LMFDB - Embedded newform 456.2.j.e.419.1

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			419.1
Character	$\chi$	$=$	456.419
Dual form			456.2.j.e.419.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34037 - 0.450999i) q^{2} +(-1.59320 + 0.679496i) q^{3} +(1.59320 + 1.20901i) q^{4} +2.84644 q^{5} +(2.44193 - 0.192246i) q^{6} -0.466225i q^{7} +(-1.59022 - 2.33906i) q^{8} +(2.07657 - 2.16515i) q^{9} +O(q^{10})$	\(q+(-1.34037 - 0.450999i) q^{2} +(-1.59320 + 0.679496i) q^{3} +(1.59320 + 1.20901i) q^{4} +2.84644 q^{5} +(2.44193 - 0.192246i) q^{6} -0.466225i q^{7} +(-1.59022 - 2.33906i) q^{8} +(2.07657 - 2.16515i) q^{9} +(-3.81529 - 1.28374i) q^{10} -4.27688i q^{11} +(-3.35981 - 0.843628i) q^{12} +4.00344i q^{13} +(-0.210267 + 0.624915i) q^{14} +(-4.53494 + 1.93414i) q^{15} +(1.07657 + 3.85240i) q^{16} -3.48404i q^{17} +(-3.75986 + 1.96557i) q^{18} +1.00000 q^{19} +(4.53494 + 3.44138i) q^{20} +(0.316798 + 0.742789i) q^{21} +(-1.92887 + 5.73261i) q^{22} -1.49782 q^{23} +(4.12292 + 2.64605i) q^{24} +3.10219 q^{25} +(1.80555 - 5.36611i) q^{26} +(-1.83719 + 4.86053i) q^{27} +(0.563672 - 0.742789i) q^{28} +8.54193 q^{29} +(6.95081 - 0.547217i) q^{30} -7.64656i q^{31} +(0.294423 - 5.64919i) q^{32} +(2.90612 + 6.81392i) q^{33} +(-1.57130 + 4.66992i) q^{34} -1.32708i q^{35} +(5.92608 - 0.938906i) q^{36} -0.360333i q^{37} +(-1.34037 - 0.450999i) q^{38} +(-2.72032 - 6.37829i) q^{39} +(-4.52645 - 6.65799i) q^{40} -3.88529i q^{41} +(-0.0896300 - 1.13849i) q^{42} +6.31001 q^{43} +(5.17081 - 6.81392i) q^{44} +(5.91082 - 6.16295i) q^{45} +(2.00764 + 0.675515i) q^{46} +3.96323 q^{47} +(-4.33288 - 5.40612i) q^{48} +6.78263 q^{49} +(-4.15810 - 1.39909i) q^{50} +(2.36739 + 5.55077i) q^{51} +(-4.84022 + 6.37829i) q^{52} +1.30160 q^{53} +(4.65461 - 5.68635i) q^{54} -12.1739i q^{55} +(-1.09053 + 0.741399i) q^{56} +(-1.59320 + 0.679496i) q^{57} +(-11.4494 - 3.85240i) q^{58} +3.00712i q^{59} +(-9.56347 - 2.40133i) q^{60} +2.20911i q^{61} +(-3.44859 + 10.2492i) q^{62} +(-1.00944 - 0.968149i) q^{63} +(-2.94241 + 7.43923i) q^{64} +11.3955i q^{65} +(-0.822214 - 10.4439i) q^{66} +11.7881 q^{67} +(4.21226 - 5.55077i) q^{68} +(2.38632 - 1.01776i) q^{69} +(-0.598511 + 1.77878i) q^{70} -6.80967 q^{71} +(-8.36661 - 1.41417i) q^{72} -1.40984 q^{73} +(-0.162510 + 0.482981i) q^{74} +(-4.94241 + 2.10793i) q^{75} +(1.59320 + 1.20901i) q^{76} -1.99399 q^{77} +(0.769648 + 9.77615i) q^{78} +14.6441i q^{79} +(3.06439 + 10.9656i) q^{80} +(-0.375707 - 8.99215i) q^{81} +(-1.75226 + 5.20773i) q^{82} +14.6883i q^{83} +(-0.393320 + 1.56642i) q^{84} -9.91710i q^{85} +(-8.45777 - 2.84581i) q^{86} +(-13.6090 + 5.80420i) q^{87} +(-10.0039 + 6.80117i) q^{88} -15.8556i q^{89} +(-10.7022 + 5.59487i) q^{90} +1.86651 q^{91} +(-2.38632 - 1.81088i) q^{92} +(5.19580 + 12.1825i) q^{93} +(-5.31221 - 1.78741i) q^{94} +2.84644 q^{95} +(3.36952 + 9.20034i) q^{96} -14.3334 q^{97} +(-9.09126 - 3.05896i) q^{98} +(-9.26006 - 8.88124i) 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 $

$2$	−1.34037	−	0.450999i	−0.947787	−	0.318904i
$2$	−1.34037	−	0.450999i	−0.947787	−	0.318904i
$3$	−1.59320	+	0.679496i	−0.919834	+	0.392307i
$3$	−1.59320	+	0.679496i	−0.919834	+	0.392307i
$4$	1.59320	+	1.20901i	0.796600	+	0.604507i
$5$	2.84644			1.27296			0.636482	−	0.771291i	$-0.280389\pi$
$5$	2.84644			1.27296			0.636482	+	0.771291i	$0.280389\pi$
$6$	2.44193	−	0.192246i	0.996915	−	0.0784842i
$7$		−	0.466225i		−	0.176216i	−0.996111	−	0.0881082i	$-0.971918\pi$
$7$		−	0.466225i		−	0.176216i	0.996111	−	0.0881082i	$-0.0280821\pi$
$8$	−1.59022	−	2.33906i	−0.562227	−	0.826983i
$9$	2.07657	−	2.16515i	0.692190	−	0.721715i
$10$	−3.81529	−	1.28374i	−1.20650	−	0.405954i
$11$		−	4.27688i		−	1.28953i	−0.764382	−	0.644764i	$-0.776956\pi$
$11$		−	4.27688i		−	1.28953i	0.764382	−	0.644764i	$-0.223044\pi$
$12$	−3.35981	−	0.843628i	−0.969892	−	0.243534i
$13$			4.00344i			1.11036i	0.831732	+	0.555178i	$0.187350\pi$
$13$			4.00344i			1.11036i	−0.831732	+	0.555178i	$0.812650\pi$
$14$	−0.210267	+	0.624915i	−0.0561962	+	0.167016i
$15$	−4.53494	+	1.93414i	−1.17092	+	0.499393i
$16$	1.07657	+	3.85240i	0.269143	+	0.963100i
$17$		−	3.48404i		−	0.845004i	−0.906362	−	0.422502i	$-0.861152\pi$
$17$		−	3.48404i		−	0.845004i	0.906362	−	0.422502i	$-0.138848\pi$
$18$	−3.75986	+	1.96557i	−0.886207	+	0.463289i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	4.53494	+	3.44138i	1.01404	+	0.769516i
$21$	0.316798	+	0.742789i	0.0691309	+	0.162090i
$22$	−1.92887	+	5.73261i	−0.411236	+	1.22220i
$23$	−1.49782			−0.312317			−0.156158	−	0.987732i	$-0.549911\pi$
$23$	−1.49782			−0.312317			−0.156158	+	0.987732i	$0.549911\pi$
$24$	4.12292	+	2.64605i	0.841587	+	0.540122i
$25$	3.10219			0.620439
$26$	1.80555	−	5.36611i	0.354097	−	1.05238i
$27$	−1.83719	+	4.86053i	−0.353566	+	0.935409i
$28$	0.563672	−	0.742789i	0.106524	−	0.140374i
$29$	8.54193			1.58620			0.793098	−	0.609094i	$-0.208467\pi$
$29$	8.54193			1.58620			0.793098	+	0.609094i	$0.208467\pi$
$30$	6.95081	−	0.547217i	1.26904	−	0.0999076i
$31$		−	7.64656i		−	1.37336i	−0.726959	−	0.686681i	$-0.759067\pi$
$31$		−	7.64656i		−	1.37336i	0.726959	−	0.686681i	$-0.240933\pi$
$32$	0.294423	−	5.64919i	0.0520471	−	0.998645i
$33$	2.90612	+	6.81392i	0.505891	+	1.18615i
$34$	−1.57130	+	4.66992i	−0.269476	+	0.800884i
$35$		−	1.32708i		−	0.224317i
$36$	5.92608	−	0.938906i	0.987680	−	0.156484i
$37$		−	0.360333i		−	0.0592385i	−0.999561	−	0.0296192i	$-0.990571\pi$
$37$		−	0.360333i		−	0.0592385i	0.999561	−	0.0296192i	$-0.00942947\pi$
$38$	−1.34037	−	0.450999i	−0.217437	−	0.0731617i
$39$	−2.72032	−	6.37829i	−0.435600	−	1.02134i
$40$	−4.52645	−	6.65799i	−0.715695	−	1.05272i
$41$		−	3.88529i		−	0.606780i	−0.952867	−	0.303390i	$-0.901882\pi$
$41$		−	3.88529i		−	0.606780i	0.952867	−	0.303390i	$-0.0981184\pi$
$42$	−0.0896300	−	1.13849i	−0.0138302	−	0.175673i
$43$	6.31001			0.962268			0.481134	−	0.876647i	$-0.340225\pi$
$43$	6.31001			0.962268			0.481134	+	0.876647i	$0.340225\pi$
$44$	5.17081	−	6.81392i	0.779528	−	1.02724i
$45$	5.91082	−	6.16295i	0.881134	−	0.918718i
$46$	2.00764	+	0.675515i	0.296010	+	0.0995992i
$47$	3.96323			0.578097			0.289048	−	0.957314i	$-0.406661\pi$
$47$	3.96323			0.578097			0.289048	+	0.957314i	$0.406661\pi$
$48$	−4.33288	−	5.40612i	−0.625398	−	0.780306i
$49$	6.78263			0.968948
$50$	−4.15810	−	1.39909i	−0.588044	−	0.197861i
$51$	2.36739	+	5.55077i	0.331501	+	0.777264i
$52$	−4.84022	+	6.37829i	−0.671218	+	0.884509i
$53$	1.30160			0.178788			0.0893940	−	0.995996i	$-0.471507\pi$
$53$	1.30160			0.178788			0.0893940	+	0.995996i	$0.471507\pi$
$54$	4.65461	−	5.68635i	0.633412	−	0.773815i
$55$		−	12.1739i		−	1.64152i
$56$	−1.09053	+	0.741399i	−0.145728	+	0.0990736i
$57$	−1.59320	+	0.679496i	−0.211024	+	0.0900014i
$58$	−11.4494	−	3.85240i	−1.50338	−	0.505845i
$59$			3.00712i			0.391494i	0.980654	+	0.195747i	$0.0627132\pi$
$59$			3.00712i			0.391494i	−0.980654	+	0.195747i	$0.937287\pi$
$60$	−9.56347	−	2.40133i	−1.23464	−	0.310011i
$61$			2.20911i			0.282848i	0.989949	+	0.141424i	$0.0451681\pi$
$61$			2.20911i			0.282848i	−0.989949	+	0.141424i	$0.954832\pi$
$62$	−3.44859	+	10.2492i	−0.437971	+	1.30165i
$63$	−1.00944	−	0.968149i	−0.127178	−	0.121975i
$64$	−2.94241	+	7.43923i	−0.367802	+	0.929904i
$65$			11.3955i			1.41344i
$66$	−0.822214	−	10.4439i	−0.101208	−	1.28555i
$67$	11.7881			1.44015			0.720073	−	0.693898i	$-0.244108\pi$
$67$	11.7881			1.44015			0.720073	+	0.693898i	$0.244108\pi$
$68$	4.21226	−	5.55077i	0.510811	−	0.673130i
$69$	2.38632	−	1.01776i	0.287280	−	0.122524i
$70$	−0.598511	+	1.77878i	−0.0715358	+	0.212605i
$71$	−6.80967			−0.808159			−0.404079	−	0.914724i	$-0.632408\pi$
$71$	−6.80967			−0.808159			−0.404079	+	0.914724i	$0.632408\pi$
$72$	−8.36661	−	1.41417i	−0.986014	−	0.166662i
$73$	−1.40984			−0.165009			−0.0825044	−	0.996591i	$-0.526292\pi$
$73$	−1.40984			−0.165009			−0.0825044	+	0.996591i	$0.526292\pi$
$74$	−0.162510	+	0.482981i	−0.0188914	+	0.0561454i
$75$	−4.94241	+	2.10793i	−0.570701	+	0.243403i
$76$	1.59320	+	1.20901i	0.182753	+	0.138683i
$77$	−1.99399			−0.227236
$78$	0.769648	+	9.77615i	0.0871454	+	1.10693i
