LMFDB - Embedded newform 828.2.q.c.397.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [828,2,Mod(73,828)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(828, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("828.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 828 = 2^{2} \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	828.q (of order $11$, degree $10$, 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:	$6.61161328736$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 8 x^{19} + 43 x^{18} - 165 x^{17} + 538 x^{16} - 1433 x^{15} + 3444 x^{14} - 7370 x^{13} + \cdots + 529 $ x^20 - 8x^19 + 43x^18 - 165x^17 + 538x^16 - 1433x^15 + 3444x^14 - 7370x^13 + 15500x^12 - 28190x^11 + 41920x^10 - 33520x^9 - 13837x^8 + 78980x^7 - 92652x^6 - 52852x^5 + 177374x^4 + 151360x^3 + 115323x^2 + 12834*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 276)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			397.2
Root			$0.302381 + 2.10310i$ of defining polynomial
Character	$\chi$	$=$	828.397
Dual form			828.2.q.c.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.52130 - 0.977682i) q^{5} +(0.485296 - 3.37531i) q^{7} +O(q^{10})$	$q+(1.52130 - 0.977682i) q^{5} +(0.485296 - 3.37531i) q^{7} +(0.800715 + 1.75332i) q^{11} +(-0.753988 - 5.24410i) q^{13} +(-0.496392 + 0.572867i) q^{17} +(-3.10335 - 3.58146i) q^{19} +(-3.36166 + 3.42041i) q^{23} +(-0.718574 + 1.57346i) q^{25} +(2.79381 - 3.22422i) q^{29} +(3.28356 - 0.964142i) q^{31} +(-2.56170 - 5.60934i) q^{35} +(-3.09318 - 1.98787i) q^{37} +(5.92232 - 3.80604i) q^{41} +(3.52444 + 1.03487i) q^{43} -10.3519 q^{47} +(-4.44075 - 1.30392i) q^{49} +(1.11911 - 7.78361i) q^{53} +(2.93232 + 1.88449i) q^{55} +(1.53778 + 10.6955i) q^{59} +(12.3748 - 3.63356i) q^{61} +(-6.27411 - 7.24071i) q^{65} +(-2.57750 + 5.64394i) q^{67} +(6.14490 - 13.4555i) q^{71} +(4.97621 + 5.74285i) q^{73} +(6.30658 - 1.85178i) q^{77} +(-0.905219 - 6.29594i) q^{79} +(8.22677 + 5.28702i) q^{83} +(-0.195081 + 1.35682i) q^{85} +(10.6954 + 3.14044i) q^{89} -18.0664 q^{91} +(-8.22267 - 2.41439i) q^{95} +(6.41054 - 4.11980i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{5}+O(q^{10}) $ 20 * q + 4 * q^5	$ 20 q + 4 q^{5} - 22 q^{13} - 7 q^{17} + 19 q^{19} - 20 q^{23} + 20 q^{25} - 32 q^{29} - 3 q^{31} + 26 q^{35} - 10 q^{37} + 40 q^{41} + 8 q^{43} + 18 q^{47} - 34 q^{49} + 34 q^{53} - 17 q^{55} + 32 q^{59} + 32 q^{61} - 49 q^{65} + 35 q^{67} - 33 q^{71} - q^{73} + 50 q^{77} + 22 q^{79} + 14 q^{83} - 9 q^{85} - 10 q^{89} - 72 q^{91} + 51 q^{95} - 4 q^{97}+O(q^{100}) $ 20 * q + 4 * q^5 - 22 * q^13 - 7 * q^17 + 19 * q^19 - 20 * q^23 + 20 * q^25 - 32 * q^29 - 3 * q^31 + 26 * q^35 - 10 * q^37 + 40 * q^41 + 8 * q^43 + 18 * q^47 - 34 * q^49 + 34 * q^53 - 17 * q^55 + 32 * q^59 + 32 * q^61 - 49 * q^65 + 35 * q^67 - 33 * q^71 - q^73 + 50 * q^77 + 22 * q^79 + 14 * q^83 - 9 * q^85 - 10 * q^89 - 72 * q^91 + 51 * q^95 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/828\mathbb{Z}\right)^\times$.

$n$	$415$	$461$	$649$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{11}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.52130	−	0.977682i	0.680348	−	0.437233i	−0.154295	−	0.988025i	$-0.549311\pi$
$5$	1.52130	−	0.977682i	0.680348	−	0.437233i	0.834643	+	0.550792i	$0.185674\pi$
$6$		0			0
$7$	0.485296	−	3.37531i	0.183425	−	1.27575i	−0.665165	−	0.746696i	$-0.731639\pi$
$7$	0.485296	−	3.37531i	0.183425	−	1.27575i	0.848590	−	0.529051i	$-0.177452\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.800715	+	1.75332i	0.241425	+	0.528646i	0.991094	−	0.133167i	$-0.0425146\pi$
$11$	0.800715	+	1.75332i	0.241425	+	0.528646i	−0.749669	+	0.661813i	$0.769787\pi$
$12$		0			0
$13$	−0.753988	−	5.24410i	−0.209119	−	1.45445i	−0.776042	−	0.630682i	$-0.782775\pi$
$13$	−0.753988	−	5.24410i	−0.209119	−	1.45445i	0.566923	−	0.823771i	$-0.308134\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.496392	+	0.572867i	−0.120393	+	0.138941i	−0.812746	−	0.582618i	$-0.802028\pi$
$17$	−0.496392	+	0.572867i	−0.120393	+	0.138941i	0.692354	+	0.721558i	$0.256574\pi$
$18$		0			0
$19$	−3.10335	−	3.58146i	−0.711958	−	0.821643i	0.278358	−	0.960477i	$-0.410210\pi$
$19$	−3.10335	−	3.58146i	−0.711958	−	0.821643i	−0.990316	+	0.138834i	$0.955664\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.36166	+	3.42041i	−0.700955	+	0.713206i
$23$	−3.36166	+	3.42041i	−0.700955	+	0.713206i
$24$		0			0
$25$	−0.718574	+	1.57346i	−0.143715	+	0.314691i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.79381	−	3.22422i	0.518797	−	0.598723i	−0.434532	−	0.900656i	$-0.643086\pi$
$29$	2.79381	−	3.22422i	0.518797	−	0.598723i	0.953329	+	0.301933i	$0.0976318\pi$
$30$		0			0
$31$	3.28356	−	0.964142i	0.589746	−	0.173165i	0.0267745	−	0.999641i	$-0.491476\pi$
$31$	3.28356	−	0.964142i	0.589746	−	0.173165i	0.562971	+	0.826477i	$0.309658\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.56170	−	5.60934i	−0.433006	−	0.948151i
$36$		0			0
$37$	−3.09318	−	1.98787i	−0.508516	−	0.326803i	0.261099	−	0.965312i	$-0.415915\pi$
$37$	−3.09318	−	1.98787i	−0.508516	−	0.326803i	−0.769614	+	0.638509i	$0.779552\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.92232	−	3.80604i	0.924911	−	0.594404i	0.0108322	−	0.999941i	$-0.496552\pi$
$41$	5.92232	−	3.80604i	0.924911	−	0.594404i	0.914079	+	0.405537i	$0.132916\pi$
$42$		0			0
$43$	3.52444	+	1.03487i	0.537472	+	0.157816i	0.539192	−	0.842183i	$-0.318730\pi$
$43$	3.52444	+	1.03487i	0.537472	+	0.157816i	−0.00172068	+	0.999999i	$0.500548\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−10.3519			−1.50998			−0.754989	−	0.655738i	$-0.772358\pi$
$47$	−10.3519			−1.50998			−0.754989	+	0.655738i	$0.772358\pi$
$48$		0			0
$49$	−4.44075	−	1.30392i	−0.634393	−	0.186275i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.11911	−	7.78361i	0.153722	−	1.06916i	−0.756187	−	0.654355i	$-0.772940\pi$
$53$	1.11911	−	7.78361i	0.153722	−	1.06916i	0.909910	−	0.414806i	$-0.136151\pi$
$54$		0			0
$55$	2.93232	+	1.88449i	0.395394	+	0.254104i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.53778	+	10.6955i	0.200202	+	1.39244i	0.803682	+	0.595059i	$0.202871\pi$
$59$	1.53778	+	10.6955i	0.200202	+	1.39244i	−0.603480	+	0.797378i	$0.706220\pi$
$60$		0			0
$61$	12.3748	−	3.63356i	1.58443	−	0.465229i	0.633268	−	0.773933i	$-0.281713\pi$
