LMFDB - Embedded newform 231.2.e.a.188.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(188,231)]

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, 1, 0]))

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

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

chi := DirichletCharacter("231.188");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			188.16
Character	$\chi$	$=$	231.188
Dual form			231.2.e.a.188.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.309769i q^{2} +(1.65749 - 0.502726i) q^{3} +1.90404 q^{4} -1.52955 q^{5} +(0.155729 + 0.513438i) q^{6} +(-0.131314 + 2.64249i) q^{7} +1.20935i q^{8} +(2.49453 - 1.66652i) q^{9} +O(q^{10})$	\(q+0.309769i q^{2} +(1.65749 - 0.502726i) q^{3} +1.90404 q^{4} -1.52955 q^{5} +(0.155729 + 0.513438i) q^{6} +(-0.131314 + 2.64249i) q^{7} +1.20935i q^{8} +(2.49453 - 1.66652i) q^{9} -0.473807i q^{10} +1.00000i q^{11} +(3.15593 - 0.957212i) q^{12} -1.78543i q^{13} +(-0.818561 - 0.0406771i) q^{14} +(-2.53521 + 0.768944i) q^{15} +3.43347 q^{16} -5.34730 q^{17} +(0.516238 + 0.772729i) q^{18} -5.87140i q^{19} -2.91233 q^{20} +(1.11080 + 4.44591i) q^{21} -0.309769 q^{22} -7.34598i q^{23} +(0.607972 + 2.00449i) q^{24} -2.66048 q^{25} +0.553070 q^{26} +(3.29685 - 4.01631i) q^{27} +(-0.250028 + 5.03142i) q^{28} +6.99353i q^{29} +(-0.238195 - 0.785329i) q^{30} +7.96010i q^{31} +3.48228i q^{32} +(0.502726 + 1.65749i) q^{33} -1.65643i q^{34} +(0.200852 - 4.04182i) q^{35} +(4.74970 - 3.17314i) q^{36} -1.02801 q^{37} +1.81878 q^{38} +(-0.897580 - 2.95932i) q^{39} -1.84976i q^{40} +1.69945 q^{41} +(-1.37721 + 0.344090i) q^{42} -10.9417 q^{43} +1.90404i q^{44} +(-3.81551 + 2.54903i) q^{45} +2.27555 q^{46} +7.18013 q^{47} +(5.69093 - 1.72609i) q^{48} +(-6.96551 - 0.693994i) q^{49} -0.824133i q^{50} +(-8.86309 + 2.68823i) q^{51} -3.39953i q^{52} -9.97413i q^{53} +(1.24413 + 1.02126i) q^{54} -1.52955i q^{55} +(-3.19570 - 0.158805i) q^{56} +(-2.95171 - 9.73178i) q^{57} -2.16638 q^{58} -6.79321 q^{59} +(-4.82715 + 1.46410i) q^{60} +2.66400i q^{61} -2.46579 q^{62} +(4.07621 + 6.81062i) q^{63} +5.78823 q^{64} +2.73090i q^{65} +(-0.513438 + 0.155729i) q^{66} -2.91745 q^{67} -10.1815 q^{68} +(-3.69301 - 12.1759i) q^{69} +(1.25203 + 0.0622177i) q^{70} +8.60295i q^{71} +(2.01541 + 3.01677i) q^{72} +4.48567i q^{73} -0.318447i q^{74} +(-4.40971 + 1.33749i) q^{75} -11.1794i q^{76} +(-2.64249 - 0.131314i) q^{77} +(0.916706 - 0.278042i) q^{78} +3.23908 q^{79} -5.25166 q^{80} +(3.44539 - 8.31440i) q^{81} +0.526436i q^{82} +8.97586 q^{83} +(2.11500 + 8.46521i) q^{84} +8.17897 q^{85} -3.38938i q^{86} +(3.51583 + 11.5917i) q^{87} -1.20935 q^{88} +0.618430 q^{89} +(-0.789611 - 1.18193i) q^{90} +(4.71797 + 0.234452i) q^{91} -13.9871i q^{92} +(4.00175 + 13.1938i) q^{93} +2.22418i q^{94} +8.98060i q^{95} +(1.75063 + 5.77184i) q^{96} -9.26798i q^{97} +(0.214978 - 2.15770i) q^{98} +(1.66652 + 2.49453i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 32 q^{4} - 8 q^{7} - 8 q^{9}+O(q^{10}) $ 28 * q - 32 * q^4 - 8 * q^7 - 8 * q^9	$ 28 q - 32 q^{4} - 8 q^{7} - 8 q^{9} - 20 q^{15} + 40 q^{16} - 12 q^{18} - 10 q^{21} + 36 q^{25} + 12 q^{28} - 4 q^{30} + 24 q^{36} - 24 q^{37} + 16 q^{39} - 40 q^{43} - 16 q^{46} + 4 q^{49} - 8 q^{51} - 4 q^{57} - 44 q^{58} + 52 q^{60} + 6 q^{63} - 68 q^{64} + 40 q^{67} + 20 q^{70} + 24 q^{72} - 28 q^{78} + 56 q^{79} + 32 q^{81} + 100 q^{84} - 8 q^{85} + 12 q^{88} + 8 q^{91} - 36 q^{93}+O(q^{100}) $ 28 * q - 32 * q^4 - 8 * q^7 - 8 * q^9 - 20 * q^15 + 40 * q^16 - 12 * q^18 - 10 * q^21 + 36 * q^25 + 12 * q^28 - 4 * q^30 + 24 * q^36 - 24 * q^37 + 16 * q^39 - 40 * q^43 - 16 * q^46 + 4 * q^49 - 8 * q^51 - 4 * q^57 - 44 * q^58 + 52 * q^60 + 6 * q^63 - 68 * q^64 + 40 * q^67 + 20 * q^70 + 24 * q^72 - 28 * q^78 + 56 * q^79 + 32 * q^81 + 100 * q^84 - 8 * q^85 + 12 * q^88 + 8 * q^91 - 36 * q^93

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$			0.309769i			0.219040i	0.993985	+	0.109520i	$0.0349313\pi$
$2$			0.309769i			0.219040i	−0.993985	+	0.109520i	$0.965069\pi$
$3$	1.65749	−	0.502726i	0.956951	−	0.290249i
$3$	1.65749	−	0.502726i	0.956951	−	0.290249i
$4$	1.90404			0.952022
$5$	−1.52955			−0.684035			−0.342018	−	0.939694i	$-0.611110\pi$
$5$	−1.52955			−0.684035			−0.342018	+	0.939694i	$0.611110\pi$
$6$	0.155729	+	0.513438i	0.0635761	+	0.209610i
$7$	−0.131314	+	2.64249i	−0.0496322	+	0.998768i
$7$	−0.131314	+	2.64249i	−0.0496322	+	0.998768i
$8$			1.20935i			0.427570i
$9$	2.49453	−	1.66652i	0.831511	−	0.555508i
$10$		−	0.473807i		−	0.149831i
$11$			1.00000i			0.301511i
$11$			1.00000i			0.301511i
$12$	3.15593	−	0.957212i	0.911038	−	0.276323i
$13$		−	1.78543i		−	0.495188i	−0.968864	−	0.247594i	$-0.920360\pi$
$13$		−	1.78543i		−	0.495188i	0.968864	−	0.247594i	$-0.0796399\pi$
$14$	−0.818561	−	0.0406771i	−0.218770	−	0.0108714i
$15$	−2.53521	+	0.768944i	−0.654588	+	0.198541i
$16$	3.43347			0.858367
$17$	−5.34730			−1.29691			−0.648456	−	0.761252i	$-0.724585\pi$
$17$	−5.34730			−1.29691			−0.648456	+	0.761252i	$0.724585\pi$
$18$	0.516238	+	0.772729i	0.121678	+	0.182134i
$19$		−	5.87140i		−	1.34699i	−0.739191	−	0.673496i	$-0.764792\pi$
$19$		−	5.87140i		−	1.34699i	0.739191	−	0.673496i	$-0.235208\pi$
$20$	−2.91233			−0.651216
$21$	1.11080	+	4.44591i	0.242396	+	0.970177i
$22$	−0.309769			−0.0660430
$23$		−	7.34598i		−	1.53174i	−0.642994	−	0.765871i	$-0.722308\pi$
$23$		−	7.34598i		−	1.53174i	0.642994	−	0.765871i	$-0.277692\pi$
$24$	0.607972	+	2.00449i	0.124102	+	0.409164i
$25$	−2.66048			−0.532096
$26$	0.553070			0.108466
$27$	3.29685	−	4.01631i	0.634480	−	0.772939i
$28$	−0.250028	+	5.03142i	−0.0472509	+	0.950848i
$29$			6.99353i			1.29867i	0.760504	+	0.649333i	$0.224952\pi$
$29$			6.99353i			1.29867i	−0.760504	+	0.649333i	$0.775048\pi$
$30$	−0.238195	−	0.785329i	−0.0434883	−	0.143381i
$31$			7.96010i			1.42968i	0.699290	+	0.714838i	$0.253500\pi$
$31$			7.96010i			1.42968i	−0.699290	+	0.714838i	$0.746500\pi$
$32$			3.48228i			0.615587i
$33$	0.502726	+	1.65749i	0.0875134	+	0.288532i
$34$		−	1.65643i		−	0.284075i
$35$	0.200852	−	4.04182i	0.0339502	−	0.683192i
$36$	4.74970	−	3.17314i	0.791616	−	0.528856i
$37$	−1.02801			−0.169004			−0.0845022	−	0.996423i	$-0.526930\pi$
$37$	−1.02801			−0.169004			−0.0845022	+	0.996423i	$0.526930\pi$
$38$	1.81878			0.295045
$39$	−0.897580	−	2.95932i	−0.143728	−	0.473871i
$40$		−	1.84976i		−	0.292473i
$41$	1.69945			0.265409			0.132704	−	0.991156i	$-0.457634\pi$
$41$	1.69945			0.265409			0.132704	+	0.991156i	$0.457634\pi$
$42$	−1.37721	+	0.344090i	−0.212507	+	0.0530943i
$43$	−10.9417			−1.66859			−0.834293	−	0.551321i	$-0.814124\pi$
$43$	−10.9417			−1.66859			−0.834293	+	0.551321i	$0.814124\pi$
$44$			1.90404i			0.287045i
$45$	−3.81551	+	2.54903i	−0.568783	+	0.379987i
$46$	2.27555			0.335512
$47$	7.18013			1.04733			0.523665	−	0.851924i	$-0.324564\pi$
$47$	7.18013			1.04733			0.523665	+	0.851924i	$0.324564\pi$
$48$	5.69093	−	1.72609i	0.821415	−	0.249140i
$49$	−6.96551	−	0.693994i	−0.995073	−	0.0991420i
$50$		−	0.824133i		−	0.116550i
$51$	−8.86309	+	2.68823i	−1.24108	+	0.376427i
$52$		−	3.39953i		−	0.471430i
$53$		−	9.97413i		−	1.37005i	−0.728519	−	0.685026i	$-0.759791\pi$
$53$		−	9.97413i		−	1.37005i	0.728519	−	0.685026i	$-0.240209\pi$
$54$	1.24413	+	1.02126i	0.169304	+	0.138976i
$55$		−	1.52955i		−	0.206244i
$56$	−3.19570	−	0.158805i	−0.427043	−	0.0212212i
$57$	−2.95171	−	9.73178i	−0.390963	−	1.28901i
$58$	−2.16638			−0.284459
$59$	−6.79321			−0.884401			−0.442200	−	0.896916i	$-0.645802\pi$
$59$	−6.79321			−0.884401			−0.442200	+	0.896916i	$0.645802\pi$
$60$	−4.82715	+	1.46410i	−0.623182	+	0.189015i
$61$			2.66400i			0.341090i	0.985350	+	0.170545i	$0.0545528\pi$
$61$			2.66400i			0.341090i	−0.985350	+	0.170545i	$0.945447\pi$
