LMFDB - Embedded newform 225.2.q.a.106.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [225,2,Mod(16,225)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("225.16"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(225, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([20, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			106.12
Character	$\chi$	$=$	225.106
Dual form			225.2.q.a.121.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.745950 - 0.158557i) q^{2} +(1.13811 - 1.30565i) q^{3} +(-1.29579 - 0.576923i) q^{4} +(-1.26382 - 1.84465i) q^{5} +(-1.05599 + 0.793494i) q^{6} +(-0.476660 + 0.825599i) q^{7} +(2.10906 + 1.53232i) q^{8} +(-0.409434 - 2.97193i) q^{9} +(0.650268 + 1.57641i) q^{10} +(-2.83092 - 0.601732i) q^{11} +(-2.22800 + 1.03525i) q^{12} +(-1.91095 + 0.406185i) q^{13} +(0.486468 - 0.540278i) q^{14} +(-3.84683 - 0.449300i) q^{15} +(0.567924 + 0.630744i) q^{16} +(-5.51944 - 4.01011i) q^{17} +(-0.165802 + 2.28183i) q^{18} +(3.77403 + 2.74200i) q^{19} +(0.573428 + 3.11941i) q^{20} +(0.535453 + 1.56197i) q^{21} +(2.01632 + 0.897723i) q^{22} +(5.89471 - 6.54674i) q^{23} +(4.40100 - 1.00975i) q^{24} +(-1.80550 + 4.66264i) q^{25} +1.48988 q^{26} +(-4.34627 - 2.84779i) q^{27} +(1.09396 - 0.794807i) q^{28} +(-0.0975850 - 0.928459i) q^{29} +(2.79831 + 0.945095i) q^{30} +(0.277775 - 2.64285i) q^{31} +(-2.93057 - 5.07590i) q^{32} +(-4.00754 + 3.01136i) q^{33} +(3.48139 + 3.86648i) q^{34} +(2.12536 - 0.164140i) q^{35} +(-1.18403 + 4.08721i) q^{36} +(0.799338 - 2.46011i) q^{37} +(-2.38048 - 2.64379i) q^{38} +(-1.64453 + 2.95731i) q^{39} +(0.161121 - 5.82706i) q^{40} +(5.30176 - 1.12692i) q^{41} +(-0.151761 - 1.25005i) q^{42} +(4.43871 - 7.68807i) q^{43} +(3.32113 + 2.41294i) q^{44} +(-4.96473 + 4.51126i) q^{45} +(-5.43519 + 3.94889i) q^{46} +(0.419452 + 3.99082i) q^{47} +(1.46989 - 0.0236566i) q^{48} +(3.04559 + 5.27512i) q^{49} +(2.08610 - 3.19182i) q^{50} +(-11.5175 + 2.64252i) q^{51} +(2.71053 + 0.576140i) q^{52} +(4.30252 - 3.12596i) q^{53} +(2.79057 + 2.81344i) q^{54} +(2.46781 + 5.98256i) q^{55} +(-2.27038 + 1.01084i) q^{56} +(7.87533 - 1.80688i) q^{57} +(-0.0744198 + 0.708057i) q^{58} +(-4.69343 + 0.997620i) q^{59} +(4.72548 + 2.80152i) q^{60} +(10.9896 + 2.33592i) q^{61} +(-0.626247 + 1.92739i) q^{62} +(2.64878 + 1.07857i) q^{63} +(0.856686 + 2.63661i) q^{64} +(3.16438 + 3.01170i) q^{65} +(3.46689 - 1.61090i) q^{66} +(-0.387024 + 3.68228i) q^{67} +(4.83851 + 8.38055i) q^{68} +(-1.83894 - 15.1473i) q^{69} +(-1.61144 - 0.214549i) q^{70} +(-0.125408 + 0.0911140i) q^{71} +(3.69042 - 6.89535i) q^{72} +(-3.09917 - 9.53828i) q^{73} +(-0.986332 + 1.70838i) q^{74} +(4.03292 + 7.66391i) q^{75} +(-3.30843 - 5.73038i) q^{76} +(1.84618 - 2.05039i) q^{77} +(1.69564 - 1.94525i) q^{78} +(-0.442202 - 4.20727i) q^{79} +(0.445747 - 1.84477i) q^{80} +(-8.66473 + 2.43362i) q^{81} -4.13353 q^{82} +(-3.01510 + 1.34241i) q^{83} +(0.207301 - 2.33290i) q^{84} +(-0.421657 + 15.2495i) q^{85} +(-4.53005 + 5.03113i) q^{86} +(-1.32330 - 0.929272i) q^{87} +(-5.04853 - 5.60696i) q^{88} +(5.32122 + 16.3770i) q^{89} +(4.41873 - 2.57798i) q^{90} +(0.575527 - 1.77129i) q^{91} +(-11.4153 + 5.08241i) q^{92} +(-3.13449 - 3.37051i) q^{93} +(0.319881 - 3.04346i) q^{94} +(0.288317 - 10.4272i) q^{95} +(-9.96263 - 1.95061i) q^{96} +(0.203049 + 1.93189i) q^{97} +(-1.43545 - 4.41787i) q^{98} +(-0.629227 + 8.65968i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20}+ \cdots - 20 q^{99}+O(q^{100}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.745950	−	0.158557i	−0.527466	−	0.112116i	−0.0635213	−	0.997980i	$-0.520233\pi$
$2$	−0.745950	−	0.158557i	−0.527466	−	0.112116i	−0.463945	+	0.885864i	$0.653566\pi$
$3$	1.13811	−	1.30565i	0.657085	−	0.753816i
$3$	1.13811	−	1.30565i	0.657085	−	0.753816i
$4$	−1.29579	−	0.576923i	−0.647895	−	0.288461i
$5$	−1.26382	−	1.84465i	−0.565200	−	0.824954i
$5$	−1.26382	−	1.84465i	−0.565200	−	0.824954i
$6$	−1.05599	+	0.793494i	−0.431105	+	0.323943i
$7$	−0.476660	+	0.825599i	−0.180161	+	0.312047i	−0.941935	−	0.335795i	$-0.890995\pi$
$7$	−0.476660	+	0.825599i	−0.180161	+	0.312047i	0.761775	+	0.647842i	$0.224328\pi$
$8$	2.10906	+	1.53232i	0.745664	+	0.541757i
$9$	−0.409434	−	2.97193i	−0.136478	−	0.990643i
$10$	0.650268	+	1.57641i	0.205633	+	0.498504i
$11$	−2.83092	−	0.601732i	−0.853556	−	0.181429i	−0.239700	−	0.970847i	$-0.577049\pi$
$11$	−2.83092	−	0.601732i	−0.853556	−	0.181429i	−0.613856	+	0.789418i	$0.710382\pi$
$12$	−2.22800	+	1.03525i	−0.643169	+	0.298850i
$13$	−1.91095	+	0.406185i	−0.530002	+	0.112655i	−0.465137	−	0.885239i	$-0.653995\pi$
$13$	−1.91095	+	0.406185i	−0.530002	+	0.112655i	−0.0648650	+	0.997894i	$0.520662\pi$
$14$	0.486468	−	0.540278i	0.130014	−	0.144395i
$15$	−3.84683	−	0.449300i	−0.993248	−	0.116009i
$16$	0.567924	+	0.630744i	0.141981	+	0.157686i
$17$	−5.51944	−	4.01011i	−1.33866	−	0.972594i	−0.999492	−	0.0318678i	$-0.989854\pi$
$17$	−5.51944	−	4.01011i	−1.33866	−	0.972594i	−0.339168	−	0.940726i	$-0.610146\pi$
$18$	−0.165802	+	2.28183i	−0.0390798	+	0.537832i
$19$	3.77403	+	2.74200i	0.865823	+	0.629057i	0.929463	−	0.368916i	$-0.120271\pi$
$19$	3.77403	+	2.74200i	0.865823	+	0.629057i	−0.0636402	+	0.997973i	$0.520271\pi$
$20$	0.573428	+	3.11941i	0.128222	+	0.697522i
$21$	0.535453	+	1.56197i	0.116845	+	0.340849i
$22$	2.01632	+	0.897723i	0.429881	+	0.191395i
$23$	5.89471	−	6.54674i	1.22913	−	1.36509i	0.320632	−	0.947204i	$-0.396105\pi$
$23$	5.89471	−	6.54674i	1.22913	−	1.36509i	0.908500	−	0.417885i	$-0.137229\pi$
$24$	4.40100	−	1.00975i	0.898350	−	0.206113i
$25$	−1.80550	+	4.66264i	−0.361099	+	0.932527i
$26$	1.48988			0.292189
$27$	−4.34627	−	2.84779i	−0.836441	−	0.548058i
$28$	1.09396	−	0.794807i	0.206739	−	0.150204i
$29$	−0.0975850	−	0.928459i	−0.0181211	−	0.172411i	0.981718	−	0.190340i	$-0.0609591\pi$
$29$	−0.0975850	−	0.928459i	−0.0181211	−	0.172411i	−0.999839	+	0.0179298i	$0.994292\pi$
$30$	2.79831	+	0.945095i	0.510898	+	0.172550i
$31$	0.277775	−	2.64285i	0.0498898	−	0.474670i	−0.940843	−	0.338843i	$-0.889964\pi$
$31$	0.277775	−	2.64285i	0.0498898	−	0.474670i	0.990733	−	0.135826i	$-0.0433689\pi$
$32$	−2.93057	−	5.07590i	−0.518057	−	0.897300i
$33$	−4.00754	+	3.01136i	−0.697623	+	0.524210i
$34$	3.48139	+	3.86648i	0.597054	+	0.663096i
$35$	2.12536	−	0.164140i	0.359251	−	0.0277447i
$36$	−1.18403	+	4.08721i	−0.197339	+	0.681201i
$37$	0.799338	−	2.46011i	0.131410	−	0.404439i	−0.863604	−	0.504171i	$-0.831798\pi$
$37$	0.799338	−	2.46011i	0.131410	−	0.404439i	0.995014	+	0.0997312i	$0.0317983\pi$
$38$	−2.38048	−	2.64379i	−0.386164	−	0.428879i
$39$	−1.64453	+	2.95731i	−0.263335	+	0.473549i
$40$	0.161121	−	5.82706i	0.0254755	−	0.921339i
$41$	5.30176	−	1.12692i	0.827996	−	0.175996i	0.225627	−	0.974214i	$-0.427557\pi$
$41$	5.30176	−	1.12692i	0.827996	−	0.175996i	0.602369	+	0.798218i	$0.294224\pi$
$42$	−0.151761	−	1.25005i	−0.0234172	−	0.192887i
$43$	4.43871	−	7.68807i	0.676897	−	1.17242i	−0.299014	−	0.954249i	$-0.596658\pi$
$43$	4.43871	−	7.68807i	0.676897	−	1.17242i	0.975911	−	0.218171i	$-0.0700090\pi$
$44$	3.32113	+	2.41294i	0.500679	+	0.363765i
$45$	−4.96473	+	4.51126i	−0.740098	+	0.672499i
$46$	−5.43519	+	3.94889i	−0.801374	+	0.582233i
$47$	0.419452	+	3.99082i	0.0611834	+	0.582121i	0.981569	+	0.191109i	$0.0612084\pi$
$47$	0.419452	+	3.99082i	0.0611834	+	0.582121i	−0.920385	+	0.391012i	$0.872125\pi$
$48$	1.46989	−	0.0236566i	0.212160	−	0.00341453i
$49$	3.04559	+	5.27512i	0.435084	+	0.753588i
$50$	2.08610	−	3.19182i	0.295019	−	0.451392i
$51$	−11.5175	+	2.64252i	−1.61277	+	0.370027i
$52$	2.71053	+	0.576140i	0.375883	+	0.0798963i
$53$	4.30252	−	3.12596i	0.590996	−	0.429384i	−0.251675	−	0.967812i	$-0.580982\pi$
$53$	4.30252	−	3.12596i	0.590996	−	0.429384i	0.842672	+	0.538428i	$0.180982\pi$
$54$	2.79057	+	2.81344i	0.379748	+	0.382861i
$55$	2.46781	+	5.98256i	0.332759	+	0.806688i
$56$	−2.27038	+	1.01084i	−0.303393	+	0.135079i
$57$	7.87533	−	1.80688i	1.04311	−	0.239327i
$58$	−0.0744198	+	0.708057i	−0.00977179	+	0.0929724i
$59$	−4.69343	+	0.997620i	−0.611033	+	0.129879i	−0.503026	−	0.864271i	$-0.667780\pi$
$59$	−4.69343	+	0.997620i	−0.611033	+	0.129879i	−0.108007	+	0.994150i	$0.534447\pi$
$60$	4.72548	+	2.80152i	0.610057	+	0.361675i
$61$	10.9896	+	2.33592i	1.40708	+	0.299084i	0.847985	−	0.530020i	$-0.177815\pi$
$61$	10.9896	+	2.33592i	1.40708	+	0.299084i	0.559095	+	0.829104i	$0.311149\pi$
$62$	−0.626247	+	1.92739i	−0.0795334	+	0.244779i
$63$	2.64878	+	1.07857i	0.333715	+	0.135887i
$64$	0.856686	+	2.63661i	0.107086	+	0.329576i
$65$	3.16438	+	3.01170i	0.392493	+	0.373555i
$66$	3.46689	−	1.61090i	0.426745	−	0.198288i
$67$	−0.387024	+	3.68228i	−0.0472824	+	0.449862i	0.945110	+	0.326751i	$0.105954\pi$
$67$	−0.387024	+	3.68228i	−0.0472824	+	0.449862i	−0.992393	+	0.123111i	$0.960713\pi$
$68$	4.83851	+	8.38055i	0.586756	+	1.01629i
$69$	−1.83894	−	15.1473i	−0.221382	−	1.82352i
$70$	−1.61144	−	0.214549i	−0.192604	−	0.0256436i
$71$	−0.125408	+	0.0911140i	−0.0148832	+	0.0108132i	−0.595202	−	0.803576i	$-0.702928\pi$
$71$	−0.125408	+	0.0911140i	−0.0148832	+	0.0108132i	0.580319	+	0.814389i	$0.302928\pi$
$72$	3.69042	−	6.89535i	0.434921	−	0.812625i
$73$	−3.09917	−	9.53828i	−0.362731	−	1.11637i	−0.951390	−	0.307989i	$-0.900344\pi$
$73$	−3.09917	−	9.53828i	−0.362731	−	1.11637i	0.588659	−	0.808381i	$-0.299656\pi$