$79$			14.6441i			1.64759i	0.566890	+	0.823794i	$0.308147\pi$
$79$			14.6441i			1.64759i	−0.566890	+	0.823794i	$0.691853\pi$
$80$	3.06439	+	10.9656i	0.342609	+	1.22599i
$81$	−0.375707	−	8.99215i	−0.0417452	−	0.999128i
$82$	−1.75226	+	5.20773i	−0.193505	+	0.575098i
$83$			14.6883i			1.61225i	0.591743	+	0.806126i	$0.298440\pi$
$83$			14.6883i			1.61225i	−0.591743	+	0.806126i	$0.701560\pi$
$84$	−0.393320	+	1.56642i	−0.0429148	+	0.170911i
$85$		−	9.91710i		−	1.07566i
$86$	−8.45777	−	2.84581i	−0.912025	−	0.306872i
$87$	−13.6090	+	5.80420i	−1.45904	+	0.622276i
$88$	−10.0039	+	6.80117i	−1.06642	+	0.725007i
$89$		−	15.8556i		−	1.68069i	−0.542050	−	0.840346i	$-0.682352\pi$
$89$		−	15.8556i		−	1.68069i	0.542050	−	0.840346i	$-0.317648\pi$
$90$	−10.7022	+	5.59487i	−1.12811	+	0.589751i
$91$	1.86651			0.195663
$92$	−2.38632	−	1.81088i	−0.248791	−	0.188798i
$93$	5.19580	+	12.1825i	0.538780	+	1.26327i
$94$	−5.31221	−	1.78741i	−0.547913	−	0.184358i
$95$	2.84644			0.292038
$96$	3.36952	+	9.20034i	0.343901	+	0.939006i
$97$	−14.3334			−1.45534			−0.727668	−	0.685930i	$-0.759396\pi$
$97$	−14.3334			−1.45534			−0.727668	+	0.685930i	$0.759396\pi$
$98$	−9.09126	−	3.05896i	−0.918356	−	0.309002i
$99$	−9.26006	−	8.88124i	−0.930671	−	0.892598i
$100$	4.94241	+	3.75060i	0.494241	+	0.375060i
$101$	−0.908973			−0.0904462			−0.0452231	−	0.998977i	$-0.514400\pi$
$101$	−0.908973			−0.0904462			−0.0452231	+	0.998977i	$0.514400\pi$
$102$	−0.669794	−	8.50780i	−0.0663195	−	0.842398i
$103$		−	19.6382i		−	1.93501i	−0.252849	−	0.967506i	$-0.581368\pi$
$103$		−	19.6382i		−	1.93501i	0.252849	−	0.967506i	$-0.418632\pi$
$104$	9.36430	−	6.36635i	0.918245	−	0.624272i
$105$	0.901744	+	2.11430i	0.0880012	+	0.206335i
$106$	−1.74463	−	0.587019i	−0.169453	−	0.0570163i
$107$			5.24428i			0.506983i	0.967338	+	0.253492i	$0.0815791\pi$
$107$			5.24428i			0.506983i	−0.967338	+	0.253492i	$0.918421\pi$
$108$	−8.80345	+	5.52261i	−0.847112	+	0.531414i
$109$			0.135163i			0.0129463i	0.999979	+	0.00647315i	$0.00206048\pi$
$109$			0.135163i			0.0129463i	−0.999979	+	0.00647315i	$0.997940\pi$
$110$	−5.49040	+	16.3175i	−0.523489	+	1.55581i
$111$	0.244845	+	0.574083i	0.0232397	+	0.0544896i
$112$	1.79608	−	0.501924i	0.169714	−	0.0474274i
$113$			16.7462i			1.57535i	0.616092	+	0.787674i	$0.288715\pi$
$113$			16.7462i			1.57535i	−0.616092	+	0.787674i	$0.711285\pi$
$114$	2.44193	−	0.192246i	0.228708	−	0.0180055i
$115$	−4.26344			−0.397568
$116$	13.6090	+	10.3273i	1.26356	+	0.958867i
$117$	8.66804	+	8.31344i	0.801361	+	0.768578i
$118$	1.35621	−	4.03067i	0.124849	−	0.371053i
$119$	−1.62435			−0.148904
$120$	11.7356	+	7.53180i	1.07131	+	0.687556i
$121$	−7.29169			−0.662881
$122$	0.996308	−	2.96104i	0.0902015	−	0.268080i
$123$	2.64004	+	6.19004i	0.238044	+	0.558137i
$124$	9.24479	−	12.1825i	0.830207	−	1.09402i
$125$	−5.40198			−0.483168
$126$	0.916398	+	1.75294i	0.0816392	+	0.156164i
$127$			2.61709i			0.232229i	0.993236	+	0.116115i	$0.0370440\pi$
$127$			2.61709i			0.232229i	−0.993236	+	0.116115i	$0.962956\pi$
$128$	7.29902	−	8.64432i	0.645148	−	0.764057i
$129$	−10.0531	+	4.28763i	−0.885127	+	0.377505i
$130$	5.13938	−	15.2743i	0.450753	−	1.33964i
$131$		−	8.90568i		−	0.778093i	−0.921218	−	0.389046i	$-0.872805\pi$
$131$		−	8.90568i		−	0.778093i	0.921218	−	0.389046i	$-0.127195\pi$
$132$	−3.60809	+	14.3695i	−0.314044	+	1.25070i
$133$		−	0.466225i		−	0.0404268i
$134$	−15.8005	−	5.31642i	−1.36495	−	0.459269i
$135$	−5.22943	+	13.8352i	−0.450078	+	1.19074i
$136$	−8.14939	+	5.54039i	−0.698804	+	0.475084i
$137$		−	6.78619i		−	0.579783i	−0.957059	−	0.289892i	$-0.906381\pi$
$137$		−	6.78619i		−	0.579783i	0.957059	−	0.289892i	$-0.0936193\pi$
$138$	−3.65757	+	0.287950i	−0.311353	+	0.0245119i
$139$	14.1008			1.19601			0.598005	−	0.801492i	$-0.295960\pi$
$139$	14.1008			1.19601			0.598005	+	0.801492i	$0.295960\pi$
$140$	1.60446	−	2.11430i	0.135601	−	0.178691i
$141$	−6.31422	+	2.69300i	−0.531753	+	0.226791i
$142$	9.12749	+	3.07115i	0.765962	+	0.257725i
$143$	17.1222			1.43183
$144$	10.5766	+	5.66885i	0.881382	+	0.472404i
$145$	24.3140			2.01917
$146$	1.88971	+	0.635834i	0.156393	+	0.0526220i
$147$	−10.8061	+	4.60877i	−0.891271	+	0.380125i
$148$	0.435648	−	0.574083i	0.0358101	−	0.0471894i
$149$	−11.5732			−0.948110			−0.474055	−	0.880495i	$-0.657210\pi$
$149$	−11.5732			−0.948110			−0.474055	+	0.880495i	$0.657210\pi$
$150$	7.57535	−	0.596385i	0.618525	−	0.0486947i
$151$			12.6407i			1.02869i	0.857585	+	0.514343i	$0.171964\pi$
$151$			12.6407i			1.02869i	−0.857585	+	0.514343i	$0.828036\pi$
$152$	−1.59022	−	2.33906i	−0.128984	−	0.189723i
$153$	−7.54346	−	7.23486i	−0.609852	−	0.584904i
$154$	2.67269	+	0.899286i	0.215371	+	0.0724665i
$155$		−	21.7654i		−	1.74824i
$156$	3.37742	−	13.4508i	0.270410	−	1.07693i
$157$		−	0.932449i		−	0.0744176i	−0.999308	−	0.0372088i	$-0.988153\pi$
$157$		−	0.932449i		−	0.0744176i	0.999308	−	0.0372088i	$-0.0118467\pi$
$158$	6.60447	−	19.6285i	0.525423	−	1.56156i
$159$	−2.07370	+	0.884429i	−0.164455	+	0.0701398i
$160$	0.838055	−	16.0800i	0.0662541	−	1.27124i
$161$			0.698320i			0.0550353i
$162$	−3.55187	+	12.2223i	−0.279061	+	0.960273i
$163$	−23.1233			−1.81115			−0.905577	−	0.424182i	$-0.860562\pi$
$163$	−23.1233			−1.81115			−0.905577	+	0.424182i	$0.860562\pi$
$164$	4.69736	−	6.19004i	0.366803	−	0.483361i
$165$	8.27209	+	19.3954i	0.643981	+	1.50993i
$166$	6.62442	−	19.6878i	0.514155	−	1.52807i
$167$	−18.6761			−1.44520			−0.722599	−	0.691268i	$-0.757053\pi$
$167$	−18.6761			−1.44520			−0.722599	+	0.691268i	$0.757053\pi$
$168$	1.23365	−	1.92221i	0.0951783	−	0.148301i
$169$	−3.02757			−0.232890
$170$	−4.47260	+	13.2926i	−0.343033	+	1.01950i
$171$	2.07657	−	2.16515i	0.158799	−	0.165573i
$172$	10.0531	+	7.62889i	0.766543	+	0.581698i
$173$	−15.6538			−1.19014			−0.595069	−	0.803675i	$-0.702875\pi$
$173$	−15.6538			−1.19014			−0.595069	+	0.803675i	$0.702875\pi$
$174$	20.8588	−	1.64215i	1.58130	−	0.124491i
$175$		−	1.44632i		−	0.109331i
$176$	16.4763	−	4.60436i	1.24194	−	0.347067i
$177$	−2.04333	−	4.79095i	−0.153586	−	0.360110i
$178$	−7.15087	+	21.2525i	−0.535981	+	1.59294i
$179$			1.31831i			0.0985351i	0.998786	+	0.0492676i	$0.0156887\pi$
$179$			1.31831i			0.0985351i	−0.998786	+	0.0492676i	$0.984311\pi$
$180$	16.8682	−	2.67253i	1.25728	−	0.199199i
$181$		−	21.7722i		−	1.61832i	−0.587591	−	0.809158i	$-0.699924\pi$
$181$		−	21.7722i		−	1.61832i	0.587591	−	0.809158i	$-0.300076\pi$
$182$	−2.50181	−	0.841792i	−0.185447	−	0.0623978i
$183$	−1.50108	−	3.51956i	−0.110963	−	0.260173i
$184$	2.38186	+	3.50349i	0.175593	+	0.258281i
$185$		−	1.02567i		−	0.0754085i
$186$	−1.47002	−	18.6724i	−0.107787	−	1.36913i
$187$	−14.9008			−1.08966
$188$	6.31422	+	4.79160i	0.460512	+	0.349464i
$189$	2.26610	+	0.856541i	0.164834	+	0.0623042i
$190$	−3.81529	−	1.28374i	−0.276790	−	0.0931323i
$191$	−3.41715			−0.247256			−0.123628	−	0.992329i	$-0.539453\pi$
$191$	−3.41715			−0.247256			−0.123628	+	0.992329i	$0.539453\pi$
$192$	−0.367075	−	13.8515i	−0.0264913	−	0.999649i
$193$	22.3929			1.61187			0.805937	−	0.592002i	$-0.201662\pi$
$193$	22.3929			1.61187			0.805937	+	0.592002i	$0.201662\pi$
$194$	19.2121	+	6.46435i	1.37935	+	0.464113i
$195$	−7.74323	−	18.1554i	−0.554504	−	1.30013i
$196$	10.8061	+	8.20030i	0.771864	+	0.585736i
$197$	−18.8339			−1.34186			−0.670930	−	0.741521i	$-0.734105\pi$
$197$	−18.8339			−1.34186			−0.670930	+	0.741521i	$0.734105\pi$
$198$	8.40651	+	16.0805i	0.597424	+	1.14279i
$199$			19.2624i			1.36547i	0.730664	+	0.682737i	$0.239211\pi$
$199$			19.2624i			1.36547i	−0.730664	+	0.682737i	$0.760789\pi$
$200$	−4.93316	−	7.25622i	−0.348827	−	0.513092i
$201$	−18.7808	+	8.00997i	−1.32470	+	0.564980i
$202$	1.21836	+	0.409946i	0.0857237	+	0.0288437i
$203$		−	3.98246i		−	0.279514i
$204$	−2.93924	+	11.7057i	−0.205788	+	0.819563i
$205$		−	11.0592i		−	0.772409i
$206$	−8.85682	+	26.3225i	−0.617084	+	1.83398i
$207$	−3.11033	+	3.24299i	−0.216183	+	0.225404i
$208$	−15.4229	+	4.30999i	−1.06938	+	0.298844i
$209$		−	4.27688i		−	0.295838i
$210$	−0.255126	−	3.24064i	−0.0176054	−	0.223625i
$211$	−14.6747			−1.01025			−0.505124	−	0.863047i	$-0.668553\pi$
