LMFDB - Embedded newform 425.2.k.b.86.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,2,Mod(86,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.86"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.k (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [76] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$19$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			86.19
Character	$\chi$	$=$	425.86
Dual form			425.2.k.b.341.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.80693 - 1.31281i) q^{2} +(-0.436131 + 1.34227i) q^{3} +(0.923486 - 2.84220i) q^{4} +(2.23360 + 0.105046i) q^{5} +(0.974092 + 2.99795i) q^{6} -2.63704 q^{7} +(-0.682224 - 2.09967i) q^{8} +(0.815568 + 0.592544i) q^{9} +(4.17386 - 2.74248i) q^{10} +(3.81797 - 2.77392i) q^{11} +(3.41224 + 2.47914i) q^{12} +(0.242146 + 0.175929i) q^{13} +(-4.76494 + 3.46193i) q^{14} +(-1.11514 + 2.95228i) q^{15} +(0.846240 + 0.614829i) q^{16} +(0.309017 + 0.951057i) q^{17} +2.25157 q^{18} +(-2.09752 - 6.45550i) q^{19} +(2.36126 - 6.25132i) q^{20} +(1.15009 - 3.53962i) q^{21} +(3.25718 - 10.0246i) q^{22} +(-6.43135 + 4.67265i) q^{23} +3.11586 q^{24} +(4.97793 + 0.469263i) q^{25} +0.668502 q^{26} +(-4.57646 + 3.32500i) q^{27} +(-2.43527 + 7.49498i) q^{28} +(-0.758704 + 2.33505i) q^{29} +(1.86081 + 6.79854i) q^{30} +(0.525379 + 1.61695i) q^{31} +6.75169 q^{32} +(2.05822 + 6.33455i) q^{33} +(1.80693 + 1.31281i) q^{34} +(-5.89008 - 0.277011i) q^{35} +(2.43729 - 1.77080i) q^{36} +(-5.77370 - 4.19484i) q^{37} +(-12.2649 - 8.91099i) q^{38} +(-0.341752 + 0.248297i) q^{39} +(-1.30325 - 4.76148i) q^{40} +(-6.57665 - 4.77822i) q^{41} +(-2.56872 - 7.90570i) q^{42} -2.93629 q^{43} +(-4.35819 - 13.4131i) q^{44} +(1.75941 + 1.40918i) q^{45} +(-5.48669 + 16.8863i) q^{46} +(2.11770 - 6.51762i) q^{47} +(-1.19434 + 0.867738i) q^{48} -0.0460344 q^{49} +(9.61082 - 5.68716i) q^{50} -1.41135 q^{51} +(0.723644 - 0.525758i) q^{52} +(-3.29447 + 10.1393i) q^{53} +(-3.90425 + 12.0161i) q^{54} +(8.81921 - 5.79476i) q^{55} +(1.79905 + 5.53690i) q^{56} +9.57983 q^{57} +(1.69456 + 5.21530i) q^{58} +(-3.67760 - 2.67194i) q^{59} +(7.36116 + 5.89585i) q^{60} +(-2.59978 + 1.88885i) q^{61} +(3.07207 + 2.23199i) q^{62} +(-2.15068 - 1.56256i) q^{63} +(10.5074 - 7.63404i) q^{64} +(0.522376 + 0.418392i) q^{65} +(12.0351 + 8.74403i) q^{66} +(-0.260847 - 0.802805i) q^{67} +2.98846 q^{68} +(-3.46705 - 10.6705i) q^{69} +(-11.0066 + 7.23203i) q^{70} +(-3.47323 + 10.6895i) q^{71} +(0.687747 - 2.11667i) q^{72} +(12.6154 - 9.16560i) q^{73} -15.9397 q^{74} +(-2.80091 + 6.47708i) q^{75} -20.2849 q^{76} +(-10.0681 + 7.31493i) q^{77} +(-0.291554 + 0.897312i) q^{78} +(-2.83142 + 8.71422i) q^{79} +(1.82558 + 1.46218i) q^{80} +(-1.53255 - 4.71672i) q^{81} -18.1564 q^{82} +(-0.322369 - 0.992151i) q^{83} +(-8.99821 - 6.53758i) q^{84} +(0.590315 + 2.15674i) q^{85} +(-5.30567 + 3.85480i) q^{86} +(-2.80338 - 2.03677i) q^{87} +(-8.42902 - 6.12404i) q^{88} +(4.17726 - 3.03496i) q^{89} +(5.02911 + 0.236519i) q^{90} +(-0.638548 - 0.463932i) q^{91} +(7.34133 + 22.5943i) q^{92} -2.39952 q^{93} +(-4.72986 - 14.5570i) q^{94} +(-4.00689 - 14.6393i) q^{95} +(-2.94462 + 9.06261i) q^{96} +(-2.75616 + 8.48259i) q^{97} +(-0.0831808 + 0.0604344i) q^{98} +4.75749 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 6 q^{2} - 7 q^{3} - 26 q^{4} + 13 q^{5} + 12 q^{6} + 22 q^{7} + 10 q^{8} - 24 q^{9} - 6 q^{10} - 16 q^{11} - 15 q^{12} - q^{13} - 19 q^{14} - 3 q^{15} + 30 q^{16} - 19 q^{17} + 6 q^{18} + 18 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) $ 76 * q - 6 * q^2 - 7 * q^3 - 26 * q^4 + 13 * q^5 + 12 * q^6 + 22 * q^7 + 10 * q^8 - 24 * q^9 - 6 * q^10 - 16 * q^11 - 15 * q^12 - q^13 - 19 * q^14 - 3 * q^15 + 30 * q^16 - 19 * q^17 + 6 * q^18 + 18 * q^19 - 23 * q^20 - 22 * q^21 - 15 * q^22 - 8 * q^23 - 22 * q^24 + 35 * q^25 - 14 * q^26 - 10 * q^27 - 29 * q^28 - 25 * q^29 + 57 * q^30 + 22 * q^31 + 54 * q^32 - 22 * q^33 - 6 * q^34 - 19 * q^35 - 91 * q^36 - 49 * q^37 + 15 * q^38 + 25 * q^39 - 2 * q^40 + 16 * q^41 - 28 * q^42 + 104 * q^43 + 18 * q^44 + 10 * q^45 - 55 * q^46 - 26 * q^47 - 86 * q^48 + 2 * q^49 - 17 * q^50 + 18 * q^51 + 53 * q^52 - 41 * q^53 - 6 * q^54 + 67 * q^55 + 115 * q^56 + 84 * q^57 - 12 * q^58 - 7 * q^59 - 32 * q^60 - 21 * q^61 - 23 * q^62 - 21 * q^63 + 6 * q^64 - 72 * q^65 + 102 * q^66 - 15 * q^67 + 74 * q^68 + 48 * q^69 - 60 * q^70 - 8 * q^71 + 9 * q^72 - 25 * q^73 - 60 * q^74 + 68 * q^75 - 76 * q^76 - 36 * q^77 - 51 * q^78 + 2 * q^79 + 217 * q^80 + 20 * q^81 - 12 * q^82 - 41 * q^83 - 48 * q^84 - 7 * q^85 - 87 * q^86 - 54 * q^87 - 4 * q^88 + 77 * q^89 - 93 * q^90 + 79 * q^91 - 19 * q^92 + 72 * q^93 + 15 * q^94 + 57 * q^95 + 28 * q^96 + 13 * q^97 - 62 * q^98 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	1.80693	−	1.31281i	1.27769	−	0.928297i	0.278211	−	0.960520i	$-0.410259\pi$
$2$	1.80693	−	1.31281i	1.27769	−	0.928297i	0.999481	+	0.0322226i	$0.0102586\pi$
$3$	−0.436131	+	1.34227i	−0.251800	+	0.774961i	0.742643	+	0.669687i	$0.233572\pi$
$3$	−0.436131	+	1.34227i	−0.251800	+	0.774961i	−0.994443	+	0.105274i	$0.966428\pi$
$4$	0.923486	−	2.84220i	0.461743	−	1.42110i
$5$	2.23360	+	0.105046i	0.998896	+	0.0469782i
$5$	2.23360	+	0.105046i	0.998896	+	0.0469782i
$6$	0.974092	+	2.99795i	0.397671	+	1.22391i
$7$	−2.63704			−0.996706			−0.498353	−	0.866974i	$-0.666062\pi$
$7$	−2.63704			−0.996706			−0.498353	+	0.866974i	$0.666062\pi$
$8$	−0.682224	−	2.09967i	−0.241202	−	0.742345i
$9$	0.815568	+	0.592544i	0.271856	+	0.197515i
$10$	4.17386	−	2.74248i	1.31989	−	0.867249i
$11$	3.81797	−	2.77392i	1.15116	−	0.836369i	0.162527	−	0.986704i	$-0.448035\pi$
$11$	3.81797	−	2.77392i	1.15116	−	0.836369i	0.988635	+	0.150336i	$0.0480354\pi$
$12$	3.41224	+	2.47914i	0.985029	+	0.715666i
$13$	0.242146	+	0.175929i	0.0671592	+	0.0487940i	0.620858	−	0.783923i	$-0.286784\pi$
$13$	0.242146	+	0.175929i	0.0671592	+	0.0487940i	−0.553699	+	0.832717i	$0.686784\pi$
$14$	−4.76494	+	3.46193i	−1.27348	+	0.925240i
$15$	−1.11514	+	2.95228i	−0.287928	+	0.762276i
$16$	0.846240	+	0.614829i	0.211560	+	0.153707i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$18$	2.25157			0.530700
$19$	−2.09752	−	6.45550i	−0.481204	−	1.48099i	−0.837404	−	0.546584i	$-0.815928\pi$
$19$	−2.09752	−	6.45550i	−0.481204	−	1.48099i	0.356200	−	0.934410i	$-0.384072\pi$
$20$	2.36126	−	6.25132i	0.527994	−	1.39784i
$21$	1.15009	−	3.53962i	0.250971	−	0.772409i
$22$	3.25718	−	10.0246i	0.694432	−	2.13724i
$23$	−6.43135	+	4.67265i	−1.34103	+	0.974314i	−0.341623	+	0.939837i	$0.610977\pi$
$23$	−6.43135	+	4.67265i	−1.34103	+	0.974314i	−0.999405	+	0.0344771i	$0.989023\pi$
$24$	3.11586			0.636023
$25$	4.97793	+	0.469263i	0.995586	+	0.0938526i
$26$	0.668502			0.131104
$27$	−4.57646	+	3.32500i	−0.880741	+	0.639896i
$28$	−2.43527	+	7.49498i	−0.460222	+	1.41642i
$29$	−0.758704	+	2.33505i	−0.140888	+	0.433608i	−0.996459	−	0.0840767i	$-0.973206\pi$
$29$	−0.758704	+	2.33505i	−0.140888	+	0.433608i	0.855572	+	0.517685i	$0.173206\pi$
$30$	1.86081	+	6.79854i	0.339735	+	1.24124i
$31$	0.525379	+	1.61695i	0.0943609	+	0.290413i	0.987087	−	0.160188i	$-0.0512099\pi$
$31$	0.525379	+	1.61695i	0.0943609	+	0.290413i	−0.892726	+	0.450600i	$0.851210\pi$
$32$	6.75169			1.19354
$33$	2.05822	+	6.33455i	0.358290	+	1.10270i
$34$	1.80693	+	1.31281i	0.309886	+	0.225145i
$35$	−5.89008	−	0.277011i	−0.995606	−	0.0468234i
$36$	2.43729	−	1.77080i	0.406216	−	0.295133i
$37$	−5.77370	−	4.19484i	−0.949190	−	0.689627i	0.00142493	−	0.999999i	$-0.499546\pi$
$37$	−5.77370	−	4.19484i	−0.949190	−	0.689627i	−0.950615	+	0.310372i	$0.899546\pi$
$38$	−12.2649	−	8.91099i	−1.98963	−	1.44555i
$39$	−0.341752	+	0.248297i	−0.0547241	+	0.0397594i
$40$	−1.30325	−	4.76148i	−0.206062	−	0.752856i
$41$	−6.57665	−	4.77822i	−1.02710	−	0.746232i	−0.0593739	−	0.998236i	$-0.518910\pi$
$41$	−6.57665	−	4.77822i	−1.02710	−	0.746232i	−0.967726	+	0.252004i	$0.918910\pi$
$42$	−2.56872	−	7.90570i	−0.396362	−	1.21988i
$43$	−2.93629			−0.447781			−0.223890	−	0.974614i	$-0.571876\pi$
$43$	−2.93629			−0.447781			−0.223890	+	0.974614i	$0.571876\pi$
$44$	−4.35819	−	13.4131i	−0.657021	−	2.02210i
$45$	1.75941	+	1.40918i	0.262277	+	0.210068i
$46$	−5.48669	+	16.8863i	−0.808968	+	2.48975i
$47$	2.11770	−	6.51762i	0.308899	−	0.950692i	−0.669295	−	0.742997i	$-0.733404\pi$
$47$	2.11770	−	6.51762i	0.308899	−	0.950692i	0.978194	−	0.207695i	$-0.0665962\pi$
$48$	−1.19434	+	0.867738i	−0.172388	+	0.125247i
$49$	−0.0460344			−0.00657634
$50$	9.61082	−	5.68716i	1.35918	−	0.804285i
$51$	−1.41135			−0.197628
$52$	0.723644	−	0.525758i	0.100351	−	0.0729096i
$53$	−3.29447	+	10.1393i	−0.452531	+	1.39275i	0.421479	+	0.906838i	$0.361511\pi$
$53$	−3.29447	+	10.1393i	−0.452531	+	1.39275i	−0.874010	+	0.485909i	$0.838489\pi$
$54$	−3.90425	+	12.0161i	−0.531302	+	1.63518i
$55$	8.81921	−	5.79476i	1.18918	−	0.781366i
$56$	1.79905	+	5.53690i	0.240408	+	0.739900i
$57$	9.57983			1.26888
$58$	1.69456	+	5.21530i	0.222506	+	0.684803i
$59$	−3.67760	−	2.67194i	−0.478783	−	0.347856i	0.322071	−	0.946715i	$-0.395621\pi$
$59$	−3.67760	−	2.67194i	−0.478783	−	0.347856i	−0.800854	+	0.598859i	$0.795621\pi$
$60$	7.36116	+	5.89585i	0.950321	+	0.761150i
