LMFDB - Embedded newform 483.2.e.a.344.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(344,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("483.344");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.e (of order $2$, degree $1$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			344.5
Character	$\chi$	$=$	483.344
Dual form			483.2.e.a.344.43

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.27845i q^{2} +(-0.307505 + 1.70454i) q^{3} -3.19131 q^{4} -0.401391 q^{5} +(3.88369 + 0.700634i) q^{6} +1.00000i q^{7} +2.71435i q^{8} +(-2.81088 - 1.04831i) q^{9} +O(q^{10})$	\(q-2.27845i q^{2} +(-0.307505 + 1.70454i) q^{3} -3.19131 q^{4} -0.401391 q^{5} +(3.88369 + 0.700634i) q^{6} +1.00000i q^{7} +2.71435i q^{8} +(-2.81088 - 1.04831i) q^{9} +0.914548i q^{10} -4.07923 q^{11} +(0.981346 - 5.43971i) q^{12} +1.08232 q^{13} +2.27845 q^{14} +(0.123430 - 0.684185i) q^{15} -0.198139 q^{16} -5.98146 q^{17} +(-2.38851 + 6.40444i) q^{18} +7.44838i q^{19} +1.28097 q^{20} +(-1.70454 - 0.307505i) q^{21} +9.29430i q^{22} +(-1.14575 - 4.65696i) q^{23} +(-4.62670 - 0.834675i) q^{24} -4.83889 q^{25} -2.46601i q^{26} +(2.65124 - 4.46889i) q^{27} -3.19131i q^{28} +4.02834i q^{29} +(-1.55888 - 0.281228i) q^{30} +2.95463 q^{31} +5.88014i q^{32} +(1.25438 - 6.95319i) q^{33} +13.6284i q^{34} -0.401391i q^{35} +(8.97041 + 3.34548i) q^{36} +11.2178i q^{37} +16.9707 q^{38} +(-0.332819 + 1.84485i) q^{39} -1.08951i q^{40} -7.74860i q^{41} +(-0.700634 + 3.88369i) q^{42} -6.27514i q^{43} +13.0181 q^{44} +(1.12826 + 0.420781i) q^{45} +(-10.6106 + 2.61054i) q^{46} +5.04148i q^{47} +(0.0609289 - 0.337735i) q^{48} -1.00000 q^{49} +11.0251i q^{50} +(1.83933 - 10.1956i) q^{51} -3.45403 q^{52} -4.33191 q^{53} +(-10.1821 - 6.04070i) q^{54} +1.63737 q^{55} -2.71435 q^{56} +(-12.6960 - 2.29041i) q^{57} +9.17836 q^{58} -1.77117i q^{59} +(-0.393904 + 2.18345i) q^{60} -6.21061i q^{61} -6.73196i q^{62} +(1.04831 - 2.81088i) q^{63} +13.0013 q^{64} -0.434434 q^{65} +(-15.8425 - 2.85804i) q^{66} -11.4332i q^{67} +19.0887 q^{68} +(8.29027 - 0.520938i) q^{69} -0.914548 q^{70} +12.7236i q^{71} +(2.84547 - 7.62970i) q^{72} -1.30237 q^{73} +25.5591 q^{74} +(1.48798 - 8.24805i) q^{75} -23.7701i q^{76} -4.07923i q^{77} +(4.20340 + 0.758310i) q^{78} -11.9223i q^{79} +0.0795314 q^{80} +(6.80211 + 5.89333i) q^{81} -17.6548 q^{82} +7.67599 q^{83} +(5.43971 + 0.981346i) q^{84} +2.40091 q^{85} -14.2976 q^{86} +(-6.86645 - 1.23874i) q^{87} -11.0724i q^{88} -13.4794 q^{89} +(0.958727 - 2.57069i) q^{90} +1.08232i q^{91} +(3.65646 + 14.8618i) q^{92} +(-0.908564 + 5.03627i) q^{93} +11.4867 q^{94} -2.98971i q^{95} +(-10.0229 - 1.80817i) q^{96} +4.86578i q^{97} +2.27845i q^{98} +(11.4662 + 4.27628i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{3} - 40 q^{4} + 6 q^{6} + 4 q^{9}+O(q^{10}) $ 48 * q - 4 * q^3 - 40 * q^4 + 6 * q^6 + 4 * q^9	$ 48 q - 4 q^{3} - 40 q^{4} + 6 q^{6} + 4 q^{9} + 22 q^{12} - 8 q^{13} + 24 q^{16} - 14 q^{18} - 12 q^{24} + 88 q^{25} - 16 q^{27} - 8 q^{31} - 10 q^{36} + 8 q^{46} - 98 q^{48} - 48 q^{49} + 28 q^{52} - 28 q^{54} - 92 q^{58} + 92 q^{64} + 8 q^{69} + 8 q^{70} + 60 q^{72} + 40 q^{73} - 80 q^{75} + 114 q^{78} - 28 q^{81} - 20 q^{82} - 40 q^{85} - 28 q^{87} - 76 q^{93} - 12 q^{94} - 6 q^{96}+O(q^{100}) $ 48 * q - 4 * q^3 - 40 * q^4 + 6 * q^6 + 4 * q^9 + 22 * q^12 - 8 * q^13 + 24 * q^16 - 14 * q^18 - 12 * q^24 + 88 * q^25 - 16 * q^27 - 8 * q^31 - 10 * q^36 + 8 * q^46 - 98 * q^48 - 48 * q^49 + 28 * q^52 - 28 * q^54 - 92 * q^58 + 92 * q^64 + 8 * q^69 + 8 * q^70 + 60 * q^72 + 40 * q^73 - 80 * q^75 + 114 * q^78 - 28 * q^81 - 20 * q^82 - 40 * q^85 - 28 * q^87 - 76 * q^93 - 12 * q^94 - 6 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$		−	2.27845i		−	1.61110i	−0.592525	−	0.805552i	$-0.701869\pi$
$2$		−	2.27845i		−	1.61110i	0.592525	−	0.805552i	$-0.298131\pi$
$3$	−0.307505	+	1.70454i	−0.177538	+	0.984114i
$3$	−0.307505	+	1.70454i	−0.177538	+	0.984114i
$4$	−3.19131			−1.59566
$5$	−0.401391			−0.179508			−0.0897538	−	0.995964i	$-0.528608\pi$
$5$	−0.401391			−0.179508			−0.0897538	+	0.995964i	$0.528608\pi$
$6$	3.88369	+	0.700634i	1.58551	+	0.286033i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$			2.71435i			0.959666i
$9$	−2.81088	−	1.04831i	−0.936960	−	0.349436i
$10$			0.914548i			0.289205i
$11$	−4.07923			−1.22993			−0.614967	−	0.788553i	$-0.710831\pi$
$11$	−4.07923			−1.22993			−0.614967	+	0.788553i	$0.710831\pi$
$12$	0.981346	−	5.43971i	0.283290	−	1.57031i
$13$	1.08232			0.300182			0.150091	−	0.988672i	$-0.452043\pi$
$13$	1.08232			0.300182			0.150091	+	0.988672i	$0.452043\pi$
$14$	2.27845			0.608940
$15$	0.123430	−	0.684185i	0.0318695	−	0.176656i
$16$	−0.198139			−0.0495348
$17$	−5.98146			−1.45072			−0.725359	−	0.688371i	$-0.758326\pi$
$17$	−5.98146			−1.45072			−0.725359	+	0.688371i	$0.758326\pi$
$18$	−2.38851	+	6.40444i	−0.562977	+	1.50954i
$19$			7.44838i			1.70877i	0.519637	+	0.854387i	$0.326067\pi$
$19$			7.44838i			1.70877i	−0.519637	+	0.854387i	$0.673933\pi$
$20$	1.28097			0.286433
$21$	−1.70454	−	0.307505i	−0.371960	−	0.0671031i
$22$			9.29430i			1.98155i
$23$	−1.14575	−	4.65696i	−0.238906	−	0.971043i
$23$	−1.14575	−	4.65696i	−0.238906	−	0.971043i
$24$	−4.62670	−	0.834675i	−0.944421	−	0.170377i
$25$	−4.83889			−0.967777
$26$		−	2.46601i		−	0.483624i
$27$	2.65124	−	4.46889i	0.510231	−	0.860038i
$28$		−	3.19131i		−	0.603102i
$29$			4.02834i			0.748045i	0.927420	+	0.374022i	$0.122022\pi$
$29$			4.02834i			0.748045i	−0.927420	+	0.374022i	$0.877978\pi$
$30$	−1.55888	−	0.281228i	−0.284611	−	0.0513450i
$31$	2.95463			0.530667			0.265334	−	0.964157i	$-0.414518\pi$
$31$	2.95463			0.530667			0.265334	+	0.964157i	$0.414518\pi$
$32$			5.88014i			1.03947i
$33$	1.25438	−	6.95319i	0.218360	−	1.21039i
$34$			13.6284i			2.33726i
$35$		−	0.401391i		−	0.0678475i
$36$	8.97041	+	3.34548i	1.49507	+	0.557579i
$37$			11.2178i			1.84419i	0.386961	+	0.922096i	$0.373525\pi$
$37$			11.2178i			1.84419i	−0.386961	+	0.922096i	$0.626475\pi$
$38$	16.9707			2.75301
$39$	−0.332819	+	1.84485i	−0.0532937	+	0.295413i
$40$		−	1.08951i		−	0.172267i
$41$		−	7.74860i		−	1.21013i	−0.796177	−	0.605064i	$-0.793148\pi$
$41$		−	7.74860i		−	1.21013i	0.796177	−	0.605064i	$-0.206852\pi$
$42$	−0.700634	+	3.88369i	−0.108110	+	0.599267i
$43$		−	6.27514i		−	0.956950i	−0.878101	−	0.478475i	$-0.841190\pi$
$43$		−	6.27514i		−	0.956950i	0.878101	−	0.478475i	$-0.158810\pi$
$44$	13.0181			1.96255
$45$	1.12826	+	0.420781i	0.168192	+	0.0627263i
$46$	−10.6106	+	2.61054i	−1.56445	+	0.384903i
$47$			5.04148i			0.735376i	0.929949	+	0.367688i	$0.119850\pi$
$47$			5.04148i			0.735376i	−0.929949	+	0.367688i	$0.880150\pi$
$48$	0.0609289	−	0.337735i	0.00879432	−	0.0487479i
$49$	−1.00000			−0.142857
$50$			11.0251i			1.55919i
$51$	1.83933	−	10.1956i	0.257558	−	1.42767i
$52$	−3.45403			−0.478987
$53$	−4.33191			−0.595034			−0.297517	−	0.954716i	$-0.596159\pi$
$53$	−4.33191			−0.595034			−0.297517	+	0.954716i	$0.596159\pi$
$54$	−10.1821	−	6.04070i	−1.38561	−	0.822035i
$55$	1.63737			0.220782
$56$	−2.71435			−0.362720
$57$	−12.6960	−	2.29041i	−1.68163	−	0.303373i
$58$	9.17836			1.20518
$59$		−	1.77117i		−	0.230586i	−0.993332	−	0.115293i	$-0.963219\pi$
$59$		−	1.77117i		−	0.230586i	0.993332	−	0.115293i	$-0.0367807\pi$
$60$	−0.393904	+	2.18345i	−0.0508527	+	0.281882i
$61$		−	6.21061i		−	0.795187i	−0.917562	−	0.397594i	$-0.869845\pi$
$61$		−	6.21061i		−	0.795187i	0.917562	−	0.397594i	$-0.130155\pi$
$62$		−	6.73196i		−	0.854960i
