LMFDB - Embedded newform 189.2.bd.a.185.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(47,189)]

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([7, 15]))

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

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

chi := DirichletCharacter("189.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.bd (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			185.1
Character	$\chi$	$=$	189.185
Dual form			189.2.bd.a.47.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.68189 + 0.472890i) q^{2} +(0.605371 - 1.62281i) q^{3} +(5.08954 - 1.85244i) q^{4} +(2.55610 - 0.930344i) q^{5} +(-0.856127 + 4.63849i) q^{6} +(2.58147 + 0.579686i) q^{7} +(-8.05677 + 4.65158i) q^{8} +(-2.26705 - 1.96481i) q^{9} +O(q^{10})$	\(q+(-2.68189 + 0.472890i) q^{2} +(0.605371 - 1.62281i) q^{3} +(5.08954 - 1.85244i) q^{4} +(2.55610 - 0.930344i) q^{5} +(-0.856127 + 4.63849i) q^{6} +(2.58147 + 0.579686i) q^{7} +(-8.05677 + 4.65158i) q^{8} +(-2.26705 - 1.96481i) q^{9} +(-6.41523 + 3.70384i) q^{10} +(0.0485071 - 0.133272i) q^{11} +(0.0748907 - 9.38079i) q^{12} +(0.695830 + 1.91178i) q^{13} +(-7.19734 - 0.333907i) q^{14} +(0.0376120 - 4.71128i) q^{15} +(11.1096 - 9.32210i) q^{16} +(2.00080 + 3.46549i) q^{17} +(7.00913 + 4.19734i) q^{18} +(-2.63555 - 1.52164i) q^{19} +(11.2860 - 9.47004i) q^{20} +(2.50347 - 3.83831i) q^{21} +(-0.0670678 + 0.380360i) q^{22} +(1.29370 + 0.228114i) q^{23} +(2.67131 + 15.8906i) q^{24} +(1.83788 - 1.54216i) q^{25} +(-2.77020 - 4.79813i) q^{26} +(-4.56093 + 2.48957i) q^{27} +(14.2123 - 1.83168i) q^{28} +(2.12744 - 5.84511i) q^{29} +(2.12704 + 12.6529i) q^{30} +(-1.45503 - 3.99766i) q^{31} +(-13.4266 + 16.0012i) q^{32} +(-0.186911 - 0.159397i) q^{33} +(-7.00474 - 8.34792i) q^{34} +(7.13779 - 0.919915i) q^{35} +(-15.1779 - 5.80039i) q^{36} -9.38062 q^{37} +(7.78784 + 2.83454i) q^{38} +(3.52369 + 0.0281311i) q^{39} +(-16.2663 + 19.3854i) q^{40} +(-0.303455 + 0.110449i) q^{41} +(-4.89893 + 11.4778i) q^{42} +(0.643705 + 3.65063i) q^{43} -0.768151i q^{44} +(-7.62276 - 2.91311i) q^{45} -3.57744 q^{46} +(-6.27238 - 2.28296i) q^{47} +(-8.40258 - 23.6722i) q^{48} +(6.32793 + 2.99288i) q^{49} +(-4.19971 + 5.00502i) q^{50} +(6.83508 - 1.14902i) q^{51} +(7.08291 + 8.44108i) q^{52} +(6.59926 + 3.81008i) q^{53} +(11.0546 - 8.83357i) q^{54} -0.385785i q^{55} +(-23.4947 + 7.33749i) q^{56} +(-4.06482 + 3.35586i) q^{57} +(-2.94149 + 16.6820i) q^{58} +(-4.94316 - 4.14781i) q^{59} +(-8.53593 - 24.0479i) q^{60} +(-3.87584 + 10.6488i) q^{61} +(5.79268 + 10.0332i) q^{62} +(-4.71335 - 6.38626i) q^{63} +(13.9394 - 24.1437i) q^{64} +(3.55722 + 4.23933i) q^{65} +(0.576653 + 0.339098i) q^{66} +(-0.311427 + 1.76619i) q^{67} +(16.6028 + 13.9314i) q^{68} +(1.15335 - 1.96134i) q^{69} +(-18.7078 + 5.84250i) q^{70} +(6.03534 + 3.48450i) q^{71} +(27.4046 + 5.28464i) q^{72} +4.24105i q^{73} +(25.1578 - 4.43600i) q^{74} +(-1.39004 - 3.91611i) q^{75} +(-16.2325 - 2.86223i) q^{76} +(0.202475 - 0.315919i) q^{77} +(-9.46347 + 1.59087i) q^{78} +(-2.60094 - 14.7507i) q^{79} +(19.7246 - 34.1640i) q^{80} +(1.27905 + 8.90865i) q^{81} +(0.761604 - 0.439712i) q^{82} +(0.966634 + 0.351826i) q^{83} +(5.63124 - 24.1728i) q^{84} +(8.33835 + 6.99670i) q^{85} +(-3.45269 - 9.48620i) q^{86} +(-8.19763 - 6.99090i) q^{87} +(0.229115 + 1.29938i) q^{88} +(-2.58608 + 4.47923i) q^{89} +(21.8210 + 4.20791i) q^{90} +(0.688030 + 5.33855i) q^{91} +(7.00690 - 1.23551i) q^{92} +(-7.36829 - 0.0588240i) q^{93} +(17.9015 + 3.15651i) q^{94} +(-8.15238 - 1.43749i) q^{95} +(17.8390 + 31.4756i) q^{96} +(7.25860 - 1.27989i) q^{97} +(-18.3861 - 5.03417i) q^{98} +(-0.371822 + 0.206828i) 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} - 15 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 - 15 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} + 30 q^{23} - 36 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} - 3 q^{30} - 9 q^{31} - 51 q^{32} - 9 q^{33} + 18 q^{34} - 9 q^{35} - 6 q^{37} - 9 q^{38} - 9 q^{39} - 9 q^{40} + 27 q^{42} - 12 q^{43} - 63 q^{45} - 6 q^{46} + 45 q^{47} + 30 q^{49} - 9 q^{50} + 33 q^{51} - 9 q^{52} + 45 q^{53} + 117 q^{54} - 51 q^{56} - 3 q^{58} - 9 q^{59} - 15 q^{60} - 63 q^{61} + 99 q^{62} - 33 q^{63} + 18 q^{64} - 102 q^{65} + 63 q^{66} - 3 q^{67} + 144 q^{68} - 108 q^{69} - 15 q^{70} + 18 q^{71} + 15 q^{72} - 33 q^{74} - 9 q^{75} - 36 q^{76} - 57 q^{77} + 66 q^{78} - 21 q^{79} - 72 q^{80} + 57 q^{81} - 18 q^{82} + 90 q^{83} + 51 q^{84} + 9 q^{85} - 33 q^{86} - 9 q^{87} + 45 q^{88} - 9 q^{89} - 81 q^{90} - 21 q^{91} + 150 q^{92} - 87 q^{93} - 9 q^{94} + 27 q^{95} - 9 q^{96} - 180 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−2.68189	+	0.472890i	−1.89638	+	0.334384i	−0.995102	−	0.0988485i	$-0.968484\pi$
$2$	−2.68189	+	0.472890i	−1.89638	+	0.334384i	−0.901282	+	0.433232i	$0.857373\pi$
$3$	0.605371	−	1.62281i	0.349511	−	0.936932i
$3$	0.605371	−	1.62281i	0.349511	−	0.936932i
$4$	5.08954	−	1.85244i	2.54477	−	0.926221i
$5$	2.55610	−	0.930344i	1.14312	−	0.416062i	0.300082	−	0.953913i	$-0.402986\pi$
$5$	2.55610	−	0.930344i	1.14312	−	0.416062i	0.843040	+	0.537851i	$0.180764\pi$
$6$	−0.856127	+	4.63849i	−0.349512	+	1.89365i
$7$	2.58147	+	0.579686i	0.975702	+	0.219101i
$7$	2.58147	+	0.579686i	0.975702	+	0.219101i
$8$	−8.05677	+	4.65158i	−2.84850	+	1.64458i
$9$	−2.26705	−	1.96481i	−0.755684	−	0.654936i
$10$	−6.41523	+	3.70384i	−2.02867	+	1.17126i
$11$	0.0485071	−	0.133272i	0.0146254	−	0.0401831i	−0.932165	−	0.362033i	$-0.882083\pi$
$11$	0.0485071	−	0.133272i	0.0146254	−	0.0401831i	0.946791	+	0.321850i	$0.104305\pi$
$12$	0.0748907	−	9.38079i	0.0216191	−	2.70800i
$13$	0.695830	+	1.91178i	0.192988	+	0.530231i	0.998013	−	0.0630103i	$-0.0200701\pi$
$13$	0.695830	+	1.91178i	0.192988	+	0.530231i	−0.805024	+	0.593242i	$0.797848\pi$
$14$	−7.19734	−	0.333907i	−1.92357	−	0.0892403i
$15$	0.0376120	−	4.71128i	0.00971138	−	1.21645i
$16$	11.1096	−	9.32210i	2.77741	−	2.33052i
$17$	2.00080	+	3.46549i	0.485266	+	0.840505i	0.999857	−	0.0169307i	$-0.00538946\pi$
$17$	2.00080	+	3.46549i	0.485266	+	0.840505i	−0.514591	+	0.857436i	$0.672056\pi$
$18$	7.00913	+	4.19734i	1.65207	+	0.989322i
$19$	−2.63555	−	1.52164i	−0.604638	−	0.349088i	0.166226	−	0.986088i	$-0.446842\pi$
$19$	−2.63555	−	1.52164i	−0.604638	−	0.349088i	−0.770864	+	0.637000i	$0.780175\pi$
$20$	11.2860	−	9.47004i	2.52362	−	2.11757i
$21$	2.50347	−	3.83831i	0.546301	−	0.837589i
$22$	−0.0670678	+	0.380360i	−0.0142989	+	0.0810931i
$23$	1.29370	+	0.228114i	0.269755	+	0.0475651i	0.306889	−	0.951745i	$-0.400712\pi$
$23$	1.29370	+	0.228114i	0.269755	+	0.0475651i	−0.0371344	+	0.999310i	$0.511823\pi$
$24$	2.67131	+	15.8906i	0.545280	+	3.24365i
$25$	1.83788	−	1.54216i	0.367575	−	0.308432i
$26$	−2.77020	−	4.79813i	−0.543281	−	0.940990i
$27$	−4.56093	+	2.48957i	−0.877751	+	0.479118i
$28$	14.2123	−	1.83168i	2.68587	−	0.346154i
$29$	2.12744	−	5.84511i	0.395056	−	1.08541i	−0.569605	−	0.821918i	$-0.692904\pi$
$29$	2.12744	−	5.84511i	0.395056	−	1.08541i	0.964662	−	0.263491i	$-0.0848738\pi$
$30$	2.12704	+	12.6529i	0.388343	+	2.31010i
$31$	−1.45503	−	3.99766i	−0.261331	−	0.718000i	−0.999078	−	0.0429236i	$-0.986333\pi$
$31$	−1.45503	−	3.99766i	−0.261331	−	0.718000i	0.737748	−	0.675077i	$-0.235889\pi$
$32$	−13.4266	+	16.0012i	−2.37352	+	2.82865i
$33$	−0.186911	−	0.159397i	−0.0325371	−	0.0277475i
$34$	−7.00474	−	8.34792i	−1.20130	−	1.43166i
$35$	7.13779	−	0.919915i	1.20651	−	0.155494i
$36$	−15.1779	−	5.80039i	−2.52966	−	0.966732i
$37$	−9.38062			−1.54217			−0.771083	−	0.636735i	$-0.780284\pi$
$37$	−9.38062			−1.54217			−0.771083	+	0.636735i	$0.780284\pi$
$38$	7.78784	+	2.83454i	1.26336	+	0.459824i
$39$	3.52369	+	0.0281311i	0.564242	+	0.00450458i
$40$	−16.2663	+	19.3854i	−2.57193	+	3.06511i
$41$	−0.303455	+	0.110449i	−0.0473917	+	0.0172492i	−0.365607	−	0.930769i	$-0.619139\pi$
$41$	−0.303455	+	0.110449i	−0.0473917	+	0.0172492i	0.318216	+	0.948018i	$0.396916\pi$
$42$	−4.89893	+	11.4778i	−0.755921	+	1.77106i
$43$	0.643705	+	3.65063i	0.0981640	+	0.556716i	0.993732	+	0.111791i	$0.0356586\pi$
$43$	0.643705	+	3.65063i	0.0981640	+	0.556716i	−0.895568	+	0.444925i	$0.853230\pi$
$44$		−	0.768151i		−	0.115803i
$45$	−7.62276	−	2.91311i	−1.13633	−	0.434260i
$46$	−3.57744			−0.527464
$47$	−6.27238	−	2.28296i	−0.914921	−	0.333004i	−0.158705	−	0.987326i	$-0.550732\pi$
$47$	−6.27238	−	2.28296i	−0.914921	−	0.333004i	−0.756216	+	0.654322i	$0.772954\pi$
$48$	−8.40258	−	23.6722i	−1.21281	−	3.41679i
$49$	6.32793	+	2.99288i	0.903990	+	0.427554i
$50$	−4.19971	+	5.00502i	−0.593929	+	0.707817i
$51$	6.83508	−	1.14902i	0.957102	−	0.160896i
$52$	7.08291	+	8.44108i	0.982222	+	1.17057i
$53$	6.59926	+	3.81008i	0.906477	+	0.523355i	0.879296	−	0.476276i	$-0.158014\pi$
$53$	6.59926	+	3.81008i	0.906477	+	0.523355i	0.0271813	+	0.999631i	$0.491347\pi$
$54$	11.0546	−	8.83357i	1.50434	−	1.20210i
$55$		−	0.385785i		−	0.0520192i
$56$	−23.4947	+	7.33749i	−3.13961	+	0.980513i
$57$	−4.06482	+	3.35586i	−0.538399	+	0.444495i
$58$	−2.94149	+	16.6820i	−0.386236	+	2.19045i
$59$	−4.94316	−	4.14781i	−0.643545	−	0.539998i	0.261560	−	0.965187i	$-0.415763\pi$
$59$	−4.94316	−	4.14781i	−0.643545	−	0.539998i	−0.905105	+	0.425189i	$0.860208\pi$
$60$	−8.53593	−	24.0479i	−1.10198	−	3.10457i
$61$	−3.87584	+	10.6488i	−0.496251	+	1.36344i	0.398621	+	0.917116i	$0.369489\pi$
$61$	−3.87584	+	10.6488i	−0.496251	+	1.36344i	−0.894872	+	0.446322i	$0.852733\pi$
$62$	5.79268	+	10.0332i	0.735671	+	1.27422i
