LMFDB - Embedded newform 507.2.m.a.40.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(40,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("507.40");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.m (of order $13$, degree $12$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$180$
Relative dimension:	$15$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			40.10
Character	$\chi$	$=$	507.40
Dual form			507.2.m.a.469.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.869211 + 0.214241i) q^{2} +(-0.120537 + 0.992709i) q^{3} +(-1.06128 - 0.557005i) q^{4} +(-1.13901 + 1.65015i) q^{5} +(-0.317451 + 0.837049i) q^{6} +(-1.32969 - 1.17800i) q^{7} +(-2.14332 - 1.89881i) q^{8} +(-0.970942 - 0.239316i) q^{9} +(-1.34357 + 1.19030i) q^{10} +(1.61061 - 0.396979i) q^{11} +(0.680867 - 0.986407i) q^{12} +(-3.02147 + 1.96741i) q^{13} +(-0.903404 - 1.30881i) q^{14} +(-1.50082 - 1.32961i) q^{15} +(-0.0944544 - 0.136841i) q^{16} +(-5.49180 - 4.86531i) q^{17} +(-0.792682 - 0.416031i) q^{18} +1.02881 q^{19} +(2.12796 - 1.11684i) q^{20} +(1.32969 - 1.17800i) q^{21} +1.48501 q^{22} -9.12340 q^{23} +(2.14332 - 1.89881i) q^{24} +(0.347396 + 0.916008i) q^{25} +(-3.04780 + 1.06277i) q^{26} +(0.354605 - 0.935016i) q^{27} +(0.755026 + 1.99084i) q^{28} +(-2.68140 - 0.660906i) q^{29} +(-1.01967 - 1.47725i) q^{30} +(2.56193 - 6.75526i) q^{31} +(1.97800 + 5.21555i) q^{32} +(0.199947 + 1.64672i) q^{33} +(-3.73118 - 5.40555i) q^{34} +(3.45841 - 0.852422i) q^{35} +(0.897145 + 0.794801i) q^{36} +(0.0568353 - 0.149862i) q^{37} +(0.894249 + 0.220413i) q^{38} +(-1.58887 - 3.23659i) q^{39} +(5.57458 - 1.37401i) q^{40} +(-0.422018 + 3.47563i) q^{41} +(1.40816 - 0.739058i) q^{42} +(3.08266 + 8.12831i) q^{43} +(-1.93043 - 0.475809i) q^{44} +(1.50082 - 1.32961i) q^{45} +(-7.93016 - 1.95461i) q^{46} +(2.45880 - 1.29048i) q^{47} +(0.147228 - 0.0772714i) q^{48} +(-0.463371 - 3.81620i) q^{49} +(0.105714 + 0.870630i) q^{50} +(5.49180 - 4.86531i) q^{51} +(4.30250 - 0.405007i) q^{52} +(8.91733 + 7.90006i) q^{53} +(0.508545 - 0.736755i) q^{54} +(-1.17943 + 3.10990i) q^{55} +(0.613140 + 5.04967i) q^{56} +(-0.124009 + 1.02131i) q^{57} +(-2.18911 - 1.14893i) q^{58} +(-8.20735 + 11.8904i) q^{59} +(0.852198 + 2.24706i) q^{60} +(-2.44268 + 2.16403i) q^{61} +(3.67412 - 5.32288i) q^{62} +(1.00914 + 1.46199i) q^{63} +(0.641995 + 5.28730i) q^{64} +(0.194983 - 7.22677i) q^{65} +(-0.178998 + 1.47418i) q^{66} +(-11.1852 + 5.87044i) q^{67} +(3.11836 + 8.22244i) q^{68} +(1.09970 - 9.05688i) q^{69} +3.18871 q^{70} +(1.00990 - 8.31728i) q^{71} +(1.62662 + 2.35657i) q^{72} +(-5.13448 + 1.26554i) q^{73} +(0.0815085 - 0.118085i) q^{74} +(-0.951203 + 0.234450i) q^{75} +(-1.09186 - 0.573050i) q^{76} +(-2.60925 - 1.36944i) q^{77} +(-0.687650 - 3.15368i) q^{78} +(15.5680 - 8.17072i) q^{79} +0.333392 q^{80} +(0.885456 + 0.464723i) q^{81} +(-1.11145 + 2.93064i) q^{82} +(0.970910 + 7.99616i) q^{83} +(-2.06733 + 0.509552i) q^{84} +(14.2837 - 3.52062i) q^{85} +(0.938063 + 7.72564i) q^{86} +(0.979294 - 2.58219i) q^{87} +(-4.20583 - 2.20739i) q^{88} -7.82265 q^{89} +(1.58939 - 0.834175i) q^{90} +(6.33524 + 0.943256i) q^{91} +(9.68252 + 5.08178i) q^{92} +(6.39720 + 3.35751i) q^{93} +(2.41369 - 0.594921i) q^{94} +(-1.17182 + 1.69768i) q^{95} +(-5.41594 + 1.33491i) q^{96} +(-0.0360998 - 0.0522996i) q^{97} +(0.414821 - 3.41636i) q^{98} -1.65881 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 180 q - q^{2} + 15 q^{3} - 15 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} - 15 q^{9} - 2 q^{10} - 4 q^{11} + 15 q^{12} - 14 q^{13} + 6 q^{14} + 2 q^{15} - 15 q^{16} - 2 q^{17} - q^{18} + 2 q^{20} - 4 q^{21}+ \cdots - 30 q^{99}+O(q^{100}) $ 180 * q - q^2 + 15 * q^3 - 15 * q^4 - 2 * q^5 + q^6 + 4 * q^7 + 3 * q^8 - 15 * q^9 - 2 * q^10 - 4 * q^11 + 15 * q^12 - 14 * q^13 + 6 * q^14 + 2 * q^15 - 15 * q^16 - 2 * q^17 - q^18 + 2 * q^20 - 4 * q^21 - 28 * q^22 - 52 * q^23 - 3 * q^24 - 67 * q^25 - 40 * q^26 + 15 * q^27 - 4 * q^28 - 27 * q^29 + 2 * q^30 + 22 * q^31 - 5 * q^32 - 9 * q^33 + 63 * q^34 - 31 * q^35 - 15 * q^36 + 2 * q^37 + 65 * q^38 + q^39 + 45 * q^40 - 6 * q^41 + 59 * q^42 - 60 * q^43 - 35 * q^44 - 2 * q^45 - 156 * q^46 + 15 * q^48 + 59 * q^49 - 51 * q^50 + 2 * q^51 + 66 * q^52 + 50 * q^53 + q^54 + 55 * q^55 - 14 * q^56 - 13 * q^57 + 36 * q^58 + 92 * q^59 - 15 * q^60 + 6 * q^61 + 61 * q^62 + 4 * q^63 - 203 * q^64 - 54 * q^65 + 54 * q^66 + 86 * q^67 + 32 * q^68 + 112 * q^70 + 39 * q^71 + 3 * q^72 - 158 * q^73 - 80 * q^74 + 15 * q^75 + 130 * q^76 - 64 * q^77 + 66 * q^78 - 10 * q^79 - 310 * q^80 - 15 * q^81 + 59 * q^82 - 82 * q^83 + 4 * q^84 + 22 * q^85 - q^86 + 40 * q^87 + 10 * q^88 + 2 * q^89 - 2 * q^90 - 100 * q^91 - 54 * q^92 + 43 * q^93 + 65 * q^94 + 58 * q^95 - 60 * q^96 + 16 * q^97 - 113 * q^98 - 30 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{13}\right)$

Coefficient data

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

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

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

$2$	0.869211	+	0.214241i	0.614625	+	0.151491i	0.534325	−	0.845279i	$-0.320566\pi$
$2$	0.869211	+	0.214241i	0.614625	+	0.151491i	0.0803001	+	0.996771i	$0.474412\pi$
$3$	−0.120537	+	0.992709i	−0.0695919	+	0.573141i
$3$	−0.120537	+	0.992709i	−0.0695919	+	0.573141i
$4$	−1.06128	−	0.557005i	−0.530642	−	0.278502i
$5$	−1.13901	+	1.65015i	−0.509382	+	0.737967i	−0.990322	−	0.138786i	$-0.955680\pi$
$5$	−1.13901	+	1.65015i	−0.509382	+	0.737967i	0.480940	+	0.876753i	$0.340295\pi$
$6$	−0.317451	+	0.837049i	−0.129599	+	0.341724i
$7$	−1.32969	−	1.17800i	−0.502576	−	0.445243i	0.373349	−	0.927691i	$-0.378209\pi$
$7$	−1.32969	−	1.17800i	−0.502576	−	0.445243i	−0.875925	+	0.482448i	$0.839748\pi$
$8$	−2.14332	−	1.89881i	−0.757777	−	0.671332i
$9$	−0.970942	−	0.239316i	−0.323647	−	0.0797719i
$10$	−1.34357	+	1.19030i	−0.424875	+	0.376406i
$11$	1.61061	−	0.396979i	0.485617	−	0.119694i	0.0110965	−	0.999938i	$-0.496468\pi$
$11$	1.61061	−	0.396979i	0.485617	−	0.119694i	0.474520	+	0.880245i	$0.342622\pi$
$12$	0.680867	−	0.986407i	0.196549	−	0.284751i
$13$	−3.02147	+	1.96741i	−0.838006	+	0.545662i
$13$	−3.02147	+	1.96741i	−0.838006	+	0.545662i
$14$	−0.903404	−	1.30881i	−0.241445	−	0.349793i
$15$	−1.50082	−	1.32961i	−0.387510	−	0.343304i
$16$	−0.0944544	−	0.136841i	−0.0236136	−	0.0342102i
$17$	−5.49180	−	4.86531i	−1.33196	−	1.18001i	−0.968675	−	0.248333i	$-0.920117\pi$
$17$	−5.49180	−	4.86531i	−1.33196	−	1.18001i	−0.363283	−	0.931679i	$-0.618344\pi$
$18$	−0.792682	−	0.416031i	−0.186837	−	0.0980595i
$19$	1.02881			0.236024			0.118012	−	0.993012i	$-0.462348\pi$
$19$	1.02881			0.236024			0.118012	+	0.993012i	$0.462348\pi$
$20$	2.12796	−	1.11684i	0.475825	−	0.249732i
$21$	1.32969	−	1.17800i	0.290162	−	0.257061i
$22$	1.48501			0.316605
$23$	−9.12340			−1.90236			−0.951180	−	0.308636i	$-0.900128\pi$
$23$	−9.12340			−1.90236			−0.951180	+	0.308636i	$0.900128\pi$
$24$	2.14332	−	1.89881i	0.437503	−	0.387593i
$25$	0.347396	+	0.916008i	0.0694792	+	0.183202i
$26$	−3.04780	+	1.06277i	−0.597722	+	0.208426i
$27$	0.354605	−	0.935016i	0.0682437	−	0.179944i
$28$	0.755026	+	1.99084i	0.142687	+	0.376233i
$29$	−2.68140	−	0.660906i	−0.497923	−	0.122727i	−0.0176470	−	0.999844i	$-0.505618\pi$
$29$	−2.68140	−	0.660906i	−0.497923	−	0.122727i	−0.480276	+	0.877117i	$0.659464\pi$
$30$	−1.01967	−	1.47725i	−0.186166	−	0.269708i
$31$	2.56193	−	6.75526i	0.460137	−	1.21328i	−0.481439	−	0.876480i	$-0.659886\pi$
$31$	2.56193	−	6.75526i	0.460137	−	1.21328i	0.941576	−	0.336802i	$-0.109345\pi$
$32$	1.97800	+	5.21555i	0.349664	+	0.921987i
$33$	0.199947	+	1.64672i	0.0348064	+	0.286656i
$34$	−3.73118	−	5.40555i	−0.639893	−	0.927044i
$35$	3.45841	−	0.852422i	0.584578	−	0.144086i
$36$	0.897145	+	0.794801i	0.149524	+	0.132467i
$37$	0.0568353	−	0.149862i	0.00934366	−	0.0246372i	−0.930263	−	0.366893i	$-0.880422\pi$
$37$	0.0568353	−	0.149862i	0.00934366	−	0.0246372i	0.939607	+	0.342256i	$0.111191\pi$
$38$	0.894249	+	0.220413i	0.145066	+	0.0357557i
$39$	−1.58887	−	3.23659i	−0.254422	−	0.518269i
$40$	5.57458	−	1.37401i	0.881419	−	0.217250i
$41$	−0.422018	+	3.47563i	−0.0659082	+	0.542803i	0.921935	+	0.387346i	$0.126608\pi$
$41$	−0.422018	+	3.47563i	−0.0659082	+	0.542803i	−0.987843	+	0.155457i	$0.950315\pi$
$42$	1.40816	−	0.739058i	0.217283	−	0.114039i
$43$	3.08266	+	8.12831i	0.470101	+	1.23956i	0.935144	+	0.354267i	$0.115270\pi$
$43$	3.08266	+	8.12831i	0.470101	+	1.23956i	−0.465043	+	0.885288i	$0.653961\pi$
$44$	−1.93043	−	0.475809i	−0.291024	−	0.0717309i
$45$	1.50082	−	1.32961i	0.223729	−	0.198207i
$46$	−7.93016	−	1.95461i	−1.16924	−	0.288191i
$47$	2.45880	−	1.29048i	0.358653	−	0.188236i	−0.275766	−	0.961225i	$-0.588932\pi$
$47$	2.45880	−	1.29048i	0.358653	−	0.188236i	0.634419	+	0.772989i	$0.281239\pi$
$48$	0.147228	−	0.0772714i	0.0212506	−	0.0111532i
$49$	−0.463371	−	3.81620i	−0.0661959	−	0.545172i
$50$	0.105714	+	0.870630i	0.0149502	+	0.123126i
$51$	5.49180	−	4.86531i	0.769006	−	0.681280i
$52$	4.30250	−	0.405007i	0.596649	−	0.0561644i
$53$	8.91733	+	7.90006i	1.22489	+	1.08516i	0.993680	+	0.112253i	$0.0358067\pi$
$53$	8.91733	+	7.90006i	1.22489	+	1.08516i	0.231209	+	0.972904i	$0.425732\pi$
$54$	0.508545	−	0.736755i	0.0692043	−	0.100260i
$55$	−1.17943	+	3.10990i	−0.159034	+	0.419339i
$56$	0.613140	+	5.04967i	0.0819343	+	0.674790i
$57$	−0.124009	+	1.02131i	−0.0164254	+	0.135275i
$58$	−2.18911	−	1.14893i	−0.287444	−	0.150862i
$59$	−8.20735	+	11.8904i	−1.06851	+	1.54800i	−0.254562	+	0.967056i	$0.581931\pi$
$59$	−8.20735	+	11.8904i	−1.06851	+	1.54800i	−0.813945	+	0.580943i	$0.802684\pi$
