LMFDB - Embedded newform 966.2.f.b.461.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(461,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("966.461");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.f (of order $2$, degree $1$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			461.9
Character	$\chi$	$=$	966.461
Dual form			966.2.f.b.461.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.950180 + 1.44816i) q^{3} -1.00000 q^{4} -0.575987 q^{5} +(1.44816 - 0.950180i) q^{6} +(2.10044 + 1.60877i) q^{7} +1.00000i q^{8} +(-1.19432 + 2.75202i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.950180 + 1.44816i) q^{3} -1.00000 q^{4} -0.575987 q^{5} +(1.44816 - 0.950180i) q^{6} +(2.10044 + 1.60877i) q^{7} +1.00000i q^{8} +(-1.19432 + 2.75202i) q^{9} +0.575987i q^{10} +6.32775i q^{11} +(-0.950180 - 1.44816i) q^{12} -2.57508i q^{13} +(1.60877 - 2.10044i) q^{14} +(-0.547291 - 0.834119i) q^{15} +1.00000 q^{16} -6.33829 q^{17} +(2.75202 + 1.19432i) q^{18} -4.31282i q^{19} +0.575987 q^{20} +(-0.333956 + 4.57039i) q^{21} +6.32775 q^{22} +1.00000i q^{23} +(-1.44816 + 0.950180i) q^{24} -4.66824 q^{25} -2.57508 q^{26} +(-5.12017 + 0.885356i) q^{27} +(-2.10044 - 1.60877i) q^{28} +10.1027i q^{29} +(-0.834119 + 0.547291i) q^{30} -1.82670i q^{31} -1.00000i q^{32} +(-9.16357 + 6.01250i) q^{33} +6.33829i q^{34} +(-1.20983 - 0.926632i) q^{35} +(1.19432 - 2.75202i) q^{36} -3.23316 q^{37} -4.31282 q^{38} +(3.72913 - 2.44679i) q^{39} -0.575987i q^{40} +10.6157 q^{41} +(4.57039 + 0.333956i) q^{42} +6.83543 q^{43} -6.32775i q^{44} +(0.687911 - 1.58513i) q^{45} +1.00000 q^{46} -1.58891 q^{47} +(0.950180 + 1.44816i) q^{48} +(1.82371 + 6.75826i) q^{49} +4.66824i q^{50} +(-6.02252 - 9.17884i) q^{51} +2.57508i q^{52} -4.99963i q^{53} +(0.885356 + 5.12017i) q^{54} -3.64470i q^{55} +(-1.60877 + 2.10044i) q^{56} +(6.24565 - 4.09796i) q^{57} +10.1027 q^{58} +2.62459 q^{59} +(0.547291 + 0.834119i) q^{60} +6.43703i q^{61} -1.82670 q^{62} +(-6.93596 + 3.85907i) q^{63} -1.00000 q^{64} +1.48321i q^{65} +(6.01250 + 9.16357i) q^{66} -1.55321 q^{67} +6.33829 q^{68} +(-1.44816 + 0.950180i) q^{69} +(-0.926632 + 1.20983i) q^{70} +4.59862i q^{71} +(-2.75202 - 1.19432i) q^{72} +13.0353i q^{73} +3.23316i q^{74} +(-4.43567 - 6.76034i) q^{75} +4.31282i q^{76} +(-10.1799 + 13.2911i) q^{77} +(-2.44679 - 3.72913i) q^{78} +16.7877 q^{79} -0.575987 q^{80} +(-6.14722 - 6.57356i) q^{81} -10.6157i q^{82} -2.97148 q^{83} +(0.333956 - 4.57039i) q^{84} +3.65078 q^{85} -6.83543i q^{86} +(-14.6302 + 9.59934i) q^{87} -6.32775 q^{88} -3.91864 q^{89} +(-1.58513 - 0.687911i) q^{90} +(4.14272 - 5.40881i) q^{91} -1.00000i q^{92} +(2.64535 - 1.73569i) q^{93} +1.58891i q^{94} +2.48413i q^{95} +(1.44816 - 0.950180i) q^{96} -17.9828i q^{97} +(6.75826 - 1.82371i) q^{98} +(-17.4141 - 7.55733i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{4} - 4 q^{7} + 8 q^{9}+O(q^{10}) $ 24 * q - 24 * q^4 - 4 * q^7 + 8 * q^9	$ 24 q - 24 q^{4} - 4 q^{7} + 8 q^{9} + 24 q^{16} + 16 q^{18} - 28 q^{21} + 8 q^{22} - 24 q^{25} + 4 q^{28} + 24 q^{30} - 8 q^{36} + 40 q^{37} + 72 q^{39} + 64 q^{43} + 24 q^{46} - 24 q^{51} + 16 q^{58} + 12 q^{63} - 24 q^{64} - 64 q^{67} + 16 q^{70} - 16 q^{72} - 32 q^{78} + 88 q^{79} + 48 q^{81} + 28 q^{84} + 64 q^{85} - 8 q^{88} - 56 q^{91} + 8 q^{93} - 8 q^{99}+O(q^{100}) $ 24 * q - 24 * q^4 - 4 * q^7 + 8 * q^9 + 24 * q^16 + 16 * q^18 - 28 * q^21 + 8 * q^22 - 24 * q^25 + 4 * q^28 + 24 * q^30 - 8 * q^36 + 40 * q^37 + 72 * q^39 + 64 * q^43 + 24 * q^46 - 24 * q^51 + 16 * q^58 + 12 * q^63 - 24 * q^64 - 64 * q^67 + 16 * q^70 - 16 * q^72 - 32 * q^78 + 88 * q^79 + 48 * q^81 + 28 * q^84 + 64 * q^85 - 8 * q^88 - 56 * q^91 + 8 * q^93 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.950180	+	1.44816i	0.548587	+	0.836094i
$3$	0.950180	+	1.44816i	0.548587	+	0.836094i
$4$	−1.00000			−0.500000
$5$	−0.575987			−0.257589			−0.128795	−	0.991671i	$-0.541111\pi$
$5$	−0.575987			−0.257589			−0.128795	+	0.991671i	$0.541111\pi$
$6$	1.44816	−	0.950180i	0.591208	−	0.387909i
$7$	2.10044	+	1.60877i	0.793892	+	0.608059i
$7$	2.10044	+	1.60877i	0.793892	+	0.608059i
$8$			1.00000i			0.353553i
$9$	−1.19432	+	2.75202i	−0.398105	+	0.917340i
$10$			0.575987i			0.182143i
$11$			6.32775i			1.90789i	0.299986	+	0.953944i	$0.403018\pi$
$11$			6.32775i			1.90789i	−0.299986	+	0.953944i	$0.596982\pi$
$12$	−0.950180	−	1.44816i	−0.274293	−	0.418047i
$13$		−	2.57508i		−	0.714200i	−0.934066	−	0.357100i	$-0.883766\pi$
$13$		−	2.57508i		−	0.714200i	0.934066	−	0.357100i	$-0.116234\pi$
$14$	1.60877	−	2.10044i	0.429962	−	0.561367i
$15$	−0.547291	−	0.834119i	−0.141310	−	0.215369i
$16$	1.00000			0.250000
$17$	−6.33829			−1.53726			−0.768631	−	0.639692i	$-0.779062\pi$
$17$	−6.33829			−1.53726			−0.768631	+	0.639692i	$0.779062\pi$
$18$	2.75202	+	1.19432i	0.648657	+	0.281503i
$19$		−	4.31282i		−	0.989430i	−0.869055	−	0.494715i	$-0.835273\pi$
$19$		−	4.31282i		−	0.989430i	0.869055	−	0.494715i	$-0.164727\pi$
$20$	0.575987			0.128795
$21$	−0.333956	+	4.57039i	−0.0728752	+	0.997341i
$22$	6.32775			1.34908
$23$			1.00000i			0.208514i
$23$			1.00000i			0.208514i
$24$	−1.44816	+	0.950180i	−0.295604	+	0.193955i
$25$	−4.66824			−0.933648
$26$	−2.57508			−0.505016
$27$	−5.12017	+	0.885356i	−0.985377	+	0.170387i
$28$	−2.10044	−	1.60877i	−0.396946	−	0.304029i
$29$			10.1027i			1.87602i	0.346613	+	0.938008i	$0.387332\pi$
$29$			10.1027i			1.87602i	−0.346613	+	0.938008i	$0.612668\pi$
$30$	−0.834119	+	0.547291i	−0.152289	+	0.0999213i
$31$		−	1.82670i		−	0.328085i	−0.986453	−	0.164042i	$-0.947547\pi$
$31$		−	1.82670i		−	0.328085i	0.986453	−	0.164042i	$-0.0524534\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−9.16357	+	6.01250i	−1.59517	+	1.04664i
$34$			6.33829i			1.08701i
$35$	−1.20983	−	0.926632i	−0.204498	−	0.156629i
$36$	1.19432	−	2.75202i	0.199053	−	0.458670i
$37$	−3.23316			−0.531529			−0.265764	−	0.964038i	$-0.585624\pi$
$37$	−3.23316			−0.531529			−0.265764	+	0.964038i	$0.585624\pi$
$38$	−4.31282			−0.699632
$39$	3.72913	−	2.44679i	0.597138	−	0.391800i
$40$		−	0.575987i		−	0.0910715i
$41$	10.6157			1.65789			0.828945	−	0.559330i	$-0.188942\pi$
$41$	10.6157			1.65789			0.828945	+	0.559330i	$0.188942\pi$
$42$	4.57039	+	0.333956i	0.705227	+	0.0515306i
$43$	6.83543			1.04239			0.521196	−	0.853437i	$-0.325486\pi$
$43$	6.83543			1.04239			0.521196	+	0.853437i	$0.325486\pi$
$44$		−	6.32775i		−	0.953944i
$45$	0.687911	−	1.58513i	0.102548	−	0.236297i
$46$	1.00000			0.147442
$47$	−1.58891			−0.231766			−0.115883	−	0.993263i	$-0.536970\pi$
$47$	−1.58891			−0.231766			−0.115883	+	0.993263i	$0.536970\pi$
$48$	0.950180	+	1.44816i	0.137147	+	0.209023i
$49$	1.82371	+	6.75826i	0.260530	+	0.965466i
$50$			4.66824i			0.660189i
$51$	−6.02252	−	9.17884i	−0.843321	−	1.28530i
$52$			2.57508i			0.357100i
$53$		−	4.99963i		−	0.686751i	−0.939198	−	0.343376i	$-0.888430\pi$
$53$		−	4.99963i		−	0.686751i	0.939198	−	0.343376i	$-0.111570\pi$
$54$	0.885356	+	5.12017i	0.120482	+	0.696767i
$55$		−	3.64470i		−	0.491451i
$56$	−1.60877	+	2.10044i	−0.214981	+	0.280683i
$57$	6.24565	−	4.09796i	0.827256	−	0.542788i
$58$	10.1027			1.32654
$59$	2.62459			0.341692			0.170846	−	0.985298i	$-0.445350\pi$
$59$	2.62459			0.341692			0.170846	+	0.985298i	$0.445350\pi$
$60$	0.547291	+	0.834119i	0.0706550	+	0.107684i
$61$			6.43703i			0.824177i	0.911144	+	0.412089i	$0.135201\pi$
$61$			6.43703i			0.824177i	−0.911144	+	0.412089i	$0.864799\pi$
$62$	−1.82670			−0.231991
$63$	−6.93596	+	3.85907i	−0.873849	+	0.486197i
$64$	−1.00000			−0.125000
$65$			1.48321i			0.183970i
$66$	6.01250	+	9.16357i	0.740087	+	1.12796i
$67$	−1.55321			−0.189754			−0.0948772	−	0.995489i	$-0.530246\pi$
