LMFDB - Embedded newform 550.2.k.d.221.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [550,2,Mod(111,550)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(550, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("550.111");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 550 = 2 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	550.k (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.39177211117$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			221.5
Character	$\chi$	$=$	550.221
Dual form			550.2.k.d.331.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(0.611300 + 0.444136i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(2.11332 - 0.730668i) q^{5} +(0.611300 - 0.444136i) q^{6} -1.28954 q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.750620 - 2.31017i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(0.611300 + 0.444136i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(2.11332 - 0.730668i) q^{5} +(0.611300 - 0.444136i) q^{6} -1.28954 q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.750620 - 2.31017i) q^{9} +(-0.0418545 - 2.23568i) q^{10} +(-0.309017 + 0.951057i) q^{11} +(-0.233496 - 0.718626i) q^{12} +(-1.74816 - 5.38028i) q^{13} +(-0.398490 + 1.22643i) q^{14} +(1.61639 + 0.491943i) q^{15} +(0.309017 + 0.951057i) q^{16} +(4.14732 - 3.01320i) q^{17} -2.42906 q^{18} +(4.91482 - 3.57083i) q^{19} +(-2.13919 - 0.651056i) q^{20} +(-0.788297 - 0.572731i) q^{21} +(0.809017 + 0.587785i) q^{22} +(-2.06020 + 6.34063i) q^{23} -0.755608 q^{24} +(3.93225 - 3.08827i) q^{25} -5.65716 q^{26} +(1.26766 - 3.90146i) q^{27} +(1.04326 + 0.757973i) q^{28} +(6.07954 + 4.41704i) q^{29} +(0.967358 - 1.38526i) q^{30} +(-5.56011 + 4.03966i) q^{31} +1.00000 q^{32} +(-0.611300 + 0.444136i) q^{33} +(-1.58413 - 4.87546i) q^{34} +(-2.72521 + 0.942226i) q^{35} +(-0.750620 + 2.31017i) q^{36} +(1.34641 + 4.14381i) q^{37} +(-1.87730 - 5.77772i) q^{38} +(1.32092 - 4.06539i) q^{39} +(-1.28024 + 1.83330i) q^{40} +(-0.578597 - 1.78074i) q^{41} +(-0.788297 + 0.572731i) q^{42} +4.79305 q^{43} +(0.809017 - 0.587785i) q^{44} +(-3.27427 - 4.33368i) q^{45} +(5.39366 + 3.91873i) q^{46} +(-1.02903 - 0.747635i) q^{47} +(-0.233496 + 0.718626i) q^{48} -5.33708 q^{49} +(-1.72199 - 4.69412i) q^{50} +3.87353 q^{51} +(-1.74816 + 5.38028i) q^{52} +(-8.16866 - 5.93488i) q^{53} +(-3.31878 - 2.41124i) q^{54} +(0.0418545 + 2.23568i) q^{55} +(1.04326 - 0.757973i) q^{56} +4.59036 q^{57} +(6.07954 - 4.41704i) q^{58} +(-0.833647 - 2.56570i) q^{59} +(-1.01853 - 1.34808i) q^{60} +(-1.72273 + 5.30201i) q^{61} +(2.12377 + 6.53630i) q^{62} +(0.967955 + 2.97906i) q^{63} +(0.309017 - 0.951057i) q^{64} +(-7.62562 - 10.0929i) q^{65} +(0.233496 + 0.718626i) q^{66} +(2.46800 - 1.79311i) q^{67} -5.12637 q^{68} +(-4.07550 + 2.96102i) q^{69} +(0.0539731 + 2.88300i) q^{70} +(8.91180 + 6.47480i) q^{71} +(1.96515 + 1.42776i) q^{72} +(-2.32255 + 7.14809i) q^{73} +4.35706 q^{74} +(3.77540 - 0.141409i) q^{75} -6.07506 q^{76} +(0.398490 - 1.22643i) q^{77} +(-3.45822 - 2.51255i) q^{78} +(9.60348 + 6.97734i) q^{79} +(1.34796 + 1.78410i) q^{80} +(-3.38774 + 2.46134i) q^{81} -1.87238 q^{82} +(-12.7031 + 9.22934i) q^{83} +(0.301102 + 0.926698i) q^{84} +(6.56296 - 9.39817i) q^{85} +(1.48113 - 4.55846i) q^{86} +(1.75466 + 5.40028i) q^{87} +(-0.309017 - 0.951057i) q^{88} +(-2.03211 + 6.25419i) q^{89} +(-5.13337 + 1.77483i) q^{90} +(2.25432 + 6.93809i) q^{91} +(5.39366 - 3.91873i) q^{92} -5.19305 q^{93} +(-1.02903 + 0.747635i) q^{94} +(7.77751 - 11.1374i) q^{95} +(0.611300 + 0.444136i) q^{96} +(-5.95215 - 4.32449i) q^{97} +(-1.64925 + 5.07587i) q^{98} +2.42906 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{2} - 2 q^{3} - 6 q^{4} + 6 q^{5} - 2 q^{6} - 6 q^{8} - 14 q^{9}+O(q^{10}) $ 24 * q - 6 * q^2 - 2 * q^3 - 6 * q^4 + 6 * q^5 - 2 * q^6 - 6 * q^8 - 14 * q^9	$ 24 q - 6 q^{2} - 2 q^{3} - 6 q^{4} + 6 q^{5} - 2 q^{6} - 6 q^{8} - 14 q^{9} + q^{10} + 6 q^{11} - 2 q^{12} - 9 q^{15} - 6 q^{16} + 13 q^{17} + 16 q^{18} - 11 q^{19} - 9 q^{20} + 33 q^{21} + 6 q^{22} - 17 q^{23} + 8 q^{24} - 16 q^{25} - 11 q^{27} + 10 q^{29} + q^{30} - 11 q^{31} + 24 q^{32} + 2 q^{33} - 12 q^{34} + 4 q^{35} - 14 q^{36} - 15 q^{37} - q^{38} + 3 q^{39} + q^{40} + 28 q^{41} + 33 q^{42} + 16 q^{43} + 6 q^{44} + 13 q^{45} + 3 q^{46} - 28 q^{47} - 2 q^{48} + 16 q^{49} - q^{50} + 26 q^{51} - 57 q^{53} + 4 q^{54} - q^{55} + 18 q^{57} + 10 q^{58} - 7 q^{59} + 46 q^{60} - q^{62} - 30 q^{63} - 6 q^{64} - 23 q^{65} + 2 q^{66} + 23 q^{67} - 2 q^{68} - 45 q^{69} - 6 q^{70} + 29 q^{71} + 6 q^{72} - 27 q^{73} + 40 q^{74} + 19 q^{75} + 24 q^{76} - 2 q^{78} - q^{79} + q^{80} - 26 q^{81} - 2 q^{82} - 47 q^{83} - 32 q^{84} + 12 q^{85} - 9 q^{86} - 14 q^{87} + 6 q^{88} - 4 q^{89} - 32 q^{90} + 27 q^{91} + 3 q^{92} + 148 q^{93} - 28 q^{94} - 6 q^{95} - 2 q^{96} - 31 q^{97} + 36 q^{98} - 16 q^{99}+O(q^{100}) $ 24 * q - 6 * q^2 - 2 * q^3 - 6 * q^4 + 6 * q^5 - 2 * q^6 - 6 * q^8 - 14 * q^9 + q^10 + 6 * q^11 - 2 * q^12 - 9 * q^15 - 6 * q^16 + 13 * q^17 + 16 * q^18 - 11 * q^19 - 9 * q^20 + 33 * q^21 + 6 * q^22 - 17 * q^23 + 8 * q^24 - 16 * q^25 - 11 * q^27 + 10 * q^29 + q^30 - 11 * q^31 + 24 * q^32 + 2 * q^33 - 12 * q^34 + 4 * q^35 - 14 * q^36 - 15 * q^37 - q^38 + 3 * q^39 + q^40 + 28 * q^41 + 33 * q^42 + 16 * q^43 + 6 * q^44 + 13 * q^45 + 3 * q^46 - 28 * q^47 - 2 * q^48 + 16 * q^49 - q^50 + 26 * q^51 - 57 * q^53 + 4 * q^54 - q^55 + 18 * q^57 + 10 * q^58 - 7 * q^59 + 46 * q^60 - q^62 - 30 * q^63 - 6 * q^64 - 23 * q^65 + 2 * q^66 + 23 * q^67 - 2 * q^68 - 45 * q^69 - 6 * q^70 + 29 * q^71 + 6 * q^72 - 27 * q^73 + 40 * q^74 + 19 * q^75 + 24 * q^76 - 2 * q^78 - q^79 + q^80 - 26 * q^81 - 2 * q^82 - 47 * q^83 - 32 * q^84 + 12 * q^85 - 9 * q^86 - 14 * q^87 + 6 * q^88 - 4 * q^89 - 32 * q^90 + 27 * q^91 + 3 * q^92 + 148 * q^93 - 28 * q^94 - 6 * q^95 - 2 * q^96 - 31 * q^97 + 36 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/550\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$	0.611300	+	0.444136i	0.352934	+	0.256422i	0.750099	−	0.661326i	$-0.230006\pi$
$3$	0.611300	+	0.444136i	0.352934	+	0.256422i	−0.397165	+	0.917747i	$0.630006\pi$
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	2.11332	−	0.730668i	0.945106	−	0.326765i
$5$	2.11332	−	0.730668i	0.945106	−	0.326765i
$6$	0.611300	−	0.444136i	0.249562	−	0.181318i
$7$	−1.28954			−0.487401			−0.243700	−	0.969851i	$-0.578361\pi$
$7$	−1.28954			−0.487401			−0.243700	+	0.969851i	$0.578361\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	−0.750620	−	2.31017i	−0.250207	−	0.770056i
$10$	−0.0418545	−	2.23568i	−0.0132356	−	0.706983i
$11$	−0.309017	+	0.951057i	−0.0931721	+	0.286754i
$11$	−0.309017	+	0.951057i	−0.0931721	+	0.286754i
$12$	−0.233496	−	0.718626i	−0.0674044	−	0.207450i
$13$	−1.74816	−	5.38028i	−0.484852	−	1.49222i	−0.832195	−	0.554483i	$-0.812916\pi$
$13$	−1.74816	−	5.38028i	−0.484852	−	1.49222i	0.347343	−	0.937738i	$-0.387084\pi$
$14$	−0.398490	+	1.22643i	−0.106501	+	0.327776i
$15$	1.61639	+	0.491943i	0.417350	+	0.127019i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	4.14732	−	3.01320i	1.00587	−	0.730809i	0.0425329	−	0.999095i	$-0.486457\pi$
$17$	4.14732	−	3.01320i	1.00587	−	0.730809i	0.963339	+	0.268286i	$0.0864573\pi$
$18$	−2.42906			−0.572534
$19$	4.91482	−	3.57083i	1.12754	−	0.819204i	0.142203	−	0.989837i	$-0.454581\pi$
$19$	4.91482	−	3.57083i	1.12754	−	0.819204i	0.985335	+	0.170633i	$0.0545814\pi$
$20$	−2.13919	−	0.651056i	−0.478337	−	0.145581i
$21$	−0.788297	−	0.572731i	−0.172020	−	0.124980i
$22$	0.809017	+	0.587785i	0.172483	+	0.125316i
$23$	−2.06020	+	6.34063i	−0.429581	+	1.32211i	0.468959	+	0.883220i	$0.344629\pi$
$23$	−2.06020	+	6.34063i	−0.429581	+	1.32211i	−0.898539	+	0.438893i	$0.855371\pi$
$24$	−0.755608			−0.154238
$25$	3.93225	−	3.08827i	0.786450	−	0.617654i
$26$	−5.65716			−1.10946
$27$	1.26766	−	3.90146i	0.243962	−	0.750837i
$28$	1.04326	+	0.757973i	0.197158	+	0.143243i
$29$	6.07954	+	4.41704i	1.12894	+	0.820225i	0.985541	−	0.169440i	$-0.0541959\pi$
$29$	6.07954	+	4.41704i	1.12894	+	0.820225i	0.143402	+	0.989665i	$0.454196\pi$
$30$	0.967358	−	1.38526i	0.176615	−	0.252912i
$31$	−5.56011	+	4.03966i	−0.998626	+	0.725544i	−0.961793	−	0.273778i	$-0.911727\pi$
$31$	−5.56011	+	4.03966i	−0.998626	+	0.725544i	−0.0368325	+	0.999321i	$0.511727\pi$
$32$	1.00000			0.176777
$33$	−0.611300	+	0.444136i	−0.106414	+	0.0773141i
$34$	−1.58413	−	4.87546i	−0.271677	−	0.836135i
$35$	−2.72521	+	0.942226i	−0.460645	+	0.159265i
$36$	−0.750620	+	2.31017i	−0.125103	+	0.385028i
$37$	1.34641	+	4.14381i	0.221348	+	0.681238i	0.998642	+	0.0521009i	$0.0165917\pi$
$37$	1.34641	+	4.14381i	0.221348	+	0.681238i	−0.777294	+	0.629137i	$0.783408\pi$
$38$	−1.87730	−	5.77772i	−0.304538	−	0.937270i
$39$	1.32092	−	4.06539i	0.211517	−	0.650983i
$40$	−1.28024	+	1.83330i	−0.202423	+	0.289870i
$41$	−0.578597	−	1.78074i	−0.0903617	−	0.278105i	0.895655	−	0.444749i	$-0.146707\pi$
$41$	−0.578597	−	1.78074i	−0.0903617	−	0.278105i	−0.986017	+	0.166644i	$0.946707\pi$
$42$	−0.788297	+	0.572731i	−0.121637	+	0.0883743i
$43$	4.79305			0.730933			0.365467	−	0.930824i	$-0.380909\pi$
$43$	4.79305			0.730933			0.365467	+	0.930824i	$0.380909\pi$
$44$	0.809017	−	0.587785i	0.121964	−	0.0886120i
$45$	−3.27427	−	4.33368i	−0.488099	−	0.646026i
$46$	5.39366	+	3.91873i	0.795252	+	0.577785i
$47$	−1.02903	−	0.747635i	−0.150100	−	0.109054i	0.510201	−	0.860055i	$-0.329571\pi$
$47$	−1.02903	−	0.747635i	−0.150100	−	0.109054i	−0.660300	+	0.751002i	$0.729571\pi$
