LMFDB - Embedded newform 912.2.cc.c.545.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(257,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 9, 17]))

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

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

chi := DirichletCharacter("912.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.cc (of order $18$, 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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{18})$
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} - x^{15} - 18 x^{14} + 36 x^{13} + 10 x^{12} + 18 x^{11} + 90 x^{10} - 567 x^{9} + 270 x^{8} + \cdots + 19683 $ x^18 - x^15 - 18x^14 + 36x^13 + 10x^12 + 18x^11 + 90x^10 - 567x^9 + 270x^8 + 162x^7 + 270x^6 + 2916x^5 - 4374x^4 - 729x^3 + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			545.1
Root			$-0.442647 - 1.67453i$ of defining polynomial
Character	$\chi$	$=$	912.545
Dual form			912.2.cc.c.497.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.57223 - 0.726702i) q^{3} +(-1.96615 + 0.346685i) q^{5} +(-0.910931 + 1.57778i) q^{7} +(1.94381 + 2.28508i) q^{9} +O(q^{10})$	\(q+(-1.57223 - 0.726702i) q^{3} +(-1.96615 + 0.346685i) q^{5} +(-0.910931 + 1.57778i) q^{7} +(1.94381 + 2.28508i) q^{9} +(4.10844 - 2.37201i) q^{11} +(0.151321 + 0.415752i) q^{13} +(3.34317 + 0.883735i) q^{15} +(-1.07476 - 1.28085i) q^{17} +(3.58212 + 2.48363i) q^{19} +(2.57877 - 1.81865i) q^{21} +(-5.93571 - 1.04663i) q^{23} +(-0.952914 + 0.346832i) q^{25} +(-1.39554 - 5.00524i) q^{27} +(-4.91935 - 4.12783i) q^{29} +(-4.88683 - 2.82141i) q^{31} +(-8.18314 + 0.743731i) q^{33} +(1.24403 - 3.41795i) q^{35} -5.80180i q^{37} +(0.0642158 - 0.763624i) q^{39} +(3.75563 + 1.36694i) q^{41} +(-2.15807 - 12.2390i) q^{43} +(-4.61402 - 3.81892i) q^{45} +(-6.92588 + 8.25394i) q^{47} +(1.84041 + 3.18768i) q^{49} +(0.758974 + 2.79482i) q^{51} +(0.424873 - 2.40957i) q^{53} +(-7.25545 + 6.08805i) q^{55} +(-3.82705 - 6.50797i) q^{57} +(-3.87172 + 3.24876i) q^{59} +(1.80210 - 10.2202i) q^{61} +(-5.37603 + 0.985349i) q^{63} +(-0.441656 - 0.764970i) q^{65} +(-5.27060 + 6.28126i) q^{67} +(8.57172 + 5.95903i) q^{69} +(-0.897109 - 5.08776i) q^{71} +(-13.5869 - 4.94524i) q^{73} +(1.75024 + 0.147184i) q^{75} +8.64294i q^{77} +(3.23544 - 8.88931i) q^{79} +(-1.44321 + 8.88353i) q^{81} +(0.523324 + 0.302141i) q^{83} +(2.55719 + 2.14574i) q^{85} +(4.73465 + 10.0648i) q^{87} +(4.07161 - 1.48195i) q^{89} +(-0.793809 - 0.139970i) q^{91} +(5.63289 + 7.98717i) q^{93} +(-7.90401 - 3.64132i) q^{95} +(1.64505 + 1.96049i) q^{97} +(13.4062 + 4.77739i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 3 q^{3} - 3 q^{9}+O(q^{10}) $ 18 * q - 3 * q^3 - 3 * q^9	$ 18 q - 3 q^{3} - 3 q^{9} - 12 q^{13} - 18 q^{15} + 6 q^{17} + 6 q^{19} - 18 q^{25} + 6 q^{27} - 6 q^{29} - 24 q^{33} + 24 q^{35} - 6 q^{39} + 3 q^{41} + 6 q^{43} - 54 q^{45} - 30 q^{47} + 21 q^{49} - 42 q^{51} - 60 q^{53} - 30 q^{55} + 12 q^{57} - 3 q^{59} + 54 q^{61} + 18 q^{63} + 24 q^{65} + 15 q^{67} + 30 q^{69} - 36 q^{71} - 42 q^{73} + 6 q^{79} - 3 q^{81} - 36 q^{83} - 60 q^{89} + 18 q^{91} - 66 q^{93} - 6 q^{95} + 9 q^{97} + 102 q^{99}+O(q^{100}) $ 18 * q - 3 * q^3 - 3 * q^9 - 12 * q^13 - 18 * q^15 + 6 * q^17 + 6 * q^19 - 18 * q^25 + 6 * q^27 - 6 * q^29 - 24 * q^33 + 24 * q^35 - 6 * q^39 + 3 * q^41 + 6 * q^43 - 54 * q^45 - 30 * q^47 + 21 * q^49 - 42 * q^51 - 60 * q^53 - 30 * q^55 + 12 * q^57 - 3 * q^59 + 54 * q^61 + 18 * q^63 + 24 * q^65 + 15 * q^67 + 30 * q^69 - 36 * q^71 - 42 * q^73 + 6 * q^79 - 3 * q^81 - 36 * q^83 - 60 * q^89 + 18 * q^91 - 66 * q^93 - 6 * q^95 + 9 * q^97 + 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$	$-1$	$1$

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
$3$	−1.57223	−	0.726702i	−0.907727	−	0.419561i
$3$	−1.57223	−	0.726702i	−0.907727	−	0.419561i
$4$		0			0
$5$	−1.96615	+	0.346685i	−0.879288	+	0.155042i	−0.595028	−	0.803705i	$-0.702859\pi$
$5$	−1.96615	+	0.346685i	−0.879288	+	0.155042i	−0.284260	+	0.958747i	$0.591748\pi$
$6$		0			0
$7$	−0.910931	+	1.57778i	−0.344300	+	0.596344i	−0.985226	−	0.171258i	$-0.945217\pi$
$7$	−0.910931	+	1.57778i	−0.344300	+	0.596344i	0.640927	+	0.767602i	$0.278550\pi$
$8$		0			0
$9$	1.94381	+	2.28508i	0.647937	+	0.761694i
$10$		0			0
$11$	4.10844	−	2.37201i	1.23874	−	0.715187i	0.269903	−	0.962887i	$-0.413008\pi$
$11$	4.10844	−	2.37201i	1.23874	−	0.715187i	0.968837	+	0.247701i	$0.0796749\pi$
$12$		0			0
$13$	0.151321	+	0.415752i	0.0419690	+	0.115309i	0.958907	−	0.283721i	$-0.0915691\pi$
$13$	0.151321	+	0.415752i	0.0419690	+	0.115309i	−0.916938	+	0.399030i	$0.869347\pi$
$14$		0			0
$15$	3.34317	+	0.883735i	0.863203	+	0.228179i
$16$		0			0
$17$	−1.07476	−	1.28085i	−0.260668	−	0.310652i	0.619798	−	0.784761i	$-0.287214\pi$
$17$	−1.07476	−	1.28085i	−0.260668	−	0.310652i	−0.880466	+	0.474110i	$0.842770\pi$
$18$		0			0
$19$	3.58212	+	2.48363i	0.821794	+	0.569785i
$19$	3.58212	+	2.48363i	0.821794	+	0.569785i
$20$		0			0
$21$	2.57877	−	1.81865i	0.562733	−	0.396863i
$22$		0			0
$23$	−5.93571	−	1.04663i	−1.23768	−	0.218237i	−0.483760	−	0.875201i	$-0.660729\pi$
$23$	−5.93571	−	1.04663i	−1.23768	−	0.218237i	−0.753922	+	0.656964i	$0.771840\pi$
$24$		0			0
$25$	−0.952914	+	0.346832i	−0.190583	+	0.0693665i
$26$		0			0
$27$	−1.39554	−	5.00524i	−0.268572	−	0.963260i
$28$		0			0
$29$	−4.91935	−	4.12783i	−0.913501	−	0.766518i	0.0592808	−	0.998241i	$-0.481119\pi$
$29$	−4.91935	−	4.12783i	−0.913501	−	0.766518i	−0.972782	+	0.231723i	$0.925564\pi$
$30$		0			0
$31$	−4.88683	−	2.82141i	−0.877700	−	0.506741i	−0.00780088	−	0.999970i	$-0.502483\pi$
$31$	−4.88683	−	2.82141i	−0.877700	−	0.506741i	−0.869899	+	0.493229i	$0.835816\pi$
$32$		0			0
$33$	−8.18314	+	0.743731i	−1.42450	+	0.129467i
$34$		0			0
$35$	1.24403	−	3.41795i	0.210280	−	0.577740i
$36$		0			0
$37$		−	5.80180i		−	0.953811i	−0.878955	−	0.476905i	$-0.841758\pi$
$37$		−	5.80180i		−	0.953811i	0.878955	−	0.476905i	$-0.158242\pi$
$38$		0			0
$39$	0.0642158	−	0.763624i	0.0102828	−	0.122278i
$40$		0			0
$41$	3.75563	+	1.36694i	0.586530	+	0.213480i	0.618203	−	0.786019i	$-0.287861\pi$
$41$	3.75563	+	1.36694i	0.586530	+	0.213480i	−0.0316723	+	0.999498i	$0.510083\pi$
$42$		0			0
$43$	−2.15807	−	12.2390i	−0.329102	−	1.86643i	−0.479125	−	0.877747i	$-0.659046\pi$
$43$	−2.15807	−	12.2390i	−0.329102	−	1.86643i	0.150023	−	0.988683i	$-0.452065\pi$
$44$		0			0
$45$	−4.61402	−	3.81892i	−0.687818	−	0.569291i
$46$		0			0
$47$	−6.92588	+	8.25394i	−1.01024	+	1.20396i	−0.0313665	+	0.999508i	$0.509986\pi$
$47$	−6.92588	+	8.25394i	−1.01024	+	1.20396i	−0.978876	+	0.204453i	$0.934459\pi$
$48$		0			0
$49$	1.84041	+	3.18768i	0.262916	+	0.455383i
$50$		0			0
$51$	0.758974	+	2.79482i	0.106278	+	0.391353i
$52$		0			0
$53$	0.424873	−	2.40957i	0.0583608	−	0.330981i	−0.941623	−	0.336669i	$-0.890700\pi$
$53$	0.424873	−	2.40957i	0.0583608	−	0.330981i	0.999984	+	0.00568857i	$0.00181074\pi$
$54$		0			0
$55$	−7.25545	+	6.08805i	−0.978325	+	0.820912i
$56$		0			0
$57$	−3.82705	−	6.50797i	−0.506905	−	0.862002i
$58$		0			0
$59$	−3.87172	+	3.24876i	−0.504055	+	0.422952i	−0.859031	−	0.511923i	$-0.828933\pi$
