i	1.63619	+	0.595526i	0.986368	−	0.164556i	$-0.0526190\pi$
$787$	45.9010	+	16.7066i	1.63619	+	0.595526i	0.649827	+	0.760082i	$0.274841\pi$
$788$		0			0
$789$	46.2639	+	17.9513i	1.64704	+	0.639083i
$790$		0			0
$791$	12.5624	−	21.7587i	0.446667	−	0.773650i
$792$		0			0
$793$	8.18979	+	14.1851i	0.290828	+	0.503729i
$794$		0			0
$795$	−18.4663	−	0.389134i	−0.654933	−	0.0138012i
$796$		0			0
$797$	−2.71436	−	15.3939i	−0.0961477	−	0.545281i	−0.994390	−	0.105779i	$-0.966266\pi$
$797$	−2.71436	−	15.3939i	−0.0961477	−	0.545281i	0.898242	−	0.439501i	$-0.144845\pi$
$798$		0			0
$799$	11.6360	+	9.76379i	0.411653	+	0.345418i
$800$		0			0
$801$	10.6357	+	4.38685i	0.375795	+	0.155002i
$802$		0			0
$803$	14.2543	−	5.18814i	0.503024	−	0.183086i
$804$		0			0
$805$	9.81422	−	8.23511i	0.345906	−	0.290249i
$806$		0			0
$807$	4.92056	+	4.30872i	0.173212	+	0.151674i
$808$		0			0
$809$	−8.18856			−0.287894			−0.143947	−	0.989585i	$-0.545980\pi$
$809$	−8.18856			−0.287894			−0.143947	+	0.989585i	$0.545980\pi$
$810$		0			0
$811$	−27.0052			−0.948279			−0.474140	−	0.880450i	$-0.657241\pi$
$811$	−27.0052			−0.948279			−0.474140	+	0.880450i	$0.657241\pi$
$812$		0			0
$813$	−33.3401	−	29.1945i	−1.16929	−	1.02389i
$814$		0			0
$815$	−2.14609	+	1.80078i	−0.0751742	+	0.0630786i
$816$		0			0
$817$	56.7300	−	20.6480i	1.98473	−	0.722383i
$818$		0			0
$819$	6.65302	−	5.12086i	0.232475	−	0.178937i
$820$		0			0
$821$	19.5852	+	16.4339i	0.683528	+	0.573548i	0.917035	−	0.398807i	$-0.130576\pi$
$821$	19.5852	+	16.4339i	0.683528	+	0.573548i	−0.233507	+	0.972355i	$0.575020\pi$
$822$		0			0
$823$	−0.615119	−	3.48851i	−0.0214417	−	0.121602i	0.972208	−	0.234118i	$-0.0752202\pi$
$823$	−0.615119	−	3.48851i	−0.0214417	−	0.121602i	−0.993650	+	0.112516i	$0.964109\pi$
$824$		0			0
$825$	23.2515	+	0.489970i	0.809513	+	0.0170586i
$826$		0			0
$827$	−15.6193	−	27.0534i	−0.543136	−	0.940739i	−0.998722	−	0.0505472i	$-0.983903\pi$
$827$	−15.6193	−	27.0534i	−0.543136	−	0.940739i	0.455586	−	0.890192i	$-0.349430\pi$
$828$		0			0
$829$	3.45938	−	5.99182i	0.120149	−	0.208104i	−0.799677	−	0.600430i	$-0.794996\pi$
$829$	3.45938	−	5.99182i	0.120149	−	0.208104i	0.919826	+	0.392326i	$0.128329\pi$
$830$		0			0
$831$	−16.3264	−	6.33497i	−0.566358	−	0.219758i
$832$		0			0
$833$	−10.7550	−	3.91451i	−0.372639	−	0.135630i
$834$		0			0
$835$	−2.89744	+	16.4322i	−0.100270	+	0.568661i
$836$		0			0