$61$	−2.59978	+	1.88885i	−0.332867	+	0.241842i	−0.741646	−	0.670791i	$-0.765955\pi$
$61$	−2.59978	+	1.88885i	−0.332867	+	0.241842i	0.408779	+	0.912633i	$0.365955\pi$
$62$	3.07207	+	2.23199i	0.390154	+	0.283463i
$63$	−2.15068	−	1.56256i	−0.270960	−	0.196864i
$64$	10.5074	−	7.63404i	1.31342	−	0.954255i
$65$	0.522376	+	0.418392i	0.0647928	+	0.0518952i
$66$	12.0351	+	8.74403i	1.48142	+	1.07632i
$67$	−0.260847	−	0.802805i	−0.0318676	−	0.0980783i	0.933858	−	0.357645i	$-0.116420\pi$
$67$	−0.260847	−	0.802805i	−0.0318676	−	0.0980783i	−0.965725	+	0.259567i	$0.916420\pi$
$68$	2.98846			0.362405
$69$	−3.46705	−	10.6705i	−0.417384	−	1.28458i
$70$	−11.0066	+	7.23203i	−1.31554	+	0.864392i
$71$	−3.47323	+	10.6895i	−0.412196	+	1.26861i	0.502538	+	0.864555i	$0.332400\pi$
$71$	−3.47323	+	10.6895i	−0.412196	+	1.26861i	−0.914735	+	0.404055i	$0.867600\pi$
$72$	0.687747	−	2.11667i	0.0810518	−	0.249452i
$73$	12.6154	−	9.16560i	1.47652	−	1.07275i	0.497859	−	0.867258i	$-0.334120\pi$
$73$	12.6154	−	9.16560i	1.47652	−	1.07275i	0.978658	−	0.205495i	$-0.0658804\pi$
$74$	−15.9397			−1.85295
$75$	−2.80091	+	6.47708i	−0.323421	+	0.747908i
$76$	−20.2849			−2.32683
$77$	−10.0681	+	7.31493i	−1.14737	+	0.833614i
$78$	−0.291554	+	0.897312i	−0.0330120	+	0.101601i
$79$	−2.83142	+	8.71422i	−0.318560	+	0.980427i	0.655704	+	0.755018i	$0.272372\pi$
$79$	−2.83142	+	8.71422i	−0.318560	+	0.980427i	−0.974264	+	0.225409i	$0.927628\pi$
$80$	1.82558	+	1.46218i	0.204106	+	0.163476i
$81$	−1.53255	−	4.71672i	−0.170284	−	0.524080i
$82$	−18.1564			−2.00504
$83$	−0.322369	−	0.992151i	−0.0353846	−	0.108903i	0.931804	−	0.362961i	$-0.118234\pi$
$83$	−0.322369	−	0.992151i	−0.0353846	−	0.108903i	−0.967189	+	0.254059i	$0.918234\pi$
$84$	−8.99821	−	6.53758i	−0.981785	−	0.713309i
$85$	0.590315	+	2.15674i	0.0640287	+	0.233931i
$86$	−5.30567	+	3.85480i	−0.572125	+	0.415673i
$87$	−2.80338	−	2.03677i	−0.300554	−	0.218365i
$88$	−8.42902	−	6.12404i	−0.898537	−	0.652825i
$89$	4.17726	−	3.03496i	0.442789	−	0.321705i	−0.343953	−	0.938987i	$-0.611766\pi$
$89$	4.17726	−	3.03496i	0.442789	−	0.321705i	0.786742	+	0.617282i	$0.211766\pi$
$90$	5.02911	+	0.236519i	0.530115	+	0.0249313i
$91$	−0.638548	−	0.463932i	−0.0669380	−	0.0486333i
$92$	7.34133	+	22.5943i	0.765386	+	2.35562i
$93$	−2.39952			−0.248819
$94$	−4.72986	−	14.5570i	−0.487848	−	1.50144i
$95$	−4.00689	−	14.6393i	−0.411099	−	1.50197i
$96$	−2.94462	+	9.06261i	−0.300534	+	0.924949i
$97$	−2.75616	+	8.48259i	−0.279846	+	0.861276i	0.708051	+	0.706162i	$0.249575\pi$
$97$	−2.75616	+	8.48259i	−0.279846	+	0.861276i	−0.987896	+	0.155115i	$0.950425\pi$
$98$	−0.0831808	+	0.0604344i	−0.00840253	+	0.00610480i
$99$	4.75749			0.478145
$100$	5.93079	−	13.7149i	0.593079	−	1.37149i
$101$	−2.05350			−0.204330			−0.102165	−	0.994767i	$-0.532577\pi$
$101$	−2.05350			−0.204330			−0.102165	+	0.994767i	$0.532577\pi$
$102$	−2.55021	+	1.85283i	−0.252508	+	0.183458i
$103$	4.87741	−	15.0111i	0.480586	−	1.47909i	−0.357688	−	0.933841i	$-0.616435\pi$
$103$	4.87741	−	15.0111i	0.480586	−	1.47909i	0.838274	−	0.545249i	$-0.183565\pi$
$104$	0.204196	−	0.628449i	0.0200230	−	0.0616245i
$105$	2.94067	−	7.78528i	0.286980	−	0.759766i
$106$	7.35817	+	22.6461i	0.714688	+	2.19958i
$107$	−14.2419			−1.37682			−0.688410	−	0.725322i	$-0.741691\pi$
$107$	−14.2419			−1.37682			−0.688410	+	0.725322i	$0.741691\pi$
$108$	5.22399	+	16.0778i	0.502679	+	1.54709i
$109$	7.13873	+	5.18659i	0.683766	+	0.496785i	0.874605	−	0.484836i	$-0.161121\pi$
$109$	7.13873	+	5.18659i	0.683766	+	0.496785i	−0.190839	+	0.981621i	$0.561121\pi$
$110$	8.32827	−	22.0487i	0.794069	−	2.10226i
$111$	8.14870	−	5.92038i	0.773440	−	0.561937i
$112$	−2.23157	−	1.62133i	−0.210863	−	0.153201i
$113$	15.7935	+	11.4746i	1.48573	+	1.07944i	0.975655	+	0.219313i	$0.0703816\pi$
$113$	15.7935	+	11.4746i	1.48573	+	1.07944i	0.510073	+	0.860131i	$0.329618\pi$
$114$	17.3101	−	12.5765i	1.62124	−	1.17790i
$115$	−14.8559	+	9.76123i	−1.38532	+	0.910239i
$116$	5.93602	+	4.31277i	0.551146	+	0.400431i
$117$	0.0932404	+	0.286964i	0.00862008	+	0.0265299i
$118$	−10.1529			−0.934652
$119$	−0.814889	−	2.50797i	−0.0747008	−	0.229905i
$120$	6.95959	+	0.327310i	0.635321	+	0.0298792i
$121$	3.48310	−	10.7199i	0.316646	−	0.974536i
$122$	−2.21791	+	6.82603i	−0.200800	+	0.618000i
$123$	9.28194	−	6.74373i	0.836924	−	0.608061i
$124$	5.08088			0.456276
$125$	11.0694	+	1.57106i	0.990078	+	0.140520i
$126$	−5.93748			−0.528953
$127$	4.22909	−	3.07261i	0.375271	−	0.272650i	−0.384122	−	0.923282i	$-0.625496\pi$
$127$	4.22909	−	3.07261i	0.375271	−	0.272650i	0.759393	+	0.650632i	$0.225496\pi$
$128$	4.79121	−	14.7458i	0.423487	−	1.30336i
$129$	1.28061	−	3.94130i	0.112751	−	0.347012i
$130$	1.49317	+	0.0702237i	0.130959	+	0.00615903i
$131$	−4.63071	−	14.2519i	−0.404587	−	1.24519i	−0.921240	−	0.388996i	$-0.872822\pi$
$131$	−4.63071	−	14.2519i	−0.404587	−	1.24519i	0.516652	−	0.856195i	$-0.327178\pi$
$132$	19.9048			1.73249
$133$	5.53124	+	17.0234i	0.479619	+	1.47612i
$134$	−1.52526	−	1.10817i	−0.131763	−	0.0957312i
$135$	−10.5713	+	6.94597i	−0.909829	+	0.597814i
$136$	1.78608	−	1.29767i	0.153155	−	0.111274i
$137$	10.7622	+	7.81919i	0.919476	+	0.668039i	0.943394	−	0.331675i	$-0.107614\pi$
$137$	10.7622	+	7.81919i	0.919476	+	0.668039i	−0.0239174	+	0.999714i	$0.507614\pi$
$138$	−20.2731	−	14.7292i	−1.72576	−	1.25384i
$139$	11.7750	−	8.55503i	0.998742	−	0.725628i	0.0369238	−	0.999318i	$-0.488244\pi$
$139$	11.7750	−	8.55503i	0.998742	−	0.725628i	0.961818	+	0.273690i	$0.0882441\pi$
$140$	−6.22673	+	16.4850i	−0.526255	+	1.39323i
$141$	7.82482	+	5.68506i	0.658968	+	0.478769i
$142$	7.75741	+	23.8749i	0.650987	+	2.00353i
$143$	1.41252			0.118121
$144$	0.325852	+	1.00287i	0.0271543	+	0.0835725i
$145$	−1.93993	+	5.13587i	−0.161102	+	0.426511i
$146$	10.7624	−	33.1232i	0.890701	−	2.74129i
$147$	0.0200770	−	0.0617906i	0.00165592	−	0.00509640i
$148$	−17.2545	+	12.5361i	−1.41831	+	1.03046i
$149$	6.35056			0.520258			0.260129	−	0.965574i	$-0.416235\pi$
$149$	6.35056			0.520258			0.260129	+	0.965574i	$0.416235\pi$
$150$	3.44214	+	15.3807i	0.281049	+	1.25583i
$151$	0.411948			0.0335238			0.0167619	−	0.999860i	$-0.494664\pi$
$151$	0.411948			0.0335238			0.0167619	+	0.999860i	$0.494664\pi$
$152$	−12.1234	+	8.80819i	−0.983341	+	0.714439i
$153$	−0.311519	+	0.958757i	−0.0251848	+	0.0775109i
$154$	−8.58929	+	26.4351i	−0.692145	+	2.13020i
$155$	1.00363	+	3.66681i	0.0806136	+	0.294525i
$156$	0.390107	+	1.20063i	0.0312336	+	0.0961271i
$157$	−12.6831			−1.01222			−0.506111	−	0.862469i	$-0.668917\pi$
$157$	−12.6831			−1.01222			−0.506111	+	0.862469i	$0.668917\pi$
$158$	6.32394	+	19.4631i	0.503106	+	1.54840i
$159$	−12.1729	−	8.84416i	−0.965377	−	0.701387i
$160$	15.0806	+	0.709241i	1.19222	+	0.0560704i
$161$	16.9597	−	12.3219i	1.33661	−	0.971105i
$162$	−8.96137	−	6.51082i	−0.704072	−	0.511538i
$163$	−7.31101	−	5.31176i	−0.572642	−	0.416049i	0.263422	−	0.964681i	$-0.415149\pi$
$163$	−7.31101	−	5.31176i	−0.572642	−	0.416049i	−0.836064	+	0.548632i	$0.815149\pi$
$164$	−19.6541	+	14.2795i	−1.53473	+	1.11504i
$165$	3.93182	+	14.3651i	0.306092	+	1.11832i
$166$	−1.88500	−	1.36954i	−0.146305	−	0.106297i
$167$	3.48328	+	10.7204i	0.269545	+	0.829573i	0.990611	+	0.136708i	$0.0436520\pi$
$167$	3.48328	+	10.7204i	0.269545	+	0.829573i	−0.721067	+	0.692866i	$0.756348\pi$
$168$	−8.21665			−0.633928
$169$	−3.98954	−	12.2785i	−0.306887	−	0.944503i
$170$	3.89805	+	3.12210i	0.298967	+	0.239454i
$171$	2.11450	−	6.50777i	0.161700	−	0.497662i
$172$	−2.71163	+	8.34553i	−0.206760	+	0.636341i
$173$	19.3918	−	14.0890i	1.47433	−	1.07116i	0.495002	−	0.868892i	$-0.335167\pi$
$173$	19.3918	−	14.0890i	1.47433	−	1.07116i	0.979329	−	0.202273i	$-0.0648328\pi$
$174$	−7.73940			−0.586723
$175$	−13.1270	−	1.23746i	−0.992307	−	0.0935435i
$176$	4.93641			0.372096
$177$	5.19038	−	3.77103i	0.390133	−	0.283448i
$178$	3.56369	−	10.9679i	0.267110	−	0.822079i
$179$	3.68494	−	11.3411i	0.275425	−	0.847671i	−0.713682	−	0.700470i	$-0.752974\pi$
$179$	3.68494	−	11.3411i	0.275425	−	0.847671i	0.989107	−	0.147201i	$-0.0470263\pi$
$180$	5.62995	−	3.69922i	0.419632	−	0.275724i
$181$	0.936764	+	2.88306i	0.0696291	+	0.214296i	0.979816	−	0.199901i	$-0.0640622\pi$
$181$	0.936764	+	2.88306i	0.0696291	+	0.214296i	−0.910187	+	0.414198i	$0.864062\pi$
$182$	−1.76287			−0.130672
$183$	−1.40151	−	4.31339i	−0.103602	−	0.318855i
$184$	14.1986	+	10.3159i	1.04674	+	0.760499i
$185$	−12.4555	−	9.97609i	−0.915745	−	0.733457i
$186$	−4.33576	+	3.15012i	−0.317914	+	0.230978i
$187$	3.81797	+	2.77392i	0.279198	+	0.202849i
$188$	−16.5687	−	12.0379i	−1.20840	−	0.877951i
$189$	12.0683	−	8.76814i	0.877840	−	0.637788i
$190$	−26.4589	−	21.1920i	−1.91953	−	1.53743i
$191$	2.54504	+	1.84908i	0.184152	+	0.133794i	0.676042	−	0.736863i	$-0.263694\pi$
$191$	2.54504	+	1.84908i	0.184152	+	0.133794i	−0.491890	+	0.870657i	$0.663694\pi$
$192$	5.66438	+	17.4332i	0.408791	+	1.25813i
$193$	−10.2137			−0.735195			−0.367597	−	0.929985i	$-0.619820\pi$
$193$	−10.2137			−0.735195			−0.367597	+	0.929985i	$0.619820\pi$
$194$	6.15585	+	18.9458i	0.441964	+	1.36023i
$195$	−0.789420	+	0.518697i	−0.0565315	+	0.0371447i