$48$	−0.233496	+	0.718626i	−0.0337022	+	0.103725i
$49$	−5.33708			−0.762441
$50$	−1.72199	−	4.69412i	−0.243526	−	0.663849i
$51$	3.87353			0.542402
$52$	−1.74816	+	5.38028i	−0.242426	+	0.746111i
$53$	−8.16866	−	5.93488i	−1.12205	−	0.815219i	−0.137533	−	0.990497i	$-0.543917\pi$
$53$	−8.16866	−	5.93488i	−1.12205	−	0.815219i	−0.984519	+	0.175279i	$0.943917\pi$
$54$	−3.31878	−	2.41124i	−0.451629	−	0.328128i
$55$	0.0418545	+	2.23568i	0.00564366	+	0.301459i
$56$	1.04326	−	0.757973i	0.139412	−	0.101288i
$57$	4.59036			0.608008
$58$	6.07954	−	4.41704i	0.798283	−	0.579986i
$59$	−0.833647	−	2.56570i	−0.108532	−	0.334026i	0.882012	−	0.471228i	$-0.156189\pi$
$59$	−0.833647	−	2.56570i	−0.108532	−	0.334026i	−0.990543	+	0.137202i	$0.956189\pi$
$60$	−1.01853	−	1.34808i	−0.131492	−	0.174036i
$61$	−1.72273	+	5.30201i	−0.220572	+	0.678852i	0.778138	+	0.628093i	$0.216164\pi$
$61$	−1.72273	+	5.30201i	−0.220572	+	0.678852i	−0.998711	+	0.0507595i	$0.983836\pi$
$62$	2.12377	+	6.53630i	0.269720	+	0.830111i
$63$	0.967955	+	2.97906i	0.121951	+	0.375326i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−7.62562	−	10.0929i	−0.945842	−	1.25187i
$66$	0.233496	+	0.718626i	0.0287414	+	0.0884568i
$67$	2.46800	−	1.79311i	0.301514	−	0.219063i	−0.426733	−	0.904378i	$-0.640335\pi$
$67$	2.46800	−	1.79311i	0.301514	−	0.219063i	0.728247	+	0.685315i	$0.240335\pi$
$68$	−5.12637			−0.621663
$69$	−4.07550	+	2.96102i	−0.490632	+	0.356465i
$70$	0.0539731	+	2.88300i	0.00645102	+	0.344584i
$71$	8.91180	+	6.47480i	1.05764	+	0.768417i	0.973649	−	0.228050i	$-0.0732349\pi$
$71$	8.91180	+	6.47480i	1.05764	+	0.768417i	0.0839861	+	0.996467i	$0.473235\pi$
$72$	1.96515	+	1.42776i	0.231595	+	0.168264i
$73$	−2.32255	+	7.14809i	−0.271834	+	0.836620i	0.718205	+	0.695831i	$0.244964\pi$
$73$	−2.32255	+	7.14809i	−0.271834	+	0.836620i	−0.990040	+	0.140789i	$0.955036\pi$
$74$	4.35706			0.506498
$75$	3.77540	−	0.141409i	0.435945	−	0.0163285i
$76$	−6.07506			−0.696857
$77$	0.398490	−	1.22643i	0.0454122	−	0.139764i
$78$	−3.45822	−	2.51255i	−0.391567	−	0.284490i
$79$	9.60348	+	6.97734i	1.08048	+	0.785012i	0.977766	−	0.209700i	$-0.0672487\pi$
$79$	9.60348	+	6.97734i	1.08048	+	0.785012i	0.102710	+	0.994711i	$0.467249\pi$
$80$	1.34796	+	1.78410i	0.150706	+	0.199468i
$81$	−3.38774	+	2.46134i	−0.376416	+	0.273482i
$82$	−1.87238			−0.206770
$83$	−12.7031	+	9.22934i	−1.39435	+	1.01305i	−0.398973	+	0.916963i	$0.630633\pi$
$83$	−12.7031	+	9.22934i	−1.39435	+	1.01305i	−0.995373	+	0.0960884i	$0.969367\pi$
$84$	0.301102	+	0.926698i	0.0328530	+	0.101111i
$85$	6.56296	−	9.39817i	0.711853	−	1.01938i
$86$	1.48113	−	4.55846i	0.159715	−	0.491552i
$87$	1.75466	+	5.40028i	0.188119	+	0.578971i
$88$	−0.309017	−	0.951057i	−0.0329413	−	0.101383i
$89$	−2.03211	+	6.25419i	−0.215403	+	0.662943i	0.783722	+	0.621112i	$0.213319\pi$
$89$	−2.03211	+	6.25419i	−0.215403	+	0.662943i	−0.999125	+	0.0418304i	$0.986681\pi$
$90$	−5.13337	+	1.77483i	−0.541105	+	0.187084i
$91$	2.25432	+	6.93809i	0.236317	+	0.727310i
$92$	5.39366	−	3.91873i	0.562328	−	0.408555i
$93$	−5.19305			−0.538494
$94$	−1.02903	+	0.747635i	−0.106136	+	0.0771126i
$95$	7.77751	−	11.1374i	0.797955	−	1.14267i
$96$	0.611300	+	0.444136i	0.0623906	+	0.0453294i
$97$	−5.95215	−	4.32449i	−0.604349	−	0.439085i	0.243071	−	0.970009i	$-0.421845\pi$
$97$	−5.95215	−	4.32449i	−0.604349	−	0.439085i	−0.847420	+	0.530923i	$0.821845\pi$
$98$	−1.64925	+	5.07587i	−0.166599	+	0.512740i
$99$	2.42906			0.244129
$100$	−4.99650	+	0.187146i	−0.499650	+	0.0187146i
$101$	12.8673			1.28034			0.640172	−	0.768232i	$-0.278863\pi$
$101$	12.8673			1.28034			0.640172	+	0.768232i	$0.278863\pi$
$102$	1.19699	−	3.68394i	0.118519	−	0.364765i
$103$	−4.76494	−	3.46193i	−0.469503	−	0.341114i	0.327744	−	0.944766i	$-0.393712\pi$
$103$	−4.76494	−	3.46193i	−0.469503	−	0.341114i	−0.797248	+	0.603652i	$0.793712\pi$
$104$	4.57674	+	3.32520i	0.448786	+	0.326062i
$105$	−2.08440	−	0.634381i	−0.203417	−	0.0619093i
$106$	−8.16866	+	5.93488i	−0.793411	+	0.576447i
$107$	−3.64619			−0.352490			−0.176245	−	0.984346i	$-0.556395\pi$
$107$	−3.64619			−0.352490			−0.176245	+	0.984346i	$0.556395\pi$
$108$	−3.31878	+	2.41124i	−0.319350	+	0.232021i
$109$	3.90847	+	12.0290i	0.374364	+	1.15217i	0.943907	+	0.330212i	$0.107120\pi$
$109$	3.90847	+	12.0290i	0.374364	+	1.15217i	−0.569543	+	0.821962i	$0.692880\pi$
$110$	2.13919	+	0.651056i	0.203964	+	0.0620757i
$111$	−1.01736	+	3.13110i	−0.0965631	+	0.297191i
$112$	−0.398490	−	1.22643i	−0.0376538	−	0.115886i
$113$	4.76291	+	14.6587i	0.448057	+	1.37898i	0.879096	+	0.476645i	$0.158147\pi$
$113$	4.76291	+	14.6587i	0.448057	+	1.37898i	−0.431038	+	0.902334i	$0.641853\pi$
$114$	1.41850	−	4.36569i	0.132855	−	0.408885i
$115$	0.279041	+	14.9051i	0.0260207	+	1.38991i
$116$	−2.32218	−	7.14693i	−0.215609	−	0.663576i
$117$	−11.1172	+	8.07709i	−1.02778	+	0.746727i
$118$	−2.69774			−0.248347
$119$	−5.34814	+	3.88565i	−0.490263	+	0.356197i
$120$	−1.59684	+	0.552099i	−0.145771	+	0.0503995i
$121$	−0.809017	−	0.587785i	−0.0735470	−	0.0534350i
$122$	4.51016	+	3.27682i	0.408330	+	0.296669i
$123$	0.437193	−	1.34554i	0.0394203	−	0.121323i
$124$	6.87268			0.617185
$125$	6.05360	−	9.39968i	0.541451	−	0.840733i
$126$	3.13237			0.279053
$127$	−0.553606	+	1.70382i	−0.0491246	+	0.151190i	−0.972610	−	0.232444i	$-0.925328\pi$
$127$	−0.553606	+	1.70382i	−0.0491246	+	0.151190i	0.923485	+	0.383634i	$0.125328\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	2.92999	+	2.12876i	0.257971	+	0.187427i
$130$	−11.9554	+	4.13351i	−1.04856	+	0.362533i
$131$	5.73434	−	4.16624i	0.501012	−	0.364006i	−0.308392	−	0.951259i	$-0.599791\pi$
$131$	5.73434	−	4.16624i	0.501012	−	0.364006i	0.809403	+	0.587253i	$0.199791\pi$
$132$	0.755608			0.0657673
$133$	−6.33787	+	4.60473i	−0.549563	+	0.399281i
$134$	−0.942693	−	2.90131i	−0.0814362	−	0.250635i
$135$	−0.171697	−	9.17128i	−0.0147773	−	0.789338i
$136$	−1.58413	+	4.87546i	−0.135838	+	0.418068i
$137$	−3.49443	−	10.7548i	−0.298550	−	0.918842i	−0.982006	−	0.188850i	$-0.939524\pi$
$137$	−3.49443	−	10.7548i	−0.298550	−	0.918842i	0.683456	−	0.729991i	$-0.260476\pi$
$138$	1.55670	+	4.79104i	0.132515	+	0.407840i
$139$	0.118509	−	0.364732i	0.0100518	−	0.0309362i	−0.945905	−	0.324444i	$-0.894823\pi$
$139$	0.118509	−	0.364732i	0.0100518	−	0.0309362i	0.955957	+	0.293508i	$0.0948227\pi$
$140$	2.75857	+	0.839563i	0.233142	+	0.0709560i
$141$	−0.296995	−	0.914058i	−0.0250115	−	0.0769776i
$142$	8.91180	−	6.47480i	0.747861	−	0.543353i
$143$	5.65716			0.473076
$144$	1.96515	−	1.42776i	0.163762	−	0.118980i
$145$	16.0754	+	4.89251i	1.33499	+	0.406301i
$146$	6.08053	+	4.41776i	0.503228	+	0.365617i
$147$	−3.26256	−	2.37039i	−0.269091	−	0.195506i
$148$	1.34641	−	4.14381i	0.110674	−	0.340619i
$149$	19.8109			1.62297			0.811485	−	0.584373i	$-0.198660\pi$
$149$	19.8109			1.62297			0.811485	+	0.584373i	$0.198660\pi$
$150$	1.03217	−	3.63431i	0.0842766	−	0.296740i
$151$	−0.502578			−0.0408992			−0.0204496	−	0.999791i	$-0.506510\pi$
$151$	−0.502578			−0.0408992			−0.0204496	+	0.999791i	$0.506510\pi$
$152$	−1.87730	+	5.77772i	−0.152269	+	0.468635i
$153$	−10.0741	−	7.31924i	−0.814440	−	0.591725i
$154$	−1.04326	−	0.757973i	−0.0840683	−	0.0610792i
$155$	−8.79865	+	12.5997i	−0.706725	+	1.01203i
$156$	−3.45822	+	2.51255i	−0.276880	+	0.201165i
$157$	11.7464			0.937467			0.468734	−	0.883340i	$-0.344710\pi$
$157$	11.7464			0.937467			0.468734	+	0.883340i	$0.344710\pi$
$158$	9.60348	−	6.97734i	0.764012	−	0.555087i
$159$	−2.35761	−	7.25599i	−0.186971	−	0.575437i
$160$	2.11332	−	0.730668i	0.167073	−	0.0577644i
$161$	2.65671	−	8.17650i	0.209378	−	0.644399i
$162$	1.29400	+	3.98253i	0.101666	+	0.312897i
$163$	−3.56958	−	10.9860i	−0.279591	−	0.860493i	−0.987968	−	0.154659i	$-0.950572\pi$
$163$	−3.56958	−	10.9860i	−0.279591	−	0.860493i	0.708377	−	0.705834i	$-0.249428\pi$
$164$	−0.578597	+	1.78074i	−0.0451808	+	0.139052i
$165$	−0.967358	+	1.38526i	−0.0753087	+	0.107842i
$166$	4.85215	+	14.9334i	0.376600	+	1.15906i
$167$	13.3216	−	9.67871i	1.03086	−	0.748961i	0.0623768	−	0.998053i	$-0.480132\pi$
$167$	13.3216	−	9.67871i	1.03086	−	0.748961i	0.968480	+	0.249091i	$0.0801320\pi$
$168$	0.974388			0.0751757
$169$	−15.3741	+	11.1700i	−1.18263	+	0.859228i
$170$	−6.91013	−	9.14594i	−0.529983	−	0.701462i
$171$	−11.9384	−	8.67374i	−0.912951	−	0.663297i
$172$	−3.87766	−	2.81728i	−0.295669	−	0.214816i
$173$	5.28159	−	16.2551i	0.401552	−	1.23585i	−0.522189	−	0.852830i	$-0.674884\pi$
$173$	5.28159	−	16.2551i	0.401552	−	1.23585i	0.923740	−	0.383019i	$-0.125116\pi$
$174$	5.67819			0.430463
$175$	−5.07080	+	3.98245i	−0.383316	+	0.301045i
$176$	−1.00000			−0.0753778
$177$	0.629911	−	1.93867i	0.0473470	−	0.145719i
$178$	5.32013	+	3.86530i	0.398761	+	0.289717i
$179$	7.35831	+	5.34613i	0.549986	+	0.399588i	0.827780	−	0.561052i	$-0.189603\pi$
$179$	7.35831	+	5.34613i	0.549986	+	0.399588i	−0.277794	+	0.960641i	$0.589603\pi$
$180$	0.101667	+	5.43058i	0.00757780	+	0.404772i
$181$	−11.2872	+	8.20064i	−0.838972	+	0.609549i	−0.922083	−	0.386991i	$-0.873514\pi$
$181$	−11.2872	+	8.20064i	−0.838972	+	0.609549i	0.0831112	+	0.996540i	$0.473514\pi$
$182$	7.29514			0.540752
$183$	−3.40791	+	2.47599i	−0.251920	+	0.183031i
$184$	−2.06020	−	6.34063i	−0.151880	−	0.467438i
$185$	5.87314	+	7.77343i	0.431802	+	0.571514i
$186$	−1.60474	+	4.93889i	−0.117665	+	0.362137i
$187$	1.58413	+	4.87546i	0.115843	+	0.356529i
$188$	0.393055	+	1.20970i	0.0286665	+	0.0882263i
$189$	−1.63470	+	5.03110i	−0.118907	+	0.365958i
