LMFDB - Embedded newform 273.2.cc.a.50.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(50,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

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

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

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

chi := DirichletCharacter("273.50");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cc (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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			50.6
Character	$\chi$	$=$	273.50
Dual form			273.2.cc.a.71.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.84038 - 0.493129i) q^{2} +(-1.11254 - 1.32750i) q^{3} +(1.41178 + 0.815092i) q^{4} +(-1.68431 + 1.68431i) q^{5} +(1.39288 + 2.99173i) q^{6} +(-0.258819 - 0.965926i) q^{7} +(0.498237 + 0.498237i) q^{8} +(-0.524491 + 2.95380i) q^{9} +O(q^{10})$	\(q+(-1.84038 - 0.493129i) q^{2} +(-1.11254 - 1.32750i) q^{3} +(1.41178 + 0.815092i) q^{4} +(-1.68431 + 1.68431i) q^{5} +(1.39288 + 2.99173i) q^{6} +(-0.258819 - 0.965926i) q^{7} +(0.498237 + 0.498237i) q^{8} +(-0.524491 + 2.95380i) q^{9} +(3.93035 - 2.26919i) q^{10} +(0.313767 - 1.17099i) q^{11} +(-0.488637 - 2.78096i) q^{12} +(0.415331 + 3.58155i) q^{13} +1.90530i q^{14} +(4.10978 + 0.362045i) q^{15} +(-2.30143 - 3.98620i) q^{16} +(-0.202536 + 0.350803i) q^{17} +(2.42187 - 5.17747i) q^{18} +(7.65849 - 2.05209i) q^{19} +(-3.75074 + 1.00501i) q^{20} +(-0.994315 + 1.41822i) q^{21} +(-1.15490 + 2.00035i) q^{22} +(-3.55196 - 6.15217i) q^{23} +(0.107097 - 1.21572i) q^{24} -0.673785i q^{25} +(1.00180 - 6.79623i) q^{26} +(4.50467 - 2.58997i) q^{27} +(0.421923 - 1.57464i) q^{28} +(5.97296 - 3.44849i) q^{29} +(-7.38503 - 2.69295i) q^{30} +(4.03416 + 4.03416i) q^{31} +(1.90507 + 7.10983i) q^{32} +(-1.90357 + 0.886258i) q^{33} +(0.545735 - 0.545735i) q^{34} +(2.06285 + 1.19099i) q^{35} +(-3.14808 + 3.74260i) q^{36} +(-1.59241 - 0.426686i) q^{37} -15.1065 q^{38} +(4.29242 - 4.53598i) q^{39} -1.67837 q^{40} +(11.4499 + 3.06798i) q^{41} +(2.52928 - 2.11973i) q^{42} +(-1.58218 - 0.913473i) q^{43} +(1.39744 - 1.39744i) q^{44} +(-4.09170 - 5.85851i) q^{45} +(3.50315 + 13.0739i) q^{46} +(7.59520 + 7.59520i) q^{47} +(-2.73122 + 7.48997i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(-0.332263 + 1.24002i) q^{50} +(0.691019 - 0.121418i) q^{51} +(-2.33294 + 5.39489i) q^{52} +0.378791i q^{53} +(-9.56751 + 2.54515i) q^{54} +(1.44383 + 2.50079i) q^{55} +(0.352307 - 0.610213i) q^{56} +(-11.2445 - 7.88358i) q^{57} +(-12.6931 + 3.40110i) q^{58} +(-8.14818 + 2.18330i) q^{59} +(5.50700 + 3.86097i) q^{60} +(-2.82748 + 4.89734i) q^{61} +(-5.43503 - 9.41375i) q^{62} +(2.98890 - 0.257879i) q^{63} -4.81852i q^{64} +(-6.73198 - 5.33289i) q^{65} +(3.94033 - 0.692349i) q^{66} +(-1.55285 + 5.79531i) q^{67} +(-0.571873 + 0.330171i) q^{68} +(-4.21528 + 11.5598i) q^{69} +(-3.20912 - 3.20912i) q^{70} +(1.83259 + 6.83932i) q^{71} +(-1.73301 + 1.21037i) q^{72} +(2.40085 - 2.40085i) q^{73} +(2.72024 + 1.57053i) q^{74} +(-0.894447 + 0.749615i) q^{75} +(12.4847 + 3.34528i) q^{76} -1.21230 q^{77} +(-10.1365 + 6.23123i) q^{78} +7.86624 q^{79} +(10.5903 + 2.83767i) q^{80} +(-8.44982 - 3.09848i) q^{81} +(-19.5592 - 11.2925i) q^{82} +(5.92256 - 5.92256i) q^{83} +(-2.55973 + 1.19175i) q^{84} +(-0.249727 - 0.931993i) q^{85} +(2.46136 + 2.46136i) q^{86} +(-11.2230 - 4.09248i) q^{87} +(0.739762 - 0.427102i) q^{88} +(0.361109 - 1.34768i) q^{89} +(4.64129 + 12.7996i) q^{90} +(3.35202 - 1.32815i) q^{91} -11.5807i q^{92} +(0.867150 - 9.84351i) q^{93} +(-10.2327 - 17.7235i) q^{94} +(-9.44291 + 16.3556i) q^{95} +(7.31879 - 10.4390i) q^{96} +(4.61523 - 1.23665i) q^{97} +(1.84038 - 0.493129i) q^{98} +(3.29431 + 1.54098i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 12 q^{6}+O(q^{10}) $ 112 * q - 12 * q^6	$ 112 q - 12 q^{6} - 48 q^{10} - 32 q^{13} + 4 q^{15} + 40 q^{16} - 16 q^{18} - 8 q^{19} - 4 q^{21} - 16 q^{22} - 88 q^{24} + 24 q^{27} - 72 q^{30} + 16 q^{31} + 48 q^{34} + 12 q^{36} + 48 q^{37} + 56 q^{39} + 32 q^{40} - 28 q^{45} + 72 q^{46} + 24 q^{48} - 144 q^{52} - 108 q^{54} - 28 q^{57} - 120 q^{58} - 116 q^{60} - 48 q^{61} + 16 q^{63} + 40 q^{66} - 16 q^{67} + 72 q^{69} + 48 q^{70} + 52 q^{72} - 16 q^{73} + 60 q^{75} + 16 q^{76} - 4 q^{78} + 16 q^{79} - 20 q^{81} + 120 q^{82} + 72 q^{84} - 40 q^{85} - 24 q^{87} + 72 q^{88} + 16 q^{91} + 92 q^{93} - 96 q^{94} + 28 q^{96} + 96 q^{97} - 144 q^{99}+O(q^{100}) $ 112 * q - 12 * q^6 - 48 * q^10 - 32 * q^13 + 4 * q^15 + 40 * q^16 - 16 * q^18 - 8 * q^19 - 4 * q^21 - 16 * q^22 - 88 * q^24 + 24 * q^27 - 72 * q^30 + 16 * q^31 + 48 * q^34 + 12 * q^36 + 48 * q^37 + 56 * q^39 + 32 * q^40 - 28 * q^45 + 72 * q^46 + 24 * q^48 - 144 * q^52 - 108 * q^54 - 28 * q^57 - 120 * q^58 - 116 * q^60 - 48 * q^61 + 16 * q^63 + 40 * q^66 - 16 * q^67 + 72 * q^69 + 48 * q^70 + 52 * q^72 - 16 * q^73 + 60 * q^75 + 16 * q^76 - 4 * q^78 + 16 * q^79 - 20 * q^81 + 120 * q^82 + 72 * q^84 - 40 * q^85 - 24 * q^87 + 72 * q^88 + 16 * q^91 + 92 * q^93 - 96 * q^94 + 28 * q^96 + 96 * q^97 - 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$	$1$

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 $

$2$	−1.84038	−	0.493129i	−1.30135	−	0.348695i	−0.459388	−	0.888236i	$-0.651931\pi$
$2$	−1.84038	−	0.493129i	−1.30135	−	0.348695i	−0.841959	+	0.539541i	$0.818598\pi$
$3$	−1.11254	−	1.32750i	−0.642328	−	0.766430i
$3$	−1.11254	−	1.32750i	−0.642328	−	0.766430i
$4$	1.41178	+	0.815092i	0.705890	+	0.407546i
$5$	−1.68431	+	1.68431i	−0.753245	+	0.753245i	−0.975083	−	0.221838i	$-0.928794\pi$
$5$	−1.68431	+	1.68431i	−0.753245	+	0.753245i	0.221838	+	0.975083i	$0.428794\pi$
$6$	1.39288	+	2.99173i	0.568641	+	1.22137i
$7$	−0.258819	−	0.965926i	−0.0978244	−	0.365086i
$7$	−0.258819	−	0.965926i	−0.0978244	−	0.365086i
$8$	0.498237	+	0.498237i	0.176153	+	0.176153i
$9$	−0.524491	+	2.95380i	−0.174830	+	0.984599i
$10$	3.93035	−	2.26919i	1.24289	−	0.717581i
$11$	0.313767	−	1.17099i	0.0946043	−	0.353068i	−0.902355	−	0.430994i	$-0.858163\pi$
$11$	0.313767	−	1.17099i	0.0946043	−	0.353068i	0.996959	+	0.0779259i	$0.0248297\pi$
$12$	−0.488637	−	2.78096i	−0.141057	−	0.802793i
$13$	0.415331	+	3.58155i	0.115192	+	0.993343i
$13$	0.415331	+	3.58155i	0.115192	+	0.993343i
$14$			1.90530i			0.509214i
$15$	4.10978	+	0.362045i	1.06114	+	0.0934796i
$16$	−2.30143	−	3.98620i	−0.575359	−	0.996550i
$17$	−0.202536	+	0.350803i	−0.0491222	+	0.0850821i	−0.889541	−	0.456855i	$-0.848976\pi$
$17$	−0.202536	+	0.350803i	−0.0491222	+	0.0850821i	0.840419	+	0.541937i	$0.182309\pi$
$18$	2.42187	−	5.17747i	0.570839	−	1.22034i
$19$	7.65849	−	2.05209i	1.75698	−	0.470781i	0.770885	−	0.636975i	$-0.219815\pi$
$19$	7.65849	−	2.05209i	1.75698	−	0.470781i	0.986093	+	0.166194i	$0.0531478\pi$
$20$	−3.75074	+	1.00501i	−0.838690	+	0.224726i
$21$	−0.994315	+	1.41822i	−0.216977	+	0.309480i
$22$	−1.15490	+	2.00035i	−0.246226	+	0.426476i
$23$	−3.55196	−	6.15217i	−0.740635	−	1.28282i	−0.952207	−	0.305455i	$-0.901192\pi$
$23$	−3.55196	−	6.15217i	−0.740635	−	1.28282i	0.211572	−	0.977362i	$-0.432142\pi$
$24$	0.107097	−	1.21572i	0.0218611	−	0.248157i
$25$		−	0.673785i		−	0.134757i
$26$	1.00180	−	6.79623i	0.196469	−	1.33285i
$27$	4.50467	−	2.58997i	0.866924	−	0.498440i
$28$	0.421923	−	1.57464i	0.0797359	−	0.297578i
$29$	5.97296	−	3.44849i	1.10915	−	0.640369i	0.170542	−	0.985350i	$-0.445448\pi$
$29$	5.97296	−	3.44849i	1.10915	−	0.640369i	0.938609	+	0.344982i	$0.112115\pi$
$30$	−7.38503	−	2.69295i	−1.34832	−	0.491664i
$31$	4.03416	+	4.03416i	0.724556	+	0.724556i	0.969530	−	0.244974i	$-0.0787793\pi$
$31$	4.03416	+	4.03416i	0.724556	+	0.724556i	−0.244974	+	0.969530i	$0.578779\pi$
$32$	1.90507	+	7.10983i	0.336773	+	1.25685i
$33$	−1.90357	+	0.886258i	−0.331369	+	0.154278i
$34$	0.545735	−	0.545735i	0.0935927	−	0.0935927i
$35$	2.06285	+	1.19099i	0.348685	+	0.201313i
$36$	−3.14808	+	3.74260i	−0.524680	+	0.623767i
$37$	−1.59241	−	0.426686i	−0.261791	−	0.0701468i	0.125536	−	0.992089i	$-0.459935\pi$
$37$	−1.59241	−	0.426686i	−0.261791	−	0.0701468i	−0.387327	+	0.921942i	$0.626602\pi$
$38$	−15.1065			−2.45060
$39$	4.29242	−	4.53598i	0.687337	−	0.726339i
$40$	−1.67837			−0.265373
$41$	11.4499	+	3.06798i	1.78817	+	0.479138i	0.992033	−	0.125979i	$-0.0402073\pi$
$41$	11.4499	+	3.06798i	1.78817	+	0.479138i	0.796136	+	0.605118i	$0.206874\pi$
$42$	2.52928	−	2.11973i	0.390277	−	0.327082i
$43$	−1.58218	−	0.913473i	−0.241280	−	0.139303i	0.374485	−	0.927233i	$-0.377820\pi$
$43$	−1.58218	−	0.913473i	−0.241280	−	0.139303i	−0.615765	+	0.787930i	$0.711153\pi$
$44$	1.39744	−	1.39744i	0.210672	−	0.210672i
$45$	−4.09170	−	5.85851i	−0.609954	−	0.873334i
$46$	3.50315	+	13.0739i	0.516511	+	1.92765i
$47$	7.59520	+	7.59520i	1.10787	+	1.10787i	0.993430	+	0.114444i	$0.0365086\pi$
$47$	7.59520	+	7.59520i	1.10787	+	1.10787i	0.114444	+	0.993430i	$0.463491\pi$
$48$	−2.73122	+	7.48997i	−0.394217	+	1.08108i
$49$	−0.866025	+	0.500000i	−0.123718	+	0.0714286i
$50$	−0.332263	+	1.24002i	−0.0469891	+	0.175366i
$51$	0.691019	−	0.121418i	0.0967621	−	0.0170019i
$52$	−2.33294	+	5.39489i	−0.323520	+	0.748137i
$53$			0.378791i			0.0520309i	0.999662	+	0.0260155i	$0.00828191\pi$
$53$			0.378791i			0.0520309i	−0.999662	+	0.0260155i	$0.991718\pi$
$54$	−9.56751	+	2.54515i	−1.30197	+	0.346351i
$55$	1.44383	+	2.50079i	0.194687	+	0.337207i
$56$	0.352307	−	0.610213i	0.0470789	−	0.0815431i
$57$	−11.2445	−	7.88358i	−1.48938	−	1.04421i
$58$	−12.6931	+	3.40110i	−1.66668	+	0.446586i