$74$	−0.986332	+	1.70838i	−0.114659	+	0.198595i
$75$	4.03292	+	7.66391i	0.465682	+	0.884952i
$76$	−3.30843	−	5.73038i	−0.379503	−	0.657319i
$77$	1.84618	−	2.05039i	0.210391	−	0.233663i
$78$	1.69564	−	1.94525i	0.191993	−	0.220257i
$79$	−0.442202	−	4.20727i	−0.0497516	−	0.473355i	−0.990825	−	0.135152i	$-0.956848\pi$
$79$	−0.442202	−	4.20727i	−0.0497516	−	0.473355i	0.941073	−	0.338203i	$-0.109819\pi$
$80$	0.445747	−	1.84477i	0.0498361	−	0.206252i
$81$	−8.66473	+	2.43362i	−0.962748	+	0.270402i
$82$	−4.13353			−0.456472
$83$	−3.01510	+	1.34241i	−0.330950	+	0.147348i	−0.565483	−	0.824760i	$-0.691310\pi$
$83$	−3.01510	+	1.34241i	−0.330950	+	0.147348i	0.234534	+	0.972108i	$0.424644\pi$
$84$	0.207301	−	2.33290i	0.0226184	−	0.254540i
$85$	−0.421657	+	15.2495i	−0.0457351	+	1.65404i
$86$	−4.53005	+	5.03113i	−0.488488	+	0.542520i
$87$	−1.32330	−	0.929272i	−0.141873	−	0.0996285i
$88$	−5.04853	−	5.60696i	−0.538176	−	0.597704i
$89$	5.32122	+	16.3770i	0.564048	+	1.73596i	0.670764	+	0.741671i	$0.265966\pi$
$89$	5.32122	+	16.3770i	0.564048	+	1.73596i	−0.106716	+	0.994290i	$0.534034\pi$
$90$	4.41873	−	2.57798i	0.465775	−	0.271743i
$91$	0.575527	−	1.77129i	0.0603317	−	0.185682i
$92$	−11.4153	+	5.08241i	−1.19012	+	0.529877i
$93$	−3.13449	−	3.37051i	−0.325032	−	0.349506i
$94$	0.319881	−	3.04346i	0.0329932	−	0.313909i
$95$	0.288317	−	10.4272i	0.0295807	−	1.06981i
$96$	−9.96263	−	1.95061i	−1.01681	−	0.199083i
$97$	0.203049	+	1.93189i	0.0206165	+	0.196153i	0.999982	−	0.00594233i	$-0.00189151\pi$
$97$	0.203049	+	1.93189i	0.0206165	+	0.196153i	−0.979366	+	0.202096i	$0.935225\pi$
$98$	−1.43545	−	4.41787i	−0.145003	−	0.446272i
$99$	−0.629227	+	8.65968i	−0.0632397	+	0.870330i
$100$	5.02952	−	5.00017i	0.502952	−	0.500017i
$101$	3.61804	−	6.26663i	0.360009	−	0.623553i	−0.627953	−	0.778251i	$-0.716107\pi$
$101$	3.61804	−	6.26663i	0.360009	−	0.623553i	0.987962	+	0.154698i	$0.0494404\pi$
$102$	9.01046	−	0.145016i	0.892168	−	0.0143587i
$103$	−16.2100	−	7.21716i	−1.59722	−	0.711128i	−0.601103	−	0.799172i	$-0.705272\pi$
$103$	−16.2100	−	7.21716i	−1.59722	−	0.711128i	−0.996117	+	0.0880440i	$0.971938\pi$
$104$	−4.65271	−	2.07152i	−0.456235	−	0.203129i
$105$	2.20457	−	2.96178i	0.215144	−	0.289040i
$106$	−3.70510	+	1.64962i	−0.359872	+	0.160225i
$107$	1.19151			0.115188			0.0575940	−	0.998340i	$-0.481657\pi$
$107$	1.19151			0.115188			0.0575940	+	0.998340i	$0.481657\pi$
$108$	3.98890	+	6.19760i	0.383832	+	0.596365i
$109$	0.597453	−	1.83877i	0.0572256	−	0.176122i	−0.918358	−	0.395751i	$-0.870484\pi$
$109$	0.597453	−	1.83877i	0.0572256	−	0.176122i	0.975584	+	0.219628i	$0.0704845\pi$
$110$	−0.892285	−	4.85398i	−0.0850761	−	0.462808i
$111$	−2.30231	−	3.84352i	−0.218525	−	0.364810i
$112$	−0.791448	+	0.168227i	−0.0747848	+	0.0158960i
$113$	−7.86072	+	1.67085i	−0.739475	+	0.157180i	−0.562223	−	0.826985i	$-0.690054\pi$
$113$	−7.86072	+	1.67085i	−0.739475	+	0.157180i	−0.177251	+	0.984166i	$0.556721\pi$
$114$	−6.16109	+	0.0991575i	−0.577039	+	0.00928695i
$115$	−19.5263	−	2.59977i	−1.82084	−	0.242430i
$116$	−0.409200	+	1.25939i	−0.0379932	+	0.116931i
$117$	1.98956	+	5.51290i	0.183935	+	0.509668i
$118$	3.65924			0.336861
$119$	5.94163	−	2.64539i	0.544669	−	0.242502i
$120$	−7.42472	−	6.84217i	−0.677781	−	0.624602i
$121$	−2.39695	−	1.06719i	−0.217904	−	0.0970172i
$122$	−7.82735	−	3.48496i	−0.708655	−	0.315513i
$123$	4.56260	−	8.20479i	0.411395	−	0.739801i
$124$	−1.88466	+	3.26432i	−0.169247	+	0.293145i
$125$	10.8828	−	2.56224i	0.973385	−	0.229174i
$126$	−1.80484	−	1.22454i	−0.160788	−	0.109091i
$127$	−4.50280	−	13.8582i	−0.399559	−	1.22972i	−0.925354	−	0.379105i	$-0.876232\pi$
$127$	−4.50280	−	13.8582i	−0.399559	−	1.22972i	0.525794	−	0.850612i	$-0.323768\pi$
$128$	1.00432	+	9.55546i	0.0887701	+	0.844591i
$129$	−4.98620	−	14.5452i	−0.439010	−	1.28064i
$130$	−1.88294	−	2.74831i	−0.165145	−	0.241042i
$131$	−1.41875	+	13.4985i	−0.123956	+	1.17937i	0.738864	+	0.673855i	$0.235363\pi$
$131$	−1.41875	+	13.4985i	−0.123956	+	1.17937i	−0.862820	+	0.505511i	$0.831304\pi$
$132$	6.93025	−	1.59005i	0.603201	−	0.138396i
$133$	−4.06272	+	1.80884i	−0.352282	+	0.156846i
$134$	0.872550	−	2.68543i	0.0753768	−	0.231986i
$135$	0.239738	+	11.6165i	0.0206334	+	0.999787i
$136$	−5.49604	−	16.9151i	−0.471282	−	1.45046i
$137$	−5.85192	−	6.49921i	−0.499963	−	0.555265i	0.439355	−	0.898314i	$-0.355207\pi$
$137$	−5.85192	−	6.49921i	−0.499963	−	0.555265i	−0.939318	+	0.343048i	$0.888541\pi$
$138$	−1.02995	+	11.5907i	−0.0876749	+	0.986665i
$139$	12.6640	−	14.0648i	1.07415	−	1.19296i	0.0938192	−	0.995589i	$-0.470092\pi$
$139$	12.6640	−	14.0648i	1.07415	−	1.19296i	0.980329	−	0.197373i	$-0.0632409\pi$
$140$	−2.84872	−	1.01348i	−0.240760	−	0.0856545i
$141$	5.68799	+	3.99432i	0.479015	+	0.336382i
$142$	0.107995	−	0.0480823i	0.00906271	−	0.00403498i
$143$	5.65417			0.472825
$144$	1.64200	−	1.94608i	0.136833	−	0.162173i
$145$	−1.58936	+	1.35342i	−0.131989	+	0.112395i
$146$	0.799472	+	7.60647i	0.0661648	+	0.629516i
$147$	10.3536	+	2.02717i	0.853955	+	0.167198i
$148$	−2.45507	+	2.72663i	−0.201805	+	0.224127i
$149$	3.03989	+	5.26524i	0.249037	+	0.431345i	0.963259	−	0.268574i	$-0.0865525\pi$
$149$	3.03989	+	5.26524i	0.249037	+	0.431345i	−0.714222	+	0.699919i	$0.753219\pi$
$150$	−1.79319	−	6.35634i	−0.146414	−	0.518993i
$151$	4.71367	−	8.16432i	0.383593	−	0.664403i	−0.607980	−	0.793952i	$-0.708020\pi$
$151$	4.71367	−	8.16432i	0.383593	−	0.664403i	0.991573	+	0.129550i	$0.0413532\pi$
$152$	3.75804	+	11.5660i	0.304817	+	0.938130i
$153$	−9.65791	+	18.0453i	−0.780795	+	1.45887i
$154$	−1.70226	+	1.23676i	−0.137172	+	0.0996612i
$155$	−5.22620	+	2.82770i	−0.419778	+	0.227126i
$156$	3.83710	−	2.88329i	0.307214	−	0.230848i
$157$	10.2999	+	17.8399i	0.822020	+	1.42378i	0.904175	+	0.427162i	$0.140486\pi$
$157$	10.2999	+	17.8399i	0.822020	+	1.42378i	−0.0821548	+	0.996620i	$0.526180\pi$
$158$	−0.337230	+	3.20853i	−0.0268285	+	0.255257i
$159$	0.815311	−	9.17525i	0.0646583	−	0.727645i
$160$	−5.65955	+	11.8209i	−0.447426	+	0.934527i
$161$	2.59521	+	7.98723i	0.204531	+	0.629482i
$162$	6.84932	−	0.441508i	0.538133	−	0.0346881i
$163$	−3.22118	+	9.91378i	−0.252302	+	0.776507i	0.742047	+	0.670348i	$0.233855\pi$
$163$	−3.22118	+	9.91378i	−0.252302	+	0.776507i	−0.994349	+	0.106159i	$0.966145\pi$
$164$	−7.52012	−	1.59845i	−0.587223	−	0.124818i
$165$	10.6197	+	3.58669i	0.826746	+	0.279224i
$166$	2.46196	−	0.523305i	0.191085	−	0.0406164i
$167$	1.61643	−	15.3793i	0.125083	−	1.19009i	−0.734325	−	0.678799i	$-0.762501\pi$
$167$	1.61643	−	15.3793i	0.125083	−	1.19009i	0.859408	−	0.511291i	$-0.170832\pi$
$168$	−1.26413	+	4.11476i	−0.0975300	+	0.317461i
$169$	−8.38935	+	3.73518i	−0.645334	+	0.287321i
$170$	2.73245	−	11.3085i	0.209569	−	0.867324i
$171$	6.60380	−	12.3388i	0.505005	−	0.943574i
$172$	−10.1871	+	7.40133i	−0.776756	+	0.564346i
$173$	14.5479	+	3.09226i	1.10606	+	0.235100i	0.724521	−	0.689253i	$-0.242061\pi$
$173$	14.5479	+	3.09226i	1.10606	+	0.235100i	0.381539	+	0.924353i	$0.375394\pi$
$174$	0.839775	+	0.903009i	0.0636632	+	0.0684569i
$175$	−2.98886	−	3.71311i	−0.225937	−	0.280685i
$176$	−1.22821	−	2.12733i	−0.0925800	−	0.160353i
$177$	−4.03908	+	7.26337i	−0.303596	+	0.545948i
$178$	−1.37268	−	13.0601i	−0.102886	−	0.978899i
$179$	−21.5801	+	15.6788i	−1.61297	+	1.17189i	−0.760016	+	0.649904i	$0.774809\pi$
$179$	−21.5801	+	15.6788i	−1.61297	+	1.17189i	−0.852954	+	0.521987i	$0.825191\pi$
$180$	9.03589	−	2.98138i	0.673496	−	0.222219i
$181$	16.0289	+	11.6457i	1.19142	+	0.865617i	0.993414	−	0.114583i	$-0.0365533\pi$
$181$	16.0289	+	11.6457i	1.19142	+	0.865617i	0.198007	+	0.980201i	$0.436553\pi$
$182$	−0.710164	+	1.23004i	−0.0526409	+	0.0911767i
$183$	15.5573	−	11.6901i	1.15003	−	0.864156i
$184$	22.4640	−	4.77486i	1.65607	−	0.352008i
$185$	−5.54827	+	1.63464i	−0.407917	+	0.120181i
$186$	1.80376	+	3.01123i	0.132258	+	0.220794i
$187$	13.2121	+	14.6735i	0.966165	+	1.07303i
$188$	1.75888	−	5.41326i	0.128279	−	0.394803i
$189$	4.42283	−	2.23085i	0.321713	−	0.162271i
$190$	−1.86837	+	7.73244i	−0.135546	+	0.560970i
$191$	−8.03506	−	8.92383i	−0.581396	−	0.645706i	0.378652	−	0.925539i	$-0.376388\pi$
$191$	−8.03506	−	8.92383i	−0.581396	−	0.645706i	−0.960049	+	0.279833i	$0.909721\pi$
$192$	4.41748	+	1.88221i	0.318804	+	0.135837i
$193$	12.6897	+	21.9792i	0.913424	+	1.58210i	0.809192	+	0.587544i	$0.199905\pi$
$193$	12.6897	+	21.9792i	0.913424	+	1.58210i	0.104232	+	0.994553i	$0.466762\pi$
$194$	0.154848	−	1.47328i	0.0111175	−	0.105776i
$195$	7.53361	−	0.703937i	0.539493	−	0.0504100i
$196$	−0.903110	−	8.59252i	−0.0645078	−	0.613751i
$197$	−1.37622	+	0.999883i	−0.0980516	+	0.0712387i	−0.635731	−	0.771911i	$-0.719301\pi$
$197$	−1.37622	+	0.999883i	−0.0980516	+	0.0712387i	0.537679	+	0.843150i	$0.319301\pi$
$198$	1.84242	−	6.35992i	0.130935	−	0.451980i
$199$	−6.51877			−0.462104			−0.231052	−	0.972941i	$-0.574217\pi$
$199$	−6.51877			−0.462104			−0.231052	+	0.972941i	$0.574217\pi$
$200$	−10.9525	+	7.06717i	−0.774461	+	0.499724i
$201$	4.36729	+	4.69614i	0.308045	+	0.331240i
$202$	−3.69249	+	4.10093i	−0.259803	+	0.288540i
$203$	0.813050	+	0.361993i	0.0570649	+	0.0254069i
$204$	16.4488	+	3.22055i	1.15164	+	0.225484i
$205$	−8.77928	−	8.35568i	−0.613172	−	0.583586i
$206$	10.9475	+	7.95384i	0.762750	+	0.554170i
$207$	−21.8699	−	14.8382i	−1.52007	−	1.03133i
$208$	−1.34147	−	0.974638i	−0.0930145	−	0.0675790i
