LMFDB - Embedded newform 189.2.ba.a.101.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(5,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5, 15]))

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

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

chi := DirichletCharacter("189.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.ba (of order $18$, degree $6$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			101.3
Character	$\chi$	$=$	189.101
Dual form			189.2.ba.a.131.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.44973 + 1.72772i) q^{2} +(0.462924 + 1.66904i) q^{3} +(-0.536009 - 3.03986i) q^{4} +(-2.61524 + 2.19445i) q^{5} +(-3.55476 - 1.61986i) q^{6} +(-0.126746 - 2.64271i) q^{7} +(2.12267 + 1.22552i) q^{8} +(-2.57140 + 1.54528i) q^{9} +O(q^{10})$	\(q+(-1.44973 + 1.72772i) q^{2} +(0.462924 + 1.66904i) q^{3} +(-0.536009 - 3.03986i) q^{4} +(-2.61524 + 2.19445i) q^{5} +(-3.55476 - 1.61986i) q^{6} +(-0.126746 - 2.64271i) q^{7} +(2.12267 + 1.22552i) q^{8} +(-2.57140 + 1.54528i) q^{9} -7.69979i q^{10} +(1.63538 - 1.94897i) q^{11} +(4.82552 - 2.30185i) q^{12} +(-2.11236 + 5.80365i) q^{13} +(4.74963 + 3.61225i) q^{14} +(-4.87329 - 3.34909i) q^{15} +(0.606533 - 0.220760i) q^{16} -2.39853 q^{17} +(1.05803 - 6.68292i) q^{18} +1.24485i q^{19} +(8.07261 + 6.77373i) q^{20} +(4.35213 - 1.43492i) q^{21} +(0.996420 + 5.65098i) q^{22} +(0.769210 - 2.11339i) q^{23} +(-1.06281 + 4.11015i) q^{24} +(1.15565 - 6.55401i) q^{25} +(-6.96475 - 12.0633i) q^{26} +(-3.76950 - 3.57643i) q^{27} +(-7.96554 + 1.80181i) q^{28} +(0.685884 + 1.88445i) q^{29} +(12.8513 - 3.56442i) q^{30} +(-1.55132 + 0.273539i) q^{31} +(-2.17451 + 5.97442i) q^{32} +(4.00997 + 1.82729i) q^{33} +(3.47723 - 4.14400i) q^{34} +(6.13078 + 6.63320i) q^{35} +(6.07573 + 6.98842i) q^{36} +(-5.01223 + 8.68144i) q^{37} +(-2.15077 - 1.80471i) q^{38} +(-10.6644 - 0.838960i) q^{39} +(-8.24065 + 1.45305i) q^{40} +(-5.39584 - 1.96393i) q^{41} +(-3.83027 + 9.59952i) q^{42} +(-0.110284 + 0.625454i) q^{43} +(-6.80118 - 3.92666i) q^{44} +(3.33380 - 9.68410i) q^{45} +(2.53620 + 4.39283i) q^{46} +(-2.09655 + 11.8901i) q^{47} +(0.649236 + 0.910134i) q^{48} +(-6.96787 + 0.669906i) q^{49} +(9.64814 + 11.4982i) q^{50} +(-1.11034 - 4.00325i) q^{51} +(18.7745 + 3.31045i) q^{52} +(4.15350 + 2.39802i) q^{53} +(11.6439 - 1.32779i) q^{54} +8.68580i q^{55} +(2.96967 - 5.76493i) q^{56} +(-2.07772 + 0.576273i) q^{57} +(-4.25016 - 1.54693i) q^{58} +(2.59194 + 0.943390i) q^{59} +(-7.56863 + 16.6093i) q^{60} +(7.26032 + 1.28019i) q^{61} +(1.77639 - 3.07681i) q^{62} +(4.40965 + 6.59962i) q^{63} +(-6.52423 - 11.3003i) q^{64} +(-7.21149 - 19.8134i) q^{65} +(-8.97045 + 4.27904i) q^{66} +(-6.14145 + 5.15329i) q^{67} +(1.28564 + 7.29120i) q^{68} +(3.88342 + 0.305506i) q^{69} +(-20.3483 + 0.975916i) q^{70} +(4.45847 - 2.57410i) q^{71} +(-7.35201 + 0.128804i) q^{72} +(11.6132 - 6.70488i) q^{73} +(-7.73274 - 21.2455i) q^{74} +(11.4739 - 1.10518i) q^{75} +(3.78418 - 0.667254i) q^{76} +(-5.35785 - 4.07482i) q^{77} +(16.9100 - 17.2089i) q^{78} +(0.740362 + 0.621237i) q^{79} +(-1.10178 + 1.90835i) q^{80} +(4.22422 - 7.94707i) q^{81} +(11.2156 - 6.47536i) q^{82} +(-2.38230 + 0.867085i) q^{83} +(-6.69474 - 12.4607i) q^{84} +(6.27275 - 5.26346i) q^{85} +(-0.920729 - 1.09728i) q^{86} +(-2.82772 + 2.01713i) q^{87} +(5.85988 - 2.13282i) q^{88} -9.95066 q^{89} +(11.8983 + 19.7992i) q^{90} +(15.6051 + 4.84676i) q^{91} +(-6.83671 - 1.20550i) q^{92} +(-1.17469 - 2.46259i) q^{93} +(-17.5034 - 20.8598i) q^{94} +(-2.73177 - 3.25560i) q^{95} +(-10.9782 - 0.863647i) q^{96} +(7.93719 + 1.39954i) q^{97} +(8.94414 - 13.0097i) q^{98} +(-1.19352 + 7.53871i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.44973	+	1.72772i	−1.02512	+	1.22169i	−0.0502858	+	0.998735i	$0.516013\pi$
$2$	−1.44973	+	1.72772i	−1.02512	+	1.22169i	−0.974830	+	0.222950i	$0.928431\pi$
$3$	0.462924	+	1.66904i	0.267269	+	0.963622i
$3$	0.462924	+	1.66904i	0.267269	+	0.963622i
$4$	−0.536009	−	3.03986i	−0.268005	−	1.51993i
$5$	−2.61524	+	2.19445i	−1.16957	+	0.981388i	−0.999991	−	0.00412812i	$-0.998686\pi$
$5$	−2.61524	+	2.19445i	−1.16957	+	0.981388i	−0.169581	+	0.985516i	$0.554242\pi$
$6$	−3.55476	−	1.61986i	−1.45122	−	0.661305i
$7$	−0.126746	−	2.64271i	−0.0479054	−	0.998852i
$7$	−0.126746	−	2.64271i	−0.0479054	−	0.998852i
$8$	2.12267	+	1.22552i	0.750477	+	0.433288i
$9$	−2.57140	+	1.54528i	−0.857134	+	0.515093i
$10$		−	7.69979i		−	2.43489i
$11$	1.63538	−	1.94897i	0.493086	−	0.587637i	−0.460913	−	0.887445i	$-0.652478\pi$
$11$	1.63538	−	1.94897i	0.493086	−	0.587637i	0.954000	+	0.299808i	$0.0969226\pi$
$12$	4.82552	−	2.30185i	1.39301	−	0.664486i
$13$	−2.11236	+	5.80365i	−0.585862	+	1.60964i	0.192131	+	0.981369i	$0.438460\pi$
$13$	−2.11236	+	5.80365i	−0.585862	+	1.60964i	−0.777993	+	0.628273i	$0.783762\pi$
$14$	4.74963	+	3.61225i	1.26939	+	0.965413i
$15$	−4.87329	−	3.34909i	−1.25828	−	0.864731i
$16$	0.606533	−	0.220760i	0.151633	−	0.0551900i
$17$	−2.39853			−0.581730			−0.290865	−	0.956764i	$-0.593943\pi$
$17$	−2.39853			−0.581730			−0.290865	+	0.956764i	$0.593943\pi$
$18$	1.05803	−	6.68292i	0.249380	−	1.57518i
$19$			1.24485i			0.285589i	0.989752	+	0.142795i	$0.0456089\pi$
$19$			1.24485i			0.285589i	−0.989752	+	0.142795i	$0.954391\pi$
$20$	8.07261	+	6.77373i	1.80509	+	1.51465i
$21$	4.35213	−	1.43492i	0.949712	−	0.313125i
$22$	0.996420	+	5.65098i	0.212437	+	1.20479i
$23$	0.769210	−	2.11339i	0.160391	−	0.440672i	−0.833300	−	0.552821i	$-0.813551\pi$
$23$	0.769210	−	2.11339i	0.160391	−	0.440672i	0.993691	+	0.112149i	$0.0357735\pi$
$24$	−1.06281	+	4.11015i	−0.216946	+	0.838980i
$25$	1.15565	−	6.55401i	0.231130	−	1.31080i
$26$	−6.96475	−	12.0633i	−1.36590	−	2.36581i
$27$	−3.76950	−	3.57643i	−0.725441	−	0.688284i
$28$	−7.96554	+	1.80181i	−1.50535	+	0.340510i
$29$	0.685884	+	1.88445i	0.127366	+	0.349934i	0.986943	−	0.161072i	$-0.0514952\pi$
$29$	0.685884	+	1.88445i	0.127366	+	0.349934i	−0.859577	+	0.511006i	$0.829273\pi$
$30$	12.8513	−	3.56442i	2.34631	−	0.650771i
$31$	−1.55132	+	0.273539i	−0.278625	+	0.0491291i	−0.311214	−	0.950340i	$-0.600736\pi$
$31$	−1.55132	+	0.273539i	−0.278625	+	0.0491291i	0.0325896	+	0.999469i	$0.489625\pi$
$32$	−2.17451	+	5.97442i	−0.384403	+	1.05614i
$33$	4.00997	+	1.82729i	0.698047	+	0.318091i
$34$	3.47723	−	4.14400i	0.596340	−	0.710691i
$35$	6.13078	+	6.63320i	1.03629	+	1.12122i
$36$	6.07573	+	6.98842i	1.01262	+	1.16474i
$37$	−5.01223	+	8.68144i	−0.824006	+	1.42722i	0.0786706	+	0.996901i	$0.474932\pi$
$37$	−5.01223	+	8.68144i	−0.824006	+	1.42722i	−0.902677	+	0.430320i	$0.858401\pi$
$38$	−2.15077	−	1.80471i	−0.348900	−	0.292762i
$39$	−10.6644	−	0.838960i	−1.70767	−	0.134341i
$40$	−8.24065	+	1.45305i	−1.30296	+	0.229747i
$41$	−5.39584	−	1.96393i	−0.842689	−	0.306714i	−0.115633	−	0.993292i	$-0.536890\pi$
$41$	−5.39584	−	1.96393i	−0.842689	−	0.306714i	−0.727056	+	0.686578i	$0.759112\pi$
$42$	−3.83027	+	9.59952i	−0.591024	+	1.48124i
$43$	−0.110284	+	0.625454i	−0.0168182	+	0.0953809i	−0.992061	−	0.125754i	$-0.959865\pi$
$43$	−0.110284	+	0.625454i	−0.0168182	+	0.0953809i	0.975243	+	0.221135i	$0.0709761\pi$
$44$	−6.80118	−	3.92666i	−1.02532	−	0.591967i
$45$	3.33380	−	9.68410i	0.496974	−	1.44362i
$46$	2.53620	+	4.39283i	0.373943	+	0.647687i
$47$	−2.09655	+	11.8901i	−0.305813	+	1.73435i	0.313839	+	0.949476i	$0.398385\pi$
$47$	−2.09655	+	11.8901i	−0.305813	+	1.73435i	−0.619653	+	0.784876i	$0.712726\pi$
$48$	0.649236	+	0.910134i	0.0937092	+	0.131366i
$49$	−6.96787	+	0.669906i	−0.995410	+	0.0957009i
$50$	9.64814	+	11.4982i	1.36445	+	1.62609i
$51$	−1.11034	−	4.00325i	−0.155479	−	0.560568i
$52$	18.7745	+	3.31045i	2.60356	+	0.459077i
$53$	4.15350	+	2.39802i	0.570527	+	0.329394i	0.757360	−	0.652998i	$-0.226489\pi$
$53$	4.15350	+	2.39802i	0.570527	+	0.329394i	−0.186833	+	0.982392i	$0.559822\pi$
$54$	11.6439	−	1.32779i	1.58453	−	0.180689i
$55$			8.68580i			1.17119i
$56$	2.96967	−	5.76493i	0.396838	−	0.770372i
$57$	−2.07772	+	0.576273i	−0.275200	+	0.0763293i
$58$	−4.25016	−	1.54693i	−0.558074	−	0.203122i
$59$	2.59194	+	0.943390i	0.337442	+	0.122819i	0.505183	−	0.863012i	$-0.331425\pi$
$59$	2.59194	+	0.943390i	0.337442	+	0.122819i	−0.167741	+	0.985831i	$0.553647\pi$
$60$	−7.56863	+	16.6093i	−0.977106	+	2.14425i
$61$	7.26032	+	1.28019i	0.929589	+	0.163912i	0.617886	−	0.786268i	$-0.287989\pi$
$61$	7.26032	+	1.28019i	0.929589	+	0.163912i	0.311703	+	0.950179i	$0.399100\pi$
$62$	1.77639	−	3.07681i	0.225602	−	0.390755i
$63$	4.40965	+	6.59962i	0.555563	+	0.831474i
$64$	−6.52423	−	11.3003i	−0.815529	−	1.41254i
$65$	−7.21149	−	19.8134i	−0.894476	−	2.45755i
$66$	−8.97045	+	4.27904i	−1.10419	+	0.526713i
$67$	−6.14145	+	5.15329i	−0.750298	+	0.629574i	−0.935582	−	0.353111i	$-0.885124\pi$
$67$	−6.14145	+	5.15329i	−0.750298	+	0.629574i	0.185284	+	0.982685i	$0.440680\pi$
$68$	1.28564	+	7.29120i	0.155906	+	0.884188i
$69$	3.88342	+	0.305506i	0.467509	+	0.0367786i
$70$	−20.3483	+	0.975916i	−2.43209	+	0.116644i
$71$	4.45847	−	2.57410i	0.529123	−	0.305489i	−0.211536	−	0.977370i	$-0.567847\pi$
$71$	4.45847	−	2.57410i	0.529123	−	0.305489i	0.740659	+	0.671881i	$0.234513\pi$
$72$	−7.35201	+	0.128804i	−0.866443	+	0.0151797i
$73$	11.6132	−	6.70488i	1.35922	−	0.784747i	0.369702	−	0.929150i	$-0.379460\pi$