$211$	−14.6747			−1.01025			−0.505124	+	0.863047i	$0.668553\pi$
$212$	2.07370	+	1.57365i	0.142423	+	0.108079i
$213$	10.8492	−	4.62714i	0.743372	−	0.317046i
$214$	2.36516	−	7.02929i	0.161679	−	0.480512i
$215$	17.9610			1.22493
$216$	14.2906	−	3.43201i	0.972352	−	0.233519i
$217$	−3.56501			−0.242009
$218$	0.0609585	−	0.181169i	0.00412863	−	0.0122703i
$219$	2.24615	−	0.957977i	0.151781	−	0.0647341i
$220$	14.7184	−	19.3954i	0.992312	−	1.30764i
$221$	13.9482			0.938255
$222$	−0.0692728	−	0.879911i	−0.00464928	−	0.0590557i
$223$		−	11.7498i		−	0.786827i	−0.919362	−	0.393414i	$-0.871294\pi$
$223$		−	11.7498i		−	0.786827i	0.919362	−	0.393414i	$-0.128706\pi$
$224$	−2.63379	−	0.137267i	−0.175978	−	0.00917154i
$225$	6.44192	−	6.71670i	0.429462	−	0.447780i
$226$	7.55251	−	22.4461i	0.502386	−	1.49309i
$227$			1.12266i			0.0745135i	0.999306	+	0.0372568i	$0.0118619\pi$
$227$			1.12266i			0.0745135i	−0.999306	+	0.0372568i	$0.988138\pi$
$228$	−3.35981	−	0.843628i	−0.222509	−	0.0558706i
$229$			25.6416i			1.69445i	0.531236	+	0.847224i	$0.321728\pi$
$229$			25.6416i			1.69445i	−0.531236	+	0.847224i	$0.678272\pi$
$230$	5.71460	+	1.92281i	0.376810	+	0.126786i
$231$	3.17682	−	1.35491i	0.209019	−	0.0891462i
$232$	−13.5835	−	19.9801i	−0.891802	−	1.31176i
$233$			9.09416i			0.595778i	0.954600	+	0.297889i	$0.0962826\pi$
$233$			9.09416i			0.595778i	−0.954600	+	0.297889i	$0.903717\pi$
$234$	−7.86905	−	15.0524i	−0.514416	−	0.984005i
$235$	11.2811			0.735897
$236$	−3.63566	+	4.79095i	−0.236661	+	0.311864i
$237$	−9.95059	−	23.3309i	−0.646360	−	1.51551i
$238$	2.17723	+	0.732579i	0.141129	+	0.0474860i
$239$	4.14167			0.267903			0.133951	−	0.990988i	$-0.457233\pi$
$239$	4.14167			0.267903			0.133951	+	0.990988i	$0.457233\pi$
$240$	−12.3333	−	15.3882i	−0.796109	−	0.993302i
$241$	−8.61961			−0.555238			−0.277619	−	0.960691i	$-0.589545\pi$
$241$	−8.61961			−0.555238			−0.277619	+	0.960691i	$0.589545\pi$
$242$	9.77359	+	3.28855i	0.628270	+	0.211396i
$243$	6.70871	+	14.0710i	0.430364	+	0.902656i
$244$	−2.67085	+	3.51956i	−0.170984	+	0.225317i
$245$	19.3063			1.23344
$246$	−0.746932	−	9.48761i	−0.0476226	−	0.604908i
$247$			4.00344i			0.254733i
$248$	−17.8858	+	12.1597i	−1.13575	+	0.772141i
$249$	−9.98065	−	23.4014i	−0.632498	−	1.48301i
$250$	7.24067	+	2.43629i	0.457940	+	0.154084i
$251$		−	3.05061i		−	0.192553i	−0.995355	−	0.0962763i	$-0.969307\pi$
$251$		−	3.05061i		−	0.192553i	0.995355	−	0.0962763i	$-0.0306932\pi$
$252$	−0.437741	−	2.76289i	−0.0275751	−	0.174045i
$253$			6.40599i			0.402741i
$254$	1.18031	−	3.50788i	0.0740590	−	0.220104i
$255$	6.73863	+	15.7999i	0.421989	+	0.989429i
$256$	−13.6820	+	8.29477i	−0.855124	+	0.518423i
$257$		−	4.18627i		−	0.261133i	−0.991440	−	0.130566i	$-0.958320\pi$
$257$		−	4.18627i		−	0.261133i	0.991440	−	0.130566i	$-0.0416795\pi$
$258$	15.4086	−	1.21308i	0.959300	−	0.0755229i
$259$	−0.167996			−0.0104388
$260$	−13.7774	+	18.1554i	−0.854436	+	1.12595i
$261$	17.7379	−	18.4945i	1.09795	−	1.14478i
$262$	−4.01645	+	11.9369i	−0.248137	+	0.737466i
$263$	21.1464			1.30394			0.651971	−	0.758244i	$-0.273943\pi$
$263$	21.1464			1.30394			0.651971	+	0.758244i	$0.273943\pi$
$264$	11.3168	−	17.6332i	0.696502	−	1.08525i
$265$	3.70491			0.227591
$266$	−0.210267	+	0.624915i	−0.0128923	+	0.0383160i
$267$	10.7738	+	25.2612i	0.659348	+	1.54596i
$268$	18.7808	+	14.2520i	1.14722	+	0.870578i
$269$	7.73388			0.471543			0.235771	−	0.971809i	$-0.424238\pi$
$269$	7.73388			0.471543			0.235771	+	0.971809i	$0.424238\pi$
$270$	13.2490	−	16.1858i	0.806311	−	0.985039i
$271$			3.05116i			0.185345i	0.995697	+	0.0926723i	$0.0295409\pi$
$271$			3.05116i			0.185345i	−0.995697	+	0.0926723i	$0.970459\pi$
$272$	13.4219	−	3.75082i	0.813824	−	0.227427i
$273$	−2.97372	+	1.26828i	−0.179977	+	0.0767599i
$274$	−3.06056	+	9.09603i	−0.184895	+	0.549511i
$275$		−	13.2677i		−	0.800073i
$276$	5.03238	+	1.26360i	0.302914	+	0.0760599i
$277$			18.8564i			1.13297i	0.824071	+	0.566487i	$0.191698\pi$
$277$			18.8564i			1.13297i	−0.824071	+	0.566487i	$0.808302\pi$
$278$	−18.9003	−	6.35943i	−1.13356	−	0.381413i
$279$	−16.5559	−	15.8786i	−0.991176	−	0.950628i
$280$	−3.10412	+	2.11034i	−0.185507	+	0.126117i
$281$			15.4367i			0.920876i	0.887692	+	0.460438i	$0.152308\pi$
$281$			15.4367i			0.920876i	−0.887692	+	0.460438i	$0.847692\pi$
$282$	9.67795	−	0.761917i	0.576314	−	0.0453715i
$283$	16.4832			0.979823			0.489911	−	0.871772i	$-0.337029\pi$
$283$	16.4832			0.979823			0.489911	+	0.871772i	$0.337029\pi$
$284$	−10.8492	−	8.23298i	−0.643779	−	0.488538i
$285$	−4.53494	+	1.93414i	−0.268627	+	0.114569i
$286$	−22.9502	−	7.72212i	−1.35707	−	0.456618i
$287$	−1.81142			−0.106925
$288$	−11.6199	−	12.3684i	−0.684710	−	0.728815i
$289$	4.86145			0.285968
$290$	−32.5899	−	10.9656i	−1.91374	−	0.643923i
$291$	22.8360	−	9.73948i	1.33867	−	0.570938i
$292$	−2.24615	−	1.70451i	−0.131446	−	0.0997489i
$293$	−29.2733			−1.71016			−0.855082	−	0.518493i	$-0.826493\pi$
$293$	−29.2733			−1.71016			−0.855082	+	0.518493i	$0.826493\pi$
$294$	16.5627	−	1.30394i	0.965959	−	0.0760471i
$295$			8.55958i			0.498358i
$296$	−0.842842	+	0.573009i	−0.0489892	+	0.0333055i
$297$	20.7879	+	7.85742i	1.20624	+	0.455934i
$298$	15.5124	+	5.21949i	0.898607	+	0.302357i
$299$		−	5.99643i		−	0.346783i
$300$	−10.4228	−	2.61710i	−0.601759	−	0.151098i
$301$		−	2.94188i		−	0.169567i
$302$	5.70094	−	16.9432i	0.328052	−	0.974974i
$303$	1.44818	−	0.617643i	0.0831955	−	0.0354827i
$304$	1.07657	+	3.85240i	0.0617456	+	0.220950i
$305$			6.28810i			0.360055i
$306$	6.84813	+	13.0995i	0.391482	+	0.748849i
$307$	−21.4068			−1.22175			−0.610875	−	0.791727i	$-0.709182\pi$
$307$	−21.4068			−1.22175			−0.610875	+	0.791727i	$0.709182\pi$
$308$	−3.17682	−	2.41076i	−0.181016	−	0.137366i
$309$	13.3441	+	31.2876i	0.759119	+	1.77989i
$310$	−9.81619	+	29.1738i	−0.557522	+	1.65696i
$311$	8.16716			0.463117			0.231559	−	0.972821i	$-0.425617\pi$
$311$	8.16716			0.463117			0.231559	+	0.972821i	$0.425617\pi$
$312$	−10.5933	+	16.5059i	−0.599727	+	0.934461i
$313$	−17.6187			−0.995866			−0.497933	−	0.867215i	$-0.665907\pi$
$313$	−17.6187			−0.995866			−0.497933	+	0.867215i	$0.665907\pi$
$314$	−0.420534	+	1.24983i	−0.0237321	+	0.0705320i
$315$	−2.87332	−	2.75577i	−0.161893	−	0.155270i
$316$	−17.7049	+	23.3309i	−0.995978	+	1.31247i
$317$	2.52671			0.141914			0.0709571	−	0.997479i	$-0.477395\pi$
$317$	2.52671			0.141914			0.0709571	+	0.997479i	$0.477395\pi$
$318$	3.17841	−	0.250227i	0.178237	−	0.0140320i
$319$		−	36.5328i		−	2.04544i
$320$	−8.37539	+	21.1753i	−0.468199	+	1.18374i
$321$	−3.56346	−	8.35518i	−0.198893	−	0.466341i
$322$	0.314942	−	0.936009i	0.0175510	−	0.0521617i
$323$		−	3.48404i		−	0.193857i
$324$	10.2731	−	14.7805i	0.570726	−	0.821141i
$325$			12.4195i			0.688908i
$326$	30.9938	+	10.4286i	1.71659	+	0.577585i
$327$	−0.0918429	−	0.215342i	−0.00507892	−	0.0119084i
$328$	−9.08792	+	6.17845i	−0.501796	+	0.341148i
$329$		−	1.84776i		−	0.101870i
$330$	−2.34038	−	29.7278i	−0.128834	−	1.63646i
$331$	19.9850			1.09848			0.549238	−	0.835666i	$-0.314918\pi$
$331$	19.9850			1.09848			0.549238	+	0.835666i	$0.314918\pi$
$332$	−17.7584	+	23.4014i	−0.974618	+	1.28432i
$333$	−0.780174	−	0.748258i	−0.0427533	−	0.0410043i
$334$	25.0329	+	8.42289i	1.36974	+	0.460880i
$335$	33.5541			1.83325
$336$	−2.52047	+	2.02010i	−0.137503	+	0.110205i
$337$	11.8512			0.645578			0.322789	−	0.946471i	$-0.395380\pi$
$337$	11.8512			0.645578			0.322789	+	0.946471i	$0.395380\pi$
$338$	4.05807	+	1.36543i	0.220730	+	0.0742697i
$339$	−11.3790	−	26.6800i	−0.618021	−	1.44906i
$340$	11.9899	−	15.7999i	0.650244	−	0.856871i
$341$	−32.7034			−1.77099
$342$	−3.75986	+	1.96557i	−0.203310	+	0.106286i
$343$		−	6.42581i		−	0.346961i
$344$	−10.0343	−	14.7595i	−0.541013	−	0.795779i
$345$	6.79252	−	2.89699i	0.365697	−	0.155969i
$346$	20.9819	+	7.05985i	1.12800	+	0.379540i
$347$			22.9770i			1.23347i	0.787170	+	0.616736i	$0.211545\pi$
$347$			22.9770i			1.23347i	−0.787170	+	0.616736i	$0.788455\pi$
$348$	−28.6992	−	7.20621i	−1.53844	−	0.386293i
$349$			21.1528i			1.13228i	0.824308	+	0.566141i	$0.191564\pi$
$349$			21.1528i			1.13228i	−0.824308	+	0.566141i	$0.808436\pi$
