LMFDB - Embedded newform 456.2.j.e.419.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [456,2,Mod(419,456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(456, 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("456.419");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.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:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			419.11
Character	$\chi$	$=$	456.419
Dual form			456.2.j.e.419.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366311 - 1.36595i) q^{2} +(1.73163 + 0.0380449i) q^{3} +(-1.73163 + 1.00072i) q^{4} +1.96235 q^{5} +(-0.582348 - 2.37926i) q^{6} +1.36779i q^{7} +(2.00125 + 1.99875i) q^{8} +(2.99711 + 0.131760i) q^{9} +O(q^{10})$	\(q+(-0.366311 - 1.36595i) q^{2} +(1.73163 + 0.0380449i) q^{3} +(-1.73163 + 1.00072i) q^{4} +1.96235 q^{5} +(-0.582348 - 2.37926i) q^{6} +1.36779i q^{7} +(2.00125 + 1.99875i) q^{8} +(2.99711 + 0.131760i) q^{9} +(-0.718829 - 2.68047i) q^{10} -3.24389i q^{11} +(-3.03663 + 1.66701i) q^{12} +6.13473i q^{13} +(1.86834 - 0.501038i) q^{14} +(3.39807 + 0.0746574i) q^{15} +(1.99711 - 3.46577i) q^{16} -1.59015i q^{17} +(-0.917895 - 4.14216i) q^{18} +1.00000 q^{19} +(-3.39807 + 1.96377i) q^{20} +(-0.0520377 + 2.36852i) q^{21} +(-4.43098 + 1.18827i) q^{22} +3.57942 q^{23} +(3.38939 + 3.53723i) q^{24} -1.14919 q^{25} +(8.37972 - 2.24722i) q^{26} +(5.18487 + 0.342184i) q^{27} +(-1.36878 - 2.36852i) q^{28} -2.53726 q^{29} +(-1.14277 - 4.66893i) q^{30} -6.19047i q^{31} +(-5.46563 - 1.45839i) q^{32} +(0.123413 - 5.61722i) q^{33} +(-2.17207 + 0.582491i) q^{34} +2.68409i q^{35} +(-5.32174 + 2.77111i) q^{36} -6.07898i q^{37} +(-0.366311 - 1.36595i) q^{38} +(-0.233395 + 10.6231i) q^{39} +(3.92715 + 3.92224i) q^{40} +5.65123i q^{41} +(3.25434 - 0.796533i) q^{42} +2.89379 q^{43} +(3.24623 + 5.61722i) q^{44} +(5.88136 + 0.258558i) q^{45} +(-1.31118 - 4.88931i) q^{46} -13.2278 q^{47} +(3.59011 - 5.92546i) q^{48} +5.12914 q^{49} +(0.420960 + 1.56973i) q^{50} +(0.0604973 - 2.75356i) q^{51} +(-6.13916 - 10.6231i) q^{52} -12.0338 q^{53} +(-1.43187 - 7.20762i) q^{54} -6.36564i q^{55} +(-2.73387 + 2.73730i) q^{56} +(1.73163 + 0.0380449i) q^{57} +(0.929427 + 3.46577i) q^{58} -6.55773i q^{59} +(-5.95892 + 3.27125i) q^{60} -2.43004i q^{61} +(-8.45587 + 2.26764i) q^{62} +(-0.180220 + 4.09942i) q^{63} +(0.0100256 + 7.99999i) q^{64} +12.0385i q^{65} +(-7.71804 + 1.88907i) q^{66} -6.04667 q^{67} +(1.59130 + 2.75356i) q^{68} +(6.19825 + 0.136179i) q^{69} +(3.66633 - 0.983211i) q^{70} +11.2654 q^{71} +(5.73461 + 6.25414i) q^{72} -13.0557 q^{73} +(-8.30358 + 2.22680i) q^{74} +(-1.98997 - 0.0437208i) q^{75} +(-1.73163 + 1.00072i) q^{76} +4.43697 q^{77} +(14.5961 - 3.57255i) q^{78} +2.08809i q^{79} +(3.91902 - 6.80105i) q^{80} +(8.96528 + 0.789796i) q^{81} +(7.71929 - 2.07010i) q^{82} -10.0230i q^{83} +(-2.28012 - 4.15348i) q^{84} -3.12044i q^{85} +(-1.06003 - 3.95277i) q^{86} +(-4.39361 - 0.0965300i) q^{87} +(6.48371 - 6.49184i) q^{88} +15.8264i q^{89} +(-1.80123 - 8.12836i) q^{90} -8.39104 q^{91} +(-6.19825 + 3.58201i) q^{92} +(0.235516 - 10.7196i) q^{93} +(4.84548 + 18.0685i) q^{94} +1.96235 q^{95} +(-9.40898 - 2.73334i) q^{96} +4.59767 q^{97} +(-1.87886 - 7.00614i) q^{98} +(0.427414 - 9.72227i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{3} - 6 q^{4} + q^{6} - 6 q^{9}+O(q^{10}) $ 24 * q + 6 * q^3 - 6 * q^4 + q^6 - 6 * q^9	$ 24 q + 6 q^{3} - 6 q^{4} + q^{6} - 6 q^{9} + 4 q^{10} - 33 q^{12} - 30 q^{16} - 19 q^{18} + 24 q^{19} - 28 q^{22} + 21 q^{24} + 96 q^{25} + 34 q^{28} + 8 q^{30} + 24 q^{33} + 58 q^{34} - 9 q^{36} - 24 q^{40} - 31 q^{42} + 16 q^{43} - 6 q^{46} + 3 q^{48} - 36 q^{49} + 38 q^{51} - 6 q^{52} - 8 q^{54} + 6 q^{57} - 42 q^{58} - 50 q^{60} + 18 q^{64} + 10 q^{66} + 20 q^{67} - 96 q^{70} - 33 q^{72} - 12 q^{73} - 30 q^{75} - 6 q^{76} - 17 q^{78} + 34 q^{81} + 68 q^{82} - 29 q^{84} - 76 q^{88} - 70 q^{90} - 36 q^{91} - 12 q^{94} + 29 q^{96} - 104 q^{97} + 56 q^{99}+O(q^{100}) $ 24 * q + 6 * q^3 - 6 * q^4 + q^6 - 6 * q^9 + 4 * q^10 - 33 * q^12 - 30 * q^16 - 19 * q^18 + 24 * q^19 - 28 * q^22 + 21 * q^24 + 96 * q^25 + 34 * q^28 + 8 * q^30 + 24 * q^33 + 58 * q^34 - 9 * q^36 - 24 * q^40 - 31 * q^42 + 16 * q^43 - 6 * q^46 + 3 * q^48 - 36 * q^49 + 38 * q^51 - 6 * q^52 - 8 * q^54 + 6 * q^57 - 42 * q^58 - 50 * q^60 + 18 * q^64 + 10 * q^66 + 20 * q^67 - 96 * q^70 - 33 * q^72 - 12 * q^73 - 30 * q^75 - 6 * q^76 - 17 * q^78 + 34 * q^81 + 68 * q^82 - 29 * q^84 - 76 * q^88 - 70 * q^90 - 36 * q^91 - 12 * q^94 + 29 * q^96 - 104 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

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 $

$2$	−0.366311	−	1.36595i	−0.259021	−	0.965872i
$2$	−0.366311	−	1.36595i	−0.259021	−	0.965872i
$3$	1.73163	+	0.0380449i	0.999759	+	0.0219653i
$3$	1.73163	+	0.0380449i	0.999759	+	0.0219653i
$4$	−1.73163	+	1.00072i	−0.865816	+	0.500362i
$5$	1.96235			0.877589			0.438794	−	0.898587i	$-0.355406\pi$
$5$	1.96235			0.877589			0.438794	+	0.898587i	$0.355406\pi$
$6$	−0.582348	−	2.37926i	−0.237743	−	0.971328i
$7$			1.36779i			0.516978i	0.966014	+	0.258489i	$0.0832245\pi$
$7$			1.36779i			0.516978i	−0.966014	+	0.258489i	$0.916775\pi$
$8$	2.00125	+	1.99875i	0.707550	+	0.706664i
$9$	2.99711	+	0.131760i	0.999035	+	0.0439199i
$10$	−0.718829	−	2.68047i	−0.227314	−	0.847638i
$11$		−	3.24389i		−	0.978069i	−0.872265	−	0.489034i	$-0.837349\pi$
$11$		−	3.24389i		−	0.978069i	0.872265	−	0.489034i	$-0.162651\pi$
$12$	−3.03663	+	1.66701i	−0.876598	+	0.481223i
$13$			6.13473i			1.70147i	0.525597	+	0.850733i	$0.323842\pi$
$13$			6.13473i			1.70147i	−0.525597	+	0.850733i	$0.676158\pi$
$14$	1.86834	−	0.501038i	0.499334	−	0.133908i
$15$	3.39807	+	0.0746574i	0.877377	+	0.0192765i
$16$	1.99711	−	3.46577i	0.499276	−	0.866443i
$17$		−	1.59015i		−	0.385669i	−0.981231	−	0.192835i	$-0.938232\pi$
$17$		−	1.59015i		−	0.385669i	0.981231	−	0.192835i	$-0.0617681\pi$
$18$	−0.917895	−	4.14216i	−0.216350	−	0.976316i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	−3.39807	+	1.96377i	−0.759831	+	0.439112i
$21$	−0.0520377	+	2.36852i	−0.0113555	+	0.516853i
$22$	−4.43098	+	1.18827i	−0.944689	+	0.253340i
$23$	3.57942			0.746362			0.373181	−	0.927759i	$-0.378267\pi$
$23$	3.57942			0.746362			0.373181	+	0.927759i	$0.378267\pi$
$24$	3.38939	+	3.53723i	0.691857	+	0.722035i
$25$	−1.14919			−0.229838
$26$	8.37972	−	2.24722i	1.64340	−	0.440715i
$27$	5.18487	+	0.342184i	0.997829	+	0.0658534i
$28$	−1.36878	−	2.36852i	−0.258676	−	0.447608i
$29$	−2.53726			−0.471158			−0.235579	−	0.971855i	$-0.575699\pi$
$29$	−2.53726			−0.471158			−0.235579	+	0.971855i	$0.575699\pi$
$30$	−1.14277	−	4.66893i	−0.208640	−	0.852427i
$31$		−	6.19047i		−	1.11184i	−0.831235	−	0.555921i	$-0.812366\pi$
$31$		−	6.19047i		−	1.11184i	0.831235	−	0.555921i	$-0.187634\pi$
$32$	−5.46563	−	1.45839i	−0.966196	−	0.257810i
$33$	0.123413	−	5.61722i	0.0214835	−	0.977833i
$34$	−2.17207	+	0.582491i	−0.372507	+	0.0998963i
$35$			2.68409i			0.453694i
$36$	−5.32174	+	2.77111i	−0.886957	+	0.461852i
$37$		−	6.07898i		−	0.999378i	−0.866205	−	0.499689i	$-0.833448\pi$
$37$		−	6.07898i		−	0.999378i	0.866205	−	0.499689i	$-0.166552\pi$
$38$	−0.366311	−	1.36595i	−0.0594234	−	0.221586i
$39$	−0.233395	+	10.6231i	−0.0373732	+	1.70106i
$40$	3.92715	+	3.92224i	0.620938	+	0.620160i
$41$			5.65123i			0.882573i	0.897366	+	0.441287i	$0.145478\pi$
$41$			5.65123i			0.882573i	−0.897366	+	0.441287i	$0.854522\pi$
$42$	3.25434	−	0.796533i	0.502155	−	0.122908i
$43$	2.89379			0.441299			0.220650	−	0.975353i	$-0.429182\pi$
$43$	2.89379			0.441299			0.220650	+	0.975353i	$0.429182\pi$
$44$	3.24623	+	5.61722i	0.489388	+	0.846828i
$45$	5.88136	+	0.258558i	0.876742	+	0.0385436i
$46$	−1.31118	−	4.88931i	−0.193323	−	0.720890i
$47$	−13.2278			−1.92947			−0.964735	−	0.263224i	$-0.915214\pi$
$47$	−13.2278			−1.92947			−0.964735	+	0.263224i	$0.915214\pi$
$48$	3.59011	−	5.92546i	0.518187	−	0.855267i
$49$	5.12914			0.732734
$50$	0.420960	+	1.56973i	0.0595328	+	0.221994i
$51$	0.0604973	−	2.75356i	0.00847132	−	0.385576i
$52$	−6.13916	−	10.6231i	−0.851349	−	1.47316i
$53$	−12.0338			−1.65297			−0.826484	−	0.562961i	$-0.809662\pi$
$53$	−12.0338			−1.65297			−0.826484	+	0.562961i	$0.809662\pi$
$54$	−1.43187	−	7.20762i	−0.194853	−	0.980833i
$55$		−	6.36564i		−	0.858342i
$56$	−2.73387	+	2.73730i	−0.365329	+	0.365787i
$57$	1.73163	+	0.0380449i	0.229360	+	0.00503917i
$58$	0.929427	+	3.46577i	0.122040	+	0.455078i
$59$		−	6.55773i		−	0.853744i	−0.904312	−	0.426872i	$-0.859616\pi$