$73$	11.6132	−	6.70488i	1.35922	−	0.784747i	0.989519	+	0.144403i	$0.0461263\pi$
$74$	−7.73274	−	21.2455i	−0.898912	−	2.46974i
$75$	11.4739	−	1.10518i	1.32489	−	0.127616i
$76$	3.78418	−	0.667254i	0.434076	−	0.0765392i
$77$	−5.35785	−	4.07482i	−0.610584	−	0.464369i
$78$	16.9100	−	17.2089i	1.91468	−	1.94852i
$79$	0.740362	+	0.621237i	0.0832972	+	0.0698946i	0.683485	−	0.729964i	$-0.260463\pi$
$79$	0.740362	+	0.621237i	0.0832972	+	0.0698946i	−0.600188	+	0.799859i	$0.704908\pi$
$80$	−1.10178	+	1.90835i	−0.123183	+	0.213360i
$81$	4.22422	−	7.94707i	0.469358	−	0.883008i
$82$	11.2156	−	6.47536i	1.23856	−	0.715084i
$83$	−2.38230	+	0.867085i	−0.261491	+	0.0951749i	−0.469439	−	0.882965i	$-0.655544\pi$
$83$	−2.38230	+	0.867085i	−0.261491	+	0.0951749i	0.207948	+	0.978140i	$0.433322\pi$
$84$	−6.69474	−	12.4607i	−0.730456	−	1.35958i
$85$	6.27275	−	5.26346i	0.680375	−	0.570903i
$86$	−0.920729	−	1.09728i	−0.0992848	−	0.118323i
$87$	−2.82772	+	2.01713i	−0.303163	+	0.216259i
$88$	5.85988	−	2.13282i	0.624666	−	0.227360i
$89$	−9.95066			−1.05477			−0.527384	−	0.849627i	$-0.676827\pi$
$89$	−9.95066			−1.05477			−0.527384	+	0.849627i	$0.676827\pi$
$90$	11.8983	+	19.7992i	1.25419	+	2.08702i
$91$	15.6051	+	4.84676i	1.63586	+	0.508079i
$92$	−6.83671	−	1.20550i	−0.712776	−	0.125682i
$93$	−1.17469	−	2.46259i	−0.121810	−	0.255358i
$94$	−17.5034	−	20.8598i	−1.80534	−	2.15152i
$95$	−2.73177	−	3.25560i	−0.280274	−	0.334017i
$96$	−10.9782	−	0.863647i	−1.12046	−	0.0881456i
$97$	7.93719	+	1.39954i	0.805899	+	0.142102i	0.561397	−	0.827547i	$-0.310264\pi$
$97$	7.93719	+	1.39954i	0.805899	+	0.142102i	0.244503	+	0.969649i	$0.421375\pi$
$98$	8.94414	−	13.0097i	0.903494	−	1.31418i
$99$	−1.19352	+	7.53871i	−0.119953	+	0.757669i
$100$	−20.5427			−2.05427
$101$	1.74962	−	0.636808i	0.174093	−	0.0633648i	−0.253503	−	0.967335i	$-0.581583\pi$
$101$	1.74962	−	0.636808i	0.174093	−	0.0633648i	0.427596	+	0.903970i	$0.359361\pi$
$102$	8.52621	+	3.88529i	0.844221	+	0.384701i
$103$	8.55538	+	10.1959i	0.842987	+	1.00463i	0.999855	+	0.0170129i	$0.00541563\pi$
$103$	8.55538	+	10.1959i	0.842987	+	1.00463i	−0.156869	+	0.987619i	$0.550140\pi$
$104$	−11.5963	+	9.73048i	−1.13711	+	0.954152i
$105$	−8.23301	+	13.3032i	−0.803460	+	1.29826i
$106$	−10.1646	+	3.69960i	−0.987271	+	0.359337i
$107$	8.41217	−	4.85677i	0.813235	−	0.469521i	−0.0348431	−	0.999393i	$-0.511093\pi$
$107$	8.41217	−	4.85677i	0.813235	−	0.469521i	0.848078	+	0.529871i	$0.177760\pi$
$108$	−8.85136	+	13.3758i	−0.851722	+	1.28708i
$109$	−3.57501	+	6.19210i	−0.342424	+	0.593095i	−0.984882	−	0.173225i	$-0.944581\pi$
$109$	−3.57501	+	6.19210i	−0.342424	+	0.593095i	0.642459	+	0.766320i	$0.277914\pi$
$110$	−15.0067	−	12.5921i	−1.43083	−	1.20061i
$111$	−16.8100	−	4.34678i	−1.59553	−	0.412578i
$112$	−0.660281	−	1.57491i	−0.0623907	−	0.148815i
$113$	1.44663	−	0.255080i	0.136088	−	0.0239959i	−0.105189	−	0.994452i	$-0.533545\pi$
$113$	1.44663	−	0.255080i	0.136088	−	0.0239959i	0.241277	+	0.970456i	$0.422434\pi$
$114$	2.01649	−	4.42516i	0.188862	−	0.414454i
$115$	2.62605	+	7.21502i	0.244881	+	0.672804i
$116$	5.36083	−	3.09508i	0.497740	−	0.287371i
$117$	−3.53655	−	18.1877i	−0.326954	−	1.68145i
$118$	−5.38754	+	3.11050i	−0.495963	+	0.286345i
$119$	0.304004	+	6.33864i	0.0278680	+	0.581062i
$120$	−6.23999	−	13.0813i	−0.569631	−	1.19416i
$121$	0.786111	+	4.45826i	0.0714646	+	0.405296i
$122$	−12.7373	+	10.6879i	−1.15319	+	0.967637i
$123$	0.780009	−	9.91503i	0.0703310	−	0.894009i
$124$	1.66304	+	4.56916i	0.149345	+	0.410323i
$125$	2.82525	+	4.89347i	0.252698	+	0.437685i
$126$	−17.7951	−	1.94903i	−1.58532	−	0.173634i
$127$	4.42813	−	7.66974i	0.392933	−	0.680580i	−0.599902	−	0.800073i	$-0.704794\pi$
$127$	4.42813	−	7.66974i	0.392933	−	0.680580i	0.992835	+	0.119494i	$0.0381271\pi$
$128$	16.4597	+	2.90229i	1.45484	+	0.256528i
$129$	−1.09496	+	0.105469i	−0.0964061	+	0.00928598i
$130$	44.6868	+	16.2647i	3.91930	+	1.42651i
$131$	17.7882	+	6.47436i	1.55416	+	0.565667i	0.969389	−	0.245532i	$-0.0789626\pi$
$131$	17.7882	+	6.47436i	1.55416	+	0.565667i	0.584770	+	0.811199i	$0.301185\pi$
$132$	3.40533	−	13.1692i	0.296396	−	1.14623i
$133$	3.28980	−	0.157780i	0.285261	−	0.0136813i
$134$		−	18.0816i		−	1.56201i
$135$	17.7065	+	1.08126i	1.52393	+	0.0930597i
$136$	−5.09129	−	2.93946i	−0.436575	−	0.252056i
$137$	1.45083	+	0.255821i	0.123953	+	0.0218562i	0.235280	−	0.971928i	$-0.424399\pi$
$137$	1.45083	+	0.255821i	0.123953	+	0.0218562i	−0.111328	+	0.993784i	$0.535510\pi$
$138$	−6.15775	+	6.26657i	−0.524182	+	0.533446i
$139$	−8.68671	−	10.3524i	−0.736798	−	0.878081i	0.259349	−	0.965784i	$-0.416492\pi$
$139$	−8.68671	−	10.3524i	−0.736798	−	0.878081i	−0.996147	+	0.0877025i	$0.972048\pi$
$140$	16.8779	−	22.1922i	1.42644	−	1.87558i
$141$	−20.8157	+	2.00500i	−1.75299	+	0.168851i
$142$	−2.01626	+	11.4348i	−0.169201	+	0.959584i
$143$	7.85664	+	13.6081i	0.657005	+	1.13797i
$144$	−1.21850	+	1.50493i	−0.101542	+	0.125410i
$145$	−5.92909	−	3.42316i	−0.492384	−	0.284278i
$146$	−5.25184	+	29.7847i	−0.434645	+	2.46500i
$147$	−4.34370	−	11.3196i	−0.358262	−	0.933621i
$148$	29.0770	+	10.5831i	2.39011	+	0.869929i
$149$	15.2390	−	2.68704i	1.24842	−	0.220131i	0.489902	−	0.871778i	$-0.337033\pi$
$149$	15.2390	−	2.68704i	1.24842	−	0.220131i	0.758523	+	0.651647i	$0.225921\pi$
$150$	−14.7246	+	21.4259i	−1.20226	+	1.74942i
$151$	4.29849	+	3.60686i	0.349806	+	0.293522i	0.800712	−	0.599049i	$-0.204455\pi$
$151$	4.29849	+	3.60686i	0.349806	+	0.293522i	−0.450906	+	0.892571i	$0.648899\pi$
$152$	−1.52560	+	2.64241i	−0.123742	+	0.214328i
$153$	6.16759	−	3.70641i	0.498620	−	0.299645i
$154$	14.8076	−	3.34949i	1.19323	−	0.269910i
$155$	3.45680	−	4.11966i	0.277657	−	0.330899i
$156$	3.16589	+	32.8679i	0.253474	+	2.63154i
$157$	−3.72781	+	10.2421i	−0.297512	+	0.817406i	0.697403	+	0.716680i	$0.254339\pi$
$157$	−3.72781	+	10.2421i	−0.297512	+	0.817406i	−0.994914	+	0.100727i	$0.967883\pi$
$158$	−2.14665	+	0.378513i	−0.170779	+	0.0301129i
$159$	−2.07965	+	8.04246i	−0.164927	+	0.637809i
$160$	−7.42370	−	20.3964i	−0.586895	−	1.61248i
$161$	−5.68257	−	1.76494i	−0.447850	−	0.139097i
$162$	7.60636	+	18.8194i	0.597612	+	1.47859i
$163$	−12.6009	−	21.8255i	−0.986982	−	1.70950i	−0.632776	−	0.774335i	$-0.718085\pi$
$163$	−12.6009	−	21.8255i	−0.986982	−	1.70950i	−0.354206	−	0.935168i	$-0.615249\pi$
$164$	−3.07784	+	17.4553i	−0.240339	+	1.36303i
$165$	−14.4970	+	4.02087i	−1.12859	+	0.313024i
$166$	1.95561	−	5.37299i	0.151785	−	0.417025i
$167$	−0.497967	−	2.82411i	−0.0385338	−	0.218536i	0.959460	−	0.281844i	$-0.0909461\pi$
$167$	−0.497967	−	2.82411i	−0.0385338	−	0.218536i	−0.997994	+	0.0633078i	$0.979835\pi$
$168$	10.9966	+	2.28777i	0.848410	+	0.176505i
$169$	−19.2617	−	16.1625i	−1.48167	−	1.24327i
$170$			18.4682i			1.41645i
$171$	−1.92365	−	3.20102i	−0.147105	−	0.244788i
$172$	1.96041			0.149480
$173$	−2.45179	+	0.892379i	−0.186406	+	0.0678463i	−0.433537	−	0.901136i	$-0.642735\pi$
$173$	−2.45179	+	0.892379i	−0.186406	+	0.0678463i	0.247131	+	0.968982i	$0.420512\pi$
$174$	0.614392	−	7.80981i	0.0465769	−	0.592060i
$175$	−17.4668	−	2.22335i	−1.32037	−	0.168070i
$176$	0.561658	−	1.54314i	0.0423366	−	0.116319i
$177$	−0.374684	+	4.76278i	−0.0281630	+	0.357992i
$178$	14.4258	−	17.1920i	1.08126	−	1.28859i
$179$			14.1803i			1.05989i	0.848033	+	0.529944i	$0.177787\pi$
$179$			14.1803i			1.05989i	−0.848033	+	0.529944i	$0.822213\pi$
$180$	−31.2252	−	4.94353i	−2.32739	−	0.368469i
$181$	5.86603	+	3.38675i	0.436018	+	0.251735i	0.701907	−	0.712268i	$-0.252332\pi$
$181$	5.86603	+	3.38675i	0.436018	+	0.251735i	−0.265889	+	0.964004i	$0.585665\pi$
$182$	−30.9971	+	19.9348i	−2.29766	+	1.47767i
$183$	1.22429	+	12.7104i	0.0905019	+	0.939581i
$184$	4.22278	−	3.54334i	0.311308	−	0.261218i
$185$	−5.94278	−	33.7032i	−0.436922	−	2.47791i
$186$	5.95765	+	1.54055i	0.436836	+	0.112959i
$187$	−3.92252	+	4.67467i	−0.286843	+	0.341846i
$188$	37.2681			2.71805
$189$	−8.97371	+	10.4150i	−0.652742	+	0.757581i
$190$	9.58512			0.695377
$191$	−10.7635	+	12.8274i	−0.778819	+	0.928160i	−0.998879	−	0.0473264i	$-0.984930\pi$
$191$	−10.7635	+	12.8274i	−0.778819	+	0.928160i	0.220061	+	0.975486i	$0.429374\pi$
$192$	15.8405	−	16.1204i	1.14319	−	1.16339i
$193$	1.99200	+	11.2972i	0.143387	+	0.813189i	0.968648	+	0.248437i	$0.0799170\pi$
$193$	1.99200	+	11.2972i	0.143387	+	0.813189i	−0.825261	+	0.564752i	$0.808972\pi$
$194$	−13.9248	+	11.6843i	−0.999744	+	0.838885i
$195$	29.7310	−	21.2084i	2.12908	−	1.51876i
$196$	5.77126	+	20.8223i	0.412233	+	1.48730i
$197$	−0.880153	−	0.508156i	−0.0627083	−	0.0362046i	0.468318	−	0.883560i	$-0.344860\pi$
$197$	−0.880153	−	0.508156i	−0.0627083	−	0.0362046i	−0.531026	+	0.847355i	$0.678193\pi$
$198$	−11.2945	−	12.9912i	−0.802668	−	0.923243i
$199$		−	5.48134i		−	0.388562i	−0.980946	−	0.194281i	$-0.937763\pi$
$199$		−	5.48134i		−	0.388562i	0.980946	−	0.194281i	$-0.0622374\pi$
$200$	10.4851	−	12.4957i	0.741412	−	0.883580i
$201$	−11.4441	−	7.86476i	−0.807203	−	0.554737i
$202$	−1.43625	+	3.94605i	−0.101054	+	0.277643i
$203$	4.89313	−	2.05144i	0.343431	−	0.143983i
$204$	−11.5742	+	5.52105i	−0.810354	+	0.386551i
$205$	18.4212	−	6.70476i	1.28659	−	0.468281i
$206$	−30.0187			−2.09150
$207$	1.28783	+	6.62302i	0.0895102	+	0.460331i
