LMFDB - Embedded newform 406.2.e.a.291.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [406,2,Mod(233,406)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(406, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("406.233");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 406 = 2 \cdot 7 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	406.e (of order $3$, degree $2$, 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:	$3.24192632206$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.3118758597603.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{8} - 16x^{6} - 34x^{5} + 43x^{4} + 155x^{3} + 199x^{2} + 124x + 43 $ x^10 - 4x^8 - 16x^6 - 34x^5 + 43x^4 + 155x^3 + 199x^2 + 124*x + 43
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			291.3
Root			$-0.676693 + 0.583217i$ of defining polynomial
Character	$\chi$	$=$	406.291
Dual form			406.2.e.a.233.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.257545 + 0.446080i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.84343 - 3.19291i) q^{5} +0.515089 q^{6} +(-2.63485 - 0.239979i) q^{7} +1.00000 q^{8} +(1.36734 + 2.36831i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.257545 + 0.446080i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.84343 - 3.19291i) q^{5} +0.515089 q^{6} +(-2.63485 - 0.239979i) q^{7} +1.00000 q^{8} +(1.36734 + 2.36831i) q^{9} +(-1.84343 + 3.19291i) q^{10} +(-3.22586 + 5.58735i) q^{11} +(-0.257545 - 0.446080i) q^{12} +2.84856 q^{13} +(1.10959 + 2.40183i) q^{14} +1.89906 q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.767706 - 1.32971i) q^{17} +(1.36734 - 2.36831i) q^{18} +(1.95949 + 3.39393i) q^{19} +3.68685 q^{20} +(0.785640 - 1.11355i) q^{21} +6.45172 q^{22} +(-0.190446 - 0.329862i) q^{23} +(-0.257545 + 0.446080i) q^{24} +(-4.29645 + 7.44167i) q^{25} +(-1.42428 - 2.46692i) q^{26} -2.95387 q^{27} +(1.52525 - 2.16185i) q^{28} -1.00000 q^{29} +(-0.949529 - 1.64463i) q^{30} +(-3.99203 + 6.91439i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.66160 - 2.87798i) q^{33} -1.53541 q^{34} +(4.09091 + 8.85521i) q^{35} -2.73468 q^{36} +(3.73448 + 6.46831i) q^{37} +(1.95949 - 3.39393i) q^{38} +(-0.733630 + 1.27069i) q^{39} +(-1.84343 - 3.19291i) q^{40} -4.98713 q^{41} +(-1.35718 - 0.123611i) q^{42} -11.5673 q^{43} +(-3.22586 - 5.58735i) q^{44} +(5.04119 - 8.73160i) q^{45} +(-0.190446 + 0.329862i) q^{46} +(-3.92931 - 6.80577i) q^{47} +0.515089 q^{48} +(6.88482 + 1.26462i) q^{49} +8.59290 q^{50} +(0.395437 + 0.684917i) q^{51} +(-1.42428 + 2.46692i) q^{52} +(0.610931 - 1.05816i) q^{53} +(1.47694 + 2.55813i) q^{54} +23.7865 q^{55} +(-2.63485 - 0.239979i) q^{56} -2.01862 q^{57} +(0.500000 + 0.866025i) q^{58} +(0.348355 - 0.603368i) q^{59} +(-0.949529 + 1.64463i) q^{60} +(1.55050 + 2.68555i) q^{61} +7.98405 q^{62} +(-3.03439 - 6.56825i) q^{63} +1.00000 q^{64} +(-5.25111 - 9.09519i) q^{65} +(-1.66160 + 2.87798i) q^{66} +(3.61247 - 6.25698i) q^{67} +(0.767706 + 1.32971i) q^{68} +0.196193 q^{69} +(5.62338 - 7.97044i) q^{70} -13.2927 q^{71} +(1.36734 + 2.36831i) q^{72} +(-7.47563 + 12.9482i) q^{73} +(3.73448 - 6.46831i) q^{74} +(-2.21305 - 3.83312i) q^{75} -3.91898 q^{76} +(9.84048 - 13.9477i) q^{77} +1.46726 q^{78} +(-2.56795 - 4.44782i) q^{79} +(-1.84343 + 3.19291i) q^{80} +(-3.34127 + 5.78725i) q^{81} +(2.49356 + 4.31898i) q^{82} +12.8154 q^{83} +(0.571540 + 1.23716i) q^{84} -5.66084 q^{85} +(5.78365 + 10.0176i) q^{86} +(0.257545 - 0.446080i) q^{87} +(-3.22586 + 5.58735i) q^{88} +(-4.69815 - 8.13744i) q^{89} -10.0824 q^{90} +(-7.50551 - 0.683594i) q^{91} +0.380892 q^{92} +(-2.05625 - 3.56153i) q^{93} +(-3.92931 + 6.80577i) q^{94} +(7.22435 - 12.5129i) q^{95} +(-0.257545 - 0.446080i) q^{96} -2.56729 q^{97} +(-2.34722 - 6.59474i) q^{98} -17.6434 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{2} - 3 q^{3} - 5 q^{4} - 7 q^{5} + 6 q^{6} - 3 q^{7} + 10 q^{8} - 8 q^{9}+O(q^{10}) $ 10 * q - 5 * q^2 - 3 * q^3 - 5 * q^4 - 7 * q^5 + 6 * q^6 - 3 * q^7 + 10 * q^8 - 8 * q^9	\( 10 q - 5 q^{2} - 3 q^{3} - 5 q^{4} - 7 q^{5} + 6 q^{6} - 3 q^{7} + 10 q^{8} - 8 q^{9} - 7 q^{10} - 3 q^{12} + 20 q^{13} + 3 q^{14} - 20 q^{15} - 5 q^{16} - 8 q^{17} - 8 q^{18} - 2 q^{19} + 14 q^{20} + 19 q^{21} - q^{23} - 3 q^{24} - 12 q^{25} - 10 q^{26} + 30 q^{27} - 10 q^{29} + 10 q^{30} - 11 q^{31} - 5 q^{32} - 9 q^{33} + 16 q^{34} + 10 q^{35} + 16 q^{36} + 8 q^{37} - 2 q^{38} - 18 q^{39} - 7 q^{40} + 46 q^{41} - 8 q^{42} - 6 q^{43} - 4 q^{45} - q^{46} - 16 q^{47} + 6 q^{48} - 11 q^{49} + 24 q^{50} - 7 q^{51} - 10 q^{52} - 7 q^{53} - 15 q^{54} + 12 q^{55} - 3 q^{56} - 68 q^{57} + 5 q^{58} + 9 q^{59} + 10 q^{60} - 15 q^{61} + 22 q^{62} - 3 q^{63} + 10 q^{64} - 5 q^{65} - 9 q^{66} + 4 q^{67} - 8 q^{68} + 28 q^{69} + 4 q^{70} - 44 q^{71} - 8 q^{72} + 8 q^{74} + 34 q^{75} + 4 q^{76} + 39 q^{77} + 36 q^{78} + 13 q^{79} - 7 q^{80} - 17 q^{81} - 23 q^{82} + 56 q^{83} - 11 q^{84} - 14 q^{85} + 3 q^{86} + 3 q^{87} - 17 q^{89} + 8 q^{90} + 6 q^{91} + 2 q^{92} - 17 q^{93} - 16 q^{94} + 9 q^{95} - 3 q^{96} + 84 q^{97} - 20 q^{98} - 84 q^{99}+O(q^{100}) \) 10 * q - 5 * q^2 - 3 * q^3 - 5 * q^4 - 7 * q^5 + 6 * q^6 - 3 * q^7 + 10 * q^8 - 8 * q^9 - 7 * q^10 - 3 * q^12 + 20 * q^13 + 3 * q^14 - 20 * q^15 - 5 * q^16 - 8 * q^17 - 8 * q^18 - 2 * q^19 + 14 * q^20 + 19 * q^21 - q^23 - 3 * q^24 - 12 * q^25 - 10 * q^26 + 30 * q^27 - 10 * q^29 + 10 * q^30 - 11 * q^31 - 5 * q^32 - 9 * q^33 + 16 * q^34 + 10 * q^35 + 16 * q^36 + 8 * q^37 - 2 * q^38 - 18 * q^39 - 7 * q^40 + 46 * q^41 - 8 * q^42 - 6 * q^43 - 4 * q^45 - q^46 - 16 * q^47 + 6 * q^48 - 11 * q^49 + 24 * q^50 - 7 * q^51 - 10 * q^52 - 7 * q^53 - 15 * q^54 + 12 * q^55 - 3 * q^56 - 68 * q^57 + 5 * q^58 + 9 * q^59 + 10 * q^60 - 15 * q^61 + 22 * q^62 - 3 * q^63 + 10 * q^64 - 5 * q^65 - 9 * q^66 + 4 * q^67 - 8 * q^68 + 28 * q^69 + 4 * q^70 - 44 * q^71 - 8 * q^72 + 8 * q^74 + 34 * q^75 + 4 * q^76 + 39 * q^77 + 36 * q^78 + 13 * q^79 - 7 * q^80 - 17 * q^81 - 23 * q^82 + 56 * q^83 - 11 * q^84 - 14 * q^85 + 3 * q^86 + 3 * q^87 - 17 * q^89 + 8 * q^90 + 6 * q^91 + 2 * q^92 - 17 * q^93 - 16 * q^94 + 9 * q^95 - 3 * q^96 + 84 * q^97 - 20 * q^98 - 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/406\mathbb{Z}\right)^\times$.

$n$	$59$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.257545	+	0.446080i	−0.148693	+	0.257545i	−0.930745	−	0.365669i	$-0.880840\pi$
$3$	−0.257545	+	0.446080i	−0.148693	+	0.257545i	0.782051	+	0.623214i	$0.214173\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.84343	−	3.19291i	−0.824406	−	1.42791i	−0.902373	−	0.430957i	$-0.858176\pi$
$5$	−1.84343	−	3.19291i	−0.824406	−	1.42791i	0.0779667	−	0.996956i	$-0.475157\pi$
$6$	0.515089			0.210284
$7$	−2.63485	−	0.239979i	−0.995878	−	0.0907036i
$7$	−2.63485	−	0.239979i	−0.995878	−	0.0907036i
$8$	1.00000			0.353553
$9$	1.36734	+	2.36831i	0.455781	+	0.789435i
$10$	−1.84343	+	3.19291i	−0.582943	+	1.00969i
$11$	−3.22586	+	5.58735i	−0.972633	+	1.68465i	−0.285098	+	0.958499i	$0.592026\pi$
$11$	−3.22586	+	5.58735i	−0.972633	+	1.68465i	−0.687535	+	0.726151i	$0.741307\pi$
$12$	−0.257545	−	0.446080i	−0.0743467	−	0.128772i
$13$	2.84856			0.790048			0.395024	−	0.918671i	$-0.370736\pi$
$13$	2.84856			0.790048			0.395024	+	0.918671i	$0.370736\pi$
$14$	1.10959	+	2.40183i	0.296552	+	0.641917i
$15$	1.89906			0.490335
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.767706	−	1.32971i	0.186196	−	0.322501i	−0.757783	−	0.652507i	$-0.773717\pi$
$17$	0.767706	−	1.32971i	0.186196	−	0.322501i	0.943979	+	0.330006i	$0.107051\pi$
$18$	1.36734	−	2.36831i	0.322286	−	0.558215i
$19$	1.95949	+	3.39393i	0.449537	+	0.778622i	0.998356	−	0.0573198i	$-0.0182555\pi$
$19$	1.95949	+	3.39393i	0.449537	+	0.778622i	−0.548818	+	0.835942i	$0.684922\pi$
$20$	3.68685			0.824406
$21$	0.785640	−	1.11355i	0.171441	−	0.242996i
$22$	6.45172			1.37551
$23$	−0.190446	−	0.329862i	−0.0397107	−	0.0687810i	0.845487	−	0.533996i	$-0.179310\pi$
$23$	−0.190446	−	0.329862i	−0.0397107	−	0.0687810i	−0.885198	+	0.465215i	$0.845977\pi$
$24$	−0.257545	+	0.446080i	−0.0525711	+	0.0910557i
$25$	−4.29645	+	7.44167i	−0.859290	+	1.48833i
$26$	−1.42428	−	2.46692i	−0.279324	−	0.483803i
$27$	−2.95387			−0.568473
$28$	1.52525	−	2.16185i	0.288245	−	0.408552i
$29$	−1.00000			−0.185695
$29$	−1.00000			−0.185695
$30$	−0.949529	−	1.64463i	−0.173360	−	0.300268i
$31$	−3.99203	+	6.91439i	−0.716989	+	1.24186i	0.245198	+	0.969473i	$0.421147\pi$
$31$	−3.99203	+	6.91439i	−0.716989	+	1.24186i	−0.962187	+	0.272388i	$0.912186\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−1.66160	−	2.87798i	−0.289248	−	0.500993i
$34$	−1.53541			−0.263321
$35$	4.09091	+	8.85521i	0.691491	+	1.49680i
$36$	−2.73468			−0.455781
$37$	3.73448	+	6.46831i	0.613945	+	1.06338i	0.990569	+	0.137017i	$0.0437516\pi$
$37$	3.73448	+	6.46831i	0.613945	+	1.06338i	−0.376624	+	0.926366i	$0.622915\pi$
$38$	1.95949	−	3.39393i	0.317871	−	0.550569i
$39$	−0.733630	+	1.27069i	−0.117475	+	0.203472i
$40$	−1.84343	−	3.19291i	−0.291471	−	0.504843i
$41$	−4.98713			−0.778859			−0.389429	−	0.921056i	$-0.627328\pi$
$41$	−4.98713			−0.778859			−0.389429	+	0.921056i	$0.627328\pi$
