LMFDB - Embedded newform 552.2.j.d.323.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(323,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("552.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.j (of order $2$, degree $1$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$42$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.3
Character	$\chi$	$=$	552.323
Dual form			552.2.j.d.323.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40766 - 0.136034i) q^{2} +(-1.50629 - 0.855045i) q^{3} +(1.96299 + 0.382978i) q^{4} -2.98020 q^{5} +(2.00402 + 1.40851i) q^{6} -1.36209i q^{7} +(-2.71112 - 0.806135i) q^{8} +(1.53780 + 2.57588i) q^{9} +O(q^{10})$	\(q+(-1.40766 - 0.136034i) q^{2} +(-1.50629 - 0.855045i) q^{3} +(1.96299 + 0.382978i) q^{4} -2.98020 q^{5} +(2.00402 + 1.40851i) q^{6} -1.36209i q^{7} +(-2.71112 - 0.806135i) q^{8} +(1.53780 + 2.57588i) q^{9} +(4.19509 + 0.405409i) q^{10} +5.80186i q^{11} +(-2.62936 - 2.25532i) q^{12} +0.852288i q^{13} +(-0.185291 + 1.91736i) q^{14} +(4.48903 + 2.54820i) q^{15} +(3.70666 + 1.50357i) q^{16} -5.38365i q^{17} +(-1.81428 - 3.83515i) q^{18} -1.59177 q^{19} +(-5.85010 - 1.14135i) q^{20} +(-1.16465 + 2.05170i) q^{21} +(0.789250 - 8.16702i) q^{22} +1.00000 q^{23} +(3.39443 + 3.53240i) q^{24} +3.88159 q^{25} +(0.115940 - 1.19973i) q^{26} +(-0.113867 - 5.19490i) q^{27} +(0.521652 - 2.67377i) q^{28} +4.01876 q^{29} +(-5.97237 - 4.19765i) q^{30} +1.32088i q^{31} +(-5.01316 - 2.62073i) q^{32} +(4.96085 - 8.73926i) q^{33} +(-0.732360 + 7.57832i) q^{34} +4.05931i q^{35} +(2.03217 + 5.64538i) q^{36} -0.210483i q^{37} +(2.24067 + 0.216535i) q^{38} +(0.728744 - 1.28379i) q^{39} +(8.07966 + 2.40244i) q^{40} -10.6401i q^{41} +(1.91853 - 2.72966i) q^{42} +3.80028 q^{43} +(-2.22199 + 11.3890i) q^{44} +(-4.58294 - 7.67665i) q^{45} +(-1.40766 - 0.136034i) q^{46} +3.46377 q^{47} +(-4.29767 - 5.43416i) q^{48} +5.14470 q^{49} +(-5.46394 - 0.528028i) q^{50} +(-4.60326 + 8.10931i) q^{51} +(-0.326408 + 1.67303i) q^{52} +12.5912 q^{53} +(-0.546399 + 7.32813i) q^{54} -17.2907i q^{55} +(-1.09803 + 3.69279i) q^{56} +(2.39766 + 1.36104i) q^{57} +(-5.65704 - 0.546689i) q^{58} -4.46664i q^{59} +(7.83602 + 6.72130i) q^{60} -14.3544i q^{61} +(0.179685 - 1.85934i) q^{62} +(3.50859 - 2.09462i) q^{63} +(6.70029 + 4.37105i) q^{64} -2.53999i q^{65} +(-8.17200 + 11.6270i) q^{66} -9.77174 q^{67} +(2.06182 - 10.5680i) q^{68} +(-1.50629 - 0.855045i) q^{69} +(0.552204 - 5.71411i) q^{70} +3.27263 q^{71} +(-2.09263 - 8.22319i) q^{72} +2.83293 q^{73} +(-0.0286329 + 0.296288i) q^{74} +(-5.84678 - 3.31893i) q^{75} +(-3.12463 - 0.609614i) q^{76} +7.90267 q^{77} +(-1.20046 + 1.70800i) q^{78} +4.99823i q^{79} +(-11.0466 - 4.48092i) q^{80} +(-4.27036 + 7.92237i) q^{81} +(-1.44742 + 14.9776i) q^{82} -3.09167i q^{83} +(-3.07195 + 3.58143i) q^{84} +16.0443i q^{85} +(-5.34949 - 0.516968i) q^{86} +(-6.05341 - 3.43622i) q^{87} +(4.67708 - 15.7295i) q^{88} +13.7100i q^{89} +(5.40692 + 11.4295i) q^{90} +1.16089 q^{91} +(1.96299 + 0.382978i) q^{92} +(1.12941 - 1.98962i) q^{93} +(-4.87579 - 0.471191i) q^{94} +4.74379 q^{95} +(5.31041 + 8.23405i) q^{96} +10.4354 q^{97} +(-7.24197 - 0.699855i) q^{98} +(-14.9449 + 8.92208i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9}+O(q^{10}) $ 42 * q + 2 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 - 9 * q^8 + 2 * q^9	$ 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9} - 4 q^{10} - 21 q^{12} - 4 q^{14} - 8 q^{15} - 12 q^{16} - 11 q^{18} + 4 q^{19} - 2 q^{20} + 8 q^{21} + 18 q^{22} + 42 q^{23} + 28 q^{24} + 22 q^{25} + 11 q^{26} - 16 q^{27} + 6 q^{28} + 2 q^{30} - 20 q^{32} + 12 q^{33} + 14 q^{34} - 24 q^{36} - 22 q^{38} + 8 q^{39} + 4 q^{40} - 44 q^{42} + 28 q^{43} + 56 q^{44} - 8 q^{45} + 30 q^{48} - 50 q^{49} + 20 q^{50} + 28 q^{51} - q^{52} + 24 q^{53} + 52 q^{54} - 34 q^{56} - 8 q^{57} - 21 q^{58} - 42 q^{60} - 79 q^{62} - 16 q^{63} + 7 q^{64} - 62 q^{66} - 4 q^{67} + 20 q^{68} + 2 q^{69} - 8 q^{70} + 22 q^{72} + 4 q^{73} + 36 q^{74} - 6 q^{75} + 14 q^{76} + 32 q^{77} + 27 q^{78} - 52 q^{80} + 18 q^{81} + 11 q^{82} - 80 q^{84} - 28 q^{86} - 48 q^{87} - 38 q^{88} - 46 q^{90} - 8 q^{91} + 4 q^{92} - 22 q^{93} + q^{94} - 16 q^{95} + 9 q^{96} + 20 q^{97} + 64 q^{98}+O(q^{100}) $ 42 * q + 2 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 - 9 * q^8 + 2 * q^9 - 4 * q^10 - 21 * q^12 - 4 * q^14 - 8 * q^15 - 12 * q^16 - 11 * q^18 + 4 * q^19 - 2 * q^20 + 8 * q^21 + 18 * q^22 + 42 * q^23 + 28 * q^24 + 22 * q^25 + 11 * q^26 - 16 * q^27 + 6 * q^28 + 2 * q^30 - 20 * q^32 + 12 * q^33 + 14 * q^34 - 24 * q^36 - 22 * q^38 + 8 * q^39 + 4 * q^40 - 44 * q^42 + 28 * q^43 + 56 * q^44 - 8 * q^45 + 30 * q^48 - 50 * q^49 + 20 * q^50 + 28 * q^51 - q^52 + 24 * q^53 + 52 * q^54 - 34 * q^56 - 8 * q^57 - 21 * q^58 - 42 * q^60 - 79 * q^62 - 16 * q^63 + 7 * q^64 - 62 * q^66 - 4 * q^67 + 20 * q^68 + 2 * q^69 - 8 * q^70 + 22 * q^72 + 4 * q^73 + 36 * q^74 - 6 * q^75 + 14 * q^76 + 32 * q^77 + 27 * q^78 - 52 * q^80 + 18 * q^81 + 11 * q^82 - 80 * q^84 - 28 * q^86 - 48 * q^87 - 38 * q^88 - 46 * q^90 - 8 * q^91 + 4 * q^92 - 22 * q^93 + q^94 - 16 * q^95 + 9 * q^96 + 20 * q^97 + 64 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.40766	−	0.136034i	−0.995363	−	0.0961907i
$2$	−1.40766	−	0.136034i	−0.995363	−	0.0961907i
$3$	−1.50629	−	0.855045i	−0.869655	−	0.493660i
$3$	−1.50629	−	0.855045i	−0.869655	−	0.493660i
$4$	1.96299	+	0.382978i	0.981495	+	0.191489i
$5$	−2.98020			−1.33279			−0.666393	−	0.745601i	$-0.732163\pi$
$5$	−2.98020			−1.33279			−0.666393	+	0.745601i	$0.732163\pi$
$6$	2.00402	+	1.40851i	0.818137	+	0.575024i
$7$		−	1.36209i		−	0.514823i	−0.966302	−	0.257411i	$-0.917130\pi$
$7$		−	1.36209i		−	0.514823i	0.966302	−	0.257411i	$-0.0828695\pi$
$8$	−2.71112	−	0.806135i	−0.958524	−	0.285012i
$9$	1.53780	+	2.57588i	0.512599	+	0.858628i
$10$	4.19509	+	0.405409i	1.32661	+	0.128202i
$11$			5.80186i			1.74933i	0.484732	+	0.874663i	$0.338917\pi$
$11$			5.80186i			1.74933i	−0.484732	+	0.874663i	$0.661083\pi$
$12$	−2.62936	−	2.25532i	−0.759031	−	0.651054i
$13$			0.852288i			0.236382i	0.992991	+	0.118191i	$0.0377095\pi$
$13$			0.852288i			0.236382i	−0.992991	+	0.118191i	$0.962290\pi$
$14$	−0.185291	+	1.91736i	−0.0495211	+	0.512435i
$15$	4.48903	+	2.54820i	1.15906	+	0.657943i
$16$	3.70666	+	1.50357i	0.926664	+	0.375891i
$17$		−	5.38365i		−	1.30573i	−0.757476	−	0.652863i	$-0.773568\pi$
$17$		−	5.38365i		−	1.30573i	0.757476	−	0.652863i	$-0.226432\pi$
$18$	−1.81428	−	3.83515i	−0.427630	−	0.903954i
$19$	−1.59177			−0.365177			−0.182589	−	0.983189i	$-0.558448\pi$
$19$	−1.59177			−0.365177			−0.182589	+	0.983189i	$0.558448\pi$
$20$	−5.85010	−	1.14135i	−1.30812	−	0.255214i
$21$	−1.16465	+	2.05170i	−0.254147	+	0.447718i
$22$	0.789250	−	8.16702i	0.168269	−	1.74121i
$23$	1.00000			0.208514
$23$	1.00000			0.208514
$24$	3.39443	+	3.53240i	0.692886	+	0.721047i
$25$	3.88159			0.776317
$26$	0.115940	−	1.19973i	0.0227377	−	0.235286i
$27$	−0.113867	−	5.19490i	−0.0219136	−	0.999760i
$28$	0.521652	−	2.67377i	0.0985830	−	0.505296i
$29$	4.01876			0.746266			0.373133	−	0.927778i	$-0.378284\pi$
$29$	4.01876			0.746266			0.373133	+	0.927778i	$0.378284\pi$
$30$	−5.97237	−	4.19765i	−1.09040	−	0.766383i
$31$			1.32088i			0.237237i	0.992940	+	0.118618i	$0.0378465\pi$
$31$			1.32088i			0.237237i	−0.992940	+	0.118618i	$0.962153\pi$
$32$	−5.01316	−	2.62073i	−0.886210	−	0.463285i
$33$	4.96085	−	8.73926i	0.863572	−	1.52131i
$34$	−0.732360	+	7.57832i	−0.125599	+	1.29967i
$35$			4.05931i			0.686148i
$36$	2.03217	+	5.64538i	0.338695	+	0.940896i
$37$		−	0.210483i		−	0.0346032i	−0.999850	−	0.0173016i	$-0.994492\pi$
$37$		−	0.210483i		−	0.0346032i	0.999850	−	0.0173016i	$-0.00550754\pi$
$38$	2.24067	+	0.216535i	0.363484	+	0.0351266i
$39$	0.728744	−	1.28379i	0.116692	−	0.205571i
$40$	8.07966	+	2.40244i	1.27751	+	0.379860i
$41$		−	10.6401i		−	1.66171i	−0.556490	−	0.830854i	$-0.687852\pi$
$41$		−	10.6401i		−	1.66171i	0.556490	−	0.830854i	$-0.312148\pi$
$42$	1.91853	−	2.72966i	0.296035	−	0.421195i
$43$	3.80028			0.579538			0.289769	−	0.957097i	$-0.406422\pi$
$43$	3.80028			0.579538			0.289769	+	0.957097i	$0.406422\pi$
$44$	−2.22199	+	11.3890i	−0.334977	+	1.71695i
$45$	−4.58294	−	7.67665i	−0.683185	−	1.14437i
$46$	−1.40766	−	0.136034i	−0.207548	−	0.0200571i
$47$	3.46377			0.505242			0.252621	−	0.967565i	$-0.418707\pi$
$47$	3.46377			0.505242			0.252621	+	0.967565i	$0.418707\pi$
$48$	−4.29767	−	5.43416i	−0.620315	−	0.784353i
$49$	5.14470			0.734958
$50$	−5.46394	−	0.528028i	−0.772717	−	0.0746745i
$51$	−4.60326	+	8.10931i	−0.644585	+	1.13553i
$52$	−0.326408	+	1.67303i	−0.0452646	+	0.232008i