$59$	−3.87172	+	3.24876i	−0.504055	+	0.422952i	0.354977	+	0.934875i	$0.384489\pi$
$60$		0			0
$61$	1.80210	−	10.2202i	0.230735	−	1.30856i	−0.620677	−	0.784067i	$-0.713142\pi$
$61$	1.80210	−	10.2202i	0.230735	−	1.30856i	0.851412	−	0.524498i	$-0.175747\pi$
$62$		0			0
$63$	−5.37603	+	0.985349i	−0.677316	+	0.124142i
$64$		0			0
$65$	−0.441656	−	0.764970i	−0.0547806	−	0.0948828i
$66$		0			0
$67$	−5.27060	+	6.28126i	−0.643906	+	0.767378i	−0.984982	−	0.172658i	$-0.944764\pi$
$67$	−5.27060	+	6.28126i	−0.643906	+	0.767378i	0.341075	+	0.940036i	$0.389209\pi$
$68$		0			0
$69$	8.57172	+	5.95903i	1.03191	+	0.717383i
$70$		0			0
$71$	−0.897109	−	5.08776i	−0.106467	−	0.603806i	−0.990624	−	0.136616i	$-0.956377\pi$
$71$	−0.897109	−	5.08776i	−0.106467	−	0.603806i	0.884157	−	0.467190i	$-0.154734\pi$
$72$		0			0
$73$	−13.5869	−	4.94524i	−1.59023	−	0.578796i	−0.612834	−	0.790212i	$-0.709971\pi$
$73$	−13.5869	−	4.94524i	−1.59023	−	0.578796i	−0.977396	+	0.211415i	$0.932193\pi$
$74$		0			0
$75$	1.75024	+	0.147184i	0.202101	+	0.0169954i
$76$		0			0
$77$			8.64294i			0.984954i
$78$		0			0
$79$	3.23544	−	8.88931i	0.364016	−	1.00013i	−0.613580	−	0.789633i	$-0.710271\pi$
$79$	3.23544	−	8.88931i	0.364016	−	1.00013i	0.977595	−	0.210493i	$-0.0675068\pi$
$80$		0			0
$81$	−1.44321	+	8.88353i	−0.160356	+	0.987059i
$82$		0			0
$83$	0.523324	+	0.302141i	0.0574423	+	0.0331643i	0.528446	−	0.848967i	$-0.322775\pi$
$83$	0.523324	+	0.302141i	0.0574423	+	0.0331643i	−0.471004	+	0.882131i	$0.656108\pi$
$84$		0			0
$85$	2.55719	+	2.14574i	0.277366	+	0.232738i
$86$		0			0
$87$	4.73465	+	10.0648i	0.507608	+	1.07906i
$88$		0			0
$89$	4.07161	−	1.48195i	0.431590	−	0.157086i	−0.117084	−	0.993122i	$-0.537355\pi$
$89$	4.07161	−	1.48195i	0.431590	−	0.157086i	0.548675	+	0.836036i	$0.315133\pi$
$90$		0			0
$91$	−0.793809	−	0.139970i	−0.0832137	−	0.0146728i
$92$		0			0
$93$	5.63289	+	7.98717i	0.584104	+	0.828231i
$94$		0			0
$95$	−7.90401	−	3.64132i	−0.810935	−	0.373592i
$96$		0			0
$97$	1.64505	+	1.96049i	0.167029	+	0.199057i	0.843066	−	0.537810i	$-0.180748\pi$
$97$	1.64505	+	1.96049i	0.167029	+	0.199057i	−0.676037	+	0.736868i	$0.736304\pi$
$98$		0			0
$99$	13.4062	+	4.77739i	1.34738	+	0.480145i
$100$		0			0
$101$	−2.72562	−	7.48859i	−0.271210	−	0.745142i	−0.998283	−	0.0585821i	$-0.981342\pi$
$101$	−2.72562	−	7.48859i	−0.271210	−	0.745142i	0.727073	−	0.686560i	$-0.240880\pi$
$102$		0			0
$103$	13.3041	−	7.68115i	1.31090	−	0.756846i	0.328651	−	0.944451i	$-0.393406\pi$
$103$	13.3041	−	7.68115i	1.31090	−	0.756846i	0.982245	+	0.187605i	$0.0600725\pi$
$104$		0			0
$105$	−4.43974	+	4.46977i	−0.433274	+	0.436204i
$106$		0			0
$107$	9.34857	−	16.1922i	0.903760	−	1.56536i	0.0811876	−	0.996699i	$-0.474129\pi$
$107$	9.34857	−	16.1922i	0.903760	−	1.56536i	0.822573	−	0.568660i	$-0.192538\pi$
$108$		0			0
$109$	−11.2420	+	1.98227i	−1.07679	+	0.189867i	−0.683795	−	0.729674i	$-0.739672\pi$
$109$	−11.2420	+	1.98227i	−1.07679	+	0.189867i	−0.392994	+	0.919541i	$0.628561\pi$
$110$		0			0
$111$	−4.21618	+	9.12177i	−0.400182	+	0.865800i
$112$		0			0
$113$	−0.594179			−0.0558957			−0.0279478	−	0.999609i	$-0.508897\pi$
$113$	−0.594179			−0.0558957			−0.0279478	+	0.999609i	$0.508897\pi$
$114$		0			0
$115$	12.0333			1.12212
$116$		0			0
$117$	−0.655888	+	1.15393i	−0.0606369	+	0.106680i
$118$		0			0
$119$	2.99993	−	0.528968i	0.275003	−	0.0484905i
$120$		0			0
$121$	5.75283	−	9.96419i	0.522984	−	0.905835i
$122$		0			0
$123$	−4.91135	−	4.87836i	−0.442842	−	0.439867i
$124$		0			0
$125$	10.3983	−	6.00348i	0.930056	−	0.536968i
$126$		0			0
$127$	−4.51501	−	12.4049i	−0.400642	−	1.10076i	−0.961968	−	0.273161i	$-0.911931\pi$
$127$	−4.51501	−	12.4049i	−0.400642	−	1.10076i	0.561326	−	0.827595i	$-0.310291\pi$
$128$		0			0
$129$	−5.50112	+	20.8108i	−0.484347	+	1.83229i
$130$		0			0
$131$	4.54726	+	5.41921i	0.397296	+	0.473479i	0.927193	−	0.374583i	$-0.122214\pi$
$131$	4.54726	+	5.41921i	0.397296	+	0.473479i	−0.529898	+	0.848062i	$0.677770\pi$
$132$		0			0
$133$	−7.18169	+	3.38937i	−0.622731	+	0.293896i
$134$		0			0
$135$	4.47908	+	9.35724i	0.385498	+	0.805343i
$136$		0			0
$137$	−9.23589	−	1.62854i	−0.789075	−	0.139135i	−0.235434	−	0.971890i	$-0.575651\pi$
$137$	−9.23589	−	1.62854i	−0.789075	−	0.139135i	−0.553641	+	0.832755i	$0.686762\pi$
$138$		0			0
$139$	−10.1792	+	3.70494i	−0.863392	+	0.314249i	−0.735488	−	0.677538i	$-0.763047\pi$
$139$	−10.1792	+	3.70494i	−0.863392	+	0.314249i	−0.127904	+	0.991787i	$0.540825\pi$
$140$		0			0
$141$	16.8872	−	7.94404i	1.42216	−	0.669009i
$142$		0			0
$143$	1.60786	+	1.34916i	0.134456	+	0.112822i
$144$		0			0
$145$	11.1032	+	6.41046i	0.922074	+	0.532359i
$146$		0			0
$147$	−0.577052	−	6.34920i	−0.0475944	−	0.523673i
$148$		0			0
$149$	−3.85231	+	10.5841i	−0.315594	+	0.867086i	0.675907	+	0.736987i	$0.263752\pi$
$149$	−3.85231	+	10.5841i	−0.315594	+	0.867086i	−0.991501	+	0.130100i	$0.958470\pi$
$150$		0			0
$151$			3.54669i			0.288625i	0.989532	+	0.144313i	$0.0460971\pi$
$151$			3.54669i			0.288625i	−0.989532	+	0.144313i	$0.953903\pi$
$152$		0			0
$153$	0.837717	−	4.94564i	0.0677254	−	0.399832i
$154$		0			0
$155$	10.5864	+	3.85312i	0.850318	+	0.309490i
$156$		0			0
$157$	−0.0548481	−	0.311059i	−0.00437736	−	0.0248252i	0.982541	−	0.186047i	$-0.0595677\pi$
$157$	−0.0548481	−	0.311059i	−0.00437736	−	0.0248252i	−0.986918	+	0.161222i	$0.948457\pi$
$158$		0			0
$159$	−2.41904	+	3.47965i	−0.191842	+	0.275954i
$160$		0			0
$161$	7.05837	−	8.41184i	0.556277	−	0.662946i
$162$		0			0
$163$	−0.624535	−	1.08173i	−0.0489174	−	0.0847274i	0.840530	−	0.541765i	$-0.182244\pi$
$163$	−0.624535	−	1.08173i	−0.0489174	−	0.0847274i	−0.889447	+	0.457038i	$0.848910\pi$
$164$		0			0
$165$	15.8314	−	4.29926i	1.23248	−	0.334697i
$166$		0			0
$167$	−0.177553	+	1.00695i	−0.0137395	+	0.0779205i	−0.990907	−	0.134552i	$-0.957040\pi$
$167$	−0.177553	+	1.00695i	−0.0137395	+	0.0779205i	0.977167	+	0.212472i	$0.0681516\pi$
$168$		0			0
$169$	9.80863	−	8.23041i	0.754510	−	0.633109i
$170$		0			0
$171$	1.28765	+	13.0131i	0.0984689	+	0.995140i
$172$		0			0
$173$	−11.5762	+	9.71361i	−0.880124	+	0.738512i	−0.966205	−	0.257776i	$-0.917010\pi$
$173$	−11.5762	+	9.71361i	−0.880124	+	0.738512i	0.0860802	+	0.996288i	$0.472566\pi$
$174$		0			0
$175$	0.320814	−	1.81943i	0.0242513	−	0.137536i
$176$		0			0
$177$	8.44811	−	2.29421i	0.634998	−	0.172443i
$178$		0			0
$179$	−2.97218	−	5.14797i	−0.222151	−	0.384777i	0.733310	−	0.679895i	$-0.237974\pi$
$179$	−2.97218	−	5.14797i	−0.222151	−	0.384777i	−0.955461	+	0.295118i	$0.904641\pi$
$180$		0			0
$181$	−4.17230	+	4.97236i	−0.310125	+	0.369593i	−0.898483	−	0.439008i	$-0.855330\pi$
$181$	−4.17230	+	4.97236i	−0.310125	+	0.369593i	0.588358	+	0.808600i	$0.299774\pi$
$182$		0			0
$183$	−10.2604	+	14.7589i	−0.758468	+	1.09101i
$184$		0			0
$185$	2.01140	+	11.4072i	0.147881	+	0.838675i
$186$		0			0
$187$	−7.45377	−	2.71295i	−0.545073	−	0.198390i
$188$		0			0
$189$	9.16841	+	2.35758i	0.666904	+	0.171488i
$190$		0			0
$191$			23.8639i			1.72673i	0.504577	+	0.863367i	$0.331648\pi$
$191$			23.8639i			1.72673i	−0.504577	+	0.863367i	$0.668352\pi$
