LMFDB - Embedded newform 324.2.i.a.253.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(37,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("324.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.i (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.58715302549$
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:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{5} $
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			253.3
Root			$-1.34999 + 1.08514i$ of defining polynomial
Character	$\chi$	$=$	324.253
Dual form			324.2.i.a.73.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.761786 + 0.639214i) q^{5} +(1.35240 + 0.492232i) q^{7} +O(q^{10})$	$q+(0.761786 + 0.639214i) q^{5} +(1.35240 + 0.492232i) q^{7} +(2.56436 - 2.15175i) q^{11} +(-0.337662 + 1.91498i) q^{13} +(-1.16107 + 2.01104i) q^{17} +(3.38586 + 5.86448i) q^{19} +(8.41184 - 3.06166i) q^{23} +(-0.696518 - 3.95015i) q^{25} +(-0.847007 - 4.80362i) q^{29} +(-5.81772 + 2.11748i) q^{31} +(0.715594 + 1.23944i) q^{35} +(-0.0829061 + 0.143598i) q^{37} +(-1.87304 + 10.6225i) q^{41} +(6.82940 - 5.73054i) q^{43} +(-6.14677 - 2.23724i) q^{47} +(-3.77563 - 3.16813i) q^{49} -10.7235 q^{53} +3.32892 q^{55} +(-3.02292 - 2.53653i) q^{59} +(-7.91547 - 2.88100i) q^{61} +(-1.48131 + 1.24296i) q^{65} +(-0.00383180 + 0.0217312i) q^{67} +(-4.53728 + 7.85879i) q^{71} +(-2.26572 - 3.92434i) q^{73} +(4.52718 - 1.64776i) q^{77} +(-1.00608 - 5.70576i) q^{79} +(-0.898927 - 5.09807i) q^{83} +(-2.16997 + 0.789806i) q^{85} +(-1.91749 - 3.32118i) q^{89} +(-1.39926 + 2.42360i) q^{91} +(-1.16936 + 6.63176i) q^{95} +(-5.40914 + 4.53881i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 3 q^{5}+O(q^{10}) $ 18 * q - 3 * q^5	$ 18 q - 3 q^{5} - 3 q^{11} + 12 q^{17} + 30 q^{23} + 9 q^{25} + 24 q^{29} + 9 q^{31} + 21 q^{35} - 21 q^{41} - 9 q^{43} - 45 q^{47} - 18 q^{49} - 66 q^{53} - 60 q^{59} - 18 q^{61} - 33 q^{65} - 27 q^{67} + 12 q^{71} + 9 q^{73} + 75 q^{77} - 36 q^{79} + 45 q^{83} - 36 q^{85} + 48 q^{89} + 9 q^{91} - 6 q^{95} - 27 q^{97}+O(q^{100}) $ 18 * q - 3 * q^5 - 3 * q^11 + 12 * q^17 + 30 * q^23 + 9 * q^25 + 24 * q^29 + 9 * q^31 + 21 * q^35 - 21 * q^41 - 9 * q^43 - 45 * q^47 - 18 * q^49 - 66 * q^53 - 60 * q^59 - 18 * q^61 - 33 * q^65 - 27 * q^67 + 12 * q^71 + 9 * q^73 + 75 * q^77 - 36 * q^79 + 45 * q^83 - 36 * q^85 + 48 * q^89 + 9 * q^91 - 6 * q^95 - 27 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$1$	$e\left(\frac{4}{9}\right)$

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
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.761786	+	0.639214i	0.340681	+	0.285865i	0.797035	−	0.603933i	$-0.206401\pi$
$5$	0.761786	+	0.639214i	0.340681	+	0.285865i	−0.456354	+	0.889798i	$0.650845\pi$
$6$		0			0
$7$	1.35240	+	0.492232i	0.511157	+	0.186046i	0.584706	−	0.811246i	$-0.301210\pi$
$7$	1.35240	+	0.492232i	0.511157	+	0.186046i	−0.0735482	+	0.997292i	$0.523432\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.56436	−	2.15175i	0.773183	−	0.648777i	−0.168339	−	0.985729i	$-0.553840\pi$
$11$	2.56436	−	2.15175i	0.773183	−	0.648777i	0.941522	+	0.336952i	$0.109396\pi$
$12$		0			0
$13$	−0.337662	+	1.91498i	−0.0936506	+	0.531119i	0.901502	+	0.432775i	$0.142466\pi$
$13$	−0.337662	+	1.91498i	−0.0936506	+	0.531119i	−0.995153	+	0.0983438i	$0.968646\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.16107	+	2.01104i	−0.281602	+	0.487749i	−0.971779	−	0.235891i	$-0.924199\pi$
$17$	−1.16107	+	2.01104i	−0.281602	+	0.487749i	0.690178	+	0.723640i	$0.257532\pi$
$18$		0			0
$19$	3.38586	+	5.86448i	0.776769	+	1.34540i	0.933795	+	0.357809i	$0.116476\pi$
$19$	3.38586	+	5.86448i	0.776769	+	1.34540i	−0.157025	+	0.987595i	$0.550190\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	8.41184	−	3.06166i	1.75399	−	0.638400i	0.754157	−	0.656694i	$-0.228046\pi$
$23$	8.41184	−	3.06166i	1.75399	−	0.638400i	0.999833	+	0.0182938i	$0.00582341\pi$
$24$		0			0
$25$	−0.696518	−	3.95015i	−0.139304	−	0.790030i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.847007	−	4.80362i	−0.157285	−	0.892009i	−0.956667	−	0.291185i	$-0.905950\pi$
$29$	−0.847007	−	4.80362i	−0.157285	−	0.892009i	0.799381	−	0.600824i	$-0.205161\pi$
$30$		0			0
$31$	−5.81772	+	2.11748i	−1.04489	+	0.380310i	−0.806733	−	0.590916i	$-0.798766\pi$
$31$	−5.81772	+	2.11748i	−1.04489	+	0.380310i	−0.238160	+	0.971226i	$0.576544\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.715594	+	1.23944i	0.120957	+	0.209504i
$36$		0			0
$37$	−0.0829061	+	0.143598i	−0.0136297	+	0.0236073i	−0.872760	−	0.488150i	$-0.837672\pi$
$37$	−0.0829061	+	0.143598i	−0.0136297	+	0.0236073i	0.859130	+	0.511757i	$0.171005\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.87304	+	10.6225i	−0.292519	+	1.65896i	0.384597	+	0.923084i	$0.374340\pi$
$41$	−1.87304	+	10.6225i	−0.292519	+	1.65896i	−0.677117	+	0.735876i	$0.736771\pi$
$42$		0			0
$43$	6.82940	−	5.73054i	1.04147	−	0.873900i	0.0493017	−	0.998784i	$-0.484300\pi$
$43$	6.82940	−	5.73054i	1.04147	−	0.873900i	0.992171	+	0.124884i	$0.0398560\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−6.14677	−	2.23724i	−0.896599	−	0.326335i	−0.147710	−	0.989031i	$-0.547190\pi$
$47$	−6.14677	−	2.23724i	−0.896599	−	0.326335i	−0.748889	+	0.662695i	$0.769412\pi$
$48$		0			0
$49$	−3.77563	−	3.16813i	−0.539376	−	0.452590i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−10.7235			−1.47299			−0.736495	−	0.676443i	$-0.763521\pi$
$53$	−10.7235			−1.47299			−0.736495	+	0.676443i	$0.763521\pi$
$54$		0			0
$55$	3.32892			0.448871
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.02292	−	2.53653i	−0.393551	−	0.330229i	0.424444	−	0.905454i	$-0.360470\pi$
$59$	−3.02292	−	2.53653i	−0.393551	−	0.330229i	−0.817995	+	0.575226i	$0.804914\pi$
