LMFDB - Embedded newform 418.2.f.g.191.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(115,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("418.115");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.f (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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 7 x^{14} - 13 x^{13} + 51 x^{12} - 74 x^{11} + 332 x^{10} - 614 x^{9} + 1832 x^{8} + \cdots + 16 $ x^16 - x^15 + 7x^14 - 13x^13 + 51x^12 - 74x^11 + 332x^10 - 614x^9 + 1832x^8 - 2960x^7 + 5348x^6 - 6872x^5 + 8232x^4 - 6344x^3 + 3984x^2 - 400x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			191.3
Root			$0.388450 - 1.19553i$ of defining polynomial
Character	$\chi$	$=$	418.191
Dual form			418.2.f.g.267.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(0.388450 - 1.19553i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.36174 + 0.989363i) q^{5} +(1.01697 - 0.738875i) q^{6} +(1.33687 + 4.11446i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(1.14866 + 0.834553i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(0.388450 - 1.19553i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.36174 + 0.989363i) q^{5} +(1.01697 - 0.738875i) q^{6} +(1.33687 + 4.11446i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(1.14866 + 0.834553i) q^{9} -1.68320 q^{10} +(-1.19982 + 3.09200i) q^{11} +1.25705 q^{12} +(-4.20413 - 3.05448i) q^{13} +(-1.33687 + 4.11446i) q^{14} +(0.653840 + 2.01231i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(5.19888 - 3.77721i) q^{17} +(0.438750 + 1.35034i) q^{18} +(0.309017 - 0.951057i) q^{19} +(-1.36174 - 0.989363i) q^{20} +5.43825 q^{21} +(-2.78810 + 1.79624i) q^{22} +1.25094 q^{23} +(1.01697 + 0.738875i) q^{24} +(-0.669585 + 2.06077i) q^{25} +(-1.60583 - 4.94225i) q^{26} +(4.49485 - 3.26570i) q^{27} +(-3.49997 + 2.54288i) q^{28} +(2.19776 + 6.76400i) q^{29} +(-0.653840 + 2.01231i) q^{30} +(2.80245 + 2.03610i) q^{31} -1.00000 q^{32} +(3.23049 + 2.63550i) q^{33} +6.42617 q^{34} +(-5.89117 - 4.28018i) q^{35} +(-0.438750 + 1.35034i) q^{36} +(-1.48261 - 4.56300i) q^{37} +(0.809017 - 0.587785i) q^{38} +(-5.28479 + 3.83963i) q^{39} +(-0.520139 - 1.60082i) q^{40} +(2.10599 - 6.48156i) q^{41} +(4.39964 + 3.19652i) q^{42} +2.38562 q^{43} +(-3.31143 - 0.185614i) q^{44} -2.38986 q^{45} +(1.01203 + 0.735283i) q^{46} +(3.72722 - 11.4712i) q^{47} +(0.388450 + 1.19553i) q^{48} +(-9.47846 + 6.88650i) q^{49} +(-1.75300 + 1.27363i) q^{50} +(-2.49624 - 7.68264i) q^{51} +(1.60583 - 4.94225i) q^{52} +(-6.09761 - 4.43018i) q^{53} +5.55594 q^{54} +(-1.42527 - 5.39755i) q^{55} -4.32620 q^{56} +(-1.01697 - 0.738875i) q^{57} +(-2.19776 + 6.76400i) q^{58} +(-4.21806 - 12.9819i) q^{59} +(-1.71178 + 1.24368i) q^{60} +(-8.31589 + 6.04185i) q^{61} +(1.07044 + 3.29447i) q^{62} +(-1.89812 + 5.84182i) q^{63} +(-0.809017 - 0.587785i) q^{64} +8.74692 q^{65} +(1.06442 + 4.03100i) q^{66} +4.78199 q^{67} +(5.19888 + 3.77721i) q^{68} +(0.485926 - 1.49553i) q^{69} +(-2.25023 - 6.92548i) q^{70} +(3.04650 - 2.21341i) q^{71} +(-1.14866 + 0.834553i) q^{72} +(1.51312 + 4.65690i) q^{73} +(1.48261 - 4.56300i) q^{74} +(2.20360 + 1.60101i) q^{75} +1.00000 q^{76} +(-14.3259 - 0.803004i) q^{77} -6.53237 q^{78} +(-1.21052 - 0.879492i) q^{79} +(0.520139 - 1.60082i) q^{80} +(-0.841952 - 2.59126i) q^{81} +(5.51354 - 4.00582i) q^{82} +(-5.68939 + 4.13358i) q^{83} +(1.68051 + 5.17208i) q^{84} +(-3.34250 + 10.2872i) q^{85} +(1.93001 + 1.40223i) q^{86} +8.94025 q^{87} +(-2.56990 - 2.09657i) q^{88} -0.194366 q^{89} +(-1.93344 - 1.40472i) q^{90} +(6.94716 - 21.3812i) q^{91} +(0.386561 + 1.18971i) q^{92} +(3.52282 - 2.55948i) q^{93} +(9.75799 - 7.08960i) q^{94} +(0.520139 + 1.60082i) q^{95} +(-0.388450 + 1.19553i) q^{96} +(-2.80336 - 2.03676i) q^{97} -11.7160 q^{98} +(-3.95862 + 2.55035i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} + q^{3} - 4 q^{4} + q^{5} - q^{6} - 12 q^{7} + 4 q^{8} - q^{9}+O(q^{10}) $ 16 * q + 4 * q^2 + q^3 - 4 * q^4 + q^5 - q^6 - 12 * q^7 + 4 * q^8 - q^9	\( 16 q + 4 q^{2} + q^{3} - 4 q^{4} + q^{5} - q^{6} - 12 q^{7} + 4 q^{8} - q^{9} + 4 q^{10} + 4 q^{11} - 4 q^{12} - 12 q^{13} + 12 q^{14} - 10 q^{15} - 4 q^{16} + 6 q^{17} + q^{18} - 4 q^{19} + q^{20} + 14 q^{21} - 9 q^{22} - 26 q^{23} - q^{24} + 33 q^{25} - 3 q^{26} + 13 q^{27} - 2 q^{28} + 10 q^{30} + 11 q^{31} - 16 q^{32} - 31 q^{33} - 6 q^{34} - 4 q^{35} - q^{36} + 4 q^{38} + 12 q^{39} - q^{40} - 7 q^{41} + 6 q^{42} + 66 q^{43} - 11 q^{44} - 42 q^{45} - 24 q^{46} + 47 q^{47} + q^{48} + 24 q^{49} + 37 q^{50} - 41 q^{51} + 3 q^{52} + 15 q^{53} - 8 q^{54} - 9 q^{55} - 28 q^{56} + q^{57} - 18 q^{59} + 5 q^{60} - 43 q^{61} + 9 q^{62} - 37 q^{63} - 4 q^{64} + 52 q^{65} - 39 q^{66} - 50 q^{67} + 6 q^{68} + 81 q^{69} - 11 q^{70} - 5 q^{71} + q^{72} - 13 q^{73} + 39 q^{75} + 16 q^{76} - 10 q^{77} - 22 q^{78} + 5 q^{79} + q^{80} + 2 q^{82} + 7 q^{83} - q^{84} - 29 q^{85} + 29 q^{86} + 4 q^{87} - 4 q^{88} - 28 q^{89} - 18 q^{90} - 11 q^{92} - 5 q^{93} + 28 q^{94} + q^{95} - q^{96} - 11 q^{97} - 24 q^{98} + 43 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + q^3 - 4 * q^4 + q^5 - q^6 - 12 * q^7 + 4 * q^8 - q^9 + 4 * q^10 + 4 * q^11 - 4 * q^12 - 12 * q^13 + 12 * q^14 - 10 * q^15 - 4 * q^16 + 6 * q^17 + q^18 - 4 * q^19 + q^20 + 14 * q^21 - 9 * q^22 - 26 * q^23 - q^24 + 33 * q^25 - 3 * q^26 + 13 * q^27 - 2 * q^28 + 10 * q^30 + 11 * q^31 - 16 * q^32 - 31 * q^33 - 6 * q^34 - 4 * q^35 - q^36 + 4 * q^38 + 12 * q^39 - q^40 - 7 * q^41 + 6 * q^42 + 66 * q^43 - 11 * q^44 - 42 * q^45 - 24 * q^46 + 47 * q^47 + q^48 + 24 * q^49 + 37 * q^50 - 41 * q^51 + 3 * q^52 + 15 * q^53 - 8 * q^54 - 9 * q^55 - 28 * q^56 + q^57 - 18 * q^59 + 5 * q^60 - 43 * q^61 + 9 * q^62 - 37 * q^63 - 4 * q^64 + 52 * q^65 - 39 * q^66 - 50 * q^67 + 6 * q^68 + 81 * q^69 - 11 * q^70 - 5 * q^71 + q^72 - 13 * q^73 + 39 * q^75 + 16 * q^76 - 10 * q^77 - 22 * q^78 + 5 * q^79 + q^80 + 2 * q^82 + 7 * q^83 - q^84 - 29 * q^85 + 29 * q^86 + 4 * q^87 - 4 * q^88 - 28 * q^89 - 18 * q^90 - 11 * q^92 - 5 * q^93 + 28 * q^94 + q^95 - q^96 - 11 * q^97 - 24 * q^98 + 43 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	0.388450	−	1.19553i	0.224272	−	0.690237i	−0.774093	−	0.633072i	$-0.781794\pi$
$3$	0.388450	−	1.19553i	0.224272	−	0.690237i	0.998365	−	0.0571651i	$-0.0182062\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−1.36174	+	0.989363i	−0.608989	+	0.442457i	−0.849058	−	0.528299i	$-0.822830\pi$
$5$	−1.36174	+	0.989363i	−0.608989	+	0.442457i	0.240069	+	0.970756i	$0.422830\pi$
$6$	1.01697	−	0.738875i	0.415178	−	0.301645i
$7$	1.33687	+	4.11446i	0.505289	+	1.55512i	0.800284	+	0.599622i	$0.204682\pi$
$7$	1.33687	+	4.11446i	0.505289	+	1.55512i	−0.294994	+	0.955499i	$0.595318\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	1.14866	+	0.834553i	0.382888	+	0.278184i
$10$	−1.68320			−0.532276
$11$	−1.19982	+	3.09200i	−0.361758	+	0.932272i
$11$	−1.19982	+	3.09200i	−0.361758	+	0.932272i
$12$	1.25705			0.362879
$13$	−4.20413	−	3.05448i	−1.16601	−	0.847159i	−0.175488	−	0.984482i	$-0.556150\pi$
$13$	−4.20413	−	3.05448i	−1.16601	−	0.847159i	−0.990526	+	0.137322i	$0.956150\pi$
$14$	−1.33687	+	4.11446i	−0.357294	+	1.09964i
$15$	0.653840	+	2.01231i	0.168821	+	0.519577i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	5.19888	−	3.77721i	1.26091	−	0.916107i	0.262111	−	0.965038i	$-0.415581\pi$
$17$	5.19888	−	3.77721i	1.26091	−	0.916107i	0.998802	+	0.0489307i	$0.0155814\pi$
$18$	0.438750	+	1.35034i	0.103414	+	0.318277i
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i
$20$	−1.36174	−	0.989363i	−0.304495	−	0.221228i
$21$	5.43825			1.18672
$22$	−2.78810	+	1.79624i	−0.594425	+	0.382960i
$23$	1.25094			0.260838			0.130419	−	0.991459i	$-0.458368\pi$
$23$	1.25094			0.260838			0.130419	+	0.991459i	$0.458368\pi$
$24$	1.01697	+	0.738875i	0.207589	+	0.150822i
$25$	−0.669585	+	2.06077i	−0.133917	+	0.412154i
$26$	−1.60583	−	4.94225i	−0.314930	−	0.969254i
$27$	4.49485	−	3.26570i	0.865034	−	0.628484i
$28$	−3.49997	+	2.54288i	−0.661432	+	0.480559i
$29$	2.19776	+	6.76400i	0.408113	+	1.25604i	0.918268	+	0.395960i	$0.129588\pi$
$29$	2.19776	+	6.76400i	0.408113	+	1.25604i	−0.510155	+	0.860083i	$0.670412\pi$
$30$	−0.653840	+	2.01231i	−0.119374	+	0.367397i
$31$	2.80245	+	2.03610i	0.503334	+	0.365694i	0.810289	−	0.586030i	$-0.199310\pi$
$31$	2.80245	+	2.03610i	0.503334	+	0.365694i	−0.306955	+	0.951724i	$0.599310\pi$
$32$	−1.00000			−0.176777
$33$	3.23049	+	2.63550i	0.562356	+	0.458781i
$34$	6.42617			1.10208
$35$	−5.89117	−	4.28018i	−0.995789	−	0.723483i
$36$	−0.438750	+	1.35034i	−0.0731251	+	0.225056i
$37$	−1.48261	−	4.56300i	−0.243739	−	0.750153i	−0.995841	−	0.0911057i	$-0.970960\pi$
$37$	−1.48261	−	4.56300i	−0.243739	−	0.750153i	0.752102	−	0.659047i	$-0.229040\pi$
$38$	0.809017	−	0.587785i	0.131240	−	0.0953514i
$39$	−5.28479	+	3.83963i	−0.846244	+	0.614833i
$40$	−0.520139	−	1.60082i	−0.0822412	−	0.253112i
$41$	2.10599	−	6.48156i	0.328900	−	1.01225i	−0.640750	−	0.767750i	$-0.721376\pi$
$41$	2.10599	−	6.48156i	0.328900	−	1.01225i	0.969649	−	0.244499i	$-0.0786236\pi$
$42$	4.39964	+	3.19652i	0.678879	+	0.493234i
$43$	2.38562			0.363803			0.181902	−	0.983317i	$-0.441775\pi$
$43$	2.38562			0.363803			0.181902	+	0.983317i	$0.441775\pi$
$44$	−3.31143	−	0.185614i	−0.499216	−	0.0279824i
$45$	−2.38986			−0.356259
$46$	1.01203	+	0.735283i	0.149216	+	0.108412i
$47$	3.72722	−	11.4712i	0.543671	−	1.67325i	−0.180457	−	0.983583i	$-0.557758\pi$
