LMFDB - Embedded newform 972.2.i.b.217.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [972,2,Mod(109,972)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(972, 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("972.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 972 = 2^{2} \cdot 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	972.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:	$7.76145907647$
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			217.1
Root			$0.472963 - 1.66622i$ of defining polynomial
Character	$\chi$	$=$	972.217
Dual form			972.2.i.b.757.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.21770 + 2.69997i) q^{5} +(-3.30269 + 1.20208i) q^{7} +O(q^{10})$	$q+(-3.21770 + 2.69997i) q^{5} +(-3.30269 + 1.20208i) q^{7} +(1.41557 + 1.18781i) q^{11} +(-0.404631 - 2.29478i) q^{13} +(0.799928 + 1.38552i) q^{17} +(2.31046 - 4.00184i) q^{19} +(-1.66845 - 0.607265i) q^{23} +(2.19551 - 12.4514i) q^{25} +(-0.200004 + 1.13428i) q^{29} +(-1.74682 - 0.635792i) q^{31} +(7.38148 - 12.7851i) q^{35} +(-4.38364 - 7.59269i) q^{37} +(-0.676508 - 3.83667i) q^{41} +(1.97156 + 1.65434i) q^{43} +(7.02002 - 2.55508i) q^{47} +(4.10044 - 3.44068i) q^{49} -8.02417 q^{53} -7.76194 q^{55} +(-0.937541 + 0.786690i) q^{59} +(4.08523 - 1.48690i) q^{61} +(7.49781 + 6.29141i) q^{65} +(-1.10248 - 6.25247i) q^{67} +(-0.871328 - 1.50918i) q^{71} +(-1.37908 + 2.38864i) q^{73} +(-6.10304 - 2.22132i) q^{77} +(-1.73125 + 9.81838i) q^{79} +(-1.96124 + 11.1227i) q^{83} +(-6.31478 - 2.29839i) q^{85} +(2.71167 - 4.69675i) q^{89} +(4.09488 + 7.09254i) q^{91} +(3.37047 + 19.1149i) q^{95} +(-9.26426 - 7.77363i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 3 q^{5}+O(q^{10}) $ 18 * q - 3 * q^5	$ 18 q - 3 q^{5} + 15 q^{11} + 12 q^{17} - 33 q^{23} + 9 q^{25} - 21 q^{29} + 9 q^{31} + 21 q^{35} + 33 q^{41} + 18 q^{43} - 9 q^{47} + 36 q^{49} - 66 q^{53} + 12 q^{59} + 36 q^{61} + 66 q^{65} + 27 q^{67} + 12 q^{71} + 9 q^{73} - 33 q^{77} + 18 q^{79} - 81 q^{83} + 18 q^{85} + 48 q^{89} + 9 q^{91} + 84 q^{95}+O(q^{100}) $ 18 * q - 3 * q^5 + 15 * q^11 + 12 * q^17 - 33 * q^23 + 9 * q^25 - 21 * q^29 + 9 * q^31 + 21 * q^35 + 33 * q^41 + 18 * q^43 - 9 * q^47 + 36 * q^49 - 66 * q^53 + 12 * q^59 + 36 * q^61 + 66 * q^65 + 27 * q^67 + 12 * q^71 + 9 * q^73 - 33 * q^77 + 18 * q^79 - 81 * q^83 + 18 * q^85 + 48 * q^89 + 9 * q^91 + 84 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/972\mathbb{Z}\right)^\times$.

$n$	$245$	$487$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−3.21770	+	2.69997i	−1.43900	+	1.20746i	−0.498856	+	0.866685i	$0.666246\pi$
$5$	−3.21770	+	2.69997i	−1.43900	+	1.20746i	−0.940143	+	0.340779i	$0.889309\pi$
$6$		0			0
$7$	−3.30269	+	1.20208i	−1.24830	+	0.454344i	−0.879827	−	0.475295i	$-0.842341\pi$
$7$	−3.30269	+	1.20208i	−1.24830	+	0.454344i	−0.368472	+	0.929639i	$0.620119\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.41557	+	1.18781i	0.426811	+	0.358137i	0.830747	−	0.556650i	$-0.187914\pi$
$11$	1.41557	+	1.18781i	0.426811	+	0.358137i	−0.403936	+	0.914787i	$0.632358\pi$
$12$		0			0
$13$	−0.404631	−	2.29478i	−0.112224	−	0.636457i	−0.988087	−	0.153896i	$-0.950818\pi$
$13$	−0.404631	−	2.29478i	−0.112224	−	0.636457i	0.875863	−	0.482561i	$-0.160293\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.799928	+	1.38552i	0.194011	+	0.336037i	0.946576	−	0.322481i	$-0.104517\pi$
$17$	0.799928	+	1.38552i	0.194011	+	0.336037i	−0.752565	+	0.658518i	$0.771184\pi$
$18$		0			0
$19$	2.31046	−	4.00184i	0.530056	−	0.918085i	−0.469329	−	0.883024i	$-0.655504\pi$
$19$	2.31046	−	4.00184i	0.530056	−	0.918085i	0.999385	−	0.0350612i	$-0.0111626\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.66845	−	0.607265i	−0.347895	−	0.126624i	0.162162	−	0.986764i	$-0.448153\pi$
$23$	−1.66845	−	0.607265i	−0.347895	−	0.126624i	−0.510057	+	0.860141i	$0.670376\pi$
$24$		0			0
$25$	2.19551	−	12.4514i	0.439102	−	2.49027i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.200004	+	1.13428i	−0.0371399	+	0.210631i	−0.997730	−	0.0673370i	$-0.978550\pi$
$29$	−0.200004	+	1.13428i	−0.0371399	+	0.210631i	0.960590	+	0.277968i	$0.0896608\pi$
$30$		0			0
$31$	−1.74682	−	0.635792i	−0.313739	−	0.114192i	0.180351	−	0.983602i	$-0.442277\pi$
$31$	−1.74682	−	0.635792i	−0.313739	−	0.114192i	−0.494090	+	0.869411i	$0.664499\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	7.38148	−	12.7851i	1.24770	−	2.16108i
$36$		0			0
$37$	−4.38364	−	7.59269i	−0.720666	−	1.24823i	−0.960733	−	0.277474i	$-0.910503\pi$
$37$	−4.38364	−	7.59269i	−0.720666	−	1.24823i	0.240067	−	0.970756i	$-0.422830\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−0.676508	−	3.83667i	−0.105653	−	0.599187i	−0.990958	−	0.134176i	$-0.957161\pi$
$41$	−0.676508	−	3.83667i	−0.105653	−	0.599187i	0.885305	−	0.465011i	$-0.153950\pi$
$42$		0			0
$43$	1.97156	+	1.65434i	0.300661	+	0.252284i	0.780619	−	0.625007i	$-0.214904\pi$
$43$	1.97156	+	1.65434i	0.300661	+	0.252284i	−0.479959	+	0.877291i	$0.659348\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	7.02002	−	2.55508i	1.02397	−	0.372696i	0.225191	−	0.974315i	$-0.427699\pi$
$47$	7.02002	−	2.55508i	1.02397	−	0.372696i	0.798784	+	0.601618i	$0.205477\pi$
$48$		0			0
$49$	4.10044	−	3.44068i	0.585778	−	0.491526i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−8.02417			−1.10220			−0.551102	−	0.834438i	$-0.685793\pi$
$53$	−8.02417			−1.10220			−0.551102	+	0.834438i	$0.685793\pi$
$54$		0			0
$55$	−7.76194			−1.04662
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−0.937541	+	0.786690i	−0.122057	+	0.102418i	−0.701773	−	0.712400i	$-0.747608\pi$
$59$	−0.937541	+	0.786690i	−0.122057	+	0.102418i	0.579716	+	0.814819i	$0.303164\pi$
$60$		0			0
$61$	4.08523	−	1.48690i	0.523060	−	0.190378i	−0.0669771	−	0.997755i	$-0.521335\pi$
$61$	4.08523	−	1.48690i	0.523060	−	0.190378i	0.590037	+	0.807376i	$0.299113\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	7.49781	+	6.29141i	0.929989	+	0.780354i
$66$		0			0
$67$	−1.10248	−	6.25247i	−0.134689	−	0.763860i	−0.975076	−	0.221873i	$-0.928783\pi$
$67$	−1.10248	−	6.25247i	−0.134689	−	0.763860i	0.840386	−	0.541988i	$-0.182328\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−0.871328	−	1.50918i	−0.103408	−	0.179107i	0.809679	−	0.586873i	$-0.199641\pi$
