LMFDB - Embedded newform 231.2.g.a.197.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(197,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, 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("231.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.g (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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			197.13
Character	$\chi$	$=$	231.197
Dual form			231.2.g.a.197.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.628865 q^{2} +(-1.53987 - 0.792976i) q^{3} -1.60453 q^{4} +1.39971i q^{5} +(-0.968369 - 0.498675i) q^{6} +1.00000i q^{7} -2.26676 q^{8} +(1.74238 + 2.44216i) q^{9} +O(q^{10})$	\(q+0.628865 q^{2} +(-1.53987 - 0.792976i) q^{3} -1.60453 q^{4} +1.39971i q^{5} +(-0.968369 - 0.498675i) q^{6} +1.00000i q^{7} -2.26676 q^{8} +(1.74238 + 2.44216i) q^{9} +0.880226i q^{10} +(-1.97997 + 2.66078i) q^{11} +(2.47076 + 1.27235i) q^{12} +5.12056i q^{13} +0.628865i q^{14} +(1.10993 - 2.15536i) q^{15} +1.78357 q^{16} -7.86626 q^{17} +(1.09572 + 1.53579i) q^{18} -5.38810i q^{19} -2.24587i q^{20} +(0.792976 - 1.53987i) q^{21} +(-1.24513 + 1.67327i) q^{22} +2.26496i q^{23} +(3.49051 + 1.79749i) q^{24} +3.04083 q^{25} +3.22014i q^{26} +(-0.746457 - 5.14226i) q^{27} -1.60453i q^{28} +2.12298 q^{29} +(0.697998 - 1.35543i) q^{30} -2.48740 q^{31} +5.65515 q^{32} +(5.15882 - 2.52717i) q^{33} -4.94682 q^{34} -1.39971 q^{35} +(-2.79569 - 3.91851i) q^{36} +1.31101 q^{37} -3.38839i q^{38} +(4.06048 - 7.88498i) q^{39} -3.17280i q^{40} -6.47026 q^{41} +(0.498675 - 0.968369i) q^{42} -4.29695i q^{43} +(3.17691 - 4.26929i) q^{44} +(-3.41830 + 2.43881i) q^{45} +1.42435i q^{46} +6.76553i q^{47} +(-2.74646 - 1.41433i) q^{48} -1.00000 q^{49} +1.91227 q^{50} +(12.1130 + 6.23776i) q^{51} -8.21608i q^{52} +7.79161i q^{53} +(-0.469421 - 3.23379i) q^{54} +(-3.72430 - 2.77137i) q^{55} -2.26676i q^{56} +(-4.27263 + 8.29695i) q^{57} +1.33507 q^{58} -14.8736i q^{59} +(-1.78092 + 3.45833i) q^{60} +9.28328i q^{61} -1.56424 q^{62} +(-2.44216 + 1.74238i) q^{63} -0.0108089 q^{64} -7.16727 q^{65} +(3.24420 - 1.58925i) q^{66} +9.60266 q^{67} +12.6216 q^{68} +(1.79606 - 3.48773i) q^{69} -0.880226 q^{70} +9.34832i q^{71} +(-3.94956 - 5.53579i) q^{72} +9.47864i q^{73} +0.824451 q^{74} +(-4.68247 - 2.41130i) q^{75} +8.64535i q^{76} +(-2.66078 - 1.97997i) q^{77} +(2.55350 - 4.95859i) q^{78} +2.26153i q^{79} +2.49647i q^{80} +(-2.92824 + 8.51031i) q^{81} -4.06892 q^{82} +5.64197 q^{83} +(-1.27235 + 2.47076i) q^{84} -11.0104i q^{85} -2.70220i q^{86} +(-3.26911 - 1.68348i) q^{87} +(4.48811 - 6.03135i) q^{88} +3.80664i q^{89} +(-2.14965 + 1.53369i) q^{90} -5.12056 q^{91} -3.63419i q^{92} +(3.83027 + 1.97245i) q^{93} +4.25461i q^{94} +7.54175 q^{95} +(-8.70818 - 4.48440i) q^{96} +15.8634 q^{97} -0.628865 q^{98} +(-9.94788 - 0.199309i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{3} + 24 q^{4} + 10 q^{9}+O(q^{10}) $ 24 * q - 6 * q^3 + 24 * q^4 + 10 * q^9	$ 24 q - 6 q^{3} + 24 q^{4} + 10 q^{9} - 20 q^{12} - 10 q^{15} - 8 q^{16} - 12 q^{25} - 20 q^{31} + 14 q^{33} - 8 q^{34} - 12 q^{36} + 4 q^{37} + 6 q^{45} - 48 q^{48} - 24 q^{49} - 28 q^{55} + 44 q^{58} + 32 q^{60} - 52 q^{64} + 12 q^{66} - 4 q^{67} + 54 q^{69} - 20 q^{70} + 68 q^{75} - 20 q^{78} + 2 q^{81} + 16 q^{82} - 44 q^{88} + 24 q^{91} + 26 q^{93} - 12 q^{97} - 6 q^{99}+O(q^{100}) $ 24 * q - 6 * q^3 + 24 * q^4 + 10 * q^9 - 20 * q^12 - 10 * q^15 - 8 * q^16 - 12 * q^25 - 20 * q^31 + 14 * q^33 - 8 * q^34 - 12 * q^36 + 4 * q^37 + 6 * q^45 - 48 * q^48 - 24 * q^49 - 28 * q^55 + 44 * q^58 + 32 * q^60 - 52 * q^64 + 12 * q^66 - 4 * q^67 + 54 * q^69 - 20 * q^70 + 68 * q^75 - 20 * q^78 + 2 * q^81 + 16 * q^82 - 44 * q^88 + 24 * q^91 + 26 * q^93 - 12 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	0.628865			0.444675			0.222337	−	0.974970i	$-0.428631\pi$
$2$	0.628865			0.444675			0.222337	+	0.974970i	$0.428631\pi$
$3$	−1.53987	−	0.792976i	−0.889042	−	0.457825i
$3$	−1.53987	−	0.792976i	−0.889042	−	0.457825i
$4$	−1.60453			−0.802264
$5$			1.39971i			0.625967i	0.949759	+	0.312984i	$0.101328\pi$
$5$			1.39971i			0.625967i	−0.949759	+	0.312984i	$0.898672\pi$
$6$	−0.968369	−	0.498675i	−0.395335	−	0.203583i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−2.26676			−0.801422
$9$	1.74238	+	2.44216i	0.580792	+	0.814052i
$10$			0.880226i			0.278352i
$11$	−1.97997	+	2.66078i	−0.596982	+	0.802254i
$11$	−1.97997	+	2.66078i	−0.596982	+	0.802254i
$12$	2.47076	+	1.27235i	0.713247	+	0.367297i
$13$			5.12056i			1.42019i	0.704107	+	0.710094i	$0.251347\pi$
$13$			5.12056i			1.42019i	−0.704107	+	0.710094i	$0.748653\pi$
$14$			0.628865i			0.168071i
$15$	1.10993	−	2.15536i	0.286583	−	0.556511i
$16$	1.78357			0.445892
$17$	−7.86626			−1.90785			−0.953924	−	0.300048i	$-0.902997\pi$
$17$	−7.86626			−1.90785			−0.953924	+	0.300048i	$0.902997\pi$
$18$	1.09572	+	1.53579i	0.258264	+	0.361988i
$19$		−	5.38810i		−	1.23611i	−0.786133	−	0.618057i	$-0.787920\pi$
$19$		−	5.38810i		−	1.23611i	0.786133	−	0.618057i	$-0.212080\pi$
$20$		−	2.24587i		−	0.502191i
$21$	0.792976	−	1.53987i	0.173042	−	0.336026i
$22$	−1.24513	+	1.67327i	−0.265463	+	0.356742i
$23$			2.26496i			0.472277i	0.971719	+	0.236138i	$0.0758818\pi$
$23$			2.26496i			0.472277i	−0.971719	+	0.236138i	$0.924118\pi$
$24$	3.49051	+	1.79749i	0.712498	+	0.366911i
$25$	3.04083			0.608165
$26$			3.22014i			0.631522i
$27$	−0.746457	−	5.14226i	−0.143656	−	0.989628i
$28$		−	1.60453i		−	0.303227i
$29$	2.12298			0.394228			0.197114	−	0.980381i	$-0.436843\pi$
$29$	2.12298			0.394228			0.197114	+	0.980381i	$0.436843\pi$
$30$	0.697998	−	1.35543i	0.127436	−	0.247467i
$31$	−2.48740			−0.446751			−0.223375	−	0.974732i	$-0.571708\pi$
$31$	−2.48740			−0.446751			−0.223375	+	0.974732i	$0.571708\pi$
$32$	5.65515			0.999699
$33$	5.15882	−	2.52717i	0.898035	−	0.439925i
$34$	−4.94682			−0.848372
$35$	−1.39971			−0.236593
$36$	−2.79569	−	3.91851i	−0.465949	−	0.653085i
$37$	1.31101			0.215529			0.107765	−	0.994176i	$-0.465631\pi$
$37$	1.31101			0.215529			0.107765	+	0.994176i	$0.465631\pi$
$38$		−	3.38839i		−	0.549669i
$39$	4.06048	−	7.88498i	0.650197	−	1.26261i
$40$		−	3.17280i		−	0.501664i
$41$	−6.47026			−1.01049			−0.505243	−	0.862977i	$-0.668597\pi$
$41$	−6.47026			−1.01049			−0.505243	+	0.862977i	$0.668597\pi$
$42$	0.498675	−	0.968369i	0.0769473	−	0.149423i
$43$		−	4.29695i		−	0.655279i	−0.944803	−	0.327639i	$-0.893747\pi$
$43$		−	4.29695i		−	0.655279i	0.944803	−	0.327639i	$-0.106253\pi$
$44$	3.17691	−	4.26929i	0.478938	−	0.643620i
$45$	−3.41830	+	2.43881i	−0.509570	+	0.363557i
$46$			1.42435i			0.210010i
$47$			6.76553i			0.986854i	0.869787	+	0.493427i	$0.164256\pi$
$47$			6.76553i			0.986854i	−0.869787	+	0.493427i	$0.835744\pi$
$48$	−2.74646	−	1.41433i	−0.396417	−	0.204141i
$49$	−1.00000			−0.142857
$50$	1.91227			0.270436
$51$	12.1130	+	6.23776i	1.69616	+	0.873461i
$52$		−	8.21608i		−	1.13937i
$53$			7.79161i			1.07026i	0.844770	+	0.535130i	$0.179737\pi$
$53$			7.79161i			1.07026i	−0.844770	+	0.535130i	$0.820263\pi$
$54$	−0.469421	−	3.23379i	−0.0638801	−	0.440063i
$55$	−3.72430	−	2.77137i	−0.502185	−	0.373691i
$56$		−	2.26676i		−	0.302909i
$57$	−4.27263	+	8.29695i	−0.565924	+	1.09896i
$58$	1.33507			0.175303
$59$		−	14.8736i		−	1.93637i	−0.250232	−	0.968186i	$-0.580507\pi$
$59$		−	14.8736i		−	1.93637i	0.250232	−	0.968186i	$-0.419493\pi$
$60$	−1.78092	+	3.45833i	−0.229916	+	0.446469i
$61$			9.28328i			1.18860i	0.804243	+	0.594301i	$0.202571\pi$
$61$			9.28328i			1.18860i	−0.804243	+	0.594301i	$0.797429\pi$
$62$	−1.56424			−0.198659
$63$	−2.44216	+	1.74238i	−0.307683	+	0.219519i