$59$	−8.14818	+	2.18330i	−1.06080	+	0.284241i	−0.746709	−	0.665151i	$-0.768367\pi$
$59$	−8.14818	+	2.18330i	−1.06080	+	0.284241i	−0.314094	+	0.949392i	$0.601701\pi$
$60$	5.50700	+	3.86097i	0.710951	+	0.498450i
$61$	−2.82748	+	4.89734i	−0.362022	+	0.627041i	−0.988294	−	0.152564i	$-0.951247\pi$
$61$	−2.82748	+	4.89734i	−0.362022	+	0.627041i	0.626271	+	0.779605i	$0.284580\pi$
$62$	−5.43503	−	9.41375i	−0.690250	−	1.19555i
$63$	2.98890	−	0.257879i	0.376565	−	0.0324897i
$64$		−	4.81852i		−	0.602315i
$65$	−6.73198	−	5.33289i	−0.834999	−	0.661463i
$66$	3.94033	−	0.692349i	0.485022	−	0.0852222i
$67$	−1.55285	+	5.79531i	−0.189711	+	0.708010i	0.803862	+	0.594816i	$0.202775\pi$
$67$	−1.55285	+	5.79531i	−0.189711	+	0.708010i	−0.993573	+	0.113194i	$0.963892\pi$
$68$	−0.571873	+	0.330171i	−0.0693497	+	0.0400391i
$69$	−4.21528	+	11.5598i	−0.507460	+	1.39163i
$70$	−3.20912	−	3.20912i	−0.383563	−	0.383563i
$71$	1.83259	+	6.83932i	0.217488	+	0.811678i	0.985276	+	0.170973i	$0.0546911\pi$
$71$	1.83259	+	6.83932i	0.217488	+	0.811678i	−0.767787	+	0.640705i	$0.778642\pi$
$72$	−1.73301	+	1.21037i	−0.204237	+	0.142643i
$73$	2.40085	−	2.40085i	0.280998	−	0.280998i	−0.552509	−	0.833507i	$-0.686329\pi$
$73$	2.40085	−	2.40085i	0.280998	−	0.280998i	0.833507	+	0.552509i	$0.186329\pi$
$74$	2.72024	+	1.57053i	0.316221	+	0.182571i
$75$	−0.894447	+	0.749615i	−0.103282	+	0.0865581i
$76$	12.4847	+	3.34528i	1.43210	+	0.383729i
$77$	−1.21230			−0.138155
$78$	−10.1365	+	6.23123i	−1.14773	+	0.705548i
$79$	7.86624			0.885021			0.442510	−	0.896763i	$-0.354088\pi$
$79$	7.86624			0.885021			0.442510	+	0.896763i	$0.354088\pi$
$80$	10.5903	+	2.83767i	1.18403	+	0.317261i
$81$	−8.44982	−	3.09848i	−0.938869	−	0.344275i
$82$	−19.5592	−	11.2925i	−2.15995	−	1.24705i
$83$	5.92256	−	5.92256i	0.650086	−	0.650086i	−0.302928	−	0.953013i	$-0.597964\pi$
$83$	5.92256	−	5.92256i	0.650086	−	0.650086i	0.953013	+	0.302928i	$0.0979641\pi$
$84$	−2.55973	+	1.19175i	−0.279290	+	0.130031i
$85$	−0.249727	−	0.931993i	−0.0270867	−	0.101089i
$86$	2.46136	+	2.46136i	0.265415	+	0.265415i
$87$	−11.2230	−	4.09248i	−1.20324	−	0.438760i
$88$	0.739762	−	0.427102i	0.0788589	−	0.0455292i
$89$	0.361109	−	1.34768i	0.0382775	−	0.142854i	−0.944143	−	0.329537i	$-0.893107\pi$
$89$	0.361109	−	1.34768i	0.0382775	−	0.142854i	0.982420	+	0.186684i	$0.0597740\pi$
$90$	4.64129	+	12.7996i	0.489235	+	1.34920i
$91$	3.35202	−	1.32815i	0.351387	−	0.139228i
$92$		−	11.5807i		−	1.20737i
$93$	0.867150	−	9.84351i	0.0899192	−	1.02072i
$94$	−10.2327	−	17.7235i	−1.05542	−	1.82804i
$95$	−9.44291	+	16.3556i	−0.968822	+	1.67805i
$96$	7.31879	−	10.4390i	0.746971	−	1.06542i
$97$	4.61523	−	1.23665i	0.468606	−	0.125563i	−0.0167864	−	0.999859i	$-0.505344\pi$
$97$	4.61523	−	1.23665i	0.468606	−	0.125563i	0.485392	+	0.874297i	$0.338677\pi$
$98$	1.84038	−	0.493129i	0.185907	−	0.0498135i
$99$	3.29431	+	1.54098i	0.331090	+	0.154874i
$100$	0.549196	−	0.951236i	0.0549196	−	0.0951236i
$101$	4.17153	+	7.22529i	0.415082	+	0.718944i	0.995437	−	0.0954201i	$-0.0304194\pi$
$101$	4.17153	+	7.22529i	0.415082	+	0.718944i	−0.580355	+	0.814364i	$0.697086\pi$
$102$	−1.33161	−	0.117307i	−0.131849	−	0.0116151i
$103$		−	9.20606i		−	0.907100i	−0.891231	−	0.453550i	$-0.850157\pi$
$103$		−	9.20606i		−	0.907100i	0.891231	−	0.453550i	$-0.149843\pi$
$104$	−1.57753	+	1.99139i	−0.154689	+	0.195272i
$105$	−0.713980	−	4.06345i	−0.0696773	−	0.396552i
$106$	0.186793	−	0.697120i	0.0181429	−	0.0677103i
$107$	7.44174	−	4.29649i	0.719420	−	0.415357i	−0.0951193	−	0.995466i	$-0.530323\pi$
$107$	7.44174	−	4.29649i	0.719420	−	0.415357i	0.814539	+	0.580109i	$0.196990\pi$
$108$	8.47067	+	0.0152543i	0.815090	+	0.00146785i
$109$	1.69810	+	1.69810i	0.162649	+	0.162649i	0.783739	−	0.621090i	$-0.213310\pi$
$109$	1.69810	+	1.69810i	0.162649	+	0.162649i	−0.621090	+	0.783739i	$0.713310\pi$
$110$	−1.42399	−	5.31441i	−0.135772	−	0.506709i
$111$	1.20521	+	2.58863i	0.114393	+	0.245702i
$112$	−3.25472	+	3.25472i	−0.307542	+	0.307542i
$113$	2.93476	+	1.69438i	0.276079	+	0.159394i	0.631647	−	0.775256i	$-0.282379\pi$
$113$	2.93476	+	1.69438i	0.276079	+	0.159394i	−0.355568	+	0.934650i	$0.615713\pi$
$114$	16.8066	+	20.0538i	1.57409	+	1.87821i
$115$	16.3447	+	4.37956i	1.52416	+	0.408396i
$116$	11.2433			1.04392
$117$	−10.7970	−	0.651687i	−0.998183	−	0.0602485i
$118$	16.0724			1.47959
$119$	0.391270	+	0.104840i	0.0358676	+	0.00961070i
$120$	1.86726	+	2.22803i	0.170457	+	0.203390i
$121$	8.25350	+	4.76516i	0.750318	+	0.433197i
$122$	7.61867	−	7.61867i	0.689762	−	0.689762i
$123$	−8.66575	−	18.6129i	−0.781364	−	1.67827i
$124$	2.40714	+	8.98355i	0.216167	+	0.806747i
$125$	−7.28668	−	7.28668i	−0.651740	−	0.651740i
$126$	−5.62788	−	0.999315i	−0.501371	−	0.0890261i
$127$	−9.26145	+	5.34710i	−0.821820	+	0.474478i	−0.851044	−	0.525095i	$-0.824030\pi$
$127$	−9.26145	+	5.34710i	−0.821820	+	0.474478i	0.0292234	+	0.999573i	$0.490697\pi$
$128$	1.43400	−	5.35175i	0.126749	−	0.473032i
$129$	0.547615	+	3.11662i	0.0482148	+	0.274403i
$130$	9.75961	+	13.1343i	0.855975	+	1.15195i
$131$			13.2796i			1.16025i	0.814529	+	0.580123i	$0.196995\pi$
$131$			13.2796i			1.16025i	−0.814529	+	0.580123i	$0.803005\pi$
$132$	−3.40980	−	0.300382i	−0.296785	−	0.0261449i
$133$	−3.96433	−	6.86641i	−0.343751	−	0.595393i
$134$	5.71567	−	9.89983i	0.493759	−	0.855215i
$135$	−3.22495	+	11.9496i	−0.277559	+	1.02845i
$136$	−0.275694	+	0.0738719i	−0.0236405	+	0.00633446i
$137$	7.96668	−	2.13467i	0.680640	−	0.182377i	0.0980968	−	0.995177i	$-0.468725\pi$
$137$	7.96668	−	2.13467i	0.680640	−	0.182377i	0.582543	+	0.812800i	$0.302058\pi$
$138$	13.4582	−	19.1957i	1.14564	−	1.63405i
$139$	5.41166	−	9.37327i	0.459011	−	0.795030i	−0.539898	−	0.841731i	$-0.681537\pi$
$139$	5.41166	−	9.37327i	0.459011	−	0.795030i	0.998909	+	0.0467000i	$0.0148705\pi$
$140$	1.94152	+	3.36282i	0.164089	+	0.284210i
$141$	1.63260	−	18.5326i	0.137490	−	1.56073i
$142$		−	13.4907i		−	1.13211i
$143$	4.32429	+	0.637421i	0.361615	+	0.0533038i
$144$	12.9815	−	4.70724i	1.08179	−	0.392270i
$145$	−4.25198	+	15.8686i	−0.353108	+	1.31782i
$146$	−5.60241	+	3.23455i	−0.463658	+	0.267693i
$147$	1.62724	+	0.593373i	0.134212	+	0.0489406i
$148$	−1.90035	−	1.90035i	−0.156208	−	0.156208i
$149$	−3.85285	−	14.3790i	−0.315638	−	1.17798i	−0.923394	−	0.383853i	$-0.874597\pi$
$149$	−3.85285	−	14.3790i	−0.315638	−	1.17798i	0.607756	−	0.794124i	$-0.292070\pi$
$150$	2.01578	−	0.938501i	0.164588	−	0.0766283i
$151$	3.06440	−	3.06440i	0.249378	−	0.249378i	−0.571338	−	0.820715i	$-0.693575\pi$
$151$	3.06440	−	3.06440i	0.249378	−	0.249378i	0.820715	+	0.571338i	$0.193575\pi$
$152$	4.83816	+	2.79332i	0.392427	+	0.226568i
$153$	−0.929971	−	0.782243i	−0.0751837	−	0.0632406i
$154$	2.23110	+	0.597821i	0.179787	+	0.0481738i
$155$	−13.5895			−1.09154
$156$	9.75719	−	2.90510i	0.781201	−	0.232594i
$157$	−18.2850			−1.45930			−0.729649	−	0.683822i	$-0.760317\pi$
$157$	−18.2850			−1.45930			−0.729649	+	0.683822i	$0.760317\pi$
$158$	−14.4769	−	3.87907i	−1.15172	−	0.308602i
$159$	0.502843	−	0.421421i	0.0398781	−	0.0334209i
$160$	−15.1839	−	8.76641i	−1.20039	−	0.693046i
$161$	−5.02323	+	5.02323i	−0.395886	+	0.395886i
$162$	14.0229	+	9.86924i	1.10175	+	0.775400i
$163$	−3.33402	−	12.4427i	−0.261141	−	0.974591i	−0.964570	−	0.263826i	$-0.915016\pi$
$163$	−3.33402	−	12.4427i	−0.261141	−	0.974591i	0.703430	−	0.710765i	$-0.251651\pi$
$164$	13.6640	+	13.6640i	1.06698	+	1.06698i
$165$	1.71346	−	4.69893i	0.133393	−	0.365811i
$166$	−13.8204	+	7.97919i	−1.07267	+	0.619305i
$167$	−3.89676	+	14.5429i	−0.301540	+	1.12536i	0.634343	+	0.773052i	$0.281271\pi$
$167$	−3.89676	+	14.5429i	−0.301540	+	1.12536i	−0.935883	+	0.352311i	$0.885396\pi$
$168$	−1.20201	+	0.211203i	−0.0927372	+	0.0162947i
$169$	−12.6550	+	2.97506i	−0.973462	+	0.228851i
$170$			1.83837i			0.140997i
$171$	2.04463	+	23.6979i	0.156357	+	1.81222i
$172$	−1.48913	−	2.57925i	−0.113545	−	0.196666i
$173$	−3.89121	+	6.73977i	−0.295843	+	0.512415i	−0.975181	−	0.221411i	$-0.928934\pi$
$173$	−3.89121	+	6.73977i	−0.295843	+	0.512415i	0.679338	+	0.733826i	$0.262267\pi$
$174$	18.6366	+	13.0661i	1.41283	+	0.990542i
$175$	−0.650826	+	0.174388i	−0.0491978	+	0.0131825i
$176$	−5.38993	+	1.44423i	−0.406281	+	0.108863i
$177$	11.9635	+	8.38766i	0.899234	+	0.630455i
$178$	−1.32916	+	2.30217i	−0.0996246	+	0.172555i
$179$	−12.1847	−	21.1045i	−0.910726	−	1.57742i	−0.813041	−	0.582206i	$-0.802190\pi$
$179$	−12.1847	−	21.1045i	−0.910726	−	1.57742i	−0.0976851	−	0.995217i	$-0.531144\pi$
$180$	−1.00136	−	11.6060i	−0.0746368	−	0.865062i
$181$		−	14.5903i		−	1.08449i	−0.840221	−	0.542244i	$-0.817575\pi$
$181$		−	14.5903i		−	1.08449i	0.840221	−	0.542244i	$-0.182425\pi$
$182$	−6.82394	+	0.791333i	−0.505824	+	0.0586575i
$183$	9.64690	−	1.69504i	0.713120	−	0.125301i
$184$	1.29552	−	4.83496i	0.0955072	−	0.356438i
$185$	3.40079	−	1.96344i	0.250031	−	0.144355i
$186$	−6.45001	+	17.6882i	−0.472937	+	1.29696i
$187$	0.347239	+	0.347239i	0.0253926	+	0.0253926i
$188$	4.53197	+	16.9135i	0.330528	+	1.23355i
$189$	−3.66761	−	3.68085i	−0.266780	−	0.267742i
$190$	25.4440	−	25.4440i	1.84590	−	1.84590i
$191$	8.63071	+	4.98294i	0.624496	+	0.360553i	0.778618	−	0.627499i	$-0.215921\pi$
$191$	8.63071	+	4.98294i	0.624496	+	0.360553i	−0.154121	+	0.988052i	$0.549255\pi$
$192$	−6.39656	+	5.36081i	−0.461632	+	0.386883i
$193$	1.34096	+	0.359309i	0.0965243	+	0.0258636i	0.306758	−	0.951788i	$-0.400756\pi$
$193$	1.34096	+	0.359309i	0.0965243	+	0.0258636i	−0.210234	+	0.977651i	$0.567422\pi$