$837$	25.9005	−	19.0804i	0.895251	−	0.659516i
$838$		0			0
$839$	−5.96637	+	33.8369i	−0.205982	+	1.16818i	0.689905	+	0.723900i	$0.257652\pi$
$839$	−5.96637	+	33.8369i	−0.205982	+	1.16818i	−0.895887	+	0.444282i	$0.853459\pi$
$840$		0			0
$841$	4.89378	+	1.78119i	0.168751	+	0.0614203i
$842$		0			0
$843$	5.05159	+	32.6584i	0.173986	+	1.12481i
$844$		0			0
$845$	−4.58380	+	7.93937i	−0.157687	+	0.273123i
$846$		0			0
$847$	0.148204	+	0.256697i	0.00509235	+	0.00882021i
$848$		0			0
$849$	−16.0094	+	26.4272i	−0.549442	+	0.906979i
$850$		0			0
$851$	0.257746	+	1.46175i	0.00883541	+	0.0501081i
$852$		0			0
$853$	−18.1440	−	15.2246i	−0.621239	−	0.521282i	0.276954	−	0.960883i	$-0.410675\pi$
$853$	−18.1440	−	15.2246i	−0.621239	−	0.521282i	−0.898193	+	0.439602i	$0.855120\pi$
$854$		0			0
$855$	−19.2581	+	6.10370i	−0.658613	+	0.208742i
$856$		0			0
$857$	−15.6873	+	5.70972i	−0.535869	+	0.195040i	−0.595757	−	0.803165i	$-0.703148\pi$
$857$	−15.6873	+	5.70972i	−0.535869	+	0.195040i	0.0598878	+	0.998205i	$0.480926\pi$
$858$		0			0
$859$	7.88524	−	6.61650i	0.269041	−	0.225752i	−0.498279	−	0.867017i	$-0.666034\pi$
$859$	7.88524	−	6.61650i	0.269041	−	0.225752i	0.767320	+	0.641265i	$0.221590\pi$
$860$		0			0
$861$	−5.22584	+	26.3750i	−0.178096	+	0.898859i
$862$		0			0
$863$	−46.7315			−1.59076			−0.795379	−	0.606112i	$-0.792728\pi$
$863$	−46.7315			−1.59076			−0.795379	+	0.606112i	$0.792728\pi$
$864$		0			0
$865$	3.46669			0.117871
$866$		0			0
$867$	19.0332	−	6.47676i	0.646401	−	0.219962i
$868$		0			0
$869$	14.8573	−	12.4668i	0.504000	−	0.422907i
$870$		0			0
$871$	−0.0403209	+	0.0146756i	−0.00136622	+	0.000497264i
$872$		0			0
$873$	11.3551	−	17.8829i	0.384313	−	0.605244i
$874$		0			0
$875$	−9.87934	−	8.28975i	−0.333982	−	0.280245i
$876$		0			0
$877$	−7.74539	−	43.9263i	−0.261543	−	1.48329i	−0.778701	−	0.627395i	$-0.784121\pi$
$877$	−7.74539	−	43.9263i	−0.261543	−	1.48329i	0.517158	−	0.855890i	$-0.326990\pi$
$878$		0			0
$879$	2.35963	+	4.29344i	0.0795885	+	0.144814i
$880$		0			0
$881$	−16.8718	−	29.2229i	−0.568426	−	0.984543i	−0.996722	−	0.0809046i	$-0.974219\pi$
$881$	−16.8718	−	29.2229i	−0.568426	−	0.984543i	0.428295	−	0.903639i	$-0.359114\pi$
$882$		0			0
$883$	−22.6765	+	39.2769i	−0.763126	+	1.32177i	0.178105	+	0.984011i	$0.443003\pi$
$883$	−22.6765	+	39.2769i	−0.763126	+	1.32177i	−0.941231	+	0.337762i	$0.890330\pi$
$884$		0			0