$64$	−0.0108089			−0.00135112
$65$	−7.16727			−0.888991
$66$	3.24420	−	1.58925i	0.399334	−	0.195623i
$67$	9.60266			1.17315			0.586576	−	0.809894i	$-0.300476\pi$
$67$	9.60266			1.17315			0.586576	+	0.809894i	$0.300476\pi$
$68$	12.6216			1.53060
$69$	1.79606	−	3.48773i	0.216220	−	0.419874i
$70$	−0.880226			−0.105207
$71$			9.34832i			1.10944i	0.832037	+	0.554721i	$0.187175\pi$
$71$			9.34832i			1.10944i	−0.832037	+	0.554721i	$0.812825\pi$
$72$	−3.94956	−	5.53579i	−0.465460	−	0.652399i
$73$			9.47864i			1.10939i	0.832054	+	0.554695i	$0.187165\pi$
$73$			9.47864i			1.10939i	−0.832054	+	0.554695i	$0.812835\pi$
$74$	0.824451			0.0958405
$75$	−4.68247	−	2.41130i	−0.540685	−	0.278433i
$76$			8.64535i			0.991690i
$77$	−2.66078	−	1.97997i	−0.303224	−	0.225638i
$78$	2.55350	−	4.95859i	0.289126	−	0.561450i
$79$			2.26153i			0.254442i	0.991874	+	0.127221i	$0.0406057\pi$
$79$			2.26153i			0.254442i	−0.991874	+	0.127221i	$0.959394\pi$
$80$			2.49647i			0.279114i
$81$	−2.92824	+	8.51031i	−0.325360	+	0.945590i
$82$	−4.06892			−0.449337
$83$	5.64197			0.619286			0.309643	−	0.950853i	$-0.399790\pi$
$83$	5.64197			0.619286			0.309643	+	0.950853i	$0.399790\pi$
$84$	−1.27235	+	2.47076i	−0.138825	+	0.269582i
$85$		−	11.0104i		−	1.19425i
$86$		−	2.70220i		−	0.291386i
$87$	−3.26911	−	1.68348i	−0.350486	−	0.180488i
$88$	4.48811	−	6.03135i	0.478435	−	0.642944i
$89$			3.80664i			0.403503i	0.979437	+	0.201751i	$0.0646633\pi$
$89$			3.80664i			0.403503i	−0.979437	+	0.201751i	$0.935337\pi$
$90$	−2.14965	+	1.53369i	−0.226593	+	0.161665i
$91$	−5.12056			−0.536780
$92$		−	3.63419i		−	0.378891i
$93$	3.83027	+	1.97245i	0.397180	+	0.204534i
$94$			4.25461i			0.438829i
$95$	7.54175			0.773767
$96$	−8.70818	−	4.48440i	−0.888774	−	0.457687i
$97$	15.8634			1.61068			0.805340	−	0.592813i	$-0.201983\pi$
$97$	15.8634			1.61068			0.805340	+	0.592813i	$0.201983\pi$
$98$	−0.628865			−0.0635250
$99$	−9.94788	−	0.199309i	−0.999799	−	0.0200313i
$100$	−4.87909			−0.487909
$101$	−0.306511			−0.0304990			−0.0152495	−	0.999884i	$-0.504854\pi$
$101$	−0.306511			−0.0304990			−0.0152495	+	0.999884i	$0.504854\pi$
$102$	7.61744	+	3.92271i	0.754239	+	0.388406i
$103$	−1.13483			−0.111819			−0.0559093	−	0.998436i	$-0.517806\pi$
$103$	−1.13483			−0.111819			−0.0559093	+	0.998436i	$0.517806\pi$
$104$		−	11.6071i		−	1.13817i
$105$	2.15536	+	1.10993i	0.210341	+	0.108318i
$106$			4.89988i			0.475918i
$107$	−7.47891			−0.723014			−0.361507	−	0.932369i	$-0.617738\pi$
$107$	−7.47891			−0.723014			−0.361507	+	0.932369i	$0.617738\pi$
$108$	1.19771	+	8.25090i	0.115250	+	0.793943i
$109$		−	11.7266i		−	1.12320i	−0.827407	−	0.561602i	$-0.810185\pi$
$109$		−	11.7266i		−	1.12320i	0.827407	−	0.561602i	$-0.189815\pi$
$110$	−2.34208	−	1.74282i	−0.223309	−	0.166171i
$111$	−2.01879	−	1.03960i	−0.191615	−	0.0986747i
$112$			1.78357i			0.168531i
$113$		−	2.16775i		−	0.203925i	−0.994788	−	0.101962i	$-0.967488\pi$
$113$		−	2.16775i		−	0.203925i	0.994788	−	0.101962i	$-0.0325122\pi$
$114$	−2.68691	+	5.21766i	−0.251652	+	0.488679i
$115$	−3.17027			−0.295630
$116$	−3.40639			−0.316275
$117$	−12.5052	+	8.92194i	−1.15611	+	0.824834i
$118$		−	9.35346i		−	0.861056i
$119$		−	7.86626i		−	0.721099i
$120$	−2.51595	+	4.88569i	−0.229674	+	0.446000i
$121$	−3.15947	−	10.5365i	−0.287224	−	0.957863i
$122$			5.83793i			0.528542i
$123$	9.96334	+	5.13077i	0.898364	+	0.462626i
$124$	3.99111			0.358412
$125$			11.2548i			1.00666i
$126$	−1.53579	+	1.09572i	−0.136819	+	0.0976145i
$127$			17.3632i			1.54074i	0.637599	+	0.770368i	$0.279928\pi$
$127$			17.3632i			1.54074i	−0.637599	+	0.770368i	$0.720072\pi$
$128$	−11.3171			−1.00030
$129$	−3.40738	+	6.61673i	−0.300003	+	0.582570i
$130$	−4.50725			−0.395312
$131$	3.16449			0.276483			0.138241	−	0.990399i	$-0.455855\pi$
$131$	3.16449			0.276483			0.138241	+	0.990399i	$0.455855\pi$
$132$	−8.27747	+	4.05492i	−0.720461	+	0.352936i
$133$	5.38810			0.467207
$134$	6.03878			0.521671
$135$	7.19764	−	1.04482i	0.619474	−	0.0899237i
$136$	17.8309			1.52899
$137$			5.63128i			0.481113i	0.970635	+	0.240556i	$0.0773299\pi$
$137$			5.63128i			0.481113i	−0.970635	+	0.240556i	$0.922670\pi$
$138$	1.12948	−	2.19332i	0.0961476	−	0.186707i
$139$			1.99470i			0.169188i	0.996415	+	0.0845942i	$0.0269594\pi$
$139$			1.99470i			0.169188i	−0.996415	+	0.0845942i	$0.973041\pi$
$140$	2.24587			0.189810
$141$	5.36491	−	10.4180i	0.451807	−	0.877355i
$142$			5.87884i			0.493341i
$143$	−13.6247	−	10.1385i	−1.13935	−	0.847827i
$144$	3.10765	+	4.35575i	0.258971	+	0.362979i
$145$			2.97155i			0.246774i
$146$			5.96079i			0.493318i
$147$	1.53987	+	0.792976i	0.127006	+	0.0654036i
$148$	−2.10356			−0.172911
$149$	19.3628			1.58626			0.793131	−	0.609050i	$-0.208449\pi$
$149$	19.3628			1.58626			0.793131	+	0.609050i	$0.208449\pi$
$150$	−2.94464	−	1.51638i	−0.240429	−	0.123812i
$151$		−	1.52076i		−	0.123757i	−0.998084	−	0.0618787i	$-0.980291\pi$
$151$		−	1.52076i		−	0.123757i	0.998084	−	0.0618787i	$-0.0197092\pi$
$152$			12.2135i			0.990649i
$153$	−13.7060	−	19.2106i	−1.10806	−	1.55309i
$154$	−1.67327	−	1.24513i	−0.134836	−	0.100336i
$155$		−	3.48163i		−	0.279651i
$156$	−6.51516	+	12.6517i	−0.521630	+	1.01294i
$157$	−15.8226			−1.26278			−0.631392	−	0.775464i	$-0.717516\pi$
$157$	−15.8226			−1.26278			−0.631392	+	0.775464i	$0.717516\pi$
$158$			1.42220i			0.113144i
$159$	6.17857	−	11.9980i	0.489992	−	0.951507i
$160$			7.91554i			0.625779i
$161$	−2.26496			−0.178504
$162$	−1.84147	+	5.35184i	−0.144680	+	0.420480i
$163$	−16.4393			−1.28762			−0.643811	−	0.765185i	$-0.722648\pi$
$163$	−16.4393			−1.28762			−0.643811	+	0.765185i	$0.722648\pi$
$164$	10.3817			0.810676
$165$	3.53730	+	7.22082i	0.275378	+	0.562140i
$166$	3.54804			0.275381
$167$	6.15137			0.476008			0.238004	−	0.971264i	$-0.423507\pi$
$167$	6.15137			0.476008			0.238004	+	0.971264i	$0.423507\pi$
$168$	−1.79749	+	3.49051i	−0.138679	+	0.269299i
$169$	−13.2201			−1.01693
$170$		−	6.92409i		−	0.531053i
$171$	13.1586	−	9.38810i	1.00626	−	0.717926i
$172$			6.89458i			0.525707i
$173$	10.1442			0.771246			0.385623	−	0.922656i	$-0.373987\pi$
$173$	10.1442			0.771246			0.385623	+	0.922656i	$0.373987\pi$
$174$	−2.05583	−	1.05868i	−0.155852	−	0.0802583i
$175$			3.04083i			0.229865i
$176$	−3.53141	+	4.74568i	−0.266190	+	0.357719i
$177$	−11.7944	+	22.9033i	−0.886520	+	1.72152i
$178$			2.39386i			0.179428i
$179$		−	9.88518i		−	0.738853i	−0.929260	−	0.369426i	$-0.879554\pi$
$179$		−	9.88518i		−	0.738853i	0.929260	−	0.369426i	$-0.120446\pi$
$180$	5.48475	−	3.91315i	0.408809	−	0.291669i
$181$	2.72524			0.202566			0.101283	−	0.994858i	$-0.467705\pi$
$181$	2.72524			0.202566			0.101283	+	0.994858i	$0.467705\pi$
$182$	−3.22014			−0.238693
$183$	7.36142	−	14.2950i	0.544172	−	1.05672i
$184$		−	5.13413i		−	0.378493i
$185$			1.83503i			0.134914i
$186$	2.40872	+	1.24041i	0.176616	+	0.0909510i
$187$	15.5749	−	20.9304i	1.13895	−	1.53058i
$188$		−	10.8555i		−	0.791718i
$189$	5.14226	−	0.746457i	0.374044	−	0.0542968i
$190$	4.74274			0.344075
$191$		−	5.91523i		−	0.428011i	−0.976832	−	0.214005i	$-0.931349\pi$
$191$		−	5.91523i		−	0.428011i	0.976832	−	0.214005i	$-0.0686510\pi$
$192$	0.0166443	+	0.00857124i	0.00120120	+	0.000618576i
$193$			21.9963i			1.58333i	0.610958	+	0.791663i	$0.290784\pi$
$193$			21.9963i			1.58333i	−0.610958	+	0.791663i	$0.709216\pi$
$194$	9.97591			0.716229
$195$	11.0366	+	5.68348i	0.790350	+	0.407002i
$196$	1.60453			0.114609
$197$	−11.5825			−0.825220			−0.412610	−	0.910908i	$-0.635383\pi$
$197$	−11.5825			−0.825220			−0.412610	+	0.910908i	$0.635383\pi$