$208$			3.98643i			0.276409i
$209$	2.42619	+	2.03581i	0.167823	+	0.140820i
$210$	−11.0486	−	33.5104i	−0.762424	−	2.31244i
$211$	0.299276	+	1.69728i	0.0206030	+	0.116845i	0.993375	−	0.114920i	$-0.0366611\pi$
$211$	0.299276	+	1.69728i	0.0206030	+	0.116845i	−0.972772	+	0.231765i	$0.925550\pi$
$212$	5.06334	−	13.9114i	0.347751	−	0.955439i
$213$	6.36021	+	6.24976i	0.435795	+	0.428227i
$214$	−3.80424	+	21.5749i	−0.260052	+	1.47483i
$215$	−1.08411	−	1.87773i	−0.0739355	−	0.128060i
$216$	−3.61840	−	12.2112i	−0.246201	−	0.830866i
$217$	0.919508	+	4.06502i	0.0624203	+	0.275951i
$218$	−5.51543	−	15.1535i	−0.373552	−	1.02633i
$219$	16.5668	+	16.2791i	1.11948	+	1.10004i
$220$	26.4036	−	4.65567i	1.78013	−	0.313885i
$221$	5.06655	−	13.9202i	0.340813	−	0.936377i
$222$	31.8800	−	22.7413i	2.13965	−	1.52630i
$223$	−14.0559	+	16.7512i	−0.941253	+	1.12174i	0.0511476	+	0.998691i	$0.483712\pi$
$223$	−14.0559	+	16.7512i	−0.941253	+	1.12174i	−0.992400	+	0.123050i	$0.960732\pi$
$224$	16.0643	+	4.98938i	1.07334	+	0.333367i
$225$	7.15614	+	18.6388i	0.477076	+	1.24259i
$226$	−1.65652	+	2.86918i	−0.110190	+	0.190855i
$227$	9.97573	+	8.37063i	0.662113	+	0.555578i	0.910719	−	0.413026i	$-0.135528\pi$
$227$	9.97573	+	8.37063i	0.662113	+	0.555578i	−0.248607	+	0.968605i	$0.579973\pi$
$228$	2.86546	+	6.00707i	0.189770	+	0.397828i
$229$	0.865476	−	0.152607i	0.0571922	−	0.0100845i	−0.144979	−	0.989435i	$-0.546311\pi$
$229$	0.865476	−	0.152607i	0.0571922	−	0.0100845i	0.202171	+	0.979350i	$0.435200\pi$
$230$	−16.2726	−	5.92275i	−1.07299	−	0.390535i
$231$	4.32077	−	10.8288i	0.284286	−	0.712484i
$232$	−0.853534	+	4.84063i	−0.0560373	+	0.317803i
$233$	7.00285	+	4.04310i	0.458772	+	0.264872i	0.711528	−	0.702658i	$-0.248004\pi$
$233$	7.00285	+	4.04310i	0.458772	+	0.264872i	−0.252756	+	0.967530i	$0.581337\pi$
$234$	36.5504	+	20.2571i	2.38937	+	1.32425i
$235$	−20.6093	−	35.6963i	−1.34440	−	2.32857i
$236$	1.47847	−	8.38481i	0.0962400	−	0.545804i
$237$	−0.694140	+	1.52328i	−0.0450892	+	0.0989477i
$238$	−11.3921	−	8.66409i	−0.738443	−	0.561610i
$239$	−4.16515	−	4.96384i	−0.269421	−	0.321084i	0.614322	−	0.789055i	$-0.289430\pi$
$239$	−4.16515	−	4.96384i	−0.269421	−	0.321084i	−0.883744	+	0.467971i	$0.844985\pi$
$240$	−3.69515	−	0.955505i	−0.238521	−	0.0616776i
$241$	−26.3927	−	4.65374i	−1.70010	−	0.299774i	−0.762372	−	0.647139i	$-0.775965\pi$
$241$	−26.3927	−	4.65374i	−1.70010	−	0.299774i	−0.937730	+	0.347365i	$0.887076\pi$
$242$	−8.84229	−	5.10510i	−0.568404	−	0.328168i
$243$	15.2195	+	3.37151i	0.976331	+	0.216282i
$244$		−	22.7566i		−	1.45684i
$245$	16.7526	−	17.0426i	1.07028	−	1.08881i
$246$	15.9996	+	15.7218i	1.02010	+	1.00238i
$247$	−7.22470	−	2.62958i	−0.459697	−	0.167316i
$248$	−3.62816	−	1.32054i	−0.230388	−	0.0838545i
$249$	−2.55002	−	3.57476i	−0.161601	−	0.226541i
$250$	−12.5504	−	2.21298i	−0.793758	−	0.139961i
$251$	10.0960	−	17.4868i	0.637253	−	1.10376i	−0.348780	−	0.937205i	$-0.613404\pi$
$251$	10.0960	−	17.4868i	0.637253	−	1.10376i	0.986033	−	0.166550i	$-0.0532628\pi$
$252$	17.6983	−	16.9422i	1.11489	−	1.06726i
$253$	−2.86098	−	4.95537i	−0.179868	−	0.311541i
$254$	6.83160	+	18.7697i	0.428653	+	1.17771i
$255$	11.6887	+	8.03290i	0.731978	+	0.503040i
$256$	−8.88507	+	7.45546i	−0.555317	+	0.465966i
$257$	−0.704449	−	3.99513i	−0.0439423	−	0.249209i	0.954922	−	0.296857i	$-0.0959386\pi$
$257$	−0.704449	−	3.99513i	−0.0439423	−	0.249209i	−0.998864	+	0.0476479i	$0.984827\pi$
$258$	1.40518	−	2.04469i	0.0874828	−	0.127297i
$259$	23.5778	+	12.1456i	1.46506	+	0.754688i
$260$	−56.3646	+	32.5421i	−3.49558	+	2.01818i
$261$	−4.67569	−	3.78580i	−0.289418	−	0.234335i
$262$	−36.9740	+	21.3469i	−2.28426	+	1.31882i
$263$	−7.38358	−	20.2862i	−0.455291	−	1.25090i	−0.928954	−	0.370195i	$-0.879291\pi$
$263$	−7.38358	−	20.2862i	−0.455291	−	1.25090i	0.473663	−	0.880706i	$-0.342931\pi$
$264$	6.27245	+	8.79306i	0.386043	+	0.541175i
$265$	−16.1247	+	2.84323i	−0.990535	+	0.174658i
$266$	−4.49672	+	5.91260i	−0.275712	+	0.362525i
$267$	−4.60640	−	16.6081i	−0.281907	−	1.01640i
$268$	18.9571	+	15.9069i	1.15799	+	0.971671i
$269$	1.05277	−	1.82346i	0.0641887	−	0.111178i	−0.832145	−	0.554558i	$-0.812887\pi$
$269$	1.05277	−	1.82346i	0.0641887	−	0.111178i	0.896334	+	0.443380i	$0.146221\pi$
$270$	−27.5378	+	29.0244i	−1.67589	+	1.76637i
$271$	11.3643	−	6.56119i	0.690333	−	0.398564i	−0.113404	−	0.993549i	$-0.536175\pi$
$271$	11.3643	−	6.56119i	0.690333	−	0.398564i	0.803737	+	0.594985i	$0.202842\pi$
$272$	−1.45479	+	0.529500i	−0.0882096	+	0.0321057i
$273$	−0.865464	+	28.2893i	−0.0523802	+	1.71214i
$274$	−2.54530	+	2.13576i	−0.153767	+	0.129026i
$275$	−10.8837	−	12.9706i	−0.656309	−	0.782159i
$276$	−1.15285	−	11.9688i	−0.0693936	−	0.720437i
$277$	3.05623	−	1.11238i	0.183631	−	0.0668363i	−0.248568	−	0.968614i	$-0.579960\pi$
$277$	3.05623	−	1.11238i	0.183631	−	0.0668363i	0.432199	+	0.901778i	$0.357738\pi$
$278$	30.4795			1.82804
$279$	3.56637	−	3.10060i	0.213513	−	0.185628i
$280$	4.88446	+	21.5935i	0.291902	+	1.29046i
$281$	15.2603	+	2.69080i	0.910351	+	0.160519i	0.609163	−	0.793045i	$-0.291506\pi$
$281$	15.2603	+	2.69080i	0.910351	+	0.160519i	0.301188	+	0.953565i	$0.402617\pi$
$282$	26.7130	−	38.8704i	1.59074	−	2.31470i
$283$	4.55485	+	5.42826i	0.270758	+	0.322677i	0.884241	−	0.467031i	$-0.154676\pi$
$283$	4.55485	+	5.42826i	0.270758	+	0.322677i	−0.613483	+	0.789708i	$0.710232\pi$
$284$	−10.2147	−	12.1734i	−0.606130	−	0.722357i
$285$	4.16913	−	6.06654i	0.246958	−	0.359351i
$286$	−34.9011	−	6.15400i	−2.06374	−	0.363894i
$287$	−4.50619	+	14.5086i	−0.265992	+	0.856415i
$288$	−3.64061	−	18.7229i	−0.214525	−	1.10326i
$289$	−11.2470			−0.661590
$290$	14.5099	−	5.28116i	0.852049	−	0.310121i
$291$	1.33843	+	13.8954i	0.0784599	+	0.814562i
$292$	−26.6067	−	31.7086i	−1.55704	−	1.85560i
$293$	−21.6105	+	18.1333i	−1.26250	+	1.05936i	−0.267085	+	0.963673i	$0.586061\pi$
$293$	−21.6105	+	18.1333i	−1.26250	+	1.05936i	−0.995411	+	0.0956878i	$0.969495\pi$
$294$	25.8543	+	8.90561i	1.50785	+	0.519386i
$295$	−8.84879	+	3.22069i	−0.515196	+	0.187516i
$296$	−21.2786	+	12.2852i	−1.23679	+	0.714064i
$297$	−13.1349	+	1.49782i	−0.762166	+	0.0869125i
$298$	−17.4500	+	30.2242i	−1.01085	+	1.75084i
$299$	10.6405	+	8.92845i	0.615357	+	0.516346i
$300$	−9.50971	−	34.2866i	−0.549044	−	1.97954i
$301$	1.66687	+	0.212176i	0.0960770	+	0.0122296i
$302$	−12.4633	+	2.19762i	−0.717184	+	0.126459i
$303$	1.87280	+	2.62539i	0.107589	+	0.150825i
$304$	0.274814	+	0.755045i	0.0157617	+	0.0433048i
$305$	−21.7968	+	12.5844i	−1.24808	+	0.720581i
$306$	−2.53772	+	16.0292i	−0.145072	+	0.916328i
$307$	−13.2261	+	7.63610i	−0.754854	+	0.435815i	−0.827445	−	0.561547i	$-0.810207\pi$
$307$	−13.2261	+	7.63610i	−0.754854	+	0.435815i	0.0725912	+	0.997362i	$0.476873\pi$
$308$	−9.51503	+	18.4713i	−0.542169	+	1.05250i
$309$	−13.0569	+	18.9992i	−0.742781	+	1.08083i
$310$	2.10619	+	11.9448i	0.119624	+	0.678419i
$311$	6.44697	−	5.40965i	0.365574	−	0.306753i	−0.441434	−	0.897294i	$-0.645530\pi$
$311$	6.44697	−	5.40965i	0.365574	−	0.306753i	0.807008	+	0.590541i	$0.201086\pi$
$312$	−21.6088	−	14.8503i	−1.22336	−	0.840732i
$313$	−4.35804	−	11.9736i	−0.246331	−	0.676789i	−0.999813	−	0.0193207i	$-0.993850\pi$
$313$	−4.35804	−	11.9736i	−0.246331	−	0.676789i	0.753482	−	0.657468i	$-0.228373\pi$
$314$	−12.2911	−	21.2889i	−0.693630	−	1.20140i
$315$	−26.0148	−	7.58287i	−1.46577	−	0.427246i
$316$	1.49163	−	2.58358i	0.0839109	−	0.145338i
$317$	−25.5640	−	4.50762i	−1.43582	−	0.253173i	−0.599041	−	0.800718i	$-0.704451\pi$
$317$	−25.5640	−	4.50762i	−1.43582	−	0.253173i	−0.836776	+	0.547545i	$0.815563\pi$
$318$	−10.8802	−	15.2525i	−0.610133	−	0.855316i
$319$	4.79443	+	1.74503i	0.268436	+	0.0977029i
$320$	41.8604	+	15.2360i	2.34007	+	0.851716i
$321$	12.0003	+	11.7919i	0.669794	+	0.658162i
$322$	11.2875	−	7.25923i	0.629030	−	0.404541i
$323$		−	2.98583i		−	0.166136i
$324$	−26.4222	−	8.58133i	−1.46790	−	0.476740i
$325$	35.5960	+	20.5514i	1.97451	+	1.13999i
$326$	55.9764	+	9.87014i	3.10024	+	0.546657i
$327$	−11.9898	−	3.10037i	−0.663039	−	0.171451i
$328$	−9.04675	−	10.7815i	−0.499523	−	0.595308i
$329$	31.6879	+	4.03355i	1.74701	+	0.222377i
$330$	14.0698	−	30.8759i	0.774516	−	1.69966i
$331$	0.512399	−	2.90596i	0.0281640	−	0.159726i	−0.967482	−	0.252939i	$-0.918603\pi$
$331$	0.512399	−	2.90596i	0.0281640	−	0.159726i	0.995646	+	0.0932133i	$0.0297138\pi$
$332$	3.91275	+	6.77708i	0.214740	+	0.371941i
$333$	−0.526791	−	30.0688i	−0.0288680	−	1.64776i
$334$	5.60120	+	3.23386i	0.306484	+	0.176949i
$335$	4.75276	−	26.9542i	0.259671	−	1.47267i
$336$	2.32293	−	1.83110i	0.126726	−	0.0998948i
$337$	2.27089	+	0.826536i	0.123703	+	0.0450243i	0.403130	−	0.915143i	$-0.367922\pi$
$337$	2.27089	+	0.826536i	0.123703	+	0.0450243i	−0.279427	+	0.960167i	$0.590144\pi$
$338$	55.8487	−	9.84762i	3.03777	−	0.535640i
$339$	1.09542	+	2.29641i	0.0594951	+	0.124724i
$340$	−19.3624	−	16.2470i	−1.05008	−	0.881118i
$341$	−2.00388	+	3.47081i	−0.108516	+	0.187955i
$342$	8.31926	+	1.31709i	0.449854	+	0.0712202i
$343$	2.65352	+	18.3292i	0.143277	+	0.989683i
$344$	−1.00061	+	1.19248i	−0.0539490	+	0.0642940i
$345$	−10.8265	+	7.72300i	−0.582880	+	0.415792i
$346$	2.01266	−	5.52973i	0.108201	−	0.297280i
