LMFDB - Embedded newform 429.2.bd.a.175.11

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			175.11
Character	$\chi$	$=$	429.175
Dual form			429.2.bd.a.76.11

$q$-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} +(-3.31482 - 0.109490i) 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} +(-4.80705 + 1.11936i) 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} +(1.75223 - 2.81597i) 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} +(-0.627837 + 0.335349i) 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} +(5.31724 - 4.97721i) 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} +(6.43338 - 6.02197i) 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} +(1.56259 + 2.92546i) 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 $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$-1$	$1$

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	$-0.406971\pi$
$2$	1.43745	−	0.385163i	1.01643	−	0.272352i	0.728314	+	0.685244i	$0.240304\pi$
$3$	−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	−0.963203	−	0.268774i	$-0.913382\pi$
$5$	−1.55279	+	1.55279i	−0.694430	+	0.694430i	0.268774	+	0.963203i	$0.413382\pi$
$6$	−0.385163	+	1.43745i	−0.157242	+	0.586836i
$7$	2.05994	+	0.551959i	0.778584	+	0.208621i	0.626160	−	0.779694i	$-0.284625\pi$
$7$	2.05994	+	0.551959i	0.778584	+	0.208621i	0.152424	+	0.988315i	$0.451292\pi$
$8$	−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
$11$	−3.31482	−	0.109490i	−0.999455	−	0.0330126i
$11$	−3.31482	−	0.109490i	−0.999455	−	0.0330126i
$12$			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	$-0.318093\pi$
$17$	−1.88830	−	3.27063i	−0.457980	−	0.793244i	−0.998854	+	0.0478595i	$0.984760\pi$
$18$	−1.05229	−	1.05229i	−0.248026	−	0.248026i
$19$	−1.33486	+	4.98175i	−0.306237	+	1.14289i	0.625638	+	0.780113i	$0.284839\pi$
$19$	−1.33486	+	4.98175i	−0.306237	+	1.14289i	−0.931875	+	0.362779i	$0.881828\pi$
$20$	−0.121977	+	0.455223i	−0.0272748	+	0.101791i
$21$	−1.50798	+	1.50798i	−0.329068	+	0.329068i
$22$	−4.80705	+	1.11936i	−1.02487	+	0.238648i
$23$	3.66864	+	2.11809i	0.764964	+	0.441652i	0.831075	−	0.556160i	$-0.187726\pi$
$23$	3.66864	+	2.11809i	0.764964	+	0.441652i	−0.0661111	+	0.997812i	$0.521059\pi$
$24$	−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	$-0.222846\pi$
$29$	3.17297	+	1.83192i	0.589206	+	0.340178i	−0.175577	+	0.984466i	$0.556179\pi$
$30$	−1.63398	−	2.83014i	−0.298323	−	0.516710i
$31$	6.23142	−	6.23142i	1.11920	−	1.11920i	0.127336	−	0.991860i	$-0.459357\pi$
$31$	6.23142	−	6.23142i	1.11920	−	1.11920i	0.991860	−	0.127336i	$-0.0406428\pi$
$32$	−0.312902	+	1.16776i	−0.0553137	+	0.206434i
$33$	1.75223	−	2.81597i	0.305024	−	0.490198i
$34$	−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	0.0891451	−	0.996019i	$-0.471587\pi$
$37$	4.04112	−	1.08282i	0.664356	−	0.178014i	0.575211	+	0.818005i	$0.304920\pi$
$38$			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	$-0.602097\pi$
$41$	−0.728757	+	0.195270i	−0.113813	+	0.0304960i	0.201463	+	0.979496i	$0.435430\pi$
$42$	−1.58683	+	2.74846i	−0.244853	+	0.424097i
$43$	2.35876	+	4.08550i	0.359708	+	0.623033i	0.987912	−	0.155016i	$-0.0495429\pi$
$43$	2.35876	+	4.08550i	0.359708	+	0.623033i	−0.628204	+	0.778049i	$0.716210\pi$
$44$	−0.627837	+	0.335349i	−0.0946499	+	0.0505557i
$45$	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	0.237233	−	0.971453i	$-0.423759\pi$
$47$	−5.03355	−	5.03355i	−0.734219	−	0.734219i	−0.971453	+	0.237233i	$0.923759\pi$
$48$	−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
$55$	5.31724	−	4.97721i	0.716976	−	0.671126i
$56$	−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	−0.742635	−	0.669697i	$-0.766424\pi$
$59$	1.80779	−	6.74676i	0.235354	−	0.878354i	0.977989	−	0.208657i	$-0.0669092\pi$
$60$	−0.333247	−	0.333247i	−0.0430220	−	0.0430220i
$61$	−1.01629	+	0.586753i	−0.130122	+	0.0751260i	−0.563648	−	0.826015i	$-0.690603\pi$
$61$	−1.01629	+	0.586753i	−0.130122	+	0.0751260i	0.433526	+	0.901141i	$0.357269\pi$
$62$	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	0.969907	−	0.243474i	$-0.0782870\pi$
$67$	0.0671688	+	0.250677i	0.00820597	+	0.0306251i	−0.961701	+	0.274099i	$0.911620\pi$
$68$	−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	0.294063	−	0.955786i	$-0.404992\pi$
$71$	0.596881	+	0.159934i	0.0708368	+	0.0189807i	−0.223227	+	0.974767i	$0.571659\pi$
$72$	2.56641	+	0.687666i	0.302454	+	0.0810423i
$73$	3.07555	−	3.07555i	0.359966	−	0.359966i	−0.503834	−	0.863800i	$-0.668078\pi$
$73$	3.07555	−	3.07555i	0.359966	−	0.359966i	0.863800	+	0.503834i	$0.168078\pi$
$74$	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	$-0.0809099\pi$