$47$	3.72722	−	11.4712i	0.543671	−	1.67325i	0.724129	−	0.689665i	$-0.242242\pi$
$48$	0.388450	+	1.19553i	0.0560679	+	0.172559i
$49$	−9.47846	+	6.88650i	−1.35407	+	0.983786i
$50$	−1.75300	+	1.27363i	−0.247911	+	0.180118i
$51$	−2.49624	−	7.68264i	−0.349544	−	1.07579i
$52$	1.60583	−	4.94225i	0.222689	−	0.685366i
$53$	−6.09761	−	4.43018i	−0.837572	−	0.608531i	0.0841196	−	0.996456i	$-0.473192\pi$
$53$	−6.09761	−	4.43018i	−0.837572	−	0.608531i	−0.921691	+	0.387924i	$0.873192\pi$
$54$	5.55594			0.756068
$55$	−1.42527	−	5.39755i	−0.192183	−	0.727806i
$56$	−4.32620			−0.578113
$57$	−1.01697	−	0.738875i	−0.134702	−	0.0978664i
$58$	−2.19776	+	6.76400i	−0.288579	+	0.888156i
$59$	−4.21806	−	12.9819i	−0.549145	−	1.69009i	−0.710926	−	0.703267i	$-0.751724\pi$
$59$	−4.21806	−	12.9819i	−0.549145	−	1.69009i	0.161782	−	0.986827i	$-0.448276\pi$
$60$	−1.71178	+	1.24368i	−0.220989	+	0.160558i
$61$	−8.31589	+	6.04185i	−1.06474	+	0.773579i	−0.974960	−	0.222382i	$-0.928617\pi$
$61$	−8.31589	+	6.04185i	−1.06474	+	0.773579i	−0.0897808	+	0.995962i	$0.528617\pi$
$62$	1.07044	+	3.29447i	0.135946	+	0.418399i
$63$	−1.89812	+	5.84182i	−0.239141	+	0.736000i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	8.74692			1.08492
$66$	1.06442	+	4.03100i	0.131021	+	0.496181i
$67$	4.78199			0.584213			0.292106	−	0.956386i	$-0.405644\pi$
$67$	4.78199			0.584213			0.292106	+	0.956386i	$0.405644\pi$
$68$	5.19888	+	3.77721i	0.630457	+	0.458054i
$69$	0.485926	−	1.49553i	0.0584986	−	0.180040i
$70$	−2.25023	−	6.92548i	−0.268953	−	0.827754i
$71$	3.04650	−	2.21341i	0.361553	−	0.262684i	−0.392146	−	0.919903i	$-0.628267\pi$
$71$	3.04650	−	2.21341i	0.361553	−	0.262684i	0.753700	+	0.657219i	$0.228267\pi$
$72$	−1.14866	+	0.834553i	−0.135371	+	0.0983530i
$73$	1.51312	+	4.65690i	0.177097	+	0.545049i	0.999723	−	0.0235342i	$-0.00749186\pi$
$73$	1.51312	+	4.65690i	0.177097	+	0.545049i	−0.822626	+	0.568583i	$0.807492\pi$
$74$	1.48261	−	4.56300i	0.172350	−	0.530438i
$75$	2.20360	+	1.60101i	0.254450	+	0.184869i
$76$	1.00000			0.114708
$77$	−14.3259	−	0.803004i	−1.63259	−	0.0915108i
$78$	−6.53237			−0.739645
$79$	−1.21052	−	0.879492i	−0.136194	−	0.0989506i	0.517602	−	0.855621i	$-0.326825\pi$
$79$	−1.21052	−	0.879492i	−0.136194	−	0.0989506i	−0.653796	+	0.756671i	$0.726825\pi$
$80$	0.520139	−	1.60082i	0.0581533	−	0.178977i
$81$	−0.841952	−	2.59126i	−0.0935502	−	0.287918i
$82$	5.51354	−	4.00582i	0.608869	−	0.442369i
$83$	−5.68939	+	4.13358i	−0.624491	+	0.453719i	−0.854487	−	0.519472i	$-0.826129\pi$
$83$	−5.68939	+	4.13358i	−0.624491	+	0.453719i	0.229996	+	0.973192i	$0.426129\pi$
$84$	1.68051	+	5.17208i	0.183359	+	0.564321i
$85$	−3.34250	+	10.2872i	−0.362545	+	1.11580i
$86$	1.93001	+	1.40223i	0.208118	+	0.151206i
$87$	8.94025			0.958495
$88$	−2.56990	−	2.09657i	−0.273952	−	0.223495i
$89$	−0.194366			−0.0206027			−0.0103014	−	0.999947i	$-0.503279\pi$
$89$	−0.194366			−0.0206027			−0.0103014	+	0.999947i	$0.503279\pi$
$90$	−1.93344	−	1.40472i	−0.203802	−	0.148071i
$91$	6.94716	−	21.3812i	0.728260	−	2.24135i
$92$	0.386561	+	1.18971i	0.0403018	+	0.124036i
$93$	3.52282	−	2.55948i	0.365299	−	0.265405i
$94$	9.75799	−	7.08960i	1.00646	−	0.731236i
$95$	0.520139	+	1.60082i	0.0533651	+	0.164241i
$96$	−0.388450	+	1.19553i	−0.0396460	+	0.122018i
$97$	−2.80336	−	2.03676i	−0.284638	−	0.206801i	0.436300	−	0.899801i	$-0.356289\pi$
$97$	−2.80336	−	2.03676i	−0.284638	−	0.206801i	−0.720938	+	0.693000i	$0.756289\pi$
$98$	−11.7160			−1.18350
$99$	−3.95862	+	2.55035i	−0.397856	+	0.256320i
$100$	−2.16682			−0.216682
$101$	7.85646	+	5.70805i	0.781747	+	0.567972i	0.905503	−	0.424341i	$-0.139494\pi$
$101$	7.85646	+	5.70805i	0.781747	+	0.567972i	−0.123756	+	0.992313i	$0.539494\pi$
$102$	2.49624	−	7.68264i	0.247165	−	0.760695i
$103$	5.16068	+	15.8829i	0.508497	+	1.56499i	0.794812	+	0.606856i	$0.207570\pi$
$103$	5.16068	+	15.8829i	0.508497	+	1.56499i	−0.286315	+	0.958136i	$0.592430\pi$
$104$	4.20413	−	3.05448i	0.412248	−	0.299516i
$105$	−7.40549	+	5.38040i	−0.722702	+	0.525074i
$106$	−2.32908	−	7.16818i	−0.226220	−	0.696235i
$107$	1.53757	−	4.73214i	0.148642	−	0.457473i	−0.848819	−	0.528683i	$-0.822686\pi$
$107$	1.53757	−	4.73214i	0.148642	−	0.457473i	0.997461	+	0.0712098i	$0.0226860\pi$
$108$	4.49485	+	3.26570i	0.432517	+	0.314242i
$109$	−2.73242			−0.261718			−0.130859	−	0.991401i	$-0.541774\pi$
$109$	−2.73242			−0.261718			−0.130859	+	0.991401i	$0.541774\pi$
$110$	2.01954	−	5.20446i	0.192555	−	0.496226i
$111$	−6.03110			−0.572447
$112$	−3.49997	−	2.54288i	−0.330716	−	0.240279i
$113$	−0.638357	+	1.96466i	−0.0600516	+	0.184820i	−0.976582	−	0.215145i	$-0.930978\pi$
$113$	−0.638357	+	1.96466i	−0.0600516	+	0.184820i	0.916531	+	0.399965i	$0.130978\pi$
$114$	−0.388450	−	1.19553i	−0.0363816	−	0.111971i
$115$	−1.70345	+	1.23763i	−0.158848	+	0.115410i
$116$	−5.75380	+	4.18038i	−0.534227	+	0.388139i
$117$	−2.28000	−	7.01713i	−0.210786	−	0.648734i
$118$	4.21806	−	12.9819i	0.388304	−	1.19508i
$119$	22.4914	+	16.3410i	2.06178	+	1.49797i
$120$	−2.11587			−0.193152
$121$	−8.12088	−	7.41966i	−0.738262	−	0.674514i
$122$	−10.2790			−0.930617
$123$	−6.93079	−	5.03552i	−0.624929	−	0.454037i
$124$	−1.07044	+	3.29447i	−0.0961283	+	0.295853i
$125$	−3.72774	−	11.4728i	−0.333419	−	1.02616i
$126$	−4.96935	+	3.61044i	−0.442705	+	0.321644i
$127$	−4.97979	+	3.61803i	−0.441885	+	0.321048i	−0.786383	−	0.617739i	$-0.788049\pi$
$127$	−4.97979	+	3.61803i	−0.441885	+	0.321048i	0.344499	+	0.938787i	$0.388049\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	0.926692	−	2.85207i	0.0815907	−	0.251110i
$130$	7.07641	+	5.14131i	0.620642	+	0.450923i
$131$	20.0218			1.74932			0.874658	−	0.484740i	$-0.161086\pi$
$131$	20.0218			1.74932			0.874658	+	0.484740i	$0.161086\pi$
$132$	−1.50823	+	3.88679i	−0.131274	+	0.338302i
$133$	4.32620			0.375129
$134$	3.86871	+	2.81078i	0.334206	+	0.242815i
$135$	−2.88986	+	8.89408i	−0.248720	+	0.765480i
$136$	1.98579	+	6.11165i	0.170280	+	0.524069i
$137$	14.4278	−	10.4824i	1.23265	−	0.895576i	0.235568	−	0.971858i	$-0.424305\pi$
$137$	14.4278	−	10.4824i	1.23265	−	0.895576i	0.997086	+	0.0762821i	$0.0243050\pi$
$138$	1.27217	−	0.924287i	0.108294	−	0.0786805i
$139$	1.15285	+	3.54812i	0.0977837	+	0.300947i	0.987969	−	0.154651i	$-0.0494253\pi$
$139$	1.15285	+	3.54812i	0.0977837	+	0.300947i	−0.890185	+	0.455598i	$0.849425\pi$
$140$	2.25023	−	6.92548i	0.190179	−	0.585310i
$141$	−12.2663	−	8.91198i	−1.03301	−	0.750524i
$142$	3.76569			0.316009
$143$	14.4886	−	9.33433i	1.21160	−	0.780576i
$144$	−1.41983			−0.118319
$145$	−9.68482	−	7.03644i	−0.804281	−	0.584344i
$146$	−1.51312	+	4.65690i	−0.125227	+	0.385408i
$147$	4.55108	+	14.0068i	0.375367	+	1.15526i
$148$	3.88152	−	2.82009i	0.319059	−	0.231810i
$149$	0.0697244	−	0.0506577i	0.00571204	−	0.00415004i	−0.584926	−	0.811087i	$-0.698876\pi$
$149$	0.0697244	−	0.0506577i	0.00571204	−	0.00415004i	0.590638	+	0.806937i	$0.298876\pi$
$150$	0.841701	+	2.59049i	0.0687246	+	0.211513i
$151$	6.71127	−	20.6552i	0.546155	−	1.68089i	−0.172072	−	0.985084i	$-0.555046\pi$
$151$	6.71127	−	20.6552i	0.546155	−	1.68089i	0.718227	−	0.695809i	$-0.244954\pi$
$152$	0.809017	+	0.587785i	0.0656199	+	0.0476757i
$153$	9.12404			0.737635
$154$	−11.1179	−	9.07020i	−0.895906	−	0.730897i
$155$	−5.83065			−0.468329
$156$	−5.28479	−	3.83963i	−0.423122	−	0.307416i
$157$	−0.945196	+	2.90901i	−0.0754348	+	0.232165i	−0.981663	−	0.190624i	$-0.938949\pi$
$157$	−0.945196	+	2.90901i	−0.0754348	+	0.232165i	0.906228	+	0.422789i	$0.138949\pi$
$158$	−0.462376	−	1.42305i	−0.0367847	−	0.113212i
$159$	−7.66500	+	5.56895i	−0.607874	+	0.441647i
$160$	1.36174	−	0.989363i	0.107655	−	0.0782160i
$161$	1.67234	+	5.14694i	0.131799	+	0.405635i
$162$	0.841952	−	2.59126i	0.0661500	−	0.203589i
$163$	−0.444837	−	0.323193i	−0.0348423	−	0.0253144i	0.570228	−	0.821487i	$-0.306855\pi$
$163$	−0.444837	−	0.323193i	−0.0348423	−	0.0253144i	−0.605070	+	0.796172i	$0.706855\pi$
$164$	6.81511			0.532171
$165$	−7.00656	−	0.392736i	−0.545460	−	0.0305744i
$166$	−7.03247			−0.545825
$167$	16.0110	+	11.6327i	1.23897	+	0.900163i	0.997529	−	0.0702535i	$-0.0223808\pi$
$167$	16.0110	+	11.6327i	1.23897	+	0.900163i	0.241438	+	0.970416i	$0.422381\pi$
$168$	−1.68051	+	5.17208i	−0.129654	+	0.399035i
$169$	4.32763	+	13.3191i	0.332894	+	1.02454i
$170$	−8.75078	+	6.35781i	−0.671154	+	0.487622i
$171$	1.14866	−	0.834553i	0.0878405	−	0.0638199i
$172$	0.737196	+	2.26886i	0.0562107	+	0.172999i
$173$	−6.08481	+	18.7271i	−0.462619	+	1.42380i	0.399333	+	0.916806i	$0.369242\pi$
$173$	−6.08481	+	18.7271i	−0.462619	+	1.42380i	−0.861952	+	0.506990i	$0.830758\pi$
$174$	7.23281	+	5.25494i	0.548318	+	0.398376i
$175$	−9.37411			−0.708616
$176$	−0.846758	−	3.20671i	−0.0638268	−	0.241715i
$177$	−17.1586			−1.28972
$178$	−0.157245	−	0.114245i	−0.0117860	−	0.00856305i
$179$	3.15060	−	9.69654i	0.235487	−	0.724754i	−0.761570	−	0.648083i	$-0.775571\pi$
$179$	3.15060	−	9.69654i	0.235487	−	0.724754i	0.997056	−	0.0766707i	$-0.0244290\pi$
$180$	−0.738507	−	2.27289i	−0.0550451	−	0.169411i
$181$	−13.8978	+	10.0973i	−1.03302	+	0.750530i	−0.968910	−	0.247413i	$-0.920419\pi$
$181$	−13.8978	+	10.0973i	−1.03302	+	0.750530i	−0.0641056	+	0.997943i	$0.520419\pi$
$182$	18.1879	−	13.2143i	1.34818	−	0.979508i
$183$	3.99288	+	12.2888i	0.295162	+	0.908415i
$184$	−0.386561	+	1.18971i	−0.0284977	+	0.0877067i
$185$	6.53339	+	4.74679i	0.480345	+	0.348991i
$186$	4.35444			0.319283