$59$		−	6.55773i		−	0.853744i	0.904312	−	0.426872i	$-0.140384\pi$
$60$	−5.95892	+	3.27125i	−0.769293	+	0.422316i
$61$		−	2.43004i		−	0.311135i	−0.987825	−	0.155567i	$-0.950279\pi$
$61$		−	2.43004i		−	0.311135i	0.987825	−	0.155567i	$-0.0497206\pi$
$62$	−8.45587	+	2.26764i	−1.07390	+	0.287990i
$63$	−0.180220	+	4.09942i	−0.0227056	+	0.516479i
$64$	0.0100256	+	7.99999i	0.00125320	+	0.999999i
$65$			12.0385i			1.49319i
$66$	−7.71804	+	1.88907i	−0.950026	+	0.232529i
$67$	−6.04667			−0.738719			−0.369359	−	0.929287i	$-0.620423\pi$
$67$	−6.04667			−0.738719			−0.369359	+	0.929287i	$0.620423\pi$
$68$	1.59130	+	2.75356i	0.192974	+	0.333919i
$69$	6.19825	+	0.136179i	0.746182	+	0.0163940i
$70$	3.66633	−	0.983211i	0.438210	−	0.117516i
$71$	11.2654			1.33696			0.668480	−	0.743730i	$-0.266945\pi$
$71$	11.2654			1.33696			0.668480	+	0.743730i	$0.266945\pi$
$72$	5.73461	+	6.25414i	0.675830	+	0.737057i
$73$	−13.0557			−1.52805			−0.764025	−	0.645186i	$-0.776780\pi$
$73$	−13.0557			−1.52805			−0.764025	+	0.645186i	$0.776780\pi$
$74$	−8.30358	+	2.22680i	−0.965271	+	0.258860i
$75$	−1.98997	−	0.0437208i	−0.229782	−	0.00504845i
$76$	−1.73163	+	1.00072i	−0.198632	+	0.114791i
$77$	4.43697			0.505640
$78$	14.5961	−	3.57255i	1.65268	−	0.404511i
$79$			2.08809i			0.234928i	0.993077	+	0.117464i	$0.0374765\pi$
$79$			2.08809i			0.234928i	−0.993077	+	0.117464i	$0.962524\pi$
$80$	3.91902	−	6.80105i	0.438159	−	0.760381i
$81$	8.96528	+	0.789796i	0.996142	+	0.0877551i
$82$	7.71929	−	2.07010i	0.852452	−	0.228605i
$83$		−	10.0230i		−	1.10017i	−0.835108	−	0.550085i	$-0.814595\pi$
$83$		−	10.0230i		−	1.10017i	0.835108	−	0.550085i	$-0.185405\pi$
$84$	−2.28012	−	4.15348i	−0.248782	−	0.453182i
$85$		−	3.12044i		−	0.338459i
$86$	−1.06003	−	3.95277i	−0.114306	−	0.426239i
$87$	−4.39361	−	0.0965300i	−0.471044	−	0.0103491i
$88$	6.48371	−	6.49184i	0.691165	−	0.692032i
$89$			15.8264i			1.67760i	0.544440	+	0.838800i	$0.316742\pi$
$89$			15.8264i			1.67760i	−0.544440	+	0.838800i	$0.683258\pi$
$90$	−1.80123	−	8.12836i	−0.189866	−	0.856804i
$91$	−8.39104			−0.879620
$92$	−6.19825	+	3.58201i	−0.646212	+	0.373451i
$93$	0.235516	−	10.7196i	0.0244219	−	1.11157i
$94$	4.84548	+	18.0685i	0.499773	+	1.86362i
$95$	1.96235			0.201333
$96$	−9.40898	−	2.73334i	−0.960300	−	0.278971i
$97$	4.59767			0.466822			0.233411	−	0.972378i	$-0.425011\pi$
$97$	4.59767			0.466822			0.233411	+	0.972378i	$0.425011\pi$
$98$	−1.87886	−	7.00614i	−0.189793	−	0.707727i
$99$	0.427414	−	9.72227i	0.0429567	−	0.977125i
$100$	1.98997	−	1.15002i	0.198997	−	0.115002i
$101$	−7.35183			−0.731535			−0.365767	−	0.930706i	$-0.619193\pi$
$101$	−7.35183			−0.731535			−0.365767	+	0.930706i	$0.619193\pi$
$102$	−3.78339	+	0.926024i	−0.374611	+	0.0916900i
$103$			7.63479i			0.752278i	0.926563	+	0.376139i	$0.122749\pi$
$103$			7.63479i			0.752278i	−0.926563	+	0.376139i	$0.877251\pi$
$104$	−12.2618	+	12.2771i	−1.20236	+	1.20387i
$105$	−0.102116	+	4.64786i	−0.00996550	+	0.453584i
$106$	4.40810	+	16.4375i	0.428153	+	1.59655i
$107$		−	5.57514i		−	0.538969i	−0.963005	−	0.269484i	$-0.913147\pi$
$107$		−	5.57514i		−	0.538969i	0.963005	−	0.269484i	$-0.0868532\pi$
$108$	−9.32073	+	4.59609i	−0.896888	+	0.442259i
$109$			5.98541i			0.573298i	0.958036	+	0.286649i	$0.0925414\pi$
$109$			5.98541i			0.573298i	−0.958036	+	0.286649i	$0.907459\pi$
$110$	−8.69513	+	2.33180i	−0.829048	+	0.222328i
$111$	0.231274	−	10.5266i	0.0219516	−	0.999137i
$112$	4.74046	+	2.73163i	0.447932	+	0.258115i
$113$			13.0901i			1.23141i	0.787977	+	0.615704i	$0.211128\pi$
$113$			13.0901i			1.23141i	−0.787977	+	0.615704i	$0.788872\pi$
$114$	−0.582348	−	2.37926i	−0.0545419	−	0.222838i
$115$	7.02408			0.654999
$116$	4.39361	−	2.53910i	0.407936	−	0.235749i
$117$	−0.808310	+	18.3864i	−0.0747283	+	1.69982i
$118$	−8.95752	+	2.40217i	−0.824607	+	0.221137i
$119$	2.17500			0.199382
$120$	6.65117	+	6.94128i	0.607166	+	0.633649i
$121$	0.477199			0.0433817
$122$	−3.31931	+	0.890149i	−0.300516	+	0.0805903i
$123$	−0.215001	+	9.78585i	−0.0193859	+	0.882360i
$124$	6.19495	+	10.7196i	0.556323	+	0.962651i
$125$	−12.0669			−1.07929
$126$	5.66562	−	1.25549i	0.504734	−	0.111848i
$127$			9.32418i			0.827387i	0.910416	+	0.413694i	$0.135762\pi$
$127$			9.32418i			0.827387i	−0.910416	+	0.413694i	$0.864238\pi$
$128$	10.9239	−	2.94418i	0.965546	−	0.260231i
$129$	5.01099	+	0.110094i	0.441193	+	0.00969325i
$130$	16.4439	−	4.40982i	1.44223	−	0.386767i
$131$		−	1.84505i		−	0.161203i	−0.996746	−	0.0806014i	$-0.974316\pi$
$131$		−	1.84505i		−	0.161203i	0.996746	−	0.0806014i	$-0.0256841\pi$
$132$	5.40758	+	9.85047i	0.470669	+	0.857373i
$133$			1.36779i			0.118603i
$134$	2.21496	+	8.25944i	0.191343	+	0.713507i
$135$	10.1745	+	0.671484i	0.875684	+	0.0577922i
$136$	3.17832	−	3.18230i	0.272538	−	0.272880i
$137$			14.8968i			1.27272i	0.771394	+	0.636358i	$0.219560\pi$
$137$			14.8968i			1.27272i	−0.771394	+	0.636358i	$0.780440\pi$
$138$	−2.08447	−	8.51638i	−0.177442	−	0.724962i
$139$	0.153834			0.0130480			0.00652402	−	0.999979i	$-0.497923\pi$
$139$	0.153834			0.0130480			0.00652402	+	0.999979i	$0.497923\pi$
$140$	−2.68603	−	4.64786i	−0.227011	−	0.392816i
$141$	−22.9057	−	0.503250i	−1.92900	−	0.0423813i
$142$	−4.12665	−	15.3880i	−0.346301	−	1.29133i
$143$	19.9004			1.66415
$144$	6.44218	−	10.1241i	0.536849	−	0.843679i
$145$	−4.97899			−0.413483
$146$	4.78243	+	17.8334i	0.395797	+	1.47590i
$147$	8.88178	+	0.195138i	0.732557	+	0.0160947i
$148$	6.08338	+	10.5266i	0.500051	+	0.865278i
$149$	−2.58143			−0.211479			−0.105739	−	0.994394i	$-0.533721\pi$
$149$	−2.58143			−0.211479			−0.105739	+	0.994394i	$0.533721\pi$
$150$	0.669229	+	2.73422i	0.0546423	+	0.223248i
$151$		−	3.53241i		−	0.287463i	−0.989617	−	0.143732i	$-0.954090\pi$
$151$		−	3.53241i		−	0.287463i	0.989617	−	0.143732i	$-0.0459102\pi$
$152$	2.00125	+	1.99875i	0.162323	+	0.162120i
$153$	0.209518	−	4.76586i	0.0169385	−	0.385297i
$154$	−1.62531	−	6.06067i	−0.130971	−	0.488383i
$155$		−	12.1479i		−	0.975740i
$156$	−10.2266	−	18.6289i	−0.818785	−	1.49150i
$157$			2.73559i			0.218324i	0.994024	+	0.109162i	$0.0348167\pi$
$157$			2.73559i			0.218324i	−0.994024	+	0.109162i	$0.965183\pi$
$158$	2.85222	−	0.764889i	0.226910	−	0.0608513i
$159$	−20.8381	−	0.457825i	−1.65257	−	0.0363078i
$160$	−10.7255	−	2.86188i	−0.847922	−	0.226251i
$161$			4.89592i			0.385852i
$162$	−2.20526	−	12.5354i	−0.173261	−	0.984876i
$163$	−2.25874			−0.176918			−0.0884592	−	0.996080i	$-0.528194\pi$
$163$	−2.25874			−0.176918			−0.0884592	+	0.996080i	$0.528194\pi$
$164$	−5.65531	−	9.78585i	−0.441606	−	0.764146i
$165$	0.242180	−	11.0229i	0.0188537	−	0.858135i
$166$	−13.6910	+	3.67154i	−1.06262	+	0.284967i
$167$	−11.3245			−0.876314			−0.438157	−	0.898898i	$-0.644369\pi$
$167$	−11.3245			−0.876314			−0.438157	+	0.898898i	$0.644369\pi$
$168$	−4.83821	+	4.63599i	−0.373276	+	0.357675i
$169$	−24.6349			−1.89499
$170$	−4.26236	+	1.14305i	−0.326908	+	0.0876679i
$171$	2.99711	+	0.131760i	0.229194	+	0.0100759i
$172$	−5.01099	+	2.89589i	−0.382084	+	0.220809i
$173$	16.3662			1.24430			0.622150	−	0.782898i	$-0.286259\pi$
$173$	16.3662			1.24430			0.622150	+	0.782898i	$0.286259\pi$
$174$	1.47757	+	6.03680i	0.112014	+	0.457649i
$175$		−	1.57186i		−	0.118821i
$176$	−11.2426	−	6.47838i	−0.847441	−	0.488326i
$177$	0.249488	−	11.3556i	0.0187527	−	0.853538i
$178$	21.6181	−	5.79739i	1.62035	−	0.434533i
$179$		−	17.9613i		−	1.34249i	−0.741235	−	0.671245i	$-0.765760\pi$
$179$		−	17.9613i		−	1.34249i	0.741235	−	0.671245i	$-0.234240\pi$
$180$	−10.4431	+	5.43789i	−0.778383	+	0.405316i
$181$		−	15.9253i		−	1.18372i	−0.806040	−	0.591861i	$-0.798393\pi$
$181$		−	15.9253i		−	1.18372i	0.806040	−	0.591861i	$-0.201607\pi$
$182$	3.07373	+	11.4617i	0.227840	+	0.849600i
$183$	0.0924507	−	4.20794i	0.00683415	−	0.311060i
$184$	7.16333	+	7.15436i	0.528088	+	0.527427i
$185$		−	11.9291i		−	0.877043i
$186$	−14.7287	+	3.60501i	−1.07996	+	0.264332i
$187$	−5.15828			−0.377211
$188$	22.9057	−	13.2373i	1.67057	−	0.965433i
$189$	−0.468038	+	7.09184i	−0.0340447	+	0.515856i
$190$	−0.718829	−	2.68047i	−0.0521493	−	0.194462i
$191$	−15.0535			−1.08923			−0.544615	−	0.838686i	$-0.683324\pi$
$191$	−15.0535			−1.08923			−0.544615	+	0.838686i	$0.683324\pi$
$192$	−0.286999	+	13.8534i	−0.0207123	+	0.999785i
$193$	4.36328			0.314076			0.157038	−	0.987593i	$-0.449806\pi$
$193$	4.36328			0.314076			0.157038	+	0.987593i	$0.449806\pi$
$194$	−1.68417	−	6.28018i	−0.120917	−	0.450891i
$195$	−0.458003	+	20.8462i	−0.0327983	+	1.49283i
$196$	−8.88178	+	5.13285i	−0.634413	+	0.366632i