$63$	−4.71335	−	6.38626i	−0.593826	−	0.804594i
$64$	13.9394	−	24.1437i	1.74242	−	3.01796i
$65$	3.55722	+	4.23933i	0.441218	+	0.525824i
$66$	0.576653	+	0.339098i	0.0709811	+	0.0417400i
$67$	−0.311427	+	1.76619i	−0.0380469	+	0.215775i	−0.997904	−	0.0647156i	$-0.979386\pi$
$67$	−0.311427	+	1.76619i	−0.0380469	+	0.215775i	0.959857	+	0.280490i	$0.0904971\pi$
$68$	16.6028	+	13.9314i	2.01338	+	1.68943i
$69$	1.15335	−	1.96134i	0.138848	−	0.236118i
$70$	−18.7078	+	5.84250i	−2.23600	+	0.698313i
$71$	6.03534	+	3.48450i	0.716263	+	0.413534i	0.813376	−	0.581739i	$-0.197627\pi$
$71$	6.03534	+	3.48450i	0.716263	+	0.413534i	−0.0971130	+	0.995273i	$0.530961\pi$
$72$	27.4046	+	5.28464i	3.22966	+	0.622800i
$73$			4.24105i			0.496377i	0.968712	+	0.248188i	$0.0798352\pi$
$73$			4.24105i			0.496377i	−0.968712	+	0.248188i	$0.920165\pi$
$74$	25.1578	−	4.43600i	2.92454	−	0.515675i
$75$	−1.39004	−	3.91611i	−0.160508	−	0.452193i
$76$	−16.2325	−	2.86223i	−1.86200	−	0.328320i
$77$	0.202475	−	0.315919i	0.0230742	−	0.0360023i
$78$	−9.46347	+	1.59087i	−1.07153	+	0.180131i
$79$	−2.60094	−	14.7507i	−0.292628	−	1.65958i	−0.676688	−	0.736270i	$-0.736585\pi$
$79$	−2.60094	−	14.7507i	−0.292628	−	1.65958i	0.384060	−	0.923308i	$-0.374526\pi$
$80$	19.7246	−	34.1640i	2.20528	−	3.81965i
$81$	1.27905	+	8.90865i	0.142117	+	0.989850i
$82$	0.761604	−	0.439712i	0.0841050	−	0.0485581i
$83$	0.966634	+	0.351826i	0.106102	+	0.0386179i	0.394526	−	0.918885i	$-0.370909\pi$
$83$	0.966634	+	0.351826i	0.106102	+	0.0386179i	−0.288424	+	0.957503i	$0.593131\pi$
$84$	5.63124	−	24.1728i	0.614419	−	2.63747i
$85$	8.33835	+	6.99670i	0.904421	+	0.758899i
$86$	−3.45269	−	9.48620i	−0.372314	−	1.02292i
$87$	−8.19763	−	6.99090i	−0.878878	−	0.749503i
$88$	0.229115	+	1.29938i	0.0244238	+	0.138514i
$89$	−2.58608	+	4.47923i	−0.274124	+	0.474797i	−0.969914	−	0.243449i	$-0.921721\pi$
$89$	−2.58608	+	4.47923i	−0.274124	+	0.474797i	0.695790	+	0.718246i	$0.255055\pi$
$90$	21.8210	+	4.20791i	2.30013	+	0.443553i
$91$	0.688030	+	5.33855i	0.0721251	+	0.559632i
$92$	7.00690	−	1.23551i	0.730520	−	0.128810i
$93$	−7.36829	−	0.0588240i	−0.764056	−	0.00609976i
$94$	17.9015	+	3.15651i	1.84639	+	0.325569i
$95$	−8.15238	−	1.43749i	−0.836417	−	0.147483i
$96$	17.8390	+	31.4756i	1.82068	+	3.21247i
$97$	7.25860	−	1.27989i	0.736999	−	0.129953i	0.207466	−	0.978242i	$-0.433478\pi$
$97$	7.25860	−	1.27989i	0.736999	−	0.129953i	0.529533	+	0.848289i	$0.322367\pi$
$98$	−18.3861	−	5.03417i	−1.85728	−	0.508528i
$99$	−0.371822	+	0.206828i	−0.0373696	+	0.0207870i
$100$	6.49718	−	11.2534i	0.649718	−	1.12534i
$101$	1.17079	+	6.63987i	0.116498	+	0.660692i	0.985998	+	0.166759i	$0.0533302\pi$
$101$	1.17079	+	6.63987i	0.116498	+	0.660692i	−0.869500	+	0.493933i	$0.835559\pi$
$102$	−17.7876	+	6.31380i	−1.76123	+	0.625159i
$103$	−3.92540	−	10.7850i	−0.386781	−	1.06267i	−0.968442	−	0.249241i	$-0.919819\pi$
$103$	−3.92540	−	10.7850i	−0.386781	−	1.06267i	0.581660	−	0.813432i	$-0.302403\pi$
$104$	−14.4989	−	12.1660i	−1.42174	−	1.19298i
$105$	2.82815	−	12.1402i	0.276000	−	1.18476i
$106$	−19.5002	−	7.09751i	−1.89403	−	0.689371i
$107$	−15.4754	+	8.93470i	−1.49606	+	0.863750i	−0.999990	−	0.00453289i	$-0.998557\pi$
$107$	−15.4754	+	8.93470i	−1.49606	+	0.863750i	−0.496069	+	0.868283i	$0.665224\pi$
$108$	−18.6012	+	21.1196i	−1.78991	+	2.03223i
$109$	−4.74241	+	8.21409i	−0.454240	+	0.786768i	−0.998644	−	0.0520558i	$-0.983423\pi$
$109$	−4.74241	+	8.21409i	−0.454240	+	0.786768i	0.544404	+	0.838823i	$0.316756\pi$
$110$	0.182434	+	1.03463i	0.0173944	+	0.0986485i
$111$	−5.67876	+	15.2230i	−0.539004	+	1.44490i
$112$	34.0830	−	17.6246i	3.22055	−	1.66536i
$113$	−1.54842	−	0.273029i	−0.145663	−	0.0256844i	0.100341	−	0.994953i	$-0.468007\pi$
$113$	−1.54842	−	0.273029i	−0.145663	−	0.0256844i	−0.246004	+	0.969269i	$0.579118\pi$
$114$	9.31447	−	10.9223i	0.872380	−	1.02296i
$115$	3.51905	−	0.620503i	0.328153	−	0.0578622i
$116$		−	33.6899i		−	3.12803i
$117$	2.17879	−	5.70127i	0.201429	−	0.527082i
$118$	15.2185	+	8.78640i	1.40098	+	0.808853i
$119$	3.15611	+	10.1059i	0.289320	+	0.926405i
$120$	21.6118	+	38.1326i	1.97288	+	3.48101i
$121$	8.41108	+	7.05773i	0.764644	+	0.641612i
$122$	5.35889	−	30.3918i	0.485171	−	2.75154i
$123$	−0.00446522	+	0.559313i	−0.000402616	+	0.0504316i
$124$	−14.8108	−	17.6509i	−1.33005	−	1.58510i
$125$	−3.53731	+	6.12679i	−0.316386	+	0.547997i
$126$	15.6607	+	14.8984i	1.39517	+	1.32725i
$127$	9.03739	+	15.6532i	0.801938	+	1.38900i	0.918339	+	0.395795i	$0.129531\pi$
$127$	9.03739	+	15.6532i	0.801938	+	1.38900i	−0.116400	+	0.993202i	$0.537136\pi$
$128$	−11.6783	+	32.0858i	−1.03222	+	2.83601i
$129$	6.31398	+	1.16537i	0.555915	+	0.102605i
$130$	−11.5448	−	9.68725i	−1.01255	−	0.849628i
$131$	0.952268	−	5.40058i	0.0832001	−	0.471851i	−0.914530	−	0.404517i	$-0.867440\pi$
$131$	0.952268	−	5.40058i	0.0832001	−	0.471851i	0.997730	−	0.0673340i	$-0.0214493\pi$
$132$	−1.24657	−	0.465016i	−0.108500	−	0.0404744i
$133$	−5.92152	−	5.45585i	−0.513461	−	0.473082i
$134$		−	4.88401i		−	0.421914i
$135$	−9.34202	+	10.6068i	−0.804033	+	0.912889i
$136$	−32.2400	−	18.6138i	−2.76456	−	1.59612i
$137$	2.69106	+	3.20708i	0.229913	+	0.273999i	0.868651	−	0.495425i	$-0.164988\pi$
$137$	2.69106	+	3.20708i	0.229913	+	0.273999i	−0.638738	+	0.769424i	$0.720543\pi$
$138$	−2.16567	+	5.80551i	−0.184354	+	0.494198i
$139$	7.34520	−	8.75367i	0.623012	−	0.742477i	−0.358573	−	0.933502i	$-0.616737\pi$
$139$	7.34520	−	8.75367i	0.623012	−	0.742477i	0.981585	+	0.191025i	$0.0611811\pi$
$140$	34.6240	−	17.9043i	2.92626	−	1.51319i
$141$	−7.50194	+	8.79688i	−0.631777	+	0.740831i
$142$	−17.8339	−	6.49101i	−1.49659	−	0.544714i
$143$	0.288539			0.0241289
$144$	−43.5023	−	0.694637i	−3.62519	−	0.0578864i
$145$		−	16.9199i		−	1.40512i
$146$	−2.00555	−	11.3740i	−0.165980	−	0.941322i
$147$	8.68763	−	8.45725i	0.716544	−	0.697542i
$148$	−47.7431	+	17.3771i	−3.92446	+	1.42839i
$149$	−14.9103	+	17.7694i	−1.22150	+	1.45572i	−0.371917	+	0.928266i	$0.621299\pi$
$149$	−14.9103	+	17.7694i	−1.22150	+	1.45572i	−0.849581	+	0.527458i	$0.823145\pi$
$150$	5.57984	+	9.84525i	0.455592	+	0.803861i
$151$	−0.216400	−	0.0787632i	−0.0176104	−	0.00640965i	0.333200	−	0.942856i	$-0.391872\pi$
$151$	−0.216400	−	0.0787632i	−0.0176104	−	0.00640965i	−0.350810	+	0.936447i	$0.614094\pi$
$152$	28.3121			2.29641
$153$	2.27310	−	11.7876i	0.183770	−	0.952975i
$154$	−0.393623	+	0.943009i	−0.0317190	+	0.0759898i
$155$	−7.43839	−	8.86472i	−0.597466	−	0.712032i
$156$	17.9861	−	6.38426i	1.44004	−	0.511150i
$157$	6.32473	−	7.53752i	0.504769	−	0.601560i	−0.452141	−	0.891947i	$-0.649340\pi$
$157$	6.32473	−	7.53752i	0.504769	−	0.601560i	0.956909	+	0.290387i	$0.0937840\pi$
$158$	13.9509	+	38.3297i	1.10987	+	3.04935i
$159$	10.1781	−	8.40285i	0.807172	−	0.666390i
$160$	−19.4332	+	53.3921i	−1.53633	+	4.22102i
$161$	3.20740	+	1.33881i	0.252779	+	0.105513i
$162$	−7.64310	−	23.2872i	−0.600499	−	1.82961i
$163$	−0.272626	−	0.472203i	−0.0213537	−	0.0369858i	0.855151	−	0.518379i	$-0.173464\pi$
$163$	−0.272626	−	0.472203i	−0.0213537	−	0.0369858i	−0.876505	+	0.481393i	$0.840131\pi$
$164$	−1.33985	+	1.12426i	−0.104624	+	0.0877903i
$165$	−0.626057	−	0.233543i	−0.0487385	−	0.0181813i
$166$	−2.75878	−	0.486448i	−0.214123	−	0.0377557i
$167$	2.22249	−	12.6044i	0.171981	−	0.975354i	−0.769590	−	0.638539i	$-0.779539\pi$
$167$	2.22249	−	12.6044i	0.171981	−	0.975354i	0.941571	−	0.336815i	$-0.109350\pi$
$168$	−2.31564	+	42.5695i	−0.178655	+	3.28431i
$169$	6.78787	−	5.69570i	0.522144	−	0.438131i
$170$	−25.6712	−	14.8213i	−1.96889	−	1.13674i
$171$	2.98521	+	8.62800i	0.228285	+	0.659799i
$172$	10.0387	+	17.3876i	0.765447	+	1.32579i
$173$	2.57625	−	2.16173i	0.195869	−	0.164353i	−0.539579	−	0.841935i	$-0.681416\pi$
$173$	2.57625	−	2.16173i	0.195869	−	0.164353i	0.735447	+	0.677582i	$0.236972\pi$
$174$	25.2911	+	14.8723i	1.91731	+	1.12746i
$175$	5.63838	−	2.91564i	0.426221	−	0.220402i
$176$	−0.703479	−	1.93279i	−0.0530268	−	0.145690i
$177$	−9.72356	+	5.51087i	−0.730868	+	0.414223i
$178$	4.81742	−	13.2357i	0.361081	−	0.992061i
$179$	−1.15514	+	0.666922i	−0.0863395	+	0.0498481i	−0.542548	−	0.840025i	$-0.682540\pi$
$179$	−1.15514	+	0.666922i	−0.0863395	+	0.0498481i	0.456209	+	0.889873i	$0.349207\pi$
$180$	−44.1927	−	0.705661i	−3.29393	−	0.0525969i
$181$	−2.64678	+	1.52812i	−0.196733	+	0.113584i	−0.595131	−	0.803629i	$-0.702900\pi$
$181$	−2.64678	+	1.52812i	−0.196733	+	0.113584i	0.398398	+	0.917213i	$0.369566\pi$
$182$	−4.36977	−	13.9920i	−0.323909	−	1.03716i
$183$	14.9347	+	12.7362i	1.10400	+	0.941490i
$184$	−11.4841	+	4.17988i	−0.846621	+	0.308145i
$185$	−23.9778	+	8.72720i	−1.76288	+	0.641637i
$186$	19.7888	−	3.32663i	1.45098	−	0.243920i
$187$	0.558907	−	0.0985503i	0.0408713	−	0.00720671i
$188$	−36.1526			−2.63670
$189$	−13.2170	+	3.78283i	−0.961398	+	0.275160i
$190$	22.5436			1.63548
$191$	14.9021	−	2.62764i	1.07828	−	0.190130i	0.393825	−	0.919186i	$-0.371152\pi$
$191$	14.9021	−	2.62764i	1.07828	−	0.190130i	0.684454	+	0.729056i	$0.260041\pi$
$192$	−30.7423	−	37.2369i	−2.21863	−	2.68734i
$193$	−4.48848	+	1.63367i	−0.323088	+	0.117594i	−0.498472	−	0.866906i	$-0.666105\pi$
$193$	−4.48848	+	1.63367i	−0.323088	+	0.117594i	0.175384	+	0.984500i	$0.443883\pi$
$194$	−18.8615	+	6.86504i	−1.35418	+	0.492881i
$195$	9.03307	−	3.20634i	0.646872	−	0.229611i
$196$	37.7504	+	3.51027i	2.69646	+	0.250733i
$197$	7.02585	−	4.05638i	0.500571	−	0.289005i	−0.228378	−	0.973572i	$-0.573342\pi$