$53$	12.5912			1.72954			0.864771	−	0.502167i	$-0.167464\pi$
$53$	12.5912			1.72954			0.864771	+	0.502167i	$0.167464\pi$
$54$	−0.546399	+	7.32813i	−0.0743555	+	0.997232i
$55$		−	17.2907i		−	2.33148i
$56$	−1.09803	+	3.69279i	−0.146731	+	0.493470i
$57$	2.39766	+	1.36104i	0.317578	+	0.180274i
$58$	−5.65704	−	0.546689i	−0.742805	−	0.0717838i
$59$		−	4.46664i		−	0.581506i	−0.956798	−	0.290753i	$-0.906094\pi$
$59$		−	4.46664i		−	0.581506i	0.956798	−	0.290753i	$-0.0939059\pi$
$60$	7.83602	+	6.72130i	1.01163	+	0.867716i
$61$		−	14.3544i		−	1.83790i	−0.394376	−	0.918949i	$-0.629039\pi$
$61$		−	14.3544i		−	1.83790i	0.394376	−	0.918949i	$-0.370961\pi$
$62$	0.179685	−	1.85934i	0.0228200	−	0.236137i
$63$	3.50859	−	2.09462i	0.442041	−	0.263898i
$64$	6.70029	+	4.37105i	0.837536	+	0.546381i
$65$		−	2.53999i		−	0.315047i
$66$	−8.17200	+	11.6270i	−1.00590	+	1.43119i
$67$	−9.77174			−1.19381			−0.596904	−	0.802313i	$-0.703603\pi$
$67$	−9.77174			−1.19381			−0.596904	+	0.802313i	$0.703603\pi$
$68$	2.06182	−	10.5680i	0.250032	−	1.28156i
$69$	−1.50629	−	0.855045i	−0.181336	−	0.102935i
$70$	0.552204	−	5.71411i	0.0660010	−	0.682966i
$71$	3.27263			0.388390			0.194195	−	0.980963i	$-0.437791\pi$
$71$	3.27263			0.388390			0.194195	+	0.980963i	$0.437791\pi$
$72$	−2.09263	−	8.22319i	−0.246619	−	0.969112i
$73$	2.83293			0.331569			0.165785	−	0.986162i	$-0.446984\pi$
$73$	2.83293			0.331569			0.165785	+	0.986162i	$0.446984\pi$
$74$	−0.0286329	+	0.296288i	−0.00332850	+	0.0344427i
$75$	−5.84678	−	3.31893i	−0.675128	−	0.383237i
$76$	−3.12463	−	0.609614i	−0.358420	−	0.0699275i
$77$	7.90267			0.900592
$78$	−1.20046	+	1.70800i	−0.135925	+	0.193393i
$79$			4.99823i			0.562345i	0.959657	+	0.281173i	$0.0907233\pi$
$79$			4.99823i			0.562345i	−0.959657	+	0.281173i	$0.909277\pi$
$80$	−11.0466	−	4.48092i	−1.23504	−	0.500983i
$81$	−4.27036	+	7.92237i	−0.474484	+	0.880264i
$82$	−1.44742	+	14.9776i	−0.159841	+	1.65400i
$83$		−	3.09167i		−	0.339355i	−0.985500	−	0.169678i	$-0.945727\pi$
$83$		−	3.09167i		−	0.339355i	0.985500	−	0.169678i	$-0.0542726\pi$
$84$	−3.07195	+	3.58143i	−0.335178	+	0.390766i
$85$			16.0443i			1.74025i
$86$	−5.34949	−	0.516968i	−0.576850	−	0.0557461i
$87$	−6.05341	−	3.43622i	−0.648994	−	0.368402i
$88$	4.67708	−	15.7295i	0.498579	−	1.67677i
$89$			13.7100i			1.45326i	0.687028	+	0.726631i	$0.258915\pi$
$89$			13.7100i			1.45326i	−0.687028	+	0.726631i	$0.741085\pi$
$90$	5.40692	+	11.4295i	0.569939	+	1.20478i
$91$	1.16089			0.121695
$92$	1.96299	+	0.382978i	0.204656	+	0.0399283i
$93$	1.12941	−	1.98962i	0.117114	−	0.206314i
$94$	−4.87579	−	0.471191i	−0.502900	−	0.0485996i
$95$	4.74379			0.486703
$96$	5.31041	+	8.23405i	0.541991	+	0.840384i
$97$	10.4354			1.05955			0.529775	−	0.848138i	$-0.322276\pi$
$97$	10.4354			1.05955			0.529775	+	0.848138i	$0.322276\pi$
$98$	−7.24197	−	0.699855i	−0.731550	−	0.0706961i
$99$	−14.9449	+	8.92208i	−1.50202	+	0.896703i
$100$	7.61951	+	1.48656i	0.761951	+	0.148656i
$101$	18.8027			1.87094			0.935468	−	0.353412i	$-0.114979\pi$
$101$	18.8027			1.87094			0.935468	+	0.353412i	$0.114979\pi$
$102$	7.58295	−	10.7889i	0.750823	−	1.06826i
$103$			13.5117i			1.33134i	0.746245	+	0.665672i	$0.231855\pi$
$103$			13.5117i			1.33134i	−0.746245	+	0.665672i	$0.768145\pi$
$104$	0.687059	−	2.31065i	0.0673717	−	0.226578i
$105$	3.47089	−	6.11448i	0.338724	−	0.596712i
$106$	−17.7241	−	1.71284i	−1.72152	−	0.166366i
$107$		−	1.99588i		−	0.192949i	−0.995335	−	0.0964746i	$-0.969243\pi$
$107$		−	1.99588i		−	0.192949i	0.995335	−	0.0964746i	$-0.0307566\pi$
$108$	1.76602	−	10.2412i	0.169935	−	0.985455i
$109$		−	9.17024i		−	0.878350i	−0.898402	−	0.439175i	$-0.855271\pi$
$109$		−	9.17024i		−	0.878350i	0.898402	−	0.439175i	$-0.144729\pi$
$110$	−2.35212	+	24.3393i	−0.224266	+	2.32066i
$111$	−0.179972	+	0.317048i	−0.0170822	+	0.0300928i
$112$	2.04800	−	5.04881i	0.193517	−	0.477067i
$113$		−	5.05032i		−	0.475094i	−0.971376	−	0.237547i	$-0.923657\pi$
$113$		−	5.05032i		−	0.475094i	0.971376	−	0.237547i	$-0.0763434\pi$
$114$	−3.18994	−	2.24203i	−0.298765	−	0.209986i
$115$	−2.98020			−0.277905
$116$	7.88879	+	1.53910i	0.732456	+	0.142902i
$117$	−2.19539	+	1.31065i	−0.202964	+	0.121169i
$118$	−0.607615	+	6.28749i	−0.0559355	+	0.578810i
$119$	−7.33302			−0.672217
$120$	−10.1161	−	10.5272i	−0.923468	−	0.961001i
$121$	−22.6615			−2.06014
$122$	−1.95269	+	20.2061i	−0.176789	+	1.82938i
$123$	−9.09778	+	16.0271i	−0.820319	+	1.44511i
$124$	−0.505868	+	2.59287i	−0.0454283	+	0.232847i
$125$	3.33310			0.298121
$126$	−5.22383	+	2.47122i	−0.465376	+	0.220154i
$127$			13.2467i			1.17545i	0.809059	+	0.587727i	$0.199977\pi$
$127$			13.2467i			1.17545i	−0.809059	+	0.587727i	$0.800023\pi$
$128$	−8.83709	−	7.06440i	−0.781096	−	0.624411i
$129$	−5.72431	−	3.24941i	−0.503998	−	0.286095i
$130$	−0.345525	+	3.57543i	−0.0303045	+	0.313586i
$131$			13.8089i			1.20649i	0.797555	+	0.603246i	$0.206126\pi$
$131$			13.8089i			1.20649i	−0.797555	+	0.603246i	$0.793874\pi$
$132$	13.0850	−	15.2552i	1.13891	−	1.32779i
$133$			2.16814i			0.188002i
$134$	13.7552	+	1.32929i	1.18827	+	0.114833i
$135$	0.339345	+	15.4818i	0.0292062	+	1.33247i
$136$	−4.33995	+	14.5957i	−0.372147	+	1.25157i
$137$			12.7826i			1.09209i	0.837755	+	0.546046i	$0.183867\pi$
$137$			12.7826i			1.09209i	−0.837755	+	0.546046i	$0.816133\pi$
$138$	2.00402	+	1.40851i	0.170593	+	0.119901i
$139$	1.50160			0.127364			0.0636821	−	0.997970i	$-0.479716\pi$
$139$	1.50160			0.127364			0.0636821	+	0.997970i	$0.479716\pi$
$140$	−1.55463	+	7.96838i	−0.131390	+	0.673451i
$141$	−5.21743	−	2.96168i	−0.439387	−	0.249418i
$142$	−4.60674	−	0.445190i	−0.386589	−	0.0373595i
$143$	−4.94485			−0.413509
$144$	1.82707	+	11.8601i	0.152256	+	0.988341i
$145$	−11.9767			−0.994612
$146$	−3.98779	−	0.385375i	−0.330032	−	0.0318939i
$147$	−7.74940	−	4.39895i	−0.639159	−	0.362819i
$148$	0.0806104	−	0.413176i	0.00662614	−	0.0339628i
$149$	−20.4255			−1.67332			−0.836661	−	0.547721i	$-0.815495\pi$
$149$	−20.4255			−1.67332			−0.836661	+	0.547721i	$0.815495\pi$
$150$	7.77877	+	5.46727i	0.635134	+	0.446401i
$151$		−	15.9023i		−	1.29411i	−0.762443	−	0.647055i	$-0.776000\pi$
$151$		−	15.9023i		−	1.29411i	0.762443	−	0.647055i	$-0.224000\pi$
$152$	4.31547	+	1.28318i	0.350031	+	0.104080i
$153$	13.8676	−	8.27896i	1.12113	−	0.669314i
$154$	−11.1242	−	1.07503i	−0.896416	−	0.0866286i
$155$		−	3.93648i		−	0.316186i
$156$	1.92218	−	2.24097i	0.153898	−	0.179421i
$157$		−	8.89088i		−	0.709569i	−0.934948	−	0.354785i	$-0.884554\pi$
$157$		−	8.89088i		−	0.709569i	0.934948	−	0.354785i	$-0.115446\pi$
$158$	0.679930	−	7.03579i	0.0540923	−	0.559738i
$159$	−18.9660	−	10.7661i	−1.50410	−	0.853806i
$160$	14.9402	+	7.81031i	1.18113	+	0.617459i
$161$		−	1.36209i		−	0.107348i
$162$	7.08891	−	10.5711i	0.556957	−	0.830541i
$163$	5.85236			0.458392			0.229196	−	0.973380i	$-0.426390\pi$
$163$	5.85236			0.458392			0.229196	+	0.973380i	$0.426390\pi$
$164$	4.07494	−	20.8865i	0.318199	−	1.63096i
$165$	−14.7843	+	26.0447i	−1.15096	+	2.02758i
$166$	−0.420573	+	4.35201i	−0.0326428	+	0.337782i
$167$	5.01615			0.388161			0.194081	−	0.980986i	$-0.437828\pi$
$167$	5.01615			0.388161			0.194081	+	0.980986i	$0.437828\pi$
$168$	4.81145	−	4.62353i	0.371211	−	0.356713i
$169$	12.2736			0.944124
$170$	2.18258	−	22.5849i	0.167396	−	1.73218i
$171$	−2.44782	−	4.10022i	−0.187190	−	0.313552i
$172$	7.45992	+	1.45543i	0.568813	+	0.110975i
$173$	−9.08009			−0.690346			−0.345173	−	0.938539i	$-0.612180\pi$
$173$	−9.08009			−0.690346			−0.345173	+	0.938539i	$0.612180\pi$
$174$	8.05367	+	5.66049i	0.610547	+	0.429121i
$175$		−	5.28708i		−	0.399666i
$176$	−8.72347	+	21.5055i	−0.657556	+	1.62104i
$177$	−3.81917	+	6.72803i	−0.287067	+	0.505710i
$178$	1.86503	−	19.2990i	0.139790	−	1.44652i
$179$		−	18.9179i		−	1.41399i	−0.707217	−	0.706996i	$-0.750050\pi$
$179$		−	18.9179i		−	1.41399i	0.707217	−	0.706996i	$-0.249950\pi$
$180$	−6.05627	−	16.8243i	−0.451408	−	1.25401i
$181$		−	13.2998i		−	0.988565i	−0.869301	−	0.494283i	$-0.835431\pi$
$181$		−	13.2998i		−	0.988565i	0.869301	−	0.494283i	$-0.164569\pi$
$182$	−1.63414	−	0.157921i	−0.121131	−	0.0117059i
$183$	−12.2737	+	21.6219i	−0.907297	+	1.59834i
$184$	−2.71112	−	0.806135i	−0.199866	−	0.0594291i
$185$			0.627281i			0.0461186i
$186$	−1.86048	+	2.64706i	−0.136417	+	0.194092i
$187$	31.2351			2.28414
$188$	6.79934	+	1.32655i	0.495893	+	0.0967485i
$189$	−7.07594	+	0.155097i	−0.514699	+	0.0112816i
$190$	−6.67763	−	0.645318i	−0.484446	−	0.0468163i
$191$	14.6288			1.05850			0.529250	−	0.848466i	$-0.322473\pi$
$191$	14.6288			1.05850			0.529250	+	0.848466i	$0.322473\pi$
$192$	−6.35511	−	12.3131i	−0.458641	−	0.888622i
