LMFDB - Embedded newform 966.2.be.a.61.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(19,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 55, 45]))

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

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

chi := DirichletCharacter("966.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.be (of order $66$, degree $20$, 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:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			61.4
Character	$\chi$	$=$	966.61
Dual form			966.2.be.a.871.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.786053 + 0.618159i) q^{2} +(-0.814576 - 0.580057i) q^{3} +(0.235759 + 0.971812i) q^{4} +(-0.436006 + 0.0840333i) q^{5} +(-0.281733 - 0.959493i) q^{6} +(-2.27972 - 1.34272i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(0.327068 + 0.945001i) q^{9} +O(q^{10})$	\(q+(0.786053 + 0.618159i) q^{2} +(-0.814576 - 0.580057i) q^{3} +(0.235759 + 0.971812i) q^{4} +(-0.436006 + 0.0840333i) q^{5} +(-0.281733 - 0.959493i) q^{6} +(-2.27972 - 1.34272i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(0.327068 + 0.945001i) q^{9} +(-0.394670 - 0.203466i) q^{10} +(-0.181297 - 0.230538i) q^{11} +(0.371662 - 0.928368i) q^{12} +(0.362355 + 0.563836i) q^{13} +(-0.961964 - 2.46468i) q^{14} +(0.403904 + 0.184457i) q^{15} +(-0.888835 + 0.458227i) q^{16} +(3.78489 + 3.60888i) q^{17} +(-0.327068 + 0.945001i) q^{18} +(-3.96499 + 3.78061i) q^{19} +(-0.184457 - 0.403904i) q^{20} +(1.07815 + 2.41611i) q^{21} -0.293286i q^{22} +(-4.36317 - 1.99066i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-4.45880 + 1.78503i) q^{25} +(-0.0637097 + 0.667198i) q^{26} +(0.281733 - 0.959493i) q^{27} +(0.767407 - 2.53201i) q^{28} +(-9.84544 + 2.89088i) q^{29} +(0.203466 + 0.394670i) q^{30} +(0.0652173 + 0.682986i) q^{31} +(-0.981929 - 0.189251i) q^{32} +(0.0139551 + 0.292954i) q^{33} +(0.744259 + 5.17643i) q^{34} +(1.10680 + 0.393862i) q^{35} +(-0.841254 + 0.540641i) q^{36} +(-5.63102 + 1.94891i) q^{37} +(-5.45372 + 0.520767i) q^{38} +(0.0318910 - 0.669474i) q^{39} +(0.104684 - 0.431514i) q^{40} +(0.302874 - 0.262442i) q^{41} +(-0.646060 + 2.56566i) q^{42} +(1.58797 - 0.725202i) q^{43} +(0.181297 - 0.230538i) q^{44} +(-0.222015 - 0.384541i) q^{45} +(-2.19914 - 4.26190i) q^{46} +(-3.66027 - 2.11325i) q^{47} +(0.989821 + 0.142315i) q^{48} +(3.39421 + 6.12204i) q^{49} +(-4.60829 - 1.35312i) q^{50} +(-0.989721 - 5.13516i) q^{51} +(-0.462514 + 0.485071i) q^{52} +(-4.18445 - 0.199330i) q^{53} +(0.814576 - 0.580057i) q^{54} +(0.0984197 + 0.0852811i) q^{55} +(2.16841 - 1.51592i) q^{56} +(5.42276 - 0.779675i) q^{57} +(-9.52607 - 3.81366i) q^{58} +(4.71831 - 9.15224i) q^{59} +(-0.0840333 + 0.436006i) q^{60} +(7.96888 + 11.1907i) q^{61} +(-0.370930 + 0.577178i) q^{62} +(0.523249 - 2.59349i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-0.205370 - 0.215386i) q^{65} +(-0.170123 + 0.238904i) q^{66} +(-2.81867 - 7.04069i) q^{67} +(-2.61483 + 4.52902i) q^{68} +(2.39944 + 4.15243i) q^{69} +(0.626537 + 0.993776i) q^{70} +(-1.41071 + 9.81174i) q^{71} +(-0.995472 - 0.0950560i) q^{72} +(9.34729 - 2.26763i) q^{73} +(-5.63102 - 1.94891i) q^{74} +(4.66745 + 1.13231i) q^{75} +(-4.60883 - 2.96191i) q^{76} +(0.103758 + 0.768994i) q^{77} +(0.438909 - 0.506528i) q^{78} +(-2.78265 + 0.132554i) q^{79} +(0.349031 - 0.274481i) q^{80} +(-0.786053 + 0.618159i) q^{81} +(0.400306 - 0.0190689i) q^{82} +(-3.44726 + 3.97835i) q^{83} +(-2.09382 + 1.61738i) q^{84} +(-1.95350 - 1.25544i) q^{85} +(1.69652 + 0.411571i) q^{86} +(9.69674 + 3.35607i) q^{87} +(0.285019 - 0.0691448i) q^{88} +(-1.29181 - 0.123353i) q^{89} +(0.0631921 - 0.439511i) q^{90} +(-0.0689938 - 1.77193i) q^{91} +(0.905888 - 4.70950i) q^{92} +(0.343046 - 0.594174i) q^{93} +(-1.57084 - 3.92376i) q^{94} +(1.41106 - 1.98156i) q^{95} +(0.690079 + 0.723734i) q^{96} +(3.64799 + 4.21000i) q^{97} +(-1.11636 + 6.91041i) q^{98} +(0.158562 - 0.246728i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9}+O(q^{10}) $ 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9	$ 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9} - 22 q^{14} + 16 q^{16} + 66 q^{17} + 16 q^{18} + 40 q^{23} - 48 q^{25} + 12 q^{26} + 44 q^{28} - 24 q^{29} + 24 q^{31} - 16 q^{32} + 98 q^{35} + 32 q^{36} - 22 q^{37} - 66 q^{38} - 8 q^{39} - 88 q^{43} + 4 q^{46} - 144 q^{47} - 24 q^{49} + 80 q^{50} - 22 q^{51} + 12 q^{52} + 44 q^{53} + 44 q^{57} + 10 q^{58} + 12 q^{59} - 32 q^{64} + 108 q^{70} - 16 q^{71} + 16 q^{72} - 180 q^{73} - 22 q^{74} - 12 q^{75} + 18 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 36 q^{82} + 22 q^{84} + 68 q^{85} - 22 q^{86} + 48 q^{87} + 22 q^{88} + 8 q^{92} + 8 q^{93} - 12 q^{94} + 66 q^{95} - 90 q^{98}+O(q^{100}) $ 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9 - 22 * q^14 + 16 * q^16 + 66 * q^17 + 16 * q^18 + 40 * q^23 - 48 * q^25 + 12 * q^26 + 44 * q^28 - 24 * q^29 + 24 * q^31 - 16 * q^32 + 98 * q^35 + 32 * q^36 - 22 * q^37 - 66 * q^38 - 8 * q^39 - 88 * q^43 + 4 * q^46 - 144 * q^47 - 24 * q^49 + 80 * q^50 - 22 * q^51 + 12 * q^52 + 44 * q^53 + 44 * q^57 + 10 * q^58 + 12 * q^59 - 32 * q^64 + 108 * q^70 - 16 * q^71 + 16 * q^72 - 180 * q^73 - 22 * q^74 - 12 * q^75 + 18 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 36 * q^82 + 22 * q^84 + 68 * q^85 - 22 * q^86 + 48 * q^87 + 22 * q^88 + 8 * q^92 + 8 * q^93 - 12 * q^94 + 66 * q^95 - 90 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{22}\right)$

Coefficient data

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

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

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

$2$	0.786053	+	0.618159i	0.555823	+	0.437104i
$2$	0.786053	+	0.618159i	0.555823	+	0.437104i
$3$	−0.814576	−	0.580057i	−0.470296	−	0.334896i
$3$	−0.814576	−	0.580057i	−0.470296	−	0.334896i
$4$	0.235759	+	0.971812i	0.117879	+	0.485906i
$5$	−0.436006	+	0.0840333i	−0.194988	+	0.0375808i	−0.285810	−	0.958286i	$-0.592263\pi$
$5$	−0.436006	+	0.0840333i	−0.194988	+	0.0375808i	0.0908222	+	0.995867i	$0.471051\pi$
$6$	−0.281733	−	0.959493i	−0.115017	−	0.391711i
$7$	−2.27972	−	1.34272i	−0.861652	−	0.507500i
$7$	−2.27972	−	1.34272i	−0.861652	−	0.507500i
$8$	−0.415415	+	0.909632i	−0.146871	+	0.321603i
$9$	0.327068	+	0.945001i	0.109023	+	0.315000i
$10$	−0.394670	−	0.203466i	−0.124806	−	0.0643417i
$11$	−0.181297	−	0.230538i	−0.0546632	−	0.0695100i	0.757953	−	0.652309i	$-0.226200\pi$
$11$	−0.181297	−	0.230538i	−0.0546632	−	0.0695100i	−0.812616	+	0.582799i	$0.801957\pi$
$12$	0.371662	−	0.928368i	0.107290	−	0.267997i
$13$	0.362355	+	0.563836i	0.100499	+	0.156380i	0.887862	−	0.460111i	$-0.152190\pi$
$13$	0.362355	+	0.563836i	0.100499	+	0.156380i	−0.787362	+	0.616491i	$0.788554\pi$
$14$	−0.961964	−	2.46468i	−0.257096	−	0.658712i
$15$	0.403904	+	0.184457i	0.104288	+	0.0476265i
$16$	−0.888835	+	0.458227i	−0.222209	+	0.114557i
$17$	3.78489	+	3.60888i	0.917970	+	0.875282i	0.992538	−	0.121933i	$-0.0389094\pi$
$17$	3.78489	+	3.60888i	0.917970	+	0.875282i	−0.0745685	+	0.997216i	$0.523758\pi$
$18$	−0.327068	+	0.945001i	−0.0770907	+	0.222739i
$19$	−3.96499	+	3.78061i	−0.909632	+	0.867332i	−0.991605	−	0.129302i	$-0.958726\pi$
$19$	−3.96499	+	3.78061i	−0.909632	+	0.867332i	0.0819731	+	0.996635i	$0.473878\pi$
$20$	−0.184457	−	0.403904i	−0.0412458	−	0.0903157i
$21$	1.07815	+	2.41611i	0.235271	+	0.527239i
$22$		−	0.293286i		−	0.0625288i
$23$	−4.36317	−	1.99066i	−0.909784	−	0.415081i
$23$	−4.36317	−	1.99066i	−0.909784	−	0.415081i
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	−4.45880	+	1.78503i	−0.891760	+	0.357007i
$26$	−0.0637097	+	0.667198i	−0.0124945	+	0.130848i
$27$	0.281733	−	0.959493i	0.0542195	−	0.184655i
$28$	0.767407	−	2.53201i	0.145026	−	0.478505i
$29$	−9.84544	+	2.89088i	−1.82825	+	0.536824i	−0.999732	−	0.0231349i	$-0.992635\pi$
$29$	−9.84544	+	2.89088i	−1.82825	+	0.536824i	−0.828521	+	0.559958i	$0.810817\pi$
$30$	0.203466	+	0.394670i	0.0371477	+	0.0720565i
$31$	0.0652173	+	0.682986i	0.0117134	+	0.122668i	0.999437	−	0.0335415i	$-0.0106786\pi$
$31$	0.0652173	+	0.682986i	0.0117134	+	0.122668i	−0.987724	+	0.156209i	$0.950073\pi$
$32$	−0.981929	−	0.189251i	−0.173582	−	0.0334552i
$33$	0.0139551	+	0.292954i	0.00242927	+	0.0509967i
$34$	0.744259	+	5.17643i	0.127639	+	0.887751i
$35$	1.10680	+	0.393862i	0.187084	+	0.0665748i
$36$	−0.841254	+	0.540641i	−0.140209	+	0.0901068i
$37$	−5.63102	+	1.94891i	−0.925733	+	0.320399i	−0.748015	−	0.663682i	$-0.768993\pi$
$37$	−5.63102	+	1.94891i	−0.925733	+	0.320399i	−0.177718	+	0.984081i	$0.556872\pi$
$38$	−5.45372	+	0.520767i	−0.884710	+	0.0844795i
$39$	0.0318910	−	0.669474i	0.00510664	−	0.107202i
$40$	0.104684	−	0.431514i	0.0165520	−	0.0682283i
$41$	0.302874	−	0.262442i	0.0473010	−	0.0409865i	−0.630890	−	0.775873i	$-0.717310\pi$
$41$	0.302874	−	0.262442i	0.0473010	−	0.0409865i	0.678190	+	0.734886i	$0.262764\pi$
$42$	−0.646060	+	2.56566i	−0.0996892	+	0.395890i
$43$	1.58797	−	0.725202i	0.242163	−	0.110592i	−0.290637	−	0.956834i	$-0.593867\pi$
$43$	1.58797	−	0.725202i	0.242163	−	0.110592i	0.532800	+	0.846241i	$0.321140\pi$
$44$	0.181297	−	0.230538i	0.0273316	−	0.0347550i
$45$	−0.222015	−	0.384541i	−0.0330961	−	0.0573240i
$46$	−2.19914	−	4.26190i	−0.324246	−	0.628383i
$47$	−3.66027	−	2.11325i	−0.533905	−	0.308250i	0.208700	−	0.977980i	$-0.433077\pi$
$47$	−3.66027	−	2.11325i	−0.533905	−	0.308250i	−0.742605	+	0.669730i	$0.766410\pi$
$48$	0.989821	+	0.142315i	0.142868	+	0.0205414i
$49$	3.39421	+	6.12204i	0.484887	+	0.874577i
$50$	−4.60829	−	1.35312i	−0.651710	−	0.191359i
$51$	−0.989721	−	5.13516i	−0.138589	−	0.719066i
$52$	−0.462514	+	0.485071i	−0.0641391	+	0.0672672i
$53$	−4.18445	−	0.199330i	−0.574779	−	0.0273801i	−0.241820	−	0.970321i	$-0.577744\pi$
$53$	−4.18445	−	0.199330i	−0.574779	−	0.0273801i	−0.332959	+	0.942941i	$0.608047\pi$
$54$	0.814576	−	0.580057i	0.110850	−	0.0789357i
$55$	0.0984197	+	0.0852811i	0.0132709	+	0.0114993i