$192$		0			0
$193$	−0.726280	+	1.99544i	−0.0522788	+	0.143635i	−0.963084	−	0.269202i	$-0.913240\pi$
$193$	−0.726280	+	1.99544i	−0.0522788	+	0.143635i	0.910805	+	0.412837i	$0.135462\pi$
$194$		0			0
$195$	0.138479	+	1.52366i	0.00991669	+	0.109112i
$196$		0			0
$197$	3.27574	+	1.89125i	0.233387	+	0.134746i	0.612133	−	0.790755i	$-0.290312\pi$
$197$	3.27574	+	1.89125i	0.233387	+	0.134746i	−0.378747	+	0.925500i	$0.623645\pi$
$198$		0			0
$199$	10.5692	+	8.86860i	0.749230	+	0.628679i	0.935299	−	0.353858i	$-0.115130\pi$
$199$	10.5692	+	8.86860i	0.749230	+	0.628679i	−0.186069	+	0.982537i	$0.559575\pi$
$200$		0			0
$201$	12.8512	−	6.04542i	0.906453	−	0.426411i
$202$		0			0
$203$	10.9940	−	4.00149i	0.771627	−	0.280849i
$204$		0			0
$205$	−7.85802	−	1.38558i	−0.548828	−	0.0967731i
$206$		0			0
$207$	−9.14627	−	15.5980i	−0.635710	−	1.08414i
$208$		0			0
$209$	20.6081	+	1.70704i	1.42549	+	0.118078i
$210$		0			0
$211$	−10.3613	−	12.3481i	−0.713299	−	0.850077i	0.280662	−	0.959807i	$-0.409446\pi$
$211$	−10.3613	−	12.3481i	−0.713299	−	0.850077i	−0.993961	+	0.109730i	$0.965002\pi$
$212$		0			0
$213$	−2.28682	+	8.65106i	−0.156690	+	0.592761i
$214$		0			0
$215$	8.48615	+	23.3155i	0.578751	+	1.59010i
$216$		0			0
$217$	8.90313	−	5.14022i	0.604384	−	0.348941i
$218$		0			0
$219$	17.7681	+	17.6487i	1.20065	+	1.19259i
$220$		0			0
$221$	0.369882	−	0.640654i	0.0248809	−	0.0430951i
$222$		0			0
$223$	−1.05803	+	0.186559i	−0.0708508	+	0.0124929i	−0.208961	−	0.977924i	$-0.567008\pi$
$223$	−1.05803	+	0.186559i	−0.0708508	+	0.0124929i	0.138110	+	0.990417i	$0.455897\pi$
$224$		0			0
$225$	−2.64482	−	1.50331i	−0.176322	−	0.100221i
$226$		0			0
$227$	18.7633			1.24536			0.622682	−	0.782475i	$-0.286043\pi$
$227$	18.7633			1.24536			0.622682	+	0.782475i	$0.286043\pi$
$228$		0			0
$229$	−11.6264			−0.768296			−0.384148	−	0.923271i	$-0.625505\pi$
$229$	−11.6264			−0.768296			−0.384148	+	0.923271i	$0.625505\pi$
$230$		0			0
$231$	6.28083	−	13.5887i	0.413249	−	0.894069i
$232$		0			0
$233$	−16.0133	+	2.82357i	−1.04907	+	0.184979i	−0.671500	−	0.741004i	$-0.734350\pi$
$233$	−16.0133	+	2.82357i	−1.04907	+	0.184979i	−0.377565	+	0.925983i	$0.623239\pi$
$234$		0			0
$235$	10.7558	−	18.6296i	0.701630	−	1.21526i
$236$		0			0
$237$	−11.5467	+	11.6248i	−0.750041	+	0.755114i
$238$		0			0
$239$	−5.90043	+	3.40661i	−0.381667	+	0.220356i	−0.678543	−	0.734560i	$-0.737388\pi$
$239$	−5.90043	+	3.40661i	−0.381667	+	0.220356i	0.296876	+	0.954916i	$0.404055\pi$
$240$		0			0
$241$	−6.63839	−	18.2388i	−0.427616	−	1.17487i	−0.947255	−	0.320480i	$-0.896156\pi$
$241$	−6.63839	−	18.2388i	−0.427616	−	1.17487i	0.519639	−	0.854386i	$-0.326066\pi$
$242$		0			0
$243$	8.72473	−	12.9182i	0.559692	−	0.828701i
$244$		0			0
$245$	−4.72364	−	5.62942i	−0.301782	−	0.359650i
$246$		0			0
$247$	−0.490525	+	1.86510i	−0.0312114	+	0.118674i
$248$		0			0
$249$	−0.603219	−	0.855336i	−0.0382274	−	0.0542047i
$250$		0			0
$251$	−16.8226	−	2.96628i	−1.06183	−	0.187230i	−0.384664	−	0.923057i	$-0.625683\pi$
$251$	−16.8226	−	2.96628i	−1.06183	−	0.187230i	−0.677170	+	0.735827i	$0.736794\pi$
$252$		0			0
$253$	−26.8691	+	9.77955i	−1.68925	+	0.614835i
$254$		0			0
$255$	−2.46118	−	5.23190i	−0.154125	−	0.327635i
$256$		0			0
$257$	12.1113	+	10.1626i	0.755485	+	0.633927i	0.936947	−	0.349471i	$-0.113639\pi$
$257$	12.1113	+	10.1626i	0.755485	+	0.633927i	−0.181462	+	0.983398i	$0.558083\pi$
$258$		0			0
$259$	9.15396	+	5.28504i	0.568800	+	0.328397i
$260$		0			0
$261$	−0.129859	−	19.2648i	−0.00803808	−	1.19246i
$262$		0			0
$263$	−0.888930	+	2.44232i	−0.0548138	+	0.150600i	−0.964078	−	0.265620i	$-0.914423\pi$
$263$	−0.888930	+	2.44232i	−0.0548138	+	0.150600i	0.909264	+	0.416220i	$0.136645\pi$
$264$		0			0
$265$			4.88488i			0.300076i
$266$		0			0
$267$	−7.47844	−	0.628889i	−0.457673	−	0.0384874i
$268$		0			0
$269$	29.9875	+	10.9146i	1.82837	+	0.665473i	0.993333	+	0.115281i	$0.0367769\pi$
$269$	29.9875	+	10.9146i	1.82837	+	0.665473i	0.835039	+	0.550191i	$0.185445\pi$
$270$		0			0
$271$	3.48942	+	19.7895i	0.211967	+	1.20212i	0.886093	+	0.463508i	$0.153410\pi$
$271$	3.48942	+	19.7895i	0.211967	+	1.20212i	−0.674126	+	0.738617i	$0.735479\pi$
$272$		0			0
$273$	1.14633	+	0.796927i	0.0693792	+	0.0482322i
$274$		0			0
$275$	−3.09230	+	3.68526i	−0.186473	+	0.222229i
$276$		0			0
$277$	4.04017	+	6.99778i	0.242750	+	0.420456i	0.961497	−	0.274816i	$-0.0886171\pi$
$277$	4.04017	+	6.99778i	0.242750	+	0.420456i	−0.718746	+	0.695272i	$0.755284\pi$
$278$		0			0
$279$	−3.05191	−	16.6511i	−0.182713	−	0.996875i
$280$		0			0
$281$	2.05091	−	11.6313i	0.122347	−	0.693866i	−0.860501	−	0.509449i	$-0.829849\pi$
$281$	2.05091	−	11.6313i	0.122347	−	0.693866i	0.982848	−	0.184417i	$-0.0590396\pi$
$282$		0			0
$283$	−11.0055	+	9.23472i	−0.654210	+	0.548947i	−0.908345	−	0.418221i	$-0.862654\pi$
$283$	−11.0055	+	9.23472i	−0.654210	+	0.548947i	0.254135	+	0.967169i	$0.418209\pi$
$284$		0			0
$285$	9.78076	+	11.4689i	0.579363	+	0.679356i
$286$		0			0
$287$	−5.57784	+	4.68036i	−0.329249	+	0.276273i
$288$		0			0
$289$	2.46655	−	13.9885i	0.145091	−	0.822854i
$290$		0			0
$291$	−1.16170	−	4.27779i	−0.0681000	−	0.250769i
$292$		0			0
$293$	−0.00324263	−	0.00561639i	−0.000189436	−	0.000328113i	0.865931	−	0.500164i	$-0.166727\pi$
$293$	−0.00324263	−	0.00561639i	−0.000189436	−	0.000328113i	−0.866120	+	0.499836i	$0.833394\pi$
$294$		0			0
$295$	6.48608	−	7.72981i	0.377634	−	0.450047i
$296$		0			0
$297$	−17.6060	−	17.2535i	−1.02160	−	1.00115i
$298$		0			0
$299$	−0.463063	−	2.62616i	−0.0267797	−	0.151875i
$300$		0			0
$301$	21.2763	+	7.74393i	1.22634	+	0.446353i
$302$		0			0
$303$	−1.15666	+	13.7545i	−0.0664486	+	0.790175i
$304$		0			0
$305$			20.7192i			1.18638i
$306$		0			0
$307$	−4.66013	+	12.8036i	−0.265968	+	0.730741i	0.732768	+	0.680478i	$0.238228\pi$
$307$	−4.66013	+	12.8036i	−0.265968	+	0.730741i	−0.998736	+	0.0502623i	$0.983994\pi$
$308$		0			0
$309$	−26.4991	+	2.40839i	−1.50748	+	0.137008i
$310$		0			0
$311$	−10.1422	−	5.85560i	−0.575111	−	0.332041i	0.184077	−	0.982912i	$-0.441070\pi$
$311$	−10.1422	−	5.85560i	−0.575111	−	0.332041i	−0.759188	+	0.650871i	$0.774404\pi$
$312$		0			0
$313$	1.34587	+	1.12932i	0.0760730	+	0.0638328i	0.680031	−	0.733183i	$-0.261966\pi$
$313$	1.34587	+	1.12932i	0.0760730	+	0.0638328i	−0.603958	+	0.797016i	$0.706411\pi$
$314$		0			0
$315$	10.2285	−	3.80113i	0.576309	−	0.214170i
$316$		0			0
$317$	−6.59148	+	2.39910i	−0.370214	+	0.134747i	−0.520426	−	0.853907i	$-0.674227\pi$
$317$	−6.59148	+	2.39910i	−0.370214	+	0.134747i	0.150211	+	0.988654i	$0.452005\pi$
$318$		0			0
$319$	−30.0021	−	5.29018i	−1.67979	−	0.296193i
$320$		0			0
$321$	−26.4650	+	18.6642i	−1.47713	+	1.04174i
$322$		0			0
$323$	−0.668758	−	7.25746i	−0.0372107	−	0.403816i
$324$		0			0
$325$	−0.288393	−	0.343693i	−0.0159971	−	0.0190647i
$326$		0			0
$327$	19.1155	+	5.05300i	1.05709	+	0.279431i
$328$		0			0
$329$	−6.71389	−	18.4463i	−0.370149	−	1.01698i
$330$		0			0
$331$	1.36720	−	0.789353i	0.0751481	−	0.0433868i	−0.461955	−	0.886903i	$-0.652852\pi$
$331$	1.36720	−	0.789353i	0.0751481	−	0.0433868i	0.537103	+	0.843517i	$0.319519\pi$
