LMFDB - Embedded newform 231.2.g.a.197.5

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			197.5
Character	$\chi$	$=$	231.197
Dual form			231.2.g.a.197.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.92194 q^{2} +(1.23500 - 1.21441i) q^{3} +1.69384 q^{4} +0.413489i q^{5} +(-2.37358 + 2.33402i) q^{6} -1.00000i q^{7} +0.588415 q^{8} +(0.0504282 - 2.99958i) q^{9} +O(q^{10})$	\(q-1.92194 q^{2} +(1.23500 - 1.21441i) q^{3} +1.69384 q^{4} +0.413489i q^{5} +(-2.37358 + 2.33402i) q^{6} -1.00000i q^{7} +0.588415 q^{8} +(0.0504282 - 2.99958i) q^{9} -0.794699i q^{10} +(3.07734 + 1.23694i) q^{11} +(2.09189 - 2.05702i) q^{12} -1.35904i q^{13} +1.92194i q^{14} +(0.502144 + 0.510656i) q^{15} -4.51858 q^{16} -1.64016 q^{17} +(-0.0969199 + 5.76500i) q^{18} -4.21243i q^{19} +0.700384i q^{20} +(-1.21441 - 1.23500i) q^{21} +(-5.91444 - 2.37731i) q^{22} -6.16223i q^{23} +(0.726690 - 0.714576i) q^{24} +4.82903 q^{25} +2.61198i q^{26} +(-3.58043 - 3.76570i) q^{27} -1.69384i q^{28} +2.73184 q^{29} +(-0.965088 - 0.981450i) q^{30} +4.56717 q^{31} +7.50760 q^{32} +(5.30264 - 2.20953i) q^{33} +3.15228 q^{34} +0.413489 q^{35} +(0.0854175 - 5.08081i) q^{36} -6.41046 q^{37} +8.09602i q^{38} +(-1.65042 - 1.67840i) q^{39} +0.243303i q^{40} -3.57034 q^{41} +(2.33402 + 2.37358i) q^{42} +1.20233i q^{43} +(5.21252 + 2.09517i) q^{44} +(1.24029 + 0.0208515i) q^{45} +11.8434i q^{46} +8.33307i q^{47} +(-5.58043 + 5.48740i) q^{48} -1.00000 q^{49} -9.28109 q^{50} +(-2.02559 + 1.99182i) q^{51} -2.30199i q^{52} -5.91727i q^{53} +(6.88136 + 7.23745i) q^{54} +(-0.511459 + 1.27244i) q^{55} -0.588415i q^{56} +(-5.11560 - 5.20233i) q^{57} -5.25043 q^{58} +10.3712i q^{59} +(0.850552 + 0.864972i) q^{60} +15.5857i q^{61} -8.77782 q^{62} +(-2.99958 - 0.0504282i) q^{63} -5.39197 q^{64} +0.561946 q^{65} +(-10.1913 + 4.24658i) q^{66} +6.12792 q^{67} -2.77817 q^{68} +(-7.48346 - 7.61032i) q^{69} -0.794699 q^{70} +8.31333i q^{71} +(0.0296727 - 1.76500i) q^{72} +0.290444i q^{73} +12.3205 q^{74} +(5.96383 - 5.86441i) q^{75} -7.13518i q^{76} +(1.23694 - 3.07734i) q^{77} +(3.17201 + 3.22579i) q^{78} +16.6717i q^{79} -1.86838i q^{80} +(-8.99491 - 0.302527i) q^{81} +6.86196 q^{82} +3.53351 q^{83} +(-2.05702 - 2.09189i) q^{84} -0.678187i q^{85} -2.31080i q^{86} +(3.37381 - 3.31757i) q^{87} +(1.81075 + 0.727832i) q^{88} -9.17912i q^{89} +(-2.38376 - 0.0400752i) q^{90} -1.35904 q^{91} -10.4378i q^{92} +(5.64044 - 5.54641i) q^{93} -16.0156i q^{94} +1.74179 q^{95} +(9.27185 - 9.11729i) q^{96} +12.9612 q^{97} +1.92194 q^{98} +(3.86547 - 9.16832i) 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 $

$2$	−1.92194			−1.35901			−0.679507	−	0.733669i	$-0.737806\pi$
$2$	−1.92194			−1.35901			−0.679507	+	0.733669i	$0.737806\pi$
$3$	1.23500	−	1.21441i	0.713025	−	0.701139i
$3$	1.23500	−	1.21441i	0.713025	−	0.701139i
$4$	1.69384			0.846921
$5$			0.413489i			0.184918i	0.995717	+	0.0924588i	$0.0294727\pi$
$5$			0.413489i			0.184918i	−0.995717	+	0.0924588i	$0.970527\pi$
$6$	−2.37358	+	2.33402i	−0.969012	+	0.952858i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	0.588415			0.208036
$9$	0.0504282	−	2.99958i	0.0168094	−	0.999859i
$10$		−	0.794699i		−	0.251306i
$11$	3.07734	+	1.23694i	0.927851	+	0.372950i
$11$	3.07734	+	1.23694i	0.927851	+	0.372950i
$12$	2.09189	−	2.05702i	0.603876	−	0.593809i
$13$		−	1.35904i		−	0.376929i	−0.982080	−	0.188464i	$-0.939649\pi$
$13$		−	1.35904i		−	0.376929i	0.982080	−	0.188464i	$-0.0603510\pi$
$14$			1.92194i			0.513659i
$15$	0.502144	+	0.510656i	0.129653	+	0.131851i
$16$	−4.51858			−1.12965
$17$	−1.64016			−0.397797			−0.198899	−	0.980020i	$-0.563736\pi$
$17$	−1.64016			−0.397797			−0.198899	+	0.980020i	$0.563736\pi$
$18$	−0.0969199	+	5.76500i	−0.0228442	+	1.35882i
$19$		−	4.21243i		−	0.966397i	−0.875511	−	0.483198i	$-0.839475\pi$
$19$		−	4.21243i		−	0.966397i	0.875511	−	0.483198i	$-0.160525\pi$
$20$			0.700384i			0.156611i
$21$	−1.21441	−	1.23500i	−0.265005	−	0.269498i
$22$	−5.91444	−	2.37731i	−1.26096	−	0.506845i
$23$		−	6.16223i		−	1.28491i	−0.766322	−	0.642457i	$-0.777915\pi$
$23$		−	6.16223i		−	1.28491i	0.766322	−	0.642457i	$-0.222085\pi$
$24$	0.726690	−	0.714576i	0.148335	−	0.145862i
$25$	4.82903			0.965805
$26$			2.61198i			0.512252i
$27$	−3.58043	−	3.76570i	−0.689054	−	0.724710i
$28$		−	1.69384i		−	0.320106i
$29$	2.73184			0.507290			0.253645	−	0.967297i	$-0.418370\pi$
$29$	2.73184			0.507290			0.253645	+	0.967297i	$0.418370\pi$
$30$	−0.965088	−	0.981450i	−0.176200	−	0.179187i
$31$	4.56717			0.820289			0.410144	−	0.912021i	$-0.365478\pi$
$31$	4.56717			0.820289			0.410144	+	0.912021i	$0.365478\pi$
$32$	7.50760			1.32717
$33$	5.30264	−	2.20953i	0.923071	−	0.384630i
$34$	3.15228			0.540612
$35$	0.413489			0.0698923
$36$	0.0854175	−	5.08081i	0.0142362	−	0.846802i
$37$	−6.41046			−1.05387			−0.526937	−	0.849904i	$-0.676660\pi$
$37$	−6.41046			−1.05387			−0.526937	+	0.849904i	$0.676660\pi$
$38$			8.09602i			1.31335i
$39$	−1.65042	−	1.67840i	−0.264279	−	0.268760i
$40$			0.243303i			0.0384696i
$41$	−3.57034			−0.557593			−0.278796	−	0.960350i	$-0.589935\pi$
$41$	−3.57034			−0.557593			−0.278796	+	0.960350i	$0.589935\pi$
$42$	2.33402	+	2.37358i	0.360146	+	0.366252i
$43$			1.20233i			0.183353i	0.995789	+	0.0916765i	$0.0292226\pi$
$43$			1.20233i			0.183353i	−0.995789	+	0.0916765i	$0.970777\pi$
$44$	5.21252	+	2.09517i	0.785817	+	0.315859i
$45$	1.24029	+	0.0208515i	0.184892	+	0.00310836i
$46$			11.8434i			1.74622i
$47$			8.33307i			1.21550i	0.794127	+	0.607752i	$0.207928\pi$
$47$			8.33307i			1.21550i	−0.794127	+	0.607752i	$0.792072\pi$
$48$	−5.58043	+	5.48740i	−0.805466	+	0.792038i
$49$	−1.00000			−0.142857
$50$	−9.28109			−1.31254
$51$	−2.02559	+	1.99182i	−0.283639	+	0.278911i
$52$		−	2.30199i		−	0.319229i
$53$		−	5.91727i		−	0.812799i	−0.913696	−	0.406399i	$-0.866784\pi$
$53$		−	5.91727i		−	0.812799i	0.913696	−	0.406399i	$-0.133216\pi$
$54$	6.88136	+	7.23745i	0.936435	+	0.984892i
$55$	−0.511459	+	1.27244i	−0.0689651	+	0.171576i
$56$		−	0.588415i		−	0.0786303i
$57$	−5.11560	−	5.20233i	−0.677578	−	0.689065i
$58$	−5.25043			−0.689415
$59$			10.3712i			1.35021i	0.737722	+	0.675105i	$0.235902\pi$
$59$			10.3712i			1.35021i	−0.737722	+	0.675105i	$0.764098\pi$
$60$	0.850552	+	0.864972i	0.109806	+	0.111667i
$61$			15.5857i			1.99555i	0.0667043	+	0.997773i	$0.478752\pi$
$61$			15.5857i			1.99555i	−0.0667043	+	0.997773i	$0.521248\pi$
$62$	−8.77782			−1.11478
$63$	−2.99958	−	0.0504282i	−0.377911	−	0.00635336i
$64$	−5.39197			−0.673997
$65$	0.561946			0.0697008
$66$	−10.1913	+	4.24658i	−1.25447	+	0.522718i
$67$	6.12792			0.748645			0.374322	−	0.927299i	$-0.377875\pi$
$67$	6.12792			0.748645			0.374322	+	0.927299i	$0.377875\pi$
$68$	−2.77817			−0.336903
$69$	−7.48346	−	7.61032i	−0.900902	−	0.916175i
$70$	−0.794699			−0.0949847
$71$			8.31333i			0.986611i	0.869856	+	0.493305i	$0.164211\pi$
$71$			8.31333i			0.986611i	−0.869856	+	0.493305i	$0.835789\pi$
$72$	0.0296727	−	1.76500i	0.00349697	−	0.208007i
$73$			0.290444i			0.0339939i	0.999856	+	0.0169969i	$0.00541056\pi$
$73$			0.290444i			0.0339939i	−0.999856	+	0.0169969i	$0.994589\pi$
$74$	12.3205			1.43223
$75$	5.96383	−	5.86441i	0.688643	−	0.677163i
$76$		−	7.13518i		−	0.818462i
$77$	1.23694	−	3.07734i	0.140962	−	0.350695i
$78$	3.17201	+	3.22579i	0.359159	+	0.365248i
$79$			16.6717i			1.87571i	0.347025	+	0.937856i	$0.387192\pi$
