LMFDB - Embedded newform 429.2.bd.a.76.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(76,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 7]))

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

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

chi := DirichletCharacter("429.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bd (of order $12$, degree $4$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			76.4
Character	$\chi$	$=$	429.76
Dual form			429.2.bd.a.175.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.43745 - 0.385163i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.185859 + 0.107306i) q^{4} +(-1.55279 - 1.55279i) q^{5} +(0.385163 + 1.43745i) q^{6} +(-2.05994 + 0.551959i) q^{7} +(1.87874 + 1.87874i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.43745 - 0.385163i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.185859 + 0.107306i) q^{4} +(-1.55279 - 1.55279i) q^{5} +(0.385163 + 1.43745i) q^{6} +(-2.05994 + 0.551959i) q^{7} +(1.87874 + 1.87874i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.63398 + 2.83014i) q^{10} +(-2.81597 - 1.75223i) q^{11} -0.214611i q^{12} +(-1.07727 + 3.44085i) q^{13} +3.17365 q^{14} +(-0.568361 + 2.12115i) q^{15} +(-2.19158 - 3.79593i) q^{16} +(1.88830 - 3.27063i) q^{17} +(1.05229 - 1.05229i) q^{18} +(1.33486 + 4.98175i) q^{19} +(-0.121977 - 0.455223i) q^{20} +(1.50798 + 1.50798i) q^{21} +(3.37292 + 3.60335i) q^{22} +(3.66864 - 2.11809i) q^{23} +(0.687666 - 2.56641i) q^{24} -0.177671i q^{25} +(2.87382 - 4.53113i) q^{26} +1.00000 q^{27} +(-0.442086 - 0.118457i) q^{28} +(-3.17297 + 1.83192i) q^{29} +(1.63398 - 2.83014i) q^{30} +(6.23142 + 6.23142i) q^{31} +(0.312902 + 1.16776i) q^{32} +(-0.109490 + 3.31482i) q^{33} +(-3.97406 + 3.97406i) q^{34} +(4.05574 + 2.34158i) q^{35} +(-0.185859 + 0.107306i) q^{36} +(4.04112 + 1.08282i) q^{37} -7.67515i q^{38} +(3.51850 - 0.787481i) q^{39} -5.83458i q^{40} +(0.728757 + 0.195270i) q^{41} +(-1.58683 - 2.74846i) q^{42} +(-2.35876 + 4.08550i) q^{43} +(-0.335349 - 0.627837i) q^{44} +(2.12115 - 0.568361i) q^{45} +(-6.08929 + 1.63162i) q^{46} +(-5.03355 + 5.03355i) q^{47} +(-2.19158 + 3.79593i) q^{48} +(-2.12348 + 1.22599i) q^{49} +(-0.0684324 + 0.255393i) q^{50} -3.77660 q^{51} +(-0.569444 + 0.523916i) q^{52} +8.86663 q^{53} +(-1.43745 - 0.385163i) q^{54} +(1.65177 + 7.09347i) q^{55} +(-4.90708 - 2.83310i) q^{56} +(3.64689 - 3.64689i) q^{57} +(5.26657 - 1.41117i) q^{58} +(1.80779 + 6.74676i) q^{59} +(-0.333247 + 0.333247i) q^{60} +(1.01629 + 0.586753i) q^{61} +(-6.55723 - 11.3575i) q^{62} +(0.551959 - 2.05994i) q^{63} +6.96721i q^{64} +(7.01572 - 3.67015i) q^{65} +(1.43413 - 4.72271i) q^{66} +(0.0671688 - 0.250677i) q^{67} +(0.701913 - 0.405250i) q^{68} +(-3.66864 - 2.11809i) q^{69} +(-4.92803 - 4.92803i) q^{70} +(0.596881 - 0.159934i) q^{71} +(-2.56641 + 0.687666i) q^{72} +(-3.07555 - 3.07555i) q^{73} +(-5.39185 - 3.11298i) q^{74} +(-0.153868 + 0.0888356i) q^{75} +(-0.286475 + 1.06914i) q^{76} +(6.76789 + 2.05519i) q^{77} +(-5.36098 - 0.223234i) q^{78} +8.01708i q^{79} +(-2.49122 + 9.29737i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.972340 - 0.561381i) q^{82} +(-6.52681 + 6.52681i) q^{83} +(0.118457 + 0.442086i) q^{84} +(-8.01074 + 2.14647i) q^{85} +(4.96419 - 4.96419i) q^{86} +(3.17297 + 1.83192i) q^{87} +(-1.99849 - 8.58246i) q^{88} +(-13.2990 - 3.56346i) q^{89} -3.26796 q^{90} +(0.319906 - 7.68257i) q^{91} +0.909132 q^{92} +(2.28086 - 8.51228i) q^{93} +(9.17422 - 5.29674i) q^{94} +(5.66287 - 9.80838i) q^{95} +(0.854863 - 0.854863i) q^{96} +(-3.58037 + 0.959356i) q^{97} +(3.52461 - 0.944416i) q^{98} +(2.92546 - 1.56259i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 28 q^{3} + 4 q^{5} - 28 q^{9}+O(q^{10}) $ 56 * q - 28 * q^3 + 4 * q^5 - 28 * q^9	$ 56 q - 28 q^{3} + 4 q^{5} - 28 q^{9} - 12 q^{11} + 24 q^{14} - 8 q^{15} + 68 q^{16} - 8 q^{20} - 10 q^{22} - 12 q^{23} - 48 q^{26} + 56 q^{27} + 4 q^{31} + 12 q^{33} + 32 q^{34} + 36 q^{37} - 12 q^{42} + 24 q^{44} + 4 q^{45} - 8 q^{47} + 68 q^{48} - 24 q^{49} - 56 q^{53} - 2 q^{55} + 72 q^{56} - 88 q^{58} + 56 q^{59} - 44 q^{60} + 20 q^{66} + 92 q^{67} + 12 q^{69} - 216 q^{70} + 72 q^{71} - 12 q^{75} - 12 q^{78} + 44 q^{80} - 28 q^{81} - 156 q^{82} - 120 q^{86} - 6 q^{88} - 56 q^{89} + 92 q^{91} + 32 q^{92} - 20 q^{93} - 44 q^{97}+O(q^{100}) $ 56 * q - 28 * q^3 + 4 * q^5 - 28 * q^9 - 12 * q^11 + 24 * q^14 - 8 * q^15 + 68 * q^16 - 8 * q^20 - 10 * q^22 - 12 * q^23 - 48 * q^26 + 56 * q^27 + 4 * q^31 + 12 * q^33 + 32 * q^34 + 36 * q^37 - 12 * q^42 + 24 * q^44 + 4 * q^45 - 8 * q^47 + 68 * q^48 - 24 * q^49 - 56 * q^53 - 2 * q^55 + 72 * q^56 - 88 * q^58 + 56 * q^59 - 44 * q^60 + 20 * q^66 + 92 * q^67 + 12 * q^69 - 216 * q^70 + 72 * q^71 - 12 * q^75 - 12 * q^78 + 44 * q^80 - 28 * q^81 - 156 * q^82 - 120 * q^86 - 6 * q^88 - 56 * q^89 + 92 * q^91 + 32 * q^92 - 20 * q^93 - 44 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.43745	−	0.385163i	−1.01643	−	0.272352i	−0.288116	−	0.957595i	$-0.593029\pi$
$2$	−1.43745	−	0.385163i	−1.01643	−	0.272352i	−0.728314	+	0.685244i	$0.759696\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.185859	+	0.107306i	0.0929294	+	0.0536528i
$5$	−1.55279	−	1.55279i	−0.694430	−	0.694430i	0.268774	−	0.963203i	$-0.413382\pi$
$5$	−1.55279	−	1.55279i	−0.694430	−	0.694430i	−0.963203	+	0.268774i	$0.913382\pi$
$6$	0.385163	+	1.43745i	0.157242	+	0.586836i
$7$	−2.05994	+	0.551959i	−0.778584	+	0.208621i	−0.626160	−	0.779694i	$-0.715375\pi$
$7$	−2.05994	+	0.551959i	−0.778584	+	0.208621i	−0.152424	+	0.988315i	$0.548708\pi$
$8$	1.87874	+	1.87874i	0.664235	+	0.664235i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.63398	+	2.83014i	0.516710	+	0.894969i
$11$	−2.81597	−	1.75223i	−0.849047	−	0.528317i
$11$	−2.81597	−	1.75223i	−0.849047	−	0.528317i
$12$		−	0.214611i		−	0.0619529i
$13$	−1.07727	+	3.44085i	−0.298782	+	0.954321i
$13$	−1.07727	+	3.44085i	−0.298782	+	0.954321i
$14$	3.17365			0.848195
$15$	−0.568361	+	2.12115i	−0.146750	+	0.547680i
$16$	−2.19158	−	3.79593i	−0.547896	−	0.948983i
$17$	1.88830	−	3.27063i	0.457980	−	0.793244i	−0.540875	−	0.841103i	$-0.681907\pi$
$17$	1.88830	−	3.27063i	0.457980	−	0.793244i	0.998854	+	0.0478595i	$0.0152400\pi$
$18$	1.05229	−	1.05229i	0.248026	−	0.248026i
$19$	1.33486	+	4.98175i	0.306237	+	1.14289i	0.931875	+	0.362779i	$0.118172\pi$
$19$	1.33486	+	4.98175i	0.306237	+	1.14289i	−0.625638	+	0.780113i	$0.715161\pi$
$20$	−0.121977	−	0.455223i	−0.0272748	−	0.101791i
$21$	1.50798	+	1.50798i	0.329068	+	0.329068i
$22$	3.37292	+	3.60335i	0.719109	+	0.768237i
$23$	3.66864	−	2.11809i	0.764964	−	0.441652i	−0.0661111	−	0.997812i	$-0.521059\pi$
$23$	3.66864	−	2.11809i	0.764964	−	0.441652i	0.831075	+	0.556160i	$0.187726\pi$
$24$	0.687666	−	2.56641i	0.140369	−	0.523865i
$25$		−	0.177671i		−	0.0355342i
$26$	2.87382	−	4.53113i	0.563602	−	0.888627i
$27$	1.00000			0.192450
$28$	−0.442086	−	0.118457i	−0.0835464	−	0.0223862i
$29$	−3.17297	+	1.83192i	−0.589206	+	0.340178i	−0.764784	−	0.644287i	$-0.777154\pi$
$29$	−3.17297	+	1.83192i	−0.589206	+	0.340178i	0.175577	+	0.984466i	$0.443821\pi$
$30$	1.63398	−	2.83014i	0.298323	−	0.516710i
$31$	6.23142	+	6.23142i	1.11920	+	1.11920i	0.991860	+	0.127336i	$0.0406428\pi$
$31$	6.23142	+	6.23142i	1.11920	+	1.11920i	0.127336	+	0.991860i	$0.459357\pi$
$32$	0.312902	+	1.16776i	0.0553137	+	0.206434i
$33$	−0.109490	+	3.31482i	−0.0190598	+	0.577036i
$34$	−3.97406	+	3.97406i	−0.681545	+	0.681545i
$35$	4.05574	+	2.34158i	0.685545	+	0.395799i
$36$	−0.185859	+	0.107306i	−0.0309765	+	0.0178843i
$37$	4.04112	+	1.08282i	0.664356	+	0.178014i	0.575211	−	0.818005i	$-0.304920\pi$
$37$	4.04112	+	1.08282i	0.664356	+	0.178014i	0.0891451	+	0.996019i	$0.471587\pi$
$38$		−	7.67515i		−	1.24507i
$39$	3.51850	−	0.787481i	0.563412	−	0.126098i
$40$		−	5.83458i		−	0.922529i
$41$	0.728757	+	0.195270i	0.113813	+	0.0304960i	0.315276	−	0.949000i	$-0.397903\pi$
$41$	0.728757	+	0.195270i	0.113813	+	0.0304960i	−0.201463	+	0.979496i	$0.564570\pi$
$42$	−1.58683	−	2.74846i	−0.244853	−	0.424097i
$43$	−2.35876	+	4.08550i	−0.359708	+	0.623033i	−0.987912	−	0.155016i	$-0.950457\pi$
$43$	−2.35876	+	4.08550i	−0.359708	+	0.623033i	0.628204	+	0.778049i	$0.283790\pi$
$44$	−0.335349	−	0.627837i	−0.0505557	−	0.0946499i
$45$	2.12115	−	0.568361i	0.316203	−	0.0847263i
$46$	−6.08929	+	1.63162i	−0.897817	+	0.240569i
$47$	−5.03355	+	5.03355i	−0.734219	+	0.734219i	−0.971453	−	0.237233i	$-0.923759\pi$
$47$	−5.03355	+	5.03355i	−0.734219	+	0.734219i	0.237233	+	0.971453i	$0.423759\pi$
$48$	−2.19158	+	3.79593i	−0.316328	+	0.547896i
$49$	−2.12348	+	1.22599i	−0.303355	+	0.175142i
$50$	−0.0684324	+	0.255393i	−0.00967781	+	0.0361181i
$51$	−3.77660			−0.528829
$52$	−0.569444	+	0.523916i	−0.0789676	+	0.0726540i
$53$	8.86663			1.21793			0.608963	−	0.793199i	$-0.291586\pi$
$53$	8.86663			1.21793			0.608963	+	0.793199i	$0.291586\pi$
$54$	−1.43745	−	0.385163i	−0.195612	−	0.0524141i
$55$	1.65177	+	7.09347i	0.222724	+	0.956483i
$56$	−4.90708	−	2.83310i	−0.655736	−	0.378589i
$57$	3.64689	−	3.64689i	0.483043	−	0.483043i
$58$	5.26657	−	1.41117i	0.691535	−	0.185296i
$59$	1.80779	+	6.74676i	0.235354	+	0.878354i	0.977989	+	0.208657i	$0.0669092\pi$
$59$	1.80779	+	6.74676i	0.235354	+	0.878354i	−0.742635	+	0.669697i	$0.766424\pi$
$60$	−0.333247	+	0.333247i	−0.0430220	+	0.0430220i
$61$	1.01629	+	0.586753i	0.130122	+	0.0751260i	0.563648	−	0.826015i	$-0.309397\pi$