$67$	−1.55321			−0.189754			−0.0948772	+	0.995489i	$0.530246\pi$
$68$	6.33829			0.768631
$69$	−1.44816	+	0.950180i	−0.174338	+	0.114388i
$70$	−0.926632	+	1.20983i	−0.110754	+	0.144602i
$71$			4.59862i			0.545756i	0.962049	+	0.272878i	$0.0879755\pi$
$71$			4.59862i			0.545756i	−0.962049	+	0.272878i	$0.912024\pi$
$72$	−2.75202	−	1.19432i	−0.324329	−	0.140752i
$73$			13.0353i			1.52567i	0.646593	+	0.762835i	$0.276193\pi$
$73$			13.0353i			1.52567i	−0.646593	+	0.762835i	$0.723807\pi$
$74$			3.23316i			0.375848i
$75$	−4.43567	−	6.76034i	−0.512187	−	0.780617i
$76$			4.31282i			0.494715i
$77$	−10.1799	+	13.2911i	−1.16011	+	1.51466i
$78$	−2.44679	−	3.72913i	−0.277045	−	0.422240i
$79$	16.7877			1.88876			0.944380	−	0.328855i	$-0.106663\pi$
$79$	16.7877			1.88876			0.944380	+	0.328855i	$0.106663\pi$
$80$	−0.575987			−0.0643973
$81$	−6.14722	−	6.57356i	−0.683024	−	0.730396i
$82$		−	10.6157i		−	1.17231i
$83$	−2.97148			−0.326163			−0.163081	−	0.986613i	$-0.552143\pi$
$83$	−2.97148			−0.326163			−0.163081	+	0.986613i	$0.552143\pi$
$84$	0.333956	−	4.57039i	0.0364376	−	0.498671i
$85$	3.65078			0.395982
$86$		−	6.83543i		−	0.737083i
$87$	−14.6302	+	9.59934i	−1.56853	+	1.02916i
$88$	−6.32775			−0.674540
$89$	−3.91864			−0.415375			−0.207688	−	0.978195i	$-0.566594\pi$
$89$	−3.91864			−0.415375			−0.207688	+	0.978195i	$0.566594\pi$
$90$	−1.58513	−	0.687911i	−0.167087	−	0.0725121i
$91$	4.14272	−	5.40881i	0.434275	−	0.566998i
$92$		−	1.00000i		−	0.104257i
$93$	2.64535	−	1.73569i	0.274310	−	0.179983i
$94$			1.58891i			0.163884i
$95$			2.48413i			0.254866i
$96$	1.44816	−	0.950180i	0.147802	−	0.0969773i
$97$		−	17.9828i		−	1.82588i	−0.408094	−	0.912940i	$-0.633806\pi$
$97$		−	17.9828i		−	1.82588i	0.408094	−	0.912940i	$-0.366194\pi$
$98$	6.75826	−	1.82371i	0.682687	−	0.184222i
$99$	−17.4141	−	7.55733i	−1.75018	−	0.759540i
$100$	4.66824			0.466824
$101$	12.9812			1.29168			0.645840	−	0.763473i	$-0.276507\pi$
$101$	12.9812			1.29168			0.645840	+	0.763473i	$0.276507\pi$
$102$	−9.17884	+	6.02252i	−0.908841	+	0.596318i
$103$			17.0461i			1.67960i	0.542894	+	0.839801i	$0.317329\pi$
$103$			17.0461i			1.67960i	−0.542894	+	0.839801i	$0.682671\pi$
$104$	2.57508			0.252508
$105$	0.192354	−	2.63249i	0.0187719	−	0.256904i
$106$	−4.99963			−0.485607
$107$		−	5.66083i		−	0.547253i	−0.961836	−	0.273627i	$-0.911777\pi$
$107$		−	5.66083i		−	0.547253i	0.961836	−	0.273627i	$-0.0882232\pi$
$108$	5.12017	−	0.885356i	0.492689	−	0.0851935i
$109$	4.62685			0.443172			0.221586	−	0.975141i	$-0.428877\pi$
$109$	4.62685			0.443172			0.221586	+	0.975141i	$0.428877\pi$
$110$	−3.64470			−0.347508
$111$	−3.07209	−	4.68213i	−0.291590	−	0.444408i
$112$	2.10044	+	1.60877i	0.198473	+	0.152015i
$113$			10.7745i			1.01358i	0.862069	+	0.506792i	$0.169169\pi$
$113$			10.7745i			1.01358i	−0.862069	+	0.506792i	$0.830831\pi$
$114$	−4.09796	−	6.24565i	−0.383809	−	0.584958i
$115$		−	0.575987i		−	0.0537111i
$116$		−	10.1027i		−	0.938008i
$117$	7.08668	+	3.07546i	0.655164	+	0.284327i
$118$		−	2.62459i		−	0.241613i
$119$	−13.3132	−	10.1969i	−1.22042	−	0.934745i
$120$	0.834119	−	0.547291i	0.0761443	−	0.0499606i
$121$	−29.0404			−2.64003
$122$	6.43703			0.582781
$123$	10.0868	+	15.3732i	0.909496	+	1.38615i
$124$			1.82670i			0.164042i
$125$	5.56878			0.498087
$126$	3.85907	+	6.93596i	0.343794	+	0.617905i
$127$	2.54100			0.225477			0.112739	−	0.993625i	$-0.464038\pi$
$127$	2.54100			0.225477			0.112739	+	0.993625i	$0.464038\pi$
$128$			1.00000i			0.0883883i
$129$	6.49488	+	9.89877i	0.571843	+	0.871538i
$130$	1.48321			0.130087
$131$	6.86505			0.599802			0.299901	−	0.953970i	$-0.403046\pi$
$131$	6.86505			0.599802			0.299901	+	0.953970i	$0.403046\pi$
$132$	9.16357	−	6.01250i	0.797586	−	0.523321i
$133$	6.93835	−	9.05883i	0.601631	−	0.785501i
$134$			1.55321i			0.134177i
$135$	2.94915	−	0.509954i	0.253823	−	0.0438898i
$136$		−	6.33829i		−	0.543504i
$137$		−	16.7248i		−	1.42890i	−0.699687	−	0.714449i	$-0.746677\pi$
$137$		−	16.7248i		−	1.42890i	0.699687	−	0.714449i	$-0.253323\pi$
$138$	0.950180	+	1.44816i	0.0808847	+	0.123275i
$139$		−	19.8476i		−	1.68345i	−0.539903	−	0.841727i	$-0.681539\pi$
$139$		−	19.8476i		−	1.68345i	0.539903	−	0.841727i	$-0.318461\pi$
$140$	1.20983	+	0.926632i	0.102249	+	0.0783147i
$141$	−1.50975	−	2.30099i	−0.127144	−	0.193778i
$142$	4.59862			0.385908
$143$	16.2945			1.36261
$144$	−1.19432	+	2.75202i	−0.0995263	+	0.229335i
$145$		−	5.81900i		−	0.483242i
$146$	13.0353			1.07881
$147$	−8.05417	+	9.06258i	−0.664297	+	0.747469i
$148$	3.23316			0.265764
$149$		−	12.9996i		−	1.06497i	−0.846439	−	0.532485i	$-0.821258\pi$
$149$		−	12.9996i		−	1.06497i	0.846439	−	0.532485i	$-0.178742\pi$
$150$	−6.76034	+	4.43567i	−0.551980	+	0.362171i
$151$	9.45996			0.769841			0.384920	−	0.922950i	$-0.374229\pi$
$151$	9.45996			0.769841			0.384920	+	0.922950i	$0.374229\pi$
$152$	4.31282			0.349816
$153$	7.56993	−	17.4431i	0.611992	−	1.41019i
$154$	13.2911	+	10.1799i	1.07102	+	0.820320i
$155$			1.05215i			0.0845111i
$156$	−3.72913	+	2.44679i	−0.298569	+	0.195900i
$157$			1.35432i			0.108086i	0.998539	+	0.0540432i	$0.0172109\pi$
$157$			1.35432i			0.108086i	−0.998539	+	0.0540432i	$0.982789\pi$
$158$		−	16.7877i		−	1.33556i
$159$	7.24024	−	4.75054i	0.574189	−	0.376743i
$160$			0.575987i			0.0455358i
$161$	−1.60877	+	2.10044i	−0.126789	+	0.165538i
$162$	−6.57356	+	6.14722i	−0.516468	+	0.482971i
$163$	0.541750			0.0424331			0.0212165	−	0.999775i	$-0.493246\pi$
$163$	0.541750			0.0424331			0.0212165	+	0.999775i	$0.493246\pi$
$164$	−10.6157			−0.828945
$165$	5.27810	−	3.46312i	0.410899	−	0.269604i
$166$			2.97148i			0.230632i
$167$	−6.77744			−0.524454			−0.262227	−	0.965006i	$-0.584457\pi$
$167$	−6.77744			−0.524454			−0.262227	+	0.965006i	$0.584457\pi$
$168$	−4.57039	−	0.333956i	−0.352613	−	0.0257653i
$169$	6.36894			0.489919
$170$		−	3.65078i		−	0.280002i
$171$	11.8690	+	5.15088i	0.907643	+	0.393897i
$172$	−6.83543			−0.521196
$173$	5.00868			0.380803			0.190401	−	0.981706i	$-0.439021\pi$
$173$	5.00868			0.380803			0.190401	+	0.981706i	$0.439021\pi$
$174$	9.59934	+	14.6302i	0.727724	+	1.10912i
$175$	−9.80536	−	7.51013i	−0.741216	−	0.567712i
$176$			6.32775i			0.476972i
$177$	2.49383	+	3.80081i	0.187448	+	0.285687i
$178$			3.91864i			0.293715i
$179$			10.7127i			0.800705i	0.916361	+	0.400353i	$0.131112\pi$
$179$			10.7127i			0.800705i	−0.916361	+	0.400353i	$0.868888\pi$
$180$	−0.687911	+	1.58513i	−0.0512738	+	0.118148i
$181$		−	16.2738i		−	1.20962i	−0.796369	−	0.604810i	$-0.793249\pi$
$181$		−	16.2738i		−	1.20962i	0.796369	−	0.604810i	$-0.206751\pi$
$182$	−5.40881	−	4.14272i	−0.400928	−	0.307079i
$183$	−9.32183	+	6.11634i	−0.689090	+	0.452133i
$184$	−1.00000			−0.0737210
$185$	1.86226			0.136916
$186$	−1.73569	−	2.64535i	−0.127267	−	0.193966i
$187$		−	40.1071i		−	2.93292i
$188$	1.58891			0.115883
$189$	−12.1790	−	6.37755i	−0.885889	−	0.463898i
$190$	2.48413			0.180218
$191$			13.4350i			0.972122i	0.873925	+	0.486061i	$0.161567\pi$
$191$			13.4350i			0.972122i	−0.873925	+	0.486061i	$0.838433\pi$
$192$	−0.950180	−	1.44816i	−0.0685733	−	0.104512i
$193$	6.91896			0.498038			0.249019	−	0.968499i	$-0.419892\pi$
$193$	6.91896			0.498038			0.249019	+	0.968499i	$0.419892\pi$
$194$	−17.9828			−1.29109
$195$	−2.14793	+	1.40932i	−0.153816	+	0.100924i
$196$	−1.82371	−	6.75826i	−0.130265	−	0.482733i
$197$		−	2.10005i		−	0.149622i	−0.997198	−	0.0748111i	$-0.976165\pi$
$197$		−	2.10005i		−	0.149622i	0.997198	−	0.0748111i	$-0.0238354\pi$
$198$	−7.55733	+	17.4141i	−0.537076	+	1.23756i
$199$		−	10.8257i		−	0.767416i	−0.923455	−	0.383708i	$-0.874647\pi$