$62$	−2.46579			−0.313156
$63$	4.07621	+	6.81062i	0.513554	+	0.858057i
$64$	5.78823			0.723529
$65$			2.73090i			0.338726i
$66$	−0.513438	+	0.155729i	−0.0631999	+	0.0191689i
$67$	−2.91745			−0.356424			−0.178212	−	0.983992i	$-0.557031\pi$
$67$	−2.91745			−0.356424			−0.178212	+	0.983992i	$0.557031\pi$
$68$	−10.1815			−1.23469
$69$	−3.69301	−	12.1759i	−0.444586	−	1.46580i
$70$	1.25203	+	0.0622177i	0.149646	+	0.00743644i
$71$			8.60295i			1.02098i	0.859883	+	0.510491i	$0.170536\pi$
$71$			8.60295i			1.02098i	−0.859883	+	0.510491i	$0.829464\pi$
$72$	2.01541	+	3.01677i	0.237519	+	0.355529i
$73$			4.48567i			0.525008i	0.964931	+	0.262504i	$0.0845483\pi$
$73$			4.48567i			0.525008i	−0.964931	+	0.262504i	$0.915452\pi$
$74$		−	0.318447i		−	0.0370187i
$75$	−4.40971	+	1.33749i	−0.509189	+	0.154440i
$76$		−	11.1794i		−	1.28237i
$77$	−2.64249	−	0.131314i	−0.301140	−	0.0149647i
$78$	0.916706	−	0.278042i	0.103797	−	0.0314821i
$79$	3.23908			0.364424			0.182212	−	0.983259i	$-0.441674\pi$
$79$	3.23908			0.364424			0.182212	+	0.983259i	$0.441674\pi$
$80$	−5.25166			−0.587153
$81$	3.44539	−	8.31440i	0.382821	−	0.923822i
$82$			0.526436i			0.0581351i
$83$	8.97586			0.985228			0.492614	−	0.870248i	$-0.336041\pi$
$83$	8.97586			0.985228			0.492614	+	0.870248i	$0.336041\pi$
$84$	2.11500	+	8.46521i	0.230766	+	0.923630i
$85$	8.17897			0.887134
$86$		−	3.38938i		−	0.365487i
$87$	3.51583	+	11.5917i	0.376936	+	1.24276i
$88$	−1.20935			−0.128917
$89$	0.618430			0.0655535			0.0327767	−	0.999463i	$-0.489565\pi$
$89$	0.618430			0.0655535			0.0327767	+	0.999463i	$0.489565\pi$
$90$	−0.789611	−	1.18193i	−0.0832323	−	0.124586i
$91$	4.71797	+	0.234452i	0.494578	+	0.0245773i
$92$		−	13.9871i		−	1.45825i
$93$	4.00175	+	13.1938i	0.414962	+	1.36813i
$94$			2.22418i			0.229407i
$95$			8.98060i			0.921390i
$96$	1.75063	+	5.77184i	0.178673	+	0.589086i
$97$		−	9.26798i		−	0.941021i	−0.882394	−	0.470510i	$-0.844070\pi$
$97$		−	9.26798i		−	0.941021i	0.882394	−	0.470510i	$-0.155930\pi$
$98$	0.214978	−	2.15770i	0.0217160	−	0.217961i
$99$	1.66652	+	2.49453i	0.167492	+	0.250710i
$100$	−5.06566			−0.506566
$101$	16.6066			1.65242			0.826210	−	0.563363i	$-0.190493\pi$
$101$	16.6066			1.65242			0.826210	+	0.563363i	$0.190493\pi$
$102$	−0.832730	−	2.74551i	−0.0824525	−	0.271846i
$103$		−	3.54269i		−	0.349071i	−0.984651	−	0.174536i	$-0.944158\pi$
$103$		−	3.54269i		−	0.349071i	0.984651	−	0.174536i	$-0.0558424\pi$
$104$	2.15921			0.211728
$105$	−1.69902	−	6.80024i	−0.165807	−	0.663636i
$106$	3.08967			0.300096
$107$		−	3.07719i		−	0.297483i	−0.988876	−	0.148742i	$-0.952478\pi$
$107$		−	3.07719i		−	0.297483i	0.988876	−	0.148742i	$-0.0475222\pi$
$108$	6.27735	−	7.64723i	0.604038	−	0.735855i
$109$	12.4813			1.19550			0.597748	−	0.801684i	$-0.296062\pi$
$109$	12.4813			1.19550			0.597748	+	0.801684i	$0.296062\pi$
$110$	0.473807			0.0451757
$111$	−1.70392	+	0.516809i	−0.161729	+	0.0490534i
$112$	−0.450864	+	9.07290i	−0.0426026	+	0.857309i
$113$			10.3842i			0.976865i	0.872602	+	0.488432i	$0.162431\pi$
$113$			10.3842i			0.976865i	−0.872602	+	0.488432i	$0.837569\pi$
$114$	3.01460	−	0.914347i	0.282343	−	0.0856364i
$115$			11.2360i			1.04777i
$116$			13.3160i			1.23636i
$117$	−2.97546	−	4.45381i	−0.275081	−	0.411754i
$118$		−	2.10433i		−	0.193719i
$119$	0.702178	−	14.1302i	0.0643686	−	1.29531i
$120$	−0.929924	−	3.06596i	−0.0848900	−	0.279883i
$121$	−1.00000			−0.0909091
$122$	−0.825224			−0.0747123
$123$	2.81681	−	0.854356i	0.253983	−	0.0770347i
$124$			15.1564i			1.36108i
$125$	11.7171			1.04801
$126$	−2.10972	+	1.26268i	−0.187949	+	0.112489i
$127$	−7.91634			−0.702462			−0.351231	−	0.936289i	$-0.614237\pi$
$127$	−7.91634			−0.702462			−0.351231	+	0.936289i	$0.614237\pi$
$128$			8.75758i			0.774068i
$129$	−18.1357	+	5.50065i	−1.59676	+	0.484306i
$130$	−0.845947			−0.0741945
$131$	−0.0428490			−0.00374373			−0.00187187	−	0.999998i	$-0.500596\pi$
$131$	−0.0428490			−0.00374373			−0.00187187	+	0.999998i	$0.500596\pi$
$132$	0.957212	+	3.15593i	0.0833146	+	0.274688i
$133$	15.5151	+	0.771000i	1.34533	+	0.0668542i
$134$		−	0.903737i		−	0.0780710i
$135$	−5.04270	+	6.14315i	−0.434007	+	0.528718i
$136$		−	6.46677i		−	0.554521i
$137$			16.6248i			1.42035i	0.704024	+	0.710176i	$0.251385\pi$
$137$			16.6248i			1.42035i	−0.704024	+	0.710176i	$0.748615\pi$
$138$	3.77170	−	1.14398i	0.321069	−	0.0973821i
$139$		−	7.58643i		−	0.643472i	−0.946829	−	0.321736i	$-0.895734\pi$
$139$		−	7.58643i		−	0.643472i	0.946829	−	0.321736i	$-0.104266\pi$
$140$	0.382431	−	7.69580i	0.0323213	−	0.650414i
$141$	11.9010	−	3.60964i	1.00224	−	0.303986i
$142$	−2.66493			−0.223636
$143$	1.78543			0.149305
$144$	8.56490	−	5.72196i	0.713741	−	0.476830i
$145$		−	10.6969i		−	0.888333i
$146$	−1.38952			−0.114998
$147$	−11.8941	+	2.35146i	−0.981012	+	0.193945i
$148$	−1.95738			−0.160896
$149$		−	3.31777i		−	0.271803i	−0.990722	−	0.135901i	$-0.956607\pi$
$149$		−	3.31777i		−	0.271803i	0.990722	−	0.135901i	$-0.0433930\pi$
$150$	−0.414313	−	1.36599i	−0.0338285	−	0.111533i
$151$	−7.40912			−0.602946			−0.301473	−	0.953475i	$-0.597478\pi$
$151$	−7.40912			−0.602946			−0.301473	+	0.953475i	$0.597478\pi$
$152$	7.10059			0.575934
$153$	−13.3390	+	8.91142i	−1.07840	+	0.720445i
$154$	0.0406771	−	0.818561i	0.00327786	−	0.0659616i
$155$		−	12.1754i		−	0.977949i
$156$	−1.70903	−	5.63468i	−0.136832	−	0.451135i
$157$			2.58008i			0.205913i	0.994686	+	0.102957i	$0.0328303\pi$
$157$			2.58008i			0.205913i	−0.994686	+	0.102957i	$0.967170\pi$
$158$			1.00336i			0.0798234i
$159$	−5.01425	−	16.5320i	−0.397656	−	1.31107i
$160$		−	5.32633i		−	0.421083i
$161$	19.4117	+	0.964632i	1.52985	+	0.0760237i
$162$	2.57554	+	1.06728i	0.202354	+	0.0838530i
$163$	10.9993			0.861531			0.430766	−	0.902464i	$-0.358244\pi$
$163$	10.9993			0.861531			0.430766	+	0.902464i	$0.358244\pi$
$164$	3.23582			0.252675
$165$	−0.768944	−	2.53521i	−0.0598622	−	0.197366i
$166$			2.78044i			0.215804i
$167$	−12.6579			−0.979496			−0.489748	−	0.871864i	$-0.662911\pi$
$167$	−12.6579			−0.979496			−0.489748	+	0.871864i	$0.662911\pi$
$168$	−5.37667	+	1.34334i	−0.414819	+	0.103641i
$169$	9.81225			0.754789
$170$			2.53359i			0.194317i
$171$	−9.78484	−	14.6464i	−0.748265	−	1.12004i
$172$	−20.8334			−1.58853
$173$	4.38058			0.333049			0.166525	−	0.986037i	$-0.446745\pi$
$173$	4.38058			0.333049			0.166525	+	0.986037i	$0.446745\pi$
$174$	−3.59074	+	1.08909i	−0.272214	+	0.0825640i
$175$	0.349359	−	7.03029i	0.0264091	−	0.531440i
$176$			3.43347i			0.258807i
$177$	−11.2597	+	3.41512i	−0.846328	+	0.256696i
$178$			0.191570i			0.0143588i
$179$			4.54399i			0.339634i	0.985476	+	0.169817i	$0.0543176\pi$
$179$			4.54399i			0.339634i	−0.985476	+	0.169817i	$0.945682\pi$
$180$	−7.26490	+	4.85347i	−0.541494	+	0.361756i
$181$			18.2780i			1.35859i	0.733864	+	0.679296i	$0.237715\pi$
$181$			18.2780i			1.35859i	−0.733864	+	0.679296i	$0.762285\pi$
$182$	−0.0726260	+	1.46148i	−0.00538340	+	0.108332i
$183$	1.33926	+	4.41555i	0.0990011	+	0.326407i
$184$	8.88386			0.654927
$185$	1.57240			0.115605
$186$	−4.08702	+	1.23962i	−0.299675	+	0.0908932i
$187$		−	5.34730i		−	0.391034i
$188$	13.6713			0.997080
$189$	10.1801	+	9.23930i	0.740496	+	0.672060i
$190$	−2.78191			−0.201821
$191$		−	11.8623i		−	0.858327i	−0.903227	−	0.429163i	$-0.858808\pi$
$191$		−	11.8623i		−	0.858327i	0.903227	−	0.429163i	$-0.141192\pi$
$192$	9.59392	−	2.90989i	0.692382	−	0.210004i
$193$	15.7880			1.13644			0.568222	−	0.822875i	$-0.307632\pi$
$193$	15.7880			1.13644			0.568222	+	0.822875i	$0.307632\pi$
$194$	2.87093			0.206121
$195$	1.37289	+	4.52643i	0.0983150	+	0.324144i
$196$	−13.2626	−	1.32140i	−0.947331	−	0.0943854i
$197$		−	6.77611i		−	0.482778i	−0.970428	−	0.241389i	$-0.922397\pi$