$83$	6.52681	+	6.52681i	0.716411	+	0.716411i	−0.251458	+	0.967868i	$0.580910\pi$
$84$	−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
$88$	6.43338	−	6.02197i	0.685801	−	0.641945i
$89$	−13.2990	+	3.56346i	−1.40969	+	0.377726i	−0.881816	−	0.471594i	$-0.843679\pi$
$89$	−13.2990	+	3.56346i	−1.40969	+	0.377726i	−0.527878	+	0.849320i	$0.677012\pi$
$90$	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	0.0724297	−	0.997374i	$-0.476925\pi$
$97$	−3.58037	−	0.959356i	−0.363531	−	0.0974079i	−0.435961	+	0.899966i	$0.643591\pi$
$98$	−3.52461	−	0.944416i	−0.356039	−	0.0954004i
$99$	1.56259	+	2.92546i	0.157046	+	0.294020i
$100$	0.0190651	+	0.0330217i	0.00190651	+	0.00330217i
$101$	0.681248	−	1.17996i	0.0677867	−	0.117410i	−0.830140	−	0.557555i	$-0.811740\pi$
$101$	0.681248	−	1.17996i	0.0677867	−	0.117410i	0.897927	+	0.440145i	$0.145073\pi$
$102$	5.42866	−	1.45461i	0.537518	−	0.144027i
$103$			17.5479i			1.72904i	0.502596	+	0.864521i	$0.332378\pi$
$103$			17.5479i			1.72904i	−0.502596	+	0.864521i	$0.667622\pi$
$104$	−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	$-0.156347\pi$
$107$	9.45649	+	5.45971i	0.914194	+	0.527810i	0.0324157	+	0.999474i	$0.489680\pi$
$108$	0.185859	−	0.107306i	0.0178843	−	0.0103255i
$109$	8.87539	+	8.87539i	0.850108	+	0.850108i	0.990146	−	0.140038i	$-0.0447226\pi$
$109$	8.87539	+	8.87539i	0.850108	+	0.850108i	−0.140038	+	0.990146i	$0.544723\pi$
$110$	5.72622	−	9.20249i	0.545974	−	0.877423i
$111$	−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	0.777341	−	0.629079i	$-0.216568\pi$
$113$	−1.65967	−	2.87463i	−0.156128	−	0.270422i	−0.933469	+	0.358657i	$0.883235\pi$
$114$	−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
$121$	10.9760	+	0.725881i	0.997820	+	0.0659892i
$122$	−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	0.0762127	−	0.997092i	$-0.475717\pi$
$127$	10.1607	−	17.5988i	0.901613	−	1.56164i	0.825400	−	0.564548i	$-0.190949\pi$
$128$	−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	$0.705495\pi$
$132$	0.0234979	−	0.711397i	0.00204523	−	0.0619191i
$133$	−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	−0.970811	−	0.239845i	$-0.922903\pi$
$137$	−0.118704	+	0.443010i	−0.0101416	+	0.0378489i	0.960670	+	0.277694i	$0.0895701\pi$
$138$	−4.45767	+	4.45767i	−0.379462	+	0.379462i
$139$	−5.16630	+	2.98277i	−0.438200	+	0.252995i	−0.702834	−	0.711354i	$-0.748082\pi$
$139$	−5.16630	+	2.98277i	−0.438200	+	0.252995i	0.264634	+	0.964349i	$0.414749\pi$
$140$	−0.502530	+	0.870407i	−0.0424715	+	0.0735628i
$141$	6.87596	−	1.84241i	0.579060	−	0.155159i
$142$	0.919587			0.0771700
$143$	−3.19422	−	11.5238i	−0.267114	−	0.963665i
$144$	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	$-0.902691\pi$
$149$	0.277338	−	1.03504i	0.0227204	−	0.0847937i	0.976355	+	0.216173i	$0.0693574\pi$
$150$	−0.255393	−	0.0684324i	−0.0208528	−	0.00558748i
$151$	−12.6595	+	12.6595i	−1.03021	+	1.03021i	−0.0306850	+	0.999529i	$0.509769\pi$
$151$	−12.6595	+	12.6595i	−1.03021	+	1.03021i	−0.999529	+	0.0306850i	$0.990231\pi$
$152$	−6.85157	−	11.8673i	−0.555735	−	0.962562i
$153$	−1.88830	+	3.27063i	−0.152660	+	0.264415i
$154$	−10.5201	−	0.347485i	−0.847732	−	0.0280011i
$155$			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	−0.518250	−	0.855229i	$-0.673416\pi$
$163$	4.57297	−	17.0665i	0.358182	−	1.33675i	0.876432	−	0.481526i	$-0.159917\pi$
$164$	−0.114492	+	0.114492i	−0.00894035	+	0.00894035i
$165$	1.65177	+	7.09347i	0.128590	+	0.552226i
$166$	11.8958	+	6.86807i	0.923297	+	0.533066i
$167$	3.06167	+	11.4263i	0.236919	+	0.884193i	0.977275	+	0.211978i	$0.0679904\pi$
$167$	3.06167	+	11.4263i	0.236919	+	0.884193i	−0.740356	+	0.672215i	$0.765343\pi$
$168$		−	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	−0.872810	−	0.488060i	$-0.837705\pi$
$173$	−11.2994	−	19.5711i	−0.859077	−	1.48797i	0.0137328	−	0.999906i	$-0.495629\pi$
$174$	−3.85540	+	3.85540i	−0.292277	+	0.292277i
$175$	−0.0980673	+	0.365992i	−0.00741319	+	0.0276664i
$176$	7.68031	−	12.3429i	0.578925	−	0.930378i
$177$	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	0.351795	−	0.936077i	$-0.385571\pi$
$179$	−3.78593	−	2.18581i	−0.282974	−	0.163375i	−0.634769	+	0.772702i	$0.718905\pi$
$180$	0.455223	−	0.121977i	0.0339303	−	0.00909161i
$181$		−	10.9274i		−	0.812231i	−0.913822	−	0.406115i	$-0.866883\pi$
$181$		−	10.9274i		−	0.812231i	0.913822	−	0.406115i	$-0.133117\pi$
$182$	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
$187$	5.90126	+	11.0483i	0.431543	+	0.807931i
$188$	−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	−0.995645	−	0.0932282i	$-0.970281\pi$
$191$	−7.99586	−	13.8492i	−0.578560	−	1.00210i	0.417084	−	0.908868i	$-0.363052\pi$
$192$	6.03378	+	3.48360i	0.435450	+	0.251407i