$79$			16.6717i			1.87571i	−0.347025	+	0.937856i	$0.612808\pi$
$80$		−	1.86838i		−	0.208891i
$81$	−8.99491	−	0.302527i	−0.999435	−	0.0336141i
$82$	6.86196			0.757777
$83$	3.53351			0.387853			0.193926	−	0.981016i	$-0.437878\pi$
$83$	3.53351			0.387853			0.193926	+	0.981016i	$0.437878\pi$
$84$	−2.05702	−	2.09189i	−0.224439	−	0.228244i
$85$		−	0.678187i		−	0.0735597i
$86$		−	2.31080i		−	0.249180i
$87$	3.37381	−	3.31757i	0.361711	−	0.355681i
$88$	1.81075	+	0.727832i	0.193027	+	0.0775871i
$89$		−	9.17912i		−	0.972985i	−0.873685	−	0.486493i	$-0.838276\pi$
$89$		−	9.17912i		−	0.972985i	0.873685	−	0.486493i	$-0.161724\pi$
$90$	−2.38376	−	0.0400752i	−0.251270	−	0.00422430i
$91$	−1.35904			−0.142466
$92$		−	10.4378i		−	1.08822i
$93$	5.64044	−	5.54641i	0.584886	−	0.575136i
$94$		−	16.0156i		−	1.65189i
$95$	1.74179			0.178704
$96$	9.27185	−	9.11729i	0.946305	−	0.930529i
$97$	12.9612			1.31601			0.658007	−	0.753012i	$-0.271400\pi$
$97$	12.9612			1.31601			0.658007	+	0.753012i	$0.271400\pi$
$98$	1.92194			0.194145
$99$	3.86547	−	9.16832i	0.388494	−	0.921451i
$100$	8.17961			0.817961
$101$	−12.6217			−1.25591			−0.627953	−	0.778251i	$-0.716107\pi$
$101$	−12.6217			−1.25591			−0.627953	+	0.778251i	$0.716107\pi$
$102$	3.89306	−	3.82816i	0.385470	−	0.379044i
$103$	−12.8103			−1.26224			−0.631120	−	0.775685i	$-0.717405\pi$
$103$	−12.8103			−1.26224			−0.631120	+	0.775685i	$0.717405\pi$
$104$		−	0.799678i		−	0.0784149i
$105$	0.510656	−	0.502144i	0.0498350	−	0.0490042i
$106$			11.3726i			1.10461i
$107$	5.35301			0.517495			0.258747	−	0.965945i	$-0.416690\pi$
$107$	5.35301			0.517495			0.258747	+	0.965945i	$0.416690\pi$
$108$	−6.06468	−	6.37851i	−0.583574	−	0.613772i
$109$		−	11.9771i		−	1.14720i	−0.819135	−	0.573601i	$-0.805546\pi$
$109$		−	11.9771i		−	1.14720i	0.819135	−	0.573601i	$-0.194454\pi$
$110$	0.982991	−	2.44555i	0.0937245	−	0.233175i
$111$	−7.91690	+	7.78492i	−0.751438	+	0.738912i
$112$			4.51858i			0.426966i
$113$			4.67841i			0.440108i	0.975488	+	0.220054i	$0.0706233\pi$
$113$			4.67841i			0.440108i	−0.975488	+	0.220054i	$0.929377\pi$
$114$	9.83186	+	9.99854i	0.920838	+	0.936449i
$115$	2.54801			0.237603
$116$	4.62731			0.429635
$117$	−4.07653	−	0.0685338i	−0.376876	−	0.00633595i
$118$		−	19.9327i		−	1.83495i
$119$			1.64016i			0.150353i
$120$	0.295469	+	0.300478i	0.0269725	+	0.0274298i
$121$	7.93998	+	7.61293i	0.721817	+	0.692084i
$122$		−	29.9548i		−	2.71198i
$123$	−4.40935	+	4.33584i	−0.397578	+	0.390950i
$124$	7.73607			0.694720
$125$			4.06419i			0.363512i
$126$	5.76500	+	0.0969199i	0.513587	+	0.00863431i
$127$		−	7.00839i		−	0.621894i	−0.950427	−	0.310947i	$-0.899354\pi$
$127$		−	7.00839i		−	0.621894i	0.950427	−	0.310947i	$-0.100646\pi$
$128$	−4.65217			−0.411198
$129$	1.46011	+	1.48487i	0.128556	+	0.130735i
$130$	−1.08002			−0.0947244
$131$	−7.89101			−0.689441			−0.344720	−	0.938705i	$-0.612026\pi$
$131$	−7.89101			−0.689441			−0.344720	+	0.938705i	$0.612026\pi$
$132$	8.98184	−	3.74260i	0.781768	−	0.325751i
$133$	−4.21243			−0.365264
$134$	−11.7775			−1.01742
$135$	1.55708	−	1.48047i	0.134012	−	0.127418i
$136$	−0.965096			−0.0827563
$137$		−	4.27223i		−	0.365002i	−0.983206	−	0.182501i	$-0.941581\pi$
$137$		−	4.27223i		−	0.365002i	0.983206	−	0.182501i	$-0.0584192\pi$
$138$	14.3827	+	14.6266i	1.22434	+	1.24510i
$139$		−	9.33606i		−	0.791874i	−0.918278	−	0.395937i	$-0.870420\pi$
$139$		−	9.33606i		−	0.791874i	0.918278	−	0.395937i	$-0.129580\pi$
$140$	0.700384			0.0591933
$141$	10.1197	+	10.2913i	0.852236	+	0.866684i
$142$		−	15.9777i		−	1.34082i
$143$	1.68104	−	4.18221i	0.140576	−	0.349734i
$144$	−0.227864	+	13.5538i	−0.0189887	+	1.12949i
$145$			1.12958i			0.0938069i
$146$		−	0.558215i		−	0.0461982i
$147$	−1.23500	+	1.21441i	−0.101861	+	0.100163i
$148$	−10.8583			−0.892548
$149$	14.6400			1.19936			0.599679	−	0.800240i	$-0.295295\pi$
$149$	14.6400			1.19936			0.599679	+	0.800240i	$0.295295\pi$
$150$	−11.4621	+	11.2710i	−0.935877	+	0.920275i
$151$			17.6272i			1.43448i	0.696827	+	0.717240i	$0.254595\pi$
$151$			17.6272i			1.43448i	−0.696827	+	0.717240i	$0.745405\pi$
$152$		−	2.47866i		−	0.201046i
$153$	−0.0827103	+	4.91978i	−0.00668673	+	0.397741i
$154$	−2.37731	+	5.91444i	−0.191569	+	0.476600i
$155$			1.88847i			0.151686i
$156$	−2.79556	−	2.84295i	−0.223824	−	0.227618i
$157$	−4.42328			−0.353016			−0.176508	−	0.984299i	$-0.556480\pi$
$157$	−4.42328			−0.353016			−0.176508	+	0.984299i	$0.556480\pi$
$158$		−	32.0419i		−	2.54912i
$159$	−7.18597	−	7.30780i	−0.569885	−	0.579546i
$160$			3.10431i			0.245417i
$161$	−6.16223			−0.485652
$162$	17.2877	+	0.581437i	1.35825	+	0.0456820i
$163$	−3.64734			−0.285682			−0.142841	−	0.989746i	$-0.545624\pi$
$163$	−3.64734			−0.285682			−0.142841	+	0.989746i	$0.545624\pi$
$164$	−6.04759			−0.472237
$165$	0.913615	+	2.19258i	0.0711248	+	0.170692i
$166$	−6.79118			−0.527097
$167$	−6.34851			−0.491262			−0.245631	−	0.969363i	$-0.578995\pi$
$167$	−6.34851			−0.491262			−0.245631	+	0.969363i	$0.578995\pi$
$168$	−0.714576	−	0.726690i	−0.0551308	−	0.0560654i
$169$	11.1530			0.857925
$170$			1.30343i			0.0999688i
$171$	−12.6355	−	0.212425i	−0.966260	−	0.0162446i
$172$			2.03655i			0.155286i
$173$	−14.2027			−1.07981			−0.539905	−	0.841726i	$-0.681540\pi$
$173$	−14.2027			−1.07981			−0.539905	+	0.841726i	$0.681540\pi$
$174$	−6.48425	+	6.37616i	−0.491570	+	0.483375i
$175$		−	4.82903i		−	0.365040i
$176$	−13.9052	−	5.58919i	−1.04814	−	0.421301i
$177$	12.5948	+	12.8083i	0.946684	+	0.962733i
$178$			17.6417i			1.32230i
$179$			25.1186i			1.87746i	0.344660	+	0.938728i	$0.387994\pi$
$179$			25.1186i			1.87746i	−0.344660	+	0.938728i	$0.612006\pi$
$180$	2.10086	+	0.0353191i	0.156589	+	0.00263253i
$181$	6.77948			0.503914			0.251957	−	0.967738i	$-0.418926\pi$
$181$	6.77948			0.503914			0.251957	+	0.967738i	$0.418926\pi$
$182$	2.61198			0.193613
$183$	18.9274	+	19.2483i	1.39915	+	1.42287i
$184$		−	3.62595i		−	0.267309i
$185$		−	2.65065i		−	0.194880i
$186$	−10.8406	+	10.6599i	−0.794869	+	0.781618i
$187$	−5.04732	−	2.02877i	−0.369097	−	0.148358i
$188$			14.1149i			1.02944i
$189$	−3.76570	+	3.58043i	−0.273915	+	0.260438i
$190$	−3.34761			−0.242861
$191$			11.1330i			0.805556i	0.915298	+	0.402778i	$0.131955\pi$
$191$			11.1330i			0.805556i	−0.915298	+	0.402778i	$0.868045\pi$
$192$	−6.65906	+	6.54805i	−0.480576	+	0.472565i
$193$		−	21.6435i		−	1.55794i	−0.627064	−	0.778968i	$-0.715744\pi$
$193$		−	21.6435i		−	1.55794i	0.627064	−	0.778968i	$-0.284256\pi$
$194$	−24.9107			−1.78848
$195$	0.694001	−	0.682431i	0.0496984	−	0.0488699i
$196$	−1.69384			−0.120989
$197$	10.0414			0.715421			0.357710	−	0.933833i	$-0.383557\pi$
$197$	10.0414			0.715421			0.357710	+	0.933833i	$0.383557\pi$
$198$	−7.42918	+	17.6209i	−0.527969	+	1.25227i
$199$	−19.8549			−1.40747			−0.703737	−	0.710461i	$-0.748486\pi$
$199$	−19.8549			−1.40747			−0.703737	+	0.710461i	$0.748486\pi$
$200$	2.84147			0.200923
$201$	7.56796	−	7.44180i	0.533803	−	0.524904i
$202$	24.2581			1.70679
$203$		−	2.73184i		−	0.191738i
$204$	−3.43103	+	3.37383i	−0.240220	+	0.236216i
$205$		−	1.47629i		−	0.103109i
$206$	24.6207			1.71540
$207$	−18.4841	−	0.310750i	−1.28473	−	0.0215986i
$208$			6.14092i			0.425796i
$209$	5.21050	−	12.9630i	0.360418	−	0.896672i
$210$	−0.981450	+	0.965088i	−0.0677265	+	0.0665974i
$211$		−	1.16287i		−	0.0800555i	−0.999199	−	0.0400278i	$-0.987255\pi$