$63$	1.04831	−	2.81088i	0.132074	−	0.354138i
$64$	13.0013			1.62516
$65$	−0.434434			−0.0538849
$66$	−15.8425	−	2.85804i	−1.95007	−	0.351801i
$67$		−	11.4332i		−	1.39679i	−0.715714	−	0.698394i	$-0.753899\pi$
$67$		−	11.4332i		−	1.39679i	0.715714	−	0.698394i	$-0.246101\pi$
$68$	19.0887			2.31485
$69$	8.29027	−	0.520938i	0.998032	−	0.0627136i
$70$	−0.914548			−0.109309
$71$			12.7236i			1.51002i	0.655714	+	0.755009i	$0.272368\pi$
$71$			12.7236i			1.51002i	−0.655714	+	0.755009i	$0.727632\pi$
$72$	2.84547	−	7.62970i	0.335342	−	0.899169i
$73$	−1.30237			−0.152431			−0.0762156	−	0.997091i	$-0.524284\pi$
$73$	−1.30237			−0.152431			−0.0762156	+	0.997091i	$0.524284\pi$
$74$	25.5591			2.97119
$75$	1.48798	−	8.24805i	0.171817	−	0.952403i
$76$		−	23.7701i		−	2.72662i
$77$		−	4.07923i		−	0.464871i
$78$	4.20340	+	0.758310i	0.475941	+	0.0858617i
$79$		−	11.9223i		−	1.34136i	−0.741745	−	0.670682i	$-0.766002\pi$
$79$		−	11.9223i		−	1.34136i	0.741745	−	0.670682i	$-0.233998\pi$
$80$	0.0795314			0.00889188
$81$	6.80211	+	5.89333i	0.755790	+	0.654815i
$82$	−17.6548			−1.94964
$83$	7.67599			0.842550			0.421275	−	0.906933i	$-0.361583\pi$
$83$	7.67599			0.842550			0.421275	+	0.906933i	$0.361583\pi$
$84$	5.43971	+	0.981346i	0.593521	+	0.107074i
$85$	2.40091			0.260415
$86$	−14.2976			−1.54175
$87$	−6.86645	−	1.23874i	−0.736161	−	0.132806i
$88$		−	11.0724i		−	1.18033i
$89$	−13.4794			−1.42882			−0.714408	−	0.699729i	$-0.753304\pi$
$89$	−13.4794			−1.42882			−0.714408	+	0.699729i	$0.753304\pi$
$90$	0.958727	−	2.57069i	0.101059	−	0.270974i
$91$			1.08232i			0.113458i
$92$	3.65646	+	14.8618i	0.381212	+	1.54945i
$93$	−0.908564	+	5.03627i	−0.0942137	+	0.522237i
$94$	11.4867			1.18477
$95$		−	2.98971i		−	0.306738i
$96$	−10.0229	−	1.80817i	−1.02296	−	0.184546i
$97$			4.86578i			0.494045i	0.969010	+	0.247022i	$0.0794521\pi$
$97$			4.86578i			0.494045i	−0.969010	+	0.247022i	$0.920548\pi$
$98$			2.27845i			0.230158i
$99$	11.4662	+	4.27628i	1.15240	+	0.429782i
$100$	15.4424			1.54424
$101$		−	9.41499i		−	0.936827i	−0.883509	−	0.468413i	$-0.844826\pi$
$101$		−	9.41499i		−	0.936827i	0.883509	−	0.468413i	$-0.155174\pi$
$102$	−23.2301	−	4.19081i	−2.30013	−	0.414952i
$103$		−	0.161539i		−	0.0159169i	−0.999968	−	0.00795844i	$-0.997467\pi$
$103$		−	0.161539i		−	0.0159169i	0.999968	−	0.00795844i	$-0.00253328\pi$
$104$			2.93779i			0.288074i
$105$	0.684185	+	0.123430i	0.0667697	+	0.0120455i
$106$			9.87003i			0.958662i
$107$	10.2686			0.992702			0.496351	−	0.868122i	$-0.334673\pi$
$107$	10.2686			0.992702			0.496351	+	0.868122i	$0.334673\pi$
$108$	−8.46093	+	14.2616i	−0.814153	+	1.37233i
$109$			14.7989i			1.41748i	0.705471	+	0.708739i	$0.250735\pi$
$109$			14.7989i			1.41748i	−0.705471	+	0.708739i	$0.749265\pi$
$110$		−	3.73065i		−	0.355703i
$111$	−19.1211	−	3.44953i	−1.81489	−	0.327414i
$112$		−	0.198139i		−	0.0187224i
$113$	−4.02762			−0.378887			−0.189443	−	0.981892i	$-0.560668\pi$
$113$	−4.02762			−0.378887			−0.189443	+	0.981892i	$0.560668\pi$
$114$	−5.21858	+	28.9272i	−0.488765	+	2.70928i
$115$	0.459895	+	1.86926i	0.0428855	+	0.174310i
$116$		−	12.8557i		−	1.19362i
$117$	−3.04227	−	1.13460i	−0.281258	−	0.104894i
$118$	−4.03550			−0.371498
$119$		−	5.98146i		−	0.548320i
$120$	1.85712	+	0.335031i	0.169531	+	0.0305840i
$121$	5.64009			0.512736
$122$	−14.1505			−1.28113
$123$	13.2078	+	2.38273i	1.19090	+	0.214844i
$124$	−9.42915			−0.846763
$125$	3.94924			0.353231
$126$	−6.40444	−	2.38851i	−0.570553	−	0.212785i
$127$	−16.3065			−1.44697			−0.723484	−	0.690341i	$-0.757461\pi$
$127$	−16.3065			−1.44697			−0.723484	+	0.690341i	$0.757461\pi$
$128$		−	17.8625i		−	1.57884i
$129$	10.6962	+	1.92964i	0.941748	+	0.169895i
$130$			0.989834i			0.0868142i
$131$			7.78903i			0.680531i	0.940329	+	0.340265i	$0.110517\pi$
$131$			7.78903i			0.680531i	−0.940329	+	0.340265i	$0.889483\pi$
$132$	−4.00313	+	22.1898i	−0.348428	+	1.93137i
$133$	−7.44838			−0.645856
$134$	−26.0499			−2.25037
$135$	−1.06418	+	1.79377i	−0.0915903	+	0.154383i
$136$		−	16.2358i		−	1.39220i
$137$	9.01203			0.769950			0.384975	−	0.922927i	$-0.374210\pi$
$137$	9.01203			0.769950			0.384975	+	0.922927i	$0.374210\pi$
$138$	−1.18693	−	18.8889i	−0.101038	−	1.60793i
$139$	−1.65195			−0.140117			−0.0700585	−	0.997543i	$-0.522319\pi$
$139$	−1.65195			−0.140117			−0.0700585	+	0.997543i	$0.522319\pi$
$140$			1.28097i			0.108261i
$141$	−8.59338	−	1.55028i	−0.723693	−	0.130557i
$142$	28.9901			2.43280
$143$	−4.41503			−0.369203
$144$	0.556946	+	0.207711i	0.0464122	+	0.0173092i
$145$		−	1.61694i		−	0.134280i
$146$			2.96738i			0.245582i
$147$	0.307505	−	1.70454i	0.0253626	−	0.140588i
$148$		−	35.7995i		−	2.94270i
$149$	−4.88154			−0.399911			−0.199955	−	0.979805i	$-0.564080\pi$
$149$	−4.88154			−0.399911			−0.199955	+	0.979805i	$0.564080\pi$
$150$	−18.7927	−	3.39029i	−1.53442	−	0.276816i
$151$	11.7045			0.952498			0.476249	−	0.879310i	$-0.341996\pi$
$151$	11.7045			0.952498			0.476249	+	0.879310i	$0.341996\pi$
$152$	−20.2175			−1.63985
$153$	16.8132	+	6.27040i	1.35926	+	0.506932i
$154$	−9.29430			−0.748956
$155$	−1.18596			−0.0952588
$156$	1.06213	−	5.88751i	0.0850385	−	0.471378i
$157$		−	5.39520i		−	0.430584i	−0.976550	−	0.215292i	$-0.930930\pi$
$157$		−	5.39520i		−	0.430584i	0.976550	−	0.215292i	$-0.0690703\pi$
$158$	−27.1643			−2.16108
$159$	1.33209	−	7.38390i	0.105641	−	0.585581i
$160$		−	2.36024i		−	0.186593i
$161$	4.65696	−	1.14575i	0.367020	−	0.0902980i
$162$	13.4276	−	15.4982i	1.05497	−	1.21766i
$163$	1.40157			0.109780			0.0548898	−	0.998492i	$-0.482519\pi$
$163$	1.40157			0.109780			0.0548898	+	0.998492i	$0.482519\pi$
$164$			24.7282i			1.93095i
$165$	−0.503498	+	2.79095i	−0.0391973	+	0.217275i
$166$		−	17.4893i		−	1.35744i
$167$			2.44287i			0.189035i	0.995523	+	0.0945175i	$0.0301308\pi$
$167$			2.44287i			0.189035i	−0.995523	+	0.0945175i	$0.969869\pi$
$168$	0.834675	−	4.62670i	0.0643966	−	0.356958i
$169$	−11.8286			−0.909891
$170$		−	5.47033i		−	0.419555i
$171$	7.80818	−	20.9365i	0.597107	−	1.60105i
$172$			20.0260i			1.52697i
$173$			21.9963i			1.67235i	0.548462	+	0.836176i	$0.315214\pi$
$173$			21.9963i			1.67235i	−0.548462	+	0.836176i	$0.684786\pi$
$174$	−2.82239	+	15.6448i	−0.213965	+	1.18603i
$175$		−	4.83889i		−	0.365785i
$176$	0.808255			0.0609245
$177$	3.01901	+	0.544642i	0.226923	+	0.0409378i
$178$			30.7121i			2.30197i
$179$			4.07869i			0.304856i	0.988315	+	0.152428i	$0.0487091\pi$
$179$			4.07869i			0.304856i	−0.988315	+	0.152428i	$0.951291\pi$
$180$	−3.60064	−	1.34284i	−0.268376	−	0.100090i
$181$		−	14.9438i		−	1.11076i	−0.831595	−	0.555382i	$-0.812572\pi$
$181$		−	14.9438i		−	1.11076i	0.831595	−	0.555382i	$-0.187428\pi$
$182$	2.46601			0.182793
$183$	10.5862	+	1.90979i	0.782555	+	0.141176i
$184$	12.6406	−	3.10997i	0.931877	−	0.229270i
$185$		−	4.50272i		−	0.331046i
$186$	11.4749	+	2.07011i	0.841378	+	0.151788i
$187$	24.3997			1.78429
$188$		−	16.0890i		−	1.17341i
$189$	4.46889	+	2.65124i	0.325064	+	0.192849i
$190$	−6.81190			−0.494187
$191$	−6.18458			−0.447500			−0.223750	−	0.974647i	$-0.571830\pi$
$191$	−6.18458			−0.447500			−0.223750	+	0.974647i	$0.571830\pi$
$192$	−3.99797	+	22.1612i	−0.288529	+	1.59935i
$193$	−1.50715			−0.108487			−0.0542436	−	0.998528i	$-0.517275\pi$
$193$	−1.50715			−0.108487			−0.0542436	+	0.998528i	$0.517275\pi$
$194$	11.0864			0.795958
$195$	0.133591	−	0.740508i	0.00956663	−	0.0530289i
$196$	3.19131			0.227951
$197$		−	10.4583i		−	0.745120i	−0.928008	−	0.372560i	$-0.878480\pi$
