LMFDB - Embedded newform 429.2.i.c.133.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(100,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("429.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.i (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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.7965937851507.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 8x^{8} - 6x^{7} + 28x^{6} - 23x^{5} + 51x^{4} - 10x^{3} + 25x^{2} - 6x + 9 $ x^10 - 2x^9 + 8x^8 - 6x^7 + 28x^6 - 23x^5 + 51x^4 - 10x^3 + 25x^2 - 6*x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			133.3
Root			$0.333779 - 0.578123i$ of defining polynomial
Character	$\chi$	$=$	429.133
Dual form			429.2.i.c.100.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.333779 - 0.578123i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.777183 - 1.34612i) q^{4} +0.849177 q^{5} +(-0.333779 + 0.578123i) q^{6} +(1.61499 - 2.79724i) q^{7} -2.37275 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.333779 - 0.578123i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.777183 - 1.34612i) q^{4} +0.849177 q^{5} +(-0.333779 + 0.578123i) q^{6} +(1.61499 - 2.79724i) q^{7} -2.37275 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.283438 - 0.490929i) q^{10} +(0.500000 + 0.866025i) q^{11} -1.55437 q^{12} +(2.86690 - 2.18653i) q^{13} -2.15620 q^{14} +(-0.424589 - 0.735409i) q^{15} +(-0.762392 - 1.32050i) q^{16} +(0.394400 - 0.683120i) q^{17} +0.667559 q^{18} +(-1.49508 + 2.58956i) q^{19} +(0.659966 - 1.14309i) q^{20} -3.22997 q^{21} +(0.333779 - 0.578123i) q^{22} +(1.75594 + 3.04137i) q^{23} +(1.18637 + 2.05486i) q^{24} -4.27890 q^{25} +(-2.22099 - 0.927601i) q^{26} +1.00000 q^{27} +(-2.51028 - 4.34793i) q^{28} +(-0.576749 - 0.998959i) q^{29} +(-0.283438 + 0.490929i) q^{30} +0.0322574 q^{31} +(-2.88169 + 4.99123i) q^{32} +(0.500000 - 0.866025i) q^{33} -0.526570 q^{34} +(1.37141 - 2.37535i) q^{35} +(0.777183 + 1.34612i) q^{36} +(-2.53312 - 4.38749i) q^{37} +1.99611 q^{38} +(-3.32704 - 1.38954i) q^{39} -2.01488 q^{40} +(-1.86665 - 3.23314i) q^{41} +(1.07810 + 1.86732i) q^{42} +(1.10048 - 1.90609i) q^{43} +1.55437 q^{44} +(-0.424589 + 0.735409i) q^{45} +(1.17219 - 2.03029i) q^{46} +1.56420 q^{47} +(-0.762392 + 1.32050i) q^{48} +(-1.71636 - 2.97282i) q^{49} +(1.42821 + 2.47373i) q^{50} -0.788800 q^{51} +(-0.715225 - 5.55852i) q^{52} +0.836264 q^{53} +(-0.333779 - 0.578123i) q^{54} +(0.424589 + 0.735409i) q^{55} +(-3.83195 + 6.63714i) q^{56} +2.99017 q^{57} +(-0.385014 + 0.666864i) q^{58} +(-4.95844 + 8.58827i) q^{59} -1.31993 q^{60} +(3.25237 - 5.63326i) q^{61} +(-0.0107668 - 0.0186487i) q^{62} +(1.61499 + 2.79724i) q^{63} +0.797823 q^{64} +(2.43450 - 1.85675i) q^{65} -0.667559 q^{66} +(4.97112 + 8.61023i) q^{67} +(-0.613041 - 1.06182i) q^{68} +(1.75594 - 3.04137i) q^{69} -1.83099 q^{70} +(-2.15009 + 3.72407i) q^{71} +(1.18637 - 2.05486i) q^{72} +6.19771 q^{73} +(-1.69100 + 2.92891i) q^{74} +(2.13945 + 3.70563i) q^{75} +(2.32391 + 4.02512i) q^{76} +3.22997 q^{77} +(0.307170 + 2.38724i) q^{78} +12.5074 q^{79} +(-0.647406 - 1.12134i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.24610 + 2.15831i) q^{82} +16.6507 q^{83} +(-2.51028 + 4.34793i) q^{84} +(0.334915 - 0.580090i) q^{85} -1.46927 q^{86} +(-0.576749 + 0.998959i) q^{87} +(-1.18637 - 2.05486i) q^{88} +(4.75163 + 8.23006i) q^{89} +0.566875 q^{90} +(-1.48624 - 11.5506i) q^{91} +5.45873 q^{92} +(-0.0161287 - 0.0279357i) q^{93} +(-0.522097 - 0.904299i) q^{94} +(-1.26959 + 2.19899i) q^{95} +5.76338 q^{96} +(-5.84903 + 10.1308i) q^{97} +(-1.14577 + 1.98453i) q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 5 q^{3} - 2 q^{4} + 16 q^{5} - 2 q^{6} - 9 q^{7} + 6 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q - 2 * q^2 - 5 * q^3 - 2 * q^4 + 16 * q^5 - 2 * q^6 - 9 * q^7 + 6 * q^8 - 5 * q^9	\( 10 q - 2 q^{2} - 5 q^{3} - 2 q^{4} + 16 q^{5} - 2 q^{6} - 9 q^{7} + 6 q^{8} - 5 q^{9} - 7 q^{10} + 5 q^{11} + 4 q^{12} + q^{13} + 6 q^{14} - 8 q^{15} + 4 q^{16} - 3 q^{17} + 4 q^{18} + 3 q^{19} - 6 q^{20} + 18 q^{21} + 2 q^{22} + q^{23} - 3 q^{24} + 18 q^{25} - 20 q^{26} + 10 q^{27} - 25 q^{28} + 2 q^{29} - 7 q^{30} - 4 q^{31} - 3 q^{32} + 5 q^{33} - 46 q^{34} - 12 q^{35} - 2 q^{36} + q^{37} + 14 q^{38} - 2 q^{39} + 50 q^{40} - 18 q^{41} - 3 q^{42} + 9 q^{43} - 4 q^{44} - 8 q^{45} + 2 q^{46} + 32 q^{47} + 4 q^{48} - 22 q^{49} - 12 q^{50} + 6 q^{51} - 7 q^{52} + 6 q^{53} - 2 q^{54} + 8 q^{55} - 25 q^{56} - 6 q^{57} - 29 q^{58} - 16 q^{59} + 12 q^{60} - 8 q^{61} - 16 q^{62} - 9 q^{63} - 2 q^{64} - 6 q^{65} - 4 q^{66} - 19 q^{67} + 22 q^{68} + q^{69} + 72 q^{70} - 25 q^{71} - 3 q^{72} + 16 q^{73} + 5 q^{74} - 9 q^{75} + 38 q^{76} - 18 q^{77} + 13 q^{78} + 36 q^{79} - 20 q^{80} - 5 q^{81} + 40 q^{82} + 44 q^{83} - 25 q^{84} + 7 q^{85} - 8 q^{86} + 2 q^{87} + 3 q^{88} + 20 q^{89} + 14 q^{90} - 25 q^{91} - 60 q^{92} + 2 q^{93} + 8 q^{94} + 7 q^{95} + 6 q^{96} - 21 q^{97} - 6 q^{98} - 10 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 - 5 * q^3 - 2 * q^4 + 16 * q^5 - 2 * q^6 - 9 * q^7 + 6 * q^8 - 5 * q^9 - 7 * q^10 + 5 * q^11 + 4 * q^12 + q^13 + 6 * q^14 - 8 * q^15 + 4 * q^16 - 3 * q^17 + 4 * q^18 + 3 * q^19 - 6 * q^20 + 18 * q^21 + 2 * q^22 + q^23 - 3 * q^24 + 18 * q^25 - 20 * q^26 + 10 * q^27 - 25 * q^28 + 2 * q^29 - 7 * q^30 - 4 * q^31 - 3 * q^32 + 5 * q^33 - 46 * q^34 - 12 * q^35 - 2 * q^36 + q^37 + 14 * q^38 - 2 * q^39 + 50 * q^40 - 18 * q^41 - 3 * q^42 + 9 * q^43 - 4 * q^44 - 8 * q^45 + 2 * q^46 + 32 * q^47 + 4 * q^48 - 22 * q^49 - 12 * q^50 + 6 * q^51 - 7 * q^52 + 6 * q^53 - 2 * q^54 + 8 * q^55 - 25 * q^56 - 6 * q^57 - 29 * q^58 - 16 * q^59 + 12 * q^60 - 8 * q^61 - 16 * q^62 - 9 * q^63 - 2 * q^64 - 6 * q^65 - 4 * q^66 - 19 * q^67 + 22 * q^68 + q^69 + 72 * q^70 - 25 * q^71 - 3 * q^72 + 16 * q^73 + 5 * q^74 - 9 * q^75 + 38 * q^76 - 18 * q^77 + 13 * q^78 + 36 * q^79 - 20 * q^80 - 5 * q^81 + 40 * q^82 + 44 * q^83 - 25 * q^84 + 7 * q^85 - 8 * q^86 + 2 * q^87 + 3 * q^88 + 20 * q^89 + 14 * q^90 - 25 * q^91 - 60 * q^92 + 2 * q^93 + 8 * q^94 + 7 * q^95 + 6 * q^96 - 21 * q^97 - 6 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.333779	−	0.578123i	−0.236018	−	0.408794i	0.723550	−	0.690272i	$-0.242509\pi$
$2$	−0.333779	−	0.578123i	−0.236018	−	0.408794i	−0.959568	+	0.281477i	$0.909176\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.777183	−	1.34612i	0.388591	−	0.673060i
$5$	0.849177			0.379764			0.189882	−	0.981807i	$-0.439190\pi$
$5$	0.849177			0.379764			0.189882	+	0.981807i	$0.439190\pi$
$6$	−0.333779	+	0.578123i	−0.136265	+	0.236018i
$7$	1.61499	−	2.79724i	0.610407	−	1.05726i	−0.380764	−	0.924672i	$-0.624339\pi$
$7$	1.61499	−	2.79724i	0.610407	−	1.05726i	0.991172	−	0.132584i	$-0.0423276\pi$
$8$	−2.37275			−0.838893
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.283438	−	0.490929i	−0.0896309	−	0.155245i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	−1.55437			−0.448707
$13$	2.86690	−	2.18653i	0.795134	−	0.606433i
$13$	2.86690	−	2.18653i	0.795134	−	0.606433i
$14$	−2.15620			−0.576267
$15$	−0.424589	−	0.735409i	−0.109628	−	0.189882i
$16$	−0.762392	−	1.32050i	−0.190598	−	0.330125i
$17$	0.394400	−	0.683120i	0.0956560	−	0.165681i	−0.814226	−	0.580548i	$-0.802838\pi$
$17$	0.394400	−	0.683120i	0.0956560	−	0.165681i	0.909882	+	0.414867i	$0.136172\pi$
$18$	0.667559			0.157345
$19$	−1.49508	+	2.58956i	−0.342996	+	0.594086i	−0.984988	−	0.172626i	$-0.944775\pi$
$19$	−1.49508	+	2.58956i	−0.342996	+	0.594086i	0.641992	+	0.766711i	$0.278108\pi$
$20$	0.659966	−	1.14309i	0.147573	−	0.255604i
$21$	−3.22997			−0.704838
$22$	0.333779	−	0.578123i	0.0711620	−	0.123256i
$23$	1.75594	+	3.04137i	0.366138	+	0.634169i	0.988958	−	0.148196i	$-0.0473465\pi$
$23$	1.75594	+	3.04137i	0.366138	+	0.634169i	−0.622820	+	0.782365i	$0.714013\pi$
$24$	1.18637	+	2.05486i	0.242167	+	0.419446i
$25$	−4.27890			−0.855780
$26$	−2.22099	−	0.927601i	−0.435572	−	0.181918i
$27$	1.00000			0.192450
$28$	−2.51028	−	4.34793i	−0.474398	−	0.821682i
$29$	−0.576749	−	0.998959i	−0.107100	−	0.185502i	0.807494	−	0.589875i	$-0.200823\pi$
$29$	−0.576749	−	0.998959i	−0.107100	−	0.185502i	−0.914594	+	0.404373i	$0.867490\pi$
$30$	−0.283438	+	0.490929i	−0.0517484	+	0.0896309i
$31$	0.0322574			0.00579360			0.00289680	−	0.999996i	$-0.499078\pi$
$31$	0.0322574			0.00579360			0.00289680	+	0.999996i	$0.499078\pi$
$32$	−2.88169	+	4.99123i	−0.509415	+	0.882333i
$33$	0.500000	−	0.866025i	0.0870388	−	0.150756i
$34$	−0.526570			−0.0903060
$35$	1.37141	−	2.37535i	0.231810	−	0.401508i
$36$	0.777183	+	1.34612i	0.129530	+	0.224353i
$37$	−2.53312	−	4.38749i	−0.416442	−	0.721299i	0.579137	−	0.815231i	$-0.303390\pi$
$37$	−2.53312	−	4.38749i	−0.416442	−	0.721299i	−0.995579	+	0.0939317i	$0.970056\pi$
$38$	1.99611			0.323812
$39$	−3.32704	−	1.38954i	−0.532752	−	0.222505i
$40$	−2.01488			−0.318581
$41$	−1.86665	−	3.23314i	−0.291522	−	0.504932i	0.682648	−	0.730748i	$-0.260828\pi$
$41$	−1.86665	−	3.23314i	−0.291522	−	0.504932i	−0.974170	+	0.225816i	$0.927495\pi$
$42$	1.07810	+	1.86732i	0.166354	+	0.288134i
$43$	1.10048	−	1.90609i	0.167822	−	0.290676i	−0.769832	−	0.638247i	$-0.779660\pi$
$43$	1.10048	−	1.90609i	0.167822	−	0.290676i	0.937654	+	0.347571i	$0.112993\pi$
$44$	1.55437			0.234329
$45$	−0.424589	+	0.735409i	−0.0632939	+	0.109628i
$46$	1.17219	−	2.03029i	0.172830	−	0.299350i
$47$	1.56420			0.228162			0.114081	−	0.993471i	$-0.463608\pi$
$47$	1.56420			0.228162			0.114081	+	0.993471i	$0.463608\pi$
$48$	−0.762392	+	1.32050i	−0.110042	+	0.190598i
$49$	−1.71636	−	2.97282i	−0.245194	−	0.424689i
$50$	1.42821	+	2.47373i	0.201979	+	0.349838i
$51$	−0.788800			−0.110454
$52$	−0.715225	−	5.55852i	−0.0991838	−	0.770828i
$53$	0.836264			0.114870			0.0574348	−	0.998349i	$-0.481708\pi$
$53$	0.836264			0.114870			0.0574348	+	0.998349i	$0.481708\pi$
$54$	−0.333779	−	0.578123i	−0.0454216	−	0.0786725i
$55$	0.424589	+	0.735409i	0.0572515	+	0.0991625i
$56$	−3.83195	+	6.63714i	−0.512066	+	0.886925i
$57$	2.99017			0.396057
$58$	−0.385014	+	0.666864i	−0.0505548	+	0.0875635i
$59$	−4.95844	+	8.58827i	−0.645534	+	1.11810i	0.338644	+	0.940914i	$0.390032\pi$
$59$	−4.95844	+	8.58827i	−0.645534	+	1.11810i	−0.984178	+	0.177183i	$0.943302\pi$
$60$	−1.31993			−0.170402
$61$	3.25237	−	5.63326i	0.416423	−	0.721266i	−0.579154	−	0.815218i	$-0.696617\pi$
