LMFDB - Embedded newform 189.2.ba.a.5.11

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			5.11
Character	$\chi$	$=$	189.5
Dual form			189.2.ba.a.38.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.220121 - 0.0388132i) q^{2} +(-0.104309 - 1.72891i) q^{3} +(-1.83244 + 0.666953i) q^{4} +(0.595276 - 3.37598i) q^{5} +(-0.0900651 - 0.376520i) q^{6} +(-2.47857 + 0.925586i) q^{7} +(-0.764613 + 0.441450i) q^{8} +(-2.97824 + 0.360682i) q^{9} +O(q^{10})$	\(q+(0.220121 - 0.0388132i) q^{2} +(-0.104309 - 1.72891i) q^{3} +(-1.83244 + 0.666953i) q^{4} +(0.595276 - 3.37598i) q^{5} +(-0.0900651 - 0.376520i) q^{6} +(-2.47857 + 0.925586i) q^{7} +(-0.764613 + 0.441450i) q^{8} +(-2.97824 + 0.360682i) q^{9} -0.766227i q^{10} +(-0.563881 + 0.0994274i) q^{11} +(1.34424 + 3.09855i) q^{12} +(0.663083 - 0.790231i) q^{13} +(-0.509659 + 0.299942i) q^{14} +(-5.89884 - 0.677031i) q^{15} +(2.83646 - 2.38007i) q^{16} +3.70384 q^{17} +(-0.641573 + 0.194989i) q^{18} -8.40493i q^{19} +(1.16081 + 6.58329i) q^{20} +(1.85879 + 4.18866i) q^{21} +(-0.120263 + 0.0437721i) q^{22} +(2.38732 - 2.84510i) q^{23} +(0.842981 + 1.27590i) q^{24} +(-6.34441 - 2.30918i) q^{25} +(0.115287 - 0.199683i) q^{26} +(0.934243 + 5.11148i) q^{27} +(3.92450 - 3.34917i) q^{28} +(2.81038 + 3.34928i) q^{29} +(-1.32474 + 0.0799245i) q^{30} +(0.645801 + 1.77433i) q^{31} +(1.66702 - 1.98668i) q^{32} +(0.230719 + 0.964526i) q^{33} +(0.815291 - 0.143758i) q^{34} +(1.64933 + 8.91856i) q^{35} +(5.21688 - 2.64727i) q^{36} +(2.08746 + 3.61558i) q^{37} +(-0.326222 - 1.85010i) q^{38} +(-1.43540 - 1.06398i) q^{39} +(1.03517 + 2.84410i) q^{40} +(0.371534 + 0.311754i) q^{41} +(0.571734 + 0.849866i) q^{42} +(-5.66998 - 2.06370i) q^{43} +(0.966963 - 0.558277i) q^{44} +(-0.555221 + 10.2692i) q^{45} +(0.415071 - 0.718925i) q^{46} +(-5.96744 - 2.17197i) q^{47} +(-4.41080 - 4.65572i) q^{48} +(5.28658 - 4.58825i) q^{49} +(-1.48616 - 0.262050i) q^{50} +(-0.386344 - 6.40359i) q^{51} +(-0.688011 + 1.89029i) q^{52} +(10.8697 - 6.27561i) q^{53} +(0.404039 + 1.08888i) q^{54} +1.96284i q^{55} +(1.48654 - 1.80188i) q^{56} +(-14.5313 + 0.876711i) q^{57} +(0.748619 + 0.628166i) q^{58} +(6.04312 + 5.07078i) q^{59} +(11.2608 - 2.69363i) q^{60} +(-1.51419 + 4.16020i) q^{61} +(0.211022 + 0.365500i) q^{62} +(7.04792 - 3.65059i) q^{63} +(-3.41290 + 5.91132i) q^{64} +(-2.27308 - 2.70896i) q^{65} +(0.0882223 + 0.203357i) q^{66} +(-1.67428 + 9.49530i) q^{67} +(-6.78705 + 2.47029i) q^{68} +(-5.16793 - 3.83069i) q^{69} +(0.709209 + 1.89915i) q^{70} +(-0.452673 - 0.261351i) q^{71} +(2.11798 - 1.59052i) q^{72} +(-6.85309 - 3.95663i) q^{73} +(0.599825 + 0.714844i) q^{74} +(-3.33057 + 11.2098i) q^{75} +(5.60569 + 15.4015i) q^{76} +(1.30559 - 0.768357i) q^{77} +(-0.357258 - 0.178491i) q^{78} +(-1.65313 - 9.37537i) q^{79} +(-6.34660 - 10.9926i) q^{80} +(8.73982 - 2.14839i) q^{81} +(0.0938826 + 0.0542032i) q^{82} +(-12.7845 + 10.7275i) q^{83} +(-6.19976 - 6.43574i) q^{84} +(2.20481 - 12.5041i) q^{85} +(-1.32818 - 0.234194i) q^{86} +(5.49744 - 5.20824i) q^{87} +(0.387258 - 0.324948i) q^{88} +11.8925 q^{89} +(0.276364 + 2.28201i) q^{90} +(-0.912067 + 2.57238i) q^{91} +(-2.47707 + 6.80570i) q^{92} +(3.00028 - 1.30161i) q^{93} +(-1.39786 - 0.246480i) q^{94} +(-28.3748 - 5.00325i) q^{95} +(-3.60866 - 2.67489i) q^{96} +(3.46606 - 9.52293i) q^{97} +(0.985601 - 1.21516i) q^{98} +(1.64351 - 0.499500i) 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 $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.220121	−	0.0388132i	0.155649	−	0.0274451i	−0.0952807	−	0.995450i	$-0.530375\pi$
$2$	0.220121	−	0.0388132i	0.155649	−	0.0274451i	0.250930	+	0.968005i	$0.419264\pi$
$3$	−0.104309	−	1.72891i	−0.0602229	−	0.998185i
$3$	−0.104309	−	1.72891i	−0.0602229	−	0.998185i
$4$	−1.83244	+	0.666953i	−0.916219	+	0.333477i
$5$	0.595276	−	3.37598i	0.266215	−	1.50978i	−0.499336	−	0.866408i	$-0.666423\pi$
$5$	0.595276	−	3.37598i	0.266215	−	1.50978i	0.765552	−	0.643375i	$-0.222466\pi$
$6$	−0.0900651	−	0.376520i	−0.0367689	−	0.153714i
$7$	−2.47857	+	0.925586i	−0.936810	+	0.349839i
$7$	−2.47857	+	0.925586i	−0.936810	+	0.349839i
$8$	−0.764613	+	0.441450i	−0.270332	+	0.156076i
$9$	−2.97824	+	0.360682i	−0.992746	+	0.120227i
$10$		−	0.766227i		−	0.242302i
$11$	−0.563881	+	0.0994274i	−0.170016	+	0.0299785i	−0.258008	−	0.966143i	$-0.583066\pi$
$11$	−0.563881	+	0.0994274i	−0.170016	+	0.0299785i	0.0879918	+	0.996121i	$0.471955\pi$
$12$	1.34424	+	3.09855i	0.388049	+	0.894473i
$13$	0.663083	−	0.790231i	0.183906	−	0.219171i	−0.666213	−	0.745762i	$-0.732086\pi$
$13$	0.663083	−	0.790231i	0.183906	−	0.219171i	0.850119	+	0.526591i	$0.176530\pi$
$14$	−0.509659	+	0.299942i	−0.136212	+	0.0801628i
$15$	−5.89884	−	0.677031i	−1.52307	−	0.174809i
$16$	2.83646	−	2.38007i	0.709116	−	0.595019i
$17$	3.70384			0.898312			0.449156	−	0.893453i	$-0.351725\pi$
$17$	3.70384			0.898312			0.449156	+	0.893453i	$0.351725\pi$
$18$	−0.641573	+	0.194989i	−0.151220	+	0.0459593i
$19$		−	8.40493i		−	1.92822i	−0.265498	−	0.964111i	$-0.585536\pi$
$19$		−	8.40493i		−	1.92822i	0.265498	−	0.964111i	$-0.414464\pi$
$20$	1.16081	+	6.58329i	0.259565	+	1.47207i
$21$	1.85879	+	4.18866i	0.405621	+	0.914041i
$22$	−0.120263	+	0.0437721i	−0.0256401	+	0.00933224i
$23$	2.38732	−	2.84510i	0.497791	−	0.593244i	−0.457390	−	0.889266i	$-0.651216\pi$
$23$	2.38732	−	2.84510i	0.497791	−	0.593244i	0.955181	+	0.296022i	$0.0956602\pi$
$24$	0.842981	+	1.27590i	0.172073	+	0.260442i
$25$	−6.34441	−	2.30918i	−1.26888	−	0.461835i
$26$	0.115287	−	0.199683i	0.0226096	−	0.0391610i
$27$	0.934243	+	5.11148i	0.179795	+	0.983704i
$28$	3.92450	−	3.34917i	0.741660	−	0.632933i
$29$	2.81038	+	3.34928i	0.521874	+	0.621945i	0.961023	−	0.276469i	$-0.0891643\pi$
$29$	2.81038	+	3.34928i	0.521874	+	0.621945i	−0.439149	+	0.898414i	$0.644720\pi$
$30$	−1.32474	+	0.0799245i	−0.241863	+	0.0145922i
$31$	0.645801	+	1.77433i	0.115989	+	0.318678i	0.984080	−	0.177728i	$-0.0568748\pi$
$31$	0.645801	+	1.77433i	0.115989	+	0.318678i	−0.868090	+	0.496406i	$0.834653\pi$
$32$	1.66702	−	1.98668i	0.294690	−	0.351198i
$33$	0.230719	+	0.964526i	0.0401630	+	0.167902i
$34$	0.815291	−	0.143758i	0.139821	−	0.0246543i
$35$	1.64933	+	8.91856i	0.278787	+	1.50751i
$36$	5.21688	−	2.64727i	0.869480	−	0.441212i
$37$	2.08746	+	3.61558i	0.343176	+	0.594398i	0.985021	−	0.172437i	$-0.0551640\pi$
$37$	2.08746	+	3.61558i	0.343176	+	0.594398i	−0.641845	+	0.766835i	$0.721831\pi$
$38$	−0.326222	−	1.85010i	−0.0529203	−	0.300126i
$39$	−1.43540	−	1.06398i	−0.229848	−	0.170373i
$40$	1.03517	+	2.84410i	0.163674	+	0.449692i
$41$	0.371534	+	0.311754i	0.0580239	+	0.0486879i	0.671338	−	0.741151i	$-0.265720\pi$
$41$	0.371534	+	0.311754i	0.0580239	+	0.0486879i	−0.613315	+	0.789839i	$0.710164\pi$
$42$	0.571734	+	0.849866i	0.0882204	+	0.131137i
$43$	−5.66998	−	2.06370i	−0.864664	−	0.314712i	−0.128660	−	0.991689i	$-0.541067\pi$
$43$	−5.66998	−	2.06370i	−0.864664	−	0.314712i	−0.736004	+	0.676977i	$0.763290\pi$
$44$	0.966963	−	0.558277i	0.145775	−	0.0841634i
$45$	−0.555221	+	10.2692i	−0.0827674	+	1.53084i
$46$	0.415071	−	0.718925i	0.0611989	−	0.106000i
$47$	−5.96744	−	2.17197i	−0.870441	−	0.316815i	−0.132095	−	0.991237i	$-0.542170\pi$
$47$	−5.96744	−	2.17197i	−0.870441	−	0.316815i	−0.738346	+	0.674422i	$0.764393\pi$
$48$	−4.41080	−	4.65572i	−0.636644	−	0.671995i
$49$	5.28658	−	4.58825i	0.755226	−	0.655465i
$50$	−1.48616	−	0.262050i	−0.210175	−	0.0370595i
$51$	−0.386344	−	6.40359i	−0.0540990	−	0.896682i
$52$	−0.688011	+	1.89029i	−0.0954100	+	0.262137i
$53$	10.8697	−	6.27561i	1.49306	−	0.862021i	0.493096	−	0.869975i	$-0.335865\pi$
$53$	10.8697	−	6.27561i	1.49306	−	0.862021i	0.999968	+	0.00795364i	$0.00253175\pi$
$54$	0.404039	+	1.08888i	0.0549828	+	0.148178i
$55$			1.96284i			0.264669i
$56$	1.48654	−	1.80188i	0.198648	−	0.240786i
$57$	−14.5313	+	0.876711i	−1.92472	+	0.116123i
$58$	0.748619	+	0.628166i	0.0982985	+	0.0824822i
$59$	6.04312	+	5.07078i	0.786747	+	0.660159i	0.944938	−	0.327249i	$-0.106122\pi$
$59$	6.04312	+	5.07078i	0.786747	+	0.660159i	−0.158191	+	0.987409i	$0.550566\pi$
$60$	11.2608	−	2.69363i	1.45377	−	0.347747i
$61$	−1.51419	+	4.16020i	−0.193872	+	0.532659i	−0.998097	−	0.0616663i	$-0.980359\pi$
$61$	−1.51419	+	4.16020i	−0.193872	+	0.532659i	0.804225	+	0.594325i	$0.202581\pi$
$62$	0.211022	+	0.365500i	0.0267998	+	0.0464186i
$63$	7.04792	−	3.65059i	0.887955	−	0.459931i
$64$	−3.41290	+	5.91132i	−0.426613	+	0.738915i
$65$	−2.27308	−	2.70896i	−0.281941	−	0.336005i
$66$	0.0882223	+	0.203357i	0.0108594	+	0.0250316i
$67$	−1.67428	+	9.49530i	−0.204546	+	1.16004i	0.693607	+	0.720353i	$0.256020\pi$
$67$	−1.67428	+	9.49530i	−0.204546	+	1.16004i	−0.898153	+	0.439683i	$0.855091\pi$
$68$	−6.78705	+	2.47029i	−0.823051	+	0.299566i
$69$	−5.16793	−	3.83069i	−0.622146	−	0.461160i
$70$	0.709209	+	1.89915i	0.0847667	+	0.226991i
$71$	−0.452673	−	0.261351i	−0.0537224	−	0.0310167i	0.472898	−	0.881117i	$-0.343208\pi$
$71$	−0.452673	−	0.261351i	−0.0537224	−	0.0310167i	−0.526621	+	0.850100i	$0.676541\pi$
$72$	2.11798	−	1.59052i	0.249606	−	0.187445i
$73$	−6.85309	−	3.95663i	−0.802094	−	0.463089i	0.0421090	−	0.999113i	$-0.486592\pi$
$73$	−6.85309	−	3.95663i	−0.802094	−	0.463089i	−0.844203	+	0.536024i	$0.819926\pi$
$74$	0.599825	+	0.714844i	0.0697282	+	0.0830989i
$75$	−3.33057	+	11.2098i	−0.384581	+	1.29439i