$61$	1.01629	+	0.586753i	0.130122	+	0.0751260i	−0.433526	+	0.901141i	$0.642731\pi$
$62$	−6.55723	−	11.3575i	−0.832770	−	1.44240i
$63$	0.551959	−	2.05994i	0.0695403	−	0.259528i
$64$			6.96721i			0.870901i
$65$	7.01572	−	3.67015i	0.870192	−	0.455226i
$66$	1.43413	−	4.72271i	0.176530	−	0.581325i
$67$	0.0671688	−	0.250677i	0.00820597	−	0.0306251i	−0.961701	−	0.274099i	$-0.911620\pi$
$67$	0.0671688	−	0.250677i	0.00820597	−	0.0306251i	0.969907	+	0.243474i	$0.0782870\pi$
$68$	0.701913	−	0.405250i	0.0851195	−	0.0491438i
$69$	−3.66864	−	2.11809i	−0.441652	−	0.254988i
$70$	−4.92803	−	4.92803i	−0.589012	−	0.589012i
$71$	0.596881	−	0.159934i	0.0708368	−	0.0189807i	−0.223227	−	0.974767i	$-0.571659\pi$
$71$	0.596881	−	0.159934i	0.0708368	−	0.0189807i	0.294063	+	0.955786i	$0.404992\pi$
$72$	−2.56641	+	0.687666i	−0.302454	+	0.0810423i
$73$	−3.07555	−	3.07555i	−0.359966	−	0.359966i	0.503834	−	0.863800i	$-0.331922\pi$
$73$	−3.07555	−	3.07555i	−0.359966	−	0.359966i	−0.863800	+	0.503834i	$0.831922\pi$
$74$	−5.39185	−	3.11298i	−0.626790	−	0.361877i
$75$	−0.153868	+	0.0888356i	−0.0177671	+	0.0102578i
$76$	−0.286475	+	1.06914i	−0.0328609	+	0.122639i
$77$	6.76789	+	2.05519i	0.771273	+	0.234210i
$78$	−5.36098	−	0.223234i	−0.607012	−	0.0252763i
$79$			8.01708i			0.901993i	0.892526	+	0.450996i	$0.148931\pi$
$79$			8.01708i			0.901993i	−0.892526	+	0.450996i	$0.851069\pi$
$80$	−2.49122	+	9.29737i	−0.278527	+	1.03948i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−0.972340	−	0.561381i	−0.107377	−	0.0619941i
$83$	−6.52681	+	6.52681i	−0.716411	+	0.716411i	−0.967868	−	0.251458i	$-0.919090\pi$
$83$	−6.52681	+	6.52681i	−0.716411	+	0.716411i	0.251458	+	0.967868i	$0.419090\pi$
$84$	0.118457	+	0.442086i	0.0129247	+	0.0482356i
$85$	−8.01074	+	2.14647i	−0.868887	+	0.232818i
$86$	4.96419	−	4.96419i	0.535302	−	0.535302i
$87$	3.17297	+	1.83192i	0.340178	+	0.196402i
$88$	−1.99849	−	8.58246i	−0.213040	−	0.914893i
$89$	−13.2990	−	3.56346i	−1.40969	−	0.377726i	−0.527878	−	0.849320i	$-0.677012\pi$
$89$	−13.2990	−	3.56346i	−1.40969	−	0.377726i	−0.881816	+	0.471594i	$0.843679\pi$
$90$	−3.26796			−0.344474
$91$	0.319906	−	7.68257i	0.0335353	−	0.805352i
$92$	0.909132			0.0947835
$93$	2.28086	−	8.51228i	0.236514	−	0.882682i
$94$	9.17422	−	5.29674i	0.946248	−	0.546317i
$95$	5.66287	−	9.80838i	0.580998	−	1.00632i
$96$	0.854863	−	0.854863i	0.0872491	−	0.0872491i
$97$	−3.58037	+	0.959356i	−0.363531	+	0.0974079i	−0.435961	−	0.899966i	$-0.643591\pi$
$97$	−3.58037	+	0.959356i	−0.363531	+	0.0974079i	0.0724297	+	0.997374i	$0.476925\pi$
$98$	3.52461	−	0.944416i	0.356039	−	0.0954004i
$99$	2.92546	−	1.56259i	0.294020	−	0.157046i
$100$	0.0190651	−	0.0330217i	0.00190651	−	0.00330217i
$101$	−0.681248	−	1.17996i	−0.0677867	−	0.117410i	0.830140	−	0.557555i	$-0.188260\pi$
$101$	−0.681248	−	1.17996i	−0.0677867	−	0.117410i	−0.897927	+	0.440145i	$0.854927\pi$
$102$	5.42866	+	1.45461i	0.537518	+	0.144027i
$103$		−	17.5479i		−	1.72904i	−0.502596	−	0.864521i	$-0.667622\pi$
$103$		−	17.5479i		−	1.72904i	0.502596	−	0.864521i	$-0.332378\pi$
$104$	−8.48839	+	4.44055i	−0.832355	+	0.435432i
$105$		−	4.68316i		−	0.457030i
$106$	−12.7453	−	3.41510i	−1.23794	−	0.331704i
$107$	−9.45649	+	5.45971i	−0.914194	+	0.527810i	−0.881778	−	0.471664i	$-0.843653\pi$
$107$	−9.45649	+	5.45971i	−0.914194	+	0.527810i	−0.0324157	+	0.999474i	$0.510320\pi$
$108$	0.185859	+	0.107306i	0.0178843	+	0.0103255i
$109$	−8.87539	+	8.87539i	−0.850108	+	0.850108i	−0.990146	−	0.140038i	$-0.955277\pi$
$109$	−8.87539	+	8.87539i	−0.850108	+	0.850108i	0.140038	+	0.990146i	$0.455277\pi$
$110$	0.357810	−	10.8327i	0.0341159	−	1.03286i
$111$	−1.08282	−	4.04112i	−0.102776	−	0.383566i
$112$	6.60973	+	6.60973i	0.624561	+	0.624561i
$113$	−1.65967	+	2.87463i	−0.156128	+	0.270422i	−0.933469	−	0.358657i	$-0.883235\pi$
$113$	−1.65967	+	2.87463i	−0.156128	+	0.270422i	0.777341	+	0.629079i	$0.216568\pi$
$114$	−6.64688	+	3.83758i	−0.622537	+	0.359422i
$115$	−8.98559	−	2.40768i	−0.837910	−	0.224517i
$116$	−0.786299			−0.0730061
$117$	−2.44123	−	2.65337i	−0.225692	−	0.245304i
$118$		−	10.3944i		−	0.956884i
$119$	−2.08453	+	7.77956i	−0.191088	+	0.713151i
$120$	−5.05290	+	2.91729i	−0.461264	+	0.266311i
$121$	4.85938	+	9.86846i	0.441762	+	0.897132i
$122$	−1.23486	−	1.23486i	−0.111799	−	0.111799i
$123$	−0.195270	−	0.728757i	−0.0176069	−	0.0657098i
$124$	0.489498	+	1.82683i	0.0439582	+	0.164054i
$125$	−8.03985	+	8.03985i	−0.719106	+	0.719106i
$126$	−1.58683	+	2.74846i	−0.141366	+	0.244853i
$127$	−10.1607	−	17.5988i	−0.901613	−	1.56164i	−0.825400	−	0.564548i	$-0.809051\pi$
$127$	−10.1607	−	17.5988i	−0.901613	−	1.56164i	−0.0762127	−	0.997092i	$-0.524283\pi$
$128$	3.30932	−	12.3505i	0.292505	−	1.09164i
$129$	4.71753			0.415355
$130$	−11.4983	+	2.57346i	−1.00847	+	0.225707i
$131$			18.2842i			1.59750i	0.601664	+	0.798749i	$0.294505\pi$
$131$			18.2842i			1.59750i	−0.601664	+	0.798749i	$0.705495\pi$
$132$	−0.376048	+	0.604339i	−0.0327308	+	0.0526009i
$133$	−5.49945	−	9.52532i	−0.476863	−	0.825950i
$134$	−0.193103	+	0.334465i	−0.0166816	+	0.0288934i
$135$	−1.55279	−	1.55279i	−0.133643	−	0.133643i
$136$	9.69228	−	2.59704i	0.831106	−	0.222694i
$137$	−0.118704	−	0.443010i	−0.0101416	−	0.0378489i	0.960670	−	0.277694i	$-0.0895701\pi$
$137$	−0.118704	−	0.443010i	−0.0101416	−	0.0378489i	−0.970811	+	0.239845i	$0.922903\pi$
$138$	4.45767	+	4.45767i	0.379462	+	0.379462i
$139$	5.16630	+	2.98277i	0.438200	+	0.252995i	0.702834	−	0.711354i	$-0.251918\pi$
$139$	5.16630	+	2.98277i	0.438200	+	0.252995i	−0.264634	+	0.964349i	$0.585251\pi$
$140$	0.502530	+	0.870407i	0.0424715	+	0.0735628i
$141$	6.87596	+	1.84241i	0.579060	+	0.155159i
$142$	−0.919587			−0.0771700
$143$	9.06274	−	7.80172i	0.757864	−	0.652412i
$144$	4.38316			0.365264
$145$	7.77155	+	2.08238i	0.645392	+	0.172932i
$146$	3.23636	+	5.60554i	0.267843	+	0.463918i
$147$	2.12348	+	1.22599i	0.175142	+	0.101118i
$148$	0.634886	+	0.634886i	0.0521873	+	0.0521873i
$149$	−0.277338	−	1.03504i	−0.0227204	−	0.0847937i	0.953635	−	0.300966i	$-0.0973092\pi$
$149$	−0.277338	−	1.03504i	−0.0227204	−	0.0847937i	−0.976355	+	0.216173i	$0.930643\pi$
$150$	0.255393	−	0.0684324i	0.0208528	−	0.00558748i
$151$	12.6595	+	12.6595i	1.03021	+	1.03021i	0.999529	+	0.0306850i	$0.00976886\pi$
$151$	12.6595	+	12.6595i	1.03021	+	1.03021i	0.0306850	+	0.999529i	$0.490231\pi$
$152$	−6.85157	+	11.8673i	−0.555735	+	0.962562i
$153$	1.88830	+	3.27063i	0.152660	+	0.264415i
$154$	−8.93692	−	5.56097i	−0.720157	−	0.448116i
$155$		−	19.3522i		−	1.55441i
$156$	0.738446	+	0.231195i	0.0591230	+	0.0185104i
$157$	15.8068			1.26152			0.630762	−	0.775977i	$-0.282743\pi$
$157$	15.8068			1.26152			0.630762	+	0.775977i	$0.282743\pi$
$158$	3.08789	−	11.5242i	0.245659	−	0.916812i
$159$	−4.43332	−	7.67873i	−0.351585	−	0.608963i
$160$	1.32743	−	2.29917i	0.104942	−	0.181765i
$161$	−6.38808	+	6.38808i	−0.503451	+	0.503451i
$162$	0.385163	+	1.43745i	0.0302613	+	0.112937i
$163$	4.57297	+	17.0665i	0.358182	+	1.33675i	0.876432	+	0.481526i	$0.159917\pi$
$163$	4.57297	+	17.0665i	0.358182	+	1.33675i	−0.518250	+	0.855229i	$0.673416\pi$
$164$	0.114492	+	0.114492i	0.00894035	+	0.00894035i
$165$	5.31724	−	4.97721i	0.413946	−	0.387475i
$166$	11.8958	−	6.86807i	0.923297	−	0.533066i
$167$	−3.06167	+	11.4263i	−0.236919	+	0.884193i	0.740356	+	0.672215i	$0.234657\pi$
$167$	−3.06167	+	11.4263i	−0.236919	+	0.884193i	−0.977275	+	0.211978i	$0.932010\pi$
$168$			5.66621i			0.437157i
$169$	−10.6790	−	7.41348i	−0.821459	−	0.570268i
$170$	12.3418			0.946571
$171$	−4.98175	−	1.33486i	−0.380964	−	0.102079i
$172$	−0.876794	+	0.506217i	−0.0668549	+	0.0385987i
$173$	11.2994	−	19.5711i	0.859077	−	1.48797i	−0.0137328	−	0.999906i	$-0.504371\pi$
$173$	11.2994	−	19.5711i	0.859077	−	1.48797i	0.872810	−	0.488060i	$-0.162295\pi$
$174$	−3.85540	−	3.85540i	−0.292277	−	0.292277i
$175$	0.0980673	+	0.365992i	0.00741319	+	0.0276664i
$176$	−0.479914	+	14.5294i	−0.0361749	+	1.09519i
$177$	4.93897	−	4.93897i	0.371236	−	0.371236i
$178$	17.7442	+	10.2446i	1.32998	+	0.767865i
$179$	−3.78593	+	2.18581i	−0.282974	+	0.163375i	−0.634769	−	0.772702i	$-0.718905\pi$
$179$	−3.78593	+	2.18581i	−0.282974	+	0.163375i	0.351795	+	0.936077i	$0.385571\pi$
$180$	0.455223	+	0.121977i	0.0339303	+	0.00909161i
$181$			10.9274i			0.812231i	0.913822	+	0.406115i	$0.133117\pi$
$181$			10.9274i			0.812231i	−0.913822	+	0.406115i	$0.866883\pi$
$182$	−3.41889	+	10.9201i	−0.253425	+	0.809450i
$183$		−	1.17351i		−	0.0867480i
$184$	10.8718	+	2.91308i	0.801476	+	0.214755i
$185$	−4.59364	−	7.95641i	−0.337731	−	0.584967i
$186$	−6.55723	+	11.3575i	−0.480800	+	0.832770i
$187$	−11.0483	+	5.90126i	−0.807931	+	0.431543i
$188$	−1.47566	+	0.395401i	−0.107623	+	0.0288376i
$189$	−2.05994	+	0.551959i	−0.149839	+	0.0401491i
$190$	−11.9179	+	11.9179i	−0.864617	+	0.864617i
$191$	−7.99586	+	13.8492i	−0.578560	+	1.00210i	0.417084	+	0.908868i	$0.363052\pi$
$191$	−7.99586	+	13.8492i	−0.578560	+	1.00210i	−0.995645	+	0.0932282i	$0.970281\pi$
$192$	6.03378	−	3.48360i	0.435450	−	0.251407i
$193$	3.95387	−	14.7561i	0.284606	−	1.06216i	−0.664521	−	0.747270i	$-0.731364\pi$
$193$	3.95387	−	14.7561i	0.284606	−	1.06216i	0.949127	−	0.314894i	$-0.101969\pi$
$194$	5.51610			0.396033
$195$	−6.68630	−	4.24071i	−0.478816	−	0.303684i
$196$	−0.526224			−0.0375874
$197$	11.6033	+	3.10910i	0.826702	+	0.221514i	0.647274	−	0.762257i	$-0.275909\pi$