$42$	−1.35718	−	0.123611i	−0.209417	−	0.0190735i
$43$	−11.5673			−1.76400			−0.881998	−	0.471254i	$-0.843802\pi$
$43$	−11.5673			−1.76400			−0.881998	+	0.471254i	$0.843802\pi$
$44$	−3.22586	−	5.58735i	−0.486316	−	0.842325i
$45$	5.04119	−	8.73160i	0.751496	−	1.30163i
$46$	−0.190446	+	0.329862i	−0.0280797	+	0.0486355i
$47$	−3.92931	−	6.80577i	−0.573149	−	0.992723i	−0.996240	−	0.0866358i	$-0.972388\pi$
$47$	−3.92931	−	6.80577i	−0.573149	−	0.992723i	0.423091	−	0.906087i	$-0.360945\pi$
$48$	0.515089			0.0743467
$49$	6.88482	+	1.26462i	0.983546	+	0.180659i
$50$	8.59290			1.21522
$51$	0.395437	+	0.684917i	0.0553723	+	0.0959076i
$52$	−1.42428	+	2.46692i	−0.197512	+	0.342101i
$53$	0.610931	−	1.05816i	0.0839179	−	0.145350i	−0.821012	−	0.570911i	$-0.806590\pi$
$53$	0.610931	−	1.05816i	0.0839179	−	0.145350i	0.904930	+	0.425561i	$0.139923\pi$
$54$	1.47694	+	2.55813i	0.200986	+	0.348117i
$55$	23.7865			3.20738
$56$	−2.63485	−	0.239979i	−0.352096	−	0.0320686i
$57$	−2.01862			−0.267373
$58$	0.500000	+	0.866025i	0.0656532	+	0.113715i
$59$	0.348355	−	0.603368i	0.0453519	−	0.0785519i	−0.842458	−	0.538761i	$-0.818892\pi$
$59$	0.348355	−	0.603368i	0.0453519	−	0.0785519i	0.887810	+	0.460210i	$0.152226\pi$
$60$	−0.949529	+	1.64463i	−0.122584	+	0.212321i
$61$	1.55050	+	2.68555i	0.198521	+	0.343849i	0.948049	−	0.318124i	$-0.103053\pi$
$61$	1.55050	+	2.68555i	0.198521	+	0.343849i	−0.749528	+	0.661973i	$0.769719\pi$
$62$	7.98405			1.01398
$63$	−3.03439	−	6.56825i	−0.382297	−	0.827522i
$64$	1.00000			0.125000
$65$	−5.25111	−	9.09519i	−0.651320	−	1.12812i
$66$	−1.66160	+	2.87798i	−0.204529	+	0.354255i
$67$	3.61247	−	6.25698i	0.441333	−	0.764412i	−0.556455	−	0.830878i	$-0.687839\pi$
$67$	3.61247	−	6.25698i	0.441333	−	0.764412i	0.997789	+	0.0664656i	$0.0211723\pi$
$68$	0.767706	+	1.32971i	0.0930980	+	0.161251i
$69$	0.196193			0.0236189
$70$	5.62338	−	7.97044i	0.672122	−	0.952650i
$71$	−13.2927			−1.57755			−0.788776	−	0.614681i	$-0.789285\pi$
$71$	−13.2927			−1.57755			−0.788776	+	0.614681i	$0.789285\pi$
$72$	1.36734	+	2.36831i	0.161143	+	0.279107i
$73$	−7.47563	+	12.9482i	−0.874956	+	1.51547i	−0.0181471	+	0.999835i	$0.505777\pi$
$73$	−7.47563	+	12.9482i	−0.874956	+	1.51547i	−0.856809	+	0.515634i	$0.827557\pi$
$74$	3.73448	−	6.46831i	0.434125	−	0.751926i
$75$	−2.21305	−	3.83312i	−0.255541	−	0.442611i
$76$	−3.91898			−0.449537
$77$	9.84048	−	13.9477i	1.12143	−	1.58948i
$78$	1.46726			0.166135
$79$	−2.56795	−	4.44782i	−0.288917	−	0.500419i	0.684635	−	0.728886i	$-0.259962\pi$
$79$	−2.56795	−	4.44782i	−0.288917	−	0.500419i	−0.973551	+	0.228468i	$0.926628\pi$
$80$	−1.84343	+	3.19291i	−0.206101	+	0.356978i
$81$	−3.34127	+	5.78725i	−0.371252	+	0.643028i
$82$	2.49356	+	4.31898i	0.275368	+	0.476952i
$83$	12.8154			1.40667			0.703334	−	0.710859i	$-0.251694\pi$
$83$	12.8154			1.40667			0.703334	+	0.710859i	$0.251694\pi$
$84$	0.571540	+	1.23716i	0.0623601	+	0.134985i
$85$	−5.66084			−0.614005
$86$	5.78365	+	10.0176i	0.623667	+	1.08022i
$87$	0.257545	−	0.446080i	0.0276117	−	0.0478248i
$88$	−3.22586	+	5.58735i	−0.343878	+	0.595614i
$89$	−4.69815	−	8.13744i	−0.498003	−	0.862566i	0.501994	−	0.864871i	$-0.332600\pi$
$89$	−4.69815	−	8.13744i	−0.498003	−	0.862566i	−0.999997	+	0.00230444i	$0.999266\pi$
$90$	−10.0824			−1.06278
$91$	−7.50551	−	0.683594i	−0.786791	−	0.0716601i
$92$	0.380892			0.0397107
$93$	−2.05625	−	3.56153i	−0.213223	−	0.369313i
$94$	−3.92931	+	6.80577i	−0.405277	+	0.701961i
$95$	7.22435	−	12.5129i	0.741203	−	1.28380i
$96$	−0.257545	−	0.446080i	−0.0262855	−	0.0455279i
$97$	−2.56729			−0.260669			−0.130334	−	0.991470i	$-0.541605\pi$
$97$	−2.56729			−0.260669			−0.130334	+	0.991470i	$0.541605\pi$
$98$	−2.34722	−	6.59474i	−0.237105	−	0.666169i
$99$	−17.6434			−1.77323
$100$	−4.29645	−	7.44167i	−0.429645	−	0.744167i
$101$	5.01718	−	8.69001i	0.499228	−	0.864688i	−0.500772	−	0.865579i	$-0.666950\pi$
$101$	5.01718	−	8.69001i	0.499228	−	0.864688i	1.00000		0.000891361i	$0.000283729\pi$
$102$	0.395437	−	0.684917i	0.0391541	−	0.0678169i
$103$	4.67177	+	8.09174i	0.460323	+	0.797302i	0.998977	−	0.0452246i	$-0.0144003\pi$
$103$	4.67177	+	8.09174i	0.460323	+	0.797302i	−0.538654	+	0.842527i	$0.681067\pi$
$104$	2.84856			0.279324
$105$	−5.00373	−	0.455734i	−0.488314	−	0.0444751i
$106$	−1.22186			−0.118678
$107$	5.89950	+	10.2182i	0.570327	+	0.987835i	0.996532	+	0.0832083i	$0.0265167\pi$
$107$	5.89950	+	10.2182i	0.570327	+	0.987835i	−0.426206	+	0.904626i	$0.640150\pi$
$108$	1.47694	−	2.55813i	0.142118	−	0.246156i
$109$	3.02724	−	5.24333i	0.289957	−	0.502219i	−0.683843	−	0.729630i	$-0.739692\pi$
$109$	3.02724	−	5.24333i	0.289957	−	0.502219i	0.973799	+	0.227410i	$0.0730258\pi$
$110$	−11.8933	−	20.5997i	−1.13398	−	1.96411i
$111$	−3.84718			−0.365158
$112$	1.10959	+	2.40183i	0.104847	+	0.226952i
$113$	−3.50810			−0.330015			−0.165007	−	0.986292i	$-0.552765\pi$
$113$	−3.50810			−0.330015			−0.165007	+	0.986292i	$0.552765\pi$
$114$	1.00931	+	1.74818i	0.0945306	+	0.163732i
$115$	−0.702146	+	1.21615i	−0.0654755	+	0.113407i
$116$	0.500000	−	0.866025i	0.0464238	−	0.0804084i
$117$	3.89495	+	6.74625i	0.360088	+	0.623691i
$118$	−0.696710			−0.0641373
$119$	−2.34189	+	3.31934i	−0.214681	+	0.304283i
$120$	1.89906			0.173360
$121$	−15.3123	−	26.5217i	−1.39203	−	2.41107i
$122$	1.55050	−	2.68555i	0.140376	−	0.243138i
$123$	1.28441	−	2.22466i	0.115811	−	0.200591i
$124$	−3.99203	−	6.91439i	−0.358494	−	0.620931i
$125$	13.2465			1.18480
$126$	−4.17108	+	5.91198i	−0.371589	+	0.526681i
$127$	2.64032			0.234291			0.117145	−	0.993115i	$-0.462626\pi$
$127$	2.64032			0.234291			0.117145	+	0.993115i	$0.462626\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	2.97909	−	5.15994i	0.262294	−	0.454307i
$130$	−5.25111	+	9.09519i	−0.460553	+	0.797701i
$131$	5.37843	+	9.31572i	0.469916	+	0.813918i	0.999408	−	0.0343963i	$-0.0109509\pi$
$131$	5.37843	+	9.31572i	0.469916	+	0.813918i	−0.529492	+	0.848315i	$0.677618\pi$
$132$	3.32321			0.289248
$133$	−4.34848	−	9.41273i	−0.377061	−	0.816187i
$134$	−7.22494			−0.624140
$135$	5.44525	+	9.43145i	0.468652	+	0.811730i
$136$	0.767706	−	1.32971i	0.0658303	−	0.114021i
$137$	−4.23619	+	7.33730i	−0.361922	+	0.626868i	−0.988277	−	0.152670i	$-0.951213\pi$
$137$	−4.23619	+	7.33730i	−0.361922	+	0.626868i	0.626355	+	0.779538i	$0.284546\pi$
$138$	−0.0980966	−	0.169908i	−0.00835054	−	0.0144636i
$139$	−2.40081			−0.203634			−0.101817	−	0.994803i	$-0.532466\pi$
$139$	−2.40081			−0.203634			−0.101817	+	0.994803i	$0.532466\pi$
$140$	−9.71429	−	0.884768i	−0.821008	−	0.0747766i
$141$	4.04789			0.340894
$142$	6.64634	+	11.5118i	0.557749	+	0.966049i
$143$	−9.18904	+	15.9159i	−0.768426	+	1.33095i
$144$	1.36734	−	2.36831i	0.113945	−	0.197359i
$145$	1.84343	+	3.19291i	0.153088	+	0.265157i
$146$	14.9513			1.23738
$147$	−2.33727	+	2.74549i	−0.192775	+	0.226444i
$148$	−7.46896			−0.613945
$149$	5.18750	+	8.98502i	0.424977	+	0.736081i	0.996418	−	0.0845614i	$-0.0269489\pi$
$149$	5.18750	+	8.98502i	0.424977	+	0.736081i	−0.571441	+	0.820643i	$0.693616\pi$
$150$	−2.21305	+	3.83312i	−0.180695	+	0.312973i
$151$	−3.37843	+	5.85162i	−0.274933	+	0.476198i	−0.970118	−	0.242633i	$-0.921989\pi$
$151$	−3.37843	+	5.85162i	−0.274933	+	0.476198i	0.695185	+	0.718831i	$0.255322\pi$
$152$	1.95949	+	3.39393i	0.158936	+	0.275284i
$153$	4.19887			0.339458
$154$	−16.9993	−	1.54828i	−1.36984	−	0.124764i
$155$	29.4360			2.36436
$156$	−0.733630	−	1.27069i	−0.0587374	−	0.101736i
$157$	1.94860	−	3.37507i	0.155515	−	0.269360i	−0.777731	−	0.628597i	$-0.783630\pi$
$157$	1.94860	−	3.37507i	0.155515	−	0.269360i	0.933246	+	0.359237i	$0.116963\pi$
$158$	−2.56795	+	4.44782i	−0.204295	+	0.353849i
$159$	0.314684	+	0.545049i	0.0249561	+	0.0432252i
$160$	3.68685			0.291471
$161$	0.422636	+	0.914838i	0.0333083	+	0.0720994i
$162$	6.68254			0.525030
$163$	−0.194658	−	0.337157i	−0.0152468	−	0.0264082i	0.858301	−	0.513146i	$-0.171520\pi$
$163$	−0.194658	−	0.337157i	−0.0152468	−	0.0264082i	−0.873548	+	0.486738i	$0.838187\pi$
$164$	2.49356	−	4.31898i	0.194715	−	0.337256i
$165$	−6.12609	+	10.6107i	−0.476916	+	0.826042i
$166$	−6.40768	−	11.0984i	−0.497333	−	0.861405i
$167$	10.3042			0.797362			0.398681	−	0.917090i	$-0.369468\pi$
$167$	10.3042			0.797362			0.398681	+	0.917090i	$0.369468\pi$
$168$	0.785640	−	1.11355i	0.0606134	−	0.0859120i
$169$	−4.88572			−0.375825
$170$	2.83042	+	4.90243i	0.217083	+	0.375999i
$171$	−5.35858	+	9.28133i	−0.409781	+	0.709761i
$172$	5.78365	−	10.0176i	0.440999	−	0.763832i
$173$	−11.5204	−	19.9538i	−0.875876	−	1.51706i	−0.855826	−	0.517263i	$-0.826951\pi$
$173$	−11.5204	−	19.9538i	−0.875876	−	1.51706i	−0.0200499	−	0.999799i	$-0.506383\pi$
$174$	−0.515089			−0.0390488
$175$	13.1063	−	18.5766i	0.990745	−	1.40426i
$176$	6.45172			0.486316
$177$	0.179434	+	0.310788i	0.0134871	+	0.0233603i
$178$	−4.69815	+	8.13744i	−0.352141	+	0.609927i
$179$	3.34900	−	5.80064i	0.250316	−	0.433560i	−0.713297	−	0.700862i	$-0.752799\pi$
$179$	3.34900	−	5.80064i	0.250316	−	0.433560i	0.963613	+	0.267302i	$0.0861321\pi$
$180$	5.04119	+	8.73160i	0.375748	+	0.650815i
$181$	13.2453			0.984513			0.492256	−	0.870450i	$-0.336172\pi$