$193$	−3.95387	−	14.7561i	−0.284606	−	1.06216i	−0.949127	−	0.314894i	$-0.898031\pi$
$193$	−3.95387	−	14.7561i	−0.284606	−	1.06216i	0.664521	−	0.747270i	$-0.268636\pi$
$194$	−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	$-0.724091\pi$
$197$	−11.6033	+	3.10910i	−0.826702	+	0.221514i	−0.179428	+	0.983771i	$0.557425\pi$
$198$	3.37292	+	3.60335i	0.239703	+	0.256079i
$199$	17.5499	−	10.1325i	1.24408	−	0.718272i	0.274160	−	0.961684i	$-0.411600\pi$
$199$	17.5499	−	10.1325i	1.24408	−	0.718272i	0.969923	+	0.243413i	$0.0782669\pi$
$200$	−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	$-0.224829\pi$
$211$	8.41117	+	4.85619i	0.579048	+	0.334314i	−0.181707	+	0.983353i	$0.558162\pi$
$212$	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	0.792383	+	0.610024i	$0.208840\pi$
$223$	6.14010	+	22.9152i	0.411171	+	1.53451i	−0.381211	+	0.924488i	$0.624493\pi$
$224$	−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	0.536824	+	0.843694i	$0.319624\pi$
$227$	−5.27217	+	19.6760i	−0.349926	+	1.30594i	−0.886751	+	0.462248i	$0.847043\pi$
$228$	−1.06914	−	0.286475i	−0.0708055	−	0.0189723i
$229$	−11.0805	−	11.0805i	−0.732218	−	0.732218i	0.238841	−	0.971059i	$-0.423233\pi$
$229$	−11.0805	−	11.0805i	−0.732218	−	0.732218i	−0.971059	+	0.238841i	$0.923233\pi$
$230$	−11.9890	+	6.92184i	−0.790530	+	0.456413i
$231$	5.16379	−	4.83357i	0.339752	−	0.318026i
$232$	−9.40288	+	2.51949i	−0.617329	+	0.165413i
$233$	−7.02154			−0.459997			−0.229998	−	0.973191i	$-0.573872\pi$
$233$	−7.02154			−0.459997			−0.229998	+	0.973191i	$0.573872\pi$
$234$	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	0.964254	+	0.264980i	$0.0853653\pi$
$239$	19.0035	+	19.0035i	1.22923	+	1.22923i	0.264980	+	0.964254i	$0.414635\pi$
$240$	9.29737	+	2.49122i	0.600142	+	0.160808i
$241$	0.955937	+	0.256142i	0.0615773	+	0.0164996i	0.289476	−	0.957185i	$-0.406519\pi$
$241$	0.955937	+	0.256142i	0.0615773	+	0.0164996i	−0.227899	+	0.973685i	$0.573186\pi$
$242$	16.0571	−	3.18415i	1.03219	−	0.204685i
$243$	−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	−0.142338	−	0.989818i	$-0.545462\pi$
$251$	10.1981	−	5.88790i	0.643701	−	0.371641i	0.786039	+	0.618177i	$0.212129\pi$
$252$	−0.323630	−	0.323630i	−0.0203867	−	0.0203867i
$253$	−11.9290	−	7.42276i	−0.749967	−	0.466665i
$254$	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	0.0503007	−	0.998734i	$-0.483982\pi$
$257$	−12.6563	−	7.30712i	−0.789478	−	0.455805i	−0.839779	+	0.542929i	$0.817315\pi$
$258$	−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	$-0.121006\pi$
$263$	17.3779	+	10.0331i	1.07156	+	0.618668i	0.142956	+	0.989729i	$0.454339\pi$
$264$	1.99849	+	8.58246i	0.122999	+	0.528214i
$265$	−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	0.999676	−	0.0254355i	$-0.00809725\pi$
$269$	7.83667	+	13.5735i	0.477810	+	0.827592i	−0.521866	+	0.853027i	$0.674764\pi$
$270$	−1.63398	+	2.83014i	−0.0994410	+	0.172237i
$271$	−3.96507	−	14.7978i	−0.240861	−	0.898904i	−0.975419	−	0.220359i	$-0.929277\pi$
$271$	−3.96507	−	14.7978i	−0.240861	−	0.898904i	0.734558	−	0.678546i	$-0.237389\pi$
$272$	16.5534			1.00370
$273$	−6.81325	−	3.56424i	−0.412357	−	0.215717i
$274$			0.682525i			0.0412328i
$275$	0.0194533	−	0.588947i	0.00117308	−	0.0355149i
$276$	−0.454566	+	0.787331i	−0.0273616	+	0.0473918i
$277$	−7.11278	−	12.3197i	−0.427365	−	0.740218i	0.569273	−	0.822149i	$-0.307225\pi$
$277$	−7.11278	−	12.3197i	−0.427365	−	0.740218i	−0.996638	+	0.0819303i	$0.973891\pi$
$278$	−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	$-0.606442\pi$
$281$	10.3329	−	10.3329i	0.616408	−	0.616408i	0.944608	+	0.328200i	$0.106442\pi$
$282$	9.17422	−	5.29674i	0.546317	−	0.315416i
$283$	3.09024	−	5.35246i	0.183696	−	0.318171i	−0.759440	−	0.650577i	$-0.774527\pi$
$283$	3.09024	−	5.35246i	0.183696	−	0.318171i	0.943136	+	0.332406i	$0.107860\pi$
$284$	0.128097	−	0.0343236i	0.00760118	−	0.00203673i
$285$	11.3257			0.670879
$286$	−9.03006	−	15.3345i	−0.533959	−	0.906749i
$287$	−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	$-0.698533\pi$
$293$	−25.6024	−	6.86015i	−1.49571	−	0.400775i	−0.911661	+	0.410943i	$0.865199\pi$
$294$	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
$297$	−3.31482	−	0.109490i	−0.192345	−	0.00635328i
$298$		−	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	−0.0400926	+	0.999196i	$0.512765\pi$
$307$	−18.2098	+	18.2098i	−1.03929	+	1.03929i	−0.999196	+	0.0400926i	$0.987235\pi$
$308$	−1.47840	+	0.344258i	−0.0842399	+	0.0196159i
$309$	−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	$0.486321\pi$
$311$			35.2378i			1.99815i	−0.0429601	+	0.999077i	$0.513679\pi$
$312$	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	−0.945495	−	0.325637i	$-0.894421\pi$