$197$		−	6.77611i		−	0.482778i	0.970428	−	0.241389i	$-0.0776030\pi$
$198$	−0.772729	+	0.516238i	−0.0549154	+	0.0366874i
$199$			6.92648i			0.491005i	0.969396	+	0.245503i	$0.0789530\pi$
$199$			6.92648i			0.491005i	−0.969396	+	0.245503i	$0.921047\pi$
$200$		−	3.21745i		−	0.227508i
$201$	−4.83565	+	1.46668i	−0.341080	+	0.103452i
$202$			5.14421i			0.361945i
$203$	−18.4803	−	0.918351i	−1.29706	−	0.0644556i
$204$	−16.8757	+	5.11850i	−1.18154	+	0.358367i
$205$	−2.59939			−0.181549
$206$	1.09741			0.0764605
$207$	−12.2422	−	18.3248i	−0.850895	−	1.27366i
$208$		−	6.13020i		−	0.425053i
$209$	5.87140			0.406133
$210$	2.10650	−	0.526303i	0.145363	−	0.0363184i
$211$	−13.7155			−0.944214			−0.472107	−	0.881541i	$-0.656506\pi$
$211$	−13.7155			−0.944214			−0.472107	+	0.881541i	$0.656506\pi$
$212$		−	18.9912i		−	1.30432i
$213$	4.32493	+	14.2593i	0.296339	+	0.977030i
$214$	0.953217			0.0651606
$215$	16.7358			1.14137
$216$	4.85713	+	3.98705i	0.330486	+	0.271285i
$217$	−21.0345	−	1.04528i	−1.42791	−	0.0709580i
$218$			3.86633i			0.261861i
$219$	2.25506	+	7.43495i	0.152383	+	0.502407i
$220$		−	2.91233i		−	0.196349i
$221$			9.54722i			0.642215i
$222$	−0.160091	−	0.527822i	−0.0107446	−	0.0354251i
$223$			12.8774i			0.862332i	0.902273	+	0.431166i	$0.141898\pi$
$223$			12.8774i			0.862332i	−0.902273	+	0.431166i	$0.858102\pi$
$224$	−9.20190	−	0.457274i	−0.614828	−	0.0305529i
$225$	−6.63665	+	4.43375i	−0.442443	+	0.295583i
$226$	−3.21671			−0.213972
$227$	−4.96491			−0.329532			−0.164766	−	0.986333i	$-0.552687\pi$
$227$	−4.96491			−0.329532			−0.164766	+	0.986333i	$0.552687\pi$
$228$	−5.62018	−	18.5297i	−0.372205	−	1.22716i
$229$		−	2.43665i		−	0.161019i	−0.996754	−	0.0805093i	$-0.974345\pi$
$229$		−	2.43665i		−	0.161019i	0.996754	−	0.0805093i	$-0.0256547\pi$
$230$	−3.48057			−0.229502
$231$	−4.44591	+	1.11080i	−0.292520	+	0.0730851i
$232$	−8.45763			−0.555271
$233$		−	18.2497i		−	1.19558i	−0.801654	−	0.597788i	$-0.796046\pi$
$233$		−	18.2497i		−	1.19558i	0.801654	−	0.597788i	$-0.203954\pi$
$234$	1.37965	−	0.921704i	0.0901906	−	0.0602537i
$235$	−10.9824			−0.716410
$236$	−12.9346			−0.841969
$237$	5.36873	−	1.62837i	0.348736	−	0.105774i
$238$	4.37710	+	0.217513i	0.283725	+	0.0140993i
$239$			12.1720i			0.787338i	0.919252	+	0.393669i	$0.128794\pi$
$239$			12.1720i			0.787338i	−0.919252	+	0.393669i	$0.871206\pi$
$240$	−8.70456	+	2.64015i	−0.561877	+	0.170421i
$241$		−	14.9027i		−	0.959970i	−0.877277	−	0.479985i	$-0.840642\pi$
$241$		−	14.9027i		−	0.959970i	0.877277	−	0.479985i	$-0.159358\pi$
$242$		−	0.309769i		−	0.0199127i
$243$	1.53083	−	15.5131i	0.0982027	−	0.995166i
$244$			5.07237i			0.324725i
$245$	10.6541	+	1.06150i	0.680665	+	0.0678167i
$246$	0.264653	+	0.872561i	0.0168737	+	0.0556324i
$247$	−10.4830			−0.667015
$248$	−9.62656			−0.611287
$249$	14.8774	−	4.51240i	0.942815	−	0.285962i
$250$			3.62959i			0.229555i
$251$	−5.12210			−0.323304			−0.161652	−	0.986848i	$-0.551682\pi$
$251$	−5.12210			−0.323304			−0.161652	+	0.986848i	$0.551682\pi$
$252$	7.76128	+	12.9677i	0.488914	+	0.816889i
$253$	7.34598			0.461838
$254$		−	2.45224i		−	0.153867i
$255$	13.5565	−	4.11178i	0.848944	−	0.257490i
$256$	8.86364			0.553977
$257$	−6.34175			−0.395587			−0.197794	−	0.980244i	$-0.563378\pi$
$257$	−6.34175			−0.395587			−0.197794	+	0.980244i	$0.563378\pi$
$258$	−1.70393	−	5.61786i	−0.106082	−	0.349753i
$259$	0.134993	−	2.71652i	0.00838806	−	0.168796i
$260$			5.19975i			0.322475i
$261$	11.6549	+	17.4456i	0.721419	+	1.07985i
$262$		−	0.0132733i		−	0.000820027i
$263$			14.9993i			0.924896i	0.886646	+	0.462448i	$0.153029\pi$
$263$			14.9993i			0.924896i	−0.886646	+	0.462448i	$0.846971\pi$
$264$	−2.00449	+	0.607972i	−0.123368	+	0.0374181i
$265$			15.2559i			0.937164i
$266$	−0.238832	+	4.80610i	−0.0146437	+	0.294681i
$267$	1.02504	−	0.310901i	0.0627315	−	0.0190268i
$268$	−5.55496			−0.339323
$269$	27.1856			1.65753			0.828767	−	0.559594i	$-0.189043\pi$
$269$	27.1856			1.65753			0.828767	+	0.559594i	$0.189043\pi$
$270$	−1.90296	−	1.56207i	−0.115810	−	0.0950647i
$271$			10.5529i			0.641044i	0.947241	+	0.320522i	$0.103858\pi$
$271$			10.5529i			0.641044i	−0.947241	+	0.320522i	$0.896142\pi$
$272$	−18.3598			−1.11323
$273$	7.93785	−	1.98325i	0.480420	−	0.120031i
$274$	−5.14985			−0.311114
$275$		−	2.66048i		−	0.160433i
$276$	−7.03166	−	23.1834i	−0.423256	−	1.39548i
$277$	11.5017			0.691073			0.345536	−	0.938405i	$-0.387697\pi$
$277$	11.5017			0.691073			0.345536	+	0.938405i	$0.387697\pi$
$278$	2.35004			0.140946
$279$	13.2657	+	19.8567i	0.794197	+	1.18879i
$280$	4.88798	+	0.242901i	0.292113	+	0.0145161i
$281$		−	20.5620i		−	1.22662i	−0.789840	−	0.613312i	$-0.789837\pi$
$281$		−	20.5620i		−	1.22662i	0.789840	−	0.613312i	$-0.210163\pi$
$282$	1.11815	+	3.68655i	0.0665851	+	0.219531i
$283$		−	19.6627i		−	1.16882i	−0.811457	−	0.584412i	$-0.801325\pi$
$283$		−	19.6627i		−	1.16882i	0.811457	−	0.584412i	$-0.198675\pi$
$284$			16.3804i			0.971997i
$285$	4.51478	+	14.8852i	0.267433	+	0.881725i
$286$			0.553070i			0.0327037i
$287$	−0.223162	+	4.49077i	−0.0131728	+	0.265082i
$288$	5.80331	+	8.68667i	0.341963	+	0.511867i
$289$	11.5937			0.681980
$290$	3.31358			0.194580
$291$	−4.65925	−	15.3616i	−0.273130	−	0.900511i
$292$			8.54091i			0.499819i
$293$	−27.6779			−1.61696			−0.808479	−	0.588525i	$-0.799709\pi$
$293$	−27.6779			−1.61696			−0.808479	+	0.588525i	$0.799709\pi$
$294$	−0.728408	−	3.68444i	−0.0424816	−	0.214881i
$295$	10.3906			0.604962
$296$		−	1.24323i		−	0.0722613i
$297$	4.01631	+	3.29685i	0.233050	+	0.191303i
$298$	1.02774			0.0595355
$299$	−13.1157			−0.758500
$300$	−8.39628	+	2.54664i	−0.484759	+	0.147030i
$301$	1.43680	−	28.9132i	0.0828156	−	1.66653i
$302$		−	2.29512i		−	0.132069i
$303$	27.5253	−	8.34857i	1.58128	−	0.479613i
$304$		−	20.1593i		−	1.15621i
$305$		−	4.07472i		−	0.233318i
$306$	−2.76048	−	4.13202i	−0.157806	−	0.236212i
$307$		−	2.98375i		−	0.170291i	−0.996369	−	0.0851457i	$-0.972864\pi$
$307$		−	2.98375i		−	0.170291i	0.996369	−	0.0851457i	$-0.0271356\pi$
$308$	−5.03142	−	0.250028i	−0.286692	−	0.0142467i
$309$	−1.78100	−	5.87196i	−0.101318	−	0.334044i
$310$	3.77155			0.214210
$311$	−26.6715			−1.51240			−0.756200	−	0.654341i	$-0.772946\pi$
$311$	−26.6715			−1.51240			−0.756200	+	0.654341i	$0.772946\pi$
$312$	3.57886	−	1.08549i	0.202613	−	0.0614538i
$313$			22.9486i			1.29713i	0.761157	+	0.648567i	$0.224631\pi$
$313$			22.9486i			1.29713i	−0.761157	+	0.648567i	$0.775369\pi$
$314$	−0.799229			−0.0451031
$315$	−6.23476	−	10.4172i	−0.351289	−	0.586942i
$316$	6.16734			0.346940
$317$		−	0.358808i		−	0.0201526i	−0.999949	−	0.0100763i	$-0.996793\pi$
$317$		−	0.358808i		−	0.0201526i	0.999949	−	0.0100763i	$-0.00320745\pi$
$318$	5.12110	−	1.55326i	0.287177	−	0.0871025i
$319$	−6.99353			−0.391562
$320$	−8.85339			−0.494919
$321$	−1.54698	−	5.10040i	−0.0863441	−	0.284677i
$322$	−0.298813	+	6.01313i	−0.0166522	+	0.335099i
$323$			31.3962i			1.74693i
$324$	6.56017	−	15.8310i	0.364454	−	0.879499i
$325$			4.75009i			0.263487i
$326$			3.40724i			0.188710i
$327$	20.6877	−	6.27470i	1.14403	−	0.346992i
$328$			2.05523i			0.113481i
$329$	−0.942854	+	18.9734i	−0.0519812	+	1.04604i
$330$	0.785329	−	0.238195i	0.0432310	−	0.0131122i
$331$	5.91675			0.325214			0.162607	−	0.986691i	$-0.448010\pi$
$331$	5.91675			0.325214			0.162607	+	0.986691i	$0.448010\pi$
$332$	17.0904			0.937959
$333$	−2.56442	+	1.71321i	−0.140529	+	0.0938834i
$334$		−	3.92102i		−	0.214548i
$335$	4.46239			0.243807
$336$	3.81388	+	15.2649i	0.208064	+	0.832768i
$337$	−4.78775			−0.260805			−0.130403	−	0.991461i	$-0.541627\pi$
$337$	−4.78775			−0.260805			−0.130403	+	0.991461i	$0.541627\pi$
$338$			3.03953i			0.165329i
$339$	5.22042	+	17.2117i	0.283534	+	0.934812i
$340$	15.5731			0.844570
$341$	−7.96010			−0.431064
