LMFDB - Embedded newform 456.2.j.e.419.5

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			419.5
Character	$\chi$	$=$	456.419
Dual form			456.2.j.e.419.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.960810 - 1.03771i) q^{2} +(0.153689 - 1.72522i) q^{3} +(-0.153689 + 1.99409i) q^{4} -1.97287 q^{5} +(-1.93794 + 1.49812i) q^{6} -2.35621i q^{7} +(2.21695 - 1.75645i) q^{8} +(-2.95276 - 0.530294i) q^{9} +O(q^{10})$	\(q+(-0.960810 - 1.03771i) q^{2} +(0.153689 - 1.72522i) q^{3} +(-0.153689 + 1.99409i) q^{4} -1.97287 q^{5} +(-1.93794 + 1.49812i) q^{6} -2.35621i q^{7} +(2.21695 - 1.75645i) q^{8} +(-2.95276 - 0.530294i) q^{9} +(1.89556 + 2.04727i) q^{10} -4.83256i q^{11} +(3.41661 + 0.571616i) q^{12} +2.14536i q^{13} +(-2.44507 + 2.26387i) q^{14} +(-0.303209 + 3.40364i) q^{15} +(-3.95276 - 0.612938i) q^{16} +5.22103i q^{17} +(2.28675 + 3.57362i) q^{18} +1.00000 q^{19} +(0.303209 - 3.93408i) q^{20} +(-4.06498 - 0.362124i) q^{21} +(-5.01481 + 4.64318i) q^{22} -8.06939 q^{23} +(-2.68954 - 4.09467i) q^{24} -1.10777 q^{25} +(2.22626 - 2.06128i) q^{26} +(-1.36868 + 5.01266i) q^{27} +(4.69849 + 0.362124i) q^{28} -0.590664 q^{29} +(3.82332 - 2.95561i) q^{30} +4.48507i q^{31} +(3.16180 + 4.69074i) q^{32} +(-8.33723 - 0.742712i) q^{33} +(5.41793 - 5.01642i) q^{34} +4.64850i q^{35} +(1.51126 - 5.80656i) q^{36} -8.77578i q^{37} +(-0.960810 - 1.03771i) q^{38} +(3.70121 + 0.329718i) q^{39} +(-4.37376 + 3.46526i) q^{40} +6.54069i q^{41} +(3.52989 + 4.56620i) q^{42} -1.36072 q^{43} +(9.63655 + 0.742712i) q^{44} +(5.82542 + 1.04620i) q^{45} +(7.75315 + 8.37370i) q^{46} +5.54780 q^{47} +(-1.66495 + 6.72517i) q^{48} +1.44828 q^{49} +(1.06436 + 1.14955i) q^{50} +(9.00743 + 0.802416i) q^{51} +(-4.27802 - 0.329718i) q^{52} -13.0520 q^{53} +(6.51673 - 3.39591i) q^{54} +9.53404i q^{55} +(-4.13857 - 5.22360i) q^{56} +(0.153689 - 1.72522i) q^{57} +(0.567516 + 0.612938i) q^{58} -14.0204i q^{59} +(-6.74055 - 1.12773i) q^{60} -10.1557i q^{61} +(4.65421 - 4.30930i) q^{62} +(-1.24948 + 6.95732i) q^{63} +(1.82975 - 7.78794i) q^{64} -4.23251i q^{65} +(7.23977 + 9.36524i) q^{66} +5.68558 q^{67} +(-10.4112 - 0.802416i) q^{68} +(-1.24018 + 13.9215i) q^{69} +(4.82380 - 4.46633i) q^{70} -3.57493 q^{71} +(-7.47756 + 4.01075i) q^{72} -3.06303 q^{73} +(-9.10673 + 8.43186i) q^{74} +(-0.170252 + 1.91115i) q^{75} +(-0.153689 + 1.99409i) q^{76} -11.3865 q^{77} +(-3.21400 - 4.15758i) q^{78} +3.01433i q^{79} +(7.79829 + 1.20925i) q^{80} +(8.43758 + 3.13166i) q^{81} +(6.78735 - 6.28436i) q^{82} +6.41871i q^{83} +(1.34685 - 8.05026i) q^{84} -10.3004i q^{85} +(1.30740 + 1.41204i) q^{86} +(-0.0907785 + 1.01902i) q^{87} +(-8.48817 - 10.7136i) q^{88} -6.77889i q^{89} +(-4.51146 - 7.05031i) q^{90} +5.05491 q^{91} +(1.24018 - 16.0911i) q^{92} +(7.73773 + 0.689307i) q^{93} +(-5.33038 - 5.75702i) q^{94} -1.97287 q^{95} +(8.57849 - 4.73388i) q^{96} -12.2390 q^{97} +(-1.39152 - 1.50289i) q^{98} +(-2.56268 + 14.2694i) 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 $

$2$	−0.960810	−	1.03771i	−0.679395	−	0.733773i
$2$	−0.960810	−	1.03771i	−0.679395	−	0.733773i
$3$	0.153689	−	1.72522i	0.0887324	−	0.996056i
$3$	0.153689	−	1.72522i	0.0887324	−	0.996056i
$4$	−0.153689	+	1.99409i	−0.0768445	+	0.997043i
$5$	−1.97287			−0.882296			−0.441148	−	0.897434i	$-0.645429\pi$
$5$	−1.97287			−0.882296			−0.441148	+	0.897434i	$0.645429\pi$
$6$	−1.93794	+	1.49812i	−0.791163	+	0.611606i
$7$		−	2.35621i		−	0.890564i	−0.895390	−	0.445282i	$-0.853104\pi$
$7$		−	2.35621i		−	0.890564i	0.895390	−	0.445282i	$-0.146896\pi$
$8$	2.21695	−	1.75645i	0.783811	−	0.621000i
$9$	−2.95276	−	0.530294i	−0.984253	−	0.176765i
$10$	1.89556	+	2.04727i	0.599427	+	0.647404i
$11$		−	4.83256i		−	1.45707i	−0.685007	−	0.728537i	$-0.740201\pi$
$11$		−	4.83256i		−	1.45707i	0.685007	−	0.728537i	$-0.259799\pi$
$12$	3.41661	+	0.571616i	0.986292	+	0.165011i
$13$			2.14536i			0.595014i	0.954720	+	0.297507i	$0.0961552\pi$
$13$			2.14536i			0.595014i	−0.954720	+	0.297507i	$0.903845\pi$
$14$	−2.44507	+	2.26387i	−0.653471	+	0.605045i
$15$	−0.303209	+	3.40364i	−0.0782882	+	0.878816i
$16$	−3.95276	−	0.612938i	−0.988190	−	0.153235i
$17$			5.22103i			1.26629i	0.774035	+	0.633143i	$0.218236\pi$
$17$			5.22103i			1.26629i	−0.774035	+	0.633143i	$0.781764\pi$
$18$	2.28675	+	3.57362i	0.538992	+	0.842311i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	0.303209	−	3.93408i	0.0677996	−	0.879687i
$21$	−4.06498	−	0.362124i	−0.887051	−	0.0790219i
$22$	−5.01481	+	4.64318i	−1.06916	+	0.989928i
$23$	−8.06939			−1.68258			−0.841292	−	0.540580i	$-0.818205\pi$
$23$	−8.06939			−1.68258			−0.841292	+	0.540580i	$0.818205\pi$
$24$	−2.68954	−	4.09467i	−0.549001	−	0.835822i
$25$	−1.10777			−0.221554
$26$	2.22626	−	2.06128i	0.436605	−	0.404250i
$27$	−1.36868	+	5.01266i	−0.263403	+	0.964686i
$28$	4.69849	+	0.362124i	0.887930	+	0.0684349i
$29$	−0.590664			−0.109684			−0.0548418	−	0.998495i	$-0.517465\pi$
$29$	−0.590664			−0.109684			−0.0548418	+	0.998495i	$0.517465\pi$
$30$	3.82332	−	2.95561i	0.698039	−	0.539617i
$31$			4.48507i			0.805543i	0.915301	+	0.402771i	$0.131953\pi$
$31$			4.48507i			0.805543i	−0.915301	+	0.402771i	$0.868047\pi$
$32$	3.16180	+	4.69074i	0.558932	+	0.829213i
$33$	−8.33723	−	0.742712i	−1.45133	−	0.129290i
$34$	5.41793	−	5.01642i	0.929167	−	0.860309i
$35$			4.64850i			0.785740i
$36$	1.51126	−	5.80656i	0.251877	−	0.967759i
$37$		−	8.77578i		−	1.44273i	−0.692555	−	0.721365i	$-0.743515\pi$
$37$		−	8.77578i		−	1.44273i	0.692555	−	0.721365i	$-0.256485\pi$
$38$	−0.960810	−	1.03771i	−0.155864	−	0.168339i
$39$	3.70121	+	0.329718i	0.592667	+	0.0527971i
$40$	−4.37376	+	3.46526i	−0.691553	+	0.547906i
$41$			6.54069i			1.02148i	0.859734	+	0.510742i	$0.170629\pi$
$41$			6.54069i			1.02148i	−0.859734	+	0.510742i	$0.829371\pi$
$42$	3.52989	+	4.56620i	0.544674	+	0.704581i
$43$	−1.36072			−0.207508			−0.103754	−	0.994603i	$-0.533086\pi$
$43$	−1.36072			−0.207508			−0.103754	+	0.994603i	$0.533086\pi$
$44$	9.63655	+	0.742712i	1.45276	+	0.111968i
$45$	5.82542	+	1.04620i	0.868402	+	0.155959i
$46$	7.75315	+	8.37370i	1.14314	+	1.23463i
$47$	5.54780			0.809230			0.404615	−	0.914487i	$-0.367406\pi$
$47$	5.54780			0.809230			0.404615	+	0.914487i	$0.367406\pi$
$48$	−1.66495	+	6.72517i	−0.240315	+	0.970695i
$49$	1.44828			0.206896
$50$	1.06436	+	1.14955i	0.150523	+	0.162570i
$51$	9.00743	+	0.802416i	1.26129	+	0.112361i
$52$	−4.27802	−	0.329718i	−0.593255	−	0.0457236i
$53$	−13.0520			−1.79283			−0.896416	−	0.443214i	$-0.853838\pi$
$53$	−13.0520			−1.79283			−0.896416	+	0.443214i	$0.853838\pi$
$54$	6.51673	−	3.39591i	0.886815	−	0.462125i
$55$			9.53404i			1.28557i
$56$	−4.13857	−	5.22360i	−0.553040	−	0.698033i
$57$	0.153689	−	1.72522i	0.0203566	−	0.228511i
$58$	0.567516	+	0.612938i	0.0745184	+	0.0804828i
$59$		−	14.0204i		−	1.82530i	−0.408744	−	0.912649i	$-0.634033\pi$
$59$		−	14.0204i		−	1.82530i	0.408744	−	0.912649i	$-0.365967\pi$
$60$	−6.74055	−	1.12773i	−0.870201	−	0.145589i
$61$		−	10.1557i		−	1.30031i	−0.759804	−	0.650153i	$-0.774705\pi$
$61$		−	10.1557i		−	1.30031i	0.759804	−	0.650153i	$-0.225295\pi$
$62$	4.65421	−	4.30930i	0.591085	−	0.547282i
$63$	−1.24948	+	6.95732i	−0.157420	+	0.876540i
$64$	1.82975	−	7.78794i	0.228718	−	0.973493i
$65$		−	4.23251i		−	0.524979i
$66$	7.23977	+	9.36524i	0.891154	+	1.15278i
$67$	5.68558			0.694604			0.347302	−	0.937753i	$-0.387098\pi$
$67$	5.68558			0.694604			0.347302	+	0.937753i	$0.387098\pi$
$68$	−10.4112	−	0.802416i	−1.26254	−	0.0973072i
$69$	−1.24018	+	13.9215i	−0.149300	+	1.67595i
$70$	4.82380	−	4.46633i	0.576555	−	0.533828i
$71$	−3.57493			−0.424266			−0.212133	−	0.977241i	$-0.568041\pi$
$71$	−3.57493			−0.424266			−0.212133	+	0.977241i	$0.568041\pi$
$72$	−7.47756	+	4.01075i	−0.881239	+	0.472671i
$73$	−3.06303			−0.358501			−0.179250	−	0.983803i	$-0.557367\pi$
$73$	−3.06303			−0.358501			−0.179250	+	0.983803i	$0.557367\pi$
$74$	−9.10673	+	8.43186i	−1.05864	+	0.980184i
$75$	−0.170252	+	1.91115i	−0.0196590	+	0.220680i
$76$	−0.153689	+	1.99409i	−0.0176293	+	0.228737i
$77$	−11.3865			−1.29762
$78$	−3.21400	−	4.15758i	−0.363914	−	0.470753i