$196$	−0.0425121	+	0.130839i	−0.00303658	+	0.00934563i
$197$	−0.535228	+	1.64726i	−0.0381334	+	0.117363i	−0.968311	−	0.249747i	$-0.919653\pi$
$197$	−0.535228	+	1.64726i	−0.0381334	+	0.117363i	0.930178	+	0.367110i	$0.119653\pi$
$198$	8.59644	−	6.24568i	0.610922	−	0.443861i
$199$	11.6694			0.827221			0.413611	−	0.910454i	$-0.364267\pi$
$199$	11.6694			0.827221			0.413611	+	0.910454i	$0.364267\pi$
$200$	−2.41076	−	10.7721i	−0.170467	−	0.761706i
$201$	1.19135			0.0840311
$202$	−3.71052	+	2.69585i	−0.261071	+	0.189679i
$203$	2.00073	−	6.15761i	0.140424	−	0.432180i
$204$	−1.30336	+	4.01133i	−0.0912535	+	0.280849i
$205$	−14.1877	−	11.3635i	−0.990910	−	0.793659i
$206$	−10.8936	−	33.5272i	−0.758995	−	2.33595i
$207$	−8.01395			−0.557008
$208$	0.0967471	+	0.297757i	0.00670820	+	0.0206457i
$209$	−25.9153	−	18.8286i	−1.79260	−	1.30240i
$210$	−4.90702	−	17.9280i	−0.338616	−	1.23715i
$211$	−11.6422	+	8.45859i	−0.801486	+	0.582313i	−0.911350	−	0.411633i	$-0.864958\pi$
$211$	−11.6422	+	8.45859i	−0.801486	+	0.582313i	0.109864	+	0.993947i	$0.464958\pi$
$212$	25.7756	+	18.7271i	1.77028	+	1.28618i
$213$	−12.8334	−	9.32403i	−0.879332	−	0.638872i
$214$	−25.7342	+	18.6970i	−1.75915	+	1.27810i
$215$	−6.55850	−	0.308447i	−0.447286	−	0.0210359i
$216$	10.1036	+	7.34066i	0.687460	+	0.499469i
$217$	−1.38544	−	4.26396i	−0.0940501	−	0.289456i
$218$	19.7082			1.33481
$219$	6.80078	+	20.9307i	0.459554	+	1.41436i
$220$	−8.32544	−	30.4173i	−0.561301	−	2.05074i
$221$	−0.0924915	+	0.284660i	−0.00622165	+	0.0191483i
$222$	6.95179	−	21.3954i	0.466573	−	1.43597i
$223$	−11.8369	+	8.60003i	−0.792659	+	0.575900i	−0.908751	−	0.417338i	$-0.862963\pi$
$223$	−11.8369	+	8.60003i	−0.792659	+	0.575900i	0.116092	+	0.993238i	$0.462963\pi$
$224$	−17.8045			−1.18961
$225$	3.78178	+	3.33236i	0.252119	+	0.222157i
$226$	43.6018			2.90035
$227$	−1.48958	+	1.08224i	−0.0988668	+	0.0718309i	−0.636120	−	0.771590i	$-0.719462\pi$
$227$	−1.48958	+	1.08224i	−0.0988668	+	0.0718309i	0.537254	+	0.843421i	$0.319462\pi$
$228$	8.84684	−	27.2278i	0.585897	−	1.80320i
$229$	−3.01583	+	9.28177i	−0.199292	+	0.613356i	0.800608	+	0.599188i	$0.204510\pi$
$229$	−3.01583	+	9.28177i	−0.199292	+	0.613356i	−0.999900	+	0.0141680i	$0.995490\pi$
$230$	−14.0289	+	37.1408i	−0.925038	+	2.44899i
$231$	−5.42760	−	16.7044i	−0.357110	−	1.09907i
$232$	5.42044			0.355869
$233$	−3.43599	−	10.5749i	−0.225099	−	0.692784i	−0.998282	−	0.0586001i	$-0.981336\pi$
$233$	−3.43599	−	10.5749i	−0.225099	−	0.692784i	0.773182	−	0.634184i	$-0.218664\pi$
$234$	0.545209	+	0.396117i	0.0356414	+	0.0258950i
$235$	5.41475	−	14.3353i	0.353219	−	0.935131i
$236$	−10.9904	+	7.98498i	−0.715413	+	0.519778i
$237$	−10.4620	−	7.60108i	−0.679579	−	0.493743i
$238$	−4.76494	−	3.46193i	−0.308865	−	0.224404i
$239$	20.8098	−	15.1192i	1.34607	−	0.977981i	0.346878	−	0.937910i	$-0.387242\pi$
$239$	20.8098	−	15.1192i	1.34607	−	0.977981i	0.999197	−	0.0400703i	$-0.0127582\pi$
$240$	−2.75883	+	1.81272i	−0.178082	+	0.117010i
$241$	7.20280	+	5.23314i	0.463973	+	0.337096i	0.795088	−	0.606494i	$-0.207425\pi$
$241$	7.20280	+	5.23314i	0.463973	+	0.337096i	−0.331115	+	0.943591i	$0.607425\pi$
$242$	−7.77947	−	23.9427i	−0.500083	−	1.53910i
$243$	−9.97095			−0.639637
$244$	2.96762	+	9.13341i	0.189983	+	0.584706i
$245$	−0.102822	−	0.00483574i	−0.00656908	−	0.000308944i
$246$	7.91857	−	24.3709i	0.504870	−	1.55383i
$247$	0.627806	−	1.93219i	0.0399464	−	0.122942i
$248$	3.03663	−	2.20624i	0.192826	−	0.140097i
$249$	1.47233			0.0933052
$250$	22.0641	−	11.6932i	1.39546	−	0.739546i
$251$	15.0651			0.950901			0.475450	−	0.879743i	$-0.342285\pi$
$251$	15.0651			0.950901			0.475450	+	0.879743i	$0.342285\pi$
$252$	−6.42724	+	4.66966i	−0.404878	+	0.294161i
$253$	−11.5932	+	35.6801i	−0.728856	+	2.24319i
$254$	3.60790	−	11.1040i	0.226380	−	0.696726i
$255$	−3.15239	−	0.148257i	−0.197410	−	0.00928421i
$256$	−2.67421	−	8.23038i	−0.167138	−	0.514399i
$257$	−11.9534			−0.745630			−0.372815	−	0.927906i	$-0.621607\pi$
$257$	−11.9534			−0.745630			−0.372815	+	0.927906i	$0.621607\pi$
$258$	−2.86022	−	8.80285i	−0.178069	−	0.548041i
$259$	15.2255	+	11.0619i	0.946064	+	0.687356i
$260$	1.67156	−	1.09832i	0.103666	−	0.0681148i
$261$	−2.00240	+	1.45483i	−0.123945	+	0.0900514i
$262$	−27.0774	−	19.6729i	−1.67285	−	1.21539i
$263$	0.727600	+	0.528632i	0.0448657	+	0.0325969i	0.609992	−	0.792407i	$-0.291173\pi$
$263$	0.727600	+	0.528632i	0.0448657	+	0.0325969i	−0.565126	+	0.825004i	$0.691173\pi$
$264$	11.8963	−	8.64316i	0.732166	−	0.531950i
$265$	−8.42364	+	22.3012i	−0.517460	+	1.36995i
$266$	32.3431	+	23.4986i	1.98308	+	1.44079i
$267$	2.25191	+	6.93065i	0.137814	+	0.424149i
$268$	−2.52262			−0.154094
$269$	−3.03859	−	9.35181i	−0.185266	−	0.570190i	0.814687	−	0.579901i	$-0.196909\pi$
$269$	−3.03859	−	9.35181i	−0.185266	−	0.570190i	−0.999953	+	0.00971108i	$0.996909\pi$
$270$	−9.98278	+	26.4289i	−0.607533	+	1.60841i
$271$	−3.92460	+	12.0787i	−0.238403	+	0.733728i	0.758249	+	0.651965i	$0.226055\pi$
$271$	−3.92460	+	12.0787i	−0.238403	+	0.733728i	−0.996652	+	0.0817628i	$0.973945\pi$
$272$	−0.323235	+	0.994815i	−0.0195990	+	0.0603195i
$273$	0.901213	−	0.654770i	0.0545439	−	0.0396285i
$274$	29.7116			1.79495
$275$	20.3073	−	12.0167i	1.22458	−	0.724637i
$276$	−33.5294			−2.01824
$277$	6.33887	−	4.60546i	0.380866	−	0.276715i	−0.380836	−	0.924642i	$-0.624364\pi$
$277$	6.33887	−	4.60546i	0.380866	−	0.276715i	0.761702	+	0.647927i	$0.224364\pi$
$278$	10.0454	−	30.9167i	0.602485	−	1.85426i
$279$	−0.529633	+	1.63004i	−0.0317083	+	0.0975881i
$280$	3.43672	+	12.5562i	0.205383	+	0.750377i
$281$	6.09211	+	18.7496i	0.363425	+	1.11851i	0.950961	+	0.309310i	$0.100098\pi$
$281$	6.09211	+	18.7496i	0.363425	+	1.11851i	−0.587536	+	0.809198i	$0.699902\pi$
$282$	21.6023			1.28640
$283$	7.88654	+	24.2723i	0.468806	+	1.44284i	0.854132	+	0.520056i	$0.174089\pi$
$283$	7.88654	+	24.2723i	0.468806	+	1.44284i	−0.385326	+	0.922780i	$0.625911\pi$
$284$	27.1742	+	19.7432i	1.61249	+	1.17154i
$285$	21.3975	+	1.00633i	1.26748	+	0.0596096i
$286$	2.55232	−	1.85437i	0.150922	−	0.109651i
$287$	17.3429	+	12.6003i	1.02372	+	0.743774i
$288$	5.50646	+	4.00068i	0.324471	+	0.235742i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	3.23711	+	11.8269i	0.190090	+	0.694500i
$291$	−10.1839	−	7.39903i	−0.596990	−	0.433739i
$292$	−14.4003	−	44.3197i	−0.842716	−	2.59361i
$293$	23.7424			1.38705			0.693523	−	0.720434i	$-0.256057\pi$
$293$	23.7424			1.38705			0.693523	+	0.720434i	$0.256057\pi$
$294$	−0.0448417	−	0.138009i	−0.00261522	−	0.00804882i
$295$	−7.93362	−	6.35435i	−0.461913	−	0.369965i
$296$	−4.86881	+	14.9847i	−0.282994	+	0.870966i
$297$	−8.24955	+	25.3895i	−0.478687	+	1.47325i
$298$	11.4750	−	8.33708i	0.664730	−	0.482954i
$299$	−2.37938			−0.137603
$300$	15.8225	+	13.9422i	0.913514	+	0.804954i
$301$	7.74311			0.446306
$302$	0.744360	−	0.540809i	0.0428331	−	0.0311201i
$303$	0.895592	−	2.75635i	0.0514504	−	0.158348i
$304$	2.19403	−	6.75252i	0.125836	−	0.387284i
$305$	−6.00528	+	3.94583i	−0.343861	+	0.225938i
$306$	0.695774	+	2.14137i	0.0397747	+	0.122414i
$307$	−5.28874			−0.301844			−0.150922	−	0.988546i	$-0.548224\pi$
$307$	−5.28874			−0.301844			−0.150922	+	0.988546i	$0.548224\pi$
$308$	11.4927	+	35.3709i	0.654857	+	2.01544i
$309$	18.0218	+	13.0936i	1.02523	+	0.744870i
$310$	6.62732	+	5.30808i	0.376406	+	0.301479i
$311$	−10.5302	+	7.65063i	−0.597112	+	0.433827i	−0.844853	−	0.534999i	$-0.820312\pi$
$311$	−10.5302	+	7.65063i	−0.597112	+	0.433827i	0.247741	+	0.968826i	$0.420312\pi$
$312$	0.754494	+	0.548172i	0.0427148	+	0.0310341i
$313$	−22.0213	−	15.9994i	−1.24472	−	0.904338i	−0.246812	−	0.969063i	$-0.579383\pi$
$313$	−22.0213	−	15.9994i	−1.24472	−	0.904338i	−0.997903	+	0.0647250i	$0.979383\pi$
$314$	−22.9175	+	16.6505i	−1.29331	+	0.939642i
$315$	−4.63962	−	3.71606i	−0.261413	−	0.209376i
$316$	22.1528	+	16.0949i	1.24619	+	0.905410i
$317$	1.23728	+	3.80794i	0.0694923	+	0.213875i	0.979771	−	0.200120i	$-0.0641331\pi$
$317$	1.23728	+	3.80794i	0.0694923	+	0.213875i	−0.910279	+	0.413995i	$0.864133\pi$
$318$	−33.6063			−1.88455
$319$	3.58053	+	11.0197i	0.200471	+	0.616987i
$320$	24.2711	−	15.9476i	1.35680	−	0.891499i
$321$	6.21134	−	19.1165i	0.346683	−	1.06698i
$322$	14.4686	−	44.5298i	0.806303	−	2.48155i
$323$	5.49138	−	3.98972i	0.305549	−	0.221994i
$324$	−14.8211			−0.823397
$325$	1.12283	+	0.989394i	0.0622833	+	0.0548817i
$326$	−20.1838			−1.11788
$327$	−10.0752	+	7.32008i	−0.557162	+	0.404802i
$328$	−5.54592	+	17.0686i	−0.306222	+	0.942455i
$329$	−5.58446	+	17.1872i	−0.307881	+	0.947561i
$330$	25.9631	+	20.7949i	1.42922	+	1.14472i
$331$	8.17617	+	25.1637i	0.449403	+	1.38312i	0.877582	+	0.479426i	$0.159155\pi$
$331$	8.17617	+	25.1637i	0.449403	+	1.38312i	−0.428179	+	0.903694i	$0.640845\pi$
$332$	−3.11759			−0.171100
$333$	−2.22321	−	6.84235i	−0.121831	−	0.374958i
$334$	20.3680	+	14.7982i	1.11449	+	0.809721i
$335$	−0.498296	−	1.82055i	−0.0272248	−	0.0994671i
$336$	3.14952	−	2.28826i	0.171820	−	0.124835i
$337$	−15.1903	−	11.0364i	−0.827469	−	0.601192i	0.0913730	−	0.995817i	$-0.470874\pi$
$337$	−15.1903	−	11.0364i	−0.827469	−	0.601192i	−0.918842	+	0.394625i	$0.870874\pi$
$338$	−23.3282	−	16.9489i	−1.26889	−	0.921900i