$197$		−	10.4583i		−	0.745120i	0.928008	−	0.372560i	$-0.121520\pi$
$198$	9.74328	−	26.1252i	0.692424	−	1.85663i
$199$		−	8.88651i		−	0.629948i	−0.949100	−	0.314974i	$-0.898004\pi$
$199$		−	8.88651i		−	0.629948i	0.949100	−	0.314974i	$-0.101996\pi$
$200$		−	13.1344i		−	0.928743i
$201$	19.4883	+	3.51577i	1.37460	+	0.247983i
$202$	−21.4516			−1.50933
$203$	−4.02834			−0.282734
$204$	−5.86988	+	32.5374i	−0.410974	+	2.27807i
$205$			3.11022i			0.217227i
$206$	−0.368057			−0.0256438
$207$	−1.66134	+	14.2913i	−0.115471	+	0.993311i
$208$	−0.214450			−0.0148695
$209$		−	30.3836i		−	2.10168i
$210$	0.281228	−	1.55888i	0.0194066	−	0.107573i
$211$	−14.7329			−1.01425			−0.507127	−	0.861871i	$-0.669292\pi$
$211$	−14.7329			−1.01425			−0.507127	+	0.861871i	$0.669292\pi$
$212$	13.8245			0.949471
$213$	−21.6879	−	3.91258i	−1.48603	−	0.268086i
$214$		−	23.3964i		−	1.59935i
$215$			2.51879i			0.171780i
$216$	12.1301	+	7.19637i	0.825349	+	0.489651i
$217$			2.95463i			0.200573i
$218$	33.7185			2.28370
$219$	0.400486	−	2.21994i	0.0270623	−	0.150010i
$220$	−5.22535			−0.352293
$221$	−6.47386			−0.435479
$222$	−7.85956	+	43.5664i	−0.527499	+	2.92398i
$223$	20.7167			1.38729			0.693645	−	0.720317i	$-0.256003\pi$
$223$	20.7167			1.38729			0.693645	+	0.720317i	$0.256003\pi$
$224$	−5.88014			−0.392884
$225$	13.6015	+	5.07264i	0.906769	+	0.338176i
$226$			9.17672i			0.610426i
$227$	15.4573			1.02594			0.512968	−	0.858408i	$-0.328546\pi$
$227$	15.4573			1.02594			0.512968	+	0.858408i	$0.328546\pi$
$228$	40.5170	+	7.30943i	2.68330	+	0.484079i
$229$			17.5993i			1.16300i	0.813548	+	0.581498i	$0.197533\pi$
$229$			17.5993i			1.16300i	−0.813548	+	0.581498i	$0.802467\pi$
$230$	4.25901	−	1.04785i	0.280831	−	0.0690929i
$231$	6.95319	+	1.25438i	0.457486	+	0.0825324i
$232$	−10.9343			−0.717873
$233$			8.82816i			0.578352i	0.957276	+	0.289176i	$0.0933813\pi$
$233$			8.82816i			0.578352i	−0.957276	+	0.289176i	$0.906619\pi$
$234$	−2.58513	+	6.93166i	−0.168995	+	0.453137i
$235$		−	2.02361i		−	0.132005i
$236$			5.65235i			0.367936i
$237$	20.3220	+	3.66617i	1.32005	+	0.238143i
$238$	−13.6284			−0.883400
$239$			13.4026i			0.866944i	0.901167	+	0.433472i	$0.142712\pi$
$239$			13.4026i			0.866944i	−0.901167	+	0.433472i	$0.857288\pi$
$240$	−0.0244563	+	0.135564i	−0.00157865	+	0.00875062i
$241$			13.6940i			0.882111i	0.897480	+	0.441055i	$0.145396\pi$
$241$			13.6940i			0.882111i	−0.897480	+	0.441055i	$0.854604\pi$
$242$		−	12.8506i		−	0.826071i
$243$	−12.1371	+	9.78220i	−0.778594	+	0.627528i
$244$			19.8200i			1.26885i
$245$	0.401391			0.0256439
$246$	5.42893	−	30.0932i	0.346136	−	1.91867i
$247$			8.06153i			0.512943i
$248$			8.01989i			0.509263i
$249$	−2.36041	+	13.0840i	−0.149585	+	0.829165i
$250$		−	8.99813i		−	0.569092i
$251$	−13.6995			−0.864702			−0.432351	−	0.901705i	$-0.642316\pi$
$251$	−13.6995			−0.864702			−0.432351	+	0.901705i	$0.642316\pi$
$252$	−3.34548	+	8.97041i	−0.210745	+	0.565083i
$253$	4.67379	+	18.9968i	0.293839	+	1.19432i
$254$			37.1535i			2.33122i
$255$	−0.738291	+	4.09243i	−0.0462336	+	0.256278i
$256$	−14.6961			−0.918506
$257$			14.4395i			0.900712i	0.892849	+	0.450356i	$0.148703\pi$
$257$			14.4395i			0.900712i	−0.892849	+	0.450356i	$0.851297\pi$
$258$	4.39658	−	24.3707i	0.273719	−	1.51725i
$259$	−11.2178			−0.697039
$260$	1.38642			0.0859818
$261$	4.22294	−	11.3232i	0.261393	−	0.700888i
$262$	17.7469			1.09641
$263$	15.4628			0.953474			0.476737	−	0.879046i	$-0.341819\pi$
$263$	15.4628			0.953474			0.476737	+	0.879046i	$0.341819\pi$
$264$	18.8734	+	3.40483i	1.16157	+	0.209553i
$265$	1.73879			0.106813
$266$			16.9707i			1.04054i
$267$	4.14499	−	22.9762i	0.253669	−	1.40612i
$268$			36.4869i			2.22879i
$269$			5.51680i			0.336365i	0.985756	+	0.168182i	$0.0537898\pi$
$269$			5.51680i			0.336365i	−0.985756	+	0.168182i	$0.946210\pi$
$270$	4.08701	+	2.42468i	0.248728	+	0.147562i
$271$	19.8878			1.20810			0.604049	−	0.796948i	$-0.293553\pi$
$271$	19.8878			1.20810			0.604049	+	0.796948i	$0.293553\pi$
$272$	1.18516			0.0718610
$273$	−1.84485	−	0.332819i	−0.111656	−	0.0201431i
$274$		−	20.5334i		−	1.24047i
$275$	19.7389			1.19030
$276$	−26.4569	+	1.66248i	−1.59252	+	0.100069i
$277$	−22.2287			−1.33559			−0.667795	−	0.744345i	$-0.732762\pi$
$277$	−22.2287			−1.33559			−0.667795	+	0.744345i	$0.732762\pi$
$278$			3.76389i			0.225743i
$279$	−8.30511	−	3.09736i	−0.497214	−	0.185434i
$280$	1.08951			0.0651110
$281$	−10.4076			−0.620868			−0.310434	−	0.950595i	$-0.600474\pi$
$281$	−10.4076			−0.620868			−0.310434	+	0.950595i	$0.600474\pi$
$282$	−3.53223	+	19.5796i	−0.210341	+	1.16595i
$283$		−	13.5153i		−	0.803401i	−0.915771	−	0.401701i	$-0.868419\pi$
$283$		−	13.5153i		−	0.803401i	0.915771	−	0.401701i	$-0.131581\pi$
$284$		−	40.6051i		−	2.40947i
$285$	5.09607	+	0.919352i	0.301865	+	0.0544577i
$286$			10.0594i			0.594825i
$287$	7.74860			0.457385
$288$	6.16419	−	16.5284i	0.363229	−	0.973944i
$289$	18.7779			1.10458
$290$	−3.68411			−0.216339
$291$	−8.29389	−	1.49625i	−0.486196	−	0.0877118i
$292$	4.15628			0.243228
$293$	−10.1597			−0.593536			−0.296768	−	0.954950i	$-0.595909\pi$
$293$	−10.1597			−0.593536			−0.296768	+	0.954950i	$0.595909\pi$
$294$	−3.88369	−	0.700634i	−0.226501	−	0.0408618i
$295$			0.710930i			0.0413919i
$296$	−30.4489			−1.76981
$297$	−10.8150	+	18.2296i	−0.627550	+	1.05779i
$298$			11.1223i			0.644298i
$299$	−1.24007	−	5.04032i	−0.0717152	−	0.291489i
$300$	−4.74862	+	26.3221i	−0.274162	+	1.51971i
$301$	6.27514			0.361693
$302$		−	26.6681i		−	1.53457i
$303$	16.0482	+	2.89516i	0.921944	+	0.166323i
$304$		−	1.47582i		−	0.0846439i
$305$			2.49288i			0.142742i
$306$	14.2868	−	38.3079i	0.816721	−	2.18992i
$307$	−19.4551			−1.11036			−0.555179	−	0.831731i	$-0.687350\pi$
$307$	−19.4551			−1.11036			−0.555179	+	0.831731i	$0.687350\pi$
$308$			13.0181i			0.741775i
$309$	0.275349	+	0.0496740i	0.0156640	+	0.00282586i
$310$			2.70215i			0.153472i
$311$		−	31.2981i		−	1.77475i	−0.461045	−	0.887377i	$-0.652525\pi$
$311$		−	31.2981i		−	1.77475i	0.461045	−	0.887377i	$-0.347475\pi$
$312$	−5.00757	−	0.903386i	−0.283498	−	0.0511442i
$313$			17.3434i			0.980307i	0.871636	+	0.490153i	$0.163059\pi$
$313$			17.3434i			0.980307i	−0.871636	+	0.490153i	$0.836941\pi$
$314$	−12.2927			−0.693715
$315$	−0.420781	+	1.12826i	−0.0237083	+	0.0635704i
$316$			38.0478i			2.14036i
$317$			2.89212i			0.162437i	0.996696	+	0.0812187i	$0.0258812\pi$
$317$			2.89212i			0.162437i	−0.996696	+	0.0812187i	$0.974119\pi$
$318$	−16.8238	−	3.03509i	−0.943433	−	0.170199i
$319$		−	16.4325i		−	0.920045i
$320$	−5.21861			−0.291729
$321$	−3.15765	+	17.5032i	−0.176243	+	0.976932i
$322$	−2.61054	−	10.6106i	−0.145480	−	0.591307i
$323$		−	44.5522i		−	2.47895i
$324$	−21.7077	−	18.8075i	−1.20598	−	1.04486i
$325$	−5.23723			−0.290509
$326$		−	3.19340i		−	0.176866i
$327$	−25.2252	−	4.55074i	−1.39496	−	0.251656i
$328$	21.0324			1.16132
$329$	−5.04148			−0.277946
$330$	6.35902	+	1.14719i	0.350053	+	0.0631509i
$331$	−34.2946			−1.88500			−0.942500	−	0.334206i	$-0.891532\pi$
$331$	−34.2946			−1.88500			−0.942500	+	0.334206i	$0.891532\pi$
$332$	−24.4965			−1.34442
$333$	11.7597	−	31.5318i	0.644426	−	1.72793i
$334$	5.56595			0.304555
$335$			4.58918i			0.250734i
$336$	0.337735	+	0.0609289i	0.0184250	+	0.00332394i
$337$		−	1.81907i		−	0.0990912i	−0.998772	−	0.0495456i	$-0.984223\pi$
$337$		−	1.81907i		−	0.0990912i	0.998772	−	0.0495456i	$-0.0157773\pi$
$338$			26.9508i			1.46593i
$339$	1.23851	−	6.86523i	0.0672669	−	0.372868i
