LMFDB - Embedded newform 231.2.p.a.10.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(10,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 3]))

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

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

chi := DirichletCharacter("231.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.p (of order $6$, degree $2$, 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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.15
Character	$\chi$	$=$	231.10
Dual form			231.2.p.a.208.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.16769 - 1.25152i) q^{2} +(0.866025 + 0.500000i) q^{3} +(2.13259 - 3.69375i) q^{4} +(-0.849508 + 0.490464i) q^{5} +2.50303 q^{6} +(-1.62716 + 2.08623i) q^{7} -5.66981i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(2.16769 - 1.25152i) q^{2} +(0.866025 + 0.500000i) q^{3} +(2.13259 - 3.69375i) q^{4} +(-0.849508 + 0.490464i) q^{5} +2.50303 q^{6} +(-1.62716 + 2.08623i) q^{7} -5.66981i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.22765 + 2.12635i) q^{10} +(-0.488650 - 3.28043i) q^{11} +(3.69375 - 2.13259i) q^{12} -0.941338 q^{13} +(-0.916236 + 6.55871i) q^{14} -0.980927 q^{15} +(-2.83068 - 4.90289i) q^{16} +(-2.58843 + 4.48329i) q^{17} +(2.16769 + 1.25152i) q^{18} +(-1.27435 - 2.20723i) q^{19} +4.18383i q^{20} +(-2.45228 + 0.993145i) q^{21} +(-5.16475 - 6.49940i) q^{22} +(0.379091 + 0.656604i) q^{23} +(2.83490 - 4.91020i) q^{24} +(-2.01889 + 3.49682i) q^{25} +(-2.04053 + 1.17810i) q^{26} +1.00000i q^{27} +(4.23594 + 10.4594i) q^{28} -8.74957i q^{29} +(-2.12635 + 1.22765i) q^{30} +(5.50826 + 3.18019i) q^{31} +(-2.45170 - 1.41549i) q^{32} +(1.21703 - 3.08526i) q^{33} +12.9578i q^{34} +(0.359069 - 2.57033i) q^{35} +4.26518 q^{36} +(-1.49424 - 2.58810i) q^{37} +(-5.52477 - 3.18973i) q^{38} +(-0.815223 - 0.470669i) q^{39} +(2.78084 + 4.81655i) q^{40} +3.80891 q^{41} +(-4.07284 + 5.22190i) q^{42} +6.73386i q^{43} +(-13.1592 - 5.19085i) q^{44} +(-0.849508 - 0.490464i) q^{45} +(1.64350 + 0.948877i) q^{46} +(8.42881 - 4.86638i) q^{47} -5.66137i q^{48} +(-1.70469 - 6.78926i) q^{49} +10.1067i q^{50} +(-4.48329 + 2.58843i) q^{51} +(-2.00749 + 3.47707i) q^{52} +(2.24816 - 3.89393i) q^{53} +(1.25152 + 2.16769i) q^{54} +(2.02404 + 2.54709i) q^{55} +(11.8285 + 9.22570i) q^{56} -2.54869i q^{57} +(-10.9502 - 18.9664i) q^{58} +(-12.7383 - 7.35448i) q^{59} +(-2.09191 + 3.62330i) q^{60} +(-2.81334 - 4.87284i) q^{61} +15.9203 q^{62} +(-2.62031 - 0.366050i) q^{63} +4.23671 q^{64} +(0.799675 - 0.461692i) q^{65} +(-1.22311 - 8.21103i) q^{66} +(-6.21261 + 10.7606i) q^{67} +(11.0401 + 19.1220i) q^{68} +0.758182i q^{69} +(-2.43846 - 6.02106i) q^{70} +10.4898 q^{71} +(4.91020 - 2.83490i) q^{72} +(-5.14984 + 8.91978i) q^{73} +(-6.47811 - 3.74014i) q^{74} +(-3.49682 + 2.01889i) q^{75} -10.8706 q^{76} +(7.63883 + 4.31836i) q^{77} -2.35620 q^{78} +(6.63084 - 3.82832i) q^{79} +(4.80938 + 2.77670i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(8.25654 - 4.76692i) q^{82} +6.28891 q^{83} +(-1.56127 + 11.1761i) q^{84} -5.07812i q^{85} +(8.42754 + 14.5969i) q^{86} +(4.37479 - 7.57735i) q^{87} +(-18.5994 + 2.77055i) q^{88} +(2.06478 - 1.19210i) q^{89} -2.45529 q^{90} +(1.53171 - 1.96385i) q^{91} +3.23378 q^{92} +(3.18019 + 5.50826i) q^{93} +(12.1807 - 21.0976i) q^{94} +(2.16513 + 1.25004i) q^{95} +(-1.41549 - 2.45170i) q^{96} -7.30005i q^{97} +(-12.1921 - 12.5836i) q^{98} +(2.59661 - 2.06340i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 12 q^{4} - 12 q^{5} + 16 q^{9}+O(q^{10}) $ 32 * q + 12 * q^4 - 12 * q^5 + 16 * q^9	$ 32 q + 12 q^{4} - 12 q^{5} + 16 q^{9} + 2 q^{11} - 32 q^{14} + 8 q^{15} - 20 q^{16} + 8 q^{22} + 24 q^{23} - 24 q^{26} - 12 q^{31} - 18 q^{33} + 24 q^{36} - 32 q^{37} + 24 q^{38} - 24 q^{42} - 28 q^{44} - 12 q^{45} + 24 q^{47} - 36 q^{49} + 36 q^{53} - 56 q^{56} + 12 q^{58} - 48 q^{59} + 8 q^{64} - 36 q^{66} + 20 q^{67} + 24 q^{70} + 72 q^{71} + 24 q^{75} - 48 q^{78} + 72 q^{80} - 16 q^{81} - 48 q^{82} + 64 q^{86} + 24 q^{88} + 60 q^{89} - 28 q^{91} - 16 q^{92} + 16 q^{93} + 4 q^{99}+O(q^{100}) $ 32 * q + 12 * q^4 - 12 * q^5 + 16 * q^9 + 2 * q^11 - 32 * q^14 + 8 * q^15 - 20 * q^16 + 8 * q^22 + 24 * q^23 - 24 * q^26 - 12 * q^31 - 18 * q^33 + 24 * q^36 - 32 * q^37 + 24 * q^38 - 24 * q^42 - 28 * q^44 - 12 * q^45 + 24 * q^47 - 36 * q^49 + 36 * q^53 - 56 * q^56 + 12 * q^58 - 48 * q^59 + 8 * q^64 - 36 * q^66 + 20 * q^67 + 24 * q^70 + 72 * q^71 + 24 * q^75 - 48 * q^78 + 72 * q^80 - 16 * q^81 - 48 * q^82 + 64 * q^86 + 24 * q^88 + 60 * q^89 - 28 * q^91 - 16 * q^92 + 16 * q^93 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	2.16769	−	1.25152i	1.53279	−	0.884956i	0.533557	−	0.845764i	$-0.320855\pi$
$2$	2.16769	−	1.25152i	1.53279	−	0.884956i	0.999232	−	0.0391917i	$-0.0124783\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	2.13259	−	3.69375i	1.06629	−	1.84688i
$5$	−0.849508	+	0.490464i	−0.379912	+	0.219342i	−0.677780	−	0.735265i	$-0.737058\pi$
$5$	−0.849508	+	0.490464i	−0.379912	+	0.219342i	0.297868	+	0.954607i	$0.403724\pi$
$6$	2.50303			1.02186
$7$	−1.62716	+	2.08623i	−0.615009	+	0.788520i
$7$	−1.62716	+	2.08623i	−0.615009	+	0.788520i
$8$		−	5.66981i		−	2.00458i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−1.22765	+	2.12635i	−0.388216	+	0.672410i
$11$	−0.488650	−	3.28043i	−0.147333	−	0.989087i
$11$	−0.488650	−	3.28043i	−0.147333	−	0.989087i
$12$	3.69375	−	2.13259i	1.06629	−	0.615625i
$13$	−0.941338			−0.261080			−0.130540	−	0.991443i	$-0.541671\pi$
$13$	−0.941338			−0.261080			−0.130540	+	0.991443i	$0.541671\pi$
$14$	−0.916236	+	6.55871i	−0.244874	+	1.75289i
$15$	−0.980927			−0.253274
$16$	−2.83068	−	4.90289i	−0.707671	−	1.22572i
$17$	−2.58843	+	4.48329i	−0.627786	+	1.08736i	0.360209	+	0.932872i	$0.382705\pi$
$17$	−2.58843	+	4.48329i	−0.627786	+	1.08736i	−0.987995	+	0.154486i	$0.950628\pi$
$18$	2.16769	+	1.25152i	0.510930	+	0.294985i
$19$	−1.27435	−	2.20723i	−0.292355	−	0.506374i	0.682011	−	0.731342i	$-0.261106\pi$
$19$	−1.27435	−	2.20723i	−0.292355	−	0.506374i	−0.974366	+	0.224968i	$0.927772\pi$
$20$			4.18383i			0.935532i
$21$	−2.45228	+	0.993145i	−0.535131	+	0.216722i
$22$	−5.16475	−	6.49940i	−1.10113	−	1.38568i
$23$	0.379091	+	0.656604i	0.0790459	+	0.136911i	0.902839	−	0.429980i	$-0.141479\pi$
$23$	0.379091	+	0.656604i	0.0790459	+	0.136911i	−0.823793	+	0.566891i	$0.808146\pi$
$24$	2.83490	−	4.91020i	0.578672	−	1.00229i
$25$	−2.01889	+	3.49682i	−0.403778	+	0.699364i
$26$	−2.04053	+	1.17810i	−0.400181	+	0.231045i
$27$			1.00000i			0.192450i
$28$	4.23594	+	10.4594i	0.800517	+	1.97664i
$29$		−	8.74957i		−	1.62475i	−0.583132	−	0.812377i	$-0.698173\pi$
$29$		−	8.74957i		−	1.62475i	0.583132	−	0.812377i	$-0.301827\pi$
$30$	−2.12635	+	1.22765i	−0.388216	+	0.224137i
$31$	5.50826	+	3.18019i	0.989312	+	0.571179i	0.905069	−	0.425266i	$-0.139819\pi$
$31$	5.50826	+	3.18019i	0.989312	+	0.571179i	0.0842433	+	0.996445i	$0.473153\pi$
$32$	−2.45170	−	1.41549i	−0.433403	−	0.250225i
$33$	1.21703	−	3.08526i	0.211858	−	0.537075i
$34$			12.9578i			2.22225i
$35$	0.359069	−	2.57033i	0.0606937	−	0.434465i
$36$	4.26518			0.710863
$37$	−1.49424	−	2.58810i	−0.245652	−	0.425481i	0.716663	−	0.697420i	$-0.245669\pi$
$37$	−1.49424	−	2.58810i	−0.245652	−	0.425481i	−0.962315	+	0.271938i	$0.912335\pi$
$38$	−5.52477	−	3.18973i	−0.896236	−	0.517442i
$39$	−0.815223	−	0.470669i	−0.130540	−	0.0753674i
$40$	2.78084	+	4.81655i	0.439689	+	0.761563i
$41$	3.80891			0.594852			0.297426	−	0.954745i	$-0.403872\pi$
$41$	3.80891			0.594852			0.297426	+	0.954745i	$0.403872\pi$
$42$	−4.07284	+	5.22190i	−0.628453	+	0.805756i
$43$			6.73386i			1.02690i	0.858118	+	0.513452i	$0.171634\pi$
$43$			6.73386i			1.02690i	−0.858118	+	0.513452i	$0.828366\pi$
$44$	−13.1592	−	5.19085i	−1.98382	−	0.782551i
$45$	−0.849508	−	0.490464i	−0.126637	−	0.0731140i
$46$	1.64350	+	0.948877i	0.242321	+	0.139904i
$47$	8.42881	−	4.86638i	1.22947	−	0.709834i	0.262550	−	0.964918i	$-0.415437\pi$
$47$	8.42881	−	4.86638i	1.22947	−	0.709834i	0.966919	+	0.255085i	$0.0821033\pi$
$48$		−	5.66137i		−	0.817148i
$49$	−1.70469	−	6.78926i	−0.243527	−	0.969894i
$50$			10.1067i			1.42930i
$51$	−4.48329	+	2.58843i	−0.627786	+	0.362452i
$52$	−2.00749	+	3.47707i	−0.278388	+	0.482183i
$53$	2.24816	−	3.89393i	0.308809	−	0.534873i	−0.669293	−	0.742998i	$-0.733403\pi$
$53$	2.24816	−	3.89393i	0.308809	−	0.534873i	0.978102	+	0.208126i	$0.0667363\pi$
$54$	1.25152	+	2.16769i	0.170310	+	0.294985i
$55$	2.02404	+	2.54709i	0.272922	+	0.343449i
$56$	11.8285	+	9.22570i	1.58065	+	1.23284i
$57$		−	2.54869i		−	0.337582i
$58$	−10.9502	−	18.9664i	−1.43784	−	2.49041i
$59$	−12.7383	−	7.35448i	−1.65839	−	0.957472i	−0.973458	−	0.228866i	$-0.926498\pi$
$59$	−12.7383	−	7.35448i	−1.65839	−	0.957472i	−0.684932	−	0.728607i	$-0.740168\pi$
$60$	−2.09191	+	3.62330i	−0.270065	+	0.467766i
$61$	−2.81334	−	4.87284i	−0.360211	−	0.623903i	0.627785	−	0.778387i	$-0.283962\pi$
