LMFDB - Embedded newform 1805.2.b.m.1084.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1084,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1805.1084");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.b (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:	$14.4129975648$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1084.6
Character	$\chi$	$=$	1805.1084
Dual form			1805.2.b.m.1084.35

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.42726i q^{2} -1.05699i q^{3} -3.89157 q^{4} +(0.123305 + 2.23267i) q^{5} -2.56557 q^{6} -4.52506i q^{7} +4.59133i q^{8} +1.88278 q^{9} +O(q^{10})$	\(q-2.42726i q^{2} -1.05699i q^{3} -3.89157 q^{4} +(0.123305 + 2.23267i) q^{5} -2.56557 q^{6} -4.52506i q^{7} +4.59133i q^{8} +1.88278 q^{9} +(5.41925 - 0.299292i) q^{10} +0.194403 q^{11} +4.11334i q^{12} +3.48815i q^{13} -10.9835 q^{14} +(2.35990 - 0.130331i) q^{15} +3.36119 q^{16} -6.60308i q^{17} -4.56999i q^{18} +(-0.479849 - 8.68858i) q^{20} -4.78292 q^{21} -0.471865i q^{22} -1.18472i q^{23} +4.85297 q^{24} +(-4.96959 + 0.550596i) q^{25} +8.46664 q^{26} -5.16103i q^{27} +17.6096i q^{28} -4.10574 q^{29} +(-0.316347 - 5.72807i) q^{30} -5.06679 q^{31} +1.02419i q^{32} -0.205481i q^{33} -16.0274 q^{34} +(10.1029 - 0.557960i) q^{35} -7.32698 q^{36} -4.20787i q^{37} +3.68693 q^{39} +(-10.2509 + 0.566132i) q^{40} -9.20454 q^{41} +11.6094i q^{42} -2.26312i q^{43} -0.756532 q^{44} +(0.232156 + 4.20362i) q^{45} -2.87562 q^{46} -5.95612i q^{47} -3.55273i q^{48} -13.4761 q^{49} +(1.33644 + 12.0625i) q^{50} -6.97936 q^{51} -13.5744i q^{52} +6.94598i q^{53} -12.5271 q^{54} +(0.0239707 + 0.434036i) q^{55} +20.7760 q^{56} +9.96568i q^{58} +2.39041 q^{59} +(-9.18370 + 0.507193i) q^{60} +4.79183 q^{61} +12.2984i q^{62} -8.51970i q^{63} +9.20835 q^{64} +(-7.78788 + 0.430105i) q^{65} -0.498754 q^{66} -5.22583i q^{67} +25.6964i q^{68} -1.25223 q^{69} +(-1.35431 - 24.5224i) q^{70} -5.85628 q^{71} +8.64448i q^{72} -6.54790i q^{73} -10.2136 q^{74} +(0.581972 + 5.25279i) q^{75} -0.879683i q^{77} -8.94912i q^{78} +5.47834 q^{79} +(0.414450 + 7.50442i) q^{80} +0.193213 q^{81} +22.3418i q^{82} +9.54544i q^{83} +18.6131 q^{84} +(14.7425 - 0.814190i) q^{85} -5.49318 q^{86} +4.33971i q^{87} +0.892567i q^{88} +14.4923 q^{89} +(10.2033 - 0.563501i) q^{90} +15.7841 q^{91} +4.61042i q^{92} +5.35552i q^{93} -14.4570 q^{94} +1.08255 q^{96} +7.41146i q^{97} +32.7101i q^{98} +0.366018 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 48 q^{4} + 6 q^{5} + 20 q^{6} - 52 q^{9}+O(q^{10}) $ 40 * q - 48 * q^4 + 6 * q^5 + 20 * q^6 - 52 * q^9	$ 40 q - 48 q^{4} + 6 q^{5} + 20 q^{6} - 52 q^{9} + 20 q^{11} + 40 q^{16} - 18 q^{20} - 92 q^{24} - 26 q^{25} + 76 q^{26} + 40 q^{30} + 4 q^{35} + 156 q^{36} - 80 q^{39} - 48 q^{44} - 22 q^{45} - 72 q^{49} - 32 q^{54} - 40 q^{55} + 80 q^{61} - 72 q^{64} + 16 q^{66} - 100 q^{74} - 66 q^{80} + 40 q^{81} + 44 q^{85} + 380 q^{96} - 128 q^{99}+O(q^{100}) $ 40 * q - 48 * q^4 + 6 * q^5 + 20 * q^6 - 52 * q^9 + 20 * q^11 + 40 * q^16 - 18 * q^20 - 92 * q^24 - 26 * q^25 + 76 * q^26 + 40 * q^30 + 4 * q^35 + 156 * q^36 - 80 * q^39 - 48 * q^44 - 22 * q^45 - 72 * q^49 - 32 * q^54 - 40 * q^55 + 80 * q^61 - 72 * q^64 + 16 * q^66 - 100 * q^74 - 66 * q^80 + 40 * q^81 + 44 * q^85 + 380 * q^96 - 128 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times$.

$n$	$362$	$1446$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	2.42726i		−	1.71633i	−0.513375	−	0.858165i	$-0.671605\pi$
$2$		−	2.42726i		−	1.71633i	0.513375	−	0.858165i	$-0.328395\pi$
$3$		−	1.05699i		−	0.610251i	−0.952312	−	0.305125i	$-0.901302\pi$
$3$		−	1.05699i		−	0.610251i	0.952312	−	0.305125i	$-0.0986984\pi$
$4$	−3.89157			−1.94579
$5$	0.123305	+	2.23267i	0.0551435	+	0.998478i
$5$	0.123305	+	2.23267i	0.0551435	+	0.998478i
$6$	−2.56557			−1.04739
$7$		−	4.52506i		−	1.71031i	−0.518371	−	0.855156i	$-0.673462\pi$
$7$		−	4.52506i		−	1.71031i	0.518371	−	0.855156i	$-0.326538\pi$
$8$			4.59133i			1.62328i
$9$	1.88278			0.627594
$10$	5.41925	−	0.299292i	1.71372	−	0.0946444i
$11$	0.194403			0.0586146			0.0293073	−	0.999570i	$-0.490670\pi$
$11$	0.194403			0.0586146			0.0293073	+	0.999570i	$0.490670\pi$
$12$			4.11334i			1.18742i
$13$			3.48815i			0.967440i	0.875223	+	0.483720i	$0.160715\pi$
$13$			3.48815i			0.967440i	−0.875223	+	0.483720i	$0.839285\pi$
$14$	−10.9835			−2.93546
$15$	2.35990	−	0.130331i	0.609322	−	0.0336513i
$16$	3.36119			0.840298
$17$		−	6.60308i		−	1.60148i	−0.599010	−	0.800741i	$-0.704439\pi$
$17$		−	6.60308i		−	1.60148i	0.599010	−	0.800741i	$-0.295561\pi$
$18$		−	4.56999i		−	1.07716i
$19$		0			0
$19$		0			0
$20$	−0.479849	−	8.68858i	−0.107297	−	1.94283i
$21$	−4.78292			−1.04372
$22$		−	0.471865i		−	0.100602i
$23$		−	1.18472i		−	0.247031i	−0.992343	−	0.123516i	$-0.960583\pi$
$23$		−	1.18472i		−	0.247031i	0.992343	−	0.123516i	$-0.0394169\pi$
$24$	4.85297			0.990608
$25$	−4.96959	+	0.550596i	−0.993918	+	0.110119i
$26$	8.46664			1.66045
$27$		−	5.16103i		−	0.993241i
$28$			17.6096i			3.32790i
$29$	−4.10574			−0.762417			−0.381208	−	0.924489i	$-0.624492\pi$
$29$	−4.10574			−0.762417			−0.381208	+	0.924489i	$0.624492\pi$
$30$	−0.316347	−	5.72807i	−0.0577568	−	1.04580i
$31$	−5.06679			−0.910023			−0.455011	−	0.890486i	$-0.650365\pi$
$31$	−5.06679			−0.910023			−0.455011	+	0.890486i	$0.650365\pi$
$32$			1.02419i			0.181052i
$33$		−	0.205481i		−	0.0357696i
$34$	−16.0274			−2.74867
$35$	10.1029	−	0.557960i	1.70771	−	0.0943125i
$36$	−7.32698			−1.22116
$37$		−	4.20787i		−	0.691770i	−0.938277	−	0.345885i	$-0.887579\pi$
$37$		−	4.20787i		−	0.691770i	0.938277	−	0.345885i	$-0.112421\pi$
$38$		0			0
$39$	3.68693			0.590381
$40$	−10.2509	+	0.566132i	−1.62081	+	0.0895133i
$41$	−9.20454			−1.43751			−0.718754	−	0.695265i	$-0.755287\pi$
$41$	−9.20454			−1.43751			−0.718754	+	0.695265i	$0.755287\pi$
$42$			11.6094i			1.79137i
$43$		−	2.26312i		−	0.345123i	−0.984999	−	0.172561i	$-0.944796\pi$
$43$		−	2.26312i		−	0.345123i	0.984999	−	0.172561i	$-0.0552043\pi$
$44$	−0.756532			−0.114052
$45$	0.232156	+	4.20362i	0.0346077	+	0.626639i
$46$	−2.87562			−0.423987
$47$		−	5.95612i		−	0.868789i	−0.900723	−	0.434394i	$-0.856962\pi$
$47$		−	5.95612i		−	0.868789i	0.900723	−	0.434394i	$-0.143038\pi$
$48$		−	3.55273i		−	0.512793i
$49$	−13.4761			−1.92516
$50$	1.33644	+	12.0625i	0.189001	+	1.70589i
$51$	−6.97936			−0.977306
$52$		−	13.5744i		−	1.88243i
$53$			6.94598i			0.954104i	0.878875	+	0.477052i	$0.158295\pi$
$53$			6.94598i			0.954104i	−0.878875	+	0.477052i	$0.841705\pi$
$54$	−12.5271			−1.70473
$55$	0.0239707	+	0.434036i	0.00323221	+	0.0585254i
$56$	20.7760			2.77632
$57$		0			0
$58$			9.96568i			1.30856i
$59$	2.39041			0.311204			0.155602	−	0.987820i	$-0.450268\pi$
$59$	2.39041			0.311204			0.155602	+	0.987820i	$0.450268\pi$
$60$	−9.18370	+	0.507193i	−1.18561	+	0.0654783i
$61$	4.79183			0.613531			0.306765	−	0.951785i	$-0.400753\pi$
$61$	4.79183			0.613531			0.306765	+	0.951785i	$0.400753\pi$