$197$	7.02585	−	4.05638i	0.500571	−	0.289005i	0.728949	+	0.684568i	$0.240009\pi$
$198$	0.899381	−	0.730521i	0.0639162	−	0.0519159i
$199$	4.36607	−	2.52075i	0.309502	−	0.178691i	−0.337201	−	0.941433i	$-0.609480\pi$
$199$	4.36607	−	2.52075i	0.309502	−	0.178691i	0.646704	+	0.762741i	$0.276147\pi$
$200$	−7.63386	+	20.9738i	−0.539795	+	1.48307i
$201$	2.67767	+	1.57459i	0.188869	+	0.111063i
$202$	−6.27986	−	17.2538i	−0.441850	−	1.21397i
$203$	8.88025	−	13.8557i	0.623271	−	0.972479i
$204$	32.6589	−	18.5096i	2.28658	−	1.29593i
$205$	−0.672905	+	0.564635i	−0.0469977	+	0.0394358i
$206$	15.6276	+	27.0678i	1.08883	+	1.88590i
$207$	−2.48468	−	3.05902i	−0.172697	−	0.212616i
$208$	25.5522	+	14.7526i	1.77172	+	1.02291i
$209$	−0.330635	+	0.277436i	−0.0228705	+	0.0191906i
$210$	−1.84383	+	33.8961i	−0.127237	+	2.33905i
$211$	−0.533965	+	3.02827i	−0.0367597	+	0.208474i	−0.997656	−	0.0684355i	$-0.978199\pi$
$211$	−0.533965	+	3.02827i	−0.0367597	+	0.208474i	0.960896	+	0.276910i	$0.0893104\pi$
$212$	40.6451	+	7.16683i	2.79152	+	0.492220i
$213$	9.30832	−	7.68481i	0.637795	−	0.526555i
$214$	37.2781	−	31.2801i	2.54828	−	2.13826i
$215$	5.04171	+	8.73250i	0.343842	+	0.595552i
$216$	25.1659	−	41.2734i	1.71232	−	2.80830i
$217$	−1.43872	−	11.1633i	−0.0976666	−	0.757812i
$218$	8.83427	−	24.2720i	0.598332	−	1.64390i
$219$	6.88243	+	2.56741i	0.465072	+	0.173489i
$220$	−0.714644	−	1.96347i	−0.0481813	−	0.132377i
$221$	−5.23303	+	6.23648i	−0.352011	+	0.419511i
$222$	8.03100	−	43.5119i	0.539006	−	2.92033i
$223$	11.4325	+	13.6247i	0.765576	+	0.912378i	0.998187	−	0.0601917i	$-0.0191712\pi$
$223$	11.4325	+	13.6247i	0.765576	+	0.912378i	−0.232611	+	0.972570i	$0.574727\pi$
$224$	−43.9361	+	33.5234i	−2.93560	+	2.23988i
$225$	−7.19661	−	0.114914i	−0.479774	−	0.00766095i
$226$	4.28182			0.284822
$227$	−6.79748	−	2.47408i	−0.451165	−	0.164211i	0.106436	−	0.994320i	$-0.466056\pi$
$227$	−6.79748	−	2.47408i	−0.451165	−	0.164211i	−0.557601	+	0.830109i	$0.688278\pi$
$228$	−14.4716	+	24.6096i	−0.958402	+	1.62981i
$229$	9.76524	−	11.6378i	0.645305	−	0.769045i	−0.339893	−	0.940464i	$-0.610391\pi$
$229$	9.76524	−	11.6378i	0.645305	−	0.769045i	0.985198	+	0.171419i	$0.0548353\pi$
$230$	−9.14427	+	3.32824i	−0.602956	+	0.219458i
$231$	−0.390105	−	0.519828i	−0.0256670	−	0.0342022i
$232$	10.0486	+	56.9886i	0.659725	+	3.74149i
$233$		−	12.3912i		−	0.811776i	−0.913923	−	0.405888i	$-0.866962\pi$
$233$		−	12.3912i		−	0.811776i	0.913923	−	0.405888i	$-0.133038\pi$
$234$	−3.14721	+	16.3205i	−0.205740	+	1.06691i
$235$	−18.1568			−1.18442
$236$	−32.8420	−	11.9535i	−2.13783	−	0.778107i
$237$	−25.5121	−	4.70877i	−1.65719	−	0.305868i
$238$	−13.2433	−	25.6104i	−0.858436	−	1.66008i
$239$	5.11974	−	6.10146i	0.331168	−	0.394671i	−0.574607	−	0.818430i	$-0.694845\pi$
$239$	5.11974	−	6.10146i	0.331168	−	0.394671i	0.905775	+	0.423759i	$0.139290\pi$
$240$	−43.5011	−	52.6912i	−2.80798	−	3.40120i
$241$	0.352467	+	0.420054i	0.0227044	+	0.0270581i	0.777277	−	0.629158i	$-0.216600\pi$
$241$	0.352467	+	0.420054i	0.0227044	+	0.0270581i	−0.754573	+	0.656216i	$0.772156\pi$
$242$	−25.8952	−	14.9506i	−1.66460	−	0.961059i
$243$	15.2314	+	3.31737i	0.977094	+	0.212809i
$244$			61.3772i			3.92927i
$245$	18.9592	+	1.76295i	1.21126	+	0.112630i
$246$	−0.252518	−	1.50213i	−0.0161000	−	0.0957723i
$247$	1.07513	−	6.09739i	0.0684092	−	0.387968i
$248$	30.3182	+	25.4400i	1.92521	+	1.61544i
$249$	1.15612	−	1.35568i	0.0732661	−	0.0859129i
$250$	6.58938	−	18.1042i	0.416749	−	1.14501i
$251$	−8.86627	−	15.3568i	−0.559634	−	0.969314i	−0.997527	−	0.0702870i	$-0.977608\pi$
$251$	−8.86627	−	15.3568i	−0.559634	−	0.969314i	0.437893	−	0.899027i	$-0.355725\pi$
$252$	−35.8189	−	23.7720i	−2.25638	−	1.49749i
$253$	0.0931548	−	0.161349i	0.00585659	−	0.0101439i
$254$	−31.6395	−	37.7065i	−1.98524	−	2.36592i
$255$	16.4021	−	9.29599i	1.02714	−	0.582137i
$256$	6.46462	−	36.6627i	0.404039	−	2.29142i
$257$	21.4325	+	17.9840i	1.33692	+	1.12181i	0.982405	+	0.186764i	$0.0597999\pi$
$257$	21.4325	+	17.9840i	1.33692	+	1.12181i	0.354519	+	0.935049i	$0.384645\pi$
$258$	−17.4845	−	0.139586i	−1.08854	−	0.00869024i
$259$	−24.2158	−	5.43782i	−1.50469	−	0.337890i
$260$	25.9577	+	14.9867i	1.60983	+	0.929435i
$261$	−16.3075	+	9.07114i	−1.00941	+	0.561489i
$262$			14.9341i			0.922632i
$263$	−10.9874	+	1.93738i	−0.677512	+	0.119464i	−0.501808	−	0.864979i	$-0.667331\pi$
$263$	−10.9874	+	1.93738i	−0.677512	+	0.119464i	−0.175705	+	0.984443i	$0.556220\pi$
$264$	2.24735	+	0.414793i	0.138315	+	0.0255288i
$265$	20.4130	+	3.59937i	1.25396	+	0.221107i
$266$	18.4609	+	11.8318i	1.13191	+	0.725453i
$267$	5.70342	+	6.90833i	0.349043	+	0.422783i
$268$	1.68675	+	9.56601i	0.103034	+	0.584337i
$269$	−2.38895	+	4.13779i	−0.145657	+	0.252286i	−0.929618	−	0.368525i	$-0.879863\pi$
$269$	−2.38895	+	4.13779i	−0.145657	+	0.252286i	0.783961	+	0.620810i	$0.213196\pi$
$270$	20.0384	−	32.8641i	1.21950	−	2.00004i
$271$	−18.5269	+	10.6965i	−1.12543	+	0.649766i	−0.942781	−	0.333412i	$-0.891800\pi$
$271$	−18.5269	+	10.6965i	−1.12543	+	0.649766i	−0.182647	+	0.983179i	$0.558467\pi$
$272$	54.5339	+	19.8487i	3.30660	+	1.20350i
$273$	9.07998	+	2.11526i	0.549546	+	0.128021i
$274$	−8.73373	−	7.32847i	−0.527624	−	0.442729i
$275$	−0.116377	−	0.319743i	−0.00701780	−	0.0192812i
$276$	2.23678	−	12.1188i	0.134638	−	0.729468i
$277$	2.15053	+	12.1962i	0.129213	+	0.732801i	0.978716	+	0.205218i	$0.0657905\pi$
$277$	2.15053	+	12.1962i	0.129213	+	0.732801i	−0.849504	+	0.527583i	$0.823098\pi$
$278$	−15.5595	+	26.9499i	−0.933198	+	1.61635i
$279$	−4.55600	+	11.9217i	−0.272761	+	0.713736i
$280$	−53.2284	+	40.6135i	−3.18101	+	2.42712i
$281$	−15.3782	+	2.71159i	−0.917385	+	0.161760i	−0.612355	−	0.790583i	$-0.709778\pi$
$281$	−15.3782	+	2.71159i	−0.917385	+	0.161760i	−0.305030	+	0.952343i	$0.598667\pi$
$282$	15.9594	−	27.1399i	0.950371	−	1.61616i
$283$	−22.5207	−	3.97101i	−1.33872	−	0.236052i	−0.541987	−	0.840387i	$-0.682328\pi$
$283$	−22.5207	−	3.97101i	−1.33872	−	0.236052i	−0.796730	+	0.604335i	$0.793439\pi$
$284$	37.1719	+	6.55441i	2.20575	+	0.388933i
$285$	−7.26799	+	12.3596i	−0.430518	+	0.732119i
$286$	−0.773831	+	0.136447i	−0.0457576	+	0.00806830i
$287$	−0.847384	+	0.109211i	−0.0500195	+	0.00644649i
$288$	61.8783	−	9.89489i	3.64621	−	0.583062i
$289$	0.493577	−	0.854901i	0.0290340	−	0.0502883i
$290$	8.00126	+	45.3774i	0.469850	+	2.66465i
$291$	2.31712	−	12.5542i	0.135832	−	0.735938i
$292$	7.85629	+	21.5850i	0.459755	+	1.26317i
$293$	−25.2580	−	21.1939i	−1.47559	−	1.23816i	−0.910749	−	0.412960i	$-0.864495\pi$
$293$	−25.2580	−	21.1939i	−1.47559	−	1.23816i	−0.564837	−	0.825203i	$-0.691061\pi$
$294$	−19.2999	+	26.7897i	−1.12560	+	1.56241i
$295$	−16.4941	−	6.00336i	−0.960323	−	0.349529i
$296$	75.5775	−	43.6347i	4.39285	−	2.53622i
$297$	0.110553	+	0.728606i	0.00641492	+	0.0422780i
$298$	31.5848	−	54.7065i	1.82966	−	3.16906i
$299$	0.464091	+	2.63199i	0.0268391	+	0.152212i
$300$	−14.3290	−	17.3562i	−0.827288	−	1.00206i
$301$	−0.454519	+	9.79712i	−0.0261980	+	0.564697i
$302$	0.617608	+	0.108901i	0.0355393	+	0.00626654i
$303$	11.4840	+	2.11961i	0.659741	+	0.121769i
$304$	−43.4649	+	7.66404i	−2.49288	+	0.439563i
$305$			30.8252i			1.76505i
$306$	−0.521958	+	32.6881i	−0.0298384	+	1.86866i
$307$	−13.5558	−	7.82647i	−0.773672	−	0.446680i	0.0605107	−	0.998168i	$-0.480727\pi$
$307$	−13.5558	−	7.82647i	−0.773672	−	0.446680i	−0.834183	+	0.551488i	$0.814060\pi$
$308$	0.445286	−	1.98295i	0.0253725	−	0.112989i
$309$	−19.8783	−	0.158696i	−1.13084	−	0.00902793i
$310$	24.1410	+	20.2567i	1.37112	+	1.15050i
$311$	4.62000	−	26.2013i	0.261976	−	1.48574i	−0.515533	−	0.856870i	$-0.672406\pi$
$311$	4.62000	−	26.2013i	0.261976	−	1.48574i	0.777509	−	0.628872i	$-0.216483\pi$
$312$	−28.5204	+	16.1641i	−1.61465	+	0.915111i
$313$	−20.0560	−	23.9018i	−1.13363	−	1.35101i	−0.928088	−	0.372362i	$-0.878548\pi$
$313$	−20.0560	−	23.9018i	−1.13363	−	1.35101i	−0.205544	−	0.978648i	$-0.565896\pi$
$314$	−13.3978	+	23.2057i	−0.756084	+	1.30958i
$315$	−17.9892	−	11.9389i	−1.01358	−	0.672680i
$316$	−40.5623	−	70.2560i	−2.28181	−	3.95221i
$317$	−4.23367	+	11.6319i	−0.237787	+	0.653313i	0.762196	+	0.647347i	$0.224121\pi$
$317$	−4.23367	+	11.6319i	−0.237787	+	0.653313i	−0.999982	+	0.00596653i	$0.998101\pi$
$318$	−23.3228	+	27.3487i	−1.30788	+	1.53364i
$319$	−0.675794	−	0.567058i	−0.0378372	−	0.0317492i
$320$	13.1685	−	74.6821i	0.736140	−	4.17486i
$321$	5.13103	+	30.5224i	0.286386	+	1.70360i
$322$	−9.23503	−	2.07379i	−0.514648	−	0.115568i
$323$		−	12.1780i		−	0.677602i
$324$	23.0125	+	42.9716i	1.27847	+	2.38731i
$325$	4.22711	+	2.44053i	0.234478	+	0.135376i
$326$	0.954455	+	1.13748i	0.0528624	+	0.0629989i
$327$	10.4590	+	12.6686i	0.578386	+	0.700576i
$328$	1.93111	−	2.30140i	0.106627	−	0.127074i
$329$	−14.8685	−	9.52940i	−0.819729	−	0.525373i
$330$	1.78946	+	0.330281i	0.0985065	+	0.0181814i
$331$	17.8661	+	6.50272i	0.982008	+	0.357422i	0.782621	−	0.622499i	$-0.213882\pi$
$331$	17.8661	+	6.50272i	0.982008	+	0.357422i	0.199388	+	0.979921i	$0.436105\pi$
$332$	5.57146			0.305774
$333$	21.2664	+	18.4311i	1.16539	+	1.01002i
$334$			34.8545i			1.90715i
$335$	0.847127	+	4.80430i	0.0462835	+	0.262487i
$336$	−7.96852	−	65.9799i	−0.434718	−	3.59950i
$337$	22.8085	−	8.30162i	1.24246	−	0.452218i	0.364612	−	0.931159i	$-0.381201\pi$
$337$	22.8085	−	8.30162i	1.24246	−	0.452218i	0.877847	+	0.478941i	$0.158979\pi$
$338$	−15.5109	+	18.4852i	−0.843682	+	1.00546i
$339$	−1.38044	+	2.34752i	−0.0749755	+	0.127500i
$340$	55.3993	+	20.1637i	3.00445	+	1.09353i
