LMFDB - Embedded newform 252.2.bj.b.103.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(103,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 5]))

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

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

chi := DirichletCharacter("252.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.bj (of order $6$, degree $2$, 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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			103.24
Character	$\chi$	$=$	252.103
Dual form			252.2.bj.b.115.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.248495 + 1.39221i) q^{2} +(1.22260 - 1.22689i) q^{3} +(-1.87650 + 0.691915i) q^{4} +(0.705906 - 0.407555i) q^{5} +(2.01189 + 1.39724i) q^{6} +(2.03393 + 1.69208i) q^{7} +(-1.42959 - 2.44055i) q^{8} +(-0.0104958 - 2.99998i) q^{9} +O(q^{10})$	\(q+(0.248495 + 1.39221i) q^{2} +(1.22260 - 1.22689i) q^{3} +(-1.87650 + 0.691915i) q^{4} +(0.705906 - 0.407555i) q^{5} +(2.01189 + 1.39724i) q^{6} +(2.03393 + 1.69208i) q^{7} +(-1.42959 - 2.44055i) q^{8} +(-0.0104958 - 2.99998i) q^{9} +(0.742817 + 0.881495i) q^{10} +(4.17670 + 2.41142i) q^{11} +(-1.44531 + 3.14819i) q^{12} +(-2.20303 - 1.27192i) q^{13} +(-1.85031 + 3.25213i) q^{14} +(0.363018 - 1.36434i) q^{15} +(3.04251 - 2.59676i) q^{16} +(-0.503257 + 0.290555i) q^{17} +(4.17400 - 0.760093i) q^{18} +(-2.24125 + 3.88195i) q^{19} +(-1.04264 + 1.25320i) q^{20} +(4.56267 - 0.426661i) q^{21} +(-2.31931 + 6.41407i) q^{22} +(5.60853 - 3.23809i) q^{23} +(-4.74209 - 1.22987i) q^{24} +(-2.16780 + 3.75474i) q^{25} +(1.22334 - 3.38315i) q^{26} +(-3.69347 - 3.65490i) q^{27} +(-4.98744 - 1.76788i) q^{28} +(-3.16210 - 5.47692i) q^{29} +(1.98966 + 0.166365i) q^{30} -9.62438 q^{31} +(4.37128 + 3.59053i) q^{32} +(8.06497 - 2.17613i) q^{33} +(-0.529571 - 0.628438i) q^{34} +(2.12538 + 0.365511i) q^{35} +(2.09543 + 5.62220i) q^{36} +(1.62993 - 2.82313i) q^{37} +(-5.96144 - 2.15564i) q^{38} +(-4.25393 + 1.14782i) q^{39} +(-2.00382 - 1.14016i) q^{40} +(-3.04709 - 1.75924i) q^{41} +(1.72780 + 6.24617i) q^{42} +(-4.72260 + 2.72659i) q^{43} +(-9.50608 - 1.63511i) q^{44} +(-1.23007 - 2.11343i) q^{45} +(5.90179 + 7.00361i) q^{46} -9.58038 q^{47} +(0.533848 - 6.90760i) q^{48} +(1.27373 + 6.88314i) q^{49} +(-5.76607 - 2.08500i) q^{50} +(-0.258804 + 0.972672i) q^{51} +(5.01405 + 0.862450i) q^{52} +(-1.09484 - 1.89632i) q^{53} +(4.17058 - 6.05031i) q^{54} +3.93115 q^{55} +(1.22191 - 7.38288i) q^{56} +(2.02256 + 7.49583i) q^{57} +(6.83926 - 5.76330i) q^{58} +11.2058 q^{59} +(0.262806 + 2.81137i) q^{60} -7.24771i q^{61} +(-2.39161 - 13.3992i) q^{62} +(5.05486 - 6.11951i) q^{63} +(-3.91253 + 6.97797i) q^{64} -2.07351 q^{65} +(5.03374 + 10.6874i) q^{66} -5.02059i q^{67} +(0.743322 - 0.893438i) q^{68} +(2.88423 - 10.8399i) q^{69} +(0.0192776 + 3.04980i) q^{70} -3.64207i q^{71} +(-7.30659 + 4.31437i) q^{72} +(2.26126 - 1.30554i) q^{73} +(4.33542 + 1.56768i) q^{74} +(1.95628 + 7.25018i) q^{75} +(1.51972 - 8.83524i) q^{76} +(4.41480 + 11.9720i) q^{77} +(-2.65508 - 5.63714i) q^{78} +10.1419i q^{79} +(1.08940 - 3.07306i) q^{80} +(-8.99978 + 0.0629746i) q^{81} +(1.69204 - 4.67935i) q^{82} +(-0.820993 - 1.42200i) q^{83} +(-8.26664 + 3.95761i) q^{84} +(-0.236835 + 0.410210i) q^{85} +(-4.96954 - 5.89731i) q^{86} +(-10.5855 - 2.81655i) q^{87} +(-0.0857994 - 13.6408i) q^{88} +(-1.90724 - 1.10115i) q^{89} +(2.63667 - 2.23769i) q^{90} +(-2.32862 - 6.31470i) q^{91} +(-8.28393 + 9.95690i) q^{92} +(-11.7668 + 11.8080i) q^{93} +(-2.38068 - 13.3379i) q^{94} +3.65373i q^{95} +(9.74950 - 0.973278i) q^{96} +(-6.14759 + 3.54931i) q^{97} +(-9.26626 + 3.48373i) q^{98} +(7.19038 - 12.5553i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 2 q^{2} - 2 q^{4} + 6 q^{5} - 16 q^{8} + 4 q^{9}+O(q^{10}) $ 84 * q + 2 * q^2 - 2 * q^4 + 6 * q^5 - 16 * q^8 + 4 * q^9	$ 84 q + 2 q^{2} - 2 q^{4} + 6 q^{5} - 16 q^{8} + 4 q^{9} - 18 q^{10} - 6 q^{12} + 18 q^{13} + 14 q^{14} + 14 q^{16} + 6 q^{17} - 10 q^{18} - 24 q^{20} + 4 q^{21} + 6 q^{22} - 6 q^{24} + 16 q^{25} - 30 q^{26} - 4 q^{28} + 10 q^{29} + 11 q^{30} - 18 q^{32} - 18 q^{33} - 24 q^{34} - 38 q^{36} + 2 q^{37} + 33 q^{38} + 6 q^{40} + 6 q^{41} - 38 q^{42} - 13 q^{44} - 54 q^{45} + 10 q^{46} + 9 q^{48} - 28 q^{49} - 17 q^{50} - 27 q^{52} - 2 q^{53} - 39 q^{54} + 58 q^{56} + 6 q^{57} - 13 q^{58} - 31 q^{60} - 8 q^{64} - 100 q^{65} + 30 q^{66} - 18 q^{68} - 18 q^{69} - 19 q^{70} + 26 q^{72} + 30 q^{73} - 23 q^{74} - 2 q^{77} + 15 q^{78} + 3 q^{80} - 32 q^{81} - 18 q^{82} + 23 q^{84} - 50 q^{85} - 9 q^{86} + q^{88} - 102 q^{89} - 39 q^{90} + 28 q^{92} - 36 q^{93} + 63 q^{96} + 6 q^{97} + 21 q^{98}+O(q^{100}) $ 84 * q + 2 * q^2 - 2 * q^4 + 6 * q^5 - 16 * q^8 + 4 * q^9 - 18 * q^10 - 6 * q^12 + 18 * q^13 + 14 * q^14 + 14 * q^16 + 6 * q^17 - 10 * q^18 - 24 * q^20 + 4 * q^21 + 6 * q^22 - 6 * q^24 + 16 * q^25 - 30 * q^26 - 4 * q^28 + 10 * q^29 + 11 * q^30 - 18 * q^32 - 18 * q^33 - 24 * q^34 - 38 * q^36 + 2 * q^37 + 33 * q^38 + 6 * q^40 + 6 * q^41 - 38 * q^42 - 13 * q^44 - 54 * q^45 + 10 * q^46 + 9 * q^48 - 28 * q^49 - 17 * q^50 - 27 * q^52 - 2 * q^53 - 39 * q^54 + 58 * q^56 + 6 * q^57 - 13 * q^58 - 31 * q^60 - 8 * q^64 - 100 * q^65 + 30 * q^66 - 18 * q^68 - 18 * q^69 - 19 * q^70 + 26 * q^72 + 30 * q^73 - 23 * q^74 - 2 * q^77 + 15 * q^78 + 3 * q^80 - 32 * q^81 - 18 * q^82 + 23 * q^84 - 50 * q^85 - 9 * q^86 + q^88 - 102 * q^89 - 39 * q^90 + 28 * q^92 - 36 * q^93 + 63 * q^96 + 6 * q^97 + 21 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.248495	+	1.39221i	0.175713	+	0.984442i
$2$	0.248495	+	1.39221i	0.175713	+	0.984442i
$3$	1.22260	−	1.22689i	0.705869	−	0.708343i
$3$	1.22260	−	1.22689i	0.705869	−	0.708343i
$4$	−1.87650	+	0.691915i	−0.938250	+	0.345957i
$5$	0.705906	−	0.407555i	0.315691	−	0.182264i	−0.333779	−	0.942651i	$-0.608324\pi$
$5$	0.705906	−	0.407555i	0.315691	−	0.182264i	0.649470	+	0.760387i	$0.274991\pi$
$6$	2.01189	+	1.39724i	0.821352	+	0.570422i
$7$	2.03393	+	1.69208i	0.768753	+	0.639546i
$7$	2.03393	+	1.69208i	0.768753	+	0.639546i
$8$	−1.42959	−	2.44055i	−0.505437	−	0.862863i
$9$	−0.0104958	−	2.99998i	−0.00349861	−	0.999994i
$10$	0.742817	+	0.881495i	0.234899	+	0.278753i
$11$	4.17670	+	2.41142i	1.25932	+	0.727070i	0.972943	−	0.231046i	$-0.0742147\pi$
$11$	4.17670	+	2.41142i	1.25932	+	0.727070i	0.286380	+	0.958116i	$0.407548\pi$
$12$	−1.44531	+	3.14819i	−0.417225	+	0.908803i
$13$	−2.20303	−	1.27192i	−0.611011	−	0.352767i	0.162350	−	0.986733i	$-0.448093\pi$
$13$	−2.20303	−	1.27192i	−0.611011	−	0.352767i	−0.773361	+	0.633966i	$0.781426\pi$
$14$	−1.85031	+	3.25213i	−0.494516	+	0.869169i
$15$	0.363018	−	1.36434i	0.0937308	−	0.352272i
$16$	3.04251	−	2.59676i	0.760627	−	0.649189i
$17$	−0.503257	+	0.290555i	−0.122058	+	0.0704700i	−0.559786	−	0.828637i	$-0.689117\pi$
$17$	−0.503257	+	0.290555i	−0.122058	+	0.0704700i	0.437728	+	0.899107i	$0.355783\pi$
$18$	4.17400	−	0.760093i	0.983821	−	0.179156i
$19$	−2.24125	+	3.88195i	−0.514177	+	0.890581i	0.485687	+	0.874133i	$0.338569\pi$
$19$	−2.24125	+	3.88195i	−0.514177	+	0.890581i	−0.999865	+	0.0164486i	$0.994764\pi$
$20$	−1.04264	+	1.25320i	−0.233141	+	0.280225i
$21$	4.56267	−	0.426661i	0.995656	−	0.0931050i
$22$	−2.31931	+	6.41407i	−0.494479	+	1.36749i
$23$	5.60853	−	3.23809i	1.16946	−	0.675188i	0.215907	−	0.976414i	$-0.430729\pi$
$23$	5.60853	−	3.23809i	1.16946	−	0.675188i	0.953553	+	0.301226i	$0.0973959\pi$
$24$	−4.74209	−	1.22987i	−0.967975	−	0.251046i
$25$	−2.16780	+	3.75474i	−0.433560	+	0.750947i
$26$	1.22334	−	3.38315i	0.239917	−	0.663490i
$27$	−3.69347	−	3.65490i	−0.710808	−	0.703386i
$28$	−4.98744	−	1.76788i	−0.942538	−	0.334098i
$29$	−3.16210	−	5.47692i	−0.587188	−	1.01704i	−0.994599	−	0.103794i	$-0.966902\pi$
$29$	−3.16210	−	5.47692i	−0.587188	−	1.01704i	0.407411	−	0.913245i	$-0.366432\pi$
$30$	1.98966	+	0.166365i	0.363261	+	0.0303739i
$31$	−9.62438			−1.72859			−0.864294	−	0.502986i	$-0.832235\pi$
$31$	−9.62438			−1.72859			−0.864294	+	0.502986i	$0.832235\pi$
$32$	4.37128	+	3.59053i	0.772741	+	0.634722i
$33$	8.06497	−	2.17613i	1.40393	−	0.378816i
$34$	−0.529571	−	0.628438i	−0.0908207	−	0.107776i
$35$	2.12538	+	0.365511i	0.359255	+	0.0617827i
$36$	2.09543	+	5.62220i	0.349238	+	0.937034i
$37$	1.62993	−	2.82313i	0.267959	−	0.464119i	−0.700375	−	0.713775i	$-0.746984\pi$
$37$	1.62993	−	2.82313i	0.267959	−	0.464119i	0.968335	+	0.249655i	$0.0803173\pi$
$38$	−5.96144	−	2.15564i	−0.967073	−	0.349691i
$39$	−4.25393	+	1.14782i	−0.681174	+	0.183798i
$40$	−2.00382	−	1.14016i	−0.316831	−	0.180275i
$41$	−3.04709	−	1.75924i	−0.475875	−	0.274747i	0.242821	−	0.970071i	$-0.421927\pi$
$41$	−3.04709	−	1.75924i	−0.475875	−	0.274747i	−0.718696	+	0.695325i	$0.755261\pi$
$42$	1.72780	+	6.24617i	0.266606	+	0.963806i
$43$	−4.72260	+	2.72659i	−0.720190	+	0.415802i	−0.814823	−	0.579710i	$-0.803166\pi$
$43$	−4.72260	+	2.72659i	−0.720190	+	0.415802i	0.0946327	+	0.995512i	$0.469832\pi$
$44$	−9.50608	−	1.63511i	−1.43310	−	0.246502i
$45$	−1.23007	−	2.11343i	−0.183368	−	0.315051i
$46$	5.90179	+	7.00361i	0.870172	+	1.03263i
$47$	−9.58038			−1.39744			−0.698721	−	0.715395i	$-0.746247\pi$
$47$	−9.58038			−1.39744			−0.698721	+	0.715395i	$0.746247\pi$
$48$	0.533848	−	6.90760i	0.0770543	−	0.997027i
$49$	1.27373	+	6.88314i	0.181962	+	0.983306i
$50$	−5.76607	−	2.08500i	−0.815445	−	0.294863i
$51$	−0.258804	+	0.972672i	−0.0362398	+	0.136201i
$52$	5.01405	+	0.862450i	0.695324	+	0.119600i
$53$	−1.09484	−	1.89632i	−0.150388	−	0.260480i	0.780982	−	0.624553i	$-0.214719\pi$
$53$	−1.09484	−	1.89632i	−0.150388	−	0.260480i	−0.931370	+	0.364074i	$0.881386\pi$