$61$	12.3748	−	3.63356i	1.58443	−	0.465229i	0.951158	+	0.308704i	$0.0998951\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−6.27411	−	7.24071i	−0.778208	−	0.898100i
$66$		0			0
$67$	−2.57750	+	5.64394i	−0.314892	+	0.689517i	−0.999213	−	0.0396637i	$-0.987371\pi$
$67$	−2.57750	+	5.64394i	−0.314892	+	0.689517i	0.684321	+	0.729181i	$0.260099\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	6.14490	−	13.4555i	0.729266	−	1.59687i	−0.0711790	−	0.997464i	$-0.522676\pi$
$71$	6.14490	−	13.4555i	0.729266	−	1.59687i	0.800445	−	0.599406i	$-0.204597\pi$
$72$		0			0
$73$	4.97621	+	5.74285i	0.582421	+	0.672150i	0.968124	−	0.250473i	$-0.0805862\pi$
$73$	4.97621	+	5.74285i	0.582421	+	0.672150i	−0.385702	+	0.922623i	$0.626041\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	6.30658	−	1.85178i	0.718702	−	0.211030i
$78$		0			0
$79$	−0.905219	−	6.29594i	−0.101845	−	0.708348i	−0.975210	−	0.221282i	$-0.928976\pi$
$79$	−0.905219	−	6.29594i	−0.101845	−	0.708348i	0.873365	−	0.487067i	$-0.161933\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	8.22677	+	5.28702i	0.903005	+	0.580326i	0.907680	−	0.419663i	$-0.137852\pi$
$83$	8.22677	+	5.28702i	0.903005	+	0.580326i	−0.00467489	+	0.999989i	$0.501488\pi$
$84$		0			0
$85$	−0.195081	+	1.35682i	−0.0211595	+	0.147168i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	10.6954	+	3.14044i	1.13371	+	0.332886i	0.794163	−	0.607704i	$-0.207909\pi$
$89$	10.6954	+	3.14044i	1.13371	+	0.332886i	0.339543	+	0.940591i	$0.389728\pi$
$90$		0			0
$91$	−18.0664			−1.89387
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−8.22267	−	2.41439i	−0.843628	−	0.247712i
$96$		0			0
$97$	6.41054	−	4.11980i	0.650892	−	0.418303i	−0.173100	−	0.984904i	$-0.555378\pi$
$97$	6.41054	−	4.11980i	0.650892	−	0.418303i	0.823992	+	0.566601i	$0.191742\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−7.49704	−	4.81805i	−0.745983	−	0.479414i	0.111604	−	0.993753i	$-0.464401\pi$
$101$	−7.49704	−	4.81805i	−0.745983	−	0.479414i	−0.857587	+	0.514339i	$0.828037\pi$
$102$		0			0
$103$	−0.367699	−	0.805149i	−0.0362305	−	0.0793337i	0.890651	−	0.454687i	$-0.150249\pi$
$103$	−0.367699	−	0.805149i	−0.0362305	−	0.0793337i	−0.926882	+	0.375353i	$0.877521\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−7.59185	+	2.22917i	−0.733932	+	0.215502i	−0.627279	−	0.778794i	$-0.715832\pi$
$107$	−7.59185	+	2.22917i	−0.733932	+	0.215502i	−0.106653	+	0.994296i	$0.534013\pi$
$108$		0			0
$109$	1.15251	−	1.33007i	0.110391	−	0.127398i	−0.697865	−	0.716229i	$-0.745866\pi$
$109$	1.15251	−	1.33007i	0.110391	−	0.127398i	0.808256	+	0.588832i	$0.200412\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−6.94750	+	15.2129i	−0.653566	+	1.43111i	0.234832	+	0.972036i	$0.424546\pi$
$113$	−6.94750	+	15.2129i	−0.653566	+	1.43111i	−0.888398	+	0.459074i	$0.848181\pi$
$114$		0			0
$115$	−1.77003	+	8.49012i	−0.165056	+	0.791708i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.69271	+	1.95349i	0.155170	+	0.179076i
$120$		0			0
$121$	4.77048	−	5.50543i	0.433680	−	0.500493i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	1.73197	+	12.0461i	0.154912	+	1.07744i
$126$		0			0
$127$	0.531324	+	1.16344i	0.0471473	+	0.103238i	0.931740	−	0.363126i	$-0.118291\pi$
$127$	0.531324	+	1.16344i	0.0471473	+	0.103238i	−0.884593	+	0.466365i	$0.845563\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−1.43523	+	9.98224i	−0.125397	+	0.872152i	0.825887	+	0.563835i	$0.190675\pi$
$131$	−1.43523	+	9.98224i	−0.125397	+	0.872152i	−0.951284	+	0.308317i	$0.900234\pi$
$132$		0			0
$133$	−13.5946	+	8.73670i	−1.17880	+	0.757568i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.53140			−0.558015			−0.279007	−	0.960289i	$-0.590005\pi$
$137$	−6.53140			−0.558015			−0.279007	+	0.960289i	$0.590005\pi$
$138$		0			0
$139$	−8.55305			−0.725461			−0.362730	−	0.931894i	$-0.618155\pi$
$139$	−8.55305			−0.725461			−0.362730	+	0.931894i	$0.618155\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	8.59086	−	5.52101i	0.718404	−	0.461690i
$144$		0			0
$145$	1.09796	−	7.63648i	0.0911806	−	0.634175i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.34464	−	2.94435i	−0.110157	−	0.241211i	0.846523	−	0.532353i	$-0.178692\pi$
$149$	−1.34464	−	2.94435i	−0.110157	−	0.241211i	−0.956680	+	0.291142i	$0.905965\pi$
$150$		0			0
$151$	−1.00038	−	6.95781i	−0.0814100	−	0.566219i	−0.989175	−	0.146740i	$-0.953122\pi$
$151$	−1.00038	−	6.95781i	−0.0814100	−	0.566219i	0.907765	−	0.419479i	$-0.137787\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	4.05267	−	4.67704i	0.325519	−	0.375668i
$156$		0			0
$157$	13.1324	+	15.1556i	1.04808	+	1.20955i	0.977257	+	0.212058i	$0.0680167\pi$
$157$	13.1324	+	15.1556i	1.04808	+	1.20955i	0.0708217	+	0.997489i	$0.477438\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	9.91356	+	13.0066i	0.781298	+	1.02506i
$162$		0			0
$163$	−6.16725	+	13.5044i	−0.483056	+	1.05775i	0.498556	+	0.866858i	$0.333864\pi$
$163$	−6.16725	+	13.5044i	−0.483056	+	1.05775i	−0.981612	+	0.190888i	$0.938863\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−16.1307	+	18.6159i	−1.24823	+	1.44054i	−0.395272	+	0.918564i	$0.629350\pi$
$167$	−16.1307	+	18.6159i	−1.24823	+	1.44054i	−0.852961	+	0.521974i	$0.825196\pi$
$168$		0			0
$169$	−14.4587	+	4.24546i	−1.11221	+	0.326574i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	6.48345	+	14.1968i	0.492928	+	1.07936i	0.978704	+	0.205278i	$0.0658098\pi$
$173$	6.48345	+	14.1968i	0.492928	+	1.07936i	−0.485776	+	0.874083i	$0.661463\pi$
$174$		0			0
$175$	4.96218	+	3.18900i	0.375106	+	0.241066i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	15.2621	−	9.80838i	1.14075	−	0.733113i	0.172970	−	0.984927i	$-0.444664\pi$
$179$	15.2621	−	9.80838i	1.14075	−	0.733113i	0.967775	+	0.251815i	$0.0810273\pi$
$180$		0			0
$181$	25.5232	+	7.49429i	1.89712	+	0.557046i	0.990967	+	0.134103i	$0.0428154\pi$
$181$	25.5232	+	7.49429i	1.89712	+	0.557046i	0.906157	+	0.422942i	$0.139003\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−6.64917			−0.488856
$186$		0			0
$187$	−1.40189	−	0.411631i	−0.102516	−	0.0301015i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−3.52838	+	24.5404i	−0.255305	+	1.77568i	0.309935	+	0.950758i	$0.399693\pi$
$191$	−3.52838	+	24.5404i	−0.255305	+	1.77568i	−0.565240	+	0.824927i	$0.691216\pi$
$192$		0			0