$317$	−11.0362	+	11.0362i	−0.619858	+	0.619858i	0.325637	+	0.945495i	$0.394421\pi$
$318$	−3.41510	+	12.7453i	−0.191509	+	0.714723i
$319$	−10.3172	−	6.41988i	−0.577655	−	0.359444i
$320$	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
$330$	5.10648	+	9.56030i	0.281102	+	0.526277i
$331$	1.47608	+	0.395513i	0.0811324	+	0.0217394i	0.299157	−	0.954204i	$-0.403295\pi$
$331$	1.47608	+	0.395513i	0.0811324	+	0.0217394i	−0.218024	+	0.975943i	$0.569961\pi$
$332$	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	$-0.446998\pi$
$337$	6.08520			0.331482			0.165741	+	0.986169i	$0.446998\pi$
$338$	−12.4951	+	14.7696i	−0.679642	+	0.803363i
$339$	3.31933			0.180281
$340$	1.71919	−	0.460657i	0.0932364	−	0.0249826i
$341$	−21.3383	+	19.9737i	−1.15553	+	1.08164i
$342$	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	$-0.489073\pi$
$347$	17.0817	−	9.86214i	0.916995	−	0.529427i	0.882675	+	0.469983i	$0.155740\pi$
$348$	−0.393150	+	0.680955i	−0.0210750	+	0.0365030i
$349$	−1.13496	−	4.23572i	−0.0607530	−	0.226733i	0.928874	−	0.370397i	$-0.120778\pi$
$349$	−1.13496	−	4.23572i	−0.0607530	−	0.226733i	−0.989627	+	0.143664i	$0.954112\pi$
$350$			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	0.928366	−	0.371667i	$-0.121214\pi$
$353$	−1.15465	−	4.30923i	−0.0614560	−	0.229357i	−0.989822	+	0.142310i	$0.954547\pi$
$354$	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	0.281084	−	0.959683i	$-0.409306\pi$
$359$	23.5092	−	23.5092i	1.24077	−	1.24077i	0.959683	−	0.281084i	$-0.0906941\pi$
$360$	−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	−0.363075	−	0.931760i	$-0.618273\pi$
$367$	11.9808	−	20.7513i	0.625391	−	1.08321i	0.988465	−	0.151448i	$-0.0483937\pi$
$368$	−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	$-0.522564\pi$
$373$	14.6319	−	8.44773i	0.757611	−	0.437407i	0.828437	+	0.560082i	$0.189230\pi$
$374$	12.7382	+	13.6084i	0.658674	+	0.703674i
$375$	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	−0.803779	−	0.594929i	$-0.797180\pi$
$379$	−7.88743	−	29.4363i	−0.405150	−	1.51204i	0.398628	−	0.917113i	$-0.369486\pi$
$380$	−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	−0.00114894	−	0.999999i	$-0.500366\pi$
$383$	−9.82714	−	2.63318i	−0.502144	−	0.134549i	−0.500995	+	0.865450i	$0.667032\pi$
$384$	12.3505	+	3.30932i	0.630261	+	0.168878i
$385$	13.7004	−	7.31785i	0.698237	−	0.372952i
$386$	−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	$-0.925719\pi$
$389$		−	9.12187i		−	0.462497i	0.972895	−	0.231249i	$-0.0742810\pi$
$390$	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
$396$	0.604339	+	0.376048i	0.0303692	+	0.0188971i
$397$	1.24375	−	4.64174i	0.0624220	−	0.232962i	−0.927666	−	0.373411i	$-0.878188\pi$
$397$	1.24375	−	4.64174i	0.0624220	−	0.232962i	0.990088	+	0.140449i	$0.0448547\pi$
$398$	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	0.377108	−	0.926169i	$-0.376919\pi$
$401$	23.3647	−	6.26055i	1.16678	−	0.312637i	0.789670	+	0.613532i	$0.210252\pi$
$402$	−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
$407$	−13.5141	+	3.14687i	−0.669871	+	0.155985i
$408$	−7.09524	+	7.09524i	−0.351267	+	0.351267i
$409$	10.1182	−	37.7615i	0.500311	−	1.86718i	0.00232802	−	0.999997i	$-0.499259\pi$
$409$	10.1182	−	37.7615i	0.500311	−	1.86718i	0.497983	−	0.867187i	$-0.334074\pi$
$410$	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
$418$	0.840355	−	25.4417i	0.0411031	−	1.24440i
$419$	13.5033	−	23.3884i	0.659679	−	1.14260i	−0.321020	−	0.947073i	$-0.604026\pi$
$419$	13.5033	−	23.3884i	0.659679	−	1.14260i	0.980699	−	0.195525i	$-0.0626411\pi$
$420$	−0.502530	−	0.870407i	−0.0245209	−	0.0424715i
$421$	−8.20360	+	8.20360i	−0.399819	+	0.399819i	−0.878169	−	0.478350i	$-0.841235\pi$
$421$	−8.20360	+	8.20360i	−0.399819	+	0.399819i	0.478350	+	0.878169i	$0.341235\pi$
$422$	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
$429$	11.5770	+	2.99560i	0.558942	+	0.144629i
$430$	−15.4167			−0.743460
$431$	34.0663	−	9.12803i	1.64092	−	0.439682i	0.683866	−	0.729608i	$-0.260297\pi$
$431$	34.0663	−	9.12803i	1.64092	−	0.439682i	0.957049	+	0.289926i	$0.0936306\pi$
$432$	−2.19158	+	3.79593i	−0.105443	+	0.182632i
$433$	20.9382	−	12.0887i	1.00623	−	0.580945i	0.0961412	−	0.995368i	$-0.469350\pi$
$433$	20.9382	−	12.0887i	1.00623	−	0.580945i	0.910084	+	0.414423i	$0.136017\pi$
$434$	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	−0.0502978	+	0.998734i	$0.516017\pi$
$439$	−18.6492	+	32.3014i	−0.890078	+	1.54166i	−0.839780	+	0.542926i	$0.817316\pi$
$440$	−0.638831	+	19.3406i	−0.0304551	+	0.922026i
$441$			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	0.789621	+	0.613595i	$0.210277\pi$