$60$	0.852198	+	2.24706i	0.110018	+	0.290094i
$61$	−2.44268	+	2.16403i	−0.312754	+	0.277075i	−0.804867	−	0.593456i	$-0.797763\pi$
$61$	−2.44268	+	2.16403i	−0.312754	+	0.277075i	0.492113	+	0.870531i	$0.336225\pi$
$62$	3.67412	−	5.32288i	0.466613	−	0.676006i
$63$	1.00914	+	1.46199i	0.127139	+	0.184193i
$64$	0.641995	+	5.28730i	0.0802493	+	0.660913i
$65$	0.194983	−	7.22677i	0.0241847	−	0.896371i
$66$	−0.178998	+	1.47418i	−0.0220331	+	0.181459i
$67$	−11.1852	+	5.87044i	−1.36649	+	0.717189i	−0.978842	−	0.204619i	$-0.934404\pi$
$67$	−11.1852	+	5.87044i	−1.36649	+	0.717189i	−0.387647	+	0.921808i	$0.626712\pi$
$68$	3.11836	+	8.22244i	0.378157	+	0.997117i
$69$	1.09970	−	9.05688i	0.132389	−	1.09032i
$70$	3.18871			0.381124
$71$	1.00990	−	8.31728i	0.119853	−	0.987079i	−0.801404	−	0.598124i	$-0.795913\pi$
$71$	1.00990	−	8.31728i	0.119853	−	0.987079i	0.921257	−	0.388955i	$-0.127164\pi$
$72$	1.62662	+	2.35657i	0.191699	+	0.277724i
$73$	−5.13448	+	1.26554i	−0.600946	+	0.148120i	−0.528041	−	0.849219i	$-0.677073\pi$
$73$	−5.13448	+	1.26554i	−0.600946	+	0.148120i	−0.0729051	+	0.997339i	$0.523227\pi$
$74$	0.0815085	−	0.118085i	0.00947517	−	0.0137272i
$75$	−0.951203	+	0.234450i	−0.109835	+	0.0270720i
$76$	−1.09186	−	0.573050i	−0.125244	−	0.0657334i
$77$	−2.60925	−	1.36944i	−0.297352	−	0.156062i
$78$	−0.687650	−	3.15368i	−0.0778611	−	0.357084i
$79$	15.5680	−	8.17072i	1.75154	−	0.919278i	0.807216	−	0.590257i	$-0.200974\pi$
$79$	15.5680	−	8.17072i	1.75154	−	0.919278i	0.944323	−	0.329021i	$-0.106719\pi$
$80$	0.333392			0.0372744
$81$	0.885456	+	0.464723i	0.0983840	+	0.0516359i
$82$	−1.11145	+	2.93064i	−0.122739	+	0.323635i
$83$	0.970910	+	7.99616i	0.106571	+	0.877693i	0.943726	+	0.330727i	$0.107294\pi$
$83$	0.970910	+	7.99616i	0.106571	+	0.877693i	−0.837155	+	0.546966i	$0.815783\pi$
$84$	−2.06733	+	0.509552i	−0.225565	+	0.0555967i
$85$	14.2837	−	3.52062i	1.54929	−	0.381865i
$86$	0.938063	+	7.72564i	0.101154	+	0.833078i
$87$	0.979294	−	2.58219i	0.104991	−	0.276839i
$88$	−4.20583	−	2.20739i	−0.448343	−	0.235309i
$89$	−7.82265			−0.829200			−0.414600	−	0.910004i	$-0.636078\pi$
$89$	−7.82265			−0.829200			−0.414600	+	0.910004i	$0.636078\pi$
$90$	1.58939	−	0.834175i	0.167536	−	0.0879297i
$91$	6.33524	+	0.943256i	0.664113	+	0.0988801i
$92$	9.68252	+	5.08178i	1.00947	+	0.529812i
$93$	6.39720	+	3.35751i	0.663359	+	0.348158i
$94$	2.41369	−	0.594921i	0.248953	−	0.0613614i
$95$	−1.17182	+	1.69768i	−0.120227	+	0.174178i
$96$	−5.41594	+	1.33491i	−0.552762	+	0.136244i
$97$	−0.0360998	−	0.0522996i	−0.00366538	−	0.00531022i	0.821147	−	0.570717i	$-0.193335\pi$
$97$	−0.0360998	−	0.0522996i	−0.00366538	−	0.00531022i	−0.824812	+	0.565407i	$0.808719\pi$
$98$	0.414821	−	3.41636i	0.0419032	−	0.345104i
$99$	−1.65881			−0.166717
$100$	0.141535	−	1.16565i	0.0141535	−	0.116565i
$101$	0.0650841	+	0.171613i	0.00647611	+	0.0170761i	0.938215	−	0.346052i	$-0.112478\pi$
$101$	0.0650841	+	0.171613i	0.00647611	+	0.0170761i	−0.931739	+	0.363128i	$0.881709\pi$
$102$	5.81588	−	3.05241i	0.575858	−	0.302234i
$103$	1.30436	−	10.7424i	0.128523	−	1.05848i	−0.775606	−	0.631218i	$-0.782555\pi$
$103$	1.30436	−	10.7424i	0.128523	−	1.05848i	0.904128	−	0.427261i	$-0.140522\pi$
$104$	10.2117	+	1.52043i	1.00134	+	0.149090i
$105$	0.429341	+	3.53594i	0.0418994	+	0.345073i
$106$	6.05852	+	8.77728i	0.588455	+	0.852525i
$107$	−7.39331	+	10.7111i	−0.714738	+	1.03548i	0.282357	+	0.959309i	$0.408884\pi$
$107$	−7.39331	+	10.7111i	−0.714738	+	1.03548i	−0.997095	+	0.0761674i	$0.975732\pi$
$108$	−0.897145	+	0.794801i	−0.0863278	+	0.0764798i
$109$	−5.43810	−	14.3391i	−0.520876	−	1.37344i	−0.895004	−	0.446059i	$-0.852827\pi$
$109$	−5.43810	−	14.3391i	−0.520876	−	1.37344i	0.374128	−	0.927377i	$-0.377942\pi$
$110$	−1.69144	+	2.45048i	−0.161273	+	0.233644i
$111$	0.141919	+	0.0744848i	0.0134703	+	0.00706978i
$112$	−0.0356038	+	0.293223i	−0.00336424	+	0.0277070i
$113$	−0.423093	−	3.48449i	−0.0398013	−	0.327793i	−0.998986	−	0.0450140i	$-0.985667\pi$
$113$	−0.423093	−	3.48449i	−0.0398013	−	0.327793i	0.959185	−	0.282779i	$-0.0912563\pi$
$114$	−0.326595	+	0.861161i	−0.0305885	+	0.0806552i
$115$	10.3917	−	15.0549i	0.969028	−	1.40388i
$116$	2.47760	+	2.19496i	0.230039	+	0.203797i
$117$	3.40451	−	1.18716i	0.314747	−	0.109753i
$118$	−9.68133	+	8.57691i	−0.891239	+	0.789569i
$119$	1.57104	+	12.9387i	0.144017	+	1.18609i
$120$	0.692051	+	5.69955i	0.0631753	+	0.520296i
$121$	−7.30355	+	3.83320i	−0.663959	+	0.348473i
$122$	−2.58683	+	1.35767i	−0.234201	+	0.122918i
$123$	−3.39942	−	0.837882i	−0.306516	−	0.0755493i
$124$	−6.48166	+	5.74225i	−0.582070	+	0.515669i
$125$	−11.6413	−	2.86932i	−1.04123	−	0.256640i
$126$	0.563935	+	1.48697i	0.0502393	+	0.132470i
$127$	9.12812	−	4.79081i	0.809990	−	0.425115i	−0.00826886	−	0.999966i	$-0.502632\pi$
$127$	9.12812	−	4.79081i	0.809990	−	0.425115i	0.818258	+	0.574850i	$0.194940\pi$
$128$	0.769985	−	6.34140i	0.0680577	−	0.560506i
$129$	−8.44062	+	2.08043i	−0.743155	+	0.183171i
$130$	1.71775	−	6.23982i	0.150657	−	0.547268i
$131$	−13.3064	−	3.27974i	−1.16259	−	0.286552i	−0.389607	−	0.920981i	$-0.627389\pi$
$131$	−13.3064	−	3.27974i	−1.16259	−	0.286552i	−0.772981	+	0.634429i	$0.781235\pi$
$132$	0.705027	−	1.85900i	0.0613648	−	0.161806i
$133$	−1.36799	−	1.21194i	−0.118620	−	0.105088i
$134$	−10.9800	+	2.70632i	−0.948526	+	0.233791i
$135$	1.13901	+	1.65015i	0.0980306	+	0.142022i
$136$	2.53235	+	20.8558i	0.217147	+	1.78837i
$137$	−4.43936	−	11.7056i	−0.379280	−	1.00008i	−0.979713	−	0.200404i	$-0.935774\pi$
$137$	−4.43936	−	11.7056i	−0.379280	−	1.00008i	0.600433	−	0.799675i	$-0.294995\pi$
$138$	2.89623	−	7.63674i	0.246544	−	0.650082i
$139$	4.02301	+	5.82833i	0.341227	+	0.494353i	0.955602	−	0.294662i	$-0.0952070\pi$
$139$	4.02301	+	5.82833i	0.341227	+	0.494353i	−0.614375	+	0.789015i	$0.710592\pi$
$140$	−4.14516	−	1.02169i	−0.350330	−	0.0863486i
$141$	0.984694	+	2.59642i	0.0829262	+	0.218658i
$142$	2.65972	−	7.01310i	0.223199	−	0.588526i
$143$	−4.08539	+	4.36819i	−0.341637	+	0.365286i
$144$	0.0589616	+	0.155469i	0.00491346	+	0.0129557i
$145$	4.14474	−	3.67192i	0.344202	−	0.304936i
$146$	−4.73408			−0.391795
$147$	3.84423			0.317067
$148$	−0.143792	+	0.127389i	−0.0118197	+	0.0104713i
$149$	10.2613	−	5.38557i	0.840642	−	0.441203i	0.0112947	−	0.999936i	$-0.496405\pi$
$149$	10.2613	−	5.38557i	0.840642	−	0.441203i	0.829347	+	0.558733i	$0.188712\pi$
$150$	−0.877025			−0.0716088
$151$	10.9126	+	5.72739i	0.888057	+	0.466088i	0.846096	−	0.533031i	$-0.178947\pi$
$151$	10.9126	+	5.72739i	0.888057	+	0.466088i	0.0419614	+	0.999119i	$0.486639\pi$
$152$	−2.20506	−	1.95351i	−0.178854	−	0.158451i
$153$	4.16787	+	6.03821i	0.336953	+	0.488160i
$154$	−1.97460	−	1.74934i	−0.159118	−	0.140966i
$155$	8.22909	+	11.9219i	0.660976	+	0.957590i
$156$	−0.116555	+	4.31995i	−0.00933186	+	0.345873i
$157$	4.86897	−	7.05392i	0.388586	−	0.562964i	−0.579057	−	0.815287i	$-0.696579\pi$
$157$	4.86897	−	7.05392i	0.388586	−	0.562964i	0.967643	+	0.252323i	$0.0811946\pi$
$158$	15.2824	−	3.76677i	1.21580	−	0.299668i
$159$	−8.91733	+	7.90006i	−0.707190	+	0.626516i
$160$	−10.8594	−	2.67660i	−0.858509	−	0.211603i
$161$	12.1313	+	10.7474i	0.956080	+	0.847013i
$162$	0.670085	+	0.593643i	0.0526468	+	0.0466410i
$163$	−5.03862	+	13.2858i	−0.394655	+	1.04062i	0.579546	+	0.814940i	$0.303230\pi$
$163$	−5.03862	+	13.2858i	−0.394655	+	1.04062i	−0.974201	+	0.225681i	$0.927539\pi$
$164$	2.38383	−	3.45357i	0.186146	−	0.269678i
$165$	−2.94506	−	1.54569i	−0.229273	−	0.120332i
$166$	−0.869182	+	7.15836i	−0.0674616	+	0.555596i
$167$	−21.0737	−	5.19419i	−1.63073	−	0.401939i	−0.685429	−	0.728140i	$-0.740385\pi$
$167$	−21.0737	−	5.19419i	−1.63073	−	0.401939i	−0.945300	+	0.326201i	$0.894231\pi$
$168$	−5.08675			−0.392452
$169$	5.25859	−	11.8890i	0.404507	−	0.914535i
$170$	13.1698			1.01008
$171$	−0.998911	−	0.246209i	−0.0763886	−	0.0188281i
$172$	1.25593	−	10.3435i	0.0957636	−	0.788685i
$173$	0.545572	+	0.286338i	0.0414791	+	0.0217699i	0.485335	−	0.874328i	$-0.338698\pi$
$173$	0.545572	+	0.286338i	0.0414791	+	0.0217699i	−0.443856	+	0.896098i	$0.646390\pi$
$174$	1.40442	−	2.03466i	0.106469	−	0.154247i
$175$	0.617131	−	1.62724i	0.0466507	−	0.123008i
$176$	−0.206452	−	0.182900i	−0.0155619	−	0.0137866i
$177$	−10.8144	−	9.58074i	−0.812862	−	0.720133i
$178$	−6.79953	−	1.67593i	−0.509647	−	0.125617i
$179$	12.4873	−	11.0628i	0.933348	−	0.826874i	−0.0517865	−	0.998658i	$-0.516492\pi$
$179$	12.4873	−	11.0628i	0.933348	−	0.826874i	0.985135	+	0.171784i	$0.0549531\pi$
$180$	−2.33340	+	0.575131i	−0.173921	+	0.0428677i
$181$	5.63170	−	8.15892i	0.418601	−	0.606448i	−0.555786	−	0.831325i	$-0.687583\pi$
$181$	5.63170	−	8.15892i	0.418601	−	0.606448i	0.974387	+	0.224877i	$0.0721981\pi$
$182$	5.30457	+	2.17716i	0.393201	+	0.161382i
$183$	−1.85382	−	2.68572i	−0.137038	−	0.198534i
$184$	19.5543	+	17.3236i	1.44156	+	1.27711i
$185$	0.182558	+	0.264482i	0.0134220	+	0.0194451i
$186$	4.84120	+	4.28893i	0.354974	+	0.314480i
$187$	−10.7766	−	5.65598i	−0.788061	−	0.413606i
$188$	−3.32829			−0.242741
$189$	−1.57297	+	0.825557i	−0.114416	+	0.0600504i
$190$	−1.38227	+	1.22459i	−0.100281	+	0.0888410i
$191$	−8.36499			−0.605270			−0.302635	−	0.953107i	$-0.597866\pi$
$191$	−8.36499			−0.605270			−0.302635	+	0.953107i	$0.597866\pi$
$192$	−5.32613			−0.384381
$193$	17.5670	−	15.5630i	1.26450	−	1.12025i	0.277298	−	0.960784i	$-0.410561\pi$
$193$	17.5670	−	15.5630i	1.26450	−	1.12025i	0.987203	−	0.159467i	$-0.0509774\pi$
$194$	−0.0201736	−	0.0531935i	−0.00144838	−	0.00381907i
$195$	7.15058	+	1.06465i	0.512064	+	0.0762414i
$196$	−1.63388	+	4.30818i	−0.116705	+	0.307727i