$187$	5.44141	+	20.6069i	0.397915	+	1.50692i
$188$	12.0615			0.879678
$189$	19.4456	+	14.1281i	1.41446	+	1.02767i
$190$	−0.520139	+	1.60082i	−0.0377348	+	0.116136i
$191$	−4.59636	−	14.1461i	−0.332581	−	1.02358i	−0.967901	−	0.251330i	$-0.919132\pi$
$191$	−4.59636	−	14.1461i	−0.332581	−	1.02358i	0.635321	−	0.772248i	$-0.280868\pi$
$192$	−1.01697	+	0.738875i	−0.0733938	+	0.0533237i
$193$	12.8622	−	9.34495i	0.925843	−	0.672664i	−0.0191288	−	0.999817i	$-0.506089\pi$
$193$	12.8622	−	9.34495i	0.925843	−	0.672664i	0.944971	+	0.327153i	$0.106089\pi$
$194$	−1.07079	−	3.29554i	−0.0768780	−	0.236606i
$195$	3.39774	−	10.4572i	0.243317	−	0.748853i
$196$	−9.47846	−	6.88650i	−0.677033	−	0.491893i
$197$	−4.17065			−0.297146			−0.148573	−	0.988901i	$-0.547468\pi$
$197$	−4.17065			−0.297146			−0.148573	+	0.988901i	$0.547468\pi$
$198$	−4.70165	−	0.263540i	−0.334132	−	0.0187290i
$199$	−24.0791			−1.70692			−0.853460	−	0.521158i	$-0.825500\pi$
$199$	−24.0791			−1.70692			−0.853460	+	0.521158i	$0.825500\pi$
$200$	−1.75300	−	1.27363i	−0.123955	−	0.0900589i
$201$	1.85756	−	5.71699i	0.131022	−	0.403245i
$202$	3.00090	+	9.23582i	0.211143	+	0.649830i
$203$	−24.8921	+	18.0852i	−1.74708	+	1.26933i
$204$	6.53525	−	4.74814i	0.457559	−	0.332436i
$205$	3.54480	+	10.9098i	0.247580	+	0.761973i
$206$	−5.16068	+	15.8829i	−0.359561	+	1.10662i
$207$	1.43691	+	1.04397i	0.0998719	+	0.0725612i
$208$	5.19659			0.360318
$209$	2.56990	+	2.09657i	0.177764	+	0.145023i
$210$	−9.15369			−0.631665
$211$	9.36337	+	6.80289i	0.644601	+	0.468330i	0.861428	−	0.507880i	$-0.169571\pi$
$211$	9.36337	+	6.80289i	0.644601	+	0.468330i	−0.216827	+	0.976210i	$0.569571\pi$
$212$	2.32908	−	7.16818i	0.159962	−	0.492312i
$213$	−1.46278	−	4.50197i	−0.100228	−	0.308470i
$214$	4.02540	−	2.92462i	0.275171	−	0.199923i
$215$	−3.24859	+	2.36024i	−0.221552	+	0.160967i
$216$	1.71688	+	5.28401i	0.116819	+	0.359532i
$217$	−4.63094	+	14.2526i	−0.314369	+	0.967527i
$218$	−2.21057	−	1.60608i	−0.149719	−	0.108777i
$219$	6.15521			0.415930
$220$	4.69295	−	3.02344i	0.316398	−	0.203841i
$221$	−33.3941			−2.24633
$222$	−4.87926	−	3.54499i	−0.327475	−	0.237924i
$223$	2.10478	−	6.47785i	0.140947	−	0.433789i	−0.855521	−	0.517768i	$-0.826763\pi$
$223$	2.10478	−	6.47785i	0.140947	−	0.433789i	0.996468	+	0.0839792i	$0.0267629\pi$
$224$	−1.33687	−	4.11446i	−0.0893234	−	0.274909i
$225$	−2.48895	+	1.80833i	−0.165930	+	0.120555i
$226$	−1.67124	+	1.21423i	−0.111169	+	0.0807692i
$227$	−3.11420	−	9.58451i	−0.206697	−	0.636147i	−0.999639	−	0.0268506i	$-0.991452\pi$
$227$	−3.11420	−	9.58451i	−0.206697	−	0.636147i	0.792943	−	0.609296i	$-0.208548\pi$
$228$	0.388450	−	1.19553i	0.0257257	−	0.0791756i
$229$	−15.8393	−	11.5079i	−1.04669	−	0.760465i	−0.0751098	−	0.997175i	$-0.523931\pi$
$229$	−15.8393	−	11.5079i	−1.04669	−	0.760465i	−0.971580	+	0.236710i	$0.923931\pi$
$230$	−2.10558			−0.138838
$231$	−6.52490	+	16.8150i	−0.429307	+	1.10635i
$232$	−7.11209			−0.466931
$233$	−5.24331	−	3.80949i	−0.343501	−	0.249568i	0.402637	−	0.915360i	$-0.368094\pi$
$233$	−5.24331	−	3.80949i	−0.343501	−	0.249568i	−0.746137	+	0.665792i	$0.768094\pi$
$234$	2.28000	−	7.01713i	0.149049	−	0.458724i
$235$	6.27368	+	19.3084i	0.409250	+	1.25954i
$236$	11.0430	−	8.02323i	0.718840	−	0.522268i
$237$	−1.52168	+	1.10557i	−0.0988437	+	0.0718142i
$238$	8.59095	+	26.4402i	0.556868	+	1.71387i
$239$	−6.38160	+	19.6406i	−0.412792	+	1.27044i	0.501420	+	0.865204i	$0.332811\pi$
$239$	−6.38160	+	19.6406i	−0.412792	+	1.27044i	−0.914211	+	0.405238i	$0.867189\pi$
$240$	−1.71178	−	1.24368i	−0.110495	−	0.0802791i
$241$	−13.1165			−0.844907			−0.422454	−	0.906385i	$-0.638831\pi$
$241$	−13.1165			−0.844907			−0.422454	+	0.906385i	$0.638831\pi$
$242$	−2.20876	−	10.7760i	−0.141985	−	0.692705i
$243$	13.2428			0.849529
$244$	−8.31589	−	6.04185i	−0.532370	−	0.386790i
$245$	6.09396	−	18.7553i	0.389329	−	1.19823i
$246$	−2.64733	−	8.14764i	−0.168787	−	0.519474i
$247$	−4.20413	+	3.05448i	−0.267502	+	0.194352i
$248$	−2.80245	+	2.03610i	−0.177956	+	0.129292i
$249$	2.73176	+	8.40749i	0.173118	+	0.532803i
$250$	3.72774	−	11.4728i	0.235763	−	0.725604i
$251$	14.8080	+	10.7587i	0.934675	+	0.679081i	0.947133	−	0.320841i	$-0.103966\pi$
$251$	14.8080	+	10.7587i	0.934675	+	0.679081i	−0.0124582	+	0.999922i	$0.503966\pi$
$252$	−6.14246			−0.386938
$253$	−1.50090	+	3.86789i	−0.0943605	+	0.243172i
$254$	−6.15535			−0.386221
$255$	11.0002	+	7.99208i	0.688857	+	0.500484i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−8.51616	−	26.2101i	−0.531224	−	1.63494i	−0.751670	−	0.659539i	$-0.770751\pi$
$257$	−8.51616	−	26.2101i	−0.531224	−	1.63494i	0.220446	−	0.975399i	$-0.429249\pi$
$258$	2.42611	−	1.76267i	0.151043	−	0.109739i
$259$	16.7922	−	12.2003i	1.04342	−	0.758088i
$260$	2.70295	+	8.31881i	0.167630	+	0.515911i
$261$	−3.12043	+	9.60370i	−0.193150	+	0.594454i
$262$	16.1980	+	11.7685i	1.00072	+	0.727063i
$263$	0.0430411			0.00265403			0.00132701	−	0.999999i	$-0.499578\pi$
$263$	0.0430411			0.00265403			0.00132701	+	0.999999i	$0.499578\pi$
$264$	−3.50478	+	2.25797i	−0.215704	+	0.138968i
$265$	12.6864			0.779321
$266$	3.49997	+	2.54288i	0.214597	+	0.155914i
$267$	−0.0755014	+	0.232369i	−0.00462061	+	0.0142208i
$268$	1.47772	+	4.54794i	0.0902659	+	0.277810i
$269$	−1.89434	+	1.37632i	−0.115500	+	0.0839158i	−0.644036	−	0.764995i	$-0.722741\pi$
$269$	−1.89434	+	1.37632i	−0.115500	+	0.0839158i	0.528536	+	0.848911i	$0.322741\pi$
$270$	−7.56575	+	5.49684i	−0.460437	+	0.334527i
$271$	1.57403	+	4.84437i	0.0956155	+	0.294274i	0.987414	−	0.158159i	$-0.0505560\pi$
$271$	1.57403	+	4.84437i	0.0956155	+	0.294274i	−0.891798	+	0.452434i	$0.850556\pi$
$272$	−1.98579	+	6.11165i	−0.120406	+	0.370573i
$273$	−22.8631	−	16.6110i	−1.38374	−	1.00534i
$274$	17.8338			1.07738
$275$	−5.56851	−	4.54290i	−0.335794	−	0.273947i
$276$	1.57249			0.0946528
$277$	26.2139	+	19.0455i	1.57504	+	1.14433i	0.922117	+	0.386912i	$0.126458\pi$
$277$	26.2139	+	19.0455i	1.57504	+	1.14433i	0.652925	+	0.757423i	$0.273542\pi$
$278$	−1.15285	+	3.54812i	−0.0691435	+	0.212802i
$279$	1.51984	+	4.67758i	0.0909904	+	0.280040i
$280$	5.89117	−	4.28018i	0.352065	−	0.255790i
$281$	−2.41768	+	1.75655i	−0.144227	+	0.104787i	−0.657559	−	0.753403i	$-0.728411\pi$
$281$	−2.41768	+	1.75655i	−0.144227	+	0.104787i	0.513332	+	0.858190i	$0.328411\pi$
$282$	−4.68530	−	14.4199i	−0.279006	−	0.858691i
$283$	5.50682	−	16.9482i	0.327346	−	1.00747i	−0.643024	−	0.765846i	$-0.722320\pi$
$283$	5.50682	−	16.9482i	0.327346	−	1.00747i	0.970370	−	0.241623i	$-0.0776796\pi$
$284$	3.04650	+	2.21341i	0.180777	+	0.131342i
$285$	2.11587			0.125333
$286$	17.2081	+	0.964560i	1.01754	+	0.0570356i
$287$	29.4835			1.74036
$288$	−1.14866	−	0.834553i	−0.0676857	−	0.0491765i
$289$	7.50776	−	23.1065i	0.441633	−	1.35921i
$290$	−3.69927	−	11.3852i	−0.217229	−	0.668562i
$291$	−3.52396	+	2.56031i	−0.206578	+	0.150088i
$292$	−3.96139	+	2.87812i	−0.231823	+	0.168429i
$293$	−4.29882	−	13.2304i	−0.251140	−	0.772929i	−0.994566	−	0.104110i	$-0.966800\pi$
$293$	−4.29882	−	13.2304i	−0.251140	−	0.772929i	0.743426	−	0.668818i	$-0.233200\pi$
$294$	−4.55108	+	14.0068i	−0.265425	+	0.816893i
$295$	18.5877	+	13.5047i	1.08222	+	0.786276i
$296$	4.79782			0.278868
$297$	4.70454	+	17.8163i	0.272985	+	1.03381i
$298$	0.0861841			0.00499251
$299$	−5.25910	−	3.82096i	−0.304142	−	0.220972i
$300$	−0.841701	+	2.59049i	−0.0485956	+	0.149562i
$301$	3.18926	+	9.81553i	0.183826	+	0.565758i
$302$	17.5703	−	12.7656i	1.01106	−	0.734577i
$303$	9.87595	−	7.17530i	0.567359	−	0.412210i
$304$	0.309017	+	0.951057i	0.0177233	+	0.0545468i
$305$	5.34651	−	16.4549i	0.306140	−	0.942203i
$306$	7.38150	+	5.36298i	0.421973	+	0.306581i
$307$	−5.07390			−0.289583			−0.144791	−	0.989462i	$-0.546251\pi$
$307$	−5.07390			−0.289583			−0.144791	+	0.989462i	$0.546251\pi$
$308$	−3.66324	−	13.8729i	−0.208733	−	0.790481i
$309$	20.9931			1.19426
$310$	−4.71709	−	3.42717i	−0.267913	−	0.194650i
$311$	2.68627	−	8.26750i	0.152325	−	0.468807i	−0.845555	−	0.533888i	$-0.820731\pi$
$311$	2.68627	−	8.26750i	0.152325	−	0.468807i	0.997880	+	0.0650809i	$0.0207305\pi$
$312$	−2.01861	−	6.21265i	−0.114281	−	0.351722i
$313$	−12.8693	+	9.35011i	−0.727417	+	0.528500i	−0.888745	−	0.458401i	$-0.848422\pi$
$313$	−12.8693	+	9.35011i	−0.727417	+	0.528500i	0.161328	+	0.986901i	$0.448422\pi$
$314$	−2.47455	+	1.79787i	−0.139647	+	0.101460i
$315$	−3.19493	−	9.83298i	−0.180014	−	0.554026i
$316$	0.462376	−	1.42305i	0.0260107	−	0.0800527i
$317$	−2.43085	−	1.76611i	−0.136530	−	0.0991948i	0.517424	−	0.855729i	$-0.326891\pi$
$317$	−2.43085	−	1.76611i	−0.136530	−	0.0991948i	−0.653954	+	0.756534i	$0.726891\pi$
$318$	−9.47446			−0.531302
$319$	−23.5512	−	1.32010i	−1.31861	−	0.0739116i
$320$	1.68320			0.0940940
$321$	−5.06013	−	3.67640i	−0.282429	−	0.205197i
$322$	−1.67234	+	5.14694i	−0.0931959	+	0.286827i
$323$	−1.98579	−	6.11165i	−0.110493	−	0.340061i
$324$	2.20426	−	1.60149i	0.122459	−	0.0889715i
$325$	9.10959	−	6.61850i	0.505309	−	0.367129i
$326$	−0.169913	−	0.522937i	−0.00941059	−	0.0289628i
$327$	−1.06141	+	3.26668i	−0.0586959	+	0.180648i
$328$	5.51354	+	4.00582i	0.304434	+	0.221184i
$329$	52.1807			2.87681
$330$	−5.43758	−	4.43608i	−0.299329	−	0.244198i
$331$	−6.10133			−0.335359			−0.167680	−	0.985842i	$-0.553627\pi$
$331$	−6.10133			−0.335359			−0.167680	+	0.985842i	$0.553627\pi$
$332$	−5.68939	−	4.13358i	−0.312246	−	0.226860i
$333$	2.10505	−	6.47867i	0.115356	−	0.355029i
$334$	6.11565	+	18.8220i	0.334634	+	1.02990i