$197$	5.19604			0.370203			0.185101	−	0.982719i	$-0.440739\pi$
$197$	5.19604			0.370203			0.185101	+	0.982719i	$0.440739\pi$
$198$	−13.4367	+	2.97755i	−0.954904	+	0.211605i
$199$		−	25.2819i		−	1.79218i	−0.443869	−	0.896092i	$-0.646394\pi$
$199$		−	25.2819i		−	1.79218i	0.443869	−	0.896092i	$-0.353606\pi$
$200$	−2.29982	−	2.29694i	−0.162622	−	0.162418i
$201$	−10.4706	−	0.230045i	−0.738540	−	0.0162261i
$202$	2.69305	+	10.0422i	0.189483	+	0.706569i
$203$		−	3.47045i		−	0.243578i
$204$	2.65080	+	4.82870i	0.185593	+	0.338077i
$205$			11.0897i			0.774536i
$206$	10.4287	−	2.79671i	0.726604	−	0.194856i
$207$	10.7279	+	0.471624i	0.745641	+	0.0327801i
$208$	21.2616	+	12.2517i	1.47422	+	0.849502i
$209$		−	3.24389i		−	0.224384i
$210$	6.38614	−	1.56307i	0.440686	−	0.107862i
$211$	−6.83636			−0.470634			−0.235317	−	0.971919i	$-0.575613\pi$
$211$	−6.83636			−0.470634			−0.235317	+	0.971919i	$0.575613\pi$
$212$	20.8381	−	12.0425i	1.43117	−	0.827082i
$213$	19.5076	+	0.428593i	1.33664	+	0.0293667i
$214$	−7.61535	+	2.04223i	−0.520575	+	0.139604i
$215$	5.67863			0.387279
$216$	9.69230	+	11.0480i	0.659478	+	0.751724i
$217$	8.46729			0.574797
$218$	8.17577	−	2.19252i	0.553733	−	0.148496i
$219$	−22.6076	−	0.496702i	−1.52768	−	0.0335640i
$220$	6.37024	+	11.0229i	0.429482	+	0.743167i
$221$	9.75516			0.656203
$222$	−14.4635	+	3.54008i	−0.970724	+	0.237595i
$223$		−	11.7214i		−	0.784926i	−0.919768	−	0.392463i	$-0.871623\pi$
$223$		−	11.7214i		−	0.784926i	0.919768	−	0.392463i	$-0.128377\pi$
$224$	1.99478	−	7.47586i	0.133282	−	0.499502i
$225$	−3.44424	−	0.151417i	−0.229616	−	0.0100945i
$226$	17.8803	−	4.79503i	1.18938	−	0.318960i
$227$			12.9812i			0.861593i	0.902449	+	0.430796i	$0.141767\pi$
$227$			12.9812i			0.861593i	−0.902449	+	0.430796i	$0.858233\pi$
$228$	−3.03663	+	1.66701i	−0.201105	+	0.110400i
$229$		−	21.1337i		−	1.39655i	−0.715828	−	0.698277i	$-0.753950\pi$
$229$		−	21.1337i		−	1.39655i	0.715828	−	0.698277i	$-0.246050\pi$
$230$	−2.57299	−	9.59453i	−0.169658	−	0.632645i
$231$	7.68320	+	0.168804i	0.505518	+	0.0111065i
$232$	−5.07770	−	5.07134i	−0.333368	−	0.332950i
$233$		−	22.7804i		−	1.49239i	−0.665725	−	0.746197i	$-0.731878\pi$
$233$		−	22.7804i		−	1.49239i	0.665725	−	0.746197i	$-0.268122\pi$
$234$	25.4110	−	5.63103i	1.66117	−	0.368112i
$235$	−25.9575			−1.69328
$236$	6.56247	+	11.3556i	0.427181	+	0.739185i
$237$	−0.0794411	+	3.61580i	−0.00516026	+	0.234871i
$238$	−0.796727	−	2.97094i	−0.0516442	−	0.192578i
$239$	4.07627			0.263672			0.131836	−	0.991272i	$-0.457913\pi$
$239$	4.07627			0.263672			0.131836	+	0.991272i	$0.457913\pi$
$240$	7.04504	−	11.6278i	0.454756	−	0.750573i
$241$	1.89906			0.122329			0.0611645	−	0.998128i	$-0.480519\pi$
$241$	1.89906			0.122329			0.0611645	+	0.998128i	$0.480519\pi$
$242$	−0.174803	−	0.651830i	−0.0112368	−	0.0419012i
$243$	15.4945	+	1.70872i	0.993974	+	0.109614i
$244$	2.43180	+	4.20794i	0.155680	+	0.269386i
$245$	10.0652			0.643039
$246$	13.4457	−	3.29098i	0.857268	−	0.209825i
$247$			6.13473i			0.390343i
$248$	12.3732	−	12.3887i	0.785698	−	0.786683i
$249$	0.381326	−	17.3562i	0.0241655	−	1.09991i
$250$	4.42022	+	16.4827i	0.279559	+	1.04246i
$251$		−	27.7824i		−	1.75361i	−0.480844	−	0.876806i	$-0.659670\pi$
$251$		−	27.7824i		−	1.75361i	0.480844	−	0.876806i	$-0.340330\pi$
$252$	−3.79031	−	7.27905i	−0.238767	−	0.458537i
$253$		−	11.6112i		−	0.729993i
$254$	12.7364	−	3.41555i	0.799150	−	0.214310i
$255$	0.118717	−	5.40345i	0.00743433	−	0.338377i
$256$	−8.02314	−	13.8430i	−0.501446	−	0.865189i
$257$			2.49223i			0.155461i	0.996974	+	0.0777305i	$0.0247674\pi$
$257$			2.49223i			0.155461i	−0.996974	+	0.0777305i	$0.975233\pi$
$258$	−1.68520	−	6.88508i	−0.104916	−	0.428647i
$259$	8.31480			0.516656
$260$	−12.0472	−	20.8462i	−0.747134	−	1.29283i
$261$	−7.60444	−	0.334309i	−0.470703	−	0.0206932i
$262$	−2.52024	+	0.675862i	−0.155701	+	0.0417549i
$263$	0.000192891	0		1.18942e−5	0		5.94708e−6	−	1.00000i	$-0.499998\pi$
$263$	0.000192891	0		1.18942e−5	0		5.94708e−6		1.00000i	$0.499998\pi$
$264$	11.4744	−	10.9948i	0.706199	−	0.676684i
$265$	−23.6145			−1.45063
$266$	1.86834	−	0.501038i	0.114555	−	0.0307206i
$267$	−0.602116	+	27.4056i	−0.0368489	+	1.67719i
$268$	10.4706	−	6.05105i	0.639595	−	0.369626i
$269$	17.0633			1.04037			0.520183	−	0.854055i	$-0.325864\pi$
$269$	17.0633			1.04037			0.520183	+	0.854055i	$0.325864\pi$
$270$	−2.80982	−	14.1439i	−0.171000	−	0.860768i
$271$			22.0286i			1.33814i	0.743199	+	0.669070i	$0.233307\pi$
$271$			22.0286i			1.33814i	−0.743199	+	0.669070i	$0.766693\pi$
$272$	−5.51111	−	3.17571i	−0.334160	−	0.192555i
$273$	−14.5302	−	0.319237i	−0.879408	−	0.0193211i
$274$	20.3482	−	5.45684i	1.22928	−	0.329660i
$275$			3.72784i			0.224797i
$276$	−10.8694	+	5.96692i	−0.654259	+	0.359166i
$277$			12.6543i			0.760323i	0.924920	+	0.380162i	$0.124132\pi$
$277$			12.6543i			0.760323i	−0.924920	+	0.380162i	$0.875868\pi$
$278$	−0.0563511	−	0.210129i	−0.00337971	−	0.0126027i
$279$	0.815655	−	18.5535i	0.0488320	−	1.11077i
$280$	−5.36481	+	5.37154i	−0.320609	+	0.321011i
$281$			18.4849i			1.10271i	0.834269	+	0.551357i	$0.185890\pi$
$281$			18.4849i			1.10271i	−0.834269	+	0.551357i	$0.814110\pi$
$282$	7.70317	+	31.4723i	0.458717	+	1.87415i
$283$	−30.3565			−1.80451			−0.902253	−	0.431207i	$-0.858088\pi$
$283$	−30.3565			−1.80451			−0.902253	+	0.431207i	$0.858088\pi$
$284$	−19.5076	+	11.2736i	−1.15756	+	0.668964i
$285$	3.39807	+	0.0746574i	0.201284	+	0.00442232i
$286$	−7.28971	−	27.1829i	−0.431050	−	1.60736i
$287$	−7.72971			−0.456271
$288$	−16.1889	−	5.09111i	−0.953940	−	0.299997i
$289$	14.4714			0.851259
$290$	1.82386	+	6.80105i	0.107101	+	0.399371i
$291$	7.96147	+	0.174918i	0.466710	+	0.0102539i
$292$	22.6076	−	13.0651i	1.32301	−	0.764578i
$293$	9.20078			0.537515			0.268758	−	0.963208i	$-0.413387\pi$
$293$	9.20078			0.537515			0.268758	+	0.963208i	$0.413387\pi$
$294$	−2.98694	−	12.2035i	−0.174202	−	0.711725i
$295$		−	12.8686i		−	0.749236i
$296$	12.1503	−	12.1656i	0.706224	−	0.707110i
$297$	1.11001	−	16.8191i	0.0644091	−	0.975946i
$298$	0.945605	+	3.52610i	0.0547774	+	0.204261i
$299$			21.9588i			1.26991i
$300$	3.48966	−	1.91571i	0.201475	−	0.110603i
$301$			3.95811i			0.228142i
$302$	−4.82509	+	1.29396i	−0.277652	+	0.0744589i
$303$	−12.7307	−	0.279700i	−0.731358	−	0.0160683i
$304$	1.99711	−	3.46577i	0.114542	−	0.198776i
$305$		−	4.76858i		−	0.273048i
$306$	−6.58667	+	1.45959i	−0.376535	+	0.0834394i
$307$	15.4755			0.883235			0.441617	−	0.897203i	$-0.354405\pi$
$307$	15.4755			0.883235			0.441617	+	0.897203i	$0.354405\pi$
$308$	−7.68320	+	4.44018i	−0.437791	+	0.253003i
$309$	−0.290465	+	13.2207i	−0.0165240	+	0.752097i
$310$	−16.5934	+	4.44989i	−0.942439	+	0.252737i
$311$	29.4009			1.66717			0.833587	−	0.552389i	$-0.186284\pi$
$311$	29.4009			1.66717			0.833587	+	0.552389i	$0.186284\pi$
$312$	−21.7000	+	20.7930i	−1.22852	+	1.17717i
$313$	1.42885			0.0807635			0.0403817	−	0.999184i	$-0.487143\pi$
$313$	1.42885			0.0807635			0.0403817	+	0.999184i	$0.487143\pi$
$314$	3.73667	−	1.00208i	0.210873	−	0.0565504i
$315$	−0.353655	+	8.04450i	−0.0199262	+	0.453256i
$316$	−2.08960	−	3.61580i	−0.117549	−	0.203405i
$317$	−23.1994			−1.30301			−0.651503	−	0.758646i	$-0.725861\pi$
$317$	−23.1994			−1.30301			−0.651503	+	0.758646i	$0.725861\pi$
$318$	7.00785	+	28.6315i	0.392981	+	1.60557i
$319$			8.23059i			0.460825i
$320$	0.0196737	+	15.6988i	0.00109979	+	0.877588i
$321$	0.212106	−	9.65409i	0.0118386	−	0.538839i
$322$	6.68757	−	1.79343i	0.372684	−	0.0999438i
$323$		−	1.59015i		−	0.0884785i
$324$	−16.3149	+	7.60413i	−0.906385	+	0.422452i
$325$		−	7.04996i		−	0.391062i
$326$	0.827402	+	3.08533i	0.0458256	+	0.170881i
$327$	−0.227715	+	10.3645i	−0.0125926	+	0.573160i
$328$	−11.2954	+	11.3095i	−0.623682	+	0.624464i
$329$		−	18.0929i		−	0.997493i
$330$	−15.1455	+	3.70702i	−0.833732	+	0.204065i
$331$	7.84420			0.431156			0.215578	−	0.976487i	$-0.430836\pi$
$331$	7.84420			0.431156			0.215578	+	0.976487i	$0.430836\pi$
$332$	10.0303	+	17.3562i	0.550483	+	0.952546i
$333$	0.800965	−	18.2193i	0.0438926	−	0.998414i
$334$	4.14828	+	15.4687i	0.226984	+	0.846407i
$335$	−11.8657			−0.648291
$336$	8.10482	+	4.91053i	0.442154	+	0.267891i
$337$	8.23132			0.448389			0.224194	−	0.974544i	$-0.428025\pi$
$337$	8.23132			0.448389			0.224194	+	0.974544i	$0.428025\pi$
$338$	9.02401	+	33.6500i	0.490842	+	1.83032i
$339$	−0.498010	+	22.6672i	−0.0270482	+	1.23111i
$340$	3.12269	+	5.40345i	0.169352	+	0.293043i
$341$	−20.0812			−1.08746
$342$	−0.917895	−	4.14216i	−0.0496341	−	0.223982i