$197$	0.713270	+	1.88074i	0.0508184	+	0.133997i	0.958022	−	0.286695i	$-0.0925566\pi$
$197$	0.713270	+	1.88074i	0.0508184	+	0.133997i	−0.907204	+	0.420692i	$0.861787\pi$
$198$	−1.44186	−	0.355385i	−0.102468	−	0.0252561i
$199$	8.24762	+	11.9487i	0.584658	+	0.847024i	0.997978	−	0.0635624i	$-0.0202462\pi$
$199$	8.24762	+	11.9487i	0.584658	+	0.847024i	−0.413320	+	0.910586i	$0.635631\pi$
$200$	0.994747	−	2.62293i	0.0703393	−	0.185469i
$201$	−4.47941	−	11.8112i	−0.315954	−	0.833101i
$202$	0.0198053	+	0.163111i	0.00139350	+	0.0114765i
$203$	2.78688	+	4.03750i	0.195601	+	0.283377i
$204$	−8.53837	+	2.10452i	−0.597805	+	0.147346i
$205$	−5.25461	−	4.65518i	−0.366998	−	0.325132i
$206$	3.43523	−	9.05795i	0.239344	−	0.631097i
$207$	8.85829	+	2.18337i	0.615694	+	0.151755i
$208$	0.554613	+	0.227630i	0.0384555	+	0.0157833i
$209$	1.65700	−	0.408415i	0.114617	−	0.0282506i
$210$	−0.384357	+	3.16546i	−0.0265231	+	0.218438i
$211$	−2.01300	+	1.05650i	−0.138581	+	0.0727328i	−0.532588	−	0.846374i	$-0.678781\pi$
$211$	−2.01300	+	1.05650i	−0.138581	+	0.0727328i	0.394008	+	0.919107i	$0.371088\pi$
$212$	−5.06345	−	13.3512i	−0.347759	−	0.916965i
$213$	8.13490	+	2.00507i	0.557394	+	0.137385i
$214$	−8.72109	+	7.72621i	−0.596161	+	0.528153i
$215$	−16.9241	−	4.17141i	−1.15421	−	0.284488i
$216$	−2.53545	+	1.33071i	−0.172516	+	0.0905432i
$217$	−11.3643	+	5.96445i	−0.771459	+	0.404893i
$218$	−1.65483	−	13.6288i	−0.112079	−	0.923056i
$219$	−0.637416	−	5.24959i	−0.0430726	−	0.354735i
$220$	2.98394	−	2.64354i	0.201177	−	0.178227i
$221$	26.1654	+	3.89578i	1.76007	+	0.262058i
$222$	0.107400	+	0.0951478i	0.00720820	+	0.00638590i
$223$	−14.4455	+	20.9280i	−0.967345	+	1.40144i	−0.0520549	+	0.998644i	$0.516577\pi$
$223$	−14.4455	+	20.9280i	−0.967345	+	1.40144i	−0.915290	+	0.402796i	$0.868038\pi$
$224$	3.51381	−	9.26515i	0.234776	−	0.619054i
$225$	−0.118086	−	0.972527i	−0.00787241	−	0.0648352i
$226$	0.378763	−	3.11940i	0.0251950	−	0.207499i
$227$	−10.2342	−	5.37131i	−0.679266	−	0.356506i	0.0895449	−	0.995983i	$-0.471459\pi$
$227$	−10.2342	−	5.37131i	−0.679266	−	0.356506i	−0.768810	+	0.639477i	$0.779151\pi$
$228$	0.700481	−	1.01482i	0.0463905	−	0.0672082i
$229$	−9.21395	−	24.2952i	−0.608875	−	1.60547i	−0.783886	−	0.620905i	$-0.786765\pi$
$229$	−9.21395	−	24.2952i	−0.608875	−	1.60547i	0.175011	−	0.984567i	$-0.444004\pi$
$230$	12.2579	−	10.8596i	0.808265	−	0.716060i
$231$	1.67397	−	2.42516i	0.110139	−	0.159564i
$232$	4.49215	+	6.50801i	0.294924	+	0.427271i
$233$	−0.290254	−	2.39045i	−0.0190151	−	0.156604i	0.980108	−	0.198463i	$-0.0635950\pi$
$233$	−0.290254	−	2.39045i	−0.0190151	−	0.156604i	−0.999124	+	0.0418592i	$0.986672\pi$
$234$	3.21357	−	0.302503i	0.210078	−	0.0197752i
$235$	−0.671130	+	5.52725i	−0.0437797	+	0.360558i
$236$	15.3334	−	8.04756i	0.998116	−	0.523852i
$237$	6.23463	+	16.4394i	0.404983	+	1.06785i
$238$	−1.40644	+	11.5831i	−0.0911658	+	0.750818i
$239$	−8.54661			−0.552834			−0.276417	−	0.961038i	$-0.589147\pi$
$239$	−8.54661			−0.552834			−0.276417	+	0.961038i	$0.589147\pi$
$240$	−0.0401860	+	0.330961i	−0.00259399	+	0.0213635i
$241$	−5.48708	−	7.94940i	−0.353454	−	0.512066i	0.605417	−	0.795908i	$-0.293006\pi$
$241$	−5.48708	−	7.94940i	−0.353454	−	0.512066i	−0.958871	+	0.283842i	$0.908391\pi$
$242$	−7.16955	+	1.76714i	−0.460876	+	0.113596i
$243$	−0.568065	+	0.822984i	−0.0364414	+	0.0527944i
$244$	3.79776	−	0.936063i	0.243126	−	0.0599253i
$245$	6.82508	+	3.58208i	0.436038	+	0.228850i
$246$	−2.77531	−	1.45659i	−0.176947	−	0.0928690i
$247$	−3.10851	+	2.02408i	−0.197790	+	0.128789i
$248$	−18.3180	+	9.61403i	−1.16319	+	0.610492i
$249$	−8.05489			−0.510458
$250$	−9.50401	−	4.98809i	−0.601086	−	0.315474i
$251$	−6.00648	+	15.8378i	−0.379126	+	0.999673i	0.600639	+	0.799520i	$0.294913\pi$
$251$	−6.00648	+	15.8378i	−0.379126	+	0.999673i	−0.979765	+	0.200152i	$0.935856\pi$
$252$	−0.256647	−	2.11368i	−0.0161673	−	0.133149i
$253$	−14.6942	+	3.62180i	−0.923818	+	0.227701i
$254$	8.96065	−	2.20860i	0.562241	−	0.138580i
$255$	1.77324	+	14.6039i	0.111044	+	0.914533i
$256$	5.80521	−	15.3071i	0.362826	−	0.956693i
$257$	−7.02181	−	3.68533i	−0.438009	−	0.229885i	0.231280	−	0.972887i	$-0.425709\pi$
$257$	−7.02181	−	3.68533i	−0.438009	−	0.229885i	−0.669289	+	0.743003i	$0.733401\pi$
$258$	−7.78239			−0.484510
$259$	−0.252112	+	0.132318i	−0.0156654	+	0.00822186i
$260$	−4.23228	+	7.56106i	−0.262475	+	0.468917i
$261$	2.44532	+	1.28340i	0.151361	+	0.0794406i
$262$	−10.8634	−	5.70157i	−0.671146	−	0.352244i
$263$	−14.0572	+	3.46479i	−0.866804	+	0.213648i	−0.647553	−	0.762020i	$-0.724208\pi$
$263$	−14.0572	+	3.46479i	−0.866804	+	0.213648i	−0.219251	+	0.975668i	$0.570361\pi$
$264$	2.69825	−	3.90909i	0.166066	−	0.240588i
$265$	−23.1932	+	5.71661i	−1.42475	+	0.351169i
$266$	−0.929428	−	1.34651i	−0.0569869	−	0.0825598i
$267$	0.942917	−	7.76562i	0.0577056	−	0.475248i
$268$	15.1405			0.924855
$269$	0.390362	−	3.21492i	0.0238008	−	0.196017i	−0.975958	−	0.217956i	$-0.930061\pi$
$269$	0.390362	−	3.21492i	0.0238008	−	0.196017i	0.999759	+	0.0219391i	$0.00698399\pi$
$270$	0.636513	+	1.67835i	0.0387370	+	0.102141i
$271$	−20.3343	+	10.6723i	−1.23522	+	0.648294i	−0.950621	−	0.310353i	$-0.899553\pi$
$271$	−20.3343	+	10.6723i	−1.23522	+	0.648294i	−0.284599	+	0.958647i	$0.591861\pi$
$272$	−0.147048	+	1.21105i	−0.00891612	+	0.0734309i
$273$	−1.70001	+	6.17535i	−0.102889	+	0.373749i
$274$	−1.35091	−	11.1257i	−0.0816115	−	0.672131i
$275$	0.923155	+	1.33742i	0.0556683	+	0.0806495i
$276$	−6.21183	+	8.99939i	−0.373908	+	0.541699i
$277$	14.0608	−	12.4567i	0.844829	−	0.748453i	−0.125022	−	0.992154i	$-0.539900\pi$
$277$	14.0608	−	12.4567i	0.844829	−	0.748453i	0.969850	+	0.243701i	$0.0783616\pi$
$278$	2.24817	+	5.92794i	0.134836	+	0.355534i
$279$	−4.10413	+	5.94586i	−0.245708	+	0.355969i
$280$	−9.03106	−	4.73986i	−0.539709	−	0.283261i
$281$	−1.29652	+	10.6778i	−0.0773439	+	0.636984i	0.901559	+	0.432657i	$0.142424\pi$
$281$	−1.29652	+	10.6778i	−0.0773439	+	0.636984i	−0.978903	+	0.204327i	$0.934499\pi$
$282$	0.299645	+	2.46780i	0.0178436	+	0.146955i
$283$	0.495804	−	1.30733i	0.0294725	−	0.0777125i	−0.919472	−	0.393155i	$-0.871384\pi$
$283$	0.495804	−	1.30733i	0.0294725	−	0.0777125i	0.948945	+	0.315442i	$0.102153\pi$
$284$	−5.70455	+	8.26447i	−0.338503	+	0.490406i
$285$	−1.54405	−	1.36791i	−0.0914619	−	0.0810281i
$286$	−4.48691	+	2.92162i	−0.265316	+	0.172759i
$287$	4.65546	−	4.12438i	0.274803	−	0.243454i
$288$	−0.672357	−	5.53736i	−0.0396190	−	0.326292i
$289$	4.43950	+	36.5626i	0.261147	+	2.15074i
$290$	4.38933	−	2.30370i	0.257750	−	0.135278i
$291$	0.0562697	−	0.0295326i	0.00329859	−	0.00173123i
$292$	6.15406	+	1.51684i	0.360139	+	0.0887663i
$293$	−4.41088	+	3.90770i	−0.257687	+	0.228290i	−0.782068	−	0.623193i	$-0.785835\pi$
$293$	−4.41088	+	3.90770i	−0.257687	+	0.228290i	0.524381	+	0.851483i	$0.324297\pi$
$294$	3.34145	+	0.823593i	0.194877	+	0.0480329i
$295$	−10.2726	−	27.0867i	−0.598095	−	1.57705i
$296$	−0.406376	+	0.213283i	−0.0236201	+	0.0123968i
$297$	0.199947	−	1.64672i	0.0116021	−	0.0955521i
$298$	10.0731	−	2.48279i	0.583518	−	0.143824i
$299$	27.5661	−	17.9495i	1.59419	−	1.03805i
$300$	1.14009	+	0.281006i	0.0658229	+	0.0162239i
$301$	5.47619	−	14.4395i	0.315642	−	0.832280i
$302$	8.25833	+	7.31624i	0.475214	+	0.421002i
$303$	−0.178207	+	0.0439240i	−0.0102377	+	0.00252337i
$304$	−0.0971753	−	0.140783i	−0.00557338	−	0.00807444i
$305$	−0.788713	−	6.49564i	−0.0451616	−	0.371939i
$306$	2.32913	+	6.14141i	0.133147	+	0.351081i
$307$	−1.57062	+	4.14137i	−0.0896398	+	0.236361i	−0.972337	−	0.233581i	$-0.924956\pi$
$307$	−1.57062	+	4.14137i	−0.0896398	+	0.236361i	0.882698	+	0.469941i	$0.155725\pi$
$308$	2.00637	+	2.90673i	0.114324	+	0.165627i
$309$	10.5068	+	2.58970i	0.597713	+	0.147323i
$310$	4.59865	+	12.1256i	0.261186	+	0.688691i
$311$	8.58358	−	22.6330i	0.486730	−	1.28340i	−0.436690	−	0.899612i	$-0.643849\pi$
$311$	8.58358	−	22.6330i	0.486730	−	1.28340i	0.923420	−	0.383790i	$-0.125381\pi$
$312$	−2.74023	+	9.95399i	−0.155135	+	0.563534i
$313$	3.10057	+	8.17552i	0.175254	+	0.462108i	0.993646	−	0.112554i	$-0.0359030\pi$
$313$	3.10057	+	8.17552i	0.175254	+	0.462108i	−0.818391	+	0.574661i	$0.805134\pi$
$314$	5.74340	−	5.08821i	0.324119	−	0.287144i
$315$	−3.56191			−0.200691
$316$	−21.0732			−1.18546
$317$	−4.25434	+	3.76902i	−0.238948	+	0.211689i	−0.774095	−	0.633070i	$-0.781795\pi$
$317$	−4.25434	+	3.76902i	−0.238948	+	0.211689i	0.535147	+	0.844759i	$0.320256\pi$
$318$	−9.44355	+	4.95636i	−0.529568	+	0.277939i
$319$	−4.58105			−0.256490
$320$	−9.45605	−	4.96292i	−0.528609	−	0.277436i
$321$	−9.74180	−	8.63048i	−0.543734	−	0.481706i
$322$	8.24212	+	11.9408i	0.459315	+	0.665433i
$323$	−5.65000	−	5.00546i	−0.314374	−	0.278511i
$324$	−0.680867	−	0.986407i	−0.0378260	−	0.0548004i
$325$	−2.85181	−	2.08422i	−0.158190	−	0.115612i
$326$	−7.22598	+	10.4686i	−0.400210	+	0.579804i
$327$	14.8900	−	3.67006i	0.823421	−	0.202955i
$328$	7.50409	−	6.64805i	0.414344	−	0.367077i
$329$	−4.78963	−	1.18054i	−0.264061	−	0.0650852i
$330$	−2.22873	−	1.97448i	−0.122688	−	0.108692i
$331$	−4.34186	−	3.84655i	−0.238650	−	0.211426i	0.535317	−	0.844651i	$-0.320192\pi$
$331$	−4.34186	−	3.84655i	−0.238650	−	0.211426i	−0.773967	+	0.633225i	$0.781731\pi$
$332$	3.42349	−	9.02700i	0.187888	−	0.495421i
$333$	−0.0910481	+	0.131906i	−0.00498941	+	0.00722840i
$334$	−17.2046	−	9.02969i	−0.941396	−	0.494083i
$335$	3.05300	−	25.1437i	0.166803	−	1.37375i
$336$	−0.286794	−	0.0706884i	−0.0156459	−	0.00385637i
$337$	4.47390			0.243709			0.121854	−	0.992548i	$-0.461116\pi$
$337$	4.47390			0.243709			0.121854	+	0.992548i	$0.461116\pi$