$199$		−	10.8257i		−	0.767416i	0.923455	−	0.383708i	$-0.125353\pi$
$200$		−	4.66824i		−	0.330094i
$201$	−1.47583	−	2.24929i	−0.104097	−	0.158652i
$202$		−	12.9812i		−	0.913356i
$203$	−16.2529	+	21.2200i	−1.14073	+	1.48936i
$204$	6.02252	+	9.17884i	0.421661	+	0.642648i
$205$	−6.11449			−0.427055
$206$	17.0461			1.18766
$207$	−2.75202	−	1.19432i	−0.191279	−	0.0830107i
$208$		−	2.57508i		−	0.178550i
$209$	27.2905			1.88772
$210$	−2.63249	−	0.192354i	−0.181659	−	0.0132737i
$211$	9.31151			0.641031			0.320516	−	0.947243i	$-0.396144\pi$
$211$	9.31151			0.641031			0.320516	+	0.947243i	$0.396144\pi$
$212$			4.99963i			0.343376i
$213$	−6.65952	+	4.36952i	−0.456303	+	0.299394i
$214$	−5.66083			−0.386966
$215$	−3.93712			−0.268509
$216$	−0.885356	−	5.12017i	−0.0602409	−	0.348383i
$217$	2.93874	−	3.83687i	0.199495	−	0.260464i
$218$		−	4.62685i		−	0.313370i
$219$	−18.8772	+	12.3859i	−1.27560	+	0.836962i
$220$			3.64470i			0.245726i
$221$			16.3216i			1.09791i
$222$	−4.68213	+	3.07209i	−0.314244	+	0.206185i
$223$			9.57697i			0.641321i	0.947194	+	0.320661i	$0.103905\pi$
$223$			9.57697i			0.641321i	−0.947194	+	0.320661i	$0.896095\pi$
$224$	1.60877	−	2.10044i	0.107491	−	0.140342i
$225$	5.57535	−	12.8471i	0.371690	−	0.856472i
$226$	10.7745			0.716712
$227$	−13.0953			−0.869167			−0.434583	−	0.900632i	$-0.643104\pi$
$227$	−13.0953			−0.869167			−0.434583	+	0.900632i	$0.643104\pi$
$228$	−6.24565	+	4.09796i	−0.413628	+	0.271394i
$229$			17.4876i			1.15561i	0.816174	+	0.577806i	$0.196091\pi$
$229$			17.4876i			1.15561i	−0.816174	+	0.577806i	$0.803909\pi$
$230$	−0.575987			−0.0379795
$231$	−28.9203	−	2.11319i	−1.90281	−	0.139038i
$232$	−10.1027			−0.663272
$233$		−	1.97242i		−	0.129218i	−0.997911	−	0.0646089i	$-0.979420\pi$
$233$		−	1.97242i		−	0.129218i	0.997911	−	0.0646089i	$-0.0205800\pi$
$234$	3.07546	−	7.08668i	0.201049	−	0.463271i
$235$	0.915191			0.0597005
$236$	−2.62459			−0.170846
$237$	15.9513	+	24.3112i	1.03615	+	1.57918i
$238$	−10.1969	+	13.3132i	−0.660965	+	0.862968i
$239$		−	1.86076i		−	0.120363i	−0.998187	−	0.0601814i	$-0.980832\pi$
$239$		−	1.86076i		−	0.120363i	0.998187	−	0.0601814i	$-0.0191679\pi$
$240$	−0.547291	−	0.834119i	−0.0353275	−	0.0538422i
$241$			15.5207i			0.999779i	0.866089	+	0.499890i	$0.166626\pi$
$241$			15.5207i			0.999779i	−0.866089	+	0.499890i	$0.833374\pi$
$242$			29.0404i			1.86679i
$243$	3.67858	−	15.1482i	0.235981	−	0.971758i
$244$		−	6.43703i		−	0.412089i
$245$	−1.05043	−	3.89267i	−0.0671096	−	0.248694i
$246$	15.3732	−	10.0868i	0.980157	−	0.643111i
$247$	−11.1059			−0.706650
$248$	1.82670			0.115995
$249$	−2.82344	−	4.30317i	−0.178928	−	0.272702i
$250$		−	5.56878i		−	0.352201i
$251$	−8.65214			−0.546118			−0.273059	−	0.961997i	$-0.588035\pi$
$251$	−8.65214			−0.546118			−0.273059	+	0.961997i	$0.588035\pi$
$252$	6.93596	−	3.85907i	0.436924	−	0.243099i
$253$	−6.32775			−0.397822
$254$		−	2.54100i		−	0.159437i
$255$	3.46889	+	5.28689i	0.217231	+	0.331078i
$256$	1.00000			0.0625000
$257$	28.2306			1.76097			0.880487	−	0.474069i	$-0.157215\pi$
$257$	28.2306			1.76097			0.880487	+	0.474069i	$0.157215\pi$
$258$	9.89877	−	6.49488i	0.616270	−	0.404354i
$259$	−6.79107	−	5.20142i	−0.421977	−	0.323201i
$260$		−	1.48321i		−	0.0919851i
$261$	−27.8027	−	12.0658i	−1.72094	−	0.746852i
$262$		−	6.86505i		−	0.424124i
$263$		−	15.5372i		−	0.958068i	−0.877796	−	0.479034i	$-0.840987\pi$
$263$		−	15.5372i		−	0.958068i	0.877796	−	0.479034i	$-0.159013\pi$
$264$	−6.01250	−	9.16357i	−0.370044	−	0.563979i
$265$			2.87972i			0.176900i
$266$	−9.05883	−	6.93835i	−0.555433	−	0.425417i
$267$	−3.72341	−	5.67481i	−0.227869	−	0.347292i
$268$	1.55321			0.0948772
$269$	−28.7294			−1.75166			−0.875831	−	0.482618i	$-0.839686\pi$
$269$	−28.7294			−1.75166			−0.875831	+	0.482618i	$0.839686\pi$
$270$	−0.509954	−	2.94915i	−0.0310348	−	0.179480i
$271$		−	28.0891i		−	1.70629i	−0.521671	−	0.853147i	$-0.674691\pi$
$271$		−	28.0891i		−	1.70629i	0.521671	−	0.853147i	$-0.325309\pi$
$272$	−6.33829			−0.384316
$273$	11.7691	+	0.859965i	0.712301	+	0.0520475i
$274$	−16.7248			−1.01038
$275$		−	29.5394i		−	1.78129i
$276$	1.44816	−	0.950180i	0.0871688	−	0.0571941i
$277$	15.1922			0.912809			0.456404	−	0.889773i	$-0.349137\pi$
$277$	15.1922			0.912809			0.456404	+	0.889773i	$0.349137\pi$
$278$	−19.8476			−1.19038
$279$	5.02711	+	2.18165i	0.300965	+	0.130612i
$280$	0.926632	−	1.20983i	0.0553768	−	0.0723010i
$281$		−	17.9523i		−	1.07094i	−0.844553	−	0.535471i	$-0.820134\pi$
$281$		−	17.9523i		−	1.07094i	0.844553	−	0.535471i	$-0.179866\pi$
$282$	−2.30099	+	1.50975i	−0.137022	+	0.0899043i
$283$			17.1778i			1.02112i	0.859844	+	0.510558i	$0.170561\pi$
$283$			17.1778i			1.02112i	−0.859844	+	0.510558i	$0.829439\pi$
$284$		−	4.59862i		−	0.272878i
$285$	−3.59741	+	2.36037i	−0.213092	+	0.139816i
$286$		−	16.2945i		−	0.963513i
$287$	22.2976	+	17.0782i	1.31619	+	1.00809i
$288$	2.75202	+	1.19432i	0.162164	+	0.0703758i
$289$	23.1740			1.36317
$290$	−5.81900			−0.341703
$291$	26.0420	−	17.0869i	1.52661	−	1.00165i
$292$		−	13.0353i		−	0.762835i
$293$	−20.9765			−1.22546			−0.612729	−	0.790293i	$-0.709928\pi$
$293$	−20.9765			−1.22546			−0.612729	+	0.790293i	$0.709928\pi$
$294$	9.06258	+	8.05417i	0.528540	+	0.469729i
$295$	−1.51173			−0.0880162
$296$		−	3.23316i		−	0.187924i
$297$	−5.60231	−	32.3991i	−0.325079	−	1.87999i
$298$	−12.9996			−0.753048
$299$	2.57508			0.148921
$300$	4.43567	+	6.76034i	0.256093	+	0.390309i
$301$	14.3574	+	10.9966i	0.827547	+	0.633836i
$302$		−	9.45996i		−	0.544360i
$303$	12.3345	+	18.7988i	0.708598	+	1.07997i
$304$		−	4.31282i		−	0.247357i
$305$		−	3.70765i		−	0.212299i
$306$	−17.4431	−	7.56993i	−0.997156	−	0.432744i
$307$		−	1.61664i		−	0.0922665i	−0.998935	−	0.0461333i	$-0.985310\pi$
$307$		−	1.61664i		−	0.0922665i	0.998935	−	0.0461333i	$-0.0146899\pi$
$308$	10.1799	−	13.2911i	0.580054	−	0.757328i
$309$	−24.6854	+	16.1969i	−1.40431	+	0.921408i
$310$	1.05215			0.0597584
$311$	2.05811			0.116705			0.0583523	−	0.998296i	$-0.481415\pi$
$311$	2.05811			0.116705			0.0583523	+	0.998296i	$0.481415\pi$
$312$	2.44679	+	3.72913i	0.138522	+	0.211120i
$313$			4.26591i			0.241124i	0.992706	+	0.120562i	$0.0384696\pi$
$313$			4.26591i			0.241124i	−0.992706	+	0.120562i	$0.961530\pi$
$314$	1.35432			0.0764286
$315$	3.99502	−	2.22278i	0.225094	−	0.125239i
$316$	−16.7877			−0.944380
$317$			7.40477i			0.415893i	0.978140	+	0.207947i	$0.0666781\pi$
$317$			7.40477i			0.415893i	−0.978140	+	0.207947i	$0.933322\pi$
$318$	−4.75054	−	7.24024i	−0.266397	−	0.406013i
$319$	−63.9271			−3.57923
$320$	0.575987			0.0321987
$321$	8.19777	−	5.37881i	0.457555	−	0.300216i
$322$	2.10044	+	1.60877i	0.117053	+	0.0896533i
$323$			27.3359i			1.52101i
$324$	6.14722	+	6.57356i	0.341512	+	0.365198i
$325$			12.0211i			0.666811i
$326$		−	0.541750i		−	0.0300047i
$327$	4.39634	+	6.70041i	0.243118	+	0.370533i
$328$			10.6157i			0.586153i
$329$	−3.33741	−	2.55619i	−0.183997	−	0.140927i
$330$	−3.46312	−	5.27810i	−0.190639	−	0.290550i
$331$	18.9342			1.04072			0.520358	−	0.853948i	$-0.325798\pi$
$331$	18.9342			1.04072			0.520358	+	0.853948i	$0.325798\pi$
$332$	2.97148			0.163081
$333$	3.86142	−	8.89773i	0.211604	−	0.487592i
$334$			6.77744i			0.370845i
$335$	0.894627			0.0488787
$336$	−0.333956	+	4.57039i	−0.0182188	+	0.249335i
$337$	0.598810			0.0326193			0.0163096	−	0.999867i	$-0.494808\pi$
$337$	0.598810			0.0326193			0.0163096	+	0.999867i	$0.494808\pi$
$338$		−	6.36894i		−	0.346425i
$339$	−15.6032	+	10.2378i	−0.847451	+	0.556038i
$340$	−3.65078			−0.197991
$341$	11.5589			0.625949
$342$	5.15088	−	11.8690i	0.278527	−	0.641801i
$343$	−7.04191	+	17.1293i	−0.380227	+	0.924893i
$344$			6.83543i			0.368541i