$60$		0			0
$61$	−7.91547	−	2.88100i	−1.01347	−	0.368874i	−0.218707	−	0.975791i	$-0.570184\pi$
$61$	−7.91547	−	2.88100i	−1.01347	−	0.368874i	−0.794765	+	0.606917i	$0.792406\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.48131	+	1.24296i	−0.183733	+	0.154171i
$66$		0			0
$67$	−0.00383180	+	0.0217312i	−0.000468128	+	0.00265489i	−0.985041	−	0.172321i	$-0.944874\pi$
$67$	−0.00383180	+	0.0217312i	−0.000468128	+	0.00265489i	0.984573	+	0.174975i	$0.0559846\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−4.53728	+	7.85879i	−0.538476	+	0.932667i	0.460511	+	0.887654i	$0.347666\pi$
$71$	−4.53728	+	7.85879i	−0.538476	+	0.932667i	−0.998986	+	0.0450131i	$0.985667\pi$
$72$		0			0
$73$	−2.26572	−	3.92434i	−0.265182	−	0.459309i	0.702429	−	0.711754i	$-0.252099\pi$
$73$	−2.26572	−	3.92434i	−0.265182	−	0.459309i	−0.967611	+	0.252445i	$0.918765\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	4.52718	−	1.64776i	0.515920	−	0.187780i
$78$		0			0
$79$	−1.00608	−	5.70576i	−0.113193	−	0.641949i	−0.987629	−	0.156808i	$-0.949880\pi$
$79$	−1.00608	−	5.70576i	−0.113193	−	0.641949i	0.874436	−	0.485140i	$-0.161232\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−0.898927	−	5.09807i	−0.0986700	−	0.559586i	−0.993561	−	0.113300i	$-0.963858\pi$
$83$	−0.898927	−	5.09807i	−0.0986700	−	0.559586i	0.894891	−	0.446285i	$-0.147253\pi$
$84$		0			0
$85$	−2.16997	+	0.789806i	−0.235367	+	0.0856664i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.91749	−	3.32118i	−0.203253	−	0.352045i	0.746322	−	0.665585i	$-0.231818\pi$
$89$	−1.91749	−	3.32118i	−0.203253	−	0.352045i	−0.949575	+	0.313541i	$0.898485\pi$
$90$		0			0
$91$	−1.39926	+	2.42360i	−0.146683	+	0.254062i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.16936	+	6.63176i	−0.119974	+	0.680405i
$96$		0			0
$97$	−5.40914	+	4.53881i	−0.549215	+	0.460846i	−0.874675	−	0.484710i	$-0.838925\pi$
$97$	−5.40914	+	4.53881i	−0.549215	+	0.460846i	0.325460	+	0.945556i	$0.394481\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	8.98129	+	3.26892i	0.893672	+	0.325270i	0.747714	−	0.664021i	$-0.231151\pi$
$101$	8.98129	+	3.26892i	0.893672	+	0.325270i	0.145958	+	0.989291i	$0.453374\pi$
$102$		0			0
$103$	−4.54565	−	3.81425i	−0.447896	−	0.375829i	0.390759	−	0.920493i	$-0.372213\pi$
$103$	−4.54565	−	3.81425i	−0.447896	−	0.375829i	−0.838654	+	0.544664i	$0.816657\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.76312			0.653815			0.326908	−	0.945056i	$-0.393993\pi$
$107$	6.76312			0.653815			0.326908	+	0.945056i	$0.393993\pi$
$108$		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			0
$112$		0			0
$113$	−13.3733	−	11.2215i	−1.25805	−	1.05563i	−0.995886	−	0.0906103i	$-0.971118\pi$
$113$	−13.3733	−	11.2215i	−1.25805	−	1.05563i	−0.262168	−	0.965022i	$-0.584437\pi$
$114$		0			0
$115$	8.36507	+	3.04464i	0.780047	+	0.283914i
$116$		0			0
$117$		0			0
$118$		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
$123$		0			0
$124$		0			0
$125$	4.48049	−	7.76044i	0.400748	−	0.694115i
$126$		0			0
$127$	1.47934	+	2.56230i	0.131270	+	0.227367i	0.924167	−	0.381990i	$-0.124761\pi$
$127$	1.47934	+	2.56230i	0.131270	+	0.227367i	−0.792896	+	0.609357i	$0.791428\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	17.7679	−	6.46697i	1.55239	−	0.565022i	0.583410	−	0.812178i	$-0.301718\pi$
$131$	17.7679	−	6.46697i	1.55239	−	0.565022i	0.968976	+	0.247156i	$0.0794959\pi$
$132$		0			0
$133$	1.69234	+	9.59772i	0.146744	+	0.832228i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.12910	+	6.40346i	0.0964658	+	0.547085i	0.994288	+	0.106727i	$0.0340372\pi$
$137$	1.12910	+	6.40346i	0.0964658	+	0.547085i	−0.897823	+	0.440358i	$0.854852\pi$
$138$		0			0
$139$	5.77063	−	2.10034i	0.489459	−	0.178148i	−0.0854880	−	0.996339i	$-0.527245\pi$
$139$	5.77063	−	2.10034i	0.489459	−	0.178148i	0.574947	+	0.818191i	$0.305023\pi$
$140$		0			0
$141$		0			0
$142$		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
$147$		0			0
$148$		0			0
$149$	−2.70785	+	15.3570i	−0.221835	+	1.25809i	0.646808	+	0.762653i	$0.276104\pi$
$149$	−2.70785	+	15.3570i	−0.221835	+	1.25809i	−0.868643	+	0.495438i	$0.835008\pi$
$150$		0			0
$151$	−3.02970	+	2.54222i	−0.246553	+	0.206883i	−0.757687	−	0.652619i	$-0.773670\pi$
$151$	−3.02970	+	2.54222i	−0.246553	+	0.206883i	0.511133	+	0.859502i	$0.329226\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−5.78537	−	2.10570i	−0.464692	−	0.169134i
$156$		0			0
$157$	18.3183	+	15.3709i	1.46196	+	1.22673i	0.923230	+	0.384248i	$0.125539\pi$
$157$	18.3183	+	15.3709i	1.46196	+	1.22673i	0.538728	+	0.842480i	$0.318905\pi$
$158$		0			0
$159$		0			0
$160$		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
$165$		0			0
$166$		0			0
$167$	−12.8535	−	10.7853i	−0.994631	−	0.834594i	−0.00839915	−	0.999965i	$-0.502674\pi$
$167$	−12.8535	−	10.7853i	−0.994631	−	0.834594i	−0.986232	+	0.165371i	$0.947118\pi$
$168$		0			0
$169$	8.66288	+	3.15303i	0.666376	+	0.242541i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2.67049	−	2.24080i	0.203033	−	0.170365i	−0.535602	−	0.844471i	$-0.679915\pi$
$173$	2.67049	−	2.24080i	0.203033	−	0.170365i	0.738635	+	0.674106i	$0.235471\pi$
$174$		0			0
$175$	1.00242	−	5.68501i	0.0757759	−	0.429747i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	6.96923	−	12.0711i	0.520905	−	0.902234i	−0.478799	−	0.877924i	$-0.658928\pi$
$179$	6.96923	−	12.0711i	0.520905	−	0.902234i	0.999704	−	0.0243097i	$-0.00773878\pi$
$180$		0			0
$181$	−8.57338	−	14.8495i	−0.637254	−	1.10376i	−0.986033	−	0.166551i	$-0.946737\pi$
$181$	−8.57338	−	14.8495i	−0.637254	−	1.10376i	0.348779	−	0.937205i	$-0.386596\pi$
$182$		0			0
$183$		0			0
$184$		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
$189$		0			0
$190$		0			0