$338$	7.11793	−	9.20740i	0.387164	−	0.500816i
$339$	3.51008			0.190641
$340$	−17.1201	−	4.21972i	−0.928466	−	0.228846i
$341$	1.44457	−	11.8971i	0.0782279	−	0.644265i
$342$	−0.815516	−	0.428016i	−0.0440980	−	0.0231444i
$343$	−10.9433	+	15.8541i	−0.590884	+	0.856043i
$344$	8.82701	−	23.2749i	0.475921	−	1.25490i
$345$	13.6926	+	12.1306i	0.737184	+	0.653088i
$346$	0.412872	+	0.365772i	0.0221961	+	0.0196640i
$347$	−2.08771	−	0.514575i	−0.112074	−	0.0276238i	0.182880	−	0.983135i	$-0.441458\pi$
$347$	−2.08771	−	0.514575i	−0.112074	−	0.0276238i	−0.294954	+	0.955511i	$0.595304\pi$
$348$	−2.47760	+	2.19496i	−0.132813	+	0.117662i
$349$	6.33836	−	1.56226i	0.339284	−	0.0836261i	−0.0659924	−	0.997820i	$-0.521021\pi$
$349$	6.33836	−	1.56226i	0.339284	−	0.0836261i	0.405277	+	0.914194i	$0.367175\pi$
$350$	0.885038	−	1.28220i	0.0473073	−	0.0685364i
$351$	0.768132	+	3.52278i	0.0409999	+	0.188032i
$352$	5.25624	+	7.61498i	0.280159	+	0.405880i
$353$	0.925181	+	0.819639i	0.0492424	+	0.0436250i	0.687385	−	0.726293i	$-0.258759\pi$
$353$	0.925181	+	0.819639i	0.0492424	+	0.0436250i	−0.638143	+	0.769918i	$0.720297\pi$
$354$	−7.34742	−	10.6446i	−0.390511	−	0.565753i
$355$	12.5744	+	11.1400i	0.667381	+	0.591248i
$356$	8.30206	+	4.35726i	0.440008	+	0.230934i
$357$	−13.0337			−0.689819
$358$	13.2242	−	6.94062i	0.698923	−	0.366823i
$359$	−26.9432	+	23.8696i	−1.42201	+	1.25979i	−0.503728	+	0.863862i	$0.668039\pi$
$359$	−26.9432	+	23.8696i	−1.42201	+	1.25979i	−0.918281	+	0.395928i	$0.870423\pi$
$360$	−5.74142			−0.302599
$361$	−17.9416			−0.944293
$362$	6.64311	−	5.88528i	0.349154	−	0.309324i
$363$	−2.92491	−	7.71234i	−0.153518	−	0.404793i
$364$	−6.19809	−	4.52982i	−0.324868	−	0.237427i
$365$	3.75992	−	9.91411i	0.196803	−	0.518928i
$366$	−1.03597	−	2.73162i	−0.0541508	−	0.142784i
$367$	22.8556	+	5.63340i	1.19305	+	0.294061i	0.785349	−	0.619053i	$-0.212483\pi$
$367$	22.8556	+	5.63340i	1.19305	+	0.294061i	0.407704	+	0.913114i	$0.366329\pi$
$368$	0.861745	+	1.24845i	0.0449216	+	0.0650801i
$369$	1.24153	−	3.27364i	0.0646314	−	0.170419i
$370$	0.102019	+	0.269002i	0.00530371	+	0.0139847i
$371$	−2.55099	−	21.0093i	−0.132441	−	1.09075i
$372$	−4.91910	−	7.12655i	−0.255044	−	0.369494i
$373$	−28.8146	+	7.10216i	−1.49196	+	0.367736i	−0.899163	−	0.437613i	$-0.855824\pi$
$373$	−28.8146	+	7.10216i	−1.49196	+	0.367736i	−0.592801	+	0.805349i	$0.701978\pi$
$374$	−8.15536	−	7.22502i	−0.421704	−	0.373597i
$375$	4.25160	−	11.2106i	0.219552	−	0.578911i
$376$	−7.72037	−	1.90290i	−0.398148	−	0.0981345i
$377$	9.40205	−	3.27851i	0.484230	−	0.168852i
$378$	−1.54411	+	0.380588i	−0.0794203	+	0.0195754i
$379$	−0.775845	+	6.38966i	−0.0398525	+	0.328215i	0.959124	+	0.282986i	$0.0913249\pi$
$379$	−0.775845	+	6.38966i	−0.0398525	+	0.328215i	−0.998977	+	0.0452292i	$0.985598\pi$
$380$	2.18925	−	1.14901i	0.112306	−	0.0589429i
$381$	3.65560	+	9.63903i	0.187282	+	0.493823i
$382$	−7.27094	−	1.79213i	−0.372014	−	0.0916931i
$383$	−7.20785	+	6.38560i	−0.368304	+	0.326289i	−0.826893	−	0.562360i	$-0.809894\pi$
$383$	−7.20785	+	6.38560i	−0.368304	+	0.326289i	0.458589	+	0.888649i	$0.348355\pi$
$384$	6.20235	+	1.52874i	0.316512	+	0.0780133i
$385$	5.23175	−	2.74583i	0.266635	−	0.139941i
$386$	18.6037	−	9.76396i	0.946902	−	0.496973i
$387$	−1.04785	−	8.62984i	−0.0532653	−	0.438680i
$388$	0.00918103	+	0.0756126i	0.000466096	+	0.00383865i
$389$	17.7885	−	15.7592i	0.901913	−	0.799025i	−0.0783086	−	0.996929i	$-0.524952\pi$
$389$	17.7885	−	15.7592i	0.901913	−	0.799025i	0.980221	+	0.197904i	$0.0634135\pi$
$390$	5.98727	+	2.45736i	0.303177	+	0.124433i
$391$	50.1039	+	44.3882i	2.53386	+	2.24481i
$392$	−6.25310	+	9.05918i	−0.315829	+	0.457558i
$393$	4.85974	−	12.8141i	0.245142	−	0.646385i
$394$	0.217050	+	1.78757i	0.0109348	+	0.0900565i
$395$	−4.24929	+	34.9960i	−0.213805	+	1.76084i
$396$	1.76047	+	0.923965i	0.0884669	+	0.0464310i
$397$	2.78847	−	4.03979i	0.139949	−	0.202751i	−0.746742	−	0.665114i	$-0.768383\pi$
$397$	2.78847	−	4.03979i	0.139949	−	0.202751i	0.886691	+	0.462363i	$0.152998\pi$
$398$	4.60901	+	12.1530i	0.231029	+	0.609172i
$399$	1.36799	−	1.21194i	0.0684854	−	0.0606727i
$400$	0.0925342	−	0.134059i	0.00462671	−	0.00670294i
$401$	10.4717	+	15.1709i	0.522934	+	0.757600i	0.992092	−	0.125514i	$-0.0400580\pi$
$401$	10.4717	+	15.1709i	0.522934	+	0.757600i	−0.469158	+	0.883114i	$0.655443\pi$
$402$	−1.36310	−	11.2261i	−0.0679852	−	0.559909i
$403$	5.54957	+	25.4512i	0.276444	+	1.26782i
$404$	0.0265164	−	0.218382i	0.00131924	−	0.0108649i
$405$	−1.77541	+	0.931805i	−0.0882207	+	0.0463018i
$406$	1.55739	+	4.10650i	0.0772920	+	0.203802i
$407$	0.0320471	−	0.263932i	0.00158852	−	0.0130826i
$408$	−21.0090			−1.04010
$409$	−0.851871	+	7.01579i	−0.0421223	+	0.346909i	0.956377	+	0.292137i	$0.0943662\pi$
$409$	−0.851871	+	7.01579i	−0.0421223	+	0.346909i	−0.998499	+	0.0547719i	$0.982557\pi$
$410$	−3.57003	−	5.17209i	−0.176311	−	0.255431i
$411$	12.1554	−	2.99603i	0.599581	−	0.147783i
$412$	−7.36786	+	10.6742i	−0.362989	+	0.525880i
$413$	24.9202	−	6.14227i	1.22624	−	0.302241i
$414$	7.23195	+	3.79562i	0.355431	+	0.186545i
$415$	−14.3007	−	7.50559i	−0.701994	−	0.368435i
$416$	−16.2376	−	11.8671i	−0.796113	−	0.581832i
$417$	−6.27076	+	3.29115i	−0.307080	+	0.161168i
$418$	1.52778			0.0747264
$419$	10.1107	+	5.30650i	0.493939	+	0.259239i	0.693250	−	0.720697i	$-0.256178\pi$
$419$	10.1107	+	5.30650i	0.493939	+	0.259239i	−0.199311	+	0.979936i	$0.563870\pi$
$420$	1.51388	−	3.99179i	0.0738700	−	0.194779i
$421$	−1.53511	−	12.6428i	−0.0748167	−	0.616171i	−0.981100	−	0.193500i	$-0.938016\pi$
$421$	−1.53511	−	12.6428i	−0.0748167	−	0.616171i	0.906284	−	0.422670i	$-0.138907\pi$
$422$	−1.97607	+	0.487057i	−0.0961935	+	0.0237096i
$423$	−2.69619	+	0.664550i	−0.131093	+	0.0323115i
$424$	−4.11191	−	33.8647i	−0.199692	−	1.64461i
$425$	2.54883	−	6.72072i	0.123637	−	0.326003i
$426$	6.64137	+	3.48566i	0.321776	+	0.168881i
$427$	5.79725			0.280548
$428$	13.8125	−	7.24937i	0.667653	−	0.350411i
$429$	−3.84390	−	4.58213i	−0.185585	−	0.221227i
$430$	−13.8169	−	7.25167i	−0.666310	−	0.349706i
$431$	16.3395	+	8.57565i	0.787048	+	0.413074i	0.809829	−	0.586666i	$-0.199560\pi$
$431$	16.3395	+	8.57565i	0.787048	+	0.413074i	−0.0227814	+	0.999740i	$0.507252\pi$
$432$	−0.161442	+	0.0397920i	−0.00776740	+	0.00191449i
$433$	−16.5596	+	23.9907i	−0.795804	+	1.15292i	0.189462	+	0.981888i	$0.439326\pi$
$433$	−16.5596	+	23.9907i	−0.795804	+	1.15292i	−0.985265	+	0.171032i	$0.945290\pi$
$434$	−11.1558	+	2.74966i	−0.535496	+	0.131988i
$435$	3.14555	+	4.55712i	0.150818	+	0.218497i
$436$	−2.21557	+	18.2469i	−0.106107	+	0.873868i
$437$	−9.38621			−0.449003
$438$	0.570630	−	4.69956i	0.0272658	−	0.224554i
$439$	−2.99854	−	7.90651i	−0.143113	−	0.377357i	0.844225	−	0.535989i	$-0.180061\pi$
$439$	−2.99854	−	7.90651i	−0.143113	−	0.377357i	−0.987338	+	0.158632i	$0.949292\pi$
$440$	8.43301	−	4.42599i	0.402028	−	0.211001i
$441$	−0.463371	+	3.81620i	−0.0220653	+	0.181724i
$442$	21.9086	+	8.99195i	1.04209	+	0.427704i
$443$	−1.44529	−	11.9031i	−0.0686680	−	0.565532i	−0.985919	−	0.167223i	$-0.946520\pi$
$443$	−1.44529	−	11.9031i	−0.0686680	−	0.565532i	0.917251	−	0.398309i	$-0.130403\pi$
$444$	−0.109128	−	0.158099i	−0.00517898	−	0.00750305i
$445$	8.91011	−	12.9085i	0.422379	−	0.611922i
$446$	−17.0398	+	15.0960i	−0.806860	+	0.714816i
$447$	4.10943	+	10.8357i	0.194370	+	0.512510i
$448$	5.37480	−	7.78674i	0.253936	−	0.367889i
$449$	7.38386	+	3.87535i	0.348466	+	0.182889i	0.629870	−	0.776700i	$-0.283108\pi$
$449$	7.38386	+	3.87535i	0.348466	+	0.182889i	−0.281405	+	0.959589i	$0.590800\pi$
$450$	0.105714	−	0.870630i	0.00498339	−	0.0410419i
$451$	0.700048	+	5.76541i	0.0329640	+	0.271483i
$452$	−1.49185	+	3.93370i	−0.0701709	+	0.185026i
$453$	−7.00100	+	10.1427i	−0.328936	+	0.476546i
$454$	−7.74489	−	6.86138i	−0.363486	−	0.322020i
$455$	−8.77243	+	9.37968i	−0.411258	+	0.439726i
$456$	2.20506	−	1.95351i	0.103261	−	0.0914815i
$457$	−0.113636	−	0.935874i	−0.00531565	−	0.0437783i	0.989810	−	0.142397i	$-0.0454808\pi$
$457$	−0.113636	−	0.935874i	−0.00531565	−	0.0437783i	−0.995125	+	0.0986182i	$0.968558\pi$
$458$	−2.80383	−	23.0916i	−0.131015	−	1.07900i
$459$	−6.49657	+	3.40966i	−0.303234	+	0.159149i
$460$	−19.4142	+	10.1894i	−0.905191	+	0.475081i
$461$	−24.4741	−	6.03231i	−1.13987	−	0.280953i	−0.376187	−	0.926544i	$-0.622765\pi$
$461$	−24.4741	−	6.03231i	−1.13987	−	0.280953i	−0.763683	+	0.645591i	$0.776611\pi$
$462$	1.97460	−	1.74934i	0.0918667	−	0.0813868i
$463$	−3.23940	−	0.798440i	−0.150548	−	0.0371066i	0.163322	−	0.986573i	$-0.447779\pi$
$463$	−3.23940	−	0.798440i	−0.150548	−	0.0371066i	−0.313869	+	0.949466i	$0.601625\pi$
$464$	0.162831	+	0.429350i	0.00755924	+	0.0199321i
$465$	−12.8269	+	6.73207i	−0.594832	+	0.312192i
$466$	0.259842	−	2.13999i	0.0120370	−	0.0991332i
$467$	6.64596	−	1.63808i	0.307538	−	0.0758014i	−0.0825263	−	0.996589i	$-0.526299\pi$
$467$	6.64596	−	1.63808i	0.307538	−	0.0758014i	0.390065	+	0.920788i	$0.372453\pi$
$468$	−4.27440	−	0.636417i	−0.197584	−	0.0294184i
$469$	21.7882	+	5.37032i	1.00609	+	0.247978i
$470$	−1.76752	+	4.66056i	−0.0815295	+	0.214976i
$471$	6.41560	+	5.68372i	0.295615	+	0.261892i
$472$	40.1686	−	9.90067i	1.84891	−	0.455715i
$473$	8.19173	+	11.8678i	0.376656	+	0.545680i
$474$	1.89722	+	15.6250i	0.0871421	+	0.717680i
$475$	0.357403	+	0.942394i	0.0163988	+	0.0432400i
$476$	5.53960	−	14.6067i	0.253907	−	0.669499i
$477$	−6.76760	−	9.80456i	−0.309867	−	0.448920i
$478$	−7.42880	−	1.83104i	−0.339785	−	0.0837496i
$479$	4.46953	+	11.7852i	0.204218	+	0.538479i	0.997523	−	0.0703460i	$-0.0224103\pi$