$56$	2.16841	−	1.51592i	0.289766	−	0.202573i
$57$	5.42276	−	0.779675i	0.718262	−	0.103271i
$58$	−9.52607	−	3.81366i	−1.25083	−	0.500758i
$59$	4.71831	−	9.15224i	0.614271	−	1.19152i	−0.352484	−	0.935818i	$-0.614663\pi$
$59$	4.71831	−	9.15224i	0.614271	−	1.19152i	0.966756	−	0.255702i	$-0.0823067\pi$
$60$	−0.0840333	+	0.436006i	−0.0108486	+	0.0562881i
$61$	7.96888	+	11.1907i	1.02031	+	1.43282i	0.897824	+	0.440355i	$0.145147\pi$
$61$	7.96888	+	11.1907i	1.02031	+	1.43282i	0.122486	+	0.992470i	$0.460913\pi$
$62$	−0.370930	+	0.577178i	−0.0471081	+	0.0733017i
$63$	0.523249	−	2.59349i	0.0659232	−	0.326750i
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	−0.205370	−	0.215386i	−0.0254730	−	0.0267153i
$66$	−0.170123	+	0.238904i	−0.0209407	+	0.0294070i
$67$	−2.81867	−	7.04069i	−0.344355	−	0.860157i	−0.994916	−	0.100704i	$-0.967891\pi$
$67$	−2.81867	−	7.04069i	−0.344355	−	0.860157i	0.650561	−	0.759454i	$-0.274534\pi$
$68$	−2.61483	+	4.52902i	−0.317095	+	0.549225i
$69$	2.39944	+	4.15243i	0.288859	+	0.499894i
$70$	0.626537	+	0.993776i	0.0748854	+	0.118779i
$71$	−1.41071	+	9.81174i	−0.167421	+	1.16444i	0.716769	+	0.697311i	$0.245620\pi$
$71$	−1.41071	+	9.81174i	−0.167421	+	1.16444i	−0.884190	+	0.467128i	$0.845289\pi$
$72$	−0.995472	−	0.0950560i	−0.117317	−	0.0112025i
$73$	9.34729	−	2.26763i	1.09402	−	0.265406i	0.352144	−	0.935946i	$-0.385453\pi$
$73$	9.34729	−	2.26763i	1.09402	−	0.265406i	0.741874	+	0.670540i	$0.233937\pi$
$74$	−5.63102	−	1.94891i	−0.654592	−	0.226557i
$75$	4.66745	+	1.13231i	0.538951	+	0.130748i
$76$	−4.60883	−	2.96191i	−0.528669	−	0.339755i
$77$	0.103758	+	0.768994i	0.0118243	+	0.0876350i
$78$	0.438909	−	0.506528i	0.0496967	−	0.0573530i
$79$	−2.78265	+	0.132554i	−0.313073	+	0.0149135i	−0.203530	−	0.979069i	$-0.565242\pi$
$79$	−2.78265	+	0.132554i	−0.313073	+	0.0149135i	−0.109542	+	0.993982i	$0.534939\pi$
$80$	0.349031	−	0.274481i	0.0390229	−	0.0306879i
$81$	−0.786053	+	0.618159i	−0.0873392	+	0.0686843i
$82$	0.400306	−	0.0190689i	0.0442064	−	0.00210581i
$83$	−3.44726	+	3.97835i	−0.378386	+	0.436681i	−0.912716	−	0.408595i	$-0.866019\pi$
$83$	−3.44726	+	3.97835i	−0.378386	+	0.436681i	0.534329	+	0.845276i	$0.320564\pi$
$84$	−2.09382	+	1.61738i	−0.228455	+	0.176470i
$85$	−1.95350	−	1.25544i	−0.211887	−	0.136171i
$86$	1.69652	+	0.411571i	0.182941	+	0.0443809i
$87$	9.69674	+	3.35607i	1.03960	+	0.359809i
$88$	0.285019	−	0.0691448i	0.0303831	−	0.00737086i
$89$	−1.29181	−	0.123353i	−0.136931	−	0.0130754i	0.0263653	−	0.999652i	$-0.491607\pi$
$89$	−1.29181	−	0.123353i	−0.136931	−	0.0130754i	−0.163297	+	0.986577i	$0.552213\pi$
$90$	0.0631921	−	0.439511i	0.00666103	−	0.0463285i
$91$	−0.0689938	−	1.77193i	−0.00723252	−	0.185748i
$92$	0.905888	−	4.70950i	0.0944453	−	0.490999i
$93$	0.343046	−	0.594174i	0.0355723	−	0.0616130i
$94$	−1.57084	−	3.92376i	−0.162019	−	0.404705i
$95$	1.41106	−	1.98156i	0.144772	−	0.203304i
$96$	0.690079	+	0.723734i	0.0704309	+	0.0738658i
$97$	3.64799	+	4.21000i	0.370397	+	0.427461i	0.910096	−	0.414397i	$-0.136007\pi$
$97$	3.64799	+	4.21000i	0.370397	+	0.427461i	−0.539699	+	0.841858i	$0.681462\pi$
$98$	−1.11636	+	6.91041i	−0.112770	+	0.698057i
$99$	0.158562	−	0.246728i	0.0159361	−	0.0247971i
$100$	−2.78592	−	3.91228i	−0.278592	−	0.391228i
$101$	2.67830	−	13.8963i	0.266501	−	1.38274i	−0.564025	−	0.825757i	$-0.690748\pi$
$101$	2.67830	−	13.8963i	0.266501	−	1.38274i	0.830526	−	0.556980i	$-0.188040\pi$
$102$	2.39637	−	4.64831i	0.237276	−	0.460251i
$103$	−1.22589	−	0.490772i	−0.120790	−	0.0483572i	0.310480	−	0.950580i	$-0.399510\pi$
$103$	−1.22589	−	0.490772i	−0.120790	−	0.0483572i	−0.431270	+	0.902223i	$0.641934\pi$
$104$	−0.663411	+	0.0953841i	−0.0650528	+	0.00935318i
$105$	−0.673113	−	0.962839i	−0.0656891	−	0.0939635i
$106$	−3.16599	−	2.74334i	−0.307508	−	0.266457i
$107$	0.243855	−	0.173648i	0.0235744	−	0.0167872i	−0.568209	−	0.822884i	$-0.692363\pi$
$107$	0.243855	−	0.173648i	0.0235744	−	0.0167872i	0.591783	+	0.806097i	$0.298424\pi$
$108$	0.998867	+	0.0475819i	0.0961161	+	0.00457857i
$109$	−4.18058	+	4.38446i	−0.400427	+	0.419956i	−0.892817	−	0.450419i	$-0.851275\pi$
$109$	−4.18058	+	4.38446i	−0.400427	+	0.419956i	0.492391	+	0.870374i	$0.336123\pi$
$110$	0.0246458	+	0.127875i	0.00234988	+	0.0121924i
$111$	5.71737	+	1.67877i	0.542669	+	0.159342i
$112$	2.64156	+	0.148830i	0.249604	+	0.0140631i
$113$	−9.94460	−	1.42982i	−0.935509	−	0.134506i	−0.342333	−	0.939579i	$-0.611217\pi$
$113$	−9.94460	−	1.42982i	−0.935509	−	0.134506i	−0.593176	+	0.805073i	$0.702126\pi$
$114$	4.74454	+	2.73926i	0.444367	+	0.256555i
$115$	2.06965	+	0.501287i	0.192996	+	0.0467453i
$116$	−5.13055	−	8.88636i	−0.476359	−	0.825078i
$117$	−0.414311	+	0.526839i	−0.0383030	+	0.0487063i
$118$	9.36638	−	4.27748i	0.862245	−	0.393774i
$119$	−3.78275	−	13.3093i	−0.346764	−	1.22006i
$120$	−0.335576	+	0.290778i	−0.0306337	+	0.0265443i
$121$	2.57307	−	10.6063i	0.233915	−	0.964212i
$122$	−0.653685	+	13.7225i	−0.0591818	+	1.24238i
$123$	−0.398945	+	0.0380946i	−0.0359717	+	0.00343488i
$124$	−0.648358	+	0.224399i	−0.0582243	+	0.0201516i
$125$	3.66177	−	2.35328i	0.327519	−	0.210484i
$126$	2.01449	−	1.71517i	0.179465	−	0.152800i
$127$	2.60807	+	18.1395i	0.231428	+	1.60962i	0.691932	+	0.721962i	$0.256760\pi$
$127$	2.60807	+	18.1395i	0.231428	+	1.60962i	−0.460504	+	0.887658i	$0.652331\pi$
$128$	−0.0475819	−	0.998867i	−0.00420569	−	0.0882882i
$129$	−1.71418	−	0.330382i	−0.150925	−	0.0290885i
$130$	−0.0282890	−	0.296256i	−0.00248111	−	0.0259834i
$131$	−1.26893	−	2.46139i	−0.110867	−	0.215052i	0.826874	−	0.562387i	$-0.190117\pi$
$131$	−1.26893	−	2.46139i	−0.110867	−	0.215052i	−0.937741	+	0.347335i	$0.887087\pi$
$132$	−0.281406	+	0.0826283i	−0.0244932	+	0.00719187i
$133$	14.1154	−	3.29485i	1.22396	−	0.285700i
$134$	2.13664	−	7.27674i	0.184578	−	0.628615i
$135$	−0.0422078	+	0.442020i	−0.00363266	+	0.0380430i
$136$	−4.85505	+	1.94367i	−0.416317	+	0.166668i
$137$	3.36148	−	1.94075i	0.287191	−	0.165810i	−0.349484	−	0.936943i	$-0.613643\pi$
$137$	3.36148	−	1.94075i	0.287191	−	0.165810i	0.636674	+	0.771133i	$0.280310\pi$
$138$	−0.680775	+	4.74727i	−0.0579514	+	0.404114i
$139$			5.18305i			0.439621i	0.975543	+	0.219810i	$0.0705439\pi$
$139$			5.18305i			0.439621i	−0.975543	+	0.219810i	$0.929456\pi$
$140$	−0.121821	+	1.16846i	−0.0102957	+	0.0987529i
$141$	1.75576	+	3.84457i	0.147861	+	0.323771i
$142$	−7.17411	+	6.84050i	−0.602038	+	0.574042i
$143$	0.0642918	−	0.185759i	0.00537635	−	0.0155339i
$144$	−0.723734	−	0.690079i	−0.0603112	−	0.0575066i
$145$	4.04974	−	2.08779i	0.336313	−	0.173381i
$146$	8.74922	+	3.99564i	0.724091	+	0.330681i
$147$	0.786289	−	6.95570i	0.0648520	−	0.573696i
$148$	−3.22154	−	5.01281i	−0.264809	−	0.412051i
$149$	−6.48873	+	16.2081i	−0.531578	+	1.32782i	0.383128	+	0.923695i	$0.374847\pi$
$149$	−6.48873	+	16.2081i	−0.531578	+	1.32782i	−0.914705	+	0.404121i	$0.867577\pi$
$150$	2.96892	+	3.77529i	0.242411	+	0.308251i
$151$	19.9633	+	10.2918i	1.62459	+	0.837536i	0.998320	+	0.0579326i	$0.0184509\pi$
$151$	19.9633	+	10.2918i	1.62459	+	0.837536i	0.626273	+	0.779604i	$0.284579\pi$
$152$	−1.79185	−	5.17721i	−0.145338	−	0.419927i
$153$	−2.17248	+	4.75707i	−0.175635	+	0.384586i
$154$	−0.393801	+	0.668609i	−0.0317334	+	0.0538781i
$155$	−0.0858287	−	0.292306i	−0.00689393	−	0.0234786i
$156$	0.658121	−	0.126842i	0.0526919	−	0.0101555i
$157$	−1.67346	−	6.89810i	−0.133557	−	0.550528i	−0.998791	−	0.0491602i	$-0.984346\pi$
$157$	−1.67346	−	6.89810i	−0.133557	−	0.550528i	0.865234	−	0.501368i	$-0.167170\pi$
$158$	−2.26925	−	1.61593i	−0.180532	−	0.128556i
$159$	3.29293	+	2.58959i	0.261147	+	0.205368i
$160$	0.444030			0.0351037
$161$	7.27390	+	10.3967i	0.573264	+	0.819371i
$162$	−1.00000			−0.0785674
$163$	8.21403	+	6.45958i	0.643372	+	0.505953i	0.885710	−	0.464238i	$-0.153672\pi$
$163$	8.21403	+	6.45958i	0.643372	+	0.505953i	−0.242338	+	0.970192i	$0.577914\pi$
$164$	0.326449	+	0.232463i	0.0254914	+	0.0181523i
$165$	−0.0307024	−	0.126557i	−0.00239018	−	0.00985245i
$166$	−5.16898	+	0.996240i	−0.401191	+	0.0773232i
$167$	−4.38905	−	14.9477i	−0.339635	−	1.15669i	−0.935418	−	0.353544i	$-0.884976\pi$
$167$	−4.38905	−	14.9477i	−0.339635	−	1.15669i	0.595783	−	0.803145i	$-0.296842\pi$
$168$	−2.64565	−	0.0229712i	−0.204116	−	0.00177226i
$169$	5.21379	−	11.4166i	0.401060	−	0.878200i
$170$	−0.759494	−	2.19441i	−0.0582505	−	0.168304i
$171$	−4.86951	−	2.51041i	−0.372380	−	0.191975i
$172$	1.07914	+	1.37224i	0.0822835	+	0.104632i
$173$	−2.91205	+	7.27394i	−0.221399	+	0.553027i	−0.996931	−	0.0782801i	$-0.975057\pi$
$173$	−2.91205	+	7.27394i	−0.221399	+	0.553027i	0.775533	+	0.631307i	$0.217481\pi$
$174$	5.54756	+	8.63218i	0.420560	+	0.654404i
$175$	12.5616	+	1.91755i	0.949568	+	0.144953i
$176$	0.266782	+	0.121835i	0.0201095	+	0.00918369i
$177$	−9.15224	+	4.71831i	−0.687924	+	0.354650i
$178$	−0.939178	−	0.895505i	−0.0703944	−	0.0671209i
$179$	8.01564	−	23.1597i	0.599117	−	1.73103i	−0.0797918	−	0.996812i	$-0.525426\pi$
$179$	8.01564	−	23.1597i	0.599117	−	1.73103i	0.678909	−	0.734223i	$-0.262453\pi$
$180$	0.321360	−	0.306416i	0.0239527	−	0.0228389i
$181$	8.04061	+	17.6065i	0.597654	+	1.30868i	0.930705	+	0.365771i	$0.119195\pi$
$181$	8.04061	+	17.6065i	0.597654	+	1.30868i	−0.333051	+	0.942909i	$0.608078\pi$
$182$	1.04110	−	1.43548i	0.0771715	−	0.106405i
$183$		−	13.7381i		−	1.01555i
$184$	3.62329	−	3.14193i	0.267113	−	0.231626i
$185$	2.29138	−	1.32293i	0.168466	−	0.0972638i
$186$	0.636947	−	0.254995i	0.0467032	−	0.0186971i
$187$	0.145796	−	1.52684i	0.0106616	−	0.111654i
$188$	1.19075	−	4.05531i	0.0868440	−	0.295764i
$189$	−1.93060	+	1.80908i	−0.140430	+	0.131591i
$190$	2.33409	−	0.685351i	0.169333	−	0.0497206i
$191$	−7.19136	−	13.9493i	−0.520348	−	1.00933i	−0.991843	−	0.127466i	$-0.959316\pi$
$191$	−7.19136	−	13.9493i	−0.520348	−	1.00933i	0.471495	−	0.881869i	$-0.343715\pi$
$192$	0.0950560	+	0.995472i	0.00686008	+	0.0718420i
$193$	15.3139	+	2.95152i	1.10232	+	0.212455i	0.707787	−	0.706426i	$-0.249694\pi$