$191$	3.94408	+	22.3680i	0.285384	+	1.61849i	0.703912	+	0.710287i	$0.251435\pi$
$191$	3.94408	+	22.3680i	0.285384	+	1.61849i	−0.418529	+	0.908204i	$0.637454\pi$
$192$		0			0
$193$	23.8297	−	8.67330i	1.71530	−	0.624318i	0.717883	−	0.696164i	$-0.245111\pi$
$193$	23.8297	−	8.67330i	1.71530	−	0.624318i	0.997416	+	0.0718466i	$0.0228892\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−4.59713	−	7.96247i	−0.327532	−	0.567303i	0.654489	−	0.756071i	$-0.272884\pi$
$197$	−4.59713	−	7.96247i	−0.327532	−	0.567303i	−0.982022	+	0.188769i	$0.939550\pi$
$198$		0			0
$199$	−8.26695	+	14.3188i	−0.586029	+	1.01503i	0.408718	+	0.912661i	$0.365976\pi$
$199$	−8.26695	+	14.3188i	−0.586029	+	1.01503i	−0.994746	+	0.102371i	$0.967357\pi$
$200$		0			0
$201$		0			0
$202$		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
$207$		0			0
$208$		0			0
$209$	21.3014	+	7.75309i	1.47345	+	0.536293i
$210$		0			0
$211$	2.60930	+	2.18947i	0.179632	+	0.150729i	0.728170	−	0.685396i	$-0.240371\pi$
$211$	2.60930	+	2.18947i	0.179632	+	0.150729i	−0.548538	+	0.836125i	$0.684816\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	8.86558			0.604627
$216$		0			0
$217$	−8.91014			−0.604860
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−3.45904	−	2.90248i	−0.232680	−	0.195242i
$222$		0			0
$223$	−9.67690	−	3.52210i	−0.648013	−	0.235858i	−0.00296060	−	0.999996i	$-0.500942\pi$
$223$	−9.67690	−	3.52210i	−0.648013	−	0.235858i	−0.645053	+	0.764138i	$0.723165\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.438383	−	0.367847i	0.0290965	−	0.0244148i	−0.628123	−	0.778114i	$-0.716177\pi$
$227$	0.438383	−	0.367847i	0.0290965	−	0.0244148i	0.657220	+	0.753699i	$0.271732\pi$
$228$		0			0
$229$	−1.18180	+	6.70231i	−0.0780955	+	0.442901i	0.920539	+	0.390652i	$0.127750\pi$
$229$	−1.18180	+	6.70231i	−0.0780955	+	0.442901i	−0.998634	+	0.0522497i	$0.983361\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	8.20978	−	14.2198i	0.537840	−	0.931567i	−0.461180	−	0.887307i	$-0.652574\pi$
$233$	8.20978	−	14.2198i	0.537840	−	0.931567i	0.999020	−	0.0442602i	$-0.0140931\pi$
$234$		0			0
$235$	−3.25245	−	5.63340i	−0.212166	−	0.367483i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−12.5301	+	4.56059i	−0.810506	+	0.295000i	−0.713833	−	0.700316i	$-0.753042\pi$
$239$	−12.5301	+	4.56059i	−0.810506	+	0.295000i	−0.0966732	+	0.995316i	$0.530820\pi$
$240$		0			0
$241$	3.34886	+	18.9923i	0.215719	+	1.22340i	0.879654	+	0.475613i	$0.157774\pi$
$241$	3.34886	+	18.9923i	0.215719	+	1.22340i	−0.663935	+	0.747790i	$0.731115\pi$
$242$		0			0
$243$		0			0
$244$		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
$249$		0			0
$250$		0			0
$251$	4.87417	+	8.44230i	0.307655	+	0.532873i	0.977849	−	0.209312i	$-0.0671225\pi$
$251$	4.87417	+	8.44230i	0.307655	+	0.532873i	−0.670194	+	0.742186i	$0.733789\pi$
$252$		0			0
$253$	14.9830	−	25.9514i	0.941975	−	1.63155i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−0.209220	+	1.18654i	−0.0130508	+	0.0740145i	−0.990638	−	0.136518i	$-0.956409\pi$
$257$	−0.209220	+	1.18654i	−0.0130508	+	0.0740145i	0.977587	+	0.210533i	$0.0675199\pi$
$258$		0			0
$259$	−0.182805	+	0.153392i	−0.0113589	+	0.00953129i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−26.9229	−	9.79914i	−1.66014	−	0.604241i	−0.669754	−	0.742583i	$-0.733600\pi$
$263$	−26.9229	−	9.79914i	−1.66014	−	0.604241i	−0.990384	+	0.138342i	$0.955823\pi$
$264$		0			0
$265$	−8.16903	−	6.85463i	−0.501820	−	0.421077i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−3.77611			−0.230233			−0.115117	−	0.993352i	$-0.536724\pi$
$269$	−3.77611			−0.230233			−0.115117	+	0.993352i	$0.536724\pi$
$270$		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			0
$274$		0			0
$275$	−10.2859	−	8.63086i	−0.620261	−	0.520461i
$276$		0			0
$277$	−9.50104	−	3.45810i	−0.570862	−	0.207777i	0.0404293	−	0.999182i	$-0.487127\pi$
$277$	−9.50104	−	3.45810i	−0.570862	−	0.207777i	−0.611291	+	0.791406i	$0.709350\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−14.6158	+	12.2641i	−0.871905	+	0.731615i	−0.964498	−	0.264089i	$-0.914929\pi$
$281$	−14.6158	+	12.2641i	−0.871905	+	0.731615i	0.0925932	+	0.995704i	$0.470484\pi$
$282$		0			0
$283$	3.09772	−	17.5681i	0.184141	−	1.04431i	−0.742914	−	0.669387i	$-0.766557\pi$
$283$	3.09772	−	17.5681i	0.184141	−	1.04431i	0.927055	−	0.374926i	$-0.122332\pi$
$284$		0			0
$285$		0			0
$286$		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
$291$		0			0
$292$		0			0
$293$	−2.65793	+	0.967409i	−0.155278	+	0.0565166i	−0.418490	−	0.908221i	$-0.637440\pi$
$293$	−2.65793	+	0.967409i	−0.155278	+	0.0565166i	0.263212	+	0.964738i	$0.415218\pi$
$294$		0			0
$295$	−0.681432	−	3.86459i	−0.0396745	−	0.225005i
$296$		0			0
$297$		0			0
$298$		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
$303$		0			0
$304$		0			0
$305$	−4.18832	−	7.25438i	−0.239822	−	0.415385i
$306$		0			0
$307$	3.85918	−	6.68429i	0.220255	−	0.381493i	−0.734630	−	0.678468i	$-0.762644\pi$
$307$	3.85918	−	6.68429i	0.220255	−	0.381493i	0.954885	+	0.296975i	$0.0959778\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−1.04067	+	5.90192i	−0.0590108	+	0.334667i	−0.999993	−	0.00378966i	$-0.998794\pi$
$311$	−1.04067	+	5.90192i	−0.0590108	+	0.334667i	0.940982	+	0.338457i	$0.109905\pi$
$312$		0			0
$313$	3.08757	−	2.59078i	0.174520	−	0.146439i	−0.551344	−	0.834278i	$-0.685885\pi$
$313$	3.08757	−	2.59078i	0.174520	−	0.146439i	0.725864	+	0.687839i	$0.241440\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	17.3768	+	6.32464i	0.975979	+	0.355227i	0.780276	−	0.625436i	$-0.215079\pi$
$317$	17.3768	+	6.32464i	0.975979	+	0.355227i	0.195704	+	0.980663i	$0.437301\pi$
$318$		0			0
$319$	−12.5082	−	10.4956i	−0.700325	−	0.587643i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−15.7249			−0.874958