$193$	8.05377			0.579723			0.289861	−	0.957069i	$-0.406391\pi$
$193$	8.05377			0.579723			0.289861	+	0.957069i	$0.406391\pi$
$194$	−14.6894	−	1.41957i	−1.05464	−	0.101919i
$195$	−2.17180	+	3.82595i	−0.155526	+	0.273982i
$196$	10.0990	+	1.97031i	0.721357	+	0.140736i
$197$	−5.98939			−0.426726			−0.213363	−	0.976973i	$-0.568442\pi$
$197$	−5.98939			−0.426726			−0.213363	+	0.976973i	$0.568442\pi$
$198$	22.2510	−	10.5262i	1.58131	−	0.748064i
$199$			20.8081i			1.47504i	0.675323	+	0.737522i	$0.264004\pi$
$199$			20.8081i			1.47504i	−0.675323	+	0.737522i	$0.735996\pi$
$200$	−10.5234	−	3.12908i	−0.744119	−	0.221260i
$201$	14.7190	+	8.35528i	1.03820	+	0.589336i
$202$	−26.4677	−	2.55780i	−1.86226	−	0.179967i
$203$		−	5.47393i		−	0.384195i
$204$	−12.1418	+	14.1555i	−0.850099	+	0.991086i
$205$			31.7097i			2.21470i
$206$	1.83805	−	19.0198i	0.128063	−	1.32517i
$207$	1.53780	+	2.57588i	0.106884	+	0.179036i
$208$	−1.28147	+	3.15914i	−0.0888540	+	0.219047i
$209$		−	9.23523i		−	0.638814i
$210$	−5.71759	+	8.13492i	−0.394552	+	0.561363i
$211$	15.6498			1.07737			0.538687	−	0.842506i	$-0.318920\pi$
$211$	15.6498			1.07737			0.538687	+	0.842506i	$0.318920\pi$
$212$	24.7165	+	4.82218i	1.69754	+	0.331188i
$213$	−4.92952	−	2.79825i	−0.337765	−	0.191733i
$214$	−0.271508	+	2.80951i	−0.0185599	+	0.192054i
$215$	−11.3256			−0.772399
$216$	−3.87909	+	14.1758i	−0.263939	+	0.964539i
$217$	1.79916			0.122135
$218$	−1.24747	+	12.9085i	−0.0844890	+	0.874277i
$219$	−4.26720	−	2.42228i	−0.288351	−	0.163683i
$220$	6.62196	−	33.9414i	0.446452	−	2.28833i
$221$	4.58842			0.308650
$222$	0.296468	−	0.421812i	0.0198977	−	0.0283101i
$223$		−	21.4944i		−	1.43937i	−0.694298	−	0.719687i	$-0.744285\pi$
$223$		−	21.4944i		−	1.43937i	0.694298	−	0.719687i	$-0.255715\pi$
$224$	−3.56968	+	6.82839i	−0.238509	+	0.456241i
$225$	5.96909	+	9.99852i	0.397939	+	0.666568i
$226$	−0.687016	+	7.10911i	−0.0456996	+	0.472891i
$227$			0.878929i			0.0583366i	0.999575	+	0.0291683i	$0.00928587\pi$
$227$			0.878929i			0.0583366i	−0.999575	+	0.0291683i	$0.990714\pi$
$228$	4.18534	+	3.58995i	0.277181	+	0.237750i
$229$			17.2682i			1.14111i	0.821259	+	0.570556i	$0.193272\pi$
$229$			17.2682i			1.14111i	−0.821259	+	0.570556i	$0.806728\pi$
$230$	4.19509	+	0.405409i	0.276616	+	0.0267319i
$231$	−11.9037	−	6.75713i	−0.783204	−	0.444587i
$232$	−10.8953	−	3.23967i	−0.715314	−	0.212695i
$233$		−	12.7832i		−	0.837454i	−0.908112	−	0.418727i	$-0.862476\pi$
$233$		−	12.7832i		−	0.837454i	0.908112	−	0.418727i	$-0.137524\pi$
$234$	3.26865	−	1.54629i	0.213678	−	0.101084i
$235$	−10.3227			−0.673380
$236$	1.71063	−	8.76796i	0.111352	−	0.570745i
$237$	4.27371	−	7.52877i	0.277607	−	0.489046i
$238$	10.3224	+	0.997542i	0.669100	+	0.0646610i
$239$	29.7037			1.92137			0.960687	−	0.277635i	$-0.0895506\pi$
$239$	29.7037			1.92137			0.960687	+	0.277635i	$0.0895506\pi$
$240$	12.8079	+	16.1949i	0.826747	+	1.04537i
$241$	9.93016			0.639658			0.319829	−	0.947475i	$-0.396375\pi$
$241$	9.93016			0.639658			0.319829	+	0.947475i	$0.396375\pi$
$242$	31.8996	+	3.08274i	2.05059	+	0.198166i
$243$	13.2064	−	8.28202i	0.847189	−	0.531292i
$244$	5.49744	−	28.1776i	0.351938	−	1.80389i
$245$	−15.3322			−0.979541
$246$	14.9868	−	21.3230i	0.955522	−	1.35950i
$247$		−	1.35665i		−	0.0863214i
$248$	1.06481	−	3.58105i	0.0676153	−	0.227397i
$249$	−2.64352	+	4.65694i	−0.167526	+	0.295122i
$250$	−4.69185	−	0.453415i	−0.296739	−	0.0286765i
$251$			3.64528i			0.230088i	0.993360	+	0.115044i	$0.0367009\pi$
$251$			3.64528i			0.230088i	−0.993360	+	0.115044i	$0.963299\pi$
$252$	7.68953	−	2.76801i	0.484395	−	0.174368i
$253$			5.80186i			0.364760i
$254$	1.80200	−	18.6468i	0.113068	−	1.17000i
$255$	13.7186	−	24.1674i	0.859094	−	1.51342i
$256$	11.4786	+	11.1464i	0.717411	+	0.696650i
$257$			6.26550i			0.390831i	0.980721	+	0.195416i	$0.0626055\pi$
$257$			6.26550i			0.390831i	−0.980721	+	0.195416i	$0.937394\pi$
$258$	7.61583	+	5.35276i	0.474141	+	0.333248i
$259$	−0.286697			−0.0178145
$260$	0.972760	−	4.98597i	0.0603280	−	0.309217i
$261$	6.18004	+	10.3519i	0.382535	+	0.640765i
$262$	1.87849	−	19.4382i	0.116053	−	1.20090i
$263$	6.89077			0.424903			0.212452	−	0.977172i	$-0.431855\pi$
$263$	6.89077			0.424903			0.212452	+	0.977172i	$0.431855\pi$
$264$	−20.4944	+	19.6940i	−1.26135	+	1.21208i
$265$	−37.5244			−2.30511
$266$	0.294941	−	3.05199i	0.0180840	−	0.187130i
$267$	11.7227	−	20.6512i	0.717418	−	1.26384i
$268$	−19.1818	−	3.74237i	−1.17172	−	0.228601i
$269$	9.20381			0.561166			0.280583	−	0.959830i	$-0.409472\pi$
$269$	9.20381			0.561166			0.280583	+	0.959830i	$0.409472\pi$
$270$	1.62838	−	21.8393i	0.0991000	−	1.32910i
$271$			5.65011i			0.343220i	0.985165	+	0.171610i	$0.0548969\pi$
$271$			5.65011i			0.343220i	−0.985165	+	0.171610i	$0.945103\pi$
$272$	8.09466	−	19.9553i	0.490811	−	1.20997i
$273$	−1.74864	−	0.992617i	−0.105833	−	0.0600759i
$274$	1.73887	−	17.9935i	0.105049	−	1.08703i
$275$			22.5204i			1.35803i
$276$	−2.62936	−	2.25532i	−0.158269	−	0.135754i
$277$		−	20.0093i		−	1.20224i	−0.799158	−	0.601121i	$-0.794721\pi$
$277$		−	20.0093i		−	1.20224i	0.799158	−	0.601121i	$-0.205279\pi$
$278$	−2.11374	−	0.204269i	−0.126774	−	0.0122512i
$279$	−3.40243	+	2.03124i	−0.203698	+	0.121607i
$280$	3.27235	−	11.0052i	0.195560	−	0.657689i
$281$		−	17.2312i		−	1.02793i	−0.857812	−	0.513963i	$-0.828177\pi$
$281$		−	17.2312i		−	1.02793i	0.857812	−	0.513963i	$-0.171823\pi$
$282$	6.94145	+	4.87877i	0.413357	+	0.290526i
$283$	12.7408			0.757363			0.378682	−	0.925527i	$-0.376378\pi$
$283$	12.7408			0.757363			0.378682	+	0.925527i	$0.376378\pi$
$284$	6.42415	+	1.25335i	0.381203	+	0.0743725i
$285$	−7.14551	−	4.05616i	−0.423264	−	0.240266i
$286$	6.96065	+	0.672668i	0.411592	+	0.0397757i
$287$	−14.4928			−0.855485
$288$	−0.958512	−	16.9435i	−0.0564809	−	0.998404i
$289$	−11.9836			−0.704920
$290$	16.8591	+	1.62924i	0.990000	+	0.0956724i
$291$	−15.7186	−	8.92270i	−0.921443	−	0.523058i
$292$	5.56101	+	1.08495i	0.325433	+	0.0634919i
$293$	−29.5288			−1.72509			−0.862544	−	0.505982i	$-0.831130\pi$
$293$	−29.5288			−1.72509			−0.862544	+	0.505982i	$0.831130\pi$
$294$	10.3101	+	7.24639i	0.601296	+	0.422618i
$295$			13.3115i			0.775023i
$296$	−0.169678	+	0.570644i	−0.00986232	+	0.0331680i
$297$	30.1401	−	0.660638i	1.74891	−	0.0383341i
$298$	28.7521	+	2.77856i	1.66556	+	0.160958i
$299$			0.852288i			0.0492891i
$300$	−10.2061	−	8.75421i	−0.589249	−	0.505425i
$301$		−	5.17634i		−	0.298359i
$302$	−2.16325	+	22.3850i	−0.124481	+	1.28811i
$303$	−28.3222	−	16.0771i	−1.62707	−	0.923607i
$304$	−5.90015	−	2.39333i	−0.338397	−	0.137267i
$305$			42.7791i			2.44952i
$306$	−20.6471	+	9.76745i	−1.18032	+	0.558368i
$307$	−24.3810			−1.39149			−0.695747	−	0.718287i	$-0.744927\pi$
$307$	−24.3810			−1.39149			−0.695747	+	0.718287i	$0.744927\pi$
$308$	15.5128	+	3.02655i	0.883927	+	0.172454i
$309$	11.5531	−	20.3524i	0.657231	−	1.15781i
$310$	−0.535496	+	5.54121i	−0.0304141	+	0.314720i
$311$	2.85460			0.161870			0.0809348	−	0.996719i	$-0.474209\pi$
$311$	2.85460			0.161870			0.0809348	+	0.996719i	$0.474209\pi$
$312$	−3.01062	+	2.89303i	−0.170443	+	0.163786i
$313$	8.10335			0.458029			0.229014	−	0.973423i	$-0.426450\pi$
$313$	8.10335			0.458029			0.229014	+	0.973423i	$0.426450\pi$
$314$	−1.20946	+	12.5153i	−0.0682539	+	0.706279i
$315$	−10.4563	+	6.24239i	−0.589146	+	0.351719i
$316$	−1.91422	+	9.81148i	−0.107683	+	0.551939i
$317$	22.9292			1.28783			0.643916	−	0.765096i	$-0.277309\pi$
$317$	22.9292			1.28783			0.643916	+	0.765096i	$0.277309\pi$
$318$	25.2331	+	17.7350i	1.41500	+	0.994527i
$319$			23.3163i			1.30546i
$320$	−19.9682	−	13.0266i	−1.11626	−	0.728209i
$321$	−1.70657	+	3.00637i	−0.0952513	+	0.167799i
$322$	−0.185291	+	1.91736i	−0.0103259	+	0.106850i
$323$			8.56953i			0.476822i
$324$	−11.4168	+	13.9161i	−0.634265	+	0.773116i
$325$			3.30823i			0.183507i
$326$	−8.23811	−	0.796121i	−0.456267	−	0.0440930i
$327$	−7.84096	+	13.8130i	−0.433606	+	0.763861i
$328$	−8.57738	+	28.8466i	−0.473607	+	1.59279i
$329$		−	4.71797i		−	0.260110i
$330$	24.3542	−	34.6508i	1.34065	−	1.90747i
$331$	0.553549			0.0304258			0.0152129	−	0.999884i	$-0.495157\pi$
$331$	0.553549			0.0304258			0.0152129	+	0.999884i	$0.495157\pi$
$332$	1.18404	−	6.06892i	0.0649829	−	0.333075i
$333$	0.542180	−	0.323680i	0.0297113	−	0.0177376i
$334$	−7.06101	−	0.682367i	−0.386361	−	0.0373375i
$335$	29.1217			1.59109
$336$	−7.40182	+	5.85382i	−0.403803	+	0.319352i
$337$	−19.3916			−1.05633			−0.528165	−	0.849142i	$-0.677120\pi$
$337$	−19.3916			−1.05633			−0.528165	+	0.849142i	$0.677120\pi$
$338$	−17.2770	−	1.66963i	−0.939746	−	0.0908159i
$339$	−4.31825	+	7.60723i	−0.234535	+	0.413168i
