LMFDB - Embedded newform 930.2.bg.i.421.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(121,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 0, 16]))

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

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

chi := DirichletCharacter("930.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bg (of order $15$, degree $8$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			421.2
Character	$\chi$	$=$	930.421
Dual form			930.2.bg.i.391.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(0.913545 - 0.406737i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(0.346545 + 0.384877i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.669131 - 0.743145i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(0.913545 - 0.406737i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(0.346545 + 0.384877i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.669131 - 0.743145i) q^{9} +(0.913545 + 0.406737i) q^{10} +(1.37238 - 0.291707i) q^{11} +(-0.104528 - 0.994522i) q^{12} +(0.710213 - 6.75723i) q^{13} +(0.506586 + 0.107678i) q^{14} +(0.809017 + 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.60681 + 0.341537i) q^{17} +(0.104528 - 0.994522i) q^{18} +(0.750150 + 7.13720i) q^{19} +(0.978148 - 0.207912i) q^{20} +(0.473128 + 0.210650i) q^{21} +(0.938814 - 1.04266i) q^{22} +(-1.43471 - 4.41557i) q^{23} +(-0.669131 - 0.743145i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-3.39722 - 5.88417i) q^{26} +(0.309017 - 0.951057i) q^{27} +(0.473128 - 0.210650i) q^{28} +(-2.09901 + 1.52502i) q^{29} +1.00000 q^{30} +(5.20799 - 1.96898i) q^{31} -1.00000 q^{32} +(1.13508 - 0.824683i) q^{33} +(1.50068 - 0.668148i) q^{34} +(-0.160041 + 0.492555i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(4.52921 - 7.84483i) q^{37} +(4.80202 + 5.33319i) q^{38} +(-2.09960 - 6.46191i) q^{39} +(0.669131 - 0.743145i) q^{40} +(6.59819 + 2.93770i) q^{41} +(0.506586 - 0.107678i) q^{42} +(0.865073 + 8.23062i) q^{43} +(0.146657 - 1.39535i) q^{44} +(0.978148 + 0.207912i) q^{45} +(-3.75611 - 2.72897i) q^{46} +(3.10749 + 2.25773i) q^{47} +(-0.978148 - 0.207912i) q^{48} +(0.703662 - 6.69490i) q^{49} +(0.104528 + 0.994522i) q^{50} +(1.60681 - 0.341537i) q^{51} +(-6.20704 - 2.76355i) q^{52} +(-9.00020 + 9.99574i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(0.938814 + 1.04266i) q^{55} +(0.258952 - 0.448518i) q^{56} +(3.58826 + 6.21504i) q^{57} +(-0.801751 + 2.46754i) q^{58} +(1.91088 - 0.850778i) q^{59} +(0.809017 - 0.587785i) q^{60} -11.8570 q^{61} +(3.05601 - 4.65411i) q^{62} +0.517903 q^{63} +(-0.809017 + 0.587785i) q^{64} +(6.20704 - 2.76355i) q^{65} +(0.433562 - 1.33437i) q^{66} +(-3.25096 - 5.63084i) q^{67} +(0.821352 - 1.42262i) q^{68} +(-3.10664 - 3.45028i) q^{69} +(0.160041 + 0.492555i) q^{70} +(-2.08376 + 2.31425i) q^{71} +(-0.913545 - 0.406737i) q^{72} +(-9.52021 + 2.02358i) q^{73} +(-0.946864 - 9.00881i) q^{74} +(-0.104528 + 0.994522i) q^{75} +(7.01969 + 1.49208i) q^{76} +(0.587861 + 0.427106i) q^{77} +(-5.49683 - 3.99368i) q^{78} +(-11.1305 - 2.36586i) q^{79} +(0.104528 - 0.994522i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(7.06478 - 1.50167i) q^{82} +(-8.74528 - 3.89365i) q^{83} +(0.346545 - 0.384877i) q^{84} +(0.507623 + 1.56230i) q^{85} +(5.53769 + 6.15023i) q^{86} +(-1.29726 + 2.24692i) q^{87} +(-0.701518 - 1.21506i) q^{88} +(-4.38230 + 13.4873i) q^{89} +(0.913545 - 0.406737i) q^{90} +(2.84682 - 2.06834i) q^{91} -4.64280 q^{92} +(3.95688 - 3.91703i) q^{93} +3.84107 q^{94} +(-5.80592 + 4.21825i) q^{95} +(-0.913545 + 0.406737i) q^{96} +(-2.17642 + 6.69832i) q^{97} +(-3.36589 - 5.82989i) q^{98} +(0.701518 - 1.21506i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{2} + 3 q^{3} - 6 q^{4} + 12 q^{5} + 12 q^{6} - 7 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q + 6 * q^2 + 3 * q^3 - 6 * q^4 + 12 * q^5 + 12 * q^6 - 7 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q + 6 q^{2} + 3 q^{3} - 6 q^{4} + 12 q^{5} + 12 q^{6} - 7 q^{7} + 6 q^{8} + 3 q^{9} + 3 q^{10} - 13 q^{11} + 3 q^{12} + 11 q^{13} - 8 q^{14} + 6 q^{15} - 6 q^{16} - 29 q^{17} - 3 q^{18} + 9 q^{19} - 3 q^{20} - 2 q^{21} - 17 q^{22} - 5 q^{23} - 3 q^{24} - 12 q^{25} + 9 q^{26} - 6 q^{27} - 2 q^{28} + 13 q^{29} + 24 q^{30} + 57 q^{31} - 24 q^{32} + 16 q^{33} + 29 q^{34} + q^{35} - 12 q^{36} - 24 q^{37} + 6 q^{38} - 17 q^{39} + 3 q^{40} + 32 q^{41} - 8 q^{42} + 49 q^{43} - 8 q^{44} - 3 q^{45} + 28 q^{47} + 3 q^{48} + 12 q^{49} - 3 q^{50} - 29 q^{51} - 19 q^{52} - 36 q^{53} + 6 q^{54} - 17 q^{55} - 3 q^{56} - 6 q^{57} + 2 q^{58} + 6 q^{60} + 33 q^{62} - 6 q^{63} - 6 q^{64} + 19 q^{65} + 4 q^{66} - 5 q^{67} + 11 q^{68} + 10 q^{69} - q^{70} - 11 q^{71} - 3 q^{72} - 13 q^{73} + 9 q^{74} + 3 q^{75} - 6 q^{76} + 4 q^{77} - 8 q^{78} - 68 q^{79} - 3 q^{80} + 3 q^{81} - 2 q^{82} + 10 q^{83} - 7 q^{84} + 2 q^{85} - 34 q^{86} + 11 q^{87} - 12 q^{88} + 55 q^{89} + 3 q^{90} + 38 q^{91} + 10 q^{92} + 19 q^{93} + 42 q^{94} + 18 q^{95} - 3 q^{96} - q^{97} + 63 q^{98} + 12 q^{99}+O(q^{100}) \) 24 * q + 6 * q^2 + 3 * q^3 - 6 * q^4 + 12 * q^5 + 12 * q^6 - 7 * q^7 + 6 * q^8 + 3 * q^9 + 3 * q^10 - 13 * q^11 + 3 * q^12 + 11 * q^13 - 8 * q^14 + 6 * q^15 - 6 * q^16 - 29 * q^17 - 3 * q^18 + 9 * q^19 - 3 * q^20 - 2 * q^21 - 17 * q^22 - 5 * q^23 - 3 * q^24 - 12 * q^25 + 9 * q^26 - 6 * q^27 - 2 * q^28 + 13 * q^29 + 24 * q^30 + 57 * q^31 - 24 * q^32 + 16 * q^33 + 29 * q^34 + q^35 - 12 * q^36 - 24 * q^37 + 6 * q^38 - 17 * q^39 + 3 * q^40 + 32 * q^41 - 8 * q^42 + 49 * q^43 - 8 * q^44 - 3 * q^45 + 28 * q^47 + 3 * q^48 + 12 * q^49 - 3 * q^50 - 29 * q^51 - 19 * q^52 - 36 * q^53 + 6 * q^54 - 17 * q^55 - 3 * q^56 - 6 * q^57 + 2 * q^58 + 6 * q^60 + 33 * q^62 - 6 * q^63 - 6 * q^64 + 19 * q^65 + 4 * q^66 - 5 * q^67 + 11 * q^68 + 10 * q^69 - q^70 - 11 * q^71 - 3 * q^72 - 13 * q^73 + 9 * q^74 + 3 * q^75 - 6 * q^76 + 4 * q^77 - 8 * q^78 - 68 * q^79 - 3 * q^80 + 3 * q^81 - 2 * q^82 + 10 * q^83 - 7 * q^84 + 2 * q^85 - 34 * q^86 + 11 * q^87 - 12 * q^88 + 55 * q^89 + 3 * q^90 + 38 * q^91 + 10 * q^92 + 19 * q^93 + 42 * q^94 + 18 * q^95 - 3 * q^96 - q^97 + 63 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{13}{15}\right)$

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 $

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	0.913545	−	0.406737i	0.527436	−	0.234830i
$3$	0.913545	−	0.406737i	0.527436	−	0.234830i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	0.346545	+	0.384877i	0.130982	+	0.145470i	0.805068	−	0.593183i	$-0.202129\pi$
$7$	0.346545	+	0.384877i	0.130982	+	0.145470i	−0.674086	+	0.738653i	$0.735462\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	0.669131	−	0.743145i	0.223044	−	0.247715i
$10$	0.913545	+	0.406737i	0.288888	+	0.128621i
$11$	1.37238	−	0.291707i	0.413787	−	0.0879531i	0.00368576	−	0.999993i	$-0.498827\pi$
$11$	1.37238	−	0.291707i	0.413787	−	0.0879531i	0.410101	+	0.912040i	$0.365493\pi$
$12$	−0.104528	−	0.994522i	−0.0301748	−	0.287094i
$13$	0.710213	−	6.75723i	0.196978	−	1.87412i	−0.234669	−	0.972075i	$-0.575401\pi$
$13$	0.710213	−	6.75723i	0.196978	−	1.87412i	0.431647	−	0.902043i	$-0.357933\pi$
$14$	0.506586	+	0.107678i	0.135391	+	0.0287782i
$15$	0.809017	+	0.587785i	0.208887	+	0.151765i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	1.60681	+	0.341537i	0.389708	+	0.0828349i	0.398598	−	0.917126i	$-0.369497\pi$
$17$	1.60681	+	0.341537i	0.389708	+	0.0828349i	−0.00889074	+	0.999960i	$0.502830\pi$
$18$	0.104528	−	0.994522i	0.0246376	−	0.234411i
$19$	0.750150	+	7.13720i	0.172096	+	1.63739i	0.650686	+	0.759347i	$0.274482\pi$
$19$	0.750150	+	7.13720i	0.172096	+	1.63739i	−0.478590	+	0.878039i	$0.658852\pi$
$20$	0.978148	−	0.207912i	0.218720	−	0.0464905i
$21$	0.473128	+	0.210650i	0.103245	+	0.0459677i
$22$	0.938814	−	1.04266i	0.200156	−	0.222295i
$23$	−1.43471	−	4.41557i	−0.299157	−	0.920710i	−0.981793	−	0.189952i	$-0.939167\pi$
$23$	−1.43471	−	4.41557i	−0.299157	−	0.920710i	0.682637	−	0.730758i	$-0.260833\pi$
$24$	−0.669131	−	0.743145i	−0.136586	−	0.151694i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−3.39722	−	5.88417i	−0.666251	−	1.15398i
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	0.473128	−	0.210650i	0.0894129	−	0.0398092i
$29$	−2.09901	+	1.52502i	−0.389777	+	0.283189i	−0.765364	−	0.643598i	$-0.777441\pi$
$29$	−2.09901	+	1.52502i	−0.389777	+	0.283189i	0.375587	+	0.926787i	$0.377441\pi$
$30$	1.00000			0.182574
$31$	5.20799	−	1.96898i	0.935382	−	0.353639i
$31$	5.20799	−	1.96898i	0.935382	−	0.353639i
$32$	−1.00000			−0.176777
$33$	1.13508	−	0.824683i	0.197592	−	0.143559i
$34$	1.50068	−	0.668148i	0.257365	−	0.114586i
$35$	−0.160041	+	0.492555i	−0.0270519	+	0.0832571i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	4.52921	−	7.84483i	0.744598	−	1.28968i	−0.205784	−	0.978597i	$-0.565974\pi$
$37$	4.52921	−	7.84483i	0.744598	−	1.28968i	0.950382	−	0.311085i	$-0.100692\pi$
$38$	4.80202	+	5.33319i	0.778991	+	0.865157i
$39$	−2.09960	−	6.46191i	−0.336205	−	1.03473i
$40$	0.669131	−	0.743145i	0.105799	−	0.117502i
$41$	6.59819	+	2.93770i	1.03046	+	0.458792i	0.851107	−	0.524992i	$-0.175932\pi$
$41$	6.59819	+	2.93770i	1.03046	+	0.458792i	0.179357	+	0.983784i	$0.442598\pi$
$42$	0.506586	−	0.107678i	0.0781679	−	0.0166151i
$43$	0.865073	+	8.23062i	0.131922	+	1.25516i	0.837465	+	0.546490i	$0.184036\pi$
$43$	0.865073	+	8.23062i	0.131922	+	1.25516i	−0.705543	+	0.708667i	$0.749297\pi$
$44$	0.146657	−	1.39535i	0.0221094	−	0.210357i
$45$	0.978148	+	0.207912i	0.145814	+	0.0309936i
$46$	−3.75611	−	2.72897i	−0.553808	−	0.402365i
$47$	3.10749	+	2.25773i	0.453274	+	0.329323i	0.790887	−	0.611962i	$-0.209619\pi$
$47$	3.10749	+	2.25773i	0.453274	+	0.329323i	−0.337613	+	0.941285i	$0.609619\pi$
$48$	−0.978148	−	0.207912i	−0.141183	−	0.0300095i
$49$	0.703662	−	6.69490i	0.100523	−	0.956414i
$50$	0.104528	+	0.994522i	0.0147826	+	0.140647i