$197$	11.6033	+	3.10910i	0.826702	+	0.221514i	0.179428	+	0.983771i	$0.442575\pi$
$198$	−4.80705	+	1.11936i	−0.341622	+	0.0795494i
$199$	17.5499	+	10.1325i	1.24408	+	0.718272i	0.969923	−	0.243413i	$-0.0782669\pi$
$199$	17.5499	+	10.1325i	1.24408	+	0.718272i	0.274160	+	0.961684i	$0.411600\pi$
$200$	0.333798	−	0.333798i	0.0236031	−	0.0236031i
$201$	−0.250677	+	0.0671688i	−0.0176814	+	0.00473772i
$202$	0.524783	+	1.95852i	0.0369236	+	0.137801i
$203$	5.52499	−	5.52499i	0.387778	−	0.387778i
$204$	−0.701913	−	0.405250i	−0.0491438	−	0.0283732i
$205$	−0.828395	−	1.43482i	−0.0578576	−	0.100212i
$206$	−6.75880	+	25.2242i	−0.470908	+	1.75745i
$207$			4.23618i			0.294435i
$208$	15.4222	−	3.45166i	1.06934	−	0.239330i
$209$	4.97026	−	16.3674i	0.343800	−	1.13216i
$210$	−1.80378	+	6.73181i	−0.124473	+	0.464539i
$211$	−8.41117	+	4.85619i	−0.579048	+	0.334314i	−0.760755	−	0.649039i	$-0.775171\pi$
$211$	−8.41117	+	4.85619i	−0.579048	+	0.334314i	0.181707	+	0.983353i	$0.441838\pi$
$212$	1.64794	+	0.951439i	0.113181	+	0.0653451i
$213$	−0.436947	−	0.436947i	−0.0299391	−	0.0299391i
$214$	15.6961	−	4.20576i	1.07296	−	0.287500i
$215$	10.0066	−	2.68126i	0.682445	−	0.182861i
$216$	1.87874	+	1.87874i	0.127832	+	0.127832i
$217$	−16.2758	−	9.39686i	−1.10488	−	0.637900i
$218$	16.1764	−	9.33944i	1.09560	−	0.632547i
$219$	−1.12573	+	4.20129i	−0.0760698	+	0.283897i
$220$	−0.454173	+	1.49563i	−0.0306203	+	0.100835i
$221$	9.21954	+	10.0207i	0.620174	+	0.674066i
$222$			6.22597i			0.417860i
$223$	6.14010	−	22.9152i	0.411171	−	1.53451i	−0.381211	−	0.924488i	$-0.624493\pi$
$223$	6.14010	−	22.9152i	0.411171	−	1.53451i	0.792383	−	0.610024i	$-0.208840\pi$
$224$	−1.28912	−	2.23282i	−0.0861328	−	0.149186i
$225$	0.153868	+	0.0888356i	0.0102578	+	0.00592237i
$226$	3.49289	−	3.49289i	0.232343	−	0.232343i
$227$	5.27217	+	19.6760i	0.349926	+	1.30594i	0.886751	+	0.462248i	$0.152957\pi$
$227$	5.27217	+	19.6760i	0.349926	+	1.30594i	−0.536824	+	0.843694i	$0.680376\pi$
$228$	1.06914	−	0.286475i	0.0708055	−	0.0189723i
$229$	−11.0805	+	11.0805i	−0.732218	+	0.732218i	−0.971059	−	0.238841i	$-0.923233\pi$
$229$	−11.0805	+	11.0805i	−0.732218	+	0.732218i	0.238841	+	0.971059i	$0.423233\pi$
$230$	11.9890	+	6.92184i	0.790530	+	0.456413i
$231$	−1.60410	−	6.88876i	−0.105542	−	0.453247i
$232$	−9.40288	−	2.51949i	−0.617329	−	0.165413i
$233$	7.02154			0.459997			0.229998	−	0.973191i	$-0.426128\pi$
$233$	7.02154			0.459997			0.229998	+	0.973191i	$0.426128\pi$
$234$	2.48716	+	4.75436i	0.162591	+	0.310802i
$235$	15.6321			1.01973
$236$	−0.387972	+	1.44793i	−0.0252548	+	0.0942523i
$237$	6.94300	−	4.00854i	0.450996	−	0.260383i
$238$	5.99280	−	10.3798i	0.388456	−	0.672825i
$239$	−19.0035	+	19.0035i	−1.22923	+	1.22923i	−0.264980	+	0.964254i	$0.585365\pi$
$239$	−19.0035	+	19.0035i	−1.22923	+	1.22923i	−0.964254	+	0.264980i	$0.914635\pi$
$240$	9.29737	−	2.49122i	0.600142	−	0.160808i
$241$	−0.955937	+	0.256142i	−0.0615773	+	0.0164996i	−0.289476	−	0.957185i	$-0.593481\pi$
$241$	−0.955937	+	0.256142i	−0.0615773	+	0.0164996i	0.227899	+	0.973685i	$0.426814\pi$
$242$	−3.18415	−	16.0571i	−0.204685	−	1.03219i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	0.125924	+	0.218106i	0.00806144	+	0.0139628i
$245$	5.20104	+	1.39362i	0.332282	+	0.0890348i
$246$			1.12276i			0.0715847i
$247$	−18.5795	−	0.773660i	−1.18218	−	0.0492268i
$248$			23.4144i			1.48682i
$249$	8.91579	+	2.38898i	0.565015	+	0.151395i
$250$	14.6535	−	8.46022i	0.926771	−	0.535071i
$251$	10.1981	+	5.88790i	0.643701	+	0.371641i	0.786039	−	0.618177i	$-0.212129\pi$
$251$	10.1981	+	5.88790i	0.643701	+	0.371641i	−0.142338	+	0.989818i	$0.545462\pi$
$252$	0.323630	−	0.323630i	0.0203867	−	0.0203867i
$253$	−14.0422	−	0.463821i	−0.882823	−	0.0291602i
$254$	7.82703	+	29.2109i	0.491112	+	1.83285i
$255$	5.86427	+	5.86427i	0.367235	+	0.367235i
$256$	−2.54674	+	4.41109i	−0.159171	+	0.275693i
$257$	−12.6563	+	7.30712i	−0.789478	+	0.455805i	−0.839779	−	0.542929i	$-0.817315\pi$
$257$	−12.6563	+	7.30712i	−0.789478	+	0.455805i	0.0503007	+	0.998734i	$0.483982\pi$
$258$	−6.78121	−	1.81702i	−0.422180	−	0.113123i
$259$	−8.92214			−0.554395
$260$	1.69776	+	0.0706957i	0.105291	+	0.00438436i
$261$		−	3.66383i		−	0.226786i
$262$	7.04241	−	26.2826i	0.435081	−	1.62375i
$263$	−17.3779	+	10.0331i	−1.07156	+	0.618668i	−0.928609	−	0.371061i	$-0.878994\pi$
$263$	−17.3779	+	10.0331i	−1.07156	+	0.618668i	−0.142956	+	0.989729i	$0.545661\pi$
$264$	−6.43338	+	6.02197i	−0.395947	+	0.370627i
$265$	−13.7680	−	13.7680i	−0.845764	−	0.845764i
$266$	4.23637	+	15.8104i	0.259749	+	0.969395i
$267$	3.56346	+	13.2990i	0.218080	+	0.813887i
$268$	0.0393830	−	0.0393830i	0.00240570	−	0.00240570i
$269$	7.83667	−	13.5735i	0.477810	−	0.827592i	−0.521866	−	0.853027i	$-0.674764\pi$
$269$	7.83667	−	13.5735i	0.477810	−	0.827592i	0.999676	+	0.0254355i	$0.00809725\pi$
$270$	1.63398	+	2.83014i	0.0994410	+	0.172237i
$271$	3.96507	−	14.7978i	0.240861	−	0.898904i	−0.734558	−	0.678546i	$-0.762611\pi$
$271$	3.96507	−	14.7978i	0.240861	−	0.898904i	0.975419	−	0.220359i	$-0.0707227\pi$
$272$	−16.5534			−1.00370
$273$	−6.81325	+	3.56424i	−0.412357	+	0.215717i
$274$			0.682525i			0.0412328i
$275$	−0.311321	+	0.500317i	−0.0187733	+	0.0301702i
$276$	−0.454566	−	0.787331i	−0.0273616	−	0.0473918i
$277$	7.11278	−	12.3197i	0.427365	−	0.740218i	−0.569273	−	0.822149i	$-0.692775\pi$
$277$	7.11278	−	12.3197i	0.427365	−	0.740218i	0.996638	+	0.0819303i	$0.0261085\pi$
$278$	−6.27744	−	6.27744i	−0.376496	−	0.376496i
$279$	−8.51228	+	2.28086i	−0.509617	+	0.136551i
$280$	3.22045	+	12.0189i	0.192459	+	0.718266i
$281$	−10.3329	−	10.3329i	−0.616408	−	0.616408i	0.328200	−	0.944608i	$-0.393558\pi$
$281$	−10.3329	−	10.3329i	−0.616408	−	0.616408i	−0.944608	+	0.328200i	$0.893558\pi$
$282$	−9.17422	−	5.29674i	−0.546317	−	0.315416i
$283$	−3.09024	−	5.35246i	−0.183696	−	0.318171i	0.759440	−	0.650577i	$-0.225473\pi$
$283$	−3.09024	−	5.35246i	−0.183696	−	0.318171i	−0.943136	+	0.332406i	$0.892140\pi$
$284$	0.128097	+	0.0343236i	0.00760118	+	0.00203673i
$285$	−11.3257			−0.670879
$286$	−16.0322	+	7.72394i	−0.948002	+	0.456726i
$287$	−1.60898			−0.0949749
$288$	−1.16776	−	0.312902i	−0.0688112	−	0.0184379i
$289$	1.36866	+	2.37059i	0.0805095	+	0.139447i
$290$	−10.3692	−	5.98663i	−0.608898	−	0.351547i
$291$	2.62101	+	2.62101i	0.153646	+	0.153646i
$292$	−0.241594	−	0.901643i	−0.0141382	−	0.0527647i
$293$	25.6024	−	6.86015i	1.49571	−	0.400775i	0.584050	−	0.811718i	$-0.301467\pi$
$293$	25.6024	−	6.86015i	1.49571	−	0.400775i	0.911661	+	0.410943i	$0.134801\pi$
$294$	−2.58019	−	2.58019i	−0.150480	−	0.150480i
$295$	7.66920	−	13.2834i	0.446518	−	0.773392i
$296$	5.55789	+	9.62654i	0.323046	+	0.559531i
$297$	−2.81597	−	1.75223i	−0.163399	−	0.101675i
$298$			1.59464i			0.0923748i
$299$	3.33591	+	14.9050i	0.192921	+	0.861979i
$300$	−0.0381302			−0.00220145
$301$	2.60388	−	9.71783i	0.150085	−	0.560126i
$302$	−13.3214	−	23.0733i	−0.766560	−	1.32772i
$303$	−0.681248	+	1.17996i	−0.0391367	+	0.0677867i
$304$	15.9849	−	15.9849i	0.916799	−	0.916799i
$305$	−0.666976	−	2.48919i	−0.0381909	−	0.142530i
$306$	−1.45461	−	5.42866i	−0.0831543	−	0.310336i
$307$	18.2098	+	18.2098i	1.03929	+	1.03929i	0.999196	+	0.0400926i	$0.0127653\pi$
$307$	18.2098	+	18.2098i	1.03929	+	1.03929i	0.0400926	+	0.999196i	$0.487235\pi$
$308$	1.03734	+	1.10821i	0.0591078	+	0.0631460i
$309$	−15.1969	+	8.77393i	−0.864521	+	0.499132i
$310$	−7.45376	+	27.8178i	−0.423345	+	1.57995i
$311$		−	35.2378i		−	1.99815i	−0.0429601	−	0.999077i	$-0.513679\pi$
$311$		−	35.2378i		−	1.99815i	0.0429601	−	0.999077i	$-0.486321\pi$
$312$	8.08983	+	5.13088i	0.457996	+	0.290479i
$313$	−17.5305			−0.990882			−0.495441	−	0.868642i	$-0.664994\pi$
$313$	−17.5305			−0.990882			−0.495441	+	0.868642i	$0.664994\pi$
$314$	−22.7215	−	6.08822i	−1.28225	−	0.343578i
$315$	−4.05574	+	2.34158i	−0.228515	+	0.131933i
$316$	−0.860278	+	1.49005i	−0.0483944	+	0.0838216i
$317$	−11.0362	−	11.0362i	−0.619858	−	0.619858i	0.325637	−	0.945495i	$-0.394421\pi$
$317$	−11.0362	−	11.0362i	−0.619858	−	0.619858i	−0.945495	+	0.325637i	$0.894421\pi$
$318$	3.41510	+	12.7453i	0.191509	+	0.714723i
$319$	12.1449	+	0.401154i	0.679986	+	0.0224603i
$320$	10.8186	−	10.8186i	0.604780	−	0.604780i
$321$	9.45649	+	5.45971i	0.527810	+	0.304731i
$322$	11.6430	−	6.72208i	0.648838	−	0.374607i
$323$	18.8141	+	5.04121i	1.04684	+	0.280501i
$324$		−	0.214611i		−	0.0119228i
$325$	0.611341	+	0.191400i	0.0339111	+	0.0106170i
$326$		−	26.2936i		−	1.45627i
$327$	12.1240	+	3.24862i	0.670459	+	0.179649i
$328$	1.00228	+	1.73601i	0.0553418	+	0.0958549i
$329$	7.59050	−	13.1471i	0.418478	−	0.724825i
$330$	−9.56030	+	5.10648i	−0.526277	+	0.281102i
$331$	1.47608	−	0.395513i	0.0811324	−	0.0217394i	−0.218024	−	0.975943i	$-0.569961\pi$
$331$	1.47608	−	0.395513i	0.0811324	−	0.0217394i	0.299157	+	0.954204i	$0.403295\pi$
$332$	−1.91343	+	0.512702i	−0.105013	+	0.0281382i
$333$	−2.95831	+	2.95831i	−0.162114	+	0.162114i
$334$	8.80198	−	15.2455i	0.481623	−	0.834195i
$335$	−0.493549	+	0.284951i	−0.0269655	+	0.0155685i
$336$	2.41933	−	9.02906i	0.131985	−	0.492575i
$337$	−6.08520			−0.331482			−0.165741	−	0.986169i	$-0.553002\pi$
$337$	−6.08520			−0.331482			−0.165741	+	0.986169i	$0.553002\pi$
$338$	12.4951	+	14.7696i	0.679642	+	0.803363i
$339$	3.31933			0.180281
$340$	−1.71919	−	0.460657i	−0.0932364	−	0.0249826i