$340$	−6.14463	+	31.4949i	−0.333240	+	1.70805i
$341$	−7.66355			−0.415004
$342$	2.88792	+	6.10468i	0.156161	+	0.330103i
$343$		−	16.5422i		−	0.893195i
$344$	−10.3030	−	3.06354i	−0.555501	−	0.165175i
$345$	4.48903	+	2.54820i	0.241681	+	0.137191i
$346$	12.7816	+	1.23520i	0.687145	+	0.0664049i
$347$		−	11.2938i		−	0.606284i	−0.952945	−	0.303142i	$-0.901964\pi$
$347$		−	11.2938i		−	0.606284i	0.952945	−	0.303142i	$-0.0980356\pi$
$348$	−10.5668	−	9.06360i	−0.566439	−	0.485860i
$349$			19.0039i			1.01725i	0.860987	+	0.508627i	$0.169847\pi$
$349$			19.0039i			1.01725i	−0.860987	+	0.508627i	$0.830153\pi$
$350$	−0.719223	+	7.44239i	−0.0384441	+	0.397812i
$351$	4.42755	−	0.0970471i	0.236325	−	0.00517999i
$352$	15.2051	−	29.0856i	0.810436	−	1.55027i
$353$		−	16.0338i		−	0.853390i	−0.904395	−	0.426695i	$-0.859678\pi$
$353$		−	16.0338i		−	0.853390i	0.904395	−	0.426695i	$-0.140322\pi$
$354$	6.29132	−	8.95122i	0.334380	−	0.475752i
$355$	−9.75310			−0.517641
$356$	−5.25065	+	26.9127i	−0.278284	+	1.42637i
$357$	11.0456	+	6.27006i	0.584597	+	0.331847i
$358$	−2.57349	+	26.6299i	−0.136013	+	1.40744i
$359$	−30.6919			−1.61986			−0.809928	−	0.586530i	$-0.800494\pi$
$359$	−30.6919			−1.61986			−0.809928	+	0.586530i	$0.800494\pi$
$360$	6.23646	+	24.5067i	0.328691	+	1.29162i
$361$	−16.4663			−0.866646
$362$	−1.80922	+	18.7215i	−0.0950907	+	0.983981i
$363$	34.1348	+	19.3766i	1.79161	+	1.01701i
$364$	2.27882	+	0.444598i	0.119443	+	0.0233033i
$365$	−8.44269			−0.441911
$366$	20.2184	−	28.7666i	1.05684	−	1.50365i
$367$		−	12.7262i		−	0.664304i	−0.943226	−	0.332152i	$-0.892225\pi$
$367$		−	12.7262i		−	0.664304i	0.943226	−	0.332152i	$-0.107775\pi$
$368$	3.70666	+	1.50357i	0.193223	+	0.0783788i
$369$	27.4077	−	16.3624i	1.42679	−	0.851790i
$370$	0.0853316	−	0.882996i	0.00443618	−	0.0459048i
$371$		−	17.1504i		−	0.890407i
$372$	2.97900	−	3.47307i	0.154454	−	0.180070i
$373$			0.102701i			0.00531768i	0.999996	+	0.00265884i	$0.000846336\pi$
$373$			0.102701i			0.00531768i	−0.999996	+	0.00265884i	$0.999154\pi$
$374$	−43.9683	−	4.24904i	−2.27355	−	0.219713i
$375$	−5.02060	−	2.84995i	−0.259263	−	0.147171i
$376$	−9.39067	−	2.79227i	−0.484287	−	0.144000i
$377$			3.42514i			0.176404i
$378$	9.98159	+	0.744247i	0.513397	+	0.0382799i
$379$	22.9132			1.17697			0.588485	−	0.808508i	$-0.299724\pi$
$379$	22.9132			1.17697			0.588485	+	0.808508i	$0.299724\pi$
$380$	9.31202	+	1.81677i	0.477696	+	0.0931984i
$381$	11.3265	−	19.9533i	0.580275	−	1.02224i
$382$	−20.5923	−	1.99001i	−1.05359	−	0.101818i
$383$	−28.1640			−1.43911			−0.719556	−	0.694435i	$-0.755654\pi$
$383$	−28.1640			−1.43911			−0.719556	+	0.694435i	$0.755654\pi$
$384$	7.27081	+	18.1971i	0.371037	+	0.928618i
$385$	−23.5515			−1.20030
$386$	−11.3369	−	1.09559i	−0.577035	−	0.0557639i
$387$	5.84406	+	9.78909i	0.297070	+	0.497607i
$388$	20.4845	+	3.99652i	1.03994	+	0.202892i
$389$	5.41823			0.274715			0.137358	−	0.990522i	$-0.456139\pi$
$389$	5.41823			0.274715			0.137358	+	0.990522i	$0.456139\pi$
$390$	3.57761	−	5.09018i	0.181159	−	0.257751i
$391$		−	5.38365i		−	0.272263i
$392$	−13.9479	−	4.14733i	−0.704475	−	0.209472i
$393$	11.8073	−	20.8002i	0.595597	−	1.04923i
$394$	8.43100	+	0.814761i	0.424748	+	0.0410471i
$395$		−	14.8957i		−	0.749485i
$396$	−32.7537	+	11.7904i	−1.64593	+	0.592488i
$397$			22.1875i			1.11356i	0.830660	+	0.556780i	$0.187963\pi$
$397$			22.1875i			1.11356i	−0.830660	+	0.556780i	$0.812037\pi$
$398$	2.83061	−	29.2906i	0.141885	−	1.46820i
$399$	1.85386	−	3.26584i	0.0928089	−	0.163496i
$400$	14.3877	+	5.83622i	0.719385	+	0.291811i
$401$		−	25.6622i		−	1.28151i	−0.767745	−	0.640755i	$-0.778621\pi$
$401$		−	25.6622i		−	1.28151i	0.767745	−	0.640755i	$-0.221379\pi$
$402$	−19.5827	−	13.7636i	−0.976698	−	0.686468i
$403$	−1.12577			−0.0560785
$404$	36.9094	+	7.20102i	1.83631	+	0.358264i
$405$	12.7265	−	23.6103i	0.632386	−	1.17320i
$406$	−0.744641	+	7.70541i	−0.0369559	+	0.382413i
$407$	1.22119			0.0605322
$408$	19.0172	−	18.2744i	0.941490	−	0.904719i
$409$	−30.4116			−1.50376			−0.751880	−	0.659300i	$-0.770853\pi$
$409$	−30.4116			−1.50376			−0.751880	+	0.659300i	$0.770853\pi$
$410$	4.31360	−	44.6363i	0.213034	−	2.20443i
$411$	10.9297	−	19.2543i	0.539122	−	0.949742i
$412$	−5.17468	+	26.5232i	−0.254938	+	1.30671i
$413$	−6.08397			−0.299373
$414$	−1.81428	−	3.83515i	−0.0891670	−	0.188487i
$415$			9.21380i			0.452288i
$416$	2.23362	−	4.27265i	0.109512	−	0.209484i
$417$	−2.26184	−	1.28394i	−0.110763	−	0.0628746i
$418$	−1.25631	+	13.0000i	−0.0614479	+	0.635852i
$419$			16.8895i			0.825105i	0.910934	+	0.412552i	$0.135363\pi$
$419$			16.8895i			0.825105i	−0.910934	+	0.412552i	$0.864637\pi$
$420$	9.15503	−	10.6734i	0.446720	−	0.520808i
$421$		−	21.1951i		−	1.03298i	−0.856292	−	0.516492i	$-0.827238\pi$
$421$		−	21.1951i		−	1.03298i	0.856292	−	0.516492i	$-0.172762\pi$
$422$	−22.0295	−	2.12890i	−1.07238	−	0.103633i
$423$	5.32657	+	8.92227i	0.258987	+	0.433815i
$424$	−34.1363	−	10.1503i	−1.65781	−	0.492940i
$425$		−	20.8971i		−	1.01366i
$426$	6.55841	+	4.60955i	0.317756	+	0.223334i
$427$	−19.5521			−0.946192
$428$	0.764379	−	3.91789i	0.0369477	−	0.189379i
$429$	7.44836	+	4.22807i	0.359610	+	0.204133i
$430$	15.9425	+	1.54067i	0.768818	+	0.0742976i
$431$	22.2205			1.07033			0.535163	−	0.844749i	$-0.320250\pi$
$431$	22.2205			1.07033			0.535163	+	0.844749i	$0.320250\pi$
$432$	7.38881	−	19.4269i	0.355494	−	0.934678i
$433$	−0.426510			−0.0204967			−0.0102484	−	0.999947i	$-0.503262\pi$
$433$	−0.426510			−0.0204967			−0.0102484	+	0.999947i	$0.503262\pi$
$434$	−2.53260	−	0.244747i	−0.121569	−	0.0117482i
$435$	18.0404	+	10.2406i	0.864969	+	0.491001i
$436$	3.51200	−	18.0011i	0.168194	−	0.862095i
$437$	−1.59177			−0.0761447
$438$	5.67724	+	3.99022i	0.271269	+	0.190660i
$439$			4.91908i			0.234775i	0.993086	+	0.117387i	$0.0374519\pi$
$439$			4.91908i			0.234775i	−0.993086	+	0.117387i	$0.962548\pi$
$440$	−13.9386	+	46.8770i	−0.664498	+	2.23478i
$441$	7.91151	+	13.2522i	0.376739	+	0.631055i
$442$	−6.45891	−	0.624181i	−0.307219	−	0.0296893i
$443$			39.8938i			1.89541i	0.319143	+	0.947707i	$0.396605\pi$
$443$			39.8938i			1.89541i	−0.319143	+	0.947707i	$0.603395\pi$
$444$	−0.474706	+	0.553436i	−0.0225286	+	0.0262649i
$445$		−	40.8587i		−	1.93689i
$446$	−2.92398	+	30.2568i	−0.138454	+	1.43270i
$447$	30.7666	+	17.4647i	1.45521	+	0.826053i
$448$	5.95378	−	9.12642i	0.281290	−	0.431183i
$449$			18.8142i			0.887899i	0.896052	+	0.443950i	$0.146423\pi$
$449$			18.8142i			0.887899i	−0.896052	+	0.443950i	$0.853577\pi$
$450$	−7.04229	−	14.8865i	−0.331977	−	0.701755i
$451$	61.7325			2.90687
$452$	1.93416	−	9.91372i	0.0909754	−	0.466302i
$453$	−13.5972	+	23.9534i	−0.638851	+	1.12543i
$454$	0.119564	−	1.23723i	0.00561143	−	0.0580660i
$455$	−3.45970			−0.162193
$456$	−5.40316	−	5.62277i	−0.253026	−	0.263310i
$457$	6.47683			0.302973			0.151487	−	0.988459i	$-0.451594\pi$
$457$	6.47683			0.302973			0.151487	+	0.988459i	$0.451594\pi$
$458$	2.34906	−	24.3076i	0.109764	−	1.13582i
$459$	−27.9675	+	0.613017i	−1.30541	+	0.0286132i
$460$	−5.85010	−	1.14135i	−0.272762	−	0.0532158i
$461$	38.5365			1.79482			0.897412	−	0.441194i	$-0.145445\pi$
$461$	38.5365			1.79482			0.897412	+	0.441194i	$0.145445\pi$
$462$	15.8371	+	11.1310i	0.736808	+	0.517862i
$463$		−	31.4845i		−	1.46321i	−0.681730	−	0.731604i	$-0.738772\pi$
$463$		−	31.4845i		−	1.46321i	0.681730	−	0.731604i	$-0.261228\pi$
$464$	14.8962	+	6.04247i	0.691537	+	0.280515i
$465$	−3.36587	+	5.92947i	−0.156088	+	0.274973i
$466$	−1.73895	+	17.9943i	−0.0805553	+	0.833571i
$467$		−	28.5861i		−	1.32281i	−0.750030	−	0.661404i	$-0.769961\pi$
$467$		−	28.5861i		−	1.32281i	0.750030	−	0.661404i	$-0.230039\pi$
$468$	−4.81149	+	1.73199i	−0.222411	+	0.0800615i
$469$			13.3100i			0.614599i
$470$	14.5308	+	1.40424i	0.670257	+	0.0647729i
$471$	−7.60210	+	13.3922i	−0.350286	+	0.617080i
$472$	−3.60071	+	12.1096i	−0.165736	+	0.557388i
$473$			22.0487i			1.01380i
$474$	−7.04009	+	10.0165i	−0.323362	+	0.460075i
$475$	−6.17860			−0.283493
$476$	−14.3946	−	2.80839i	−0.659778	−	0.128722i
$477$	19.3628	+	32.4336i	0.886561	+	1.48503i
$478$	−41.8126	−	4.04072i	−1.91246	−	0.184818i
$479$	−17.8359			−0.814943			−0.407471	−	0.913218i	$-0.633589\pi$
$479$	−17.8359			−0.814943			−0.407471	+	0.913218i	$0.633589\pi$
$480$	−15.8261	−	24.5391i	−0.722358	−	1.12005i
$481$	0.179392			0.00817957
$482$	−13.9783	−	1.35084i	−0.636692	−	0.0615291i
$483$	−1.16465	+	2.05170i	−0.0529934	+	0.0933557i
$484$	−44.4844	−	8.67888i	−2.02202	−	0.394495i
$485$	−31.0995			−1.41215
$486$	−19.7167	+	9.86171i	−0.894366	+	0.447336i
$487$			4.21929i			0.191194i	0.995420	+	0.0955972i	$0.0304761\pi$
