LMFDB - Embedded newform 297.2.f.b.163.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(82,297)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(297, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([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("297.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.f (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 9x^{14} + 51x^{12} - 249x^{10} + 1476x^{8} - 2875x^{6} + 2335x^{4} + 125x^{2} + 25 $ x^16 - 9x^14 + 51x^12 - 249x^10 + 1476x^8 - 2875x^6 + 2335x^4 + 125*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			163.1
Root			$-1.18970 + 0.386556i$ of defining polynomial
Character	$\chi$	$=$	297.163
Dual form			297.2.f.b.82.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.760284 + 2.33991i) q^{2} +(-3.27913 - 2.38243i) q^{4} +(-0.305860 - 0.941339i) q^{5} +(-3.49672 - 2.54052i) q^{7} +(4.08684 - 2.96926i) q^{8} +2.43519 q^{10} +(2.79120 + 1.79142i) q^{11} +(1.11803 - 3.44095i) q^{13} +(8.60310 - 6.25052i) q^{14} +(1.33563 + 4.11065i) q^{16} +(-0.816208 - 2.51203i) q^{17} +(3.09629 - 2.24958i) q^{19} +(-1.23972 + 3.81546i) q^{20} +(-6.31388 + 5.16917i) q^{22} -3.45011 q^{23} +(3.25252 - 2.36309i) q^{25} +(7.20151 + 5.23221i) q^{26} +(5.41361 + 16.6614i) q^{28} +(-8.43168 - 6.12597i) q^{29} +(-0.521582 + 1.60526i) q^{31} -0.530785 q^{32} +6.49848 q^{34} +(-1.32198 + 4.06865i) q^{35} +(-2.61803 - 1.90211i) q^{37} +(2.90977 + 8.95537i) q^{38} +(-4.04508 - 2.93893i) q^{40} +(-9.63335 + 6.99904i) q^{41} -2.12307 q^{43} +(-4.88477 - 12.5241i) q^{44} +(2.62307 - 8.07297i) q^{46} +(3.47861 - 2.52736i) q^{47} +(3.60973 + 11.1096i) q^{49} +(3.05659 + 9.40723i) q^{50} +(-11.8640 + 8.61970i) q^{52} +(2.93021 - 9.01826i) q^{53} +(0.832623 - 3.17539i) q^{55} -21.8340 q^{56} +(20.7447 - 15.0719i) q^{58} +(5.23607 + 3.80423i) q^{59} +(-1.48656 - 4.57516i) q^{61} +(-3.35963 - 2.44091i) q^{62} +(-2.26771 + 6.97930i) q^{64} -3.58107 q^{65} +0.854102 q^{67} +(-3.30828 + 10.1818i) q^{68} +(-8.51520 - 6.18665i) q^{70} +(1.16751 + 3.59324i) q^{71} +(-9.22952 - 6.70564i) q^{73} +(6.44123 - 4.67983i) q^{74} -15.5126 q^{76} +(-5.20891 - 13.3552i) q^{77} +(1.89841 - 5.84272i) q^{79} +(3.46100 - 2.51456i) q^{80} +(-9.05306 - 27.8625i) q^{82} +(-1.03831 - 3.19558i) q^{83} +(-2.11503 + 1.53666i) q^{85} +(1.61413 - 4.96779i) q^{86} +(16.7264 - 0.966542i) q^{88} +13.2605 q^{89} +(-12.6513 + 9.19169i) q^{91} +(11.3134 + 8.21964i) q^{92} +(3.26907 + 10.0612i) q^{94} +(-3.06465 - 2.22660i) q^{95} +(-0.114759 + 0.353191i) q^{97} -28.7399 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 10 q^{4} + 12 q^{10} - 10 q^{16} - 2 q^{19} - 36 q^{22} + 32 q^{25} + 42 q^{28} - 26 q^{31} - 48 q^{34} - 24 q^{37} - 20 q^{40} + 24 q^{43} - 16 q^{46} + 24 q^{49} - 40 q^{52} - 16 q^{55} + 106 q^{58}+ \cdots + 72 q^{97}+O(q^{100}) $ 16 * q - 10 * q^4 + 12 * q^10 - 10 * q^16 - 2 * q^19 - 36 * q^22 + 32 * q^25 + 42 * q^28 - 26 * q^31 - 48 * q^34 - 24 * q^37 - 20 * q^40 + 24 * q^43 - 16 * q^46 + 24 * q^49 - 40 * q^52 - 16 * q^55 + 106 * q^58 - 6 * q^61 + 62 * q^64 - 40 * q^67 - 58 * q^70 + 60 * q^76 + 64 * q^79 - 84 * q^82 - 18 * q^85 + 80 * q^88 - 10 * q^91 + 90 * q^94 + 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.760284	+	2.33991i	−0.537602	+	1.65457i	0.200357	+	0.979723i	$0.435790\pi$
$2$	−0.760284	+	2.33991i	−0.537602	+	1.65457i	−0.737959	+	0.674846i	$0.764210\pi$
$3$		0			0
$3$		0			0
$4$	−3.27913	−	2.38243i	−1.63956	−	1.19121i
$5$	−0.305860	−	0.941339i	−0.136785	−	0.420980i	0.859079	−	0.511843i	$-0.171037\pi$
$5$	−0.305860	−	0.941339i	−0.136785	−	0.420980i	−0.995863	+	0.0908638i	$0.971037\pi$
$6$		0			0
$7$	−3.49672	−	2.54052i	−1.32164	−	0.960226i	−0.999910	−	0.0133937i	$-0.995737\pi$
$7$	−3.49672	−	2.54052i	−1.32164	−	0.960226i	−0.321727	−	0.946832i	$-0.604263\pi$
$8$	4.08684	−	2.96926i	1.44492	−	1.04979i
$9$		0			0
$10$	2.43519			0.770075
$11$	2.79120	+	1.79142i	0.841578	+	0.540135i
$11$	2.79120	+	1.79142i	0.841578	+	0.540135i
$12$		0			0
$13$	1.11803	−	3.44095i	0.310087	−	0.954349i	−0.667643	−	0.744482i	$-0.732697\pi$
$13$	1.11803	−	3.44095i	0.310087	−	0.954349i	0.977730	−	0.209868i	$-0.0673033\pi$
$14$	8.60310	−	6.25052i	2.29927	−	1.67052i
$15$		0			0
$16$	1.33563	+	4.11065i	0.333908	+	1.02766i
$17$	−0.816208	−	2.51203i	−0.197959	−	0.609257i	−0.999929	−	0.0118921i	$-0.996215\pi$
$17$	−0.816208	−	2.51203i	−0.197959	−	0.609257i	0.801970	−	0.597365i	$-0.203785\pi$
$18$		0			0
$19$	3.09629	−	2.24958i	0.710337	−	0.516090i	−0.172945	−	0.984931i	$-0.555328\pi$
$19$	3.09629	−	2.24958i	0.710337	−	0.516090i	0.883282	+	0.468841i	$0.155328\pi$
$20$	−1.23972	+	3.81546i	−0.277209	+	0.853163i
$21$		0			0
$22$	−6.31388	+	5.16917i	−1.34612	+	1.10207i
$23$	−3.45011			−0.719398			−0.359699	−	0.933068i	$-0.617121\pi$
$23$	−3.45011			−0.719398			−0.359699	+	0.933068i	$0.617121\pi$
$24$		0			0
$25$	3.25252	−	2.36309i	0.650503	−	0.472618i
$26$	7.20151	+	5.23221i	1.41233	+	1.02612i
$27$		0			0
$28$	5.41361	+	16.6614i	1.02308	+	3.14870i
$29$	−8.43168	−	6.12597i	−1.56572	−	1.13756i	−0.931112	−	0.364733i	$-0.881160\pi$
$29$	−8.43168	−	6.12597i	−1.56572	−	1.13756i	−0.634611	−	0.772832i	$-0.718840\pi$
$30$		0			0
$31$	−0.521582	+	1.60526i	−0.0936788	+	0.288314i	−0.986907	−	0.161290i	$-0.948435\pi$
$31$	−0.521582	+	1.60526i	−0.0936788	+	0.288314i	0.893228	+	0.449603i	$0.148435\pi$
$32$	−0.530785			−0.0938305
$33$		0			0
$34$	6.49848			1.11448
$35$	−1.32198	+	4.06865i	−0.223456	+	0.687727i
$36$		0			0
$37$	−2.61803	−	1.90211i	−0.430402	−	0.312705i	0.351408	−	0.936223i	$-0.385703\pi$
$37$	−2.61803	−	1.90211i	−0.430402	−	0.312705i	−0.781810	+	0.623517i	$0.785703\pi$
$38$	2.90977	+	8.95537i	0.472028	+	1.45275i
$39$		0			0
$40$	−4.04508	−	2.93893i	−0.639584	−	0.464685i
$41$	−9.63335	+	6.99904i	−1.50448	+	1.09307i	−0.535921	+	0.844268i	$0.680035\pi$
$41$	−9.63335	+	6.99904i	−1.50448	+	1.09307i	−0.968555	+	0.248798i	$0.919965\pi$
$42$		0			0
$43$	−2.12307			−0.323764			−0.161882	−	0.986810i	$-0.551756\pi$
$43$	−2.12307			−0.323764			−0.161882	+	0.986810i	$0.551756\pi$
$44$	−4.88477	−	12.5241i	−0.736406	−	1.88809i
$45$		0			0
$46$	2.62307	−	8.07297i	0.386750	−	1.19029i
$47$	3.47861	−	2.52736i	0.507407	−	0.368653i	−0.304432	−	0.952534i	$-0.598467\pi$
$47$	3.47861	−	2.52736i	0.507407	−	0.368653i	0.811839	+	0.583881i	$0.198467\pi$
$48$		0			0
$49$	3.60973	+	11.1096i	0.515675	+	1.58709i
$50$	3.05659	+	9.40723i	0.432267	+	1.33038i
$51$		0			0
$52$	−11.8640	+	8.61970i	−1.64524	+	1.19534i
$53$	2.93021	−	9.01826i	0.402496	−	1.23875i	−0.520473	−	0.853878i	$-0.674244\pi$
$53$	2.93021	−	9.01826i	0.402496	−	1.23875i	0.922968	−	0.384876i	$-0.125756\pi$
$54$		0			0
$55$	0.832623	−	3.17539i	0.112271	−	0.428170i
$56$	−21.8340			−2.91770
$57$		0			0
$58$	20.7447	−	15.0719i	2.72391	−	1.97904i
$59$	5.23607	+	3.80423i	0.681679	+	0.495269i	0.873914	−	0.486080i	$-0.161574\pi$
$59$	5.23607	+	3.80423i	0.681679	+	0.495269i	−0.192235	+	0.981349i	$0.561574\pi$
$60$		0			0
$61$	−1.48656	−	4.57516i	−0.190334	−	0.585789i	0.809665	−	0.586892i	$-0.199649\pi$
$61$	−1.48656	−	4.57516i	−0.190334	−	0.585789i	−0.999999	+	0.00110319i	$0.999649\pi$
$62$	−3.35963	−	2.44091i	−0.426673	−	0.309996i
$63$		0			0
$64$	−2.26771	+	6.97930i	−0.283464	+	0.872413i
$65$	−3.58107			−0.444177
$66$		0			0
$67$	0.854102			0.104345			0.0521726	−	0.998638i	$-0.483385\pi$
$67$	0.854102			0.104345			0.0521726	+	0.998638i	$0.483385\pi$
$68$	−3.30828	+	10.1818i	−0.401187	+	1.23473i
$69$		0			0