$347$	3.14361	−	0.554304i	0.168758	−	0.0297566i	−0.0886307	−	0.996065i	$-0.528249\pi$
$347$	3.14361	−	0.554304i	0.168758	−	0.0297566i	0.257389	+	0.966308i	$0.417138\pi$
$348$	7.64747	+	7.51466i	0.409947	+	0.402828i
$349$	−8.87089	−	24.3726i	−0.474848	−	1.30463i	−0.913815	−	0.406130i	$-0.866878\pi$
$349$	−8.87089	−	24.3726i	−0.474848	−	1.30463i	0.438967	−	0.898503i	$-0.355344\pi$
$350$	29.1636	−	26.9546i	1.55886	−	1.44078i
$351$	28.7189	−	14.3222i	1.53290	−	0.764461i
$352$	8.08783	+	14.0085i	0.431083	+	0.746657i
$353$	4.51456	−	25.6033i	0.240286	−	1.36273i	−0.590906	−	0.806741i	$-0.701229\pi$
$353$	4.51456	−	25.6033i	0.240286	−	1.36273i	0.831191	−	0.555987i	$-0.187659\pi$
$354$	−7.68558	−	7.55211i	−0.408484	−	0.401390i
$355$	−6.01126	+	16.5158i	−0.319044	+	0.876567i
$356$	5.33365	+	30.2486i	0.282683	+	1.60317i
$357$	−10.4387	+	3.44170i	−0.552476	+	0.182154i
$358$	−24.4997	−	20.5577i	−1.29485	−	1.08651i
$359$			19.0535i			1.00560i	0.864402	+	0.502802i	$0.167697\pi$
$359$			19.0535i			1.00560i	−0.864402	+	0.502802i	$0.832303\pi$
$360$	18.9446	−	16.4705i	0.998471	−	0.868070i
$361$	17.4503			0.918439
$362$	−14.3555	+	5.22499i	−0.754510	+	0.274619i
$363$	−7.07711	+	3.37589i	−0.371452	+	0.177188i
$364$	6.36899	−	50.0353i	0.333826	−	2.62256i
$365$	−15.6578	+	43.0195i	−0.819567	+	2.25174i
$366$	−23.7350	−	16.3115i	−1.24065	−	0.852614i
$367$	6.08788	−	7.25525i	0.317785	−	0.378721i	−0.583379	−	0.812200i	$-0.698270\pi$
$367$	6.08788	−	7.25525i	0.317785	−	0.378721i	0.901164	+	0.433479i	$0.142714\pi$
$368$		−	1.45165i		−	0.0756725i
$369$	16.9097	−	3.28804i	0.880284	−	0.171169i
$370$	66.8452	+	38.5931i	3.47512	+	2.00636i
$371$	5.81085	−	11.2804i	0.301684	−	0.585651i
$372$	−6.85627	+	4.89086i	−0.355481	+	0.253579i
$373$	15.0894	−	12.6615i	0.781301	−	0.655590i	−0.162275	−	0.986746i	$-0.551883\pi$
$373$	15.0894	−	12.6615i	0.781301	−	0.655590i	0.943576	+	0.331156i	$0.107439\pi$
$374$	−2.38995	−	13.5541i	−0.123581	−	0.700864i
$375$	−6.85954	+	6.98076i	−0.354225	+	0.360485i
$376$	−19.0219	+	22.6694i	−0.980979	+	1.16909i
$377$	−12.3855			−0.637887
$378$	−4.98478	−	30.6031i	−0.256389	−	1.57405i
$379$	−24.3431			−1.25042			−0.625211	−	0.780456i	$-0.714987\pi$
$379$	−24.3431			−1.25042			−0.625211	+	0.780456i	$0.714987\pi$
$380$	−8.43231	+	10.0492i	−0.432568	+	0.515515i
$381$	14.8510	+	3.84022i	0.760840	+	0.196741i
$382$	−6.55807	−	37.1927i	−0.335540	−	1.90294i
$383$	−8.34437	+	7.00176i	−0.426378	+	0.357773i	−0.830583	−	0.556895i	$-0.811993\pi$
$383$	−8.34437	+	7.00176i	−0.426378	+	0.357773i	0.404205	+	0.914668i	$0.367548\pi$
$384$	2.77555	+	28.8154i	0.141639	+	1.47048i
$385$	22.9541	−	1.10089i	1.16985	−	0.0561065i
$386$	−22.4063	−	12.9363i	−1.14045	−	0.658439i
$387$	−0.682916	−	1.77871i	−0.0347146	−	0.0904171i
$388$		−	24.8781i		−	1.26299i
$389$	−5.08402	+	6.05890i	−0.257770	+	0.307198i	−0.879372	−	0.476135i	$-0.842038\pi$
$389$	−5.08402	+	6.05890i	−0.257770	+	0.307198i	0.621602	+	0.783333i	$0.286482\pi$
$390$	−6.45981	+	82.1135i	−0.327105	+	4.15798i
$391$	−1.84498	+	5.06903i	−0.0933045	+	0.256352i
$392$	−15.6115	−	7.11730i	−0.788498	−	0.359478i
$393$	−2.57141	+	32.6863i	−0.129710	+	1.64881i
$394$	2.15394	−	0.783970i	0.108514	−	0.0394958i
$395$	−3.29950			−0.166016
$396$	23.5564	−	0.412697i	1.18375	−	0.0207388i
$397$		−	3.33022i		−	0.167139i	−0.996502	−	0.0835695i	$-0.973368\pi$
$397$		−	3.33022i		−	0.167139i	0.996502	−	0.0835695i	$-0.0266321\pi$
$398$	9.47024	+	7.94648i	0.474700	+	0.398321i
$399$	1.78627	+	5.41777i	0.0894252	+	0.271228i
$400$	−0.745924	−	4.23034i	−0.0372962	−	0.211517i
$401$	−11.8310	+	32.5054i	−0.590812	+	1.62324i	0.178189	+	0.983996i	$0.442976\pi$
$401$	−11.8310	+	32.5054i	−0.590812	+	1.62324i	−0.769001	+	0.639247i	$0.779246\pi$
$402$	30.1790	−	8.37042i	1.50519	−	0.417479i
$403$	1.68941	−	9.58111i	0.0841554	−	0.477269i
$404$	−2.87362	−	4.97725i	−0.142968	−	0.247627i
$405$	6.39209	+	30.0534i	0.317626	+	1.49336i
$406$	−3.54941	+	11.4280i	−0.176154	+	0.567163i
$407$	8.72297	+	23.9662i	0.432382	+	1.18796i
$408$	2.54920	−	9.85832i	0.126204	−	0.488060i
$409$	17.7722	−	3.13371i	0.878776	−	0.154952i	0.283982	−	0.958830i	$-0.408344\pi$
$409$	17.7722	−	3.13371i	0.878776	−	0.154952i	0.594795	+	0.803878i	$0.297233\pi$
$410$	−15.1218	+	41.5468i	−0.746813	+	2.05185i
$411$	0.244649	+	2.53992i	0.0120677	+	0.125285i
$412$	26.4084	−	31.4722i	1.30105	−	1.55053i
$413$	2.16459	−	6.96933i	0.106513	−	0.342938i
$414$	−13.3097	−	7.37659i	−0.654138	−	0.362540i
$415$	4.32751	−	7.49547i	0.212429	−	0.367938i
$416$	−30.0801	−	25.2402i	−1.47480	−	1.23750i
$417$	13.2573	−	19.2909i	0.649215	−	0.944678i
$418$	−7.03465	+	1.24040i	−0.344076	+	0.0606698i
$419$	−8.67340	−	3.15686i	−0.423724	−	0.154223i	0.121352	−	0.992609i	$-0.461277\pi$
$419$	−8.67340	−	3.15686i	−0.423724	−	0.154223i	−0.545076	+	0.838387i	$0.683499\pi$
$420$	44.8528	+	17.8966i	2.18859	+	0.873263i
$421$	−4.17891	+	23.6998i	−0.203668	+	1.15506i	0.695855	+	0.718182i	$0.255026\pi$
$421$	−4.17891	+	23.6998i	−0.203668	+	1.15506i	−0.899523	+	0.436874i	$0.856086\pi$
$422$	−3.36629	−	1.94353i	−0.163869	−	0.0946096i
$423$	−12.9825	−	33.8140i	−0.631230	−	1.64409i
$424$	5.87766	+	10.1804i	0.285445	+	0.494404i
$425$	−2.77186	+	15.7200i	−0.134455	+	0.762532i
$426$	−20.0185	+	1.92821i	−0.969898	+	0.0934221i
$427$	2.46296	−	19.3492i	0.119191	−	0.936374i
$428$	−19.2729	−	22.9685i	−0.931590	−	1.11023i
$429$	−19.0755	+	19.4126i	−0.920972	+	0.937249i
$430$	4.81586	+	0.849166i	0.232242	+	0.0409504i
$431$	19.5471	+	11.2855i	0.941552	+	0.543605i	0.890447	−	0.455088i	$-0.150392\pi$
$431$	19.5471	+	11.2855i	0.941552	+	0.543605i	0.0511056	+	0.998693i	$0.483726\pi$
$432$	−3.07586	−	1.33707i	−0.147987	−	0.0643297i
$433$		−	18.7792i		−	0.902469i	−0.892405	−	0.451234i	$-0.850984\pi$
$433$		−	18.7792i		−	0.902469i	0.892405	−	0.451234i	$-0.149016\pi$
$434$	−8.35627	−	4.30453i	−0.401114	−	0.206624i
$435$	2.96868	−	11.4806i	0.142337	−	0.550451i
$436$	20.7393	+	7.54850i	0.993234	+	0.361508i
$437$	2.63086	+	0.957555i	0.125851	+	0.0458061i
$438$	−52.1431	+	5.02250i	−2.49149	+	0.239984i
$439$	6.52614	+	1.15074i	0.311476	+	0.0549216i	0.327201	−	0.944955i	$-0.393895\pi$
$439$	6.52614	+	1.15074i	0.311476	+	0.0549216i	−0.0157251	+	0.999876i	$0.505006\pi$
$440$	−10.6447	+	18.4371i	−0.507464	+	0.878953i
$441$	16.8820	−	12.4899i	0.803905	−	0.594758i
$442$	16.7052	+	28.9342i	0.794585	+	1.37626i
$443$	6.08341	+	16.7140i	0.289031	+	0.794107i	0.996203	+	0.0870648i	$0.0277487\pi$
$443$	6.08341	+	16.7140i	0.289031	+	0.794107i	−0.707171	+	0.707042i	$0.750029\pi$
$444$	−4.20329	+	53.4299i	−0.199479	+	2.53567i
$445$	26.0234	−	21.8362i	1.23363	−	1.03514i
$446$	−8.56410	−	48.5694i	−0.405522	−	2.29983i
$447$	11.5393	+	24.1906i	0.545789	+	1.14418i
$448$	−29.0366	+	18.6740i	−1.37185	+	0.882261i
$449$	28.0035	−	16.1678i	1.32157	−	0.763007i	0.337589	−	0.941294i	$-0.390389\pi$
$449$	28.0035	−	16.1678i	1.32157	−	0.763007i	0.983979	+	0.178286i	$0.0570554\pi$
$450$	−42.5772	−	14.6574i	−2.00711	−	0.690958i
$451$	−12.6519	+	7.30458i	−0.595755	+	0.343959i
$452$	−1.55082	−	4.26083i	−0.0729443	−	0.200413i
$453$	−4.03013	+	8.84407i	−0.189352	+	0.415531i
$454$	−28.9243	+	5.10013i	−1.35748	+	0.239361i
$455$	−51.4472	+	21.5692i	−2.41188	+	1.01118i
$456$	−5.11654	−	1.32305i	−0.239604	−	0.0619575i
$457$	6.87283	+	5.76699i	0.321498	+	0.269769i	0.789225	−	0.614104i	$-0.210483\pi$
$457$	6.87283	+	5.76699i	0.321498	+	0.269769i	−0.467727	+	0.883873i	$0.654927\pi$
$458$	−0.991046	+	1.71654i	−0.0463085	+	0.0802087i
$459$	9.04127	+	8.57819i	0.422011	+	0.400396i
$460$	20.5251	−	11.8501i	0.956986	−	0.552516i
$461$	32.7872	−	11.9336i	1.52705	−	0.555801i	0.564154	−	0.825670i	$-0.309203\pi$
$461$	32.7872	−	11.9336i	1.52705	−	0.555801i	0.962897	+	0.269869i	$0.0869803\pi$
$462$	12.4452	+	23.1640i	0.579005	+	1.07769i
$463$	−21.5412	+	18.0752i	−1.00111	+	0.840028i	−0.987137	−	0.159875i	$-0.948891\pi$
$463$	−21.5412	+	18.0752i	−1.00111	+	0.840028i	−0.0139685	+	0.999902i	$0.504446\pi$
$464$	0.832023	+	0.991566i	0.0386257	+	0.0460323i
$465$	8.47612	+	3.86246i	0.393071	+	0.179117i
$466$	−17.1376	+	6.23759i	−0.793885	+	0.288951i
$467$	−24.5729			−1.13710			−0.568549	−	0.822649i	$-0.692495\pi$
$467$	−24.5729			−1.13710			−0.568549	+	0.822649i	$0.692495\pi$
$468$	−53.3924	+	20.4994i	−2.46806	+	0.947584i
$469$	14.3971	+	15.5769i	0.664795	+	0.719276i
$470$	91.5514	+	16.1430i	4.22295	+	0.744620i
$471$	−18.8201	−	1.48057i	−0.867186	−	0.0682209i
$472$	4.34569	+	5.17899i	0.200027	+	0.238382i
$473$	1.03864	+	1.23780i	0.0477565	+	0.0569140i
$474$	−1.62549	−	3.40763i	−0.0746613	−	0.156518i
$475$	8.15879	+	1.43861i	0.374351	+	0.0660082i
$476$	19.1056	−	4.32170i	0.875704	−	0.198085i
$477$	−14.3859	+	0.252035i	−0.658686	+	0.0115399i
$478$	14.6145			0.668452
$479$	−30.1019	+	10.9562i	−1.37539	+	0.500602i	−0.920778	−	0.390087i	$-0.872445\pi$
$479$	−30.1019	+	10.9562i	−1.37539	+	0.500602i	−0.454614	+	0.890689i	$0.650223\pi$
$480$	30.6059	−	21.8325i	1.39696	−	0.996511i
$481$	−39.7964	−	47.4275i	−1.81456	−	2.16251i
$482$	46.3027	−	38.8526i	2.10903	−	1.76969i
$483$	0.315157	−	10.3015i	0.0143401	−	0.468734i
$484$	13.1311	−	4.77933i	0.596869	−	0.217242i
$485$	−23.8289	+	13.7576i	−1.08202	+	0.624702i
$486$	−27.8892	+	21.4073i	−1.26508	+	0.971055i