$190$	−8.18892	−	10.8385i	−0.594087	−	0.786307i
$191$	7.99337	+	24.6011i	0.578380	+	1.78007i	0.624370	+	0.781128i	$0.285356\pi$
$191$	7.99337	+	24.6011i	0.578380	+	1.78007i	−0.0459905	+	0.998942i	$0.514644\pi$
$192$	0.611300	−	0.444136i	0.0441168	−	0.0320527i
$193$	1.20476			0.0867209			0.0433604	−	0.999059i	$-0.486194\pi$
$193$	1.20476			0.0867209			0.0433604	+	0.999059i	$0.486194\pi$
$194$	−5.95215	+	4.32449i	−0.427339	+	0.310480i
$195$	−0.178911	−	9.55662i	−0.0128121	−	0.684364i
$196$	4.31779	+	3.13706i	0.308414	+	0.224076i
$197$	−15.8525	−	11.5175i	−1.12945	−	0.820591i	−0.143832	−	0.989602i	$-0.545942\pi$
$197$	−15.8525	−	11.5175i	−1.12945	−	0.820591i	−0.985614	+	0.169012i	$0.945942\pi$
$198$	0.750620	−	2.31017i	0.0533442	−	0.164177i
$199$	8.34088			0.591270			0.295635	−	0.955301i	$-0.404469\pi$
$199$	8.34088			0.591270			0.295635	+	0.955301i	$0.404469\pi$
$200$	−1.36602	+	4.80978i	−0.0965919	+	0.340103i
$201$	2.30507			0.162587
$202$	3.97621	−	12.2375i	0.279765	−	0.861030i
$203$	−7.83982	−	5.69596i	−0.550247	−	0.399778i
$204$	−3.13375	−	2.27680i	−0.219406	−	0.159408i
$205$	−2.52389	−	3.34051i	−0.176276	−	0.233311i
$206$	−4.76494	+	3.46193i	−0.331989	+	0.241204i
$207$	16.1944			1.12559
$208$	4.57674	−	3.32520i	0.317340	−	0.230561i
$209$	1.87730	+	5.77772i	0.129855	+	0.399653i
$210$	−1.24745	+	1.78635i	−0.0860820	+	0.123270i
$211$	−2.79297	+	8.59588i	−0.192276	+	0.591764i	0.807722	+	0.589564i	$0.200700\pi$
$211$	−2.79297	+	8.59588i	−0.192276	+	0.591764i	−0.999998	+	0.00220046i	$0.999300\pi$
$212$	3.12015	+	9.60284i	0.214293	+	0.659526i
$213$	2.57209	+	7.91609i	0.176237	+	0.542402i
$214$	−1.12673	+	3.46773i	−0.0770219	+	0.237049i
$215$	10.1293	−	3.50213i	0.690809	−	0.238843i
$216$	1.26766	+	3.90146i	0.0862535	+	0.265461i
$217$	7.16999	−	5.20930i	0.486731	−	0.353631i
$218$	12.6481			0.856636
$219$	−4.59450	+	3.33810i	−0.310467	+	0.225568i
$220$	1.28024	−	1.83330i	0.0863135	−	0.123601i
$221$	−23.4620	−	17.0462i	−1.57823	−	1.14665i
$222$	2.66347	+	1.93513i	0.178761	+	0.129877i
$223$	−8.20309	+	25.2465i	−0.549320	+	1.69063i	0.161172	+	0.986926i	$0.448473\pi$
$223$	−8.20309	+	25.2465i	−0.549320	+	1.69063i	−0.710492	+	0.703705i	$0.751527\pi$
$224$	−1.28954			−0.0861611
$225$	−10.0861	−	6.76604i	−0.672404	−	0.451070i
$226$	15.4131			1.02527
$227$	5.08518	−	15.6506i	0.337516	−	1.03877i	−0.627954	−	0.778250i	$-0.716107\pi$
$227$	5.08518	−	15.6506i	0.337516	−	1.03877i	0.965470	−	0.260516i	$-0.0838926\pi$
$228$	−3.71368	−	2.69815i	−0.245945	−	0.178689i
$229$	−6.74678	−	4.90182i	−0.445840	−	0.323922i	0.342111	−	0.939659i	$-0.388858\pi$
$229$	−6.74678	−	4.90182i	−0.445840	−	0.323922i	−0.787951	+	0.615738i	$0.788858\pi$
$230$	14.2618	+	4.34055i	0.940397	+	0.286207i
$231$	0.788297	−	0.572731i	0.0518661	−	0.0376829i
$232$	−7.51473			−0.493366
$233$	2.88131	−	2.09340i	0.188761	−	0.137143i	−0.489391	−	0.872064i	$-0.662781\pi$
$233$	2.88131	−	2.09340i	0.188761	−	0.137143i	0.678152	+	0.734921i	$0.262781\pi$
$234$	4.24638	+	13.0690i	0.277594	+	0.854347i
$235$	−2.72094	−	0.828112i	−0.177495	−	0.0540201i
$236$	−0.833647	+	2.56570i	−0.0542658	+	0.167013i
$237$	2.77172	+	8.53049i	0.180043	+	0.554115i
$238$	2.04281	+	6.28711i	0.132415	+	0.407533i
$239$	−7.41084	+	22.8082i	−0.479367	+	1.47534i	0.360609	+	0.932717i	$0.382569\pi$
$239$	−7.41084	+	22.8082i	−0.479367	+	1.47534i	−0.839976	+	0.542623i	$0.817431\pi$
$240$	0.0316256	+	1.68930i	0.00204142	+	0.109044i
$241$	−7.59040	−	23.3608i	−0.488941	−	1.50480i	−0.826191	−	0.563389i	$-0.809497\pi$
$241$	−7.59040	−	23.3608i	−0.488941	−	1.50480i	0.337251	−	0.941415i	$-0.390503\pi$
$242$	−0.809017	+	0.587785i	−0.0520056	+	0.0377843i
$243$	−15.4708			−0.992453
$244$	4.51016	−	3.27682i	0.288733	−	0.209777i
$245$	−11.2790	+	3.89964i	−0.720587	+	0.249139i
$246$	−1.14459	−	0.831590i	−0.0729761	−	0.0530202i
$247$	−27.8040	−	20.2008i	−1.76912	−	1.28534i
$248$	2.12377	−	6.53630i	0.134860	−	0.415056i
$249$	−11.8645			−0.751881
$250$	−7.06896	−	8.66198i	−0.447080	−	0.547832i
$251$	−8.40940			−0.530797			−0.265398	−	0.964139i	$-0.585503\pi$
$251$	−8.40940			−0.530797			−0.265398	+	0.964139i	$0.585503\pi$
$252$	0.967955	−	2.97906i	0.0609754	−	0.187663i
$253$	−5.39366	−	3.91873i	−0.339097	−	0.246368i
$254$	1.44936	+	1.05302i	0.0909408	+	0.0660724i
$255$	8.18600	−	2.83026i	0.512627	−	0.177238i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−8.40530			−0.524308			−0.262154	−	0.965026i	$-0.584433\pi$
$257$	−8.40530			−0.524308			−0.262154	+	0.965026i	$0.584433\pi$
$258$	2.92999	−	2.12876i	0.182413	−	0.132531i
$259$	−1.73625	−	5.34361i	−0.107885	−	0.332036i
$260$	0.236778	+	12.6476i	0.0146843	+	0.784370i
$261$	5.64070	−	17.3603i	0.349151	−	1.07457i
$262$	−2.19032	−	6.74112i	−0.135319	−	0.416468i
$263$	−8.61751	−	26.5220i	−0.531378	−	1.63541i	−0.751347	−	0.659908i	$-0.770595\pi$
$263$	−8.61751	−	26.5220i	−0.531378	−	1.63541i	0.219968	−	0.975507i	$-0.429405\pi$
$264$	0.233496	−	0.718626i	0.0143707	−	0.0442284i
$265$	−21.5994	−	6.57373i	−1.32684	−	0.403821i
$266$	2.42085	+	7.45061i	0.148432	+	0.456826i
$267$	−4.01994	+	2.92065i	−0.246016	+	0.178741i
$268$	−3.05062			−0.186346
$269$	20.8595	−	15.1553i	1.27183	−	0.924035i	0.272552	−	0.962141i	$-0.412132\pi$
$269$	20.8595	−	15.1553i	1.27183	−	0.924035i	0.999274	+	0.0381059i	$0.0121324\pi$
$270$	−8.77546	−	2.67079i	−0.534058	−	0.162539i
$271$	−0.0651103	−	0.0473054i	−0.00395517	−	0.00287360i	0.585806	−	0.810451i	$-0.300778\pi$
$271$	−0.0651103	−	0.0473054i	−0.00395517	−	0.00287360i	−0.589761	+	0.807578i	$0.700778\pi$
$272$	4.14732	+	3.01320i	0.251468	+	0.182702i
$273$	−1.70339	+	5.24248i	−0.103094	+	0.317289i
$274$	−11.3082			−0.683155
$275$	1.72199	+	4.69412i	0.103840	+	0.283066i
$276$	5.03759			0.303227
$277$	−3.02394	+	9.30673i	−0.181691	+	0.559187i	−0.999876	−	0.0157683i	$-0.994981\pi$
$277$	−3.02394	+	9.30673i	−0.181691	+	0.559187i	0.818185	+	0.574955i	$0.194981\pi$
$278$	−0.310260	−	0.225417i	−0.0186081	−	0.0135196i
$279$	13.5058	+	9.81255i	0.808572	+	0.587462i
$280$	1.65092	−	2.36412i	0.0986612	−	0.141283i
$281$	15.1107	−	10.9786i	0.901429	−	0.654927i	−0.0374034	−	0.999300i	$-0.511909\pi$
$281$	15.1107	−	10.9786i	0.901429	−	0.654927i	0.938833	+	0.344374i	$0.111909\pi$
$282$	−0.961098			−0.0572325
$283$	−6.93053	+	5.03533i	−0.411977	+	0.299319i	−0.774402	−	0.632694i	$-0.781949\pi$
$283$	−6.93053	+	5.03533i	−0.411977	+	0.299319i	0.362424	+	0.932013i	$0.381949\pi$
$284$	−3.40400	−	10.4764i	−0.201990	−	0.621663i
$285$	9.70091	−	3.35403i	0.574632	−	0.198676i
$286$	1.74816	−	5.38028i	0.103371	−	0.318143i
$287$	0.746125	+	2.29634i	0.0440423	+	0.135548i
$288$	−0.750620	−	2.31017i	−0.0442307	−	0.136128i
$289$	2.86756	−	8.82545i	0.168680	−	0.519144i
$290$	9.62063	−	13.7768i	0.564943	−	0.808999i
$291$	−1.71789	−	5.28712i	−0.100704	−	0.309936i
$292$	6.08053	−	4.41776i	0.355836	−	0.258530i
$293$	−17.1271			−1.00058			−0.500288	−	0.865859i	$-0.666773\pi$
$293$	−17.1271			−1.00058			−0.500288	+	0.865859i	$0.666773\pi$
$294$	−3.26256	+	2.37039i	−0.190276	+	0.138244i
$295$	−3.63644	−	4.81303i	−0.211722	−	0.280225i
$296$	−3.52494	−	2.56102i	−0.204883	−	0.148856i
$297$	3.31878	+	2.41124i	0.192575	+	0.139914i
$298$	6.12190	−	18.8413i	0.354632	−	1.09144i
$299$	37.7159			2.18117
$300$	−3.13748	−	2.10472i	−0.181142	−	0.121516i
$301$	−6.18083			−0.356257
$302$	−0.155305	+	0.477980i	−0.00893680	+	0.0275046i
$303$	7.86578	+	5.71483i	0.451877	+	0.328308i
$304$	4.91482	+	3.57083i	0.281884	+	0.204801i
$305$	0.233333	+	12.4636i	0.0133606	+	0.713662i
$306$	−10.0741	+	7.31924i	−0.575896	+	0.418413i
$307$	−4.57034			−0.260843			−0.130421	−	0.991459i	$-0.541633\pi$
$307$	−4.57034			−0.260843			−0.130421	+	0.991459i	$0.541633\pi$
$308$	−1.04326	+	0.757973i	−0.0594453	+	0.0431895i
$309$	−1.37524	−	4.23256i	−0.0782347	−	0.240782i
$310$	9.26408	+	12.2615i	0.526164	+	0.696408i
$311$	9.75901	−	30.0351i	0.553382	−	1.70314i	−0.146795	−	0.989167i	$-0.546896\pi$
$311$	9.75901	−	30.0351i	0.553382	−	1.70314i	0.700177	−	0.713969i	$-0.253104\pi$
$312$	1.32092	+	4.06539i	0.0747826	+	0.230157i
$313$	7.98006	+	24.5601i	0.451060	+	1.38822i	0.875699	+	0.482857i	$0.160401\pi$
$313$	7.98006	+	24.5601i	0.451060	+	1.38822i	−0.424639	+	0.905363i	$0.639599\pi$
$314$	3.62985	−	11.1715i	0.204844	−	0.630445i
$315$	4.22230	+	5.58845i	0.237900	+	0.314874i
$316$	−3.66820	−	11.2896i	−0.206353	−	0.635088i
$317$	13.3031	−	9.66526i	0.747176	−	0.542855i	−0.147774	−	0.989021i	$-0.547211\pi$
$317$	13.3031	−	9.66526i	0.747176	−	0.542855i	0.894950	+	0.446166i	$0.147211\pi$
$318$	−7.62940			−0.427835
$319$	−6.07954	+	4.41704i	−0.340389	+	0.247307i
$320$	−0.0418545	−	2.23568i	−0.00233974	−	0.124978i
$321$	−2.22891	−	1.61940i	−0.124406	−	0.0903861i
$322$	−6.95535	−	5.05336i	−0.387606	−	0.281613i
$323$	9.62370	−	29.6187i	0.535477	−	1.64803i
$324$	4.18748			0.232638
$325$	−23.4900	−	15.7578i	−1.30299	−	0.874086i
$326$	−11.5514			−0.639773
$327$	−2.95328	+	9.08925i	−0.163317	+	0.502637i
$328$	1.51479	+	1.10056i	0.0836401	+	0.0607681i
$329$	1.32698	+	0.964105i	0.0731586	+	0.0531528i
$330$	1.01853	+	1.34808i	0.0560682	+	0.0742094i
$331$	0.460935	−	0.334889i	0.0253353	−	0.0184072i	−0.575046	−	0.818121i	$-0.695016\pi$
$331$	0.460935	−	0.334889i	0.0253353	−	0.0184072i	0.600381	+	0.799714i	$0.295016\pi$
$332$	15.7019			0.861753
$333$	8.56227	−	6.22085i	0.469209	−	0.340901i
$334$	−5.08840	−	15.6605i	−0.278425	−	0.856904i
$335$	3.90551	−	5.59270i	0.213381	−	0.305562i