$51$	1.60681	−	0.341537i	0.224998	−	0.0478248i
$52$	−6.20704	−	2.76355i	−0.860761	−	0.383236i
$53$	−9.00020	+	9.99574i	−1.23627	+	1.37302i	−0.333587	+	0.942719i	$0.608259\pi$
$53$	−9.00020	+	9.99574i	−1.23627	+	1.37302i	−0.902686	+	0.430301i	$0.858407\pi$
$54$	−0.309017	−	0.951057i	−0.0420519	−	0.129422i
$55$	0.938814	+	1.04266i	0.126590	+	0.140592i
$56$	0.258952	−	0.448518i	0.0346039	−	0.0599357i
$57$	3.58826	+	6.21504i	0.475276	+	0.823202i
$58$	−0.801751	+	2.46754i	−0.105275	+	0.324003i
$59$	1.91088	−	0.850778i	0.248775	−	0.110762i	−0.278561	−	0.960419i	$-0.589857\pi$
$59$	1.91088	−	0.850778i	0.248775	−	0.110762i	0.527336	+	0.849657i	$0.323191\pi$
$60$	0.809017	−	0.587785i	0.104444	−	0.0758827i
$61$	−11.8570			−1.51814			−0.759068	−	0.651012i	$-0.774345\pi$
$61$	−11.8570			−1.51814			−0.759068	+	0.651012i	$0.774345\pi$
$62$	3.05601	−	4.65411i	0.388114	−	0.591073i
$63$	0.517903			0.0652497
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	6.20704	−	2.76355i	0.769888	−	0.342776i
$66$	0.433562	−	1.33437i	0.0533678	−	0.164249i
$67$	−3.25096	−	5.63084i	−0.397169	−	0.687916i	0.596207	−	0.802831i	$-0.296674\pi$
$67$	−3.25096	−	5.63084i	−0.397169	−	0.687916i	−0.993375	+	0.114915i	$0.963340\pi$
$68$	0.821352	−	1.42262i	0.0996035	−	0.172518i
$69$	−3.10664	−	3.45028i	−0.373996	−	0.415364i
$70$	0.160041	+	0.492555i	0.0191286	+	0.0588716i
$71$	−2.08376	+	2.31425i	−0.247296	+	0.274651i	−0.853995	−	0.520282i	$-0.825827\pi$
$71$	−2.08376	+	2.31425i	−0.247296	+	0.274651i	0.606698	+	0.794932i	$0.292494\pi$
$72$	−0.913545	−	0.406737i	−0.107662	−	0.0479344i
$73$	−9.52021	+	2.02358i	−1.11426	+	0.236843i	−0.728019	−	0.685557i	$-0.759559\pi$
$73$	−9.52021	+	2.02358i	−1.11426	+	0.236843i	−0.386237	+	0.922399i	$0.626225\pi$
$74$	−0.946864	−	9.00881i	−0.110071	−	1.04725i
$75$	−0.104528	+	0.994522i	−0.0120699	+	0.114837i
$76$	7.01969	+	1.49208i	0.805214	+	0.171153i
$77$	0.587861	+	0.427106i	0.0669930	+	0.0486733i
$78$	−5.49683	−	3.99368i	−0.622393	−	0.452195i
$79$	−11.1305	−	2.36586i	−1.25228	−	0.266181i	−0.466409	−	0.884569i	$-0.654452\pi$
$79$	−11.1305	−	2.36586i	−1.25228	−	0.266181i	−0.785872	+	0.618389i	$0.787786\pi$
$80$	0.104528	−	0.994522i	0.0116866	−	0.111191i
$81$	−0.104528	−	0.994522i	−0.0116143	−	0.110502i
$82$	7.06478	−	1.50167i	0.780175	−	0.165831i
$83$	−8.74528	−	3.89365i	−0.959920	−	0.427384i	−0.133881	−	0.990997i	$-0.542744\pi$
$83$	−8.74528	−	3.89365i	−0.959920	−	0.427384i	−0.826039	+	0.563614i	$0.809411\pi$
$84$	0.346545	−	0.384877i	0.0378112	−	0.0419936i
$85$	0.507623	+	1.56230i	0.0550595	+	0.169456i
$86$	5.53769	+	6.15023i	0.597145	+	0.663196i
$87$	−1.29726	+	2.24692i	−0.139081	+	0.240895i
$88$	−0.701518	−	1.21506i	−0.0747820	−	0.129526i
$89$	−4.38230	+	13.4873i	−0.464523	+	1.42965i	0.395058	+	0.918656i	$0.370724\pi$
$89$	−4.38230	+	13.4873i	−0.464523	+	1.42965i	−0.859581	+	0.510999i	$0.829276\pi$
$90$	0.913545	−	0.406737i	0.0962961	−	0.0428738i
$91$	2.84682	−	2.06834i	0.298428	−	0.216821i
$92$	−4.64280			−0.484046
$93$	3.95688	−	3.91703i	0.410309	−	0.406177i
$94$	3.84107			0.396176
$95$	−5.80592	+	4.21825i	−0.595675	+	0.432783i
$96$	−0.913545	+	0.406737i	−0.0932383	+	0.0415124i
$97$	−2.17642	+	6.69832i	−0.220982	+	0.680112i	0.777693	+	0.628644i	$0.216390\pi$
$97$	−2.17642	+	6.69832i	−0.220982	+	0.680112i	−0.998675	+	0.0514675i	$0.983610\pi$
$98$	−3.36589	−	5.82989i	−0.340006	−	0.588908i
$99$	0.701518	−	1.21506i	0.0705052	−	0.122119i
$100$	0.669131	+	0.743145i	0.0669131	+	0.0743145i
$101$	0.827144	+	2.54569i	0.0823039	+	0.253305i	0.983738	−	0.179612i	$-0.0574842\pi$
$101$	0.827144	+	2.54569i	0.0823039	+	0.253305i	−0.901434	+	0.432917i	$0.857484\pi$
$102$	1.09918	−	1.22077i	0.108835	−	0.120874i
$103$	12.8372	+	5.71549i	1.26489	+	0.563164i	0.925950	−	0.377646i	$-0.123266\pi$
$103$	12.8372	+	5.71549i	1.26489	+	0.563164i	0.338936	+	0.940809i	$0.389933\pi$
$104$	−6.64597	+	1.41265i	−0.651691	+	0.138521i
$105$	0.0541357	+	0.515066i	0.00528310	+	0.0502653i
$106$	−1.40597	+	13.3769i	−0.136560	+	1.29928i
$107$	12.5883	+	2.67573i	1.21696	+	0.258672i	0.771265	−	0.636514i	$-0.219624\pi$
$107$	12.5883	+	2.67573i	1.21696	+	0.258672i	0.445692	+	0.895186i	$0.352958\pi$
$108$	−0.809017	−	0.587785i	−0.0778477	−	0.0565597i
$109$	3.25821	+	2.36723i	0.312080	+	0.226740i	0.732789	−	0.680456i	$-0.238218\pi$
$109$	3.25821	+	2.36723i	0.312080	+	0.226740i	−0.420708	+	0.907196i	$0.638218\pi$
$110$	1.37238	+	0.291707i	0.130851	+	0.0278132i
$111$	0.946864	−	9.00881i	0.0898723	−	0.855078i
$112$	−0.0541357	−	0.515066i	−0.00511534	−	0.0486692i
$113$	−3.03655	+	0.645439i	−0.285655	+	0.0607177i	−0.348511	−	0.937305i	$-0.613312\pi$
$113$	−3.03655	+	0.645439i	−0.285655	+	0.0607177i	0.0628560	+	0.998023i	$0.479979\pi$
$114$	6.55607	+	2.91895i	0.614032	+	0.273385i
$115$	3.10664	−	3.45028i	0.289696	−	0.321740i
$116$	0.801751	+	2.46754i	0.0744407	+	0.229105i
$117$	−4.54637	−	5.04926i	−0.420312	−	0.466804i
$118$	1.04586	−	1.81148i	0.0962791	−	0.166760i
$119$	0.425381	+	0.736781i	0.0389946	+	0.0675406i
$120$	0.309017	−	0.951057i	0.0282093	−	0.0868192i
$121$	−8.25068	+	3.67344i	−0.750062	+	0.333949i
$122$	−9.59253	+	6.96938i	−0.868467	+	0.630978i
$123$	7.22261			0.651241
$124$	−0.263252	−	5.56154i	−0.0236407	−	0.499441i
$125$	−1.00000			−0.0894427
$126$	0.418993	−	0.304416i	0.0373268	−	0.0271195i
$127$	−1.60865	+	0.716218i	−0.142745	+	0.0635540i	−0.476866	−	0.878976i	$-0.658227\pi$
$127$	−1.60865	+	0.716218i	−0.142745	+	0.0635540i	0.334121	+	0.942530i	$0.391561\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	4.13798	+	7.16719i	0.364328	+	0.631035i
$130$	3.39722	−	5.88417i	0.297956	−	0.516075i
$131$	8.83111	+	9.80794i	0.771578	+	0.856924i	0.992983	−	0.118258i	$-0.0377310\pi$
$131$	8.83111	+	9.80794i	0.771578	+	0.856924i	−0.221405	+	0.975182i	$0.571064\pi$
$132$	−0.433562	−	1.33437i	−0.0377367	−	0.116142i
$133$	−2.48699	+	2.76208i	−0.215649	+	0.239502i
$134$	−5.93981	−	2.64457i	−0.513121	−	0.228456i
$135$	0.978148	−	0.207912i	0.0841855	−	0.0178942i
$136$	−0.171709	−	1.63370i	−0.0147239	−	0.140089i
$137$	−0.497386	+	4.73231i	−0.0424946	+	0.404309i	0.952512	+	0.304501i	$0.0984896\pi$
$137$	−0.497386	+	4.73231i	−0.0424946	+	0.404309i	−0.995007	+	0.0998082i	$0.968177\pi$
$138$	−4.54135	−	0.965293i	−0.386585	−	0.0821712i
$139$	−8.31520	−	6.04134i	−0.705286	−	0.512420i	0.176364	−	0.984325i	$-0.443567\pi$
$139$	−8.31520	−	6.04134i	−0.705286	−	0.512420i	−0.881649	+	0.471905i	$0.843567\pi$
$140$	0.418993	+	0.304416i	0.0354113	+	0.0257278i
$141$	3.75714	+	0.798604i	0.316408	+	0.0672546i
$142$	−0.325515	+	3.09707i	−0.0273166	+	0.259900i
$143$	−0.996454	−	9.48063i	−0.0833277	−	0.792810i
$144$	−0.978148	+	0.207912i	−0.0815123	+	0.0173260i
$145$	−2.37021	−	1.05529i	−0.196836	−	0.0876368i
$146$	−6.51258	+	7.23295i	−0.538985	+	0.598603i
$147$	−2.08023	−	6.40230i	−0.171575	−	0.528053i
$148$	−6.06127	−	6.73172i	−0.498234	−	0.553344i
$149$	−6.95654	+	12.0491i	−0.569902	+	0.987099i	0.426673	+	0.904406i	$0.359686\pi$
$149$	−6.95654	+	12.0491i	−0.569902	+	0.987099i	−0.996575	+	0.0826934i	$0.973648\pi$
$150$	0.500000	+	0.866025i	0.0408248	+	0.0707107i
$151$	3.89055	−	11.9739i	0.316609	−	0.974421i	−0.658479	−	0.752599i	$-0.728800\pi$
$151$	3.89055	−	11.9739i	0.316609	−	0.974421i	0.975087	−	0.221822i	$-0.0712002\pi$
$152$	6.55607	−	2.91895i	0.531768	−	0.236758i
$153$	1.32897	−	0.965557i	0.107441	−	0.0780606i
$154$	0.726637			0.0585541
$155$	4.30918	+	3.52576i	0.346121	+	0.283196i
$156$	−6.79445			−0.543991
$157$	10.9764	−	7.97482i	0.876012	−	0.636460i	−0.0561814	−	0.998421i	$-0.517893\pi$
$157$	10.9764	−	7.97482i	0.876012	−	0.636460i	0.932193	+	0.361961i	$0.117893\pi$
$158$	−10.3954	+	4.62833i	−0.827013	+	0.368210i
$159$	−4.15646	+	12.7923i	−0.329629	+	1.01449i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	1.20226	−	2.08238i	0.0947515	−	0.164114i
$162$	−0.669131	−	0.743145i	−0.0525719	−	0.0583870i
$163$	−3.18655	−	9.80720i	−0.249590	−	0.768159i	−0.994848	−	0.101382i	$-0.967673\pi$
$163$	−3.18655	−	9.80720i	−0.249590	−	0.768159i	0.745258	−	0.666777i	$-0.232327\pi$
$164$	4.83287	−	5.36745i	0.377384	−	0.419127i
$165$	1.28174	+	0.570666i	0.0997830	+	0.0444263i
$166$	−9.36371	+	1.99032i	−0.726765	+	0.154479i
$167$	−0.169631	−	1.61393i	−0.0131265	−	0.124890i	0.985996	−	0.166767i	$-0.0533328\pi$
$167$	−0.169631	−	1.61393i	−0.0131265	−	0.124890i	−0.999123	+	0.0418773i	$0.986666\pi$
$168$	0.0541357	−	0.515066i	0.00417666	−	0.0397382i
$169$	−32.4398	−	6.89530i	−2.49537	−	0.530407i
$170$	1.32897	+	0.965557i	0.101928	+	0.0740548i
$171$	5.80592	+	4.21825i	0.443990	+	0.322578i
$172$	8.09510	+	1.72067i	0.617246	+	0.131200i
$173$	−1.81888	+	17.3055i	−0.138287	+	1.31571i	0.676711	+	0.736249i	$0.263405\pi$
$173$	−1.81888	+	17.3055i	−0.138287	+	1.31571i	−0.814998	+	0.579464i	$0.803262\pi$
$174$	0.271201	+	2.58031i	0.0205597	+	0.195613i
$175$	−0.506586	+	0.107678i	−0.0382943	+	0.00813971i
$176$	−1.28174	−	0.570666i	−0.0966145	−	0.0430156i
$177$	1.39963	−	1.55445i	0.105203	−	0.116839i
$178$	4.38230	+	13.4873i	0.328467	+	1.01092i
$179$	12.6668	+	14.0679i	0.946763	+	1.05149i	0.998603	+	0.0528318i	$0.0168247\pi$
$179$	12.6668	+	14.0679i	0.946763	+	1.05149i	−0.0518401	+	0.998655i	$0.516509\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	8.35502	+	14.4713i	0.621024	+	1.07564i	0.989295	+	0.145926i	$0.0466162\pi$
$181$	8.35502	+	14.4713i	0.621024	+	1.07564i	−0.368272	+	0.929718i	$0.620050\pi$
$182$	1.08739	−	3.34664i	0.0806027	−	0.248070i
$183$	−10.8319	+	4.82268i	−0.800719	+	0.356503i
$184$	−3.75611	+	2.72897i	−0.276904	+	0.201182i
$185$	9.05843			0.665989
$186$	0.898809	−	5.49474i	0.0659039	−	0.402894i
$187$	2.30477			0.168541
$188$	3.10749	−	2.25773i	0.226637	−	0.164662i
$189$	0.473128	−	0.210650i	0.0344150	−	0.0153226i
$190$	−2.21766	+	6.82527i	−0.160886	+	0.495157i
$191$	7.05781	+	12.2245i	0.510685	+	0.884532i	0.999923	+	0.0123822i	$0.00394147\pi$