$342$	4.53700	−	3.03104i	0.245333	−	0.163900i
$343$	2.74855	−	18.3152i	0.148408	−	0.988926i
$344$		−	13.2323i		−	0.713438i
$345$	5.64865	+	18.6236i	0.304113	+	1.00266i
$346$			1.35697i			0.0729510i
$347$		−	5.40348i		−	0.290074i	−0.989426	−	0.145037i	$-0.953670\pi$
$347$		−	5.40348i		−	0.290074i	0.989426	−	0.145037i	$-0.0463301\pi$
$348$	6.69429	+	22.0711i	0.358852	+	1.18313i
$349$			10.3697i			0.555075i	0.960715	+	0.277538i	$0.0895183\pi$
$349$			10.3697i			0.555075i	−0.960715	+	0.277538i	$0.910482\pi$
$350$	2.17776	+	0.108221i	0.116406	+	0.00578463i
$351$	−7.17083	−	5.88629i	−0.382751	−	0.314187i
$352$	−3.48228			−0.185606
$353$	−5.80434			−0.308934			−0.154467	−	0.987998i	$-0.549366\pi$
$353$	−5.80434			−0.308934			−0.154467	+	0.987998i	$0.549366\pi$
$354$	−1.05790	−	3.48789i	−0.0562267	−	0.185380i
$355$		−	13.1586i		−	0.698388i
$356$	1.17752			0.0624083
$357$	−5.93977	−	23.7736i	−0.314366	−	1.25823i
$358$	−1.40759			−0.0743933
$359$		−	21.9202i		−	1.15691i	−0.815716	−	0.578453i	$-0.803657\pi$
$359$		−	21.9202i		−	1.15691i	0.815716	−	0.578453i	$-0.196343\pi$
$360$	−3.08268	−	4.61429i	−0.162471	−	0.243195i
$361$	−15.4734			−0.814388
$362$	−5.66195			−0.297586
$363$	−1.65749	+	0.502726i	−0.0869956	+	0.0263863i
$364$	8.98322	+	0.446407i	0.470849	+	0.0233981i
$365$		−	6.86106i		−	0.359124i
$366$	−1.36780	+	0.414862i	−0.0714960	+	0.0216852i
$367$		−	8.55895i		−	0.446774i	−0.974730	−	0.223387i	$-0.928289\pi$
$367$		−	8.55895i		−	0.446774i	0.974730	−	0.223387i	$-0.0717113\pi$
$368$		−	25.2222i		−	1.31480i
$369$	4.23932	−	2.83217i	0.220690	−	0.147437i
$370$			0.487080i			0.0253221i
$371$	26.3565	+	1.30975i	1.36836	+	0.0679987i
$372$	7.61951	+	25.1215i	0.395053	+	1.30249i
$373$	4.56725			0.236483			0.118242	−	0.992985i	$-0.462274\pi$
$373$	4.56725			0.236483			0.118242	+	0.992985i	$0.462274\pi$
$374$	1.65643			0.0856519
$375$	19.4209	−	5.89048i	1.00289	−	0.304183i
$376$			8.68330i			0.447807i
$377$	12.4864			0.643084
$378$	−2.86205	+	3.15349i	−0.147208	+	0.162198i
$379$	27.7952			1.42775			0.713873	−	0.700275i	$-0.246939\pi$
$379$	27.7952			1.42775			0.713873	+	0.700275i	$0.246939\pi$
$380$			17.0995i			0.877183i
$381$	−13.1212	+	3.97975i	−0.672221	+	0.203889i
$382$	3.67458			0.188008
$383$	−22.9129			−1.17079			−0.585397	−	0.810747i	$-0.699061\pi$
$383$	−22.9129			−1.17079			−0.585397	+	0.810747i	$0.699061\pi$
$384$	4.40266	+	14.5156i	0.224673	+	0.740745i
$385$	4.04182	+	0.200852i	0.205990	+	0.0102364i
$386$			4.89063i			0.248926i
$387$	−27.2943	+	18.2345i	−1.38745	+	0.926914i
$388$		−	17.6466i		−	0.895872i
$389$			15.5053i			0.786150i	0.919506	+	0.393075i	$0.128589\pi$
$389$			15.5053i			0.786150i	−0.919506	+	0.393075i	$0.871411\pi$
$390$	−1.40215	+	0.425280i	−0.0710005	+	0.0215349i
$391$			39.2812i			1.98653i
$392$	0.839283	−	8.42375i	0.0423902	−	0.425464i
$393$	−0.0710217	+	0.0215413i	−0.00358257	+	0.00108662i
$394$	2.09903			0.105748
$395$	−4.95433			−0.249279
$396$	3.17314	+	4.74970i	0.159456	+	0.238681i
$397$			10.4562i			0.524780i	0.964962	+	0.262390i	$0.0845107\pi$
$397$			10.4562i			0.524780i	−0.964962	+	0.262390i	$0.915489\pi$
$398$	−2.14561			−0.107550
$399$	26.1037	−	6.52193i	1.30682	−	0.326505i
$400$	−9.13466			−0.456733
$401$		−	15.3593i		−	0.767007i	−0.923539	−	0.383504i	$-0.874717\pi$
$401$		−	15.3593i		−	0.767007i	0.923539	−	0.383504i	$-0.125283\pi$
$402$	−0.454332	−	1.49793i	−0.0226600	−	0.0747101i
$403$	14.2122			0.707959
$404$	31.6197			1.57314
$405$	−5.26990	+	12.7173i	−0.261863	+	0.631927i
$406$	0.284477	−	5.72463i	0.0141183	−	0.284109i
$407$		−	1.02801i		−	0.0509568i
$408$	−3.25101	−	10.7186i	−0.160949	−	0.530649i
$409$			32.8989i			1.62675i	0.581742	+	0.813373i	$0.302371\pi$
$409$			32.8989i			1.62675i	−0.581742	+	0.813373i	$0.697629\pi$
$410$		−	0.805209i		−	0.0397665i
$411$	8.35772	+	27.5554i	0.412256	+	1.35921i
$412$		−	6.74543i		−	0.332323i
$413$	0.892047	−	17.9510i	0.0438947	−	0.883311i
$414$	5.67645	−	3.79227i	0.278982	−	0.186380i
$415$	−13.7290			−0.673931
$416$	6.21736			0.304831
$417$	−3.81389	−	12.5744i	−0.186767	−	0.615772i
$418$			1.81878i			0.0889593i
$419$	−15.8940			−0.776471			−0.388236	−	0.921560i	$-0.626915\pi$
$419$	−15.8940			−0.776471			−0.388236	+	0.921560i	$0.626915\pi$
$420$	−3.23500	−	12.9480i	−0.157852	−	0.631796i
$421$	−3.45819			−0.168542			−0.0842709	−	0.996443i	$-0.526856\pi$
$421$	−3.45819			−0.168542			−0.0842709	+	0.996443i	$0.526856\pi$
$422$		−	4.24864i		−	0.206820i
$423$	17.9111	−	11.9659i	0.870866	−	0.581800i
$424$	12.0622			0.585793
$425$	14.2264			0.690081
$426$	−4.41708	+	1.33973i	−0.214008	+	0.0649100i
$427$	−7.03959	−	0.349822i	−0.340670	−	0.0169291i
$428$		−	5.85910i		−	0.283210i
$429$	2.95932	−	0.897580i	0.142877	−	0.0433356i
$430$			5.18423i			0.250006i
$431$			28.1589i			1.35637i	0.734892	+	0.678184i	$0.237233\pi$
$431$			28.1589i			1.35637i	−0.734892	+	0.678184i	$0.762767\pi$
$432$	11.3196	−	13.7899i	0.544616	−	0.663466i
$433$		−	41.4315i		−	1.99107i	−0.0943873	−	0.995536i	$-0.530089\pi$
$433$		−	41.4315i		−	1.99107i	0.0943873	−	0.995536i	$-0.469911\pi$
$434$	0.323794	−	6.51583i	0.0155426	−	0.312770i
$435$	−5.37763	−	17.7301i	−0.257838	−	0.850091i
$436$	23.7650			1.13814
$437$	−43.1312			−2.06324
$438$	−2.30312	+	0.698549i	−0.110047	+	0.0333779i
$439$		−	32.8032i		−	1.56561i	−0.622266	−	0.782806i	$-0.713788\pi$
$439$		−	32.8032i		−	1.56561i	0.622266	−	0.782806i	$-0.286212\pi$
$440$	1.84976			0.0881840
$441$	−18.5323	+	9.87701i	−0.882489	+	0.470334i
$442$	−2.95743			−0.140671
$443$			26.5210i			1.26005i	0.776574	+	0.630026i	$0.216956\pi$
$443$			26.5210i			1.26005i	−0.776574	+	0.630026i	$0.783044\pi$
$444$	−3.24434	+	0.984028i	−0.153970	+	0.0466999i
$445$	−0.945920			−0.0448409
$446$	−3.98901			−0.188885
$447$	−1.66793	−	5.49917i	−0.0788904	−	0.260102i
$448$	−0.760078	+	15.2953i	−0.0359103	+	0.722637i
$449$			13.5518i			0.639548i	0.947494	+	0.319774i	$0.103607\pi$
$449$			13.5518i			0.639548i	−0.947494	+	0.319774i	$0.896393\pi$
$450$	−1.37344	−	2.05583i	−0.0647445	−	0.0969127i
$451$			1.69945i			0.0800238i
$452$			19.7720i			0.929996i
$453$	−12.2805	+	3.72476i	−0.576990	+	0.175004i
$454$		−	1.53797i		−	0.0721807i
$455$	−7.21637	−	0.358606i	−0.338309	−	0.0168117i
$456$	11.7691	−	3.56965i	0.551140	−	0.167164i
$457$	−29.0229			−1.35763			−0.678817	−	0.734307i	$-0.737507\pi$
$457$	−29.0229			−1.35763			−0.678817	+	0.734307i	$0.737507\pi$
$458$	0.754799			0.0352694
$459$	−17.6293	+	21.4764i	−0.822864	+	1.00243i
$460$			21.3939i			0.997495i
$461$	14.6582			0.682702			0.341351	−	0.939936i	$-0.389116\pi$
$461$	14.6582			0.682702			0.341351	+	0.939936i	$0.389116\pi$
$462$	−0.344090	−	1.37721i	−0.0160085	−	0.0640734i
$463$	−4.59145			−0.213383			−0.106691	−	0.994292i	$-0.534026\pi$
$463$	−4.59145			−0.213383			−0.106691	+	0.994292i	$0.534026\pi$
$464$			24.0120i			1.11473i
$465$	−6.12088	−	20.1805i	−0.283849	−	0.935850i
$466$	5.65318			0.261879
$467$	−32.2257			−1.49123			−0.745613	−	0.666379i	$-0.767843\pi$
$467$	−32.2257			−1.49123			−0.745613	+	0.666379i	$0.767843\pi$
$468$	−5.66540	−	8.48024i	−0.261883	−	0.391999i
$469$	0.383104	−	7.70935i	0.0176901	−	0.355985i
$470$		−	3.40199i		−	0.156922i
$471$	1.29707	+	4.27646i	0.0597661	+	0.197049i
$472$		−	8.21538i		−	0.378143i
$473$		−	10.9417i		−	0.503098i
$474$	0.504418	+	1.66307i	0.0231687	+	0.0763871i
$475$			15.6207i			0.716728i
$476$	1.33698	−	26.9045i	0.0612803	−	1.23317i
$477$	−16.6221	−	24.8808i	−0.761075	−	1.13921i
$478$	−3.77049			−0.172458
$479$	−35.5761			−1.62551			−0.812756	−	0.582604i	$-0.802034\pi$
$479$	−35.5761			−1.62551			−0.812756	+	0.582604i	$0.802034\pi$
$480$	−2.67768	−	8.82832i	−0.122219	−	0.402956i
$481$			1.83544i			0.0836890i
$482$	4.61640			0.210271