$193$	−3.96991	−	2.55131i	−0.285761	−	0.183647i	0.389906	−	0.920855i	$-0.372508\pi$
$193$	−3.96991	−	2.55131i	−0.285761	−	0.183647i	−0.675666	+	0.737208i	$0.736144\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−1.58426	−	11.0188i	−0.112874	−	0.785055i	−0.965100	−	0.261882i	$-0.915657\pi$
$197$	−1.58426	−	11.0188i	−0.112874	−	0.785055i	0.852226	−	0.523174i	$-0.175252\pi$
$198$		0			0
$199$	7.56852	−	2.22232i	0.536518	−	0.157536i	−0.00223844	−	0.999997i	$-0.500713\pi$
$199$	7.56852	−	2.22232i	0.536518	−	0.157536i	0.538756	+	0.842462i	$0.318894\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−9.52693	−	10.9947i	−0.668660	−	0.771674i
$204$		0			0
$205$	5.28854	−	11.5803i	0.369368	−	0.808803i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	3.79455	−	8.30890i	0.262474	−	0.574738i
$210$		0			0
$211$	12.2185	+	14.1009i	0.841159	+	0.970749i	0.999863	−	0.0165774i	$-0.00527698\pi$
$211$	12.2185	+	14.1009i	0.841159	+	0.970749i	−0.158704	+	0.987326i	$0.550732\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	6.37351	−	1.87143i	0.434670	−	0.127631i
$216$		0			0
$217$	−1.66077	−	11.5509i	−0.112741	−	0.784129i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	3.37845	+	2.17120i	0.227259	+	0.146050i
$222$		0			0
$223$	−3.29264	+	22.9008i	−0.220491	+	1.53355i	0.515694	+	0.856773i	$0.327534\pi$
$223$	−3.29264	+	22.9008i	−0.220491	+	1.53355i	−0.736186	+	0.676779i	$0.763375\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	11.8332	+	3.47453i	0.785394	+	0.230613i	0.649753	−	0.760145i	$-0.274872\pi$
$227$	11.8332	+	3.47453i	0.785394	+	0.230613i	0.135641	+	0.990758i	$0.456691\pi$
$228$		0			0
$229$	−11.4857			−0.758998			−0.379499	−	0.925192i	$-0.623904\pi$
$229$	−11.4857			−0.758998			−0.379499	+	0.925192i	$0.623904\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−5.13434	−	1.50758i	−0.336362	−	0.0987647i	0.109190	−	0.994021i	$-0.465174\pi$
$233$	−5.13434	−	1.50758i	−0.336362	−	0.0987647i	−0.445552	+	0.895256i	$0.646992\pi$
$234$		0			0
$235$	−15.7484	+	10.1209i	−1.02731	+	0.660212i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−9.62507	−	6.18565i	−0.622594	−	0.400117i	0.190967	−	0.981596i	$-0.438838\pi$
$239$	−9.62507	−	6.18565i	−0.622594	−	0.400117i	−0.813561	+	0.581480i	$0.802474\pi$
$240$		0			0
$241$	1.45687	+	3.19010i	0.0938452	+	0.205492i	0.950733	−	0.310010i	$-0.100333\pi$
$241$	1.45687	+	3.19010i	0.0938452	+	0.205492i	−0.856888	+	0.515503i	$0.827605\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−8.03055	+	2.35798i	−0.513053	+	0.150646i
$246$		0			0
$247$	−16.4416	+	18.9747i	−1.04616	+	1.20733i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	4.91943	−	10.7720i	0.310512	−	0.679925i	−0.688460	−	0.725275i	$-0.741713\pi$
$251$	4.91943	−	10.7720i	0.310512	−	0.679925i	0.998971	+	0.0453492i	$0.0144401\pi$
$252$		0			0
$253$	−8.68881	−	3.15529i	−0.546261	−	0.198371i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−16.7144	−	19.2895i	−1.04262	−	1.20324i	−0.978702	−	0.205287i	$-0.934187\pi$
$257$	−16.7144	−	19.2895i	−1.04262	−	1.20324i	−0.0639142	−	0.997955i	$-0.520358\pi$
$258$		0			0
$259$	−8.21077	+	9.47573i	−0.510192	+	0.588794i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−0.511613	−	3.55835i	−0.0315474	−	0.219417i	0.967949	−	0.251147i	$-0.0808076\pi$
$263$	−0.511613	−	3.55835i	−0.0315474	−	0.219417i	−0.999496	+	0.0317294i	$0.989899\pi$
$264$		0			0
$265$	−5.90739	−	12.9354i	−0.362888	−	0.794614i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	2.30719	−	16.0468i	0.140672	−	0.978393i	−0.790148	−	0.612915i	$-0.789997\pi$
$269$	2.30719	−	16.0468i	0.140672	−	0.978393i	0.930820	−	0.365478i	$-0.119094\pi$
$270$		0			0
$271$	−3.65183	+	2.34689i	−0.221833	+	0.142563i	−0.646838	−	0.762628i	$-0.723909\pi$
$271$	−3.65183	+	2.34689i	−0.221833	+	0.142563i	0.425005	+	0.905191i	$0.360272\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−3.33415			−0.201057
$276$		0			0
$277$	28.6009			1.71846			0.859230	−	0.511589i	$-0.170943\pi$
$277$	28.6009			1.71846			0.859230	+	0.511589i	$0.170943\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	9.53062	−	6.12496i	0.568549	−	0.365384i	−0.224563	−	0.974459i	$-0.572096\pi$
$281$	9.53062	−	6.12496i	0.568549	−	0.365384i	0.793113	+	0.609075i	$0.208459\pi$
$282$		0			0
$283$	0.759137	−	5.27992i	0.0451260	−	0.313858i	−0.954739	−	0.297444i	$-0.903866\pi$
$283$	0.759137	−	5.27992i	0.0451260	−	0.313858i	0.999865	−	0.0164143i	$-0.00522508\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−9.97249	−	21.8367i	−0.588658	−	1.28898i
$288$		0			0
$289$	2.33758	+	16.2582i	0.137505	+	0.956367i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−15.4905	+	17.8770i	−0.904963	+	1.04438i	0.0938455	+	0.995587i	$0.470084\pi$
$293$	−15.4905	+	17.8770i	−0.904963	+	1.04438i	−0.998809	+	0.0487965i	$0.984461\pi$
$294$		0			0
$295$	12.7963	+	14.7677i	0.745027	+	0.859806i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	20.4717	+	15.0499i	1.18391	+	0.870361i
$300$		0			0
$301$	5.20340	−	11.3939i	0.299919	−	0.656731i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	15.2733	−	17.6263i	0.874547	−	1.00928i
$306$		0			0
$307$	18.7890	−	5.51696i	1.07235	−	0.314870i	0.302534	−	0.953139i	$-0.402167\pi$
$307$	18.7890	−	5.51696i	1.07235	−	0.314870i	0.769813	+	0.638269i	$0.220349\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	0.797463	+	1.74620i	0.0452200	+	0.0990179i	0.930894	−	0.365290i	$-0.119030\pi$
$311$	0.797463	+	1.74620i	0.0452200	+	0.0990179i	−0.885674	+	0.464308i	$0.846303\pi$
$312$		0			0
$313$	−10.6720	−	6.85849i	−0.603219	−	0.387665i	0.203090	−	0.979160i	$-0.434902\pi$
$313$	−10.6720	−	6.85849i	−0.603219	−	0.387665i	−0.806309	+	0.591495i	$0.798538\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.62869	+	1.68936i	−0.147642	+	0.0948838i	−0.612376	−	0.790566i	$-0.709786\pi$
$317$	−2.62869	+	1.68936i	−0.147642	+	0.0948838i	0.464734	+	0.885450i	$0.346150\pi$
$318$		0			0
$319$	7.89014	+	2.31675i	0.441763	+	0.129713i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	3.59218			0.199874
$324$		0			0
$325$	8.79317	+	2.58191i	0.487757	+	0.143218i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−5.02373	+	34.9408i	−0.276967	+	1.92635i
$330$		0			0
$331$	−10.8260	−	6.95744i	−0.595050	−	0.382415i	0.208175	−	0.978092i	$-0.433248\pi$