$340$	−7.66204			−0.415533
$341$	−12.0526			−0.652685
$342$	−47.7027	−	17.7905i	−2.57947	−	0.962001i
$343$		−	1.00000i		−	0.0539949i
$344$	17.0329			0.918353
$345$	−3.32764	+	0.209100i	−0.179154	+	0.0112576i
$346$	50.1175			2.69433
$347$			25.9993i			1.39572i	0.716236	+	0.697858i	$0.245863\pi$
$347$			25.9993i			1.39572i	−0.716236	+	0.697858i	$0.754137\pi$
$348$	21.9130	+	3.95320i	1.17466	+	0.211914i
$349$	22.7532			1.21795			0.608974	−	0.793190i	$-0.291581\pi$
$349$	22.7532			1.21795			0.608974	+	0.793190i	$0.291581\pi$
$350$	−11.0251			−0.589318
$351$	2.86949	−	4.83677i	0.153162	−	0.258168i
$352$		−	23.9864i		−	1.27848i
$353$			23.1351i			1.23136i	0.787997	+	0.615680i	$0.211118\pi$
$353$			23.1351i			1.23136i	−0.787997	+	0.615680i	$0.788882\pi$
$354$	1.24094	−	6.87866i	0.0659551	−	0.365597i
$355$		−	5.10716i		−	0.271060i
$356$	43.0171			2.27990
$357$	10.1956	+	1.83933i	0.539609	+	0.0973477i
$358$	9.29307			0.491154
$359$	−32.9159			−1.73723			−0.868616	−	0.495485i	$-0.834990\pi$
$359$	−32.9159			−1.73723			−0.868616	+	0.495485i	$0.834990\pi$
$360$	−1.14215	+	3.06250i	−0.0601964	+	0.161408i
$361$	−36.4783			−1.91991
$362$	−34.0486			−1.78956
$363$	−1.73436	+	9.61374i	−0.0910302	+	0.504590i
$364$		−	3.45403i		−	0.181040i
$365$	0.522761			0.0273625
$366$	4.35136	−	24.1201i	0.227449	−	1.26078i
$367$			28.1557i			1.46972i	0.678221	+	0.734858i	$0.262751\pi$
$367$			28.1557i			1.46972i	−0.678221	+	0.734858i	$0.737249\pi$
$368$	0.227019	+	0.922726i	0.0118342	+	0.0481004i
$369$	−8.12291	+	21.7804i	−0.422862	+	1.13384i
$370$	−10.2592			−0.533350
$371$		−	4.33191i		−	0.224902i
$372$	2.89951	−	16.0723i	0.150333	−	0.833311i
$373$			10.4269i			0.539887i	0.962876	+	0.269943i	$0.0870049\pi$
$373$			10.4269i			0.539887i	−0.962876	+	0.269943i	$0.912995\pi$
$374$		−	55.5935i		−	2.87467i
$375$	−1.21441	+	6.73162i	−0.0627120	+	0.347619i
$376$	−13.6843			−0.705715
$377$			4.35996i			0.224549i
$378$	6.04070	−	10.1821i	0.310700	−	0.523711i
$379$		−	19.4658i		−	0.999889i	−0.866057	−	0.499945i	$-0.833354\pi$
$379$		−	19.4658i		−	0.999889i	0.866057	−	0.499945i	$-0.166646\pi$
$380$			9.54111i			0.489449i
$381$	5.01434	−	27.7950i	0.256892	−	1.42398i
$382$			14.0912i			0.720970i
$383$	−4.49745			−0.229809			−0.114904	−	0.993377i	$-0.536656\pi$
$383$	−4.49745			−0.229809			−0.114904	+	0.993377i	$0.536656\pi$
$384$	30.4472	+	5.49281i	1.55375	+	0.280304i
$385$			1.63737i			0.0834479i
$386$			3.43396i			0.174784i
$387$	−6.57828	+	17.6387i	−0.334393	+	0.896625i
$388$		−	15.5282i		−	0.788326i
$389$	−19.1495			−0.970916			−0.485458	−	0.874260i	$-0.661347\pi$
$389$	−19.1495			−0.970916			−0.485458	+	0.874260i	$0.661347\pi$
$390$	−1.68721	−	0.304379i	−0.0854351	−	0.0154128i
$391$	6.85328	+	27.8554i	0.346585	+	1.40871i
$392$		−	2.71435i		−	0.137095i
$393$	−13.2767	−	2.39517i	−0.669720	−	0.120820i
$394$	−23.8286			−1.20047
$395$			4.78551i			0.240785i
$396$	−36.5923	−	13.6470i	−1.83883	−	0.685786i
$397$	25.7330			1.29150			0.645752	−	0.763547i	$-0.276544\pi$
$397$	25.7330			1.29150			0.645752	+	0.763547i	$0.276544\pi$
$398$	−20.2474			−1.01491
$399$	2.29041	−	12.6960i	0.114664	−	0.635596i
$400$	0.958773			0.0479387
$401$	−12.4439			−0.621420			−0.310710	−	0.950505i	$-0.600567\pi$
$401$	−12.4439			−0.621420			−0.310710	+	0.950505i	$0.600567\pi$
$402$	8.01048	−	44.4030i	0.399527	−	2.21462i
$403$	3.19786			0.159297
$404$			30.0462i			1.49485i
$405$	−2.73031	−	2.36553i	−0.135670	−	0.117544i
$406$			9.17836i			0.455514i
$407$		−	45.7599i		−	2.26823i
$408$	27.6744	+	4.99258i	1.37009	+	0.247169i
$409$	−20.1487			−0.996288			−0.498144	−	0.867094i	$-0.665985\pi$
$409$	−20.1487			−0.996288			−0.498144	+	0.867094i	$0.665985\pi$
$410$	7.08647			0.349976
$411$	−2.77125	+	15.3613i	−0.136695	+	0.757718i
$412$			0.515521i			0.0253979i
$413$	1.77117			0.0871533
$414$	32.5618	+	3.78528i	1.60033	+	0.186036i
$415$	−3.08108			−0.151244
$416$			6.36420i			0.312031i
$417$	0.507984	−	2.81581i	0.0248761	−	0.137891i
$418$	−69.2274			−3.38602
$419$	−20.6978			−1.01115			−0.505577	−	0.862782i	$-0.668720\pi$
$419$	−20.6978			−1.01115			−0.505577	+	0.862782i	$0.668720\pi$
$420$	−2.18345	−	0.393904i	−0.106542	−	0.0192205i
$421$			0.387187i			0.0188704i	0.999955	+	0.00943518i	$0.00300336\pi$
$421$			0.387187i			0.0188704i	−0.999955	+	0.00943518i	$0.996997\pi$
$422$			33.5681i			1.63407i
$423$	5.28502	−	14.1710i	0.256966	−	0.689018i
$424$		−	11.7583i		−	0.571034i
$425$	28.9436			1.40397
$426$	−8.91461	+	49.4147i	−0.431914	+	2.39415i
$427$	6.21061			0.300553
$428$	−32.7703			−1.58401
$429$	1.35764	−	7.52558i	0.0655477	−	0.363338i
$430$	5.73892			0.276755
$431$	−25.0930			−1.20869			−0.604343	−	0.796724i	$-0.706564\pi$
$431$	−25.0930			−1.20869			−0.604343	+	0.796724i	$0.706564\pi$
$432$	−0.525314	+	0.885462i	−0.0252742	+	0.0426018i
$433$			36.5226i			1.75517i	0.479425	+	0.877583i	$0.340845\pi$
$433$			36.5226i			1.75517i	−0.479425	+	0.877583i	$0.659155\pi$
$434$	6.73196			0.323145
$435$	2.75613	+	0.497218i	0.132147	+	0.0238398i
$436$		−	47.2279i		−	2.26181i
$437$	34.6868	−	8.53400i	1.65929	−	0.408237i
$438$	−5.05801	−	0.912486i	−0.241681	−	0.0436003i
$439$	3.89309			0.185807			0.0929036	−	0.995675i	$-0.470385\pi$
$439$	3.89309			0.185807			0.0929036	+	0.995675i	$0.470385\pi$
$440$			4.44438i			0.211877i
$441$	2.81088	+	1.04831i	0.133851	+	0.0499194i
$442$			14.7503i			0.701602i
$443$			11.3758i			0.540481i	0.962793	+	0.270240i	$0.0871032\pi$
$443$			11.3758i			0.540481i	−0.962793	+	0.270240i	$0.912897\pi$
$444$	61.0215	+	11.0085i	2.89595	+	0.522441i
$445$	5.41052			0.256483
$446$		−	47.2018i		−	2.23507i
$447$	1.50110	−	8.32075i	0.0709995	−	0.393558i
$448$			13.0013i			0.614254i
$449$		−	10.8861i		−	0.513749i	−0.966445	−	0.256874i	$-0.917307\pi$
$449$		−	10.8861i		−	0.513749i	0.966445	−	0.256874i	$-0.0826927\pi$
$450$	11.5577	−	30.9903i	0.544836	−	1.46090i
$451$			31.6083i			1.48838i
$452$	12.8534			0.604574
$453$	−3.59919	+	19.9507i	−0.169105	+	0.937367i
$454$		−	35.2186i		−	1.65289i
$455$		−	0.434434i		−	0.0203666i
$456$	6.21698	−	34.4614i	0.291137	−	1.61380i
$457$		−	14.6334i		−	0.684523i	−0.939605	−	0.342261i	$-0.888807\pi$
$457$		−	14.6334i		−	0.684523i	0.939605	−	0.342261i	$-0.111193\pi$
$458$	40.0991			1.87371
$459$	−15.8583	+	26.7305i	−0.740200	+	1.24767i
$460$	−1.46767	−	5.96540i	−0.0684305	−	0.278138i
$461$			1.61338i			0.0751427i	0.999294	+	0.0375714i	$0.0119622\pi$
$461$			1.61338i			0.0751427i	−0.999294	+	0.0375714i	$0.988038\pi$
$462$	2.85804	−	15.8425i	0.132968	−	0.737058i
$463$	−5.07317			−0.235770			−0.117885	−	0.993027i	$-0.537611\pi$
$463$	−5.07317			−0.235770			−0.117885	+	0.993027i	$0.537611\pi$
$464$		−	0.798173i		−	0.0370543i
$465$	0.364690	−	2.02151i	0.0169121	−	0.0937455i
$466$	20.1145			0.931786
$467$	23.0228			1.06537			0.532683	−	0.846315i	$-0.321184\pi$
$467$	23.0228			1.06537			0.532683	+	0.846315i	$0.321184\pi$
$468$	9.70886	+	3.62088i	0.448792	+	0.167375i
$469$	11.4332			0.527936
$470$	−4.61068			−0.212675
$471$	9.19630	+	1.65905i	0.423743	+	0.0764450i
$472$	4.80756			0.221286
$473$			25.5977i			1.17699i
$474$	8.35317	−	46.3025i	0.383674	−	2.12675i
$475$		−	36.0418i		−	1.65371i
$476$			19.0887i			0.874930i
$477$	12.1765	+	4.54118i	0.557523	+	0.207926i
$478$	30.5372			1.39674
$479$	−31.2281			−1.42685			−0.713425	−	0.700731i	$-0.752857\pi$
$479$	−31.2281			−1.42685			−0.713425	+	0.700731i	$0.752857\pi$
$480$	4.02311	+	0.725785i	0.183629	+	0.0331274i
$481$			12.1412i			0.553593i
$482$	31.2011			1.42117