$211$		−	1.16287i		−	0.0800555i	0.999199	−	0.0400278i	$-0.0127446\pi$
$212$		−	10.0229i		−	0.688377i
$213$	10.0958	+	10.2669i	0.691751	+	0.703478i
$214$	−10.2881			−0.703283
$215$	−0.497148			−0.0339052
$216$	−2.10678	−	2.21580i	−0.143348	−	0.150766i
$217$		−	4.56717i		−	0.310040i
$218$			23.0193i			1.55907i
$219$	0.352717	+	0.358697i	0.0238344	+	0.0242385i
$220$	−0.866330	+	2.15532i	−0.0584080	+	0.145311i
$221$			2.22904i			0.149941i
$222$	15.2158	−	14.9621i	1.02122	−	1.00419i
$223$	−12.4329			−0.832568			−0.416284	−	0.909235i	$-0.636668\pi$
$223$	−12.4329			−0.832568			−0.416284	+	0.909235i	$0.636668\pi$
$224$		−	7.50760i		−	0.501623i
$225$	0.243519	−	14.4850i	0.0162346	−	0.965669i
$226$		−	8.99161i		−	0.598113i
$227$	27.4133			1.81948			0.909742	−	0.415174i	$-0.136279\pi$
$227$	27.4133			1.81948			0.909742	+	0.415174i	$0.136279\pi$
$228$	−8.66502	−	8.81192i	−0.573855	−	0.583584i
$229$	−27.2215			−1.79885			−0.899423	−	0.437080i	$-0.856013\pi$
$229$	−27.2215			−1.79885			−0.899423	+	0.437080i	$0.856013\pi$
$230$	−4.89712			−0.322906
$231$	−2.20953	−	5.30264i	−0.145376	−	0.348888i
$232$	1.60746			0.105535
$233$	10.8221			0.708982			0.354491	−	0.935059i	$-0.384654\pi$
$233$	10.8221			0.708982			0.354491	+	0.935059i	$0.384654\pi$
$234$	7.83484	+	0.131718i	0.512179	+	0.00861065i
$235$	−3.44563			−0.224768
$236$			17.5671i			1.14352i
$237$	20.2462	+	20.5895i	1.31513	+	1.33743i
$238$		−	3.15228i		−	0.204332i
$239$	19.9099			1.28786			0.643931	−	0.765083i	$-0.277302\pi$
$239$	19.9099			1.28786			0.643931	+	0.765083i	$0.277302\pi$
$240$	−2.26898	−	2.30744i	−0.146462	−	0.148945i
$241$		−	7.69265i		−	0.495527i	−0.968821	−	0.247764i	$-0.920304\pi$
$241$		−	7.69265i		−	0.495527i	0.968821	−	0.247764i	$-0.0796956\pi$
$242$	−15.2601	−	14.6316i	−0.980959	−	0.940553i
$243$	−11.4761	+	10.5499i	−0.736190	+	0.676775i
$244$			26.3997i			1.69007i
$245$		−	0.413489i		−	0.0264168i
$246$	8.47449	−	8.33322i	0.540314	−	0.531307i
$247$	−5.72484			−0.364263
$248$	2.68740			0.170650
$249$	4.36386	−	4.29112i	0.276549	−	0.271938i
$250$		−	7.81112i		−	0.494018i
$251$			9.61917i			0.607157i	0.952806	+	0.303578i	$0.0981814\pi$
$251$			9.61917i			0.607157i	−0.952806	+	0.303578i	$0.901819\pi$
$252$	−5.08081	−	0.0854175i	−0.320061	−	0.00538079i
$253$	7.62228	−	18.9632i	0.479208	−	1.19221i
$254$			13.4697i			0.845164i
$255$	−0.823596	−	0.837558i	−0.0515756	−	0.0524499i
$256$	19.7251			1.23282
$257$		−	12.9172i		−	0.805751i	−0.915255	−	0.402875i	$-0.868011\pi$
$257$		−	12.9172i		−	0.805751i	0.915255	−	0.402875i	$-0.131989\pi$
$258$	−2.80625	−	2.85382i	−0.174709	−	0.177671i
$259$			6.41046i			0.398327i
$260$	0.951848			0.0590311
$261$	0.137762	−	8.19437i	0.00852725	−	0.507218i
$262$	15.1660			0.936960
$263$	1.86943			0.115274			0.0576369	−	0.998338i	$-0.481643\pi$
$263$	1.86943			0.115274			0.0576369	+	0.998338i	$0.481643\pi$
$264$	3.12015	−	1.30012i	0.192032	−	0.0800169i
$265$	2.44672			0.150301
$266$	8.09602			0.496399
$267$	−11.1472	−	11.3362i	−0.682197	−	0.693763i
$268$	10.3797			0.634043
$269$			12.9253i			0.788071i	0.919095	+	0.394036i	$0.128921\pi$
$269$			12.9253i			0.788071i	−0.919095	+	0.394036i	$0.871079\pi$
$270$	−2.99260	+	2.84536i	−0.182124	+	0.173163i
$271$		−	20.2282i		−	1.22878i	−0.789003	−	0.614389i	$-0.789403\pi$
$271$		−	20.2282i		−	1.22878i	0.789003	−	0.614389i	$-0.210597\pi$
$272$	7.41120			0.449370
$273$	−1.67840	+	1.65042i	−0.101582	+	0.0998882i
$274$			8.21097i			0.496043i
$275$	14.8605	+	5.97319i	0.896124	+	0.360197i
$276$	−12.6758	−	12.8907i	−0.762993	−	0.775928i
$277$		−	7.26198i		−	0.436330i	−0.975912	−	0.218165i	$-0.929993\pi$
$277$		−	7.26198i		−	0.436330i	0.975912	−	0.218165i	$-0.0700071\pi$
$278$			17.9433i			1.07617i
$279$	0.230314	−	13.6996i	0.0137886	−	0.820173i
$280$	0.243303			0.0145401
$281$	−25.5479			−1.52406			−0.762030	−	0.647541i	$-0.775797\pi$
$281$	−25.5479			−1.52406			−0.762030	+	0.647541i	$0.775797\pi$
$282$	−19.4495	−	19.7792i	−1.15820	−	1.17784i
$283$			19.3170i			1.14828i	0.818758	+	0.574139i	$0.194663\pi$
$283$			19.3170i			1.14828i	−0.818758	+	0.574139i	$0.805337\pi$
$284$			14.0815i			0.835582i
$285$	2.15110	−	2.11524i	0.127420	−	0.125296i
$286$	−3.23085	+	8.03794i	−0.191044	+	0.475294i
$287$			3.57034i			0.210750i
$288$	0.378595	−	22.5196i	0.0223089	−	1.32698i
$289$	−14.3099			−0.841757
$290$		−	2.17099i		−	0.127485i
$291$	16.0071	−	15.7402i	0.938351	−	0.922708i
$292$			0.491966i			0.0287902i
$293$	−19.4631			−1.13705			−0.568523	−	0.822667i	$-0.692485\pi$
$293$	−19.4631			−1.13705			−0.568523	+	0.822667i	$0.692485\pi$
$294$	2.37358	−	2.33402i	0.138430	−	0.136123i
$295$	−4.28835			−0.249678
$296$	−3.77202			−0.219244
$297$	−6.36025	−	16.0171i	−0.369059	−	0.929406i
$298$	−28.1372			−1.62995
$299$	−8.37469			−0.484321
$300$	10.1018	−	9.93338i	0.583227	−	0.573504i
$301$	1.20233			0.0693009
$302$		−	33.8783i		−	1.94948i
$303$	−15.5877	+	15.3279i	−0.895492	+	0.880564i
$304$			19.0342i			1.09169i
$305$	−6.44451			−0.369012
$306$	0.158964	−	9.45552i	0.00908737	−	0.540536i
$307$			8.73827i			0.498719i	0.968411	+	0.249360i	$0.0802201\pi$
$307$			8.73827i			0.498719i	−0.968411	+	0.249360i	$0.919780\pi$
$308$	2.09517	−	5.21252i	0.119384	−	0.297011i
$309$	−15.8207	+	15.5570i	−0.900009	+	0.885005i
$310$		−	3.62953i		−	0.206143i
$311$			10.6726i			0.605185i	0.953120	+	0.302593i	$0.0978522\pi$
$311$			10.6726i			0.605185i	−0.953120	+	0.302593i	$0.902148\pi$
$312$	−0.971135	−	0.987599i	−0.0549797	−	0.0559118i
$313$	26.7253			1.51060			0.755302	−	0.655377i	$-0.227490\pi$
$313$	26.7253			1.51060			0.755302	+	0.655377i	$0.227490\pi$
$314$	8.50127			0.479754
$315$	0.0208515	−	1.24029i	0.00117485	−	0.0698824i
$316$			28.2392i			1.58858i
$317$		−	16.7346i		−	0.939907i	−0.882691	−	0.469953i	$-0.844271\pi$
$317$		−	16.7346i		−	0.939907i	0.882691	−	0.469953i	$-0.155729\pi$
$318$	13.8110	+	14.0451i	0.774482	+	0.787612i
$319$	8.40679	+	3.37911i	0.470690	+	0.189194i
$320$		−	2.22952i		−	0.124634i
$321$	6.61094	−	6.50073i	0.368987	−	0.362835i
$322$	11.8434			0.660008
$323$			6.90905i			0.384430i
$324$	−15.2360	−	0.512432i	−0.846443	−	0.0284685i
$325$		−	6.56282i		−	0.364040i
$326$	7.00996			0.388246
$327$	−14.5451	−	14.7917i	−0.804348	−	0.817984i
$328$	−2.10084			−0.116000
$329$	8.33307			0.459417
$330$	−1.75591	−	4.21400i	−0.0966597	−	0.231973i
$331$	−0.0281857			−0.00154923			−0.000774613	−	1.00000i	$-0.500247\pi$
$331$	−0.0281857			−0.00154923			−0.000774613		1.00000i	$0.500247\pi$
$332$	5.98520			0.328481
$333$	−0.323268	+	19.2287i	−0.0177150	+	1.05372i
$334$	12.2014			0.667633
$335$			2.53383i			0.138438i
$336$	5.48740	+	5.58043i	0.299362	+	0.304437i
$337$			28.5132i			1.55321i	0.629987	+	0.776606i	$0.283060\pi$
$337$			28.5132i			1.55321i	−0.629987	+	0.776606i	$0.716940\pi$
$338$	−21.4354			−1.16593
$339$	5.68149	+	5.77781i	0.308576	+	0.313808i
$340$		−	1.14874i		−	0.0622993i
$341$	14.0547	+	5.64930i	0.761106	+	0.305927i
$342$	24.2846	+	0.408268i	1.31316	+	0.0220766i
$343$			1.00000i			0.0539949i
$344$			0.707467i			0.0381441i
$345$	3.14678	−	3.09432i	0.169417	−	0.166593i
$346$	27.2967			1.46748
$347$	−32.0737			−1.72181			−0.860903	−	0.508769i	$-0.830101\pi$
$347$	−32.0737			−1.72181			−0.860903	+	0.508769i	$0.830101\pi$
$348$	5.71471	−	5.61944i	0.306340	−	0.301234i