$193$	15.3139	+	2.95152i	1.10232	+	0.212455i	0.394535	+	0.918881i	$0.370906\pi$
$194$	0.265061	+	5.56432i	0.0190303	+	0.399495i
$195$	0.0423534	+	0.294575i	0.00303299	+	0.0210949i
$196$	−5.14925	+	4.74186i	−0.367804	+	0.338704i
$197$	8.95686	−	5.75623i	0.638150	−	0.410114i	−0.181169	−	0.983452i	$-0.557988\pi$
$197$	8.95686	−	5.75623i	0.638150	−	0.410114i	0.819319	+	0.573338i	$0.194352\pi$
$198$	0.277156	−	0.0959245i	0.0196966	−	0.00681706i
$199$	−13.1431	+	1.25502i	−0.931692	+	0.0889658i	−0.549851	−	0.835263i	$-0.685316\pi$
$199$	−13.1431	+	1.25502i	−0.931692	+	0.0889658i	−0.381840	+	0.924228i	$0.624710\pi$
$200$	0.228528	−	4.79740i	0.0161594	−	0.339227i
$201$	−1.78798	+	7.37017i	−0.126115	+	0.519851i
$202$	10.6954	−	9.26764i	0.752528	−	0.652069i
$203$	26.3265	+	6.62928i	1.84776	+	0.465284i
$204$	4.75707	−	2.17248i	0.333062	−	0.152104i
$205$	−0.110001	+	0.139878i	−0.00768281	+	0.00976948i
$206$	−0.660239	−	1.14357i	−0.0460010	−	0.0796761i
$207$	0.454120	−	4.77428i	0.0315635	−	0.331836i
$208$	−0.580439	−	0.335117i	−0.0402462	−	0.0232362i
$209$	1.59042	+	0.228668i	0.110012	+	0.0158173i
$210$	0.0660852	−	1.17293i	0.00456031	−	0.0809401i
$211$	−21.1865	−	6.22091i	−1.45854	−	0.428265i	−0.546182	−	0.837666i	$-0.683919\pi$
$211$	−21.1865	−	6.22091i	−1.45854	−	0.428265i	−0.912354	+	0.409401i	$0.865738\pi$
$212$	−0.792811	−	4.11350i	−0.0544505	−	0.282516i
$213$	6.84050	−	7.17411i	0.468703	−	0.491562i
$214$	0.299025	+	0.0142443i	0.0204410	+	0.000973723i
$215$	−0.631424	+	0.449635i	−0.0430628	+	0.0306649i
$216$	0.755750	+	0.654861i	0.0514222	+	0.0445576i
$217$	0.768382	−	1.64458i	0.0521612	−	0.111642i
$218$	−5.99645	+	0.862160i	−0.406131	+	0.0583928i
$219$	−8.92943	−	3.57481i	−0.603395	−	0.241563i
$220$	−0.0596739	+	0.115751i	−0.00402321	+	0.00780394i
$221$	−0.663344	+	3.44175i	−0.0446213	+	0.231517i
$222$	3.45641	+	4.85385i	0.231979	+	0.325769i
$223$	12.2076	−	18.9953i	0.817479	−	1.27202i	−0.141894	−	0.989882i	$-0.545319\pi$
$223$	12.2076	−	18.9953i	0.817479	−	1.27202i	0.959373	−	0.282140i	$-0.0910444\pi$
$224$	1.98441	+	1.74989i	0.132589	+	0.116920i
$225$	−3.14519	−	3.62974i	−0.209679	−	0.241983i
$226$	−6.93313	−	7.27125i	−0.461185	−	0.483677i
$227$	2.26499	−	3.18073i	0.150332	−	0.211112i	−0.732542	−	0.680722i	$-0.761666\pi$
$227$	2.26499	−	3.18073i	0.150332	−	0.211112i	0.882874	+	0.469610i	$0.155605\pi$
$228$	2.03616	+	5.08609i	0.134848	+	0.336834i
$229$	−3.96296	+	6.86404i	−0.261880	+	0.453589i	−0.966741	−	0.255756i	$-0.917676\pi$
$229$	−3.96296	+	6.86404i	−0.261880	+	0.453589i	0.704862	+	0.709345i	$0.251009\pi$
$230$	1.31698	+	1.67341i	0.0868391	+	0.110342i
$231$	0.361541	−	0.686590i	0.0237877	−	0.0451743i
$232$	1.46031	−	10.1566i	0.0958737	−	0.666817i
$233$	−9.07266	−	0.866334i	−0.594370	−	0.0567555i	−0.206464	−	0.978454i	$-0.566196\pi$
$233$	−9.07266	−	0.866334i	−0.594370	−	0.0567555i	−0.387906	+	0.921699i	$0.626802\pi$
$234$	−0.651340	+	0.158013i	−0.0425794	+	0.0103297i
$235$	1.77348	+	0.613808i	0.115689	+	0.0400404i
$236$	10.0066	+	2.42758i	0.651376	+	0.158022i
$237$	2.34357	+	1.50612i	0.152231	+	0.0978330i
$238$	5.25380	−	12.8001i	0.340553	−	0.829709i
$239$	−3.57662	+	4.12764i	−0.231353	+	0.266995i	−0.859542	−	0.511066i	$-0.829251\pi$
$239$	−3.57662	+	4.12764i	−0.231353	+	0.266995i	0.628189	+	0.778061i	$0.283796\pi$
$240$	−0.443527	+	0.0211278i	−0.0286296	+	0.00136379i
$241$	−9.87988	+	7.76962i	−0.636419	+	0.500485i	−0.883452	−	0.468522i	$-0.844787\pi$
$241$	−9.87988	+	7.76962i	−0.636419	+	0.500485i	0.247033	+	0.969007i	$0.420544\pi$
$242$	8.57897	−	6.74658i	0.551477	−	0.433686i
$243$	0.998867	−	0.0475819i	0.0640774	−	0.00305238i
$244$	−8.99654	+	10.3826i	−0.575944	+	0.664675i
$245$	−1.99435	−	2.38402i	−0.127414	−	0.152309i
$246$	−0.337141	−	0.216667i	−0.0214953	−	0.0138142i
$247$	−3.56838	−	0.865681i	−0.227051	−	0.0550819i
$248$	−0.648358	−	0.224399i	−0.0411708	−	0.0142494i
$249$	5.11573	−	1.24106i	0.324196	−	0.0786491i
$250$	4.33305	+	0.413756i	0.274046	+	0.0261682i
$251$	−1.48878	+	10.3547i	−0.0939710	+	0.653582i	0.887335	+	0.461126i	$0.152554\pi$
$251$	−1.48878	+	10.3547i	−0.0939710	+	0.653582i	−0.981306	+	0.192456i	$0.938355\pi$
$252$	2.64375	−	0.102940i	0.166540	−	0.00648461i
$253$	0.332109	+	1.36678i	0.0208795	+	0.0859288i
$254$	−9.16301	+	15.8708i	−0.574939	+	0.995823i
$255$	0.863048	+	2.15579i	0.0540462	+	0.135001i
$256$	0.580057	−	0.814576i	0.0362536	−	0.0509110i
$257$	17.8749	+	18.7466i	1.11500	+	1.16938i	0.984031	+	0.177996i	$0.0569615\pi$
$257$	17.8749	+	18.7466i	1.11500	+	1.16938i	0.130973	+	0.991386i	$0.458190\pi$
$258$	−1.14321	−	1.31933i	−0.0711731	−	0.0821382i
$259$	15.4540	+	3.11791i	0.960262	+	0.193737i
$260$	0.160897	−	0.250360i	0.00997839	−	0.0155267i
$261$	−5.95202	−	8.35844i	−0.368421	−	0.517374i
$262$	0.524080	−	2.71918i	0.0323777	−	0.167992i
$263$	13.3538	−	25.9028i	0.823432	−	1.59724i	0.0215398	−	0.999768i	$-0.493143\pi$
$263$	13.3538	−	25.9028i	0.823432	−	1.59724i	0.801893	−	0.597468i	$-0.203827\pi$
$264$	−0.272277	−	0.109003i	−0.0167575	−	0.00670870i
$265$	1.84120	−	0.264724i	0.113104	−	0.0162619i
$266$	13.1322	+	6.13561i	0.805185	+	0.376198i
$267$	0.980724	+	0.849802i	0.0600194	+	0.0520071i
$268$	6.17770	−	4.39912i	0.377363	−	0.268719i
$269$	−27.8654	−	1.32739i	−1.69898	−	0.0809324i	−0.824460	−	0.565920i	$-0.808521\pi$
$269$	−27.8654	−	1.32739i	−1.69898	−	0.0809324i	−0.874521	+	0.484988i	$0.838824\pi$
$270$	−0.306416	+	0.321360i	−0.0186479	+	0.0195573i
$271$	1.93770	+	10.0537i	0.117707	+	0.610721i	0.992094	+	0.125493i	$0.0400513\pi$
$271$	1.93770	+	10.0537i	0.117707	+	0.610721i	−0.874388	+	0.485228i	$0.838737\pi$
$272$	−5.01783	−	1.47337i	−0.304250	−	0.0893360i
$273$	−0.971618	+	1.48339i	−0.0588050	+	0.0897788i
$274$	3.84200	+	0.552396i	0.232103	+	0.0333714i
$275$	1.21989	+	0.704303i	0.0735620	+	0.0424711i
$276$	−3.46969	+	3.31078i	−0.208851	+	0.199285i
$277$	2.06804	+	3.58195i	0.124257	+	0.215219i	0.921442	−	0.388516i	$-0.127012\pi$
$277$	2.06804	+	3.58195i	0.124257	+	0.215219i	−0.797186	+	0.603734i	$0.793679\pi$
$278$	−3.20395	+	4.07416i	−0.192160	+	0.244352i
$279$	−0.624092	+	0.285013i	−0.0373634	+	0.0170633i
$280$	−0.818052	+	0.843167i	−0.0488879	+	0.0503889i
$281$	−13.8330	+	11.9864i	−0.825207	+	0.715046i	−0.961256	−	0.275656i	$-0.911105\pi$
$281$	−13.8330	+	11.9864i	−0.825207	+	0.715046i	0.136049	+	0.990702i	$0.456559\pi$
$282$	−0.996437	+	4.10737i	−0.0593370	+	0.244590i
$283$	−0.109992	+	2.30902i	−0.00653835	+	0.137257i	0.993238	+	0.116098i	$0.0370386\pi$
$283$	−0.109992	+	2.30902i	−0.00653835	+	0.137257i	−0.999776	+	0.0211589i	$0.993264\pi$
$284$	−9.86775	+	0.942256i	−0.585543	+	0.0559126i
$285$	−2.29884	+	0.795635i	−0.136171	+	0.0471294i
$286$	0.165365	−	0.106274i	0.00977825	−	0.00628410i
$287$	−1.04285	+	0.191618i	−0.0615576	+	0.0113109i
$288$	−0.142315	−	0.989821i	−0.00838598	−	0.0583258i
$289$	0.492444	+	10.3377i	0.0289673	+	0.608098i
$290$	4.47390	+	0.862273i	0.262716	+	0.0506344i
$291$	−0.529522	−	5.54541i	−0.0310411	−	0.325078i
$292$	4.40742	+	8.54919i	0.257924	+	0.500304i
$293$	−23.2590	+	6.82946i	−1.35881	+	0.398981i	−0.878342	−	0.478033i	$-0.841350\pi$
$293$	−23.2590	+	6.82946i	−1.35881	+	0.398981i	−0.480464	+	0.877014i	$0.659532\pi$
$294$	4.91779	−	4.98150i	0.286812	−	0.290527i
$295$	−1.28812	+	4.38693i	−0.0749971	+	0.255417i
$296$	0.566414	−	5.93176i	0.0329222	−	0.344777i
$297$	−0.272277	+	0.109003i	−0.0157991	+	0.00632502i
$298$	−15.1197	+	8.72933i	−0.875858	+	0.505677i
$299$	−0.458614	−	3.18144i	−0.0265224	−	0.183987i
$300$			4.80284i			0.277292i
$301$	−4.59387	−	0.478945i	−0.264786	−	0.0276059i
$302$	9.33027	+	20.4304i	0.536897	+	1.17564i
$303$	−10.2423	+	9.76605i	−0.588407	+	0.561045i
$304$	1.79185	−	5.17721i	0.102770	−	0.296933i
$305$	−4.41487	−	4.20957i	−0.252795	−	0.241039i
$306$	−4.64831	+	2.39637i	−0.265726	+	0.136991i
$307$	20.7536	+	9.47786i	1.18447	+	0.540930i	0.907543	−	0.419960i	$-0.137956\pi$
$307$	20.7536	+	9.47786i	1.18447	+	0.540930i	0.276929	+	0.960890i	$0.410683\pi$
$308$	−0.722855	+	0.282131i	−0.0411885	+	0.0160759i
$309$	0.713904	+	1.11086i	0.0406126	+	0.0631944i
$310$	0.113225	−	0.282824i	0.00643077	−	0.0160633i
$311$	−16.9800	−	21.5918i	−0.962846	−	1.22436i	−0.974491	−	0.224426i	$-0.927949\pi$
$311$	−16.9800	−	21.5918i	−0.962846	−	1.22436i	0.0116452	−	0.999932i	$-0.496293\pi$
$312$	0.595727	+	0.307119i	0.0337264	+	0.0173872i
$313$	−4.55345	−	13.1563i	−0.257376	−	0.743640i	−0.997467	−	0.0711327i	$-0.977339\pi$
$313$	−4.55345	−	13.1563i	−0.257376	−	0.743640i	0.740091	−	0.672507i	$-0.234783\pi$
$314$	2.94869	−	6.45673i	0.166404	−	0.364375i
$315$	−0.0101999	+	1.17475i	−0.000574699	+	0.0661896i
$316$	−0.784852	−	2.67296i	−0.0441514	−	0.150366i
$317$	2.20296	−	0.424585i	0.123730	−	0.0238471i	−0.127010	−	0.991901i	$-0.540538\pi$
$317$	2.20296	−	0.424585i	0.123730	−	0.0238471i	0.250740	+	0.968054i	$0.419326\pi$
$318$	0.987641	+	4.07111i	0.0553842	+	0.228297i
$319$	2.45141	+	1.74564i	0.137253	+	0.0977373i
$320$	0.349031	+	0.274481i	0.0195114	+	0.0153440i
$321$	−0.299365			−0.0167089
$322$	−0.709113	+	12.6687i	−0.0395173	+	0.706002i
$323$	−28.6508			−1.59418
$324$	−0.786053	−	0.618159i	−0.0436696	−	0.0343422i
$325$	−2.62214	−	1.86722i	−0.145450	−	0.103574i
$326$	2.46361	+	10.1551i	0.136447	+	0.562442i
$327$	5.94864	−	1.14651i	0.328960	−	0.0634019i
$328$	0.112907	+	0.384526i	0.00623425	+	0.0212319i
$329$	5.50686	+	9.73233i	0.303603	+	0.536561i
$330$	0.0540986	−	0.118459i	0.00297803	−	0.00652098i
$331$	6.89676	+	19.9269i	0.379080	+	1.09528i	0.959681	+	0.281092i	$0.0906965\pi$
$331$	6.89676	+	19.9269i	0.379080	+	1.09528i	−0.580601	+	0.814188i	$0.697182\pi$
$332$	−4.67893	−	2.41216i	−0.256790	−	0.132384i
$333$	−3.68345	−	4.68389i	−0.201852	−	0.256675i
$334$	5.79005	−	14.4628i	0.316817	−	0.791371i
$335$	1.82061	+	2.83292i	0.0994705	+	0.154779i
$336$	−2.06542	−	1.65349i	−0.112678	−	0.0902053i
$337$	18.6516	+	8.51789i	1.01602	+	0.463999i	0.852603	−	0.522559i	$-0.175023\pi$