$191$	7.05781	+	12.2245i	0.510685	+	0.884532i	−0.489238	+	0.872150i	$0.662725\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	1.10985	+	1.23261i	0.0798886	+	0.0887253i	0.781764	−	0.623575i	$-0.214320\pi$
$193$	1.10985	+	1.23261i	0.0798886	+	0.0887253i	−0.701875	+	0.712300i	$0.747654\pi$
$194$	2.17642	+	6.69832i	0.156258	+	0.480912i
$195$	4.54637	−	5.04926i	0.325573	−	0.361585i
$196$	−6.14978	−	2.73806i	−0.439270	−	0.195576i
$197$	22.0839	−	4.69407i	1.57341	−	0.334438i	0.663153	−	0.748484i	$-0.269218\pi$
$197$	22.0839	−	4.69407i	1.57341	−	0.334438i	0.910256	+	0.414045i	$0.135885\pi$
$198$	−0.146657	−	1.39535i	−0.0104225	−	0.0991631i
$199$	0.628204	−	5.97696i	0.0445322	−	0.423696i	−0.949430	−	0.313977i	$-0.898338\pi$
$199$	0.628204	−	5.97696i	0.0445322	−	0.423696i	0.993963	−	0.109718i	$-0.0349949\pi$
$200$	0.978148	+	0.207912i	0.0691655	+	0.0147016i
$201$	−5.26017	−	3.82174i	−0.371024	−	0.269565i
$202$	2.16549	+	1.57332i	0.152363	+	0.110699i
$203$	−1.31435	−	0.279373i	−0.0922492	−	0.0196082i
$204$	0.171709	−	1.63370i	0.0120221	−	0.114382i
$205$	0.754969	+	7.18305i	0.0527293	+	0.501686i
$206$	13.7450	−	2.92159i	0.957659	−	0.203557i
$207$	−4.24141	−	1.88840i	−0.294799	−	0.131253i
$208$	−4.54637	+	5.04926i	−0.315234	+	0.350103i
$209$	3.11146	+	9.57609i	0.215224	+	0.662392i
$210$	0.346545	+	0.384877i	0.0239139	+	0.0265591i
$211$	−11.7704	+	20.3870i	−0.810310	+	1.40350i	0.102338	+	0.994750i	$0.467368\pi$
$211$	−11.7704	+	20.3870i	−0.810310	+	1.40350i	−0.912647	+	0.408748i	$0.865966\pi$
$212$	6.72530	+	11.6486i	0.461895	+	0.800026i
$213$	−0.962318	+	2.96171i	−0.0659369	+	0.202933i
$214$	11.7569	−	5.23451i	0.803685	−	0.357824i
$215$	−6.69539	+	4.86448i	−0.456622	+	0.331755i
$216$	−1.00000			−0.0680414
$217$	2.56262	+	1.32210i	0.173962	+	0.0897498i
$218$	4.02738			0.272768
$219$	−7.87408	+	5.72085i	−0.532081	+	0.386580i
$220$	1.28174	−	0.570666i	0.0864146	−	0.0384743i
$221$	3.44902	−	10.6150i	0.232006	−	0.714042i
$222$	−4.52921	−	7.84483i	−0.303981	−	0.526511i
$223$	6.77292	−	11.7310i	0.453548	−	0.785568i	−0.545055	−	0.838400i	$-0.683491\pi$
$223$	6.77292	−	11.7310i	0.453548	−	0.785568i	0.998603	+	0.0528317i	$0.0168247\pi$
$224$	−0.346545	−	0.384877i	−0.0231545	−	0.0257157i
$225$	0.309017	+	0.951057i	0.0206011	+	0.0634038i
$226$	−2.07724	+	2.30701i	−0.138176	+	0.153460i
$227$	−18.4291	−	8.20515i	−1.22318	−	0.544595i	−0.309450	−	0.950916i	$-0.600145\pi$
$227$	−18.4291	−	8.20515i	−1.22318	−	0.544595i	−0.913731	+	0.406321i	$0.866812\pi$
$228$	7.01969	−	1.49208i	0.464890	−	0.0988155i
$229$	−2.21709	−	21.0942i	−0.146510	−	1.39395i	−0.782693	−	0.622408i	$-0.786155\pi$
$229$	−2.21709	−	21.0942i	−0.146510	−	1.39395i	0.636184	−	0.771538i	$-0.280512\pi$
$230$	0.485305	−	4.61737i	0.0320001	−	0.304460i
$231$	0.710758	+	0.151076i	0.0467644	+	0.00994009i
$232$	2.09901	+	1.52502i	0.137807	+	0.100123i
$233$	−21.5825	−	15.6806i	−1.41392	−	1.02727i	−0.992739	−	0.120292i	$-0.961617\pi$
$233$	−21.5825	−	15.6806i	−1.41392	−	1.02727i	−0.421178	−	0.906978i	$-0.638383\pi$
$234$	−6.64597	−	1.41265i	−0.434461	−	0.0923475i
$235$	−0.401501	+	3.82003i	−0.0261911	+	0.249191i
$236$	−0.218644	−	2.08026i	−0.0142325	−	0.135413i
$237$	−11.1305	+	2.36586i	−0.723005	+	0.153679i
$238$	0.777209	+	0.346036i	0.0503790	+	0.0224302i
$239$	−9.70377	+	10.7771i	−0.627685	+	0.697114i	−0.970175	−	0.242407i	$-0.922063\pi$
$239$	−9.70377	+	10.7771i	−0.627685	+	0.697114i	0.342490	+	0.939521i	$0.388730\pi$
$240$	−0.309017	−	0.951057i	−0.0199470	−	0.0613904i
$241$	−12.9581	−	14.3914i	−0.834702	−	0.927031i	0.163525	−	0.986539i	$-0.447713\pi$
$241$	−12.9581	−	14.3914i	−0.834702	−	0.927031i	−0.998228	+	0.0595081i	$0.981047\pi$
$242$	−4.51575	+	7.82150i	−0.290283	+	0.502785i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−3.66402	+	11.2767i	−0.234565	+	0.721916i
$245$	6.14978	−	2.73806i	0.392895	−	0.174928i
$246$	5.84322	−	4.24535i	0.372550	−	0.270673i
$247$	48.7605			3.10255
$248$	−3.48197	−	4.34464i	−0.221105	−	0.275885i
$249$	−9.57291			−0.606658
$250$	−0.809017	+	0.587785i	−0.0511667	+	0.0371748i
$251$	−7.66952	+	3.41469i	−0.484096	+	0.215533i	−0.634248	−	0.773130i	$-0.718690\pi$
$251$	−7.66952	+	3.41469i	−0.484096	+	0.215533i	0.150152	+	0.988663i	$0.452024\pi$
$252$	0.160041	−	0.492555i	0.0100816	−	0.0310281i
$253$	−3.25701	−	5.64130i	−0.204766	−	0.354666i
$254$	−0.880444	+	1.52497i	−0.0552440	+	0.0956854i
$255$	1.09918	+	1.22077i	0.0688335	+	0.0764474i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−17.7004	+	19.6583i	−1.10412	+	1.22625i	−0.132129	+	0.991232i	$0.542181\pi$
$257$	−17.7004	+	19.6583i	−1.10412	+	1.22625i	−0.971991	+	0.235017i	$0.924485\pi$
$258$	7.56046	+	3.36613i	0.470694	+	0.209566i
$259$	4.58887	−	0.975395i	0.285139	−	0.0606081i
$260$	−0.710213	−	6.75723i	−0.0440456	−	0.419066i
$261$	−0.271201	+	2.58031i	−0.0167869	+	0.159717i
$262$	12.9095	+	2.74399i	0.797550	+	0.169525i
$263$	25.9353	+	18.8431i	1.59924	+	1.16192i	0.888949	+	0.458006i	$0.151436\pi$
$263$	25.9353	+	18.8431i	1.59924	+	1.16192i	0.710290	+	0.703909i	$0.248564\pi$
$264$	−1.13508	−	0.824683i	−0.0698593	−	0.0507558i
$265$	−13.1567	−	2.79654i	−0.808207	−	0.171790i
$266$	−0.388505	+	3.69638i	−0.0238208	+	0.226640i
$267$	1.48236	+	14.1037i	0.0907191	+	0.863135i
$268$	−6.35985	+	1.35183i	−0.388489	+	0.0825760i
$269$	−24.1664	−	10.7596i	−1.47345	−	0.656022i	−0.496217	−	0.868198i	$-0.665278\pi$
$269$	−24.1664	−	10.7596i	−1.47345	−	0.656022i	−0.977231	+	0.212177i	$0.931945\pi$
$270$	0.669131	−	0.743145i	0.0407220	−	0.0452264i
$271$	−1.34570	−	4.14165i	−0.0817457	−	0.251587i	0.901828	−	0.432096i	$-0.142226\pi$
$271$	−1.34570	−	4.14165i	−0.0817457	−	0.251587i	−0.983573	+	0.180508i	$0.942226\pi$
$272$	−1.09918	−	1.22077i	−0.0666478	−	0.0740198i
$273$	1.75943	−	3.04743i	0.106486	−	0.184439i
$274$	2.37919	+	4.12088i	0.143732	+	0.248951i
$275$	−0.433562	+	1.33437i	−0.0261448	+	0.0804653i
$276$	−4.24141	+	1.88840i	−0.255303	+	0.113668i
$277$	19.2201	−	13.9642i	1.15482	−	0.839027i	0.165707	−	0.986175i	$-0.447009\pi$
$277$	19.2201	−	13.9642i	1.15482	−	0.839027i	0.989114	+	0.147148i	$0.0470094\pi$
$278$	−10.2781			−0.616442
$279$	2.02159	−	5.18779i	0.121029	−	0.310585i
$280$	0.517903			0.0309507
$281$	15.7964	−	11.4768i	0.942337	−	0.684648i	−0.00664513	−	0.999978i	$-0.502115\pi$
$281$	15.7964	−	11.4768i	0.942337	−	0.684648i	0.948982	+	0.315330i	$0.102115\pi$
$282$	3.50899	−	1.56230i	0.208958	−	0.0930339i
$283$	0.610454	−	1.87878i	0.0362877	−	0.111682i	−0.931272	−	0.364325i	$-0.881300\pi$
$283$	0.610454	−	1.87878i	0.0362877	−	0.111682i	0.967560	+	0.252643i	$0.0812998\pi$
$284$	1.55706	+	2.69691i	0.0923947	+	0.160032i
$285$	−3.58826	+	6.21504i	−0.212550	+	0.368147i
$286$	−6.37872	−	7.08429i	−0.377182	−	0.418903i
$287$	1.15591	+	3.55754i	0.0682315	+	0.209995i
$288$	−0.669131	+	0.743145i	−0.0394289	+	0.0437902i
$289$	−13.0651	−	5.81695i	−0.768535	−	0.342174i
$290$	−2.53783	+	0.539431i	−0.149026	+	0.0316765i
$291$	0.736198	+	7.00445i	0.0431567	+	0.410608i
$292$	−1.01736	+	9.67958i	−0.0595368	+	0.566455i
$293$	−9.56096	−	2.03224i	−0.558557	−	0.118725i	−0.0800215	−	0.996793i	$-0.525499\pi$
$293$	−9.56096	−	2.03224i	−0.558557	−	0.118725i	−0.478536	+	0.878068i	$0.658832\pi$
$294$	−5.44612	−	3.95684i	−0.317624	−	0.230768i
$295$	1.69223	+	1.22948i	0.0985257	+	0.0715831i
$296$	−8.86048	−	1.88335i	−0.515005	−	0.109468i
$297$	0.146657	−	1.39535i	0.00850991	−	0.0809664i
$298$	1.45431	+	13.8369i	0.0842461	+	0.801548i
$299$	−30.8560	+	6.55864i	−1.78445	+	0.379296i
$300$	0.913545	+	0.406737i	0.0527436	+	0.0234830i
$301$	−2.86799	+	3.18523i	−0.165308	+	0.183593i
$302$	−3.89055	−	11.9739i	−0.223876	−	0.689020i
$303$	1.79106	+	1.98917i	0.102894	+	0.114275i
$304$	3.58826	−	6.21504i	0.205801	−	0.356457i
$305$	−5.92851	−	10.2685i	−0.339465	−	0.587971i
$306$	0.507623	−	1.56230i	0.0290189	−	0.0893109i
$307$	0.472208	−	0.210240i	0.0269503	−	0.0119991i	−0.393217	−	0.919446i	$-0.628638\pi$
$307$	0.472208	−	0.210240i	0.0269503	−	0.0119991i	0.420168	+	0.907447i	$0.361971\pi$
$308$	0.587861	−	0.427106i	0.0334965	−	0.0243366i
$309$	14.0521			0.799394
$310$	5.55859	+	0.319529i	0.315707	+	0.0181480i
$311$	18.4787			1.04783			0.523917	−	0.851769i	$-0.324470\pi$
$311$	18.4787			1.04783			0.523917	+	0.851769i	$0.324470\pi$
$312$	−5.49683	+	3.99368i	−0.311196	+	0.226097i
$313$	21.3140	−	9.48961i	1.20474	−	0.536385i	0.296580	−	0.955008i	$-0.404154\pi$
$313$	21.3140	−	9.48961i	1.20474	−	0.536385i	0.908160	+	0.418624i	$0.137487\pi$
$314$	4.19261	−	12.9035i	0.236603	−	0.728188i
$315$	0.258952	+	0.448518i	0.0145903	+	0.0252711i
$316$	−5.68959	+	9.85466i	−0.320064	+	0.554368i
$317$	3.24783	+	3.60708i	0.182416	+	0.202594i	0.827417	−	0.561588i	$-0.189809\pi$
$317$	3.24783	+	3.60708i	0.182416	+	0.202594i	−0.645000	+	0.764182i	$0.723143\pi$
$318$	4.15646	+	12.7923i	0.233083	+	0.717355i
$319$	−2.43577	+	2.70520i	−0.136377	+	0.151462i
$320$	−0.913545	−	0.406737i	−0.0510687	−	0.0227373i
$321$	12.5883	−	2.67573i	0.702611	−	0.149344i
$322$	−0.251341	−	2.39135i	−0.0140067	−	0.133265i
$323$	−1.23227	+	11.7243i	−0.0685655	+	0.652357i
$324$	−0.978148	−	0.207912i	−0.0543415	−	0.0115506i
$325$	5.49683	+	3.99368i	0.304909	+	0.221529i
$326$	−8.34250	−	6.06118i	−0.462048	−	0.335698i
$327$	3.93937	+	0.837338i	0.217848	+	0.0463049i
$328$	0.754969	−	7.18305i	0.0416862	−	0.396617i
$329$	0.207939	+	1.97841i	0.0114640	+	0.109073i
$330$	1.37238	−	0.291707i	0.0755468	−	0.0160580i
$331$	9.17870	+	4.08662i	0.504507	+	0.224621i	0.643177	−	0.765718i	$-0.277616\pi$
$331$	9.17870	+	4.08662i	0.504507	+	0.224621i	−0.138670	+	0.990339i	$0.544283\pi$
$332$	−6.40552	+	7.11406i	−0.351549	+	0.390435i
$333$	−2.79921	−	8.61508i	−0.153396	−	0.472103i
$334$	−1.08588	−	1.20599i	−0.0594167	−	0.0659890i
$335$	3.25096	−	5.63084i	0.177619	−	0.307645i
$336$	−0.258952	−	0.448518i	−0.0141270	−	0.0244686i