$79$			3.01433i			0.339139i	0.985518	+	0.169570i	$0.0542377\pi$
$79$			3.01433i			0.339139i	−0.985518	+	0.169570i	$0.945762\pi$
$80$	7.79829	+	1.20925i	0.871876	+	0.135198i
$81$	8.43758	+	3.13166i	0.937508	+	0.347963i
$82$	6.78735	−	6.28436i	0.749538	−	0.693992i
$83$			6.41871i			0.704545i	0.935898	+	0.352272i	$0.114591\pi$
$83$			6.41871i			0.704545i	−0.935898	+	0.352272i	$0.885409\pi$
$84$	1.34685	−	8.05026i	0.146953	−	0.878355i
$85$		−	10.3004i		−	1.11724i
$86$	1.30740	+	1.41204i	0.140980	+	0.152264i
$87$	−0.0907785	+	1.01902i	−0.00973248	+	0.109251i
$88$	−8.48817	−	10.7136i	−0.904842	−	1.14207i
$89$		−	6.77889i		−	0.718561i	−0.933230	−	0.359280i	$-0.883022\pi$
$89$		−	6.77889i		−	0.718561i	0.933230	−	0.359280i	$-0.116978\pi$
$90$	−4.51146	−	7.05031i	−0.475550	−	0.743168i
$91$	5.05491			0.529898
$92$	1.24018	−	16.0911i	0.129297	−	1.67761i
$93$	7.73773	+	0.689307i	0.802365	+	0.0714778i
$94$	−5.33038	−	5.75702i	−0.549787	−	0.593791i
$95$	−1.97287			−0.202413
$96$	8.57849	−	4.73388i	0.875538	−	0.483149i
$97$	−12.2390			−1.24268			−0.621340	−	0.783541i	$-0.713411\pi$
$97$	−12.2390			−1.24268			−0.621340	+	0.783541i	$0.713411\pi$
$98$	−1.39152	−	1.50289i	−0.140564	−	0.151815i
$99$	−2.56268	+	14.2694i	−0.257559	+	1.43413i
$100$	0.170252	−	2.20899i	0.0170252	−	0.220899i
$101$	−1.74580			−0.173714			−0.0868568	−	0.996221i	$-0.527682\pi$
$101$	−1.74580			−0.173714			−0.0868568	+	0.996221i	$0.527682\pi$
$102$	−7.82175	−	10.1181i	−0.774468	−	1.00184i
$103$		−	13.1313i		−	1.29387i	−0.762547	−	0.646933i	$-0.776051\pi$
$103$		−	13.1313i		−	1.29387i	0.762547	−	0.646933i	$-0.223949\pi$
$104$	3.76821	+	4.75615i	0.369504	+	0.466379i
$105$	8.01969	+	0.714424i	0.782641	+	0.0697206i
$106$	12.5405	+	13.5442i	1.21804	+	1.31553i
$107$		−	9.99113i		−	0.965879i	−0.875654	−	0.482940i	$-0.839569\pi$
$107$		−	9.99113i		−	0.965879i	0.875654	−	0.482940i	$-0.160431\pi$
$108$	−9.78532	−	3.49966i	−0.941592	−	0.336755i
$109$		−	4.66192i		−	0.446531i	−0.974758	−	0.223266i	$-0.928328\pi$
$109$		−	4.66192i		−	0.446531i	0.974758	−	0.223266i	$-0.0716717\pi$
$110$	9.89358	−	9.16040i	0.943316	−	0.873410i
$111$	−15.1401	−	1.34874i	−1.43704	−	0.128017i
$112$	−1.44421	+	9.31353i	−0.136465	+	0.880046i
$113$		−	15.4604i		−	1.45439i	−0.686432	−	0.727194i	$-0.740824\pi$
$113$		−	15.4604i		−	1.45439i	0.686432	−	0.727194i	$-0.259176\pi$
$114$	−1.93794	+	1.49812i	−0.181505	+	0.140312i
$115$	15.9199			1.48454
$116$	0.0907785	−	1.17783i	0.00842858	−	0.109359i
$117$	1.13767	−	6.33472i	0.105178	−	0.585645i
$118$	−14.5491	+	13.4709i	−1.33935	+	1.24010i
$119$	12.3019			1.12771
$120$	5.30613	+	8.07827i	0.484381	+	0.737442i
$121$	−12.3537			−1.12306
$122$	−10.5387	+	9.75770i	−0.954128	+	0.883421i
$123$	11.2841	+	1.00523i	1.01746	+	0.0906388i
$124$	−8.94362	−	0.689307i	−0.803161	−	0.0619016i
$125$	12.0499			1.07777
$126$	8.42021	−	5.38806i	0.750132	−	0.480006i
$127$		−	11.0587i		−	0.981300i	−0.871357	−	0.490650i	$-0.836759\pi$
$127$		−	11.0587i		−	0.981300i	0.871357	−	0.490650i	$-0.163241\pi$
$128$	−9.83967	+	5.58398i	−0.869712	+	0.493559i
$129$	−0.209128	+	2.34754i	−0.0184127	+	0.206690i
$130$	−4.39213	+	4.06664i	−0.385215	+	0.356668i
$131$			5.46142i			0.477166i	0.971122	+	0.238583i	$0.0766829\pi$
$131$			5.46142i			0.477166i	−0.971122	+	0.238583i	$0.923317\pi$
$132$	2.76237	−	16.5110i	0.240434	−	1.43710i
$133$		−	2.35621i		−	0.204309i
$134$	−5.46276	−	5.89999i	−0.471911	−	0.509681i
$135$	2.70023	−	9.88933i	0.232399	−	0.851138i
$136$	9.17050	+	11.5748i	0.786364	+	0.992529i
$137$		−	1.19513i		−	0.102106i	−0.998696	−	0.0510532i	$-0.983742\pi$
$137$		−	1.19513i		−	0.102106i	0.998696	−	0.0510532i	$-0.0162578\pi$
$138$	15.6380	−	12.0889i	1.33120	−	1.02908i
$139$	−4.81905			−0.408746			−0.204373	−	0.978893i	$-0.565516\pi$
$139$	−4.81905			−0.408746			−0.204373	+	0.978893i	$0.565516\pi$
$140$	−9.26952	−	0.714424i	−0.783417	−	0.0603799i
$141$	0.852636	−	9.57117i	0.0718049	−	0.806038i
$142$	3.43483	+	3.70974i	0.288244	+	0.311315i
$143$	10.3676			0.866980
$144$	11.3465	+	3.90599i	0.945542	+	0.325499i
$145$	1.16530			0.0967733
$146$	2.94299	+	3.17854i	0.243564	+	0.263058i
$147$	0.222584	−	2.49859i	0.0183584	−	0.206080i
$148$	17.4997	+	1.34874i	1.43846	+	0.110866i
$149$	23.1362			1.89539			0.947697	−	0.319172i	$-0.103405\pi$
$149$	23.1362			1.89539			0.947697	+	0.319172i	$0.103405\pi$
$150$	2.14680	−	1.65958i	0.175285	−	0.135504i
$151$			5.63190i			0.458317i	0.973389	+	0.229159i	$0.0735975\pi$
$151$			5.63190i			0.458317i	−0.973389	+	0.229159i	$0.926403\pi$
$152$	2.21695	−	1.75645i	0.179819	−	0.142467i
$153$	2.76869	−	15.4165i	0.223835	−	1.24635i
$154$	10.9403	+	11.8159i	0.881594	+	0.952155i
$155$		−	8.84848i		−	0.710727i
$156$	−1.22632	+	7.32985i	−0.0981842	+	0.586858i
$157$		−	4.71242i		−	0.376092i	−0.982160	−	0.188046i	$-0.939785\pi$
$157$		−	4.71242i		−	0.376092i	0.982160	−	0.188046i	$-0.0602154\pi$
$158$	3.12801	−	2.89620i	0.248851	−	0.230409i
$159$	−2.00595	+	22.5176i	−0.159082	+	1.78576i
$160$	−6.23782	−	9.25424i	−0.493143	−	0.731612i
$161$			19.0132i			1.49845i
$162$	−4.85714	−	11.7647i	−0.381613	−	0.924322i
$163$	−21.8296			−1.70983			−0.854913	−	0.518771i	$-0.826390\pi$
$163$	−21.8296			−1.70983			−0.854913	+	0.518771i	$0.826390\pi$
$164$	−13.0427	−	1.00523i	−1.01846	−	0.0784955i
$165$	16.4483	+	1.46528i	1.28050	+	0.114072i
$166$	6.66077	−	6.16716i	0.516976	−	0.478664i
$167$	−0.772221			−0.0597562			−0.0298781	−	0.999554i	$-0.509512\pi$
$167$	−0.772221			−0.0597562			−0.0298781	+	0.999554i	$0.509512\pi$
$168$	−9.64791	+	6.33713i	−0.744352	+	0.488920i
$169$	8.39745			0.645958
$170$	−10.6889	+	9.89676i	−0.819800	+	0.759047i
$171$	−2.95276	−	0.530294i	−0.225803	−	0.0405526i
$172$	0.209128	−	2.71340i	0.0159459	−	0.206895i
$173$	−2.64330			−0.200966			−0.100483	−	0.994939i	$-0.532039\pi$
$173$	−2.64330			−0.200966			−0.100483	+	0.994939i	$0.532039\pi$
$174$	1.14467	−	0.884886i	0.0867775	−	0.0670831i
$175$			2.61014i			0.197308i
$176$	−2.96206	+	19.1020i	−0.223274	+	1.43986i
$177$	−24.1882	−	2.15478i	−1.81810	−	0.161963i
$178$	−7.03453	+	6.51322i	−0.527260	+	0.488187i
$179$			13.7988i			1.03137i	0.856778	+	0.515686i	$0.172463\pi$
$179$			13.7988i			1.03137i	−0.856778	+	0.515686i	$0.827537\pi$
$180$	−2.98152	+	11.4556i	−0.222230	+	0.853850i
$181$			12.3871i			0.920729i	0.887730	+	0.460365i	$0.152281\pi$
$181$			12.3871i			0.920729i	−0.887730	+	0.460365i	$0.847719\pi$
$182$	−4.85680	−	5.24553i	−0.360010	−	0.388825i
$183$	−17.5208	−	1.56082i	−1.29518	−	0.115379i
$184$	−17.8895	+	14.1735i	−1.31883	+	1.04488i
$185$			17.3135i			1.27291i
$186$	−6.71919	−	8.69182i	−0.492675	−	0.637315i
$187$	25.2310			1.84507
$188$	−0.852636	+	11.0628i	−0.0621849	+	0.806837i
$189$	11.8109	+	3.22490i	0.859114	+	0.234577i
$190$	1.89556	+	2.04727i	0.137518	+	0.148525i
$191$	−0.794407			−0.0574813			−0.0287406	−	0.999587i	$-0.509150\pi$
$191$	−0.794407			−0.0574813			−0.0287406	+	0.999587i	$0.509150\pi$
$192$	−13.1547	−	4.35364i	−0.949358	−	0.314197i
$193$	−10.5422			−0.758842			−0.379421	−	0.925224i	$-0.623877\pi$
$193$	−10.5422			−0.758842			−0.379421	+	0.925224i	$0.623877\pi$
$194$	11.7593	+	12.7005i	0.844271	+	0.911845i
$195$	−7.30201	−	0.650491i	−0.522908	−	0.0465826i
$196$	−0.222584	+	2.88799i	−0.0158989	+	0.206285i
$197$	−10.3447			−0.737032			−0.368516	−	0.929621i	$-0.620134\pi$
$197$	−10.3447			−0.737032			−0.368516	+	0.929621i	$0.620134\pi$
$198$	17.2698	−	11.0509i	1.22731	−	0.785350i
$199$		−	11.1911i		−	0.793315i	−0.917967	−	0.396657i	$-0.870170\pi$
$199$		−	11.1911i		−	0.793315i	0.917967	−	0.396657i	$-0.129830\pi$
$200$	−2.45587	+	1.94575i	−0.173657	+	0.137585i
$201$	0.873811	−	9.80887i	0.0616339	−	0.691864i
$202$	1.67738	+	1.81164i	0.118020	+	0.127466i
$203$			1.39173i			0.0976801i
$204$	−2.98443	+	17.8383i	−0.208952	+	1.24893i
$205$		−	12.9040i		−	0.901252i
$206$	−13.6265	+	12.6167i	−0.949403	+	0.879046i
$207$	23.8270	+	4.27915i	1.65609	+	0.297422i
$208$	1.31497	−	8.48007i	0.0911768	−	0.587987i
$209$		−	4.83256i		−	0.334275i
$210$	−6.96403	−	9.00854i	−0.480563	−	0.621649i
$211$	−5.93112			−0.408315			−0.204158	−	0.978938i	$-0.565446\pi$