$61$	3.25237	−	5.63326i	0.416423	−	0.721266i	0.995577	+	0.0939527i	$0.0299503\pi$
$62$	−0.0107668	−	0.0186487i	−0.00136739	−	0.00236839i
$63$	1.61499	+	2.79724i	0.203469	+	0.352419i
$64$	0.797823			0.0997279
$65$	2.43450	−	1.85675i	0.301963	−	0.230301i
$66$	−0.667559			−0.0821708
$67$	4.97112	+	8.61023i	0.607319	+	1.05191i	0.991680	+	0.128724i	$0.0410882\pi$
$67$	4.97112	+	8.61023i	0.607319	+	1.05191i	−0.384362	+	0.923183i	$0.625579\pi$
$68$	−0.613041	−	1.06182i	−0.0743422	−	0.128764i
$69$	1.75594	−	3.04137i	0.211390	−	0.366138i
$70$	−1.83099			−0.218845
$71$	−2.15009	+	3.72407i	−0.255169	+	0.441966i	−0.964941	−	0.262465i	$-0.915464\pi$
$71$	−2.15009	+	3.72407i	−0.255169	+	0.441966i	0.709772	+	0.704431i	$0.248798\pi$
$72$	1.18637	−	2.05486i	0.139815	−	0.242167i
$73$	6.19771			0.725388			0.362694	−	0.931908i	$-0.381857\pi$
$73$	6.19771			0.725388			0.362694	+	0.931908i	$0.381857\pi$
$74$	−1.69100	+	2.92891i	−0.196575	+	0.340478i
$75$	2.13945	+	3.70563i	0.247042	+	0.427890i
$76$	2.32391	+	4.02512i	0.266570	+	0.461713i
$77$	3.22997			0.368090
$78$	0.307170	+	2.38724i	0.0347801	+	0.270301i
$79$	12.5074			1.40719			0.703597	−	0.710600i	$-0.251576\pi$
$79$	12.5074			1.40719			0.703597	+	0.710600i	$0.251576\pi$
$80$	−0.647406	−	1.12134i	−0.0723822	−	0.125370i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.24610	+	2.15831i	−0.137609	+	0.238345i
$83$	16.6507			1.82765			0.913824	−	0.406110i	$-0.133115\pi$
$83$	16.6507			1.82765			0.913824	+	0.406110i	$0.133115\pi$
$84$	−2.51028	+	4.34793i	−0.273894	+	0.474398i
$85$	0.334915	−	0.580090i	0.0363267	−	0.0629196i
$86$	−1.46927			−0.158436
$87$	−0.576749	+	0.998959i	−0.0618340	+	0.107100i
$88$	−1.18637	−	2.05486i	−0.126468	−	0.219049i
$89$	4.75163	+	8.23006i	0.503671	+	0.872384i	0.999991	+	0.00424439i	$0.00135104\pi$
$89$	4.75163	+	8.23006i	0.503671	+	0.872384i	−0.496320	+	0.868140i	$0.665316\pi$
$90$	0.566875			0.0597539
$91$	−1.48624	−	11.5506i	−0.155800	−	1.21083i
$92$	5.45873			0.569112
$93$	−0.0161287	−	0.0279357i	−0.00167247	−	0.00289680i
$94$	−0.522097	−	0.904299i	−0.0538502	−	0.0932714i
$95$	−1.26959	+	2.19899i	−0.130257	+	0.225612i
$96$	5.76338			0.588222
$97$	−5.84903	+	10.1308i	−0.593879	+	1.02863i	0.399826	+	0.916591i	$0.369071\pi$
$97$	−5.84903	+	10.1308i	−0.593879	+	1.02863i	−0.993704	+	0.112037i	$0.964263\pi$
$98$	−1.14577	+	1.98453i	−0.115740	+	0.200468i
$99$	−1.00000			−0.100504
$100$	−3.32549	+	5.75991i	−0.332549	+	0.575991i
$101$	−7.10926	−	12.3136i	−0.707398	−	1.22525i	−0.965819	−	0.259217i	$-0.916536\pi$
$101$	−7.10926	−	12.3136i	−0.707398	−	1.22525i	0.258421	−	0.966032i	$-0.416798\pi$
$102$	0.263285	+	0.456023i	0.0260691	+	0.0451530i
$103$	11.7245			1.15525			0.577623	−	0.816304i	$-0.303980\pi$
$103$	11.7245			1.15525			0.577623	+	0.816304i	$0.303980\pi$
$104$	−6.80242	+	5.18808i	−0.667032	+	0.508733i
$105$	−2.74282			−0.267672
$106$	−0.279128	−	0.483463i	−0.0271113	−	0.0469581i
$107$	5.84391	+	10.1219i	0.564952	+	0.978525i	0.997054	+	0.0767006i	$0.0244386\pi$
$107$	5.84391	+	10.1219i	0.564952	+	0.978525i	−0.432102	+	0.901825i	$0.642228\pi$
$108$	0.777183	−	1.34612i	0.0747845	−	0.129530i
$109$	6.84618			0.655745			0.327872	−	0.944722i	$-0.393668\pi$
$109$	6.84618			0.655745			0.327872	+	0.944722i	$0.393668\pi$
$110$	0.283438	−	0.490929i	0.0270247	−	0.0468082i
$111$	−2.53312	+	4.38749i	−0.240433	+	0.416442i
$112$	−4.92501			−0.465370
$113$	5.17459	−	8.96265i	0.486784	−	0.843135i	−0.513100	−	0.858329i	$-0.671503\pi$
$113$	5.17459	−	8.96265i	0.486784	−	0.843135i	0.999885	+	0.0151934i	$0.00483638\pi$
$114$	−0.998055	−	1.72868i	−0.0934764	−	0.161906i
$115$	1.49110	+	2.58266i	0.139046	+	0.240834i
$116$	−1.79296			−0.166472
$117$	0.460139	+	3.57607i	0.0425399	+	0.330608i
$118$	6.62009			0.609429
$119$	−1.27390	−	2.20646i	−0.116778	−	0.202266i
$120$	1.00744	+	1.74494i	0.0919664	+	0.159290i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−4.34229			−0.393132
$123$	−1.86665	+	3.23314i	−0.168311	+	0.291522i
$124$	0.0250699	−	0.0434223i	0.00225134	−	0.00389944i
$125$	−7.87943			−0.704757
$126$	1.07810	−	1.86732i	0.0960446	−	0.166354i
$127$	−4.32301	−	7.48768i	−0.383605	−	0.664424i	0.607969	−	0.793961i	$-0.291984\pi$
$127$	−4.32301	−	7.48768i	−0.383605	−	0.664424i	−0.991575	+	0.129537i	$0.958651\pi$
$128$	5.49708	+	9.52122i	0.485878	+	0.841565i
$129$	−2.20096			−0.193784
$130$	−1.88602	−	0.787697i	−0.165414	−	0.0690856i
$131$	−10.1086			−0.883196			−0.441598	−	0.897213i	$-0.645588\pi$
$131$	−10.1086			−0.883196			−0.441598	+	0.897213i	$0.645588\pi$
$132$	−0.777183	−	1.34612i	−0.0676451	−	0.117165i
$133$	4.82908	+	8.36421i	0.418734	+	0.725269i
$134$	3.31851	−	5.74783i	0.286676	−	0.496537i
$135$	0.849177			0.0730855
$136$	−0.935811	+	1.62087i	−0.0802451	+	0.138989i
$137$	−6.91951	+	11.9849i	−0.591174	+	1.02394i	0.402901	+	0.915244i	$0.368002\pi$
$137$	−6.91951	+	11.9849i	−0.591174	+	1.02394i	−0.994075	+	0.108699i	$0.965331\pi$
$138$	−2.34438			−0.199567
$139$	−3.42922	+	5.93958i	−0.290863	+	0.503789i	−0.974014	−	0.226488i	$-0.927276\pi$
$139$	−3.42922	+	5.93958i	−0.290863	+	0.503789i	0.683151	+	0.730277i	$0.260609\pi$
$140$	−2.13167	−	3.69216i	−0.180159	−	0.312045i