$198$	−6.25588	−	0.125338i	−0.444586	−	0.00890740i
$199$	−5.35255			−0.379432			−0.189716	−	0.981839i	$-0.560757\pi$
$199$	−5.35255			−0.379432			−0.189716	+	0.981839i	$0.560757\pi$
$200$	−6.89283			−0.487397
$201$	−14.7868	−	7.61468i	−1.04298	−	0.537098i
$202$	−0.192754			−0.0135621
$203$			2.12298i			0.149004i
$204$	−19.4356	−	10.0087i	−1.36077	−	0.700746i
$205$		−	9.05646i		−	0.632531i
$206$	−0.713658			−0.0497229
$207$	−5.53138	+	3.94641i	−0.384458	+	0.274295i
$208$			9.13287i			0.633250i
$209$	14.3365	+	10.6683i	0.991678	+	0.737938i
$210$	1.35543	+	0.697998i	0.0935336	+	0.0481665i
$211$		−	10.7037i		−	0.736872i	−0.929653	−	0.368436i	$-0.879893\pi$
$211$		−	10.7037i		−	0.736872i	0.929653	−	0.368436i	$-0.120107\pi$
$212$		−	12.5019i		−	0.858632i
$213$	7.41300	−	14.3952i	0.507930	−	0.986341i
$214$	−4.70323			−0.321506
$215$	6.01446			0.410183
$216$	1.69204	+	11.6563i	0.115129	+	0.793109i
$217$		−	2.48740i		−	0.168856i
$218$		−	7.37445i		−	0.499461i
$219$	7.51634	−	14.5958i	0.507907	−	0.986295i
$220$	5.97575	+	4.44674i	0.402885	+	0.299799i
$221$		−	40.2796i		−	2.70950i
$222$	−1.26954	−	0.653770i	−0.0852062	−	0.0438782i
$223$	−2.20941			−0.147953			−0.0739764	−	0.997260i	$-0.523569\pi$
$223$	−2.20941			−0.147953			−0.0739764	+	0.997260i	$0.523569\pi$
$224$			5.65515i			0.377851i
$225$	5.29827	+	7.42617i	0.353218	+	0.495078i
$226$		−	1.36322i		−	0.0906803i
$227$	9.90328			0.657304			0.328652	−	0.944451i	$-0.393406\pi$
$227$	9.90328			0.657304			0.328652	+	0.944451i	$0.393406\pi$
$228$	6.85556	−	13.3127i	0.454021	−	0.881654i
$229$	−8.82851			−0.583405			−0.291702	−	0.956509i	$-0.594222\pi$
$229$	−8.82851			−0.583405			−0.291702	+	0.956509i	$0.594222\pi$
$230$	−1.99368			−0.131459
$231$	2.52717	+	5.15882i	0.166276	+	0.339425i
$232$	−4.81230			−0.315943
$233$	3.51336			0.230168			0.115084	−	0.993356i	$-0.463286\pi$
$233$	3.51336			0.230168			0.115084	+	0.993356i	$0.463286\pi$
$234$	−7.86409	+	5.61070i	−0.514091	+	0.366783i
$235$	−9.46975			−0.617738
$236$			23.8650i			1.55348i
$237$	1.79334	−	3.48245i	0.116490	−	0.226210i
$238$		−	4.94682i		−	0.320655i
$239$	25.8002			1.66888			0.834439	−	0.551101i	$-0.185792\pi$
$239$	25.8002			1.66888			0.834439	+	0.551101i	$0.185792\pi$
$240$	1.97964	−	3.84423i	0.127785	−	0.248144i
$241$		−	12.6023i		−	0.811786i	−0.913921	−	0.405893i	$-0.866960\pi$
$241$		−	12.6023i		−	0.811786i	0.913921	−	0.405893i	$-0.133040\pi$
$242$	−1.98688	−	6.62604i	−0.127721	−	0.425938i
$243$	11.2576	−	10.7827i	0.722174	−	0.691711i
$244$		−	14.8953i		−	0.953573i
$245$		−	1.39971i		−	0.0894239i
$246$	6.26560	+	3.22656i	0.399480	+	0.205718i
$247$	27.5901			1.75551
$248$	5.63835			0.358036
$249$	−8.68787	−	4.47395i	−0.550572	−	0.283525i
$250$			7.07774i			0.447636i
$251$			2.24802i			0.141894i	0.997480	+	0.0709469i	$0.0226021\pi$
$251$			2.24802i			0.141894i	−0.997480	+	0.0709469i	$0.977398\pi$
$252$	3.91851	−	2.79569i	0.246843	−	0.176112i
$253$	−6.02655	−	4.48454i	−0.378886	−	0.281941i
$254$			10.9191i			0.685127i
$255$	−8.73102	+	16.9546i	−0.546758	+	1.06174i
$256$	−7.09531			−0.443457
$257$		−	2.20944i		−	0.137821i	−0.997623	−	0.0689106i	$-0.978048\pi$
$257$		−	2.20944i		−	0.137821i	0.997623	−	0.0689106i	$-0.0219523\pi$
$258$	−2.14278	+	4.16103i	−0.133404	+	0.259054i
$259$			1.31101i			0.0814624i
$260$	11.5001			0.713205
$261$	3.69904	+	5.18466i	0.228965	+	0.320922i
$262$	1.99004			0.122945
$263$	−22.5624			−1.39126			−0.695629	−	0.718401i	$-0.744874\pi$
$263$	−22.5624			−1.39126			−0.695629	+	0.718401i	$0.744874\pi$
$264$	−11.6938	+	5.72850i	−0.719705	+	0.352565i
$265$	−10.9060			−0.669948
$266$	3.38839			0.207755
$267$	3.01857	−	5.86171i	0.184734	−	0.358731i
$268$	−15.4077			−0.941178
$269$		−	3.79522i		−	0.231399i	−0.993284	−	0.115699i	$-0.963089\pi$
$269$		−	3.79522i		−	0.231399i	0.993284	−	0.115699i	$-0.0369109\pi$
$270$	4.52635	−	0.657051i	0.275465	−	0.0399868i
$271$			13.4820i			0.818972i	0.912316	+	0.409486i	$0.134292\pi$
$271$			13.4820i			0.818972i	−0.912316	+	0.409486i	$0.865708\pi$
$272$	−14.0300			−0.850694
$273$	7.88498	+	4.06048i	0.477220	+	0.245752i
$274$			3.54132i			0.213939i
$275$	−6.02073	+	8.09096i	−0.363064	+	0.487903i
$276$	−2.88183	+	5.59617i	−0.173466	+	0.336850i
$277$		−	0.0725150i		−	0.00435700i	−0.999998	−	0.00217850i	$-0.999307\pi$
$277$		−	0.0725150i		−	0.00435700i	0.999998	−	0.00217850i	$-0.000693439\pi$
$278$			1.25440i			0.0752338i
$279$	−4.33400	−	6.07463i	−0.259470	−	0.363678i
$280$	3.17280			0.189611
$281$	−10.1465			−0.605287			−0.302644	−	0.953104i	$-0.597869\pi$
$281$	−10.1465			−0.605287			−0.302644	+	0.953104i	$0.597869\pi$
$282$	3.37380	−	6.55153i	0.200907	−	0.390138i
$283$		−	0.711086i		−	0.0422697i	−0.999777	−	0.0211348i	$-0.993272\pi$
$283$		−	0.711086i		−	0.0422697i	0.999777	−	0.0211348i	$-0.00672793\pi$
$284$		−	14.9996i		−	0.890065i
$285$	−11.6133	−	5.98043i	−0.687911	−	0.354250i
$286$	−8.56808	−	6.37577i	−0.506641	−	0.377007i
$287$		−	6.47026i		−	0.381928i
$288$	9.85340	+	13.8108i	0.580617	+	0.813806i
$289$	44.8780			2.63988
$290$			1.86871i			0.109734i
$291$	−24.4274	−	12.5793i	−1.43196	−	0.737410i
$292$		−	15.2087i		−	0.890024i
$293$	5.24916			0.306659			0.153330	−	0.988175i	$-0.451000\pi$
$293$	5.24916			0.306659			0.153330	+	0.988175i	$0.451000\pi$
$294$	0.968369	+	0.498675i	0.0564764	+	0.0290833i
$295$	20.8186			1.21211
$296$	−2.97176			−0.172730
$297$	15.1604	+	8.19534i	0.879693	+	0.475542i
$298$	12.1766			0.705371
$299$	−11.5979			−0.670721
$300$	7.51315	+	3.86900i	0.433772	+	0.223377i
$301$	4.29695			0.247672
$302$		−	0.956351i		−	0.0550318i
$303$	0.471986	+	0.243056i	0.0271149	+	0.0139632i
$304$		−	9.61004i		−	0.551174i
$305$	−12.9939			−0.744026
$306$	−8.61922	−	12.0809i	−0.492728	−	0.690619i
$307$			9.12897i			0.521018i	0.965471	+	0.260509i	$0.0838904\pi$
$307$			9.12897i			0.521018i	−0.965471	+	0.260509i	$0.916110\pi$
$308$	4.26929	+	3.17691i	0.243265	+	0.181021i
$309$	1.74749	+	0.899897i	0.0994114	+	0.0511933i
$310$		−	2.18948i		−	0.124354i
$311$			27.3166i			1.54898i	0.632586	+	0.774490i	$0.281993\pi$
$311$			27.3166i			1.54898i	−0.632586	+	0.774490i	$0.718007\pi$
$312$	−9.20415	+	17.8734i	−0.521082	+	1.01188i
$313$	−17.8132			−1.00686			−0.503430	−	0.864036i	$-0.667929\pi$
$313$	−17.8132			−1.00686			−0.503430	+	0.864036i	$0.667929\pi$
$314$	−9.95031			−0.561528
$315$	−2.43881	−	3.41830i	−0.137412	−	0.192599i
$316$		−	3.62869i		−	0.204130i
$317$			4.33844i			0.243671i	0.992550	+	0.121835i	$0.0388780\pi$
$317$			4.33844i			0.243671i	−0.992550	+	0.121835i	$0.961122\pi$
$318$	3.88549	−	7.54515i	0.217887	−	0.423111i
$319$	−4.20344	+	5.64879i	−0.235347	+	0.316271i
$320$		−	0.0151293i		−	0.000845756i
$321$	11.5165	+	5.93060i	0.642790	+	0.331014i
$322$	−1.42435			−0.0793762
$323$			42.3842i			2.35832i
$324$	4.69845	−	13.6550i	0.261025	−	0.758613i
$325$			15.5707i			0.863709i
$326$	−10.3381			−0.572573
$327$	−9.29892	+	18.0574i	−0.514231	+	0.998577i
$328$	14.6666			0.809825
$329$	−6.76553			−0.372996
$330$	2.22448	+	4.54092i	0.122454	+	0.249970i
$331$	−25.5248			−1.40297			−0.701486	−	0.712683i	$-0.747480\pi$
$331$	−25.5248			−1.40297			−0.701486	+	0.712683i	$0.747480\pi$
$332$	−9.05269			−0.496831
$333$	2.28428	+	3.20170i	0.125178	+	0.175452i
$334$	3.86839			0.211669
$335$			13.4409i			0.734355i
$336$	1.41433	−	2.74646i	0.0771579	−	0.149832i
$337$			9.72472i			0.529739i	0.964284	+	0.264870i	$0.0853289\pi$
$337$			9.72472i			0.529739i	−0.964284	+	0.264870i	$0.914671\pi$
$338$	−8.31368			−0.452204
$339$	−1.71898	+	3.33805i	−0.0933619	+	0.181298i
$340$			17.6666i			0.958104i