$349$			24.5954i			1.31656i	0.752773	+	0.658280i	$0.228716\pi$
$349$			24.5954i			1.31656i	−0.752773	+	0.658280i	$0.771284\pi$
$350$			9.28109i			0.496095i
$351$	−5.11773	+	4.86593i	−0.273164	+	0.259724i
$352$	23.1034	+	9.28642i	1.23142	+	0.494968i
$353$		−	21.2100i		−	1.12889i	−0.825470	−	0.564446i	$-0.809090\pi$
$353$		−	21.2100i		−	1.12889i	0.825470	−	0.564446i	$-0.190910\pi$
$354$	−24.2064	−	24.6168i	−1.28656	−	1.30837i
$355$	−3.43747			−0.182442
$356$		−	15.5480i		−	0.824042i
$357$	1.99182	+	2.02559i	0.105418	+	0.107206i
$358$		−	48.2764i		−	2.55149i
$359$	12.0531			0.636141			0.318070	−	0.948067i	$-0.396965\pi$
$359$	12.0531			0.636141			0.318070	+	0.948067i	$0.396965\pi$
$360$	0.729806	+	0.0122693i	0.0384642	+	0.000646651i
$361$	1.25547			0.0660776
$362$	−13.0297			−0.684827
$363$	19.0510	−	0.240442i	0.999920	−	0.0126199i
$364$	−2.30199			−0.120657
$365$	−0.120095			−0.00628607
$366$	−36.3773	−	36.9940i	−1.90147	−	1.93371i
$367$	−13.3568			−0.697219			−0.348609	−	0.937268i	$-0.613346\pi$
$367$	−13.3568			−0.697219			−0.348609	+	0.937268i	$0.613346\pi$
$368$			27.8445i			1.45150i
$369$	−0.180046	+	10.7095i	−0.00937281	+	0.557514i
$370$			5.09439i			0.264845i
$371$	−5.91727			−0.307209
$372$	9.55402	−	9.39475i	0.495353	−	0.487095i
$373$		−	1.91862i		−	0.0993425i	−0.998766	−	0.0496713i	$-0.984183\pi$
$373$		−	1.91862i		−	0.0993425i	0.998766	−	0.0496713i	$-0.0158174\pi$
$374$	9.70064	+	3.89917i	0.501608	+	0.201621i
$375$	4.93558	+	5.01926i	0.254872	+	0.259193i
$376$			4.90331i			0.252869i
$377$		−	3.71267i		−	0.191212i
$378$	7.23745	−	6.88136i	0.372254	−	0.353939i
$379$	23.5384			1.20909			0.604544	−	0.796572i	$-0.293355\pi$
$379$	23.5384			1.20909			0.604544	+	0.796572i	$0.293355\pi$
$380$	2.95032			0.151348
$381$	−8.51105	−	8.65533i	−0.436034	−	0.443426i
$382$		−	21.3969i		−	1.09476i
$383$			10.1166i			0.516932i	0.966020	+	0.258466i	$0.0832170\pi$
$383$			10.1166i			0.516932i	−0.966020	+	0.258466i	$0.916783\pi$
$384$	−5.74541	+	5.64963i	−0.293194	+	0.288307i
$385$	1.27244	+	0.511459i	0.0648497	+	0.0260663i
$386$			41.5975i			2.11726i
$387$	3.60647	+	0.0606312i	0.183327	+	0.00308206i
$388$	21.9543			1.11456
$389$			5.43831i			0.275733i	0.990451	+	0.137867i	$0.0440246\pi$
$389$			5.43831i			0.275733i	−0.990451	+	0.137867i	$0.955975\pi$
$390$	−1.33383	+	1.31159i	−0.0675409	+	0.0664149i
$391$			10.1070i			0.511135i
$392$	−0.588415			−0.0297195
$393$	−9.74536	+	9.58290i	−0.491588	+	0.483393i
$394$	−19.2990			−0.972268
$395$	−6.89355			−0.346852
$396$	6.54749	−	15.5297i	0.329024	−	0.780397i
$397$	25.7021			1.28995			0.644975	−	0.764204i	$-0.276868\pi$
$397$	25.7021			1.28995			0.644975	+	0.764204i	$0.276868\pi$
$398$	38.1598			1.91278
$399$	−5.20233	+	5.11560i	−0.260442	+	0.256100i
$400$	−21.8204			−1.09102
$401$		−	35.2490i		−	1.76025i	−0.474741	−	0.880125i	$-0.657458\pi$
$401$		−	35.2490i		−	1.76025i	0.474741	−	0.880125i	$-0.342542\pi$
$402$	−14.5451	+	14.3027i	−0.725446	+	0.713352i
$403$		−	6.20695i		−	0.309190i
$404$	−21.3792			−1.06365
$405$	0.125091	−	3.71929i	0.00621583	−	0.184813i
$406$			5.25043i			0.260574i
$407$	−19.7271	−	7.92933i	−0.977838	−	0.393042i
$408$	−1.19189	+	1.17202i	−0.0590073	+	0.0580236i
$409$		−	29.2925i		−	1.44842i	−0.689579	−	0.724210i	$-0.742205\pi$
$409$		−	29.2925i		−	1.44842i	0.689579	−	0.724210i	$-0.257795\pi$
$410$			2.83734i			0.140126i
$411$	−5.18823	−	5.27619i	−0.255917	−	0.260255i
$412$	−21.6987			−1.06902
$413$	10.3712			0.510331
$414$	35.5252	+	0.597242i	1.74597	+	0.0293529i
$415$			1.46106i			0.0717208i
$416$		−	10.2031i		−	0.500248i
$417$	−11.3378	−	11.5300i	−0.555214	−	0.564626i
$418$	−10.0142	+	24.9142i	−0.489813	+	1.21859i
$419$		−	7.55837i		−	0.369250i	−0.982809	−	0.184625i	$-0.940893\pi$
$419$		−	7.55837i		−	0.369250i	0.982809	−	0.184625i	$-0.0591071\pi$
$420$	0.864972	−	0.850552i	0.0422063	−	0.0415027i
$421$	−2.30918			−0.112542			−0.0562712	−	0.998416i	$-0.517921\pi$
$421$	−2.30918			−0.112542			−0.0562712	+	0.998416i	$0.517921\pi$
$422$			2.23497i			0.108797i
$423$	24.9957	+	0.420222i	1.21533	+	0.0204319i
$424$		−	3.48181i		−	0.169092i
$425$	−7.92038			−0.384195
$426$	−19.4034	−	19.7324i	−0.940100	−	0.956037i
$427$	15.5857			0.754245
$428$	9.06715			0.438277
$429$	−3.00283	−	7.20648i	−0.144978	−	0.347932i
$430$	0.955488			0.0460777
$431$	16.2294			0.781745			0.390872	−	0.920445i	$-0.372173\pi$
$431$	16.2294			0.781745			0.390872	+	0.920445i	$0.372173\pi$
$432$	16.1785	+	17.0156i	0.778387	+	0.818666i
$433$	1.66823			0.0801698			0.0400849	−	0.999196i	$-0.487237\pi$
$433$	1.66823			0.0801698			0.0400849	+	0.999196i	$0.487237\pi$
$434$			8.77782i			0.421349i
$435$	1.37178	+	1.39503i	0.0657717	+	0.0668867i
$436$		−	20.2874i		−	0.971590i
$437$	−25.9579			−1.24174
$438$	−0.677901	−	0.689393i	−0.0323913	−	0.0329405i
$439$		−	34.5341i		−	1.64822i	−0.566426	−	0.824112i	$-0.691674\pi$
$439$		−	34.5341i		−	1.64822i	0.566426	−	0.824112i	$-0.308326\pi$
$440$	−0.300950	+	0.748725i	−0.0143472	+	0.0356941i
$441$	−0.0504282	+	2.99958i	−0.00240134	+	0.142837i
$442$		−	4.28407i		−	0.203772i
$443$		−	23.1357i		−	1.09921i	−0.835424	−	0.549606i	$-0.814778\pi$
$443$		−	23.1357i		−	1.09921i	0.835424	−	0.549606i	$-0.185222\pi$
$444$	−13.4100	+	13.1864i	−0.636409	+	0.625800i
$445$	3.79546			0.179922
$446$	23.8952			1.13147
$447$	18.0804	−	17.7790i	0.855173	−	0.840916i
$448$			5.39197i			0.254747i
$449$		−	14.1968i		−	0.669989i	−0.942220	−	0.334995i	$-0.891266\pi$
$449$		−	14.1968i		−	0.669989i	0.942220	−	0.334995i	$-0.108734\pi$
$450$	−0.468029	+	27.8393i	−0.0220631	+	1.31236i
$451$	−10.9871	−	4.41628i	−0.517363	−	0.207954i
$452$			7.92449i			0.372737i
$453$	21.4066	+	21.7695i	1.00577	+	1.02282i
$454$	−52.6866			−2.47271
$455$		−	0.561946i		−	0.0263444i
$456$	−3.01010	−	3.06113i	−0.140961	−	0.143351i
$457$			15.8942i			0.743500i	0.928333	+	0.371750i	$0.121242\pi$
$457$			15.8942i			0.743500i	−0.928333	+	0.371750i	$0.878758\pi$
$458$	52.3180			2.44466
$459$	5.87248	+	6.17636i	0.274104	+	0.288288i
$460$	4.31593			0.201231
$461$	25.5065			1.18795			0.593977	−	0.804482i	$-0.297557\pi$
$461$	25.5065			1.18795			0.593977	+	0.804482i	$0.297557\pi$
$462$	4.24658	+	10.1913i	0.197569	+	0.474144i
$463$	13.2452			0.615558			0.307779	−	0.951458i	$-0.400414\pi$
$463$	13.2452			0.615558			0.307779	+	0.951458i	$0.400414\pi$
$464$	−12.3440			−0.573058
$465$	2.29338	+	2.33226i	0.106353	+	0.108156i
$466$	−20.7995			−0.963517
$467$			28.3407i			1.31145i	0.754999	+	0.655726i	$0.227637\pi$
$467$			28.3407i			1.31145i	−0.754999	+	0.655726i	$0.772363\pi$
$468$	−6.90500	−	0.116085i	−0.319184	−	0.00536605i
$469$		−	6.12792i		−	0.282961i
$470$	6.62228			0.305463
$471$	−5.46273	+	5.37167i	−0.251710	+	0.247513i
$472$			6.10255i			0.280892i
$473$	−1.48720	+	3.69996i	−0.0683815	+	0.170124i
$474$	−38.9120	−	39.5717i	−1.78729	−	1.81759i
$475$		−	20.3419i		−	0.933351i
$476$			2.77817i			0.127337i
$477$	−17.7493	−	0.298397i	−0.812684	−	0.0136627i
$478$	−38.2655			−1.75022
$479$	1.53713			0.0702331			0.0351165	−	0.999383i	$-0.488820\pi$
$479$	1.53713			0.0702331			0.0351165	+	0.999383i	$0.488820\pi$
$480$	3.76989	+	3.83381i	0.172071	+	0.174988i
$481$			8.71205i			0.397235i
$482$			14.7848i			0.673429i
$483$	−7.61032	+	7.48346i	−0.346282	+	0.340509i
$484$	13.4491	+	12.8951i	0.611322	+	0.586141i
$485$			5.35932i			0.243354i