$141$	−0.782100	−	1.35464i	−0.0658647	−	0.114081i
$142$	2.87062			0.240897
$143$	3.32704	+	1.38954i	0.278221	+	0.116199i
$144$	1.52478			0.127065
$145$	−0.489762	−	0.848293i	−0.0406725	−	0.0704469i
$146$	−2.06867	−	3.58304i	−0.171204	−	0.296534i
$147$	−1.71636	+	2.97282i	−0.141563	+	0.245194i
$148$	−7.87478			−0.647303
$149$	8.21454	−	14.2280i	0.672962	−	1.16560i	−0.304099	−	0.952641i	$-0.598355\pi$
$149$	8.21454	−	14.2280i	0.672962	−	1.16560i	0.977060	−	0.212963i	$-0.0683114\pi$
$150$	1.42821	−	2.47373i	0.116613	−	0.201979i
$151$	7.36374			0.599253			0.299627	−	0.954057i	$-0.403138\pi$
$151$	7.36374			0.599253			0.299627	+	0.954057i	$0.403138\pi$
$152$	3.54745	−	6.14437i	0.287736	−	0.498374i
$153$	0.394400	+	0.683120i	0.0318853	+	0.0552270i
$154$	−1.07810	−	1.86732i	−0.0868756	−	0.150473i
$155$	0.0273922			0.00220020
$156$	−4.45621	+	3.39866i	−0.356782	+	0.272111i
$157$	21.5732			1.72173			0.860865	−	0.508833i	$-0.169923\pi$
$157$	21.5732			1.72173			0.860865	+	0.508833i	$0.169923\pi$
$158$	−4.17471	−	7.23082i	−0.332122	−	0.575253i
$159$	−0.418132	−	0.724226i	−0.0331600	−	0.0574348i
$160$	−2.44706	+	4.23844i	−0.193457	+	0.335078i
$161$	11.3432			0.893973
$162$	−0.333779	+	0.578123i	−0.0262242	+	0.0454216i
$163$	−6.87689	+	11.9111i	−0.538640	+	0.932951i	0.460338	+	0.887744i	$0.347728\pi$
$163$	−6.87689	+	11.9111i	−0.538640	+	0.932951i	−0.998978	+	0.0452074i	$0.985605\pi$
$164$	−5.80293			−0.453132
$165$	0.424589	−	0.735409i	0.0330542	−	0.0572515i
$166$	−5.55765	−	9.62613i	−0.431357	−	0.747132i
$167$	−5.29848	−	9.17724i	−0.410009	−	0.710156i	0.584881	−	0.811119i	$-0.301141\pi$
$167$	−5.29848	−	9.17724i	−0.410009	−	0.710156i	−0.994890	+	0.100963i	$0.967808\pi$
$168$	7.66391			0.591283
$169$	3.43820	−	12.5371i	0.264477	−	0.964392i
$170$	−0.447151			−0.0342949
$171$	−1.49508	−	2.58956i	−0.114332	−	0.198029i
$172$	−1.71055	−	2.96276i	−0.130428	−	0.225908i
$173$	2.18012	−	3.77608i	0.165751	−	0.287090i	−0.771170	−	0.636629i	$-0.780328\pi$
$173$	2.18012	−	3.77608i	0.165751	−	0.287090i	0.936922	+	0.349539i	$0.113662\pi$
$174$	0.770028			0.0583756
$175$	−6.91036	+	11.9691i	−0.522374	+	0.904779i
$176$	0.762392	−	1.32050i	0.0574675	−	0.0995365i
$177$	9.91687			0.745398
$178$	3.17199	−	5.49404i	0.237751	−	0.411796i
$179$	−6.87137	−	11.9016i	−0.513590	−	0.889564i	−0.999876	−	0.0157641i	$-0.994982\pi$
$179$	−6.87137	−	11.9016i	−0.513590	−	0.889564i	0.486286	−	0.873800i	$-0.338351\pi$
$180$	0.659966	+	1.14309i	0.0491910	+	0.0852012i
$181$	−15.1610			−1.12691			−0.563453	−	0.826148i	$-0.690527\pi$
$181$	−15.1610			−1.12691			−0.563453	+	0.826148i	$0.690527\pi$
$182$	−6.18159	+	4.71458i	−0.458210	+	0.349468i
$183$	−6.50473			−0.480844
$184$	−4.16639	−	7.21640i	−0.307150	−	0.532000i
$185$	−2.15107	−	3.72576i	−0.158150	−	0.273923i
$186$	−0.0107668	+	0.0186487i	−0.000789464	+	0.00136739i
$187$	0.788800			0.0576827
$188$	1.21567	−	2.10560i	0.0886618	−	0.153567i
$189$	1.61499	−	2.79724i	0.117473	−	0.203469i
$190$	1.69505			0.122972
$191$	1.48435	−	2.57097i	0.107404	−	0.186029i	−0.807314	−	0.590122i	$-0.799080\pi$
$191$	1.48435	−	2.57097i	0.107404	−	0.186029i	0.914718	+	0.404093i	$0.132413\pi$
$192$	−0.398912	−	0.690935i	−0.0287890	−	0.0498640i
$193$	2.90711	+	5.03526i	0.209258	+	0.362446i	0.951481	−	0.307707i	$-0.0995617\pi$
$193$	2.90711	+	5.03526i	0.209258	+	0.362446i	−0.742223	+	0.670153i	$0.766228\pi$
$194$	7.80913			0.560663
$195$	−2.82524	−	1.17997i	−0.202320	−	0.0844992i
$196$	−5.33570			−0.381122
$197$	−4.22473	−	7.31745i	−0.301000	−	0.521346i	0.675363	−	0.737485i	$-0.263987\pi$
$197$	−4.22473	−	7.31745i	−0.301000	−	0.521346i	−0.976363	+	0.216139i	$0.930654\pi$
$198$	0.333779	+	0.578123i	0.0237207	+	0.0410854i
$199$	−7.28654	+	12.6207i	−0.516529	+	0.894654i	0.483287	+	0.875462i	$0.339443\pi$
$199$	−7.28654	+	12.6207i	−0.516529	+	0.894654i	−0.999816	+	0.0191922i	$0.993891\pi$
$200$	10.1527			0.717907
$201$	4.97112	−	8.61023i	0.350636	−	0.607319i
$202$	−4.74585	+	8.22005i	−0.333917	+	0.578361i
$203$	−3.72577			−0.261498
$204$	−0.613041	+	1.06182i	−0.0429215	+	0.0743422i
$205$	−1.58512	−	2.74551i	−0.110710	−	0.191755i
$206$	−3.91338	−	6.77818i	−0.272658	−	0.472258i
$207$	−3.51187			−0.244092
$208$	−5.07301	−	2.11875i	−0.351750	−	0.146909i
$209$	−2.99017			−0.206834
$210$	0.915496	+	1.58569i	0.0631752	+	0.109423i
$211$	−4.79309	−	8.30187i	−0.329970	−	0.571524i	0.652536	−	0.757758i	$-0.273705\pi$
$211$	−4.79309	−	8.30187i	−0.329970	−	0.571524i	−0.982506	+	0.186234i	$0.940372\pi$
$212$	0.649930	−	1.12571i	0.0446374	−	0.0773142i
$213$	4.30018			0.294644
$214$	3.90115	−	6.75699i	0.266677	−	0.461898i
$215$	0.934504	−	1.61861i	0.0637326	−	0.110388i
$216$	−2.37275			−0.161445
$217$	0.0520952	−	0.0902316i	0.00353646	−	0.00612532i
$218$	−2.28511	−	3.95793i	−0.154767	−	0.268065i
$219$	−3.09886	−	5.36738i	−0.209401	−	0.362694i
$220$	1.31993			0.0889898
$221$	−0.362958	−	2.82080i	−0.0244152	−	0.189748i
$222$	3.38201			0.226986
$223$	4.60905	+	7.98311i	0.308645	+	0.534589i	0.978066	−	0.208294i	$-0.0667912\pi$
$223$	4.60905	+	7.98311i	0.308645	+	0.534589i	−0.669421	+	0.742883i	$0.733458\pi$