$487$	−2.41488	+	4.18270i	−0.109429	+	0.189536i	−0.915539	−	0.402229i	$-0.868235\pi$
$487$	−2.41488	+	4.18270i	−0.109429	+	0.189536i	0.806110	+	0.591765i	$0.201569\pi$
$488$	13.8424	+	11.6151i	0.626614	+	0.525792i
$489$	30.5943	−	31.1350i	1.38352	−	1.40797i
$490$	5.15813	+	53.6511i	0.233021	+	2.42371i
$491$	11.4709	−	2.02263i	0.517675	−	0.0912800i	0.0912942	−	0.995824i	$-0.470900\pi$
$491$	11.4709	−	2.02263i	0.517675	−	0.0912800i	0.426380	+	0.904544i	$0.359789\pi$
$492$	−30.5584	+	2.94343i	−1.37768	+	0.132700i
$493$	−1.64512	−	4.51992i	−0.0740923	−	0.203567i
$494$	15.0171	−	8.67011i	0.675650	−	0.390086i
$495$	−13.4220	−	22.3347i	−0.603274	−	1.00387i
$496$	−0.880538	+	0.508379i	−0.0395373	+	0.0228269i
$497$	−7.36770	−	11.4562i	−0.330487	−	0.513881i
$498$	9.87305	+	0.776706i	0.442422	+	0.0348050i
$499$	1.83083	+	10.3831i	0.0819591	+	0.464813i	0.997971	+	0.0636632i	$0.0202783\pi$
$499$	1.83083	+	10.3831i	0.0819591	+	0.464813i	−0.916012	+	0.401150i	$0.868611\pi$
$500$	13.3611	−	11.2113i	0.597527	−	0.501385i
$501$	4.48304	−	2.13848i	0.200287	−	0.0955401i
$502$	15.5758	+	42.7942i	0.695183	+	1.91000i
$503$	3.57408	+	6.19049i	0.159360	+	0.276020i	0.934638	−	0.355600i	$-0.115723\pi$
$503$	3.57408	+	6.19049i	0.159360	+	0.276020i	−0.775278	+	0.631620i	$0.782390\pi$
$504$	1.27223	+	19.4129i	0.0566696	+	0.864721i
$505$	−3.17823	+	5.50485i	−0.141429	+	0.244963i
$506$	12.7092	+	2.24097i	0.564991	+	0.0996232i
$507$	18.0592	−	39.6306i	0.802036	−	1.76006i
$508$	−25.6885	−	9.34983i	−1.13974	−	0.414832i
$509$	−17.0659	−	6.21149i	−0.756434	−	0.275319i	−0.0651232	−	0.997877i	$-0.520744\pi$
$509$	−17.0659	−	6.21149i	−0.756434	−	0.275319i	−0.691310	+	0.722558i	$0.742966\pi$
$510$	−30.8242	+	8.54937i	−1.36492	+	0.378573i
$511$	−19.1910	−	29.8405i	−0.848960	−	1.32007i
$512$			7.26783i			0.321196i
$513$	4.45214	−	4.69248i	0.196567	−	0.207178i
$514$	7.92375	+	4.57478i	0.349501	+	0.201785i
$515$	−44.7488	−	7.89042i	−1.97187	−	0.347694i
$516$	0.907519	+	3.27200i	0.0399513	+	0.144042i
$517$	19.7449	+	23.5310i	0.868378	+	1.03489i
$518$	−55.1657	+	23.1282i	−2.42384	+	1.01619i
$519$	−2.62441	−	3.67904i	−0.115199	−	0.161492i
$520$	8.97419	−	50.8952i	0.393544	−	2.23190i
$521$	−1.45387	−	2.51818i	−0.0636953	−	0.110323i	0.832419	−	0.554146i	$-0.186955\pi$
$521$	−1.45387	−	2.51818i	−0.0636953	−	0.110323i	−0.896114	+	0.443823i	$0.853622\pi$
$522$	13.3193	−	2.58990i	0.582971	−	0.113357i
$523$	−22.4146	−	12.9411i	−0.980123	−	0.565875i	−0.0778161	−	0.996968i	$-0.524795\pi$
$523$	−22.4146	−	12.9411i	−0.980123	−	0.565875i	−0.902307	+	0.431093i	$0.858128\pi$
$524$	10.1465	−	57.5438i	0.443253	−	2.51381i
$525$	−4.37495	−	30.1821i	−0.190939	−	1.31726i
$526$	45.7532	+	16.6528i	1.99493	+	0.726096i
$527$	3.72088	−	0.656092i	0.162084	−	0.0285798i
$528$	2.83557	+	0.223073i	0.123403	+	0.00970799i
$529$	13.7443	+	11.5328i	0.597578	+	0.501428i
$530$	18.4643	−	31.9810i	0.802036	−	1.38917i
$531$	−8.12273	+	1.57944i	−0.352496	+	0.0685419i
$532$	−2.24299	−	9.91594i	−0.0972459	−	0.429911i
$533$	22.7959	−	27.1671i	0.987399	−	1.17674i
$534$	35.3722	+	16.1187i	1.53071	+	0.697523i
$535$	−11.3419	+	31.1617i	−0.490355	+	1.34724i
$536$	−19.3517	+	3.41223i	−0.835868	+	0.147386i
$537$	−23.6676	+	6.56442i	−1.02133	+	0.283276i
$538$	1.62419	+	4.46243i	0.0700238	+	0.192389i
$539$	−10.0895	+	14.6757i	−0.434586	+	0.632129i
$540$	−6.20396	−	54.4047i	−0.266976	−	2.34121i
$541$	−9.36987	−	16.2291i	−0.402842	−	0.697743i	0.591225	−	0.806506i	$-0.298644\pi$
$541$	−9.36987	−	16.2291i	−0.402842	−	0.697743i	−0.994068	+	0.108763i	$0.965311\pi$
$542$	−5.13929	+	29.1464i	−0.220751	+	1.25194i
$543$	−2.93711	+	11.3585i	−0.126043	+	0.487438i
$544$	5.21564	−	14.3299i	0.223619	−	0.614387i
$545$	−4.23873	−	24.0390i	−0.181567	−	1.02972i
$546$	−47.6214	−	42.5072i	−2.03801	−	1.81914i
$547$	33.4456	+	28.0642i	1.43003	+	1.19994i	0.945695	+	0.325055i	$0.105383\pi$
$547$	33.4456	+	28.0642i	1.43003	+	1.19994i	0.484335	+	0.874882i	$0.339061\pi$
$548$		−	4.54744i		−	0.194257i
$549$	−20.6475	+	7.92735i	−0.881213	+	0.338331i
$550$	38.1881			1.62834
$551$	−2.34587	+	0.853827i	−0.0999374	+	0.0363742i
$552$	7.86881	+	5.40771i	0.334919	+	0.230167i
$553$	1.54791	−	2.03530i	0.0658240	−	0.0865499i
$554$	−2.50884	+	6.89298i	−0.106590	+	0.292855i
$555$	53.5010	−	25.5208i	2.27099	−	1.08330i
$556$	−26.8137	+	31.9554i	−1.13716	+	1.35521i
$557$			2.74059i			0.116122i	0.998313	+	0.0580612i	$0.0184918\pi$
$557$			2.74059i			0.116122i	−0.998313	+	0.0580612i	$0.981508\pi$
$558$	0.186701	+	10.6567i	0.00790368	+	0.451135i
$559$	−3.39696	−	1.96123i	−0.143676	−	0.0829513i
$560$	5.18286	+	2.66983i	0.219016	+	0.112821i
$561$	−9.61806	−	4.38283i	−0.406075	−	0.185043i
$562$	−26.7723	+	22.4646i	−1.12932	+	0.947612i
$563$	2.31668	+	13.1385i	0.0976363	+	0.553723i	0.993908	+	0.110217i	$0.0351544\pi$
$563$	2.31668	+	13.1385i	0.0976363	+	0.553723i	−0.896271	+	0.443506i	$0.853734\pi$
$564$	17.2523	+	62.2020i	0.726452	+	2.61917i
$565$	−3.22354	+	3.84166i	−0.135615	+	0.161620i
$566$	−15.9819			−0.671767
$567$	−21.5372	−	10.1561i	−0.904479	−	0.426518i
$568$	12.6185			0.529459
$569$	−6.61733	+	7.88623i	−0.277413	+	0.330608i	−0.886703	−	0.462339i	$-0.847010\pi$
$569$	−6.61733	+	7.88623i	−0.277413	+	0.330608i	0.609290	+	0.792948i	$0.291455\pi$
$570$	4.43718	+	15.9980i	0.185853	+	0.670081i
$571$	−3.76232	−	21.3372i	−0.157448	−	0.892933i	−0.956513	−	0.291689i	$-0.905783\pi$
$571$	−3.76232	−	21.3372i	−0.157448	−	0.892933i	0.799065	−	0.601244i	$-0.205328\pi$
$572$	37.1555	−	31.1772i	1.55355	−	1.30358i
$573$	−26.3922	−	12.0266i	−1.10255	−	0.502418i
$574$	−18.5341	−	28.8190i	−0.773596	−	1.20288i
$575$	−12.9622	−	7.48375i	−0.540562	−	0.312094i
$576$	34.2386	+	18.9759i	1.42661	+	0.790661i
$577$			5.13708i			0.213860i	0.994267	+	0.106930i	$0.0341020\pi$
$577$			5.13708i			0.213860i	−0.994267	+	0.106930i	$0.965898\pi$
$578$	16.3052	−	19.4318i	0.678207	−	0.808255i
$579$	−17.9333	+	8.55447i	−0.745284	+	0.355512i
$580$	−7.22788	+	19.8584i	−0.300122	+	0.824577i
$581$	2.59340	+	6.18583i	0.107593	+	0.256631i
$582$	−25.9477	−	17.8322i	−1.07557	−	0.739167i
$583$	11.4662	−	4.17337i	0.474883	−	0.172843i
$584$	32.8679			1.36008
$585$	49.1609	+	39.8045i	2.03255	+	1.64571i
$586$		−	63.6254i		−	2.62834i
$587$	26.0870	+	21.8896i	1.07672	+	0.903479i	0.995645	−	0.0932285i	$-0.0297187\pi$
$587$	26.0870	+	21.8896i	1.07672	+	0.903479i	0.0810798	+	0.996708i	$0.474163\pi$
$588$	−32.0816	+	19.2716i	−1.32302	+	0.794748i
$589$	−0.340516	−	1.93116i	−0.0140307	−	0.0795722i
$590$	7.26390	−	19.9574i	0.299050	−	0.821633i
$591$	0.440690	−	1.70425i	0.0181276	−	0.0701035i
$592$	−1.12357	+	6.37208i	−0.0461784	+	0.261891i
$593$	−2.84168	−	4.92193i	−0.116694	−	0.202119i	0.801762	−	0.597644i	$-0.203896\pi$
$593$	−2.84168	−	4.92193i	−0.116694	−	0.202119i	−0.918456	+	0.395524i	$0.870563\pi$
$594$	16.4543	−	24.8650i	0.675129	−	1.02022i
$595$	−14.7049	−	15.9100i	−0.602841	−	0.652245i
$596$	−16.3365	−	44.8840i	−0.669167	−	1.83852i
$597$	9.14859	−	2.53745i	0.374427	−	0.103851i
$598$	−30.8518	+	5.44000i	−1.26162	+	0.222458i
$599$	13.3705	−	36.7351i	0.546303	−	1.50096i	−0.292362	−	0.956308i	$-0.594441\pi$
$599$	13.3705	−	36.7351i	0.546303	−	1.50096i	0.838665	−	0.544648i	$-0.183337\pi$
$600$	25.7097	+	11.7156i	1.04959	+	0.478287i
$601$	−14.1568	+	16.8714i	−0.577468	+	0.688199i	−0.973146	−	0.230190i	$-0.926065\pi$
$601$	−14.1568	+	16.8714i	−0.577468	+	0.688199i	0.395678	+	0.918389i	$0.370510\pi$
$602$	−2.78310	+	2.57230i	−0.113431	+	0.104839i
$603$	7.82887	−	22.7414i	0.318816	−	0.926103i
$604$	8.66033	−	15.0001i	0.352384	−	0.610346i
$605$	−11.8393	−	9.93435i	−0.481336	−	0.403889i
$606$	−7.25100	−	0.570431i	−0.294552	−	0.0231722i
$607$	23.9714	−	4.22680i	0.972969	−	0.171561i	0.335503	−	0.942039i	$-0.391094\pi$
$607$	23.9714	−	4.22680i	0.972969	−	0.171561i	0.637466	+	0.770479i	$0.279983\pi$
$608$	−7.43729	−	2.70695i	−0.301622	−	0.109781i
$609$	5.68909	+	7.21718i	0.230534	+	0.292455i
$610$	9.85720	−	55.9029i	0.399106	−	2.26344i
$611$	−64.5774	−	37.2838i	−2.61252	−	1.50834i
$612$	−14.5728	−	16.7619i	−0.589072	−	0.677562i
$613$	7.28902	+	12.6250i	0.294401	+	0.509917i	0.974845	−	0.222882i	$-0.0715466\pi$
$613$	7.28902	+	12.6250i	0.294401	+	0.509917i	−0.680444	+	0.732800i	$0.738213\pi$
$614$	5.98125	−	33.9214i	0.241384	−	1.36895i
$615$	19.7181	+	27.6419i	0.795112	+	1.11463i
$616$	−6.37916	−	15.2157i	−0.257024	−	0.613057i
$617$	−17.1824	−	20.4772i	−0.691739	−	0.824383i	0.299826	−	0.953994i	$-0.403072\pi$
$617$	−17.1824	−	20.4772i	−0.691739	−	0.824383i	−0.991565	+	0.129611i	$0.958627\pi$
$618$	−13.8964	−	50.1025i	−0.558995	−	2.01542i
$619$	17.9845	+	3.17115i	0.722857	+	0.127459i	0.522959	−	0.852358i	$-0.324828\pi$
$619$	17.9845	+	3.17115i	0.722857	+	0.127459i	0.199898	+	0.979817i	$0.435939\pi$
$620$	−14.3761	−	8.30002i	−0.577357	−	0.333337i
$621$	−10.4579	+	5.21539i	−0.419662	+	0.209286i
$622$			18.9811i			0.761074i
$623$	1.26121	+	26.2967i	0.0505291	+	1.05356i
$624$	−6.65351	+	1.84541i	−0.266354	+	0.0738757i
$625$	13.1416	+	4.78316i	0.525665	+	0.191326i
$626$	27.0051	+	9.82905i	1.07934	+	0.392848i
$627$	−2.27472	+	4.99184i	−0.0908434	+	0.199355i
$628$	33.1326	+	5.84217i	1.32213	+	0.233128i
$629$	12.0220	−	20.8227i	0.479349	−	0.830256i