$331$	−10.8260	−	6.95744i	−0.595050	−	0.382415i	−0.803225	+	0.595676i	$0.796884\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	1.59682	+	11.1061i	0.0872436	+	0.606792i
$336$		0			0
$337$	14.8281	−	4.35393i	0.807739	−	0.237174i	0.148311	−	0.988941i	$-0.452616\pi$
$337$	14.8281	−	4.35393i	0.807739	−	0.237174i	0.659429	+	0.751767i	$0.270798\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	4.31965	+	4.98514i	0.233922	+	0.269960i
$342$		0			0
$343$	3.35979	−	7.35691i	0.181412	−	0.397236i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	7.54167	−	16.5140i	0.404858	−	0.886516i	−0.591896	−	0.806014i	$-0.701620\pi$
$347$	7.54167	−	16.5140i	0.404858	−	0.886516i	0.996754	−	0.0805017i	$-0.0256522\pi$
$348$		0			0
$349$	−14.3287	−	16.5361i	−0.766995	−	0.885160i	0.229104	−	0.973402i	$-0.426420\pi$
$349$	−14.3287	−	16.5361i	−0.766995	−	0.885160i	−0.996099	+	0.0882423i	$0.971875\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	11.6096	−	3.40888i	0.617916	−	0.181436i	0.0422305	−	0.999108i	$-0.486554\pi$
$353$	11.6096	−	3.40888i	0.617916	−	0.181436i	0.575685	+	0.817672i	$0.304735\pi$
$354$		0			0
$355$	−3.80691	−	26.4776i	−0.202050	−	1.40529i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	2.98260	+	1.91680i	0.157415	+	0.101165i	0.616977	−	0.786981i	$-0.288357\pi$
$359$	2.98260	+	1.91680i	0.157415	+	0.101165i	−0.459562	+	0.888146i	$0.651993\pi$
$360$		0			0
$361$	−0.492073	+	3.42244i	−0.0258986	+	0.180129i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	13.1850	+	3.87147i	0.690135	+	0.202642i
$366$		0			0
$367$	−26.1379			−1.36439			−0.682194	−	0.731171i	$-0.738974\pi$
$367$	−26.1379			−1.36439			−0.682194	+	0.731171i	$0.738974\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−25.7290	−	7.55472i	−1.33578	−	0.392221i
$372$		0			0
$373$	12.1660	−	7.81858i	0.629929	−	0.404831i	−0.186354	−	0.982483i	$-0.559667\pi$
$373$	12.1660	−	7.81858i	0.629929	−	0.404831i	0.816283	+	0.577652i	$0.196031\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−19.0147	−	12.2200i	−0.979305	−	0.629361i
$378$		0			0
$379$	−11.6229	−	25.4505i	−0.597026	−	1.30730i	−0.931102	−	0.364758i	$-0.881152\pi$
$379$	−11.6229	−	25.4505i	−0.597026	−	1.30730i	0.334076	−	0.942546i	$-0.391576\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−17.7316	+	5.20645i	−0.906040	+	0.266037i	−0.701373	−	0.712794i	$-0.747429\pi$
$383$	−17.7316	+	5.20645i	−0.906040	+	0.266037i	−0.204667	+	0.978832i	$0.565611\pi$
$384$		0			0
$385$	7.78377	−	8.98295i	0.396698	−	0.457814i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−10.6824	+	23.3913i	−0.541621	+	1.18598i	0.418965	+	0.908002i	$0.362393\pi$
$389$	−10.6824	+	23.3913i	−0.541621	+	1.18598i	−0.960586	+	0.277982i	$0.910334\pi$
$390$		0			0
$391$	−0.290741	−	3.62365i	−0.0147034	−	0.183256i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−7.53254	−	8.69302i	−0.379003	−	0.437393i
$396$		0			0
$397$	18.2955	−	21.1141i	0.918225	−	1.05969i	−0.0797958	−	0.996811i	$-0.525427\pi$
$397$	18.2955	−	21.1141i	0.918225	−	1.05969i	0.998021	−	0.0628775i	$-0.0200277\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	3.47619	+	24.1775i	0.173593	+	1.20737i	0.871216	+	0.490900i	$0.163332\pi$
$401$	3.47619	+	24.1775i	0.173593	+	1.20737i	−0.697623	+	0.716465i	$0.745759\pi$
$402$		0			0
$403$	−7.53183	−	16.4924i	−0.375187	−	0.821545i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.00861	−	7.01505i	0.0499950	−	0.347723i
$408$		0			0
$409$	−30.4357	+	19.5599i	−1.50495	+	0.967173i	−0.510738	+	0.859736i	$0.670628\pi$
$409$	−30.4357	+	19.5599i	−1.50495	+	0.967173i	−0.994212	+	0.107437i	$0.965736\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	36.8470			1.81312
$414$		0			0
$415$	17.6844			0.868095
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−6.96574	+	4.47661i	−0.340299	+	0.218697i	−0.699617	−	0.714519i	$-0.746646\pi$
$419$	−6.96574	+	4.47661i	−0.340299	+	0.218697i	0.359318	+	0.933215i	$0.383009\pi$
$420$		0			0
$421$	−5.08820	+	35.3892i	−0.247984	+	1.72476i	0.361852	+	0.932236i	$0.382145\pi$
$421$	−5.08820	+	35.3892i	−0.247984	+	1.72476i	−0.609836	+	0.792528i	$0.708765\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.544687	−	1.19270i	−0.0264212	−	0.0578544i
$426$		0			0
$427$	−6.25896	−	43.5320i	−0.302892	−	2.10666i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	14.2907	−	16.4924i	0.688361	−	0.794411i	−0.298770	−	0.954325i	$-0.596576\pi$
$431$	14.2907	−	16.4924i	0.688361	−	0.794411i	0.987131	+	0.159914i	$0.0511218\pi$
$432$		0			0
$433$	−19.9066	−	22.9735i	−0.956651	−	1.10403i	−0.994499	−	0.104751i	$-0.966596\pi$
$433$	−19.9066	−	22.9735i	−0.956651	−	1.10403i	0.0378476	−	0.999284i	$-0.487950\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	22.6825	+	1.42490i	1.08505	+	0.0681621i
$438$		0			0
$439$	8.60356	−	18.8392i	0.410626	−	0.899145i	−0.585456	−	0.810704i	$-0.699084\pi$
$439$	8.60356	−	18.8392i	0.410626	−	0.899145i	0.996081	−	0.0884405i	$-0.0281883\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	16.1133	−	18.5958i	0.765567	−	0.883512i	−0.230412	−	0.973093i	$-0.574007\pi$
$443$	16.1133	−	18.5958i	0.765567	−	0.883512i	0.995980	+	0.0895812i	$0.0285529\pi$
$444$		0			0
$445$	19.3412	−	5.67910i	0.916863	−	0.269215i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−16.3387	−	35.7767i	−0.771070	−	1.68841i	−0.724283	−	0.689502i	$-0.757829\pi$
$449$	−16.3387	−	35.7767i	−0.771070	−	1.68841i	−0.0467864	−	0.998905i	$-0.514898\pi$
$450$		0			0
$451$	11.4153	+	7.33617i	0.537525	+	0.345447i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−27.4844	+	17.6632i	−1.28849	+	0.828063i
$456$		0			0
$457$	−16.4781	−	4.83841i	−0.770814	−	0.226331i	−0.127401	−	0.991851i	$-0.540664\pi$
$457$	−16.4781	−	4.83841i	−0.770814	−	0.226331i	−0.643412	+	0.765520i	$0.722482\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−1.59212			−0.0741524			−0.0370762	−	0.999312i	$-0.511804\pi$
$461$	−1.59212			−0.0741524			−0.0370762	+	0.999312i	$0.511804\pi$
$462$		0			0
$463$	14.0004	+	4.11088i	0.650653	+	0.191049i	0.590371	−	0.807132i	$-0.298982\pi$
$463$	14.0004	+	4.11088i	0.650653	+	0.191049i	0.0602827	+	0.998181i	$0.480800\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−4.20501	+	29.2465i	−0.194585	+	1.35337i	0.625097	+	0.780547i	$0.285060\pi$