$339$	−22.2901	+	16.1947i	−1.21063	+	0.879577i
$340$	6.67503	+	0.313927i	0.362004	+	0.0170251i
$341$	6.49118	+	4.71612i	0.351517	+	0.255392i
$342$	−4.72272	−	14.5350i	−0.255375	−	0.785964i
$343$	18.5807			1.00326
$344$	2.00321	+	6.16524i	0.108006	+	0.332408i
$345$	−6.62311	−	24.1978i	−0.356576	−	1.30277i
$346$	16.5435	−	50.9155i	0.889382	−	2.73724i
$347$	1.88456	−	5.80008i	0.101169	−	0.311365i	−0.887644	−	0.460531i	$-0.847659\pi$
$347$	1.88456	−	5.80008i	0.101169	−	0.311365i	0.988812	+	0.149166i	$0.0476590\pi$
$348$	−8.37779	+	6.08682i	−0.449097	+	0.326288i
$349$	−7.92015			−0.423956			−0.211978	−	0.977274i	$-0.567991\pi$
$349$	−7.92015			−0.423956			−0.211978	+	0.977274i	$0.567991\pi$
$350$	−25.3441	+	14.9972i	−1.35470	+	0.801636i
$351$	−1.69314			−0.0903729
$352$	25.7778	−	18.7287i	1.37396	−	0.998241i
$353$	−4.78440	+	14.7249i	−0.254648	+	0.783726i	0.739251	+	0.673430i	$0.235180\pi$
$353$	−4.78440	+	14.7249i	−0.254648	+	0.783726i	−0.993899	+	0.110296i	$0.964820\pi$
$354$	4.42800	−	13.6280i	0.235345	−	0.724318i
$355$	−8.88069	+	23.5112i	−0.471338	+	1.24785i
$356$	−4.76831	−	14.6753i	−0.252720	−	0.777791i
$357$	3.72178			0.196977
$358$	−8.23025	−	25.3301i	−0.434982	−	1.33874i
$359$	18.0338	+	13.1023i	0.951786	+	0.691513i	0.951229	−	0.308487i	$-0.0998227\pi$
$359$	18.0338	+	13.1023i	0.951786	+	0.691513i	0.000557146		1.00000i	$0.499823\pi$
$360$	1.75850	−	4.65554i	0.0926811	−	0.245369i
$361$	−21.9026	+	15.9132i	−1.15277	+	0.837536i
$362$	5.47758	+	3.97970i	0.287895	+	0.209168i
$363$	12.8699	+	9.35054i	0.675496	+	0.490776i
$364$	−1.90828	+	1.38644i	−0.100021	+	0.0726694i
$365$	29.1405	−	19.1471i	1.52528	−	1.00220i
$366$	−8.19509	−	5.95408i	−0.428364	−	0.311225i
$367$	6.95657	+	21.4101i	0.363130	+	1.11760i	0.951144	+	0.308748i	$0.0999100\pi$
$367$	6.95657	+	21.4101i	0.363130	+	1.11760i	−0.588014	+	0.808851i	$0.700090\pi$
$368$	−8.31534			−0.433467
$369$	−2.53240	−	7.79392i	−0.131831	−	0.405735i
$370$	−35.6029	−	1.67441i	−1.85091	−	0.0870483i
$371$	8.68765	−	26.7378i	0.451040	−	1.38816i
$372$	−2.21592	+	6.81991i	−0.114890	+	0.353596i
$373$	16.9642	−	12.3252i	0.878374	−	0.638176i	−0.0544470	−	0.998517i	$-0.517340\pi$
$373$	16.9642	−	12.3252i	0.878374	−	0.638176i	0.932821	+	0.360341i	$0.117340\pi$
$374$	10.5404			0.545033
$375$	−6.93649	+	14.1730i	−0.358199	+	0.731889i
$376$	−15.1296			−0.780248
$377$	−0.594521	+	0.431945i	−0.0306194	+	0.0222463i
$378$	10.2957	−	31.6868i	0.529552	−	1.62979i
$379$	−5.95714	+	18.3342i	−0.305998	+	0.941765i	0.673305	+	0.739365i	$0.264874\pi$
$379$	−5.95714	+	18.3342i	−0.305998	+	0.941765i	−0.979303	+	0.202400i	$0.935126\pi$
$380$	−45.3082	−	2.13085i	−2.32426	−	0.109310i
$381$	2.27985	+	7.01665i	0.116800	+	0.359474i
$382$	7.02618			0.359491
$383$	2.96004	+	9.11007i	0.151251	+	0.465503i	0.997762	−	0.0668688i	$-0.0213009\pi$
$383$	2.96004	+	9.11007i	0.151251	+	0.465503i	−0.846511	+	0.532372i	$0.821301\pi$
$384$	17.7033	+	12.8622i	0.903419	+	0.656373i
$385$	−23.2566	+	15.2810i	−1.18527	+	0.778792i
$386$	−18.4553	+	13.4086i	−0.939352	+	0.682480i
$387$	−2.39475	−	1.73988i	−0.121732	−	0.0884433i
$388$	21.5639	+	15.6671i	1.09474	+	0.795377i
$389$	28.4307	−	20.6561i	1.44149	−	1.04731i	0.453766	−	0.891121i	$-0.350080\pi$
$389$	28.4307	−	20.6561i	1.44149	−	1.04731i	0.987728	−	0.156186i	$-0.0499199\pi$
$390$	−0.745475	+	1.97361i	−0.0377486	+	0.0999375i
$391$	−6.43135	−	4.67265i	−0.325247	−	0.236306i
$392$	0.0314057	+	0.0966569i	0.00158623	+	0.00488191i
$393$	21.1495			1.06685
$394$	1.19542	+	3.67914i	0.0602246	+	0.185352i
$395$	−7.23966	+	19.1666i	−0.364267	+	0.964379i
$396$	4.39347	−	13.5217i	0.220780	−	0.679492i
$397$	2.70289	−	8.31865i	0.135654	−	0.417501i	−0.860037	−	0.510232i	$-0.829560\pi$
$397$	2.70289	−	8.31865i	0.135654	−	0.417501i	0.995691	+	0.0927308i	$0.0295596\pi$
$398$	21.0858	−	15.3197i	1.05693	−	0.767907i
$399$	−25.2624			−1.26470
$400$	3.92401	+	3.45769i	0.196200	+	0.172884i
$401$	−9.40866			−0.469846			−0.234923	−	0.972014i	$-0.575484\pi$
$401$	−9.40866			−0.469846			−0.234923	+	0.972014i	$0.575484\pi$
$402$	2.15268	−	1.56401i	0.107366	−	0.0780058i
$403$	−0.157251	+	0.483968i	−0.00783321	+	0.0241081i
$404$	−1.89638	+	5.83644i	−0.0943482	+	0.290374i
$405$	−2.92764	−	10.6962i	−0.145476	−	0.531501i
$406$	−4.46860	−	13.7530i	−0.221773	−	0.682548i
$407$	−33.6800			−1.66945
$408$	0.962855	+	2.96336i	0.0476684	+	0.146708i
$409$	−14.1342	−	10.2691i	−0.698892	−	0.507775i	0.180679	−	0.983542i	$-0.442171\pi$
$409$	−14.1342	−	10.2691i	−0.698892	−	0.507775i	−0.879571	+	0.475767i	$0.842171\pi$
$410$	−40.5542	−	1.90727i	−2.00283	−	0.0941932i
$411$	−15.1892	+	11.0356i	−0.749228	+	0.544346i
$412$	−38.1604	−	27.7251i	−1.88003	−	1.36592i
$413$	9.69798	+	7.04599i	0.477206	+	0.346711i
$414$	−14.4806	+	10.5208i	−0.711684	+	0.517069i
$415$	−0.615822	−	2.24993i	−0.0302295	−	0.110445i
$416$	1.63490	+	1.18782i	0.0801573	+	0.0582377i
$417$	6.34775	+	19.5364i	0.310850	+	0.956699i
$418$	−71.5455			−3.49941
$419$	−10.3384	−	31.8182i	−0.505062	−	1.55442i	−0.800666	−	0.599111i	$-0.795521\pi$
$419$	−10.3384	−	31.8182i	−0.505062	−	1.55442i	0.295604	−	0.955311i	$-0.404479\pi$
$420$	−19.4116	−	15.5476i	−0.947191	−	0.758644i
$421$	−4.19230	+	12.9026i	−0.204320	+	0.628833i	0.795420	+	0.606058i	$0.207250\pi$
$421$	−4.19230	+	12.9026i	−0.204320	+	0.628833i	−0.999741	+	0.0227747i	$0.992750\pi$
$422$	−9.93219	+	30.5681i	−0.483491	+	1.48803i
$423$	5.58911	−	4.06072i	0.271752	−	0.197439i
$424$	23.5368			1.14305
$425$	1.09197	+	4.87930i	0.0529683	+	0.236681i
$426$	−35.4298			−1.71658
$427$	6.85571	−	4.98096i	0.331771	−	0.241046i
$428$	−13.1522	+	40.4784i	−0.635737	+	1.95660i
$429$	−0.616043	+	1.89599i	−0.0297429	+	0.0915391i
$430$	−12.2557	+	8.05273i	−0.591021	+	0.388337i
$431$	−2.47099	−	7.60492i	−0.119023	−	0.366316i	0.873742	−	0.486390i	$-0.161687\pi$
$431$	−2.47099	−	7.60492i	−0.119023	−	0.366316i	−0.992765	+	0.120074i	$0.961687\pi$
$432$	−5.91709			−0.284686
$433$	5.53960	+	17.0491i	0.266216	+	0.819329i	0.991411	+	0.130785i	$0.0417498\pi$
$433$	5.53960	+	17.0491i	0.266216	+	0.819329i	−0.725194	+	0.688544i	$0.758250\pi$
$434$	−8.10117	−	5.88585i	−0.388869	−	0.282530i
$435$	−6.04767	−	4.84382i	−0.289963	−	0.232243i
$436$	21.3338	−	15.4999i	1.02171	−	0.742313i
$437$	43.6542	+	31.7166i	2.08826	+	1.51721i
$438$	39.7665	+	28.8921i	1.90012	+	1.38052i
$439$	28.3234	−	20.5782i	1.35180	−	0.982142i	0.352883	−	0.935667i	$-0.385201\pi$
$439$	28.3234	−	20.5782i	1.35180	−	0.982142i	0.998919	−	0.0464748i	$-0.0147987\pi$
$440$	−18.1838	−	14.5641i	−0.866876	−	0.694316i
$441$	−0.0375441	−	0.0272774i	−0.00178782	−	0.00129892i
$442$	0.206579	+	0.635784i	0.00982594	+	0.0302411i
$443$	17.7013			0.841015			0.420508	−	0.907289i	$-0.361852\pi$
$443$	17.7013			0.841015			0.420508	+	0.907289i	$0.361852\pi$
$444$	−9.30167	−	28.6276i	−0.441438	−	1.35861i
$445$	9.64913	−	6.34007i	0.457413	−	0.300548i
$446$	−10.0983	+	31.0793i	−0.478167	+	1.47165i
$447$	−2.76967	+	8.52418i	−0.131001	+	0.403180i
$448$	−27.7083	+	20.1312i	−1.30909	+	0.951112i
$449$	2.14273			0.101122			0.0505608	−	0.998721i	$-0.483899\pi$
$449$	2.14273			0.101122			0.0505608	+	0.998721i	$0.483899\pi$
$450$	11.2082	+	1.05658i	0.528358	+	0.0498076i
$451$	−38.3639			−1.80648
$452$	47.1983	−	34.2916i	2.22002	−	1.61294i
$453$	−0.179663	+	0.552946i	−0.00844130	+	0.0259797i
$454$	−1.27078	+	3.91107i	−0.0596408	+	0.183556i
$455$	−1.37753	−	1.10332i	−0.0645794	−	0.0517242i
$456$	−6.53559	−	20.1145i	−0.306057	−	0.941946i
$457$	8.31166			0.388803			0.194401	−	0.980922i	$-0.437724\pi$
$457$	8.31166			0.388803			0.194401	+	0.980922i	$0.437724\pi$
$458$	6.73581	+	20.7307i	0.314744	+	0.968682i
$459$	−4.57646	−	3.32500i	−0.213611	−	0.155197i
$460$	14.0241	+	51.2378i	0.653879	+	2.38897i
$461$	−7.03345	+	5.11010i	−0.327580	+	0.238001i	−0.739403	−	0.673263i	$-0.764892\pi$
$461$	−7.03345	+	5.11010i	−0.327580	+	0.238001i	0.411823	+	0.911264i	$0.364892\pi$
$462$	−31.7371	−	23.0583i	−1.47654	−	1.07277i
$463$	1.73175	+	1.25819i	0.0804812	+	0.0584730i	0.627298	−	0.778779i	$-0.284161\pi$
$463$	1.73175	+	1.25819i	0.0804812	+	0.0584730i	−0.546817	+	0.837252i	$0.684161\pi$
$464$	−2.07770	+	1.50954i	−0.0964550	+	0.0700786i
$465$	−5.35957	−	0.252061i	−0.248544	−	0.0116890i
$466$	−20.0914	−	14.5973i	−0.930717	−	0.676205i
$467$	2.74973	+	8.46279i	0.127242	+	0.391611i	0.994303	−	0.106591i	$-0.0339936\pi$
$467$	2.74973	+	8.46279i	0.127242	+	0.391611i	−0.867061	+	0.498203i	$0.833994\pi$
$468$	0.901716			0.0416818
$469$	0.687864	+	2.11703i	0.0317626	+	0.0977552i
$470$	−9.03545	−	33.0114i	−0.416774	−	1.52270i
$471$	5.53149	−	17.0242i	0.254877	−	0.784432i
$472$	−3.10123	+	9.54461i	−0.142746	+	0.439326i
$473$	−11.2107	+	8.14504i	−0.515468	+	0.374510i
$474$	−28.8828			−1.32663
$475$	−7.41198	−	33.1193i	−0.340085	−	1.51962i
$476$	−7.88069			−0.361211
$477$	−8.69488	+	6.31720i	−0.398111	+	0.289245i
$478$	17.7532	−	54.6387i	0.812012	−	2.49912i
$479$	−3.74135	+	11.5147i	−0.170947	+	0.526119i	−0.999425	−	0.0339014i	$-0.989207\pi$
$479$	−3.74135	+	11.5147i	−0.170947	+	0.526119i	0.828479	+	0.560021i	$0.189207\pi$
$480$	−7.52909	+	19.9329i	−0.343655	+	0.909809i