$345$	0.834119	−	0.547291i	0.0449075	−	0.0294652i
$346$		−	5.00868i		−	0.269268i
$347$		−	22.0310i		−	1.18268i	−0.806421	−	0.591342i	$-0.798598\pi$
$347$		−	22.0310i		−	1.18268i	0.806421	−	0.591342i	$-0.201402\pi$
$348$	14.6302	−	9.59934i	0.784263	−	0.514579i
$349$			11.9800i			0.641276i	0.947202	+	0.320638i	$0.103897\pi$
$349$			11.9800i			0.641276i	−0.947202	+	0.320638i	$0.896103\pi$
$350$	−7.51013	+	9.80536i	−0.401433	+	0.524119i
$351$	2.27987	+	13.1849i	0.121690	+	0.703756i
$352$	6.32775			0.337270
$353$	24.9427			1.32756			0.663782	−	0.747926i	$-0.268950\pi$
$353$	24.9427			1.32756			0.663782	+	0.747926i	$0.268950\pi$
$354$	3.80081	−	2.49383i	0.202011	−	0.132546i
$355$		−	2.64875i		−	0.140581i
$356$	3.91864			0.207688
$357$	2.11671	−	28.9685i	0.112028	−	1.53317i
$358$	10.7127			0.566184
$359$		−	11.9216i		−	0.629196i	−0.949225	−	0.314598i	$-0.898130\pi$
$359$		−	11.9216i		−	0.629196i	0.949225	−	0.314598i	$-0.101870\pi$
$360$	1.58513	+	0.687911i	0.0835435	+	0.0362561i
$361$	0.399548			0.0210288
$362$	−16.2738			−0.855331
$363$	−27.5936	−	42.0550i	−1.44829	−	2.20732i
$364$	−4.14272	+	5.40881i	−0.217138	+	0.283499i
$365$		−	7.50818i		−	0.392996i
$366$	6.11634	+	9.32183i	0.319706	+	0.487260i
$367$			2.68705i			0.140263i	0.997538	+	0.0701316i	$0.0223419\pi$
$367$			2.68705i			0.140263i	−0.997538	+	0.0701316i	$0.977658\pi$
$368$			1.00000i			0.0521286i
$369$	−12.6785	+	29.2145i	−0.660015	+	1.52085i
$370$		−	1.86226i		−	0.0968143i
$371$	8.04326	−	10.5014i	0.417585	−	0.545207i
$372$	−2.64535	+	1.73569i	−0.137155	+	0.0899914i
$373$	0.108765			0.00563166			0.00281583	−	0.999996i	$-0.499104\pi$
$373$	0.108765			0.00563166			0.00281583	+	0.999996i	$0.499104\pi$
$374$	−40.1071			−2.07389
$375$	5.29134	+	8.06447i	0.273244	+	0.416447i
$376$		−	1.58891i		−	0.0819418i
$377$	26.0152			1.33985
$378$	−6.37755	+	12.1790i	−0.328026	+	0.626418i
$379$	−15.3323			−0.787570			−0.393785	−	0.919203i	$-0.628835\pi$
$379$	−15.3323			−0.787570			−0.393785	+	0.919203i	$0.628835\pi$
$380$		−	2.48413i		−	0.127433i
$381$	2.41441	+	3.67977i	0.123694	+	0.188520i
$382$	13.4350			0.687394
$383$	−20.3454			−1.03960			−0.519801	−	0.854287i	$-0.673994\pi$
$383$	−20.3454			−1.03960			−0.519801	+	0.854287i	$0.673994\pi$
$384$	−1.44816	+	0.950180i	−0.0739009	+	0.0484887i
$385$	5.86349	−	7.65548i	0.298831	−	0.390159i
$386$		−	6.91896i		−	0.352166i
$387$	−8.16366	+	18.8112i	−0.414982	+	0.956228i
$388$			17.9828i			0.912940i
$389$			1.58847i			0.0805388i	0.999189	+	0.0402694i	$0.0128216\pi$
$389$			1.58847i			0.0805388i	−0.999189	+	0.0402694i	$0.987178\pi$
$390$	1.40932	+	2.14793i	0.0713637	+	0.108765i
$391$		−	6.33829i		−	0.320541i
$392$	−6.75826	+	1.82371i	−0.341344	+	0.0921112i
$393$	6.52303	+	9.94167i	0.329043	+	0.501491i
$394$	−2.10005			−0.105799
$395$	−9.66948			−0.486524
$396$	17.4141	+	7.55733i	0.875090	+	0.379770i
$397$			6.14813i			0.308566i	0.988027	+	0.154283i	$0.0493067\pi$
$397$			6.14813i			0.308566i	−0.988027	+	0.154283i	$0.950693\pi$
$398$	−10.8257			−0.542645
$399$	19.7113	+	1.44029i	0.986799	+	0.0721049i
$400$	−4.66824			−0.233412
$401$		−	1.10369i		−	0.0551156i	−0.999620	−	0.0275578i	$-0.991227\pi$
$401$		−	1.10369i		−	0.0551156i	0.999620	−	0.0275578i	$-0.00877303\pi$
$402$	−2.24929	+	1.47583i	−0.112184	+	0.0736075i
$403$	−4.70390			−0.234318
$404$	−12.9812			−0.645840
$405$	3.54072	+	3.78629i	0.175940	+	0.188142i
$406$	21.2200	+	16.2529i	1.05313	+	0.806616i
$407$		−	20.4586i		−	1.01410i
$408$	9.17884	−	6.02252i	0.454420	−	0.298159i
$409$			33.1984i			1.64155i	0.571250	+	0.820776i	$0.306459\pi$
$409$			33.1984i			1.64155i	−0.571250	+	0.820776i	$0.693541\pi$
$410$			6.11449i			0.301973i
$411$	24.2202	−	15.8916i	1.19469	−	0.783875i
$412$		−	17.0461i		−	0.839801i
$413$	5.51279	+	4.22236i	0.271267	+	0.207769i
$414$	−1.19432	+	2.75202i	−0.0586974	+	0.135254i
$415$	1.71154			0.0840160
$416$	−2.57508			−0.126254
$417$	28.7425	−	18.8588i	1.40753	−	0.923520i
$418$		−	27.2905i		−	1.33482i
$419$	−0.222549			−0.0108722			−0.00543612	−	0.999985i	$-0.501730\pi$
$419$	−0.222549			−0.0108722			−0.00543612	+	0.999985i	$0.501730\pi$
$420$	−0.192354	+	2.63249i	−0.00938594	+	0.128452i
$421$	19.8267			0.966296			0.483148	−	0.875539i	$-0.339493\pi$
$421$	19.8267			0.966296			0.483148	+	0.875539i	$0.339493\pi$
$422$		−	9.31151i		−	0.453277i
$423$	1.89766	−	4.37271i	0.0922674	−	0.212608i
$424$	4.99963			0.242803
$425$	29.5887			1.43526
$426$	4.36952	+	6.65952i	0.211704	+	0.322655i
$427$	−10.3557	+	13.5206i	−0.501148	+	0.654308i
$428$			5.66083i			0.273627i
$429$	15.4827	+	23.5970i	0.747511	+	1.13927i
$430$			3.93712i			0.189865i
$431$			22.5397i			1.08570i	0.839830	+	0.542849i	$0.182655\pi$
$431$			22.5397i			1.08570i	−0.839830	+	0.542849i	$0.817345\pi$
$432$	−5.12017	+	0.885356i	−0.246344	+	0.0425967i
$433$		−	12.5261i		−	0.601965i	−0.953630	−	0.300983i	$-0.902685\pi$
$433$		−	12.5261i		−	0.601965i	0.953630	−	0.300983i	$-0.0973146\pi$
$434$	−3.83687	−	2.93874i	−0.184176	−	0.141064i
$435$	8.42682	−	5.52910i	0.404035	−	0.265100i
$436$	−4.62685			−0.221586
$437$	4.31282			0.206310
$438$	12.3859	+	18.8772i	0.591822	+	0.901987i
$439$			31.3680i			1.49711i	0.663070	+	0.748557i	$0.269253\pi$
$439$			31.3680i			1.49711i	−0.663070	+	0.748557i	$0.730747\pi$
$440$	3.64470			0.173754
$441$	−20.7769	−	3.05262i	−0.989378	−	0.145363i
$442$	16.3216			0.776341
$443$			18.5795i			0.882739i	0.897325	+	0.441370i	$0.145507\pi$
$443$			18.5795i			0.882739i	−0.897325	+	0.441370i	$0.854493\pi$
$444$	3.07209	+	4.68213i	0.145795	+	0.222204i
$445$	2.25709			0.106996
$446$	9.57697			0.453482
$447$	18.8255	−	12.3520i	0.890415	−	0.584229i
$448$	−2.10044	−	1.60877i	−0.0992365	−	0.0760073i
$449$		−	22.1240i		−	1.04410i	−0.852915	−	0.522049i	$-0.825168\pi$
$449$		−	22.1240i		−	1.04410i	0.852915	−	0.522049i	$-0.174832\pi$
$450$	−12.8471	−	5.57535i	−0.605617	−	0.262825i
$451$			67.1733i			3.16307i
$452$		−	10.7745i		−	0.506792i
$453$	8.98866	+	13.6995i	0.422324	+	0.643659i
$454$			13.0953i			0.614594i
$455$	−2.38615	+	3.11541i	−0.111865	+	0.146052i
$456$	4.09796	+	6.24565i	0.191905	+	0.292479i
$457$	14.3877			0.673030			0.336515	−	0.941678i	$-0.390752\pi$
$457$	14.3877			0.673030			0.336515	+	0.941678i	$0.390752\pi$
$458$	17.4876			0.817141
$459$	32.4531	−	5.61165i	1.51478	−	0.261929i
$460$			0.575987i			0.0268555i
$461$	−21.3872			−0.996103			−0.498052	−	0.867147i	$-0.665951\pi$
$461$	−21.3872			−0.996103			−0.498052	+	0.867147i	$0.665951\pi$
$462$	−2.11319	+	28.9203i	−0.0983145	+	1.34549i
$463$	−9.49725			−0.441375			−0.220687	−	0.975345i	$-0.570830\pi$
$463$	−9.49725			−0.441375			−0.220687	+	0.975345i	$0.570830\pi$
$464$			10.1027i			0.469004i
$465$	−1.52368	+	0.999736i	−0.0706592	+	0.0463616i
$466$	−1.97242			−0.0913708
$467$	7.11700			0.329335			0.164668	−	0.986349i	$-0.447345\pi$
$467$	7.11700			0.329335			0.164668	+	0.986349i	$0.447345\pi$
$468$	−7.08668	−	3.07546i	−0.327582	−	0.142163i
$469$	−3.26242	−	2.49876i	−0.150645	−	0.115382i
$470$		−	0.915191i		−	0.0422146i
$471$	−1.96126	+	1.28685i	−0.0903703	+	0.0592947i
$472$			2.62459i			0.120806i
$473$			43.2528i			1.98877i
$474$	24.3112	−	15.9513i	1.11665	−	0.732668i
$475$			20.1333i			0.923779i
$476$	13.3132	+	10.1969i	0.610210	+	0.467373i
$477$	13.7591	+	5.97113i	0.629984	+	0.273399i
$478$	−1.86076			−0.0851093
$479$	−32.0987			−1.46663			−0.733314	−	0.679890i	$-0.762028\pi$
$479$	−32.0987			−1.46663			−0.733314	+	0.679890i	$0.762028\pi$
$480$	−0.834119	+	0.547291i	−0.0380722	+	0.0249803i
$481$			8.32567i			0.379618i
$482$	15.5207			0.706951
$483$	−4.57039	−	0.333956i	−0.207960	−	0.0151955i
$484$	29.0404			1.32002