$181$	13.2453			0.984513			0.492256	+	0.870450i	$0.336172\pi$
$182$	3.16074	+	6.84176i	0.234290	+	0.507145i
$183$	−1.59729			−0.118075
$184$	−0.190446	−	0.329862i	−0.0140399	−	0.0243177i
$185$	13.7685	−	23.8477i	1.01228	−	1.75332i
$186$	−2.05625	+	3.56153i	−0.150771	+	0.261144i
$187$	4.95302	+	8.57889i	0.362201	+	0.627350i
$188$	7.85862			0.573149
$189$	7.78300	+	0.708868i	0.566130	+	0.0515625i
$190$	−14.4487			−1.04822
$191$	10.1673	+	17.6103i	0.735681	+	1.27424i	0.954424	+	0.298454i	$0.0964711\pi$
$191$	10.1673	+	17.6103i	0.735681	+	1.27424i	−0.218743	+	0.975783i	$0.570196\pi$
$192$	−0.257545	+	0.446080i	−0.0185867	+	0.0321931i
$193$	−6.60202	+	11.4350i	−0.475224	+	0.823112i	−0.999597	−	0.0283762i	$-0.990966\pi$
$193$	−6.60202	+	11.4350i	−0.475224	+	0.823112i	0.524373	+	0.851489i	$0.324300\pi$
$194$	1.28365	+	2.22334i	0.0921604	+	0.159626i
$195$	5.40958			0.387388
$196$	−4.53760	+	5.33012i	−0.324114	+	0.380723i
$197$	−9.01237			−0.642104			−0.321052	−	0.947061i	$-0.604037\pi$
$197$	−9.01237			−0.642104			−0.321052	+	0.947061i	$0.604037\pi$
$198$	8.82170	+	15.2796i	0.626931	+	1.08588i
$199$	2.93180	−	5.07802i	0.207830	−	0.359972i	−0.743201	−	0.669068i	$-0.766693\pi$
$199$	2.93180	−	5.07802i	0.207830	−	0.359972i	0.951031	+	0.309097i	$0.100027\pi$
$200$	−4.29645	+	7.44167i	−0.303805	+	0.526205i
$201$	1.86074	+	3.22290i	0.131247	+	0.227326i
$202$	−10.0344			−0.706015
$203$	2.63485	+	0.239979i	0.184930	+	0.0168432i
$204$	−0.790874			−0.0553723
$205$	9.19341	+	15.9235i	0.642096	+	1.11214i
$206$	4.67177	−	8.09174i	0.325497	−	0.563778i
$207$	0.520809	−	0.902068i	0.0361987	−	0.0626981i
$208$	−1.42428	−	2.46692i	−0.0987560	−	0.171050i
$209$	−25.2841			−1.74894
$210$	2.10719	+	4.56122i	0.145410	+	0.314754i
$211$	20.9741			1.44391			0.721957	−	0.691938i	$-0.243243\pi$
$211$	20.9741			1.44391			0.721957	+	0.691938i	$0.243243\pi$
$212$	0.610931	+	1.05816i	0.0419589	+	0.0726750i
$213$	3.42346	−	5.92960i	0.234572	−	0.406290i
$214$	5.89950	−	10.2182i	0.403282	−	0.698505i
$215$	21.3235	+	36.9333i	1.45425	+	2.51883i
$216$	−2.95387			−0.200986
$217$	12.1777	−	17.2603i	0.826675	−	1.17171i
$218$	−6.05447			−0.410060
$219$	−3.85062	−	6.66946i	−0.260200	−	0.450680i
$220$	−11.8933	+	20.5997i	−0.801844	+	1.38883i
$221$	2.18685	−	3.78774i	0.147104	−	0.254791i
$222$	1.92359	+	3.33176i	0.129103	+	0.223613i
$223$	−1.10629			−0.0740825			−0.0370412	−	0.999314i	$-0.511793\pi$
$223$	−1.10629			−0.0740825			−0.0370412	+	0.999314i	$0.511793\pi$
$224$	1.52525	−	2.16185i	0.101910	−	0.144445i
$225$	−23.4989			−1.56659
$226$	1.75405	+	3.03811i	0.116678	+	0.202092i
$227$	0.434814	−	0.753121i	0.0288596	−	0.0499864i	−0.851235	−	0.524785i	$-0.824146\pi$
$227$	0.434814	−	0.753121i	0.0288596	−	0.0499864i	0.880095	+	0.474799i	$0.157479\pi$
$228$	1.00931	−	1.74818i	0.0668433	−	0.115776i
$229$	3.50178	+	6.06526i	0.231404	+	0.400804i	0.958222	−	0.286027i	$-0.0923347\pi$
$229$	3.50178	+	6.06526i	0.231404	+	0.400804i	−0.726817	+	0.686831i	$0.759001\pi$
$230$	1.40429			0.0925963
$231$	3.68741	+	7.98179i	0.242614	+	0.525163i
$232$	−1.00000			−0.0656532
$233$	−0.205639	−	0.356178i	−0.0134719	−	0.0233340i	0.859211	−	0.511622i	$-0.170955\pi$
$233$	−0.205639	−	0.356178i	−0.0134719	−	0.0233340i	−0.872683	+	0.488288i	$0.837622\pi$
$234$	3.89495	−	6.74625i	0.254621	−	0.441016i
$235$	−14.4868	+	25.0919i	−0.945014	+	1.63681i
$236$	0.348355	+	0.603368i	0.0226760	+	0.0392759i
$237$	2.64545			0.171840
$238$	4.04557	+	0.368467i	0.262236	+	0.0238842i
$239$	−12.6415			−0.817713			−0.408857	−	0.912599i	$-0.634072\pi$
$239$	−12.6415			−0.817713			−0.408857	+	0.912599i	$0.634072\pi$
$240$	−0.949529	−	1.64463i	−0.0612919	−	0.106161i
$241$	−10.4546	+	18.1079i	−0.673439	+	1.16643i	0.303483	+	0.952837i	$0.401850\pi$
$241$	−10.4546	+	18.1079i	−0.673439	+	1.16643i	−0.976922	+	0.213594i	$0.931483\pi$
$242$	−15.3123	+	26.5217i	−0.984313	+	1.70488i
$243$	−6.15186	−	10.6553i	−0.394642	−	0.683540i
$244$	−3.10100			−0.198521
$245$	−8.65386	−	24.3138i	−0.552875	−	1.55335i
$246$	−2.56882			−0.163782
$247$	5.58172	+	9.66781i	0.355156	+	0.615148i
$248$	−3.99203	+	6.91439i	−0.253494	+	0.439064i
$249$	−3.30053	+	5.71668i	−0.209162	+	0.362280i
$250$	−6.62325	−	11.4718i	−0.418891	−	0.725541i
$251$	−23.2297			−1.46624			−0.733121	−	0.680098i	$-0.761937\pi$
$251$	−23.2297			−1.46624			−0.733121	+	0.680098i	$0.761937\pi$
$252$	7.20547	+	0.656267i	0.453902	+	0.0413409i
$253$	2.45741			0.154496
$254$	−1.32016	−	2.28659i	−0.0828343	−	0.143473i
$255$	1.45792	−	2.52519i	0.0912984	−	0.158134i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.75738	+	13.4362i	0.483892	+	0.838126i	0.999829	−	0.0185011i	$-0.00588942\pi$
$257$	7.75738	+	13.4362i	0.483892	+	0.838126i	−0.515937	+	0.856627i	$0.672556\pi$
$258$	−5.95819			−0.370940
$259$	−8.28752	−	17.9392i	−0.514961	−	1.11469i
$260$	10.5022			0.651320
$261$	−1.36734	−	2.36831i	−0.0846363	−	0.146594i
$262$	5.37843	−	9.31572i	0.332281	−	0.575527i
$263$	1.47256	−	2.55055i	0.0908021	−	0.157274i	−0.817047	−	0.576571i	$-0.804390\pi$
$263$	1.47256	−	2.55055i	0.0908021	−	0.157274i	0.907849	+	0.419298i	$0.137724\pi$
$264$	−1.66160	−	2.87798i	−0.102265	−	0.177128i
$265$	−4.50483			−0.276729
$266$	−5.97742	+	8.47225i	−0.366499	+	0.519467i
$267$	4.83993			0.296199
$268$	3.61247	+	6.25698i	0.220667	+	0.382206i
$269$	3.38459	−	5.86228i	0.206362	−	0.357429i	−0.744204	−	0.667953i	$-0.767171\pi$
$269$	3.38459	−	5.86228i	0.206362	−	0.357429i	0.950566	+	0.310523i	$0.100504\pi$
$270$	5.44525	−	9.43145i	0.331387	−	0.573980i
$271$	−8.43787	−	14.6148i	−0.512564	−	0.887787i	−0.999894	−	0.0145687i	$-0.995362\pi$
$271$	−8.43787	−	14.6148i	−0.512564	−	0.887787i	0.487330	−	0.873218i	$-0.337971\pi$
$272$	−1.53541			−0.0930980
$273$	2.23794	−	3.17200i	0.135446	−	0.191978i
$274$	8.47238			0.511835
$275$	−27.7195	−	48.0115i	−1.67155	−	2.89520i
$276$	−0.0980966	+	0.169908i	−0.00590472	+	0.0102273i
$277$	−13.1578	+	22.7899i	−0.790573	+	1.36931i	0.135039	+	0.990840i	$0.456884\pi$
$277$	−13.1578	+	22.7899i	−0.790573	+	1.36931i	−0.925612	+	0.378473i	$0.876449\pi$
$278$	1.20041	+	2.07916i	0.0719955	+	0.124700i
$279$	−21.8338			−1.30716
$280$	4.09091	+	8.85521i	0.244479	+	0.529200i
$281$	0.662563			0.0395252			0.0197626	−	0.999805i	$-0.493709\pi$
$281$	0.662563			0.0395252			0.0197626	+	0.999805i	$0.493709\pi$
$282$	−2.02394	−	3.50558i	−0.120524	−	0.208754i
$283$	12.4648	−	21.5897i	0.740955	−	1.28337i	−0.211106	−	0.977463i	$-0.567706\pi$
$283$	12.4648	−	21.5897i	0.740955	−	1.28337i	0.952061	−	0.305909i	$-0.0989602\pi$
$284$	6.64634	−	11.5118i	0.394388	−	0.683100i
$285$	3.72118	+	6.44528i	0.220424	+	0.381785i
$286$	18.3781			1.08672
$287$	13.1403	+	1.19681i	0.775648	+	0.0706453i
$288$	−2.73468			−0.161143
$289$	7.32125	+	12.6808i	0.430662	+	0.745929i
$290$	1.84343	−	3.19291i	0.108250	−	0.187494i
$291$	0.661192	−	1.14522i	0.0387598	−	0.0671339i
$292$	−7.47563	−	12.9482i	−0.437478	−	0.757734i
$293$	9.98069			0.583078			0.291539	−	0.956559i	$-0.405833\pi$
$293$	9.98069			0.583078			0.291539	+	0.956559i	$0.405833\pi$
$294$	3.54630	+	0.651390i	0.206824	+	0.0379898i
$295$	−2.56867			−0.149554
$296$	3.73448	+	6.46831i	0.217062	+	0.375963i
$297$	9.52877	−	16.5043i	0.552916	−	0.957678i
$298$	5.18750	−	8.98502i	0.300504	−	0.520488i
$299$	−0.542496	−	0.939631i	−0.0313734	−	0.0543402i
$300$	4.42611			0.255541
$301$	30.4780	+	2.77591i	1.75672	+	0.160001i
$302$	6.75687			0.388814
$303$	2.58429	+	4.47613i	0.148464	+	0.257147i
$304$	1.95949	−	3.39393i	0.112384	−	0.194655i
$305$	5.71647	−	9.90122i	0.327324	−	0.566942i
$306$	−2.09943	−	3.63632i	−0.120017	−	0.207875i
$307$	−2.78572			−0.158990			−0.0794948	−	0.996835i	$-0.525331\pi$
$307$	−2.78572			−0.158990			−0.0794948	+	0.996835i	$0.525331\pi$
$308$	7.15879	+	15.4959i	0.407910	+	0.882963i
$309$	−4.81275			−0.273788
$310$	−14.7180	−	25.4924i	−0.835927	−	1.44787i
$311$	−7.62907	+	13.2139i	−0.432605	+	0.749293i	−0.997097	−	0.0761452i	$-0.975739\pi$
$311$	−7.62907	+	13.2139i	−0.432605	+	0.749293i	0.564492	+	0.825439i	$0.309072\pi$
$312$	−0.733630	+	1.27069i	−0.0415336	+	0.0719384i
$313$	−17.1512	−	29.7067i	−0.969443	−	1.67912i	−0.697173	−	0.716903i	$-0.745559\pi$
$313$	−17.1512	−	29.7067i	−0.969443	−	1.67912i	−0.272270	−	0.962221i	$-0.587774\pi$
$314$	−3.89720			−0.219931
$315$	−15.3782	+	21.7966i	−0.866461	+	1.22810i
$316$	5.13590			0.288917
$317$	11.7602	+	20.3692i	0.660516	+	1.14405i	0.980480	+	0.196617i	$0.0629957\pi$
$317$	11.7602	+	20.3692i	0.660516	+	1.14405i	−0.319964	+	0.947430i	$0.603671\pi$
$318$	0.314684	−	0.545049i	0.0176466	−	0.0305648i
$319$	3.22586	−	5.58735i	0.180613	−	0.312832i
$320$	−1.84343	−	3.19291i	−0.103051	−	0.178489i
$321$	−6.07754			−0.339215
$322$	0.580955	−	0.823432i	0.0323754	−	0.0458881i
$323$	6.01725			0.334808
$324$	−3.34127	−	5.78725i	−0.185626	−	0.321514i
$325$	−12.2387	+	21.1980i	−0.678880	+	1.17585i
$326$	−0.194658	+	0.337157i	−0.0107811	+	0.0186734i
$327$	1.55930	+	2.70078i	0.0862293	+	0.149353i
$328$	−4.98713			−0.275368
$329$	8.71988	+	18.8751i	0.480743	+	1.04062i
$330$	12.2522			0.674461
$331$	10.4585	+	18.1146i	0.574851	+	0.995670i	0.996058	+	0.0887060i	$0.0282732\pi$