$343$			16.5902i			0.895785i
$344$	5.79121	+	5.78396i	0.312241	+	0.311850i
$345$	12.1631	+	0.267231i	0.654841	+	0.0143872i
$346$	−5.99512	−	22.3554i	−0.322300	−	1.20183i
$347$			37.1146i			1.99242i	0.0869959	+	0.996209i	$0.472273\pi$
$347$			37.1146i			1.99242i	−0.0869959	+	0.996209i	$0.527727\pi$
$348$	7.70472	−	4.22963i	0.413016	−	0.226732i
$349$		−	29.4520i		−	1.57653i	−0.615338	−	0.788263i	$-0.710980\pi$
$349$		−	29.4520i		−	1.57653i	0.615338	−	0.788263i	$-0.289020\pi$
$350$	−2.14707	+	0.575787i	−0.114766	+	0.0307771i
$351$	−2.09921	+	31.8078i	−0.112047	+	1.69777i
$352$	−4.73087	+	17.7299i	−0.252156	+	0.945006i
$353$		−	33.5116i		−	1.78364i	−0.452388	−	0.891821i	$-0.649428\pi$
$353$		−	33.5116i		−	1.78364i	0.452388	−	0.891821i	$-0.350572\pi$
$354$	−15.6025	+	3.81888i	−0.829265	+	0.202971i
$355$	22.1067			1.17330
$356$	−15.8379	−	27.4056i	−0.839406	−	1.45249i
$357$	3.76631	+	0.0827479i	0.199334	+	0.00437948i
$358$	−24.5342	+	6.57941i	−1.29667	+	0.347733i
$359$	−16.6668			−0.879638			−0.439819	−	0.898087i	$-0.644957\pi$
$359$	−16.6668			−0.879638			−0.439819	+	0.898087i	$0.644957\pi$
$360$	11.2533	+	12.2728i	0.593101	+	0.646833i
$361$	1.00000			0.0526316
$362$	−21.7532	+	5.83363i	−1.14332	+	0.306609i
$363$	0.826334	+	0.0181550i	0.0433713	+	0.000952891i
$364$	14.5302	−	8.39711i	0.761590	−	0.440128i
$365$	−25.6198			−1.34100
$366$	−5.78169	+	1.41513i	−0.302214	+	0.0739700i
$367$			16.7895i			0.876403i	0.898877	+	0.438201i	$0.144384\pi$
$367$			16.7895i			0.876403i	−0.898877	+	0.438201i	$0.855616\pi$
$368$	7.14849	−	12.4055i	0.372641	−	0.646680i
$369$	−0.744604	+	16.9373i	−0.0387625	+	0.881721i
$370$	−16.2945	+	4.36975i	−0.847111	+	0.227172i
$371$		−	16.4597i		−	0.854547i
$372$	10.3196	+	18.7981i	0.535044	+	0.974638i
$373$			33.0710i			1.71235i	0.516684	+	0.856176i	$0.327166\pi$
$373$			33.0710i			1.71235i	−0.516684	+	0.856176i	$0.672834\pi$
$374$	1.88953	+	7.04595i	0.0977054	+	0.364337i
$375$	−20.8954	−	0.459083i	−1.07903	−	0.0237069i
$376$	−26.4721	−	26.4390i	−1.36520	−	1.36349i
$377$		−	15.5654i		−	0.801659i
$378$	9.85854	−	1.95850i	0.507069	−	0.100734i
$379$	−22.6250			−1.16217			−0.581085	−	0.813843i	$-0.697372\pi$
$379$	−22.6250			−1.16217			−0.581085	+	0.813843i	$0.697372\pi$
$380$	−3.39807	+	1.96377i	−0.174317	+	0.100739i
$381$	−0.354738	+	16.1461i	−0.0181738	+	0.827188i
$382$	5.51424	+	20.5623i	0.282133	+	1.05206i
$383$	16.5208			0.844173			0.422086	−	0.906556i	$-0.361298\pi$
$383$	16.5208			0.844173			0.422086	+	0.906556i	$0.361298\pi$
$384$	19.0282	−	4.68264i	0.971029	−	0.238960i
$385$	8.70688			0.443744
$386$	−1.59832	−	5.96002i	−0.0813521	−	0.303357i
$387$	8.67300	+	0.381285i	0.440874	+	0.0193818i
$388$	−7.96147	+	4.60099i	−0.404183	+	0.233580i
$389$	−6.35808			−0.322367			−0.161184	−	0.986924i	$-0.551531\pi$
$389$	−6.35808			−0.322367			−0.161184	+	0.986924i	$0.551531\pi$
$390$	28.6426	−	7.01058i	1.45038	−	0.354995i
$391$		−	5.69184i		−	0.287849i
$392$	10.2647	+	10.2518i	0.518446	+	0.517796i
$393$	0.0701948	−	3.19495i	0.00354086	−	0.161164i
$394$	−1.90337	−	7.09753i	−0.0958902	−	0.357568i
$395$			4.09755i			0.206170i
$396$	8.98918	+	17.2631i	0.451723	+	0.867505i
$397$		−	26.9035i		−	1.35025i	−0.737704	−	0.675124i	$-0.764090\pi$
$397$		−	26.9035i		−	1.35025i	0.737704	−	0.675124i	$-0.235910\pi$
$398$	−34.5337	+	9.26102i	−1.73102	+	0.464213i
$399$	−0.0520377	+	2.36852i	−0.00260514	+	0.118574i
$400$	−2.29505	+	3.98283i	−0.114753	+	0.199141i
$401$			13.1856i			0.658456i	0.944250	+	0.329228i	$0.106789\pi$
$401$			13.1856i			0.658456i	−0.944250	+	0.329228i	$0.893211\pi$
$402$	3.52127	+	14.3866i	0.175625	+	0.717538i
$403$	37.9768			1.89176
$404$	12.7307	−	7.35715i	0.633375	−	0.366032i
$405$	17.5930	+	1.54985i	0.874203	+	0.0770129i
$406$	−4.74046	+	1.27126i	−0.235265	+	0.0630918i
$407$	−19.7195			−0.977461
$408$	5.62475	−	5.38966i	0.278466	−	0.266828i
$409$	−21.3283			−1.05462			−0.527309	−	0.849673i	$-0.676799\pi$
$409$	−21.3283			−1.05462			−0.527309	+	0.849673i	$0.676799\pi$
$410$	15.1479	−	4.06227i	0.748103	−	0.200621i
$411$	−0.566746	+	25.7957i	−0.0279555	+	1.27241i
$412$	−7.64031	−	13.2207i	−0.376411	−	0.651335i
$413$	8.96963			0.441367
$414$	−3.28553	−	14.8265i	−0.161475	−	0.728685i
$415$		−	19.6687i		−	0.965498i
$416$	8.94685	−	33.5301i	0.438655	−	1.64395i
$417$	0.266384	+	0.00585261i	0.0130449	+	0.000286603i
$418$	−4.43098	+	1.18827i	−0.216726	+	0.0581202i
$419$			21.5519i			1.05288i	0.850212	+	0.526441i	$0.176474\pi$
$419$			21.5519i			1.05288i	−0.850212	+	0.526441i	$0.823526\pi$
$420$	−4.47439	−	8.15057i	−0.218328	−	0.397707i
$421$			10.4934i			0.511418i	0.966754	+	0.255709i	$0.0823089\pi$
$421$			10.4934i			0.511418i	−0.966754	+	0.255709i	$0.917691\pi$
$422$	2.50423	+	9.33812i	0.121904	+	0.454572i
$423$	−39.6450	−	1.74289i	−1.92761	−	0.0847421i
$424$	−24.0826	−	24.0525i	−1.16956	−	1.16809i
$425$			1.82739i			0.0886414i
$426$	−6.56040	−	26.8034i	−0.317853	−	1.29863i
$427$	3.32379			0.160850
$428$	5.57917	+	9.65409i	0.269679	+	0.466648i
$429$	34.4601	+	0.757108i	1.66375	+	0.0365535i
$430$	−2.08014	−	7.75672i	−0.100313	−	0.374062i
$431$	16.0363			0.772441			0.386220	−	0.922407i	$-0.373780\pi$
$431$	16.0363			0.772441			0.386220	+	0.922407i	$0.373780\pi$
$432$	11.5407	−	17.2862i	0.555251	−	0.831683i
$433$	23.5481			1.13165			0.565824	−	0.824526i	$-0.308558\pi$
$433$	23.5481			1.13165			0.565824	+	0.824526i	$0.308558\pi$
$434$	−3.10166	−	11.5659i	−0.148884	−	0.555180i
$435$	−8.62179	−	0.189425i	−0.413383	−	0.00908226i
$436$	−5.98974	−	10.3645i	−0.286857	−	0.496371i
$437$	3.57942			0.171227
$438$	7.60295	+	31.0628i	0.363283	+	1.48424i
$439$			11.7334i			0.560007i	0.959999	+	0.280003i	$0.0903356\pi$
$439$			11.7334i			0.560007i	−0.959999	+	0.280003i	$0.909664\pi$
$440$	12.7233	−	12.7392i	0.606559	−	0.607320i
$441$	15.3726	+	0.675814i	0.732027	+	0.0321816i
$442$	−3.57342	−	13.3251i	−0.169970	−	0.633808i
$443$		−	10.7030i		−	0.508514i	−0.967137	−	0.254257i	$-0.918169\pi$
$443$		−	10.7030i		−	0.508514i	0.967137	−	0.254257i	$-0.0818308\pi$
$444$	10.1337	+	18.4596i	0.480924	+	0.876053i
$445$			31.0570i			1.47224i
$446$	−16.0109	+	4.29369i	−0.758138	+	0.203312i
$447$	−4.47009	−	0.0982103i	−0.211428	−	0.00464519i
$448$	−10.9423	+	0.0137129i	−0.516977	+	0.000647875i
$449$		−	17.2656i		−	0.814816i	−0.913246	−	0.407408i	$-0.866433\pi$
$449$		−	17.2656i		−	0.814816i	0.913246	−	0.407408i	$-0.133567\pi$
$450$	1.05483	+	4.76012i	0.0497254	+	0.224394i
$451$	18.3319			0.863217
$452$	−13.0995	−	22.6672i	−0.616150	−	1.06617i
$453$	0.134390	−	6.11683i	0.00631420	−	0.287394i
$454$	17.7317	−	4.75515i	0.832188	−	0.223170i
$455$	−16.4661			−0.771945
$456$	3.38939	+	3.53723i	0.158723	+	0.165646i
$457$	23.1891			1.08474			0.542371	−	0.840139i	$-0.317527\pi$
$457$	23.1891			1.08474			0.542371	+	0.840139i	$0.317527\pi$
$458$	−28.8676	+	7.74150i	−1.34889	+	0.361737i
$459$	0.544126	−	8.24475i	0.0253976	−	0.384832i
$460$	−12.1631	+	7.02916i	−0.567109	+	0.327736i
$461$	26.3227			1.22597			0.612986	−	0.790094i	$-0.289968\pi$
$461$	26.3227			1.22597			0.612986	+	0.790094i	$0.289968\pi$
$462$	−2.58386	−	10.5567i	−0.120212	−	0.491142i
$463$		−	9.10122i		−	0.422970i	−0.977381	−	0.211485i	$-0.932170\pi$
$463$		−	9.10122i		−	0.422970i	0.977381	−	0.211485i	$-0.0678299\pi$
$464$	−5.06718	+	8.79357i	−0.235238	+	0.408231i
$465$	0.462165	−	21.0356i	0.0214324	−	0.975504i
$466$	−31.1169	+	8.34471i	−1.44146	+	0.386561i
$467$			19.8707i			0.919507i	0.888047	+	0.459753i	$0.152062\pi$
$467$			19.8707i			0.919507i	−0.888047	+	0.459753i	$0.847938\pi$
$468$	−17.0000	−	32.6474i	−0.785826	−	1.50913i
$469$		−	8.27060i		−	0.381901i
$470$	9.50851	+	35.4566i	0.438595	+	1.63549i
$471$	−0.104075	+	4.73704i	−0.00479554	+	0.218271i
$472$	13.1072	−	13.1237i	0.603310	−	0.604066i
$473$		−	9.38714i		−	0.431621i
$474$	4.96810	−	1.21599i	0.228192	−	0.0558524i
$475$	−1.14919			−0.0527284
$476$	−3.76631	+	2.17658i	−0.172628	+	0.0997633i
$477$	−36.0665	−	1.58557i	−1.65137	−	0.0725982i
$478$	−1.49318	−	5.56797i	−0.0682965	−	0.254673i
$479$	32.8657			1.50167			0.750836	−	0.660488i	$-0.229651\pi$
$479$	32.8657			1.50167			0.750836	+	0.660488i	$0.229651\pi$
$480$	−18.4637	−	5.36377i	−0.842748	−	0.244822i
$481$	37.2929			1.70041
$482$	−0.695645	−	2.59401i	−0.0316858	−	0.118154i
$483$	−0.186265	+	8.47793i	−0.00847534	+	0.385759i
$484$	−0.826334	+	0.477544i	−0.0375606	+	0.0217066i
$485$	9.02222			0.409678
$486$	−3.34179	−	21.7907i	−0.151587	−	0.988444i
$487$			15.9272i			0.721731i	0.932618	+	0.360865i	$0.117519\pi$