$62$			12.2984i			1.56190i
$63$		−	8.51970i		−	1.07338i
$64$	9.20835			1.15104
$65$	−7.78788	+	0.430105i	−0.965968	+	0.0533480i
$66$	−0.498754			−0.0613924
$67$		−	5.22583i		−	0.638437i	−0.947681	−	0.319219i	$-0.896580\pi$
$67$		−	5.22583i		−	0.638437i	0.947681	−	0.319219i	$-0.103420\pi$
$68$			25.6964i			3.11614i
$69$	−1.25223			−0.150751
$70$	−1.35431	−	24.5224i	−0.161871	−	2.93099i
$71$	−5.85628			−0.695012			−0.347506	−	0.937678i	$-0.612971\pi$
$71$	−5.85628			−0.695012			−0.347506	+	0.937678i	$0.612971\pi$
$72$			8.64448i			1.01876i
$73$		−	6.54790i		−	0.766374i	−0.923671	−	0.383187i	$-0.874827\pi$
$73$		−	6.54790i		−	0.766374i	0.923671	−	0.383187i	$-0.125173\pi$
$74$	−10.2136			−1.18730
$75$	0.581972	+	5.25279i	0.0672003	+	0.606540i
$76$		0			0
$77$		−	0.879683i		−	0.100249i
$78$		−	8.94912i		−	1.01329i
$79$	5.47834			0.616362			0.308181	−	0.951328i	$-0.400280\pi$
$79$	5.47834			0.616362			0.308181	+	0.951328i	$0.400280\pi$
$80$	0.414450	+	7.50442i	0.0463370	+	0.839020i
$81$	0.193213			0.0214681
$82$			22.3418i			2.46724i
$83$			9.54544i			1.04775i	0.851796	+	0.523874i	$0.175514\pi$
$83$			9.54544i			1.04775i	−0.851796	+	0.523874i	$0.824486\pi$
$84$	18.6131			2.03085
$85$	14.7425	−	0.814190i	1.59905	−	0.0883113i
$86$	−5.49318			−0.592345
$87$			4.33971i			0.465265i
$88$			0.892567i			0.0951480i
$89$	14.4923			1.53618			0.768091	−	0.640341i	$-0.221207\pi$
$89$	14.4923			1.53618			0.768091	+	0.640341i	$0.221207\pi$
$90$	10.2033	−	0.563501i	1.07552	−	0.0593982i
$91$	15.7841			1.65462
$92$			4.61042i			0.480670i
$93$			5.35552i			0.555342i
$94$	−14.4570			−1.49113
$95$		0			0
$96$	1.08255			0.110487
$97$			7.41146i			0.752520i	0.926514	+	0.376260i	$0.122790\pi$
$97$			7.41146i			0.752520i	−0.926514	+	0.376260i	$0.877210\pi$
$98$			32.7101i			3.30422i
$99$	0.366018			0.0367862
$100$	19.3395	−	2.14268i	1.93395	−	0.214268i
$101$	−12.2199			−1.21593			−0.607963	−	0.793965i	$-0.708013\pi$
$101$	−12.2199			−1.21593			−0.607963	+	0.793965i	$0.708013\pi$
$102$			16.9407i			1.67738i
$103$			10.1826i			1.00332i	0.865065	+	0.501660i	$0.167277\pi$
$103$			10.1826i			1.00332i	−0.865065	+	0.501660i	$0.832723\pi$
$104$	−16.0153			−1.57043
$105$	−0.589756	−	10.6787i	−0.0575543	−	1.04213i
$106$	16.8597			1.63756
$107$			0.779264i			0.0753343i	0.999290	+	0.0376671i	$0.0119927\pi$
$107$			0.779264i			0.0753343i	−0.999290	+	0.0376671i	$0.988007\pi$
$108$			20.0845i			1.93263i
$109$	−3.46937			−0.332305			−0.166153	−	0.986100i	$-0.553134\pi$
$109$	−3.46937			−0.332305			−0.166153	+	0.986100i	$0.553134\pi$
$110$	1.05352	−	0.0581831i	0.100449	−	0.00554754i
$111$	−4.44766			−0.422153
$112$		−	15.2096i		−	1.43717i
$113$			14.5203i			1.36595i	0.730441	+	0.682976i	$0.239315\pi$
$113$			14.5203i			1.36595i	−0.730441	+	0.682976i	$0.760685\pi$
$114$		0			0
$115$	2.64508	−	0.146081i	0.246655	−	0.0136221i
$116$	15.9778			1.48350
$117$			6.56743i			0.607159i
$118$		−	5.80213i		−	0.534129i
$119$	−29.8793			−2.73903
$120$	0.598393	+	10.8351i	0.0546256	+	0.989101i
$121$	−10.9622			−0.996564
$122$		−	11.6310i		−	1.05302i
$123$			9.72906i			0.877240i
$124$	19.7178			1.77071
$125$	−1.84207	−	11.0275i	−0.164760	−	0.986334i
$126$	−20.6795			−1.84228
$127$		−	18.7617i		−	1.66484i	−0.554149	−	0.832418i	$-0.686956\pi$
$127$		−	18.7617i		−	1.66484i	0.554149	−	0.832418i	$-0.313044\pi$
$128$		−	20.3027i		−	1.79452i
$129$	−2.39209			−0.210612
$130$	1.04398	+	18.9032i	0.0915627	+	1.65792i
$131$	14.0733			1.22959			0.614795	−	0.788687i	$-0.289239\pi$
$131$	14.0733			1.22959			0.614795	+	0.788687i	$0.289239\pi$
$132$			0.799643i			0.0696000i
$133$		0			0
$134$	−12.6844			−1.09577
$135$	11.5229	−	0.636378i	0.991729	−	0.0547707i
$136$	30.3169			2.59966
$137$		−	6.71499i		−	0.573700i	−0.957975	−	0.286850i	$-0.907392\pi$
$137$		−	6.71499i		−	0.573700i	0.957975	−	0.286850i	$-0.0926082\pi$
$138$			3.03949i			0.258738i
$139$	6.33776			0.537562			0.268781	−	0.963201i	$-0.413379\pi$
$139$	6.33776			0.537562			0.268781	+	0.963201i	$0.413379\pi$
$140$	−39.3163	+	2.17134i	−3.32284	+	0.183512i
$141$	−6.29553			−0.530179
$142$			14.2147i			1.19287i
$143$			0.678106i			0.0567061i
$144$	6.32839			0.527366
$145$	−0.506256	−	9.16674i	−0.0420423	−	0.761257i
$146$	−15.8934			−1.31535
$147$			14.2441i			1.17483i
$148$			16.3752i			1.34604i
$149$	−6.51608			−0.533818			−0.266909	−	0.963722i	$-0.586002\pi$
$149$	−6.51608			−0.533818			−0.266909	+	0.963722i	$0.586002\pi$
$150$	12.7499	−	1.41259i	1.04102	−	0.115338i
$151$	−15.0078			−1.22132			−0.610660	−	0.791893i	$-0.709096\pi$
$151$	−15.0078			−1.22132			−0.610660	+	0.791893i	$0.709096\pi$
$152$		0			0
$153$		−	12.4322i		−	1.00508i
$154$	−2.13522			−0.172061
$155$	−0.624758	−	11.3125i	−0.0501818	−	0.908638i
$156$	−14.3479			−1.14876
$157$		−	15.9224i		−	1.27074i	−0.772207	−	0.635371i	$-0.780847\pi$
$157$		−	15.9224i		−	1.27074i	0.772207	−	0.635371i	$-0.219153\pi$
$158$		−	13.2973i		−	1.05788i
$159$	7.34180			0.582243
$160$	−2.28667	+	0.126287i	−0.180777	+	0.00998386i
$161$	−5.36092			−0.422500
$162$		−	0.468978i		−	0.0368464i
$163$			17.6799i			1.38480i	0.721514	+	0.692400i	$0.243447\pi$
$163$			17.6799i			1.38480i	−0.721514	+	0.692400i	$0.756553\pi$
$164$	35.8201			2.79708
$165$	0.458770	−	0.0253367i	0.0357152	−	0.00197246i
$166$	23.1692			1.79828
$167$			12.5103i			0.968075i	0.875047	+	0.484038i	$0.160830\pi$
$167$			12.5103i			0.968075i	−0.875047	+	0.484038i	$0.839170\pi$
$168$		−	21.9600i		−	1.69425i
$169$	0.832781			0.0640601
$170$	−1.97625	−	35.7838i	−0.151571	−	2.74449i
$171$		0			0
$172$			8.80710i			0.671535i
$173$		−	6.09199i		−	0.463166i	−0.972815	−	0.231583i	$-0.925610\pi$
$173$		−	6.09199i		−	0.463166i	0.972815	−	0.231583i	$-0.0743904\pi$
$174$	10.5336			0.798549
$175$	2.49148	+	22.4877i	0.188338	+	1.69991i
$176$	0.653425			0.0492538
$177$		−	2.52662i		−	0.189913i
$178$		−	35.1765i		−	2.63659i
$179$	5.35886			0.400540			0.200270	−	0.979741i	$-0.435818\pi$
$179$	5.35886			0.400540			0.200270	+	0.979741i	$0.435818\pi$
$180$	−0.903450	−	16.3587i	−0.0673392	−	1.21931i
$181$	−15.8763			−1.18007			−0.590037	−	0.807376i	$-0.700887\pi$
$181$	−15.8763			−1.18007			−0.590037	+	0.807376i	$0.700887\pi$
$182$		−	38.3121i		−	2.83988i
$183$		−	5.06489i		−	0.374408i
$184$	5.43944			0.401001
$185$	9.39477	−	0.518850i	0.690717	−	0.0381466i
$186$	12.9992			0.953150
$187$		−	1.28366i		−	0.0938703i
$188$			23.1787i			1.69048i
$189$	−23.3540			−1.69875
$190$		0			0
$191$	22.2361			1.60895			0.804475	−	0.593987i	$-0.202447\pi$
$191$	22.2361			1.60895			0.804475	+	0.593987i	$0.202447\pi$
$192$		−	9.73309i		−	0.702425i
$193$		−	14.4423i		−	1.03958i	−0.854293	−	0.519791i	$-0.826010\pi$
$193$		−	14.4423i		−	1.03958i	0.854293	−	0.519791i	$-0.173990\pi$
$194$	17.9895			1.29157
$195$	0.454615	+	8.23168i	0.0325557	+	0.589483i
$196$	52.4434			3.74596
$197$		−	10.7740i		−	0.767613i	−0.923414	−	0.383806i	$-0.874613\pi$