$479$	4.46953	+	11.7852i	0.204218	+	0.538479i	−0.793304	+	0.608825i	$0.791641\pi$
$480$	3.96603	−	10.4576i	0.181024	−	0.477321i
$481$	0.123114	+	0.564623i	0.00561354	+	0.0257446i
$482$	−3.06634	−	8.08526i	−0.139668	−	0.368274i
$483$	−12.1313	+	10.7474i	−0.551993	+	0.489023i
$484$	9.88625			0.449375
$485$	0.127420			0.00578585
$486$	−0.670085	+	0.593643i	−0.0303957	+	0.0269282i
$487$	16.9306	−	8.88586i	0.767199	−	0.402657i	−0.0352497	−	0.999379i	$-0.511223\pi$
$487$	16.9306	−	8.88586i	0.767199	−	0.402657i	0.802448	+	0.596722i	$0.203530\pi$
$488$	9.34453			0.423007
$489$	−12.5815	−	6.60331i	−0.568957	−	0.298612i
$490$	5.16500	+	4.57579i	0.233331	+	0.206713i
$491$	9.97104	+	14.4455i	0.449987	+	0.651918i	0.980674	−	0.195649i	$-0.0626814\pi$
$491$	9.97104	+	14.4455i	0.449987	+	0.651918i	−0.530687	+	0.847568i	$0.678066\pi$
$492$	3.14105	+	2.78273i	0.141609	+	0.125455i
$493$	11.5102	+	16.6754i	0.518394	+	0.751023i
$494$	−3.13559	+	1.09338i	−0.141077	+	0.0491937i
$495$	1.88941	−	2.73728i	0.0849225	−	0.123031i
$496$	−1.16638	+	0.287487i	−0.0523721	+	0.0129086i
$497$	−11.1406	+	9.86974i	−0.499726	+	0.442718i
$498$	−7.00140	−	1.72569i	−0.313740	−	0.0773300i
$499$	20.1668	+	17.8662i	0.902789	+	0.799801i	0.980366	−	0.197185i	$-0.0631800\pi$
$499$	20.1668	+	17.8662i	0.902789	+	0.799801i	−0.0775774	+	0.996986i	$0.524718\pi$
$500$	10.7565	+	9.52942i	0.481045	+	0.426169i
$501$	7.69647	−	20.2939i	0.343853	−	0.906666i
$502$	−8.61401	+	12.4795i	−0.384462	+	0.556989i
$503$	33.8466	+	17.7641i	1.50915	+	0.792061i	0.997735	−	0.0672744i	$-0.0214303\pi$
$503$	33.8466	+	17.7641i	1.50915	+	0.792061i	0.511412	+	0.859336i	$0.329123\pi$
$504$	0.613140	−	5.04967i	0.0273114	−	0.224930i
$505$	−0.357318	−	0.0880709i	−0.0159004	−	0.00391910i
$506$	−13.5483			−0.602296
$507$	11.1684	+	6.65330i	0.496007	+	0.295484i
$508$	−12.3560			−0.548210
$509$	−18.9435	−	4.66916i	−0.839656	−	0.206957i	−0.204041	−	0.978962i	$-0.565408\pi$
$509$	−18.9435	−	4.66916i	−0.839656	−	0.206957i	−0.635616	+	0.772006i	$0.719254\pi$
$510$	−1.58745	+	13.0738i	−0.0702932	+	0.578917i
$511$	8.31808	+	4.36567i	0.367970	+	0.193126i
$512$	1.06780	−	1.54697i	0.0471905	−	0.0683672i
$513$	0.364820	−	0.961951i	0.0161072	−	0.0424712i
$514$	−5.31388	−	4.70769i	−0.234385	−	0.207647i
$515$	16.2408	+	14.3881i	0.715656	+	0.634016i
$516$	10.1167	+	2.49354i	0.445363	+	0.109772i
$517$	3.44787	−	3.05455i	0.151637	−	0.134339i
$518$	−0.247486	+	0.0609998i	−0.0108739	+	0.00268018i
$519$	−0.350012	+	0.507080i	−0.0153638	+	0.0222583i
$520$	−14.1402	+	15.1190i	−0.620089	+	0.663013i
$521$	8.62357	+	12.4934i	0.377805	+	0.547346i	0.965051	−	0.262063i	$-0.0844029\pi$
$521$	8.62357	+	12.4934i	0.377805	+	0.547346i	−0.587245	+	0.809409i	$0.699788\pi$
$522$	1.85054	+	1.63943i	0.0809959	+	0.0717561i
$523$	15.0158	+	21.7541i	0.656593	+	0.951240i	0.999928	+	0.0120263i	$0.00382820\pi$
$523$	15.0158	+	21.7541i	0.656593	+	0.951240i	−0.343334	+	0.939213i	$0.611556\pi$
$524$	12.2951	+	10.8925i	0.537113	+	0.475841i
$525$	1.54099	+	0.808773i	0.0672543	+	0.0352978i
$526$	−12.9610			−0.565125
$527$	−46.9361	+	24.6340i	−2.04457	+	1.07307i
$528$	0.206452	−	0.182900i	0.00898467	−	0.00795972i
$529$	60.2365			2.61898
$530$	−21.3845			−0.928884
$531$	10.8144	−	9.58074i	0.469306	−	0.415769i
$532$	0.776776	+	2.04819i	0.0336775	+	0.0888002i
$533$	−5.56288	−	11.3318i	−0.240955	−	0.490835i
$534$	2.48331	−	6.54795i	0.107463	−	0.283357i
$535$	−9.25372	−	24.4001i	−0.400073	−	1.05491i
$536$	35.1203	+	8.65637i	1.51696	+	0.373898i
$537$	9.47698	+	13.7298i	0.408962	+	0.592484i
$538$	1.02808	−	2.71081i	0.0443235	−	0.116872i
$539$	−2.26126	−	5.96246i	−0.0973995	−	0.256821i
$540$	−0.289678	−	2.38571i	−0.0124657	−	0.102665i
$541$	6.00088	+	8.69377i	0.257998	+	0.373774i	0.930482	−	0.366337i	$-0.119388\pi$
$541$	6.00088	+	8.69377i	0.257998	+	0.373774i	−0.672484	+	0.740111i	$0.734773\pi$
$542$	−19.9612	+	4.92000i	−0.857408	+	0.211332i
$543$	7.42061	+	6.57409i	0.318449	+	0.282121i
$544$	14.5125	−	38.2663i	0.622218	−	1.64066i
$545$	29.8556	+	7.35876i	1.27888	+	0.315215i
$546$	−2.80068	+	5.00347i	−0.119858	+	0.214129i
$547$	−6.72303	+	1.65708i	−0.287456	+	0.0708515i	−0.380407	−	0.924819i	$-0.624216\pi$
$547$	−6.72303	+	1.65708i	−0.287456	+	0.0708515i	0.0929512	+	0.995671i	$0.470370\pi$
$548$	−1.80867	+	14.8957i	−0.0772626	+	0.636315i
$549$	2.88959	−	1.51657i	0.123325	−	0.0647258i
$550$	0.515885	+	1.36028i	0.0219974	+	0.0580024i
$551$	−2.75864	−	0.679944i	−0.117522	−	0.0289666i
$552$	−19.5543	+	17.3236i	−0.832288	+	0.737343i
$553$	−30.3258	−	7.47463i	−1.28958	−	0.317854i
$554$	14.8905	−	7.81514i	0.632637	−	0.332033i
$555$	−0.284558	+	0.149348i	−0.0120788	+	0.00633945i
$556$	−1.02314	−	8.42635i	−0.0433910	−	0.357357i
$557$	−3.81069	−	31.3839i	−0.161464	−	1.32978i	−0.817885	−	0.575382i	$-0.804853\pi$
$557$	−3.81069	−	31.3839i	−0.161464	−	1.32978i	0.656421	−	0.754395i	$-0.272070\pi$
$558$	−4.84120	+	4.28893i	−0.204944	+	0.181565i
$559$	−25.3059	−	18.4946i	−1.07033	−	0.782238i
$560$	−0.443308	−	0.392737i	−0.0187332	−	0.0165962i
$561$	6.91371	−	10.0162i	0.291897	−	0.422886i
$562$	−3.41457	+	9.00349i	−0.144035	+	0.379789i
$563$	−0.341883	−	2.81566i	−0.0144086	−	0.118666i	0.983730	−	0.179654i	$-0.0574978\pi$
$563$	−0.341883	−	2.81566i	−0.0144086	−	0.118666i	−0.998138	+	0.0609883i	$0.980575\pi$
$564$	0.401181	−	3.30402i	0.0168928	−	0.139125i
$565$	6.23182	+	3.27071i	0.262175	+	0.137600i
$566$	0.711041	−	1.03012i	0.0298873	−	0.0432992i
$567$	−0.629937	−	1.66101i	−0.0264549	−	0.0697558i
$568$	−17.9575	+	15.9089i	−0.753479	+	0.667524i
$569$	15.7115	−	22.7620i	0.658661	−	0.954235i	−0.341238	−	0.939977i	$-0.610846\pi$
$569$	15.7115	−	22.7620i	0.658661	−	0.954235i	0.999898	−	0.0142576i	$-0.00453850\pi$
$570$	−1.04904	−	1.51980i	−0.0439397	−	0.0636576i
$571$	4.62214	+	38.0667i	0.193430	+	1.59304i	0.689189	+	0.724582i	$0.257967\pi$
$571$	4.62214	+	38.0667i	0.193430	+	1.59304i	−0.495758	+	0.868460i	$0.665110\pi$
$572$	6.76886	−	2.36031i	0.283020	−	0.0986895i
$573$	1.00829	−	8.30400i	0.0421219	−	0.346905i
$574$	4.93019	−	2.58756i	0.205782	−	0.108003i
$575$	−3.16943	−	8.35711i	−0.132174	−	0.348515i
$576$	0.641995	−	5.28730i	0.0267498	−	0.220304i
$577$	15.1379			0.630200			0.315100	−	0.949058i	$-0.397962\pi$
$577$	15.1379			0.630200			0.315100	+	0.949058i	$0.397962\pi$
$578$	−3.97435	+	32.7317i	−0.165311	+	1.36146i
$579$	13.3321	+	19.3148i	0.554062	+	0.802698i
$580$	−6.44402	+	1.58831i	−0.267574	+	0.0659510i
$581$	8.12849	−	11.7762i	0.337227	−	0.488557i
$582$	0.0552373	−	0.0136148i	0.00228966	−	0.000564350i
$583$	17.4985	+	9.18391i	0.724713	+	0.380359i
$584$	13.4078	+	7.03698i	0.554820	+	0.291192i
$585$	−1.91880	+	6.97011i	−0.0793325	+	0.288179i
$586$	−4.67118	+	2.45162i	−0.192965	+	0.101276i
$587$	14.3020			0.590307			0.295154	−	0.955450i	$-0.404629\pi$
$587$	14.3020			0.590307			0.295154	+	0.955450i	$0.404629\pi$
$588$	−4.07982	−	2.14126i	−0.168249	−	0.0883039i
$589$	2.63573	−	6.94986i	0.108604	−	0.286364i
$590$	−3.12599	−	25.7448i	−0.128695	−	1.05990i
$591$	−1.95300	+	0.481372i	−0.0803357	+	0.0198010i
$592$	−0.0258756	+	0.00637777i	−0.00106348	+	0.000262125i
$593$	2.56425	+	21.1185i	0.105301	+	0.867232i	0.945650	+	0.325186i	$0.105427\pi$
$593$	2.56425	+	21.1185i	0.105301	+	0.867232i	−0.840349	+	0.542046i	$0.817650\pi$
$594$	0.526591	−	1.38851i	0.0216063	−	0.0569711i
$595$	−23.1402	−	12.1449i	−0.948656	−	0.497893i
$596$	−13.8900			−0.568956
$597$	−12.8558	+	6.74722i	−0.526151	+	0.276145i
$598$	27.8063	−	9.69608i	1.13708	−	0.396502i
$599$	−11.1225	−	5.83754i	−0.454453	−	0.238515i	0.221934	−	0.975062i	$-0.428763\pi$
$599$	−11.1225	−	5.83754i	−0.454453	−	0.238515i	−0.676387	+	0.736546i	$0.736455\pi$
$600$	2.48391	+	1.30365i	0.101405	+	0.0532215i
$601$	−30.1907	+	7.44134i	−1.23150	+	0.303539i	−0.800787	−	0.598949i	$-0.795585\pi$
$601$	−30.1907	+	7.44134i	−1.23150	+	0.303539i	−0.430717	+	0.902487i	$0.641739\pi$
$602$	7.85350	−	11.3778i	0.320085	−	0.463723i
$603$	12.2651	−	3.02307i	0.499472	−	0.123109i
$604$	−8.39122	−	12.1568i	−0.341434	−	0.494652i
$605$	1.99350	−	16.4180i	0.0810475	−	0.667486i
$606$	−0.164309			−0.00667461
$607$	1.42877	−	11.7670i	0.0579921	−	0.477608i	−0.934562	−	0.355801i	$-0.884208\pi$
$607$	1.42877	−	11.7670i	0.0579921	−	0.477608i	0.992554	−	0.121807i	$-0.0388689\pi$
$608$	2.03497	+	5.36579i	0.0825291	+	0.217611i
$609$	−4.34398	+	2.27990i	−0.176027	+	0.0923861i
$610$	0.706075	−	5.81505i	0.0285882	−	0.235445i
$611$	−4.89030	+	8.73662i	−0.197840	+	0.353446i
$612$	−1.05999	−	8.72978i	−0.0428475	−	0.352881i
$613$	−14.2701	−	20.6738i	−0.576363	−	0.835006i	0.421039	−	0.907043i	$-0.361666\pi$
$613$	−14.2701	−	20.6738i	−0.576363	−	0.835006i	−0.997402	+	0.0720367i	$0.977050\pi$
$614$	−2.25245	+	3.26324i	−0.0909014	+	0.131693i
$615$	5.25461	−	4.65518i	0.211887	−	0.187715i
$616$	2.99214	+	7.88963i	0.120557	+	0.317882i
$617$	9.59790	−	13.9050i	0.386397	−	0.559793i	−0.580727	−	0.814098i	$-0.697232\pi$
$617$	9.59790	−	13.9050i	0.386397	−	0.559793i	0.967124	+	0.254306i	$0.0818470\pi$
$618$	8.57784	+	4.50200i	0.345051	+	0.181097i
$619$	2.38484	−	19.6409i	0.0958549	−	0.789436i	−0.862934	−	0.505317i	$-0.831376\pi$
$619$	2.38484	−	19.6409i	0.0958549	−	0.789436i	0.958789	−	0.284120i	$-0.0917013\pi$
$620$	−2.09285	−	17.2362i	−0.0840509	−	0.692221i
$621$	−3.23520	+	8.53053i	−0.129824	+	0.342318i
$622$	12.3099	−	17.8339i	0.493581	−	0.715075i
$623$	10.4017	+	9.21511i	0.416736	+	0.369196i
$624$	−0.292822	+	0.523132i	−0.0117222	+	0.0209420i
$625$	14.3279	−	12.6934i	0.573117	−	0.507737i
$626$	0.943512	+	7.77052i	0.0377103	+	0.310572i