$211$	−5.93112			−0.408315			−0.204158	+	0.978938i	$0.565446\pi$
$212$	2.00595	−	26.0268i	0.137769	−	1.78753i
$213$	−0.549427	+	6.16753i	−0.0376461	+	0.422592i
$214$	−10.3679	+	9.59958i	−0.708736	+	0.656214i
$215$	2.68453			0.183084
$216$	5.77019	+	13.5168i	0.392612	+	0.919704i
$217$	10.5678			0.717387
$218$	−4.83773	+	4.47922i	−0.327652	+	0.303371i
$219$	−0.470754	+	5.28440i	−0.0318106	+	0.357087i
$220$	−19.0117	−	1.46528i	−1.28177	−	0.0987890i
$221$	−11.2010			−0.753459
$222$	13.1472	+	17.0070i	0.882382	+	1.14143i
$223$			3.45829i			0.231584i	0.993273	+	0.115792i	$0.0369406\pi$
$223$			3.45829i			0.231584i	−0.993273	+	0.115792i	$0.963059\pi$
$224$	11.0524	−	7.44986i	0.738467	−	0.497765i
$225$	3.27098	+	0.587445i	0.218065	+	0.0391630i
$226$	−16.0434	+	14.8545i	−1.06719	+	0.988104i
$227$		−	14.3152i		−	0.950130i	−0.879951	−	0.475065i	$-0.842424\pi$
$227$		−	14.3152i		−	0.950130i	0.879951	−	0.475065i	$-0.157576\pi$
$228$	3.41661	+	0.571616i	0.226271	+	0.0378562i
$229$		−	13.4895i		−	0.891412i	−0.895179	−	0.445706i	$-0.852953\pi$
$229$		−	13.4895i		−	0.891412i	0.895179	−	0.445706i	$-0.147047\pi$
$230$	−15.2960	−	16.5202i	−1.00859	−	1.08931i
$231$	−1.74999	+	19.6443i	−0.115141	+	1.29250i
$232$	−1.30947	+	1.03747i	−0.0859711	+	0.0681134i
$233$			14.0612i			0.921181i	0.887613	+	0.460591i	$0.152362\pi$
$233$			14.0612i			0.921181i	−0.887613	+	0.460591i	$0.847638\pi$
$234$	−7.66669	+	4.90589i	−0.501187	+	0.320708i
$235$	−10.9451			−0.713980
$236$	27.9579	+	2.15478i	1.81990	+	0.140264i
$237$	5.20039	+	0.463270i	0.337801	+	0.0300926i
$238$	−11.8197	−	12.7658i	−0.766160	−	0.827482i
$239$	10.9776			0.710079			0.355040	−	0.934851i	$-0.384467\pi$
$239$	10.9776			0.710079			0.355040	+	0.934851i	$0.384467\pi$
$240$	3.28473	−	13.2679i	0.212029	−	0.856440i
$241$	−12.3554			−0.795878			−0.397939	−	0.917412i	$-0.630275\pi$
$241$	−12.3554			−0.795878			−0.397939	+	0.917412i	$0.630275\pi$
$242$	11.8695	+	12.8196i	0.763003	+	0.824072i
$243$	6.69957	−	14.0754i	0.429777	−	0.902935i
$244$	20.2514	+	1.56082i	1.29646	+	0.0999213i
$245$	−2.85726			−0.182544
$246$	−9.79876	−	12.6755i	−0.624746	−	0.808161i
$247$			2.14536i			0.136506i
$248$	7.87782	+	9.94319i	0.500242	+	0.631393i
$249$	11.0737	+	0.986485i	0.701766	+	0.0625160i
$250$	−11.5776	−	12.5043i	−0.732233	−	0.790840i
$251$		−	3.35841i		−	0.211981i	−0.994367	−	0.105991i	$-0.966199\pi$
$251$		−	3.35841i		−	0.211981i	0.994367	−	0.105991i	$-0.0338013\pi$
$252$	−13.6815	−	3.56084i	−0.861851	−	0.224312i
$253$			38.9959i			2.45165i
$254$	−11.4757	+	10.6253i	−0.720051	+	0.666691i
$255$	−17.7705	−	1.58306i	−1.11283	−	0.0991354i
$256$	15.2486	+	4.84560i	0.953038	+	0.302850i
$257$			5.93733i			0.370360i	0.982705	+	0.185180i	$0.0592868\pi$
$257$			5.93733i			0.370360i	−0.982705	+	0.185180i	$0.940713\pi$
$258$	2.63700	−	2.03853i	0.164173	−	0.126913i
$259$	−20.6776			−1.28484
$260$	8.44000	+	0.650491i	0.523426	+	0.0403417i
$261$	1.74409	+	0.313226i	0.107956	+	0.0193882i
$262$	5.66737	−	5.24738i	0.350132	−	0.324184i
$263$	21.0419			1.29750			0.648749	−	0.761002i	$-0.275293\pi$
$263$	21.0419			1.29750			0.648749	+	0.761002i	$0.275293\pi$
$264$	−19.7878	+	12.9974i	−1.21785	+	0.799934i
$265$	25.7500			1.58181
$266$	−2.44507	+	2.26387i	−0.149917	+	0.138807i
$267$	−11.6951	−	1.04184i	−0.715727	−	0.0637596i
$268$	−0.873811	+	11.3375i	−0.0533765	+	0.692550i
$269$	10.4505			0.637180			0.318590	−	0.947893i	$-0.396791\pi$
$269$	10.4505			0.637180			0.318590	+	0.947893i	$0.396791\pi$
$270$	−12.8567	+	6.69971i	−0.782433	+	0.407731i
$271$		−	31.8860i		−	1.93694i	−0.249131	−	0.968470i	$-0.580145\pi$
$271$		−	31.8860i		−	1.93694i	0.249131	−	0.968470i	$-0.419855\pi$
$272$	3.20017	−	20.6375i	0.194039	−	1.25133i
$273$	0.776884	−	8.72082i	0.0470191	−	0.527808i
$274$	−1.24020	+	1.14829i	−0.0749229	+	0.0693706i
$275$			5.35337i			0.322821i
$276$	−27.5700	−	4.61260i	−1.65952	−	0.277646i
$277$			19.3036i			1.15984i	0.814674	+	0.579920i	$0.196916\pi$
$277$			19.3036i			1.15984i	−0.814674	+	0.579920i	$0.803084\pi$
$278$	4.63019	+	5.00078i	0.277700	+	0.299927i
$279$	2.37841	−	13.2433i	0.142392	−	0.792858i
$280$	8.16488	+	10.3055i	0.487945	+	0.615872i
$281$			3.94758i			0.235493i	0.993044	+	0.117747i	$0.0375670\pi$
$281$			3.94758i			0.235493i	−0.993044	+	0.117747i	$0.962433\pi$
$282$	−10.7513	+	8.31129i	−0.640233	+	0.494930i
$283$	−16.8230			−1.00002			−0.500011	−	0.866019i	$-0.666671\pi$
$283$	−16.8230			−1.00002			−0.500011	+	0.866019i	$0.666671\pi$
$284$	0.549427	−	7.12872i	0.0326025	−	0.423011i
$285$	−0.303209	+	3.40364i	−0.0179606	+	0.201614i
$286$	−9.96126	−	10.7585i	−0.589022	−	0.636166i
$287$	15.4112			0.909697
$288$	−6.84855	−	15.5273i	−0.403555	−	0.914955i
$289$	−10.2592			−0.603482
$290$	−1.11964	−	1.20925i	−0.0657473	−	0.0710096i
$291$	−1.88100	+	21.1149i	−0.110266	+	1.23778i
$292$	0.470754	−	6.10795i	0.0275488	−	0.357441i
$293$	10.1353			0.592112			0.296056	−	0.955171i	$-0.404329\pi$
$293$	10.1353			0.592112			0.296056	+	0.955171i	$0.404329\pi$
$294$	−2.80668	+	2.16969i	−0.163689	+	0.126539i
$295$			27.6604i			1.61045i
$296$	−15.4142	−	19.4555i	−0.895935	−	1.13083i
$297$	24.2240	+	6.61424i	1.40562	+	0.383797i
$298$	−22.2295	−	24.0087i	−1.28772	−	1.39079i
$299$		−	17.3117i		−	1.00116i
$300$	−3.78483	−	0.633220i	−0.218517	−	0.0365590i
$301$			3.20615i			0.184799i
$302$	5.84428	−	5.41118i	0.336301	−	0.311379i
$303$	−0.268310	+	3.01189i	−0.0154140	+	0.173028i
$304$	−3.95276	−	0.612938i	−0.226706	−	0.0351544i
$305$			20.0359i			1.14725i
$306$	−18.6580	+	11.9392i	−1.06661	+	0.682518i
$307$	26.0177			1.48491			0.742454	−	0.669897i	$-0.233662\pi$
$307$	26.0177			1.48491			0.742454	+	0.669897i	$0.233662\pi$
$308$	1.74999	−	22.7057i	0.0997147	−	1.29378i
$309$	−22.6544	−	2.01814i	−1.28876	−	0.114808i
$310$	−9.18217	+	8.50171i	−0.521512	+	0.482865i
$311$	24.6649			1.39862			0.699309	−	0.714819i	$-0.253491\pi$
$311$	24.6649			1.39862			0.699309	+	0.714819i	$0.253491\pi$
$312$	8.78453	−	5.77003i	0.497326	−	0.326663i
$313$	23.7033			1.33979			0.669894	−	0.742456i	$-0.266339\pi$
$313$	23.7033			1.33979			0.669894	+	0.742456i	$0.266339\pi$
$314$	−4.89013	+	4.52774i	−0.275966	+	0.255515i
$315$	2.46508	−	13.7259i	0.138891	−	0.773368i
$316$	−6.01084	−	0.463270i	−0.338136	−	0.0260610i
$317$	−24.2250			−1.36061			−0.680306	−	0.732928i	$-0.738153\pi$
$317$	−24.2250			−1.36061			−0.680306	+	0.732928i	$0.738153\pi$
$318$	25.2941	−	19.5535i	1.41842	−	1.09651i
$319$			2.85442i			0.159817i
$320$	−3.60986	+	15.3646i	−0.201797	+	0.858908i
$321$	−17.2369	−	1.53553i	−0.962069	−	0.0857048i
$322$	19.7302	−	18.2681i	1.09952	−	1.01804i
$323$			5.22103i			0.290506i
$324$	−7.54157	+	16.3440i	−0.418976	+	0.907997i
$325$		−	2.37656i		−	0.131828i
$326$	20.9741	+	22.6528i	1.16165	+	1.25462i
$327$	−8.04283	−	0.716486i	−0.444770	−	0.0396218i
$328$	11.4884	+	14.5004i	0.634342	+	0.800651i
$329$		−	13.0718i		−	0.720671i
$330$	−14.2832	−	18.4764i	−0.786262	−	1.01709i
$331$	−19.4306			−1.06800			−0.534001	−	0.845484i	$-0.679312\pi$
$331$	−19.4306			−1.06800			−0.534001	+	0.845484i	$0.679312\pi$
$332$	−12.7995	−	0.986485i	−0.702462	−	0.0541404i
$333$	−4.65375	+	25.9128i	−0.255024	+	1.42001i
$334$	0.741957	+	0.801342i	0.0405981	+	0.0438475i
$335$	−11.2169			−0.612846
$336$	15.8459	+	3.92297i	0.864466	+	0.214015i
$337$	3.54860			0.193305			0.0966524	−	0.995318i	$-0.469186\pi$
$337$	3.54860			0.193305			0.0966524	+	0.995318i	$0.469186\pi$
$338$	−8.06835	−	8.71413i	−0.438861	−	0.473986i
$339$	−26.6725	−	2.37609i	−1.44865	−	0.129051i
$340$	20.5400	+	1.58306i	1.11394	+	0.0858537i
$341$	21.6744			1.17373
$342$	2.28675	+	3.57362i	0.123653	+	0.193239i
$343$		−	19.9059i		−	1.07482i
$344$	−3.01666	+	2.39004i	−0.162647	+	0.128863i
$345$	2.44671	−	27.4653i	0.131727	−	1.47868i
$346$	2.53971	+	2.74298i	0.136535	+	0.147463i
$347$		−	19.3122i		−	1.03673i	−0.855158	−	0.518367i	$-0.826540\pi$
$347$		−	19.3122i		−	1.03673i	0.855158	−	0.518367i	$-0.173460\pi$
$348$	−2.01807	−	0.337633i	−0.108180	−	0.0180990i
$349$			13.9086i			0.744510i	0.928130	+	0.372255i	$0.121415\pi$
$349$			13.9086i			0.744510i	−0.928130	+	0.372255i	$0.878585\pi$