$194$	−9.10362			−0.653602
$195$	0.410237	+	14.8697i	0.0293777	+	1.06484i
$196$	−1.63018			−0.116442
$197$	0.694195	+	0.186009i	0.0494594	+	0.0132526i	0.283464	−	0.958983i	$-0.408516\pi$
$197$	0.694195	+	0.186009i	0.0494594	+	0.0132526i	−0.234005	+	0.972236i	$0.575183\pi$
$198$	−5.30289	−	4.46051i	−0.376860	−	0.316995i
$199$	7.67315	+	4.43010i	0.543935	+	0.314041i	0.746672	−	0.665192i	$-0.231650\pi$
$199$	7.67315	+	4.43010i	0.543935	+	0.314041i	−0.202737	+	0.979233i	$0.564984\pi$
$200$	0.335704	−	0.335704i	0.0237379	−	0.0237379i
$201$	9.42086	−	4.38614i	0.664496	−	0.309374i
$202$	−4.11420	−	15.3544i	−0.289474	−	1.08033i
$203$	−4.87690	−	4.87690i	−0.342291	−	0.342291i
$204$	1.07453	+	0.391829i	0.0752324	+	0.0274335i
$205$	−24.4525	+	14.1177i	−1.70784	+	0.986021i
$206$	−4.53977	+	16.9427i	−0.316301	+	1.18045i
$207$	20.0352	−	7.26500i	1.39255	−	0.504953i
$208$	13.3209	−	9.89830i	0.923640	−	0.686323i
$209$		−	9.61192i		−	0.664870i
$210$	−0.689806	+	7.83038i	−0.0476011	+	0.540347i
$211$	−5.15604	−	8.93052i	−0.354956	−	0.614802i	0.632154	−	0.774843i	$-0.282171\pi$
$211$	−5.15604	−	8.93052i	−0.354956	−	0.614802i	−0.987110	+	0.160040i	$0.948838\pi$
$212$	−0.308749	+	0.534769i	−0.0212050	+	0.0367281i
$213$	7.04033	−	10.0418i	0.482396	−	0.688053i
$214$	−15.8144	+	4.23745i	−1.08105	+	0.289666i
$215$	4.20345	−	1.12631i	0.286673	−	0.0768137i
$216$	3.53481	+	0.953975i	0.240513	+	0.0649098i
$217$	2.85258	−	4.94081i	0.193646	−	0.335404i
$218$	−2.28778	−	3.96255i	−0.154948	−	0.268377i
$219$	−5.85817	−	0.516067i	−0.395858	−	0.0348726i
$220$			4.70743i			0.317375i
$221$	−1.34054	−	0.579693i	−0.0901743	−	0.0389944i
$222$	−0.941513	−	5.35839i	−0.0631902	−	0.359632i
$223$	−6.52641	+	24.3569i	−0.437040	+	1.63106i	0.299095	+	0.954223i	$0.403315\pi$
$223$	−6.52641	+	24.3569i	−0.437040	+	1.63106i	−0.736136	+	0.676834i	$0.763352\pi$
$224$	6.37450	−	3.68032i	0.425914	−	0.245902i
$225$	1.99022	+	0.353394i	0.132682	+	0.0235596i
$226$	−4.56552	−	4.56552i	−0.303694	−	0.303694i
$227$	2.43594	+	9.09107i	0.161679	+	0.603395i	0.998440	+	0.0558274i	$0.0177796\pi$
$227$	2.43594	+	9.09107i	0.161679	+	0.603395i	−0.836761	+	0.547568i	$0.815554\pi$
$228$	−9.44898	−	20.2952i	−0.625774	−	1.34408i
$229$	−7.20916	+	7.20916i	−0.476395	+	0.476395i	−0.903977	−	0.427582i	$-0.859366\pi$
$229$	−7.20916	+	7.20916i	−0.476395	+	0.476395i	0.427582	+	0.903977i	$0.359366\pi$
$230$	−27.9209	−	16.1201i	−1.84105	−	1.06293i
$231$	1.34874	+	1.60933i	0.0887405	+	0.105886i
$232$	4.69411	+	1.25778i	0.308184	+	0.0825775i
$233$	−11.0759			−0.725609			−0.362804	−	0.931865i	$-0.618181\pi$
$233$	−11.0759			−0.725609			−0.362804	+	0.931865i	$0.618181\pi$
$234$	19.5493	+	6.52367i	1.27797	+	0.426466i
$235$	−25.5853			−1.66900
$236$	−13.2830	−	3.55918i	−0.864652	−	0.231683i
$237$	−8.75153	−	10.4424i	−0.568473	−	0.678307i
$238$	−0.668386	−	0.385893i	−0.0433250	−	0.0250137i
$239$	−17.4165	+	17.4165i	−1.12658	+	1.12658i	−0.135848	+	0.990730i	$0.543376\pi$
$239$	−17.4165	+	17.4165i	−1.12658	+	1.12658i	−0.990730	+	0.135848i	$0.956624\pi$
$240$	−8.01520	−	17.2156i	−0.517379	−	1.11126i
$241$	0.217953	+	0.813411i	0.0140396	+	0.0523964i	0.972590	−	0.232526i	$-0.0746990\pi$
$241$	0.217953	+	0.813411i	0.0140396	+	0.0523964i	−0.958551	+	0.284922i	$0.908032\pi$
$242$	−12.8398	−	12.8398i	−0.825371	−	0.825371i
$243$	5.28758	+	14.6643i	0.339198	+	0.940715i
$244$	−7.98357	+	4.60932i	−0.511096	+	0.295081i
$245$	0.616499	−	2.30081i	0.0393867	−	0.146993i
$246$	6.76972	+	38.5282i	0.431622	+	2.45647i
$247$	10.5305	+	26.5770i	0.670037	+	1.69105i
$248$			4.01993i			0.255266i
$249$	−14.4513	−	1.27307i	−0.915813	−	0.0806773i
$250$	9.81700	+	17.0035i	0.620882	+	1.07540i
$251$	12.4451	−	21.5555i	0.785525	−	1.36057i	−0.143161	−	0.989699i	$-0.545727\pi$
$251$	12.4451	−	21.5555i	0.785525	−	1.36057i	0.928685	−	0.370869i	$-0.120940\pi$
$252$	4.42986	+	2.07216i	0.279055	+	0.130534i
$253$	−8.31865	+	2.22897i	−0.522989	+	0.140134i
$254$	19.6814	−	5.27362i	1.23492	−	0.330896i
$255$	−0.959384	+	1.36839i	−0.0600790	+	0.0856922i
$256$	−10.0967	+	17.4880i	−0.631045	+	1.09300i
$257$	2.96660	+	5.13831i	0.185052	+	0.320519i	0.943594	−	0.331105i	$-0.107421\pi$
$257$	2.96660	+	5.13831i	0.185052	+	0.320519i	−0.758542	+	0.651624i	$0.774088\pi$
$258$	0.529073	−	6.00581i	0.0329387	−	0.373906i
$259$			1.64859i			0.102438i
$260$	−5.15728	−	13.0160i	−0.319841	−	0.807221i
$261$	7.05337	+	19.4516i	0.436593	+	1.20402i
$262$	6.54856	−	24.4396i	0.404572	−	1.50988i
$263$	12.0679	−	6.96738i	0.744136	−	0.429627i	−0.0794354	−	0.996840i	$-0.525312\pi$
$263$	12.0679	−	6.96738i	0.744136	−	0.429627i	0.823571	+	0.567213i	$0.191978\pi$
$264$	−1.38999	−	0.506862i	−0.0855482	−	0.0311952i
$265$	−0.638000	−	0.638000i	−0.0391920	−	0.0391920i
$266$	3.90985	+	14.5917i	0.239728	+	0.894677i
$267$	−2.19079	+	1.01998i	−0.134074	+	0.0624217i
$268$	−6.91599	+	6.91599i	−0.422461	+	0.422461i
$269$	0.776875	+	0.448529i	0.0473669	+	0.0273473i	0.523496	−	0.852028i	$-0.324627\pi$
$269$	0.776875	+	0.448529i	0.0473669	+	0.0273473i	−0.476130	+	0.879375i	$0.657961\pi$
$270$	11.8278	−	20.4014i	0.719818	−	1.24159i
$271$	20.8889	+	5.59715i	1.26891	+	0.340003i	0.829612	−	0.558340i	$-0.188561\pi$
$271$	20.8889	+	5.59715i	1.26891	+	0.340003i	0.439295	+	0.898343i	$0.355228\pi$
$272$	1.86449			0.113052
$273$	−5.49238	−	2.97216i	−0.332414	−	0.179883i
$274$	−15.7144			−0.949342
$275$	−0.788998	−	0.211411i	−0.0475784	−	0.0127486i
$276$	−15.3733	+	12.8840i	−0.925365	+	0.775528i
$277$	1.30024	+	0.750692i	0.0781237	+	0.0451047i	0.538553	−	0.842592i	$-0.318971\pi$
$277$	1.30024	+	0.750692i	0.0781237	+	0.0451047i	−0.460429	+	0.887696i	$0.652305\pi$
$278$	−14.5818	+	14.5818i	−0.874556	+	0.874556i
$279$	−14.0320	+	9.80020i	−0.840071	+	0.586723i
$280$	0.434394	+	1.62118i	0.0259600	+	0.0968840i
$281$	−2.21026	−	2.21026i	−0.131853	−	0.131853i	0.638100	−	0.769953i	$-0.279721\pi$
$281$	−2.21026	−	2.21026i	−0.131853	−	0.131853i	−0.769953	+	0.638100i	$0.779721\pi$
$282$	−12.1436	+	33.3020i	−0.723139	+	1.98310i
$283$	−4.15612	+	2.39954i	−0.247056	+	0.142638i	−0.618415	−	0.785851i	$-0.712225\pi$
$283$	−4.15612	+	2.39954i	−0.247056	+	0.142638i	0.371360	+	0.928489i	$0.378892\pi$
$284$	−2.98746	+	11.1493i	−0.177273	+	0.661592i
$285$	32.2176	−	5.66090i	1.90841	−	0.335323i
$286$	−7.64402	−	3.30553i	−0.452000	−	0.195460i
$287$		−	11.8538i		−	0.699706i
$288$	−22.0002	+	1.89815i	−1.29637	+	0.111850i
$289$	8.41796	+	14.5803i	0.495174	+	0.857667i
$290$	15.6506	−	27.1076i	0.919032	−	1.59181i
$291$	−6.77629	−	4.75088i	−0.397233	−	0.278501i
$292$	5.34638	−	1.43256i	0.312873	−	0.0838341i
$293$	−14.1650	+	3.79550i	−0.827528	+	0.221736i	−0.647635	−	0.761951i	$-0.724242\pi$
$293$	−14.1650	+	3.79550i	−0.827528	+	0.221736i	−0.179893	+	0.983686i	$0.557575\pi$
$294$	−2.70213	−	1.89447i	−0.157592	−	0.110488i
$295$	10.0467	−	17.4014i	0.584942	−	1.01315i
$296$	−0.580808	−	1.00599i	−0.0337588	−	0.0584720i
$297$	−1.61942	−	6.08759i	−0.0939683	−	0.353238i
$298$			28.3629i			1.64302i
$299$	20.5591	−	15.2767i	1.18896	−	0.883475i
$300$	−1.87377	+	0.329236i	−0.108182	+	0.0190085i
$301$	−0.472848	+	1.76469i	−0.0272545	+	0.101715i
$302$	−7.15082	+	4.12853i	−0.411483	+	0.237570i
$303$	4.95054	−	13.5761i	0.284401	−	0.779929i
$304$	−25.8055	−	25.8055i	−1.48005	−	1.48005i
$305$	−3.48628	−	13.0110i	−0.199624	−	0.745007i
$306$	1.32576	+	1.89822i	0.0757884	+	0.108514i
$307$	7.99714	−	7.99714i	0.456421	−	0.456421i	−0.441058	−	0.897479i	$-0.645397\pi$
$307$	7.99714	−	7.99714i	0.456421	−	0.456421i	0.897479	+	0.441058i	$0.145397\pi$
$308$	−1.71150	−	0.988137i	−0.0975220	−	0.0563044i
$309$	−12.2210	+	10.2421i	−0.695229	+	0.582655i
$310$	25.0099	+	6.70139i	1.42047	+	0.380613i
$311$	−8.88181			−0.503641			−0.251821	−	0.967774i	$-0.581029\pi$
$311$	−8.88181			−0.503641			−0.251821	+	0.967774i	$0.581029\pi$
$312$	4.39863	−	0.121353i	0.249024	−	0.00687024i
$313$	9.83190			0.555732			0.277866	−	0.960620i	$-0.410373\pi$
$313$	9.83190			0.555732			0.277866	+	0.960620i	$0.410373\pi$
$314$	33.6513	+	9.01684i	1.89905	+	0.508850i
$315$	−4.59987	+	5.46857i	−0.259173	+	0.308119i
$316$	11.1054	+	6.41170i	0.624727	+	0.360686i
$317$	12.4429	−	12.4429i	0.698862	−	0.698862i	−0.265303	−	0.964165i	$-0.585472\pi$
$317$	12.4429	−	12.4429i	0.698862	−	0.698862i	0.964165	+	0.265303i	$0.0854721\pi$
$318$	−1.13324	+	0.527610i	−0.0635489	+	0.0295869i
$319$	−2.16404	−	8.07632i	−0.121163	−	0.452187i
$320$	8.11586	+	8.11586i	0.453691	+	0.453691i
$321$	−13.9828	−	5.09884i	−0.780445	−	0.284590i
$322$	11.7218	−	6.76756i	0.653228	−	0.377142i
$323$	−0.831242	+	3.10224i	−0.0462516	+	0.172613i
$324$	−9.40374	−	11.2617i	−0.522430	−	0.625653i
$325$	2.41319	−	0.279844i	0.133860	−	0.0155230i
$326$			24.5435i			1.35934i
$327$	0.365011	−	4.14344i	0.0201851	−	0.229133i
$328$	4.17616	+	7.23332i	0.230590	+	0.399394i
$329$	5.37062	−	9.30218i	0.296092	−	0.512846i
$330$	−5.47061	+	7.80286i	−0.301147	+	0.429534i
$331$	−14.5325	+	3.89398i	−0.798781	+	0.214033i	−0.635049	−	0.772472i	$-0.719020\pi$
$331$	−14.5325	+	3.89398i	−0.798781	+	0.214033i	−0.163732	+	0.986505i	$0.552353\pi$
$332$	13.1888	−	3.53393i	0.723829	−	0.193949i
$333$	2.09555	−	4.47987i	0.114835	−	0.245496i
$334$	14.3430	−	24.8429i	0.784817	−	1.35934i
$335$	−7.14561	−	12.3766i	−0.390406	−	0.676204i
$336$	7.94165	+	0.699608i	0.433252	+	0.0381667i
$337$		−	13.8619i		−	0.755104i	−0.925988	−	0.377552i	$-0.876766\pi$
$337$		−	13.8619i		−	0.755104i	0.925988	−	0.377552i	$-0.123234\pi$