$487$			4.21929i			0.191194i	−0.995420	+	0.0955972i	$0.969524\pi$
$488$	−11.5716	+	38.9166i	−0.523823	+	1.76167i
$489$	−8.81533	−	5.00403i	−0.398643	−	0.226290i
$490$	21.5825	+	2.08571i	0.974999	+	0.0942227i
$491$			19.7601i			0.891763i	0.895092	+	0.445881i	$0.147110\pi$
$491$			19.7601i			0.891763i	−0.895092	+	0.445881i	$0.852890\pi$
$492$	−23.9969	+	27.9767i	−1.08186	+	1.26129i
$493$		−	21.6356i		−	0.974419i
$494$	−0.184550	+	1.90969i	−0.00830331	+	0.0859211i
$495$	44.5388	−	26.5896i	2.00187	−	1.19511i
$496$	−1.98603	+	4.89604i	−0.0891753	+	0.219839i
$497$		−	4.45763i		−	0.199952i
$498$	4.35467	−	6.19577i	0.195137	−	0.277639i
$499$	−13.1506			−0.588701			−0.294351	−	0.955697i	$-0.595103\pi$
$499$	−13.1506			−0.588701			−0.294351	+	0.955697i	$0.595103\pi$
$500$	6.54283	+	1.27650i	0.292604	+	0.0570870i
$501$	−7.55575	−	4.28903i	−0.337566	−	0.191620i
$502$	0.495883	−	5.13130i	0.0221323	−	0.229021i
$503$	−40.6941			−1.81446			−0.907230	−	0.420634i	$-0.861808\pi$
$503$	−40.6941			−1.81446			−0.907230	+	0.420634i	$0.861808\pi$
$504$	−11.2007	+	2.85036i	−0.498921	+	0.126965i
$505$	−56.0357			−2.49356
$506$	0.789250	−	8.16702i	0.0350865	−	0.363068i
$507$	−18.4876	−	10.4945i	−0.821062	−	0.466076i
$508$	−5.07320	+	26.0031i	−0.225087	+	1.15370i
$509$	−6.52138			−0.289055			−0.144528	−	0.989501i	$-0.546166\pi$
$509$	−6.52138			−0.289055			−0.144528	+	0.989501i	$0.546166\pi$
$510$	−22.5987	+	32.1531i	−1.00069	+	1.42376i
$511$		−	3.85871i		−	0.170699i
$512$	−14.6416	−	17.2518i	−0.647074	−	0.762428i
$513$	0.181250	+	8.26910i	0.00800236	+	0.365090i
$514$	0.852322	−	8.81966i	0.0375943	−	0.389019i
$515$		−	40.2674i		−	1.77440i
$516$	−9.99231	−	8.57085i	−0.439887	−	0.377311i
$517$			20.0963i			0.883834i
$518$	0.403571	+	0.0390006i	0.0177319	+	0.00171359i
$519$	13.6772	+	7.76388i	0.600363	+	0.340797i
$520$	−2.04757	+	6.88620i	−0.0897920	+	0.301980i
$521$			9.55394i			0.418566i	0.977855	+	0.209283i	$0.0671129\pi$
$521$			9.55394i			0.418566i	−0.977855	+	0.209283i	$0.932887\pi$
$522$	−7.29117	−	15.4126i	−0.319126	−	0.674590i
$523$	18.5211			0.809871			0.404935	−	0.914345i	$-0.367294\pi$
$523$	18.5211			0.809871			0.404935	+	0.914345i	$0.367294\pi$
$524$	−5.28852	+	27.1068i	−0.231030	+	1.18417i
$525$	−4.52069	+	7.96386i	−0.197299	+	0.347571i
$526$	−9.69983	−	0.937380i	−0.422933	−	0.0408717i
$527$	7.11114			0.309766
$528$	31.5282	−	24.9345i	1.37209	−	1.08513i
$529$	1.00000			0.0434783
$530$	52.8215	+	5.10460i	2.29442	+	0.221730i
$531$	11.5055	−	6.86878i	0.499298	−	0.298080i
$532$	−0.830351	+	4.25604i	−0.0360003	+	0.184523i
$533$	9.06845			0.392798
$534$	−19.3108	+	27.4752i	−0.835660	+	1.18897i
$535$			5.94812i			0.257160i
$536$	26.4923	+	7.87735i	1.14429	+	0.340250i
$537$	−16.1757	+	28.4958i	−0.698032	+	1.22969i
$538$	−12.9558	−	1.25203i	−0.558564	−	0.0539790i
$539$			29.8488i			1.28568i
$540$	−5.26308	+	30.5207i	−0.226487	+	1.31340i
$541$		−	6.54485i		−	0.281385i	−0.990053	−	0.140693i	$-0.955067\pi$
$541$		−	6.54485i		−	0.281385i	0.990053	−	0.140693i	$-0.0449329\pi$
$542$	0.768608	−	7.95341i	0.0330145	−	0.341628i
$543$	−11.3719	+	20.0333i	−0.488015	+	0.859711i
$544$	−14.1091	+	26.9891i	−0.604923	+	1.15715i
$545$			27.3291i			1.17065i
$546$	2.32645	+	1.63514i	0.0995630	+	0.0699774i
$547$	22.1440			0.946808			0.473404	−	0.880845i	$-0.343025\pi$
$547$	22.1440			0.946808			0.473404	+	0.880845i	$0.343025\pi$
$548$	−4.89546	+	25.0921i	−0.209124	+	1.07188i
$549$	36.9754	−	22.0742i	1.57807	−	0.942105i
$550$	3.06354	−	31.7010i	0.130630	−	1.35173i
$551$	−6.39695			−0.272519
$552$	3.39443	+	3.53240i	0.144477	+	0.150349i
$553$	6.80806			0.289508
$554$	−2.72195	+	28.1662i	−0.115644	+	1.19667i
$555$	0.536353	−	0.944865i	0.0227669	−	0.0401073i
$556$	2.94763	+	0.575081i	0.125007	+	0.0243889i
$557$	−13.7714			−0.583514			−0.291757	−	0.956492i	$-0.594240\pi$
$557$	−13.7714			−0.583514			−0.291757	+	0.956492i	$0.594240\pi$
$558$	5.06577	−	2.39645i	0.214451	−	0.101450i
$559$			3.23893i			0.136992i
$560$	−6.10343	+	15.0465i	−0.257917	+	0.635829i
$561$	−47.0491	−	26.7074i	−1.98641	−	1.12759i
$562$	−2.34403	+	24.2556i	−0.0988768	+	1.02316i
$563$		−	43.5521i		−	1.83550i	−0.397155	−	0.917752i	$-0.630002\pi$
$563$		−	43.5521i		−	1.83550i	0.397155	−	0.917752i	$-0.369998\pi$
$564$	−9.10749	−	7.81190i	−0.383495	−	0.328940i
$565$			15.0510i			0.633198i
$566$	−17.9347	−	1.73319i	−0.753851	−	0.0728513i
$567$	10.7910	+	5.81663i	0.453180	+	0.244275i
$568$	−8.87249	−	2.63819i	−0.372281	−	0.110696i
$569$			36.7256i			1.53962i	0.638274	+	0.769809i	$0.279649\pi$
$569$			36.7256i			1.53962i	−0.638274	+	0.769809i	$0.720351\pi$
$570$	9.50665	+	6.68171i	0.398190	+	0.279866i
$571$	−6.35399			−0.265906			−0.132953	−	0.991122i	$-0.542446\pi$
$571$	−6.35399			−0.265906			−0.132953	+	0.991122i	$0.542446\pi$
$572$	−9.70669	−	1.89377i	−0.405857	−	0.0791826i
$573$	−22.0351	−	12.5082i	−0.920530	−	0.522540i
$574$	20.4009	+	1.97152i	0.851518	+	0.0822897i
$575$	3.88159			0.161873
$576$	−0.955635	+	23.9810i	−0.0398181	+	0.999207i
$577$	36.0375			1.50026			0.750130	−	0.661290i	$-0.229991\pi$
$577$	36.0375			1.50026			0.750130	+	0.661290i	$0.229991\pi$
$578$	16.8688	+	1.63018i	0.701651	+	0.0678067i
$579$	−12.1313	−	6.88633i	−0.504159	−	0.286186i
$580$	−23.5102	−	4.58682i	−0.976207	−	0.190458i
$581$	−4.21114			−0.174708
$582$	20.9126	+	14.6984i	0.866857	+	0.609267i
$583$			73.0526i			3.02553i
$584$	−7.68039	−	2.28372i	−0.317817	−	0.0945012i
$585$	6.54271	−	3.90598i	0.270508	−	0.161493i
$586$	41.5663	+	4.01692i	1.71709	+	0.165937i
$587$		−	0.173544i		−	0.00716291i	−0.999994	−	0.00358146i	$-0.998860\pi$
$587$		−	0.173544i		−	0.00716291i	0.999994	−	0.00358146i	$-0.00114002\pi$
$588$	−13.5273	−	11.6029i	−0.557856	−	0.478497i
$589$		−	2.10254i		−	0.0866335i
$590$	1.81081	−	18.7380i	0.0745500	−	0.771429i
$591$	9.02174	+	5.12120i	0.371105	+	0.210658i
$592$	0.316475	−	0.780188i	0.0130070	−	0.0320655i
$593$			26.2045i			1.07609i	0.842917	+	0.538044i	$0.180837\pi$
$593$			26.2045i			1.07609i	−0.842917	+	0.538044i	$0.819163\pi$
$594$	−42.5167	−	3.17013i	−1.74448	−	0.130072i
$595$	21.8539			0.895921
$596$	−40.0950	−	7.82253i	−1.64236	−	0.320423i
$597$	17.7918	−	31.3429i	0.728171	−	1.28278i
$598$	0.115940	−	1.19973i	0.00474115	−	0.0490605i
$599$	10.2797			0.420016			0.210008	−	0.977700i	$-0.432651\pi$
$599$	10.2797			0.420016			0.210008	+	0.977700i	$0.432651\pi$
$600$	13.1758	+	13.7113i	0.537899	+	0.559761i
$601$	−14.5446			−0.593287			−0.296644	−	0.954988i	$-0.595867\pi$
$601$	−14.5446			−0.593287			−0.296644	+	0.954988i	$0.595867\pi$
$602$	−0.704159	+	7.28650i	−0.0286994	+	0.296976i
$603$	−15.0270	−	25.1709i	−0.611945	−	1.02504i
$604$	6.09023	−	31.2160i	0.247808	−	1.27016i
$605$	67.5359			2.74572
$606$	37.6809	+	26.4838i	1.53068	+	1.07583i
$607$		−	37.4693i		−	1.52083i	−0.649436	−	0.760417i	$-0.724995\pi$
$607$		−	37.4693i		−	1.52083i	0.649436	−	0.760417i	$-0.275005\pi$
$608$	7.97980	+	4.17161i	0.323624	+	0.169181i
$609$	−4.68045	+	8.24531i	−0.189662	+	0.334117i
$610$	5.81942	−	60.2182i	0.235621	−	2.43817i
$611$			2.95213i			0.119430i
$612$	30.3927	−	10.9405i	1.22855	−	0.442243i
$613$			35.8106i			1.44638i	0.690651	+	0.723188i	$0.257324\pi$
$613$			35.8106i			1.44638i	−0.690651	+	0.723188i	$0.742676\pi$
$614$	34.3200	+	3.31664i	1.38504	+	0.133849i
$615$	27.1132	−	47.7639i	1.09331	−	1.92603i
$616$	−21.4250	−	6.37062i	−0.863239	−	0.256680i
$617$			17.1786i			0.691583i	0.938311	+	0.345791i	$0.112390\pi$
$617$			17.1786i			0.691583i	−0.938311	+	0.345791i	$0.887610\pi$
$618$	−19.0314	+	27.0776i	−0.765554	+	1.08922i
$619$	−30.4234			−1.22282			−0.611410	−	0.791314i	$-0.709398\pi$
$619$	−30.4234			−1.22282			−0.611410	+	0.791314i	$0.709398\pi$
$620$	1.50759	−	7.72727i	0.0605462	−	0.310335i
$621$	−0.113867	−	5.19490i	−0.00456931	−	0.208464i
$622$	−4.01830	−	0.388323i	−0.161119	−	0.0155703i
$623$	18.6743			0.748172
$624$	4.63146	−	3.66285i	0.185407	−	0.146631i
$625$	−29.3412			−1.17365
$626$	−11.4067	−	1.10233i	−0.455905	−	0.0440581i
$627$	−7.89653	+	13.9109i	−0.315357	+	0.555548i
$628$	3.40502	−	17.4527i	0.135875	−	0.696439i
$629$	−1.13317			−0.0451823
$630$	15.5681	−	7.36472i	0.620246	−	0.293418i
$631$		−	34.7687i		−	1.38412i	−0.721839	−	0.692061i	$-0.756703\pi$
$631$		−	34.7687i		−	1.38412i	0.721839	−	0.692061i	$-0.243297\pi$
$632$	4.02925	−	13.5508i	0.160275	−	0.539021i
$633$	−23.5730	−	13.3813i	−0.936944	−	0.531857i
$634$	−32.2764	−	3.11915i	−1.28186	−	0.123877i
$635$		−	39.4778i		−	1.56663i
$636$	−33.1069	−	28.3973i	−1.31278	−	1.12603i
$637$			4.38477i			0.173731i
$638$	3.17181	−	32.8213i	0.125573	−	1.29941i
$639$	5.03265	+	8.42993i	0.199088	+	0.333483i