$350$	−0.652289	+	1.93861i	−0.0348663	+	0.103623i
$351$	−19.4589	−	7.35507i	−1.03864	−	0.392585i
$352$	−24.1609	−	1.25921i	−1.28778	−	0.0671161i
$353$		−	18.5723i		−	0.988504i	−0.869319	−	0.494252i	$-0.835442\pi$
$353$		−	18.5723i		−	0.988504i	0.869319	−	0.494252i	$-0.164558\pi$
$354$	0.578109	+	7.34320i	0.0307261	+	0.390287i
$355$	−19.3833			−1.02876
$356$	19.1697	−	25.2612i	1.01599	−	1.33884i
$357$	2.58791	−	1.10374i	0.136967	−	0.0584159i
$358$	0.594557	−	1.76703i	0.0314233	−	0.0933903i
$359$	−7.11376			−0.375450			−0.187725	−	0.982222i	$-0.560111\pi$
$359$	−7.11376			−0.375450			−0.187725	+	0.982222i	$0.560111\pi$
$360$	−23.8150	−	4.02535i	−1.25516	−	0.212155i
$361$	1.00000			0.0526316
$362$	−9.81925	+	29.1829i	−0.516088	+	1.53382i
$363$	11.6171	−	4.95467i	0.609741	−	0.260053i
$364$	2.97372	+	2.25663i	0.155865	+	0.118280i
$365$	−4.01301			−0.210050
$366$	0.424694	+	5.39451i	0.0221991	+	0.281975i
$367$			0.517055i			0.0269900i	0.999909	+	0.0134950i	$0.00429573\pi$
$367$			0.517055i			0.0269900i	−0.999909	+	0.0134950i	$0.995704\pi$
$368$	−1.61251	−	5.77020i	−0.0840578	−	0.300792i
$369$	−8.41221	−	8.06807i	−0.437922	−	0.420007i
$370$	−0.462574	+	1.37477i	−0.0240481	+	0.0714711i
$371$		−	0.606837i		−	0.0315054i
$372$	−6.45085	+	25.6909i	−0.334461	+	1.33201i
$373$		−	27.1084i		−	1.40362i	−0.712364	−	0.701810i	$-0.752376\pi$
$373$		−	27.1084i		−	1.40362i	0.712364	−	0.701810i	$-0.247624\pi$
$374$	19.9727	+	6.72026i	1.03276	+	0.347496i
$375$	8.60644	−	3.67062i	0.444435	−	0.189550i
$376$	−6.30240	−	9.27024i	−0.325022	−	0.478076i
$377$			34.1971i			1.76124i
$378$	−2.65112	−	2.17009i	−0.136359	−	0.111618i
$379$	−4.55933			−0.234197			−0.117098	−	0.993120i	$-0.537359\pi$
$379$	−4.55933			−0.234197			−0.117098	+	0.993120i	$0.537359\pi$
$380$	4.53494	+	3.44138i	0.232638	+	0.176539i
$381$	−1.77830	−	4.16955i	−0.0911052	−	0.213612i
$382$	4.58025	+	1.54113i	0.234346	+	0.0788511i
$383$	−8.31238			−0.424743			−0.212371	−	0.977189i	$-0.568119\pi$
$383$	−8.31238			−0.424743			−0.212371	+	0.977189i	$0.568119\pi$
$384$	−5.75502	+	18.7318i	−0.293684	+	0.955902i
$385$	−5.67575			−0.289263
$386$	−30.0148	−	10.0992i	−1.52771	−	0.514034i
$387$	13.1032	−	13.6621i	0.666073	−	0.694483i
$388$	−22.8360	−	17.3293i	−1.15932	−	0.879760i
$389$	−18.9309			−0.959835			−0.479918	−	0.877314i	$-0.659333\pi$
$389$	−18.9309			−0.959835			−0.479918	+	0.877314i	$0.659333\pi$
$390$	2.19075	+	27.8272i	0.110933	+	1.40908i
$391$			5.21846i			0.263909i
$392$	−10.7859	−	15.8650i	−0.544769	−	0.801303i
$393$	6.05137	+	14.1885i	0.305251	+	0.715717i
$394$	25.2444	+	8.49407i	1.27180	+	0.427925i
$395$			41.6834i			2.09732i
$396$	−4.01559	−	25.3451i	−0.201791	−	1.27364i
$397$			19.7700i			0.992227i	0.868258	+	0.496113i	$0.165240\pi$
$397$			19.7700i			0.992227i	−0.868258	+	0.496113i	$0.834760\pi$
$398$	8.68732	−	25.8188i	0.435456	−	1.29418i
$399$	0.316798	+	0.742789i	0.0158597	+	0.0371860i
$400$	3.33973	+	11.9509i	0.166987	+	0.597545i
$401$			8.03205i			0.401102i	0.979683	+	0.200551i	$0.0642732\pi$
$401$			8.03205i			0.401102i	−0.979683	+	0.200551i	$0.935727\pi$
$402$	28.7858	−	2.26622i	1.43570	−	0.113029i
$403$	30.6126			1.52492
$404$	−1.44818	−	1.09896i	−0.0720494	−	0.0546753i
$405$	−1.06942	−	25.5956i	−0.0531401	−	1.27185i
$406$	−1.79608	+	5.33798i	−0.0891382	+	0.264919i
$407$	−1.54110			−0.0763896
$408$	9.21893	−	14.3644i	0.456405	−	0.711145i
$409$	−29.4278			−1.45511			−0.727556	−	0.686048i	$-0.759344\pi$
$409$	−29.4278			−1.45511			−0.727556	+	0.686048i	$0.759344\pi$
$410$	−4.98769	+	14.8235i	−0.246325	+	0.732079i
$411$	4.61119	+	10.8118i	0.227453	+	0.533305i
$412$	23.7429	−	31.2876i	1.16973	−	1.54143i
$413$	1.40200			0.0689877
$414$	5.63158	−	2.94407i	0.276777	−	0.144693i
$415$			41.8094i			2.05234i
$416$	22.6162	+	1.17870i	1.10885	+	0.0577908i
$417$	−22.4653	+	9.58140i	−1.10013	+	0.469203i
$418$	−1.92887	+	5.73261i	−0.0943440	+	0.280391i
$419$			12.7128i			0.621062i	0.950563	+	0.310531i	$0.100507\pi$
$419$			12.7128i			0.621062i	−0.950563	+	0.310531i	$0.899493\pi$
$420$	−1.11956	+	4.45873i	−0.0546290	+	0.217564i
$421$		−	26.4745i		−	1.29029i	−0.764061	−	0.645143i	$-0.776798\pi$
$421$		−	26.4745i		−	1.29029i	0.764061	−	0.645143i	$-0.223202\pi$
$422$	19.6696	+	6.61828i	0.957500	+	0.322173i
$423$	8.22993	−	8.58097i	0.400153	−	0.417221i
$424$	−2.06982	−	3.04451i	−0.100519	−	0.147855i
$425$		−	10.8082i		−	0.524273i
$426$	−16.6288	+	1.30913i	−0.805666	+	0.0634277i
$427$	1.02994			0.0498424
$428$	−6.34040	+	8.35518i	−0.306475	+	0.403863i
$429$	−27.2792	+	11.6345i	−1.31705	+	0.561719i
$430$	−24.0745	−	8.10041i	−1.16098	−	0.390637i
$431$	−4.48203			−0.215892			−0.107946	−	0.994157i	$-0.534427\pi$
$431$	−4.48203			−0.215892			−0.107946	+	0.994157i	$0.534427\pi$
$432$	−20.7026	−	1.84487i	−0.996053	−	0.0887613i
$433$	31.5853			1.51789			0.758947	−	0.651152i	$-0.225714\pi$
$433$	31.5853			1.51789			0.758947	+	0.651152i	$0.225714\pi$
$434$	4.77845	+	1.60782i	0.229373	+	0.0771777i
$435$	−38.7371	+	16.5213i	−1.85730	+	0.792135i
$436$	−0.163414	+	0.215342i	−0.00782613	+	0.0103130i
$437$	−1.49782			−0.0716504
$438$	−3.44273	+	0.271036i	−0.164500	+	0.0129506i
$439$			30.8696i			1.47333i	0.676259	+	0.736664i	$0.263600\pi$
$439$			30.8696i			1.47333i	−0.676259	+	0.736664i	$0.736400\pi$
$440$	−28.4754	+	19.3591i	−1.35751	+	0.922908i
$441$	14.0846	−	14.6854i	0.670696	−	0.699304i
$442$	−18.6958	−	6.29061i	−0.889266	−	0.299214i
$443$			13.5157i			0.642152i	0.947053	+	0.321076i	$0.104045\pi$
$443$			13.5157i			0.642152i	−0.947053	+	0.321076i	$0.895955\pi$
$444$	−0.303987	+	1.21065i	−0.0144266	+	0.0574549i
$445$		−	45.1320i		−	2.13946i
$446$	−5.29917	+	15.7492i	−0.250923	+	0.745745i
$447$	18.4384	−	7.86392i	0.872105	−	0.371950i
$448$	3.46835	+	1.37183i	0.163864	+	0.0648127i
$449$			39.6229i			1.86992i	0.354753	+	0.934960i	$0.384565\pi$
$449$			39.6229i			1.86992i	−0.354753	+	0.934960i	$0.615435\pi$
$450$	−11.6638	+	6.09758i	−0.549837	+	0.287443i
$451$	−16.6169			−0.782459
$452$	−20.2464	+	26.6800i	−0.952309	+	1.25492i
$453$	−8.58930	−	20.1392i	−0.403561	−	0.946220i
$454$	0.506318	−	1.50478i	0.0237627	−	0.0706229i
$455$	5.31289			0.249072
$456$	4.12292	+	2.64605i	0.193073	+	0.123912i
$457$	−35.9360			−1.68102			−0.840508	−	0.541799i	$-0.817743\pi$
$457$	−35.9360			−1.68102			−0.840508	+	0.541799i	$0.817743\pi$
$458$	11.5644	−	34.3694i	0.540367	−	1.60598i
$459$	16.9343	+	6.40083i	0.790425	+	0.298765i
$460$	−6.79252	−	5.15456i	−0.316703	−	0.240333i
$461$	−40.7343			−1.89719			−0.948593	−	0.316499i	$-0.897493\pi$
$461$	−40.7343			−1.89719			−0.948593	+	0.316499i	$0.897493\pi$
$462$	−4.86918	+	0.383337i	−0.226535	+	0.0178344i
$463$		−	11.2414i		−	0.522433i	−0.965280	−	0.261216i	$-0.915876\pi$
$463$		−	11.2414i		−	0.522433i	0.965280	−	0.261216i	$-0.0841236\pi$
$464$	9.19599	+	32.9069i	0.426913	+	1.52767i
$465$	14.7895	+	34.6767i	0.685847	+	1.60809i
$466$	4.10146	−	12.1896i	0.189996	−	0.564671i
$467$		−	22.1470i		−	1.02484i	−0.858734	−	0.512421i	$-0.828749\pi$
$467$		−	22.1470i		−	1.02484i	0.858734	−	0.512421i	$-0.171251\pi$
$468$	3.75886	+	23.7247i	0.173753	+	1.09668i
$469$		−	5.49591i		−	0.253777i
$470$	−15.1209	−	5.08776i	−0.697473	−	0.234681i
$471$	0.633596	+	1.48558i	0.0291945	+	0.0684518i
$472$	7.03385	−	4.78198i	0.323759	−	0.220109i
$473$		−	26.9872i		−	1.24087i
$474$	2.81527	+	35.7599i	0.129310	+	1.64251i
$475$	3.10219			0.142338
$476$	−2.58791	−	1.96386i	−0.118617	−	0.0900133i
$477$	2.70286	−	2.81815i	0.123755	−	0.129034i
$478$	−5.55139	−	1.86789i	−0.253915	−	0.0854353i
$479$	14.4920			0.662158			0.331079	−	0.943603i	$-0.392587\pi$
$479$	14.4920			0.662158			0.331079	+	0.943603i	$0.392587\pi$
$480$	9.59113	+	26.1882i	0.437773	+	1.19532i
$481$	1.44258			0.0657758
$482$	11.5535	+	3.88744i	0.526247	+	0.177068i
$483$	−0.474505	−	1.11256i	−0.0215907	−	0.0506234i
$484$	−11.6171	−	8.81576i	−0.528051	−	0.400716i
$485$	−40.7991			−1.85259
$486$	−2.64616	−	21.8860i	−0.120032	−	0.992770i
$487$		−	21.3493i		−	0.967431i	−0.875225	−	0.483716i	$-0.839287\pi$
$487$		−	21.3493i		−	0.967431i	0.875225	−	0.483716i	$-0.160713\pi$
$488$	5.16725	−	3.51297i	0.233910	−	0.159025i