$341$	4.92498	−	6.61843i	0.266702	−	0.358408i
$342$	8.27497	−	5.90385i	0.447459	−	0.319244i
$343$		−	1.00000i		−	0.0539949i
$344$			9.74016i			0.525154i
$345$	4.88180	+	2.51395i	0.262827	+	0.135347i
$346$	6.37931			0.342954
$347$	−20.4532			−1.09799			−0.548994	−	0.835826i	$-0.684989\pi$
$347$	−20.4532			−1.09799			−0.548994	+	0.835826i	$0.684989\pi$
$348$	5.24538	+	2.70119i	0.281182	+	0.144799i
$349$			17.2193i			0.921726i	0.887471	+	0.460863i	$0.152460\pi$
$349$			17.2193i			0.921726i	−0.887471	+	0.460863i	$0.847540\pi$
$350$			1.91227i			0.102215i
$351$	26.3312	−	3.82228i	1.40546	−	0.204018i
$352$	−11.1970	+	15.0471i	−0.596802	+	0.802013i
$353$			12.2957i			0.654435i	0.944949	+	0.327217i	$0.106111\pi$
$353$			12.2957i			0.654435i	−0.944949	+	0.327217i	$0.893889\pi$
$354$	−7.41707	+	14.4031i	−0.394213	+	0.765515i
$355$	−13.0849			−0.694474
$356$		−	6.10786i		−	0.323716i
$357$	−6.23776	+	12.1130i	−0.330137	+	0.641087i
$358$		−	6.21644i		−	0.328549i
$359$	−17.0719			−0.901018			−0.450509	−	0.892772i	$-0.648757\pi$
$359$	−17.0719			−0.901018			−0.450509	+	0.892772i	$0.648757\pi$
$360$	7.74847	−	5.52821i	0.408380	−	0.291362i
$361$	−10.0316			−0.527978
$362$	1.71381			0.0900759
$363$	−3.49004	+	18.7302i	−0.183179	+	0.983079i
$364$	8.21608			0.430640
$365$	−13.2673			−0.694442
$366$	4.62934	−	8.98964i	0.241980	−	0.469896i
$367$	25.9213			1.35308			0.676539	−	0.736406i	$-0.263479\pi$
$367$	25.9213			1.35308			0.676539	+	0.736406i	$0.263479\pi$
$368$			4.03971i			0.210584i
$369$	−11.2736	−	15.8014i	−0.586882	−	0.822587i
$370$			1.15399i			0.0599930i
$371$	−7.79161			−0.404520
$372$	−6.14578	−	3.16486i	−0.318644	−	0.164090i
$373$			6.27775i			0.325049i	0.986704	+	0.162525i	$0.0519637\pi$
$373$			6.27775i			0.325049i	−0.986704	+	0.162525i	$0.948036\pi$
$374$	9.79453	−	13.1624i	0.506463	−	0.680610i
$375$	8.92478	−	17.3309i	0.460874	−	0.894962i
$376$		−	15.3359i		−	0.790886i
$377$			10.8709i			0.559878i
$378$	3.23379	−	0.469421i	0.166328	−	0.0241444i
$379$	3.81760			0.196097			0.0980484	−	0.995182i	$-0.468740\pi$
$379$	3.81760			0.196097			0.0980484	+	0.995182i	$0.468740\pi$
$380$	−12.1009			−0.620765
$381$	13.7686	−	26.7370i	0.705388	−	1.36978i
$382$		−	3.71988i		−	0.190326i
$383$			4.10141i			0.209572i	0.994495	+	0.104786i	$0.0334158\pi$
$383$			4.10141i			0.209572i	−0.994495	+	0.104786i	$0.966584\pi$
$384$	17.4268	+	8.97419i	0.889309	+	0.457962i
$385$	2.77137	−	3.72430i	0.141242	−	0.189808i
$386$			13.8327i			0.704065i
$387$	10.4938	−	7.48691i	0.533431	−	0.380581i
$388$	−25.4532			−1.29219
$389$		−	21.1329i		−	1.07148i	−0.844383	−	0.535741i	$-0.820032\pi$
$389$		−	21.1329i		−	1.07148i	0.844383	−	0.535741i	$-0.179968\pi$
$390$	6.94056	+	3.57414i	0.351449	+	0.180984i
$391$		−	17.8168i		−	0.901032i
$392$	2.26676			0.114489
$393$	−4.87289	−	2.50936i	−0.245805	−	0.126581i
$394$	−7.28384			−0.366955
$395$	−3.16548			−0.159272
$396$	15.9617	+	0.319796i	0.802103	+	0.0160704i
$397$	−2.00808			−0.100783			−0.0503913	−	0.998730i	$-0.516047\pi$
$397$	−2.00808			−0.100783			−0.0503913	+	0.998730i	$0.516047\pi$
$398$	−3.36603			−0.168724
$399$	−8.29695	−	4.27263i	−0.415367	−	0.213899i
$400$	5.42352			0.271176
$401$		−	7.68132i		−	0.383587i	−0.981435	−	0.191793i	$-0.938570\pi$
$401$		−	7.68132i		−	0.383587i	0.981435	−	0.191793i	$-0.0614303\pi$
$402$	−9.29892	−	4.78861i	−0.463788	−	0.238834i
$403$		−	12.7369i		−	0.634470i
$404$	0.491806			0.0244683
$405$	−11.9119	−	4.09868i	−0.591908	−	0.203665i
$406$			1.33507i			0.0662585i
$407$	−2.59576	+	3.48831i	−0.128667	+	0.172909i
$408$	−27.4573	−	14.1395i	−1.35934	−	0.700010i
$409$		−	22.3006i		−	1.10269i	−0.834276	−	0.551347i	$-0.814114\pi$
$409$		−	22.3006i		−	1.10269i	0.834276	−	0.551347i	$-0.185886\pi$
$410$		−	5.69529i		−	0.281270i
$411$	4.46547	−	8.67142i	0.220265	−	0.427730i
$412$	1.82087			0.0897080
$413$	14.8736			0.731880
$414$	−3.47849	+	2.48176i	−0.170959	+	0.121972i
$415$			7.89709i			0.387653i
$416$			28.9575i			1.41976i
$417$	1.58175	−	3.07157i	0.0774587	−	0.150416i
$418$	9.01574	+	6.70889i	0.440974	+	0.328143i
$419$			16.6237i			0.812120i	0.913846	+	0.406060i	$0.133098\pi$
$419$			16.6237i			0.812120i	−0.913846	+	0.406060i	$0.866902\pi$
$420$	−3.45833	−	1.78092i	−0.168749	−	0.0868999i
$421$	13.0467			0.635857			0.317929	−	0.948115i	$-0.397013\pi$
$421$	13.0467			0.635857			0.317929	+	0.948115i	$0.397013\pi$
$422$		−	6.73117i		−	0.327668i
$423$	−16.5225	+	11.7881i	−0.803350	+	0.573157i
$424$		−	17.6617i		−	0.857730i
$425$	−23.9199			−1.16029
$426$	4.66178	−	9.05262i	0.225864	−	0.438601i
$427$	−9.28328			−0.449249
$428$	12.0001			0.580048
$429$	12.9405	+	26.4160i	0.624775	+	1.27538i
$430$	3.78229			0.182398
$431$	−6.33438			−0.305116			−0.152558	−	0.988295i	$-0.548751\pi$
$431$	−6.33438			−0.305116			−0.152558	+	0.988295i	$0.548751\pi$
$432$	−1.33136	−	9.17157i	−0.0640549	−	0.441267i
$433$	10.2252			0.491390			0.245695	−	0.969347i	$-0.420984\pi$
$433$	10.2252			0.491390			0.245695	+	0.969347i	$0.420984\pi$
$434$		−	1.56424i		−	0.0750860i
$435$	2.35637	−	4.57579i	0.112979	−	0.219393i
$436$			18.8157i			0.901107i
$437$	12.2038			0.583788
$438$	4.72676	−	9.17882i	0.225853	−	0.438581i
$439$			13.5977i			0.648984i	0.945888	+	0.324492i	$0.105193\pi$
$439$			13.5977i			0.648984i	−0.945888	+	0.324492i	$0.894807\pi$
$440$	8.44211	+	6.28204i	0.402462	+	0.299484i
$441$	−1.74238	−	2.44216i	−0.0829703	−	0.116293i
$442$		−	25.3305i		−	1.20485i
$443$		−	37.4083i		−	1.77732i	−0.458563	−	0.888662i	$-0.651636\pi$
$443$		−	37.4083i		−	1.77732i	0.458563	−	0.888662i	$-0.348364\pi$
$444$	3.23920	+	1.66807i	0.153726	+	0.0791632i
$445$	−5.32817			−0.252580
$446$	−1.38942			−0.0657909
$447$	−29.8161	−	15.3542i	−1.41025	−	0.726231i
$448$		−	0.0108089i		−	0.000510675i
$449$		−	21.2272i		−	1.00177i	−0.865513	−	0.500886i	$-0.833008\pi$
$449$		−	21.2272i		−	1.00177i	0.865513	−	0.500886i	$-0.166992\pi$
$450$	3.33190	+	4.67006i	0.157067	+	0.220149i
$451$	12.8109	−	17.2159i	0.603242	−	0.810666i
$452$			3.47822i			0.163602i
$453$	−1.20592	+	2.34176i	−0.0566592	+	0.110026i
$454$	6.22783			0.292286
$455$		−	7.16727i		−	0.336007i
$456$	9.68505	−	18.8072i	0.453544	−	0.880729i
$457$			25.3347i			1.18511i	0.805531	+	0.592553i	$0.201880\pi$
$457$			25.3347i			1.18511i	−0.805531	+	0.592553i	$0.798120\pi$
$458$	−5.55195			−0.259425
$459$	5.87182	+	40.4503i	0.274073	+	1.88806i
$460$	5.08680			0.237173
$461$	32.9044			1.53251			0.766255	−	0.642537i	$-0.222118\pi$
$461$	32.9044			1.53251			0.766255	+	0.642537i	$0.222118\pi$
$462$	1.58925	+	3.24420i	0.0739387	+	0.150934i
$463$	7.10290			0.330100			0.165050	−	0.986285i	$-0.447222\pi$
$463$	7.10290			0.330100			0.165050	+	0.986285i	$0.447222\pi$
$464$	3.78649			0.175783
$465$	−2.76085	+	5.36125i	−0.128031	+	0.248622i
$466$	2.20943			0.102350
$467$		−	8.26658i		−	0.382532i	−0.981538	−	0.191266i	$-0.938741\pi$
$467$		−	8.26658i		−	0.382532i	0.981538	−	0.191266i	$-0.0612592\pi$
$468$	20.0649	−	14.3155i	0.927503	−	0.661735i
$469$			9.60266i			0.443410i
$470$	−5.95520			−0.274693
$471$	24.3647	+	12.5470i	1.12267	+	0.578134i
$472$			33.7148i			1.55185i
$473$	11.4332	+	8.50782i	0.525700	+	0.391190i
$474$	1.12777	−	2.18999i	0.0518002	−	0.100590i
$475$		−	16.3843i		−	0.751762i
$476$			12.6216i			0.578512i
$477$	−19.0283	+	13.5759i	−0.871247	+	0.621599i
$478$	16.2249			0.742108
$479$	−20.8747			−0.953792			−0.476896	−	0.878960i	$-0.658238\pi$
$479$	−20.8747			−0.953792			−0.476896	+	0.878960i	$0.658238\pi$
$480$	6.27684	−	12.1889i	0.286497	−	0.556344i
$481$			6.71312i			0.306092i
$482$		−	7.92516i		−	0.360981i
$483$	3.48773	+	1.79606i	0.158697	+	0.0817235i