$336$	0.301102	−	0.926698i	0.0164265	−	0.0505555i
$337$	−2.51513	−	7.74079i	−0.137008	−	0.421667i	0.858889	−	0.512162i	$-0.171155\pi$
$337$	−2.51513	−	7.74079i	−0.137008	−	0.421667i	−0.995897	+	0.0904945i	$0.971155\pi$
$338$	5.87240	+	18.0734i	0.319416	+	0.983063i
$339$	−3.59890	+	11.0763i	−0.195465	+	0.601580i
$340$	−10.8337	+	3.74567i	−0.587537	+	0.203138i
$341$	−2.12377	−	6.53630i	−0.115009	−	0.353961i
$342$	−11.9384	+	8.67374i	−0.645554	+	0.469022i
$343$	15.9092			0.859015
$344$	−3.87766	+	2.81728i	−0.209069	+	0.151898i
$345$	−6.44931	+	9.23543i	−0.347219	+	0.497219i
$346$	−13.8274	−	10.0462i	−0.743365	−	0.540086i
$347$	−14.4827	−	10.5223i	−0.777474	−	0.564868i	0.126746	−	0.991935i	$-0.459547\pi$
$347$	−14.4827	−	10.5223i	−0.777474	−	0.564868i	−0.904220	+	0.427067i	$0.859547\pi$
$348$	1.75466	−	5.40028i	0.0940595	−	0.289485i
$349$	−26.8805			−1.43888			−0.719440	−	0.694554i	$-0.755602\pi$
$349$	−26.8805			−1.43888			−0.719440	+	0.694554i	$0.755602\pi$
$350$	2.22058	+	6.05326i	0.118695	+	0.323560i
$351$	−23.2070			−1.23870
$352$	−0.309017	+	0.951057i	−0.0164707	+	0.0506915i
$353$	5.98337	+	4.34717i	0.318463	+	0.231377i	0.735519	−	0.677504i	$-0.236938\pi$
$353$	5.98337	+	4.34717i	0.318463	+	0.231377i	−0.417056	+	0.908881i	$0.636938\pi$
$354$	−1.64913	−	1.19816i	−0.0876501	−	0.0636815i
$355$	23.5644	+	7.17176i	1.25067	+	0.380638i
$356$	5.32013	−	3.86530i	0.281966	−	0.204861i
$357$	−4.99507			−0.264367
$358$	7.35831	−	5.34613i	0.388899	−	0.282552i
$359$	−3.15495	−	9.70993i	−0.166512	−	0.512470i	0.832633	−	0.553825i	$-0.186832\pi$
$359$	−3.15495	−	9.70993i	−0.166512	−	0.512470i	−0.999145	+	0.0413551i	$0.986832\pi$
$360$	5.19621	+	1.58145i	0.273864	+	0.0833498i
$361$	5.53335	−	17.0299i	0.291229	−	0.896311i
$362$	4.31133	+	13.2689i	0.226599	+	0.697399i
$363$	−0.233496	−	0.718626i	−0.0122554	−	0.0377181i
$364$	2.25432	−	6.93809i	0.118159	−	0.363655i
$365$	0.314576	+	16.8032i	0.0164657	+	0.879521i
$366$	1.30171	+	4.00624i	0.0680413	+	0.209410i
$367$	−12.2598	+	8.90723i	−0.639954	+	0.464954i	−0.859834	−	0.510573i	$-0.829433\pi$
$367$	−12.2598	+	8.90723i	−0.639954	+	0.464954i	0.219880	+	0.975527i	$0.429433\pi$
$368$	−6.66693			−0.347538
$369$	−3.67950	+	2.67331i	−0.191547	+	0.139167i
$370$	9.20787	−	3.18356i	0.478694	−	0.165506i
$371$	10.5338	+	7.65327i	0.546889	+	0.397338i
$372$	4.20127	+	3.05240i	0.217826	+	0.158260i
$373$	−6.61501	+	20.3589i	−0.342512	+	1.05414i	0.620390	+	0.784294i	$0.286974\pi$
$373$	−6.61501	+	20.3589i	−0.342512	+	1.05414i	−0.962902	+	0.269851i	$0.913026\pi$
$374$	5.12637			0.265078
$375$	7.87530	−	3.05740i	0.406679	−	0.157884i
$376$	1.27195			0.0655959
$377$	13.1369	−	40.4313i	0.676587	−	2.08232i
$378$	4.27971	+	3.10939i	0.220124	+	0.159930i
$379$	18.6494	+	13.5496i	0.957955	+	0.695995i	0.952675	−	0.303991i	$-0.0983192\pi$
$379$	18.6494	+	13.5496i	0.957955	+	0.695995i	0.00528034	+	0.999986i	$0.498319\pi$
$380$	−12.8385	+	4.43885i	−0.658603	+	0.227708i
$381$	−1.09515	+	0.795671i	−0.0561061	+	0.0407635i
$382$	25.8671			1.32348
$383$	−5.80379	+	4.21670i	−0.296560	+	0.215463i	−0.726108	−	0.687581i	$-0.758673\pi$
$383$	−5.80379	+	4.21670i	−0.296560	+	0.215463i	0.429548	+	0.903044i	$0.358673\pi$
$384$	−0.233496	−	0.718626i	−0.0119155	−	0.0366722i
$385$	−0.0539731	−	2.88300i	−0.00275072	−	0.146931i
$386$	0.372293	−	1.14580i	0.0189492	−	0.0583197i
$387$	−3.59776	−	11.0728i	−0.182884	−	0.562860i
$388$	2.27352	+	6.99717i	0.115420	+	0.355227i
$389$	−7.15549	+	22.0223i	−0.362798	+	1.11658i	0.588551	+	0.808460i	$0.299699\pi$
$389$	−7.15549	+	22.0223i	−0.362798	+	1.11658i	−0.951349	+	0.308117i	$0.900301\pi$
$390$	−9.14417	−	2.78300i	−0.463033	−	0.140923i
$391$	10.5613	+	32.5044i	0.534109	+	1.64382i
$392$	4.31779	−	3.13706i	0.218081	−	0.158445i
$393$	5.35578			0.270163
$394$	−15.8525	+	11.5175i	−0.798639	+	0.580245i
$395$	25.3933	+	7.72839i	1.27768	+	0.388858i
$396$	−1.96515	−	1.42776i	−0.0987524	−	0.0717478i
$397$	−3.77252	−	2.74090i	−0.189337	−	0.137562i	0.489078	−	0.872240i	$-0.337333\pi$
$397$	−3.77252	−	2.74090i	−0.189337	−	0.137562i	−0.678416	+	0.734678i	$0.737333\pi$
$398$	2.57747	−	7.93265i	0.129197	−	0.397628i
$399$	−5.91946			−0.296344
$400$	4.15225	+	2.78546i	0.207613	+	0.139273i
$401$	−28.6503			−1.43073			−0.715364	−	0.698752i	$-0.753739\pi$
$401$	−28.6503			−1.43073			−0.715364	+	0.698752i	$0.753739\pi$
$402$	0.712307	−	2.19225i	0.0355266	−	0.109340i
$403$	31.4545	+	22.8530i	1.56686	+	1.13839i
$404$	−10.4099	−	7.56321i	−0.517910	−	0.376284i
$405$	−5.36096	+	7.67691i	−0.266388	+	0.381469i
$406$	−7.83982	+	5.69596i	−0.389084	+	0.282686i
$407$	−4.35706			−0.215971
$408$	−3.13375	+	2.27680i	−0.155144	+	0.112718i
$409$	−9.07979	−	27.9447i	−0.448967	−	1.38178i	−0.878074	−	0.478524i	$-0.841172\pi$
$409$	−9.07979	−	27.9447i	−0.448967	−	1.38178i	0.429108	−	0.903253i	$-0.358828\pi$
$410$	−3.95694	+	1.36809i	−0.195419	+	0.0675650i
$411$	2.64042	−	8.12639i	0.130243	−	0.400845i
$412$	1.82004	+	5.60152i	0.0896672	+	0.275967i
$413$	1.07502	+	3.30858i	0.0528984	+	0.162804i
$414$	5.00433	−	15.4017i	0.245949	−	0.756955i
$415$	−20.1021	+	28.7863i	−0.986775	+	1.41306i
$416$	−1.74816	−	5.38028i	−0.0857106	−	0.263790i
$417$	0.234435	−	0.170327i	0.0114803	−	0.00834095i
$418$	6.07506			0.297141
$419$	−5.24071	+	3.80760i	−0.256026	+	0.186013i	−0.708393	−	0.705818i	$-0.750580\pi$
$419$	−5.24071	+	3.80760i	−0.256026	+	0.186013i	0.452368	+	0.891832i	$0.350580\pi$
$420$	1.31343	+	1.73840i	0.0640891	+	0.0848254i
$421$	25.5535	+	18.5657i	1.24540	+	0.904837i	0.997946	−	0.0640621i	$-0.0204056\pi$
$421$	25.5535	+	18.5657i	1.24540	+	0.904837i	0.247456	+	0.968899i	$0.420406\pi$
$422$	7.31209	+	5.31254i	0.355947	+	0.258611i
$423$	−0.954752	+	2.93842i	−0.0464216	+	0.142871i
$424$	10.0970			0.490355
$425$	7.00270	−	24.6567i	0.339681	−	1.19603i
$426$	8.32347			0.403273
$427$	2.22153	−	6.83715i	0.107507	−	0.330873i
$428$	2.94983	+	2.14317i	0.142585	+	0.103594i
$429$	3.45822	+	2.51255i	0.166965	+	0.121307i
$430$	−0.200611	−	10.7157i	−0.00967431	−	0.516757i
$431$	−4.16153	+	3.02353i	−0.200454	+	0.145638i	−0.683484	−	0.729966i	$-0.739536\pi$
$431$	−4.16153	+	3.02353i	−0.200454	+	0.145638i	0.483030	+	0.875604i	$0.339536\pi$
$432$	4.10224			0.197369
$433$	16.8667	−	12.2544i	0.810564	−	0.588909i	−0.103430	−	0.994637i	$-0.532982\pi$
$433$	16.8667	−	12.2544i	0.810564	−	0.588909i	0.913994	+	0.405728i	$0.132982\pi$
$434$	−2.73869	−	8.42883i	−0.131461	−	0.404597i
$435$	7.65397	+	10.1305i	0.366980	+	0.485718i
$436$	3.90847	−	12.0290i	0.187182	−	0.576087i
$437$	12.5158	+	38.5197i	0.598712	+	1.84265i
$438$	1.75494	+	5.40116i	0.0838544	+	0.258077i
$439$	0.311335	−	0.958190i	0.0148592	−	0.0457319i	−0.943352	−	0.331794i	$-0.892346\pi$
$439$	0.311335	−	0.958190i	0.0148592	−	0.0457319i	0.958211	+	0.286062i	$0.0923462\pi$
$440$	−1.34796	−	1.78410i	−0.0642614	−	0.0850536i
$441$	4.00612	+	12.3296i	0.190768	+	0.587122i
$442$	−23.4620	+	17.0462i	−1.11598	+	0.810804i
$443$	30.9840			1.47210			0.736048	−	0.676929i	$-0.236690\pi$
$443$	30.9840			1.47210			0.736048	+	0.676929i	$0.236690\pi$
$444$	2.66347	−	1.93513i	0.126403	−	0.0918370i
$445$	0.275237	+	14.7019i	0.0130475	+	0.696937i
$446$	21.4760	+	15.6032i	1.01692	+	0.738833i
$447$	12.1104	+	8.79871i	0.572802	+	0.416165i
$448$	−0.398490	+	1.22643i	−0.0188269	+	0.0579432i
$449$	0.350339			0.0165335			0.00826677	−	0.999966i	$-0.497369\pi$
$449$	0.350339			0.0165335			0.00826677	+	0.999966i	$0.497369\pi$
$450$	−9.55165	+	7.50158i	−0.450269	+	0.353628i
$451$	1.87238			0.0881669
$452$	4.76291	−	14.6587i	0.224029	−	0.689489i
$453$	−0.307226	−	0.223213i	−0.0144347	−	0.0104874i
$454$	−13.3132	−	9.67260i	−0.624819	−	0.453957i
$455$	9.83355	+	13.0153i	0.461004	+	0.610164i
$456$	−3.71368	+	2.69815i	−0.173909	+	0.126352i
$457$	6.70498			0.313646			0.156823	−	0.987627i	$-0.449875\pi$
$457$	6.70498			0.313646			0.156823	+	0.987627i	$0.449875\pi$
$458$	−6.74678	+	4.90182i	−0.315256	+	0.229047i
$459$	−6.49850	−	20.0003i	−0.303324	−	0.933535i
$460$	8.53525	−	12.2225i	0.397958	−	0.569877i
$461$	−3.12016	+	9.60286i	−0.145320	+	0.447250i	−0.997052	−	0.0767284i	$-0.975553\pi$
$461$	−3.12016	+	9.60286i	−0.145320	+	0.447250i	0.851732	+	0.523978i	$0.175553\pi$
$462$	−0.301102	−	0.926698i	−0.0140086	−	0.0431139i
$463$	−2.81422	−	8.66127i	−0.130788	−	0.402523i	0.864123	−	0.503280i	$-0.167874\pi$
$463$	−2.81422	−	8.66127i	−0.130788	−	0.402523i	−0.994911	+	0.100757i	$0.967874\pi$
$464$	−2.32218	+	7.14693i	−0.107804	+	0.331788i
$465$	−10.9746	+	3.79440i	−0.508934	+	0.175961i
$466$	−1.10056	−	3.38719i	−0.0509826	−	0.156908i
$467$	−27.3449	+	19.8672i	−1.26537	+	0.919346i	−0.999008	−	0.0445269i	$-0.985822\pi$
$467$	−27.3449	+	19.8672i	−1.26537	+	0.919346i	−0.266363	+	0.963873i	$0.585822\pi$
$468$	13.7416			0.635204
$469$	−3.18259	+	2.31229i	−0.146958	+	0.106771i
$470$	−1.62840	+	2.33187i	−0.0751125	+	0.107561i
$471$	7.18059	+	5.21701i	0.330864	+	0.240387i
$472$	2.18252	+	1.58569i	0.100458	+	0.0729873i
$473$	−1.48113	+	4.55846i	−0.0681026	+	0.209598i
$474$	8.96949			0.411982
$475$	8.29862	−	29.2197i	0.380767	−	1.34069i
$476$	6.61066			0.302999
$477$	−7.57902	+	23.3258i	−0.347020	+	1.06802i
$478$	19.4018	+	14.0962i	0.887419	+	0.644747i
$479$	−0.0558317	−	0.0405641i	−0.00255101	−	0.00185342i	0.586509	−	0.809943i	$-0.300502\pi$
$479$	−0.0558317	−	0.0405641i	−0.00255101	−	0.00185342i	−0.589060	+	0.808089i	$0.700502\pi$
$480$	1.61639	+	0.491943i	0.0737777	+	0.0224540i
$481$	19.9411	−	14.4881i	0.909238	−	0.660600i