$341$	−6.62861	−	28.4664i	−0.358960	−	1.54154i
$342$	6.64688	+	3.83758i	0.359422	+	0.207512i
$343$	14.2534	−	14.2534i	0.769612	−	0.769612i
$344$	−12.1071	+	3.24409i	−0.652771	+	0.174909i
$345$	2.40768	+	8.98559i	0.129625	+	0.483768i
$346$	−23.7804	+	23.7804i	−1.27844	+	1.27844i
$347$	−17.0817	−	9.86214i	−0.916995	−	0.529427i	−0.0343200	−	0.999411i	$-0.510927\pi$
$347$	−17.0817	−	9.86214i	−0.916995	−	0.529427i	−0.882675	+	0.469983i	$0.844260\pi$
$348$	0.393150	+	0.680955i	0.0210750	+	0.0365030i
$349$	1.13496	−	4.23572i	0.0607530	−	0.226733i	−0.928874	−	0.370397i	$-0.879222\pi$
$349$	1.13496	−	4.23572i	0.0607530	−	0.226733i	0.989627	+	0.143664i	$0.0458884\pi$
$350$		−	0.563867i		−	0.0301399i
$351$	−1.07727	+	3.44085i	−0.0575006	+	0.183659i
$352$	1.16507	−	3.83667i	0.0620985	−	0.204495i
$353$	−1.15465	+	4.30923i	−0.0614560	+	0.229357i	−0.989822	−	0.142310i	$-0.954547\pi$
$353$	−1.15465	+	4.30923i	−0.0614560	+	0.229357i	0.928366	+	0.371667i	$0.121214\pi$
$354$	−9.00183	+	5.19721i	−0.478442	+	0.276229i
$355$	−1.17518	−	0.678489i	−0.0623719	−	0.0360104i
$356$	−2.08936	−	2.08936i	−0.110736	−	0.110736i
$357$	7.77956	−	2.08453i	0.411738	−	0.110325i
$358$	6.28398	−	1.68379i	0.332119	−	0.0889909i
$359$	−23.5092	−	23.5092i	−1.24077	−	1.24077i	−0.959683	−	0.281084i	$-0.909306\pi$
$359$	−23.5092	−	23.5092i	−1.24077	−	1.24077i	−0.281084	−	0.959683i	$-0.590694\pi$
$360$	5.05290	+	2.91729i	0.266311	+	0.153755i
$361$	−6.58152	+	3.79984i	−0.346396	+	0.199992i
$362$	4.20885	−	15.7076i	0.221212	−	0.825576i
$363$	6.11664	−	9.14257i	0.321041	−	0.479861i
$364$	0.883840	−	1.39354i	0.0463258	−	0.0730416i
$365$			9.55139i			0.499943i
$366$	−0.451991	+	1.68686i	−0.0236260	+	0.0881733i
$367$	11.9808	+	20.7513i	0.625391	+	1.08321i	0.988465	+	0.151448i	$0.0483937\pi$
$367$	11.9808	+	20.7513i	0.625391	+	1.08321i	−0.363075	+	0.931760i	$0.618273\pi$
$368$	−16.0802	−	9.28394i	−0.838241	−	0.483959i
$369$	−0.533487	+	0.533487i	−0.0277722	+	0.0277722i
$370$	3.53860	+	13.2062i	0.183963	+	0.686560i
$371$	−18.2647	+	4.89402i	−0.948258	+	0.254085i
$372$	1.33733	−	1.33733i	0.0693375	−	0.0693375i
$373$	−14.6319	−	8.44773i	−0.757611	−	0.437407i	0.0708262	−	0.997489i	$-0.477436\pi$
$373$	−14.6319	−	8.44773i	−0.757611	−	0.437407i	−0.828437	+	0.560082i	$0.810770\pi$
$374$	18.1543	−	4.22737i	0.938736	−	0.218592i
$375$	10.9826	+	2.94279i	0.567141	+	0.151965i
$376$	−18.9135			−0.975388
$377$	−2.88520	−	12.8912i	−0.148595	−	0.663931i
$378$	3.17365			0.163235
$379$	−7.88743	+	29.4363i	−0.405150	+	1.51204i	0.398628	+	0.917113i	$0.369486\pi$
$379$	−7.88743	+	29.4363i	−0.405150	+	1.51204i	−0.803779	+	0.594929i	$0.797180\pi$
$380$	2.10499	−	1.21532i	0.107984	−	0.0623444i
$381$	−10.1607	+	17.5988i	−0.520547	+	0.901613i
$382$	16.8279	−	16.8279i	0.860989	−	0.860989i
$383$	−9.82714	+	2.63318i	−0.502144	+	0.134549i	−0.500995	−	0.865450i	$-0.667032\pi$
$383$	−9.82714	+	2.63318i	−0.502144	+	0.134549i	−0.00114894	+	0.999999i	$0.500366\pi$
$384$	−12.3505	+	3.30932i	−0.630261	+	0.168878i
$385$	−7.31785	−	13.7004i	−0.372952	−	0.698237i
$386$	−11.3670	+	19.6882i	−0.578564	+	1.00210i
$387$	−2.35876	−	4.08550i	−0.119903	−	0.207678i
$388$	−0.768387	−	0.205889i	−0.0390089	−	0.0104524i
$389$			9.12187i			0.462497i	0.972895	+	0.231249i	$0.0742810\pi$
$389$			9.12187i			0.462497i	−0.972895	+	0.231249i	$0.925719\pi$
$390$	7.97785	+	8.67113i	0.403974	+	0.439080i
$391$		−	15.9983i		−	0.809071i
$392$	−6.29280	−	1.68615i	−0.317834	−	0.0851634i
$393$	15.8346	−	9.14210i	0.798749	−	0.461158i
$394$	−15.4817	−	8.93834i	−0.779955	−	0.450307i
$395$	12.4489	−	12.4489i	0.626371	−	0.626371i
$396$	0.711397	+	0.0234979i	0.0357490	+	0.00118081i
$397$	1.24375	+	4.64174i	0.0624220	+	0.232962i	0.990088	−	0.140449i	$-0.0448547\pi$
$397$	1.24375	+	4.64174i	0.0624220	+	0.232962i	−0.927666	+	0.373411i	$0.878188\pi$
$398$	−21.3245	−	21.3245i	−1.06890	−	1.06890i
$399$	−5.49945	+	9.52532i	−0.275317	+	0.476863i
$400$	−0.674428	+	0.389381i	−0.0337214	+	0.0194690i
$401$	23.3647	+	6.26055i	1.16678	+	0.312637i	0.789670	−	0.613532i	$-0.210252\pi$
$401$	23.3647	+	6.26055i	1.16678	+	0.312637i	0.377108	+	0.926169i	$0.376919\pi$
$402$	0.386207			0.0192622
$403$	−28.1543	+	14.7285i	−1.40247	+	0.733677i
$404$		−	0.292407i		−	0.0145478i
$405$	−0.568361	+	2.12115i	−0.0282421	+	0.105401i
$406$	−10.0699	+	5.81387i	−0.499761	+	0.288537i
$407$	−9.48234	−	10.1302i	−0.470022	−	0.502133i
$408$	−7.09524	−	7.09524i	−0.351267	−	0.351267i
$409$	−10.1182	−	37.7615i	−0.500311	−	1.86718i	−0.497983	−	0.867187i	$-0.665926\pi$
$409$	−10.1182	−	37.7615i	−0.500311	−	1.86718i	−0.00232802	−	0.999997i	$-0.500741\pi$
$410$	0.638135	+	2.38155i	0.0315152	+	0.117616i
$411$	−0.324306	+	0.324306i	−0.0159968	+	0.0159968i
$412$	1.88298	−	3.26142i	0.0927680	−	0.160679i
$413$	−7.44788	−	12.9001i	−0.366486	−	0.634772i
$414$	1.63162	−	6.08929i	0.0801898	−	0.299272i
$415$	20.2696			0.994994
$416$	−4.35519	−	0.181353i	−0.213531	−	0.00889154i
$417$		−	5.96553i		−	0.292133i
$418$	−13.4486	+	21.6130i	−0.657794	+	1.05713i
$419$	13.5033	+	23.3884i	0.659679	+	1.14260i	0.980699	+	0.195525i	$0.0626411\pi$
$419$	13.5033	+	23.3884i	0.659679	+	1.14260i	−0.321020	+	0.947073i	$0.604026\pi$
$420$	0.502530	−	0.870407i	0.0245209	−	0.0424715i
$421$	−8.20360	−	8.20360i	−0.399819	−	0.399819i	0.478350	−	0.878169i	$-0.341235\pi$
$421$	−8.20360	−	8.20360i	−0.399819	−	0.399819i	−0.878169	+	0.478350i	$0.841235\pi$
$422$	13.9610	−	3.74085i	0.679613	−	0.182102i
$423$	−1.84241	−	6.87596i	−0.0895810	−	0.334321i
$424$	16.6581	+	16.6581i	0.808989	+	0.808989i
$425$	−0.581096	−	0.335496i	−0.0281873	−	0.0162740i
$426$	0.459794	+	0.796386i	0.0222771	+	0.0385850i
$427$	−2.41735	−	0.647727i	−0.116984	−	0.0313457i
$428$	−2.34343			−0.113274
$429$	−11.2879	−	3.94770i	−0.544983	−	0.190597i
$430$	−15.4167			−0.743460
$431$	−34.0663	−	9.12803i	−1.64092	−	0.439682i	−0.683866	−	0.729608i	$-0.739703\pi$
$431$	−34.0663	−	9.12803i	−1.64092	−	0.439682i	−0.957049	+	0.289926i	$0.906369\pi$
$432$	−2.19158	−	3.79593i	−0.105443	−	0.182632i
$433$	20.9382	+	12.0887i	1.00623	+	0.580945i	0.910084	−	0.414423i	$-0.136017\pi$
$433$	20.9382	+	12.0887i	1.00623	+	0.580945i	0.0961412	+	0.995368i	$0.469350\pi$
$434$	19.7764	+	19.7764i	0.949296	+	0.949296i
$435$	−2.08238	−	7.77155i	−0.0998425	−	0.372617i
$436$	−2.60195	+	0.697190i	−0.124611	+	0.0333893i
$437$	15.4489	+	15.4489i	0.739021	+	0.739021i
$438$	3.23636	−	5.60554i	0.154639	−	0.267843i
$439$	18.6492	+	32.3014i	0.890078	+	1.54166i	0.839780	+	0.542926i	$0.182684\pi$
$439$	18.6492	+	32.3014i	0.890078	+	1.54166i	0.0502978	+	0.998734i	$0.483983\pi$
$440$	−10.2235	+	16.4300i	−0.487388	+	0.783270i
$441$		−	2.45199i		−	0.116761i
$442$	−9.39301	−	17.9553i	−0.446780	−	0.854047i
$443$	23.4549			1.11438			0.557189	−	0.830386i	$-0.311880\pi$
$443$	23.4549			1.11438			0.557189	+	0.830386i	$0.311880\pi$
$444$	0.232384	−	0.867270i	0.0110285	−	0.0411588i
$445$	15.1173	+	26.1839i	0.716629	+	1.24124i
$446$	−17.6522	+	30.5744i	−0.835854	+	1.44774i
$447$	−0.757701	+	0.757701i	−0.0358380	+	0.0358380i
$448$	−3.84562	−	14.3520i	−0.181688	−	0.678070i
$449$	−4.25929	−	15.8959i	−0.201008	−	0.750173i	−0.990629	−	0.136578i	$-0.956390\pi$
$449$	−4.25929	−	15.8959i	−0.201008	−	0.750173i	0.789621	−	0.613595i	$-0.210277\pi$
$450$	−0.186961	−	0.186961i	−0.00881342	−	0.00881342i
$451$	−1.71000	−	1.82682i	−0.0805208	−	0.0860218i
$452$	−0.616927	+	0.356183i	−0.0290178	+	0.0167534i
$453$	4.63369	−	17.2932i	0.217710	−	0.812504i
$454$		−	30.3139i		−	1.42270i
$455$	−12.4262	+	11.4327i	−0.582548	+	0.535972i
$456$	13.7031			0.641708
$457$	−12.9917	−	3.48110i	−0.607724	−	0.162839i	−0.0581829	−	0.998306i	$-0.518531\pi$
$457$	−12.9917	−	3.48110i	−0.607724	−	0.162839i	−0.549541	+	0.835467i	$0.685197\pi$
$458$	20.1954	−	11.6598i	0.943670	−	0.544828i
$459$	1.88830	−	3.27063i	0.0881382	−	0.152660i
$460$	−1.41169	−	1.41169i	−0.0658205	−	0.0658205i
$461$	−8.83809	−	32.9842i	−0.411631	−	1.53623i	−0.791489	−	0.611183i	$-0.790694\pi$
$461$	−8.83809	−	32.9842i	−0.411631	−	1.53623i	0.379858	−	0.925045i	$-0.375973\pi$
$462$	−0.347485	+	10.5201i	−0.0161664	+	0.489439i
$463$	−11.9794	+	11.9794i	−0.556729	+	0.556729i	−0.928375	−	0.371646i	$-0.878794\pi$
$463$	−11.9794	+	11.9794i	−0.556729	+	0.556729i	0.371646	+	0.928375i	$0.378794\pi$
$464$	13.9077	+	8.02959i	0.645647	+	0.372764i
$465$	−16.7595	+	9.67610i	−0.777203	+	0.448718i
$466$	−10.0931	−	2.70444i	−0.467554	−	0.125281i
$467$			6.10787i			0.282639i	0.989964	+	0.141319i	$0.0451344\pi$
$467$			6.10787i			0.282639i	−0.989964	+	0.141319i	$0.954866\pi$
$468$	−0.169002	−	0.755110i	−0.00781214	−	0.0349050i
$469$			0.553455i			0.0255562i
$470$	−22.4704	−	6.02092i	−1.03648	−	0.277724i
$471$	−7.90342	−	13.6891i	−0.364170	−	0.630762i
$472$	−9.27904	+	16.0718i	−0.427103	+	0.739763i
$473$	13.8009	−	7.37155i	0.634568	−	0.338944i
$474$	−11.5242	+	3.08789i	−0.529322	+	0.141831i
$475$	0.885114	−	0.237165i	0.0406118	−	0.0108819i
$476$	−1.22222	+	1.22222i	−0.0560203	+	0.0560203i
$477$	−4.43332	+	7.67873i	−0.202988	+	0.351585i
$478$	34.6360	−	19.9971i	1.58421	−	0.914646i
$479$	3.41205	−	12.7339i	0.155901	−	0.581829i	−0.843126	−	0.537716i	$-0.819287\pi$
$479$	3.41205	−	12.7339i	0.155901	−	0.581829i	0.999027	−	0.0441128i	$-0.0140461\pi$
$480$	−2.65485			−0.121177
$481$	−8.07920	+	12.7384i	−0.368380	+	0.580822i
$482$	1.47277			0.0670827
$483$	8.72628	+	2.33820i	0.397059	+	0.106392i