$481$	−0.660083	−	2.03153i	−0.0300972	−	0.0926296i
$482$	19.8851			0.905740
$483$	9.14275	+	28.1385i	0.416010	+	1.28035i
$484$	−27.2515	−	19.7993i	−1.23870	−	0.899970i
$485$	−7.04722	+	18.6572i	−0.319998	+	0.847179i
$486$	−18.0168	+	13.0900i	−0.817258	+	0.593773i
$487$	−4.75015	−	3.45119i	−0.215250	−	0.156388i	0.474936	−	0.880020i	$-0.342471\pi$
$487$	−4.75015	−	3.45119i	−0.215250	−	0.156388i	−0.690186	+	0.723632i	$0.742471\pi$
$488$	5.73958	+	4.17005i	0.259819	+	0.188769i
$489$	10.3184	−	7.49674i	0.466613	−	0.339014i
$490$	−0.192141	+	0.126248i	−0.00868005	+	0.00570332i
$491$	−2.43833	−	1.77155i	−0.110040	−	0.0799491i	0.531404	−	0.847118i	$-0.321665\pi$
$491$	−2.43833	−	1.77155i	−0.110040	−	0.0799491i	−0.641445	+	0.767169i	$0.721665\pi$
$492$	−10.5953	−	32.6089i	−0.477671	−	1.47012i
$493$	−2.45522			−0.110577
$494$	−1.40220	−	4.31552i	−0.0630878	−	0.194164i
$495$	10.6263	+	0.499757i	0.477618	+	0.0224624i
$496$	−0.549552	+	1.69135i	−0.0246756	+	0.0759437i
$497$	9.15903	−	28.1886i	0.410839	−	1.26443i
$498$	2.66040	−	1.93289i	0.119215	−	0.0866150i
$499$	−34.4090			−1.54036			−0.770179	−	0.637828i	$-0.779833\pi$
$499$	−34.4090			−1.54036			−0.770179	+	0.637828i	$0.779833\pi$
$500$	14.6877	−	30.0106i	0.656854	−	1.34211i
$501$	−15.9089			−0.710758
$502$	27.2216	−	19.7776i	1.21496	−	0.882719i
$503$	−8.84241	+	27.2141i	−0.394263	+	1.21342i	0.535270	+	0.844681i	$0.320210\pi$
$503$	−8.84241	+	27.2141i	−0.394263	+	1.21342i	−0.929534	+	0.368737i	$0.879790\pi$
$504$	−1.81362	+	5.58173i	−0.0807849	+	0.248630i
$505$	−4.58669	−	0.215712i	−0.204105	−	0.00959907i
$506$	25.8932	+	79.6910i	1.15109	+	3.54270i
$507$	18.2211			0.809227
$508$	−4.82747	−	14.8574i	−0.214184	−	0.659192i
$509$	4.18137	+	3.03795i	0.185336	+	0.134655i	0.676585	−	0.736365i	$-0.263459\pi$
$509$	4.18137	+	3.03795i	0.185336	+	0.134655i	−0.491249	+	0.871019i	$0.663459\pi$
$510$	−5.89077	+	3.87060i	−0.260848	+	0.171393i
$511$	−33.2672	+	24.1700i	−1.47165	+	1.06922i
$512$	9.45008	+	6.86589i	0.417639	+	0.303432i
$513$	31.0637	+	22.5691i	1.37150	+	0.996452i
$514$	−21.5989	+	15.6925i	−0.952686	+	0.692167i
$515$	12.4710	−	33.0165i	0.549540	−	1.45488i
$516$	−10.0193	−	7.27948i	−0.441077	−	0.320461i
$517$	−9.99402	−	30.7584i	−0.439536	−	1.35275i
$518$	42.0336			1.84685
$519$	10.4539	+	32.1737i	0.458874	+	1.41227i
$520$	0.522107	−	1.38225i	0.0228959	−	0.0606158i
$521$	−2.55499	+	7.86344i	−0.111936	+	0.344504i	−0.991296	−	0.131654i	$-0.957971\pi$
$521$	−2.55499	+	7.86344i	−0.111936	+	0.344504i	0.879360	+	0.476158i	$0.157971\pi$
$522$	−1.70828	+	5.25753i	−0.0747692	+	0.230116i
$523$	−15.3662	+	11.1642i	−0.671916	+	0.488176i	−0.870666	−	0.491875i	$-0.836312\pi$
$523$	−15.3662	+	11.1642i	−0.671916	+	0.488176i	0.198750	+	0.980050i	$0.436312\pi$
$524$	−44.7830			−1.95636
$525$	7.38609	−	17.0803i	0.322356	−	0.745445i
$526$	2.00872			0.0875842
$527$	−1.37546	+	0.999331i	−0.0599160	+	0.0435315i
$528$	−2.15292	+	6.62601i	−0.0936938	+	0.288360i
$529$	12.4212	−	38.2285i	0.540052	−	1.66211i
$530$	14.0563	+	51.3553i	0.610567	+	2.23073i
$531$	−1.41609	−	4.35829i	−0.0614532	−	0.189134i
$532$	53.4919			2.31917
$533$	−0.751881	−	2.31405i	−0.0325676	−	0.100233i
$534$	13.1677	+	9.56687i	0.569821	+	0.413999i
$535$	−31.8108	−	1.49606i	−1.37530	−	0.0646805i
$536$	−1.50767	+	1.09539i	−0.0651214	+	0.0473134i
$537$	13.6157	+	9.89237i	0.587560	+	0.426887i
$538$	−17.7677	−	12.9090i	−0.766019	−	0.556545i
$539$	−0.175758	+	0.127696i	−0.00757043	+	0.00550024i
$540$	9.97940	+	36.4601i	0.429445	+	1.56899i
$541$	−2.85484	−	2.07416i	−0.122739	−	0.0891752i	0.524722	−	0.851274i	$-0.324169\pi$
$541$	−2.85484	−	2.07416i	−0.122739	−	0.0891752i	−0.647461	+	0.762098i	$0.724169\pi$
$542$	8.76555	+	26.9776i	0.376512	+	1.15879i
$543$	−4.27840			−0.183604
$544$	2.08639	+	6.42124i	0.0894532	+	0.275309i
$545$	15.4002	+	12.3347i	0.659673	+	0.528359i
$546$	0.768839	−	2.36624i	0.0329033	−	0.101266i
$547$	10.1801	−	31.3311i	0.435269	−	1.33962i	−0.457541	−	0.889189i	$-0.651270\pi$
$547$	10.1801	−	31.3311i	0.435269	−	1.33962i	0.892810	−	0.450433i	$-0.148730\pi$
$548$	32.1624	−	23.3674i	1.37391	−	0.998205i
$549$	−3.23952			−0.138259
$550$	20.9181	−	48.3731i	0.891953	−	2.06263i
$551$	16.6653			0.709967
$552$	−20.0392	+	14.5593i	−0.852925	+	0.619686i
$553$	7.46657	−	22.9797i	0.317511	−	0.977197i
$554$	5.40779	−	16.6435i	0.229755	−	0.707114i
$555$	18.8228	−	12.3678i	0.798985	−	0.524982i
$556$	−13.4411	−	41.3673i	−0.570028	−	1.75437i
$557$	−40.5482			−1.71808			−0.859041	−	0.511907i	$-0.828939\pi$
$557$	−40.5482			−1.71808			−0.859041	+	0.511907i	$0.828939\pi$
$558$	1.18293	+	3.64068i	0.0500774	+	0.154122i
$559$	−0.711011	−	0.516580i	−0.0300726	−	0.0218490i
$560$	−4.81411	−	3.85582i	−0.203433	−	0.162938i
$561$	−5.38849	+	3.91497i	−0.227502	+	0.165290i
$562$	35.6227	+	25.8814i	1.50265	+	1.09174i
$563$	−2.91220	−	2.11584i	−0.122735	−	0.0891720i	0.524724	−	0.851272i	$-0.324168\pi$
$563$	−2.91220	−	2.11584i	−0.122735	−	0.0891720i	−0.647459	+	0.762100i	$0.724168\pi$
$564$	23.3842	−	16.9896i	0.984652	−	0.715391i
$565$	34.0710	+	27.2888i	1.43338	+	1.14805i
$566$	46.1153	+	33.5047i	1.93837	+	1.40831i
$567$	4.04140	+	12.4382i	0.169723	+	0.522354i
$568$	24.8139			1.04117
$569$	2.21703	+	6.82331i	0.0929427	+	0.286048i	0.986712	−	0.162479i	$-0.0519489\pi$
$569$	2.21703	+	6.82331i	0.0929427	+	0.286048i	−0.893769	+	0.448527i	$0.851949\pi$
$570$	39.9849	−	26.2725i	1.67478	−	1.10043i
$571$	−6.22070	+	19.1453i	−0.260328	+	0.801208i	0.732405	+	0.680869i	$0.238398\pi$
$571$	−6.22070	+	19.1453i	−0.260328	+	0.801208i	−0.992733	+	0.120338i	$0.961602\pi$
$572$	1.30444	−	4.01466i	0.0545415	−	0.167862i
$573$	−3.59193	+	2.60969i	−0.150055	+	0.109021i
$574$	47.8792			1.99844
$575$	−34.2075	+	20.2421i	−1.42655	+	0.844155i
$576$	13.0930			0.545540
$577$	−23.5825	+	17.1337i	−0.981753	+	0.713286i	−0.958100	−	0.286435i	$-0.907530\pi$
$577$	−23.5825	+	17.1337i	−0.981753	+	0.713286i	−0.0236535	+	0.999720i	$0.507530\pi$
$578$	−0.690185	+	2.12417i	−0.0287079	+	0.0883539i
$579$	4.45449	−	13.7095i	0.185122	−	0.569747i
$580$	12.8057	+	10.2566i	0.531726	+	0.425881i
$581$	0.850100	+	2.61634i	0.0352681	+	0.108544i
$582$	−28.1151			−1.16541
$583$	15.5475	+	47.8504i	0.643913	+	1.98176i
$584$	−27.8512	−	20.2351i	−1.15249	−	0.837335i
$585$	0.178117	+	0.650758i	0.00736424	+	0.0269055i
$586$	42.9009	−	31.1693i	1.77222	−	1.28759i
$587$	−18.5847	−	13.5026i	−0.767074	−	0.557312i	0.133998	−	0.990982i	$-0.457218\pi$
$587$	−18.5847	−	13.5026i	−0.767074	−	0.557312i	−0.901072	+	0.433670i	$0.857218\pi$
$588$	−0.157080	−	0.114126i	−0.00647789	−	0.00470646i
$589$	9.33624	−	6.78317i	0.384693	−	0.279496i
$590$	−22.6775	−	1.06653i	−0.933620	−	0.0439082i
$591$	−1.97764	−	1.43684i	−0.0813494	−	0.0591038i
$592$	−2.30683	−	7.09968i	−0.0948100	−	0.291795i
$593$	10.2524			0.421015			0.210507	−	0.977592i	$-0.432488\pi$
$593$	10.2524			0.421015			0.210507	+	0.977592i	$0.432488\pi$
$594$	18.4253	+	56.7071i	0.755997	+	2.32672i
$595$	−1.55668	−	5.68740i	−0.0638178	−	0.233161i
$596$	5.86465	−	18.0496i	0.240226	−	0.739338i
$597$	−5.08938	+	15.6635i	−0.208294	+	0.641064i
$598$	−4.29937	+	3.12368i	−0.175814	+	0.127737i
$599$	−30.8395			−1.26007			−0.630035	−	0.776567i	$-0.716959\pi$
$599$	−30.8395			−1.26007			−0.630035	+	0.776567i	$0.716959\pi$
$600$	15.5106	+	1.46216i	0.633216	+	0.0596924i
$601$	2.25852			0.0921270			0.0460635	−	0.998939i	$-0.485332\pi$
$601$	2.25852			0.0921270			0.0460635	+	0.998939i	$0.485332\pi$
$602$	13.9913	−	10.1652i	0.570241	−	0.414304i
$603$	0.262959	−	0.809305i	0.0107085	−	0.0329575i
$604$	0.380428	−	1.17084i	0.0154794	−	0.0476407i
$605$	8.90594	−	23.5781i	0.362078	−	0.958584i
$606$	−2.00029	−	6.15627i	−0.0812564	−	0.250081i
$607$	14.3154			0.581046			0.290523	−	0.956868i	$-0.406171\pi$
$607$	14.3154			0.581046			0.290523	+	0.956868i	$0.406171\pi$
$608$	−14.1618	−	43.5856i	−0.574338	−	1.76763i
$609$	7.39261	+	5.37105i	0.299564	+	0.217646i
$610$	−5.67097	+	15.0136i	−0.229611	+	0.607884i
$611$	1.65943	−	1.20565i	0.0671335	−	0.0487753i
$612$	2.43729	+	1.77080i	0.0985218	+	0.0715803i
$613$	−14.0464	−	10.2053i	−0.567327	−	0.412187i	0.266806	−	0.963750i	$-0.414032\pi$
$613$	−14.0464	−	10.2053i	−0.567327	−	0.412187i	−0.834133	+	0.551563i	$0.814032\pi$
$614$	−9.55637	+	6.94311i	−0.385664	+	0.280201i
$615$	21.4405	−	14.0877i	0.864566	−	0.568073i
$616$	22.2277	+	16.1493i	0.895578	+	0.650675i
$617$	−10.4814	−	32.2586i	−0.421967	−	1.29868i	−0.905869	−	0.423558i	$-0.860781\pi$
$617$	−10.4814	−	32.2586i	−0.421967	−	1.29868i	0.483902	−	0.875122i	$-0.339219\pi$
$618$	49.7536			2.00138
$619$	11.5708	+	35.6113i	0.465070	+	1.43134i	0.858895	+	0.512152i	$0.171152\pi$
$619$	11.5708	+	35.6113i	0.465070	+	1.43134i	−0.393825	+	0.919185i	$0.628848\pi$
$620$	11.3486	+	0.533727i	0.455772	+	0.0214350i
$621$	13.8963	−	42.7684i	0.557639	−	1.71624i
$622$	−8.98347	+	27.6483i	−0.360204	+	1.10859i
$623$	−11.0156	+	8.00329i	−0.441330	+	0.320645i
$624$	−0.441865			−0.0176888
$625$	24.5596	+	4.67192i	0.982383	+	0.186877i
$626$	−60.7950			−2.42986
$627$	36.5756	−	26.5737i	1.46069	−	1.06125i
$628$	−11.7127	+	36.0479i	−0.467386	+	1.43847i
$629$	2.20536	−	6.78739i	0.0879333	−	0.270631i