$54$	4.17058	−	6.05031i	0.567545	−	0.823343i
$55$	3.93115			0.530076
$56$	1.22191	−	7.38288i	0.163284	−	0.986579i
$57$	2.02256	+	7.49583i	0.267895	+	0.992847i
$58$	6.83926	−	5.76330i	0.898039	−	0.756759i
$59$	11.2058			1.45886			0.729432	−	0.684053i	$-0.239784\pi$
$59$	11.2058			1.45886			0.729432	+	0.684053i	$0.239784\pi$
$60$	0.262806	+	2.81137i	0.0339281	+	0.362946i
$61$		−	7.24771i		−	0.927974i	−0.885842	−	0.463987i	$-0.846418\pi$
$61$		−	7.24771i		−	0.927974i	0.885842	−	0.463987i	$-0.153582\pi$
$62$	−2.39161	−	13.3992i	−0.303735	−	1.70169i
$63$	5.05486	−	6.11951i	0.636852	−	0.770986i
$64$	−3.91253	+	6.97797i	−0.489066	+	0.872247i
$65$	−2.07351			−0.257187
$66$	5.03374	+	10.6874i	0.619610	+	1.31553i
$67$		−	5.02059i		−	0.613363i	−0.951812	−	0.306682i	$-0.900781\pi$
$67$		−	5.02059i		−	0.613363i	0.951812	−	0.306682i	$-0.0992187\pi$
$68$	0.743322	−	0.893438i	0.0901410	−	0.108345i
$69$	2.88423	−	10.8399i	0.347221	−	1.30497i
$70$	0.0192776	+	3.04980i	0.00230411	+	0.364521i
$71$		−	3.64207i		−	0.432234i	−0.976367	−	0.216117i	$-0.930661\pi$
$71$		−	3.64207i		−	0.432234i	0.976367	−	0.216117i	$-0.0693392\pi$
$72$	−7.30659	+	4.31437i	−0.861090	+	0.508453i
$73$	2.26126	−	1.30554i	0.264661	−	0.152802i	−0.361798	−	0.932257i	$-0.617837\pi$
$73$	2.26126	−	1.30554i	0.264661	−	0.152802i	0.626459	+	0.779454i	$0.284504\pi$
$74$	4.33542	+	1.56768i	0.503982	+	0.182239i
$75$	1.95628	+	7.25018i	0.225892	+	0.837179i
$76$	1.51972	−	8.83524i	0.174324	−	1.01347i
$77$	4.41480	+	11.9720i	0.503113	+	1.36433i
$78$	−2.65508	−	5.63714i	−0.300629	−	0.638280i
$79$			10.1419i			1.14105i	0.821280	+	0.570526i	$0.193260\pi$
$79$			10.1419i			1.14105i	−0.821280	+	0.570526i	$0.806740\pi$
$80$	1.08940	−	3.07306i	0.121799	−	0.343578i
$81$	−8.99978	+	0.0629746i	−0.999976	+	0.00699717i
$82$	1.69204	−	4.67935i	0.186855	−	0.516747i
$83$	−0.820993	−	1.42200i	−0.0901157	−	0.156085i	0.817444	−	0.576008i	$-0.195390\pi$
$83$	−0.820993	−	1.42200i	−0.0901157	−	0.156085i	−0.907560	+	0.419923i	$0.862057\pi$
$84$	−8.26664	+	3.95761i	−0.901964	+	0.431810i
$85$	−0.236835	+	0.410210i	−0.0256883	+	0.0444935i
$86$	−4.96954	−	5.89731i	−0.535879	−	0.635923i
$87$	−10.5855	−	2.81655i	−1.13489	−	0.301966i
$88$	−0.0857994	−	13.6408i	−0.00914624	−	1.45411i
$89$	−1.90724	−	1.10115i	−0.202167	−	0.116721i	0.395499	−	0.918466i	$-0.370572\pi$
$89$	−1.90724	−	1.10115i	−0.202167	−	0.116721i	−0.597666	+	0.801745i	$0.703905\pi$
$90$	2.63667	−	2.23769i	0.277930	−	0.235873i
$91$	−2.32862	−	6.31470i	−0.244106	−	0.661961i
$92$	−8.28393	+	9.95690i	−0.863660	+	1.03808i
$93$	−11.7668	+	11.8080i	−1.22016	+	1.22443i
$94$	−2.38068	−	13.3379i	−0.245548	−	1.37570i
$95$			3.65373i			0.374864i
$96$	9.74950	−	0.973278i	0.995054	−	0.0993347i
$97$	−6.14759	+	3.54931i	−0.624193	+	0.360378i	−0.778500	−	0.627645i	$-0.784019\pi$
$97$	−6.14759	+	3.54931i	−0.624193	+	0.360378i	0.154307	+	0.988023i	$0.450686\pi$
$98$	−9.26626	+	3.48373i	−0.936034	+	0.351910i
$99$	7.19038	−	12.5553i	0.722660	−	1.26186i
$100$	1.46992	−	8.54569i	0.146992	−	0.854569i
$101$	8.15564	+	4.70866i	0.811516	+	0.468529i	0.847482	−	0.530824i	$-0.178117\pi$
$101$	8.15564	+	4.70866i	0.811516	+	0.468529i	−0.0359658	+	0.999353i	$0.511451\pi$
$102$	−1.41848	−	0.118605i	−0.140450	−	0.0117437i
$103$	2.57609	+	4.46191i	0.253829	+	0.439645i	0.964577	−	0.263802i	$-0.0849765\pi$
$103$	2.57609	+	4.46191i	0.253829	+	0.439645i	−0.710748	+	0.703447i	$0.751643\pi$
$104$	0.0452555	+	7.19493i	0.00443767	+	0.705521i
$105$	3.04693	−	2.16072i	0.297350	−	0.210865i
$106$	2.36802	−	1.99548i	0.230002	−	0.193818i
$107$	10.4663	+	6.04271i	1.01181	+	0.584170i	0.911722	−	0.410808i	$-0.134753\pi$
$107$	10.4663	+	6.04271i	1.01181	+	0.584170i	0.100091	+	0.994978i	$0.468087\pi$
$108$	9.45967	+	4.30286i	0.910257	+	0.414043i
$109$	1.83950	+	3.18610i	0.176192	+	0.305173i	0.940573	−	0.339591i	$-0.110289\pi$
$109$	1.83950	+	3.18610i	0.176192	+	0.305173i	−0.764381	+	0.644764i	$0.776955\pi$
$110$	0.976870	+	5.47298i	0.0931409	+	0.521828i
$111$	−1.47090	−	5.45130i	−0.139611	−	0.517414i
$112$	10.5822	−	0.133455i	0.999920	−	0.0126103i
$113$	−2.77892	+	4.81323i	−0.261419	+	0.452790i	−0.966619	−	0.256218i	$-0.917524\pi$
$113$	−2.77892	+	4.81323i	−0.261419	+	0.452790i	0.705201	+	0.709008i	$0.250857\pi$
$114$	−9.93318	+	4.67851i	−0.930327	+	0.438183i
$115$	2.63940	−	4.57157i	0.246125	−	0.426301i
$116$	9.72325	+	8.08954i	0.902781	+	0.751095i
$117$	−3.79262	+	6.62241i	−0.350628	+	0.612242i
$118$	2.78457	+	15.6008i	0.256341	+	1.43617i
$119$	−1.51523	−	0.260581i	−0.138901	−	0.0238875i
$120$	−3.84871	+	1.06449i	−0.351338	+	0.0971744i
$121$	6.12989	+	10.6173i	0.557263	+	0.965207i
$122$	10.0903	−	1.80102i	0.913537	−	0.163057i
$123$	−5.88375	+	1.58758i	−0.530520	+	0.143148i
$124$	18.0601	−	6.65925i	1.62185	−	0.598018i
$125$			7.60954i			0.680618i
$126$	9.77575	+	5.51676i	0.870893	+	0.491472i
$127$			1.07938i			0.0957798i	0.998853	+	0.0478899i	$0.0152497\pi$
$127$			1.07938i			0.0957798i	−0.998853	+	0.0478899i	$0.984750\pi$
$128$	−10.6871	−	3.71308i	−0.944611	−	0.328193i
$129$	−2.42863	+	9.12763i	−0.213829	+	0.803643i
$130$	−0.515257	−	2.88677i	−0.0451911	−	0.253186i
$131$	4.37411	+	7.57619i	0.382168	+	0.661935i	0.991372	−	0.131079i	$-0.0418442\pi$
$131$	4.37411	+	7.57619i	0.382168	+	0.661935i	−0.609204	+	0.793014i	$0.708511\pi$
$132$	−13.6282	+	9.66379i	−1.18618	+	0.841125i
$133$	−11.1271	+	4.10325i	−0.964843	+	0.355797i
$134$	6.98972	−	1.24759i	0.603820	−	0.107776i
$135$	−4.09681	−	1.07473i	−0.352598	−	0.0924978i
$136$	1.42857	+	0.812846i	0.122499	+	0.0697009i
$137$	4.31047	−	7.46595i	0.368268	−	0.637859i	−0.621027	−	0.783789i	$-0.713284\pi$
$137$	4.31047	−	7.46595i	0.368268	−	0.637859i	0.989295	+	0.145930i	$0.0466174\pi$
$138$	15.8082	+	1.32179i	1.34568	+	0.112518i
$139$	−4.64043	+	8.03745i	−0.393596	+	0.681728i	−0.992921	−	0.118778i	$-0.962102\pi$
$139$	−4.64043	+	8.03745i	−0.393596	+	0.681728i	0.599325	+	0.800506i	$0.295436\pi$
$140$	−4.24118	+	0.784699i	−0.358445	+	0.0663192i
$141$	−11.7130	+	11.7540i	−0.986410	+	0.989867i
$142$	5.07053	−	0.905036i	0.425509	−	0.0759489i
$143$	−6.13427	−	10.6249i	−0.512974	−	0.888496i
$144$	−7.82216	−	9.10021i	−0.651846	−	0.758351i
$145$	−4.46430	−	2.57746i	−0.370740	−	0.214047i
$146$	2.37950	+	2.82374i	0.196929	+	0.233694i
$147$	10.0021	+	6.85260i	0.824959	+	0.565193i
$148$	−1.10521	+	6.42538i	−0.0908474	+	0.528163i
$149$	−5.47269	−	9.47898i	−0.448340	−	0.776548i	0.549938	−	0.835206i	$-0.314651\pi$
$149$	−5.47269	−	9.47898i	−0.448340	−	0.776548i	−0.998278	+	0.0586572i	$0.981318\pi$
$150$	−9.60765	+	4.52519i	−0.784462	+	0.369480i
$151$	0.329198	+	0.190062i	0.0267897	+	0.0154671i	0.513335	−	0.858188i	$-0.328410\pi$
$151$	0.329198	+	0.190062i	0.0267897	+	0.0154671i	−0.486545	+	0.873655i	$0.661743\pi$
$152$	12.6782	−	0.0797446i	1.02833	−	0.00646814i
$153$	0.876943	+	1.50671i	0.0708966	+	0.121810i
$154$	−15.5704	+	9.12131i	−1.25470	+	0.735016i
$155$	−6.79391	+	3.92246i	−0.545700	+	0.315060i
$156$	7.18831	−	5.09724i	0.575525	−	0.408105i
$157$		−	4.96221i		−	0.396028i	−0.980199	−	0.198014i	$-0.936551\pi$
$157$		−	4.96221i		−	0.396028i	0.980199	−	0.198014i	$-0.0634491\pi$
$158$	−14.1196	+	2.52021i	−1.12330	+	0.200497i
$159$	−3.66512	−	0.975198i	−0.290663	−	0.0773382i
$160$	4.54905	+	0.753039i	0.359634	+	0.0595330i
$161$	16.8865	+	2.90404i	1.33084	+	0.228871i
$162$	−2.32407	−	12.5139i	−0.182597	−	0.983188i
$163$	17.9942	+	10.3890i	1.40942	+	0.813727i	0.995332	−	0.0965111i	$-0.0307683\pi$
$163$	17.9942	+	10.3890i	1.40942	+	0.813727i	0.414085	+	0.910238i	$0.364102\pi$
$164$	6.93510	+	1.19288i	0.541540	+	0.0931485i
$165$	4.80622	−	4.82307i	0.374164	−	0.375475i
$166$	1.77571	−	1.49636i	0.137822	−	0.116140i
$167$	−1.02852	+	1.78145i	−0.0795893	+	0.137853i	−0.903073	−	0.429487i	$-0.858694\pi$
$167$	−1.02852	+	1.78145i	−0.0795893	+	0.137853i	0.823483	+	0.567340i	$0.192028\pi$
$168$	−7.56404	−	10.5255i	−0.583579	−	0.812057i
$169$	−3.26443	−	5.65416i	−0.251110	−	0.434936i
$170$	−0.629951	−	0.227789i	−0.0483150	−	0.0174706i
$171$	11.6693	+	6.68296i	0.892375	+	0.511058i
$172$	6.97539	−	8.38409i	0.531869	−	0.639281i
$173$			14.4260i			1.09679i	0.836220	+	0.548395i	$0.184761\pi$
$173$			14.4260i			1.09679i	−0.836220	+	0.548395i	$0.815239\pi$
$174$	1.29078	−	15.4372i	0.0978535	−	1.17029i
$175$	−10.7625	+	3.96878i	−0.813565	+	0.300012i
$176$	18.9695	−	3.50912i	1.42988	−	0.264510i
$177$	13.7002	−	13.7482i	1.02977	−	1.03338i
$178$	1.05909	−	2.92891i	0.0793819	−	0.219531i
$179$	−3.35237	+	1.93549i	−0.250568	+	0.144666i	−0.620024	−	0.784583i	$-0.712877\pi$
$179$	−3.35237	+	1.93549i	−0.250568	+	0.144666i	0.369456	+	0.929248i	$0.379544\pi$
$180$	3.77053	+	3.11475i	0.281039	+	0.232159i
$181$		−	24.8665i		−	1.84831i	−0.382012	−	0.924157i	$-0.624769\pi$
$181$		−	24.8665i		−	1.84831i	0.382012	−	0.924157i	$-0.375231\pi$
$182$	8.21275	−	4.81110i	0.608769	−	0.356623i
$183$	−8.89211	−	8.86106i	−0.657324	−	0.655028i
$184$	−15.9206	−	9.05874i	−1.17368	−	0.667819i
$185$		−	2.65715i		−	0.195358i
$186$	−19.3632	−	13.4476i	−1.41978	−	0.986025i
$187$	−2.80260			−0.204947
$188$	17.9776	−	6.62880i	1.31115	−	0.483455i
$189$	−1.32786	−	13.6834i	−0.0965878	−	0.995324i
$190$	−5.08676	+	0.907933i	−0.369032	+	0.0658684i
$191$			18.5339i			1.34107i	0.741880	+	0.670533i	$0.233935\pi$
$191$			18.5339i			1.34107i	−0.741880	+	0.670533i	$0.766065\pi$
$192$	3.77771	+	13.3315i	0.272633	+	0.962118i
$193$	26.3504			1.89674			0.948371	−	0.317163i	$-0.102730\pi$
$193$	26.3504			1.89674			0.948371	+	0.317163i	$0.102730\pi$
$194$	−6.46904	−	7.67675i	−0.464450	−	0.551159i
$195$	−2.53508	+	2.54396i	−0.181541	+	0.182177i