$467$	−4.20501	+	29.2465i	−0.194585	+	1.35337i	−0.819681	+	0.572820i	$0.805850\pi$
$468$		0			0
$469$	17.7992	+	11.4388i	0.821890	+	0.528197i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.00761	+	7.00810i	0.0463301	+	0.322233i
$474$		0			0
$475$	7.86526	−	2.30945i	0.360883	−	0.105965i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	2.07544	+	2.39519i	0.0948293	+	0.109439i	0.801181	−	0.598423i	$-0.204206\pi$
$479$	2.07544	+	2.39519i	0.0948293	+	0.109439i	−0.706351	+	0.707861i	$0.749660\pi$
$480$		0			0
$481$	−8.09235	+	17.7198i	−0.368979	+	0.807952i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	5.72452	−	12.5349i	0.259937	−	0.569183i
$486$		0			0
$487$	−20.8452	−	24.0567i	−0.944586	−	1.09011i	−0.995812	−	0.0914238i	$-0.970858\pi$
$487$	−20.8452	−	24.0567i	−0.944586	−	1.09011i	0.0512256	−	0.998687i	$-0.483687\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	10.7015	−	3.14225i	0.482953	−	0.141808i	−0.0311880	−	0.999514i	$-0.509929\pi$
$491$	10.7015	−	3.14225i	0.482953	−	0.141808i	0.514141	+	0.857706i	$0.328111\pi$
$492$		0			0
$493$	0.460228	+	3.20096i	0.0207276	+	0.144164i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−42.4343	−	27.2708i	−1.90344	−	1.22326i
$498$		0			0
$499$	−0.553581	+	3.85024i	−0.0247817	+	0.172360i	−0.998453	−	0.0555942i	$-0.982295\pi$
$499$	−0.553581	+	3.85024i	−0.0247817	+	0.172360i	0.973672	+	0.227955i	$0.0732038\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	36.0920	+	10.5976i	1.60926	+	0.472523i	0.958105	−	0.286418i	$-0.0924645\pi$
$503$	36.0920	+	10.5976i	1.60926	+	0.472523i	0.651160	+	0.758940i	$0.274283\pi$
$504$		0			0
$505$	−16.1158			−0.717143
$506$		0			0
$507$		0			0
$508$		0			0
$509$	18.9608	+	5.56740i	0.840424	+	0.246771i	0.673489	−	0.739197i	$-0.264795\pi$
$509$	18.9608	+	5.56740i	0.840424	+	0.246771i	0.166935	+	0.985968i	$0.446613\pi$
$510$		0			0
$511$	21.7988	−	14.0093i	0.964324	−	0.619733i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−1.34656	−	0.865383i	−0.0593366	−	0.0381333i
$516$		0			0
$517$	−8.28891	−	18.1502i	−0.364546	−	0.798244i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	26.3779	−	7.74525i	1.15564	−	0.339326i	0.352901	−	0.935660i	$-0.385195\pi$
$521$	26.3779	−	7.74525i	1.15564	−	0.339326i	0.802736	+	0.596335i	$0.203377\pi$
$522$		0			0
$523$	5.32266	−	6.14267i	0.232744	−	0.268600i	−0.627349	−	0.778738i	$-0.715860\pi$
$523$	5.32266	−	6.14267i	0.232744	−	0.268600i	0.860093	+	0.510138i	$0.170406\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.07761	+	2.35964i	−0.0469414	+	0.102787i
$528$		0			0
$529$	−0.398477	−	22.9965i	−0.0173251	−	0.999850i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−24.4246	−	28.1875i	−1.05795	−	1.22094i
$534$		0			0
$535$	−9.37009	+	10.8137i	−0.405104	+	0.467515i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−1.26958	−	8.83013i	−0.0546847	−	0.380341i
$540$		0			0
$541$	9.72352	+	21.2915i	0.418047	+	0.915395i	0.995117	+	0.0987006i	$0.0314686\pi$
$541$	9.72352	+	21.2915i	0.418047	+	0.915395i	−0.577070	+	0.816695i	$0.695804\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	0.452935	−	3.15023i	0.0194016	−	0.134941i
$546$		0			0
$547$	13.7794	−	8.85546i	0.589163	−	0.378632i	−0.211829	−	0.977307i	$-0.567942\pi$
$547$	13.7794	−	8.85546i	0.589163	−	0.378632i	0.800992	+	0.598675i	$0.204306\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−20.2176			−0.861298
$552$		0			0
$553$	−21.6900			−0.922354
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−16.0768	+	10.3319i	−0.681196	+	0.437778i	−0.834946	−	0.550332i	$-0.814501\pi$
$557$	−16.0768	+	10.3319i	−0.681196	+	0.437778i	0.153750	+	0.988110i	$0.450865\pi$
$558$		0			0
$559$	2.76957	−	19.2628i	0.117140	−	0.814729i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−8.42062	−	18.4386i	−0.354887	−	0.777094i	−0.999916	−	0.0129360i	$-0.995882\pi$
$563$	−8.42062	−	18.4386i	−0.354887	−	0.777094i	0.645030	−	0.764158i	$-0.276845\pi$
$564$		0			0
$565$	4.30413	+	29.9359i	0.181076	+	1.25941i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−12.1549	+	14.0276i	−0.509562	+	0.588066i	−0.950986	−	0.309233i	$-0.899928\pi$
$569$	−12.1549	+	14.0276i	−0.509562	+	0.588066i	0.441425	+	0.897298i	$0.354473\pi$
$570$		0			0
$571$	30.6110	+	35.3269i	1.28103	+	1.47839i	0.797838	+	0.602872i	$0.205977\pi$
$571$	30.6110	+	35.3269i	1.28103	+	1.47839i	0.483191	+	0.875515i	$0.339478\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−2.96628	−	7.74725i	−0.123702	−	0.323083i
$576$		0			0
$577$	−14.8811	+	32.5851i	−0.619509	+	1.35653i	0.296368	+	0.955074i	$0.404225\pi$
$577$	−14.8811	+	32.5851i	−0.619509	+	1.35653i	−0.915876	+	0.401461i	$0.868503\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	21.8378	−	25.2021i	0.905983	−	1.04556i
$582$		0			0
$583$	14.5433	−	4.27029i	0.602320	−	0.176857i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.00770622	−	0.0168743i	−0.000318070	−	0.000696476i	0.909473	−	0.415763i	$-0.136485\pi$
$587$	−0.00770622	−	0.0168743i	−0.000318070	−	0.000696476i	−0.909791	+	0.415067i	$0.863758\pi$
$588$		0			0
$589$	−13.6431	−	8.76788i	−0.562154	−	0.361274i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	5.46726	−	3.51359i	0.224513	−	0.144286i	−0.423549	−	0.905873i	$-0.639216\pi$
$593$	5.46726	−	3.51359i	0.224513	−	0.144286i	0.648063	+	0.761587i	$0.275580\pi$
$594$		0			0
$595$	4.48501	+	1.31692i	0.183867	+	0.0539883i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	7.49989			0.306437			0.153219	−	0.988192i	$-0.451036\pi$
$599$	7.49989			0.306437			0.153219	+	0.988192i	$0.451036\pi$
$600$		0			0
$601$	−24.6872	−	7.24882i	−1.00701	−	0.295686i	−0.263682	−	0.964610i	$-0.584937\pi$
$601$	−24.6872	−	7.24882i	−1.00701	−	0.295686i	−0.743331	+	0.668924i	$0.766755\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	1.87479	−	13.0394i	0.0762210	−	0.530129i
$606$		0			0
$607$	24.3740	+	15.6642i	0.989309	+	0.635790i	0.931959	−	0.362564i	$-0.118098\pi$
$607$	24.3740	+	15.6642i	0.989309	+	0.635790i	0.0573502	+	0.998354i	$0.481735\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	7.80520	+	54.2863i	0.315765	+	2.19619i
$612$		0			0
$613$	−2.25859	+	0.663181i	−0.0912235	+	0.0267856i	−0.327026	−	0.945015i	$-0.606046\pi$
$613$	−2.25859	+	0.663181i	−0.0912235	+	0.0267856i	0.235802	+	0.971801i	$0.424228\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	9.99989	+	11.5405i	0.402580	+	0.464603i	0.920452	−	0.390856i	$-0.127821\pi$