$486$	22.0563	−	20.2762i	1.00049	−	0.919747i
$487$	−7.17846			−0.325287			−0.162643	−	0.986685i	$-0.552002\pi$
$487$	−7.17846			−0.325287			−0.162643	+	0.986685i	$0.552002\pi$
$488$			9.17087i			0.415146i
$489$	−4.50445	+	4.42936i	−0.203698	+	0.200303i
$490$			0.794699i			0.0359008i
$491$	37.4970			1.69221			0.846107	−	0.533013i	$-0.178940\pi$
$491$	37.4970			1.69221			0.846107	+	0.533013i	$0.178940\pi$
$492$	−7.46875	+	7.34424i	−0.336717	+	0.331104i
$493$	−4.48066			−0.201799
$494$	11.0028			0.495038
$495$	3.79100	+	1.59833i	0.170393	+	0.0718394i
$496$	−20.6372			−0.926635
$497$	8.31333			0.372904
$498$	−8.38707	+	8.24726i	−0.375834	+	0.369568i
$499$	13.2712			0.594100			0.297050	−	0.954862i	$-0.403997\pi$
$499$	13.2712			0.594100			0.297050	+	0.954862i	$0.403997\pi$
$500$			6.88410i			0.307866i
$501$	−7.84038	+	7.70968i	−0.350282	+	0.344443i
$502$		−	18.4874i		−	0.825135i
$503$	−39.4829			−1.76046			−0.880228	−	0.474551i	$-0.842610\pi$
$503$	−39.4829			−1.76046			−0.880228	+	0.474551i	$0.842610\pi$
$504$	−1.76500	−	0.0296727i	−0.0786192	−	0.00132173i
$505$		−	5.21893i		−	0.232239i
$506$	−14.6495	+	36.4462i	−0.651251	+	1.62023i
$507$	13.7739	−	13.5443i	0.611722	−	0.601524i
$508$		−	11.8711i		−	0.526696i
$509$			0.384496i			0.0170425i	0.999964	+	0.00852125i	$0.00271243\pi$
$509$			0.384496i			0.0170425i	−0.999964	+	0.00852125i	$0.997288\pi$
$510$	1.58290	+	1.60973i	0.0700920	+	0.0712802i
$511$	0.290444			0.0128485
$512$	−28.6061			−1.26422
$513$	−15.8627	+	15.0823i	−0.700357	+	0.665899i
$514$			24.8260i			1.09503i
$515$		−	5.29693i		−	0.233411i
$516$	2.47320	+	2.51513i	0.108877	+	0.110723i
$517$	−10.3075	+	25.6437i	−0.453322	+	1.12781i
$518$		−	12.3205i		−	0.541332i
$519$	−17.5403	+	17.2478i	−0.769932	+	0.757097i
$520$	0.330658			0.0145003
$521$			21.4053i			0.937783i	0.883256	+	0.468892i	$0.155347\pi$
$521$			21.4053i			0.937783i	−0.883256	+	0.468892i	$0.844653\pi$
$522$	−0.264770	+	15.7491i	−0.0115887	+	0.689317i
$523$		−	38.1637i		−	1.66878i	−0.551174	−	0.834390i	$-0.685820\pi$
$523$		−	38.1637i		−	1.66878i	0.551174	−	0.834390i	$-0.314180\pi$
$524$	−13.3661			−0.583902
$525$	−5.86441	−	5.96383i	−0.255944	−	0.260283i
$526$	−3.59292			−0.156659
$527$	−7.49090			−0.326309
$528$	−23.9604	+	9.98394i	−1.04274	+	0.434495i
$529$	−14.9730			−0.651002
$530$	−4.70244			−0.204261
$531$	31.1091	+	0.522999i	1.35002	+	0.0226962i
$532$	−7.13518			−0.309349
$533$			4.85222i			0.210173i
$534$	21.4242	+	21.7874i	0.927116	+	0.942834i
$535$			2.21341i			0.0956939i
$536$	3.60576			0.155745
$537$	30.5043	+	31.0214i	1.31636	+	1.33867i
$538$		−	24.8417i		−	1.07100i
$539$	−3.07734	−	1.23694i	−0.132550	−	0.0532786i
$540$	2.63744	−	2.50768i	0.113497	−	0.107913i
$541$			9.20566i			0.395782i	0.980224	+	0.197891i	$0.0634092\pi$
$541$			9.20566i			0.395782i	−0.980224	+	0.197891i	$0.936591\pi$
$542$			38.8774i			1.66993i
$543$	8.37262	−	8.23305i	0.359304	−	0.353314i
$544$	−12.3137			−0.527944
$545$	4.95241			0.212138
$546$	3.22579	−	3.17201i	0.138051	−	0.135750i
$547$			38.8699i			1.66196i	0.556305	+	0.830978i	$0.312219\pi$
$547$			38.8699i			1.66196i	−0.556305	+	0.830978i	$0.687781\pi$
$548$		−	7.23649i		−	0.309128i
$549$	46.7505	+	0.785959i	1.99526	+	0.0335439i
$550$	−28.5610	−	11.4801i	−1.21785	−	0.489513i
$551$		−	11.5077i		−	0.490243i
$552$	−4.40338	−	4.47803i	−0.187420	−	0.190598i
$553$	16.6717			0.708952
$554$			13.9571i			0.592979i
$555$	−3.21897	−	3.27355i	−0.136638	−	0.138954i
$556$		−	15.8138i		−	0.670655i
$557$	−29.6798			−1.25757			−0.628787	−	0.777578i	$-0.716448\pi$
$557$	−29.6798			−1.25757			−0.628787	+	0.777578i	$0.716448\pi$
$558$	−0.442650	+	26.3297i	−0.0187389	+	1.11463i
$559$	1.63400			0.0691110
$560$	−1.86838			−0.0789535
$561$	−8.69718	+	3.62398i	−0.367195	+	0.153005i
$562$	49.1015			2.07122
$563$	−22.9672			−0.967954			−0.483977	−	0.875081i	$-0.660808\pi$
$563$	−22.9672			−0.967954			−0.483977	+	0.875081i	$0.660808\pi$
$564$	17.1413	+	17.4319i	0.721777	+	0.734013i
$565$	−1.93447			−0.0813837
$566$		−	37.1261i		−	1.56053i
$567$	−0.302527	+	8.99491i	−0.0127049	+	0.377751i
$568$			4.89169i			0.205251i
$569$	−18.5180			−0.776314			−0.388157	−	0.921593i	$-0.626888\pi$
$569$	−18.5180			−0.776314			−0.388157	+	0.921593i	$0.626888\pi$
$570$	−4.13428	+	4.06536i	−0.173166	+	0.170279i
$571$			9.78122i			0.409332i	0.978832	+	0.204666i	$0.0656107\pi$
$571$			9.78122i			0.409332i	−0.978832	+	0.204666i	$0.934389\pi$
$572$	2.84742	−	7.08400i	0.119056	−	0.296197i
$573$	13.5200	+	13.7492i	0.564806	+	0.574382i
$574$		−	6.86196i		−	0.286413i
$575$		−	29.7576i		−	1.24098i
$576$	−0.271908	+	16.1736i	−0.0113295	+	0.673901i
$577$	−32.9536			−1.37188			−0.685938	−	0.727660i	$-0.740608\pi$
$577$	−32.9536			−1.37188			−0.685938	+	0.727660i	$0.740608\pi$
$578$	27.5027			1.14396
$579$	−26.2841	−	26.7297i	−1.09233	−	1.11085i
$580$			1.91334i			0.0794471i
$581$		−	3.53351i		−	0.146595i
$582$	−30.7646	+	30.2517i	−1.27523	+	1.25397i
$583$	7.31927	−	18.2094i	0.303133	−	0.754157i
$584$			0.170902i			0.00707196i
$585$	0.0283379	−	1.68560i	0.00117163	−	0.0696910i
$586$	37.4069			1.54526
$587$			12.3669i			0.510438i	0.966883	+	0.255219i	$0.0821476\pi$
$587$			12.3669i			0.510438i	−0.966883	+	0.255219i	$0.917852\pi$
$588$	−2.09189	+	2.05702i	−0.0862680	+	0.0848299i
$589$		−	19.2389i		−	0.792724i
$590$	8.24194			0.339315
$591$	12.4011	−	12.1944i	0.510113	−	0.501609i
$592$	28.9662			1.19050
$593$	−0.769454			−0.0315977			−0.0157988	−	0.999875i	$-0.505029\pi$
$593$	−0.769454			−0.0315977			−0.0157988	+	0.999875i	$0.505029\pi$
$594$	12.2240	+	30.7838i	0.501557	+	1.26308i
$595$	−0.678187			−0.0278030
$596$	24.7979			1.01576
$597$	−24.5207	+	24.1119i	−1.00356	+	0.986834i
$598$	16.0956			0.658199
$599$		−	23.1559i		−	0.946123i	−0.881029	−	0.473062i	$-0.843149\pi$
$599$		−	23.1559i		−	0.946123i	0.881029	−	0.473062i	$-0.156851\pi$
$600$	3.50921	−	3.45071i	0.143263	−	0.140875i
$601$		−	37.3517i		−	1.52361i	−0.647809	−	0.761803i	$-0.724314\pi$
$601$		−	37.3517i		−	1.52361i	0.647809	−	0.761803i	$-0.275686\pi$
$602$	−2.31080			−0.0941810
$603$	0.309020	−	18.3812i	0.0125843	−	0.748539i
$604$			29.8577i			1.21489i
$605$	−3.14786	+	3.28309i	−0.127979	+	0.133477i
$606$	29.9587	−	29.4592i	1.21699	−	1.19670i
$607$			34.6424i			1.40609i	0.711144	+	0.703046i	$0.248177\pi$
$607$			34.6424i			1.40609i	−0.711144	+	0.703046i	$0.751823\pi$
$608$		−	31.6252i		−	1.28257i
$609$	−3.31757	−	3.37381i	−0.134435	−	0.136714i
$610$	12.3859			0.501492
$611$	11.3249			0.458158
$612$	−0.140098	+	8.33334i	−0.00566314	+	0.336855i
$613$			21.0615i			0.850668i	0.905037	+	0.425334i	$0.139843\pi$
$613$			21.0615i			0.850668i	−0.905037	+	0.425334i	$0.860157\pi$
$614$		−	16.7944i		−	0.677767i
$615$	−1.79282	−	1.82322i	−0.0722936	−	0.0735192i
$616$	0.727832	−	1.81075i	0.0293252	−	0.0729573i
$617$		−	38.2694i		−	1.54067i	−0.637640	−	0.770334i	$-0.720089\pi$
$617$		−	38.2694i		−	1.54067i	0.637640	−	0.770334i	$-0.279911\pi$
$618$	30.4064	−	29.8995i	1.22313	−	1.20274i
$619$	14.3645			0.577357			0.288679	−	0.957426i	$-0.406784\pi$
$619$	14.3645			0.577357			0.288679	+	0.957426i	$0.406784\pi$
$620$			3.19878i			0.128466i
$621$	−23.2051	+	22.0634i	−0.931189	+	0.885375i
$622$		−	20.5120i		−	0.822456i
$623$	−9.17912			−0.367754
$624$	7.45758	+	7.58400i	0.298542	+	0.303603i
$625$	22.4646			0.898586
$626$	−51.3644			−2.05293