$337$	18.6516	+	8.51789i	1.01602	+	0.463999i	0.163413	+	0.986558i	$0.447750\pi$
$338$	11.1556	−	5.75110i	0.606784	−	0.312819i
$339$	7.27125	+	6.93313i	0.394920	+	0.376556i
$340$	0.759494	−	2.19441i	0.0411893	−	0.119009i
$341$	0.145631	−	0.138859i	0.00788635	−	0.00751962i
$342$	−2.27586	−	4.98344i	−0.123064	−	0.269474i
$343$	0.482346	−	18.5140i	0.0260442	−	0.999661i
$344$			1.74573i			0.0941234i
$345$	−1.39511	−	1.60885i	−0.0751103	−	0.0866177i
$346$	−6.78547	+	3.91759i	−0.364789	+	0.210611i
$347$	−0.393131	+	0.157386i	−0.0211044	+	0.00844892i	−0.382191	−	0.924084i	$-0.624830\pi$
$347$	−0.393131	+	0.157386i	−0.0211044	+	0.00844892i	0.361086	+	0.932532i	$0.382406\pi$
$348$	−0.975379	+	10.2146i	−0.0522858	+	0.547561i
$349$	0.995900	−	3.39173i	0.0533093	−	0.181555i	−0.928534	−	0.371246i	$-0.878931\pi$
$349$	0.995900	−	3.39173i	0.0533093	−	0.181555i	0.981844	+	0.189691i	$0.0607487\pi$
$350$	8.68873	+	9.27236i	0.464432	+	0.495628i
$351$	0.643084	−	0.188826i	0.0343253	−	0.0100788i
$352$	0.134391	+	0.260683i	0.00716309	+	0.0138945i
$353$	−1.01801	−	10.6611i	−0.0541831	−	0.567431i	−0.981277	−	0.192602i	$-0.938307\pi$
$353$	−1.01801	−	10.6611i	−0.0541831	−	0.567431i	0.927094	−	0.374829i	$-0.122299\pi$
$354$	−10.1108	−	1.94870i	−0.537384	−	0.103572i
$355$	−0.209432	−	4.39652i	−0.0111155	−	0.233343i
$356$	−0.184680	−	1.28448i	−0.00978801	−	0.0680771i
$357$	−4.63879	+	13.0356i	−0.245511	+	0.689918i
$358$	20.6171	−	13.2498i	1.08965	−	0.700273i
$359$	−23.5391	+	8.14696i	−1.24235	+	0.429980i	−0.867654	−	0.497169i	$-0.834373\pi$
$359$	−23.5391	+	8.14696i	−1.24235	+	0.429980i	−0.374692	+	0.927149i	$0.622252\pi$
$360$	0.442020	−	0.0422078i	0.0232965	−	0.00222454i
$361$	0.524078	−	11.0018i	0.0275831	−	0.579040i
$362$	−4.56326	+	18.8100i	−0.239840	+	0.988632i
$363$	−8.24824	+	7.14714i	−0.432920	+	0.375128i
$364$	1.70571	−	0.484797i	0.0894037	−	0.0254103i
$365$	−3.88492	+	1.77418i	−0.203346	+	0.0928650i
$366$	8.49233	−	10.7989i	0.443901	−	0.564466i
$367$	7.21809	+	12.5021i	0.376781	+	0.652604i	0.990592	−	0.136849i	$-0.0436976\pi$
$367$	7.21809	+	12.5021i	0.376781	+	0.652604i	−0.613811	+	0.789453i	$0.710364\pi$
$368$	4.79032	−	0.229954i	0.249712	−	0.0119872i
$369$	0.347068	+	0.200380i	0.0180676	+	0.0104314i
$370$	2.61893	+	0.376545i	0.136152	+	0.0195757i
$371$	9.27172	+	6.07296i	0.481364	+	0.315293i
$372$	0.658301	+	0.193295i	0.0341313	+	0.0100219i
$373$	−2.57493	−	13.3600i	−0.133325	−	0.691755i	−0.985658	−	0.168756i	$-0.946025\pi$
$373$	−2.57493	−	13.3600i	−0.133325	−	0.691755i	0.852333	−	0.522999i	$-0.175187\pi$
$374$	1.05844	−	1.11005i	0.0547304	−	0.0573996i
$375$	−4.34783	−	0.207112i	−0.224521	−	0.0106952i
$376$	3.44281	−	2.45162i	0.177550	−	0.126432i
$377$	−5.19753	−	4.50369i	−0.267687	−	0.231952i
$378$	−2.63586	+	0.228618i	−0.135574	+	0.0117588i
$379$	−33.3087	+	4.78907i	−1.71095	+	0.245998i	−0.927064	−	0.374904i	$-0.877676\pi$
$379$	−33.3087	+	4.78907i	−1.71095	+	0.245998i	−0.783888	+	0.620902i	$0.786767\pi$
$380$	2.25838	+	0.904117i	0.115852	+	0.0463802i
$381$	8.39747	−	16.2888i	0.430215	−	0.834502i
$382$	2.97009	−	15.4103i	0.151963	−	0.788459i
$383$	14.9707	+	21.0233i	0.764965	+	1.07424i	0.994883	+	0.101033i	$0.0322148\pi$
$383$	14.9707	+	21.0233i	0.764965	+	1.07424i	−0.229918	+	0.973210i	$0.573846\pi$
$384$	−0.540641	+	0.841254i	−0.0275895	+	0.0429300i
$385$	−0.109860	−	0.326567i	−0.00559900	−	0.0166434i
$386$	10.2131	+	11.7865i	0.519831	+	0.599917i
$387$	1.20469	+	1.26344i	0.0612379	+	0.0642245i
$388$	−3.23128	+	4.53770i	−0.164044	+	0.230367i
$389$	8.21630	+	20.5233i	0.416583	+	1.04057i	0.977166	+	0.212476i	$0.0681527\pi$
$389$	8.21630	+	20.5233i	0.416583	+	1.04057i	−0.560583	+	0.828098i	$0.689423\pi$
$390$	−0.148802	+	0.257732i	−0.00753488	+	0.0130508i
$391$	−9.33006	−	23.2806i	−0.471842	−	1.17735i
$392$	−6.97881	+	0.544295i	−0.352483	+	0.0274910i
$393$	−0.394102	+	2.74104i	−0.0198798	+	0.138267i
$394$	10.5988	+	1.01207i	0.533961	+	0.0509871i
$395$	1.20211	−	0.291630i	0.0604849	−	0.0146735i
$396$	0.277156	+	0.0959245i	0.0139276	+	0.00482039i
$397$	−17.1116	−	4.15123i	−0.858808	−	0.208344i	−0.217908	−	0.975969i	$-0.569923\pi$
$397$	−17.1116	−	4.15123i	−0.858808	−	0.208344i	−0.640900	+	0.767625i	$0.721438\pi$
$398$	−11.1070	−	7.13803i	−0.556743	−	0.357797i
$399$	−13.4092	−	5.50381i	−0.671302	−	0.275535i
$400$	3.14519	−	3.62974i	0.157259	−	0.181487i
$401$	−0.930792	+	0.0443391i	−0.0464815	+	0.00221419i	−0.0708098	−	0.997490i	$-0.522558\pi$
$401$	−0.930792	+	0.0443391i	−0.0464815	+	0.00221419i	0.0243283	+	0.999704i	$0.492255\pi$
$402$	−5.96138	+	4.68808i	−0.297327	+	0.233820i
$403$	−0.361460	+	0.284256i	−0.0180056	+	0.0141598i
$404$	14.1361	−	0.673383i	0.703295	−	0.0335021i
$405$	0.290778	−	0.335576i	0.0144489	−	0.0166749i
$406$	16.5960	+	21.4849i	0.823648	+	1.06628i
$407$	1.47019	+	0.944833i	0.0728745	+	0.0468336i
$408$	5.08225	+	1.23294i	0.251609	+	0.0610396i
$409$	11.3821	+	3.93940i	0.562811	+	0.194791i	0.593635	−	0.804734i	$-0.297692\pi$
$409$	11.3821	+	3.93940i	0.562811	+	0.194791i	−0.0308247	+	0.999525i	$0.509813\pi$
$410$	−0.172933	+	0.0419532i	−0.00854057	+	0.00207192i
$411$	−3.86393	−	0.368960i	−0.190594	−	0.0181995i
$412$	0.187924	−	1.30704i	0.00925833	−	0.0643931i
$413$	−23.0453	+	14.5291i	−1.13398	+	0.714932i
$414$	3.30823	−	3.47212i	0.162591	−	0.170645i
$415$	1.16871	−	2.02427i	0.0573699	−	0.0993675i
$416$	−0.249100	−	0.622223i	−0.0122132	−	0.0305070i
$417$	3.00647	−	4.22199i	0.147227	−	0.206752i
$418$	1.10880	+	1.16288i	0.0542333	+	0.0568782i
$419$	−16.0958	−	18.5756i	−0.786333	−	0.907477i	0.211217	−	0.977439i	$-0.432257\pi$
$419$	−16.0958	−	18.5756i	−0.786333	−	0.907477i	−0.997550	+	0.0699627i	$0.977712\pi$
$420$	0.777006	−	0.881137i	0.0379140	−	0.0429951i
$421$	−3.40810	+	5.30310i	−0.166100	+	0.258457i	−0.914319	−	0.404995i	$-0.867273\pi$
$421$	−3.40810	+	5.30310i	−0.166100	+	0.258457i	0.748218	+	0.663453i	$0.230910\pi$
$422$	−12.8082	−	17.9866i	−0.623492	−	0.875573i
$423$	0.799872	−	4.15013i	0.0388911	−	0.201786i
$424$	1.91960	−	3.72351i	0.0932241	−	0.180830i
$425$	−23.3180	−	9.33513i	−1.13109	−	0.452820i
$426$	9.81174	−	1.41071i	0.475380	−	0.0683494i
$427$	−3.14078	−	36.2116i	−0.151993	−	1.75240i
$428$	0.226245	+	0.196042i	0.0109359	+	0.00947605i
$429$	−0.160121	+	0.114022i	−0.00773073	+	0.00550503i
$430$	−0.774279	−	0.0368834i	−0.0373390	−	0.00177868i
$431$	−0.878484	+	0.921327i	−0.0423151	+	0.0443788i	−0.744551	−	0.667565i	$-0.767337\pi$
$431$	−0.878484	+	0.921327i	−0.0423151	+	0.0443788i	0.702236	+	0.711944i	$0.252185\pi$
$432$	0.189251	+	0.981929i	0.00910535	+	0.0472431i
$433$	10.7450	+	3.15501i	0.516370	+	0.151620i	0.529526	−	0.848294i	$-0.322370\pi$
$433$	10.7450	+	3.15501i	0.516370	+	0.151620i	−0.0131563	+	0.999913i	$0.504188\pi$
$434$	1.62060	−	0.817747i	0.0777914	−	0.0392531i
$435$	−4.50986	−	0.648420i	−0.216231	−	0.0310893i
$436$	−5.24648	−	3.02906i	−0.251261	−	0.145066i
$437$	24.8259	−	8.60253i	1.18758	−	0.411515i
$438$	−4.80921	−	8.32980i	−0.229793	−	0.398013i
$439$	−24.6552	+	31.3516i	−1.17673	+	1.49633i	−0.347264	+	0.937767i	$0.612889\pi$
$439$	−24.6552	+	31.3516i	−1.17673	+	1.49633i	−0.829462	+	0.558563i	$0.811353\pi$
$440$	−0.118459	+	0.0540986i	−0.00564733	+	0.00257905i
$441$	−4.67519	+	5.20985i	−0.222628	+	0.248088i
$442$	−2.64897	+	2.29535i	−0.125999	+	0.109179i
$443$	−3.44240	+	14.1897i	−0.163553	+	0.674175i	0.829700	+	0.558209i	$0.188511\pi$
$443$	−3.44240	+	14.1897i	−0.163553	+	0.674175i	−0.993253	+	0.115966i	$0.963004\pi$
$444$	−0.283528	+	5.95199i	−0.0134557	+	0.282469i
$445$	0.573602	−	0.0547723i	0.0271913	−	0.00259646i
$446$	21.3379	−	7.38513i	1.01038	−	0.349696i
$447$	14.6872	−	9.43887i	0.694679	−	0.446443i
$448$	0.478137	+	2.60219i	0.0225898	+	0.122942i
$449$	1.41610	+	9.84917i	0.0668297	+	0.464811i	0.995566	+	0.0940691i	$0.0299875\pi$
$449$	1.41610	+	9.84917i	0.0668297	+	0.464811i	−0.928736	+	0.370742i	$0.879103\pi$
$450$	−0.228528	−	4.79740i	−0.0107729	−	0.226151i
$451$	−0.115413	−	0.0222441i	−0.00543460	−	0.00104743i
$452$	−0.955015	−	10.0014i	−0.0449201	−	0.470425i
$453$	−10.2918	−	19.9633i	−0.483552	−	0.937960i
$454$	3.74660	−	1.10010i	0.175837	−	0.0516303i
$455$	0.178983	+	0.766773i	0.00839083	+	0.0359469i
$456$	−1.54348	+	5.25661i	−0.0722800	+	0.246163i
$457$	1.66846	−	17.4729i	0.0780472	−	0.817348i	−0.868693	−	0.495350i	$-0.835040\pi$
$457$	1.66846	−	17.4729i	0.0780472	−	0.817348i	0.946741	−	0.321997i	$-0.104354\pi$
$458$	−7.35816	+	2.94576i	−0.343824	+	0.137647i
$459$	4.52902	−	2.61483i	0.211397	−	0.122050i
$460$	0.000781914		2.12949i	3.64569e−5		0.0992882i
$461$		−	9.32993i		−	0.434538i	−0.976112	−	0.217269i	$-0.930285\pi$
$461$		−	9.32993i		−	0.434538i	0.976112	−	0.217269i	$-0.0697149\pi$
$462$	0.708612	−	0.316206i	0.0329676	−	0.0147112i
$463$	−5.60730	−	12.2783i	−0.260593	−	0.570620i	0.733433	−	0.679762i	$-0.237917\pi$
$463$	−5.60730	−	12.2783i	−0.260593	−	0.570620i	−0.994026	+	0.109142i	$0.965190\pi$
$464$	7.42630	−	7.08096i	0.344757	−	0.328725i
$465$	−0.0996399	+	0.287891i	−0.00462069	+	0.0133506i
$466$	−6.59606	−	6.28933i	−0.305557	−	0.291348i
$467$	17.4155	−	8.97832i	0.805894	−	0.415467i	−0.00548687	−	0.999985i	$-0.501747\pi$
$467$	17.4155	−	8.97832i	0.805894	−	0.415467i	0.811381	+	0.584518i	$0.198716\pi$
$468$	−0.609666	−	0.278425i	−0.0281818	−	0.0128702i
$469$	−3.02791	+	19.8355i	−0.139816	+	0.915916i
$470$	1.01462	+	1.57878i	0.0468009	+	0.0728236i
$471$	−2.63813	+	6.58973i	−0.121559	+	0.303639i
$472$	6.36511	+	8.09390i	0.292978	+	0.372552i
$473$	−0.455082	−	0.234611i	−0.0209247	−	0.0107874i
$474$	0.911148	+	2.63259i	0.0418504	+	0.120919i
$475$	10.9306	−	23.9347i	0.501530	−	1.09820i
$476$	12.0423	−	6.81390i	0.551957	−	0.312315i
$477$	−1.18023	−	4.01951i	−0.0540392	−	0.184041i
$478$	−5.36296	+	1.03363i	−0.245296	+	0.0472769i
$479$	2.33292	+	9.61643i	0.106594	+	0.439386i	0.999950	−	0.00996273i	$-0.00317129\pi$
$479$	2.33292	+	9.61643i	0.106594	+	0.439386i	−0.893357	+	0.449349i	$0.851656\pi$