$617$	9.99989	+	11.5405i	0.402580	+	0.464603i	−0.517871	+	0.855458i	$0.673275\pi$
$618$		0			0
$619$	−4.77631	+	10.4587i	−0.191976	+	0.420369i	−0.981004	−	0.193988i	$-0.937858\pi$
$619$	−4.77631	+	10.4587i	−0.191976	+	0.420369i	0.789028	+	0.614358i	$0.210585\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	15.7904	−	34.5761i	0.632628	−	1.38526i
$624$		0			0
$625$	8.74830	+	10.0961i	0.349932	+	0.403843i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	2.67421	−	0.785219i	0.106628	−	0.0313087i
$630$		0			0
$631$	2.01067	+	13.9845i	0.0800436	+	0.556715i	0.989897	+	0.141786i	$0.0452845\pi$
$631$	2.01067	+	13.9845i	0.0800436	+	0.556715i	−0.909854	+	0.414929i	$0.863806\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.94578	+	1.25047i	0.0772158	+	0.0496235i
$636$		0			0
$637$	−3.48963	+	24.2709i	−0.138264	+	0.961648i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−23.8830	−	7.01267i	−0.943320	−	0.276984i	−0.226317	−	0.974054i	$-0.572669\pi$
$641$	−23.8830	−	7.01267i	−0.943320	−	0.276984i	−0.717003	+	0.697070i	$0.754487\pi$
$642$		0			0
$643$	23.5235			0.927678			0.463839	−	0.885919i	$-0.346472\pi$
$643$	23.5235			0.927678			0.463839	+	0.885919i	$0.346472\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−19.2110	−	5.64087i	−0.755264	−	0.221766i	−0.118637	−	0.992938i	$-0.537853\pi$
$647$	−19.2110	−	5.64087i	−0.755264	−	0.221766i	−0.636627	+	0.771172i	$0.719671\pi$
$648$		0			0
$649$	−17.5213	+	11.2603i	−0.687773	+	0.442005i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	6.28245	+	4.03749i	0.245851	+	0.157999i	0.657764	−	0.753224i	$-0.271503\pi$
$653$	6.28245	+	4.03749i	0.245851	+	0.157999i	−0.411912	+	0.911224i	$0.635139\pi$
$654$		0			0
$655$	7.57604	+	16.5892i	0.296020	+	0.648194i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	10.4634	−	3.07234i	0.407597	−	0.119681i	−0.0715057	−	0.997440i	$-0.522780\pi$
$659$	10.4634	−	3.07234i	0.407597	−	0.119681i	0.479102	+	0.877759i	$0.340962\pi$
$660$		0			0
$661$	−11.3039	+	13.0454i	−0.439672	+	0.507409i	−0.931729	−	0.363154i	$-0.881700\pi$
$661$	−11.3039	+	13.0454i	−0.439672	+	0.507409i	0.492057	+	0.870563i	$0.336245\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−12.1398	+	26.5824i	−0.470759	+	1.03082i
$666$		0			0
$667$	1.63636	+	20.3947i	0.0633600	+	0.789687i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	16.2794	+	18.7875i	0.628461	+	0.725283i
$672$		0			0
$673$	4.61892	−	5.33051i	0.178046	−	0.205476i	−0.659711	−	0.751520i	$-0.729321\pi$
$673$	4.61892	−	5.33051i	0.178046	−	0.205476i	0.837757	+	0.546043i	$0.183867\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	3.71912	+	25.8671i	0.142937	+	0.994152i	0.927426	+	0.374008i	$0.122017\pi$
$677$	3.71912	+	25.8671i	0.142937	+	0.994152i	−0.784488	+	0.620144i	$0.787074\pi$
$678$		0			0
$679$	−10.7946	−	23.6369i	−0.414259	−	0.907100i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.601211	+	4.18151i	−0.0230047	+	0.160001i	−0.998086	−	0.0618487i	$-0.980300\pi$
$683$	−0.601211	+	4.18151i	−0.0230047	+	0.160001i	0.975081	+	0.221850i	$0.0712095\pi$
$684$		0			0
$685$	−9.93623	+	6.38563i	−0.379644	+	0.243982i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−41.6619			−1.58719
$690$		0			0
$691$	35.2154			1.33966			0.669829	−	0.742516i	$-0.266367\pi$
$691$	35.2154			1.33966			0.669829	+	0.742516i	$0.266367\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−13.0118	+	8.36217i	−0.493565	+	0.317195i
$696$		0			0
$697$	−0.759435	+	5.28199i	−0.0287657	+	0.200070i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−16.0954	−	35.2441i	−0.607917	−	1.33115i	−0.923990	−	0.382417i	$-0.875092\pi$
$701$	−16.0954	−	35.2441i	−0.607917	−	1.33115i	0.316073	−	0.948735i	$-0.397635\pi$
$702$		0			0
$703$	2.47976	+	17.2471i	0.0935261	+	0.650488i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−19.9007	+	22.9666i	−0.748443	+	0.863749i
$708$		0			0
$709$	9.24611	+	10.6706i	0.347245	+	0.400742i	0.902326	−	0.431054i	$-0.141858\pi$
$709$	9.24611	+	10.6706i	0.347245	+	0.400742i	−0.555081	+	0.831796i	$0.687313\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−7.74047	+	14.4723i	−0.289883	+	0.541991i
$714$		0			0
$715$	7.67151	−	16.7983i	0.286898	−	0.628220i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	31.2454	−	36.0591i	1.16526	−	1.34478i	0.237590	−	0.971365i	$-0.423642\pi$
$719$	31.2454	−	36.0591i	1.16526	−	1.34478i	0.927666	−	0.373412i	$-0.121812\pi$
$720$		0			0
$721$	−2.89607	+	0.850363i	−0.107855	+	0.0316692i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	3.06562	+	6.71278i	0.113854	+	0.249306i
$726$		0			0
$727$	−30.9527	−	19.8921i	−1.14797	−	0.737756i	−0.178736	−	0.983897i	$-0.557201\pi$
$727$	−30.9527	−	19.8921i	−1.14797	−	0.737756i	−0.969234	+	0.246141i	$0.920837\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−2.34234	+	1.50533i	−0.0866347	+	0.0556768i
$732$		0			0
$733$	−23.7585	−	6.97613i	−0.877541	−	0.257669i	−0.188221	−	0.982127i	$-0.560272\pi$
$733$	−23.7585	−	6.97613i	−0.877541	−	0.257669i	−0.689320	+	0.724457i	$0.742090\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−11.9595			−0.440533
$738$		0			0
$739$	−18.0128	−	5.28903i	−0.662611	−	0.194560i	−0.0669010	−	0.997760i	$-0.521311\pi$
$739$	−18.0128	−	5.28903i	−0.662611	−	0.194560i	−0.595710	+	0.803199i	$0.703129\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−4.33086	+	30.1218i	−0.158884	+	1.10506i	0.741811	+	0.670609i	$0.233967\pi$
$743$	−4.33086	+	30.1218i	−0.158884	+	1.10506i	−0.900695	+	0.434452i	$0.856942\pi$
$744$		0			0
$745$	−4.92425	−	3.16462i	−0.180411	−	0.115943i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	3.83984	+	26.7067i	0.140305	+	0.975840i
$750$		0			0
$751$	−34.7928	+	10.2161i	−1.26961	+	0.372790i	−0.846062	−	0.533085i	$-0.821033\pi$
$751$	−34.7928	+	10.2161i	−1.26961	+	0.372790i	−0.423545	+	0.905875i	$0.639215\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−8.32442	−	9.60689i	−0.302957	−	0.349631i
$756$		0			0
$757$	−18.1304	+	39.7001i	−0.658961	+	1.44292i	0.224526	+	0.974468i	$0.427917\pi$
$757$	−18.1304	+	39.7001i	−0.658961	+	1.44292i	−0.883487	+	0.468456i	$0.844811\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.29149	−	2.82797i	0.0468164	−	0.102514i	−0.884779	−	0.466012i	$-0.845690\pi$