$224$	9.30777	+	16.1215i	0.621902	+	1.07717i
$225$	2.13945	−	3.70563i	0.142630	−	0.247042i
$226$	−6.90868			−0.459559
$227$	−10.2799	+	17.8054i	−0.682304	+	1.18179i	0.291972	+	0.956427i	$0.405689\pi$
$227$	−10.2799	+	17.8054i	−0.682304	+	1.18179i	−0.974276	+	0.225359i	$0.927645\pi$
$228$	2.32391	−	4.02512i	0.153904	−	0.266570i
$229$	−6.92737			−0.457774			−0.228887	−	0.973453i	$-0.573509\pi$
$229$	−6.92737			−0.457774			−0.228887	+	0.973453i	$0.573509\pi$
$230$	0.995397	−	1.72408i	0.0656345	−	0.113682i
$231$	−1.61499	−	2.79724i	−0.106258	−	0.184045i
$232$	1.36848	+	2.37028i	0.0898451	+	0.155616i
$233$	−9.94449			−0.651485			−0.325743	−	0.945459i	$-0.605614\pi$
$233$	−9.94449			−0.651485			−0.325743	+	0.945459i	$0.605614\pi$
$234$	1.91382	−	1.45963i	0.125110	−	0.0954193i
$235$	1.32828			0.0866476
$236$	7.70722	+	13.3493i	0.501698	+	0.868966i
$237$	−6.25370	−	10.8317i	−0.406222	−	0.703597i
$238$	−0.850403	+	1.47294i	−0.0551234	+	0.0954766i
$239$	−10.7017			−0.692237			−0.346118	−	0.938191i	$-0.612500\pi$
$239$	−10.7017			−0.692237			−0.346118	+	0.938191i	$0.612500\pi$
$240$	−0.647406	+	1.12134i	−0.0417899	+	0.0723822i
$241$	−12.2124	+	21.1525i	−0.786670	+	1.36255i	0.141327	+	0.989963i	$0.454863\pi$
$241$	−12.2124	+	21.1525i	−0.786670	+	1.36255i	−0.927997	+	0.372589i	$0.878470\pi$
$242$	0.667559			0.0429123
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−5.05537	−	8.75615i	−0.323637	−	0.560555i
$245$	−1.45749	−	2.52445i	−0.0931159	−	0.161281i
$246$	2.49220			0.158897
$247$	1.37589	+	10.6930i	0.0875459	+	0.680382i
$248$	−0.0765386			−0.00486021
$249$	−8.32533	−	14.4199i	−0.527597	−	0.913824i
$250$	2.62999	+	4.55528i	0.166335	+	0.288101i
$251$	−2.44258	+	4.23068i	−0.154175	+	0.267038i	−0.932758	−	0.360503i	$-0.882605\pi$
$251$	−2.44258	+	4.23068i	−0.154175	+	0.267038i	0.778584	+	0.627541i	$0.215938\pi$
$252$	5.02056			0.316265
$253$	−1.75594	+	3.04137i	−0.110395	+	0.191209i
$254$	−2.88586	+	4.99846i	−0.181075	+	0.313631i
$255$	−0.669831			−0.0419464
$256$	4.46745	−	7.73784i	0.279215	−	0.483615i
$257$	−11.6952	−	20.2567i	−0.729526	−	1.26358i	−0.957084	−	0.289812i	$-0.906407\pi$
$257$	−11.6952	−	20.2567i	−0.729526	−	1.26358i	0.227557	−	0.973765i	$-0.426926\pi$
$258$	0.734636	+	1.27243i	0.0457364	+	0.0792178i
$259$	−16.3638			−1.01680
$260$	−0.607352	−	4.72017i	−0.0376664	−	0.292732i
$261$	1.15350			0.0713998
$262$	3.37406	+	5.84404i	0.208450	+	0.361046i
$263$	2.67363	+	4.63086i	0.164863	+	0.285551i	0.936607	−	0.350383i	$-0.113948\pi$
$263$	2.67363	+	4.63086i	0.164863	+	0.285551i	−0.771744	+	0.635934i	$0.780615\pi$
$264$	−1.18637	+	2.05486i	−0.0730162	+	0.126468i
$265$	0.710136			0.0436233
$266$	3.22369	−	5.58360i	0.197657	−	0.342352i
$267$	4.75163	−	8.23006i	0.290795	−	0.503671i
$268$	15.4539			0.943995
$269$	5.66999	−	9.82071i	0.345705	−	0.598779i	−0.639776	−	0.768561i	$-0.720973\pi$
$269$	5.66999	−	9.82071i	0.345705	−	0.598779i	0.985482	+	0.169782i	$0.0543063\pi$
$270$	−0.283438	−	0.490929i	−0.0172495	−	0.0298770i
$271$	−6.23570	−	10.8005i	−0.378792	−	0.656086i	0.612095	−	0.790784i	$-0.290327\pi$
$271$	−6.23570	−	10.8005i	−0.378792	−	0.656086i	−0.990887	+	0.134698i	$0.956994\pi$
$272$	−1.20275			−0.0729274
$273$	−9.26000	+	7.06242i	−0.560441	+	0.427437i
$274$	9.23835			0.558109
$275$	−2.13945	−	3.70563i	−0.129014	−	0.223458i
$276$	−2.72937	−	4.72740i	−0.164288	−	0.284556i
$277$	9.94564	−	17.2264i	0.597576	−	1.03503i	−0.395602	−	0.918422i	$-0.629464\pi$
$277$	9.94564	−	17.2264i	0.597576	−	1.03503i	0.993178	−	0.116609i	$-0.0372026\pi$
$278$	4.57841			0.274595
$279$	−0.0161287	+	0.0279357i	−0.000965600	+	0.00167247i
$280$	−3.25401	+	5.63611i	−0.194464	+	0.336822i
$281$	19.7804			1.18000			0.590001	−	0.807402i	$-0.299127\pi$
$281$	19.7804			1.18000			0.590001	+	0.807402i	$0.299127\pi$
$282$	−0.522097	+	0.904299i	−0.0310905	+	0.0538502i
$283$	−2.55376	−	4.42324i	−0.151805	−	0.262934i	0.780086	−	0.625672i	$-0.215175\pi$
$283$	−2.55376	−	4.42324i	−0.151805	−	0.262934i	−0.931891	+	0.362738i	$0.881842\pi$
$284$	3.34203	+	5.78856i	0.198313	+	0.343488i
$285$	2.53918			0.150408
$286$	−0.307170	−	2.38724i	−0.0181633	−	0.141160i
$287$	−12.0585			−0.711790
$288$	−2.88169	−	4.99123i	−0.169805	−	0.294111i
$289$	8.18890	+	14.1836i	0.481700	+	0.834329i
$290$	−0.326945	+	0.566285i	−0.0191989	+	0.0332534i
$291$	11.6981			0.685752
$292$	4.81676	−	8.34287i	0.281879	−	0.488229i
$293$	−3.49191	+	6.04816i	−0.203999	+	0.353337i	−0.949813	−	0.312817i	$-0.898727\pi$
$293$	−3.49191	+	6.04816i	−0.203999	+	0.353337i	0.745814	+	0.666154i	$0.232061\pi$
$294$	2.29154			0.133645
$295$	−4.21059	+	7.29296i	−0.245150	+	0.424612i
$296$	6.01045	+	10.4104i	0.349350	+	0.605092i
$297$	0.500000	+	0.866025i	0.0290129	+	0.0502519i
$298$	−10.9674			−0.635323
$299$	11.6841	+	4.87989i	0.675710	+	0.282212i
$300$	6.65097			0.383994
$301$	−3.55452	−	6.15662i	−0.204879	−	0.354861i
$302$	−2.45787	−	4.25715i	−0.141434	−	0.244971i
$303$	−7.10926	+	12.3136i	−0.408416	+	0.707398i
$304$	4.55936			0.261497
$305$	2.76184	−	4.78364i	0.158142	−	0.273910i
$306$	0.263285	−	0.456023i	0.0150510	−	0.0260691i
$307$	−18.8576			−1.07626			−0.538129	−	0.842862i	$-0.680869\pi$