$337$	−1.86380	+	5.73620i	−0.101528	+	0.312471i	−0.988900	−	0.148583i	$-0.952529\pi$
$337$	−1.86380	+	5.73620i	−0.101528	+	0.312471i	0.887372	+	0.461054i	$0.152529\pi$
$338$	−30.2973	+	13.4892i	−1.64796	+	0.733718i
$339$	−2.51150	+	1.82471i	−0.136406	+	0.0991048i
$340$	1.64270			0.0890881
$341$	6.57295	−	4.22138i	0.355945	−	0.228601i
$342$	7.17651			0.388061
$343$	5.75351	−	4.18017i	0.310661	−	0.225708i
$344$	7.56046	−	3.36613i	0.407633	−	0.181490i
$345$	1.43471	−	4.41557i	0.0772419	−	0.237726i
$346$	8.70042	+	15.0696i	0.467737	+	0.810145i
$347$	7.49939	−	12.9893i	0.402588	−	0.697303i	−0.591449	−	0.806342i	$-0.701444\pi$
$347$	7.49939	−	12.9893i	0.402588	−	0.697303i	0.994037	+	0.109039i	$0.0347773\pi$
$348$	1.73607	+	1.92811i	0.0930633	+	0.103357i
$349$	3.69454	+	11.3706i	0.197764	+	0.608656i	0.999933	+	0.0115587i	$0.00367932\pi$
$349$	3.69454	+	11.3706i	0.197764	+	0.608656i	−0.802169	+	0.597097i	$0.796321\pi$
$350$	−0.346545	+	0.384877i	−0.0185236	+	0.0205726i
$351$	−6.20704	−	2.76355i	−0.331307	−	0.147507i
$352$	−1.37238	+	0.291707i	−0.0731479	+	0.0155481i
$353$	−1.28716	−	12.2466i	−0.0685089	−	0.651818i	−0.973859	−	0.227153i	$-0.927058\pi$
$353$	−1.28716	−	12.2466i	−0.0685089	−	0.651818i	0.905350	−	0.424666i	$-0.139608\pi$
$354$	0.218644	−	2.08026i	0.0116208	−	0.110564i
$355$	−3.04607	−	0.647463i	−0.161669	−	0.0343638i
$356$	11.4730	+	8.33563i	0.608069	+	0.441788i
$357$	0.688281	+	0.500065i	0.0364277	+	0.0264663i
$358$	18.5166	+	3.93583i	0.978633	+	0.208015i
$359$	0.797635	−	7.58899i	0.0420976	−	0.400532i	−0.953101	−	0.302653i	$-0.902128\pi$
$359$	0.797635	−	7.58899i	0.0420976	−	0.400532i	0.995198	−	0.0978786i	$-0.0312057\pi$
$360$	−0.104528	−	0.994522i	−0.00550913	−	0.0524159i
$361$	−31.7921	+	6.75762i	−1.67327	+	0.355664i
$362$	15.2654	+	6.79658i	0.802330	+	0.357221i
$363$	−6.04325	+	6.71171i	−0.317188	+	0.352273i
$364$	−1.08739	−	3.34664i	−0.0569947	−	0.175412i
$365$	−6.51258	−	7.23295i	−0.340884	−	0.378590i
$366$	−5.92851	+	10.2685i	−0.309888	+	0.536742i
$367$	−11.3054	−	19.5815i	−0.590136	−	1.02215i	−0.994214	−	0.107421i	$-0.965741\pi$
$367$	−11.3054	−	19.5815i	−0.590136	−	1.02215i	0.404078	−	0.914725i	$-0.367592\pi$
$368$	−1.43471	+	4.41557i	−0.0747892	+	0.230177i
$369$	6.59819	−	2.93770i	0.343488	−	0.152931i
$370$	7.32842	−	5.32441i	0.380987	−	0.276803i
$371$	−6.96611			−0.361662
$372$	−2.50257	−	4.97364i	−0.129752	−	0.257871i
$373$	−3.59182			−0.185977			−0.0929886	−	0.995667i	$-0.529642\pi$
$373$	−3.59182			−0.185977			−0.0929886	+	0.995667i	$0.529642\pi$
$374$	1.86460	−	1.35471i	0.0964161	−	0.0700504i
$375$	−0.913545	+	0.406737i	−0.0471753	+	0.0210038i
$376$	1.18696	−	3.65308i	0.0612126	−	0.188393i
$377$	8.81417	+	15.2666i	0.453953	+	0.786270i
$378$	0.258952	−	0.448518i	0.0133190	−	0.0230693i
$379$	10.1297	+	11.2502i	0.520330	+	0.577885i	0.944837	−	0.327540i	$-0.106219\pi$
$379$	10.1297	+	11.2502i	0.520330	+	0.577885i	−0.424508	+	0.905424i	$0.639553\pi$
$380$	2.21766	+	6.82527i	0.113764	+	0.350129i
$381$	−1.17826	+	1.30859i	−0.0603643	+	0.0670413i
$382$	12.8953	+	5.74134i	0.659779	+	0.293752i
$383$	−2.43066	+	0.516654i	−0.124201	+	0.0263998i	−0.269593	−	0.962974i	$-0.586889\pi$
$383$	−2.43066	+	0.516654i	−0.124201	+	0.0263998i	0.145392	+	0.989374i	$0.453556\pi$
$384$	0.104528	+	0.994522i	0.00533420	+	0.0507515i
$385$	−0.0759542	+	0.722656i	−0.00387099	+	0.0368300i
$386$	1.62240	+	0.344851i	0.0825778	+	0.0175525i
$387$	6.69539	+	4.86448i	0.340346	+	0.247276i
$388$	5.69793	+	4.13979i	0.289269	+	0.210166i
$389$	−28.5289	−	6.06401i	−1.44647	−	0.307458i	−0.583256	−	0.812288i	$-0.698222\pi$
$389$	−28.5289	−	6.06401i	−1.44647	−	0.307458i	−0.863219	+	0.504830i	$0.831555\pi$
$390$	0.710213	−	6.75723i	0.0359631	−	0.342166i
$391$	−0.797212	−	7.58497i	−0.0403168	−	0.383588i
$392$	−6.58467	+	1.39961i	−0.332576	+	0.0706912i
$393$	12.0569	+	5.36806i	0.608189	+	0.270783i
$394$	15.1071	−	16.7781i	0.761085	−	0.845271i
$395$	−3.51636	−	10.8222i	−0.176927	−	0.544526i
$396$	−0.938814	−	1.04266i	−0.0471772	−	0.0523955i
$397$	−13.8994	+	24.0745i	−0.697591	+	1.20826i	0.271709	+	0.962379i	$0.412411\pi$
$397$	−13.8994	+	24.0745i	−0.697591	+	1.20826i	−0.969300	+	0.245883i	$0.920922\pi$
$398$	−3.00494	−	5.20472i	−0.150624	−	0.260889i
$399$	−1.14854	+	3.53483i	−0.0574987	+	0.176963i
$400$	0.913545	−	0.406737i	0.0456773	−	0.0203368i
$401$	3.46187	−	2.51519i	0.172877	−	0.125603i	−0.497982	−	0.867187i	$-0.665925\pi$
$401$	3.46187	−	2.51519i	0.172877	−	0.125603i	0.670859	+	0.741585i	$0.265925\pi$
$402$	−6.50193			−0.324287
$403$	−9.60605	−	36.5900i	−0.478511	−	1.82268i
$404$	2.67669			0.133171
$405$	0.809017	−	0.587785i	0.0402004	−	0.0292073i
$406$	−1.22754	+	0.546537i	−0.0609219	+	0.0271242i
$407$	3.92739	−	12.0873i	0.194673	−	0.599143i
$408$	−0.821352	−	1.42262i	−0.0406630	−	0.0704303i
$409$	−2.83791	+	4.91541i	−0.140326	+	0.243051i	−0.927619	−	0.373527i	$-0.878148\pi$
$409$	−2.83791	+	4.91541i	−0.140326	+	0.243051i	0.787293	+	0.616578i	$0.211482\pi$
$410$	4.83287	+	5.36745i	0.238679	+	0.265079i
$411$	1.47042	+	4.52549i	0.0725305	+	0.223226i
$412$	9.40266	−	10.4427i	0.463236	−	0.514476i
$413$	0.989650	+	0.440621i	0.0486975	+	0.0216815i
$414$	−4.54135	+	0.965293i	−0.223195	+	0.0474416i
$415$	−1.00064	−	9.52046i	−0.0491195	−	0.467341i
$416$	−0.710213	+	6.75723i	−0.0348211	+	0.331300i
$417$	−10.0535	−	2.13695i	−0.492324	−	0.104647i
$418$	8.14591	+	5.91835i	0.398430	+	0.289476i
$419$	−8.27988	−	6.01569i	−0.404499	−	0.293886i	0.366872	−	0.930271i	$-0.380429\pi$
$419$	−8.27988	−	6.01569i	−0.404499	−	0.293886i	−0.771371	+	0.636386i	$0.780429\pi$
$420$	0.506586	+	0.107678i	0.0247189	+	0.00525416i
$421$	1.15699	−	11.0080i	0.0563883	−	0.536499i	−0.929468	−	0.368904i	$-0.879733\pi$
$421$	1.15699	−	11.0080i	0.0563883	−	0.536499i	0.985856	−	0.167595i	$-0.0536002\pi$
$422$	2.46069	+	23.4119i	0.119784	+	1.13967i
$423$	3.75714	−	0.798604i	0.182678	−	0.0388294i
$424$	12.2877	+	5.47085i	0.596745	+	0.265688i
$425$	−1.09918	+	1.22077i	−0.0533182	+	0.0592159i
$426$	0.962318	+	2.96171i	0.0466244	+	0.143495i
$427$	−4.10899	−	4.56350i	−0.198848	−	0.220843i
$428$	6.43477	−	11.1453i	0.311036	−	0.538730i
$429$	−4.76643	−	8.25569i	−0.230125	−	0.398589i
$430$	−2.55741	+	7.87090i	−0.123329	+	0.379568i
$431$	11.4620	−	5.10322i	0.552106	−	0.245814i	−0.111669	−	0.993745i	$-0.535620\pi$
$431$	11.4620	−	5.10322i	0.552106	−	0.245814i	0.663775	+	0.747932i	$0.268953\pi$
$432$	−0.809017	+	0.587785i	−0.0389238	+	0.0282798i
$433$	24.5624			1.18039			0.590197	−	0.807259i	$-0.299050\pi$
$433$	24.5624			1.18039			0.590197	+	0.807259i	$0.299050\pi$
$434$	2.85031	−	0.436670i	0.136819	−	0.0209608i
$435$	−2.59452			−0.124398
$436$	3.25821	−	2.36723i	0.156040	−	0.113370i
$437$	30.4386	−	13.5521i	1.45607	−	0.648286i
$438$	−3.00763	+	9.25654i	−0.143710	+	0.442294i
$439$	−1.09881	−	1.90319i	−0.0524431	−	0.0908342i	0.838612	−	0.544729i	$-0.183367\pi$
$439$	−1.09881	−	1.90319i	−0.0524431	−	0.0908342i	−0.891055	+	0.453895i	$0.850034\pi$
$440$	0.701518	−	1.21506i	0.0334435	−	0.0579259i
$441$	−4.50444	−	5.00268i	−0.214497	−	0.238223i
$442$	−3.44902	−	10.6150i	−0.164053	−	0.504904i
$443$	12.4373	−	13.8131i	0.590916	−	0.656279i	−0.371317	−	0.928506i	$-0.621094\pi$
$443$	12.4373	−	13.8131i	0.590916	−	0.656279i	0.962233	+	0.272228i	$0.0877603\pi$
$444$	−8.27529	−	3.68440i	−0.392728	−	0.174854i
$445$	−13.8715	+	2.94848i	−0.657574	+	0.139772i
$446$	−1.41593	−	13.4716i	−0.0670460	−	0.637900i
$447$	−1.45431	+	13.8369i	−0.0687867	+	0.654461i
$448$	−0.506586	−	0.107678i	−0.0239339	−	0.00508732i
$449$	−16.9098	−	12.2857i	−0.798024	−	0.579798i	0.112310	−	0.993673i	$-0.464175\pi$
$449$	−16.9098	−	12.2857i	−0.798024	−	0.579798i	−0.910334	+	0.413875i	$0.864175\pi$
$450$	0.809017	+	0.587785i	0.0381374	+	0.0277085i
$451$	9.91214	+	2.10689i	0.466744	+	0.0992096i
$452$	−0.324497	+	3.08738i	−0.0152631	+	0.145218i
$453$	−1.31602	−	12.5211i	−0.0618321	−	0.588293i
$454$	−19.7323	+	4.19423i	−0.926083	+	0.196845i
$455$	3.21465	+	1.43125i	0.150705	+	0.0670982i
$456$	4.80202	−	5.33319i	0.224875	−	0.249749i
$457$	4.43801	+	13.6588i	0.207601	+	0.638931i	0.999597	+	0.0284039i	$0.00904247\pi$
$457$	4.43801	+	13.6588i	0.207601	+	0.638931i	−0.791995	+	0.610527i	$0.790958\pi$
$458$	−14.1925	−	15.7624i	−0.663174	−	0.736529i
$459$	0.821352	−	1.42262i	0.0383374	−	0.0664023i
$460$	−2.32140	−	4.02079i	−0.108236	−	0.187470i
$461$	9.37876	−	28.8649i	0.436812	−	1.34437i	−0.454405	−	0.890795i	$-0.650148\pi$
$461$	9.37876	−	28.8649i	0.436812	−	1.34437i	0.891218	−	0.453575i	$-0.149852\pi$
$462$	0.663816	−	0.295550i	0.0308835	−	0.0137502i
$463$	−22.9564	+	16.6788i	−1.06687	+	0.775129i	−0.975348	−	0.220674i	$-0.929174\pi$
$463$	−22.9564	+	16.6788i	−1.06687	+	0.775129i	−0.0915257	+	0.995803i	$0.529174\pi$
$464$	2.59452			0.120448
$465$	5.37069	+	1.46824i	0.249060	+	0.0680881i
$466$	−26.6774			−1.23581
$467$	31.5503	−	22.9226i	1.45997	−	1.06073i	0.476605	−	0.879117i	$-0.341867\pi$
$467$	31.5503	−	22.9226i	1.45997	−	1.06073i	0.983369	−	0.181616i	$-0.0581329\pi$
$468$	−6.20704	+	2.76355i	−0.286920	+	0.127745i
$469$	1.04057	−	3.20256i	0.0480493	−	0.147881i
$470$	1.92054	+	3.32647i	0.0885877	+	0.153438i
$471$	6.78379	−	11.7499i	0.312580	−	0.541405i
$472$	−1.39963	−	1.55445i	−0.0644233	−	0.0715493i
$473$	3.58814	+	11.0431i	0.164983	+	0.507764i
$474$	−7.61416	+	8.45638i	−0.349730	+	0.388414i
$475$	−6.55607	−	2.91895i	−0.300813	−	0.133931i
$476$	0.832170	−	0.176883i	0.0381425	−	0.00810743i
$477$	1.40597	+	13.3769i	0.0643749	+	0.612487i
$478$	−1.51588	+	14.4226i	−0.0693346	+	0.659675i
$479$	22.8367	+	4.85409i	1.04344	+	0.221789i	0.697586	−	0.716501i	$-0.254257\pi$
$479$	22.8367	+	4.85409i	1.04344	+	0.221789i	0.345850	+	0.938290i	$0.387591\pi$
$480$	−0.809017	−	0.587785i	−0.0369264	−	0.0268286i
$481$	−49.7926	−	36.1764i	−2.27035	−	1.64950i
$482$	−18.9423	−	4.02632i	−0.862800	−	0.183394i