$489$	36.8400	−	15.7122i	1.66596	−	0.710529i
$490$	−25.8777	−	8.70714i	−1.16903	−	0.393348i
$491$			18.0569i			0.814896i	0.913228	+	0.407448i	$0.133581\pi$
$491$			18.0569i			0.814896i	−0.913228	+	0.407448i	$0.866419\pi$
$492$	−3.27774	+	13.0538i	−0.147772	+	0.588511i
$493$		−	29.7604i		−	1.34034i
$494$	1.80555	−	5.36611i	0.0812355	−	0.241433i
$495$	−26.3582	−	25.2799i	−1.18471	−	1.13625i
$496$	29.4576	−	8.23206i	1.32269	−	0.369630i
$497$			3.17484i			0.142411i
$498$	2.82378	+	35.8679i	0.126536	+	1.60728i
$499$	2.30123			0.103017			0.0515086	−	0.998673i	$-0.483597\pi$
$499$	2.30123			0.103017			0.0515086	+	0.998673i	$0.483597\pi$
$500$	−8.60644	−	6.53107i	−0.384892	−	0.292078i
$501$	29.7547	−	12.6903i	1.32934	−	0.566961i
$502$	−1.37582	+	4.08895i	−0.0614059	+	0.182499i
$503$	42.1587			1.87976			0.939881	−	0.341502i	$-0.110936\pi$
$503$	42.1587			1.87976			0.939881	+	0.341502i	$0.110936\pi$
$504$	−0.659323	+	3.90072i	−0.0293686	+	0.173752i
$505$	−2.58733			−0.115135
$506$	2.88909	−	8.58641i	0.128436	−	0.381713i
$507$	4.82353	−	2.05722i	0.214220	−	0.0913644i
$508$	−3.16410	+	4.16955i	−0.140384	+	0.184994i
$509$	39.0804			1.73221			0.866104	−	0.499863i	$-0.166616\pi$
$509$	39.0804			1.73221			0.866104	+	0.499863i	$0.166616\pi$
$510$	−1.90653	−	24.2169i	−0.0844224	−	1.07234i
$511$			0.657300i			0.0290772i
$512$	22.0799	−	4.94752i	0.975803	−	0.218651i
$513$	−1.83719	+	4.86053i	−0.0811137	+	0.214598i
$514$	−1.88801	+	5.61117i	−0.0832764	+	0.247498i
$515$		−	55.8989i		−	2.46320i
$516$	−21.2004	−	5.32330i	−0.933296	−	0.234345i
$517$		−	16.9503i		−	0.745472i
$518$	0.225178	+	0.0757662i	0.00989375	+	0.00332898i
$519$	24.9397	−	10.6367i	1.09473	−	0.466899i
$520$	26.6549	−	18.1214i	1.16889	−	0.794676i
$521$			26.5526i			1.16329i	0.813443	+	0.581645i	$0.197591\pi$
$521$			26.5526i			1.16329i	−0.813443	+	0.581645i	$0.802409\pi$
$522$	−32.1164	+	16.7898i	−1.40570	+	0.734868i
$523$	30.8111			1.34728			0.673639	−	0.739061i	$-0.264730\pi$
$523$	30.8111			1.34728			0.673639	+	0.739061i	$0.264730\pi$
$524$	10.7671	−	14.1885i	0.470363	−	0.619829i
$525$	0.982768	+	2.30428i	0.0428915	+	0.100567i
$526$	−28.3440	−	9.53699i	−1.23586	−	0.415833i
$527$	−26.6409			−1.16050
$528$	−23.1213	+	18.5312i	−1.00623	+	0.806468i
$529$	−20.7565			−0.902458
$530$	−4.96596	−	1.67091i	−0.215708	−	0.0725797i
$531$	6.51086	+	6.24451i	0.282547	+	0.270989i
$532$	0.563672	−	0.742789i	0.0244383	−	0.0322040i
$533$	15.5545			0.673741
$534$	−3.04819	−	38.7184i	−0.131908	−	1.67551i
$535$			14.9275i			0.645372i
$536$	−18.7457	−	27.5731i	−0.809689	−	1.19098i
$537$	−0.895786	−	2.10033i	−0.0386560	−	0.0906360i
$538$	−10.3663	−	3.48797i	−0.446922	−	0.150377i
$539$		−	29.0085i		−	1.24948i
$540$	−25.0585	+	15.7198i	−1.07834	+	0.676471i
$541$			23.5736i			1.01351i	0.862091	+	0.506753i	$0.169155\pi$
$541$			23.5736i			1.01351i	−0.862091	+	0.506753i	$0.830845\pi$
$542$	1.37607	−	4.08969i	0.0591072	−	0.175667i
$543$	14.7941	+	34.6875i	0.634877	+	1.48858i
$544$	−19.6820	−	1.02578i	−0.843859	−	0.0439800i
$545$			0.384734i			0.0164802i
$546$	4.55788	−	0.358829i	0.195059	−	0.0153565i
$547$	−6.72108			−0.287373			−0.143686	−	0.989623i	$-0.545896\pi$
$547$	−6.72108			−0.287373			−0.143686	+	0.989623i	$0.545896\pi$
$548$	8.20460	−	10.8118i	0.350483	−	0.461855i
$549$	4.78305	+	4.58738i	0.204136	+	0.195785i
$550$	−5.98372	+	17.7837i	−0.255147	+	0.758298i
$551$	8.54193			0.363898
$552$	−6.17538	−	3.96329i	−0.262842	−	0.168689i
$553$	6.82743			0.290332
$554$	8.50424	−	25.2747i	0.361310	−	1.07382i
$555$	0.696936	+	1.63409i	0.0295833	+	0.0693633i
$556$	22.4653	+	17.0480i	0.952742	+	0.722997i
$557$	16.6408			0.705093			0.352547	−	0.935794i	$-0.385316\pi$
$557$	16.6408			0.705093			0.352547	+	0.935794i	$0.385316\pi$
$558$	15.0298	+	28.7500i	0.636264	+	1.21708i
$559$			25.2618i			1.06846i
$560$	5.11244	−	1.42869i	0.216040	−	0.0603733i
$561$	23.7400	−	10.1250i	1.00230	−	0.427480i
$562$	6.96193	−	20.6909i	0.293671	−	0.872794i
$563$		−	36.2254i		−	1.52672i	−0.645973	−	0.763360i	$-0.723548\pi$
$563$		−	36.2254i		−	1.52672i	0.645973	−	0.763360i	$-0.276452\pi$
$564$	−13.3157	−	3.34349i	−0.560692	−	0.140786i
$565$			47.6669i			2.00536i
$566$	−22.0936	−	7.43389i	−0.928663	−	0.312470i
$567$	−4.19236	+	0.175164i	−0.176063	+	0.00735618i
$568$	10.8289	+	15.9282i	0.454369	+	0.668334i
$569$		−	17.6565i		−	0.740200i	−0.928992	−	0.370100i	$-0.879323\pi$
$569$		−	17.6565i		−	0.740200i	0.928992	−	0.370100i	$-0.120677\pi$
$570$	6.95081	−	0.547217i	0.291137	−	0.0229204i
$571$	24.7456			1.03557			0.517786	−	0.855510i	$-0.326757\pi$
$571$	24.7456			1.03557			0.517786	+	0.855510i	$0.326757\pi$
$572$	27.2792	+	20.7010i	1.14060	+	0.865554i
$573$	5.44420	−	2.32194i	0.227435	−	0.0970003i
$574$	2.42797	+	0.816947i	0.101342	+	0.0340987i
$575$	−4.64652			−0.193773
$576$	9.99689	+	21.8188i	0.416537	+	0.909119i
$577$	17.4071			0.724669			0.362335	−	0.932048i	$-0.381980\pi$
$577$	17.4071			0.724669			0.362335	+	0.932048i	$0.381980\pi$
$578$	−6.51616	−	2.19251i	−0.271036	−	0.0911964i
$579$	−35.6763	+	15.2159i	−1.48266	+	0.632349i
$580$	38.7371	+	29.3960i	1.60847	+	1.22060i
$581$	6.84806			0.284105
$582$	−35.0012	+	2.75554i	−1.45085	+	0.114221i
$583$		−	5.56677i		−	0.230552i
$584$	2.24195	+	3.29769i	0.0927724	+	0.136459i
$585$	24.6730	+	23.6637i	1.02010	+	0.978372i
$586$	39.2371	+	13.2022i	1.62087	+	0.545379i
$587$		−	15.1652i		−	0.625936i	−0.949764	−	0.312968i	$-0.898677\pi$
$587$		−	15.1652i		−	0.625936i	0.949764	−	0.312968i	$-0.101323\pi$
$588$	−22.7883	−	5.72202i	−0.939775	−	0.235972i
$589$		−	7.64656i		−	0.315071i
$590$	3.86036	−	11.4730i	0.158929	−	0.472337i
$591$	30.0062	−	12.7976i	1.23429	−	0.526421i
$592$	1.38815	−	0.387925i	0.0570526	−	0.0159436i
$593$		−	2.75839i		−	0.113274i	−0.998395	−	0.0566368i	$-0.981962\pi$
$593$		−	2.75839i		−	0.113274i	0.998395	−	0.0566368i	$-0.0180377\pi$
$594$	−24.3198	−	19.9072i	−0.997855	−	0.816802i
$595$	−4.62360			−0.189549
$596$	−18.4384	−	13.9921i	−0.755265	−	0.573139i
$597$	−13.0887	−	30.6888i	−0.535685	−	1.25601i
$598$	−2.70439	+	8.03746i	−0.110591	+	0.328676i
$599$	10.8449			0.443110			0.221555	−	0.975148i	$-0.428887\pi$
$599$	10.8449			0.443110			0.221555	+	0.975148i	$0.428887\pi$
$600$	12.7901	+	8.20854i	0.522153	+	0.335112i
$601$	18.9772			0.774096			0.387048	−	0.922060i	$-0.373495\pi$
$601$	18.9772			0.774096			0.387048	+	0.922060i	$0.373495\pi$
$602$	−1.32679	+	3.94322i	−0.0540758	+	0.160714i
$603$	24.4788	−	25.5230i	0.996855	−	1.03938i
$604$	−15.2828	+	20.1392i	−0.621847	+	0.819451i
$605$	−20.7553			−0.843824
$606$	−2.21965	+	0.174747i	−0.0901672	+	0.00709860i
$607$			11.5022i			0.466860i	0.972374	+	0.233430i	$0.0749950\pi$
$607$			11.5022i			0.466860i	−0.972374	+	0.233430i	$0.925005\pi$
$608$	0.294423	−	5.64919i	0.0119404	−	0.229105i
$609$	2.70606	+	6.34485i	0.109655	+	0.257106i
$610$	2.83593	−	8.42840i	0.114823	−	0.341256i
$611$			15.8666i			0.641893i
$612$	−3.27119	−	20.6467i	−0.132230	−	0.834594i
$613$		−	27.9553i		−	1.12911i	−0.825397	−	0.564553i	$-0.809049\pi$
$613$		−	27.9553i		−	1.12911i	0.825397	−	0.564553i	$-0.190951\pi$
$614$	28.6931	+	9.65443i	1.15796	+	0.389621i
$615$	7.51469	+	17.6195i	0.303022	+	0.710488i
$616$	3.17087	+	4.66406i	0.127758	+	0.187920i
$617$			8.63436i			0.347606i	0.984780	+	0.173803i	$0.0556056\pi$
$617$			8.63436i			0.347606i	−0.984780	+	0.173803i	$0.944394\pi$
$618$	−3.77538	−	47.9552i	−0.151868	−	1.92904i
$619$	−23.5198			−0.945342			−0.472671	−	0.881239i	$-0.656710\pi$
$619$	−23.5198			−0.945342			−0.472671	+	0.881239i	$0.656710\pi$
$620$	26.3147	−	34.6767i	1.05682	−	1.39265i
$621$	2.75177	−	7.28019i	0.110425	−	0.292144i
$622$	−10.9470	−	3.68338i	−0.438937	−	0.147690i
$623$	−7.39228			−0.296166
$624$	21.6431	−	17.3465i	0.866417	−	0.694414i
$625$	−30.8874			−1.23549
$626$	23.6156	+	7.94600i	0.943869	+	0.317586i
$627$	2.90612	+	6.81392i	0.116059	+	0.272122i
$628$	1.12734	−	1.48558i	0.0449859	−	0.0592810i
$629$	−1.25542			−0.0500568
$630$	2.60847	+	4.98963i	0.103924	+	0.198791i
$631$		−	17.9945i		−	0.716351i	−0.933654	−	0.358176i	$-0.883399\pi$