$341$	−0.603356			−0.0326735
$342$	−12.0861	−	21.7277i	−0.653542	−	1.17490i
$343$	14.6004	+	11.3942i	0.788347	+	0.615230i
$344$	−22.1674	−	26.4180i	−1.19518	−	1.42437i
$345$	1.12337	−	6.08639i	0.0604800	−	0.327680i
$346$	−5.88697	+	7.01582i	−0.316485	+	0.377173i
$347$	−10.4256	−	28.6441i	−0.559675	−	1.53769i	−0.820112	−	0.572203i	$-0.806089\pi$
$347$	−10.4256	−	28.6441i	−0.559675	−	1.53769i	0.260438	−	0.965491i	$-0.416133\pi$
$348$	−54.6724	−	20.3949i	−2.93075	−	1.09328i
$349$	3.07591	−	8.45099i	0.164650	−	0.452371i	−0.829740	−	0.558150i	$-0.811511\pi$
$349$	3.07591	−	8.45099i	0.164650	−	0.452371i	0.994390	+	0.105779i	$0.0337336\pi$
$350$	−13.7428	+	10.4858i	−0.734581	+	0.560488i
$351$	−7.93312	−	6.98716i	−0.423439	−	0.372947i
$352$	1.48123	+	2.56557i	0.0789500	+	0.136745i
$353$	−13.7471	+	11.5352i	−0.731685	+	0.613957i	−0.930590	−	0.366062i	$-0.880706\pi$
$353$	−13.7471	+	11.5352i	−0.731685	+	0.613957i	0.198905	+	0.980019i	$0.436261\pi$
$354$	23.4715	−	19.3778i	1.24750	−	1.02992i
$355$	18.6687	+	3.29179i	0.990831	+	0.174710i
$356$	−4.86447	+	27.5878i	−0.257816	+	1.46215i
$357$	18.3106	+	0.996034i	0.969099	+	0.0527157i
$358$	2.78259	−	2.33487i	0.147064	−	0.123402i
$359$	23.3898	+	13.5041i	1.23447	+	0.712719i	0.967958	−	0.251114i	$-0.0807969\pi$
$359$	23.3898	+	13.5041i	1.23447	+	0.712719i	0.266508	+	0.963833i	$0.414130\pi$
$360$	74.9653	−	11.9876i	3.95102	−	0.631803i
$361$	−4.86923	−	8.43376i	−0.256275	−	0.443882i
$362$	6.37574	−	5.34988i	0.335101	−	0.281184i
$363$	16.5452	−	9.37708i	0.868399	−	0.492169i
$364$	13.3911	+	25.8962i	0.701884	+	1.35733i
$365$	3.94563	+	10.8405i	0.206524	+	0.567419i
$366$	−46.0761	−	27.0948i	−2.40844	−	1.41627i
$367$	−5.49659	+	15.1017i	−0.286920	+	0.788305i	0.709574	+	0.704631i	$0.248888\pi$
$367$	−5.49659	+	15.1017i	−0.286920	+	0.788305i	−0.996493	+	0.0836737i	$0.973335\pi$
$368$	16.4990	−	9.52572i	0.860072	−	0.496563i
$369$	0.904958	+	0.345838i	0.0471103	+	0.0180036i
$370$	60.1789	−	34.7443i	3.12855	−	1.80627i
$371$	14.8271	+	13.6611i	0.769785	+	0.709249i
$372$	−37.6102	+	13.3499i	−1.95000	+	0.692161i
$373$	18.4113	−	6.70115i	0.953299	−	0.346972i	0.181895	−	0.983318i	$-0.441777\pi$
$373$	18.4113	−	6.70115i	0.953299	−	0.346972i	0.771404	+	0.636346i	$0.219555\pi$
$374$	−1.45232	+	0.528603i	−0.0750979	+	0.0273334i
$375$	7.80127	+	9.44937i	0.402856	+	0.487964i
$376$	61.1545	−	10.7832i	3.15380	−	0.556101i
$377$	12.6549			0.651759
$378$	33.6578	−	16.3953i	1.73117	−	0.843286i
$379$	4.00603			0.205776			0.102888	−	0.994693i	$-0.467192\pi$
$379$	4.00603			0.205776			0.102888	+	0.994693i	$0.467192\pi$
$380$	−44.1547	+	7.78567i	−2.26509	+	0.399397i
$381$	30.8732	−	5.19000i	1.58168	−	0.265892i
$382$	−38.7233	+	14.0941i	−1.98126	+	0.721118i
$383$	−19.9066	+	7.24540i	−1.01718	+	0.370222i	−0.796185	−	0.605053i	$-0.793152\pi$
$383$	−19.9066	+	7.24540i	−1.01718	+	0.370222i	−0.220993	+	0.975275i	$0.570930\pi$
$384$	44.9996	+	38.3754i	2.29637	+	1.95834i
$385$	0.223634	−	0.995891i	0.0113975	−	0.0507553i
$386$	11.2651	−	6.50390i	0.573377	−	0.331040i
$387$	5.71348	−	9.54093i	0.290432	−	0.484993i
$388$	34.5720	−	19.9602i	1.75513	−	1.01332i
$389$	6.11758	−	16.8079i	0.310174	−	0.852195i	−0.682447	−	0.730935i	$-0.739084\pi$
$389$	6.11758	−	16.8079i	0.310174	−	0.852195i	0.992621	−	0.121260i	$-0.0386936\pi$
$390$	−22.7095	+	12.8707i	−1.14994	+	0.651734i
$391$	1.79791	+	4.93971i	0.0909242	+	0.249812i
$392$	−64.9043	+	5.32191i	−3.27816	+	0.268797i
$393$	−8.18767	−	4.81471i	−0.413013	−	0.242870i
$394$	−16.9244	+	14.2012i	−0.852637	+	0.715447i
$395$	−20.3714	−	35.2844i	−1.02500	−	1.77535i
$396$	−1.50927	+	1.74144i	−0.0758436	+	0.0875105i
$397$	−13.9690	−	8.06502i	−0.701085	−	0.404772i	0.106666	−	0.994295i	$-0.465982\pi$
$397$	−13.9690	−	8.06502i	−0.701085	−	0.404772i	−0.807752	+	0.589523i	$0.799316\pi$
$398$	−10.5173	+	8.82505i	−0.527184	+	0.442360i
$399$	−12.4385	+	6.30672i	−0.622706	+	0.315731i
$400$	6.04197	−	34.2657i	0.302098	−	1.71328i
$401$	2.93174	+	0.516945i	0.146404	+	0.0258150i	0.246370	−	0.969176i	$-0.420762\pi$
$401$	2.93174	+	0.516945i	0.146404	+	0.0258150i	−0.0999658	+	0.994991i	$0.531873\pi$
$402$	−7.92584	−	2.95664i	−0.395305	−	0.147464i
$403$	6.63017	−	5.56337i	0.330272	−	0.277131i
$404$	18.2588	+	31.6251i	0.908407	+	1.57341i
$405$	11.5575	+	21.5814i	0.574296	+	1.07239i
$406$	−17.2637	+	41.3589i	−0.856781	+	2.05261i
$407$	−0.455027	+	1.25018i	−0.0225548	+	0.0619689i
$408$	−49.7239	+	41.0513i	−2.46170	+	2.03234i
$409$	−7.88805	−	21.6722i	−0.390039	−	1.07162i	−0.966983	−	0.254840i	$-0.917977\pi$
$409$	−7.88805	−	21.6722i	−0.390039	−	1.07162i	0.576944	−	0.816783i	$-0.304245\pi$
$410$	1.53765	−	1.83250i	0.0759391	−	0.0905007i
$411$	6.83358	−	2.42562i	0.337076	−	0.119647i
$412$	−39.9570	−	47.6189i	−1.96854	−	2.34601i
$413$	−10.3562	−	13.5729i	−0.509594	−	0.667879i
$414$	8.11023	+	7.02898i	0.398596	+	0.345455i
$415$	2.79813			0.137355
$416$	−39.9335	−	14.5346i	−1.95790	−	0.712617i
$417$	−9.75901	−	17.2191i	−0.477901	−	0.843224i
$418$	0.755532	−	0.900407i	0.0369543	−	0.0440404i
$419$	7.21684	−	2.62672i	0.352566	−	0.128323i	−0.159665	−	0.987171i	$-0.551041\pi$
$419$	7.21684	−	2.62672i	0.352566	−	0.128323i	0.512231	+	0.858848i	$0.328819\pi$
$420$	−8.09498	−	67.0270i	−0.394995	−	3.27058i
$421$	6.15920	+	34.9305i	0.300181	+	1.70241i	0.645364	+	0.763875i	$0.276706\pi$
$421$	6.15920	+	34.9305i	0.300181	+	1.70241i	−0.345183	+	0.938535i	$0.612183\pi$
$422$		−	8.37399i		−	0.407639i
$423$	9.73424	+	17.4996i	0.473295	+	0.850861i
$424$	−70.8916			−3.44280
$425$	9.02157	+	3.28358i	0.437610	+	0.159277i
$426$	−21.3298	+	25.0117i	−1.03343	+	1.21182i
$427$	−16.1783	+	25.2427i	−0.782923	+	1.22158i
$428$	−62.2114	+	74.1407i	−3.00710	+	3.58373i
$429$	0.174673	−	0.468246i	0.00843330	−	0.0226071i
$430$	−17.6508	−	21.0355i	−0.851200	−	1.01442i
$431$	12.6881	+	7.32548i	0.611164	+	0.352856i	0.773421	−	0.633893i	$-0.218544\pi$
$431$	12.6881	+	7.32548i	0.611164	+	0.352856i	−0.162257	+	0.986749i	$0.551877\pi$
$432$	−27.4623	+	70.1756i	−1.32128	+	3.37633i
$433$		−	20.7962i		−	0.999403i	−0.866198	−	0.499701i	$-0.833443\pi$
$433$		−	20.7962i		−	0.999403i	0.866198	−	0.499701i	$-0.166557\pi$
$434$	9.13749	+	29.2583i	0.438614	+	1.40445i
$435$	−27.4579	−	10.2428i	−1.31650	−	0.491106i
$436$	−8.92056	+	50.5910i	−0.427217	+	2.42287i
$437$	−3.06251	−	2.56975i	−0.146500	−	0.122928i
$438$	−19.6720	−	3.63087i	−0.939967	−	0.173490i
$439$	−8.96881	+	24.6416i	−0.428058	+	1.17608i	0.518932	+	0.854815i	$0.326330\pi$
$439$	−8.96881	+	24.6416i	−0.428058	+	1.17608i	−0.946990	+	0.321263i	$0.895892\pi$
$440$	1.79451	+	3.10818i	0.0855498	+	0.148177i
$441$	−8.46531	−	19.2182i	−0.403110	−	0.915152i
$442$	11.0852	−	19.2002i	0.527272	−	0.913261i
$443$	−0.0928329	−	0.110634i	−0.00441063	−	0.00525638i	0.763835	−	0.645412i	$-0.223314\pi$
$443$	−0.0928329	−	0.110634i	−0.00441063	−	0.00525638i	−0.768245	+	0.640156i	$0.778870\pi$
$444$	−0.702521	+	87.9977i	−0.0333402	+	4.17619i
$445$	−2.44306	+	13.8553i	−0.115812	+	0.656804i
$446$	−37.1037	−	31.1337i	−1.75691	−	1.47422i
$447$	19.8102	+	34.9537i	0.936988	+	1.65325i
$448$	49.9798	−	54.2457i	2.36132	−	2.56287i
$449$	15.6193	+	9.01783i	0.737122	+	0.425578i	0.821022	−	0.570897i	$-0.193404\pi$
$449$	15.6193	+	9.01783i	0.737122	+	0.425578i	−0.0838999	+	0.996474i	$0.526738\pi$
$450$	19.3549	−	3.09502i	0.912398	−	0.145901i
$451$			0.0457996i			0.00215662i
$452$	−8.38653	+	1.47877i	−0.394469	+	0.0695556i
$453$	−0.258820	+	0.303496i	−0.0121604	+	0.0142595i
$454$	19.4001	+	3.42076i	0.910492	+	0.160544i
$455$	6.72535	+	13.0057i	0.315289	+	0.609719i
$456$	17.1393	−	45.9452i	0.802621	−	2.15158i
$457$	−3.40011	−	19.2830i	−0.159050	−	0.902020i	−0.954989	−	0.296642i	$-0.904133\pi$
$457$	−3.40011	−	19.2830i	−0.159050	−	0.902020i	0.795938	−	0.605378i	$-0.206978\pi$
$458$	−20.6860	+	35.8291i	−0.966591	+	1.67418i
$459$	−17.7531	−	10.8247i	−0.828643	−	0.505255i
$460$	16.7609	−	9.67690i	0.781480	−	0.451188i
$461$	−12.6847	−	4.61684i	−0.590784	−	0.215028i	0.0292902	−	0.999571i	$-0.490675\pi$
$461$	−12.6847	−	4.61684i	−0.590784	−	0.215028i	−0.620074	+	0.784543i	$0.712898\pi$
$462$	1.29204	+	1.20965i	0.0601111	+	0.0562778i
$463$	−6.46334	−	5.42339i	−0.300377	−	0.252046i	0.480124	−	0.877200i	$-0.340592\pi$
$463$	−6.46334	−	5.42339i	−0.300377	−	0.252046i	−0.780501	+	0.625154i	$0.785036\pi$
$464$	−30.8535	−	84.7693i	−1.43234	−	3.93531i
$465$	−18.8888	+	6.70468i	−0.875946	+	0.310922i
$466$	5.85969	+	33.2319i	0.271445	+	1.53944i
$467$	6.97283	−	12.0773i	0.322664	−	0.558870i	−0.658373	−	0.752692i	$-0.728755\pi$
$467$	6.97283	−	12.0773i	0.322664	−	0.558870i	0.981037	+	0.193822i	$0.0620883\pi$
$468$	0.527783	−	33.0529i	0.0243968	−	1.52787i
$469$	−1.82778	+	4.37883i	−0.0843989	+	0.202196i
$470$	48.6945	−	8.58616i	2.24611	−	0.396050i
$471$	−8.40319	−	14.8269i	−0.387199	−	0.683186i
$472$	59.1197	+	10.4244i	2.72121	+	0.479822i
$473$	0.517752	+	0.0912936i	0.0238063	+	0.00419768i
$474$	70.6475	+	0.564007i	3.24495	+	0.0259057i
$475$	−7.19043	+	1.26787i	−0.329920	+	0.0581737i
$476$	34.7837	+	45.5878i	1.59431	+	2.08951i
$477$	−7.47478	−	21.6039i	−0.342247	−	0.989176i
$478$	−10.8453	+	18.7845i	−0.496051	+	0.859185i
$479$	−3.80300	−	21.5679i	−0.173764	−	0.985462i	−0.939561	−	0.342381i	$-0.888767\pi$
$479$	−3.80300	−	21.5679i	−0.173764	−	0.985462i	0.765798	−	0.643082i	$-0.222344\pi$
$480$	74.8813	+	63.8584i	3.41785	+	2.91473i
$481$	−6.52732	−	17.9337i	−0.297620	−	0.817704i
$482$	−1.14392	−	0.959862i	−0.0521041	−	0.0437205i