$196$	−7.15271	−	12.0349i	−0.510908	−	0.859636i
$197$	−5.05586			−0.360215			−0.180107	−	0.983647i	$-0.557645\pi$
$197$	−5.05586			−0.360215			−0.180107	+	0.983647i	$0.557645\pi$
$198$	19.2664	+	6.89058i	1.36921	+	0.489692i
$199$	−10.9222	−	18.9178i	−0.774255	−	1.34105i	−0.935212	−	0.354088i	$-0.884791\pi$
$199$	−10.9222	−	18.9178i	−0.774255	−	1.34105i	0.160957	−	0.986961i	$-0.448542\pi$
$200$	12.2627	−	0.0771312i	0.867102	−	0.00545400i
$201$	−6.15969	−	6.13818i	−0.434471	−	0.432954i
$202$	−4.52881	+	12.5244i	−0.318646	+	0.881217i
$203$	2.83590	−	16.4902i	0.199041	−	1.15739i
$204$	−0.187361	−	2.00429i	−0.0131179	−	0.140328i
$205$	−2.86794			−0.200306
$206$	−5.57178	+	4.69522i	−0.388204	+	0.327131i
$207$	−9.77307	−	16.7915i	−0.679275	−	1.16709i
$208$	−10.0056	+	1.85091i	−0.693764	+	0.128338i
$209$	−18.7220	+	10.8092i	−1.29503	+	0.747686i
$210$	3.76533	+	3.70504i	0.259832	+	0.255672i
$211$	22.2066	+	12.8210i	1.52876	+	0.882632i	0.999414	+	0.0342290i	$0.0108975\pi$
$211$	22.2066	+	12.8210i	1.52876	+	0.882632i	0.529350	+	0.848403i	$0.322436\pi$
$212$	3.36656	+	2.80091i	0.231217	+	0.192367i
$213$	−4.46840	−	4.45279i	−0.306170	−	0.305100i
$214$	−5.81190	+	16.0728i	−0.397293	+	1.09872i
$215$	−2.22248	+	3.84944i	−0.151572	+	0.262530i
$216$	−3.63981	+	14.2391i	−0.247657	+	0.968848i
$217$	−19.5753	−	16.2852i	−1.32886	−	1.10551i
$218$	−3.97862	+	3.35269i	−0.269466	+	0.227073i
$219$	1.16287	−	4.37047i	0.0785797	−	0.295329i
$220$	−7.37680	+	2.72002i	−0.497344	+	0.183384i
$221$	1.47825			0.0994382
$222$	7.22385	−	3.40242i	0.484833	−	0.228355i
$223$	−12.3031	−	21.3096i	−0.823876	−	1.42699i	−0.902776	−	0.430112i	$-0.858474\pi$
$223$	−12.3031	−	21.3096i	−0.823876	−	1.42699i	0.0789002	−	0.996883i	$-0.474859\pi$
$224$	2.81541	+	14.6994i	0.188113	+	0.982147i
$225$	11.2869	+	6.46394i	0.752459	+	0.430930i
$226$	−7.39157	−	2.67278i	−0.491680	−	0.177790i
$227$	10.9776	−	19.0138i	0.728611	−	1.26199i	−0.228859	−	0.973459i	$-0.573500\pi$
$227$	10.9776	−	19.0138i	0.728611	−	1.26199i	0.957470	−	0.288532i	$-0.0931670\pi$
$228$	−8.98182	−	12.6665i	−0.594835	−	0.838859i
$229$	9.27254	−	5.35350i	0.612747	−	0.353769i	−0.161293	−	0.986907i	$-0.551566\pi$
$229$	9.27254	−	5.35350i	0.612747	−	0.353769i	0.774040	+	0.633137i	$0.218233\pi$
$230$	7.02047	+	2.53858i	0.462916	+	0.167389i
$231$	20.0858	+	9.22048i	1.32155	+	0.606663i
$232$	−8.84617	+	15.5470i	−0.580779	+	1.02071i
$233$	2.17122	−	3.76066i	0.142241	−	0.246369i	−0.786099	−	0.618101i	$-0.787902\pi$
$233$	2.17122	−	3.76066i	0.142241	−	0.246369i	0.928340	+	0.371731i	$0.121236\pi$
$234$	−10.1622	−	3.63449i	−0.664326	−	0.237594i
$235$	−6.76285	+	3.90453i	−0.441159	+	0.254704i
$236$	−21.0276	+	7.75343i	−1.36878	+	0.504705i
$237$	12.4429	+	12.3995i	0.808255	+	0.805432i
$238$	−0.0137434	−	2.17427i	−0.000890855	−	0.140937i
$239$	−9.17613	−	5.29784i	−0.593554	−	0.342689i	0.172947	−	0.984931i	$-0.444671\pi$
$239$	−9.17613	−	5.29784i	−0.593554	−	0.342689i	−0.766502	+	0.642242i	$0.778004\pi$
$240$	−2.43838	−	5.09369i	−0.157397	−	0.328796i
$241$	−5.90935	−	3.41177i	−0.380655	−	0.219771i	0.297448	−	0.954738i	$-0.403864\pi$
$241$	−5.90935	−	3.41177i	−0.380655	−	0.219771i	−0.678103	+	0.734967i	$0.737198\pi$
$242$	−13.2582	+	11.1724i	−0.852272	+	0.718192i
$243$	−10.9259	+	11.1187i	−0.700895	+	0.713264i
$244$	5.01480	+	13.6003i	0.321040	+	0.870672i
$245$	3.70440	+	4.33973i	0.236665	+	0.277255i
$246$	−3.67233	−	7.79691i	−0.234139	−	0.497113i
$247$	9.87508	−	5.70138i	0.628336	−	0.362770i
$248$	13.7589	+	23.4887i	0.873693	+	1.49154i
$249$	−2.74838	−	0.731276i	−0.174172	−	0.0463427i
$250$	−10.5941	+	1.89093i	−0.670028	+	0.119593i
$251$	−9.85832			−0.622252			−0.311126	−	0.950369i	$-0.600706\pi$
$251$	−9.85832			−0.622252			−0.311126	+	0.950369i	$0.600706\pi$
$252$	−5.25127	+	14.9808i	−0.330799	+	0.943701i
$253$	31.2336			1.96364
$254$	−1.50273	+	0.268221i	−0.0942896	+	0.0168297i
$255$	0.213726	+	0.792092i	0.0133840	+	0.0496027i
$256$	2.51370	−	15.8013i	0.157106	−	0.987582i
$257$	11.8534	−	6.84354i	0.739392	−	0.426888i	−0.0824560	−	0.996595i	$-0.526276\pi$
$257$	11.8534	−	6.84354i	0.739392	−	0.426888i	0.821848	+	0.569706i	$0.192943\pi$
$258$	−13.3111	−	1.11300i	−0.828712	−	0.0692924i
$259$	8.09213	−	2.98406i	0.502820	−	0.185421i
$260$	3.89095	−	1.43469i	0.241306	−	0.0889759i
$261$	−16.3975	+	9.54374i	−1.01498	+	0.590742i
$262$	−9.46070	+	7.97233i	−0.584484	+	0.492532i
$263$	13.5112	+	7.80071i	0.833138	+	0.481013i	0.854926	−	0.518750i	$-0.173602\pi$
$263$	13.5112	+	7.80071i	0.833138	+	0.481013i	−0.0217878	+	0.999763i	$0.506936\pi$
$264$	−16.8406	−	16.5720i	−1.03647	−	1.01993i
$265$	−1.54571	−	0.892417i	−0.0949523	−	0.0548207i
$266$	−8.47762	−	14.4716i	−0.519796	−	0.887313i
$267$	−3.68277	+	0.993704i	−0.225382	+	0.0608137i
$268$	3.47382	+	9.42115i	0.212198	+	0.575488i
$269$	18.5276	−	10.6969i	1.12965	−	0.652202i	0.185801	−	0.982587i	$-0.440512\pi$
$269$	18.5276	−	10.6969i	1.12965	−	0.652202i	0.943846	+	0.330386i	$0.107179\pi$
$270$	0.478208	−	5.97069i	0.0291028	−	0.363365i
$271$	−1.36221	+	2.35942i	−0.0827485	+	0.143325i	−0.904430	−	0.426623i	$-0.859703\pi$
$271$	−1.36221	+	2.35942i	−0.0827485	+	0.143325i	0.821681	+	0.569948i	$0.193036\pi$
$272$	−0.776661	+	2.19085i	−0.0470920	+	0.132840i
$273$	−10.5944	−	4.86341i	−0.641202	−	0.294347i
$274$	11.4653	+	4.14583i	0.692645	+	0.250459i
$275$	−18.1085	+	10.4549i	−1.09198	+	0.630457i
$276$	2.08804	+	22.3367i	0.125685	+	1.34451i
$277$	−5.69546	+	9.86482i	−0.342207	+	0.592720i	−0.984842	−	0.173453i	$-0.944508\pi$
$277$	−5.69546	+	9.86482i	−0.342207	+	0.592720i	0.642635	+	0.766172i	$0.277841\pi$
$278$	−12.3429	−	4.46318i	−0.740281	−	0.267684i
$279$	0.101016	+	28.8730i	0.00604766	+	1.72858i
$280$	−2.14638	−	5.70962i	−0.128271	−	0.341215i
$281$	−15.5146	−	26.8721i	−0.925524	−	1.60305i	−0.790716	−	0.612183i	$-0.790292\pi$
$281$	−15.5146	−	26.8721i	−0.925524	−	1.60305i	−0.134808	−	0.990872i	$-0.543042\pi$
$282$	−19.2747	−	13.3861i	−1.14779	−	0.797131i
$283$	4.05561			0.241081			0.120540	−	0.992708i	$-0.461537\pi$
$283$	4.05561			0.241081			0.120540	+	0.992708i	$0.461537\pi$
$284$	2.52000	+	6.83434i	0.149535	+	0.405544i
$285$	4.48270	+	4.46705i	0.265532	+	0.264605i
$286$	13.2677	−	11.1804i	0.784537	−	0.661112i
$287$	−3.22079	−	8.73407i	−0.190117	−	0.515556i
$288$	10.7256	−	13.1514i	0.632015	−	0.774957i
$289$	−8.33116	+	14.4300i	−0.490068	+	0.848823i
$290$	2.47901	−	6.85573i	0.145573	−	0.402582i
$291$	−3.16145	+	11.8818i	−0.185327	+	0.696522i
$292$	−3.33994	+	4.01445i	−0.195455	+	0.234928i
$293$	18.5526	+	10.7113i	1.08385	+	0.625762i	0.931933	−	0.362631i	$-0.118121\pi$
$293$	18.5526	+	10.7113i	1.08385	+	0.625762i	0.151919	+	0.988393i	$0.451455\pi$
$294$	−7.05480	+	15.6279i	−0.411444	+	0.911435i
$295$	7.91021	−	4.56696i	0.460550	−	0.265899i
$296$	−9.22011	+	0.0579938i	−0.535908	+	0.00337082i
$297$	−6.61300	−	24.1719i	−0.383725	−	1.40260i
$298$	11.8368	−	9.97462i	0.685687	−	0.577814i
$299$	−16.4744			−0.952737
$300$	−8.68747	−	12.2514i	−0.501571	−	0.707334i
$301$	−14.2190	−	2.44532i	−0.819572	−	0.140946i
$302$	−0.182803	+	0.505542i	−0.0105191	+	0.0290907i
$303$	15.7481	−	4.24922i	0.904703	−	0.244112i
$304$	3.26148	+	17.6308i	0.187059	+	1.01120i
$305$	−2.95384	−	5.11620i	−0.169137	−	0.292953i
$306$	−1.87974	+	1.59530i	−0.107458	+	0.0911972i
$307$	19.4087			1.10771			0.553856	−	0.832613i	$-0.313156\pi$
$307$	19.4087			1.10771			0.553856	+	0.832613i	$0.313156\pi$
$308$	−16.5680	−	19.4107i	−0.944047	−	1.10603i
$309$	8.62378	+	2.29457i	0.490590	+	0.130534i
$310$	−7.14915	−	8.48383i	−0.406044	−	0.481849i
$311$	−10.7296			−0.608419			−0.304209	−	0.952605i	$-0.598392\pi$
$311$	−10.7296			−0.608419			−0.304209	+	0.952605i	$0.598392\pi$
$312$	8.88268	+	8.74100i	0.502883	+	0.494862i
$313$			24.4060i			1.37951i	0.724044	+	0.689754i	$0.242281\pi$
$313$			24.4060i			1.37951i	−0.724044	+	0.689754i	$0.757719\pi$
$314$	6.90844	−	1.23309i	0.389866	−	0.0695870i
$315$	1.07422	−	6.37993i	0.0605254	−	0.359469i
$316$	−7.01732	−	19.0312i	−0.394755	−	1.07059i
$317$	32.1240			1.80426			0.902132	−	0.431460i	$-0.142001\pi$
$317$	32.1240			1.80426			0.902132	+	0.431460i	$0.142001\pi$
$318$	0.446916	−	5.34495i	0.0250618	−	0.299730i
$319$		−	30.5006i		−	1.70771i
$320$	0.0820284	+	6.52037i	0.00458553	+	0.364500i
$321$	20.2098	−	5.45310i	1.12800	−	0.304363i
$322$	0.153163	+	24.2311i	0.00853546	+	1.35035i
$323$		−	2.60483i		−	0.144936i
$324$	16.8445	−	6.34525i	0.935807	−	0.352514i
$325$	9.55146	−	5.51454i	0.529819	−	0.305891i
$326$	−9.99216	+	27.6334i	−0.553415	+	1.53047i
$327$	6.15795	+	1.63848i	0.340535	+	0.0906080i
$328$	0.0625944	+	9.95154i	0.00345620	+	0.549482i
$329$	−19.4858	−	16.2108i	−1.07429	−	0.893728i
$330$	7.90904	+	5.49276i	0.435379	+	0.302367i
$331$		−	26.1463i		−	1.43713i	−0.695460	−	0.718565i	$-0.744799\pi$
$331$		−	26.1463i		−	1.43713i	0.695460	−	0.718565i	$-0.255201\pi$
$332$	2.52450	+	2.10033i	0.138550	+	0.115271i
$333$	−8.48644	−	4.86014i	−0.465054	−	0.266334i
$334$	−2.73574	−	0.989236i	−0.149693	−	0.0541286i
$335$	−2.04617	−	3.54407i	−0.111794	−	0.193633i
$336$	12.7740	−	13.1463i	0.696880	−	0.717188i
$337$	2.89594	−	5.01591i	0.157752	−	0.273234i	−0.776306	−	0.630356i	$-0.782909\pi$
$337$	2.89594	−	5.01591i	0.157752	−	0.273234i	0.934058	+	0.357122i	$0.116242\pi$
$338$	7.06059	−	5.94981i	0.384046	−	0.323627i
$339$	2.50777	+	9.29407i	0.136203	+	0.504784i
$340$	0.160590	−	0.933628i	0.00870923	−	0.0506331i
$341$	−40.1981	−	23.2084i	−2.17685	−	1.25681i
$342$	−6.40431	+	17.9068i	−0.346306	+	0.968290i
$343$	−9.05613	+	16.1551i	−0.488985	+	0.872292i