$61$	−2.81334	−	4.87284i	−0.360211	−	0.623903i	−0.987995	+	0.154484i	$0.950629\pi$
$62$	15.9203			2.02187
$63$	−2.62031	−	0.366050i	−0.330128	−	0.0461180i
$64$	4.23671			0.529588
$65$	0.799675	−	0.461692i	0.0991874	−	0.0572659i
$66$	−1.22311	−	8.21103i	−0.150554	−	1.01071i
$67$	−6.21261	+	10.7606i	−0.758991	+	1.31461i	0.184375	+	0.982856i	$0.440974\pi$
$67$	−6.21261	+	10.7606i	−0.758991	+	1.31461i	−0.943366	+	0.331755i	$0.892359\pi$
$68$	11.0401	+	19.1220i	1.33881	+	2.31888i
$69$			0.758182i			0.0912743i
$70$	−2.43846	−	6.02106i	−0.291452	−	0.719654i
$71$	10.4898			1.24491			0.622455	−	0.782656i	$-0.286135\pi$
$71$	10.4898			1.24491			0.622455	+	0.782656i	$0.286135\pi$
$72$	4.91020	−	2.83490i	0.578672	−	0.334097i
$73$	−5.14984	+	8.91978i	−0.602743	+	1.04398i	0.389661	+	0.920958i	$0.372592\pi$
$73$	−5.14984	+	8.91978i	−0.602743	+	1.04398i	−0.992404	+	0.123023i	$0.960741\pi$
$74$	−6.47811	−	3.74014i	−0.753065	−	0.434782i
$75$	−3.49682	+	2.01889i	−0.403778	+	0.233121i
$76$	−10.8706			−1.24694
$77$	7.63883	+	4.31836i	0.870526	+	0.492122i
$78$	−2.35620			−0.266787
$79$	6.63084	−	3.82832i	0.746028	−	0.430719i	−0.0782290	−	0.996935i	$-0.524927\pi$
$79$	6.63084	−	3.82832i	0.746028	−	0.430719i	0.824257	+	0.566216i	$0.191593\pi$
$80$	4.80938	+	2.77670i	0.537705	+	0.310444i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	8.25654	−	4.76692i	0.911783	−	0.526418i
$83$	6.28891			0.690297			0.345149	−	0.938548i	$-0.387828\pi$
$83$	6.28891			0.690297			0.345149	+	0.938548i	$0.387828\pi$
$84$	−1.56127	+	11.1761i	−0.170348	+	1.21941i
$85$		−	5.07812i		−	0.550799i
$86$	8.42754	+	14.5969i	0.908765	+	1.57403i
$87$	4.37479	−	7.57735i	0.469026	−	0.812377i
$88$	−18.5994	+	2.77055i	−1.98270	+	0.295342i
$89$	2.06478	−	1.19210i	0.218867	−	0.126363i	−0.386559	−	0.922265i	$-0.626336\pi$
$89$	2.06478	−	1.19210i	0.218867	−	0.126363i	0.605425	+	0.795902i	$0.293003\pi$
$90$	−2.45529			−0.258811
$91$	1.53171	−	1.96385i	0.160567	−	0.205867i
$92$	3.23378			0.337145
$93$	3.18019	+	5.50826i	0.329771	+	0.571179i
$94$	12.1807	−	21.0976i	1.25634	−	2.17605i
$95$	2.16513	+	1.25004i	0.222138	+	0.128251i
$96$	−1.41549	−	2.45170i	−0.144468	−	0.250225i
$97$		−	7.30005i		−	0.741208i	−0.928791	−	0.370604i	$-0.879151\pi$
$97$		−	7.30005i		−	0.741208i	0.928791	−	0.370604i	$-0.120849\pi$
$98$	−12.1921	−	12.5836i	−1.23159	−	1.27113i
$99$	2.59661	−	2.06340i	0.260969	−	0.207379i
$100$	8.61092	+	14.9146i	0.861092	+	1.49146i
$101$	−2.63999	+	4.57260i	−0.262689	+	0.454991i	−0.966956	−	0.254945i	$-0.917943\pi$
$101$	−2.63999	+	4.57260i	−0.262689	+	0.454991i	0.704267	+	0.709936i	$0.251276\pi$
$102$	−6.47892	+	11.2218i	−0.641509	+	1.11113i
$103$	−14.8650	+	8.58231i	−1.46469	+	0.845641i	−0.999223	−	0.0394233i	$-0.987448\pi$
$103$	−14.8650	+	8.58231i	−1.46469	+	0.845641i	−0.465470	+	0.885064i	$0.654115\pi$
$104$			5.33721i			0.523356i
$105$	1.59613	−	2.04644i	0.155766	−	0.199712i
$106$		−	11.2545i		−	1.09313i
$107$	11.0757	−	6.39455i	1.07073	−	0.618184i	0.142346	−	0.989817i	$-0.454535\pi$
$107$	11.0757	−	6.39455i	1.07073	−	0.618184i	0.928380	+	0.371633i	$0.121202\pi$
$108$	3.69375	+	2.13259i	0.355431	+	0.205208i
$109$	−1.54302	−	0.890861i	−0.147794	−	0.0853291i	0.424279	−	0.905531i	$-0.360527\pi$
$109$	−1.54302	−	0.890861i	−0.147794	−	0.0853291i	−0.572074	+	0.820202i	$0.693861\pi$
$110$	7.57522	+	2.98817i	0.722269	+	0.284911i
$111$		−	2.98848i		−	0.283654i
$112$	14.8345	+	2.07235i	1.40173	+	0.195818i
$113$	−15.0553			−1.41628			−0.708140	−	0.706073i	$-0.750465\pi$
$113$	−15.0553			−1.41628			−0.708140	+	0.706073i	$0.750465\pi$
$114$	−3.18973	−	5.52477i	−0.298745	−	0.517442i
$115$	−0.644081	−	0.371861i	−0.0600609	−	0.0346762i
$116$	−32.3187	−	18.6592i	−3.00072	−	1.73247i
$117$	−0.470669	−	0.815223i	−0.0435134	−	0.0753674i
$118$	−36.8170			−3.38928
$119$	−5.14137	−	12.6951i	−0.471308	−	1.16376i
$120$			5.56167i			0.507709i
$121$	−10.5224	+	3.20596i	−0.956586	+	0.291451i
$122$	−12.1969	−	7.04187i	−1.10425	−	0.637541i
$123$	3.29861	+	1.90446i	0.297426	+	0.171719i
$124$	23.4937	−	13.5641i	2.10979	−	1.21809i
$125$		−	8.86541i		−	0.792946i
$126$	−6.13813	+	2.48587i	−0.546828	+	0.221459i
$127$		−	5.11223i		−	0.453637i	−0.973937	−	0.226818i	$-0.927168\pi$
$127$		−	5.11223i		−	0.453637i	0.973937	−	0.226818i	$-0.0728324\pi$
$128$	14.0873	−	8.13329i	1.24515	−	0.718888i
$129$	−3.36693	+	5.83169i	−0.296442	+	0.513452i
$130$	1.15563	−	2.00161i	0.101356	−	0.175553i
$131$	−6.09581	−	10.5582i	−0.532593	−	0.922478i	−0.999276	−	0.0380535i	$-0.987884\pi$
$131$	−6.09581	−	10.5582i	−0.532593	−	0.922478i	0.466683	−	0.884425i	$-0.345449\pi$
$132$	−8.80076	−	11.0750i	−0.766007	−	0.963955i
$133$	6.67835	+	0.932949i	0.579087	+	0.0808969i
$134$			31.1007i			2.68669i
$135$	−0.490464	−	0.849508i	−0.0422124	−	0.0731140i
$136$	25.4194	+	14.6759i	2.17969	+	1.25845i
$137$	−1.51095	+	2.61705i	−0.129089	+	0.223590i	−0.923324	−	0.384022i	$-0.874539\pi$
$137$	−1.51095	+	2.61705i	−0.129089	+	0.223590i	0.794235	+	0.607611i	$0.207872\pi$
$138$	0.948877	+	1.64350i	0.0807738	+	0.139904i
$139$	11.6396			0.987260			0.493630	−	0.869672i	$-0.335670\pi$
$139$	11.6396			0.987260			0.493630	+	0.869672i	$0.335670\pi$
$140$	−8.72841	−	6.80776i	−0.737686	−	0.575361i
$141$	9.73275			0.819646
$142$	22.7386	−	13.1282i	1.90818	−	1.10169i
$143$	0.459985	+	3.08800i	0.0384659	+	0.258231i
$144$	2.83068	−	4.90289i	0.235890	−	0.408574i
$145$	4.29135	+	7.43283i	0.356377	+	0.617263i
$146$			25.7804i			2.13360i
$147$	1.91833	−	6.73201i	0.158221	−	0.555247i
$148$	−12.7464			−1.04775
$149$	−1.10635	+	0.638749i	−0.0906354	+	0.0523284i	−0.544633	−	0.838675i	$-0.683331\pi$
$149$	−1.10635	+	0.638749i	−0.0906354	+	0.0523284i	0.453997	+	0.891003i	$0.349998\pi$
$150$	−5.05335	+	8.75266i	−0.412604	+	0.714652i
$151$	19.7164	+	11.3833i	1.60450	+	0.926357i	0.990572	+	0.136992i	$0.0437435\pi$
$151$	19.7164	+	11.3833i	1.60450	+	0.926357i	0.613925	+	0.789365i	$0.289590\pi$
$152$	−12.5146	+	7.22529i	−1.01507	+	0.586049i
$153$	−5.17686			−0.418524
$154$	21.9631	−	0.199268i	1.76984	−	0.0160575i
$155$	−6.23908			−0.501135
$156$	−3.47707	+	2.00749i	−0.278388	+	0.160728i
$157$	−8.40005	−	4.84977i	−0.670397	−	0.387054i	0.125830	−	0.992052i	$-0.459841\pi$
$157$	−8.40005	−	4.84977i	−0.670397	−	0.387054i	−0.796227	+	0.604998i	$0.793174\pi$
$158$	9.58241	−	16.5972i	0.762335	−	1.32040i
$159$	3.89393	−	2.24816i	0.308809	−	0.178291i
$160$	2.77698			0.219540
$161$	−1.98667	−	0.277533i	−0.156571	−	0.0218726i
$162$			2.50303i			0.196657i
$163$	8.64263	+	14.9695i	0.676943	+	1.17250i	0.975897	+	0.218232i	$0.0700291\pi$
$163$	8.64263	+	14.9695i	0.676943	+	1.17250i	−0.298954	+	0.954268i	$0.596638\pi$
$164$	8.12284	−	14.0692i	0.634287	−	1.09862i
$165$	0.479330	+	3.21786i	0.0373158	+	0.250510i
$166$	13.6324	−	7.87067i	1.05808	−	0.610883i
$167$	−4.94196			−0.382420			−0.191210	−	0.981549i	$-0.561241\pi$
$167$	−4.94196			−0.382420			−0.191210	+	0.981549i	$0.561241\pi$
$168$	5.63094	+	13.9039i	0.434436	+	1.07271i
$169$	−12.1139			−0.931837
$170$	−6.35535	−	11.0078i	−0.487433	−	0.844259i
$171$	1.27435	−	2.20723i	0.0974516	−	0.168791i
$172$	24.8732	+	14.3605i	1.89656	+	1.09498i
$173$	−0.579680	−	1.00403i	−0.0440722	−	0.0763354i	0.843148	−	0.537682i	$-0.180700\pi$
$173$	−0.579680	−	1.00403i	−0.0440722	−	0.0763354i	−0.887220	+	0.461346i	$0.847367\pi$
$174$		−	21.9005i		−	1.66027i
$175$	−4.01010	−	9.90176i	−0.303135	−	0.748503i
$176$	−14.7004	+	11.6817i	−1.10808	+	0.880538i
$177$	−7.35448	−	12.7383i	−0.552797	−	0.957472i
$178$	2.98387	−	5.16822i	0.223651	−	0.387374i
$179$	−9.62679	+	16.6741i	−0.719540	+	1.24628i	0.241642	+	0.970365i	$0.422314\pi$
$179$	−9.62679	+	16.6741i	−0.719540	+	1.24628i	−0.961182	+	0.275915i	$0.911019\pi$
$180$	−3.62330	+	2.09191i	−0.270065	+	0.155922i
$181$		−	0.999542i		−	0.0742954i	−0.999310	−	0.0371477i	$-0.988173\pi$
$181$		−	0.999542i		−	0.0742954i	0.999310	−	0.0371477i	$-0.0118272\pi$
$182$	0.862488	−	6.17397i	0.0639319	−	0.457645i
$183$		−	5.62667i		−	0.415935i
$184$	3.72282	−	2.14937i	0.274450	−	0.158454i
$185$	2.53874	+	1.46574i	0.186652	+	0.107764i
$186$	13.7873	+	7.96013i	1.01094	+	0.583665i
$187$	15.9720	+	6.30040i	1.16798	+	0.460731i
$188$		−	41.5119i		−	3.02757i
$189$	−2.08623	−	1.62716i	−0.151751	−	0.118359i
$190$	6.25778			0.453987
$191$	11.0819	+	19.1944i	0.801858	+	1.38886i	0.918392	+	0.395673i	$0.129489\pi$
$191$	11.0819	+	19.1944i	0.801858	+	1.38886i	−0.116533	+	0.993187i	$0.537178\pi$
$192$	3.66910	+	2.11835i	0.264794	+	0.152879i
$193$	10.4318	+	6.02278i	0.750894	+	0.433529i	0.826017	−	0.563645i	$-0.190601\pi$
$193$	10.4318	+	6.02278i	0.750894	+	0.433529i	−0.0751226	+	0.997174i	$0.523935\pi$
$194$	−9.13613	−	15.8242i	−0.655936	−	1.13611i
$195$	0.923385			0.0661249
$196$	−28.7132	−	8.18200i	−2.05094	−	0.584429i
$197$		−	0.892906i		−	0.0636169i	−0.999494	−	0.0318085i	$-0.989873\pi$
$197$		−	0.892906i		−	0.0636169i	0.999494	−	0.0318085i	$-0.0101267\pi$