$640$	26.3363	+	21.0533i	1.04103	+	0.832206i
$641$		−	12.0542i		−	0.476112i	−0.971251	−	0.238056i	$-0.923490\pi$
$641$		−	12.0542i		−	0.476112i	0.971251	−	0.238056i	$-0.0765102\pi$
$642$	2.81123	−	3.99978i	0.110950	−	0.157859i
$643$	−11.6786			−0.460561			−0.230280	−	0.973124i	$-0.573964\pi$
$643$	−11.6786			−0.460561			−0.230280	+	0.973124i	$0.573964\pi$
$644$	0.521652	−	2.67377i	0.0205560	−	0.105361i
$645$	17.0596	+	9.68389i	0.671721	+	0.381303i
$646$	1.16575	−	12.0630i	0.0458658	−	0.474610i
$647$	−23.7356			−0.933142			−0.466571	−	0.884484i	$-0.654511\pi$
$647$	−23.7356			−0.933142			−0.466571	+	0.884484i	$0.654511\pi$
$648$	17.9639	−	18.0360i	0.705690	−	0.708520i
$649$	25.9148			1.01724
$650$	0.450032	−	4.65685i	0.0176517	−	0.182657i
$651$	−2.71005	−	1.53836i	−0.106215	−	0.0602932i
$652$	11.4881	+	2.24133i	0.449909	+	0.0877772i
$653$	−19.7060			−0.771157			−0.385578	−	0.922675i	$-0.625998\pi$
$653$	−19.7060			−0.771157			−0.385578	+	0.922675i	$0.625998\pi$
$654$	12.9164	−	18.3773i	0.505072	−	0.718610i
$655$		−	41.1534i		−	1.60799i
$656$	15.9981	−	39.4393i	0.624622	−	1.53984i
$657$	4.35647	+	7.29730i	0.169962	+	0.284695i
$658$	−0.641805	+	6.64128i	−0.0250202	+	0.258904i
$659$			22.9550i			0.894198i	0.894484	+	0.447099i	$0.147543\pi$
$659$			22.9550i			0.894198i	−0.894484	+	0.447099i	$0.852457\pi$
$660$	−38.9960	+	45.4634i	−1.51792	+	1.76966i
$661$			25.4471i			0.989777i	0.868956	+	0.494889i	$0.164791\pi$
$661$			25.4471i			0.989777i	−0.868956	+	0.494889i	$0.835209\pi$
$662$	−0.779206	−	0.0753015i	−0.0302847	−	0.00292668i
$663$	−6.91147	−	3.92330i	−0.268419	−	0.152368i
$664$	−2.49231	+	8.38188i	−0.0967203	+	0.325280i
$665$		−	6.46149i		−	0.250566i
$666$	−0.807234	+	0.381875i	−0.0312797	+	0.0147974i
$667$	4.01876			0.155607
$668$	9.84664	+	1.92108i	0.380978	+	0.0743287i
$669$	−18.3787	+	32.3768i	−0.710562	+	1.25176i
$670$	−40.9934	−	3.96155i	−1.58371	−	0.153048i
$671$	83.2824			3.21508
$672$	11.2155	−	7.23327i	0.432649	−	0.279029i
$673$	15.0164			0.578838			0.289419	−	0.957202i	$-0.406538\pi$
$673$	15.0164			0.578838			0.289419	+	0.957202i	$0.406538\pi$
$674$	27.2967	+	2.63792i	1.05143	+	0.101609i
$675$	−0.441983	−	20.1645i	−0.0170119	−	0.776131i
$676$	24.0930	+	4.70053i	0.926652	+	0.180789i
$677$	−4.56679			−0.175516			−0.0877581	−	0.996142i	$-0.527970\pi$
$677$	−4.56679			−0.175516			−0.0877581	+	0.996142i	$0.527970\pi$
$678$	7.11345	−	10.1209i	0.273190	−	0.388692i
$679$		−	14.2139i		−	0.545480i
$680$	12.9339	−	43.4980i	0.495993	−	1.66807i
$681$	0.751523	−	1.32392i	0.0287984	−	0.0507327i
$682$	10.7876	+	1.04250i	0.413080	+	0.0399196i
$683$		−	24.9270i		−	0.953804i	−0.878956	−	0.476902i	$-0.841760\pi$
$683$		−	24.9270i		−	0.953804i	0.878956	−	0.476902i	$-0.158240\pi$
$684$	−3.23475	−	8.98615i	−0.123684	−	0.343594i
$685$		−	38.0947i		−	1.45552i
$686$	−2.25031	+	23.2857i	−0.0859171	+	0.889054i
$687$	14.7650	−	26.0108i	0.563322	−	0.992374i
$688$	14.0863	+	5.71397i	0.537037	+	0.217843i
$689$			10.7314i			0.408833i
$690$	−5.97237	−	4.19765i	−0.227364	−	0.159802i
$691$	33.0419			1.25697			0.628486	−	0.777821i	$-0.283675\pi$
$691$	33.0419			1.25697			0.628486	+	0.777821i	$0.283675\pi$
$692$	−17.8241	−	3.47748i	−0.677571	−	0.132194i
$693$	12.1527	+	20.3564i	0.461643	+	0.773274i
$694$	−1.53634	+	15.8978i	−0.0583188	+	0.603472i
$695$	−4.47507			−0.169749
$696$	13.6414	+	14.1959i	0.517077	+	0.538093i
$697$	−57.2827			−2.16974
$698$	2.58518	−	26.7509i	0.0978503	−	1.01254i
$699$	−10.9302	+	19.2551i	−0.413418	+	0.728296i
$700$	2.02484	−	10.3785i	0.0765317	−	0.392270i
$701$	−4.39569			−0.166023			−0.0830114	−	0.996549i	$-0.526454\pi$
$701$	−4.39569			−0.166023			−0.0830114	+	0.996549i	$0.526454\pi$
$702$	−6.24567	−	0.465690i	−0.235728	−	0.0175763i
$703$			0.335041i			0.0126363i
$704$	−25.3602	+	38.8741i	−0.955799	+	1.46512i
$705$	15.5490	+	8.82639i	0.585608	+	0.332421i
$706$	−2.18114	+	22.5700i	−0.0820882	+	0.849433i
$707$		−	25.6110i		−	0.963200i
$708$	−10.0737	+	11.7444i	−0.378592	+	0.441381i
$709$		−	6.77578i		−	0.254470i	−0.991873	−	0.127235i	$-0.959390\pi$
$709$		−	6.77578i		−	0.254470i	0.991873	−	0.127235i	$-0.0406102\pi$
$710$	13.7290	+	1.32675i	0.515240	+	0.0497922i
$711$	−12.8749	+	7.68627i	−0.482845	+	0.288258i
$712$	11.0521	−	37.1695i	0.414197	−	1.39299i
$713$			1.32088i			0.0494673i
$714$	−14.6955	−	10.3287i	−0.549966	−	0.386541i
$715$	14.7366			0.551119
$716$	7.24516	−	37.1357i	0.270764	−	1.38783i
$717$	−44.7423	−	25.3980i	−1.67093	−	0.948506i
$718$	43.2036	+	4.17514i	1.61234	+	0.155815i
$719$	−30.9094			−1.15273			−0.576363	−	0.817194i	$-0.695529\pi$
$719$	−30.9094			−1.15273			−0.576363	+	0.817194i	$0.695529\pi$
$720$	−5.44504	−	35.3454i	−0.202925	−	1.31725i
$721$	18.4041			0.685406
$722$	23.1788	+	2.23997i	0.862627	+	0.0833632i
$723$	−14.9577	−	8.49073i	−0.556282	−	0.315774i
$724$	5.09353	−	26.1073i	0.189300	−	0.970272i
$725$	15.5992			0.579339
$726$	−45.4141	−	31.9191i	−1.68548	−	1.18463i
$727$			12.8729i			0.477429i	0.971090	+	0.238714i	$0.0767260\pi$
$727$			12.8729i			0.477429i	−0.971090	+	0.238714i	$0.923274\pi$
$728$	−3.14732	−	0.935838i	−0.116647	−	0.0346845i
$729$	−26.9741	+	1.18305i	−0.999040	+	0.0438167i
$730$	11.8844	+	1.14849i	0.439861	+	0.0425077i
$731$		−	20.4594i		−	0.756717i
$732$	−32.3738	+	37.7430i	−1.19657	+	1.39502i
$733$		−	16.9056i		−	0.624424i	−0.950012	−	0.312212i	$-0.898930\pi$
$733$		−	16.9056i		−	0.624424i	0.950012	−	0.312212i	$-0.101070\pi$
$734$	−1.73120	+	17.9142i	−0.0638999	+	0.661224i
$735$	23.0947	+	13.1098i	0.851862	+	0.483560i
$736$	−5.01316	−	2.62073i	−0.184787	−	0.0966015i
$737$		−	56.6942i		−	2.08836i
$738$	−40.8065	+	19.3042i	−1.50211	+	0.710596i
$739$	41.2310			1.51671			0.758353	−	0.651844i	$-0.226004\pi$
$739$	41.2310			1.51671			0.758353	+	0.651844i	$0.226004\pi$
$740$	−0.240235	+	1.23135i	−0.00883122	+	0.0452652i
$741$	−1.15999	+	2.04350i	−0.0426134	+	0.0750698i
$742$	−2.33305	+	24.1419i	−0.0856488	+	0.886278i
$743$	−31.9621			−1.17258			−0.586289	−	0.810102i	$-0.699412\pi$
$743$	−31.9621			−1.17258			−0.586289	+	0.810102i	$0.699412\pi$
$744$	−4.66587	+	4.48364i	−0.171059	+	0.164378i
$745$	60.8720			2.23018
$746$	0.0139709	−	0.144568i	0.000511511	−	0.00529302i
$747$	7.96379	−	4.75437i	0.291380	−	0.173953i
$748$	61.3142	+	11.9624i	2.24187	+	0.437388i
$749$	−2.71857			−0.0993346
$750$	6.67958	+	4.69472i	0.243904	+	0.171427i
$751$		−	22.7550i		−	0.830341i	−0.909744	−	0.415171i	$-0.863722\pi$
$751$		−	22.7550i		−	0.830341i	0.909744	−	0.415171i	$-0.136278\pi$
$752$	12.8390	+	5.20800i	0.468190	+	0.189916i
$753$	3.11688	−	5.49084i	0.113585	−	0.200097i
$754$	0.465936	−	4.82142i	0.0169684	−	0.175586i
$755$			47.3920i			1.72477i
$756$	−13.9494	−	2.40548i	−0.507335	−	0.0874865i
$757$		−	19.6164i		−	0.712969i	−0.934301	−	0.356485i	$-0.883975\pi$
$757$		−	19.6164i		−	0.712969i	0.934301	−	0.356485i	$-0.116025\pi$
$758$	−32.2539	−	3.11697i	−1.17151	−	0.113214i
$759$	4.96085	−	8.73926i	0.180067	−	0.317215i
$760$	−12.8610	−	3.82414i	−0.466517	−	0.138716i
$761$		−	2.64074i		−	0.0957268i	−0.998854	−	0.0478634i	$-0.984759\pi$
$761$		−	2.64074i		−	0.0957268i	0.998854	−	0.0478634i	$-0.0152412\pi$
$762$	−18.6582	+	26.5466i	−0.675914	+	0.961682i
$763$	−12.4907			−0.452194
$764$	28.7161	+	5.60250i	1.03891	+	0.202691i
$765$	−41.3284	+	24.6729i	−1.49423	+	0.892052i
$766$	39.6452	+	3.83126i	1.43244	+	0.138429i
$767$	3.80686			0.137458
$768$	−7.75937	−	26.6044i	−0.279992	−	0.960002i
$769$	17.6328			0.635856			0.317928	−	0.948115i	$-0.397013\pi$
$769$	17.6328			0.635856			0.317928	+	0.948115i	$0.397013\pi$
$770$	33.1524	+	3.20381i	1.19473	+	0.115457i
$771$	5.35728	−	9.43763i	0.192938	−	0.339888i
$772$	15.8095	+	3.08442i	0.568995	+	0.111011i
$773$	10.4930			0.377407			0.188704	−	0.982034i	$-0.439571\pi$
$773$	10.4930			0.377407			0.188704	+	0.982034i	$0.439571\pi$
$774$	−6.89478	−	14.5747i	−0.247828	−	0.523875i
$775$			5.12710i			0.184171i
$776$	−28.2915	−	8.41231i	−1.01560	−	0.301984i
$777$	0.431848	+	0.245139i	0.0154925	+	0.00879431i
$778$	−7.62700	−	0.737064i	−0.273441	−	0.0264250i
$779$			16.9366i			0.606818i
$780$	−5.72848	+	6.67854i	−0.205113	+	0.239130i
$781$			18.9873i			0.679421i
$782$	−0.732360	+	7.57832i	−0.0261891	+	0.271000i
$783$	−0.457603	−	20.8771i	−0.0163534	−	0.746087i
$784$	19.0696	+	7.73540i	0.681059	+	0.276264i
$785$			26.4966i			0.945704i
$786$	−19.4501	+	27.6733i	−0.693762	+	0.987075i
$787$	30.6123			1.09121			0.545606	−	0.838042i	$-0.316299\pi$
$787$	30.6123			1.09121			0.545606	+	0.838042i	$0.316299\pi$
$788$	−11.7571	−	2.29381i	−0.418830	−	0.0817135i
$789$	−10.3795	−	5.89192i	−0.369519	−	0.209758i