$487$			15.9272i			0.721731i	−0.932618	+	0.360865i	$0.882481\pi$
$488$	4.85703	−	4.86312i	0.219868	−	0.220143i
$489$	−3.91131	−	0.0859337i	−0.176876	−	0.00388606i
$490$	−3.68697	−	13.7485i	−0.166561	−	0.621093i
$491$		−	11.7100i		−	0.528464i	−0.964459	−	0.264232i	$-0.914882\pi$
$491$		−	11.7100i		−	0.528464i	0.964459	−	0.264232i	$-0.0851184\pi$
$492$	−9.42063	−	17.1607i	−0.424715	−	0.773662i
$493$			4.03464i			0.181711i
$494$	8.37972	−	2.24722i	0.377022	−	0.101107i
$495$	0.838734	−	19.0785i	0.0376983	−	0.857514i
$496$	−21.4548	−	12.3630i	−0.963347	−	0.555116i
$497$			15.4088i			0.691179i
$498$	−23.8474	+	5.83690i	−1.06863	+	0.261558i
$499$	25.8509			1.15724			0.578622	−	0.815596i	$-0.303591\pi$
$499$	25.8509			1.15724			0.578622	+	0.815596i	$0.303591\pi$
$500$	20.8954	−	12.0756i	0.934469	−	0.540036i
$501$	−19.6098	−	0.430839i	−0.876103	−	0.0192485i
$502$	−37.9494	+	10.1770i	−1.69376	+	0.454222i
$503$	17.2709			0.770069			0.385035	−	0.922902i	$-0.374189\pi$
$503$	17.2709			0.770069			0.385035	+	0.922902i	$0.374189\pi$
$504$	−8.55437	+	7.84377i	−0.381042	+	0.349389i
$505$	−14.4269			−0.641986
$506$	−15.8604	+	4.25332i	−0.705079	+	0.189083i
$507$	−42.6585	−	0.937232i	−1.89453	−	0.0416239i
$508$	−9.33093	−	16.1461i	−0.413993	−	0.716365i
$509$	−5.42339			−0.240388			−0.120194	−	0.992750i	$-0.538352\pi$
$509$	−5.42339			−0.240388			−0.120194	+	0.992750i	$0.538352\pi$
$510$	−7.42432	+	1.81718i	−0.328755	+	0.0804661i
$511$		−	17.8575i		−	0.789968i
$512$	−15.9699	+	16.0300i	−0.705776	+	0.708435i
$513$	5.18487	+	0.342184i	0.228918	+	0.0151078i
$514$	3.40426	−	0.912930i	0.150155	−	0.0402676i
$515$			14.9821i			0.660191i
$516$	−8.78737	+	4.82397i	−0.386842	+	0.212363i
$517$			42.9094i			1.88715i
$518$	−3.04580	−	11.3576i	−0.133825	−	0.499024i
$519$	28.3403	+	0.622652i	1.24400	+	0.0273314i
$520$	−24.0618	+	24.0920i	−1.05518	+	1.05650i
$521$			13.0272i			0.570732i	0.958419	+	0.285366i	$0.0921151\pi$
$521$			13.0272i			0.570732i	−0.958419	+	0.285366i	$0.907885\pi$
$522$	2.32894	+	10.5097i	0.101935	+	0.459999i
$523$	21.7560			0.951322			0.475661	−	0.879629i	$-0.342209\pi$
$523$	21.7560			0.951322			0.475661	+	0.879629i	$0.342209\pi$
$524$	1.84638	+	3.19495i	0.0806597	+	0.139572i
$525$	0.0598011	−	2.72188i	0.00260994	−	0.118792i
$526$	−7.06580e−5	0	0.000263479i	−3.08084e−6	0	1.14882e-5i
$527$	−9.84380			−0.428803
$528$	−19.2215	−	11.6459i	−0.836510	−	0.506823i
$529$	−10.1877			−0.442944
$530$	8.65023	+	32.2562i	0.375742	+	1.40112i
$531$	0.864045	−	19.6542i	0.0374964	−	0.852920i
$532$	−1.36878	−	2.36852i	−0.0593443	−	0.102688i
$533$	−34.6687			−1.50167
$534$	37.6552	−	9.21650i	1.62950	−	0.398837i
$535$		−	10.9404i		−	0.472993i
$536$	−12.1009	−	12.0858i	−0.522680	−	0.522025i
$537$	0.683336	−	31.1024i	0.0294881	−	1.34217i
$538$	−6.25046	−	23.3076i	−0.269477	−	1.00486i
$539$		−	16.6383i		−	0.716664i
$540$	−18.2905	+	9.01912i	−0.787098	+	0.388121i
$541$			14.5132i			0.623971i	0.950087	+	0.311986i	$0.100994\pi$
$541$			14.5132i			0.623971i	−0.950087	+	0.311986i	$0.899006\pi$
$542$	30.0899	−	8.06930i	1.29247	−	0.346606i
$543$	0.605879	−	27.5769i	0.0260007	−	1.18344i
$544$	−2.31907	+	8.69119i	−0.0994294	+	0.372632i
$545$			11.7455i			0.503120i
$546$	4.88651	+	19.9645i	0.209123	+	0.854400i
$547$	30.4946			1.30385			0.651927	−	0.758282i	$-0.273961\pi$
$547$	30.4946			1.30385			0.651927	+	0.758282i	$0.273961\pi$
$548$	−14.9075	−	25.7957i	−0.636818	−	1.10194i
$549$	0.320181	−	7.28308i	0.0136650	−	0.310834i
$550$	5.09204	−	1.36555i	0.217125	−	0.0582272i
$551$	−2.53726			−0.108091
$552$	12.1321	+	12.6613i	0.516375	+	0.538899i
$553$	−2.85607			−0.121453
$554$	17.2851	−	4.63541i	0.734375	−	0.196939i
$555$	0.453841	−	20.6568i	0.0192645	−	0.876832i
$556$	−0.266384	+	0.153945i	−0.0112972	+	0.00652874i
$557$	35.7858			1.51629			0.758147	−	0.652084i	$-0.226105\pi$
$557$	35.7858			1.51629			0.758147	+	0.652084i	$0.226105\pi$
$558$	−25.6419	+	5.68220i	−1.08551	+	0.240547i
$559$			17.7526i			0.750856i
$560$	9.30244	+	5.36041i	0.393100	+	0.226519i
$561$	−8.93225	−	0.196246i	−0.377120	−	0.00828553i
$562$	25.2494	−	6.77120i	1.06508	−	0.285626i
$563$			40.9452i			1.72563i	0.505516	+	0.862817i	$0.331302\pi$
$563$			40.9452i			1.72563i	−0.505516	+	0.862817i	$0.668698\pi$
$564$	40.1678	−	22.0508i	1.69137	−	0.928505i
$565$			25.6872i			1.08067i
$566$	11.1199	+	41.4654i	0.467405	+	1.74292i
$567$	−1.08028	+	12.2627i	−0.0453674	+	0.514983i
$568$	22.5450	+	22.5167i	0.945966	+	0.944781i
$569$			35.8823i			1.50426i	0.659013	+	0.752132i	$0.270974\pi$
$569$			35.8823i			1.50426i	−0.659013	+	0.752132i	$0.729026\pi$
$570$	−1.14277	−	4.66893i	−0.0478654	−	0.195560i
$571$	−1.85306			−0.0775483			−0.0387741	−	0.999248i	$-0.512345\pi$
$571$	−1.85306			−0.0775483			−0.0387741	+	0.999248i	$0.512345\pi$
$572$	−34.4601	+	19.9148i	−1.44085	+	0.832678i
$573$	−26.0671	−	0.572708i	−1.08897	−	0.0239252i
$574$	2.83148	+	10.5584i	0.118184	+	0.440699i
$575$	−4.11344			−0.171542
$576$	−1.02403	+	23.9781i	−0.0426679	+	0.999089i
$577$	−18.7853			−0.782044			−0.391022	−	0.920381i	$-0.627878\pi$
$577$	−18.7853			−0.782044			−0.391022	+	0.920381i	$0.627878\pi$
$578$	−5.30103	−	19.7672i	−0.220494	−	0.822207i
$579$	7.55560	+	0.166001i	0.314000	+	0.00689875i
$580$	8.62179	−	4.98260i	0.358000	−	0.206891i
$581$	13.7095			0.568764
$582$	−2.67744	−	10.9390i	−0.110984	−	0.453438i
$583$			39.0362i			1.61672i
$584$	−26.1277	−	26.0950i	−1.08117	−	1.07982i
$585$	−1.58619	+	36.0806i	−0.0655807	+	1.49175i
$586$	−3.37034	−	12.5678i	−0.139228	−	0.519171i
$587$			1.87515i			0.0773957i	0.999251	+	0.0386979i	$0.0123210\pi$
$587$			1.87515i			0.0773957i	−0.999251	+	0.0386979i	$0.987679\pi$
$588$	−15.5753	+	8.55030i	−0.642313	+	0.352609i
$589$		−	6.19047i		−	0.255074i
$590$	−17.5778	+	4.71389i	−0.723666	+	0.194068i
$591$	8.99764	+	0.197683i	0.370113	+	0.00813160i
$592$	−21.0684	−	12.1404i	−0.865904	−	0.498966i
$593$			21.6626i			0.889577i	0.895636	+	0.444788i	$0.146721\pi$
$593$			21.6626i			0.889577i	−0.895636	+	0.444788i	$0.853279\pi$
$594$	−23.3807	+	4.64482i	−0.959322	+	0.190579i
$595$	4.26812			0.174976
$596$	4.47009	−	2.58330i	0.183102	−	0.105816i
$597$	0.961847	−	43.7789i	0.0393658	−	1.79175i
$598$	29.9946	−	8.04374i	1.22657	−	0.328933i
$599$	−30.5641			−1.24882			−0.624408	−	0.781099i	$-0.714660\pi$
$599$	−30.5641			−1.24882			−0.624408	+	0.781099i	$0.714660\pi$
$600$	−3.89506	−	4.06495i	−0.159015	−	0.165951i
$601$	42.3311			1.72672			0.863360	−	0.504588i	$-0.168356\pi$
$601$	42.3311			1.72672			0.863360	+	0.504588i	$0.168356\pi$
$602$	5.40658	−	1.44990i	0.220356	−	0.0590935i
$603$	−18.1225	−	0.796708i	−0.738006	−	0.0324445i
$604$	3.53496	+	6.11683i	0.143836	+	0.248890i
$605$	0.936431			0.0380713
$606$	4.28133	+	17.4919i	0.173917	+	0.710560i
$607$		−	24.5533i		−	0.996589i	−0.867008	−	0.498295i	$-0.833960\pi$
$607$		−	24.5533i		−	0.996589i	0.867008	−	0.498295i	$-0.166040\pi$
$608$	−5.46563	−	1.45839i	−0.221660	−	0.0591457i
$609$	0.132033	−	6.00955i	0.00535026	−	0.243519i
$610$	−6.51364	+	1.74678i	−0.263730	+	0.0707252i
$611$		−	81.1488i		−	3.28293i
$612$	4.40650	+	8.46239i	0.178122	+	0.342072i
$613$		−	21.7529i		−	0.878593i	−0.898342	−	0.439296i	$-0.855228\pi$
$613$		−	21.7529i		−	0.878593i	0.898342	−	0.439296i	$-0.144772\pi$
$614$	−5.66885	−	21.1388i	−0.228776	−	0.853092i
$615$	−0.421906	+	19.2032i	−0.0170129	+	0.774349i
$616$	8.87950	+	8.86838i	0.357765	+	0.357317i
$617$			17.3983i			0.700429i	0.936670	+	0.350214i	$0.113891\pi$
$617$			17.3983i			0.700429i	−0.936670	+	0.350214i	$0.886109\pi$
$618$	18.1651	−	4.44611i	0.730709	−	0.178849i
$619$	−38.4734			−1.54638			−0.773188	−	0.634177i	$-0.781339\pi$
$619$	−38.4734			−1.54638			−0.773188	+	0.634177i	$0.781339\pi$
$620$	12.1566	+	21.0356i	0.488223	+	0.844811i
$621$	18.5589	+	1.22482i	0.744741	+	0.0491504i
$622$	−10.7699	−	40.1602i	−0.431833	−	1.61028i
$623$	−21.6473			−0.867281
$624$	36.3511	+	22.0243i	1.45521	+	0.881679i
$625$	−17.9334			−0.717337
$626$	−0.523404	−	1.95174i	−0.0209194	−	0.0780072i
$627$	0.123413	−	5.61722i	0.00492866	−	0.224330i
$628$	−2.73757	−	4.73704i	−0.109241	−	0.189028i
$629$	−9.66652			−0.385429
$630$	11.1179	−	2.46371i	0.442949	−	0.0981566i
$631$		−	9.53328i		−	0.379514i	−0.981831	−	0.189757i	$-0.939230\pi$
$631$		−	9.53328i		−	0.379514i	0.981831	−	0.189757i	$-0.0607700\pi$
$632$	−4.17356	+	4.17879i	−0.166015	+	0.166223i
$633$	−11.8381	−	0.260089i	−0.470521	−	0.0103376i
$634$	8.49818	+	31.6892i	0.337506	+	1.25854i
$635$			18.2973i			0.726106i