$335$	−6.51183	+	4.73112i	−0.355779	+	0.258489i
$336$	−4.39964	+	3.19652i	−0.240020	+	0.174385i
$337$	9.49657	+	29.2274i	0.517311	+	1.59212i	0.779037	+	0.626978i	$0.215709\pi$
$337$	9.49657	+	29.2274i	0.517311	+	1.59212i	−0.261725	+	0.965142i	$0.584291\pi$
$338$	−4.32763	+	13.3191i	−0.235392	+	0.724462i
$339$	2.10083	+	1.52634i	0.114102	+	0.0828997i
$340$	−10.8166			−0.586610
$341$	−9.65803	+	6.22221i	−0.523012	+	0.336952i
$342$	1.41983			0.0767754
$343$	−16.5059	−	11.9923i	−0.891237	−	0.647522i
$344$	−0.737196	+	2.26886i	−0.0397470	+	0.122329i
$345$	0.817913	+	2.51728i	0.0440350	+	0.135526i
$346$	−15.9302	+	11.5740i	−0.856414	+	0.622222i
$347$	−9.33347	+	6.78116i	−0.501047	+	0.364032i	−0.809417	−	0.587235i	$-0.800217\pi$
$347$	−9.33347	+	6.78116i	−0.501047	+	0.364032i	0.308370	+	0.951267i	$0.400217\pi$
$348$	2.76269	+	8.50268i	0.148096	+	0.455791i
$349$	−6.58019	+	20.2518i	−0.352230	+	1.08405i	0.605369	+	0.795945i	$0.293026\pi$
$349$	−6.58019	+	20.2518i	−0.352230	+	1.08405i	−0.957598	+	0.288106i	$0.906974\pi$
$350$	−7.58381	−	5.50996i	−0.405372	−	0.294520i
$351$	−28.8719			−1.54107
$352$	1.19982	−	3.09200i	0.0639504	−	0.164804i
$353$	−32.0203			−1.70427			−0.852134	−	0.523324i	$-0.824692\pi$
$353$	−32.0203			−1.70427			−0.852134	+	0.523324i	$0.824692\pi$
$354$	−13.8816	−	10.0856i	−0.737800	−	0.536043i
$355$	−1.95868	+	6.02820i	−0.103956	+	0.319943i
$356$	−0.0600624	−	0.184853i	−0.00318330	−	0.00979719i
$357$	28.2728	−	20.5414i	1.49636	−	1.08717i
$358$	8.24837	−	5.99279i	0.435940	−	0.316729i
$359$	1.29663	+	3.99061i	0.0684335	+	0.210617i	0.979425	−	0.201808i	$-0.0646819\pi$
$359$	1.29663	+	3.99061i	0.0684335	+	0.210617i	−0.910992	+	0.412425i	$0.864682\pi$
$360$	0.738507	−	2.27289i	0.0389227	−	0.119792i
$361$	−0.809017	−	0.587785i	−0.0425798	−	0.0309361i
$362$	−17.1786			−0.902889
$363$	−12.0249	+	6.82655i	−0.631146	+	0.358301i
$364$	22.4815			1.17835
$365$	−6.66784	−	4.84447i	−0.349011	−	0.253571i
$366$	−3.99288	+	12.2888i	−0.208711	+	0.642346i
$367$	−8.66084	−	26.6553i	−0.452092	−	1.39140i	−0.874515	−	0.484998i	$-0.838820\pi$
$367$	−8.66084	−	26.6553i	−0.452092	−	1.39140i	0.422423	−	0.906399i	$-0.361180\pi$
$368$	−1.01203	+	0.735283i	−0.0527557	+	0.0383293i
$369$	7.82827	−	5.68757i	0.407523	−	0.296083i
$370$	2.49553	+	7.68046i	0.129737	+	0.399288i
$371$	10.0761	−	31.0110i	0.523124	−	1.61001i
$372$	3.52282	+	2.55948i	0.182649	+	0.132703i
$373$	−35.2091			−1.82306			−0.911529	−	0.411235i	$-0.865097\pi$
$373$	−35.2091			−1.82306			−0.911529	+	0.411235i	$0.865097\pi$
$374$	−7.71022	+	19.8697i	−0.398686	+	1.02744i
$375$	−15.1641			−0.783070
$376$	9.75799	+	7.08960i	0.503230	+	0.365618i
$377$	11.4208	−	35.1497i	0.588202	−	1.81030i
$378$	7.42757	+	22.8597i	0.382033	+	1.17578i
$379$	−1.85214	+	1.34566i	−0.0951382	+	0.0691220i	−0.634337	−	0.773056i	$-0.718727\pi$
$379$	−1.85214	+	1.34566i	−0.0951382	+	0.0691220i	0.539199	+	0.842178i	$0.318727\pi$
$380$	−1.36174	+	0.989363i	−0.0698559	+	0.0507533i
$381$	2.39105	+	7.35888i	0.122497	+	0.377007i
$382$	4.59636	−	14.1461i	0.235170	−	0.723779i
$383$	−6.34080	−	4.60686i	−0.324000	−	0.235399i	0.413881	−	0.910331i	$-0.364173\pi$
$383$	−6.34080	−	4.60686i	−0.324000	−	0.235399i	−0.737880	+	0.674932i	$0.764173\pi$
$384$	−1.25705			−0.0641485
$385$	20.3026	−	13.0800i	1.03472	−	0.666620i
$386$	15.8986			0.809216
$387$	2.74027	+	1.99092i	0.139296	+	0.101204i
$388$	1.07079	−	3.29554i	0.0543610	−	0.167306i
$389$	0.145316	+	0.447235i	0.00736779	+	0.0226757i	0.954673	−	0.297657i	$-0.0962052\pi$
$389$	0.145316	+	0.447235i	0.00736779	+	0.0226757i	−0.947305	+	0.320333i	$0.896205\pi$
$390$	8.89539	−	6.46288i	0.450436	−	0.327261i
$391$	6.50347	−	4.72505i	0.328895	−	0.238956i
$392$	−3.62045	−	11.1426i	−0.182860	−	0.562786i
$393$	7.77748	−	23.9366i	0.392322	−	1.20744i
$394$	−3.37413	−	2.45145i	−0.169986	−	0.123502i
$395$	2.51855			0.126722
$396$	−3.64881	−	2.97677i	−0.183360	−	0.149588i
$397$	20.8498			1.04642			0.523211	−	0.852203i	$-0.324734\pi$
$397$	20.8498			1.04642			0.523211	+	0.852203i	$0.324734\pi$
$398$	−19.4804	−	14.1533i	−0.976463	−	0.709442i
$399$	1.68051	−	5.17208i	0.0841308	−	0.258928i
$400$	−0.669585	−	2.06077i	−0.0334792	−	0.103038i
$401$	−28.1517	+	20.4534i	−1.40583	+	1.02140i	−0.411918	+	0.911221i	$0.635141\pi$
$401$	−28.1517	+	20.4534i	−1.40583	+	1.02140i	−0.993912	+	0.110175i	$0.964859\pi$
$402$	4.86316	−	3.53329i	0.242552	−	0.176225i
$403$	−5.56263	−	17.1200i	−0.277094	−	0.852809i
$404$	−3.00090	+	9.23582i	−0.149300	+	0.459499i
$405$	3.71022	+	2.69563i	0.184362	+	0.133947i
$406$	−30.7683			−1.52701
$407$	15.8876	+	0.890544i	0.787521	+	0.0441426i
$408$	8.07801			0.399921
$409$	−23.5145	−	17.0843i	−1.16272	−	0.844762i	−0.172597	−	0.984993i	$-0.555216\pi$
$409$	−23.5145	−	17.0843i	−1.16272	−	0.844762i	−0.990119	+	0.140230i	$0.955216\pi$
$410$	−3.54480	+	10.9098i	−0.175065	+	0.538796i
$411$	−6.92753	−	21.3208i	−0.341710	−	1.05168i
$412$	−13.5108	+	9.81619i	−0.665631	+	0.483609i
$413$	47.7743	−	34.7101i	2.35082	−	1.70797i
$414$	0.548849	+	1.68918i	0.0269745	+	0.0830189i
$415$	3.65786	−	11.2577i	0.179557	−	0.552620i
$416$	4.20413	+	3.05448i	0.206124	+	0.149758i
$417$	4.68969			0.229655
$418$	0.846758	+	3.20671i	0.0414163	+	0.156845i
$419$	−21.9160			−1.07067			−0.535333	−	0.844641i	$-0.679814\pi$
$419$	−21.9160			−1.07067			−0.535333	+	0.844641i	$0.679814\pi$
$420$	−7.40549	−	5.38040i	−0.361351	−	0.262537i
$421$	−1.15648	+	3.55927i	−0.0563633	+	0.173468i	−0.975275	−	0.220995i	$-0.929070\pi$
$421$	−1.15648	+	3.55927i	−0.0563633	+	0.173468i	0.918912	+	0.394463i	$0.129070\pi$
$422$	3.57649	+	11.0073i	0.174101	+	0.535827i
$423$	13.8547	−	10.0660i	0.673636	−	0.489426i
$424$	6.09761	−	4.43018i	0.296126	−	0.215148i
$425$	4.30286	+	13.2428i	0.208719	+	0.642372i
$426$	1.46278	−	4.50197i	0.0708719	−	0.218121i
$427$	−35.9762	−	26.1382i	−1.74101	−	1.26492i
$428$	4.97567			0.240508
$429$	−5.53133	−	20.9474i	−0.267055	−	1.01135i
$430$	−4.01548			−0.193644
$431$	2.96666	+	2.15541i	0.142899	+	0.103822i	0.656938	−	0.753945i	$-0.271851\pi$
$431$	2.96666	+	2.15541i	0.142899	+	0.103822i	−0.514039	+	0.857767i	$0.671851\pi$
$432$	−1.71688	+	5.28401i	−0.0826034	+	0.254227i
$433$	3.90587	+	12.0210i	0.187704	+	0.577694i	0.999984	−	0.00557318i	$-0.00177401\pi$
$433$	3.90587	+	12.0210i	0.187704	+	0.577694i	−0.812280	+	0.583267i	$0.801774\pi$
$434$	−12.1240	+	8.80857i	−0.581968	+	0.422825i
$435$	−12.1743	+	8.84515i	−0.583713	+	0.424092i
$436$	−0.844364	−	2.59868i	−0.0404377	−	0.124454i
$437$	0.386561	−	1.18971i	0.0184917	−	0.0569117i
$438$	4.97967	+	3.61794i	0.237938	+	0.172872i
$439$	8.83165			0.421512			0.210756	−	0.977539i	$-0.432407\pi$
$439$	8.83165			0.421512			0.210756	+	0.977539i	$0.432407\pi$
$440$	5.57381	+	0.312427i	0.265721	+	0.0148944i
$441$	−16.6347			−0.792129
$442$	−27.0164	−	19.6286i	−1.28504	−	0.933636i
$443$	−7.11885	+	21.9096i	−0.338227	+	1.04096i	0.626884	+	0.779113i	$0.284330\pi$
$443$	−7.11885	+	21.9096i	−0.338227	+	1.04096i	−0.965111	+	0.261842i	$0.915670\pi$
$444$	−1.86371	−	5.73592i	−0.0884479	−	0.272215i
$445$	0.264676	−	0.192298i	0.0125468	−	0.00911582i
$446$	5.51039	−	4.00353i	0.260925	−	0.189573i
$447$	−0.0334782	−	0.103035i	−0.00158346	−	0.00487340i
$448$	1.33687	−	4.11446i	0.0631612	−	0.194390i
$449$	−10.7490	−	7.80959i	−0.507276	−	0.368557i	0.304513	−	0.952508i	$-0.401506\pi$
$449$	−10.7490	−	7.80959i	−0.507276	−	0.368557i	−0.811789	+	0.583951i	$0.801506\pi$
$450$	−3.07651			−0.145028
$451$	17.5141	+	14.2884i	0.824709	+	0.672813i
$452$	−2.06577			−0.0971656
$453$	−22.0868	−	16.0470i	−1.03773	−	0.753953i
$454$	3.11420	−	9.58451i	0.146157	−	0.449824i
$455$	11.6935	+	35.9889i	0.548199	+	1.68718i
$456$	1.01697	−	0.738875i	0.0476242	−	0.0346010i
$457$	−21.1126	+	15.3392i	−0.987607	+	0.717538i	−0.959396	−	0.282064i	$-0.908981\pi$
$457$	−21.1126	+	15.3392i	−0.987607	+	0.717538i	−0.0282111	+	0.999602i	$0.508981\pi$
$458$	−6.05007	−	18.6202i	−0.282701	−	0.870065i
$459$	11.0330	−	33.9560i	0.514974	−	1.58493i
$460$	−1.70345	−	1.23763i	−0.0794239	−	0.0577049i
$461$	7.15168			0.333087			0.166543	−	0.986034i	$-0.446739\pi$
$461$	7.15168			0.333087			0.166543	+	0.986034i	$0.446739\pi$
$462$	−15.1624	+	9.76842i	−0.705418	+	0.454468i
$463$	5.35809			0.249012			0.124506	−	0.992219i	$-0.460265\pi$
$463$	5.35809			0.249012			0.124506	+	0.992219i	$0.460265\pi$
$464$	−5.75380	−	4.18038i	−0.267113	−	0.194069i
$465$	−2.26491	+	6.97069i	−0.105033	+	0.323258i
$466$	−2.00277	−	6.16388i	−0.0927764	−	0.285536i
$467$	30.4287	−	22.1077i	1.40807	−	1.02302i	0.414472	−	0.910062i	$-0.363966\pi$
$467$	30.4287	−	22.1077i	1.40807	−	1.02302i	0.993599	−	0.112962i	$-0.0360339\pi$
$468$	5.96913	−	4.33683i	0.275923	−	0.200470i
$469$	6.39290	+	19.6753i	0.295197	+	0.908522i
$470$	−6.27368	+	19.3084i	−0.289383	+	0.890630i
$471$	3.11064	+	2.26001i	0.143331	+	0.104136i
$472$	13.6499			0.628289
$473$	−2.86230	+	7.37632i	−0.131609	+	0.339164i
$474$	−1.88090			−0.0863926
$475$	1.75300	+	1.27363i	0.0804329	+	0.0584379i
$476$	−8.59095	+	26.4402i	−0.393765	+	1.21189i
$477$	−3.30689	−	10.1776i	−0.151412	−	0.465999i
$478$	−16.7073	+	12.1385i	−0.764172	+	0.555204i
$479$	−17.2366	+	12.5231i	−0.787560	+	0.572196i	−0.907238	−	0.420617i	$-0.861814\pi$
$479$	−17.2366	+	12.5231i	−0.787560	+	0.572196i	0.119678	+	0.992813i	$0.461814\pi$
$480$	−0.653840	−	2.01231i	−0.0298436	−	0.0918491i
$481$	−7.70450	+	23.7120i	−0.351295	+	1.08118i