$76$	5.60569	+	15.4015i	0.643017	+	1.76668i
$77$	1.30559	−	0.768357i	0.148785	−	0.0875625i
$78$	−0.357258	−	0.178491i	−0.0404515	−	0.0202102i
$79$	−1.65313	−	9.37537i	−0.185992	−	1.05481i	−0.924675	−	0.380758i	$-0.875663\pi$
$79$	−1.65313	−	9.37537i	−0.185992	−	1.05481i	0.738683	−	0.674053i	$-0.235448\pi$
$80$	−6.34660	−	10.9926i	−0.709571	−	1.22901i
$81$	8.73982	−	2.14839i	0.971091	−	0.238710i
$82$	0.0938826	+	0.0542032i	0.0103676	+	0.00598574i
$83$	−12.7845	+	10.7275i	−1.40328	+	1.17749i	−0.443660	+	0.896195i	$0.646320\pi$
$83$	−12.7845	+	10.7275i	−1.40328	+	1.17749i	−0.959621	+	0.281297i	$0.909235\pi$
$84$	−6.19976	−	6.43574i	−0.676449	−	0.702197i
$85$	2.20481	−	12.5041i	0.239145	−	1.35626i
$86$	−1.32818	−	0.234194i	−0.143221	−	0.0252538i
$87$	5.49744	−	5.20824i	0.589388	−	0.558382i
$88$	0.387258	−	0.324948i	0.0412819	−	0.0346396i
$89$	11.8925			1.26060			0.630302	−	0.776350i	$-0.282931\pi$
$89$	11.8925			1.26060			0.630302	+	0.776350i	$0.282931\pi$
$90$	0.276364	+	2.28201i	0.0291313	+	0.240545i
$91$	−0.912067	+	2.57238i	−0.0956106	+	0.269659i
$92$	−2.47707	+	6.80570i	−0.258253	+	0.709543i
$93$	3.00028	−	1.30161i	0.311115	−	0.134971i
$94$	−1.39786	−	0.246480i	−0.144178	−	0.0254225i
$95$	−28.3748	−	5.00325i	−2.91120	−	0.513323i
$96$	−3.60866	−	2.67489i	−0.368308	−	0.273005i
$97$	3.46606	−	9.52293i	0.351926	−	0.966907i	−0.629826	−	0.776737i	$-0.716874\pi$
$97$	3.46606	−	9.52293i	0.351926	−	0.966907i	0.981751	−	0.190171i	$-0.0609042\pi$
$98$	0.985601	−	1.21516i	0.0995608	−	0.122750i
$99$	1.64351	−	0.499500i	0.165179	−	0.0502016i
$100$	13.1658			1.31658
$101$	12.0960	−	10.1498i	1.20360	−	1.00994i	0.204077	−	0.978955i	$-0.434581\pi$
$101$	12.0960	−	10.1498i	1.20360	−	1.00994i	0.999520	−	0.0309832i	$-0.00986382\pi$
$102$	−0.333586	−	1.39457i	−0.0330300	−	0.138083i
$103$	−4.08844	−	0.720902i	−0.402846	−	0.0710326i	−0.0314457	−	0.999505i	$-0.510011\pi$
$103$	−4.08844	−	0.720902i	−0.402846	−	0.0710326i	−0.371400	+	0.928473i	$0.621122\pi$
$104$	−0.158154	+	0.896938i	−0.0155083	+	0.0879520i
$105$	15.2473	−	3.78182i	1.48799	−	0.369068i
$106$	2.14906	−	1.80328i	0.208736	−	0.175150i
$107$	−2.22494	−	1.28457i	−0.215093	−	0.124184i	0.388583	−	0.921414i	$-0.372965\pi$
$107$	−2.22494	−	1.28457i	−0.215093	−	0.124184i	−0.603676	+	0.797230i	$0.706298\pi$
$108$	−5.12106	−	8.74337i	−0.492774	−	0.841331i
$109$	0.237244	+	0.410919i	0.0227239	+	0.0393589i	0.877164	−	0.480191i	$-0.159433\pi$
$109$	0.237244	+	0.410919i	0.0227239	+	0.0393589i	−0.854440	+	0.519550i	$0.826099\pi$
$110$	0.0761840	+	0.432061i	0.00726386	+	0.0411954i
$111$	6.03326	−	3.98616i	0.572652	−	0.378349i
$112$	−4.82740	+	8.52456i	−0.456146	+	0.805495i
$113$	−5.70443	−	15.6728i	−0.536628	−	1.47437i	−0.851047	−	0.525089i	$-0.824032\pi$
$113$	−5.70443	−	15.6728i	−0.536628	−	1.47437i	0.314420	−	0.949284i	$-0.398190\pi$
$114$	−3.16462	+	0.756991i	−0.296394	+	0.0708987i
$115$	−8.18387	−	9.75316i	−0.763150	−	0.909487i
$116$	−7.38366	−	4.26296i	−0.685555	−	0.395806i
$117$	−1.68980	+	2.59266i	−0.156222	+	0.239691i
$118$	1.52703	+	0.881631i	0.140574	+	0.0811607i
$119$	−9.18021	+	3.42822i	−0.841548	+	0.314264i
$120$	4.80921	−	2.08638i	0.439019	−	0.190459i
$121$	−10.0285	+	3.65009i	−0.911686	+	0.331826i
$122$	−0.171834	+	0.974517i	−0.0155571	+	0.0882286i
$123$	0.500240	−	0.674867i	0.0451051	−	0.0608507i
$124$	−2.36678	−	2.82062i	−0.212543	−	0.253299i
$125$	−3.00225	+	5.20005i	−0.268530	+	0.465107i
$126$	1.40970	−	1.07712i	0.125586	−	0.0959578i
$127$	2.88122	+	4.99042i	0.255667	+	0.442828i	0.965076	−	0.261969i	$-0.0843717\pi$
$127$	2.88122	+	4.99042i	0.255667	+	0.442828i	−0.709410	+	0.704796i	$0.751038\pi$
$128$	−2.29582	+	6.30771i	−0.202924	+	0.557528i
$129$	−2.97652	+	10.0181i	−0.262068	+	0.882047i
$130$	−0.605497	−	0.508072i	−0.0531056	−	0.0445609i
$131$	11.3834	+	9.55180i	0.994572	+	0.834545i	0.986223	−	0.165420i	$-0.0528980\pi$
$131$	11.3834	+	9.55180i	0.994572	+	0.834545i	0.00834879	+	0.999965i	$0.497342\pi$
$132$	−1.06607	−	1.61356i	−0.0927896	−	0.140442i
$133$	7.77948	+	20.8322i	0.674567	+	1.80638i
$134$			2.15510i			0.186172i
$135$	17.8124	−	0.111244i	1.53304	−	0.00957439i
$136$	−2.83200	+	1.63506i	−0.242842	+	0.140205i
$137$	−1.73524	+	4.76754i	−0.148252	+	0.407319i	−0.991484	−	0.130232i	$-0.958428\pi$
$137$	−1.73524	+	4.76754i	−0.148252	+	0.407319i	0.843232	+	0.537550i	$0.180650\pi$
$138$	−1.28625	−	0.642629i	−0.109493	−	0.0547042i
$139$	9.50632	+	1.67622i	0.806315	+	0.142175i	0.561588	−	0.827417i	$-0.310191\pi$
$139$	9.50632	+	1.67622i	0.806315	+	0.142175i	0.244727	+	0.969592i	$0.421302\pi$
$140$	−8.97055	−	15.2427i	−0.758150	−	1.28824i
$141$	−3.13268	+	10.5437i	−0.263819	+	0.887941i
$142$	−0.109787	−	0.0399591i	−0.00921309	−	0.00335329i
$143$	−0.295329	+	0.511525i	−0.0246966	+	0.0427758i
$144$	−7.58921	+	8.11149i	−0.632434	+	0.675958i
$145$	12.9800	−	7.49403i	1.07793	−	0.622345i
$146$	−1.66208	−	0.604947i	−0.137555	−	0.0500658i
$147$	−8.48410	−	8.66141i	−0.699757	−	0.714381i
$148$	−6.23656	−	5.23310i	−0.512642	−	0.430158i
$149$	3.91052	+	10.7441i	0.320363	+	0.880189i	0.990446	+	0.137903i	$0.0440362\pi$
$149$	3.91052	+	10.7441i	0.320363	+	0.880189i	−0.670083	+	0.742286i	$0.733742\pi$
$150$	−0.298041	+	2.59677i	−0.0243349	+	0.212025i
$151$	3.17852	+	18.0263i	0.258664	+	1.46696i	0.786489	+	0.617604i	$0.211897\pi$
$151$	3.17852	+	18.0263i	0.258664	+	1.46696i	−0.527825	+	0.849353i	$0.676992\pi$
$152$	3.71035	+	6.42652i	0.300949	+	0.521259i
$153$	−11.0309	+	1.33591i	−0.891796	+	0.108002i
$154$	0.257564	−	0.219805i	0.0207551	−	0.0177124i
$155$	6.37451	−	1.12400i	0.512013	−	0.0902817i
$156$	3.33991	+	0.992332i	0.267407	+	0.0794501i
$157$	−2.48225	+	2.95823i	−0.198105	+	0.236093i	−0.855947	−	0.517063i	$-0.827025\pi$
$157$	−2.48225	+	2.95823i	−0.198105	+	0.236093i	0.657842	+	0.753156i	$0.271470\pi$
$158$	−0.727776	−	1.99955i	−0.0578988	−	0.159076i
$159$	−11.9838	−	18.1381i	−0.950373	−	1.43844i
$160$	−5.71464	−	6.81044i	−0.451782	−	0.538412i
$161$	−3.28375	+	9.26143i	−0.258796	+	0.729903i
$162$	1.84043	−	0.812126i	0.144598	−	0.0638067i
$163$	−2.90913	+	5.03875i	−0.227860	+	0.394666i	−0.957174	−	0.289514i	$-0.906506\pi$
$163$	−2.90913	+	5.03875i	−0.227860	+	0.394666i	0.729313	+	0.684180i	$0.239840\pi$
$164$	−0.888739	−	0.323475i	−0.0693989	−	0.0252591i
$165$	3.39356	−	0.204742i	0.264188	−	0.0159391i
$166$	−2.39777	+	2.85755i	−0.186103	+	0.221789i
$167$	15.0821	−	5.48942i	1.16709	−	0.424784i	0.315462	−	0.948938i	$-0.397841\pi$
$167$	15.0821	−	5.48942i	1.16709	−	0.424784i	0.851623	+	0.524154i	$0.175618\pi$
$168$	−3.27034	−	2.38215i	−0.252312	−	0.183786i
$169$	2.07264	+	11.7545i	0.159434	+	0.904194i
$170$		−	2.83798i		−	0.217663i
$171$	3.03150	+	25.0319i	0.231825	+	1.91424i
$172$	11.7663			0.897171
$173$	6.80689	−	5.71166i	0.517519	−	0.434250i	−0.346247	−	0.938143i	$-0.612544\pi$
$173$	6.80689	−	5.71166i	0.517519	−	0.434250i	0.863766	+	0.503894i	$0.168100\pi$
$174$	1.00795	−	1.35982i	0.0764127	−	0.103087i
$175$	17.8624	−	0.148850i	1.35027	−	0.0112520i
$176$	−1.36278	+	1.62410i	−0.102724	+	0.122421i
$177$	8.13656	−	10.9769i	0.611581	−	0.825076i
$178$	2.61779	−	0.461587i	0.196212	−	0.0345974i
$179$		−	18.2842i		−	1.36663i	−0.730125	−	0.683313i	$-0.760538\pi$
$179$		−	18.2842i		−	1.36663i	0.730125	−	0.683313i	$-0.239462\pi$
$180$	−5.83165	−	19.1879i	−0.434665	−	1.43018i
$181$	1.41108	−	0.814685i	0.104884	−	0.0605551i	−0.446640	−	0.894714i	$-0.647380\pi$
$181$	1.41108	−	0.814685i	0.104884	−	0.0605551i	0.551525	+	0.834159i	$0.314046\pi$
$182$	−0.100923	+	0.601634i	−0.00748088	+	0.0445961i
$183$	7.35054	+	2.18394i	0.543368	+	0.161442i
$184$	−0.569409	+	3.22928i	−0.0419774	+	0.238066i
$185$	13.4487	−	4.89494i	0.988771	−	0.359883i
$186$	0.609904	−	0.402962i	0.0447204	−	0.0295466i
$187$	−2.08852	+	0.368263i	−0.152728	+	0.0269300i
$188$	12.3836			0.903165
$189$	−7.04669	−	11.8044i	−0.512572	−	0.858645i
$190$	−6.44009			−0.467213
$191$	5.58893	−	0.985480i	0.404401	−	0.0713068i	0.0322519	−	0.999480i	$-0.489732\pi$
$191$	5.58893	−	0.985480i	0.404401	−	0.0713068i	0.372149	+	0.928173i	$0.378621\pi$
$192$	10.5761	+	5.28399i	0.763266	+	0.381339i
$193$	−6.66273	+	2.42504i	−0.479594	+	0.174558i	−0.570494	−	0.821302i	$-0.693248\pi$
$193$	−6.66273	+	2.42504i	−0.479594	+	0.174558i	0.0908994	+	0.995860i	$0.471026\pi$
$194$	0.393337	−	2.23072i	0.0282399	−	0.160157i
$195$	−4.44643	+	4.21252i	−0.318416	+	0.301665i
$196$	−6.62719	+	11.9336i	−0.473370	+	0.852399i
$197$	−3.44056	+	1.98641i	−0.245130	+	0.141526i	−0.617532	−	0.786546i	$-0.711867\pi$
$197$	−3.44056	+	1.98641i	−0.245130	+	0.141526i	0.372402	+	0.928071i	$0.378534\pi$
$198$	0.342383	−	0.173740i	0.0243321	−	0.0123472i
$199$		−	19.0362i		−	1.34944i	−0.738075	−	0.674719i	$-0.764265\pi$
$199$		−	19.0362i		−	1.34944i	0.738075	−	0.674719i	$-0.235735\pi$
$200$	5.87040	−	1.03511i	0.415100	−	0.0731933i
$201$	16.5911	+	1.90422i	1.17025	+	0.134314i
$202$	2.26864	−	2.70366i	0.159621	−	0.190229i
$203$	−10.0658	−	5.70016i	−0.706477	−	0.400073i
$204$	4.97885	+	11.4765i	0.348589	+	0.803517i
$205$	1.27364	−	1.06871i	0.0889550	−	0.0746421i
$206$	−0.927931			−0.0646520
$207$	−6.08384	+	9.33444i	−0.422856	+	0.648789i
$208$		−	3.81965i		−	0.264845i
$209$	0.835680	+	4.73938i	0.0578052	+	0.327830i
$210$	3.20947	−	1.42426i	0.221474	−	0.0982829i
$211$	2.90837	−	1.05856i	0.200221	−	0.0728743i	−0.239963	−	0.970782i	$-0.577135\pi$