$71$	−0.871328	−	1.50918i	−0.103408	−	0.179107i	−0.913087	+	0.407766i	$0.866308\pi$
$72$		0			0
$73$	−1.37908	+	2.38864i	−0.161409	+	0.279569i	−0.935374	−	0.353659i	$-0.884937\pi$
$73$	−1.37908	+	2.38864i	−0.161409	+	0.279569i	0.773965	+	0.633228i	$0.218271\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−6.10304	−	2.22132i	−0.695506	−	0.253143i
$78$		0			0
$79$	−1.73125	+	9.81838i	−0.194780	+	1.10465i	0.717951	+	0.696094i	$0.245080\pi$
$79$	−1.73125	+	9.81838i	−0.194780	+	1.10465i	−0.912731	+	0.408561i	$0.866031\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−1.96124	+	11.1227i	−0.215274	+	1.22088i	0.665157	+	0.746703i	$0.268364\pi$
$83$	−1.96124	+	11.1227i	−0.215274	+	1.22088i	−0.880431	+	0.474174i	$0.842747\pi$
$84$		0			0
$85$	−6.31478	−	2.29839i	−0.684934	−	0.249296i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	2.71167	−	4.69675i	0.287436	−	0.497854i	−0.685761	−	0.727827i	$-0.740530\pi$
$89$	2.71167	−	4.69675i	0.287436	−	0.497854i	0.973197	+	0.229973i	$0.0738637\pi$
$90$		0			0
$91$	4.09488	+	7.09254i	0.429260	+	0.743500i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	3.37047	+	19.1149i	0.345803	+	1.96115i
$96$		0			0
$97$	−9.26426	−	7.77363i	−0.940643	−	0.789293i	0.0370544	−	0.999313i	$-0.488203\pi$
$97$	−9.26426	−	7.77363i	−0.940643	−	0.789293i	−0.977697	+	0.210020i	$0.932647\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−13.3096	+	4.84430i	−1.32435	+	0.482026i	−0.904851	−	0.425728i	$-0.860018\pi$
$101$	−13.3096	+	4.84430i	−1.32435	+	0.482026i	−0.419503	+	0.907754i	$0.637796\pi$
$102$		0			0
$103$	1.15620	−	0.970163i	0.113923	−	0.0955930i	−0.584046	−	0.811720i	$-0.698531\pi$
$103$	1.15620	−	0.970163i	0.113923	−	0.0955930i	0.697970	+	0.716127i	$0.254087\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−19.4114			−1.87658			−0.938288	−	0.345856i	$-0.887589\pi$
$107$	−19.4114			−1.87658			−0.938288	+	0.345856i	$0.887589\pi$
$108$		0			0
$109$	15.2590			1.46155			0.730775	−	0.682619i	$-0.239159\pi$
$109$	15.2590			1.46155			0.730775	+	0.682619i	$0.239159\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	8.72188	−	7.31853i	0.820485	−	0.688469i	−0.132600	−	0.991170i	$-0.542333\pi$
$113$	8.72188	−	7.31853i	0.820485	−	0.688469i	0.953086	+	0.302701i	$0.0978882\pi$
$114$		0			0
$115$	7.00816	−	2.55076i	0.653514	−	0.237860i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−4.30741	−	3.61435i	−0.394860	−	0.331327i
$120$		0			0
$121$	−1.31717	−	7.47003i	−0.119743	−	0.679094i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	16.0528	+	27.8042i	1.43581	+	2.48689i
$126$		0			0
$127$	0.804999	−	1.39430i	0.0714321	−	0.123724i	−0.828097	−	0.560585i	$-0.810576\pi$
$127$	0.804999	−	1.39430i	0.0714321	−	0.123724i	0.899529	+	0.436861i	$0.143910\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−4.94924	−	1.80138i	−0.432417	−	0.157387i	0.116635	−	0.993175i	$-0.462789\pi$
$131$	−4.94924	−	1.80138i	−0.432417	−	0.157387i	−0.549053	+	0.835788i	$0.685011\pi$
$132$		0			0
$133$	−2.82021	+	15.9942i	−0.244543	+	1.38687i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.71499	−	15.3975i	0.231958	−	1.31550i	−0.616969	−	0.786987i	$-0.711640\pi$
$137$	2.71499	−	15.3975i	0.231958	−	1.31550i	0.848927	−	0.528510i	$-0.177249\pi$
$138$		0			0
$139$	11.5151	+	4.19114i	0.976696	+	0.355488i	0.780555	−	0.625087i	$-0.214937\pi$
$139$	11.5151	+	4.19114i	0.976696	+	0.355488i	0.196141	+	0.980576i	$0.437159\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	2.15297	−	3.72905i	0.180040	−	0.311839i
$144$		0			0
$145$	−2.41897	−	4.18978i	−0.200885	−	0.347943i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.63622	−	20.6221i	−0.297891	−	1.68942i	−0.655214	−	0.755443i	$-0.727422\pi$
$149$	−3.63622	−	20.6221i	−0.297891	−	1.68942i	0.357323	−	0.933981i	$-0.383690\pi$
$150$		0			0
$151$	−7.38748	−	6.19883i	−0.601184	−	0.504454i	0.290642	−	0.956832i	$-0.406131\pi$
$151$	−7.38748	−	6.19883i	−0.601184	−	0.504454i	−0.891826	+	0.452378i	$0.850576\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	7.33738	−	2.67059i	0.589352	−	0.214507i
$156$		0			0
$157$	−9.00929	+	7.55969i	−0.719019	+	0.603329i	−0.927114	−	0.374780i	$-0.877718\pi$
$157$	−9.00929	+	7.55969i	−0.719019	+	0.603329i	0.208094	+	0.978109i	$0.433274\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	6.24034			0.491808
$162$		0			0
$163$	−14.3539			−1.12429			−0.562143	−	0.827040i	$-0.690023\pi$
$163$	−14.3539			−1.12429			−0.562143	+	0.827040i	$0.690023\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.48095	+	5.43816i	−0.501511	+	0.420818i	−0.858130	−	0.513432i	$-0.828374\pi$
$167$	−6.48095	+	5.43816i	−0.501511	+	0.420818i	0.356619	+	0.934250i	$0.383929\pi$
$168$		0			0
$169$	7.11373	−	2.58919i	0.547210	−	0.199168i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−19.1950	−	16.1065i	−1.45937	−	1.22455i	−0.925370	−	0.379066i	$-0.876245\pi$
$173$	−19.1950	−	16.1065i	−1.45937	−	1.22455i	−0.533996	−	0.845487i	$-0.679310\pi$
$174$		0			0
$175$	7.71645	+	43.7621i	0.583308	+	3.30811i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	4.84160	+	8.38590i	0.361878	+	0.626792i	0.988270	−	0.152717i	$-0.0488023\pi$
$179$	4.84160	+	8.38590i	0.361878	+	0.626792i	−0.626392	+	0.779508i	$0.715469\pi$
$180$		0			0
$181$	0.302082	−	0.523221i	0.0224535	−	0.0388907i	−0.854580	−	0.519319i	$-0.826186\pi$
$181$	0.302082	−	0.523221i	0.0224535	−	0.0388907i	0.877034	+	0.480429i	$0.159519\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	34.6053	+	12.5953i	2.54423	+	0.926024i
$186$		0			0
$187$	−0.513369	+	2.91146i	−0.0375412	+	0.212907i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	3.59590	−	20.3934i	0.260190	−	1.47561i	−0.522199	−	0.852824i	$-0.674888\pi$
$191$	3.59590	−	20.3934i	0.260190	−	1.47561i	0.782390	−	0.622789i	$-0.214001\pi$
$192$		0			0
$193$	10.4636	+	3.80845i	0.753189	+	0.274138i	0.689947	−	0.723860i	$-0.257634\pi$
$193$	10.4636	+	3.80845i	0.753189	+	0.274138i	0.0632420	+	0.997998i	$0.479856\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	6.31196	−	10.9326i	0.449709	−	0.778918i	−0.548658	−	0.836047i	$-0.684861\pi$
$197$	6.31196	−	10.9326i	0.449709	−	0.778918i	0.998367	+	0.0571286i	$0.0181945\pi$
$198$		0			0
$199$	10.5243	+	18.2286i	0.746049	+	1.29219i	0.949703	+	0.313152i	$0.101385\pi$