$209$	−9.03406	−	10.0333i	−0.624899	−	0.694020i
$210$	−2.11411	+	1.85979i	−0.145887	+	0.128338i
$211$	5.33924	−	5.92982i	0.367568	−	0.408226i	−0.530780	−	0.847510i	$-0.678101\pi$
$211$	5.33924	−	5.92982i	0.367568	−	0.408226i	0.898348	+	0.439284i	$0.144768\pi$
$212$	−7.37860	+	1.56837i	−0.506764	+	0.107716i
$213$	−0.0237643	+	0.267436i	−0.00162830	+	0.0183244i
$214$	−0.888810	−	0.188922i	−0.0607578	−	0.0129145i
$215$	−19.7916	+	1.52849i	−1.34977	+	0.104242i
$216$	−4.80281	−	12.6660i	−0.326790	−	0.861814i
$217$	2.04953	+	1.48907i	0.139131	+	0.101085i
$218$	−0.737219	+	1.27690i	−0.0499307	+	0.0864826i
$219$	−15.9808	−	6.80913i	−1.07988	−	0.460118i
$220$	0.253717	−	9.17587i	0.0171056	−	0.618637i
$221$	12.1762	+	5.42120i	0.819061	+	0.364669i
$222$	1.10799	+	3.23212i	0.0743634	+	0.216925i
$223$	9.23109	+	1.96213i	0.618160	+	0.131394i	0.506339	−	0.862335i	$-0.330998\pi$
$223$	9.23109	+	1.96213i	0.618160	+	0.131394i	0.111821	+	0.993728i	$0.464332\pi$
$224$	5.58754			0.373333
$225$	14.5963	+	3.45676i	0.973084	+	0.230451i
$226$	6.12863			0.407670
$227$	23.0879	+	4.90748i	1.53240	+	0.325721i	0.895441	−	0.445180i	$-0.146860\pi$
$227$	23.0879	+	4.90748i	1.53240	+	0.325721i	0.636955	+	0.770901i	$0.280194\pi$
$228$	−11.2472	−	2.20212i	−0.744864	−	0.145839i
$229$	−14.3491	−	6.38865i	−0.948218	−	0.422174i	−0.126435	−	0.991975i	$-0.540354\pi$
$229$	−14.3491	−	6.38865i	−0.948218	−	0.422174i	−0.821783	+	0.569801i	$0.807020\pi$
$230$	14.1535	+	5.03533i	0.933252	+	0.332020i
$231$	−0.575941	−	4.74401i	−0.0378941	−	0.312133i
$232$	1.21688	−	2.10770i	0.0798923	−	0.138378i
$233$	−1.52687	−	1.10933i	−0.100028	−	0.0726749i	0.536647	−	0.843807i	$-0.319691\pi$
$233$	−1.52687	−	1.10933i	−0.100028	−	0.0726749i	−0.636675	+	0.771132i	$0.719691\pi$
$234$	−0.610006	−	4.42781i	−0.0398773	−	0.289455i
$235$	6.83157	−	5.81744i	0.445643	−	0.379488i
$236$	6.65725	+	1.41504i	0.433350	+	0.0921115i
$237$	−5.99649	−	4.21095i	−0.389514	−	0.273531i
$238$	−4.85160	+	1.03124i	−0.314483	+	0.0668454i
$239$	−0.959065	+	1.06515i	−0.0620368	+	0.0688988i	−0.773364	−	0.633962i	$-0.781428\pi$
$239$	−0.959065	+	1.06515i	−0.0620368	+	0.0688988i	0.711328	+	0.702861i	$0.248094\pi$
$240$	−1.90132	−	2.68153i	−0.122729	−	0.173092i
$241$	7.32923	+	8.13993i	0.472117	+	0.524339i	0.931423	−	0.363939i	$-0.118568\pi$
$241$	7.32923	+	8.13993i	0.472117	+	0.524339i	−0.459306	+	0.888278i	$0.651902\pi$
$242$	1.61879	+	1.17612i	0.104060	+	0.0756039i
$243$	−6.68392	+	14.0828i	−0.428774	+	0.903412i
$244$	−12.8926	−	9.36704i	−0.825366	−	0.599663i
$245$	5.88167	−	12.2849i	0.375766	−	0.784852i
$246$	−4.70439	+	5.39694i	−0.299941	+	0.344096i
$247$	−8.32575	−	3.70686i	−0.529755	−	0.235862i
$248$	4.63553	−	5.14828i	0.294356	−	0.326916i
$249$	−1.67879	+	5.46446i	−0.106389	+	0.346296i
$250$	−8.52427	+	0.185768i	−0.539122	+	0.0117490i
$251$	9.34568			0.589894			0.294947	−	0.955514i	$-0.404698\pi$
$251$	9.34568			0.589894			0.294947	+	0.955514i	$0.404698\pi$
$252$	−2.81001	−	2.92575i	−0.177014	−	0.184305i
$253$	−20.6269	+	14.9863i	−1.29680	+	0.942180i
$254$	1.16156	+	11.0515i	0.0728825	+	0.693431i
$255$	19.4306	+	17.9061i	1.21679	+	1.12132i
$256$	1.34548	−	12.8013i	0.0840922	−	0.800084i
$257$	−3.12162	−	5.40681i	−0.194722	−	0.337268i	0.752088	−	0.659063i	$-0.229047\pi$
$257$	−3.12162	−	5.40681i	−0.194722	−	0.337268i	−0.946809	+	0.321795i	$0.895714\pi$
$258$	1.41321	+	11.6406i	0.0879828	+	0.724712i
$259$	1.65005	+	1.83257i	0.102529	+	0.113870i
$260$	−2.36285	−	5.72813i	−0.146538	−	0.355243i
$261$	−2.71936	+	0.670159i	−0.168324	+	0.0414818i
$262$	3.19858	−	9.84422i	0.197609	−	0.608178i
$263$	1.24587	+	1.38368i	0.0768239	+	0.0853216i	0.780331	−	0.625366i	$-0.215050\pi$
$263$	1.24587	+	1.38368i	0.0768239	+	0.0853216i	−0.703507	+	0.710688i	$0.748384\pi$
$264$	−13.0665	+	0.210294i	−0.804187	+	0.0129427i
$265$	−11.2039	−	3.98599i	−0.688253	−	0.244857i
$266$	3.31739	−	0.705133i	0.203402	−	0.0432345i
$267$	27.4387	+	11.6911i	1.67922	+	0.715486i
$268$	2.62589	−	4.54818i	0.160402	−	0.277824i
$269$	3.89397	+	2.82914i	0.237420	+	0.172496i	0.700133	−	0.714012i	$-0.253124\pi$
$269$	3.89397	+	2.82914i	0.237420	+	0.172496i	−0.462713	+	0.886508i	$0.653124\pi$
$270$	1.66304	−	8.70332i	0.101209	−	0.529667i
$271$	18.4402	−	13.3976i	1.12016	−	0.813846i	0.135929	−	0.990719i	$-0.456598\pi$
$271$	18.4402	−	13.3976i	1.12016	−	0.813846i	0.984234	+	0.176873i	$0.0565982\pi$
$272$	−0.605273	−	5.75879i	−0.0367001	−	0.349178i
$273$	−1.65767	−	2.76735i	−0.100327	−	0.167488i
$274$	3.33474	+	5.77595i	0.201459	+	0.348938i
$275$	7.91688	−	12.1132i	0.477406	−	0.730451i
$276$	−6.35594	+	20.6886i	−0.382583	+	1.24531i
$277$	−7.64077	−	1.62410i	−0.459089	−	0.0975825i	−0.0274391	−	0.999623i	$-0.508735\pi$
$277$	−7.64077	−	1.62410i	−0.459089	−	0.0975825i	−0.431650	+	0.902041i	$0.642069\pi$
$278$	−11.6768	+	8.48368i	−0.700327	+	0.508817i
$279$	−7.96809	+	0.256546i	−0.477037	+	0.0153590i
$280$	4.73402	+	2.91055i	0.282912	+	0.173938i
$281$	−1.44142	+	0.641761i	−0.0859878	+	0.0382842i	−0.449280	−	0.893391i	$-0.648319\pi$
$281$	−1.44142	+	0.641761i	−0.0859878	+	0.0382842i	0.363292	+	0.931675i	$0.381653\pi$
$282$	−3.60963	−	3.88143i	−0.214950	−	0.231136i
$283$	0.811572	−	7.72159i	0.0482429	−	0.459001i	−0.943558	−	0.331208i	$-0.892544\pi$
$283$	0.811572	−	7.72159i	0.0482429	−	0.459001i	0.991801	−	0.127793i	$-0.0407894\pi$
$284$	0.215068	−	0.0457141i	0.0127619	−	0.00271263i
$285$	−13.2861	−	12.2437i	−0.787001	−	0.725253i
$286$	−4.21773	−	0.896506i	−0.249399	−	0.0530115i
$287$	−1.59675	+	4.91429i	−0.0942532	+	0.290081i
$288$	−13.8853	+	10.7877i	−0.818201	+	0.635671i
$289$	9.12995	+	28.0991i	0.537056	+	1.65289i
$290$	1.40017	−	0.757581i	0.0822210	−	0.0444867i
$291$	2.75345	+	1.93358i	0.161410	+	0.113348i
$292$	−1.48697	+	14.1476i	−0.0870184	+	0.827925i
$293$	5.25540	+	9.10262i	0.307024	+	0.531781i	0.977710	−	0.209961i	$-0.0673336\pi$
$293$	5.25540	+	9.10262i	0.307024	+	0.531781i	−0.670686	+	0.741741i	$0.734000\pi$
$294$	−7.40188	−	3.15380i	−0.431687	−	0.183934i
$295$	7.77194	+	7.39694i	0.452500	+	0.430667i
$296$	5.45552	−	3.96367i	0.317096	−	0.230383i
$297$	10.5904	+	10.6772i	0.614515	+	0.619552i
$298$	−1.43276	−	4.40960i	−0.0829978	−	0.255441i
$299$	−8.60531	+	14.9048i	−0.497658	+	0.861969i
$300$	−0.804332	−	12.2575i	−0.0464381	−	0.707687i
$301$	4.23151	+	7.32919i	0.243900	+	0.422447i
$302$	−4.81067	+	5.34279i	−0.276823	+	0.307443i
$303$	−4.06431	−	11.8560i	−0.233488	−	0.681108i
$304$	0.413868	+	3.93769i	0.0237370	+	0.225842i
$305$	−9.58002	−	23.2243i	−0.548550	−	1.32982i
$306$	10.0655	−	11.9295i	0.575407	−	0.681966i
$307$	3.00205			0.171336			0.0856680	−	0.996324i	$-0.472698\pi$
$307$	3.00205			0.171336			0.0856680	+	0.996324i	$0.472698\pi$
$308$	−3.57517	+	1.59177i	−0.203714	+	0.0906995i
$309$	−27.8718	+	12.9507i	−1.58557	+	0.736738i
$310$	4.34683	−	1.28067i	0.246883	−	0.0727373i
$311$	−9.37603	+	10.4131i	−0.531666	+	0.590475i	−0.947815	−	0.318822i	$-0.896713\pi$
$311$	−9.37603	+	10.4131i	−0.531666	+	0.590475i	0.416149	+	0.909297i	$0.363380\pi$
$312$	−7.99994	+	3.71719i	−0.452908	+	0.210445i
$313$	−3.71665	−	4.12776i	−0.210077	−	0.233315i	0.628893	−	0.777492i	$-0.283508\pi$
$313$	−3.71665	−	4.12776i	−0.210077	−	0.233315i	−0.838970	+	0.544178i	$0.816842\pi$
$314$	−4.85456	−	14.9408i	−0.273959	−	0.843158i
$315$	−1.35801	−	6.24921i	−0.0765150	−	0.352103i
$316$	−1.85427	+	5.70685i	−0.104311	+	0.321036i
$317$	4.15158	−	1.84840i	0.233176	−	0.103817i	−0.286823	−	0.957984i	$-0.592599\pi$
$317$	4.15158	−	1.84840i	0.233176	−	0.103817i	0.519999	+	0.854167i	$0.325932\pi$
$318$	−2.06298	+	6.71500i	−0.115686	+	0.376559i
$319$	−0.282427	+	2.68712i	−0.0158129	+	0.150450i
$320$	3.78093	−	4.91250i	0.211360	−	0.274617i
$321$	1.35607	−	1.55570i	0.0756884	−	0.0868307i
$322$	−0.669468	−	6.36956i	−0.0373080	−	0.354962i
$323$	−9.83485	−	30.2685i	−0.547226	−	1.68419i
$324$	12.6317	+	1.84542i	0.701760	+	0.102523i
$325$	1.55632	−	9.64343i	0.0863290	−	0.534921i
$326$	3.97473	−	6.88444i	0.220140	−	0.381294i
$327$	−1.72082	−	2.87278i	−0.0951617	−	0.158865i
$328$	12.9085	+	5.74724i	0.712754	+	0.317338i
$329$	−3.49476	−	1.55597i	−0.192672	−	0.0857832i
$330$	−7.35310	−	4.35932i	−0.404775	−	0.239973i
$331$	5.29985	−	2.35964i	0.291306	−	0.129698i	−0.255881	−	0.966708i	$-0.582365\pi$
$331$	5.29985	−	2.35964i	0.291306	−	0.129698i	0.547187	+	0.837011i	$0.315699\pi$
$332$	4.68140			0.256925
$333$	−7.63855	−	1.36832i	−0.418590	−	0.0749837i
$334$	−3.64427	+	11.2159i	−0.199406	+	0.613708i
$335$	7.28167	−	3.93983i	0.397840	−	0.215256i
$336$	−0.681105	+	1.22481i	−0.0371573	+	0.0668190i
$337$	−4.80717	+	1.02179i	−0.261863	+	0.0556607i	−0.336972	−	0.941515i	$-0.609403\pi$
$337$	−4.80717	+	1.02179i	−0.261863	+	0.0556607i	0.0751092	+	0.997175i	$0.476069\pi$
$338$	6.85027	−	1.45607i	0.372605	−	0.0791997i
$339$	−6.76479	+	12.1649i	−0.367413	+	0.660709i
$340$	9.34418	−	19.5169i	0.506759	−	1.05845i
$341$	−2.37664	+	7.31456i	−0.128702	+	0.396106i
$342$	−6.88250	+	8.15707i	−0.372163	+	0.441084i
$343$	−12.4801			−0.673861
$344$	21.1421	−	9.41305i	1.13990	−	0.507518i
$345$	−25.6174	+	22.5357i	−1.37920	+	1.21328i
$346$	−10.3617	−	4.61334i	−0.557050	−	0.248015i
$347$	9.10712	+	4.05475i	0.488896	+	0.217670i	0.636353	−	0.771398i	$-0.280442\pi$
$347$	9.10712	+	4.05475i	0.488896	+	0.217670i	−0.147457	+	0.989068i	$0.547109\pi$