$198$	3.04627	−	7.72251i	0.216489	−	0.548815i
$199$	8.84669	+	5.10764i	0.627125	+	0.362071i	0.779638	−	0.626231i	$-0.215403\pi$
$199$	8.84669	+	5.10764i	0.627125	+	0.362071i	−0.152513	+	0.988302i	$0.548736\pi$
$200$	19.8263	+	11.4467i	1.40193	+	0.809406i
$201$	−10.7606	+	6.21261i	−0.758991	+	0.438204i
$202$			13.2160i			0.929872i
$203$	18.2536	+	14.2370i	1.28115	+	0.999240i
$204$			22.0802i			1.54592i
$205$	−3.23570	+	1.86813i	−0.225991	+	0.130476i
$206$	−21.4818	+	37.2076i	−1.49671	+	2.59238i
$207$	−0.379091	+	0.656604i	−0.0263486	+	0.0456372i
$208$	2.66463	+	4.61528i	0.184759	+	0.320012i
$209$	−6.61796	+	5.25896i	−0.457774	+	0.363770i
$210$	0.898761	−	6.43362i	0.0620204	−	0.443962i
$211$		−	5.90844i		−	0.406754i	−0.979101	−	0.203377i	$-0.934808\pi$
$211$		−	5.90844i		−	0.406754i	0.979101	−	0.203377i	$-0.0651917\pi$
$212$	−9.58881	−	16.6083i	−0.658562	−	1.14066i
$213$	9.08443	+	5.24490i	0.622455	+	0.359374i
$214$	16.0058	−	27.7228i	1.09413	−	1.89509i
$215$	−3.30271	−	5.72047i	−0.225243	−	0.390133i
$216$	5.66981			0.385782
$217$	−15.5974	+	6.31678i	−1.05882	+	0.428811i
$218$	−4.45971			−0.302050
$219$	−8.91978	+	5.14984i	−0.602743	+	0.347994i
$220$	13.7248	−	2.04443i	0.925323	−	0.137835i
$221$	2.43659	−	4.22029i	0.163903	−	0.283888i
$222$	−3.74014	−	6.47811i	−0.251022	−	0.434782i
$223$		−	13.1739i		−	0.882191i	−0.897460	−	0.441096i	$-0.854590\pi$
$223$		−	13.1739i		−	0.882191i	0.897460	−	0.441096i	$-0.145410\pi$
$224$	6.94234	−	2.81157i	0.463855	−	0.187856i
$225$	−4.03778			−0.269185
$226$	−32.6351	+	18.8419i	−2.17086	+	1.25334i
$227$	−13.2144	+	22.8880i	−0.877071	+	1.51913i	−0.0225308	+	0.999746i	$0.507172\pi$
$227$	−13.2144	+	22.8880i	−0.877071	+	1.51913i	−0.854540	+	0.519385i	$0.826161\pi$
$228$	−9.41423	−	5.43531i	−0.623472	−	0.359962i
$229$	−9.58709	+	5.53511i	−0.633532	+	0.365770i	−0.782119	−	0.623129i	$-0.785861\pi$
$229$	−9.58709	+	5.53511i	−0.633532	+	0.365770i	0.148586	+	0.988899i	$0.452528\pi$
$230$	−1.86156			−0.122748
$231$	4.45625	+	7.55922i	0.293199	+	0.497360i
$232$	−49.6084			−3.25695
$233$	6.70503	−	3.87115i	0.439261	−	0.253607i	−0.264023	−	0.964516i	$-0.585050\pi$
$233$	6.70503	−	3.87115i	0.439261	−	0.253607i	0.703284	+	0.710909i	$0.251716\pi$
$234$	−2.04053	−	1.17810i	−0.133394	−	0.0770149i
$235$	−4.77356	+	8.26805i	−0.311393	+	0.539348i
$236$	−54.3312	+	31.3682i	−3.53666	+	2.04189i
$237$	7.65664			0.497352
$238$	−27.0330	−	21.0845i	−1.75229	−	1.36671i
$239$		−	12.7580i		−	0.825249i	−0.910901	−	0.412625i	$-0.864612\pi$
$239$		−	12.7580i		−	0.825249i	0.910901	−	0.412625i	$-0.135388\pi$
$240$	2.77670	+	4.80938i	0.179235	+	0.310444i
$241$	−12.8053	+	22.1794i	−0.824861	+	1.42870i	0.0771645	+	0.997018i	$0.475413\pi$
$241$	−12.8053	+	22.1794i	−0.824861	+	1.42870i	−0.902025	+	0.431683i	$0.857920\pi$
$242$	−18.7971	+	20.1185i	−1.20832	+	1.29327i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−23.9987			−1.53636
$245$	4.77803	+	4.93144i	0.305257	+	0.315058i
$246$	9.53383			0.607855
$247$	1.19959	+	2.07775i	0.0763281	+	0.132204i
$248$	18.0311	−	31.2308i	1.14497	−	1.98315i
$249$	5.44636	+	3.14445i	0.345149	+	0.199272i
$250$	−11.0952	−	19.2175i	−0.701722	−	1.21542i
$251$			6.48260i			0.409178i	0.978848	+	0.204589i	$0.0655857\pi$
$251$			6.48260i			0.409178i	−0.978848	+	0.204589i	$0.934414\pi$
$252$	−6.94013	+	8.89812i	−0.437187	+	0.560529i
$253$	1.96870	−	1.56443i	0.123771	−	0.0983549i
$254$	−6.39804	−	11.0817i	−0.401449	−	0.695330i
$255$	2.53906	−	4.39778i	0.159002	−	0.275400i
$256$	16.1212	−	27.9227i	1.00757	−	1.74517i
$257$	−13.9410	+	8.04882i	−0.869613	+	0.502071i	−0.867220	−	0.497926i	$-0.834095\pi$
$257$	−13.9410	+	8.04882i	−0.869613	+	0.502071i	−0.00239339	+	0.999997i	$0.500762\pi$
$258$			16.8551i			1.04935i
$259$	7.83074	+	1.09394i	0.486579	+	0.0679738i
$260$		−	3.93840i		−	0.244249i
$261$	7.57735	−	4.37479i	0.469026	−	0.270792i
$262$	−26.4276	−	15.2580i	−1.63271	−	0.942643i
$263$	5.41725	+	3.12765i	0.334042	+	0.192859i	0.657634	−	0.753337i	$-0.271557\pi$
$263$	5.41725	+	3.12765i	0.334042	+	0.192859i	−0.323592	+	0.946197i	$0.604891\pi$
$264$	−17.4928	−	6.90034i	−1.07661	−	0.424686i
$265$			4.41057i			0.270939i
$266$	15.6442	−	6.33572i	0.959207	−	0.388468i
$267$	2.38421			0.145911
$268$	26.4979	+	45.8956i	1.61861	+	2.80352i
$269$	8.20794	+	4.73886i	0.500447	+	0.288933i	0.728898	−	0.684622i	$-0.240033\pi$
$269$	8.20794	+	4.73886i	0.500447	+	0.288933i	−0.228451	+	0.973555i	$0.573366\pi$
$270$	−2.12635	−	1.22765i	−0.129405	−	0.0747122i
$271$	9.33691	+	16.1720i	0.567177	+	0.982379i	0.996844	+	0.0793913i	$0.0252977\pi$
$271$	9.33691	+	16.1720i	0.567177	+	0.982379i	−0.429667	+	0.902987i	$0.641369\pi$
$272$	29.3081			1.77706
$273$	2.30842	−	0.934885i	0.139712	−	0.0565818i
$274$			7.56393i			0.456954i
$275$	12.4576	+	4.91411i	0.751222	+	0.296332i
$276$	2.80053	+	1.61689i	0.168572	+	0.0973253i
$277$	−15.2590	−	8.80980i	−0.916826	−	0.529330i	−0.0342049	−	0.999415i	$-0.510890\pi$
$277$	−15.2590	−	8.80980i	−0.916826	−	0.529330i	−0.882621	+	0.470085i	$0.844223\pi$
$278$	25.2311	−	14.5672i	1.51326	−	0.873682i
$279$			6.36039i			0.380786i
$280$	−14.5733	−	2.03585i	−0.870920	−	0.121665i
$281$			10.9532i			0.653414i	0.945126	+	0.326707i	$0.105939\pi$
$281$			10.9532i			0.653414i	−0.945126	+	0.326707i	$0.894061\pi$
$282$	21.0976	−	12.1807i	1.25634	−	0.725350i
$283$	13.8367	−	23.9659i	0.822507	−	1.42462i	−0.0813030	−	0.996689i	$-0.525908\pi$
$283$	13.8367	−	23.9659i	0.822507	−	1.42462i	0.903810	−	0.427934i	$-0.140759\pi$
$284$	22.3704	−	38.7467i	1.32744	−	2.29919i
$285$	1.25004	+	2.16513i	0.0740460	+	0.128251i
$286$	4.86178	+	6.11814i	0.287483	+	0.361773i
$287$	−6.19772	+	7.94626i	−0.365840	+	0.469053i
$288$		−	2.83098i		−	0.166817i
$289$	−4.89992	−	8.48691i	−0.288231	−	0.499230i
$290$	18.6046	+	10.7414i	1.09250	+	0.630756i
$291$	3.65002	−	6.32203i	0.213968	−	0.370604i
$292$	21.9650	+	38.0444i	1.28540	+	2.22638i
$293$	−21.3408			−1.24674			−0.623370	−	0.781927i	$-0.714237\pi$
$293$	−21.3408			−1.24674			−0.623370	+	0.781927i	$0.714237\pi$
$294$	−4.26689	−	16.9937i	−0.248850	−	0.991095i
$295$	14.4284			0.840056
$296$	−14.6740	+	8.47207i	−0.852912	+	0.492429i
$297$	3.28043	−	0.488650i	0.190350	−	0.0283543i
$298$	−1.59881	+	2.76922i	−0.0926166	+	0.160417i
$299$	−0.356853	−	0.618087i	−0.0206373	−	0.0357449i
$300$			17.2218i			0.994304i
$301$	−14.0484	−	10.9571i	−0.809734	−	0.631556i
$302$	56.9854			3.27914
$303$	−4.57260	+	2.63999i	−0.262689	+	0.151664i
$304$	−7.21454	+	12.4959i	−0.413782	+	0.716692i
$305$	4.77990	+	2.75968i	0.273696	+	0.158019i
$306$	−11.2218	+	6.47892i	−0.641509	+	0.370375i
$307$	24.9793			1.42565			0.712823	−	0.701344i	$-0.247416\pi$
$307$	24.9793			1.42565			0.712823	+	0.701344i	$0.247416\pi$
$308$	32.2414	−	19.0067i	1.83713	−	1.08301i
$309$	−17.1646			−0.976462
$310$	−13.5244	+	7.80831i	−0.768133	+	0.443482i
$311$	−20.9351	−	12.0869i	−1.18712	−	0.685383i	−0.229468	−	0.973316i	$-0.573698\pi$
$311$	−20.9351	−	12.0869i	−1.18712	−	0.685383i	−0.957650	+	0.287933i	$0.907032\pi$
$312$	−2.66860	+	4.62216i	−0.151080	+	0.261678i
$313$	19.1163	−	11.0368i	1.08052	−	0.623838i	0.149482	−	0.988764i	$-0.452239\pi$
$313$	19.1163	−	11.0368i	1.08052	−	0.623838i	0.931036	+	0.364927i	$0.118906\pi$
$314$	−24.2783			−1.37010
$315$	2.40551	−	0.974203i	0.135535	−	0.0548901i
$316$		−	32.6569i		−	1.83709i
$317$	3.43604	+	5.95139i	0.192987	+	0.334263i	0.946239	−	0.323469i	$-0.104849\pi$
$317$	3.43604	+	5.95139i	0.192987	+	0.334263i	−0.753252	+	0.657732i	$0.771516\pi$
$318$	5.62723	−	9.74664i	0.315559	−	0.546565i
$319$	−28.7024	+	4.27548i	−1.60702	+	0.239381i
$320$	−3.59912	+	2.07795i	−0.201197	+	0.116161i
$321$	12.7891			0.713817
$322$	−4.65382	+	1.88474i	−0.259347	+	0.105033i
$323$	13.1942			0.734145
$324$	2.13259	+	3.69375i	0.118477	+	0.205208i
$325$	1.90046	−	3.29169i	0.105419	−	0.182590i
$326$	37.4691	+	21.6328i	2.07522	+	1.19813i
$327$	−0.890861	−	1.54302i	−0.0492648	−	0.0853291i
$328$		−	21.5958i		−	1.19243i
$329$	−3.56268	+	25.5028i	−0.196417	+	1.40601i
$330$	5.06625	+	6.37544i	0.278888	+	0.350957i
$331$	2.38784	+	4.13586i	0.131248	+	0.227328i	0.924158	−	0.382011i	$-0.124768\pi$
$331$	2.38784	+	4.13586i	0.131248	+	0.227328i	−0.792910	+	0.609339i	$0.791435\pi$
$332$	13.4117	−	23.2297i	0.736060	−	1.27489i
$333$	1.49424	−	2.58810i	0.0818840	−	0.141827i
$334$	−10.7126	+	6.18494i	−0.586169	+	0.338425i
$335$		−	12.1882i		−	0.665914i
$336$	11.8109	+	9.21197i	0.644337	+	0.502554i
$337$		−	16.3128i		−	0.888613i	−0.895875	−	0.444306i	$-0.853450\pi$
$337$		−	16.3128i		−	0.888613i	0.895875	−	0.444306i	$-0.146550\pi$
$338$	−26.2591	+	15.1607i	−1.42831	+	0.824635i
$339$	−13.0382	−	7.52763i	−0.708140	−	0.408845i
$340$	−18.7573	−	10.8295i	−1.01726	−	0.587314i
$341$	7.74079	−	19.6234i	0.419187	−	1.06267i
$342$		−	6.37946i		−	0.344962i
$343$	16.9377	+	7.49086i	0.914552	+	0.404469i
$344$	38.1797			2.05851
$345$	−0.371861	−	0.644081i	−0.0200203	−	0.0346762i