$482$	−10.6115	−	7.70968i	−0.483339	−	0.351166i
$483$	6.80291			0.309543
$484$	4.54702	−	10.0162i	0.206683	−	0.455283i
$485$	5.83254			0.264842
$486$	10.7137	+	7.78395i	0.485983	+	0.353087i
$487$	−0.735205	+	2.26273i	−0.0333153	+	0.102534i	−0.966331	−	0.257301i	$-0.917167\pi$
$487$	−0.735205	+	2.26273i	−0.0333153	+	0.102534i	0.933016	+	0.359835i	$0.117167\pi$
$488$	−3.17639	−	9.77591i	−0.143788	−	0.442535i
$489$	−0.559182	+	0.406270i	−0.0252871	+	0.0183722i
$490$	15.9542	−	11.5914i	0.720737	−	0.523646i
$491$	−3.89416	−	11.9850i	−0.175741	−	0.540876i	0.823925	−	0.566698i	$-0.191780\pi$
$491$	−3.89416	−	11.9850i	−0.175741	−	0.540876i	−0.999667	+	0.0258226i	$0.991780\pi$
$492$	2.64733	−	8.14764i	0.119351	−	0.367324i
$493$	36.9749	+	26.8638i	1.66526	+	1.20989i
$494$	−5.19659			−0.233805
$495$	2.86739	−	7.38943i	0.128880	−	0.332130i
$496$	−3.46402			−0.155539
$497$	13.1798	+	9.57568i	0.591194	+	0.429528i
$498$	−2.73176	+	8.40749i	−0.122413	+	0.376749i
$499$	−8.94586	−	27.5325i	−0.400472	−	1.23252i	−0.924618	−	0.380897i	$-0.875615\pi$
$499$	−8.94586	−	27.5325i	−0.400472	−	1.23252i	0.524146	−	0.851628i	$-0.324385\pi$
$500$	9.75936	−	7.09059i	0.436452	−	0.317101i
$501$	20.1266	−	14.6228i	0.899191	−	0.653300i
$502$	5.65616	+	17.4079i	0.252447	+	0.776952i
$503$	4.23754	−	13.0418i	0.188943	−	0.581506i	−0.811051	−	0.584975i	$-0.801104\pi$
$503$	4.23754	−	13.0418i	0.188943	−	0.581506i	0.999994	+	0.00346916i	$0.00110427\pi$
$504$	−4.96935	−	3.61044i	−0.221352	−	0.160822i
$505$	−16.3458			−0.727378
$506$	−3.48774	+	2.24699i	−0.155049	+	0.0998908i
$507$	17.6043			0.781837
$508$	−4.97979	−	3.61803i	−0.220942	−	0.160524i
$509$	0.760627	−	2.34097i	0.0337142	−	0.103762i	−0.932783	−	0.360438i	$-0.882627\pi$
$509$	0.760627	−	2.34097i	0.0337142	−	0.103762i	0.966498	+	0.256676i	$0.0826273\pi$
$510$	4.20169	+	12.9315i	0.186054	+	0.572615i
$511$	−17.1378	+	12.4513i	−0.758131	+	0.550815i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−1.71688	−	5.28401i	−0.0758021	−	0.233295i
$514$	8.51616	−	26.2101i	0.375632	−	1.15608i
$515$	−22.7415	−	16.5227i	−1.00211	−	0.728076i
$516$	2.99884			0.132017
$517$	30.9970	+	25.2879i	1.36324	+	1.11216i
$518$	20.7563			0.911982
$519$	20.0251	+	14.5491i	0.879004	+	0.638634i
$520$	−2.70295	+	8.31881i	−0.118532	+	0.364804i
$521$	5.49959	+	16.9260i	0.240942	+	0.741542i	0.996278	+	0.0862040i	$0.0274737\pi$
$521$	5.49959	+	16.9260i	0.240942	+	0.741542i	−0.755336	+	0.655338i	$0.772526\pi$
$522$	−8.16940	+	5.93541i	−0.357565	+	0.259786i
$523$	−28.2398	+	20.5174i	−1.23484	+	0.897164i	−0.997243	−	0.0741996i	$-0.976360\pi$
$523$	−28.2398	+	20.5174i	−1.23484	+	0.897164i	−0.237597	+	0.971364i	$0.576360\pi$
$524$	6.18709	+	19.0419i	0.270284	+	0.831850i
$525$	−3.64137	+	11.2070i	−0.158922	+	0.489113i
$526$	0.0348210	+	0.0252989i	0.00151827	+	0.00110309i
$527$	22.2603			0.969676
$528$	−4.16263	−	0.233326i	−0.181155	−	0.0101542i
$529$	−21.4352			−0.931963
$530$	10.2635	+	7.45689i	0.445819	+	0.323907i
$531$	5.98891	−	18.4320i	0.259897	−	0.799880i
$532$	1.33687	+	4.11446i	0.0579607	+	0.178385i
$533$	−28.6516	+	20.8166i	−1.24104	+	0.901667i
$534$	−0.197665	+	0.143612i	−0.00855381	+	0.00621470i
$535$	2.58804	+	7.96516i	0.111891	+	0.344364i
$536$	−1.47772	+	4.54794i	−0.0638276	+	0.196441i
$537$	−10.3686	−	7.53324i	−0.447439	−	0.325083i
$538$	−2.34154			−0.100951
$539$	−9.92063	−	37.5699i	−0.427312	−	1.61825i
$540$	−9.35179			−0.402437
$541$	11.4963	+	8.35252i	0.494263	+	0.359103i	0.806821	−	0.590796i	$-0.201186\pi$
$541$	11.4963	+	8.35252i	0.494263	+	0.359103i	−0.312558	+	0.949899i	$0.601186\pi$
$542$	−1.57403	+	4.84437i	−0.0676104	+	0.208083i
$543$	6.67303	+	20.5375i	0.286367	+	0.881348i
$544$	−5.19888	+	3.77721i	−0.222900	+	0.161946i
$545$	3.72085	−	2.70335i	0.159384	−	0.115799i
$546$	−8.73292	−	26.8772i	−0.373735	−	1.15024i
$547$	1.90241	−	5.85502i	0.0813412	−	0.250342i	−0.902113	−	0.431500i	$-0.857984\pi$
$547$	1.90241	−	5.85502i	0.0813412	−	0.250342i	0.983454	+	0.181158i	$0.0579844\pi$
$548$	14.4278	+	10.4824i	0.616327	+	0.447788i
$549$	−14.5944			−0.622874
$550$	−1.83477	−	6.94837i	−0.0782350	−	0.296280i
$551$	7.11209			0.302985
$552$	1.27217	+	0.924287i	0.0541472	+	0.0393403i
$553$	2.00033	−	6.15639i	0.0850628	−	0.261796i
$554$	10.0128	+	30.8163i	0.425404	+	1.30926i
$555$	8.21280	−	5.96695i	0.348614	−	0.253283i
$556$	−3.01821	+	2.19286i	−0.128001	+	0.0929978i
$557$	−6.38243	−	19.6431i	−0.270432	−	0.832304i	−0.990392	−	0.138289i	$-0.955840\pi$
$557$	−6.38243	−	19.6431i	−0.270432	−	0.832304i	0.719960	−	0.694016i	$-0.244160\pi$
$558$	−1.51984	+	4.67758i	−0.0643399	+	0.198018i
$559$	−10.0294	−	7.28681i	−0.424200	−	0.308199i
$560$	7.28188			0.307716
$561$	26.7497	+	1.49939i	1.12937	+	0.0633044i
$562$	−2.98842			−0.126059
$563$	14.6508	+	10.6445i	0.617459	+	0.448610i	0.852033	−	0.523488i	$-0.175369\pi$
$563$	14.6508	+	10.6445i	0.617459	+	0.448610i	−0.234574	+	0.972098i	$0.575369\pi$
$564$	4.68530	−	14.4199i	0.197287	−	0.607186i
$565$	−1.07449	−	3.30693i	−0.0452040	−	0.139124i
$566$	14.4170	−	10.4746i	0.605993	−	0.440280i
$567$	9.53607	−	6.92836i	0.400477	−	0.290964i
$568$	1.16366	+	3.58138i	0.0488261	+	0.150271i
$569$	−2.17732	+	6.70112i	−0.0912782	+	0.280925i	−0.986266	−	0.165165i	$-0.947184\pi$
$569$	−2.17732	+	6.70112i	−0.0912782	+	0.280925i	0.894988	+	0.446091i	$0.147184\pi$
$570$	1.71178	+	1.24368i	0.0716984	+	0.0520920i
$571$	−23.1098			−0.967115			−0.483558	−	0.875312i	$-0.660656\pi$
$571$	−23.1098			−0.967115			−0.483558	+	0.875312i	$0.660656\pi$
$572$	13.3547	+	10.8950i	0.558388	+	0.455544i
$573$	−18.6975			−0.781100
$574$	23.8527	+	17.3300i	0.995592	+	0.723340i
$575$	−0.837608	+	2.57789i	−0.0349307	+	0.107506i
$576$	−0.438750	−	1.35034i	−0.0182813	−	0.0562640i
$577$	3.78114	−	2.74716i	0.157411	−	0.114366i	−0.506292	−	0.862362i	$-0.668984\pi$
$577$	3.78114	−	2.74716i	0.157411	−	0.114366i	0.663703	+	0.747997i	$0.268984\pi$
$578$	19.6556	−	14.2806i	0.817564	−	0.593995i
$579$	−6.17580	−	19.0071i	−0.256657	−	0.789910i
$580$	3.69927	−	11.3852i	0.153604	−	0.472744i
$581$	−24.6134	−	17.8827i	−1.02114	−	0.741900i
$582$	−4.35585			−0.180556
$583$	21.0141	−	13.5384i	0.870315	−	0.560703i
$584$	−4.89655			−0.202621
$585$	10.0473	+	7.29977i	0.415403	+	0.301808i
$586$	4.29882	−	13.2304i	0.177583	−	0.546543i
$587$	5.48608	+	16.8844i	0.226435	+	0.696894i	0.998143	+	0.0609175i	$0.0194027\pi$
$587$	5.48608	+	16.8844i	0.226435	+	0.696894i	−0.771708	+	0.635977i	$0.780597\pi$
$588$	−11.9149	+	8.65668i	−0.491362	+	0.356995i
$589$	2.80245	−	2.03610i	0.115473	−	0.0838959i
$590$	7.09986	+	21.8511i	0.292297	+	0.899596i
$591$	−1.62009	+	4.98612i	−0.0666415	+	0.205101i
$592$	3.88152	+	2.82009i	0.159529	+	0.115905i
$593$	−6.01368			−0.246952			−0.123476	−	0.992348i	$-0.539404\pi$
$593$	−6.01368			−0.246952			−0.123476	+	0.992348i	$0.539404\pi$
$594$	−6.66611	+	17.1789i	−0.273514	+	0.704861i
$595$	−46.7946			−1.91839
$596$	0.0697244	+	0.0506577i	0.00285602	+	0.00207502i
$597$	−9.35351	+	28.7871i	−0.382814	+	1.17818i
$598$	−2.00880	−	6.18244i	−0.0821458	−	0.252819i
$599$	−25.4426	+	18.4851i	−1.03956	+	0.755283i	−0.970199	−	0.242309i	$-0.922095\pi$
$599$	−25.4426	+	18.4851i	−1.03956	+	0.755283i	−0.0693582	+	0.997592i	$0.522095\pi$
$600$	−2.20360	+	1.60101i	−0.0899617	+	0.0653610i
$601$	−7.64742	−	23.5363i	−0.311945	−	0.960067i	−0.976994	−	0.213268i	$-0.931589\pi$
$601$	−7.64742	−	23.5363i	−0.311945	−	0.960067i	0.665049	−	0.746800i	$-0.268411\pi$
$602$	−3.18926	+	9.81553i	−0.129985	+	0.400051i
$603$	5.49290	+	3.99082i	0.223688	+	0.162519i
$604$	21.7181			0.883698
$605$	18.3993	+	2.06916i	0.748037	+	0.0841232i
$606$	12.2074			0.495890
$607$	14.1845	+	10.3056i	0.575729	+	0.418292i	0.837182	−	0.546925i	$-0.184202\pi$
$607$	14.1845	+	10.3056i	0.575729	+	0.418292i	−0.261453	+	0.965216i	$0.584202\pi$
$608$	−0.309017	+	0.951057i	−0.0125323	+	0.0385704i
$609$	11.9519	+	36.7843i	0.484317	+	1.49058i
$610$	13.9973	−	10.1697i	0.566736	−	0.411758i
$611$	−50.7082	+	36.8417i	−2.05144	+	1.49046i
$612$	2.81948	+	8.67748i	0.113971	+	0.350766i
$613$	7.03607	−	21.6548i	0.284184	−	0.874629i	−0.702458	−	0.711725i	$-0.747914\pi$
$613$	7.03607	−	21.6548i	0.284184	−	0.874629i	0.986642	−	0.162904i	$-0.0520860\pi$
$614$	−4.10487	−	2.98236i	−0.165659	−	0.120358i
$615$	14.4199			0.581467
$616$	5.19065	−	13.3766i	0.209137	−	0.538959i
$617$	7.62010			0.306774			0.153387	−	0.988166i	$-0.450982\pi$
$617$	7.62010			0.306774			0.153387	+	0.988166i	$0.450982\pi$
$618$	16.9838	+	12.3394i	0.683188	+	0.496365i
$619$	−1.21635	+	3.74355i	−0.0488894	+	0.150466i	−0.972521	−	0.232816i	$-0.925206\pi$
$619$	−1.21635	+	3.74355i	−0.0488894	+	0.150466i	0.923631	+	0.383282i	$0.125206\pi$
$620$	−1.80177	−	5.54528i	−0.0723608	−	0.222704i
$621$	5.62278	−	4.08519i	0.225634	−	0.163933i
$622$	7.03275	−	5.10959i	0.281988	−	0.204876i
$623$	−0.259842	−	0.799711i	−0.0104103	−	0.0320397i
$624$	2.01861	−	6.21265i	0.0808091	−	0.248705i
$625$	7.66202	+	5.56678i	0.306481	+	0.222671i
$626$	−15.9074			−0.635786
$627$	3.50478	−	2.25797i	0.139968	−	0.0901745i
$628$	−3.05872			−0.122056
$629$	−24.9433	−	18.1224i	−0.994554	−	0.722586i
$630$	3.19493	−	9.83298i	0.127289	−	0.391755i
$631$	11.4361	+	35.1968i	0.455265	+	1.40116i	0.870824	+	0.491595i	$0.163586\pi$
$631$	11.4361	+	35.1968i	0.455265	+	1.40116i	−0.415559	+	0.909566i	$0.636414\pi$
$632$	1.21052	−	0.879492i	0.0481518	−	0.0349843i