$70$	−8.51520	−	6.18665i	−1.01776	−	0.739446i
$71$	1.16751	+	3.59324i	0.138558	+	0.426439i	0.996127	−	0.0879314i	$-0.0280256\pi$
$71$	1.16751	+	3.59324i	0.138558	+	0.426439i	−0.857568	+	0.514371i	$0.828026\pi$
$72$		0			0
$73$	−9.22952	−	6.70564i	−1.08023	−	0.784835i	−0.102510	−	0.994732i	$-0.532687\pi$
$73$	−9.22952	−	6.70564i	−1.08023	−	0.784835i	−0.977724	+	0.209897i	$0.932687\pi$
$74$	6.44123	−	4.67983i	0.748778	−	0.544019i
$75$		0			0
$76$	−15.5126			−1.77942
$77$	−5.20891	−	13.3552i	−0.593610	−	1.52197i
$78$		0			0
$79$	1.89841	−	5.84272i	0.213588	−	0.657357i	−0.785663	−	0.618655i	$-0.787678\pi$
$79$	1.89841	−	5.84272i	0.213588	−	0.657357i	0.999251	−	0.0387017i	$-0.0123222\pi$
$80$	3.46100	−	2.51456i	0.386951	−	0.281137i
$81$		0			0
$82$	−9.05306	−	27.8625i	−0.999743	−	3.07689i
$83$	−1.03831	−	3.19558i	−0.113969	−	0.350761i	0.877762	−	0.479098i	$-0.159036\pi$
$83$	−1.03831	−	3.19558i	−0.113969	−	0.350761i	−0.991731	+	0.128337i	$0.959036\pi$
$84$		0			0
$85$	−2.11503	+	1.53666i	−0.229407	+	0.166674i
$86$	1.61413	−	4.96779i	0.174056	−	0.535690i
$87$		0			0
$88$	16.7264	−	0.966542i	1.78304	−	0.103034i
$89$	13.2605			1.40561			0.702806	−	0.711381i	$-0.251930\pi$
$89$	13.2605			1.40561			0.702806	+	0.711381i	$0.251930\pi$
$90$		0			0
$91$	−12.6513	+	9.19169i	−1.32621	+	0.963550i
$92$	11.3134	+	8.21964i	1.17950	+	0.856957i
$93$		0			0
$94$	3.26907	+	10.0612i	0.337178	+	1.03773i
$95$	−3.06465	−	2.22660i	−0.314427	−	0.228444i
$96$		0			0
$97$	−0.114759	+	0.353191i	−0.0116520	+	0.0358612i	−0.956713	−	0.291031i	$-0.906002\pi$
$97$	−0.114759	+	0.353191i	−0.0116520	+	0.0358612i	0.945061	+	0.326893i	$0.106002\pi$
$98$	−28.7399			−2.90317
$99$		0			0
$100$	−16.2953			−1.62953
$101$	−4.01546	+	12.3583i	−0.399553	+	1.22970i	0.525805	+	0.850605i	$0.323764\pi$
$101$	−4.01546	+	12.3583i	−0.399553	+	1.22970i	−0.925358	+	0.379094i	$0.876236\pi$
$102$		0			0
$103$	9.54968	+	6.93825i	0.940958	+	0.683646i	0.948651	−	0.316324i	$-0.102449\pi$
$103$	9.54968	+	6.93825i	0.940958	+	0.683646i	−0.00769290	+	0.999970i	$0.502449\pi$
$104$	−5.64788	−	17.3824i	−0.553820	−	1.70448i
$105$		0			0
$106$	18.8742	+	13.7129i	1.83322	+	1.33191i
$107$	−3.82493	+	2.77898i	−0.369770	+	0.268654i	−0.757116	−	0.653281i	$-0.773392\pi$
$107$	−3.82493	+	2.77898i	−0.369770	+	0.268654i	0.387345	+	0.921935i	$0.373392\pi$
$108$		0			0
$109$	16.1864			1.55037			0.775186	−	0.631733i	$-0.217656\pi$
$109$	16.1864			1.55037			0.775186	+	0.631733i	$0.217656\pi$
$110$	6.79711	+	4.36246i	0.648079	+	0.415945i
$111$		0			0
$112$	5.77285	−	17.7670i	0.545483	−	1.67882i
$113$	0.687408	−	0.499431i	0.0646659	−	0.0469825i	−0.554983	−	0.831862i	$-0.687275\pi$
$113$	0.687408	−	0.499431i	0.0646659	−	0.0469825i	0.619649	+	0.784879i	$0.287275\pi$
$114$		0			0
$115$	1.05525	+	3.24773i	0.0984026	+	0.302852i
$116$	13.0539	+	40.1757i	1.21202	+	3.73022i
$117$		0			0
$118$	−12.8825	+	9.35966i	−1.18593	+	0.861627i
$119$	−3.52781	+	10.8575i	−0.323393	+	0.995302i
$120$		0			0
$121$	4.58160	+	10.0004i	0.416509	+	0.909132i
$122$	11.8357			1.07155
$123$		0			0
$124$	5.53475	−	4.02123i	0.497036	−	0.361117i
$125$	−7.22304	−	5.24784i	−0.646048	−	0.469381i
$126$		0			0
$127$	3.60148	+	11.0842i	0.319580	+	0.983566i	0.973828	+	0.227286i	$0.0729853\pi$
$127$	3.60148	+	11.0842i	0.319580	+	0.983566i	−0.654248	+	0.756280i	$0.727015\pi$
$128$	−15.4657	−	11.2365i	−1.36699	−	0.993174i
$129$		0			0
$130$	2.72263	−	8.37939i	0.238790	−	0.734921i
$131$	0.242802			0.0212137			0.0106068	−	0.999944i	$-0.496624\pi$
$131$	0.242802			0.0212137			0.0106068	+	0.999944i	$0.496624\pi$
$132$		0			0
$133$	−16.5420			−1.43437
$134$	−0.649360	+	1.99852i	−0.0560962	+	0.172646i
$135$		0			0
$136$	−10.7946	−	7.84273i	−0.925629	−	0.672509i
$137$	−0.140507	−	0.432435i	−0.0120043	−	0.0369454i	0.944875	−	0.327431i	$-0.106183\pi$
$137$	−0.140507	−	0.432435i	−0.0120043	−	0.0369454i	−0.956879	+	0.290486i	$0.906183\pi$
$138$		0			0
$139$	14.4337	+	10.4867i	1.22425	+	0.889468i	0.996446	−	0.0842390i	$-0.0268459\pi$
$139$	14.4337	+	10.4867i	1.22425	+	0.889468i	0.227803	+	0.973707i	$0.426846\pi$
$140$	14.0282	−	10.1921i	1.18560	−	0.861389i
$141$		0			0
$142$	−9.29551			−0.780062
$143$	9.28487	−	7.60152i	0.776440	−	0.635671i
$144$		0			0
$145$	−3.18771	+	9.81076i	−0.264725	+	0.814739i
$146$	22.7077	−	16.4981i	1.87930	−	1.36539i
$147$		0			0
$148$	4.05323	+	12.4745i	0.333173	+	1.02540i
$149$	−4.92523	−	15.1583i	−0.403491	−	1.24182i	−0.922149	−	0.386835i	$-0.873568\pi$
$149$	−4.92523	−	15.1583i	−0.403491	−	1.24182i	0.518658	−	0.854982i	$-0.326432\pi$
$150$		0			0
$151$	−4.89743	+	3.55819i	−0.398547	+	0.289562i	−0.768949	−	0.639310i	$-0.779220\pi$
$151$	−4.89743	+	3.55819i	−0.398547	+	0.289562i	0.370402	+	0.928872i	$0.379220\pi$
$152$	5.97443	−	18.3874i	0.484590	−	1.49141i
$153$		0			0
$154$	35.2103	−	2.03464i	2.83733	−	0.163956i
$155$	1.67063			0.134188
$156$		0			0
$157$	−6.05296	+	4.39773i	−0.483079	+	0.350977i	−0.802516	−	0.596630i	$-0.796506\pi$
$157$	−6.05296	+	4.39773i	−0.483079	+	0.350977i	0.319438	+	0.947607i	$0.396506\pi$
$158$	12.2281	+	8.88425i	0.972817	+	0.706793i
$159$		0			0
$160$	0.162346	+	0.499649i	0.0128346	+	0.0395007i
$161$	12.0641	+	8.76508i	0.950784	+	0.690785i
$162$		0			0
$163$	4.31902	−	13.2926i	0.338292	−	1.04115i	−0.626786	−	0.779191i	$-0.715630\pi$
$163$	4.31902	−	13.2926i	0.338292	−	1.04115i	0.965078	−	0.261963i	$-0.0843699\pi$
$164$	48.2637			3.76876
$165$		0			0
$166$	8.26679			0.641628
$167$	−1.97499	+	6.07840i	−0.152829	+	0.470361i	−0.997935	−	0.0642395i	$-0.979538\pi$
$167$	−1.97499	+	6.07840i	−0.152829	+	0.470361i	0.845105	+	0.534600i	$0.179538\pi$
$168$		0			0
$169$	−0.0729490	−	0.0530006i	−0.00561146	−	0.00407697i
$170$	−1.98762	−	6.11727i	−0.152444	−	0.469174i
$171$		0			0
$172$	6.96181	+	5.05805i	0.530833	+	0.385673i
$173$	6.34726	−	4.61155i	0.482573	−	0.350610i	−0.319748	−	0.947503i	$-0.603598\pi$
$173$	6.34726	−	4.61155i	0.482573	−	0.350610i	0.802321	+	0.596893i	$0.203598\pi$
$174$		0			0
$175$	−17.3766			−1.31355
$176$	−3.63590	+	13.8663i	−0.274066	+	1.04521i
$177$		0			0
$178$	−10.0818	+	31.0285i	−0.755660	+	2.32568i
$179$	−3.94392	+	2.86542i	−0.294782	+	0.214172i	−0.725339	−	0.688392i	$-0.758317\pi$
$179$	−3.94392	+	2.86542i	−0.294782	+	0.214172i	0.430557	+	0.902563i	$0.358317\pi$
$180$		0			0
$181$	2.79558	+	8.60390i	0.207794	+	0.639523i	0.999587	+	0.0287340i	$0.00914758\pi$
$181$	2.79558	+	8.60390i	0.207794	+	0.639523i	−0.791794	+	0.610789i	$0.790852\pi$
$182$	−11.8892	−	36.5912i	−0.881285	−	2.71232i
$183$		0			0
$184$	−14.1001	+	10.2443i	−1.03947	+	0.755220i
$185$	−0.989783	+	3.04624i	−0.0727703	+	0.223964i
$186$		0			0
$187$	2.22191	−	8.47375i	0.162482	−	0.619662i
$188$	−17.4280			−1.27107
$189$		0			0
$190$	7.54005	−	5.47817i	0.547013	−	0.397428i
$191$	−15.1833	−	11.0313i	−1.09863	−	0.798200i	−0.117793	−	0.993038i	$-0.537582\pi$
$191$	−15.1833	−	11.0313i	−1.09863	−	0.798200i	−0.980835	+	0.194838i	$0.937582\pi$
$192$		0			0
$193$	−5.34678	−	16.4557i	−0.384870	−	1.18451i	−0.936575	−	0.350468i	$-0.886023\pi$
$193$	−5.34678	−	16.4557i	−0.384870	−	1.18451i	0.551705	−	0.834039i	$-0.313977\pi$
$194$	−0.739188	−	0.537051i	−0.0530706	−	0.0385580i
$195$		0			0
$196$	14.6310	−	45.0297i	1.04507	−	3.21641i
$197$	6.06800			0.432327			0.216164	−	0.976357i	$-0.430646\pi$
$197$	6.06800			0.432327			0.216164	+	0.976357i	$0.430646\pi$
$198$		0			0
$199$	−10.1108			−0.716738			−0.358369	−	0.933580i	$-0.616667\pi$