$307$	−18.8576			−1.07626			−0.538129	+	0.842862i	$0.680869\pi$
$308$	2.51028	−	4.34793i	0.143036	−	0.247746i
$309$	−5.86223	−	10.1537i	−0.333491	−	0.577623i
$310$	−0.00914296	−	0.0158361i	−0.000519285	−	0.000899429i
$311$	−30.2366			−1.71456			−0.857281	−	0.514849i	$-0.827848\pi$
$311$	−30.2366			−1.71456			−0.857281	+	0.514849i	$0.827848\pi$
$312$	7.89422	+	3.29703i	0.446922	+	0.186658i
$313$	28.6369			1.61865			0.809326	−	0.587360i	$-0.199833\pi$
$313$	28.6369			1.61865			0.809326	+	0.587360i	$0.199833\pi$
$314$	−7.20069	−	12.4720i	−0.406359	−	0.703834i
$315$	1.37141	+	2.37535i	0.0772702	+	0.133836i
$316$	9.72054	−	16.8365i	0.546823	−	0.947126i
$317$	19.6824			1.10547			0.552736	−	0.833357i	$-0.313584\pi$
$317$	19.6824			1.10547			0.552736	+	0.833357i	$0.313584\pi$
$318$	−0.279128	+	0.483463i	−0.0156527	+	0.0271113i
$319$	0.576749	−	0.998959i	0.0322918	−	0.0559310i
$320$	0.677493			0.0378730
$321$	5.84391	−	10.1219i	0.326175	−	0.564952i
$322$	−3.78614	−	6.55779i	−0.210993	−	0.365451i
$323$	1.17932	+	2.04264i	0.0656192	+	0.113656i
$324$	−1.55437			−0.0863536
$325$	−12.2672	+	9.35593i	−0.680460	+	0.518973i
$326$	9.18145			0.508514
$327$	−3.42309	−	5.92896i	−0.189297	−	0.327872i
$328$	4.42910	+	7.67142i	0.244556	+	0.423584i
$329$	2.52616	−	4.37544i	0.139272	−	0.241226i
$330$	−0.566875			−0.0312055
$331$	−10.7824	+	18.6756i	−0.592652	+	1.02650i	0.401222	+	0.915981i	$0.368586\pi$
$331$	−10.7824	+	18.6756i	−0.592652	+	1.02650i	−0.993874	+	0.110522i	$0.964748\pi$
$332$	12.9406	−	22.4138i	0.710208	−	1.23012i
$333$	5.06624			0.277628
$334$	−3.53705	+	6.12635i	−0.193539	+	0.335219i
$335$	4.22136	+	7.31161i	0.230637	+	0.399476i
$336$	2.46250	+	4.26518i	0.134341	+	0.232685i
$337$	−34.0883			−1.85691			−0.928453	−	0.371449i	$-0.878861\pi$
$337$	−34.0883			−1.85691			−0.928453	+	0.371449i	$0.878861\pi$
$338$	−8.39558	+	2.19692i	−0.456659	+	0.119497i
$339$	−10.3492			−0.562090
$340$	−0.520581	−	0.901672i	−0.0282325	−	0.0489000i
$341$	0.0161287	+	0.0279357i	0.000873418	+	0.00151280i
$342$	−0.998055	+	1.72868i	−0.0539687	+	0.0934764i
$343$	11.5222			0.622141
$344$	−2.61116	+	4.52267i	−0.140785	+	0.243846i
$345$	1.49110	−	2.58266i	0.0802781	−	0.139046i
$346$	−2.91071			−0.156481
$347$	13.1839	−	22.8352i	0.707751	−	1.22586i	−0.257939	−	0.966161i	$-0.583043\pi$
$347$	13.1839	−	22.8352i	0.707751	−	1.22586i	0.965690	−	0.259699i	$-0.0836234\pi$
$348$	0.896479	+	1.55275i	0.0480563	+	0.0832360i
$349$	5.01891	+	8.69300i	0.268656	+	0.465326i	0.968515	−	0.248955i	$-0.0800872\pi$
$349$	5.01891	+	8.69300i	0.268656	+	0.465326i	−0.699859	+	0.714281i	$0.746754\pi$
$350$	9.22614			0.493158
$351$	2.86690	−	2.18653i	0.153024	−	0.116708i
$352$	−5.76338			−0.307189
$353$	10.2221	+	17.7052i	0.544069	+	0.942355i	0.998665	+	0.0516571i	$0.0164503\pi$
$353$	10.2221	+	17.7052i	0.544069	+	0.942355i	−0.454596	+	0.890698i	$0.650216\pi$
$354$	−3.31005	−	5.73317i	−0.175927	−	0.304715i
$355$	−1.82581	+	3.16239i	−0.0969039	+	0.167842i
$356$	14.7715			0.782889
$357$	−1.27390	+	2.20646i	−0.0674220	+	0.116778i
$358$	−4.58704	+	7.94498i	−0.242433	+	0.419905i
$359$	27.9740			1.47641			0.738206	−	0.674575i	$-0.235673\pi$
$359$	27.9740			1.47641			0.738206	+	0.674575i	$0.235673\pi$
$360$	1.00744	−	1.74494i	0.0530968	−	0.0919664i
$361$	5.02945	+	8.71127i	0.264708	+	0.458488i
$362$	5.06042	+	8.76490i	0.265970	+	0.460673i
$363$	1.00000			0.0524864
$364$	−16.7036	−	6.97628i	−0.875505	−	0.365656i
$365$	5.26296			0.275476
$366$	2.17115	+	3.76053i	0.113488	+	0.196566i
$367$	13.3717	+	23.1604i	0.697995	+	1.20896i	0.969161	+	0.246430i	$0.0792576\pi$
$367$	13.3717	+	23.1604i	0.697995	+	1.20896i	−0.271165	+	0.962533i	$0.587409\pi$
$368$	2.67742	−	4.63743i	0.139570	−	0.241743i
$369$	3.73331			0.194348
$370$	−1.43596	+	2.48716i	−0.0746521	+	0.129301i
$371$	1.35055	−	2.33923i	0.0701173	−	0.121447i
$372$	−0.0501398			−0.00259963
$373$	−11.8299	+	20.4900i	−0.612531	+	1.06093i	0.378282	+	0.925691i	$0.376515\pi$
$373$	−11.8299	+	20.4900i	−0.612531	+	1.06093i	−0.990812	+	0.135244i	$0.956818\pi$
$374$	−0.263285	−	0.456023i	−0.0136141	−	0.0235804i
$375$	3.93971	+	6.82378i	0.203446	+	0.352379i
$376$	−3.71145			−0.191403
$377$	−3.83773	−	1.60284i	−0.197653	−	0.0825502i
$378$	−2.15620			−0.110903
$379$	13.3469	+	23.1175i	0.685583	+	1.18746i	0.973253	+	0.229735i	$0.0737859\pi$
$379$	13.3469	+	23.1175i	0.685583	+	1.18746i	−0.287670	+	0.957730i	$0.592881\pi$
$380$	1.97341	+	3.41804i	0.101234	+	0.175342i
$381$	−4.32301	+	7.48768i	−0.221475	+	0.383605i
$382$	−1.98178			−0.101397
$383$	−14.4494	+	25.0271i	−0.738329	+	1.27882i	0.214919	+	0.976632i	$0.431051\pi$
$383$	−14.4494	+	25.0271i	−0.738329	+	1.27882i	−0.953247	+	0.302191i	$0.902282\pi$
$384$	5.49708	−	9.52122i	0.280522	−	0.485878i
$385$	2.74282			0.139787
$386$	1.94067	−	3.36133i	0.0987773	−	0.171087i
$387$	1.10048	+	1.90609i	0.0559406	+	0.0968920i
$388$	9.09152	+	15.7470i	0.461552	+	0.799432i
$389$	−24.7751			−1.25615			−0.628073	−	0.778154i	$-0.716156\pi$
$389$	−24.7751			−1.25615			−0.628073	+	0.778154i	$0.716156\pi$
$390$	0.260842	+	2.02719i	0.0132082	+	0.102651i
$391$	2.77016			0.140093
$392$	4.07249	+	7.05376i	0.205692	+	0.356269i