$324$		0			0
$325$	7.79963			0.432646
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−7.21162	−	6.05127i	−0.397590	−	0.333617i
$330$		0			0
$331$	2.97650	+	1.08336i	0.163603	+	0.0595466i	0.422523	−	0.906352i	$-0.361144\pi$
$331$	2.97650	+	1.08336i	0.163603	+	0.0595466i	−0.258920	+	0.965899i	$0.583367\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.0168099	+	0.0141052i	−0.000918422	+	0.000770648i
$336$		0			0
$337$	0.734248	−	4.16413i	0.0399971	−	0.226835i	−0.958256	−	0.285910i	$-0.907704\pi$
$337$	0.734248	−	4.16413i	0.0399971	−	0.226835i	0.998254	+	0.0590754i	$0.0188153\pi$
$338$		0			0
$339$		0			0
$340$		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
$345$		0			0
$346$		0			0
$347$	−4.83722	+	1.76060i	−0.259676	+	0.0945142i	−0.468577	−	0.883422i	$-0.655233\pi$
$347$	−4.83722	+	1.76060i	−0.259676	+	0.0945142i	0.208902	+	0.977937i	$0.433011\pi$
$348$		0			0
$349$	−4.41135	−	25.0180i	−0.236134	−	1.33918i	−0.840212	−	0.542257i	$-0.817570\pi$
$349$	−4.41135	−	25.0180i	−0.236134	−	1.33918i	0.604079	−	0.796925i	$-0.293541\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−4.54522	−	25.7772i	−0.241918	−	1.37198i	−0.827543	−	0.561402i	$-0.810262\pi$
$353$	−4.54522	−	25.7772i	−0.241918	−	1.37198i	0.585626	−	0.810582i	$-0.300849\pi$
$354$		0			0
$355$	−8.47988	+	3.08642i	−0.450065	+	0.163810i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−0.586533	−	1.01590i	−0.0309560	−	0.0536174i	0.850132	−	0.526569i	$-0.176522\pi$
$359$	−0.586533	−	1.01590i	−0.0309560	−	0.0536174i	−0.881088	+	0.472952i	$0.843189\pi$
$360$		0			0
$361$	−13.4281	+	23.2581i	−0.706741	+	1.22411i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	0.782501	−	4.43778i	0.0409580	−	0.232284i
$366$		0			0
$367$	4.40016	−	3.69217i	0.229686	−	0.192730i	−0.520680	−	0.853752i	$-0.674322\pi$
$367$	4.40016	−	3.69217i	0.229686	−	0.192730i	0.750366	+	0.661022i	$0.229877\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−14.5024	−	5.27846i	−0.752930	−	0.274044i
$372$		0			0
$373$	16.3175	+	13.6920i	0.844888	+	0.708945i	0.958658	−	0.284562i	$-0.0918483\pi$
$373$	16.3175	+	13.6920i	0.844888	+	0.708945i	−0.113770	+	0.993507i	$0.536293\pi$
$374$		0			0
$375$		0			0
$376$		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
$381$		0			0
$382$		0			0
$383$	18.8004	+	15.7754i	0.960658	+	0.806087i	0.981060	−	0.193704i	$-0.0620503\pi$
$383$	18.8004	+	15.7754i	0.960658	+	0.806087i	−0.0204024	+	0.999792i	$0.506495\pi$
$384$		0			0
$385$	4.50201	+	1.63860i	0.229444	+	0.0835107i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	1.21272	−	1.01760i	0.0614875	−	0.0515942i	−0.611526	−	0.791224i	$-0.709444\pi$
$389$	1.21272	−	1.01760i	0.0614875	−	0.0515942i	0.673013	+	0.739630i	$0.265000\pi$
$390$		0			0
$391$	−3.60965	+	20.4713i	−0.182548	+	1.03528i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	2.88079	−	4.98967i	0.144948	−	0.251057i
$396$		0			0
$397$	5.40150	+	9.35568i	0.271094	+	0.469548i	0.969142	−	0.246503i	$-0.0792814\pi$
$397$	5.40150	+	9.35568i	0.271094	+	0.469548i	−0.698049	+	0.716050i	$0.745948\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	2.13798	−	0.778161i	0.106766	−	0.0388595i	−0.288085	−	0.957605i	$-0.593019\pi$
$401$	2.13798	−	0.778161i	0.106766	−	0.0388595i	0.394851	+	0.918745i	$0.370796\pi$
$402$		0			0
$403$	−2.09049	−	11.8558i	−0.104135	−	0.590578i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	0.0963853	+	0.546628i	0.00477764	+	0.0270954i
$408$		0			0
$409$	−32.1074	+	11.6861i	−1.58761	+	0.577842i	−0.976841	−	0.213968i	$-0.931361\pi$
$409$	−32.1074	+	11.6861i	−1.58761	+	0.577842i	−0.610767	+	0.791810i	$0.709139\pi$
$410$		0			0
$411$		0			0
$412$		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
$417$		0			0
$418$		0			0
$419$	1.82203	−	10.3333i	0.0890121	−	0.504813i	−0.907406	−	0.420254i	$-0.861941\pi$
$419$	1.82203	−	10.3333i	0.0890121	−	0.504813i	0.996419	−	0.0845586i	$-0.0269480\pi$
$420$		0			0
$421$	−16.0206	+	13.4429i	−0.780798	+	0.655167i	−0.943449	−	0.331516i	$-0.892440\pi$
$421$	−16.0206	+	13.4429i	−0.780798	+	0.655167i	0.162652	+	0.986684i	$0.447995\pi$
$422$		0			0
$423$		0			0
$424$		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
$429$		0			0
$430$		0			0
$431$	−7.25638			−0.349528			−0.174764	−	0.984610i	$-0.555916\pi$
$431$	−7.25638			−0.349528			−0.174764	+	0.984610i	$0.555916\pi$
$432$		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
$435$		0			0
$436$		0			0
$437$	46.4363	+	38.9647i	2.22135	+	1.86394i
$438$		0			0
$439$	9.20682	+	3.35101i	0.439417	+	0.159935i	0.552249	−	0.833679i	$-0.313770\pi$
$439$	9.20682	+	3.35101i	0.439417	+	0.159935i	−0.112831	+	0.993614i	$0.535992\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	21.8385	−	18.3247i	1.03758	−	0.870633i	0.0458469	−	0.998948i	$-0.485401\pi$
$443$	21.8385	−	18.3247i	1.03758	−	0.870633i	0.991733	+	0.128315i	$0.0409569\pi$
$444$		0			0
$445$	0.662234	−	3.75571i	0.0313929	−	0.178038i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	9.03115	−	15.6424i	0.426206	−	0.738211i	−0.570326	−	0.821418i	$-0.693183\pi$
$449$	9.03115	−	15.6424i	0.426206	−	0.738211i	0.996532	+	0.0832075i	$0.0265164\pi$
$450$		0			0
$451$	18.0539	+	31.2703i	0.850125	+	1.47246i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−2.61514	+	0.951832i	−0.122599	+	0.0446226i
$456$		0			0
$457$	1.52536	+	8.65075i	0.0713534	+	0.404665i	0.999475	+	0.0323889i	$0.0103115\pi$
$457$	1.52536	+	8.65075i	0.0713534	+	0.404665i	−0.928122	+	0.372276i	$0.878577\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−6.91883	−	39.2386i	−0.322242	−	1.82753i	−0.528386	−	0.849004i	$-0.677203\pi$