$761$	1.29149	−	2.82797i	0.0468164	−	0.102514i	0.931595	+	0.363498i	$0.118418\pi$
$762$		0			0
$763$	−3.93009	−	4.53557i	−0.142279	−	0.164198i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	54.9289	−	16.1286i	1.98337	−	0.582369i
$768$		0			0
$769$	6.34944	+	44.1613i	0.228967	+	1.59250i	0.702475	+	0.711709i	$0.252078\pi$
$769$	6.34944	+	44.1613i	0.228967	+	1.59250i	−0.473508	+	0.880790i	$0.657012\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−14.3965	−	9.25209i	−0.517807	−	0.332774i	0.255497	−	0.966810i	$-0.417761\pi$
$773$	−14.3965	−	9.25209i	−0.517807	−	0.332774i	−0.773304	+	0.634035i	$0.781397\pi$
$774$		0			0
$775$	−0.842448	+	5.85936i	−0.0302616	+	0.210474i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−32.0102	−	9.39905i	−1.14689	−	0.336756i
$780$		0			0
$781$	28.5121			1.02024
$782$		0			0
$783$		0			0
$784$		0			0
$785$	34.7957	+	10.2169i	1.24191	+	0.364658i
$786$		0			0
$787$	−36.8248	+	23.6658i	−1.31266	+	0.843596i	−0.994530	−	0.104451i	$-0.966692\pi$
$787$	−36.8248	+	23.6658i	−1.31266	+	0.843596i	−0.318131	+	0.948047i	$0.603055\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	47.9767	+	30.8327i	1.70585	+	1.09629i
$792$		0			0
$793$	−28.3852	−	62.1549i	−1.00799	−	2.20718i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	27.6054	−	8.10566i	0.977832	−	0.287117i	0.246503	−	0.969142i	$-0.420719\pi$
$797$	27.6054	−	8.10566i	0.977832	−	0.287117i	0.731329	+	0.682025i	$0.238900\pi$
$798$		0			0
$799$	5.13859	−	5.93025i	0.181790	−	0.209797i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−6.08454	+	13.3233i	−0.214719	+	0.470168i
$804$		0			0
$805$	27.7978	+	10.0946i	0.979744	+	0.355788i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−8.71151	−	10.0536i	−0.306280	−	0.353466i	0.581654	−	0.813436i	$-0.302406\pi$
$809$	−8.71151	−	10.0536i	−0.306280	−	0.353466i	−0.887935	+	0.459970i	$0.847860\pi$
$810$		0			0
$811$	30.0940	−	34.7303i	1.05674	−	1.21955i	0.0819035	−	0.996640i	$-0.473900\pi$
$811$	30.0940	−	34.7303i	1.05674	−	1.21955i	0.974840	−	0.222907i	$-0.0715545\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	3.82075	+	26.5739i	0.133835	+	0.930842i
$816$		0			0
$817$	−7.23123	−	15.8342i	−0.252989	−	0.553968i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−6.84569	+	47.6128i	−0.238916	+	1.66170i	0.418534	+	0.908201i	$0.362544\pi$
$821$	−6.84569	+	47.6128i	−0.238916	+	1.66170i	−0.657451	+	0.753498i	$0.728365\pi$
$822$		0			0
$823$	24.2085	−	15.5579i	0.843856	−	0.542313i	−0.0457968	−	0.998951i	$-0.514583\pi$
$823$	24.2085	−	15.5579i	0.843856	−	0.542313i	0.889653	+	0.456637i	$0.150946\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−47.0915			−1.63753			−0.818766	−	0.574128i	$-0.805341\pi$
$827$	−47.0915			−1.63753			−0.818766	+	0.574128i	$0.805341\pi$
$828$		0			0
$829$	−27.9669			−0.971330			−0.485665	−	0.874145i	$-0.661423\pi$
$829$	−27.9669			−0.971330			−0.485665	+	0.874145i	$0.661423\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	2.95133	−	1.89670i	0.102257	−	0.0657169i
$834$		0			0
$835$	−6.33934	+	44.0911i	−0.219382	+	1.52584i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−7.71830	−	16.9007i	−0.266465	−	0.583477i	0.728347	−	0.685209i	$-0.240289\pi$
$839$	−7.71830	−	16.9007i	−0.266465	−	0.583477i	−0.994812	+	0.101731i	$0.967562\pi$
$840$		0			0
$841$	1.53686	+	10.6891i	0.0529952	+	0.368590i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−17.8454	+	20.5947i	−0.613899	+	0.708478i
$846$		0			0
$847$	−16.2674	−	18.7736i	−0.558955	−	0.645069i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	17.1975	−	3.89743i	0.589524	−	0.133602i
$852$		0			0
$853$	18.1531	−	39.7498i	0.621551	−	1.36101i	−0.292834	−	0.956163i	$-0.594598\pi$
$853$	18.1531	−	39.7498i	0.621551	−	1.36101i	0.914386	−	0.404844i	$-0.132674\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−23.5393	+	27.1658i	−0.804087	+	0.927966i	−0.998598	−	0.0529347i	$-0.983142\pi$
$857$	−23.5393	+	27.1658i	−0.804087	+	0.927966i	0.194511	+	0.980900i	$0.437688\pi$
$858$		0			0
$859$	26.6711	−	7.83135i	0.910008	−	0.267202i	0.206964	−	0.978349i	$-0.433642\pi$
$859$	26.6711	−	7.83135i	0.910008	−	0.267202i	0.703044	+	0.711146i	$0.251824\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	2.79661	+	6.12373i	0.0951979	+	0.208454i	0.951240	−	0.308452i	$-0.0998109\pi$
$863$	2.79661	+	6.12373i	0.0951979	+	0.208454i	−0.856042	+	0.516906i	$0.827084\pi$
$864$		0			0
$865$	23.7432	+	15.2589i	0.807294	+	0.518817i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	10.3140	−	6.62839i	0.349878	−	0.224853i
$870$		0			0
$871$	31.5408	+	9.26122i	1.06872	+	0.313804i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	41.4998			1.40295
$876$		0			0
$877$	−12.0177	−	3.52871i	−0.405808	−	0.119156i	0.0724571	−	0.997372i	$-0.476916\pi$
$877$	−12.0177	−	3.52871i	−0.405808	−	0.119156i	−0.478265	+	0.878216i	$0.658734\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−4.25497	+	29.5939i	−0.143353	+	0.997045i	0.783438	+	0.621470i	$0.213464\pi$
$881$	−4.25497	+	29.5939i	−0.143353	+	0.997045i	−0.926792	+	0.375576i	$0.877445\pi$
$882$		0			0
$883$	16.2520	+	10.4445i	0.546923	+	0.351486i	0.784741	−	0.619824i	$-0.212796\pi$
$883$	16.2520	+	10.4445i	0.546923	+	0.351486i	−0.237818	+	0.971310i	$0.576432\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−7.50812	−	52.2201i	−0.252098	−	1.75338i	−0.585572	−	0.810620i	$-0.699130\pi$
$887$	−7.50812	−	52.2201i	−0.252098	−	1.75338i	0.333474	−	0.942759i	$-0.391779\pi$
$888$		0			0
$889$	4.18481	−	1.22877i	0.140354	−	0.0412116i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	32.1255	+	37.0748i	1.07504	+	1.24066i
$894$		0			0
$895$	13.6289	−	29.8430i	0.455562	−	0.997543i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	6.06504	−	13.2806i	0.202280	−	0.442932i
$900$		0			0
$901$	3.90345	+	4.50483i	0.130043	+	0.150078i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	46.1555	−	13.5525i	1.53426	−	0.450500i
$906$		0			0
$907$	−0.829035	−	5.76607i	−0.0275277	−	0.191459i	0.971418	−	0.237377i	$-0.0762878\pi$
$907$	−0.829035	−	5.76607i	−0.0275277	−	0.191459i	−0.998945	+	0.0459181i	$0.985379\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	30.2223	+	19.4227i	1.00131	+	0.643503i	0.935130	−	0.354305i	$-0.115283\pi$