$449$	−4.25929	+	15.8959i	−0.201008	+	0.750173i	−0.990629	+	0.136578i	$0.956390\pi$
$450$	0.186961	−	0.186961i	0.00881342	−	0.00881342i
$451$	2.43708	−	0.567492i	0.114757	−	0.0267221i
$452$	−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	$-0.481469\pi$
$457$	12.9917	−	3.48110i	0.607724	−	0.162839i	0.549541	+	0.835467i	$0.314803\pi$
$458$	−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	−0.379858	−	0.925045i	$-0.624027\pi$
$461$	8.83809	−	32.9842i	0.411631	−	1.53623i	0.791489	−	0.611183i	$-0.209306\pi$
$462$	5.56097	−	8.93692i	0.258720	−	0.415783i
$463$	−11.9794	−	11.9794i	−0.556729	−	0.556729i	0.371646	−	0.928375i	$-0.378794\pi$
$463$	−11.9794	−	11.9794i	−0.556729	−	0.556729i	−0.928375	+	0.371646i	$0.878794\pi$
$464$	−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	$-0.954866\pi$
$467$		−	6.10787i		−	0.282639i	0.989964	−	0.141319i	$-0.0451344\pi$
$468$	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
$473$	−7.37155	−	13.8009i	−0.338944	−	0.634568i
$474$	−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	−0.999027	−	0.0441128i	$-0.985954\pi$
$479$	−3.41205	−	12.7339i	−0.155901	−	0.581829i	0.843126	−	0.537716i	$-0.180713\pi$
$480$	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
$484$	2.11788	−	1.04288i	0.0962673	−	0.0474035i
$485$	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	−0.0875747	−	0.996158i	$-0.527912\pi$
$487$	−14.5979	−	3.91151i	−0.661496	−	0.177247i	−0.573921	+	0.818911i	$0.694578\pi$
$488$	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	$-0.838523\pi$
$491$	−0.361278	+	0.625752i	−0.0163043	+	0.0282398i	0.857758	+	0.514053i	$0.171857\pi$
$492$	−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	−0.917791	−	0.397063i	$-0.870030\pi$
$499$	−11.6322	+	11.6322i	−0.520729	+	0.520729i	0.397063	+	0.917791i	$0.370030\pi$
$500$	−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	$-0.751797\pi$
$503$	−10.2657	+	5.92689i	−0.457724	+	0.264267i	0.253363	+	0.967371i	$0.418463\pi$
$504$	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	−0.993972	−	0.109631i	$-0.965033\pi$
$509$	−4.24107	−	15.8279i	−0.187982	−	0.701560i	0.805990	−	0.591929i	$-0.201633\pi$
$510$	−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
$517$	16.1342	+	17.2364i	0.709581	+	0.758058i
$518$	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	$-0.471551\pi$
$523$	−16.6644	−	9.62120i	−0.728684	−	0.420706i	−0.817940	+	0.575303i	$0.804884\pi$
$524$	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
$528$	6.84908	+	12.8228i	0.298068	+	0.558040i
$529$	−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
$539$	6.90473	+	4.29645i	0.297408	+	0.185061i
$540$	−0.121977	+	0.455223i	−0.00524904	+	0.0195897i
$541$	−18.0899	+	18.0899i	−0.777744	+	0.777744i	−0.979447	−	0.201703i	$-0.935352\pi$
$541$	−18.0899	+	18.0899i	−0.777744	+	0.777744i	0.201703	+	0.979447i	$0.435352\pi$
$542$	−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
$550$	−0.198878	−	0.854075i	−0.00848018	−	0.0364179i
$551$	−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	$-0.0601436\pi$
$557$	0.889232	+	3.31866i	0.0376780	+	0.140616i	−0.944525	+	0.328441i	$0.893477\pi$
$558$	−13.1145			−0.555180
$559$	−11.5166	+	12.5174i	−0.487099	+	0.529428i
$560$		−	20.5271i		−	0.867427i
$561$	−12.5187	−	0.413501i	−0.528541	−	0.0174580i
$562$	10.8731	−	18.8328i	0.458656	−	0.794415i
$563$	−1.45958	−	2.52807i	−0.0615140	−	0.106545i	0.833628	−	0.552326i	$-0.186260\pi$
$563$	−1.45958	−	2.52807i	−0.0615140	−	0.106545i	−0.895142	+	0.445780i	$0.852926\pi$
$564$	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	0.412048	+	0.911162i	$0.364814\pi$
$569$	−13.9083	+	24.0899i	−0.583066	+	1.00990i	−0.995114	+	0.0987372i	$0.968520\pi$
$570$	16.2802	−	4.36226i	0.681902	−	0.182715i
$571$	47.0769			1.97011			0.985054	−	0.172246i	$-0.0551023\pi$
$571$	47.0769			1.97011			0.985054	+	0.172246i	$0.0551023\pi$
$572$	−1.83024	−	1.79903i	−0.0765261	−	0.0752213i
$573$	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	−0.0188334	−	0.999823i	$-0.505995\pi$
$577$	23.5642	−	23.5642i	0.980989	−	0.980989i	0.999823	+	0.0188334i	$0.00599521\pi$
$578$	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
$583$	−29.3913	−	0.970811i	−1.21726	−	0.0402069i
$584$			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	0.998783	+	0.0493127i	$0.0157031\pi$
$587$	3.83937	+	14.3287i	0.158468	+	0.591410i	−0.840315	+	0.542098i	$0.817630\pi$
$588$	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	$-0.732250\pi$
$593$	1.91944	−	1.91944i	0.0788218	−	0.0788218i	0.745419	+	0.666597i	$0.232250\pi$
$594$	−4.80705	+	1.11936i	−0.197236	+	0.0459279i
$595$	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	$-0.301648\pi$