$885$	−5.29764	+	4.25832i	−0.178078	+	0.143142i
$886$		0			0
$887$	−9.30614	−	3.38716i	−0.312470	−	0.113730i	0.181025	−	0.983478i	$-0.442059\pi$
$887$	−9.30614	−	3.38716i	−0.312470	−	0.113730i	−0.493495	+	0.869749i	$0.664281\pi$
$888$		0			0
$889$	0.739412	−	4.19342i	0.0247991	−	0.140643i
$890$		0			0
$891$	27.3430	+	12.6509i	0.916024	+	0.423821i
$892$		0			0
$893$	7.69184	−	43.6226i	0.257398	−	1.45977i
$894$		0			0
$895$	13.0251	+	4.74073i	0.435380	+	0.158465i
$896$		0			0
$897$	−23.4989	+	18.8887i	−0.784605	+	0.630677i
$898$		0			0
$899$	−15.0992	+	26.1526i	−0.503586	+	0.872237i
$900$		0			0
$901$	12.4508	+	21.5654i	0.414797	+	0.718449i
$902$		0			0
$903$	10.7037	+	19.4757i	0.356196	+	0.648110i
$904$		0			0
$905$	−2.96095	−	16.7924i	−0.0984252	−	0.558197i
$906$		0			0
$907$	−35.8255	−	30.0612i	−1.18957	−	0.998165i	−0.999867	−	0.0163231i	$-0.994804\pi$
$907$	−35.8255	−	30.0612i	−1.18957	−	0.998165i	−0.189700	−	0.981842i	$-0.560752\pi$
$908$		0			0
$909$	−13.2777	−	25.4135i	−0.440395	−	0.842913i
$910$		0			0
$911$	−25.6491	+	9.33551i	−0.849793	+	0.309299i	−0.729956	−	0.683494i	$-0.760459\pi$
$911$	−25.6491	+	9.33551i	−0.849793	+	0.309299i	−0.119837	+	0.992794i	$0.538237\pi$
$912$		0			0
$913$	−13.2749	+	11.1390i	−0.439336	+	0.368647i
$914$		0			0
$915$	13.7353	−	4.67395i	0.454075	−	0.154516i
$916$		0			0
$917$	−27.2124			−0.898633
$918$		0			0
$919$	14.5356			0.479487			0.239743	−	0.970836i	$-0.422937\pi$
$919$	14.5356			0.479487			0.239743	+	0.970836i	$0.422937\pi$
$920$		0			0
$921$	−2.59828	+	13.1137i	−0.0856164	+	0.432110i
$922$		0			0
$923$	13.5173	−	11.3424i	0.444929	−	0.373339i
$924$		0			0
$925$	0.624977	−	0.227473i	0.0205491	−	0.00747927i
$926$		0			0
$927$	−13.1428	−	12.0071i	−0.431666	−	0.394364i
$928$		0			0
$929$	10.3804	+	8.71015i	0.340568	+	0.285771i	0.796990	−	0.603993i	$-0.206425\pi$
$929$	10.3804	+	8.71015i	0.340568	+	0.285771i	−0.456421	+	0.889764i	$0.650869\pi$
$930$		0			0
$931$	5.79568	+	32.8690i	0.189946	+	1.07724i
$932$		0			0
$933$	−5.37829	+	8.87810i	−0.176077	+	0.290656i
$934$		0			0
$935$	3.86512	+	6.69458i	0.126403	+	0.218936i
$936$		0			0
$937$	15.4561	−	26.7707i	0.504927	−	0.874560i	−0.495056	−	0.868861i	$-0.664853\pi$
$937$	15.4561	−	26.7707i	0.504927	−	0.874560i	0.999984	−	0.00569901i	$-0.00181406\pi$
$938$		0			0
$939$	1.06714	+	6.89905i	0.0348249	+	0.225142i
$940$		0			0