$199$	−10.1108			−0.716738			−0.358369	+	0.933580i	$0.616667\pi$
$200$	6.27588	−	19.3152i	0.443771	−	1.36579i
$201$		0			0
$202$	−25.8645	−	18.7917i	−1.81982	−	1.32218i
$203$	13.9201	+	42.8417i	0.977000	+	3.00690i
$204$		0			0
$205$	9.53492	+	6.92752i	0.665948	+	0.483839i
$206$	−23.4954	+	17.0704i	−1.63700	+	1.18935i
$207$		0			0
$208$	15.6378			1.08429
$209$	12.6723	−	0.732275i	0.876562	−	0.0506525i
$210$		0			0
$211$	4.55535	−	14.0199i	0.313603	−	0.965172i	−0.662722	−	0.748865i	$-0.730599\pi$
$211$	4.55535	−	14.0199i	0.313603	−	0.965172i	0.976325	−	0.216307i	$-0.0694011\pi$
$212$	−31.0939	+	22.5910i	−2.13554	+	1.55156i
$213$		0			0
$214$	−3.59453	−	11.0628i	−0.245717	−	0.756239i
$215$	0.649360	+	1.99852i	0.0442860	+	0.136298i
$216$		0			0
$217$	5.90203	−	4.28807i	0.400656	−	0.291093i
$218$	−12.3062	+	37.8747i	−0.833483	+	2.56520i
$219$		0			0
$220$	−10.2954	+	8.42885i	−0.694116	+	0.568273i
$221$	−9.55633			−0.642828
$222$		0			0
$223$	−0.496725	+	0.360892i	−0.0332632	+	0.0241671i	−0.604293	−	0.796762i	$-0.706544\pi$
$223$	−0.496725	+	0.360892i	−0.0332632	+	0.0241671i	0.571029	+	0.820930i	$0.306544\pi$
$224$	1.85601	+	1.34847i	0.124010	+	0.0900985i
$225$		0			0
$226$	0.646000	+	1.98818i	0.0429713	+	0.132252i
$227$	9.39297	+	6.82439i	0.623433	+	0.452951i	0.854119	−	0.520078i	$-0.174097\pi$
$227$	9.39297	+	6.82439i	0.623433	+	0.452951i	−0.230686	+	0.973028i	$0.574097\pi$
$228$		0			0
$229$	0.251367	−	0.773628i	0.0166108	−	0.0511228i	−0.942408	−	0.334467i	$-0.891444\pi$
$229$	0.251367	−	0.773628i	0.0166108	−	0.0511228i	0.959018	+	0.283344i	$0.0914438\pi$
$230$	−8.40169			−0.553991
$231$		0			0
$232$	−52.6486			−3.45655
$233$	5.33097	−	16.4070i	0.349243	−	1.07486i	−0.610029	−	0.792379i	$-0.708842\pi$
$233$	5.33097	−	16.4070i	0.349243	−	1.07486i	0.959273	−	0.282482i	$-0.0911577\pi$
$234$		0			0
$235$	−3.44307	−	2.50153i	−0.224601	−	0.163182i
$236$	−8.10646	−	24.9491i	−0.527686	−	1.62405i
$237$		0			0
$238$	−22.7234	−	16.5095i	−1.47294	−	1.07015i
$239$	−0.161603	+	0.117411i	−0.0104532	+	0.00759470i	−0.593000	−	0.805203i	$-0.702056\pi$
$239$	−0.161603	+	0.117411i	−0.0104532	+	0.00759470i	0.582546	+	0.812797i	$0.302056\pi$
$240$		0			0
$241$	14.8309			0.955345			0.477672	−	0.878538i	$-0.341481\pi$
$241$	14.8309			0.955345			0.477672	+	0.878538i	$0.341481\pi$
$242$	−26.8835	+	3.11736i	−1.72814	+	0.200391i
$243$		0			0
$244$	−6.02536	+	18.5442i	−0.385734	+	1.18717i
$245$	9.35383	−	6.79596i	0.597594	−	0.434178i
$246$		0			0
$247$	−4.27896	−	13.1693i	−0.272264	−	0.837942i
$248$	2.63483	+	8.10917i	0.167312	+	0.514933i
$249$		0			0
$250$	17.7711	−	12.9114i	1.12394	−	0.816591i
$251$	−2.63483	+	8.10917i	−0.166309	+	0.511846i	−0.999130	−	0.0416955i	$-0.986724\pi$
$251$	−2.63483	+	8.10917i	−0.166309	+	0.511846i	0.832821	+	0.553542i	$0.186724\pi$
$252$		0			0
$253$	−9.62996	−	6.18062i	−0.605430	−	0.388572i
$254$	−28.6743			−1.79918
$255$		0			0
$256$	26.1768	−	19.0186i	1.63605	−	1.18866i
$257$	−10.5161	−	7.64039i	−0.655976	−	0.476595i	0.209325	−	0.977846i	$-0.432873\pi$
$257$	−10.5161	−	7.64039i	−0.655976	−	0.476595i	−0.865302	+	0.501251i	$0.832873\pi$
$258$		0			0
$259$	4.32219	+	13.3023i	0.268568	+	0.826567i
$260$	11.7428	+	8.53163i	0.728256	+	0.529109i
$261$		0			0
$262$	−0.184598	+	0.568135i	−0.0114045	+	0.0350995i
$263$	14.8529			0.915868			0.457934	−	0.888986i	$-0.348590\pi$
$263$	14.8529			0.915868			0.457934	+	0.888986i	$0.348590\pi$
$264$		0			0
$265$	−9.38548			−0.576545
$266$	12.5766	−	38.7068i	0.771121	−	2.37327i
$267$		0			0
$268$	−2.80071	−	2.03484i	−0.171081	−	0.124297i
$269$	1.17789	+	3.62517i	0.0718172	+	0.221031i	0.980522	−	0.196408i	$-0.0629278\pi$
$269$	1.17789	+	3.62517i	0.0718172	+	0.221031i	−0.908705	+	0.417439i	$0.862928\pi$
$270$		0			0
$271$	11.1948	+	8.13347i	0.680033	+	0.494073i	0.873369	−	0.487060i	$-0.161931\pi$
$271$	11.1948	+	8.13347i	0.680033	+	0.494073i	−0.193335	+	0.981133i	$0.561931\pi$
$272$	9.23591	−	6.71028i	0.560010	−	0.406871i
$273$		0			0
$274$	1.11869			0.0675823
$275$	13.3117	−	0.769223i	0.802727	−	0.0463859i
$276$		0			0
$277$	0.759571	−	2.33772i	0.0456382	−	0.140460i	−0.925641	−	0.378403i	$-0.876473\pi$
$277$	0.759571	−	2.33772i	0.0456382	−	0.140460i	0.971279	+	0.237943i	$0.0764732\pi$
$278$	−35.5116	+	25.8007i	−2.12984	+	1.54742i
$279$		0			0
$280$	6.67815	+	20.5532i	0.399096	+	1.22829i
$281$	−6.15581	−	18.9456i	−0.367225	−	1.13020i	−0.948576	−	0.316549i	$-0.897476\pi$
$281$	−6.15581	−	18.9456i	−0.367225	−	1.13020i	0.581352	−	0.813652i	$-0.302524\pi$
$282$		0			0
$283$	−5.81564	+	4.22531i	−0.345704	+	0.251169i	−0.747065	−	0.664752i	$-0.768537\pi$
$283$	−5.81564	+	4.22531i	−0.345704	+	0.251169i	0.401361	+	0.915920i	$0.368537\pi$
$284$	4.73220	−	14.5642i	0.280804	−	0.864227i
$285$		0			0
$286$	10.7278	+	27.5051i	0.634346	+	1.62641i
$287$	51.4664			3.03796
$288$		0			0
$289$	8.10919	−	5.89167i	0.477011	−	0.346569i
$290$	−20.5328	−	14.9179i	−1.20572	−	0.876010i
$291$		0			0
$292$	14.2891	+	43.9773i	0.836206	+	2.57358i
$293$	−13.8033	−	10.0287i	−0.806396	−	0.585881i	0.106387	−	0.994325i	$-0.466072\pi$
$293$	−13.8033	−	10.0287i	−0.806396	−	0.585881i	−0.912784	+	0.408444i	$0.866072\pi$
$294$		0			0
$295$	1.97957	−	6.09248i	0.115255	−	0.354718i
$296$	−16.3474			−0.950172
$297$		0			0
$298$	39.2137			2.27159
$299$	−3.85734	+	11.8717i	−0.223076	+	0.686557i
$300$		0			0
$301$	7.42378	+	5.39369i	0.427899	+	0.310887i
$302$	−4.60242	−	14.1648i	−0.264840	−	0.815093i
$303$		0			0
$304$	13.3827	+	9.72313i	0.767553	+	0.557660i
$305$	−3.85210	+	2.79871i	−0.220571	+	0.160254i
$306$		0			0
$307$	7.48842			0.427387			0.213693	−	0.976901i	$-0.431451\pi$
$307$	7.48842			0.427387			0.213693	+	0.976901i	$0.431451\pi$
$308$	−14.7371	+	56.2033i	−0.839726	+	3.20248i
$309$		0			0
$310$	−1.27015	+	3.90912i	−0.0721397	+	0.222023i
$311$	8.51155	−	6.18400i	0.482645	−	0.350662i	−0.319704	−	0.947518i	$-0.603583\pi$
$311$	8.51155	−	6.18400i	0.482645	−	0.350662i	0.802349	+	0.596855i	$0.203583\pi$
$312$		0			0
$313$	−3.22449	−	9.92395i	−0.182259	−	0.560935i	0.817632	−	0.575742i	$-0.195287\pi$
$313$	−3.22449	−	9.92395i	−0.182259	−	0.560935i	−0.999890	+	0.0148070i	$0.995287\pi$
$314$	−5.68834	−	17.5069i	−0.321012	−	0.987973i
$315$		0			0
$316$	−20.1450	+	14.6362i	−1.13324	+	0.823350i
$317$	−3.95173	+	12.1622i	−0.221951	+	0.683096i	0.776635	+	0.629950i	$0.216925\pi$
$317$	−3.95173	+	12.1622i	−0.221951	+	0.683096i	−0.998587	+	0.0531456i	$0.983075\pi$
$318$		0			0
$319$	−12.5603	−	32.2035i	−0.703241	−	1.80305i
$320$	7.26349			0.406042
$321$		0			0
$322$	−29.6817	+	21.5650i	−1.65409	+	1.20177i
$323$	−8.17824	−	5.94184i	−0.455049	−	0.330613i
$324$		0			0
$325$	−4.49487	−	13.8338i	−0.249330	−	0.767360i
$326$	27.8198	+	20.2122i	1.54079	+	1.11945i
$327$		0			0
$328$	−18.5880	+	57.2079i	−1.02635	+	3.15878i
$329$	−18.5845			−1.02460
$330$		0			0
$331$	16.3849			0.900598			0.450299	−	0.892878i	$-0.351317\pi$
$331$	16.3849			0.900598			0.450299	+	0.892878i	$0.351317\pi$
$332$	−4.20849	+	12.9524i	−0.230971	+	0.710856i
$333$		0			0
$334$	−12.7214	−	9.24262i	−0.696083	−	0.505734i
$335$	−0.261235	−	0.804000i	−0.0142728	−	0.0439272i
$336$		0			0
$337$	−23.5160	−	17.0854i	−1.28100	−	0.930698i	−0.281414	−	0.959586i	$-0.590803\pi$
$337$	−23.5160	−	17.0854i	−1.28100	−	0.930698i	−0.999583	+	0.0288881i	$0.990803\pi$
$338$	0.179479	−	0.130399i	0.00976235	−	0.00709277i
$339$		0			0
$340$	10.5964			0.574671
$341$	−4.33155	+	3.54624i	−0.234566	+	0.192039i
$342$		0			0
$343$	6.25252	−	19.2433i	0.337604	−	1.03904i