$211$	2.90837	−	1.05856i	0.200221	−	0.0728743i	0.440184	+	0.897908i	$0.354913\pi$
$212$	−15.7325	+	18.7492i	−1.08051	+	1.28770i
$213$	−0.404634	+	0.809892i	−0.0277250	+	0.0554929i
$214$	−0.539615	−	0.196404i	−0.0368873	−	0.0134259i
$215$	−10.3422	+	17.9133i	−0.705334	+	1.22167i
$216$	−2.97079	−	3.49588i	−0.202137	−	0.237865i
$217$	−3.24295	−	3.80004i	−0.220146	−	0.257963i
$218$	0.0681715	+	0.0812437i	0.00461716	+	0.00550252i
$219$	−6.12581	+	12.2611i	−0.413944	+	0.828527i
$220$	−1.30912	−	3.59678i	−0.0882608	−	0.242495i
$221$	2.45595	−	2.92689i	0.165205	−	0.196884i
$222$	1.17333	−	1.11161i	0.0787488	−	0.0746061i
$223$	15.3831	−	2.71245i	1.03013	−	0.181639i	0.367059	−	0.930198i	$-0.380365\pi$
$223$	15.3831	−	2.71245i	1.03013	−	0.181639i	0.663069	+	0.748558i	$0.269254\pi$
$224$	−2.29298	+	6.46708i	−0.153206	+	0.432100i
$225$	19.7280	+	4.58896i	1.31520	+	0.305931i
$226$	−1.86398	−	3.22850i	−0.123990	−	0.214757i
$227$	1.12879	+	6.40170i	0.0749206	+	0.424896i	0.999080	+	0.0428884i	$0.0136560\pi$
$227$	1.12879	+	6.40170i	0.0749206	+	0.424896i	−0.924159	+	0.382007i	$0.875233\pi$
$228$	26.0431	−	11.2982i	1.72474	−	0.748244i
$229$	2.66740	+	7.32862i	0.176267	+	0.484289i	0.996092	−	0.0883255i	$-0.0281516\pi$
$229$	2.66740	+	7.32862i	0.176267	+	0.484289i	−0.819825	+	0.572614i	$0.805929\pi$
$230$	−2.17999	−	1.82923i	−0.143744	−	0.120616i
$231$	−1.46460	−	2.17709i	−0.0963638	−	0.143242i
$232$	−3.62739	−	1.32026i	−0.238150	−	0.0866794i
$233$	−16.2549	+	9.38477i	−1.06489	+	0.614817i	−0.926782	−	0.375600i	$-0.877437\pi$
$233$	−16.2549	+	9.38477i	−1.06489	+	0.614817i	−0.138112	+	0.990417i	$0.544103\pi$
$234$	−0.271330	+	0.636284i	−0.0177374	+	0.0415952i
$235$	−10.8848	+	18.8530i	−0.710046	+	1.22984i
$236$	−14.4556	−	5.26142i	−0.940981	−	0.342489i
$237$	−16.0367	+	3.83604i	−1.04170	+	0.249178i
$238$	−1.88769	+	1.11094i	−0.122361	+	0.0720113i
$239$	19.0385	+	3.35699i	1.23150	+	0.217146i	0.751268	−	0.659998i	$-0.229443\pi$
$239$	19.0385	+	3.35699i	1.23150	+	0.217146i	0.480228	+	0.877144i	$0.340554\pi$
$240$	−18.3432	+	12.1193i	−1.18405	+	0.782298i
$241$	−7.14845	+	19.6402i	−0.460472	+	1.26514i	0.464660	+	0.885489i	$0.346177\pi$
$241$	−7.14845	+	19.6402i	−0.460472	+	1.26514i	−0.925131	+	0.379647i	$0.876046\pi$
$242$	−2.06582	+	1.19270i	−0.132796	+	0.0766697i
$243$	−4.62602	−	14.8862i	−0.296759	−	0.954952i
$244$		−	8.63320i		−	0.552684i
$245$	−12.3429	−	20.5787i	−0.788557	−	1.31472i
$246$	0.0839194	−	0.167968i	0.00535051	−	0.0107093i
$247$	−6.64184	−	5.57316i	−0.422610	−	0.354612i
$248$	−1.27706	−	1.07158i	−0.0810936	−	0.0680456i
$249$	19.8803	+	20.9842i	1.25986	+	1.32982i
$250$	−0.459027	+	1.26117i	−0.0290314	+	0.0797632i
$251$	−8.90271	−	15.4199i	−0.561934	−	0.973298i	−0.997328	−	0.0730578i	$-0.976724\pi$
$251$	−8.90271	−	15.4199i	−0.561934	−	0.973298i	0.435394	−	0.900240i	$-0.356609\pi$
$252$	−10.4801	+	11.3901i	−0.660185	+	0.717510i
$253$	−1.06328	+	1.84166i	−0.0668481	+	0.115784i
$254$	0.827910	+	0.986665i	0.0519477	+	0.0619089i
$255$	−21.8484	−	2.50761i	−1.36820	−	0.157033i
$256$	2.11004	−	11.9666i	0.131878	−	0.747915i
$257$	17.9820	−	6.54491i	1.12169	−	0.408260i	0.286419	−	0.958105i	$-0.407535\pi$
$257$	17.9820	−	6.54491i	1.12169	−	0.408260i	0.835267	+	0.549844i	$0.185313\pi$
$258$	−0.266358	+	2.32073i	−0.0165827	+	0.144482i
$259$	−8.52043	−	7.02934i	−0.529434	−	0.436782i
$260$	5.97204	+	3.44796i	0.370370	+	0.213833i
$261$	−9.57800	−	8.96130i	−0.592863	−	0.554691i
$262$	2.87646	+	1.66072i	0.177708	+	0.102600i
$263$	−4.87984	−	5.81557i	−0.300904	−	0.358604i	0.594313	−	0.804234i	$-0.297424\pi$
$263$	−4.87984	−	5.81557i	−0.300904	−	0.358604i	−0.895217	+	0.445630i	$0.852980\pi$
$264$	−0.602200	−	0.635639i	−0.0370629	−	0.0391209i
$265$	−14.7159	−	40.4315i	−0.903988	−	2.48369i
$266$	2.52099	+	4.28365i	0.154572	+	0.262647i
$267$	−1.24050	−	20.5610i	−0.0759172	−	1.25832i
$268$	−3.26491	−	18.5162i	−0.199436	−	1.13106i
$269$	12.7935	+	22.1590i	0.780034	+	1.35106i	0.931921	+	0.362660i	$0.118131\pi$
$269$	12.7935	+	22.1590i	0.780034	+	1.35106i	−0.151888	+	0.988398i	$0.548535\pi$
$270$	3.91655	−	0.715842i	0.238354	−	0.0435648i
$271$	−10.6282	−	6.13617i	−0.645615	−	0.372746i	0.141159	−	0.989987i	$-0.454917\pi$
$271$	−10.6282	−	6.13617i	−0.645615	−	0.372746i	−0.786774	+	0.617241i	$0.788250\pi$
$272$	10.5058	−	8.81541i	0.637007	−	0.534513i
$273$	4.54254	+	1.30856i	0.274927	+	0.0791974i
$274$	−0.196919	+	1.11679i	−0.0118963	+	0.0674675i
$275$	3.80708	+	0.671292i	0.229576	+	0.0404804i
$276$	12.0248	+	3.57273i	0.723808	+	0.215053i
$277$	12.3425	−	10.3566i	0.741591	−	0.622269i	−0.191673	−	0.981459i	$-0.561391\pi$
$277$	12.3425	−	10.3566i	0.741591	−	0.622269i	0.933264	+	0.359190i	$0.116947\pi$
$278$	2.15760			0.129404
$279$	−2.56332	−	5.05144i	−0.153462	−	0.302422i
$280$	−5.19819	−	6.09115i	−0.310651	−	0.364016i
$281$	3.58019	−	9.83649i	0.213576	−	0.586796i	−0.785927	−	0.618319i	$-0.787814\pi$
$281$	3.58019	−	9.83649i	0.213576	−	0.586796i	0.999503	+	0.0315239i	$0.0100360\pi$
$282$	−0.280332	+	2.44248i	−0.0166935	+	0.145448i
$283$	−3.79010	−	0.668296i	−0.225298	−	0.0397261i	0.0598595	−	0.998207i	$-0.480935\pi$
$283$	−3.79010	−	0.668296i	−0.225298	−	0.0397261i	−0.285157	+	0.958481i	$0.592046\pi$
$284$	1.00381	+	0.176998i	0.0595649	+	0.0105029i
$285$	−5.69040	+	49.5794i	−0.337070	+	2.93683i
$286$	−0.0451541	+	0.124060i	−0.00267002	+	0.00733581i
$287$	−1.20943	−	0.428817i	−0.0713903	−	0.0253123i
$288$	−4.24822	+	6.51806i	−0.250329	+	0.384080i
$289$	−3.28159			−0.193035
$290$	2.56631	−	2.15339i	0.150699	−	0.126451i
$291$	−16.8258	−	4.99917i	−0.986346	−	0.293057i
$292$	15.1968	+	2.67960i	0.889323	+	0.156812i
$293$	−1.89493	+	10.7467i	−0.110703	+	0.627828i	0.878085	+	0.478504i	$0.158821\pi$
$293$	−1.89493	+	10.7467i	−0.110703	+	0.627828i	−0.988788	+	0.149324i	$0.952290\pi$
$294$	−2.20370	−	1.57726i	−0.128523	−	0.0919877i
$295$	20.7162	−	17.3829i	1.20614	−	1.01207i
$296$	−3.19219	−	1.84301i	−0.185542	−	0.107123i
$297$	−1.03502	−	2.78937i	−0.0600581	−	0.161856i
$298$	1.27780	+	2.21321i	0.0740209	+	0.128208i
$299$	−0.665294	−	3.77307i	−0.0384749	−	0.218202i
$300$	−1.37332	−	22.7625i	−0.0792886	−	1.31419i
$301$	15.9636	−	0.133027i	0.920124	−	0.00766756i
$302$	1.39932	+	3.84459i	0.0805216	+	0.221231i
$303$	−18.8097	−	19.8542i	−1.08059	−	1.14059i
$304$	−20.0044	−	23.8403i	−1.14733	−	1.36733i
$305$	13.1434	+	7.58833i	0.752588	+	0.434507i
$306$	−2.37628	+	0.722206i	−0.135843	+	0.0412858i
$307$	−18.4024	−	10.6246i	−1.05028	−	0.606378i	−0.127551	−	0.991832i	$-0.540712\pi$
$307$	−18.4024	−	10.6246i	−1.05028	−	0.606378i	−0.922727	+	0.385454i	$0.874045\pi$
$308$	−1.87995	+	2.27873i	−0.107120	+	0.129843i
$309$	−0.819911	+	7.14373i	−0.0466431	+	0.406393i
$310$	1.35954	−	0.494831i	0.0772165	−	0.0281045i
$311$	−3.47779	+	19.7235i	−0.197207	+	1.11842i	0.712032	+	0.702147i	$0.247775\pi$
$311$	−3.47779	+	19.7235i	−0.197207	+	1.11842i	−0.909240	+	0.416273i	$0.863336\pi$
$312$	1.56722	+	0.179875i	0.0887264	+	0.0101834i
$313$	−13.8341	−	16.4868i	−0.781949	−	0.931890i	0.217071	−	0.976156i	$-0.430350\pi$
$313$	−13.8341	−	16.4868i	−0.781949	−	0.931890i	−0.999020	+	0.0442656i	$0.985905\pi$
$314$	−0.431577	+	0.747513i	−0.0243553	+	0.0421846i
$315$	−8.12885	−	25.9667i	−0.458009	−	1.46306i
$316$	9.28219	+	16.0772i	0.522164	+	0.904414i
$317$	3.18437	−	8.74899i	0.178852	−	0.491392i	−0.817578	−	0.575818i	$-0.804684\pi$
$317$	3.18437	−	8.74899i	0.178852	−	0.491392i	0.996430	+	0.0844263i	$0.0269058\pi$
$318$	−3.34187	−	3.52743i	−0.187403	−	0.197809i
$319$	−1.91773	−	1.60917i	−0.107372	−	0.0900959i
$320$	17.9249	+	15.0407i	1.00203	+	0.840803i
$321$	−1.98882	+	3.98071i	−0.111005	+	0.222182i
$322$	−0.363355	+	2.16609i	−0.0202490	+	0.120711i
$323$		−	31.1305i		−	1.73215i
$324$	−14.5823	+	9.76585i	−0.810128	+	0.542547i
$325$	−6.03165	+	3.48237i	−0.334576	+	0.193167i
$326$	−0.444789	+	1.22205i	−0.0246346	+	0.0676829i
$327$	0.685695	−	0.453036i	0.0379190	−	0.0250530i
$328$	−0.421704	−	0.0743578i	−0.0232847	−	0.00410572i
$329$	16.8011	−	0.140006i	0.926272	−	0.00771879i
$330$	0.739046	−	0.176783i	0.0406832	−	0.00973158i
$331$	13.1635	+	4.79114i	0.723534	+	0.263345i	0.677425	−	0.735592i	$-0.263096\pi$
$331$	13.1635	+	4.79114i	0.723534	+	0.263345i	0.0461086	+	0.998936i	$0.485318\pi$
$332$	16.2721	−	28.1841i	0.893047	−	1.54680i
$333$	−7.52102	−	10.0152i	−0.412149	−	0.548827i
$334$	3.10681	−	1.79372i	0.169997	−	0.0981480i
$335$	31.0593	+	11.3047i	1.69695	+	0.617639i
$336$	15.2417	+	7.45693i	0.831504	+	0.406809i
$337$	−7.66325	−	6.43023i	−0.417444	−	0.350277i	0.409746	−	0.912200i	$-0.365617\pi$
$337$	−7.66325	−	6.43023i	−0.417444	−	0.350277i	−0.827190	+	0.561923i	$0.810062\pi$
$338$	0.912462	+	2.50697i	0.0496314	+	0.136361i
$339$	−26.5018	+	11.4973i	−1.43938	+	0.624445i
$340$	4.29946	+	24.3834i	0.233171	+	1.32238i
$341$	−0.540572	−	0.936297i	−0.0292736	−	0.0507033i
$342$	1.63887	+	5.39238i	0.0886197	+	0.291586i
$343$	−8.85632	+	16.2655i	−0.478196	+	0.878253i
$344$	5.24636	−	0.925075i	0.282865	−	0.0498767i
$345$	−16.0087	+	15.1665i	−0.861877	+	0.816537i
$346$	1.27665	−	1.52145i	0.0686332	−	0.0817938i
$347$	3.40057	+	9.34298i	0.182552	+	0.501558i	0.996888	−	0.0788368i	$-0.0251206\pi$
$347$	3.40057	+	9.34298i	0.182552	+	0.501558i	−0.814336	+	0.580394i	$0.802898\pi$