$332$		0			0
$333$	13.2576	−	11.2776i	0.726512	−	0.618009i
$334$		0			0
$335$	8.18517	−	14.1771i	0.447203	−	0.774579i
$336$		0			0
$337$	32.2083	−	5.67918i	1.75450	−	0.309365i	0.798336	−	0.602212i	$-0.205714\pi$
$337$	32.2083	−	5.67918i	1.75450	−	0.309365i	0.956159	+	0.292847i	$0.0946028\pi$
$338$		0			0
$339$	0.934186	+	0.431791i	0.0507380	+	0.0234517i
$340$		0			0
$341$	−26.7696			−1.44966
$342$		0			0
$343$	−19.4590			−1.05069
$344$		0			0
$345$	−18.9192	−	8.74465i	−1.01857	−	0.470796i
$346$		0			0
$347$	−2.28496	+	0.402900i	−0.122663	+	0.0216288i	−0.234643	−	0.972082i	$-0.575392\pi$
$347$	−2.28496	+	0.402900i	−0.122663	+	0.0216288i	0.111980	+	0.993711i	$0.464281\pi$
$348$		0			0
$349$	6.90604	−	11.9616i	0.369672	−	0.640291i	−0.619842	−	0.784727i	$-0.712803\pi$
$349$	6.90604	−	11.9616i	0.369672	−	0.640291i	0.989514	+	0.144436i	$0.0461367\pi$
$350$		0			0
$351$	1.86977	−	1.33760i	0.0998007	−	0.0713958i
$352$		0			0
$353$	−12.6233	+	7.28806i	−0.671870	+	0.387904i	−0.796785	−	0.604263i	$-0.793468\pi$
$353$	−12.6233	+	7.28806i	−0.671870	+	0.387904i	0.124915	+	0.992167i	$0.460134\pi$
$354$		0			0
$355$	3.52770	+	9.69228i	0.187231	+	0.514413i
$356$		0			0
$357$	−5.10098	−	1.34839i	−0.269972	−	0.0713645i
$358$		0			0
$359$	−12.4925	−	14.8880i	−0.659331	−	0.785760i	0.327959	−	0.944692i	$-0.393639\pi$
$359$	−12.4925	−	14.8880i	−0.659331	−	0.785760i	−0.987290	+	0.158932i	$0.949195\pi$
$360$		0			0
$361$	6.66313	+	17.7933i	0.350691	+	0.936491i
$362$		0			0
$363$	−16.2858	+	11.4854i	−0.854780	+	0.602827i
$364$		0			0
$365$	28.4284	+	5.01269i	1.48801	+	0.262376i
$366$		0			0
$367$	7.10474	−	2.58591i	0.370865	−	0.134984i	−0.149863	−	0.988707i	$-0.547883\pi$
$367$	7.10474	−	2.58591i	0.370865	−	0.134984i	0.520727	+	0.853723i	$0.325661\pi$
$368$		0			0
$369$	4.17666	+	11.2390i	0.217428	+	0.585078i
$370$		0			0
$371$	3.41475	+	2.86531i	0.177285	+	0.148760i
$372$		0			0
$373$	−5.00566	−	2.89002i	−0.259183	−	0.149640i	0.364779	−	0.931094i	$-0.381145\pi$
$373$	−5.00566	−	2.89002i	−0.259183	−	0.149640i	−0.623962	+	0.781455i	$0.714478\pi$
$374$		0			0
$375$	−20.7113	+	1.88236i	−1.06953	+	0.0972049i
$376$		0			0
$377$	0.971750	−	2.66986i	0.0500477	−	0.137505i
$378$		0			0
$379$		−	31.0884i		−	1.59690i	−0.602058	−	0.798452i	$-0.705653\pi$
$379$		−	31.0884i		−	1.59690i	0.602058	−	0.798452i	$-0.294347\pi$
$380$		0			0
$381$	−1.91602	+	22.7844i	−0.0981607	+	1.16728i
$382$		0			0
$383$	6.29971	+	2.29291i	0.321900	+	0.117162i	0.497916	−	0.867225i	$-0.334099\pi$
$383$	6.29971	+	2.29291i	0.321900	+	0.117162i	−0.176016	+	0.984387i	$0.556321\pi$
$384$		0			0
$385$	−2.99638	−	16.9933i	−0.152709	−	0.866058i
$386$		0			0
$387$	23.7722	−	28.7216i	1.20841	−	1.46000i
$388$		0			0
$389$	22.9366	−	27.3348i	1.16293	−	1.38593i	0.254933	−	0.966959i	$-0.417947\pi$
$389$	22.9366	−	27.3348i	1.16293	−	1.38593i	0.908000	−	0.418971i	$-0.137609\pi$
$390$		0			0
$391$	5.03890	+	8.72763i	0.254828	+	0.441375i
$392$		0			0
$393$	−3.21118	−	11.8247i	−0.161983	−	0.596479i
$394$		0			0
$395$	−3.27957	+	18.5994i	−0.165013	+	0.935837i
$396$		0			0
$397$	−23.1763	+	19.4472i	−1.16319	+	0.976029i	−0.999944	−	0.0105571i	$-0.996640\pi$
$397$	−23.1763	+	19.4472i	−1.16319	+	0.976029i	−0.163242	+	0.986586i	$0.552195\pi$
$398$		0			0
$399$	13.7543	−	0.109926i	0.688577	−	0.00550318i
$400$		0			0
$401$	−14.3394	+	12.0322i	−0.716074	+	0.600858i	−0.926296	−	0.376796i	$-0.877026\pi$
$401$	−14.3394	+	12.0322i	−0.716074	+	0.600858i	0.210222	+	0.977654i	$0.432581\pi$
$402$		0			0
$403$	0.433526	−	2.45865i	0.0215955	−	0.122474i
$404$		0			0
$405$	−0.242228	−	17.9667i	−0.0120364	−	0.892772i
$406$		0			0
$407$	−13.7619	−	23.8363i	−0.682153	−	1.18152i
$408$		0			0
$409$	−9.76955	+	11.6429i	−0.483073	+	0.575704i	−0.951442	−	0.307829i	$-0.900398\pi$
$409$	−9.76955	+	11.6429i	−0.483073	+	0.575704i	0.468369	+	0.883533i	$0.344842\pi$
$410$		0			0
$411$	13.3375	+	9.27216i	0.657889	+	0.457362i
$412$		0			0
$413$	−1.59895	−	9.06811i	−0.0786793	−	0.446212i
$414$		0			0
$415$	−1.13368	−	0.412626i	−0.0556502	−	0.0202550i
$416$		0			0
$417$	18.6965	+	1.57225i	0.915571	+	0.0769936i
$418$		0			0
$419$			6.74268i			0.329402i	0.986344	+	0.164701i	$0.0526659\pi$
$419$			6.74268i			0.329402i	−0.986344	+	0.164701i	$0.947334\pi$
$420$		0			0
$421$	5.11036	−	14.0406i	0.249064	−	0.684297i	−0.750658	−	0.660691i	$-0.770263\pi$
$421$	5.11036	−	14.0406i	0.249064	−	0.684297i	0.999721	−	0.0236056i	$-0.00751459\pi$
$422$		0			0
$423$	−32.3235	+	0.217884i	−1.57162	+	0.0105939i
$424$		0			0
$425$	1.46839	+	0.847778i	0.0712276	+	0.0411233i
$426$		0			0
$427$	14.4836	+	12.1532i	0.700913	+	0.588136i
$428$		0			0
$429$	−1.54749	−	3.28962i	−0.0747137	−	0.158824i
$430$		0			0
$431$	12.6508	−	4.60452i	0.609368	−	0.221792i	−0.0188586	−	0.999822i	$-0.506003\pi$
$431$	12.6508	−	4.60452i	0.609368	−	0.221792i	0.628227	+	0.778030i	$0.283781\pi$
$432$		0			0
$433$	16.6663	+	2.93872i	0.800933	+	0.141226i	0.559109	−	0.829094i	$-0.311143\pi$
$433$	16.6663	+	2.93872i	0.800933	+	0.141226i	0.241824	+	0.970320i	$0.422254\pi$
$434$		0			0
$435$	−12.7983	−	18.1474i	−0.613634	−	0.870103i
$436$		0			0
$437$	−18.6630	−	18.4913i	−0.892772	−	0.884558i
$438$		0			0
$439$	9.65722	+	11.5090i	0.460914	+	0.549296i	0.945574	−	0.325407i	$-0.105501\pi$
$439$	9.65722	+	11.5090i	0.460914	+	0.549296i	−0.484660	+	0.874702i	$0.661057\pi$
$440$		0			0
$441$	−3.70671	+	10.4017i	−0.176510	+	0.495321i
$442$		0			0
$443$	−12.6699	−	34.8103i	−0.601966	−	1.65389i	−0.747286	−	0.664503i	$-0.768643\pi$
$443$	−12.6699	−	34.8103i	−0.601966	−	1.65389i	0.145320	−	0.989385i	$-0.453579\pi$
$444$		0			0
$445$	−7.49163	+	4.32529i	−0.355137	+	0.205039i
$446$		0			0
$447$	13.7482	−	13.8412i	0.650269	−	0.654667i
$448$		0			0
$449$	−5.81501	+	10.0719i	−0.274427	+	0.475322i	−0.969991	−	0.243143i	$-0.921822\pi$
$449$	−5.81501	+	10.0719i	−0.274427	+	0.475322i	0.695563	+	0.718465i	$0.255155\pi$
$450$		0			0
$451$	18.6721	−	3.29240i	0.879236	−	0.155033i
$452$		0			0
$453$	2.57738	−	5.57621i	0.121096	−	0.261993i
$454$		0			0
$455$	1.60927			0.0754438
$456$		0			0
$457$	15.7379			0.736189			0.368094	−	0.929788i	$-0.380010\pi$
$457$	15.7379			0.736189			0.368094	+	0.929788i	$0.380010\pi$
$458$		0			0
$459$	−4.91109	+	7.16692i	−0.229230	+	0.334523i
$460$		0			0
$461$	−5.96078	+	1.05105i	−0.277621	+	0.0489521i	−0.310725	−	0.950500i	$-0.600572\pi$
$461$	−5.96078	+	1.05105i	−0.277621	+	0.0489521i	0.0331039	+	0.999452i	$0.489461\pi$
$462$		0			0
$463$	−4.59401	+	7.95705i	−0.213502	+	0.369796i	−0.952808	−	0.303574i	$-0.901820\pi$
$463$	−4.59401	+	7.95705i	−0.213502	+	0.369796i	0.739306	+	0.673369i	$0.235154\pi$
$464$		0			0
$465$	−13.8441	−	13.7511i	−0.642006	−	0.637693i
$466$		0			0
$467$	−0.179338	+	0.103541i	−0.00829879	+	0.00479131i	−0.504144	−	0.863620i	$-0.668192\pi$
$467$	−0.179338	+	0.103541i	−0.00829879	+	0.00479131i	0.495845	+	0.868411i	$0.334858\pi$
$468$		0			0
$469$	−5.10928	−	14.0376i	−0.235925	−	0.648198i
$470$		0			0
$471$	−0.139813	+	0.528915i	−0.00644226	+	0.0243711i
$472$		0			0
$473$	−37.8972	−	45.1642i	−1.74252	−	2.07665i