$344$	−8.67663	+	6.30394i	−0.467813	+	0.339886i
$345$		0			0
$346$	5.96491	+	18.3581i	0.320676	+	0.986939i
$347$	6.66940	+	20.5263i	0.358032	+	1.10191i	0.954231	+	0.299072i	$0.0966771\pi$
$347$	6.66940	+	20.5263i	0.358032	+	1.10191i	−0.596199	+	0.802837i	$0.703323\pi$
$348$		0			0
$349$	−19.5785	+	14.2246i	−1.04801	+	0.761426i	−0.971833	−	0.235669i	$-0.924272\pi$
$349$	−19.5785	+	14.2246i	−1.04801	+	0.761426i	−0.0761789	+	0.997094i	$0.524272\pi$
$350$	13.2112	−	40.6598i	0.706167	−	2.17336i
$351$		0			0
$352$	−1.48153	−	0.950862i	−0.0789657	−	0.0506811i
$353$	20.9800			1.11666			0.558328	−	0.829621i	$-0.311443\pi$
$353$	20.9800			1.11666			0.558328	+	0.829621i	$0.311443\pi$
$354$		0			0
$355$	3.02536	−	2.19805i	0.160570	−	0.116661i
$356$	−43.4830	−	31.5922i	−2.30459	−	1.67438i
$357$		0			0
$358$	−3.70635	−	11.4070i	−0.195886	−	0.602876i
$359$	12.6882	+	9.21850i	0.669657	+	0.486534i	0.869910	−	0.493210i	$-0.164177\pi$
$359$	12.6882	+	9.21850i	0.669657	+	0.486534i	−0.200254	+	0.979744i	$0.564177\pi$
$360$		0			0
$361$	−1.34496	+	4.13936i	−0.0707873	+	0.217861i
$362$	−22.2578			−1.16984
$363$		0			0
$364$	63.3837			3.32221
$365$	−3.48934	+	10.7391i	−0.182640	+	0.562110i
$366$		0			0
$367$	6.62952	+	4.81663i	0.346058	+	0.251426i	0.747214	−	0.664584i	$-0.231391\pi$
$367$	6.62952	+	4.81663i	0.346058	+	0.251426i	−0.401155	+	0.916010i	$0.631391\pi$
$368$	−4.60807	−	14.1822i	−0.240212	−	0.739298i
$369$		0			0
$370$	−6.37542	−	4.63201i	−0.331442	−	0.240807i
$371$	−33.1572	+	24.0901i	−1.72144	+	1.25070i
$372$		0			0
$373$	30.8172			1.59565			0.797826	−	0.602888i	$-0.205983\pi$
$373$	30.8172			1.59565			0.797826	+	0.602888i	$0.205983\pi$
$374$	18.1386	+	11.6415i	0.937923	+	0.601970i
$375$		0			0
$376$	6.71213	−	20.6578i	0.346152	−	1.06535i
$377$	−30.5061	+	22.1640i	−1.57114	+	1.14150i
$378$		0			0
$379$	6.12378	+	18.8470i	0.314557	+	0.968108i	0.975936	+	0.218056i	$0.0699715\pi$
$379$	6.12378	+	18.8470i	0.314557	+	0.968108i	−0.661379	+	0.750052i	$0.730029\pi$
$380$	4.74468	+	14.6026i	0.243397	+	0.749098i
$381$		0			0
$382$	37.3560	−	27.1407i	1.91130	−	1.38864i
$383$	7.31619	−	22.5169i	0.373840	−	1.15056i	−0.570418	−	0.821354i	$-0.693219\pi$
$383$	7.31619	−	22.5169i	0.373840	−	1.15056i	0.944258	−	0.329206i	$-0.106781\pi$
$384$		0			0
$385$	−10.9786	+	8.98817i	−0.559521	+	0.458080i
$386$	42.5700			2.16675
$387$		0			0
$388$	1.21776	−	0.884756i	0.0618225	−	0.0449167i
$389$	6.89001	+	5.00589i	0.349338	+	0.253809i	0.748591	−	0.663032i	$-0.230731\pi$
$389$	6.89001	+	5.00589i	0.349338	+	0.253809i	−0.399254	+	0.916841i	$0.630731\pi$
$390$		0			0
$391$	2.81601	+	8.66679i	0.142412	+	0.438298i
$392$	47.7397	+	34.6849i	2.41122	+	1.75185i
$393$		0			0
$394$	−4.61341	+	14.1986i	−0.232420	+	0.715315i
$395$	−6.08063			−0.305949
$396$		0			0
$397$	−3.78373			−0.189900			−0.0949499	−	0.995482i	$-0.530269\pi$
$397$	−3.78373			−0.189900			−0.0949499	+	0.995482i	$0.530269\pi$
$398$	7.68710	−	23.6585i	0.385320	−	1.18589i
$399$		0			0
$400$	14.0580	+	10.2137i	0.702899	+	0.510686i
$401$	−5.42428	−	16.6942i	−0.270876	−	0.833670i	−0.990281	−	0.139079i	$-0.955586\pi$
$401$	−5.42428	−	16.6942i	−0.270876	−	0.833670i	0.719405	−	0.694590i	$-0.244414\pi$
$402$		0			0
$403$	4.94049	+	3.58948i	0.246103	+	0.178805i
$404$	42.6100	−	30.9580i	2.11993	−	1.54022i
$405$		0			0
$406$	−110.829			−5.50035
$407$	−3.89996	−	9.99919i	−0.193314	−	0.495641i
$408$		0			0
$409$	8.74225	−	26.9059i	0.432276	−	1.33041i	−0.463576	−	0.886057i	$-0.653434\pi$
$409$	8.74225	−	26.9059i	0.432276	−	1.33041i	0.895852	−	0.444352i	$-0.146566\pi$
$410$	−23.4591	+	17.0440i	−1.15856	+	0.841743i
$411$		0			0
$412$	−14.7848	−	45.5028i	−0.728393	−	2.24176i
$413$	−8.64439	−	26.6047i	−0.425363	−	1.30913i
$414$		0			0
$415$	−2.69055	+	1.95480i	−0.132074	+	0.0959573i
$416$	−0.593436	+	1.82641i	−0.0290956	+	0.0895470i
$417$		0			0
$418$	−7.92110	+	30.2089i	−0.387434	+	1.47756i
$419$	32.2357			1.57482			0.787409	−	0.616430i	$-0.211422\pi$
$419$	32.2357			1.57482			0.787409	+	0.616430i	$0.211422\pi$
$420$		0			0
$421$	23.0100	−	16.7177i	1.12144	−	0.814772i	0.137011	−	0.990570i	$-0.456250\pi$
$421$	23.0100	−	16.7177i	1.12144	−	0.814772i	0.984426	+	0.175798i	$0.0562504\pi$
$422$	29.3421	+	21.3183i	1.42835	+	1.03776i
$423$		0			0
$424$	−14.8023	−	45.5568i	−0.718863	−	2.21243i
$425$	−8.59088	−	6.24164i	−0.416719	−	0.302764i
$426$		0			0
$427$	−6.42519	+	19.7747i	−0.310937	+	0.956965i
$428$	19.1632			0.926286
$429$		0			0
$430$	−5.17007			−0.249323
$431$	8.27921	−	25.4808i	0.398796	−	1.22737i	−0.527170	−	0.849760i	$-0.676747\pi$
$431$	8.27921	−	25.4808i	0.398796	−	1.22737i	0.925966	−	0.377607i	$-0.123253\pi$
$432$		0			0
$433$	7.60672	+	5.52661i	0.365556	+	0.265592i	0.755366	−	0.655304i	$-0.227459\pi$
$433$	7.60672	+	5.52661i	0.365556	+	0.265592i	−0.389810	+	0.920895i	$0.627459\pi$
$434$	5.54651	+	17.0704i	0.266241	+	0.819405i
$435$		0			0
$436$	−53.0771	−	38.5628i	−2.54193	−	1.84682i
$437$	−10.6825	+	7.76132i	−0.511015	+	0.371274i
$438$		0			0
$439$	−17.8962			−0.854139			−0.427069	−	0.904219i	$-0.640454\pi$
$439$	−17.8962			−0.854139			−0.427069	+	0.904219i	$0.640454\pi$
$440$	−6.02578	−	15.4496i	−0.287268	−	0.736531i
$441$		0			0
$442$	7.26552	−	22.3610i	0.345586	−	1.06360i
$443$	−14.8708	+	10.8042i	−0.706531	+	0.513325i	−0.882053	−	0.471151i	$-0.843839\pi$
$443$	−14.8708	+	10.8042i	−0.706531	+	0.513325i	0.175522	+	0.984476i	$0.443839\pi$
$444$		0			0
$445$	−4.05586	−	12.4826i	−0.192266	−	0.591734i
$446$	−0.466803	−	1.43667i	−0.0221038	−	0.0680285i
$447$		0			0
$448$	25.6606	−	18.6435i	1.21235	−	0.880824i
$449$	−1.85302	+	5.70301i	−0.0874494	+	0.269142i	−0.985212	−	0.171337i	$-0.945191\pi$
$449$	−1.85302	+	5.70301i	−0.0874494	+	0.269142i	0.897763	+	0.440479i	$0.145191\pi$
$450$		0			0
$451$	−39.4268	+	2.27830i	−1.85654	+	0.107281i
$452$	−3.44396			−0.161990
$453$		0			0
$454$	−23.1098	+	16.7903i	−1.08460	+	0.788006i
$455$	12.5220	+	9.09777i	0.587041	+	0.426510i
$456$		0			0
$457$	7.89068	+	24.2850i	0.369110	+	1.13600i	0.947367	+	0.320150i	$0.103733\pi$
$457$	7.89068	+	24.2850i	0.369110	+	1.13600i	−0.578257	+	0.815855i	$0.696267\pi$
$458$	1.61911	+	1.17635i	0.0756562	+	0.0549674i
$459$		0			0
$460$	4.27717	−	13.1638i	0.199424	−	0.613764i
$461$	31.5683			1.47028			0.735142	−	0.677913i	$-0.237115\pi$
$461$	31.5683			1.47028			0.735142	+	0.677913i	$0.237115\pi$
$462$		0			0
$463$	3.76414			0.174934			0.0874671	−	0.996167i	$-0.472123\pi$
$463$	3.76414			0.174934			0.0874671	+	0.996167i	$0.472123\pi$
$464$	13.9201	−	42.8417i	0.646225	−	1.98888i
$465$		0			0
$466$	34.3380	+	24.9480i	1.59068	+	1.15569i
$467$	−1.80825	−	5.56521i	−0.0836756	−	0.257527i	0.900462	−	0.434935i	$-0.143229\pi$
$467$	−1.80825	−	5.56521i	−0.0836756	−	0.257527i	−0.984137	+	0.177408i	$0.943229\pi$
$468$		0			0
$469$	−2.98656	−	2.16986i	−0.137907	−	0.100195i
$470$	8.47108	−	6.15460i	0.390742	−	0.283890i
$471$		0			0
$472$	32.6948			1.50490
$473$	−5.92590	−	3.80331i	−0.272473	−	0.174876i
$474$		0			0
$475$	4.75475	−	14.6336i	0.218163	−	0.671436i
$476$	37.4352	−	27.1983i	1.71584	−	1.24663i
$477$		0			0
$478$	−0.151868	−	0.467402i	−0.00694629	−	0.0213785i
$479$	−7.93853	−	24.4323i	−0.362721	−	1.11634i	−0.951396	−	0.307970i	$-0.900350\pi$
$479$	−7.93853	−	24.4323i	−0.362721	−	1.11634i	0.588675	−	0.808370i	$-0.299650\pi$
$480$		0			0
$481$	−9.47214	+	6.88191i	−0.431892	+	0.313788i
$482$	−11.2757	+	34.7031i	−0.513595	+	1.58068i
$483$		0			0
$484$	8.80169	−	43.7081i	0.400077	−	1.98673i