$480$	−0.361696	−	0.257563i	−0.0165091	−	0.0117561i
$481$	−3.13930	−	2.46877i	−0.143140	−	0.112566i
$482$	−12.5690			−0.572501
$483$	0.105507	−	12.6881i	0.00480074	−	0.577330i
$484$	10.9140			0.496090
$485$	−1.94433	−	1.52903i	−0.0882873	−	0.0694299i
$486$	0.814576	+	0.580057i	0.0369499	+	0.0263119i
$487$	−7.42278	−	30.5971i	−0.336358	−	1.38649i	−0.849231	−	0.528022i	$-0.822934\pi$
$487$	−7.42278	−	30.5971i	−0.336358	−	1.38649i	0.512872	−	0.858465i	$-0.328581\pi$
$488$	−13.4898	+	2.59995i	−0.610656	+	0.117694i
$489$	−2.94402	−	10.0264i	−0.133133	−	0.453411i
$490$	−0.0939627	−	3.10679i	−0.00424480	−	0.140350i
$491$	14.1551	−	30.9953i	0.638810	−	1.39880i	−0.262205	−	0.965012i	$-0.584450\pi$
$491$	14.1551	−	30.9953i	0.638810	−	1.39880i	0.901015	−	0.433787i	$-0.142823\pi$
$492$	−0.131076	−	0.378718i	−0.00590935	−	0.0170739i
$493$	−47.6967	−	24.5894i	−2.14815	−	1.10745i
$494$	−2.26981	−	2.88630i	−0.102124	−	0.129861i
$495$	−0.0484008	+	0.120899i	−0.00217546	+	0.00543402i
$496$	−0.370930	−	0.577178i	−0.0166552	−	0.0259161i
$497$	16.3904	−	20.4738i	0.735212	−	0.918374i
$498$	4.78841	+	2.18679i	0.214574	+	0.0979925i
$499$	−24.8023	+	12.7865i	−1.11030	+	0.572400i	−0.913007	−	0.407944i	$-0.866246\pi$
$499$	−24.8023	+	12.7865i	−1.11030	+	0.572400i	−0.197295	+	0.980344i	$0.563216\pi$
$500$	3.15024	+	3.00375i	0.140883	+	0.134332i
$501$	−5.09532	+	14.7220i	−0.227642	+	0.657728i
$502$	−7.57111	+	7.21904i	−0.337915	+	0.322201i
$503$	4.16133	+	9.11204i	0.185544	+	0.406286i	0.979431	−	0.201781i	$-0.0646728\pi$
$503$	4.16133	+	9.11204i	0.185544	+	0.406286i	−0.793886	+	0.608066i	$0.791946\pi$
$504$	2.14176	+	1.55334i	0.0954016	+	0.0691913i
$505$			6.28395i			0.279632i
$506$	−0.583833	+	1.27966i	−0.0259545	+	0.0568877i
$507$	−10.8693	+	6.27539i	−0.482723	+	0.278700i
$508$	−17.0133	+	6.81110i	−0.754843	+	0.302194i
$509$	−3.22618	+	33.7861i	−0.142998	+	1.49754i	0.584479	+	0.811409i	$0.301299\pi$
$509$	−3.22618	+	33.7861i	−0.142998	+	1.49754i	−0.727477	+	0.686132i	$0.759307\pi$
$510$	−0.654219	+	2.22807i	−0.0289693	+	0.0986604i
$511$	−24.3540	−	7.38124i	−1.07736	−	0.326527i
$512$	0.959493	−	0.281733i	0.0424040	−	0.0124509i
$513$	2.51041	+	4.86951i	0.110837	+	0.214994i
$514$	2.46220	+	25.7854i	0.108603	+	1.13734i
$515$	0.575736	+	0.110964i	0.0253700	+	0.00488966i
$516$	−0.0830652	−	1.74375i	−0.00365674	−	0.0767644i
$517$	0.176410	+	1.22696i	0.00775851	+	0.0539616i
$518$	10.2203	+	12.0038i	0.449053	+	0.527419i
$519$	6.59138	−	4.23602i	0.289330	−	0.185941i
$520$	0.281236	−	0.0973366i	0.0123330	−	0.00426849i
$521$	3.94901	−	0.377085i	0.173009	−	0.0165204i	−0.00819176	−	0.999966i	$-0.502608\pi$
$521$	3.94901	−	0.377085i	0.173009	−	0.0165204i	0.181201	+	0.983446i	$0.442001\pi$
$522$	0.488242	−	10.2495i	0.0213698	−	0.448607i
$523$	−9.85183	+	40.6098i	−0.430791	+	1.77574i	0.179702	+	0.983721i	$0.442487\pi$
$523$	−9.85183	+	40.6098i	−0.430791	+	1.77574i	−0.610492	+	0.792022i	$0.709028\pi$
$524$	2.09284	−	1.81346i	0.0914262	−	0.0792213i
$525$	−9.12009	−	8.84843i	−0.398033	−	0.386177i
$526$	26.5089	−	12.1062i	1.15584	−	0.527855i
$527$	−2.21798	+	2.82039i	−0.0966166	+	0.122858i
$528$	−0.146643	−	0.253993i	−0.00638182	−	0.0110536i
$529$	15.0746	+	17.3712i	0.655416	+	0.755268i
$530$	1.61092	+	0.930065i	0.0699739	+	0.0403995i
$531$	10.1921	+	1.46540i	0.442299	+	0.0635929i
$532$	6.52980	+	12.9407i	0.283103	+	0.561050i
$533$	0.257722	+	0.0756741i	0.0111632	+	0.00327781i
$534$	0.245588	+	1.27423i	0.0106276	+	0.0551415i
$535$	−0.0917300	+	0.0962037i	−0.00396584	+	0.00415925i
$536$	7.57536	+	0.360859i	0.327206	+	0.0155867i
$537$	−19.9633	+	14.2158i	−0.861479	+	0.613456i
$538$	−21.0831	−	18.2686i	−0.908957	−	0.787616i
$539$	0.796004	−	1.89241i	0.0342863	−	0.0815117i
$540$	−0.439511	+	0.0631921i	−0.0189135	+	0.00271935i
$541$	−23.6917	−	9.48471i	−1.01858	−	0.407780i	−0.198548	−	0.980091i	$-0.563623\pi$
$541$	−23.6917	−	9.48471i	−1.01858	−	0.407780i	−0.820036	+	0.572312i	$0.806047\pi$
$542$	−4.69167	+	9.10058i	−0.201525	+	0.390903i
$543$	3.66307	−	19.0058i	0.157198	−	0.815618i
$544$	−3.03350	−	4.25996i	−0.130060	−	0.182644i
$545$	1.45432	−	2.26296i	0.0622961	−	0.0969346i
$546$	−1.68071	+	0.565409i	−0.0719279	+	0.0241973i
$547$	−12.7218	−	14.6817i	−0.543943	−	0.627744i	0.415518	−	0.909585i	$-0.363600\pi$
$547$	−12.7218	−	14.6817i	−0.543943	−	0.627744i	−0.959461	+	0.281841i	$0.909055\pi$
$548$	2.67854	+	2.80918i	0.114422	+	0.120002i
$549$	−7.96888	+	11.1907i	−0.340103	+	0.477608i
$550$	0.523526	+	1.30770i	0.0223232	+	0.0557607i
$551$	28.1078	−	48.6842i	1.19743	−	2.07402i
$552$	−4.77395	+	0.457626i	−0.203193	+	0.0194778i
$553$	6.52164	+	3.43413i	0.277328	+	0.146034i
$554$	−0.588626	+	4.09398i	−0.0250083	+	0.173937i
$555$	−2.63388	−	0.251505i	−0.111802	−	0.0106758i
$556$	−5.03695	+	1.22195i	−0.213614	+	0.0518223i
$557$	3.52332	+	1.21943i	0.149288	+	0.0516690i	0.400690	−	0.916214i	$-0.368770\pi$
$557$	3.52332	+	1.21943i	0.149288	+	0.0516690i	−0.251402	+	0.967883i	$0.580892\pi$
$558$	−0.666753	−	0.161753i	−0.0282259	−	0.00684753i
$559$	0.984305	+	0.632575i	0.0416317	+	0.0267551i
$560$	−1.16424	+	0.157088i	−0.0491983	+	0.00663819i
$561$	−1.00442	+	1.15916i	−0.0424065	+	0.0489398i
$562$	−18.2829	+	0.870924i	−0.771219	+	0.0367377i
$563$	16.8751	−	13.2708i	0.711202	−	0.559296i	−0.195686	−	0.980667i	$-0.562693\pi$
$563$	16.8751	−	13.2708i	0.711202	−	0.559296i	0.906888	+	0.421371i	$0.138451\pi$
$564$	−3.32226	+	2.61266i	−0.139892	+	0.110013i
$565$	4.45606	−	0.212268i	0.187468	−	0.00893018i
$566$	−1.51380	+	1.74702i	−0.0636297	+	0.0734326i
$567$	2.62199	−	0.353778i	0.110113	−	0.0148573i
$568$	−8.33904	−	5.35917i	−0.349898	−	0.224866i
$569$	2.18214	+	0.529381i	0.0914801	+	0.0221928i	0.281238	−	0.959638i	$-0.409255\pi$
$569$	2.18214	+	0.529381i	0.0914801	+	0.0221928i	−0.189758	+	0.981831i	$0.560770\pi$
$570$	−2.29884	−	0.795635i	−0.0962877	−	0.0333255i
$571$	8.40702	−	2.03952i	0.351823	−	0.0853513i	−0.0559528	−	0.998433i	$-0.517820\pi$
$571$	8.40702	−	2.03952i	0.351823	−	0.0853513i	0.407776	+	0.913082i	$0.366304\pi$
$572$	0.195680	+	0.0186852i	0.00818179	+	0.000781266i
$573$	−2.23347	+	15.5341i	−0.0933047	+	0.648948i
$574$	−0.938188	−	0.494027i	−0.0391592	−	0.0206203i
$575$	23.0079	+	1.08753i	0.959496	+	0.0453533i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	13.9791	+	34.9180i	0.581956	+	1.45366i	0.868549	+	0.495604i	$0.165053\pi$
$577$	13.9791	+	34.9180i	0.581956	+	1.45366i	−0.286592	+	0.958053i	$0.592523\pi$
$578$	−6.00324	+	8.43037i	−0.249702	+	0.350657i
$579$	−10.7623	−	11.2872i	−0.447267	−	0.469080i
$580$	2.98370	+	3.44337i	0.123891	+	0.142978i
$581$	13.2006	−	4.44081i	0.547653	−	0.184236i
$582$	3.01171	−	4.68631i	0.124839	−	0.194254i
$583$	0.712678	+	1.00082i	0.0295161	+	0.0414496i
$584$	−1.82030	+	9.44460i	−0.0753245	+	0.390820i
$585$	0.136370	−	0.264521i	0.00563820	−	0.0109366i
$586$	−22.5045	−	9.00945i	−0.929653	−	0.372177i
$587$	−17.3362	+	2.49257i	−0.715542	+	0.102879i	−0.490464	−	0.871461i	$-0.663173\pi$
$587$	−17.3362	+	2.49257i	−0.715542	+	0.102879i	−0.225078	+	0.974341i	$0.572264\pi$
$588$	6.94500	−	0.875743i	0.286407	−	0.0361150i
$589$	−2.84069	−	2.46148i	−0.117049	−	0.101423i
$590$	−3.72435	+	2.65210i	−0.153329	+	0.109185i
$591$	−10.6350	−	0.506607i	−0.437465	−	0.0208390i
$592$	4.11200	−	4.31254i	0.169002	−	0.177244i
$593$	2.46085	+	12.7681i	0.101055	+	0.524323i	0.996812	+	0.0797800i	$0.0254218\pi$
$593$	2.46085	+	12.7681i	0.101055	+	0.524323i	−0.895758	+	0.444543i	$0.853366\pi$
$594$	−0.281406	−	0.0826283i	−0.0115462	−	0.00339028i
$595$	2.76772	+	5.48504i	0.113466	+	0.224865i
$596$	−17.2810	−	2.48463i	−0.707856	−	0.101774i
$597$	11.4341	+	6.60146i	0.467965	+	0.270180i
$598$	1.60614	−	2.78428i	0.0656800	−	0.113858i
$599$	17.8564	+	30.9282i	0.729593	+	1.26369i	0.957056	+	0.289905i	$0.0936236\pi$
$599$	17.8564	+	30.9282i	0.729593	+	1.26369i	−0.227463	+	0.973787i	$0.573043\pi$
$600$	−2.96892	+	3.77529i	−0.121206	+	0.154125i
$601$	3.98655	−	1.82060i	0.162615	−	0.0742637i	−0.332445	−	0.943123i	$-0.607873\pi$
$601$	3.98655	−	1.82060i	0.162615	−	0.0742637i	0.495060	+	0.868859i	$0.335146\pi$
$602$	−3.31496	−	3.21622i	−0.135108	−	0.131083i
$603$	5.73156	−	4.96643i	0.233407	−	0.202249i
$604$	−5.29517	+	21.8270i	−0.215457	+	0.888128i
$605$	−0.230589	+	4.84065i	−0.00937476	+	0.196800i
$606$	−14.0880	+	1.34524i	−0.572286	+	0.0546467i
$607$	−10.1082	+	3.49848i	−0.410279	+	0.141999i	−0.524408	−	0.851467i	$-0.675713\pi$
$607$	−10.1082	+	3.49848i	−0.410279	+	0.141999i	0.114130	+	0.993466i	$0.463592\pi$
$608$	4.60883	−	2.96191i	0.186913	−	0.120121i
$609$	−17.5995	−	20.6709i	−0.713169	−	0.837627i
$610$	−0.868139	−	6.03804i	−0.0351499	−	0.244473i
$611$	−0.134788	−	2.82954i	−0.00545292	−	0.114471i
$612$	−5.13516	−	0.989721i	−0.207576	−	0.0400071i
$613$	2.91719	+	30.5502i	0.117824	+	1.23391i	0.840149	+	0.542356i	$0.182468\pi$
$613$	2.91719	+	30.5502i	0.117824	+	1.23391i	−0.722324	+	0.691554i	$0.756926\pi$
$614$	10.4546	+	20.2791i	0.421914	+	0.818399i
$615$	0.170741	−	0.0501342i	0.00688495	−	0.00202160i
$616$	−0.742604	−	0.225070i	−0.0299204	−	0.00906832i
$617$	−9.72281	+	33.1128i	−0.391426	+	1.33307i	0.494473	+	0.869193i	$0.335361\pi$
$617$	−9.72281	+	33.1128i	−0.391426	+	1.33307i	−0.885898	+	0.463880i	$0.846457\pi$
$618$	−0.125519	+	1.31450i	−0.00504913	+	0.0528769i
$619$	−41.0501	+	16.4340i	−1.64994	+	0.660537i	−0.995428	−	0.0955141i	$-0.969551\pi$
$619$	−41.0501	+	16.4340i	−1.64994	+	0.660537i	−0.654513	+	0.756051i	$0.727126\pi$
$620$	0.263831	−	0.152323i	0.0105957	−	0.00611744i
$621$	−3.13927	+	3.62560i	−0.125975	+	0.145490i
$622$		−	27.4686i		−	1.10139i
$623$	2.77933	+	2.01575i	0.111351	+	0.0807591i
$624$	0.278425	+	0.609666i	0.0111459	+	0.0244062i
$625$	15.9811	−	15.2379i	0.639243	−	0.609517i
$626$	4.55345	−	13.1563i	0.181992	−	0.525833i
$627$	−1.16288	−	1.10880i	−0.0464409	−	0.0442813i
$628$	6.30912	−	3.25258i	0.251761	−	0.129792i
$629$	−28.3462	−	12.9453i	−1.13024	−	0.516161i