$199$	10.5243	+	18.2286i	0.746049	+	1.29219i	−0.203654	+	0.979043i	$0.565282\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−0.702945	−	3.98660i	−0.0493371	−	0.279804i
$204$		0			0
$205$	12.5357	+	10.5187i	0.875531	+	0.734658i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	8.02404	−	2.92051i	0.555035	−	0.202016i
$210$		0			0
$211$	−16.9822	+	14.2497i	−1.16910	+	0.980992i	−0.999989	−	0.00460533i	$-0.998534\pi$
$211$	−16.9822	+	14.2497i	−1.16910	+	0.980992i	−0.169111	+	0.985597i	$0.554090\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−10.8106			−0.737275
$216$		0			0
$217$	6.53349			0.443522
$218$		0			0
$219$		0			0
$220$		0			0
$221$	2.85577	−	2.39628i	0.192100	−	0.161191i
$222$		0			0
$223$	−12.9567	+	4.71584i	−0.867643	+	0.315796i	−0.737212	−	0.675661i	$-0.763858\pi$
$223$	−12.9567	+	4.71584i	−0.867643	+	0.315796i	−0.130431	+	0.991457i	$0.541636\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	7.12191	+	5.97599i	0.472698	+	0.396641i	0.847778	−	0.530352i	$-0.177940\pi$
$227$	7.12191	+	5.97599i	0.472698	+	0.396641i	−0.375080	+	0.926993i	$0.622385\pi$
$228$		0			0
$229$	−0.0257158	−	0.145841i	−0.00169935	−	0.00963747i	0.983946	−	0.178465i	$-0.0571131\pi$
$229$	−0.0257158	−	0.145841i	−0.00169935	−	0.00963747i	−0.985646	+	0.168827i	$0.946002\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.824403	−	1.42791i	−0.0540084	−	0.0935454i	0.837757	−	0.546043i	$-0.183866\pi$
$233$	−0.824403	−	1.42791i	−0.0540084	−	0.0935454i	−0.891766	+	0.452498i	$0.850533\pi$
$234$		0			0
$235$	−15.6897	+	27.1753i	−1.02348	+	1.77272i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−11.4292	−	4.15988i	−0.739293	−	0.269081i	−0.0551997	−	0.998475i	$-0.517580\pi$
$239$	−11.4292	−	4.15988i	−0.739293	−	0.269081i	−0.684093	+	0.729395i	$0.739802\pi$
$240$		0			0
$241$	0.168569	−	0.956002i	0.0108585	−	0.0615815i	−0.978897	−	0.204354i	$-0.934491\pi$
$241$	0.168569	−	0.956002i	0.0108585	−	0.0615815i	0.989756	+	0.142773i	$0.0456017\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−3.90426	+	22.1422i	−0.249434	+	1.41461i
$246$		0			0
$247$	−10.1182	−	3.68273i	−0.643806	−	0.234326i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−12.1814	+	21.0988i	−0.768884	+	1.33175i	0.169284	+	0.985567i	$0.445855\pi$
$251$	−12.1814	+	21.0988i	−0.768884	+	1.33175i	−0.938168	+	0.346180i	$0.887479\pi$
$252$		0			0
$253$	−1.64050	−	2.84142i	−0.103137	−	0.178639i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	0.159344	+	0.903686i	0.00993961	+	0.0563704i	0.989374	−	0.145392i	$-0.0464443\pi$
$257$	0.159344	+	0.903686i	0.00993961	+	0.0563704i	−0.979435	+	0.201762i	$0.935333\pi$
$258$		0			0
$259$	23.6048	+	19.8068i	1.46673	+	1.23073i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−22.0362	+	8.02050i	−1.35881	+	0.494565i	−0.915685	−	0.401896i	$-0.868351\pi$
$263$	−22.0362	+	8.02050i	−1.35881	+	0.494565i	−0.443122	+	0.896461i	$0.646129\pi$
$264$		0			0
$265$	25.8194	−	21.6650i	1.58607	−	1.33087i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−16.5865			−1.01130			−0.505649	−	0.862739i	$-0.668747\pi$
$269$	−16.5865			−1.01130			−0.505649	+	0.862739i	$0.668747\pi$
$270$		0			0
$271$	17.5443			1.06574			0.532869	−	0.846198i	$-0.321114\pi$
$271$	17.5443			1.06574			0.532869	+	0.846198i	$0.321114\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	17.8977	−	15.0180i	1.07927	−	0.905618i
$276$		0			0
$277$	−22.7716	+	8.28817i	−1.36821	+	0.497988i	−0.918583	−	0.395228i	$-0.870666\pi$
$277$	−22.7716	+	8.28817i	−1.36821	+	0.497988i	−0.449628	+	0.893216i	$0.648443\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−16.1800	−	13.5766i	−0.965218	−	0.809914i	0.0165762	−	0.999863i	$-0.494723\pi$
$281$	−16.1800	−	13.5766i	−0.965218	−	0.809914i	−0.981794	+	0.189949i	$0.939168\pi$
$282$		0			0
$283$	−4.46832	−	25.3411i	−0.265614	−	1.50637i	−0.767281	−	0.641311i	$-0.778391\pi$
$283$	−4.46832	−	25.3411i	−0.265614	−	1.50637i	0.501667	−	0.865061i	$-0.332720\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	6.84628	+	11.8581i	0.404123	+	0.699962i
$288$		0			0
$289$	7.22023	−	12.5058i	0.424720	−	0.735636i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	17.1968	+	6.25911i	1.00464	+	0.365661i	0.791374	−	0.611332i	$-0.209366\pi$
$293$	17.1968	+	6.25911i	1.00464	+	0.365661i	0.213271	+	0.976993i	$0.431588\pi$
$294$		0			0
$295$	0.892685	−	5.06267i	0.0519741	−	0.294760i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.718432	+	4.07443i	−0.0415480	+	0.235631i
$300$		0			0
$301$	−8.50011	−	3.09379i	−0.489938	−	0.178323i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−9.13045	+	15.8144i	−0.522808	+	0.905530i
$306$		0			0
$307$	6.26334	+	10.8484i	0.357468	+	0.619152i	0.987537	−	0.157387i	$-0.0503069\pi$
$307$	6.26334	+	10.8484i	0.357468	+	0.619152i	−0.630069	+	0.776539i	$0.716974\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	1.36185	+	7.72343i	0.0772234	+	0.437956i	0.998765	+	0.0496769i	$0.0158191\pi$
$311$	1.36185	+	7.72343i	0.0772234	+	0.437956i	−0.921542	+	0.388279i	$0.873070\pi$
$312$		0			0
$313$	4.92505	+	4.13261i	0.278380	+	0.233589i	0.771278	−	0.636498i	$-0.219618\pi$
$313$	4.92505	+	4.13261i	0.278380	+	0.233589i	−0.492898	+	0.870087i	$0.664062\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−17.9168	+	6.52118i	−1.00631	+	0.366266i	−0.792014	−	0.610503i	$-0.790967\pi$
$317$	−17.9168	+	6.52118i	−1.00631	+	0.366266i	−0.214294	+	0.976769i	$0.568745\pi$
$318$		0			0
$319$	−1.63043	+	1.36809i	−0.0912865	+	0.0765984i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	7.39281			0.411347
$324$		0			0
$325$	−29.4615			−1.63423
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−20.1135	+	16.8772i	−1.10889	+	0.930473i
$330$		0			0
$331$	−14.1739	+	5.15888i	−0.779069	+	0.283558i	−0.700784	−	0.713373i	$-0.747166\pi$
$331$	−14.1739	+	5.15888i	−0.779069	+	0.283558i	−0.0782845	+	0.996931i	$0.524944\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	20.4289	+	17.1419i	1.11615	+	0.936562i
$336$		0			0
$337$	−0.631777	−	3.58299i	−0.0344151	−	0.195178i	0.962753	−	0.270382i	$-0.0871501\pi$
$337$	−0.631777	−	3.58299i	−0.0344151	−	0.195178i	−0.997168	+	0.0752046i	$0.976039\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−1.71756	−	2.97490i	−0.0930111	−	0.161100i
$342$		0			0
$343$	2.89475	−	5.01386i	0.156302	−	0.270723i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−10.6147	−	3.86345i	−0.569829	−	0.207401i	0.0410055	−	0.999159i	$-0.486944\pi$