$393$	5.05432	+	8.75434i	0.254957	+	0.441598i
$394$	−2.82025	+	4.88482i	−0.142082	+	0.246094i
$395$	10.6210			0.534401
$396$	−0.777183	+	1.34612i	−0.0390549	+	0.0676451i
$397$	−2.56512	+	4.44292i	−0.128740	+	0.222984i	−0.923189	−	0.384347i	$-0.874427\pi$
$397$	−2.56512	+	4.44292i	−0.128740	+	0.222984i	0.794449	+	0.607331i	$0.207760\pi$
$398$	9.72838			0.487640
$399$	4.82908	−	8.36421i	0.241756	−	0.418734i
$400$	3.26220	+	5.65029i	0.163110	+	0.282515i
$401$	−3.87725	−	6.71559i	−0.193621	−	0.335361i	0.752827	−	0.658219i	$-0.228690\pi$
$401$	−3.87725	−	6.71559i	−0.193621	−	0.335361i	−0.946447	+	0.322858i	$0.895356\pi$
$402$	−6.63702			−0.331025
$403$	0.0924786	−	0.0705317i	0.00460669	−	0.00351343i
$404$	−22.1008			−1.09955
$405$	−0.424589	−	0.735409i	−0.0210980	−	0.0365428i
$406$	1.24358	+	2.15395i	0.0617180	+	0.106899i
$407$	2.53312	−	4.38749i	0.125562	−	0.217480i
$408$	1.87162			0.0926591
$409$	−2.73670	+	4.74011i	−0.135321	+	0.234383i	−0.925720	−	0.378209i	$-0.876540\pi$
$409$	−2.73670	+	4.74011i	−0.135321	+	0.234383i	0.790399	+	0.612593i	$0.209873\pi$
$410$	−1.05816	+	1.83279i	−0.0522588	+	0.0905149i
$411$	13.8390			0.682628
$412$	9.11205	−	15.7825i	0.448919	−	0.777550i
$413$	16.0156	+	27.7399i	0.788077	+	1.36499i
$414$	1.17219	+	2.03029i	0.0576100	+	0.0997834i
$415$	14.1394			0.694074
$416$	2.65196	+	20.6102i	0.130023	+	1.01050i
$417$	6.85844			0.335859
$418$	0.998055	+	1.72868i	0.0488165	+	0.0845526i
$419$	−16.8067	−	29.1100i	−0.821060	−	1.42212i	−0.904893	−	0.425639i	$-0.860049\pi$
$419$	−16.8067	−	29.1100i	−0.821060	−	1.42212i	0.0838327	−	0.996480i	$-0.473284\pi$
$420$	−2.13167	+	3.69216i	−0.104015	+	0.180159i
$421$	−31.5135			−1.53587			−0.767937	−	0.640526i	$-0.778717\pi$
$421$	−31.5135			−1.53587			−0.767937	+	0.640526i	$0.778717\pi$
$422$	−3.19967	+	5.54199i	−0.155757	+	0.269780i
$423$	−0.782100	+	1.35464i	−0.0380270	+	0.0658647i
$424$	−1.98424			−0.0963633
$425$	−1.68760	+	2.92300i	−0.0818605	+	0.141786i
$426$	−1.43531	−	2.48603i	−0.0695411	−	0.120449i
$427$	−10.5051	−	18.1953i	−0.508375	−	0.880532i
$428$	18.1671			0.878142
$429$	−0.460139	−	3.57607i	−0.0222157	−	0.172654i
$430$	−1.24767			−0.0601681
$431$	14.6349	+	25.3483i	0.704937	+	1.22099i	0.966714	+	0.255858i	$0.0823580\pi$
$431$	14.6349	+	25.3483i	0.704937	+	1.22099i	−0.261778	+	0.965128i	$0.584309\pi$
$432$	−0.762392	−	1.32050i	−0.0366806	−	0.0635327i
$433$	10.7335	−	18.5910i	0.515820	−	0.893426i	−0.484011	−	0.875062i	$-0.660821\pi$
$433$	10.7335	−	18.5910i	0.515820	−	0.893426i	0.999831	−	0.0183648i	$-0.00584601\pi$
$434$	−0.0695533			−0.00333866
$435$	−0.489762	+	0.848293i	−0.0234823	+	0.0406725i
$436$	5.32073	−	9.21578i	0.254817	−	0.441356i
$437$	−10.5011			−0.502335
$438$	−2.06867	+	3.58304i	−0.0988448	+	0.171204i
$439$	1.16422	+	2.01649i	0.0555653	+	0.0962419i	0.892470	−	0.451107i	$-0.148971\pi$
$439$	1.16422	+	2.01649i	0.0555653	+	0.0962419i	−0.836905	+	0.547348i	$0.815637\pi$
$440$	−1.00744	−	1.74494i	−0.0480279	−	0.0831867i
$441$	3.43272			0.163463
$442$	−1.50962	+	1.15136i	−0.0718054	+	0.0547646i
$443$	12.4928			0.593550			0.296775	−	0.954947i	$-0.404089\pi$
$443$	12.4928			0.593550			0.296775	+	0.954947i	$0.404089\pi$
$444$	3.93739	+	6.81976i	0.186860	+	0.323652i
$445$	4.03497	+	6.98878i	0.191276	+	0.331300i
$446$	3.07681	−	5.32919i	0.145691	−	0.252345i
$447$	−16.4291			−0.777069
$448$	1.28847	−	2.23170i	0.0608747	−	0.105438i
$449$	13.8002	−	23.9027i	0.651273	−	1.12804i	−0.331541	−	0.943441i	$-0.607569\pi$
$449$	13.8002	−	23.9027i	0.651273	−	1.12804i	0.982814	−	0.184598i	$-0.0590982\pi$
$450$	−2.85641			−0.134653
$451$	1.86665	−	3.23314i	0.0878973	−	0.152243i
$452$	−8.04320	−	13.9312i	−0.378321	−	0.655270i
$453$	−3.68187	−	6.37719i	−0.172989	−	0.299627i
$454$	13.7249			0.644143
$455$	−1.26208	−	9.80851i	−0.0591671	−	0.459830i
$456$	−7.09491			−0.332249
$457$	−5.36694	−	9.29581i	−0.251055	−	0.434840i	0.712762	−	0.701406i	$-0.247444\pi$
$457$	−5.36694	−	9.29581i	−0.251055	−	0.434840i	−0.963816	+	0.266567i	$0.914111\pi$
$458$	2.31221	+	4.00487i	0.108043	+	0.187135i
$459$	0.394400	−	0.683120i	0.0184090	−	0.0318853i
$460$	4.63543			0.216128
$461$	−17.0750	+	29.5747i	−0.795260	+	1.37743i	0.127413	+	0.991850i	$0.459333\pi$
$461$	−17.0750	+	29.5747i	−0.795260	+	1.37743i	−0.922674	+	0.385582i	$0.874001\pi$
$462$	−1.07810	+	1.86732i	−0.0501576	+	0.0868756i
$463$	26.5280			1.23286			0.616431	−	0.787409i	$-0.288578\pi$
$463$	26.5280			1.23286			0.616431	+	0.787409i	$0.288578\pi$
$464$	−0.879418	+	1.52320i	−0.0408259	+	0.0707126i
$465$	−0.0136961	−	0.0237224i	−0.000635142	−	0.00110010i
$466$	3.31926	+	5.74913i	0.153762	+	0.266323i
$467$	−36.6740			−1.69707			−0.848536	−	0.529138i	$-0.822515\pi$
$467$	−36.6740			−1.69707			−0.848536	+	0.529138i	$0.822515\pi$
$468$	5.17143	+	2.15986i	0.239049	+	0.0998394i
$469$	32.1131			1.48285
$470$	−0.443353	−	0.767910i	−0.0204504	−	0.0354211i
$471$	−10.7866	−	18.6830i	−0.497021	−	0.860865i
$472$	11.7651	−	20.3778i	0.541533	−	0.937963i
$473$	2.20096			0.101200
$474$	−4.17471	+	7.23082i	−0.191751	+	0.332122i
$475$	6.39731	−	11.0805i	0.293529	−	0.508406i
$476$	−3.96021			−0.181516