$633$	11.7702	−	8.55157i	0.467824	−	0.339894i
$634$	−0.928500	−	2.85763i	−0.0368755	−	0.113491i
$635$	3.20164	−	9.85363i	0.127053	−	0.391030i
$636$	−7.66500	−	5.56895i	−0.303937	−	0.220823i
$637$	60.8833			2.41228
$638$	−18.2773	−	14.9110i	−0.723607	−	0.590332i
$639$	5.34662			0.211509
$640$	1.36174	+	0.989363i	0.0538276	+	0.0391080i
$641$	−2.54136	+	7.82149i	−0.100378	+	0.308930i	−0.988618	−	0.150449i	$-0.951928\pi$
$641$	−2.54136	+	7.82149i	−0.100378	+	0.308930i	0.888240	+	0.459379i	$0.151928\pi$
$642$	−1.93280	−	5.94854i	−0.0762814	−	0.234770i
$643$	19.2257	−	13.9683i	0.758186	−	0.550854i	−0.140167	−	0.990128i	$-0.544764\pi$
$643$	19.2257	−	13.9683i	0.758186	−	0.550854i	0.898353	+	0.439273i	$0.144764\pi$
$644$	−4.37824	+	3.18098i	−0.172527	+	0.125348i
$645$	1.55981	+	4.80061i	0.0614176	+	0.189024i
$646$	1.98579	−	6.11165i	0.0781300	−	0.240460i
$647$	37.7654	+	27.4381i	1.48471	+	1.07870i	0.976001	+	0.217766i	$0.0698768\pi$
$647$	37.7654	+	27.4381i	1.48471	+	1.07870i	0.508708	+	0.860939i	$0.330123\pi$
$648$	2.72461			0.107033
$649$	45.2007	+	2.53362i	1.77428	+	0.0994533i
$650$	11.2601			0.441656
$651$	15.2404	+	11.0728i	0.597319	+	0.433978i
$652$	0.169913	−	0.522937i	0.00665429	−	0.0204798i
$653$	5.70681	+	17.5638i	0.223325	+	0.687323i	0.998457	+	0.0555244i	$0.0176831\pi$
$653$	5.70681	+	17.5638i	0.223325	+	0.687323i	−0.775133	+	0.631799i	$0.782317\pi$
$654$	−2.77880	+	2.01892i	−0.108660	+	0.0789459i
$655$	−27.2646	+	19.8089i	−1.06532	+	0.773997i
$656$	2.10599	+	6.48156i	0.0822249	+	0.253062i
$657$	−2.14836	+	6.61199i	−0.0838157	+	0.257958i
$658$	42.2150	+	30.6710i	1.64571	+	1.19568i
$659$	13.6550			0.531923			0.265961	−	0.963984i	$-0.414311\pi$
$659$	13.6550			0.531923			0.265961	+	0.963984i	$0.414311\pi$
$660$	−1.79163	−	6.78499i	−0.0697391	−	0.264105i
$661$	30.3635			1.18100			0.590502	−	0.807036i	$-0.298930\pi$
$661$	30.3635			1.18100			0.590502	+	0.807036i	$0.298930\pi$
$662$	−4.93608	−	3.58627i	−0.191846	−	0.139384i
$663$	−12.9719	+	39.9235i	−0.503788	+	1.55050i
$664$	−2.17315	−	6.68827i	−0.0843346	−	0.259555i
$665$	−5.89117	+	4.28018i	−0.228450	+	0.165978i
$666$	5.51108	−	4.00404i	0.213550	−	0.155153i
$667$	2.74926	+	8.46134i	0.106452	+	0.327624i
$668$	−6.11565	+	18.8220i	−0.236622	+	0.728247i
$669$	−6.92683	−	5.03264i	−0.267807	−	0.194573i
$670$	−8.04907			−0.310963
$671$	−8.70382	−	32.9618i	−0.336007	−	1.27248i
$672$	−5.43825			−0.209785
$673$	8.60285	+	6.25034i	0.331616	+	0.240933i	0.741116	−	0.671377i	$-0.234297\pi$
$673$	8.60285	+	6.25034i	0.331616	+	0.240933i	−0.409500	+	0.912310i	$0.634297\pi$
$674$	−9.49657	+	29.2274i	−0.365794	+	1.12580i
$675$	3.72017	+	11.4495i	0.143189	+	0.440692i
$676$	−11.3299	+	8.23164i	−0.435765	+	0.316601i
$677$	−16.0572	+	11.6663i	−0.617130	+	0.448371i	−0.851918	−	0.523676i	$-0.824560\pi$
$677$	−16.0572	+	11.6663i	−0.617130	+	0.448371i	0.234788	+	0.972047i	$0.424560\pi$
$678$	0.802447	+	2.46968i	0.0308178	+	0.0948474i
$679$	4.63244	−	14.2572i	0.177777	−	0.547141i
$680$	−8.75078	−	6.35781i	−0.335577	−	0.243811i
$681$	−12.6682			−0.485448
$682$	−11.4708	−	0.642970i	−0.439241	−	0.0246206i
$683$	−1.05707			−0.0404475			−0.0202238	−	0.999795i	$-0.506438\pi$
$683$	−1.05707			−0.0404475			−0.0202238	+	0.999795i	$0.506438\pi$
$684$	1.14866	+	0.834553i	0.0439203	+	0.0319099i
$685$	−9.27605	+	28.5488i	−0.354420	+	1.09079i
$686$	−6.30471	−	19.4039i	−0.240715	−	0.740844i
$687$	−19.9108	+	14.4660i	−0.759644	+	0.551913i
$688$	−1.93001	+	1.40223i	−0.0735808	+	0.0534595i
$689$	12.1033	+	37.2500i	0.461098	+	1.41911i
$690$	−0.817913	+	2.51728i	−0.0311374	+	0.0958312i
$691$	−30.0364	−	21.8227i	−1.14264	−	0.830174i	−0.155152	−	0.987891i	$-0.549587\pi$
$691$	−30.0364	−	21.8227i	−1.14264	−	0.830174i	−0.987484	+	0.157716i	$0.949587\pi$
$692$	−19.6908			−0.748534
$693$	−15.7855	−	12.8781i	−0.599641	−	0.489199i
$694$	−11.5368			−0.437931
$695$	−5.08026	−	3.69103i	−0.192705	−	0.140009i
$696$	−2.76269	+	8.50268i	−0.104719	+	0.322293i
$697$	−13.5334	−	41.6516i	−0.512614	−	1.57767i
$698$	−17.2272	+	12.5163i	−0.652058	+	0.473748i
$699$	−6.59110	+	4.78872i	−0.249298	+	0.181126i
$700$	−2.89676	−	8.91530i	−0.109487	−	0.336967i
$701$	6.69117	−	20.5933i	0.252722	−	0.777799i	−0.741548	−	0.670900i	$-0.765908\pi$
$701$	6.69117	−	20.5933i	0.252722	−	0.777799i	0.994270	−	0.106899i	$-0.0340921\pi$
$702$	−23.3579	−	16.9705i	−0.881586	−	0.640510i
$703$	−4.79782			−0.180953
$704$	2.78810	−	1.79624i	0.105081	−	0.0676984i
$705$	25.5207			0.961164
$706$	−25.9049	−	18.8210i	−0.974945	−	0.708339i
$707$	−12.9825	+	39.9560i	−0.488257	+	1.50270i
$708$	−5.30231	−	16.3188i	−0.199273	−	0.613299i
$709$	26.5378	−	19.2808i	0.996647	−	0.724106i	0.0352804	−	0.999377i	$-0.488768\pi$
$709$	26.5378	−	19.2808i	0.996647	−	0.724106i	0.961367	+	0.275271i	$0.0887676\pi$
$710$	−5.12789	+	3.72563i	−0.192446	+	0.139820i
$711$	−0.656494	−	2.02048i	−0.0246205	−	0.0757740i
$712$	0.0600624	−	0.184853i	0.00225093	−	0.00692766i
$713$	3.50569	+	2.54703i	0.131289	+	0.0953870i
$714$	34.9471			1.30786
$715$	−10.4947	+	27.0454i	−0.392479	+	1.01144i
$716$	10.1955			0.381026
$717$	21.0019	+	15.2587i	0.784328	+	0.569848i
$718$	−1.29663	+	3.99061i	−0.0483898	+	0.148928i
$719$	−14.5111	−	44.6604i	−0.541171	−	1.66555i	−0.729924	−	0.683528i	$-0.760445\pi$
$719$	−14.5111	−	44.6604i	−0.541171	−	1.66555i	0.188753	−	0.982025i	$-0.439555\pi$
$720$	1.93344	−	1.40472i	0.0720549	−	0.0523510i
$721$	−58.4506	+	42.4668i	−2.17681	+	1.58155i
$722$	−0.309017	−	0.951057i	−0.0115004	−	0.0353947i
$723$	−5.09510	+	15.6811i	−0.189489	+	0.583186i
$724$	−13.8978	−	10.0973i	−0.516508	−	0.375265i
$725$	−15.4106			−0.572336
$726$	−13.7409	−	1.54529i	−0.509974	−	0.0573509i
$727$	−2.77227			−0.102818			−0.0514089	−	0.998678i	$-0.516371\pi$
$727$	−2.77227			−0.102818			−0.0514089	+	0.998678i	$0.516371\pi$
$728$	18.1879	+	13.2143i	0.674088	+	0.489754i
$729$	7.67004	−	23.6059i	0.284075	−	0.874294i
$730$	−2.54689	−	7.83851i	−0.0942645	−	0.290116i
$731$	12.4025	−	9.01097i	0.458724	−	0.333283i
$732$	−10.4535	+	7.59490i	−0.386372	+	0.280716i
$733$	−9.86954	−	30.3753i	−0.364540	−	1.12194i	−0.950269	−	0.311431i	$-0.899192\pi$
$733$	−9.86954	−	30.3753i	−0.364540	−	1.12194i	0.585729	−	0.810507i	$-0.300808\pi$
$734$	8.66084	−	26.6553i	0.319677	−	0.983866i
$735$	−20.0552	−	14.5710i	−0.739748	−	0.537458i
$736$	−1.25094			−0.0461102
$737$	−5.73751	+	14.7859i	−0.211344	+	0.544645i
$738$	9.67627			0.356189
$739$	−9.27443	−	6.73827i	−0.341165	−	0.247871i	0.403988	−	0.914764i	$-0.367624\pi$
$739$	−9.27443	−	6.73827i	−0.341165	−	0.247871i	−0.745153	+	0.666893i	$0.767624\pi$
$740$	−2.49553	+	7.68046i	−0.0917377	+	0.282339i
$741$	2.01861	+	6.21265i	0.0741556	+	0.228227i
$742$	26.3795	−	19.1658i	0.968422	−	0.703600i
$743$	−28.4008	+	20.6344i	−1.04192	+	0.757001i	−0.970660	−	0.240456i	$-0.922703\pi$
$743$	−28.4008	+	20.6344i	−1.04192	+	0.757001i	−0.0712631	+	0.997458i	$0.522703\pi$
$744$	1.34560	+	4.14132i	0.0493319	+	0.151828i
$745$	−0.0448277	+	0.137965i	−0.00164236	+	0.00505466i
$746$	−28.4848	−	20.6954i	−1.04290	−	0.757712i
$747$	−9.98488			−0.365328
$748$	−17.9168	+	11.5430i	−0.655103	+	0.422052i
$749$	21.5257			0.786534
$750$	−12.2680	−	8.91322i	−0.447964	−	0.325465i
$751$	2.43316	−	7.48850i	0.0887873	−	0.273259i	−0.896798	−	0.442441i	$-0.854113\pi$
$751$	2.43316	−	7.48850i	0.0887873	−	0.273259i	0.985585	+	0.169182i	$0.0541125\pi$
$752$	3.72722	+	11.4712i	0.135918	+	0.418312i
$753$	18.6144	−	13.5242i	0.678348	−	0.492848i
$754$	29.9001	−	21.7237i	1.08890	−	0.791131i
$755$	11.2964	+	34.7669i	0.411120	+	1.26530i
$756$	−7.42757	+	22.8597i	−0.270138	+	0.831400i
$757$	26.3877	+	19.1718i	0.959077	+	0.696810i	0.952936	−	0.303171i	$-0.0980454\pi$
$757$	26.3877	+	19.1718i	0.959077	+	0.696810i	0.00614054	+	0.999981i	$0.498045\pi$
$758$	−2.28938			−0.0831539
$759$	4.04114	+	3.29684i	0.146684	+	0.119668i
$760$	−1.68320			−0.0610563
$761$	−17.3637	−	12.6155i	−0.629433	−	0.457310i	0.226771	−	0.973948i	$-0.427183\pi$
$761$	−17.3637	−	12.6155i	−0.629433	−	0.457310i	−0.856204	+	0.516638i	$0.827183\pi$
$762$	−2.39105	+	7.35888i	−0.0866184	+	0.266584i
$763$	−3.65289	−	11.2424i	−0.132243	−	0.407003i
$764$	12.0334	−	8.74279i	0.435354	−	0.316303i
$765$	−12.4246	+	9.02699i	−0.449212	+	0.326371i
$766$	−2.42197	−	7.45405i	−0.0875093	−	0.269326i
$767$	−21.9195	+	67.4613i	−0.791468	+	2.43589i
$768$	−1.01697	−	0.738875i	−0.0366969	−	0.0266619i
$769$	27.8521			1.00437			0.502187	−	0.864759i	$-0.332529\pi$
$769$	27.8521			1.00437			0.502187	+	0.864759i	$0.332529\pi$
$770$	24.1134	+	1.35162i	0.868988	+	0.0487090i
$771$	−34.6429			−1.24763
$772$	12.8622	+	9.34495i	0.462921	+	0.336332i
$773$	−6.30825	+	19.4148i	−0.226892	+	0.698302i	0.771202	+	0.636590i	$0.219656\pi$
$773$	−6.30825	+	19.4148i	−0.226892	+	0.698302i	−0.998094	+	0.0617112i	$0.980344\pi$
$774$	1.04669	+	3.22138i	0.0376225	+	0.115790i
$775$	−6.07240	+	4.41186i	−0.218127	+	0.158479i
$776$	2.80336	−	2.03676i	0.100635	−	0.0731154i
$777$	−8.06280	−	24.8147i	−0.289251	−	0.890224i
$778$	−0.145316	+	0.447235i	−0.00520981	+	0.0160342i
$779$	−5.51354	−	4.00582i	−0.197543	−	0.143523i
$780$	10.9953			0.393695
$781$	3.18862	+	12.0755i	0.114098	+	0.432094i
$782$	8.03873			0.287464
$783$	31.9678	+	23.2259i	1.14243	+	0.830028i
$784$	3.62045	−	11.1426i	0.129302	−	0.397950i
$785$	−1.59096	−	4.89647i	−0.0567837	−	0.174762i
$786$	20.3617	−	14.7936i	0.726278	−	0.527672i
$787$	8.07849	−	5.86937i	0.287967	−	0.209220i	−0.434418	−	0.900711i	$-0.643046\pi$