$484$	5.06945	+	16.9061i	0.230430	+	0.768460i
$485$			22.2040i			1.00823i
$486$	7.07950	−	6.78087i	0.321133	−	0.307587i
$487$	−30.7746			−1.39453			−0.697265	−	0.716813i	$-0.745600\pi$
$487$	−30.7746			−1.39453			−0.697265	+	0.716813i	$0.745600\pi$
$488$		−	21.0430i		−	0.952572i
$489$	25.3143	+	13.0359i	1.14475	+	0.589506i
$490$		−	0.880226i		−	0.0397646i
$491$	18.5678			0.837954			0.418977	−	0.907997i	$-0.362389\pi$
$491$	18.5678			0.837954			0.418977	+	0.907997i	$0.362389\pi$
$492$	−15.9865	−	8.23246i	−0.720725	−	0.371148i
$493$	−16.6999			−0.752128
$494$	17.3504			0.780633
$495$	0.278973	−	13.9241i	0.0125389	−	0.625842i
$496$	−4.43645			−0.199203
$497$	−9.34832			−0.419330
$498$	−5.46350	−	2.81351i	−0.244825	−	0.126076i
$499$	−18.1861			−0.814123			−0.407061	−	0.913401i	$-0.633446\pi$
$499$	−18.1861			−0.814123			−0.407061	+	0.913401i	$0.633446\pi$
$500$		−	18.0586i		−	0.807606i
$501$	−9.47229	−	4.87789i	−0.423191	−	0.217928i
$502$			1.41370i			0.0630966i
$503$	8.70284			0.388040			0.194020	−	0.980998i	$-0.437847\pi$
$503$	8.70284			0.388040			0.194020	+	0.980998i	$0.437847\pi$
$504$	5.53579	−	3.94956i	0.246584	−	0.175927i
$505$		−	0.429025i		−	0.0190914i
$506$	−3.78989	−	2.82017i	−0.168481	−	0.125372i
$507$	20.3572	+	10.4832i	0.904096	+	0.465577i
$508$		−	27.8598i		−	1.23608i
$509$			3.53507i			0.156689i	0.996926	+	0.0783446i	$0.0249634\pi$
$509$			3.53507i			0.156689i	−0.996926	+	0.0783446i	$0.975037\pi$
$510$	−5.49064	+	10.6622i	−0.243129	+	0.472129i
$511$	−9.47864			−0.419310
$512$	18.1722			0.803105
$513$	−27.7070	+	4.02198i	−1.22329	+	0.177575i
$514$		−	1.38944i		−	0.0612857i
$515$		−	1.58843i		−	0.0699947i
$516$	5.46724	−	10.6167i	0.240682	−	0.467375i
$517$	−18.0016	−	13.3955i	−0.791708	−	0.589135i
$518$			0.824451i			0.0362243i
$519$	−15.6207	−	8.04408i	−0.685670	−	0.353096i
$520$	16.2465			0.712456
$521$		−	9.80310i		−	0.429482i	−0.976671	−	0.214741i	$-0.931109\pi$
$521$		−	9.80310i		−	0.429482i	0.976671	−	0.214741i	$-0.0688907\pi$
$522$	2.32620	+	3.26045i	0.101815	+	0.142706i
$523$			11.4083i			0.498848i	0.968394	+	0.249424i	$0.0802413\pi$
$523$			11.4083i			0.498848i	−0.968394	+	0.249424i	$0.919759\pi$
$524$	−5.07751			−0.221812
$525$	2.41130	−	4.68247i	0.105238	−	0.204360i
$526$	−14.1887			−0.618657
$527$	19.5666			0.852333
$528$	9.20110	−	4.50739i	0.400427	−	0.196159i
$529$	17.8700			0.776955
$530$	−6.85838			−0.297909
$531$	36.3235	−	25.9153i	1.57631	−	1.12463i
$532$	−8.64535			−0.374824
$533$		−	33.1314i		−	1.43508i
$534$	1.89828	−	3.68623i	0.0821465	−	0.159519i
$535$		−	10.4683i		−	0.452583i
$536$	−21.7670			−0.940190
$537$	−7.83871	+	15.2219i	−0.338265	+	0.656871i
$538$		−	2.38668i		−	0.102897i
$539$	1.97997	−	2.66078i	0.0852832	−	0.114608i
$540$	−11.5488	+	1.67644i	−0.496982	+	0.0721426i
$541$		−	40.4431i		−	1.73878i	−0.494123	−	0.869392i	$-0.664511\pi$
$541$		−	40.4431i		−	1.73878i	0.494123	−	0.869392i	$-0.335489\pi$
$542$			8.47835i			0.364176i
$543$	−4.19651	−	2.16105i	−0.180090	−	0.0927397i
$544$	−44.4849			−1.90727
$545$	16.4138			0.703089
$546$	4.95859	+	2.55350i	0.212208	+	0.109280i
$547$			24.9225i			1.06561i	0.846239	+	0.532804i	$0.178862\pi$
$547$			24.9225i			1.06561i	−0.846239	+	0.532804i	$0.821138\pi$
$548$		−	9.03555i		−	0.385979i
$549$	−22.6712	+	16.1750i	−0.967584	+	0.690331i
$550$	−3.78623	+	5.08812i	−0.161445	+	0.216958i
$551$		−	11.4388i		−	0.487311i
$552$	−4.07124	+	7.90587i	−0.173283	+	0.336496i
$553$	−2.26153			−0.0961701
$554$		−	0.0456022i		−	0.00193745i
$555$	1.45514	−	2.82570i	0.0617671	−	0.119944i
$556$		−	3.20055i		−	0.135734i
$557$	15.4996			0.656739			0.328369	−	0.944549i	$-0.393501\pi$
$557$	15.4996			0.656739			0.328369	+	0.944549i	$0.393501\pi$
$558$	−2.72550	−	3.82012i	−0.115380	−	0.161719i
$559$	22.0028			0.930618
$560$	−2.49647			−0.105495
$561$	−40.5806	+	19.8794i	−1.71331	+	0.839309i
$562$	−6.38076			−0.269156
$563$	26.6916			1.12492			0.562459	−	0.826825i	$-0.309856\pi$
$563$	26.6916			1.12492			0.562459	+	0.826825i	$0.309856\pi$
$564$	−8.60814	+	16.7160i	−0.362468	+	0.703871i
$565$	3.03421			0.127650
$566$		−	0.447177i		−	0.0187963i
$567$	−8.51031	−	2.92824i	−0.357399	−	0.122975i
$568$		−	21.1904i		−	0.889131i
$569$	43.6405			1.82951			0.914753	−	0.404013i	$-0.132385\pi$
$569$	43.6405			1.82951			0.914753	+	0.404013i	$0.132385\pi$
$570$	−7.30319	−	3.76088i	−0.305897	−	0.157526i
$571$			32.7971i			1.37252i	0.727359	+	0.686258i	$0.240748\pi$
$571$			32.7971i			1.37252i	−0.727359	+	0.686258i	$0.759252\pi$
$572$	21.8612	+	16.2676i	0.914061	+	0.680181i
$573$	−4.69064	+	9.10866i	−0.195954	+	0.380520i
$574$		−	4.06892i		−	0.169834i
$575$			6.88735i			0.287222i
$576$	−0.0188333	−	0.0263971i	−0.000784719	−	0.00109988i
$577$	−10.9774			−0.456994			−0.228497	−	0.973545i	$-0.573381\pi$
$577$	−10.9774			−0.456994			−0.228497	+	0.973545i	$0.573381\pi$
$578$	28.2222			1.17389
$579$	17.4425	−	33.8713i	0.724886	−	1.40764i
$580$		−	4.76794i		−	0.197978i
$581$			5.64197i			0.234068i
$582$	−15.3616	−	7.91066i	−0.636758	−	0.327908i
$583$	−20.7317	−	15.4271i	−0.858621	−	0.638927i
$584$		−	21.4858i		−	0.889090i
$585$	−12.4881	−	17.5036i	−0.516319	−	0.723684i
$586$	3.30102			0.136364
$587$			26.7840i			1.10549i	0.833349	+	0.552747i	$0.186420\pi$
$587$			26.7840i			1.10549i	−0.833349	+	0.552747i	$0.813580\pi$
$588$	−2.47076	−	1.27235i	−0.101892	−	0.0524710i
$589$			13.4024i			0.552235i
$590$	13.0921			0.538993
$591$	17.8355	+	9.18466i	0.733655	+	0.377806i
$592$	2.33828			0.0961028
$593$	−12.1102			−0.497308			−0.248654	−	0.968592i	$-0.579988\pi$
$593$	−12.1102			−0.497308			−0.248654	+	0.968592i	$0.579988\pi$
$594$	9.53382	+	5.15377i	0.391177	+	0.211462i
$595$	11.0104			0.451384
$596$	−31.0682			−1.27260
$597$	8.24221	+	4.24444i	0.337331	+	0.173714i
$598$	−7.29349			−0.298253
$599$			23.1293i			0.945036i	0.881321	+	0.472518i	$0.156655\pi$
$599$			23.1293i			0.945036i	−0.881321	+	0.472518i	$0.843345\pi$
$600$	10.6140	+	5.46585i	0.433316	+	0.223142i
$601$		−	8.96690i		−	0.365768i	−0.983135	−	0.182884i	$-0.941457\pi$
$601$		−	8.96690i		−	0.365768i	0.983135	−	0.182884i	$-0.0585432\pi$
$602$	2.70220			0.110134
$603$	16.7315	+	23.4512i	0.681358	+	0.955006i
$604$			2.44010i			0.0992861i
$605$	14.7480	−	4.42232i	0.599591	−	0.179793i
$606$	0.296816	+	0.152850i	0.0120573	+	0.00620909i
$607$		−	14.0694i		−	0.571058i	−0.958370	−	0.285529i	$-0.907831\pi$
$607$		−	14.0694i		−	0.571058i	0.958370	−	0.285529i	$-0.0921693\pi$
$608$		−	30.4705i		−	1.23574i
$609$	1.68348	−	3.26911i	0.0682179	−	0.132471i
$610$	−8.17138			−0.330850
$611$	−34.6433			−1.40152
$612$	21.9917	+	30.8240i	0.888960	+	1.24599i
$613$		−	13.7427i		−	0.555061i	−0.960717	−	0.277531i	$-0.910484\pi$
$613$		−	13.7427i		−	0.555061i	0.960717	−	0.277531i	$-0.0895160\pi$
$614$			5.74090i			0.231684i
$615$	−7.18156	+	13.9457i	−0.289588	+	0.562346i
$616$	6.03135	+	4.48811i	0.243010	+	0.180831i
$617$		−	31.2137i		−	1.25661i	−0.777965	−	0.628307i	$-0.783748\pi$
$617$		−	31.2137i		−	1.25661i	0.777965	−	0.628307i	$-0.216252\pi$
$618$	1.09894	+	0.565914i	0.0442058	+	0.0227644i
$619$	−17.3133			−0.695880			−0.347940	−	0.937517i	$-0.613119\pi$
$619$	−17.3133			−0.695880			−0.347940	+	0.937517i	$0.613119\pi$
$620$			5.58638i			0.224354i
$621$	11.6470	−	1.69069i	0.467378	−	0.0678452i
$622$			17.1784i			0.688792i
$623$	−3.80664			−0.152510
$624$	7.24215	−	14.0634i	0.289918	−	0.562986i
$625$	−0.549248			−0.0219699
$626$	−11.2021			−0.447726
$627$	−13.6167	−	27.7962i	−0.543797	−	1.11007i
$628$	25.3879			1.01309
$629$	−10.3128			−0.411197