$630$	−13.2619	−	0.623710i	−0.528369	−	0.0248492i
$631$	−2.33627	−	7.19031i	−0.0930055	−	0.286242i	0.893723	−	0.448619i	$-0.148084\pi$
$631$	−2.33627	−	7.19031i	−0.0930055	−	0.286242i	−0.986729	+	0.162377i	$0.948084\pi$
$632$	20.2286			0.804652
$633$	−6.27618	−	19.3161i	−0.249456	−	0.767746i
$634$	7.23478	+	5.25637i	0.287330	+	0.208757i
$635$	9.76886	−	6.41874i	0.387665	−	0.254720i
$636$	−36.3784	+	26.4305i	−1.44250	+	1.04804i
$637$	−0.0111470	−	0.00809879i	−0.000441662	−	0.000320886i
$638$	20.9366	+	15.2113i	0.828888	+	0.602223i
$639$	−9.16666	+	6.65996i	−0.362627	+	0.263464i
$640$	12.2506	−	32.4330i	0.484249	−	1.28203i
$641$	5.83033	+	4.23598i	0.230284	+	0.167311i	0.696944	−	0.717126i	$-0.254543\pi$
$641$	5.83033	+	4.23598i	0.230284	+	0.167311i	−0.466660	+	0.884437i	$0.654543\pi$
$642$	−13.8730	−	42.6966i	−0.547522	−	1.68510i
$643$	0.302163			0.0119161			0.00595807	−	0.999982i	$-0.498103\pi$
$643$	0.302163			0.0119161			0.00595807	+	0.999982i	$0.498103\pi$
$644$	−19.3594	−	59.5820i	−0.762866	−	2.34786i
$645$	3.27438	−	8.66877i	0.128929	−	0.341332i
$646$	4.68478	−	14.4183i	0.184320	−	0.567280i
$647$	6.52102	−	20.0696i	0.256368	−	0.789019i	−0.737189	−	0.675686i	$-0.763847\pi$
$647$	6.52102	−	20.0696i	0.256368	−	0.789019i	0.993557	−	0.113333i	$-0.0361525\pi$
$648$	−8.85800	+	6.43571i	−0.347975	+	0.252819i
$649$	−21.4527			−0.842093
$650$	3.32776	+	0.313703i	0.130525	+	0.0123045i
$651$	6.32763			0.247999
$652$	−21.8487	+	15.8740i	−0.855661	+	0.621674i
$653$	14.9125	−	45.8959i	0.583571	−	1.79605i	−0.0213656	−	0.999772i	$-0.506801\pi$
$653$	14.9125	−	45.8959i	0.583571	−	1.79605i	0.604936	−	0.796274i	$-0.293199\pi$
$654$	−8.59534	+	26.4537i	−0.336104	+	1.03442i
$655$	−8.84605	−	32.3194i	−0.345644	−	1.26282i
$656$	−2.62764	−	8.08704i	−0.102592	−	0.315746i
$657$	15.7197			0.613284
$658$	12.4728	+	38.3874i	0.486241	+	1.49650i
$659$	6.96863	+	5.06301i	0.271459	+	0.197227i	0.715184	−	0.698937i	$-0.246343\pi$
$659$	6.96863	+	5.06301i	0.271459	+	0.197227i	−0.443724	+	0.896163i	$0.646343\pi$
$660$	44.4593	+	2.09093i	1.73058	+	0.0813892i
$661$	29.4433	−	21.3918i	1.14521	−	0.832046i	0.157376	−	0.987539i	$-0.449697\pi$
$661$	29.4433	−	21.3918i	1.14521	−	0.832046i	0.987837	+	0.155493i	$0.0496965\pi$
$662$	47.8089	+	34.7352i	1.85814	+	1.35002i
$663$	−0.341752	−	0.248297i	−0.0132726	−	0.00964308i
$664$	−1.86326	+	1.35374i	−0.0723085	+	0.0525352i
$665$	10.5663	+	38.6045i	0.409745	+	1.49702i
$666$	−12.9999	−	9.44498i	−0.503736	−	0.365985i
$667$	−6.03138	−	18.5627i	−0.233536	−	0.718750i
$668$	33.6864			1.30337
$669$	−6.38113	−	19.6391i	−0.246709	−	0.759291i
$670$	−3.29042	−	2.63543i	−0.127120	−	0.101815i
$671$	−4.68636	+	14.4231i	−0.180915	+	0.556799i
$672$	7.76507	−	23.8984i	0.299544	−	0.921902i
$673$	6.41196	−	4.65856i	0.247163	−	0.179574i	−0.457306	−	0.889310i	$-0.651185\pi$
$673$	6.41196	−	4.65856i	0.247163	−	0.179574i	0.704468	+	0.709735i	$0.251185\pi$
$674$	−41.9365			−1.61534
$675$	−24.3416	+	14.4040i	−0.936909	+	0.554411i
$676$	−38.5823			−1.48393
$677$	−10.4549	+	7.59591i	−0.401813	+	0.291934i	−0.770279	−	0.637707i	$-0.779883\pi$
$677$	−10.4549	+	7.59591i	−0.401813	+	0.291934i	0.368466	+	0.929641i	$0.379883\pi$
$678$	−19.0161	+	58.5254i	−0.730308	+	2.24766i
$679$	7.26810	−	22.3689i	0.278924	−	0.858440i
$680$	4.12571	−	2.71084i	0.158214	−	0.103956i
$681$	−0.803012	−	2.47142i	−0.0307715	−	0.0947049i
$682$	17.9205			0.686210
$683$	−13.7839	−	42.4226i	−0.527427	−	1.62325i	−0.759466	−	0.650548i	$-0.774539\pi$
$683$	−13.7839	−	42.4226i	−0.527427	−	1.62325i	0.232038	−	0.972707i	$-0.425461\pi$
$684$	−16.5437	−	12.0197i	−0.632563	−	0.459584i
$685$	23.2170	+	18.5955i	0.887078	+	0.710496i
$686$	33.5739	−	24.3929i	1.28186	−	0.931325i
$687$	−11.1434	−	8.09612i	−0.425146	−	0.308886i
$688$	−2.48481	−	1.80532i	−0.0947325	−	0.0688272i
$689$	−2.58155	+	1.87561i	−0.0983493	+	0.0714550i
$690$	−43.7346	−	35.0288i	−1.66495	−	1.33353i
$691$	−17.2409	−	12.5263i	−0.655875	−	0.476521i	0.209392	−	0.977832i	$-0.432851\pi$
$691$	−17.2409	−	12.5263i	−0.655875	−	0.476521i	−0.865267	+	0.501311i	$0.832851\pi$
$692$	−22.1356	−	68.1263i	−0.841469	−	2.58977i
$693$	−12.5457			−0.476571
$694$	−4.20914	−	12.9544i	−0.159777	−	0.491743i
$695$	27.1993	−	17.8716i	1.03173	−	0.677908i
$696$	−2.36402	+	7.27570i	−0.0896079	+	0.275785i
$697$	2.51206	−	7.73132i	0.0951509	−	0.292844i
$698$	−14.3112	+	10.3977i	−0.541685	+	0.393557i
$699$	15.6929			0.593560
$700$	−15.6397	+	36.1667i	−0.591125	+	1.36697i
$701$	−36.8974			−1.39360			−0.696798	−	0.717267i	$-0.745393\pi$
$701$	−36.8974			−1.39360			−0.696798	+	0.717267i	$0.745393\pi$
$702$	−3.05938	+	2.22277i	−0.115469	+	0.0838929i
$703$	−14.9693	+	46.0709i	−0.564579	+	1.73760i
$704$	18.9406	−	58.2931i	0.713850	−	2.19700i
$705$	16.8803	+	13.5201i	0.635749	+	0.509197i
$706$	10.6859	+	32.8878i	0.402169	+	1.23775i
$707$	5.41515			0.203657
$708$	−5.92477	−	18.2346i	−0.222667	−	0.685298i
$709$	2.60019	+	1.88915i	0.0976522	+	0.0709484i	0.635540	−	0.772068i	$-0.280778\pi$
$709$	2.60019	+	1.88915i	0.0976522	+	0.0709484i	−0.537888	+	0.843016i	$0.680778\pi$
$710$	14.8190	+	54.1417i	0.556146	+	2.03190i
$711$	−7.47278	+	5.42929i	−0.280251	+	0.203614i
$712$	−9.22223	−	6.70034i	−0.345618	−	0.251106i
$713$	−10.9343	−	7.94426i	−0.409494	−	0.297515i
$714$	6.72499	−	4.88599i	0.251676	−	0.182854i
$715$	3.15501	+	0.148380i	0.117991	+	0.00554910i
$716$	−28.8306	−	20.9466i	−1.07745	−	0.782812i
$717$	11.2183	+	34.5264i	0.418955	+	1.28941i
$718$	49.7866			1.85802
$719$	15.7283	+	48.4068i	0.586568	+	1.80527i	0.592881	+	0.805290i	$0.297990\pi$
$719$	15.7283	+	48.4068i	0.586568	+	1.80527i	−0.00631317	+	0.999980i	$0.502010\pi$
$720$	0.622475	+	2.27424i	0.0231983	+	0.0847559i
$721$	−12.8619	+	39.5849i	−0.479003	+	1.47422i
$722$	−18.6855	+	57.5080i	−0.695402	+	2.14023i
$723$	−10.1657	+	7.38578i	−0.378065	+	0.274680i
$724$	9.05932			0.336687
$725$	−4.87253	+	11.2677i	−0.180961	+	0.418471i
$726$	35.5305			1.31866
$727$	24.0194	−	17.4511i	0.890831	−	0.647227i	−0.0452633	−	0.998975i	$-0.514413\pi$
$727$	24.0194	−	17.4511i	0.890831	−	0.647227i	0.936095	+	0.351748i	$0.114413\pi$
$728$	−0.538471	+	1.65724i	−0.0199571	+	0.0614215i
$729$	8.94630	−	27.5339i	0.331344	−	1.01977i
$730$	27.5183	−	72.8534i	1.01850	−	2.69642i
$731$	−0.907364	−	2.79258i	−0.0335601	−	0.103287i
$732$	−13.5538			−0.500962
$733$	−8.31355	−	25.5865i	−0.307068	−	0.945059i	−0.978897	−	0.204352i	$-0.934491\pi$
$733$	−8.31355	−	25.5865i	−0.307068	−	0.945059i	0.671829	−	0.740706i	$-0.265509\pi$
$734$	40.6775	+	29.5539i	1.50143	+	1.09085i
$735$	0.0513348	−	0.135906i	0.00189351	−	0.00501299i
$736$	−43.4225	+	31.5483i	−1.60057	+	1.16289i
$737$	−3.22283	−	2.34152i	−0.118714	−	0.0862510i
$738$	−14.8078	−	10.7585i	−0.545083	−	0.396026i
$739$	−6.38348	+	4.63787i	−0.234820	+	0.170607i	−0.698972	−	0.715149i	$-0.746359\pi$
$739$	−6.38348	+	4.63787i	−0.234820	+	0.170607i	0.464152	+	0.885755i	$0.346359\pi$
$740$	−39.8565	+	26.1882i	−1.46515	+	0.962696i
$741$	2.31972	+	1.68537i	0.0852170	+	0.0619137i
$742$	−19.4038	−	59.7186i	−0.712334	−	2.19234i
$743$	39.3592			1.44395			0.721975	−	0.691919i	$-0.243235\pi$
$743$	39.3592			1.44395			0.721975	+	0.691919i	$0.243235\pi$
$744$	1.63701	+	5.03820i	0.0600157	+	0.184709i
$745$	14.1846	+	0.667103i	0.519684	+	0.0244408i
$746$	14.4724	−	44.5416i	0.529874	−	1.63078i
$747$	0.324980	−	1.00018i	0.0118904	−	0.0365948i
$748$	11.4099	−	8.28976i	0.417186	−	0.303104i
$749$	37.5565			1.37229
$750$	6.07267	+	34.7158i	0.221743	+	1.26764i
$751$	23.4980			0.857456			0.428728	−	0.903434i	$-0.358962\pi$
$751$	23.4980			0.857456			0.428728	+	0.903434i	$0.358962\pi$
$752$	5.79931	−	4.21344i	0.211479	−	0.153648i
$753$	−6.57035	+	20.2215i	−0.239437	+	0.736911i
$754$	−0.507195	+	1.56099i	−0.0184710	+	0.0568478i
$755$	0.920126	+	0.0432736i	0.0334868	+	0.00157489i
$756$	−13.7759	−	42.3978i	−0.501024	−	1.54199i
$757$	−46.6817			−1.69667			−0.848337	−	0.529456i	$-0.822396\pi$
$757$	−46.6817			−1.69667			−0.848337	+	0.529456i	$0.822396\pi$
$758$	13.3052	+	40.9492i	0.483267	+	1.48734i
$759$	−42.8362	−	31.1223i	−1.55486	−	1.12967i
$760$	−28.0042	+	18.4005i	−1.01582	+	0.667455i
$761$	−20.3039	+	14.7517i	−0.736017	+	0.534748i	−0.891461	−	0.453097i	$-0.850319\pi$
$761$	−20.3039	+	14.7517i	−0.736017	+	0.534748i	0.155444	+	0.987845i	$0.450319\pi$
$762$	13.3311	+	9.68558i	0.482933	+	0.350871i
$763$	−18.8251	−	13.6772i	−0.681514	−	0.495149i
$764$	7.60575	−	5.52590i	0.275166	−	0.199920i
$765$	−0.796523	+	2.10876i	−0.0287983	+	0.0762422i
$766$	17.3084	+	12.5753i	0.625377	+	0.454363i
$767$	−0.420445	−	1.29400i	−0.0151814	−	0.0467235i
$768$	12.2137			0.440724
$769$	−2.86216	−	8.80881i	−0.103212	−	0.317654i	0.886095	−	0.463504i	$-0.153408\pi$
$769$	−2.86216	−	8.80881i	−0.103212	−	0.317654i	−0.989307	+	0.145850i	$0.953408\pi$
$770$	−21.9620	+	58.1432i	−0.791454	+	2.09534i
$771$	5.21323	−	16.0447i	0.187750	−	0.577834i
$772$	−9.43217	+	29.0292i	−0.339471	+	1.04478i
$773$	28.6362	−	20.8054i	1.02997	−	0.748319i	0.0616699	−	0.998097i	$-0.480357\pi$
$773$	28.6362	−	20.8054i	1.02997	−	0.748319i	0.968303	+	0.249777i	$0.0803574\pi$
$774$	−6.61127			−0.237637