$484$	−0.155782	+	2.35558i	−0.00708101	+	0.107072i
$485$	7.04925	+	4.06988i	0.320090	+	0.184804i
$486$	1.05229	−	1.05229i	0.0477327	−	0.0477327i
$487$	−14.5979	+	3.91151i	−0.661496	+	0.177247i	−0.573921	−	0.818911i	$-0.694578\pi$
$487$	−14.5979	+	3.91151i	−0.661496	+	0.177247i	−0.0875747	+	0.996158i	$0.527912\pi$
$488$	0.806980	+	3.01169i	0.0365303	+	0.136333i
$489$	12.4936	−	12.4936i	0.564979	−	0.564979i
$490$	−6.93947	−	4.00650i	−0.313493	−	0.180995i
$491$	0.361278	+	0.625752i	0.0163043	+	0.0282398i	0.874062	−	0.485814i	$-0.161477\pi$
$491$	0.361278	+	0.625752i	0.0163043	+	0.0282398i	−0.857758	+	0.514053i	$0.828143\pi$
$492$	0.0419071	−	0.156399i	0.00188932	−	0.00705103i
$493$			13.8368i			0.623179i
$494$	26.4091	+	8.26824i	1.18820	+	0.372005i
$495$	−6.96901	−	2.11626i	−0.313234	−	0.0951188i
$496$	9.99737	−	37.3107i	0.448895	−	1.67530i
$497$	−1.14126	+	0.658908i	−0.0511926	+	0.0295561i
$498$	−11.8958	−	6.86807i	−0.533066	−	0.307766i
$499$	−11.6322	−	11.6322i	−0.520729	−	0.520729i	0.397063	−	0.917791i	$-0.370030\pi$
$499$	−11.6322	−	11.6322i	−0.520729	−	0.520729i	−0.917791	+	0.397063i	$0.870030\pi$
$500$	−2.35700	+	0.631555i	−0.105408	+	0.0282440i
$501$	11.4263	−	3.06167i	0.510489	−	0.136785i
$502$	−12.3915	−	12.3915i	−0.553060	−	0.553060i
$503$	10.2657	+	5.92689i	0.457724	+	0.264267i	0.711087	−	0.703104i	$-0.248203\pi$
$503$	10.2657	+	5.92689i	0.457724	+	0.264267i	−0.253363	+	0.967371i	$0.581537\pi$
$504$	4.90708	−	2.83310i	0.218579	−	0.126196i
$505$	−0.774390	+	2.89006i	−0.0344599	+	0.128606i
$506$	20.0062	+	6.07524i	0.889386	+	0.270078i
$507$	−1.08078	+	12.9550i	−0.0479992	+	0.575352i
$508$		−	4.36118i		−	0.193496i
$509$	−4.24107	+	15.8279i	−0.187982	+	0.701560i	0.805990	+	0.591929i	$0.201633\pi$
$509$	−4.24107	+	15.8279i	−0.187982	+	0.701560i	−0.993972	+	0.109631i	$0.965033\pi$
$510$	−6.17089	−	10.6883i	−0.273252	−	0.473286i
$511$	8.03304	+	4.63788i	0.355361	+	0.205168i
$512$	−12.7226	+	12.7226i	−0.562267	+	0.562267i
$513$	1.33486	+	4.98175i	0.0589353	+	0.219950i
$514$	21.0072	−	5.62887i	0.926589	−	0.248279i
$515$	−27.2482	+	27.2482i	−1.20070	+	1.20070i
$516$	0.876794	+	0.506217i	0.0385987	+	0.0222850i
$517$	22.9943	−	5.35440i	1.01129	−	0.235486i
$518$	12.8251	+	3.43648i	0.563504	+	0.150990i
$519$	−22.5988			−0.991977
$520$	20.0760	+	6.28544i	0.880389	+	0.275635i
$521$	2.82770			0.123884			0.0619419	−	0.998080i	$-0.480271\pi$
$521$	2.82770			0.123884			0.0619419	+	0.998080i	$0.480271\pi$
$522$	−1.41117	+	5.26657i	−0.0617654	+	0.230512i
$523$	16.6644	−	9.62120i	0.728684	−	0.420706i	−0.0892567	−	0.996009i	$-0.528449\pi$
$523$	16.6644	−	9.62120i	0.728684	−	0.420706i	0.817940	+	0.575303i	$0.195116\pi$
$524$	−1.96200	+	3.39828i	−0.0857103	+	0.148455i
$525$	0.267925	−	0.267925i	0.0116932	−	0.0116932i
$526$	28.8442	−	7.72877i	1.25767	−	0.336991i
$527$	32.1474	−	8.61388i	1.40036	−	0.375226i
$528$	12.8228	−	6.84908i	0.558040	−	0.298068i
$529$	−2.52739	+	4.37757i	−0.109887	+	0.190329i
$530$	14.4879	+	25.0938i	0.629315	+	1.09001i
$531$	−6.74676	−	1.80779i	−0.292785	−	0.0784514i
$532$		−	2.36049i		−	0.102340i
$533$	−1.45697	+	2.29719i	−0.0631082	+	0.0995022i
$534$		−	20.4892i		−	0.886654i
$535$	23.1618	+	6.20618i	1.00137	+	0.268316i
$536$	0.597150	−	0.344765i	0.0257929	−	0.0148916i
$537$	3.78593	+	2.18581i	0.163375	+	0.0943246i
$538$	−16.4928	+	16.4928i	−0.711057	+	0.711057i
$539$	8.12789	+	0.268469i	0.350093	+	0.0115638i
$540$	−0.121977	−	0.455223i	−0.00524904	−	0.0195897i
$541$	18.0899	+	18.0899i	0.777744	+	0.777744i	0.979447	−	0.201703i	$-0.0646476\pi$
$541$	18.0899	+	18.0899i	0.777744	+	0.777744i	−0.201703	+	0.979447i	$0.564648\pi$
$542$	−11.3992	+	19.7439i	−0.489636	+	0.848074i
$543$	9.46344	−	5.46372i	0.406115	−	0.234471i
$544$	4.41018	+	1.18170i	0.189085	+	0.0506651i
$545$	27.5633			1.18068
$546$	11.1665	−	2.49919i	0.477883	−	0.106956i
$547$			21.9952i			0.940446i	0.882548	+	0.470223i	$0.155827\pi$
$547$			21.9952i			0.940446i	−0.882548	+	0.470223i	$0.844173\pi$
$548$	0.0254752	−	0.0950749i	0.00108825	−	0.00406140i
$549$	−1.01629	+	0.586753i	−0.0433740	+	0.0250420i
$550$	0.640211	−	0.599271i	0.0272987	−	0.0255530i
$551$	−13.3616	−	13.3616i	−0.569224	−	0.569224i
$552$	−2.91308	−	10.8718i	−0.123989	−	0.462733i
$553$	−4.42510	−	16.5147i	−0.188175	−	0.702277i
$554$	−14.9693	+	14.9693i	−0.635987	+	0.635987i
$555$	−4.59364	+	7.95641i	−0.194989	+	0.337731i
$556$	0.640135	+	1.10875i	0.0271478	+	0.0470213i
$557$	−0.889232	+	3.31866i	−0.0376780	+	0.140616i	−0.982203	−	0.187824i	$-0.939856\pi$
$557$	−0.889232	+	3.31866i	−0.0376780	+	0.140616i	0.944525	+	0.328441i	$0.106523\pi$
$558$	13.1145			0.555180
$559$	−11.5166	−	12.5174i	−0.487099	−	0.529428i
$560$		−	20.5271i		−	0.867427i
$561$	10.6348	+	6.61746i	0.449001	+	0.279390i
$562$	10.8731	+	18.8328i	0.458656	+	0.794415i
$563$	1.45958	−	2.52807i	0.0615140	−	0.106545i	−0.833628	−	0.552326i	$-0.813740\pi$
$563$	1.45958	−	2.52807i	0.0615140	−	0.106545i	0.895142	+	0.445780i	$0.147074\pi$
$564$	1.08026	+	1.08026i	0.0454870	+	0.0454870i
$565$	7.04082	−	1.88658i	0.296209	−	0.0793691i
$566$	2.38050	+	8.88414i	0.100060	+	0.373428i
$567$	1.50798	+	1.50798i	0.0633292	+	0.0633292i
$568$	1.42186	+	0.820910i	0.0596599	+	0.0344446i
$569$	13.9083	+	24.0899i	0.583066	+	1.00990i	0.995114	+	0.0987372i	$0.0314803\pi$
$569$	13.9083	+	24.0899i	0.583066	+	1.00990i	−0.412048	+	0.911162i	$0.635186\pi$
$570$	16.2802	+	4.36226i	0.681902	+	0.182715i
$571$	−47.0769			−1.97011			−0.985054	−	0.172246i	$-0.944898\pi$
$571$	−47.0769			−1.97011			−0.985054	+	0.172246i	$0.944898\pi$
$572$	2.52156	−	0.477535i	0.105432	−	0.0199667i
$573$	15.9917			0.668064
$574$	2.31282	+	0.619719i	0.0965353	+	0.0258666i
$575$	−0.376323	−	0.651811i	−0.0156938	−	0.0271824i
$576$	−6.03378	−	3.48360i	−0.251407	−	0.145150i
$577$	23.5642	+	23.5642i	0.980989	+	0.980989i	0.999823	−	0.0188334i	$-0.00599521\pi$
$577$	23.5642	+	23.5642i	0.980989	+	0.980989i	−0.0188334	+	0.999823i	$0.505995\pi$
$578$	−1.05432	−	3.93476i	−0.0438538	−	0.163665i
$579$	−14.7561	+	3.95387i	−0.613241	+	0.164317i
$580$	1.22096	+	1.22096i	0.0506976	+	0.0506976i
$581$	9.84231	−	17.0474i	0.408328	−	0.707244i
$582$	−2.75805	−	4.77709i	−0.114325	−	0.198017i
$583$	−24.9682	−	15.5364i	−1.03408	−	0.643451i
$584$		−	11.5563i		−	0.478204i
$585$	−0.329413	+	7.91086i	−0.0136195	+	0.327074i
$586$	−39.4445			−1.62944
$587$	3.83937	−	14.3287i	0.158468	−	0.591410i	−0.840315	−	0.542098i	$-0.817630\pi$
$587$	3.83937	−	14.3287i	0.158468	−	0.591410i	0.998783	−	0.0493127i	$-0.0157031\pi$
$588$	0.263112	+	0.455723i	0.0108506	+	0.0187937i
$589$	−22.7253	+	39.3614i	−0.936381	+	1.62186i
$590$	−16.1404	+	16.1404i	−0.664489	+	0.664489i
$591$	−3.10910	−	11.6033i	−0.127891	−	0.477297i
$592$	−4.74616	−	17.7129i	−0.195066	−	0.727996i
$593$	−1.91944	−	1.91944i	−0.0788218	−	0.0788218i	0.666597	−	0.745419i	$-0.267750\pi$
$593$	−1.91944	−	1.91944i	−0.0788218	−	0.0788218i	−0.745419	+	0.666597i	$0.767750\pi$
$594$	3.37292	+	3.60335i	0.138393	+	0.147847i
$595$	15.3169	−	8.84321i	0.627931	−	0.362536i
$596$	0.0595198	−	0.222131i	0.00243803	−	0.00909884i
$597$		−	20.2649i		−	0.829388i
$598$	0.945661	−	22.7101i	0.0386709	−	0.928684i
$599$	28.2902			1.15591			0.577953	−	0.816070i	$-0.303852\pi$
$599$	28.2902			1.15591			0.577953	+	0.816070i	$0.303852\pi$
$600$	−0.455976	−	0.122178i	−0.0186152	−	0.00498792i
$601$	−4.21977	+	2.43629i	−0.172128	+	0.0993782i	−0.583589	−	0.812049i	$-0.698352\pi$
$601$	−4.21977	+	2.43629i	−0.172128	+	0.0993782i	0.411461	+	0.911427i	$0.365019\pi$
$602$	−7.48590	+	12.9660i	−0.305103	+	0.528453i
$603$	0.183508	+	0.183508i	0.00747304	+	0.00747304i
$604$	0.994442	+	3.71131i	0.0404633	+	0.151011i
$605$	7.77805	−	22.8693i	0.316223	−	0.929768i
$606$	1.43373	−	1.43373i	0.0582415	−	0.0582415i
$607$	−3.22008	−	1.85911i	−0.130699	−	0.0754591i	0.433225	−	0.901286i	$-0.357376\pi$
$607$	−3.22008	−	1.85911i	−0.130699	−	0.0754591i	−0.563924	+	0.825827i	$0.690709\pi$
$608$	−5.39983	+	3.11760i	−0.218992	+	0.126435i
$609$	−7.54727	−	2.02229i	−0.305831	−	0.0819472i
$610$			3.83497i			0.155274i
$611$	−11.8972	−	22.7422i	−0.481310	−	0.920053i
$612$			0.810500i			0.0327625i
$613$	10.6995	+	2.86693i	0.432149	+	0.115794i	0.468335	−	0.883551i	$-0.344854\pi$
$613$	10.6995	+	2.86693i	0.432149	+	0.115794i	−0.0361857	+	0.999345i	$0.511521\pi$
$614$	−19.1619	−	33.1894i	−0.773312	−	1.33942i
$615$	−0.828395	+	1.43482i	−0.0334041	+	0.0578576i
$616$	8.85394	+	16.5763i	0.356735	+	0.667877i
$617$	−4.34149	+	1.16330i	−0.174782	+	0.0468327i	−0.345149	−	0.938548i	$-0.612171\pi$
$617$	−4.34149	+	1.16330i	−0.174782	+	0.0468327i	0.170367	+	0.985381i	$0.445505\pi$
$618$	25.2242	−	6.75880i	1.01466	−	0.271879i
$619$	3.19312	−	3.19312i	0.128342	−	0.128342i	−0.640018	−	0.768360i	$-0.721073\pi$
$619$	3.19312	−	3.19312i	0.128342	−	0.128342i	0.768360	+	0.640018i	$0.221073\pi$
$620$	2.07660	−	3.59678i	0.0833982	−	0.144450i
$621$	3.66864	−	2.11809i	0.147217	−	0.0849960i
$622$	−13.5723	+	50.6526i	−0.544200	+	2.03098i
$623$	29.3621			1.17637
$624$	−10.7003	−	11.6302i	−0.428356	−	0.465579i
$625$	24.0801			0.963203
$626$	25.1992	+	6.75210i	1.00716	+	0.269868i
$627$	−16.6597	+	3.87935i	−0.665326	+	0.154926i
$628$	2.93784	+	1.69616i	0.117233	+	0.0676843i
$629$	11.1723	−	11.1723i	0.445470	−	0.445470i
$630$	6.73181	−	1.80378i	0.268202	−	0.0718644i
$631$	−0.947745	−	3.53703i	−0.0377291	−	0.140807i	0.944492	−	0.328534i	$-0.106555\pi$