$197$		−	10.7740i		−	0.767613i	0.923414	−	0.383806i	$-0.125387\pi$
$198$		−	0.888419i		−	0.0631372i
$199$	−2.09938			−0.148821			−0.0744105	−	0.997228i	$-0.523707\pi$
$199$	−2.09938			−0.148821			−0.0744105	+	0.997228i	$0.523707\pi$
$200$	−2.52797	−	22.8170i	−0.178754	−	1.61341i
$201$	−5.52363			−0.389607
$202$			29.6609i			2.08693i
$203$			18.5787i			1.30397i
$204$	27.1607			1.90163
$205$	−1.13496	−	20.5507i	−0.0792692	−	1.43532i
$206$	24.7157			1.72203
$207$		−	2.23057i		−	0.155035i
$208$			11.7244i			0.812938i
$209$		0			0
$210$	−25.9198	+	1.43149i	−1.78864	+	0.0987821i
$211$	6.30512			0.434062			0.217031	−	0.976165i	$-0.430363\pi$
$211$	6.30512			0.434062			0.217031	+	0.976165i	$0.430363\pi$
$212$		−	27.0308i		−	1.85648i
$213$			6.19000i			0.424132i
$214$	1.89147			0.129298
$215$	5.05279	−	0.279053i	0.344598	−	0.0190313i
$216$	23.6960			1.61231
$217$			22.9275i			1.55642i
$218$			8.42105i			0.570346i
$219$	−6.92103			−0.467680
$220$	−0.0932839	−	1.68908i	−0.00628920	−	0.113878i
$221$	23.0326			1.54934
$222$			10.7956i			0.724553i
$223$		−	12.6960i		−	0.850187i	−0.905149	−	0.425094i	$-0.860241\pi$
$223$		−	12.6960i		−	0.850187i	0.905149	−	0.425094i	$-0.139759\pi$
$224$	4.63450			0.309656
$225$	−9.35666	+	1.03665i	−0.623777	+	0.0691101i
$226$	35.2444			2.34442
$227$		−	10.8208i		−	0.718201i	−0.933299	−	0.359101i	$-0.883084\pi$
$227$		−	10.8208i		−	0.718201i	0.933299	−	0.359101i	$-0.116916\pi$
$228$		0			0
$229$	−1.66903			−0.110293			−0.0551463	−	0.998478i	$-0.517563\pi$
$229$	−1.66903			−0.110293			−0.0551463	+	0.998478i	$0.517563\pi$
$230$	−0.354577	−	6.42029i	−0.0233801	−	0.423341i
$231$	−0.929812			−0.0611772
$232$		−	18.8508i		−	1.23762i
$233$		−	10.3979i		−	0.681192i	−0.940210	−	0.340596i	$-0.889371\pi$
$233$		−	10.3979i		−	0.681192i	0.940210	−	0.340596i	$-0.110629\pi$
$234$	15.9408			1.04209
$235$	13.2980	−	0.734416i	0.867467	−	0.0479080i
$236$	−9.30244			−0.605537
$237$		−	5.79053i		−	0.376135i
$238$			72.5248i			4.70108i
$239$	−9.94852			−0.643516			−0.321758	−	0.946822i	$-0.604274\pi$
$239$	−9.94852			−0.643516			−0.321758	+	0.946822i	$0.604274\pi$
$240$	7.93206	−	0.438068i	0.512012	−	0.0282772i
$241$	5.01351			0.322949			0.161474	−	0.986877i	$-0.448375\pi$
$241$	5.01351			0.322949			0.161474	+	0.986877i	$0.448375\pi$
$242$			26.6081i			1.71043i
$243$		−	15.6873i		−	1.00634i
$244$	−18.6478			−1.19380
$245$	−1.66167	−	30.0877i	−0.106160	−	1.92224i
$246$	23.6149			1.50563
$247$		0			0
$248$		−	23.2633i		−	1.47722i
$249$	10.0894			0.639389
$250$	−26.7667	+	4.47117i	−1.69287	+	0.282782i
$251$	24.2323			1.52953			0.764766	−	0.644308i	$-0.222855\pi$
$251$	24.2323			1.52953			0.764766	+	0.644308i	$0.222855\pi$
$252$			33.1550i			2.08857i
$253$		−	0.230313i		−	0.0144796i
$254$	−45.5396			−2.85741
$255$	−0.860587	−	15.5826i	−0.0538920	−	0.975819i
$256$	−30.8630			−1.92894
$257$		−	13.2309i		−	0.825323i	−0.910884	−	0.412662i	$-0.864599\pi$
$257$		−	13.2309i		−	0.825323i	0.910884	−	0.412662i	$-0.135401\pi$
$258$			5.80621i			0.361479i
$259$	−19.0409			−1.18314
$260$	30.3071	−	1.67379i	1.87957	−	0.103804i
$261$	−7.73021			−0.478488
$262$		−	34.1595i		−	2.11038i
$263$		−	14.8787i		−	0.917461i	−0.888575	−	0.458730i	$-0.848304\pi$
$263$		−	14.8787i		−	0.917461i	0.888575	−	0.458730i	$-0.151696\pi$
$264$	0.943430			0.0580641
$265$	−15.5081	+	0.856471i	−0.952652	+	0.0526126i
$266$		0			0
$267$		−	15.3182i		−	0.937456i
$268$			20.3367i			1.24226i
$269$	−3.82602			−0.233277			−0.116638	−	0.993174i	$-0.537212\pi$
$269$	−3.82602			−0.233277			−0.116638	+	0.993174i	$0.537212\pi$
$270$	−1.54465	−	27.9689i	−0.0940046	−	1.70213i
$271$	−20.6532			−1.25459			−0.627297	−	0.778780i	$-0.715839\pi$
$271$	−20.6532			−1.25459			−0.627297	+	0.778780i	$0.715839\pi$
$272$		−	22.1942i		−	1.34572i
$273$		−	16.6836i		−	1.00974i
$274$	−16.2990			−0.984659
$275$	−0.966102	+	0.107037i	−0.0582581	+	0.00645459i
$276$	4.87315			0.293329
$277$			12.9777i			0.779757i	0.920866	+	0.389879i	$0.127483\pi$
$277$			12.9777i			0.779757i	−0.920866	+	0.389879i	$0.872517\pi$
$278$		−	15.3834i		−	0.922633i
$279$	−9.53966			−0.571125
$280$	2.56178	+	46.3860i	0.153096	+	2.77209i
$281$	−12.4242			−0.741165			−0.370582	−	0.928800i	$-0.620842\pi$
$281$	−12.4242			−0.741165			−0.370582	+	0.928800i	$0.620842\pi$
$282$			15.2809i			0.909962i
$283$		−	19.2541i		−	1.14454i	−0.820066	−	0.572268i	$-0.806064\pi$
$283$		−	19.2541i		−	1.14454i	0.820066	−	0.572268i	$-0.193936\pi$
$284$	22.7901			1.35235
$285$		0			0
$286$	1.64594			0.0973264
$287$			41.6511i			2.45859i
$288$			1.92832i			0.113627i
$289$	−26.6007			−1.56475
$290$	−22.2500	+	1.22881i	−1.30657	+	0.0721584i
$291$	7.83381			0.459226
$292$			25.4816i			1.49120i
$293$		−	13.2897i		−	0.776395i	−0.921576	−	0.388197i	$-0.873098\pi$
$293$		−	13.2897i		−	0.776395i	0.921576	−	0.388197i	$-0.126902\pi$
$294$	34.5741			2.01640
$295$	0.294748	+	5.33698i	0.0171609	+	0.310731i
$296$	19.3197			1.12294
$297$		−	1.00332i		−	0.0582184i
$298$			15.8162i			0.916208i
$299$	4.13248			0.238988
$300$	−2.26478	−	20.4416i	−0.130757	−	1.18020i
$301$	−10.2408			−0.590267
$302$			36.4278i			2.09619i
$303$			12.9163i			0.742020i
$304$		0			0
$305$	0.590854	+	10.6986i	0.0338322	+	0.612597i
$306$	−30.1760			−1.72505
$307$		−	15.3103i		−	0.873802i	−0.899510	−	0.436901i	$-0.856076\pi$
$307$		−	15.3103i		−	0.873802i	0.899510	−	0.436901i	$-0.143924\pi$
$308$			3.42335i			0.195064i
$309$	10.7628			0.612276
$310$	−27.4582	+	1.51645i	−1.55952	+	0.0861285i
$311$	25.6272			1.45319			0.726594	−	0.687067i	$-0.241102\pi$
$311$	25.6272			1.45319			0.726594	+	0.687067i	$0.241102\pi$
$312$			16.9279i			0.958354i
$313$			4.64058i			0.262301i	0.991362	+	0.131150i	$0.0418671\pi$
$313$			4.64058i			0.262301i	−0.991362	+	0.131150i	$0.958133\pi$
$314$	−38.6476			−2.18101
$315$	19.0216	−	1.05052i	1.07175	−	0.0591900i
$316$	−21.3194			−1.19931
$317$			7.58665i			0.426109i	0.977040	+	0.213054i	$0.0683411\pi$
$317$			7.58665i			0.426109i	−0.977040	+	0.213054i	$0.931659\pi$
$318$		−	17.8204i		−	0.999320i
$319$	−0.798167			−0.0446888
$320$	1.13543	+	20.5592i	0.0634725	+	1.14929i
$321$	0.823670			0.0459728
$322$			13.0123i			0.725149i
$323$		0			0
$324$	−0.751903			−0.0417724
$325$	−1.92056	−	17.3347i	−0.106534	−	0.961556i
$326$	42.9137			2.37677
$327$			3.66707i			0.202790i
$328$		−	42.2611i		−	2.33348i
$329$	−26.9518			−1.48590
$330$	−0.0614987	−	1.11355i	−0.00338539	−	0.0612990i
$331$	−7.17378			−0.394307			−0.197153	−	0.980373i	$-0.563170\pi$
$331$	−7.17378			−0.394307			−0.197153	+	0.980373i	$0.563170\pi$
$332$		−	37.1468i		−	2.03869i
$333$		−	7.92250i		−	0.434150i
$334$	30.3657			1.66154
$335$	11.6675	−	0.644369i	0.637466	−	0.0352056i
$336$	−16.0763			−0.877035
$337$			8.16394i			0.444718i	0.974965	+	0.222359i	$0.0713758\pi$
$337$			8.16394i			0.444718i	−0.974965	+	0.222359i	$0.928624\pi$
$338$		−	2.02137i		−	0.109948i
$339$	15.3477			0.833573