$483$	32.6596	−	8.15988i	1.48606	−	0.371288i
$484$	−1.90404			−0.0865474
$485$			14.1758i			0.643691i
$486$	4.80548	+	0.474203i	0.217981	+	0.0215103i
$487$	−33.5902			−1.52212			−0.761060	−	0.648682i	$-0.775321\pi$
$487$	−33.5902			−1.52212			−0.761060	+	0.648682i	$0.775321\pi$
$488$	−3.22171			−0.145840
$489$	18.2312	−	5.52963i	0.824443	−	0.250059i
$490$	−0.328819	+	3.30031i	−0.0148545	+	0.149093i
$491$		−	43.1793i		−	1.94865i	−0.225138	−	0.974327i	$-0.572283\pi$
$491$		−	43.1793i		−	1.94865i	0.225138	−	0.974327i	$-0.427717\pi$
$492$	5.36333	−	1.62673i	0.241798	−	0.0733387i
$493$		−	37.3965i		−	1.68425i
$494$		−	3.24729i		−	0.146103i
$495$	−2.54903	−	3.81551i	−0.114570	−	0.171495i
$496$			27.3307i			1.22719i
$497$	−22.7332	−	1.12969i	−1.01972	−	0.0506736i
$498$	1.39780	+	4.60855i	0.0626369	+	0.206514i
$499$	−29.6100			−1.32552			−0.662762	−	0.748830i	$-0.730616\pi$
$499$	−29.6100			−1.32552			−0.662762	+	0.748830i	$0.730616\pi$
$500$	22.3098			0.997726
$501$	−20.9803	+	6.36344i	−0.937329	+	0.284298i
$502$		−	1.58667i		−	0.0708164i
$503$	−9.07805			−0.404770			−0.202385	−	0.979306i	$-0.564869\pi$
$503$	−9.07805			−0.404770			−0.202385	+	0.979306i	$0.564869\pi$
$504$	−8.23643	+	4.92957i	−0.366880	+	0.219580i
$505$	−25.4006			−1.13031
$506$			2.27555i			0.101161i
$507$	16.2637	−	4.93287i	0.722296	−	0.219077i
$508$	−15.0731			−0.668759
$509$	11.4120			0.505828			0.252914	−	0.967489i	$-0.418611\pi$
$509$	11.4120			0.505828			0.252914	+	0.967489i	$0.418611\pi$
$510$	1.27370	+	4.19940i	0.0564005	+	0.185952i
$511$	−11.8533	−	0.589033i	−0.524361	−	0.0260573i
$512$			20.2608i			0.895411i
$513$	−23.5814	−	19.3572i	−1.04114	−	0.854639i
$514$		−	1.96448i		−	0.0866493i
$515$			5.41871i			0.238777i
$516$	−34.5311	+	10.4735i	−1.52015	+	0.461069i
$517$			7.18013i			0.315782i
$518$	0.841493	+	0.0418167i	0.0369731	+	0.00183732i
$519$	7.26076	−	2.20223i	0.318712	−	0.0966672i
$520$	−3.30262			−0.144829
$521$	40.7990			1.78744			0.893719	−	0.448627i	$-0.148087\pi$
$521$	40.7990			1.78744			0.893719	+	0.448627i	$0.148087\pi$
$522$	−5.40410	+	3.61032i	−0.236531	+	0.158019i
$523$			10.6257i			0.464631i	0.972640	+	0.232316i	$0.0746302\pi$
$523$			10.6257i			0.464631i	−0.972640	+	0.232316i	$0.925370\pi$
$524$	−0.0815864			−0.00356412
$525$	−2.95525	−	11.8282i	−0.128978	−	0.516227i
$526$	−4.64631			−0.202589
$527$		−	42.5651i		−	1.85416i
$528$	1.72609	+	5.69093i	0.0751186	+	0.247666i
$529$	−30.9634			−1.34623
$530$	−4.72581			−0.205276
$531$	−16.9459	+	11.3211i	−0.735389	+	0.491292i
$532$	29.5415	+	1.46802i	1.28079	+	0.0636466i
$533$		−	3.03424i		−	0.131427i
$534$	0.0963075	+	0.317526i	0.00416763	+	0.0137407i
$535$			4.70671i			0.203489i
$536$		−	3.52823i		−	0.152396i
$537$	2.28438	+	7.53161i	0.0985784	+	0.325013i
$538$			8.42125i			0.363066i
$539$	0.693994	−	6.96551i	0.0298924	−	0.300026i
$540$	−9.60152	+	11.6968i	−0.413184	+	0.503351i
$541$	4.46361			0.191906			0.0959529	−	0.995386i	$-0.469410\pi$
$541$	4.46361			0.191906			0.0959529	+	0.995386i	$0.469410\pi$
$542$	−3.26896			−0.140414
$543$	9.18882	+	30.2956i	0.394330	+	1.30011i
$544$		−	18.6208i		−	0.798362i
$545$	−19.0908			−0.817762
$546$	0.614348	+	2.45890i	0.0262917	+	0.105231i
$547$	11.2009			0.478917			0.239459	−	0.970907i	$-0.423030\pi$
$547$	11.2009			0.478917			0.239459	+	0.970907i	$0.423030\pi$
$548$			31.6543i			1.35221i
$549$	4.43962	+	6.64543i	0.189478	+	0.283620i
$550$	0.824133			0.0351412
$551$	41.0618			1.74929
$552$	14.7249	−	4.46615i	0.626733	−	0.190092i
$553$	−0.425337	+	8.55923i	−0.0180872	+	0.363975i
$554$			3.56288i			0.151372i
$555$	2.60623	−	0.790486i	0.110628	−	0.0335542i
$556$		−	14.4449i		−	0.612600i
$557$		−	26.7712i		−	1.13433i	−0.823603	−	0.567167i	$-0.808039\pi$
$557$		−	26.7712i		−	1.13433i	0.823603	−	0.567167i	$-0.191961\pi$
$558$	−6.15100	+	4.10930i	−0.260393	+	0.173961i
$559$			19.5355i			0.826264i
$560$	0.689618	−	13.8775i	0.0291417	−	0.586430i
$561$	−2.68823	−	8.86309i	−0.113497	−	0.374200i
$562$	6.36946			0.268680
$563$	43.7568			1.84413			0.922064	−	0.387037i	$-0.126501\pi$
$563$	43.7568			1.84413			0.922064	+	0.387037i	$0.126501\pi$
$564$	22.6600	−	6.87291i	0.954157	−	0.289402i
$565$		−	15.8832i		−	0.668210i
$566$	6.09088			0.256019
$567$	21.5183	+	10.1962i	0.903684	+	0.428201i
$568$	−10.4040			−0.436542
$569$		−	4.40585i		−	0.184703i	−0.995726	−	0.0923515i	$-0.970562\pi$
$569$		−	4.40585i		−	0.184703i	0.995726	−	0.0923515i	$-0.0294383\pi$
$570$	−4.61098	+	1.39854i	−0.193133	+	0.0585784i
$571$	1.01701			0.0425603			0.0212802	−	0.999774i	$-0.493226\pi$
$571$	1.01701			0.0425603			0.0212802	+	0.999774i	$0.493226\pi$
$572$	3.39953			0.142141
$573$	−5.96349	−	19.6616i	−0.249128	−	0.821377i
$574$	−1.39110	−	0.0691286i	−0.0580634	−	0.00288537i
$575$			19.5438i			0.815033i
$576$	14.4389	−	9.64623i	0.601622	−	0.401926i
$577$			31.5090i			1.31174i	0.754875	+	0.655869i	$0.227698\pi$
$577$			31.5090i			1.31174i	−0.754875	+	0.655869i	$0.772302\pi$
$578$			3.59136i			0.149381i
$579$	26.1684	−	7.93703i	1.08752	−	0.329852i
$580$		−	20.3674i		−	0.845712i
$581$	−1.17866	+	23.7186i	−0.0488990	+	0.984014i
$582$	4.75853	−	1.44329i	0.197248	−	0.0598264i
$583$	9.97413			0.413086
$584$	−5.42475			−0.224478
$585$	4.55111	+	6.81232i	0.188165	+	0.281655i
$586$		−	8.57374i		−	0.354178i
$587$	−18.0891			−0.746617			−0.373309	−	0.927707i	$-0.621777\pi$
$587$	−18.0891			−0.746617			−0.373309	+	0.927707i	$0.621777\pi$
$588$	−22.6470	+	4.47728i	−0.933945	+	0.184640i
$589$	46.7370			1.92576
$590$			3.21867i			0.132511i
$591$	−3.40653	−	11.2313i	−0.140126	−	0.461995i
$592$	−3.52965			−0.145068
$593$	7.63812			0.313660			0.156830	−	0.987626i	$-0.449873\pi$
$593$	7.63812			0.313660			0.156830	+	0.987626i	$0.449873\pi$
$594$	−1.02126	+	1.24413i	−0.0419029	+	0.0510472i
$595$	−1.07402	+	21.6128i	−0.0440304	+	0.886040i
$596$		−	6.31718i		−	0.258762i
$597$	3.48212	+	11.4806i	0.142514	+	0.469868i
$598$		−	4.06284i		−	0.166142i
$599$		−	8.08842i		−	0.330484i	−0.986253	−	0.165242i	$-0.947160\pi$
$599$		−	8.08842i		−	0.330484i	0.986253	−	0.165242i	$-0.0528405\pi$
$600$	−1.61750	−	5.33289i	−0.0660340	−	0.217714i
$601$		−	7.02002i		−	0.286353i	−0.989697	−	0.143176i	$-0.954268\pi$
$601$		−	7.02002i		−	0.286353i	0.989697	−	0.143176i	$-0.0457316\pi$
$602$	8.95642	+	0.445075i	0.365036	+	0.0181399i
$603$	−7.27769	+	4.86201i	−0.296370	+	0.197996i
$604$	−14.1073			−0.574017
$605$	1.52955			0.0621850
$606$	2.58613	+	8.52647i	0.105054	+	0.346364i
$607$		−	18.9533i		−	0.769290i	−0.923065	−	0.384645i	$-0.874324\pi$
$607$		−	18.9533i		−	0.769290i	0.923065	−	0.384645i	$-0.125676\pi$
$608$	20.4459			0.829190
$609$	−31.0926	+	7.76839i	−1.25994	+	0.314791i
$610$	1.26222			0.0511058
$611$		−	12.8196i		−	0.518625i
$612$	−25.3981	+	16.9677i	−1.02666	+	0.685879i
$613$	29.0589			1.17368			0.586838	−	0.809704i	$-0.300372\pi$
$613$	29.0589			1.17368			0.586838	+	0.809704i	$0.300372\pi$
$614$	0.924272			0.0373006
$615$	−4.30845	+	1.30678i	−0.173734	+	0.0526944i
$616$	0.158805	−	3.19570i	0.00639845	−	0.128758i
$617$			22.5816i			0.909103i	0.890720	+	0.454551i	$0.150200\pi$
$617$			22.5816i			0.909103i	−0.890720	+	0.454551i	$0.849800\pi$
$618$	1.81895	−	0.551699i	0.0731689	−	0.0221926i
$619$			36.7173i			1.47579i	0.674914	+	0.737897i	$0.264181\pi$
$619$			36.7173i			1.47579i	−0.674914	+	0.737897i	$0.735819\pi$
$620$		−	23.1824i		−	0.931029i
$621$	−29.5037	−	24.2186i	−1.18394	−	0.971859i
$622$		−	8.26199i		−	0.331275i
$623$	−0.0812088	+	1.63420i	−0.00325356	+	0.0654727i
$624$	−3.08181	−	10.1607i	−0.123371	−	0.406755i
$625$	−4.61947			−0.184779
$626$	−7.10878			−0.284124
$627$	9.73178	−	2.95171i	0.388650	−	0.117880i
$628$			4.91259i			0.196034i
$629$	5.49710			0.219184
$630$	3.22692	−	1.93134i	0.128564	−	0.0769462i