$483$	0.251341	−	2.39135i	0.0114364	−	0.108810i
$484$	0.944048	+	8.98202i	0.0429113	+	0.408274i
$485$	−6.88913	+	1.46433i	−0.312819	+	0.0664918i
$486$	−0.913545	−	0.406737i	−0.0414393	−	0.0184499i
$487$	13.3657	−	14.8441i	0.605658	−	0.672652i	−0.359854	−	0.933009i	$-0.617174\pi$
$487$	13.3657	−	14.8441i	0.605658	−	0.672652i	0.965512	+	0.260357i	$0.0838402\pi$
$488$	3.66402	+	11.2767i	0.165862	+	0.510472i
$489$	−6.90001	−	7.66323i	−0.312029	−	0.346543i
$490$	3.36589	−	5.82989i	0.152055	−	0.263368i
$491$	3.78225	+	6.55104i	0.170690	+	0.295644i	0.938661	−	0.344840i	$-0.112067\pi$
$491$	3.78225	+	6.55104i	0.170690	+	0.295644i	−0.767971	+	0.640485i	$0.778734\pi$
$492$	2.23191	−	6.86911i	0.100622	−	0.309684i
$493$	−3.89356	+	1.73352i	−0.175357	+	0.0780740i
$494$	39.4480	−	28.6607i	1.77485	−	1.28950i
$495$	1.40304			0.0630617
$496$	−5.37069	−	1.46824i	−0.241151	−	0.0659260i
$497$	−1.61282			−0.0723447
$498$	−7.74464	+	5.62681i	−0.347046	+	0.252144i
$499$	12.5968	−	5.60843i	0.563908	−	0.251068i	−0.104926	−	0.994480i	$-0.533460\pi$
$499$	12.5968	−	5.60843i	0.563908	−	0.251068i	0.668834	+	0.743412i	$0.266794\pi$
$500$	−0.309017	+	0.951057i	−0.0138197	+	0.0425325i
$501$	−0.811411	−	1.40541i	−0.0362512	−	0.0627889i
$502$	−4.19767	+	7.27057i	−0.187351	+	0.324501i
$503$	−3.17599	−	3.52729i	−0.141610	−	0.157274i	0.668167	−	0.744011i	$-0.267079\pi$
$503$	−3.17599	−	3.52729i	−0.141610	−	0.157274i	−0.809778	+	0.586737i	$0.800412\pi$
$504$	−0.160041	−	0.492555i	−0.00712879	−	0.0219402i
$505$	−1.79106	+	1.98917i	−0.0797010	+	0.0885170i
$506$	−5.95085	−	2.64949i	−0.264548	−	0.117784i
$507$	−32.4398	+	6.89530i	−1.44070	+	0.306231i
$508$	0.184063	+	1.75124i	0.00816647	+	0.0776988i
$509$	0.183276	−	1.74375i	0.00812355	−	0.0772904i	−0.989709	−	0.143095i	$-0.954295\pi$
$509$	0.183276	−	1.74375i	0.00812355	−	0.0772904i	0.997833	+	0.0658043i	$0.0209613\pi$
$510$	1.60681	+	0.341537i	0.0711506	+	0.0151235i
$511$	−4.07801	−	2.96285i	−0.180401	−	0.131069i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	7.01969	+	1.49208i	0.309927	+	0.0658770i
$514$	−2.76507	+	26.3079i	−0.121962	+	1.16039i
$515$	1.46884	+	13.9751i	0.0647248	+	0.615816i
$516$	8.09510	−	1.72067i	0.356367	−	0.0757482i
$517$	4.92324	+	2.19197i	0.216524	+	0.0964027i
$518$	3.13915	−	3.48638i	0.137927	−	0.153183i
$519$	5.37715	+	16.5492i	0.236031	+	0.726428i
$520$	−4.54637	−	5.04926i	−0.199372	−	0.221425i
$521$	4.32917	−	7.49834i	0.189664	−	0.328508i	−0.755474	−	0.655179i	$-0.772593\pi$
$521$	4.32917	−	7.49834i	0.189664	−	0.328508i	0.945138	+	0.326670i	$0.105927\pi$
$522$	1.29726	+	2.24692i	0.0567796	+	0.0983451i
$523$	12.2512	−	37.7053i	0.535707	−	1.64874i	−0.206408	−	0.978466i	$-0.566177\pi$
$523$	12.2512	−	37.7053i	0.535707	−	1.64874i	0.742116	−	0.670272i	$-0.233823\pi$
$524$	12.0569	−	5.36806i	0.526707	−	0.234505i
$525$	−0.418993	+	0.304416i	−0.0182863	+	0.0132858i
$526$	32.0578			1.39779
$527$	9.04070	−	1.38504i	0.393819	−	0.0603334i
$528$	−1.40304			−0.0610593
$529$	1.16852	−	0.848979i	0.0508052	−	0.0369121i
$530$	−12.2877	+	5.47085i	−0.533745	+	0.237638i
$531$	0.646376	−	1.98934i	0.0280503	−	0.0863300i
$532$	1.85837	+	3.21879i	0.0805706	+	0.139552i
$533$	24.5368	−	42.4991i	1.06281	−	1.84084i
$534$	9.48923	+	10.5389i	0.410639	+	0.456061i
$535$	3.97690	+	12.2397i	0.171937	+	0.529166i
$536$	−4.35064	+	4.83187i	−0.187919	+	0.208705i
$537$	17.2937	+	7.69964i	0.746277	+	0.332264i
$538$	−25.8753	+	5.49996i	−1.11556	+	0.237120i
$539$	−0.987263	−	9.39318i	−0.0425244	−	0.404593i
$540$	0.104528	−	0.994522i	0.00449819	−	0.0427974i
$541$	−13.7617	−	2.92513i	−0.591660	−	0.125761i	−0.0976550	−	0.995220i	$-0.531134\pi$
$541$	−13.7617	−	2.92513i	−0.591660	−	0.125761i	−0.494005	+	0.869459i	$0.664468\pi$
$542$	−3.52310	−	2.55968i	−0.151330	−	0.109948i
$543$	13.5187	+	9.82191i	0.580143	+	0.421499i
$544$	−1.60681	−	0.341537i	−0.0688912	−	0.0146433i
$545$	−0.420975	+	4.00531i	−0.0180326	+	0.171569i
$546$	−0.367822	−	3.49959i	−0.0157413	−	0.149769i
$547$	23.9213	−	5.08462i	1.02280	−	0.217403i	0.334167	−	0.942514i	$-0.391545\pi$
$547$	23.9213	−	5.08462i	1.02280	−	0.217403i	0.688632	+	0.725111i	$0.258212\pi$
$548$	4.34700	+	1.93541i	0.185695	+	0.0826765i
$549$	−7.93389	+	8.81148i	−0.338610	+	0.376065i
$550$	0.433562	+	1.33437i	0.0184871	+	0.0568975i
$551$	−12.4590	−	13.8371i	−0.530769	−	0.589479i
$552$	−2.32140	+	4.02079i	−0.0988054	+	0.171136i
$553$	−2.94666	−	5.10376i	−0.125305	−	0.217034i
$554$	7.34141	−	22.5945i	0.311907	−	0.959950i
$555$	8.27529	−	3.68440i	0.351266	−	0.156394i
$556$	−8.31520	+	6.04134i	−0.352643	+	0.256210i
$557$	−39.4675			−1.67229			−0.836145	−	0.548509i	$-0.815196\pi$
$557$	−39.4675			−1.67229			−0.836145	+	0.548509i	$0.815196\pi$
$558$	−1.41381	−	5.38527i	−0.0598513	−	0.227977i
$559$	56.2305			2.37830
$560$	0.418993	−	0.304416i	0.0177057	−	0.0128639i
$561$	2.10551	−	0.937434i	0.0888948	−	0.0395785i
$562$	6.03371	−	18.5698i	0.254516	−	0.783321i
$563$	10.7289	+	18.5830i	0.452168	+	0.783179i	0.998520	−	0.0543769i	$-0.0173173\pi$
$563$	10.7289	+	18.5830i	0.452168	+	0.783179i	−0.546352	+	0.837556i	$0.683984\pi$
$564$	1.92054	−	3.32647i	0.0808692	−	0.140070i
$565$	−2.07724	−	2.30701i	−0.0873902	−	0.0970566i
$566$	−0.610454	−	1.87878i	−0.0256593	−	0.0789712i
$567$	0.346545	−	0.384877i	0.0145535	−	0.0161633i
$568$	2.84490	+	1.26663i	0.119369	+	0.0531466i
$569$	−21.1695	+	4.49972i	−0.887472	+	0.188638i	−0.629023	−	0.777387i	$-0.716545\pi$
$569$	−21.1695	+	4.49972i	−0.887472	+	0.188638i	−0.258449	+	0.966025i	$0.583212\pi$
$570$	0.750150	+	7.13720i	0.0314203	+	0.298944i
$571$	−3.68034	+	35.0161i	−0.154017	+	1.46538i	0.595480	+	0.803370i	$0.296962\pi$
$571$	−3.68034	+	35.0161i	−0.154017	+	1.46538i	−0.749497	+	0.662008i	$0.769705\pi$
$572$	−9.32454	−	1.98199i	−0.389878	−	0.0828712i
$573$	11.4198	+	8.29695i	0.477068	+	0.346610i
$574$	3.02622	+	2.19868i	0.126312	+	0.0917711i
$575$	4.54135	+	0.965293i	0.189387	+	0.0402555i
$576$	−0.104528	+	0.994522i	−0.00435535	+	0.0414384i
$577$	−2.35620	−	22.4178i	−0.0980899	−	0.933263i	−0.927298	−	0.374323i	$-0.877875\pi$
$577$	−2.35620	−	22.4178i	−0.0980899	−	0.933263i	0.829208	−	0.558940i	$-0.188792\pi$
$578$	−13.9890	+	2.97345i	−0.581866	+	0.123679i
$579$	1.51524	+	0.674630i	0.0629714	+	0.0280367i
$580$	−1.73607	+	1.92811i	−0.0720866	+	0.0800602i
$581$	−1.53206	−	4.71519i	−0.0635604	−	0.195619i
$582$	4.71271	+	5.23399i	0.195348	+	0.216956i
$583$	−9.43583	+	16.3433i	−0.390792	+	0.676872i
$584$	4.86645	+	8.42894i	0.201375	+	0.348792i
$585$	2.09960	−	6.46191i	0.0868078	−	0.267167i
$586$	−8.92950	+	3.97567i	−0.368874	+	0.164233i
$587$	−11.8000	+	8.57320i	−0.487038	+	0.353854i	−0.804044	−	0.594570i	$-0.797322\pi$
$587$	−11.8000	+	8.57320i	−0.487038	+	0.353854i	0.317006	+	0.948424i	$0.397322\pi$
$588$	−6.73178			−0.277614
$589$	17.9598	+	35.6934i	0.740019	+	1.47072i
$590$	2.09172			0.0861146
$591$	18.2654	−	13.2706i	0.751336	−	0.545878i
$592$	−8.27529	+	3.68440i	−0.340112	+	0.151428i
$593$	2.65959	−	8.18537i	0.109216	−	0.336133i	−0.881481	−	0.472220i	$-0.843453\pi$
$593$	2.65959	−	8.18537i	0.109216	−	0.336133i	0.990697	+	0.136087i	$0.0434527\pi$
$594$	−0.701518	−	1.21506i	−0.0287836	−	0.0498547i
$595$	−0.425381	+	0.736781i	−0.0174389	+	0.0302051i
$596$	9.30967	+	10.3394i	0.381339	+	0.423520i
$597$	−1.85716	−	5.71574i	−0.0760084	−	0.233930i
$598$	−21.1079	+	23.4427i	−0.863167	+	0.958644i
$599$	−29.7871	−	13.2621i	−1.21707	−	0.541874i	−0.305174	−	0.952297i	$-0.598715\pi$
$599$	−29.7871	−	13.2621i	−1.21707	−	0.541874i	−0.911896	+	0.410422i	$0.865381\pi$
$600$	0.978148	−	0.207912i	0.0399327	−	0.00848796i
$601$	−1.30850	−	12.4495i	−0.0533746	−	0.507826i	−0.988250	−	0.152849i	$-0.951155\pi$
$601$	−1.30850	−	12.4495i	−0.0533746	−	0.507826i	0.934875	−	0.354977i	$-0.115511\pi$
$602$	−0.448024	+	4.26266i	−0.0182601	+	0.173733i
$603$	−6.35985	−	1.35183i	−0.258993	−	0.0550507i
$604$	−10.1856	−	7.40027i	−0.414446	−	0.301113i
$605$	−7.30663	−	5.30858i	−0.297057	−	0.215824i
$606$	2.61820	+	0.556516i	0.106357	+	0.0226069i
$607$	2.39427	−	22.7799i	0.0971803	−	0.924609i	−0.831949	−	0.554853i	$-0.812775\pi$
$607$	2.39427	−	22.7799i	0.0971803	−	0.924609i	0.929129	−	0.369756i	$-0.120559\pi$
$608$	−0.750150	−	7.13720i	−0.0304226	−	0.289452i
$609$	−1.31435	+	0.279373i	−0.0532601	+	0.0113208i
$610$	−10.8319	−	4.82268i	−0.438572	−	0.195265i
$611$	17.4630	−	19.3946i	0.706475	−	0.784620i
$612$	−0.507623	−	1.56230i	−0.0205195	−	0.0631524i
$613$	11.8954	+	13.2111i	0.480449	+	0.533593i	0.933827	−	0.357726i	$-0.116448\pi$
$613$	11.8954	+	13.2111i	0.480449	+	0.533593i	−0.453377	+	0.891319i	$0.649781\pi$
$614$	0.258448	−	0.447645i	0.0104301	−	0.0180655i
$615$	3.61131	+	6.25497i	0.145622	+	0.252225i
$616$	0.224543	−	0.691073i	0.00904710	−	0.0278441i
$617$	6.88409	−	3.06500i	0.277143	−	0.123392i	−0.263459	−	0.964671i	$-0.584863\pi$
$617$	6.88409	−	3.06500i	0.277143	−	0.123392i	0.540602	+	0.841279i	$0.318197\pi$
$618$	11.3684	−	8.25959i	0.457302	−	0.332250i
$619$	−16.4919			−0.662866			−0.331433	−	0.943479i	$-0.607532\pi$
$619$	−16.4919			−0.662866			−0.331433	+	0.943479i	$0.607532\pi$
$620$	4.68481	−	3.00875i	0.188146	−	0.120834i
$621$	−4.64280			−0.186309
$622$	14.9496	−	10.8615i	0.599425	−	0.435508i
$623$	−6.70964	+	2.98732i	−0.268816	+	0.119685i
$624$	−2.09960	+	6.46191i	−0.0840513	+	0.258683i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	11.6655	−	20.2053i	0.466249	−	0.807567i
$627$	6.73741	+	7.48265i	0.269066	+	0.298828i
$628$	−4.19261	−	12.9035i	−0.167303	−	0.514907i
$629$	9.95687	−	11.0582i	0.397006	−	0.440920i
$630$	0.473128	+	0.210650i	0.0188499	+	0.00839251i
$631$	3.87204	−	0.823028i	0.154144	−	0.0327642i	−0.130193	−	0.991489i	$-0.541560\pi$
$631$	3.87204	−	0.823028i	0.154144	−	0.0327642i	0.284337	+	0.958724i	$0.408227\pi$
$632$	1.18945	+	11.3168i	0.0473137	+	0.450160i
$633$	−2.46069	+	23.4119i	−0.0978036	+	0.930539i