$340$	−57.3714	+	3.16848i	−3.11140	+	0.171835i
$341$	−0.984998			−0.0533406
$342$		0			0
$343$			29.3050i			1.58232i
$344$	10.3907			0.560231
$345$	−0.154406	−	2.79581i	−0.00831293	−	0.150521i
$346$	−14.7868			−0.794945
$347$			3.02384i			0.162328i	0.996701	+	0.0811642i	$0.0258638\pi$
$347$			3.02384i			0.162328i	−0.996701	+	0.0811642i	$0.974136\pi$
$348$		−	16.8883i		−	0.905307i
$349$	−23.1629			−1.23988			−0.619940	−	0.784650i	$-0.712843\pi$
$349$	−23.1629			−1.23988			−0.619940	+	0.784650i	$0.712843\pi$
$350$	54.5834	−	6.04745i	2.91760	−	0.323250i
$351$	18.0025			0.960901
$352$			0.199105i			0.0106123i
$353$		−	2.14345i		−	0.114084i	−0.998372	−	0.0570421i	$-0.981833\pi$
$353$		−	2.14345i		−	0.114084i	0.998372	−	0.0570421i	$-0.0181669\pi$
$354$	−6.13276			−0.325953
$355$	−0.722106	−	13.0751i	−0.0383254	−	0.693955i
$356$	−56.3979			−2.98908
$357$			31.5820i			1.67150i
$358$		−	13.0073i		−	0.687458i
$359$	6.89505			0.363907			0.181953	−	0.983307i	$-0.441758\pi$
$359$	6.89505			0.363907			0.181953	+	0.983307i	$0.441758\pi$
$360$	−19.3002	+	1.06590i	−1.01721	+	0.0561780i
$361$		0			0
$362$			38.5358i			2.02540i
$363$			11.5869i			0.608154i
$364$	−61.4250			−3.21954
$365$	14.6193	−	0.807386i	0.765208	−	0.0422605i
$366$	−12.2938			−0.642607
$367$			12.3423i			0.644263i	0.946695	+	0.322132i	$0.104399\pi$
$367$			12.3423i			0.644263i	−0.946695	+	0.322132i	$0.895601\pi$
$368$		−	3.98207i		−	0.207580i
$369$	−17.3301			−0.902171
$370$	−1.25938	−	22.8035i	−0.0654721	−	1.18550i
$371$	31.4310			1.63181
$372$		−	20.8414i		−	1.08058i
$373$		−	21.5626i		−	1.11647i	−0.829683	−	0.558234i	$-0.811479\pi$
$373$		−	21.5626i		−	1.11647i	0.829683	−	0.558234i	$-0.188521\pi$
$374$	−3.11576			−0.161112
$375$	−11.6560	+	1.94704i	−0.601911	+	0.100545i
$376$	27.3465			1.41029
$377$		−	14.3215i		−	0.737592i
$378$			56.6860i			2.91562i
$379$	28.3040			1.45388			0.726939	−	0.686703i	$-0.240942\pi$
$379$	28.3040			1.45388			0.726939	+	0.686703i	$0.240942\pi$
$380$		0			0
$381$	−19.8309			−1.01597
$382$		−	53.9728i		−	2.76149i
$383$		−	8.08490i		−	0.413119i	−0.978434	−	0.206560i	$-0.933773\pi$
$383$		−	8.08490i		−	0.413119i	0.978434	−	0.206560i	$-0.0662267\pi$
$384$	−21.4596			−1.09511
$385$	1.96404	−	0.108469i	0.100097	−	0.00552809i
$386$	−35.0552			−1.78426
$387$		−	4.26097i		−	0.216597i
$388$		−	28.8422i		−	1.46424i
$389$	−1.83534			−0.0930556			−0.0465278	−	0.998917i	$-0.514816\pi$
$389$	−1.83534			−0.0930556			−0.0465278	+	0.998917i	$0.514816\pi$
$390$	19.9804	−	1.10347i	1.01175	−	0.0558762i
$391$	−7.82280			−0.395616
$392$		−	61.8735i		−	3.12508i
$393$		−	14.8753i		−	0.750359i
$394$	−26.1512			−1.31748
$395$	0.675504	+	12.2313i	0.0339883	+	0.615424i
$396$	−1.42438			−0.0715780
$397$			4.86954i			0.244395i	0.992506	+	0.122198i	$0.0389942\pi$
$397$			4.86954i			0.244395i	−0.992506	+	0.122198i	$0.961006\pi$
$398$			5.09573i			0.255426i
$399$		0			0
$400$	−16.7038	+	1.85066i	−0.835188	+	0.0925329i
$401$	18.0028			0.899016			0.449508	−	0.893276i	$-0.351599\pi$
$401$	18.0028			0.899016			0.449508	+	0.893276i	$0.351599\pi$
$402$			13.4073i			0.668693i
$403$		−	17.6737i		−	0.880392i
$404$	47.5547			2.36593
$405$	0.0238241	+	0.431380i	0.00118383	+	0.0214355i
$406$	45.0953			2.23804
$407$		−	0.818021i		−	0.0405478i
$408$		−	32.0446i		−	1.58644i
$409$	11.3247			0.559969			0.279985	−	0.960005i	$-0.409671\pi$
$409$	11.3247			0.559969			0.279985	+	0.960005i	$0.409671\pi$
$410$	−49.8817	+	2.75484i	−2.46348	+	0.136052i
$411$	−7.09765			−0.350101
$412$		−	39.6262i		−	1.95224i
$413$		−	10.8167i		−	0.532256i
$414$	−5.41416			−0.266091
$415$	−21.3118	+	1.17700i	−1.04615	+	0.0577765i
$416$	−3.57252			−0.175157
$417$		−	6.69892i		−	0.328048i
$418$		0			0
$419$	3.64977			0.178303			0.0891514	−	0.996018i	$-0.471584\pi$
$419$	3.64977			0.178303			0.0891514	+	0.996018i	$0.471584\pi$
$420$	2.29508	+	41.5568i	0.111988	+	2.02776i
$421$	14.5023			0.706799			0.353400	−	0.935472i	$-0.385026\pi$
$421$	14.5023			0.706799			0.353400	+	0.935472i	$0.385026\pi$
$422$		−	15.3041i		−	0.744994i
$423$		−	11.2141i		−	0.545247i
$424$	−31.8913			−1.54878
$425$	3.63563	+	32.8146i	0.176354	+	1.59174i
$426$	15.0247			0.727950
$427$		−	21.6833i		−	1.04933i
$428$		−	3.03256i		−	0.146584i
$429$	0.716749			0.0346049
$430$	−0.677334	−	12.2644i	−0.0326639	−	0.591443i
$431$	0.227835			0.0109744			0.00548721	−	0.999985i	$-0.498253\pi$
$431$	0.227835			0.0109744			0.00548721	+	0.999985i	$0.498253\pi$
$432$		−	17.3472i		−	0.834618i
$433$			33.0508i			1.58832i	0.607709	+	0.794160i	$0.292089\pi$
$433$			33.0508i			1.58832i	−0.607709	+	0.794160i	$0.707911\pi$
$434$	55.6510			2.67133
$435$	−9.68911	+	0.535106i	−0.464557	+	0.0256564i
$436$	13.5013			0.646595
$437$		0			0
$438$			16.7991i			0.802693i
$439$	−29.8555			−1.42493			−0.712464	−	0.701709i	$-0.752421\pi$
$439$	−29.8555			−1.42493			−0.712464	+	0.701709i	$0.752421\pi$
$440$	−1.99280	+	0.110058i	−0.0950032	+	0.00524679i
$441$	−25.3727			−1.20822
$442$		−	55.9059i		−	2.65917i
$443$		−	16.1507i		−	0.767342i	−0.923470	−	0.383671i	$-0.874660\pi$
$443$		−	16.1507i		−	0.767342i	0.923470	−	0.383671i	$-0.125340\pi$
$444$	17.3084			0.821419
$445$	1.78697	+	32.3565i	0.0847104	+	1.53384i
$446$	−30.8164			−1.45920
$447$			6.88740i			0.325763i
$448$		−	41.6683i		−	1.96864i
$449$	−23.8916			−1.12752			−0.563758	−	0.825940i	$-0.690645\pi$
$449$	−23.8916			−1.12752			−0.563758	+	0.825940i	$0.690645\pi$
$450$	2.51622	+	22.7110i	0.118616	+	1.07061i
$451$	−1.78939			−0.0842589
$452$		−	56.5067i		−	2.65785i
$453$			15.8631i			0.745311i
$454$	−26.2648			−1.23267
$455$	1.94625	+	35.2406i	0.0912417	+	1.65211i
$456$		0			0
$457$		−	15.1145i		−	0.707027i	−0.935429	−	0.353514i	$-0.884987\pi$
$457$		−	15.1145i		−	0.707027i	0.935429	−	0.353514i	$-0.115013\pi$
$458$			4.05116i			0.189298i
$459$	−34.0787			−1.59066
$460$	−10.2935	+	0.568486i	−0.479938	+	0.0265058i
$461$	25.2228			1.17474			0.587372	−	0.809317i	$-0.300162\pi$
$461$	25.2228			1.17474			0.587372	+	0.809317i	$0.300162\pi$
$462$			2.25689i			0.105000i
$463$			40.2723i			1.87161i	0.352513	+	0.935807i	$0.385327\pi$
$463$			40.2723i			1.87161i	−0.352513	+	0.935807i	$0.614673\pi$
$464$	−13.8002			−0.640657
$465$	−11.9571	+	0.660361i	−0.554497	+	0.0306235i
$466$	−25.2385			−1.16915
$467$			20.5304i			0.950035i	0.879976	+	0.475017i	$0.157558\pi$
$467$			20.5304i			0.950035i	−0.879976	+	0.475017i	$0.842442\pi$
$468$		−	25.5576i		−	1.18140i
$469$	−23.6472			−1.09193
$470$	−1.78262	−	32.2777i	−0.0822260	−	1.48886i
$471$	−16.8297			−0.775472
$472$			10.9751i			0.505172i
$473$		−	0.439957i		−	0.0202292i
$474$	−14.0551			−0.645572
$475$		0			0
$476$	116.278			5.32957
$477$			13.0778i			0.598790i
$478$			24.1476i			1.10449i
$479$	21.6877			0.990936			0.495468	−	0.868626i	$-0.334997\pi$
$479$	21.6877			0.990936			0.495468	+	0.868626i	$0.334997\pi$
$480$	0.133483	+	2.41697i	0.00609266	+	0.110319i
$481$	14.6777			0.669245
$482$		−	12.1691i		−	0.554286i