$485$	0.367573			0.0166906
$486$		0			0
$487$	4.29919	−	3.12355i	0.194815	−	0.141541i	−0.486102	−	0.873902i	$-0.661582\pi$
$487$	4.29919	−	3.12355i	0.194815	−	0.141541i	0.680917	+	0.732361i	$0.261582\pi$
$488$	−19.6602	−	14.2840i	−0.889975	−	0.646605i
$489$		0			0
$490$	8.79038	+	27.0540i	0.397109	+	1.22218i
$491$	−1.99393	−	1.44868i	−0.0899850	−	0.0653779i	0.541883	−	0.840454i	$-0.317712\pi$
$491$	−1.99393	−	1.44868i	−0.0899850	−	0.0653779i	−0.631868	+	0.775076i	$0.717712\pi$
$492$		0			0
$493$	−8.50662	+	26.1807i	−0.383119	+	1.17912i
$494$	34.0682			1.53280
$495$		0			0
$496$	−7.29531			−0.327569
$497$	5.04622	−	15.5307i	0.226354	−	0.696646i
$498$		0			0
$499$	−18.0431	−	13.1091i	−0.807722	−	0.586844i	0.105448	−	0.994425i	$-0.466372\pi$
$499$	−18.0431	−	13.1091i	−0.807722	−	0.586844i	−0.913169	+	0.407581i	$0.866372\pi$
$500$	11.1827	+	34.4167i	0.500104	+	1.53916i
$501$		0			0
$502$	−16.9715	−	12.3305i	−0.757477	−	0.550339i
$503$	−21.0129	+	15.2667i	−0.936917	+	0.680710i	−0.947677	−	0.319232i	$-0.896575\pi$
$503$	−21.0129	+	15.2667i	−0.936917	+	0.680710i	0.0107594	+	0.999942i	$0.496575\pi$
$504$		0			0
$505$	12.8615			0.572331
$506$	21.7836	−	17.8342i	0.968400	−	0.792829i
$507$		0			0
$508$	14.5976	−	44.9269i	0.647665	−	1.99331i
$509$	22.5506	−	16.3840i	0.999538	−	0.726207i	0.0375492	−	0.999295i	$-0.488045\pi$
$509$	22.5506	−	16.3840i	0.999538	−	0.726207i	0.961989	+	0.273088i	$0.0880449\pi$
$510$		0			0
$511$	15.2373	+	46.8955i	0.674058	+	2.07454i
$512$	12.7852	+	39.3489i	0.565033	+	1.73899i
$513$		0			0
$514$	25.8731	−	18.7979i	1.14121	−	0.829139i
$515$	3.61038	−	11.1116i	0.159093	−	0.489637i
$516$		0			0
$517$	14.2371	−	0.822694i	0.626145	−	0.0361820i
$518$	−34.4124			−1.51199
$519$		0			0
$520$	−14.6353	+	10.6331i	−0.641798	+	0.466294i
$521$	−20.9287	−	15.2056i	−0.916902	−	0.666168i	0.0258491	−	0.999666i	$-0.491771\pi$
$521$	−20.9287	−	15.2056i	−0.916902	−	0.666168i	−0.942751	+	0.333498i	$0.891771\pi$
$522$		0			0
$523$	−8.42503	−	25.9296i	−0.368401	−	1.13382i	−0.947824	−	0.318794i	$-0.896722\pi$
$523$	−8.42503	−	25.9296i	−0.368401	−	1.13382i	0.579423	−	0.815027i	$-0.303278\pi$
$524$	−0.796178	−	0.578457i	−0.0347812	−	0.0252700i
$525$		0			0
$526$	−11.2924	+	34.7544i	−0.492372	+	1.51537i
$527$	4.45819			0.194202
$528$		0			0
$529$	−11.0967			−0.482466
$530$	7.13563	−	21.9612i	0.309952	−	0.953934i
$531$		0			0
$532$	54.2433	+	39.4100i	2.35174	+	1.70864i
$533$	13.3130	+	40.9731i	0.576648	+	1.77474i
$534$		0			0
$535$	3.78585	+	2.75058i	0.163677	+	0.118918i
$536$	3.49058	−	2.53605i	0.150770	−	0.109541i
$537$		0			0
$538$	−9.37812			−0.404320
$539$	−9.82654	+	37.4757i	−0.423259	+	1.61419i
$540$		0			0
$541$	−7.22580	+	22.2387i	−0.310661	+	0.956118i	0.666842	+	0.745199i	$0.267646\pi$
$541$	−7.22580	+	22.2387i	−0.310661	+	0.956118i	−0.977504	+	0.210919i	$0.932354\pi$
$542$	−27.5428	+	20.0110i	−1.18307	+	0.859547i
$543$		0			0
$544$	0.433231	+	1.33335i	0.0185746	+	0.0571668i
$545$	−4.95075	−	15.2368i	−0.212067	−	0.652675i
$546$		0			0
$547$	−12.3642	+	8.98309i	−0.528654	+	0.384089i	−0.819854	−	0.572573i	$-0.805945\pi$
$547$	−12.3642	+	8.98309i	−0.528654	+	0.384089i	0.291200	+	0.956662i	$0.405945\pi$
$548$	−0.569506	+	1.75276i	−0.0243281	+	0.0748741i
$549$		0			0
$550$	−8.32077	+	31.7331i	−0.354799	+	1.35310i
$551$	−39.8878			−1.69928
$552$		0			0
$553$	−21.4818	+	15.6074i	−0.913498	+	0.663695i
$554$	4.89257	+	3.55466i	0.207866	+	0.151023i
$555$		0			0
$556$	−22.3461	−	68.7743i	−0.947687	−	2.91668i
$557$	−5.85761	−	4.25580i	−0.248195	−	0.180324i	0.456732	−	0.889605i	$-0.349020\pi$
$557$	−5.85761	−	4.25580i	−0.248195	−	0.180324i	−0.704926	+	0.709280i	$0.749020\pi$
$558$		0			0
$559$	−2.37366	+	7.30537i	−0.100395	+	0.308984i
$560$	−18.4904			−0.781364
$561$		0			0
$562$	49.0113			2.06742
$563$	−9.74643	+	29.9964i	−0.410763	+	1.26420i	0.505223	+	0.862989i	$0.331410\pi$
$563$	−9.74643	+	29.9964i	−0.410763	+	1.26420i	−0.915986	+	0.401210i	$0.868590\pi$
$564$		0			0
$565$	−0.680384	−	0.494328i	−0.0286240	−	0.0207965i
$566$	−5.46532	−	16.8205i	−0.229725	−	0.707019i
$567$		0			0
$568$	15.4407	+	11.2183i	0.647879	+	0.470711i
$569$	9.04664	−	6.57277i	0.379255	−	0.275545i	−0.381783	−	0.924252i	$-0.624690\pi$
$569$	9.04664	−	6.57277i	0.379255	−	0.275545i	0.761038	+	0.648707i	$0.224690\pi$
$570$		0			0
$571$	11.5906			0.485052			0.242526	−	0.970145i	$-0.422024\pi$
$571$	11.5906			0.485052			0.242526	+	0.970145i	$0.422024\pi$
$572$	−48.5563	+	2.80585i	−2.03024	+	0.117318i
$573$		0			0
$574$	−39.1290	+	120.427i	−1.63321	+	5.02652i
$575$	−11.2215	+	8.15293i	−0.467971	+	0.340001i
$576$		0			0
$577$	5.23344	+	16.1069i	0.217871	+	0.670537i	0.998937	+	0.0460895i	$0.0146760\pi$
$577$	5.23344	+	16.1069i	0.217871	+	0.670537i	−0.781067	+	0.624448i	$0.785324\pi$
$578$	7.62072	+	23.4541i	0.316980	+	0.975564i
$579$		0			0
$580$	33.8263	−	24.5763i	1.40456	−	1.02047i
$581$	−4.48776	+	13.8119i	−0.186184	+	0.573015i
$582$		0			0
$583$	24.3343	−	19.9225i	1.00783	−	0.825107i
$584$	−57.6304			−2.38476
$585$		0			0
$586$	33.9606	−	24.6738i	1.40290	−	1.01927i
$587$	7.31900	+	5.31756i	0.302087	+	0.219479i	0.728494	−	0.685052i	$-0.240221\pi$
$587$	7.31900	+	5.31756i	0.302087	+	0.219479i	−0.426406	+	0.904532i	$0.640221\pi$
$588$		0			0
$589$	1.99621	+	6.14370i	0.0822523	+	0.253147i
$590$	12.7508	+	9.26403i	0.524944	+	0.381394i
$591$		0			0
$592$	4.32219	−	13.3023i	0.177641	−	0.546722i
$593$	20.4127			0.838248			0.419124	−	0.907929i	$-0.362337\pi$
$593$	20.4127			0.838248			0.419124	+	0.907929i	$0.362337\pi$
$594$		0			0
$595$	11.2996			0.463237
$596$	−19.9631	+	61.4401i	−0.817720	+	2.51668i
$597$		0			0
$598$	−24.8460	−	18.0517i	−1.01603	−	0.738189i
$599$	−12.9855	−	39.9652i	−0.530573	−	1.63293i	−0.753026	−	0.657991i	$-0.771406\pi$
$599$	−12.9855	−	39.9652i	−0.530573	−	1.63293i	0.222453	−	0.974943i	$-0.428594\pi$
$600$		0			0
$601$	8.65252	+	6.28642i	0.352944	+	0.256429i	0.750103	−	0.661321i	$-0.230004\pi$
$601$	8.65252	+	6.28642i	0.352944	+	0.256429i	−0.397159	+	0.917750i	$0.630004\pi$
$602$	−18.2649	+	13.2703i	−0.744423	+	0.540855i
$603$		0			0
$604$	24.5364			0.998373
$605$	8.01249	−	7.37157i	0.325754	−	0.299697i
$606$		0			0
$607$	−14.0910	+	43.3676i	−0.571936	+	1.76024i	0.0744490	+	0.997225i	$0.476280\pi$
$607$	−14.0910	+	43.3676i	−0.571936	+	1.76024i	−0.646385	+	0.763012i	$0.723720\pi$
$608$	−1.64346	+	1.19405i	−0.0666513	+	0.0484250i
$609$		0			0
$610$	−3.62006	−	11.1414i	−0.146572	−	0.451102i
$611$	−4.80732	−	14.7954i	−0.194483	−	0.598558i
$612$		0			0
$613$	−21.9790	+	15.9687i	−0.887725	+	0.644970i	−0.935284	−	0.353899i	$-0.884856\pi$
$613$	−21.9790	+	15.9687i	−0.887725	+	0.644970i	0.0475592	+	0.998868i	$0.484856\pi$
$614$	−5.69332	+	17.5222i	−0.229764	+	0.707140i
$615$		0			0
$616$	−60.9432	−	39.1140i	−2.45547	−	1.57595i
$617$	7.83117			0.315271			0.157636	−	0.987497i	$-0.449613\pi$
$617$	7.83117			0.315271			0.157636	+	0.987497i	$0.449613\pi$
$618$		0			0
$619$	−30.6835	+	22.2929i	−1.23327	+	0.896027i	−0.997131	−	0.0756915i	$-0.975884\pi$
$619$	−30.6835	+	22.2929i	−1.23327	+	0.896027i	−0.236144	+	0.971718i	$0.575884\pi$
$620$	−5.47820	−	3.98015i	−0.220010	−	0.159847i
$621$		0			0
$622$	7.99883	+	24.6179i	0.320724	+	0.987087i
$623$	−46.3684	−	33.6886i	−1.85771	−	1.34971i
$624$		0			0
$625$	3.48099	−	10.7134i	0.139239	−	0.428535i
$626$	25.6727			1.02609
$627$		0			0
$628$	30.3257			1.21013
$629$	−2.64130	+	8.12910i	−0.105316	+	0.324128i
$630$		0			0