$485$			10.3579i			0.470327i
$486$	−15.1482	−	3.67858i	−0.687136	−	0.166864i
$487$	−24.5101			−1.11066			−0.555328	−	0.831631i	$-0.687407\pi$
$487$	−24.5101			−1.11066			−0.555328	+	0.831631i	$0.687407\pi$
$488$	−6.43703			−0.291391
$489$	0.514760	+	0.784538i	0.0232782	+	0.0354780i
$490$	−3.89267	+	1.05043i	−0.175853	+	0.0474537i
$491$		−	7.49990i		−	0.338466i	−0.985576	−	0.169233i	$-0.945871\pi$
$491$		−	7.49990i		−	0.338466i	0.985576	−	0.169233i	$-0.0541290\pi$
$492$	−10.0868	−	15.3732i	−0.454748	−	0.693076i
$493$		−	64.0336i		−	2.88393i
$494$			11.1059i			0.499677i
$495$	10.0303	+	4.35292i	0.450828	+	0.195649i
$496$		−	1.82670i		−	0.0820212i
$497$	−7.39813	+	9.65913i	−0.331852	+	0.433271i
$498$	−4.30317	+	2.82344i	−0.192830	+	0.126522i
$499$	36.8663			1.65036			0.825180	−	0.564870i	$-0.191074\pi$
$499$	36.8663			1.65036			0.825180	+	0.564870i	$0.191074\pi$
$500$	−5.56878			−0.249043
$501$	−6.43979	−	9.81480i	−0.287709	−	0.438493i
$502$			8.65214i			0.386164i
$503$	22.0936			0.985104			0.492552	−	0.870283i	$-0.336064\pi$
$503$	22.0936			0.985104			0.492552	+	0.870283i	$0.336064\pi$
$504$	−3.85907	−	6.93596i	−0.171897	−	0.308952i
$505$	−7.47702			−0.332723
$506$			6.32775i			0.281303i
$507$	6.05164	+	9.22323i	0.268763	+	0.409618i
$508$	−2.54100			−0.112739
$509$	18.7859			0.832671			0.416335	−	0.909211i	$-0.363314\pi$
$509$	18.7859			0.832671			0.416335	+	0.909211i	$0.363314\pi$
$510$	5.28689	−	3.46889i	0.234108	−	0.153605i
$511$	−20.9709	+	27.3799i	−0.927696	+	1.21122i
$512$		−	1.00000i		−	0.0441942i
$513$	3.81839	+	22.0824i	0.168586	+	0.974962i
$514$		−	28.2306i		−	1.24520i
$515$		−	9.81834i		−	0.432648i
$516$	−6.49488	−	9.89877i	−0.285921	−	0.435769i
$517$		−	10.0542i		−	0.442184i
$518$	−5.20142	+	6.79107i	−0.228537	+	0.298382i
$519$	4.75915	+	7.25335i	0.208903	+	0.318387i
$520$	−1.48321			−0.0650433
$521$	15.2366			0.667530			0.333765	−	0.942656i	$-0.391681\pi$
$521$	15.2366			0.667530			0.333765	+	0.942656i	$0.391681\pi$
$522$	−12.0658	+	27.8027i	−0.528104	+	1.21689i
$523$			8.92095i			0.390086i	0.980795	+	0.195043i	$0.0624847\pi$
$523$			8.92095i			0.390086i	−0.980795	+	0.195043i	$0.937515\pi$
$524$	−6.86505			−0.299901
$525$	1.55899	−	21.3357i	0.0680398	−	0.931165i
$526$	−15.5372			−0.677456
$527$			11.5781i			0.504352i
$528$	−9.16357	+	6.01250i	−0.398793	+	0.261660i
$529$	−1.00000			−0.0434783
$530$	2.87972			0.125087
$531$	−3.13459	+	7.22291i	−0.136029	+	0.313448i
$532$	−6.93835	+	9.05883i	−0.300816	+	0.392750i
$533$		−	27.3363i		−	1.18406i
$534$	−5.67481	+	3.72341i	−0.245573	+	0.161128i
$535$			3.26056i			0.140967i
$536$		−	1.55321i		−	0.0670883i
$537$	−15.5137	+	10.1790i	−0.669464	+	0.439256i
$538$			28.7294i			1.23861i
$539$	−42.7646	+	11.5400i	−1.84200	+	0.497061i
$540$	−2.94915	+	0.509954i	−0.126911	+	0.0219449i
$541$	−22.8979			−0.984458			−0.492229	−	0.870466i	$-0.663818\pi$
$541$	−22.8979			−0.984458			−0.492229	+	0.870466i	$0.663818\pi$
$542$	−28.0891			−1.20653
$543$	23.5670	−	15.4630i	1.01136	−	0.663582i
$544$			6.33829i			0.271752i
$545$	−2.66501			−0.114156
$546$	0.859965	−	11.7691i	0.0368031	−	0.503673i
$547$	−9.42675			−0.403059			−0.201529	−	0.979482i	$-0.564591\pi$
$547$	−9.42675			−0.403059			−0.201529	+	0.979482i	$0.564591\pi$
$548$			16.7248i			0.714449i
$549$	−17.7148	−	7.68785i	−0.756051	−	0.328109i
$550$	−29.5394			−1.25957
$551$	43.5710			1.85619
$552$	−0.950180	−	1.44816i	−0.0404423	−	0.0616376i
$553$	35.2615	+	27.0075i	1.49947	+	1.14848i
$554$		−	15.1922i		−	0.645453i
$555$	1.76948	+	2.69684i	0.0751103	+	0.114475i
$556$			19.8476i			0.841727i
$557$			21.1295i			0.895284i	0.894213	+	0.447642i	$0.147736\pi$
$557$			21.1295i			0.895284i	−0.894213	+	0.447642i	$0.852264\pi$
$558$	2.18165	−	5.02711i	0.0923568	−	0.212814i
$559$		−	17.6018i		−	0.744477i
$560$	−1.20983	−	0.926632i	−0.0511245	−	0.0391573i
$561$	58.0814	−	38.1090i	2.45220	−	1.60896i
$562$	−17.9523			−0.757271
$563$	−7.73577			−0.326024			−0.163012	−	0.986624i	$-0.552121\pi$
$563$	−7.73577			−0.326024			−0.163012	+	0.986624i	$0.552121\pi$
$564$	1.50975	+	2.30099i	0.0635719	+	0.0968892i
$565$		−	6.20599i		−	0.261088i
$566$	17.1778			0.722038
$567$	−2.33651	−	23.6969i	−0.0981243	−	0.995174i
$568$	−4.59862			−0.192954
$569$			12.0964i			0.507107i	0.967321	+	0.253553i	$0.0815994\pi$
$569$			12.0964i			0.507107i	−0.967321	+	0.253553i	$0.918401\pi$
$570$	2.36037	+	3.59741i	0.0988651	+	0.150679i
$571$	−8.76433			−0.366776			−0.183388	−	0.983041i	$-0.558706\pi$
$571$	−8.76433			−0.366776			−0.183388	+	0.983041i	$0.558706\pi$
$572$	−16.2945			−0.681306
$573$	−19.4560	+	12.7657i	−0.812785	+	0.533293i
$574$	17.0782	−	22.2976i	0.712830	−	0.930684i
$575$		−	4.66824i		−	0.194679i
$576$	1.19432	−	2.75202i	0.0497632	−	0.114667i
$577$			18.7515i			0.780636i	0.920680	+	0.390318i	$0.127635\pi$
$577$			18.7515i			0.780636i	−0.920680	+	0.390318i	$0.872365\pi$
$578$		−	23.1740i		−	0.963910i
$579$	6.57426	+	10.0197i	0.273217	+	0.416406i
$580$			5.81900i			0.241621i
$581$	−6.24142	−	4.78044i	−0.258938	−	0.198326i
$582$	−17.0869	−	26.0420i	−0.708276	−	1.07947i
$583$	31.6364			1.31024
$584$	−13.0353			−0.539406
$585$	−4.08184	−	1.77143i	−0.168763	−	0.0732395i
$586$			20.9765i			0.866530i
$587$	−28.3953			−1.17200			−0.585999	−	0.810312i	$-0.699298\pi$
$587$	−28.3953			−1.17200			−0.585999	+	0.810312i	$0.699298\pi$
$588$	8.05417	−	9.06258i	0.332148	−	0.373734i
$589$	−7.87823			−0.324617
$590$			1.51173i			0.0622369i
$591$	3.04120	−	1.99542i	0.125098	−	0.0820807i
$592$	−3.23316			−0.132882
$593$	28.0926			1.15362			0.576812	−	0.816877i	$-0.304297\pi$
$593$	28.0926			1.15362			0.576812	+	0.816877i	$0.304297\pi$
$594$	−32.3991	+	5.60231i	−1.32935	+	0.229866i
$595$	7.66824	+	5.87326i	0.314367	+	0.240780i
$596$			12.9996i			0.532485i
$597$	15.6774	−	10.2864i	0.641632	−	0.420994i
$598$		−	2.57508i		−	0.105303i
$599$			11.2202i			0.458443i	0.973374	+	0.229222i	$0.0736180\pi$
$599$			11.2202i			0.458443i	−0.973374	+	0.229222i	$0.926382\pi$
$600$	6.76034	−	4.43567i	0.275990	−	0.181085i
$601$		−	23.2289i		−	0.947525i	−0.880653	−	0.473763i	$-0.842895\pi$
$601$		−	23.2289i		−	0.947525i	0.880653	−	0.473763i	$-0.157105\pi$
$602$	10.9966	−	14.3574i	0.448190	−	0.585164i
$603$	1.85502	−	4.27445i	0.0755423	−	0.174069i
$604$	−9.45996			−0.384920
$605$	16.7269			0.680044
$606$	18.7988	−	12.3345i	0.763651	−	0.501055i
$607$			10.2126i			0.414517i	0.978286	+	0.207259i	$0.0664542\pi$
$607$			10.2126i			0.414517i	−0.978286	+	0.207259i	$0.933546\pi$
$608$	−4.31282			−0.174908
$609$	−46.1731	−	3.37385i	−1.87103	−	0.136715i
$610$	−3.70765			−0.150118
$611$			4.09158i			0.165527i
$612$	−7.56993	+	17.4431i	−0.305996	+	0.705096i
$613$	−3.92971			−0.158720			−0.0793598	−	0.996846i	$-0.525288\pi$
$613$	−3.92971			−0.158720			−0.0793598	+	0.996846i	$0.525288\pi$
$614$	−1.61664			−0.0652423
$615$	−5.80987	−	8.85474i	−0.234276	−	0.357058i
$616$	−13.2911	−	10.1799i	−0.535512	−	0.410160i
$617$		−	26.7652i		−	1.07753i	−0.842457	−	0.538763i	$-0.818892\pi$
$617$		−	26.7652i		−	1.07753i	0.842457	−	0.538763i	$-0.181108\pi$
$618$	16.1969	+	24.6854i	0.651534	+	0.992994i
$619$		−	34.4649i		−	1.38526i	−0.721293	−	0.692630i	$-0.756452\pi$
$619$		−	34.4649i		−	1.38526i	0.721293	−	0.692630i	$-0.243548\pi$
$620$		−	1.05215i		−	0.0422555i
$621$	−0.885356	−	5.12017i	−0.0355281	−	0.205465i
$622$		−	2.05811i		−	0.0825227i
$623$	−8.23087	−	6.30420i	−0.329763	−	0.252572i
$624$	3.72913	−	2.44679i	0.149284	−	0.0979501i
$625$	20.1336			0.805346
$626$	4.26591			0.170500
$627$	25.9308	+	39.5209i	1.03558	+	1.57831i
$628$		−	1.35432i		−	0.0540432i
$629$	20.4927			0.817099
$630$	−2.22278	−	3.99502i	−0.0885575	−	0.159166i