$348$	1.17860	+	1.96759i	0.0631798	+	0.105474i
$349$	7.15701	−	12.3963i	0.383106	−	0.663559i	−0.608398	−	0.793632i	$-0.708188\pi$
$349$	7.15701	−	12.3963i	0.383106	−	0.663559i	0.991504	+	0.130073i	$0.0415210\pi$
$350$	1.64080	+	3.24370i	0.0877046	+	0.173383i
$351$	9.46224	+	3.67660i	0.505057	+	0.196242i
$352$	5.24190	+	16.1329i	0.279394	+	0.859887i
$353$	−2.64975	−	25.2107i	−0.141032	−	1.34183i	−0.804646	−	0.593755i	$-0.797645\pi$
$353$	−2.64975	−	25.2107i	−0.141032	−	1.34183i	0.663614	−	0.748075i	$-0.269022\pi$
$354$	4.16460	−	4.77769i	0.221346	−	0.253931i
$355$	0.326567	+	0.116182i	0.0173324	+	0.00616628i
$356$	2.55310	−	24.2911i	0.135314	−	1.28743i
$357$	3.30826	−	10.7684i	0.175092	−	0.569925i
$358$	18.5836	−	8.27396i	0.982175	−	0.437293i
$359$	6.35182	−	19.5489i	0.335236	−	1.03175i	−0.631369	−	0.775482i	$-0.717507\pi$
$359$	6.35182	−	19.5489i	0.335236	−	1.03175i	0.966606	−	0.256269i	$-0.0824933\pi$
$360$	−17.3836	+	1.90696i	−0.916195	+	0.100505i
$361$	0.853463	+	2.62669i	0.0449191	+	0.138247i
$362$	−10.1103	−	11.2286i	−0.531384	−	0.590162i
$363$	−4.12135	+	1.91500i	−0.216315	+	0.100511i
$364$	−1.76766	+	1.96319i	−0.0926506	+	0.102899i
$365$	−13.6780	+	17.7716i	−0.715940	+	0.930209i
$366$	−13.4585	+	6.25351i	−0.703486	+	0.326876i
$367$	26.2996	−	11.7093i	1.37283	−	0.611221i	0.418016	−	0.908440i	$-0.362725\pi$
$367$	26.2996	−	11.7093i	1.37283	−	0.611221i	0.954810	+	0.297218i	$0.0960588\pi$
$368$	7.47706			0.389769
$369$	−5.51986	−	15.2951i	−0.287353	−	0.796229i
$370$	4.39792	−	0.339648i	0.228637	−	0.0176575i
$371$	0.529954	+	5.04218i	0.0275138	+	0.261777i
$372$	2.11712	+	6.17584i	0.109767	+	0.320202i
$373$	7.64527	−	8.49093i	0.395857	−	0.439644i	−0.511961	−	0.859009i	$-0.671081\pi$
$373$	7.64527	−	8.49093i	0.395857	−	0.439644i	0.907818	+	0.419365i	$0.137747\pi$
$374$	−7.52898	−	13.0406i	−0.389314	−	0.674312i
$375$	9.04036	−	17.1252i	0.466842	−	0.884341i
$376$	−5.23057	+	9.05960i	−0.269746	+	0.467213i
$377$	0.563606	+	1.73460i	0.0290272	+	0.0893365i
$378$	−3.65292	+	0.962835i	−0.187886	+	0.0495229i
$379$	2.90335	−	2.10941i	0.149135	−	0.108353i	−0.510716	−	0.859750i	$-0.670620\pi$
$379$	2.90335	−	2.10941i	0.149135	−	0.108353i	0.659851	+	0.751397i	$0.270620\pi$
$380$	−6.38928	+	13.3451i	−0.327763	+	0.684590i
$381$	−23.2186	−	9.89301i	−1.18953	−	0.506834i
$382$	4.57882	+	7.93074i	0.234273	+	0.405772i
$383$	−0.535221	+	5.09229i	−0.0273485	+	0.260204i	0.972301	+	0.233732i	$0.0750939\pi$
$383$	−0.535221	+	5.09229i	−0.0273485	+	0.260204i	−0.999650	+	0.0264718i	$0.991573\pi$
$384$	13.6191	+	9.56383i	0.694996	+	0.488052i
$385$	−6.11550	−	0.814228i	−0.311675	−	0.0414969i
$386$	−5.98093	−	18.4074i	−0.304421	−	0.936912i
$387$	−24.6658	−	10.0438i	−1.25383	−	0.510554i
$388$	0.851440	−	2.62046i	0.0432253	−	0.133034i
$389$	−30.2263	−	6.42479i	−1.53253	−	0.325750i	−0.637041	−	0.770830i	$-0.719842\pi$
$389$	−30.2263	−	6.42479i	−1.53253	−	0.325750i	−0.895491	+	0.445080i	$0.853175\pi$
$390$	−5.73131	−	0.669401i	−0.290216	−	0.0338964i
$391$	−58.7886	+	12.4959i	−2.97307	+	0.631945i
$392$	−1.65984	+	15.7923i	−0.0838346	+	0.797633i
$393$	16.0096	+	17.2150i	0.807575	+	0.868384i
$394$	1.18513	−	0.527653i	0.0597059	−	0.0265828i
$395$	−7.20209	+	6.13296i	−0.362376	+	0.308583i
$396$	5.81131	−	10.8581i	0.292029	−	0.545640i
$397$	−5.15821	+	3.74766i	−0.258883	+	0.188090i	−0.709654	−	0.704550i	$-0.751149\pi$
$397$	−5.15821	+	3.74766i	−0.258883	+	0.188090i	0.450771	+	0.892639i	$0.351149\pi$
$398$	4.86268	+	1.03359i	0.243744	+	0.0518094i
$399$	−2.26209	+	7.36313i	−0.113246	+	0.368618i
$400$	−3.96631	+	1.50922i	−0.198316	+	0.0754610i
$401$	8.96136	+	15.5215i	0.447509	+	0.775108i	0.998223	−	0.0595856i	$-0.0189779\pi$
$401$	8.96136	+	15.5215i	0.447509	+	0.775108i	−0.550714	+	0.834694i	$0.685645\pi$
$402$	−2.51318	−	4.19555i	−0.125346	−	0.209255i
$403$	0.542672	+	5.16318i	0.0270324	+	0.257196i
$404$	−8.30359	+	6.03291i	−0.413119	+	0.300149i
$405$	15.4399	+	12.9078i	0.767214	+	0.641392i
$406$	−0.549098	−	0.398943i	−0.0272513	−	0.0197992i
$407$	−3.74319	+	6.48340i	−0.185543	+	0.321370i
$408$	−28.3402	−	12.0752i	−1.40305	−	0.597813i
$409$	37.5919	−	7.99041i	1.85880	−	0.395101i	0.864585	−	0.502487i	$-0.167582\pi$
$409$	37.5919	−	7.99041i	1.85880	−	0.395101i	0.994217	+	0.107387i	$0.0342483\pi$
$410$	5.22406	+	7.62493i	0.257998	+	0.376569i
$411$	−15.1458	+	0.243758i	−0.747086	+	0.0120237i
$412$	16.8410	+	18.7038i	0.829697	+	0.921472i
$413$	1.41354	−	4.35042i	0.0695556	−	0.214070i
$414$	13.9612	+	14.5362i	0.686155	+	0.714414i
$415$	6.28683	+	3.86524i	0.308608	+	0.189737i
$416$	7.66193	+	8.50943i	0.375657	+	0.417209i
$417$	−3.95072	−	32.5420i	−0.193468	−	1.59359i
$418$	5.14810	+	8.91677i	0.251802	+	0.436134i
$419$	−0.552525	+	5.25693i	−0.0269926	+	0.256818i	0.972701	+	0.232062i	$0.0745473\pi$
$419$	−0.552525	+	5.25693i	−0.0269926	+	0.256818i	−0.999694	+	0.0247553i	$0.992119\pi$
$420$	−4.56538	+	2.56598i	−0.222768	+	0.125207i
$421$	2.83193	+	26.9440i	0.138020	+	1.31317i	0.815984	+	0.578075i	$0.196196\pi$
$421$	2.83193	+	26.9440i	0.138020	+	1.31317i	−0.677964	+	0.735095i	$0.737137\pi$
$422$	−4.92301	+	3.57678i	−0.239649	+	0.174115i
$423$	11.6887	−	2.88056i	0.568324	−	0.140058i
$424$	13.8642			0.673306
$425$	28.6630	−	18.4949i	1.39036	−	0.897135i
$426$	0.0601306	−	0.195726i	0.00291334	−	0.00948294i
$427$	−7.16686	+	7.95960i	−0.346829	+	0.385192i
$428$	−1.54395	−	0.687412i	−0.0746298	−	0.0332273i
$429$	6.43504	−	7.38236i	0.310687	−	0.356424i
$430$	15.0059	+	1.99791i	0.723647	+	0.0963476i
$431$	−28.0178	−	20.3561i	−1.34957	−	0.980518i	−0.999033	−	0.0439685i	$-0.986000\pi$
$431$	−28.0178	−	20.3561i	−1.34957	−	0.980518i	−0.350535	−	0.936550i	$-0.614000\pi$
$432$	−0.672127	−	4.35871i	−0.0323377	−	0.209709i
$433$	−7.43160	−	5.39937i	−0.357140	−	0.259477i	0.394718	−	0.918802i	$-0.370842\pi$
$433$	−7.43160	−	5.39937i	−0.357140	−	0.259477i	−0.751858	+	0.659325i	$0.770842\pi$
$434$	−1.29274	−	1.43574i	−0.0620537	−	0.0689176i
$435$	−0.0417631	+	3.61547i	−0.00200239	+	0.173349i
$436$	−1.83500	+	2.03798i	−0.0878806	+	0.0976013i
$437$	40.1980	−	8.54434i	1.92293	−	0.408731i
$438$	10.8413	+	7.61313i	0.518015	+	0.363769i
$439$	−7.02176	−	1.49252i	−0.335130	−	0.0712342i	0.0372730	−	0.999305i	$-0.488133\pi$
$439$	−7.02176	−	1.49252i	−0.335130	−	0.0712342i	−0.372403	+	0.928071i	$0.621466\pi$
$440$	−3.96245	+	16.3990i	−0.188902	+	0.781792i
$441$	14.4303	−	11.2111i	0.687158	−	0.533862i
$442$	−8.22328	−	5.97456i	−0.391141	−	0.284181i
$443$	12.6804	−	21.9630i	0.602462	−	1.04349i	−0.389985	−	0.920821i	$-0.627520\pi$
$443$	12.6804	−	21.9630i	0.602462	−	1.04349i	0.992447	−	0.122673i	$-0.0391468\pi$
$444$	0.765893	+	6.30864i	0.0363477	+	0.299395i
$445$	23.4848	−	30.5135i	1.11329	−	1.44648i
$446$	−6.57482	−	2.92730i	−0.311327	−	0.138612i
$447$	10.3343	+	2.02337i	0.488793	+	0.0957022i
$448$	−2.58513	−	0.549486i	−0.122136	−	0.0259608i
$449$	−7.13943			−0.336930			−0.168465	−	0.985708i	$-0.553881\pi$
$449$	−7.13943			−0.336930			−0.168465	+	0.985708i	$0.553881\pi$
$450$	−10.3400	−	4.89290i	−0.487432	−	0.230654i
$451$	−15.6870			−0.738672
$452$	11.1498	+	2.36996i	0.524442	+	0.111474i
$453$	−5.29507	−	15.4462i	−0.248784	−	0.725728i
$454$	−16.4443	−	7.32147i	−0.771768	−	0.343613i
$455$	−3.99478	+	1.17695i	−0.187278	+	0.0551764i
$456$	19.3782	+	8.25670i	0.907468	+	0.386655i
$457$	−17.8907	+	30.9875i	−0.836890	+	1.44954i	0.0555925	+	0.998454i	$0.482295\pi$
$457$	−17.8907	+	30.9875i	−0.836890	+	1.44954i	−0.892482	+	0.451082i	$0.851038\pi$
$458$	9.69078	+	7.04076i	0.452820	+	0.328993i
$459$	12.5690	+	33.1472i	0.586672	+	1.54718i
$460$	23.8022	+	14.6340i	1.10978	+	0.682311i
$461$	14.9012	+	3.16735i	0.694018	+	0.147518i	0.541397	−	0.840767i	$-0.317895\pi$
$461$	14.9012	+	3.16735i	0.694018	+	0.147518i	0.152621	+	0.988285i	$0.451229\pi$
$462$	−0.322571	+	3.63012i	−0.0150074	+	0.168888i
$463$	24.3097	−	5.16720i	1.12977	−	0.240140i	0.395148	−	0.918617i	$-0.370693\pi$
$463$	24.3097	−	5.16720i	1.12977	−	0.240140i	0.734621	+	0.678477i	$0.237360\pi$
$464$	0.530199	−	0.588846i	0.0246139	−	0.0273365i
$465$	−2.25598	+	10.0418i	−0.104619	+	0.465677i
$466$	0.963075	+	1.06960i	0.0446136	+	0.0495484i
$467$	−21.1648	−	15.3771i	−0.979389	−	0.711568i	−0.0218169	−	0.999762i	$-0.506945\pi$
$467$	−21.1648	−	15.3771i	−0.979389	−	0.711568i	−0.957572	+	0.288194i	$0.906945\pi$
$468$	0.602466	−	8.29139i	0.0278490	−	0.383270i
$469$	−2.85561	−	2.07472i	−0.131860	−	0.0958018i
$470$	−6.01840	+	3.25633i	−0.277608	+	0.150203i
$471$	35.0150	+	6.85568i	1.61341	+	0.315893i
$472$	−11.4274	−	5.08780i	−0.525988	−	0.234185i
$473$	−17.1918	+	19.0934i	−0.790480	+	0.877917i
$474$	3.80540	+	4.09194i	0.174788	+	0.187949i
$475$	−19.5989	+	12.6463i	−0.899261	+	0.580251i
$476$	−9.22529			−0.422841
$477$	−11.0517	−	11.5069i	−0.506024	−	0.526865i
$478$	0.884301	−	0.642482i	0.0404470	−	0.0293865i
$479$	1.00563	+	9.56794i	0.0459484	+	0.437170i	0.993177	+	0.116613i	$0.0372036\pi$
$479$	1.00563	+	9.56794i	0.0459484	+	0.437170i	−0.947229	+	0.320558i	$0.896130\pi$
$480$	8.99282	+	20.8428i	0.410464	+	0.951341i
$481$	−0.528235	+	5.02583i	−0.0240855	+	0.229158i
$482$	−4.17660	−	7.23408i	−0.190239	−	0.329503i
$483$	13.3821	+	5.70188i	0.608908	+	0.259445i
$484$	2.49025	+	2.76571i	0.113193	+	0.125714i
$485$	3.30704	−	2.81612i	0.150165	−	0.127873i