$346$	−2.51313	−	1.45096i	−0.135107	−	0.0780040i
$347$	−10.0904	−	5.82568i	−0.541680	−	0.312739i	0.204080	−	0.978954i	$-0.434580\pi$
$347$	−10.0904	−	5.82568i	−0.541680	−	0.312739i	−0.745759	+	0.666215i	$0.767913\pi$
$348$	−18.6592	−	32.3187i	−1.00024	−	1.73247i
$349$	12.3693			0.662111			0.331056	−	0.943611i	$-0.392595\pi$
$349$	12.3693			0.662111			0.331056	+	0.943611i	$0.392595\pi$
$350$	−21.0849	−	16.4452i	−1.12703	−	0.879035i
$351$		−	0.941338i		−	0.0502449i
$352$	−3.44539	+	8.73430i	−0.183640	+	0.465540i
$353$	−11.6310	−	6.71514i	−0.619053	−	0.357411i	0.157447	−	0.987527i	$-0.449674\pi$
$353$	−11.6310	−	6.71514i	−0.619053	−	0.357411i	−0.776500	+	0.630117i	$0.783007\pi$
$354$	−31.8845	−	18.4085i	−1.69464	−	0.978402i
$355$	−8.91116	+	5.14486i	−0.472956	+	0.273061i
$356$		−	10.1691i		−	0.538959i
$357$	1.89499	−	13.5650i	0.100293	−	0.717933i
$358$			48.1924i			2.54704i
$359$	−1.71367	+	0.989386i	−0.0904439	+	0.0522178i	−0.544540	−	0.838735i	$-0.683296\pi$
$359$	−1.71367	+	0.989386i	−0.0904439	+	0.0522178i	0.454096	+	0.890953i	$0.349962\pi$
$360$	−2.78084	+	4.81655i	−0.146563	+	0.253854i
$361$	6.25209	−	10.8289i	0.329057	−	0.569944i
$362$	−1.25094	−	2.16670i	−0.0657481	−	0.113879i
$363$	−10.7157	−	2.48478i	−0.562428	−	0.130417i
$364$	−3.98745	−	9.84583i	−0.208999	−	0.516062i
$365$		−	10.1032i		−	0.528827i
$366$	−7.04187	−	12.1969i	−0.368084	−	0.637541i
$367$	−10.4906	−	6.05676i	−0.547605	−	0.316160i	0.200550	−	0.979683i	$-0.435727\pi$
$367$	−10.4906	−	6.05676i	−0.547605	−	0.316160i	−0.748156	+	0.663523i	$0.769060\pi$
$368$	2.14617	−	3.71728i	0.111877	−	0.193777i
$369$	1.90446	+	3.29861i	0.0991420	+	0.171719i
$370$	7.33761			0.381464
$371$	4.46550	+	11.0262i	0.231837	+	0.572454i
$372$	27.1282			1.40653
$373$	−13.0833	+	7.55367i	−0.677429	+	0.391114i	−0.798886	−	0.601483i	$-0.794577\pi$
$373$	−13.0833	+	7.55367i	−0.677429	+	0.391114i	0.121456	+	0.992597i	$0.461244\pi$
$374$	42.5073	−	6.33185i	2.19800	−	0.327412i
$375$	4.43270	−	7.67767i	0.228904	−	0.396473i
$376$	−27.5914	−	47.7897i	−1.42292	−	2.46457i
$377$			8.23631i			0.424192i
$378$	−6.55871	−	0.916236i	−0.337344	−	0.0471261i
$379$	−0.0566884			−0.00291189			−0.00145594	−	0.999999i	$-0.500463\pi$
$379$	−0.0566884			−0.00291189			−0.00145594	+	0.999999i	$0.500463\pi$
$380$	9.23467	−	5.33164i	0.473729	−	0.273507i
$381$	2.55611	−	4.42732i	0.130954	−	0.226818i
$382$	48.0443	+	27.7384i	2.45816	+	1.41922i
$383$	8.35611	−	4.82440i	0.426977	−	0.246516i	−0.271081	−	0.962557i	$-0.587381\pi$
$383$	8.35611	−	4.82440i	0.426977	−	0.246516i	0.698058	+	0.716041i	$0.254048\pi$
$384$	16.2666			0.830100
$385$	−8.60725	+	0.0780921i	−0.438666	+	0.00397994i
$386$	30.1504			1.53462
$387$	−5.83169	+	3.36693i	−0.296442	+	0.171151i
$388$	−26.9646	−	15.5680i	−1.36892	−	0.790345i
$389$	−4.50920	+	7.81017i	−0.228626	+	0.395991i	−0.957401	−	0.288762i	$-0.906757\pi$
$389$	−4.50920	+	7.81017i	−0.228626	+	0.395991i	0.728775	+	0.684753i	$0.240090\pi$
$390$	2.00161	−	1.15563i	0.101356	−	0.0585177i
$391$	−3.92500			−0.198496
$392$	−38.4938	+	9.66525i	−1.94423	+	0.488169i
$393$		−	12.1916i		−	0.614986i
$394$	−1.11749	−	1.93554i	−0.0562982	−	0.0975113i
$395$	−3.75530	+	6.50437i	−0.188950	+	0.327271i
$396$	−2.08418	−	13.9916i	−0.104734	−	0.703105i
$397$	12.6565	−	7.30722i	0.635211	−	0.366739i	−0.147557	−	0.989054i	$-0.547141\pi$
$397$	12.6565	−	7.30722i	0.635211	−	0.366739i	0.782767	+	0.622315i	$0.213808\pi$
$398$	25.5692			1.28167
$399$	5.31715	+	4.14713i	0.266190	+	0.207616i
$400$	22.8594			1.14297
$401$	7.11226	+	12.3188i	0.355169	+	0.615171i	0.987147	−	0.159815i	$-0.0510899\pi$
$401$	7.11226	+	12.3188i	0.355169	+	0.615171i	−0.631978	+	0.774987i	$0.717757\pi$
$402$	−15.5504	+	26.9340i	−0.775582	+	1.34335i
$403$	−5.18513	−	2.99364i	−0.258290	−	0.149124i
$404$	11.2600	+	19.5029i	0.560207	+	0.970307i
$405$		−	0.980927i		−	0.0487427i
$406$	57.3860	+	8.01667i	2.84802	+	0.397861i
$407$	−7.75993	+	6.16643i	−0.384645	+	0.305659i
$408$	14.6759	+	25.4194i	0.726565	+	1.25845i
$409$	−1.79313	+	3.10579i	−0.0886646	+	0.153572i	−0.906947	−	0.421245i	$-0.861593\pi$
$409$	−1.79313	+	3.10579i	−0.0886646	+	0.153572i	0.818282	+	0.574817i	$0.194927\pi$
$410$	−4.67600	+	8.09907i	−0.230931	+	0.399984i
$411$	−2.61705	+	1.51095i	−0.129089	+	0.0745299i
$412$			73.2101i			3.60680i
$413$	36.0705	−	14.6081i	1.77491	−	0.718819i
$414$			1.89775i			0.0932695i
$415$	−5.34248	+	3.08448i	−0.262252	+	0.151411i
$416$	2.30788	+	1.33245i	0.113153	+	0.0653289i
$417$	10.0802	+	5.81981i	0.493630	+	0.284997i
$418$	−7.76400	+	19.6823i	−0.379750	+	0.962692i
$419$		−	29.6711i		−	1.44953i	−0.688997	−	0.724764i	$-0.741949\pi$
$419$		−	29.6711i		−	1.44953i	0.688997	−	0.724764i	$-0.258051\pi$
$420$	−4.15515	−	10.2599i	−0.202750	−	0.500632i
$421$	−6.62829			−0.323043			−0.161521	−	0.986869i	$-0.551640\pi$
$421$	−6.62829			−0.323043			−0.161521	+	0.986869i	$0.551640\pi$
$422$	−7.39451	−	12.8077i	−0.359959	−	0.623467i
$423$	8.42881	+	4.86638i	0.409823	+	0.236611i
$424$	−22.0779	−	12.7467i	−1.07220	−	0.619032i
$425$	−10.4515	−	18.1025i	−0.506973	−	0.878102i
$426$	26.2563			1.27212
$427$	14.7436	+	2.05964i	0.713493	+	0.0996731i
$428$		−	54.5477i		−	2.63666i
$429$	−1.14564	+	2.90427i	−0.0553120	+	0.140220i
$430$	−14.3185	−	8.26680i	−0.690500	−	0.398661i
$431$	−31.1534	−	17.9864i	−1.50061	−	0.866375i	−1.00000		0.000700603i	$-0.999777\pi$
$431$	−31.1534	−	17.9864i	−1.50061	−	0.866375i	−0.500607	−	0.865675i	$-0.666890\pi$
$432$	4.90289	−	2.83068i	0.235890	−	0.136191i
$433$		−	17.4731i		−	0.839702i	−0.907593	−	0.419851i	$-0.862082\pi$
$433$		−	17.4731i		−	0.839702i	0.907593	−	0.419851i	$-0.137918\pi$
$434$	−25.9048	+	33.2133i	−1.24347	+	1.59429i
$435$			8.58270i			0.411509i
$436$	−6.58124	+	3.79968i	−0.315184	+	0.181972i
$437$	0.966185	−	1.67348i	0.0462189	−	0.0800535i
$438$	−12.8902	+	22.3265i	−0.615918	+	1.06680i
$439$	−16.2702	−	28.1808i	−0.776533	−	1.34499i	−0.933929	−	0.357459i	$-0.883643\pi$
$439$	−16.2702	−	28.1808i	−0.776533	−	1.34499i	0.157396	−	0.987536i	$-0.449690\pi$
$440$	14.4415	−	11.4759i	0.688471	−	0.547094i
$441$	5.02733	−	4.87093i	0.239397	−	0.231949i
$442$		−	12.1977i		−	0.580186i
$443$	−1.33063	−	2.30472i	−0.0632201	−	0.109500i	0.832683	−	0.553750i	$-0.186804\pi$
$443$	−1.33063	−	2.30472i	−0.0632201	−	0.109500i	−0.895903	+	0.444250i	$0.853470\pi$
$444$	−11.0387	−	6.37320i	−0.523874	−	0.302459i
$445$	−1.16937	+	2.02540i	−0.0554333	+	0.0960133i
$446$	−16.4874	−	28.5570i	−0.780700	−	1.35221i
$447$	−1.27750			−0.0604236
$448$	−6.89381	+	8.83873i	−0.325702	+	0.417591i
$449$	−40.5312			−1.91278			−0.956392	−	0.292086i	$-0.905651\pi$
$449$	−40.5312			−1.91278			−0.956392	+	0.292086i	$0.905651\pi$
$450$	−8.75266	+	5.05335i	−0.412604	+	0.238217i
$451$	−1.86122	−	12.4949i	−0.0876416	−	0.588360i
$452$	−32.1066	+	55.6103i	−1.51017	+	2.61569i
$453$	11.3833	+	19.7164i	0.534832	+	0.926357i
$454$			66.1522i			3.10468i
$455$	−0.338005	+	2.41955i	−0.0158459	+	0.113430i
$456$	−14.4506			−0.676711
$457$	−12.7651	+	7.36996i	−0.597128	+	0.344752i	−0.767911	−	0.640556i	$-0.778704\pi$
$457$	−12.7651	+	7.36996i	−0.597128	+	0.344752i	0.170783	+	0.985309i	$0.445370\pi$
$458$	−13.8546	+	23.9968i	−0.647381	+	1.12130i
$459$	−4.48329	−	2.58843i	−0.209262	−	0.120817i
$460$	−2.74712	+	1.58605i	−0.128085	+	0.0739500i
$461$	5.02966			0.234255			0.117127	−	0.993117i	$-0.462631\pi$
$461$	5.02966			0.234255			0.117127	+	0.993117i	$0.462631\pi$
$462$	19.1203	+	10.8090i	0.889555	+	0.502880i
$463$	2.81117			0.130646			0.0653230	−	0.997864i	$-0.479192\pi$
$463$	2.81117			0.130646			0.0653230	+	0.997864i	$0.479192\pi$
$464$	−42.8982	+	24.7673i	−1.99150	+	1.14979i
$465$	−5.40320	−	3.11954i	−0.250567	−	0.144665i
$466$	9.68962	−	16.7829i	0.448863	−	0.777453i
$467$	12.1818	−	7.03319i	0.563708	−	0.325457i	−0.190924	−	0.981605i	$-0.561149\pi$
$467$	12.1818	−	7.03319i	0.563708	−	0.325457i	0.754633	+	0.656148i	$0.227815\pi$
$468$	−4.01497			−0.185592
$469$	−12.3400	−	30.4701i	−0.569810	−	1.40698i
$470$			23.8968i			1.10228i
$471$	−4.84977	−	8.40005i	−0.223466	−	0.387054i
$472$	−41.6985	+	72.2239i	−1.91933	+	3.32438i
$473$	22.0900	−	3.29050i	1.01570	−	0.151297i
$474$	16.5972	−	9.58241i	0.762335	−	0.440134i
$475$	10.2911			0.472186
$476$	−57.8569	−	8.08246i	−2.65187	−	0.370459i
$477$	4.49633			0.205873
$478$	−15.9669	−	27.6555i	−0.730309	−	1.26493i
$479$	20.0630	−	34.7502i	0.916703	−	1.58778i	0.112313	−	0.993673i	$-0.464174\pi$
$479$	20.0630	−	34.7502i	0.916703	−	1.58778i	0.804389	−	0.594103i	$-0.202493\pi$
$480$	2.40494	+	1.38849i	0.109770	+	0.0633757i
$481$	1.40659	+	2.43628i	0.0641349	+	0.111085i
$482$			64.1041i			2.91986i
$483$	−1.58174	−	1.23368i	−0.0719716	−	0.0561346i
$484$	−10.5980	+	45.7043i	−0.481727	+	2.07747i
$485$	3.58041	+	6.20145i	0.162578	+	0.281593i
$486$	−1.25152	+	2.16769i	−0.0567699	+	0.0983284i
$487$	−1.30070	+	2.25289i	−0.0589405	+	0.102088i	−0.893990	−	0.448087i	$-0.852106\pi$