$344$	13.4058	+	7.62781i	0.722791	+	0.411264i
$345$	−2.38187	−	8.82745i	−0.128235	−	0.475254i
$346$	−20.0840	+	3.58479i	−1.07973	+	0.192720i
$347$			14.9047i			0.800126i	0.916488	+	0.400063i	$0.131012\pi$
$347$			14.9047i			0.800126i	−0.916488	+	0.400063i	$0.868988\pi$
$348$	21.8126	−	2.03904i	1.16928	−	0.109304i
$349$	2.24929	−	1.29863i	0.120402	−	0.0695140i	−0.438590	−	0.898687i	$-0.644522\pi$
$349$	2.24929	−	1.29863i	0.120402	−	0.0695140i	0.558991	+	0.829173i	$0.311188\pi$
$350$	−8.19979	−	13.9974i	−0.438297	−	0.748192i
$351$	3.48808	+	12.7497i	0.186180	+	0.680527i
$352$	9.59926	+	25.5376i	0.511642	+	1.36116i
$353$	−11.6633	−	6.73382i	−0.620775	−	0.358405i	0.156395	−	0.987695i	$-0.450013\pi$
$353$	−11.6633	−	6.73382i	−0.620775	−	0.358405i	−0.777171	+	0.629290i	$0.783346\pi$
$354$	22.5448	+	15.6572i	1.19824	+	0.832168i
$355$	−1.48434	−	2.57096i	−0.0787808	−	0.136452i
$356$	4.34084	+	0.746652i	0.230064	+	0.0395725i
$357$	−2.17223	+	1.54043i	−0.114966	+	0.0815281i
$358$	−3.52766	−	4.18625i	−0.186443	−	0.221250i
$359$	−15.7293	−	9.08130i	−0.830159	−	0.479293i	0.0237479	−	0.999718i	$-0.492440\pi$
$359$	−15.7293	−	9.08130i	−0.830159	−	0.479293i	−0.853907	+	0.520425i	$0.825773\pi$
$360$	−3.39942	+	6.02338i	−0.179165	+	0.317460i
$361$	−0.546375	−	0.946350i	−0.0287566	−	0.0498079i
$362$	34.6194	−	6.17921i	1.81956	−	0.324772i
$363$	20.5206	+	5.46002i	1.07705	+	0.286577i
$364$	8.73889	+	10.2383i	0.458042	+	0.536635i
$365$	1.06416	−	1.84318i	0.0557007	−	0.0964764i
$366$	10.1268	−	14.5816i	0.529337	−	0.762194i
$367$	−5.58683	+	9.67667i	−0.291630	+	0.505118i	−0.974195	−	0.225707i	$-0.927531\pi$
$367$	−5.58683	+	9.67667i	−0.291630	+	0.505118i	0.682565	+	0.730825i	$0.260864\pi$
$368$	8.65547	−	24.4159i	0.451198	−	1.27277i
$369$	−5.24569	+	9.15967i	−0.273080	+	0.476833i
$370$	3.69931	−	0.660289i	0.192318	−	0.0343268i
$371$	0.981896	−	5.70954i	0.0509775	−	0.296425i
$372$	13.9102	−	30.2993i	0.721211	−	1.57095i
$373$	15.4012	+	26.6757i	0.797445	+	1.38121i	0.921275	+	0.388911i	$0.127149\pi$
$373$	15.4012	+	26.6757i	0.797445	+	1.38121i	−0.123831	+	0.992303i	$0.539518\pi$
$374$	−0.696433	−	3.90182i	−0.0360117	−	0.201758i
$375$	9.33603	+	9.30343i	0.482111	+	0.480427i
$376$	13.6960	+	23.3813i	0.706319	+	1.20580i
$377$			16.0878i			0.828563i
$378$	18.7203	−	5.24893i	0.962867	−	0.269976i
$379$		−	5.54837i		−	0.285001i	−0.989795	−	0.142500i	$-0.954486\pi$
$379$		−	5.54837i		−	0.285001i	0.989795	−	0.142500i	$-0.0455142\pi$
$380$	−2.52807	−	6.85622i	−0.129687	−	0.351717i
$381$	1.32428	+	1.31965i	0.0678449	+	0.0676080i
$382$	−25.8031	+	4.60558i	−1.32020	+	0.235642i
$383$	−4.30672	−	7.45945i	−0.220063	−	0.381160i	0.734764	−	0.678323i	$-0.237293\pi$
$383$	−4.30672	−	7.45945i	−0.220063	−	0.381160i	−0.954827	+	0.297163i	$0.903960\pi$
$384$	−17.6215	+	8.57218i	−0.899244	+	0.437447i
$385$	7.99567	+	6.65181i	0.407497	+	0.339008i
$386$	6.54794	+	36.6853i	0.333281	+	1.86723i
$387$	8.22930	+	14.1391i	0.418319	+	0.718731i
$388$	9.08013	−	10.9139i	0.460974	−	0.554069i
$389$	−1.74069	+	3.01496i	−0.0882563	+	0.152864i	−0.906774	−	0.421617i	$-0.861463\pi$
$389$	−1.74069	+	3.01496i	−0.0882563	+	0.152864i	0.818518	+	0.574481i	$0.194796\pi$
$390$	−4.17168	−	2.89720i	−0.211241	−	0.146705i
$391$	−1.88169	+	3.25918i	−0.0951611	+	0.164824i
$392$	14.9777	−	12.9487i	0.756488	−	0.654008i
$393$	14.6429	+	3.89611i	0.738637	+	0.196533i
$394$	−1.25636	−	7.03882i	−0.0632943	−	0.354611i
$395$	4.13338	+	7.15922i	0.207973	+	0.360219i
$396$	−4.80552	+	28.5352i	−0.241486	+	1.43395i
$397$	−15.5989	−	9.00601i	−0.782885	−	0.451999i	0.0545667	−	0.998510i	$-0.482622\pi$
$397$	−15.5989	−	9.00601i	−0.782885	−	0.451999i	−0.837452	+	0.546511i	$0.815956\pi$
$398$	23.6235	−	19.9070i	1.18414	−	0.997848i
$399$	−8.56979	+	18.6683i	−0.429026	+	0.934585i
$400$	3.15460	+	17.0531i	0.157730	+	0.852653i
$401$	−7.15282	−	12.3891i	−0.357195	−	0.618680i	0.630296	−	0.776355i	$-0.282933\pi$
$401$	−7.15282	−	12.3891i	−0.357195	−	0.618680i	−0.987491	+	0.157675i	$0.949600\pi$
$402$	7.01499	−	10.1009i	0.349876	−	0.503787i
$403$	21.2028	+	12.2414i	1.05619	+	0.609790i
$404$	−18.5621	−	3.19279i	−0.923497	−	0.158847i
$405$	−6.32733	+	3.71236i	−0.314408	+	0.184469i
$406$	23.6625	−	0.149569i	1.17435	−	0.00742300i
$407$	13.6155	−	7.86091i	0.674895	−	0.389651i
$408$	2.74383	−	0.758901i	0.135840	−	0.0375712i
$409$			39.1722i			1.93694i	0.249133	+	0.968469i	$0.419854\pi$
$409$			39.1722i			1.93694i	−0.249133	+	0.968469i	$0.580146\pi$
$410$	−0.712670	−	3.99278i	−0.0351962	−	0.197189i
$411$	−3.88989	−	14.4163i	−0.191874	−	0.711105i
$412$	−7.92129	−	6.59035i	−0.390254	−	0.324683i
$413$	22.7917	+	18.9610i	1.12151	+	0.933011i
$414$	20.9488	−	17.7788i	1.02958	−	0.873779i
$415$	−1.15909	−	0.669200i	−0.0568974	−	0.0328497i
$416$	−5.06320	−	13.4700i	−0.248244	−	0.660420i
$417$	4.18765	+	15.5199i	0.205070	+	0.760011i
$418$	−19.7010	−	23.3790i	−0.963606	−	1.14350i
$419$	−11.3503	+	19.6592i	−0.554497	+	0.960417i	0.443446	+	0.896301i	$0.353756\pi$
$419$	−11.3503	+	19.6592i	−0.554497	+	0.960417i	−0.997942	+	0.0641156i	$0.979577\pi$
$420$	−4.22253	+	6.16281i	−0.206038	+	0.300714i
$421$	−0.931761	−	1.61386i	−0.0454113	−	0.0786546i	0.842426	−	0.538811i	$-0.181126\pi$
$421$	−0.931761	−	1.61386i	−0.0454113	−	0.0786546i	−0.887838	+	0.460157i	$0.847793\pi$
$422$	−12.3313	+	34.1022i	−0.600277	+	1.66007i
$423$	0.100554	+	28.7410i	0.00488910	+	1.39743i
$424$	−3.06288	+	5.38298i	−0.148747	+	0.261421i
$425$		−	2.51946i		−	0.122212i
$426$	5.08885	−	7.32745i	0.246556	−	0.355016i
$427$	12.2637	−	14.7413i	0.593482	−	0.713383i
$428$	−23.8210	−	4.09737i	−1.15143	−	0.198054i
$429$	−20.5353	−	5.46392i	−0.991452	−	0.263801i
$430$	−5.91150	−	2.13759i	−0.285078	−	0.103084i
$431$	−3.78493	+	2.18523i	−0.182314	+	0.105259i	−0.588379	−	0.808585i	$-0.700234\pi$
$431$	−3.78493	+	2.18523i	−0.182314	+	0.105259i	0.406065	+	0.913844i	$0.366900\pi$
$432$	−20.7283	−	1.52903i	−0.997290	−	0.0735656i
$433$			9.78275i			0.470129i	0.971980	+	0.235065i	$0.0755302\pi$
$433$			9.78275i			0.470129i	−0.971980	+	0.235065i	$0.924470\pi$
$434$	17.8081	−	31.2997i	0.854815	−	1.50244i
$435$	−8.62030	+	2.32597i	−0.413312	+	0.111522i
$436$	−5.65632	−	4.70594i	−0.270889	−	0.225374i
$437$			29.0294i			1.38867i
$438$	6.37358	+	0.532924i	0.304541	+	0.0254641i
$439$	0.385147			0.0183821			0.00919103	−	0.999958i	$-0.497074\pi$
$439$	0.385147			0.0183821			0.00919103	+	0.999958i	$0.497074\pi$
$440$	−5.61994	−	9.59414i	−0.267920	−	0.457383i
$441$	20.6359	−	3.89342i	0.982663	−	0.185401i
$442$	0.367339	+	2.05804i	0.0174725	+	0.0978911i
$443$		−	16.1931i		−	0.769360i	−0.923050	−	0.384680i	$-0.874312\pi$
$443$		−	16.1931i		−	0.769360i	0.923050	−	0.384680i	$-0.125688\pi$
$444$	6.53197	+	9.21163i	0.309994	+	0.437165i
$445$	−1.79511			−0.0850964
$446$	26.6101	−	22.4238i	1.26003	−	1.06180i
$447$	−18.3205	−	4.87464i	−0.866532	−	0.230563i
$448$	−19.7651	+	7.57239i	−0.933813	+	0.357762i
$449$	−33.2361			−1.56851			−0.784253	−	0.620441i	$-0.786954\pi$
$449$	−33.2361			−1.56851			−0.784253	+	0.620441i	$0.786954\pi$
$450$	−6.19443	+	17.3200i	−0.292008	+	0.816472i
$451$	−8.48451	−	14.6956i	−0.399520	−	0.691989i
$452$	1.88430	−	10.9548i	0.0886299	−	0.515270i
$453$	0.635662	−	0.171518i	0.0298660	−	0.00805860i
$454$	29.1991	+	10.5583i	1.37038	+	0.495527i
$455$	−4.21738	−	3.50855i	−0.197714	−	0.164483i
$456$	15.4025	−	15.6521i	0.721287	−	0.732979i
$457$	−5.53862			−0.259086			−0.129543	−	0.991574i	$-0.541351\pi$
$457$	−5.53862			−0.259086			−0.129543	+	0.991574i	$0.541351\pi$
$458$	9.75738	+	11.5790i	0.455933	+	0.541051i
$459$	2.92071	+	0.766198i	0.136327	+	0.0357630i
$460$	−1.78969	+	10.4048i	−0.0834449	+	0.485126i
$461$	−5.35007	+	3.08886i	−0.249178	+	0.143863i	−0.619388	−	0.785085i	$-0.712619\pi$
$461$	−5.35007	+	3.08886i	−0.249178	+	0.143863i	0.370210	+	0.928948i	$0.379286\pi$
$462$	−7.84563	+	30.2549i	−0.365012	+	1.40758i
$463$	10.1830	+	5.87914i	0.473243	+	0.273227i	0.717596	−	0.696459i	$-0.245242\pi$
$463$	10.1830	+	5.87914i	0.473243	+	0.273227i	−0.244353	+	0.969686i	$0.578576\pi$
$464$	−23.8430	−	8.45237i	−1.10688	−	0.392391i
$465$	−3.49382	+	13.1310i	−0.162022	+	0.608933i
$466$	5.77517	+	2.08829i	0.267530	+	0.0967381i
$467$	13.8715	−	24.0262i	0.641897	−	1.11180i	−0.343112	−	0.939295i	$-0.611481\pi$
$467$	13.8715	−	24.0262i	0.641897	−	1.11180i	0.985009	−	0.172504i	$-0.0551858\pi$
$468$	2.53471	−	15.0511i	0.117167	−	0.695738i
$469$	8.49524	−	10.2115i	0.392274	−	0.471525i
$470$	−7.11646	−	8.44505i	−0.328258	−	0.389541i
$471$	−6.08807	−	6.06680i	−0.280523	−	0.279544i
$472$	−16.0197	−	27.3482i	−0.737365	−	1.25880i
$473$	−26.2999			−1.20927
$474$	−14.1707	+	20.4044i	−0.650880	+	0.937205i
$475$	−9.71714	−	16.8306i	−0.445853	−	0.772240i
$476$	3.02363	−	0.559430i	0.138588	−	0.0256414i
$477$	−5.67744	+	3.30441i	−0.259952	+	0.151298i
$478$	5.09549	−	14.0916i	0.233062	−	0.644534i
$479$	−3.57520	+	6.19243i	−0.163355	+	0.282939i	−0.936070	−	0.351814i	$-0.885565\pi$
$479$	−3.57520	+	6.19243i	−0.163355	+	0.282939i	0.772715	+	0.634753i	$0.218898\pi$
$480$	6.48557	−	4.66050i	0.296024	−	0.212722i
$481$	−7.18159	+	4.14629i	−0.327452	+	0.189055i
$482$	3.28145	−	9.07487i	0.149466	−	0.413349i
$483$	24.2083	−	17.1673i	1.10152	−	0.781138i
$484$	−18.8490	−	15.6820i	−0.856773	−	0.712817i
$485$	−2.89308	+	5.01096i	−0.131368	+	0.227536i
$486$	−18.1946	−	12.4482i	−0.825323	−	0.564661i
$487$	6.67495	−	3.85379i	0.302471	−	0.174632i	−0.341081	−	0.940034i	$-0.610793\pi$
$487$	6.67495	−	3.85379i	0.302471	−	0.174632i	0.643552	+	0.765402i	$0.277460\pi$
$488$	−17.6884	+	10.3613i	−0.800715	+	0.469033i