$350$	2.70857	−	2.50785i	0.144779	−	0.134050i
$351$	−10.7539	−	2.93631i	−0.574002	−	0.156728i
$352$	22.6683	−	15.2796i	1.20822	−	0.814405i
$353$			17.9380i			0.954744i	0.878701	+	0.477372i	$0.158411\pi$
$353$			17.9380i			0.954744i	−0.878701	+	0.477372i	$0.841589\pi$
$354$	21.0042	+	27.1707i	1.11636	+	1.44411i
$355$	7.05288			0.374328
$356$	13.5177	+	1.04184i	0.716436	+	0.0552175i
$357$	1.89066	−	21.2234i	0.100064	−	1.12326i
$358$	14.3192	−	13.2580i	0.756792	−	0.700709i
$359$	32.0012			1.68896			0.844479	−	0.535589i	$-0.179910\pi$
$359$	32.0012			1.68896			0.844479	+	0.535589i	$0.179910\pi$
$360$	14.7523	−	7.91269i	0.777513	−	0.417035i
$361$	1.00000			0.0526316
$362$	12.8543	−	11.9017i	0.675606	−	0.625539i
$363$	−1.89863	+	21.3128i	−0.0996520	+	1.11863i
$364$	−0.776884	+	10.0799i	−0.0407198	+	0.528331i
$365$	6.04297			0.316304
$366$	15.2145	+	19.6812i	0.795274	+	1.02875i
$367$			14.3595i			0.749558i	0.927114	+	0.374779i	$0.122281\pi$
$367$			14.3595i			0.749558i	−0.927114	+	0.374779i	$0.877719\pi$
$368$	31.8964	+	4.94604i	1.66271	+	0.257830i
$369$	3.46849	−	19.3131i	0.180563	−	1.00540i
$370$	17.9664	−	16.6350i	0.934030	−	0.864812i
$371$			30.7533i			1.59663i
$372$	−2.56374	+	15.3238i	−0.132924	+	0.794500i
$373$			22.3799i			1.15879i	0.815048	+	0.579393i	$0.196710\pi$
$373$			22.3799i			1.15879i	−0.815048	+	0.579393i	$0.803290\pi$
$374$	−24.2422	−	26.1825i	−1.25353	−	1.35386i
$375$	1.85193	−	20.7886i	0.0956333	−	1.07352i
$376$	12.2992	−	9.74445i	0.634283	−	0.502532i
$377$		−	1.26718i		−	0.0652633i
$378$	−8.00148	−	15.3548i	−0.411552	−	0.789765i
$379$	27.5634			1.41583			0.707917	−	0.706295i	$-0.249635\pi$
$379$	27.5634			1.41583			0.707917	+	0.706295i	$0.249635\pi$
$380$	0.303209	−	3.93408i	0.0155543	−	0.201814i
$381$	−19.0787	−	1.69960i	−0.977430	−	0.0870731i
$382$	0.763274	+	0.824365i	0.0390525	+	0.0421782i
$383$	−34.4356			−1.75958			−0.879788	−	0.475367i	$-0.842315\pi$
$383$	−34.4356			−1.75958			−0.879788	+	0.475367i	$0.842315\pi$
$384$	8.12134	+	17.8338i	0.414440	+	0.910077i
$385$	22.4642			1.14488
$386$	10.1290	+	10.9397i	0.515554	+	0.556817i
$387$	4.01789	+	0.721583i	0.204241	+	0.0366801i
$388$	1.88100	−	24.4056i	0.0954932	−	1.23901i
$389$	−9.55684			−0.484551			−0.242276	−	0.970207i	$-0.577894\pi$
$389$	−9.55684			−0.484551			−0.242276	+	0.970207i	$0.577894\pi$
$390$	6.34082	+	8.20238i	0.321080	+	0.415344i
$391$		−	42.1306i		−	2.13063i
$392$	3.21076	−	2.54383i	0.162168	−	0.128483i
$393$	9.42214	+	0.839360i	0.475284	+	0.0423401i
$394$	9.93932	+	10.7348i	0.500736	+	0.540814i
$395$		−	5.94690i		−	0.299221i
$396$	−28.0606	−	7.30326i	−1.41010	−	0.367003i
$397$		−	17.6792i		−	0.887295i	−0.896201	−	0.443647i	$-0.853684\pi$
$397$		−	17.6792i		−	0.887295i	0.896201	−	0.443647i	$-0.146316\pi$
$398$	−11.6131	+	10.7525i	−0.582113	+	0.538974i
$399$	−4.06498	−	0.362124i	−0.203503	−	0.0181289i
$400$	4.37875	+	0.678995i	0.218938	+	0.0339498i
$401$		−	34.3290i		−	1.71431i	−0.515058	−	0.857155i	$-0.672230\pi$
$401$		−	34.3290i		−	1.71431i	0.515058	−	0.857155i	$-0.327770\pi$
$402$	−11.0183	+	8.51769i	−0.549545	+	0.424824i
$403$	−9.62207			−0.479310
$404$	0.268310	−	3.48127i	0.0133489	−	0.173200i
$405$	−16.6463	−	6.17838i	−0.827160	−	0.307006i
$406$	1.44421	−	1.33719i	0.0716750	−	0.0663634i
$407$	−42.4095			−2.10216
$408$	21.3784	−	14.0422i	1.05839	−	0.695193i
$409$	−21.2316			−1.04983			−0.524917	−	0.851154i	$-0.675904\pi$
$409$	−21.2316			−1.04983			−0.524917	+	0.851154i	$0.675904\pi$
$410$	−13.3906	+	12.3983i	−0.661314	+	0.612306i
$411$	−2.06185	−	0.183678i	−0.101704	−	0.00906015i
$412$	26.1850	+	2.01814i	1.29004	+	0.0994265i
$413$	−33.0350			−1.62554
$414$	−18.4527	−	28.8370i	−0.906899	−	1.41726i
$415$		−	12.6633i		−	0.621617i
$416$	−10.0633	+	6.78318i	−0.493394	+	0.332573i
$417$	−0.740635	+	8.31391i	−0.0362690	+	0.407134i
$418$	−5.01481	+	4.64318i	−0.245282	+	0.227105i
$419$		−	16.7076i		−	0.816219i	−0.912933	−	0.408110i	$-0.866188\pi$
$419$		−	16.7076i		−	0.816219i	0.912933	−	0.408110i	$-0.133812\pi$
$420$	−2.65716	+	15.8821i	−0.129656	+	0.774969i
$421$			3.19194i			0.155565i	0.996970	+	0.0777827i	$0.0247840\pi$
$421$			3.19194i			0.155565i	−0.996970	+	0.0777827i	$0.975216\pi$
$422$	5.69868	+	6.15479i	0.277407	+	0.299611i
$423$	−16.3813	−	2.94197i	−0.796487	−	0.143043i
$424$	−28.9357	+	22.9252i	−1.40524	+	1.11335i
$425$		−	5.78371i		−	0.280551i
$426$	6.92801	−	5.35568i	0.335663	−	0.259484i
$427$	−23.9290			−1.15800
$428$	19.9232	+	1.53553i	0.963023	+	0.0742225i
$429$	1.59338	−	17.8863i	0.0769292	−	0.863560i
$430$	−2.57933	−	2.78577i	−0.124386	−	0.134342i
$431$	17.4859			0.842267			0.421133	−	0.906999i	$-0.361632\pi$
$431$	17.4859			0.842267			0.421133	+	0.906999i	$0.361632\pi$
$432$	8.48251	−	18.9749i	0.408115	−	0.912930i
$433$	−5.03086			−0.241768			−0.120884	−	0.992667i	$-0.538573\pi$
$433$	−5.03086			−0.241768			−0.120884	+	0.992667i	$0.538573\pi$
$434$	−10.1536	−	10.9663i	−0.487389	−	0.526399i
$435$	0.179095	−	2.01041i	0.00858693	−	0.0963916i
$436$	9.29627	+	0.716486i	0.445211	+	0.0343135i
$437$	−8.06939			−0.386011
$438$	5.93599	−	4.58880i	0.283632	−	0.219261i
$439$		−	1.24339i		−	0.0593439i	−0.999560	−	0.0296719i	$-0.990554\pi$
$439$		−	1.24339i		−	0.0593439i	0.999560	−	0.0296719i	$-0.00944625\pi$
$440$	16.7461	+	21.1365i	0.798338	+	1.00764i
$441$	−4.27641	−	0.768012i	−0.203639	−	0.0365720i
$442$	10.7620	+	11.6234i	0.511896	+	0.552868i
$443$		−	7.28527i		−	0.346134i	−0.984910	−	0.173067i	$-0.944632\pi$
$443$		−	7.28527i		−	0.346134i	0.984910	−	0.173067i	$-0.0553677\pi$
$444$	5.01638	−	29.9835i	0.238067	−	1.42295i
$445$			13.3739i			0.633983i
$446$	3.58870	−	3.32276i	0.169930	−	0.157337i
$447$	3.55578	−	39.9151i	0.168183	−	1.88792i
$448$	−18.3500	−	4.31127i	−0.866957	−	0.203688i
$449$			35.0658i			1.65486i	0.561571	+	0.827429i	$0.310197\pi$
$449$			35.0658i			1.65486i	−0.561571	+	0.827429i	$0.689803\pi$
$450$	−2.53319	−	3.95876i	−0.119416	−	0.186618i
$451$	31.6083			1.48838
$452$	30.8293	+	2.37609i	1.45009	+	0.111762i
$453$	9.71626	+	0.865561i	0.456510	+	0.0406676i
$454$	−14.8550	+	13.7541i	−0.697180	+	0.645514i
$455$	−9.97269			−0.467527
$456$	−2.68954	−	4.09467i	−0.125949	−	0.191751i
$457$	−2.98914			−0.139826			−0.0699130	−	0.997553i	$-0.522272\pi$
$457$	−2.98914			−0.139826			−0.0699130	+	0.997553i	$0.522272\pi$
$458$	−13.9982	+	12.9609i	−0.654094	+	0.605621i
$459$	−26.1712	−	7.14593i	−1.22157	−	0.333543i
$460$	−2.44671	+	31.7456i	−0.114079	+	1.48015i
$461$	−21.9864			−1.02401			−0.512005	−	0.858983i	$-0.671097\pi$
$461$	−21.9864			−1.02401			−0.512005	+	0.858983i	$0.671097\pi$
$462$	22.0665	−	17.0584i	1.02663	−	0.793630i
$463$			14.2465i			0.662089i	0.943615	+	0.331045i	$0.107401\pi$
$463$			14.2465i			0.662089i	−0.943615	+	0.331045i	$0.892599\pi$
$464$	2.33475	+	0.362040i	0.108388	+	0.0168073i
$465$	−15.2656	−	1.35991i	−0.707924	−	0.0630645i
$466$	14.5915	−	13.5102i	0.675938	−	0.625846i
$467$			7.12691i			0.329794i	0.986311	+	0.164897i	$0.0527292\pi$
$467$			7.12691i			0.329794i	−0.986311	+	0.164897i	$0.947271\pi$
$468$	12.4571	+	3.24219i	0.575831	+	0.149870i
$469$		−	13.3964i		−	0.618589i
$470$	10.5162	+	11.3579i	0.485075	+	0.523899i
$471$	−8.12995	−	0.724247i	−0.374609	−	0.0333716i
$472$	−24.6261	−	31.0825i	−1.13351	−	1.43069i
$473$			6.57578i			0.302355i
$474$	−4.51584	−	5.84161i	−0.207419	−	0.268314i
$475$	−1.10777			−0.0508280
$476$	−1.89066	+	24.5310i	−0.0866583	+	1.12437i
$477$	38.5395	+	6.92141i	1.76460	+	0.316910i
$478$	−10.5473	−	11.3915i	−0.482424	−	0.521037i
$479$	1.78303			0.0814687			0.0407344	−	0.999170i	$-0.487030\pi$
$479$	1.78303			0.0814687			0.0407344	+	0.999170i	$0.487030\pi$
$480$	−16.9243	+	9.33934i	−0.772484	+	0.426280i
$481$	18.8272			0.858445
$482$	11.8711	+	12.8213i	0.540716	+	0.583994i
$483$	32.8019	+	2.92212i	1.49254	+	0.132961i
$484$	1.89863	−	24.6343i	0.0863011	−	1.11974i
$485$	24.1460			1.09641
$486$	−21.0432	+	6.57153i	−0.954538	+	0.298091i
$487$			14.2210i			0.644417i	0.946669	+	0.322208i	$0.104425\pi$
$487$			14.2210i			0.644417i	−0.946669	+	0.322208i	$0.895575\pi$
$488$	−17.8380	−	22.5147i	−0.807489	−	1.01919i