$631$		−	17.9945i		−	0.716351i	0.933654	−	0.358176i	$-0.116601\pi$
$632$	34.2534	−	23.2873i	1.36253	−	0.926318i
$633$	23.3797	−	9.97140i	0.929261	−	0.396328i
$634$	−3.38674	−	1.13954i	−0.134504	−	0.0452571i
$635$			7.44938i			0.295620i
$636$	−4.37311	−	1.09806i	−0.173405	−	0.0435410i
$637$			27.1539i			1.07588i
$638$	−16.4763	+	48.9676i	−0.652301	+	1.93864i
$639$	−14.1408	+	14.7439i	−0.559400	+	0.583260i
$640$	20.7762	−	24.6055i	0.821251	−	0.972618i
$641$		−	19.8114i		−	0.782505i	−0.920283	−	0.391253i	$-0.872042\pi$
$641$		−	19.8114i		−	0.782505i	0.920283	−	0.391253i	$-0.127958\pi$
$642$	1.00819	+	12.8062i	0.0397902	+	0.505420i
$643$	−14.6875			−0.579219			−0.289610	−	0.957145i	$-0.593526\pi$
$643$	−14.6875			−0.579219			−0.289610	+	0.957145i	$0.593526\pi$
$644$	−0.844278	+	1.11256i	−0.0332692	+	0.0438411i
$645$	−28.6155	+	12.2045i	−1.12674	+	0.480550i
$646$	−1.57130	+	4.66992i	−0.0618220	+	0.183735i
$647$	−12.3332			−0.484868			−0.242434	−	0.970168i	$-0.577946\pi$
$647$	−12.3332			−0.484868			−0.242434	+	0.970168i	$0.577946\pi$
$648$	−20.4357	+	15.1783i	−0.802792	+	0.596259i
$649$	12.8611			0.504843
$650$	5.60116	−	16.6467i	0.219696	−	0.652938i
$651$	5.67978	−	2.42241i	0.222608	−	0.0949418i
$652$	−36.8400	−	27.9564i	−1.44277	−	1.09486i
$653$	9.77352			0.382467			0.191234	−	0.981545i	$-0.438751\pi$
$653$	9.77352			0.382467			0.191234	+	0.981545i	$0.438751\pi$
$654$	0.0259846	+	0.330060i	0.00101608	+	0.0129064i
$655$		−	25.3494i		−	0.990485i
$656$	14.9677	−	4.18279i	0.584390	−	0.163310i
$657$	−2.92762	+	3.05250i	−0.114217	+	0.119089i
$658$	−0.833337	+	2.47668i	−0.0324868	+	0.0965512i
$659$			26.5173i			1.03297i	0.856297	+	0.516484i	$0.172759\pi$
$659$			26.5173i			1.03297i	−0.856297	+	0.516484i	$0.827241\pi$
$660$	−10.2702	+	40.9018i	−0.399767	+	1.59210i
$661$			43.9961i			1.71125i	0.517597	+	0.855625i	$0.326827\pi$
$661$			43.9961i			1.71125i	−0.517597	+	0.855625i	$0.673173\pi$
$662$	−26.7874	−	9.01323i	−1.04112	−	0.350309i
$663$	−22.2222	+	9.47772i	−0.863040	+	0.368084i
$664$	34.3569	−	23.3576i	1.33331	−	0.906452i
$665$		−	1.32708i		−	0.0514619i
$666$	0.708261	+	1.35480i	0.0274446	+	0.0524975i
$667$	−12.7943			−0.495396
$668$	−29.7547	−	22.5796i	−1.15124	−	0.873632i
$669$	7.98397	+	18.7198i	0.308678	+	0.723751i
$670$	−44.9750	−	15.1329i	−1.73753	−	0.584633i
$671$	9.44811			0.364740
$672$	4.28943	−	1.57096i	0.165468	−	0.0606009i
$673$	7.50506			0.289299			0.144649	−	0.989483i	$-0.453795\pi$
$673$	7.50506			0.289299			0.144649	+	0.989483i	$0.453795\pi$
$674$	−15.8851	−	5.34490i	−0.611870	−	0.205878i
$675$	−5.69930	+	15.0783i	−0.219366	+	0.580364i
$676$	−4.82353	−	3.66038i	−0.185520	−	0.140784i
$677$	−3.17793			−0.122138			−0.0610690	−	0.998134i	$-0.519451\pi$
$677$	−3.17793			−0.122138			−0.0610690	+	0.998134i	$0.519451\pi$
$678$	3.21939	+	40.8931i	0.123640	+	1.57049i
$679$			6.68258i			0.256454i
$680$	−23.1967	+	15.7704i	−0.889553	+	0.604765i
$681$	−0.762842	−	1.78862i	−0.0292322	−	0.0685401i
$682$	43.8347	+	14.7492i	1.67852	+	0.564776i
$683$			16.3890i			0.627107i	0.949571	+	0.313554i	$0.101520\pi$
$683$			16.3890i			0.627107i	−0.949571	+	0.313554i	$0.898480\pi$
$684$	5.92608	−	0.938906i	0.226589	−	0.0359000i
$685$		−	19.3164i		−	0.738044i
$686$	−2.89803	+	8.61298i	−0.110647	+	0.328845i
$687$	−17.4234	−	40.8523i	−0.664744	−	1.55861i
$688$	6.79318	+	24.3087i	0.258987	+	0.926761i
$689$			5.21087i			0.198518i
$690$	−10.4110	+	0.819631i	−0.396342	+	0.0312028i
$691$	−13.2798			−0.505186			−0.252593	−	0.967573i	$-0.581283\pi$
$691$	−13.2798			−0.505186			−0.252593	+	0.967573i	$0.581283\pi$
$692$	−24.9397	−	18.9257i	−0.948063	−	0.719446i
$693$	−4.14065	+	4.31727i	−0.157290	+	0.164000i
$694$	10.3626	−	30.7978i	0.393360	−	1.16907i
$695$	40.1369			1.52248
$696$	35.2177	+	22.6023i	1.33492	+	0.856739i
$697$	−13.5365			−0.512731
$698$	9.53988	−	28.3526i	0.361090	−	1.07316i
$699$	−6.17944	−	14.4888i	−0.233728	−	0.548017i
$700$	1.74862	−	2.30428i	0.0660916	−	0.0870934i
$701$	26.1554			0.987875			0.493938	−	0.869497i	$-0.335557\pi$
$701$	26.1554			0.987875			0.493938	+	0.869497i	$0.335557\pi$
$702$	22.7650	+	18.6345i	0.859210	+	0.703313i
$703$		−	0.360333i		−	0.0135902i
$704$	31.8167	+	12.5843i	1.19914	+	0.474290i
$705$	−17.9730	+	7.66545i	−0.676903	+	0.288698i
$706$	−8.37609	+	24.8938i	−0.315238	+	0.936891i
$707$			0.423786i			0.0159381i
$708$	2.53689	−	10.1034i	0.0953423	−	0.379707i
$709$		−	3.81405i		−	0.143240i	−0.997432	−	0.0716198i	$-0.977183\pi$
$709$		−	3.81405i		−	0.143240i	0.997432	−	0.0716198i	$-0.0228168\pi$
$710$	25.9808	+	8.74184i	0.975043	+	0.328075i
$711$	31.7066	+	30.4095i	1.18909	+	1.14044i
$712$	−37.0873	+	25.2139i	−1.38990	+	0.944931i
$713$			11.4532i			0.428924i
$714$	−3.96655	+	0.312275i	−0.148444	+	0.0116866i
$715$	48.7374			1.82267
$716$	−1.59386	+	2.10033i	−0.0595652	+	0.0784931i
$717$	−6.59851	+	2.81425i	−0.246426	+	0.105100i
$718$	9.53509	+	3.20830i	0.355847	+	0.119733i
$719$	−35.8564			−1.33722			−0.668609	−	0.743614i	$-0.733110\pi$
$719$	−35.8564			−1.33722			−0.668609	+	0.743614i	$0.733110\pi$
$720$	30.1056	+	16.1360i	1.12197	+	0.601354i
$721$	−9.15582			−0.340981
$722$	−1.34037	−	0.450999i	−0.0498835	−	0.0167844i
$723$	13.7328	−	5.85699i	0.510727	−	0.217824i
$724$	26.3229	−	34.6875i	0.978283	−	1.28915i
$725$	26.4987			0.984138
$726$	−17.8058	+	1.40180i	−0.660836	+	0.0520257i
$727$		−	31.0603i		−	1.15196i	−0.817463	−	0.575982i	$-0.804620\pi$
$727$		−	31.0603i		−	1.15196i	0.817463	−	0.575982i	$-0.195380\pi$
$728$	−2.96815	−	4.36587i	−0.110007	−	0.161810i
$729$	−20.2495	−	17.8594i	−0.749982	−	0.661459i
$730$	5.37892	+	1.80986i	0.199083	+	0.0669860i
$731$		−	21.9844i		−	0.813121i
$732$	1.86367	−	7.42219i	0.0688832	−	0.274332i
$733$		−	11.3722i		−	0.420043i	−0.977697	−	0.210022i	$-0.932647\pi$
$733$		−	11.3722i		−	0.420043i	0.977697	−	0.210022i	$-0.0673534\pi$
$734$	0.233191	−	0.693046i	0.00860724	−	0.0255808i
$735$	−30.7588	+	13.1186i	−1.13456	+	0.483886i
$736$	−0.440992	+	8.46145i	−0.0162552	+	0.311893i
$737$		−	50.4163i		−	1.85711i
$738$	7.63680	+	14.6081i	0.281115	+	0.537732i
$739$	−14.8112			−0.544840			−0.272420	−	0.962178i	$-0.587824\pi$
$739$	−14.8112			−0.544840			−0.272420	+	0.962178i	$0.587824\pi$
$740$	1.24004	−	1.63409i	0.0455849	−	0.0600704i
$741$	−2.72032	−	6.37829i	−0.0999336	−	0.234312i
$742$	−0.273683	+	0.813387i	−0.0100472	+	0.0298604i
$743$	14.6124			0.536075			0.268038	−	0.963408i	$-0.413625\pi$
$743$	14.6124			0.536075			0.268038	+	0.963408i	$0.413625\pi$
$744$	20.2331	−	31.5261i	0.741783	−	1.15580i
$745$	−32.9423			−1.20691
$746$	−12.2259	+	36.3354i	−0.447621	+	1.33033i
$747$	31.8024	+	30.5013i	1.16359	+	1.11599i
$748$	−23.7400	−	18.0153i	−0.868020	−	0.658705i
$749$	2.44501			0.0893388
$750$	−13.1913	+	1.03851i	−0.481678	+	0.0379211i
$751$			16.2098i			0.591503i	0.955265	+	0.295751i	$0.0955700\pi$
$751$			16.2098i			0.591503i	−0.955265	+	0.295751i	$0.904430\pi$
$752$	4.26670	+	15.2680i	0.155591	+	0.556765i
$753$	2.07287	+	4.86022i	0.0755397	+	0.177116i
$754$	15.4229	−	45.8369i	0.561668	−	1.66928i
$755$			35.9809i			1.30948i
$756$	2.57478	+	4.10439i	0.0936438	+	0.149275i
$757$			25.0524i			0.910547i	0.890352	+	0.455273i	$0.150458\pi$
$757$			25.0524i			0.910547i	−0.890352	+	0.455273i	$0.849542\pi$
$758$	6.11120	+	2.05625i	0.221969	+	0.0746864i
$759$	−4.35284	−	10.2060i	−0.157998	−	0.370455i
$760$	−4.52645	−	6.65799i	−0.164192	−	0.241511i
$761$		−	5.42352i		−	0.196602i	−0.995157	−	0.0983012i	$-0.968659\pi$
$761$		−	5.42352i		−	0.196602i	0.995157	−	0.0983012i	$-0.0313408\pi$
$762$	0.503126	+	6.39076i	0.0182263	+	0.231513i
$763$	0.0630165			0.00228135
$764$	−5.44420	−	4.13138i	−0.196964	−	0.149468i
$765$	−21.4720	−	20.5936i	−0.776320	−	0.744562i
$766$	11.1417	+	3.74887i	0.402566	+	0.135452i
$767$	−12.0389			−0.434698
$768$	16.1619	−	22.5121i	0.583192	−	0.812335i
$769$	−29.2196			−1.05369			−0.526843	−	0.849963i	$-0.676624\pi$
$769$	−29.2196			−1.05369			−0.526843	+	0.849963i	$0.676624\pi$
$770$	7.60763	+	2.55976i	0.274160	+	0.0922473i
$771$	2.84456	+	6.66957i	0.102444	+	0.240199i
$772$	35.6763	+	27.0733i	1.28402	+	0.974389i
$773$	14.1117			0.507564			0.253782	−	0.967262i	$-0.418325\pi$