$486$	7.21879	−	9.44528i	0.327451	−	0.428447i
$487$	12.1864	−	37.5059i	0.552219	−	1.69956i	−0.150958	−	0.988540i	$-0.548236\pi$
$487$	12.1864	−	37.5059i	0.552219	−	1.69956i	0.703177	−	0.711015i	$-0.251764\pi$
$488$	19.5984	+	21.7662i	0.887178	+	0.985311i
$489$	9.27786	+	15.4887i	0.419560	+	0.700421i
$490$	−6.33528	+	8.23133i	−0.286199	+	0.371854i
$491$	−9.52590	+	2.02479i	−0.429898	+	0.0913776i	−0.417778	−	0.908549i	$-0.637191\pi$
$491$	−9.52590	+	2.02479i	−0.429898	+	0.0913776i	−0.0121194	+	0.999927i	$0.503858\pi$
$492$	−10.6457	+	7.99943i	−0.479945	+	0.360642i
$493$	−3.18461	+	5.51590i	−0.143427	+	0.248424i
$494$	5.62284	+	4.08523i	0.252984	+	0.183803i
$495$	16.7693	−	9.78361i	0.753726	−	0.439740i
$496$	1.82471	−	1.32573i	0.0819321	−	0.0595272i
$497$	−0.0154468	−	0.146967i	−0.000692886	−	0.00659237i
$498$	2.11871	−	3.81003i	0.0949419	−	0.170731i
$499$	−4.37718	−	7.58149i	−0.195949	−	0.339394i	0.751262	−	0.660004i	$-0.229445\pi$
$499$	−4.37718	−	7.58149i	−0.195949	−	0.339394i	−0.947211	+	0.320610i	$0.896112\pi$
$500$	−15.5800	−	2.95840i	−0.696759	−	0.132304i
$501$	−18.2403	−	19.6138i	−0.814918	−	0.876280i
$502$	−6.97140	−	1.48182i	−0.311149	−	0.0661368i
$503$	−16.1674	+	11.7463i	−0.720867	+	0.523741i	−0.886661	−	0.462420i	$-0.846981\pi$
$503$	−16.1674	+	11.7463i	−0.720867	+	0.523741i	0.165794	+	0.986160i	$0.446981\pi$
$504$	3.93372	+	6.33355i	0.175222	+	0.282119i
$505$	−16.1323	+	1.24589i	−0.717880	+	0.0554414i
$506$	17.7628	−	7.90850i	0.789652	−	0.351576i
$507$	−4.67113	+	15.2046i	−0.207452	+	0.675258i
$508$	−2.16043	+	20.5551i	−0.0958535	+	0.911985i
$509$	32.6145	−	6.93243i	1.44561	−	0.307274i	0.582725	−	0.812670i	$-0.301987\pi$
$509$	32.6145	−	6.93243i	1.44561	−	0.307274i	0.862888	+	0.505395i	$0.168653\pi$
$510$	−11.6551	−	16.4379i	−0.516098	−	0.727882i
$511$	9.35204	+	1.98784i	0.413710	+	0.0879368i
$512$	2.90473	−	8.93985i	0.128372	−	0.395089i
$513$	−8.59435	−	22.6651i	−0.379450	−	1.00069i
$514$	1.47129	+	4.52816i	0.0648958	+	0.199729i
$515$	7.17344	+	39.0231i	0.316100	+	1.71956i
$516$	−1.93041	+	21.7242i	−0.0849815	+	0.956355i
$517$	1.21397	−	11.5501i	0.0533902	−	0.507974i
$518$	−0.940290	−	1.62863i	−0.0413140	−	0.0715579i
$519$	20.5945	−	15.4752i	0.903998	−	0.679285i
$520$	2.05897	+	11.2007i	0.0902918	+	0.491182i
$521$	−18.9750	+	13.7861i	−0.831308	+	0.603981i	−0.919929	−	0.392085i	$-0.871754\pi$
$521$	−18.9750	+	13.7861i	−0.831308	+	0.603981i	0.0886210	+	0.996065i	$0.471754\pi$
$522$	2.13476	−	0.0687322i	0.0934361	−	0.00300833i
$523$	6.59815	+	20.3070i	0.288517	+	0.887963i	0.985322	+	0.170703i	$0.0546040\pi$
$523$	6.59815	+	20.3070i	0.288517	+	0.887963i	−0.696806	+	0.717260i	$0.745396\pi$
$524$	9.62597	−	16.6727i	0.420512	−	0.728349i
$525$	−8.24965	−	0.323504i	−0.360044	−	0.0141189i
$526$	−0.709968	−	1.22970i	−0.0309561	−	0.0536175i
$527$	−12.1313	+	13.4731i	−0.528446	+	0.586899i
$528$	−4.17537	−	0.817507i	−0.181710	−	0.0355774i
$529$	−5.70803	−	54.3082i	−0.248175	−	2.36123i
$530$	7.72558	+	4.74981i	0.335578	+	0.206318i
$531$	4.88651	+	13.5401i	0.212056	+	0.587590i
$532$	6.30799			0.273486
$533$	−9.67366	+	4.30699i	−0.419013	+	0.186557i
$534$	−18.6142	−	13.0716i	−0.805515	−	0.565663i
$535$	−1.50587	−	2.19793i	−0.0651042	−	0.0950249i
$536$	−6.45869	+	7.17310i	−0.278973	+	0.309831i
$537$	−4.08934	+	46.0201i	−0.176468	+	1.98592i
$538$	−2.45613	−	2.72781i	−0.105891	−	0.117604i
$539$	−5.44763	−	16.7661i	−0.234646	−	0.722167i
$540$	6.39116	−	15.1908i	0.275032	−	0.653709i
$541$	10.3808	−	31.9488i	0.446305	−	1.37358i	−0.434742	−	0.900555i	$-0.643160\pi$
$541$	10.3808	−	31.9488i	0.446305	−	1.37358i	0.881047	−	0.473029i	$-0.156840\pi$
$542$	−15.8797	+	7.07012i	−0.682093	+	0.303687i
$543$	33.4478	−	7.67411i	1.43538	−	0.329328i
$544$	−4.17979	+	39.7680i	−0.179207	+	1.70504i
$545$	−4.14697	+	1.22179i	−0.177637	+	0.0523357i
$546$	0.797759	+	2.32714i	0.0341409	+	0.0995924i
$547$	−3.47767	−	33.0878i	−0.148694	−	1.41473i	−0.773423	−	0.633890i	$-0.781457\pi$
$547$	−3.47767	−	33.0878i	−0.148694	−	1.41473i	0.624729	−	0.780842i	$-0.285210\pi$
$548$	3.83331	+	11.7977i	0.163751	+	0.503974i
$549$	2.44266	−	33.6169i	0.104250	−	1.43473i
$550$	−7.82621	+	7.78053i	−0.333711	+	0.331763i
$551$	2.17754	−	3.77161i	0.0927664	−	0.160676i
$552$	19.3321	−	34.7643i	0.822827	−	1.47967i
$553$	3.68430	+	1.64036i	0.156672	+	0.0697550i
$554$	5.44212	+	2.42299i	0.231214	+	0.102943i
$555$	−4.18025	+	9.10449i	−0.177442	+	0.386464i
$556$	−24.5242	+	10.9189i	−1.04006	+	0.463064i
$557$	29.7702			1.26140			0.630702	−	0.776025i	$-0.282767\pi$
$557$	29.7702			1.26140			0.630702	+	0.776025i	$0.282767\pi$
$558$	5.98447	+	1.07202i	0.253343	+	0.0453823i
$559$	−5.35937	+	16.4945i	−0.226677	+	0.697641i
$560$	1.31057	+	1.24734i	0.0553818	+	0.0527096i
$561$	34.1952	−	0.550343i	1.44372	−	0.0232355i
$562$	1.17698	−	0.250175i	0.0496479	−	0.0105530i
$563$	−23.2130	+	4.93408i	−0.978312	+	0.207947i	−0.669203	−	0.743080i	$-0.733364\pi$
$563$	−23.2130	+	4.93408i	−0.978312	+	0.207947i	−0.309109	+	0.951027i	$0.600031\pi$
$564$	−5.06603	−	8.45733i	−0.213318	−	0.356118i
$565$	13.0167	+	12.3887i	0.547617	+	0.521195i
$566$	−1.82970	+	5.63124i	−0.0769080	+	0.236699i
$567$	2.12094	−	8.31360i	0.0890709	−	0.349138i
$568$	−0.404108			−0.0169560
$569$	26.6550	−	11.8676i	1.11744	−	0.497515i	0.236920	−	0.971529i	$-0.423862\pi$
$569$	26.6550	−	11.8676i	1.11744	−	0.497515i	0.880517	+	0.474014i	$0.157195\pi$
$570$	7.96945	+	11.2398i	0.333804	+	0.470782i
$571$	−2.43726	−	1.08514i	−0.101996	−	0.0454116i	0.355104	−	0.934827i	$-0.384445\pi$
$571$	−2.43726	−	1.08514i	−0.101996	−	0.0454116i	−0.457100	+	0.889415i	$0.651112\pi$
$572$	−7.32662	−	3.26202i	−0.306341	−	0.136392i
$573$	−20.7961	+	0.334696i	−0.868771	+	0.0139821i
$574$	1.97029	−	3.41264i	0.0822382	−	0.142441i
$575$	19.8822	+	39.3050i	0.829145	+	1.63913i
$576$	7.48506	−	3.62553i	0.311877	−	0.151064i
$577$	−10.1294	−	31.1750i	−0.421692	−	1.29783i	−0.906127	−	0.423007i	$-0.860975\pi$
$577$	−10.1294	−	31.1750i	−0.421692	−	1.29783i	0.484435	−	0.874827i	$-0.339025\pi$
$578$	−2.35519	−	22.4081i	−0.0979630	−	0.932055i
$579$	43.1393	+	8.44636i	1.79281	+	0.351019i
$580$	2.84029	−	0.836813i	0.117937	−	0.0347468i
$581$	0.328885	−	3.12913i	0.0136445	−	0.129818i
$582$	−1.74736	−	1.87893i	−0.0724303	−	0.0778841i
$583$	−14.0611	+	6.26040i	−0.582351	+	0.259279i
$584$	8.07935	−	24.8657i	0.334326	−	1.02895i
$585$	7.65494	−	10.6374i	0.316493	−	0.439802i
$586$	−2.47698	−	7.62337i	−0.102323	−	0.314919i
$587$	−2.85518	−	3.17100i	−0.117846	−	0.130881i	0.681335	−	0.731972i	$-0.261400\pi$
$587$	−2.85518	−	3.17100i	−0.117846	−	0.130881i	−0.799181	+	0.601091i	$0.794733\pi$
$588$	−12.2466	−	8.60004i	−0.505043	−	0.354660i
$589$	8.29501	−	9.21254i	0.341790	−	0.379596i
$590$	−4.62464	−	6.75004i	−0.190394	−	0.277895i
$591$	−0.260788	+	2.93483i	−0.0107274	+	0.120723i
$592$	2.00566	−	0.892978i	0.0824322	−	0.0367012i
$593$	−7.81313			−0.320847			−0.160423	−	0.987048i	$-0.551286\pi$
$593$	−7.81313			−0.320847			−0.160423	+	0.987048i	$0.551286\pi$
$594$	−6.20695	−	9.64380i	−0.254674	−	0.395690i
$595$	−12.3890	−	7.61695i	−0.507900	−	0.312265i
$596$	−0.901418	−	8.57642i	−0.0369235	−	0.351304i
$597$	−7.41905	+	8.51123i	−0.303642	+	0.348341i
$598$	8.78239	−	9.75383i	0.359139	−	0.398864i
$599$	22.2102	+	38.4691i	0.907483	+	1.57181i	0.817550	+	0.575858i	$0.195332\pi$
$599$	22.2102	+	38.4691i	0.907483	+	1.57181i	0.0899331	+	0.995948i	$0.471335\pi$
$600$	−3.23790	+	22.3433i	−0.132187	+	0.912163i
$601$	−7.98356	+	13.8279i	−0.325656	+	0.564053i	−0.981645	−	0.190718i	$-0.938919\pi$
$601$	−7.98356	+	13.8279i	−0.325656	+	0.564053i	0.655989	+	0.754771i	$0.272252\pi$
$602$	−1.99440	−	6.13814i	−0.0812858	−	0.250172i
$603$	11.1019	−	0.357445i	0.452106	−	0.0145563i
$604$	−10.8181	+	7.85982i	−0.440183	+	0.319811i
$605$	1.06073	+	5.77028i	0.0431246	+	0.234595i
$606$	1.15193	+	9.48839i	0.0467938	+	0.385439i
$607$	−5.79724	−	10.0411i	−0.235303	−	0.407557i	0.724058	−	0.689739i	$-0.242275\pi$
$607$	−5.79724	−	10.0411i	−0.235303	−	0.407557i	−0.959361	+	0.282183i	$0.908942\pi$
$608$	2.85802	−	27.1922i	0.115908	−	1.10279i
$609$	1.39797	−	0.649571i	0.0566487	−	0.0263219i
$610$	3.46385	+	18.8431i	0.140247	+	0.762936i
$611$	−2.42257	−	7.45589i	−0.0980065	−	0.301633i
$612$	22.9253	−	17.8110i	0.926702	−	0.719967i
$613$	0.0509077	−	0.156678i	0.00205614	−	0.00632816i	−0.950023	−	0.312179i	$-0.898941\pi$
$613$	0.0509077	−	0.156678i	0.00205614	−	0.00632816i	0.952079	+	0.305851i	$0.0989410\pi$
$614$	−2.23938	−	0.475994i	−0.0903739	−	0.0192096i
$615$	−20.9013	+	1.95301i	−0.842823	+	0.0787530i
$616$	7.03554	−	1.49545i	0.283470	−	0.0602534i
$617$	−3.76370	+	35.8092i	−0.151521	+	1.44162i	0.609444	+	0.792829i	$0.291393\pi$
$617$	−3.76370	+	35.8092i	−0.151521	+	1.44162i	−0.760965	+	0.648794i	$0.775274\pi$
$618$	22.8443	−	5.24131i	0.918934	−	0.210836i
$619$	−43.6439	+	19.4315i	−1.75420	+	0.781019i	−0.763358	+	0.645976i	$0.776451\pi$
$619$	−43.6439	+	19.4315i	−1.75420	+	0.781019i	−0.990840	+	0.135043i	$0.956883\pi$
$620$	8.40342	−	0.648990i	0.337489	−	0.0260641i
$621$	−44.2638	+	11.6670i	−1.77624	+	0.468181i
$622$	8.64512	−	6.28105i	0.346638	−	0.251847i
$623$	−16.0573	−	3.41308i	−0.643321	−	0.136742i
$624$	−2.79927	+	0.642252i	−0.112061	+	0.0257107i
$625$	−18.4804	−	16.8367i	−0.739215	−	0.673470i
$626$	2.11795	+	3.66840i	0.0846503	+	0.146619i