$601$	4.21977	+	2.43629i	0.172128	+	0.0993782i	−0.411461	+	0.911427i	$0.634981\pi$
$602$	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
$605$	−18.1706	+	15.9163i	−0.738741	+	0.647091i
$606$	1.43373	+	1.43373i	0.0582415	+	0.0582415i
$607$	3.22008	−	1.85911i	0.130699	−	0.0754591i	−0.433225	−	0.901286i	$-0.642624\pi$
$607$	3.22008	−	1.85911i	0.130699	−	0.0754591i	0.563924	+	0.825827i	$0.309291\pi$
$608$	−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	$-0.655146\pi$
$613$	−10.6995	+	2.86693i	−0.432149	+	0.115794i	0.0361857	+	0.999345i	$0.488479\pi$
$614$	−19.1619	+	33.1894i	−0.773312	+	1.33942i
$615$	0.828395	+	1.43482i	0.0334041	+	0.0578576i
$616$	16.5763	−	8.85394i	0.667877	−	0.356735i
$617$	−4.34149	−	1.16330i	−0.174782	−	0.0468327i	0.170367	−	0.985381i	$-0.445505\pi$
$617$	−4.34149	−	1.16330i	−0.174782	−	0.0468327i	−0.345149	+	0.938548i	$0.612171\pi$
$618$	−25.2242	−	6.75880i	−1.01466	−	0.271879i
$619$	3.19312	+	3.19312i	0.128342	+	0.128342i	0.768360	−	0.640018i	$-0.221073\pi$
$619$	3.19312	+	3.19312i	0.128342	+	0.128342i	−0.640018	+	0.768360i	$0.721073\pi$
$620$	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
$627$	11.6895	+	12.4881i	0.466833	+	0.498726i
$628$	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	−0.982221	−	0.187727i	$-0.939888\pi$
$631$	−0.947745	+	3.53703i	−0.0377291	+	0.140807i	0.944492	+	0.328534i	$0.106555\pi$
$632$	−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	−0.332003	−	0.943278i	$-0.607724\pi$
$641$	8.07386	−	4.66144i	0.318898	−	0.184116i	0.650901	+	0.759162i	$0.274391\pi$
$642$	−11.4904	+	11.4904i	−0.453488	+	0.453488i
$643$	−38.7770	−	10.3903i	−1.52922	−	0.409752i	−0.606452	−	0.795120i	$-0.707408\pi$
$643$	−38.7770	−	10.3903i	−1.52922	−	0.409752i	−0.922763	+	0.385368i	$0.874075\pi$
$644$	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	0.218516	−	0.975833i	$-0.429878\pi$
$647$	−13.1587	−	7.59719i	−0.517323	−	0.298676i	−0.735839	+	0.677157i	$0.763212\pi$
$648$	−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	−0.973525	−	0.228583i	$-0.926591\pi$
$653$	−7.38005	+	12.7826i	−0.288804	+	0.500223i	0.684721	+	0.728806i	$0.259924\pi$
$654$	−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	$-0.366649\pi$
$659$	35.9732	−	20.7691i	1.40132	−	0.809050i	0.994528	+	0.104472i	$0.0333154\pi$
$660$	1.06816	+	1.14114i	0.0415782	+	0.0444188i
$661$	5.04286	−	1.35123i	0.196145	−	0.0525568i	−0.159409	−	0.987213i	$-0.550959\pi$
$661$	5.04286	−	1.35123i	0.196145	−	0.0525568i	0.355554	+	0.934656i	$0.384292\pi$
$662$	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
$671$	3.43305	−	1.83371i	0.132531	−	0.0707894i
$672$	−1.28912	−	2.23282i	−0.0497288	−	0.0861328i
$673$	0.500379	−	0.866681i	0.0192882	−	0.0334081i	−0.856220	−	0.516611i	$-0.827193\pi$
$673$	0.500379	−	0.866681i	0.0192882	−	0.0334081i	0.875508	+	0.483203i	$0.160527\pi$
$674$	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
$682$	−22.9796	+	36.9300i	−0.879933	+	1.41412i
$683$	−4.81235	+	17.9599i	−0.184139	+	0.687217i	0.810674	+	0.585498i	$0.199101\pi$
$683$	−4.81235	+	17.9599i	−0.184139	+	0.687217i	−0.994813	+	0.101719i	$0.967566\pi$
$684$	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	1.00000		0.000963213i	$-0.000306600\pi$
$691$	3.50911	+	13.0962i	0.133493	+	0.498202i	−0.866507	+	0.499166i	$0.833640\pi$
$692$	−4.20018	−	2.42498i	−0.159667	−	0.0921838i
$693$	1.60410	+	6.88876i	0.0609347	+	0.261682i
$694$	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	$-0.357735\pi$
$701$	22.8866			0.864415			0.432208	+	0.901774i	$0.357735\pi$
$702$	2.87382	+	4.53113i	0.108465	+	0.171016i
$703$			21.5773i			0.813802i
$704$	−0.762842	+	23.0950i	−0.0287507	+	0.870426i
$705$	−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	0.682473	+	0.730911i	$0.260905\pi$
$709$	−7.29639	+	27.2305i	−0.274022	+	1.02266i	−0.956494	+	0.291751i	$0.905762\pi$
$710$	−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
$715$	22.8540	+	12.9340i	0.854690	+	0.483705i
$716$	−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	−0.114724	−	0.993397i	$-0.536598\pi$
$719$	18.4541	−	10.6545i	0.688222	−	0.397345i	0.802945	+	0.596053i	$0.203265\pi$
$720$	−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
$726$	−5.27098	+	15.4979i	−0.195624	+	0.575181i
$727$		−	33.9014i		−	1.25733i	−0.777674	−	0.628667i	$-0.783601\pi$
$727$		−	33.9014i		−	1.25733i	0.777674	−	0.628667i	$-0.216399\pi$
$728$	−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	0.995906	+	0.0903930i	$0.0288123\pi$
$733$	29.4104	+	29.4104i	1.08630	+	1.08630i	0.0903930	+	0.995906i	$0.471188\pi$
$734$	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