$338$	24.7571	+	0.765299i	1.34661	+	0.0416268i
$339$	−1.01576	−	5.78095i	−0.0551685	−	0.313978i
$340$	0.407100	−	1.51932i	0.0220781	−	0.0823966i
$341$	5.98976	−	3.45819i	0.324364	−	0.187271i
$342$	7.92322	−	44.6215i	0.428439	−	2.41285i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	−0.333175	−	1.24343i	−0.0179636	−	0.0670410i
$345$	−12.3704	−	26.5700i	−0.666000	−	1.43048i
$346$	10.4849	−	10.4849i	0.563671	−	0.563671i
$347$	28.7779	+	16.6149i	1.54488	+	0.891935i	0.998520	+	0.0543815i	$0.0173187\pi$
$347$	28.7779	+	16.6149i	1.54488	+	0.891935i	0.546356	+	0.837553i	$0.316015\pi$
$348$	−12.5087	−	14.9255i	−0.670538	−	0.800090i
$349$	−29.6725	−	7.95071i	−1.58833	−	0.425592i	−0.646839	−	0.762627i	$-0.723909\pi$
$349$	−29.6725	−	7.95071i	−1.58833	−	0.425592i	−0.941492	+	0.337035i	$0.890576\pi$
$350$	1.28377			0.0686201
$351$	11.1470	+	15.0580i	0.594985	+	0.803737i
$352$	8.92332			0.475614
$353$	7.94279	+	2.12826i	0.422752	+	0.113276i	0.463922	−	0.885876i	$-0.346442\pi$
$353$	7.94279	+	2.12826i	0.422752	+	0.113276i	−0.0411698	+	0.999152i	$0.513108\pi$
$354$	−17.8813	−	21.3361i	−0.950379	−	1.13400i
$355$	−14.6062	−	8.43287i	−0.775215	−	0.447570i
$356$	1.60829	−	1.60829i	0.0852391	−	0.0852391i
$357$	−0.296129	−	0.636048i	−0.0156728	−	0.0336632i
$358$	12.0172	+	44.8490i	0.635131	+	2.37034i
$359$	−18.7210	−	18.7210i	−0.988056	−	0.988056i	0.0118733	−	0.999930i	$-0.496221\pi$
$359$	−18.7210	−	18.7210i	−0.988056	−	0.988056i	−0.999930	+	0.0118733i	$0.996221\pi$
$360$	0.880289	−	4.95756i	0.0463953	−	0.261286i
$361$	37.9869	−	21.9317i	1.99931	−	1.15430i
$362$	−7.19489	+	26.8517i	−0.378155	+	1.41129i
$363$	−2.85665	−	16.2579i	−0.149935	−	0.853321i
$364$	5.81488	+	0.857141i	0.304782	+	0.0449264i
$365$			8.08753i			0.423321i
$366$	−18.5899	−	1.63765i	−0.971708	−	0.0856012i
$367$	3.90108	+	6.75688i	0.203635	+	0.352706i	0.949697	−	0.313170i	$-0.101391\pi$
$367$	3.90108	+	6.75688i	0.203635	+	0.352706i	−0.746062	+	0.665876i	$0.768058\pi$
$368$	−16.3492	+	28.3177i	−0.852261	+	1.47616i
$369$	−15.0675	+	32.2114i	−0.784385	+	1.67686i
$370$	−7.22698	+	1.93646i	−0.375713	+	0.100672i
$371$	0.365884	−	0.0980383i	0.0189957	−	0.00508989i
$372$	9.24759	−	13.1901i	0.479465	−	0.683873i
$373$	5.90692	−	10.2311i	0.305849	−	0.529745i	−0.671601	−	0.740913i	$-0.734393\pi$
$373$	5.90692	−	10.2311i	0.305849	−	0.529745i	0.977450	+	0.211167i	$0.0677265\pi$
$374$	−0.467818	−	0.810285i	−0.0241903	−	0.0418989i
$375$	−1.56628	+	17.7798i	−0.0808826	+	0.918144i
$376$			7.56841i			0.390311i
$377$	14.8317	+	19.9602i	0.763871	+	1.02800i
$378$	4.93468	+	8.58277i	0.253812	+	0.441450i
$379$	9.37858	−	35.0013i	0.481745	−	1.79790i	−0.112544	−	0.993647i	$-0.535900\pi$
$379$	9.37858	−	35.0013i	0.481745	−	1.79790i	0.594290	−	0.804251i	$-0.297433\pi$
$380$	−26.6626	+	15.3937i	−1.36776	+	0.789679i
$381$	17.4020	+	6.34565i	0.891532	+	0.325097i
$382$	−13.4266	−	13.4266i	−0.686963	−	0.686963i
$383$	−3.90095	−	14.5586i	−0.199329	−	0.743908i	−0.991103	−	0.133094i	$-0.957509\pi$
$383$	−3.90095	−	14.5586i	−0.199329	−	0.743908i	0.791774	−	0.610814i	$-0.209158\pi$
$384$	−8.69981	+	4.05043i	−0.443960	+	0.206698i
$385$	2.04189	−	2.04189i	0.104064	−	0.104064i
$386$	−2.29069	−	1.32253i	−0.116593	−	0.0673151i
$387$	3.52805	−	4.19433i	0.179341	−	0.213210i
$388$	7.52367	+	2.01596i	0.381957	+	0.102345i
$389$	19.7437			1.00104			0.500522	−	0.865724i	$-0.333141\pi$
$389$	19.7437			1.00104			0.500522	+	0.865724i	$0.333141\pi$
$390$	6.57771	−	27.5683i	0.333075	−	1.39598i
$391$	2.87760			0.145526
$392$	−0.680604	−	0.182367i	−0.0343757	−	0.00921094i
$393$	17.6286	−	14.7742i	0.889247	−	0.745258i
$394$	−1.18586	−	0.684656i	−0.0597427	−	0.0344925i
$395$	−13.2492	+	13.2492i	−0.666638	+	0.666638i
$396$	3.39480	+	4.86069i	0.170595	+	0.244259i
$397$	7.90610	+	29.5060i	0.396796	+	1.48086i	0.818700	+	0.574221i	$0.194695\pi$
$397$	7.90610	+	29.5060i	0.396796	+	1.48086i	−0.421904	+	0.906640i	$0.638638\pi$
$398$	−11.9369	−	11.9369i	−0.598344	−	0.598344i
$399$	−4.70465	+	12.9018i	−0.235527	+	0.645898i
$400$	−2.68584	+	1.55067i	−0.134292	+	0.0775336i
$401$	−8.56375	+	31.9603i	−0.427653	+	1.59602i	0.330407	+	0.943839i	$0.392814\pi$
$401$	−8.56375	+	31.9603i	−0.427653	+	1.59602i	−0.758060	+	0.652185i	$0.773853\pi$
$402$	−19.5009	+	3.42647i	−0.972618	+	0.170897i
$403$	−12.7730	+	16.1241i	−0.636270	+	0.803196i
$404$			13.6007i			0.676660i
$405$	19.4509	−	9.01330i	0.966522	−	0.447875i
$406$	6.57042	+	11.3803i	0.326085	+	0.564795i
$407$	−0.999294	+	1.73083i	−0.0495331	+	0.0857939i
$408$	0.404786	+	0.283796i	0.0200399	+	0.0140500i
$409$	18.5869	−	4.98035i	0.919064	−	0.246263i	0.231879	−	0.972745i	$-0.425513\pi$
$409$	18.5869	−	4.98035i	0.919064	−	0.246263i	0.687185	+	0.726482i	$0.258846\pi$
$410$	51.9638	−	13.9237i	2.56631	−	0.687641i
$411$	−11.6970	−	8.20083i	−0.576973	−	0.404517i
$412$	7.50378	−	12.9969i	0.369685	−	0.640313i
$413$	4.21781	+	7.30546i	0.207545	+	0.359478i
$414$	−40.4551	+	3.49043i	−1.98826	+	0.171545i
$415$			19.9508i			0.979348i
$416$	−24.6730	+	9.77605i	−1.20969	+	0.479310i
$417$	−18.4637	+	3.24422i	−0.904171	+	0.158870i
$418$	−4.73992	+	17.6896i	−0.231837	+	0.865227i
$419$	10.0245	−	5.78767i	0.489731	−	0.282746i	−0.234732	−	0.972060i	$-0.575421\pi$
$419$	10.0245	−	5.78767i	0.489731	−	0.282746i	0.724463	+	0.689314i	$0.242088\pi$
$420$	2.30410	−	6.31865i	0.112428	−	0.308319i
$421$	21.9724	+	21.9724i	1.07087	+	1.07087i	0.997289	+	0.0735824i	$0.0234432\pi$
$421$	21.9724	+	21.9724i	1.07087	+	1.07087i	0.0735824	+	0.997289i	$0.476557\pi$
$422$	5.08518	+	18.9782i	0.247543	+	0.923842i
$423$	−26.4183	+	18.4511i	−1.28450	+	0.897121i
$424$	−0.188727	+	0.188727i	−0.00916541	+	0.00916541i
$425$	0.236366	+	0.136466i	0.0114654	+	0.00661956i
$426$	−17.9088	+	15.0090i	−0.867684	+	0.727187i
$427$	5.46228	+	1.46361i	0.264338	+	0.0708292i
$428$	14.0081			0.677108
$429$	−3.96479	−	6.44964i	−0.191422	−	0.311391i
$430$	−8.29137			−0.399845
$431$	−38.3132	−	10.2660i	−1.84548	−	0.494496i	−0.846219	−	0.532835i	$-0.821127\pi$
$431$	−38.3132	−	10.2660i	−1.84548	−	0.494496i	−0.999265	+	0.0383392i	$0.987793\pi$
$432$	−20.6913	−	11.9959i	−0.995513	−	0.577152i
$433$	−26.1277	−	15.0848i	−1.25562	−	0.724930i	−0.283397	−	0.959003i	$-0.591461\pi$
$433$	−26.1277	−	15.0848i	−1.25562	−	0.724930i	−0.972219	+	0.234072i	$0.924795\pi$
$434$	−7.68630	+	7.68630i	−0.368954	+	0.368954i
$435$	25.7961	−	12.0101i	1.23683	−	0.575838i
$436$	1.01324	+	3.78146i	0.0485254	+	0.181099i
$437$	−39.8274	−	39.8274i	−1.90520	−	1.90520i
$438$	10.5268	+	3.83859i	0.502989	+	0.183415i
$439$	−5.17775	+	2.98938i	−0.247121	+	0.142675i	−0.618445	−	0.785828i	$-0.712237\pi$
$439$	−5.17775	+	2.98938i	−0.247121	+	0.142675i	0.371325	+	0.928503i	$0.378904\pi$
$440$	−0.526616	+	1.96536i	−0.0251054	+	0.0936948i
$441$	−1.02268	−	2.82031i	−0.0486988	−	0.134300i
$442$	2.18124	+	1.72792i	0.103751	+	0.0821885i
$443$			17.0966i			0.812283i	0.913810	+	0.406141i	$0.133126\pi$
$443$			17.0966i			0.812283i	−0.913810	+	0.406141i	$0.866874\pi$
$444$	−0.408484	+	4.63693i	−0.0193858	+	0.220059i
$445$	1.66168	+	2.87812i	0.0787714	+	0.136436i
$446$	24.0222	−	41.6076i	1.13748	−	1.97018i
$447$	−14.8016	+	21.1120i	−0.700094	+	0.998561i
$448$	−4.65433	+	1.24712i	−0.219896	+	0.0589211i
$449$	25.4478	−	6.81871i	1.20095	−	0.321795i	0.397748	−	0.917495i	$-0.369792\pi$
$449$	25.4478	−	6.81871i	1.20095	−	0.321795i	0.803207	+	0.595700i	$0.203125\pi$
$450$	−3.48850	−	1.63182i	−0.164450	−	0.0769246i
$451$	7.18518	−	12.4451i	0.338337	−	0.586017i
$452$	2.76215	+	4.78419i	0.129921	+	0.225029i
$453$	−7.47726	−	0.658699i	−0.351313	−	0.0309484i
$454$		−	17.9323i		−	0.841604i
$455$	−3.40881	+	7.88284i	−0.159807	+	0.369553i
$456$	−1.67456	−	9.53033i	−0.0784183	−	0.446299i
$457$	2.05677	−	7.67597i	0.0962116	−	0.359067i	−0.900989	−	0.433842i	$-0.857157\pi$
$457$	2.05677	−	7.67597i	0.0962116	−	0.359067i	0.997200	+	0.0747759i	$0.0238241\pi$
$458$	16.8227	−	9.71257i	0.786071	−	0.453838i
$459$	−0.00379043	+	2.10481i	−0.000176922	+	0.0982442i
$460$	19.5054	+	19.5054i	0.909446	+	0.909446i
$461$	3.44573	+	12.8597i	0.160484	+	0.598934i	0.998573	+	0.0534007i	$0.0170061\pi$
$461$	3.44573	+	12.8597i	0.160484	+	0.598934i	−0.838089	+	0.545533i	$0.816327\pi$
$462$	−1.68859	−	3.62688i	−0.0785604	−	0.168738i
$463$	9.74682	−	9.74682i	0.452973	−	0.452973i	−0.443367	−	0.896340i	$-0.646216\pi$
$463$	9.74682	−	9.74682i	0.452973	−	0.452973i	0.896340	+	0.443367i	$0.146216\pi$
$464$	−27.4928	−	15.8730i	−1.27632	−	0.736883i
$465$	15.1189	+	18.0400i	0.701124	+	0.836587i
$466$	20.3840	+	5.46187i	0.944269	+	0.253016i
$467$	−29.5667			−1.36818			−0.684092	−	0.729396i	$-0.739801\pi$
$467$	−29.5667			−1.36818			−0.684092	+	0.729396i	$0.739801\pi$
$468$	−14.7118	−	9.72059i	−0.680054	−	0.449334i
$469$	5.99975			0.277043
$470$	47.0867	+	12.6169i	2.17195	+	0.581972i
$471$	20.3428	+	24.2732i	0.937348	+	1.11845i
$472$	−5.14752	−	2.97192i	−0.236934	−	0.136794i
$473$	−1.56611	+	1.56611i	−0.0720097	+	0.0720097i
$474$	10.9567	+	23.5336i	0.503259	+	1.08094i
$475$	−1.38266	−	5.16017i	−0.0634410	−	0.236765i
$476$	0.466932	+	0.466932i	0.0214018	+	0.0214018i
$477$	−1.11887	−	0.198672i	−0.0512296	−	0.00909658i
$478$	40.6415	−	23.4644i	1.85890	−	1.07324i
$479$	4.44967	−	16.6064i	0.203311	−	0.758766i	−0.786647	−	0.617403i	$-0.788185\pi$
$479$	4.44967	−	16.6064i	0.203311	−	0.758766i	0.989958	−	0.141363i	$-0.0451485\pi$
$480$	5.25535	+	29.9096i	0.239873	+	1.36518i