$487$	−1.30070	+	2.25289i	−0.0589405	+	0.102088i	0.835050	+	0.550175i	$0.185439\pi$
$488$	−27.6281	+	15.9511i	−1.25066	+	0.722071i
$489$			17.2853i			0.781667i
$490$	16.5291	+	4.71006i	0.746707	+	0.212779i
$491$			20.4535i			0.923052i	0.887127	+	0.461526i	$0.152698\pi$
$491$			20.4535i			0.923052i	−0.887127	+	0.461526i	$0.847302\pi$
$492$	14.0692	−	8.12284i	0.634287	−	0.366206i
$493$	39.2269	+	22.6476i	1.76669	+	1.02000i
$494$	5.20068	+	3.00261i	0.233990	+	0.135094i
$495$	−1.19382	+	3.02642i	−0.0536582	+	0.136027i
$496$		−	36.0085i		−	1.61683i
$497$	−17.0686	+	21.8841i	−0.765631	+	0.981636i
$498$	15.7413			0.705387
$499$	−16.8600	−	29.2024i	−0.754758	−	1.30728i	−0.945495	−	0.325638i	$-0.894421\pi$
$499$	−16.8600	−	29.2024i	−0.754758	−	1.30728i	0.190737	−	0.981641i	$-0.438912\pi$
$500$	−32.7466	−	18.9063i	−1.46447	−	0.845514i
$501$	−4.27986	−	2.47098i	−0.191210	−	0.110395i
$502$	8.11308	+	14.0523i	0.362104	+	0.627183i
$503$	13.4051			0.597705			0.298852	−	0.954299i	$-0.403396\pi$
$503$	13.4051			0.597705			0.298852	+	0.954299i	$0.403396\pi$
$504$	−2.07543	+	14.8566i	−0.0924472	+	0.661767i
$505$		−	5.17928i		−	0.230475i
$506$	2.30963	−	5.85506i	0.102675	−	0.260289i
$507$	−10.4909	−	6.05694i	−0.465919	−	0.268998i
$508$	−18.8833	−	10.9023i	−0.837811	−	0.483710i
$509$	6.62764	−	3.82647i	0.293765	−	0.169605i	−0.345874	−	0.938281i	$-0.612417\pi$
$509$	6.62764	−	3.82647i	0.293765	−	0.169605i	0.639638	+	0.768676i	$0.279084\pi$
$510$		−	12.7107i		−	0.562839i
$511$	−10.2291	−	25.2577i	−0.452507	−	1.11733i
$512$		−	48.1706i		−	2.12886i
$513$	2.20723	−	1.27435i	0.0974516	−	0.0562637i
$514$	−20.1465	+	34.8947i	−0.888622	+	1.53914i
$515$	8.41863	−	14.5815i	0.370969	−	0.642537i
$516$	14.3605	+	24.8732i	0.632188	+	1.09498i
$517$	−20.0825	−	25.2722i	−0.883229	−	1.11147i
$518$	18.3437	−	7.42899i	0.805976	−	0.326411i
$519$		−	1.15936i		−	0.0508902i
$520$	−2.61771	−	4.53400i	−0.114794	−	0.198829i
$521$	7.71648	+	4.45511i	0.338065	+	0.195182i	0.659416	−	0.751778i	$-0.270804\pi$
$521$	7.71648	+	4.45511i	0.338065	+	0.195182i	−0.321351	+	0.946960i	$0.604137\pi$
$522$	10.9502	−	18.9664i	0.479279	−	0.830135i
$523$	5.12728	+	8.88071i	0.224200	+	0.388326i	0.956079	−	0.293108i	$-0.0946897\pi$
$523$	5.12728	+	8.88071i	0.224200	+	0.388326i	−0.731879	+	0.681435i	$0.761356\pi$
$524$	−51.9994			−2.27160
$525$	1.47803	−	10.5802i	0.0645066	−	0.461759i
$526$	15.6572			0.682688
$527$	−28.5154	+	16.4634i	−1.24215	+	0.717157i
$528$	−18.5717	+	2.76643i	−0.808231	+	0.120393i
$529$	11.2126	−	19.4208i	0.487503	−	0.844381i
$530$	5.51990	+	9.56075i	0.239769	+	0.415292i
$531$		−	14.7090i		−	0.638315i
$532$	17.6882	−	22.6786i	0.766883	−	0.983241i
$533$	−3.58548			−0.155304
$534$	5.16822	−	2.98387i	0.223651	−	0.129125i
$535$	−6.27258	+	10.8644i	−0.271187	+	0.469710i
$536$	61.0103	+	35.2243i	2.63524	+	1.52146i
$537$	−16.6741	+	9.62679i	−0.719540	+	0.415427i
$538$	23.7230			1.02277
$539$	−21.4387	+	8.90968i	−0.923430	+	0.383767i
$540$	−4.18383			−0.180043
$541$	7.63198	−	4.40633i	0.328125	−	0.189443i	−0.326884	−	0.945065i	$-0.605998\pi$
$541$	7.63198	−	4.40633i	0.328125	−	0.189443i	0.655008	+	0.755622i	$0.272665\pi$
$542$	40.4790	+	23.3706i	1.73872	+	1.00385i
$543$	0.499771	−	0.865629i	0.0214472	−	0.0371477i
$544$	12.6921	−	7.32778i	0.544169	−	0.314176i
$545$	1.74774			0.0748650
$546$	3.83392	−	4.91557i	0.164077	−	0.210367i
$547$		−	1.13200i		−	0.0484007i	−0.999707	−	0.0242004i	$-0.992296\pi$
$547$		−	1.13200i		−	0.0484007i	0.999707	−	0.0242004i	$-0.00770397\pi$
$548$	6.44448	+	11.1622i	0.275295	+	0.476824i
$549$	2.81334	−	4.87284i	0.120070	−	0.207968i
$550$	33.1543	−	4.93864i	1.41371	−	0.210584i
$551$	−19.3123	+	11.1500i	−0.822733	+	0.475005i
$552$	4.29874			0.182967
$553$	−2.80271	+	20.0627i	−0.119183	+	0.853154i
$554$	−44.1025			−1.87373
$555$	1.46574	+	2.53874i	0.0622173	+	0.107764i
$556$	24.8225	−	42.9939i	1.05271	−	1.82335i
$557$	6.52655	+	3.76810i	0.276539	+	0.159660i	0.631855	−	0.775086i	$-0.282294\pi$
$557$	6.52655	+	3.76810i	0.276539	+	0.159660i	−0.355317	+	0.934746i	$0.615627\pi$
$558$	7.96013	+	13.7873i	0.336979	+	0.583665i
$559$		−	6.33884i		−	0.268104i
$560$	−13.6185	+	5.51532i	−0.575485	+	0.233065i
$561$	10.6819	+	13.4423i	0.450991	+	0.567534i
$562$	13.7081	+	23.7432i	0.578243	+	1.00155i
$563$	2.38645	−	4.13346i	0.100577	−	0.174204i	−0.811346	−	0.584567i	$-0.801264\pi$
$563$	2.38645	−	4.13346i	0.100577	−	0.174204i	0.911923	+	0.410362i	$0.134598\pi$
$564$	20.7559	−	35.9504i	0.873983	−	1.51378i
$565$	12.7896	−	7.38405i	0.538061	−	0.310650i
$566$		−	69.2675i		−	2.91153i
$567$	−0.993145	−	2.45228i	−0.0417082	−	0.102986i
$568$		−	59.4751i		−	2.49552i
$569$	19.1415	−	11.0513i	0.802452	−	0.463296i	−0.0418756	−	0.999123i	$-0.513333\pi$
$569$	19.1415	−	11.0513i	0.802452	−	0.463296i	0.844328	+	0.535827i	$0.180000\pi$
$570$	5.41940	+	3.12889i	0.226994	+	0.131055i
$571$	−20.9597	−	12.1011i	−0.877134	−	0.506414i	−0.00742170	−	0.999972i	$-0.502362\pi$
$571$	−20.9597	−	12.1011i	−0.877134	−	0.506414i	−0.869712	+	0.493559i	$0.835696\pi$
$572$	12.3872	+	4.88635i	0.517937	+	0.204309i
$573$			22.1638i			0.925906i
$574$	−3.48986	+	24.9816i	−0.145664	+	1.04271i
$575$	−3.06137			−0.127668
$576$	2.11835	+	3.66910i	0.0882647	+	0.152879i
$577$	10.2401	+	5.91215i	0.426303	+	0.246126i	0.697770	−	0.716322i	$-0.254176\pi$
$577$	10.2401	+	5.91215i	0.426303	+	0.246126i	−0.271468	+	0.962448i	$0.587509\pi$
$578$	−21.2430	−	12.2647i	−0.883593	−	0.510143i
$579$	6.02278	+	10.4318i	0.250298	+	0.433529i
$580$	36.6067			1.52001
$581$	−10.2331	+	13.1201i	−0.424539	+	0.544313i
$582$		−	18.2723i		−	0.757410i
$583$	−13.8723	−	5.47217i	−0.574534	−	0.226634i
$584$	50.5734	+	29.1986i	2.09274	+	1.20825i
$585$	0.799675	+	0.461692i	0.0330625	+	0.0190886i
$586$	−46.2602	+	26.7083i	−1.91099	+	1.10331i
$587$			3.24719i			0.134026i	0.997752	+	0.0670130i	$0.0213469\pi$
$587$			3.24719i			0.134026i	−0.997752	+	0.0670130i	$0.978653\pi$
$588$	−20.7754	−	21.4424i	−0.856762	−	0.884271i
$589$		−	16.2107i		−	0.667948i
$590$	31.2764	−	18.0574i	1.28763	−	0.743412i
$591$	0.446453	−	0.773280i	0.0183646	−	0.0318085i
$592$	−8.45945	+	14.6522i	−0.347681	+	0.602202i
$593$	−4.44715	−	7.70270i	−0.182623	−	0.316312i	0.760150	−	0.649747i	$-0.225125\pi$
$593$	−4.44715	−	7.70270i	−0.182623	−	0.316312i	−0.942773	+	0.333436i	$0.891792\pi$
$594$	6.49940	−	5.16475i	0.266674	−	0.211912i
$595$	10.5941	+	8.26292i	0.434316	+	0.338747i
$596$			5.44876i			0.223190i
$597$	5.10764	+	8.84669i	0.209042	+	0.362071i
$598$	−1.54709	−	0.893214i	−0.0632653	−	0.0365262i
$599$	−1.23981	+	2.14741i	−0.0506571	+	0.0877407i	−0.890242	−	0.455488i	$-0.849465\pi$
$599$	−1.23981	+	2.14741i	−0.0506571	+	0.0877407i	0.839585	+	0.543228i	$0.182798\pi$
$600$	11.4467	+	19.8263i	0.467311	+	0.809406i
$601$	27.6199			1.12664			0.563319	−	0.826239i	$-0.309524\pi$
$601$	27.6199			1.12664			0.563319	+	0.826239i	$0.309524\pi$
$602$	−44.1655	−	6.16980i	−1.80005	−	0.251462i
$603$	−12.4252			−0.505994
$604$	84.0938	−	48.5516i	3.42173	−	1.97554i
$605$	7.36649	−	7.88437i	0.299490	−	0.320545i
$606$	−6.60798	+	11.4454i	−0.268431	+	0.464936i
$607$	0.907807	+	1.57237i	0.0368467	+	0.0638204i	0.883861	−	0.467750i	$-0.154935\pi$
$607$	0.907807	+	1.57237i	0.0368467	+	0.0638204i	−0.847014	+	0.531571i	$0.821602\pi$
$608$			7.21529i			0.292618i
$609$	8.68959	+	21.4564i	0.352120	+	0.869456i
$610$	13.8151			0.559358
$611$	−7.93436	+	4.58091i	−0.320990	+	0.185324i
$612$	−11.0401	+	19.1220i	−0.446270	+	0.772962i
$613$	−25.3612	−	14.6423i	−1.02433	−	0.591397i	−0.108974	−	0.994045i	$-0.534757\pi$
$613$	−25.3612	−	14.6423i	−1.02433	−	0.591397i	−0.915355	+	0.402648i	$0.868090\pi$
$614$	54.1475	−	31.2621i	2.18521	−	1.26163i
$615$	−3.73627			−0.150661
$616$	24.4843	−	43.3107i	0.986499	−	1.74504i
$617$	2.57805			0.103788			0.0518941	−	0.998653i	$-0.483474\pi$
$617$	2.57805			0.103788			0.0518941	+	0.998653i	$0.483474\pi$
$618$	−37.2076	+	21.4818i	−1.49671	+	0.864125i
$619$	35.8142	+	20.6774i	1.43950	+	0.831093i	0.997814	−	0.0660784i	$-0.0210488\pi$
$619$	35.8142	+	20.6774i	1.43950	+	0.831093i	0.441682	+	0.897172i	$0.354382\pi$
$620$	−13.3054	+	23.0456i	−0.534357	+	0.925533i
$621$	−0.656604	+	0.379091i	−0.0263486	+	0.0152124i
$622$	−60.5076			−2.42613
$623$	−0.872739	+	6.24735i	−0.0349656	+	0.250295i
$624$			5.32926i			0.213341i
$625$	−5.74629	−	9.95287i	−0.229852	−	0.398115i
$626$	27.6255	−	47.8488i	1.10414	−	1.91242i
$627$	−8.36080	+	1.24542i	−0.333898	+	0.0497372i
$628$	−35.8277	+	20.6851i	−1.42968	+	0.825426i
$629$	15.4710			0.616867
$630$	3.99516	−	5.12230i	0.159171	−	0.204077i
$631$	−2.44038			−0.0971500			−0.0485750	−	0.998820i	$-0.515468\pi$
$631$	−2.44038			−0.0971500			−0.0485750	+	0.998820i	$0.515468\pi$
$632$	−21.7058	−	37.5956i	−0.863411	−	1.49547i
$633$	2.95422	−	5.11686i	0.117420	−	0.203377i
$634$	14.8965	+	8.60051i	0.591617	+	0.341570i
$635$	2.50736	+	4.34288i	0.0995016	+	0.172342i