$631$	−0.947745	−	3.53703i	−0.0377291	−	0.140807i	−0.982221	+	0.187727i	$0.939888\pi$
$632$	−15.0620	+	15.0620i	−0.599135	+	0.599135i
$633$	8.41117	+	4.85619i	0.334314	+	0.193016i
$634$	11.6133	+	20.1148i	0.461223	+	0.798861i
$635$	−11.5499	+	43.1047i	−0.458342	+	1.71056i
$636$		−	1.90288i		−	0.0754541i
$637$	−1.93090	−	8.62733i	−0.0765048	−	0.341827i
$638$	−17.3032	−	5.25442i	−0.685041	−	0.208025i
$639$	−0.159934	+	0.596881i	−0.00632689	+	0.0236123i
$640$	−24.3165	+	14.0391i	−0.961194	+	0.554946i
$641$	8.07386	+	4.66144i	0.318898	+	0.184116i	0.650901	−	0.759162i	$-0.274391\pi$
$641$	8.07386	+	4.66144i	0.318898	+	0.184116i	−0.332003	+	0.943278i	$0.607724\pi$
$642$	−11.4904	−	11.4904i	−0.453488	−	0.453488i
$643$	−38.7770	+	10.3903i	−1.52922	+	0.409752i	−0.922763	−	0.385368i	$-0.874075\pi$
$643$	−38.7770	+	10.3903i	−1.52922	+	0.409752i	−0.606452	+	0.795120i	$0.707408\pi$
$644$	−1.87276	+	0.501804i	−0.0737969	+	0.0197738i
$645$	−7.32534	−	7.32534i	−0.288435	−	0.288435i
$646$	−25.1026	−	14.4930i	−0.987647	−	0.570218i
$647$	−13.1587	+	7.59719i	−0.517323	+	0.298676i	−0.735839	−	0.677157i	$-0.763212\pi$
$647$	−13.1587	+	7.59719i	−0.517323	+	0.298676i	0.218516	+	0.975833i	$0.429878\pi$
$648$	0.687666	−	2.56641i	0.0270141	−	0.100818i
$649$	6.73120	−	22.1663i	0.264223	−	0.870105i
$650$	−0.805051	−	0.510594i	−0.0315767	−	0.0200272i
$651$			18.7937i			0.736584i
$652$	−0.981410	+	3.66267i	−0.0384350	+	0.143441i
$653$	−7.38005	−	12.7826i	−0.288804	−	0.500223i	0.684721	−	0.728806i	$-0.259924\pi$
$653$	−7.38005	−	12.7826i	−0.288804	−	0.500223i	−0.973525	+	0.228583i	$0.926591\pi$
$654$	−16.1764	−	9.33944i	−0.632547	−	0.365201i
$655$	28.3916	−	28.3916i	1.10935	−	1.10935i
$656$	−0.855900	−	3.19426i	−0.0334173	−	0.124715i
$657$	4.20129	−	1.12573i	0.163908	−	0.0439189i
$658$	−15.9748	+	15.9748i	−0.622761	+	0.622761i
$659$	−35.9732	−	20.7691i	−1.40132	−	0.809050i	−0.406788	−	0.913523i	$-0.633351\pi$
$659$	−35.9732	−	20.7691i	−1.40132	−	0.809050i	−0.994528	+	0.104472i	$0.966685\pi$
$660$	1.52234	−	0.354488i	0.0592569	−	0.0137984i
$661$	5.04286	+	1.35123i	0.196145	+	0.0525568i	0.355554	−	0.934656i	$-0.384292\pi$
$661$	5.04286	+	1.35123i	0.196145	+	0.0525568i	−0.159409	+	0.987213i	$0.550959\pi$
$662$	−2.27412			−0.0883862
$663$	4.06843	−	12.9947i	0.158005	−	0.504673i
$664$	−24.5244			−0.951729
$665$	−6.25135	+	23.3303i	−0.242417	+	0.904712i
$666$	5.39185	−	3.11298i	0.208930	−	0.120626i
$667$	−7.76033	+	13.4413i	−0.300481	+	0.520448i
$668$	−1.79514	+	1.79514i	−0.0694562	+	0.0694562i
$669$	−22.9152	+	6.14010i	−0.885951	+	0.237390i
$670$	0.819204	−	0.219505i	0.0316486	−	0.00848022i
$671$	−1.83371	−	3.43305i	−0.0707894	−	0.132531i
$672$	−1.28912	+	2.23282i	−0.0497288	+	0.0861328i
$673$	−0.500379	−	0.866681i	−0.0192882	−	0.0334081i	0.856220	−	0.516611i	$-0.172807\pi$
$673$	−0.500379	−	0.866681i	−0.0192882	−	0.0334081i	−0.875508	+	0.483203i	$0.839473\pi$
$674$	8.74717	+	2.34380i	0.336928	+	0.0902797i
$675$		−	0.177671i		−	0.00683857i
$676$	−1.18927	−	2.52377i	−0.0457412	−	0.0970682i
$677$			45.1463i			1.73511i	0.497340	+	0.867556i	$0.334310\pi$
$677$			45.1463i			1.73511i	−0.497340	+	0.867556i	$0.665690\pi$
$678$	−4.77137	−	1.27849i	−0.183243	−	0.0490999i
$679$	6.84581	−	3.95243i	0.262718	−	0.151680i
$680$	−19.0828	−	11.0174i	−0.731790	−	0.422499i
$681$	14.4038	−	14.4038i	0.551956	−	0.551956i
$682$	−1.43591	+	43.4721i	−0.0549838	+	1.66463i
$683$	−4.81235	−	17.9599i	−0.184139	−	0.687217i	−0.994813	−	0.101719i	$-0.967566\pi$
$683$	−4.81235	−	17.9599i	−0.184139	−	0.687217i	0.810674	−	0.585498i	$-0.199101\pi$
$684$	−0.782664	−	0.782664i	−0.0299259	−	0.0299259i
$685$	−0.503579	+	0.872225i	−0.0192408	+	0.0333260i
$686$	−25.9785	+	14.9987i	−0.991862	+	0.572652i
$687$	15.1362	+	4.05573i	0.577482	+	0.154736i
$688$	20.6777			0.788330
$689$	−9.55179	+	30.5088i	−0.363894	+	1.16229i
$690$		−	13.8437i		−	0.527020i
$691$	3.50911	−	13.0962i	0.133493	−	0.498202i	−0.866507	−	0.499166i	$-0.833640\pi$
$691$	3.50911	−	13.0962i	0.133493	−	0.498202i	1.00000		0.000963213i	$0.000306600\pi$
$692$	4.20018	−	2.42498i	0.159667	−	0.0921838i
$693$	−5.16379	+	4.83357i	−0.196156	+	0.183612i
$694$	20.7556	+	20.7556i	0.787871	+	0.787871i
$695$	−3.39058	−	12.6538i	−0.128612	−	0.479986i
$696$	2.51949	+	9.40288i	0.0955012	+	0.356415i
$697$	2.01476	−	2.01476i	0.0763147	−	0.0763147i
$698$	−3.26289	+	5.65149i	−0.123502	+	0.213912i
$699$	−3.51077	−	6.08084i	−0.132790	−	0.229998i
$700$	−0.0210463	+	0.0785460i	−0.000795477	+	0.00296876i
$701$	−22.8866			−0.864415			−0.432208	−	0.901774i	$-0.642265\pi$
$701$	−22.8866			−0.864415			−0.432208	+	0.901774i	$0.642265\pi$
$702$	2.87382	−	4.53113i	0.108465	−	0.171016i
$703$			21.5773i			0.813802i
$704$	12.2082	−	19.6195i	0.460112	−	0.739436i
$705$	−7.81606	−	13.5378i	−0.294370	−	0.509864i
$706$	3.31951	−	5.74957i	0.124932	−	0.216388i
$707$	2.05462	+	2.05462i	0.0772718	+	0.0772718i
$708$	1.44793	−	0.387972i	0.0544166	−	0.0145809i
$709$	−7.29639	−	27.2305i	−0.274022	−	1.02266i	−0.956494	−	0.291751i	$-0.905762\pi$
$709$	−7.29639	−	27.2305i	−0.274022	−	1.02266i	0.682473	−	0.730911i	$-0.260905\pi$
$710$	1.42793	+	1.42793i	0.0535892	+	0.0535892i
$711$	−6.94300	−	4.00854i	−0.260383	−	0.150332i
$712$	−18.2906	−	31.6802i	−0.685469	−	1.18727i
$713$	36.0595	+	9.66212i	1.35044	+	0.361849i
$714$	−11.9856			−0.448550
$715$	−26.1870	−	1.95811i	−0.979338	−	0.0732290i
$716$	−0.938198			−0.0350621
$717$	25.9593	+	6.95576i	0.969466	+	0.259768i
$718$	24.7384	+	42.8481i	0.923228	+	1.59908i
$719$	18.4541	+	10.6545i	0.688222	+	0.397345i	0.802945	−	0.596053i	$-0.203265\pi$
$719$	18.4541	+	10.6545i	0.688222	+	0.397345i	−0.114724	+	0.993397i	$0.536598\pi$
$720$	−6.80614	−	6.80614i	−0.253650	−	0.253650i
$721$	9.68571	+	36.1476i	0.360715	+	1.34621i
$722$	10.9242	−	2.92712i	0.406555	−	0.108936i
$723$	0.699794	+	0.699794i	0.0260256	+	0.0260256i
$724$	−1.17258	+	2.03096i	−0.0435784	+	0.0754801i
$725$	0.325479	+	0.563746i	0.0120880	+	0.0209370i
$726$	−12.3137	+	10.7861i	−0.457006	+	0.400309i
$727$			33.9014i			1.25733i	0.777674	+	0.628667i	$0.216399\pi$
$727$			33.9014i			1.25733i	−0.777674	+	0.628667i	$0.783601\pi$
$728$	15.0346	−	13.8325i	0.557218	−	0.512667i
$729$	1.00000			0.0370370
$730$	3.67885	−	13.7296i	0.136160	−	0.508157i
$731$	8.90810	+	15.4293i	0.329478	+	0.570673i
$732$	0.125924	−	0.218106i	0.00465428	−	0.00806144i
$733$	−29.4104	+	29.4104i	−1.08630	+	1.08630i	−0.0903930	+	0.995906i	$0.528812\pi$
$733$	−29.4104	+	29.4104i	−1.08630	+	1.08630i	−0.995906	+	0.0903930i	$0.971188\pi$
$734$	−9.22910	−	34.4435i	−0.340652	−	1.27133i
$735$	−1.39362	−	5.20104i	−0.0514043	−	0.191843i
$736$	3.62135	+	3.62135i	0.133485	+	0.133485i
$737$	−0.628389	+	0.588205i	−0.0231470	+	0.0216668i
$738$	0.972340	−	0.561381i	0.0357923	−	0.0206647i
$739$	−0.224918	+	0.839407i	−0.00827376	+	0.0308781i	−0.969939	−	0.243347i	$-0.921755\pi$
$739$	−0.224918	+	0.839407i	−0.00827376	+	0.0308781i	0.961666	+	0.274225i	$0.0884213\pi$
$740$		−	1.97169i		−	0.0724808i
$741$	8.61973	+	16.4771i	0.316654	+	0.605303i
$742$	28.1396			1.03304
$743$	33.2275	+	8.90329i	1.21900	+	0.326630i	0.810287	−	0.586033i	$-0.199311\pi$
$743$	33.2275	+	8.90329i	1.21900	+	0.326630i	0.408713	+	0.912663i	$0.365978\pi$
$744$	20.2775	−	11.7072i	0.743409	−	0.429207i
$745$	−1.17655	+	2.03785i	−0.0431056	+	0.0746610i
$746$	17.7789	+	17.7789i	0.650930	+	0.650930i
$747$	−2.38898	−	8.91579i	−0.0874082	−	0.326212i
$748$	−2.68666	−	0.0887419i	−0.0982340	−	0.00324473i
$749$	16.4663	−	16.4663i	0.601665	−	0.601665i
$750$	−14.6535	−	8.46022i	−0.535071	−	0.308924i
$751$	37.8220	−	21.8366i	1.38014	−	0.796827i	0.387969	−	0.921673i	$-0.373177\pi$
$751$	37.8220	−	21.8366i	1.38014	−	0.796827i	0.992176	+	0.124845i	$0.0398435\pi$
$752$	30.1385	+	8.07558i	1.09904	+	0.294486i
$753$		−	11.7758i		−	0.429134i
$754$	−0.817893	+	19.6417i	−0.0297859	+	0.715310i
$755$		−	39.3151i		−	1.43082i
$756$	−0.442086	−	0.118457i	−0.0160785	−	0.00430823i
$757$	2.16030	+	3.74176i	0.0785176	+	0.135996i	0.902611	−	0.430458i	$-0.141648\pi$
$757$	2.16030	+	3.74176i	0.0785176	+	0.135996i	−0.824093	+	0.566455i	$0.808315\pi$
$758$	22.6756	−	39.2752i	0.823614	−	1.42654i
$759$	6.61940	+	12.3928i	0.240269	+	0.449829i
$760$	29.0664	−	7.78833i	1.05435	−	0.282512i
$761$	−2.85242	+	0.764305i	−0.103400	+	0.0277060i	−0.310148	−	0.950688i	$-0.600379\pi$
$761$	−2.85242	+	0.764305i	−0.103400	+	0.0277060i	0.206748	+	0.978394i	$0.433712\pi$
$762$	21.3838	−	21.3838i	0.774655	−	0.774655i
$763$	13.3839	−	23.1816i	0.484530	−	0.839231i
$764$	−2.97220	+	1.71600i	−0.107531	+	0.0620828i
$765$	2.14647	−	8.01074i	0.0776058	−	0.289629i
$766$	15.1402			0.547039
$767$	−25.1621	−	1.04776i	−0.908551	−	0.0378326i
$768$	5.09348			0.183795
$769$	−0.929157	−	0.248967i	−0.0335063	−	0.00897797i	0.242027	−	0.970270i	$-0.422188\pi$
$769$	−0.929157	−	0.248967i	−0.0335063	−	0.00897797i	−0.275533	+	0.961292i	$0.588854\pi$
$770$	5.24214	+	22.5122i	0.188914	+	0.811284i
$771$	12.6563	+	7.30712i	0.455805	+	0.263159i
$772$	2.31827	−	2.31827i	0.0834363	−	0.0834363i
$773$	−20.1021	+	5.38633i	−0.723021	+	0.193733i	−0.601519	−	0.798858i	$-0.705438\pi$
$773$	−20.1021	+	5.38633i	−0.723021	+	0.193733i	−0.121502	+	0.992591i	$0.538771\pi$
$774$	1.81702	+	6.78121i	0.0653114	+	0.243746i
$775$	1.10714	−	1.10714i	0.0397698	−	0.0397698i
$776$	−8.52896	−	4.92419i	−0.306172	−	0.176768i