$773$	14.1117			0.507564			0.253782	+	0.967262i	$0.418325\pi$
$774$	−23.7248	+	12.4028i	−0.852769	+	0.445809i
$775$		−	23.7211i		−	0.852087i
$776$	22.7932	+	33.5267i	0.818229	+	1.20354i
$777$	0.267652	−	0.114153i	0.00960195	−	0.00409521i
$778$	25.3745	+	8.53782i	0.909719	+	0.306096i
$779$		−	3.88529i		−	0.139205i
$780$	9.61360	−	38.2868i	0.344222	−	1.37089i
$781$			29.1241i			1.04214i
$782$	2.35352	−	6.99468i	0.0841617	−	0.250129i
$783$	−15.6931	+	41.5183i	−0.560826	+	1.48374i
$784$	7.30199	+	26.1294i	0.260785	+	0.933194i
$785$		−	2.65416i		−	0.0947309i
$786$	−1.71208	−	21.7471i	−0.0610680	−	0.775693i
$787$	1.16977			0.0416978			0.0208489	−	0.999783i	$-0.493363\pi$
$787$	1.16977			0.0416978			0.0208489	+	0.999783i	$0.493363\pi$
$788$	−30.0062	−	22.7704i	−1.06893	−	0.811163i
$789$	−33.6904	+	14.3689i	−1.19941	+	0.511545i
$790$	18.7992	−	55.8713i	0.668845	−	1.98781i
$791$	7.80749			0.277602
$792$	−6.04825	+	35.7830i	−0.214915	+	1.27149i
$793$	−8.84406			−0.314062
$794$	8.91624	−	26.4992i	0.316426	−	0.940420i
$795$	−5.90266	+	2.51747i	−0.209346	+	0.0892855i
$796$	−23.2885	+	30.6888i	−0.825438	+	1.08774i
$797$	27.3497			0.968776			0.484388	−	0.874853i	$-0.339042\pi$
$797$	27.3497			0.968776			0.484388	+	0.874853i	$0.339042\pi$
$798$	−0.0896300	−	1.13849i	−0.00317287	−	0.0403021i
$799$		−	13.8081i		−	0.488494i
$800$	0.913356	−	17.5249i	0.0322920	−	0.619598i
$801$	−34.3297	−	32.9253i	−1.21298	−	1.16336i
$802$	3.62245	−	10.7659i	0.127913	−	0.380159i
$803$			6.02970i			0.212783i
$804$	−39.6057	−	9.94478i	−1.39679	−	0.350725i
$805$			1.98772i			0.0700580i
$806$	−41.0323	−	13.8062i	−1.44530	−	0.486304i
$807$	−12.3216	+	5.25514i	−0.433741	+	0.184990i
$808$	1.44547	+	2.12614i	0.0508513	+	0.0747975i
$809$		−	20.4291i		−	0.718249i	−0.933290	−	0.359124i	$-0.883075\pi$
$809$		−	20.4291i		−	0.718249i	0.933290	−	0.359124i	$-0.116925\pi$
$810$	−10.1102	+	34.7899i	−0.355235	+	1.22239i
$811$	−15.2642			−0.535998			−0.267999	−	0.963419i	$-0.586362\pi$
$811$	−15.2642			−0.535998			−0.267999	+	0.963419i	$0.586362\pi$
$812$	4.81485	−	6.34485i	0.168968	−	0.222661i
$813$	−2.07325	−	4.86110i	−0.0727120	−	0.170486i
$814$	2.06565	+	0.695036i	0.0724011	+	0.0243610i
$815$	−65.8189			−2.30554
$816$	−18.8351	+	15.0959i	−0.659362	+	0.528464i
$817$	6.31001			0.220759
$818$	39.4442	+	13.2719i	1.37914	+	0.464042i
$819$	3.87593	−	4.04125i	0.135436	−	0.141213i
$820$	13.3707	−	17.6195i	0.466927	−	0.615301i
$821$	22.7493			0.793956			0.396978	−	0.917828i	$-0.370059\pi$
$821$	22.7493			0.793956			0.396978	+	0.917828i	$0.370059\pi$
$822$	−1.30462	−	16.5714i	−0.0455038	−	0.577995i
$823$			10.0940i			0.351854i	0.984403	+	0.175927i	$0.0562923\pi$
$823$			10.0940i			0.351854i	−0.984403	+	0.175927i	$0.943708\pi$
$824$	−45.9350	+	31.2290i	−1.60022	+	1.08792i
$825$	9.01535	+	21.1381i	0.313874	+	0.735934i
$826$	−1.87920	−	0.632299i	−0.0653856	−	0.0220005i
$827$			8.22962i			0.286172i	0.989710	+	0.143086i	$0.0457026\pi$
$827$			8.22962i			0.286172i	−0.989710	+	0.143086i	$0.954297\pi$
$828$	−8.87619	+	1.40631i	−0.308469	+	0.0488726i
$829$		−	26.0198i		−	0.903706i	−0.892092	−	0.451853i	$-0.850763\pi$
$829$		−	26.0198i		−	0.903706i	0.892092	−	0.451853i	$-0.149237\pi$
$830$	18.8560	−	56.0401i	0.654501	−	1.94518i
$831$	−12.8129	−	30.0421i	−0.444474	−	1.04215i
$832$	−29.7826	−	11.7798i	−1.03252	−	0.408391i
$833$		−	23.6310i		−	0.818765i
$834$	34.4331	−	2.71082i	1.19232	−	0.0938680i
$835$	−53.1602			−1.83969
$836$	5.17081	−	6.81392i	0.178836	−	0.235664i
$837$	37.1663	+	14.0481i	1.28466	+	0.485575i
$838$	5.73347	−	17.0399i	0.198060	−	0.588635i
$839$	−37.2701			−1.28671			−0.643353	−	0.765569i	$-0.722457\pi$
$839$	−37.2701			−1.28671			−0.643353	+	0.765569i	$0.722457\pi$
$840$	3.51151	−	5.47143i	0.121159	−	0.188782i
$841$	43.9645			1.51602
$842$	−11.9400	+	35.4857i	−0.411478	+	1.22292i
$843$	−10.4892	−	24.5937i	−0.361266	−	0.847053i
$844$	−23.3797	−	17.7419i	−0.804764	−	0.610702i
$845$	−8.61779			−0.296461
$846$	−14.9012	+	7.79001i	−0.512313	+	0.267826i
$847$			3.39957i			0.116810i
$848$	1.40126	+	5.01427i	0.0481195	+	0.172191i
$849$	−26.2610	+	11.2002i	−0.901275	+	0.384391i
$850$	−4.87448	+	14.4870i	−0.167193	+	0.496899i
$851$			0.539714i			0.0185012i
$852$	22.8792	+	5.74483i	0.783827	+	0.196815i
$853$			49.0827i			1.68056i	0.542153	+	0.840280i	$0.317609\pi$
$853$			49.0827i			1.68056i	−0.542153	+	0.840280i	$0.682391\pi$
$854$	−1.38051	−	0.464503i	−0.0472400	−	0.0158950i
$855$	5.91082	−	6.16295i	0.202146	−	0.210768i
$856$	12.2667	−	8.33954i	0.419267	−	0.285040i
$857$		−	23.7686i		−	0.811919i	−0.913891	−	0.405959i	$-0.866937\pi$
$857$		−	23.7686i		−	0.811919i	0.913891	−	0.405959i	$-0.133063\pi$
$858$	41.8114	−	3.29169i	1.42742	−	0.112376i
$859$	−3.42519			−0.116866			−0.0584330	−	0.998291i	$-0.518610\pi$
$859$	−3.42519			−0.116866			−0.0584330	+	0.998291i	$0.518610\pi$
$860$	28.6155	+	21.7152i	0.975782	+	0.740481i
$861$	2.88595	−	1.23085i	0.0983528	−	0.0419472i
$862$	6.00760	+	2.02139i	0.204620	+	0.0688489i
$863$	46.0387			1.56717			0.783587	−	0.621282i	$-0.213388\pi$
$863$	46.0387			1.56717			0.783587	+	0.621282i	$0.213388\pi$
$864$	26.9171	+	11.8097i	0.915739	+	0.401773i
$865$	−44.5576			−1.51500
$866$	−42.3361	−	14.2450i	−1.43864	−	0.484063i
$867$	−7.74526	+	3.30334i	−0.263043	+	0.112187i
$868$	−5.67978	−	4.31015i	−0.192784	−	0.146296i
$869$	62.6310			2.12461
$870$	59.3733	−	4.67429i	2.01294	−	0.158473i
$871$			47.1930i			1.59907i
$872$	0.316155	−	0.214939i	0.0107064	−	0.00727876i
$873$	−29.7643	+	31.0339i	−1.00737	+	1.05034i
$874$	2.00764	+	0.675515i	0.0679093	+	0.0228496i
$875$			2.51854i			0.0851421i
$876$	4.73677	+	1.18938i	0.160041	+	0.0401853i
$877$			41.7008i			1.40814i	0.710132	+	0.704068i	$0.248635\pi$
$877$			41.7008i			1.40814i	−0.710132	+	0.704068i	$0.751365\pi$
$878$	13.9222	−	41.3768i	0.469851	−	1.39640i
$879$	46.6382	−	19.8911i	1.57307	−	0.670909i
$880$	46.8986	−	13.1060i	1.58095	−	0.441804i
$881$			30.3385i			1.02213i	0.859542	+	0.511065i	$0.170749\pi$
$881$			30.3385i			1.02213i	−0.859542	+	0.511065i	$0.829251\pi$
$882$	−25.5017	+	13.3317i	−0.858688	+	0.448903i
$883$	30.8512			1.03823			0.519113	−	0.854706i	$-0.326262\pi$
$883$	30.8512			1.03823			0.519113	+	0.854706i	$0.326262\pi$
$884$	22.2222	+	16.8635i	0.747414	+	0.567182i
$885$	−5.81620	−	13.6371i	−0.195509	−	0.458407i
$886$	6.09559	−	18.1161i	0.204785	−	0.608623i
$887$	−49.1511			−1.65033			−0.825166	−	0.564890i	$-0.808919\pi$
$887$	−49.1511			−1.65033			−0.825166	+	0.564890i	$0.808919\pi$
$888$	0.953459	−	1.48563i	0.0319960	−	0.0498543i
$889$	1.22015			0.0409226
$890$	−20.3545	+	60.4937i	−0.682284	+	2.02775i
$891$	−38.4584	+	1.60685i	−1.28840	+	0.0538316i
$892$	14.2057	−	18.7198i	0.475643	−	0.626787i
$893$	3.96323			0.132625
$894$	−28.2609	+	2.22490i	−0.945186	+	0.0744117i
$895$			3.75248i			0.125432i
$896$	−4.03020	−	3.40298i	−0.134639	−	0.113686i
$897$	4.07455	+	9.55351i	0.136045	+	0.318983i
$898$	17.8699	−	53.1095i	0.596326	−	1.77229i
$899$		−	65.3163i		−	2.17842i
$900$	18.3839	−	2.91267i	0.612795	−	0.0970889i
$901$		−	4.53482i		−	0.151077i
$902$	22.2728	+	7.49420i	0.741604	+	0.249530i
$903$	1.99900	+	4.68701i	0.0665225	+	0.155974i
$904$	39.1704	−	26.6301i	1.30279	−	0.885704i
$905$		−	61.9732i		−	2.06006i
$906$	2.43013	+	30.8677i	0.0807356	+	1.02551i
$907$	−0.778059			−0.0258350			−0.0129175	−	0.999917i	$-0.504112\pi$
$907$	−0.778059			−0.0258350			−0.0129175	+	0.999917i	$0.504112\pi$
$908$	−1.35731	+	1.78862i	−0.0450439	+	0.0593575i
$909$	−1.88755	+	1.96806i	−0.0626060	+	0.0652764i
$910$	−7.12125	−	2.39611i	−0.236067	−	0.0794302i
$911$	−30.2563			−1.00243			−0.501217	−	0.865321i	$-0.667114\pi$
$911$	−30.2563			−1.00243			−0.501217	+	0.865321i	$0.667114\pi$
$912$	−4.33288	−	5.40612i	−0.143476	−	0.179014i
$913$	62.8202			2.07904
$914$	48.1677	+	16.2071i	1.59325	+	0.536084i
$915$	−4.27274	−	10.0182i	−0.141252	−	0.331191i
$916$	−31.0011	+	40.8523i	−1.02431	+	1.34980i
$917$	−4.15205			−0.137113
$918$	−19.8115	−	16.2168i	−0.653877	−	0.535236i
$919$		−	3.71572i		−	0.122570i	−0.998120	−	0.0612851i	$-0.980480\pi$