$627$	−9.30748	−	22.3370i	−0.371705	−	0.892053i
$628$	−7.49234			−0.298977
$629$	10.5142			0.419228
$630$	−0.0400752	+	2.38376i	−0.00159664	+	0.0949713i
$631$	12.9501			0.515536			0.257768	−	0.966207i	$-0.417013\pi$
$631$	12.9501			0.515536			0.257768	+	0.966207i	$0.417013\pi$
$632$			9.80988i			0.390216i
$633$	−1.41220	−	1.43614i	−0.0561300	−	0.0570816i
$634$			32.1628i			1.27735i
$635$	2.89789			0.114999
$636$	−12.1719	−	12.3783i	−0.482647	−	0.490830i
$637$			1.35904i			0.0538470i
$638$	−16.1573	−	6.49444i	−0.639675	−	0.257117i
$639$	24.9365	+	0.419226i	0.986471	+	0.0165843i
$640$		−	1.92362i		−	0.0760377i
$641$		−	34.7902i		−	1.37413i	−0.726596	−	0.687065i	$-0.758899\pi$
$641$		−	34.7902i		−	1.37413i	0.726596	−	0.687065i	$-0.241101\pi$
$642$	−12.7058	+	12.4940i	−0.501458	+	0.493099i
$643$	−19.3039			−0.761273			−0.380637	−	0.924725i	$-0.624295\pi$
$643$	−19.3039			−0.761273			−0.380637	+	0.924725i	$0.624295\pi$
$644$	−10.4378			−0.411309
$645$	−0.613976	+	0.603741i	−0.0241753	+	0.0237723i
$646$		−	13.2788i		−	0.522446i
$647$		−	44.4284i		−	1.74666i	−0.487128	−	0.873331i	$-0.661956\pi$
$647$		−	44.4284i		−	1.74666i	0.487128	−	0.873331i	$-0.338044\pi$
$648$	−5.29275	−	0.178011i	−0.207919	−	0.00699294i
$649$	−12.8284	+	31.9155i	−0.503561	+	1.25279i
$650$			12.6133i			0.494736i
$651$	−5.54641	−	5.64044i	−0.217381	−	0.221066i
$652$	−6.17802			−0.241950
$653$			25.8911i			1.01320i	0.862182	+	0.506599i	$0.169098\pi$
$653$			25.8911i			1.01320i	−0.862182	+	0.506599i	$0.830902\pi$
$654$	27.9548	+	28.4288i	1.09312	+	1.11165i
$655$		−	3.26284i		−	0.127490i
$656$	16.1329			0.629882
$657$	0.871209	+	0.0146466i	0.0339891	+	0.000571417i
$658$	−16.0156			−0.624355
$659$	36.4163			1.41858			0.709289	−	0.704917i	$-0.249016\pi$
$659$	36.4163			1.41858			0.709289	+	0.704917i	$0.249016\pi$
$660$	1.54752	+	3.71389i	0.0602371	+	0.144563i
$661$	−31.8343			−1.23821			−0.619105	−	0.785308i	$-0.712505\pi$
$661$	−31.8343			−1.23821			−0.619105	+	0.785308i	$0.712505\pi$
$662$	0.0541711			0.00210542
$663$	2.70696	+	2.75285i	0.105130	+	0.106912i
$664$	2.07917			0.0806874
$665$		−	1.74179i		−	0.0675437i
$666$	0.621301	−	36.9563i	0.0240749	−	1.43203i
$667$		−	16.8342i		−	0.651824i
$668$	−10.7534			−0.416061
$669$	−15.3546	+	15.0986i	−0.593642	+	0.583745i
$670$		−	4.86985i		−	0.188139i
$671$	−19.2785	+	47.9624i	−0.744239	+	1.85157i
$672$	−9.11729	−	9.27185i	−0.351707	−	0.357670i
$673$		−	12.2118i		−	0.470732i	−0.971907	−	0.235366i	$-0.924371\pi$
$673$		−	12.2118i		−	0.470732i	0.971907	−	0.235366i	$-0.0756289\pi$
$674$		−	54.8005i		−	2.11084i
$675$	−17.2900	−	18.1847i	−0.665492	−	0.699929i
$676$	18.8915			0.726595
$677$	−1.16457			−0.0447582			−0.0223791	−	0.999750i	$-0.507124\pi$
$677$	−1.16457			−0.0447582			−0.0223791	+	0.999750i	$0.507124\pi$
$678$	−10.9195	−	11.1046i	−0.419360	−	0.426469i
$679$		−	12.9612i		−	0.497407i
$680$		−	0.399056i		−	0.0153031i
$681$	33.8553	−	33.2909i	1.29734	−	1.27571i
$682$	−27.0123	−	10.8576i	−1.03435	−	0.415759i
$683$		−	17.1511i		−	0.656269i	−0.944631	−	0.328135i	$-0.893580\pi$
$683$		−	17.1511i		−	0.656269i	0.944631	−	0.328135i	$-0.106420\pi$
$684$	−21.4025	−	0.359815i	−0.818346	−	0.0137579i
$685$	1.76652			0.0674952
$686$		−	1.92194i		−	0.0733799i
$687$	−33.6184	+	33.0580i	−1.28262	+	1.26124i
$688$		−	5.43281i		−	0.207124i
$689$	−8.04178			−0.306367
$690$	−6.04792	+	5.94709i	−0.230240	+	0.226402i
$691$	3.24097			0.123292			0.0616461	−	0.998098i	$-0.480365\pi$
$691$	3.24097			0.123292			0.0616461	+	0.998098i	$0.480365\pi$
$692$	−24.0571			−0.914514
$693$	−9.16832	−	3.86547i	−0.348276	−	0.146837i
$694$	61.6436			2.33996
$695$	3.86035			0.146432
$696$	1.98520	−	1.95211i	0.0752489	−	0.0739945i
$697$	5.85592			0.221809
$698$		−	47.2708i		−	1.78922i
$699$	13.3653	−	13.1425i	0.505522	−	0.497095i
$700$		−	8.17961i		−	0.309160i
$701$	1.96664			0.0742788			0.0371394	−	0.999310i	$-0.488175\pi$
$701$	1.96664			0.0742788			0.0371394	+	0.999310i	$0.488175\pi$
$702$	9.83595	−	9.35202i	0.371234	−	0.352969i
$703$			27.0036i			1.01846i
$704$	−16.5929	−	6.66952i	−0.625369	−	0.251367i
$705$	−4.25534	+	4.18440i	−0.160265	+	0.157594i
$706$			40.7642i			1.53418i
$707$			12.6217i			0.474688i
$708$	21.3336	+	21.6953i	0.801767	+	0.815359i
$709$	−25.8765			−0.971812			−0.485906	−	0.874011i	$-0.661510\pi$
$709$	−25.8765			−0.971812			−0.485906	+	0.874011i	$0.661510\pi$
$710$	6.60659			0.247941
$711$	50.0080	+	0.840724i	1.87545	+	0.0315296i
$712$		−	5.40114i		−	0.202416i
$713$		−	28.1440i		−	1.05400i
$714$	−3.82816	−	3.89306i	−0.143265	−	0.145694i
$715$	1.72930	+	0.695091i	0.0646720	+	0.0259949i
$716$			42.5470i			1.59006i
$717$	24.5886	−	24.1787i	0.918279	−	0.902970i
$718$	−23.1654			−0.864524
$719$		−	25.2880i		−	0.943085i	−0.881843	−	0.471542i	$-0.843697\pi$
$719$		−	25.2880i		−	0.943085i	0.881843	−	0.471542i	$-0.156303\pi$
$720$	−5.60435	−	0.0942192i	−0.208862	−	0.00351134i
$721$			12.8103i			0.477082i
$722$	−2.41294			−0.0898005
$723$	−9.34202	−	9.50039i	−0.347433	−	0.353323i
$724$	11.4834			0.426776
$725$	13.1921			0.489944
$726$	−36.6149	+	0.462115i	−1.35891	+	0.0171507i
$727$	44.7443			1.65948			0.829738	−	0.558154i	$-0.188490\pi$
$727$	44.7443			1.65948			0.829738	+	0.558154i	$0.188490\pi$
$728$	−0.799678			−0.0296380
$729$	−1.36105	+	26.9657i	−0.0504092	+	0.998729i
$730$	0.230816			0.00854287
$731$		−	1.97201i		−	0.0729373i
$732$	32.0600	+	32.6036i	1.18497	+	1.20506i
$733$			7.08238i			0.261594i	0.991409	+	0.130797i	$0.0417536\pi$
$733$			7.08238i			0.261594i	−0.991409	+	0.130797i	$0.958246\pi$
$734$	25.6709			0.947531
$735$	−0.502144	−	0.510656i	−0.0185218	−	0.0188358i
$736$		−	46.2635i		−	1.70530i
$737$	18.8577	+	7.57984i	0.694631	+	0.279207i
$738$	0.346037	−	20.5830i	0.0127378	−	0.757670i
$739$		−	4.71652i		−	0.173500i	−0.996230	−	0.0867499i	$-0.972352\pi$
$739$		−	4.71652i		−	0.173500i	0.996230	−	0.0867499i	$-0.0276481\pi$
$740$		−	4.48979i		−	0.165048i
$741$	−7.07015	+	6.95229i	−0.259728	+	0.255399i
$742$	11.3726			0.417502
$743$	−6.91850			−0.253815			−0.126908	−	0.991915i	$-0.540505\pi$
$743$	−6.91850			−0.253815			−0.126908	+	0.991915i	$0.540505\pi$
$744$	3.31892	−	3.26359i	0.121678	−	0.119649i
$745$			6.05349i			0.221783i
$746$			3.68747i			0.135008i
$747$	0.178188	−	10.5990i	0.00651957	−	0.387798i
$748$	−8.54937	−	3.43642i	−0.312596	−	0.125648i
$749$		−	5.35301i		−	0.195595i
$750$	−9.48588	−	9.64670i	−0.346375	−	0.352248i
$751$	27.8696			1.01698			0.508488	−	0.861069i	$-0.330204\pi$
$751$	27.8696			1.01698			0.508488	+	0.861069i	$0.330204\pi$
$752$		−	37.6537i		−	1.37309i
$753$	11.6816	+	11.8796i	0.425701	+	0.432918i
$754$			7.13552i			0.259860i
$755$	−7.28864			−0.265261
$756$	−6.37851	+	6.06468i	−0.231984	+	0.220570i
$757$	−29.8479			−1.08484			−0.542420	−	0.840107i	$-0.682492\pi$
$757$	−29.8479			−1.08484			−0.542420	+	0.840107i	$0.682492\pi$
$758$	−45.2394			−1.64317
$759$	−13.6156	−	32.6761i	−0.494216	−	1.18607i
$760$	1.02490			0.0371769
$761$	41.1535			1.49181			0.745906	−	0.666051i	$-0.232017\pi$
$761$	41.1535			1.49181			0.745906	+	0.666051i	$0.232017\pi$
$762$	16.3577	+	16.6350i	0.592577	+	0.602623i
$763$	−11.9771			−0.433602
$764$			18.8576i			0.682243i
$765$	−2.03427	−	0.0341998i	−0.0735494	−	0.00123650i
$766$		−	19.4434i		−	0.702519i
$767$	14.0948			0.508933
$768$	24.3604	−	23.9543i	0.879032	−	0.864378i