$481$	0.866818	−	5.88053i	0.0395235	−	0.268129i
$482$		−	1.60447i		−	0.0730814i
$483$	12.2569	+	1.07975i	0.557707	+	0.0491304i
$484$	7.76809	+	13.4547i	0.353095	+	0.611578i
$485$	−5.69057	+	9.85636i	−0.258396	+	0.447554i
$486$	−2.49977	−	29.5954i	−0.113392	−	1.34247i
$487$	19.1059	−	5.11940i	0.865769	−	0.231982i	0.201512	−	0.979486i	$-0.435415\pi$
$487$	19.1059	−	5.11940i	0.865769	−	0.231982i	0.664257	+	0.747504i	$0.268748\pi$
$488$	−3.84879	+	1.03128i	−0.174227	+	0.0466839i
$489$	−12.8084	+	18.2690i	−0.579218	+	0.826153i
$490$	−2.26919	+	3.93035i	−0.102512	+	0.177555i
$491$	1.17988	+	2.04362i	0.0532475	+	0.0922273i	0.891421	−	0.453177i	$-0.149709\pi$
$491$	1.17988	+	2.04362i	0.0532475	+	0.0922273i	−0.838173	+	0.545404i	$0.816376\pi$
$492$	2.93710	−	33.3407i	0.132415	−	1.50312i
$493$			2.79377i			0.125825i
$494$	−6.27420	−	54.1046i	−0.282290	−	2.43428i
$495$	−8.14411	+	2.95315i	−0.366051	+	0.132734i
$496$	6.79662	−	25.3653i	0.305177	−	1.13894i
$497$	6.13197	−	3.54029i	0.275056	−	0.158804i
$498$	25.9681	+	9.46928i	1.16366	+	0.424328i
$499$	13.3107	+	13.3107i	0.595867	+	0.595867i	0.939210	−	0.343343i	$-0.111559\pi$
$499$	13.3107	+	13.3107i	0.595867	+	0.595867i	−0.343343	+	0.939210i	$0.611559\pi$
$500$	−4.34788	−	16.2265i	−0.194443	−	0.725671i
$501$	23.6409	−	11.0067i	1.05620	−	0.491742i
$502$	−33.5333	+	33.5333i	−1.49666	+	1.49666i
$503$	17.0443	+	9.84053i	0.759967	+	0.438767i	0.829284	−	0.558827i	$-0.188749\pi$
$503$	17.0443	+	9.84053i	0.759967	+	0.438767i	−0.0693166	+	0.997595i	$0.522082\pi$
$504$	1.61766	+	1.36069i	0.0720564	+	0.0606101i
$505$	−19.1958	−	5.14349i	−0.854200	−	0.228882i
$506$	16.4087			0.729454
$507$	18.0286	+	13.4896i	0.800679	+	0.599093i
$508$	−17.4335			−0.773487
$509$	−28.3330	−	7.59181i	−1.25584	−	0.336501i	−0.431250	−	0.902233i	$-0.641927\pi$
$509$	−28.3330	−	7.59181i	−1.25584	−	0.336501i	−0.824590	+	0.565731i	$0.808594\pi$
$510$	2.44043	−	2.04527i	0.108064	−	0.0905660i
$511$	−2.94043	−	1.69766i	−0.130077	−	0.0750999i
$512$	19.3702	−	19.3702i	0.856049	−	0.856049i
$513$	29.1841	−	29.0792i	1.28851	−	1.28388i
$514$	−2.92584	−	10.9194i	−0.129053	−	0.481633i
$515$	15.5058	+	15.5058i	0.683269	+	0.683269i
$516$	−1.76722	+	4.84634i	−0.0777974	+	0.213348i
$517$	11.2771	−	6.51081i	0.495964	−	0.286345i
$518$	0.812967	−	3.03403i	0.0357197	−	0.133308i
$519$	13.2762	−	2.33273i	0.582759	−	0.102395i
$520$	−0.697079	−	6.01116i	−0.0305689	−	0.263607i
$521$		−	1.90472i		−	0.0834473i	−0.999129	−	0.0417236i	$-0.986715\pi$
$521$		−	1.90472i		−	0.0834473i	0.999129	−	0.0417236i	$-0.0132849\pi$
$522$	−3.38875	−	39.2766i	−0.148322	−	1.71909i
$523$	−20.0890	−	34.7951i	−0.878430	−	1.52148i	−0.853064	−	0.521807i	$-0.825258\pi$
$523$	−20.0890	−	34.7951i	−0.878430	−	1.52148i	−0.0253660	−	0.999678i	$-0.508075\pi$
$524$	−10.8241	+	18.7479i	−0.472853	+	0.819006i
$525$	0.955573	+	0.669954i	0.0417046	+	0.0292392i
$526$	−25.6453	+	6.87163i	−1.11819	+	0.299617i
$527$	−2.23226	+	0.598131i	−0.0972386	+	0.0260550i
$528$	7.91374	+	5.54834i	0.344401	+	0.241461i
$529$	−13.7328	+	23.7860i	−0.597080	+	1.03417i
$530$	0.859548	+	1.48878i	0.0373364	+	0.0646685i
$531$	−2.17537	−	25.2132i	−0.0944030	−	1.09416i
$532$		−	12.9252i		−	0.560376i
$533$	−6.23264	+	42.2825i	−0.269966	+	1.83146i
$534$	4.53487	−	0.796813i	0.196243	−	0.0344815i
$535$	−5.29756	+	19.7708i	−0.229034	+	0.854765i
$536$	−3.66112	+	2.11375i	−0.158136	+	0.0913001i
$537$	−14.4601	+	39.6548i	−0.624001	+	1.71123i
$538$	−1.20856	−	1.20856i	−0.0521049	−	0.0521049i
$539$	0.313767	+	1.17099i	0.0135149	+	0.0504383i
$540$	−14.2929	+	14.2415i	−0.615069	+	0.612857i
$541$	−30.4164	+	30.4164i	−1.30770	+	1.30770i	−0.384632	+	0.923070i	$0.625672\pi$
$541$	−30.4164	+	30.4164i	−1.30770	+	1.30770i	−0.923070	+	0.384632i	$0.874328\pi$
$542$	−35.6834	−	20.6018i	−1.53273	−	0.884923i
$543$	−19.3685	+	16.2323i	−0.831184	+	0.696596i
$544$	−2.87999	−	0.771692i	−0.123479	−	0.0330860i
$545$	−5.72026			−0.245029
$546$	8.64243	+	8.17836i	0.369862	+	0.350002i
$547$	−19.0332			−0.813802			−0.406901	−	0.913472i	$-0.633391\pi$
$547$	−19.0332			−0.813802			−0.406901	+	0.913472i	$0.633391\pi$
$548$	12.9872	+	3.47990i	0.554784	+	0.148654i
$549$	−12.9828	−	10.9204i	−0.554091	−	0.466072i
$550$	1.34780	+	0.778155i	0.0574706	+	0.0331807i
$551$	38.6673	−	38.6673i	1.64728	−	1.64728i
$552$	−7.85971	+	3.65930i	−0.334531	+	0.155750i
$553$	−2.03593	−	7.59820i	−0.0865766	−	0.323108i
$554$	−2.02275	−	2.02275i	−0.0859382	−	0.0859382i
$555$	−6.38999	−	2.33011i	−0.271240	−	0.0989077i
$556$	15.2802	−	8.82200i	0.648023	−	0.374136i
$557$	−6.22582	+	23.2351i	−0.263797	+	0.984502i	0.699186	+	0.714940i	$0.253546\pi$
$557$	−6.22582	+	23.2351i	−0.263797	+	0.984502i	−0.962983	+	0.269563i	$0.913121\pi$
$558$	30.6569	−	11.1165i	1.29781	−	0.470601i
$559$	2.61452	−	6.04605i	0.110582	−	0.255721i
$560$		−	10.9639i		−	0.463309i
$561$	0.0746396	−	0.847276i	0.00315129	−	0.0357720i
$562$	2.97778	+	5.15767i	0.125610	+	0.217563i
$563$	3.60600	−	6.24578i	0.151975	−	0.263228i	−0.779978	−	0.625806i	$-0.784770\pi$
$563$	3.60600	−	6.24578i	0.151975	−	0.263228i	0.931953	+	0.362578i	$0.118103\pi$
$564$	17.4106	−	24.8332i	0.733120	−	1.04567i
$565$	−7.79689	+	2.08917i	−0.328018	+	0.0878921i
$566$	8.83213	−	2.36656i	0.371242	−	0.0994740i
$567$	−0.805927	+	8.96384i	−0.0338458	+	0.376446i
$568$	−2.49454	+	4.32066i	−0.104668	+	0.181291i
$569$	−4.81313	−	8.33658i	−0.201777	−	0.349488i	0.747324	−	0.664460i	$-0.231338\pi$
$569$	−4.81313	−	8.33658i	−0.201777	−	0.349488i	−0.949101	+	0.314972i	$0.898005\pi$
$570$	−62.0843	−	5.46923i	−2.60043	−	0.229081i
$571$		−	24.2313i		−	1.01405i	−0.861931	−	0.507025i	$-0.830745\pi$
$571$		−	24.2313i		−	1.01405i	0.861931	−	0.507025i	$-0.169255\pi$
$572$	5.58539	+	4.42459i	0.233537	+	0.185001i
$573$	−2.98721	−	17.0010i	−0.124792	−	0.710226i
$574$	−5.84544	+	21.8155i	−0.243984	+	0.910560i
$575$	−4.14524	+	2.39326i	−0.172869	+	0.0998057i
$576$	14.2329	+	2.52727i	0.593038	+	0.105303i
$577$	3.63464	+	3.63464i	0.151312	+	0.151312i	0.778704	−	0.627392i	$-0.215878\pi$
$577$	3.63464	+	3.63464i	0.151312	+	0.151312i	−0.627392	+	0.778704i	$0.715878\pi$
$578$	−8.30228	−	30.9845i	−0.345329	−	1.28879i
$579$	−1.01489	−	2.17986i	−0.0421776	−	0.0905921i
$580$	−18.9373	+	18.9373i	−0.786327	+	0.786327i
$581$	−7.25363	−	4.18788i	−0.300931	−	0.173743i
$582$	10.1282	+	12.0850i	0.419826	+	0.500940i
$583$	0.443562	+	0.118852i	0.0183704	+	0.00492235i
$584$	2.39238			0.0989974
$585$	19.2831	−	17.0878i	0.797259	−	0.706495i
$586$	27.9407			1.15422
$587$	−14.3382	−	3.84192i	−0.591803	−	0.158573i	−0.0495257	−	0.998773i	$-0.515771\pi$
$587$	−14.3382	−	3.84192i	−0.591803	−	0.158573i	−0.542277	+	0.840200i	$0.682438\pi$
$588$	1.81365	+	2.16406i	0.0747937	+	0.0892444i
$589$	39.1740	+	22.6171i	1.61414	+	0.931922i
$590$	−27.0709	+	27.0709i	−1.11449	+	1.11449i
$591$	−0.525397	−	1.12848i	−0.0216119	−	0.0464197i
$592$	1.96398	+	7.32967i	0.0807191	+	0.301248i
$593$	−20.8228	−	20.8228i	−0.855089	−	0.855089i	0.135666	−	0.990755i	$-0.456683\pi$
$593$	−20.8228	−	20.8228i	−0.855089	−	0.855089i	−0.990755	+	0.135666i	$0.956683\pi$
$594$	−0.0216138	+	12.0021i	−0.000886827	+	0.492451i
$595$	−0.835602	+	0.482435i	−0.0342563	+	0.0197779i
$596$	6.28086	−	23.4405i	0.257274	−	0.960159i
$597$	−2.65578	−	15.1148i	−0.108694	−	0.618606i
$598$	−45.3700	+	17.9767i	−1.85532	+	0.735122i
$599$		−	21.3335i		−	0.871665i	−0.900028	−	0.435832i	$-0.856454\pi$
$599$		−	21.3335i		−	0.871665i	0.900028	−	0.435832i	$-0.143546\pi$
$600$	−0.819132	−	0.0721603i	−0.0334409	−	0.00294593i
$601$	5.12815	+	8.88221i	0.209181	+	0.362313i	0.951457	−	0.307782i	$-0.0995867\pi$
$601$	5.12815	+	8.88221i	0.209181	+	0.362313i	−0.742275	+	0.670095i	$0.766253\pi$
$602$	1.74044	−	3.01454i	0.0709352	−	0.122863i
$603$	−16.3037	−	7.62639i	−0.663938	−	0.310570i
$604$	6.82403	−	1.82849i	0.277666	−	0.0744004i
$605$	−21.9274	+	5.87544i	−0.891477	+	0.238871i
$606$	−15.8057	+	22.5440i	−0.642062	+	0.915789i
$607$	16.5914	−	28.7371i	0.673422	−	1.16640i	−0.303505	−	0.952830i	$-0.598157\pi$
$607$	16.5914	−	28.7371i	0.673422	−	1.16640i	0.976927	−	0.213572i	$-0.0685097\pi$
$608$	29.1800	+	50.5412i	1.18340	+	2.04972i
$609$	−1.04830	+	11.8998i	−0.0424792	+	0.482206i
$610$			25.6644i			1.03912i
$611$	−24.0481	+	30.3571i	−0.972880	+	1.22812i
$612$	−0.675315	−	1.86237i	−0.0272980	−	0.0752817i
$613$	3.15498	−	11.7746i	0.127428	−	0.475570i	−0.872486	−	0.488639i	$-0.837494\pi$
$613$	3.15498	−	11.7746i	0.127428	−	0.475570i	0.999915	+	0.0130693i	$0.00416021\pi$
$614$	−18.6614	+	10.7742i	−0.753114	+	0.434810i
$615$	45.9457	+	16.7541i	1.85271	+	0.675590i
$616$	−0.604013	−	0.604013i	−0.0243364	−	0.0243364i
$617$	3.20991	+	11.9795i	0.129226	+	0.482278i	0.999955	−	0.00948517i	$-0.00301927\pi$
$617$	3.20991	+	11.9795i	0.129226	+	0.482278i	−0.870729	+	0.491763i	$0.836353\pi$
$618$	27.5420	−	12.8229i	1.10790	−	0.515814i
$619$	8.03568	−	8.03568i	0.322981	−	0.322981i	−0.526928	−	0.849910i	$-0.676656\pi$
$619$	8.03568	−	8.03568i	0.322981	−	0.322981i	0.849910	+	0.526928i	$0.176656\pi$
$620$	−19.1854	−	11.0767i	−0.770505	−	0.444851i
$621$	−31.9343	−	18.5141i	−1.28148	−	0.742944i
$622$	16.3459	+	4.37988i	0.655412	+	0.175617i
$623$	−1.39522			−0.0558982
$624$	−27.9601	−	6.67118i	−1.11930	−	0.267061i
$625$	27.9149			1.11660
$626$	−18.0944	−	4.84839i	−0.723200	−	0.193781i
$627$	−12.7598	+	10.6937i	−0.509577	+	0.427065i
$628$	−25.8143	−	14.9039i	−1.03010	−	0.594731i
$629$	0.472204	−	0.472204i	0.0188280	−	0.0188280i