$483$	4.11431	−	4.39455i	0.187207	−	0.199959i
$484$	55.8826	+	20.3396i	2.54012	+	0.924527i
$485$	17.3630	−	10.0245i	0.788411	−	0.455189i
$486$	−42.4177	−	1.69405i	−1.92411	−	0.0768438i
$487$	4.85645	−	8.41162i	0.220067	−	0.381167i	−0.734761	−	0.678326i	$-0.762706\pi$
$487$	4.85645	−	8.41162i	0.220067	−	0.381167i	0.954828	+	0.297159i	$0.0960392\pi$
$488$	−18.3069	−	103.824i	−0.828715	−	4.69987i
$489$	−0.931337	+	0.156564i	−0.0421165	+	0.00708008i
$490$	−51.6803	+	4.23759i	−2.33468	+	0.191435i
$491$	26.7581	+	4.71818i	1.20758	+	0.212928i	0.740971	−	0.671537i	$-0.234366\pi$
$491$	26.7581	+	4.71818i	1.20758	+	0.212928i	0.466606	+	0.884465i	$0.345477\pi$
$492$	1.01337	+	2.85492i	0.0456862	+	0.128710i
$493$	24.5128	−	4.32226i	1.10400	−	0.194665i
$494$			16.8610i			0.758611i
$495$	−0.757994	+	0.874595i	−0.0340693	+	0.0393101i
$496$	−53.4314	−	30.8486i	−2.39914	−	1.38514i
$497$	13.5601	+	12.4937i	0.608253	+	0.560420i
$498$	−2.45950	+	4.18251i	−0.110213	+	0.187423i
$499$	−24.8714	−	20.8696i	−1.11340	−	0.934253i	−0.115147	−	0.993349i	$-0.536734\pi$
$499$	−24.8714	−	20.8696i	−1.11340	−	0.934253i	−0.998252	+	0.0590959i	$0.981178\pi$
$500$	−6.65374	+	37.7352i	−0.297564	+	1.68757i
$501$	−19.1091	−	11.2370i	−0.853731	−	0.502032i
$502$	31.0405	+	36.9926i	1.38540	+	1.65106i
$503$	−12.9131	+	22.3661i	−0.575764	+	0.997253i	0.420194	+	0.907434i	$0.361962\pi$
$503$	−12.9131	+	22.3661i	−0.575764	+	0.997253i	−0.995958	+	0.0898189i	$0.971371\pi$
$504$	67.6805	+	29.5282i	3.01473	+	1.31529i
$505$	9.17002	+	15.8829i	0.408060	+	0.706781i
$506$	−0.173531	+	0.476773i	−0.00771439	+	0.0211951i
$507$	−5.13388	−	14.4635i	−0.228004	−	0.642345i
$508$	74.9928	+	62.9264i	3.32727	+	2.79191i
$509$	5.07095	−	28.7588i	0.224766	−	1.27471i	−0.638367	−	0.769733i	$-0.720390\pi$
$509$	5.07095	−	28.7588i	0.224766	−	1.27471i	0.863132	−	0.504978i	$-0.168499\pi$
$510$	−39.5928	+	32.6873i	−1.75320	+	1.44742i
$511$	−2.45848	+	10.9481i	−0.108757	+	0.484316i
$512$			33.0926i			1.46250i
$513$	15.8088	+	0.378688i	0.697975	+	0.0167195i
$514$	−65.9842	−	38.0960i	−2.91044	−	1.68034i
$515$	−20.0674	−	23.9154i	−0.884276	−	1.05384i
$516$	34.2940	−	5.76506i	1.50971	−	0.253793i
$517$	−0.608510	+	0.725194i	−0.0267623	+	0.0318940i
$518$	67.5156	+	3.13225i	2.96646	+	0.137623i
$519$	−1.94850	−	5.48943i	−0.0855297	−	0.240959i
$520$	−48.3792	−	17.6086i	−2.12157	−	0.772188i
$521$	−2.87036			−0.125753			−0.0628763	−	0.998021i	$-0.520027\pi$
$521$	−2.87036			−0.125753			−0.0628763	+	0.998021i	$0.520027\pi$
$522$	39.4454	−	32.0395i	1.72648	−	1.40233i
$523$		−	7.76370i		−	0.339483i	−0.985489	−	0.169742i	$-0.945707\pi$
$523$		−	7.76370i		−	0.339483i	0.985489	−	0.169742i	$-0.0542933\pi$
$524$	−5.15765	−	29.2505i	−0.225313	−	1.27781i
$525$	−1.31824	−	10.9151i	−0.0575326	−	0.476374i
$526$	28.5509	−	10.3917i	1.24488	−	0.453098i
$527$	10.9426	−	13.0409i	0.476668	−	0.568071i
$528$	−3.56243	−	0.0284403i	−0.155035	−	0.00123771i
$529$	−19.9913	−	7.27624i	−0.869187	−	0.316358i
$530$	−56.4477			−2.45193
$531$	3.05676	+	19.1157i	0.132652	+	0.829549i
$532$	−40.2445	−	16.7985i	−1.74482	−	0.728308i
$533$	−0.422306	−	0.503284i	−0.0182921	−	0.0217997i
$534$	−18.5628	−	15.8303i	−0.803292	−	0.685044i
$535$	−31.2442	+	37.2354i	−1.35080	+	1.60983i
$536$	−5.70648	−	15.6784i	−0.246482	−	0.677205i
$537$	0.383001	+	2.27832i	0.0165277	+	0.0983167i
$538$	4.45020	−	12.2268i	0.191862	−	0.527136i
$539$	0.705817	−	0.698161i	0.0304017	−	0.0300719i
$540$	−27.8981	+	71.2893i	−1.20054	+	3.06780i
$541$	0.0411054	+	0.0711966i	0.00176726	+	0.00306098i	0.866908	−	0.498469i	$-0.166104\pi$
$541$	0.0411054	+	0.0711966i	0.00176726	+	0.00306098i	−0.865140	+	0.501530i	$0.832771\pi$
$542$	44.6289	−	37.4481i	1.91697	−	1.60853i
$543$	0.877569	+	5.22030i	0.0376601	+	0.224025i
$544$	−82.3163	−	14.5146i	−3.52928	−	0.622307i
$545$	−4.48013	+	25.4081i	−0.191908	+	1.08836i
$546$	−25.3518	−	1.37905i	−1.08496	−	0.0590180i
$547$	0.989409	−	0.830213i	0.0423041	−	0.0354973i	−0.621390	−	0.783501i	$-0.713432\pi$
$547$	0.989409	−	0.830213i	0.0423041	−	0.0354973i	0.663695	+	0.748004i	$0.268987\pi$
$548$	19.6372	+	11.3375i	0.838859	+	0.484315i
$549$	29.7096	−	16.5261i	1.26797	−	0.705316i
$550$	0.463314	+	0.802484i	0.0197558	+	0.0342180i
$551$	−14.5011	+	12.1679i	−0.617769	+	0.518370i
$552$	−0.168985	+	21.1670i	−0.00719246	+	0.900926i
$553$	1.83652	−	39.5860i	0.0780967	−	1.68337i
$554$	−11.5350	−	31.6921i	−0.490074	−	1.34647i
$555$	−0.352824	+	44.1947i	−0.0149766	+	1.87596i
$556$	21.1680	−	58.1587i	0.897725	−	2.46648i
$557$	35.2510	−	20.3522i	1.49363	−	0.862350i	0.493660	−	0.869655i	$-0.335659\pi$
$557$	35.2510	−	20.3522i	1.49363	−	0.862350i	0.999973	+	0.00730507i	$0.00232530\pi$
$558$	6.58104	−	34.1273i	0.278598	−	1.44473i
$559$	−6.53128	+	3.77084i	−0.276244	+	0.159489i
$560$	70.7227	−	76.7591i	2.98858	−	3.24366i
$561$	0.178417	−	0.966661i	0.00753277	−	0.0408125i
$562$	39.9603	−	14.5444i	1.68563	−	0.613517i
$563$	32.9305	−	11.9857i	1.38786	−	0.505138i	0.463306	−	0.886198i	$-0.346663\pi$
$563$	32.9305	−	11.9857i	1.38786	−	0.505138i	0.924550	+	0.381060i	$0.124441\pi$
$564$	−21.8857	+	58.6690i	−0.921555	+	2.47041i
$565$	−4.21193	+	0.742677i	−0.177197	+	0.0312447i
$566$	62.2760			2.61765
$567$	−1.86238	+	23.7388i	−0.0782128	+	0.996937i
$568$	−64.8337			−2.72036
$569$	−5.97075	+	1.05280i	−0.250307	+	0.0441359i	−0.297394	−	0.954755i	$-0.596117\pi$
$569$	−5.97075	+	1.05280i	−0.250307	+	0.0441359i	0.0470868	+	0.998891i	$0.485006\pi$
$570$	13.6472	−	36.5841i	0.571620	−	1.53234i
$571$	7.29077	−	2.65362i	0.305109	−	0.111051i	−0.184928	−	0.982752i	$-0.559205\pi$
$571$	7.29077	−	2.65362i	0.305109	−	0.111051i	0.490038	+	0.871701i	$0.336983\pi$
$572$	1.46853	−	0.534502i	0.0614024	−	0.0223486i
$573$	4.75712	−	25.7741i	0.198732	−	1.07673i
$574$	2.22095	−	0.693610i	0.0927006	−	0.0289507i
$575$	2.72945	−	1.57585i	0.113826	−	0.0657173i
$576$	−79.0391	+	27.3468i	−3.29329	+	1.13945i
$577$	24.3850	−	14.0787i	1.01516	−	0.586104i	0.102463	−	0.994737i	$-0.467328\pi$
$577$	24.3850	−	14.0787i	1.01516	−	0.586104i	0.912699	+	0.408633i	$0.133994\pi$
$578$	−0.919447	+	2.52616i	−0.0382440	+	0.105074i
$579$	−0.0660463	+	8.27295i	−0.00274479	+	0.343812i
$580$	−31.3431	−	86.1146i	−1.30145	−	3.57571i
$581$	2.29138	+	1.46857i	0.0950626	+	0.0609266i
$582$	−0.277540	+	34.7647i	−0.0115044	+	1.44104i
$583$	0.827889	−	0.694681i	0.0342876	−	0.0287707i
$584$	−19.7276	−	34.1691i	−0.816332	−	1.41393i
$585$	0.265066	−	16.6000i	0.0109591	−	0.686327i
$586$	77.7615	+	44.8956i	3.21230	+	1.85462i
$587$	14.0329	−	11.7750i	0.579200	−	0.486006i	−0.305484	−	0.952197i	$-0.598818\pi$
$587$	14.0329	−	11.7750i	0.579200	−	0.486006i	0.884684	+	0.466191i	$0.154374\pi$
$588$	28.5495	−	59.1368i	1.17736	−	2.43876i
$589$	−2.24818	+	12.7501i	−0.0926347	+	0.525357i
$590$	47.0743	+	8.30047i	1.93802	+	0.341725i
$591$	−2.32950	−	13.8573i	−0.0958229	−	0.570011i
$592$	−104.215	+	87.4471i	−4.28323	+	3.59405i
$593$	−10.2123	−	17.6882i	−0.419367	−	0.726366i	0.576509	−	0.817091i	$-0.304415\pi$
$593$	−10.2123	−	17.6882i	−0.419367	−	0.726366i	−0.995876	+	0.0907255i	$0.971081\pi$
$594$	−0.641041	−	1.90176i	−0.0263022	−	0.0780304i
$595$	17.4693	+	22.8954i	0.716170	+	0.938619i
$596$	−42.9697	+	118.058i	−1.76011	+	4.83586i
$597$	−1.44762	−	8.61130i	−0.0592471	−	0.352437i
$598$	−2.48929	−	6.83925i	−0.101794	−	0.279678i
$599$	−19.6942	+	23.4706i	−0.804684	+	0.958985i	−0.999762	−	0.0218030i	$-0.993059\pi$
$599$	−19.6942	+	23.4706i	−0.804684	+	0.958985i	0.195079	+	0.980788i	$0.437504\pi$
$600$	29.4153	+	25.0853i	1.20088	+	1.02410i
$601$	2.11771	+	2.52379i	0.0863832	+	0.102947i	0.807505	−	0.589861i	$-0.200818\pi$
$601$	2.11771	+	2.52379i	0.0863832	+	0.102947i	−0.721122	+	0.692809i	$0.756373\pi$
$602$	−3.41399	−	26.4898i	−0.139144	−	1.07964i
$603$	4.17625	−	3.39216i	0.170070	−	0.138139i
$604$	−1.24728			−0.0507511
$605$	28.0657	+	10.2151i	1.14103	+	0.415301i
$606$	−31.8013	−	0.253883i	−1.29184	−	0.0103133i
$607$	−28.1092	+	33.4993i	−1.14092	+	1.35969i	−0.217427	+	0.976077i	$0.569766\pi$
$607$	−28.1092	+	33.4993i	−1.14092	+	1.35969i	−0.923492	+	0.383618i	$0.874678\pi$
$608$	59.7348	−	21.7417i	2.42256	−	0.881741i
$609$	−17.1094	−	22.7988i	−0.693306	−	0.923855i
$610$	−14.5769	−	82.6699i	−0.590203	−	3.34721i
$611$		−	13.5799i		−	0.549386i
$612$	−10.2669	−	64.2045i	−0.415014	−	2.59531i
$613$	−20.8813			−0.843387			−0.421694	−	0.906738i	$-0.638564\pi$
$613$	−20.8813			−0.843387			−0.421694	+	0.906738i	$0.638564\pi$
$614$	40.0564	+	14.5793i	1.61654	+	0.588374i
$615$	0.508940	+	1.43381i	0.0205224	+	0.0578169i
$616$	−0.161778	+	3.48711i	−0.00651822	+	0.140500i
$617$	13.6109	−	16.2208i	0.547954	−	0.653026i	−0.418997	−	0.907988i	$-0.637618\pi$
$617$	13.6109	−	16.2208i	0.547954	−	0.653026i	0.966951	+	0.254961i	$0.0820627\pi$
$618$	53.3865	−	8.97464i	2.14752	−	0.361013i
$619$	2.45683	+	2.92793i	0.0987483	+	0.117684i	0.813155	−	0.582047i	$-0.197748\pi$
$619$	2.45683	+	2.92793i	0.0987483	+	0.117684i	−0.714407	+	0.699730i	$0.753303\pi$
$620$	−54.2794	−	31.3382i	−2.17991	−	1.25857i
$621$	−6.46837	+	2.18034i	−0.259567	+	0.0874940i
$622$			72.4539i			2.90514i
$623$	−9.27243	+	10.0639i	−0.371492	+	0.403200i
$624$	39.4092	−	32.5357i	1.57763	−	1.30247i
$625$	−5.42474	+	30.7652i	−0.216990	+	1.23061i
$626$	65.0910	+	54.6178i	2.60156	+	2.18297i
$627$	0.250070	+	0.704511i	0.00998683	+	0.0281355i
$628$	18.2272	−	50.0787i	0.727343	−	1.99836i
$629$	−18.7688	−	32.5085i	−0.748360	−	1.29620i