$631$	12.2459			0.487502			0.243751	−	0.969838i	$-0.421622\pi$
$631$	12.2459			0.487502			0.243751	+	0.969838i	$0.421622\pi$
$632$			16.7877i			0.667778i
$633$	8.84761	+	13.4845i	0.351661	+	0.535962i
$634$	7.40477			0.294081
$635$	−1.46358			−0.0580806
$636$	−7.24024	+	4.75054i	−0.287094	+	0.188371i
$637$	17.4031	−	4.69620i	0.689535	−	0.186070i
$638$			63.9271i			2.53090i
$639$	−12.6555	−	5.49221i	−0.500644	−	0.217268i
$640$		−	0.575987i		−	0.0227679i
$641$			30.1319i			1.19014i	0.803675	+	0.595069i	$0.202875\pi$
$641$			30.1319i			1.19014i	−0.803675	+	0.595069i	$0.797125\pi$
$642$	−5.37881	−	8.19777i	−0.212285	−	0.323540i
$643$			10.7702i			0.424734i	0.977190	+	0.212367i	$0.0681173\pi$
$643$			10.7702i			0.424734i	−0.977190	+	0.212367i	$0.931883\pi$
$644$	1.60877	−	2.10044i	0.0633945	−	0.0827690i
$645$	−3.74097	−	5.70156i	−0.147301	−	0.224499i
$646$	27.3359			1.07552
$647$	40.4816			1.59150			0.795748	−	0.605627i	$-0.207078\pi$
$647$	40.4816			1.59150			0.795748	+	0.605627i	$0.207078\pi$
$648$	6.57356	−	6.14722i	0.258234	−	0.241486i
$649$			16.6077i			0.651910i
$650$	12.0211			0.471507
$651$	8.34872	+	0.610037i	0.327212	+	0.0239092i
$652$	−0.541750			−0.0212165
$653$		−	27.9445i		−	1.09355i	−0.837279	−	0.546776i	$-0.815855\pi$
$653$		−	27.9445i		−	1.09355i	0.837279	−	0.546776i	$-0.184145\pi$
$654$	6.70041	−	4.39634i	0.262007	−	0.171911i
$655$	−3.95418			−0.154503
$656$	10.6157			0.414472
$657$	−35.8735	−	15.5683i	−1.39956	−	0.607377i
$658$	−2.55619	+	3.33741i	−0.0996508	+	0.130106i
$659$		−	17.3255i		−	0.674906i	−0.941342	−	0.337453i	$-0.890435\pi$
$659$		−	17.3255i		−	0.674906i	0.941342	−	0.337453i	$-0.109565\pi$
$660$	−5.27810	+	3.46312i	−0.205450	+	0.134802i
$661$		−	44.8011i		−	1.74256i	−0.490785	−	0.871281i	$-0.663290\pi$
$661$		−	44.8011i		−	1.74256i	0.490785	−	0.871281i	$-0.336710\pi$
$662$		−	18.9342i		−	0.735898i
$663$	−23.6363	+	15.5085i	−0.917958	+	0.602300i
$664$		−	2.97148i		−	0.115316i
$665$	−3.99640	+	5.21777i	−0.154974	+	0.202336i
$666$	−8.89773	−	3.86142i	−0.344780	−	0.149627i
$667$	−10.1027			−0.391177
$668$	6.77744			0.262227
$669$	−13.8689	+	9.09984i	−0.536205	+	0.351820i
$670$		−	0.894627i		−	0.0345625i
$671$	−40.7319			−1.57244
$672$	4.57039	+	0.333956i	0.176307	+	0.0128826i
$673$	16.0260			0.617759			0.308879	−	0.951101i	$-0.400046\pi$
$673$	16.0260			0.617759			0.308879	+	0.951101i	$0.400046\pi$
$674$		−	0.598810i		−	0.0230653i
$675$	23.9022	−	4.13305i	0.919995	−	0.159081i
$676$	−6.36894			−0.244959
$677$	−44.6643			−1.71659			−0.858294	−	0.513159i	$-0.828475\pi$
$677$	−44.6643			−1.71659			−0.858294	+	0.513159i	$0.828475\pi$
$678$	10.2378	+	15.6032i	0.393178	+	0.599238i
$679$	28.9303	−	37.7719i	1.11024	−	1.44955i
$680$			3.65078i			0.140001i
$681$	−12.4429	−	18.9641i	−0.476813	−	0.726705i
$682$		−	11.5589i		−	0.442612i
$683$		−	34.8122i		−	1.33205i	−0.745929	−	0.666026i	$-0.767994\pi$
$683$		−	34.8122i		−	1.33205i	0.745929	−	0.666026i	$-0.232006\pi$
$684$	−11.8690	−	5.15088i	−0.453822	−	0.196949i
$685$			9.63328i			0.368069i
$686$	17.1293	+	7.04191i	0.653998	+	0.268861i
$687$	−25.3248	+	16.6163i	−0.966200	+	0.633953i
$688$	6.83543			0.260598
$689$	−12.8745			−0.490478
$690$	−0.547291	−	0.834119i	−0.0208350	−	0.0317544i
$691$			12.0488i			0.458357i	0.973384	+	0.229179i	$0.0736040\pi$
$691$			12.0488i			0.458357i	−0.973384	+	0.229179i	$0.926396\pi$
$692$	−5.00868			−0.190401
$693$	−24.4192	−	43.8890i	−0.927610	−	1.66721i
$694$	−22.0310			−0.836284
$695$			11.4320i			0.433640i
$696$	−9.59934	−	14.6302i	−0.363862	−	0.554558i
$697$	−67.2853			−2.54861
$698$	11.9800			0.453451
$699$	2.85638	−	1.87416i	0.108038	−	0.0708872i
$700$	9.80536	+	7.51013i	0.370608	+	0.283856i
$701$			22.3683i			0.844841i	0.906400	+	0.422420i	$0.138819\pi$
$701$			22.3683i			0.844841i	−0.906400	+	0.422420i	$0.861181\pi$
$702$	13.1849	−	2.27987i	0.497631	−	0.0860480i
$703$			13.9441i			0.525910i
$704$		−	6.32775i		−	0.238486i
$705$	0.869596	+	1.32534i	0.0327509	+	0.0499152i
$706$		−	24.9427i		−	0.938730i
$707$	27.2663	+	20.8838i	1.02545	+	0.785417i
$708$	−2.49383	−	3.80081i	−0.0937239	−	0.142843i
$709$	16.9134			0.635195			0.317598	−	0.948226i	$-0.397124\pi$
$709$	16.9134			0.635195			0.317598	+	0.948226i	$0.397124\pi$
$710$	−2.64875			−0.0994057
$711$	−20.0498	+	46.2000i	−0.751926	+	1.73264i
$712$		−	3.91864i		−	0.146857i
$713$	1.82670			0.0684104
$714$	−28.9685	−	2.11671i	−1.08412	−	0.0792160i
$715$	−9.38541			−0.350994
$716$		−	10.7127i		−	0.400353i
$717$	2.69468	−	1.76806i	0.100635	−	0.0660294i
$718$	−11.9216			−0.444909
$719$	−4.63983			−0.173037			−0.0865183	−	0.996250i	$-0.527574\pi$
$719$	−4.63983			−0.173037			−0.0865183	+	0.996250i	$0.527574\pi$
$720$	0.687911	−	1.58513i	0.0256369	−	0.0590742i
$721$	−27.4233	+	35.8043i	−1.02130	+	1.33342i
$722$		−	0.399548i		−	0.0148696i
$723$	−22.4765	+	14.7475i	−0.835909	+	0.548465i
$724$			16.2738i			0.604810i
$725$		−	47.1616i		−	1.75154i
$726$	−42.0550	+	27.5936i	−1.56081	+	1.02409i
$727$		−	16.1797i		−	0.600073i	−0.953928	−	0.300037i	$-0.903001\pi$
$727$		−	16.1797i		−	0.600073i	0.953928	−	0.300037i	$-0.0969989\pi$
$728$	5.40881	+	4.14272i	0.200464	+	0.153539i
$729$	25.4323	−	9.06635i	0.941937	−	0.335791i
$730$	−7.50818			−0.277890
$731$	−43.3249			−1.60243
$732$	9.32183	−	6.11634i	0.344545	−	0.226066i
$733$		−	12.8967i		−	0.476352i	−0.971222	−	0.238176i	$-0.923450\pi$
$733$		−	12.8967i		−	0.476352i	0.971222	−	0.238176i	$-0.0765495\pi$
$734$	2.68705			0.0991810
$735$	4.63910	−	5.21993i	0.171116	−	0.192540i
$736$	1.00000			0.0368605
$737$		−	9.82830i		−	0.362030i
$738$	29.2145	+	12.6785i	1.07540	+	0.466701i
$739$	40.4583			1.48828			0.744141	−	0.668022i	$-0.232859\pi$
$739$	40.4583			1.48828			0.744141	+	0.668022i	$0.232859\pi$
$740$	−1.86226			−0.0684580
$741$	−10.5526	−	16.0831i	−0.387659	−	0.590826i
$742$	−10.5014	−	8.04326i	−0.385519	−	0.295277i
$743$			41.9796i			1.54008i	0.637994	+	0.770041i	$0.279764\pi$
$743$			41.9796i			1.54008i	−0.637994	+	0.770041i	$0.720236\pi$
$744$	1.73569	+	2.64535i	0.0636336	+	0.0969831i
$745$			7.48762i			0.274325i
$746$		−	0.108765i		−	0.00398219i
$747$	3.54889	−	8.17758i	0.129847	−	0.299202i
$748$			40.1071i			1.46646i
$749$	9.10698	−	11.8902i	0.332762	−	0.434460i
$750$	8.06447	−	5.29134i	0.294473	−	0.193213i
$751$	−32.8907			−1.20020			−0.600099	−	0.799925i	$-0.704872\pi$
$751$	−32.8907			−1.20020			−0.600099	+	0.799925i	$0.704872\pi$
$752$	−1.58891			−0.0579416
$753$	−8.22109	−	12.5297i	−0.299593	−	0.456606i
$754$		−	26.0152i		−	0.947418i
$755$	−5.44881			−0.198303
$756$	12.1790	+	6.37755i	0.442944	+	0.231949i
$757$	−51.1991			−1.86086			−0.930431	−	0.366467i	$-0.880567\pi$
$757$	−51.1991			−1.86086			−0.930431	+	0.366467i	$0.880567\pi$
$758$			15.3323i			0.556896i
$759$	−6.01250	−	9.16357i	−0.218240	−	0.332616i
$760$	−2.48413			−0.0901089
$761$	40.9757			1.48537			0.742685	−	0.669641i	$-0.233552\pi$
$761$	40.9757			1.48537			0.742685	+	0.669641i	$0.233552\pi$
$762$	3.67977	−	2.41441i	0.133304	−	0.0874648i
$763$	9.71843	+	7.44355i	0.351831	+	0.269475i
$764$		−	13.4350i		−	0.486061i
$765$	−4.36018	+	10.0470i	−0.157643	+	0.363250i
$766$			20.3454i			0.735110i
$767$		−	6.75853i		−	0.244036i
$768$	0.950180	+	1.44816i	0.0342867	+	0.0522559i
$769$			35.6701i			1.28630i	0.765742	+	0.643148i	$0.222372\pi$
$769$			35.6701i			1.28630i	−0.765742	+	0.643148i	$0.777628\pi$
$770$	−7.65548	−	5.86349i	−0.275884	−	0.211305i
$771$	26.8241	+	40.8823i	0.966047	+	1.47234i
$772$	−6.91896			−0.249019
$773$	−35.8989			−1.29119			−0.645596	−	0.763679i	$-0.723391\pi$
$773$	−35.8989			−1.29119			−0.645596	+	0.763679i	$0.723391\pi$