$630$	11.1622	−	7.79593i	0.444714	−	0.310597i
$631$	10.0860	+	37.6415i	0.401518	+	1.49849i	0.810388	+	0.585894i	$0.199256\pi$
$631$	10.0860	+	37.6415i	0.401518	+	1.49849i	−0.408870	+	0.912593i	$0.634077\pi$
$632$	3.91925	+	3.91925i	0.155899	+	0.155899i
$633$	−6.11891	+	16.7802i	−0.243205	+	0.666954i
$634$	−29.0356	+	16.7637i	−1.15315	+	0.665772i
$635$	6.59297	−	24.6053i	0.261634	−	0.976431i
$636$	1.05340	−	0.185091i	0.0417701	−	0.00733934i
$637$	−2.15046	−	2.89405i	−0.0852044	−	0.114666i
$638$			15.9307i			0.630701i
$639$	−21.1631	+	1.82593i	−0.837200	+	0.0722329i
$640$	6.59870	+	11.4293i	0.260837	+	0.451782i
$641$	−17.7657	+	30.7711i	−0.701703	+	1.21538i	0.266166	+	0.963927i	$0.414243\pi$
$641$	−17.7657	+	30.7711i	−0.701703	+	1.21538i	−0.967868	+	0.251457i	$0.919090\pi$
$642$	23.2194	+	16.2792i	0.916395	+	0.642487i
$643$	4.68474	−	1.25527i	0.184748	−	0.0495031i	−0.165259	−	0.986250i	$-0.552846\pi$
$643$	4.68474	−	1.25527i	0.184748	−	0.0495031i	0.350007	+	0.936747i	$0.386179\pi$
$644$	−11.1861	+	2.99730i	−0.440794	+	0.118110i
$645$	−6.17169	−	4.32699i	−0.243010	−	0.170375i
$646$	3.05961	−	5.29940i	0.120379	−	0.208502i
$647$	15.7066	+	27.2046i	0.617489	+	1.06952i	0.989942	+	0.141472i	$0.0451835\pi$
$647$	15.7066	+	27.2046i	0.617489	+	1.06952i	−0.372453	+	0.928051i	$0.621483\pi$
$648$	−2.66623	−	5.75378i	−0.104740	−	0.226030i
$649$			10.2265i			0.401426i
$650$	−4.57920	−	0.674996i	−0.179611	−	0.0264755i
$651$	−9.73253	+	1.71008i	−0.381448	+	0.0670235i
$652$	5.43507	−	20.2839i	0.212854	−	0.794381i
$653$	22.9127	−	13.2287i	0.896643	−	0.517677i	0.0205337	−	0.999789i	$-0.493463\pi$
$653$	22.9127	−	13.2287i	0.896643	−	0.517677i	0.876110	+	0.482112i	$0.160130\pi$
$654$	−2.71501	+	7.44552i	−0.106165	+	0.291143i
$655$	−22.3670	−	22.3670i	−0.873949	−	0.873949i
$656$	−14.1215	−	52.7022i	−0.551353	−	2.05768i
$657$	5.83239	+	8.35084i	0.227543	+	0.325797i
$658$	−14.4712	+	14.4712i	−0.564145	+	0.564145i
$659$	−16.7845	−	9.69055i	−0.653833	−	0.377490i	0.136090	−	0.990696i	$-0.456546\pi$
$659$	−16.7845	−	9.69055i	−0.653833	−	0.377490i	−0.789923	+	0.613206i	$0.789880\pi$
$660$	6.24909	−	5.23722i	0.243246	−	0.203859i
$661$	−14.9627	−	4.00925i	−0.581983	−	0.155942i	−0.0441962	−	0.999023i	$-0.514073\pi$
$661$	−14.9627	−	4.00925i	−0.581983	−	0.155942i	−0.537786	+	0.843081i	$0.680739\pi$
$662$	28.6657			1.11412
$663$	0.721866	+	2.42449i	0.0280349	+	0.0941595i
$664$	5.90168			0.229029
$665$	18.2423	+	4.88801i	0.707406	+	0.189549i
$666$	−6.06577	+	7.21130i	−0.235044	+	0.279432i
$667$	−42.4314	−	24.4978i	−1.64295	−	0.948559i
$668$	−17.3552	+	17.3552i	−0.671491	+	0.671491i
$669$	39.5946	−	18.4343i	1.53081	−	0.712712i
$670$	7.04741	+	26.3013i	0.272265	+	1.01611i
$671$	4.84759	+	4.84759i	0.187139	+	0.187139i
$672$	−11.9775	−	4.36761i	−0.462043	−	0.168484i
$673$	12.6667	−	7.31311i	0.488264	−	0.281900i	−0.235590	−	0.971853i	$-0.575702\pi$
$673$	12.6667	−	7.31311i	0.488264	−	0.281900i	0.723854	+	0.689953i	$0.242369\pi$
$674$	−6.83569	+	25.5111i	−0.263301	+	0.982652i
$675$	−1.74508	−	3.03518i	−0.0671682	−	0.116824i
$676$	−20.2910	−	6.11485i	−0.780424	−	0.235187i
$677$			21.2376i			0.816227i	0.912931	+	0.408113i	$0.133813\pi$
$677$			21.2376i			0.816227i	−0.912931	+	0.408113i	$0.866187\pi$
$678$	−0.981368	+	11.1401i	−0.0376892	+	0.427832i
$679$	−2.38902	−	4.13790i	−0.0916822	−	0.158798i
$680$	0.339930	−	0.588776i	0.0130357	−	0.0225785i
$681$	9.35826	−	13.3479i	0.358609	−	0.511494i
$682$	−12.7288	+	3.41067i	−0.487410	+	0.130601i
$683$	−5.63183	+	1.50904i	−0.215496	+	0.0577419i	−0.364952	−	0.931026i	$-0.618914\pi$
$683$	−5.63183	+	1.50904i	−0.215496	+	0.0577419i	0.149456	+	0.988768i	$0.452248\pi$
$684$	−16.4294	+	35.1228i	−0.628194	+	1.34295i
$685$	−9.82291	+	17.0138i	−0.375314	+	0.650063i
$686$	−0.952652	−	1.65004i	−0.0363724	−	0.0629989i
$687$	17.5906	+	1.54962i	0.671125	+	0.0591218i
$688$			8.40919i			0.320597i
$689$	−1.35666	+	0.157324i	−0.0516846	+	0.00599355i
$690$	9.66381	+	54.9992i	0.367895	+	2.09379i
$691$	10.3359	−	38.5740i	0.393195	−	1.46742i	−0.431639	−	0.902047i	$-0.642064\pi$
$691$	10.3359	−	38.5740i	0.393195	−	1.46742i	0.824833	−	0.565376i	$-0.191269\pi$
$692$	−10.9871	+	6.34338i	−0.417665	+	0.241139i
$693$	0.635842	−	3.58089i	0.0241536	−	0.136027i
$694$	−44.7690	−	44.7690i	−1.69941	−	1.69941i
$695$	6.67257	+	24.9024i	0.253105	+	0.944601i
$696$	−3.55270	−	7.63076i	−0.134665	−	0.289243i
$697$	−3.39527	+	3.39527i	−0.128605	+	0.128605i
$698$	50.6880	+	29.2647i	1.91857	+	1.10769i
$699$	12.3225	+	14.7033i	0.466079	+	0.556128i
$700$	−1.06097	−	0.284285i	−0.0401007	−	0.0107450i
$701$	−49.1141			−1.85501			−0.927506	−	0.373807i	$-0.878052\pi$
$701$	−49.1141			−1.85501			−0.927506	+	0.373807i	$0.878052\pi$
$702$	−13.0893	−	33.2094i	−0.494022	−	1.25341i
$703$	−13.0711			−0.492985
$704$	−5.64245	−	1.51189i	−0.212658	−	0.0569815i
$705$	28.4648	+	33.9644i	1.07205	+	1.27917i
$706$	−13.5683	−	7.83364i	−0.510648	−	0.294823i
$707$	5.89943	−	5.89943i	0.221871	−	0.221871i
$708$	10.0532	+	21.5929i	0.377821	+	0.811512i
$709$	−4.21754	−	15.7401i	−0.158393	−	0.591131i	−0.998791	−	0.0491608i	$-0.984345\pi$
$709$	−4.21754	−	15.7401i	−0.158393	−	0.591131i	0.840398	−	0.541970i	$-0.182321\pi$
$710$	22.7224	+	22.7224i	0.852758	+	0.852758i
$711$	−4.12577	+	23.2353i	−0.154728	+	0.871390i
$712$	0.851380	−	0.491544i	0.0319068	−	0.0184214i
$713$	10.4897	−	39.1480i	0.392842	−	1.46610i
$714$	0.231338	+	1.31660i	0.00865759	+	0.0492726i
$715$	−8.35705	+	6.20982i	−0.312536	+	0.232234i
$716$		−	39.7265i		−	1.48465i
$717$	42.4969	+	3.74370i	1.58708	+	0.139811i
$718$	25.2219	+	43.6857i	0.941274	+	1.63033i
$719$	−8.87193	+	15.3666i	−0.330867	+	0.573078i	−0.982682	−	0.185299i	$-0.940674\pi$
$719$	−8.87193	+	15.3666i	−0.330867	+	0.573078i	0.651815	+	0.758378i	$0.274008\pi$
$720$	−13.9364	+	29.7933i	−0.519379	+	1.11033i
$721$	−8.89237	+	2.38270i	−0.331169	+	0.0887365i
$722$	−80.7256	+	21.6304i	−3.00430	+	0.804999i
$723$	0.837318	−	1.19429i	0.0311402	−	0.0444160i
$724$	11.8924	−	20.5983i	0.441978	−	0.765529i
$725$	−2.32354	−	4.02449i	−0.0862941	−	0.149466i
$726$	−2.75993	+	31.3295i	−0.102431	+	1.16275i
$727$		−	33.9659i		−	1.25972i	−0.776707	−	0.629862i	$-0.783111\pi$
$727$		−	33.9659i		−	1.25972i	0.776707	−	0.629862i	$-0.216889\pi$
$728$	2.33183	+	1.00836i	0.0864234	+	0.0373724i
$729$	13.5841	−	23.3339i	0.503116	−	0.864219i
$730$	3.98820	−	14.8842i	0.147610	−	0.550887i
$731$	0.640897	−	0.370022i	0.0237044	−	0.0136858i
$732$	15.0009	+	5.47009i	0.554450	+	0.202180i
$733$	26.0012	+	26.0012i	0.960378	+	0.960378i	0.999244	−	0.0388665i	$-0.0123747\pi$
$733$	26.0012	+	26.0012i	0.960378	+	0.960378i	−0.0388665	+	0.999244i	$0.512375\pi$
$734$	−3.84747	−	14.3590i	−0.142013	−	0.529999i
$735$	−3.74019	+	1.74135i	−0.137959	+	0.0642306i
$736$	36.9742	−	36.9742i	1.36289	−	1.36289i
$737$	6.29904	+	3.63675i	0.232028	+	0.133961i
$738$	43.6144	−	51.8511i	1.60547	−	1.90867i
$739$	−10.4676	−	2.80478i	−0.385056	−	0.103175i	0.0610978	−	0.998132i	$-0.480540\pi$
$739$	−10.4676	−	2.80478i	−0.385056	−	0.103175i	−0.446154	+	0.894956i	$0.647207\pi$
$740$	6.40155			0.235326
$741$	23.5652	−	43.5472i	0.865690	−	1.59975i
$742$	−0.721712			−0.0264949
$743$	4.24251	+	1.13678i	0.155643	+	0.0417043i	0.335799	−	0.941934i	$-0.390994\pi$
$743$	4.24251	+	1.13678i	0.155643	+	0.0417043i	−0.180156	+	0.983638i	$0.557660\pi$
$744$	5.33644	−	4.47235i	0.195643	−	0.163964i
$745$	30.7081	+	17.7293i	1.12506	+	0.649553i
$746$	−15.9162	+	15.9162i	−0.582735	+	0.582735i
$747$	14.3877	+	20.6004i	0.526419	+	0.753728i
$748$	0.207193	+	0.773256i	0.00757574	+	0.0282730i
$749$	−6.07615	−	6.07615i	−0.222018	−	0.222018i
$750$	11.6503	−	31.9492i	0.425408	−	1.16662i
$751$	6.90441	−	3.98626i	0.251945	−	0.145461i	−0.368709	−	0.929545i	$-0.620200\pi$
$751$	6.90441	−	3.98626i	0.251945	−	0.145461i	0.620655	+	0.784084i	$0.286867\pi$
$752$	12.7961	−	47.7558i	0.466627	−	1.74148i
$753$	−42.4605	+	7.46065i	−1.54734	+	0.271881i
$754$	−17.4530	−	44.0483i	−0.635603	−	1.60415i
$755$			10.3228i			0.375685i
$756$	−2.17764	−	8.18598i	−0.0791998	−	0.297721i
$757$	3.40444	+	5.89667i	0.123737	+	0.214318i	0.921238	−	0.388999i	$-0.127179\pi$
$757$	3.40444	+	5.89667i	0.123737	+	0.214318i	−0.797502	+	0.603317i	$0.793846\pi$
$758$	−34.5203	+	59.7910i	−1.25384	+	2.17171i
$759$	12.2138	+	8.56314i	0.443333	+	0.310822i
$760$	−12.8538	+	3.44415i	−0.466255	+	0.124933i
$761$	15.9847	−	4.28310i	0.579446	−	0.155262i	0.0428209	−	0.999083i	$-0.486366\pi$
$761$	15.9847	−	4.28310i	0.579446	−	0.155262i	0.536625	+	0.843821i	$0.319699\pi$
$762$	−28.8971	−	20.2599i	−1.04683	−	0.733937i
$763$	1.20074	−	2.07974i	0.0434697	−	0.0752918i
$764$	8.12311	+	14.0696i	0.293884	+	0.509022i
$765$	2.88389	−	0.248820i	0.104267	−	0.00899609i
$766$			28.7170i			1.03759i
$767$	−11.2038	−	28.2763i	−0.404545	−	1.02100i
$768$	34.4483	−	6.05285i	1.24305	−	0.218414i
$769$	−11.1169	+	41.4887i	−0.400885	+	1.49612i	0.410636	+	0.911799i	$0.365307\pi$
$769$	−11.1169	+	41.4887i	−0.400885	+	1.49612i	−0.811521	+	0.584323i	$0.801360\pi$
$770$	−4.76477	+	2.75094i	−0.171710	+	0.0991371i
$771$	3.52061	−	9.65475i	0.126792	−	0.347707i
$772$	1.60027	+	1.60027i	0.0575950	+	0.0575950i
$773$	9.49602	+	35.4396i	0.341548	+	1.27467i	0.896593	+	0.442855i	$0.146034\pi$
$773$	9.49602	+	35.4396i	0.341548	+	1.27467i	−0.555045	+	0.831820i	$0.687299\pi$
$774$	−8.56131	+	5.97939i	−0.307730	+	0.214925i
$775$	2.71815	−	2.71815i	0.0976390	−	0.0976390i
$776$	2.91562	+	1.68333i	0.104665	+	0.0604282i