$347$	−10.6147	−	3.86345i	−0.569829	−	0.207401i	−0.610835	+	0.791758i	$0.709166\pi$
$348$		0			0
$349$	4.62824	−	26.2480i	0.247744	−	1.40503i	−0.566289	−	0.824207i	$-0.691621\pi$
$349$	4.62824	−	26.2480i	0.247744	−	1.40503i	0.814033	−	0.580819i	$-0.197267\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.332020	+	1.88298i	−0.0176716	+	0.100221i	−0.992368	−	0.123313i	$-0.960648\pi$
$353$	−0.332020	+	1.88298i	−0.0176716	+	0.100221i	0.974696	+	0.223534i	$0.0717592\pi$
$354$		0			0
$355$	6.87843	+	2.50354i	0.365069	+	0.132874i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	13.2372	−	22.9275i	0.698631	−	1.21006i	−0.270310	−	0.962773i	$-0.587126\pi$
$359$	13.2372	−	22.9275i	0.698631	−	1.21006i	0.968941	−	0.247291i	$-0.0795405\pi$
$360$		0			0
$361$	−1.17647	−	2.03771i	−0.0619197	−	0.107248i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2.01179	−	11.4094i	−0.105302	−	0.597196i
$366$		0			0
$367$	9.57522	+	8.03457i	0.499823	+	0.419401i	0.857531	−	0.514432i	$-0.171997\pi$
$367$	9.57522	+	8.03457i	0.499823	+	0.419401i	−0.357708	+	0.933833i	$0.616442\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	26.5013	−	9.64570i	1.37588	−	0.500780i
$372$		0			0
$373$	−2.45390	+	2.05907i	−0.127058	+	0.106614i	−0.704102	−	0.710098i	$-0.748650\pi$
$373$	−2.45390	+	2.05907i	−0.127058	+	0.106614i	0.577044	+	0.816713i	$0.304206\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	2.68385			0.138225
$378$		0			0
$379$	10.7650			0.552963			0.276481	−	0.961019i	$-0.410832\pi$
$379$	10.7650			0.552963			0.276481	+	0.961019i	$0.410832\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	23.0996	−	19.3829i	1.18033	−	0.990418i	0.180358	−	0.983601i	$-0.442275\pi$
$383$	23.0996	−	19.3829i	1.18033	−	0.990418i	0.999977	−	0.00681699i	$-0.00216993\pi$
$384$		0			0
$385$	25.6353	−	9.33047i	1.30649	−	0.475525i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	14.0029	+	11.7498i	0.709975	+	0.595739i	0.924592	−	0.380959i	$-0.124406\pi$
$389$	14.0029	+	11.7498i	0.709975	+	0.595739i	−0.214617	+	0.976698i	$0.568850\pi$
$390$		0			0
$391$	−0.493262	−	2.79743i	−0.0249453	−	0.141472i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−20.9387	−	36.2669i	−1.05354	−	1.82479i
$396$		0			0
$397$	−4.90869	+	8.50210i	−0.246360	+	0.426708i	−0.962513	−	0.271235i	$-0.912568\pi$
$397$	−4.90869	+	8.50210i	−0.246360	+	0.426708i	0.716153	+	0.697943i	$0.245901\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−21.6780	−	7.89014i	−1.08255	−	0.394015i	−0.261692	−	0.965151i	$-0.584280\pi$
$401$	−21.6780	−	7.89014i	−1.08255	−	0.394015i	−0.820855	+	0.571137i	$0.806503\pi$
$402$		0			0
$403$	−0.752182	+	4.26583i	−0.0374688	+	0.212496i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	2.81328	−	15.9549i	0.139449	−	0.790856i
$408$		0			0
$409$	17.6497	+	6.42397i	0.872723	+	0.317645i	0.739269	−	0.673410i	$-0.235171\pi$
$409$	17.6497	+	6.42397i	0.872723	+	0.317645i	0.133453	+	0.991055i	$0.457393\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	2.15074	−	3.72519i	0.105831	−	0.183305i
$414$		0			0
$415$	−23.7204	−	41.0849i	−1.16439	−	2.01678i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	5.44953	+	30.9058i	0.266227	+	1.50985i	0.765519	+	0.643414i	$0.222482\pi$
$419$	5.44953	+	30.9058i	0.266227	+	1.50985i	−0.499292	+	0.866434i	$0.666407\pi$
$420$		0			0
$421$	−15.9472	−	13.3813i	−0.777217	−	0.652162i	0.165329	−	0.986238i	$-0.447131\pi$
$421$	−15.9472	−	13.3813i	−0.777217	−	0.652162i	−0.942546	+	0.334076i	$0.891576\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	19.0078	−	6.91827i	0.922013	−	0.335585i
$426$		0			0
$427$	−11.7049	+	9.82154i	−0.566438	+	0.475298i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	30.8928			1.48806			0.744028	−	0.668149i	$-0.232913\pi$
$431$	30.8928			1.48806			0.744028	+	0.668149i	$0.232913\pi$
$432$		0			0
$433$	−15.5840			−0.748917			−0.374459	−	0.927244i	$-0.622171\pi$
$433$	−15.5840			−0.748917			−0.374459	+	0.927244i	$0.622171\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−6.28506	+	5.27379i	−0.300655	+	0.252280i
$438$		0			0
$439$	10.4878	−	3.81726i	0.500557	−	0.182188i	−0.0793875	−	0.996844i	$-0.525296\pi$
$439$	10.4878	−	3.81726i	0.500557	−	0.182188i	0.579945	+	0.814656i	$0.303074\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−11.0896	−	9.30524i	−0.526881	−	0.442105i	0.340142	−	0.940374i	$-0.389525\pi$
$443$	−11.0896	−	9.30524i	−0.526881	−	0.442105i	−0.867023	+	0.498269i	$0.833969\pi$
$444$		0			0
$445$	3.95575	+	22.4341i	0.187520	+	1.06348i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−18.6936	−	32.3783i	−0.882207	−	1.52803i	−0.848882	−	0.528583i	$-0.822724\pi$
$449$	−18.6936	−	32.3783i	−0.882207	−	1.52803i	−0.0333252	−	0.999445i	$-0.510610\pi$
$450$		0			0
$451$	3.59958	−	6.23465i	0.169497	−	0.293578i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−32.3257	−	11.7656i	−1.51545	−	0.551580i
$456$		0			0
$457$	2.38128	−	13.5049i	0.111392	−	0.631734i	−0.877082	−	0.480341i	$-0.840513\pi$
$457$	2.38128	−	13.5049i	0.111392	−	0.631734i	0.988474	−	0.151393i	$-0.0483760\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−0.928212	+	5.26415i	−0.0432312	+	0.245176i	−0.998764	−	0.0497096i	$-0.984170\pi$
$461$	−0.928212	+	5.26415i	−0.0432312	+	0.245176i	0.955533	+	0.294886i	$0.0952815\pi$
$462$		0			0
$463$	−34.1845	−	12.4422i	−1.58869	−	0.578236i	−0.611620	−	0.791152i	$-0.709482\pi$
$463$	−34.1845	−	12.4422i	−1.58869	−	0.578236i	−0.977070	+	0.212916i	$0.931704\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	2.61809	−	4.53466i	0.121151	−	0.209839i	−0.799071	−	0.601237i	$-0.794675\pi$
$467$	2.61809	−	4.53466i	0.121151	−	0.209839i	0.920222	+	0.391397i	$0.128008\pi$
$468$		0			0
$469$	11.1571	+	19.3247i	0.515188	+	0.892331i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.825859	+	4.68368i	0.0379730	+	0.215356i
$474$		0			0
$475$	−44.7557	−	37.5545i	−2.05353	−	1.72312i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	10.9912	−	4.00046i	0.502199	−	0.182786i	−0.0784836	−	0.996915i	$-0.525008\pi$
$479$	10.9912	−	4.00046i	0.502199	−	0.182786i	0.580683	+	0.814130i	$0.302786\pi$
$480$		0			0
$481$	−15.6498	+	13.1317i	−0.713568	+	0.598754i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	50.7982			2.30663