$461$	−6.91883	−	39.2386i	−0.322242	−	1.82753i	0.206144	−	0.978522i	$-0.433909\pi$
$462$		0			0
$463$	22.3956	−	8.15134i	1.04081	−	0.378825i	0.235624	−	0.971844i	$-0.424286\pi$
$463$	22.3956	−	8.15134i	1.04081	−	0.378825i	0.805188	+	0.593019i	$0.202064\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	5.35121	+	9.26856i	0.247624	+	0.428898i	0.962866	−	0.269979i	$-0.0870168\pi$
$467$	5.35121	+	9.26856i	0.247624	+	0.428898i	−0.715242	+	0.698877i	$0.753683\pi$
$468$		0			0
$469$	−0.0158789	+	0.0275030i	−0.000733219	+	0.00126997i
$470$		0			0
$471$		0			0
$472$		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
$477$		0			0
$478$		0			0
$479$	11.9843	+	4.36195i	0.547579	+	0.199302i	0.600970	−	0.799271i	$-0.294781\pi$
$479$	11.9843	+	4.36195i	0.547579	+	0.199302i	−0.0533916	+	0.998574i	$0.517003\pi$
$480$		0			0
$481$	−0.246992	−	0.207251i	−0.0112618	−	0.00944981i
$482$		0			0
$483$		0			0
$484$		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
$489$		0			0
$490$		0			0
$491$	24.0693	+	20.1965i	1.08623	+	0.911457i	0.996423	−	0.0845017i	$-0.0269298\pi$
$491$	24.0693	+	20.1965i	1.08623	+	0.911457i	0.0898092	+	0.995959i	$0.471374\pi$
$492$		0			0
$493$	10.6437	+	3.87399i	0.479368	+	0.174476i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−10.0045	+	8.39480i	−0.448765	+	0.376558i
$498$		0			0
$499$	−5.93176	+	33.6407i	−0.265542	+	1.50596i	0.501945	+	0.864900i	$0.332618\pi$
$499$	−5.93176	+	33.6407i	−0.265542	+	1.50596i	−0.767487	+	0.641065i	$0.778493\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−10.1654	+	17.6069i	−0.453252	+	0.785055i	−0.998586	−	0.0531640i	$-0.983069\pi$
$503$	−10.1654	+	17.6069i	−0.453252	+	0.785055i	0.545334	+	0.838219i	$0.316403\pi$
$504$		0			0
$505$	4.75228	+	8.23119i	0.211474	+	0.366283i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−7.69531	+	2.80086i	−0.341088	+	0.124146i	−0.506884	−	0.862014i	$-0.669203\pi$
$509$	−7.69531	+	2.80086i	−0.341088	+	0.124146i	0.165796	+	0.986160i	$0.446981\pi$
$510$		0			0
$511$	−1.13246	−	6.42251i	−0.0500972	−	0.284115i
$512$		0			0
$513$		0			0
$514$		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			0
$520$		0			0
$521$	16.5346	+	28.6387i	0.724392	+	1.25468i	0.959224	+	0.282648i	$0.0912128\pi$
$521$	16.5346	+	28.6387i	0.724392	+	1.25468i	−0.234832	+	0.972036i	$0.575454\pi$
$522$		0			0
$523$	−2.92714	+	5.06995i	−0.127995	+	0.221693i	−0.922900	−	0.385041i	$-0.874187\pi$
$523$	−2.92714	+	5.06995i	−0.127995	+	0.221693i	0.794905	+	0.606734i	$0.207521\pi$
$524$		0			0
$525$		0			0
$526$		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
$531$		0			0
$532$		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
$537$		0			0
$538$		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
$543$		0			0
$544$		0			0
$545$	−1.32101	−	1.10846i	−0.0565860	−	0.0474813i
$546$		0			0
$547$	−23.9504	−	8.71722i	−1.02404	−	0.372721i	−0.225234	−	0.974305i	$-0.572315\pi$
$547$	−23.9504	−	8.71722i	−1.02404	−	0.372721i	−0.798810	+	0.601583i	$0.794537\pi$
$548$		0			0
$549$		0			0
$550$		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			0
$556$		0			0
$557$	−18.5450	+	32.1208i	−0.785775	+	1.36100i	0.142760	+	0.989757i	$0.454402\pi$
$557$	−18.5450	+	32.1208i	−0.785775	+	1.36100i	−0.928535	+	0.371245i	$0.878931\pi$
$558$		0			0
$559$	8.66783	+	15.0131i	0.366610	+	0.634987i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	11.6768	−	4.25002i	0.492120	−	0.179117i	−0.0840264	−	0.996464i	$-0.526778\pi$
$563$	11.6768	−	4.25002i	0.492120	−	0.179117i	0.576146	+	0.817346i	$0.304556\pi$
$564$		0			0
$565$	−3.01463	−	17.0968i	−0.126826	−	0.719268i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	4.64088	+	26.3198i	0.194556	+	1.10338i	0.913050	+	0.407848i	$0.133721\pi$
$569$	4.64088	+	26.3198i	0.194556	+	1.10338i	−0.718494	+	0.695533i	$0.755168\pi$
$570$		0			0
$571$	−6.28728	+	2.28838i	−0.263115	+	0.0957659i	−0.470209	−	0.882555i	$-0.655821\pi$
$571$	−6.28728	+	2.28838i	−0.263115	+	0.0957659i	0.207094	+	0.978321i	$0.433599\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−17.9530	−	31.0955i	−0.748693	−	1.29677i
$576$		0			0
$577$	−14.5989	+	25.2860i	−0.607760	+	1.05267i	0.383849	+	0.923396i	$0.374598\pi$
$577$	−14.5989	+	25.2860i	−0.607760	+	1.05267i	−0.991609	+	0.129275i	$0.958735\pi$
$578$		0			0
$579$		0			0
$580$		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
$585$		0			0
$586$		0			0
$587$	−7.33702	−	2.67046i	−0.302831	−	0.110222i	0.186135	−	0.982524i	$-0.440404\pi$
$587$	−7.33702	−	2.67046i	−0.302831	−	0.110222i	−0.488967	+	0.872303i	$0.662626\pi$
$588$		0			0
$589$	−32.1159	−	26.9484i	−1.32331	−	1.11039i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−6.64855			−0.273023			−0.136512	−	0.990638i	$-0.543589\pi$
$593$	−6.64855			−0.273023			−0.136512	+	0.990638i	$0.543589\pi$
$594$		0			0
$595$	−3.32343			−0.136247
$596$		0			0
$597$		0			0
$598$		0			0
$599$	11.1040	+	9.31733i	0.453696	+	0.380696i	0.840805	−	0.541338i	$-0.182082\pi$
$599$	11.1040	+	9.31733i	0.453696	+	0.380696i	−0.387110	+	0.922034i	$0.626526\pi$
$600$		0			0
$601$	−3.52740	−	1.28387i	−0.143886	−	0.0523701i	0.269073	−	0.963120i	$-0.413283\pi$
$601$	−3.52740	−	1.28387i	−0.143886	−	0.0523701i	−0.412959	+	0.910750i	$0.635505\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.156894	−	0.131649i	0.00637863	−	0.00535231i
$606$		0			0
$607$	4.47607	−	25.3851i	0.181678	−	1.03035i	−0.748472	−	0.663167i	$-0.769212\pi$
$607$	4.47607	−	25.3851i	0.181678	−	1.03035i	0.930150	−	0.367181i	$-0.119677\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	6.35980	−	11.0155i	0.257290	−	0.445639i
$612$		0			0
$613$	−7.07992	−	12.2628i	−0.285955	−	0.495289i	0.686885	−	0.726766i	$-0.258978\pi$