$630$	50.8157	−	33.9533i	2.02455	−	1.35273i
$631$	−8.50860	−	14.7373i	−0.338722	−	0.586684i	0.645471	−	0.763785i	$-0.276661\pi$
$631$	−8.50860	−	14.7373i	−0.338722	−	0.586684i	−0.984193	+	0.177101i	$0.943328\pi$
$632$	0.810202	+	2.22601i	0.0322281	+	0.0885460i
$633$	−2.69428	+	1.28521i	−0.107088	+	0.0510827i
$634$	44.8489	−	37.6327i	1.78118	−	1.49459i
$635$	5.25023	+	29.7756i	0.208349	+	1.18161i
$636$	25.5627	+	2.01100i	1.01363	+	0.0797412i
$637$	10.8307	−	41.8542i	0.429129	−	1.65832i
$638$	−9.96556	+	5.75362i	−0.394540	+	0.227788i
$639$	−7.48682	+	13.5086i	−0.296174	+	0.534393i
$640$	−49.4150	+	28.5298i	−1.95330	+	1.12774i
$641$	15.4740	+	42.5145i	0.611187	+	1.67922i	0.727584	+	0.686019i	$0.240643\pi$
$641$	15.4740	+	42.5145i	0.611187	+	1.67922i	−0.116397	+	0.993203i	$0.537135\pi$
$642$	−37.7705	+	3.63811i	−1.49068	+	0.143585i
$643$	−1.26736	+	0.223470i	−0.0499799	+	0.00881280i	−0.198582	−	0.980084i	$-0.563634\pi$
$643$	−1.26736	+	0.223470i	−0.0499799	+	0.00881280i	0.148602	+	0.988897i	$0.452523\pi$
$644$	−2.31926	+	18.2202i	−0.0913915	+	0.717978i
$645$	2.63215	−	2.67867i	0.103641	−	0.105472i
$646$	5.15868	+	4.32865i	0.202966	+	0.170308i
$647$	11.2984	−	19.5694i	0.444185	−	0.769351i	−0.553810	−	0.832643i	$-0.686827\pi$
$647$	11.2984	−	19.5694i	0.444185	−	0.769351i	0.997995	+	0.0632923i	$0.0201600\pi$
$648$	18.7059	−	11.6921i	0.734839	−	0.459310i
$649$	6.07746	−	3.50882i	0.238561	−	0.137733i
$650$	−87.1118	+	31.7061i	−3.41681	+	1.24362i
$651$	−6.35902	+	3.41649i	−0.249230	+	0.133903i
$652$	−59.5921	+	50.0037i	−2.33381	+	1.95830i
$653$	−30.4541	−	36.2937i	−1.19176	−	1.42028i	−0.883148	−	0.469095i	$-0.844580\pi$
$653$	−30.4541	−	36.2937i	−1.19176	−	1.42028i	−0.308612	−	0.951188i	$-0.599864\pi$
$654$	22.7386	−	16.2204i	0.889150	−	0.634268i
$655$	−60.7280	+	22.1032i	−2.37284	+	0.863643i
$656$	−3.70631			−0.144707
$657$	−19.5013	+	35.1866i	−0.760817	+	1.37276i
$658$	−52.9079	+	48.9004i	−2.06256	+	1.90634i
$659$	6.94728	+	1.22499i	0.270628	+	0.0477190i	0.307315	−	0.951608i	$-0.400569\pi$
$659$	6.94728	+	1.22499i	0.270628	+	0.0477190i	−0.0366873	+	0.999327i	$0.511681\pi$
$660$	19.9934	+	41.9135i	0.778241	+	1.63148i
$661$	12.6732	+	15.1034i	0.492932	+	0.587454i	0.953961	−	0.299932i	$-0.0969639\pi$
$661$	12.6732	+	15.1034i	0.492932	+	0.587454i	−0.461029	+	0.887385i	$0.652519\pi$
$662$	4.27785	+	5.09815i	0.166263	+	0.198145i
$663$	25.5789	+	2.01227i	0.993402	+	0.0781502i
$664$	−6.11946	−	1.07903i	−0.237481	−	0.0418743i
$665$	−8.25738	+	7.63193i	−0.320207	+	0.295953i
$666$	52.7143	+	42.6815i	2.04264	+	1.65388i
$667$	4.51017			0.174634
$668$	−8.31799	+	3.02750i	−0.321833	+	0.117137i
$669$	−34.4652	−	15.7054i	−1.33250	−	0.607205i
$670$	39.6792	+	47.2879i	1.53294	+	1.82689i
$671$	14.3685	−	12.0566i	0.554688	−	0.465439i
$672$	−0.890930	+	29.1217i	−0.0343684	+	1.12339i
$673$	41.0196	−	14.9299i	1.58119	−	0.575506i	0.605727	−	0.795673i	$-0.292883\pi$
$673$	41.0196	−	14.9299i	1.58119	−	0.575506i	0.975462	+	0.220167i	$0.0706603\pi$
$674$	−4.72021	+	2.72521i	−0.181816	+	0.104971i
$675$	−27.7962	+	20.5723i	−1.06988	+	0.791826i
$676$	−38.8073	+	67.2161i	−1.49259	+	2.58524i
$677$	16.1115	+	13.5191i	0.619215	+	0.519583i	0.897557	−	0.440899i	$-0.145340\pi$
$677$	16.1115	+	13.5191i	0.619215	+	0.519583i	−0.278342	+	0.960482i	$0.589785\pi$
$678$	−5.55563	−	1.43659i	−0.213363	−	0.0551720i
$679$	2.69258	−	21.1531i	0.103332	−	0.811782i
$680$	19.7655	−	3.48518i	0.757971	−	0.133651i
$681$	−9.35293	+	20.5249i	−0.358405	+	0.786515i
$682$	−3.09153	−	8.49390i	−0.118381	−	0.325248i
$683$	13.8112	−	7.97392i	0.528472	−	0.305114i	−0.211922	−	0.977287i	$-0.567972\pi$
$683$	13.8112	−	7.97392i	0.528472	−	0.305114i	0.740394	+	0.672173i	$0.234639\pi$
$684$	−8.69956	+	7.56340i	−0.332636	+	0.289194i
$685$	−4.35566	+	2.51474i	−0.166421	+	0.0960834i
$686$	−35.5147	−	21.9879i	−1.35596	−	0.839500i
$687$	0.655357	+	1.37387i	0.0250034	+	0.0524164i
$688$	0.0711841	+	0.403705i	0.00271387	+	0.0153911i
$689$	−22.6909	+	19.0400i	−0.864456	+	0.725365i
$690$	2.35233	−	29.9015i	0.0895516	−	1.13833i
$691$	4.61731	+	12.6860i	0.175651	+	0.482597i	0.996009	−	0.0892535i	$-0.0284481\pi$
$691$	4.61731	+	12.6860i	0.175651	+	0.482597i	−0.820358	+	0.571850i	$0.806226\pi$
$692$	4.02689	+	6.97478i	0.153079	+	0.265141i
$693$	20.0739	+	2.19862i	0.762546	+	0.0835188i
$694$	−3.59971	+	6.23488i	−0.136643	+	0.236673i
$695$	45.4358	+	8.01155i	1.72348	+	0.303895i
$696$	−8.47434	+	0.816262i	−0.321219	+	0.0309403i
$697$	12.9421	+	4.71054i	0.490217	+	0.178424i
$698$	54.9695	+	20.0073i	2.08063	+	0.757286i
$699$	−3.50631	+	13.5597i	−0.132621	+	0.512875i
$700$	2.60370	+	54.2885i	0.0984107	+	2.05191i
$701$		−	5.13366i		−	0.193896i	−0.995289	−	0.0969478i	$-0.969092\pi$
$701$		−	5.13366i		−	0.193896i	0.995289	−	0.0969478i	$-0.0309080\pi$
$702$	−16.8899	+	70.3816i	−0.637469	+	2.65638i
$703$	−10.8071	−	6.23950i	−0.407599	−	0.235327i
$704$	−32.6936	−	5.76476i	−1.23219	−	0.217268i
$705$	50.0382	−	50.9225i	1.88455	−	1.91785i
$706$	37.6906	+	44.9179i	1.41850	+	1.69051i
$707$	−1.90466	−	4.54302i	−0.0716320	−	0.170858i
$708$	14.6790	−	1.41391i	0.551671	−	0.0531378i
$709$	−3.27838	+	18.5926i	−0.123122	+	0.698260i	0.859283	+	0.511500i	$0.170910\pi$
$709$	−3.27838	+	18.5926i	−0.123122	+	0.698260i	−0.982406	+	0.186760i	$0.940201\pi$
$710$	−19.8200	−	34.3293i	−0.743832	−	1.28835i
$711$	−2.86375	−	0.453385i	−0.107399	−	0.0170033i
$712$	−21.1220	−	12.1948i	−0.791579	−	0.457018i
$713$	−0.615195	+	3.48894i	−0.0230392	+	0.130662i
$714$	9.18704	−	23.0248i	0.343816	−	0.861681i
$715$	−50.4093	−	18.3475i	−1.88520	−	0.686158i
$716$	43.1062	−	7.60079i	1.61096	−	0.284055i
$717$	6.35670	−	9.24970i	0.237395	−	0.345436i
$718$	−32.9191	−	27.6224i	−1.22853	−	1.03086i
$719$	−2.15856	+	3.73874i	−0.0805007	+	0.139431i	−0.903465	−	0.428662i	$-0.858985\pi$
$719$	−2.15856	+	3.73874i	−0.0805007	+	0.139431i	0.822964	+	0.568093i	$0.192319\pi$
$720$	−0.115799	−	6.60969i	−0.00431557	−	0.246329i
$721$	25.8605	−	23.9017i	0.963095	−	0.890146i
$722$	−25.2983	+	30.1494i	−0.941506	+	1.12204i
$723$	−4.45052	−	46.2048i	−0.165517	−	1.71838i
$724$	7.15100	−	19.6472i	0.265765	−	0.730183i
$725$	13.1434	−	2.31753i	0.488132	−	0.0860708i
$726$	4.42731	−	17.1214i	0.164313	−	0.635436i
$727$	10.4652	+	28.7528i	0.388131	+	1.06638i	0.967842	+	0.251560i	$0.0809435\pi$
$727$	10.4652	+	28.7528i	0.388131	+	1.06638i	−0.579710	+	0.814823i	$0.696834\pi$
$728$	27.1847	+	29.4125i	1.00753	+	1.09010i
$729$	1.41828	+	26.9627i	0.0525290	+	0.998619i
$730$	−51.6261	−	89.4191i	−1.91077	−	3.30955i
$731$	0.264521	−	1.50017i	0.00978366	−	0.0554859i
$732$	37.9816	−	10.5346i	1.40384	−	0.389369i
$733$	−6.38753	+	17.5496i	−0.235929	+	0.648210i	0.764066	+	0.645138i	$0.223200\pi$
$733$	−6.38753	+	17.5496i	−0.235929	+	0.648210i	−0.999995	+	0.00307180i	$0.999022\pi$
$734$	3.70928	+	21.0364i	0.136912	+	0.776466i
$735$	36.2000	+	20.0714i	1.33526	+	0.740344i
$736$	10.9536	+	9.19118i	0.403756	+	0.338791i
$737$			20.3971i			0.751337i
$738$	−18.8337	+	33.9821i	−0.693278	+	1.25090i
$739$	40.3186			1.48315			0.741573	−	0.670873i	$-0.234080\pi$
$739$	40.3186			1.48315			0.741573	+	0.670873i	$0.234080\pi$
$740$	−99.2676	+	36.1304i	−3.64915	+	1.32818i
$741$	1.04438	−	13.2756i	0.0383664	−	0.487692i
$742$	11.0653	+	26.3932i	0.406220	+	0.968923i
$743$	9.56525	−	26.2803i	0.350915	−	0.964131i	−0.631162	−	0.775651i	$-0.717422\pi$
$743$	9.56525	−	26.2803i	0.350915	−	0.964131i	0.982077	−	0.188480i	$-0.0603562\pi$
$744$	0.524477	−	6.66686i	0.0192283	−	0.244419i
$745$	−33.9570	+	40.4684i	−1.24409	+	1.48265i
$746$			44.4262i			1.62656i
$747$	4.78595	−	5.91094i	0.175109	−	0.216270i
$748$	16.3129	+	9.41823i	0.596457	+	0.344365i
$749$	−13.9013	−	21.6154i	−0.507941	−	0.789809i
$750$	−2.11634	−	21.9716i	−0.0772779	−	0.802290i
$751$	28.7061	−	24.0873i	1.04750	−	0.878959i	0.0546735	−	0.998504i	$-0.482588\pi$
$751$	28.7061	−	24.0873i	1.04750	−	0.878959i	0.992829	+	0.119546i	$0.0381438\pi$
$752$	1.35324	+	7.67458i	0.0493474	+	0.279863i
$753$	33.8598	+	8.75558i	1.23392	+	0.319071i
$754$	17.9557	−	21.3988i	0.653908	−	0.779297i
$755$	−19.1567			−0.697184
$756$	36.4702	+	21.6963i	1.32641	+	0.789086i
$757$	31.2917			1.13732			0.568659	−	0.822574i	$-0.307463\pi$
$757$	31.2917			1.13732			0.568659	+	0.822574i	$0.307463\pi$
$758$	35.2910	−	42.0582i	1.28183	−	1.52762i
$759$	6.94630	−	7.06906i	0.252135	−	0.256591i
$760$	−1.80883	−	10.2584i	−0.0656133	−	0.372112i
$761$	−26.8763	+	22.5519i	−0.974265	+	0.817505i	−0.983214	−	0.182455i	$-0.941596\pi$
$761$	−26.8763	+	22.5519i	−0.974265	+	0.817505i	0.00894931	+	0.999960i	$0.497151\pi$
$762$	−28.1648	+	20.0912i	−1.02030	+	0.727826i
$763$	16.8171	+	8.66290i	0.608818	+	0.313618i
$764$	44.7629	+	25.8439i	1.61946	+	0.934998i
$765$	−7.99624	+	23.2276i	−0.289105	+	0.839797i
$766$		−	24.5674i		−	0.887658i
$767$	−10.9502	+	13.0500i	−0.395389	+	0.471206i
$768$	−16.5566	−	11.3782i	−0.597435	−	0.410577i
$769$	4.55125	−	12.5045i	0.164122	−	0.450923i	−0.830183	−	0.557491i	$-0.811764\pi$
$769$	4.55125	−	12.5045i	0.164122	−	0.450923i	0.994305	+	0.106568i	$0.0339863\pi$
$770$	−31.3753	+	41.2543i	−1.13069	+	1.48670i
$771$	6.34194	−	3.02520i	0.228399	−	0.108950i
$772$	33.2741	−	12.1108i	1.19756	−	0.435877i