$631$	22.3432	+	16.2333i	0.889468	+	0.646237i	0.935739	−	0.352692i	$-0.114734\pi$
$631$	22.3432	+	16.2333i	0.889468	+	0.646237i	−0.0462710	+	0.998929i	$0.514734\pi$
$632$	−9.59006	−	29.5152i	−0.381472	−	1.17405i
$633$		0			0
$634$	−25.4540	−	18.4934i	−1.01091	−	0.734467i
$635$	9.33247	−	6.78044i	0.370348	−	0.269073i
$636$		0			0
$637$	42.2634			1.67454
$638$	84.9029	−	4.90614i	3.36134	−	0.194236i
$639$		0			0
$640$	−5.84701	+	17.9952i	−0.231123	+	0.711324i
$641$	−3.61805	+	2.62867i	−0.142904	+	0.103826i	−0.656940	−	0.753942i	$-0.728150\pi$
$641$	−3.61805	+	2.62867i	−0.142904	+	0.103826i	0.514036	+	0.857769i	$0.328150\pi$
$642$		0			0
$643$	−2.30885	−	7.10591i	−0.0910522	−	0.280230i	0.895153	−	0.445760i	$-0.147067\pi$
$643$	−2.30885	−	7.10591i	−0.0910522	−	0.280230i	−0.986205	+	0.165530i	$0.947067\pi$
$644$	−18.6776	−	57.4836i	−0.735999	−	2.26517i
$645$		0			0
$646$	20.1212	−	14.6189i	0.791657	−	0.575172i
$647$	3.55862	−	10.9523i	0.139904	−	0.430579i	−0.856417	−	0.516285i	$-0.827314\pi$
$647$	3.55862	−	10.9523i	0.139904	−	0.430579i	0.996320	+	0.0857057i	$0.0273145\pi$
$648$		0			0
$649$	7.79994	+	19.9984i	0.306174	+	0.785006i
$650$	35.7872			1.40369
$651$		0			0
$652$	−45.8312	+	33.2983i	−1.79489	+	1.30406i
$653$	17.1013	+	12.4248i	0.669226	+	0.486221i	0.869766	−	0.493464i	$-0.164270\pi$
$653$	17.1013	+	12.4248i	0.669226	+	0.486221i	−0.200540	+	0.979686i	$0.564270\pi$
$654$		0			0
$655$	−0.0742632	−	0.228559i	−0.00290170	−	0.00893053i
$656$	−41.6372	−	30.2512i	−1.62566	−	1.18111i
$657$		0			0
$658$	14.1295	−	43.4862i	0.550826	−	1.69527i
$659$	−27.0354			−1.05315			−0.526575	−	0.850129i	$-0.676524\pi$
$659$	−27.0354			−1.05315			−0.526575	+	0.850129i	$0.676524\pi$
$660$		0			0
$661$	−26.7618			−1.04091			−0.520456	−	0.853888i	$-0.674238\pi$
$661$	−26.7618			−1.04091			−0.520456	+	0.853888i	$0.674238\pi$
$662$	−12.4572	+	38.3393i	−0.484163	+	1.49010i
$663$		0			0
$664$	−13.7319	−	9.97683i	−0.532902	−	0.387176i
$665$	5.05952	+	15.5716i	0.196200	+	0.603841i
$666$		0			0
$667$	29.0902	+	21.1353i	1.12638	+	0.818362i
$668$	20.9576	−	15.2266i	0.810874	−	0.589134i
$669$		0			0
$670$	2.07990			0.0803536
$671$	4.04677	−	15.4332i	0.156224	−	0.595794i
$672$		0			0
$673$	15.1845	−	46.7332i	0.585321	−	1.80143i	−0.0126574	−	0.999920i	$-0.504029\pi$
$673$	15.1845	−	46.7332i	0.585321	−	1.80143i	0.597978	−	0.801512i	$-0.295971\pi$
$674$	57.8571	−	42.0356i	2.22857	−	1.61915i
$675$		0			0
$676$	0.112939	+	0.347591i	0.00434382	+	0.0133689i
$677$	14.1181	+	43.4511i	0.542603	+	1.66996i	0.726622	+	0.687038i	$0.241089\pi$
$677$	14.1181	+	43.4511i	0.542603	+	1.66996i	−0.184019	+	0.982923i	$0.558911\pi$
$678$		0			0
$679$	1.29857	−	0.943466i	0.0498345	−	0.0362069i
$680$	−4.08104	+	12.5601i	−0.156501	+	0.481660i
$681$		0			0
$682$	−5.00468	−	12.8316i	−0.191639	−	0.491347i
$683$	−47.1991			−1.80602			−0.903012	−	0.429615i	$-0.858649\pi$
$683$	−47.1991			−1.80602			−0.903012	+	0.429615i	$0.858649\pi$
$684$		0			0
$685$	−0.364093	+	0.264529i	−0.0139113	+	0.0101071i
$686$	40.2739	+	29.2607i	1.53766	+	1.11718i
$687$		0			0
$688$	−2.83563	−	8.72717i	−0.108107	−	0.332720i
$689$	−27.7554	−	20.1655i	−1.05740	−	0.768243i
$690$		0			0
$691$	9.20361	−	28.3258i	0.350122	−	1.07756i	−0.608662	−	0.793429i	$-0.708294\pi$
$691$	9.20361	−	28.3258i	0.350122	−	1.07756i	0.958784	−	0.284135i	$-0.0917065\pi$
$692$	−31.8002			−1.20886
$693$		0			0
$694$	−53.1004			−2.01566
$695$	5.45684	−	16.7944i	0.206990	−	0.637049i
$696$		0			0
$697$	25.4446	+	18.4866i	0.963783	+	0.700229i
$698$	−18.3991	−	56.6267i	−0.696417	−	2.14335i
$699$		0			0
$700$	56.9802	+	41.3985i	2.15365	+	1.56472i
$701$	−0.479434	+	0.348329i	−0.0181080	+	0.0131562i	−0.596802	−	0.802388i	$-0.703562\pi$
$701$	−0.479434	+	0.348329i	−0.0181080	+	0.0131562i	0.578694	+	0.815544i	$0.303562\pi$
$702$		0			0
$703$	−12.3851			−0.467115
$704$	−18.8325	+	15.4182i	−0.709778	+	0.581095i
$705$		0			0
$706$	−15.9508	+	49.0915i	−0.600316	+	1.84758i
$707$	45.4375	−	33.0123i	1.70885	−	1.24155i
$708$		0			0
$709$	−10.4557	−	32.1793i	−0.392672	−	1.20852i	−0.930760	−	0.365631i	$-0.880853\pi$
$709$	−10.4557	−	32.1793i	−0.392672	−	1.20852i	0.538088	−	0.842888i	$-0.319147\pi$
$710$	2.84312	+	8.75023i	0.106700	+	0.328390i
$711$		0			0
$712$	54.1937	−	39.3740i	2.03099	−	1.47560i
$713$	1.79952	−	5.53834i	0.0673924	−	0.207412i
$714$		0			0
$715$	−9.99547	−	6.41521i	−0.373810	−	0.239915i
$716$	19.7593			0.738439
$717$		0			0
$718$	−31.2171	+	22.6806i	−1.16501	+	0.846431i
$719$	−39.3929	−	28.6206i	−1.46911	−	1.06737i	−0.980871	−	0.194657i	$-0.937641\pi$
$719$	−39.3929	−	28.6206i	−1.46911	−	1.06737i	−0.488236	−	0.872712i	$-0.662359\pi$
$720$		0			0
$721$	−15.7659	−	48.5223i	−0.587151	−	1.80707i
$722$	−8.66319	−	6.29417i	−0.322410	−	0.234245i
$723$		0			0
$724$	11.3311	−	34.8736i	0.421117	−	1.29607i
$725$	−41.9004			−1.55614
$726$		0			0
$727$	−38.4706			−1.42680			−0.713399	−	0.700758i	$-0.752845\pi$
$727$	−38.4706			−1.42680			−0.713399	+	0.700758i	$0.752845\pi$
$728$	−24.4112	+	75.1299i	−0.904739	+	2.78450i
$729$		0			0
$730$	−22.4756	−	16.3295i	−0.831861	−	0.604382i
$731$	1.73286	+	5.33320i	0.0640922	+	0.197256i
$732$		0			0
$733$	−7.72793	−	5.61467i	−0.285437	−	0.207382i	0.435848	−	0.900020i	$-0.356448\pi$
$733$	−7.72793	−	5.61467i	−0.285437	−	0.207382i	−0.721286	+	0.692638i	$0.756448\pi$
$734$	−16.3108	+	11.8505i	−0.602043	+	0.437410i
$735$		0			0
$736$	1.83127			0.0675015
$737$	2.38397	+	1.53006i	0.0878146	+	0.0563605i
$738$		0			0
$739$	5.87978	−	18.0961i	0.216291	−	0.665675i	−0.782768	−	0.622313i	$-0.786193\pi$
$739$	5.87978	−	18.0961i	0.216291	−	0.665675i	0.999059	−	0.0433623i	$-0.0138070\pi$
$740$	10.5031	−	7.63092i	0.386100	−	0.280518i
$741$		0			0
$742$	−31.1599	−	95.9004i	−1.14392	−	3.52061i
$743$	3.92913	+	12.0926i	0.144146	+	0.443635i	0.996900	−	0.0786769i	$-0.0250695\pi$
$743$	3.92913	+	12.0926i	0.144146	+	0.443635i	−0.852754	+	0.522312i	$0.825070\pi$
$744$		0			0
$745$	−12.7627	+	9.27263i	−0.467588	+	0.339723i
$746$	−23.4298	+	72.1095i	−0.857826	+	2.64012i
$747$		0			0
$748$	−27.4740	+	22.4930i	−1.00455	+	0.822425i
$749$	20.4348			0.746671
$750$		0			0
$751$	30.8657	−	22.4252i	1.12630	−	0.818308i	0.141151	−	0.989988i	$-0.454920\pi$
$751$	30.8657	−	22.4252i	1.12630	−	0.818308i	0.985153	+	0.171680i	$0.0549196\pi$
$752$	15.0352	+	10.9237i	0.548277	+	0.398347i
$753$		0			0
$754$	−28.6685	−	88.2325i	−1.04404	−	3.21324i
$755$	4.84739	+	3.52184i	0.176415	+	0.128173i
$756$		0			0
$757$	2.01311	−	6.19571i	0.0731677	−	0.225187i	−0.907784	−	0.419437i	$-0.862227\pi$
$757$	2.01311	−	6.19571i	0.0731677	−	0.225187i	0.980952	+	0.194250i	$0.0622274\pi$
$758$	−48.7563			−1.77091
$759$		0			0
$760$	−19.1361			−0.694140
$761$	−13.8835	+	42.7291i	−0.503278	+	1.54893i	0.300369	+	0.953823i	$0.402890\pi$
$761$	−13.8835	+	42.7291i	−0.503278	+	1.54893i	−0.803646	+	0.595107i	$0.797110\pi$
$762$		0			0
$763$	−56.5992	−	41.1217i	−2.04903	−	1.48871i
$764$	23.5068	+	72.3464i	0.850445	+	2.61740i
$765$		0			0
$766$	47.1252	+	34.2385i	1.70270	+	1.23709i
$767$	18.9443	−	13.7638i	0.684039	−	0.496983i
$768$		0			0
$769$	−0.0822779			−0.00296702			−0.00148351	−	0.999999i	$-0.500472\pi$
$769$	−0.0822779			−0.00296702			−0.00148351	+	0.999999i	$0.500472\pi$
$770$	−12.6847	−	32.5225i	−0.457125	−	1.17203i
$771$		0			0
$772$	−21.6717	+	66.6986i	−0.779982	+	2.40054i
$773$	−15.3850	+	11.1779i	−0.553361	+	0.402040i	−0.829023	−	0.559215i	$-0.811103\pi$
$773$	−15.3850	+	11.1779i	−0.553361	+	0.402040i	0.275662	+	0.961255i	$0.411103\pi$