$331$	10.4585	+	18.1146i	0.574851	+	0.995670i	−0.421207	+	0.906964i	$0.638394\pi$
$332$	−6.40768	+	11.0984i	−0.351667	+	0.609105i
$333$	−10.2126	+	17.6888i	−0.559648	+	0.969339i
$334$	−5.15209	−	8.92368i	−0.281910	−	0.488282i
$335$	−26.6373			−1.45535
$336$	−1.35718	−	0.123611i	−0.0740402	−	0.00674351i
$337$	35.1825			1.91651			0.958256	−	0.285910i	$-0.0922959\pi$
$337$	35.1825			1.91651			0.958256	+	0.285910i	$0.0922959\pi$
$338$	2.44286	+	4.23116i	0.132874	+	0.230145i
$339$	0.903493	−	1.56490i	0.0490710	−	0.0849935i
$340$	2.83042	−	4.90243i	0.153501	−	0.265872i
$341$	−25.7554	−	44.6097i	−1.39473	−	2.41575i
$342$	10.7172			0.579518
$343$	−17.8370	−	4.98428i	−0.963105	−	0.269126i
$344$	−11.5673			−0.623667
$345$	−0.361668	−	0.626427i	−0.0194715	−	0.0337257i
$346$	−11.5204	+	19.9538i	−0.619338	+	1.07272i
$347$	7.43304	−	12.8744i	0.399026	−	0.691134i	−0.594580	−	0.804037i	$-0.702682\pi$
$347$	7.43304	−	12.8744i	0.399026	−	0.691134i	0.993606	+	0.112903i	$0.0360149\pi$
$348$	0.257545	+	0.446080i	0.0138058	+	0.0239124i
$349$	−20.1456			−1.07837			−0.539185	−	0.842187i	$-0.681268\pi$
$349$	−20.1456			−1.07837			−0.539185	+	0.842187i	$0.681268\pi$
$350$	−22.6410	−	2.06212i	−1.21021	−	0.110225i
$351$	−8.41428			−0.449121
$352$	−3.22586	−	5.58735i	−0.171939	−	0.297807i
$353$	4.77791	−	8.27558i	0.254302	−	0.440465i	−0.710403	−	0.703795i	$-0.751487\pi$
$353$	4.77791	−	8.27558i	0.254302	−	0.440465i	0.964706	+	0.263330i	$0.0848208\pi$
$354$	0.179434	−	0.310788i	0.00953680	−	0.0165182i
$355$	24.5041	+	42.4424i	1.30054	+	2.25261i
$356$	9.39630			0.498003
$357$	−0.877550	−	1.89955i	−0.0464449	−	0.100535i
$358$	−6.69801			−0.354001
$359$	−6.34390	−	10.9880i	−0.334818	−	0.579923i	0.648632	−	0.761103i	$-0.275342\pi$
$359$	−6.34390	−	10.9880i	−0.334818	−	0.579923i	−0.983450	+	0.181180i	$0.942008\pi$
$360$	5.04119	−	8.73160i	0.265694	−	0.460196i
$361$	1.82081	−	3.15373i	0.0958321	−	0.165986i
$362$	−6.62263	−	11.4707i	−0.348078	−	0.602888i
$363$	15.7744			0.827942
$364$	4.34476	−	6.15816i	0.227728	−	0.322775i
$365$	55.1231			2.88528
$366$	0.798646	+	1.38330i	0.0417459	+	0.0723060i
$367$	16.5126	−	28.6007i	0.861953	−	1.49295i	−0.00808862	−	0.999967i	$-0.502575\pi$
$367$	16.5126	−	28.6007i	0.861953	−	1.49295i	0.870041	−	0.492979i	$-0.164092\pi$
$368$	−0.190446	+	0.329862i	−0.00992768	+	0.0171952i
$369$	−6.81911	−	11.8110i	−0.354989	−	0.614858i
$370$	−27.5370			−1.43158
$371$	−1.86365	+	2.64149i	−0.0967557	+	0.137139i
$372$	4.11250			0.213223
$373$	9.97372	+	17.2750i	0.516420	+	0.894465i	0.999818	+	0.0190646i	$0.00606880\pi$
$373$	9.97372	+	17.2750i	0.516420	+	0.894465i	−0.483399	+	0.875400i	$0.660598\pi$
$374$	4.95302	−	8.57889i	0.256115	−	0.443604i
$375$	−3.41156	+	5.90900i	−0.176172	+	0.305139i
$376$	−3.92931	−	6.80577i	−0.202639	−	0.350981i
$377$	−2.84856			−0.146708
$378$	−3.27760	−	7.09471i	−0.168582	−	0.364912i
$379$	27.8725			1.43171			0.715857	−	0.698247i	$-0.246036\pi$
$379$	27.8725			1.43171			0.715857	+	0.698247i	$0.246036\pi$
$380$	7.22435	+	12.5129i	0.370601	+	0.641900i
$381$	−0.680001	+	1.17780i	−0.0348375	+	0.0603403i
$382$	10.1673	−	17.6103i	0.520205	−	0.901022i
$383$	−10.5799	−	18.3250i	−0.540609	−	0.936362i	−0.998869	−	0.0475439i	$-0.984861\pi$
$383$	−10.5799	−	18.3250i	−0.540609	−	0.936362i	0.458260	−	0.888818i	$-0.348473\pi$
$384$	0.515089			0.0262855
$385$	−62.6739	−	5.70827i	−3.19416	−	0.290921i
$386$	13.2040			0.672068
$387$	−15.8164	−	27.3949i	−0.803995	−	1.39256i
$388$	1.28365	−	2.22334i	0.0651672	−	0.112873i
$389$	−4.39902	+	7.61932i	−0.223039	+	0.386315i	−0.955729	−	0.294247i	$-0.904931\pi$
$389$	−4.39902	+	7.61932i	−0.223039	+	0.386315i	0.732690	+	0.680562i	$0.238264\pi$
$390$	−2.70479	−	4.68483i	−0.136962	−	0.237226i
$391$	−0.584826			−0.0295759
$392$	6.88482	+	1.26462i	0.347736	+	0.0638727i
$393$	−5.54075			−0.279494
$394$	4.50618	+	7.80494i	0.227018	+	0.393207i
$395$	−9.46766	+	16.3985i	−0.476369	+	0.825096i
$396$	8.82170	−	15.2796i	0.443307	−	0.767830i
$397$	3.79207	+	6.56805i	0.190318	+	0.329641i	0.945356	−	0.326041i	$-0.105715\pi$
$397$	3.79207	+	6.56805i	0.190318	+	0.329641i	−0.755037	+	0.655682i	$0.772381\pi$
$398$	−5.86360			−0.293916
$399$	5.31876	+	0.484427i	0.266271	+	0.0242517i
$400$	8.59290			0.429645
$401$	−5.91354	−	10.2426i	−0.295308	−	0.511489i	0.679748	−	0.733445i	$-0.262089\pi$
$401$	−5.91354	−	10.2426i	−0.295308	−	0.511489i	−0.975057	+	0.221957i	$0.928756\pi$
$402$	1.86074	−	3.22290i	0.0928055	−	0.160744i
$403$	−11.3715	+	19.6960i	−0.566455	+	0.981130i
$404$	5.01718	+	8.69001i	0.249614	+	0.432344i
$405$	24.6376			1.22425
$406$	−1.10959	−	2.40183i	−0.0550683	−	0.119201i
$407$	−48.1876			−2.38857
$408$	0.395437	+	0.684917i	0.0195771	+	0.0339084i
$409$	−5.92530	+	10.2629i	−0.292987	+	0.507469i	−0.974515	−	0.224324i	$-0.927983\pi$
$409$	−5.92530	+	10.2629i	−0.292987	+	0.507469i	0.681527	+	0.731793i	$0.261316\pi$
$410$	9.19341	−	15.9235i	0.454030	−	0.786403i
$411$	−2.18202	−	3.77936i	−0.107631	−	0.186422i
$412$	−9.34353			−0.460323
$413$	−1.06266	+	1.50618i	−0.0522899	+	0.0741145i
$414$	−1.04162			−0.0511928
$415$	−23.6242	−	40.9183i	−1.15967	−	2.00860i
$416$	−1.42428	+	2.46692i	−0.0698310	+	0.120951i
$417$	0.618316	−	1.07095i	0.0302790	−	0.0524448i
$418$	12.6421	+	21.8967i	0.618344	+	1.07100i
$419$	0.933145			0.0455871			0.0227935	−	0.999740i	$-0.492744\pi$
$419$	0.933145			0.0455871			0.0227935	+	0.999740i	$0.492744\pi$
$420$	2.89654	−	4.10549i	0.141337	−	0.200327i
$421$	−3.17478			−0.154729			−0.0773647	−	0.997003i	$-0.524651\pi$
$421$	−3.17478			−0.154729			−0.0773647	+	0.997003i	$0.524651\pi$
$422$	−10.4870	−	18.1641i	−0.510501	−	0.884213i
$423$	10.7454	−	18.6116i	0.522460	−	0.904928i
$424$	0.610931	−	1.05816i	0.0296694	−	0.0513890i
$425$	6.59682	+	11.4260i	0.319993	+	0.554244i
$426$	−6.84692			−0.331734
$427$	−3.44086	−	7.44809i	−0.166515	−	0.360438i
$428$	−11.7990			−0.570327
$429$	−4.73318	−	8.19810i	−0.228520	−	0.395808i
$430$	21.3235	−	36.9333i	1.02831	−	1.78108i
$431$	12.6441	−	21.9002i	0.609044	−	1.05489i	−0.382355	−	0.924016i	$-0.624887\pi$
$431$	12.6441	−	21.9002i	0.609044	−	1.05489i	0.991398	−	0.130879i	$-0.0417799\pi$
$432$	1.47694	+	2.55813i	0.0710591	+	0.123078i
$433$	25.3900			1.22017			0.610084	−	0.792337i	$-0.291136\pi$
$433$	25.3900			1.22017			0.610084	+	0.792337i	$0.291136\pi$
$434$	−21.0367	−	1.91601i	−1.00980	−	0.0919712i
$435$	−1.89906			−0.0910529
$436$	3.02724	+	5.24333i	0.144978	+	0.251110i
$437$	0.746353	−	1.29272i	0.0357029	−	0.0618393i
$438$	−3.85062	+	6.66946i	−0.183990	+	0.318679i
$439$	4.97971	+	8.62511i	0.237668	+	0.411654i	0.960045	−	0.279846i	$-0.0902835\pi$
$439$	4.97971	+	8.62511i	0.237668	+	0.411654i	−0.722376	+	0.691500i	$0.756950\pi$
$440$	23.7865			1.13398
$441$	6.41891	+	18.0345i	0.305662	+	0.858786i
$442$	−4.37371			−0.208036
$443$	4.84527	+	8.39225i	0.230206	+	0.398728i	0.957869	−	0.287207i	$-0.0927268\pi$
$443$	4.84527	+	8.39225i	0.230206	+	0.398728i	−0.727663	+	0.685935i	$0.759393\pi$
$444$	1.92359	−	3.33176i	0.0912896	−	0.158118i
$445$	−17.3214	+	30.0015i	−0.821113	+	1.42221i
$446$	0.553144	+	0.958073i	0.0261921	+	0.0453661i
$447$	−5.34405			−0.252765
$448$	−2.63485	−	0.239979i	−0.124485	−	0.0113379i
$449$	13.7314			0.648025			0.324013	−	0.946053i	$-0.394968\pi$
$449$	13.7314			0.648025			0.324013	+	0.946053i	$0.394968\pi$
$450$	11.7494	+	20.3506i	0.553873	+	0.959337i
$451$	16.0878	−	27.8648i	0.757543	−	1.31210i
$452$	1.75405	−	3.03811i	0.0825037	−	0.142901i
$453$	−1.74019	−	3.01411i	−0.0817615	−	0.141615i
$454$	−0.869629			−0.0408137
$455$	11.6532	+	25.2246i	0.546311	+	1.18255i
$456$	−2.01862			−0.0945306
$457$	−6.16944	−	10.6858i	−0.288594	−	0.499860i	0.684880	−	0.728656i	$-0.259854\pi$
$457$	−6.16944	−	10.6858i	−0.288594	−	0.499860i	−0.973474	+	0.228796i	$0.926521\pi$
$458$	3.50178	−	6.06526i	0.163628	−	0.283411i
$459$	−2.26771	+	3.92778i	−0.105847	+	0.183333i
$460$	−0.702146	−	1.21615i	−0.0327377	−	0.0567034i
$461$	−11.8322			−0.551081			−0.275540	−	0.961290i	$-0.588857\pi$
$461$	−11.8322			−0.551081			−0.275540	+	0.961290i	$0.588857\pi$
$462$	5.06873	−	7.18429i	0.235818	−	0.334243i
$463$	−30.3189			−1.40904			−0.704519	−	0.709685i	$-0.748837\pi$
$463$	−30.3189			−1.40904			−0.704519	+	0.709685i	$0.748837\pi$
$464$	0.500000	+	0.866025i	0.0232119	+	0.0402042i
$465$	−7.58109	+	13.1308i	−0.351565	+	0.608928i
$466$	−0.205639	+	0.356178i	−0.00952605	+	0.0164996i
$467$	4.15548	+	7.19751i	0.192293	+	0.333061i	0.946010	−	0.324138i	$-0.105074\pi$
$467$	4.15548	+	7.19751i	0.192293	+	0.333061i	−0.753717	+	0.657199i	$0.771741\pi$
$468$	−7.78990			−0.360088
$469$	−11.0198	+	15.6193i	−0.508849	+	0.721231i
$470$	28.9736			1.33645
$471$	1.00370	+	1.73846i	0.0462481	+	0.0801041i
$472$	0.348355	−	0.603368i	0.0160343	−	0.0277723i
$473$	37.3144	−	64.6305i	1.71572	−	2.97171i
$474$	−1.32272	−	2.29102i	−0.0607547	−	0.105230i
$475$	−33.6754			−1.54513
$476$	−1.70369	−	3.68780i	−0.0780883	−	0.169030i
$477$	3.34141			0.152992
$478$	6.32077	+	10.9479i	0.289105	+	0.500745i
$479$	−15.6548	+	27.1149i	−0.715286	+	1.23891i	0.247563	+	0.968872i	$0.420370\pi$