$775$	1.85653	+	8.29561i	0.0666884	+	0.297987i
$776$	19.6909			0.706864
$777$	−21.4884	+	15.6123i	−0.770893	+	0.560086i
$778$	24.2547	−	74.6483i	0.869573	−	2.67627i
$779$	−17.0511	+	52.4780i	−0.610920	+	1.88022i
$780$	0.745222	+	2.72270i	0.0266832	+	0.0974882i
$781$	16.3911	+	50.4467i	0.586520	+	1.80512i
$782$	−17.7553			−0.634928
$783$	−4.29185	−	13.2090i	−0.153378	−	0.472050i
$784$	−0.0389561	−	0.0283033i	−0.00139129	−	0.00101083i
$785$	−28.3290	−	1.33231i	−1.01110	−	0.0475523i
$786$	38.2156	−	27.7652i	1.36310	−	0.990354i
$787$	26.0533	+	18.9288i	0.928699	+	0.674739i	0.945674	−	0.325117i	$-0.105404\pi$
$787$	26.0533	+	18.9288i	0.928699	+	0.674739i	−0.0169748	+	0.999856i	$0.505404\pi$
$788$	4.18757	+	3.04245i	0.149176	+	0.108383i
$789$	−1.02690	+	0.746084i	−0.0365585	+	0.0265613i
$790$	12.0806	+	44.1371i	0.429810	+	1.57033i
$791$	−41.6480	−	30.2591i	−1.48083	−	1.07589i
$792$	−3.24567	−	9.98914i	−0.115330	−	0.354949i
$793$	−0.961829			−0.0341556
$794$	−6.03688	−	18.5796i	−0.214241	−	0.659365i
$795$	−26.2604	−	21.0330i	−0.931361	−	0.745965i
$796$	10.7765	−	33.1667i	0.381964	−	1.17556i
$797$	1.77810	−	5.47241i	0.0629834	−	0.193843i	−0.914613	−	0.404330i	$-0.867505\pi$
$797$	1.77810	−	5.47241i	0.0629834	−	0.193843i	0.977597	+	0.210487i	$0.0675049\pi$
$798$	−45.6473	+	33.1647i	−1.61590	+	1.17402i
$799$	6.85303			0.242443
$800$	33.6095	+	3.16832i	1.18827	+	0.112017i
$801$	5.20518			0.183916
$802$	−17.0008	+	12.3518i	−0.600318	+	0.436157i
$803$	22.7405	−	69.9881i	0.802495	−	2.46983i
$804$	1.10019	−	3.38604i	0.0388008	−	0.119416i
$805$	39.1755	−	25.7407i	1.38076	−	0.907241i
$806$	0.351217	+	1.08094i	0.0123711	+	0.0380743i
$807$	13.8779			0.488525
$808$	1.40094	+	4.31166i	0.0492850	+	0.151684i
$809$	−28.3362	−	20.5875i	−0.996249	−	0.723817i	−0.0349685	−	0.999388i	$-0.511133\pi$
$809$	−28.3362	−	20.5875i	−0.996249	−	0.723817i	−0.961281	+	0.275571i	$0.911133\pi$
$810$	−19.3322	−	15.4839i	−0.679264	−	0.544049i
$811$	29.5709	−	21.4845i	1.03838	−	0.754424i	0.0684080	−	0.997657i	$-0.478208\pi$
$811$	29.5709	−	21.4845i	1.03838	−	0.754424i	0.969968	+	0.243233i	$0.0782080\pi$
$812$	−15.6535	−	11.3729i	−0.549331	−	0.399112i
$813$	−14.5012	−	10.5358i	−0.508580	−	0.369505i
$814$	−60.8573	+	44.2154i	−2.13305	+	1.54975i
$815$	−15.7719	−	12.6323i	−0.552465	−	0.442491i
$816$	−1.19434	−	0.867738i	−0.0418102	−	0.0303769i
$817$	6.15894	+	18.9553i	0.215474	+	0.663160i
$818$	−39.0209			−1.36434
$819$	−0.245878	−	0.756736i	−0.00859169	−	0.0264425i
$820$	−45.3994	+	29.8301i	−1.58541	+	1.04171i
$821$	10.0028	−	30.7855i	0.349100	−	1.07442i	−0.610252	−	0.792207i	$-0.708932\pi$
$821$	10.0028	−	30.7855i	0.349100	−	1.07442i	0.959352	−	0.282212i	$-0.0910683\pi$
$822$	−12.9581	+	39.8811i	−0.451967	+	1.39101i
$823$	−22.4578	+	16.3165i	−0.782829	+	0.568759i	−0.905827	−	0.423648i	$-0.860749\pi$
$823$	−22.4578	+	16.3165i	−0.782829	+	0.568759i	0.122998	+	0.992407i	$0.460749\pi$
$824$	−34.8459			−1.21391
$825$	7.27311	+	32.4988i	0.253217	+	1.13146i
$826$	26.7736			0.931573
$827$	37.1852	−	27.0167i	1.29306	−	0.939461i	0.293195	−	0.956053i	$-0.405281\pi$
$827$	37.1852	−	27.0167i	1.29306	−	0.939461i	0.999862	+	0.0165915i	$0.00528149\pi$
$828$	−7.40077	+	22.7772i	−0.257195	+	0.791563i
$829$	−12.2506	+	37.7033i	−0.425479	+	1.30949i	0.477056	+	0.878873i	$0.341704\pi$
$829$	−12.2506	+	37.7033i	−0.425479	+	1.30949i	−0.902535	+	0.430617i	$0.858296\pi$
$830$	−4.06648	−	3.25701i	−0.141150	−	0.113052i
$831$	3.41720	+	10.5171i	0.118541	+	0.364833i
$832$	3.88736			0.134770
$833$	−0.0142254	−	0.0437813i	−0.000492881	−	0.00151693i
$834$	37.1175	+	26.9674i	1.28527	+	0.933805i
$835$	6.65412	+	24.3111i	0.230275	+	0.841320i
$836$	−77.4471	+	56.2686i	−2.67856	+	1.94609i
$837$	−7.78073	−	5.65303i	−0.268941	−	0.195397i
$838$	−60.4520	−	43.9209i	−2.08828	−	1.51722i
$839$	−8.37681	+	6.08611i	−0.289200	+	0.210116i	−0.722920	−	0.690932i	$-0.757201\pi$
$839$	−8.37681	+	6.08611i	−0.289200	+	0.210116i	0.433721	+	0.901047i	$0.357201\pi$
$840$	−18.3527	−	0.863129i	−0.633228	−	0.0297808i
$841$	18.5847	+	13.5025i	0.640851	+	0.465605i
$842$	9.36344	+	28.8177i	0.322686	+	0.993124i
$843$	−27.8240			−0.958310
$844$	13.2895	+	40.9010i	0.457445	+	1.40787i
$845$	−7.62121	−	27.8444i	−0.262178	−	0.957877i
$846$	4.76816	−	14.6749i	0.163933	−	0.504533i
$847$	−9.18507	+	28.2688i	−0.315603	+	0.971326i
$848$	−9.02189	+	6.55479i	−0.309813	+	0.225092i
$849$	−36.0195			−1.23619
$850$	8.37871	+	7.38301i	0.287387	+	0.253235i
$851$	56.7337			1.94480
$852$	−38.3522	+	27.8645i	−1.31393	+	0.954623i
$853$	−0.695423	+	2.14029i	−0.0238108	+	0.0732822i	−0.962256	−	0.272146i	$-0.912266\pi$
$853$	−0.695423	+	2.14029i	−0.0238108	+	0.0732822i	0.938445	+	0.345429i	$0.112266\pi$
$854$	5.84871	−	18.0005i	0.200139	−	0.615964i
$855$	5.40657	−	14.3136i	0.184901	−	0.489516i
$856$	9.71618	+	29.9033i	0.332092	+	1.02207i
$857$	−39.7546			−1.35799			−0.678995	−	0.734143i	$-0.737584\pi$
$857$	−39.7546			−1.35799			−0.678995	+	0.734143i	$0.737584\pi$
$858$	1.37592	+	4.23466i	0.0469733	+	0.144569i
$859$	9.05693	+	6.58024i	0.309018	+	0.224515i	0.731475	−	0.681868i	$-0.238832\pi$
$859$	9.05693	+	6.58024i	0.309018	+	0.224515i	−0.422457	+	0.906383i	$0.638832\pi$
$860$	−6.93335	+	18.3557i	−0.236425	+	0.625925i
$861$	−24.4768	+	17.7835i	−0.834168	+	0.606059i
$862$	−14.4487	−	10.4976i	−0.492125	−	0.357550i
$863$	−18.7497	−	13.6225i	−0.638249	−	0.463715i	0.220999	−	0.975274i	$-0.429068\pi$
$863$	−18.7497	−	13.6225i	−0.638249	−	0.463715i	−0.859248	+	0.511559i	$0.829068\pi$
$864$	−30.8989	+	22.4493i	−1.05120	+	0.763742i
$865$	44.7935	−	29.4321i	1.52303	−	1.00072i
$866$	32.3920	+	23.5341i	1.10072	+	0.799722i
$867$	−0.436131	−	1.34227i	−0.0148118	−	0.0455859i
$868$	−13.3985			−0.454773
$869$	13.3623	+	41.1248i	0.453284	+	1.39506i
$870$	−17.2867	−	0.812996i	−0.586075	−	0.0275631i
$871$	0.0780739	−	0.240287i	0.00264543	−	0.00814180i
$872$	6.01991	−	18.5274i	0.203860	−	0.627416i
$873$	−7.27415	+	5.28498i	−0.246193	+	0.178869i
$874$	120.518			4.07658
$875$	−29.1904	−	4.14294i	−0.986817	−	0.140057i
$876$	65.7695			2.22215
$877$	27.8284	−	20.2185i	0.939698	−	0.682730i	−0.00865012	−	0.999963i	$-0.502753\pi$
$877$	27.8284	−	20.2185i	0.939698	−	0.682730i	0.948348	+	0.317232i	$0.102753\pi$
$878$	24.1632	−	74.3666i	0.815467	−	2.50975i
$879$	−10.3548	+	31.8688i	−0.349258	+	1.07491i
$880$	11.0260	+	0.518552i	0.371685	+	0.0174804i
$881$	−3.97930	−	12.2470i	−0.134066	−	0.412613i	0.861377	−	0.507965i	$-0.169602\pi$
$881$	−3.97930	−	12.2470i	−0.134066	−	0.412613i	−0.995444	+	0.0953523i	$0.969602\pi$
$882$	−0.103650			−0.00349006
$883$	4.41592	+	13.5908i	0.148607	+	0.457367i	0.997457	−	0.0712675i	$-0.0227044\pi$
$883$	4.41592	+	13.5908i	0.148607	+	0.457367i	−0.848850	+	0.528634i	$0.822704\pi$
$884$	0.723644	+	0.525758i	0.0243388	+	0.0176832i
$885$	11.9894	−	7.87774i	0.403018	−	0.264807i
$886$	31.9850	−	23.2385i	1.07456	−	0.780712i
$887$	−37.3614	−	27.1447i	−1.25447	−	0.911429i	−0.256001	−	0.966676i	$-0.582405\pi$
$887$	−37.3614	−	27.1447i	−1.25447	−	0.911429i	−0.998473	+	0.0552477i	$0.982405\pi$
$888$	−17.9901	−	13.0705i	−0.603707	−	0.438619i
$889$	−11.1523	+	8.10260i	−0.374035	+	0.271752i
$890$	9.11199	−	24.1235i	0.305434	−	0.808623i
$891$	−18.9351	−	13.7571i	−0.634348	−	0.460881i
$892$	13.5117	+	41.5849i	0.452407	+	1.39236i
$893$	−46.5164			−1.55661
$894$	6.18603	+	19.0386i	0.206892	+	0.636747i
$895$	9.42201	−	24.9443i	0.314943	−	0.833796i
$896$	−12.6346	+	38.8853i	−0.422093	+	1.29907i
$897$	1.03772	−	3.19377i	0.0346485	−	0.106637i
$898$	3.87176	−	2.81299i	0.129202	−	0.0938709i
$899$	−4.17427			−0.139220
$900$	12.9637	−	7.67118i	0.432122	−	0.255706i
$901$	−10.6611			−0.355174
$902$	−69.3208	+	50.3645i	−2.30813	+	1.67695i
$903$	−3.37701	+	10.3934i	−0.112380	+	0.345869i
$904$	13.3183	−	40.9894i	0.442959	−	1.36329i
$905$	1.78950	+	6.53801i	0.0594850	+	0.217331i
$906$	0.401275	+	1.23500i	0.0133315	+	0.0410300i
$907$	15.9730			0.530374			0.265187	−	0.964197i	$-0.414566\pi$
$907$	15.9730			0.530374			0.265187	+	0.964197i	$0.414566\pi$
$908$	1.70034	+	5.23311i	0.0564278	+	0.173667i
$909$	−1.67476	−	1.21679i	−0.0555484	−	0.0403583i
$910$	−3.93754	−	0.185183i	−0.130528	−	0.00613874i
$911$	20.5525	−	14.9323i	0.680935	−	0.494729i	−0.192732	−	0.981251i	$-0.561735\pi$
$911$	20.5525	−	14.9323i	0.680935	−	0.494729i	0.873668	+	0.486523i	$0.161735\pi$
$912$	8.10684	+	5.88996i	0.268444	+	0.195036i
$913$	−3.98295	−	2.89378i	−0.131816	−	0.0957701i
$914$	15.0186	−	10.9116i	0.496770	−	0.360925i
$915$	−2.67730	−	9.78161i	−0.0885087	−	0.323370i
$916$	23.5955	+	17.1432i	0.779619	+	0.566426i
$917$	12.2114	+	37.5827i	0.403255	+	1.24109i
$918$	−12.6344			−0.416998
$919$	8.09429	+	24.9117i	0.267006	+	0.821760i	0.991225	+	0.132189i	$0.0422006\pi$
$919$	8.09429	+	24.9117i	0.267006	+	0.821760i	−0.724219	+	0.689570i	$0.757799\pi$
$920$	30.6304	+	24.5331i	1.00985	+	0.808833i
$921$	2.30658	−	7.09892i	0.0760044	−	0.233917i
$922$	−6.00035	+	18.4672i	−0.197611	+	0.608184i
$923$	−2.72162	+	1.97738i	−0.0895833	+	0.0650861i
$924$	−52.4897			−1.72678
$925$	−26.7726	−	23.5910i	−0.880277	−	0.775667i
$926$	4.78091			0.157110