$627$	0.205707	+	1.69415i	0.00821515	+	0.0676579i
$628$	−9.09642	+	4.77417i	−0.362987	+	0.190510i
$629$	−1.04125	+	0.546493i	−0.0415175	+	0.0217901i
$630$	−3.09605	−	0.763109i	−0.123350	−	0.0304030i
$631$	−28.1826	+	24.9676i	−1.12193	+	0.993944i	−0.121932	+	0.992538i	$0.538909\pi$
$631$	−28.1826	+	24.9676i	−1.12193	+	0.993944i	−0.999999	+	0.00140596i	$0.999552\pi$
$632$	−48.8818	−	12.0483i	−1.94441	−	0.479255i
$633$	−0.806161	−	2.12567i	−0.0320420	−	0.0844879i
$634$	−4.50540	+	2.36461i	−0.178932	+	0.0939108i
$635$	−2.49152	+	20.5195i	−0.0988730	+	0.814292i
$636$	13.8642	−	3.41722i	0.549751	−	0.135501i
$637$	8.90810	+	10.6189i	0.352952	+	0.420737i
$638$	−3.98190	−	0.981449i	−0.157645	−	0.0388560i
$639$	−2.97101	+	7.83391i	−0.117531	+	0.309905i
$640$	9.58720	+	8.49352i	0.378967	+	0.335736i
$641$	−12.4496	+	3.06854i	−0.491728	+	0.121200i	−0.477380	−	0.878697i	$-0.658414\pi$
$641$	−12.4496	+	3.06854i	−0.491728	+	0.121200i	−0.0143483	+	0.999897i	$0.504567\pi$
$642$	−6.61867	−	9.58880i	−0.261218	−	0.378440i
$643$	−2.63309	−	21.6854i	−0.103839	−	0.855189i	−0.947818	−	0.318813i	$-0.896716\pi$
$643$	−2.63309	−	21.6854i	−0.103839	−	0.855189i	0.843979	−	0.536376i	$-0.180207\pi$
$644$	−6.88841	−	18.1632i	−0.271441	−	0.715732i
$645$	6.18097	−	16.2979i	0.243375	−	0.641728i
$646$	−3.83866	−	5.56126i	−0.151030	−	0.218805i
$647$	−5.53740	−	1.36485i	−0.217698	−	0.0536576i	0.128958	−	0.991650i	$-0.458837\pi$
$647$	−5.53740	−	1.36485i	−0.217698	−	0.0536576i	−0.346656	+	0.937992i	$0.612683\pi$
$648$	−1.01539	−	2.67736i	−0.0398883	−	0.105177i
$649$	−8.49859	+	22.4089i	−0.333599	+	0.879627i
$650$	−2.03230	−	2.42260i	−0.0797133	−	0.0950223i
$651$	−4.55114	−	12.0004i	−0.178373	−	0.470332i
$652$	12.7476	−	11.2934i	0.499236	−	0.442285i
$653$	45.5469			1.78239			0.891195	−	0.453621i	$-0.149868\pi$
$653$	45.5469			1.78239			0.891195	+	0.453621i	$0.149868\pi$
$654$	13.7289			0.536841
$655$	20.5683	−	18.2219i	0.803668	−	0.711988i
$656$	0.515470	−	0.270539i	0.0201257	−	0.0105628i
$657$	5.28815			0.206310
$658$	−3.91028	−	2.05227i	−0.152439	−	0.0800059i
$659$	19.9814	+	17.7020i	0.778364	+	0.689570i	0.955623	−	0.294594i	$-0.0951844\pi$
$659$	19.9814	+	17.7020i	0.778364	+	0.689570i	−0.177258	+	0.984164i	$0.556723\pi$
$660$	2.26459	+	3.28083i	0.0881491	+	0.127706i
$661$	−28.5602	−	25.3022i	−1.11086	−	0.984140i	−0.110911	−	0.993830i	$-0.535377\pi$
$661$	−28.5602	−	25.3022i	−1.11086	−	0.984140i	−0.999953	+	0.00969039i	$0.996915\pi$
$662$	−2.94990	−	4.27367i	−0.114651	−	0.166101i
$663$	−7.02126	+	25.5050i	−0.272683	+	0.990534i
$664$	13.1022	−	18.9819i	0.508466	−	0.736640i
$665$	3.55803	−	0.876977i	0.137975	−	0.0340077i
$666$	−0.107400	+	0.0951478i	−0.00416165	+	0.00368690i
$667$	24.4635	+	6.02971i	0.947230	+	0.233471i
$668$	19.4720	+	17.2506i	0.753393	+	0.667448i
$669$	−19.0342	−	16.8628i	−0.735903	−	0.651953i
$670$	8.04052	−	21.2011i	0.310632	−	0.819070i
$671$	−3.07513	+	4.45510i	−0.118714	+	0.171987i
$672$	8.77405	+	4.60498i	0.338466	+	0.177641i
$673$	3.75338	−	30.9119i	0.144682	−	1.19156i	−0.721708	−	0.692197i	$-0.756643\pi$
$673$	3.75338	−	30.9119i	0.144682	−	1.19156i	0.866390	−	0.499367i	$-0.166434\pi$
$674$	3.88876	+	0.958494i	0.149790	+	0.0369198i
$675$	0.979670			0.0377075
$676$	−12.2031	+	9.68850i	−0.469349	+	0.372635i
$677$	−45.6997			−1.75638			−0.878192	−	0.478309i	$-0.841250\pi$
$677$	−45.6997			−1.75638			−0.878192	+	0.478309i	$0.841250\pi$
$678$	3.05100	+	0.752004i	0.117173	+	0.0288805i
$679$	−0.0136075	+	0.112068i	−0.000522209	+	0.00430078i
$680$	−37.2995	−	19.5763i	−1.43037	−	0.750716i
$681$	6.56574	−	9.51211i	0.251600	−	0.364505i
$682$	3.80449	−	10.0316i	0.145681	−	0.384130i
$683$	−22.2507	−	19.7124i	−0.851398	−	0.754273i	0.119736	−	0.992806i	$-0.461795\pi$
$683$	−22.2507	−	19.7124i	−0.851398	−	0.754273i	−0.971134	+	0.238533i	$0.923334\pi$
$684$	0.922989	+	0.817697i	0.0352914	+	0.0312654i
$685$	24.3725	+	6.00727i	0.931224	+	0.229526i
$686$	−12.9087	+	11.4361i	−0.492855	+	0.436631i
$687$	25.2287	−	6.21831i	0.962534	−	0.237243i
$688$	0.821113	−	1.18959i	0.0313047	−	0.0453526i
$689$	−42.4861	−	6.32578i	−1.61859	−	0.240993i
$690$	9.30288	+	13.4775i	0.354154	+	0.513081i
$691$	−26.1092	−	23.1307i	−0.993241	−	0.879935i	−0.000475187	−	1.00000i	$-0.500151\pi$
$691$	−26.1092	−	23.1307i	−0.993241	−	0.879935i	−0.992766	+	0.120065i	$0.961690\pi$
$692$	−0.419515	−	0.607773i	−0.0159476	−	0.0231041i
$693$	2.20570	+	1.95408i	0.0837878	+	0.0742295i
$694$	−1.70442	−	0.894548i	−0.0646988	−	0.0339566i
$695$	−14.1999			−0.538631
$696$	−7.00202	+	3.67495i	−0.265411	+	0.139298i
$697$	19.2277	−	17.0342i	0.728300	−	0.645218i
$698$	5.84407			0.221201
$699$	2.40801			0.0910793
$700$	−1.56133	+	1.38322i	−0.0590128	+	0.0522808i
$701$	11.6266	+	30.6567i	0.439129	+	1.15789i	0.953784	+	0.300492i	$0.0971508\pi$
$701$	11.6266	+	30.6567i	0.439129	+	1.15789i	−0.514655	+	0.857397i	$0.672080\pi$
$702$	−0.0870558	+	3.22660i	−0.00328571	+	0.121780i
$703$	0.0584725	−	0.154179i	0.00220533	−	0.00581498i
$704$	3.13295	+	8.26091i	0.118077	+	0.311345i
$705$	−5.40606	−	1.33247i	−0.203604	−	0.0501838i
$706$	0.628577	+	0.910650i	0.0236568	+	0.0342728i
$707$	0.115619	−	0.304861i	0.00434828	−	0.0114655i
$708$	6.14066	+	16.1916i	0.230780	+	0.608517i
$709$	5.51696	+	45.4362i	0.207194	+	1.70639i	0.611068	+	0.791578i	$0.290740\pi$
$709$	5.51696	+	45.4362i	0.207194	+	1.70639i	−0.403874	+	0.914815i	$0.632337\pi$
$710$	8.54318	+	12.3769i	0.320620	+	0.464498i
$711$	−17.0710	+	4.20763i	−0.640213	+	0.157798i
$712$	16.7664	+	14.8538i	0.628348	+	0.556668i
$713$	−23.3736	+	61.6310i	−0.875346	+	2.30810i
$714$	−11.3291	−	2.79237i	−0.423980	−	0.104502i
$715$	−2.55484	−	11.7169i	−0.0955455	−	0.438187i
$716$	−19.4147	+	4.78529i	−0.725560	+	0.178835i
$717$	1.03018	−	8.48429i	0.0384728	−	0.316852i
$718$	−28.5332	+	14.9754i	−1.06485	+	0.558876i
$719$	5.34281	+	14.0878i	0.199253	+	0.525387i	0.996982	−	0.0776286i	$-0.0247348\pi$
$719$	5.34281	+	14.0878i	0.199253	+	0.525387i	−0.797729	+	0.603016i	$0.793966\pi$
$720$	−0.323704	−	0.0797859i	−0.0120637	−	0.00297345i
$721$	−14.3890	+	12.7475i	−0.535873	+	0.474742i
$722$	−15.5950	−	3.84382i	−0.580386	−	0.143052i
$723$	8.55284	−	4.48887i	0.318083	−	0.166943i
$724$	−10.5214	+	5.52205i	−0.391025	+	0.205226i
$725$	−0.326113	−	2.68578i	−0.0121115	−	0.0997473i
$726$	−0.890058	−	7.33028i	−0.0330331	−	0.272052i
$727$	−22.1037	+	19.5822i	−0.819781	+	0.726263i	−0.964748	−	0.263174i	$-0.915231\pi$
$727$	−22.1037	+	19.5822i	−0.819781	+	0.726263i	0.144967	+	0.989436i	$0.453692\pi$
$728$	−11.7874	−	14.0511i	−0.436868	−	0.520769i
$729$	−0.748511	−	0.663123i	−0.0277226	−	0.0245601i
$730$	5.39218	−	7.81192i	0.199573	−	0.289132i
$731$	22.6174	−	59.6372i	0.836534	−	2.20576i
$732$	0.471469	+	3.88290i	0.0174260	+	0.143516i
$733$	−1.23532	+	10.1738i	−0.0456276	+	0.375777i	0.951952	+	0.306247i	$0.0990732\pi$
$733$	−1.23532	+	10.1738i	−0.0456276	+	0.375777i	−0.997580	+	0.0695306i	$0.977850\pi$
$734$	18.6594	+	9.79323i	0.688733	+	0.361475i
$735$	−4.37863	+	6.34354i	−0.161508	+	0.233985i
$736$	−18.0461	−	47.5835i	−0.665186	−	1.75395i
$737$	−15.6845	+	13.8953i	−0.577747	+	0.511839i
$738$	1.78050	−	2.57950i	0.0655411	−	0.0949526i
$739$	−15.2763	−	22.1316i	−0.561949	−	0.814124i	0.434290	−	0.900773i	$-0.356999\pi$
$739$	−15.2763	−	22.1316i	−0.561949	−	0.814124i	−0.996239	+	0.0866493i	$0.972384\pi$
$740$	−0.0464289	−	0.382376i	−0.00170676	−	0.0140564i
$741$	−1.63464	−	3.32982i	−0.0600499	−	0.122324i
$742$	2.28371	−	18.8080i	0.0838375	−	0.690464i
$743$	−15.4370	+	8.10195i	−0.566328	+	0.297232i	−0.723483	−	0.690342i	$-0.757460\pi$
$743$	−15.4370	+	8.10195i	−0.566328	+	0.297232i	0.157155	+	0.987574i	$0.449768\pi$
$744$	−7.33595	−	19.3433i	−0.268949	−	0.709160i
$745$	−2.80083	+	23.0669i	−0.102615	+	0.845107i
$746$	−26.5675			−0.972707
$747$	0.970910	−	7.99616i	0.0355237	−	0.292564i
$748$	8.28659	+	12.0052i	0.302988	+	0.438954i
$749$	22.4485	−	5.53305i	0.820249	−	0.202173i
$750$	6.09730	−	8.83347i	0.222642	−	0.322553i
$751$	32.7980	−	8.08398i	1.19682	−	0.294989i	0.409947	−	0.912109i	$-0.365547\pi$
$751$	32.7980	−	8.08398i	1.19682	−	0.294989i	0.786869	+	0.617121i	$0.211701\pi$
$752$	−0.408835	−	0.214573i	−0.0149087	−	0.00782467i
$753$	−14.9983	−	7.87173i	−0.546569	−	0.286862i
$754$	8.87475	−	0.835407i	0.323199	−	0.0304237i
$755$	−21.8807	+	11.4839i	−0.796319	+	0.417940i
$756$	2.12920			0.0774384
$757$	−47.1556	−	24.7492i	−1.71390	−	0.899524i	−0.973919	−	0.226898i	$-0.927142\pi$
$757$	−47.1556	−	24.7492i	−1.71390	−	0.899524i	−0.739982	−	0.672627i	$-0.765166\pi$
$758$	−2.04330	+	5.38774i	−0.0742161	+	0.195692i
$759$	−1.82420	−	15.0236i	−0.0662143	−	0.545324i
$760$	5.73516	−	1.41359i	0.208036	−	0.0512763i
$761$	−0.657452	+	0.162047i	−0.0238326	+	0.00587421i	−0.251214	−	0.967932i	$-0.580830\pi$
$761$	−0.657452	+	0.162047i	−0.0238326	+	0.00587421i	0.227381	+	0.973806i	$0.426984\pi$
$762$	1.11241	+	9.16153i	0.0402984	+	0.331887i
$763$	−9.66050	+	25.4727i	−0.349734	+	0.922172i
$764$	8.87764	+	4.65934i	0.321182	+	0.168569i
$765$	−14.7112			−0.531884
$766$	−7.63320	+	4.00621i	−0.275799	+	0.144750i
$767$	1.40498	−	52.0738i	0.0507310	−	1.88027i
$768$	14.4957	+	7.60795i	0.523070	+	0.274528i
$769$	−38.5162	−	20.2149i	−1.38893	−	0.728967i	−0.406161	−	0.913801i	$-0.633133\pi$
$769$	−38.5162	−	20.2149i	−1.38893	−	0.728967i	−0.982770	+	0.184834i	$0.940825\pi$
$770$	5.13576	−	1.26585i	0.185080	−	0.0456181i
$771$	4.50485	−	6.52640i	0.162238	−	0.235042i
$772$	−27.3123	+	6.73187i	−0.982990	+	0.242285i
$773$	−1.39604	−	2.02252i	−0.0502122	−	0.0727449i	0.797074	−	0.603882i	$-0.206380\pi$