$790$	−2.02633	+	20.9681i	−0.0720935	+	0.746010i
$791$	−6.87900			−0.244589
$792$	47.7098	−	12.1412i	1.69529	−	0.431417i
$793$	12.2341			0.434446
$794$	3.01826	−	31.2324i	0.107114	−	1.10840i
$795$	56.5225	+	32.0851i	2.00465	+	1.13794i
$796$	−7.96904	+	40.8460i	−0.282455	+	1.44775i
$797$	10.4447			0.369971			0.184985	−	0.982741i	$-0.440776\pi$
$797$	10.4447			0.369971			0.184985	+	0.982741i	$0.440776\pi$
$798$	−3.05386	+	4.34499i	−0.108105	+	0.153811i
$799$		−	18.6477i		−	0.659708i
$800$	−19.4590	−	10.1726i	−0.687980	−	0.359656i
$801$	−35.3155	+	21.0833i	−1.24781	+	0.744940i
$802$	−3.49094	+	36.1236i	−0.123269	+	1.27557i
$803$			16.4362i			0.580022i
$804$	25.6934	+	22.0384i	0.906137	+	0.777234i
$805$			4.05931i			0.143072i
$806$	1.58470	+	0.153143i	0.0558185	+	0.00539423i
$807$	−13.8636	−	7.86967i	−0.488021	−	0.277026i
$808$	−50.9762	−	15.1575i	−1.79334	−	0.533239i
$809$		−	48.5755i		−	1.70782i	−0.520418	−	0.853911i	$-0.674224\pi$
$809$		−	48.5755i		−	1.70782i	0.520418	−	0.853911i	$-0.325776\pi$
$810$	−21.1264	+	31.5039i	−0.742305	+	1.10693i
$811$	26.2605			0.922132			0.461066	−	0.887366i	$-0.347467\pi$
$811$	26.2605			0.922132			0.461066	+	0.887366i	$0.347467\pi$
$812$	2.09640	−	10.7453i	0.0735691	−	0.377085i
$813$	4.83110	−	8.51069i	0.169434	−	0.298483i
$814$	−1.71902	−	0.166124i	−0.0602515	−	0.00582264i
$815$	−17.4412			−0.610938
$816$	−29.2556	+	23.1371i	−1.02415	+	0.809961i
$817$	−6.04918			−0.211634
$818$	42.8091	+	4.13702i	1.49679	+	0.144648i
$819$	1.78522	+	2.99033i	0.0623807	+	0.104491i
$820$	−12.1441	+	62.2458i	−0.424091	+	2.17372i
$821$	1.69169			0.0590404			0.0295202	−	0.999564i	$-0.490602\pi$
$821$	1.69169			0.0590404			0.0295202	+	0.999564i	$0.490602\pi$
$822$	−18.0045	+	25.6166i	−0.627978	+	0.893480i
$823$			11.4145i			0.397883i	0.980011	+	0.198942i	$0.0637504\pi$
$823$			11.4145i			0.397883i	−0.980011	+	0.198942i	$0.936250\pi$
$824$	10.8922	−	36.6317i	0.379449	−	1.27612i
$825$	19.2560	−	33.9222i	0.670406	−	1.18102i
$826$	8.56414	+	0.827628i	0.297984	+	0.0287969i
$827$			15.8926i			0.552640i	0.961066	+	0.276320i	$0.0891150\pi$
$827$			15.8926i			0.552640i	−0.961066	+	0.276320i	$0.910885\pi$
$828$	2.03217	+	5.64538i	0.0706228	+	0.196190i
$829$		−	35.6637i		−	1.23865i	−0.785134	−	0.619326i	$-0.787406\pi$
$829$		−	35.6637i		−	1.23865i	0.785134	−	0.619326i	$-0.212594\pi$
$830$	1.25339	−	12.9699i	0.0435058	−	0.450190i
$831$	−17.1088	+	30.1397i	−0.593499	+	1.04553i
$832$	−3.72539	+	5.71058i	−0.129155	+	0.197979i
$833$		−	27.6973i		−	0.959653i
$834$	3.00924	+	2.11503i	0.104201	+	0.0732374i
$835$	−14.9491			−0.517335
$836$	3.53689	−	18.1287i	0.122326	−	0.626993i
$837$	6.86184	−	0.150404i	0.237180	−	0.00519872i
$838$	2.29754	−	23.7746i	0.0793674	−	0.821279i
$839$	−22.4175			−0.773939			−0.386969	−	0.922093i	$-0.626478\pi$
$839$	−22.4175			−0.773939			−0.386969	+	0.922093i	$0.626478\pi$
$840$	−14.3391	+	13.7791i	−0.494745	+	0.475422i
$841$	−12.8495			−0.443087
$842$	−2.88325	+	29.8353i	−0.0993634	+	1.02819i
$843$	−14.7334	+	25.9551i	−0.507446	+	0.893940i
$844$	30.7203	+	5.99352i	1.05744	+	0.206306i
$845$	−36.5778			−1.25831
$846$	−6.28425	−	13.2841i	−0.216057	−	0.456716i
$847$			30.8671i			1.06061i
$848$	46.6714	+	18.9318i	1.60270	+	0.650119i
$849$	−19.1913	−	10.8940i	−0.658645	−	0.373880i
$850$	−2.84272	+	29.4159i	−0.0975044	+	1.00896i
$851$		−	0.210483i		−	0.00721526i
$852$	−8.60493	−	7.38083i	−0.294800	−	0.252863i
$853$			33.3784i			1.14285i	0.820653	+	0.571427i	$0.193610\pi$
$853$			33.3784i			1.14285i	−0.820653	+	0.571427i	$0.806390\pi$
$854$	27.5226	+	2.65975i	0.941804	+	0.0910148i
$855$	7.29499	+	12.2195i	0.249484	+	0.417897i
$856$	−1.60895	+	5.41106i	−0.0549928	+	0.184946i
$857$		−	28.8345i		−	0.984966i	−0.870322	−	0.492483i	$-0.836089\pi$
$857$		−	28.8345i		−	0.984966i	0.870322	−	0.492483i	$-0.163911\pi$
$858$	−9.90957	−	6.96490i	−0.338307	−	0.237778i
$859$	−20.3286			−0.693602			−0.346801	−	0.937939i	$-0.612732\pi$
$859$	−20.3286			−0.693602			−0.346801	+	0.937939i	$0.612732\pi$
$860$	−22.2320	−	4.33746i	−0.758106	−	0.147906i
$861$	21.8304	+	12.3920i	0.743977	+	0.422319i
$862$	−31.2789	−	3.02275i	−1.06536	−	0.102955i
$863$	−13.9426			−0.474612			−0.237306	−	0.971435i	$-0.576264\pi$
$863$	−13.9426			−0.474612			−0.237306	+	0.971435i	$0.576264\pi$
$864$	−13.0436	+	26.3413i	−0.443753	+	0.896149i
$865$	27.0605			0.920084
$866$	0.600379	+	0.0580199i	0.0204017	+	0.00197160i
$867$	18.0508	+	10.2465i	0.613037	+	0.347991i
$868$	3.53173	+	0.689039i	0.119875	+	0.0233875i
$869$	−28.9990			−0.983725
$870$	−24.0015	−	16.8694i	−0.813729	−	0.571926i
$871$		−	8.32834i		−	0.282195i
$872$	−7.39245	+	24.8616i	−0.250340	+	0.841919i
$873$	16.0475	+	26.8803i	0.543124	+	0.909760i
$874$	2.24067	+	0.216535i	0.0757917	+	0.00732441i
$875$		−	4.53999i		−	0.153480i
$876$	−7.44879	−	6.38916i	−0.251671	−	0.215870i
$877$			4.44841i			0.150212i	0.997176	+	0.0751061i	$0.0239295\pi$
$877$			4.44841i			0.150212i	−0.997176	+	0.0751061i	$0.976070\pi$
$878$	0.669163	−	6.92437i	0.0225832	−	0.233686i
$879$	44.4788	+	25.2484i	1.50023	+	0.851608i
$880$	25.9977	−	64.0906i	0.876381	−	2.16049i
$881$			8.99796i			0.303149i	0.988446	+	0.151575i	$0.0484344\pi$
$881$			8.99796i			0.303149i	−0.988446	+	0.151575i	$0.951566\pi$
$882$	−9.33394	−	19.7307i	−0.314290	−	0.664368i
$883$	−10.7222			−0.360832			−0.180416	−	0.983590i	$-0.557744\pi$
$883$	−10.7222			−0.360832			−0.180416	+	0.983590i	$0.557744\pi$
$884$	9.00701	+	1.75726i	0.302939	+	0.0591032i
$885$	11.3819	−	20.0509i	0.382598	−	0.674003i
$886$	5.42692	−	56.1568i	0.182321	−	1.88662i
$887$	9.72570			0.326557			0.163278	−	0.986580i	$-0.447793\pi$
$887$	9.72570			0.326557			0.163278	+	0.986580i	$0.447793\pi$
$888$	0.743509	−	0.714471i	0.0249505	−	0.0239761i
$889$	18.0432			0.605151
$890$	−5.55817	+	57.5149i	−0.186310	+	1.92790i
$891$	−45.9645	−	24.7760i	−1.53987	−	0.830028i
$892$	8.23191	−	42.1934i	0.275625	−	1.41274i
$893$	−5.51353			−0.184503
$894$	−40.9331	−	28.7696i	−1.36901	−	0.962200i
$895$			56.3792i			1.88455i
$896$	−9.62237	+	12.0369i	−0.321461	+	0.402126i
$897$	0.728744	−	1.28379i	0.0243321	−	0.0428645i
$898$	2.55938	−	26.4840i	0.0854076	−	0.883782i
$899$			5.30830i			0.177042i
$900$	7.88805	+	21.9130i	0.262935	+	0.730434i
$901$		−	67.7868i		−	2.25831i
$902$	−86.8981	−	8.39772i	−2.89339	−	0.279614i
$903$	−4.42600	+	7.79705i	−0.147288	+	0.259469i
$904$	−4.07124	+	13.6920i	−0.135407	+	0.455389i
$905$			39.6360i			1.31755i
$906$	22.3986	−	31.8685i	0.744144	−	1.05876i
$907$	−28.4008			−0.943033			−0.471516	−	0.881857i	$-0.656293\pi$
$907$	−28.4008			−0.943033			−0.471516	+	0.881857i	$0.656293\pi$
$908$	−0.336611	+	1.72533i	−0.0111708	+	0.0572570i
$909$	28.9147	+	48.4335i	0.959040	+	1.60644i
$910$	4.87006	+	0.470637i	0.161441	+	0.0156015i
$911$	15.7823			0.522892			0.261446	−	0.965218i	$-0.415801\pi$
$911$	15.7823			0.522892			0.261446	+	0.965218i	$0.415801\pi$
$912$	6.84090	+	8.64993i	0.226525	+	0.286428i
$913$	17.9374			0.593643
$914$	−9.11715	−	0.881070i	−0.301568	−	0.0291432i
$915$	36.5780	−	64.4376i	1.20923	−	2.13024i
$916$	−6.61333	+	33.8972i	−0.218511	+	1.12000i
$917$	18.8090			0.621129
$918$	39.4520	+	2.94162i	1.30211	+	0.0970880i
$919$			9.07586i			0.299385i	0.988733	+	0.149692i	$0.0478284\pi$
$919$			9.07586i			0.299385i	−0.988733	+	0.149692i	$0.952172\pi$
$920$	8.07966	+	2.40244i	0.266379	+	0.0792062i
$921$	36.7247	+	20.8468i	1.21012	+	0.686926i
$922$	−54.2461	−	5.24228i	−1.78650	−	0.172645i
$923$			2.78923i			0.0918085i
$924$	−20.7790	−	17.8230i	−0.683577	−	0.586335i
$925$		−	0.817008i		−	0.0268630i
$926$	−4.28296	+	44.3193i	−0.140747	+	1.45642i
$927$	−34.8045	+	20.7782i	−1.14313	+	0.682445i
$928$	−20.1467	−	10.5321i	−0.661348	−	0.345734i
$929$		−	9.96935i		−	0.327084i	−0.986536	−	0.163542i	$-0.947708\pi$
$929$		−	9.96935i		−	0.327084i	0.986536	−	0.163542i	$-0.0522919\pi$
$930$	5.54459	−	7.88878i	0.181814	−	0.258683i
$931$	−8.18919			−0.268390
$932$	4.89569	−	25.0933i	0.160363	−	0.821957i
$933$	−4.29985	−	2.44081i	−0.140771	−	0.0799086i
$934$	−3.88869	+	40.2394i	−0.127242	+	1.31667i
$935$	−93.0869			−3.04427
$936$	7.00853	−	1.78353i	0.229081	−	0.0582964i
$937$	−8.42781			−0.275324			−0.137662	−	0.990479i	$-0.543959\pi$
$937$	−8.42781			−0.275324			−0.137662	+	0.990479i	$0.543959\pi$
$938$	1.81062	−	18.7359i	0.0591187	−	0.611750i
$939$	−12.2060	−	6.92873i	−0.398327	−	0.226111i
$940$	−20.2634	−	3.95338i	−0.660919	−	0.128945i
$941$	26.7191			0.871018			0.435509	−	0.900184i	$-0.356568\pi$
$941$	26.7191			0.871018			0.435509	+	0.900184i	$0.356568\pi$
$942$	12.5229	−	17.8175i	0.408019	−	0.580525i
$943$		−	10.6401i		−	0.346490i
$944$	6.71588	−	16.5563i	0.218583	−	0.538861i