$737$	−0.195205	−	0.838304i	−0.00719048	−	0.0308793i
$738$	0.972340	+	0.561381i	0.0357923	+	0.0206647i
$739$	0.224918	+	0.839407i	0.00827376	+	0.0308781i	0.969939	−	0.243347i	$-0.0782454\pi$
$739$	0.224918	+	0.839407i	0.00827376	+	0.0308781i	−0.961666	+	0.274225i	$0.911579\pi$
$740$			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	$-0.800689\pi$
$743$	−33.2275	+	8.90329i	−1.21900	+	0.326630i	−0.408713	+	0.912663i	$0.634022\pi$
$744$	−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
$748$	2.28234	+	1.42018i	0.0834507	+	0.0519270i
$749$	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	0.992176	−	0.124845i	$-0.0398435\pi$
$751$	37.8220	+	21.8366i	1.38014	+	0.796827i	0.387969	+	0.921673i	$0.373177\pi$
$752$	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	−0.824093	−	0.566455i	$-0.808315\pi$
$757$	2.16030	−	3.74176i	0.0785176	−	0.135996i	0.902611	+	0.430458i	$0.141648\pi$
$758$	−22.6756	−	39.2752i	−0.823614	−	1.42654i
$759$	12.3928	−	6.61940i	0.449829	−	0.240269i
$760$	29.0664	+	7.78833i	1.05435	+	0.282512i
$761$	2.85242	+	0.764305i	0.103400	+	0.0277060i	0.310148	−	0.950688i	$-0.399621\pi$
$761$	2.85242	+	0.764305i	0.103400	+	0.0277060i	−0.206748	+	0.978394i	$0.566288\pi$
$762$	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	$-0.577812\pi$
$769$	0.929157	−	0.248967i	0.0335063	−	0.00897797i	0.275533	+	0.961292i	$0.411146\pi$
$770$	16.8751	−	15.7959i	0.608135	−	0.569246i
$771$	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	−0.121502	−	0.992591i	$-0.538771\pi$
$773$	−20.1021	−	5.38633i	−0.723021	−	0.193733i	−0.601519	+	0.798858i	$0.705438\pi$
$774$	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	$-0.670336\pi$
$787$	−38.7610	−	10.3860i	−1.38168	−	0.370220i	−0.871731	+	0.489984i	$0.837002\pi$
$788$	−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	−0.634405	+	0.773000i	$0.718755\pi$
$797$	−45.7641	+	26.4219i	−1.62105	+	0.935911i	−0.986641	+	0.162911i	$0.947912\pi$
$798$	−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
$803$	−10.5316	+	9.85816i	−0.371654	+	0.347887i
$804$	−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	$-0.223759\pi$
$809$	16.6258	+	9.59890i	0.584531	+	0.337479i	−0.178401	+	0.983958i	$0.557092\pi$
$810$	−1.63398	−	2.83014i	−0.0574123	−	0.0994410i
$811$	6.04032	+	6.04032i	0.212104	+	0.212104i	0.805161	−	0.593057i	$-0.202079\pi$
$811$	6.04032	+	6.04032i	0.212104	+	0.212104i	−0.593057	+	0.805161i	$0.702079\pi$
$812$	1.61973	+	0.434005i	0.0568414	+	0.0152306i
$813$	14.7978	+	3.96507i	0.518983	+	0.139061i
$814$	−18.2138	+	9.72862i	−0.638394	+	0.340988i
$815$	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	$-0.950528\pi$
$821$	−50.6052	+	13.5596i	−1.76613	+	0.473234i	−0.778189	+	0.628031i	$0.783861\pi$
$822$	−0.591084	−	0.341262i	−0.0206164	−	0.0119029i
$823$	−19.7563	+	11.4063i	−0.688662	+	0.397599i	−0.803111	−	0.595830i	$-0.796823\pi$
$823$	−19.7563	+	11.4063i	−0.688662	+	0.397599i	0.114448	+	0.993429i	$0.463490\pi$
$824$	−32.9679	−	32.9679i	−1.14849	−	1.14849i
$825$	0.500317	+	0.311321i	0.0174188	+	0.0108388i
$826$	5.73730	−	21.4119i	0.199626	−	0.745015i
$827$	−2.51770	+	2.51770i	−0.0875491	+	0.0875491i	−0.749525	−	0.661976i	$-0.769718\pi$
$827$	−2.51770	+	2.51770i	−0.0875491	+	0.0875491i	0.661976	+	0.749525i	$0.269718\pi$
$828$	−0.454566	−	0.787331i	−0.0157973	−	0.0273616i
$829$	−46.0743	−	26.6010i	−1.60023	−	0.923892i	−0.991441	−	0.130559i	$-0.958323\pi$
$829$	−46.0743	−	26.6010i	−1.60023	−	0.923892i	−0.608787	−	0.793333i	$-0.708344\pi$
$830$	−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
$836$	−0.832552	−	3.57537i	−0.0287944	−	0.123657i
$837$	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	−0.726851	−	0.686795i	$-0.759017\pi$
$839$	7.12603	−	26.5947i	0.246018	−	0.918152i	0.972869	−	0.231356i	$-0.0743164\pi$
$840$	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
$847$	22.2093	+	7.55359i	0.763120	+	0.259544i
$848$	−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	$-0.607209\pi$
$853$	17.9133	−	17.9133i	0.613341	−	0.613341i	0.943815	+	0.330474i	$0.107209\pi$
$854$	−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	$-0.149170\pi$
$857$	52.2368			1.78438			0.892188	+	0.451665i	$0.149170\pi$
$858$	17.7951	−	0.153005i	0.607515	−	0.00522351i
$859$	−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	−0.512469	−	0.858705i	$-0.671269\pi$
$863$	10.1713	−	10.1713i	0.346236	−	0.346236i	0.858705	+	0.512469i	$0.171269\pi$
$864$	−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
$869$	0.877794	−	26.5752i	0.0297771	−	0.901501i
$870$		−	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	$-0.953307\pi$
$877$	−1.76068	+	6.57095i	−0.0594540	+	0.221885i	0.929806	+	0.368049i	$0.119974\pi$