$482$	−24.5630			−1.11882
$483$	5.25552	−	3.81836i	0.239135	−	0.173741i
$484$	0.309017	+	0.951057i	0.0140462	+	0.0432298i
$485$	−15.7386	−	4.78999i	−0.714651	−	0.217502i
$486$	−4.78075	+	14.7136i	−0.216859	+	0.667423i
$487$	4.22526	+	13.0040i	0.191465	+	0.589268i	1.00000		0.000819588i	$0.000260883\pi$
$487$	4.22526	+	13.0040i	0.191465	+	0.589268i	−0.808535	+	0.588448i	$0.799739\pi$
$488$	−1.72273	−	5.30201i	−0.0779841	−	0.240011i
$489$	2.69721	−	8.30115i	0.121972	−	0.375391i
$490$	0.223381	+	11.9320i	0.0100913	+	0.539032i
$491$	−4.85364	−	14.9380i	−0.219042	−	0.674142i	−0.998842	−	0.0481130i	$-0.984679\pi$
$491$	−4.85364	−	14.9380i	−0.219042	−	0.674142i	0.779800	−	0.626029i	$-0.215321\pi$
$492$	−1.14459	+	0.831590i	−0.0516019	+	0.0374910i
$493$	38.5232			1.73500
$494$	−27.8040	+	20.2008i	−1.25096	+	0.908875i
$495$	5.13337	−	1.77483i	0.230728	−	0.0797728i
$496$	−5.56011	−	4.03966i	−0.249656	−	0.181386i
$497$	−11.4921	−	8.34952i	−0.515492	−	0.374527i
$498$	−3.66633	+	11.2838i	−0.164292	+	0.505639i
$499$	−20.6968			−0.926514			−0.463257	−	0.886224i	$-0.653319\pi$
$499$	−20.6968			−0.926514			−0.463257	+	0.886224i	$0.653319\pi$
$500$	−10.4225	+	4.04628i	−0.466106	+	0.180955i
$501$	12.4422			0.555875
$502$	−2.59865	+	7.99782i	−0.115983	+	0.356960i
$503$	−30.9482	−	22.4852i	−1.37991	−	1.00257i	−0.996888	−	0.0788288i	$-0.974882\pi$
$503$	−30.9482	−	22.4852i	−1.37991	−	1.00257i	−0.383026	−	0.923738i	$-0.625118\pi$
$504$	−2.53414	−	1.84116i	−0.112879	−	0.0820117i
$505$	27.1927	−	9.40172i	1.21006	−	0.418371i
$506$	−5.39366	+	3.91873i	−0.239778	+	0.174209i
$507$	−14.3592			−0.637714
$508$	1.44936	−	1.05302i	0.0643049	−	0.0467202i
$509$	−6.57556	−	20.2375i	−0.291457	−	0.897012i	−0.984389	−	0.176009i	$-0.943681\pi$
$509$	−6.57556	−	20.2375i	−0.291457	−	0.897012i	0.692932	−	0.721003i	$-0.256319\pi$
$510$	−0.162124	−	8.65995i	−0.00717899	−	0.383469i
$511$	2.99503	−	9.21775i	0.132492	−	0.407769i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	−7.70112	−	23.7016i	−0.340013	−	1.04645i
$514$	−2.59738	+	7.99391i	−0.114566	+	0.352596i
$515$	−12.5994	−	3.83458i	−0.555194	−	0.168972i
$516$	−1.11916	−	3.44441i	−0.0492682	−	0.151632i
$517$	1.02903	−	0.747635i	0.0452567	−	0.0328809i
$518$	−5.61861			−0.246867
$519$	10.4481	−	7.59098i	0.458620	−	0.333207i
$520$	12.1017	+	3.68313i	0.530696	+	0.161516i
$521$	−30.9303	−	22.4722i	−1.35508	−	0.984525i	−0.998741	−	0.0501690i	$-0.984024\pi$
$521$	−30.9303	−	22.4722i	−1.35508	−	0.984525i	−0.356341	−	0.934356i	$-0.615976\pi$
$522$	−14.7675	−	10.7292i	−0.646358	−	0.469606i
$523$	−10.9484	+	33.6956i	−0.478738	+	1.47341i	0.362110	+	0.932135i	$0.382056\pi$
$523$	−10.9484	+	33.6956i	−0.478738	+	1.47341i	−0.840849	+	0.541270i	$0.817944\pi$
$524$	−7.08803			−0.309642
$525$	−4.86853	+	0.182353i	−0.212480	+	0.00795854i
$526$	−27.8869			−1.21592
$527$	−10.8872	+	33.5075i	−0.474256	+	1.45961i
$528$	−0.611300	−	0.444136i	−0.0266034	−	0.0193285i
$529$	−17.3518	−	12.6068i	−0.754427	−	0.548123i
$530$	−12.9266	+	18.5109i	−0.561495	+	0.804061i
$531$	−5.30145	+	3.85173i	−0.230063	+	0.167151i
$532$	7.83403			0.339648
$533$	−8.56939	+	6.22603i	−0.371182	+	0.269679i
$534$	1.53548	+	4.72572i	0.0664467	+	0.204502i
$535$	−7.70556	+	2.66415i	−0.333140	+	0.115181i
$536$	−0.942693	+	2.90131i	−0.0407181	+	0.125317i
$537$	2.12373	+	6.53618i	0.0916458	+	0.282057i
$538$	−7.96762	−	24.5218i	−0.343508	−	1.05721i
$539$	1.64925	−	5.07587i	0.0710382	−	0.218633i
$540$	−5.25184	+	7.52064i	−0.226003	+	0.323637i
$541$	−2.46316	−	7.58083i	−0.105900	−	0.325925i	0.884041	−	0.467409i	$-0.154813\pi$
$541$	−2.46316	−	7.58083i	−0.105900	−	0.325925i	−0.989941	+	0.141484i	$0.954813\pi$
$542$	−0.0651103	+	0.0473054i	−0.00279673	+	0.00203194i
$543$	−10.5421			−0.452404
$544$	4.14732	−	3.01320i	0.177815	−	0.129190i
$545$	17.0491	+	22.5654i	0.730303	+	0.966597i
$546$	4.45952	+	3.24003i	0.190850	+	0.138661i
$547$	9.04522	+	6.57174i	0.386746	+	0.280987i	0.764121	−	0.645073i	$-0.223173\pi$
$547$	9.04522	+	6.57174i	0.386746	+	0.280987i	−0.377375	+	0.926061i	$0.623173\pi$
$548$	−3.49443	+	10.7548i	−0.149275	+	0.459421i
$549$	13.5416			0.577943
$550$	4.99650	−	0.187146i	0.213051	−	0.00797994i
$551$	45.6524			1.94486
$552$	1.55670	−	4.79104i	0.0662576	−	0.203920i
$553$	−12.3841	−	8.99756i	−0.526625	−	0.382615i
$554$	7.91677	+	5.75187i	0.336352	+	0.244374i
$555$	0.137795	+	7.36036i	0.00584906	+	0.312430i
$556$	−0.310260	+	0.225417i	−0.0131579	+	0.00955981i
$557$	36.1018			1.52968			0.764840	−	0.644220i	$-0.222818\pi$
$557$	36.1018			1.52968			0.764840	+	0.644220i	$0.222818\pi$
$558$	13.5058	−	9.81255i	0.571747	−	0.415399i
$559$	−8.37901	−	25.7880i	−0.354395	−	1.09071i
$560$	−1.73825	−	2.30067i	−0.0734544	−	0.0972210i
$561$	−1.19699	+	3.68394i	−0.0505368	+	0.155536i
$562$	−5.77178	−	17.7637i	−0.243468	−	0.749317i
$563$	5.23297	+	16.1054i	0.220543	+	0.678763i	0.998713	+	0.0507091i	$0.0161481\pi$
$563$	5.23297	+	16.1054i	0.220543	+	0.678763i	−0.778170	+	0.628054i	$0.783852\pi$
$564$	−0.296995	+	0.914058i	−0.0125058	+	0.0384888i
$565$	20.7762	+	27.4985i	0.874063	+	1.15687i
$566$	2.64723	+	8.14733i	0.111271	+	0.342458i
$567$	4.36863	−	3.17400i	0.183465	−	0.133295i
$568$	−11.0156			−0.462204
$569$	−16.0468	+	11.6587i	−0.672716	+	0.488757i	−0.870933	−	0.491401i	$-0.836485\pi$
$569$	−16.0468	+	11.6587i	−0.672716	+	0.488757i	0.198217	+	0.980158i	$0.436485\pi$
$570$	−0.192127	−	10.2626i	−0.00804733	−	0.429852i
$571$	−30.0022	−	21.7979i	−1.25555	−	0.912213i	−0.257023	−	0.966405i	$-0.582742\pi$
$571$	−30.0022	−	21.7979i	−1.25555	−	0.912213i	−0.998531	+	0.0541923i	$0.982742\pi$
$572$	−4.57674	−	3.32520i	−0.191363	−	0.139033i
$573$	−6.03986	+	18.5888i	−0.252319	+	0.776557i
$574$	2.41451			0.100780
$575$	11.4804	+	31.2954i	0.478765	+	1.30511i
$576$	−2.42906			−0.101211
$577$	3.82405	−	11.7692i	0.159197	−	0.489959i	−0.839365	−	0.543569i	$-0.817073\pi$
$577$	3.82405	−	11.7692i	0.159197	−	0.489959i	0.998562	+	0.0536098i	$0.0170727\pi$
$578$	−7.50738	−	5.45443i	−0.312266	−	0.226874i
$579$	0.736473	+	0.535079i	0.0306068	+	0.0222371i
$580$	−10.1295	−	13.4070i	−0.420606	−	0.556696i
$581$	16.3812	−	11.9016i	0.679605	−	0.493762i
$582$	−5.55921			−0.230437
$583$	8.16866	−	5.93488i	0.338311	−	0.245798i
$584$	−2.32255	−	7.14809i	−0.0961080	−	0.295790i
$585$	−17.5925	+	25.1924i	−0.727358	+	1.04158i
$586$	−5.29257	+	16.2889i	−0.218634	+	0.672886i
$587$	7.63752	+	23.5059i	0.315234	+	0.970191i	0.975658	+	0.219298i	$0.0703767\pi$
$587$	7.63752	+	23.5059i	0.315234	+	0.970191i	−0.660424	+	0.750893i	$0.729623\pi$
$588$	1.24619	+	3.83537i	0.0513919	+	0.158168i
$589$	−12.9020	+	39.7084i	−0.531619	+	1.63616i
$590$	−5.70118	+	1.97115i	−0.234714	+	0.0811510i
$591$	−4.57531	−	14.0813i	−0.188203	−	0.579229i
$592$	−3.52494	+	2.56102i	−0.144874	+	0.105257i
$593$	22.9383			0.941964			0.470982	−	0.882143i	$-0.343900\pi$
$593$	22.9383			0.941964			0.470982	+	0.882143i	$0.343900\pi$
$594$	3.31878	−	2.41124i	0.136171	−	0.0989342i
$595$	−8.46321	+	12.1193i	−0.346958	+	0.496844i
$596$	−16.0273	−	11.6445i	−0.656505	−	0.476979i
$597$	5.09878	+	3.70448i	0.208679	+	0.151614i
$598$	11.6549	−	35.8700i	0.476603	−	1.46683i
$599$	38.3460			1.56678			0.783388	−	0.621533i	$-0.213490\pi$
$599$	38.3460			1.56678			0.783388	+	0.621533i	$0.213490\pi$
$600$	−2.97124	+	2.33352i	−0.121300	+	0.0952657i
$601$	22.2687			0.908360			0.454180	−	0.890910i	$-0.349932\pi$
$601$	22.2687			0.908360			0.454180	+	0.890910i	$0.349932\pi$
$602$	−1.90998	+	5.87832i	−0.0778451	+	0.239583i
$603$	−5.99491	−	4.35556i	−0.244132	−	0.177372i
$604$	0.406594	+	0.295408i	0.0165441	+	0.0120200i
$605$	−2.13919	−	0.651056i	−0.0869704	−	0.0264692i
$606$	7.86578	−	5.71483i	0.319526	−	0.232149i
$607$	−23.8201			−0.966826			−0.483413	−	0.875392i	$-0.660603\pi$
$607$	−23.8201			−0.966826			−0.483413	+	0.875392i	$0.660603\pi$
$608$	4.91482	−	3.57083i	0.199322	−	0.144816i
$609$	−2.26270	−	6.96388i	−0.0916893	−	0.282191i
$610$	11.9257	+	3.62955i	0.482856	+	0.146956i
$611$	−2.22357	+	6.84346i	−0.0899562	+	0.276857i
$612$	3.84795	+	11.8428i	0.155544	+	0.478716i
$613$	4.70009	+	14.4654i	0.189835	+	0.584252i	0.999998	−	0.00195265i	$-0.000621548\pi$
$613$	4.70009	+	14.4654i	0.189835	+	0.584252i	−0.810163	+	0.586204i	$0.800622\pi$
$614$	−1.41231	+	4.34665i	−0.0569962	+	0.175416i
$615$	−0.0592151	−	3.16300i	−0.00238779	−	0.127545i
$616$	0.398490	+	1.22643i	0.0160556	+	0.0494141i
$617$	−13.5914	+	9.87472i	−0.547169	+	0.397541i	−0.826740	−	0.562583i	$-0.809808\pi$
$617$	−13.5914	+	9.87472i	−0.547169	+	0.397541i	0.279572	+	0.960125i	$0.409808\pi$
$618$	−4.45037			−0.179020
$619$	−7.14436	+	5.19068i	−0.287156	+	0.208631i	−0.722033	−	0.691859i	$-0.756792\pi$
$619$	−7.14436	+	5.19068i	−0.287156	+	0.208631i	0.434876	+	0.900490i	$0.356792\pi$
$620$	14.5242	−	5.02164i	0.583305	−	0.201674i
$621$	22.1261	+	16.0756i	0.887890	+	0.645090i
$622$	−25.5494	−	18.5627i	−1.02444	−	0.744298i
$623$	2.62049	−	8.06503i	0.104988	−	0.323119i
$624$	4.27460			0.171121
$625$	5.92516	−	24.2877i	0.237006	−	0.971508i
$626$	25.8240			1.03214
$627$	−1.41850	+	4.36569i	−0.0566494	+	0.174349i
$628$	−9.50306	−	6.90438i	−0.379213	−	0.275515i
$629$	18.0701	+	13.1287i	0.720503	+	0.523476i
$630$	6.61970	−	2.28872i	0.263735	−	0.0911848i
$631$	−22.3966	+	16.2721i	−0.891595	+	0.647782i	−0.936293	−	0.351219i	$-0.885767\pi$
$631$	−22.3966	+	16.2721i	−0.891595	+	0.647782i	0.0446985	+	0.999001i	$0.485767\pi$
$632$	−11.8706			−0.472185
$633$	−5.52508	+	4.01420i	−0.219602	+	0.159550i