$474$		0			0
$475$	−4.27485	−	1.12429i	−0.196144	−	0.0515862i
$476$		0			0
$477$	6.33195	−	3.71288i	0.289920	−	0.170001i
$478$		0			0
$479$	−4.92232	−	0.867938i	−0.224907	−	0.0396571i	0.0600591	−	0.998195i	$-0.480871\pi$
$479$	−4.92232	−	0.867938i	−0.224907	−	0.0396571i	−0.284966	+	0.958538i	$0.591982\pi$
$480$		0			0
$481$	2.41211	−	0.877937i	0.109983	−	0.0400305i
$482$		0			0
$483$	−17.2103	+	8.09601i	−0.783094	+	0.368381i
$484$		0			0
$485$	−3.91408	−	3.28430i	−0.177729	−	0.149132i
$486$		0			0
$487$	23.4422	+	13.5344i	1.06227	+	0.613300i	0.926059	−	0.377380i	$-0.123175\pi$
$487$	23.4422	+	13.5344i	1.06227	+	0.613300i	0.136209	+	0.990680i	$0.456508\pi$
$488$		0			0
$489$	0.195820	+	2.15457i	0.00885529	+	0.0974332i
$490$		0			0
$491$	−2.14701	+	5.89886i	−0.0968931	+	0.266212i	−0.978664	−	0.205466i	$-0.934129\pi$
$491$	−2.14701	+	5.89886i	−0.0968931	+	0.266212i	0.881771	+	0.471677i	$0.156351\pi$
$492$		0			0
$493$			10.7374i			0.483587i
$494$		0			0
$495$	−28.0149	−	4.74531i	−1.25918	−	0.213286i
$496$		0			0
$497$	8.84457	+	3.21916i	0.396733	+	0.144399i
$498$		0			0
$499$	3.81949	+	21.6614i	0.170984	+	0.969699i	0.942678	+	0.333704i	$0.108299\pi$
$499$	3.81949	+	21.6614i	0.170984	+	0.969699i	−0.771694	+	0.635994i	$0.780590\pi$
$500$		0			0
$501$	1.01091	−	1.45414i	0.0451641	−	0.0649660i
$502$		0			0
$503$	6.51623	−	7.76574i	0.290544	−	0.346257i	−0.600952	−	0.799285i	$-0.705212\pi$
$503$	6.51623	−	7.76574i	0.290544	−	0.346257i	0.891496	+	0.453028i	$0.149656\pi$
$504$		0			0
$505$	7.95516	+	13.7787i	0.354000	+	0.613146i
$506$		0			0
$507$	−21.4025	+	5.81216i	−0.950517	+	0.258127i
$508$		0			0
$509$	−1.94826	+	11.0492i	−0.0863553	+	0.489745i	0.910701	+	0.413067i	$0.135543\pi$
$509$	−1.94826	+	11.0492i	−0.0863553	+	0.489745i	−0.997056	+	0.0766782i	$0.975569\pi$
$510$		0			0
$511$	20.1793	−	16.9324i	0.892678	−	0.749045i
$512$		0			0
$513$	7.43220	−	21.3954i	0.328139	−	0.944629i
$514$		0			0
$515$	−23.4950	+	19.7146i	−1.03531	+	0.868730i
$516$		0			0
$517$	−8.87612	+	50.3390i	−0.390371	+	2.21391i
$518$		0			0
$519$	25.2594	−	6.85956i	1.10876	−	0.301101i
$520$		0			0
$521$	−22.3984	−	38.7951i	−0.981290	−	1.69964i	−0.657386	−	0.753554i	$-0.728338\pi$
$521$	−22.3984	−	38.7951i	−0.981290	−	1.69964i	−0.323904	−	0.946090i	$-0.604995\pi$
$522$		0			0
$523$	−25.4174	+	30.2913i	−1.11143	+	1.32455i	−0.170721	+	0.985319i	$0.554610\pi$
$523$	−25.4174	+	30.2913i	−1.11143	+	1.32455i	−0.940705	+	0.339226i	$0.889835\pi$
$524$		0			0
$525$	−1.82657	+	2.62742i	−0.0797182	+	0.114670i
$526$		0			0
$527$	1.63837	+	9.29163i	0.0713683	+	0.404750i
$528$		0			0
$529$	12.5243	+	4.55849i	0.544536	+	0.198195i
$530$		0			0
$531$	−14.9496	−	2.53223i	−0.648756	−	0.109889i
$532$		0			0
$533$			1.76826i			0.0765917i
$534$		0			0
$535$	−12.7671	+	35.0773i	−0.551969	+	1.51652i
$536$		0			0
$537$	0.931913	+	10.2537i	0.0402150	+	0.442479i
$538$		0			0
$539$	15.1224	+	8.73093i	0.651368	+	0.376068i
$540$		0			0
$541$	9.00083	+	7.55259i	0.386976	+	0.324711i	0.815434	−	0.578850i	$-0.196499\pi$
$541$	9.00083	+	7.55259i	0.386976	+	0.324711i	−0.428458	+	0.903562i	$0.640943\pi$
$542$		0			0
$543$	10.1732	−	4.78567i	0.436576	−	0.205373i
$544$		0			0
$545$	21.4162	−	7.79487i	0.917370	−	0.333895i
$546$		0			0
$547$	−3.60851	−	0.636278i	−0.154289	−	0.0272053i	0.0959702	−	0.995384i	$-0.469405\pi$
$547$	−3.60851	−	0.636278i	−0.154289	−	0.0272053i	−0.250259	+	0.968179i	$0.580516\pi$
$548$		0			0
$549$	26.8570	−	15.7482i	1.14623	−	0.672117i
$550$		0			0
$551$	−7.36969	−	27.0042i	−0.313959	−	1.15042i
$552$		0			0
$553$	11.0781	+	13.2024i	0.471089	+	0.561422i
$554$		0			0
$555$	5.12726	−	19.3964i	0.217640	−	0.823333i
$556$		0			0
$557$	4.53013	+	12.4464i	0.191948	+	0.527372i	0.997912	−	0.0645925i	$-0.0205747\pi$
$557$	4.53013	+	12.4464i	0.191948	+	0.527372i	−0.805964	+	0.591965i	$0.798353\pi$
$558$		0			0
$559$	4.76183	−	2.74924i	0.201404	−	0.116281i
$560$		0			0
$561$	9.74752	+	9.68204i	0.411541	+	0.408776i
$562$		0			0
$563$	2.30395	−	3.99056i	0.0970999	−	0.168182i	−0.813383	−	0.581728i	$-0.802377\pi$
$563$	2.30395	−	3.99056i	0.0970999	−	0.168182i	0.910483	+	0.413546i	$0.135710\pi$
$564$		0			0
$565$	1.16824	−	0.205993i	0.0491484	−	0.00866619i
$566$		0			0
$567$	−12.7016	−	10.3693i	−0.533416	−	0.435472i
$568$		0			0
$569$	24.3659			1.02147			0.510736	−	0.859738i	$-0.329373\pi$
$569$	24.3659			1.02147			0.510736	+	0.859738i	$0.329373\pi$
$570$		0			0
$571$	20.9944			0.878589			0.439294	−	0.898343i	$-0.355228\pi$
$571$	20.9944			0.878589			0.439294	+	0.898343i	$0.355228\pi$
$572$		0			0
$573$	17.3420	−	37.5196i	0.724470	−	1.56740i
$574$		0			0
$575$	6.01923	−	1.06135i	0.251019	−	0.0442614i
$576$		0			0
$577$	−2.59042	+	4.48675i	−0.107841	+	0.186786i	−0.914895	−	0.403691i	$-0.867727\pi$
$577$	−2.59042	+	4.48675i	−0.107841	+	0.186786i	0.807055	+	0.590477i	$0.201060\pi$
$578$		0			0
$579$	2.59197	−	2.60950i	0.107718	−	0.108447i
$580$		0			0
$581$	−0.953424	+	0.550460i	−0.0395547	+	0.0228369i
$582$		0			0
$583$	−3.96996	−	10.9074i	−0.164419	−	0.451738i
$584$		0			0
$585$	0.889525	−	2.49618i	0.0367773	−	0.103204i
$586$		0			0
$587$	−19.9370	−	23.7599i	−0.822887	−	0.980678i	0.177107	−	0.984192i	$-0.443326\pi$
$587$	−19.9370	−	23.7599i	−0.822887	−	0.980678i	−0.999994	+	0.00351357i	$0.998882\pi$
$588$		0			0
$589$	−10.4978	−	22.2437i	−0.432556	−	0.916536i
$590$		0			0
$591$	−3.77584	−	5.35396i	−0.155317	−	0.220232i
$592$		0			0
$593$	−19.0316	−	3.35579i	−0.781536	−	0.137806i	−0.231375	−	0.972865i	$-0.574322\pi$
$593$	−19.0316	−	3.35579i	−0.781536	−	0.137806i	−0.550161	+	0.835059i	$0.685434\pi$
$594$		0			0
$595$	−5.71492	+	2.08006i	−0.234289	+	0.0852742i
$596$		0			0
$597$	−10.1724	−	21.6241i	−0.416327	−	0.885016i
$598$		0			0
$599$	14.4631	+	12.1360i	0.590946	+	0.495863i	0.888521	−	0.458836i	$-0.151733\pi$
$599$	14.4631	+	12.1360i	0.590946	+	0.495863i	−0.297575	+	0.954698i	$0.596178\pi$
$600$		0			0
$601$	−9.35958	−	5.40376i	−0.381785	−	0.220424i	0.296809	−	0.954937i	$-0.404077\pi$
$601$	−9.35958	−	5.40376i	−0.381785	−	0.220424i	−0.678595	+	0.734513i	$0.737411\pi$
$602$		0			0
$603$	−24.5982	+	0.165810i	−1.00172	+	0.00675231i
$604$		0			0
$605$	−7.85648	+	21.5855i	−0.319411	+	0.877575i
$606$		0			0
$607$		−	7.06408i		−	0.286722i	−0.989670	−	0.143361i	$-0.954209\pi$
$607$		−	7.06408i		−	0.286722i	0.989670	−	0.143361i	$-0.0457910\pi$
$608$		0			0
$609$	−20.1930	−	1.69810i	−0.818260	−	0.0688104i
$610$		0			0
$611$	−4.47963	−	1.63045i	−0.181226	−	0.0659610i
$612$		0			0
$613$	−5.48141	−	31.0866i	−0.221392	−	1.25558i	−0.869463	−	0.493998i	$-0.835535\pi$
$613$	−5.48141	−	31.0866i	−0.221392	−	1.25558i	0.648071	−	0.761580i	$-0.275576\pi$
$614$		0			0
$615$	11.3477	+	7.88888i	0.457583	+	0.318110i
$616$		0			0
$617$	−19.6647	+	23.4355i	−0.791672	+	0.943478i	−0.999397	−	0.0347092i	$-0.988950\pi$
$617$	−19.6647	+	23.4355i	−0.791672	+	0.943478i	0.207725	+	0.978187i	$0.433394\pi$
$618$		0			0
$619$	−21.8906	−	37.9157i	−0.879859	−	1.52396i	−0.851494	−	0.524364i	$-0.824303\pi$
$619$	−21.8906	−	37.9157i	−0.879859	−	1.52396i	−0.0283650	−	0.999598i	$-0.509030\pi$