$627$	−23.3817	+	0.376309i	−0.933776	+	0.0150283i
$628$	−3.05423	−	29.0590i	−0.121877	−	1.15958i
$629$	−14.2772	+	10.3730i	−0.569269	+	0.413598i
$630$	0.0221514	+	4.87692i	0.000882534	+	0.194301i
$631$	−12.6855	−	9.21654i	−0.505001	−	0.366905i	0.305923	−	0.952056i	$-0.401035\pi$
$631$	−12.6855	−	9.21654i	−0.505001	−	0.366905i	−0.810924	+	0.585152i	$0.801035\pi$
$632$	5.51425	−	9.55096i	0.219345	−	0.379917i
$633$	−1.66565	−	13.7199i	−0.0662037	−	0.545318i
$634$	−3.38994	+	0.720555i	−0.134632	+	0.0286169i
$635$	−19.8728	+	25.8205i	−0.788629	+	1.02465i
$636$	−6.34988	+	11.4188i	−0.251789	+	0.452786i
$637$	−7.96265	−	8.84341i	−0.315492	−	0.350389i
$638$	0.636737	−	1.95967i	0.0252087	−	0.0775843i
$639$	0.322131	+	0.335398i	0.0127433	+	0.0132681i
$640$	16.3572	−	13.9290i	0.646576	−	0.550594i
$641$	−24.8019	−	27.5453i	−0.979616	−	1.08797i	−0.996111	−	0.0881103i	$-0.971917\pi$
$641$	−24.8019	−	27.5453i	−0.979616	−	1.08797i	0.0164943	−	0.999864i	$-0.494749\pi$
$642$	−1.25823	+	0.945460i	−0.0496582	+	0.0373143i
$643$	3.29095	+	5.70009i	0.129782	+	0.224790i	0.923592	−	0.383376i	$-0.125239\pi$
$643$	3.29095	+	5.70009i	0.129782	+	0.224790i	−0.793810	+	0.608166i	$0.791905\pi$
$644$	1.24517	−	11.8470i	0.0490666	−	0.466838i
$645$	−20.5292	+	27.5804i	−0.808337	+	1.08598i
$646$	2.53703	+	24.1382i	0.0998180	+	0.949705i
$647$	2.22736	−	1.61827i	0.0875666	−	0.0636209i	−0.543141	−	0.839642i	$-0.682765\pi$
$647$	2.22736	−	1.61827i	0.0875666	−	0.0636209i	0.630707	+	0.776021i	$0.282765\pi$
$648$	−22.0035	−	8.14449i	−0.864378	−	0.319946i
$649$	13.8871			0.545115
$650$	−2.68996	+	6.94675i	−0.105509	+	0.272474i
$651$	4.27678	−	0.981246i	0.167620	−	0.0384581i
$652$	9.89346	−	10.9878i	0.387458	−	0.430316i
$653$	5.91127	+	2.63187i	0.231326	+	0.102993i	0.519126	−	0.854697i	$-0.326257\pi$
$653$	5.91127	+	2.63187i	0.231326	+	0.102993i	−0.287801	+	0.957690i	$0.592924\pi$
$654$	0.828150	+	2.41579i	0.0323832	+	0.0944650i
$655$	26.6930	−	14.4426i	1.04298	−	0.564319i
$656$	3.72180	+	2.70405i	0.145312	+	0.105575i
$657$	−27.0782	+	13.1158i	−1.05642	+	0.511697i
$658$	2.36020	+	1.71479i	0.0920103	+	0.0668494i
$659$	6.54526	+	7.26924i	0.254967	+	0.283170i	0.857016	−	0.515289i	$-0.172316\pi$
$659$	6.54526	+	7.26924i	0.254967	+	0.283170i	−0.602049	+	0.798459i	$0.705649\pi$
$660$	−11.6917	−	10.7744i	−0.455099	−	0.419392i
$661$	−0.222630	+	0.247256i	−0.00865932	+	0.00961714i	−0.747459	−	0.664308i	$-0.768726\pi$
$661$	−0.222630	+	0.247256i	−0.00865932	+	0.00961714i	0.738800	+	0.673925i	$0.235393\pi$
$662$	−4.32756	+	0.919851i	−0.168195	+	0.0357510i
$663$	20.9360	−	9.72796i	0.813087	−	0.377803i
$664$	−8.41601	−	1.78888i	−0.326604	−	0.0694219i
$665$	8.47125	+	5.20826i	0.328501	+	0.201967i
$666$	5.48102	+	2.23184i	0.212385	+	0.0864821i
$667$	−6.65361	−	4.83413i	−0.257629	−	0.187178i
$668$	−10.9673	+	18.9958i	−0.424336	+	0.734971i
$669$	13.0678	−	9.81945i	0.505230	−	0.379642i
$670$	−6.05644	+	1.78436i	−0.233981	+	0.0689360i
$671$	−29.7053	−	13.2256i	−1.14676	−	0.510570i
$672$	6.35921	−	7.29536i	0.245312	−	0.281425i
$673$	6.03084	+	1.28189i	0.232472	+	0.0494134i	0.322674	−	0.946510i	$-0.395418\pi$
$673$	6.03084	+	1.28189i	0.232472	+	0.0494134i	−0.0902026	+	0.995923i	$0.528751\pi$
$674$	3.74792			0.144364
$675$	21.1254	−	15.1234i	0.813117	−	0.582101i
$676$	13.0257			0.500990
$677$	14.2930	+	3.03808i	0.549326	+	0.116763i	0.474210	−	0.880412i	$-0.342734\pi$
$677$	14.2930	+	3.03808i	0.549326	+	0.116763i	0.0751165	+	0.997175i	$0.476067\pi$
$678$	6.97502	−	8.00183i	0.267874	−	0.307309i
$679$	−1.69175	−	0.753215i	−0.0649233	−	0.0289057i
$680$	−24.2564	+	31.5160i	−0.930192	+	1.20858i
$681$	32.6839	−	24.5594i	1.25245	−	0.941119i
$682$	2.93263	−	5.07946i	0.112296	−	0.194503i
$683$	16.7839	+	12.1942i	0.642217	+	0.466598i	0.860611	−	0.509263i	$-0.170082\pi$
$683$	16.7839	+	12.1942i	0.642217	+	0.466598i	−0.218394	+	0.975861i	$0.570082\pi$
$684$	−15.6757	+	12.1786i	−0.599375	+	0.465662i
$685$	−4.59300	+	19.0086i	−0.175490	+	0.726282i
$686$	9.30951	+	1.97880i	0.355439	+	0.0755509i
$687$	−24.6722	+	11.4640i	−0.941301	+	0.437378i
$688$	7.37005	−	1.56655i	0.280981	−	0.0597243i
$689$	−6.95218	+	7.72118i	−0.264857	+	0.294153i
$690$	22.6825	−	12.7487i	0.863508	−	0.485335i
$691$	17.5081	+	19.4447i	0.666040	+	0.739713i	0.977590	−	0.210517i	$-0.0675148\pi$
$691$	17.5081	+	19.4447i	0.666040	+	0.739713i	−0.311550	+	0.950230i	$0.600848\pi$
$692$	−17.0671	−	12.4000i	−0.648793	−	0.471376i
$693$	−6.84949	−	4.64721i	−0.260191	−	0.176533i
$694$	−6.15055	−	4.46863i	−0.233472	−	0.169627i
$695$	−41.9498	−	5.58527i	−1.59125	−	0.211861i
$696$	−1.36698	−	3.98761i	−0.0518152	−	0.151150i
$697$	−33.7818	−	15.0406i	−1.27958	−	0.569705i
$698$	−7.30429	+	8.11223i	−0.276471	+	0.307053i
$699$	−3.18614	+	0.731013i	−0.120511	+	0.0276495i
$700$	1.73076	+	6.53575i	0.0654166	+	0.247028i
$701$	−24.6481			−0.930945			−0.465472	−	0.885062i	$-0.654116\pi$
$701$	−24.6481			−0.930945			−0.465472	+	0.885062i	$0.654116\pi$
$702$	−6.47541	−	4.24286i	−0.244399	−	0.160136i
$703$	9.76234	−	7.09275i	0.368193	−	0.267508i
$704$	−0.838683	−	7.97954i	−0.0316091	−	0.300740i
$705$	0.179512	−	15.5405i	0.00676080	−	0.585289i
$706$	−2.02074	+	19.2260i	−0.0760515	+	0.723582i
$707$	3.44915	+	5.97411i	0.129719	+	0.224679i
$708$	9.42420	−	7.08156i	0.354183	−	0.266141i
$709$	−18.3812	−	20.4144i	−0.690321	−	0.766680i	0.291483	−	0.956576i	$-0.405851\pi$
$709$	−18.3812	−	20.4144i	−0.690321	−	0.766680i	−0.981804	+	0.189897i	$0.939185\pi$
$710$	−0.225181	−	0.138445i	−0.00845091	−	0.00519575i
$711$	−12.3227	+	3.03679i	−0.462136	+	0.113889i
$712$	−13.8721	+	42.6938i	−0.519878	+	1.60002i
$713$	−15.6646	−	17.3973i	−0.586645	−	0.651535i
$714$	−4.17520	+	7.50815i	−0.156253	+	0.280985i
$715$	−7.14588	−	10.4300i	−0.267241	−	0.390059i
$716$	37.0087	−	7.86644i	1.38308	−	0.293983i
$717$	0.299194	+	2.46445i	0.0111736	+	0.0920367i
$718$	−7.83774	+	13.5754i	−0.292502	+	0.506628i
$719$	29.6588	+	21.5483i	1.10609	+	0.803618i	0.982043	−	0.188659i	$-0.0604141\pi$
$719$	29.6588	+	21.5483i	1.10609	+	0.803618i	0.124042	+	0.992277i	$0.460414\pi$
$720$	−5.66504	−	0.569417i	−0.211124	−	0.0212209i
$721$	13.6851	−	9.94284i	0.509661	−	0.370291i
$722$	−0.220162	−	2.09470i	−0.00819358	−	0.0779567i
$723$	18.9693	−	0.305295i	0.705476	−	0.0113540i
$724$	−14.0514	−	24.3378i	−0.522218	−	0.904508i
$725$	4.50526	+	1.22133i	0.167321	+	0.0453589i
$726$	3.37796	−	0.775023i	0.125368	−	0.0287638i
$727$	−9.30118	−	1.97703i	−0.344962	−	0.0733239i	0.0321730	−	0.999482i	$-0.489757\pi$
$727$	−9.30118	−	1.97703i	−0.344962	−	0.0733239i	−0.377135	+	0.926158i	$0.623091\pi$
$728$	3.92800	−	2.85386i	0.145581	−	0.105771i
$729$	10.7802	+	24.7546i	0.399266	+	0.916835i
$730$	13.0209	−	11.0880i	0.481925	−	0.410385i
$731$	−55.3291	+	24.6341i	−2.04642	+	0.911126i
$732$	−26.9032	+	6.17256i	−0.994372	+	0.228144i
$733$	−1.05311	+	10.0197i	−0.0388976	+	0.370086i	0.957707	+	0.287746i	$0.0929059\pi$
$733$	−1.05311	+	10.0197i	−0.0388976	+	0.370086i	−0.996604	+	0.0823398i	$0.973761\pi$
$734$	−21.4747	+	4.56460i	−0.792647	+	0.168482i
$735$	−9.34577	−	21.6609i	−0.344724	−	0.798974i
$736$	−50.5054	−	10.7353i	−1.86166	−	0.395707i
$737$	3.31138	−	10.1914i	0.121976	−	0.375404i
$738$	1.69241	+	12.2846i	0.0622984	+	0.452201i
$739$	−5.85917	−	18.0327i	−0.215533	−	0.663342i	−0.999115	−	0.0420544i	$-0.986610\pi$
$739$	−5.85917	−	18.0327i	−0.215533	−	0.663342i	0.783582	−	0.621288i	$-0.213390\pi$
$740$	8.13246	+	1.08277i	0.298955	+	0.0398034i
$741$	−14.3154	+	6.65170i	−0.525890	+	0.244356i
$742$	0.404151	−	3.84524i	0.0148368	−	0.141163i
$743$	−10.9750	−	19.0092i	−0.402633	−	0.697381i	0.591410	−	0.806371i	$-0.298572\pi$
$743$	−10.9750	−	19.0092i	−0.402633	−	0.697381i	−0.994043	+	0.108990i	$0.965238\pi$
$744$	−1.44612	−	11.9116i	−0.0530173	−	0.436702i
$745$	5.87066	−	12.2619i	0.215084	−	0.449240i
$746$	−7.04928	+	5.12160i	−0.258092	+	0.187515i
$747$	5.22402	+	8.41103i	0.191137	+	0.307743i
$748$	−8.65462	−	26.6362i	−0.316444	−	0.973915i
$749$	−0.567947	+	0.983714i	−0.0207523	+	0.0359441i
$750$	−9.45896	+	11.3411i	−0.345393	+	0.414119i
$751$	−6.43136	−	11.1394i	−0.234684	−	0.406484i	0.724497	−	0.689278i	$-0.242072\pi$
$751$	−6.43136	−	11.1394i	−0.234684	−	0.406484i	−0.959181	+	0.282794i	$0.908739\pi$
$752$	−2.27897	+	2.53105i	−0.0831055	+	0.0922980i
$753$	10.6364	−	12.2022i	0.387611	−	0.444672i
$754$	−0.145390	−	1.38329i	−0.00529478	−	0.0503764i
$755$	−21.0176	+	1.62317i	−0.764908	+	0.0590733i
$756$	−7.01809	+	0.339085i	−0.255245	+	0.0123324i
$757$	−3.01935			−0.109740			−0.0548701	−	0.998494i	$-0.517474\pi$
$757$	−3.01935			−0.109740			−0.0548701	+	0.998494i	$0.517474\pi$
$758$	−2.50021	+	1.11317i	−0.0908118	+	0.0404320i
$759$	−3.90871	+	43.9874i	−0.141877	+	1.59664i
$760$	16.5858	−	21.5497i	0.601632	−	0.781691i
$761$	28.0099	−	31.1081i	1.01536	−	1.12767i	0.0235764	−	0.999722i	$-0.492495\pi$
$761$	28.0099	−	31.1081i	1.01536	−	1.12767i	0.991781	−	0.127947i	$-0.0408386\pi$
$762$	15.7513	+	11.0612i	0.570610	+	0.400703i
$763$	1.23331	+	1.36972i	0.0446486	+	0.0495873i
$764$	5.26338	+	16.1990i	0.190422	+	0.586060i
$765$	45.4931	−	4.99054i	1.64481	−	0.180433i
$766$	1.20666	−	3.71373i	0.0435985	−	0.134183i
$767$	8.56370	−	3.81280i	0.309217	−	0.137672i
$768$	−15.1828	−	16.3260i	−0.547861	−	0.589114i