$774$	18.8112	+	8.16366i	0.676155	+	0.293437i
$775$			8.52746i			0.306316i
$776$	17.9828			0.645546
$777$	1.07974	−	14.7768i	0.0387353	−	0.530115i
$778$	1.58847			0.0569495
$779$		−	45.7835i		−	1.64037i
$780$	2.14793	−	1.40932i	0.0769081	−	0.0504618i
$781$	−29.0989			−1.04124
$782$	−6.33829			−0.226657
$783$	−8.94445	−	51.7273i	−0.319649	−	1.84858i
$784$	1.82371	+	6.75826i	0.0651324	+	0.241366i
$785$		−	0.780069i		−	0.0278419i
$786$	9.94167	−	6.52303i	0.354607	−	0.232669i
$787$		−	39.8679i		−	1.42114i	−0.703629	−	0.710568i	$-0.748438\pi$
$787$		−	39.8679i		−	1.42114i	0.703629	−	0.710568i	$-0.251562\pi$
$788$			2.10005i			0.0748111i
$789$	22.5004	−	14.7632i	0.801034	−	0.525583i
$790$			9.66948i			0.344025i
$791$	−17.3338	+	22.6313i	−0.616318	+	0.804676i
$792$	7.55733	−	17.4141i	0.268538	−	0.618782i
$793$	16.5759			0.588627
$794$	6.14813			0.218189
$795$	−4.17029	+	2.73625i	−0.147905	+	0.0970449i
$796$			10.8257i			0.383708i
$797$	10.4720			0.370936			0.185468	−	0.982650i	$-0.440620\pi$
$797$	10.4720			0.370936			0.185468	+	0.982650i	$0.440620\pi$
$798$	1.44029	−	19.7113i	0.0509859	−	0.697772i
$799$	10.0710			0.356286
$800$			4.66824i			0.165047i
$801$	4.68010	−	10.7842i	0.165363	−	0.381040i
$802$	−1.10369			−0.0389726
$803$	−82.4842			−2.91081
$804$	1.47583	+	2.24929i	0.0520484	+	0.0793262i
$805$	0.926632	−	1.20983i	0.0326595	−	0.0426408i
$806$			4.70390i			0.165688i
$807$	−27.2981	−	41.6047i	−0.960938	−	1.46455i
$808$			12.9812i			0.456678i
$809$			6.58175i			0.231402i	0.993284	+	0.115701i	$0.0369115\pi$
$809$			6.58175i			0.231402i	−0.993284	+	0.115701i	$0.963089\pi$
$810$	3.78629	−	3.54072i	0.133037	−	0.124408i
$811$		−	26.7024i		−	0.937647i	−0.883292	−	0.468823i	$-0.844678\pi$
$811$		−	26.7024i		−	0.937647i	0.883292	−	0.468823i	$-0.155322\pi$
$812$	16.2529	−	21.2200i	0.570364	−	0.744678i
$813$	40.6775	−	26.6897i	1.42662	−	0.936050i
$814$	−20.4586			−0.717075
$815$	−0.312041			−0.0109303
$816$	−6.02252	−	9.17884i	−0.210830	−	0.321324i
$817$		−	29.4800i		−	1.03137i
$818$	33.1984			1.16075
$819$	9.93744	+	17.8607i	0.347242	+	0.624103i
$820$	6.11449			0.213527
$821$			47.2065i			1.64752i	0.566940	+	0.823759i	$0.308127\pi$
$821$			47.2065i			1.64752i	−0.566940	+	0.823759i	$0.691873\pi$
$822$	−15.8916	−	24.2202i	−0.554283	−	0.844776i
$823$	−15.8180			−0.551381			−0.275690	−	0.961247i	$-0.588906\pi$
$823$	−15.8180			−0.551381			−0.275690	+	0.961247i	$0.588906\pi$
$824$	−17.0461			−0.593829
$825$	42.7777	−	28.0678i	1.48933	−	0.977194i
$826$	4.22236	−	5.51279i	0.146915	−	0.191815i
$827$		−	9.90702i		−	0.344501i	−0.985053	−	0.172250i	$-0.944896\pi$
$827$		−	9.90702i		−	0.344501i	0.985053	−	0.172250i	$-0.0551038\pi$
$828$	2.75202	+	1.19432i	0.0956393	+	0.0415054i
$829$			3.38713i			0.117640i	0.998269	+	0.0588200i	$0.0187338\pi$
$829$			3.38713i			0.117640i	−0.998269	+	0.0588200i	$0.981266\pi$
$830$		−	1.71154i		−	0.0594083i
$831$	14.4353	+	22.0006i	0.500755	+	0.763194i
$832$			2.57508i			0.0892750i
$833$	−11.5592	−	42.8358i	−0.400502	−	1.48417i
$834$	−18.8588	−	28.7425i	−0.653027	−	0.995271i
$835$	3.90372			0.135094
$836$	−27.2905			−0.943860
$837$	1.61728	+	9.35301i	0.0559013	+	0.323287i
$838$			0.222549i			0.00768784i
$839$	−4.95773			−0.171160			−0.0855799	−	0.996331i	$-0.527274\pi$
$839$	−4.95773			−0.171160			−0.0855799	+	0.996331i	$0.527274\pi$
$840$	2.63249	+	0.192354i	0.0908294	+	0.00663686i
$841$	−73.0637			−2.51944
$842$		−	19.8267i		−	0.683275i
$843$	25.9977	−	17.0579i	0.895408	−	0.587505i
$844$	−9.31151			−0.320516
$845$	−3.66843			−0.126198
$846$	−4.37271	−	1.89766i	−0.150337	−	0.0652429i
$847$	−60.9976	−	46.7193i	−2.09590	−	1.60529i
$848$		−	4.99963i		−	0.171688i
$849$	−24.8762	+	16.3220i	−0.853748	+	0.560170i
$850$		−	29.5887i		−	1.01488i
$851$		−	3.23316i		−	0.110831i
$852$	6.65952	−	4.36952i	0.228152	−	0.149697i
$853$		−	31.5392i		−	1.07988i	−0.841703	−	0.539942i	$-0.818446\pi$
$853$		−	31.5392i		−	1.07988i	0.841703	−	0.539942i	$-0.181554\pi$
$854$	13.5206	+	10.3557i	0.462666	+	0.354365i
$855$	−6.83637	−	2.96684i	−0.233799	−	0.101464i
$856$	5.66083			0.193483
$857$	−18.6484			−0.637018			−0.318509	−	0.947920i	$-0.603182\pi$
$857$	−18.6484			−0.637018			−0.318509	+	0.947920i	$0.603182\pi$
$858$	23.5970	−	15.4827i	0.805587	−	0.528570i
$859$			43.4893i			1.48384i	0.670490	+	0.741918i	$0.266084\pi$
$859$			43.4893i			1.48384i	−0.670490	+	0.741918i	$0.733916\pi$
$860$	3.93712			0.134255
$861$	−3.54517	+	48.5178i	−0.120819	+	1.65348i
$862$	22.5397			0.767705
$863$		−	30.6235i		−	1.04243i	−0.853424	−	0.521217i	$-0.825478\pi$
$863$		−	30.6235i		−	1.04243i	0.853424	−	0.521217i	$-0.174522\pi$
$864$	0.885356	+	5.12017i	0.0301204	+	0.174192i
$865$	−2.88493			−0.0980907
$866$	−12.5261			−0.425654
$867$	22.0194	+	33.5595i	0.747820	+	1.13974i
$868$	−2.93874	+	3.83687i	−0.0997473	+	0.130232i
$869$			106.228i			3.60354i
$870$	−5.52910	−	8.42682i	−0.187454	−	0.285696i
$871$			3.99964i			0.135523i
$872$			4.62685i			0.156685i
$873$	49.4891	+	21.4772i	1.67495	+	0.726893i
$874$		−	4.31282i		−	0.145883i
$875$	11.6969	+	8.95890i	0.395427	+	0.302866i
$876$	18.8772	−	12.3859i	0.637801	−	0.418481i
$877$	0.152370			0.00514516			0.00257258	−	0.999997i	$-0.499181\pi$
$877$	0.152370			0.00514516			0.00257258	+	0.999997i	$0.499181\pi$
$878$	31.3680			1.05862
$879$	−19.9314	−	30.3772i	−0.672270	−	1.02460i
$880$		−	3.64470i		−	0.122863i
$881$	45.2237			1.52362			0.761812	−	0.647798i	$-0.224310\pi$
$881$	45.2237			1.52362			0.761812	+	0.647798i	$0.224310\pi$
$882$	−3.05262	+	20.7769i	−0.102787	+	0.699596i
$883$	−35.9287			−1.20910			−0.604549	−	0.796568i	$-0.706647\pi$
$883$	−35.9287			−1.20910			−0.604549	+	0.796568i	$0.706647\pi$
$884$		−	16.3216i		−	0.548956i
$885$	−1.43641	−	2.18922i	−0.0482845	−	0.0735898i
$886$	18.5795			0.624191
$887$	17.9212			0.601733			0.300867	−	0.953666i	$-0.402724\pi$
$887$	17.9212			0.601733			0.300867	+	0.953666i	$0.402724\pi$
$888$	4.68213	−	3.07209i	0.157122	−	0.103092i
$889$	5.33723	+	4.08789i	0.179005	+	0.137103i
$890$		−	2.25709i		−	0.0756577i
$891$	41.5958	−	38.8980i	1.39351	−	1.30313i
$892$		−	9.57697i		−	0.320661i
$893$			6.85269i			0.229316i
$894$	−12.3520	−	18.8255i	−0.413112	−	0.629619i
$895$		−	6.17038i		−	0.206253i
$896$	−1.60877	+	2.10044i	−0.0537453	+	0.0701708i
$897$	2.44679	+	3.72913i	0.0816960	+	0.124512i
$898$	−22.1240			−0.738289
$899$	18.4545			0.615492
$900$	−5.57535	+	12.8471i	−0.185845	+	0.428236i
$901$			31.6891i			1.05572i
$902$	67.1733			2.23663
$903$	−2.28273	+	31.2406i	−0.0759646	+	1.03962i
$904$	−10.7745			−0.358356
$905$			9.37349i			0.311585i
$906$	13.6995	−	8.98866i	0.455136	−	0.298628i
$907$	−39.9417			−1.32624			−0.663121	−	0.748512i	$-0.730769\pi$
$907$	−39.9417			−1.32624			−0.663121	+	0.748512i	$0.730769\pi$
$908$	13.0953			0.434583
$909$	−15.5037	+	35.7246i	−0.514225	+	1.18491i
$910$	3.11541	+	2.38615i	0.103275	+	0.0791002i
$911$		−	14.9796i		−	0.496295i	−0.968722	−	0.248148i	$-0.920178\pi$
$911$		−	14.9796i		−	0.496295i	0.968722	−	0.248148i	$-0.0798218\pi$
$912$	6.24565	−	4.09796i	0.206814	−	0.135697i
$913$		−	18.8028i		−	0.622281i
$914$		−	14.3877i		−	0.475904i
$915$	5.36925	−	3.52293i	0.177502	−	0.116465i
$916$		−	17.4876i		−	0.577806i
$917$	14.4196	+	11.0443i	0.476178	+	0.364715i
$918$	−5.61165	−	32.4531i	−0.185212	−	1.07111i
$919$	4.67542			0.154228			0.0771140	−	0.997022i	$-0.475429\pi$
$919$	4.67542			0.154228			0.0771140	+	0.997022i	$0.475429\pi$
$920$	0.575987			0.0189897
$921$	2.34115	−	1.53610i	0.0771434	−	0.0506162i
$922$			21.3872i			0.704351i
$923$	11.8418			0.389779
$924$	28.9203	+	2.11319i	0.951407	+	0.0695189i
$925$	15.0932			0.496261