$630$	53.8909	+	23.5119i	2.14706	+	0.936737i
$631$	−20.3234	+	35.2011i	−0.809061	+	1.40133i	0.104454	+	0.994530i	$0.466690\pi$
$631$	−20.3234	+	35.2011i	−0.809061	+	1.40133i	−0.913515	+	0.406805i	$0.866643\pi$
$632$	89.5690	+	106.744i	3.56286	+	4.24605i
$633$	4.59107	+	2.69975i	0.182478	+	0.107305i
$634$	5.85363	−	33.1976i	0.232478	−	1.31845i
$635$	37.6633	+	31.6033i	1.49462	+	1.25414i
$636$	36.2358	−	61.6209i	1.43684	−	2.44343i
$637$	−1.31856	+	14.1801i	−0.0522431	+	0.561837i
$638$	2.08056	+	1.20121i	0.0823703	+	0.0475565i
$639$	−6.83604	−	19.7578i	−0.270430	−	0.781608i
$640$			92.8792i			3.67137i
$641$	10.4719	−	1.84648i	0.413616	−	0.0729316i	0.0370316	−	0.999314i	$-0.488210\pi$
$641$	10.4719	−	1.84648i	0.413616	−	0.0729316i	0.376584	+	0.926383i	$0.377099\pi$
$642$	−28.1946	−	79.4315i	−1.11275	−	3.13491i
$643$	−41.6989	−	7.35263i	−1.64444	−	0.289960i	−0.726646	−	0.687012i	$-0.758922\pi$
$643$	−41.6989	−	7.35263i	−1.64444	−	0.289960i	−0.917796	+	0.397052i	$0.870033\pi$
$644$	18.8043	+	0.872388i	0.740992	+	0.0343769i
$645$	17.2233	−	2.89536i	0.678168	−	0.114005i
$646$	5.75885	+	32.6601i	0.226579	+	1.28499i
$647$	−20.0622	+	34.7487i	−0.788726	+	1.36611i	0.138021	+	0.990429i	$0.455926\pi$
$647$	−20.0622	+	34.7487i	−0.788726	+	1.36611i	−0.926748	+	0.375685i	$0.877408\pi$
$648$	−51.7443	−	65.8253i	−2.03271	−	2.58586i
$649$	−0.792565	+	0.457588i	−0.0311109	+	0.0179619i
$650$	−12.4908	−	4.54627i	−0.489928	−	0.178319i
$651$	−18.9869	−	4.42314i	−0.744154	−	0.173357i
$652$	−2.26227	−	1.89827i	−0.0885974	−	0.0743420i
$653$	7.62691	+	20.9548i	0.298464	+	0.820023i	0.994757	+	0.102266i	$0.0326092\pi$
$653$	7.62691	+	20.9548i	0.298464	+	0.820023i	−0.696293	+	0.717758i	$0.745169\pi$
$654$	−34.0409	−	29.0299i	−1.33110	−	1.13516i
$655$	−2.59031	−	14.6904i	−0.101212	−	0.574000i
$656$	−2.34166	+	4.05588i	−0.0914266	+	0.158355i
$657$	8.33284	−	9.61468i	0.325095	−	0.375104i
$658$	44.3822	+	18.5256i	1.73020	+	0.722205i
$659$	−14.8769	+	2.62320i	−0.579522	+	0.102185i	−0.455723	−	0.890122i	$-0.650619\pi$
$659$	−14.8769	+	2.62320i	−0.579522	+	0.102185i	−0.123800	+	0.992307i	$0.539508\pi$
$660$	−3.61897	−	0.0288917i	−0.140868	−	0.00112461i
$661$	−19.6850	−	3.47099i	−0.765656	−	0.135006i	−0.222837	−	0.974856i	$-0.571532\pi$
$661$	−19.6850	−	3.47099i	−0.765656	−	0.135006i	−0.542819	+	0.839850i	$0.682643\pi$
$662$	−50.9900	−	8.99091i	−1.98178	−	0.349442i
$663$	6.95273	+	12.2676i	0.270021	+	0.476435i
$664$	−9.42449	+	1.66179i	−0.365741	+	0.0644900i
$665$	−20.2118	−	8.43664i	−0.783780	−	0.327159i
$666$	−65.7500	−	39.3737i	−2.54776	−	1.52570i
$667$	4.08562	−	7.07651i	0.158196	−	0.274003i
$668$	−12.0374	−	68.2674i	−0.465740	−	2.64134i
$669$	29.0313	−	10.3048i	1.12241	−	0.398407i
$670$	−4.54381	−	12.4840i	−0.175543	−	0.482299i
$671$	1.23118	+	1.03308i	0.0475292	+	0.0398818i
$672$	27.8047	+	91.5943i	1.07259	+	3.53332i
$673$	38.6509	+	14.0678i	1.48988	+	0.542273i	0.953418	−	0.301651i	$-0.0975377\pi$
$673$	38.6509	+	14.0678i	1.48988	+	0.542273i	0.536463	+	0.843924i	$0.319760\pi$
$674$	−57.2443	+	33.0500i	−2.20497	+	1.27304i
$675$	−4.54310	+	11.6092i	−0.174864	+	0.446838i
$676$	23.9962	−	41.5626i	0.922930	−	1.59856i
$677$	3.61587	+	20.5066i	0.138969	+	0.788134i	0.972013	+	0.234927i	$0.0754850\pi$
$677$	3.61587	+	20.5066i	0.138969	+	0.788134i	−0.833044	+	0.553207i	$0.813404\pi$
$678$	2.59209	−	6.94859i	0.0995485	−	0.266859i
$679$	19.4798	+	0.903726i	0.747564	+	0.0346818i
$680$	−99.7258	−	17.5844i	−3.82431	−	0.674329i
$681$	−8.12997	+	9.53332i	−0.311541	+	0.365318i
$682$	1.61813	−	0.285321i	0.0619616	−	0.0109255i
$683$			26.1374i			1.00012i	0.865991	+	0.500060i	$0.166689\pi$
$683$			26.1374i			1.00012i	−0.865991	+	0.500060i	$0.833311\pi$
$684$	31.1762	+	38.3826i	1.19205	+	1.46760i
$685$	9.86230	+	5.69400i	0.376819	+	0.217557i
$686$	−44.5449	−	23.6537i	−1.70073	−	0.903103i
$687$	−12.9743	−	22.8923i	−0.495002	−	0.873397i
$688$	41.1829	+	34.5565i	1.57008	+	1.31746i
$689$	−2.69207	+	15.2675i	−0.102560	+	0.581644i
$690$	−0.134555	+	16.8543i	−0.00512240	+	0.641631i
$691$	19.9455	+	23.7702i	0.758764	+	0.904260i	0.997769	−	0.0667585i	$-0.0212657\pi$
$691$	19.9455	+	23.7702i	0.758764	+	0.904260i	−0.239005	+	0.971018i	$0.576821\pi$
$692$	9.10745	−	15.7746i	0.346213	−	0.599659i
$693$	−1.07974	+	0.318379i	−0.0410160	+	0.0120942i
$694$	41.5058	+	71.8901i	1.57554	+	2.72891i
$695$	10.6311	−	29.2088i	0.403262	−	1.10795i
$696$	98.5651	+	18.1922i	3.73610	+	0.689573i
$697$	−0.989912	−	0.830635i	−0.0374956	−	0.0314625i
$698$	−4.25287	+	24.1192i	−0.160974	+	0.912926i
$699$	−20.1087	−	7.50129i	−0.760579	−	0.283725i
$700$	23.2957	−	25.2841i	0.880495	−	0.955647i
$701$		−	35.8873i		−	1.35545i	−0.735317	−	0.677723i	$-0.762967\pi$
$701$		−	35.8873i		−	1.35545i	0.735317	−	0.677723i	$-0.237033\pi$
$702$	24.5799	+	14.9873i	0.927710	+	0.565660i
$703$	24.7232	+	14.2739i	0.932451	+	0.538351i
$704$	−2.54153	−	3.02887i	−0.0957873	−	0.114155i
$705$	−10.9916	+	29.4651i	−0.413967	+	1.10972i
$706$	31.4134	−	37.4370i	1.18226	−	1.40896i
$707$	−0.826692	+	17.8193i	−0.0310909	+	0.670164i
$708$	−39.2799	+	46.0601i	−1.47623	+	1.73105i
$709$	47.5071	+	17.2912i	1.78417	+	0.649384i	0.999568	+	0.0293794i	$0.00935309\pi$
$709$	47.5071	+	17.2912i	1.78417	+	0.649384i	0.784598	+	0.620004i	$0.212869\pi$
$710$	−51.6241			−1.93742
$711$	−23.0857	+	38.5509i	−0.865783	+	1.44577i
$712$		−	48.1175i		−	1.80328i
$713$	−0.970447	−	5.50368i	−0.0363435	−	0.206114i
$714$	−49.5781	+	5.98764i	−1.85541	+	0.224082i
$715$	0.737535	−	0.268441i	0.0275822	−	0.0100391i
$716$	−4.64371	+	5.53416i	−0.173544	+	0.206821i
$717$	−6.80221	−	12.0020i	−0.254033	−	0.448224i
$718$	−69.1148	−	25.1557i	−2.57934	−	0.938804i
$719$	41.8931			1.56235			0.781175	−	0.624312i	$-0.214621\pi$
$719$	41.8931			1.56235			0.781175	+	0.624312i	$0.214621\pi$
$720$	−111.842	+	38.6965i	−4.16812	+	1.44213i
$721$	−3.88140	−	30.1165i	−0.144551	−	1.12160i
$722$	17.0470	+	20.3158i	0.634424	+	0.756077i
$723$	0.895043	−	0.317700i	0.0332870	−	0.0118154i
$724$	−10.6401	+	12.6804i	−0.395437	+	0.471264i
$725$	−5.10411	−	14.0234i	−0.189562	−	0.520817i
$726$	−39.9382	+	32.9724i	−1.48224	+	1.22372i
$727$	4.61680	−	12.6846i	0.171228	−	0.470444i	−0.824162	−	0.566354i	$-0.808354\pi$
$727$	4.61680	−	12.6846i	0.171228	−	0.470444i	0.995390	+	0.0959094i	$0.0305759\pi$
$728$	−30.3760	−	39.8110i	−1.12581	−	1.47549i
$729$	14.6041	−	22.7095i	0.540893	−	0.841092i
$730$	−15.7081	−	27.2073i	−0.581384	−	1.00699i
$731$	−11.3633	+	9.53495i	−0.420287	+	0.352663i
$732$	99.6038	+	37.1560i	3.68146	+	1.37332i
$733$	−26.9369	−	4.74970i	−0.994936	−	0.175434i	−0.347603	−	0.937642i	$-0.613004\pi$
$733$	−26.9369	−	4.74970i	−0.994936	−	0.175434i	−0.647333	+	0.762208i	$0.724116\pi$
$734$	7.59979	−	43.1006i	0.280513	−	1.59087i
$735$	14.3383	−	29.7000i	0.528876	−	1.09550i
$736$	−21.0201	+	17.6380i	−0.774813	+	0.650145i
$737$	0.220278	+	0.127177i	0.00811404	+	0.00468464i
$738$	−2.59055	−	0.499555i	−0.0953593	−	0.0183889i
$739$	−8.53378	−	14.7809i	−0.313920	−	0.543726i	0.665287	−	0.746588i	$-0.268309\pi$
$739$	−8.53378	−	14.7809i	−0.313920	−	0.543726i	−0.979207	+	0.202862i	$0.934976\pi$
$740$	−105.869	+	88.8349i	−3.89183	+	3.26564i
$741$	−9.24408	−	5.43593i	−0.339590	−	0.199694i
$742$	−46.2249	−	29.6260i	−1.69697	−	1.08760i
$743$	2.70067	+	7.42004i	0.0990781	+	0.272215i	0.979322	−	0.202306i	$-0.0648436\pi$
$743$	2.70067	+	7.42004i	0.0990781	+	0.272215i	−0.880244	+	0.474521i	$0.842621\pi$
$744$	59.6382	−	33.8002i	2.18644	−	1.23918i
$745$	−21.5805	+	59.2920i	−0.790649	+	2.17229i
$746$	−46.2081	+	26.6783i	−1.69180	+	0.976761i
$747$	−1.50014	−	2.69686i	−0.0548872	−	0.0986729i
$748$	2.66202	−	1.53692i	0.0973331	−	0.0561953i
$749$	−45.1284	+	14.0938i	−1.64896	+	0.514975i
$750$	−25.3907	−	21.6531i	−0.927137	−	0.790658i
$751$	6.02030	−	2.19121i	0.219684	−	0.0799584i	−0.229834	−	0.973230i	$-0.573818\pi$
$751$	6.02030	−	2.19121i	0.219684	−	0.0799584i	0.449517	+	0.893272i	$0.351596\pi$
$752$	−90.9659	+	33.1089i	−3.31719	+	1.20736i
$753$	−30.2886	+	5.09173i	−1.10378	+	0.185553i
$754$	−33.9390	+	5.98436i	−1.23599	+	0.217938i
$755$	−0.626416			−0.0227976
$756$	−60.2612	+	43.7366i	−2.19168	+	1.59069i
$757$	−31.0889			−1.12994			−0.564972	−	0.825110i	$-0.691113\pi$
$757$	−31.0889			−1.12994			−0.564972	+	0.825110i	$0.691113\pi$
$758$	−10.7437	+	1.89441i	−0.390230	+	0.0688081i
$759$	−0.205446	−	0.248849i	−0.00745722	−	0.00903264i
$760$	72.3684	−	26.3400i	2.62508	−	0.955451i
$761$	9.23274	−	3.36044i	0.334687	−	0.121816i	−0.169210	−	0.985580i	$-0.554122\pi$
$761$	9.23274	−	3.36044i	0.334687	−	0.121816i	0.503896	+	0.863764i	$0.331899\pi$
$762$	−80.3444	+	28.5187i	−2.91057	+	1.03312i
$763$	−17.0040	+	18.4553i	−0.615585	+	0.668126i
$764$	70.9773	−	40.9788i	2.56787	−	1.48256i
$765$	−5.15629	−	32.2451i	−0.186426	−	1.16583i
$766$	49.9610	−	28.8450i	1.80516	−	1.04221i
$767$	4.49008	−	12.3364i	0.162127	−	0.445441i
$768$	−55.5833	−	32.6854i	−2.00569	−	1.17943i
$769$	7.53988	+	20.7157i	0.271895	+	0.747026i	0.998218	+	0.0596720i	$0.0190055\pi$
$769$	7.53988	+	20.7157i	0.271895	+	0.747026i	−0.726323	+	0.687354i	$0.758772\pi$
$770$	−0.128816	+	2.77663i	−0.00464221	+	0.100063i
$771$	42.1594	−	23.8940i	1.51833	−	0.860522i
$772$	−19.8180	+	16.6293i	−0.713266	+	0.598501i
$773$	−4.62590	−	8.01229i	−0.166382	−	0.288182i	0.770763	−	0.637122i	$-0.219875\pi$
$773$	−4.62590	−	8.01229i	−0.166382	−	0.288182i	−0.937145	+	0.348940i	$0.886542\pi$
$774$	−10.8111	+	28.2896i	−0.388598	+	1.01685i