$769$	−4.91139	+	46.7288i	−0.177109	+	1.68508i	0.439837	+	0.898077i	$0.355036\pi$
$769$	−4.91139	+	46.7288i	−0.177109	+	1.68508i	−0.616947	+	0.787005i	$0.711631\pi$
$770$	4.43275	+	1.57703i	0.159745	+	0.0568320i
$771$	−10.6121	−	2.07778i	−0.382187	−	0.0748293i
$772$	−3.76288	−	35.8014i	−0.135429	−	1.28852i
$773$	8.38597	+	25.8093i	0.301622	+	0.928298i	0.980916	+	0.194431i	$0.0622862\pi$
$773$	8.38597	+	25.8093i	0.301622	+	0.928298i	−0.679294	+	0.733866i	$0.737714\pi$
$774$	16.8069	+	11.4031i	0.604112	+	0.409875i
$775$	11.8211	+	6.06681i	0.424627	+	0.217926i
$776$	−2.53202	+	4.38559i	−0.0908943	+	0.157434i
$777$	4.27062	−	0.0687320i	0.153208	−	0.00246575i
$778$	21.5286	+	9.58514i	0.771837	+	0.343644i
$779$	23.0990	+	10.2844i	0.827609	+	0.368475i
$780$	−10.1681	−	3.43416i	−0.364076	−	0.122962i
$781$	0.409846	−	0.182475i	0.0146654	−	0.00652948i
$782$	45.8346			1.63904
$783$	−2.21993	+	4.31324i	−0.0793337	+	0.154143i
$784$	−1.59758	+	4.91685i	−0.0570565	+	0.175602i
$785$	19.8912	−	41.5463i	0.709949	−	1.48285i
$786$	−9.21277	−	15.3800i	−0.328609	−	0.548586i
$787$	8.70721	−	1.85077i	0.310378	−	0.0659730i	−0.0500890	−	0.998745i	$-0.515951\pi$
$787$	8.70721	−	1.85077i	0.310378	−	0.0659730i	0.360467	+	0.932772i	$0.382617\pi$
$788$	2.36015	−	0.501665i	0.0840768	−	0.0178711i
$789$	3.22454	−	0.0518962i	0.114797	−	0.00184755i
$790$	6.34482	−	3.43294i	0.225738	−	0.122139i
$791$	2.36744	−	7.28623i	0.0841765	−	0.259069i
$792$	−14.5965	+	17.2996i	−0.518663	+	0.614713i
$793$	−21.9495			−0.779449
$794$	4.44198	−	1.97770i	0.157640	−	0.0701858i
$795$	−17.9556	+	10.0919i	−0.636818	+	0.357924i
$796$	8.44696	+	3.76083i	0.299395	+	0.133299i
$797$	34.5778	+	15.3950i	1.22481	+	0.545320i	0.914217	−	0.405224i	$-0.132807\pi$
$797$	34.5778	+	15.3950i	1.22481	+	0.545320i	0.310590	+	0.950544i	$0.399473\pi$
$798$	2.85488	−	5.13386i	0.101062	−	0.181737i
$799$	13.6885	−	23.7091i	0.484264	−	0.838769i
$800$	28.9582	−	4.49968i	1.02383	−	0.159088i
$801$	46.4926	−	22.5196i	1.64274	−	0.795690i
$802$	−4.22368	−	12.9992i	−0.149143	−	0.459016i
$803$	3.03405	+	28.8670i	0.107069	+	1.01869i
$804$	−2.94978	−	8.60480i	−0.104031	−	0.303468i
$805$	11.4538	−	14.8817i	0.403693	−	0.524512i
$806$	0.413850	−	3.93752i	0.0145772	−	0.138693i
$807$	8.12561	−	1.86430i	0.286035	−	0.0656266i
$808$	17.2331	−	7.67269i	0.606260	−	0.269924i
$809$	5.78411	−	17.8016i	0.203358	−	0.625873i	−0.796418	−	0.604746i	$-0.793275\pi$
$809$	5.78411	−	17.8016i	0.203358	−	0.625873i	0.999777	−	0.0211267i	$-0.00672534\pi$
$810$	−9.47076	−	12.0766i	−0.332769	−	0.424330i
$811$	13.0270	+	40.0931i	0.457441	+	1.40786i	0.868245	+	0.496135i	$0.165248\pi$
$811$	13.0270	+	40.0931i	0.457441	+	1.40786i	−0.410804	+	0.911723i	$0.634752\pi$
$812$	−0.844700	−	0.938134i	−0.0296432	−	0.0329221i
$813$	3.49435	−	39.3243i	0.122552	−	1.37916i
$814$	3.82022	−	4.24278i	0.133899	−	0.148709i
$815$	22.3585	−	6.58731i	0.783184	−	0.230743i
$816$	−8.20781	−	5.76383i	−0.287331	−	0.201774i
$817$	37.8325	−	16.8441i	1.32359	−	0.589301i
$818$	−29.3086			−1.02475
$819$	−5.49979	−	0.985200i	−0.192178	−	0.0344257i
$820$	6.55552	+	15.8922i	0.228929	+	0.554979i
$821$	3.02671	+	28.7972i	0.105633	+	1.00503i	0.911043	+	0.412311i	$0.135278\pi$
$821$	3.02671	+	28.7972i	0.105633	+	1.00503i	−0.805410	+	0.592718i	$0.798055\pi$
$822$	11.3366	+	2.21963i	0.395411	+	0.0774185i
$823$	−8.17299	+	9.07702i	−0.284892	+	0.316405i	−0.868557	−	0.495590i	$-0.834952\pi$
$823$	−8.17299	+	9.07702i	−0.284892	+	0.316405i	0.583664	+	0.811995i	$0.301618\pi$
$824$	−23.1288	−	40.0603i	−0.805731	−	1.39557i
$825$	−6.80528	−	24.1227i	−0.236929	−	0.839844i
$826$	−1.74422	+	3.02107i	−0.0606890	+	0.105116i
$827$	5.83473	+	17.9575i	0.202894	+	0.624442i	0.999793	+	0.0203307i	$0.00647191\pi$
$827$	5.83473	+	17.9575i	0.202894	+	0.624442i	−0.796900	+	0.604112i	$0.793528\pi$
$828$	19.7783	+	31.8445i	0.687345	+	1.10667i
$829$	−10.2118	+	7.41933i	−0.354672	+	0.257684i	−0.750826	−	0.660500i	$-0.770344\pi$
$829$	−10.2118	+	7.41933i	−0.354672	+	0.257684i	0.396155	+	0.918184i	$0.370344\pi$
$830$	−4.07680	−	3.88010i	−0.141508	−	0.134680i
$831$	−10.8165	+	8.12777i	−0.375220	+	0.281949i
$832$	−2.70804	−	4.69045i	−0.0938842	−	0.162612i
$833$	4.34383	−	41.3288i	0.150505	−	1.43196i
$834$	−2.21271	+	24.9011i	−0.0766197	+	0.862254i
$835$	−30.4124	+	16.4550i	−1.05247	+	0.569450i
$836$	5.91778	+	18.2131i	0.204671	+	0.629912i
$837$	−8.73356	+	10.6955i	−0.301876	+	0.369690i
$838$	1.24568	−	3.83380i	0.0430312	−	0.132436i
$839$	43.0383	+	9.14808i	1.48585	+	0.315827i	0.878167	−	0.478354i	$-0.158766\pi$
$839$	43.0383	+	9.14808i	1.48585	+	0.315827i	0.607681	+	0.794181i	$0.292100\pi$
$840$	9.18796	−	2.86845i	0.317015	−	0.0989709i
$841$	27.5138	−	5.84823i	0.948751	−	0.201663i
$842$	2.15967	−	20.5479i	0.0744272	−	0.708127i
$843$	−0.802571	+	2.61238i	−0.0276420	+	0.0899750i
$844$	−10.3396	+	4.60348i	−0.355903	+	0.158458i
$845$	17.4928	+	10.7548i	0.601770	+	0.369977i
$846$	−9.17592	+	0.295434i	−0.315475	+	0.0101572i
$847$	2.02360	−	1.47023i	0.0695317	−	0.0505177i
$848$	4.41519	+	0.938477i	0.151618	+	0.0322274i
$849$	−9.15803	−	9.84761i	−0.314303	−	0.337969i
$850$	−24.3136	+	9.25157i	−0.833951	+	0.317326i
$851$	−11.3938	−	19.7347i	−0.390575	−	0.676496i
$852$	0.185083	−	0.332830i	0.00634085	−	0.0114026i
$853$	5.01106	+	47.6771i	0.171576	+	1.63243i	0.654000	+	0.756494i	$0.273090\pi$
$853$	5.01106	+	47.6771i	0.171576	+	1.63243i	−0.482425	+	0.875938i	$0.660244\pi$
$854$	6.60816	−	4.80111i	0.226127	−	0.164291i
$855$	−31.1069	+	3.41239i	−1.06383	+	0.116701i
$856$	2.51297	+	1.82578i	0.0858916	+	0.0624039i
$857$	−12.6888	+	21.9776i	−0.433440	+	0.750741i	−0.997167	−	0.0752208i	$-0.976034\pi$
$857$	−12.6888	+	21.9776i	−0.433440	+	0.750741i	0.563727	+	0.825961i	$0.309367\pi$
$858$	−5.97074	+	4.48655i	−0.203838	+	0.153168i
$859$	8.22330	−	1.74792i	0.280575	−	0.0596382i	−0.0654745	−	0.997854i	$-0.520856\pi$
$859$	8.22330	−	1.74792i	0.280575	−	0.0596382i	0.346050	+	0.938216i	$0.387523\pi$
$860$	26.5275	+	9.43761i	0.904582	+	0.321820i
$861$	4.59907	+	7.67777i	0.156736	+	0.261658i
$862$	17.6722	+	19.6270i	0.601919	+	0.668499i
$863$	−9.08240	+	27.9528i	−0.309168	+	0.951523i	0.668920	+	0.743334i	$0.266757\pi$
$863$	−9.08240	+	27.9528i	−0.309168	+	0.951523i	−0.978089	+	0.208189i	$0.933243\pi$
$864$	−1.71803	+	30.4069i	−0.0584487	+	1.03446i
$865$	−12.6819	−	30.7440i	−0.431197	−	1.04533i
$866$	4.68749	+	5.20599i	0.159288	+	0.176907i
$867$	47.0784	+	20.0592i	1.59887	+	0.681247i
$868$	−1.79668	−	3.11194i	−0.0609833	−	0.105626i
$869$	−1.27981	+	12.1765i	−0.0434145	+	0.413061i
$870$	0.604410	−	2.69034i	0.0204914	−	0.0912111i
$871$	−0.756105	−	7.19386i	−0.0256197	−	0.243755i
$872$	4.07764	−	2.96258i	0.138086	−	0.100326i
$873$	5.65829	−	1.39443i	0.191504	−	0.0471942i
$874$	−31.3404			−1.06011
$875$	−3.07200	+	10.2061i	−0.103853	+	0.345030i
$876$	16.7794	+	18.0429i	0.566925	+	0.609613i
$877$	−30.6214	+	34.0085i	−1.03401	+	1.14838i	−0.0452341	+	0.998976i	$0.514403\pi$
$877$	−30.6214	+	34.0085i	−1.03401	+	1.14838i	−0.988776	+	0.149408i	$0.952263\pi$
$878$	5.00123	+	2.22669i	0.168783	+	0.0751472i
$879$	17.8660	+	3.49803i	0.602606	+	0.117986i
$880$	−2.37193	+	4.95419i	−0.0799579	+	0.167006i
$881$	22.8783	+	16.6220i	0.770789	+	0.560011i	0.902200	−	0.431317i	$-0.141951\pi$
$881$	22.8783	+	16.6220i	0.770789	+	0.560011i	−0.131412	+	0.991328i	$0.541951\pi$
$882$	−12.5419	+	6.07489i	−0.422307	+	0.204552i
$883$	9.86953	+	7.17063i	0.332136	+	0.241311i	0.741336	−	0.671134i	$-0.234192\pi$
$883$	9.86953	+	7.17063i	0.332136	+	0.241311i	−0.409200	+	0.912445i	$0.634192\pi$
$884$	−12.6502	−	14.0495i	−0.425472	−	0.472535i
$885$	18.5031	−	1.72892i	0.621975	−	0.0581170i
$886$	−12.9413	+	14.3728i	−0.434771	+	0.482862i
$887$	−10.8668	+	2.30982i	−0.364873	+	0.0775561i	−0.386700	−	0.922206i	$-0.626385\pi$
$887$	−10.8668	+	2.30982i	−0.364873	+	0.0775561i	0.0218271	+	0.999762i	$0.493052\pi$
$888$	1.03380	−	11.6341i	0.0346920	−	0.390413i
$889$	13.5876	+	2.88814i	0.455714	+	0.0968651i
$890$	−22.3566	+	19.0378i	−0.749396	+	0.638150i
$891$	25.9936	−	1.67555i	0.870818	−	0.0561330i
$892$	−10.8296	−	7.86813i	−0.362600	−	0.263445i
$893$	−9.35979	+	16.2116i	−0.313214	+	0.542502i
$894$	−7.38802	−	3.14790i	−0.247092	−	0.105281i
$895$	56.1954	+	19.9925i	1.87841	+	0.668274i
$896$	−8.36770	−	3.72554i	−0.279545	−	0.124461i
$897$	9.66672	+	28.1988i	0.322762	+	0.941530i
$898$	5.32566	+	1.13200i	0.177719	+	0.0377754i
$899$	−2.48088			−0.0827421
$900$	−16.9194	−	12.9002i	−0.563980	−	0.430005i
$901$	−36.2829			−1.20876
$902$	11.7017	+	2.48728i	0.389624	+	0.0828172i
$903$	14.3852	+	2.81652i	0.478711	+	0.0937281i
$904$	−19.1390	−	8.52122i	−0.636553	−	0.283412i
$905$	1.22453	−	44.2859i	0.0407047	−	1.47211i
$906$	1.50076	+	12.3617i	0.0498593	+	0.410690i
$907$	20.6216	−	35.7176i	0.684728	−	1.18598i	−0.288794	−	0.957391i	$-0.593254\pi$
$907$	20.6216	−	35.7176i	0.684728	−	1.18598i	0.973522	−	0.228593i	$-0.0734125\pi$
$908$	−27.0858	−	19.6790i	−0.898874	−	0.653070i
$909$	−20.1053	−	8.18680i	−0.666852	−	0.271539i
$910$	3.16652	−	0.244548i	0.104969	−	0.00810670i
$911$	11.7894	+	2.50591i	0.390600	+	0.0830245i	0.399025	−	0.916940i	$-0.369349\pi$
$911$	11.7894	+	2.50591i	0.390600	+	0.0830245i	−0.00842543	+	0.999965i	$0.502682\pi$
$912$	5.61227	+	3.94114i	0.185841	+	0.130504i
$913$	9.34328	−	1.98598i	0.309218	−	0.0657262i