$777$	4.46107	+	7.72680i	0.160040	+	0.277197i
$778$	3.51341	−	13.1122i	0.125962	−	0.470096i
$779$			3.89114i			0.139415i
$780$	−0.787656	−	1.50565i	−0.0282026	−	0.0539110i
$781$	−1.96104	−	0.595504i	−0.0701716	−	0.0213088i
$782$	−6.16197	+	22.9968i	−0.220352	+	0.822364i
$783$	−3.17297	+	1.83192i	−0.113393	+	0.0654673i
$784$	9.30758	+	5.37373i	0.332414	+	0.191919i
$785$	−24.5447	−	24.5447i	−0.876039	−	0.876039i
$786$	−26.2826	+	7.04241i	−0.937470	+	0.251194i
$787$	38.7610	−	10.3860i	1.38168	−	0.370220i	0.509949	−	0.860205i	$-0.329664\pi$
$787$	38.7610	−	10.3860i	1.38168	−	0.370220i	0.871731	+	0.489984i	$0.162998\pi$
$788$	1.82295	+	1.82295i	0.0649400	+	0.0649400i
$789$	17.3779	+	10.0331i	0.618668	+	0.357188i
$790$	−22.6895	+	13.0998i	−0.807255	+	0.466069i
$791$	1.83214	−	6.83763i	0.0651433	−	0.243118i
$792$	8.43187	+	2.56048i	0.299614	+	0.0909829i
$793$	−3.11375	+	2.86480i	−0.110572	+	0.101732i
$794$		−	7.15131i		−	0.253790i
$795$	−5.03945	+	18.8075i	−0.178731	+	0.667033i
$796$	2.17454	+	3.76642i	0.0770746	+	0.133497i
$797$	−45.7641	−	26.4219i	−1.62105	−	0.935911i	−0.986641	−	0.162911i	$-0.947912\pi$
$797$	−45.7641	−	26.4219i	−1.62105	−	0.935911i	−0.634405	−	0.773000i	$-0.718755\pi$
$798$	11.5740	−	11.5740i	0.409715	−	0.409715i
$799$	6.95803	+	25.9677i	0.246157	+	0.918672i
$800$	0.207478	−	0.0555936i	0.00733546	−	0.00196553i
$801$	9.73556	−	9.73556i	0.343989	−	0.343989i
$802$	−31.1742	−	17.9984i	−1.10080	−	0.635547i
$803$	3.27159	+	14.0497i	0.115452	+	0.495805i
$804$	−0.0537981	−	0.0144152i	−0.00189731	−	0.000508384i
$805$	19.8387			0.699223
$806$	46.1433	−	10.3274i	1.62533	−	0.363767i
$807$	−15.6733			−0.551728
$808$	0.936942	−	3.49672i	0.0329615	−	0.123014i
$809$	−16.6258	+	9.59890i	−0.584531	+	0.337479i	−0.762932	−	0.646479i	$-0.776241\pi$
$809$	−16.6258	+	9.59890i	−0.584531	+	0.337479i	0.178401	+	0.983958i	$0.442908\pi$
$810$	1.63398	−	2.83014i	0.0574123	−	0.0994410i
$811$	−6.04032	+	6.04032i	−0.212104	+	0.212104i	−0.805161	−	0.593057i	$-0.797921\pi$
$811$	−6.04032	+	6.04032i	−0.212104	+	0.212104i	0.593057	+	0.805161i	$0.297921\pi$
$812$	1.61973	−	0.434005i	0.0568414	−	0.0152306i
$813$	−14.7978	+	3.96507i	−0.518983	+	0.139061i
$814$	9.72862	+	18.2138i	0.340988	+	0.638394i
$815$	19.3999	−	33.6017i	0.679550	−	1.17702i
$816$	8.27672	+	14.3357i	0.289743	+	0.501850i
$817$	−23.5016	−	6.29722i	−0.822215	−	0.220312i
$818$			58.1773i			2.03412i
$819$	6.49334	+	4.11833i	0.226896	+	0.143906i
$820$		−	0.355566i		−	0.0124169i
$821$	50.6052	+	13.5596i	1.76613	+	0.473234i	0.987946	−	0.154796i	$-0.0494721\pi$
$821$	50.6052	+	13.5596i	1.76613	+	0.473234i	0.778189	+	0.628031i	$0.216139\pi$
$822$	0.591084	−	0.341262i	0.0206164	−	0.0119029i
$823$	−19.7563	−	11.4063i	−0.688662	−	0.397599i	0.114448	−	0.993429i	$-0.463490\pi$
$823$	−19.7563	−	11.4063i	−0.688662	−	0.397599i	−0.803111	+	0.595830i	$0.796823\pi$
$824$	32.9679	−	32.9679i	1.14849	−	1.14849i
$825$	0.588947	+	0.0194533i	0.0205045	+	0.000677276i
$826$	5.73730	+	21.4119i	0.199626	+	0.745015i
$827$	2.51770	+	2.51770i	0.0875491	+	0.0875491i	0.749525	−	0.661976i	$-0.230282\pi$
$827$	2.51770	+	2.51770i	0.0875491	+	0.0875491i	−0.661976	+	0.749525i	$0.730282\pi$
$828$	−0.454566	+	0.787331i	−0.0157973	+	0.0273616i
$829$	−46.0743	+	26.6010i	−1.60023	+	0.923892i	−0.608787	+	0.793333i	$0.708344\pi$
$829$	−46.0743	+	26.6010i	−1.60023	+	0.923892i	−0.991441	+	0.130559i	$0.958323\pi$
$830$	−29.1365	−	7.80709i	−1.01134	−	0.270988i
$831$	−14.2256			−0.493479
$832$	−23.9732	−	7.50559i	−0.831119	−	0.260209i
$833$			9.26017i			0.320846i
$834$	−2.29770	+	8.57515i	−0.0795630	+	0.296933i
$835$	22.4968	−	12.9885i	0.778534	−	0.449487i
$836$	2.68008	−	2.50870i	0.0926926	−	0.0867650i
$837$	6.23142	+	6.23142i	0.215389	+	0.215389i
$838$	−10.4019	−	38.8206i	−0.359329	−	1.34104i
$839$	7.12603	+	26.5947i	0.246018	+	0.918152i	0.972869	+	0.231356i	$0.0743164\pi$
$839$	7.12603	+	26.5947i	0.246018	+	0.918152i	−0.726851	+	0.686795i	$0.759017\pi$
$840$	8.79844	−	8.79844i	0.303575	−	0.303575i
$841$	−7.78817	+	13.4895i	−0.268557	+	0.465155i
$842$	8.63253	+	14.9520i	0.297497	+	0.515279i
$843$	−3.78210	+	14.1150i	−0.130262	+	0.486145i
$844$	−2.08438			−0.0717475
$845$	5.07062	+	28.0938i	0.174435	+	0.966457i
$846$			10.5935i			0.364211i
$847$	−15.4570	−	17.6462i	−0.531109	−	0.606332i
$848$	−19.4320	−	33.6571i	−0.667296	−	1.15579i
$849$	−3.09024	+	5.35246i	−0.106057	+	0.183696i
$850$	0.706076	+	0.706076i	0.0242182	+	0.0242182i
$851$	17.1189	−	4.58700i	0.586829	−	0.157240i
$852$	−0.0343236	−	0.128097i	−0.00117591	−	0.00438855i
$853$	−17.9133	−	17.9133i	−0.613341	−	0.613341i	0.330474	−	0.943815i	$-0.392791\pi$
$853$	−17.9133	−	17.9133i	−0.613341	−	0.613341i	−0.943815	+	0.330474i	$0.892791\pi$
$854$	3.22534	+	1.86215i	0.110369	+	0.0637215i
$855$	5.66287	+	9.80838i	0.193666	+	0.335440i
$856$	−28.0237	−	7.50892i	−0.957829	−	0.256650i
$857$	−52.2368			−1.78438			−0.892188	−	0.451665i	$-0.850830\pi$
$857$	−52.2368			−1.78438			−0.892188	+	0.451665i	$0.850830\pi$
$858$	14.7052	+	10.0223i	0.502027	+	0.342155i
$859$	−46.5779			−1.58922			−0.794608	−	0.607123i	$-0.792324\pi$
$859$	−46.5779			−1.58922			−0.794608	+	0.607123i	$0.792324\pi$
$860$	2.14753	+	0.575429i	0.0732302	+	0.0196220i
$861$	0.804488	+	1.39341i	0.0274169	+	0.0474874i
$862$	45.4528	+	26.2422i	1.54813	+	0.893812i
$863$	10.1713	+	10.1713i	0.346236	+	0.346236i	0.858705	−	0.512469i	$-0.171269\pi$
$863$	10.1713	+	10.1713i	0.346236	+	0.346236i	−0.512469	+	0.858705i	$0.671269\pi$
$864$	0.312902	+	1.16776i	0.0106451	+	0.0397282i
$865$	−47.9355	+	12.8443i	−1.62986	+	0.436719i
$866$	−25.4415	−	25.4415i	−0.864537	−	0.864537i
$867$	1.36866	−	2.37059i	0.0464822	−	0.0805095i
$868$	−2.01667	−	3.49298i	−0.0684503	−	0.118559i
$869$	14.0478	−	22.5759i	0.476538	−	0.765834i
$870$			11.9733i			0.405932i
$871$	0.790185	+	0.501166i	0.0267744	+	0.0169814i
$872$	−33.3491			−1.12934
$873$	0.959356	−	3.58037i	0.0324693	−	0.121177i
$874$	−16.2567	−	28.1574i	−0.549890	−	0.952437i
$875$	12.1239	−	20.9993i	0.409864	−	0.709905i
$876$	−0.660048	+	0.660048i	−0.0223010	+	0.0223010i
$877$	1.76068	+	6.57095i	0.0594540	+	0.221885i	0.989260	−	0.146164i	$-0.0466926\pi$
$877$	1.76068	+	6.57095i	0.0594540	+	0.221885i	−0.929806	+	0.368049i	$0.880026\pi$
$878$	−14.3660	−	53.6146i	−0.484828	−	1.80940i
$879$	−18.7423	−	18.7423i	−0.632162	−	0.632162i
$880$	23.3063	−	21.8159i	0.785656	−	0.735414i
$881$	−10.4899	+	6.05636i	−0.353414	+	0.204044i	−0.666188	−	0.745784i	$-0.732075\pi$
$881$	−10.4899	+	6.05636i	−0.353414	+	0.204044i	0.312774	+	0.949828i	$0.398742\pi$
$882$	−0.944416	+	3.52461i	−0.0318001	+	0.118680i
$883$		−	19.3576i		−	0.651436i	−0.945467	−	0.325718i	$-0.894394\pi$
$883$		−	19.3576i		−	0.651436i	0.945467	−	0.325718i	$-0.105606\pi$
$884$	0.638254	+	2.85175i	0.0214668	+	0.0959146i
$885$	−15.3384			−0.515595
$886$	−33.7153	−	9.03398i	−1.13269	−	0.303503i
$887$	−8.17204	+	4.71813i	−0.274390	+	0.158419i	−0.630881	−	0.775880i	$-0.717306\pi$
$887$	−8.17204	+	4.71813i	−0.274390	+	0.158419i	0.356491	+	0.934299i	$0.383973\pi$
$888$	5.55789	−	9.62654i	0.186510	−	0.323046i
$889$	30.6442	+	30.6442i	1.02777	+	1.02777i
$890$	−11.6453	−	43.4607i	−0.390350	−	1.45681i
$891$	−0.109490	+	3.31482i	−0.00366807	+	0.111051i
$892$	3.60012	−	3.60012i	0.120541	−	0.120541i
$893$	−31.7950	−	18.3568i	−1.06398	−	0.614288i
$894$	1.38100	−	0.797319i	0.0461874	−	0.0266663i
$895$	9.27288	+	2.48466i	0.309958	+	0.0830530i
$896$			27.2680i			0.910959i
$897$	11.2402	−	10.3415i	0.375298	−	0.345292i
$898$			24.4900i			0.817243i
$899$	−31.1876	−	8.35668i	−1.04016	−	0.278711i
$900$	0.0190651	+	0.0330217i	0.000635504	+	0.00110072i
$901$	16.7428	−	28.9995i	0.557785	−	0.966112i
$902$	1.75441	+	3.28460i	0.0584156	+	0.109365i
$903$	−9.71783	+	2.60388i	−0.323389	+	0.0866518i
$904$	−8.51875	+	2.28259i	−0.283330	+	0.0759179i
$905$	16.9681	−	16.9681i	0.564037	−	0.564037i
$906$	−13.3214	+	23.0733i	−0.442574	+	0.766560i
$907$	16.4207	−	9.48051i	0.545241	−	0.314795i	−0.201959	−	0.979394i	$-0.564731\pi$
$907$	16.4207	−	9.48051i	0.545241	−	0.314795i	0.747200	+	0.664599i	$0.231398\pi$
$908$	−1.13147	+	4.22269i	−0.0375490	+	0.140135i
$909$	1.36250			0.0451911
$910$	22.2655	−	11.6478i	0.738093	−	0.386121i
$911$	−2.45950			−0.0814868			−0.0407434	−	0.999170i	$-0.512973\pi$
$911$	−2.45950			−0.0814868			−0.0407434	+	0.999170i	$0.512973\pi$
$912$	−21.8358	−	5.85089i	−0.723057	−	0.193742i
$913$	29.8158	−	6.94283i	0.986758	−	0.229774i
$914$	17.3340	+	10.0078i	0.573359	+	0.331029i
$915$	−1.82221	+	1.82221i	−0.0602404	+	0.0602404i
$916$	−3.24840	+	0.870406i	−0.107330	+	0.0287590i
$917$	−10.0921	−	37.6644i	−0.333272	−	1.24379i
$918$	−3.97406	+	3.97406i	−0.131163	+	0.131163i
$919$	24.0472	+	13.8836i	0.793243	+	0.457979i	0.841103	−	0.540875i	$-0.181907\pi$
$919$	24.0472	+	13.8836i	0.793243	+	0.457979i	−0.0478598	+	0.998854i	$0.515240\pi$
$920$	−12.3582	−	21.4050i	−0.407437	−	0.705701i
$921$	6.66525	−	24.8751i	0.219628	−	0.819661i
$922$			50.8172i			1.67358i
$923$	−0.0926950	+	2.22607i	−0.00305109	+	0.0732721i
$924$	0.441066	−	1.45247i	0.0145100	−	0.0477826i
$925$	0.192385	−	0.717991i	0.00632558	−	0.0236074i
$926$	21.8338	−	12.6057i	0.717502	−	0.414250i
$927$	15.1969	+	8.77393i	0.499132	+	0.288174i
$928$	−3.13208	−	3.13208i	−0.102815	−	0.102815i
$929$	42.0325	−	11.2626i	1.37904	−	0.369513i	0.508269	−	0.861199i	$-0.330286\pi$