$483$	0.520938	+	8.29027i	0.0237035	+	0.377220i
$484$	−17.9993			−0.818151
$485$		−	1.95308i		−	0.0886848i
$486$	22.2882	+	27.6537i	1.01101	+	1.25440i
$487$	−24.0319			−1.08899			−0.544494	−	0.838765i	$-0.683278\pi$
$487$	−24.0319			−1.08899			−0.544494	+	0.838765i	$0.683278\pi$
$488$	16.8577			0.763114
$489$	−0.430990	+	2.38903i	−0.0194901	+	0.108036i
$490$		−	0.914548i		−	0.0413151i
$491$			26.9518i			1.21632i	0.793815	+	0.608159i	$0.208092\pi$
$491$			26.9518i			1.21632i	−0.793815	+	0.608159i	$0.791908\pi$
$492$	−42.1501	−	7.60406i	−1.90027	−	0.342817i
$493$		−	24.0954i		−	1.08520i
$494$	18.3678			0.826405
$495$	−4.60244	−	1.71646i	−0.206864	−	0.0771492i
$496$	−0.585428			−0.0262865
$497$	−12.7236			−0.570733
$498$	29.8112	+	5.37806i	1.33587	+	0.240997i
$499$	1.82878			0.0818672			0.0409336	−	0.999162i	$-0.486967\pi$
$499$	1.82878			0.0818672			0.0409336	+	0.999162i	$0.486967\pi$
$500$	−12.6033			−0.563636
$501$	−4.16396	−	0.751195i	−0.186032	−	0.0335609i
$502$			31.2135i			1.39312i
$503$	39.0045			1.73912			0.869562	−	0.493823i	$-0.164401\pi$
$503$	39.0045			1.73912			0.869562	+	0.493823i	$0.164401\pi$
$504$	7.62970	+	2.84547i	0.339854	+	0.126747i
$505$			3.77910i			0.168168i
$506$	43.2831	−	10.6490i	1.92417	−	0.473405i
$507$	3.63735	−	20.1622i	0.161540	−	0.895436i
$508$	52.0392			2.30887
$509$			10.6040i			0.470015i	0.971993	+	0.235008i	$0.0755116\pi$
$509$			10.6040i			0.470015i	−0.971993	+	0.235008i	$0.924488\pi$
$510$	9.32437	+	1.68216i	0.412890	+	0.0744871i
$511$		−	1.30237i		−	0.0576135i
$512$		−	2.24072i		−	0.0990270i
$513$	33.2859	+	19.7474i	1.46961	+	0.871869i
$514$	32.8996			1.45114
$515$			0.0648402i			0.00285720i
$516$	−34.1350	−	6.15809i	−1.50271	−	0.271095i
$517$		−	20.5653i		−	0.904463i
$518$			25.5591i			1.12300i
$519$	−37.4935	−	6.76399i	−1.64578	−	0.296906i
$520$		−	1.17920i		−	0.0517115i
$521$	−42.4688			−1.86059			−0.930295	−	0.366811i	$-0.880449\pi$
$521$	−42.4688			−1.86059			−0.930295	+	0.366811i	$0.880449\pi$
$522$	−25.7993	−	9.62174i	−1.12920	−	0.421132i
$523$		−	15.3784i		−	0.672452i	−0.941781	−	0.336226i	$-0.890849\pi$
$523$		−	15.3784i		−	0.672452i	0.941781	−	0.336226i	$-0.109151\pi$
$524$		−	24.8573i		−	1.08589i
$525$	8.24805	+	1.48798i	0.359974	+	0.0649409i
$526$		−	35.2310i		−	1.53615i
$527$	−17.6730			−0.769848
$528$	−0.248543	+	1.37770i	−0.0108164	+	0.0599567i
$529$	−20.3745	+	10.6714i	−0.885848	+	0.463976i
$530$		−	3.96174i		−	0.172087i
$531$	−1.85672	+	4.97853i	−0.0805750	+	0.216050i
$532$	23.7701			1.03057
$533$		−	8.38647i		−	0.363258i
$534$	−52.3499	−	9.44414i	−2.26540	−	0.408688i
$535$	−4.12172			−0.178198
$536$	31.0336			1.34045
$537$	−6.95227	−	1.25422i	−0.300013	−	0.0541235i
$538$	12.5697			0.541919
$539$	4.07923			0.175705
$540$	3.39614	−	5.72449i	0.146147	−	0.246343i
$541$	−2.37632			−0.102166			−0.0510829	−	0.998694i	$-0.516267\pi$
$541$	−2.37632			−0.102166			−0.0510829	+	0.998694i	$0.516267\pi$
$542$		−	45.3132i		−	1.94637i
$543$	25.4722	+	4.59530i	1.09312	+	0.197203i
$544$		−	35.1718i		−	1.50798i
$545$		−	5.94015i		−	0.254448i
$546$	−0.758310	+	4.20340i	−0.0324527	+	0.179889i
$547$	12.9615			0.554194			0.277097	−	0.960842i	$-0.410628\pi$
$547$	12.9615			0.554194			0.277097	+	0.960842i	$0.410628\pi$
$548$	−28.7602			−1.22858
$549$	−6.51063	+	17.4573i	−0.277867	+	0.745059i
$550$		−	44.9740i		−	1.91770i
$551$	−30.0046			−1.27824
$552$	1.41401	+	22.5027i	0.0601841	+	0.957777i
$553$	11.9223			0.506988
$554$			50.6468i			2.15178i
$555$	7.67504	+	1.38461i	0.325787	+	0.0587734i
$556$	5.27191			0.223579
$557$	−22.9363			−0.971844			−0.485922	−	0.874002i	$-0.661516\pi$
$557$	−22.9363			−0.971844			−0.485922	+	0.874002i	$0.661516\pi$
$558$	−7.05716	+	18.9227i	−0.298754	+	0.801064i
$559$		−	6.79172i		−	0.287259i
$560$			0.0795314i			0.00336081i
$561$	−7.50304	+	41.5902i	−0.316779	+	1.75594i
$562$			23.7132i			1.00028i
$563$	27.7083			1.16777			0.583883	−	0.811838i	$-0.301533\pi$
$563$	27.7083			1.16777			0.583883	+	0.811838i	$0.301533\pi$
$564$	27.4242	+	4.94744i	1.15477	+	0.208325i
$565$	1.61665			0.0680131
$566$	−30.7939			−1.29436
$567$	−5.89333	+	6.80211i	−0.247497	+	0.285662i
$568$	−34.5364			−1.44911
$569$	2.96527			0.124311			0.0621554	−	0.998066i	$-0.480203\pi$
$569$	2.96527			0.124311			0.0621554	+	0.998066i	$0.480203\pi$
$570$	2.09469	−	11.6111i	0.0877371	−	0.486336i
$571$		−	3.31200i		−	0.138603i	−0.997596	−	0.0693015i	$-0.977923\pi$
$571$		−	3.31200i		−	0.138603i	0.997596	−	0.0693015i	$-0.0220770\pi$
$572$	14.0898			0.589122
$573$	1.90179	−	10.5418i	0.0794484	−	0.440391i
$574$		−	17.6548i		−	0.736896i
$575$	5.54417	+	22.5345i	0.231208	+	0.939753i
$576$	−36.5451	−	13.6294i	−1.52271	−	0.567890i
$577$	19.0098			0.791388			0.395694	−	0.918382i	$-0.370504\pi$
$577$	19.0098			0.791388			0.395694	+	0.918382i	$0.370504\pi$
$578$		−	42.7843i		−	1.77959i
$579$	0.463457	−	2.56899i	0.0192606	−	0.106764i
$580$			5.16017i			0.214264i
$581$			7.67599i			0.318454i
$582$	−3.40913	+	18.8972i	−0.141313	+	0.783313i
$583$	17.6709			0.731852
$584$		−	3.53509i		−	0.146283i
$585$	1.22114	+	0.455420i	0.0504880	+	0.0188293i
$586$			23.1483i			0.956248i
$587$			14.1732i			0.584992i	0.956267	+	0.292496i	$0.0944858\pi$
$587$			14.1732i			0.584992i	−0.956267	+	0.292496i	$0.905514\pi$
$588$	−0.981346	+	5.43971i	−0.0404700	+	0.224330i
$589$			22.0072i			0.906791i
$590$	1.61982			0.0666868
$591$	17.8265	+	3.21597i	0.733283	+	0.132287i
$592$		−	2.22268i		−	0.0913517i
$593$		−	27.0452i		−	1.11061i	−0.831646	−	0.555306i	$-0.812601\pi$
$593$		−	27.0452i		−	1.11061i	0.831646	−	0.555306i	$-0.187399\pi$
$594$	41.5352	+	24.6414i	1.70421	+	1.01105i
$595$			2.40091i			0.0984275i
$596$	15.5785			0.638121
$597$	15.1474	+	2.73265i	0.619941	+	0.111840i
$598$	−11.4841	+	2.82544i	−0.469620	+	0.115541i
$599$			15.3154i			0.625772i	0.949791	+	0.312886i	$0.101296\pi$
$599$			15.3154i			0.625772i	−0.949791	+	0.312886i	$0.898704\pi$
$600$	22.3881	+	4.03890i	0.913989	+	0.164887i
$601$	−30.7671			−1.25502			−0.627508	−	0.778610i	$-0.715925\pi$
$601$	−30.7671			−1.25502			−0.627508	+	0.778610i	$0.715925\pi$
$602$		−	14.2976i		−	0.582726i
$603$	−11.9855	+	32.1374i	−0.488087	+	1.30873i
$604$	−37.3527			−1.51986
$605$	−2.26388			−0.0920400
$606$	6.59646	−	36.5649i	0.267963	−	1.48535i
$607$	28.2704			1.14746			0.573729	−	0.819045i	$-0.305496\pi$
$607$	28.2704			1.14746			0.573729	+	0.819045i	$0.305496\pi$
$608$	−43.7975			−1.77622
$609$	1.23874	−	6.86645i	0.0501961	−	0.278243i
$610$	5.67990			0.229972
$611$			5.45650i			0.220746i
$612$	−53.6561	−	20.0108i	−2.16892	−	0.808890i
$613$		−	11.6874i		−	0.472049i	−0.971747	−	0.236024i	$-0.924155\pi$
$613$		−	11.6874i		−	0.472049i	0.971747	−	0.236024i	$-0.0758445\pi$
$614$			44.3273i			1.78890i
$615$	−5.30148	−	0.956409i	−0.213776	−	0.0385661i
$616$	11.0724			0.446121
$617$	44.0896			1.77498			0.887490	−	0.460827i	$-0.152447\pi$
$617$	44.0896			1.77498			0.887490	+	0.460827i	$0.152447\pi$
$618$	0.113180	−	0.627367i	0.00455275	−	0.0252364i
$619$		−	42.2920i		−	1.69986i	−0.526896	−	0.849930i	$-0.676644\pi$
$619$		−	42.2920i		−	1.69986i	0.526896	−	0.849930i	$-0.323356\pi$
$620$	3.78478			0.152000
$621$	−23.8491	−	7.22645i	−0.957030	−	0.289988i
$622$	−71.3111			−2.85931
$623$		−	13.4794i		−	0.540042i
$624$	0.0659446	−	0.365538i	0.00263990	−	0.0146332i
$625$	22.6092			0.904369
$626$	39.5160			1.57938
$627$	51.7900	+	9.34312i	2.06829	+	0.373128i
$628$			17.2178i			0.687064i
$629$		−	67.0987i		−	2.67540i