$634$	−5.08133	−	15.6387i	−0.201805	−	0.621093i
$635$	0.0749826	+	4.00523i	0.00297559	+	0.158943i
$636$	−2.35761	+	7.25599i	−0.0934854	+	0.287719i
$637$	9.33007	+	28.7150i	0.369671	+	1.13773i
$638$	2.32218	+	7.14693i	0.0919359	+	0.282950i
$639$	8.26851	−	25.4479i	0.327097	−	1.00670i
$640$	−2.13919	−	0.651056i	−0.0845588	−	0.0257352i
$641$	−5.33536	−	16.4206i	−0.210734	−	0.648573i	−0.999429	−	0.0337883i	$-0.989243\pi$
$641$	−5.33536	−	16.4206i	−0.210734	−	0.648573i	0.788695	−	0.614785i	$-0.210757\pi$
$642$	−2.22891	+	1.61940i	−0.0879682	+	0.0639126i
$643$	7.21031			0.284347			0.142173	−	0.989842i	$-0.454591\pi$
$643$	7.21031			0.284347			0.142173	+	0.989842i	$0.454591\pi$
$644$	−6.95535	+	5.05336i	−0.274079	+	0.199130i
$645$	7.74743	+	2.35791i	0.305055	+	0.0928426i
$646$	−25.1952	−	18.3054i	−0.991291	−	0.720215i
$647$	−17.8441	−	12.9645i	−0.701526	−	0.509688i	0.178903	−	0.983867i	$-0.442745\pi$
$647$	−17.8441	−	12.9645i	−0.701526	−	0.509688i	−0.880429	+	0.474178i	$0.842745\pi$
$648$	1.29400	−	3.98253i	0.0508332	−	0.156449i
$649$	2.69774			0.105895
$650$	−22.2454	+	17.4709i	−0.872535	+	0.685263i
$651$	6.69665			0.262463
$652$	−3.56958	+	10.9860i	−0.139796	+	0.430247i
$653$	25.3706	+	18.4328i	0.992827	+	0.721331i	0.960538	−	0.278148i	$-0.0897204\pi$
$653$	25.3706	+	18.4328i	0.992827	+	0.721331i	0.0322886	+	0.999479i	$0.489720\pi$
$654$	7.73178	+	5.61746i	0.302336	+	0.219660i
$655$	9.07436	−	12.9945i	0.354565	−	0.507737i
$656$	1.51479	−	1.10056i	0.0591425	−	0.0429695i
$657$	18.2566			0.712260
$658$	1.32698	−	0.964105i	0.0517310	−	0.0375847i
$659$	−10.5061	−	32.3345i	−0.409260	−	1.25957i	−0.917285	−	0.398231i	$-0.869624\pi$
$659$	−10.5061	−	32.3345i	−0.409260	−	1.25957i	0.508025	−	0.861342i	$-0.330376\pi$
$660$	1.59684	−	0.552099i	0.0621570	−	0.0214904i
$661$	−5.01120	+	15.4229i	−0.194913	+	0.599881i	0.805064	+	0.593187i	$0.202131\pi$
$661$	−5.01120	+	15.4229i	−0.194913	+	0.599881i	−0.999978	+	0.00669370i	$0.997869\pi$
$662$	−0.176061	−	0.541861i	−0.00684282	−	0.0210600i
$663$	−6.77154	−	20.8407i	−0.262985	−	0.809384i
$664$	4.85215	−	14.9334i	0.188300	−	0.579528i
$665$	−10.0294	+	14.3621i	−0.388924	+	0.556940i
$666$	−3.27049	−	10.0655i	−0.126729	−	0.390032i
$667$	−40.5319	+	29.4481i	−1.56940	+	1.14024i
$668$	−16.4664			−0.637105
$669$	−16.2274	+	11.7899i	−0.627388	+	0.455824i
$670$	−4.11211	−	5.44260i	−0.158865	−	0.210266i
$671$	−4.51016	−	3.27682i	−0.174113	−	0.126500i
$672$	−0.788297	−	0.572731i	−0.0304092	−	0.0220936i
$673$	7.72251	−	23.7675i	0.297681	−	0.916168i	−0.684627	−	0.728894i	$-0.740035\pi$
$673$	7.72251	−	23.7675i	0.297681	−	0.916168i	0.982308	−	0.187274i	$-0.0599653\pi$
$674$	−8.13914			−0.313508
$675$	−7.06401	−	19.2564i	−0.271894	−	0.741179i
$676$	19.0035			0.730903
$677$	−6.08413	+	18.7250i	−0.233832	+	0.719661i	0.763442	+	0.645876i	$0.223508\pi$
$677$	−6.08413	+	18.7250i	−0.233832	+	0.719661i	−0.997274	+	0.0737849i	$0.976492\pi$
$678$	9.42204	+	6.84551i	0.361851	+	0.262900i
$679$	7.67554	+	5.57660i	0.294560	+	0.214010i
$680$	0.214561	+	11.4609i	0.00822806	+	0.439505i
$681$	10.0596	−	7.30870i	0.385483	−	0.280070i
$682$	−6.87268			−0.263168
$683$	−15.4521	+	11.2266i	−0.591257	+	0.429573i	−0.842765	−	0.538282i	$-0.819074\pi$
$683$	−15.4521	+	11.2266i	−0.591257	+	0.429573i	0.251508	+	0.967855i	$0.419074\pi$
$684$	4.56006	+	14.0344i	0.174358	+	0.536619i
$685$	−15.2430	−	20.1750i	−0.582406	−	0.770847i
$686$	4.91621	−	15.1305i	0.187702	−	0.577686i
$687$	−1.94723	−	5.99297i	−0.0742916	−	0.228646i
$688$	1.48113	+	4.55846i	0.0564677	+	0.173790i
$689$	−17.6512	+	54.3248i	−0.672457	+	2.06961i
$690$	6.79047	+	8.98756i	0.258509	+	0.342151i
$691$	10.7276	+	33.0160i	0.408095	+	1.25599i	0.918283	+	0.395925i	$0.129576\pi$
$691$	10.7276	+	33.0160i	0.408095	+	1.25599i	−0.510187	+	0.860063i	$0.670424\pi$
$692$	−13.8274	+	10.0462i	−0.525638	+	0.381898i
$693$	−3.13237			−0.118989
$694$	−14.4827	+	10.5223i	−0.549757	+	0.399422i
$695$	−0.0160513	−	0.857387i	−0.000608860	−	0.0325225i
$696$	−4.59375	−	3.33756i	−0.174126	−	0.126510i
$697$	−7.76535	−	5.64186i	−0.294134	−	0.213701i
$698$	−8.30653	+	25.5649i	−0.314407	+	0.967645i
$699$	2.69110			0.101787
$700$	6.44319	−	0.241333i	0.243530	−	0.00912152i
$701$	27.1209			1.02434			0.512170	−	0.858884i	$-0.328842\pi$
$701$	27.1209			1.02434			0.512170	+	0.858884i	$0.328842\pi$
$702$	−7.17137	+	22.0712i	−0.270666	+	0.833024i
$703$	21.4142	+	15.5583i	0.807651	+	0.586793i
$704$	0.809017	+	0.587785i	0.0304910	+	0.0221530i
$705$	−1.29552	−	1.71469i	−0.0487921	−	0.0645791i
$706$	5.98337	−	4.34717i	0.225187	−	0.163608i
$707$	−16.5929			−0.624041
$708$	−1.64913	+	1.19816i	−0.0619780	+	0.0450297i
$709$	4.10932	+	12.6472i	0.154329	+	0.474975i	0.998092	−	0.0617404i	$-0.0196651\pi$
$709$	4.10932	+	12.6472i	0.154329	+	0.474975i	−0.843764	+	0.536715i	$0.819665\pi$
$710$	14.1026	−	20.1949i	0.529259	−	0.757901i
$711$	8.91027	−	27.4230i	0.334161	−	1.02844i
$712$	−2.03211	−	6.25419i	−0.0761565	−	0.234386i
$713$	−14.1591	−	43.5771i	−0.530261	−	1.63198i
$714$	−1.54356	+	4.75059i	−0.0577663	+	0.177787i
$715$	11.9554	−	4.13351i	0.447107	−	0.154584i
$716$	−2.81063	−	8.65022i	−0.105038	−	0.323274i
$717$	−14.6602	+	10.6512i	−0.547494	+	0.397778i
$718$	−10.2096			−0.381020
$719$	0.558635	−	0.405872i	0.0208336	−	0.0151365i	−0.577320	−	0.816518i	$-0.695901\pi$
$719$	0.558635	−	0.405872i	0.0208336	−	0.0151365i	0.598153	+	0.801382i	$0.295901\pi$
$720$	3.10977	−	4.45319i	0.115894	−	0.165961i
$721$	6.14458	+	4.46430i	0.228836	+	0.166259i
$722$	−14.4865	−	10.5251i	−0.539132	−	0.391702i
$723$	5.73537	−	17.6517i	0.213301	−	0.656472i
$724$	13.9518			0.518513
$725$	37.5473	−	1.40635i	1.39447	−	0.0522306i
$726$	−0.755608			−0.0280433
$727$	13.1360	−	40.4286i	0.487189	−	1.49941i	−0.341597	−	0.939847i	$-0.610968\pi$
$727$	13.1360	−	40.4286i	0.487189	−	1.49941i	0.828786	−	0.559566i	$-0.189032\pi$
$728$	−5.90189	−	4.28798i	−0.218739	−	0.158923i
$729$	0.705915	+	0.512877i	0.0261450	+	0.0189954i
$730$	16.0780	+	4.89330i	0.595074	+	0.181109i
$731$	19.8783	−	14.4424i	0.735225	−	0.534173i
$732$	4.21241			0.155695
$733$	11.5466	−	8.38913i	0.426485	−	0.309860i	−0.353757	−	0.935337i	$-0.615096\pi$
$733$	11.5466	−	8.38913i	0.426485	−	0.309860i	0.780242	+	0.625478i	$0.215096\pi$
$734$	4.68281	+	14.4122i	0.172846	+	0.531964i
$735$	−8.62680	−	2.62554i	−0.318204	−	0.0968446i
$736$	−2.06020	+	6.34063i	−0.0759398	+	0.233719i
$737$	0.942693	+	2.90131i	0.0347245	+	0.106871i
$738$	1.40544	+	4.32551i	0.0517351	+	0.159224i
$739$	9.93490	−	30.5765i	0.365461	−	1.12477i	−0.584231	−	0.811588i	$-0.698604\pi$
$739$	9.93490	−	30.5765i	0.365461	−	1.12477i	0.949692	−	0.313186i	$-0.101396\pi$
$740$	−0.182363	−	9.74098i	−0.00670378	−	0.358085i
$741$	−8.02469	−	24.6974i	−0.294794	−	0.907283i
$742$	10.5338	−	7.65327i	0.386709	−	0.280960i
$743$	−28.7756			−1.05568			−0.527838	−	0.849345i	$-0.676997\pi$
$743$	−28.7756			−1.05568			−0.527838	+	0.849345i	$0.676997\pi$
$744$	4.20127	−	3.05240i	0.154026	−	0.111906i
$745$	41.8667	−	14.4752i	1.53388	−	0.530329i
$746$	17.3183	+	12.5825i	0.634069	+	0.460678i
$747$	30.8565	+	22.4186i	1.12898	+	0.820253i
$748$	1.58413	−	4.87546i	0.0579217	−	0.178265i
$749$	4.70191			0.171804
$750$	−0.474163	−	8.43464i	−0.0173140	−	0.307990i
$751$	23.0748			0.842013			0.421006	−	0.907058i	$-0.361677\pi$
$751$	23.0748			0.842013			0.421006	+	0.907058i	$0.361677\pi$
$752$	0.393055	−	1.20970i	0.0143332	−	0.0441132i
$753$	−5.14067	−	3.73491i	−0.187336	−	0.136108i
$754$	−34.3929	−	24.9879i	−1.25252	−	0.910007i
$755$	−1.06211	+	0.367217i	−0.0386540	+	0.0133644i
$756$	4.27971	−	3.10939i	0.155651	−	0.113087i
$757$	−9.34514			−0.339655			−0.169827	−	0.985474i	$-0.554321\pi$
$757$	−9.34514			−0.339655			−0.169827	+	0.985474i	$0.554321\pi$
$758$	18.6494	−	13.5496i	0.677377	−	0.492143i
$759$	−1.55670	−	4.79104i	−0.0565047	−	0.173904i
$760$	0.254268	+	13.5819i	0.00922328	+	0.492666i
$761$	−3.85811	+	11.8740i	−0.139856	+	0.430433i	−0.996314	−	0.0857843i	$-0.972660\pi$
$761$	−3.85811	+	11.8740i	−0.139856	+	0.430433i	0.856457	+	0.516218i	$0.172660\pi$
$762$	0.418309	+	1.28742i	0.0151537	+	0.0466384i
$763$	−5.04014	−	15.5119i	−0.182465	−	0.561570i
$764$	7.99337	−	24.6011i	0.289190	−	0.890035i
$765$	−26.6377	−	8.10710i	−0.963087	−	0.293113i
$766$	2.21685	+	6.82276i	0.0800981	+	0.246516i
$767$	−12.3468	+	8.97051i	−0.445819	+	0.323906i
$768$	−0.755608			−0.0272657
$769$	−24.8585	+	18.0608i	−0.896420	+	0.651288i	−0.937544	−	0.347866i	$-0.886906\pi$
$769$	−24.8585	+	18.0608i	−0.896420	+	0.651288i	0.0411236	+	0.999154i	$0.486906\pi$
$770$	−2.75857	−	0.839563i	−0.0994120	−	0.0302558i
$771$	−5.13816	−	3.73309i	−0.185046	−	0.134444i
$772$	−0.974675	−	0.708143i	−0.0350793	−	0.0254866i
$773$	−12.0874	+	37.2013i	−0.434754	+	1.33804i	0.458584	+	0.888651i	$0.348357\pi$
$773$	−12.0874	+	37.2013i	−0.434754	+	1.33804i	−0.893338	+	0.449385i	$0.851643\pi$
$774$	−11.6426			−0.418484
$775$	−9.38818	+	33.0561i	−0.337233	+	1.18741i
$776$	7.35726			0.264110
$777$	1.31192	−	4.03768i	0.0470649	−	0.144851i
$778$	18.7333	+	13.6106i	0.671622	+	0.487962i
$779$	−9.20241	−	6.68594i	−0.329711	−	0.239549i
$780$	−5.47250	+	7.83663i	−0.195947	+	0.280596i
$781$	−8.91180	+	6.47480i	−0.318889	+	0.231687i
$782$	34.1771			1.22217
$783$	24.9397	−	18.1198i	0.891274	−	0.647548i
$784$	−1.64925	−	5.07587i	−0.0589018	−	0.181281i
$785$	24.8240	−	8.58274i	0.886006	−	0.306331i
$786$	1.65503	−	5.09365i	0.0590328	−	0.181684i