$941$	−50.4209	−	18.3517i	−1.64367	−	0.598248i	−0.655998	−	0.754763i	$-0.727752\pi$
$941$	−50.4209	−	18.3517i	−1.64367	−	0.598248i	−0.987676	+	0.156515i	$0.949974\pi$
$942$		0			0
$943$	16.7669	−	95.0896i	0.546004	−	3.09654i
$944$		0			0
$945$	−3.30409	−	6.66236i	−0.107482	−	0.216726i
$946$		0			0
$947$	−5.62722	+	31.9135i	−0.182860	+	1.03705i	0.745814	+	0.666154i	$0.232061\pi$
$947$	−5.62722	+	31.9135i	−0.182860	+	1.03705i	−0.928674	+	0.370896i	$0.879050\pi$
$948$		0			0
$949$	8.28006	+	3.01370i	0.268782	+	0.0978287i
$950$		0			0
$951$	−29.8601	−	11.5863i	−0.968279	−	0.375710i
$952$		0			0
$953$	−14.3386	+	24.8351i	−0.464472	+	0.804489i	−0.999178	−	0.0405492i	$-0.987089\pi$
$953$	−14.3386	+	24.8351i	−0.464472	+	0.804489i	0.534705	+	0.845039i	$0.320423\pi$
$954$		0			0
$955$	−11.2934	−	19.5607i	−0.365445	−	0.632970i
$956$		0			0
$957$	−28.2752	−	0.595833i	−0.914007	−	0.0192605i
$958$		0			0
$959$	1.62499	+	9.21579i	0.0524738	+	0.297593i
$960$		0			0
$961$	5.61474	+	4.71132i	0.181121	+	0.151978i
$962$		0			0
$963$	−2.67835	−	20.1118i	−0.0863085	−	0.648094i
$964$		0			0
$965$	−23.6972	+	8.62508i	−0.762840	+	0.277651i
$966$		0			0
$967$	31.6019	−	26.5171i	1.01625	−	0.852733i	0.0270967	−	0.999633i	$-0.491374\pi$
$967$	31.6019	−	26.5171i	1.01625	−	0.852733i	0.989151	+	0.146899i	$0.0469293\pi$
$968$		0			0
$969$	20.4908	+	17.9429i	0.658259	+	0.576408i
$970$		0			0
$971$	29.1919			0.936814			0.468407	−	0.883513i	$-0.344828\pi$
$971$	29.1919			0.936814			0.468407	+	0.883513i	$0.344828\pi$
$972$		0			0
$973$	8.83803			0.283334
$974$		0			0
$975$	10.1635	+	8.89975i	0.325493	+	0.285020i
$976$		0			0
$977$	12.4794	−	10.4715i	0.399253	−	0.335013i	−0.420952	−	0.907083i	$-0.638304\pi$
$977$	12.4794	−	10.4715i	0.399253	−	0.335013i	0.820205	+	0.572070i	$0.193859\pi$
$978$		0			0
$979$	−12.0635	+	4.39075i	−0.385550	+	0.140329i
$980$		0			0
$981$	−0.686743	−	5.15678i	−0.0219260	−	0.164643i
$982$		0			0
$983$	−8.25670	−	6.92820i	−0.263348	−	0.220975i	0.501547	−	0.865131i	$-0.332765\pi$
$983$	−8.25670	−	6.92820i	−0.263348	−	0.220975i	−0.764895	+	0.644155i	$0.777209\pi$
$984$		0			0
$985$	1.58769	+	9.00425i	0.0505881	+	0.286899i
$986$		0			0
$987$	16.3021	+	0.343528i	0.518901	+	0.0109346i
$988$		0			0
$989$	−39.9028	−	69.1137i	−1.26884	−	2.19769i
$990$		0			0
$991$	−27.6415	+	47.8765i	−0.878062	+	1.52085i	−0.0245976	+	0.999697i	$0.507830\pi$