$630$	−0.734199	+	0.917110i	−0.0292512	+	0.0365385i
$631$	−9.86400	−	15.3487i	−0.392679	−	0.611021i	0.587478	−	0.809240i	$-0.300121\pi$
$631$	−9.86400	−	15.3487i	−0.392679	−	0.611021i	−0.980158	+	0.198219i	$0.936484\pi$
$632$	1.03538	−	2.58625i	0.0411852	−	0.102876i
$633$	13.6495	+	17.3568i	0.542519	+	0.689869i
$634$	1.99410	+	1.02803i	0.0791960	+	0.0408284i
$635$	−2.66145	−	7.68976i	−0.105617	−	0.305159i
$636$	−1.74026	+	3.81063i	−0.0690057	+	0.151101i
$637$	−2.22192	+	4.13213i	−0.0880355	+	0.163721i
$638$	0.847856	+	2.88753i	0.0335669	+	0.114318i
$639$	−9.73350	+	1.87598i	−0.385051	+	0.0742125i
$640$	0.104684	+	0.431514i	0.00413800	+	0.0170571i
$641$	16.5306	+	11.7714i	0.652919	+	0.464942i	0.857895	−	0.513825i	$-0.171772\pi$
$641$	16.5306	+	11.7714i	0.652919	+	0.464942i	−0.204976	+	0.978767i	$0.565711\pi$
$642$	−0.235316	−	0.185055i	−0.00928720	−	0.00730353i
$643$	−16.2034			−0.639001			−0.319501	−	0.947586i	$-0.603515\pi$
$643$	−16.2034			−0.639001			−0.319501	+	0.947586i	$0.603515\pi$
$644$	−8.38870	+	9.51996i	−0.330561	+	0.375139i
$645$	0.775157			0.0305218
$646$	−22.5211	−	17.7108i	−0.886080	−	0.696821i
$647$	23.3612	+	16.6354i	0.918422	+	0.654005i	0.938309	−	0.345797i	$-0.112391\pi$
$647$	23.3612	+	16.6354i	0.918422	+	0.654005i	−0.0198876	+	0.999802i	$0.506331\pi$
$648$	−0.235759	−	0.971812i	−0.00926149	−	0.0381764i
$649$	−2.96536	+	0.571526i	−0.116401	+	0.0224344i
$650$	−0.906903	−	3.08863i	−0.0355717	−	0.121146i
$651$	−1.57986	+	0.893933i	−0.0619195	+	0.0350360i
$652$	−4.34097	+	9.50539i	−0.170005	+	0.372260i
$653$	−3.18239	−	9.19492i	−0.124537	−	0.359825i	0.865448	−	0.500998i	$-0.167034\pi$
$653$	−3.18239	−	9.19492i	−0.124537	−	0.359825i	−0.989985	+	0.141173i	$0.954912\pi$
$654$	5.38467	+	2.77599i	0.210557	+	0.108550i
$655$	0.760101	+	0.966547i	0.0296996	+	0.0377661i
$656$	−0.148947	+	0.372053i	−0.00581542	+	0.0145262i
$657$	5.20011	+	8.09153i	0.202876	+	0.315681i
$658$	−1.68745	+	11.0542i	−0.0657835	+	0.430939i
$659$	−2.59709	−	1.18605i	−0.101168	−	0.0462020i	0.364188	−	0.931325i	$-0.381347\pi$
$659$	−2.59709	−	1.18605i	−0.101168	−	0.0462020i	−0.465356	+	0.885123i	$0.654074\pi$
$660$	0.115751	−	0.0596739i	0.00450561	−	0.00232280i
$661$	−26.4573	−	25.2270i	−1.02907	−	0.981216i	−0.0292378	−	0.999572i	$-0.509308\pi$
$661$	−26.4573	−	25.2270i	−1.02907	−	0.981216i	−0.999831	+	0.0183569i	$0.994157\pi$
$662$	−6.89676	+	19.9269i	−0.268050	+	0.774480i
$663$	2.53676	−	2.41879i	0.0985195	−	0.0939381i
$664$	−2.18679	−	4.78841i	−0.0848640	−	0.185826i
$665$	−5.87751	+	2.62274i	−0.227920	+	0.101705i
$666$		−	5.95874i		−	0.230897i
$667$	48.7121	+	6.98549i	1.88614	+	0.270479i
$668$	13.4916	−	7.78939i	0.522006	−	0.301380i
$669$	−20.9624	+	8.39207i	−0.810452	+	0.324456i
$670$	−0.320101	+	3.35225i	−0.0123666	+	0.129509i
$671$	1.13515	−	3.86598i	0.0438222	−	0.149245i
$672$	−0.601412	−	2.57649i	−0.0232000	−	0.0993903i
$673$	−13.0293	+	3.82576i	−0.502244	+	0.147472i	−0.523034	−	0.852312i	$-0.675200\pi$
$673$	−13.0293	+	3.82576i	−0.502244	+	0.147472i	0.0207899	+	0.999784i	$0.493382\pi$
$674$	9.39572	+	18.2251i	0.361909	+	0.702006i
$675$	0.456539	+	4.78109i	0.0175722	+	0.184024i
$676$	12.3240	+	2.37525i	0.473999	+	0.0913559i
$677$	−1.69101	−	35.4987i	−0.0649908	−	1.36433i	−0.762146	−	0.647405i	$-0.775854\pi$
$677$	−1.69101	−	35.4987i	−0.0649908	−	1.36433i	0.697155	−	0.716920i	$-0.254449\pi$
$678$	1.42982	+	9.94460i	0.0549118	+	0.381920i
$679$	−2.66352	−	14.4958i	−0.102217	−	0.556299i
$680$	1.95350	−	1.25544i	0.0749133	−	0.0481438i
$681$	−3.69001	+	1.27712i	−0.141401	+	0.0489395i
$682$	0.200310	−	0.0191273i	0.00767028	−	0.000732423i
$683$	−0.531163	+	11.1505i	−0.0203244	+	0.426662i	0.965658	+	0.259815i	$0.0836615\pi$
$683$	−0.531163	+	11.1505i	−0.0203244	+	0.426662i	−0.985983	+	0.166847i	$0.946642\pi$
$684$	1.29161	−	5.32409i	0.0493860	−	0.203572i
$685$	−1.30254	+	1.12866i	−0.0497674	+	0.0431237i
$686$	11.8237	−	14.2548i	0.451432	−	0.544251i
$687$	7.20967	−	3.29254i	0.275066	−	0.125618i
$688$	−1.07914	+	1.37224i	−0.0411418	+	0.0523160i
$689$	−1.40387	−	2.43157i	−0.0534832	−	0.0926356i
$690$	−0.102106	−	2.12704i	−0.00388712	−	0.0809752i
$691$	16.7352	+	9.66207i	0.636637	+	0.367563i	0.783318	−	0.621621i	$-0.213526\pi$
$691$	16.7352	+	9.66207i	0.636637	+	0.367563i	−0.146681	+	0.989184i	$0.546859\pi$
$692$	−7.75544	−	1.11506i	−0.294818	−	0.0423884i
$693$	−0.692764	+	0.349565i	−0.0263159	+	0.0132789i
$694$	−0.406311	−	0.119304i	−0.0154234	−	0.00452871i
$695$	−0.435549	−	2.25984i	−0.0165213	−	0.0857207i
$696$	−7.08096	+	7.42630i	−0.268403	+	0.281493i
$697$	2.09347	+	0.0997241i	0.0792957	+	0.00377732i
$698$	2.87946	−	2.05045i	0.108989	−	0.0776107i
$699$	6.88785	+	5.96836i	0.260522	+	0.225744i
$700$	1.09802	+	12.6596i	0.0415011	+	0.478487i
$701$	34.9184	−	5.02050i	1.31885	−	0.189622i	0.553290	−	0.832988i	$-0.313372\pi$
$701$	34.9184	−	5.02050i	1.31885	−	0.189622i	0.765558	+	0.643367i	$0.222463\pi$
$702$	0.622223	+	0.249100i	0.0234843	+	0.00940169i
$703$	14.9589	−	29.0161i	0.564184	−	1.09436i
$704$	−0.0555048	+	0.287986i	−0.00209191	+	0.0108539i
$705$	−1.08859	−	1.52871i	−0.0409987	−	0.0575747i
$706$	5.79003	−	9.00945i	0.217910	−	0.339075i
$707$	−24.7646	+	28.0835i	−0.931370	+	1.05619i
$708$	−6.74303	−	7.78187i	−0.253419	−	0.292461i
$709$	14.2859	+	14.9826i	0.536517	+	0.562683i	0.935070	−	0.354462i	$-0.115336\pi$
$709$	14.2859	+	14.9826i	0.536517	+	0.562683i	−0.398553	+	0.917145i	$0.630488\pi$
$710$	2.55313	−	3.58536i	0.0958171	−	0.134556i
$711$	−1.03538	−	2.58625i	−0.0388298	−	0.0969921i
$712$	0.648842	−	1.12383i	0.0243164	−	0.0421172i
$713$	1.07504	−	3.10981i	0.0402605	−	0.116463i
$714$	−11.7044	+	7.37918i	−0.438027	+	0.276159i
$715$	−0.0124217	+	0.0863946i	−0.000464544	+	0.00323098i
$716$	24.3966	+	2.32959i	0.911743	+	0.0870609i
$717$	5.30770	−	1.28763i	0.198220	−	0.0480876i
$718$	−23.5391	−	8.14696i	−0.878471	−	0.304042i
$719$	11.3216	+	2.74658i	0.422223	+	0.102430i	0.441241	−	0.897389i	$-0.354539\pi$
$719$	11.3216	+	2.74658i	0.422223	+	0.102430i	−0.0190172	+	0.999819i	$0.506054\pi$
$720$	0.373542	+	0.240061i	0.0139211	+	0.00894654i
$721$	2.13571	+	2.76485i	0.0795380	+	0.102968i
$722$	7.21278	−	8.32400i	0.268432	−	0.309787i
$723$	12.5547	−	0.598056i	0.466916	−	0.0222419i
$724$	−15.2145	+	11.9648i	−0.565444	+	0.444670i
$725$	38.7385	−	30.4643i	1.43871	−	1.13142i
$726$	−10.9016	+	0.519308i	−0.404597	+	0.0192733i
$727$	2.47700	−	2.85861i	0.0918667	−	0.106020i	−0.707955	−	0.706258i	$-0.750382\pi$
$727$	2.47700	−	2.85861i	0.0918667	−	0.106020i	0.799822	+	0.600238i	$0.204927\pi$
$728$	1.64046	+	0.673326i	0.0607996	+	0.0249551i
$729$	−0.841254	−	0.540641i	−0.0311575	−	0.0200237i
$730$	−4.15048	−	1.00690i	−0.153616	−	0.0372669i
$731$	8.62746	+	2.98599i	0.319098	+	0.110441i
$732$	13.3508	−	3.23888i	0.493461	−	0.119712i
$733$	34.0571	+	3.25206i	1.25793	+	0.120118i	0.702644	−	0.711542i	$-0.252003\pi$
$733$	34.0571	+	3.25206i	1.25793	+	0.120118i	0.555286	+	0.831660i	$0.312609\pi$
$734$	−2.05448	+	14.2892i	−0.0758323	+	0.527425i
$735$	0.241683	+	3.09880i	0.00891462	+	0.114301i
$736$	3.90759	+	2.78042i	0.144036	+	0.102488i
$737$	−1.11213	+	1.92627i	−0.0409659	+	0.0709551i
$738$	0.148947	+	0.372053i	0.00548283	+	0.0136954i
$739$	−23.9713	+	33.6630i	−0.881799	+	1.23831i	0.0884197	+	0.996083i	$0.471818\pi$
$739$	−23.9713	+	33.6630i	−0.881799	+	1.23831i	−0.970219	+	0.242230i	$0.922121\pi$
$740$	1.82585	+	1.91490i	0.0671197	+	0.0703931i
$741$	2.40458	+	2.77503i	0.0883343	+	0.101943i
$742$	3.53401	+	10.5051i	0.129738	+	0.385653i
$743$	−16.6071	+	25.8411i	−0.609255	+	0.948019i	0.390371	+	0.920658i	$0.372347\pi$
$743$	−16.6071	+	25.8411i	−0.609255	+	0.948019i	−0.999626	+	0.0273610i	$0.991290\pi$
$744$	0.397973	+	0.558875i	0.0145904	+	0.0204893i
$745$	1.46711	−	7.61208i	0.0537507	−	0.278885i
$746$	6.23458	−	12.0934i	0.228264	−	0.442771i
$747$	−4.88703	−	1.95647i	−0.178807	−	0.0715836i
$748$	1.51818	−	0.218281i	0.0555100	−	0.00798114i
$749$	−0.789082	+	0.0684401i	−0.0288324	+	0.00250075i
$750$	−3.28959	−	2.85045i	−0.120119	−	0.104084i
$751$	−27.5417	+	19.6124i	−1.00501	+	0.715665i	−0.959038	−	0.283277i	$-0.908578\pi$
$751$	−27.5417	+	19.6124i	−1.00501	+	0.715665i	−0.0459733	+	0.998943i	$0.514639\pi$
$752$	4.22172	+	0.201105i	0.153950	+	0.00733356i
$753$	7.21904	−	7.57111i	0.263076	−	0.275906i
$754$	−1.30154	−	6.75304i	−0.0473994	−	0.245931i
$755$	−9.56899	−	2.80971i	−0.348251	−	0.102256i
$756$	−2.21324	−	1.44967i	−0.0804949	−	0.0527241i
$757$	−38.6425	−	5.55596i	−1.40449	−	0.201935i	−0.601949	−	0.798535i	$-0.705609\pi$
$757$	−38.6425	−	5.55596i	−1.40449	−	0.201935i	−0.802539	+	0.596600i	$0.796518\pi$
$758$	−29.1428	−	16.8256i	−1.05851	−	0.611133i
$759$	0.522283	−	1.30599i	0.0189577	−	0.0474044i
$760$	1.21631	+	2.10672i	0.0441204	+	0.0764187i
$761$	5.11486	−	6.50408i	0.185414	−	0.235773i	−0.684456	−	0.729054i	$-0.739960\pi$
$761$	5.11486	−	6.50408i	0.185414	−	0.235773i	0.869870	+	0.493281i	$0.164203\pi$
$762$	16.6699	−	7.61291i	0.603888	−	0.275787i
$763$	15.4176	−	4.38199i	0.558156	−	0.158639i
$764$	11.8607	−	10.2773i	0.429103	−	0.371820i
$765$	0.547463	−	2.25667i	0.0197936	−	0.0815901i
$766$	−1.22804	+	25.7797i	−0.0443709	+	0.931459i
$767$	6.87007	−	0.656012i	0.248064	−	0.0236872i
$768$	−0.945001	+	0.327068i	−0.0340998	+	0.0118020i
$769$	−31.2544	+	20.0860i	−1.12706	+	0.724319i	−0.964945	−	0.262453i	$-0.915469\pi$
$769$	−31.2544	+	20.0860i	−1.12706	+	0.724319i	−0.162117	+	0.986771i	$0.551832\pi$
$770$	0.115514	−	0.324610i	0.00416284	−	0.0116981i
$771$	−3.68633	−	25.6390i	−0.132760	−	0.923366i
$772$	0.742077	+	15.5781i	0.0267079	+	0.560669i
$773$	6.39382	+	1.23231i	0.229970	+	0.0443230i	0.302934	−	0.953012i	$-0.402034\pi$
$773$	6.39382	+	1.23231i	0.229970	+	0.0443230i	−0.0729643	+	0.997335i	$0.523246\pi$
$774$	0.165942	+	1.73783i	0.00596467	+	0.0624648i
$775$	−1.50994	−	2.92888i	−0.0542388	−	0.105209i
$776$	−5.34498	+	1.56943i	−0.191874	+	0.0563392i
$777$	−10.7799	−	11.5039i	−0.386725	−	0.412702i