$489$	−3.35497	+	37.6608i	−0.151717	+	1.70308i
$490$	2.74529	+	2.96501i	0.124019	+	0.133946i
$491$		−	6.44379i		−	0.290804i	−0.989373	−	0.145402i	$-0.953552\pi$
$491$		−	6.44379i		−	0.290804i	0.989373	−	0.145402i	$-0.0464476\pi$
$492$	−3.73877	+	22.3470i	−0.168557	+	1.00748i
$493$		−	3.08388i		−	0.138891i
$494$	2.22626	−	2.06128i	0.100164	−	0.0927413i
$495$	5.05585	−	28.1517i	0.227243	−	1.26533i
$496$	2.74907	−	17.7284i	0.123437	−	0.796029i
$497$			8.42328i			0.377836i
$498$	−9.61601	−	12.4391i	−0.430904	−	0.557410i
$499$	−36.1251			−1.61718			−0.808592	−	0.588370i	$-0.799770\pi$
$499$	−36.1251			−1.61718			−0.808592	+	0.588370i	$0.799770\pi$
$500$	−1.85193	+	24.0285i	−0.0828209	+	1.07459i
$501$	−0.118682	+	1.33225i	−0.00530232	+	0.0595205i
$502$	−3.48506	+	3.22680i	−0.155546	+	0.144019i
$503$	−30.4980			−1.35984			−0.679919	−	0.733288i	$-0.737985\pi$
$503$	−30.4980			−1.35984			−0.679919	+	0.733288i	$0.737985\pi$
$504$	9.45016	+	17.6187i	0.420943	+	0.784799i
$505$	3.44424			0.153267
$506$	40.4664	−	37.4676i	1.79895	−	1.66564i
$507$	1.29060	−	14.4874i	0.0573174	−	0.643410i
$508$	22.0520	+	1.69960i	0.978399	+	0.0754076i
$509$	−10.9622			−0.485889			−0.242944	−	0.970040i	$-0.578113\pi$
$509$	−10.9622			−0.485889			−0.242944	+	0.970040i	$0.578113\pi$
$510$	15.4313	+	19.9617i	0.683310	+	0.883918i
$511$			7.21714i			0.319268i
$512$	−9.62269	−	20.4794i	−0.425267	−	0.905068i
$513$	−1.36868	+	5.01266i	−0.0604287	+	0.221314i
$514$	6.16123	−	5.70464i	0.271760	−	0.251621i
$515$			25.9064i			1.14157i
$516$	−4.64906	−	0.777811i	−0.204664	−	0.0342412i
$517$		−	26.8101i		−	1.17911i
$518$	19.8672	+	21.4574i	0.872916	+	0.942782i
$519$	−0.406246	+	4.56026i	−0.0178322	+	0.200173i
$520$	−7.43421	−	9.38328i	−0.326012	−	0.411484i
$521$		−	8.00895i		−	0.350879i	−0.984490	−	0.175439i	$-0.943865\pi$
$521$		−	8.00895i		−	0.350879i	0.984490	−	0.175439i	$-0.0561346\pi$
$522$	−1.35070	−	2.11081i	−0.0591185	−	0.0923876i
$523$	−14.1920			−0.620572			−0.310286	−	0.950643i	$-0.600425\pi$
$523$	−14.1920			−0.620572			−0.310286	+	0.950643i	$0.600425\pi$
$524$	−10.8905	−	0.839360i	−0.475755	−	0.0366676i
$525$	4.50306	+	0.401150i	0.196530	+	0.0175076i
$526$	−20.2172	−	21.8354i	−0.881514	−	0.952069i
$527$	−23.4167			−1.02005
$528$	32.4998	+	8.04597i	1.41437	+	0.350156i
$529$	42.1151			1.83109
$530$	−24.7408	−	26.7210i	−1.07467	−	1.16069i
$531$	−7.43493	+	41.3988i	−0.322649	+	1.79656i
$532$	4.69849	+	0.362124i	0.203705	+	0.0157001i
$533$	−14.0321			−0.607798
$534$	10.1556	+	13.1371i	0.439476	+	0.568499i
$535$			19.7112i			0.852191i
$536$	12.6047	−	9.98645i	0.544438	−	0.431349i
$537$	23.8060	+	2.12073i	1.02730	+	0.0915161i
$538$	−10.0410	−	10.8446i	−0.432897	−	0.467546i
$539$		−	6.99888i		−	0.301463i
$540$	19.3052	+	6.90438i	0.830763	+	0.297117i
$541$		−	17.1733i		−	0.738337i	−0.929362	−	0.369168i	$-0.879643\pi$
$541$		−	17.1733i		−	0.738337i	0.929362	−	0.369168i	$-0.120357\pi$
$542$	−33.0885	+	30.6364i	−1.42127	+	1.31595i
$543$	21.3705	+	1.90377i	0.917098	+	0.0816985i
$544$	−24.4905	+	16.5079i	−1.05002	+	0.707768i
$545$			9.19738i			0.393972i
$546$	−9.79613	+	7.57287i	−0.419236	+	0.324089i
$547$	20.0528			0.857394			0.428697	−	0.903448i	$-0.358973\pi$
$547$	20.0528			0.857394			0.428697	+	0.903448i	$0.358973\pi$
$548$	2.38318	+	0.183678i	0.101805	+	0.00784632i
$549$	−5.38551	+	29.9874i	−0.229848	+	1.27983i
$550$	5.55526	−	5.14357i	0.236877	−	0.219323i
$551$	−0.590664			−0.0251631
$552$	21.7030	+	33.0415i	0.923741	+	1.40634i
$553$	7.10241			0.302025
$554$	20.0315	−	18.5471i	0.851058	−	0.787989i
$555$	29.8696	+	2.66090i	1.26789	+	0.112949i
$556$	0.740635	−	9.60960i	0.0314099	−	0.407538i
$557$	−20.5897			−0.872414			−0.436207	−	0.899846i	$-0.643678\pi$
$557$	−20.5897			−0.872414			−0.436207	+	0.899846i	$0.643678\pi$
$558$	−16.0280	+	10.2562i	−0.678518	+	0.434181i
$559$		−	2.91923i		−	0.123470i
$560$	2.84925	−	18.3744i	0.120403	−	0.776461i
$561$	3.87773	−	43.5290i	0.163718	−	1.83779i
$562$	4.09645	−	3.79288i	0.172798	−	0.159993i
$563$		−	3.87489i		−	0.163307i	−0.996661	−	0.0816536i	$-0.973980\pi$
$563$		−	3.87489i		−	0.163307i	0.996661	−	0.0816536i	$-0.0260201\pi$
$564$	18.9547	+	3.17121i	0.798137	+	0.133532i
$565$			30.5013i			1.28320i
$566$	16.1637	+	17.4574i	0.679411	+	0.733789i
$567$	7.37886	−	19.8807i	0.309883	−	0.834911i
$568$	−7.92544	+	6.27919i	−0.332544	+	0.263469i
$569$		−	0.630264i		−	0.0264220i	−0.999913	−	0.0132110i	$-0.995795\pi$
$569$		−	0.630264i		−	0.0264220i	0.999913	−	0.0132110i	$-0.00420532\pi$
$570$	3.82332	−	2.95561i	0.160141	−	0.123797i
$571$	10.7705			0.450731			0.225365	−	0.974274i	$-0.427642\pi$
$571$	10.7705			0.450731			0.225365	+	0.974274i	$0.427642\pi$
$572$	−1.59338	+	20.6738i	−0.0666226	+	0.864416i
$573$	−0.122092	+	1.37053i	−0.00510045	+	0.0572545i
$574$	−14.8073	−	15.9924i	−0.618044	−	0.667511i
$575$	8.93904			0.372784
$576$	−9.53271	+	22.0256i	−0.397196	+	0.917734i
$577$	34.5776			1.43948			0.719742	−	0.694241i	$-0.244260\pi$
$577$	34.5776			1.43948			0.719742	+	0.694241i	$0.244260\pi$
$578$	9.85714	+	10.6461i	0.410003	+	0.442819i
$579$	−1.62022	+	18.1875i	−0.0673339	+	0.755849i
$580$	−0.179095	+	2.32372i	−0.00743650	+	0.0964871i
$581$	15.1238			0.627442
$582$	23.7185	−	18.3355i	0.983162	−	0.760030i
$583$			63.0747i			2.61229i
$584$	−6.79059	+	5.38007i	−0.280997	+	0.222629i
$585$	−2.24448	+	12.4976i	−0.0927978	+	0.516712i
$586$	−9.73812	−	10.5175i	−0.402278	−	0.434476i
$587$		−	15.2181i		−	0.628116i	−0.949404	−	0.314058i	$-0.898311\pi$
$587$		−	15.2181i		−	0.628116i	0.949404	−	0.314058i	$-0.101689\pi$
$588$	4.94820	+	0.827858i	0.204060	+	0.0341403i
$589$			4.48507i			0.184804i
$590$	28.7035	−	26.5764i	1.18171	−	1.09413i
$591$	−1.58987	+	17.8469i	−0.0653986	+	0.734124i
$592$	−5.37901	+	34.6886i	−0.221076	+	1.42569i
$593$		−	4.83383i		−	0.198502i	−0.995062	−	0.0992509i	$-0.968355\pi$
$593$		−	4.83383i		−	0.198502i	0.995062	−	0.0992509i	$-0.0316446\pi$
$594$	−16.4110	−	31.4925i	−0.673350	−	1.29215i
$595$	−24.2700			−0.994973
$596$	−3.55578	+	46.1356i	−0.145651	+	1.88979i
$597$	−19.3071	−	1.71995i	−0.790185	−	0.0703927i
$598$	−17.9646	+	16.6333i	−0.734625	+	0.680185i
$599$	−42.3775			−1.73150			−0.865748	−	0.500480i	$-0.833157\pi$
$599$	−42.3775			−1.73150			−0.865748	+	0.500480i	$0.833157\pi$
$600$	2.97940	+	4.53596i	0.121633	+	0.185180i
$601$	−6.13637			−0.250308			−0.125154	−	0.992137i	$-0.539942\pi$
$601$	−6.13637			−0.250308			−0.125154	+	0.992137i	$0.539942\pi$
$602$	3.32706	−	3.08050i	0.135601	−	0.125552i
$603$	−16.7881	−	3.01503i	−0.683666	−	0.122782i
$604$	−11.2305	−	0.865561i	−0.456962	−	0.0352192i
$605$	24.3722			0.990873
$606$	3.38326	−	2.61542i	0.137436	−	0.106244i
$607$		−	40.2074i		−	1.63197i	−0.578074	−	0.815985i	$-0.696195\pi$
$607$		−	40.2074i		−	1.63197i	0.578074	−	0.815985i	$-0.303805\pi$
$608$	3.16180	+	4.69074i	0.128228	+	0.190235i
$609$	2.40103	+	0.213893i	0.0972948	+	0.00866739i
$610$	20.7915	−	19.2507i	0.841823	−	0.779439i
$611$			11.9020i			0.481504i
$612$	30.3162	+	7.89034i	1.22546	+	0.318948i
$613$			41.5016i			1.67623i	0.545491	+	0.838117i	$0.316343\pi$
$613$			41.5016i			1.67623i	−0.545491	+	0.838117i	$0.683657\pi$
$614$	−24.9981	−	26.9989i	−1.00884	−	1.08959i
$615$	−22.2622	−	1.98320i	−0.897697	−	0.0799702i
$616$	−25.2434	+	19.9999i	−1.01709	+	0.805819i
$617$		−	43.6944i		−	1.75907i	−0.475834	−	0.879535i	$-0.657854\pi$
$617$		−	43.6944i		−	1.75907i	0.475834	−	0.879535i	$-0.342146\pi$
$618$	19.6723	+	25.4477i	0.791336	+	1.02366i
$619$	−7.56093			−0.303900			−0.151950	−	0.988388i	$-0.548555\pi$
$619$	−7.56093			−0.303900			−0.151950	+	0.988388i	$0.548555\pi$
$620$	17.6446	+	1.35991i	0.708626	+	0.0546155i
$621$	11.0444	−	40.4491i	0.443197	−	1.62317i
$622$	−23.6983	−	25.5951i	−0.950215	−	1.02627i
$623$	−15.9725			−0.639924
$624$	−14.4279	−	3.57191i	−0.577578	−	0.142991i
$625$	−18.2340			−0.729360
$626$	−22.7743	−	24.5972i	−0.910246	−	0.983100i
$627$	−8.33723	−	0.742712i	−0.332957	−	0.0296611i
$628$	9.39697	+	0.724247i	0.374980	+	0.0289006i
$629$	45.8187			1.82691
$630$	−16.6120	+	10.6300i	−0.661838	+	0.423508i