$479$	−15.6548	+	27.1149i	−0.715286	+	1.23891i	−0.962849	+	0.270040i	$0.912963\pi$
$480$	−0.949529	+	1.64463i	−0.0433399	+	0.0750669i
$481$	10.6379	+	18.4254i	0.485046	+	0.840124i
$482$	20.9092			0.952387
$483$	−0.516939	−	0.0470823i	−0.0235215	−	0.00214232i
$484$	30.6246			1.39203
$485$	4.73262	+	8.19713i	0.214897	+	0.372213i
$486$	−6.15186	+	10.6553i	−0.279054	+	0.483336i
$487$	10.8547	−	18.8009i	0.491874	−	0.851951i	−0.508082	−	0.861309i	$-0.669645\pi$
$487$	10.8547	−	18.8009i	0.491874	−	0.851951i	0.999956	+	0.00935780i	$0.00297872\pi$
$488$	1.55050	+	2.68555i	0.0701879	+	0.121569i
$489$	0.200532			0.00906838
$490$	−16.7295	+	19.6514i	−0.755760	+	0.887759i
$491$	−28.6142			−1.29134			−0.645670	−	0.763616i	$-0.723422\pi$
$491$	−28.6142			−1.29134			−0.645670	+	0.763616i	$0.723422\pi$
$492$	1.28441	+	2.22466i	0.0579056	+	0.100295i
$493$	−0.767706	+	1.32971i	−0.0345757	+	0.0598869i
$494$	5.58172	−	9.66781i	0.251133	−	0.434976i
$495$	32.5243	+	56.3338i	1.46186	+	2.53202i
$496$	7.98405			0.358494
$497$	35.0242	+	3.18997i	1.57105	+	0.143090i
$498$	6.60105			0.295800
$499$	11.1644	+	19.3373i	0.499786	+	0.865655i	1.00000		0.000247177i	$-7.86790e-5\pi$
$499$	11.1644	+	19.3373i	0.499786	+	0.865655i	−0.500214	+	0.865902i	$0.666745\pi$
$500$	−6.62325	+	11.4718i	−0.296201	+	0.513035i
$501$	−2.65379	+	4.59649i	−0.118562	+	0.205356i
$502$	11.6148	+	20.1175i	0.518395	+	0.897887i
$503$	−13.7215			−0.611810			−0.305905	−	0.952062i	$-0.598959\pi$
$503$	−13.7215			−0.611810			−0.305905	+	0.952062i	$0.598959\pi$
$504$	−3.03439	−	6.56825i	−0.135162	−	0.292573i
$505$	−36.9952			−1.64627
$506$	−1.22870	−	2.12818i	−0.0546225	−	0.0946090i
$507$	1.25829	−	2.17942i	0.0558827	−	0.0967916i
$508$	−1.32016	+	2.28659i	−0.0585727	+	0.101451i
$509$	3.40302	+	5.89421i	0.150836	+	0.261256i	0.931535	−	0.363651i	$-0.118470\pi$
$509$	3.40302	+	5.89421i	0.150836	+	0.261256i	−0.780699	+	0.624908i	$0.785137\pi$
$510$	−2.91584			−0.129115
$511$	22.8044	−	32.3224i	1.00881	−	1.42986i
$512$	1.00000			0.0441942
$513$	−5.78808	−	10.0252i	−0.255550	−	0.442626i
$514$	7.75738	−	13.4362i	0.342163	−	0.592644i
$515$	17.2241	−	29.8331i	0.758986	−	1.31460i
$516$	2.97909	+	5.15994i	0.131147	+	0.227154i
$517$	50.7016			2.22985
$518$	−11.3920	+	16.1468i	−0.500537	+	0.709450i
$519$	11.8680			0.520948
$520$	−5.25111	−	9.09519i	−0.230276	−	0.398850i
$521$	−2.77962	+	4.81444i	−0.121777	+	0.210925i	−0.920469	−	0.390816i	$-0.872193\pi$
$521$	−2.77962	+	4.81444i	−0.121777	+	0.210925i	0.798691	+	0.601741i	$0.205526\pi$
$522$	−1.36734	+	2.36831i	−0.0598469	+	0.103658i
$523$	6.04000	+	10.4616i	0.264111	+	0.457453i	0.967330	−	0.253520i	$-0.0815882\pi$
$523$	6.04000	+	10.4616i	0.264111	+	0.457453i	−0.703220	+	0.710973i	$0.748255\pi$
$524$	−10.7569			−0.469916
$525$	4.91119	+	10.6308i	0.214342	+	0.463965i
$526$	−2.94512			−0.128414
$527$	6.12940	+	10.6164i	0.267001	+	0.462459i
$528$	−1.66160	+	2.87798i	−0.0723120	+	0.125248i
$529$	11.4275	−	19.7929i	0.496846	−	0.860563i
$530$	2.25241	+	3.90130i	0.0978386	+	0.169461i
$531$	1.90528			0.0826821
$532$	10.3259	+	0.940473i	0.447684	+	0.0407747i
$533$	−14.2061			−0.615335
$534$	−2.41997	−	4.19150i	−0.104722	−	0.181384i
$535$	21.7506	−	37.6732i	0.940361	−	1.62875i
$536$	3.61247	−	6.25698i	0.156035	−	0.270260i
$537$	1.72503	+	2.98785i	0.0744407	+	0.128935i
$538$	−6.76917			−0.291840
$539$	−29.2753	+	34.3884i	−1.26098	+	1.48121i
$540$	−10.8905			−0.468652
$541$	−14.1881	−	24.5745i	−0.609994	−	1.05654i	−0.991241	−	0.132068i	$-0.957838\pi$
$541$	−14.1881	−	24.5745i	−0.609994	−	1.05654i	0.381246	−	0.924474i	$-0.375495\pi$
$542$	−8.43787	+	14.6148i	−0.362437	+	0.627760i
$543$	−3.41125	+	5.90845i	−0.146391	+	0.253556i
$544$	0.767706	+	1.32971i	0.0329151	+	0.0570107i
$545$	−22.3220			−0.956167
$546$	−3.86601	−	0.352112i	−0.165450	−	0.0150690i
$547$	−19.5396			−0.835455			−0.417727	−	0.908572i	$-0.637173\pi$
$547$	−19.5396			−0.835455			−0.417727	+	0.908572i	$0.637173\pi$
$548$	−4.23619	−	7.33730i	−0.180961	−	0.313434i
$549$	−4.24013	+	7.34412i	−0.180964	+	0.313439i
$550$	−27.7195	+	48.0115i	−1.18196	+	2.04722i
$551$	−1.95949	−	3.39393i	−0.0834770	−	0.144586i
$552$	0.196193			0.00835054
$553$	5.69877	+	12.3356i	0.242336	+	0.524562i
$554$	26.3155			1.11804
$555$	7.09200	+	12.2837i	0.301039	+	0.521414i
$556$	1.20041	−	2.07916i	0.0509085	−	0.0881761i
$557$	−8.14870	+	14.1140i	−0.345272	+	0.598028i	−0.985403	−	0.170238i	$-0.945547\pi$
$557$	−8.14870	+	14.1140i	−0.345272	+	0.598028i	0.640132	+	0.768265i	$0.278880\pi$
$558$	10.9169	+	18.9087i	0.462150	+	0.800468i
$559$	−32.9501			−1.39364
$560$	5.62338	−	7.97044i	0.237631	−	0.336813i
$561$	−5.10250			−0.215428
$562$	−0.331281	−	0.573796i	−0.0139743	−	0.0242041i
$563$	6.92621	−	11.9966i	0.291905	−	0.505594i	−0.682355	−	0.731021i	$-0.739044\pi$
$563$	6.92621	−	11.9966i	0.291905	−	0.505594i	0.974260	+	0.225426i	$0.0723775\pi$
$564$	−2.02394	+	3.50558i	−0.0852235	+	0.147611i
$565$	6.46693	+	11.2011i	0.272066	+	0.471232i
$566$	−24.9296			−1.04787
$567$	10.1926	−	14.4467i	0.428047	−	0.606703i
$568$	−13.2927			−0.557749
$569$	20.2209	+	35.0236i	0.847703	+	1.46826i	0.883253	+	0.468896i	$0.155348\pi$
$569$	20.2209	+	35.0236i	0.847703	+	1.46826i	−0.0355506	+	0.999368i	$0.511318\pi$
$570$	3.72118	−	6.44528i	0.155863	−	0.269963i
$571$	−9.42791	+	16.3296i	−0.394546	+	0.683373i	−0.993043	−	0.117752i	$-0.962431\pi$
$571$	−9.42791	+	16.3296i	−0.394546	+	0.683373i	0.598497	+	0.801125i	$0.295765\pi$
$572$	−9.18904	−	15.9159i	−0.384213	−	0.665477i
$573$	−10.4741			−0.437564
$574$	−5.53369	−	11.9782i	−0.230972	−	0.499962i
$575$	3.27296			0.136492
$576$	1.36734	+	2.36831i	0.0569726	+	0.0986794i
$577$	9.23715	−	15.9992i	0.384548	−	0.666056i	−0.607159	−	0.794581i	$-0.707691\pi$
$577$	9.23715	−	15.9992i	0.384548	−	0.666056i	0.991706	+	0.128524i	$0.0410241\pi$
$578$	7.32125	−	12.6808i	0.304524	−	0.527451i
$579$	−3.40063	−	5.89007i	−0.141325	−	0.244783i
$580$	−3.68685			−0.153088
$581$	−33.7665	−	3.07542i	−1.40087	−	0.127590i
$582$	−1.32238			−0.0548146
$583$	3.94155	+	6.82697i	0.163243	+	0.282744i
$584$	−7.47563	+	12.9482i	−0.309344	+	0.535799i
$585$	14.3601	−	24.8725i	0.593718	−	1.02835i
$586$	−4.99035	−	8.64354i	−0.206149	−	0.357061i
$587$	29.5731			1.22061			0.610306	−	0.792166i	$-0.291046\pi$
$587$	29.5731			1.22061			0.610306	+	0.792166i	$0.291046\pi$
$588$	−1.20903	−	3.39688i	−0.0498595	−	0.140085i
$589$	−31.2893			−1.28925
$590$	1.28433	+	2.22453i	0.0528752	+	0.0915825i
$591$	2.32109	−	4.02024i	0.0954767	−	0.165370i
$592$	3.73448	−	6.46831i	0.153486	−	0.265846i
$593$	−17.7735	−	30.7846i	−0.729869	−	1.26417i	−0.956938	−	0.290292i	$-0.906248\pi$
$593$	−17.7735	−	30.7846i	−0.729869	−	1.26417i	0.227069	−	0.973879i	$-0.427086\pi$
$594$	−19.0575			−0.781941
$595$	14.9154	+	1.35848i	0.611474	+	0.0556924i
$596$	−10.3750			−0.424977
$597$	1.51014	+	2.61563i	0.0618058	+	0.107051i
$598$	−0.542496	+	0.939631i	−0.0221843	+	0.0384244i
$599$	0.559363	−	0.968846i	0.0228550	−	0.0395860i	−0.854372	−	0.519662i	$-0.826058\pi$
$599$	0.559363	−	0.968846i	0.0228550	−	0.0395860i	0.877227	+	0.480076i	$0.159391\pi$
$600$	−2.21305	−	3.83312i	−0.0903476	−	0.156487i
$601$	−5.46816			−0.223051			−0.111525	−	0.993762i	$-0.535574\pi$
$601$	−5.46816			−0.223051			−0.111525	+	0.993762i	$0.535574\pi$
$602$	−12.8350	−	27.7827i	−0.523116	−	1.13234i
$603$	19.7579			0.804605
$604$	−3.37843	−	5.85162i	−0.137467	−	0.238099i
$605$	−56.4543	+	97.7817i	−2.29519	+	3.97539i
$606$	2.58429	−	4.47613i	0.104980	−	0.181830i
$607$	12.0159	+	20.8121i	0.487710	+	0.844739i	0.999900	−	0.0141333i	$-0.00449890\pi$
$607$	12.0159	+	20.8121i	0.487710	+	0.844739i	−0.512190	+	0.858872i	$0.671166\pi$
$608$	−3.91898			−0.158936
$609$	−0.785640	+	1.11355i	−0.0318357	+	0.0451232i
$610$	−11.4329			−0.462906
$611$	−11.1929	−	19.3866i	−0.452815	−	0.784298i
$612$	−2.09943	+	3.63632i	−0.0848646	+	0.146990i
$613$	−5.95398	+	10.3126i	−0.240479	+	0.416522i	−0.960851	−	0.277066i	$-0.910638\pi$
$613$	−5.95398	+	10.3126i	−0.240479	+	0.416522i	0.720372	+	0.693588i	$0.243971\pi$
$614$	1.39286	+	2.41251i	0.0562113	+	0.0973609i
$615$	−9.47085			−0.381902
$616$	9.84048	−	13.9477i	0.396484	−	0.561967i
$617$	−40.3723			−1.62533			−0.812664	−	0.582733i	$-0.801983\pi$
$617$	−40.3723			−1.62533			−0.812664	+	0.582733i	$0.801983\pi$
$618$	2.40638	+	4.16796i	0.0967986	+	0.167660i
$619$	12.8716	−	22.2942i	0.517353	−	0.896081i	−0.482444	−	0.875927i	$-0.660251\pi$
$619$	12.8716	−	22.2942i	0.517353	−	0.896081i	0.999797	−	0.0201545i	$-0.00641581\pi$
$620$	−14.7180	+	25.4924i	−0.591090	+	1.02380i
$621$	0.562553	+	0.974370i	0.0225745	+	0.0391001i
$622$	15.2581			0.611795
$623$	10.4261	+	22.5683i	0.417712	+	0.904182i
$624$	1.46726			0.0587374
$625$	−2.93671	−	5.08653i	−0.117468	−	0.203461i
$626$	−17.1512	+	29.7067i	−0.685500	+	1.18732i
$627$	6.51179	−	11.2787i	0.260056	−	0.450430i
$628$	1.94860	+	3.37507i	0.0777575	+	0.134680i
$629$	11.4679			0.457257
$630$	26.5655	+	2.41956i	1.05840	+	0.0963976i
$631$	26.6745			1.06189			0.530947	−	0.847405i	$-0.321836\pi$
$631$	26.6745			1.06189			0.530947	+	0.847405i	$0.321836\pi$
$632$	−2.56795	−	4.44782i	−0.102148	−	0.176925i