$613$	−7.07992	−	12.2628i	−0.285955	−	0.495289i	−0.972840	+	0.231477i	$0.925644\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−26.1322	+	9.51134i	−1.05204	+	0.382912i	−0.809433	−	0.587212i	$-0.800226\pi$
$617$	−26.1322	+	9.51134i	−1.05204	+	0.382912i	−0.242609	+	0.970124i	$0.578003\pi$
$618$		0			0
$619$	5.54233	+	31.4321i	0.222765	+	1.26336i	0.866912	+	0.498462i	$0.166102\pi$
$619$	5.54233	+	31.4321i	0.222765	+	1.26336i	−0.644146	+	0.764902i	$0.722787\pi$
$620$		0			0
$621$		0			0
$622$		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
$627$		0			0
$628$		0			0
$629$	−0.192520	−	0.333455i	−0.00767628	−	0.0132957i
$630$		0			0
$631$	10.6272	−	18.4068i	0.423062	−	0.732765i	−0.573175	−	0.819433i	$-0.694289\pi$
$631$	10.6272	−	18.4068i	0.423062	−	0.732765i	0.996237	+	0.0866680i	$0.0276219\pi$
$632$		0			0
$633$		0			0
$634$		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
$639$		0			0
$640$		0			0
$641$	−14.8823	−	5.41670i	−0.587814	−	0.213947i	0.0309539	−	0.999521i	$-0.490145\pi$
$641$	−14.8823	−	5.41670i	−0.587814	−	0.213947i	−0.618768	+	0.785574i	$0.712368\pi$
$642$		0			0
$643$	22.4373	+	18.8271i	0.884839	+	0.742468i	0.967168	−	0.254137i	$-0.0817914\pi$
$643$	22.4373	+	18.8271i	0.884839	+	0.742468i	−0.0823289	+	0.996605i	$0.526236\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	20.4322			0.803272			0.401636	−	0.915799i	$-0.368442\pi$
$647$	20.4322			0.803272			0.401636	+	0.915799i	$0.368442\pi$
$648$		0			0
$649$	−13.2098			−0.518532
$650$		0			0
$651$		0			0
$652$		0			0
$653$	13.7302	+	11.5210i	0.537306	+	0.450853i	0.870615	−	0.491964i	$-0.163721\pi$
$653$	13.7302	+	11.5210i	0.537306	+	0.450853i	−0.333309	+	0.942817i	$0.608165\pi$
$654$		0			0
$655$	17.6691	+	6.43102i	0.690388	+	0.251281i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	9.71001	−	8.14766i	0.378248	−	0.317388i	−0.433766	−	0.901026i	$-0.642816\pi$
$659$	9.71001	−	8.14766i	0.378248	−	0.317388i	0.812014	+	0.583638i	$0.198371\pi$
$660$		0			0
$661$	−3.10157	+	17.5899i	−0.120637	+	0.684167i	0.863167	+	0.504919i	$0.168478\pi$
$661$	−3.10157	+	17.5899i	−0.120637	+	0.684167i	−0.983804	+	0.179248i	$0.942634\pi$
$662$		0			0
$663$		0			0
$664$		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
$669$		0			0
$670$		0			0
$671$	−26.4973	+	9.64422i	−1.02292	+	0.372311i
$672$		0			0
$673$	−4.94149	−	28.0246i	−0.190480	−	1.08027i	−0.918709	−	0.394934i	$-0.870767\pi$
$673$	−4.94149	−	28.0246i	−0.190480	−	1.08027i	0.728229	−	0.685334i	$-0.240344\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−3.73652	−	21.1909i	−0.143606	−	0.814431i	−0.968476	−	0.249108i	$-0.919863\pi$
$677$	−3.73652	−	21.1909i	−0.143606	−	0.814431i	0.824869	−	0.565323i	$-0.191249\pi$
$678$		0			0
$679$	−9.54944	+	3.47571i	−0.366474	+	0.133386i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	2.31436	+	4.00859i	0.0885566	+	0.153384i	0.906901	−	0.421343i	$-0.138441\pi$
$683$	2.31436	+	4.00859i	0.0885566	+	0.153384i	−0.818345	+	0.574728i	$0.805108\pi$
$684$		0			0
$685$	−3.23305	+	5.59980i	−0.123528	+	0.213958i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	3.62093	−	20.5353i	0.137946	−	0.782333i
$690$		0			0
$691$	−13.4054	+	11.2485i	−0.509966	+	0.427913i	−0.861117	−	0.508406i	$-0.830235\pi$
$691$	−13.4054	+	11.2485i	−0.509966	+	0.427913i	0.351151	+	0.936319i	$0.385790\pi$
$692$		0			0
$693$		0			0
$694$		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
$699$		0			0
$700$		0			0
$701$	−20.6892			−0.781420			−0.390710	−	0.920514i	$-0.627771\pi$
$701$	−20.6892			−0.781420			−0.390710	+	0.920514i	$0.627771\pi$
$702$		0			0
$703$	−1.12283			−0.0423484
$704$		0			0
$705$		0			0
$706$		0			0
$707$	10.5372	+	8.84175i	0.396292	+	0.332528i
$708$		0			0
$709$	−41.9234	−	15.2589i	−1.57447	−	0.573059i	−0.600476	−	0.799643i	$-0.705022\pi$
$709$	−41.9234	−	15.2589i	−1.57447	−	0.573059i	−0.973992	+	0.226584i	$0.927244\pi$
$710$		0			0
$711$		0			0
$712$		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
$717$		0			0
$718$		0			0
$719$	15.0646	−	26.0926i	0.561814	−	0.973091i	−0.435524	−	0.900177i	$-0.643437\pi$
$719$	15.0646	−	26.0926i	0.561814	−	0.973091i	0.997338	−	0.0729139i	$-0.0232298\pi$
$720$		0			0
$721$	−4.27002	−	7.39588i	−0.159024	−	0.275437i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−18.3851	+	6.69161i	−0.682804	+	0.248520i
$726$		0			0
$727$	−3.07006	−	17.4112i	−0.113862	−	0.645745i	−0.987307	−	0.158822i	$-0.949230\pi$
$727$	−3.07006	−	17.4112i	−0.113862	−	0.645745i	0.873445	−	0.486923i	$-0.161881\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	3.59491	+	20.3878i	0.132963	+	0.754069i
$732$		0			0
$733$	7.47895	−	2.72211i	0.276241	−	0.100544i	−0.200185	−	0.979758i	$-0.564154\pi$
$733$	7.47895	−	2.72211i	0.276241	−	0.100544i	0.476426	+	0.879215i	$0.341932\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.0369340	+	0.0639716i	0.00136048	+	0.00235642i
$738$		0			0
$739$	6.81386	−	11.8019i	0.250652	−	0.434142i	−0.713054	−	0.701109i	$-0.752688\pi$
$739$	6.81386	−	11.8019i	0.250652	−	0.434142i	0.963705	+	0.266968i	$0.0860218\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	3.87103	−	21.9537i	0.142014	−	0.805403i	−0.827702	−	0.561168i	$-0.810352\pi$
$743$	3.87103	−	21.9537i	0.142014	−	0.805403i	0.969716	−	0.244235i	$-0.0785369\pi$
$744$		0			0
$745$	−11.8792	+	9.96782i	−0.435220	+	0.365193i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	9.14641	+	3.32902i	0.334203	+	0.121640i
$750$		0			0
$751$	12.8736	+	10.8023i	0.469766	+	0.394180i	0.846709	−	0.532056i	$-0.178580\pi$
$751$	12.8736	+	10.8023i	0.469766	+	0.394180i	−0.376943	+	0.926236i	$0.623025\pi$
$752$		0			0
$753$		0			0
$754$		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
$759$		0			0
$760$		0			0