$787$	−7.45910	−	22.9568i	−0.265888	−	0.818320i	−0.991487	−	0.130203i	$-0.958437\pi$
$787$	−7.45910	−	22.9568i	−0.265888	−	0.818320i	0.725599	−	0.688118i	$-0.241563\pi$
$788$	6.05513	+	18.6358i	0.215705	+	0.663872i
$789$	6.51146	−	20.0402i	0.231814	−	0.713451i
$790$	15.1971	−	21.7623i	0.540689	−	0.774268i
$791$	−6.14197	−	18.9031i	−0.218383	−	0.672115i
$792$	−1.96515	+	1.42776i	−0.0698285	+	0.0507334i
$793$	31.5379			1.11994
$794$	−3.77252	+	2.74090i	−0.133882	+	0.0972708i
$795$	−10.2841	−	13.6116i	−0.364740	−	0.482753i
$796$	−6.74792	−	4.90265i	−0.239174	−	0.173770i
$797$	−24.0487	−	17.4724i	−0.851848	−	0.618904i	0.0738071	−	0.997273i	$-0.476485\pi$
$797$	−24.0487	−	17.4724i	−0.851848	−	0.618904i	−0.925655	+	0.378369i	$0.876485\pi$
$798$	−1.82921	+	5.62974i	−0.0647535	+	0.199291i
$799$	−6.52049			−0.230678
$800$	3.93225	−	3.08827i	0.139026	−	0.109187i
$801$	15.9736			0.564399
$802$	−8.85343	+	27.2481i	−0.312626	+	0.962163i
$803$	−6.08053	−	4.41776i	−0.214577	−	0.155899i
$804$	−1.86484	−	1.35489i	−0.0657679	−	0.0477832i
$805$	−0.359835	−	19.2207i	−0.0126825	−	0.677442i
$806$	31.4545	−	22.8530i	1.10794	−	0.804963i
$807$	19.4824			0.685814
$808$	−10.4099	+	7.56321i	−0.366218	+	0.266073i
$809$	−14.2705	−	43.9200i	−0.501723	−	1.54414i	−0.806211	−	0.591627i	$-0.798486\pi$
$809$	−14.2705	−	43.9200i	−0.501723	−	1.54414i	0.304489	−	0.952516i	$-0.401514\pi$
$810$	5.64455	+	7.47088i	0.198329	+	0.262500i
$811$	−7.33107	+	22.5627i	−0.257429	+	0.792284i	0.735913	+	0.677076i	$0.236753\pi$
$811$	−7.33107	+	22.5627i	−0.257429	+	0.792284i	−0.993341	+	0.115207i	$0.963247\pi$
$812$	2.99454	+	9.21626i	0.105088	+	0.323427i
$813$	−0.0187919	−	0.0578356i	−0.000659061	−	0.00202838i
$814$	−1.34641	+	4.14381i	−0.0471915	+	0.145240i
$815$	−15.5708	−	20.6088i	−0.545422	−	0.721896i
$816$	1.19699	+	3.68394i	0.0419029	+	0.128964i
$817$	23.5570	−	17.1152i	0.824155	−	0.598784i
$818$	−29.3828			−1.02735
$819$	14.3360	−	10.4157i	0.500941	−	0.363955i
$820$	0.0783675	+	4.18603i	0.00273671	+	0.146183i
$821$	−7.80539	−	5.67095i	−0.272410	−	0.197917i	0.443190	−	0.896428i	$-0.353847\pi$
$821$	−7.80539	−	5.67095i	−0.272410	−	0.197917i	−0.715600	+	0.698510i	$0.753847\pi$
$822$	−6.91272	−	5.02239i	−0.241109	−	0.175176i
$823$	7.17282	−	22.0757i	0.250029	−	0.769509i	−0.744740	−	0.667355i	$-0.767426\pi$
$823$	7.17282	−	22.0757i	0.250029	−	0.769509i	0.994769	−	0.102154i	$-0.0325736\pi$
$824$	5.88979			0.205181
$825$	−1.03217	+	3.63431i	−0.0359357	+	0.126531i
$826$	3.47884			0.121044
$827$	−2.39449	+	7.36947i	−0.0832645	+	0.256262i	−0.984018	−	0.178069i	$-0.943015\pi$
$827$	−2.39449	+	7.36947i	−0.0832645	+	0.256262i	0.900754	+	0.434331i	$0.143015\pi$
$828$	−13.1015	−	9.51880i	−0.455309	−	0.330801i
$829$	−28.8620	−	20.9695i	−1.00242	−	0.728301i	−0.0398146	−	0.999207i	$-0.512677\pi$
$829$	−28.8620	−	20.9695i	−1.00242	−	0.728301i	−0.962606	+	0.270906i	$0.912677\pi$
$830$	21.1655	+	28.0137i	0.734665	+	0.972370i
$831$	−5.98198	+	4.34616i	−0.207513	+	0.150767i
$832$	−5.65716			−0.196127
$833$	−22.1346	+	16.0817i	−0.766918	+	0.557198i
$834$	−0.0895462	−	0.275595i	−0.00310073	−	0.00954307i
$835$	21.0809	−	30.1879i	0.729535	−	1.04470i
$836$	1.87730	−	5.77772i	0.0649276	−	0.199827i
$837$	8.71223	+	26.8135i	0.301139	+	0.926810i
$838$	2.00177	+	6.16083i	0.0691501	+	0.212822i
$839$	16.4918	−	50.7566i	0.569360	−	1.75231i	−0.0852652	−	0.996358i	$-0.527174\pi$
$839$	16.4918	−	50.7566i	0.569360	−	1.75231i	0.654626	−	0.755953i	$-0.272826\pi$
$840$	2.05919	−	0.711954i	0.0710490	−	0.0245648i
$841$	8.48904	+	26.1266i	0.292725	+	0.900916i
$842$	25.5535	−	18.5657i	0.880632	−	0.639817i
$843$	14.1132			0.486083
$844$	7.31209	−	5.31254i	0.251692	−	0.182865i
$845$	−24.3290	+	34.8391i	−0.836942	+	1.19850i
$846$	2.49957	+	1.81605i	0.0859371	+	0.0624369i
$847$	1.04326	+	0.757973i	0.0358469	+	0.0260443i
$848$	3.12015	−	9.60284i	0.107146	−	0.329763i
$849$	−6.47300			−0.222153
$850$	−21.2860	−	14.2793i	−0.730103	−	0.489776i
$851$	−29.0482			−0.995761
$852$	2.57209	−	7.91609i	0.0881185	−	0.271201i
$853$	41.5871	+	30.2148i	1.42391	+	1.03453i	0.991110	+	0.133046i	$0.0424760\pi$
$853$	41.5871	+	30.2148i	1.42391	+	1.03453i	0.432804	+	0.901488i	$0.357524\pi$
$854$	−5.81603	−	4.22559i	−0.199020	−	0.144597i
$855$	−31.5672	−	9.60740i	−1.07958	−	0.328566i
$856$	2.94983	−	2.14317i	0.100823	−	0.0732522i
$857$	31.9429			1.09115			0.545575	−	0.838062i	$-0.316311\pi$
$857$	31.9429			1.09115			0.545575	+	0.838062i	$0.316311\pi$
$858$	3.45822	−	2.51255i	0.118062	−	0.0857769i
$859$	−8.89253	−	27.3684i	−0.303409	−	0.933798i	−0.980266	−	0.197683i	$-0.936658\pi$
$859$	−8.89253	−	27.3684i	−0.303409	−	0.933798i	0.676857	−	0.736115i	$-0.263342\pi$
$860$	−10.2532	−	3.12054i	−0.349632	−	0.106410i
$861$	−0.563778	+	1.73513i	−0.0192135	+	0.0591331i
$862$	1.58956	+	4.89217i	0.0541407	+	0.166628i
$863$	−9.40233	−	28.9374i	−0.320059	−	0.985040i	−0.973622	−	0.228168i	$-0.926726\pi$
$863$	−9.40233	−	28.9374i	−0.320059	−	0.985040i	0.653563	−	0.756872i	$-0.273274\pi$
$864$	1.26766	−	3.90146i	0.0431267	−	0.132730i
$865$	−0.715360	−	38.2112i	−0.0243230	−	1.29922i
$866$	−6.44252	−	19.8280i	−0.218926	−	0.673784i
$867$	5.67264	−	4.12141i	0.192653	−	0.139971i
$868$	−8.86260			−0.300816
$869$	−9.60348	+	6.97734i	−0.325776	+	0.236690i
$870$	11.9998	−	4.14887i	0.406833	−	0.140660i
$871$	−13.9619	−	10.1439i	−0.473080	−	0.343713i
$872$	−10.2325	−	7.43436i	−0.346517	−	0.251759i
$873$	−5.52250	+	16.9965i	−0.186908	+	0.575245i
$874$	40.5020			1.37000
$875$	−7.80637	+	12.1213i	−0.263903	+	0.409774i
$876$	5.67911			0.191879
$877$	5.05071	−	15.5445i	0.170550	−	0.524900i	−0.828852	−	0.559468i	$-0.811005\pi$
$877$	5.05071	−	15.5445i	0.170550	−	0.524900i	0.999402	+	0.0345677i	$0.0110054\pi$
$878$	−0.815086	−	0.592194i	−0.0275078	−	0.0199856i
$879$	−10.4698	−	7.60676i	−0.353138	−	0.256570i
$880$	−2.11332	+	0.730668i	−0.0712400	+	0.0246308i
$881$	27.8547	−	20.2376i	0.938447	−	0.681822i	−0.00959926	−	0.999954i	$-0.503056\pi$
$881$	27.8547	−	20.2376i	0.938447	−	0.681822i	0.948046	+	0.318132i	$0.103056\pi$
$882$	12.9641			0.436523
$883$	−37.0014	+	26.8831i	−1.24520	+	0.904687i	−0.997933	−	0.0642612i	$-0.979531\pi$
$883$	−37.0014	+	26.8831i	−1.24520	+	0.904687i	−0.247262	+	0.968949i	$0.579531\pi$
$884$	8.96170	+	27.5813i	0.301415	+	0.927659i
$885$	−0.0853176	−	4.55728i	−0.00286792	−	0.153191i
$886$	9.57460	−	29.4676i	0.321665	−	0.989983i
$887$	−12.7436	−	39.2206i	−0.427887	−	1.31690i	−0.900203	−	0.435471i	$-0.856582\pi$
$887$	−12.7436	−	39.2206i	−0.427887	−	1.31690i	0.472316	−	0.881429i	$-0.343418\pi$
$888$	−1.01736	−	3.13110i	−0.0341402	−	0.105073i
$889$	0.713897	−	2.19715i	0.0239433	−	0.0736900i
$890$	14.0674	+	4.28137i	0.471540	+	0.143512i
$891$	−1.29400	−	3.98253i	−0.0433507	−	0.133420i
$892$	21.4760	−	15.6032i	0.719069	−	0.522434i
$893$	−7.72718			−0.258580
$894$	12.1104	−	8.79871i	0.405032	−	0.294273i
$895$	19.4567	+	5.92160i	0.650366	+	0.197937i
$896$	1.04326	+	0.757973i	0.0348529	+	0.0253221i
$897$	23.0558	+	16.7510i	0.769809	+	0.559299i
$898$	0.108261	−	0.333192i	0.00361271	−	0.0111188i
$899$	−51.6463			−1.72250
$900$	4.18281	+	11.4023i	0.139427	+	0.380076i
$901$	−51.7610			−1.72441
$902$	0.578597	−	1.78074i	0.0192652	−	0.0592921i
$903$	−3.77834	−	2.74513i	−0.125735	−	0.0913521i
$904$	−12.4695	−	9.05960i	−0.414728	−	0.301318i
$905$	−17.8616	+	25.5778i	−0.593738	+	0.850235i
$906$	−0.307226	+	0.223213i	−0.0102069	+	0.00741574i
$907$	2.67085			0.0886840			0.0443420	−	0.999016i	$-0.485881\pi$
$907$	2.67085			0.0886840			0.0443420	+	0.999016i	$0.485881\pi$
$908$	−13.3132	+	9.67260i	−0.441814	+	0.320996i
$909$	−9.65845	−	29.7256i	−0.320350	−	0.985937i
$910$	15.4170	−	5.33033i	0.511068	−	0.176699i
$911$	−17.9435	+	55.2245i	−0.594496	+	1.82967i	−0.0372758	+	0.999305i	$0.511868\pi$
$911$	−17.9435	+	55.2245i	−0.594496	+	1.82967i	−0.557220	+	0.830365i	$0.688132\pi$
$912$	1.41850	+	4.36569i	0.0469712	+	0.144563i
$913$	−4.85215	−	14.9334i	−0.160583	−	0.494223i
$914$	2.07195	−	6.37682i	0.0685341	−	0.210926i
$915$	−5.39288	+	7.72262i	−0.178283	+	0.255302i
$916$	2.57704	+	7.93132i	0.0851478	+	0.262058i
$917$	−7.39467	+	5.37254i	−0.244193	+	0.177417i
$918$	−21.0296			−0.694080
$919$	−34.0306	+	24.7247i	−1.12257	+	0.815591i	−0.984596	−	0.174845i	$-0.944057\pi$
$919$	−34.0306	+	24.7247i	−1.12257	+	0.815591i	−0.137969	+	0.990437i	$0.544057\pi$
$920$	−8.98675	−	11.8945i	−0.296284	−	0.392149i
$921$	−2.79385	−	2.02985i	−0.0920604	−	0.0668858i
$922$	8.16868	+	5.93489i	0.269021	+	0.195455i
$923$	19.2570	−	59.2669i	0.633852	−	1.95080i
$924$	−0.974388			−0.0320550
$925$	18.0916	+	12.1364i	0.594849	+	0.399043i
$926$	−9.10700			−0.299274
$927$	−4.42099	+	13.6064i	−0.145204	+	0.446893i
$928$	6.07954	+	4.41704i	0.199571	+	0.144997i
$929$	−7.19811	−	5.22973i	−0.236162	−	0.171582i	0.463410	−	0.886144i	$-0.346626\pi$
$929$	−7.19811	−	5.22973i	−0.236162	−	0.171582i	−0.699572	+	0.714562i	$0.746626\pi$
$930$	0.217353	+	11.6100i	0.00712727	+	0.380706i
$931$	−26.2308	+	19.0578i	−0.859681	+	0.624594i
$932$	−3.56150			−0.116661
$933$	19.3053	−	14.0262i	0.632029	−	0.459196i
$934$	10.4448	+	32.1459i	0.341765	+	1.05184i
$935$	6.91013	+	9.14594i	0.225985	+	0.299104i
$936$	4.24638	−	13.0690i	0.138797	−	0.427174i
$937$	−3.63170	−	11.1772i	−0.118643	−	0.365144i	0.874047	−	0.485842i	$-0.161487\pi$
$937$	−3.63170	−	11.1772i	−0.118643	−	0.365144i	−0.992689	+	0.120697i	$0.961487\pi$
$938$	1.21564	+	3.74136i	0.0396921	+	0.122160i
$939$	−6.02980	+	18.5578i	−0.196775	+	0.605612i