$631$	19.3150			0.768918			0.384459	−	0.923142i	$-0.374388\pi$
$631$	19.3150			0.768918			0.384459	+	0.923142i	$0.374388\pi$
$632$			3.91718i			0.155817i
$633$	−22.7333	+	6.89514i	−0.903567	+	0.274057i
$634$	0.111147			0.00441423
$635$	12.1084			0.480509
$636$	−9.54736	−	31.4776i	−0.378577	−	1.24817i
$637$	−1.23908	+	12.4364i	−0.0490940	+	0.492749i
$638$		−	2.16638i		−	0.0857677i
$639$	14.3370	+	21.4603i	0.567164	+	0.848958i
$640$		−	13.3952i		−	0.529490i
$641$		−	23.1228i		−	0.913295i	−0.889648	−	0.456648i	$-0.849050\pi$
$641$		−	23.1228i		−	0.913295i	0.889648	−	0.456648i	$-0.150950\pi$
$642$	1.57995	−	0.479207i	0.0623555	−	0.0189128i
$643$			17.3528i			0.684326i	0.939641	+	0.342163i	$0.111160\pi$
$643$			17.3528i			0.684326i	−0.939641	+	0.342163i	$0.888840\pi$
$644$	36.9607	+	1.83670i	1.45645	+	0.0723762i
$645$	27.7394	−	8.41352i	1.09224	−	0.331282i
$646$	−9.72556			−0.382647
$647$	1.70554			0.0670516			0.0335258	−	0.999438i	$-0.489326\pi$
$647$	1.70554			0.0670516			0.0335258	+	0.999438i	$0.489326\pi$
$648$	10.0550	+	4.16669i	0.394999	+	0.163683i
$649$		−	6.79321i		−	0.266657i
$650$	−1.47143			−0.0577142
$651$	−35.3899	+	8.84206i	−1.38704	+	0.346547i
$652$	20.9431			0.820196
$653$			28.9224i			1.13182i	0.824467	+	0.565910i	$0.191475\pi$
$653$			28.9224i			1.13182i	−0.824467	+	0.565910i	$0.808525\pi$
$654$	1.94371	+	6.40840i	0.0760049	+	0.250588i
$655$	0.0655397			0.00256085
$656$	5.83499			0.227818
$657$	7.47548	+	11.1897i	0.291646	+	0.436550i
$658$	−5.87738	−	0.292067i	−0.229124	−	0.0113860i
$659$		−	14.9487i		−	0.582320i	−0.956674	−	0.291160i	$-0.905959\pi$
$659$		−	14.9487i		−	0.582320i	0.956674	−	0.291160i	$-0.0940412\pi$
$660$	−1.46410	−	4.82715i	−0.0569901	−	0.187897i
$661$		−	18.2706i		−	0.710644i	−0.934744	−	0.355322i	$-0.884371\pi$
$661$		−	18.2706i		−	0.710644i	0.934744	−	0.355322i	$-0.115629\pi$
$662$			1.83282i			0.0712347i
$663$	4.79964	+	15.8244i	0.186402	+	0.614569i
$664$			10.8550i			0.421254i
$665$	−23.7312	−	1.17928i	−0.920255	−	0.0457306i
$666$	−0.530699	−	0.794376i	−0.0205642	−	0.0307814i
$667$	51.3743			1.98922
$668$	−24.1011			−0.932501
$669$	6.47379	+	21.3441i	0.250291	+	0.825210i
$670$			1.38231i			0.0534033i
$671$	−2.66400			−0.102843
$672$	−15.4819	+	3.86811i	−0.597228	+	0.149216i
$673$	−25.2541			−0.973475			−0.486737	−	0.873548i	$-0.661813\pi$
$673$	−25.2541			−0.973475			−0.486737	+	0.873548i	$0.661813\pi$
$674$		−	1.48310i		−	0.0571267i
$675$	−8.77121	+	10.6853i	−0.337604	+	0.411278i
$676$	18.6830			0.718575
$677$	26.8161			1.03063			0.515313	−	0.857002i	$-0.327676\pi$
$677$	26.8161			1.03063			0.515313	+	0.857002i	$0.327676\pi$
$678$	−5.33165	+	1.61712i	−0.204761	+	0.0621052i
$679$	24.4905	+	1.21702i	0.939861	+	0.0467049i
$680$			9.89124i			0.379312i
$681$	−8.22927	+	2.49599i	−0.315346	+	0.0956465i
$682$		−	2.46579i		−	0.0944201i
$683$		−	23.7243i		−	0.907785i	−0.891057	−	0.453892i	$-0.850035\pi$
$683$		−	23.7243i		−	0.907785i	0.891057	−	0.453892i	$-0.149965\pi$
$684$	−18.6308	−	27.8874i	−0.712365	−	1.06630i
$685$		−	25.4285i		−	0.971571i
$686$	5.67347	+	0.851414i	0.216614	+	0.0325071i
$687$	−1.22497	−	4.03872i	−0.0467355	−	0.154087i
$688$	−37.5678			−1.43226
$689$	−17.8081			−0.678434
$690$	−5.76901	+	1.74978i	−0.219622	+	0.0666128i
$691$		−	33.9271i		−	1.29065i	−0.763909	−	0.645324i	$-0.776722\pi$
$691$		−	33.9271i		−	1.29065i	0.763909	−	0.645324i	$-0.223278\pi$
$692$	8.34081			0.317070
$693$	−6.81062	+	4.07621i	−0.258714	+	0.154842i
$694$	1.67383			0.0635377
$695$			11.6038i			0.440158i
$696$	−14.0184	+	4.25187i	−0.531367	+	0.161167i
$697$	−9.08746			−0.344212
$698$	−3.21220			−0.121584
$699$	−9.17459	−	30.2486i	−0.347015	−	1.14411i
$700$	0.665195	−	13.3860i	0.0251420	−	0.505942i
$701$			29.4861i			1.11367i	0.830622	+	0.556837i	$0.187985\pi$
$701$			29.4861i			1.11367i	−0.830622	+	0.556837i	$0.812015\pi$
$702$	1.82339	−	2.22130i	0.0688194	−	0.0838376i
$703$			6.03588i			0.227648i
$704$			5.78823i			0.218152i
$705$	−18.2031	+	5.52112i	−0.685570	+	0.207937i
$706$		−	1.79800i		−	0.0676688i
$707$	−2.18069	+	43.8828i	−0.0820132	+	1.65038i
$708$	−21.4389	+	6.50254i	−0.805723	+	0.244381i
$709$	11.8547			0.445211			0.222605	−	0.974909i	$-0.428544\pi$
$709$	11.8547			0.445211			0.222605	+	0.974909i	$0.428544\pi$
$710$	4.07614			0.152975
$711$	8.07998	−	5.39800i	0.303023	−	0.202441i
$712$			0.747899i			0.0280287i
$713$	58.4747			2.18990
$714$	7.36434	−	1.83996i	0.275603	−	0.0688586i
$715$	−2.73090			−0.102130
$716$			8.65196i			0.323339i
$717$	6.11916	+	20.1749i	0.228524	+	0.753444i
$718$	6.79021			0.253408
$719$	−35.3278			−1.31751			−0.658753	−	0.752359i	$-0.728916\pi$
$719$	−35.3278			−1.31751			−0.658753	+	0.752359i	$0.728916\pi$
$720$	−13.1004	+	8.75202i	−0.488224	+	0.326168i
$721$	9.36151	+	0.465206i	0.348641	+	0.0173252i
$722$		−	4.79317i		−	0.178383i
$723$	−7.49199	−	24.7011i	−0.278630	−	0.918644i
$724$			34.8021i			1.29341i
$725$		−	18.6061i		−	0.691014i
$726$	−0.155729	−	0.513438i	−0.00577964	−	0.0190555i
$727$		−	39.1244i		−	1.45104i	−0.688200	−	0.725521i	$-0.741599\pi$
$727$		−	39.1244i		−	1.45104i	0.688200	−	0.725521i	$-0.258401\pi$
$728$	−0.283535	+	5.70569i	−0.0105085	+	0.211467i
$729$	−5.26151	−	26.4824i	−0.194871	−	0.980829i
$730$	2.12534			0.0786624
$731$	58.5084			2.16401
$732$	2.55001	+	8.40739i	0.0942512	+	0.310746i
$733$			25.5939i			0.945332i	0.881242	+	0.472666i	$0.156708\pi$
$733$			25.5939i			0.945332i	−0.881242	+	0.472666i	$0.843292\pi$
$734$	2.65130			0.0978612
$735$	18.1927	−	3.59667i	0.671047	−	0.132665i
$736$	25.5808			0.942920
$737$		−	2.91745i		−	0.107466i
$738$	0.877318	+	1.31321i	0.0322945	+	0.0483400i
$739$	19.3001			0.709966			0.354983	−	0.934873i	$-0.384487\pi$
$739$	19.3001			0.709966			0.354983	+	0.934873i	$0.384487\pi$
$740$	2.99392			0.110059
$741$	−17.3754	+	5.27005i	−0.638300	+	0.193600i
$742$	−0.405719	+	8.16444i	−0.0148944	+	0.299726i
$743$			17.6637i			0.648020i	0.946054	+	0.324010i	$0.105031\pi$
$743$			17.6637i			0.648020i	−0.946054	+	0.324010i	$0.894969\pi$
$744$	−15.9559	+	4.83952i	−0.584972	+	0.177425i
$745$			5.07470i			0.185923i
$746$			1.41479i			0.0517992i
$747$	22.3906	−	14.9585i	0.819228	−	0.547302i
$748$		−	10.1815i		−	0.372272i
$749$	8.13144	+	0.404079i	0.297116	+	0.0147647i
$750$	1.82469	+	6.01600i	0.0666282	+	0.219673i
$751$	13.4932			0.492374			0.246187	−	0.969222i	$-0.420822\pi$
$751$	13.4932			0.492374			0.246187	+	0.969222i	$0.420822\pi$
$752$	24.6527			0.898993
$753$	−8.48982	+	2.57501i	−0.309386	+	0.0938387i
$754$			3.86791i			0.140861i
$755$	11.3326			0.412436
$756$	19.3834	+	17.5920i	0.704968	+	0.639816i
$757$	−8.96895			−0.325982			−0.162991	−	0.986628i	$-0.552114\pi$
$757$	−8.96895			−0.325982			−0.162991	+	0.986628i	$0.552114\pi$
$758$			8.61010i			0.312733i
$759$	12.1759	−	3.69301i	0.441956	−	0.134048i
$760$	−10.8607			−0.393959
$761$	−4.15986			−0.150795			−0.0753973	−	0.997154i	$-0.524023\pi$
$761$	−4.15986			−0.150795			−0.0753973	+	0.997154i	$0.524023\pi$
$762$	−1.23280	−	4.06455i	−0.0446597	−	0.147243i
$763$	−1.63898	+	32.9818i	−0.0593351	+	1.19402i
$764$		−	22.5864i		−	0.817146i
$765$	20.4027	−	13.6305i	0.737661	−	0.492810i
$766$		−	7.09770i		−	0.256450i
$767$			12.1288i			0.437945i
$768$	14.6914	−	4.45598i	0.530129	−	0.160791i
$769$		−	35.1795i		−	1.26861i	−0.773084	−	0.634303i	$-0.781287\pi$
$769$		−	35.1795i		−	1.26861i	0.773084	−	0.634303i	$-0.218713\pi$
$770$	−0.0622177	+	1.25203i	−0.00224217	+	0.0451200i
$771$	−10.5114	+	3.18816i	−0.378558	+	0.114819i
$772$	30.0610			1.08192
$773$	−43.0709			−1.54915			−0.774576	−	0.632481i	$-0.782037\pi$
$773$	−43.0709			−1.54915			−0.774576	+	0.632481i	$0.782037\pi$
$774$	−5.64849	−	8.45493i	−0.203031	−	0.303906i