$775$	−8.83919	−	5.10331i	−0.317513	−	0.183316i
$776$	−52.5274	+	44.0757i	−1.88562	+	1.58222i
$777$	−23.4841	+	36.0058i	−0.842487	+	1.29170i
$778$	−8.45840	+	47.9700i	−0.303248	+	1.71981i
$779$	0.967835	+	0.170655i	0.0346763	+	0.00611436i
$780$	40.0346	−	33.0520i	1.43347	−	1.18345i
$781$	0.757144	−	0.635319i	0.0270927	−	0.0227335i
$782$	−7.15774	−	12.3976i	−0.255960	−	0.443336i
$783$	4.84867	+	31.9555i	0.173277	+	1.14200i
$784$	98.2009	−	25.7397i	3.50718	−	0.919276i
$785$	9.15415	−	25.1508i	0.326726	−	0.897671i
$786$	24.2353	+	9.04067i	0.864444	+	0.322470i
$787$	0.471591	+	1.29569i	0.0168104	+	0.0461862i	0.947814	−	0.318824i	$-0.103288\pi$
$787$	0.471591	+	1.29569i	0.0168104	+	0.0461862i	−0.931004	+	0.365010i	$0.881066\pi$
$788$	28.2441	−	33.6601i	1.00616	−	1.19909i
$789$	−3.50745	+	19.0033i	−0.124869	+	0.676537i
$790$	71.3196	+	84.9954i	2.53744	+	3.02400i
$791$	−3.83893	−	1.60241i	−0.136497	−	0.0569753i
$792$	2.03361	−	3.39592i	0.0722612	−	0.120669i
$793$	−23.0550			−0.818708
$794$	41.2773	+	15.0237i	1.46488	+	0.533172i
$795$	18.1986	−	30.9476i	0.645436	−	1.09760i
$796$	17.5517	−	20.9173i	0.622105	−	0.741395i
$797$	13.4666	−	4.90146i	0.477013	−	0.173619i	−0.0923136	−	0.995730i	$-0.529426\pi$
$797$	13.4666	−	4.90146i	0.477013	−	0.173619i	0.569327	+	0.822111i	$0.307204\pi$
$798$	30.3765	−	22.7960i	1.07532	−	0.806970i
$799$	−4.63822	−	26.3047i	−0.164088	−	0.930592i
$800$			50.1143i			1.77181i
$801$	14.6636	−	5.07349i	0.518113	−	0.179263i
$802$	−8.10707			−0.286271
$803$	0.565214	+	0.205721i	0.0199460	+	0.00725973i
$804$	16.5450	+	3.05371i	0.583496	+	0.107696i
$805$	9.44399	+	0.438136i	0.332857	+	0.0154423i
$806$	−15.1505	+	18.0557i	−0.533655	+	0.635986i
$807$	5.26866	+	6.38173i	0.185466	+	0.224647i
$808$	−40.3187	−	48.0499i	−1.41841	−	1.69039i
$809$	25.1012	+	14.4922i	0.882512	+	0.509519i	0.871486	−	0.490420i	$-0.163157\pi$
$809$	25.1012	+	14.4922i	0.882512	+	0.509519i	0.0110264	+	0.999939i	$0.496490\pi$
$810$	−41.2016	−	52.4136i	−1.44768	−	1.84163i
$811$		−	16.8829i		−	0.592840i	−0.955058	−	0.296420i	$-0.904207\pi$
$811$		−	16.8829i		−	0.592840i	0.955058	−	0.296420i	$-0.0957928\pi$
$812$	19.5295	−	86.9692i	0.685353	−	3.05202i
$813$	6.14280	+	36.5411i	0.215438	+	1.28155i
$814$	0.629138	−	3.56802i	0.0220513	−	0.125059i
$815$	−1.13617	−	0.953360i	−0.0397983	−	0.0333948i
$816$	65.2239	−	76.4825i	2.28329	−	2.67742i
$817$	3.85842	−	10.6009i	0.134989	−	0.370879i
$818$	31.4035	+	54.3924i	1.09800	+	1.90179i
$819$	8.92942	−	13.4546i	0.312019	−	0.470142i
$820$	−2.37883	+	4.12025i	−0.0830722	+	0.143885i
$821$	2.60378	+	3.10306i	0.0908725	+	0.108298i	0.809564	−	0.587031i	$-0.199703\pi$
$821$	2.60378	+	3.10306i	0.0908725	+	0.108298i	−0.718692	+	0.695329i	$0.755259\pi$
$822$	−17.1799	+	9.73678i	−0.599217	+	0.339609i
$823$	−2.15078	+	12.1977i	−0.0749715	+	0.425184i	0.924102	+	0.382146i	$0.124815\pi$
$823$	−2.15078	+	12.1977i	−0.0749715	+	0.425184i	−0.999073	+	0.0430383i	$0.986296\pi$
$824$	81.7931	+	68.6325i	2.84940	+	2.39093i
$825$	−0.589335	−	0.00470490i	−0.0205180	−	0.000163804i
$826$	34.1926	+	31.5037i	1.18971	+	1.09615i
$827$	−5.99133	−	3.45910i	−0.208339	−	0.120285i	0.392200	−	0.919880i	$-0.371714\pi$
$827$	−5.99133	−	3.45910i	−0.208339	−	0.120285i	−0.600539	+	0.799595i	$0.705047\pi$
$828$	−18.3125	−	10.9663i	−0.636405	−	0.381104i
$829$		−	53.3178i		−	1.85180i	−0.377765	−	0.925901i	$-0.623307\pi$
$829$		−	53.3178i		−	1.85180i	0.377765	−	0.925901i	$-0.376693\pi$
$830$	−7.50429	+	1.32321i	−0.260478	+	0.0459292i
$831$	21.0941	+	3.89334i	0.731747	+	0.135059i
$832$	55.8568	+	9.84906i	1.93649	+	0.341455i
$833$	2.28914	+	27.9175i	0.0793139	+	0.967286i
$834$	34.3154	+	41.5649i	1.18824	+	1.43927i
$835$	−6.04548	−	34.2856i	−0.209213	−	1.18650i
$836$	−1.16885	+	2.02450i	−0.0404254	+	0.0700189i
$837$	16.5887	+	14.6106i	0.573390	+	0.505017i
$838$	−18.1127	+	10.4573i	−0.625691	+	0.361243i
$839$	−40.8924	−	14.8836i	−1.41176	−	0.513840i	−0.480116	−	0.877205i	$-0.659406\pi$
$839$	−40.8924	−	14.8836i	−1.41176	−	0.513840i	−0.931647	+	0.363365i	$0.881628\pi$
$840$	33.6852	+	110.966i	1.16225	+	3.82869i
$841$	−7.42395	−	6.22943i	−0.255998	−	0.214808i
$842$	−33.0366	−	90.7674i	−1.13852	−	3.12805i
$843$	−4.90909	+	26.5974i	−0.169078	+	0.916064i
$844$	2.89205	+	16.4016i	0.0995484	+	0.564567i
$845$	12.0515	−	20.8738i	0.414584	−	0.718081i
$846$	−34.3816	−	42.3289i	−1.18206	−	1.45530i
$847$	17.6216	+	23.0951i	0.605487	+	0.793556i
$848$	108.833	−	19.1902i	3.73735	−	0.658996i
$849$	−20.0776	+	34.1430i	−0.689061	+	1.17178i
$850$	−25.7477	−	4.54001i	−0.883137	−	0.155721i
$851$	−12.1357	−	2.13985i	−0.416007	−	0.0733532i
$852$	33.1394	−	56.3553i	1.13534	−	1.93070i
$853$	−52.2783	+	9.21807i	−1.78997	+	0.315621i	−0.967441	−	0.253097i	$-0.918551\pi$
$853$	−52.2783	+	9.21807i	−1.78997	+	0.315621i	−0.822533	+	0.568718i	$0.807440\pi$
$854$	31.4515	−	75.3488i	1.07625	−	2.57838i
$855$	15.6575	+	19.2767i	0.535475	+	0.659250i
$856$	83.1209	−	143.970i	2.84101	−	4.92078i
$857$	6.95408	+	39.4386i	0.237547	+	1.34720i	0.837183	+	0.546923i	$0.184201\pi$
$857$	6.95408	+	39.4386i	0.237547	+	1.34720i	−0.599636	+	0.800273i	$0.704688\pi$
$858$	−0.247026	+	1.33839i	−0.00843333	+	0.0456917i
$859$	3.46257	+	9.51334i	0.118141	+	0.324591i	0.984642	−	0.174585i	$-0.0558584\pi$
$859$	3.46257	+	9.51334i	0.118141	+	0.324591i	−0.866501	+	0.499176i	$0.833636\pi$
$860$	41.8364	+	35.1049i	1.42661	+	1.19707i
$861$	−0.335753	+	1.44126i	−0.0114424	+	0.0491180i
$862$	−37.4923	−	13.6461i	−1.27699	−	0.464787i
$863$	26.6005	−	15.3578i	0.905490	−	0.522785i	0.0265129	−	0.999648i	$-0.491560\pi$
$863$	26.6005	−	15.3578i	0.905490	−	0.522785i	0.878977	+	0.476863i	$0.158226\pi$
$864$	21.4017	−	106.407i	0.728102	−	3.62004i
$865$	4.57400	−	7.92240i	0.155521	−	0.269370i
$866$	9.83433	+	55.7732i	0.334184	+	1.89525i
$867$	−1.08855	−	1.31852i	−0.0369690	−	0.0447792i
$868$	−28.0017	−	54.1508i	−0.950440	−	1.83800i
$869$	−2.09202	−	0.368879i	−0.0709668	−	0.0125134i
$870$	78.4828	+	14.4856i	2.66082	+	0.491108i
$871$	−3.59326	+	0.633590i	−0.121753	+	0.0214684i
$872$		−	88.2387i		−	2.98814i
$873$	−18.9704	−	11.3602i	−0.642049	−	0.384484i
$874$	9.42853	+	5.44356i	0.318925	+	0.184131i
$875$	−12.6831	+	13.7656i	−0.428765	+	0.465362i
$876$	39.7844	+	0.317615i	1.34419	+	0.0107312i
$877$	−18.2996	−	15.3552i	−0.617935	−	0.518509i	0.279219	−	0.960228i	$-0.409925\pi$
$877$	−18.2996	−	15.3552i	−0.617935	−	0.518509i	−0.897154	+	0.441718i	$0.854369\pi$
$878$	12.4006	−	70.3274i	0.418500	−	2.37343i
$879$	−49.6843	+	28.1588i	−1.67581	+	0.949772i
$880$	−3.59632	−	4.28593i	−0.121232	−	0.144479i
$881$	1.24040	−	2.14844i	0.0417902	−	0.0723828i	−0.844374	−	0.535755i	$-0.820027\pi$
$881$	1.24040	−	2.14844i	0.0417902	−	0.0723828i	0.886164	+	0.463372i	$0.153361\pi$
$882$	31.7911	+	47.5379i	1.07046	+	1.60069i
$883$	−17.2245	−	29.8337i	−0.579650	−	1.00398i	−0.995519	−	0.0945585i	$-0.969856\pi$
$883$	−17.2245	−	29.8337i	−0.579650	−	1.00398i	0.415870	−	0.909424i	$-0.363477\pi$
$884$	−15.0810	+	41.4347i	−0.507229	+	1.39360i
$885$	−19.7274	+	23.1326i	−0.663128	+	0.777593i
$886$	0.301286	+	0.252809i	0.0101219	+	0.00849327i
$887$	−2.84453	+	16.1321i	−0.0955099	+	0.541664i	0.899080	+	0.437784i	$0.144237\pi$
$887$	−2.84453	+	16.1321i	−0.0955099	+	0.541664i	−0.994590	+	0.103879i	$0.966874\pi$
$888$	−25.0586	−	149.063i	−0.840911	−	5.00224i
$889$	14.2557	+	45.6471i	0.478122	+	1.53095i
$890$		−	38.3137i		−	1.28428i
$891$	1.24932	+	0.261670i	0.0418537	+	0.00876629i
$892$	83.4251	+	48.1655i	2.79328	+	1.61270i
$893$	13.0574	+	15.5612i	0.436948	+	0.520735i
$894$	−69.6580	−	84.3740i	−2.32971	−	2.82189i
$895$	−2.33219	+	2.77940i	−0.0779566	+	0.0929050i
$896$	−48.7467	+	76.0586i	−1.62851	+	2.54094i
$897$	4.55218	+	0.840197i	0.151993	+	0.0280534i
$898$	−46.1538	−	16.7986i	−1.54017	−	0.560577i
$899$	−26.4622			−0.882564
$900$	−36.8403	+	12.7464i	−1.22801	+	0.424881i
$901$			30.4929i			1.01587i
$902$	−0.0216582	−	0.122830i	−0.000721139	−	0.00408978i
$903$	15.6238	+	6.66849i	0.519926	+	0.221913i
$904$	13.7453	−	5.00288i	0.457162	−	0.166393i
$905$	−5.34375	+	6.36843i	−0.177632	+	0.211694i
$906$	0.550608	−	0.936338i	0.0182927	−	0.0311077i
$907$	31.8395	+	11.5886i	1.05721	+	0.384794i	0.811380	−	0.584519i	$-0.198717\pi$
$907$	31.8395	+	11.5886i	1.05721	+	0.384794i	0.245832	+	0.969312i	$0.420939\pi$
$908$	−39.1792			−1.30021
$909$	10.3918	−	17.3533i	0.344676	−	0.575573i
$910$	−24.1870	−	31.6997i	−0.801790	−	1.05083i
$911$	−4.91968	−	5.86305i	−0.162996	−	0.194251i	0.678364	−	0.734726i	$-0.262689\pi$
$911$	−4.91968	−	5.86305i	−0.162996	−	0.194251i	−0.841360	+	0.540474i	$0.818245\pi$
$912$	−13.8751	+	75.1751i	−0.459450	+	2.48930i
$913$	0.0937772	−	0.111759i	0.00310357	−	0.00369869i
$914$	18.2375	+	50.1070i	0.603242	+	1.65739i
$915$	50.0236	+	18.6607i	1.65373	+	0.616903i
$916$	28.1423	−	77.3204i	0.929848	−	2.55474i
$917$	5.58889	−	13.3894i	0.184561	−	0.442157i
$918$	52.7308	+	20.6355i	1.74038	+	0.681072i
$919$	9.69700	+	16.7957i	0.319874	+	0.554039i	0.980462	−	0.196711i	$-0.0630260\pi$
$919$	9.69700	+	16.7957i	0.319874	+	0.554039i	−0.660587	+	0.750749i	$0.729693\pi$
$920$	−25.4658	+	21.3684i	−0.839583	+	0.704494i
$921$	−20.9072	+	17.2607i	−0.688916	+	0.568759i
$922$	36.2022	+	6.38342i	1.19226	+	0.210227i
$923$	−2.46202	+	13.9628i	−0.0810385	+	0.459592i
$924$	−2.94840	−	1.92304i	−0.0969954	−	0.0632634i
$925$	−17.2404	+	14.4664i	−0.566861	+	0.475653i
$926$	19.8987	+	11.4885i	0.653910	+	0.377535i
$927$	−12.2913	+	32.1627i	−0.403698	+	1.05636i