$636$		−	19.1776i		−	0.760442i
$637$	1.60469	+	6.39099i	0.0635800	+	0.253220i
$638$	−56.8670	+	45.1894i	−2.25139	+	1.78907i
$639$	5.24490	+	9.08443i	0.207485	+	0.359374i
$640$	−7.97816	+	13.8186i	−0.315365	+	0.546228i
$641$	16.6553	−	28.8479i	0.657846	−	1.13942i	−0.323326	−	0.946288i	$-0.604801\pi$
$641$	16.6553	−	28.8479i	0.657846	−	1.13942i	0.981172	−	0.193135i	$-0.0618656\pi$
$642$	27.7228	−	16.0058i	1.09413	−	0.631697i
$643$			14.8370i			0.585116i	0.956248	+	0.292558i	$0.0945064\pi$
$643$			14.8370i			0.585116i	−0.956248	+	0.292558i	$0.905494\pi$
$644$	−5.26188	+	6.74639i	−0.207347	+	0.265845i
$645$		−	6.60543i		−	0.260088i
$646$	28.6010	−	16.5128i	1.12529	−	0.649686i
$647$	6.86747	+	3.96494i	0.269988	+	0.155878i	0.628882	−	0.777501i	$-0.283513\pi$
$647$	6.86747	+	3.96494i	0.269988	+	0.155878i	−0.358894	+	0.933378i	$0.616846\pi$
$648$	4.91020	+	2.83490i	0.192891	+	0.111366i
$649$	−17.9013	+	45.3810i	−0.702687	+	1.78136i
$650$		−	9.51383i		−	0.373163i
$651$	−16.6662	−	2.32822i	−0.653198	−	0.0912501i
$652$	73.7247			2.88728
$653$	−6.57416	−	11.3868i	−0.257267	−	0.445599i	0.708242	−	0.705970i	$-0.249489\pi$
$653$	−6.57416	−	11.3868i	−0.257267	−	0.445599i	−0.965509	+	0.260371i	$0.916155\pi$
$654$	−3.86222	−	2.22986i	−0.151025	−	0.0871943i
$655$	10.3569	+	5.97954i	0.404677	+	0.233640i
$656$	−10.7818	−	18.6747i	−0.420960	−	0.729124i
$657$	−10.2997			−0.401829
$658$	24.1944	+	59.7409i	0.943196	+	2.32894i
$659$		−	1.07554i		−	0.0418972i	−0.999781	−	0.0209486i	$-0.993331\pi$
$659$		−	1.07554i		−	0.0418972i	0.999781	−	0.0209486i	$-0.00666864\pi$
$660$	12.9082	+	5.09185i	0.502451	+	0.198200i
$661$	44.0089	+	25.4085i	1.71175	+	0.988278i	0.932207	+	0.361925i	$0.117880\pi$
$661$	44.0089	+	25.4085i	1.71175	+	0.988278i	0.779540	+	0.626353i	$0.215453\pi$
$662$	10.3522	+	5.97685i	0.402350	+	0.232297i
$663$	4.22029	−	2.43659i	0.163903	−	0.0946292i
$664$		−	35.6569i		−	1.38376i
$665$	−6.13089	+	2.48294i	−0.237746	+	0.0962843i
$666$		−	7.48027i		−	0.289855i
$667$	5.74501	−	3.31688i	0.222448	−	0.128430i
$668$	−10.5392	+	18.2544i	−0.407772	+	0.706282i
$669$	6.58696	−	11.4090i	0.254667	−	0.441096i
$670$	−15.2538	−	26.4203i	−0.589305	−	1.02071i
$671$	−14.6103	+	11.6101i	−0.564023	+	0.448201i
$672$	7.41803	+	1.03628i	0.286157	+	0.0399754i
$673$			29.6755i			1.14391i	0.820287	+	0.571953i	$0.193814\pi$
$673$			29.6755i			1.14391i	−0.820287	+	0.571953i	$0.806186\pi$
$674$	−20.4157	−	35.3610i	−0.786383	−	1.36206i
$675$	−3.49682	−	2.01889i	−0.134593	−	0.0777071i
$676$	−25.8339	+	44.7457i	−0.993612	+	1.72099i
$677$	−12.5710	−	21.7736i	−0.483143	−	0.836827i	0.516670	−	0.856185i	$-0.327171\pi$
$677$	−12.5710	−	21.7736i	−0.483143	−	0.836827i	−0.999813	+	0.0193571i	$0.993838\pi$
$678$	−37.6838			−1.44724
$679$	15.2296	+	11.8784i	0.584457	+	0.455850i
$680$	−28.7920			−1.10412
$681$	−22.8880	+	13.2144i	−0.877071	+	0.506377i
$682$	−7.77943	−	52.2253i	−0.297890	−	1.99981i
$683$	0.452546	−	0.783833i	0.0173162	−	0.0299926i	−0.857237	−	0.514921i	$-0.827821\pi$
$683$	0.452546	−	0.783833i	0.0173162	−	0.0299926i	0.874554	+	0.484929i	$0.161154\pi$
$684$	−5.43531	−	9.41423i	−0.207824	−	0.359962i
$685$		−	2.96427i		−	0.113259i
$686$	46.0907	−	4.95999i	1.75975	−	0.189373i
$687$	−11.0702			−0.422355
$688$	33.0154	−	19.0614i	1.25870	−	0.726710i
$689$	−2.11628	+	3.66551i	−0.0806240	+	0.139645i
$690$	−1.61216	−	0.930779i	−0.0613738	−	0.0354342i
$691$	−4.05268	+	2.33982i	−0.154171	+	0.0890109i	−0.575101	−	0.818082i	$-0.695037\pi$
$691$	−4.05268	+	2.33982i	−0.154171	+	0.0890109i	0.420930	+	0.907093i	$0.361704\pi$
$692$	−4.94487			−0.187976
$693$	0.0796105	+	8.77460i	0.00302415	+	0.333320i
$694$	−29.1637			−1.10704
$695$	−9.88796	+	5.70881i	−0.375072	+	0.216548i
$696$	−42.9621	−	24.8042i	−1.62848	−	0.940201i
$697$	−9.85910	+	17.0765i	−0.373440	+	0.646817i
$698$	26.8127	−	15.4803i	1.01488	−	0.585939i
$699$	7.74230			0.292841
$700$	−45.1265	−	6.30406i	−1.70562	−	0.238271i
$701$			0.533229i			0.0201398i	0.999949	+	0.0100699i	$0.00320540\pi$
$701$			0.533229i			0.0201398i	−0.999949	+	0.0100699i	$0.996795\pi$
$702$	−1.17810	−	2.04053i	−0.0444645	−	0.0770149i
$703$	−3.80836	+	6.59627i	−0.143635	+	0.248783i
$704$	−2.07027	−	13.8982i	−0.0780261	−	0.523809i
$705$	−8.26805	+	4.77356i	−0.311393	+	0.179783i
$706$	−33.6164			−1.26517
$707$	−5.24379	−	12.9480i	−0.197213	−	0.486959i
$708$	−62.7363			−2.35778
$709$	−6.35361	−	11.0048i	−0.238615	−	0.413293i	0.721702	−	0.692204i	$-0.243360\pi$
$709$	−6.35361	−	11.0048i	−0.238615	−	0.413293i	−0.960317	+	0.278911i	$0.910027\pi$
$710$	−12.8778	+	22.3049i	−0.483294	+	0.837090i
$711$	6.63084	+	3.82832i	0.248676	+	0.143573i
$712$	−6.75900	−	11.7069i	−0.253304	−	0.438736i
$713$			4.82233i			0.180598i
$714$	−12.8690	−	31.7762i	−0.481611	−	1.18920i
$715$	−1.90531	−	2.39767i	−0.0712546	−	0.0896678i
$716$	41.0599	+	71.1179i	1.53448	+	2.65780i
$717$	6.37902	−	11.0488i	0.238229	−	0.412625i
$718$	−2.47647	+	4.28936i	−0.0924209	+	0.160078i
$719$	27.9083	−	16.1129i	1.04081	−	0.600909i	0.120744	−	0.992684i	$-0.461472\pi$
$719$	27.9083	−	16.1129i	1.04081	−	0.600909i	0.920061	+	0.391774i	$0.128139\pi$
$720$			5.55339i			0.206963i
$721$	6.28312	−	44.9766i	0.233995	−	1.67502i
$722$		−	31.2984i		−	1.16480i
$723$	−22.1794	+	12.8053i	−0.824861	+	0.476234i
$724$	−3.69206	−	2.13161i	−0.137214	−	0.0792207i
$725$	30.5957	+	17.6644i	1.13630	+	0.656041i
$726$	−26.3380	+	8.02463i	−0.977496	+	0.297822i
$727$			34.5072i			1.27980i	0.768457	+	0.639902i	$0.221025\pi$
$727$			34.5072i			1.27980i	−0.768457	+	0.639902i	$0.778975\pi$
$728$	−11.1346	−	8.68450i	−0.412677	−	0.321869i
$729$	−1.00000			−0.0370370
$730$	−12.6444	−	21.9007i	−0.467989	−	0.810580i
$731$	−30.1898	−	17.4301i	−1.11661	−	0.644676i
$732$	−20.7835	−	11.9994i	−0.768181	−	0.443509i
$733$	−15.9487	−	27.6239i	−0.589078	−	1.02031i	−0.994354	−	0.106118i	$-0.966158\pi$
$733$	−15.9487	−	27.6239i	−0.589078	−	1.02031i	0.405276	−	0.914194i	$-0.367176\pi$
$734$	−30.3205			−1.11915
$735$	1.67217	+	6.65977i	0.0616791	+	0.245649i
$736$		−	2.14639i		−	0.0791172i
$737$	38.3350	+	15.1219i	1.41209	+	0.557022i
$738$	8.25654	+	4.76692i	0.303928	+	0.175473i
$739$	−37.4773	−	21.6375i	−1.37862	−	0.795948i	−0.386629	−	0.922235i	$-0.626361\pi$
$739$	−37.4773	−	21.6375i	−1.37862	−	0.795948i	−0.991994	+	0.126287i	$0.959694\pi$
$740$	10.8282	−	6.25165i	0.398052	−	0.229815i
$741$			2.39918i			0.0881361i
$742$	23.4794	+	18.3128i	0.861954	+	0.672285i
$743$			50.2625i			1.84395i	0.387246	+	0.921976i	$0.373426\pi$
$743$			50.2625i			1.84395i	−0.387246	+	0.921976i	$0.626574\pi$
$744$	31.2308	−	18.0311i	1.14497	−	0.661052i
$745$	0.626567	−	1.08525i	0.0229556	−	0.0397603i
$746$	−18.9071	+	32.7480i	−0.692237	+	1.19899i
$747$	3.14445	+	5.44636i	0.115050	+	0.199272i
$748$	57.3337	−	45.5602i	2.09633	−	1.66585i
$749$	−4.68145	+	33.5113i	−0.171056	+	1.22448i
$750$		−	22.1904i		−	0.810279i
$751$	18.5875	+	32.1944i	0.678266	+	1.17479i	0.975503	+	0.219988i	$0.0706017\pi$
$751$	18.5875	+	32.1944i	0.678266	+	1.17479i	−0.297236	+	0.954804i	$0.596065\pi$
$752$	−47.7186	−	27.5503i	−1.74012	−	1.00466i
$753$	−3.24130	+	5.61409i	−0.118119	+	0.204589i
$754$	10.3079	+	17.8538i	0.375391	+	0.650196i
$755$	−22.3323			−0.812756
$756$	−10.4594	+	4.23594i	−0.380404	+	0.154059i
$757$	−5.95539			−0.216452			−0.108226	−	0.994126i	$-0.534517\pi$
$757$	−5.95539			−0.216452			−0.108226	+	0.994126i	$0.534517\pi$
$758$	−0.122883	+	0.0709464i	−0.00446330	+	0.00257689i
$759$	2.48716	−	0.370485i	0.0902782	−	0.0134478i
$760$	7.08749	−	12.2759i	0.257090	−	0.445293i
$761$	12.8060	+	22.1807i	0.464217	+	0.804048i	0.999166	−	0.0408367i	$-0.0130023\pi$
$761$	12.8060	+	22.1807i	0.464217	+	0.804048i	−0.534949	+	0.844885i	$0.679669\pi$
$762$		−	12.7961i		−	0.463553i
$763$	4.36928	−	1.76951i	0.158179	−	0.0640605i
$764$	94.5325			3.42007
$765$	4.39778	−	2.53906i	0.159002	−	0.0917999i
$766$	12.0756	−	20.9156i	0.436311	−	0.755712i
$767$	11.9911	+	6.92306i	0.432973	+	0.249977i
$768$	27.9227	−	16.1212i	1.00757	−	0.581723i
$769$	−52.0469			−1.87686			−0.938429	−	0.345472i	$-0.887719\pi$
$769$	−52.0469			−1.87686			−0.938429	+	0.345472i	$0.887719\pi$
$770$	−18.5601	+	10.9414i	−0.668860	+	0.394300i
$771$	−16.0976			−0.579742
$772$	44.4933	−	25.6882i	1.60135	−	0.924539i
$773$	30.4779	+	17.5964i	1.09621	+	0.632899i	0.935224	−	0.354058i	$-0.115198\pi$
$773$	30.4779	+	17.5964i	1.09621	+	0.632899i	0.160989	+	0.986956i	$0.448532\pi$
$774$	−8.42754	+	14.5969i	−0.302922	+	0.524676i
$775$	−22.2411	+	12.8409i	−0.798925	+	0.461260i
$776$	−41.3899			−1.48581
$777$	6.23466	+	4.86275i	0.223667	+	0.174450i
$778$			22.5734i			0.809295i
$779$	−4.85387	−	8.40715i	−0.173908	−	0.301217i
$780$	1.96920	−	3.41075i	0.0705086	−	0.122125i
$781$	−5.12584	−	34.4110i	−0.183417	−	1.23132i
$782$	−8.50818	+	4.91220i	−0.304252	+	0.175660i
$783$	8.74957			0.312684
$784$	−28.4616	+	27.5761i	−1.01648	+	0.984862i
$785$	9.51454			0.339589