$761$	−5.72263	−	4.80186i	−0.207445	−	0.174067i	0.533146	−	0.846024i	$-0.321010\pi$
$761$	−5.72263	−	4.80186i	−0.207445	−	0.174067i	−0.740591	+	0.671956i	$0.765454\pi$
$762$		0			0
$763$	−2.34519	−	0.853579i	−0.0849016	−	0.0309016i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	5.87813	−	4.93234i	0.212247	−	0.178096i
$768$		0			0
$769$	8.44440	−	47.8906i	0.304513	−	1.72698i	−0.321276	−	0.946986i	$-0.604112\pi$
$769$	8.44440	−	47.8906i	0.304513	−	1.72698i	0.625789	−	0.779993i	$-0.284777\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−14.2586	+	24.6966i	−0.512846	+	0.888276i	0.487043	+	0.873378i	$0.338076\pi$
$773$	−14.2586	+	24.6966i	−0.512846	+	0.888276i	−0.999889	+	0.0148977i	$0.995258\pi$
$774$		0			0
$775$	12.4165	+	21.5060i	0.446014	+	0.772518i
$776$		0			0
$777$		0			0
$778$		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
$783$		0			0
$784$		0			0
$785$	4.12933	+	23.4186i	0.147382	+	0.835845i
$786$		0			0
$787$	45.9010	−	16.7066i	1.63619	−	0.595526i	0.649827	−	0.760082i	$-0.274841\pi$
$787$	45.9010	−	16.7066i	1.63619	−	0.595526i	0.986368	+	0.164556i	$0.0526190\pi$
$788$		0			0
$789$		0			0
$790$		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
$795$		0			0
$796$		0			0
$797$	2.71436	−	15.3939i	0.0961477	−	0.545281i	−0.898242	−	0.439501i	$-0.855155\pi$
$797$	2.71436	−	15.3939i	0.0961477	−	0.545281i	0.994390	−	0.105779i	$-0.0337337\pi$
$798$		0			0
$799$	11.6360	−	9.76379i	0.411653	−	0.345418i
$800$		0			0
$801$		0			0
$802$		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
$807$		0			0
$808$		0			0
$809$	8.18856			0.287894			0.143947	−	0.989585i	$-0.454020\pi$
$809$	8.18856			0.287894			0.143947	+	0.989585i	$0.454020\pi$
$810$		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
$813$		0			0
$814$		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
$819$		0			0
$820$		0			0
$821$	−19.5852	+	16.4339i	−0.683528	+	0.573548i	−0.917035	−	0.398807i	$-0.869424\pi$
$821$	−19.5852	+	16.4339i	−0.683528	+	0.573548i	0.233507	+	0.972355i	$0.424980\pi$
$822$		0			0
$823$	−0.615119	+	3.48851i	−0.0214417	+	0.121602i	−0.993650	−	0.112516i	$-0.964109\pi$
$823$	−0.615119	+	3.48851i	−0.0214417	+	0.121602i	0.972208	+	0.234118i	$0.0752202\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	15.6193	−	27.0534i	0.543136	−	0.940739i	−0.455586	−	0.890192i	$-0.650570\pi$
$827$	15.6193	−	27.0534i	0.543136	−	0.940739i	0.998722	−	0.0505472i	$-0.0160965\pi$
$828$		0			0
$829$	3.45938	+	5.99182i	0.120149	+	0.208104i	0.919826	−	0.392326i	$-0.128329\pi$
$829$	3.45938	+	5.99182i	0.120149	+	0.208104i	−0.799677	+	0.600430i	$0.794996\pi$
$830$		0			0
$831$		0			0
$832$		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
$837$		0			0
$838$		0			0
$839$	5.96637	+	33.8369i	0.205982	+	1.16818i	0.895887	+	0.444282i	$0.146541\pi$
$839$	5.96637	+	33.8369i	0.205982	+	1.16818i	−0.689905	+	0.723900i	$0.742348\pi$
$840$		0			0
$841$	4.89378	−	1.78119i	0.168751	−	0.0614203i
$842$		0			0
$843$		0			0
$844$		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
$849$		0			0
$850$		0			0
$851$	−0.257746	+	1.46175i	−0.00883541	+	0.0501081i
$852$		0			0
$853$	−18.1440	+	15.2246i	−0.621239	+	0.521282i	−0.898193	−	0.439602i	$-0.855120\pi$
$853$	−18.1440	+	15.2246i	−0.621239	+	0.521282i	0.276954	+	0.960883i	$0.410675\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	15.6873	+	5.70972i	0.535869	+	0.195040i	0.595757	−	0.803165i	$-0.296852\pi$
$857$	15.6873	+	5.70972i	0.535869	+	0.195040i	−0.0598878	+	0.998205i	$0.519074\pi$
$858$		0			0
$859$	7.88524	+	6.61650i	0.269041	+	0.225752i	0.767320	−	0.641265i	$-0.221590\pi$
$859$	7.88524	+	6.61650i	0.269041	+	0.225752i	−0.498279	+	0.867017i	$0.666034\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	46.7315			1.59076			0.795379	−	0.606112i	$-0.207272\pi$
$863$	46.7315			1.59076			0.795379	+	0.606112i	$0.207272\pi$
$864$		0			0
$865$	3.46669			0.117871
$866$		0			0
$867$		0			0
$868$		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
$873$		0			0
$874$		0			0
$875$	9.87934	−	8.28975i	0.333982	−	0.280245i
$876$		0			0
$877$	−7.74539	+	43.9263i	−0.261543	+	1.48329i	0.517158	+	0.855890i	$0.326990\pi$
$877$	−7.74539	+	43.9263i	−0.261543	+	1.48329i	−0.778701	+	0.627395i	$0.784121\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	16.8718	−	29.2229i	0.568426	−	0.984543i	−0.428295	−	0.903639i	$-0.640886\pi$
$881$	16.8718	−	29.2229i	0.568426	−	0.984543i	0.996722	−	0.0809046i	$-0.0257809\pi$
$882$		0			0
$883$	−22.6765	−	39.2769i	−0.763126	−	1.32177i	−0.941231	−	0.337762i	$-0.890330\pi$
$883$	−22.6765	−	39.2769i	−0.763126	−	1.32177i	0.178105	−	0.984011i	$-0.443003\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	9.30614	−	3.38716i	0.312470	−	0.113730i	−0.181025	−	0.983478i	$-0.557941\pi$
$887$	9.30614	−	3.38716i	0.312470	−	0.113730i	0.493495	+	0.869749i	$0.335719\pi$
$888$		0			0
$889$	0.739412	+	4.19342i	0.0247991	+	0.140643i
$890$		0			0
$891$		0			0
$892$		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
$897$		0			0
$898$		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
$903$		0			0
$904$		0			0
$905$	2.96095	−	16.7924i	0.0984252	−	0.558197i
$906$		0			0
$907$	−35.8255	+	30.0612i	−1.18957	+	0.998165i	−0.189700	+	0.981842i	$0.560752\pi$
$907$	−35.8255	+	30.0612i	−1.18957	+	0.998165i	−0.999867	+	0.0163231i	$0.994804\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	25.6491	+	9.33551i	0.849793	+	0.309299i	0.729956	−	0.683494i	$-0.239541\pi$
$911$	25.6491	+	9.33551i	0.849793	+	0.309299i	0.119837	+	0.992794i	$0.461763\pi$
$912$		0			0
$913$	−13.2749	−	11.1390i	−0.439336	−	0.368647i
$914$		0			0
$915$		0			0
$916$		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
$921$		0			0