$348$	−6.60007	+	13.2103i	−0.353801	+	0.708148i
$349$	14.2950	+	17.0361i	0.765192	+	0.911920i	0.998164	−	0.0605633i	$-0.0192897\pi$
$349$	14.2950	+	17.0361i	0.765192	+	0.911920i	−0.232973	+	0.972483i	$0.574845\pi$
$350$	3.92610	−	0.726061i	0.209859	−	0.0388096i
$351$	4.65873	+	2.65106i	0.248664	+	0.141503i
$352$	−0.742470	+	1.28600i	−0.0395738	+	0.0685438i
$353$	−0.983396	−	0.357927i	−0.0523409	−	0.0190505i	0.315717	−	0.948853i	$-0.397755\pi$
$353$	−0.983396	−	0.357927i	−0.0523409	−	0.0190505i	−0.368058	+	0.929803i	$0.619977\pi$
$354$	1.36497	−	2.73205i	0.0725476	−	0.145207i
$355$	−1.15178	+	1.37264i	−0.0611302	+	0.0728521i
$356$	−21.7923	+	7.93175i	−1.15499	+	0.420382i
$357$	6.88465	+	15.5141i	0.364375	+	0.821095i
$358$	−0.709670	−	4.02474i	−0.0375072	−	0.212714i
$359$			0.361634i			0.0190863i	0.999954	+	0.00954315i	$0.00303772\pi$
$359$			0.361634i			0.0190863i	−0.999954	+	0.00954315i	$0.996962\pi$
$360$	−4.10879	−	8.09705i	−0.216552	−	0.426752i
$361$	−51.6428			−2.71804
$362$	0.278987	−	0.234098i	0.0146632	−	0.0123039i
$363$	7.35674	+	16.9577i	0.386129	+	0.890047i
$364$	−0.0443495	−	5.32203i	−0.00232454	−	0.278950i
$365$	−17.4370	+	20.7806i	−0.912694	+	1.08771i
$366$	1.70277	+	0.195433i	0.0890054	+	0.0102155i
$367$	31.0458	−	5.47421i	1.62058	−	0.285751i	0.711595	−	0.702590i	$-0.247973\pi$
$367$	31.0458	−	5.47421i	1.62058	−	0.285751i	0.908981	+	0.416838i	$0.136862\pi$
$368$		−	13.7520i		−	0.716873i
$369$	−1.21896	−	0.794473i	−0.0634566	−	0.0413586i
$370$	2.77036	−	1.59947i	0.144024	−	0.0831523i
$371$	−21.1326	+	25.6153i	−1.09715	+	1.32988i
$372$	−4.62972	+	4.38616i	−0.240040	+	0.227412i
$373$	−2.78601	+	15.8002i	−0.144254	+	0.818106i	0.823709	+	0.567013i	$0.191901\pi$
$373$	−2.78601	+	15.8002i	−0.144254	+	0.818106i	−0.967963	+	0.251093i	$0.919210\pi$
$374$	−0.445434	+	0.162125i	−0.0230328	+	0.00838326i
$375$	9.30357	+	4.64820i	0.480434	+	0.240032i
$376$	5.52160	−	0.973607i	0.284755	−	0.0502100i
$377$	4.51022			0.232288
$378$	−2.00929	−	2.32489i	−0.103347	−	0.119579i
$379$	19.2286			0.987705			0.493852	−	0.869546i	$-0.335588\pi$
$379$	19.2286			0.987705			0.493852	+	0.869546i	$0.335588\pi$
$380$	55.3321	−	9.75654i	2.83848	−	0.500500i
$381$	8.32743	−	5.50191i	0.426627	−	0.281871i
$382$	1.19199	−	0.433849i	0.0609875	−	0.0221976i
$383$	4.56911	−	25.9127i	0.233471	−	1.32408i	−0.612339	−	0.790595i	$-0.709771\pi$
$383$	4.56911	−	25.9127i	0.233471	−	1.32408i	0.845810	−	0.533484i	$-0.179118\pi$
$384$	11.1449	+	3.31130i	0.568737	+	0.168979i
$385$	−1.81677	−	4.86502i	−0.0925913	−	0.247944i
$386$	−1.37248	+	0.792403i	−0.0698575	+	0.0403323i
$387$	17.6309	+	4.10115i	0.896229	+	0.208473i
$388$			19.7619i			1.00326i
$389$	−1.59220	+	0.280748i	−0.0807278	+	0.0142345i	−0.213866	−	0.976863i	$-0.568606\pi$
$389$	−1.59220	+	0.280748i	−0.0807278	+	0.0142345i	0.133138	+	0.991097i	$0.457495\pi$
$390$	−0.815250	+	1.09984i	−0.0412818	+	0.0556928i
$391$	8.84225	−	10.5378i	0.447172	−	0.532918i
$392$	−2.01671	+	5.84200i	−0.101859	+	0.295065i
$393$	15.3268	−	20.6772i	0.773134	−	1.04303i
$394$	−0.680240	+	0.570789i	−0.0342700	+	0.0287559i
$395$	−32.6351			−1.64205
$396$	−2.67849	+	2.01145i	−0.134599	+	0.101079i
$397$			2.97650i			0.149386i	0.997207	+	0.0746932i	$0.0237978\pi$
$397$			2.97650i			0.149386i	−0.997207	+	0.0746932i	$0.976202\pi$
$398$	−0.738855	−	4.19025i	−0.0370354	−	0.210038i
$399$	35.2054	−	15.6230i	1.76248	−	0.782128i
$400$	−23.4917	+	8.55027i	−1.17458	+	0.427514i
$401$	−4.05799	+	4.83612i	−0.202646	+	0.241505i	−0.857791	−	0.513999i	$-0.828163\pi$
$401$	−4.05799	+	4.83612i	−0.202646	+	0.241505i	0.655144	+	0.755504i	$0.272608\pi$
$402$	3.72596	−	0.224796i	0.185834	−	0.0112118i
$403$	1.83035	+	0.666192i	0.0911760	+	0.0331854i
$404$	−15.3958	+	26.6663i	−0.765968	+	1.32670i
$405$	−2.05032	−	30.7843i	−0.101881	−	1.52968i
$406$	−2.43692	−	0.864040i	−0.120942	−	0.0428816i
$407$	−1.53656	−	1.83121i	−0.0761647	−	0.0907695i
$408$	3.12227	+	4.72572i	0.154575	+	0.233958i
$409$	−4.42973	−	12.1706i	−0.219036	−	0.601796i	0.780697	−	0.624910i	$-0.214864\pi$
$409$	−4.42973	−	12.1706i	−0.219036	−	0.601796i	−0.999733	+	0.0231135i	$0.992642\pi$
$410$	0.238875	−	0.284680i	0.0117972	−	0.0140593i
$411$	8.42364	+	2.50278i	0.415507	+	0.123453i
$412$	7.97262	−	1.40579i	0.392783	−	0.0692582i
$413$	−19.6717	−	6.97484i	−0.967982	−	0.343209i
$414$	−0.976879	+	2.29084i	−0.0480110	+	0.112589i
$415$	28.6054	+	49.5460i	1.40418	+	2.43212i
$416$	−0.464562	−	2.63466i	−0.0227770	−	0.129175i
$417$	1.90643	−	16.6104i	0.0933584	−	0.813414i
$418$	0.367901	+	1.01080i	0.0179946	+	0.0494398i
$419$	−9.08276	−	7.62134i	−0.443722	−	0.372327i	0.393378	−	0.919377i	$-0.371306\pi$
$419$	−9.08276	−	7.62134i	−0.443722	−	0.372327i	−0.837100	+	0.547050i	$0.815751\pi$
$420$	−25.4175	+	17.0992i	−1.24025	+	0.834356i
$421$	9.85568	+	3.58717i	0.480337	+	0.174828i	0.570829	−	0.821069i	$-0.306622\pi$
$421$	9.85568	+	3.58717i	0.480337	+	0.174828i	−0.0904925	+	0.995897i	$0.528844\pi$
$422$	0.599107	−	0.345895i	0.0291641	−	0.0168379i
$423$	18.5559	+	4.31630i	0.902217	+	0.209866i
$424$	−5.54073	+	9.59683i	−0.269082	+	0.466063i
$425$	−23.4986	−	8.55281i	−1.13985	−	0.414872i
$426$	−0.0576338	+	0.193979i	−0.00279237	+	0.00939832i
$427$	−0.0976052	−	11.7128i	−0.00472345	−	0.566824i
$428$	4.93382	+	0.869966i	0.238485	+	0.0420514i
$429$	0.915184	+	0.457239i	0.0441855	+	0.0220757i
$430$	−1.58127	+	4.34449i	−0.0762554	+	0.209510i
$431$	−10.8779	+	6.28037i	−0.523971	+	0.302515i	−0.738558	−	0.674190i	$-0.764493\pi$
$431$	−10.8779	+	6.28037i	−0.523971	+	0.302515i	0.214587	+	0.976705i	$0.431159\pi$
$432$	14.8156	+	12.2749i	0.712818	+	0.590578i
$433$			2.84286i			0.136619i	0.997664	+	0.0683097i	$0.0217606\pi$
$433$			2.84286i			0.136619i	−0.997664	+	0.0683097i	$0.978239\pi$
$434$	−0.861333	−	0.710598i	−0.0413453	−	0.0341098i
$435$	−14.3104	−	21.6596i	−0.686132	−	1.03850i
$436$	−0.708800	−	0.594754i	−0.0339454	−	0.0284835i
$437$	−23.9128	−	20.0653i	−1.14391	−	0.959852i
$438$	−0.872527	+	2.93668i	−0.0416909	+	0.140320i
$439$	0.0910994	−	0.250294i	0.00434794	−	0.0119459i	−0.937500	−	0.347986i	$-0.886866\pi$
$439$	0.0910994	−	0.250294i	0.00434794	−	0.0119459i	0.941848	+	0.336040i	$0.109088\pi$
$440$	−0.866493	−	1.50081i	−0.0413084	−	0.0715483i
$441$	−14.0898	+	15.5717i	−0.670943	+	0.741509i
$442$	0.427004	−	0.739592i	0.0203105	−	0.0351788i
$443$	−22.8541	−	27.2364i	−1.08583	−	1.29404i	−0.953022	−	0.302901i	$-0.902045\pi$
$443$	−22.8541	−	27.2364i	−1.08583	−	1.29404i	−0.132809	−	0.991142i	$-0.542400\pi$
$444$	−8.39700	+	11.3283i	−0.398504	+	0.537617i
$445$	7.07932	−	40.1488i	0.335592	−	1.90324i
$446$	3.28086	−	1.19414i	0.155353	−	0.0565439i
$447$	18.1676	−	7.88164i	0.859298	−	0.372789i
$448$	2.98767	−	17.8105i	0.141154	−	0.841469i
$449$	25.2684	+	14.5887i	1.19249	+	0.688483i	0.958870	−	0.283845i	$-0.0916101\pi$
$449$	25.2684	+	14.5887i	1.19249	+	0.688483i	0.233618	+	0.972328i	$0.424943\pi$
$450$	4.52066	+	0.244417i	0.213106	+	0.0115219i
$451$	−0.240498	−	0.138852i	−0.0113246	−	0.00653827i
$452$	20.9060	+	24.9149i	0.983338	+	1.17190i
$453$	30.8342	−	7.37567i	1.44872	−	0.346539i
$454$	0.496941	+	1.36533i	0.0233226	+	0.0640783i
$455$	8.14136	+	4.61039i	0.381673	+	0.216139i
$456$	10.7238	−	7.08520i	0.502189	−	0.331795i
$457$	0.498786	+	2.82876i	0.0233322	+	0.132324i	0.994249	−	0.107094i	$-0.0341546\pi$
$457$	0.498786	+	2.82876i	0.0233322	+	0.132324i	−0.970917	+	0.239418i	$0.923043\pi$
$458$	0.871597	+	1.50965i	0.0407271	+	0.0705413i
$459$	3.46028	+	18.9321i	0.161512	+	0.883674i
$460$	21.5013	+	12.4138i	1.00251	+	0.578797i
$461$	−6.62406	+	5.55824i	−0.308513	+	0.258873i	−0.783877	−	0.620916i	$-0.786761\pi$
$461$	−6.62406	+	5.55824i	−0.308513	+	0.258873i	0.475364	+	0.879789i	$0.342316\pi$
$462$	−0.406890	−	0.422377i	−0.0189302	−	0.0196508i
$463$	−5.41640	+	30.7179i	−0.251721	+	1.42758i	0.552629	+	0.833427i	$0.313625\pi$
$463$	−5.41640	+	30.7179i	−0.251721	+	1.42758i	−0.804350	+	0.594155i	$0.797487\pi$
$464$	15.9431	+	2.81119i	0.740138	+	0.130506i
$465$	−2.60821	−	10.9037i	−0.120953	−	0.505647i
$466$	−3.21379	+	2.69669i	−0.148876	+	0.124922i
$467$	−24.9065			−1.15253			−0.576267	−	0.817261i	$-0.695491\pi$
$467$	−24.9065			−1.15253			−0.576267	+	0.817261i	$0.695491\pi$
$468$	1.36727	−	5.87790i	0.0632019	−	0.271706i
$469$	−4.63891	−	25.0844i	−0.214205	−	1.15829i
$470$	−1.66422	+	4.57242i	−0.0767649	+	0.210910i
$471$	5.37343	+	3.98301i	0.247595	+	0.183528i
$472$	−6.85914	−	1.20945i	−0.315718	−	0.0556695i
$473$	3.40238	+	0.599932i	0.156442	+	0.0275849i
$474$	−3.38112	+	1.46683i	−0.155300	+	0.0673737i
$475$	−19.4085	+	53.3243i	−0.890521	+	2.44669i
$476$	14.5357	−	12.4048i	0.666243	−	0.568572i
$477$	−30.1090	+	22.6108i	−1.37860	+	1.03528i
$478$	4.32106			0.197641
$479$	17.9386	−	15.0523i	0.819635	−	0.687756i	−0.133251	−	0.991082i	$-0.542542\pi$
$479$	17.9386	−	15.0523i	0.819635	−	0.687756i	0.952887	+	0.303327i	$0.0980973\pi$
$480$	−11.1785	+	10.5905i	−0.510228	+	0.483386i
$481$	4.24130	+	0.747856i	0.193387	+	0.0340993i
$482$	−0.811222	+	4.60067i	−0.0369502	+	0.209555i
$483$	16.3547	+	4.71124i	0.744164	+	0.214369i
$484$	15.9422	−	13.3771i	0.724648	−	0.608052i
$485$	−30.0859	−	17.3701i	−1.36613	−	0.788737i
$486$	−1.59606	−	3.09722i	−0.0723990	−	0.140493i
$487$	7.63610	+	13.2261i	0.346025	+	0.599333i	0.985539	−	0.169446i	$-0.0541980\pi$