$773$	−17.3597			−0.624384			−0.312192	−	0.950019i	$-0.601063\pi$
$773$	−17.3597			−0.624384			−0.312192	+	0.950019i	$0.601063\pi$
$774$	4.06317	+	1.39877i	0.146048	+	0.0502777i
$775$			10.4835i			0.376577i
$776$	15.1329	+	12.6980i	0.543238	+	0.455831i
$777$	−9.35669	+	44.9749i	−0.335669	+	1.61347i
$778$	−3.09764	−	17.5676i	−0.111056	−	0.629828i
$779$	2.44480	−	6.71704i	0.0875941	−	0.240663i
$780$	−80.4067	−	79.0103i	−2.87902	−	2.82902i
$781$	2.27445	−	12.8991i	0.0813864	−	0.461565i
$782$	−6.08316	−	10.5363i	−0.217534	−	0.376779i
$783$	4.15417	−	9.55646i	0.148458	−	0.341520i
$784$	−4.07835	+	1.94455i	−0.145656	+	0.0694481i
$785$	−12.7266	−	34.9660i	−0.454231	−	1.24799i
$786$	−52.7451	−	51.8291i	−1.88135	−	1.84868i
$787$	14.3977	−	2.53870i	0.513221	−	0.0904948i	0.0889612	−	0.996035i	$-0.471645\pi$
$787$	14.3977	−	2.53870i	0.513221	−	0.0904948i	0.424260	+	0.905540i	$0.360534\pi$
$788$	−1.07295	+	2.94792i	−0.0382224	+	0.105015i
$789$	30.4405	−	21.7145i	1.08371	−	0.773056i
$790$	4.78339	−	5.70063i	0.170185	−	0.202819i
$791$	−0.857459	−	3.79071i	−0.0304877	−	0.134782i
$792$	−11.7723	+	14.5395i	−0.418311	+	0.516639i
$793$	−22.7662	+	39.4322i	−0.808450	+	1.40028i
$794$	5.75370	+	4.82793i	0.204191	+	0.171337i
$795$	−12.2100	−	25.5967i	−0.433044	−	0.907821i
$796$	−16.6625	+	2.93805i	−0.590587	+	0.104136i
$797$	−29.7715	−	10.8359i	−1.05456	−	0.383828i	−0.244178	−	0.969731i	$-0.578518\pi$
$797$	−29.7715	−	10.8359i	−1.05456	−	0.383828i	−0.810382	+	0.585902i	$0.800740\pi$
$798$	−11.9500	−	4.76813i	−0.423026	−	0.168790i
$799$	5.02864	−	28.5188i	0.177901	−	1.00892i
$800$	36.6435	+	21.1561i	1.29554	+	0.747981i
$801$	25.5872	−	15.3766i	0.904078	−	0.543304i
$802$	−39.0086	−	67.5649i	−1.37744	−	2.38580i
$803$	5.92438	−	33.5988i	0.209067	−	1.18568i
$804$	−17.7736	+	39.0040i	−0.626827	+	1.37556i
$805$	18.7344	−	7.85438i	0.660300	−	0.276830i
$806$	14.1043	+	16.8089i	0.496803	+	0.592067i
$807$	3.53078	+	0.913001i	0.124289	+	0.0321391i
$808$	4.49428	+	0.792462i	0.158108	+	0.0278787i
$809$	40.0677	+	23.1331i	1.40870	+	0.813316i	0.995263	−	0.0972146i	$-0.0309933\pi$
$809$	40.0677	+	23.1331i	1.40870	+	0.813316i	0.413441	+	0.910531i	$0.364327\pi$
$810$	−61.1908	−	32.5256i	−2.15002	−	1.14283i
$811$		−	33.8813i		−	1.18973i	−0.803825	−	0.594866i	$-0.797205\pi$
$811$		−	33.8813i		−	1.18973i	0.803825	−	0.594866i	$-0.202795\pi$
$812$	−8.85886	−	13.7748i	−0.310885	−	0.483402i
$813$	16.2117	+	15.9302i	0.568570	+	0.558696i
$814$	−54.0529	−	19.6737i	−1.89455	−	0.689561i
$815$	80.8494	+	29.4268i	2.83203	+	1.03078i
$816$	−1.55721	−	2.18299i	−0.0545134	−	0.0764198i
$817$	−0.778600	−	0.137288i	−0.0272398	−	0.00480310i
$818$	−20.3507	+	35.2484i	−0.711545	+	1.23243i
$819$	−47.6166	+	11.6513i	−1.66386	+	0.407129i
$820$	−30.2555	−	52.4040i	−1.05657	−	1.83003i
$821$	16.0558	+	44.1131i	0.560353	+	1.53956i	0.819123	+	0.573618i	$0.194460\pi$
$821$	16.0558	+	44.1131i	0.560353	+	1.53956i	−0.258771	+	0.965939i	$0.583317\pi$
$822$	−4.74296	−	3.25952i	−0.165430	−	0.113689i
$823$	−25.7167	+	21.5789i	−0.896428	+	0.752192i	−0.969489	−	0.245135i	$-0.921168\pi$
$823$	−25.7167	+	21.5789i	−0.896428	+	0.752192i	0.0730613	+	0.997327i	$0.476723\pi$
$824$	5.66492	+	32.1273i	0.197347	+	1.11921i
$825$	16.6102	−	24.1697i	0.578294	−	0.841481i
$826$	8.90301	+	13.8435i	0.309775	+	0.481676i
$827$	9.24493	−	5.33756i	0.321478	−	0.185605i	−0.330573	−	0.943780i	$-0.607242\pi$
$827$	9.24493	−	5.33756i	0.321478	−	0.185605i	0.652051	+	0.758175i	$0.273909\pi$
$828$	19.4427	−	7.46481i	0.675682	−	0.259420i
$829$	−30.1265	+	17.3936i	−1.04634	+	0.604103i	−0.921622	−	0.388089i	$-0.873135\pi$
$829$	−30.1265	+	17.3936i	−1.04634	+	0.604103i	−0.124716	+	0.992192i	$0.539802\pi$
$830$	6.67637	+	18.3432i	0.231740	+	0.636701i
$831$	3.27141	+	4.58603i	0.113484	+	0.159088i
$832$	79.3645	−	13.9941i	2.75147	−	0.485158i
$833$	16.7127	−	1.60679i	0.579060	−	0.0556720i
$834$	14.1097	+	50.8716i	0.488580	+	1.76154i
$835$	7.49968	+	6.29298i	0.259537	+	0.217777i
$836$	4.88813	−	8.46648i	0.169059	−	0.292819i
$837$	6.82598	+	4.51707i	0.235941	+	0.156133i
$838$	18.0283	−	10.4086i	0.622777	−	0.359561i
$839$	−14.6918	+	5.34740i	−0.507219	+	0.184613i	−0.582938	−	0.812517i	$-0.698097\pi$
$839$	−14.6918	+	5.34740i	−0.507219	+	0.184613i	0.0757191	+	0.997129i	$0.475875\pi$
$840$	−33.7793	+	18.1485i	−1.16550	+	0.626183i
$841$	19.1346	−	16.0558i	0.659813	−	0.553649i
$842$	−34.8884	−	41.5783i	−1.20233	−	1.43288i
$843$	2.57329	+	26.7157i	0.0886290	+	0.920136i
$844$	4.99907	−	1.81951i	0.172075	−	0.0626302i
$845$	85.8419			2.95305
$846$	77.2425	+	26.5911i	2.65565	+	0.914222i
$847$	11.6823	−	2.64253i	0.401407	−	0.0907985i
$848$	3.04862	+	0.537554i	0.104690	+	0.0184597i
$849$	−6.95144	+	10.1151i	−0.238573	+	0.347150i
$850$	−23.1414	−	27.5788i	−0.793743	−	0.945946i
$851$	14.4918	+	17.2706i	0.496772	+	0.592030i
$852$	15.5893	−	22.6841i	0.534079	−	0.777144i
$853$	13.0053	+	2.29319i	0.445294	+	0.0785174i	0.391799	−	0.920051i	$-0.371853\pi$
$853$	13.0053	+	2.29319i	0.445294	+	0.0785174i	0.0534951	+	0.998568i	$0.482964\pi$
$854$	29.8595	+	32.3065i	1.02177	+	1.10551i
$855$	12.0553	+	4.15010i	0.412283	+	0.141931i
$856$	23.8083			0.813752
$857$	32.5929	−	11.8629i	1.11335	−	0.405228i	0.281131	−	0.959669i	$-0.409290\pi$
$857$	32.5929	−	11.8629i	1.11335	−	0.405228i	0.832222	+	0.554442i	$0.187068\pi$
$858$	−5.88527	−	61.1002i	−0.200920	−	2.08593i
$859$	0.903326	+	1.07654i	0.0308211	+	0.0367311i	0.781235	−	0.624237i	$-0.214590\pi$
$859$	0.903326	+	1.07654i	0.0308211	+	0.0367311i	−0.750414	+	0.660968i	$0.770146\pi$
$860$	−5.12694	+	4.30201i	−0.174827	+	0.146697i
$861$	−26.3015	−	0.804650i	−0.896351	−	0.0274224i
$862$	−47.8364	+	17.4110i	−1.62931	+	0.593022i
$863$	30.4192	−	17.5625i	1.03548	−	0.597836i	0.116931	−	0.993140i	$-0.462694\pi$
$863$	30.4192	−	17.5625i	1.03548	−	0.597836i	0.918550	+	0.395304i	$0.129361\pi$
$864$	29.5639	−	14.7436i	1.00579	−	0.501588i
$865$	4.45375	−	7.71412i	0.151432	−	0.262288i
$866$	32.4452	+	27.2248i	1.10253	+	0.925135i
$867$	−5.20653	−	18.7718i	−0.176823	−	0.637523i
$868$	11.8642	−	4.97406i	0.402698	−	0.168831i
$869$	2.42155	−	0.426984i	0.0821454	−	0.0144844i
$870$	15.5315	+	21.7728i	0.526566	+	0.738168i
$871$	−16.9350	−	46.5284i	−0.573819	−	1.57655i
$872$	−15.1771	+	8.76251i	−0.513962	+	0.296736i
$873$	−22.5724	+	8.66640i	−0.763960	+	0.293313i
$874$	−5.46844	+	3.15720i	−0.184973	+	0.106794i
$875$	12.5740	−	8.08655i	0.425077	−	0.273375i
$876$	40.6061	−	59.0863i	1.37195	−	1.99634i
$877$	−7.31819	−	41.5035i	−0.247118	−	1.40147i	−0.815522	−	0.578726i	$-0.803550\pi$
$877$	−7.31819	−	41.5035i	−0.247118	−	1.40147i	0.568404	−	0.822749i	$-0.307561\pi$
$878$	−11.4493	+	9.60712i	−0.386396	+	0.324225i
$879$	−40.2693	−	27.6744i	−1.35825	−	0.933435i
$880$	1.91748	+	5.26823i	0.0646381	+	0.177592i
$881$	28.1569	+	48.7691i	0.948629	+	1.64307i	0.748317	+	0.663342i	$0.230862\pi$
$881$	28.1569	+	48.7691i	0.948629	+	1.64307i	0.200313	+	0.979732i	$0.435804\pi$
$882$	−2.89528	+	47.2745i	−0.0974891	+	1.59181i
$883$	−17.5215	+	30.3481i	−0.589645	+	1.02130i	0.404634	+	0.914479i	$0.367399\pi$
$883$	−17.5215	+	30.3481i	−0.589645	+	1.02130i	−0.994279	+	0.106816i	$0.965934\pi$
$884$	−45.0313	−	7.94023i	−1.51457	−	0.267059i
$885$	−9.47179	−	13.2781i	−0.318391	−	0.446337i
$886$	−37.6965	−	13.7204i	−1.26644	−	0.460946i
$887$	−40.3117	−	14.6722i	−1.35353	−	0.492646i	−0.439484	−	0.898250i	$-0.644839\pi$
$887$	−40.3117	−	14.6722i	−1.35353	−	0.492646i	−0.914049	+	0.405605i	$0.867061\pi$
$888$	−30.3549	−	29.8278i	−1.01864	−	1.00095i
$889$	−20.8302	−	10.7302i	−0.698622	−	0.359878i
$890$			76.6180i			2.56824i
$891$	−8.58041	−	21.2294i	−0.287455	−	0.711211i
$892$	58.4553	+	33.7492i	1.95723	+	1.13001i
$893$	−14.8015	−	2.60990i	−0.495312	−	0.0873370i
$894$	−58.5235	−	15.1332i	−1.95732	−	0.506130i
$895$	−31.1181	−	37.0850i	−1.04016	−	1.23962i
$896$	5.58371	−	43.8661i	0.186539	−	1.46546i
$897$	−9.97621	+	21.8927i	−0.333096	+	0.730975i
$898$	−12.6640	+	71.8214i	−0.422605	+	2.39671i
$899$	−1.57950	−	2.73577i	−0.0526791	−	0.0912429i
$900$	52.8236	−	31.7442i	1.76079	−	1.05814i
$901$	−9.96230	−	5.75174i	−0.331892	−	0.191618i
$902$	5.72158	−	32.4487i	0.190508	−	1.08042i
$903$	0.417505	+	2.88030i	0.0138937	+	0.0958505i
$904$	3.38333	+	1.23143i	0.112528	+	0.0409568i
$905$	−22.7732	+	4.01552i	−0.757005	+	0.133480i
$906$	−9.43750	−	19.7845i	−0.313540	−	0.657296i
$907$	−10.3157	−	8.65588i	−0.342526	−	0.287414i	0.455254	−	0.890361i	$-0.349548\pi$
$907$	−10.3157	−	8.65588i	−0.342526	−	0.287414i	−0.797781	+	0.602948i	$0.793993\pi$
$908$	20.0985	−	34.8116i	0.666991	−	1.15526i
$909$	−3.51492	+	4.34114i	−0.116583	+	0.143986i
$910$	37.3190	−	120.156i	1.23711	−	3.98313i
$911$	−36.2342	+	43.1823i	−1.20049	+	1.43069i	−0.326197	+	0.945302i	$0.605767\pi$
$911$	−36.2342	+	43.1823i	−1.20049	+	1.43069i	−0.874297	+	0.485391i	$0.838677\pi$
$912$	−1.13298	+	0.808205i	−0.0375169	+	0.0267623i
$913$	−2.20604	+	6.06105i	−0.0730093	+	0.200591i
$914$	−19.9275	+	3.51376i	−0.659144	+	0.116225i
$915$	−31.0942	−	30.5542i	−1.02794	−	1.01009i
$916$	−0.927806	−	2.54913i	−0.0306556	−	0.0842255i
$917$	14.8553	−	47.8296i	0.490565	−	1.57947i
$918$	−27.9282	+	3.18475i	−0.921767	+	0.105112i