$777$	2.18849	−	1.83413i	0.0785118	−	0.0657990i
$778$	−36.3359	−	9.73617i	−1.30271	−	0.349059i
$779$	93.9844			3.36734
$780$	−11.5410	+	21.3272i	−0.413236	+	0.763636i
$781$	8.58381			0.307153
$782$	−5.29588	−	1.41903i	−0.189380	−	0.0507443i
$783$	17.9747	−	31.0041i	0.642365	−	1.10800i
$784$	3.98620	+	2.30143i	0.142364	+	0.0821941i
$785$	30.7975	−	30.7975i	1.09921	−	1.09921i
$786$	−39.7290	+	18.4969i	−1.41709	+	0.659763i
$787$	0.942915	+	3.51901i	0.0336113	+	0.125439i	0.980693	−	0.195553i	$-0.0626503\pi$
$787$	0.942915	+	3.51901i	0.0336113	+	0.125439i	−0.947082	+	0.320992i	$0.895984\pi$
$788$	0.828437	+	0.828437i	0.0295118	+	0.0295118i
$789$	−22.6752	−	8.26851i	−0.807258	−	0.294367i
$790$	30.9171	−	17.8500i	1.09998	−	0.635074i
$791$	0.877077	−	3.27329i	0.0311853	−	0.116385i
$792$	0.873573	+	2.40912i	0.0310411	+	0.0856043i
$793$	−18.7144	−	8.09275i	−0.664569	−	0.287382i
$794$		−	58.2010i		−	2.06548i
$795$	−0.137139	+	1.55675i	−0.00486383	+	0.0552121i
$796$	7.22187	+	12.5086i	0.255972	+	0.443357i
$797$	22.7531	−	39.4095i	0.805956	−	1.39596i	−0.109688	−	0.993966i	$-0.534985\pi$
$797$	22.7531	−	39.4095i	0.805956	−	1.39596i	0.915644	−	0.401990i	$-0.131681\pi$
$798$	15.0206	−	21.4243i	0.531724	−	0.758411i
$799$	−4.20272	+	1.12611i	−0.148681	+	0.0398391i
$800$	4.79050	−	1.28361i	0.169370	−	0.0453825i
$801$	3.79137	+	1.77349i	0.133961	+	0.0626631i
$802$	31.5211	−	54.5962i	1.11305	−	1.92786i
$803$	−2.05807	−	3.56468i	−0.0726278	−	0.125795i
$804$	16.8753	+	1.48660i	0.595146	+	0.0524285i
$805$		−	16.9213i		−	0.596398i
$806$	31.4585	−	23.3757i	1.10808	−	0.823373i
$807$	−0.268887	−	1.53031i	−0.00946528	−	0.0538694i
$808$	−1.52150	+	5.67831i	−0.0535262	+	0.199762i
$809$	−21.4988	+	12.4123i	−0.755856	+	0.436394i	−0.827806	−	0.561014i	$-0.810411\pi$
$809$	−21.4988	+	12.4123i	−0.755856	+	0.436394i	0.0719497	+	0.997408i	$0.477078\pi$
$810$	−40.2418	+	6.99613i	−1.41395	+	0.245819i
$811$	−18.4890	−	18.4890i	−0.649236	−	0.649236i	0.303572	−	0.952808i	$-0.401821\pi$
$811$	−18.4890	−	18.4890i	−0.649236	−	0.649236i	−0.952808	+	0.303572i	$0.901821\pi$
$812$	−2.90999	−	10.8602i	−0.102121	−	0.381120i
$813$	−15.8096	−	33.9570i	−0.554466	−	1.19092i
$814$	2.69260	−	2.69260i	0.0943757	−	0.0943757i
$815$	26.5729	+	15.3419i	0.930809	+	0.537403i
$816$	−2.07433	−	2.47511i	−0.0726161	−	0.0866461i
$817$	−13.9916	−	3.74905i	−0.489505	−	0.131163i
$818$	−36.6630			−1.28189
$819$	2.16499	+	10.5978i	0.0756508	+	0.370316i
$820$	−46.0288			−1.60740
$821$	−9.49140	−	2.54321i	−0.331252	−	0.0887588i	0.0893597	−	0.995999i	$-0.471518\pi$
$821$	−9.49140	−	2.54321i	−0.331252	−	0.0887588i	−0.420612	+	0.907241i	$0.638185\pi$
$822$	17.4830	+	20.8608i	0.609789	+	0.727604i
$823$	5.10504	+	2.94740i	0.177951	+	0.102740i	0.586329	−	0.810073i	$-0.300572\pi$
$823$	5.10504	+	2.94740i	0.177951	+	0.102740i	−0.408379	+	0.912813i	$0.633906\pi$
$824$	4.58680	−	4.58680i	0.159789	−	0.159789i
$825$	0.597147	+	1.28260i	0.0207900	+	0.0446543i
$826$	−4.15985	−	15.5248i	−0.144740	−	0.540176i
$827$	33.0075	+	33.0075i	1.14778	+	1.14778i	0.986987	+	0.160797i	$0.0514065\pi$
$827$	33.0075	+	33.0075i	1.14778	+	1.14778i	0.160797	+	0.986987i	$0.448594\pi$
$828$	34.2070	+	6.07397i	1.18878	+	0.211085i
$829$	2.24655	−	1.29705i	0.0780261	−	0.0450484i	−0.460479	−	0.887670i	$-0.652322\pi$
$829$	2.24655	−	1.29705i	0.0780261	−	0.0450484i	0.538505	+	0.842622i	$0.318989\pi$
$830$	9.83833	−	36.7172i	0.341494	−	1.27447i
$831$	−0.450030	−	2.56124i	−0.0156114	−	0.0888484i
$832$	17.2578	−	2.00128i	0.598305	−	0.0693819i
$833$		−	0.405072i		−	0.0140349i
$834$	35.5801	+	3.13438i	1.23204	+	0.108535i
$835$	−17.9314	−	31.0580i	−0.620541	−	1.07481i
$836$	7.83460	−	13.5699i	0.270965	−	0.469325i
$837$	28.6209	+	7.72422i	0.989283	+	0.266988i
$838$	−21.3030	+	5.70813i	−0.735902	+	0.197184i
$839$	−29.2690	+	7.84260i	−1.01048	+	0.270757i	−0.725829	−	0.687875i	$-0.758544\pi$
$839$	−29.2690	+	7.84260i	−1.01048	+	0.270757i	−0.284649	+	0.958632i	$0.591877\pi$
$840$	1.66883	−	2.38029i	0.0575800	−	0.0821278i
$841$	9.28418	−	16.0807i	0.320144	−	0.554506i
$842$	−29.6025	−	51.2730i	−1.02017	−	1.76698i
$843$	−0.475099	+	5.39312i	−0.0163633	+	0.185749i
$844$		−	16.8106i		−	0.578644i
$845$	16.3040	−	26.3258i	0.560875	−	0.905636i
$846$	57.7185	−	20.9294i	1.98440	−	0.719567i
$847$	2.46663	−	9.20559i	0.0847544	−	0.316308i
$848$	1.50994	−	0.871762i	0.0518514	−	0.0299364i
$849$	7.80924	+	2.84764i	0.268012	+	0.0977308i
$850$	−0.367708	−	0.367708i	−0.0126123	−	0.0126123i
$851$	3.03114	+	11.3124i	0.103906	+	0.387783i
$852$	18.1244	−	8.43830i	0.620931	−	0.289091i
$853$	−24.1217	+	24.1217i	−0.825913	+	0.825913i	−0.986949	−	0.161036i	$-0.948517\pi$
$853$	−24.1217	+	24.1217i	−0.825913	+	0.825913i	0.161036	+	0.986949i	$0.448517\pi$
$854$	−9.33093	−	5.38721i	−0.319298	−	0.184347i
$855$	−43.3584	−	36.4708i	−1.48282	−	1.24727i
$856$	5.84841	+	1.56708i	0.199895	+	0.0535616i
$857$	14.7900			0.505216			0.252608	−	0.967569i	$-0.418712\pi$
$857$	14.7900			0.505216			0.252608	+	0.967569i	$0.418712\pi$
$858$	4.11623	+	13.8250i	0.140526	+	0.471976i
$859$	−13.8781			−0.473513			−0.236757	−	0.971569i	$-0.576084\pi$
$859$	−13.8781			−0.473513			−0.236757	+	0.971569i	$0.576084\pi$
$860$	6.85239	+	1.83609i	0.233665	+	0.0626102i
$861$	−15.7358	+	13.1878i	−0.536276	+	0.449441i
$862$	65.4485	+	37.7867i	2.22919	+	1.28702i
$863$	27.1564	−	27.1564i	0.924414	−	0.924414i	−0.0729239	−	0.997338i	$-0.523233\pi$
$863$	27.1564	−	27.1564i	0.924414	−	0.924414i	0.997338	+	0.0729239i	$0.0232330\pi$
$864$	26.9960	+	27.0934i	0.918421	+	0.921735i
$865$	−4.79785	−	17.9058i	−0.163132	−	0.608817i
$866$	40.6462	+	40.6462i	1.38121	+	1.38121i
$867$	9.98998	−	27.3961i	0.339278	−	0.930419i
$868$	8.05443	−	4.65023i	0.273385	−	0.157839i
$869$	2.46816	−	9.21131i	0.0837267	−	0.312472i
$870$	−53.3971	+	9.38230i	−1.81033	+	0.318090i
$871$	−21.4011	−	3.15463i	−0.725150	−	0.106891i
$872$			1.69212i			0.0573023i
$873$	1.23216	+	14.2811i	0.0417022	+	0.483341i
$874$	53.6576	+	92.9378i	1.81500	+	3.14367i
$875$	−5.15246	+	8.92432i	−0.174185	+	0.301697i
$876$	−7.84980	−	5.50351i	−0.265220	−	0.185947i
$877$	4.48695	−	1.20227i	0.151513	−	0.0405979i	−0.182265	−	0.983249i	$-0.558343\pi$
$877$	4.48695	−	1.20227i	0.151513	−	0.0405979i	0.333779	+	0.942652i	$0.391676\pi$
$878$	11.0032	−	2.94830i	0.371340	−	0.0995001i
$879$	20.7977	+	14.5813i	0.701489	+	0.491816i
$880$	6.64578	−	11.5108i	0.224029	−	0.388030i
$881$	9.43842	+	16.3478i	0.317988	+	0.550772i	0.980068	−	0.198661i	$-0.0636594\pi$
$881$	9.43842	+	16.3478i	0.317988	+	0.550772i	−0.662080	+	0.749433i	$0.730326\pi$
$882$	0.491338	+	5.69476i	0.0165442	+	0.191752i
$883$			18.4148i			0.619708i	0.950784	+	0.309854i	$0.100280\pi$
$883$			18.4148i			0.619708i	−0.950784	+	0.309854i	$0.899720\pi$
$884$	−1.42004	−	1.91106i	−0.0477611	−	0.0642759i
$885$	−34.2777	+	6.02287i	−1.15223	+	0.202456i
$886$	8.43081	−	31.4642i	0.283239	−	1.05706i
$887$	−20.8960	+	12.0643i	−0.701619	+	0.405080i	−0.807950	−	0.589251i	$-0.799423\pi$
$887$	−20.8960	+	12.0643i	−0.701619	+	0.405080i	0.106331	+	0.994331i	$0.466090\pi$
$888$	−0.689272	+	1.89023i	−0.0231305	+	0.0634319i
$889$	7.56194	+	7.56194i	0.253619	+	0.253619i
$890$	−1.63885	−	6.11627i	−0.0549344	−	0.205018i
$891$	−6.27957	+	8.92249i	−0.210374	+	0.298914i
$892$	−29.0669	+	29.0669i	−0.973233	+	0.973233i
$893$	73.7537	+	42.5817i	2.46807	+	1.42494i
$894$	37.6516	−	31.5550i	1.25926	−	1.05536i
$895$	56.0692	+	15.0237i	1.87419	+	0.502187i
$896$	−5.54054			−0.185096
$897$	−43.1527	−	10.2961i	−1.44083	−	0.343776i
$898$	−50.1961			−1.67507
$899$	38.0076	+	10.1841i	1.26763	+	0.339659i
$900$	2.52171	+	2.12113i	0.0840570	+	0.0707043i
$901$	−0.132881	−	0.0767188i	−0.00442690	−	0.00255587i
$902$	−19.3605	+	19.3605i	−0.644634	+	0.644634i
$903$	2.86869	−	1.33560i	0.0954640	−	0.0444458i
$904$	0.618000	+	2.30641i	0.0205544	+	0.0767099i
$905$	24.5745	+	24.5745i	0.816885	+	0.816885i
$906$	13.4362	+	4.89951i	0.446388	+	0.162775i
$907$	6.93158	−	4.00195i	0.230159	−	0.132883i	−0.380486	−	0.924787i	$-0.624243\pi$
$907$	6.93158	−	4.00195i	0.230159	−	0.132883i	0.610646	+	0.791904i	$0.290910\pi$
$908$	−3.97104	+	14.8201i	−0.131783	+	0.491823i
$909$	−23.5300	+	8.53223i	−0.780440	+	0.282996i
$910$	10.1608	−	12.8265i	0.336826	−	0.425193i
$911$		−	33.0998i		−	1.09665i	−0.836267	−	0.548323i	$-0.815266\pi$
$911$		−	33.0998i		−	1.09665i	0.836267	−	0.548323i	$-0.184734\pi$
$912$	−5.54695	+	62.9665i	−0.183678	+	2.08503i
$913$	−5.07698	−	8.79359i	−0.168024	−	0.291025i
$914$	−7.57048	+	13.1125i	−0.250409	+	0.433722i
$915$	−13.3934	+	19.1033i	−0.442772	+	0.631536i
$916$	−16.0539	+	4.30162i	−0.530435	+	0.142130i
$917$	12.8271	−	3.43702i	0.423589	−	0.113500i
$918$	1.04492	−	3.87179i	0.0344875	−	0.127788i
$919$	−9.01337	+	15.6116i	−0.297324	+	0.514980i	−0.975523	−	0.219899i	$-0.929427\pi$
$919$	−9.01337	+	15.6116i	−0.297324	+	0.514980i	0.678199	+	0.734878i	$0.262761\pi$
$920$	5.96149	+	10.3256i	0.196545	+	0.340425i
$921$	−19.5133	−	1.71900i	−0.642987	−	0.0566430i
$922$		−	25.3659i		−	0.835380i
$923$	−23.7342	+	9.40410i	−0.781222	+	0.309540i
$924$	0.592375	+	3.37136i	0.0194877	+	0.110910i
$925$	−0.287495	+	1.07294i	−0.00945277	+	0.0352782i
$926$	−22.7443	+	13.1314i	−0.747425	+	0.431526i
$927$	27.1928	+	4.82850i	0.893129	+	0.158589i
$928$	35.8971	+	35.8971i	1.17838	+	1.17838i
$929$	−3.55731	−	13.2761i	−0.116712	−	0.435574i	0.882698	−	0.469941i	$-0.155725\pi$
$929$	−3.55731	−	13.2761i	−0.116712	−	0.435574i	−0.999409	+	0.0343678i	$0.989058\pi$