$630$	2.57069	+	0.958727i	0.102419	+	0.0381966i
$631$		−	6.21589i		−	0.247451i	−0.992316	−	0.123725i	$-0.960516\pi$
$631$		−	6.21589i		−	0.247451i	0.992316	−	0.123725i	$-0.0394842\pi$
$632$	32.3613			1.28726
$633$	4.53044	−	25.1127i	0.180069	−	0.998141i
$634$	6.58953			0.261704
$635$	6.54529			0.259742
$636$	−4.25111	+	23.5644i	−0.168567	+	0.934387i
$637$	−1.08232			−0.0428831
$638$	−37.4406			−1.48229
$639$	13.3383	−	35.7646i	0.527654	−	1.41483i
$640$			7.16984i			0.283413i
$641$	29.3975			1.16113			0.580565	−	0.814214i	$-0.302832\pi$
$641$	29.3975			1.16113			0.580565	+	0.814214i	$0.302832\pi$
$642$	39.8800	+	7.19452i	1.57394	+	0.283945i
$643$			2.56346i			0.101093i	0.998722	+	0.0505466i	$0.0160963\pi$
$643$			2.56346i			0.101093i	−0.998722	+	0.0505466i	$0.983904\pi$
$644$	−14.8618	+	3.65646i	−0.585638	+	0.144085i
$645$	−4.29336	−	0.774540i	−0.169051	−	0.0304975i
$646$	−101.510			−3.99385
$647$			31.4797i			1.23759i	0.785551	+	0.618797i	$0.212380\pi$
$647$			31.4797i			1.23759i	−0.785551	+	0.618797i	$0.787620\pi$
$648$	−15.9965	+	18.4633i	−0.628404	+	0.725306i
$649$			7.22498i			0.283605i
$650$			11.9327i			0.468040i
$651$	−5.03627	−	0.908564i	−0.197387	−	0.0356094i
$652$	−4.47286			−0.175171
$653$		−	15.2353i		−	0.596205i	−0.954534	−	0.298102i	$-0.903646\pi$
$653$		−	15.2353i		−	0.596205i	0.954534	−	0.298102i	$-0.0963537\pi$
$654$	−10.3686	+	57.4743i	−0.405445	+	2.24742i
$655$		−	3.12645i		−	0.122160i
$656$			1.53530i			0.0599435i
$657$	3.66081	+	1.36529i	0.142822	+	0.0532649i
$658$			11.4867i			0.447800i
$659$	−35.0017			−1.36347			−0.681737	−	0.731597i	$-0.738775\pi$
$659$	−35.0017			−1.36347			−0.681737	+	0.731597i	$0.738775\pi$
$660$	1.60682	−	8.90679i	0.0625455	−	0.346696i
$661$		−	33.0763i		−	1.28652i	−0.765648	−	0.643260i	$-0.777582\pi$
$661$		−	33.0763i		−	1.28652i	0.765648	−	0.643260i	$-0.222418\pi$
$662$			78.1383i			3.03693i
$663$	1.99074	−	11.0349i	0.0773141	−	0.428561i
$664$			20.8353i			0.808567i
$665$	2.98971			0.115936
$666$	−71.8436	−	26.7938i	−2.78388	−	1.03824i
$667$	18.7598	−	4.61549i	0.726383	−	0.178712i
$668$		−	7.79597i		−	0.301635i
$669$	−6.37048	+	35.3123i	−0.246297	+	1.36525i
$670$	10.4562			0.403958
$671$			25.3345i			0.978027i
$672$	1.80817	−	10.0229i	0.0697518	−	0.386642i
$673$	−14.7737			−0.569483			−0.284742	−	0.958604i	$-0.591908\pi$
$673$	−14.7737			−0.569483			−0.284742	+	0.958604i	$0.591908\pi$
$674$	−4.14466			−0.159646
$675$	−12.8290	+	21.6244i	−0.493790	+	0.832325i
$676$	37.7487			1.45187
$677$	−20.8941			−0.803025			−0.401512	−	0.915854i	$-0.631515\pi$
$677$	−20.8941			−0.803025			−0.401512	+	0.915854i	$0.631515\pi$
$678$	−15.6420	−	2.82189i	−0.600729	−	0.108374i
$679$	−4.86578			−0.186731
$680$			6.51689i			0.249911i
$681$	−4.75319	+	26.3475i	−0.182143	+	1.00964i
$682$			27.4612i			1.05154i
$683$		−	29.9778i		−	1.14707i	−0.819182	−	0.573534i	$-0.805572\pi$
$683$		−	29.9778i		−	1.14707i	0.819182	−	0.573534i	$-0.194428\pi$
$684$	−24.9184	+	66.8150i	−0.952778	+	2.55473i
$685$	−3.61735			−0.138212
$686$	−2.27845			−0.0869915
$687$	−29.9987	−	5.41189i	−1.14452	−	0.206476i
$688$			1.24335i			0.0474024i
$689$	−4.68852			−0.178618
$690$	0.476423	+	7.58185i	0.0181371	+	0.288636i
$691$	43.2636			1.64582			0.822912	−	0.568169i	$-0.192348\pi$
$691$	43.2636			1.64582			0.822912	+	0.568169i	$0.192348\pi$
$692$		−	70.1973i		−	2.66850i
$693$	−4.27628	+	11.4662i	−0.162443	+	0.435566i
$694$	59.2380			2.24864
$695$	0.663080			0.0251521
$696$	3.36236	−	18.6379i	0.127450	−	0.706469i
$697$			46.3479i			1.75555i
$698$		−	51.8418i		−	1.96224i
$699$	−15.0479	−	2.71471i	−0.569164	−	0.102680i
$700$			15.4424i			0.583668i
$701$	8.63263			0.326050			0.163025	−	0.986622i	$-0.447875\pi$
$701$	8.63263			0.326050			0.163025	+	0.986622i	$0.447875\pi$
$702$	−11.0203	−	6.53797i	−0.415935	−	0.246760i
$703$	−83.5543			−3.15131
$704$	−53.0353			−1.99884
$705$	3.44931	+	0.622269i	0.129908	+	0.0234360i
$706$	52.7122			1.98385
$707$	9.41499			0.354087
$708$	−9.63462	−	1.73813i	−0.362091	−	0.0653228i
$709$		−	23.5821i		−	0.885644i	−0.896609	−	0.442822i	$-0.853977\pi$
$709$		−	23.5821i		−	0.885644i	0.896609	−	0.442822i	$-0.146023\pi$
$710$	−11.6364			−0.436706
$711$	−12.4982	+	33.5122i	−0.468720	+	1.25680i
$712$		−	36.5878i		−	1.37119i
$713$	−3.38528	−	13.7596i	−0.126780	−	0.515300i
$714$	4.19081	−	23.2301i	0.156837	−	0.869366i
$715$	1.77215			0.0662748
$716$		−	13.0164i		−	0.486445i
$717$	−22.8453	−	4.12138i	−0.853172	−	0.153916i
$718$			74.9970i			2.79886i
$719$		−	24.4649i		−	0.912387i	−0.889881	−	0.456193i	$-0.849213\pi$
$719$		−	24.4649i		−	0.912387i	0.889881	−	0.456193i	$-0.150787\pi$
$720$	−0.223553	−	0.0833733i	−0.00833134	−	0.00310714i
$721$	0.161539			0.00601602
$722$			83.1139i			3.09318i
$723$	−23.3420	−	4.21099i	−0.868097	−	0.156608i
$724$			47.6904i			1.77240i
$725$		−	19.4927i		−	0.723940i
$726$	21.9044	+	3.95164i	0.812948	+	0.146659i
$727$		−	11.7507i		−	0.435811i	−0.975970	−	0.217905i	$-0.930078\pi$
$727$		−	11.7507i		−	0.435811i	0.975970	−	0.217905i	$-0.0699224\pi$
$728$	−2.93779			−0.108882
$729$	−12.9419	−	23.6961i	−0.479329	−	0.877635i
$730$		−	1.19108i		−	0.0440839i
$731$			37.5345i			1.38826i
$732$	−33.7839	−	6.09476i	−1.24869	−	0.225269i
$733$		−	24.6937i		−	0.912084i	−0.889958	−	0.456042i	$-0.849267\pi$
$733$		−	24.6937i		−	0.912084i	0.889958	−	0.456042i	$-0.150733\pi$
$734$	64.1513			2.36787
$735$	−0.123430	+	0.684185i	−0.00455278	+	0.0252366i
$736$	27.3836	−	6.73719i	1.00937	−	0.248336i
$737$			46.6386i			1.71795i
$738$	49.6254	+	18.5076i	1.82674	+	0.681274i
$739$	38.3065			1.40913			0.704564	−	0.709640i	$-0.251142\pi$
$739$	38.3065			1.40913			0.704564	+	0.709640i	$0.251142\pi$
$740$			14.3696i			0.528237i
$741$	−13.7412	−	2.47896i	−0.504794	−	0.0910670i
$742$	−9.87003			−0.362340
$743$	−0.715971			−0.0262664			−0.0131332	−	0.999914i	$-0.504181\pi$
$743$	−0.715971			−0.0262664			−0.0131332	+	0.999914i	$0.504181\pi$
$744$	−13.6702	−	2.46616i	−0.501173	−	0.0904137i
$745$	1.95941			0.0717871
$746$	23.7572			0.869814
$747$	−21.5763	−	8.04680i	−0.789436	−	0.294417i
$748$	−77.8672			−2.84711
$749$			10.2686i			0.375206i
$750$	15.3376	+	2.76697i	0.560051	+	0.101036i
$751$		−	29.7182i		−	1.08443i	−0.840239	−	0.542216i	$-0.817586\pi$
$751$		−	29.7182i		−	1.08443i	0.840239	−	0.542216i	$-0.182414\pi$
$752$		−	0.998916i		−	0.0364267i
$753$	4.21265	−	23.3512i	0.153518	−	0.850965i
$754$	9.93393			0.361772
$755$	−4.69808			−0.170981
$756$	−14.2616	−	8.46093i	−0.518690	−	0.307721i
$757$		−	15.3459i		−	0.557755i	−0.960327	−	0.278877i	$-0.910038\pi$
$757$		−	15.3459i		−	0.557755i	0.960327	−	0.278877i	$-0.0899623\pi$
$758$	−44.3517			−1.61093
$759$	−33.8179	+	2.12503i	−1.22751	+	0.0771336i
$760$	8.11512			0.294366
$761$		−	44.0409i		−	1.59648i	−0.602339	−	0.798240i	$-0.705764\pi$
$761$		−	44.0409i		−	1.59648i	0.602339	−	0.798240i	$-0.294236\pi$
$762$	−63.3295	−	11.4249i	−2.29418	−	0.413880i
$763$	−14.7989			−0.535756
$764$	19.7369			0.714057
$765$	−6.74866	−	2.51689i	−0.243998	−	0.0909982i
$766$			10.2472i			0.370246i
$767$		−	1.91697i		−	0.0692177i
$768$	4.51912	−	25.0500i	0.163070	−	0.903914i
$769$			15.4202i			0.556066i	0.960572	+	0.278033i	$0.0896824\pi$
$769$			15.4202i			0.556066i	−0.960572	+	0.278033i	$0.910318\pi$
$770$	3.73065			0.134443
$771$	−24.6126	−	4.44022i	−0.886403	−	0.159911i
$772$	4.80980			0.173108
$773$	11.7595			0.422961			0.211481	−	0.977382i	$-0.432171\pi$
$773$	11.7595			0.422961			0.211481	+	0.977382i	$0.432171\pi$