$787$	8.07849	−	5.86937i	0.287967	−	0.209220i	0.722385	+	0.691491i	$0.243046\pi$
$788$	−1.28880	−	3.96652i	−0.0459116	−	0.141302i
$789$	0.0167193	−	0.0514567i	0.000595223	−	0.00183191i
$790$	2.03755	+	1.48037i	0.0724927	+	0.0526690i
$791$	−8.93693			−0.317761
$792$	−1.20225	−	4.55297i	−0.0427201	−	0.161783i
$793$	53.4157			1.89685
$794$	16.8679	+	12.2552i	0.598618	+	0.434921i
$795$	4.92804	−	15.1669i	0.174779	−	0.537916i
$796$	−7.44084	−	22.9006i	−0.263734	−	0.811689i
$797$	−1.46326	+	1.06312i	−0.0518312	+	0.0376576i	−0.613399	−	0.789773i	$-0.710198\pi$
$797$	−1.46326	+	1.06312i	−0.0518312	+	0.0376576i	0.561568	+	0.827431i	$0.310198\pi$
$798$	4.39964	−	3.19652i	0.155745	−	0.113156i
$799$	−23.9517	−	73.7159i	−0.847352	−	2.60788i
$800$	0.669585	−	2.06077i	0.0236734	−	0.0728592i
$801$	−0.223261	−	0.162209i	−0.00788854	−	0.00573136i
$802$	−34.7975			−1.22874
$803$	−16.2146	−	0.908869i	−0.572200	−	0.0320733i
$804$	6.01120			0.211999
$805$	−7.36948	−	5.35424i	−0.259740	−	0.188712i
$806$	5.56263	−	17.1200i	0.195935	−	0.603027i
$807$	0.909570	+	2.79937i	0.0320184	+	0.0985424i
$808$	−7.85646	+	5.70805i	−0.276389	+	0.200808i
$809$	14.4318	−	10.4853i	0.507397	−	0.368645i	−0.304439	−	0.952532i	$-0.598469\pi$
$809$	14.4318	−	10.4853i	0.507397	−	0.368645i	0.811835	+	0.583887i	$0.198469\pi$
$810$	1.41718	+	4.36162i	0.0497945	+	0.153252i
$811$	−15.5186	+	47.7613i	−0.544931	+	1.67713i	0.176222	+	0.984350i	$0.443612\pi$
$811$	−15.5186	+	47.7613i	−0.544931	+	1.67713i	−0.721153	+	0.692775i	$0.756388\pi$
$812$	−24.8921	−	18.0852i	−0.873541	−	0.634665i
$813$	6.40299			0.224563
$814$	12.3299	+	10.0590i	0.432163	+	0.352567i
$815$	0.925508			0.0324191
$816$	6.53525	+	4.74814i	0.228779	+	0.166218i
$817$	0.737196	−	2.26886i	0.0257912	−	0.0793773i
$818$	−8.98173	−	27.6429i	−0.314039	−	0.966512i
$819$	25.8237	−	18.7620i	0.902352	−	0.655597i
$820$	−9.28042	+	6.74262i	−0.324086	+	0.235462i
$821$	−10.7933	−	33.2183i	−0.376688	−	1.15933i	−0.942333	−	0.334677i	$-0.891373\pi$
$821$	−10.7933	−	33.2183i	−0.376688	−	1.15933i	0.565645	−	0.824649i	$-0.308627\pi$
$822$	6.92753	−	21.3208i	0.241626	−	0.743647i
$823$	18.6348	+	13.5390i	0.649568	+	0.471939i	0.863124	−	0.504992i	$-0.168505\pi$
$823$	18.6348	+	13.5390i	0.649568	+	0.471939i	−0.213556	+	0.976931i	$0.568505\pi$
$824$	−16.7003			−0.581783
$825$	−7.59424	+	4.89261i	−0.264397	+	0.170339i
$826$	59.0523			2.05469
$827$	19.1825	+	13.9369i	0.667041	+	0.484634i	0.869033	−	0.494753i	$-0.164742\pi$
$827$	19.1825	+	13.9369i	0.667041	+	0.484634i	−0.201992	+	0.979387i	$0.564742\pi$
$828$	−0.548849	+	1.68918i	−0.0190738	+	0.0587032i
$829$	−8.37165	−	25.7653i	−0.290760	−	0.894866i	−0.984613	−	0.174750i	$-0.944088\pi$
$829$	−8.37165	−	25.7653i	−0.290760	−	0.894866i	0.693853	−	0.720116i	$-0.255912\pi$
$830$	9.57640	−	6.95766i	0.332402	−	0.241504i
$831$	32.9522	−	23.9412i	1.14310	−	0.830510i
$832$	1.60583	+	4.94225i	0.0556722	+	0.171342i
$833$	−23.2656	+	71.6042i	−0.806106	+	2.48094i
$834$	3.79404	+	2.75653i	0.131377	+	0.0954508i
$835$	−33.3118			−1.15280
$836$	−1.19982	+	3.09200i	−0.0414965	+	0.106939i
$837$	19.2459			0.665234
$838$	−17.7304	−	12.8819i	−0.612487	−	0.444998i
$839$	−3.40594	+	10.4824i	−0.117586	+	0.361893i	−0.992478	−	0.122426i	$-0.960933\pi$
$839$	−3.40594	+	10.4824i	−0.117586	+	0.361893i	0.874891	+	0.484319i	$0.160933\pi$
$840$	−2.82865	−	8.70568i	−0.0975975	−	0.300374i
$841$	−17.4600	+	12.6855i	−0.602070	+	0.437429i
$842$	−3.02770	+	2.19975i	−0.104341	+	0.0758084i
$843$	1.16085	+	3.57273i	0.0399818	+	0.123051i
$844$	−3.57649	+	11.0073i	−0.123108	+	0.378887i
$845$	−19.0705	−	13.8555i	−0.656045	−	0.476645i
$846$	17.1253			0.588780
$847$	19.6713	−	43.3322i	0.675915	−	1.48891i
$848$	7.53707			0.258824
$849$	−18.1229	−	13.1671i	−0.621977	−	0.451893i
$850$	−4.30286	+	13.2428i	−0.147587	+	0.454226i
$851$	−1.85465	−	5.70803i	−0.0635766	−	0.195669i
$852$	3.82961	−	2.78237i	0.131200	−	0.0953225i
$853$	38.8807	−	28.2485i	1.33125	−	0.967209i	0.331532	−	0.943444i	$-0.392435\pi$
$853$	38.8807	−	28.2485i	1.33125	−	0.967209i	0.999718	−	0.0237651i	$-0.00756538\pi$
$854$	−13.7417	−	42.2926i	−0.470231	−	1.44722i
$855$	−0.738507	+	2.27289i	−0.0252564	+	0.0777312i
$856$	4.02540	+	2.92462i	0.137585	+	0.0999616i
$857$	54.2341			1.85260			0.926301	−	0.376785i	$-0.122971\pi$
$857$	54.2341			1.85260			0.926301	+	0.376785i	$0.122971\pi$
$858$	7.83764	−	20.1980i	0.267573	−	0.689550i
$859$	−20.3733			−0.695128			−0.347564	−	0.937656i	$-0.612991\pi$
$859$	−20.3733			−0.695128			−0.347564	+	0.937656i	$0.612991\pi$
$860$	−3.24859	−	2.36024i	−0.110776	−	0.0804836i
$861$	11.4529	−	35.2483i	0.390313	−	1.20126i
$862$	1.13316	+	3.48752i	0.0385957	+	0.118785i
$863$	15.8445	−	11.5117i	0.539354	−	0.391864i	−0.284491	−	0.958679i	$-0.591825\pi$
$863$	15.8445	−	11.5117i	0.539354	−	0.391864i	0.823845	+	0.566815i	$0.191825\pi$
$864$	−4.49485	+	3.26570i	−0.152918	+	0.111101i
$865$	−10.2420	−	31.5216i	−0.348238	−	1.07177i
$866$	−3.90587	+	12.0210i	−0.132727	+	0.408491i
$867$	−24.7080	−	17.9514i	−0.839128	−	0.609663i
$868$	−14.9860			−0.508659
$869$	4.17178	−	2.68768i	0.141518	−	0.0911735i
$870$	−15.0483			−0.510184
$871$	−20.1041	−	14.6065i	−0.681201	−	0.494921i
$872$	0.844364	−	2.59868i	0.0285938	−	0.0880026i
$873$	−1.52033	−	4.67910i	−0.0514554	−	0.158364i
$874$	1.01203	−	0.735283i	0.0342324	−	0.0248713i
$875$	42.2209	−	30.6753i	1.42733	−	1.03701i
$876$	1.90206	+	5.85395i	0.0642648	+	0.197787i
$877$	15.8044	−	48.6409i	0.533677	−	1.64249i	−0.212815	−	0.977093i	$-0.568263\pi$
$877$	15.8044	−	48.6409i	0.533677	−	1.64249i	0.746491	−	0.665395i	$-0.231737\pi$
$878$	7.14496	+	5.19112i	0.241131	+	0.175192i
$879$	−17.4872			−0.589827
$880$	4.32567	+	3.52896i	0.145818	+	0.118961i
$881$	−22.4055			−0.754859			−0.377430	−	0.926038i	$-0.623192\pi$
$881$	−22.4055			−0.754859			−0.377430	+	0.926038i	$0.623192\pi$
$882$	−13.4578	−	9.77764i	−0.453147	−	0.329230i
$883$	−5.63241	+	17.3348i	−0.189546	+	0.583361i	−0.999997	−	0.00244462i	$-0.999222\pi$
$883$	−5.63241	+	17.3348i	−0.189546	+	0.583361i	0.810451	+	0.585806i	$0.199222\pi$
$884$	−10.3194	−	31.7597i	−0.347077	−	1.06819i
$885$	23.3656	−	16.9761i	0.785427	−	0.570646i
$886$	−18.6374	+	13.5409i	−0.626135	+	0.454914i
$887$	−9.03416	−	27.8043i	−0.303337	−	0.933577i	−0.980292	−	0.197552i	$-0.936701\pi$
$887$	−9.03416	−	27.8043i	−0.303337	−	0.933577i	0.676955	−	0.736024i	$-0.263299\pi$
$888$	1.86371	−	5.73592i	0.0625421	−	0.192485i
$889$	−21.5436	−	15.6523i	−0.722548	−	0.524962i
$890$	0.327158			0.0109663
$891$	9.02236	+	0.505727i	0.302260	+	0.0169425i
$892$	6.81122			0.228056
$893$	−9.75799	−	7.08960i	−0.326539	−	0.237244i
$894$	0.0334782	−	0.103035i	0.00111968	−	0.00344601i
$895$	5.30310	+	16.3213i	0.177263	+	0.545560i
$896$	3.49997	−	2.54288i	0.116926	−	0.0849516i
$897$	−6.61095	+	4.80313i	−0.220733	+	0.160372i
$898$	−4.10575	−	12.6362i	−0.137010	−	0.421675i
$899$	−7.61306	+	23.4306i	−0.253910	+	0.781454i
$900$	−2.48895	−	1.80833i	−0.0829650	−	0.0602776i
$901$	−48.4344			−1.61359
$902$	5.77075	+	21.8541i	0.192145	+	0.727662i
$903$	12.9736			0.431734
$904$	−1.67124	−	1.21423i	−0.0555847	−	0.0403846i
$905$	8.93527	−	27.4999i	0.297019	−	0.914129i
$906$	−8.43640	−	25.9646i	−0.280281	−	0.862615i
$907$	12.7711	−	9.27875i	0.424058	−	0.308096i	−0.355211	−	0.934786i	$-0.615591\pi$
$907$	12.7711	−	9.27875i	0.424058	−	0.308096i	0.779268	+	0.626690i	$0.215591\pi$
$908$	8.15307	−	5.92356i	0.270569	−	0.196580i
$909$	4.26076	+	13.1133i	0.141320	+	0.434939i
$910$	−11.6935	+	35.9889i	−0.387635	+	1.19302i
$911$	−0.135518	−	0.0984595i	−0.00448991	−	0.00326211i	0.585538	−	0.810645i	$-0.300883\pi$
$911$	−0.135518	−	0.0984595i	−0.00448991	−	0.00326211i	−0.590028	+	0.807383i	$0.700883\pi$
$912$	1.25705			0.0416251
$913$	−5.95479	−	22.5511i	−0.197075	−	0.746332i
$914$	−26.0966			−0.863200
$915$	−17.5954	−	12.7838i	−0.581684	−	0.422619i
$916$	6.05007	−	18.6202i	0.199900	−	0.615229i
$917$	26.7666	+	82.3791i	0.883911	+	2.72040i
$918$	28.8847	−	20.9859i	0.953336	−	0.692639i
$919$	−41.7140	+	30.3070i	−1.37602	+	0.999737i	−0.378780	+	0.925487i	$0.623656\pi$
$919$	−41.7140	+	30.3070i	−1.37602	+	0.999737i	−0.997240	+	0.0742496i	$0.976344\pi$
$920$	−0.650661	−	2.00253i	−0.0214517	−	0.0660214i
$921$	−1.97096	+	6.06598i	−0.0649452	+	0.199881i
$922$	5.78583	+	4.20365i	0.190546	+	0.138440i
$923$	−19.5687			−0.644112
$924$	−18.0084	−	1.00942i	−0.592432	−	0.0332074i
$925$	10.3960			0.341819
$926$	4.33479	+	3.14941i	0.142450	+	0.103496i
$927$	−7.32727	+	22.5510i	−0.240659	+	0.740672i
$928$	−2.19776	−	6.76400i	−0.0721449	−	0.222039i
$929$	−20.5607	+	14.9382i	−0.674574	+	0.490107i	−0.871553	−	0.490301i	$-0.836887\pi$
$929$	−20.5607	+	14.9382i	−0.674574	+	0.490107i	0.196979	+	0.980408i	$0.436887\pi$
$930$	−5.92962	+	4.30812i	−0.194440	+	0.141269i
$931$	3.62045	+	11.1426i	0.118655	+	0.365184i
$932$	2.00277	−	6.16388i	0.0656028	−	0.201905i
$933$	−8.84052	−	6.42301i	−0.289426	−	0.210280i
$934$	37.6119			1.23070
$935$	−27.7975	−	22.6777i	−0.909074	−	0.741640i
$936$	7.37825			0.241166
$937$	−11.7694	−	8.55100i	−0.384491	−	0.279349i	0.378703	−	0.925518i	$-0.376370\pi$
$937$	−11.7694	−	8.55100i	−0.384491	−	0.279349i	−0.763194	+	0.646169i	$0.776370\pi$
$938$	−6.39290	+	19.6753i	−0.208736	+	0.642422i
$939$	6.17921	+	19.0176i	0.201651	+	0.620617i
$940$	−16.4247	+	11.9332i	−0.535715	+	0.389220i