$489$	34.7458	−	9.37529i	1.57126	−	0.423965i
$490$	−5.12130	+	6.23570i	−0.231357	+	0.281700i
$491$	−22.3770	−	12.9194i	−1.00986	−	0.583043i	−0.0987099	−	0.995116i	$-0.531472\pi$
$491$	−22.3770	−	12.9194i	−1.00986	−	0.583043i	−0.911151	+	0.412073i	$0.864805\pi$
$492$	9.94239	−	7.05015i	0.448237	−	0.317846i
$493$	3.18270	+	1.83753i	0.143342	+	0.0827583i
$494$	10.3914	+	12.3314i	0.467532	+	0.554817i
$495$	−0.0412606	−	11.7934i	−0.00185453	−	0.530072i
$496$	−29.2822	+	24.9922i	−1.31481	+	1.12218i
$497$	6.16267	−	7.40771i	0.276433	−	0.332281i
$498$	0.335131	−	4.00804i	0.0150176	−	0.179605i
$499$	−32.2276	+	18.6066i	−1.44271	+	0.832947i	−0.998030	−	0.0627448i	$-0.980015\pi$
$499$	−32.2276	+	18.6066i	−1.44271	+	0.832947i	−0.444676	+	0.895691i	$0.646681\pi$
$500$	−5.26515	−	14.2793i	−0.235465	−	0.638590i
$501$	0.928166	+	3.43988i	0.0414674	+	0.153683i
$502$	−2.44974	−	13.7249i	−0.109337	−	0.612571i
$503$	11.8075			0.526469			0.263235	−	0.964732i	$-0.415211\pi$
$503$	11.8075			0.526469			0.263235	+	0.964732i	$0.415211\pi$
$504$	−22.1613	−	3.58821i	−0.987144	−	0.159832i
$505$	7.67615			0.341584
$506$	7.76138	+	43.4837i	0.345036	+	1.93309i
$507$	−10.9281	−	2.90770i	−0.485334	−	0.129135i
$508$	−0.746842	−	2.02546i	−0.0331357	−	0.0898654i
$509$	3.18924	−	1.84131i	0.141361	−	0.0816146i	−0.427652	−	0.903944i	$-0.640659\pi$
$509$	3.18924	−	1.84131i	0.141361	−	0.0816146i	0.569012	+	0.822329i	$0.307326\pi$
$510$	−1.04965	+	0.494383i	−0.0464792	+	0.0218916i
$511$	6.80833	+	1.17086i	0.301183	+	0.0517958i
$512$	22.6234	−	0.426943i	0.999822	−	0.0188684i
$513$	22.4661	−	6.14633i	0.991904	−	0.271367i
$514$	12.4732	+	14.8018i	0.550167	+	0.652879i
$515$	3.63695	+	2.09979i	0.160263	+	0.0925280i
$516$	−1.75821	−	18.8084i	−0.0774007	−	0.827994i
$517$	−40.0144	−	23.1023i	−1.75983	−	1.01604i
$518$	6.16530	+	10.5244i	0.270888	+	0.462416i
$519$	17.6991	+	17.6373i	0.776903	+	0.774189i
$520$	2.96428	+	5.06050i	0.129992	+	0.221918i
$521$	−10.9116	+	6.29980i	−0.478045	+	0.275999i	−0.719601	−	0.694387i	$-0.755675\pi$
$521$	−10.9116	+	6.29980i	−0.478045	+	0.275999i	0.241557	+	0.970387i	$0.422342\pi$
$522$	−17.3616	−	20.4572i	−0.759896	−	0.895386i
$523$	−9.32093	+	16.1443i	−0.407576	+	0.705942i	−0.994618	−	0.103615i	$-0.966959\pi$
$523$	−9.32093	+	16.1443i	−0.407576	+	0.705942i	0.587042	+	0.809557i	$0.300292\pi$
$524$	−13.4501	−	11.1902i	−0.587571	−	0.488846i
$525$	−8.28895	+	18.0565i	−0.361759	+	0.788052i
$526$	−7.50276	+	20.7489i	−0.327136	+	0.904696i
$527$	4.84353	−	2.79641i	0.210988	−	0.121814i
$528$	18.8869	−	27.5637i	0.821945	−	1.19955i
$529$	9.47042	−	16.4033i	0.411758	−	0.713185i
$530$	0.858330	−	2.37372i	0.0372835	−	0.103108i
$531$	−0.117614	−	33.6171i	−0.00510400	−	1.45886i
$532$	18.0409	−	15.3988i	0.782173	−	0.667621i
$533$	4.47522	+	7.75131i	0.193843	+	0.335746i
$534$	−2.29860	−	4.88026i	−0.0994700	−	0.211190i
$535$	9.85094			0.425893
$536$	−12.2530	+	7.17740i	−0.529249	+	0.310017i
$537$	−1.72398	+	6.47931i	−0.0743954	+	0.279603i
$538$	19.4964	+	23.1362i	0.840548	+	0.997471i
$539$	−11.2781	+	31.8203i	−0.485783	+	1.37060i
$540$	8.43129	−	0.817922i	0.362825	−	0.0351977i
$541$	−9.06775	+	15.7058i	−0.389853	+	0.675245i	−0.992429	−	0.122816i	$-0.960807\pi$
$541$	−9.06775	+	15.7058i	−0.389853	+	0.675245i	0.602577	+	0.798061i	$0.294141\pi$
$542$	−3.62331	−	1.31018i	−0.155635	−	0.0562771i
$543$	−30.5084	−	30.4018i	−1.30924	−	1.30467i
$544$	−3.24312	−	0.536859i	−0.139048	−	0.0230176i
$545$	2.59702	+	1.49939i	0.111244	+	0.0642269i
$546$	4.13824	−	15.9582i	0.177100	−	0.682946i
$547$	−24.9748	+	14.4192i	−1.06784	+	0.616520i	−0.927592	−	0.373596i	$-0.878125\pi$
$547$	−24.9748	+	14.4192i	−1.06784	+	0.616520i	−0.140252	+	0.990116i	$0.544791\pi$
$548$	−2.92279	+	16.9923i	−0.124856	+	0.725877i
$549$	−21.7430	+	0.0760707i	−0.927969	+	0.00324662i
$550$	−19.0553	−	22.6128i	−0.812523	−	0.964214i
$551$	28.3482			1.20767
$552$	−30.5786	+	8.45756i	−1.30151	+	0.359978i
$553$	−17.1609	+	20.6279i	−0.729755	+	0.877186i
$554$	−15.1492	−	5.47792i	−0.643628	−	0.232734i
$555$	−3.26002	−	3.24863i	−0.138380	−	0.137897i
$556$	3.14653	−	18.2931i	0.133442	−	0.775799i
$557$	−6.31355	−	10.9354i	−0.267514	−	0.463347i	0.700705	−	0.713451i	$-0.252869\pi$
$557$	−6.31355	−	10.9354i	−0.267514	−	0.463347i	−0.968219	+	0.250103i	$0.919535\pi$
$558$	−40.1721	+	7.31542i	−1.70062	+	0.309686i
$559$	13.8721			0.586725
$560$	7.41562	−	4.40702i	0.313367	−	0.186231i
$561$	−3.42647	+	3.43847i	−0.144666	+	0.145173i
$562$	33.5563	−	28.2772i	1.41549	−	1.19280i
$563$	−9.37380			−0.395059			−0.197529	−	0.980297i	$-0.563292\pi$
$563$	−9.37380			−0.395059			−0.197529	+	0.980297i	$0.563292\pi$
$564$	13.8466	−	30.1608i	0.583048	−	1.27000i
$565$			4.53025i			0.190589i
$566$	1.00780	+	5.64626i	0.0423609	+	0.237330i
$567$	−18.4115	−	15.1003i	−0.773209	−	0.634151i
$568$	−8.88863	+	5.20667i	−0.372959	+	0.218467i
$569$	39.3939			1.65148			0.825739	−	0.564053i	$-0.190759\pi$
$569$	39.3939			1.65148			0.825739	+	0.564053i	$0.190759\pi$
$570$	−5.10514	+	7.35091i	−0.213831	+	0.307896i
$571$		−	5.77562i		−	0.241702i	−0.992671	−	0.120851i	$-0.961438\pi$
$571$		−	5.77562i		−	0.241702i	0.992671	−	0.120851i	$-0.0385624\pi$
$572$	18.8625	+	15.6932i	0.788679	+	0.656165i
$573$	22.7390	+	22.6596i	0.949934	+	0.946617i
$574$	11.3593	−	6.65439i	0.474129	−	0.277749i
$575$			28.0781i			1.17094i
$576$	20.9749	+	11.6643i	0.873952	+	0.486012i
$577$	−25.4955	+	14.7198i	−1.06139	+	0.612794i	−0.925817	−	0.377973i	$-0.876621\pi$
$577$	−25.4955	+	14.7198i	−1.06139	+	0.612794i	−0.135574	+	0.990767i	$0.543288\pi$
$578$	−22.1598	−	8.01294i	−0.921727	−	0.333294i
$579$	32.2160	−	32.3289i	1.33885	−	1.34354i
$580$	10.1606	+	1.74770i	0.421898	+	0.0725691i
$581$	0.736299	−	4.28144i	0.0305468	−	0.177624i
$582$	−17.3275	−	1.44884i	−0.718250	−	0.0600562i
$583$		−	10.5605i		−	0.437371i
$584$	−6.41892	−	3.65233i	−0.265617	−	0.151134i
$585$	0.0217632	+	6.22050i	0.000899798	+	0.257186i
$586$	−10.3022	+	28.4908i	−0.425580	+	1.17694i
$587$	−2.66633	−	4.61821i	−0.110051	−	0.190614i	0.805740	−	0.592270i	$-0.201768\pi$
$587$	−2.66633	−	4.61821i	−0.110051	−	0.190614i	−0.915791	+	0.401656i	$0.868435\pi$
$588$	−23.5103	−	5.93832i	−0.969550	−	0.244892i
$589$	21.5706	−	37.3614i	0.888801	−	1.53945i
$590$	8.32382	+	9.87781i	0.342686	+	0.406663i
$591$	−6.18129	+	6.20296i	−0.254264	+	0.255156i
$592$	−2.37189	−	12.8219i	−0.0974842	−	0.526978i
$593$	37.9363	+	21.9025i	1.55786	+	0.899429i	0.997462	+	0.0712043i	$0.0226842\pi$
$593$	37.9363	+	21.9025i	1.55786	+	0.899429i	0.560396	+	0.828225i	$0.310649\pi$
$594$	32.0091	−	15.2133i	1.31335	−	0.624209i
$595$	−1.17581	+	0.433594i	−0.0482036	+	0.0177756i
$596$	16.8282	+	14.0007i	0.689308	+	0.573490i
$597$	−36.5635	−	9.72865i	−1.49645	−	0.398167i
$598$	−4.09380	−	22.9358i	−0.167408	−	0.937914i
$599$		−	22.8992i		−	0.935635i	−0.883825	−	0.467817i	$-0.845041\pi$
$599$		−	22.8992i		−	0.935635i	0.883825	−	0.467817i	$-0.154959\pi$
$600$	14.8977	−	15.1392i	0.608197	−	0.618055i
$601$	23.6446	−	13.6512i	0.964482	−	0.556844i	0.0669322	−	0.997758i	$-0.478679\pi$
$601$	23.6446	−	13.6512i	0.964482	−	0.556844i	0.897549	+	0.440914i	$0.145346\pi$
$602$	−0.128969	−	20.4036i	−0.00525640	−	0.831587i
$603$	−15.0617	+	0.0526953i	−0.613359	+	0.00214592i
$604$	−0.749247	−	0.128875i	−0.0304864	−	0.00524386i
$605$	8.65425	+	4.99654i	0.351845	+	0.203138i
$606$	9.82913	+	20.8687i	0.399281	+	0.847734i
$607$	5.86613	+	10.1604i	0.238099	+	0.412399i	0.960169	−	0.279421i	$-0.0901424\pi$
$607$	5.86613	+	10.1604i	0.238099	+	0.412399i	−0.722070	+	0.691820i	$0.756809\pi$
$608$	−23.7354	+	8.92185i	−0.962597	+	0.361829i
$609$	−16.7644	−	23.6403i	−0.679329	−	0.957951i
$610$	6.38882	−	5.38372i	0.258676	−	0.217981i
$611$	21.1059	+	12.1855i	0.853852	+	0.492972i
$612$	−2.68810	−	2.22057i	−0.108660	−	0.0897614i
$613$	−1.66771	−	2.88856i	−0.0673582	−	0.116668i	0.830379	−	0.557198i	$-0.188124\pi$
$613$	−1.66771	−	2.88856i	−0.0673582	−	0.116668i	−0.897738	+	0.440531i	$0.854790\pi$
$614$	4.82296	+	27.0210i	0.194639	+	1.09048i
$615$	−3.50635	+	3.51864i	−0.141390	+	0.141885i
$616$	22.9068	−	27.8896i	0.922940	−	1.12370i
$617$	14.7956	−	25.6267i	0.595648	−	1.03169i	−0.397807	−	0.917469i	$-0.630229\pi$
$617$	14.7956	−	25.6267i	0.595648	−	1.03169i	0.993455	−	0.114224i	$-0.0364381\pi$
$618$	−1.05156	+	12.5763i	−0.0423001	+	0.505893i
$619$	−15.8213	+	27.4033i	−0.635912	+	1.10143i	0.350410	+	0.936597i	$0.386042\pi$
$619$	−15.8213	+	27.4033i	−0.635912	+	1.10143i	−0.986321	+	0.164835i	$0.947291\pi$
$620$	10.0348	−	12.0613i	0.403006	−	0.484394i
$621$	−32.5498	−	8.53887i	−1.30618	−	0.342653i
$622$	−2.66625	−	14.9378i	−0.106907	−	0.598952i
$623$	−2.01596	−	5.46685i	−0.0807679	−	0.219025i
$624$	−9.96201	+	14.5387i	−0.398800	+	0.582012i
$625$	−7.73768	−	13.4021i	−0.309507	−	0.536082i
$626$	−33.9783	+	6.06477i	−1.35804	+	0.242397i
$627$	−9.62796	+	36.1851i	−0.384504	+	1.44509i
$628$	3.43343	+	9.31159i	0.137009	+	0.371573i
$629$			1.89434i			0.0755325i
$630$	9.14915	−	0.0898426i	0.364511	−	0.00357941i
$631$			6.61866i			0.263485i	0.991284	+	0.131742i	$0.0420572\pi$
$631$			6.61866i			0.263485i	−0.991284	+	0.131742i	$0.957943\pi$
$632$	24.7517	−	14.4988i	0.984571	−	0.576730i
$633$	42.8796	−	11.5700i	1.70431	−	0.459866i
$634$	7.98266	+	44.7234i	0.317032	+	1.77619i
$635$	0.439908	+	0.761943i	0.0174572	+	0.0302368i
$636$	7.55236	−	0.705993i	0.299470	−	0.0279945i
$637$	5.94873	−	16.7839i	0.235697	−	0.665001i
$638$	42.4633	−	7.57926i	1.68114	−	0.300066i
$639$	−10.9261	+	0.0382265i	−0.432231	+	0.00151222i
$640$	−9.05734	+	1.73448i	−0.358023	+	0.0685613i