$636$	36.5421	−	20.0604i	1.44899	−	0.795446i
$637$			31.4659i			1.24672i
$638$	11.2426	−	3.01495i	0.445098	−	0.119363i
$639$	33.7637	+	1.48433i	1.33567	+	0.0587192i
$640$	21.4365	−	5.77750i	0.847353	−	0.228376i
$641$			8.63282i			0.340976i	0.985360	+	0.170488i	$0.0545344\pi$
$641$			8.63282i			0.340976i	−0.985360	+	0.170488i	$0.945466\pi$
$642$	−13.2647	+	3.24667i	−0.523515	+	0.128136i
$643$	−22.0445			−0.869351			−0.434676	−	0.900587i	$-0.643137\pi$
$643$	−22.0445			−0.869351			−0.434676	+	0.900587i	$0.643137\pi$
$644$	−4.89946	−	8.47793i	−0.193066	−	0.334077i
$645$	9.83330	+	0.216043i	0.387186	+	0.00850669i
$646$	−2.17207	+	0.582491i	−0.0854589	+	0.0229178i
$647$	17.5205			0.688801			0.344401	−	0.938823i	$-0.388082\pi$
$647$	17.5205			0.688801			0.344401	+	0.938823i	$0.388082\pi$
$648$	16.3632	+	19.4999i	0.642807	+	0.766028i
$649$	−21.2725			−0.835020
$650$	−9.62989	+	2.58248i	−0.377715	+	0.101293i
$651$	14.6622	+	0.322138i	0.574659	+	0.0126256i
$652$	3.91131	−	2.26038i	0.153179	−	0.0885232i
$653$	−15.0230			−0.587894			−0.293947	−	0.955822i	$-0.594969\pi$
$653$	−15.0230			−0.587894			−0.293947	+	0.955822i	$0.594969\pi$
$654$	14.2408	−	3.48559i	0.556861	−	0.136297i
$655$		−	3.62063i		−	0.141470i
$656$	19.5859	+	11.2861i	0.764699	+	0.440648i
$657$	−39.1292	−	1.72021i	−1.52658	−	0.0671118i
$658$	−24.7140	+	6.62762i	−0.963450	+	0.258371i
$659$		−	24.1769i		−	0.941796i	−0.882188	−	0.470898i	$-0.843930\pi$
$659$		−	24.1769i		−	0.941796i	0.882188	−	0.470898i	$-0.156070\pi$
$660$	10.6116	+	19.3300i	0.413054	+	0.752421i
$661$		−	38.1321i		−	1.48317i	−0.670861	−	0.741583i	$-0.734075\pi$
$661$		−	38.1321i		−	1.48317i	0.670861	−	0.741583i	$-0.265925\pi$
$662$	−2.87342	−	10.7148i	−0.111678	−	0.416442i
$663$	16.8924	+	0.371134i	0.656045	+	0.0144137i
$664$	20.0335	−	20.0586i	0.777451	−	0.778426i
$665$			2.68409i			0.104085i
$666$	−25.1801	+	5.57986i	−0.975709	+	0.216215i
$667$	−9.08194			−0.351654
$668$	19.6098	−	11.3327i	0.758727	−	0.438474i
$669$	0.445941	−	20.2972i	0.0172411	−	0.784736i
$670$	4.34652	+	16.2079i	0.167921	+	0.626166i
$671$	−7.88277			−0.304311
$672$	3.73865	−	12.8695i	0.144222	−	0.496453i
$673$	49.9085			1.92383			0.961916	−	0.273343i	$-0.0881296\pi$
$673$	49.9085			1.92383			0.961916	+	0.273343i	$0.0881296\pi$
$674$	−3.01522	−	11.2436i	−0.116142	−	0.433086i
$675$	−5.95840	−	0.393234i	−0.229339	−	0.0151356i
$676$	42.6585	−	24.6527i	1.64071	−	0.948180i
$677$	−17.2494			−0.662949			−0.331474	−	0.943464i	$-0.607546\pi$
$677$	−17.2494			−0.662949			−0.331474	+	0.943464i	$0.607546\pi$
$678$	31.1446	−	7.62297i	1.19610	−	0.292758i
$679$			6.28866i			0.241337i
$680$	6.23696	−	6.24478i	0.239177	−	0.239476i
$681$	−0.493869	+	22.4787i	−0.0189251	+	0.861385i
$682$	7.35595	+	27.4299i	0.281674	+	1.05034i
$683$			11.2494i			0.430448i	0.976565	+	0.215224i	$0.0690481\pi$
$683$			11.2494i			0.430448i	−0.976565	+	0.215224i	$0.930952\pi$
$684$	−5.32174	+	2.77111i	−0.203482	+	0.105956i
$685$			29.2326i			1.11692i
$686$	22.6613	−	6.07716i	0.865213	−	0.232027i
$687$	0.804030	−	36.5958i	0.0306757	−	1.39622i
$688$	5.77921	−	10.0292i	0.220330	−	0.382361i
$689$		−	73.8240i		−	2.81247i
$690$	−4.09046	−	16.7121i	−0.155721	−	0.636219i
$691$	11.1897			0.425675			0.212838	−	0.977088i	$-0.431729\pi$
$691$	11.1897			0.425675			0.212838	+	0.977088i	$0.431729\pi$
$692$	−28.3403	+	16.3781i	−1.07734	+	0.622600i
$693$	13.2981	+	0.584614i	0.505152	+	0.0222076i
$694$	50.6967	−	13.5955i	1.92442	−	0.516078i
$695$	0.301876			0.0114508
$696$	−8.59978	−	8.97489i	−0.325974	−	0.340192i
$697$	8.98632			0.340381
$698$	−40.2299	+	10.7886i	−1.52272	+	0.408353i
$699$	0.866679	−	39.4473i	0.0327808	−	1.49203i
$700$	1.57299	+	2.72188i	0.0594535	+	0.102877i
$701$	46.6253			1.76101			0.880507	−	0.474032i	$-0.157202\pi$
$701$	46.6253			1.76101			0.880507	+	0.474032i	$0.157202\pi$
$702$	44.2168	−	8.78412i	1.66885	−	0.331535i
$703$		−	6.07898i		−	0.229273i
$704$	25.9511	−	0.0325218i	0.978068	−	0.00122571i
$705$	−44.9489	−	0.987552i	−1.69287	−	0.0371933i
$706$	−45.7751	+	12.2757i	−1.72277	+	0.462000i
$707$		−	10.0558i		−	0.378187i
$708$	10.9318	+	19.9134i	0.410841	+	0.748390i
$709$			43.2621i			1.62474i	0.583142	+	0.812371i	$0.301823\pi$
$709$			43.2621i			1.62474i	−0.583142	+	0.812371i	$0.698177\pi$
$710$	−8.09792	−	30.1966i	−0.303910	−	1.13326i
$711$	−0.275126	+	6.25822i	−0.0103180	+	0.234701i
$712$	−31.6330	+	31.6727i	−1.18550	+	1.18698i
$713$		−	22.1583i		−	0.829836i
$714$	−1.26661	−	5.17490i	−0.0474017	−	0.193666i
$715$	39.0514			1.46044
$716$	17.9743	+	31.1024i	0.671731	+	1.16235i
$717$	7.05860	+	0.155081i	0.263608	+	0.00579162i
$718$	6.10521	+	22.7659i	0.227844	+	0.849617i
$719$	−11.8551			−0.442121			−0.221060	−	0.975260i	$-0.570952\pi$
$719$	−11.8551			−0.442121			−0.221060	+	0.975260i	$0.570952\pi$
$720$	12.6418	−	19.8671i	0.471132	−	0.740403i
$721$	−10.4428			−0.388911
$722$	−0.366311	−	1.36595i	−0.0136327	−	0.0508354i
$723$	3.28847	+	0.0722495i	0.122299	+	0.00268699i
$724$	15.9369	+	27.5769i	0.592289	+	1.02489i
$725$	2.91580			0.108290
$726$	−0.277896	−	1.13538i	−0.0103137	−	0.0421379i
$727$		−	16.5461i		−	0.613661i	−0.951764	−	0.306831i	$-0.900731\pi$
$727$		−	16.5461i		−	0.613661i	0.951764	−	0.306831i	$-0.0992685\pi$
$728$	−16.7926	−	16.7716i	−0.622375	−	0.621596i
$729$	26.7658	+	3.54836i	0.991327	+	0.131421i
$730$	9.38480	+	34.9953i	0.347347	+	1.29523i
$731$		−	4.60158i		−	0.170196i
$732$	4.05089	+	7.37912i	0.149725	+	0.272740i
$733$		−	39.8130i		−	1.47053i	−0.677782	−	0.735263i	$-0.737059\pi$
$733$		−	39.8130i		−	1.47053i	0.677782	−	0.735263i	$-0.262941\pi$
$734$	22.9335	−	6.15016i	0.846493	−	0.227007i
$735$	17.4292	+	0.382928i	0.642884	+	0.0141245i
$736$	−19.5638	−	5.22021i	−0.721131	−	0.192420i
$737$			19.6147i			0.722517i
$738$	23.4083	−	5.18723i	0.861670	−	0.190945i
$739$	−21.1287			−0.777232			−0.388616	−	0.921400i	$-0.627047\pi$
$739$	−21.1287			−0.777232			−0.388616	+	0.921400i	$0.627047\pi$
$740$	11.9377	+	20.6568i	0.438839	+	0.759358i
$741$	−0.233395	+	10.6231i	−0.00857399	+	0.390249i
$742$	−22.4832	+	6.02938i	−0.825383	+	0.221345i
$743$	−17.8534			−0.654978			−0.327489	−	0.944855i	$-0.606202\pi$
$743$	−17.8534			−0.654978			−0.327489	+	0.944855i	$0.606202\pi$
$744$	21.8971	−	20.9819i	0.802788	−	0.769235i
$745$	−5.06566			−0.185591
$746$	45.1733	−	12.1143i	1.65391	−	0.443535i
$747$	1.32063	−	30.0401i	0.0483194	−	1.09911i
$748$	8.93225	−	5.16201i	0.326595	−	0.188742i
$749$	7.62564			0.278635
$750$	7.02711	+	28.7102i	0.256594	+	1.04835i
$751$			38.4146i			1.40177i	0.713276	+	0.700884i	$0.247211\pi$
$751$			38.4146i			1.40177i	−0.713276	+	0.700884i	$0.752789\pi$
$752$	−26.4173	+	45.8445i	−0.963338	+	1.67178i
$753$	1.05698	−	48.1090i	0.0385185	−	1.75319i
$754$	−21.2616	+	5.70178i	−0.774300	+	0.207646i
$755$		−	6.93181i		−	0.252274i
$756$	−6.28650	−	12.7488i	−0.228638	−	0.463671i
$757$		−	19.2895i		−	0.701088i	−0.936546	−	0.350544i	$-0.885997\pi$
$757$		−	19.2895i		−	0.701088i	0.936546	−	0.350544i	$-0.114003\pi$
$758$	8.28780	+	30.9047i	0.301026	+	1.12251i
$759$	0.441749	−	20.1064i	0.0160345	−	0.729817i
$760$	3.92715	+	3.92224i	0.142453	+	0.142274i
$761$		−	0.138065i		−	0.00500487i	−0.999997	−	0.00250243i	$-0.999203\pi$
$761$		−	0.138065i		−	0.00500487i	0.999997	−	0.00250243i	$-0.000796550\pi$
$762$	22.1846	−	5.42992i	0.803664	−	0.196705i
$763$	−8.18681			−0.296382
$764$	26.0671	−	15.0644i	0.943073	−	0.545009i
$765$	0.411148	−	9.35228i	0.0148651	−	0.338132i
$766$	−6.05174	−	22.5665i	−0.218658	−	0.815363i
$767$	40.2299			1.45262
$768$	−13.3665	−	24.2763i	−0.482321	−	0.875994i
$769$	−19.5952			−0.706621			−0.353310	−	0.935506i	$-0.614944\pi$
$769$	−19.5952			−0.706621			−0.353310	+	0.935506i	$0.614944\pi$
$770$	−3.18942	−	11.8932i	−0.114939	−	0.428600i
$771$	−0.0948167	+	4.31563i	−0.00341474	+	0.155423i
$772$	−7.55560	+	4.36643i	−0.271932	+	0.157151i
$773$	−9.09036			−0.326958			−0.163479	−	0.986547i	$-0.552272\pi$
$773$	−9.09036			−0.326958			−0.163479	+	0.986547i	$0.552272\pi$
$774$	−2.65620	−	11.9865i	−0.0954751	−	0.430848i
$775$			7.11402i			0.255543i
$776$	9.20109	+	9.18957i	0.330300	+	0.329886i
$777$	14.3982	+	0.316336i	0.516532	+	0.0113485i
$778$	2.32903	+	8.68481i	0.0834998	+	0.311365i
$779$			5.65123i			0.202476i
$780$	−20.0682	−	36.5563i	−0.718557	−	1.30893i
$781$		−	36.5438i		−	1.30764i
$782$	−7.77476	+	2.08498i	−0.278025	+	0.0745588i
$783$	−13.1554	−	0.868211i	−0.470135	−	0.0310273i
$784$	10.2434	−	17.7764i	0.365837	−	0.634872i
$785$			5.36818i			0.191598i