$928$	64.9645	+	112.522i	2.13257	+	3.69371i
$929$	−8.05873	+	6.76208i	−0.264398	+	0.221857i	−0.765343	−	0.643623i	$-0.777431\pi$
$929$	−8.05873	+	6.76208i	−0.264398	+	0.221857i	0.500944	+	0.865479i	$0.332986\pi$
$930$	47.4871	−	26.9135i	1.55716	−	0.882530i
$931$	−12.1235	−	17.5167i	−0.397332	−	0.574087i
$932$	−22.9540	−	63.0656i	−0.751884	−	2.06578i
$933$	−39.7231	−	23.3589i	−1.30048	−	0.764737i
$934$	−12.9891	+	35.6874i	−0.425018	+	1.16773i
$935$	1.33693	−	0.771880i	0.0437224	−	0.0252432i
$936$	8.96587	+	56.0686i	0.293059	+	1.83266i
$937$	42.2539	−	24.3953i	1.38038	−	0.796960i	0.388172	−	0.921587i	$-0.373107\pi$
$937$	42.2539	−	24.3953i	1.38038	−	0.796960i	0.992204	+	0.124627i	$0.0397733\pi$
$938$	2.83119	−	12.6079i	0.0924417	−	0.411663i
$939$	−50.9295	+	18.0777i	−1.66202	+	0.589944i
$940$	−92.4096	+	33.6343i	−3.01407	+	1.09703i
$941$	1.76308	−	0.641710i	0.0574749	−	0.0209192i	−0.313123	−	0.949713i	$-0.601375\pi$
$941$	1.76308	−	0.641710i	0.0574749	−	0.0209192i	0.370598	+	0.928794i	$0.379153\pi$
$942$	29.5479	+	35.7903i	0.962724	+	1.16611i
$943$	−0.417774	+	0.0736649i	−0.0136046	+	0.00239886i
$944$	−93.5830			−3.04587
$945$	−30.2647	+	21.9657i	−0.984512	+	0.714543i
$946$	−1.43173			−0.0465494
$947$	−50.0909	+	8.83238i	−1.62774	+	0.287014i	−0.911640	−	0.410989i	$-0.865184\pi$
$947$	−50.0909	+	8.83238i	−1.62774	+	0.287014i	−0.716095	+	0.698002i	$0.754072\pi$
$948$	−138.568	+	23.2942i	−4.50047	+	0.756560i
$949$	−8.10793	+	2.95105i	−0.263195	+	0.0957950i
$950$	18.6844	−	6.80057i	0.606202	−	0.220640i
$951$	16.3135	+	13.9121i	0.529001	+	0.451130i
$952$	−72.4363	−	66.7399i	−2.34767	−	2.16305i
$953$	−42.4743	+	24.5225i	−1.37588	+	0.794363i	−0.991660	−	0.128880i	$-0.958862\pi$
$953$	−42.4743	+	24.5225i	−1.37588	+	0.794363i	−0.384216	+	0.923243i	$0.625528\pi$
$954$	30.2628	+	54.4047i	0.979796	+	1.76142i
$955$	35.6466	−	20.5806i	1.15350	−	0.665973i
$956$	14.7545	−	40.5377i	0.477195	−	1.31108i
$957$	−1.32934	+	0.753407i	−0.0429713	+	0.0243542i
$958$	20.3985	+	56.0444i	0.659045	+	1.81071i
$959$	5.08778	+	9.83893i	0.164293	+	0.317716i
$960$	−113.223	−	66.5803i	−3.65427	−	2.14887i
$961$	9.88323	−	8.29301i	0.318814	−	0.267517i
$962$	25.9862	+	45.0094i	0.837829	+	1.45116i
$963$	52.6384	+	10.1507i	1.69625	+	0.327101i
$964$	2.57202	+	1.48496i	0.0828393	+	0.0478273i
$965$	−9.95312	+	8.35166i	−0.320402	+	0.268849i
$966$	−8.95599	+	13.7313i	−0.288154	+	0.441798i
$967$	9.57744	−	54.3164i	0.307990	−	1.74670i	−0.301098	−	0.953593i	$-0.597353\pi$
$967$	9.57744	−	54.3164i	0.307990	−	1.74670i	0.609088	−	0.793103i	$-0.291536\pi$
$968$	−100.596	−	17.7377i	−3.23327	−	0.570113i
$969$	−19.7626	−	7.37220i	−0.634867	−	0.236829i
$970$	−41.8251	+	35.0954i	−1.34292	+	1.12685i
$971$	−10.1506	−	17.5814i	−0.325749	−	0.564214i	0.655915	−	0.754835i	$-0.272283\pi$
$971$	−10.1506	−	17.5814i	−0.325749	−	0.564214i	−0.981664	+	0.190621i	$0.938950\pi$
$972$	83.6660	−	11.3314i	2.68359	−	0.363454i
$973$	24.0358	−	18.3394i	0.770552	−	0.587934i
$974$	−9.04671	+	24.8556i	−0.289875	+	0.796426i
$975$	6.51949	−	5.38240i	0.208791	−	0.172375i
$976$	56.2098	+	154.435i	1.79923	+	4.94335i
$977$	14.5379	−	17.3256i	0.465108	−	0.554294i	−0.481598	−	0.876392i	$-0.659944\pi$
$977$	14.5379	−	17.3256i	0.465108	−	0.554294i	0.946706	+	0.322098i	$0.104388\pi$
$978$	2.42371	−	0.860309i	0.0775017	−	0.0275096i
$979$	0.471513	+	0.561927i	0.0150696	+	0.0179593i
$980$	99.7594	−	26.1482i	3.18670	−	0.835275i
$981$	26.8904	−	9.30386i	0.858545	−	0.297049i
$982$	−73.9936			−2.36123
$983$	9.86200	+	3.58948i	0.314549	+	0.114487i	0.494470	−	0.869195i	$-0.335362\pi$
$983$	9.86200	+	3.58948i	0.314549	+	0.114487i	−0.179921	+	0.983681i	$0.557584\pi$
$984$	−2.56571	−	4.52703i	−0.0817920	−	0.144316i
$985$	14.1849	−	16.9049i	0.451970	−	0.538636i
$986$	−63.6966	+	23.1837i	−2.02851	+	0.738319i
$987$	−24.4654	+	18.3601i	−0.778743	+	0.584407i
$988$	−5.82312	−	33.0245i	−0.185258	−	1.05065i
$989$			4.86966i			0.154846i
$990$	1.61927	−	2.70402i	0.0514638	−	0.0859393i
$991$	−1.56002			−0.0495557			−0.0247779	−	0.999693i	$-0.507888\pi$
$991$	−1.56002			−0.0495557			−0.0247779	+	0.999693i	$0.507888\pi$
$992$	83.5036	+	30.3928i	2.65124	+	0.964973i
$993$	21.3683	−	25.0568i	0.678103	−	0.795153i
$994$	−42.2749	−	27.0944i	−1.34088	−	0.859382i
$995$	8.81493	−	10.5052i	0.279452	−	0.333038i
$996$	3.37280	−	9.04144i	0.106871	−	0.286489i
$997$	19.9910	+	23.8243i	0.633121	+	0.754524i	0.983267	−	0.182171i	$-0.0583125\pi$
$997$	19.9910	+	23.8243i	0.633121	+	0.754524i	−0.350146	+	0.936695i	$0.613868\pi$
$998$	76.5716	+	44.2086i	2.42383	+	1.39940i
$999$	42.7843	−	23.3537i	1.35364	−	0.738878i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.bd.a.185.1	yes	132
3.2	odd	2		567.2.bd.a.17.22		132
7.5	odd	6		189.2.ba.a.131.22	yes	132
21.5	even	6		567.2.ba.a.341.1		132
27.7	even	9		567.2.ba.a.143.1		132
27.20	odd	18		189.2.ba.a.101.22	✓	132
189.47	even	18	inner	189.2.bd.a.47.1	yes	132
189.61	odd	18		567.2.bd.a.467.22		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.22	✓	132	27.20	odd	18
189.2.ba.a.131.22	yes	132	7.5	odd	6
189.2.bd.a.47.1	yes	132	189.47	even	18	inner
189.2.bd.a.185.1	yes	132	1.1	even	1	trivial
567.2.ba.a.143.1		132	27.7	even	9
567.2.ba.a.341.1		132	21.5	even	6
567.2.bd.a.17.22		132	3.2	odd	2
567.2.bd.a.467.22		132	189.61	odd	18

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.bd (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.68189 + 0.472890i) q^{2} +(0.605371 - 1.62281i) q^{3} +(5.08954 - 1.85244i) q^{4} +(2.55610 - 0.930344i) q^{5} +(-0.856127 + 4.63849i) q^{6} +(2.58147 + 0.579686i) q^{7} +(-8.05677 + 4.65158i) q^{8} +(-2.26705 - 1.96481i) q^{9} +O(q^{10})\)	\(q+(-2.68189 + 0.472890i) q^{2} +(0.605371 - 1.62281i) q^{3} +(5.08954 - 1.85244i) q^{4} +(2.55610 - 0.930344i) q^{5} +(-0.856127 + 4.63849i) q^{6} +(2.58147 + 0.579686i) q^{7} +(-8.05677 + 4.65158i) q^{8} +(-2.26705 - 1.96481i) q^{9} +(-6.41523 + 3.70384i) q^{10} +(0.0485071 - 0.133272i) q^{11} +(0.0748907 - 9.38079i) q^{12} +(0.695830 + 1.91178i) q^{13} +(-7.19734 - 0.333907i) q^{14} +(0.0376120 - 4.71128i) q^{15} +(11.1096 - 9.32210i) q^{16} +(2.00080 + 3.46549i) q^{17} +(7.00913 + 4.19734i) q^{18} +(-2.63555 - 1.52164i) q^{19} +(11.2860 - 9.47004i) q^{20} +(2.50347 - 3.83831i) q^{21} +(-0.0670678 + 0.380360i) q^{22} +(1.29370 + 0.228114i) q^{23} +(2.67131 + 15.8906i) q^{24} +(1.83788 - 1.54216i) q^{25} +(-2.77020 - 4.79813i) q^{26} +(-4.56093 + 2.48957i) q^{27} +(14.2123 - 1.83168i) q^{28} +(2.12744 - 5.84511i) q^{29} +(2.12704 + 12.6529i) q^{30} +(-1.45503 - 3.99766i) q^{31} +(-13.4266 + 16.0012i) q^{32} +(-0.186911 - 0.159397i) q^{33} +(-7.00474 - 8.34792i) q^{34} +(7.13779 - 0.919915i) q^{35} +(-15.1779 - 5.80039i) q^{36} -9.38062 q^{37} +(7.78784 + 2.83454i) q^{38} +(3.52369 + 0.0281311i) q^{39} +(-16.2663 + 19.3854i) q^{40} +(-0.303455 + 0.110449i) q^{41} +(-4.89893 + 11.4778i) q^{42} +(0.643705 + 3.65063i) q^{43} -0.768151i q^{44} +(-7.62276 - 2.91311i) q^{45} -3.57744 q^{46} +(-6.27238 - 2.28296i) q^{47} +(-8.40258 - 23.6722i) q^{48} +(6.32793 + 2.99288i) q^{49} +(-4.19971 + 5.00502i) q^{50} +(6.83508 - 1.14902i) q^{51} +(7.08291 + 8.44108i) q^{52} +(6.59926 + 3.81008i) q^{53} +(11.0546 - 8.83357i) q^{54} -0.385785i q^{55} +(-23.4947 + 7.33749i) q^{56} +(-4.06482 + 3.35586i) q^{57} +(-2.94149 + 16.6820i) q^{58} +(-4.94316 - 4.14781i) q^{59} +(-8.53593 - 24.0479i) q^{60} +(-3.87584 + 10.6488i) q^{61} +(5.79268 + 10.0332i) q^{62} +(-4.71335 - 6.38626i) q^{63} +(13.9394 - 24.1437i) q^{64} +(3.55722 + 4.23933i) q^{65} +(0.576653 + 0.339098i) q^{66} +(-0.311427 + 1.76619i) q^{67} +(16.6028 + 13.9314i) q^{68} +(1.15335 - 1.96134i) q^{69} +(-18.7078 + 5.84250i) q^{70} +(6.03534 + 3.48450i) q^{71} +(27.4046 + 5.28464i) q^{72} +4.24105i q^{73} +(25.1578 - 4.43600i) q^{74} +(-1.39004 - 3.91611i) q^{75} +(-16.2325 - 2.86223i) q^{76} +(0.202475 - 0.315919i) q^{77} +(-9.46347 + 1.59087i) q^{78} +(-2.60094 - 14.7507i) q^{79} +(19.7246 - 34.1640i) q^{80} +(1.27905 + 8.90865i) q^{81} +(0.761604 - 0.439712i) q^{82} +(0.966634 + 0.351826i) q^{83} +(5.63124 - 24.1728i) q^{84} +(8.33835 + 6.99670i) q^{85} +(-3.45269 - 9.48620i) q^{86} +(-8.19763 - 6.99090i) q^{87} +(0.229115 + 1.29938i) q^{88} +(-2.58608 + 4.47923i) q^{89} +(21.8210 + 4.20791i) q^{90} +(0.688030 + 5.33855i) q^{91} +(7.00690 - 1.23551i) q^{92} +(-7.36829 - 0.0588240i) q^{93} +(17.9015 + 3.15651i) q^{94} +(-8.15238 - 1.43749i) q^{95} +(17.8390 + 31.4756i) q^{96} +(7.25860 - 1.27989i) q^{97} +(-18.3861 - 5.03417i) q^{98} +(-0.371822 + 0.206828i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} + 30 q^{23} - 36 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} - 3 q^{30} - 9 q^{31} - 51 q^{32} - 9 q^{33} + 18 q^{34} - 9 q^{35} - 6 q^{37} - 9 q^{38} - 9 q^{39} - 9 q^{40} + 27 q^{42} - 12 q^{43} - 63 q^{45} - 6 q^{46} + 45 q^{47} + 30 q^{49} - 9 q^{50} + 33 q^{51} - 9 q^{52} + 45 q^{53} + 117 q^{54} - 51 q^{56} - 3 q^{58} - 9 q^{59} - 15 q^{60} - 63 q^{61} + 99 q^{62} - 33 q^{63} + 18 q^{64} - 102 q^{65} + 63 q^{66} - 3 q^{67} + 144 q^{68} - 108 q^{69} - 15 q^{70} + 18 q^{71} + 15 q^{72} - 33 q^{74} - 9 q^{75} - 36 q^{76} - 57 q^{77} + 66 q^{78} - 21 q^{79} - 72 q^{80} + 57 q^{81} - 18 q^{82} + 90 q^{83} + 51 q^{84} + 9 q^{85} - 33 q^{86} - 9 q^{87} + 45 q^{88} - 9 q^{89} - 81 q^{90} - 21 q^{91} + 150 q^{92} - 87 q^{93} - 9 q^{94} + 27 q^{95} - 9 q^{96} - 180 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more