$487$	7.63610	+	13.2261i	0.346025	+	0.599333i	−0.639515	+	0.768779i	$0.720865\pi$
$488$	−0.678750	−	3.84938i	−0.0307256	−	0.174253i
$489$	9.01498	+	4.50402i	0.407672	+	0.203679i
$490$	−3.51564	−	4.05072i	−0.158821	−	0.182993i
$491$	8.86288	+	24.3506i	0.399976	+	1.09893i	0.962296	+	0.272005i	$0.0876869\pi$
$491$	8.86288	+	24.3506i	0.399976	+	1.09893i	−0.562320	+	0.826920i	$0.690091\pi$
$492$	−0.466554	+	1.57029i	−0.0210339	+	0.0707941i
$493$	10.4092	+	12.4052i	0.468806	+	0.558701i
$494$	−1.67832	−	0.968977i	−0.0755111	−	0.0435964i
$495$	−0.707959	−	5.84579i	−0.0318204	−	0.262749i
$496$	6.05482	+	3.49575i	0.271869	+	0.156964i
$497$	1.36388	+	0.228788i	0.0611786	+	0.0102625i
$498$	5.19054	+	3.84744i	0.232594	+	0.172408i
$499$	−5.27779	+	1.92096i	−0.236266	+	0.0859939i	−0.457440	−	0.889241i	$-0.651233\pi$
$499$	−5.27779	+	1.92096i	−0.236266	+	0.0859939i	0.221174	+	0.975234i	$0.429011\pi$
$500$	2.03325	−	11.5311i	0.0909297	−	0.515688i
$501$	−11.0639	−	25.5029i	−0.494299	−	1.13939i
$502$	−2.55817	−	3.04871i	−0.114177	−	0.136070i
$503$	−12.0053	+	20.7938i	−0.535291	+	0.927151i	0.463858	+	0.885909i	$0.346465\pi$
$503$	−12.0053	+	20.7938i	−0.535291	+	0.927151i	−0.999149	+	0.0412418i	$0.986869\pi$
$504$	−3.77738	+	5.90259i	−0.168258	+	0.262922i
$505$	−27.0649	−	46.8777i	−1.20437	−	2.08603i
$506$	−0.162570	+	0.446657i	−0.00722712	+	0.0198563i
$507$	20.1063	−	4.80951i	0.892951	−	0.213598i
$508$	−8.60803	−	7.22300i	−0.381920	−	0.320469i
$509$	−0.229469	−	0.192548i	−0.0101711	−	0.00853452i	0.637688	−	0.770295i	$-0.279891\pi$
$509$	−0.229469	−	0.192548i	−0.0101711	−	0.00853452i	−0.647859	+	0.761760i	$0.724335\pi$
$510$	−4.90661	+	0.296027i	−0.217268	+	0.0131083i
$511$	20.6480	+	3.46365i	0.913416	+	0.153223i
$512$		−	16.1410i		−	0.713340i
$513$	42.9616	−	7.85225i	1.89680	−	0.346685i
$514$	3.70418	−	2.13861i	0.163384	−	0.0943300i
$515$	−4.86750	+	13.3733i	−0.214488	+	0.589300i
$516$	−1.22733	−	20.3428i	−0.0540303	−	0.895542i
$517$	3.58088	+	0.631406i	0.157487	+	0.0277692i
$518$	−2.14836	−	1.21660i	−0.0943933	−	0.0534542i
$519$	−10.5850	−	11.1727i	−0.464628	−	0.490427i
$520$	2.93390	+	1.06785i	0.128660	+	0.0468284i
$521$	−8.16132	+	14.1358i	−0.357554	+	0.619302i	−0.987552	−	0.157295i	$-0.949723\pi$
$521$	−8.16132	+	14.1358i	−0.357554	+	0.619302i	0.629998	+	0.776597i	$0.283056\pi$
$522$	−2.45613	−	1.60081i	−0.107502	−	0.0700658i
$523$	8.49648	−	4.90545i	0.371525	−	0.214500i	−0.302599	−	0.953118i	$-0.597854\pi$
$523$	8.49648	−	4.90545i	0.371525	−	0.214500i	0.674125	+	0.738618i	$0.264521\pi$
$524$	−27.2300	−	9.91090i	−1.18955	−	0.432960i
$525$	−2.12056	−	30.8669i	−0.0925487	−	1.34714i
$526$	−1.29988	−	1.09073i	−0.0566773	−	0.0475579i
$527$	2.39194	+	6.57181i	0.104195	+	0.286273i
$528$	2.95007	+	2.18671i	0.128385	+	0.0951645i
$529$	1.59863	+	9.06626i	0.0695055	+	0.394185i
$530$	−4.80854	−	8.32864i	−0.208870	−	0.361773i
$531$	−19.8268	−	12.9224i	−0.860410	−	0.560782i
$532$	−28.1495	−	32.9851i	−1.22044	−	1.43009i
$533$	0.492716	−	0.0868791i	0.0213419	−	0.00376315i
$534$	−1.07110	−	4.47776i	−0.0463510	−	0.193772i
$535$	−5.66114	+	6.74668i	−0.244752	+	0.291685i
$536$	−2.91152	−	7.99934i	−0.125759	−	0.345519i
$537$	−31.6117	+	1.90721i	−1.36415	+	0.0823023i
$538$	3.67618	+	4.38110i	0.158491	+	0.188883i
$539$	−2.52480	+	3.11286i	−0.108751	+	0.134080i
$540$	−32.5659	+	12.0839i	−1.40141	+	0.520006i
$541$	7.28065	−	12.6105i	0.313019	−	0.542166i	−0.665995	−	0.745956i	$-0.731993\pi$
$541$	7.28065	−	12.6105i	0.313019	−	0.542166i	0.979015	+	0.203791i	$0.0653262\pi$
$542$	−2.57764	−	0.938186i	−0.110719	−	0.0402985i
$543$	−1.55570	−	2.35464i	−0.0667616	−	0.101047i
$544$	6.17437	−	7.35832i	0.264724	−	0.315486i
$545$	1.52848	−	0.556322i	0.0654729	−	0.0238302i
$546$	1.05070	+	0.111730i	0.0449657	+	0.00478159i
$547$	4.82647	+	27.3723i	0.206365	+	1.17035i	0.895277	+	0.445509i	$0.146977\pi$
$547$	4.82647	+	27.3723i	0.206365	+	1.17035i	−0.688912	+	0.724845i	$0.741912\pi$
$548$		−	9.89355i		−	0.422632i
$549$	3.00911	−	12.9362i	0.128426	−	0.552104i
$550$	0.864073			0.0368442
$551$	28.1504	−	23.6210i	1.19925	−	1.00629i
$552$	5.64252	+	0.647612i	0.240162	+	0.0275642i
$553$	12.7751	+	21.7074i	0.543252	+	0.923090i
$554$	2.31487	−	2.75876i	0.0983496	−	0.117208i
$555$	−9.86572	−	22.7410i	−0.418777	−	0.965303i
$556$	−18.5377	+	3.26870i	−0.786174	+	0.138624i
$557$			1.80913i			0.0766554i	0.999265	+	0.0383277i	$0.0122031\pi$
$557$			1.80913i			0.0766554i	−0.999265	+	0.0383277i	$0.987797\pi$
$558$	−0.760302	−	1.01244i	−0.0321862	−	0.0428598i
$559$	−5.39047	+	3.11219i	−0.227993	+	0.131632i
$560$	25.9051	+	21.3716i	1.09469	+	0.903117i
$561$	0.854544	+	3.57245i	0.0360789	+	0.150829i
$562$	0.406288	−	2.30417i	0.0171382	−	0.0971957i
$563$	−3.11242	+	1.13283i	−0.131173	+	0.0477430i	−0.406773	−	0.913529i	$-0.633346\pi$
$563$	−3.11242	+	1.13283i	−0.131173	+	0.0477430i	0.275600	+	0.961273i	$0.411124\pi$
$564$	−1.29172	−	21.4101i	−0.0543913	−	0.901526i
$565$	−56.3067	+	9.92840i	−2.36884	+	0.417691i
$566$	−0.860218			−0.0361576
$567$	−19.6737	+	13.4144i	−0.826217	+	0.563351i
$568$	0.461493			0.0193638
$569$	−10.6572	+	1.87916i	−0.446774	+	0.0787784i	−0.392509	−	0.919748i	$-0.628393\pi$
$569$	−10.6572	+	1.87916i	−0.446774	+	0.0787784i	−0.0542654	+	0.998527i	$0.517282\pi$
$570$	0.671760	+	11.1343i	0.0281369	+	0.466365i
$571$	21.9958	−	8.00582i	0.920496	−	0.335033i	0.162060	−	0.986781i	$-0.448186\pi$
$571$	21.9958	−	8.00582i	0.920496	−	0.335033i	0.758436	+	0.651748i	$0.225964\pi$
$572$	0.200009	−	1.13431i	0.00836280	−	0.0474278i
$573$	−2.28678	−	9.55995i	−0.0955316	−	0.399373i
$574$	−0.282864	−	0.0474497i	−0.0118065	−	0.00198051i
$575$	−21.7160	+	12.5377i	−0.905618	+	0.522859i
$576$	8.03233	−	18.8363i	0.334681	−	0.784846i
$577$			39.9309i			1.66234i	0.556015	+	0.831172i	$0.312330\pi$
$577$			39.9309i			1.66234i	−0.556015	+	0.831172i	$0.687670\pi$
$578$	−0.722346	+	0.127369i	−0.0300456	+	0.00529785i
$579$	4.88765	+	11.2663i	0.203124	+	0.468211i
$580$	−18.7870	+	22.3894i	−0.780086	+	0.929670i
$581$	21.7580	−	38.4219i	0.902675	−	1.59401i
$582$	−3.89774	−	0.447358i	−0.161567	−	0.0185436i
$583$	−5.50523	+	4.61944i	−0.228003	+	0.191318i
$584$	6.98662			0.289108
$585$	7.74686	+	7.24806i	0.320293	+	0.299670i
$586$			2.43912i			0.100759i
$587$	−6.40324	−	36.3146i	−0.264290	−	1.49886i	−0.771050	−	0.636775i	$-0.780268\pi$
$587$	−6.40324	−	36.3146i	−0.264290	−	1.49886i	0.506760	−	0.862087i	$-0.330843\pi$
$588$	21.3233	+	10.2130i	0.879360	+	0.421177i
$589$	14.9131	−	5.42792i	0.614483	−	0.223653i
$590$	3.88537	−	4.63040i	0.159958	−	0.190631i
$591$	3.79320	+	5.74121i	0.156031	+	0.236162i
$592$	14.5263	+	5.28716i	0.597029	+	0.217301i
$593$	−5.87281	+	10.1720i	−0.241167	+	0.417714i	−0.961047	−	0.276385i	$-0.910864\pi$
$593$	−5.87281	+	10.1720i	−0.241167	+	0.417714i	0.719880	+	0.694099i	$0.244197\pi$
$594$	−0.336095	−	0.573827i	−0.0137901	−	0.0235444i
$595$	6.10884	+	33.0329i	0.250438	+	1.35422i
$596$	−14.3316	−	17.0797i	−0.587045	−	0.699613i
$597$	−32.9117	+	1.98565i	−1.34699	+	0.0812671i
$598$	−0.292890	−	0.804709i	−0.0119772	−	0.0329070i
$599$	−6.84754	+	8.16058i	−0.279783	+	0.333432i	−0.887574	−	0.460664i	$-0.847611\pi$
$599$	−6.84754	+	8.16058i	−0.279783	+	0.333432i	0.607792	+	0.794097i	$0.292056\pi$
$600$	−2.40195	−	10.0414i	−0.0980590	−	0.409939i
$601$	−22.3746	+	3.94524i	−0.912678	+	0.160930i	−0.610219	−	0.792233i	$-0.708919\pi$
$601$	−22.3746	+	3.94524i	−0.912678	+	0.160930i	−0.302459	+	0.953162i	$0.597808\pi$
$602$	3.50875	−	0.648879i	0.143006	−	0.0264463i
$603$	1.56162	−	28.8832i	0.0635940	−	1.17621i
$604$	−17.8471	−	30.9121i	−0.726189	−	1.25780i
$605$	6.35288	+	36.0289i	0.258281	+	1.46478i
$606$	−4.91101	−	3.64025i	−0.199496	−	0.147875i
$607$	7.42432	+	20.3981i	0.301344	+	0.827935i	0.994267	+	0.106924i	$0.0341001\pi$
$607$	7.42432	+	20.3981i	0.301344	+	0.827935i	−0.692924	+	0.721011i	$0.743678\pi$
$608$	−16.6979	−	14.0112i	−0.677188	−	0.568228i
$609$	−8.80510	+	17.9973i	−0.356801	+	0.729289i
$610$	3.18766	+	1.16021i	0.129064	+	0.0469756i
$611$	−5.67327	+	3.27546i	−0.229516	+	0.132511i
$612$	19.3225	−	9.80507i	0.781065	−	0.396346i
$613$	3.87628	−	6.71392i	0.156562	−	0.271173i	−0.777065	−	0.629420i	$-0.783292\pi$
$613$	3.87628	−	6.71392i	0.156562	−	0.271173i	0.933627	+	0.358248i	$0.116626\pi$
$614$	−4.46312	−	1.62444i	−0.180117	−	0.0655571i
$615$	−1.98056	−	2.09053i	−0.0798637	−	0.0842983i
$616$	−0.659078	+	1.16385i	−0.0265550	+	0.0468927i
$617$	−26.9142	−	4.74570i	−1.08352	−	0.191055i	−0.396751	−	0.917926i	$-0.629862\pi$
$617$	−26.9142	−	4.74570i	−1.08352	−	0.191055i	−0.686773	+	0.726872i	$0.740974\pi$
$618$	0.0967917	+	1.60431i	0.00389353	+	0.0645347i
$619$	7.51496	−	20.6472i	0.302052	−	0.829880i	−0.692092	−	0.721810i	$-0.743311\pi$
$619$	7.51496	−	20.6472i	0.302052	−	0.829880i	0.994143	−	0.108070i	$-0.0344672\pi$
$620$	−10.9312	+	6.31116i	−0.439009	+	0.253462i
$621$	16.7730	+	9.54472i	0.673077	+	0.383016i
$622$			4.47654i			0.179493i
$623$	−29.4764	+	11.0075i	−1.18095	+	0.441008i
$624$	−6.60381	+	0.398424i	−0.264364	+	0.0159497i
$625$	−10.0919	−	8.46815i	−0.403678	−	0.338726i
$626$	−3.68508	−	3.09215i	−0.147285	−	0.123587i
$627$	8.10677	−	1.93917i	0.323753	−	0.0774431i
$628$	2.57557	−	7.07633i	0.102777	−	0.282376i
$629$	7.73160	+	13.3915i	0.308279	+	0.533955i
$630$	−2.79718	−	5.40031i	−0.111442	−	0.215153i