$911$	30.2223	+	19.4227i	1.00131	+	0.643503i	0.0661796	+	0.997808i	$0.478919\pi$
$912$		0			0
$913$	−2.68255	+	18.6576i	−0.0887795	+	0.617475i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	32.9966	+	9.68868i	1.08964	+	0.319949i
$918$		0			0
$919$	−5.76019			−0.190011			−0.0950055	−	0.995477i	$-0.530287\pi$
$919$	−5.76019			−0.190011			−0.0950055	+	0.995477i	$0.530287\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−75.1950	−	22.0792i	−2.47507	−	0.726747i
$924$		0			0
$925$	5.35050	−	3.43856i	0.175923	−	0.113059i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−16.6393	−	10.6934i	−0.545917	−	0.350839i	0.238432	−	0.971159i	$-0.423366\pi$
$929$	−16.6393	−	10.6934i	−0.545917	−	0.350839i	−0.784349	+	0.620320i	$0.787003\pi$
$930$		0			0
$931$	9.11127	+	19.9509i	0.298610	+	0.653864i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−2.53514	+	0.744384i	−0.0829080	+	0.0243440i
$936$		0			0
$937$	−0.359201	+	0.414540i	−0.0117346	+	0.0135424i	−0.761587	−	0.648063i	$-0.775579\pi$
$937$	−0.359201	+	0.414540i	−0.0117346	+	0.0135424i	0.749852	+	0.661606i	$0.230125\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−18.7468	+	41.0498i	−0.611129	+	1.33819i	0.310670	+	0.950518i	$0.399447\pi$
$941$	−18.7468	+	41.0498i	−0.611129	+	1.33819i	−0.921799	+	0.387669i	$0.873281\pi$
$942$		0			0
$943$	−6.89058	+	33.0514i	−0.224388	+	1.07630i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	2.55059	+	2.94354i	0.0828832	+	0.0956523i	0.795676	−	0.605722i	$-0.207116\pi$
$947$	2.55059	+	2.94354i	0.0828832	+	0.0956523i	−0.712793	+	0.701374i	$0.752570\pi$
$948$		0			0
$949$	26.3641	−	30.4258i	0.855815	−	0.987663i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−6.86795	−	47.7677i	−0.222475	−	1.54735i	−0.728632	−	0.684905i	$-0.759843\pi$
$953$	−6.86795	−	47.7677i	−0.222475	−	1.54735i	0.506157	−	0.862441i	$-0.331066\pi$
$954$		0			0
$955$	18.6250	+	40.7831i	0.602692	+	1.31971i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−3.16966	+	22.0455i	−0.102354	+	0.711886i
$960$		0			0
$961$	−16.2266	+	10.4282i	−0.523440	+	0.336394i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−8.53381			−0.274713
$966$		0			0
$967$	−52.3950			−1.68491			−0.842456	−	0.538766i	$-0.818891\pi$
$967$	−52.3950			−1.68491			−0.842456	+	0.538766i	$0.818891\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−0.372738	+	0.239544i	−0.0119617	+	0.00768733i	−0.546608	−	0.837389i	$-0.684081\pi$
$971$	−0.372738	+	0.239544i	−0.0119617	+	0.00768733i	0.534646	+	0.845076i	$0.320445\pi$
$972$		0			0
$973$	−4.15077	+	28.8692i	−0.133067	+	0.925504i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−21.8870	−	47.9259i	−0.700228	−	1.53329i	−0.839695	−	0.543058i	$-0.817266\pi$
$977$	−21.8870	−	47.9259i	−0.700228	−	1.53329i	0.139467	−	0.990227i	$-0.455461\pi$
$978$		0			0
$979$	3.05773	+	21.2670i	0.0977255	+	0.679696i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	10.4554	−	12.0662i	0.333475	−	0.384851i	−0.564104	−	0.825704i	$-0.690778\pi$
$983$	10.4554	−	12.0662i	0.333475	−	0.384851i	0.897580	+	0.440853i	$0.145324\pi$
$984$		0			0
$985$	−13.1830	−	15.2140i	−0.420046	−	0.484758i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−15.3876	+	8.57617i	−0.489299	+	0.272706i
$990$		0			0
$991$	−9.03107	+	19.7753i	−0.286881	+	0.628183i	−0.997125	−	0.0757732i	$-0.975857\pi$
$991$	−9.03107	+	19.7753i	−0.286881	+	0.628183i	0.710244	+	0.703956i	$0.248585\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	9.34129	−	10.7804i	0.296139	−	0.341762i
$996$		0			0
$997$	−30.8973	+	9.07225i	−0.978526	+	0.287321i	−0.731616	−	0.681717i	$-0.761233\pi$
$997$	−30.8973	+	9.07225i	−0.978526	+	0.287321i	−0.246910	+	0.969038i	$0.579415\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	828.2.q.c.397.2		20
3.2	odd	2		276.2.i.a.121.1	yes	20
23.4	even	11	inner	828.2.q.c.73.2		20
69.2	odd	22		6348.2.a.s.1.3		10
69.44	even	22		6348.2.a.t.1.8		10
69.50	odd	22		276.2.i.a.73.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.i.a.73.1	✓	20	69.50	odd	22
276.2.i.a.121.1	yes	20	3.2	odd	2
828.2.q.c.73.2		20	23.4	even	11	inner
828.2.q.c.397.2		20	1.1	even	1	trivial
6348.2.a.s.1.3		10	69.2	odd	22
6348.2.a.t.1.8		10	69.44	even	22

Overview	Random
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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:	\( N \)	\(=\)	\( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	828.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.52130 - 0.977682i) q^{5} +(0.485296 - 3.37531i) q^{7} +O(q^{10})\)	\(q+(1.52130 - 0.977682i) q^{5} +(0.485296 - 3.37531i) q^{7} +(0.800715 + 1.75332i) q^{11} +(-0.753988 - 5.24410i) q^{13} +(-0.496392 + 0.572867i) q^{17} +(-3.10335 - 3.58146i) q^{19} +(-3.36166 + 3.42041i) q^{23} +(-0.718574 + 1.57346i) q^{25} +(2.79381 - 3.22422i) q^{29} +(3.28356 - 0.964142i) q^{31} +(-2.56170 - 5.60934i) q^{35} +(-3.09318 - 1.98787i) q^{37} +(5.92232 - 3.80604i) q^{41} +(3.52444 + 1.03487i) q^{43} -10.3519 q^{47} +(-4.44075 - 1.30392i) q^{49} +(1.11911 - 7.78361i) q^{53} +(2.93232 + 1.88449i) q^{55} +(1.53778 + 10.6955i) q^{59} +(12.3748 - 3.63356i) q^{61} +(-6.27411 - 7.24071i) q^{65} +(-2.57750 + 5.64394i) q^{67} +(6.14490 - 13.4555i) q^{71} +(4.97621 + 5.74285i) q^{73} +(6.30658 - 1.85178i) q^{77} +(-0.905219 - 6.29594i) q^{79} +(8.22677 + 5.28702i) q^{83} +(-0.195081 + 1.35682i) q^{85} +(10.6954 + 3.14044i) q^{89} -18.0664 q^{91} +(-8.22267 - 2.41439i) q^{95} +(6.41054 - 4.11980i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{5}+O(q^{10}) \) 20 * q + 4 * q^5	\( 20 q + 4 q^{5} - 22 q^{13} - 7 q^{17} + 19 q^{19} - 20 q^{23} + 20 q^{25} - 32 q^{29} - 3 q^{31} + 26 q^{35} - 10 q^{37} + 40 q^{41} + 8 q^{43} + 18 q^{47} - 34 q^{49} + 34 q^{53} - 17 q^{55} + 32 q^{59} + 32 q^{61} - 49 q^{65} + 35 q^{67} - 33 q^{71} - q^{73} + 50 q^{77} + 22 q^{79} + 14 q^{83} - 9 q^{85} - 10 q^{89} - 72 q^{91} + 51 q^{95} - 4 q^{97}+O(q^{100}) \) 20 * q + 4 * q^5 - 22 * q^13 - 7 * q^17 + 19 * q^19 - 20 * q^23 + 20 * q^25 - 32 * q^29 - 3 * q^31 + 26 * q^35 - 10 * q^37 + 40 * q^41 + 8 * q^43 + 18 * q^47 - 34 * q^49 + 34 * q^53 - 17 * q^55 + 32 * q^59 + 32 * q^61 - 49 * q^65 + 35 * q^67 - 33 * q^71 - q^73 + 50 * q^77 + 22 * q^79 + 14 * q^83 - 9 * q^85 - 10 * q^89 - 72 * q^91 + 51 * q^95 - 4 * q^97

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