$922$		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
$927$		0			0
$928$		0			0
$929$	−10.3804	+	8.71015i	−0.340568	+	0.285771i	−0.796990	−	0.603993i	$-0.793575\pi$
$929$	−10.3804	+	8.71015i	−0.340568	+	0.285771i	0.456421	+	0.889764i	$0.349131\pi$
$930$		0			0
$931$	5.79568	−	32.8690i	0.189946	−	1.07724i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−3.86512	+	6.69458i	−0.126403	+	0.218936i
$936$		0			0
$937$	15.4561	+	26.7707i	0.504927	+	0.874560i	0.999984	+	0.00569901i	$0.00181406\pi$
$937$	15.4561	+	26.7707i	0.504927	+	0.874560i	−0.495056	+	0.868861i	$0.664853\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	50.4209	−	18.3517i	1.64367	−	0.598248i	0.655998	−	0.754763i	$-0.272248\pi$
$941$	50.4209	−	18.3517i	1.64367	−	0.598248i	0.987676	+	0.156515i	$0.0500259\pi$
$942$		0			0
$943$	16.7669	+	95.0896i	0.546004	+	3.09654i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	5.62722	+	31.9135i	0.182860	+	1.03705i	0.928674	+	0.370896i	$0.120950\pi$
$947$	5.62722	+	31.9135i	0.182860	+	1.03705i	−0.745814	+	0.666154i	$0.767939\pi$
$948$		0			0
$949$	8.28006	−	3.01370i	0.268782	−	0.0978287i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	14.3386	+	24.8351i	0.464472	+	0.804489i	0.999178	−	0.0405492i	$-0.0129108\pi$
$953$	14.3386	+	24.8351i	0.464472	+	0.804489i	−0.534705	+	0.845039i	$0.679577\pi$
$954$		0			0
$955$	−11.2934	+	19.5607i	−0.365445	+	0.632970i
$956$		0			0
$957$		0			0
$958$		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
$963$		0			0
$964$		0			0
$965$	23.6972	+	8.62508i	0.762840	+	0.277651i
$966$		0			0
$967$	31.6019	+	26.5171i	1.01625	+	0.852733i	0.989151	−	0.146899i	$-0.0469293\pi$
$967$	31.6019	+	26.5171i	1.01625	+	0.852733i	0.0270967	+	0.999633i	$0.491374\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−29.1919			−0.936814			−0.468407	−	0.883513i	$-0.655172\pi$
$971$	−29.1919			−0.936814			−0.468407	+	0.883513i	$0.655172\pi$
$972$		0			0
$973$	8.83803			0.283334
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−12.4794	−	10.4715i	−0.399253	−	0.335013i	0.420952	−	0.907083i	$-0.361696\pi$
$977$	−12.4794	−	10.4715i	−0.399253	−	0.335013i	−0.820205	+	0.572070i	$0.806141\pi$
$978$		0			0
$979$	−12.0635	−	4.39075i	−0.385550	−	0.140329i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	8.25670	−	6.92820i	0.263348	−	0.220975i	−0.501547	−	0.865131i	$-0.667235\pi$
$983$	8.25670	−	6.92820i	0.263348	−	0.220975i	0.764895	+	0.644155i	$0.222791\pi$
$984$		0			0
$985$	1.58769	−	9.00425i	0.0505881	−	0.286899i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	39.9028	−	69.1137i	1.26884	−	2.19769i
$990$		0			0
$991$	−27.6415	−	47.8765i	−0.878062	−	1.52085i	−0.853465	−	0.521151i	$-0.825503\pi$
$991$	−27.6415	−	47.8765i	−0.878062	−	1.52085i	−0.0245976	−	0.999697i	$-0.507830\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−15.4504	+	5.62349i	−0.489811	+	0.178277i
$996$		0			0
$997$	2.60909	+	14.7969i	0.0826307	+	0.468622i	0.997843	+	0.0656495i	$0.0209119\pi$
$997$	2.60909	+	14.7969i	0.0826307	+	0.468622i	−0.915212	+	0.402973i	$0.867977\pi$
$998$		0			0
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.i.a.13.3	✓	18	3.2	odd	2
108.2.i.a.25.3	yes	18	27.2	odd	18
324.2.i.a.73.3		18	27.25	even	9	inner
324.2.i.a.253.3		18	1.1	even	1	trivial
432.2.u.d.241.1		18	108.83	even	18
432.2.u.d.337.1		18	12.11	even	2
972.2.i.a.109.3		18	9.2	odd	6
972.2.i.a.865.3		18	27.20	odd	18
972.2.i.b.433.3		18	9.4	even	3
972.2.i.b.541.3		18	27.16	even	9
972.2.i.c.433.1		18	9.5	odd	6
972.2.i.c.541.1		18	27.11	odd	18
972.2.i.d.109.1		18	9.7	even	3
972.2.i.d.865.1		18	27.7	even	9
2916.2.a.c.1.7		9	27.22	even	9
2916.2.a.d.1.3		9	27.5	odd	18
2916.2.e.c.973.7		18	27.14	odd	18
2916.2.e.c.1945.7		18	27.23	odd	18
2916.2.e.d.973.3		18	27.13	even	9
2916.2.e.d.1945.3		18	27.4	even	9

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.i (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.761786 + 0.639214i) q^{5} +(1.35240 + 0.492232i) q^{7} +O(q^{10})\)	\(q+(0.761786 + 0.639214i) q^{5} +(1.35240 + 0.492232i) q^{7} +(2.56436 - 2.15175i) q^{11} +(-0.337662 + 1.91498i) q^{13} +(-1.16107 + 2.01104i) q^{17} +(3.38586 + 5.86448i) q^{19} +(8.41184 - 3.06166i) q^{23} +(-0.696518 - 3.95015i) q^{25} +(-0.847007 - 4.80362i) q^{29} +(-5.81772 + 2.11748i) q^{31} +(0.715594 + 1.23944i) q^{35} +(-0.0829061 + 0.143598i) q^{37} +(-1.87304 + 10.6225i) q^{41} +(6.82940 - 5.73054i) q^{43} +(-6.14677 - 2.23724i) q^{47} +(-3.77563 - 3.16813i) q^{49} -10.7235 q^{53} +3.32892 q^{55} +(-3.02292 - 2.53653i) q^{59} +(-7.91547 - 2.88100i) q^{61} +(-1.48131 + 1.24296i) q^{65} +(-0.00383180 + 0.0217312i) q^{67} +(-4.53728 + 7.85879i) q^{71} +(-2.26572 - 3.92434i) q^{73} +(4.52718 - 1.64776i) q^{77} +(-1.00608 - 5.70576i) q^{79} +(-0.898927 - 5.09807i) q^{83} +(-2.16997 + 0.789806i) q^{85} +(-1.91749 - 3.32118i) q^{89} +(-1.39926 + 2.42360i) q^{91} +(-1.16936 + 6.63176i) q^{95} +(-5.40914 + 4.53881i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 3 q^{5}+O(q^{10}) \) 18 * q - 3 * q^5	\( 18 q - 3 q^{5} - 3 q^{11} + 12 q^{17} + 30 q^{23} + 9 q^{25} + 24 q^{29} + 9 q^{31} + 21 q^{35} - 21 q^{41} - 9 q^{43} - 45 q^{47} - 18 q^{49} - 66 q^{53} - 60 q^{59} - 18 q^{61} - 33 q^{65} - 27 q^{67} + 12 q^{71} + 9 q^{73} + 75 q^{77} - 36 q^{79} + 45 q^{83} - 36 q^{85} + 48 q^{89} + 9 q^{91} - 6 q^{95} - 27 q^{97}+O(q^{100}) \) 18 * q - 3 * q^5 - 3 * q^11 + 12 * q^17 + 30 * q^23 + 9 * q^25 + 24 * q^29 + 9 * q^31 + 21 * q^35 - 21 * q^41 - 9 * q^43 - 45 * q^47 - 18 * q^49 - 66 * q^53 - 60 * q^59 - 18 * q^61 - 33 * q^65 - 27 * q^67 + 12 * q^71 + 9 * q^73 + 75 * q^77 - 36 * q^79 + 45 * q^83 - 36 * q^85 + 48 * q^89 + 9 * q^91 - 6 * q^95 - 27 * q^97

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