$631$	1.06343	−	1.84192i	0.0423346	−	0.0733256i	−0.844082	−	0.536215i	$-0.819854\pi$
$631$	1.06343	−	1.84192i	0.0423346	−	0.0733256i	0.886416	+	0.462889i	$0.153187\pi$
$632$	5.40276	+	6.43875i	0.214910	+	0.256120i
$633$	−2.13352	−	4.91789i	−0.0847999	−	0.195468i
$634$	0.361370	−	2.04943i	0.0143518	−	0.0813932i
$635$	18.5627	−	6.75625i	0.736637	−	0.268114i
$636$	34.0567	+	25.2443i	1.35044	+	1.00100i
$637$	−0.120340	−	7.22001i	−0.00476803	−	0.286067i
$638$	−0.484589	−	0.279777i	−0.0191851	−	0.0110765i
$639$	1.44243	+	0.615095i	0.0570618	+	0.0243328i
$640$	19.9280	+	11.5055i	0.787725	+	0.454793i
$641$	−12.7840	−	15.2354i	−0.504938	−	0.601762i	0.452013	−	0.892011i	$-0.350706\pi$
$641$	−12.7840	−	15.2354i	−0.504938	−	0.601762i	−0.956951	+	0.290250i	$0.906262\pi$
$642$	−0.283277	+	0.953430i	−0.0111800	+	0.0376289i
$643$	5.26568	+	14.4673i	0.207658	+	0.570536i	0.999175	−	0.0406114i	$-0.0129306\pi$
$643$	5.26568	+	14.4673i	0.207658	+	0.570536i	−0.791517	+	0.611147i	$0.790708\pi$
$644$	−0.159673	−	19.1611i	−0.00629200	−	0.755054i
$645$	32.0491	+	16.0122i	1.26193	+	0.630481i
$646$	−1.20827	−	6.85247i	−0.0475389	−	0.269607i
$647$	4.32630	+	7.49338i	0.170084	+	0.294595i	0.938449	−	0.345417i	$-0.112263\pi$
$647$	4.32630	+	7.49338i	0.170084	+	0.294595i	−0.768365	+	0.640012i	$0.778929\pi$
$648$	−5.73417	+	5.50088i	−0.225260	+	0.216095i
$649$	−3.91177	−	2.25846i	−0.153551	−	0.0886525i
$650$	−1.19253	+	1.00065i	−0.0467748	+	0.0392487i
$651$	−6.23164	+	6.00314i	−0.244237	+	0.235282i
$652$	1.97018	−	11.1735i	0.0771583	−	0.437586i
$653$	−7.99326	−	1.40943i	−0.312800	−	0.0551551i	0.0150442	−	0.999887i	$-0.495211\pi$
$653$	−7.99326	−	1.40943i	−0.312800	−	0.0551551i	−0.327845	+	0.944732i	$0.606322\pi$
$654$	0.133352	−	0.126337i	0.00521447	−	0.00494016i
$655$	39.0229	−	32.7441i	1.52475	−	1.27942i
$656$	1.79584			0.0701158
$657$	21.8372	+	9.31202i	0.851952	+	0.363296i
$658$	3.69283	−	0.682921i	0.143961	−	0.0266230i
$659$	−9.97657	+	27.4104i	−0.388632	+	1.06776i	0.578986	+	0.815337i	$0.303449\pi$
$659$	−9.97657	+	27.4104i	−0.388632	+	1.06776i	−0.967618	+	0.252420i	$0.918774\pi$
$660$	−6.08194	+	2.63852i	−0.236739	+	0.102704i
$661$	19.2197	+	3.38895i	0.747559	+	0.131815i	0.534434	−	0.845210i	$-0.320525\pi$
$661$	19.2197	+	3.38895i	0.747559	+	0.131815i	0.213125	+	0.977025i	$0.431636\pi$
$662$	3.08353	+	0.543709i	0.119845	+	0.0211319i
$663$	−5.31649	−	3.94081i	−0.206476	−	0.153048i
$664$	5.03956	−	13.8461i	0.195573	−	0.537332i
$665$	74.9599	−	13.8625i	2.90682	−	0.537564i
$666$	−2.04425	−	1.91263i	−0.0792132	−	0.0741129i
$667$	16.2383			0.628749
$668$	−23.9758	+	20.1181i	−0.927650	+	0.778391i
$669$	−6.29418	−	26.3130i	−0.243347	−	1.01732i
$670$	7.27556	+	1.28288i	0.281079	+	0.0495619i
$671$	0.440184	−	2.49641i	0.0169931	−	0.0963728i
$672$	11.4202	+	3.28977i	0.440542	+	0.126906i
$673$	−12.4902	+	10.4805i	−0.481462	+	0.403995i	−0.850955	−	0.525239i	$-0.823976\pi$
$673$	−12.4902	+	10.4805i	−0.481462	+	0.403995i	0.369492	+	0.929234i	$0.379532\pi$
$674$	−1.93642	−	1.11799i	−0.0745881	−	0.0430634i
$675$	5.87608	−	34.5866i	0.226170	−	1.33124i
$676$	−11.6377	−	20.1571i	−0.447604	−	0.775273i
$677$	1.93545	+	10.9765i	0.0743854	+	0.421861i	0.999146	+	0.0413120i	$0.0131538\pi$
$677$	1.93545	+	10.9765i	0.0743854	+	0.421861i	−0.924761	+	0.380549i	$0.875735\pi$
$678$	−5.38735	+	3.55940i	−0.206900	+	0.136698i
$679$	0.223424	+	26.8114i	0.00857422	+	1.02893i
$680$	3.83409	+	10.5341i	0.147031	+	0.403964i
$681$	10.9502	−	2.61933i	0.419613	−	0.100373i
$682$	−0.155332	−	0.185117i	−0.00594796	−	0.00708850i
$683$	29.6313	+	17.1076i	1.13381	+	0.654606i	0.944890	−	0.327387i	$-0.106168\pi$
$683$	29.6313	+	17.1076i	1.13381	+	0.654606i	0.188920	+	0.981993i	$0.439501\pi$
$684$	−22.2501	−	43.8475i	−0.850755	−	1.67655i
$685$	15.0622	+	8.69614i	0.575496	+	0.332263i
$686$	−1.31814	+	3.92411i	−0.0503270	+	0.149823i
$687$	12.3923	−	5.37613i	0.472794	−	0.205112i
$688$	−20.9945	+	7.64136i	−0.800406	+	0.291324i
$689$	2.24831	−	12.7508i	0.0856538	−	0.485767i
$690$	−2.93518	+	3.95981i	−0.111740	+	0.150747i
$691$	−22.4978	−	26.8118i	−0.855856	−	1.01997i	−0.999539	−	0.0303456i	$-0.990339\pi$
$691$	−22.4978	−	26.8118i	−0.855856	−	1.01997i	0.143684	−	0.989624i	$-0.454105\pi$
$692$	−8.66380	+	15.0062i	−0.329348	+	0.570448i
$693$	−3.61122	+	2.75925i	−0.137179	+	0.104815i
$694$	1.11117	+	1.92460i	0.0421793	+	0.0730567i
$695$	11.3178	−	31.0953i	0.429307	−	1.17951i
$696$	−1.90424	+	6.40913i	−0.0721800	+	0.242938i
$697$	1.37610	+	1.15469i	0.0521236	+	0.0437369i
$698$	3.80784	+	3.19516i	0.144129	+	0.120939i
$699$	17.9209	+	27.1243i	0.677832	+	1.02593i
$700$	−32.6324	+	12.1861i	−1.23339	+	0.460592i
$701$		−	49.9356i		−	1.88604i	−0.332736	−	0.943020i	$-0.607972\pi$
$701$		−	49.9356i		−	1.88604i	0.332736	−	0.943020i	$-0.392028\pi$
$702$	1.12838	+	0.402734i	0.0425879	+	0.0152002i
$703$	30.3887	−	17.5449i	1.14613	−	0.661719i
$704$	1.33672	−	3.67262i	0.0503796	−	0.138417i
$705$	33.7305	+	16.8523i	1.27036	+	0.634693i
$706$	−0.230358	−	0.0406184i	−0.00866965	−	0.00152869i
$707$	−20.5863	+	36.3527i	−0.774227	+	1.36718i
$708$	−7.58864	+	25.5412i	−0.285199	+	0.959899i
$709$	−32.4827	−	11.8227i	−1.21991	−	0.444012i	−0.349782	−	0.936831i	$-0.613744\pi$
$709$	−32.4827	−	11.8227i	−1.21991	−	0.444012i	−0.870132	+	0.492819i	$0.835966\pi$
$710$	−0.200254	+	0.346851i	−0.00751541	+	0.0130171i
$711$	8.30494	+	27.3258i	0.311460	+	1.02480i
$712$	−9.09317	+	5.24994i	−0.340781	+	0.196750i
$713$	6.58986	+	2.39851i	0.246792	+	0.0898251i
$714$	2.11761	+	3.14777i	0.0792495	+	0.117802i
$715$	1.55109	+	1.30152i	0.0580076	+	0.0486742i
$716$	12.1947	+	33.5047i	0.455738	+	1.25213i
$717$	3.81805	−	33.2659i	0.142588	−	1.24234i
$718$	0.0140362	+	0.0796031i	0.000523825	+	0.00297076i
$719$	−3.18608	−	5.51846i	−0.118821	−	0.205804i	0.800480	−	0.599360i	$-0.204578\pi$
$719$	−3.18608	−	5.51846i	−0.118821	−	0.205804i	−0.919301	+	0.393556i	$0.871245\pi$
$720$	22.8665	+	30.4496i	0.852185	+	1.13479i
$721$	10.8007	−	1.99740i	0.402240	−	0.0743870i
$722$	−11.3677	+	2.00442i	−0.423060	+	0.0745970i
$723$	34.7017	+	10.3103i	1.29057	+	0.383446i
$724$	−2.04235	+	2.43398i	−0.0759035	+	0.0904583i
$725$	−10.0961	−	27.7388i	−0.374960	−	1.03019i
$726$	2.27755	+	3.44720i	0.0845279	+	0.127938i
$727$	1.07036	+	1.27560i	0.0396973	+	0.0473094i	0.785528	−	0.618826i	$-0.212392\pi$
$727$	1.07036	+	1.27560i	0.0396973	+	0.0473094i	−0.745830	+	0.666136i	$0.767947\pi$
$728$	−0.438197	−	2.36951i	−0.0162407	−	0.0878198i
$729$	−25.2544	+	9.55072i	−0.935347	+	0.353730i
$730$	−3.03168	+	5.25103i	−0.112208	+	0.194349i
$731$	−21.0007	−	7.64362i	−0.776738	−	0.282710i
$732$	−14.9260	+	0.900522i	−0.551681	+	0.0332843i
$733$	−18.5213	+	22.0728i	−0.684098	+	0.815276i	−0.990628	−	0.136584i	$-0.956387\pi$
$733$	−18.5213	+	22.0728i	−0.684098	+	0.815276i	0.306530	+	0.951861i	$0.400832\pi$
$734$	6.62135	−	2.40997i	0.244398	−	0.0889537i
$735$	−34.2911	+	23.4862i	−1.26485	+	0.866302i
$736$	−1.67258	−	9.48566i	−0.0616521	−	0.349646i
$737$		−	5.52069i		−	0.203357i
$738$	−0.299155	−	0.127568i	−0.0110120	−	0.00469585i
$739$	−6.33508			−0.233040			−0.116520	−	0.993188i	$-0.537174\pi$
$739$	−6.33508			−0.233040			−0.116520	+	0.993188i	$0.537174\pi$
$740$	−21.3793	+	17.9393i	−0.785918	+	0.659464i
$741$	−8.94267	+	12.0644i	−0.328517	+	0.443199i
$742$	−3.65751	+	6.45869i	−0.134271	+	0.237106i
$743$	−29.0460	+	34.6157i	−1.06560	+	1.26993i	−0.104259	+	0.994550i	$0.533247\pi$
$743$	−29.0460	+	34.6157i	−1.06560	+	1.26993i	−0.961336	+	0.275377i	$0.911197\pi$
$744$	−1.71946	+	2.31970i	−0.0630384	+	0.0850443i
$745$	38.5996	−	6.80615i	1.41418	−	0.249358i
$746$			3.58610i			0.131296i
$747$	34.2061	−	36.5601i	1.25154	−	1.33766i
$748$	3.58148	−	2.06777i	0.130952	−	0.0756050i
$749$	6.70365	+	1.12452i	0.244946	+	0.0410890i
$750$	2.22832	+	0.662064i	0.0813668	+	0.0241752i
$751$	−0.0285057	+	0.161664i	−0.00104019	+	0.00589920i	−0.985323	−	0.170698i	$-0.945398\pi$
$751$	−0.0285057	+	0.161664i	−0.00104019	+	0.00589920i	0.984283	+	0.176597i	$0.0565089\pi$
$752$	−22.0959	+	8.04224i	−0.805754	+	0.293270i
$753$	−25.7310	+	17.0004i	−0.937690	+	0.619529i
$754$	0.992792	−	0.175056i	0.0361554	−	0.00637517i
$755$	62.7484			2.28365
$756$	20.7856	+	16.9310i	0.755966	+	0.615776i
$757$	−35.2242			−1.28025			−0.640123	−	0.768272i	$-0.721117\pi$
$757$	−35.2242			−1.28025			−0.640123	+	0.768272i	$0.721117\pi$
$758$	4.23260	−	0.746322i	0.153735	−	0.0271076i
$759$	3.29497	+	1.64622i	0.119600	+	0.0597539i
$760$	23.9045	−	8.70051i	0.867106	−	0.315601i
$761$	0.652342	−	3.69962i	0.0236474	−	0.134111i	−0.970699	−	0.240301i	$-0.922754\pi$
$761$	0.652342	−	3.69962i	0.0236474	−	0.134111i	0.994346	+	0.106190i	$0.0338651\pi$
$762$	1.61949	−	1.53430i	0.0586681	−	0.0555818i
$763$	−0.968367	−	0.798901i	−0.0350573	−	0.0289222i
$764$	−9.58411	+	5.53339i	−0.346741	+	0.200191i
$765$	−2.05645	+	38.0353i	−0.0743510	+	1.37517i
$766$		−	5.88127i		−	0.212499i
$767$	8.01418	−	1.41312i	0.289375	−	0.0510246i
$768$	−20.9093	−	2.39984i	−0.754500	−	0.0865966i
$769$	7.05501	−	8.40783i	0.254410	−	0.303194i	−0.623689	−	0.781672i	$-0.714367\pi$
$769$	7.05501	−	8.40783i	0.254410	−	0.303194i	0.878099	+	0.478478i	$0.158811\pi$
$770$	−0.588736	−	1.00038i	−0.0212166	−	0.0360511i
$771$	−13.1912	−	30.4065i	−0.475070	−	1.09506i
$772$	10.5917	−	8.88746i	0.381202	−	0.319867i