$945$	21.0877	−	0.462219i	0.685983	−	0.0150360i
$946$	2.99938	−	31.0370i	0.0975181	−	1.00910i
$947$			37.2705i			1.21113i	0.795797	+	0.605564i	$0.207052\pi$
$947$			37.2705i			1.21113i	−0.795797	+	0.605564i	$0.792948\pi$
$948$	11.2726	−	13.1422i	0.366117	−	0.426837i
$949$			2.41447i			0.0783770i
$950$	8.69734	+	0.840500i	0.282179	+	0.0272694i
$951$	−34.5379	−	19.6055i	−1.11997	−	0.635751i
$952$	19.8807	+	5.91141i	0.644336	+	0.191590i
$953$			28.9414i			0.937505i	0.883330	+	0.468753i	$0.155296\pi$
$953$			28.9414i			0.937505i	−0.883330	+	0.468753i	$0.844704\pi$
$954$	−22.8441	−	48.2893i	−0.739604	−	1.56343i
$955$	−43.5966			−1.41075
$956$	58.3081	+	11.3759i	1.88582	+	0.367922i
$957$	19.9365	−	35.1210i	0.644455	−	1.13530i
$958$	25.1068	+	2.42629i	0.811164	+	0.0783899i
$959$	17.4111			0.562233
$960$	18.9395	+	36.6955i	0.611270	+	1.18434i
$961$	29.2553			0.943719
$962$	−0.252522	−	0.0244034i	−0.00814164	−	0.000786799i
$963$	5.14116	−	3.06926i	0.165672	−	0.0989055i
$964$	19.4928	+	3.80304i	0.627821	+	0.122488i
$965$	−24.0018			−0.772646
$966$	1.91853	−	2.72966i	0.0617276	−	0.0878253i
$967$			8.93046i			0.287184i	0.989637	+	0.143592i	$0.0458653\pi$
$967$			8.93046i			0.287184i	−0.989637	+	0.143592i	$0.954135\pi$
$968$	61.4380	+	18.2683i	1.97469	+	0.587164i
$969$	7.32733	−	12.9082i	0.235388	−	0.414670i
$970$	43.7773	+	4.23059i	1.40561	+	0.135836i
$971$		−	35.2297i		−	1.13058i	−0.824893	−	0.565288i	$-0.808765\pi$
$971$		−	35.2297i		−	1.13058i	0.824893	−	0.565288i	$-0.191235\pi$
$972$	29.0958	−	11.1998i	0.933248	−	0.359232i
$973$		−	2.04532i		−	0.0655700i
$974$	0.573968	−	5.93931i	0.0183911	−	0.190308i
$975$	2.82868	−	4.98314i	0.0905903	−	0.159588i
$976$	21.5828	−	53.2070i	0.690850	−	1.70311i
$977$			32.5344i			1.04087i	0.853902	+	0.520434i	$0.174230\pi$
$977$			32.5344i			1.04087i	−0.853902	+	0.520434i	$0.825770\pi$
$978$	11.7282	+	8.24314i	0.375027	+	0.263586i
$979$	−79.5437			−2.54223
$980$	−30.0970	−	5.87192i	−0.961414	−	0.187572i
$981$	23.6215	−	14.1020i	0.754176	−	0.450241i
$982$	2.68805	−	27.8155i	0.0857792	−	0.887627i
$983$	27.1694			0.866570			0.433285	−	0.901257i	$-0.357354\pi$
$983$	27.1694			0.866570			0.433285	+	0.901257i	$0.357354\pi$
$984$	37.5851	−	36.1172i	1.19817	−	1.15137i
$985$	17.8496			0.568735
$986$	−2.94318	+	30.4555i	−0.0937300	+	0.969900i
$987$	−4.03408	+	7.10662i	−0.128406	+	0.226206i
$988$	0.519567	−	2.66308i	0.0165296	−	0.0847240i
$989$	3.80028			0.120842
$990$	−66.3124	+	31.3702i	−2.10755	+	0.997009i
$991$		−	40.3567i		−	1.28197i	−0.767553	−	0.640986i	$-0.778526\pi$
$991$		−	40.3567i		−	1.28197i	0.767553	−	0.640986i	$-0.221474\pi$
$992$	3.46167	−	6.62177i	0.109908	−	0.210242i
$993$	−0.833803	−	0.473309i	−0.0264599	−	0.0150200i
$994$	−0.606390	+	6.27481i	−0.0192335	+	0.199025i
$995$		−	62.0122i		−	1.96592i
$996$	−6.97271	+	8.12912i	−0.220939	+	0.257581i
$997$		−	40.2642i		−	1.27518i	−0.770376	−	0.637589i	$-0.779932\pi$
$997$		−	40.2642i		−	1.27518i	0.770376	−	0.637589i	$-0.220068\pi$
$998$	18.5115	+	1.78893i	0.585971	+	0.0566276i
$999$	−1.09344	+	0.0239670i	−0.0345949	+	0.000758282i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.j.d.323.3	yes	42
3.2	odd	2		552.2.j.c.323.40	yes	42
4.3	odd	2		2208.2.j.d.47.36		42
8.3	odd	2		552.2.j.c.323.39	✓	42
8.5	even	2		2208.2.j.c.47.36		42
12.11	even	2		2208.2.j.c.47.35		42
24.5	odd	2		2208.2.j.d.47.35		42
24.11	even	2	inner	552.2.j.d.323.4	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.j.c.323.39	✓	42	8.3	odd	2
552.2.j.c.323.40	yes	42	3.2	odd	2
552.2.j.d.323.3	yes	42	1.1	even	1	trivial
552.2.j.d.323.4	yes	42	24.11	even	2	inner
2208.2.j.c.47.35		42	12.11	even	2
2208.2.j.c.47.36		42	8.5	even	2
2208.2.j.d.47.35		42	24.5	odd	2
2208.2.j.d.47.36		42	4.3	odd	2

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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40766 - 0.136034i) q^{2} +(-1.50629 - 0.855045i) q^{3} +(1.96299 + 0.382978i) q^{4} -2.98020 q^{5} +(2.00402 + 1.40851i) q^{6} -1.36209i q^{7} +(-2.71112 - 0.806135i) q^{8} +(1.53780 + 2.57588i) q^{9} +O(q^{10})\)	\(q+(-1.40766 - 0.136034i) q^{2} +(-1.50629 - 0.855045i) q^{3} +(1.96299 + 0.382978i) q^{4} -2.98020 q^{5} +(2.00402 + 1.40851i) q^{6} -1.36209i q^{7} +(-2.71112 - 0.806135i) q^{8} +(1.53780 + 2.57588i) q^{9} +(4.19509 + 0.405409i) q^{10} +5.80186i q^{11} +(-2.62936 - 2.25532i) q^{12} +0.852288i q^{13} +(-0.185291 + 1.91736i) q^{14} +(4.48903 + 2.54820i) q^{15} +(3.70666 + 1.50357i) q^{16} -5.38365i q^{17} +(-1.81428 - 3.83515i) q^{18} -1.59177 q^{19} +(-5.85010 - 1.14135i) q^{20} +(-1.16465 + 2.05170i) q^{21} +(0.789250 - 8.16702i) q^{22} +1.00000 q^{23} +(3.39443 + 3.53240i) q^{24} +3.88159 q^{25} +(0.115940 - 1.19973i) q^{26} +(-0.113867 - 5.19490i) q^{27} +(0.521652 - 2.67377i) q^{28} +4.01876 q^{29} +(-5.97237 - 4.19765i) q^{30} +1.32088i q^{31} +(-5.01316 - 2.62073i) q^{32} +(4.96085 - 8.73926i) q^{33} +(-0.732360 + 7.57832i) q^{34} +4.05931i q^{35} +(2.03217 + 5.64538i) q^{36} -0.210483i q^{37} +(2.24067 + 0.216535i) q^{38} +(0.728744 - 1.28379i) q^{39} +(8.07966 + 2.40244i) q^{40} -10.6401i q^{41} +(1.91853 - 2.72966i) q^{42} +3.80028 q^{43} +(-2.22199 + 11.3890i) q^{44} +(-4.58294 - 7.67665i) q^{45} +(-1.40766 - 0.136034i) q^{46} +3.46377 q^{47} +(-4.29767 - 5.43416i) q^{48} +5.14470 q^{49} +(-5.46394 - 0.528028i) q^{50} +(-4.60326 + 8.10931i) q^{51} +(-0.326408 + 1.67303i) q^{52} +12.5912 q^{53} +(-0.546399 + 7.32813i) q^{54} -17.2907i q^{55} +(-1.09803 + 3.69279i) q^{56} +(2.39766 + 1.36104i) q^{57} +(-5.65704 - 0.546689i) q^{58} -4.46664i q^{59} +(7.83602 + 6.72130i) q^{60} -14.3544i q^{61} +(0.179685 - 1.85934i) q^{62} +(3.50859 - 2.09462i) q^{63} +(6.70029 + 4.37105i) q^{64} -2.53999i q^{65} +(-8.17200 + 11.6270i) q^{66} -9.77174 q^{67} +(2.06182 - 10.5680i) q^{68} +(-1.50629 - 0.855045i) q^{69} +(0.552204 - 5.71411i) q^{70} +3.27263 q^{71} +(-2.09263 - 8.22319i) q^{72} +2.83293 q^{73} +(-0.0286329 + 0.296288i) q^{74} +(-5.84678 - 3.31893i) q^{75} +(-3.12463 - 0.609614i) q^{76} +7.90267 q^{77} +(-1.20046 + 1.70800i) q^{78} +4.99823i q^{79} +(-11.0466 - 4.48092i) q^{80} +(-4.27036 + 7.92237i) q^{81} +(-1.44742 + 14.9776i) q^{82} -3.09167i q^{83} +(-3.07195 + 3.58143i) q^{84} +16.0443i q^{85} +(-5.34949 - 0.516968i) q^{86} +(-6.05341 - 3.43622i) q^{87} +(4.67708 - 15.7295i) q^{88} +13.7100i q^{89} +(5.40692 + 11.4295i) q^{90} +1.16089 q^{91} +(1.96299 + 0.382978i) q^{92} +(1.12941 - 1.98962i) q^{93} +(-4.87579 - 0.471191i) q^{94} +4.74379 q^{95} +(5.31041 + 8.23405i) q^{96} +10.4354 q^{97} +(-7.24197 - 0.699855i) q^{98} +(-14.9449 + 8.92208i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9}+O(q^{10}) \) 42 * q + 2 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 - 9 * q^8 + 2 * q^9	\( 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9} - 4 q^{10} - 21 q^{12} - 4 q^{14} - 8 q^{15} - 12 q^{16} - 11 q^{18} + 4 q^{19} - 2 q^{20} + 8 q^{21} + 18 q^{22} + 42 q^{23} + 28 q^{24} + 22 q^{25} + 11 q^{26} - 16 q^{27} + 6 q^{28} + 2 q^{30} - 20 q^{32} + 12 q^{33} + 14 q^{34} - 24 q^{36} - 22 q^{38} + 8 q^{39} + 4 q^{40} - 44 q^{42} + 28 q^{43} + 56 q^{44} - 8 q^{45} + 30 q^{48} - 50 q^{49} + 20 q^{50} + 28 q^{51} - q^{52} + 24 q^{53} + 52 q^{54} - 34 q^{56} - 8 q^{57} - 21 q^{58} - 42 q^{60} - 79 q^{62} - 16 q^{63} + 7 q^{64} - 62 q^{66} - 4 q^{67} + 20 q^{68} + 2 q^{69} - 8 q^{70} + 22 q^{72} + 4 q^{73} + 36 q^{74} - 6 q^{75} + 14 q^{76} + 32 q^{77} + 27 q^{78} - 52 q^{80} + 18 q^{81} + 11 q^{82} - 80 q^{84} - 28 q^{86} - 48 q^{87} - 38 q^{88} - 46 q^{90} - 8 q^{91} + 4 q^{92} - 22 q^{93} + q^{94} - 16 q^{95} + 9 q^{96} + 20 q^{97} + 64 q^{98}+O(q^{100}) \) 42 * q + 2 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 - 9 * q^8 + 2 * q^9 - 4 * q^10 - 21 * q^12 - 4 * q^14 - 8 * q^15 - 12 * q^16 - 11 * q^18 + 4 * q^19 - 2 * q^20 + 8 * q^21 + 18 * q^22 + 42 * q^23 + 28 * q^24 + 22 * q^25 + 11 * q^26 - 16 * q^27 + 6 * q^28 + 2 * q^30 - 20 * q^32 + 12 * q^33 + 14 * q^34 - 24 * q^36 - 22 * q^38 + 8 * q^39 + 4 * q^40 - 44 * q^42 + 28 * q^43 + 56 * q^44 - 8 * q^45 + 30 * q^48 - 50 * q^49 + 20 * q^50 + 28 * q^51 - q^52 + 24 * q^53 + 52 * q^54 - 34 * q^56 - 8 * q^57 - 21 * q^58 - 42 * q^60 - 79 * q^62 - 16 * q^63 + 7 * q^64 - 62 * q^66 - 4 * q^67 + 20 * q^68 + 2 * q^69 - 8 * q^70 + 22 * q^72 + 4 * q^73 + 36 * q^74 - 6 * q^75 + 14 * q^76 + 32 * q^77 + 27 * q^78 - 52 * q^80 + 18 * q^81 + 11 * q^82 - 80 * q^84 - 28 * q^86 - 48 * q^87 - 38 * q^88 - 46 * q^90 - 8 * q^91 + 4 * q^92 - 22 * q^93 + q^94 - 16 * q^95 + 9 * q^96 + 20 * q^97 + 64 * q^98

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