$486$		0			0
$487$	20.7362			0.939645			0.469823	−	0.882761i	$-0.344318\pi$
$487$	20.7362			0.939645			0.469823	+	0.882761i	$0.344318\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−7.57101	+	6.35283i	−0.341675	+	0.286699i	−0.797437	−	0.603402i	$-0.793811\pi$
$491$	−7.57101	+	6.35283i	−0.341675	+	0.286699i	0.455762	+	0.890102i	$0.349367\pi$
$492$		0			0
$493$	−1.73155	+	0.630234i	−0.0779852	+	0.0283843i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	4.69189	+	3.93696i	0.210460	+	0.176597i
$498$		0			0
$499$	−3.51947	−	19.9599i	−0.157553	−	0.893529i	−0.956414	−	0.292013i	$-0.905675\pi$
$499$	−3.51947	−	19.9599i	−0.157553	−	0.893529i	0.798861	−	0.601516i	$-0.205436\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	1.34704	+	2.33314i	0.0600614	+	0.104029i	0.894493	−	0.447083i	$-0.147537\pi$
$503$	1.34704	+	2.33314i	0.0600614	+	0.104029i	−0.834431	+	0.551112i	$0.814204\pi$
$504$		0			0
$505$	29.7468	−	51.5230i	1.32372	−	2.29274i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−2.21633	−	0.806680i	−0.0982373	−	0.0357555i	0.292434	−	0.956286i	$-0.405535\pi$
$509$	−2.21633	−	0.806680i	−0.0982373	−	0.0357555i	−0.390671	+	0.920530i	$0.627757\pi$
$510$		0			0
$511$	1.68334	−	9.54670i	0.0744666	−	0.422321i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−1.10088	+	6.24339i	−0.0485105	+	0.275117i
$516$		0			0
$517$	12.9723	+	4.72153i	0.570521	+	0.207652i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−17.5589	+	30.4129i	−0.769270	+	1.33241i	0.168690	+	0.985669i	$0.446046\pi$
$521$	−17.5589	+	30.4129i	−0.769270	+	1.33241i	−0.937959	+	0.346745i	$0.887287\pi$
$522$		0			0
$523$	−14.8599	−	25.7381i	−0.649777	−	1.12545i	−0.983176	−	0.182661i	$-0.941529\pi$
$523$	−14.8599	−	25.7381i	−0.649777	−	1.12545i	0.333399	−	0.942786i	$-0.391804\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−0.516433	−	2.92884i	−0.0224962	−	0.127582i
$528$		0			0
$529$	−15.2041	−	12.7577i	−0.661047	−	0.554684i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−8.53056	+	3.10487i	−0.369500	+	0.134487i
$534$		0			0
$535$	62.4602	−	52.4103i	2.70039	−	2.26590i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	9.89135			0.426050
$540$		0			0
$541$	−4.06242			−0.174657			−0.0873286	−	0.996180i	$-0.527833\pi$
$541$	−4.06242			−0.174657			−0.0873286	+	0.996180i	$0.527833\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−49.0990	+	41.1989i	−2.10317	+	1.76477i
$546$		0			0
$547$	35.0232	−	12.7474i	1.49748	−	0.545040i	0.542077	−	0.840329i	$-0.317638\pi$
$547$	35.0232	−	12.7474i	1.49748	−	0.545040i	0.955408	+	0.295289i	$0.0954160\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	4.07711	+	3.42110i	0.173691	+	0.145744i
$552$		0			0
$553$	−6.08472	−	34.5082i	−0.258749	−	1.46744i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	4.81761	+	8.34434i	0.204128	+	0.353561i	0.949855	−	0.312692i	$-0.101231\pi$
$557$	4.81761	+	8.34434i	0.204128	+	0.353561i	−0.745726	+	0.666253i	$0.767897\pi$
$558$		0			0
$559$	2.99858	−	5.19370i	0.126827	−	0.219670i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	15.0427	+	5.47511i	0.633976	+	0.230748i	0.638961	−	0.769239i	$-0.279365\pi$
$563$	15.0427	+	5.47511i	0.633976	+	0.230748i	−0.00498517	+	0.999988i	$0.501587\pi$
$564$		0			0
$565$	−8.30459	+	47.0977i	−0.349377	+	1.98141i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−3.35361	+	19.0193i	−0.140591	+	0.797329i	0.830212	+	0.557448i	$0.188219\pi$
$569$	−3.35361	+	19.0193i	−0.140591	+	0.797329i	−0.970802	+	0.239881i	$0.922892\pi$
$570$		0			0
$571$	8.74110	+	3.18150i	0.365804	+	0.133142i	0.518381	−	0.855150i	$-0.326535\pi$
$571$	8.74110	+	3.18150i	0.365804	+	0.133142i	−0.152577	+	0.988292i	$0.548757\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−11.2244	+	19.4412i	−0.468089	+	0.810753i
$576$		0			0
$577$	−3.05082	−	5.28418i	−0.127007	−	0.219983i	0.795508	−	0.605943i	$-0.207204\pi$
$577$	−3.05082	−	5.28418i	−0.127007	−	0.219983i	−0.922516	+	0.385959i	$0.873871\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−6.89305	−	39.0925i	−0.285972	−	1.62183i
$582$		0			0
$583$	−11.3588	−	9.53117i	−0.470434	−	0.394741i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−21.3843	+	7.78325i	−0.882625	+	0.321249i	−0.743268	−	0.668993i	$-0.766725\pi$
$587$	−21.3843	+	7.78325i	−0.882625	+	0.321249i	−0.139356	+	0.990242i	$0.544503\pi$
$588$		0			0
$589$	−6.58031	+	5.52154i	−0.271137	+	0.227511i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−16.4186			−0.674233			−0.337117	−	0.941463i	$-0.609452\pi$
$593$	−16.4186			−0.674233			−0.337117	+	0.941463i	$0.609452\pi$
$594$		0			0
$595$	23.6186			0.968268
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−25.3603	+	21.2798i	−1.03619	+	0.869469i	−0.991575	−	0.129535i	$-0.958652\pi$
$599$	−25.3603	+	21.2798i	−1.03619	+	0.869469i	−0.0446184	+	0.999004i	$0.514207\pi$
$600$		0			0
$601$	−21.3505	+	7.77094i	−0.870904	+	0.316983i	−0.738533	−	0.674217i	$-0.764481\pi$
$601$	−21.3505	+	7.77094i	−0.870904	+	0.316983i	−0.132371	+	0.991200i	$0.542259\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	24.4071	+	20.4800i	0.992290	+	0.832630i
$606$		0			0
$607$	−2.97342	−	16.8631i	−0.120688	−	0.684453i	−0.983776	−	0.179401i	$-0.942584\pi$
$607$	−2.97342	−	16.8631i	−0.120688	−	0.684453i	0.863089	−	0.505053i	$-0.168527\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−8.70385	−	15.0755i	−0.352120	−	0.609890i
$612$		0			0
$613$	−20.8362	+	36.0893i	−0.841564	+	1.45763i	0.0470074	+	0.998895i	$0.485032\pi$
$613$	−20.8362	+	36.0893i	−0.841564	+	1.45763i	−0.888572	+	0.458738i	$0.848302\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	17.0470	+	6.20458i	0.686285	+	0.249787i	0.661544	−	0.749907i	$-0.269902\pi$
$617$	17.0470	+	6.20458i	0.686285	+	0.249787i	0.0247410	+	0.999694i	$0.492124\pi$
$618$		0			0
$619$	−1.38552	+	7.85765i	−0.0556886	+	0.315826i	−0.999909	−	0.0134883i	$-0.995706\pi$
$619$	−1.38552	+	7.85765i	−0.0556886	+	0.315826i	0.944220	+	0.329314i	$0.106818\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−3.30993	+	18.7715i	−0.132609	+	0.752066i
$624$		0			0
$625$	−67.3190	−	24.5021i	−2.69276	−	0.980084i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	7.01319	−	12.1472i	0.279634	−	0.484340i
$630$		0			0
$631$	0.118628	+	0.205470i	0.00472251	+	0.00817962i	0.868377	−	0.495905i	$-0.165163\pi$