$914$	18.2588	−	20.2785i	0.603948	−	0.670752i
$915$	−41.2258	−	13.9235i	−1.36288	−	0.460298i
$916$	14.9077	+	16.5567i	0.492565	+	0.547049i
$917$	−10.4681	−	7.60549i	−0.345686	−	0.251155i
$918$	−4.12016	−	26.7191i	−0.135986	−	0.881860i
$919$	31.2727	+	22.7209i	1.03159	+	0.749494i	0.968626	−	0.248522i	$-0.0799448\pi$
$919$	31.2727	+	22.7209i	1.03159	+	0.749494i	0.0629636	+	0.998016i	$0.479945\pi$
$920$	−37.1985	−	35.4036i	−1.22640	−	1.16722i
$921$	3.41665	−	3.91962i	0.112582	−	0.129156i
$922$	−10.6133	−	4.72536i	−0.349532	−	0.155622i
$923$	0.202639	−	0.225053i	0.00666994	−	0.00740771i
$924$	−1.99063	+	6.47952i	−0.0654870	+	0.213161i
$925$	10.0274	+	8.16874i	0.329699	+	0.268586i
$926$	−18.9531			−0.622839
$927$	−14.8120	+	51.1299i	−0.486489	+	1.67933i
$928$	−4.42678	+	3.21625i	−0.145316	+	0.105578i
$929$	4.76162	+	45.3038i	0.156224	+	1.48637i	0.738983	+	0.673724i	$0.235306\pi$
$929$	4.76162	+	45.3038i	0.156224	+	1.48637i	−0.582759	+	0.812645i	$0.698027\pi$
$930$	3.27504	−	7.13297i	0.107393	−	0.233899i
$931$	−2.97019	+	28.2595i	−0.0973440	+	0.926167i
$932$	1.33850	+	2.31835i	0.0438440	+	0.0759401i
$933$	2.92499	+	24.0930i	0.0957597	+	0.788771i
$934$	13.3497	+	14.8264i	0.436816	+	0.485133i
$935$	10.3698	−	42.9165i	0.339129	−	1.40352i
$936$	−4.25143	+	14.6757i	−0.138962	+	0.479689i
$937$	−10.9573	+	33.7230i	−0.357958	+	1.10168i	0.596316	+	0.802750i	$0.296630\pi$
$937$	−10.9573	+	33.7230i	−0.357958	+	1.10168i	−0.954274	+	0.298932i	$0.903370\pi$
$938$	1.80118	+	2.00041i	0.0588107	+	0.0653159i
$939$	−9.61933	+	0.154815i	−0.313915	+	0.00505219i
$940$	−12.2085	+	3.59690i	−0.398197	+	0.117318i
$941$	−19.6924	+	4.18575i	−0.641954	+	0.136452i	−0.517376	−	0.855758i	$-0.673091\pi$
$941$	−19.6924	+	4.18575i	−0.641954	+	0.136452i	−0.124578	+	0.992210i	$0.539758\pi$
$942$	−25.0324	−	10.6659i	−0.815601	−	0.347512i
$943$	23.8747	−	41.3521i	0.777466	−	1.34661i
$944$	−3.29476	−	2.39378i	−0.107235	−	0.0779109i
$945$	−9.70483	−	5.33918i	−0.315698	−	0.173684i
$946$	15.8516	−	11.5169i	0.515380	−	0.374446i
$947$	2.53012	+	24.0725i	0.0822179	+	0.782251i	0.955491	+	0.295020i	$0.0953263\pi$
$947$	2.53012	+	24.0725i	0.0822179	+	0.782251i	−0.873273	+	0.487231i	$0.838007\pi$
$948$	5.34079	+	8.91602i	0.173461	+	0.289579i
$949$	9.79667	+	16.9683i	0.318013	+	0.550815i
$950$	16.6250	−	6.32596i	0.539385	−	0.205241i
$951$	2.31157	−	7.52417i	0.0749578	−	0.243988i
$952$	16.5848	+	3.52521i	0.537517	+	0.114253i
$953$	−14.5798	+	10.5929i	−0.472287	+	0.343137i	−0.798332	−	0.602218i	$-0.794284\pi$
$953$	−14.5798	+	10.5929i	−0.472287	+	0.343137i	0.326045	+	0.945354i	$0.394284\pi$
$954$	6.41955	+	10.3359i	0.207840	+	0.334637i
$955$	−6.30648	+	26.1001i	−0.204073	+	0.844578i
$956$	1.85726	−	0.826904i	0.0600680	−	0.0267440i
$957$	3.18700	+	3.42697i	0.103021	+	0.110778i
$958$	0.766909	−	7.29665i	0.0247777	−	0.235744i
$959$	8.15512	−	1.73342i	0.263343	−	0.0559752i
$960$	−2.11090	−	10.5275i	−0.0681291	−	0.339774i
$961$	23.4151	+	4.97703i	0.755325	+	0.160549i
$962$	1.19091	−	3.66526i	0.0383966	−	0.118173i
$963$	−0.487847	−	3.54110i	−0.0157206	−	0.114110i
$964$	−4.80103	−	14.7760i	−0.154631	−	0.475904i
$965$	24.5065	−	51.1859i	0.788891	−	1.64773i
$966$	−9.07833	−	6.37514i	−0.292091	−	0.205117i
$967$	3.80122	−	36.1662i	0.122239	−	1.16303i	−0.745675	−	0.666310i	$-0.767873\pi$
$967$	3.80122	−	36.1662i	0.122239	−	1.16303i	0.867913	−	0.496715i	$-0.165461\pi$
$968$	−3.42002	−	5.92365i	−0.109924	−	0.190393i
$969$	−50.7132	−	21.6079i	−1.62914	−	0.694147i
$970$	−2.91340	+	1.57633i	−0.0935436	+	0.0506129i
$971$	46.1160	−	33.5052i	1.47993	−	1.07523i	0.502354	−	0.864662i	$-0.332467\pi$
$971$	46.1160	−	33.5052i	1.47993	−	1.07523i	0.977578	−	0.210572i	$-0.0675327\pi$
$972$	16.7856	−	14.3922i	0.538400	−	0.461631i
$973$	5.57547	+	17.1595i	0.178741	+	0.550109i
$974$	−15.0373	+	26.0453i	−0.481825	+	0.834545i
$975$	−10.8197	−	13.0072i	−0.346507	−	0.416565i
$976$	4.76792	+	8.25828i	0.152617	+	0.264341i
$977$	−10.3645	+	11.5109i	−0.331588	+	0.368266i	−0.885766	−	0.464132i	$-0.846366\pi$
$977$	−10.3645	+	11.5109i	−0.331588	+	0.368266i	0.554177	+	0.832399i	$0.313033\pi$
$978$	−4.46499	−	13.0248i	−0.142775	−	0.416488i
$979$	−5.20939	−	49.5640i	−0.166493	−	1.58407i
$980$	−14.7088	+	12.5254i	−0.469857	+	0.400108i
$981$	−5.70931	−	1.02273i	−0.182284	−	0.0326533i
$982$	7.42689			0.237001
$983$	−14.3663	+	6.39631i	−0.458215	+	0.204011i	−0.622846	−	0.782345i	$-0.714024\pi$
$983$	−14.3663	+	6.39631i	−0.458215	+	0.204011i	0.164630	+	0.986355i	$0.447357\pi$
$984$	22.1951	−	10.3130i	0.707555	−	0.328767i
$985$	3.58374	+	1.27497i	0.114187	+	0.0406240i
$986$	3.25014	−	3.60964i	0.103505	−	0.114954i
$987$	−6.00894	+	2.79207i	−0.191267	+	0.0888726i
$988$	8.64985	+	9.60663i	0.275188	+	0.305628i
$989$	−24.1669	−	74.3780i	−0.768462	−	2.36508i
$990$	−14.0603	+	4.63919i	−0.446867	+	0.147443i
$991$	6.23054	−	19.1756i	0.197920	−	0.609134i	−0.802010	−	0.597310i	$-0.796236\pi$
$991$	6.23054	−	19.1756i	0.197920	−	0.609134i	0.999930	−	0.0118242i	$-0.00376384\pi$
$992$	−14.2289	+	6.33510i	−0.451767	+	0.201140i
$993$	2.95092	−	9.60526i	0.0936446	−	0.304814i
$994$	−0.0117800	+	0.112079i	−0.000373639	+	0.00355493i
$995$	8.23859	+	12.0249i	0.261181	+	0.381214i
$996$	5.32792	−	6.11226i	0.168822	−	0.193674i
$997$	4.26567	+	40.5852i	0.135095	+	1.28534i	0.826525	+	0.562901i	$0.190315\pi$
$997$	4.26567	+	40.5852i	0.135095	+	1.28534i	−0.691429	+	0.722444i	$0.743019\pi$
$998$	2.06306	+	6.34944i	0.0653050	+	0.200988i
$999$	−10.4800	+	8.41596i	−0.331573	+	0.266269i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.106.12	yes	224
3.2	odd	2		675.2.r.a.181.17		224
9.4	even	3	inner	225.2.q.a.31.17	✓	224
9.5	odd	6		675.2.r.a.631.12		224
25.21	even	5	inner	225.2.q.a.196.17	yes	224
75.71	odd	10		675.2.r.a.46.12		224
225.121	even	15	inner	225.2.q.a.121.12	yes	224
225.221	odd	30		675.2.r.a.496.17		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.17	✓	224	9.4	even	3	inner
225.2.q.a.106.12	yes	224	1.1	even	1	trivial
225.2.q.a.121.12	yes	224	225.121	even	15	inner
225.2.q.a.196.17	yes	224	25.21	even	5	inner
675.2.r.a.46.12		224	75.71	odd	10
675.2.r.a.181.17		224	3.2	odd	2
675.2.r.a.496.17		224	225.221	odd	30
675.2.r.a.631.12		224	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.745950 - 0.158557i) q^{2} +(1.13811 - 1.30565i) q^{3} +(-1.29579 - 0.576923i) q^{4} +(-1.26382 - 1.84465i) q^{5} +(-1.05599 + 0.793494i) q^{6} +(-0.476660 + 0.825599i) q^{7} +(2.10906 + 1.53232i) q^{8} +(-0.409434 - 2.97193i) q^{9} +(0.650268 + 1.57641i) q^{10} +(-2.83092 - 0.601732i) q^{11} +(-2.22800 + 1.03525i) q^{12} +(-1.91095 + 0.406185i) q^{13} +(0.486468 - 0.540278i) q^{14} +(-3.84683 - 0.449300i) q^{15} +(0.567924 + 0.630744i) q^{16} +(-5.51944 - 4.01011i) q^{17} +(-0.165802 + 2.28183i) q^{18} +(3.77403 + 2.74200i) q^{19} +(0.573428 + 3.11941i) q^{20} +(0.535453 + 1.56197i) q^{21} +(2.01632 + 0.897723i) q^{22} +(5.89471 - 6.54674i) q^{23} +(4.40100 - 1.00975i) q^{24} +(-1.80550 + 4.66264i) q^{25} +1.48988 q^{26} +(-4.34627 - 2.84779i) q^{27} +(1.09396 - 0.794807i) q^{28} +(-0.0975850 - 0.928459i) q^{29} +(2.79831 + 0.945095i) q^{30} +(0.277775 - 2.64285i) q^{31} +(-2.93057 - 5.07590i) q^{32} +(-4.00754 + 3.01136i) q^{33} +(3.48139 + 3.86648i) q^{34} +(2.12536 - 0.164140i) q^{35} +(-1.18403 + 4.08721i) q^{36} +(0.799338 - 2.46011i) q^{37} +(-2.38048 - 2.64379i) q^{38} +(-1.64453 + 2.95731i) q^{39} +(0.161121 - 5.82706i) q^{40} +(5.30176 - 1.12692i) q^{41} +(-0.151761 - 1.25005i) q^{42} +(4.43871 - 7.68807i) q^{43} +(3.32113 + 2.41294i) q^{44} +(-4.96473 + 4.51126i) q^{45} +(-5.43519 + 3.94889i) q^{46} +(0.419452 + 3.99082i) q^{47} +(1.46989 - 0.0236566i) q^{48} +(3.04559 + 5.27512i) q^{49} +(2.08610 - 3.19182i) q^{50} +(-11.5175 + 2.64252i) q^{51} +(2.71053 + 0.576140i) q^{52} +(4.30252 - 3.12596i) q^{53} +(2.79057 + 2.81344i) q^{54} +(2.46781 + 5.98256i) q^{55} +(-2.27038 + 1.01084i) q^{56} +(7.87533 - 1.80688i) q^{57} +(-0.0744198 + 0.708057i) q^{58} +(-4.69343 + 0.997620i) q^{59} +(4.72548 + 2.80152i) q^{60} +(10.9896 + 2.33592i) q^{61} +(-0.626247 + 1.92739i) q^{62} +(2.64878 + 1.07857i) q^{63} +(0.856686 + 2.63661i) q^{64} +(3.16438 + 3.01170i) q^{65} +(3.46689 - 1.61090i) q^{66} +(-0.387024 + 3.68228i) q^{67} +(4.83851 + 8.38055i) q^{68} +(-1.83894 - 15.1473i) q^{69} +(-1.61144 - 0.214549i) q^{70} +(-0.125408 + 0.0911140i) q^{71} +(3.69042 - 6.89535i) q^{72} +(-3.09917 - 9.53828i) q^{73} +(-0.986332 + 1.70838i) q^{74} +(4.03292 + 7.66391i) q^{75} +(-3.30843 - 5.73038i) q^{76} +(1.84618 - 2.05039i) q^{77} +(1.69564 - 1.94525i) q^{78} +(-0.442202 - 4.20727i) q^{79} +(0.445747 - 1.84477i) q^{80} +(-8.66473 + 2.43362i) q^{81} -4.13353 q^{82} +(-3.01510 + 1.34241i) q^{83} +(0.207301 - 2.33290i) q^{84} +(-0.421657 + 15.2495i) q^{85} +(-4.53005 + 5.03113i) q^{86} +(-1.32330 - 0.929272i) q^{87} +(-5.04853 - 5.60696i) q^{88} +(5.32122 + 16.3770i) q^{89} +(4.41873 - 2.57798i) q^{90} +(0.575527 - 1.77129i) q^{91} +(-11.4153 + 5.08241i) q^{92} +(-3.13449 - 3.37051i) q^{93} +(0.319881 - 3.04346i) q^{94} +(0.288317 - 10.4272i) q^{95} +(-9.96263 - 1.95061i) q^{96} +(0.203049 + 1.93189i) q^{97} +(-1.43545 - 4.41787i) q^{98} +(-0.629227 + 8.65968i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20}+ \cdots - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more