$878$	−14.3660	+	53.6146i	−0.484828	+	1.80940i
$879$	18.7423	−	18.7423i	0.632162	−	0.632162i
$880$	7.23997	+	31.0918i	0.244059	+	1.04811i
$881$	−10.4899	−	6.05636i	−0.353414	−	0.204044i	0.312774	−	0.949828i	$-0.398742\pi$
$881$	−10.4899	−	6.05636i	−0.353414	−	0.204044i	−0.666188	+	0.745784i	$0.732075\pi$
$882$	0.944416	+	3.52461i	0.0318001	+	0.118680i
$883$			19.3576i			0.651436i	0.945467	+	0.325718i	$0.105606\pi$
$883$			19.3576i			0.651436i	−0.945467	+	0.325718i	$0.894394\pi$
$884$	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	$-0.282694\pi$
$887$	8.17204	+	4.71813i	0.274390	+	0.158419i	−0.356491	+	0.934299i	$0.616027\pi$
$888$	−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
$891$	1.75223	−	2.81597i	0.0587019	−	0.0943386i
$892$	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
$902$	3.28460	−	1.75441i	0.109365	−	0.0584156i
$903$	−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	0.747200	−	0.664599i	$-0.231398\pi$
$907$	16.4207	+	9.48051i	0.545241	+	0.314795i	−0.201959	+	0.979394i	$0.564731\pi$
$908$	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
$913$	−20.9206	−	22.3498i	−0.692369	−	0.739671i
$914$	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	$-0.818093\pi$
$919$	−24.0472	+	13.8836i	−0.793243	+	0.457979i	0.0478598	+	0.998854i	$0.484760\pi$
$920$	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	0.870773	−	0.491686i	$-0.163619\pi$
$929$	42.0325	+	11.2626i	1.37904	+	0.369513i	0.508269	+	0.861199i	$0.330286\pi$
$930$	−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	0.999682	+	0.0252128i	$0.00802634\pi$
$941$	31.4394	+	31.4394i	1.02489	+	1.02489i	0.0252128	+	0.999682i	$0.491974\pi$
$942$	−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
$946$	−15.9119	−	16.9989i	−0.517339	−	0.552682i
$947$	−50.4947	+	13.5300i	−1.64086	+	0.439666i	−0.957033	−	0.289980i	$-0.906351\pi$
$947$	−50.4947	+	13.5300i	−1.64086	+	0.439666i	−0.683825	+	0.729646i	$0.739685\pi$
$948$	−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	$-0.0166385\pi$
$953$	14.0174	+	24.2789i	0.454069	+	0.786471i	−0.544565	+	0.838719i	$0.683305\pi$
$954$	−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
$957$	10.7184	−	5.72506i	0.346477	−	0.185065i
$958$	−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	$-0.490229\pi$
$967$	−30.1275	−	30.1275i	−0.968836	−	0.968836i	−0.999529	+	0.0306928i	$0.990229\pi$
$968$	−21.9848	+	19.2573i	−0.706619	+	0.618955i
$969$	−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	0.858802	−	0.512308i	$-0.171210\pi$
$971$	−0.444706	−	0.770254i	−0.0142713	−	0.0247186i	−0.873073	+	0.487590i	$0.837876\pi$
$972$	−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	0.904438	−	0.426605i	$-0.140291\pi$
$977$	−2.87974	−	10.7473i	−0.0921309	−	0.343837i	−0.996569	+	0.0827680i	$0.973624\pi$
$978$	22.7710	+	13.1468i	0.728135	+	0.420389i
$979$	44.4740	−	10.3561i	1.42139	−	0.330983i
$980$	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	0.943932	+	0.330139i	$0.107096\pi$
$983$	39.9457	+	39.9457i	1.27407	+	1.27407i	0.330139	+	0.943932i	$0.392904\pi$
$984$	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
$990$	−10.8327	−	0.357810i	−0.344286	−	0.0113720i
$991$	15.1873	−	26.3051i	0.482440	−	0.835610i	−0.517357	−	0.855770i	$-0.673084\pi$
$991$	15.1873	−	26.3051i	0.482440	−	0.835610i	0.999797	+	0.0201594i	$0.00641737\pi$
$992$	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	−0.640758	+	0.767743i	$0.721380\pi$
$997$	−51.3421	+	29.6424i	−1.62602	+	0.938784i	−0.985264	+	0.171041i	$0.945287\pi$
$998$	−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.175.11	yes	56
11.10	odd	2	inner	429.2.bd.a.175.4	yes	56
13.11	odd	12	inner	429.2.bd.a.76.4	✓	56
143.76	even	12	inner	429.2.bd.a.76.11	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bd.a.76.4	✓	56	13.11	odd	12	inner
429.2.bd.a.76.11	yes	56	143.76	even	12	inner
429.2.bd.a.175.4	yes	56	11.10	odd	2	inner
429.2.bd.a.175.11	yes	56	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
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} +(-3.31482 - 0.109490i) 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} +(-4.80705 + 1.11936i) 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} +(1.75223 - 2.81597i) 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} +(-0.627837 + 0.335349i) 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} +(5.31724 - 4.97721i) 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} +(6.43338 - 6.02197i) 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} +(1.56259 + 2.92546i) 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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