$927$	12.8726	−	9.35251i	0.422792	−	0.307177i
$928$	−5.12254	+	15.7655i	−0.168155	+	0.517529i
$929$	12.7795	−	39.3313i	0.419283	−	1.29042i	−0.489081	−	0.872238i	$-0.662668\pi$
$929$	12.7795	−	39.3313i	0.419283	−	1.29042i	0.908364	−	0.418181i	$-0.137332\pi$
$930$	−10.0153	+	6.58064i	−0.328414	+	0.215788i
$931$	0.0965580	+	0.297175i	0.00316456	+	0.00973952i
$932$	−33.2290			−1.08845
$933$	−5.67668	−	17.4710i	−0.185846	−	0.571976i
$934$	16.0786	+	11.6818i	0.526108	+	0.382240i
$935$	8.23643	+	6.59689i	0.269360	+	0.215741i
$936$	0.538919	−	0.391548i	0.0176151	−	0.0127981i
$937$	−35.8277	−	26.0303i	−1.17044	−	0.850374i	−0.179378	−	0.983780i	$-0.557409\pi$
$937$	−35.8277	−	26.0303i	−1.17044	−	0.850374i	−0.991061	+	0.133406i	$0.957409\pi$
$938$	4.02218	+	2.92228i	0.131329	+	0.0954159i
$939$	31.0797	−	22.5807i	1.01425	−	0.736893i
$940$	−35.7433	−	28.6282i	−1.16582	−	0.933750i
$941$	−42.9769	−	31.2246i	−1.40101	−	1.01789i	−0.994554	−	0.104220i	$-0.966765\pi$
$941$	−42.9769	−	31.2246i	−1.40101	−	1.01789i	−0.406453	−	0.913672i	$-0.633235\pi$
$942$	−12.3545	−	38.0232i	−0.402531	−	1.23886i
$943$	64.6236			2.10443
$944$	−1.46935	−	4.52220i	−0.0478233	−	0.147185i
$945$	27.8768	−	18.3168i	0.906833	−	0.595845i
$946$	−9.56402	+	29.4350i	−0.310953	+	0.957015i
$947$	10.9586	−	33.7270i	0.356105	−	1.09598i	−0.599260	−	0.800554i	$-0.704539\pi$
$947$	10.9586	−	33.7270i	0.356105	−	1.09598i	0.955366	−	0.295426i	$-0.0954614\pi$
$948$	−31.2653	+	22.7155i	−1.01545	+	0.737767i
$949$	4.66726			0.151506
$950$	−56.8724	−	50.1138i	−1.84518	−	1.62591i
$951$	−5.65091			−0.183243
$952$	−4.70997	+	3.42199i	−0.152651	+	0.110907i
$953$	4.77955	−	14.7100i	0.154825	−	0.476502i	−0.843318	−	0.537415i	$-0.819401\pi$
$953$	4.77955	−	14.7100i	0.154825	−	0.476502i	0.998143	+	0.0609125i	$0.0194011\pi$
$954$	−7.41774	+	22.8295i	−0.240158	+	0.739131i
$955$	5.49035	+	4.39744i	0.177664	+	0.142298i
$956$	−23.7542	−	73.1080i	−0.768267	−	2.36448i
$957$	−16.3531			−0.528620
$958$	8.35625	+	25.7179i	0.269978	+	0.830907i
$959$	−28.3803	−	20.6195i	−0.916448	−	0.665838i
$960$	10.8207	+	39.5337i	0.349235	+	1.27594i
$961$	22.7410	−	16.5223i	0.733581	−	0.532978i
$962$	−3.85973	−	2.80426i	−0.124443	−	0.0904129i
$963$	−11.6153	−	8.43898i	−0.374296	−	0.271942i
$964$	21.5253	−	15.6391i	0.693283	−	0.503700i
$965$	−22.8132	−	1.07291i	−0.734383	−	0.0345381i
$966$	53.4608	+	38.8416i	1.72007	+	1.24971i
$967$	8.94036	+	27.5156i	0.287503	+	0.884842i	0.985637	+	0.168876i	$0.0540136\pi$
$967$	8.94036	+	27.5156i	0.287503	+	0.884842i	−0.698135	+	0.715966i	$0.745986\pi$
$968$	−24.8845			−0.799817
$969$	2.96033	+	9.11096i	0.0950995	+	0.292686i
$970$	11.7595	+	42.9639i	0.377575	+	1.37949i
$971$	−16.3985	+	50.4695i	−0.526254	+	1.61964i	0.235570	+	0.971857i	$0.424304\pi$
$971$	−16.3985	+	50.4695i	−0.526254	+	1.61964i	−0.761823	+	0.647785i	$0.775696\pi$
$972$	−9.20803	+	28.3394i	−0.295348	+	0.908987i
$973$	−31.0511	+	22.5599i	−0.995452	+	0.723239i
$974$	−13.1140			−0.420198
$975$	−1.81774	+	1.07564i	−0.0582141	+	0.0344479i
$976$	−3.36136			−0.107594
$977$	20.5174	−	14.9068i	0.656411	−	0.476911i	−0.209038	−	0.977908i	$-0.567033\pi$
$977$	20.5174	−	14.9068i	0.656411	−	0.476911i	0.865449	+	0.500997i	$0.167033\pi$
$978$	8.80278	−	27.0922i	0.281482	−	0.866312i
$979$	7.52994	−	23.1748i	0.240658	−	0.740669i
$980$	−0.108699	+	0.287776i	−0.00347227	+	0.00919266i
$981$	2.74883	+	8.46003i	0.0877634	+	0.270108i
$982$	−6.73161			−0.214814
$983$	−5.16583	−	15.8988i	−0.164764	−	0.507093i	0.834254	−	0.551380i	$-0.185898\pi$
$983$	−5.16583	−	15.8988i	−0.164764	−	0.507093i	−0.999019	+	0.0442869i	$0.985898\pi$
$984$	−20.4919	−	14.8883i	−0.653259	−	0.474621i
$985$	−1.36852	+	3.62310i	−0.0436048	+	0.115442i
$986$	−4.43640	+	3.22324i	−0.141284	+	0.102649i
$987$	−20.6343	−	14.9917i	−0.656798	−	0.477192i
$988$	−4.91189	−	3.56870i	−0.156268	−	0.113535i
$989$	18.8843	−	13.7203i	0.600486	−	0.436279i
$990$	19.8571	−	13.0473i	0.631100	−	0.414671i
$991$	−20.0244	−	14.5486i	−0.636096	−	0.462151i	0.222410	−	0.974953i	$-0.428607\pi$
$991$	−20.0244	−	14.5486i	−0.636096	−	0.462151i	−0.858507	+	0.512802i	$0.828607\pi$
$992$	3.54720	+	10.9172i	0.112624	+	0.346620i
$993$	−37.3423			−1.18502
$994$	−20.4566	−	62.9589i	−0.648843	−	1.99693i
$995$	26.0647	+	1.22583i	0.826308	+	0.0388613i
$996$	1.35968	−	4.18466i	0.0430830	−	0.132596i
$997$	0.232117	−	0.714383i	0.00735122	−	0.0226247i	−0.947314	−	0.320308i	$-0.896214\pi$
$997$	0.232117	−	0.714383i	0.00735122	−	0.0226247i	0.954665	+	0.297683i	$0.0962138\pi$
$998$	−62.1746	+	45.1725i	−1.96810	+	1.42991i
$999$	40.3709			1.27728

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.k.b.86.19	✓	76
25.16	even	5	inner	425.2.k.b.341.19	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.k.b.86.19	✓	76	1.1	even	1	trivial
425.2.k.b.341.19	yes	76	25.16	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.80693 - 1.31281i) q^{2} +(-0.436131 + 1.34227i) q^{3} +(0.923486 - 2.84220i) q^{4} +(2.23360 + 0.105046i) q^{5} +(0.974092 + 2.99795i) q^{6} -2.63704 q^{7} +(-0.682224 - 2.09967i) q^{8} +(0.815568 + 0.592544i) q^{9} +(4.17386 - 2.74248i) q^{10} +(3.81797 - 2.77392i) q^{11} +(3.41224 + 2.47914i) q^{12} +(0.242146 + 0.175929i) q^{13} +(-4.76494 + 3.46193i) q^{14} +(-1.11514 + 2.95228i) q^{15} +(0.846240 + 0.614829i) q^{16} +(0.309017 + 0.951057i) q^{17} +2.25157 q^{18} +(-2.09752 - 6.45550i) q^{19} +(2.36126 - 6.25132i) q^{20} +(1.15009 - 3.53962i) q^{21} +(3.25718 - 10.0246i) q^{22} +(-6.43135 + 4.67265i) q^{23} +3.11586 q^{24} +(4.97793 + 0.469263i) q^{25} +0.668502 q^{26} +(-4.57646 + 3.32500i) q^{27} +(-2.43527 + 7.49498i) q^{28} +(-0.758704 + 2.33505i) q^{29} +(1.86081 + 6.79854i) q^{30} +(0.525379 + 1.61695i) q^{31} +6.75169 q^{32} +(2.05822 + 6.33455i) q^{33} +(1.80693 + 1.31281i) q^{34} +(-5.89008 - 0.277011i) q^{35} +(2.43729 - 1.77080i) q^{36} +(-5.77370 - 4.19484i) q^{37} +(-12.2649 - 8.91099i) q^{38} +(-0.341752 + 0.248297i) q^{39} +(-1.30325 - 4.76148i) q^{40} +(-6.57665 - 4.77822i) q^{41} +(-2.56872 - 7.90570i) q^{42} -2.93629 q^{43} +(-4.35819 - 13.4131i) q^{44} +(1.75941 + 1.40918i) q^{45} +(-5.48669 + 16.8863i) q^{46} +(2.11770 - 6.51762i) q^{47} +(-1.19434 + 0.867738i) q^{48} -0.0460344 q^{49} +(9.61082 - 5.68716i) q^{50} -1.41135 q^{51} +(0.723644 - 0.525758i) q^{52} +(-3.29447 + 10.1393i) q^{53} +(-3.90425 + 12.0161i) q^{54} +(8.81921 - 5.79476i) q^{55} +(1.79905 + 5.53690i) q^{56} +9.57983 q^{57} +(1.69456 + 5.21530i) q^{58} +(-3.67760 - 2.67194i) q^{59} +(7.36116 + 5.89585i) q^{60} +(-2.59978 + 1.88885i) q^{61} +(3.07207 + 2.23199i) q^{62} +(-2.15068 - 1.56256i) q^{63} +(10.5074 - 7.63404i) q^{64} +(0.522376 + 0.418392i) q^{65} +(12.0351 + 8.74403i) q^{66} +(-0.260847 - 0.802805i) q^{67} +2.98846 q^{68} +(-3.46705 - 10.6705i) q^{69} +(-11.0066 + 7.23203i) q^{70} +(-3.47323 + 10.6895i) q^{71} +(0.687747 - 2.11667i) q^{72} +(12.6154 - 9.16560i) q^{73} -15.9397 q^{74} +(-2.80091 + 6.47708i) q^{75} -20.2849 q^{76} +(-10.0681 + 7.31493i) q^{77} +(-0.291554 + 0.897312i) q^{78} +(-2.83142 + 8.71422i) q^{79} +(1.82558 + 1.46218i) q^{80} +(-1.53255 - 4.71672i) q^{81} -18.1564 q^{82} +(-0.322369 - 0.992151i) q^{83} +(-8.99821 - 6.53758i) q^{84} +(0.590315 + 2.15674i) q^{85} +(-5.30567 + 3.85480i) q^{86} +(-2.80338 - 2.03677i) q^{87} +(-8.42902 - 6.12404i) q^{88} +(4.17726 - 3.03496i) q^{89} +(5.02911 + 0.236519i) q^{90} +(-0.638548 - 0.463932i) q^{91} +(7.34133 + 22.5943i) q^{92} -2.39952 q^{93} +(-4.72986 - 14.5570i) q^{94} +(-4.00689 - 14.6393i) q^{95} +(-2.94462 + 9.06261i) q^{96} +(-2.75616 + 8.48259i) q^{97} +(-0.0831808 + 0.0604344i) q^{98} +4.75749 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 6 q^{2} - 7 q^{3} - 26 q^{4} + 13 q^{5} + 12 q^{6} + 22 q^{7} + 10 q^{8} - 24 q^{9} - 6 q^{10} - 16 q^{11} - 15 q^{12} - q^{13} - 19 q^{14} - 3 q^{15} + 30 q^{16} - 19 q^{17} + 6 q^{18} + 18 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) \) 76 * q - 6 * q^2 - 7 * q^3 - 26 * q^4 + 13 * q^5 + 12 * q^6 + 22 * q^7 + 10 * q^8 - 24 * q^9 - 6 * q^10 - 16 * q^11 - 15 * q^12 - q^13 - 19 * q^14 - 3 * q^15 + 30 * q^16 - 19 * q^17 + 6 * q^18 + 18 * q^19 - 23 * q^20 - 22 * q^21 - 15 * q^22 - 8 * q^23 - 22 * q^24 + 35 * q^25 - 14 * q^26 - 10 * q^27 - 29 * q^28 - 25 * q^29 + 57 * q^30 + 22 * q^31 + 54 * q^32 - 22 * q^33 - 6 * q^34 - 19 * q^35 - 91 * q^36 - 49 * q^37 + 15 * q^38 + 25 * q^39 - 2 * q^40 + 16 * q^41 - 28 * q^42 + 104 * q^43 + 18 * q^44 + 10 * q^45 - 55 * q^46 - 26 * q^47 - 86 * q^48 + 2 * q^49 - 17 * q^50 + 18 * q^51 + 53 * q^52 - 41 * q^53 - 6 * q^54 + 67 * q^55 + 115 * q^56 + 84 * q^57 - 12 * q^58 - 7 * q^59 - 32 * q^60 - 21 * q^61 - 23 * q^62 - 21 * q^63 + 6 * q^64 - 72 * q^65 + 102 * q^66 - 15 * q^67 + 74 * q^68 + 48 * q^69 - 60 * q^70 - 8 * q^71 + 9 * q^72 - 25 * q^73 - 60 * q^74 + 68 * q^75 - 76 * q^76 - 36 * q^77 - 51 * q^78 + 2 * q^79 + 217 * q^80 + 20 * q^81 - 12 * q^82 - 41 * q^83 - 48 * q^84 - 7 * q^85 - 87 * q^86 - 54 * q^87 - 4 * q^88 + 77 * q^89 - 93 * q^90 + 79 * q^91 - 19 * q^92 + 72 * q^93 + 15 * q^94 + 57 * q^95 + 28 * q^96 + 13 * q^97 - 62 * q^98 - 64 * q^99

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