$634$	4.74774	+	1.00916i	0.188557	+	0.0400790i
$635$	−1.42459	−	1.03502i	−0.0565331	−	0.0410737i
$636$	10.8818	+	7.90606i	0.431490	+	0.313496i
$637$	−44.7392	−	9.50961i	−1.77263	−	0.376785i
$638$	−0.380505	+	3.62026i	−0.0150643	+	0.143328i
$639$	0.325515	+	3.09707i	0.0128772	+	0.122518i
$640$	−0.978148	+	0.207912i	−0.0386647	+	0.00821843i
$641$	−20.3541	−	9.06223i	−0.803938	−	0.357936i	−0.0367226	−	0.999325i	$-0.511692\pi$
$641$	−20.3541	−	9.06223i	−0.803938	−	0.357936i	−0.767216	+	0.641389i	$0.778358\pi$
$642$	8.61140	−	9.56393i	0.339865	−	0.377458i
$643$	6.35310	+	19.5528i	0.250542	+	0.771088i	0.994675	+	0.103057i	$0.0328625\pi$
$643$	6.35310	+	19.5528i	0.250542	+	0.771088i	−0.744134	+	0.668031i	$0.767138\pi$
$644$	−1.60894	−	1.78691i	−0.0634012	−	0.0704141i
$645$	−4.13798	+	7.16719i	−0.162933	+	0.282208i
$646$	5.89444	+	10.2095i	0.231914	+	0.401686i
$647$	9.63975	−	29.6681i	0.378978	−	1.16637i	−0.561778	−	0.827288i	$-0.689883\pi$
$647$	9.63975	−	29.6681i	0.378978	−	1.16637i	0.940756	−	0.339085i	$-0.110117\pi$
$648$	−0.913545	+	0.406737i	−0.0358875	+	0.0159781i
$649$	2.37426	−	1.72500i	0.0931980	−	0.0677123i
$650$	6.79445			0.266500
$651$	2.87881	+	0.165485i	0.112830	+	0.00648587i
$652$	−10.3119			−0.403845
$653$	19.5667	−	14.2160i	0.765703	−	0.556316i	−0.134951	−	0.990852i	$-0.543088\pi$
$653$	19.5667	−	14.2160i	0.765703	−	0.556316i	0.900654	+	0.434536i	$0.143088\pi$
$654$	3.67919	−	1.63808i	0.143868	−	0.0640540i
$655$	−4.07837	+	12.5519i	−0.159355	+	0.490445i
$656$	−3.61131	−	6.25497i	−0.140998	−	0.244215i
$657$	−4.86645	+	8.42894i	−0.189858	+	0.328844i
$658$	1.33110	+	1.47834i	0.0518919	+	0.0576318i
$659$	−4.87050	−	14.9899i	−0.189728	−	0.583922i	0.810270	−	0.586057i	$-0.199321\pi$
$659$	−4.87050	−	14.9899i	−0.189728	−	0.583922i	−0.999998	+	0.00213464i	$0.999321\pi$
$660$	0.938814	−	1.04266i	0.0365433	−	0.0405854i
$661$	−30.1711	−	13.4330i	−1.17352	−	0.522484i	−0.275010	−	0.961441i	$-0.588681\pi$
$661$	−30.1711	−	13.4330i	−1.17352	−	0.522484i	−0.898508	+	0.438957i	$0.855348\pi$
$662$	9.82778	−	2.08896i	0.381968	−	0.0811897i
$663$	−1.16667	−	11.1001i	−0.0453097	−	0.431093i
$664$	−1.00064	+	9.52046i	−0.0388324	+	0.369466i
$665$	−3.63552	−	0.772754i	−0.140979	−	0.0299661i
$666$	−7.32842	−	5.32441i	−0.283971	−	0.206317i
$667$	9.74530	+	7.08038i	0.377340	+	0.274153i
$668$	−1.58736	−	0.337404i	−0.0614168	−	0.0130545i
$669$	1.41593	−	13.4716i	0.0547428	−	0.520843i
$670$	−0.679637	−	6.46631i	−0.0262567	−	0.249815i
$671$	−16.2723	+	3.45878i	−0.628184	+	0.133525i
$672$	−0.473128	−	0.210650i	−0.0182513	−	0.00812601i
$673$	10.2422	−	11.3752i	0.394809	−	0.438480i	−0.512664	−	0.858589i	$-0.671341\pi$
$673$	10.2422	−	11.3752i	0.394809	−	0.438480i	0.907474	+	0.420109i	$0.138008\pi$
$674$	1.86380	+	5.73620i	0.0717911	+	0.220950i
$675$	0.669131	+	0.743145i	0.0257548	+	0.0286037i
$676$	−16.5823	+	28.7213i	−0.637780	+	1.10467i
$677$	3.20564	+	5.55233i	0.123203	+	0.213394i	0.921029	−	0.389494i	$-0.127350\pi$
$677$	3.20564	+	5.55233i	0.123203	+	0.213394i	−0.797826	+	0.602888i	$0.794017\pi$
$678$	−0.959309	+	2.95245i	−0.0368420	+	0.113388i
$679$	−3.33226	+	1.48362i	−0.127880	+	0.0569360i
$680$	1.32897	−	0.965557i	0.0509639	−	0.0370274i
$681$	−20.1731			−0.773036
$682$	2.83636	−	7.27865i	0.108610	−	0.278714i
$683$	−35.5676			−1.36096			−0.680479	−	0.732768i	$-0.738228\pi$
$683$	−35.5676			−1.36096			−0.680479	+	0.732768i	$0.738228\pi$
$684$	5.80592	−	4.21825i	0.221995	−	0.161289i
$685$	−4.34700	+	1.93541i	−0.166090	+	0.0739481i
$686$	2.19765	−	6.76366i	0.0839065	−	0.258238i
$687$	−10.6052	−	18.3688i	−0.404614	−	0.700812i
$688$	4.13798	−	7.16719i	0.157759	−	0.273246i
$689$	61.1514	+	67.9155i	2.32968	+	2.58738i
$690$	−1.43471	−	4.41557i	−0.0546183	−	0.168098i
$691$	−29.7059	+	32.9918i	−1.13007	+	1.25507i	−0.166955	+	0.985965i	$0.553393\pi$
$691$	−29.7059	+	32.9918i	−1.13007	+	1.25507i	−0.963112	+	0.269102i	$0.913273\pi$
$692$	15.8964	+	7.07756i	0.604292	+	0.269048i
$693$	0.710758	−	0.151076i	0.0269995	−	0.00573891i
$694$	−1.56780	−	14.9166i	−0.0595129	−	0.566227i
$695$	1.07436	−	10.2218i	0.0407528	−	0.387737i
$696$	2.53783	+	0.539431i	0.0961960	+	0.0204471i
$697$	9.59867	+	6.97384i	0.363576	+	0.264153i
$698$	9.67243	+	7.02743i	0.366107	+	0.265992i
$699$	−26.0945	−	5.54655i	−0.986983	−	0.209790i
$700$	−0.0541357	+	0.515066i	−0.00204614	+	0.0194677i
$701$	0.284998	+	2.71157i	0.0107642	+	0.102415i	0.998585	−	0.0531824i	$-0.0169365\pi$
$701$	0.284998	+	2.71157i	0.0107642	+	0.102415i	−0.987821	+	0.155597i	$0.950270\pi$
$702$	−6.64597	+	1.41265i	−0.250836	+	0.0533169i
$703$	59.3877	+	26.4411i	2.23985	+	0.997245i
$704$	−0.938814	+	1.04266i	−0.0353829	+	0.0392967i
$705$	1.18696	+	3.65308i	0.0447034	+	0.137583i
$706$	−8.23968	−	9.15109i	−0.310104	−	0.344406i
$707$	−0.693135	+	1.20054i	−0.0260680	+	0.0451511i
$708$	−1.04586	−	1.81148i	−0.0393058	−	0.0680796i
$709$	−2.60729	+	8.02441i	−0.0979188	+	0.301363i	−0.988003	−	0.154432i	$-0.950645\pi$
$709$	−2.60729	+	8.02441i	−0.0979188	+	0.301363i	0.890085	+	0.455795i	$0.150645\pi$
$710$	−2.84490	+	1.26663i	−0.106767	+	0.0475357i
$711$	−9.20595	+	6.68851i	−0.345250	+	0.250839i
$712$	14.1814			0.531471
$713$	−16.1661	−	20.1713i	−0.605425	−	0.755422i
$714$	0.850762			0.0318390
$715$	7.71224	−	5.60327i	0.288421	−	0.209550i
$716$	17.2937	−	7.69964i	0.646295	−	0.287749i
$717$	−4.48138	+	13.7923i	−0.167360	+	0.515082i
$718$	−3.81540	−	6.60846i	−0.142389	−	0.246626i
$719$	20.6084	−	35.6949i	0.768565	−	1.33119i	−0.169776	−	0.985483i	$-0.554304\pi$
$719$	20.6084	−	35.6949i	0.768565	−	1.33119i	0.938341	−	0.345711i	$-0.112362\pi$
$720$	−0.669131	−	0.743145i	−0.0249370	−	0.0276954i
$721$	2.24890	+	6.92142i	0.0837536	+	0.257767i
$722$	−21.7483	+	24.1539i	−0.809388	+	0.898917i
$723$	−17.6913	−	7.87667i	−0.657946	−	0.292936i
$724$	16.3449	−	3.47421i	0.607453	−	0.129118i
$725$	−0.271201	−	2.58031i	−0.0100722	−	0.0958303i
$726$	−0.944048	+	8.98202i	−0.0350369	+	0.333354i
$727$	−0.608231	−	0.129284i	−0.0225580	−	0.00479486i	0.196619	−	0.980480i	$-0.437004\pi$
$727$	−0.608231	−	0.129284i	−0.0225580	−	0.00479486i	−0.219177	+	0.975685i	$0.570337\pi$
$728$	−2.84682	−	2.06834i	−0.105510	−	0.0766578i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−9.52021	−	2.02358i	−0.352359	−	0.0748962i
$731$	−1.42106	+	13.5205i	−0.0525597	+	0.500072i
$732$	1.23940	+	11.7921i	0.0458094	+	0.435847i
$733$	16.4600	−	3.49867i	0.607962	−	0.129226i	0.106364	−	0.994327i	$-0.466079\pi$
$733$	16.4600	−	3.49867i	0.607962	−	0.129226i	0.501598	+	0.865101i	$0.332746\pi$
$734$	−20.6560	−	9.19662i	−0.762425	−	0.339454i
$735$	4.50444	−	5.00268i	0.166149	−	0.184527i
$736$	1.43471	+	4.41557i	0.0528839	+	0.162760i
$737$	−6.10410	−	6.77929i	−0.224847	−	0.249718i
$738$	3.61131	−	6.25497i	0.132934	−	0.230249i
$739$	22.1540	+	38.3719i	0.814950	+	1.41153i	0.909364	+	0.416001i	$0.136569\pi$
$739$	22.1540	+	38.3719i	0.814950	+	1.41153i	−0.0944142	+	0.995533i	$0.530098\pi$
$740$	2.79921	−	8.61508i	0.102901	−	0.316697i
$741$	44.5449	−	19.8327i	1.63640	−	0.728571i
$742$	−5.63570	+	4.09458i	−0.206893	+	0.150317i
$743$	26.3167			0.965467			0.482734	−	0.875767i	$-0.339644\pi$
$743$	26.3167			0.965467			0.482734	+	0.875767i	$0.339644\pi$
$744$	−4.94806	−	2.55279i	−0.181405	−	0.0935897i
$745$	−13.9131			−0.509736
$746$	−2.90584	+	2.11122i	−0.106390	+	0.0772971i
$747$	−8.74528	+	3.89365i	−0.319973	+	0.142461i
$748$	0.712213	−	2.19197i	0.0260411	−	0.0801462i
$749$	3.33259	+	5.77221i	0.121770	+	0.210912i
$750$	−0.500000	+	0.866025i	−0.0182574	+	0.0316228i
$751$	15.0451	+	16.7093i	0.549005	+	0.609731i	0.952235	−	0.305367i	$-0.0987792\pi$
$751$	15.0451	+	16.7093i	0.549005	+	0.609731i	−0.403230	+	0.915099i	$0.632113\pi$
$752$	−1.18696	−	3.65308i	−0.0432839	−	0.133214i
$753$	−5.61757	+	6.23895i	−0.204716	+	0.227360i
$754$	16.1043	+	7.17010i	0.586484	+	0.261119i
$755$	12.3150	−	2.61763i	0.448187	−	0.0952652i
$756$	−0.0541357	−	0.515066i	−0.00196889	−	0.0187328i
$757$	−2.92092	+	27.7907i	−0.106163	+	1.01007i	0.803664	+	0.595083i	$0.202881\pi$
$757$	−2.92092	+	27.7907i	−0.106163	+	1.01007i	−0.909827	+	0.414988i	$0.863786\pi$
$758$	14.8078	+	3.14750i	0.537845	+	0.114322i
$759$	−5.26995	−	3.82884i	−0.191287	−	0.138978i
$760$	5.80592	+	4.21825i	0.210603	+	0.153012i
$761$	38.8347	+	8.25457i	1.40776	+	0.299228i	0.848249	−	0.529597i	$-0.177657\pi$
$761$	38.8347	+	8.25457i	1.40776	+	0.299228i	0.559507	+	0.828825i	$0.310990\pi$
$762$	−0.184063	+	1.75124i	−0.00666790	+	0.0634408i
$763$	0.218025	+	2.07437i	0.00789302	+	0.0750971i
$764$	13.8072	−	2.93480i	0.499525	−	0.106177i
$765$	1.50068	+	0.668148i	0.0542573	+	0.0241569i
$766$	−1.66277	+	1.84669i	−0.0600782	+	0.0667236i
$767$	−4.39177	−	13.5165i	−0.158578	−	0.488052i
$768$	0.669131	+	0.743145i	0.0241452	+	0.0268159i
$769$	21.5035	−	37.2451i	0.775435	−	1.34309i	−0.159115	−	0.987260i	$-0.550864\pi$
$769$	21.5035	−	37.2451i	0.775435	−	1.34309i	0.934550	−	0.355833i	$-0.115803\pi$
$770$	0.363318	+	0.629286i	0.0130931	+	0.0226779i
$771$	−8.17437	+	25.1581i	−0.294393	+	0.906048i
$772$	1.51524	−	0.674630i	0.0545348	−	0.0242805i
$773$	0.0133268	−	0.00968247i	0.000479331	−	0.000348254i	−0.587546	−	0.809191i	$-0.699906\pi$
$773$	0.0133268	−	0.00968247i	0.000479331	−	0.000348254i	0.588025	+	0.808843i	$0.299906\pi$
$774$	8.27595			0.297473
$775$	−0.898809	+	5.49474i	−0.0322862	+	0.197377i
$776$	7.04303			0.252830
$777$	3.79542	−	2.75753i	0.136160	−	0.0989259i
$778$	−26.6447	+	11.8630i	−0.955260	+	0.425309i
$779$	−16.0173	+	49.2963i	−0.573881	+	1.76622i
$780$	−3.39722	−	5.88417i	−0.121640	−	0.210687i
$781$	−2.18461	+	3.78386i	−0.0781716	+	0.135397i
$782$	−5.10329	−	5.66778i	−0.182493	−	0.202679i
$783$	0.801751	+	2.46754i	0.0286523	+	0.0881826i
$784$	−4.50444	+	5.00268i	−0.160873	+	0.178667i
$785$	12.3946	+	5.51843i	0.442382	+	0.196961i
$786$	12.9095	−	2.74399i	0.460466	−	0.0978751i