$641$	−15.1406	+	26.2243i	−0.598018	+	1.03580i	0.395096	+	0.918640i	$0.370711\pi$
$641$	−15.1406	+	26.2243i	−0.598018	+	1.03580i	−0.993113	+	0.117157i	$0.962622\pi$
$642$	12.6139	+	26.7812i	0.497831	+	1.05697i
$643$	−8.34512	+	14.4542i	−0.329099	+	0.570017i	−0.982333	−	0.187139i	$-0.940078\pi$
$643$	−8.34512	+	14.4542i	−0.329099	+	0.570017i	0.653234	+	0.757156i	$0.273412\pi$
$644$	−33.6968	+	6.23456i	−1.32784	+	0.245676i
$645$	2.00562	+	7.43305i	0.0789713	+	0.292676i
$646$	3.62647	−	0.647286i	0.142681	−	0.0254671i
$647$	14.3660	+	24.8826i	0.564786	+	0.978237i	0.997070	+	0.0764997i	$0.0243744\pi$
$647$	14.3660	+	24.8826i	0.564786	+	0.978237i	−0.432284	+	0.901737i	$0.642292\pi$
$648$	13.0197	+	21.8743i	0.511462	+	0.859306i
$649$	46.8031	+	27.0218i	1.83718	+	1.06070i
$650$	10.0509	+	11.9273i	0.394228	+	0.467827i
$651$	−43.9129	+	4.10634i	−1.72108	+	0.160940i
$652$	−40.9545	−	7.04444i	−1.60390	−	0.275881i
$653$	4.63161	+	8.02218i	0.181249	+	0.313932i	0.942306	−	0.334753i	$-0.108653\pi$
$653$	4.63161	+	8.02218i	0.181249	+	0.313932i	−0.761057	+	0.648685i	$0.775319\pi$
$654$	−0.750885	+	8.98031i	−0.0293619	+	0.351158i
$655$	6.17543	+	3.56538i	0.241294	+	0.139311i
$656$	−13.8391	+	2.56005i	−0.540326	+	0.0999533i
$657$	−3.94033	−	6.77005i	−0.153727	−	0.264125i
$658$	17.7267	−	31.1566i	0.691057	−	1.21461i
$659$	0.465951	−	0.269017i	0.0181509	−	0.0104794i	−0.490897	−	0.871218i	$-0.663331\pi$
$659$	0.465951	−	0.269017i	0.0181509	−	0.0104794i	0.509048	+	0.860738i	$0.329998\pi$
$660$	−5.68172	+	12.3760i	−0.221161	+	0.481734i
$661$		−	23.1477i		−	0.900342i	−0.892942	−	0.450171i	$-0.851363\pi$
$661$		−	23.1477i		−	0.900342i	0.892942	−	0.450171i	$-0.148637\pi$
$662$	36.4011	−	6.49722i	1.41477	−	0.252522i
$663$	1.80731	−	1.81365i	0.0701903	−	0.0704363i
$664$	−2.29678	+	4.03656i	−0.0891322	+	0.156649i
$665$	−6.18240	+	7.43142i	−0.239743	+	0.288178i
$666$	4.65750	−	13.0226i	0.180474	−	0.504617i
$667$	−35.4695	−	20.4783i	−1.37339	−	0.792924i
$668$	0.697408	−	4.05454i	0.0269835	−	0.156875i
$669$	−41.1862	−	10.9586i	−1.59235	−	0.423684i
$670$	4.42563	−	3.72938i	0.170977	−	0.144079i
$671$	17.4773	−	30.2715i	0.674703	−	1.16862i
$672$	21.4767	+	14.5173i	0.828480	+	0.560019i
$673$	−11.9724	−	20.7368i	−0.461503	−	0.799346i	0.537533	−	0.843243i	$-0.319356\pi$
$673$	−11.9724	−	20.7368i	−0.461503	−	0.799346i	−0.999036	+	0.0438961i	$0.986023\pi$
$674$	7.70283	+	2.78533i	0.296702	+	0.107287i
$675$	21.7299	−	5.94490i	0.836383	−	0.228819i
$676$	10.0379	+	8.35133i	0.386073	+	0.321205i
$677$		−	35.0977i		−	1.34891i	−0.738314	−	0.674457i	$-0.764378\pi$
$677$		−	35.0977i		−	1.34891i	0.738314	−	0.674457i	$-0.235622\pi$
$678$	−12.3161	+	5.80088i	−0.472998	+	0.222781i
$679$	−18.5095	−	3.18316i	−0.710329	−	0.122159i
$680$	1.33971	−	0.00842668i	0.0513756	−	0.000323149i
$681$	−9.90651	−	36.7146i	−0.379618	−	1.40691i
$682$	22.3220	−	61.7315i	0.854752	−	2.36382i
$683$	21.2103	−	12.2458i	0.811591	−	0.468572i	−0.0359174	−	0.999355i	$-0.511435\pi$
$683$	21.2103	−	12.2458i	0.811591	−	0.468572i	0.847508	+	0.530783i	$0.178102\pi$
$684$	−26.5215	−	4.46640i	−1.01408	−	0.170777i
$685$		−	7.02702i		−	0.268488i
$686$	−24.7417	−	8.59359i	−0.944641	−	0.328105i
$687$	4.76848	−	17.9215i	0.181929	−	0.683749i
$688$	−7.28824	+	20.5591i	−0.277862	+	0.783810i
$689$			5.57021i			0.212208i
$690$	11.6978	−	5.50963i	0.445327	−	0.209748i
$691$	17.2066			0.654569			0.327285	−	0.944926i	$-0.393866\pi$
$691$	17.2066			0.654569			0.327285	+	0.944926i	$0.393866\pi$
$692$	−9.98157	−	27.0704i	−0.379443	−	1.02906i
$693$	35.8693	−	13.3700i	1.36256	−	0.507883i
$694$	−20.7505	+	3.70374i	−0.787677	+	0.140592i
$695$			7.56492i			0.286954i
$696$	8.25909	+	29.8610i	0.313060	+	1.13188i
$697$	2.04462			0.0774456
$698$	2.36690	+	2.80878i	0.0895886	+	0.106314i
$699$	−1.95937	−	7.26162i	−0.0741101	−	0.274660i
$700$	17.4497	−	14.8941i	0.659537	−	0.562945i
$701$	3.54331			0.133829			0.0669145	−	0.997759i	$-0.478685\pi$
$701$	3.54331			0.133829			0.0669145	+	0.997759i	$0.478685\pi$
$702$	−16.8834	+	8.02437i	−0.637225	+	0.302860i
$703$	7.30617	+	12.6547i	0.275557	+	0.477279i
$704$	−33.1683	+	19.7102i	−1.25008	+	0.742854i
$705$	−3.47785	+	13.0709i	−0.130983	+	0.492279i
$706$	6.47661	−	17.9111i	0.243751	−	0.674093i
$707$	8.62056	+	23.3771i	0.324210	+	0.879185i
$708$	−16.1958	+	35.2778i	−0.608675	+	1.32582i
$709$	−3.01099			−0.113080			−0.0565401	−	0.998400i	$-0.518007\pi$
$709$	−3.01099			−0.113080			−0.0565401	+	0.998400i	$0.518007\pi$
$710$	3.21046	−	2.70539i	0.120487	−	0.101531i
$711$	30.4255	−	0.106447i	1.14104	−	0.00399209i
$712$	0.0391792	+	6.22890i	0.00146830	+	0.233438i
$713$	−53.9786	+	31.1646i	−2.02152	+	1.16712i
$714$	−2.68439	−	2.64141i	−0.100461	−	0.0988522i
$715$	−8.66044	−	5.00011i	−0.323882	−	0.186993i
$716$	4.95153	−	5.95151i	0.185047	−	0.222418i
$717$	−17.7186	+	4.78092i	−0.661713	+	0.178547i
$718$	8.73444	−	24.1551i	0.325966	−	0.901461i
$719$	−8.34116	+	14.4473i	−0.311073	+	0.538794i	−0.978595	−	0.205796i	$-0.934022\pi$
$719$	−8.34116	+	14.4473i	−0.311073	+	0.538794i	0.667522	+	0.744590i	$0.267355\pi$
$720$	−9.23055	−	3.23593i	−0.344002	−	0.120596i
$721$	−2.31033	+	13.4342i	−0.0860413	+	0.500314i
$722$	1.18175	−	0.995833i	0.0439800	−	0.0370611i
$723$	−11.4106	+	3.07887i	−0.424366	+	0.114504i
$724$	17.2055	+	46.6620i	0.639438	+	1.73418i
$725$	27.4192			1.01832
$726$	−2.50223	+	29.9258i	−0.0928665	+	1.11065i
$727$	18.9577	+	32.8358i	0.703104	+	1.21781i	0.967372	+	0.253362i	$0.0815364\pi$
$727$	18.9577	+	32.8358i	0.703104	+	1.21781i	−0.264268	+	0.964449i	$0.585130\pi$
$728$	−12.0823	+	14.7106i	−0.447802	+	0.545209i
$729$	0.283383	+	26.9985i	0.0104957	+	0.999945i
$730$	2.83053	+	1.02351i	0.104763	+	0.0378820i
$731$	1.58445	−	2.74435i	0.0586031	−	0.101504i
$732$	22.8172	+	10.4752i	0.843346	+	0.387174i
$733$	20.3825	−	11.7678i	0.752845	−	0.434655i	−0.0738758	−	0.997267i	$-0.523537\pi$
$733$	20.3825	−	11.7678i	0.752845	−	0.434655i	0.826721	+	0.562612i	$0.190204\pi$
$734$	−14.8603	−	5.37344i	−0.548502	−	0.198337i
$735$	9.85335	+	0.760892i	0.363446	+	0.0280659i
$736$	36.1429	+	5.98301i	1.33225	+	0.220537i
$737$	12.1068	−	20.9695i	0.445958	−	0.772422i
$738$	−14.0557	−	5.02698i	−0.517398	−	0.185046i
$739$	−24.3790	+	14.0752i	−0.896797	+	0.517766i	−0.876160	−	0.482021i	$-0.839903\pi$
$739$	−24.3790	+	14.0752i	−0.896797	+	0.517766i	−0.0206373	+	0.999787i	$0.506570\pi$
$740$	1.83852	+	4.98614i	0.0675854	+	0.183294i
$741$	5.07834	−	19.0861i	0.186557	−	0.701145i
$742$	8.19288	−	0.0517866i	0.300770	−	0.00190115i
$743$	43.7349	+	25.2504i	1.60448	+	0.926347i	0.990576	+	0.136966i	$0.0437350\pi$
$743$	43.7349	+	25.2504i	1.60448	+	0.926347i	0.613904	+	0.789381i	$0.289598\pi$
$744$	45.6397	+	11.8367i	1.67323	+	0.433955i
$745$	−7.72641	−	4.46085i	−0.283074	−	0.163433i
$746$	−33.3110	+	28.0705i	−1.21960	+	1.02773i
$747$	−4.25736	+	2.47789i	−0.155769	+	0.0906612i
$748$	5.25909	−	1.93916i	0.192291	−	0.0709029i
$749$	11.0629	+	30.0002i	0.404230	+	1.09618i
$750$	−10.6324	+	15.3096i	−0.388239	+	0.559027i
$751$	−3.53155	+	2.03894i	−0.128868	+	0.0744020i	−0.563048	−	0.826424i	$-0.690371\pi$
$751$	−3.53155	+	2.03894i	−0.128868	+	0.0744020i	0.434180	+	0.900826i	$0.357038\pi$
$752$	−29.1484	+	24.8779i	−1.06293	+	0.907204i
$753$	−12.0528	+	12.0950i	−0.439228	+	0.440767i
$754$	−22.3976	+	3.99774i	−0.815672	+	0.145589i
$755$	0.309844			0.0112764
$756$	11.9595	+	24.7582i	0.434963	+	0.900448i
$757$	−6.31380			−0.229479			−0.114739	−	0.993396i	$-0.536603\pi$
$757$	−6.31380			−0.229479			−0.114739	+	0.993396i	$0.536603\pi$
$758$	7.72450	−	1.37874i	0.280566	−	0.0500782i
$759$	38.1862	−	38.3200i	1.38607	−	1.39093i
$760$	8.91709	−	5.22334i	0.323457	−	0.189470i
$761$	15.3919	−	8.88652i	0.557956	−	0.322136i	−0.194368	−	0.980929i	$-0.562266\pi$
$761$	15.3919	−	8.88652i	0.557956	−	0.322136i	0.752325	+	0.658792i	$0.228932\pi$
$762$	−1.50816	+	2.17160i	−0.0546349	+	0.0786689i
$763$	−1.64973	+	9.59287i	−0.0597243	+	0.347285i
$764$	−12.8239	−	34.7789i	−0.463952	−	1.25826i
$765$	1.23311	+	0.706194i	0.0445831	+	0.0255325i
$766$	9.31493	−	7.84949i	0.336562	−	0.283614i
$767$	−24.6866	−	14.2528i	−0.891383	−	0.514640i
$768$	−16.3131	−	22.4027i	−0.588650	−	0.808388i
$769$	−21.8160	−	12.5955i	−0.786706	−	0.454205i	0.0520959	−	0.998642i	$-0.483410\pi$
$769$	−21.8160	−	12.5955i	−0.786706	−	0.454205i	−0.838801	+	0.544437i	$0.816743\pi$
$770$	−7.27384	+	12.7846i	−0.262131	+	0.460725i
$771$	6.09568	−	22.9096i	0.219531	−	0.825070i
$772$	−49.4465	+	18.2322i	−1.77962	+	0.656192i
$773$	35.8079	−	20.6737i	1.28792	−	0.743582i	0.309639	−	0.950854i	$-0.399792\pi$
$773$	35.8079	−	20.6737i	1.28792	−	0.743582i	0.978283	+	0.207272i	$0.0664585\pi$
$774$	−17.6397	+	14.9704i	−0.634044	+	0.538101i
$775$	20.8637	−	36.1370i	0.749446	−	1.29808i
$776$	17.4508	+	9.92941i	0.626448	+	0.356445i
$777$	6.23233	−	13.5764i	0.223584	−	0.487052i
$778$	−4.63001	−	1.67420i	−0.165994	−	0.0600230i
$779$	13.6585	−	7.88576i	0.489368	−	0.282537i
$780$	2.99687	−	6.52780i	0.107305	−	0.233733i
$781$	8.78255	−	15.2118i	0.314264	−	0.544322i
$782$	−5.00505	−	1.80982i	−0.178980	−	0.0647189i
$783$	−8.33850	+	31.7860i	−0.297994	+	1.13594i
$784$	21.7492	+	17.6344i	0.776757	+	0.629801i
$785$	−2.02238	−	3.50286i	−0.0721817	−	0.125022i
$786$	−1.78552	+	21.3542i	−0.0636874	+	0.761678i
$787$	19.4885			0.694690			0.347345	−	0.937737i	$-0.387083\pi$
$787$	19.4885			0.694690			0.347345	+	0.937737i	$0.387083\pi$
$788$	9.48732	−	3.49822i	0.337972	−	0.124619i
$789$	26.0894	−	7.03958i	0.928808	−	0.250616i
$790$	−8.94002	+	7.53356i	−0.318071	+	0.268032i
$791$	−13.7965	+	5.08761i	−0.490547	+	0.180895i