$620$		0			0
$621$	3.04491	+	31.1703i	0.122188	+	1.25082i
$622$		0			0
$623$	−1.37078	+	7.77406i	−0.0549190	+	0.311461i
$624$		0			0
$625$	−14.4792	+	12.1495i	−0.579170	+	0.485981i
$626$		0			0
$627$	−31.1601	−	17.6598i	−1.24442	−	0.705264i
$628$		0			0
$629$	−7.43124	+	6.23555i	−0.296303	+	0.248628i
$630$		0			0
$631$	−0.0934107	+	0.529758i	−0.00371862	+	0.0210893i	−0.986611	−	0.163094i	$-0.947853\pi$
$631$	−0.0934107	+	0.529758i	−0.00371862	+	0.0210893i	0.982892	+	0.184183i	$0.0589639\pi$
$632$		0			0
$633$	7.31692	+	26.9436i	0.290822	+	1.07091i
$634$		0			0
$635$	13.1778	+	22.8246i	0.522944	+	0.905765i
$636$		0			0
$637$	−1.04679	+	1.24752i	−0.0414755	+	0.0494285i
$638$		0			0
$639$	9.88214	−	11.9396i	0.390932	−	0.472324i
$640$		0			0
$641$	4.01897	+	22.7927i	0.158740	+	0.900259i	0.955287	+	0.295682i	$0.0955467\pi$
$641$	4.01897	+	22.7927i	0.158740	+	0.900259i	−0.796547	+	0.604577i	$0.793342\pi$
$642$		0			0
$643$	8.18931	+	2.98066i	0.322955	+	0.117546i	0.498410	−	0.866941i	$-0.333917\pi$
$643$	8.18931	+	2.98066i	0.322955	+	0.117546i	−0.175455	+	0.984487i	$0.556140\pi$
$644$		0			0
$645$	3.60124	−	42.8242i	0.141799	−	1.68620i
$646$		0			0
$647$			39.9441i			1.57037i	0.619264	+	0.785183i	$0.287431\pi$
$647$			39.9441i			1.57037i	−0.619264	+	0.785183i	$0.712569\pi$
$648$		0			0
$649$	−8.20063	+	22.5310i	−0.321903	+	0.884421i
$650$		0			0
$651$	−17.7332	+	1.61169i	−0.695018	+	0.0631672i
$652$		0			0
$653$	1.49337	+	0.862200i	0.0584402	+	0.0337405i	0.528935	−	0.848662i	$-0.322591\pi$
$653$	1.49337	+	0.862200i	0.0584402	+	0.0337405i	−0.470495	+	0.882403i	$0.655925\pi$
$654$		0			0
$655$	−10.8193	−	9.07851i	−0.422747	−	0.354727i
$656$		0			0
$657$	−15.1101	−	40.6599i	−0.589502	−	1.58629i
$658$		0			0
$659$	22.0705	−	8.03300i	0.859744	−	0.312921i	0.125737	−	0.992064i	$-0.459870\pi$
$659$	22.0705	−	8.03300i	0.859744	−	0.312921i	0.734006	+	0.679142i	$0.237648\pi$
$660$		0			0
$661$	10.0686	+	1.77536i	0.391622	+	0.0690535i	0.365992	−	0.930618i	$-0.380730\pi$
$661$	10.0686	+	1.77536i	0.391622	+	0.0690535i	0.0256300	+	0.999671i	$0.491841\pi$
$662$		0			0
$663$	−1.04710	+	0.738461i	−0.0406661	+	0.0286795i
$664$		0			0
$665$	12.9452	−	9.15379i	0.501994	−	0.354969i
$666$		0			0
$667$	24.8796	+	29.6503i	0.963341	+	1.14807i
$668$		0			0
$669$	1.79904	+	0.475558i	0.0695548	+	0.0183861i
$670$		0			0
$671$	−16.8386	−	46.2637i	−0.650047	−	1.78599i
$672$		0			0
$673$	−32.9000	+	18.9948i	−1.26820	+	0.732197i	−0.974648	−	0.223745i	$-0.928172\pi$
$673$	−32.9000	+	18.9948i	−1.26820	+	0.732197i	−0.293555	+	0.955942i	$0.594838\pi$
$674$		0			0
$675$	3.06581	+	4.28555i	0.118003	+	0.164951i
$676$		0			0
$677$	16.1698	−	28.0070i	0.621457	−	1.07640i	−0.367757	−	0.929922i	$-0.619874\pi$
$677$	16.1698	−	28.0070i	0.621457	−	1.07640i	0.989215	−	0.146474i	$-0.0467925\pi$
$678$		0			0
$679$	−4.59174	+	0.809648i	−0.176215	+	0.0310714i
$680$		0			0
$681$	−29.5002	−	13.6353i	−1.13045	−	0.522506i
$682$		0			0
$683$	−27.4952			−1.05208			−0.526038	−	0.850461i	$-0.676323\pi$
$683$	−27.4952			−1.05208			−0.526038	+	0.850461i	$0.676323\pi$
$684$		0			0
$685$	18.7237			0.715396
$686$		0			0
$687$	18.2794	+	8.44895i	0.697403	+	0.322347i
$688$		0			0
$689$	1.06608	−	0.187978i	0.0406144	−	0.00716141i
$690$		0			0
$691$	−8.55714	+	14.8214i	−0.325529	+	0.563833i	−0.981619	−	0.190850i	$-0.938876\pi$
$691$	−8.55714	+	14.8214i	−0.325529	+	0.563833i	0.656090	+	0.754682i	$0.272209\pi$
$692$		0			0
$693$	−19.7498	+	16.8002i	−0.750234	+	0.638188i
$694$		0			0
$695$	18.7294	−	10.8134i	0.710448	−	0.410178i
$696$		0			0
$697$	−2.28556	−	6.27952i	−0.0865717	−	0.237854i
$698$		0			0
$699$	27.2285	+	7.19757i	1.02987	+	0.272237i
$700$		0			0
$701$	−24.3781	−	29.0527i	−0.920748	−	1.09730i	−0.994981	−	0.100064i	$-0.968095\pi$
$701$	−24.3781	−	29.0527i	−0.920748	−	1.09730i	0.0742333	−	0.997241i	$-0.476349\pi$
$702$		0			0
$703$	14.4096	−	20.7827i	0.543467	−	0.783836i
$704$		0			0
$705$	−30.4487	+	21.4737i	−1.14676	+	0.808746i
$706$		0			0
$707$	14.2982	+	2.52116i	0.537739	+	0.0948178i
$708$		0			0
$709$	−18.3247	+	6.66963i	−0.688197	+	0.250483i	−0.662363	−	0.749183i	$-0.730446\pi$
$709$	−18.3247	+	6.66963i	−0.688197	+	0.250483i	−0.0258338	+	0.999666i	$0.508224\pi$
$710$		0			0
$711$	26.6019	−	9.88587i	0.997649	−	0.370749i
$712$		0			0
$713$	26.0539	+	21.8618i	0.975724	+	0.818730i
$714$		0			0
$715$	−3.62903	−	2.09522i	−0.135718	−	0.0783568i
$716$		0			0
$717$	11.7524	−	1.06813i	0.438902	−	0.0398900i
$718$		0			0
$719$	0.618865	−	1.70032i	0.0230798	−	0.0634111i	−0.927618	−	0.373531i	$-0.878147\pi$
$719$	0.618865	−	1.70032i	0.0230798	−	0.0634111i	0.950697	+	0.310120i	$0.100369\pi$
$720$		0			0
$721$			27.9880i			1.04233i
$722$		0			0
$723$	−2.81711	+	33.4997i	−0.104769	+	1.24587i
$724$		0			0
$725$	6.11938	+	2.22727i	0.227268	+	0.0827189i
$726$		0			0
$727$	−2.39063	−	13.5580i	−0.0886637	−	0.502837i	−0.996506	−	0.0835244i	$-0.973382\pi$
$727$	−2.39063	−	13.5580i	−0.0886637	−	0.502837i	0.907842	−	0.419312i	$-0.137729\pi$
$728$		0			0
$729$	−23.1049	+	13.9700i	−0.855738	+	0.517409i
$730$		0			0
$731$	−13.3569	+	15.9181i	−0.494023	+	0.588754i
$732$		0			0
$733$	3.00825	+	5.21044i	0.111112	+	0.192452i	0.916219	−	0.400678i	$-0.131225\pi$
$733$	3.00825	+	5.21044i	0.111112	+	0.192452i	−0.805107	+	0.593130i	$0.797892\pi$
$734$		0			0
$735$	3.33574	+	12.2834i	0.123041	+	0.453080i
$736$		0			0
$737$	−6.75474	+	38.3080i	−0.248814	+	1.41109i
$738$		0			0
$739$	−16.5397	+	13.8784i	−0.608421	+	0.510526i	−0.894140	−	0.447788i	$-0.852212\pi$
$739$	−16.5397	+	13.8784i	−0.608421	+	0.510526i	0.285719	+	0.958313i	$0.407768\pi$
$740$		0			0
$741$	2.12659	−	2.57590i	0.0781222	−	0.0946281i
$742$		0			0
$743$	18.9259	−	15.8807i	0.694322	−	0.582606i	−0.225830	−	0.974167i	$-0.572509\pi$
$743$	18.9259	−	15.8807i	0.694322	−	0.582606i	0.920152	+	0.391561i	$0.128065\pi$
$744$		0			0
$745$	3.90485	−	22.1455i	0.143063	−	0.811349i
$746$		0			0
$747$	0.326825	+	1.78314i	0.0119579	+	0.0652418i
$748$		0			0
$749$	17.0318	+	29.4999i	0.622329	+	1.07790i
$750$		0			0
$751$	14.8918	−	17.7473i	0.543409	−	0.647609i	−0.422540	−	0.906344i	$-0.638861\pi$
$751$	14.8918	−	17.7473i	0.543409	−	0.647609i	0.965948	+	0.258735i	$0.0833057\pi$
$752$		0			0
$753$	24.2934	+	16.8887i	0.885300	+	0.615458i
$754$		0			0
$755$	−1.22958	−	6.97331i	−0.0447491	−	0.253785i
$756$		0			0
$757$	−11.1562	−	4.06054i	−0.405480	−	0.147583i	0.131225	−	0.991353i	$-0.458109\pi$
$757$	−11.1562	−	4.06054i	−0.405480	−	0.147583i	−0.536705	+	0.843770i	$0.680331\pi$
$758$		0			0
$759$	49.3512	+	4.15012i	1.79134	+	0.150640i
$760$		0			0
$761$			6.51835i			0.236290i	0.992996	+	0.118145i	$0.0376948\pi$
$761$			6.51835i			0.236290i	−0.992996	+	0.118145i	$0.962305\pi$
$762$		0			0
$763$	7.11311	−	19.5431i	0.257512	−	0.707508i
$764$		0			0
$765$	0.0675037	+	10.0143i	0.00244060	+	0.362068i
$766$		0			0
$767$	−1.93655	−	1.11807i	−0.0699249	−	0.0403711i
$768$		0			0
$769$	6.42301	+	5.38954i	0.231620	+	0.194352i	0.751209	−	0.660064i	$-0.229471\pi$
$769$	6.42301	+	5.38954i	0.231620	+	0.194352i	−0.519590	+	0.854416i	$0.673915\pi$