$787$	3.32138	+	31.6009i	0.118395	+	1.12645i	0.878863	+	0.477074i	$0.158303\pi$
$787$	3.32138	+	31.6009i	0.118395	+	1.12645i	−0.760468	+	0.649375i	$0.775031\pi$
$788$	2.35996	−	22.4535i	0.0840702	−	0.799874i
$789$	31.3573	+	6.66519i	1.11635	+	0.237287i
$790$	−9.20595	−	6.68851i	−0.327533	−	0.237967i
$791$	−1.30072	−	0.945025i	−0.0462481	−	0.0336012i
$792$	−1.37238	−	0.291707i	−0.0487652	−	0.0103654i
$793$	−8.42101	+	80.1206i	−0.299039	+	2.84517i
$794$	2.90576	+	27.6465i	0.103122	+	0.981138i
$795$	−13.1567	+	2.79654i	−0.466619	+	0.0991829i
$796$	−5.49031	−	2.44444i	−0.194599	−	0.0866409i
$797$	−13.7222	+	15.2400i	−0.486064	+	0.539828i	−0.935427	−	0.353521i	$-0.884984\pi$
$797$	−13.7222	+	15.2400i	−0.486064	+	0.539828i	0.449363	+	0.893349i	$0.351651\pi$
$798$	1.14854	+	3.53483i	0.0406577	+	0.125132i
$799$	4.22204	+	4.68905i	0.149365	+	0.165887i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	7.09071	+	12.2815i	0.250538	+	0.433945i
$802$	1.32232	−	4.06967i	0.0466926	−	0.143705i
$803$	−12.4750	+	5.55423i	−0.440234	+	0.196005i
$804$	−5.26017	+	3.82174i	−0.185512	+	0.134782i
$805$	2.40452			0.0847483
$806$	−29.2785	−	23.9556i	−1.03129	−	0.843800i
$807$	−26.4534			−0.931203
$808$	2.16549	−	1.57332i	0.0761817	−	0.0553493i
$809$	30.8568	−	13.7383i	1.08487	−	0.483013i	0.215158	−	0.976579i	$-0.430974\pi$
$809$	30.8568	−	13.7383i	1.08487	−	0.483013i	0.869708	+	0.493566i	$0.164307\pi$
$810$	0.309017	−	0.951057i	0.0108578	−	0.0334167i
$811$	3.16273	+	5.47800i	0.111058	+	0.192359i	0.916197	−	0.400728i	$-0.131243\pi$
$811$	3.16273	+	5.47800i	0.111058	+	0.192359i	−0.805139	+	0.593086i	$0.797909\pi$
$812$	−0.671856	+	1.16369i	−0.0235775	+	0.0408375i
$813$	−2.91392	−	3.23624i	−0.102196	−	0.113500i
$814$	−3.92739	−	12.0873i	−0.137655	−	0.423658i
$815$	6.90001	−	7.66323i	0.241697	−	0.268431i
$816$	−1.50068	−	0.668148i	−0.0525344	−	0.0233898i
$817$	−58.0946	+	12.3484i	−2.03247	+	0.432016i
$818$	0.593286	+	5.64474i	0.0207437	+	0.197364i
$819$	0.367822	−	3.49959i	0.0128527	−	0.122286i
$820$	7.06478	+	1.50167i	0.246713	+	0.0524404i
$821$	22.2021	+	16.1308i	0.774860	+	0.562969i	0.903432	−	0.428731i	$-0.141039\pi$
$821$	22.2021	+	16.1308i	0.774860	+	0.562969i	−0.128572	+	0.991700i	$0.541039\pi$
$822$	3.84961	+	2.79691i	0.134271	+	0.0975533i
$823$	−0.835369	−	0.177563i	−0.0291191	−	0.00618946i	0.193329	−	0.981134i	$-0.438071\pi$
$823$	−0.835369	−	0.177563i	−0.0291191	−	0.00618946i	−0.222448	+	0.974945i	$0.571405\pi$
$824$	1.46884	−	13.9751i	0.0511695	−	0.486845i
$825$	0.146657	+	1.39535i	0.00510594	+	0.0485798i
$826$	1.05963	−	0.225232i	0.0368694	−	0.00783683i
$827$	−6.27951	−	2.79582i	−0.218360	−	0.0972202i	0.294641	−	0.955608i	$-0.404800\pi$
$827$	−6.27951	−	2.79582i	−0.218360	−	0.0972202i	−0.513001	+	0.858388i	$0.671466\pi$
$828$	−3.10664	+	3.45028i	−0.107963	+	0.119905i
$829$	−13.7673	−	42.3714i	−0.478158	−	1.47162i	−0.841651	−	0.540022i	$-0.818416\pi$
$829$	−13.7673	−	42.3714i	−0.478158	−	1.47162i	0.363493	−	0.931597i	$-0.381584\pi$
$830$	−6.40552	−	7.11406i	−0.222339	−	0.246932i
$831$	11.8786	−	20.5744i	0.412066	−	0.713719i
$832$	3.39722	+	5.88417i	0.117778	+	0.203997i
$833$	3.41721	−	10.5171i	0.118399	−	0.364395i
$834$	−9.38956	+	4.18050i	−0.325134	+	0.144759i
$835$	1.31289	−	0.953871i	0.0454345	−	0.0330101i
$836$	10.0689			0.348240
$837$	−0.263252	−	5.56154i	−0.00909932	−	0.192235i
$838$	−10.2345			−0.353545
$839$	−3.73771	+	2.71560i	−0.129040	+	0.0937531i	−0.650433	−	0.759564i	$-0.725413\pi$
$839$	−3.73771	+	2.71560i	−0.129040	+	0.0937531i	0.521393	+	0.853317i	$0.325413\pi$
$840$	0.473128	−	0.210650i	0.0163245	−	0.00726813i
$841$	−6.88133	+	21.1786i	−0.237287	+	0.730295i
$842$	−5.53434	−	9.58576i	−0.190726	−	0.330347i
$843$	9.76274	−	16.9096i	0.336247	−	0.582396i
$844$	15.7519	+	17.4943i	0.542203	+	0.602177i
$845$	−10.2484	−	31.5414i	−0.352556	−	1.08506i
$846$	2.57018	−	2.85447i	0.0883646	−	0.0981388i
$847$	−4.27306	−	1.90249i	−0.146824	−	0.0653702i
$848$	13.1567	−	2.79654i	0.451802	−	0.0960334i
$849$	−0.206493	−	1.96465i	−0.00708682	−	0.0674266i
$850$	−0.171709	+	1.63370i	−0.00588958	+	0.0560356i
$851$	−41.1375	−	8.74404i	−1.41017	−	0.299742i
$852$	2.51938	+	1.83044i	0.0863126	+	0.0627097i
$853$	−22.1717	−	16.1087i	−0.759145	−	0.551551i	0.139503	−	0.990222i	$-0.455449\pi$
$853$	−22.1717	−	16.1087i	−0.759145	−	0.551551i	−0.898648	+	0.438671i	$0.855449\pi$
$854$	−6.00660	−	1.27674i	−0.205542	−	0.0436892i
$855$	−0.750150	+	7.13720i	−0.0256546	+	0.244087i
$856$	−1.34523	−	12.7990i	−0.0459791	−	0.437462i
$857$	−34.5118	+	7.33571i	−1.17890	+	0.250583i	−0.755370	−	0.655298i	$-0.772543\pi$
$857$	−34.5118	+	7.33571i	−1.17890	+	0.250583i	−0.423531	+	0.905882i	$0.639210\pi$
$858$	−8.70869	−	3.87736i	−0.297310	−	0.132371i
$859$	8.78142	−	9.75275i	0.299618	−	0.332760i	−0.574471	−	0.818525i	$-0.694792\pi$
$859$	8.78142	−	9.75275i	0.299618	−	0.332760i	0.874089	+	0.485765i	$0.161459\pi$
$860$	2.55741	+	7.87090i	0.0872070	+	0.268395i
$861$	2.50296	+	2.77982i	0.0853007	+	0.0947360i
$862$	6.27337	−	10.8658i	0.213672	−	0.370091i
$863$	27.8880	+	48.3034i	0.949318	+	1.64427i	0.746867	+	0.664974i	$0.231557\pi$
$863$	27.8880	+	48.3034i	0.949318	+	1.64427i	0.202451	+	0.979292i	$0.435109\pi$
$864$	−0.309017	+	0.951057i	−0.0105130	+	0.0323556i
$865$	−15.8964	+	7.07756i	−0.540496	+	0.240644i
$866$	19.8714	−	14.4374i	0.675258	−	0.490604i
$867$	−14.3015			−0.485705
$868$	2.04928	−	2.02864i	0.0695571	−	0.0688566i
$869$	−15.9654			−0.541589
$870$	−2.09901	+	1.52502i	−0.0711632	+	0.0517031i
$871$	−40.3577	+	17.9684i	−1.36747	+	0.608837i
$872$	1.24453	−	3.83026i	0.0421450	−	0.129709i
$873$	3.52152	+	6.09945i	0.119185	+	0.206435i
$874$	16.6596	−	28.8552i	0.563518	−	0.976043i
$875$	−0.346545	−	0.384877i	−0.0117154	−	0.0130112i
$876$	3.00763	+	9.25654i	0.101618	+	0.312749i
$877$	−24.1612	+	26.8337i	−0.815865	+	0.906110i	−0.997004	−	0.0773478i	$-0.975355\pi$
$877$	−24.1612	+	26.8337i	−0.815865	+	0.906110i	0.181139	+	0.983457i	$0.442021\pi$
$878$	−2.00762	−	0.893849i	−0.0677538	−	0.0301659i
$879$	−9.56096	+	2.03224i	−0.322483	+	0.0685459i
$880$	−0.146657	−	1.39535i	−0.00494381	−	0.0470372i
$881$	2.99045	−	28.4523i	0.100751	−	0.958581i	−0.821034	−	0.570880i	$-0.806602\pi$
$881$	2.99045	−	28.4523i	0.100751	−	0.958581i	0.921785	−	0.387702i	$-0.126731\pi$
$882$	−6.58467	−	1.39961i	−0.221717	−	0.0471275i
$883$	−8.14442	−	5.91727i	−0.274082	−	0.199132i	0.442250	−	0.896892i	$-0.354180\pi$
$883$	−8.14442	−	5.91727i	−0.274082	−	0.199132i	−0.716332	+	0.697760i	$0.754180\pi$
$884$	−9.02965	−	6.56043i	−0.303700	−	0.220651i
$885$	2.04601	+	0.434892i	0.0687758	+	0.0146187i
$886$	1.94290	−	18.4855i	0.0652731	−	0.621032i
$887$	−2.46594	−	23.4618i	−0.0827980	−	0.787771i	−0.954596	−	0.297905i	$-0.903712\pi$
$887$	−2.46594	−	23.4618i	−0.0827980	−	0.787771i	0.871798	−	0.489866i	$-0.162954\pi$
$888$	−8.86048	+	1.88335i	−0.297338	+	0.0632012i
$889$	−0.833126	−	0.370932i	−0.0279421	−	0.0124406i
$890$	−9.48923	+	10.5389i	−0.318080	+	0.353263i
$891$	−0.433562	−	1.33437i	−0.0145249	−	0.0447029i
$892$	−9.06393	−	10.0665i	−0.303483	−	0.337052i
$893$	−13.7828	+	23.8724i	−0.461222	+	0.798860i
$894$	6.95654	+	12.0491i	0.232662	+	0.402982i
$895$	−5.84978	+	18.0038i	−0.195537	+	0.601800i
$896$	−0.473128	+	0.210650i	−0.0158061	+	0.00703733i
$897$	−25.5207	+	18.5419i	−0.852111	+	0.619095i
$898$	−20.9017			−0.697498
$899$	−7.92890	+	12.0752i	−0.264443	+	0.402731i
$900$	1.00000			0.0333333
$901$	−17.8755	+	12.9873i	−0.595519	+	0.432670i
$902$	9.25749	−	4.12170i	0.308241	−	0.137238i
$903$	−1.32449	+	4.07637i	−0.0440763	+	0.135653i
$904$	1.55219	+	2.68848i	0.0516252	+	0.0894175i
$905$	−8.35502	+	14.4713i	−0.277730	+	0.481043i
$906$	−8.42441	−	9.35626i	−0.279882	−	0.310841i
$907$	0.825382	+	2.54026i	0.0274063	+	0.0843481i	0.963824	−	0.266539i	$-0.0858801\pi$
$907$	0.825382	+	2.54026i	0.0274063	+	0.0843481i	−0.936418	+	0.350887i	$0.885880\pi$
$908$	−13.4985	+	14.9916i	−0.447962	+	0.497512i
$909$	2.44528	+	1.08871i	0.0811049	+	0.0361102i
$910$	3.44197	−	0.731614i	0.114100	−	0.0242528i
$911$	−0.762685	−	7.25646i	−0.0252689	−	0.240417i	−0.999865	−	0.0164466i	$-0.994765\pi$
$911$	−0.762685	−	7.25646i	−0.0252689	−	0.240417i	0.974596	−	0.223971i	$-0.0719020\pi$
$912$	0.750150	−	7.13720i	0.0248399	−	0.236336i
$913$	−13.1376	−	2.79249i	−0.434792	−	0.0924178i
$914$	11.6189	+	8.44160i	0.384318	+	0.279223i
$915$	−9.59253	−	6.96938i	−0.317119	−	0.230401i
$916$	−20.7469	−	4.40989i	−0.685497	−	0.145707i
$917$	−0.714476	+	6.79779i	−0.0235941	+	0.224483i
$918$	−0.171709	−	1.63370i	−0.00566725	−	0.0539203i
$919$	−16.5162	+	3.51063i	−0.544820	+	0.115805i	−0.472096	−	0.881547i	$-0.656503\pi$
$919$	−16.5162	+	3.51063i	−0.544820	+	0.115805i	−0.0727240	+	0.997352i	$0.523169\pi$
$920$	−4.24141	−	1.88840i	−0.139835	−	0.0622587i
$921$	0.345871	−	0.384128i	0.0113968	−	0.0126575i
$922$	−9.37876	−	28.8649i	−0.308873	−	0.950613i
$923$	14.1580	+	15.7240i	0.466016	+	0.517563i
$924$	0.363318	−	0.629286i	0.0119523	−	0.0207020i
$925$	4.52921	+	7.84483i	0.148920	+	0.257936i
$926$	−8.76856	+	26.9868i	−0.288153	+	0.886843i
$927$	12.8372	−	5.71549i	0.421629	−	0.187721i
$928$	2.09901	−	1.52502i	0.0689035	−	0.0500613i
$929$	7.70989			0.252953			0.126477	−	0.991970i	$-0.459633\pi$
$929$	7.70989			0.252953			0.126477	+	0.991970i	$0.459633\pi$
$930$	5.20799	−	1.96898i	0.170777	−	0.0645653i
$931$	48.3107			1.58332
$932$	−21.5825	+	15.6806i	−0.706958	+	0.513635i
$933$	16.8812	−	7.51598i	0.552665	−	0.246062i
$934$	12.0511	−	37.0896i	0.394326	−	1.21361i
$935$	1.15239	+	1.99599i	0.0376870	+	0.0652758i
$936$	−3.39722	+	5.88417i	−0.111042	+	0.192330i
$937$	23.5291	+	26.1317i	0.768662	+	0.853686i	0.992664	−	0.120903i	$-0.0385790\pi$
$937$	23.5291	+	26.1317i	0.768662	+	0.853686i	−0.224002	+	0.974589i	$0.571912\pi$
$938$	−1.04057	−	3.20256i	−0.0339760	−	0.104567i
$939$	15.6115	−	17.3384i	0.509464	−	0.565817i
$940$	3.50899	+	1.56230i	0.114451	+	0.0509568i