$792$	−40.9212	+	0.400568i	−1.45407	+	0.0142336i
$793$	−9.21852	+	15.9669i	−0.327359	+	0.567003i
$794$	8.66202	−	23.9549i	0.307404	−	0.850126i
$795$	−2.98468	+	0.805341i	−0.105856	+	0.0285625i
$796$	33.5851	+	27.9421i	1.19039	+	0.990381i
$797$	−19.1331	−	11.0465i	−0.677729	−	0.391287i	0.121270	−	0.992620i	$-0.461303\pi$
$797$	−19.1331	−	11.0465i	−0.677729	−	0.391287i	−0.798999	+	0.601333i	$0.794637\pi$
$798$	−28.1198	−	7.29197i	−0.995430	−	0.258133i
$799$	4.82139	−	2.78363i	0.170568	−	0.0984778i
$800$	−22.9575	+	8.62946i	−0.811672	+	0.305098i
$801$	−3.28340	+	5.73324i	−0.116013	+	0.202574i
$802$	15.4707	−	13.0369i	0.546290	−	0.460347i
$803$	12.5928			0.444392
$804$	15.8058	+	7.25631i	0.557426	+	0.255910i
$805$	13.1038	−	4.83218i	0.461849	−	0.170312i
$806$	−11.7739	+	32.5607i	−0.414717	+	1.14690i
$807$	9.52796	−	35.8093i	0.335400	−	1.26055i
$808$	−0.167536	−	26.6357i	−0.00589390	−	0.937040i
$809$	−3.36792	−	5.83340i	−0.118410	−	0.205091i	0.800728	−	0.599028i	$-0.204446\pi$
$809$	−3.36792	−	5.83340i	−0.118410	−	0.205091i	−0.919138	+	0.393937i	$0.871113\pi$
$810$	−6.74070	−	7.88648i	−0.236844	−	0.277103i
$811$	52.9099			1.85792			0.928960	−	0.370181i	$-0.120704\pi$
$811$	52.9099			1.85792			0.928960	+	0.370181i	$0.120704\pi$
$812$	6.08826	+	32.9061i	0.213656	+	1.15478i
$813$	1.22930	+	4.55591i	0.0431133	+	0.159783i
$814$	14.3274	+	17.0022i	0.502176	+	0.595928i
$815$	16.9363			0.593253
$816$	1.73838	+	3.63141i	0.0608555	+	0.127125i
$817$		−	24.4439i		−	0.855183i
$818$	−54.5359	+	9.73409i	−1.90680	+	0.340344i
$819$	−18.9196	+	7.05209i	−0.661103	+	0.246420i
$820$	5.38170	−	1.98437i	0.187937	−	0.0692973i
$821$	11.8882			0.414903			0.207451	−	0.978245i	$-0.433483\pi$
$821$	11.8882			0.414903			0.207451	+	0.978245i	$0.433483\pi$
$822$	19.1040	−	8.99793i	0.666327	−	0.313839i
$823$			27.8356i			0.970287i	0.874435	+	0.485143i	$0.161233\pi$
$823$			27.8356i			0.970287i	−0.874435	+	0.485143i	$0.838767\pi$
$824$	7.20675	−	12.6658i	0.251059	−	0.441233i
$825$	−9.31243	+	34.9993i	−0.324217	+	1.21852i
$826$	−20.7341	+	36.4426i	−0.721432	+	1.26800i
$827$		−	30.7186i		−	1.06819i	−0.845424	−	0.534095i	$-0.820652\pi$
$827$		−	30.7186i		−	1.06819i	0.845424	−	0.534095i	$-0.179348\pi$
$828$	29.9575	+	24.7471i	1.04109	+	0.860022i
$829$	11.1106	−	6.41474i	0.385889	−	0.222793i	−0.294488	−	0.955655i	$-0.595149\pi$
$829$	11.1106	−	6.41474i	0.385889	−	0.222793i	0.680377	+	0.732862i	$0.261816\pi$
$830$	0.643640	−	1.77999i	0.0223411	−	0.0617843i
$831$	5.13974	+	19.0484i	0.178295	+	0.660782i
$832$	17.4949	−	10.3963i	0.606525	−	0.360426i
$833$	−2.64095	−	3.09390i	−0.0915035	−	0.107197i
$834$	−20.5663	+	9.68670i	−0.712153	+	0.335423i
$835$			1.67672i			0.0580252i
$836$	27.6529	−	33.2375i	0.956395	−	1.14954i
$837$	35.5473	+	35.1762i	1.22869	+	1.21587i
$838$	−30.1903	−	10.9167i	−1.04291	−	0.377113i
$839$	1.26520	+	2.19139i	0.0436795	+	0.0756551i	0.887039	−	0.461695i	$-0.152759\pi$
$839$	1.26520	+	2.19139i	0.0436795	+	0.0756551i	−0.843359	+	0.537350i	$0.819425\pi$
$840$	−9.62921	−	4.34722i	−0.332239	−	0.149993i
$841$	−5.49779	+	9.52246i	−0.189579	+	0.328361i
$842$	2.01529	−	1.69824i	0.0694515	−	0.0585253i
$843$	−51.9371	−	13.8192i	−1.78881	−	0.475958i
$844$	−50.5417	−	8.69350i	−1.73972	−	0.299243i
$845$	−4.60877	−	2.66087i	−0.158546	−	0.0915368i
$846$	−39.9885	+	7.28198i	−1.37483	+	0.250360i
$847$	−5.49752	+	31.9671i	−0.188897	+	1.09840i
$848$	−8.25535	−	2.92653i	−0.283490	−	0.100498i
$849$	4.95839	−	4.97577i	0.170171	−	0.170768i
$850$	3.50762	−	0.626074i	0.120310	−	0.0214742i
$851$		−	21.1115i		−	0.723692i
$852$	11.4659	+	5.26392i	0.392816	+	0.180339i
$853$	−15.4010	+	8.89177i	−0.527320	+	0.304448i	−0.739924	−	0.672690i	$-0.765139\pi$
$853$	−15.4010	+	8.89177i	−0.527320	+	0.304448i	0.212605	+	0.977138i	$0.431805\pi$
$854$	23.5705	+	13.4105i	0.806566	+	0.458898i
$855$	10.9611	−	0.0383489i	0.374862	−	0.00131150i
$856$	−0.215002	−	34.1820i	−0.00734862	−	1.16832i
$857$	−20.7330	−	11.9702i	−0.708224	−	0.408894i	0.102179	−	0.994766i	$-0.467419\pi$
$857$	−20.7330	−	11.9702i	−0.708224	−	0.408894i	−0.810403	+	0.585873i	$0.800752\pi$
$858$	2.50402	−	29.9472i	0.0854858	−	1.02238i
$859$	−23.3482	−	40.4402i	−0.796629	−	1.37980i	−0.921799	−	0.387667i	$-0.873281\pi$
$859$	−23.3482	−	40.4402i	−0.796629	−	1.37980i	0.125170	−	0.992135i	$-0.460052\pi$
$860$	1.50699	−	8.76124i	0.0513880	−	0.298756i
$861$	−14.6534	−	6.72674i	−0.499388	−	0.229247i
$862$	−3.98284	−	4.72641i	−0.135656	−	0.160982i
$863$	−34.3329	−	19.8221i	−1.16870	−	0.674752i	−0.215330	−	0.976541i	$-0.569083\pi$
$863$	−34.3329	−	19.8221i	−1.16870	−	0.674752i	−0.953375	+	0.301789i	$0.902416\pi$
$864$	−3.02214	−	29.2381i	−0.102815	−	0.994700i
$865$	5.87940	+	10.1834i	0.199905	+	0.346246i
$866$	−13.6197	+	2.43097i	−0.462815	+	0.0826076i
$867$	7.51826	+	27.8635i	0.255334	+	0.946293i
$868$	48.0010	+	17.0148i	1.62926	+	0.577519i
$869$	−24.4563	+	42.3596i	−0.829624	+	1.43695i
$870$	−5.38035	−	11.4233i	−0.182411	−	0.387286i
$871$	−6.38580	+	11.0605i	−0.216375	+	0.374772i
$872$	5.14609	−	9.04420i	0.174269	−	0.306275i
$873$	10.7124	+	18.4054i	0.362560	+	0.622929i
$874$	−40.4151	+	7.21367i	−1.36706	+	0.244006i
$875$	−12.8759	+	15.4773i	−0.435286	+	0.523227i
$876$	0.841860	+	9.00579i	0.0284438	+	0.304278i
$877$	−15.0927	−	26.1413i	−0.509644	−	0.882730i	−0.999938	−	0.0111721i	$-0.996444\pi$
$877$	−15.0927	−	26.1413i	−0.509644	−	0.882730i	0.490293	−	0.871557i	$-0.336890\pi$
$878$	0.0957071	+	0.536206i	0.00322996	+	0.0180961i
$879$	35.8239	−	9.66619i	1.20831	−	0.326033i
$880$	11.9605	−	10.2082i	0.403190	−	0.344119i
$881$		−	15.0652i		−	0.507560i	−0.967262	−	0.253780i	$-0.918326\pi$
$881$		−	15.0652i		−	0.507560i	0.967262	−	0.253780i	$-0.0816739\pi$
$882$	10.5484	+	27.7621i	0.355183	+	0.934797i
$883$		−	16.1352i		−	0.542993i	−0.962439	−	0.271497i	$-0.912481\pi$
$883$		−	16.1352i		−	0.542993i	0.962439	−	0.271497i	$-0.0875186\pi$
$884$	−2.77395	+	1.02283i	−0.0932979	+	0.0344014i
$885$	4.06789	−	15.2885i	0.136741	−	0.513917i
$886$	22.5443	−	4.02392i	0.757390	−	0.135186i
$887$	10.9762	+	19.0114i	0.368545	+	0.638339i	0.989338	−	0.145636i	$-0.0465227\pi$
$887$	10.9762	+	19.0114i	0.368545	+	0.638339i	−0.620793	+	0.783974i	$0.713189\pi$
$888$	−11.2014	+	11.3829i	−0.375893	+	0.381986i
$889$	−1.82640	+	2.19539i	−0.0612556	+	0.0736310i
$890$	−0.446076	−	2.49917i	−0.0149525	−	0.0837724i
$891$	−37.7413	−	21.4392i	−1.26438	−	0.718241i
$892$	37.8312	+	31.4747i	1.26668	+	1.05385i
$893$	21.4720	−	37.1906i	0.718533	−	1.24454i
$894$	2.23396	−	26.7174i	0.0747149	−	0.893563i
$895$	−1.57764	+	2.73255i	−0.0527347	+	0.0913392i
$896$	−15.4539	−	25.6355i	−0.516278	−	0.856421i
$897$	−20.1416	+	20.2122i	−0.672508	+	0.674865i
$898$	−8.25900	−	46.2716i	−0.275606	−	1.54410i
$899$	30.4333	+	52.7120i	1.01501	+	1.75804i
$900$	−25.6524	−	4.32003i	−0.855079	−	0.144001i
$901$	1.10197	+	0.636224i	0.0367120	+	0.0211957i
$902$	18.3510	−	15.4640i	0.611022	−	0.514895i
$903$	−20.3843	+	14.4555i	−0.678348	+	0.481049i
$904$	15.7196	−	0.0988751i	0.522827	−	0.00328854i
$905$	−10.1345	−	17.5534i	−0.336882	−	0.583496i
$906$	0.396747	+	0.842354i	0.0131810	+	0.0279853i
$907$	17.6385	+	10.1836i	0.585676	+	0.338140i	0.763386	−	0.645943i	$-0.223536\pi$
$907$	17.6385	+	10.1836i	0.585676	+	0.338140i	−0.177710	+	0.984083i	$0.556869\pi$
$908$	−7.44359	+	43.2750i	−0.247024	+	1.43613i
$909$	14.0403	−	24.5162i	0.465687	−	0.813151i
$910$	3.83664	−	6.74333i	0.127183	−	0.223539i
$911$	−12.6090	+	7.27984i	−0.417756	+	0.241192i	−0.694117	−	0.719862i	$-0.744205\pi$
$911$	−12.6090	+	7.27984i	−0.417756	+	0.241192i	0.276361	+	0.961054i	$0.410872\pi$
$912$	25.6185	+	17.5540i	0.848314	+	0.581272i
$913$		−	7.91904i		−	0.262082i
$914$	−1.37632	−	7.71093i	−0.0455246	−	0.255055i
$915$	−9.88837	−	2.63105i	−0.326899	−	0.0869798i
$916$	−13.6958	+	16.4617i	−0.452520	+	0.543909i
$917$	−3.92287	+	22.8108i	−0.129545	+	0.753278i
$918$	−0.340925	+	4.25664i	−0.0112522	+	0.140490i
$919$	9.46004	+	5.46176i	0.312058	+	0.180167i	0.647847	−	0.761770i	$-0.275670\pi$
$919$	9.46004	+	5.46176i	0.312058	+	0.180167i	−0.335789	+	0.941937i	$0.609003\pi$
$920$	−14.9304	+	0.0939110i	−0.492241	+	0.00309615i
$921$	23.7291	−	23.8122i	0.781899	−	0.784639i
$922$	−5.62982	−	6.68086i	−0.185408	−	0.220022i
$923$	−4.63242	+	8.02359i	−0.152478	+	0.264100i
$924$	−44.0707	−	3.40459i	−1.44982	−	0.112003i
$925$	7.06673	+	12.2399i	0.232353	+	0.402447i
$926$	−5.65459	+	15.6378i	−0.185821	+	0.513889i
$927$	13.3586	−	7.77504i	0.438755	−	0.255366i
$928$	5.84261	−	35.2948i	0.191793	−	1.15861i
$929$			36.7280i			1.20501i	0.798117	+	0.602503i	$0.205830\pi$
$929$			36.7280i			1.20501i	−0.798117	+	0.602503i	$0.794170\pi$
$930$	−19.1492	−	1.60116i	−0.627928	−	0.0525040i
$931$	−29.5748	−	10.4822i	−0.969274	−	0.343541i
$932$	−1.47224	+	8.55918i	−0.0482247	+	0.280365i
$933$	−13.1180	+	13.1640i	−0.429464	+	0.430969i
$934$	36.8965	+	13.3417i	1.20729	+	0.436553i
$935$	−1.97838	+	1.14222i	−0.0646998	+	0.0373544i
$936$	21.5842	−	0.211282i	0.705501	−	0.00690598i
$937$		−	9.07200i		−	0.296369i	−0.988960	−	0.148185i	$-0.952657\pi$
$937$		−	9.07200i		−	0.296369i	0.988960	−	0.148185i	$-0.0473430\pi$
$938$	16.3276	+	9.28965i	0.533116	+	0.303318i
$939$	29.9433	+	29.8388i	0.977164	+	0.973752i
$940$	9.98888	−	12.0062i	0.325801	−	0.391598i
$941$			9.27264i			0.302280i	0.988512	+	0.151140i	$0.0482944\pi$
$941$			9.27264i			0.302280i	−0.988512	+	0.151140i	$0.951706\pi$
$942$	6.93341	−	9.98344i	0.225903	−	0.325278i
$943$	−22.7862			−0.742022
$944$	34.0936	−	29.0986i	1.10965	−	0.947079i
$945$	−6.51411	−	9.11805i	−0.211904	−	0.296610i