$631$	0.118628	+	0.205470i	0.00472251	+	0.00817962i	−0.863654	+	0.504084i	$0.831830\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.17432	+	6.65991i	0.0466016	+	0.264291i
$636$		0			0
$637$	−9.55476	−	8.01740i	−0.378574	−	0.317661i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	22.4754	−	8.18038i	0.887725	−	0.323105i	0.142402	−	0.989809i	$-0.454517\pi$
$641$	22.4754	−	8.18038i	0.887725	−	0.323105i	0.745323	+	0.666704i	$0.232295\pi$
$642$		0			0
$643$	−19.7687	+	16.5879i	−0.779600	+	0.654162i	−0.943148	−	0.332373i	$-0.892151\pi$
$643$	−19.7687	+	16.5879i	−0.779600	+	0.654162i	0.163548	+	0.986535i	$0.447706\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−6.60899			−0.259826			−0.129913	−	0.991525i	$-0.541470\pi$
$647$	−6.60899			−0.259826			−0.129913	+	0.991525i	$0.541470\pi$
$648$		0			0
$649$	−2.26159			−0.0887753
$650$		0			0
$651$		0			0
$652$		0			0
$653$	19.0986	−	16.0257i	0.747388	−	0.627133i	−0.187423	−	0.982279i	$-0.560014\pi$
$653$	19.0986	−	16.0257i	0.747388	−	0.627133i	0.934811	+	0.355147i	$0.115569\pi$
$654$		0			0
$655$	20.7888	−	7.56652i	0.812287	−	0.295648i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−5.91373	−	4.96221i	−0.230366	−	0.193300i	0.520297	−	0.853985i	$-0.325821\pi$
$659$	−5.91373	−	4.96221i	−0.230366	−	0.193300i	−0.750663	+	0.660685i	$0.770266\pi$
$660$		0			0
$661$	3.10169	+	17.5905i	0.120642	+	0.684193i	0.983801	+	0.179262i	$0.0573709\pi$
$661$	3.10169	+	17.5905i	0.120642	+	0.684193i	−0.863160	+	0.504931i	$0.831518\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−34.1093	−	59.0790i	−1.32270	−	2.29098i
$666$		0			0
$667$	1.02251	−	1.77103i	0.0395916	−	0.0685747i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	7.54909	+	2.74764i	0.291429	+	0.106072i
$672$		0			0
$673$	0.849501	−	4.81776i	0.0327459	−	0.185711i	−0.964047	−	0.265730i	$-0.914387\pi$
$673$	0.849501	−	4.81776i	0.0327459	−	0.185711i	0.996793	+	0.0800190i	$0.0254981\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	2.93348	−	16.6366i	0.112743	−	0.639397i	−0.875100	−	0.483942i	$-0.839205\pi$
$677$	2.93348	−	16.6366i	0.112743	−	0.639397i	0.987843	−	0.155455i	$-0.0496843\pi$
$678$		0			0
$679$	39.9415	+	14.5375i	1.53281	+	0.557898i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−16.8279	+	29.1467i	−0.643900	+	1.11527i	0.340654	+	0.940189i	$0.389352\pi$
$683$	−16.8279	+	29.1467i	−0.643900	+	1.11527i	−0.984554	+	0.175080i	$0.943982\pi$
$684$		0			0
$685$	32.8368	+	56.8750i	1.25463	+	2.17308i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	3.24683	+	18.4137i	0.123694	+	0.701506i
$690$		0			0
$691$	12.5613	+	10.5402i	0.477856	+	0.400968i	0.849650	−	0.527347i	$-0.176813\pi$
$691$	12.5613	+	10.5402i	0.477856	+	0.400968i	−0.371795	+	0.928315i	$0.621257\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−48.3680	+	17.6045i	−1.83470	+	0.667778i
$696$		0			0
$697$	4.77461	−	4.00637i	0.180851	−	0.151752i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	34.9743			1.32096			0.660481	−	0.750843i	$-0.270352\pi$
$701$	34.9743			1.32096			0.660481	+	0.750843i	$0.270352\pi$
$702$		0			0
$703$	−40.5129			−1.52797
$704$		0			0
$705$		0			0
$706$		0			0
$707$	38.1342	−	31.9984i	1.43419	−	1.20342i
$708$		0			0
$709$	25.1183	−	9.14232i	0.943338	−	0.343347i	0.175855	−	0.984416i	$-0.443731\pi$
$709$	25.1183	−	9.14232i	0.943338	−	0.343347i	0.767483	+	0.641069i	$0.221509\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	2.52839	+	2.12157i	0.0946889	+	0.0794535i
$714$		0			0
$715$	3.14072	+	17.8119i	0.117456	+	0.666128i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−13.0563	−	22.6141i	−0.486916	−	0.843364i	0.512970	−	0.858406i	$-0.328545\pi$
$719$	−13.0563	−	22.6141i	−0.486916	−	0.843364i	−0.999887	+	0.0150424i	$0.995212\pi$
$720$		0			0
$721$	−2.65234	+	4.59399i	−0.0987783	+	0.171089i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	13.6842	+	4.98065i	0.508220	+	0.184977i
$726$		0			0
$727$	2.37371	−	13.4620i	0.0880359	−	0.499277i	−0.908624	−	0.417615i	$-0.862866\pi$
$727$	2.37371	−	13.4620i	0.0880359	−	0.499277i	0.996660	−	0.0816618i	$-0.0260227\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−0.715003	+	4.05498i	−0.0264453	+	0.149979i
$732$		0			0
$733$	10.8582	+	3.95207i	0.401058	+	0.145973i	0.534671	−	0.845060i	$-0.320436\pi$
$733$	10.8582	+	3.95207i	0.401058	+	0.145973i	−0.133613	+	0.991034i	$0.542658\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	5.86609	−	10.1604i	0.216080	−	0.374262i
$738$		0			0
$739$	−25.2426	−	43.7215i	−0.928566	−	1.60832i	−0.785724	−	0.618577i	$-0.787709\pi$
$739$	−25.2426	−	43.7215i	−0.928566	−	1.60832i	−0.142841	−	0.989746i	$-0.545624\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−3.64696	−	20.6829i	−0.133794	−	0.758783i	−0.975692	−	0.219146i	$-0.929673\pi$
$743$	−3.64696	−	20.6829i	−0.133794	−	0.758783i	0.841898	−	0.539637i	$-0.181438\pi$
$744$		0			0
$745$	67.3792	+	56.5379i	2.46858	+	2.07139i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	64.1100	−	23.3341i	2.34253	−	0.852610i
$750$		0			0
$751$	−8.57159	+	7.19242i	−0.312782	+	0.262455i	−0.785641	−	0.618683i	$-0.787666\pi$
$751$	−8.57159	+	7.19242i	−0.312782	+	0.262455i	0.472859	+	0.881138i	$0.343222\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	40.5073			1.47421
$756$		0			0
$757$	−22.2619			−0.809123			−0.404561	−	0.914511i	$-0.632576\pi$
$757$	−22.2619			−0.809123			−0.404561	+	0.914511i	$0.632576\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	4.53901	−	3.80868i	0.164539	−	0.138065i	−0.556801	−	0.830646i	$-0.687971\pi$
$761$	4.53901	−	3.80868i	0.164539	−	0.138065i	0.721339	+	0.692582i	$0.243527\pi$
$762$		0			0
$763$	−50.3958	+	18.3426i	−1.82445	+	0.664046i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	2.18464	+	1.83313i	0.0788827	+	0.0661904i
$768$		0			0
$769$	0.393789	+	2.23329i	0.0142004	+	0.0805345i	0.991084	−	0.133236i	$-0.0425367\pi$
$769$	0.393789	+	2.23329i	0.0142004	+	0.0805345i	−0.976884	+	0.213770i	$0.931426\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−4.63951	−	8.03586i	−0.166872	−	0.289030i	0.770447	−	0.637504i	$-0.220033\pi$
$773$	−4.63951	−	8.03586i	−0.166872	−	0.289030i	−0.937318	+	0.348474i	$0.886700\pi$
$774$		0			0