$773$	−1.39604	−	2.02252i	−0.0502122	−	0.0727449i	−0.847286	+	0.531137i	$0.821765\pi$
$774$	0.938063	−	7.72564i	0.0337180	−	0.277693i
$775$	7.07788			0.254245
$776$	−0.0219338	+	0.180641i	−0.000787379	+	0.00648465i
$777$	−0.100965	−	0.266223i	−0.00362210	−	0.00955068i
$778$	18.8382	−	9.88707i	0.675383	−	0.354468i
$779$	−0.434175	+	3.57575i	−0.0155559	+	0.128115i
$780$	−6.99578	−	5.11281i	−0.250489	−	0.183068i
$781$	−1.67523	−	13.7968i	−0.0599445	−	0.493688i
$782$	34.0411	+	49.3170i	1.21731	+	1.76357i
$783$	−1.56880	+	2.27279i	−0.0560642	+	0.0812230i
$784$	−0.478445	+	0.423865i	−0.0170873	+	0.0151380i
$785$	6.09417	+	16.0690i	0.217510	+	0.573527i
$786$	6.96944	−	10.0970i	0.248592	−	0.360147i
$787$	14.8656	+	7.80206i	0.529901	+	0.278113i	0.708381	−	0.705830i	$-0.249426\pi$
$787$	14.8656	+	7.80206i	0.529901	+	0.278113i	−0.178480	+	0.983943i	$0.557118\pi$
$788$	0.290598	−	2.39329i	0.0103521	−	0.0852575i
$789$	−1.74512	−	14.3723i	−0.0621279	−	0.511669i
$790$	−11.1911	+	29.5086i	−0.398162	+	1.04987i
$791$	−3.54215	+	5.13169i	−0.125944	+	0.182462i
$792$	3.55535	+	3.14977i	0.126334	+	0.111922i
$793$	3.12297	−	11.3443i	0.110900	−	0.402848i
$794$	3.28926	−	2.91403i	0.116731	−	0.103415i
$795$	−2.87930	−	23.7132i	−0.102118	−	0.841019i
$796$	−2.09756	−	17.2750i	−0.0743461	−	0.612295i
$797$	−29.9812	+	15.7354i	−1.06199	+	0.557375i	−0.902883	−	0.429886i	$-0.858554\pi$
$797$	−29.9812	+	15.7354i	−1.06199	+	0.557375i	−0.159106	+	0.987261i	$0.550861\pi$
$798$	1.44872	−	0.760348i	0.0512842	−	0.0269160i
$799$	−19.7818	−	4.87578i	−0.699831	−	0.172493i
$800$	−4.09033	+	3.62372i	−0.144615	+	0.128118i
$801$	7.59534	+	1.87208i	0.268368	+	0.0661468i
$802$	5.85191	+	15.4302i	0.206638	+	0.544860i
$803$	−7.76725	+	4.07657i	−0.274100	+	0.143859i
$804$	−1.82499	+	15.0301i	−0.0643624	+	0.530072i
$805$	−31.5525	+	7.77699i	−1.11208	+	0.274103i
$806$	−0.628957	+	23.3114i	−0.0221541	+	0.821110i
$807$	3.14443	+	0.775033i	0.110689	+	0.0272824i
$808$	0.186365	−	0.491403i	0.00655628	−	0.0172875i
$809$	−28.7407	−	25.4620i	−1.01047	−	0.895198i	−0.0159629	−	0.999873i	$-0.505081\pi$
$809$	−28.7407	−	25.4620i	−1.01047	−	0.895198i	−0.994507	+	0.104675i	$0.966620\pi$
$810$	−1.74283	+	0.429570i	−0.0612369	+	0.0150935i
$811$	−15.1206	−	21.9059i	−0.530955	−	0.769221i	0.462106	−	0.886825i	$-0.347094\pi$
$811$	−15.1206	−	21.9059i	−0.530955	−	0.769221i	−0.993061	+	0.117604i	$0.962479\pi$
$812$	−0.708769	−	5.83724i	−0.0248729	−	0.204847i
$813$	−8.14342	−	21.4724i	−0.285602	−	0.753071i
$814$	0.0844008	−	0.222546i	0.00295824	−	0.00780025i
$815$	−16.1844	−	23.4471i	−0.566914	−	0.821316i
$816$	−1.18450	−	0.291953i	−0.0414657	−	0.0102204i
$817$	3.17146	+	8.36245i	0.110955	+	0.292565i
$818$	−2.24353	+	5.91570i	−0.0784431	+	0.206837i
$819$	−5.92541	−	2.43197i	−0.207051	−	0.0849799i
$820$	2.98368	+	7.86732i	0.104195	+	0.274739i
$821$	−7.39057	+	6.54747i	−0.257933	+	0.228508i	−0.782172	−	0.623063i	$-0.785888\pi$
$821$	−7.39057	+	6.54747i	−0.257933	+	0.228508i	0.524239	+	0.851571i	$0.324350\pi$
$822$	11.2075			0.390905
$823$	6.60687			0.230301			0.115151	−	0.993348i	$-0.463265\pi$
$823$	6.60687			0.230301			0.115151	+	0.993348i	$0.463265\pi$
$824$	−23.1934	+	20.5476i	−0.807982	+	0.715809i
$825$	−1.43894	+	0.755216i	−0.0500976	+	0.0262932i
$826$	22.9768			0.799465
$827$	−28.2605	−	14.8322i	−0.982713	−	0.515768i	−0.104752	−	0.994498i	$-0.533405\pi$
$827$	−28.2605	−	14.8322i	−0.982713	−	0.515768i	−0.877962	+	0.478731i	$0.841097\pi$
$828$	−8.18502	−	7.25129i	−0.284449	−	0.252000i
$829$	15.3203	+	22.1954i	0.532098	+	0.770876i	0.993194	−	0.116474i	$-0.0371591\pi$
$829$	15.3203	+	22.1954i	0.532098	+	0.770876i	−0.461096	+	0.887350i	$0.652544\pi$
$830$	−10.8223	−	9.58774i	−0.375648	−	0.332795i
$831$	10.6711	+	15.4597i	0.370176	+	0.536292i
$832$	−12.3421	−	14.7124i	−0.427884	−	0.510060i
$833$	−16.0223	+	23.2123i	−0.555139	+	0.804258i
$834$	−6.15571	+	1.51725i	−0.213155	+	0.0525379i
$835$	32.5743	−	28.8584i	1.12728	−	0.998685i
$836$	−1.98604	−	0.489515i	−0.0686887	−	0.0169302i
$837$	−5.40781	−	4.79090i	−0.186921	−	0.165598i
$838$	7.65144	+	6.77859i	0.264315	+	0.234162i
$839$	5.62230	−	14.8248i	0.194104	−	0.511809i	−0.802264	−	0.596970i	$-0.796371\pi$
$839$	5.62230	−	14.8248i	0.194104	−	0.511809i	0.996367	+	0.0851609i	$0.0271404\pi$
$840$	5.79388	−	8.39388i	0.199908	−	0.289616i
$841$	−18.9251	−	9.93267i	−0.652590	−	0.342506i
$842$	1.37427	−	11.3181i	0.0473604	−	0.390048i
$843$	−10.4437	−	2.57413i	−0.359699	−	0.0886578i
$844$	2.72484			0.0937930
$845$	13.6289	+	22.2191i	0.468848	+	0.764361i
$846$	−2.48593			−0.0854679
$847$	14.2270	+	3.50664i	0.488845	+	0.120489i
$848$	0.238770	−	1.96645i	0.00819940	−	0.0675282i
$849$	1.23803	+	0.649770i	0.0424892	+	0.0223000i
$850$	3.65533	−	5.29566i	0.125377	−	0.181640i
$851$	−0.518531	+	1.36725i	−0.0177750	+	0.0468689i
$852$	−7.51661	−	6.65913i	−0.257515	−	0.228138i
$853$	−6.98184	−	6.18537i	−0.239054	−	0.211783i	0.535086	−	0.844797i	$-0.320279\pi$
$853$	−6.98184	−	6.18537i	−0.239054	−	0.211783i	−0.774140	+	0.633014i	$0.781817\pi$
$854$	5.03903	+	1.24201i	0.172432	+	0.0425007i
$855$	1.54405	−	1.36791i	0.0528055	−	0.0467816i
$856$	36.1845	−	8.91867i	1.23676	−	0.304834i
$857$	−14.2818	+	20.6908i	−0.487858	+	0.706784i	−0.987176	−	0.159634i	$-0.948969\pi$
$857$	−14.2818	+	20.6908i	−0.487858	+	0.706784i	0.499318	+	0.866419i	$0.333584\pi$
$858$	−2.35948	−	4.80635i	−0.0805513	−	0.164086i
$859$	−0.499612	−	0.723813i	−0.0170465	−	0.0246962i	0.814368	−	0.580349i	$-0.197084\pi$
$859$	−0.499612	−	0.723813i	−0.0170465	−	0.0246962i	−0.831414	+	0.555653i	$0.812468\pi$
$860$	15.6378	+	13.8538i	0.533243	+	0.472412i
$861$	3.53315	+	5.11865i	0.120410	+	0.174443i
$862$	12.3652	+	10.9546i	0.421162	+	0.373117i
$863$	27.1747	+	14.2624i	0.925036	+	0.485497i	0.858802	−	0.512308i	$-0.171209\pi$
$863$	27.1747	+	14.2624i	0.925036	+	0.485497i	0.0662344	+	0.997804i	$0.478902\pi$
$864$	5.57803			0.189768
$865$	−1.09391	+	0.574130i	−0.0371942	+	0.0195210i
$866$	−19.5336	+	17.3052i	−0.663778	+	0.588056i
$867$	−36.8312			−1.25085
$868$	15.3830			0.522132
$869$	21.8304	−	19.3400i	0.740544	−	0.656065i
$870$	1.75783	+	4.63500i	0.0595959	+	0.157141i
$871$	22.2462	−	39.7433i	0.753783	−	1.34665i
$872$	−15.5717	+	41.0591i	−0.527324	+	1.39044i
$873$	0.0225347	+	0.0594192i	0.000762685	+	0.00201103i
$874$	−8.15860	−	2.01091i	−0.275969	−	0.0680202i
$875$	12.0992	+	17.5288i	0.409029	+	0.592581i
$876$	−2.24757	+	5.92635i	−0.0759383	+	0.200233i
$877$	18.0420	+	47.5728i	0.609234	+	1.60642i	0.783272	+	0.621679i	$0.213549\pi$
$877$	18.0420	+	47.5728i	0.609234	+	1.60642i	−0.174038	+	0.984739i	$0.555682\pi$
$878$	−0.912466	−	7.51483i	−0.0307942	−	0.253613i
$879$	−3.34754	−	4.84975i	−0.112910	−	0.163578i
$880$	0.536964	−	0.132350i	0.0181010	−	0.00446151i
$881$	−19.9946	−	17.7137i	−0.673636	−	0.596789i	0.255375	−	0.966842i	$-0.417801\pi$
$881$	−19.9946	−	17.7137i	−0.673636	−	0.596789i	−0.929011	+	0.370053i	$0.879340\pi$
$882$	−1.22035	+	3.21781i	−0.0410915	+	0.108349i
$883$	−2.54819	−	0.628073i	−0.0857535	−	0.0211363i	0.196205	−	0.980563i	$-0.437138\pi$
$883$	−2.54819	−	0.628073i	−0.0857535	−	0.0211363i	−0.281959	+	0.959426i	$0.590984\pi$
$884$	−25.5990	−	18.7088i	−0.860986	−	0.629244i
$885$	28.1274	−	6.93278i	0.945492	−	0.233043i
$886$	1.29386	−	10.6559i	0.0434682	−	0.357992i
$887$	−10.7584	+	5.64643i	−0.361231	+	0.189588i	−0.635568	−	0.772045i	$-0.719234\pi$
$887$	−10.7584	+	5.64643i	−0.361231	+	0.189588i	0.274337	+	0.961634i	$0.411542\pi$
$888$	−0.162744	−	0.429122i	−0.00546134	−	0.0144004i
$889$	−17.7812	−	4.38266i	−0.596361	−	0.146990i
$890$	10.5103	−	9.31131i	0.352306	−	0.312116i
$891$	1.61061	+	0.396979i	0.0539574	+	0.0132993i
$892$	26.9878	−	14.1643i	0.903618	−	0.474256i
$893$	2.52963	−	1.32765i	0.0846509	−	0.0444282i
$894$	1.25051	+	10.2989i	0.0418234	+	0.344447i
$895$	4.03202	+	33.2066i	0.134775	+	1.10998i
$896$	−8.49403	+	7.52505i	−0.283766	+	0.251394i
$897$	14.4959	+	29.5287i	0.484003	+	0.985934i
$898$	5.58787	+	4.95042i	0.186470	+	0.165198i
$899$	−11.3342	+	16.4204i	−0.378015	+	0.547650i
$900$	−0.416380	+	1.09790i	−0.0138793	+	0.0365968i
$901$	−10.5359	−	86.7712i	−0.351003	−	2.89077i
$902$	−0.626700	+	5.16134i	−0.0208668	+	0.171854i
$903$	13.6742	+	7.17675i	0.455047	+	0.238827i
$904$	−5.70956	+	8.27173i	−0.189897	+	0.275114i
$905$	7.04883	+	18.5862i	0.234311	+	0.617828i
$906$	−8.25833	+	7.31624i	−0.274365	+	0.243066i
$907$	4.25709	−	6.16747i	0.141354	−	0.204787i	−0.745912	−	0.666045i	$-0.767986\pi$
$907$	4.25709	−	6.16747i	0.141354	−	0.204787i	0.887266	+	0.461257i	$0.152601\pi$
$908$	7.86952	+	11.4010i	0.261159	+	0.378354i
$909$	−0.0221233	−	0.182202i	−0.000733783	−	0.00604325i
$910$	−9.63460	+	6.27350i	−0.319384	+	0.207965i
$911$	2.56855	−	21.1539i	0.0850998	−	0.700860i	−0.886250	−	0.463207i	$-0.846699\pi$
$911$	2.56855	−	21.1539i	0.0850998	−	0.700860i	0.971350	−	0.237653i	$-0.0763781\pi$
$912$	0.151469	−	0.0794973i	0.00501565	−	0.00263242i
$913$	4.73807	+	12.4933i	0.156807	+	0.413466i
$914$	0.101729	−	0.837817i	0.00336491	−	0.0277125i
$915$	6.54335			0.216316
$916$	−3.75392	+	30.9163i	−0.124033	+	1.02150i
$917$	13.8299	+	20.0361i	0.456703	+	0.661649i
$918$	−6.37737	+	1.57188i	−0.210485	+	0.0518798i
$919$	20.1385	−	29.1756i	0.664307	−	0.962415i	−0.335486	−	0.942045i	$-0.608900\pi$
$919$	20.1385	−	29.1756i	0.664307	−	0.962415i	0.999793	−	0.0203693i	$-0.00648421\pi$
$920$	−50.8591	+	12.5357i	−1.67678	+	0.413288i
$921$	−3.92186	−	2.05835i	−0.129230	−	0.0678250i
$922$	−19.9807	−	10.4867i	−0.658031	−	0.345361i
$923$	13.3121	+	27.1173i	0.438173	+	0.892577i