$774$		0			0
$775$	2.09693	+	6.45369i	0.0753240	+	0.231823i
$776$	0.579717	+	1.78419i	0.0208106	+	0.0640486i
$777$		0			0
$778$	−16.9517	+	12.3161i	−0.607748	+	0.441555i
$779$	−14.0827	+	43.3421i	−0.504565	+	1.55289i
$780$		0			0
$781$	−3.17825	+	12.1210i	−0.113727	+	0.433722i
$782$	−22.4205			−0.801755
$783$		0			0
$784$	−40.8464	+	29.6766i	−1.45880	+	1.05988i
$785$	5.99111	+	4.35280i	0.213832	+	0.155358i
$786$		0			0
$787$	2.66677	+	8.20747i	0.0950601	+	0.292565i	0.987269	−	0.159057i	$-0.0508455\pi$
$787$	2.66677	+	8.20747i	0.0950601	+	0.292565i	−0.892209	+	0.451622i	$0.850845\pi$
$788$	−19.8978	−	14.4566i	−0.708829	−	0.514994i
$789$		0			0
$790$	4.62300	−	14.2281i	0.164479	−	0.506214i
$791$	−3.67249			−0.130579
$792$		0			0
$793$	−17.4049			−0.618068
$794$	2.87671	−	8.85359i	0.102091	−	0.314202i
$795$		0			0
$796$	33.1547	+	24.0883i	1.17514	+	0.853788i
$797$	5.12156	+	15.7626i	0.181415	+	0.558338i	0.999868	−	0.0162351i	$-0.00516802\pi$
$797$	5.12156	+	15.7626i	0.181415	+	0.558338i	−0.818453	+	0.574573i	$0.805168\pi$
$798$		0			0
$799$	−9.18806	−	6.67552i	−0.325050	−	0.236163i
$800$	−1.72639	+	1.25429i	−0.0610370	+	0.0443460i
$801$		0			0
$802$	43.1870			1.52499
$803$	−13.7488	−	35.2508i	−0.485184	−	1.24397i
$804$		0			0
$805$	4.56099	−	14.0373i	0.160754	−	0.494749i
$806$	−12.1552	+	8.83130i	−0.428150	+	0.311069i
$807$		0			0
$808$	20.2846	+	62.4295i	0.713608	+	2.19626i
$809$	6.99703	+	21.5347i	0.246003	+	0.757118i	0.995470	+	0.0950768i	$0.0303097\pi$
$809$	6.99703	+	21.5347i	0.246003	+	0.757118i	−0.749467	+	0.662041i	$0.769690\pi$
$810$		0			0
$811$	45.7773	−	33.2592i	1.60746	−	1.16789i	0.736635	−	0.676290i	$-0.236413\pi$
$811$	45.7773	−	33.2592i	1.60746	−	1.16789i	0.870823	−	0.491597i	$-0.163587\pi$
$812$	56.4213	−	173.647i	1.98000	−	6.09382i
$813$		0			0
$814$	26.3623	−	1.52336i	0.923999	−	0.0533936i
$815$	−13.8338			−0.484578
$816$		0			0
$817$	−6.57362	+	4.77601i	−0.229982	+	0.167092i
$818$	56.3108	+	40.9122i	1.96886	+	1.43046i
$819$		0			0
$820$	−14.7619	−	45.4325i	−0.515508	−	1.58657i
$821$	38.3065	+	27.8313i	1.33690	+	0.971318i	0.999552	+	0.0299397i	$0.00953152\pi$
$821$	38.3065	+	27.8313i	1.33690	+	0.971318i	0.337353	+	0.941378i	$0.390468\pi$
$822$		0			0
$823$	−2.15721	+	6.63922i	−0.0751957	+	0.231429i	−0.981589	−	0.191007i	$-0.938825\pi$
$823$	−2.15721	+	6.63922i	−0.0751957	+	0.231429i	0.906393	+	0.422435i	$0.138825\pi$
$824$	59.6296			2.07729
$825$		0			0
$826$	68.8249			2.39472
$827$	12.3062	−	37.8747i	0.427929	−	1.31703i	−0.472232	−	0.881474i	$-0.656551\pi$
$827$	12.3062	−	37.8747i	0.427929	−	1.31703i	0.900161	−	0.435557i	$-0.143449\pi$
$828$		0			0
$829$	26.7634	+	19.4447i	0.929530	+	0.675343i	0.945878	−	0.324524i	$-0.105204\pi$
$829$	26.7634	+	19.4447i	0.929530	+	0.675343i	−0.0163480	+	0.999866i	$0.505204\pi$
$830$	−2.52848	−	7.78186i	−0.0877648	−	0.270112i
$831$		0			0
$832$	21.4801	+	15.6062i	0.744688	+	0.541047i
$833$	24.9614	−	18.1355i	0.864860	−	0.628357i
$834$		0			0
$835$	6.32591			0.218917
$836$	−43.2987	−	27.7896i	−1.49752	−	0.961125i
$837$		0			0
$838$	−24.5083	+	75.4288i	−0.846626	+	2.60565i
$839$	27.6635	−	20.0987i	0.955052	−	0.693886i	0.00305543	−	0.999995i	$-0.499027\pi$
$839$	27.6635	−	20.0987i	0.955052	−	0.693886i	0.951996	+	0.306110i	$0.0990274\pi$
$840$		0			0
$841$	24.6042	+	75.7238i	0.848419	+	2.61117i
$842$	21.6239	+	66.5515i	0.745209	+	2.29352i
$843$		0			0
$844$	−48.3390	+	35.1204i	−1.66390	+	1.20889i
$845$	−0.0275793	+	0.0848805i	−0.000948758	+	0.00291998i
$846$		0			0
$847$	9.38576	−	46.6085i	0.322498	−	1.60149i
$848$	40.9846			1.40742
$849$		0			0
$850$	21.1364	−	15.3565i	0.724973	−	0.526724i
$851$	9.03251	+	6.56250i	0.309631	+	0.224960i
$852$		0			0
$853$	−2.36127	−	7.26723i	−0.0808482	−	0.248825i	0.902460	−	0.430774i	$-0.141759\pi$
$853$	−2.36127	−	7.26723i	−0.0808482	−	0.248825i	−0.983308	+	0.181949i	$0.941759\pi$
$854$	−41.3861	−	30.0688i	−1.41620	−	1.02893i
$855$		0			0
$856$	−7.38038	+	22.7145i	−0.252256	+	0.776365i
$857$	−27.6052			−0.942976			−0.471488	−	0.881873i	$-0.656283\pi$
$857$	−27.6052			−0.942976			−0.471488	+	0.881873i	$0.656283\pi$
$858$		0			0
$859$	−17.0244			−0.580864			−0.290432	−	0.956896i	$-0.593799\pi$
$859$	−17.0244			−0.580864			−0.290432	+	0.956896i	$0.593799\pi$
$860$	2.63200	−	8.10047i	0.0897506	−	0.276224i
$861$		0			0
$862$	53.3283	+	38.7453i	1.81637	+	1.31967i
$863$	−3.17117	−	9.75984i	−0.107948	−	0.332229i	0.882463	−	0.470381i	$-0.155884\pi$
$863$	−3.17117	−	9.75984i	−0.107948	−	0.332229i	−0.990411	+	0.138152i	$0.955884\pi$
$864$		0			0
$865$	−6.28240	−	4.56443i	−0.213608	−	0.155195i
$866$	−18.7150	+	13.5973i	−0.635963	+	0.462054i
$867$		0			0
$868$	−29.5695			−1.00366
$869$	15.7656	−	12.9073i	0.534813	−	0.437851i
$870$		0			0
$871$	0.954915	−	2.93893i	0.0323561	−	0.0995817i
$872$	66.1511	−	48.0616i	2.24016	−	1.62757i
$873$		0			0
$874$	−10.0391	−	30.8970i	−0.339576	−	1.04511i
$875$	11.9247	+	36.7005i	0.403129	+	1.24070i
$876$		0			0
$877$	18.0108	−	13.0856i	0.608181	−	0.441869i	−0.240592	−	0.970626i	$-0.577342\pi$
$877$	18.0108	−	13.0856i	0.608181	−	0.441869i	0.848773	+	0.528757i	$0.177342\pi$
$878$	13.6062	−	41.8755i	0.459187	−	1.41323i
$879$		0			0
$880$	14.1650	−	0.818529i	0.477501	−	0.0275926i
$881$	3.58540			0.120795			0.0603976	−	0.998174i	$-0.480763\pi$
$881$	3.58540			0.120795			0.0603976	+	0.998174i	$0.480763\pi$
$882$		0			0
$883$	−36.3972	+	26.4441i	−1.22486	+	0.889916i	−0.996495	−	0.0836583i	$-0.973340\pi$
$883$	−36.3972	+	26.4441i	−1.22486	+	0.889916i	−0.228370	+	0.973574i	$0.573340\pi$
$884$	31.3364	+	22.7673i	1.05396	+	0.765745i
$885$		0			0
$886$	−13.9750	−	43.0106i	−0.469499	−	1.44497i
$887$	11.9764	+	8.70139i	0.402129	+	0.292164i	0.770408	−	0.637551i	$-0.220053\pi$
$887$	11.9764	+	8.70139i	0.402129	+	0.292164i	−0.368278	+	0.929716i	$0.620053\pi$
$888$		0			0
$889$	15.5663	−	47.9081i	0.522077	−	1.60679i
$890$	32.2919			1.08243
$891$		0			0
$892$	2.48862			0.0833253
$893$	5.08527	−	15.6508i	0.170172	−	0.523735i
$894$		0			0
$895$	3.90362	+	2.83615i	0.130484	+	0.0948019i
$896$	25.5328	+	78.5817i	0.852989	+	2.62523i
$897$		0			0
$898$	−11.9357	−	8.67181i	−0.398300	−	0.289382i
$899$	14.2316	−	10.3399i	0.474651	−	0.344854i
$900$		0			0
$901$	−25.0458			−0.834397
$902$	24.6446	−	93.9876i	0.820575	−	3.12944i
$903$		0			0
$904$	1.32638	−	4.08219i	0.0441149	−	0.135772i
$905$	7.24413	−	5.26317i	0.240803	−	0.174954i
$906$		0			0
$907$	7.40837	+	22.8006i	0.245991	+	0.757083i	0.995472	+	0.0950565i	$0.0303032\pi$
$907$	7.40837	+	22.8006i	0.245991	+	0.757083i	−0.749481	+	0.662026i	$0.769697\pi$
$908$	−14.5421	−	44.7561i	−0.482598	−	1.48528i
$909$		0			0
$910$	−30.8083	+	22.3835i	−1.02128	+	0.742006i
$911$	6.93704	−	21.3500i	0.229835	−	0.707358i	−0.767930	−	0.640534i	$-0.778713\pi$
$911$	6.93704	−	21.3500i	0.229835	−	0.707358i	0.997765	−	0.0668244i	$-0.0212867\pi$
$912$		0			0
$913$	2.82652	−	10.7796i	0.0935442	−	0.356751i
$914$	−62.8240			−2.07803
$915$		0			0
$916$	−2.66738	+	1.93796i	−0.0881326	+	0.0640321i
$917$	−0.849011	−	0.616842i	−0.0280368	−	0.0203699i
$918$		0			0
$919$	5.84951	+	18.0029i	0.192958	+	0.593862i	0.999994	+	0.00336124i	$0.00106992\pi$
$919$	5.84951	+	18.0029i	0.192958	+	0.593862i	−0.807037	+	0.590501i	$0.798930\pi$
$920$	13.9560	+	10.1396i	0.460116	+	0.334294i
$921$		0			0
$922$	−24.0009	+	73.8672i	−0.790428	+	2.43269i
$923$	13.6695			0.449937
$924$		0			0
$925$	−13.0101			−0.427768
$926$	−2.86181	+	8.80775i	−0.0940450	+	0.289441i