$770$		0			0
$771$	−11.6566	−	24.7793i	−0.419803	−	0.892405i
$772$		0			0
$773$	15.1689	−	5.52103i	0.545588	−	0.198578i	−0.0544971	−	0.998514i	$-0.517356\pi$
$773$	15.1689	−	5.52103i	0.545588	−	0.198578i	0.600085	+	0.799936i	$0.295133\pi$
$774$		0			0
$775$	5.63528	+	0.993653i	0.202425	+	0.0356931i
$776$		0			0
$777$	−10.5515	−	14.9615i	−0.378532	−	0.536741i
$778$		0			0
$779$	10.0581	+	14.2241i	0.360370	+	0.509632i
$780$		0			0
$781$	−15.7539	−	18.7748i	−0.563719	−	0.671815i
$782$		0			0
$783$	−13.7956	+	30.3831i	−0.493015	+	1.08580i
$784$		0			0
$785$	0.215679	+	0.592574i	0.00769792	+	0.0211499i
$786$		0			0
$787$	−19.4065	+	11.2044i	−0.691768	+	0.399392i	−0.804274	−	0.594259i	$-0.797446\pi$
$787$	−19.4065	+	11.2044i	−0.691768	+	0.399392i	0.112506	+	0.993651i	$0.464112\pi$
$788$		0			0
$789$	3.17244	−	3.19389i	0.112942	−	0.113706i
$790$		0			0
$791$	0.541256	−	0.937483i	0.0192449	−	0.0333331i
$792$		0			0
$793$	4.52177	−	0.797311i	0.160573	−	0.0283133i
$794$		0			0
$795$	3.54985	−	7.68015i	0.125900	−	0.272387i
$796$		0			0
$797$	33.1888			1.17561			0.587804	−	0.809003i	$-0.299993\pi$
$797$	33.1888			1.17561			0.587804	+	0.809003i	$0.299993\pi$
$798$		0			0
$799$	18.0157			0.637350
$800$		0			0
$801$	11.3008	+	6.42335i	0.399295	+	0.226958i
$802$		0			0
$803$	−67.5512	+	11.9111i	−2.38383	+	0.420333i
$804$		0			0
$805$	−10.9615	+	18.9860i	−0.386344	+	0.669167i
$806$		0			0
$807$	−39.2156	−	38.9522i	−1.38046	−	1.37118i
$808$		0			0
$809$	35.2784	−	20.3680i	1.24032	−	0.716101i	0.271164	−	0.962533i	$-0.412591\pi$
$809$	35.2784	−	20.3680i	1.24032	−	0.716101i	0.969160	+	0.246432i	$0.0792581\pi$
$810$		0			0
$811$	6.36968	+	17.5006i	0.223670	+	0.614528i	0.999873	−	0.0159555i	$-0.00507902\pi$
$811$	6.36968	+	17.5006i	0.223670	+	0.614528i	−0.776203	+	0.630483i	$0.782857\pi$
$812$		0			0
$813$	8.89488	−	33.6494i	0.311957	−	1.18013i
$814$		0			0
$815$	1.60295	+	1.91032i	0.0561488	+	0.0669155i
$816$		0			0
$817$	22.6667	−	49.2014i	0.793009	−	1.72134i
$818$		0			0
$819$	−1.22317	−	2.08599i	−0.0427410	−	0.0728905i
$820$		0			0
$821$	17.1780	+	3.02894i	0.599515	+	0.105711i	0.465166	−	0.885223i	$-0.345995\pi$
$821$	17.1780	+	3.02894i	0.599515	+	0.105711i	0.134349	+	0.990934i	$0.457106\pi$
$822$		0			0
$823$	−13.0772	+	4.75972i	−0.455844	+	0.165914i	−0.559729	−	0.828676i	$-0.689095\pi$
$823$	−13.0772	+	4.75972i	−0.455844	+	0.165914i	0.103885	+	0.994589i	$0.466873\pi$
$824$		0			0
$825$	7.53988	−	3.54689i	0.262505	−	0.123487i
$826$		0			0
$827$	−3.80513	−	3.19288i	−0.132317	−	0.111027i	0.574227	−	0.818696i	$-0.305303\pi$
$827$	−3.80513	−	3.19288i	−0.132317	−	0.111027i	−0.706545	+	0.707669i	$0.749747\pi$
$828$		0			0
$829$	36.2878	+	20.9508i	1.26033	+	0.727650i	0.973138	−	0.230224i	$-0.0739460\pi$
$829$	36.2878	+	20.9508i	1.26033	+	0.727650i	0.287189	+	0.957874i	$0.407279\pi$
$830$		0			0
$831$	−1.26678	−	13.9381i	−0.0439440	−	0.483508i
$832$		0			0
$833$	2.10494	−	5.78328i	0.0729319	−	0.200379i
$834$		0			0
$835$		−	2.04138i		−	0.0706448i
$836$		0			0
$837$	−7.30208	+	28.3972i	−0.252397	+	0.981550i
$838$		0			0
$839$	37.7944	+	13.7560i	1.30481	+	0.474912i	0.898560	−	0.438851i	$-0.144614\pi$
$839$	37.7944	+	13.7560i	1.30481	+	0.474912i	0.406249	+	0.913763i	$0.366837\pi$
$840$		0			0
$841$	2.12528	+	12.0531i	0.0732855	+	0.415623i
$842$		0			0
$843$	−11.6770	+	16.7967i	−0.402177	+	0.578509i
$844$		0			0
$845$	−16.4319	+	19.5827i	−0.565273	+	0.673666i
$846$		0			0
$847$	10.4809	+	18.1534i	0.360126	+	0.623757i
$848$		0			0
$849$	24.0141	−	6.52138i	0.824161	−	0.223813i
$850$		0			0
$851$	−6.07232	+	34.4378i	−0.208156	+	1.18051i
$852$		0			0
$853$	25.6859	−	21.5531i	0.879470	−	0.737963i	−0.0866001	−	0.996243i	$-0.527600\pi$
$853$	25.6859	−	21.5531i	0.879470	−	0.737963i	0.966070	+	0.258280i	$0.0831558\pi$
$854$		0			0
$855$	−7.04317	−	25.1394i	−0.240871	−	0.859748i
$856$		0			0
$857$	0.680362	−	0.570892i	0.0232407	−	0.0195013i	−0.631093	−	0.775707i	$-0.717393\pi$
$857$	0.680362	−	0.570892i	0.0232407	−	0.0195013i	0.654334	+	0.756206i	$0.272949\pi$
$858$		0			0
$859$	0.641169	−	3.63625i	0.0218764	−	0.124067i	−0.971914	−	0.235337i	$-0.924381\pi$
$859$	0.641169	−	3.63625i	0.0218764	−	0.124067i	0.993790	+	0.111270i	$0.0354917\pi$
$860$		0			0
$861$	12.1709	−	3.30518i	0.414782	−	0.112640i
$862$		0			0
$863$	9.90600	+	17.1577i	0.337204	+	0.584055i	0.983906	−	0.178688i	$-0.0571854\pi$
$863$	9.90600	+	17.1577i	0.337204	+	0.584055i	−0.646701	+	0.762743i	$0.723852\pi$
$864$		0			0
$865$	19.3930	−	23.1117i	0.659383	−	0.785822i
$866$		0			0
$867$	−14.0435	+	20.2007i	−0.476941	+	0.686052i
$868$		0			0
$869$	−7.79289	−	44.1957i	−0.264356	−	1.49923i
$870$		0			0
$871$	−3.40900	−	1.24078i	−0.115510	−	0.0420421i
$872$		0			0
$873$	−1.28222	+	7.56988i	−0.0433967	+	0.256202i
$874$		0			0
$875$			21.8750i			0.739511i
$876$		0			0
$877$	−11.7852	+	32.3795i	−0.397958	+	1.09338i	0.565320	+	0.824872i	$0.308753\pi$
$877$	−11.7852	+	32.3795i	−0.397958	+	1.09338i	−0.963278	+	0.268508i	$0.913470\pi$
$878$		0			0
$879$	0.00101671	+	0.0111867i	3.42928e−5	+	0.000377317i
$880$		0			0
$881$	18.5560	+	10.7133i	0.625166	+	0.360940i	0.778878	−	0.627176i	$-0.215789\pi$
$881$	18.5560	+	10.7133i	0.625166	+	0.360940i	−0.153711	+	0.988116i	$0.549123\pi$
$882$		0			0
$883$	26.4524	+	22.1962i	0.890193	+	0.746960i	0.968249	−	0.249989i	$-0.0804269\pi$
$883$	26.4524	+	22.1962i	0.890193	+	0.746960i	−0.0780562	+	0.996949i	$0.524871\pi$
$884$		0			0
$885$	−15.8149	+	7.43958i	−0.531611	+	0.250079i
$886$		0			0
$887$	28.3275	−	10.3104i	0.951145	−	0.346189i	0.180588	−	0.983559i	$-0.442200\pi$
$887$	28.3275	−	10.3104i	0.951145	−	0.346189i	0.770558	+	0.637370i	$0.219978\pi$
$888$		0			0
$889$	23.6850	+	4.17631i	0.794370	+	0.140069i
$890$		0			0
$891$	15.1425	+	39.9207i	0.507292	+	1.33739i
$892$		0			0
$893$	−45.3091	+	12.3652i	−1.51621	+	0.413787i
$894$		0			0
$895$	7.62847	+	9.09125i	0.254992	+	0.303887i
$896$		0			0
$897$	−1.18040	+	4.46544i	−0.0394122	+	0.149097i
$898$		0			0
$899$	12.3937	+	34.0515i	0.413354	+	1.13568i
$900$		0			0
$901$	−3.54294	+	2.04552i	−0.118032	+	0.0681460i
$902$		0			0
$903$	−27.8237	−	27.6367i	−0.925913	−	0.919693i
$904$		0			0
$905$	6.47953	−	11.2229i	0.215387	−	0.373061i
$906$		0			0
$907$	56.6712	−	9.99267i	1.88174	−	0.331801i	0.889579	−	0.456782i	$-0.150998\pi$
$907$	56.6712	−	9.99267i	1.88174	−	0.331801i	0.992159	+	0.124981i	$0.0398869\pi$
$908$		0			0
$909$	11.8139	−	20.7847i	0.391844	−	0.689384i
$910$		0			0
$911$	38.7915			1.28522			0.642610	−	0.766194i	$-0.277852\pi$
$911$	38.7915			1.28522			0.642610	+	0.766194i	$0.277852\pi$
$912$		0			0
$913$	2.86672			0.0948747
$914$		0			0
$915$	15.0567	−	32.5754i	0.497759	−	1.07691i
$916$		0			0
$917$	−12.6926	+	2.23804i	−0.419145	+	0.0739066i
$918$		0			0
$919$	−28.1669	+	48.7865i	−0.929141	+	1.60932i	−0.144379	+	0.989522i	$0.546118\pi$
$919$	−28.1669	+	48.7865i	−0.929141	+	1.60932i	−0.784762	+	0.619797i	$0.787215\pi$
$920$		0			0
$921$	16.6312	−	16.7437i	0.548017	−	0.551723i
$922$		0			0
$923$	1.97950	−	1.14286i	0.0651559	−	0.0376178i
$924$		0			0