$631$			36.6940i			1.46077i	0.683038	+	0.730383i	$0.260658\pi$
$631$			36.6940i			1.46077i	−0.683038	+	0.730383i	$0.739342\pi$
$632$	5.29454	+	6.68263i	0.210605	+	0.265821i
$633$	−0.911549	+	10.2325i	−0.0362308	+	0.406705i
$634$	23.2756	+	25.1386i	0.924393	+	0.998380i
$635$			21.8174i			0.865797i
$636$	−44.5937	−	7.46075i	−1.76826	−	0.295838i
$637$			3.10707i			0.123106i
$638$	2.96206	−	2.74256i	0.117269	−	0.108579i
$639$	10.5559	+	1.89576i	0.417585	+	0.0749953i
$640$	19.4124	−	11.0165i	0.767344	−	0.435465i
$641$		−	17.5329i		−	0.692508i	−0.938141	−	0.346254i	$-0.887454\pi$
$641$		−	17.5329i		−	0.692508i	0.938141	−	0.346254i	$-0.112546\pi$
$642$	14.9679	+	19.3623i	0.590737	+	0.764167i
$643$	−42.2395			−1.66576			−0.832882	−	0.553451i	$-0.813311\pi$
$643$	−42.2395			−1.66576			−0.832882	+	0.553451i	$0.813311\pi$
$644$	−37.9139	−	2.92212i	−1.49402	−	0.115148i
$645$	0.412583	−	4.63141i	0.0162455	−	0.182361i
$646$	5.41793	−	5.01642i	0.213165	−	0.197368i
$647$	46.4035			1.82431			0.912156	−	0.409844i	$-0.134417\pi$
$647$	46.4035			1.82431			0.912156	+	0.409844i	$0.134417\pi$
$648$	24.2063	−	7.87746i	0.950914	−	0.309456i
$649$	−67.7544			−2.65959
$650$	−2.46619	+	2.28342i	−0.0967317	+	0.0895633i
$651$	1.62415	−	18.2317i	0.0636555	−	0.714557i
$652$	3.35497	−	43.5301i	0.131391	−	1.70477i
$653$	21.8338			0.854422			0.427211	−	0.904152i	$-0.359496\pi$
$653$	21.8338			0.854422			0.427211	+	0.904152i	$0.359496\pi$
$654$	6.98413	+	9.03454i	0.273101	+	0.353279i
$655$		−	10.7747i		−	0.421002i
$656$	4.00904	−	25.8538i	0.156527	−	1.00942i
$657$	9.04440	+	1.62431i	0.352855	+	0.0633703i
$658$	−13.5647	+	12.5595i	−0.528809	+	0.489620i
$659$		−	6.39325i		−	0.249046i	−0.992217	−	0.124523i	$-0.960260\pi$
$659$		−	6.39325i		−	0.249046i	0.992217	−	0.124523i	$-0.0397400\pi$
$660$	−5.44981	+	32.5741i	−0.212134	+	1.26795i
$661$		−	12.6013i		−	0.490136i	−0.969506	−	0.245068i	$-0.921190\pi$
$661$		−	12.6013i		−	0.490136i	0.969506	−	0.245068i	$-0.0788102\pi$
$662$	18.6691	+	20.1633i	0.725595	+	0.783671i
$663$	−1.72147	+	19.3241i	−0.0668562	+	0.750487i
$664$	11.2742	+	14.2300i	0.437522	+	0.552230i
$665$			4.64850i			0.180261i
$666$	31.3613	−	20.0680i	1.21523	−	0.777619i
$667$	4.76630			0.184552
$668$	0.118682	−	1.53987i	0.00459194	−	0.0595795i
$669$	5.96630	+	0.531501i	0.230671	+	0.0205490i
$670$	10.7773	+	11.6399i	0.416365	+	0.449690i
$671$	−49.0781			−1.89464
$672$	−11.1540	−	20.2127i	−0.430275	−	0.779722i
$673$	18.0854			0.697141			0.348571	−	0.937282i	$-0.386667\pi$
$673$	18.0854			0.697141			0.348571	+	0.937282i	$0.386667\pi$
$674$	−3.40953	−	3.68242i	−0.131330	−	0.141842i
$675$	1.51618	−	5.55287i	0.0583580	−	0.213730i
$676$	−1.29060	+	16.7452i	−0.0496383	+	0.644048i
$677$	−49.8380			−1.91543			−0.957715	−	0.287717i	$-0.907104\pi$
$677$	−49.8380			−1.91543			−0.957715	+	0.287717i	$0.907104\pi$
$678$	23.1615	+	29.9613i	0.889512	+	1.15066i
$679$			28.8376i			1.10669i
$680$	−18.0922	−	22.8356i	−0.693806	−	0.875704i
$681$	−24.6968	−	2.20008i	−0.946382	−	0.0843073i
$682$	−20.8250	−	22.4918i	−0.797430	−	0.861254i
$683$		−	13.6776i		−	0.523359i	−0.965155	−	0.261680i	$-0.915724\pi$
$683$		−	13.6776i		−	0.523359i	0.965155	−	0.261680i	$-0.0842764\pi$
$684$	1.51126	−	5.80656i	0.0577845	−	0.222019i
$685$			2.35783i			0.0900881i
$686$	−20.6566	+	19.1258i	−0.788672	+	0.730226i
$687$	−23.2724	−	2.07319i	−0.887896	−	0.0790971i
$688$	5.37861	+	0.834039i	0.205058	+	0.0317974i
$689$		−	28.0012i		−	1.06676i
$690$	−30.8519	+	23.8499i	−1.17451	+	0.907952i
$691$	14.8089			0.563357			0.281679	−	0.959509i	$-0.409109\pi$
$691$	14.8089			0.563357			0.281679	+	0.959509i	$0.409109\pi$
$692$	0.406246	−	5.27096i	0.0154431	−	0.200372i
$693$	33.6217	+	6.03822i	1.27718	+	0.229373i
$694$	−20.0405	+	18.5554i	−0.760727	+	0.704352i
$695$	9.50737			0.360635
$696$	1.58862	+	2.41858i	0.0602163	+	0.0916759i
$697$	−34.1492			−1.29349
$698$	14.4331	−	13.3635i	0.546301	−	0.505817i
$699$	24.2587	+	2.16106i	0.917548	+	0.0817386i
$700$	−5.20485	−	0.401150i	−0.196725	−	0.0151620i
$701$	35.9252			1.35688			0.678438	−	0.734658i	$-0.262657\pi$
$701$	35.9252			1.35688			0.678438	+	0.734658i	$0.262657\pi$
$702$	7.28544	+	13.9807i	0.274971	+	0.527668i
$703$		−	8.77578i		−	0.330985i
$704$	−37.6357	−	8.84237i	−1.41845	−	0.333260i
$705$	−1.68214	+	18.8827i	−0.0633532	+	0.711164i
$706$	18.6145	−	17.2350i	0.700565	−	0.648649i
$707$			4.11347i			0.154703i
$708$	8.01428	−	47.9022i	0.301195	−	1.80028i
$709$			31.3446i			1.17717i	0.808435	+	0.588585i	$0.200315\pi$
$709$			31.3446i			1.17717i	−0.808435	+	0.588585i	$0.799685\pi$
$710$	−6.77648	−	7.31885i	−0.254317	−	0.274672i
$711$	1.59848	−	8.90061i	0.0599479	−	0.333799i
$712$	−11.9068	−	15.0285i	−0.446226	−	0.563216i
$713$		−	36.1918i		−	1.35539i
$714$	−23.8403	+	18.4297i	−0.892201	+	0.689713i
$715$	−20.4539			−0.764932
$716$	−27.5160	−	2.12073i	−1.02832	−	0.0792552i
$717$	1.68713	−	18.9387i	0.0630070	−	0.707278i
$718$	−30.7470	−	33.2080i	−1.14747	−	1.23931i
$719$	33.9669			1.26675			0.633377	−	0.773844i	$-0.281668\pi$
$719$	33.9669			1.26675			0.633377	+	0.773844i	$0.281668\pi$
$720$	−22.3852	−	7.70602i	−0.834248	−	0.287186i
$721$	−30.9401			−1.15227
$722$	−0.960810	−	1.03771i	−0.0357576	−	0.0386196i
$723$	−1.89888	+	21.3157i	−0.0706202	+	0.792739i
$724$	−24.7010	−	1.90377i	−0.918007	−	0.0707530i
$725$	0.654320			0.0243008
$726$	23.9407	−	18.5073i	0.888525	−	0.686871i
$727$			4.72559i			0.175263i	0.996153	+	0.0876313i	$0.0279297\pi$
$727$			4.72559i			0.175263i	−0.996153	+	0.0876313i	$0.972070\pi$
$728$	11.2065	−	8.87870i	0.415340	−	0.329067i
$729$	−23.2534	−	13.7214i	−0.861238	−	0.508202i
$730$	−5.80615	−	6.27086i	−0.214895	−	0.232095i
$731$		−	7.10438i		−	0.262765i
$732$	5.80517	−	34.6981i	0.214565	−	1.28248i
$733$			32.6808i			1.20709i	0.797328	+	0.603546i	$0.206246\pi$
$733$			32.6808i			1.20709i	−0.797328	+	0.603546i	$0.793754\pi$
$734$	14.9010	−	13.7967i	0.550005	−	0.509246i
$735$	−0.439130	+	4.92941i	−0.0161976	+	0.181824i
$736$	−25.5138	−	37.8514i	−0.940451	−	1.39522i
$737$		−	27.4759i		−	1.01209i
$738$	−23.3740	+	14.9569i	−0.860408	+	0.550572i
$739$	36.5392			1.34412			0.672059	−	0.740498i	$-0.265410\pi$
$739$	36.5392			1.34412			0.672059	+	0.740498i	$0.265410\pi$
$740$	−34.5246	−	2.66090i	−1.26915	−	0.0978165i
$741$	3.70121	+	0.329718i	0.135967	+	0.0121125i
$742$	31.9130	−	29.5481i	1.17156	−	1.08474i
$743$	20.4413			0.749917			0.374958	−	0.927042i	$-0.377657\pi$
$743$	20.4413			0.749917			0.374958	+	0.927042i	$0.377657\pi$
$744$	18.3649	−	12.0628i	0.673290	−	0.442244i
$745$	−45.6448			−1.67230
$746$	23.2239	−	21.5028i	0.850286	−	0.787274i
$747$	3.40381	−	18.9529i	0.124539	−	0.693450i
$748$	−3.87773	+	50.3128i	−0.141784	+	1.83962i
$749$	−23.5412			−0.860177
$750$	−23.3520	+	18.0522i	−0.852693	+	0.659172i
$751$			16.0510i			0.585709i	0.956157	+	0.292855i	$0.0946052\pi$
$751$			16.0510i			0.585709i	−0.956157	+	0.292855i	$0.905395\pi$
$752$	−21.9291	−	3.40046i	−0.799673	−	0.124002i
$753$	−5.79400	−	0.516151i	−0.211145	−	0.0188096i
$754$	−1.31497	+	1.21752i	−0.0478884	+	0.0443395i
$755$		−	11.1110i		−	0.404371i
$756$	−8.24593	+	23.0563i	−0.299901	+	0.838548i
$757$			11.7433i			0.426817i	0.976963	+	0.213408i	$0.0684565\pi$
$757$			11.7433i			0.426817i	−0.976963	+	0.213408i	$0.931543\pi$
$758$	−26.4832	−	28.6028i	−0.961911	−	1.03890i
$759$	67.2764	+	5.99324i	2.44198	+	0.217541i
$760$	−4.37376	+	3.46526i	−0.158653	+	0.125698i
$761$			35.7369i			1.29546i	0.761870	+	0.647730i	$0.224282\pi$
$761$			35.7369i			1.29546i	−0.761870	+	0.647730i	$0.775718\pi$
$762$	16.5673	+	21.4311i	0.600169	+	0.776368i
$763$	−10.9845			−0.397664
$764$	0.122092	−	1.58412i	0.00441712	−	0.0573113i
$765$	−5.46227	+	30.4147i	−0.197489	+	1.09965i
$766$	33.0860	+	35.7342i	1.19545	+	1.29113i
$767$	30.0787			1.08608
$768$	10.7033	−	25.5625i	0.386221	−	0.922406i
$769$	40.1108			1.44643			0.723216	−	0.690622i	$-0.242663\pi$
$769$	40.1108			1.44643			0.723216	+	0.690622i	$0.242663\pi$
$770$	−21.5838	−	23.3113i	−0.777827	−	0.840083i
$771$	10.2432	+	0.912502i	0.368899	+	0.0328630i
$772$	1.62022	−	21.0220i	0.0583128	−	0.756598i