$633$	−5.40175	+	9.35611i	−0.214700	+	0.371872i
$634$	11.7602	−	20.3692i	0.467055	−	0.808963i
$635$	−4.86724	−	8.43031i	−0.193151	−	0.334547i
$636$	−0.629368			−0.0249561
$637$	19.6118	+	3.60233i	0.777048	+	0.142730i
$638$	−6.45172			−0.255426
$639$	−18.1756	−	31.4811i	−0.719017	−	1.24537i
$640$	−1.84343	+	3.19291i	−0.0728679	+	0.126211i
$641$	−11.6911	+	20.2495i	−0.461769	+	0.799807i	−0.999049	−	0.0435964i	$-0.986118\pi$
$641$	−11.6911	+	20.2495i	−0.461769	+	0.799807i	0.537280	+	0.843404i	$0.319452\pi$
$642$	3.03877	+	5.26330i	0.119931	+	0.207726i
$643$	−5.26893			−0.207786			−0.103893	−	0.994588i	$-0.533130\pi$
$643$	−5.26893			−0.207786			−0.103893	+	0.994588i	$0.533130\pi$
$644$	−1.00359	−	0.0914061i	−0.0395470	−	0.00360190i
$645$	−21.9670			−0.864948
$646$	−3.00862	−	5.21109i	−0.118373	−	0.205027i
$647$	−5.23077	+	9.05996i	−0.205643	+	0.356184i	−0.950337	−	0.311222i	$-0.899262\pi$
$647$	−5.23077	+	9.05996i	−0.205643	+	0.356184i	0.744695	+	0.667405i	$0.232595\pi$
$648$	−3.34127	+	5.78725i	−0.131258	+	0.227345i
$649$	2.24749	+	3.89276i	0.0882216	+	0.152804i
$650$	24.4774			0.960081
$651$	4.56321	+	9.87753i	0.178846	+	0.387131i
$652$	0.389316			0.0152468
$653$	−6.32751	−	10.9596i	−0.247615	−	0.428881i	0.715249	−	0.698870i	$-0.246313\pi$
$653$	−6.32751	−	10.9596i	−0.247615	−	0.428881i	−0.962863	+	0.269989i	$0.912980\pi$
$654$	1.55930	−	2.70078i	0.0609733	−	0.105609i
$655$	19.8295	−	34.3457i	0.774803	−	1.34200i
$656$	2.49356	+	4.31898i	0.0973573	+	0.168628i
$657$	−40.8870			−1.59515
$658$	11.9864	−	16.9892i	0.467277	−	0.662307i
$659$	27.0561			1.05396			0.526978	−	0.849879i	$-0.323325\pi$
$659$	27.0561			1.05396			0.526978	+	0.849879i	$0.323325\pi$
$660$	−6.12609	−	10.6107i	−0.238458	−	0.413021i
$661$	10.5975	−	18.3554i	0.412194	−	0.713942i	−0.582935	−	0.812519i	$-0.698096\pi$
$661$	10.5975	−	18.3554i	0.412194	−	0.713942i	0.995129	+	0.0985771i	$0.0314291\pi$
$662$	10.4585	−	18.1146i	0.406481	−	0.704045i
$663$	1.12643	+	1.95103i	0.0437467	+	0.0757715i
$664$	12.8154			0.497333
$665$	−22.0379	+	31.2360i	−0.854593	+	1.21128i
$666$	20.4252			0.791462
$667$	0.190446	+	0.329862i	0.00737409	+	0.0127723i
$668$	−5.15209	+	8.92368i	−0.199340	+	0.345268i
$669$	0.284918	−	0.493493i	0.0110156	−	0.0190795i
$670$	13.3187	+	23.0686i	0.514544	+	0.891217i
$671$	−20.0068			−0.772354
$672$	0.571540	+	1.23716i	0.0220476	+	0.0477244i
$673$	6.95037			0.267917			0.133959	−	0.990987i	$-0.457231\pi$
$673$	6.95037			0.267917			0.133959	+	0.990987i	$0.457231\pi$
$674$	−17.5912	−	30.4689i	−0.677590	−	1.17362i
$675$	12.6912	−	21.9817i	0.488483	−	0.846078i
$676$	2.44286	−	4.23116i	0.0939562	−	0.162737i
$677$	22.9685	+	39.7826i	0.882752	+	1.52897i	0.848269	+	0.529565i	$0.177645\pi$
$677$	22.9685	+	39.7826i	0.882752	+	1.52897i	0.0344824	+	0.999405i	$0.489022\pi$
$678$	−1.80699			−0.0693969
$679$	6.76442	+	0.616096i	0.259594	+	0.0236436i
$680$	−5.66084			−0.217083
$681$	0.223968	+	0.387924i	0.00858248	+	0.0148653i
$682$	−25.7554	+	44.6097i	−0.986226	+	1.70819i
$683$	−0.750913	+	1.30062i	−0.0287329	+	0.0497668i	−0.880034	−	0.474910i	$-0.842481\pi$
$683$	−0.750913	+	1.30062i	−0.0287329	+	0.0497668i	0.851301	+	0.524677i	$0.175814\pi$
$684$	−5.35858	−	9.28133i	−0.204890	−	0.354881i
$685$	31.2364			1.19348
$686$	4.60196	+	17.9394i	0.175704	+	0.684929i
$687$	−3.60746			−0.137633
$688$	5.78365	+	10.0176i	0.220499	+	0.381916i
$689$	1.74027	−	3.01424i	0.0662991	−	0.114833i
$690$	−0.361668	+	0.626427i	−0.0137685	+	0.0238477i
$691$	16.0131	+	27.7355i	0.609167	+	1.05511i	0.991378	+	0.131033i	$0.0418294\pi$
$691$	16.0131	+	27.7355i	0.609167	+	1.05511i	−0.382211	+	0.924075i	$0.624837\pi$
$692$	23.0407			0.875876
$693$	46.4876	+	4.23405i	1.76592	+	0.160838i
$694$	−14.8661			−0.564308
$695$	4.42572	+	7.66557i	0.167877	+	0.290772i
$696$	0.257545	−	0.446080i	0.00976220	−	0.0169086i
$697$	−3.82865	+	6.63141i	−0.145020	+	0.251183i
$698$	10.0728	+	17.4466i	0.381261	+	0.660364i
$699$	0.211845			0.00801271
$700$	9.53464	+	20.6387i	0.360375	+	0.780070i
$701$	20.1243			0.760083			0.380042	−	0.924969i	$-0.375910\pi$
$701$	20.1243			0.760083			0.380042	+	0.924969i	$0.375910\pi$
$702$	4.20714	+	7.28698i	0.158788	+	0.275029i
$703$	−14.6353	+	25.3492i	−0.551982	+	0.956062i
$704$	−3.22586	+	5.58735i	−0.121579	+	0.210581i
$705$	−7.46199	−	12.9245i	−0.281035	−	0.486767i
$706$	−9.55582			−0.359638
$707$	−15.3049	+	21.6928i	−0.575600	+	0.815842i
$708$	−0.358868			−0.0134871
$709$	2.03054	+	3.51699i	0.0762584	+	0.132083i	0.901633	−	0.432502i	$-0.142369\pi$
$709$	2.03054	+	3.51699i	0.0762584	+	0.132083i	−0.825374	+	0.564586i	$0.809036\pi$
$710$	24.5041	−	42.4424i	0.919623	−	1.59283i
$711$	7.02253	−	12.1634i	0.263365	−	0.456162i
$712$	−4.69815	−	8.13744i	−0.176071	−	0.304963i
$713$	3.04106			0.113889
$714$	−1.20628	+	1.70975i	−0.0451439	+	0.0639859i
$715$	67.7573			2.53398
$716$	3.34900	+	5.80064i	0.125158	+	0.216780i
$717$	3.25576	−	5.63914i	0.121589	−	0.210598i
$718$	−6.34390	+	10.9880i	−0.236752	+	0.410067i
$719$	−0.755948	−	1.30934i	−0.0281921	−	0.0488301i	0.851585	−	0.524216i	$-0.175642\pi$
$719$	−0.755948	−	1.30934i	−0.0281921	−	0.0488301i	−0.879777	+	0.475386i	$0.842308\pi$
$720$	−10.0824			−0.375748
$721$	−10.3675	−	22.4416i	−0.386107	−	0.835769i
$722$	−3.64162			−0.135527
$723$	−5.38505	−	9.32717i	−0.200272	−	0.346881i
$724$	−6.62263	+	11.4707i	−0.246128	+	0.426306i
$725$	4.29645	−	7.44167i	0.159566	−	0.276377i
$726$	−7.88721	−	13.6610i	−0.292722	−	0.507009i
$727$	−28.1717			−1.04483			−0.522414	−	0.852692i	$-0.674969\pi$
$727$	−28.1717			−1.04483			−0.522414	+	0.852692i	$0.674969\pi$
$728$	−7.50551	−	0.683594i	−0.278173	−	0.0253357i
$729$	−13.7101			−0.507782
$730$	−27.5616	−	47.7380i	−1.02010	−	1.76686i
$731$	−8.88028	+	15.3811i	−0.328449	+	0.568890i
$732$	0.798646	−	1.38330i	0.0295188	−	0.0511281i
$733$	−3.15772	−	5.46934i	−0.116633	−	0.202015i	0.801798	−	0.597595i	$-0.203877\pi$
$733$	−3.15772	−	5.46934i	−0.116633	−	0.202015i	−0.918431	+	0.395580i	$0.870544\pi$
$734$	−33.0253			−1.21899
$735$	13.0747	+	2.40158i	0.482267	+	0.0885836i
$736$	0.380892			0.0140399
$737$	23.3066	+	40.3683i	0.858511	+	1.48698i
$738$	−6.81911	+	11.8110i	−0.251015	+	0.434770i
$739$	−4.32273	+	7.48719i	−0.159014	+	0.275421i	−0.934513	−	0.355928i	$-0.884165\pi$
$739$	−4.32273	+	7.48719i	−0.159014	+	0.275421i	0.775499	+	0.631349i	$0.217498\pi$
$740$	13.7685	+	23.8477i	0.506140	+	0.876660i
$741$	−5.75016			−0.211237
$742$	3.21942	+	0.293221i	0.118189	+	0.0107645i
$743$	18.3123			0.671814			0.335907	−	0.941895i	$-0.390957\pi$
$743$	18.3123			0.671814			0.335907	+	0.941895i	$0.390957\pi$
$744$	−2.05625	−	3.56153i	−0.0753857	−	0.130572i
$745$	19.1256	−	33.1265i	0.700707	−	1.21366i
$746$	9.97372	−	17.2750i	0.365164	−	0.632482i
$747$	17.5230	+	30.3507i	0.641132	+	1.11047i
$748$	−9.90604			−0.362201
$749$	−13.0921	−	28.3392i	−0.478376	−	1.03549i
$750$	6.82313			0.249145
$751$	1.15487	+	2.00029i	0.0421417	+	0.0729916i	0.886327	−	0.463060i	$-0.153249\pi$
$751$	1.15487	+	2.00029i	0.0421417	+	0.0729916i	−0.844185	+	0.536052i	$0.819915\pi$
$752$	−3.92931	+	6.80577i	−0.143287	+	0.248181i
$753$	5.98267	−	10.3623i	0.218021	−	0.377623i
$754$	1.42428	+	2.46692i	0.0518692	+	0.0898400i
$755$	24.9116			0.906626
$756$	−4.50540	+	6.38584i	−0.163860	+	0.232251i
$757$	53.8978			1.95895			0.979474	−	0.201573i	$-0.0646052\pi$
$757$	53.8978			1.95895			0.979474	+	0.201573i	$0.0646052\pi$
$758$	−13.9362	−	24.1383i	−0.506187	−	0.876742i
$759$	−0.632891	+	1.09620i	−0.0229725	+	0.0397895i
$760$	7.22435	−	12.5129i	0.262055	−	0.453892i
$761$	15.4567	+	26.7718i	0.560305	+	0.970477i	0.997470	+	0.0710954i	$0.0226495\pi$
$761$	15.4567	+	26.7718i	0.560305	+	0.970477i	−0.437164	+	0.899382i	$0.644017\pi$
$762$	1.36000			0.0492677
$763$	−9.23459	+	13.0889i	−0.334314	+	0.473849i
$764$	−20.3346			−0.735681
$765$	−7.74031	−	13.4066i	−0.279851	−	0.484717i
$766$	−10.5799	+	18.3250i	−0.382268	+	0.662108i
$767$	0.992309	−	1.71873i	0.0358302	−	0.0620597i
$768$	−0.257545	−	0.446080i	−0.00929334	−	0.0160965i
$769$	8.51208			0.306953			0.153477	−	0.988152i	$-0.450953\pi$
$769$	8.51208			0.306953			0.153477	+	0.988152i	$0.450953\pi$
$770$	26.3934	+	57.1313i	0.951153	+	2.05887i
$771$	−7.99148			−0.287806
$772$	−6.60202	−	11.4350i	−0.237612	−	0.411556i
$773$	−1.25764	+	2.17830i	−0.0452343	+	0.0783480i	−0.887756	−	0.460314i	$-0.847737\pi$
$773$	−1.25764	+	2.17830i	−0.0452343	+	0.0783480i	0.842522	+	0.538662i	$0.181070\pi$
$774$	−15.8164	+	27.3949i	−0.568510	+	0.984688i
$775$	−34.3031	−	59.4147i	−1.23220	−	2.13424i
$776$	−2.56729			−0.0921604
$777$	10.1367	+	0.923243i	0.363653	+	0.0331212i
$778$	8.79804			0.315425
$779$	−9.77222	−	16.9260i	−0.350126	−	0.606436i
$780$	−2.70479	+	4.68483i	−0.0968470	+	0.167744i
$781$	42.8803	−	74.2709i	1.53438	−	2.65762i
$782$	0.292413	+	0.506474i	0.0104567	+	0.0181115i
$783$	2.95387			0.105563
$784$	−2.34722	−	6.59474i	−0.0838293	−	0.235526i
$785$	−14.3684			−0.512830
$786$	2.77037	+	4.79843i	0.0988159	+	0.171154i
$787$	−2.99152	+	5.18147i	−0.106636	+	0.184699i	−0.914406	−	0.404799i	$-0.867341\pi$