$483$			5.66642i			0.257831i
$484$	42.6602			1.93910
$485$	−16.5473	+	0.913867i	−0.751375	+	0.0414966i
$486$	−38.0771			−1.72721
$487$			6.84733i			0.310282i	0.987892	+	0.155141i	$0.0495832\pi$
$487$			6.84733i			0.310282i	−0.987892	+	0.155141i	$0.950417\pi$
$488$			22.0009i			0.995933i
$489$	18.6874			0.845075
$490$	−73.0306	+	4.03330i	−3.29919	+	0.182206i
$491$	25.4609			1.14904			0.574518	−	0.818492i	$-0.305190\pi$
$491$	25.4609			1.14904			0.574518	+	0.818492i	$0.305190\pi$
$492$		−	37.8614i		−	1.70692i
$493$			27.1105i			1.22100i
$494$		0			0
$495$	0.0451317	+	0.817195i	0.00202852	+	0.0367302i
$496$	−17.0305			−0.764690
$497$			26.5000i			1.18869i
$498$		−	24.4895i		−	1.09740i
$499$	43.7606			1.95899			0.979496	−	0.201465i	$-0.0645702\pi$
$499$	43.7606			1.95899			0.979496	+	0.201465i	$0.0645702\pi$
$500$	7.16855	+	42.9145i	0.320587	+	1.91919i
$501$	13.2232			0.590769
$502$		−	58.8181i		−	2.62518i
$503$		−	1.49740i		−	0.0667657i	−0.999443	−	0.0333828i	$-0.989372\pi$
$503$		−	1.49740i		−	0.0667657i	0.999443	−	0.0333828i	$-0.0106281\pi$
$504$	39.1168			1.74240
$505$	−1.50677	−	27.2830i	−0.0670504	−	1.21408i
$506$	−0.559028			−0.0248518
$507$		−	0.880237i		−	0.0390927i
$508$			73.0127i			3.23941i
$509$	28.0342			1.24259			0.621297	−	0.783575i	$-0.286606\pi$
$509$	28.0342			1.24259			0.621297	+	0.783575i	$0.286606\pi$
$510$	−37.8229	+	2.08887i	−1.67483	+	0.0924965i
$511$	−29.6296			−1.31074
$512$			34.3072i			1.51618i
$513$		0			0
$514$	−32.1149			−1.41653
$515$	−22.7343	+	1.25556i	−1.00179	+	0.0553265i
$516$	9.30898			0.409805
$517$		−	1.15788i		−	0.0509237i
$518$			46.2170i			2.03066i
$519$	−6.43915			−0.282647
$520$	−1.97476	−	35.7567i	−0.0865988	−	1.56804i
$521$	−5.17980			−0.226931			−0.113466	−	0.993542i	$-0.536195\pi$
$521$	−5.17980			−0.226931			−0.113466	+	0.993542i	$0.536195\pi$
$522$			18.7632i			0.821243i
$523$		−	24.3654i		−	1.06543i	−0.846296	−	0.532713i	$-0.821172\pi$
$523$		−	24.3654i		−	1.06543i	0.846296	−	0.532713i	$-0.178828\pi$
$524$	−54.7673			−2.39252
$525$	23.7692	−	2.63346i	1.03737	−	0.114933i
$526$	−36.1145			−1.57466
$527$			33.4564i			1.45739i
$528$		−	0.690661i		−	0.0300571i
$529$	21.5964			0.938976
$530$	2.07887	+	37.6420i	0.0903006	+	1.63506i
$531$	4.50061			0.195310
$532$		0			0
$533$		−	32.1069i		−	1.39070i
$534$	−37.1811			−1.60898
$535$	−1.73984	+	0.0960868i	−0.0752196	+	0.00415419i
$536$	23.9935			1.03636
$537$		−	5.66423i		−	0.244430i
$538$			9.28673i			0.400379i
$539$	−2.61980			−0.112843
$540$	−44.8420	+	2.47651i	−1.92969	+	0.106572i
$541$	24.8099			1.06666			0.533330	−	0.845907i	$-0.320940\pi$
$541$	24.8099			1.06666			0.533330	+	0.845907i	$0.320940\pi$
$542$			50.1307i			2.15330i
$543$			16.7810i			0.720141i
$544$	6.76279			0.289952
$545$	−0.427789	−	7.74595i	−0.0183245	−	0.331800i
$546$	−40.4953			−1.73304
$547$		−	9.73496i		−	0.416237i	−0.978104	−	0.208118i	$-0.933266\pi$
$547$		−	9.73496i		−	0.416237i	0.978104	−	0.208118i	$-0.0667339\pi$
$548$			26.1319i			1.11630i
$549$	9.02197			0.385048
$550$	0.259807	+	2.34498i	0.0110782	+	0.0999901i
$551$		0			0
$552$		−	5.74941i		−	0.244711i
$553$		−	24.7898i		−	1.05417i
$554$	31.5003			1.33832
$555$	−0.548416	−	9.93013i	−0.0232790	−	0.421511i
$556$	−24.6639			−1.04598
$557$			17.7327i			0.751359i	0.926750	+	0.375679i	$0.122591\pi$
$557$			17.7327i			0.751359i	−0.926750	+	0.375679i	$0.877409\pi$
$558$			23.1552i			0.980238i
$559$	7.89412			0.333886
$560$	33.9579	−	1.87541i	1.43498	−	0.0792506i
$561$	−1.35681			−0.0572844
$562$			30.1567i			1.27208i
$563$			30.7541i			1.29613i	0.761585	+	0.648065i	$0.224422\pi$
$563$			30.7541i			1.29613i	−0.761585	+	0.648065i	$0.775578\pi$
$564$	24.4995			1.03162
$565$	−32.4189	+	1.79041i	−1.36387	+	0.0753233i
$566$	−46.7346			−1.96440
$567$		−	0.874300i		−	0.0367172i
$568$		−	26.8881i		−	1.12820i
$569$	34.2367			1.43528			0.717639	−	0.696415i	$-0.245223\pi$
$569$	34.2367			1.43528			0.717639	+	0.696415i	$0.245223\pi$
$570$		0			0
$571$	−36.7211			−1.53673			−0.768366	−	0.640011i	$-0.778930\pi$
$571$	−36.7211			−1.53673			−0.768366	+	0.640011i	$0.778930\pi$
$572$		−	2.63890i		−	0.110338i
$573$		−	23.5033i		−	0.981863i
$574$	101.098			4.21974
$575$	0.652301	+	5.88757i	0.0272028	+	0.245529i
$576$	17.3373			0.722388
$577$		−	41.5983i		−	1.73176i	−0.500252	−	0.865880i	$-0.666759\pi$
$577$		−	41.5983i		−	1.73176i	0.500252	−	0.865880i	$-0.333241\pi$
$578$			64.5667i			2.68562i
$579$	−15.2653			−0.634406
$580$	1.97013	+	35.6731i	0.0818053	+	1.48124i
$581$	43.1937			1.79197
$582$		−	19.0147i		−	0.788183i
$583$			1.35032i			0.0559244i
$584$	30.0636			1.24404
$585$	−14.6629	+	0.809794i	−0.606236	+	0.0334809i
$586$	−32.2576			−1.33255
$587$			13.3401i			0.550604i	0.961358	+	0.275302i	$0.0887778\pi$
$587$			13.3401i			0.550604i	−0.961358	+	0.275302i	$0.911222\pi$
$588$		−	55.4319i		−	2.28597i
$589$		0			0
$590$	12.9542	−	0.715429i	0.533316	−	0.0294537i
$591$	−11.3879			−0.468436
$592$		−	14.1435i		−	0.581293i
$593$		−	5.69252i		−	0.233764i	−0.993146	−	0.116882i	$-0.962710\pi$
$593$		−	5.69252i		−	0.233764i	0.993146	−	0.116882i	$-0.0372899\pi$
$594$	−2.43531			−0.0999220
$595$	−3.68426	−	66.7106i	−0.151040	−	2.73487i
$596$	25.3578			1.03870
$597$			2.21901i			0.0908181i
$598$		−	10.0306i		−	0.410182i
$599$	42.1070			1.72044			0.860222	−	0.509919i	$-0.170325\pi$
$599$	42.1070			1.72044			0.860222	+	0.509919i	$0.170325\pi$
$600$	−24.1173	+	2.67202i	−0.984584	+	0.109085i
$601$	−36.0751			−1.47153			−0.735767	−	0.677235i	$-0.763178\pi$
$601$	−36.0751			−1.47153			−0.735767	+	0.677235i	$0.763178\pi$
$602$			24.8569i			1.01309i
$603$		−	9.83910i		−	0.400679i
$604$	58.4041			2.37643
$605$	−1.35169	−	24.4749i	−0.0549540	−	0.995048i
$606$	31.3511			1.27355
$607$		−	32.4019i		−	1.31515i	−0.753388	−	0.657577i	$-0.771582\pi$
$607$		−	32.4019i		−	1.31515i	0.753388	−	0.657577i	$-0.228418\pi$
$608$		0			0
$609$	19.6374			0.795749
$610$	25.9681	−	1.43416i	1.05142	−	0.0580672i
$611$	20.7759			0.840501
$612$			48.3807i			1.95567i
$613$			25.1069i			1.01406i	0.861929	+	0.507030i	$0.169257\pi$
$613$			25.1069i			1.01406i	−0.861929	+	0.507030i	$0.830743\pi$
$614$	−37.1619			−1.49973
$615$	−21.7217	+	1.19964i	−0.875905	+	0.0483741i
$616$	4.03892			0.162733
$617$		−	11.0213i		−	0.443703i	−0.975080	−	0.221851i	$-0.928790\pi$
$617$		−	11.0213i		−	0.443703i	0.975080	−	0.221851i	$-0.0712100\pi$
$618$		−	26.1242i		−	1.05087i
$619$	15.0846			0.606302			0.303151	−	0.952942i	$-0.401961\pi$
$619$	15.0846			0.606302			0.303151	+	0.952942i	$0.401961\pi$
$620$	2.43129	+	44.0232i	0.0976431	+	1.76802i
$621$	−6.11437			−0.245361
$622$		−	62.2039i		−	2.49415i
$623$		−	65.5785i		−	2.62735i
$624$	12.3925			0.496096
$625$	24.3937	−	5.47247i	0.975748	−	0.218899i
$626$	11.2639			0.450195
$627$		0			0
$628$			61.9630i			2.47259i
$629$	−27.7849			−1.10786
$630$	−2.54988	−	46.1704i	−0.101589	−	1.83947i
$631$	−43.2378			−1.72127			−0.860635	−	0.509223i	$-0.829933\pi$