$926$			9.49725i			0.312099i
$927$	−46.9112	−	20.3584i	−1.54077	−	0.668659i
$928$	10.1027			0.331636
$929$	28.2294			0.926176			0.463088	−	0.886312i	$-0.346741\pi$
$929$	28.2294			0.926176			0.463088	+	0.886312i	$0.346741\pi$
$930$	0.999736	+	1.52368i	0.0327826	+	0.0499636i
$931$	29.1472	−	7.86533i	0.955261	−	0.257776i
$932$			1.97242i			0.0646089i
$933$	1.95557	+	2.98047i	0.0640226	+	0.0975761i
$934$		−	7.11700i		−	0.232875i
$935$			23.1012i			0.755489i
$936$	−3.07546	+	7.08668i	−0.100525	+	0.231635i
$937$			38.9520i			1.27251i	0.771481	+	0.636253i	$0.219516\pi$
$937$			38.9520i			1.27251i	−0.771481	+	0.636253i	$0.780484\pi$
$938$	−2.49876	+	3.26242i	−0.0815872	+	0.106522i
$939$	−6.17771	+	4.05338i	−0.201602	+	0.132277i
$940$	−0.915191			−0.0298502
$941$	−9.79514			−0.319313			−0.159656	−	0.987173i	$-0.551039\pi$
$941$	−9.79514			−0.319313			−0.159656	+	0.987173i	$0.551039\pi$
$942$	1.28685	+	1.96126i	0.0419277	+	0.0639015i
$943$			10.6157i			0.345694i
$944$	2.62459			0.0854230
$945$	7.01492	+	3.67338i	0.228195	+	0.119495i
$946$	43.2528			1.40627
$947$		−	13.2368i		−	0.430137i	−0.976599	−	0.215068i	$-0.931003\pi$
$947$		−	13.2368i		−	0.430137i	0.976599	−	0.215068i	$-0.0689975\pi$
$948$	−15.9513	−	24.3112i	−0.518074	−	0.789590i
$949$	33.5671			1.08963
$950$	20.1333			0.653210
$951$	−10.7233	+	7.03587i	−0.347726	+	0.228154i
$952$	10.1969	−	13.3132i	0.330482	−	0.431484i
$953$			27.7246i			0.898089i	0.893509	+	0.449044i	$0.148235\pi$
$953$			27.7246i			0.898089i	−0.893509	+	0.449044i	$0.851765\pi$
$954$	5.97113	−	13.7591i	0.193323	−	0.445466i
$955$		−	7.73838i		−	0.250408i
$956$			1.86076i			0.0601814i
$957$	−60.7422	−	92.5764i	−1.96352	−	2.99257i
$958$			32.0987i			1.03706i
$959$	26.9064	−	35.1295i	0.868854	−	1.13439i
$960$	0.547291	+	0.834119i	0.0176638	+	0.0269211i
$961$	27.6632			0.892360
$962$	8.32567			0.268430
$963$	15.5787	+	6.76082i	0.502017	+	0.217864i
$964$		−	15.5207i		−	0.499890i
$965$	−3.98523			−0.128289
$966$	−0.333956	+	4.57039i	−0.0107449	+	0.147050i
$967$	−3.92545			−0.126234			−0.0631169	−	0.998006i	$-0.520104\pi$
$967$	−3.92545			−0.126234			−0.0631169	+	0.998006i	$0.520104\pi$
$968$		−	29.0404i		−	0.933393i
$969$	−39.5867	+	25.9741i	−1.27171	+	0.834407i
$970$	10.3579			0.332571
$971$	−15.4401			−0.495497			−0.247748	−	0.968824i	$-0.579691\pi$
$971$	−15.4401			−0.495497			−0.247748	+	0.968824i	$0.579691\pi$
$972$	−3.67858	+	15.1482i	−0.117991	+	0.485879i
$973$	31.9303	−	41.6888i	1.02364	−	1.33648i
$974$			24.5101i			0.785353i
$975$	−17.4084	+	11.4222i	−0.557517	+	0.365804i
$976$			6.43703i			0.206044i
$977$			26.9366i			0.861779i	0.902405	+	0.430889i	$0.141800\pi$
$977$			26.9366i			0.861779i	−0.902405	+	0.430889i	$0.858200\pi$
$978$	0.784538	−	0.514760i	0.0250868	−	0.0164602i
$979$		−	24.7962i		−	0.792489i
$980$	1.05043	+	3.89267i	0.0335548	+	0.124347i
$981$	−5.52592	+	12.7332i	−0.176429	+	0.406539i
$982$	−7.49990			−0.239331
$983$	10.0671			0.321090			0.160545	−	0.987028i	$-0.448675\pi$
$983$	10.0671			0.321090			0.160545	+	0.987028i	$0.448675\pi$
$984$	−15.3732	+	10.0868i	−0.490078	+	0.321555i
$985$			1.20960i			0.0385411i
$986$	−64.0336			−2.03925
$987$	0.530626	−	7.26194i	0.0168900	−	0.231150i
$988$	11.1059			0.353325
$989$			6.83543i			0.217354i
$990$	4.35292	−	10.0303i	0.138345	−	0.318783i
$991$	49.2206			1.56354			0.781771	−	0.623565i	$-0.214316\pi$
$991$	49.2206			1.56354			0.781771	+	0.623565i	$0.214316\pi$
$992$	−1.82670			−0.0579977
$993$	17.9909	+	27.4197i	0.570923	+	0.870137i
$994$	9.65913	+	7.39813i	0.306369	+	0.234654i
$995$			6.23548i			0.197678i
$996$	2.82344	+	4.30317i	0.0894642	+	0.136351i
$997$			14.2273i			0.450584i	0.974291	+	0.225292i	$0.0723336\pi$
$997$			14.2273i			0.450584i	−0.974291	+	0.225292i	$0.927666\pi$
$998$		−	36.8663i		−	1.16698i
$999$	16.5543	−	2.86250i	0.523756	−	0.0905655i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.f.b.461.9	yes	24
3.2	odd	2	inner	966.2.f.b.461.16	yes	24
7.6	odd	2	inner	966.2.f.b.461.4	✓	24
21.20	even	2	inner	966.2.f.b.461.21	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.f.b.461.4	✓	24	7.6	odd	2	inner
966.2.f.b.461.9	yes	24	1.1	even	1	trivial
966.2.f.b.461.16	yes	24	3.2	odd	2	inner
966.2.f.b.461.21	yes	24	21.20	even	2	inner

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.950180 + 1.44816i) q^{3} -1.00000 q^{4} -0.575987 q^{5} +(1.44816 - 0.950180i) q^{6} +(2.10044 + 1.60877i) q^{7} +1.00000i q^{8} +(-1.19432 + 2.75202i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.950180 + 1.44816i) q^{3} -1.00000 q^{4} -0.575987 q^{5} +(1.44816 - 0.950180i) q^{6} +(2.10044 + 1.60877i) q^{7} +1.00000i q^{8} +(-1.19432 + 2.75202i) q^{9} +0.575987i q^{10} +6.32775i q^{11} +(-0.950180 - 1.44816i) q^{12} -2.57508i q^{13} +(1.60877 - 2.10044i) q^{14} +(-0.547291 - 0.834119i) q^{15} +1.00000 q^{16} -6.33829 q^{17} +(2.75202 + 1.19432i) q^{18} -4.31282i q^{19} +0.575987 q^{20} +(-0.333956 + 4.57039i) q^{21} +6.32775 q^{22} +1.00000i q^{23} +(-1.44816 + 0.950180i) q^{24} -4.66824 q^{25} -2.57508 q^{26} +(-5.12017 + 0.885356i) q^{27} +(-2.10044 - 1.60877i) q^{28} +10.1027i q^{29} +(-0.834119 + 0.547291i) q^{30} -1.82670i q^{31} -1.00000i q^{32} +(-9.16357 + 6.01250i) q^{33} +6.33829i q^{34} +(-1.20983 - 0.926632i) q^{35} +(1.19432 - 2.75202i) q^{36} -3.23316 q^{37} -4.31282 q^{38} +(3.72913 - 2.44679i) q^{39} -0.575987i q^{40} +10.6157 q^{41} +(4.57039 + 0.333956i) q^{42} +6.83543 q^{43} -6.32775i q^{44} +(0.687911 - 1.58513i) q^{45} +1.00000 q^{46} -1.58891 q^{47} +(0.950180 + 1.44816i) q^{48} +(1.82371 + 6.75826i) q^{49} +4.66824i q^{50} +(-6.02252 - 9.17884i) q^{51} +2.57508i q^{52} -4.99963i q^{53} +(0.885356 + 5.12017i) q^{54} -3.64470i q^{55} +(-1.60877 + 2.10044i) q^{56} +(6.24565 - 4.09796i) q^{57} +10.1027 q^{58} +2.62459 q^{59} +(0.547291 + 0.834119i) q^{60} +6.43703i q^{61} -1.82670 q^{62} +(-6.93596 + 3.85907i) q^{63} -1.00000 q^{64} +1.48321i q^{65} +(6.01250 + 9.16357i) q^{66} -1.55321 q^{67} +6.33829 q^{68} +(-1.44816 + 0.950180i) q^{69} +(-0.926632 + 1.20983i) q^{70} +4.59862i q^{71} +(-2.75202 - 1.19432i) q^{72} +13.0353i q^{73} +3.23316i q^{74} +(-4.43567 - 6.76034i) q^{75} +4.31282i q^{76} +(-10.1799 + 13.2911i) q^{77} +(-2.44679 - 3.72913i) q^{78} +16.7877 q^{79} -0.575987 q^{80} +(-6.14722 - 6.57356i) q^{81} -10.6157i q^{82} -2.97148 q^{83} +(0.333956 - 4.57039i) q^{84} +3.65078 q^{85} -6.83543i q^{86} +(-14.6302 + 9.59934i) q^{87} -6.32775 q^{88} -3.91864 q^{89} +(-1.58513 - 0.687911i) q^{90} +(4.14272 - 5.40881i) q^{91} -1.00000i q^{92} +(2.64535 - 1.73569i) q^{93} +1.58891i q^{94} +2.48413i q^{95} +(1.44816 - 0.950180i) q^{96} -17.9828i q^{97} +(6.75826 - 1.82371i) q^{98} +(-17.4141 - 7.55733i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} - 4 q^{7} + 8 q^{9}+O(q^{10}) \) 24 * q - 24 * q^4 - 4 * q^7 + 8 * q^9	\( 24 q - 24 q^{4} - 4 q^{7} + 8 q^{9} + 24 q^{16} + 16 q^{18} - 28 q^{21} + 8 q^{22} - 24 q^{25} + 4 q^{28} + 24 q^{30} - 8 q^{36} + 40 q^{37} + 72 q^{39} + 64 q^{43} + 24 q^{46} - 24 q^{51} + 16 q^{58} + 12 q^{63} - 24 q^{64} - 64 q^{67} + 16 q^{70} - 16 q^{72} - 32 q^{78} + 88 q^{79} + 48 q^{81} + 28 q^{84} + 64 q^{85} - 8 q^{88} - 56 q^{91} + 8 q^{93} - 8 q^{99}+O(q^{100}) \) 24 * q - 24 * q^4 - 4 * q^7 + 8 * q^9 + 24 * q^16 + 16 * q^18 - 28 * q^21 + 8 * q^22 - 24 * q^25 + 4 * q^28 + 24 * q^30 - 8 * q^36 + 40 * q^37 + 72 * q^39 + 64 * q^43 + 24 * q^46 - 24 * q^51 + 16 * q^58 + 12 * q^63 - 24 * q^64 - 64 * q^67 + 16 * q^70 - 16 * q^72 - 32 * q^78 + 88 * q^79 + 48 * q^81 + 28 * q^84 + 64 * q^85 - 8 * q^88 - 56 * q^91 + 8 * q^93 - 8 * q^99

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