$775$	−11.7516	+	20.3544i	−0.422132	+	0.731153i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−16.9168	−	6.15720i	−0.606106	−	0.220605i
$780$		0			0
$781$	0.559191	−	3.17133i	0.0200094	−	0.113479i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	8.57824	−	48.6496i	0.306171	−	1.73638i
$786$		0			0
$787$	21.6788	+	7.89045i	0.772767	+	0.281264i	0.698153	−	0.715948i	$-0.254005\pi$
$787$	21.6788	+	7.89045i	0.772767	+	0.281264i	0.0746139	+	0.997212i	$0.476228\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−20.0082	+	34.6552i	−0.711410	+	1.23220i
$792$		0			0
$793$	−5.06512	−	8.77304i	−0.179868	−	0.311540i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−3.52552	−	19.9942i	−0.124880	−	0.708232i	−0.981379	−	0.192082i	$-0.938476\pi$
$797$	−3.52552	−	19.9942i	−0.124880	−	0.708232i	0.856499	−	0.516149i	$-0.172635\pi$
$798$		0			0
$799$	9.15560	+	7.68246i	0.323902	+	0.271786i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−4.78944	+	1.74321i	−0.169016	+	0.0615166i
$804$		0			0
$805$	−20.0796	+	16.8487i	−0.707711	+	0.593840i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−35.2976			−1.24100			−0.620499	−	0.784207i	$-0.713070\pi$
$809$	−35.2976			−1.24100			−0.620499	+	0.784207i	$0.713070\pi$
$810$		0			0
$811$	−40.1846			−1.41107			−0.705536	−	0.708675i	$-0.749293\pi$
$811$	−40.1846			−1.41107			−0.705536	+	0.708675i	$0.749293\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	46.1867	−	38.7552i	1.61785	−	1.35754i
$816$		0			0
$817$	11.1756	−	4.06759i	0.390986	−	0.142307i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−10.3898	−	8.71810i	−0.362608	−	0.304264i	0.443221	−	0.896412i	$-0.353836\pi$
$821$	−10.3898	−	8.71810i	−0.362608	−	0.304264i	−0.805829	+	0.592148i	$0.798280\pi$
$822$		0			0
$823$	3.69938	+	20.9802i	0.128952	+	0.731324i	0.978882	+	0.204428i	$0.0655334\pi$
$823$	3.69938	+	20.9802i	0.128952	+	0.731324i	−0.849929	+	0.526897i	$0.823356\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	26.2719	+	45.5043i	0.913564	+	1.58234i	0.808990	+	0.587822i	$0.200014\pi$
$827$	26.2719	+	45.5043i	0.913564	+	1.58234i	0.104573	+	0.994517i	$0.466652\pi$
$828$		0			0
$829$	−6.89163	+	11.9366i	−0.239356	+	0.414577i	−0.960530	−	0.278177i	$-0.910270\pi$
$829$	−6.89163	+	11.9366i	−0.239356	+	0.414577i	0.721174	+	0.692754i	$0.243603\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	8.04718	+	2.92893i	0.278818	+	0.101481i
$834$		0			0
$835$	6.17087	−	34.9967i	0.213552	−	1.21111i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−4.32925	+	24.5524i	−0.149462	+	0.847643i	0.814213	+	0.580566i	$0.197169\pi$
$839$	−4.32925	+	24.5524i	−0.149462	+	0.847643i	−0.963675	+	0.267077i	$0.913942\pi$
$840$		0			0
$841$	26.0045	+	9.46486i	0.896707	+	0.326375i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−15.8991	+	27.5381i	−0.546946	+	0.947339i
$846$		0			0
$847$	13.3298	+	23.0878i	0.458016	+	0.793308i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	2.70310	+	15.3300i	0.0926610	+	0.525506i
$852$		0			0
$853$	−3.55496	−	2.98297i	−0.121720	−	0.102135i	0.579896	−	0.814690i	$-0.303093\pi$
$853$	−3.55496	−	2.98297i	−0.121720	−	0.102135i	−0.701616	+	0.712556i	$0.747538\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−34.0597	+	12.3967i	−1.16346	+	0.423464i	−0.850331	−	0.526248i	$-0.823598\pi$
$857$	−34.0597	+	12.3967i	−1.16346	+	0.423464i	−0.313126	+	0.949712i	$0.601376\pi$
$858$		0			0
$859$	20.9740	−	17.5993i	0.715623	−	0.600479i	−0.210547	−	0.977584i	$-0.567525\pi$
$859$	20.9740	−	17.5993i	0.715623	−	0.600479i	0.926171	+	0.377104i	$0.123080\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	20.9476			0.713065			0.356532	−	0.934283i	$-0.383959\pi$
$863$	20.9476			0.713065			0.356532	+	0.934283i	$0.383959\pi$
$864$		0			0
$865$	105.251			3.57863
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−14.1130	+	11.8423i	−0.478752	+	0.401721i
$870$		0			0
$871$	−13.9019	+	5.05989i	−0.471049	+	0.171448i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−86.4403	−	72.5320i	−2.92222	−	2.45203i
$876$		0			0
$877$	3.16206	+	17.9329i	0.106775	+	0.605551i	0.990496	+	0.137538i	$0.0439190\pi$
$877$	3.16206	+	17.9329i	0.106775	+	0.605551i	−0.883721	+	0.468013i	$0.844970\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	23.0582	+	39.9380i	0.776851	+	1.34555i	0.933748	+	0.357931i	$0.116518\pi$
$881$	23.0582	+	39.9380i	0.776851	+	1.34555i	−0.156897	+	0.987615i	$0.550149\pi$
$882$		0			0
$883$	9.03494	−	15.6490i	0.304050	−	0.526630i	−0.672999	−	0.739643i	$-0.734994\pi$
$883$	9.03494	−	15.6490i	0.304050	−	0.526630i	0.977049	+	0.213013i	$0.0683277\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	24.8303	+	9.03750i	0.833721	+	0.303450i	0.723385	−	0.690445i	$-0.242585\pi$
$887$	24.8303	+	9.03750i	0.833721	+	0.303450i	0.110336	+	0.993894i	$0.464807\pi$
$888$		0			0
$889$	−0.982602	+	5.57261i	−0.0329554	+	0.186899i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	5.99448	−	33.9964i	0.200598	−	1.13765i
$894$		0			0
$895$	−38.2205	−	13.9111i	−1.27757	−	0.464998i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	1.07054	−	1.85423i	0.0357045	−	0.0618420i
$900$		0			0
$901$	−6.41876	−	11.1176i	−0.213840	−	0.370381i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.440673	+	2.49918i	0.0146485	+	0.0830755i
$906$		0			0
$907$	28.7563	+	24.1294i	0.954838	+	0.801204i	0.980106	−	0.198477i	$-0.0635994\pi$
$907$	28.7563	+	24.1294i	0.954838	+	0.801204i	−0.0252678	+	0.999681i	$0.508044\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−15.0435	+	5.47539i	−0.498414	+	0.181408i	−0.578980	−	0.815342i	$-0.696549\pi$
$911$	−15.0435	+	5.47539i	−0.498414	+	0.181408i	0.0805668	+	0.996749i	$0.474327\pi$
$912$		0			0
$913$	−15.9879	+	13.4155i	−0.529123	+	0.443987i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	18.5112			0.611294
$918$		0			0
$919$	36.8859			1.21675			0.608377	−	0.793648i	$-0.291821\pi$
$919$	36.8859			1.21675			0.608377	+	0.793648i	$0.291821\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−3.11068	+	2.61017i	−0.102389	+	0.0859147i
$924$		0			0
$925$	−104.164	+	37.9124i	−3.42488	+	1.24655i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	26.0445	+	21.8539i	0.854492	+	0.717004i	0.960774	−	0.277332i	$-0.0894501\pi$
$929$	26.0445	+	21.8539i	0.854492	+	0.717004i	−0.106282	+	0.994336i	$0.533895\pi$
$930$		0			0