$775$		−	21.1777i		−	0.760725i
$776$	11.2082			0.402352
$777$	−1.14191	−	4.57046i	−0.0409660	−	0.163964i
$778$	−4.80306			−0.172198
$779$		−	9.97813i		−	0.357504i
$780$	2.61405	+	8.61852i	0.0935980	+	0.308593i
$781$	−8.60295			−0.307838
$782$	−12.1681			−0.435130
$783$	28.0882	+	23.0566i	1.00379	+	0.823977i
$784$	−23.9159	−	2.38281i	−0.854138	−	0.0851002i
$785$		−	3.94636i		−	0.140852i
$786$	−0.00667283	−	0.0220003i	−0.000238012	−	0.000784725i
$787$		−	8.87150i		−	0.316235i	−0.987420	−	0.158117i	$-0.949458\pi$
$787$		−	8.87150i		−	0.316235i	0.987420	−	0.158117i	$-0.0505424\pi$
$788$		−	12.9020i		−	0.459615i
$789$	7.54053	+	24.8611i	0.268450	+	0.885080i
$790$		−	1.53470i		−	0.0546021i
$791$	−27.4402	−	1.36360i	−0.975661	−	0.0484839i
$792$	−3.01677	+	2.01541i	−0.107196	+	0.0716146i
$793$	4.75637			0.168904
$794$	−3.23900			−0.114948
$795$	7.66955	+	25.2865i	0.272011	+	0.896820i
$796$			13.1883i			0.467448i
$797$	17.2013			0.609301			0.304650	−	0.952464i	$-0.401460\pi$
$797$	17.2013			0.609301			0.304650	+	0.952464i	$0.401460\pi$
$798$	2.02029	+	8.08613i	0.0715176	+	0.286246i
$799$	−38.3943			−1.35829
$800$		−	9.26454i		−	0.327551i
$801$	1.54269	−	1.03063i	0.0545084	−	0.0364155i
$802$	4.75784			0.168005
$803$	−4.48567			−0.158296
$804$	−9.20728	+	2.79262i	−0.324716	+	0.0984882i
$805$	−29.6911	−	1.47545i	−1.04647	−	0.0520029i
$806$			4.40249i			0.155071i
$807$	45.0598	−	13.6669i	1.58618	−	0.481097i
$808$			20.0832i			0.706525i
$809$		−	45.6731i		−	1.60578i	−0.596126	−	0.802891i	$-0.703294\pi$
$809$		−	45.6731i		−	1.60578i	0.596126	−	0.802891i	$-0.296706\pi$
$810$	−3.93942	−	1.63245i	−0.138417	−	0.0573585i
$811$		−	19.8027i		−	0.695367i	−0.937612	−	0.347683i	$-0.886968\pi$
$811$		−	19.8027i		−	0.695367i	0.937612	−	0.347683i	$-0.113032\pi$
$812$	−35.1873	−	1.74858i	−1.23483	−	0.0613631i
$813$	5.30522	+	17.4913i	0.186062	+	0.613447i
$814$	0.318447			0.0111616
$815$	−16.8240			−0.589318
$816$	−30.4311	+	9.22995i	−1.06530	+	0.323113i
$817$			64.2428i			2.24757i
$818$	−10.1911			−0.356322
$819$	12.1599	−	7.27777i	0.424900	−	0.254306i
$820$	−4.94935			−0.172839
$821$		−	11.1103i		−	0.387751i	−0.981026	−	0.193876i	$-0.937894\pi$
$821$		−	11.1103i		−	0.387751i	0.981026	−	0.193876i	$-0.0621058\pi$
$822$	−8.53581	+	2.58896i	−0.297721	+	0.0903004i
$823$	33.2550			1.15919			0.579597	−	0.814903i	$-0.303210\pi$
$823$	33.2550			1.15919			0.579597	+	0.814903i	$0.303210\pi$
$824$	4.28435			0.149252
$825$	−1.33749	−	4.40971i	−0.0465655	−	0.153526i
$826$	5.56066	+	0.276328i	0.193480	+	0.00961469i
$827$			55.6100i			1.93375i	0.255253	+	0.966874i	$0.417841\pi$
$827$			55.6100i			1.93375i	−0.255253	+	0.966874i	$0.582159\pi$
$828$	−23.3098	−	34.8912i	−0.810071	−	1.21255i
$829$			41.3978i			1.43781i	0.695110	+	0.718903i	$0.255356\pi$
$829$			41.3978i			1.43781i	−0.695110	+	0.718903i	$0.744644\pi$
$830$		−	4.25282i		−	0.147618i
$831$	19.0640	−	5.78223i	0.661323	−	0.200583i
$832$		−	10.3345i		−	0.358283i
$833$	37.2467	+	3.71100i	1.29052	+	0.128578i
$834$	3.89516	−	1.18143i	0.134878	−	0.0409094i
$835$	19.3608			0.670010
$836$	11.1794			0.386648
$837$	31.9702	+	26.2433i	1.10505	+	0.907101i
$838$		−	4.92346i		−	0.170078i
$839$	−33.8886			−1.16997			−0.584983	−	0.811046i	$-0.698899\pi$
$839$	−33.8886			−1.16997			−0.584983	+	0.811046i	$0.698899\pi$
$840$	8.22388	−	2.05471i	0.283751	−	0.0708942i
$841$	−19.9094			−0.686532
$842$		−	1.07124i		−	0.0369173i
$843$	−10.3370	−	34.0812i	−0.356027	−	1.17382i
$844$	−26.1149			−0.898912
$845$	−15.0083			−0.516302
$846$	3.70665	+	5.54829i	0.127437	+	0.190754i
$847$	0.131314	−	2.64249i	0.00451202	−	0.0907971i
$848$		−	34.2458i		−	1.17601i
$849$	−9.88494	−	32.5906i	−0.339250	−	1.11851i
$850$			4.40689i			0.151155i
$851$			7.55177i			0.258871i
$852$	8.23485	+	27.1503i	0.282121	+	0.930154i
$853$		−	48.0064i		−	1.64371i	−0.569698	−	0.821854i	$-0.692940\pi$
$853$		−	48.0064i		−	1.64371i	0.569698	−	0.821854i	$-0.307060\pi$
$854$	0.108364	−	2.18065i	0.00370813	−	0.0746202i
$855$	14.9664	+	22.4024i	0.511840	+	0.766146i
$856$	3.72140			0.127195
$857$	−3.20934			−0.109629			−0.0548144	−	0.998497i	$-0.517457\pi$
$857$	−3.20934			−0.109629			−0.0548144	+	0.998497i	$0.517457\pi$
$858$	0.278042	+	0.916706i	0.00949221	+	0.0312958i
$859$		−	29.6133i		−	1.01039i	−0.863004	−	0.505197i	$-0.831420\pi$
$859$		−	29.6133i		−	1.01039i	0.863004	−	0.505197i	$-0.168580\pi$
$860$	31.8657			1.08661
$861$	1.88774	+	7.55559i	0.0643340	+	0.257494i
$862$	−8.72277			−0.297099
$863$		−	5.46456i		−	0.186016i	−0.995665	−	0.0930079i	$-0.970352\pi$
$863$		−	5.46456i		−	0.186016i	0.995665	−	0.0930079i	$-0.0296482\pi$
$864$	13.9859	+	11.4806i	0.475811	+	0.390577i
$865$	−6.70031			−0.227817
$866$	12.8342			0.436124
$867$	19.2164	−	5.82844i	0.652622	−	0.197944i
$868$	−40.0506	−	1.99025i	−1.35941	−	0.0675535i
$869$			3.23908i			0.109878i
$870$	5.49222	−	1.66582i	0.186204	−	0.0564767i
$871$			5.20890i			0.176497i
$872$			15.0943i			0.511159i
$873$	−15.4453	−	23.1193i	−0.522745	−	0.782469i
$874$		−	13.3607i		−	0.451932i
$875$	−1.53862	+	30.9623i	−0.0520149	+	1.04672i
$876$	4.29374	+	14.1565i	0.145072	+	0.478302i
$877$	−30.9585			−1.04539			−0.522697	−	0.852519i	$-0.675074\pi$
$877$	−30.9585			−1.04539			−0.522697	+	0.852519i	$0.675074\pi$
$878$	10.1614			0.342931
$879$	−45.8757	+	13.9144i	−1.54735	+	0.469320i
$880$		−	5.25166i		−	0.177033i
$881$	−14.8915			−0.501708			−0.250854	−	0.968025i	$-0.580711\pi$
$881$	−14.8915			−0.501708			−0.250854	+	0.968025i	$0.580711\pi$
$882$	−3.05959	−	5.74072i	−0.103022	−	0.193300i
$883$	−21.7631			−0.732388			−0.366194	−	0.930539i	$-0.619339\pi$
$883$	−21.7631			−0.732388			−0.366194	+	0.930539i	$0.619339\pi$
$884$			18.1783i			0.611403i
$885$	17.2222	−	5.22360i	0.578919	−	0.175589i
$886$	−8.21539			−0.276001
$887$	−7.63375			−0.256316			−0.128158	−	0.991754i	$-0.540906\pi$
$887$	−7.63375			−0.256316			−0.128158	+	0.991754i	$0.540906\pi$
$888$	−0.625004	−	2.06064i	−0.0209738	−	0.0691505i
$889$	1.03953	−	20.9189i	0.0348647	−	0.701596i
$890$		−	0.293017i		−	0.00982194i
$891$	8.31440	+	3.44539i	0.278543	+	0.115425i
$892$			24.5191i			0.820959i
$893$		−	42.1574i		−	1.41074i
$894$	1.70347	−	0.516673i	0.0569726	−	0.0172801i
$895$		−	6.95026i		−	0.232322i
$896$	−23.1418	−	1.15000i	−0.773114	−	0.0384187i
$897$	−21.7391	+	6.59360i	−0.725848	+	0.220154i
$898$	−4.19792			−0.140086
$899$	−55.6692			−1.85667
$900$	−12.6365	+	8.44206i	−0.421216	+	0.281402i
$901$			53.3347i			1.77684i
$902$	−0.526436			−0.0175284
$903$	−12.1540	−	48.6456i	−0.404458	−	1.61883i
$904$	−12.5582			−0.417678
$905$		−	27.9571i		−	0.929325i
$906$	−1.15381	−	3.80413i	−0.0383329	−	0.126384i
$907$	24.3248			0.807691			0.403845	−	0.914827i	$-0.367673\pi$
$907$	24.3248			0.807691			0.403845	+	0.914827i	$0.367673\pi$
$908$	−9.45340			−0.313722
$909$	41.4257	−	27.6753i	1.37400	−	0.917932i
$910$	0.111085	−	2.23541i	0.00368243	−	0.0741031i
$911$		−	55.6786i		−	1.84471i	−0.386338	−	0.922357i	$-0.626260\pi$
$911$		−	55.6786i		−	1.84471i	0.386338	−	0.922357i	$-0.373740\pi$
$912$	−10.1346	−	33.4137i	−0.335590	−	1.10644i
$913$			8.97586i			0.297058i
$914$		−	8.99040i		−	0.297376i
$915$	−2.04847	−	6.75380i	−0.0677202	−	0.223274i
$916$		−	4.63949i		−	0.153293i
$917$	0.00562669	−	0.113228i	0.000185810	−	0.00373912i
$918$	−6.65273	−	5.46100i	−0.219573	−	0.180240i
$919$	−34.5297			−1.13903			−0.569515	−	0.821981i	$-0.692869\pi$
$919$	−34.5297			−1.13903			−0.569515	+	0.821981i	$0.692869\pi$
$920$	−13.5883			−0.447993
$921$	−1.50001	−	4.94552i	−0.0494269	−	0.162961i
$922$			4.54066i			0.149539i
$923$	15.3599			0.505579
$924$	−8.46521	+	2.11500i	−0.278485	+	0.0695786i
$925$	2.73501			0.0899265
$926$		−	1.42229i		−	0.0467393i
$927$	−5.90397	−	8.83735i	−0.193912	−	0.290257i