$778$	−6.22823	+	21.2114i	−0.223293	+	0.760466i
$779$	−0.208702	+	2.18563i	−0.00747754	+	0.0783083i
$780$	−0.276286	+	0.110608i	−0.00989262	+	0.00396041i
$781$	2.51774	−	1.45362i	0.0900919	−	0.0520146i
$782$	7.05718	−	24.0672i	0.252364	−	0.860643i
$783$			10.2611i			0.366701i
$784$	−5.82217	−	3.88617i	−0.207935	−	0.138792i
$785$	1.30931	+	2.86698i	0.0467312	+	0.102327i
$786$	−2.00418	+	1.91099i	−0.0714869	+	0.0681626i
$787$	−0.353561	+	1.02155i	−0.0126031	+	0.0364143i	−0.951127	−	0.308800i	$-0.900073\pi$
$787$	−0.353561	+	1.02155i	−0.0126031	+	0.0364143i	0.938524	+	0.345214i	$0.112194\pi$
$788$	7.70563	+	7.34730i	0.274502	+	0.261737i
$789$	−25.9028	+	13.3538i	−0.922165	+	0.475409i
$790$	1.12520	+	0.513861i	0.0400328	+	0.0182823i
$791$	20.7510	+	16.6124i	0.737821	+	0.590668i
$792$	0.158562	+	0.246728i	0.00563427	+	0.00876710i
$793$	−3.42217	+	8.54816i	−0.121525	+	0.303554i
$794$	−10.8845	−	13.8408i	−0.386277	−	0.491191i
$795$	−1.65335	−	0.852361i	−0.0586383	−	0.0302301i
$796$	−4.31825	−	12.4768i	−0.153056	−	0.442227i
$797$	−5.19039	+	11.3654i	−0.183853	+	0.402582i	−0.979007	−	0.203825i	$-0.934663\pi$
$797$	−5.19039	+	11.3654i	−0.183853	+	0.402582i	0.795154	+	0.606407i	$0.207390\pi$
$798$	−7.13815	−	12.6153i	−0.252688	−	0.446578i
$799$	−6.22720	−	21.2079i	−0.220302	−	0.750281i
$800$	4.71604	−	0.908943i	0.166737	−	0.0321360i
$801$	−0.305941	−	1.26110i	−0.0108099	−	0.0445589i
$802$	−0.759061	−	0.540525i	−0.0268034	−	0.0190866i
$803$	−2.21742	−	1.74380i	−0.0782509	−	0.0615372i
$804$	−7.58395			−0.267465
$805$	−4.04513	−	3.92175i	−0.142572	−	0.138224i
$806$	−0.459842			−0.0161973
$807$	21.9285	+	17.2448i	0.771919	+	0.607044i
$808$	11.5279	+	8.20901i	0.405552	+	0.288792i
$809$	2.37407	+	9.78607i	0.0834680	+	0.344060i	0.998198	−	0.0600058i	$-0.0191119\pi$
$809$	2.37407	+	9.78607i	0.0834680	+	0.344060i	−0.914730	+	0.404066i	$0.867597\pi$
$810$	0.436006	−	0.0840333i	0.0153197	−	0.00295263i
$811$	−3.47911	−	11.8488i	−0.122168	−	0.416066i	0.875585	−	0.483064i	$-0.160476\pi$
$811$	−3.47911	−	11.8488i	−0.122168	−	0.416066i	−0.997753	+	0.0669979i	$0.978658\pi$
$812$	−0.235709	+	27.1473i	−0.00827177	+	0.952682i
$813$	4.25334	−	9.31351i	0.149171	−	0.326639i
$814$	0.571589	+	1.65150i	0.0200342	+	0.0578850i
$815$	−4.12418	−	2.12616i	−0.144464	−	0.0744763i
$816$	3.23276	+	4.11079i	0.113169	+	0.143907i
$817$	−3.55459	+	8.87893i	−0.124359	+	0.310635i
$818$	6.51179	+	10.1325i	0.227680	+	0.354276i
$819$	1.65191	−	0.644740i	0.0577223	−	0.0225290i
$820$	−0.161869	−	0.0739229i	−0.00565269	−	0.00258150i
$821$	−28.8933	+	14.8956i	−1.00838	+	0.519858i	−0.881563	−	0.472067i	$-0.843508\pi$
$821$	−28.8933	+	14.8956i	−1.00838	+	0.519858i	−0.126822	+	0.991925i	$0.540478\pi$
$822$	−2.80918	−	2.67854i	−0.0979813	−	0.0934250i
$823$	−7.83915	+	22.6497i	−0.273256	+	0.789520i	0.721970	+	0.691924i	$0.243237\pi$
$823$	−7.83915	+	22.6497i	−0.273256	+	0.789520i	−0.995226	+	0.0975964i	$0.968885\pi$
$824$	0.955675	−	0.911234i	0.0332925	−	0.0317443i
$825$	−0.585156	−	1.28131i	−0.0203725	−	0.0446096i
$826$	−27.0961	−	2.82498i	−0.942795	−	0.0982935i
$827$			39.1713i			1.36212i	0.732228	+	0.681060i	$0.238481\pi$
$827$			39.1713i			1.36212i	−0.732228	+	0.681060i	$0.761519\pi$
$828$	4.74677	−	0.684261i	0.164962	−	0.0237797i
$829$	−13.8940	+	8.02173i	−0.482560	+	0.278606i	−0.721483	−	0.692432i	$-0.756539\pi$
$829$	−13.8940	+	8.02173i	−0.482560	+	0.278606i	0.238923	+	0.971039i	$0.423206\pi$
$830$	2.16999	−	0.868733i	0.0753215	−	0.0301542i
$831$	0.393160	−	4.11736i	0.0136386	−	0.142829i
$832$	0.188826	−	0.643084i	0.00654638	−	0.0222949i
$833$	−9.24701	+	35.4205i	−0.320390	+	1.22725i
$834$	4.97310	−	1.46023i	0.172204	−	0.0505638i
$835$	3.16976	+	6.14847i	0.109694	+	0.212777i
$836$	0.152734	+	1.59950i	0.00528241	+	0.0553199i
$837$	0.673694	+	0.129844i	0.0232863	+	0.00448806i
$838$	−1.16952	−	24.5512i	−0.0404003	−	0.848106i
$839$	−2.76455	−	19.2278i	−0.0954427	−	0.663819i	−0.980236	−	0.197834i	$-0.936609\pi$
$839$	−2.76455	−	19.2278i	−0.0954427	−	0.663819i	0.884793	−	0.465985i	$-0.154300\pi$
$840$	1.15545	−	0.212307i	0.0398668	−	0.00732529i
$841$	64.1792	−	41.2455i	2.21308	−	1.42226i
$842$	−5.95711	+	2.06177i	−0.205295	+	0.0710534i
$843$	18.2208	−	1.73987i	0.627557	−	0.0599245i
$844$	1.05065	−	22.0559i	0.0361649	−	0.759195i
$845$	−1.31387	+	5.41584i	−0.0451984	+	0.186310i
$846$	3.19418	−	2.76778i	0.109818	−	0.0951581i
$847$	−20.1072	+	20.7245i	−0.690892	+	0.712103i
$848$	3.81063	−	1.74026i	0.130858	−	0.0597606i
$849$	1.42896	−	1.81707i	0.0490417	−	0.0623616i
$850$	−12.5586	−	21.7522i	−0.430757	−	0.746093i
$851$	28.4487	+	2.70598i	0.975209	+	0.0927599i
$852$	8.58459	+	4.95632i	0.294103	+	0.169801i
$853$	2.05349	+	0.295247i	0.0703100	+	0.0101091i	0.177380	−	0.984142i	$-0.443238\pi$
$853$	2.05349	+	0.295247i	0.0703100	+	0.0101091i	−0.107070	+	0.994251i	$0.534147\pi$
$854$	19.9157	−	30.4058i	0.681502	−	1.04046i
$855$	2.33409	+	0.685351i	0.0798242	+	0.0234385i
$856$	0.0566551	+	0.293955i	0.00193643	+	0.0100472i
$857$	36.4695	−	38.2481i	1.24577	−	1.30653i	0.311381	−	0.950285i	$-0.399208\pi$
$857$	36.4695	−	38.2481i	1.24577	−	1.30653i	0.934393	−	0.356245i	$-0.115943\pi$
$858$	−0.196347	−	0.00935318i	−0.00670319	−	0.000319312i
$859$	−1.29755	+	0.923984i	−0.0442720	+	0.0315259i	−0.601979	−	0.798512i	$-0.705621\pi$
$859$	−1.29755	+	0.923984i	−0.0442720	+	0.0315259i	0.557707	+	0.830038i	$0.311681\pi$
$860$	−0.585824	−	0.507620i	−0.0199764	−	0.0173097i
$861$	0.960632	+	0.448826i	0.0327383	+	0.0152960i
$862$	−1.26006	+	0.181170i	−0.0429179	+	0.00617066i
$863$	9.61895	+	3.85085i	0.327433	+	0.131084i	0.529554	−	0.848276i	$-0.322359\pi$
$863$	9.61895	+	3.85085i	0.327433	+	0.131084i	−0.202121	+	0.979361i	$0.564783\pi$
$864$	−0.458227	+	0.888835i	−0.0155892	+	0.0302388i
$865$	0.658417	−	3.41619i	0.0223868	−	0.116154i
$866$	6.49582	+	9.12210i	0.220737	+	0.309982i
$867$	5.59531	−	8.70647i	0.190027	−	0.295687i
$868$	1.77938	+	0.358997i	0.0603960	+	0.0121852i
$869$	0.535046	+	0.617476i	0.0181502	+	0.0209464i
$870$	−3.14416	−	3.29750i	−0.106597	−	0.111796i
$871$	2.94844	−	4.14050i	0.0999039	−	0.140295i
$872$	−2.25157	−	5.62416i	−0.0762479	−	0.190458i
$873$	−2.78532	+	4.82431i	−0.0942687	+	0.163278i
$874$	24.8322	+	8.58429i	0.839961	+	0.290368i
$875$	−11.5076	+	0.448073i	−0.389027	+	0.0151476i
$876$	1.36884	−	9.52052i	0.0462490	−	0.321669i
$877$	5.19979	+	0.496519i	0.175584	+	0.0167663i	0.182478	−	0.983210i	$-0.441588\pi$
$877$	5.19979	+	0.496519i	0.175584	+	0.0167663i	−0.00689353	+	0.999976i	$0.502194\pi$
$878$	−38.7605	+	9.40320i	−1.30810	+	0.317343i
$879$	22.9077	+	7.92843i	0.772658	+	0.267419i
$880$	−0.126557	−	0.0307024i	−0.00426623	−	0.00103498i
$881$	15.3897	+	9.89036i	0.518492	+	0.333215i	0.773575	−	0.633704i	$-0.218466\pi$
$881$	15.3897	+	9.89036i	0.518492	+	0.333215i	−0.255083	+	0.966919i	$0.582103\pi$
$882$	−6.89547	+	1.20521i	−0.232182	+	0.0405815i
$883$	−1.95060	+	2.25111i	−0.0656428	+	0.0757558i	−0.787621	−	0.616160i	$-0.788688\pi$
$883$	−1.95060	+	2.25111i	−0.0656428	+	0.0757558i	0.721978	+	0.691916i	$0.243233\pi$
$884$	−3.50112	+	0.166779i	−0.117756	+	0.00560939i
$885$	3.59394	−	2.82630i	0.120809	−	0.0950051i
$886$	−11.4774	+	9.02595i	−0.385592	+	0.303233i
$887$	52.5687	−	2.50416i	1.76508	−	0.0840813i	0.860257	−	0.509861i	$-0.170303\pi$
$887$	52.5687	−	2.50416i	1.76508	−	0.0840813i	0.904827	+	0.425779i	$0.140000\pi$
$888$	−3.90215	+	4.50332i	−0.130947	+	0.151121i
$889$	18.4106	−	44.8548i	0.617472	−	1.50438i
$890$	0.484740	+	0.311523i	0.0162485	+	0.0104423i
$891$	0.285019	+	0.0691448i	0.00954849	+	0.00231644i
$892$	21.3379	+	7.38513i	0.714447	+	0.247273i
$893$	22.5023	−	5.45901i	0.753012	−	0.182679i
$894$	17.3796	+	1.65955i	0.581261	+	0.0555037i
$895$	−1.54868	+	10.7713i	−0.0517668	+	0.360046i
$896$	−1.23273	+	2.34102i	−0.0411825	+	0.0782081i
$897$	−1.47184	+	2.85755i	−0.0491433	+	0.0954107i
$898$	−4.97523	+	8.61734i	−0.166025	+	0.287564i
$899$	−2.61653	−	6.53577i	−0.0872660	−	0.217980i
$900$	2.78592	−	3.91228i	0.0928640	−	0.130409i
$901$	−15.1183	−	15.8556i	−0.503664	−	0.528228i
$902$	−0.0769706	−	0.0888288i	−0.00256284	−	0.00295767i
$903$	3.46424	+	3.05484i	0.115283	+	0.101659i
$904$	5.43174	−	8.45196i	0.180657	−	0.281108i
$905$	−4.98528	−	7.00085i	−0.165716	−	0.232716i
$906$	4.25060	−	22.0542i	0.141217	−	0.732703i
$907$	−2.60122	+	5.04567i	−0.0863723	+	0.167539i	−0.928065	−	0.372418i	$-0.878529\pi$
$907$	−2.60122	+	5.04567i	−0.0863723	+	0.167539i	0.841693	+	0.539956i	$0.181559\pi$
$908$	3.62506	+	1.45126i	0.120302	+	0.0481616i
$909$	14.0080	−	2.01405i	0.464617	−	0.0668019i
$910$	−0.333298	+	0.713364i	−0.0110487	+	0.0236478i
$911$	−10.6446	−	9.22362i	−0.352672	−	0.305592i	0.460449	−	0.887686i	$-0.347688\pi$
$911$	−10.6446	−	9.22362i	−0.352672	−	0.305592i	−0.813122	+	0.582094i	$0.802234\pi$
$912$	−4.46267	+	3.17786i	−0.147774	+	0.105229i
$913$	1.54214	+	0.0734613i	0.0510375	+	0.00243122i
$914$	12.1125	−	12.7033i	0.400647	−	0.420186i
$915$	1.15446	+	5.98989i	0.0381652	+	0.198020i
$916$	−7.60486	−	2.23299i	−0.251272	−	0.0737800i
$917$	−0.412145	+	7.31508i	−0.0136102	+	0.241565i
$918$	5.17643	+	0.744259i	0.170848	+	0.0245642i
$919$	12.7623	+	7.36830i	0.420989	+	0.243058i	0.695500	−	0.718526i	$-0.255183\pi$
$919$	12.7623	+	7.36830i	0.420989	+	0.243058i	−0.274512	+	0.961584i	$0.588516\pi$
$920$	−1.31575	+	1.67438i	−0.0433790	+	0.0552026i
$921$	−11.4077	−	19.7587i	−0.375897	−	0.651072i
$922$	5.76738	−	7.33382i	0.189938	−	0.241526i
$923$	−6.04339	+	2.75992i	−0.198921	+	0.0908440i
$924$	0.752472	+	0.189480i	0.0247545	+	0.00623345i
$925$	21.6287	−	18.7414i	0.711147	−	0.616212i
$926$	3.18229	−	13.1176i	0.104577	−	0.431070i
$927$	0.0628309	−	1.31898i	0.00206364	−	0.0433211i
$928$	10.2146	−	0.975379i	0.335312	−	0.0320184i
$929$	51.9752	−	17.9888i	1.70525	−	0.590193i	0.711588	−	0.702597i	$-0.247976\pi$
$929$	51.9752	−	17.9888i	1.70525	−	0.590193i	0.993663	+	0.112404i	$0.0358550\pi$
$930$	−0.256284	+	0.164704i	−0.00840390	+	0.00540086i