$631$	−43.2378			−1.72127			−0.860635	+	0.509223i	$0.829933\pi$
$632$			25.1529i			1.00053i
$633$		−	6.66442i		−	0.264887i
$634$	18.4147			0.731343
$635$	41.8887	−	2.31341i	1.66230	−	0.0918048i
$636$	−28.5712			−1.13292
$637$		−	47.0069i		−	1.86248i
$638$			1.93736i			0.0767006i
$639$	−11.0261			−0.436185
$640$	45.3290	−	2.50341i	1.79179	−	0.0989559i
$641$	29.9485			1.18290			0.591448	−	0.806343i	$-0.298556\pi$
$641$	29.9485			1.18290			0.591448	+	0.806343i	$0.298556\pi$
$642$		−	1.99926i		−	0.0789044i
$643$		−	31.5665i		−	1.24486i	−0.782675	−	0.622430i	$-0.786145\pi$
$643$		−	31.5665i		−	1.24486i	0.782675	−	0.622430i	$-0.213855\pi$
$644$	20.8624			0.822095
$645$	−0.294955	−	5.34073i	−0.0116139	−	0.210291i
$646$		0			0
$647$		−	17.5232i		−	0.688907i	−0.938803	−	0.344453i	$-0.888064\pi$
$647$		−	17.5232i		−	0.688907i	0.938803	−	0.344453i	$-0.111936\pi$
$648$			0.887105i			0.0348488i
$649$	0.464701			0.0182411
$650$	−42.0758	+	4.66170i	−1.65035	+	0.182847i
$651$	24.2341			0.949808
$652$		−	68.8028i		−	2.69452i
$653$		−	31.0328i		−	1.21441i	−0.794547	−	0.607203i	$-0.792291\pi$
$653$		−	31.0328i		−	1.21441i	0.794547	−	0.607203i	$-0.207709\pi$
$654$	8.90093			0.348054
$655$	1.73530	+	31.4210i	0.0678039	+	1.22772i
$656$	−30.9382			−1.20794
$657$		−	12.3283i		−	0.480972i
$658$			65.4189i			2.55029i
$659$	47.0487			1.83276			0.916379	−	0.400311i	$-0.131098\pi$
$659$	47.0487			1.83276			0.916379	+	0.400311i	$0.131098\pi$
$660$	−1.78534	+	0.0985997i	−0.0694941	+	0.00383799i
$661$	11.9223			0.463723			0.231861	−	0.972749i	$-0.425518\pi$
$661$	11.9223			0.463723			0.231861	+	0.972749i	$0.425518\pi$
$662$			17.4126i			0.676760i
$663$		−	24.3451i		−	0.945485i
$664$	−43.8263			−1.70079
$665$		0			0
$666$	−19.2299			−0.745145
$667$			4.86415i			0.188341i
$668$		−	48.6847i		−	1.88367i
$669$	−13.4195			−0.518827
$670$	−1.56405	−	28.3201i	−0.0604245	−	1.09410i
$671$	0.931544			0.0359619
$672$		−	4.89860i		−	0.188968i
$673$		−	27.0397i		−	1.04230i	−0.853464	−	0.521152i	$-0.825503\pi$
$673$		−	27.0397i		−	1.04230i	0.853464	−	0.521152i	$-0.174497\pi$
$674$	19.8160			0.763283
$675$	2.84164	+	25.6482i	0.109375	+	0.987200i
$676$	−3.24083			−0.124647
$677$		−	20.0588i		−	0.770924i	−0.922724	−	0.385462i	$-0.874042\pi$
$677$		−	20.0588i		−	0.770924i	0.922724	−	0.385462i	$-0.125958\pi$
$678$		−	37.2528i		−	1.43069i
$679$	33.5373			1.28704
$680$	3.73822	+	67.6876i	0.143354	+	2.59570i
$681$	−11.4374			−0.438283
$682$			2.39084i			0.0915501i
$683$		−	39.5059i		−	1.51165i	−0.654773	−	0.755825i	$-0.727236\pi$
$683$		−	39.5059i		−	1.51165i	0.654773	−	0.755825i	$-0.272764\pi$
$684$		0			0
$685$	14.9923	−	0.827989i	0.572827	−	0.0316358i
$686$	71.1306			2.71578
$687$			1.76414i			0.0673061i
$688$		−	7.60679i		−	0.290006i
$689$	−24.2287			−0.923038
$690$	−6.78615	+	0.374782i	−0.258344	+	0.0142677i
$691$	−22.2396			−0.846035			−0.423018	−	0.906121i	$-0.639029\pi$
$691$	−22.2396			−0.846035			−0.423018	+	0.906121i	$0.639029\pi$
$692$			23.7074i			0.901222i
$693$		−	1.65625i		−	0.0629158i
$694$	7.33964			0.278609
$695$	0.781475	+	14.1501i	0.0296430	+	0.536744i
$696$	−19.9250			−0.755256
$697$			60.7783i			2.30214i
$698$			56.2222i			2.12804i
$699$	−10.9905			−0.415698
$700$	−9.69577	−	87.5125i	−0.366465	−	3.30766i
$701$	−28.0887			−1.06090			−0.530448	−	0.847717i	$-0.677976\pi$
$701$	−28.0887			−1.06090			−0.530448	+	0.847717i	$0.677976\pi$
$702$		−	43.6966i		−	1.64922i
$703$		0			0
$704$	1.79013			0.0674680
$705$	−0.776267	−	14.0558i	−0.0292359	−	0.529372i
$706$	−5.20270			−0.195806
$707$			55.2958i			2.07961i
$708$			9.83254i			0.369529i
$709$	39.9125			1.49894			0.749472	−	0.662036i	$-0.230307\pi$
$709$	39.9125			1.49894			0.749472	+	0.662036i	$0.230307\pi$
$710$	−31.7366	+	1.75274i	−1.19105	+	0.0657790i
$711$	10.3145			0.386825
$712$			66.5390i			2.49365i
$713$			6.00272i			0.224804i
$714$	76.6576			2.86884
$715$	−1.51398	+	0.0836136i	−0.0566198	+	0.00312697i
$716$	−20.8544			−0.779365
$717$			10.5154i			0.392706i
$718$		−	16.7361i		−	0.624584i
$719$	−6.17844			−0.230417			−0.115208	−	0.993341i	$-0.536754\pi$
$719$	−6.17844			−0.230417			−0.115208	+	0.993341i	$0.536754\pi$
$720$	0.780320	+	14.1292i	0.0290808	+	0.526564i
$721$	46.0767			1.71599
$722$		0			0
$723$		−	5.29921i		−	0.197080i
$724$	61.7837			2.29617
$725$	20.4039	−	2.26060i	0.757780	−	0.0839567i
$726$	28.1244			1.04379
$727$		−	9.21771i		−	0.341866i	−0.985283	−	0.170933i	$-0.945322\pi$
$727$		−	9.21771i		−	0.341866i	0.985283	−	0.170933i	$-0.0546782\pi$
$728$			72.4700i			2.68592i
$729$	−16.0016			−0.592653
$730$	−1.95973	−	35.4847i	−0.0725330	−	1.31335i
$731$	−14.9436			−0.552708
$732$			19.7104i			0.728518i
$733$		−	20.5865i		−	0.760381i	−0.924908	−	0.380190i	$-0.875858\pi$
$733$		−	20.5865i		−	0.760381i	0.924908	−	0.380190i	$-0.124142\pi$
$734$	29.9579			1.10577
$735$	−31.8023	+	1.75636i	−1.17305	+	0.0647844i
$736$	1.21337			0.0447255
$737$		−	1.01592i		−	0.0374217i
$738$			42.0647i			1.54842i
$739$	14.4627			0.532021			0.266010	−	0.963970i	$-0.414294\pi$
$739$	14.4627			0.532021			0.266010	+	0.963970i	$0.414294\pi$
$740$	−36.5604	+	2.01914i	−1.34399	+	0.0742251i
$741$		0			0
$742$		−	76.2910i		−	2.80073i
$743$		−	4.23224i		−	0.155266i	−0.996982	−	0.0776329i	$-0.975264\pi$
$743$		−	4.23224i		−	0.155266i	0.996982	−	0.0776329i	$-0.0247362\pi$
$744$	−24.5890			−0.901476
$745$	−0.803463	−	14.5482i	−0.0294366	−	0.533006i
$746$	−52.3379			−1.91623
$747$			17.9720i			0.657560i
$748$			4.99544i			0.182651i
$749$	3.52621			0.128845
$750$	4.72597	+	28.2920i	0.172568	+	1.03308i
$751$	−22.0045			−0.802956			−0.401478	−	0.915869i	$-0.631503\pi$
$751$	−22.0045			−0.802956			−0.401478	+	0.915869i	$0.631503\pi$
$752$		−	20.0197i		−	0.730042i
$753$		−	25.6132i		−	0.933398i
$754$	−34.7618			−1.26595
$755$	−1.85053	−	33.5075i	−0.0673478	−	1.21946i
$756$	90.8836			3.30541
$757$		−	1.19032i		−	0.0432628i	−0.999766	−	0.0216314i	$-0.993114\pi$
$757$		−	1.19032i		−	0.0432628i	0.999766	−	0.0216314i	$-0.00688603\pi$
$758$		−	68.7010i		−	2.49533i
$759$	−0.243437			−0.00883620
$760$		0			0
$761$	−19.5355			−0.708161			−0.354080	−	0.935215i	$-0.615206\pi$
$761$	−19.5355			−0.708161			−0.354080	+	0.935215i	$0.615206\pi$
$762$			48.1346i			1.74373i
$763$			15.6991i			0.568346i
$764$	−86.5335			−3.13067
$765$	27.7569	−	1.53294i	1.00355	−	0.0554236i
$766$	−19.6241			−0.709049
$767$			8.33810i			0.301071i
$768$			32.6218i			1.17714i
$769$	−53.9907			−1.94696			−0.973478	−	0.228780i	$-0.926526\pi$
$769$	−53.9907			−1.94696			−0.973478	+	0.228780i	$0.926526\pi$
$770$	−0.263282	−	4.76723i	−0.00948802	−	0.171799i
$771$	−13.9849			−0.503654
$772$			56.2034i			2.02280i
$773$		−	17.3893i		−	0.625451i	−0.949844	−	0.312725i	$-0.898758\pi$
$773$		−	17.3893i		−	0.625451i	0.949844	−	0.312725i	$-0.101242\pi$
$774$	−10.3425			−0.371752
$775$	25.1799	−	2.78975i	0.904488	−	0.100211i
$776$	−34.0285			−1.22155