$919$		−	3.71572i		−	0.122570i	0.998120	−	0.0612851i	$-0.0195199\pi$
$920$	6.77980	+	9.97245i	0.223523	+	0.328782i
$921$	34.1053	−	14.5458i	1.12381	−	0.479301i
$922$	54.5992	+	18.3711i	1.79813	+	0.605021i
$923$		−	27.2621i		−	0.897344i
$924$	6.69941	+	1.68218i	0.220394	+	0.0553398i
$925$		−	1.11782i		−	0.0367538i
$926$	−5.06986	+	15.0677i	−0.166606	+	0.495155i
$927$	−42.5196	−	40.7802i	−1.39653	−	1.33940i
$928$	2.51494	−	48.2549i	0.0825568	−	1.58405i
$929$		−	47.2890i		−	1.55150i	−0.631039	−	0.775751i	$-0.717371\pi$
$929$		−	47.2890i		−	1.55150i	0.631039	−	0.775751i	$-0.282629\pi$
$930$	−4.18432	−	53.1497i	−0.137209	−	1.74285i
$931$	6.78263			0.222292
$932$	−10.9950	+	14.4888i	−0.360152	+	0.474597i
$933$	−13.0119	+	5.54955i	−0.425991	+	0.181684i
$934$	−9.98829	+	29.6853i	−0.326827	+	0.971332i
$935$	−42.4142			−1.38709
$936$	5.66157	−	33.4953i	0.185054	−	1.09483i
$937$	14.3287			0.468099			0.234049	−	0.972225i	$-0.424802\pi$
$937$	14.3287			0.468099			0.234049	+	0.972225i	$0.424802\pi$
$938$	−2.47865	+	7.36656i	−0.0809307	+	0.240527i
$939$	28.0701	−	11.9718i	0.916032	−	0.390685i
$940$	17.9730	+	13.6390i	0.586215	+	0.444855i
$941$	12.3295			0.401931			0.200965	−	0.979598i	$-0.435592\pi$
$941$	12.3295			0.401931			0.200965	+	0.979598i	$0.435592\pi$
$942$	−0.179260	−	2.27698i	−0.00584061	−	0.0741880i
$943$			5.81945i			0.189507i
$944$	−11.5846	+	3.23738i	−0.377048	+	0.105368i
$945$	6.45030	+	2.43809i	0.209828	+	0.0793110i
$946$	−12.1712	+	36.1729i	−0.395719	+	1.17608i
$947$		−	22.0884i		−	0.717776i	−0.933381	−	0.358888i	$-0.883156\pi$
$947$		−	22.0884i		−	0.717776i	0.933381	−	0.358888i	$-0.116844\pi$
$948$	12.3542	−	49.2013i	0.401244	−	1.59798i
$949$		−	5.64420i		−	0.183218i
$950$	−4.15810	−	1.39909i	−0.134906	−	0.0453924i
$951$	−4.02556	+	1.71689i	−0.130538	+	0.0556740i
$952$	2.58307	+	3.79945i	0.0837176	+	0.123141i
$953$			51.7883i			1.67759i	0.544449	+	0.838794i	$0.316739\pi$
$953$			51.7883i			1.67759i	−0.544449	+	0.838794i	$0.683261\pi$
$954$	−4.89382	+	2.55838i	−0.158443	+	0.0828306i
$955$	−9.72669			−0.314748
$956$	6.59851	+	5.00734i	0.213411	+	0.161949i
$957$	24.8239	+	58.2040i	0.802442	+	1.88147i
$958$	−19.4247	−	6.53590i	−0.627585	−	0.211165i
$959$	−3.16389			−0.102167
$960$	−1.04485	−	39.4275i	−0.0337225	−	1.27252i
$961$	−27.4698			−0.886123
$962$	−1.93359	−	0.650600i	−0.0623414	−	0.0209762i
$963$	11.3546	+	10.8901i	0.365898	+	0.350929i
$964$	−13.7328	−	10.4212i	−0.442303	−	0.335645i
$965$	63.7398			2.05186
$966$	0.134249	+	1.70525i	0.00431940	+	0.0548656i
$967$			7.70555i			0.247794i	0.992295	+	0.123897i	$0.0395392\pi$
$967$			7.70555i			0.247794i	−0.992295	+	0.123897i	$0.960461\pi$
$968$	11.5954	+	17.0557i	0.372690	+	0.548191i
$969$	2.36739	+	5.55077i	0.0760516	+	0.178317i
$970$	54.6860	+	18.4003i	1.75586	+	0.590799i
$971$			56.4878i			1.81278i	0.422443	+	0.906389i	$0.361173\pi$
$971$			56.4878i			1.81278i	−0.422443	+	0.906389i	$0.638827\pi$
$972$	−6.32373	+	30.5288i	−0.202834	+	0.979213i
$973$		−	6.57412i		−	0.210757i
$974$	−9.62853	+	28.6161i	−0.308518	+	0.916919i
$975$	−8.43897	−	19.7867i	−0.270263	−	0.633681i
$976$	−8.51039	+	2.37827i	−0.272411	+	0.0761265i
$977$		−	15.5457i		−	0.497352i	−0.968587	−	0.248676i	$-0.920005\pi$
$977$		−	15.5457i		−	0.497352i	0.968587	−	0.248676i	$-0.0799954\pi$
$978$	−56.4655	+	4.44536i	−1.80557	+	0.142147i
$979$	−67.8126			−2.16730
$980$	30.7588	+	23.3416i	0.982555	+	0.745621i
$981$	0.292648	+	0.280676i	0.00934354	+	0.00896130i
$982$	8.14364	−	24.2030i	0.259874	−	0.772348i
$983$	−18.2981			−0.583618			−0.291809	−	0.956477i	$-0.594257\pi$
$983$	−18.2981			−0.583618			−0.291809	+	0.956477i	$0.594257\pi$
$984$	10.2806	−	16.0187i	0.327735	−	0.510658i
$985$	−53.6095			−1.70814
$986$	−13.4219	+	39.8901i	−0.427441	+	1.27036i
$987$	1.25554	+	2.94385i	0.0399644	+	0.0937036i
$988$	−4.84022	+	6.37829i	−0.153988	+	0.202920i
$989$	−9.45125			−0.300532
$990$	23.9286	+	45.7720i	0.760500	+	1.45473i
$991$		−	57.6946i		−	1.83273i	−0.400346	−	0.916364i	$-0.631110\pi$
$991$		−	57.6946i		−	1.83273i	0.400346	−	0.916364i	$-0.368890\pi$
$992$	−43.1968	−	2.25132i	−1.37150	−	0.0714795i
$993$	−31.8401	+	13.5797i	−1.01042	+	0.430940i
$994$	1.43185	−	4.25546i	0.0454155	−	0.134975i
$995$			54.8291i			1.73820i
$996$	12.3915	−	49.3499i	0.392639	−	1.56371i
$997$			36.9642i			1.17067i	0.810793	+	0.585333i	$0.199036\pi$
$997$			36.9642i			1.17067i	−0.810793	+	0.585333i	$0.800964\pi$
$998$	−3.08451	−	1.03785i	−0.0976383	−	0.0328526i
$999$	1.75141	+	0.661999i	0.0554122	+	0.0209447i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.j.e.419.1	✓	24
3.2	odd	2	inner	456.2.j.e.419.24	yes	24
4.3	odd	2		1824.2.j.d.1103.22		24
8.3	odd	2	inner	456.2.j.e.419.23	yes	24
8.5	even	2		1824.2.j.d.1103.21		24
12.11	even	2		1824.2.j.d.1103.23		24
24.5	odd	2		1824.2.j.d.1103.24		24
24.11	even	2	inner	456.2.j.e.419.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.j.e.419.1	✓	24	1.1	even	1	trivial
456.2.j.e.419.2	yes	24	24.11	even	2	inner
456.2.j.e.419.23	yes	24	8.3	odd	2	inner
456.2.j.e.419.24	yes	24	3.2	odd	2	inner
1824.2.j.d.1103.21		24	8.5	even	2
1824.2.j.d.1103.22		24	4.3	odd	2
1824.2.j.d.1103.23		24	12.11	even	2
1824.2.j.d.1103.24		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)

\(f(q)\)	\(=\)	\(q+(-1.34037 - 0.450999i) q^{2} +(-1.59320 + 0.679496i) q^{3} +(1.59320 + 1.20901i) q^{4} +2.84644 q^{5} +(2.44193 - 0.192246i) q^{6} -0.466225i q^{7} +(-1.59022 - 2.33906i) q^{8} +(2.07657 - 2.16515i) q^{9} +O(q^{10})\)	\(q+(-1.34037 - 0.450999i) q^{2} +(-1.59320 + 0.679496i) q^{3} +(1.59320 + 1.20901i) q^{4} +2.84644 q^{5} +(2.44193 - 0.192246i) q^{6} -0.466225i q^{7} +(-1.59022 - 2.33906i) q^{8} +(2.07657 - 2.16515i) q^{9} +(-3.81529 - 1.28374i) q^{10} -4.27688i q^{11} +(-3.35981 - 0.843628i) q^{12} +4.00344i q^{13} +(-0.210267 + 0.624915i) q^{14} +(-4.53494 + 1.93414i) q^{15} +(1.07657 + 3.85240i) q^{16} -3.48404i q^{17} +(-3.75986 + 1.96557i) q^{18} +1.00000 q^{19} +(4.53494 + 3.44138i) q^{20} +(0.316798 + 0.742789i) q^{21} +(-1.92887 + 5.73261i) q^{22} -1.49782 q^{23} +(4.12292 + 2.64605i) q^{24} +3.10219 q^{25} +(1.80555 - 5.36611i) q^{26} +(-1.83719 + 4.86053i) q^{27} +(0.563672 - 0.742789i) q^{28} +8.54193 q^{29} +(6.95081 - 0.547217i) q^{30} -7.64656i q^{31} +(0.294423 - 5.64919i) q^{32} +(2.90612 + 6.81392i) q^{33} +(-1.57130 + 4.66992i) q^{34} -1.32708i q^{35} +(5.92608 - 0.938906i) q^{36} -0.360333i q^{37} +(-1.34037 - 0.450999i) q^{38} +(-2.72032 - 6.37829i) q^{39} +(-4.52645 - 6.65799i) q^{40} -3.88529i q^{41} +(-0.0896300 - 1.13849i) q^{42} +6.31001 q^{43} +(5.17081 - 6.81392i) q^{44} +(5.91082 - 6.16295i) q^{45} +(2.00764 + 0.675515i) q^{46} +3.96323 q^{47} +(-4.33288 - 5.40612i) q^{48} +6.78263 q^{49} +(-4.15810 - 1.39909i) q^{50} +(2.36739 + 5.55077i) q^{51} +(-4.84022 + 6.37829i) q^{52} +1.30160 q^{53} +(4.65461 - 5.68635i) q^{54} -12.1739i q^{55} +(-1.09053 + 0.741399i) q^{56} +(-1.59320 + 0.679496i) q^{57} +(-11.4494 - 3.85240i) q^{58} +3.00712i q^{59} +(-9.56347 - 2.40133i) q^{60} +2.20911i q^{61} +(-3.44859 + 10.2492i) q^{62} +(-1.00944 - 0.968149i) q^{63} +(-2.94241 + 7.43923i) q^{64} +11.3955i q^{65} +(-0.822214 - 10.4439i) q^{66} +11.7881 q^{67} +(4.21226 - 5.55077i) q^{68} +(2.38632 - 1.01776i) q^{69} +(-0.598511 + 1.77878i) q^{70} -6.80967 q^{71} +(-8.36661 - 1.41417i) q^{72} -1.40984 q^{73} +(-0.162510 + 0.482981i) q^{74} +(-4.94241 + 2.10793i) q^{75} +(1.59320 + 1.20901i) q^{76} -1.99399 q^{77} +(0.769648 + 9.77615i) q^{78} +14.6441i q^{79} +(3.06439 + 10.9656i) q^{80} +(-0.375707 - 8.99215i) q^{81} +(-1.75226 + 5.20773i) q^{82} +14.6883i q^{83} +(-0.393320 + 1.56642i) q^{84} -9.91710i q^{85} +(-8.45777 - 2.84581i) q^{86} +(-13.6090 + 5.80420i) q^{87} +(-10.0039 + 6.80117i) q^{88} -15.8556i q^{89} +(-10.7022 + 5.59487i) q^{90} +1.86651 q^{91} +(-2.38632 - 1.81088i) q^{92} +(5.19580 + 12.1825i) q^{93} +(-5.31221 - 1.78741i) q^{94} +2.84644 q^{95} +(3.36952 + 9.20034i) q^{96} -14.3334 q^{97} +(-9.09126 - 3.05896i) q^{98} +(-9.26006 - 8.88124i) 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

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