$946$	−6.53538	−	36.6149i	−0.212484	−	1.19045i
$947$		−	3.29975i		−	0.107227i	−0.998562	−	0.0536137i	$-0.982926\pi$
$947$		−	3.29975i		−	0.107227i	0.998562	−	0.0536137i	$-0.0170739\pi$
$948$	−31.9285	−	14.6582i	−1.03699	−	0.476075i
$949$	−6.64218			−0.215614
$950$	21.0170	−	17.7106i	0.681883	−	0.574608i
$951$	39.2748	−	39.4125i	1.27357	−	1.27804i
$952$	1.53020	+	4.07052i	0.0495941	+	0.131926i
$953$	−16.0636			−0.520349			−0.260175	−	0.965562i	$-0.583780\pi$
$953$	−16.0636			−0.520349			−0.260175	+	0.965562i	$0.583780\pi$
$954$	−6.01125	−	7.08306i	−0.194621	−	0.229323i
$955$	7.55359	+	13.0832i	0.244428	+	0.423362i
$956$	20.8847	+	3.59230i	0.675458	+	0.116183i
$957$	−37.4208	−	37.2901i	−1.20964	−	1.20542i
$958$	−9.50959	−	3.43865i	−0.307241	−	0.111098i
$959$	21.4002	−	7.89156i	0.691048	−	0.254832i
$960$	8.10003	+	7.87116i	0.261427	+	0.254041i
$961$	61.6286			1.98802
$962$	−7.55710	−	8.96795i	−0.243651	−	0.289138i
$963$	18.0182	−	31.4621i	0.580627	−	1.01385i
$964$	13.4496	+	2.31341i	0.433181	+	0.0745100i
$965$	18.6009	−	10.7392i	0.598784	−	0.345708i
$966$	29.9161	+	29.4371i	0.962535	+	0.947123i
$967$	−13.4318	−	7.75487i	−0.431938	−	0.249380i	0.268234	−	0.963354i	$-0.413560\pi$
$967$	−13.4318	−	7.75487i	−0.431938	−	0.249380i	−0.700172	+	0.713974i	$0.746893\pi$
$968$	17.1487	−	30.1387i	0.551181	−	0.968693i
$969$	−3.19582	−	3.18466i	−0.102665	−	0.102306i
$970$	−7.69523	−	2.78258i	−0.247079	−	0.0893432i
$971$	15.4979	−	26.8432i	0.497352	−	0.861439i	−0.502643	−	0.864494i	$-0.667639\pi$
$971$	15.4979	−	26.8432i	0.497352	−	0.861439i	0.999995	+	0.00305480i	$0.000972375\pi$
$972$	12.8092	−	28.4240i	0.410856	−	0.911700i
$973$	−23.0383	+	8.49564i	−0.738574	+	0.272358i
$974$	7.02397	+	8.33529i	0.225063	+	0.267080i
$975$	4.91191	−	18.4606i	0.157307	−	0.591213i
$976$	−18.8205	−	22.0512i	−0.602431	−	0.705842i
$977$	34.0008			1.08778			0.543891	−	0.839156i	$-0.316950\pi$
$977$	34.0008			1.08778			0.543891	+	0.839156i	$0.316950\pi$
$978$	21.6866	+	46.0438i	0.693459	+	1.47232i
$979$	−5.31065	−	9.19831i	−0.169729	−	0.293979i
$980$	−9.95402	−	5.58038i	−0.317970	−	0.178259i
$981$	9.53893	−	5.55189i	0.304555	−	0.177258i
$982$	12.4259	−	34.3639i	0.396527	−	1.09660i
$983$	−17.2885	+	29.9445i	−0.551416	+	0.955081i	0.446756	+	0.894656i	$0.352579\pi$
$983$	−17.2885	+	29.9445i	−0.551416	+	0.955081i	−0.998173	+	0.0604255i	$0.980754\pi$
$984$	12.2859	+	12.0900i	0.391661	+	0.385414i
$985$	−3.56896	+	2.06054i	−0.113717	+	0.0656543i
$986$	−1.76735	+	4.88761i	−0.0562838	+	0.155653i
$987$	−43.7121	+	4.08757i	−1.39137	+	0.130109i
$988$	−14.5857	+	17.5314i	−0.464034	+	0.557747i
$989$	−17.6579	+	30.5844i	−0.561489	+	0.972527i
$990$	16.4086	−	2.98804i	0.521499	−	0.0949660i
$991$	−46.4705	+	26.8297i	−1.47618	+	0.852275i	−0.999639	−	0.0268752i	$-0.991444\pi$
$991$	−46.4705	+	26.8297i	−1.47618	+	0.852275i	−0.476545	+	0.879150i	$0.658111\pi$
$992$	−42.0709	−	34.5566i	−1.33575	−	1.09717i
$993$	−32.0785	−	31.9664i	−1.01798	−	1.01442i
$994$	11.8445	+	6.73895i	0.375684	+	0.213747i
$995$	−15.4201	−	8.90281i	−0.488851	−	0.282238i
$996$	5.66332	−	0.529406i	0.179449	−	0.0167749i
$997$	38.1596	+	22.0314i	1.20853	+	0.697742i	0.962437	−	0.271505i	$-0.0875214\pi$
$997$	38.1596	+	22.0314i	1.20853	+	0.697742i	0.246088	+	0.969247i	$0.420855\pi$
$998$	−33.9127	−	40.2440i	−1.07349	−	1.27390i
$999$	−16.3384	+	4.46988i	−0.516923	+	0.141421i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.bj.b.103.24	yes	84
3.2	odd	2		756.2.bj.b.523.19		84
4.3	odd	2	inner	252.2.bj.b.103.23	yes	84
7.3	odd	6		252.2.n.b.31.6	✓	84
9.2	odd	6		756.2.n.b.19.9		84
9.7	even	3		252.2.n.b.187.34	yes	84
12.11	even	2		756.2.bj.b.523.20		84
21.17	even	6		756.2.n.b.199.37		84
28.3	even	6		252.2.n.b.31.34	yes	84
36.7	odd	6		252.2.n.b.187.6	yes	84
36.11	even	6		756.2.n.b.19.37		84
63.38	even	6		756.2.bj.b.451.19		84
63.52	odd	6	inner	252.2.bj.b.115.24	yes	84
84.59	odd	6		756.2.n.b.199.9		84
252.115	even	6	inner	252.2.bj.b.115.23	yes	84
252.227	odd	6		756.2.bj.b.451.20		84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.n.b.31.6	✓	84	7.3	odd	6
252.2.n.b.31.34	yes	84	28.3	even	6
252.2.n.b.187.6	yes	84	36.7	odd	6
252.2.n.b.187.34	yes	84	9.7	even	3
252.2.bj.b.103.23	yes	84	4.3	odd	2	inner
252.2.bj.b.103.24	yes	84	1.1	even	1	trivial
252.2.bj.b.115.23	yes	84	252.115	even	6	inner
252.2.bj.b.115.24	yes	84	63.52	odd	6	inner
756.2.n.b.19.9		84	9.2	odd	6
756.2.n.b.19.37		84	36.11	even	6
756.2.n.b.199.9		84	84.59	odd	6
756.2.n.b.199.37		84	21.17	even	6
756.2.bj.b.451.19		84	63.38	even	6
756.2.bj.b.451.20		84	252.227	odd	6
756.2.bj.b.523.19		84	3.2	odd	2
756.2.bj.b.523.20		84	12.11	even	2

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.248495 + 1.39221i) q^{2} +(1.22260 - 1.22689i) q^{3} +(-1.87650 + 0.691915i) q^{4} +(0.705906 - 0.407555i) q^{5} +(2.01189 + 1.39724i) q^{6} +(2.03393 + 1.69208i) q^{7} +(-1.42959 - 2.44055i) q^{8} +(-0.0104958 - 2.99998i) q^{9} +O(q^{10})\)	\(q+(0.248495 + 1.39221i) q^{2} +(1.22260 - 1.22689i) q^{3} +(-1.87650 + 0.691915i) q^{4} +(0.705906 - 0.407555i) q^{5} +(2.01189 + 1.39724i) q^{6} +(2.03393 + 1.69208i) q^{7} +(-1.42959 - 2.44055i) q^{8} +(-0.0104958 - 2.99998i) q^{9} +(0.742817 + 0.881495i) q^{10} +(4.17670 + 2.41142i) q^{11} +(-1.44531 + 3.14819i) q^{12} +(-2.20303 - 1.27192i) q^{13} +(-1.85031 + 3.25213i) q^{14} +(0.363018 - 1.36434i) q^{15} +(3.04251 - 2.59676i) q^{16} +(-0.503257 + 0.290555i) q^{17} +(4.17400 - 0.760093i) q^{18} +(-2.24125 + 3.88195i) q^{19} +(-1.04264 + 1.25320i) q^{20} +(4.56267 - 0.426661i) q^{21} +(-2.31931 + 6.41407i) q^{22} +(5.60853 - 3.23809i) q^{23} +(-4.74209 - 1.22987i) q^{24} +(-2.16780 + 3.75474i) q^{25} +(1.22334 - 3.38315i) q^{26} +(-3.69347 - 3.65490i) q^{27} +(-4.98744 - 1.76788i) q^{28} +(-3.16210 - 5.47692i) q^{29} +(1.98966 + 0.166365i) q^{30} -9.62438 q^{31} +(4.37128 + 3.59053i) q^{32} +(8.06497 - 2.17613i) q^{33} +(-0.529571 - 0.628438i) q^{34} +(2.12538 + 0.365511i) q^{35} +(2.09543 + 5.62220i) q^{36} +(1.62993 - 2.82313i) q^{37} +(-5.96144 - 2.15564i) q^{38} +(-4.25393 + 1.14782i) q^{39} +(-2.00382 - 1.14016i) q^{40} +(-3.04709 - 1.75924i) q^{41} +(1.72780 + 6.24617i) q^{42} +(-4.72260 + 2.72659i) q^{43} +(-9.50608 - 1.63511i) q^{44} +(-1.23007 - 2.11343i) q^{45} +(5.90179 + 7.00361i) q^{46} -9.58038 q^{47} +(0.533848 - 6.90760i) q^{48} +(1.27373 + 6.88314i) q^{49} +(-5.76607 - 2.08500i) q^{50} +(-0.258804 + 0.972672i) q^{51} +(5.01405 + 0.862450i) q^{52} +(-1.09484 - 1.89632i) q^{53} +(4.17058 - 6.05031i) q^{54} +3.93115 q^{55} +(1.22191 - 7.38288i) q^{56} +(2.02256 + 7.49583i) q^{57} +(6.83926 - 5.76330i) q^{58} +11.2058 q^{59} +(0.262806 + 2.81137i) q^{60} -7.24771i q^{61} +(-2.39161 - 13.3992i) q^{62} +(5.05486 - 6.11951i) q^{63} +(-3.91253 + 6.97797i) q^{64} -2.07351 q^{65} +(5.03374 + 10.6874i) q^{66} -5.02059i q^{67} +(0.743322 - 0.893438i) q^{68} +(2.88423 - 10.8399i) q^{69} +(0.0192776 + 3.04980i) q^{70} -3.64207i q^{71} +(-7.30659 + 4.31437i) q^{72} +(2.26126 - 1.30554i) q^{73} +(4.33542 + 1.56768i) q^{74} +(1.95628 + 7.25018i) q^{75} +(1.51972 - 8.83524i) q^{76} +(4.41480 + 11.9720i) q^{77} +(-2.65508 - 5.63714i) q^{78} +10.1419i q^{79} +(1.08940 - 3.07306i) q^{80} +(-8.99978 + 0.0629746i) q^{81} +(1.69204 - 4.67935i) q^{82} +(-0.820993 - 1.42200i) q^{83} +(-8.26664 + 3.95761i) q^{84} +(-0.236835 + 0.410210i) q^{85} +(-4.96954 - 5.89731i) q^{86} +(-10.5855 - 2.81655i) q^{87} +(-0.0857994 - 13.6408i) q^{88} +(-1.90724 - 1.10115i) q^{89} +(2.63667 - 2.23769i) q^{90} +(-2.32862 - 6.31470i) q^{91} +(-8.28393 + 9.95690i) q^{92} +(-11.7668 + 11.8080i) q^{93} +(-2.38068 - 13.3379i) q^{94} +3.65373i q^{95} +(9.74950 - 0.973278i) q^{96} +(-6.14759 + 3.54931i) q^{97} +(-9.26626 + 3.48373i) q^{98} +(7.19038 - 12.5553i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 2 q^{2} - 2 q^{4} + 6 q^{5} - 16 q^{8} + 4 q^{9}+O(q^{10}) \) 84 * q + 2 * q^2 - 2 * q^4 + 6 * q^5 - 16 * q^8 + 4 * q^9	\( 84 q + 2 q^{2} - 2 q^{4} + 6 q^{5} - 16 q^{8} + 4 q^{9} - 18 q^{10} - 6 q^{12} + 18 q^{13} + 14 q^{14} + 14 q^{16} + 6 q^{17} - 10 q^{18} - 24 q^{20} + 4 q^{21} + 6 q^{22} - 6 q^{24} + 16 q^{25} - 30 q^{26} - 4 q^{28} + 10 q^{29} + 11 q^{30} - 18 q^{32} - 18 q^{33} - 24 q^{34} - 38 q^{36} + 2 q^{37} + 33 q^{38} + 6 q^{40} + 6 q^{41} - 38 q^{42} - 13 q^{44} - 54 q^{45} + 10 q^{46} + 9 q^{48} - 28 q^{49} - 17 q^{50} - 27 q^{52} - 2 q^{53} - 39 q^{54} + 58 q^{56} + 6 q^{57} - 13 q^{58} - 31 q^{60} - 8 q^{64} - 100 q^{65} + 30 q^{66} - 18 q^{68} - 18 q^{69} - 19 q^{70} + 26 q^{72} + 30 q^{73} - 23 q^{74} - 2 q^{77} + 15 q^{78} + 3 q^{80} - 32 q^{81} - 18 q^{82} + 23 q^{84} - 50 q^{85} - 9 q^{86} + q^{88} - 102 q^{89} - 39 q^{90} + 28 q^{92} - 36 q^{93} + 63 q^{96} + 6 q^{97} + 21 q^{98}+O(q^{100}) \) 84 * q + 2 * q^2 - 2 * q^4 + 6 * q^5 - 16 * q^8 + 4 * q^9 - 18 * q^10 - 6 * q^12 + 18 * q^13 + 14 * q^14 + 14 * q^16 + 6 * q^17 - 10 * q^18 - 24 * q^20 + 4 * q^21 + 6 * q^22 - 6 * q^24 + 16 * q^25 - 30 * q^26 - 4 * q^28 + 10 * q^29 + 11 * q^30 - 18 * q^32 - 18 * q^33 - 24 * q^34 - 38 * q^36 + 2 * q^37 + 33 * q^38 + 6 * q^40 + 6 * q^41 - 38 * q^42 - 13 * q^44 - 54 * q^45 + 10 * q^46 + 9 * q^48 - 28 * q^49 - 17 * q^50 - 27 * q^52 - 2 * q^53 - 39 * q^54 + 58 * q^56 + 6 * q^57 - 13 * q^58 - 31 * q^60 - 8 * q^64 - 100 * q^65 + 30 * q^66 - 18 * q^68 - 18 * q^69 - 19 * q^70 + 26 * q^72 + 30 * q^73 - 23 * q^74 - 2 * q^77 + 15 * q^78 + 3 * q^80 - 32 * q^81 - 18 * q^82 + 23 * q^84 - 50 * q^85 - 9 * q^86 + q^88 - 102 * q^89 - 39 * q^90 + 28 * q^92 - 36 * q^93 + 63 * q^96 + 6 * q^97 + 21 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more