$931$	−36.6031	−	11.4416i	−1.19962	−	0.374985i
$932$	−1.29705	−	9.02117i	−0.0424862	−	0.295498i
$933$	1.30701	+	27.4375i	0.0427896	+	0.898264i
$934$	19.2396	+	3.70812i	0.629537	+	0.121333i
$935$	0.0647378	+	0.677964i	0.00211715	+	0.0221718i
$936$	−0.307119	−	0.595727i	−0.0100385	−	0.0194719i
$937$	25.7581	−	7.56327i	0.841482	−	0.247081i	0.167540	−	0.985865i	$-0.446418\pi$
$937$	25.7581	−	7.56327i	0.841482	−	0.247081i	0.673942	+	0.738784i	$0.264600\pi$
$938$	−14.6416	+	13.7200i	−0.478064	+	0.447974i
$939$	−3.92229	+	13.3581i	−0.127999	+	0.435925i
$940$	−0.178391	+	1.86820i	−0.00581849	+	0.0609340i
$941$	43.7682	−	17.5222i	1.42680	−	0.571206i	0.475570	−	0.879678i	$-0.342242\pi$
$941$	43.7682	−	17.5222i	1.42680	−	0.571206i	0.951234	+	0.308472i	$0.0998175\pi$
$942$	−6.14721	+	3.54909i	−0.200287	+	0.115636i
$943$	−1.84392	+	0.542160i	−0.0600464	+	0.0176552i
$944$			10.2969i			0.335135i
$945$	0.689730	−	0.951006i	0.0224369	−	0.0309362i
$946$	−0.212692	−	0.465730i	−0.00691521	−	0.0151422i
$947$	−1.04421	+	0.995656i	−0.0339324	+	0.0323545i	−0.706856	−	0.707358i	$-0.749887\pi$
$947$	−1.04421	+	0.995656i	−0.0339324	+	0.0323545i	0.672923	+	0.739712i	$0.265038\pi$
$948$	−0.911148	+	2.63259i	−0.0295927	+	0.0855025i
$949$	4.66561	+	4.44865i	0.151452	+	0.144409i
$950$	23.3874	−	12.0571i	0.758789	−	0.391183i
$951$	−2.04076	−	0.931984i	−0.0661762	−	0.0302217i
$952$	13.6779	+	2.08796i	0.443305	+	0.0676711i
$953$	−25.0526	−	38.9827i	−0.811535	−	1.26277i	−0.961698	−	0.274112i	$-0.911616\pi$
$953$	−25.0526	−	38.9827i	−0.811535	−	1.26277i	0.150163	−	0.988661i	$-0.452020\pi$
$954$	1.55697	−	3.88912i	0.0504087	−	0.125915i
$955$	4.30768	+	5.47766i	0.139393	+	0.177253i
$956$	−4.85451	−	2.50268i	−0.157006	−	0.0809423i
$957$	−0.984290	−	2.84392i	−0.0318176	−	0.0919308i
$958$	−4.11068	+	9.00114i	−0.132810	+	0.290814i
$959$	−10.2691	−	0.0891627i	−0.331607	−	0.00287921i
$960$	−0.125098	−	0.426044i	−0.00403751	−	0.0137505i
$961$	29.9776	−	5.77770i	0.967018	−	0.186378i
$962$	−0.941561	−	3.88117i	−0.0303572	−	0.125134i
$963$	0.243855	+	0.173648i	0.00785812	+	0.00559574i
$964$	−9.87988	−	7.76962i	−0.318210	−	0.250243i
$965$	−6.92500			−0.222924
$966$	7.92622	−	9.90833i	0.255022	−	0.318795i
$967$	21.8056			0.701221			0.350611	−	0.936521i	$-0.385974\pi$
$967$	21.8056			0.701221			0.350611	+	0.936521i	$0.385974\pi$
$968$	8.57897	+	6.74658i	0.275739	+	0.216843i
$969$	23.3383	+	16.6191i	0.749734	+	0.533883i
$970$	−0.583157	−	2.40380i	−0.0187240	−	0.0771815i
$971$	−39.0630	+	7.52878i	−1.25359	+	0.241610i	−0.772475	−	0.635046i	$-0.780981\pi$
$971$	−39.0630	+	7.52878i	−1.25359	+	0.241610i	−0.481118	+	0.876656i	$0.659769\pi$
$972$	0.281733	+	0.959493i	0.00903658	+	0.0307758i
$973$	6.95939	−	11.8159i	0.223108	−	0.378800i
$974$	13.0792	−	28.6394i	0.419084	−	0.917666i
$975$	1.05284	+	3.04198i	0.0337178	+	0.0974212i
$976$	−12.2109	−	6.29516i	−0.390862	−	0.201503i
$977$	−23.6639	−	30.0911i	−0.757076	−	0.962701i	0.242897	−	0.970052i	$-0.421902\pi$
$977$	−23.6639	−	30.0911i	−0.757076	−	0.962701i	−0.999973	+	0.00735117i	$0.997660\pi$
$978$	3.88376	−	9.70118i	0.124189	−	0.310209i
$979$	0.205764	+	0.320175i	0.00657625	+	0.0102328i
$980$	1.84663	−	2.50019i	0.0589885	−	0.0798655i
$981$	−5.51066	−	2.51663i	−0.175942	−	0.0803499i
$982$	30.2867	−	15.6139i	0.966487	−	0.498259i
$983$	18.0702	+	17.2299i	0.576349	+	0.549548i	0.921190	−	0.389113i	$-0.127219\pi$
$983$	18.0702	+	17.2299i	0.576349	+	0.549548i	−0.344841	+	0.938661i	$0.612067\pi$
$984$	0.131076	−	0.378718i	0.00417854	−	0.0120731i
$985$	−3.42153	+	3.26242i	−0.109019	+	0.103949i
$986$	−22.2920	−	48.8127i	−0.709923	−	1.55451i
$987$	1.15955	−	11.1220i	0.0369090	−	0.354018i
$988$		−	3.67189i		−	0.116818i
$989$	−8.37223	+	0.00307414i	−0.266221	+	9.77520e-5i
$990$	−0.112781	+	0.0651139i	−0.00358440	+	0.00206946i
$991$	25.7701	−	10.3168i	0.818614	−	0.327724i	0.0757173	−	0.997129i	$-0.475875\pi$
$991$	25.7701	−	10.3168i	0.818614	−	0.327724i	0.742897	+	0.669406i	$0.233451\pi$
$992$	0.0652173	−	0.682986i	0.00207065	−	0.0216848i
$993$	5.94079	−	20.2325i	0.188525	−	0.642058i
$994$	25.5398	−	5.96158i	0.810073	−	0.189090i
$995$	5.62502	−	1.65165i	0.178325	−	0.0523610i
$996$	2.41216	+	4.67893i	0.0764321	+	0.148258i
$997$	−2.79876	−	29.3099i	−0.0886376	−	0.928255i	−0.924972	−	0.380035i	$-0.875912\pi$
$997$	−2.79876	−	29.3099i	−0.0886376	−	0.928255i	0.836334	−	0.548220i	$-0.184694\pi$
$998$	−27.4000	−	5.28091i	−0.867331	−	0.167164i
$999$	0.283528	+	5.95199i	0.00897044	+	0.188313i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.be.a.61.4	✓	320
7.3	odd	6	inner	966.2.be.a.199.12	yes	320
23.20	odd	22	inner	966.2.be.a.733.12	yes	320
161.66	even	66	inner	966.2.be.a.871.4	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.be.a.61.4	✓	320	1.1	even	1	trivial
966.2.be.a.199.12	yes	320	7.3	odd	6	inner
966.2.be.a.733.12	yes	320	23.20	odd	22	inner
966.2.be.a.871.4	yes	320	161.66	even	66	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.be (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.786053 + 0.618159i) q^{2} +(-0.814576 - 0.580057i) q^{3} +(0.235759 + 0.971812i) q^{4} +(-0.436006 + 0.0840333i) q^{5} +(-0.281733 - 0.959493i) q^{6} +(-2.27972 - 1.34272i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(0.327068 + 0.945001i) q^{9} +O(q^{10})\)	\(q+(0.786053 + 0.618159i) q^{2} +(-0.814576 - 0.580057i) q^{3} +(0.235759 + 0.971812i) q^{4} +(-0.436006 + 0.0840333i) q^{5} +(-0.281733 - 0.959493i) q^{6} +(-2.27972 - 1.34272i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(0.327068 + 0.945001i) q^{9} +(-0.394670 - 0.203466i) q^{10} +(-0.181297 - 0.230538i) q^{11} +(0.371662 - 0.928368i) q^{12} +(0.362355 + 0.563836i) q^{13} +(-0.961964 - 2.46468i) q^{14} +(0.403904 + 0.184457i) q^{15} +(-0.888835 + 0.458227i) q^{16} +(3.78489 + 3.60888i) q^{17} +(-0.327068 + 0.945001i) q^{18} +(-3.96499 + 3.78061i) q^{19} +(-0.184457 - 0.403904i) q^{20} +(1.07815 + 2.41611i) q^{21} -0.293286i q^{22} +(-4.36317 - 1.99066i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-4.45880 + 1.78503i) q^{25} +(-0.0637097 + 0.667198i) q^{26} +(0.281733 - 0.959493i) q^{27} +(0.767407 - 2.53201i) q^{28} +(-9.84544 + 2.89088i) q^{29} +(0.203466 + 0.394670i) q^{30} +(0.0652173 + 0.682986i) q^{31} +(-0.981929 - 0.189251i) q^{32} +(0.0139551 + 0.292954i) q^{33} +(0.744259 + 5.17643i) q^{34} +(1.10680 + 0.393862i) q^{35} +(-0.841254 + 0.540641i) q^{36} +(-5.63102 + 1.94891i) q^{37} +(-5.45372 + 0.520767i) q^{38} +(0.0318910 - 0.669474i) q^{39} +(0.104684 - 0.431514i) q^{40} +(0.302874 - 0.262442i) q^{41} +(-0.646060 + 2.56566i) q^{42} +(1.58797 - 0.725202i) q^{43} +(0.181297 - 0.230538i) q^{44} +(-0.222015 - 0.384541i) q^{45} +(-2.19914 - 4.26190i) q^{46} +(-3.66027 - 2.11325i) q^{47} +(0.989821 + 0.142315i) q^{48} +(3.39421 + 6.12204i) q^{49} +(-4.60829 - 1.35312i) q^{50} +(-0.989721 - 5.13516i) q^{51} +(-0.462514 + 0.485071i) q^{52} +(-4.18445 - 0.199330i) q^{53} +(0.814576 - 0.580057i) q^{54} +(0.0984197 + 0.0852811i) q^{55} +(2.16841 - 1.51592i) q^{56} +(5.42276 - 0.779675i) q^{57} +(-9.52607 - 3.81366i) q^{58} +(4.71831 - 9.15224i) q^{59} +(-0.0840333 + 0.436006i) q^{60} +(7.96888 + 11.1907i) q^{61} +(-0.370930 + 0.577178i) q^{62} +(0.523249 - 2.59349i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-0.205370 - 0.215386i) q^{65} +(-0.170123 + 0.238904i) q^{66} +(-2.81867 - 7.04069i) q^{67} +(-2.61483 + 4.52902i) q^{68} +(2.39944 + 4.15243i) q^{69} +(0.626537 + 0.993776i) q^{70} +(-1.41071 + 9.81174i) q^{71} +(-0.995472 - 0.0950560i) q^{72} +(9.34729 - 2.26763i) q^{73} +(-5.63102 - 1.94891i) q^{74} +(4.66745 + 1.13231i) q^{75} +(-4.60883 - 2.96191i) q^{76} +(0.103758 + 0.768994i) q^{77} +(0.438909 - 0.506528i) q^{78} +(-2.78265 + 0.132554i) q^{79} +(0.349031 - 0.274481i) q^{80} +(-0.786053 + 0.618159i) q^{81} +(0.400306 - 0.0190689i) q^{82} +(-3.44726 + 3.97835i) q^{83} +(-2.09382 + 1.61738i) q^{84} +(-1.95350 - 1.25544i) q^{85} +(1.69652 + 0.411571i) q^{86} +(9.69674 + 3.35607i) q^{87} +(0.285019 - 0.0691448i) q^{88} +(-1.29181 - 0.123353i) q^{89} +(0.0631921 - 0.439511i) q^{90} +(-0.0689938 - 1.77193i) q^{91} +(0.905888 - 4.70950i) q^{92} +(0.343046 - 0.594174i) q^{93} +(-1.57084 - 3.92376i) q^{94} +(1.41106 - 1.98156i) q^{95} +(0.690079 + 0.723734i) q^{96} +(3.64799 + 4.21000i) q^{97} +(-1.11636 + 6.91041i) q^{98} +(0.158562 - 0.246728i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9}+O(q^{10}) \) 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9	\( 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9} - 22 q^{14} + 16 q^{16} + 66 q^{17} + 16 q^{18} + 40 q^{23} - 48 q^{25} + 12 q^{26} + 44 q^{28} - 24 q^{29} + 24 q^{31} - 16 q^{32} + 98 q^{35} + 32 q^{36} - 22 q^{37} - 66 q^{38} - 8 q^{39} - 88 q^{43} + 4 q^{46} - 144 q^{47} - 24 q^{49} + 80 q^{50} - 22 q^{51} + 12 q^{52} + 44 q^{53} + 44 q^{57} + 10 q^{58} + 12 q^{59} - 32 q^{64} + 108 q^{70} - 16 q^{71} + 16 q^{72} - 180 q^{73} - 22 q^{74} - 12 q^{75} + 18 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 36 q^{82} + 22 q^{84} + 68 q^{85} - 22 q^{86} + 48 q^{87} + 22 q^{88} + 8 q^{92} + 8 q^{93} - 12 q^{94} + 66 q^{95} - 90 q^{98}+O(q^{100}) \) 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9 - 22 * q^14 + 16 * q^16 + 66 * q^17 + 16 * q^18 + 40 * q^23 - 48 * q^25 + 12 * q^26 + 44 * q^28 - 24 * q^29 + 24 * q^31 - 16 * q^32 + 98 * q^35 + 32 * q^36 - 22 * q^37 - 66 * q^38 - 8 * q^39 - 88 * q^43 + 4 * q^46 - 144 * q^47 - 24 * q^49 + 80 * q^50 - 22 * q^51 + 12 * q^52 + 44 * q^53 + 44 * q^57 + 10 * q^58 + 12 * q^59 - 32 * q^64 + 108 * q^70 - 16 * q^71 + 16 * q^72 - 180 * q^73 - 22 * q^74 - 12 * q^75 + 18 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 36 * q^82 + 22 * q^84 + 68 * q^85 - 22 * q^86 + 48 * q^87 + 22 * q^88 + 8 * q^92 + 8 * q^93 - 12 * q^94 + 66 * q^95 - 90 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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