$786$	−15.2580	−	26.4276i	−0.544235	−	0.942643i
$787$	−1.71802	+	2.97569i	−0.0612406	+	0.106072i	−0.895020	−	0.446026i	$-0.852839\pi$
$787$	−1.71802	+	2.97569i	−0.0612406	+	0.106072i	0.833780	+	0.552097i	$0.186172\pi$
$788$	−3.29817	−	1.90420i	−0.117493	−	0.0678344i
$789$	3.12765	+	5.41725i	0.111347	+	0.192859i
$790$			18.7993i			0.668849i
$791$	24.4973	−	31.4087i	0.871025	−	1.11676i
$792$	−11.6991	−	14.7223i	−0.415708	−	0.523134i
$793$	2.64830	+	4.58699i	0.0940439	+	0.162889i
$794$	18.2902	−	31.6796i	0.649096	−	1.12427i
$795$	−2.20529	+	3.81967i	−0.0782134	+	0.135470i
$796$	37.7327	−	21.7850i	1.33740	−	0.772148i
$797$		−	20.0096i		−	0.708777i	−0.935098	−	0.354388i	$-0.884689\pi$
$797$		−	20.0096i		−	0.708777i	0.935098	−	0.354388i	$-0.115311\pi$
$798$	16.7161	+	2.33520i	0.591745	+	0.0826652i
$799$			50.3851i			1.78250i
$800$	9.89942	−	5.71543i	0.349997	−	0.202071i
$801$	2.06478	+	1.19210i	0.0729555	+	0.0421209i
$802$	30.8344	+	17.8022i	1.08880	+	0.628618i
$803$	31.7772	+	12.5350i	1.12139	+	0.442352i
$804$			52.9957i			1.86902i
$805$	1.82381	−	0.738622i	0.0642809	−	0.0260330i
$806$	−14.9863			−0.527872
$807$	4.73886	+	8.20794i	0.166816	+	0.288933i
$808$	25.9258	+	14.9682i	0.912065	+	0.526581i
$809$	13.5836	+	7.84252i	0.477576	+	0.275728i	0.719406	−	0.694590i	$-0.244414\pi$
$809$	13.5836	+	7.84252i	0.477576	+	0.275728i	−0.241830	+	0.970319i	$0.577748\pi$
$810$	−1.22765	−	2.12635i	−0.0431351	−	0.0747122i
$811$	−23.1967			−0.814545			−0.407272	−	0.913307i	$-0.633520\pi$
$811$	−23.1967			−0.814545			−0.407272	+	0.913307i	$0.633520\pi$
$812$	91.5152	−	37.0626i	3.21155	−	1.30064i
$813$			18.6738i			0.654919i
$814$	−9.10373	+	23.0786i	−0.319086	+	0.808904i
$815$	−14.6840	−	8.47780i	−0.514357	−	0.296964i
$816$	25.3816	+	14.6540i	0.888532	+	0.512994i
$817$	14.8632	−	8.58126i	0.519997	−	0.300220i
$818$			8.97653i			0.313857i
$819$	2.46660	+	0.344577i	0.0861898	+	0.0120405i
$820$			15.9358i			0.556503i
$821$	23.4614	−	13.5454i	0.818808	−	0.472739i	−0.0311971	−	0.999513i	$-0.509932\pi$
$821$	23.4614	−	13.5454i	0.818808	−	0.472739i	0.850005	+	0.526774i	$0.176599\pi$
$822$	−3.78197	+	6.55056i	−0.131911	+	0.228477i
$823$	−22.8215	+	39.5280i	−0.795508	+	1.37786i	0.127008	+	0.991902i	$0.459463\pi$
$823$	−22.8215	+	39.5280i	−0.795508	+	1.37786i	−0.922516	+	0.385959i	$0.873871\pi$
$824$	48.6601	+	84.2817i	1.69515	+	2.93609i
$825$	8.33155	+	10.4845i	0.290067	+	0.365025i
$826$	59.9073	−	76.8087i	2.08444	−	2.67252i
$827$			11.3712i			0.395415i	0.980261	+	0.197707i	$0.0633496\pi$
$827$			11.3712i			0.395415i	−0.980261	+	0.197707i	$0.936650\pi$
$828$	1.61689	+	2.80053i	0.0561908	+	0.0973253i
$829$	−24.9489	−	14.4043i	−0.866511	−	0.500280i	−0.000323761	−	1.00000i	$-0.500103\pi$
$829$	−24.9489	−	14.4043i	−0.866511	−	0.500280i	−0.866187	+	0.499720i	$0.833436\pi$
$830$	−7.72056	+	13.3724i	−0.267985	+	0.464163i
$831$	−8.80980	−	15.2590i	−0.305609	−	0.529330i
$832$	−3.98818			−0.138265
$833$	34.8507	+	9.93091i	1.20750	+	0.344086i
$834$	29.1344			1.00884
$835$	4.19823	−	2.42385i	0.145286	−	0.0838808i
$836$	5.31192	+	35.6603i	0.183717	+	1.23334i
$837$	−3.18019	+	5.50826i	−0.109924	+	0.190393i
$838$	−37.1339	−	64.3178i	−1.28277	−	2.22182i
$839$		−	12.9826i		−	0.448211i	−0.974565	−	0.224105i	$-0.928054\pi$
$839$		−	12.9826i		−	0.448211i	0.974565	−	0.224105i	$-0.0719460\pi$
$840$	−11.6029	−	9.04974i	−0.400338	−	0.312246i
$841$	−47.5550			−1.63983
$842$	−14.3681	+	8.29541i	−0.495156	+	0.285879i
$843$	−5.47661	+	9.48577i	−0.188624	+	0.326707i
$844$	−21.8243	−	12.6003i	−0.751223	−	0.433719i
$845$	10.2908	−	5.94142i	0.354016	−	0.204391i
$846$	24.3614			0.837562
$847$	10.4334	−	27.1688i	0.358494	−	0.933532i
$848$	−25.4554			−0.874141
$849$	23.9659	−	13.8367i	0.822507	−	0.474875i
$850$	−45.3113	−	26.1605i	−1.55416	−	0.897297i
$851$	1.13291	−	1.96225i	0.0388355	−	0.0672651i
$852$	38.7467	−	22.3704i	1.32744	−	0.766397i
$853$	38.9986			1.33529			0.667644	−	0.744481i	$-0.267303\pi$
$853$	38.9986			1.33529			0.667644	+	0.744481i	$0.267303\pi$
$854$	34.5372	−	13.9872i	1.18184	−	0.478632i
$855$			2.50008i			0.0855010i
$856$	−36.2558	−	62.7970i	−1.23920	−	2.14636i
$857$	−0.248529	+	0.430465i	−0.00848959	+	0.0147044i	−0.870239	−	0.492630i	$-0.836036\pi$
$857$	−0.248529	+	0.430465i	−0.00848959	+	0.0147044i	0.861749	+	0.507334i	$0.169369\pi$
$858$	1.15136	+	7.72935i	0.0393067	+	0.263876i
$859$	19.7134	−	11.3815i	0.672613	−	0.388333i	−0.124453	−	0.992225i	$-0.539718\pi$
$859$	19.7134	−	11.3815i	0.672613	−	0.388333i	0.797066	+	0.603892i	$0.206384\pi$
$860$	−28.1733			−0.960702
$861$	−9.34051	+	3.78280i	−0.318324	+	0.128918i
$862$	−90.0412			−3.06682
$863$	−10.3490	−	17.9250i	−0.352284	−	0.610174i	0.634365	−	0.773034i	$-0.281262\pi$
$863$	−10.3490	−	17.9250i	−0.352284	−	0.610174i	−0.986649	+	0.162859i	$0.947928\pi$
$864$	1.41549	−	2.45170i	0.0481559	−	0.0834085i
$865$	0.984885	+	0.568624i	0.0334871	+	0.0193338i
$866$	−21.8678	−	37.8762i	−0.743099	−	1.28709i
$867$		−	9.79984i		−	0.332820i
$868$	−9.93027	+	71.0841i	−0.337055	+	2.41275i
$869$	−15.7987	−	19.8813i	−0.535934	−	0.674427i
$870$	10.7414	+	18.6046i	0.364167	+	0.630756i
$871$	5.84817	−	10.1293i	0.198158	−	0.343219i
$872$	−5.05101	+	8.74861i	−0.171049	+	0.296265i
$873$	6.32203	−	3.65002i	0.213968	−	0.123535i
$874$		−	4.83679i		−	0.163607i
$875$	18.4953	+	14.4255i	0.625254	+	0.487669i
$876$			43.9299i			1.48425i
$877$	28.9691	−	16.7253i	0.978218	−	0.564774i	0.0764860	−	0.997071i	$-0.475630\pi$
$877$	28.9691	−	16.7253i	0.978218	−	0.564774i	0.901732	+	0.432297i	$0.142297\pi$
$878$	−70.5374	−	40.7248i	−2.38052	−	1.37440i
$879$	−18.4816	−	10.6704i	−0.623370	−	0.359903i
$880$	6.75865	−	17.1337i	0.227834	−	0.577576i
$881$		−	39.1311i		−	1.31836i	−0.751984	−	0.659181i	$-0.770903\pi$
$881$		−	39.1311i		−	1.31836i	0.751984	−	0.659181i	$-0.229097\pi$
$882$	4.80164	−	16.8505i	0.161680	−	0.567384i
$883$	38.6223			1.29974			0.649872	−	0.760044i	$-0.274823\pi$
$883$	38.6223			1.29974			0.649872	+	0.760044i	$0.274823\pi$
$884$	−10.3925	−	18.0003i	−0.349537	−	0.605415i
$885$	12.4954	+	7.21421i	0.420028	+	0.242503i
$886$	−5.76879	−	3.33061i	−0.193806	−	0.111894i
$887$	5.87619	+	10.1779i	0.197303	+	0.341739i	0.947653	−	0.319302i	$-0.103448\pi$
$887$	5.87619	+	10.1779i	0.197303	+	0.341739i	−0.750350	+	0.661041i	$0.770115\pi$
$888$	−16.9441			−0.568608
$889$	10.6653	+	8.31843i	0.357702	+	0.278991i
$890$			5.85393i			0.196224i
$891$	3.08526	+	1.21703i	0.103360	+	0.0407721i
$892$	−48.6612	−	28.0945i	−1.62930	−	0.940675i
$893$	−21.4824	−	12.4029i	−0.718882	−	0.415047i
$894$	−2.76922	+	1.59881i	−0.0926166	+	0.0534722i
$895$		−	18.8864i		−	0.631302i
$896$	−5.95438	+	42.6234i	−0.198922	+	1.42395i
$897$		−	0.713705i		−	0.0238299i
$898$	−87.8590	+	50.7254i	−2.93189	+	1.69273i
$899$	27.8253	−	48.1949i	0.928027	−	1.60739i
$900$	−8.61092	+	14.9146i	−0.287031	+	0.497152i
$901$	11.6384	+	20.1583i	0.387732	+	0.671571i
$902$	−19.6721	−	24.7557i	−0.655009	−	0.824273i
$903$	−6.68770	−	16.5133i	−0.222553	−	0.549528i
$904$			85.3604i			2.83904i
$905$	0.490239	+	0.849119i	0.0162961	+	0.0282257i
$906$	49.3508	+	28.4927i	1.63957	+	0.946606i
$907$	−16.4781	+	28.5410i	−0.547147	+	0.947687i	0.451321	+	0.892362i	$0.350953\pi$
$907$	−16.4781	+	28.5410i	−0.547147	+	0.947687i	−0.998468	+	0.0553253i	$0.982380\pi$
$908$	56.3618	+	97.6214i	1.87043	+	3.23968i
$909$	−5.27998			−0.175126
$910$	2.29542	+	5.66786i	0.0760924	+	0.187888i
$911$	2.79047			0.0924525			0.0462263	−	0.998931i	$-0.485280\pi$
$911$	2.79047			0.0924525			0.0462263	+	0.998931i	$0.485280\pi$
$912$	−12.4959	+	7.21454i	−0.413782	+	0.238897i
$913$	−3.07307	−	20.6303i	−0.101704	−	0.682764i
$914$	−18.4473	+	31.9516i	−0.610181	+	1.05686i
$915$	2.75968	+	4.77990i	0.0912321	+	0.158019i
$916$			47.2164i			1.56007i
$917$	31.9458	+	4.46274i	1.05494	+	0.147373i
$918$	−12.9578			−0.427673
$919$	−40.5986	+	23.4396i	−1.33922	+	0.773202i	−0.986692	−	0.162598i	$-0.948013\pi$
$919$	−40.5986	+	23.4396i	−1.33922	+	0.773202i	−0.352532	+	0.935800i	$0.614679\pi$
$920$	−2.10838	+	3.65182i	−0.0695112	+	0.120397i
$921$	21.6327	+	12.4897i	0.712823	+	0.411549i
$922$	10.9027	−	6.29470i	0.359063	−	0.207305i
$923$	−9.87445			−0.325021
$924$	37.4252	−	0.339553i	1.23120	−	0.0111705i
$925$	12.0668			0.396755
$926$	6.09374	−	3.51822i	0.200253	−	0.115616i
$927$	−14.8650	−	8.58231i	−0.488231	−	0.281880i
$928$	−12.3849	+	21.4513i	−0.406555	+	0.704174i
$929$	−40.3911	+	23.3198i	−1.32519	+	0.765099i	−0.984552	−	0.175095i	$-0.943977\pi$
$929$	−40.3911	+	23.3198i	−1.32519	+	0.765099i	−0.340639	+	0.940194i	$0.610643\pi$
$930$	−15.6166			−0.512089
$931$	−12.8131	+	12.4145i	−0.419933	+	0.406869i
$932$		−	33.0223i		−	1.08168i
$933$	−12.0869	−	20.9351i	−0.395706	−	0.685383i
$934$	17.6043	−	30.4915i	0.576030	−	0.997714i
$935$	−16.6584	+	2.48142i	−0.544788	+	0.0811512i
$936$	−4.62216	+	2.66860i	−0.151080	+	0.0872261i
$937$	−1.36302			−0.0445280			−0.0222640	−	0.999752i	$-0.507087\pi$