$773$	−23.0364			−0.828561			−0.414280	−	0.910149i	$-0.635967\pi$
$773$	−23.0364			−0.828561			−0.414280	+	0.910149i	$0.635967\pi$
$774$	−3.11163	−	4.86271i	−0.111845	−	0.174786i
$775$		−	4.96843i		−	0.178471i
$776$	−27.1332	+	21.4972i	−0.974026	+	0.771704i
$777$	−3.17792	+	35.6734i	−0.114007	+	1.27977i
$778$	9.18231	+	9.91724i	0.329202	+	0.355550i
$779$			6.54069i			0.234345i
$780$	2.41937	−	14.4609i	0.0866275	−	0.517782i
$781$			17.2761i			0.618187i
$782$	−43.7194	+	40.4795i	−1.56340	+	1.44754i
$783$	0.808430	−	2.96079i	0.0288909	−	0.105810i
$784$	−5.72468	−	0.887704i	−0.204453	−	0.0317037i
$785$			9.29701i			0.331824i
$786$	−8.18187	−	10.5839i	−0.291838	−	0.377516i
$787$	28.5826			1.01886			0.509430	−	0.860512i	$-0.329856\pi$
$787$	28.5826			1.01886			0.509430	+	0.860512i	$0.329856\pi$
$788$	1.58987	−	20.6283i	0.0566368	−	0.734852i
$789$	3.23391	−	36.3018i	0.115130	−	1.29238i
$790$	−6.17117	+	5.71384i	−0.219560	+	0.203289i
$791$	−36.4278			−1.29522
$792$	19.3822	+	36.1358i	0.688716	+	1.28403i
$793$	21.7876			0.773700
$794$	−18.3459	+	16.9864i	−0.651073	+	0.602824i
$795$	3.95749	−	44.4243i	0.140358	−	1.57557i
$796$	22.3160	+	1.71995i	0.790969	+	0.0609619i
$797$	−4.29989			−0.152310			−0.0761549	−	0.997096i	$-0.524264\pi$
$797$	−4.29989			−0.152310			−0.0761549	+	0.997096i	$0.524264\pi$
$798$	3.52989	+	4.56620i	0.124957	+	0.161642i
$799$			28.9653i			1.02472i
$800$	−3.50255	−	5.19627i	−0.123834	−	0.183716i
$801$	−3.59481	+	20.0164i	−0.127016	+	0.707246i
$802$	−35.6236	+	32.9837i	−1.25791	+	1.16469i
$803$			14.8023i			0.522362i
$804$	19.4254	+	3.24997i	0.685082	+	0.114618i
$805$		−	37.5106i		−	1.32208i
$806$	9.24498	+	9.98493i	0.325641	+	0.351704i
$807$	1.60613	−	18.0295i	0.0565386	−	0.634667i
$808$	−3.87035	+	3.06641i	−0.136159	+	0.107876i
$809$			15.9007i			0.559038i	0.960140	+	0.279519i	$0.0901750\pi$
$809$			15.9007i			0.559038i	−0.960140	+	0.279519i	$0.909825\pi$
$810$	9.58253	+	23.2103i	0.336696	+	0.815525i
$811$	31.8029			1.11675			0.558376	−	0.829588i	$-0.311425\pi$
$811$	31.8029			1.11675			0.558376	+	0.829588i	$0.311425\pi$
$812$	−2.77523	−	0.213893i	−0.0973913	−	0.00750618i
$813$	−55.0104	−	4.90054i	−1.92930	−	0.171869i
$814$	40.7475	+	44.0089i	1.42820	+	1.54251i
$815$	43.0670			1.50857
$816$	−35.1124	−	8.69275i	−1.22918	−	0.304307i
$817$	−1.36072			−0.0476056
$818$	20.3995	+	22.0322i	0.713252	+	0.770339i
$819$	−14.9259	−	2.68059i	−0.521554	−	0.0936674i
$820$	25.7316	+	1.98320i	0.898587	+	0.0692562i
$821$	−12.9857			−0.453204			−0.226602	−	0.973987i	$-0.572762\pi$
$821$	−12.9857			−0.453204			−0.226602	+	0.973987i	$0.572762\pi$
$822$	1.79044	+	2.31609i	0.0624489	+	0.0807828i
$823$		−	27.8018i		−	0.969108i	−0.874761	−	0.484554i	$-0.838982\pi$
$823$		−	27.8018i		−	0.969108i	0.874761	−	0.484554i	$-0.161018\pi$
$824$	−23.0645	−	29.1115i	−0.803491	−	1.01415i
$825$	9.23574	+	0.822755i	0.321547	+	0.0286447i
$826$	31.7403	+	34.2808i	1.10439	+	1.19278i
$827$		−	10.5836i		−	0.368028i	−0.982924	−	0.184014i	$-0.941091\pi$
$827$		−	10.5836i		−	0.368028i	0.982924	−	0.184014i	$-0.0589092\pi$
$828$	−12.1949	+	46.8554i	−0.423804	+	1.62834i
$829$		−	4.56921i		−	0.158695i	−0.996847	−	0.0793477i	$-0.974716\pi$
$829$		−	4.56921i		−	0.158695i	0.996847	−	0.0793477i	$-0.0252837\pi$
$830$	−13.1408	+	12.1670i	−0.456125	+	0.422323i
$831$	33.3029	+	2.96675i	1.15526	+	0.102915i
$832$	16.7079	+	3.92546i	0.579242	+	0.136091i
$833$			7.56150i			0.261990i
$834$	9.33905	−	7.21952i	0.323385	−	0.249992i
$835$	1.52349			0.0527227
$836$	9.63655	+	0.742712i	0.333287	+	0.0256872i
$837$	−22.4821	−	6.13863i	−0.777096	−	0.212182i
$838$	−17.3377	+	16.0528i	−0.598919	+	0.554535i
$839$	32.2093			1.11199			0.555994	−	0.831187i	$-0.312338\pi$
$839$	32.2093			1.11199			0.555994	+	0.831187i	$0.312338\pi$
$840$	19.0341	−	12.5024i	0.656739	−	0.431372i
$841$	−28.6511			−0.987970
$842$	3.31231	−	3.06684i	0.114150	−	0.105690i
$843$	6.81044	+	0.606700i	0.234564	+	0.0208959i
$844$	0.911549	−	11.8272i	0.0313768	−	0.407108i
$845$	−16.5671			−0.569926
$846$	12.6864	+	19.8258i	0.436168	+	0.681624i
$847$			29.1079i			1.00016i
$848$	51.5915	+	8.00008i	1.77166	+	0.274724i
$849$	−2.58551	+	29.0233i	−0.0887344	+	0.996078i
$850$	−6.00182	+	5.55705i	−0.205861	+	0.190605i
$851$			70.8152i			2.42752i
$852$	−12.2142	−	2.04349i	−0.418450	−	0.0700087i
$853$		−	32.0084i		−	1.09595i	−0.836496	−	0.547974i	$-0.815399\pi$
$853$		−	32.0084i		−	1.09595i	0.836496	−	0.547974i	$-0.184601\pi$
$854$	22.9912	+	24.8314i	0.786742	+	0.849712i
$855$	5.82542	+	1.04620i	0.199225	+	0.0357794i
$856$	−17.5489	−	22.1499i	−0.599811	−	0.757066i
$857$			23.9200i			0.817092i	0.912738	+	0.408546i	$0.133964\pi$
$857$			23.9200i			0.817092i	−0.912738	+	0.408546i	$0.866036\pi$
$858$	−20.0918	+	15.5319i	−0.685922	+	0.530250i
$859$	42.0614			1.43512			0.717559	−	0.696498i	$-0.245259\pi$
$859$	42.0614			1.43512			0.717559	+	0.696498i	$0.245259\pi$
$860$	−0.412583	+	5.35319i	−0.0140690	+	0.182542i
$861$	2.36854	−	26.5878i	0.0807196	−	0.906109i
$862$	−16.8006	−	18.1453i	−0.572232	−	0.618032i
$863$	29.7612			1.01308			0.506542	−	0.862215i	$-0.330924\pi$
$863$	29.7612			1.01308			0.506542	+	0.862215i	$0.330924\pi$
$864$	−27.8406	+	9.42887i	−0.947155	+	0.320777i
$865$	5.21489			0.177312
$866$	4.83370	+	5.22058i	0.164256	+	0.177403i
$867$	−1.57673	+	17.6994i	−0.0535484	+	0.601102i
$868$	−1.62415	+	21.0731i	−0.0551273	+	0.715266i
$869$	14.5670			0.494151
$870$	−2.25830	+	1.74577i	−0.0765634	+	0.0591871i
$871$			12.1976i			0.413299i
$872$	−8.18844	−	10.3353i	−0.277296	−	0.349996i
$873$	36.1388	+	6.49026i	1.22311	+	0.219662i
$874$	7.75315	+	8.37370i	0.262254	+	0.283245i
$875$		−	28.3920i		−	0.959825i
$876$	−10.4652	−	1.75088i	−0.353586	−	0.0591567i
$877$		−	48.6451i		−	1.64263i	−0.570476	−	0.821314i	$-0.693241\pi$
$877$		−	48.6451i		−	1.64263i	0.570476	−	0.821314i	$-0.306759\pi$
$878$	−1.29028	+	1.19466i	−0.0435449	+	0.0403179i
$879$	1.55769	−	17.4857i	0.0525395	−	0.589776i
$880$	5.84378	−	37.6858i	0.196994	−	1.27039i
$881$			26.7539i			0.901362i	0.892685	+	0.450681i	$0.148819\pi$
$881$			26.7539i			0.901362i	−0.892685	+	0.450681i	$0.851181\pi$
$882$	3.31184	+	5.17559i	0.111515	+	0.174271i
$883$	17.6253			0.593139			0.296569	−	0.955011i	$-0.404157\pi$
$883$	17.6253			0.593139			0.296569	+	0.955011i	$0.404157\pi$
$884$	1.72147	−	22.3357i	0.0578992	−	0.751231i
$885$	47.7203	+	4.25111i	1.60410	+	0.142899i
$886$	−7.56001	+	6.99976i	−0.253983	+	0.235162i
$887$	25.2876			0.849075			0.424538	−	0.905410i	$-0.360437\pi$
$887$	25.2876			0.849075			0.424538	+	0.905410i	$0.360437\pi$
$888$	−35.9340	+	23.6029i	−1.20587	+	0.792060i
$889$	−26.0566			−0.873910
$890$	13.8782	−	12.8498i	0.465200	−	0.430725i
$891$	15.1340	−	40.7751i	0.507007	−	1.36602i
$892$	−6.89612	−	0.531501i	−0.230899	−	0.0177960i
$893$	5.54780			0.185650
$894$	−44.8367	+	34.6609i	−1.49956	+	1.15923i
$895$		−	27.2233i		−	0.909975i
$896$	13.1570	+	23.1843i	0.439545	+	0.774534i
$897$	−29.8665	−	2.66062i	−0.997213	−	0.0888355i
$898$	36.3882	−	33.6916i	1.21429	−	1.12430i
$899$		−	2.64917i		−	0.0883548i
$900$	−1.67413	+	6.43233i	−0.0558043	+	0.214411i
$901$		−	68.1450i		−	2.27024i
$902$	−30.3696	−	32.8003i	−1.01120	−	1.09213i
$903$	5.53131	+	0.492750i	0.184070	+	0.0163977i
$904$	−27.1554	−	34.2749i	−0.903175	−	1.13996i
$905$		−	24.4383i		−	0.812356i
$906$	−8.43727	−	10.9143i	−0.280310	−	0.362604i
$907$	−51.6403			−1.71469			−0.857344	−	0.514744i	$-0.827887\pi$
$907$	−51.6403			−1.71469			−0.857344	+	0.514744i	$0.827887\pi$
$908$	28.5457	+	2.20008i	0.947321	+	0.0730123i
$909$	5.15493	+	0.925788i	0.170978	+	0.0307064i
$910$	9.58186	+	10.3488i	0.317636	+	0.343058i
$911$	−37.8190			−1.25300			−0.626500	−	0.779421i	$-0.715513\pi$
$911$	−37.8190			−1.25300			−0.626500	+	0.779421i	$0.715513\pi$
$912$	−1.66495	+	6.72517i	−0.0551320	+	0.222693i
$913$	31.0188			1.02657
$914$	2.87199	+	3.10186i	0.0949970	+	0.102600i
$915$	34.5663	+	3.07930i	1.14273	+	0.101799i
$916$	26.8993	+	2.07319i	0.888776	+	0.0685001i
$917$	12.8682			0.424947
$918$	17.7302	+	34.0241i	0.585183	+	1.12296i
$919$		−	20.0850i		−	0.662543i	−0.943535	−	0.331272i	$-0.892522\pi$