$941$	−6.77356	+	4.92128i	−0.220812	+	0.160429i	−0.692692	−	0.721234i	$-0.743575\pi$
$941$	−6.77356	+	4.92128i	−0.220812	+	0.160429i	0.471880	+	0.881663i	$0.343575\pi$
$942$	1.18816	+	3.65677i	0.0387123	+	0.119144i
$943$	2.63446	−	8.10802i	0.0857897	−	0.264033i
$944$	11.0430	+	8.02323i	0.359420	+	0.261134i
$945$	−40.4577			−1.31609
$946$	−6.65134	+	4.28515i	−0.216254	+	0.139322i
$947$	−10.8678			−0.353155			−0.176577	−	0.984287i	$-0.556503\pi$
$947$	−10.8678			−0.353155			−0.176577	+	0.984287i	$0.556503\pi$
$948$	−1.52168	−	1.10557i	−0.0494219	−	0.0359071i
$949$	7.86305	−	24.2000i	0.255245	−	0.785564i
$950$	0.669585	+	2.06077i	0.0217242	+	0.0668602i
$951$	−3.05569	+	2.22009i	−0.0990876	+	0.0719914i
$952$	−22.4914	+	16.3410i	−0.728950	+	0.529613i
$953$	7.98735	+	24.5825i	0.258736	+	0.796306i	0.993071	+	0.117519i	$0.0374941\pi$
$953$	7.98735	+	24.5825i	0.258736	+	0.796306i	−0.734335	+	0.678787i	$0.762506\pi$
$954$	3.30689	−	10.1776i	0.107065	−	0.329511i
$955$	20.2547	+	14.7159i	0.655427	+	0.476196i
$956$	−20.6513			−0.667911
$957$	−10.7267	+	27.6432i	−0.346744	+	0.893578i
$958$	−21.3056			−0.688353
$959$	62.4178	+	45.3492i	2.01558	+	1.46440i
$960$	0.653840	−	2.01231i	0.0211026	−	0.0649472i
$961$	−5.87151	−	18.0706i	−0.189403	−	0.582924i
$962$	−20.1706	+	14.6548i	−0.650328	+	0.472491i
$963$	5.71537	−	4.15246i	0.184175	−	0.133811i
$964$	−4.05322	−	12.4745i	−0.130545	−	0.401777i
$965$	−8.26947	+	25.4508i	−0.266204	+	0.819290i
$966$	5.50367	+	3.99865i	0.177078	+	0.128654i
$967$	−44.2634			−1.42341			−0.711707	−	0.702476i	$-0.752078\pi$
$967$	−44.2634			−1.42341			−0.711707	+	0.702476i	$0.752078\pi$
$968$	9.56600	−	5.43062i	0.307463	−	0.174547i
$969$	−8.07801			−0.259503
$970$	4.71862	+	3.42828i	0.151506	+	0.110075i
$971$	4.26829	−	13.1365i	0.136976	−	0.421569i	−0.858916	−	0.512116i	$-0.828862\pi$
$971$	4.26829	−	13.1365i	0.136976	−	0.421569i	0.995892	+	0.0905475i	$0.0288617\pi$
$972$	4.09227	+	12.5947i	0.131259	+	0.403975i
$973$	−13.0574	+	9.48674i	−0.418600	+	0.304131i
$974$	−1.92479	+	1.39844i	−0.0616743	+	0.0448090i
$975$	−4.37397	−	13.4617i	−0.140079	−	0.431119i
$976$	3.17639	−	9.77591i	0.101674	−	0.312919i
$977$	−16.5808	−	12.0467i	−0.530468	−	0.385407i	0.290065	−	0.957007i	$-0.406323\pi$
$977$	−16.5808	−	12.0467i	−0.530468	−	0.385407i	−0.820533	+	0.571600i	$0.806323\pi$
$978$	−0.691187			−0.0221017
$979$	0.233203	−	0.600978i	0.00745321	−	0.0192074i
$980$	19.7205			0.629947
$981$	−3.13863	−	2.28035i	−0.100209	−	0.0728059i
$982$	3.89416	−	11.9850i	0.124268	−	0.382457i
$983$	−11.7124	−	36.0472i	−0.373569	−	1.14973i	−0.944439	−	0.328687i	$-0.893394\pi$
$983$	−11.7124	−	36.0472i	−0.373569	−	1.14973i	0.570870	−	0.821041i	$-0.306606\pi$
$984$	6.93079	−	5.03552i	0.220946	−	0.160526i
$985$	5.67934	−	4.12629i	0.180959	−	0.131474i
$986$	14.1231	+	43.4666i	0.449773	+	1.38426i
$987$	20.2696	−	62.3833i	0.645187	−	1.98568i
$988$	−4.20413	−	3.05448i	−0.133751	−	0.0971758i
$989$	2.98426			0.0948939
$990$	6.66317	−	4.29277i	0.211769	−	0.136433i
$991$	2.15975			0.0686067			0.0343033	−	0.999411i	$-0.489079\pi$
$991$	2.15975			0.0686067			0.0343033	+	0.999411i	$0.489079\pi$
$992$	−2.80245	−	2.03610i	−0.0889778	−	0.0646462i
$993$	−2.37006	+	7.29430i	−0.0752116	+	0.231477i
$994$	5.03423	+	15.4938i	0.159676	+	0.491433i
$995$	32.7895	−	23.8230i	1.03950	−	0.755238i
$996$	−7.15184	+	5.19612i	−0.226615	+	0.164645i
$997$	1.57586	+	4.84999i	0.0499079	+	0.153601i	0.972904	−	0.231207i	$-0.0742676\pi$
$997$	1.57586	+	4.84999i	0.0499079	+	0.153601i	−0.922997	+	0.384808i	$0.874268\pi$
$998$	8.94586	−	27.5325i	0.283176	−	0.871527i
$999$	−21.5655	−	15.6682i	−0.682302	−	0.495721i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.f.g.191.3	✓	16
11.3	even	5	inner	418.2.f.g.267.3	yes	16
11.5	even	5		4598.2.a.bw.1.6		8
11.6	odd	10		4598.2.a.bz.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.g.191.3	✓	16	1.1	even	1	trivial
418.2.f.g.267.3	yes	16	11.3	even	5	inner
4598.2.a.bw.1.6		8	11.5	even	5
4598.2.a.bz.1.6		8	11.6	odd	10

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.388450 - 1.19553i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.36174 + 0.989363i) q^{5} +(1.01697 - 0.738875i) q^{6} +(1.33687 + 4.11446i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(1.14866 + 0.834553i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.388450 - 1.19553i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.36174 + 0.989363i) q^{5} +(1.01697 - 0.738875i) q^{6} +(1.33687 + 4.11446i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(1.14866 + 0.834553i) q^{9} -1.68320 q^{10} +(-1.19982 + 3.09200i) q^{11} +1.25705 q^{12} +(-4.20413 - 3.05448i) q^{13} +(-1.33687 + 4.11446i) q^{14} +(0.653840 + 2.01231i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(5.19888 - 3.77721i) q^{17} +(0.438750 + 1.35034i) q^{18} +(0.309017 - 0.951057i) q^{19} +(-1.36174 - 0.989363i) q^{20} +5.43825 q^{21} +(-2.78810 + 1.79624i) q^{22} +1.25094 q^{23} +(1.01697 + 0.738875i) q^{24} +(-0.669585 + 2.06077i) q^{25} +(-1.60583 - 4.94225i) q^{26} +(4.49485 - 3.26570i) q^{27} +(-3.49997 + 2.54288i) q^{28} +(2.19776 + 6.76400i) q^{29} +(-0.653840 + 2.01231i) q^{30} +(2.80245 + 2.03610i) q^{31} -1.00000 q^{32} +(3.23049 + 2.63550i) q^{33} +6.42617 q^{34} +(-5.89117 - 4.28018i) q^{35} +(-0.438750 + 1.35034i) q^{36} +(-1.48261 - 4.56300i) q^{37} +(0.809017 - 0.587785i) q^{38} +(-5.28479 + 3.83963i) q^{39} +(-0.520139 - 1.60082i) q^{40} +(2.10599 - 6.48156i) q^{41} +(4.39964 + 3.19652i) q^{42} +2.38562 q^{43} +(-3.31143 - 0.185614i) q^{44} -2.38986 q^{45} +(1.01203 + 0.735283i) q^{46} +(3.72722 - 11.4712i) q^{47} +(0.388450 + 1.19553i) q^{48} +(-9.47846 + 6.88650i) q^{49} +(-1.75300 + 1.27363i) q^{50} +(-2.49624 - 7.68264i) q^{51} +(1.60583 - 4.94225i) q^{52} +(-6.09761 - 4.43018i) q^{53} +5.55594 q^{54} +(-1.42527 - 5.39755i) q^{55} -4.32620 q^{56} +(-1.01697 - 0.738875i) q^{57} +(-2.19776 + 6.76400i) q^{58} +(-4.21806 - 12.9819i) q^{59} +(-1.71178 + 1.24368i) q^{60} +(-8.31589 + 6.04185i) q^{61} +(1.07044 + 3.29447i) q^{62} +(-1.89812 + 5.84182i) q^{63} +(-0.809017 - 0.587785i) q^{64} +8.74692 q^{65} +(1.06442 + 4.03100i) q^{66} +4.78199 q^{67} +(5.19888 + 3.77721i) q^{68} +(0.485926 - 1.49553i) q^{69} +(-2.25023 - 6.92548i) q^{70} +(3.04650 - 2.21341i) q^{71} +(-1.14866 + 0.834553i) q^{72} +(1.51312 + 4.65690i) q^{73} +(1.48261 - 4.56300i) q^{74} +(2.20360 + 1.60101i) q^{75} +1.00000 q^{76} +(-14.3259 - 0.803004i) q^{77} -6.53237 q^{78} +(-1.21052 - 0.879492i) q^{79} +(0.520139 - 1.60082i) q^{80} +(-0.841952 - 2.59126i) q^{81} +(5.51354 - 4.00582i) q^{82} +(-5.68939 + 4.13358i) q^{83} +(1.68051 + 5.17208i) q^{84} +(-3.34250 + 10.2872i) q^{85} +(1.93001 + 1.40223i) q^{86} +8.94025 q^{87} +(-2.56990 - 2.09657i) q^{88} -0.194366 q^{89} +(-1.93344 - 1.40472i) q^{90} +(6.94716 - 21.3812i) q^{91} +(0.386561 + 1.18971i) q^{92} +(3.52282 - 2.55948i) q^{93} +(9.75799 - 7.08960i) q^{94} +(0.520139 + 1.60082i) q^{95} +(-0.388450 + 1.19553i) q^{96} +(-2.80336 - 2.03676i) q^{97} -11.7160 q^{98} +(-3.95862 + 2.55035i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} + q^{3} - 4 q^{4} + q^{5} - q^{6} - 12 q^{7} + 4 q^{8} - q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 + q^3 - 4 * q^4 + q^5 - q^6 - 12 * q^7 + 4 * q^8 - q^9	\( 16 q + 4 q^{2} + q^{3} - 4 q^{4} + q^{5} - q^{6} - 12 q^{7} + 4 q^{8} - q^{9} + 4 q^{10} + 4 q^{11} - 4 q^{12} - 12 q^{13} + 12 q^{14} - 10 q^{15} - 4 q^{16} + 6 q^{17} + q^{18} - 4 q^{19} + q^{20} + 14 q^{21} - 9 q^{22} - 26 q^{23} - q^{24} + 33 q^{25} - 3 q^{26} + 13 q^{27} - 2 q^{28} + 10 q^{30} + 11 q^{31} - 16 q^{32} - 31 q^{33} - 6 q^{34} - 4 q^{35} - q^{36} + 4 q^{38} + 12 q^{39} - q^{40} - 7 q^{41} + 6 q^{42} + 66 q^{43} - 11 q^{44} - 42 q^{45} - 24 q^{46} + 47 q^{47} + q^{48} + 24 q^{49} + 37 q^{50} - 41 q^{51} + 3 q^{52} + 15 q^{53} - 8 q^{54} - 9 q^{55} - 28 q^{56} + q^{57} - 18 q^{59} + 5 q^{60} - 43 q^{61} + 9 q^{62} - 37 q^{63} - 4 q^{64} + 52 q^{65} - 39 q^{66} - 50 q^{67} + 6 q^{68} + 81 q^{69} - 11 q^{70} - 5 q^{71} + q^{72} - 13 q^{73} + 39 q^{75} + 16 q^{76} - 10 q^{77} - 22 q^{78} + 5 q^{79} + q^{80} + 2 q^{82} + 7 q^{83} - q^{84} - 29 q^{85} + 29 q^{86} + 4 q^{87} - 4 q^{88} - 28 q^{89} - 18 q^{90} - 11 q^{92} - 5 q^{93} + 28 q^{94} + q^{95} - q^{96} - 11 q^{97} - 24 q^{98} + 43 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + q^3 - 4 * q^4 + q^5 - q^6 - 12 * q^7 + 4 * q^8 - q^9 + 4 * q^10 + 4 * q^11 - 4 * q^12 - 12 * q^13 + 12 * q^14 - 10 * q^15 - 4 * q^16 + 6 * q^17 + q^18 - 4 * q^19 + q^20 + 14 * q^21 - 9 * q^22 - 26 * q^23 - q^24 + 33 * q^25 - 3 * q^26 + 13 * q^27 - 2 * q^28 + 10 * q^30 + 11 * q^31 - 16 * q^32 - 31 * q^33 - 6 * q^34 - 4 * q^35 - q^36 + 4 * q^38 + 12 * q^39 - q^40 - 7 * q^41 + 6 * q^42 + 66 * q^43 - 11 * q^44 - 42 * q^45 - 24 * q^46 + 47 * q^47 + q^48 + 24 * q^49 + 37 * q^50 - 41 * q^51 + 3 * q^52 + 15 * q^53 - 8 * q^54 - 9 * q^55 - 28 * q^56 + q^57 - 18 * q^59 + 5 * q^60 - 43 * q^61 + 9 * q^62 - 37 * q^63 - 4 * q^64 + 52 * q^65 - 39 * q^66 - 50 * q^67 + 6 * q^68 + 81 * q^69 - 11 * q^70 - 5 * q^71 + q^72 - 13 * q^73 + 39 * q^75 + 16 * q^76 - 10 * q^77 - 22 * q^78 + 5 * q^79 + q^80 + 2 * q^82 + 7 * q^83 - q^84 - 29 * q^85 + 29 * q^86 + 4 * q^87 - 4 * q^88 - 28 * q^89 - 18 * q^90 - 11 * q^92 - 5 * q^93 + 28 * q^94 + q^95 - q^96 - 11 * q^97 - 24 * q^98 + 43 * q^99

Introduction

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