$777$			20.1259i			0.722013i
$778$			4.45485i			0.159714i
$779$		0			0
$780$	−1.76917	−	32.0342i	−0.0633464	−	1.14701i
$781$	−1.13848			−0.0407379
$782$			18.9879i			0.679007i
$783$			21.1898i			0.757263i
$784$	−45.2959			−1.61771
$785$	35.5493	−	1.96330i	1.26881	−	0.0700732i
$786$	−36.1061			−1.28786
$787$		−	48.0664i		−	1.71338i	−0.515830	−	0.856691i	$-0.672516\pi$
$787$		−	48.0664i		−	1.71338i	0.515830	−	0.856691i	$-0.327484\pi$
$788$			41.9276i			1.49361i
$789$	−15.7266			−0.559881
$790$	29.6885	−	1.63962i	1.05627	−	0.0583352i
$791$	65.7050			2.33620
$792$			1.68051i			0.0597143i
$793$			16.7146i			0.593554i
$794$	11.8196			0.419463
$795$	0.905277	+	16.3918i	0.0321069	+	0.581357i
$796$	8.16988			0.289574
$797$			27.1546i			0.961866i	0.876757	+	0.480933i	$0.159702\pi$
$797$			27.1546i			0.961866i	−0.876757	+	0.480933i	$0.840298\pi$
$798$		0			0
$799$	−39.3287			−1.39135
$800$	−0.563913	−	5.08979i	−0.0199373	−	0.179951i
$801$	27.2859			0.964098
$802$		−	43.6974i		−	1.54301i
$803$		−	1.27293i		−	0.0449207i
$804$	21.4956			0.758091
$805$	−0.661026	−	11.9691i	−0.0232981	−	0.421857i
$806$	−42.8987			−1.51104
$807$			4.04405i			0.142357i
$808$		−	56.1057i		−	1.97379i
$809$	2.22424			0.0782001			0.0391001	−	0.999235i	$-0.487551\pi$
$809$	2.22424			0.0782001			0.0391001	+	0.999235i	$0.487551\pi$
$810$	1.04707	−	0.0578271i	0.0367903	−	0.00203184i
$811$	16.5337			0.580577			0.290289	−	0.956939i	$-0.406249\pi$
$811$	16.5337			0.580577			0.290289	+	0.956939i	$0.406249\pi$
$812$		−	72.3004i		−	2.53725i
$813$			21.8301i			0.765617i
$814$	−1.98555			−0.0695934
$815$	−39.4734	+	2.18002i	−1.38269	+	0.0763627i
$816$	−23.4590			−0.821229
$817$		0			0
$818$		−	27.4879i		−	0.961091i
$819$	29.7180			1.03843
$820$	4.41679	+	79.9744i	0.154241	+	2.79283i
$821$	40.6846			1.41990			0.709952	−	0.704250i	$-0.248717\pi$
$821$	40.6846			1.41990			0.709952	+	0.704250i	$0.248717\pi$
$822$			17.2278i			0.600889i
$823$			15.8784i			0.553486i	0.960944	+	0.276743i	$0.0892551\pi$
$823$			15.8784i			0.553486i	−0.960944	+	0.276743i	$0.910745\pi$
$824$	−46.7516			−1.62867
$825$	0.113137	+	1.02116i	0.00393892	+	0.0355521i
$826$	−26.2550			−0.913527
$827$			2.03295i			0.0706926i	0.999375	+	0.0353463i	$0.0112534\pi$
$827$			2.03295i			0.0706926i	−0.999375	+	0.0353463i	$0.988747\pi$
$828$			8.68042i			0.301665i
$829$	17.2280			0.598354			0.299177	−	0.954198i	$-0.403288\pi$
$829$	17.2280			0.598354			0.299177	+	0.954198i	$0.403288\pi$
$830$	2.85687	+	51.7291i	0.0991634	+	1.79554i
$831$	13.7173			0.475847
$832$			32.1201i			1.11357i
$833$			88.9841i			3.08312i
$834$	−16.2600			−0.563038
$835$	−27.9313	+	1.54258i	−0.966602	+	0.0533830i
$836$		0			0
$837$			26.1499i			0.903871i
$838$		−	8.85893i		−	0.306026i
$839$	0.456894			0.0157737			0.00788687	−	0.999969i	$-0.497490\pi$
$839$	0.456894			0.0157737			0.00788687	+	0.999969i	$0.497490\pi$
$840$	49.0293	−	2.70776i	1.69167	−	0.0934268i
$841$	−12.1429			−0.418721
$842$		−	35.2008i		−	1.21310i
$843$			13.1322i			0.452296i
$844$	−24.5368			−0.844592
$845$	0.102686	+	1.85932i	0.00353249	+	0.0639626i
$846$	−27.2194			−0.935823
$847$			49.6046i			1.70444i
$848$			23.3468i			0.801732i
$849$	−20.3513			−0.698454
$850$	79.6495	−	8.82460i	2.73196	−	0.302681i
$851$	−4.98514			−0.170889
$852$		−	24.0888i		−	0.825270i
$853$		−	29.8966i		−	1.02364i	−0.859093	−	0.511820i	$-0.828971\pi$
$853$		−	29.8966i		−	1.02364i	0.859093	−	0.511820i	$-0.171029\pi$
$854$	−52.6309			−1.80099
$855$		0			0
$856$	−3.57786			−0.122289
$857$		−	15.6100i		−	0.533226i	−0.963804	−	0.266613i	$-0.914095\pi$
$857$		−	15.6100i		−	0.533226i	0.963804	−	0.266613i	$-0.0859046\pi$
$858$		−	1.73973i		−	0.0593935i
$859$	−35.1240			−1.19842			−0.599208	−	0.800594i	$-0.704518\pi$
$859$	−35.1240			−1.19842			−0.599208	+	0.800594i	$0.704518\pi$
$860$	−19.6633	+	1.08596i	−0.670514	+	0.0370308i
$861$	44.0246			1.50035
$862$		−	0.553014i		−	0.0188357i
$863$			15.1704i			0.516406i	0.966091	+	0.258203i	$0.0831303\pi$
$863$			15.1704i			0.516406i	−0.966091	+	0.258203i	$0.916870\pi$
$864$	5.28586			0.179829
$865$	13.6014	−	0.751171i	0.462461	−	0.0255406i
$866$	80.2227			2.72608
$867$			28.1165i			0.954888i
$868$		−	89.2241i		−	3.02846i
$869$	1.06500			0.0361278
$870$	1.29884	+	23.5180i	0.0440347	+	0.797334i
$871$	18.2285			0.617649
$872$		−	15.9290i		−	0.539425i
$873$			13.9542i			0.472277i
$874$		0			0
$875$	−49.9003	+	8.33547i	−1.68694	+	0.281790i
$876$	26.9337			0.910006
$877$			29.3157i			0.989922i	0.868915	+	0.494961i	$0.164818\pi$
$877$			29.3157i			0.989922i	−0.868915	+	0.494961i	$0.835182\pi$
$878$			72.4671i			2.44564i
$879$	−14.0471			−0.473795
$880$	0.0805703	+	1.45888i	0.00271602	+	0.0491788i
$881$	29.7218			1.00135			0.500676	−	0.865634i	$-0.333085\pi$
$881$	29.7218			1.00135			0.500676	+	0.865634i	$0.333085\pi$
$882$			61.5859i			2.07371i
$883$		−	49.1965i		−	1.65559i	−0.561027	−	0.827797i	$-0.689594\pi$
$883$		−	49.1965i		−	1.65559i	0.561027	−	0.827797i	$-0.310406\pi$
$884$	−89.6329			−3.01468
$885$	5.64111	−	0.311544i	0.189624	−	0.0104724i
$886$	−39.2018			−1.31701
$887$		−	45.2035i		−	1.51779i	−0.651215	−	0.758893i	$-0.725741\pi$
$887$		−	45.2035i		−	1.51779i	0.651215	−	0.758893i	$-0.274259\pi$
$888$		−	20.4207i		−	0.685273i
$889$	−84.8980			−2.84739
$890$	78.5375	−	4.33743i	2.63258	−	0.145391i
$891$	0.0375611			0.00125835
$892$			49.4074i			1.65428i
$893$		0			0
$894$	16.7175			0.559117
$895$	0.660771	+	11.9645i	0.0220872	+	0.399930i
$896$	−91.8707			−3.06918
$897$		−	4.36797i		−	0.145842i
$898$			57.9911i			1.93519i
$899$	20.8029			0.693816
$900$	36.4121	−	4.03421i	1.21374	−	0.134474i
$901$	45.8649			1.52798
$902$			4.34330i			0.144616i
$903$			10.8243i			0.360211i
$904$	−66.6673			−2.21732
$905$	−1.95762	−	35.4464i	−0.0650734	−	1.17828i
$906$	38.5037			1.27920
$907$			52.8789i			1.75581i	0.478831	+	0.877907i	$0.341061\pi$
$907$			52.8789i			1.75581i	−0.478831	+	0.877907i	$0.658939\pi$
$908$			42.1099i			1.39747i
$909$	−23.0074			−0.763108
$910$	85.5380	−	4.72405i	2.83556	−	0.156601i
$911$	−13.9927			−0.463597			−0.231799	−	0.972764i	$-0.574461\pi$
$911$	−13.9927			−0.463597			−0.231799	+	0.972764i	$0.574461\pi$
$912$		0			0
$913$			1.85566i			0.0614133i
$914$	−36.6868			−1.21349
$915$	11.3082	−	0.624525i	0.373838	−	0.0206461i
$916$	6.49515			0.214606
$917$		−	63.6825i		−	2.10298i
$918$			82.7177i			2.73009i
$919$	−28.2198			−0.930884			−0.465442	−	0.885078i	$-0.654105\pi$
$919$	−28.2198			−0.930884			−0.465442	+	0.885078i	$0.654105\pi$
$920$	0.670708	+	12.1444i	0.0221126	+	0.400391i
$921$	−16.1827			−0.533238
$922$		−	61.2223i		−	2.01625i
$923$		−	20.4276i		−	0.672382i
$924$	3.61843			0.119038
$925$	2.31684	+	20.9114i	0.0761771	+	0.687562i
$926$	97.7512			3.21231
$927$			19.1716i			0.629677i
$928$		−	4.20504i		−	0.138037i
$929$	22.9113			0.751696			0.375848	−	0.926681i	$-0.377351\pi$
$929$	22.9113			0.751696			0.375848	+	0.926681i	$0.377351\pi$