$919$		−	20.0850i		−	0.662543i	0.943535	−	0.331272i	$-0.107478\pi$
$920$	35.2936	−	27.9625i	1.16360	−	0.921897i
$921$	3.99864	−	44.8862i	0.131760	−	1.47905i
$922$	21.1248	+	22.8155i	0.695707	+	0.751390i
$923$		−	7.66949i		−	0.252444i
$924$	−38.9034	−	6.50873i	−1.27983	−	0.214122i
$925$			9.72156i			0.319643i
$926$	14.7837	−	13.6881i	0.485823	−	0.449820i
$927$	−6.96346	+	38.7736i	−0.228710	+	1.27349i
$928$	−1.86756	−	2.77065i	−0.0613056	−	0.0909510i
$929$		−	18.8526i		−	0.618533i	−0.950975	−	0.309267i	$-0.899916\pi$
$929$		−	18.8526i		−	0.618533i	0.950975	−	0.309267i	$-0.100084\pi$
$930$	13.2561	+	17.1479i	0.434685	+	0.562301i
$931$	1.44828			0.0474653
$932$	−28.0393	−	2.16106i	−0.918457	−	0.0707877i
$933$	3.79073	−	42.5524i	0.124103	−	1.39310i
$934$	7.39568	−	6.84761i	0.241994	−	0.224061i
$935$	−49.7775			−1.62790
$936$	−8.60447	−	16.0420i	−0.281246	−	0.524350i
$937$	23.1082			0.754911			0.377456	−	0.926028i	$-0.376799\pi$
$937$	23.1082			0.754911			0.377456	+	0.926028i	$0.376799\pi$
$938$	−13.9016	+	12.8714i	−0.453904	+	0.420266i
$939$	3.64294	−	40.8934i	0.118883	−	1.33450i
$940$	1.68214	−	21.8255i	0.0548655	−	0.711869i
$941$	49.7606			1.62215			0.811075	−	0.584942i	$-0.198883\pi$
$941$	49.7606			1.62215			0.811075	+	0.584942i	$0.198883\pi$
$942$	7.05978	+	9.13241i	0.230020	+	0.297550i
$943$		−	52.7794i		−	1.71873i
$944$	−8.59363	+	55.4192i	−0.279699	+	1.80374i
$945$	−23.3013	−	6.36232i	−0.757993	−	0.206966i
$946$	6.82376	−	6.31807i	0.221860	−	0.205418i
$947$			35.0676i			1.13954i	0.821803	+	0.569772i	$0.192969\pi$
$947$			35.0676i			1.13954i	−0.821803	+	0.569772i	$0.807031\pi$
$948$	−1.72304	+	10.2988i	−0.0559618	+	0.334490i
$949$		−	6.57129i		−	0.213313i
$950$	1.06436	+	1.14955i	0.0345323	+	0.0372962i
$951$	−3.72312	+	41.7934i	−0.120730	+	1.35525i
$952$	27.2726	−	21.6076i	0.883910	−	0.700307i
$953$			23.3921i			0.757745i	0.925449	+	0.378872i	$0.123688\pi$
$953$			23.3921i			0.757745i	−0.925449	+	0.378872i	$0.876312\pi$
$954$	−29.8467	−	46.6430i	−0.966321	−	1.51012i
$955$	1.56726			0.0507155
$956$	−1.68713	+	21.8902i	−0.0545657	+	0.707979i
$957$	4.92450	+	0.438693i	0.159186	+	0.0141809i
$958$	−1.71315	−	1.85027i	−0.0553494	−	0.0597795i
$959$	−2.81597			−0.0909323
$960$	25.9525	+	8.58917i	0.837614	+	0.277214i
$961$	10.8841			0.351101
$962$	−18.0893	−	19.5372i	−0.583223	−	0.629904i
$963$	−5.29824	+	29.5014i	−0.170733	+	0.950669i
$964$	1.89888	−	24.6376i	0.0611589	−	0.793525i
$965$	20.7984			0.669523
$966$	−28.4841	−	36.8465i	−0.916460	−	1.18552i
$967$		−	17.4787i		−	0.562076i	−0.959697	−	0.281038i	$-0.909321\pi$
$967$		−	17.4787i		−	0.562076i	0.959697	−	0.281038i	$-0.0906786\pi$
$968$	−27.3875	+	21.6987i	−0.880268	+	0.697421i
$969$	9.00743	+	0.802416i	0.289360	+	0.0257773i
$970$	−23.1997	−	25.0565i	−0.744897	−	0.804517i
$971$		−	13.4578i		−	0.431882i	−0.976406	−	0.215941i	$-0.930718\pi$
$971$		−	13.4578i		−	0.431882i	0.976406	−	0.215941i	$-0.0692819\pi$
$972$	27.0378	+	15.5227i	0.867239	+	0.497892i
$973$			11.3547i			0.364015i
$974$	14.7573	−	13.6637i	0.472855	−	0.437814i
$975$	−4.10009	−	0.365252i	−0.131308	−	0.0116974i
$976$	−6.22482	+	40.1431i	−0.199252	+	1.28495i
$977$		−	16.8194i		−	0.538101i	−0.963126	−	0.269051i	$-0.913290\pi$
$977$		−	16.8194i		−	0.538101i	0.963126	−	0.269051i	$-0.0867099\pi$
$978$	42.3046	−	32.7034i	1.35275	−	1.04574i
$979$	−32.7594			−1.04700
$980$	0.439130	−	5.69763i	0.0140275	−	0.182004i
$981$	−2.47219	+	13.7655i	−0.0789310	+	0.439500i
$982$	−6.68679	+	6.19126i	−0.213384	+	0.197571i
$983$	21.2785			0.678678			0.339339	−	0.940664i	$-0.389797\pi$
$983$	21.2785			0.678678			0.339339	+	0.940664i	$0.389797\pi$
$984$	26.7820	−	17.5915i	0.853779	−	0.560796i
$985$	20.4088			0.650280
$986$	−3.20017	+	2.96302i	−0.101914	+	0.0943617i
$987$	−22.5517	−	2.00899i	−0.717828	−	0.0639469i
$988$	−4.27802	−	0.329718i	−0.136102	−	0.0104897i
$989$	10.9802			0.349150
$990$	−34.0711	+	21.8019i	−1.08285	+	0.692911i
$991$			25.4403i			0.808139i	0.914728	+	0.404069i	$0.132405\pi$
$991$			25.4403i			0.808139i	−0.914728	+	0.404069i	$0.867595\pi$
$992$	−21.0383	+	14.1809i	−0.667967	+	0.450244i
$993$	−2.98627	+	33.5220i	−0.0947664	+	1.06379i
$994$	8.74093	−	8.09317i	0.277246	−	0.256700i
$995$			22.0786i			0.699938i
$996$	−3.66904	+	21.9303i	−0.116258	+	0.694887i
$997$			44.9174i			1.42255i	0.702915	+	0.711274i	$0.251881\pi$
$997$			44.9174i			1.42255i	−0.702915	+	0.711274i	$0.748119\pi$
$998$	34.7094	+	37.4875i	1.09871	+	1.18664i
$999$	43.9900	+	12.0112i	1.39178	+	0.380019i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.j.e.419.5	✓	24
3.2	odd	2	inner	456.2.j.e.419.20	yes	24
4.3	odd	2		1824.2.j.d.1103.15		24
8.3	odd	2	inner	456.2.j.e.419.19	yes	24
8.5	even	2		1824.2.j.d.1103.16		24
12.11	even	2		1824.2.j.d.1103.14		24
24.5	odd	2		1824.2.j.d.1103.13		24
24.11	even	2	inner	456.2.j.e.419.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.j.e.419.5	✓	24	1.1	even	1	trivial
456.2.j.e.419.6	yes	24	24.11	even	2	inner
456.2.j.e.419.19	yes	24	8.3	odd	2	inner
456.2.j.e.419.20	yes	24	3.2	odd	2	inner
1824.2.j.d.1103.13		24	24.5	odd	2
1824.2.j.d.1103.14		24	12.11	even	2
1824.2.j.d.1103.15		24	4.3	odd	2
1824.2.j.d.1103.16		24	8.5	even	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)

\(f(q)\)	\(=\)	\(q+(-0.960810 - 1.03771i) q^{2} +(0.153689 - 1.72522i) q^{3} +(-0.153689 + 1.99409i) q^{4} -1.97287 q^{5} +(-1.93794 + 1.49812i) q^{6} -2.35621i q^{7} +(2.21695 - 1.75645i) q^{8} +(-2.95276 - 0.530294i) q^{9} +O(q^{10})\)	\(q+(-0.960810 - 1.03771i) q^{2} +(0.153689 - 1.72522i) q^{3} +(-0.153689 + 1.99409i) q^{4} -1.97287 q^{5} +(-1.93794 + 1.49812i) q^{6} -2.35621i q^{7} +(2.21695 - 1.75645i) q^{8} +(-2.95276 - 0.530294i) q^{9} +(1.89556 + 2.04727i) q^{10} -4.83256i q^{11} +(3.41661 + 0.571616i) q^{12} +2.14536i q^{13} +(-2.44507 + 2.26387i) q^{14} +(-0.303209 + 3.40364i) q^{15} +(-3.95276 - 0.612938i) q^{16} +5.22103i q^{17} +(2.28675 + 3.57362i) q^{18} +1.00000 q^{19} +(0.303209 - 3.93408i) q^{20} +(-4.06498 - 0.362124i) q^{21} +(-5.01481 + 4.64318i) q^{22} -8.06939 q^{23} +(-2.68954 - 4.09467i) q^{24} -1.10777 q^{25} +(2.22626 - 2.06128i) q^{26} +(-1.36868 + 5.01266i) q^{27} +(4.69849 + 0.362124i) q^{28} -0.590664 q^{29} +(3.82332 - 2.95561i) q^{30} +4.48507i q^{31} +(3.16180 + 4.69074i) q^{32} +(-8.33723 - 0.742712i) q^{33} +(5.41793 - 5.01642i) q^{34} +4.64850i q^{35} +(1.51126 - 5.80656i) q^{36} -8.77578i q^{37} +(-0.960810 - 1.03771i) q^{38} +(3.70121 + 0.329718i) q^{39} +(-4.37376 + 3.46526i) q^{40} +6.54069i q^{41} +(3.52989 + 4.56620i) q^{42} -1.36072 q^{43} +(9.63655 + 0.742712i) q^{44} +(5.82542 + 1.04620i) q^{45} +(7.75315 + 8.37370i) q^{46} +5.54780 q^{47} +(-1.66495 + 6.72517i) q^{48} +1.44828 q^{49} +(1.06436 + 1.14955i) q^{50} +(9.00743 + 0.802416i) q^{51} +(-4.27802 - 0.329718i) q^{52} -13.0520 q^{53} +(6.51673 - 3.39591i) q^{54} +9.53404i q^{55} +(-4.13857 - 5.22360i) q^{56} +(0.153689 - 1.72522i) q^{57} +(0.567516 + 0.612938i) q^{58} -14.0204i q^{59} +(-6.74055 - 1.12773i) q^{60} -10.1557i q^{61} +(4.65421 - 4.30930i) q^{62} +(-1.24948 + 6.95732i) q^{63} +(1.82975 - 7.78794i) q^{64} -4.23251i q^{65} +(7.23977 + 9.36524i) q^{66} +5.68558 q^{67} +(-10.4112 - 0.802416i) q^{68} +(-1.24018 + 13.9215i) q^{69} +(4.82380 - 4.46633i) q^{70} -3.57493 q^{71} +(-7.47756 + 4.01075i) q^{72} -3.06303 q^{73} +(-9.10673 + 8.43186i) q^{74} +(-0.170252 + 1.91115i) q^{75} +(-0.153689 + 1.99409i) q^{76} -11.3865 q^{77} +(-3.21400 - 4.15758i) q^{78} +3.01433i q^{79} +(7.79829 + 1.20925i) q^{80} +(8.43758 + 3.13166i) q^{81} +(6.78735 - 6.28436i) q^{82} +6.41871i q^{83} +(1.34685 - 8.05026i) q^{84} -10.3004i q^{85} +(1.30740 + 1.41204i) q^{86} +(-0.0907785 + 1.01902i) q^{87} +(-8.48817 - 10.7136i) q^{88} -6.77889i q^{89} +(-4.51146 - 7.05031i) q^{90} +5.05491 q^{91} +(1.24018 - 16.0911i) q^{92} +(7.73773 + 0.689307i) q^{93} +(-5.33038 - 5.75702i) q^{94} -1.97287 q^{95} +(8.57849 - 4.73388i) q^{96} -12.2390 q^{97} +(-1.39152 - 1.50289i) q^{98} +(-2.56268 + 14.2694i) 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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