$941$	−22.6743	+	4.81957i	−0.739161	+	0.157114i	−0.562080	−	0.827083i	$-0.689999\pi$
$941$	−22.6743	+	4.81957i	−0.739161	+	0.157114i	−0.177081	+	0.984196i	$0.556665\pi$
$942$	−1.41820	−	13.4932i	−0.0462074	−	0.439634i
$943$	3.50517	−	33.3495i	0.114144	−	1.08601i
$944$	−2.04601	−	0.434892i	−0.0665919	−	0.0141545i
$945$	0.418993	+	0.304416i	0.0136298	+	0.00990265i
$946$	9.39386	+	6.82504i	0.305421	+	0.221901i
$947$	−19.9067	−	4.23129i	−0.646879	−	0.137498i	−0.127223	−	0.991874i	$-0.540607\pi$
$947$	−19.9067	−	4.23129i	−0.646879	−	0.137498i	−0.519656	+	0.854376i	$0.673940\pi$
$948$	−1.18945	+	11.3168i	−0.0386315	+	0.367554i
$949$	6.91243	+	65.7674i	0.224387	+	2.13490i
$950$	−7.01969	+	1.49208i	−0.227749	+	0.0484095i
$951$	4.43417	+	1.97422i	0.143788	+	0.0640185i
$952$	0.569271	−	0.632239i	0.0184502	−	0.0204910i
$953$	0.397432	+	1.22317i	0.0128741	+	0.0396224i	0.957287	−	0.289139i	$-0.0933689\pi$
$953$	0.397432	+	1.22317i	0.0128741	+	0.0396224i	−0.944413	+	0.328761i	$0.893369\pi$
$954$	9.00020	+	9.99574i	0.291392	+	0.323624i
$955$	−7.05781	+	12.2245i	−0.228385	+	0.395575i
$956$	7.25103	+	12.5591i	0.234515	+	0.406192i
$957$	−1.12489	+	3.46204i	−0.0363624	+	0.111912i
$958$	21.3285	−	9.49604i	0.689091	−	0.306803i
$959$	−1.99373	+	1.44853i	−0.0643808	+	0.0467754i
$960$	−1.00000			−0.0322749
$961$	23.2463	−	20.5088i	0.749879	−	0.661575i
$962$	−61.5470			−1.98436
$963$	10.4117	−	7.56452i	0.335511	−	0.243763i
$964$	−17.6913	+	7.87667i	−0.569798	+	0.253690i
$965$	−0.512548	+	1.57746i	−0.0164995	+	0.0507803i
$966$	−1.20226	−	2.08238i	−0.0386822	−	0.0669995i
$967$	19.5882	−	33.9278i	0.629914	−	1.09104i	−0.357654	−	0.933854i	$-0.616423\pi$
$967$	19.5882	−	33.9278i	0.629914	−	1.09104i	0.987569	−	0.157189i	$-0.0502432\pi$
$968$	6.04325	+	6.71171i	0.194237	+	0.215722i
$969$	3.64296	+	11.2119i	0.117029	+	0.360178i
$970$	−4.71271	+	5.23399i	−0.151316	+	0.168053i
$971$	30.2617	+	13.4734i	0.971144	+	0.432381i	0.830095	−	0.557622i	$-0.188286\pi$
$971$	30.2617	+	13.4734i	0.971144	+	0.432381i	0.141049	+	0.990003i	$0.454953\pi$
$972$	−0.978148	+	0.207912i	−0.0313741	+	0.00666877i
$973$	−0.556414	−	5.29393i	−0.0178378	−	0.169716i
$974$	2.08793	−	19.8653i	0.0669016	−	0.636526i
$975$	6.64597	+	1.41265i	0.212842	+	0.0452409i
$976$	9.59253	+	6.96938i	0.307049	+	0.223084i
$977$	−15.7090	−	11.4133i	−0.502575	−	0.365142i	0.307425	−	0.951572i	$-0.400533\pi$
$977$	−15.7090	−	11.4133i	−0.502575	−	0.365142i	−0.810000	+	0.586430i	$0.800533\pi$
$978$	−10.0866	−	2.14396i	−0.322533	−	0.0685564i
$979$	−2.07981	+	19.7880i	−0.0664709	+	0.632429i
$980$	−0.703662	−	6.69490i	−0.0224777	−	0.213861i
$981$	3.93937	−	0.837338i	0.125774	−	0.0267342i
$982$	6.91051	+	3.07676i	0.220523	+	0.0981832i
$983$	−7.26591	+	8.06962i	−0.231747	+	0.257381i	−0.847791	−	0.530331i	$-0.822068\pi$
$983$	−7.26591	+	8.06962i	−0.231747	+	0.257381i	0.616044	+	0.787712i	$0.288734\pi$
$984$	−2.23191	−	6.86911i	−0.0711507	−	0.218979i
$985$	15.1071	+	16.7781i	0.481352	+	0.534596i
$986$	−2.13101	+	3.69103i	−0.0678653	+	0.117546i
$987$	0.994652	+	1.72279i	0.0316601	+	0.0548370i
$988$	15.0678	−	46.3739i	0.479371	−	1.47535i
$989$	35.1017	−	15.6283i	1.11617	−	0.496951i
$990$	1.13508	−	0.824683i	0.0360752	−	0.0262102i
$991$	−9.26400			−0.294281			−0.147140	−	0.989116i	$-0.547007\pi$
$991$	−9.26400			−0.294281			−0.147140	+	0.989116i	$0.547007\pi$
$992$	−5.20799	+	1.96898i	−0.165354	+	0.0625151i
$993$	10.0473			0.318843
$994$	−1.30480	+	0.947990i	−0.0413856	+	0.0300684i
$995$	5.49031	−	2.44444i	0.174054	−	0.0774940i
$996$	−2.95819	+	9.10437i	−0.0937339	+	0.288483i
$997$	11.3940	+	19.7349i	0.360850	+	0.625011i	0.988101	−	0.153806i	$-0.0491532\pi$
$997$	11.3940	+	19.7349i	0.360850	+	0.625011i	−0.627251	+	0.778817i	$0.715820\pi$
$998$	6.89443	−	11.9415i	0.218239	−	0.378002i
$999$	−6.06127	−	6.73172i	−0.191770	−	0.212982i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.i.421.2	yes	24
31.19	even	15	inner	930.2.bg.i.391.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.i.391.2	✓	24	31.19	even	15	inner
930.2.bg.i.421.2	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.913545 - 0.406737i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(0.346545 + 0.384877i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.669131 - 0.743145i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.913545 - 0.406737i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(0.346545 + 0.384877i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.669131 - 0.743145i) q^{9} +(0.913545 + 0.406737i) q^{10} +(1.37238 - 0.291707i) q^{11} +(-0.104528 - 0.994522i) q^{12} +(0.710213 - 6.75723i) q^{13} +(0.506586 + 0.107678i) q^{14} +(0.809017 + 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.60681 + 0.341537i) q^{17} +(0.104528 - 0.994522i) q^{18} +(0.750150 + 7.13720i) q^{19} +(0.978148 - 0.207912i) q^{20} +(0.473128 + 0.210650i) q^{21} +(0.938814 - 1.04266i) q^{22} +(-1.43471 - 4.41557i) q^{23} +(-0.669131 - 0.743145i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-3.39722 - 5.88417i) q^{26} +(0.309017 - 0.951057i) q^{27} +(0.473128 - 0.210650i) q^{28} +(-2.09901 + 1.52502i) q^{29} +1.00000 q^{30} +(5.20799 - 1.96898i) q^{31} -1.00000 q^{32} +(1.13508 - 0.824683i) q^{33} +(1.50068 - 0.668148i) q^{34} +(-0.160041 + 0.492555i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(4.52921 - 7.84483i) q^{37} +(4.80202 + 5.33319i) q^{38} +(-2.09960 - 6.46191i) q^{39} +(0.669131 - 0.743145i) q^{40} +(6.59819 + 2.93770i) q^{41} +(0.506586 - 0.107678i) q^{42} +(0.865073 + 8.23062i) q^{43} +(0.146657 - 1.39535i) q^{44} +(0.978148 + 0.207912i) q^{45} +(-3.75611 - 2.72897i) q^{46} +(3.10749 + 2.25773i) q^{47} +(-0.978148 - 0.207912i) q^{48} +(0.703662 - 6.69490i) q^{49} +(0.104528 + 0.994522i) q^{50} +(1.60681 - 0.341537i) q^{51} +(-6.20704 - 2.76355i) q^{52} +(-9.00020 + 9.99574i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(0.938814 + 1.04266i) q^{55} +(0.258952 - 0.448518i) q^{56} +(3.58826 + 6.21504i) q^{57} +(-0.801751 + 2.46754i) q^{58} +(1.91088 - 0.850778i) q^{59} +(0.809017 - 0.587785i) q^{60} -11.8570 q^{61} +(3.05601 - 4.65411i) q^{62} +0.517903 q^{63} +(-0.809017 + 0.587785i) q^{64} +(6.20704 - 2.76355i) q^{65} +(0.433562 - 1.33437i) q^{66} +(-3.25096 - 5.63084i) q^{67} +(0.821352 - 1.42262i) q^{68} +(-3.10664 - 3.45028i) q^{69} +(0.160041 + 0.492555i) q^{70} +(-2.08376 + 2.31425i) q^{71} +(-0.913545 - 0.406737i) q^{72} +(-9.52021 + 2.02358i) q^{73} +(-0.946864 - 9.00881i) q^{74} +(-0.104528 + 0.994522i) q^{75} +(7.01969 + 1.49208i) q^{76} +(0.587861 + 0.427106i) q^{77} +(-5.49683 - 3.99368i) q^{78} +(-11.1305 - 2.36586i) q^{79} +(0.104528 - 0.994522i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(7.06478 - 1.50167i) q^{82} +(-8.74528 - 3.89365i) q^{83} +(0.346545 - 0.384877i) q^{84} +(0.507623 + 1.56230i) q^{85} +(5.53769 + 6.15023i) q^{86} +(-1.29726 + 2.24692i) q^{87} +(-0.701518 - 1.21506i) q^{88} +(-4.38230 + 13.4873i) q^{89} +(0.913545 - 0.406737i) q^{90} +(2.84682 - 2.06834i) q^{91} -4.64280 q^{92} +(3.95688 - 3.91703i) q^{93} +3.84107 q^{94} +(-5.80592 + 4.21825i) q^{95} +(-0.913545 + 0.406737i) q^{96} +(-2.17642 + 6.69832i) q^{97} +(-3.36589 - 5.82989i) q^{98} +(0.701518 - 1.21506i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} + 3 q^{3} - 6 q^{4} + 12 q^{5} + 12 q^{6} - 7 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q + 6 * q^2 + 3 * q^3 - 6 * q^4 + 12 * q^5 + 12 * q^6 - 7 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q + 6 q^{2} + 3 q^{3} - 6 q^{4} + 12 q^{5} + 12 q^{6} - 7 q^{7} + 6 q^{8} + 3 q^{9} + 3 q^{10} - 13 q^{11} + 3 q^{12} + 11 q^{13} - 8 q^{14} + 6 q^{15} - 6 q^{16} - 29 q^{17} - 3 q^{18} + 9 q^{19} - 3 q^{20} - 2 q^{21} - 17 q^{22} - 5 q^{23} - 3 q^{24} - 12 q^{25} + 9 q^{26} - 6 q^{27} - 2 q^{28} + 13 q^{29} + 24 q^{30} + 57 q^{31} - 24 q^{32} + 16 q^{33} + 29 q^{34} + q^{35} - 12 q^{36} - 24 q^{37} + 6 q^{38} - 17 q^{39} + 3 q^{40} + 32 q^{41} - 8 q^{42} + 49 q^{43} - 8 q^{44} - 3 q^{45} + 28 q^{47} + 3 q^{48} + 12 q^{49} - 3 q^{50} - 29 q^{51} - 19 q^{52} - 36 q^{53} + 6 q^{54} - 17 q^{55} - 3 q^{56} - 6 q^{57} + 2 q^{58} + 6 q^{60} + 33 q^{62} - 6 q^{63} - 6 q^{64} + 19 q^{65} + 4 q^{66} - 5 q^{67} + 11 q^{68} + 10 q^{69} - q^{70} - 11 q^{71} - 3 q^{72} - 13 q^{73} + 9 q^{74} + 3 q^{75} - 6 q^{76} + 4 q^{77} - 8 q^{78} - 68 q^{79} - 3 q^{80} + 3 q^{81} - 2 q^{82} + 10 q^{83} - 7 q^{84} + 2 q^{85} - 34 q^{86} + 11 q^{87} - 12 q^{88} + 55 q^{89} + 3 q^{90} + 38 q^{91} + 10 q^{92} + 19 q^{93} + 42 q^{94} + 18 q^{95} - 3 q^{96} - q^{97} + 63 q^{98} + 12 q^{99}+O(q^{100}) \) 24 * q + 6 * q^2 + 3 * q^3 - 6 * q^4 + 12 * q^5 + 12 * q^6 - 7 * q^7 + 6 * q^8 + 3 * q^9 + 3 * q^10 - 13 * q^11 + 3 * q^12 + 11 * q^13 - 8 * q^14 + 6 * q^15 - 6 * q^16 - 29 * q^17 - 3 * q^18 + 9 * q^19 - 3 * q^20 - 2 * q^21 - 17 * q^22 - 5 * q^23 - 3 * q^24 - 12 * q^25 + 9 * q^26 - 6 * q^27 - 2 * q^28 + 13 * q^29 + 24 * q^30 + 57 * q^31 - 24 * q^32 + 16 * q^33 + 29 * q^34 + q^35 - 12 * q^36 - 24 * q^37 + 6 * q^38 - 17 * q^39 + 3 * q^40 + 32 * q^41 - 8 * q^42 + 49 * q^43 - 8 * q^44 - 3 * q^45 + 28 * q^47 + 3 * q^48 + 12 * q^49 - 3 * q^50 - 29 * q^51 - 19 * q^52 - 36 * q^53 + 6 * q^54 - 17 * q^55 - 3 * q^56 - 6 * q^57 + 2 * q^58 + 6 * q^60 + 33 * q^62 - 6 * q^63 - 6 * q^64 + 19 * q^65 + 4 * q^66 - 5 * q^67 + 11 * q^68 + 10 * q^69 - q^70 - 11 * q^71 - 3 * q^72 - 13 * q^73 + 9 * q^74 + 3 * q^75 - 6 * q^76 + 4 * q^77 - 8 * q^78 - 68 * q^79 - 3 * q^80 + 3 * q^81 - 2 * q^82 + 10 * q^83 - 7 * q^84 + 2 * q^85 - 34 * q^86 + 11 * q^87 - 12 * q^88 + 55 * q^89 + 3 * q^90 + 38 * q^91 + 10 * q^92 + 19 * q^93 + 42 * q^94 + 18 * q^95 - 3 * q^96 - q^97 + 63 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

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Database

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