$773$	12.1325			0.436376			0.218188	−	0.975907i	$-0.429985\pi$
$773$	12.1325			0.436376			0.218188	+	0.975907i	$0.429985\pi$
$774$	4.04011	+	0.218435i	0.145219	+	0.00785149i
$775$		−	12.7483i		−	0.457933i
$776$	1.55370	+	8.81145i	0.0557745	+	0.316313i
$777$	−11.2643	+	15.4643i	−0.404105	+	0.554777i
$778$	−0.339580	+	0.123597i	−0.0121745	+	0.00443117i
$779$	2.62027	−	3.12272i	0.0938810	−	0.111883i
$780$	5.33826	−	10.6847i	0.191140	−	0.382575i
$781$	0.281239	+	0.102363i	0.0100635	+	0.00366283i
$782$	1.53736	−	2.66278i	0.0549758	−	0.0952208i
$783$	−14.4942	+	17.4942i	−0.517980	+	0.625192i
$784$	4.07481	−	25.5969i	0.145529	−	0.914174i
$785$	8.50931	+	10.1410i	0.303710	+	0.361948i
$786$	2.57120	−	5.14636i	0.0917115	−	0.183564i
$787$	−7.87995	−	21.6500i	−0.280890	−	0.771739i	−0.997257	−	0.0740152i	$-0.976419\pi$
$787$	−7.87995	−	21.6500i	−0.280890	−	0.771739i	0.716367	−	0.697723i	$-0.245804\pi$
$788$	4.97977	−	5.93466i	0.177397	−	0.211414i
$789$	−9.54557	+	9.04341i	−0.339831	+	0.321954i
$790$	−7.18366	+	1.26667i	−0.255583	+	0.0450662i
$791$	28.6453	+	33.5661i	1.01851	+	1.19347i
$792$	−1.03615	+	1.10745i	−0.0368178	+	0.0393516i
$793$	2.28349	+	3.95511i	0.0810890	+	0.140450i
$794$	0.115528	+	0.655190i	0.00409993	+	0.0232518i
$795$	−68.3673	+	29.6597i	−2.42474	+	1.05192i
$796$	12.6962	+	34.8826i	0.450006	+	1.23638i
$797$	2.90031	+	2.43365i	0.102734	+	0.0862042i	0.692708	−	0.721218i	$-0.256417\pi$
$797$	2.90031	+	2.43365i	0.102734	+	0.0862042i	−0.589974	+	0.807422i	$0.700862\pi$
$798$	7.14306	−	4.80538i	0.252862	−	0.170109i
$799$	−22.1024	−	8.04463i	−0.781928	−	0.284599i
$800$	−15.1638	+	8.75484i	−0.536122	+	0.309530i
$801$	−35.4187	+	4.28941i	−1.25146	+	0.151559i
$802$	−0.705542	+	1.22203i	−0.0249136	+	0.0431516i
$803$	4.25772	+	1.54969i	0.150252	+	0.0546872i
$804$	−31.6723	+	7.57614i	−1.11700	+	0.267190i
$805$	29.3117	+	16.5990i	1.03310	+	0.585037i
$806$	0.428754	+	0.0756009i	0.0151022	+	0.00266293i
$807$	36.9764	−	24.4302i	1.30163	−	0.859983i
$808$	−4.76816	+	13.1004i	−0.167743	+	0.460871i
$809$	40.5003	−	23.3829i	1.42391	−	0.822097i	0.427284	−	0.904118i	$-0.359471\pi$
$809$	40.5003	−	23.3829i	1.42391	−	0.822097i	0.996631	+	0.0820201i	$0.0261372\pi$
$810$	−1.64616	−	6.69669i	−0.0578401	−	0.235298i
$811$		−	1.11378i		−	0.0391100i	−0.999809	−	0.0195550i	$-0.993775\pi$
$811$		−	1.11378i		−	0.0391100i	0.999809	−	0.0195550i	$-0.00622495\pi$
$812$	22.2466	+	3.73181i	0.780703	+	0.130961i
$813$	−9.50026	+	19.0152i	−0.333189	+	0.666891i
$814$	−0.409305	−	0.343448i	−0.0143461	−	0.0120378i
$815$	15.2790	+	12.8206i	0.535199	+	0.449086i
$816$	−16.3369	−	17.2440i	−0.571905	−	0.603661i
$817$	−17.3453	+	47.6558i	−0.606835	+	1.66726i
$818$	−1.44745	−	2.50706i	−0.0506091	−	0.0876575i
$819$	1.78854	−	7.99013i	0.0624968	−	0.279198i
$820$	−1.62109	+	2.80781i	−0.0566109	+	0.0980529i
$821$	3.80821	+	4.53845i	0.132908	+	0.158393i	0.828393	−	0.560147i	$-0.189255\pi$
$821$	3.80821	+	4.53845i	0.132908	+	0.158393i	−0.695486	+	0.718540i	$0.744811\pi$
$822$	1.95136	+	0.223964i	0.0680614	+	0.00781165i
$823$	3.09761	−	17.5674i	0.107976	−	0.612362i	−0.882014	−	0.471223i	$-0.843813\pi$
$823$	3.09761	−	17.5674i	0.107976	−	0.612362i	0.989990	−	0.141138i	$-0.0450763\pi$
$824$	3.44432	−	1.25363i	0.119988	−	0.0436722i
$825$	0.763487	−	6.65212i	0.0265812	−	0.231597i
$826$	−4.60087	−	0.771784i	−0.160085	−	0.0268538i
$827$	−18.0119	−	10.3992i	−0.626336	−	0.361615i	0.152996	−	0.988227i	$-0.451108\pi$
$827$	−18.0119	−	10.3992i	−0.626336	−	0.361615i	−0.779332	+	0.626612i	$0.784441\pi$
$828$	4.92262	−	21.1624i	0.171073	−	0.735445i
$829$	19.5966	+	11.3141i	0.680619	+	0.392955i	0.800088	−	0.599882i	$-0.204786\pi$
$829$	19.5966	+	11.3141i	0.680619	+	0.392955i	−0.119469	+	0.992838i	$0.538119\pi$
$830$	8.21968	+	9.79583i	0.285309	+	0.340018i
$831$	−19.1931	−	20.2588i	−0.665800	−	0.702770i
$832$	2.40827	+	6.61667i	0.0834918	+	0.229392i
$833$	19.5806	−	16.9941i	0.678429	−	0.588812i
$834$	−0.225057	−	3.73029i	−0.00779309	−	0.129169i
$835$	−9.55418	−	54.1844i	−0.330636	−	1.87513i
$836$	−4.69228	−	8.12726i	−0.162286	−	0.281087i
$837$	−8.46608	+	4.95865i	−0.292631	+	0.171396i
$838$	−2.29511	−	1.32508i	−0.0792833	−	0.0457742i
$839$	1.56279	−	1.31133i	0.0539533	−	0.0452722i	−0.615412	−	0.788205i	$-0.711010\pi$
$839$	1.56279	−	1.31133i	0.0539533	−	0.0452722i	0.669366	+	0.742933i	$0.266566\pi$
$840$	−9.98882	+	9.62255i	−0.344647	+	0.332010i
$841$	1.71636	−	9.73395i	0.0591847	−	0.335653i
$842$	2.30867	+	0.407081i	0.0795620	+	0.0140289i
$843$	−17.3798	−	5.16378i	−0.598593	−	0.177850i
$844$	−4.62340	+	3.87950i	−0.159144	+	0.133538i
$845$	40.9168			1.40758
$846$	4.25206	+	0.229895i	0.146189	+	0.00790395i
$847$	21.4779	−	18.3293i	0.737991	−	0.629801i
$848$	15.8950	−	43.6712i	0.545837	−	1.49967i
$849$	−0.760080	+	6.62243i	−0.0260859	+	0.227281i
$850$	−5.50450	−	0.970592i	−0.188803	−	0.0332910i
$851$	15.2701	+	2.69253i	0.523453	+	0.0922988i
$852$	0.201307	−	1.75395i	0.00689666	−	0.0600893i
$853$	2.46977	−	6.78563i	0.0845632	−	0.232335i	−0.890203	−	0.455564i	$-0.849438\pi$
$853$	2.46977	−	6.78563i	0.0845632	−	0.232335i	0.974766	+	0.223229i	$0.0716597\pi$
$854$	−0.476098	−	2.57445i	−0.0162917	−	0.0880959i
$855$	86.3117	+	4.66659i	2.95180	+	0.159594i
$856$	2.26829			0.0775287
$857$	−12.4405	+	10.4388i	−0.424958	+	0.356582i	−0.830045	−	0.557696i	$-0.811686\pi$
$857$	−12.4405	+	10.4388i	−0.424958	+	0.356582i	0.405087	+	0.914278i	$0.367241\pi$
$858$	0.219198	+	0.0651266i	0.00748329	+	0.00222339i
$859$	14.4896	+	2.55491i	0.494378	+	0.0871722i	0.415278	−	0.909694i	$-0.363684\pi$
$859$	14.4896	+	2.55491i	0.494378	+	0.0871722i	0.0791001	+	0.996867i	$0.474795\pi$
$860$	7.00419	−	39.7227i	0.238841	−	1.35453i
$861$	−0.615230	+	2.13572i	−0.0209670	+	0.0727851i
$862$	−2.15069	+	1.80465i	−0.0732529	+	0.0614665i
$863$	24.5666	+	14.1836i	0.836258	+	0.482814i	0.855991	−	0.516992i	$-0.172948\pi$
$863$	24.5666	+	14.1836i	0.836258	+	0.482814i	−0.0197325	+	0.999805i	$0.506281\pi$
$864$	11.7122	+	6.66489i	0.398459	+	0.226744i
$865$	−15.2305	−	26.3799i	−0.517851	−	0.896945i
$866$	0.110341	+	0.625773i	0.00374953	+	0.0212646i
$867$	0.342300	+	5.67356i	0.0116251	+	0.192684i
$868$	8.47696	+	4.80044i	0.287727	+	0.162937i
$869$	1.86434	+	5.12222i	0.0632433	+	0.173759i
$870$	−3.99070	−	4.21229i	−0.135297	−	0.142810i
$871$	6.39330	+	7.61924i	0.216629	+	0.258168i
$872$	−0.362800	−	0.209463i	−0.0122860	−	0.00709331i
$873$	−6.88802	+	29.6117i	−0.233124	+	1.00220i
$874$	−6.04251	−	3.48865i	−0.204391	−	0.118005i
$875$	2.62818	−	15.6675i	0.0888488	−	0.529659i
$876$	3.04762	−	26.5533i	0.102969	−	0.897153i
$877$	−22.0771	+	8.03542i	−0.745492	+	0.271337i	−0.686708	−	0.726934i	$-0.740945\pi$
$877$	−22.0771	+	8.03542i	−0.745492	+	0.271337i	−0.0587844	+	0.998271i	$0.518722\pi$
$878$	0.0103382	−	0.0586307i	0.000348896	−	0.00197869i
$879$	18.7777	+	2.15518i	0.633356	+	0.0726925i
$880$	4.67169	+	5.56751i	0.157483	+	0.187681i
$881$	6.70899	−	11.6203i	0.226032	−	0.391498i	−0.730597	−	0.682809i	$-0.760758\pi$
$881$	6.70899	−	11.6203i	0.226032	−	0.391498i	0.956628	+	0.291311i	$0.0940914\pi$
$882$	−2.49707	+	3.97452i	−0.0840808	+	0.133829i
$883$	26.5625	+	46.0075i	0.893898	+	1.54828i	0.835163	+	0.550003i	$0.185373\pi$
$883$	26.5625	+	46.0075i	0.893898	+	1.54828i	0.0587354	+	0.998274i	$0.481293\pi$
$884$	−2.54828	+	7.00134i	−0.0857080	+	0.235481i
$885$	−32.2144	−	34.0031i	−1.08287	−	1.14300i
$886$	−6.08779	−	5.10827i	−0.204523	−	0.171616i
$887$	−26.5308	−	22.2620i	−0.890817	−	0.747485i	0.0775565	−	0.996988i	$-0.475288\pi$
$887$	−26.5308	−	22.2620i	−0.890817	−	0.747485i	−0.968374	+	0.249503i	$0.919733\pi$
$888$	−2.85342	+	5.71125i	−0.0957547	+	0.191657i
$889$	−11.7604	−	9.70226i	−0.394430	−	0.325403i
$890$		−	9.11236i		−	0.305447i
$891$	−4.71461	+	2.08041i	−0.157945	+	0.0696965i
$892$	−26.3795	+	15.2302i	−0.883251	+	0.509945i
$893$	−18.2553	+	50.1559i	−0.610889	+	1.67840i
$894$	3.69315	−	2.44006i	0.123518	−	0.0816077i
$895$	−61.7271	−	10.8842i	−2.06331	−	0.363817i
$896$	−0.147989	−	17.7590i	−0.00494398	−	0.593288i
$897$	−6.45389	+	1.54380i	−0.215489	+	0.0515459i
$898$	6.12833	+	2.23053i	0.204505	+	0.0744337i
$899$	−4.12776	+	7.14949i	−0.137669	+	0.238449i
$900$	−39.2110	+	4.74868i	−1.30703	+	0.158289i
$901$	40.2595	−	23.2438i	1.34124	−	0.774364i
$902$	−0.0583279	−	0.0212296i	−0.00194211	−	0.000706869i
$903$	−1.89514	−	27.5856i	−0.0630662	−	0.917992i
$904$	11.2804	+	9.46541i	0.375182	+	0.314815i
$905$	−1.91038	−	5.24872i	−0.0635032	−	0.174474i
$906$	6.50097	−	2.82031i	0.215980	−	0.0936986i
$907$	−2.57706	−	14.6152i	−0.0855699	−	0.485291i	−0.997232	−	0.0743506i	$-0.976312\pi$
$907$	−2.57706	−	14.6152i	−0.0855699	−	0.485291i	0.911662	−	0.410940i	$-0.134800\pi$
$908$	−6.33808	−	10.9779i	−0.210336	−	0.364313i
$909$	−32.3640	+	34.5912i	−1.07344	+	1.14732i
$910$	1.97103	+	0.698851i	0.0653389	+	0.0231667i
$911$	50.2361	−	8.85799i	1.66440	−	0.293478i	0.739348	−	0.673324i	$-0.235134\pi$
$911$	50.2361	−	8.85799i	1.66440	−	0.293478i	0.925050	+	0.379845i	$0.124023\pi$
$912$	−39.1310	+	37.0724i	−1.29576	+	1.22759i
$913$	6.14233	−	7.32014i	0.203281	−	0.242261i
$914$	0.219587	+	0.603309i	0.00726328	+	0.0199557i
$915$	11.7485	−	23.5152i	0.388395	−	0.777389i
$916$	−9.77569	−	11.6502i	−0.322998	−	0.384934i
$917$	−37.0555	−	13.1385i	−1.22368	−	0.433870i