$991$	−27.6415	+	47.8765i	−0.878062	+	1.52085i	−0.853465	+	0.521151i	$0.825503\pi$
$992$		0			0
$993$	5.11476	+	1.98463i	0.162312	+	0.0629802i
$994$		0			0
$995$	15.4504	+	5.62349i	0.489811	+	0.178277i
$996$		0			0
$997$	2.60909	−	14.7969i	0.0826307	−	0.468622i	−0.915212	−	0.402973i	$-0.867977\pi$
$997$	2.60909	−	14.7969i	0.0826307	−	0.468622i	0.997843	−	0.0656495i	$-0.0209119\pi$
$998$		0			0
$999$	0.859865	+	0.0544233i	0.0272049	+	0.00172188i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.2.i.a.25.3	yes	18
3.2	odd	2		324.2.i.a.73.3		18
4.3	odd	2		432.2.u.d.241.1		18
9.2	odd	6		972.2.i.b.541.3		18
9.4	even	3		972.2.i.a.865.3		18
9.5	odd	6		972.2.i.d.865.1		18
9.7	even	3		972.2.i.c.541.1		18
27.2	odd	18		2916.2.e.d.1945.3		18
27.4	even	9		972.2.i.a.109.3		18
27.5	odd	18		972.2.i.b.433.3		18
27.7	even	9		2916.2.e.c.973.7		18
27.11	odd	18		2916.2.a.c.1.7		9
27.13	even	9	inner	108.2.i.a.13.3	✓	18
27.14	odd	18		324.2.i.a.253.3		18
27.16	even	9		2916.2.a.d.1.3		9
27.20	odd	18		2916.2.e.d.973.3		18
27.22	even	9		972.2.i.c.433.1		18
27.23	odd	18		972.2.i.d.109.1		18
27.25	even	9		2916.2.e.c.1945.7		18
108.67	odd	18		432.2.u.d.337.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.i.a.13.3	✓	18	27.13	even	9	inner
108.2.i.a.25.3	yes	18	1.1	even	1	trivial
324.2.i.a.73.3		18	3.2	odd	2
324.2.i.a.253.3		18	27.14	odd	18
432.2.u.d.241.1		18	4.3	odd	2
432.2.u.d.337.1		18	108.67	odd	18
972.2.i.a.109.3		18	27.4	even	9
972.2.i.a.865.3		18	9.4	even	3
972.2.i.b.433.3		18	27.5	odd	18
972.2.i.b.541.3		18	9.2	odd	6
972.2.i.c.433.1		18	27.22	even	9
972.2.i.c.541.1		18	9.7	even	3
972.2.i.d.109.1		18	27.23	odd	18
972.2.i.d.865.1		18	9.5	odd	6
2916.2.a.c.1.7		9	27.11	odd	18
2916.2.a.d.1.3		9	27.16	even	9
2916.2.e.c.973.7		18	27.7	even	9
2916.2.e.c.1945.7		18	27.25	even	9
2916.2.e.d.973.3		18	27.20	odd	18
2916.2.e.d.1945.3		18	27.2	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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	108.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30308 + 1.14105i) q^{3} +(-0.761786 + 0.639214i) q^{5} +(1.35240 - 0.492232i) q^{7} +(0.396022 + 2.97375i) q^{9} +O(q^{10})\)	\(q+(1.30308 + 1.14105i) q^{3} +(-0.761786 + 0.639214i) q^{5} +(1.35240 - 0.492232i) q^{7} +(0.396022 + 2.97375i) q^{9} +(-2.56436 - 2.15175i) q^{11} +(-0.337662 - 1.91498i) q^{13} +(-1.72204 - 0.0362879i) q^{15} +(1.16107 + 2.01104i) q^{17} +(3.38586 - 5.86448i) q^{19} +(2.32394 + 0.901731i) q^{21} +(-8.41184 - 3.06166i) q^{23} +(-0.696518 + 3.95015i) q^{25} +(-2.87714 + 4.32690i) q^{27} +(0.847007 - 4.80362i) q^{29} +(-5.81772 - 2.11748i) q^{31} +(-0.886306 - 5.72995i) q^{33} +(-0.715594 + 1.23944i) q^{35} +(-0.0829061 - 0.143598i) q^{37} +(1.74508 - 2.88065i) q^{39} +(1.87304 + 10.6225i) q^{41} +(6.82940 + 5.73054i) q^{43} +(-2.20254 - 2.01221i) q^{45} +(6.14677 - 2.23724i) q^{47} +(-3.77563 + 3.16813i) q^{49} +(-0.781721 + 3.94538i) q^{51} +10.7235 q^{53} +3.32892 q^{55} +(11.1037 - 3.77845i) q^{57} +(3.02292 - 2.53653i) q^{59} +(-7.91547 + 2.88100i) q^{61} +(1.99935 + 3.82674i) q^{63} +(1.48131 + 1.24296i) q^{65} +(-0.00383180 - 0.0217312i) q^{67} +(-7.46778 - 13.5879i) q^{69} +(4.53728 + 7.85879i) q^{71} +(-2.26572 + 3.92434i) q^{73} +(-5.41493 + 4.35259i) q^{75} +(-4.52718 - 1.64776i) q^{77} +(-1.00608 + 5.70576i) q^{79} +(-8.68633 + 2.35534i) q^{81} +(0.898927 - 5.09807i) q^{83} +(-2.16997 - 0.789806i) q^{85} +(6.58487 - 5.29301i) q^{87} +(1.91749 - 3.32118i) q^{89} +(-1.39926 - 2.42360i) q^{91} +(-5.16480 - 9.39752i) q^{93} +(1.16936 + 6.63176i) q^{95} +(-5.40914 - 4.53881i) q^{97} +(5.38322 - 8.47789i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) 18 * q + 3 * q^5 + 6 * q^9	\( 18 q + 3 q^{5} + 6 q^{9} + 3 q^{11} - 9 q^{15} - 12 q^{17} - 30 q^{21} - 30 q^{23} + 9 q^{25} - 27 q^{27} - 24 q^{29} + 9 q^{31} - 18 q^{33} - 21 q^{35} + 3 q^{39} + 21 q^{41} - 9 q^{43} + 45 q^{45} + 45 q^{47} - 18 q^{49} + 63 q^{51} + 66 q^{53} + 54 q^{57} + 60 q^{59} - 18 q^{61} + 57 q^{63} + 33 q^{65} - 27 q^{67} - 9 q^{69} - 12 q^{71} + 9 q^{73} - 33 q^{75} - 75 q^{77} - 36 q^{79} - 54 q^{81} - 45 q^{83} - 36 q^{85} - 63 q^{87} - 48 q^{89} + 9 q^{91} - 33 q^{93} + 6 q^{95} - 27 q^{97} + 27 q^{99}+O(q^{100}) \) 18 * q + 3 * q^5 + 6 * q^9 + 3 * q^11 - 9 * q^15 - 12 * q^17 - 30 * q^21 - 30 * q^23 + 9 * q^25 - 27 * q^27 - 24 * q^29 + 9 * q^31 - 18 * q^33 - 21 * q^35 + 3 * q^39 + 21 * q^41 - 9 * q^43 + 45 * q^45 + 45 * q^47 - 18 * q^49 + 63 * q^51 + 66 * q^53 + 54 * q^57 + 60 * q^59 - 18 * q^61 + 57 * q^63 + 33 * q^65 - 27 * q^67 - 9 * q^69 - 12 * q^71 + 9 * q^73 - 33 * q^75 - 75 * q^77 - 36 * q^79 - 54 * q^81 - 45 * q^83 - 36 * q^85 - 63 * q^87 - 48 * q^89 + 9 * q^91 - 33 * q^93 + 6 * q^95 - 27 * q^97 + 27 * q^99

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