$930$	1.60286	+	29.0229i	0.0525600	+	0.951700i
$931$		0			0
$932$			40.4643i			1.32545i
$933$		−	27.0876i		−	0.886809i
$934$	49.8326			1.63057
$935$	2.86598	−	0.158281i	0.0937274	−	0.00517633i
$936$	−30.1533			−0.985590
$937$			48.7586i			1.59287i	0.604722	+	0.796437i	$0.293284\pi$
$937$			48.7586i			1.59287i	−0.604722	+	0.796437i	$0.706716\pi$
$938$			57.3978i			1.87410i
$939$	4.90502			0.160069
$940$	−51.7502	+	2.85803i	−1.68791	+	0.0932188i
$941$	−5.26228			−0.171545			−0.0857727	−	0.996315i	$-0.527336\pi$
$941$	−5.26228			−0.171545			−0.0857727	+	0.996315i	$0.527336\pi$
$942$			40.8500i			1.33096i
$943$			10.9048i			0.355109i
$944$	8.03461			0.261504
$945$	−2.87965	−	52.1416i	−0.0936750	−	1.69617i
$946$	−1.06789			−0.0347200
$947$		−	55.3080i		−	1.79727i	−0.438700	−	0.898634i	$-0.644561\pi$
$947$		−	55.3080i		−	1.79727i	0.438700	−	0.898634i	$-0.355439\pi$
$948$			22.5343i			0.731879i
$949$	22.8401			0.741421
$950$		0			0
$951$	8.01898			0.260033
$952$		−	137.186i		−	4.44622i
$953$		−	15.8248i		−	0.512616i	−0.966595	−	0.256308i	$-0.917494\pi$
$953$		−	15.8248i		−	0.512616i	0.966595	−	0.256308i	$-0.0825061\pi$
$954$	31.7431			1.02772
$955$	2.74182	+	49.6458i	0.0887231	+	1.60650i
$956$	38.7154			1.25215
$957$			0.843651i			0.0272713i
$958$		−	52.6416i		−	1.70077i
$959$	−30.3857			−0.981206
$960$	21.7307	−	1.20013i	0.701357	−	0.0387342i
$961$	−5.32763			−0.171859
$962$		−	35.6265i		−	1.14865i
$963$			1.46718i			0.0472793i
$964$	−19.5104			−0.628389
$965$	32.2449	−	1.78081i	1.03800	−	0.0573262i
$966$	13.7538			0.442523
$967$			42.2128i			1.35747i	0.734382	+	0.678736i	$0.237472\pi$
$967$			42.2128i			1.35747i	−0.734382	+	0.678736i	$0.762528\pi$
$968$		−	50.3311i		−	1.61770i
$969$		0			0
$970$	2.21819	+	40.1646i	0.0712218	+	1.28961i
$971$	−10.0408			−0.322224			−0.161112	−	0.986936i	$-0.551508\pi$
$971$	−10.0408			−0.322224			−0.161112	+	0.986936i	$0.551508\pi$
$972$			61.0483i			1.95813i
$973$		−	28.6787i		−	0.919398i
$974$	16.6202			0.532546
$975$	−18.3225	+	2.03001i	−0.586791	+	0.0650122i
$976$	16.1063			0.515549
$977$			47.5795i			1.52220i	0.648632	+	0.761102i	$0.275341\pi$
$977$			47.5795i			1.52220i	−0.648632	+	0.761102i	$0.724659\pi$
$978$		−	45.3592i		−	1.45043i
$979$	2.81734			0.0900427
$980$	6.46651	+	117.089i	0.206565	+	3.74026i
$981$	−6.53207			−0.208553
$982$		−	61.8002i		−	1.97212i
$983$		−	48.8895i		−	1.55933i	−0.626194	−	0.779667i	$-0.715388\pi$
$983$		−	48.8895i		−	1.55933i	0.626194	−	0.779667i	$-0.284612\pi$
$984$	−44.6694			−1.42401
$985$	24.0546	−	1.32848i	0.766445	−	0.0423288i
$986$	65.8042			2.09563
$987$			28.4876i			0.906771i
$988$		0			0
$989$	−2.68116			−0.0852561
$990$	1.98354	−	0.109546i	0.0630411	−	0.00348160i
$991$	7.28600			0.231447			0.115724	−	0.993281i	$-0.463081\pi$
$991$	7.28600			0.231447			0.115724	+	0.993281i	$0.463081\pi$
$992$		−	5.18934i		−	0.164762i
$993$			7.58258i			0.240626i
$994$	64.3223			2.04018
$995$	−0.258863	−	4.68721i	−0.00820650	−	0.148594i
$996$	−39.2636			−1.24411
$997$			20.4024i			0.646151i	0.946373	+	0.323075i	$0.104717\pi$
$997$			20.4024i			0.646151i	−0.946373	+	0.323075i	$0.895283\pi$
$998$		−	106.218i		−	3.36227i
$999$	−21.7169			−0.687094

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.b.m.1084.6	yes	40
5.2	odd	4		9025.2.a.cv.1.36		40
5.3	odd	4		9025.2.a.cv.1.5		40
5.4	even	2	inner	1805.2.b.m.1084.35	yes	40
19.18	odd	2	inner	1805.2.b.m.1084.36	yes	40
95.18	even	4		9025.2.a.cv.1.35		40
95.37	even	4		9025.2.a.cv.1.6		40
95.94	odd	2	inner	1805.2.b.m.1084.5	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1805.2.b.m.1084.5	✓	40	95.94	odd	2	inner
1805.2.b.m.1084.6	yes	40	1.1	even	1	trivial
1805.2.b.m.1084.35	yes	40	5.4	even	2	inner
1805.2.b.m.1084.36	yes	40	19.18	odd	2	inner
9025.2.a.cv.1.5		40	5.3	odd	4
9025.2.a.cv.1.6		40	95.37	even	4
9025.2.a.cv.1.35		40	95.18	even	4
9025.2.a.cv.1.36		40	5.2	odd	4

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:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.42726i q^{2} -1.05699i q^{3} -3.89157 q^{4} +(0.123305 + 2.23267i) q^{5} -2.56557 q^{6} -4.52506i q^{7} +4.59133i q^{8} +1.88278 q^{9} +O(q^{10})\)	\(q-2.42726i q^{2} -1.05699i q^{3} -3.89157 q^{4} +(0.123305 + 2.23267i) q^{5} -2.56557 q^{6} -4.52506i q^{7} +4.59133i q^{8} +1.88278 q^{9} +(5.41925 - 0.299292i) q^{10} +0.194403 q^{11} +4.11334i q^{12} +3.48815i q^{13} -10.9835 q^{14} +(2.35990 - 0.130331i) q^{15} +3.36119 q^{16} -6.60308i q^{17} -4.56999i q^{18} +(-0.479849 - 8.68858i) q^{20} -4.78292 q^{21} -0.471865i q^{22} -1.18472i q^{23} +4.85297 q^{24} +(-4.96959 + 0.550596i) q^{25} +8.46664 q^{26} -5.16103i q^{27} +17.6096i q^{28} -4.10574 q^{29} +(-0.316347 - 5.72807i) q^{30} -5.06679 q^{31} +1.02419i q^{32} -0.205481i q^{33} -16.0274 q^{34} +(10.1029 - 0.557960i) q^{35} -7.32698 q^{36} -4.20787i q^{37} +3.68693 q^{39} +(-10.2509 + 0.566132i) q^{40} -9.20454 q^{41} +11.6094i q^{42} -2.26312i q^{43} -0.756532 q^{44} +(0.232156 + 4.20362i) q^{45} -2.87562 q^{46} -5.95612i q^{47} -3.55273i q^{48} -13.4761 q^{49} +(1.33644 + 12.0625i) q^{50} -6.97936 q^{51} -13.5744i q^{52} +6.94598i q^{53} -12.5271 q^{54} +(0.0239707 + 0.434036i) q^{55} +20.7760 q^{56} +9.96568i q^{58} +2.39041 q^{59} +(-9.18370 + 0.507193i) q^{60} +4.79183 q^{61} +12.2984i q^{62} -8.51970i q^{63} +9.20835 q^{64} +(-7.78788 + 0.430105i) q^{65} -0.498754 q^{66} -5.22583i q^{67} +25.6964i q^{68} -1.25223 q^{69} +(-1.35431 - 24.5224i) q^{70} -5.85628 q^{71} +8.64448i q^{72} -6.54790i q^{73} -10.2136 q^{74} +(0.581972 + 5.25279i) q^{75} -0.879683i q^{77} -8.94912i q^{78} +5.47834 q^{79} +(0.414450 + 7.50442i) q^{80} +0.193213 q^{81} +22.3418i q^{82} +9.54544i q^{83} +18.6131 q^{84} +(14.7425 - 0.814190i) q^{85} -5.49318 q^{86} +4.33971i q^{87} +0.892567i q^{88} +14.4923 q^{89} +(10.2033 - 0.563501i) q^{90} +15.7841 q^{91} +4.61042i q^{92} +5.35552i q^{93} -14.4570 q^{94} +1.08255 q^{96} +7.41146i q^{97} +32.7101i q^{98} +0.366018 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 48 q^{4} + 6 q^{5} + 20 q^{6} - 52 q^{9}+O(q^{10}) \) 40 * q - 48 * q^4 + 6 * q^5 + 20 * q^6 - 52 * q^9	\( 40 q - 48 q^{4} + 6 q^{5} + 20 q^{6} - 52 q^{9} + 20 q^{11} + 40 q^{16} - 18 q^{20} - 92 q^{24} - 26 q^{25} + 76 q^{26} + 40 q^{30} + 4 q^{35} + 156 q^{36} - 80 q^{39} - 48 q^{44} - 22 q^{45} - 72 q^{49} - 32 q^{54} - 40 q^{55} + 80 q^{61} - 72 q^{64} + 16 q^{66} - 100 q^{74} - 66 q^{80} + 40 q^{81} + 44 q^{85} + 380 q^{96} - 128 q^{99}+O(q^{100}) \) 40 * q - 48 * q^4 + 6 * q^5 + 20 * q^6 - 52 * q^9 + 20 * q^11 + 40 * q^16 - 18 * q^20 - 92 * q^24 - 26 * q^25 + 76 * q^26 + 40 * q^30 + 4 * q^35 + 156 * q^36 - 80 * q^39 - 48 * q^44 - 22 * q^45 - 72 * q^49 - 32 * q^54 - 40 * q^55 + 80 * q^61 - 72 * q^64 + 16 * q^66 - 100 * q^74 - 66 * q^80 + 40 * q^81 + 44 * q^85 + 380 * q^96 - 128 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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