$769$			7.21978i			0.260352i	0.991491	+	0.130176i	$0.0415543\pi$
$769$			7.21978i			0.260352i	−0.991491	+	0.130176i	$0.958446\pi$
$770$	−2.44555	−	0.982991i	−0.0881317	−	0.0354245i
$771$	−15.6867	−	15.9526i	−0.564943	−	0.574520i
$772$		−	36.6607i		−	1.31945i
$773$		−	8.26163i		−	0.297150i	−0.988901	−	0.148575i	$-0.952531\pi$
$773$		−	8.26163i		−	0.297150i	0.988901	−	0.148575i	$-0.0474687\pi$
$774$	−6.93141	−	0.116529i	−0.249144	−	0.00418856i
$775$	22.0550			0.792239
$776$	7.62659			0.273779
$777$	7.78492	+	7.91690i	0.279282	+	0.284017i
$778$		−	10.4521i		−	0.374726i
$779$			15.0398i			0.538856i
$780$	1.17553	−	1.15593i	0.0420906	−	0.0413890i
$781$	−10.2830	+	25.5829i	−0.367956	+	0.915428i
$782$		−	19.4251i		−	0.694640i
$783$	−9.78116	−	10.2873i	−0.349550	−	0.367638i
$784$	4.51858			0.161378
$785$		−	1.82898i		−	0.0652790i
$786$	18.7300	−	18.4177i	0.668076	−	0.656939i
$787$			27.8702i			0.993465i	0.867904	+	0.496733i	$0.165467\pi$
$787$			27.8702i			0.993465i	−0.867904	+	0.496733i	$0.834533\pi$
$788$	17.0086			0.605905
$789$	2.30873	−	2.27025i	0.0821931	−	0.0808229i
$790$	13.2490			0.471377
$791$	4.67841			0.166345
$792$	2.27450	−	5.39478i	0.0808208	−	0.191695i
$793$	21.1815			0.752179
$794$	−49.3977			−1.75306
$795$	3.02169	−	2.97132i	0.107168	−	0.105382i
$796$	−33.6310			−1.19202
$797$			1.97594i			0.0699914i	0.999387	+	0.0349957i	$0.0111418\pi$
$797$			1.97594i			0.0699914i	−0.999387	+	0.0349957i	$0.988858\pi$
$798$	9.99854	−	9.83186i	0.353945	−	0.348044i
$799$		−	13.6676i		−	0.483524i
$800$	36.2544			1.28179
$801$	−27.5335	−	0.462887i	−0.972848	−	0.0163553i
$802$			67.7464i			2.39221i
$803$	−0.359260	+	0.893793i	−0.0126780	+	0.0315413i
$804$	12.8189	−	12.6052i	0.452089	−	0.444552i
$805$		−	2.54801i		−	0.0898056i
$806$			11.9294i			0.420194i
$807$	15.6966	+	15.9627i	0.552547	+	0.561915i
$808$	−7.42680			−0.261274
$809$	−26.8892			−0.945373			−0.472687	−	0.881231i	$-0.656716\pi$
$809$	−26.8892			−0.945373			−0.472687	+	0.881231i	$0.656716\pi$
$810$	−0.240418	+	7.14825i	−0.00844741	+	0.251164i
$811$			6.63605i			0.233023i	0.993189	+	0.116512i	$0.0371712\pi$
$811$			6.63605i			0.233023i	−0.993189	+	0.116512i	$0.962829\pi$
$812$		−	4.62731i		−	0.162387i
$813$	−24.5653	−	24.9818i	−0.861543	−	0.876149i
$814$	37.9143	+	15.2397i	1.32890	+	0.534150i
$815$		−	1.50813i		−	0.0528276i
$816$	9.15280	−	9.00022i	0.320412	−	0.315071i
$817$	5.06471			0.177192
$818$			56.2983i			1.96842i
$819$	−0.0685338	+	4.07653i	−0.00239476	+	0.142446i
$820$		−	2.50061i		−	0.0873250i
$821$	−0.765204			−0.0267058			−0.0133529	−	0.999911i	$-0.504250\pi$
$821$	−0.765204			−0.0267058			−0.0133529	+	0.999911i	$0.504250\pi$
$822$	9.97146	+	10.1405i	0.347795	+	0.353691i
$823$	46.9375			1.63614			0.818069	−	0.575120i	$-0.195045\pi$
$823$	46.9375			1.63614			0.818069	+	0.575120i	$0.195045\pi$
$824$	−7.53780			−0.262592
$825$	25.6066	−	10.6699i	0.891507	−	0.371477i
$826$	−19.9327			−0.693548
$827$	−2.55853			−0.0889688			−0.0444844	−	0.999010i	$-0.514164\pi$
$827$	−2.55853			−0.0889688			−0.0444844	+	0.999010i	$0.514164\pi$
$828$	−31.3091	−	0.526362i	−1.08807	−	0.0182923i
$829$	−21.0300			−0.730402			−0.365201	−	0.930929i	$-0.619000\pi$
$829$	−21.0300			−0.730402			−0.365201	+	0.930929i	$0.619000\pi$
$830$		−	2.80807i		−	0.0974696i
$831$	−8.81900	−	8.96851i	−0.305928	−	0.311114i
$832$			7.32788i			0.254049i
$833$	1.64016			0.0568282
$834$	21.7905	+	22.1599i	0.754544	+	0.767335i
$835$		−	2.62504i		−	0.0908431i
$836$	8.82576	−	21.9574i	0.305245	−	0.759411i
$837$	−16.3524	−	17.1986i	−0.565223	−	0.594471i
$838$			14.5267i			0.501817i
$839$		−	16.4101i		−	0.566538i	−0.959040	−	0.283269i	$-0.908581\pi$
$839$		−	16.4101i		−	0.566538i	0.959040	−	0.283269i	$-0.0914190\pi$
$840$	0.300478	−	0.295469i	0.0103675	−	0.0101947i
$841$	−21.5370			−0.742657
$842$	4.43809			0.152947
$843$	−31.5516	+	31.0256i	−1.08669	+	1.06858i
$844$		−	1.96973i		−	0.0678007i
$845$			4.61165i			0.158645i
$846$	−48.0401	−	0.807640i	−1.65165	−	0.0277672i
$847$	7.61293	−	7.93998i	0.261583	−	0.272821i
$848$			26.7377i			0.918175i
$849$	23.4587	+	23.8564i	0.805102	+	0.818751i
$850$	15.2225			0.522126
$851$			39.5027i			1.35414i
$852$	17.1006	+	17.3906i	0.585858	+	0.595791i
$853$			37.0834i			1.26971i	0.772630	+	0.634856i	$0.218941\pi$
$853$			37.0834i			1.26971i	−0.772630	+	0.634856i	$0.781059\pi$
$854$	−29.9548			−1.02503
$855$	0.0878353	−	5.22463i	0.00300390	−	0.178679i
$856$	3.14979			0.107658
$857$	−51.6425			−1.76407			−0.882037	−	0.471180i	$-0.843828\pi$
$857$	−51.6425			−1.76407			−0.882037	+	0.471180i	$0.843828\pi$
$858$	5.77125	+	13.8504i	0.197027	+	0.472845i
$859$	−20.1363			−0.687043			−0.343522	−	0.939145i	$-0.611620\pi$
$859$	−20.1363			−0.687043			−0.343522	+	0.939145i	$0.611620\pi$
$860$	−0.842091			−0.0287151
$861$	4.33584	+	4.40935i	0.147765	+	0.150270i
$862$	−31.1920			−1.06240
$863$			1.50058i			0.0510803i	0.999674	+	0.0255402i	$0.00813057\pi$
$863$			1.50058i			0.0510803i	−0.999674	+	0.0255402i	$0.991869\pi$
$864$	−26.8804	−	28.2714i	−0.914491	−	0.961813i
$865$		−	5.87265i		−	0.199676i
$866$	−3.20623			−0.108952
$867$	−17.6726	+	17.3780i	−0.600194	+	0.590189i
$868$		−	7.73607i		−	0.262579i
$869$	−20.6218	+	51.3044i	−0.699547	+	1.74038i
$870$	−2.63647	−	2.68116i	−0.0893846	−	0.0909000i
$871$		−	8.32807i		−	0.282186i
$872$		−	7.04754i		−	0.238660i
$873$	0.653612	−	38.8782i	0.0221214	−	1.31583i
$874$	49.8895			1.68754
$875$	4.06419			0.137395
$876$	0.597448	+	0.607576i	0.0201859	+	0.0205281i
$877$			10.2813i			0.347176i	0.984818	+	0.173588i	$0.0555360\pi$
$877$			10.2813i			0.347176i	−0.984818	+	0.173588i	$0.944464\pi$
$878$			66.3725i			2.23996i
$879$	−24.0369	+	23.6361i	−0.810743	+	0.797227i
$880$	2.31107	−	5.74964i	0.0779061	−	0.193820i
$881$			58.2128i			1.96124i	0.195920	+	0.980620i	$0.437231\pi$
$881$			58.2128i			1.96124i	−0.195920	+	0.980620i	$0.562769\pi$
$882$	0.0969199	−	5.76500i	0.00326346	−	0.194118i
$883$	−4.96966			−0.167243			−0.0836213	−	0.996498i	$-0.526649\pi$
$883$	−4.96966			−0.167243			−0.0836213	+	0.996498i	$0.526649\pi$
$884$			3.77564i			0.126988i
$885$	−5.29610	+	5.20781i	−0.178026	+	0.175059i
$886$			44.4654i			1.49384i
$887$	39.5512			1.32800			0.664000	−	0.747733i	$-0.268858\pi$
$887$	39.5512			1.32800			0.664000	+	0.747733i	$0.268858\pi$
$888$	−4.65842	+	4.58077i	−0.156326	+	0.153720i
$889$	−7.00839			−0.235054
$890$	−7.29464			−0.244517
$891$	−27.3062	−	12.0571i	−0.914791	−	0.403928i
$892$	−21.0594			−0.705119
$893$	35.1024			1.17466
$894$	−34.7494	+	34.1701i	−1.16219	+	1.14282i
$895$	−10.3863			−0.347175
$896$			4.65217i			0.155418i
$897$	−10.3427	+	10.1703i	−0.345333	+	0.339576i
$898$			27.2854i			0.910525i
$899$	12.4768			0.416124
$900$	0.412483	−	24.5354i	0.0137494	−	0.817846i
$901$			9.70526i			0.323329i
$902$	21.1166	+	8.48780i	0.703105	+	0.282613i
$903$	1.48487	−	1.46011i	0.0494133	−	0.0485896i
$904$			2.75285i			0.0915583i
$905$			2.80324i			0.0931827i
$906$	−41.1421	−	41.8396i	−1.36685	−	1.39003i
$907$	−17.3361			−0.575634			−0.287817	−	0.957685i	$-0.592930\pi$
$907$	−17.3361			−0.575634			−0.287817	+	0.957685i	$0.592930\pi$
$908$	46.4338			1.54096
$909$	−0.636490	+	37.8597i	−0.0211110	+	1.25573i
$910$			1.08002i			0.0358025i
$911$		−	24.3870i		−	0.807976i	−0.914764	−	0.403988i	$-0.867624\pi$
$911$		−	24.3870i		−	0.807976i	0.914764	−	0.403988i	$-0.132376\pi$