$937$	−1.36302			−0.0445280			−0.0222640	+	0.999752i	$0.507087\pi$
$938$	−64.8832	−	50.6059i	−2.11851	−	1.65234i
$939$	22.0736			0.720346
$940$	20.3601	+	35.2647i	0.664072	+	1.15021i
$941$	−19.6223	+	33.9868i	−0.639668	+	1.10794i	0.345838	+	0.938294i	$0.387595\pi$
$941$	−19.6223	+	33.9868i	−0.639668	+	1.10794i	−0.985506	+	0.169642i	$0.945739\pi$
$942$	−21.0256	−	12.1391i	−0.685051	−	0.395514i
$943$	1.44392	+	2.50095i	0.0470206	+	0.0814421i
$944$			83.2729i			2.71030i
$945$	2.57033	+	0.359069i	0.0836129	+	0.0116805i
$946$	43.7661	−	34.7787i	1.42296	−	1.13075i
$947$	−8.40850	−	14.5640i	−0.273240	−	0.473265i	0.696450	−	0.717605i	$-0.254762\pi$
$947$	−8.40850	−	14.5640i	−0.273240	−	0.473265i	−0.969689	+	0.244341i	$0.921429\pi$
$948$	16.3284	−	28.2817i	0.530323	−	0.918547i
$949$	4.84774	−	8.39653i	0.157364	−	0.272563i
$950$	22.3078	−	12.8794i	0.723761	−	0.417864i
$951$			6.87207i			0.222842i
$952$	−71.9787	+	29.1506i	−2.33284	+	0.944775i
$953$		−	46.5459i		−	1.50777i	−0.657007	−	0.753884i	$-0.728178\pi$
$953$		−	46.5459i		−	1.50777i	0.657007	−	0.753884i	$-0.271822\pi$
$954$	9.74664	−	5.62723i	0.315559	−	0.182188i
$955$	−18.8283	−	10.8705i	−0.609271	−	0.351763i
$956$	−47.1250	−	27.2076i	−1.52413	−	0.879958i
$957$	−26.9947	−	10.6485i	−0.872615	−	0.344217i
$958$		−	100.437i		−	3.24497i
$959$	−3.00119	−	7.41056i	−0.0969135	−	0.239299i
$960$	−4.15590			−0.134131
$961$	4.72725	+	8.18784i	0.152492	+	0.264124i
$962$	6.09809	+	3.52073i	0.196610	+	0.113513i
$963$	11.0757	+	6.39455i	0.356909	+	0.206061i
$964$	54.6168	+	94.5991i	1.75909	+	3.04683i
$965$	−11.8158			−0.380365
$966$	−4.97270	−	0.694673i	−0.159994	−	0.0223507i
$967$			41.2782i			1.32742i	0.747991	+	0.663709i	$0.231019\pi$
$967$			41.2782i			1.32742i	−0.747991	+	0.663709i	$0.768981\pi$
$968$	18.1772	+	59.6602i	0.584237	+	1.91755i
$969$	11.4265	+	6.59710i	0.367073	+	0.211929i
$970$	15.5224	+	8.96188i	0.498395	+	0.287749i
$971$	−43.7908	+	25.2826i	−1.40531	+	0.811358i	−0.994931	−	0.100556i	$-0.967938\pi$
$971$	−43.7908	+	25.2826i	−1.40531	+	0.811358i	−0.410381	+	0.911914i	$0.634604\pi$
$972$			4.26518i			0.136806i
$973$	−18.9396	+	24.2829i	−0.607174	+	0.778474i
$974$			6.51141i			0.208639i
$975$	3.29169	−	1.90046i	0.105419	−	0.0608634i
$976$	−15.9273	+	27.5869i	−0.509821	+	0.883036i
$977$	−4.78051	+	8.28009i	−0.152942	+	0.264904i	−0.932308	−	0.361666i	$-0.882208\pi$
$977$	−4.78051	+	8.28009i	−0.152942	+	0.264904i	0.779366	+	0.626569i	$0.215541\pi$
$978$	21.6328	+	37.4691i	0.691741	+	1.19813i
$979$	−4.91957	−	6.19086i	−0.157230	−	0.197861i
$980$	28.4051	−	7.13211i	0.907367	−	0.227827i
$981$		−	1.78172i		−	0.0568860i
$982$	25.5979	+	44.3368i	0.816860	+	1.41484i
$983$	−3.85461	−	2.22546i	−0.122943	−	0.0709811i	0.437267	−	0.899332i	$-0.355946\pi$
$983$	−3.85461	−	2.22546i	−0.122943	−	0.0709811i	−0.560210	+	0.828350i	$0.689280\pi$
$984$	10.7979	−	18.7025i	0.344225	−	0.596214i
$985$	0.437938	+	0.758531i	0.0139539	+	0.0241688i
$986$	113.376			3.61061
$987$	−15.8368	+	20.3047i	−0.504090	+	0.646307i
$988$	10.2329			0.325553
$989$	−4.42148	+	2.55274i	−0.140595	+	0.0811725i
$990$	1.19978	+	8.05442i	0.0381315	+	0.255986i
$991$	22.6534	−	39.2369i	0.719610	−	1.24640i	−0.241544	−	0.970390i	$-0.577654\pi$
$991$	22.6534	−	39.2369i	0.719610	−	1.24640i	0.961154	−	0.276012i	$-0.0890129\pi$
$992$	−9.00305	−	15.5937i	−0.285847	−	0.495102i
$993$			4.77568i			0.151552i
$994$	−9.61113	+	68.7996i	−0.304846	+	2.18219i
$995$	−10.0204			−0.317669
$996$	23.2297	−	13.4117i	0.736060	−	0.424964i
$997$	19.6051	−	33.9570i	0.620900	−	1.07543i	−0.368418	−	0.929660i	$-0.620101\pi$
$997$	19.6051	−	33.9570i	0.620900	−	1.07543i	0.989318	−	0.145770i	$-0.0465660\pi$
$998$	−73.0946	−	42.2012i	−2.31377	−	1.33586i
$999$	2.58810	−	1.49424i	0.0818840	−	0.0472757i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.p.a.10.15	yes	32
3.2	odd	2		693.2.bg.b.10.2		32
7.3	odd	6		1617.2.c.a.538.30		32
7.4	even	3		1617.2.c.a.538.29		32
7.5	odd	6	inner	231.2.p.a.208.2	yes	32
11.10	odd	2	inner	231.2.p.a.10.2	✓	32
21.5	even	6		693.2.bg.b.208.15		32
33.32	even	2		693.2.bg.b.10.15		32
77.10	even	6		1617.2.c.a.538.4		32
77.32	odd	6		1617.2.c.a.538.3		32
77.54	even	6	inner	231.2.p.a.208.15	yes	32
231.131	odd	6		693.2.bg.b.208.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.p.a.10.2	✓	32	11.10	odd	2	inner
231.2.p.a.10.15	yes	32	1.1	even	1	trivial
231.2.p.a.208.2	yes	32	7.5	odd	6	inner
231.2.p.a.208.15	yes	32	77.54	even	6	inner
693.2.bg.b.10.2		32	3.2	odd	2
693.2.bg.b.10.15		32	33.32	even	2
693.2.bg.b.208.2		32	231.131	odd	6
693.2.bg.b.208.15		32	21.5	even	6
1617.2.c.a.538.3		32	77.32	odd	6
1617.2.c.a.538.4		32	77.10	even	6
1617.2.c.a.538.29		32	7.4	even	3
1617.2.c.a.538.30		32	7.3	odd	6

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.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.16769 - 1.25152i) q^{2} +(0.866025 + 0.500000i) q^{3} +(2.13259 - 3.69375i) q^{4} +(-0.849508 + 0.490464i) q^{5} +2.50303 q^{6} +(-1.62716 + 2.08623i) q^{7} -5.66981i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(2.16769 - 1.25152i) q^{2} +(0.866025 + 0.500000i) q^{3} +(2.13259 - 3.69375i) q^{4} +(-0.849508 + 0.490464i) q^{5} +2.50303 q^{6} +(-1.62716 + 2.08623i) q^{7} -5.66981i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.22765 + 2.12635i) q^{10} +(-0.488650 - 3.28043i) q^{11} +(3.69375 - 2.13259i) q^{12} -0.941338 q^{13} +(-0.916236 + 6.55871i) q^{14} -0.980927 q^{15} +(-2.83068 - 4.90289i) q^{16} +(-2.58843 + 4.48329i) q^{17} +(2.16769 + 1.25152i) q^{18} +(-1.27435 - 2.20723i) q^{19} +4.18383i q^{20} +(-2.45228 + 0.993145i) q^{21} +(-5.16475 - 6.49940i) q^{22} +(0.379091 + 0.656604i) q^{23} +(2.83490 - 4.91020i) q^{24} +(-2.01889 + 3.49682i) q^{25} +(-2.04053 + 1.17810i) q^{26} +1.00000i q^{27} +(4.23594 + 10.4594i) q^{28} -8.74957i q^{29} +(-2.12635 + 1.22765i) q^{30} +(5.50826 + 3.18019i) q^{31} +(-2.45170 - 1.41549i) q^{32} +(1.21703 - 3.08526i) q^{33} +12.9578i q^{34} +(0.359069 - 2.57033i) q^{35} +4.26518 q^{36} +(-1.49424 - 2.58810i) q^{37} +(-5.52477 - 3.18973i) q^{38} +(-0.815223 - 0.470669i) q^{39} +(2.78084 + 4.81655i) q^{40} +3.80891 q^{41} +(-4.07284 + 5.22190i) q^{42} +6.73386i q^{43} +(-13.1592 - 5.19085i) q^{44} +(-0.849508 - 0.490464i) q^{45} +(1.64350 + 0.948877i) q^{46} +(8.42881 - 4.86638i) q^{47} -5.66137i q^{48} +(-1.70469 - 6.78926i) q^{49} +10.1067i q^{50} +(-4.48329 + 2.58843i) q^{51} +(-2.00749 + 3.47707i) q^{52} +(2.24816 - 3.89393i) q^{53} +(1.25152 + 2.16769i) q^{54} +(2.02404 + 2.54709i) q^{55} +(11.8285 + 9.22570i) q^{56} -2.54869i q^{57} +(-10.9502 - 18.9664i) q^{58} +(-12.7383 - 7.35448i) q^{59} +(-2.09191 + 3.62330i) q^{60} +(-2.81334 - 4.87284i) q^{61} +15.9203 q^{62} +(-2.62031 - 0.366050i) q^{63} +4.23671 q^{64} +(0.799675 - 0.461692i) q^{65} +(-1.22311 - 8.21103i) q^{66} +(-6.21261 + 10.7606i) q^{67} +(11.0401 + 19.1220i) q^{68} +0.758182i q^{69} +(-2.43846 - 6.02106i) q^{70} +10.4898 q^{71} +(4.91020 - 2.83490i) q^{72} +(-5.14984 + 8.91978i) q^{73} +(-6.47811 - 3.74014i) q^{74} +(-3.49682 + 2.01889i) q^{75} -10.8706 q^{76} +(7.63883 + 4.31836i) q^{77} -2.35620 q^{78} +(6.63084 - 3.82832i) q^{79} +(4.80938 + 2.77670i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(8.25654 - 4.76692i) q^{82} +6.28891 q^{83} +(-1.56127 + 11.1761i) q^{84} -5.07812i q^{85} +(8.42754 + 14.5969i) q^{86} +(4.37479 - 7.57735i) q^{87} +(-18.5994 + 2.77055i) q^{88} +(2.06478 - 1.19210i) q^{89} -2.45529 q^{90} +(1.53171 - 1.96385i) q^{91} +3.23378 q^{92} +(3.18019 + 5.50826i) q^{93} +(12.1807 - 21.0976i) q^{94} +(2.16513 + 1.25004i) q^{95} +(-1.41549 - 2.45170i) q^{96} -7.30005i q^{97} +(-12.1921 - 12.5836i) q^{98} +(2.59661 - 2.06340i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{4} - 12 q^{5} + 16 q^{9}+O(q^{10}) \) 32 * q + 12 * q^4 - 12 * q^5 + 16 * q^9	\( 32 q + 12 q^{4} - 12 q^{5} + 16 q^{9} + 2 q^{11} - 32 q^{14} + 8 q^{15} - 20 q^{16} + 8 q^{22} + 24 q^{23} - 24 q^{26} - 12 q^{31} - 18 q^{33} + 24 q^{36} - 32 q^{37} + 24 q^{38} - 24 q^{42} - 28 q^{44} - 12 q^{45} + 24 q^{47} - 36 q^{49} + 36 q^{53} - 56 q^{56} + 12 q^{58} - 48 q^{59} + 8 q^{64} - 36 q^{66} + 20 q^{67} + 24 q^{70} + 72 q^{71} + 24 q^{75} - 48 q^{78} + 72 q^{80} - 16 q^{81} - 48 q^{82} + 64 q^{86} + 24 q^{88} + 60 q^{89} - 28 q^{91} - 16 q^{92} + 16 q^{93} + 4 q^{99}+O(q^{100}) \) 32 * q + 12 * q^4 - 12 * q^5 + 16 * q^9 + 2 * q^11 - 32 * q^14 + 8 * q^15 - 20 * q^16 + 8 * q^22 + 24 * q^23 - 24 * q^26 - 12 * q^31 - 18 * q^33 + 24 * q^36 - 32 * q^37 + 24 * q^38 - 24 * q^42 - 28 * q^44 - 12 * q^45 + 24 * q^47 - 36 * q^49 + 36 * q^53 - 56 * q^56 + 12 * q^58 - 48 * q^59 + 8 * q^64 - 36 * q^66 + 20 * q^67 + 24 * q^70 + 72 * q^71 + 24 * q^75 - 48 * q^78 + 72 * q^80 - 16 * q^81 - 48 * q^82 + 64 * q^86 + 24 * q^88 + 60 * q^89 - 28 * q^91 - 16 * q^92 + 16 * q^93 + 4 * q^99

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