$787$	−2.99152	+	5.18147i	−0.106636	+	0.184699i	0.807769	+	0.589499i	$0.200675\pi$
$788$	4.50618	−	7.80494i	0.160526	−	0.278039i
$789$	0.758501	+	1.31376i	0.0270033	+	0.0467712i
$790$	18.9353			0.673688
$791$	9.24331	+	0.841871i	0.328654	+	0.0299335i
$792$	−17.6434			−0.626931
$793$	4.41669	+	7.64993i	0.156841	+	0.271657i
$794$	3.79207	−	6.56805i	0.134575	−	0.233091i
$795$	1.16019	−	2.00952i	0.0411478	−	0.0712702i
$796$	2.93180	+	5.07802i	0.103915	+	0.179986i
$797$	−0.207213			−0.00733988			−0.00366994	−	0.999993i	$-0.501168\pi$
$797$	−0.207213			−0.00733988			−0.00366994	+	0.999993i	$0.501168\pi$
$798$	−2.23985	−	4.84839i	−0.0792899	−	0.171631i
$799$	−12.0662			−0.426872
$800$	−4.29645	−	7.44167i	−0.151902	−	0.263103i
$801$	12.8480	−	22.2533i	0.453960	−	0.786282i
$802$	−5.91354	+	10.2426i	−0.208814	+	0.361677i
$803$	−48.2306	−	83.5379i	−1.70202	−	2.94799i
$804$	−3.72149			−0.131247
$805$	2.14190	−	3.03588i	0.0754920	−	0.107001i
$806$	22.7430			0.801089
$807$	1.74336	+	3.01959i	0.0613693	+	0.106295i
$808$	5.01718	−	8.69001i	0.176504	−	0.305713i
$809$	−15.9180	+	27.5707i	−0.559646	+	0.969336i	0.437879	+	0.899034i	$0.355730\pi$
$809$	−15.9180	+	27.5707i	−0.559646	+	0.969336i	−0.997526	+	0.0703021i	$0.977604\pi$
$810$	−12.3188	−	21.3368i	−0.432838	−	0.749697i
$811$	−19.8976			−0.698699			−0.349350	−	0.936992i	$-0.613597\pi$
$811$	−19.8976			−0.698699			−0.349350	+	0.936992i	$0.613597\pi$
$812$	−1.52525	+	2.16185i	−0.0535258	+	0.0758662i
$813$	8.69250			0.304859
$814$	24.0938	+	41.7317i	0.844488	+	1.46270i
$815$	−0.717675	+	1.24305i	−0.0251391	+	0.0435421i
$816$	0.395437	−	0.684917i	0.0138431	−	0.0239769i
$817$	−22.6660	−	39.2586i	−0.792982	−	1.37349i
$818$	11.8506			0.414347
$819$	−8.64363	−	18.7100i	−0.302033	−	0.653782i
$820$	−18.3868			−0.642096
$821$	12.1951	+	21.1225i	0.425610	+	0.737179i	0.996477	−	0.0838640i	$-0.0267261\pi$
$821$	12.1951	+	21.1225i	0.425610	+	0.737179i	−0.570867	+	0.821043i	$0.693393\pi$
$822$	−2.18202	+	3.77936i	−0.0761065	+	0.131820i
$823$	25.0794	−	43.4388i	0.874213	−	1.51418i	0.0166149	−	0.999862i	$-0.494711\pi$
$823$	25.0794	−	43.4388i	0.874213	−	1.51418i	0.857598	−	0.514320i	$-0.171956\pi$
$824$	4.67177	+	8.09174i	0.162749	+	0.281889i
$825$	28.5560			0.994192
$826$	1.83572	+	0.167196i	0.0638730	+	0.00581749i
$827$	−12.5847			−0.437612			−0.218806	−	0.975768i	$-0.570216\pi$
$827$	−12.5847			−0.437612			−0.218806	+	0.975768i	$0.570216\pi$
$828$	0.520809	+	0.902068i	0.0180994	+	0.0313490i
$829$	25.0488	−	43.3859i	0.869982	−	1.50685i	0.00796884	−	0.999968i	$-0.497463\pi$
$829$	25.0488	−	43.3859i	0.869982	−	1.50685i	0.862013	−	0.506885i	$-0.169203\pi$
$830$	−23.6242	+	40.9183i	−0.820008	+	1.42029i
$831$	−6.77742	−	11.7388i	−0.235106	−	0.407216i
$832$	2.84856			0.0987560
$833$	6.96709	−	8.18393i	0.241395	−	0.283556i
$834$	−1.23663			−0.0428210
$835$	−18.9950	−	32.9003i	−0.657349	−	1.13856i
$836$	12.6421	−	21.8967i	0.437235	−	0.757313i
$837$	11.7919	−	20.4242i	0.407589	−	0.705965i
$838$	−0.466572	−	0.808127i	−0.0161175	−	0.0279163i
$839$	−26.7756			−0.924397			−0.462199	−	0.886776i	$-0.652939\pi$
$839$	−26.7756			−0.924397			−0.462199	+	0.886776i	$0.652939\pi$
$840$	−5.00373	−	0.455734i	−0.172645	−	0.0157243i
$841$	1.00000			0.0344828
$842$	1.58739	+	2.74944i	0.0547051	+	0.0947520i
$843$	−0.170639	+	0.295556i	−0.00587713	+	0.0101795i
$844$	−10.4870	+	18.1641i	−0.360978	+	0.625233i
$845$	9.00647	+	15.5997i	0.309832	+	0.536645i
$846$	−21.4908			−0.738870
$847$	33.9809	+	73.5553i	1.16760	+	2.52739i
$848$	−1.22186			−0.0419589
$849$	6.42048	+	11.1206i	0.220350	+	0.381658i
$850$	6.59682	−	11.4260i	0.226269	−	0.391910i
$851$	1.42243	−	2.46373i	0.0487604	−	0.0844555i
$852$	3.42346	+	5.92960i	0.117286	+	0.203145i
$853$	−16.8716			−0.577673			−0.288837	−	0.957378i	$-0.593268\pi$
$853$	−16.8716			−0.577673			−0.288837	+	0.957378i	$0.593268\pi$
$854$	−4.72981	+	6.70391i	−0.161851	+	0.229403i
$855$	39.5126			1.35130
$856$	5.89950	+	10.2182i	0.201641	+	0.349252i
$857$	−4.05728	+	7.02742i	−0.138594	+	0.240052i	−0.926965	−	0.375149i	$-0.877592\pi$
$857$	−4.05728	+	7.02742i	−0.138594	+	0.240052i	0.788371	+	0.615201i	$0.210925\pi$
$858$	−4.73318	+	8.19810i	−0.161588	+	0.279879i
$859$	−24.7626	−	42.8901i	−0.844889	−	1.46339i	−0.885718	−	0.464224i	$-0.846333\pi$
$859$	−24.7626	−	42.8901i	−0.844889	−	1.46339i	0.0408294	−	0.999166i	$-0.487000\pi$
$860$	−42.6469			−1.45425
$861$	−3.91809	+	5.55340i	−0.133528	+	0.189259i
$862$	−25.2882			−0.861318
$863$	−18.3327	−	31.7531i	−0.624051	−	1.08089i	−0.988723	−	0.149753i	$-0.952152\pi$
$863$	−18.3327	−	31.7531i	−0.624051	−	1.08089i	0.364672	−	0.931136i	$-0.381181\pi$
$864$	1.47694	−	2.55813i	0.0502464	−	0.0870293i
$865$	−42.4739	+	73.5669i	−1.44416	+	2.50135i
$866$	−12.6950	−	21.9884i	−0.431394	−	0.747197i
$867$	−7.54220			−0.256146
$868$	8.85906	+	19.1764i	0.300696	+	0.650888i
$869$	33.1354			1.12404
$870$	0.949529	+	1.64463i	0.0321921	+	0.0557583i
$871$	10.2903	−	17.8234i	0.348674	−	0.603922i
$872$	3.02724	−	5.24333i	0.102515	−	0.177561i
$873$	−3.51036	−	6.08013i	−0.118808	−	0.205781i
$874$	−1.49271			−0.0504915
$875$	−34.9025	−	3.17888i	−1.17992	−	0.107466i
$876$	7.70123			0.260200
$877$	−1.49721	−	2.59324i	−0.0505570	−	0.0875674i	0.839639	−	0.543144i	$-0.182766\pi$
$877$	−1.49721	−	2.59324i	−0.0505570	−	0.0875674i	−0.890196	+	0.455577i	$0.849433\pi$
$878$	4.97971	−	8.62511i	0.168057	−	0.291083i
$879$	−2.57047	+	4.45219i	−0.0866999	+	0.150169i
$880$	−11.8933	−	20.5997i	−0.400922	−	0.694417i
$881$	14.1339			0.476183			0.238092	−	0.971243i	$-0.423478\pi$
$881$	14.1339			0.476183			0.238092	+	0.971243i	$0.423478\pi$
$882$	12.4089	−	14.5762i	0.417829	−	0.490806i
$883$	−15.9154			−0.535596			−0.267798	−	0.963475i	$-0.586296\pi$
$883$	−15.9154			−0.535596			−0.267798	+	0.963475i	$0.586296\pi$
$884$	2.18685	+	3.78774i	0.0735519	+	0.127396i
$885$	0.661546	−	1.14583i	0.0222376	−	0.0385167i
$886$	4.84527	−	8.39225i	0.162780	−	0.281943i
$887$	−1.07296	−	1.85843i	−0.0360266	−	0.0623999i	0.847450	−	0.530875i	$-0.178137\pi$
$887$	−1.07296	−	1.85843i	−0.0360266	−	0.0623999i	−0.883477	+	0.468475i	$0.844803\pi$
$888$	−3.84718			−0.129103
$889$	−6.95684	−	0.633622i	−0.233325	−	0.0212510i
$890$	34.6428			1.16123
$891$	−21.5569	−	37.3377i	−0.722184	−	1.25086i
$892$	0.553144	−	0.958073i	0.0185206	−	0.0320787i
$893$	15.3989	−	26.6716i	0.515304	−	0.892532i
$894$	2.67203	+	4.62808i	0.0893659	+	0.154786i
$895$	−24.6946			−0.825449
$896$	1.10959	+	2.40183i	0.0370690	+	0.0802396i
$897$	0.558868			0.0186600
$898$	−6.86570	−	11.8917i	−0.229112	−	0.396833i
$899$	3.99203	−	6.91439i	0.133142	−	0.230608i
$900$	11.7494	−	20.3506i	0.391648	−	0.678354i
$901$	−0.938031	−	1.62472i	−0.0312504	−	0.0541272i
$902$	−32.1755			−1.07133
$903$	−9.08773	+	12.8807i	−0.302421	+	0.428644i
$904$	−3.50810			−0.116678
$905$	−24.4167	−	42.2909i	−0.811638	−	1.40580i
$906$	−1.74019	+	3.01411i	−0.0578141	+	0.100137i
$907$	−9.71293	+	16.8233i	−0.322513	+	0.558608i	−0.981006	−	0.193979i	$-0.937861\pi$
$907$	−9.71293	+	16.8233i	−0.322513	+	0.558608i	0.658493	+	0.752587i	$0.271194\pi$
$908$	0.434814	+	0.753121i	0.0144298	+	0.0249932i
$909$	27.4408			0.910153
$910$	16.0185	−	22.7043i	0.531009	−	0.752639i
$911$	−1.60092			−0.0530408			−0.0265204	−	0.999648i	$-0.508443\pi$
$911$	−1.60092			−0.0530408			−0.0265204	+	0.999648i	$0.508443\pi$
$912$	1.00931	+	1.74818i	0.0334216	+	0.0578880i
$913$	−41.3405	+	71.6039i	−1.36817	+	2.36974i
$914$	−6.16944	+	10.6858i	−0.204067	+	0.353454i
$915$	2.94449	+	5.10001i	0.0973419	+	0.168601i
$916$	−7.00356			−0.231404
$917$	−11.9358	−	25.8362i	−0.394154	−	0.853186i
$918$	4.53541			0.149691
$919$	25.4312	+	44.0482i	0.838899	+	1.45302i	0.890816	+	0.454365i	$0.150134\pi$
$919$	25.4312	+	44.0482i	0.838899	+	1.45302i	−0.0519167	+	0.998651i	$0.516533\pi$
$920$	−0.702146	+	1.21615i	−0.0231491	+	0.0400954i
$921$	0.717448	−	1.24266i	0.0236407	−	0.0409469i
$922$	5.91610	+	10.2470i	0.194836	+	0.337467i
$923$	−37.8650			−1.24634
$924$	−8.75614	−	0.797501i	−0.288056	−	0.0262358i
$925$	−64.1800			−2.11023
$926$	15.1594	+	26.2569i	0.498170	+	0.862856i
$927$	−12.7758	+	22.1283i	−0.419612	+	0.726790i
$928$	0.500000	−	0.866025i	0.0164133	−	0.0284287i
$929$	13.9859	+	24.2242i	0.458861	+	0.794771i	0.998901	−	0.0468683i	$-0.0149241\pi$
$929$	13.9859	+	24.2242i	0.458861	+	0.794771i	−0.540040	+	0.841640i	$0.681591\pi$
$930$	15.1622			0.497187
$931$	9.19870	+	25.8446i	0.301475	+	0.847023i
$932$	0.411278			0.0134719
$933$	−3.92965	−	6.80635i	−0.128651	−	0.222830i
$934$	4.15548	−	7.19751i	0.135972	−	0.235510i
$935$	18.2611	−	31.6291i	0.597201	−	1.03438i
$936$	3.89495	+	6.74625i	0.127310	+	0.220508i
$937$	42.4694			1.38741			0.693707	−	0.720258i	$-0.255976\pi$
$937$	42.4694			1.38741			0.693707	+	0.720258i	$0.255976\pi$
$938$	19.0366	+	1.73383i	0.621567	+	0.0566117i
$939$	17.6688			0.576599
$940$	−14.4868	−	25.0919i	−0.472507	−	0.818407i
$941$	−17.2136	+	29.8149i	−0.561149	+	0.971938i	0.436248	+	0.899827i	$0.356307\pi$
$941$	−17.2136	+	29.8149i	−0.561149	+	0.971938i	−0.997397	+	0.0721116i	$0.977026\pi$
$942$	1.00370	−	1.73846i	0.0327024	−	0.0566421i