$924$	−3.12738	+	1.64138i	−0.102883	+	0.0539973i
$925$	0.157019			0.00516276
$926$	−2.64466	−	1.38802i	−0.0869089	−	0.0456133i
$927$	−3.83728	+	10.1181i	−0.126033	+	0.332321i
$928$	−1.85681	−	15.2922i	−0.0609529	−	0.501992i
$929$	39.9292	−	9.84167i	1.31004	−	0.322895i	0.478364	−	0.878162i	$-0.341230\pi$
$929$	39.9292	−	9.84167i	1.31004	−	0.322895i	0.831672	+	0.555267i	$0.187384\pi$
$930$	−12.5915	+	3.10354i	−0.412893	+	0.101769i
$931$	−0.476719	−	3.92613i	−0.0156238	−	0.128674i
$932$	−1.02345	+	2.69862i	−0.0335243	+	0.0883963i
$933$	21.4334	+	11.2491i	0.701697	+	0.368279i
$934$	6.12768			0.200504
$935$	21.6078	−	11.3407i	0.706652	−	0.370879i
$936$	−9.55112	−	3.92007i	−0.312188	−	0.128131i
$937$	−12.5178	−	6.56985i	−0.408939	−	0.214627i	0.247694	−	0.968838i	$-0.420327\pi$
$937$	−12.5178	−	6.56985i	−0.408939	−	0.214627i	−0.656632	+	0.754211i	$0.728020\pi$
$938$	17.7880	+	9.33588i	0.580800	+	0.304827i
$939$	−8.48965	+	2.09251i	−0.277049	+	0.0682865i
$940$	3.79097	−	5.49216i	0.123648	−	0.179135i
$941$	9.85160	−	2.42820i	0.321153	−	0.0791571i	−0.0754437	−	0.997150i	$-0.524037\pi$
$941$	9.85160	−	2.42820i	0.321153	−	0.0791571i	0.396597	+	0.917993i	$0.370191\pi$
$942$	4.35882	+	6.31484i	0.142018	+	0.205748i
$943$	3.85024	−	31.7096i	0.125381	−	1.03261i
$944$	2.40231			0.0781886
$945$	0.429341	−	3.53594i	0.0139665	−	0.115024i
$946$	4.57777	+	12.0706i	0.148836	+	0.392449i
$947$	−38.7857	+	20.3563i	−1.26036	+	0.661490i	−0.956641	−	0.291270i	$-0.905922\pi$
$947$	−38.7857	+	20.3563i	−1.26036	+	0.661490i	−0.303724	+	0.952760i	$0.598230\pi$
$948$	2.54010	−	20.9196i	0.0824985	−	0.679436i
$949$	13.0239	−	13.9254i	0.422773	−	0.452038i
$950$	0.108759	+	0.895710i	0.00352860	+	0.0290607i
$951$	−3.22873	−	4.67763i	−0.104699	−	0.151682i
$952$	21.2010	−	30.7149i	0.687127	−	0.995475i
$953$	39.6187	−	35.0991i	1.28338	−	1.13697i	0.300287	−	0.953849i	$-0.402918\pi$
$953$	39.6187	−	35.0991i	1.28338	−	1.13697i	0.983090	−	0.183124i	$-0.0586209\pi$
$954$	−3.78193	−	9.97212i	−0.122444	−	0.322859i
$955$	9.52784	−	13.8035i	0.308314	−	0.446669i
$956$	9.07038	+	4.76050i	0.293357	+	0.153966i
$957$	0.552185	−	4.54765i	0.0178496	−	0.147005i
$958$	1.36009	+	11.2014i	0.0439426	+	0.361900i
$959$	−7.88629	+	20.7944i	−0.254662	+	0.671487i
$960$	6.06654	−	8.78889i	0.195797	−	0.283660i
$961$	−15.8663	−	14.0563i	−0.511815	−	0.453428i
$962$	−0.0139531	+	0.517153i	−0.000449866	+	0.0166737i
$963$	9.74180	−	8.63048i	0.313925	−	0.278113i
$964$	1.39549	+	11.4929i	0.0449457	+	0.370162i
$965$	5.67218	+	46.7146i	0.182594	+	1.50380i
$966$	−12.8472	+	6.74273i	−0.413352	+	0.216944i
$967$	9.37388	−	4.91979i	0.301444	−	0.158210i	−0.307219	−	0.951639i	$-0.599399\pi$
$967$	9.37388	−	4.91979i	0.301444	−	0.158210i	0.608663	+	0.793429i	$0.291706\pi$
$968$	22.9323	+	5.65232i	0.737073	+	0.181672i
$969$	5.65000	−	5.00546i	0.181504	−	0.160799i
$970$	0.110755	+	0.0272987i	0.00355613	+	0.000876507i
$971$	−1.58896	−	4.18974i	−0.0509921	−	0.134455i	0.907100	−	0.420915i	$-0.138291\pi$
$971$	−1.58896	−	4.18974i	−0.0509921	−	0.134455i	−0.958092	+	0.286459i	$0.907522\pi$
$972$	1.06128	−	0.557005i	0.0340407	−	0.0178659i
$973$	1.51644	−	12.4890i	0.0486148	−	0.400379i
$974$	16.6200	−	4.09646i	0.532538	−	0.131259i
$975$	2.41277	−	2.57979i	0.0772706	−	0.0826195i
$976$	0.526850	+	0.129857i	0.0168640	+	0.00415661i
$977$	16.1957	−	42.7046i	0.518147	−	1.36624i	−0.379364	−	0.925248i	$-0.623857\pi$
$977$	16.1957	−	42.7046i	0.518147	−	1.36624i	0.897511	−	0.440993i	$-0.145374\pi$
$978$	−9.52131	−	8.43515i	−0.304458	−	0.269726i
$979$	−12.5992	+	3.10543i	−0.402673	+	0.0992500i
$980$	−5.24811	−	7.60320i	−0.167645	−	0.242875i
$981$	1.84851	+	15.2238i	0.0590184	+	0.486060i
$982$	5.57210	+	14.6924i	0.177813	+	0.468854i
$983$	−0.800598	+	2.11100i	−0.0255351	+	0.0673305i	−0.947178	−	0.320710i	$-0.896079\pi$
$983$	−0.800598	+	2.11100i	−0.0255351	+	0.0673305i	0.921642	+	0.388040i	$0.126848\pi$
$984$	5.69506	+	8.25071i	0.181552	+	0.263023i
$985$	−3.91592	−	0.965187i	−0.124771	−	0.0307534i
$986$	6.43223	+	16.9604i	0.204844	+	0.540129i
$987$	1.74926	−	4.61241i	0.0556795	−	0.146815i
$988$	4.42644	−	0.416674i	0.140824	−	0.0132562i
$989$	−28.1243	−	74.1578i	−0.894302	−	2.35808i
$990$	2.22873	−	1.97448i	0.0708337	−	0.0627532i
$991$	−3.70705			−0.117758			−0.0588791	−	0.998265i	$-0.518753\pi$
$991$	−3.70705			−0.117758			−0.0588791	+	0.998265i	$0.518753\pi$
$992$	40.2999			1.27952
$993$	4.34186	−	3.84655i	0.137785	−	0.122067i
$994$	−11.7981	+	6.19210i	−0.374212	+	0.196401i
$995$	−29.1113			−0.922890
$996$	8.54853	+	4.48661i	0.270871	+	0.142164i
$997$	41.3616	+	36.6432i	1.30993	+	1.16050i	0.975968	+	0.217915i	$0.0699256\pi$
$997$	41.3616	+	36.6432i	1.30993	+	1.16050i	0.333966	+	0.942585i	$0.391613\pi$
$998$	13.7015	+	19.8500i	0.433713	+	0.628342i
$999$	−0.119970	−	0.106284i	−0.00379567	−	0.00336267i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.m.a.40.10	✓	180
169.131	even	13	inner	507.2.m.a.469.10	yes	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.m.a.40.10	✓	180	1.1	even	1	trivial
507.2.m.a.469.10	yes	180	169.131	even	13	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.m (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.869211 + 0.214241i) q^{2} +(-0.120537 + 0.992709i) q^{3} +(-1.06128 - 0.557005i) q^{4} +(-1.13901 + 1.65015i) q^{5} +(-0.317451 + 0.837049i) q^{6} +(-1.32969 - 1.17800i) q^{7} +(-2.14332 - 1.89881i) q^{8} +(-0.970942 - 0.239316i) q^{9} +(-1.34357 + 1.19030i) q^{10} +(1.61061 - 0.396979i) q^{11} +(0.680867 - 0.986407i) q^{12} +(-3.02147 + 1.96741i) q^{13} +(-0.903404 - 1.30881i) q^{14} +(-1.50082 - 1.32961i) q^{15} +(-0.0944544 - 0.136841i) q^{16} +(-5.49180 - 4.86531i) q^{17} +(-0.792682 - 0.416031i) q^{18} +1.02881 q^{19} +(2.12796 - 1.11684i) q^{20} +(1.32969 - 1.17800i) q^{21} +1.48501 q^{22} -9.12340 q^{23} +(2.14332 - 1.89881i) q^{24} +(0.347396 + 0.916008i) q^{25} +(-3.04780 + 1.06277i) q^{26} +(0.354605 - 0.935016i) q^{27} +(0.755026 + 1.99084i) q^{28} +(-2.68140 - 0.660906i) q^{29} +(-1.01967 - 1.47725i) q^{30} +(2.56193 - 6.75526i) q^{31} +(1.97800 + 5.21555i) q^{32} +(0.199947 + 1.64672i) q^{33} +(-3.73118 - 5.40555i) q^{34} +(3.45841 - 0.852422i) q^{35} +(0.897145 + 0.794801i) q^{36} +(0.0568353 - 0.149862i) q^{37} +(0.894249 + 0.220413i) q^{38} +(-1.58887 - 3.23659i) q^{39} +(5.57458 - 1.37401i) q^{40} +(-0.422018 + 3.47563i) q^{41} +(1.40816 - 0.739058i) q^{42} +(3.08266 + 8.12831i) q^{43} +(-1.93043 - 0.475809i) q^{44} +(1.50082 - 1.32961i) q^{45} +(-7.93016 - 1.95461i) q^{46} +(2.45880 - 1.29048i) q^{47} +(0.147228 - 0.0772714i) q^{48} +(-0.463371 - 3.81620i) q^{49} +(0.105714 + 0.870630i) q^{50} +(5.49180 - 4.86531i) q^{51} +(4.30250 - 0.405007i) q^{52} +(8.91733 + 7.90006i) q^{53} +(0.508545 - 0.736755i) q^{54} +(-1.17943 + 3.10990i) q^{55} +(0.613140 + 5.04967i) q^{56} +(-0.124009 + 1.02131i) q^{57} +(-2.18911 - 1.14893i) q^{58} +(-8.20735 + 11.8904i) q^{59} +(0.852198 + 2.24706i) q^{60} +(-2.44268 + 2.16403i) q^{61} +(3.67412 - 5.32288i) q^{62} +(1.00914 + 1.46199i) q^{63} +(0.641995 + 5.28730i) q^{64} +(0.194983 - 7.22677i) q^{65} +(-0.178998 + 1.47418i) q^{66} +(-11.1852 + 5.87044i) q^{67} +(3.11836 + 8.22244i) q^{68} +(1.09970 - 9.05688i) q^{69} +3.18871 q^{70} +(1.00990 - 8.31728i) q^{71} +(1.62662 + 2.35657i) q^{72} +(-5.13448 + 1.26554i) q^{73} +(0.0815085 - 0.118085i) q^{74} +(-0.951203 + 0.234450i) q^{75} +(-1.09186 - 0.573050i) q^{76} +(-2.60925 - 1.36944i) q^{77} +(-0.687650 - 3.15368i) q^{78} +(15.5680 - 8.17072i) q^{79} +0.333392 q^{80} +(0.885456 + 0.464723i) q^{81} +(-1.11145 + 2.93064i) q^{82} +(0.970910 + 7.99616i) q^{83} +(-2.06733 + 0.509552i) q^{84} +(14.2837 - 3.52062i) q^{85} +(0.938063 + 7.72564i) q^{86} +(0.979294 - 2.58219i) q^{87} +(-4.20583 - 2.20739i) q^{88} -7.82265 q^{89} +(1.58939 - 0.834175i) q^{90} +(6.33524 + 0.943256i) q^{91} +(9.68252 + 5.08178i) q^{92} +(6.39720 + 3.35751i) q^{93} +(2.41369 - 0.594921i) q^{94} +(-1.17182 + 1.69768i) q^{95} +(-5.41594 + 1.33491i) q^{96} +(-0.0360998 - 0.0522996i) q^{97} +(0.414821 - 3.41636i) q^{98} -1.65881 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 180 q - q^{2} + 15 q^{3} - 15 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} - 15 q^{9} - 2 q^{10} - 4 q^{11} + 15 q^{12} - 14 q^{13} + 6 q^{14} + 2 q^{15} - 15 q^{16} - 2 q^{17} - q^{18} + 2 q^{20} - 4 q^{21}+ \cdots - 30 q^{99}+O(q^{100}) \) 180 * q - q^2 + 15 * q^3 - 15 * q^4 - 2 * q^5 + q^6 + 4 * q^7 + 3 * q^8 - 15 * q^9 - 2 * q^10 - 4 * q^11 + 15 * q^12 - 14 * q^13 + 6 * q^14 + 2 * q^15 - 15 * q^16 - 2 * q^17 - q^18 + 2 * q^20 - 4 * q^21 - 28 * q^22 - 52 * q^23 - 3 * q^24 - 67 * q^25 - 40 * q^26 + 15 * q^27 - 4 * q^28 - 27 * q^29 + 2 * q^30 + 22 * q^31 - 5 * q^32 - 9 * q^33 + 63 * q^34 - 31 * q^35 - 15 * q^36 + 2 * q^37 + 65 * q^38 + q^39 + 45 * q^40 - 6 * q^41 + 59 * q^42 - 60 * q^43 - 35 * q^44 - 2 * q^45 - 156 * q^46 + 15 * q^48 + 59 * q^49 - 51 * q^50 + 2 * q^51 + 66 * q^52 + 50 * q^53 + q^54 + 55 * q^55 - 14 * q^56 - 13 * q^57 + 36 * q^58 + 92 * q^59 - 15 * q^60 + 6 * q^61 + 61 * q^62 + 4 * q^63 - 203 * q^64 - 54 * q^65 + 54 * q^66 + 86 * q^67 + 32 * q^68 + 112 * q^70 + 39 * q^71 + 3 * q^72 - 158 * q^73 - 80 * q^74 + 15 * q^75 + 130 * q^76 - 64 * q^77 + 66 * q^78 - 10 * q^79 - 310 * q^80 - 15 * q^81 + 59 * q^82 - 82 * q^83 + 4 * q^84 + 22 * q^85 - q^86 + 40 * q^87 + 10 * q^88 + 2 * q^89 - 2 * q^90 - 100 * q^91 - 54 * q^92 + 43 * q^93 + 65 * q^94 + 58 * q^95 - 60 * q^96 + 16 * q^97 - 113 * q^98 - 30 * q^99

Introduction

L-functions

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