$630$	−1.53369	−	2.14965i	−0.0611035	−	0.0856440i
$631$	−26.3186			−1.04773			−0.523863	−	0.851803i	$-0.675510\pi$
$631$	−26.3186			−1.04773			−0.523863	+	0.851803i	$0.675510\pi$
$632$		−	5.12635i		−	0.203915i
$633$	−8.48776	+	16.4822i	−0.337358	+	0.655110i
$634$			2.72829i			0.108354i
$635$	−24.3034			−0.964451
$636$	−9.91368	+	19.2512i	−0.393103	+	0.763360i
$637$		−	5.12056i		−	0.202884i
$638$	−2.64340	+	3.55233i	−0.104653	+	0.140638i
$639$	−22.8301	+	16.2883i	−0.903143	+	0.644355i
$640$		−	15.8406i		−	0.626155i
$641$			4.98595i			0.196933i	0.995140	+	0.0984665i	$0.0313937\pi$
$641$			4.98595i			0.196933i	−0.995140	+	0.0984665i	$0.968606\pi$
$642$	7.24235	+	3.72955i	0.285833	+	0.147194i
$643$	13.3724			0.527355			0.263678	−	0.964611i	$-0.415064\pi$
$643$	13.3724			0.527355			0.263678	+	0.964611i	$0.415064\pi$
$644$	3.63419			0.143207
$645$	−9.26147	−	4.76933i	−0.364670	−	0.187792i
$646$			26.6539i			1.04868i
$647$		−	39.6125i		−	1.55733i	−0.627441	−	0.778664i	$-0.715897\pi$
$647$		−	39.6125i		−	1.55733i	0.627441	−	0.778664i	$-0.284103\pi$
$648$	6.63763	−	19.2909i	0.260751	−	0.757816i
$649$	39.5752	+	29.4491i	1.55346	+	1.15598i
$650$			9.79189i			0.384070i
$651$	−1.97245	+	3.83027i	−0.0773065	+	0.150120i
$652$	26.3773			1.03301
$653$		−	3.15327i		−	0.123397i	−0.998095	−	0.0616985i	$-0.980348\pi$
$653$		−	3.15327i		−	0.123397i	0.998095	−	0.0616985i	$-0.0196517\pi$
$654$	−5.84777	+	11.3557i	−0.228666	+	0.444042i
$655$			4.42935i			0.173069i
$656$	−11.5402			−0.450567
$657$	−23.1483	+	16.5154i	−0.903101	+	0.644326i
$658$	−4.25461			−0.165862
$659$	3.35808			0.130812			0.0654060	−	0.997859i	$-0.479166\pi$
$659$	3.35808			0.130812			0.0654060	+	0.997859i	$0.479166\pi$
$660$	−5.67570	−	11.5860i	−0.220926	−	0.450985i
$661$	49.9542			1.94299			0.971496	−	0.237056i	$-0.0761824\pi$
$661$	49.9542			1.94299			0.971496	+	0.237056i	$0.0761824\pi$
$662$	−16.0517			−0.623867
$663$	−31.9408	+	62.0253i	−1.24048	+	2.40886i
$664$	−12.7890			−0.496309
$665$			7.54175i			0.292456i
$666$	1.43650	+	2.01344i	0.0556634	+	0.0780191i
$667$			4.80847i			0.186185i
$668$	−9.87005			−0.381884
$669$	3.40219	+	1.75201i	0.131536	+	0.0677365i
$670$			8.45251i			0.326549i
$671$	−24.7007	−	18.3806i	−0.953561	−	0.709575i
$672$	4.48440	−	8.70818i	0.172989	−	0.335925i
$673$			43.2951i			1.66890i	0.551082	+	0.834451i	$0.314215\pi$
$673$			43.2951i			1.66890i	−0.551082	+	0.834451i	$0.685785\pi$
$674$			6.11554i			0.235562i
$675$	−2.26985	−	15.6367i	−0.0873664	−	0.601857i
$676$	21.2121			0.815849
$677$	51.5345			1.98063			0.990316	−	0.138829i	$-0.0443339\pi$
$677$	51.5345			1.98063			0.990316	+	0.138829i	$0.0443339\pi$
$678$	−1.08100	+	2.09918i	−0.0415157	+	0.0806186i
$679$			15.8634i			0.608780i
$680$			24.9581i			0.957098i
$681$	−15.2497	−	7.85307i	−0.584371	−	0.300930i
$682$	3.09715	−	4.16210i	0.118596	−	0.159375i
$683$			39.8186i			1.52362i	0.647803	+	0.761808i	$0.275688\pi$
$683$			39.8186i			1.52362i	−0.647803	+	0.761808i	$0.724312\pi$
$684$	−21.1133	+	15.0635i	−0.807287	+	0.575966i
$685$	−7.88213			−0.301161
$686$		−	0.628865i		−	0.0240102i
$687$	13.5947	+	7.00080i	0.518671	+	0.267097i
$688$		−	7.66390i		−	0.292184i
$689$	−39.8974			−1.51997
$690$	3.06999	+	1.58094i	0.116873	+	0.0601853i
$691$	12.7423			0.484741			0.242370	−	0.970184i	$-0.422075\pi$
$691$	12.7423			0.484741			0.242370	+	0.970184i	$0.422075\pi$
$692$	−16.2766			−0.618743
$693$	0.199309	−	9.94788i	0.00757111	−	0.377889i
$694$	−12.8623			−0.488248
$695$	−2.79199			−0.105906
$696$	7.41030	+	3.81604i	0.280887	+	0.144647i
$697$	50.8968			1.92785
$698$			10.8286i			0.409868i
$699$	−5.41010	−	2.78601i	−0.204629	−	0.105377i
$700$		−	4.87909i		−	0.184412i
$701$	9.93928			0.375402			0.187701	−	0.982226i	$-0.439896\pi$
$701$	9.93928			0.375402			0.187701	+	0.982226i	$0.439896\pi$
$702$	16.5588	−	2.40370i	0.624971	−	0.0907217i
$703$		−	7.06387i		−	0.266419i
$704$	0.0214013	−	0.0287602i	0.000806594	−	0.00108394i
$705$	14.5821	+	7.50929i	0.549195	+	0.282816i
$706$			7.73235i			0.291011i
$707$		−	0.306511i		−	0.0115275i
$708$	18.9244	−	36.7490i	0.711223	−	1.38111i
$709$	32.0156			1.20237			0.601186	−	0.799109i	$-0.294695\pi$
$709$	32.0156			1.20237			0.601186	+	0.799109i	$0.294695\pi$
$710$	−8.22864			−0.308815
$711$	−5.52301	+	3.94044i	−0.207129	+	0.147778i
$712$		−	8.62875i		−	0.323376i
$713$		−	5.63387i		−	0.210990i
$714$	−3.92271	+	7.61744i	−0.146804	+	0.285075i
$715$	14.1910	−	19.0705i	0.530712	−	0.713197i
$716$			15.8610i			0.592755i
$717$	−39.7289	−	20.4590i	−1.48370	−	0.764054i
$718$	−10.7359			−0.400660
$719$		−	15.3992i		−	0.574292i	−0.957887	−	0.287146i	$-0.907293\pi$
$719$		−	15.3992i		−	0.574292i	0.957887	−	0.287146i	$-0.0927065\pi$
$720$	−6.09677	+	4.34979i	−0.227213	+	0.162107i
$721$		−	1.13483i		−	0.0422634i
$722$	−6.30852			−0.234779
$723$	−9.99334	+	19.4059i	−0.371656	+	0.721712i
$724$	−4.37273			−0.162511
$725$	6.45563			0.239756
$726$	−2.19476	+	11.7788i	−0.0814553	+	0.437151i
$727$	−50.7874			−1.88360			−0.941801	−	0.336171i	$-0.890868\pi$
$727$	−50.7874			−1.88360			−0.941801	+	0.336171i	$0.890868\pi$
$728$	11.6071			0.430187
$729$	−25.8856	+	7.67695i	−0.958726	+	0.284331i
$730$	−8.34334			−0.308801
$731$			33.8009i			1.25017i
$732$	−11.8116	+	22.9368i	−0.436570	+	0.847767i
$733$		−	29.6659i		−	1.09573i	−0.836566	−	0.547867i	$-0.815440\pi$
$733$		−	29.6659i		−	1.09573i	0.836566	−	0.547867i	$-0.184560\pi$
$734$	16.3010			0.601680
$735$	−1.10993	+	2.15536i	−0.0409405	+	0.0795016i
$736$			12.8087i			0.472134i
$737$	−19.0130	+	25.5505i	−0.700351	+	0.941166i
$738$	−7.08960	−	9.93694i	−0.260972	−	0.365784i
$739$		−	9.64470i		−	0.354786i	−0.984140	−	0.177393i	$-0.943234\pi$
$739$		−	9.64470i		−	0.354786i	0.984140	−	0.177393i	$-0.0567664\pi$
$740$		−	2.94436i		−	0.108237i
$741$	−42.4850	−	21.8783i	−1.56073	−	0.803718i
$742$	−4.89988			−0.179880
$743$	−27.6201			−1.01328			−0.506641	−	0.862157i	$-0.669113\pi$
$743$	−27.6201			−1.01328			−0.506641	+	0.862157i	$0.669113\pi$
$744$	−8.68231	−	4.47108i	−0.318309	−	0.163918i
$745$			27.1022i			0.992948i
$746$			3.94786i			0.144541i
$747$	9.83043	+	13.7786i	0.359677	+	0.504131i
$748$	−24.9904	+	33.5834i	−0.913740	+	1.22793i
$749$		−	7.47891i		−	0.273274i
$750$	5.61248	−	10.8988i	0.204939	−	0.397967i
$751$	48.0476			1.75328			0.876642	−	0.481144i	$-0.159779\pi$
$751$	48.0476			1.75328			0.876642	+	0.481144i	$0.159779\pi$
$752$			12.0668i			0.440030i
$753$	1.78263	−	3.46165i	0.0649626	−	0.126150i
$754$			6.83631i			0.248964i
$755$	2.12861			0.0774680
$756$	−8.25090	+	1.19771i	−0.300082	+	0.0435603i
$757$	−8.06808			−0.293239			−0.146620	−	0.989193i	$-0.546839\pi$
$757$	−8.06808			−0.293239			−0.146620	+	0.989193i	$0.546839\pi$
$758$	2.40075			0.0871993
$759$	5.72395	+	11.6845i	0.207766	+	0.424121i
$760$	−17.0953			−0.620114
$761$	30.3643			1.10071			0.550353	−	0.834932i	$-0.314493\pi$
$761$	30.3643			1.10071			0.550353	+	0.834932i	$0.314493\pi$
$762$	8.65861	−	16.8140i	0.313668	−	0.609107i
$763$	11.7266			0.424532
$764$			9.49115i			0.343378i
$765$	26.8892	−	19.1843i	0.972181	−	0.693611i
$766$			2.57924i			0.0931916i
$767$	76.1609			2.75001
$768$	10.9258	+	5.62641i	0.394252	+	0.203026i
$769$		−	32.0281i		−	1.15496i	−0.816404	−	0.577481i	$-0.804036\pi$
$769$		−	32.0281i		−	1.15496i	0.816404	−	0.577481i	$-0.195964\pi$
$770$	1.74282	−	2.34208i	0.0628068	−	0.0844029i
$771$	−1.75204	+	3.40225i	−0.0630980	+	0.122529i
$772$		−	35.2936i		−	1.27025i
$773$		−	24.5910i		−	0.884477i	−0.896897	−	0.442239i	$-0.854184\pi$
$773$		−	24.5910i		−	0.884477i	0.896897	−	0.442239i	$-0.145816\pi$