$774$	40.1888	+	14.9882i	1.44456	+	0.538741i
$775$	−14.2971			−0.513567
$776$	−13.2074			−0.474118
$777$	3.44953	−	19.1211i	0.123751	−	0.685966i
$778$			43.6310i			1.56425i
$779$	57.7145			2.06784
$780$	−0.426330	+	2.36319i	−0.0152651	+	0.0846159i
$781$		−	51.9026i		−	1.85722i
$782$	63.4670	−	15.6148i	2.26958	−	0.558385i
$783$	18.0022	+	10.6801i	0.643346	+	0.381675i
$784$	0.198139			0.00707640
$785$			2.16558i			0.0772930i
$786$	−5.45726	+	30.2502i	−0.194654	+	1.07899i
$787$			39.6898i			1.41479i	0.706819	+	0.707394i	$0.250129\pi$
$787$			39.6898i			1.41479i	−0.706819	+	0.707394i	$0.749871\pi$
$788$			33.3756i			1.18896i
$789$	−4.75488	+	26.3568i	−0.169278	+	0.938327i
$790$	10.9035			0.387930
$791$		−	4.02762i		−	0.143206i
$792$	−11.6073	+	31.1233i	−0.412448	+	1.10592i
$793$		−	6.72187i		−	0.238701i
$794$		−	58.6313i		−	2.08075i
$795$	−0.534688	+	2.96383i	−0.0189634	+	0.105116i
$796$			28.3597i			1.00518i
$797$	12.9779			0.459700			0.229850	−	0.973226i	$-0.426176\pi$
$797$	12.9779			0.459700			0.229850	+	0.973226i	$0.426176\pi$
$798$	−28.9272	−	5.21858i	−1.02401	−	0.184736i
$799$		−	30.1554i		−	1.06682i
$800$		−	28.4533i		−	1.00598i
$801$	37.8891	+	14.1306i	1.33874	+	0.499279i
$802$			28.3528i			1.00117i
$803$	5.31267			0.187480
$804$	−62.1932	−	11.2199i	−2.19339	−	0.395696i
$805$	−1.86926	+	0.459895i	−0.0658828	+	0.0162092i
$806$		−	7.28614i		−	0.256643i
$807$	−9.40357	−	1.69644i	−0.331021	−	0.0597176i
$808$	25.5556			0.899041
$809$			6.56922i			0.230962i	0.993310	+	0.115481i	$0.0368409\pi$
$809$			6.56922i			0.230962i	−0.993310	+	0.115481i	$0.963159\pi$
$810$	−5.38973	+	6.22085i	−0.189376	+	0.218578i
$811$	−23.4473			−0.823345			−0.411673	−	0.911332i	$-0.635055\pi$
$811$	−23.4473			−0.823345			−0.411673	+	0.911332i	$0.635055\pi$
$812$	12.8557			0.451147
$813$	−6.11560	+	33.8994i	−0.214483	+	1.18891i
$814$	−104.261			−3.65436
$815$	−0.562578			−0.0197063
$816$	−0.364444	+	2.02015i	−0.0127581	+	0.0707194i
$817$	46.7396			1.63521
$818$			45.9077i			1.60512i
$819$	1.13460	−	3.04227i	0.0396463	−	0.106306i
$820$		−	9.92569i		−	0.346620i
$821$			21.5940i			0.753637i	0.926287	+	0.376819i	$0.122982\pi$
$821$			21.5940i			0.753637i	−0.926287	+	0.376819i	$0.877018\pi$
$822$	34.9999	+	6.31413i	1.22076	+	0.220231i
$823$	18.6019			0.648422			0.324211	−	0.945985i	$-0.394901\pi$
$823$	18.6019			0.648422			0.324211	+	0.945985i	$0.394901\pi$
$824$	0.438472			0.0152749
$825$	−6.06982	+	33.6457i	−0.211324	+	1.17139i
$826$		−	4.03550i		−	0.140413i
$827$	28.4757			0.990196			0.495098	−	0.868837i	$-0.335132\pi$
$827$	28.4757			0.990196			0.495098	+	0.868837i	$0.335132\pi$
$828$	5.30187	−	45.6079i	0.184253	−	1.58498i
$829$	27.5852			0.958075			0.479038	−	0.877794i	$-0.340986\pi$
$829$	27.5852			0.958075			0.479038	+	0.877794i	$0.340986\pi$
$830$			7.02006i			0.243670i
$831$	6.83543	−	37.8895i	0.237118	−	1.31437i
$832$	14.0716			0.487844
$833$	5.98146			0.207245
$834$	−6.41568	−	1.15742i	−0.222157	−	0.0400780i
$835$		−	0.980547i		−	0.0339332i
$836$			96.9637i			3.35356i
$837$	7.83342	−	13.2039i	0.270763	−	0.456394i
$838$			47.1588i			1.62907i
$839$	17.9942			0.621229			0.310614	−	0.950536i	$-0.399465\pi$
$839$	17.9942			0.621229			0.310614	+	0.950536i	$0.399465\pi$
$840$	−0.335031	+	1.85712i	−0.0115597	+	0.0640766i
$841$	12.7724			0.440429
$842$	0.882185			0.0304021
$843$	3.20040	−	17.7402i	0.110228	−	0.611004i
$844$	47.0173			1.61840
$845$	4.74789			0.163332
$846$	−32.2879	−	12.0416i	−1.11008	−	0.414000i
$847$			5.64009i			0.193796i
$848$	0.858323			0.0294749
$849$	23.0373	+	4.15602i	0.790638	+	0.142634i
$850$		−	65.9464i		−	2.26194i
$851$	52.2407	−	12.8528i	1.79079	−	0.440589i
$852$	69.2129	+	12.4863i	2.37119	+	0.427773i
$853$	22.7456			0.778795			0.389398	−	0.921070i	$-0.372683\pi$
$853$	22.7456			0.778795			0.389398	+	0.921070i	$0.372683\pi$
$854$		−	14.1505i		−	0.484221i
$855$	−3.13414	+	8.40373i	−0.107185	+	0.287401i
$856$			27.8725i			0.952663i
$857$			16.8163i			0.574433i	0.957866	+	0.287216i	$0.0927299\pi$
$857$			16.8163i			0.574433i	−0.957866	+	0.287216i	$0.907270\pi$
$858$	−17.1466	−	3.09332i	−0.585376	−	0.105604i
$859$	6.40087			0.218395			0.109197	−	0.994020i	$-0.465172\pi$
$859$	6.40087			0.218395			0.109197	+	0.994020i	$0.465172\pi$
$860$		−	8.03824i		−	0.274102i
$861$	−2.38273	+	13.2078i	−0.0812034	+	0.450119i
$862$			57.1730i			1.94732i
$863$			15.7675i			0.536731i	0.963317	+	0.268365i	$0.0864835\pi$
$863$			15.7675i			0.536731i	−0.963317	+	0.268365i	$0.913517\pi$
$864$	26.2777	+	15.5896i	0.893985	+	0.530371i
$865$		−	8.82914i		−	0.300200i
$866$	83.2148			2.82776
$867$	−5.77429	+	32.0075i	−0.196105	+	1.08703i
$868$		−	9.42915i		−	0.320046i
$869$			48.6338i			1.64979i
$870$	1.13288	−	6.27970i	0.0384084	−	0.212902i
$871$		−	12.3744i		−	0.419290i
$872$	−40.1693			−1.36030
$873$	5.10083	−	13.6771i	0.172637	−	0.462900i
$874$	−19.4443	−	79.0319i	−0.657712	−	2.67329i
$875$			3.94924i			0.133509i
$876$	−1.27808	+	7.08452i	−0.0431822	+	0.239364i
$877$	−34.5472			−1.16658			−0.583288	−	0.812265i	$-0.698234\pi$
$877$	−34.5472			−1.16658			−0.583288	+	0.812265i	$0.698234\pi$
$878$		−	8.87020i		−	0.299355i
$879$	3.12416	−	17.3176i	0.105375	−	0.584107i
$880$	−0.324427			−0.0109364
$881$	15.8201			0.532993			0.266497	−	0.963836i	$-0.414134\pi$
$881$	15.8201			0.532993			0.266497	+	0.963836i	$0.414134\pi$
$882$	2.38851	−	6.40444i	0.0804253	−	0.215649i
$883$	−3.65540			−0.123014			−0.0615069	−	0.998107i	$-0.519591\pi$
$883$	−3.65540			−0.123014			−0.0615069	+	0.998107i	$0.519591\pi$
$884$	20.6601			0.694875
$885$	−1.21181	−	0.218615i	−0.0407344	−	0.00734865i
$886$	25.9192			0.870771
$887$		−	52.0439i		−	1.74746i	−0.486408	−	0.873732i	$-0.661693\pi$
$887$		−	52.0439i		−	1.74746i	0.486408	−	0.873732i	$-0.338307\pi$
$888$	9.36321	−	51.9013i	0.314209	−	1.74169i
$889$		−	16.3065i		−	0.546903i
$890$		−	12.3276i		−	0.413222i
$891$	−27.7473	−	24.0402i	−0.929571	−	0.805378i
$892$	−66.1134			−2.21364
$893$	−37.5508			−1.25659
$894$	−18.9584	−	3.42017i	−0.634063	−	0.114388i
$895$		−	1.63715i		−	0.0547239i
$896$	17.8625			0.596744
$897$	8.97273	−	0.563822i	0.299591	−	0.0188255i
$898$	−24.8035			−0.827703
$899$			11.9023i			0.396963i
$900$	−43.4068	−	16.1884i	−1.44689	−	0.539613i
$901$	25.9112			0.863226
$902$	72.0178			2.39793
$903$	−1.92964	+	10.6962i	−0.0642144	+	0.355947i
$904$		−	10.9324i		−	0.363605i
$905$			5.99831i			0.199391i
$906$	45.4566	+	8.20057i	1.51020	+	0.272446i
$907$		−	10.7410i		−	0.356648i	−0.983972	−	0.178324i	$-0.942932\pi$
$907$		−	10.7410i		−	0.356648i	0.983972	−	0.178324i	$-0.0570676\pi$
$908$	−49.3290			−1.63704
$909$	−9.86980	+	26.4644i	−0.327361	+	0.877770i
$910$	−0.989834			−0.0328127
$911$	−13.1393			−0.435324			−0.217662	−	0.976024i	$-0.569843\pi$
$911$	−13.1393			−0.435324			−0.217662	+	0.976024i	$0.569843\pi$
$912$	2.51558	+	0.453821i	0.0832992	+	0.0150275i
$913$	−31.3121			−1.03628
$914$	−33.3415			−1.10284
$915$	−4.24921	−	0.766575i	−0.140475	−	0.0253422i
$916$		−	56.1650i		−	1.85574i
$917$	−7.78903			−0.257217
$918$	60.9039	+	36.1322i	2.01013	+	1.19254i
$919$			35.4767i			1.17027i	0.810936	+	0.585134i	$0.198958\pi$
$919$			35.4767i			1.17027i	−0.810936	+	0.585134i	$0.801042\pi$
$920$	−5.07382	+	1.24831i	−0.167279	+	0.0411557i
$921$	5.98253	−	33.1618i	0.197131	−	1.09272i
$922$	3.67601			0.121063
$923$			13.7711i			0.453280i
$924$	−22.1898	−	4.00313i	−0.729991	−	0.131693i
$925$		−	54.2816i		−	1.78477i
$926$			11.5590i			0.379851i