$930$	−18.9286	−	40.6562i	−0.620693	−	1.33317i
$931$	−5.60640	+	5.60640i	−0.183742	+	0.183742i
$932$	−15.6368	−	9.02790i	−0.512200	−	0.295719i
$933$	9.88140	+	11.7906i	0.323503	+	0.386006i
$934$	54.4140	+	14.5802i	1.78048	+	0.477079i
$935$	−1.16971			−0.0382537
$936$	−5.05477	−	5.70416i	−0.165220	−	0.186446i
$937$	−43.2902			−1.41423			−0.707115	−	0.707098i	$-0.750004\pi$
$937$	−43.2902			−1.41423			−0.707115	+	0.707098i	$0.750004\pi$
$938$	−11.0418	−	2.95865i	−0.360528	−	0.0966033i
$939$	−10.9384	−	13.0518i	−0.356962	−	0.425929i
$940$	−36.1208	−	20.8544i	−1.17813	−	0.680195i
$941$	−0.790417	+	0.790417i	−0.0257669	+	0.0257669i	−0.719873	−	0.694106i	$-0.755800\pi$
$941$	−0.790417	+	0.790417i	−0.0257669	+	0.0257669i	0.694106	+	0.719873i	$0.255800\pi$
$942$	−25.4687	−	54.7036i	−0.829817	−	1.78234i
$943$	−21.7947	−	81.3389i	−0.709733	−	2.64876i
$944$	27.4556	+	27.4556i	0.893603	+	0.893603i
$945$	12.3771	+	0.0222891i	0.402626	+	0.000725066i
$946$	3.65453	−	2.10994i	0.118819	−	0.0686002i
$947$	4.09616	−	15.2871i	0.133107	−	0.496763i	−0.866891	−	0.498497i	$-0.833885\pi$
$947$	4.09616	−	15.2871i	0.133107	−	0.496763i	0.999998	+	0.00173422i	$0.000552018\pi$
$948$	−3.84373	−	21.8757i	−0.124839	−	0.710489i
$949$	9.59590	+	7.60161i	0.311496	+	0.246759i
$950$			10.1785i			0.330235i
$951$	−30.3611	−	2.67462i	−0.984527	−	0.0867305i
$952$	0.142710	+	0.247180i	0.00462524	+	0.00801115i
$953$	7.87177	−	13.6343i	0.254992	−	0.441658i	−0.709902	−	0.704301i	$-0.751261\pi$
$953$	7.87177	−	13.6343i	0.254992	−	0.441658i	0.964893	+	0.262642i	$0.0845940\pi$
$954$	1.96118	+	0.917381i	0.0634955	+	0.0297013i
$955$	−22.9296	+	6.14396i	−0.741984	+	0.198814i
$956$	−38.7842	+	10.3922i	−1.25437	+	0.336108i
$957$	−8.31369	+	11.8580i	−0.268743	+	0.383316i
$958$	−16.3782	+	28.3679i	−0.529155	+	0.916524i
$959$	−4.12386	−	7.14273i	−0.133166	−	0.230651i
$960$	1.74452	−	19.8030i	0.0563041	−	0.639140i
$961$			1.54886i			0.0499633i
$962$	−4.49514	+	10.3950i	−0.144929	+	0.335147i
$963$	8.78782	+	24.2348i	0.283184	+	0.780957i
$964$	−0.355303	+	1.32601i	−0.0114435	+	0.0427079i
$965$	−2.86377	+	1.65340i	−0.0921882	+	0.0532249i
$966$	−22.0249	−	8.03138i	−0.708639	−	0.258405i
$967$	−15.3767	−	15.3767i	−0.494482	−	0.494482i	0.415233	−	0.909715i	$-0.363700\pi$
$967$	−15.3767	−	15.3767i	−0.494482	−	0.494482i	−0.909715	+	0.415233i	$0.863700\pi$
$968$	1.73802	+	6.48638i	0.0558621	+	0.208480i
$969$	5.04300	−	2.34791i	0.162005	−	0.0754256i
$970$	15.3333	−	15.3333i	0.492322	−	0.492322i
$971$	−25.2390	−	14.5717i	−0.809958	−	0.467629i	0.0369833	−	0.999316i	$-0.488225\pi$
$971$	−25.2390	−	14.5717i	−0.809958	−	0.467629i	−0.846941	+	0.531686i	$0.821558\pi$
$972$	−4.48785	+	25.0126i	−0.143948	+	0.802280i
$973$	−10.4545	−	2.80128i	−0.335157	−	0.0898050i
$974$	−37.6866			−1.20756
$975$	−3.05628	−	2.89217i	−0.0978792	−	0.0926235i
$976$	26.0291			0.833170
$977$	−22.6664	−	6.07344i	−0.725162	−	0.194307i	−0.122688	−	0.992445i	$-0.539152\pi$
$977$	−22.6664	−	6.07344i	−0.725162	−	0.194307i	−0.602474	+	0.798139i	$0.705818\pi$
$978$	32.5814	−	27.3057i	1.04184	−	0.873141i
$979$	−1.46482	−	0.845713i	−0.0468158	−	0.0270291i
$980$	2.74573	−	2.74573i	0.0877091	−	0.0877091i
$981$	−5.90649	+	4.12521i	−0.188580	+	0.131708i
$982$	−1.16367	−	4.34288i	−0.0371342	−	0.138587i
$983$	10.1026	+	10.1026i	0.322223	+	0.322223i	0.849619	−	0.527396i	$-0.176832\pi$
$983$	10.1026	+	10.1026i	0.322223	+	0.322223i	−0.527396	+	0.849619i	$0.676832\pi$
$984$	4.95604	−	13.5912i	0.157993	−	0.433273i
$985$	−1.48254	+	0.855942i	−0.0472375	+	0.0272726i
$986$	1.37769	−	5.14161i	0.0438746	−	0.163742i
$987$	−18.3237	+	3.21961i	−0.583248	+	0.102481i
$988$	−6.79597	+	46.1041i	−0.216209	+	1.46677i
$989$			12.9785i			0.412691i
$990$	16.4446	−	1.41882i	0.522643	−	0.0450931i
$991$	4.68686	+	8.11789i	0.148883	+	0.257873i	0.930815	−	0.365491i	$-0.119099\pi$
$991$	4.68686	+	8.11789i	0.148883	+	0.257873i	−0.781932	+	0.623364i	$0.785766\pi$
$992$	−20.9968	+	36.3675i	−0.666650	+	1.15467i
$993$	21.3373	+	14.9597i	0.677120	+	0.474730i
$994$	−13.0310	+	3.49164i	−0.413318	+	0.110748i
$995$	−20.3856	+	5.46230i	−0.646267	+	0.173167i
$996$	−19.3644	−	13.5764i	−0.613584	−	0.430185i
$997$	4.60015	−	7.96768i	0.145688	−	0.252339i	−0.783941	−	0.620835i	$-0.786794\pi$
$997$	4.60015	−	7.96768i	0.145688	−	0.252339i	0.929629	+	0.368496i	$0.120127\pi$
$998$	−17.9328	−	31.0606i	−0.567654	−	0.983205i
$999$	−8.27841	+	2.20222i	−0.261917	+	0.0696752i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cc.a.50.6	✓	112
3.2	odd	2	inner	273.2.cc.a.50.23	yes	112
13.6	odd	12	inner	273.2.cc.a.71.23	yes	112
39.32	even	12	inner	273.2.cc.a.71.6	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.cc.a.50.6	✓	112	1.1	even	1	trivial
273.2.cc.a.50.23	yes	112	3.2	odd	2	inner
273.2.cc.a.71.6	yes	112	39.32	even	12	inner
273.2.cc.a.71.23	yes	112	13.6	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.84038 - 0.493129i) q^{2} +(-1.11254 - 1.32750i) q^{3} +(1.41178 + 0.815092i) q^{4} +(-1.68431 + 1.68431i) q^{5} +(1.39288 + 2.99173i) q^{6} +(-0.258819 - 0.965926i) q^{7} +(0.498237 + 0.498237i) q^{8} +(-0.524491 + 2.95380i) q^{9} +O(q^{10})\)	\(q+(-1.84038 - 0.493129i) q^{2} +(-1.11254 - 1.32750i) q^{3} +(1.41178 + 0.815092i) q^{4} +(-1.68431 + 1.68431i) q^{5} +(1.39288 + 2.99173i) q^{6} +(-0.258819 - 0.965926i) q^{7} +(0.498237 + 0.498237i) q^{8} +(-0.524491 + 2.95380i) q^{9} +(3.93035 - 2.26919i) q^{10} +(0.313767 - 1.17099i) q^{11} +(-0.488637 - 2.78096i) q^{12} +(0.415331 + 3.58155i) q^{13} +1.90530i q^{14} +(4.10978 + 0.362045i) q^{15} +(-2.30143 - 3.98620i) q^{16} +(-0.202536 + 0.350803i) q^{17} +(2.42187 - 5.17747i) q^{18} +(7.65849 - 2.05209i) q^{19} +(-3.75074 + 1.00501i) q^{20} +(-0.994315 + 1.41822i) q^{21} +(-1.15490 + 2.00035i) q^{22} +(-3.55196 - 6.15217i) q^{23} +(0.107097 - 1.21572i) q^{24} -0.673785i q^{25} +(1.00180 - 6.79623i) q^{26} +(4.50467 - 2.58997i) q^{27} +(0.421923 - 1.57464i) q^{28} +(5.97296 - 3.44849i) q^{29} +(-7.38503 - 2.69295i) q^{30} +(4.03416 + 4.03416i) q^{31} +(1.90507 + 7.10983i) q^{32} +(-1.90357 + 0.886258i) q^{33} +(0.545735 - 0.545735i) q^{34} +(2.06285 + 1.19099i) q^{35} +(-3.14808 + 3.74260i) q^{36} +(-1.59241 - 0.426686i) q^{37} -15.1065 q^{38} +(4.29242 - 4.53598i) q^{39} -1.67837 q^{40} +(11.4499 + 3.06798i) q^{41} +(2.52928 - 2.11973i) q^{42} +(-1.58218 - 0.913473i) q^{43} +(1.39744 - 1.39744i) q^{44} +(-4.09170 - 5.85851i) q^{45} +(3.50315 + 13.0739i) q^{46} +(7.59520 + 7.59520i) q^{47} +(-2.73122 + 7.48997i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(-0.332263 + 1.24002i) q^{50} +(0.691019 - 0.121418i) q^{51} +(-2.33294 + 5.39489i) q^{52} +0.378791i q^{53} +(-9.56751 + 2.54515i) q^{54} +(1.44383 + 2.50079i) q^{55} +(0.352307 - 0.610213i) q^{56} +(-11.2445 - 7.88358i) q^{57} +(-12.6931 + 3.40110i) q^{58} +(-8.14818 + 2.18330i) q^{59} +(5.50700 + 3.86097i) q^{60} +(-2.82748 + 4.89734i) q^{61} +(-5.43503 - 9.41375i) q^{62} +(2.98890 - 0.257879i) q^{63} -4.81852i q^{64} +(-6.73198 - 5.33289i) q^{65} +(3.94033 - 0.692349i) q^{66} +(-1.55285 + 5.79531i) q^{67} +(-0.571873 + 0.330171i) q^{68} +(-4.21528 + 11.5598i) q^{69} +(-3.20912 - 3.20912i) q^{70} +(1.83259 + 6.83932i) q^{71} +(-1.73301 + 1.21037i) q^{72} +(2.40085 - 2.40085i) q^{73} +(2.72024 + 1.57053i) q^{74} +(-0.894447 + 0.749615i) q^{75} +(12.4847 + 3.34528i) q^{76} -1.21230 q^{77} +(-10.1365 + 6.23123i) q^{78} +7.86624 q^{79} +(10.5903 + 2.83767i) q^{80} +(-8.44982 - 3.09848i) q^{81} +(-19.5592 - 11.2925i) q^{82} +(5.92256 - 5.92256i) q^{83} +(-2.55973 + 1.19175i) q^{84} +(-0.249727 - 0.931993i) q^{85} +(2.46136 + 2.46136i) q^{86} +(-11.2230 - 4.09248i) q^{87} +(0.739762 - 0.427102i) q^{88} +(0.361109 - 1.34768i) q^{89} +(4.64129 + 12.7996i) q^{90} +(3.35202 - 1.32815i) q^{91} -11.5807i q^{92} +(0.867150 - 9.84351i) q^{93} +(-10.2327 - 17.7235i) q^{94} +(-9.44291 + 16.3556i) q^{95} +(7.31879 - 10.4390i) q^{96} +(4.61523 - 1.23665i) q^{97} +(1.84038 - 0.493129i) q^{98} +(3.29431 + 1.54098i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 12 q^{6}+O(q^{10}) \) 112 * q - 12 * q^6	\( 112 q - 12 q^{6} - 48 q^{10} - 32 q^{13} + 4 q^{15} + 40 q^{16} - 16 q^{18} - 8 q^{19} - 4 q^{21} - 16 q^{22} - 88 q^{24} + 24 q^{27} - 72 q^{30} + 16 q^{31} + 48 q^{34} + 12 q^{36} + 48 q^{37} + 56 q^{39} + 32 q^{40} - 28 q^{45} + 72 q^{46} + 24 q^{48} - 144 q^{52} - 108 q^{54} - 28 q^{57} - 120 q^{58} - 116 q^{60} - 48 q^{61} + 16 q^{63} + 40 q^{66} - 16 q^{67} + 72 q^{69} + 48 q^{70} + 52 q^{72} - 16 q^{73} + 60 q^{75} + 16 q^{76} - 4 q^{78} + 16 q^{79} - 20 q^{81} + 120 q^{82} + 72 q^{84} - 40 q^{85} - 24 q^{87} + 72 q^{88} + 16 q^{91} + 92 q^{93} - 96 q^{94} + 28 q^{96} + 96 q^{97} - 144 q^{99}+O(q^{100}) \) 112 * q - 12 * q^6 - 48 * q^10 - 32 * q^13 + 4 * q^15 + 40 * q^16 - 16 * q^18 - 8 * q^19 - 4 * q^21 - 16 * q^22 - 88 * q^24 + 24 * q^27 - 72 * q^30 + 16 * q^31 + 48 * q^34 + 12 * q^36 + 48 * q^37 + 56 * q^39 + 32 * q^40 - 28 * q^45 + 72 * q^46 + 24 * q^48 - 144 * q^52 - 108 * q^54 - 28 * q^57 - 120 * q^58 - 116 * q^60 - 48 * q^61 + 16 * q^63 + 40 * q^66 - 16 * q^67 + 72 * q^69 + 48 * q^70 + 52 * q^72 - 16 * q^73 + 60 * q^75 + 16 * q^76 - 4 * q^78 + 16 * q^79 - 20 * q^81 + 120 * q^82 + 72 * q^84 - 40 * q^85 - 24 * q^87 + 72 * q^88 + 16 * q^91 + 92 * q^93 - 96 * q^94 + 28 * q^96 + 96 * q^97 - 144 * q^99

Introduction

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