$774$	6.59920	−	4.70826i	0.237203	−	0.169235i
$775$	−7.56376			−0.271698
$776$	−35.9585			−1.29083
$777$	1.03960	−	2.01879i	0.0372955	−	0.0724235i
$778$		−	13.2898i		−	0.476461i
$779$			34.8624i			1.24908i
$780$	−17.7086	−	9.11930i	−0.634070	−	0.326523i
$781$	−24.8738	−	18.5094i	−0.890054	−	0.662317i
$782$		−	11.2043i		−	0.400666i
$783$	−1.58472	−	10.9169i	−0.0566332	−	0.390139i
$784$	−1.78357			−0.0636989
$785$		−	22.1470i		−	0.790461i
$786$	−3.06439	−	1.57805i	−0.109303	−	0.0562873i
$787$			0.407568i			0.0145282i	0.999974	+	0.00726411i	$0.00231226\pi$
$787$			0.407568i			0.0145282i	−0.999974	+	0.00726411i	$0.997688\pi$
$788$	18.5845			0.662044
$789$	34.7431	+	17.8915i	1.23689	+	0.636953i
$790$	−1.99066			−0.0708244
$791$	2.16775			0.0770764
$792$	22.5495	+	0.451785i	0.801261	+	0.0160535i
$793$	−47.5356			−1.68804
$794$	−1.26281			−0.0448155
$795$	16.7937	+	8.64817i	0.595612	+	0.306719i
$796$	8.58832			0.304405
$797$		−	47.3952i		−	1.67882i	−0.543496	−	0.839412i	$-0.682900\pi$
$797$		−	47.3952i		−	1.67882i	0.543496	−	0.839412i	$-0.317100\pi$
$798$	−5.21766	−	2.68691i	−0.184703	−	0.0951156i
$799$		−	53.2194i		−	1.88277i
$800$	17.1963			0.607982
$801$	−9.29640	+	6.63260i	−0.328472	+	0.234351i
$802$		−	4.83051i		−	0.170571i
$803$	−25.2205	−	18.7674i	−0.890014	−	0.662287i
$804$	23.7259	+	12.2180i	0.836747	+	0.430895i
$805$		−	3.17027i		−	0.111737i
$806$		−	8.00979i		−	0.282133i
$807$	−3.00952	+	5.84413i	−0.105940	+	0.205723i
$808$	0.694788			0.0244426
$809$	10.9905			0.386404			0.193202	−	0.981159i	$-0.438113\pi$
$809$	10.9905			0.386404			0.193202	+	0.981159i	$0.438113\pi$
$810$	−7.49100	−	2.57752i	−0.263207	−	0.0905647i
$811$			14.8192i			0.520371i	0.965559	+	0.260186i	$0.0837838\pi$
$811$			14.8192i			0.520371i	−0.965559	+	0.260186i	$0.916216\pi$
$812$		−	3.40639i		−	0.119541i
$813$	10.6909	−	20.7604i	0.374946	−	0.728101i
$814$	−1.63238	+	2.19368i	−0.0572151	+	0.0768884i
$815$		−	23.0101i		−	0.806009i
$816$	21.6043	+	11.1255i	0.756303	+	0.389469i
$817$	−23.1524			−0.809999
$818$		−	14.0241i		−	0.490340i
$819$	−8.92194	−	12.5052i	−0.311758	−	0.436967i
$820$			14.5313i			0.507457i
$821$	7.81630			0.272791			0.136395	−	0.990654i	$-0.456448\pi$
$821$	7.81630			0.272791			0.136395	+	0.990654i	$0.456448\pi$
$822$	2.80818	−	5.45315i	0.0979465	−	0.190201i
$823$	37.5890			1.31027			0.655135	−	0.755512i	$-0.272612\pi$
$823$	37.5890			1.31027			0.655135	+	0.755512i	$0.272612\pi$
$824$	2.57240			0.0896138
$825$	15.6871	−	7.68470i	0.546153	−	0.267547i
$826$	9.35346			0.325449
$827$	19.5391			0.679440			0.339720	−	0.940527i	$-0.389668\pi$
$827$	19.5391			0.679440			0.339720	+	0.940527i	$0.389668\pi$
$828$	8.87526	−	6.33213i	0.308437	−	0.220057i
$829$	−29.5391			−1.02593			−0.512967	−	0.858408i	$-0.671454\pi$
$829$	−29.5391			−1.02593			−0.512967	+	0.858408i	$0.671454\pi$
$830$			4.96620i			0.172379i
$831$	−0.0575027	+	0.111663i	−0.00199475	+	0.00387356i
$832$		−	0.0553478i		−	0.00191884i
$833$	7.86626			0.272550
$834$	0.994708	−	1.93161i	0.0344439	−	0.0668860i
$835$			8.61011i			0.297965i
$836$	−23.0034	−	17.1175i	−0.795588	−	0.592022i
$837$	1.85674	+	12.7909i	0.0641783	+	0.442117i
$838$			10.4541i			0.361129i
$839$		−	38.3305i		−	1.32332i	−0.749805	−	0.661659i	$-0.769853\pi$
$839$		−	38.3305i		−	1.32332i	0.749805	−	0.661659i	$-0.230147\pi$
$840$	−4.88569	−	2.51595i	−0.168572	−	0.0868087i
$841$	−24.4929			−0.844584
$842$	8.20462			0.282750
$843$	15.6242	+	8.04591i	0.538126	+	0.277116i
$844$			17.1744i			0.591166i
$845$		−	18.5043i		−	0.636566i
$846$	−10.3904	+	7.41313i	−0.357230	+	0.254869i
$847$	10.5365	−	3.15947i	0.362038	−	0.108561i
$848$			13.8969i			0.477221i
$849$	−0.563874	+	1.09498i	−0.0193521	+	0.0375795i
$850$	−15.0424			−0.515950
$851$			2.96939i			0.101789i
$852$	−11.8944	+	23.0975i	−0.407494	+	0.791306i
$853$			31.0549i			1.06330i	0.846964	+	0.531651i	$0.178428\pi$
$853$			31.0549i			1.06330i	−0.846964	+	0.531651i	$0.821572\pi$
$854$	−5.83793			−0.199770
$855$	13.1406	+	18.4181i	0.449398	+	0.629886i
$856$	16.9529			0.579439
$857$	55.5681			1.89817			0.949086	−	0.315018i	$-0.102010\pi$
$857$	55.5681			1.89817			0.949086	+	0.315018i	$0.102010\pi$
$858$	8.13786	+	16.6121i	0.277822	+	0.567128i
$859$	1.65947			0.0566205			0.0283102	−	0.999599i	$-0.490987\pi$
$859$	1.65947			0.0566205			0.0283102	+	0.999599i	$0.490987\pi$
$860$	−9.65037			−0.329075
$861$	−5.13077	+	9.96334i	−0.174856	+	0.339550i
$862$	−3.98347			−0.135678
$863$		−	45.7736i		−	1.55815i	−0.626930	−	0.779075i	$-0.715689\pi$
$863$		−	45.7736i		−	1.55815i	0.626930	−	0.779075i	$-0.284311\pi$
$864$	−4.22133	−	29.0802i	−0.143612	−	0.989330i
$865$			14.1988i			0.482775i
$866$	6.43025			0.218509
$867$	−69.1062	−	35.5872i	−2.34697	−	1.20861i
$868$			3.99111i			0.135467i
$869$	−6.01743	−	4.47775i	−0.204127	−	0.151897i
$870$	1.48184	−	2.87756i	0.0502391	−	0.0975584i
$871$			49.1710i			1.66610i
$872$			26.5814i			0.900161i
$873$	27.6399	+	38.7408i	0.935471	+	1.31118i
$874$	7.67456			0.259596
$875$	−11.2548			−0.380481
$876$	−12.0602	+	23.4194i	−0.407476	+	0.791269i
$877$		−	49.7260i		−	1.67913i	−0.543261	−	0.839564i	$-0.682810\pi$
$877$		−	49.7260i		−	1.67913i	0.543261	−	0.839564i	$-0.317190\pi$
$878$			8.55114i			0.288587i
$879$	−8.08301	−	4.16246i	−0.272633	−	0.140396i
$880$	−6.64255	−	4.94293i	−0.223920	−	0.166626i
$881$			37.6862i			1.26968i	0.772644	+	0.634840i	$0.218934\pi$
$881$			37.6862i			1.26968i	−0.772644	+	0.634840i	$0.781066\pi$
$882$	−1.09572	−	1.53579i	−0.0368948	−	0.0517126i
$883$	40.5420			1.36435			0.682174	−	0.731190i	$-0.261035\pi$
$883$	40.5420			1.36435			0.682174	+	0.731190i	$0.261035\pi$
$884$			64.6298i			2.17374i
$885$	−32.0578	−	16.5086i	−1.07761	−	0.554932i
$886$		−	23.5248i		−	0.790331i
$887$	−30.9079			−1.03779			−0.518893	−	0.854839i	$-0.673656\pi$
$887$	−30.9079			−1.03779			−0.518893	+	0.854839i	$0.673656\pi$
$888$	4.57611	+	2.35653i	0.153564	+	0.0790800i
$889$	−17.3632			−0.582344
$890$	−3.35070			−0.112316
$891$	−16.8462	−	24.6415i	−0.564369	−	0.825522i
$892$	3.54506			0.118697
$893$	36.4533			1.21986
$894$	−18.7503	−	9.65575i	−0.627105	−	0.322937i
$895$	13.8363			0.462498
$896$		−	11.3171i		−	0.378078i
$897$	17.8591	+	9.19683i	0.596300	+	0.307073i
$898$		−	13.3490i		−	0.445463i
$899$	−5.28072			−0.176122
$900$	−8.50122	−	11.9155i	−0.283374	−	0.397183i
$901$		−	61.2909i		−	2.04189i
$902$	8.05633	−	10.8265i	0.268247	−	0.360483i
$903$	−6.61673	−	3.40738i	−0.220191	−	0.113390i
$904$			4.91378i			0.163430i
$905$			3.81454i			0.126800i
$906$	−0.758363	+	1.47265i	−0.0251949	+	0.0489256i
$907$	−9.99470			−0.331869			−0.165934	−	0.986137i	$-0.553064\pi$
$907$	−9.99470			−0.331869			−0.165934	+	0.986137i	$0.553064\pi$
$908$	−15.8901			−0.527331
$909$	−0.534058	−	0.748548i	−0.0177136	−	0.0248278i
$910$		−	4.50725i		−	0.149414i
$911$			6.81919i			0.225930i	0.993599	+	0.112965i	$0.0360347\pi$
$911$			6.81919i			0.225930i	−0.993599	+	0.112965i	$0.963965\pi$
$912$	−7.62053	+	14.7982i	−0.252341	+	0.490017i
$913$	−11.1709	+	15.0120i	−0.369703	+	0.496825i
$914$			15.9321i			0.526987i
$915$	20.0088	+	10.3038i	0.661470	+	0.340634i
$916$	14.1656			0.468045
$917$			3.16449i			0.104501i
$918$	3.69259	+	25.4378i	0.121874	+	0.839573i
$919$		−	26.6008i		−	0.877478i	−0.898614	−	0.438739i	$-0.855425\pi$
$919$		−	26.6008i		−	0.877478i	0.898614	−	0.438739i	$-0.144575\pi$
$920$	7.18626			0.236924
$921$	7.23906	−	14.0574i	0.238535	−	0.463207i
$922$	20.6924			0.681469
$923$	−47.8686			−1.57562
$924$	−4.05492	−	8.27747i	−0.133397	−	0.272309i
$925$	3.98656			0.131077
$926$	4.46677			0.146787