$912$	23.1153	+	23.5071i	0.765423	+	0.778399i
$913$	10.8738	+	4.37072i	0.359870	+	0.144650i
$914$		−	30.5477i		−	1.01043i
$915$	−7.95894	+	7.82626i	−0.263115	+	0.258728i
$916$	−46.1089			−1.52348
$917$			7.89101i			0.260584i
$918$	−11.2865	−	11.8706i	−0.372511	−	0.391787i
$919$			5.37606i			0.177340i	0.996061	+	0.0886700i	$0.0282616\pi$
$919$			5.37606i			0.177340i	−0.996061	+	0.0886700i	$0.971738\pi$
$920$	1.49929			0.0494301
$921$	10.6118	+	10.7917i	0.349671	+	0.355599i
$922$	−49.0218			−1.61445
$923$	11.2981			0.371882
$924$	−3.74260	−	8.98184i	−0.123122	−	0.295481i
$925$	−30.9563			−1.01784
$926$	−25.4565			−0.836553
$927$	−0.646003	+	38.4256i	−0.0212175	+	1.26206i
$928$	20.5096			0.673260
$929$			23.9905i			0.787101i	0.919303	+	0.393551i	$0.128753\pi$
$929$			23.9905i			0.787101i	−0.919303	+	0.393551i	$0.871247\pi$
$930$	−4.40773	−	4.48245i	−0.144535	−	0.146985i
$931$			4.21243i			0.138057i
$932$	18.3310			0.600452
$933$	12.9608	+	13.1806i	0.424319	+	0.431512i
$934$		−	54.4691i		−	1.78228i
$935$	0.838874	−	2.08701i	0.0274341	−	0.0682525i
$936$	−2.39869	−	0.0403263i	−0.0784038	−	0.00131811i
$937$		−	25.8520i		−	0.844546i	−0.906469	−	0.422273i	$-0.861232\pi$
$937$		−	25.8520i		−	0.844546i	0.906469	−	0.422273i	$-0.138768\pi$
$938$			11.7775i			0.384548i
$939$	33.0056	−	32.4554i	1.07710	−	1.05914i
$940$	−5.83635			−0.190361
$941$	21.1934			0.690884			0.345442	−	0.938440i	$-0.387729\pi$
$941$	21.1934			0.690884			0.345442	+	0.938440i	$0.387729\pi$
$942$	10.4990	−	10.3240i	0.342077	−	0.336374i
$943$			22.0012i			0.716459i
$944$		−	46.8629i		−	1.52526i
$945$	−1.48047	−	1.55708i	−0.0481596	−	0.0506517i
$946$	2.85830	−	7.11109i	0.0929315	−	0.231202i
$947$			44.9355i			1.46021i	0.683336	+	0.730104i	$0.260528\pi$
$947$			44.9355i			1.46021i	−0.683336	+	0.730104i	$0.739472\pi$
$948$	34.2939	+	34.8753i	1.11381	+	1.13270i
$949$	0.394724			0.0128133
$950$			39.0959i			1.26844i
$951$	−20.3226	−	20.6671i	−0.659005	−	0.670177i
$952$			0.965096i			0.0312789i
$953$	−43.7243			−1.41637			−0.708184	−	0.706028i	$-0.750485\pi$
$953$	−43.7243			−1.41637			−0.708184	+	0.706028i	$0.750485\pi$
$954$	34.1130	+	0.573501i	1.10445	+	0.0185678i
$955$	−4.60337			−0.148962
$956$	33.7242			1.09072
$957$	14.4860	−	6.03608i	0.468265	−	0.195119i
$958$	−2.95426			−0.0954478
$959$	−4.27223			−0.137958
$960$	−2.70754	−	2.75345i	−0.0873856	−	0.0888671i
$961$	−10.1409			−0.327127
$962$		−	16.7440i		−	0.539849i
$963$	0.269943	−	16.0567i	0.00869878	−	0.517422i
$964$		−	13.0301i		−	0.419673i
$965$	8.94935			0.288090
$966$	14.6266	−	14.3827i	0.470602	−	0.462757i
$967$			17.8707i			0.574682i	0.957828	+	0.287341i	$0.0927714\pi$
$967$			17.8707i			0.574682i	−0.957828	+	0.287341i	$0.907229\pi$
$968$	4.67201	+	4.47956i	0.150164	+	0.143979i
$969$	8.39040	+	8.53265i	0.269539	+	0.274108i
$970$		−	10.3003i		−	0.330722i
$971$		−	25.6948i		−	0.824586i	−0.911051	−	0.412293i	$-0.864728\pi$
$971$		−	25.6948i		−	0.824586i	0.911051	−	0.412293i	$-0.135272\pi$
$972$	−19.4387	+	17.8698i	−0.623495	+	0.573175i
$973$	−9.33606			−0.299300
$974$	13.7965			0.442070
$975$	−7.96994	−	8.10506i	−0.255242	−	0.259570i
$976$		−	70.4253i		−	2.25426i
$977$			30.5104i			0.976114i	0.872812	+	0.488057i	$0.162294\pi$
$977$			30.5104i			0.976114i	−0.872812	+	0.488057i	$0.837706\pi$
$978$	8.65727	−	8.51295i	0.276829	−	0.272214i
$979$	11.3540	−	28.2472i	0.362875	−	0.902786i
$980$		−	0.700384i		−	0.0223730i
$981$	−35.9264	−	0.603986i	−1.14704	−	0.0192838i
$982$	−72.0668			−2.29974
$983$		−	7.50598i		−	0.239404i	−0.992810	−	0.119702i	$-0.961806\pi$
$983$		−	7.50598i		−	0.239404i	0.992810	−	0.119702i	$-0.0381938\pi$
$984$	−2.59453	+	2.55128i	−0.0827106	+	0.0813318i
$985$			4.15201i			0.132294i
$986$	8.61154			0.274247
$987$	10.2913	−	10.1197i	0.327576	−	0.322115i
$988$	−9.69697			−0.308502
$989$	7.40901			0.235593
$990$	−7.28606	−	3.07188i	−0.231566	−	0.0976308i
$991$	−39.5227			−1.25548			−0.627740	−	0.778423i	$-0.716020\pi$
$991$	−39.5227			−1.25548			−0.627740	+	0.778423i	$0.716020\pi$
$992$	34.2885			1.08866
$993$	−0.0348092	+	0.0342289i	−0.00110464	+	0.00108622i
$994$	−15.9777			−0.506782
$995$		−	8.20975i		−	0.260267i
$996$	7.39170	−	7.26847i	0.234215	−	0.230310i
$997$			16.1240i			0.510652i	0.966855	+	0.255326i	$0.0821828\pi$
$997$			16.1240i			0.510652i	−0.966855	+	0.255326i	$0.917817\pi$
$998$	−25.5064			−0.807391
$999$	22.9522	+	24.1399i	0.726176	+	0.763753i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.g.a.197.5	✓	24
3.2	odd	2	inner	231.2.g.a.197.20	yes	24
11.10	odd	2	inner	231.2.g.a.197.19	yes	24
33.32	even	2	inner	231.2.g.a.197.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.g.a.197.5	✓	24	1.1	even	1	trivial
231.2.g.a.197.6	yes	24	33.32	even	2	inner
231.2.g.a.197.19	yes	24	11.10	odd	2	inner
231.2.g.a.197.20	yes	24	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.92194 q^{2} +(1.23500 - 1.21441i) q^{3} +1.69384 q^{4} +0.413489i q^{5} +(-2.37358 + 2.33402i) q^{6} -1.00000i q^{7} +0.588415 q^{8} +(0.0504282 - 2.99958i) q^{9} +O(q^{10})\)	\(q-1.92194 q^{2} +(1.23500 - 1.21441i) q^{3} +1.69384 q^{4} +0.413489i q^{5} +(-2.37358 + 2.33402i) q^{6} -1.00000i q^{7} +0.588415 q^{8} +(0.0504282 - 2.99958i) q^{9} -0.794699i q^{10} +(3.07734 + 1.23694i) q^{11} +(2.09189 - 2.05702i) q^{12} -1.35904i q^{13} +1.92194i q^{14} +(0.502144 + 0.510656i) q^{15} -4.51858 q^{16} -1.64016 q^{17} +(-0.0969199 + 5.76500i) q^{18} -4.21243i q^{19} +0.700384i q^{20} +(-1.21441 - 1.23500i) q^{21} +(-5.91444 - 2.37731i) q^{22} -6.16223i q^{23} +(0.726690 - 0.714576i) q^{24} +4.82903 q^{25} +2.61198i q^{26} +(-3.58043 - 3.76570i) q^{27} -1.69384i q^{28} +2.73184 q^{29} +(-0.965088 - 0.981450i) q^{30} +4.56717 q^{31} +7.50760 q^{32} +(5.30264 - 2.20953i) q^{33} +3.15228 q^{34} +0.413489 q^{35} +(0.0854175 - 5.08081i) q^{36} -6.41046 q^{37} +8.09602i q^{38} +(-1.65042 - 1.67840i) q^{39} +0.243303i q^{40} -3.57034 q^{41} +(2.33402 + 2.37358i) q^{42} +1.20233i q^{43} +(5.21252 + 2.09517i) q^{44} +(1.24029 + 0.0208515i) q^{45} +11.8434i q^{46} +8.33307i q^{47} +(-5.58043 + 5.48740i) q^{48} -1.00000 q^{49} -9.28109 q^{50} +(-2.02559 + 1.99182i) q^{51} -2.30199i q^{52} -5.91727i q^{53} +(6.88136 + 7.23745i) q^{54} +(-0.511459 + 1.27244i) q^{55} -0.588415i q^{56} +(-5.11560 - 5.20233i) q^{57} -5.25043 q^{58} +10.3712i q^{59} +(0.850552 + 0.864972i) q^{60} +15.5857i q^{61} -8.77782 q^{62} +(-2.99958 - 0.0504282i) q^{63} -5.39197 q^{64} +0.561946 q^{65} +(-10.1913 + 4.24658i) q^{66} +6.12792 q^{67} -2.77817 q^{68} +(-7.48346 - 7.61032i) q^{69} -0.794699 q^{70} +8.31333i q^{71} +(0.0296727 - 1.76500i) q^{72} +0.290444i q^{73} +12.3205 q^{74} +(5.96383 - 5.86441i) q^{75} -7.13518i q^{76} +(1.23694 - 3.07734i) q^{77} +(3.17201 + 3.22579i) q^{78} +16.6717i q^{79} -1.86838i q^{80} +(-8.99491 - 0.302527i) q^{81} +6.86196 q^{82} +3.53351 q^{83} +(-2.05702 - 2.09189i) q^{84} -0.678187i q^{85} -2.31080i q^{86} +(3.37381 - 3.31757i) q^{87} +(1.81075 + 0.727832i) q^{88} -9.17912i q^{89} +(-2.38376 - 0.0400752i) q^{90} -1.35904 q^{91} -10.4378i q^{92} +(5.64044 - 5.54641i) q^{93} -16.0156i q^{94} +1.74179 q^{95} +(9.27185 - 9.11729i) q^{96} +12.9612 q^{97} +1.92194 q^{98} +(3.86547 - 9.16832i) 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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