$925$	2.01225	+	5.52862i	0.0661625	+	0.181780i
$926$		0			0
$927$	43.4128	+	15.4704i	1.42586	+	0.508114i
$928$		0			0
$929$	31.8205	+	37.9221i	1.04400	+	1.24418i	0.969016	+	0.247000i	$0.0794447\pi$
$929$	31.8205	+	37.9221i	1.04400	+	1.24418i	0.0749796	+	0.997185i	$0.476111\pi$
$930$		0			0
$931$	−1.32447	+	15.9896i	−0.0434078	+	0.524037i
$932$		0			0
$933$	11.6906	+	16.5767i	0.382733	+	0.542697i
$934$		0			0
$935$	15.5957	+	2.74995i	0.510035	+	0.0899330i
$936$		0			0
$937$	21.2381	−	7.73002i	0.693817	−	0.252529i	0.0290486	−	0.999578i	$-0.490752\pi$
$937$	21.2381	−	7.73002i	0.693817	−	0.252529i	0.664769	+	0.747049i	$0.268530\pi$
$938$		0			0
$939$	−1.29534	−	2.75359i	−0.0422717	−	0.0898601i
$940$		0			0
$941$	40.2199	+	33.7485i	1.31113	+	1.10017i	0.988105	+	0.153778i	$0.0491440\pi$
$941$	40.2199	+	33.7485i	1.31113	+	1.10017i	0.323024	+	0.946391i	$0.395300\pi$
$942$		0			0
$943$	−20.8617	−	12.0445i	−0.679349	−	0.392222i
$944$		0			0
$945$	−18.8438	−	1.45679i	−0.612988	−	0.0473895i
$946$		0			0
$947$	−9.84314	+	27.0438i	−0.319859	+	0.878805i	0.670701	+	0.741728i	$0.265993\pi$
$947$	−9.84314	+	27.0438i	−0.319859	+	0.878805i	−0.990560	+	0.137078i	$0.956229\pi$
$948$		0			0
$949$		−	6.39712i		−	0.207659i
$950$		0			0
$951$	12.1067	+	1.01810i	0.392588	+	0.0330141i
$952$		0			0
$953$	−1.95076	−	0.710020i	−0.0631914	−	0.0229998i	0.310231	−	0.950661i	$-0.399594\pi$
$953$	−1.95076	−	0.710020i	−0.0631914	−	0.0229998i	−0.373422	+	0.927661i	$0.621816\pi$
$954$		0			0
$955$	−8.27327	−	46.9200i	−0.267717	−	1.51830i
$956$		0			0
$957$	43.3258	+	30.1199i	1.40052	+	0.973639i
$958$		0			0
$959$	10.9827	−	13.0887i	0.354651	−	0.422656i
$960$		0			0
$961$	0.420731	+	0.728727i	0.0135720	+	0.0235073i
$962$		0			0
$963$	55.1724	−	10.1123i	1.77790	−	0.325864i
$964$		0			0
$965$	0.736186	−	4.17512i	0.0236987	−	0.134402i
$966$		0			0
$967$	2.18110	−	1.83016i	0.0701395	−	0.0588540i	−0.607044	−	0.794668i	$-0.707645\pi$
$967$	2.18110	−	1.83016i	0.0701395	−	0.0588540i	0.677183	+	0.735814i	$0.263200\pi$
$968$		0			0
$969$	−4.22257	+	11.8964i	−0.135648	+	0.382167i
$970$		0			0
$971$	−0.796470	+	0.668318i	−0.0255599	+	0.0214473i	−0.655478	−	0.755214i	$-0.727533\pi$
$971$	−0.796470	+	0.668318i	−0.0255599	+	0.0214473i	0.629918	+	0.776661i	$0.283088\pi$
$972$		0			0
$973$	3.42701	−	19.4355i	0.109865	−	0.623074i
$974$		0			0
$975$	0.203657	+	0.749940i	0.00652225	+	0.0240173i
$976$		0			0
$977$	−17.5242	−	30.3529i	−0.560650	−	0.971074i	−0.997440	−	0.0715108i	$-0.977218\pi$
$977$	−17.5242	−	30.3529i	−0.560650	−	0.971074i	0.436790	−	0.899564i	$-0.356115\pi$
$978$		0			0
$979$	13.2128	−	15.7464i	0.422282	−	0.503256i
$980$		0			0
$981$	−26.3820	−	21.8357i	−0.842311	−	0.697162i
$982$		0			0
$983$	3.51109	+	19.9124i	0.111986	+	0.635106i	0.988198	+	0.153180i	$0.0489515\pi$
$983$	3.51109	+	19.9124i	0.111986	+	0.635106i	−0.876212	+	0.481926i	$0.839937\pi$
$984$		0			0
$985$	−7.09625	−	2.58283i	−0.226105	−	0.0822957i
$986$		0			0
$987$	−2.84915	+	33.8808i	−0.0906895	+	1.07844i
$988$		0			0
$989$			74.9059i			2.38187i
$990$		0			0
$991$	−4.51355	+	12.4009i	−0.143378	+	0.393926i	−0.990507	−	0.137459i	$-0.956106\pi$
$991$	−4.51355	+	12.4009i	−0.143378	+	0.393926i	0.847130	+	0.531386i	$0.178329\pi$
$992$		0			0
$993$	−2.72317	+	0.247498i	−0.0864173	+	0.00785411i
$994$		0			0
$995$	−23.8552	−	13.7728i	−0.756261	−	0.436627i
$996$		0			0
$997$	20.9990	+	17.6202i	0.665045	+	0.558039i	0.911594	−	0.411091i	$-0.134852\pi$
$997$	20.9990	+	17.6202i	0.665045	+	0.558039i	−0.246549	+	0.969130i	$0.579297\pi$
$998$		0			0
$999$	−29.0394	+	8.09666i	−0.918767	+	0.256167i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.cc.c.545.1		18
3.2	odd	2		912.2.cc.d.545.3		18
4.3	odd	2		114.2.l.b.89.3	yes	18
12.11	even	2		114.2.l.a.89.1	yes	18
19.3	odd	18		912.2.cc.d.497.3		18
57.41	even	18	inner	912.2.cc.c.497.1		18
76.3	even	18		114.2.l.a.41.1	✓	18
228.155	odd	18		114.2.l.b.41.3	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.l.a.41.1	✓	18	76.3	even	18
114.2.l.a.89.1	yes	18	12.11	even	2
114.2.l.b.41.3	yes	18	228.155	odd	18
114.2.l.b.89.3	yes	18	4.3	odd	2
912.2.cc.c.497.1		18	57.41	even	18	inner
912.2.cc.c.545.1		18	1.1	even	1	trivial
912.2.cc.d.497.3		18	19.3	odd	18
912.2.cc.d.545.3		18	3.2	odd	2

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.cc (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.57223 - 0.726702i) q^{3} +(-1.96615 + 0.346685i) q^{5} +(-0.910931 + 1.57778i) q^{7} +(1.94381 + 2.28508i) q^{9} +O(q^{10})\)	\(q+(-1.57223 - 0.726702i) q^{3} +(-1.96615 + 0.346685i) q^{5} +(-0.910931 + 1.57778i) q^{7} +(1.94381 + 2.28508i) q^{9} +(4.10844 - 2.37201i) q^{11} +(0.151321 + 0.415752i) q^{13} +(3.34317 + 0.883735i) q^{15} +(-1.07476 - 1.28085i) q^{17} +(3.58212 + 2.48363i) q^{19} +(2.57877 - 1.81865i) q^{21} +(-5.93571 - 1.04663i) q^{23} +(-0.952914 + 0.346832i) q^{25} +(-1.39554 - 5.00524i) q^{27} +(-4.91935 - 4.12783i) q^{29} +(-4.88683 - 2.82141i) q^{31} +(-8.18314 + 0.743731i) q^{33} +(1.24403 - 3.41795i) q^{35} -5.80180i q^{37} +(0.0642158 - 0.763624i) q^{39} +(3.75563 + 1.36694i) q^{41} +(-2.15807 - 12.2390i) q^{43} +(-4.61402 - 3.81892i) q^{45} +(-6.92588 + 8.25394i) q^{47} +(1.84041 + 3.18768i) q^{49} +(0.758974 + 2.79482i) q^{51} +(0.424873 - 2.40957i) q^{53} +(-7.25545 + 6.08805i) q^{55} +(-3.82705 - 6.50797i) q^{57} +(-3.87172 + 3.24876i) q^{59} +(1.80210 - 10.2202i) q^{61} +(-5.37603 + 0.985349i) q^{63} +(-0.441656 - 0.764970i) q^{65} +(-5.27060 + 6.28126i) q^{67} +(8.57172 + 5.95903i) q^{69} +(-0.897109 - 5.08776i) q^{71} +(-13.5869 - 4.94524i) q^{73} +(1.75024 + 0.147184i) q^{75} +8.64294i q^{77} +(3.23544 - 8.88931i) q^{79} +(-1.44321 + 8.88353i) q^{81} +(0.523324 + 0.302141i) q^{83} +(2.55719 + 2.14574i) q^{85} +(4.73465 + 10.0648i) q^{87} +(4.07161 - 1.48195i) q^{89} +(-0.793809 - 0.139970i) q^{91} +(5.63289 + 7.98717i) q^{93} +(-7.90401 - 3.64132i) q^{95} +(1.64505 + 1.96049i) q^{97} +(13.4062 + 4.77739i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 3 q^{3} - 3 q^{9}+O(q^{10}) \) 18 * q - 3 * q^3 - 3 * q^9	\( 18 q - 3 q^{3} - 3 q^{9} - 12 q^{13} - 18 q^{15} + 6 q^{17} + 6 q^{19} - 18 q^{25} + 6 q^{27} - 6 q^{29} - 24 q^{33} + 24 q^{35} - 6 q^{39} + 3 q^{41} + 6 q^{43} - 54 q^{45} - 30 q^{47} + 21 q^{49} - 42 q^{51} - 60 q^{53} - 30 q^{55} + 12 q^{57} - 3 q^{59} + 54 q^{61} + 18 q^{63} + 24 q^{65} + 15 q^{67} + 30 q^{69} - 36 q^{71} - 42 q^{73} + 6 q^{79} - 3 q^{81} - 36 q^{83} - 60 q^{89} + 18 q^{91} - 66 q^{93} - 6 q^{95} + 9 q^{97} + 102 q^{99}+O(q^{100}) \) 18 * q - 3 * q^3 - 3 * q^9 - 12 * q^13 - 18 * q^15 + 6 * q^17 + 6 * q^19 - 18 * q^25 + 6 * q^27 - 6 * q^29 - 24 * q^33 + 24 * q^35 - 6 * q^39 + 3 * q^41 + 6 * q^43 - 54 * q^45 - 30 * q^47 + 21 * q^49 - 42 * q^51 - 60 * q^53 - 30 * q^55 + 12 * q^57 - 3 * q^59 + 54 * q^61 + 18 * q^63 + 24 * q^65 + 15 * q^67 + 30 * q^69 - 36 * q^71 - 42 * q^73 + 6 * q^79 - 3 * q^81 - 36 * q^83 - 60 * q^89 + 18 * q^91 - 66 * q^93 - 6 * q^95 + 9 * q^97 + 102 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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