$928$	−24.3534			−0.799441
$929$	−45.5234			−1.49358			−0.746788	−	0.665062i	$-0.768405\pi$
$929$	−45.5234			−1.49358			−0.746788	+	0.665062i	$0.768405\pi$
$930$	6.25130	−	1.89606i	0.204988	−	0.0621742i
$931$	−4.07472	+	40.8973i	−0.133544	+	1.34036i
$932$		−	34.7482i		−	1.13821i
$933$	−44.2076	+	13.4084i	−1.44729	+	0.438972i
$934$		−	9.98251i		−	0.326638i
$935$			8.17897i			0.267481i
$936$	5.38621	−	3.59837i	0.176054	−	0.117616i
$937$		−	30.2841i		−	0.989340i	−0.869081	−	0.494670i	$-0.835289\pi$
$937$		−	30.2841i		−	0.989340i	0.869081	−	0.494670i	$-0.164711\pi$
$938$	2.38812	+	0.118674i	0.0779748	+	0.00387483i
$939$	11.5369	+	38.0371i	0.376492	+	1.24129i
$940$	−20.9109			−0.682038
$941$	26.4415			0.861969			0.430985	−	0.902359i	$-0.358166\pi$
$941$	26.4415			0.861969			0.430985	+	0.902359i	$0.358166\pi$
$942$	−1.32471	+	0.401793i	−0.0431615	+	0.0130911i
$943$		−	12.4841i		−	0.406538i
$944$	−23.3243			−0.759140
$945$	−15.5710	−	14.1320i	−0.506526	−	0.459713i
$946$	3.38938			0.110198
$947$		−	11.1090i		−	0.360993i	−0.983576	−	0.180496i	$-0.942230\pi$
$947$		−	11.1090i		−	0.360993i	0.983576	−	0.180496i	$-0.0577704\pi$
$948$	10.2223	−	3.10048i	0.332005	−	0.100699i
$949$	8.00884			0.259978
$950$	−4.83882			−0.156992
$951$	−0.180382	−	0.594719i	−0.00584928	−	0.0192851i
$952$	17.0884	+	0.849180i	0.553837	+	0.0275221i
$953$			42.0838i			1.36323i	0.731711	+	0.681614i	$0.238722\pi$
$953$			42.0838i			1.36323i	−0.731711	+	0.681614i	$0.761278\pi$
$954$	7.70730	−	5.14902i	0.249533	−	0.166706i
$955$			18.1440i			0.587126i
$956$			23.1759i			0.749563i
$957$	−11.5917	+	3.51583i	−0.374706	+	0.113651i
$958$		−	11.0204i		−	0.356052i
$959$	−43.9309	−	2.18308i	−1.41860	−	0.0704952i
$960$	−14.6744	+	4.45083i	−0.473614	+	0.143650i
$961$	−32.3632			−1.04398
$962$	−0.568563			−0.0183312
$963$	−5.12821	−	7.67615i	−0.165254	−	0.247360i
$964$		−	28.3755i		−	0.913912i
$965$	−24.1485			−0.777368
$966$	2.52768	+	10.1169i	0.0813267	+	0.325506i
$967$	54.0265			1.73737			0.868687	−	0.495362i	$-0.164964\pi$
$967$	54.0265			1.73737			0.868687	+	0.495362i	$0.164964\pi$
$968$		−	1.20935i		−	0.0388700i
$969$	15.7837	+	52.0388i	0.507045	+	1.67173i
$970$	−4.39123			−0.140994
$971$	33.7859			1.08424			0.542121	−	0.840300i	$-0.317621\pi$
$971$	33.7859			1.08424			0.542121	+	0.840300i	$0.317621\pi$
$972$	2.91476	−	29.5376i	0.0934911	−	0.947420i
$973$	20.0471	+	0.996207i	0.642679	+	0.0319369i
$974$		−	10.4052i		−	0.333404i
$975$	2.38799	+	7.87321i	0.0764770	+	0.252145i
$976$			9.14675i			0.292780i
$977$		−	11.4408i		−	0.366024i	−0.983111	−	0.183012i	$-0.941415\pi$
$977$		−	11.4408i		−	0.366024i	0.983111	−	0.183012i	$-0.0585847\pi$
$978$	1.71291	+	5.64746i	0.0547727	+	0.180586i
$979$			0.618430i			0.0197651i
$980$	20.2859	+	2.02114i	0.648008	+	0.0645629i
$981$	31.1351	−	20.8005i	0.994068	−	0.664108i
$982$	13.3756			0.426833
$983$	38.1822			1.21782			0.608911	−	0.793238i	$-0.291607\pi$
$983$	38.1822			1.21782			0.608911	+	0.793238i	$0.291607\pi$
$984$	1.03322	+	3.40651i	0.0329377	+	0.108596i
$985$			10.3644i			0.330237i
$986$	11.5843			0.368919
$987$	7.97566	+	31.9222i	0.253868	+	1.01610i
$988$	−19.9600			−0.635012
$989$			80.3771i			2.55584i
$990$	1.18193	−	0.789611i	0.0375641	−	0.0250955i
$991$	−7.72743			−0.245470			−0.122735	−	0.992439i	$-0.539167\pi$
$991$	−7.72743			−0.245470			−0.122735	+	0.992439i	$0.539167\pi$
$992$	−27.7193			−0.880090
$993$	9.80694	−	2.97450i	0.311214	−	0.0943930i
$994$	0.349943	−	7.04204i	0.0110995	−	0.223360i
$995$		−	10.5944i		−	0.335865i
$996$	28.3272	−	8.59180i	0.897581	−	0.272242i
$997$			0.399776i			0.0126610i	0.999980	+	0.00633051i	$0.00201508\pi$
$997$			0.399776i			0.0126610i	−0.999980	+	0.00633051i	$0.997985\pi$
$998$		−	9.17224i		−	0.290342i
$999$	−3.38921	+	4.12882i	−0.107230	+	0.130630i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.e.a.188.16	yes	28
3.2	odd	2	inner	231.2.e.a.188.13	✓	28
7.6	odd	2	inner	231.2.e.a.188.15	yes	28
21.20	even	2	inner	231.2.e.a.188.14	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.e.a.188.13	✓	28	3.2	odd	2	inner
231.2.e.a.188.14	yes	28	21.20	even	2	inner
231.2.e.a.188.15	yes	28	7.6	odd	2	inner
231.2.e.a.188.16	yes	28	1.1	even	1	trivial

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.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.309769i q^{2} +(1.65749 - 0.502726i) q^{3} +1.90404 q^{4} -1.52955 q^{5} +(0.155729 + 0.513438i) q^{6} +(-0.131314 + 2.64249i) q^{7} +1.20935i q^{8} +(2.49453 - 1.66652i) q^{9} +O(q^{10})\)	\(q+0.309769i q^{2} +(1.65749 - 0.502726i) q^{3} +1.90404 q^{4} -1.52955 q^{5} +(0.155729 + 0.513438i) q^{6} +(-0.131314 + 2.64249i) q^{7} +1.20935i q^{8} +(2.49453 - 1.66652i) q^{9} -0.473807i q^{10} +1.00000i q^{11} +(3.15593 - 0.957212i) q^{12} -1.78543i q^{13} +(-0.818561 - 0.0406771i) q^{14} +(-2.53521 + 0.768944i) q^{15} +3.43347 q^{16} -5.34730 q^{17} +(0.516238 + 0.772729i) q^{18} -5.87140i q^{19} -2.91233 q^{20} +(1.11080 + 4.44591i) q^{21} -0.309769 q^{22} -7.34598i q^{23} +(0.607972 + 2.00449i) q^{24} -2.66048 q^{25} +0.553070 q^{26} +(3.29685 - 4.01631i) q^{27} +(-0.250028 + 5.03142i) q^{28} +6.99353i q^{29} +(-0.238195 - 0.785329i) q^{30} +7.96010i q^{31} +3.48228i q^{32} +(0.502726 + 1.65749i) q^{33} -1.65643i q^{34} +(0.200852 - 4.04182i) q^{35} +(4.74970 - 3.17314i) q^{36} -1.02801 q^{37} +1.81878 q^{38} +(-0.897580 - 2.95932i) q^{39} -1.84976i q^{40} +1.69945 q^{41} +(-1.37721 + 0.344090i) q^{42} -10.9417 q^{43} +1.90404i q^{44} +(-3.81551 + 2.54903i) q^{45} +2.27555 q^{46} +7.18013 q^{47} +(5.69093 - 1.72609i) q^{48} +(-6.96551 - 0.693994i) q^{49} -0.824133i q^{50} +(-8.86309 + 2.68823i) q^{51} -3.39953i q^{52} -9.97413i q^{53} +(1.24413 + 1.02126i) q^{54} -1.52955i q^{55} +(-3.19570 - 0.158805i) q^{56} +(-2.95171 - 9.73178i) q^{57} -2.16638 q^{58} -6.79321 q^{59} +(-4.82715 + 1.46410i) q^{60} +2.66400i q^{61} -2.46579 q^{62} +(4.07621 + 6.81062i) q^{63} +5.78823 q^{64} +2.73090i q^{65} +(-0.513438 + 0.155729i) q^{66} -2.91745 q^{67} -10.1815 q^{68} +(-3.69301 - 12.1759i) q^{69} +(1.25203 + 0.0622177i) q^{70} +8.60295i q^{71} +(2.01541 + 3.01677i) q^{72} +4.48567i q^{73} -0.318447i q^{74} +(-4.40971 + 1.33749i) q^{75} -11.1794i q^{76} +(-2.64249 - 0.131314i) q^{77} +(0.916706 - 0.278042i) q^{78} +3.23908 q^{79} -5.25166 q^{80} +(3.44539 - 8.31440i) q^{81} +0.526436i q^{82} +8.97586 q^{83} +(2.11500 + 8.46521i) q^{84} +8.17897 q^{85} -3.38938i q^{86} +(3.51583 + 11.5917i) q^{87} -1.20935 q^{88} +0.618430 q^{89} +(-0.789611 - 1.18193i) q^{90} +(4.71797 + 0.234452i) q^{91} -13.9871i q^{92} +(4.00175 + 13.1938i) q^{93} +2.22418i q^{94} +8.98060i q^{95} +(1.75063 + 5.77184i) q^{96} -9.26798i q^{97} +(0.214978 - 2.15770i) q^{98} +(1.66652 + 2.49453i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 32 q^{4} - 8 q^{7} - 8 q^{9}+O(q^{10}) \) 28 * q - 32 * q^4 - 8 * q^7 - 8 * q^9	\( 28 q - 32 q^{4} - 8 q^{7} - 8 q^{9} - 20 q^{15} + 40 q^{16} - 12 q^{18} - 10 q^{21} + 36 q^{25} + 12 q^{28} - 4 q^{30} + 24 q^{36} - 24 q^{37} + 16 q^{39} - 40 q^{43} - 16 q^{46} + 4 q^{49} - 8 q^{51} - 4 q^{57} - 44 q^{58} + 52 q^{60} + 6 q^{63} - 68 q^{64} + 40 q^{67} + 20 q^{70} + 24 q^{72} - 28 q^{78} + 56 q^{79} + 32 q^{81} + 100 q^{84} - 8 q^{85} + 12 q^{88} + 8 q^{91} - 36 q^{93}+O(q^{100}) \) 28 * q - 32 * q^4 - 8 * q^7 - 8 * q^9 - 20 * q^15 + 40 * q^16 - 12 * q^18 - 10 * q^21 + 36 * q^25 + 12 * q^28 - 4 * q^30 + 24 * q^36 - 24 * q^37 + 16 * q^39 - 40 * q^43 - 16 * q^46 + 4 * q^49 - 8 * q^51 - 4 * q^57 - 44 * q^58 + 52 * q^60 + 6 * q^63 - 68 * q^64 + 40 * q^67 + 20 * q^70 + 24 * q^72 - 28 * q^78 + 56 * q^79 + 32 * q^81 + 100 * q^84 - 8 * q^85 + 12 * q^88 + 8 * q^91 - 36 * q^93

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