$918$	1.49650	+	4.03304i	0.0493917	+	0.133110i
$919$	5.49891	−	9.52438i	0.181392	−	0.314180i	−0.760963	−	0.648796i	$-0.775273\pi$
$919$	5.49891	−	9.52438i	0.181392	−	0.314180i	0.942355	+	0.334615i	$0.108606\pi$
$920$	10.5630	+	3.84463i	0.348253	+	0.126754i
$921$	−16.4494	+	32.9242i	−0.542027	+	1.08489i
$922$	−1.24236	+	1.48059i	−0.0409149	+	0.0487605i
$923$	−0.506688	+	0.184419i	−0.0166778	+	0.00607023i
$924$	4.13581	+	3.01257i	0.136058	+	0.0991061i
$925$	−4.89466	−	27.7590i	−0.160936	−	0.912711i
$926$			6.97188i			0.229110i
$927$	12.4364	+	0.672394i	0.408464	+	0.0220843i
$928$	11.3389			0.372217
$929$	−15.1986	+	12.7531i	−0.498649	+	0.418416i	−0.857114	−	0.515127i	$-0.827745\pi$
$929$	−15.1986	+	12.7531i	−0.498649	+	0.418416i	0.358465	+	0.933543i	$0.383300\pi$
$930$	−0.997328	−	2.29890i	−0.0327037	−	0.0753838i
$931$	−38.5639	−	44.4333i	−1.26388	−	1.45624i
$932$	23.5269	−	28.0383i	0.770649	−	0.918424i
$933$	34.4629	+	3.95543i	1.12827	+	0.129495i
$934$	−5.48243	+	0.966701i	−0.179391	+	0.0316314i
$935$			7.27002i			0.237755i
$936$	0.147512	−	2.72834i	0.00482159	−	0.0891786i
$937$	−28.8058	+	16.6311i	−0.941045	+	0.543313i	−0.890288	−	0.455398i	$-0.849497\pi$
$937$	−28.8058	+	16.6311i	−0.941045	+	0.543313i	−0.0507575	+	0.998711i	$0.516164\pi$
$938$	−1.99473	−	5.34155i	−0.0651302	−	0.174408i
$939$	−27.0612	+	25.6376i	−0.883108	+	0.836651i
$940$	7.37164	−	41.8067i	0.240437	−	1.36358i
$941$	−36.3251	+	13.2213i	−1.18417	+	0.431001i	−0.857671	−	0.514198i	$-0.828089\pi$
$941$	−36.3251	+	13.2213i	−1.18417	+	0.431001i	−0.326494	+	0.945199i	$0.605867\pi$
$942$	1.33740	+	0.668184i	0.0435748	+	0.0217706i
$943$	1.77394	−	0.312794i	0.0577675	−	0.0101860i
$944$	29.2099			0.950702
$945$	−44.0461	+	16.7626i	−1.43282	+	0.545287i
$946$	0.772220			0.0251070
$947$	25.7311	−	4.53709i	0.836148	−	0.147436i	0.260850	−	0.965379i	$-0.415997\pi$
$947$	25.7311	−	4.53709i	0.836148	−	0.147436i	0.575298	+	0.817944i	$0.304886\pi$
$948$	26.8278	−	17.7250i	0.871327	−	0.575683i
$949$	−7.67082	+	2.79195i	−0.249005	+	0.0906306i
$950$	−2.20252	+	12.4911i	−0.0714590	+	0.405264i
$951$	−15.4583	−	4.59288i	−0.501271	−	0.148934i
$952$	5.50592	−	6.67386i	0.178448	−	0.216301i
$953$	−22.3002	+	12.8750i	−0.722373	+	0.417062i	−0.815625	−	0.578580i	$-0.803607\pi$
$953$	−22.3002	+	12.8750i	−0.722373	+	0.417062i	0.0932526	+	0.995642i	$0.470274\pi$
$954$	−5.75002	+	6.14572i	−0.186164	+	0.198975i
$955$		−	19.4547i		−	0.629541i
$956$	−37.1258	+	6.54627i	−1.20073	+	0.211722i
$957$	−2.58206	+	3.48342i	−0.0834662	+	0.112603i
$958$	3.36443	−	4.00957i	0.108700	−	0.129543i
$959$	−0.111854	−	13.4228i	−0.00361197	−	0.433444i
$960$	24.1343	−	32.5593i	0.778932	−	1.05085i
$961$	21.0162	−	17.6347i	0.677942	−	0.568861i
$962$	0.962625			0.0310363
$963$	7.08973	+	3.02326i	0.228464	+	0.0974234i
$964$		−	40.7571i		−	1.31270i
$965$	4.22071	+	23.9368i	0.135869	+	0.770553i
$966$	3.78286	+	0.402265i	0.121712	+	0.0129427i
$967$	−38.5487	+	14.0306i	−1.23964	+	0.451193i	−0.876889	−	0.480693i	$-0.840385\pi$
$967$	−38.5487	+	14.0306i	−1.23964	+	0.451193i	−0.362752	+	0.931886i	$0.618163\pi$
$968$	6.05662	−	7.21800i	0.194667	−	0.231995i
$969$	−53.8217	+	3.24720i	−1.72900	+	0.104315i
$970$	−7.29673	−	2.65579i	−0.234284	−	0.0852724i
$971$	−21.5973	+	37.4076i	−0.693091	+	1.20047i	0.277730	+	0.960659i	$0.410418\pi$
$971$	−21.5973	+	37.4076i	−0.693091	+	1.20047i	−0.970820	+	0.239809i	$0.922915\pi$
$972$	18.4053	+	24.1928i	0.590351	+	0.775984i
$973$	−25.1135	+	4.64429i	−0.805103	+	0.148889i
$974$	2.19421	+	2.61496i	0.0703071	+	0.0837888i
$975$	6.64986	+	10.0649i	0.212966	+	0.322335i
$976$	5.60664	+	15.4041i	0.179464	+	0.493074i
$977$	−21.4760	+	25.5941i	−0.687077	+	0.818827i	−0.990999	−	0.133870i	$-0.957260\pi$
$977$	−21.4760	+	25.5941i	−0.687077	+	0.818827i	0.303921	+	0.952697i	$0.401704\pi$
$978$	2.15920	+	0.641527i	0.0690436	+	0.0205138i
$979$	−6.70596	+	1.18244i	−0.214323	+	0.0377910i
$980$	36.3425	+	29.4770i	1.16092	+	0.941609i
$981$	−0.854782	−	1.13825i	−0.0272911	−	0.0363414i
$982$	2.89603	+	5.01607i	0.0924160	+	0.160069i
$983$	−2.10645	−	11.9463i	−0.0671852	−	0.381026i	−0.999797	−	0.0201452i	$-0.993587\pi$
$983$	−2.10645	−	11.9463i	−0.0671852	−	0.381026i	0.932612	−	0.360881i	$-0.117524\pi$
$984$	−0.0845701	+	0.736843i	−0.00269600	+	0.0234897i
$985$	4.65799	+	12.7977i	0.148416	+	0.407769i
$986$	2.77276	+	2.32662i	0.0883028	+	0.0740948i
$987$	−1.99456	−	29.0328i	−0.0634876	−	0.924126i
$988$	15.8878	+	5.78268i	0.505458	+	0.183972i
$989$	−19.4075	+	11.2049i	−0.617123	+	0.356296i
$990$	−0.382731	−	1.25930i	−0.0121640	−	0.0400233i
$991$	24.7079	−	42.7953i	0.784872	−	1.35944i	−0.144203	−	0.989548i	$-0.546062\pi$
$991$	24.7079	−	42.7953i	0.784872	−	1.35944i	0.929075	−	0.369890i	$-0.120605\pi$
$992$	4.60157	+	1.67484i	0.146100	+	0.0531761i
$993$	6.91035	−	23.2583i	0.219293	−	0.738080i
$994$	0.309099	−	0.00257578i	0.00980403	−	8.16987e-5i
$995$	−64.2656	−	11.3318i	−2.03736	−	0.359241i
$996$	−50.4250	−	25.1931i	−1.59778	−	0.798273i
$997$	15.5890	−	42.8305i	0.493709	−	1.35646i	−0.403553	−	0.914956i	$-0.632225\pi$
$997$	15.5890	−	42.8305i	0.493709	−	1.35646i	0.897262	−	0.441499i	$-0.145553\pi$
$998$	−1.08719	+	0.627691i	−0.0344145	+	0.0198692i
$999$	−16.5308	+	14.0478i	−0.523010	+	0.444453i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.ba.a.5.11	✓	132
3.2	odd	2		567.2.ba.a.530.12		132
7.3	odd	6		189.2.bd.a.59.12	yes	132
21.17	even	6		567.2.bd.a.206.11		132
27.11	odd	18		189.2.bd.a.173.12	yes	132
27.16	even	9		567.2.bd.a.278.11		132
189.38	even	18	inner	189.2.ba.a.38.11	yes	132
189.178	odd	18		567.2.ba.a.521.12		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.5.11	✓	132	1.1	even	1	trivial
189.2.ba.a.38.11	yes	132	189.38	even	18	inner
189.2.bd.a.59.12	yes	132	7.3	odd	6
189.2.bd.a.173.12	yes	132	27.11	odd	18
567.2.ba.a.521.12		132	189.178	odd	18
567.2.ba.a.530.12		132	3.2	odd	2
567.2.bd.a.206.11		132	21.17	even	6
567.2.bd.a.278.11		132	27.16	even	9

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)

\(f(q)\)	\(=\)	\(q+(0.220121 - 0.0388132i) q^{2} +(-0.104309 - 1.72891i) q^{3} +(-1.83244 + 0.666953i) q^{4} +(0.595276 - 3.37598i) q^{5} +(-0.0900651 - 0.376520i) q^{6} +(-2.47857 + 0.925586i) q^{7} +(-0.764613 + 0.441450i) q^{8} +(-2.97824 + 0.360682i) q^{9} +O(q^{10})\)	\(q+(0.220121 - 0.0388132i) q^{2} +(-0.104309 - 1.72891i) q^{3} +(-1.83244 + 0.666953i) q^{4} +(0.595276 - 3.37598i) q^{5} +(-0.0900651 - 0.376520i) q^{6} +(-2.47857 + 0.925586i) q^{7} +(-0.764613 + 0.441450i) q^{8} +(-2.97824 + 0.360682i) q^{9} -0.766227i q^{10} +(-0.563881 + 0.0994274i) q^{11} +(1.34424 + 3.09855i) q^{12} +(0.663083 - 0.790231i) q^{13} +(-0.509659 + 0.299942i) q^{14} +(-5.89884 - 0.677031i) q^{15} +(2.83646 - 2.38007i) q^{16} +3.70384 q^{17} +(-0.641573 + 0.194989i) q^{18} -8.40493i q^{19} +(1.16081 + 6.58329i) q^{20} +(1.85879 + 4.18866i) q^{21} +(-0.120263 + 0.0437721i) q^{22} +(2.38732 - 2.84510i) q^{23} +(0.842981 + 1.27590i) q^{24} +(-6.34441 - 2.30918i) q^{25} +(0.115287 - 0.199683i) q^{26} +(0.934243 + 5.11148i) q^{27} +(3.92450 - 3.34917i) q^{28} +(2.81038 + 3.34928i) q^{29} +(-1.32474 + 0.0799245i) q^{30} +(0.645801 + 1.77433i) q^{31} +(1.66702 - 1.98668i) q^{32} +(0.230719 + 0.964526i) q^{33} +(0.815291 - 0.143758i) q^{34} +(1.64933 + 8.91856i) q^{35} +(5.21688 - 2.64727i) q^{36} +(2.08746 + 3.61558i) q^{37} +(-0.326222 - 1.85010i) q^{38} +(-1.43540 - 1.06398i) q^{39} +(1.03517 + 2.84410i) q^{40} +(0.371534 + 0.311754i) q^{41} +(0.571734 + 0.849866i) q^{42} +(-5.66998 - 2.06370i) q^{43} +(0.966963 - 0.558277i) q^{44} +(-0.555221 + 10.2692i) q^{45} +(0.415071 - 0.718925i) q^{46} +(-5.96744 - 2.17197i) q^{47} +(-4.41080 - 4.65572i) q^{48} +(5.28658 - 4.58825i) q^{49} +(-1.48616 - 0.262050i) q^{50} +(-0.386344 - 6.40359i) q^{51} +(-0.688011 + 1.89029i) q^{52} +(10.8697 - 6.27561i) q^{53} +(0.404039 + 1.08888i) q^{54} +1.96284i q^{55} +(1.48654 - 1.80188i) q^{56} +(-14.5313 + 0.876711i) q^{57} +(0.748619 + 0.628166i) q^{58} +(6.04312 + 5.07078i) q^{59} +(11.2608 - 2.69363i) q^{60} +(-1.51419 + 4.16020i) q^{61} +(0.211022 + 0.365500i) q^{62} +(7.04792 - 3.65059i) q^{63} +(-3.41290 + 5.91132i) q^{64} +(-2.27308 - 2.70896i) q^{65} +(0.0882223 + 0.203357i) q^{66} +(-1.67428 + 9.49530i) q^{67} +(-6.78705 + 2.47029i) q^{68} +(-5.16793 - 3.83069i) q^{69} +(0.709209 + 1.89915i) q^{70} +(-0.452673 - 0.261351i) q^{71} +(2.11798 - 1.59052i) q^{72} +(-6.85309 - 3.95663i) q^{73} +(0.599825 + 0.714844i) q^{74} +(-3.33057 + 11.2098i) q^{75} +(5.60569 + 15.4015i) q^{76} +(1.30559 - 0.768357i) q^{77} +(-0.357258 - 0.178491i) q^{78} +(-1.65313 - 9.37537i) q^{79} +(-6.34660 - 10.9926i) q^{80} +(8.73982 - 2.14839i) q^{81} +(0.0938826 + 0.0542032i) q^{82} +(-12.7845 + 10.7275i) q^{83} +(-6.19976 - 6.43574i) q^{84} +(2.20481 - 12.5041i) q^{85} +(-1.32818 - 0.234194i) q^{86} +(5.49744 - 5.20824i) q^{87} +(0.387258 - 0.324948i) q^{88} +11.8925 q^{89} +(0.276364 + 2.28201i) q^{90} +(-0.912067 + 2.57238i) q^{91} +(-2.47707 + 6.80570i) q^{92} +(3.00028 - 1.30161i) q^{93} +(-1.39786 - 0.246480i) q^{94} +(-28.3748 - 5.00325i) q^{95} +(-3.60866 - 2.67489i) q^{96} +(3.46606 - 9.52293i) q^{97} +(0.985601 - 1.21516i) q^{98} +(1.64351 - 0.499500i) 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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