$919$	19.3698	+	33.5495i	0.638951	+	1.10670i	0.985663	+	0.168725i	$0.0539649\pi$
$919$	19.3698	+	33.5495i	0.638951	+	1.10670i	−0.346712	+	0.937972i	$0.612702\pi$
$920$	−3.26794	+	18.5334i	−0.107741	+	0.611028i
$921$	−18.8677	−	18.5400i	−0.621710	−	0.610914i
$922$	−26.9147	+	73.9476i	−0.886390	+	2.43534i
$923$	5.52129	+	31.3128i	0.181736	+	1.03067i
$924$	−35.2340	−	7.33018i	−1.15912	−	0.241145i
$925$	51.1059	+	42.8829i	1.68035	+	1.40998i
$926$		−	63.4216i		−	2.08416i
$927$	−37.7549	−	12.9973i	−1.24003	−	0.426888i
$928$	−12.7500			−0.418539
$929$	−40.8960	+	14.8849i	−1.34175	+	0.488358i	−0.910364	−	0.413807i	$-0.864199\pi$
$929$	−40.8960	+	14.8849i	−1.34175	+	0.488358i	−0.431389	+	0.902166i	$0.641976\pi$
$930$	−18.9614	+	9.04486i	−0.621768	+	0.296593i
$931$	−0.833936	−	8.67399i	−0.0273311	−	0.284278i
$932$	8.53686	−	23.4548i	0.279634	−	0.768288i
$933$	12.0134	+	8.25600i	0.393301	+	0.270289i
$934$	35.6241	−	42.4552i	1.16566	−	1.38918i
$935$		−	20.8332i		−	0.681318i
$936$	14.7825	−	42.9406i	0.483182	−	1.40356i
$937$	−29.8016	−	17.2060i	−0.973576	−	0.562094i	−0.0732512	−	0.997314i	$-0.523337\pi$
$937$	−29.8016	−	17.2060i	−0.973576	−	0.562094i	−0.900324	+	0.435219i	$0.856671\pi$
$938$	−47.7845	+	2.29177i	−1.56022	+	0.0748290i
$939$	17.9670	−	12.8166i	0.586332	−	0.418255i
$940$	−97.4651	+	81.7829i	−3.17896	+	2.66746i
$941$	9.69222	+	54.9673i	0.315957	+	1.79188i	0.566801	+	0.823855i	$0.308181\pi$
$941$	9.69222	+	54.9673i	0.315957	+	1.79188i	−0.250843	+	0.968028i	$0.580708\pi$
$942$	29.8422	−	30.3696i	0.972311	−	0.989495i
$943$	−8.30107	+	9.89283i	−0.270320	+	0.322155i
$944$	1.78036			0.0579458
$945$	0.613228	−	46.9302i	0.0199483	−	1.52664i
$946$	−3.64432			−0.118487
$947$	3.33361	−	3.97284i	0.108328	−	0.129100i	−0.709156	−	0.705051i	$-0.750924\pi$
$947$	3.33361	−	3.97284i	0.108328	−	0.129100i	0.817484	+	0.575952i	$0.195368\pi$
$948$	5.00262	+	1.29359i	0.162478	+	0.0420140i
$949$	14.3816	+	81.5620i	0.466846	+	2.64761i
$950$	−14.3136	+	12.0105i	−0.464394	+	0.389673i
$951$	−4.31078	−	44.7541i	−0.139787	−	1.45125i
$952$	−7.12285	+	13.8274i	−0.230853	+	0.448148i
$953$	−38.7728	−	22.3855i	−1.25598	−	0.725138i	−0.283686	−	0.958917i	$-0.591557\pi$
$953$	−38.7728	−	22.3855i	−1.25598	−	0.725138i	−0.972290	+	0.233779i	$0.924891\pi$
$954$	20.4203	−	25.2203i	0.661131	−	0.816537i
$955$		−	57.1668i		−	1.84987i
$956$	−12.8568	+	15.3221i	−0.415819	+	0.495554i
$957$	−0.693070	+	8.80992i	−0.0224038	+	0.284784i
$958$	24.7104	−	67.8914i	0.798358	−	2.19347i
$959$	0.492174	−	3.86655i	0.0158931	−	0.124858i
$960$	−6.05123	+	76.9199i	−0.195303	+	2.48258i
$961$	−26.7987	+	9.75393i	−0.864475	+	0.314643i
$962$	139.636			4.50204
$963$	−14.1260	+	25.4879i	−0.455204	+	0.821335i
$964$			82.7245i			2.66438i
$965$	−30.0007	−	25.1735i	−0.965756	−	0.810365i
$966$	17.3412	+	15.4789i	0.557945	+	0.498026i
$967$	3.09720	+	17.5651i	0.0995992	+	0.564855i	0.993241	+	0.116074i	$0.0370308\pi$
$967$	3.09720	+	17.5651i	0.0995992	+	0.564855i	−0.893641	+	0.448782i	$0.851858\pi$
$968$	−3.79504	+	10.4268i	−0.121977	+	0.335130i
$969$	4.98347	−	1.38221i	0.160092	−	0.0444030i
$970$	10.7762	−	61.1147i	0.346002	−	1.96227i
$971$	4.65514	+	8.06294i	0.149391	+	0.258752i	0.931002	−	0.365013i	$-0.118935\pi$
$971$	4.65514	+	8.06294i	0.149391	+	0.258752i	−0.781612	+	0.623765i	$0.785602\pi$
$972$	2.09112	−	48.0723i	0.0670727	−	1.54192i
$973$	−26.2575	+	24.2686i	−0.841776	+	0.778016i
$974$	−3.72561	−	10.2360i	−0.119376	−	0.327984i
$975$	−17.8228	+	68.9250i	−0.570788	+	2.20737i
$976$	4.68624	−	0.826311i	0.150003	−	0.0264496i
$977$	1.23209	−	3.38515i	0.0394182	−	0.108300i	−0.918422	−	0.395602i	$-0.870536\pi$
$977$	1.23209	−	3.38515i	0.0394182	−	0.108300i	0.957840	+	0.287302i	$0.0927582\pi$
$978$	9.43913	+	97.9960i	0.301830	+	3.13357i
$979$	−16.2731	+	19.3936i	−0.520092	+	0.619821i
$980$	−60.7867	−	41.7906i	−1.94176	−	1.33495i
$981$	−0.375737	−	21.4468i	−0.0119964	−	0.684742i
$982$	−13.1352	+	22.7508i	−0.419161	+	0.726008i
$983$	−2.94241	−	2.46898i	−0.0938484	−	0.0787481i	0.594656	−	0.803980i	$-0.297288\pi$
$983$	−2.94241	−	2.46898i	−0.0938484	−	0.0787481i	−0.688505	+	0.725232i	$0.741733\pi$
$984$	13.8068	−	20.0904i	0.440145	−	0.640459i
$985$	3.41694	−	0.602498i	0.108873	−	0.0191972i
$986$	10.1942	+	3.71037i	0.324648	+	0.118162i
$987$	7.93693	+	54.7557i	0.252635	+	1.74289i
$988$	−4.12103	+	23.3715i	−0.131108	+	0.743548i
$989$	1.23700	+	0.714180i	0.0393342	+	0.0227096i
$990$	58.0465	+	9.18983i	1.84484	+	0.292072i
$991$	3.17566	+	5.50041i	0.100878	+	0.174726i	0.912047	−	0.410086i	$-0.134501\pi$
$991$	3.17566	+	5.50041i	0.100878	+	0.174726i	−0.811168	+	0.584813i	$0.801168\pi$
$992$	1.73912	−	9.86304i	0.0552171	−	0.313152i
$993$	5.08737	−	0.490023i	0.161443	−	0.0155504i
$994$	30.4744	+	3.87908i	0.966588	+	0.123037i
$995$	12.0285	+	14.3350i	0.381330	+	0.454452i
$996$	−9.49993	+	9.66782i	−0.301017	+	0.306337i
$997$	−53.6156	−	9.45388i	−1.69802	−	0.299407i	−0.761021	−	0.648728i	$-0.775301\pi$
$997$	−53.6156	−	9.45388i	−1.69802	−	0.299407i	−0.937003	+	0.349320i	$0.886413\pi$
$998$	−20.5934	−	11.8896i	−0.651873	−	0.376359i
$999$	49.9422	−	14.7988i	1.58010	−	0.468213i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.ba.a.101.3	✓	132
3.2	odd	2		567.2.ba.a.143.20		132
7.5	odd	6		189.2.bd.a.47.20	yes	132
21.5	even	6		567.2.bd.a.467.3		132
27.4	even	9		567.2.bd.a.17.3		132
27.23	odd	18		189.2.bd.a.185.20	yes	132
189.131	even	18	inner	189.2.ba.a.131.3	yes	132
189.166	odd	18		567.2.ba.a.341.20		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.3	✓	132	1.1	even	1	trivial
189.2.ba.a.131.3	yes	132	189.131	even	18	inner
189.2.bd.a.47.20	yes	132	7.5	odd	6
189.2.bd.a.185.20	yes	132	27.23	odd	18
567.2.ba.a.143.20		132	3.2	odd	2
567.2.ba.a.341.20		132	189.166	odd	18
567.2.bd.a.17.3		132	27.4	even	9
567.2.bd.a.467.3		132	21.5	even	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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.ba (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.44973 + 1.72772i) q^{2} +(0.462924 + 1.66904i) q^{3} +(-0.536009 - 3.03986i) q^{4} +(-2.61524 + 2.19445i) q^{5} +(-3.55476 - 1.61986i) q^{6} +(-0.126746 - 2.64271i) q^{7} +(2.12267 + 1.22552i) q^{8} +(-2.57140 + 1.54528i) q^{9} +O(q^{10})\)	\(q+(-1.44973 + 1.72772i) q^{2} +(0.462924 + 1.66904i) q^{3} +(-0.536009 - 3.03986i) q^{4} +(-2.61524 + 2.19445i) q^{5} +(-3.55476 - 1.61986i) q^{6} +(-0.126746 - 2.64271i) q^{7} +(2.12267 + 1.22552i) q^{8} +(-2.57140 + 1.54528i) q^{9} -7.69979i q^{10} +(1.63538 - 1.94897i) q^{11} +(4.82552 - 2.30185i) q^{12} +(-2.11236 + 5.80365i) q^{13} +(4.74963 + 3.61225i) q^{14} +(-4.87329 - 3.34909i) q^{15} +(0.606533 - 0.220760i) q^{16} -2.39853 q^{17} +(1.05803 - 6.68292i) q^{18} +1.24485i q^{19} +(8.07261 + 6.77373i) q^{20} +(4.35213 - 1.43492i) q^{21} +(0.996420 + 5.65098i) q^{22} +(0.769210 - 2.11339i) q^{23} +(-1.06281 + 4.11015i) q^{24} +(1.15565 - 6.55401i) q^{25} +(-6.96475 - 12.0633i) q^{26} +(-3.76950 - 3.57643i) q^{27} +(-7.96554 + 1.80181i) q^{28} +(0.685884 + 1.88445i) q^{29} +(12.8513 - 3.56442i) q^{30} +(-1.55132 + 0.273539i) q^{31} +(-2.17451 + 5.97442i) q^{32} +(4.00997 + 1.82729i) q^{33} +(3.47723 - 4.14400i) q^{34} +(6.13078 + 6.63320i) q^{35} +(6.07573 + 6.98842i) q^{36} +(-5.01223 + 8.68144i) q^{37} +(-2.15077 - 1.80471i) q^{38} +(-10.6644 - 0.838960i) q^{39} +(-8.24065 + 1.45305i) q^{40} +(-5.39584 - 1.96393i) q^{41} +(-3.83027 + 9.59952i) q^{42} +(-0.110284 + 0.625454i) q^{43} +(-6.80118 - 3.92666i) q^{44} +(3.33380 - 9.68410i) q^{45} +(2.53620 + 4.39283i) q^{46} +(-2.09655 + 11.8901i) q^{47} +(0.649236 + 0.910134i) q^{48} +(-6.96787 + 0.669906i) q^{49} +(9.64814 + 11.4982i) q^{50} +(-1.11034 - 4.00325i) q^{51} +(18.7745 + 3.31045i) q^{52} +(4.15350 + 2.39802i) q^{53} +(11.6439 - 1.32779i) q^{54} +8.68580i q^{55} +(2.96967 - 5.76493i) q^{56} +(-2.07772 + 0.576273i) q^{57} +(-4.25016 - 1.54693i) q^{58} +(2.59194 + 0.943390i) q^{59} +(-7.56863 + 16.6093i) q^{60} +(7.26032 + 1.28019i) q^{61} +(1.77639 - 3.07681i) q^{62} +(4.40965 + 6.59962i) q^{63} +(-6.52423 - 11.3003i) q^{64} +(-7.21149 - 19.8134i) q^{65} +(-8.97045 + 4.27904i) q^{66} +(-6.14145 + 5.15329i) q^{67} +(1.28564 + 7.29120i) q^{68} +(3.88342 + 0.305506i) q^{69} +(-20.3483 + 0.975916i) q^{70} +(4.45847 - 2.57410i) q^{71} +(-7.35201 + 0.128804i) q^{72} +(11.6132 - 6.70488i) q^{73} +(-7.73274 - 21.2455i) q^{74} +(11.4739 - 1.10518i) q^{75} +(3.78418 - 0.667254i) q^{76} +(-5.35785 - 4.07482i) q^{77} +(16.9100 - 17.2089i) q^{78} +(0.740362 + 0.621237i) q^{79} +(-1.10178 + 1.90835i) q^{80} +(4.22422 - 7.94707i) q^{81} +(11.2156 - 6.47536i) q^{82} +(-2.38230 + 0.867085i) q^{83} +(-6.69474 - 12.4607i) q^{84} +(6.27275 - 5.26346i) q^{85} +(-0.920729 - 1.09728i) q^{86} +(-2.82772 + 2.01713i) q^{87} +(5.85988 - 2.13282i) q^{88} -9.95066 q^{89} +(11.8983 + 19.7992i) q^{90} +(15.6051 + 4.84676i) q^{91} +(-6.83671 - 1.20550i) q^{92} +(-1.17469 - 2.46259i) q^{93} +(-17.5034 - 20.8598i) q^{94} +(-2.73177 - 3.25560i) q^{95} +(-10.9782 - 0.863647i) q^{96} +(7.93719 + 1.39954i) q^{97} +(8.94414 - 13.0097i) q^{98} +(-1.19352 + 7.53871i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Introduction

L-functions

Modular forms

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