$943$	0.949778	+	1.64506i	0.0309290	+	0.0535707i
$944$	−0.696710			−0.0226760
$945$	−12.0840	−	26.1572i	−0.393094	−	0.850892i
$946$	−74.6289			−2.42639
$947$	14.0179	+	24.2797i	0.455520	+	0.788984i	0.998718	−	0.0506209i	$-0.0161200\pi$
$947$	14.0179	+	24.2797i	0.455520	+	0.788984i	−0.543198	+	0.839605i	$0.682787\pi$
$948$	−1.32272	+	2.29102i	−0.0429600	+	0.0744090i
$949$	−21.2948	+	36.8836i	−0.691257	+	1.19729i
$950$	16.8377	+	29.1637i	0.546287	+	0.946196i
$951$	−12.1150			−0.392857
$952$	−2.34189	+	3.31934i	−0.0759010	+	0.107580i
$953$	50.4431			1.63401			0.817007	−	0.576628i	$-0.195632\pi$
$953$	50.4431			1.63401			0.817007	+	0.576628i	$0.195632\pi$
$954$	−1.67070	−	2.89374i	−0.0540910	−	0.0936884i
$955$	37.4854	−	64.9266i	1.21300	−	2.10098i
$956$	6.32077	−	10.9479i	0.204428	−	0.354080i
$957$	1.66160	+	2.87798i	0.0537120	+	0.0930320i
$958$	31.3096			1.01157
$959$	12.9225	−	18.3161i	0.417290	−	0.591456i
$960$	1.89906			0.0612919
$961$	−16.3725	−	28.3581i	−0.528146	−	0.914776i
$962$	10.6379	−	18.4254i	0.342979	−	0.594057i
$963$	−16.1333	+	27.9437i	−0.519888	+	0.900472i
$964$	−10.4546	−	18.1079i	−0.336720	−	0.583216i
$965$	48.6814			1.56711
$966$	0.217695	+	0.471223i	0.00700422	+	0.0151614i
$967$	40.9091			1.31555			0.657774	−	0.753215i	$-0.271498\pi$
$967$	40.9091			1.31555			0.657774	+	0.753215i	$0.271498\pi$
$968$	−15.3123	−	26.5217i	−0.492157	−	0.852440i
$969$	−1.54971	+	2.68417i	−0.0497838	+	0.0862281i
$970$	4.73262	−	8.19713i	0.151955	−	0.263194i
$971$	−21.5569	−	37.3376i	−0.691794	−	1.19822i	−0.971250	−	0.238063i	$-0.923487\pi$
$971$	−21.5569	−	37.3376i	−0.691794	−	1.19822i	0.279456	−	0.960158i	$-0.409846\pi$
$972$	12.3037			0.394642
$973$	6.32576	+	0.576144i	0.202795	+	0.0184703i
$974$	−21.7094			−0.695615
$975$	−6.30401	−	10.9189i	−0.201890	−	0.349684i
$976$	1.55050	−	2.68555i	0.0496303	−	0.0859623i
$977$	−24.5842	+	42.5811i	−0.786519	+	1.36229i	0.141568	+	0.989929i	$0.454786\pi$
$977$	−24.5842	+	42.5811i	−0.786519	+	1.36229i	−0.928087	+	0.372363i	$0.878548\pi$
$978$	−0.100266	−	0.173666i	−0.00320616	−	0.00555323i
$979$	60.6223			1.93750
$980$	25.3833	+	4.66245i	0.810841	+	0.148937i
$981$	16.5571			0.528626
$982$	14.3071	+	24.7806i	0.456558	+	0.790781i
$983$	−2.70859	+	4.69142i	−0.0863907	+	0.149633i	−0.905983	−	0.423314i	$-0.860867\pi$
$983$	−2.70859	+	4.69142i	−0.0863907	+	0.149633i	0.819592	+	0.572947i	$0.194200\pi$
$984$	1.28441	−	2.22466i	0.0409454	−	0.0709196i
$985$	16.6136	+	28.7757i	0.529355	+	0.916869i
$986$	1.53541			0.0488975
$987$	−10.6656	−	0.971409i	−0.339489	−	0.0309203i
$988$	−11.1634			−0.355156
$989$	2.20294	+	3.81561i	0.0700495	+	0.121329i
$990$	32.5243	−	56.3338i	1.03369	−	1.79041i
$991$	−3.14438	+	5.44623i	−0.0998845	+	0.173005i	−0.911637	−	0.410997i	$-0.865181\pi$
$991$	−3.14438	+	5.44623i	−0.0998845	+	0.173005i	0.811752	+	0.584002i	$0.198514\pi$
$992$	−3.99203	−	6.91439i	−0.126747	−	0.219532i
$993$	−10.7741			−0.341906
$994$	−14.7495	−	31.9268i	−0.467826	−	1.01266i
$995$	−21.6182			−0.685344
$996$	−3.30053	−	5.71668i	−0.104581	−	0.181140i
$997$	−3.55717	+	6.16120i	−0.112657	+	0.195127i	−0.916841	−	0.399253i	$-0.869269\pi$
$997$	−3.55717	+	6.16120i	−0.112657	+	0.195127i	0.804184	+	0.594381i	$0.202603\pi$
$998$	11.1644	−	19.3373i	0.353402	−	0.612110i
$999$	−11.0312	−	19.1066i	−0.349011	−	0.604505i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	406.2.e.a.291.3	yes	10
7.2	even	3	inner	406.2.e.a.233.3	✓	10
7.3	odd	6		2842.2.a.x.1.3		5
7.4	even	3		2842.2.a.z.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
406.2.e.a.233.3	✓	10	7.2	even	3	inner
406.2.e.a.291.3	yes	10	1.1	even	1	trivial
2842.2.a.x.1.3		5	7.3	odd	6
2842.2.a.z.1.3		5	7.4	even	3

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:	\( N \)	\(=\)	\( 406 = 2 \cdot 7 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	406.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.257545 + 0.446080i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.84343 - 3.19291i) q^{5} +0.515089 q^{6} +(-2.63485 - 0.239979i) q^{7} +1.00000 q^{8} +(1.36734 + 2.36831i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.257545 + 0.446080i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.84343 - 3.19291i) q^{5} +0.515089 q^{6} +(-2.63485 - 0.239979i) q^{7} +1.00000 q^{8} +(1.36734 + 2.36831i) q^{9} +(-1.84343 + 3.19291i) q^{10} +(-3.22586 + 5.58735i) q^{11} +(-0.257545 - 0.446080i) q^{12} +2.84856 q^{13} +(1.10959 + 2.40183i) q^{14} +1.89906 q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.767706 - 1.32971i) q^{17} +(1.36734 - 2.36831i) q^{18} +(1.95949 + 3.39393i) q^{19} +3.68685 q^{20} +(0.785640 - 1.11355i) q^{21} +6.45172 q^{22} +(-0.190446 - 0.329862i) q^{23} +(-0.257545 + 0.446080i) q^{24} +(-4.29645 + 7.44167i) q^{25} +(-1.42428 - 2.46692i) q^{26} -2.95387 q^{27} +(1.52525 - 2.16185i) q^{28} -1.00000 q^{29} +(-0.949529 - 1.64463i) q^{30} +(-3.99203 + 6.91439i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.66160 - 2.87798i) q^{33} -1.53541 q^{34} +(4.09091 + 8.85521i) q^{35} -2.73468 q^{36} +(3.73448 + 6.46831i) q^{37} +(1.95949 - 3.39393i) q^{38} +(-0.733630 + 1.27069i) q^{39} +(-1.84343 - 3.19291i) q^{40} -4.98713 q^{41} +(-1.35718 - 0.123611i) q^{42} -11.5673 q^{43} +(-3.22586 - 5.58735i) q^{44} +(5.04119 - 8.73160i) q^{45} +(-0.190446 + 0.329862i) q^{46} +(-3.92931 - 6.80577i) q^{47} +0.515089 q^{48} +(6.88482 + 1.26462i) q^{49} +8.59290 q^{50} +(0.395437 + 0.684917i) q^{51} +(-1.42428 + 2.46692i) q^{52} +(0.610931 - 1.05816i) q^{53} +(1.47694 + 2.55813i) q^{54} +23.7865 q^{55} +(-2.63485 - 0.239979i) q^{56} -2.01862 q^{57} +(0.500000 + 0.866025i) q^{58} +(0.348355 - 0.603368i) q^{59} +(-0.949529 + 1.64463i) q^{60} +(1.55050 + 2.68555i) q^{61} +7.98405 q^{62} +(-3.03439 - 6.56825i) q^{63} +1.00000 q^{64} +(-5.25111 - 9.09519i) q^{65} +(-1.66160 + 2.87798i) q^{66} +(3.61247 - 6.25698i) q^{67} +(0.767706 + 1.32971i) q^{68} +0.196193 q^{69} +(5.62338 - 7.97044i) q^{70} -13.2927 q^{71} +(1.36734 + 2.36831i) q^{72} +(-7.47563 + 12.9482i) q^{73} +(3.73448 - 6.46831i) q^{74} +(-2.21305 - 3.83312i) q^{75} -3.91898 q^{76} +(9.84048 - 13.9477i) q^{77} +1.46726 q^{78} +(-2.56795 - 4.44782i) q^{79} +(-1.84343 + 3.19291i) q^{80} +(-3.34127 + 5.78725i) q^{81} +(2.49356 + 4.31898i) q^{82} +12.8154 q^{83} +(0.571540 + 1.23716i) q^{84} -5.66084 q^{85} +(5.78365 + 10.0176i) q^{86} +(0.257545 - 0.446080i) q^{87} +(-3.22586 + 5.58735i) q^{88} +(-4.69815 - 8.13744i) q^{89} -10.0824 q^{90} +(-7.50551 - 0.683594i) q^{91} +0.380892 q^{92} +(-2.05625 - 3.56153i) q^{93} +(-3.92931 + 6.80577i) q^{94} +(7.22435 - 12.5129i) q^{95} +(-0.257545 - 0.446080i) q^{96} -2.56729 q^{97} +(-2.34722 - 6.59474i) q^{98} -17.6434 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{2} - 3 q^{3} - 5 q^{4} - 7 q^{5} + 6 q^{6} - 3 q^{7} + 10 q^{8} - 8 q^{9}+O(q^{10}) \) 10 * q - 5 * q^2 - 3 * q^3 - 5 * q^4 - 7 * q^5 + 6 * q^6 - 3 * q^7 + 10 * q^8 - 8 * q^9	\( 10 q - 5 q^{2} - 3 q^{3} - 5 q^{4} - 7 q^{5} + 6 q^{6} - 3 q^{7} + 10 q^{8} - 8 q^{9} - 7 q^{10} - 3 q^{12} + 20 q^{13} + 3 q^{14} - 20 q^{15} - 5 q^{16} - 8 q^{17} - 8 q^{18} - 2 q^{19} + 14 q^{20} + 19 q^{21} - q^{23} - 3 q^{24} - 12 q^{25} - 10 q^{26} + 30 q^{27} - 10 q^{29} + 10 q^{30} - 11 q^{31} - 5 q^{32} - 9 q^{33} + 16 q^{34} + 10 q^{35} + 16 q^{36} + 8 q^{37} - 2 q^{38} - 18 q^{39} - 7 q^{40} + 46 q^{41} - 8 q^{42} - 6 q^{43} - 4 q^{45} - q^{46} - 16 q^{47} + 6 q^{48} - 11 q^{49} + 24 q^{50} - 7 q^{51} - 10 q^{52} - 7 q^{53} - 15 q^{54} + 12 q^{55} - 3 q^{56} - 68 q^{57} + 5 q^{58} + 9 q^{59} + 10 q^{60} - 15 q^{61} + 22 q^{62} - 3 q^{63} + 10 q^{64} - 5 q^{65} - 9 q^{66} + 4 q^{67} - 8 q^{68} + 28 q^{69} + 4 q^{70} - 44 q^{71} - 8 q^{72} + 8 q^{74} + 34 q^{75} + 4 q^{76} + 39 q^{77} + 36 q^{78} + 13 q^{79} - 7 q^{80} - 17 q^{81} - 23 q^{82} + 56 q^{83} - 11 q^{84} - 14 q^{85} + 3 q^{86} + 3 q^{87} - 17 q^{89} + 8 q^{90} + 6 q^{91} + 2 q^{92} - 17 q^{93} - 16 q^{94} + 9 q^{95} - 3 q^{96} + 84 q^{97} - 20 q^{98} - 84 q^{99}+O(q^{100}) \) 10 * q - 5 * q^2 - 3 * q^3 - 5 * q^4 - 7 * q^5 + 6 * q^6 - 3 * q^7 + 10 * q^8 - 8 * q^9 - 7 * q^10 - 3 * q^12 + 20 * q^13 + 3 * q^14 - 20 * q^15 - 5 * q^16 - 8 * q^17 - 8 * q^18 - 2 * q^19 + 14 * q^20 + 19 * q^21 - q^23 - 3 * q^24 - 12 * q^25 - 10 * q^26 + 30 * q^27 - 10 * q^29 + 10 * q^30 - 11 * q^31 - 5 * q^32 - 9 * q^33 + 16 * q^34 + 10 * q^35 + 16 * q^36 + 8 * q^37 - 2 * q^38 - 18 * q^39 - 7 * q^40 + 46 * q^41 - 8 * q^42 - 6 * q^43 - 4 * q^45 - q^46 - 16 * q^47 + 6 * q^48 - 11 * q^49 + 24 * q^50 - 7 * q^51 - 10 * q^52 - 7 * q^53 - 15 * q^54 + 12 * q^55 - 3 * q^56 - 68 * q^57 + 5 * q^58 + 9 * q^59 + 10 * q^60 - 15 * q^61 + 22 * q^62 - 3 * q^63 + 10 * q^64 - 5 * q^65 - 9 * q^66 + 4 * q^67 - 8 * q^68 + 28 * q^69 + 4 * q^70 - 44 * q^71 - 8 * q^72 + 8 * q^74 + 34 * q^75 + 4 * q^76 + 39 * q^77 + 36 * q^78 + 13 * q^79 - 7 * q^80 - 17 * q^81 - 23 * q^82 + 56 * q^83 - 11 * q^84 - 14 * q^85 + 3 * q^86 + 3 * q^87 - 17 * q^89 + 8 * q^90 + 6 * q^91 + 2 * q^92 - 17 * q^93 - 16 * q^94 + 9 * q^95 - 3 * q^96 + 84 * q^97 - 20 * q^98 - 84 * q^99

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