$927$		0			0
$928$	4.47541	+	3.25158i	0.146913	+	0.106738i
$929$	−6.82412	−	21.0025i	−0.223892	−	0.689069i	−0.998402	−	0.0565076i	$-0.982003\pi$
$929$	−6.82412	−	21.0025i	−0.223892	−	0.689069i	0.774510	−	0.632562i	$-0.217997\pi$
$930$		0			0
$931$	36.1687	+	26.2781i	1.18538	+	0.861231i
$932$	−56.5695	+	41.1001i	−1.85300	+	1.34628i
$933$		0			0
$934$	14.3969			0.471080
$935$	−8.65627	+	0.500206i	−0.283090	+	0.0163585i
$936$		0			0
$937$	3.73772	−	11.5035i	0.122106	−	0.375804i	−0.871257	−	0.490828i	$-0.836694\pi$
$937$	3.73772	−	11.5035i	0.122106	−	0.375804i	0.993363	+	0.115024i	$0.0366945\pi$
$938$	7.34792	−	5.33858i	0.239918	−	0.174311i
$939$		0			0
$940$	5.33054	+	16.4057i	0.173863	+	0.535095i
$941$	6.37683	+	19.6259i	0.207879	+	0.639785i	0.999583	+	0.0288803i	$0.00919417\pi$
$941$	6.37683	+	19.6259i	0.207879	+	0.639785i	−0.791704	+	0.610905i	$0.790806\pi$
$942$		0			0
$943$	33.2361	−	24.1475i	1.08232	−	0.786350i
$944$	−8.64439	+	26.6047i	−0.281351	+	0.865909i
$945$		0			0
$946$	13.4048	−	10.9745i	0.435827	−	0.356812i
$947$	5.27445			0.171397			0.0856983	−	0.996321i	$-0.472688\pi$
$947$	5.27445			0.171397			0.0856983	+	0.996321i	$0.472688\pi$
$948$		0			0
$949$	−33.3927	+	24.2612i	−1.08397	+	0.787553i
$950$	30.6264	+	22.2514i	0.993653	+	0.721931i
$951$		0			0
$952$	17.8211	+	54.8477i	0.577586	+	1.77763i
$953$	43.2076	+	31.3922i	1.39963	+	1.01689i	0.994730	+	0.102532i	$0.0326945\pi$
$953$	43.2076	+	31.3922i	1.39963	+	1.01689i	0.404902	+	0.914360i	$0.367306\pi$
$954$		0			0
$955$	−5.74026	+	17.6667i	−0.185751	+	0.571681i
$956$	0.809640			0.0261856
$957$		0			0
$958$	63.2050			2.04206
$959$	−0.607297	+	1.86907i	−0.0196106	+	0.0603553i
$960$		0			0
$961$	22.7747	+	16.5468i	0.734668	+	0.533767i
$962$	−8.90156	−	27.3962i	−0.286998	−	0.883288i
$963$		0			0
$964$	−48.6326	−	35.3336i	−1.56635	−	1.13802i
$965$	−13.8550	+	10.0663i	−0.446009	+	0.324044i
$966$		0			0
$967$	44.5529			1.43273			0.716363	−	0.697728i	$-0.245806\pi$
$967$	44.5529			1.43273			0.716363	+	0.697728i	$0.245806\pi$
$968$	48.4182	+	27.2663i	1.55622	+	0.876372i
$969$		0			0
$970$	−0.279460	+	0.860089i	−0.00897291	+	0.0276158i
$971$	−32.0517	+	23.2869i	−1.02859	+	0.747313i	−0.968026	−	0.250852i	$-0.919289\pi$
$971$	−32.0517	+	23.2869i	−1.02859	+	0.747313i	−0.0605623	+	0.998164i	$0.519289\pi$
$972$		0			0
$973$	−23.8290	−	73.3381i	−0.763922	−	2.35111i
$974$	4.04022	+	12.4345i	0.129457	+	0.398428i
$975$		0			0
$976$	16.8214	−	12.2214i	0.538439	−	0.391199i
$977$	17.5677	−	54.0679i	0.562041	−	1.72979i	−0.114541	−	0.993418i	$-0.536540\pi$
$977$	17.5677	−	54.0679i	0.562041	−	1.72979i	0.676583	−	0.736367i	$-0.263460\pi$
$978$		0			0
$979$	37.0128	+	23.7552i	1.18293	+	0.759220i
$980$	−46.8633			−1.49699
$981$		0			0
$982$	4.90574	−	3.56423i	0.156548	−	0.113739i
$983$	9.04164	+	6.56913i	0.288383	+	0.209523i	0.722566	−	0.691302i	$-0.242963\pi$
$983$	9.04164	+	6.56913i	0.288383	+	0.209523i	−0.434182	+	0.900825i	$0.642963\pi$
$984$		0			0
$985$	−1.85596	−	5.71205i	−0.0591357	−	0.182001i
$986$	−54.7931	−	39.8095i	−1.74497	−	1.26779i
$987$		0			0
$988$	−17.3436	+	53.3781i	−0.551774	+	1.69818i
$989$	7.32482			0.232916
$990$		0			0
$991$	−37.0475			−1.17685			−0.588426	−	0.808551i	$-0.700252\pi$
$991$	−37.0475			−1.17685			−0.588426	+	0.808551i	$0.700252\pi$
$992$	0.276848	−	0.852050i	0.00878993	−	0.0270526i
$993$		0			0
$994$	32.5039	+	23.6154i	1.03096	+	0.749036i
$995$	3.09250	+	9.51772i	0.0980387	+	0.301732i
$996$		0			0
$997$	−34.8630	−	25.3294i	−1.10412	−	0.802191i	−0.122394	−	0.992482i	$-0.539057\pi$
$997$	−34.8630	−	25.3294i	−1.10412	−	0.802191i	−0.981728	+	0.190290i	$0.939057\pi$
$998$	44.3921	−	32.2527i	1.40521	−	1.02094i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.f.b.163.1	yes	16
3.2	odd	2	inner	297.2.f.b.163.4	yes	16
9.2	odd	6		891.2.n.h.757.1		32
9.4	even	3		891.2.n.h.460.1		32
9.5	odd	6		891.2.n.h.460.4		32
9.7	even	3		891.2.n.h.757.4		32
11.4	even	5		3267.2.a.bj.1.1		8
11.5	even	5	inner	297.2.f.b.82.1	✓	16
11.7	odd	10		3267.2.a.bi.1.8		8
33.5	odd	10	inner	297.2.f.b.82.4	yes	16
33.26	odd	10		3267.2.a.bj.1.8		8
33.29	even	10		3267.2.a.bi.1.1		8
99.5	odd	30		891.2.n.h.379.1		32
99.16	even	15		891.2.n.h.676.1		32
99.38	odd	30		891.2.n.h.676.4		32
99.49	even	15		891.2.n.h.379.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.f.b.82.1	✓	16	11.5	even	5	inner
297.2.f.b.82.4	yes	16	33.5	odd	10	inner
297.2.f.b.163.1	yes	16	1.1	even	1	trivial
297.2.f.b.163.4	yes	16	3.2	odd	2	inner
891.2.n.h.379.1		32	99.5	odd	30
891.2.n.h.379.4		32	99.49	even	15
891.2.n.h.460.1		32	9.4	even	3
891.2.n.h.460.4		32	9.5	odd	6
891.2.n.h.676.1		32	99.16	even	15
891.2.n.h.676.4		32	99.38	odd	30
891.2.n.h.757.1		32	9.2	odd	6
891.2.n.h.757.4		32	9.7	even	3
3267.2.a.bi.1.1		8	33.29	even	10
3267.2.a.bi.1.8		8	11.7	odd	10
3267.2.a.bj.1.1		8	11.4	even	5
3267.2.a.bj.1.8		8	33.26	odd	10

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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.760284 + 2.33991i) q^{2} +(-3.27913 - 2.38243i) q^{4} +(-0.305860 - 0.941339i) q^{5} +(-3.49672 - 2.54052i) q^{7} +(4.08684 - 2.96926i) q^{8} +2.43519 q^{10} +(2.79120 + 1.79142i) q^{11} +(1.11803 - 3.44095i) q^{13} +(8.60310 - 6.25052i) q^{14} +(1.33563 + 4.11065i) q^{16} +(-0.816208 - 2.51203i) q^{17} +(3.09629 - 2.24958i) q^{19} +(-1.23972 + 3.81546i) q^{20} +(-6.31388 + 5.16917i) q^{22} -3.45011 q^{23} +(3.25252 - 2.36309i) q^{25} +(7.20151 + 5.23221i) q^{26} +(5.41361 + 16.6614i) q^{28} +(-8.43168 - 6.12597i) q^{29} +(-0.521582 + 1.60526i) q^{31} -0.530785 q^{32} +6.49848 q^{34} +(-1.32198 + 4.06865i) q^{35} +(-2.61803 - 1.90211i) q^{37} +(2.90977 + 8.95537i) q^{38} +(-4.04508 - 2.93893i) q^{40} +(-9.63335 + 6.99904i) q^{41} -2.12307 q^{43} +(-4.88477 - 12.5241i) q^{44} +(2.62307 - 8.07297i) q^{46} +(3.47861 - 2.52736i) q^{47} +(3.60973 + 11.1096i) q^{49} +(3.05659 + 9.40723i) q^{50} +(-11.8640 + 8.61970i) q^{52} +(2.93021 - 9.01826i) q^{53} +(0.832623 - 3.17539i) q^{55} -21.8340 q^{56} +(20.7447 - 15.0719i) q^{58} +(5.23607 + 3.80423i) q^{59} +(-1.48656 - 4.57516i) q^{61} +(-3.35963 - 2.44091i) q^{62} +(-2.26771 + 6.97930i) q^{64} -3.58107 q^{65} +0.854102 q^{67} +(-3.30828 + 10.1818i) q^{68} +(-8.51520 - 6.18665i) q^{70} +(1.16751 + 3.59324i) q^{71} +(-9.22952 - 6.70564i) q^{73} +(6.44123 - 4.67983i) q^{74} -15.5126 q^{76} +(-5.20891 - 13.3552i) q^{77} +(1.89841 - 5.84272i) q^{79} +(3.46100 - 2.51456i) q^{80} +(-9.05306 - 27.8625i) q^{82} +(-1.03831 - 3.19558i) q^{83} +(-2.11503 + 1.53666i) q^{85} +(1.61413 - 4.96779i) q^{86} +(16.7264 - 0.966542i) q^{88} +13.2605 q^{89} +(-12.6513 + 9.19169i) q^{91} +(11.3134 + 8.21964i) q^{92} +(3.26907 + 10.0612i) q^{94} +(-3.06465 - 2.22660i) q^{95} +(-0.114759 + 0.353191i) q^{97} -28.7399 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 10 q^{4} + 12 q^{10} - 10 q^{16} - 2 q^{19} - 36 q^{22} + 32 q^{25} + 42 q^{28} - 26 q^{31} - 48 q^{34} - 24 q^{37} - 20 q^{40} + 24 q^{43} - 16 q^{46} + 24 q^{49} - 40 q^{52} - 16 q^{55} + 106 q^{58}+ \cdots + 72 q^{97}+O(q^{100}) \) 16 * q - 10 * q^4 + 12 * q^10 - 10 * q^16 - 2 * q^19 - 36 * q^22 + 32 * q^25 + 42 * q^28 - 26 * q^31 - 48 * q^34 - 24 * q^37 - 20 * q^40 + 24 * q^43 - 16 * q^46 + 24 * q^49 - 40 * q^52 - 16 * q^55 + 106 * q^58 - 6 * q^61 + 62 * q^64 - 40 * q^67 - 58 * q^70 + 60 * q^76 + 64 * q^79 - 84 * q^82 - 18 * q^85 + 80 * q^88 - 10 * q^91 + 90 * q^94 + 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more