$786$	−4.38985	+	1.07446i	−0.156581	+	0.0383248i
$787$	8.58829			0.306139			0.153070	−	0.988215i	$-0.451084\pi$
$787$	8.58829			0.306139			0.153070	+	0.988215i	$0.451084\pi$
$788$	−8.99764	+	5.19980i	−0.320528	+	0.185235i
$789$	0.000334016	0	7.33852e-6i	1.18913e−5	0	2.61258e-7i
$790$	5.59705	−	1.50098i	0.199134	−	0.0534024i
$791$	−17.9045			−0.636611
$792$	20.2877	−	18.6024i	0.720893	−	0.661008i
$793$	14.9076			0.529385
$794$	−36.7488	+	9.85504i	−1.30417	+	0.349742i
$795$	−40.8916	−	0.898411i	−1.45028	−	0.0318634i
$796$	25.3001	+	43.7789i	0.896740	+	1.55170i
$797$	−28.0592			−0.993909			−0.496955	−	0.867777i	$-0.665548\pi$
$797$	−28.0592			−0.993909			−0.496955	+	0.867777i	$0.665548\pi$
$798$	3.25434	−	0.796533i	0.115202	−	0.0281970i
$799$			21.0342i			0.744137i
$800$	6.28104	+	1.67597i	0.222068	+	0.0592545i
$801$	−2.08529	+	47.4335i	−0.0736800	+	1.67598i
$802$	18.0108	−	4.83002i	0.635984	−	0.170554i
$803$			42.3511i			1.49454i
$804$	18.3615	−	10.0798i	0.647559	−	0.355488i
$805$			9.60749i			0.338620i
$806$	−13.9113	−	51.8744i	−0.490005	−	1.82720i
$807$	29.5473	+	0.649171i	1.04012	+	0.0228519i
$808$	−14.7129	−	14.6944i	−0.517597	−	0.516949i
$809$		−	14.2427i		−	0.500745i	−0.968150	−	0.250373i	$-0.919447\pi$
$809$		−	14.2427i		−	0.500745i	0.968150	−	0.250373i	$-0.0805531\pi$
$810$	−4.32748	−	24.5989i	−0.152052	−	0.864316i
$811$	−13.8687			−0.486995			−0.243497	−	0.969902i	$-0.578295\pi$
$811$	−13.8687			−0.486995			−0.243497	+	0.969902i	$0.578295\pi$
$812$	3.47296	+	6.00955i	0.121877	+	0.210894i
$813$	−0.838075	+	38.1454i	−0.0293926	+	1.33782i
$814$	7.22347	+	26.9359i	0.253183	+	0.944102i
$815$	−4.43244			−0.155262
$816$	−9.42240	−	5.70883i	−0.329850	−	0.199849i
$817$	2.89379			0.101241
$818$	7.81280	+	29.1334i	0.273168	+	1.01863i
$819$	−25.1488	−	1.10560i	−0.878772	−	0.0386328i
$820$	−11.0977	−	19.2032i	−0.387548	−	0.670606i
$821$	−5.37340			−0.187533			−0.0937665	−	0.995594i	$-0.529891\pi$
$821$	−5.37340			−0.187533			−0.0937665	+	0.995594i	$0.529891\pi$
$822$	35.4432	−	8.67510i	1.23622	−	0.302579i
$823$			14.2483i			0.496666i	0.968675	+	0.248333i	$0.0798827\pi$
$823$			14.2483i			0.496666i	−0.968675	+	0.248333i	$0.920117\pi$
$824$	−15.2600	+	15.2791i	−0.531608	+	0.532274i
$825$	−0.141825	+	6.45525i	−0.00493773	+	0.224743i
$826$	−3.28567	−	12.2521i	−0.114323	−	0.426303i
$827$			15.8458i			0.551013i	0.961299	+	0.275506i	$0.0888455\pi$
$827$			15.8458i			0.551013i	−0.961299	+	0.275506i	$0.911155\pi$
$828$	−19.0488	+	9.91899i	−0.661991	+	0.344709i
$829$		−	5.86645i		−	0.203750i	−0.994797	−	0.101875i	$-0.967516\pi$
$829$		−	5.86645i		−	0.203750i	0.994797	−	0.101875i	$-0.0324842\pi$
$830$	−26.8664	+	7.20485i	−0.932547	+	0.250084i
$831$	−0.481432	+	21.9126i	−0.0167007	+	0.760140i
$832$	−49.0778	+	0.0615042i	−1.70147	+	0.00213227i
$833$		−	8.15612i		−	0.282593i
$834$	−0.0895850	−	0.366011i	−0.00310207	−	0.0126739i
$835$	−22.2226			−0.769044
$836$	3.24623	+	5.61722i	0.112273	+	0.194276i
$837$	2.11828	−	32.0968i	0.0732185	−	1.10943i
$838$	29.4389	−	7.89471i	1.01695	−	0.272718i
$839$	10.4522			0.360850			0.180425	−	0.983589i	$-0.442253\pi$
$839$	10.4522			0.360850			0.180425	+	0.983589i	$0.442253\pi$
$840$	−9.49425	+	9.09743i	−0.327583	+	0.313891i
$841$	−22.5623			−0.778010
$842$	14.3335	−	3.84385i	0.493964	−	0.132468i
$843$	−0.703255	+	32.0090i	−0.0242214	+	1.10245i
$844$	11.8381	−	6.84131i	0.407483	−	0.235487i
$845$	−48.3422			−1.66302
$846$	12.1417	+	54.7915i	0.417440	+	1.88377i
$847$			0.652710i			0.0224274i
$848$	−24.0327	+	41.7063i	−0.825287	+	1.43220i
$849$	−52.5663	−	1.15491i	−1.80407	−	0.0396364i
$850$	2.49612	−	0.669392i	0.0856162	−	0.0229600i
$851$		−	21.7593i		−	0.745898i
$852$	−34.2089	+	18.7795i	−1.17198	+	0.643376i
$853$			36.7335i			1.25773i	0.777513	+	0.628866i	$0.216481\pi$
$853$			36.7335i			1.25773i	−0.777513	+	0.628866i	$0.783519\pi$
$854$	−1.21754	−	4.54013i	−0.0416634	−	0.155360i
$855$	5.88136	+	0.258558i	0.201138	+	0.00884251i
$856$	11.1433	−	11.1573i	0.380870	−	0.381347i
$857$			18.6507i			0.637097i	0.947907	+	0.318549i	$0.103195\pi$
$857$			18.6507i			0.637097i	−0.947907	+	0.318549i	$0.896805\pi$
$858$	−11.5889	−	47.3481i	−0.395640	−	1.61644i
$859$	−54.3062			−1.85291			−0.926453	−	0.376411i	$-0.877158\pi$
$859$	−54.3062			−1.85291			−0.926453	+	0.376411i	$0.877158\pi$
$860$	−9.83330	+	5.68274i	−0.335313	+	0.193780i
$861$	−13.3850	−	0.294076i	−0.456161	−	0.0100221i
$862$	−5.87426	−	21.9048i	−0.200078	−	0.746079i
$863$	25.9376			0.882926			0.441463	−	0.897279i	$-0.354460\pi$
$863$	25.9376			0.882926			0.441463	+	0.897279i	$0.354460\pi$
$864$	−27.8395	−	9.43184i	−0.947121	−	0.320878i
$865$	32.1162			1.09198
$866$	−8.62592	−	32.1655i	−0.293121	−	1.09303i
$867$	25.0592	+	0.550564i	0.851054	+	0.0186981i
$868$	−14.6622	+	8.47342i	−0.497669	+	0.287607i
$869$	6.77352			0.229776
$870$	2.89951	+	11.8463i	0.0983025	+	0.401628i
$871$		−	37.0947i		−	1.25691i
$872$	−11.9633	+	11.9783i	−0.405129	+	0.405637i
$873$	13.7797	+	0.605787i	0.466372	+	0.0205028i
$874$	−1.31118	−	4.88931i	−0.0443514	−	0.165383i
$875$		−	16.5050i		−	0.557970i
$876$	39.6452	−	21.7639i	1.33949	−	0.735333i
$877$		−	53.3820i		−	1.80258i	−0.433213	−	0.901292i	$-0.642620\pi$
$877$		−	53.3820i		−	1.80258i	0.433213	−	0.901292i	$-0.357380\pi$
$878$	16.0273	−	4.29808i	0.540894	−	0.145053i
$879$	15.9324	+	0.350043i	0.537386	+	0.0118067i
$880$	−22.0618	−	12.7128i	−0.743704	−	0.428550i
$881$			46.8795i			1.57941i	0.613486	+	0.789706i	$0.289767\pi$
$881$			46.8795i			1.57941i	−0.613486	+	0.789706i	$0.710233\pi$
$882$	−4.70801	−	21.2457i	−0.158527	−	0.715380i
$883$	9.33911			0.314286			0.157143	−	0.987576i	$-0.449772\pi$
$883$	9.33911			0.314286			0.157143	+	0.987576i	$0.449772\pi$
$884$	−16.8924	+	9.76222i	−0.568151	+	0.328339i
$885$	0.489583	−	22.2836i	0.0164572	−	0.749055i
$886$	−14.6197	+	3.92061i	−0.491159	+	0.131716i
$887$	−44.9373			−1.50885			−0.754423	−	0.656388i	$-0.772083\pi$
$887$	−44.9373			−1.50885			−0.754423	+	0.656388i	$0.772083\pi$
$888$	21.5028	−	20.6041i	0.721586	−	0.691427i
$889$	−12.7536			−0.427741
$890$	42.4223	−	11.3765i	1.42200	−	0.381341i
$891$	2.56201	−	29.0823i	0.0858305	−	0.974295i
$892$	11.7299	+	20.2972i	0.392747	+	0.679602i
$893$	−13.2278			−0.442651
$894$	1.50329	+	6.14189i	0.0502776	+	0.205415i
$895$		−	35.2463i		−	1.17815i
$896$	4.02703	+	14.9417i	0.134534	+	0.499166i
$897$	−0.835421	+	38.0246i	−0.0278939	+	1.26960i
$898$	−23.5840	+	6.32459i	−0.787008	+	0.211054i
$899$			15.7069i			0.523853i
$900$	6.11569	−	3.18454i	0.203856	−	0.106151i
$901$			19.1356i			0.637498i
$902$	−6.71518	−	25.0405i	−0.223591	−	0.833757i
$903$	−0.150586	+	6.85400i	−0.00501120	+	0.228087i
$904$	−26.1637	+	26.1965i	−0.870192	+	0.871283i
$905$		−	31.2511i		−	1.03882i
$906$	−8.40451	+	2.05709i	−0.279221	+	0.0683422i
$907$	16.6996			0.554500			0.277250	−	0.960798i	$-0.410577\pi$
$907$	16.6996			0.554500			0.277250	+	0.960798i	$0.410577\pi$
$908$	−12.9906	−	22.4787i	−0.431108	−	0.745981i
$909$	−22.0342	−	0.968675i	−0.730829	−	0.0321289i
$910$	6.03173	+	22.4919i	0.199950	+	0.745600i
$911$	10.7179			0.355102			0.177551	−	0.984112i	$-0.443183\pi$
$911$	10.7179			0.355102			0.177551	+	0.984112i	$0.443183\pi$
$912$	3.59011	−	5.92546i	0.118880	−	0.196212i
$913$	−32.5136			−1.07604
$914$	−8.49442	−	31.6751i	−0.280970	−	1.04772i
$915$	0.181420	−	8.25744i	0.00599758	−	0.272982i
$916$	21.1490	+	36.5958i	0.698782	+	1.20916i
$917$	2.52365			0.0833382
$918$	−11.4612	+	2.27689i	−0.378277	+	0.0751486i
$919$		−	35.7102i		−	1.17797i	−0.808144	−	0.588985i	$-0.799528\pi$
$919$		−	35.7102i		−	1.17797i	0.808144	−	0.588985i	$-0.200472\pi$
$920$	14.0570	+	14.0393i	0.463444	+	0.462864i
$921$	26.7979	+	0.588765i	0.883022	+	0.0194005i
$922$	−9.64230	−	35.9555i	−0.317552	−	1.18413i
$923$			69.1103i			2.27479i
$924$	−13.4734	+	7.39646i	−0.443243	+	0.243326i
$925$			6.98590i			0.229695i
$926$	−12.4318	+	3.33388i	−0.408535	+	0.109558i
$927$	−1.00596	+	22.8823i	−0.0330400	+	0.751552i
$928$	13.8677	+	3.70033i	0.455231	+	0.121469i
$929$			1.59209i			0.0522348i	0.999659	+	0.0261174i	$0.00831437\pi$
$929$			1.59209i			0.0522348i	−0.999659	+	0.0261174i	$0.991686\pi$
$930$	−28.9029	+	7.07428i	−0.947763	+	0.231975i
$931$	5.12914			0.168101
$932$	22.7969	+	39.4473i	0.746737	+	1.29214i
$933$	50.9116	+	1.11856i	1.66677	+	0.0366199i
$934$	27.1424	−	7.27885i	0.888126	−	0.238171i
$935$	−10.1223			−0.331036
$936$	−38.3674	+	35.1803i	−1.25408	+	1.14990i
$937$	13.6128			0.444711			0.222355	−	0.974966i	$-0.428626\pi$