$940$	1.71454	+	2.26929i	0.0559221	+	0.0740160i
$941$	0.952237	+	2.93068i	0.0310420	+	0.0955376i	0.965377	−	0.260858i	$-0.0840055\pi$
$941$	0.952237	+	2.93068i	0.0310420	+	0.0955376i	−0.934335	+	0.356396i	$0.884005\pi$
$942$	7.18059	−	5.21701i	0.233956	−	0.169979i
$943$	12.4830			0.406503
$944$	2.18252	−	1.58569i	0.0710348	−	0.0516098i
$945$	0.221411	+	11.8267i	0.00720249	+	0.384724i
$946$	3.87766	+	2.81728i	0.126074	+	0.0915978i
$947$	−23.0468	−	16.7445i	−0.748919	−	0.544122i	0.146572	−	0.989200i	$-0.453176\pi$
$947$	−23.0468	−	16.7445i	−0.748919	−	0.544122i	−0.895492	+	0.445078i	$0.853176\pi$
$948$	2.77172	−	8.53049i	0.0900214	−	0.277057i
$949$	42.5189			1.38022
$950$	−25.2252	−	16.9218i	−0.818412	−	0.549017i
$951$	12.4249			0.402904
$952$	2.04281	−	6.28711i	0.0662077	−	0.203766i
$953$	8.09890	+	5.88420i	0.262349	+	0.190608i	0.711182	−	0.703008i	$-0.248160\pi$
$953$	8.09890	+	5.88420i	0.262349	+	0.190608i	−0.448833	+	0.893616i	$0.648160\pi$
$954$	19.8421	+	14.4162i	0.642413	+	0.466740i
$955$	34.8678	+	46.1494i	1.12829	+	1.49336i
$956$	19.4018	−	14.0962i	0.627500	−	0.455905i
$957$	−5.67819			−0.183550
$958$	−0.0558317	+	0.0405641i	−0.00180384	+	0.00131057i
$959$	4.50622	+	13.8687i	0.145513	+	0.447844i
$960$	0.967358	−	1.38526i	0.0312213	−	0.0447090i
$961$	5.01648	−	15.4391i	0.161822	−	0.498037i
$962$	−7.61684	−	23.4422i	−0.245577	−	0.755807i
$963$	2.73690	+	8.42331i	0.0881953	+	0.271437i
$964$	−7.59040	+	23.3608i	−0.244470	+	0.752402i
$965$	2.54605	−	0.880283i	0.0819604	−	0.0283373i
$966$	−2.00743	−	6.17824i	−0.0645880	−	0.198781i
$967$	−18.8197	+	13.6733i	−0.605201	+	0.439705i	−0.847721	−	0.530442i	$-0.822026\pi$
$967$	−18.8197	+	13.6733i	−0.605201	+	0.439705i	0.242520	+	0.970146i	$0.422026\pi$
$968$	1.00000			0.0321412
$969$	19.0377	−	13.8317i	0.611579	−	0.444338i
$970$	−9.41903	+	13.4881i	−0.302427	+	0.433076i
$971$	6.89896	+	5.01239i	0.221398	+	0.160855i	0.692956	−	0.720980i	$-0.256308\pi$
$971$	6.89896	+	5.01239i	0.221398	+	0.160855i	−0.471558	+	0.881835i	$0.656308\pi$
$972$	12.5162	+	9.09352i	0.401456	+	0.291675i
$973$	−0.152822	+	0.470337i	−0.00489924	+	0.0150783i
$974$	13.6732			0.438118
$975$	−7.36081	−	20.0655i	−0.235735	−	0.642610i
$976$	−5.57486			−0.178447
$977$	−0.342542	+	1.05424i	−0.0109589	+	0.0337280i	−0.956386	−	0.292104i	$-0.905645\pi$
$977$	−0.342542	+	1.05424i	−0.0109589	+	0.0337280i	0.945428	+	0.325832i	$0.105645\pi$
$978$	−7.06138	−	5.13039i	−0.225798	−	0.164052i
$979$	−5.32013	−	3.86530i	−0.170032	−	0.123536i
$980$	11.4170	+	3.47474i	0.364704	+	0.110997i
$981$	24.8554	−	18.0585i	0.793570	−	0.576563i
$982$	−15.7067			−0.501222
$983$	−3.14696	+	2.28640i	−0.100373	+	0.0729249i	−0.636840	−	0.770996i	$-0.719759\pi$
$983$	−3.14696	+	2.28640i	−0.100373	+	0.0729249i	0.536467	+	0.843921i	$0.319759\pi$
$984$	0.437193	+	1.34554i	0.0139372	+	0.0428943i
$985$	−41.9170	−	12.7573i	−1.33559	−	0.406482i
$986$	11.9043	−	36.6378i	0.379111	−	1.16678i
$987$	0.382988	+	1.17872i	0.0121906	+	0.0375189i
$988$	10.6202	+	32.6855i	0.337872	+	1.03986i
$989$	−9.87462	+	30.3910i	−0.313995	+	0.966376i
$990$	−0.101667	−	5.43058i	−0.00323119	−	0.172595i
$991$	−2.47807	−	7.62670i	−0.0787184	−	0.242270i	0.903951	−	0.427635i	$-0.140653\pi$
$991$	−2.47807	−	7.62670i	−0.0787184	−	0.242270i	−0.982670	+	0.185365i	$0.940653\pi$
$992$	−5.56011	+	4.03966i	−0.176534	+	0.128259i
$993$	0.430505			0.0136617
$994$	−11.4921	+	8.34952i	−0.364508	+	0.264831i
$995$	17.6270	−	6.09442i	0.558812	−	0.193206i
$996$	9.59856	+	6.97376i	0.304142	+	0.220972i
$997$	15.5673	+	11.3103i	0.493022	+	0.358201i	0.806345	−	0.591445i	$-0.201442\pi$
$997$	15.5673	+	11.3103i	0.493022	+	0.358201i	−0.313323	+	0.949646i	$0.601442\pi$
$998$	−6.39565	+	19.6838i	−0.202451	+	0.623080i
$999$	17.8737			0.565499

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	550.2.k.d.221.5	✓	24
25.6	even	5	inner	550.2.k.d.331.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
550.2.k.d.221.5	✓	24	1.1	even	1	trivial
550.2.k.d.331.5	yes	24	25.6	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	550.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(0.611300 + 0.444136i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(2.11332 - 0.730668i) q^{5} +(0.611300 - 0.444136i) q^{6} -1.28954 q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.750620 - 2.31017i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(0.611300 + 0.444136i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(2.11332 - 0.730668i) q^{5} +(0.611300 - 0.444136i) q^{6} -1.28954 q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.750620 - 2.31017i) q^{9} +(-0.0418545 - 2.23568i) q^{10} +(-0.309017 + 0.951057i) q^{11} +(-0.233496 - 0.718626i) q^{12} +(-1.74816 - 5.38028i) q^{13} +(-0.398490 + 1.22643i) q^{14} +(1.61639 + 0.491943i) q^{15} +(0.309017 + 0.951057i) q^{16} +(4.14732 - 3.01320i) q^{17} -2.42906 q^{18} +(4.91482 - 3.57083i) q^{19} +(-2.13919 - 0.651056i) q^{20} +(-0.788297 - 0.572731i) q^{21} +(0.809017 + 0.587785i) q^{22} +(-2.06020 + 6.34063i) q^{23} -0.755608 q^{24} +(3.93225 - 3.08827i) q^{25} -5.65716 q^{26} +(1.26766 - 3.90146i) q^{27} +(1.04326 + 0.757973i) q^{28} +(6.07954 + 4.41704i) q^{29} +(0.967358 - 1.38526i) q^{30} +(-5.56011 + 4.03966i) q^{31} +1.00000 q^{32} +(-0.611300 + 0.444136i) q^{33} +(-1.58413 - 4.87546i) q^{34} +(-2.72521 + 0.942226i) q^{35} +(-0.750620 + 2.31017i) q^{36} +(1.34641 + 4.14381i) q^{37} +(-1.87730 - 5.77772i) q^{38} +(1.32092 - 4.06539i) q^{39} +(-1.28024 + 1.83330i) q^{40} +(-0.578597 - 1.78074i) q^{41} +(-0.788297 + 0.572731i) q^{42} +4.79305 q^{43} +(0.809017 - 0.587785i) q^{44} +(-3.27427 - 4.33368i) q^{45} +(5.39366 + 3.91873i) q^{46} +(-1.02903 - 0.747635i) q^{47} +(-0.233496 + 0.718626i) q^{48} -5.33708 q^{49} +(-1.72199 - 4.69412i) q^{50} +3.87353 q^{51} +(-1.74816 + 5.38028i) q^{52} +(-8.16866 - 5.93488i) q^{53} +(-3.31878 - 2.41124i) q^{54} +(0.0418545 + 2.23568i) q^{55} +(1.04326 - 0.757973i) q^{56} +4.59036 q^{57} +(6.07954 - 4.41704i) q^{58} +(-0.833647 - 2.56570i) q^{59} +(-1.01853 - 1.34808i) q^{60} +(-1.72273 + 5.30201i) q^{61} +(2.12377 + 6.53630i) q^{62} +(0.967955 + 2.97906i) q^{63} +(0.309017 - 0.951057i) q^{64} +(-7.62562 - 10.0929i) q^{65} +(0.233496 + 0.718626i) q^{66} +(2.46800 - 1.79311i) q^{67} -5.12637 q^{68} +(-4.07550 + 2.96102i) q^{69} +(0.0539731 + 2.88300i) q^{70} +(8.91180 + 6.47480i) q^{71} +(1.96515 + 1.42776i) q^{72} +(-2.32255 + 7.14809i) q^{73} +4.35706 q^{74} +(3.77540 - 0.141409i) q^{75} -6.07506 q^{76} +(0.398490 - 1.22643i) q^{77} +(-3.45822 - 2.51255i) q^{78} +(9.60348 + 6.97734i) q^{79} +(1.34796 + 1.78410i) q^{80} +(-3.38774 + 2.46134i) q^{81} -1.87238 q^{82} +(-12.7031 + 9.22934i) q^{83} +(0.301102 + 0.926698i) q^{84} +(6.56296 - 9.39817i) q^{85} +(1.48113 - 4.55846i) q^{86} +(1.75466 + 5.40028i) q^{87} +(-0.309017 - 0.951057i) q^{88} +(-2.03211 + 6.25419i) q^{89} +(-5.13337 + 1.77483i) q^{90} +(2.25432 + 6.93809i) q^{91} +(5.39366 - 3.91873i) q^{92} -5.19305 q^{93} +(-1.02903 + 0.747635i) q^{94} +(7.77751 - 11.1374i) q^{95} +(0.611300 + 0.444136i) q^{96} +(-5.95215 - 4.32449i) q^{97} +(-1.64925 + 5.07587i) q^{98} +2.42906 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{2} - 2 q^{3} - 6 q^{4} + 6 q^{5} - 2 q^{6} - 6 q^{8} - 14 q^{9}+O(q^{10}) \) 24 * q - 6 * q^2 - 2 * q^3 - 6 * q^4 + 6 * q^5 - 2 * q^6 - 6 * q^8 - 14 * q^9	\( 24 q - 6 q^{2} - 2 q^{3} - 6 q^{4} + 6 q^{5} - 2 q^{6} - 6 q^{8} - 14 q^{9} + q^{10} + 6 q^{11} - 2 q^{12} - 9 q^{15} - 6 q^{16} + 13 q^{17} + 16 q^{18} - 11 q^{19} - 9 q^{20} + 33 q^{21} + 6 q^{22} - 17 q^{23} + 8 q^{24} - 16 q^{25} - 11 q^{27} + 10 q^{29} + q^{30} - 11 q^{31} + 24 q^{32} + 2 q^{33} - 12 q^{34} + 4 q^{35} - 14 q^{36} - 15 q^{37} - q^{38} + 3 q^{39} + q^{40} + 28 q^{41} + 33 q^{42} + 16 q^{43} + 6 q^{44} + 13 q^{45} + 3 q^{46} - 28 q^{47} - 2 q^{48} + 16 q^{49} - q^{50} + 26 q^{51} - 57 q^{53} + 4 q^{54} - q^{55} + 18 q^{57} + 10 q^{58} - 7 q^{59} + 46 q^{60} - q^{62} - 30 q^{63} - 6 q^{64} - 23 q^{65} + 2 q^{66} + 23 q^{67} - 2 q^{68} - 45 q^{69} - 6 q^{70} + 29 q^{71} + 6 q^{72} - 27 q^{73} + 40 q^{74} + 19 q^{75} + 24 q^{76} - 2 q^{78} - q^{79} + q^{80} - 26 q^{81} - 2 q^{82} - 47 q^{83} - 32 q^{84} + 12 q^{85} - 9 q^{86} - 14 q^{87} + 6 q^{88} - 4 q^{89} - 32 q^{90} + 27 q^{91} + 3 q^{92} + 148 q^{93} - 28 q^{94} - 6 q^{95} - 2 q^{96} - 31 q^{97} + 36 q^{98} - 16 q^{99}+O(q^{100}) \) 24 * q - 6 * q^2 - 2 * q^3 - 6 * q^4 + 6 * q^5 - 2 * q^6 - 6 * q^8 - 14 * q^9 + q^10 + 6 * q^11 - 2 * q^12 - 9 * q^15 - 6 * q^16 + 13 * q^17 + 16 * q^18 - 11 * q^19 - 9 * q^20 + 33 * q^21 + 6 * q^22 - 17 * q^23 + 8 * q^24 - 16 * q^25 - 11 * q^27 + 10 * q^29 + q^30 - 11 * q^31 + 24 * q^32 + 2 * q^33 - 12 * q^34 + 4 * q^35 - 14 * q^36 - 15 * q^37 - q^38 + 3 * q^39 + q^40 + 28 * q^41 + 33 * q^42 + 16 * q^43 + 6 * q^44 + 13 * q^45 + 3 * q^46 - 28 * q^47 - 2 * q^48 + 16 * q^49 - q^50 + 26 * q^51 - 57 * q^53 + 4 * q^54 - q^55 + 18 * q^57 + 10 * q^58 - 7 * q^59 + 46 * q^60 - q^62 - 30 * q^63 - 6 * q^64 - 23 * q^65 + 2 * q^66 + 23 * q^67 - 2 * q^68 - 45 * q^69 - 6 * q^70 + 29 * q^71 + 6 * q^72 - 27 * q^73 + 40 * q^74 + 19 * q^75 + 24 * q^76 - 2 * q^78 - q^79 + q^80 - 26 * q^81 - 2 * q^82 - 47 * q^83 - 32 * q^84 + 12 * q^85 - 9 * q^86 - 14 * q^87 + 6 * q^88 - 4 * q^89 - 32 * q^90 + 27 * q^91 + 3 * q^92 + 148 * q^93 - 28 * q^94 - 6 * q^95 - 2 * q^96 - 31 * q^97 + 36 * q^98 - 16 * q^99

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