$931$	−4.29513	−	24.3589i	−0.140767	−	0.798330i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−6.20899	−	10.7543i	−0.203056	−	0.351703i
$936$		0			0
$937$	−6.09208	+	10.5518i	−0.199020	+	0.344712i	−0.948211	−	0.317642i	$-0.897109\pi$
$937$	−6.09208	+	10.5518i	−0.199020	+	0.344712i	0.749191	+	0.662354i	$0.230442\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	10.1068	+	3.67857i	0.329472	+	0.119918i	0.501459	−	0.865181i	$-0.332797\pi$
$941$	10.1068	+	3.67857i	0.329472	+	0.119918i	−0.171988	+	0.985099i	$0.555019\pi$
$942$		0			0
$943$	−1.20116	+	6.81210i	−0.0391151	+	0.221832i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−6.66262	+	37.7856i	−0.216506	+	1.22787i	0.661768	+	0.749709i	$0.269806\pi$
$947$	−6.66262	+	37.7856i	−0.216506	+	1.22787i	−0.878274	+	0.478158i	$0.841305\pi$
$948$		0			0
$949$	6.03942	+	2.19817i	0.196048	+	0.0713556i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−11.2733	+	19.5259i	−0.365177	+	0.632506i	−0.988805	−	0.149216i	$-0.952325\pi$
$953$	−11.2733	+	19.5259i	−0.365177	+	0.632506i	0.623627	+	0.781722i	$0.285658\pi$
$954$		0			0
$955$	43.4910	+	75.3286i	1.40734	+	2.43758i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	9.54225	+	54.1168i	0.308135	+	1.74752i
$960$		0			0
$961$	−21.1002	−	17.7052i	−0.680652	−	0.571135i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−43.9516	+	15.9971i	−1.41485	+	0.514964i
$966$		0			0
$967$	−22.4315	+	18.8223i	−0.721349	+	0.605284i	−0.927758	−	0.373182i	$-0.878267\pi$
$967$	−22.4315	+	18.8223i	−0.721349	+	0.605284i	0.206409	+	0.978466i	$0.433822\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−33.2319			−1.06646			−0.533232	−	0.845969i	$-0.679023\pi$
$971$	−33.2319			−1.06646			−0.533232	+	0.845969i	$0.679023\pi$
$972$		0			0
$973$	−43.0688			−1.38072
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−4.81204	+	4.03778i	−0.153951	+	0.129180i	−0.716510	−	0.697577i	$-0.754261\pi$
$977$	−4.81204	+	4.03778i	−0.153951	+	0.129180i	0.562559	+	0.826757i	$0.309817\pi$
$978$		0			0
$979$	9.41739	−	3.42765i	0.300981	−	0.109548i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−1.09263	−	0.916828i	−0.0348496	−	0.0292423i	0.625197	−	0.780467i	$-0.285019\pi$
$983$	−1.09263	−	0.916828i	−0.0348496	−	0.0292423i	−0.660046	+	0.751225i	$0.729463\pi$
$984$		0			0
$985$	9.20781	+	52.2201i	0.293385	+	1.66387i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−2.28483	−	3.95744i	−0.0726533	−	0.125839i
$990$		0			0
$991$	5.58886	−	9.68018i	0.177536	−	0.307501i	−0.763500	−	0.645808i	$-0.776521\pi$
$991$	5.58886	−	9.68018i	0.177536	−	0.307501i	0.941036	+	0.338307i	$0.109854\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−83.0809	−	30.2390i	−2.63384	−	0.958640i
$996$		0			0
$997$	−7.00066	+	39.7027i	−0.221713	+	1.25740i	0.647157	+	0.762357i	$0.275958\pi$
$997$	−7.00066	+	39.7027i	−0.221713	+	1.25740i	−0.868870	+	0.495041i	$0.835153\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	972.2.i.b.217.1		18
3.2	odd	2		972.2.i.c.217.3		18
9.2	odd	6		972.2.i.a.541.3		18
9.4	even	3		324.2.i.a.289.3		18
9.5	odd	6		108.2.i.a.97.2	yes	18
9.7	even	3		972.2.i.d.541.1		18
27.2	odd	18		2916.2.e.c.1945.1		18
27.4	even	9		324.2.i.a.37.3		18
27.5	odd	18		972.2.i.a.433.3		18
27.7	even	9		2916.2.e.d.973.9		18
27.11	odd	18		2916.2.a.d.1.9		9
27.13	even	9	inner	972.2.i.b.757.1		18
27.14	odd	18		972.2.i.c.757.3		18
27.16	even	9		2916.2.a.c.1.1		9
27.20	odd	18		2916.2.e.c.973.1		18
27.22	even	9		972.2.i.d.433.1		18
27.23	odd	18		108.2.i.a.49.2	✓	18
27.25	even	9		2916.2.e.d.1945.9		18
36.23	even	6		432.2.u.d.97.2		18
108.23	even	18		432.2.u.d.49.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.i.a.49.2	✓	18	27.23	odd	18
108.2.i.a.97.2	yes	18	9.5	odd	6
324.2.i.a.37.3		18	27.4	even	9
324.2.i.a.289.3		18	9.4	even	3
432.2.u.d.49.2		18	108.23	even	18
432.2.u.d.97.2		18	36.23	even	6
972.2.i.a.433.3		18	27.5	odd	18
972.2.i.a.541.3		18	9.2	odd	6
972.2.i.b.217.1		18	1.1	even	1	trivial
972.2.i.b.757.1		18	27.13	even	9	inner
972.2.i.c.217.3		18	3.2	odd	2
972.2.i.c.757.3		18	27.14	odd	18
972.2.i.d.433.1		18	27.22	even	9
972.2.i.d.541.1		18	9.7	even	3
2916.2.a.c.1.1		9	27.16	even	9
2916.2.a.d.1.9		9	27.11	odd	18
2916.2.e.c.973.1		18	27.20	odd	18
2916.2.e.c.1945.1		18	27.2	odd	18
2916.2.e.d.973.9		18	27.7	even	9
2916.2.e.d.1945.9		18	27.25	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:	\( N \)	\(=\)	\( 972 = 2^{2} \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	972.i (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.21770 + 2.69997i) q^{5} +(-3.30269 + 1.20208i) q^{7} +O(q^{10})\)	\(q+(-3.21770 + 2.69997i) q^{5} +(-3.30269 + 1.20208i) q^{7} +(1.41557 + 1.18781i) q^{11} +(-0.404631 - 2.29478i) q^{13} +(0.799928 + 1.38552i) q^{17} +(2.31046 - 4.00184i) q^{19} +(-1.66845 - 0.607265i) q^{23} +(2.19551 - 12.4514i) q^{25} +(-0.200004 + 1.13428i) q^{29} +(-1.74682 - 0.635792i) q^{31} +(7.38148 - 12.7851i) q^{35} +(-4.38364 - 7.59269i) q^{37} +(-0.676508 - 3.83667i) q^{41} +(1.97156 + 1.65434i) q^{43} +(7.02002 - 2.55508i) q^{47} +(4.10044 - 3.44068i) q^{49} -8.02417 q^{53} -7.76194 q^{55} +(-0.937541 + 0.786690i) q^{59} +(4.08523 - 1.48690i) q^{61} +(7.49781 + 6.29141i) q^{65} +(-1.10248 - 6.25247i) q^{67} +(-0.871328 - 1.50918i) q^{71} +(-1.37908 + 2.38864i) q^{73} +(-6.10304 - 2.22132i) q^{77} +(-1.73125 + 9.81838i) q^{79} +(-1.96124 + 11.1227i) q^{83} +(-6.31478 - 2.29839i) q^{85} +(2.71167 - 4.69675i) q^{89} +(4.09488 + 7.09254i) q^{91} +(3.37047 + 19.1149i) q^{95} +(-9.26426 - 7.77363i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 3 q^{5}+O(q^{10}) \) 18 * q - 3 * q^5	\( 18 q - 3 q^{5} + 15 q^{11} + 12 q^{17} - 33 q^{23} + 9 q^{25} - 21 q^{29} + 9 q^{31} + 21 q^{35} + 33 q^{41} + 18 q^{43} - 9 q^{47} + 36 q^{49} - 66 q^{53} + 12 q^{59} + 36 q^{61} + 66 q^{65} + 27 q^{67} + 12 q^{71} + 9 q^{73} - 33 q^{77} + 18 q^{79} - 81 q^{83} + 18 q^{85} + 48 q^{89} + 9 q^{91} + 84 q^{95}+O(q^{100}) \) 18 * q - 3 * q^5 + 15 * q^11 + 12 * q^17 - 33 * q^23 + 9 * q^25 - 21 * q^29 + 9 * q^31 + 21 * q^35 + 33 * q^41 + 18 * q^43 - 9 * q^47 + 36 * q^49 - 66 * q^53 + 12 * q^59 + 36 * q^61 + 66 * q^65 + 27 * q^67 + 12 * q^71 + 9 * q^73 - 33 * q^77 + 18 * q^79 - 81 * q^83 + 18 * q^85 + 48 * q^89 + 9 * q^91 + 84 * q^95

Introduction

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