$929$	42.0325	−	11.2626i	1.37904	−	0.369513i	0.870773	+	0.491686i	$0.163619\pi$
$930$	27.8178	−	7.45376i	0.912182	−	0.244418i
$931$	−8.94214	−	8.94214i	−0.293067	−	0.293067i
$932$	1.30502	+	0.753451i	0.0427472	+	0.0246801i
$933$	−30.5168	+	17.6189i	−0.999077	+	0.576817i
$934$	2.35253	−	8.77976i	0.0769771	−	0.287282i
$935$	26.3191	+	7.99226i	0.860727	+	0.261375i
$936$	0.398560	−	9.57143i	0.0130273	−	0.312852i
$937$		−	32.9194i		−	1.07543i	−0.843127	−	0.537714i	$-0.819288\pi$
$937$		−	32.9194i		−	1.07543i	0.843127	−	0.537714i	$-0.180712\pi$
$938$	0.213170	−	0.795563i	0.00696026	−	0.0259760i
$939$	8.76525	+	15.1819i	0.286043	+	0.495441i
$940$	2.90537	+	1.67741i	0.0947626	+	0.0547112i
$941$	−31.4394	+	31.4394i	−1.02489	+	1.02489i	−0.0252128	+	0.999682i	$0.508026\pi$
$941$	−31.4394	+	31.4394i	−1.02489	+	1.02489i	−0.999682	+	0.0252128i	$0.991974\pi$
$942$	6.08822	+	22.7215i	0.198365	+	0.740307i
$943$	3.08714	−	0.827198i	0.100531	−	0.0269373i
$944$	21.6483	−	21.6483i	0.704593	−	0.704593i
$945$	4.05574	+	2.34158i	0.131933	+	0.0761716i
$946$	−22.6774	+	5.28061i	−0.737306	+	0.171687i
$947$	−50.4947	−	13.5300i	−1.64086	−	0.439666i	−0.683825	−	0.729646i	$-0.739685\pi$
$947$	−50.4947	−	13.5300i	−1.64086	−	0.439666i	−0.957033	+	0.289980i	$0.906351\pi$
$948$	1.72056			0.0558811
$949$	13.8957	−	7.26932i	0.451075	−	0.235972i
$950$	−1.36365			−0.0442428
$951$	−4.03955	+	15.0758i	−0.130991	+	0.488866i
$952$	−18.5321	+	10.6995i	−0.600627	+	0.346772i
$953$	−14.0174	+	24.2789i	−0.454069	+	0.786471i	−0.998634	−	0.0522477i	$-0.983361\pi$
$953$	−14.0174	+	24.2789i	−0.454069	+	0.786471i	0.544565	+	0.838719i	$0.316695\pi$
$954$	9.33023	−	9.33023i	0.302077	−	0.302077i
$955$	33.9209	−	9.08908i	1.09766	−	0.294116i
$956$	−5.57115	+	1.49278i	−0.180184	+	0.0482801i
$957$	−5.72506	−	10.7184i	−0.185065	−	0.346477i
$958$	−9.80930	+	16.9902i	−0.316924	+	0.548929i
$959$	0.489047	+	0.847054i	0.0157921	+	0.0273528i
$960$	−14.7785	−	3.95989i	−0.476975	−	0.127805i
$961$			46.6612i			1.50520i
$962$	16.5198	−	15.1990i	0.532620	−	0.490036i
$963$		−	10.9194i		−	0.351873i
$964$	−0.205155	−	0.0549710i	−0.00660759	−	0.00177050i
$965$	−29.0526	+	16.7735i	−0.935237	+	0.539960i
$966$	−11.6430	−	6.72208i	−0.374607	−	0.216279i
$967$	30.1275	−	30.1275i	0.968836	−	0.968836i	−0.0306928	−	0.999529i	$-0.509771\pi$
$967$	30.1275	−	30.1275i	0.968836	−	0.968836i	0.999529	+	0.0306928i	$0.00977137\pi$
$968$	−9.41075	+	27.6698i	−0.302473	+	0.889340i
$969$	−5.04121	−	18.8141i	−0.161947	−	0.604395i
$970$	−8.56536	−	8.56536i	−0.275017	−	0.275017i
$971$	−0.444706	+	0.770254i	−0.0142713	+	0.0247186i	−0.873073	−	0.487590i	$-0.837876\pi$
$971$	−0.444706	+	0.770254i	−0.0142713	+	0.0247186i	0.858802	+	0.512308i	$0.171210\pi$
$972$	−0.185859	+	0.107306i	−0.00596142	+	0.00344183i
$973$	−12.2886	−	3.29273i	−0.393956	−	0.105560i
$974$	22.4904			0.720638
$975$	−0.139913	−	0.625137i	−0.00448079	−	0.0200204i
$976$		−	5.14367i		−	0.164645i
$977$	−2.87974	+	10.7473i	−0.0921309	+	0.343837i	−0.996569	−	0.0827680i	$-0.973624\pi$
$977$	−2.87974	+	10.7473i	−0.0921309	+	0.343837i	0.904438	+	0.426605i	$0.140291\pi$
$978$	−22.7710	+	13.1468i	−0.728135	+	0.420389i
$979$	31.2057	+	33.3376i	0.997337	+	1.06547i
$980$	0.817117	+	0.817117i	0.0261018	+	0.0261018i
$981$	−3.24862	−	12.1240i	−0.103720	−	0.387090i
$982$	−0.278302	−	1.03864i	−0.00888098	−	0.0331443i
$983$	39.9457	−	39.9457i	1.27407	−	1.27407i	0.330139	−	0.943932i	$-0.392904\pi$
$983$	39.9457	−	39.9457i	1.27407	−	1.27407i	0.943932	−	0.330139i	$-0.107096\pi$
$984$	1.00228	−	1.73601i	0.0319516	−	0.0553418i
$985$	−13.1898	−	22.8453i	−0.420261	−	0.727913i
$986$	5.32943	−	19.8897i	0.169724	−	0.633418i
$987$	−15.1810			−0.483217
$988$	−3.37014	−	2.13747i	−0.107219	−	0.0680021i
$989$			19.9843i			0.635464i
$990$	9.20249	+	5.72622i	0.292474	+	0.181991i
$991$	15.1873	+	26.3051i	0.482440	+	0.835610i	0.999797	−	0.0201594i	$-0.00641737\pi$
$991$	15.1873	+	26.3051i	0.482440	+	0.835610i	−0.517357	+	0.855770i	$0.673084\pi$
$992$	−5.32701	+	9.22665i	−0.169133	+	0.292947i
$993$	−1.08056	−	1.08056i	−0.0342906	−	0.0342906i
$994$	1.89429	−	0.507575i	0.0600834	−	0.0160993i
$995$	−11.5178	−	42.9850i	−0.365139	−	1.36272i
$996$	1.40073	+	1.40073i	0.0443837	+	0.0443837i
$997$	51.3421	+	29.6424i	1.62602	+	0.938784i	0.985264	+	0.171041i	$0.0547131\pi$
$997$	51.3421	+	29.6424i	1.62602	+	0.938784i	0.640758	+	0.767743i	$0.278620\pi$
$998$	12.2404	+	21.2010i	0.387463	+	0.671106i
$999$	4.04112	+	1.08282i	0.127855	+	0.0342588i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bd.a.76.4	✓	56
11.10	odd	2	inner	429.2.bd.a.76.11	yes	56
13.6	odd	12	inner	429.2.bd.a.175.11	yes	56
143.32	even	12	inner	429.2.bd.a.175.4	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bd.a.76.4	✓	56	1.1	even	1	trivial
429.2.bd.a.76.11	yes	56	11.10	odd	2	inner
429.2.bd.a.175.4	yes	56	143.32	even	12	inner
429.2.bd.a.175.11	yes	56	13.6	odd	12	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.43745 - 0.385163i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.185859 + 0.107306i) q^{4} +(-1.55279 - 1.55279i) q^{5} +(0.385163 + 1.43745i) q^{6} +(-2.05994 + 0.551959i) q^{7} +(1.87874 + 1.87874i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.43745 - 0.385163i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.185859 + 0.107306i) q^{4} +(-1.55279 - 1.55279i) q^{5} +(0.385163 + 1.43745i) q^{6} +(-2.05994 + 0.551959i) q^{7} +(1.87874 + 1.87874i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.63398 + 2.83014i) q^{10} +(-2.81597 - 1.75223i) q^{11} -0.214611i q^{12} +(-1.07727 + 3.44085i) q^{13} +3.17365 q^{14} +(-0.568361 + 2.12115i) q^{15} +(-2.19158 - 3.79593i) q^{16} +(1.88830 - 3.27063i) q^{17} +(1.05229 - 1.05229i) q^{18} +(1.33486 + 4.98175i) q^{19} +(-0.121977 - 0.455223i) q^{20} +(1.50798 + 1.50798i) q^{21} +(3.37292 + 3.60335i) q^{22} +(3.66864 - 2.11809i) q^{23} +(0.687666 - 2.56641i) q^{24} -0.177671i q^{25} +(2.87382 - 4.53113i) q^{26} +1.00000 q^{27} +(-0.442086 - 0.118457i) q^{28} +(-3.17297 + 1.83192i) q^{29} +(1.63398 - 2.83014i) q^{30} +(6.23142 + 6.23142i) q^{31} +(0.312902 + 1.16776i) q^{32} +(-0.109490 + 3.31482i) q^{33} +(-3.97406 + 3.97406i) q^{34} +(4.05574 + 2.34158i) q^{35} +(-0.185859 + 0.107306i) q^{36} +(4.04112 + 1.08282i) q^{37} -7.67515i q^{38} +(3.51850 - 0.787481i) q^{39} -5.83458i q^{40} +(0.728757 + 0.195270i) q^{41} +(-1.58683 - 2.74846i) q^{42} +(-2.35876 + 4.08550i) q^{43} +(-0.335349 - 0.627837i) q^{44} +(2.12115 - 0.568361i) q^{45} +(-6.08929 + 1.63162i) q^{46} +(-5.03355 + 5.03355i) q^{47} +(-2.19158 + 3.79593i) q^{48} +(-2.12348 + 1.22599i) q^{49} +(-0.0684324 + 0.255393i) q^{50} -3.77660 q^{51} +(-0.569444 + 0.523916i) q^{52} +8.86663 q^{53} +(-1.43745 - 0.385163i) q^{54} +(1.65177 + 7.09347i) q^{55} +(-4.90708 - 2.83310i) q^{56} +(3.64689 - 3.64689i) q^{57} +(5.26657 - 1.41117i) q^{58} +(1.80779 + 6.74676i) q^{59} +(-0.333247 + 0.333247i) q^{60} +(1.01629 + 0.586753i) q^{61} +(-6.55723 - 11.3575i) q^{62} +(0.551959 - 2.05994i) q^{63} +6.96721i q^{64} +(7.01572 - 3.67015i) q^{65} +(1.43413 - 4.72271i) q^{66} +(0.0671688 - 0.250677i) q^{67} +(0.701913 - 0.405250i) q^{68} +(-3.66864 - 2.11809i) q^{69} +(-4.92803 - 4.92803i) q^{70} +(0.596881 - 0.159934i) q^{71} +(-2.56641 + 0.687666i) q^{72} +(-3.07555 - 3.07555i) q^{73} +(-5.39185 - 3.11298i) q^{74} +(-0.153868 + 0.0888356i) q^{75} +(-0.286475 + 1.06914i) q^{76} +(6.76789 + 2.05519i) q^{77} +(-5.36098 - 0.223234i) q^{78} +8.01708i q^{79} +(-2.49122 + 9.29737i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.972340 - 0.561381i) q^{82} +(-6.52681 + 6.52681i) q^{83} +(0.118457 + 0.442086i) q^{84} +(-8.01074 + 2.14647i) q^{85} +(4.96419 - 4.96419i) q^{86} +(3.17297 + 1.83192i) q^{87} +(-1.99849 - 8.58246i) q^{88} +(-13.2990 - 3.56346i) q^{89} -3.26796 q^{90} +(0.319906 - 7.68257i) q^{91} +0.909132 q^{92} +(2.28086 - 8.51228i) q^{93} +(9.17422 - 5.29674i) q^{94} +(5.66287 - 9.80838i) q^{95} +(0.854863 - 0.854863i) q^{96} +(-3.58037 + 0.959356i) q^{97} +(3.52461 - 0.944416i) q^{98} +(2.92546 - 1.56259i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 28 q^{3} + 4 q^{5} - 28 q^{9}+O(q^{10}) \) 56 * q - 28 * q^3 + 4 * q^5 - 28 * q^9	\( 56 q - 28 q^{3} + 4 q^{5} - 28 q^{9} - 12 q^{11} + 24 q^{14} - 8 q^{15} + 68 q^{16} - 8 q^{20} - 10 q^{22} - 12 q^{23} - 48 q^{26} + 56 q^{27} + 4 q^{31} + 12 q^{33} + 32 q^{34} + 36 q^{37} - 12 q^{42} + 24 q^{44} + 4 q^{45} - 8 q^{47} + 68 q^{48} - 24 q^{49} - 56 q^{53} - 2 q^{55} + 72 q^{56} - 88 q^{58} + 56 q^{59} - 44 q^{60} + 20 q^{66} + 92 q^{67} + 12 q^{69} - 216 q^{70} + 72 q^{71} - 12 q^{75} - 12 q^{78} + 44 q^{80} - 28 q^{81} - 156 q^{82} - 120 q^{86} - 6 q^{88} - 56 q^{89} + 92 q^{91} + 32 q^{92} - 20 q^{93} - 44 q^{97}+O(q^{100}) \) 56 * q - 28 * q^3 + 4 * q^5 - 28 * q^9 - 12 * q^11 + 24 * q^14 - 8 * q^15 + 68 * q^16 - 8 * q^20 - 10 * q^22 - 12 * q^23 - 48 * q^26 + 56 * q^27 + 4 * q^31 + 12 * q^33 + 32 * q^34 + 36 * q^37 - 12 * q^42 + 24 * q^44 + 4 * q^45 - 8 * q^47 + 68 * q^48 - 24 * q^49 - 56 * q^53 - 2 * q^55 + 72 * q^56 - 88 * q^58 + 56 * q^59 - 44 * q^60 + 20 * q^66 + 92 * q^67 + 12 * q^69 - 216 * q^70 + 72 * q^71 - 12 * q^75 - 12 * q^78 + 44 * q^80 - 28 * q^81 - 156 * q^82 - 120 * q^86 - 6 * q^88 - 56 * q^89 + 92 * q^91 + 32 * q^92 - 20 * q^93 - 44 * q^97

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