$937$	13.6128			0.444711			0.222355	+	0.974966i	$0.428626\pi$
$938$	−11.2972	+	3.02961i	−0.368867	+	0.0989203i
$939$	2.47425	+	0.0543606i	0.0807440	+	0.00177399i
$940$	44.9489	−	25.9763i	1.46607	−	0.847253i
$941$	−20.3717			−0.664100			−0.332050	−	0.943262i	$-0.607740\pi$
$941$	−20.3717			−0.664100			−0.332050	+	0.943262i	$0.607740\pi$
$942$	6.50867	−	1.59307i	0.212064	−	0.0519049i
$943$			20.2281i			0.658719i
$944$	−22.7276	−	13.0965i	−0.739720	−	0.426254i
$945$	−0.918453	+	13.9167i	−0.0298773	+	0.452709i
$946$	−12.8224	+	3.43861i	−0.416891	+	0.111799i
$947$			18.7160i			0.608189i	0.952642	+	0.304094i	$0.0983539\pi$
$947$			18.7160i			0.608189i	−0.952642	+	0.304094i	$0.901646\pi$
$948$	−3.48085	−	6.34074i	−0.113053	−	0.205938i
$949$		−	80.0930i		−	2.59993i
$950$	0.420960	+	1.56973i	0.0136578	+	0.0509289i
$951$	−40.1728	−	0.882619i	−1.30269	−	0.0286209i
$952$	4.35273	+	4.34728i	0.141073	+	0.140896i
$953$			17.0131i			0.551109i	0.961285	+	0.275555i	$0.0888615\pi$
$953$			17.0131i			0.551109i	−0.961285	+	0.275555i	$0.911138\pi$
$954$	11.0457	+	49.8458i	0.357619	+	1.61382i
$955$	−29.5401			−0.955896
$956$	−7.05860	+	4.07922i	−0.228291	+	0.131931i
$957$	−0.313132	+	14.2524i	−0.0101221	+	0.460714i
$958$	−12.0391	−	44.8929i	−0.388964	−	1.45042i
$959$	−20.3757			−0.657966
$960$	−0.563191	+	27.1853i	−0.0181769	+	0.877401i
$961$	−7.32193			−0.236191
$962$	−13.6608	−	50.9402i	−0.440441	−	1.64238i
$963$	0.734578	−	16.7093i	0.0236715	−	0.538449i
$964$	−3.28847	+	1.90043i	−0.105914	+	0.0612087i
$965$	8.56227			0.275629
$966$	11.6487	−	2.85113i	0.374789	−	0.0917336i
$967$		−	22.8375i		−	0.734406i	−0.930141	−	0.367203i	$-0.880315\pi$
$967$		−	22.8375i		−	0.734406i	0.930141	−	0.367203i	$-0.119685\pi$
$968$	0.954996	+	0.953800i	0.0306947	+	0.0306563i
$969$	0.0604973	−	2.75356i	0.00194345	−	0.0884572i
$970$	−3.30494	−	12.3239i	−0.106115	−	0.395696i
$971$		−	15.4353i		−	0.495341i	−0.968844	−	0.247670i	$-0.920335\pi$
$971$		−	15.4353i		−	0.495341i	0.968844	−	0.247670i	$-0.0796650\pi$
$972$	−28.5408	+	12.5469i	−0.915446	+	0.402441i
$973$			0.210413i			0.00674554i
$974$	21.7558	−	5.83431i	0.697099	−	0.186943i
$975$	0.268215	−	12.2079i	0.00858977	−	0.390967i
$976$	−8.42196	−	4.85304i	−0.269580	−	0.155342i
$977$		−	37.4754i		−	1.19895i	−0.800395	−	0.599473i	$-0.795377\pi$
$977$		−	37.4754i		−	1.19895i	0.800395	−	0.599473i	$-0.204623\pi$
$978$	1.31538	+	5.37413i	0.0420611	+	0.171846i
$979$	51.3392			1.64081
$980$	−17.4292	+	10.0724i	−0.556754	+	0.321752i
$981$	−0.788636	+	17.9389i	−0.0251792	+	0.572745i
$982$	−15.9952	+	4.28949i	−0.510428	+	0.136883i
$983$	15.5892			0.497217			0.248609	−	0.968604i	$-0.420027\pi$
$983$	15.5892			0.497217			0.248609	+	0.968604i	$0.420027\pi$
$984$	−19.9897	+	19.1542i	−0.637248	+	0.610614i
$985$	10.1964			0.324886
$986$	5.51111	−	1.47793i	0.175510	−	0.0470669i
$987$	0.688343	−	31.3302i	0.0219102	−	0.997252i
$988$	−6.13916	−	10.6231i	−0.195313	−	0.337966i
$989$	10.3581			0.329369
$990$	−26.3675	+	5.84298i	−0.838013	+	0.185702i
$991$			36.6363i			1.16379i	0.813264	+	0.581896i	$0.197689\pi$
$991$			36.6363i			1.16379i	−0.813264	+	0.581896i	$0.802311\pi$
$992$	−9.02815	+	33.8348i	−0.286644	+	1.07426i
$993$	13.5833	+	0.298432i	0.431052	+	0.00947046i
$994$	21.0476	−	5.64441i	0.667590	−	0.179030i
$995$		−	49.6118i		−	1.57280i
$996$	16.7085	+	30.4362i	0.529428	+	0.964408i
$997$		−	17.3420i		−	0.549228i	−0.961555	−	0.274614i	$-0.911450\pi$
$997$		−	17.3420i		−	0.549228i	0.961555	−	0.274614i	$-0.0885501\pi$
$998$	−9.46945	−	35.3110i	−0.299750	−	1.11775i
$999$	2.08013	−	31.5187i	0.0658124	−	0.997209i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.j.e.419.11	✓	24
3.2	odd	2	inner	456.2.j.e.419.14	yes	24
4.3	odd	2		1824.2.j.d.1103.2		24
8.3	odd	2	inner	456.2.j.e.419.13	yes	24
8.5	even	2		1824.2.j.d.1103.1		24
12.11	even	2		1824.2.j.d.1103.3		24
24.5	odd	2		1824.2.j.d.1103.4		24
24.11	even	2	inner	456.2.j.e.419.12	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.j.e.419.11	✓	24	1.1	even	1	trivial
456.2.j.e.419.12	yes	24	24.11	even	2	inner
456.2.j.e.419.13	yes	24	8.3	odd	2	inner
456.2.j.e.419.14	yes	24	3.2	odd	2	inner
1824.2.j.d.1103.1		24	8.5	even	2
1824.2.j.d.1103.2		24	4.3	odd	2
1824.2.j.d.1103.3		24	12.11	even	2
1824.2.j.d.1103.4		24	24.5	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:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.366311 - 1.36595i) q^{2} +(1.73163 + 0.0380449i) q^{3} +(-1.73163 + 1.00072i) q^{4} +1.96235 q^{5} +(-0.582348 - 2.37926i) q^{6} +1.36779i q^{7} +(2.00125 + 1.99875i) q^{8} +(2.99711 + 0.131760i) q^{9} +O(q^{10})\)	\(q+(-0.366311 - 1.36595i) q^{2} +(1.73163 + 0.0380449i) q^{3} +(-1.73163 + 1.00072i) q^{4} +1.96235 q^{5} +(-0.582348 - 2.37926i) q^{6} +1.36779i q^{7} +(2.00125 + 1.99875i) q^{8} +(2.99711 + 0.131760i) q^{9} +(-0.718829 - 2.68047i) q^{10} -3.24389i q^{11} +(-3.03663 + 1.66701i) q^{12} +6.13473i q^{13} +(1.86834 - 0.501038i) q^{14} +(3.39807 + 0.0746574i) q^{15} +(1.99711 - 3.46577i) q^{16} -1.59015i q^{17} +(-0.917895 - 4.14216i) q^{18} +1.00000 q^{19} +(-3.39807 + 1.96377i) q^{20} +(-0.0520377 + 2.36852i) q^{21} +(-4.43098 + 1.18827i) q^{22} +3.57942 q^{23} +(3.38939 + 3.53723i) q^{24} -1.14919 q^{25} +(8.37972 - 2.24722i) q^{26} +(5.18487 + 0.342184i) q^{27} +(-1.36878 - 2.36852i) q^{28} -2.53726 q^{29} +(-1.14277 - 4.66893i) q^{30} -6.19047i q^{31} +(-5.46563 - 1.45839i) q^{32} +(0.123413 - 5.61722i) q^{33} +(-2.17207 + 0.582491i) q^{34} +2.68409i q^{35} +(-5.32174 + 2.77111i) q^{36} -6.07898i q^{37} +(-0.366311 - 1.36595i) q^{38} +(-0.233395 + 10.6231i) q^{39} +(3.92715 + 3.92224i) q^{40} +5.65123i q^{41} +(3.25434 - 0.796533i) q^{42} +2.89379 q^{43} +(3.24623 + 5.61722i) q^{44} +(5.88136 + 0.258558i) q^{45} +(-1.31118 - 4.88931i) q^{46} -13.2278 q^{47} +(3.59011 - 5.92546i) q^{48} +5.12914 q^{49} +(0.420960 + 1.56973i) q^{50} +(0.0604973 - 2.75356i) q^{51} +(-6.13916 - 10.6231i) q^{52} -12.0338 q^{53} +(-1.43187 - 7.20762i) q^{54} -6.36564i q^{55} +(-2.73387 + 2.73730i) q^{56} +(1.73163 + 0.0380449i) q^{57} +(0.929427 + 3.46577i) q^{58} -6.55773i q^{59} +(-5.95892 + 3.27125i) q^{60} -2.43004i q^{61} +(-8.45587 + 2.26764i) q^{62} +(-0.180220 + 4.09942i) q^{63} +(0.0100256 + 7.99999i) q^{64} +12.0385i q^{65} +(-7.71804 + 1.88907i) q^{66} -6.04667 q^{67} +(1.59130 + 2.75356i) q^{68} +(6.19825 + 0.136179i) q^{69} +(3.66633 - 0.983211i) q^{70} +11.2654 q^{71} +(5.73461 + 6.25414i) q^{72} -13.0557 q^{73} +(-8.30358 + 2.22680i) q^{74} +(-1.98997 - 0.0437208i) q^{75} +(-1.73163 + 1.00072i) q^{76} +4.43697 q^{77} +(14.5961 - 3.57255i) q^{78} +2.08809i q^{79} +(3.91902 - 6.80105i) q^{80} +(8.96528 + 0.789796i) q^{81} +(7.71929 - 2.07010i) q^{82} -10.0230i q^{83} +(-2.28012 - 4.15348i) q^{84} -3.12044i q^{85} +(-1.06003 - 3.95277i) q^{86} +(-4.39361 - 0.0965300i) q^{87} +(6.48371 - 6.49184i) q^{88} +15.8264i q^{89} +(-1.80123 - 8.12836i) q^{90} -8.39104 q^{91} +(-6.19825 + 3.58201i) q^{92} +(0.235516 - 10.7196i) q^{93} +(4.84548 + 18.0685i) q^{94} +1.96235 q^{95} +(-9.40898 - 2.73334i) q^{96} +4.59767 q^{97} +(-1.87886 - 7.00614i) q^{98} +(0.427414 - 9.72227i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{3} - 6 q^{4} + q^{6} - 6 q^{9}+O(q^{10}) \) 24 * q + 6 * q^3 - 6 * q^4 + q^6 - 6 * q^9	\( 24 q + 6 q^{3} - 6 q^{4} + q^{6} - 6 q^{9} + 4 q^{10} - 33 q^{12} - 30 q^{16} - 19 q^{18} + 24 q^{19} - 28 q^{22} + 21 q^{24} + 96 q^{25} + 34 q^{28} + 8 q^{30} + 24 q^{33} + 58 q^{34} - 9 q^{36} - 24 q^{40} - 31 q^{42} + 16 q^{43} - 6 q^{46} + 3 q^{48} - 36 q^{49} + 38 q^{51} - 6 q^{52} - 8 q^{54} + 6 q^{57} - 42 q^{58} - 50 q^{60} + 18 q^{64} + 10 q^{66} + 20 q^{67} - 96 q^{70} - 33 q^{72} - 12 q^{73} - 30 q^{75} - 6 q^{76} - 17 q^{78} + 34 q^{81} + 68 q^{82} - 29 q^{84} - 76 q^{88} - 70 q^{90} - 36 q^{91} - 12 q^{94} + 29 q^{96} - 104 q^{97} + 56 q^{99}+O(q^{100}) \) 24 * q + 6 * q^3 - 6 * q^4 + q^6 - 6 * q^9 + 4 * q^10 - 33 * q^12 - 30 * q^16 - 19 * q^18 + 24 * q^19 - 28 * q^22 + 21 * q^24 + 96 * q^25 + 34 * q^28 + 8 * q^30 + 24 * q^33 + 58 * q^34 - 9 * q^36 - 24 * q^40 - 31 * q^42 + 16 * q^43 - 6 * q^46 + 3 * q^48 - 36 * q^49 + 38 * q^51 - 6 * q^52 - 8 * q^54 + 6 * q^57 - 42 * q^58 - 50 * q^60 + 18 * q^64 + 10 * q^66 + 20 * q^67 - 96 * q^70 - 33 * q^72 - 12 * q^73 - 30 * q^75 - 6 * q^76 - 17 * q^78 + 34 * q^81 + 68 * q^82 - 29 * q^84 - 76 * q^88 - 70 * q^90 - 36 * q^91 - 12 * q^94 + 29 * q^96 - 104 * q^97 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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