$927$	−0.169342	+	0.454066i	−0.00556193	+	0.0149135i
$928$	−23.6872			−0.777571
$929$			2.88165i			0.0945439i	0.998882	+	0.0472720i	$0.0150527\pi$
$929$			2.88165i			0.0945439i	−0.998882	+	0.0472720i	$0.984947\pi$
$930$	−4.60591	−	0.830925i	−0.151034	−	0.0272471i
$931$		−	7.44838i		−	0.244111i
$932$		−	28.1735i		−	0.922852i
$933$	53.3488	+	9.62433i	1.74656	+	0.315087i
$934$		−	52.4561i		−	1.71642i
$935$	−9.79384			−0.320293
$936$	3.07971	−	8.25779i	0.100663	−	0.269914i
$937$			4.26047i			0.139183i	0.997576	+	0.0695917i	$0.0221696\pi$
$937$			4.26047i			0.139183i	−0.997576	+	0.0695917i	$0.977830\pi$
$938$		−	26.0499i		−	0.850560i
$939$	−29.5624	−	5.33318i	−0.964734	−	0.174042i
$940$			6.45796i			0.210636i
$941$	−7.69462			−0.250837			−0.125419	−	0.992104i	$-0.540027\pi$
$941$	−7.69462			−0.250837			−0.125419	+	0.992104i	$0.540027\pi$
$942$	3.78006	−	20.9533i	0.123161	−	0.682695i
$943$	−36.0849	+	8.87798i	−1.17509	+	0.289107i
$944$			0.350937i			0.0114220i
$945$	−1.79377	−	1.06418i	−0.0583514	−	0.0346179i
$946$	58.3231			1.89625
$947$		−	36.9765i		−	1.20157i	−0.799409	−	0.600787i	$-0.794854\pi$
$947$		−	36.9765i		−	1.20157i	0.799409	−	0.600787i	$-0.205146\pi$
$948$	−64.8538	−	11.6999i	−2.10635	−	0.379995i
$949$	−1.40958			−0.0457570
$950$	−82.1194			−2.66430
$951$	−4.92972	−	0.889341i	−0.159857	−	0.0288389i
$952$	16.2358			0.526204
$953$	−31.6780			−1.02615			−0.513076	−	0.858343i	$-0.671494\pi$
$953$	−31.6780			−1.02615			−0.513076	+	0.858343i	$0.671494\pi$
$954$	10.3468	−	27.7435i	0.334991	−	0.898229i
$955$	2.48243			0.0803297
$956$		−	42.7720i		−	1.38335i
$957$	28.0098	+	5.05309i	0.905429	+	0.163343i
$958$			71.1516i			2.29881i
$959$			9.01203i			0.291014i
$960$	1.60475	−	8.89530i	0.0517931	−	0.287095i
$961$	−22.2702			−0.718392
$962$	27.6631			0.891896
$963$	−28.8638	−	10.7646i	−0.930123	−	0.346886i
$964$		−	43.7020i		−	1.40755i
$965$	0.604957			0.0194743
$966$	18.8889	−	1.18693i	0.607742	−	0.0381888i
$967$	−43.3391			−1.39369			−0.696845	−	0.717221i	$-0.745414\pi$
$967$	−43.3391			−1.39369			−0.696845	+	0.717221i	$0.745414\pi$
$968$			15.3092i			0.492055i
$969$	75.9407	+	13.7000i	2.43957	+	0.440108i
$970$	−4.44999			−0.142880
$971$	33.6735			1.08063			0.540317	−	0.841461i	$-0.318304\pi$
$971$	33.6735			1.08063			0.540317	+	0.841461i	$0.318304\pi$
$972$	38.7332	−	31.2181i	1.24237	−	1.00132i
$973$		−	1.65195i		−	0.0529592i
$974$			54.7553i			1.75447i
$975$	1.61047	−	8.92704i	0.0515764	−	0.285894i
$976$			1.23057i			0.0393895i
$977$	42.9550			1.37425			0.687126	−	0.726538i	$-0.258872\pi$
$977$	42.9550			1.37425			0.687126	+	0.726538i	$0.258872\pi$
$978$	5.44327	+	0.981988i	0.174057	+	0.0314005i
$979$	54.9856			1.75735
$980$	−1.28097			−0.0409189
$981$	15.5138	−	41.5979i	0.495317	−	1.32812i
$982$	61.4082			1.95961
$983$	−21.8584			−0.697173			−0.348587	−	0.937277i	$-0.613338\pi$
$983$	−21.8584			−0.697173			−0.348587	+	0.937277i	$0.613338\pi$
$984$	−6.46757	+	35.8504i	−0.206178	+	1.14287i
$985$			4.19785i			0.133755i
$986$	−54.9000			−1.74837
$987$	1.55028	−	8.59338i	0.0493460	−	0.273530i
$988$		−	25.7269i		−	0.818481i
$989$	−29.2231	+	7.18977i	−0.929240	+	0.228621i
$990$	−3.91086	+	10.4864i	−0.124295	+	0.333280i
$991$	10.3004			0.327204			0.163602	−	0.986526i	$-0.447689\pi$
$991$	10.3004			0.327204			0.163602	+	0.986526i	$0.447689\pi$
$992$			17.3736i			0.551614i
$993$	10.5458	−	58.4563i	0.334659	−	1.85505i
$994$			28.9901i			0.919511i
$995$			3.56697i			0.113080i
$996$	7.53280	−	41.7552i	0.238686	−	1.32306i
$997$	−16.0790			−0.509227			−0.254613	−	0.967043i	$-0.581948\pi$
$997$	−16.0790			−0.509227			−0.254613	+	0.967043i	$0.581948\pi$
$998$		−	4.16676i		−	0.131897i
$999$	50.1310	+	29.7410i	1.58607	+	0.940963i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.e.a.344.5	✓	48
3.2	odd	2	inner	483.2.e.a.344.44	yes	48
23.22	odd	2	inner	483.2.e.a.344.6	yes	48
69.68	even	2	inner	483.2.e.a.344.43	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.e.a.344.5	✓	48	1.1	even	1	trivial
483.2.e.a.344.6	yes	48	23.22	odd	2	inner
483.2.e.a.344.43	yes	48	69.68	even	2	inner
483.2.e.a.344.44	yes	48	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.27845i q^{2} +(-0.307505 + 1.70454i) q^{3} -3.19131 q^{4} -0.401391 q^{5} +(3.88369 + 0.700634i) q^{6} +1.00000i q^{7} +2.71435i q^{8} +(-2.81088 - 1.04831i) q^{9} +O(q^{10})\)	\(q-2.27845i q^{2} +(-0.307505 + 1.70454i) q^{3} -3.19131 q^{4} -0.401391 q^{5} +(3.88369 + 0.700634i) q^{6} +1.00000i q^{7} +2.71435i q^{8} +(-2.81088 - 1.04831i) q^{9} +0.914548i q^{10} -4.07923 q^{11} +(0.981346 - 5.43971i) q^{12} +1.08232 q^{13} +2.27845 q^{14} +(0.123430 - 0.684185i) q^{15} -0.198139 q^{16} -5.98146 q^{17} +(-2.38851 + 6.40444i) q^{18} +7.44838i q^{19} +1.28097 q^{20} +(-1.70454 - 0.307505i) q^{21} +9.29430i q^{22} +(-1.14575 - 4.65696i) q^{23} +(-4.62670 - 0.834675i) q^{24} -4.83889 q^{25} -2.46601i q^{26} +(2.65124 - 4.46889i) q^{27} -3.19131i q^{28} +4.02834i q^{29} +(-1.55888 - 0.281228i) q^{30} +2.95463 q^{31} +5.88014i q^{32} +(1.25438 - 6.95319i) q^{33} +13.6284i q^{34} -0.401391i q^{35} +(8.97041 + 3.34548i) q^{36} +11.2178i q^{37} +16.9707 q^{38} +(-0.332819 + 1.84485i) q^{39} -1.08951i q^{40} -7.74860i q^{41} +(-0.700634 + 3.88369i) q^{42} -6.27514i q^{43} +13.0181 q^{44} +(1.12826 + 0.420781i) q^{45} +(-10.6106 + 2.61054i) q^{46} +5.04148i q^{47} +(0.0609289 - 0.337735i) q^{48} -1.00000 q^{49} +11.0251i q^{50} +(1.83933 - 10.1956i) q^{51} -3.45403 q^{52} -4.33191 q^{53} +(-10.1821 - 6.04070i) q^{54} +1.63737 q^{55} -2.71435 q^{56} +(-12.6960 - 2.29041i) q^{57} +9.17836 q^{58} -1.77117i q^{59} +(-0.393904 + 2.18345i) q^{60} -6.21061i q^{61} -6.73196i q^{62} +(1.04831 - 2.81088i) q^{63} +13.0013 q^{64} -0.434434 q^{65} +(-15.8425 - 2.85804i) q^{66} -11.4332i q^{67} +19.0887 q^{68} +(8.29027 - 0.520938i) q^{69} -0.914548 q^{70} +12.7236i q^{71} +(2.84547 - 7.62970i) q^{72} -1.30237 q^{73} +25.5591 q^{74} +(1.48798 - 8.24805i) q^{75} -23.7701i q^{76} -4.07923i q^{77} +(4.20340 + 0.758310i) q^{78} -11.9223i q^{79} +0.0795314 q^{80} +(6.80211 + 5.89333i) q^{81} -17.6548 q^{82} +7.67599 q^{83} +(5.43971 + 0.981346i) q^{84} +2.40091 q^{85} -14.2976 q^{86} +(-6.86645 - 1.23874i) q^{87} -11.0724i q^{88} -13.4794 q^{89} +(0.958727 - 2.57069i) q^{90} +1.08232i q^{91} +(3.65646 + 14.8618i) q^{92} +(-0.908564 + 5.03627i) q^{93} +11.4867 q^{94} -2.98971i q^{95} +(-10.0229 - 1.80817i) q^{96} +4.86578i q^{97} +2.27845i q^{98} +(11.4662 + 4.27628i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{3} - 40 q^{4} + 6 q^{6} + 4 q^{9}+O(q^{10}) \) 48 * q - 4 * q^3 - 40 * q^4 + 6 * q^6 + 4 * q^9	\( 48 q - 4 q^{3} - 40 q^{4} + 6 q^{6} + 4 q^{9} + 22 q^{12} - 8 q^{13} + 24 q^{16} - 14 q^{18} - 12 q^{24} + 88 q^{25} - 16 q^{27} - 8 q^{31} - 10 q^{36} + 8 q^{46} - 98 q^{48} - 48 q^{49} + 28 q^{52} - 28 q^{54} - 92 q^{58} + 92 q^{64} + 8 q^{69} + 8 q^{70} + 60 q^{72} + 40 q^{73} - 80 q^{75} + 114 q^{78} - 28 q^{81} - 20 q^{82} - 40 q^{85} - 28 q^{87} - 76 q^{93} - 12 q^{94} - 6 q^{96}+O(q^{100}) \) 48 * q - 4 * q^3 - 40 * q^4 + 6 * q^6 + 4 * q^9 + 22 * q^12 - 8 * q^13 + 24 * q^16 - 14 * q^18 - 12 * q^24 + 88 * q^25 - 16 * q^27 - 8 * q^31 - 10 * q^36 + 8 * q^46 - 98 * q^48 - 48 * q^49 + 28 * q^52 - 28 * q^54 - 92 * q^58 + 92 * q^64 + 8 * q^69 + 8 * q^70 + 60 * q^72 + 40 * q^73 - 80 * q^75 + 114 * q^78 - 28 * q^81 - 20 * q^82 - 40 * q^85 - 28 * q^87 - 76 * q^93 - 12 * q^94 - 6 * q^96

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