$927$	−1.97731	−	2.77144i	−0.0649433	−	0.0910261i
$928$	12.0058			0.394110
$929$		−	15.9862i		−	0.524490i	−0.965001	−	0.262245i	$-0.915537\pi$
$929$		−	15.9862i		−	0.524490i	0.965001	−	0.262245i	$-0.0844629\pi$
$930$	−1.73620	+	3.37150i	−0.0569324	+	0.110556i
$931$			5.38810i			0.176588i
$932$	−5.63728			−0.184655
$933$	21.6614	−	42.0638i	0.709162	−	1.37711i
$934$		−	5.19856i		−	0.170102i
$935$	29.2963	+	21.8003i	0.958092	+	0.712946i
$936$	28.3463	−	20.2239i	0.926528	−	0.661040i
$937$		−	12.5427i		−	0.409751i	−0.978788	−	0.204875i	$-0.934321\pi$
$937$		−	12.5427i		−	0.409751i	0.978788	−	0.204875i	$-0.0656789\pi$
$938$			6.03878i			0.197173i
$939$	27.4299	+	14.1254i	0.895142	+	0.460966i
$940$	15.1945			0.495589
$941$	42.6383			1.38997			0.694985	−	0.719024i	$-0.255411\pi$
$941$	42.6383			1.38997			0.694985	+	0.719024i	$0.255411\pi$
$942$	15.3221	+	7.89036i	0.499222	+	0.257082i
$943$		−	14.6549i		−	0.477229i
$944$		−	26.5280i		−	0.863413i
$945$	1.04482	+	7.19764i	0.0339880	+	0.234139i
$946$	7.18996	+	5.35027i	0.233766	+	0.173952i
$947$		−	14.3923i		−	0.467685i	−0.972274	−	0.233843i	$-0.924870\pi$
$947$		−	14.3923i		−	0.467685i	0.972274	−	0.233843i	$-0.0751301\pi$
$948$	−2.87746	+	5.58770i	−0.0934557	+	0.181480i
$949$	−48.5359			−1.57554
$950$		−	10.3035i		−	0.334290i
$951$	3.44028	−	6.68062i	0.111559	−	0.216634i
$952$			17.8309i			0.577904i
$953$	0.524444			0.0169884			0.00849421	−	0.999964i	$-0.497296\pi$
$953$	0.524444			0.0169884			0.00849421	+	0.999964i	$0.497296\pi$
$954$	−11.9663	+	8.53743i	−0.387422	+	0.276410i
$955$	8.27957			0.267921
$956$	−41.3972			−1.33888
$957$	10.9521	−	5.36515i	0.354031	−	0.173431i
$958$	−13.1274			−0.424127
$959$	−5.63128			−0.181844
$960$	−0.0119972	+	0.0232972i	−0.000387208	+	0.000751912i
$961$	−24.8128			−0.800414
$962$			4.22165i			0.136111i
$963$	−13.0311	−	18.2647i	−0.419921	−	0.588571i
$964$			20.2208i			0.651267i
$965$	−30.7883			−0.991110
$966$	2.19332	+	1.12948i	0.0705688	+	0.0363404i
$967$			26.1107i			0.839664i	0.907602	+	0.419832i	$0.137911\pi$
$967$			26.1107i			0.839664i	−0.907602	+	0.419832i	$0.862089\pi$
$968$	7.16176	+	23.8837i	0.230188	+	0.767653i
$969$	33.6096	−	65.2660i	1.07970	−	2.09664i
$970$			13.9633i			0.448336i
$971$			22.9199i			0.735534i	0.929918	+	0.367767i	$0.119878\pi$
$971$			22.9199i			0.735534i	−0.929918	+	0.367767i	$0.880122\pi$
$972$	−18.0631	+	17.3012i	−0.579374	+	0.554935i
$973$	−1.99470			−0.0639472
$974$	−19.3531			−0.620113
$975$	12.3472	−	23.9768i	0.395427	−	0.767873i
$976$			16.5574i			0.529988i
$977$			32.2825i			1.03281i	0.856345	+	0.516404i	$0.172730\pi$
$977$			32.2825i			1.03281i	−0.856345	+	0.516404i	$0.827270\pi$
$978$	15.9193	+	8.19785i	0.509042	+	0.262138i
$979$	−10.1286	−	7.53702i	−0.323712	−	0.240884i
$980$			2.24587i			0.0717416i
$981$	28.6382	−	20.4322i	0.914347	−	0.652349i
$982$	11.6767			0.372617
$983$			31.9474i			1.01896i	0.860482	+	0.509481i	$0.170163\pi$
$983$			31.9474i			1.01896i	−0.860482	+	0.509481i	$0.829837\pi$
$984$	−22.5845	−	11.6302i	−0.719969	−	0.370758i
$985$		−	16.2121i		−	0.516560i
$986$	−10.5020			−0.334452
$987$	10.4180	+	5.36491i	0.331609	+	0.170767i
$988$	−44.2690			−1.40839
$989$	9.73241			0.309473
$990$	0.175437	−	8.75638i	0.00557574	−	0.278296i
$991$	25.0152			0.794634			0.397317	−	0.917681i	$-0.369941\pi$
$991$	25.0152			0.794634			0.397317	+	0.917681i	$0.369941\pi$
$992$	−14.0666			−0.446616
$993$	39.3048	+	20.2406i	1.24730	+	0.642316i
$994$	−5.87884			−0.186465
$995$		−	7.49199i		−	0.237512i
$996$	13.9399	+	7.17857i	0.441704	+	0.227462i
$997$		−	11.9884i		−	0.379676i	−0.981815	−	0.189838i	$-0.939204\pi$
$997$		−	11.9884i		−	0.379676i	0.981815	−	0.189838i	$-0.0607962\pi$
$998$	−11.4366			−0.362020
$999$	−0.978615	−	6.74157i	−0.0309620	−	0.213294i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.g.a.197.13	yes	24
3.2	odd	2	inner	231.2.g.a.197.12	yes	24
11.10	odd	2	inner	231.2.g.a.197.11	✓	24
33.32	even	2	inner	231.2.g.a.197.14	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.g.a.197.11	✓	24	11.10	odd	2	inner
231.2.g.a.197.12	yes	24	3.2	odd	2	inner
231.2.g.a.197.13	yes	24	1.1	even	1	trivial
231.2.g.a.197.14	yes	24	33.32	even	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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.628865 q^{2} +(-1.53987 - 0.792976i) q^{3} -1.60453 q^{4} +1.39971i q^{5} +(-0.968369 - 0.498675i) q^{6} +1.00000i q^{7} -2.26676 q^{8} +(1.74238 + 2.44216i) q^{9} +O(q^{10})\)	\(q+0.628865 q^{2} +(-1.53987 - 0.792976i) q^{3} -1.60453 q^{4} +1.39971i q^{5} +(-0.968369 - 0.498675i) q^{6} +1.00000i q^{7} -2.26676 q^{8} +(1.74238 + 2.44216i) q^{9} +0.880226i q^{10} +(-1.97997 + 2.66078i) q^{11} +(2.47076 + 1.27235i) q^{12} +5.12056i q^{13} +0.628865i q^{14} +(1.10993 - 2.15536i) q^{15} +1.78357 q^{16} -7.86626 q^{17} +(1.09572 + 1.53579i) q^{18} -5.38810i q^{19} -2.24587i q^{20} +(0.792976 - 1.53987i) q^{21} +(-1.24513 + 1.67327i) q^{22} +2.26496i q^{23} +(3.49051 + 1.79749i) q^{24} +3.04083 q^{25} +3.22014i q^{26} +(-0.746457 - 5.14226i) q^{27} -1.60453i q^{28} +2.12298 q^{29} +(0.697998 - 1.35543i) q^{30} -2.48740 q^{31} +5.65515 q^{32} +(5.15882 - 2.52717i) q^{33} -4.94682 q^{34} -1.39971 q^{35} +(-2.79569 - 3.91851i) q^{36} +1.31101 q^{37} -3.38839i q^{38} +(4.06048 - 7.88498i) q^{39} -3.17280i q^{40} -6.47026 q^{41} +(0.498675 - 0.968369i) q^{42} -4.29695i q^{43} +(3.17691 - 4.26929i) q^{44} +(-3.41830 + 2.43881i) q^{45} +1.42435i q^{46} +6.76553i q^{47} +(-2.74646 - 1.41433i) q^{48} -1.00000 q^{49} +1.91227 q^{50} +(12.1130 + 6.23776i) q^{51} -8.21608i q^{52} +7.79161i q^{53} +(-0.469421 - 3.23379i) q^{54} +(-3.72430 - 2.77137i) q^{55} -2.26676i q^{56} +(-4.27263 + 8.29695i) q^{57} +1.33507 q^{58} -14.8736i q^{59} +(-1.78092 + 3.45833i) q^{60} +9.28328i q^{61} -1.56424 q^{62} +(-2.44216 + 1.74238i) q^{63} -0.0108089 q^{64} -7.16727 q^{65} +(3.24420 - 1.58925i) q^{66} +9.60266 q^{67} +12.6216 q^{68} +(1.79606 - 3.48773i) q^{69} -0.880226 q^{70} +9.34832i q^{71} +(-3.94956 - 5.53579i) q^{72} +9.47864i q^{73} +0.824451 q^{74} +(-4.68247 - 2.41130i) q^{75} +8.64535i q^{76} +(-2.66078 - 1.97997i) q^{77} +(2.55350 - 4.95859i) q^{78} +2.26153i q^{79} +2.49647i q^{80} +(-2.92824 + 8.51031i) q^{81} -4.06892 q^{82} +5.64197 q^{83} +(-1.27235 + 2.47076i) q^{84} -11.0104i q^{85} -2.70220i q^{86} +(-3.26911 - 1.68348i) q^{87} +(4.48811 - 6.03135i) q^{88} +3.80664i q^{89} +(-2.14965 + 1.53369i) q^{90} -5.12056 q^{91} -3.63419i q^{92} +(3.83027 + 1.97245i) q^{93} +4.25461i q^{94} +7.54175 q^{95} +(-8.70818 - 4.48440i) q^{96} +15.8634 q^{97} -0.628865 q^{98} +(-9.94788 - 0.199309i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{3} + 24 q^{4} + 10 q^{9}+O(q^{10}) \) 24 * q - 6 * q^3 + 24 * q^4 + 10 * q^9	\( 24 q - 6 q^{3} + 24 q^{4} + 10 q^{9} - 20 q^{12} - 10 q^{15} - 8 q^{16} - 12 q^{25} - 20 q^{31} + 14 q^{33} - 8 q^{34} - 12 q^{36} + 4 q^{37} + 6 q^{45} - 48 q^{48} - 24 q^{49} - 28 q^{55} + 44 q^{58} + 32 q^{60} - 52 q^{64} + 12 q^{66} - 4 q^{67} + 54 q^{69} - 20 q^{70} + 68 q^{75} - 20 q^{78} + 2 q^{81} + 16 q^{82} - 44 q^{88} + 24 q^{91} + 26 q^{93} - 12 q^{97} - 6 q^{99}+O(q^{100}) \) 24 * q - 6 * q^3 + 24 * q^4 + 10 * q^9 - 20 * q^12 - 10 * q^15 - 8 * q^16 - 12 * q^25 - 20 * q^31 + 14 * q^33 - 8 * q^34 - 12 * q^36 + 4 * q^37 + 6 * q^45 - 48 * q^48 - 24 * q^49 - 28 * q^55 + 44 * q^58 + 32 * q^60 - 52 * q^64 + 12 * q^66 - 4 * q^67 + 54 * q^69 - 20 * q^70 + 68 * q^75 - 20 * q^78 + 2 * q^81 + 16 * q^82 - 44 * q^88 + 24 * q^91 + 26 * q^93 - 12 * q^97 - 6 * q^99

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