$477$	−0.418132	+	0.724226i	−0.0191449	+	0.0331600i
$478$	3.57201	+	6.18691i	0.163380	+	0.282983i
$479$	2.58285	+	4.47362i	0.118013	+	0.204405i	0.918980	−	0.394303i	$-0.129014\pi$
$479$	2.58285	+	4.47362i	0.118013	+	0.204405i	−0.800967	+	0.598709i	$0.795681\pi$
$480$	4.89413			0.223385
$481$	−16.8556	−	7.03975i	−0.768547	−	0.320985i
$482$	16.3050			0.742671
$483$	−5.67162	−	9.82354i	−0.258068	−	0.446986i
$484$	0.777183	+	1.34612i	0.0353265	+	0.0611873i
$485$	−4.96686	+	8.60285i	−0.225533	+	0.390635i
$486$	0.667559			0.0302811
$487$	10.1561	−	17.5909i	0.460217	−	0.797120i	−0.538754	−	0.842463i	$-0.681105\pi$
$487$	10.1561	−	17.5909i	0.460217	−	0.797120i	0.998971	+	0.0453431i	$0.0144381\pi$
$488$	−7.71704	+	13.3663i	−0.349334	+	0.605064i
$489$	13.7538			0.621967
$490$	−0.972963	+	1.68522i	−0.0439540	+	0.0761305i
$491$	−15.4868	−	26.8240i	−0.698910	−	1.21055i	−0.968845	−	0.247669i	$-0.920335\pi$
$491$	−15.4868	−	26.8240i	−0.698910	−	1.21055i	0.269934	−	0.962879i	$-0.412998\pi$
$492$	2.90146	+	5.02548i	0.130808	+	0.226566i
$493$	−0.909879			−0.0409789
$494$	5.72264	−	4.36455i	0.257474	−	0.196370i
$495$	−0.849177			−0.0381677
$496$	−0.0245928	−	0.0425959i	−0.00110425	−	0.00191261i
$497$	6.94474	+	12.0286i	0.311514	+	0.539558i
$498$	−5.55765	+	9.62613i	−0.249044	+	0.431357i
$499$	−24.8190			−1.11105			−0.555525	−	0.831500i	$-0.687483\pi$
$499$	−24.8190			−1.11105			−0.555525	+	0.831500i	$0.687483\pi$
$500$	−6.12376	+	10.6067i	−0.273863	+	0.474344i
$501$	−5.29848	+	9.17724i	−0.236719	+	0.410009i
$502$	3.26114			0.145552
$503$	−17.3306	+	30.0174i	−0.772732	+	1.33841i	0.163328	+	0.986572i	$0.447777\pi$
$503$	−17.3306	+	30.0174i	−0.772732	+	1.33841i	−0.936060	+	0.351840i	$0.885556\pi$
$504$	−3.83195	−	6.63714i	−0.170689	−	0.295642i
$505$	−6.03702	−	10.4564i	−0.268644	−	0.465305i
$506$	2.34438			0.104220
$507$	−12.5765	+	3.29098i	−0.558544	+	0.146158i
$508$	−13.4391			−0.596263
$509$	−3.49940	−	6.06114i	−0.155108	−	0.268655i	0.777990	−	0.628276i	$-0.216239\pi$
$509$	−3.49940	−	6.06114i	−0.155108	−	0.268655i	−0.933098	+	0.359621i	$0.882906\pi$
$510$	0.223576	+	0.387244i	0.00990009	+	0.0171475i
$511$	10.0092	−	17.3365i	0.442782	−	0.766921i
$512$	16.0238			0.708157
$513$	−1.49508	+	2.58956i	−0.0660095	+	0.114332i
$514$	−7.80723	+	13.5225i	−0.344362	+	0.596453i
$515$	9.95615			0.438720
$516$	−1.71055	+	2.96276i	−0.0753028	+	0.130428i
$517$	0.782100	+	1.35464i	0.0343967	+	0.0595769i
$518$	5.46190	+	9.46028i	0.239982	+	0.415661i
$519$	−4.36024			−0.191393
$520$	−5.77646	+	4.40559i	−0.253315	+	0.193198i
$521$	−25.6505			−1.12377			−0.561885	−	0.827215i	$-0.689924\pi$
$521$	−25.6505			−1.12377			−0.561885	+	0.827215i	$0.689924\pi$
$522$	−0.385014	−	0.666864i	−0.0168516	−	0.0291878i
$523$	8.57502	+	14.8524i	0.374959	+	0.649449i	0.990321	−	0.138796i	$-0.0443233\pi$
$523$	8.57502	+	14.8524i	0.374959	+	0.649449i	−0.615362	+	0.788245i	$0.710990\pi$
$524$	−7.85627	+	13.6075i	−0.343203	+	0.594444i
$525$	13.8207			0.603186
$526$	1.78480	−	3.09137i	0.0778212	−	0.134790i
$527$	0.0127223	−	0.0220357i	0.000554193	−	0.000959890i
$528$	−1.52478			−0.0663577
$529$	5.33338	−	9.23769i	0.231886	−	0.401639i
$530$	−0.237029	−	0.410546i	−0.0102959	−	0.0178330i
$531$	−4.95844	−	8.58827i	−0.215178	−	0.372699i
$532$	15.0123			0.650866
$533$	−12.4209	−	5.18759i	−0.538007	−	0.224700i
$534$	−6.34398			−0.274531
$535$	4.96251	+	8.59532i	0.214548	+	0.371608i
$536$	−11.7952	−	20.4299i	−0.509475	−	0.882437i
$537$	−6.87137	+	11.9016i	−0.296521	+	0.513590i
$538$	−7.57010			−0.326370
$539$	1.71636	−	2.97282i	0.0739289	−	0.128049i
$540$	0.659966	−	1.14309i	0.0284004	−	0.0491910i
$541$	−39.4496			−1.69607			−0.848035	−	0.529941i	$-0.822214\pi$
$541$	−39.4496			−1.69607			−0.848035	+	0.529941i	$0.822214\pi$
$542$	−4.16269	+	7.21000i	−0.178803	+	0.309696i
$543$	7.58049	+	13.1298i	0.325310	+	0.563453i
$544$	2.27307	+	3.93708i	0.0974573	+	0.168801i
$545$	5.81362			0.249028
$546$	7.17374	+	2.99613i	0.307008	+	0.128222i
$547$	38.6045			1.65061			0.825305	−	0.564686i	$-0.191003\pi$
$547$	38.6045			1.65061			0.825305	+	0.564686i	$0.191003\pi$
$548$	10.7554	+	18.6290i	0.459450	+	0.795791i
$549$	3.25237	+	5.63326i	0.138808	+	0.240422i
$550$	−1.42821	+	2.47373i	−0.0608990	+	0.105480i
$551$	3.44915			0.146939
$552$	−4.16639	+	7.21640i	−0.177333	+	0.307150i
$553$	20.1993	−	34.9862i	0.858961	−	1.48776i
$554$	−13.2786			−0.564153
$555$	−2.15107	+	3.72576i	−0.0913077	+	0.158150i
$556$	5.33026	+	9.23228i	0.226053	+	0.391536i
$557$	−23.1516	−	40.0998i	−0.980967	−	1.69908i	−0.658644	−	0.752454i	$-0.728870\pi$
$557$	−23.1516	−	40.0998i	−0.980967	−	1.69908i	−0.322322	−	0.946630i	$-0.604464\pi$
$558$	0.0215337			0.000911594
$559$	−1.01275	−	7.87080i	−0.0428347	−	0.332899i
$560$	−4.18221			−0.176730
$561$	−0.394400	−	0.683120i	−0.0166516	−	0.0288414i
$562$	−6.60230	−	11.4355i	−0.278501	−	0.482378i
$563$	−19.5560	+	33.8719i	−0.824186	+	1.42753i	0.0783546	+	0.996926i	$0.475033\pi$
$563$	−19.5560	+	33.8719i	−0.824186	+	1.42753i	−0.902540	+	0.430606i	$0.858300\pi$
$564$	−2.43134			−0.102378
$565$	4.39414	−	7.61088i	0.184863	−	0.320192i
$566$	−1.70478	+	2.95277i	−0.0716574	+	0.124114i
$567$	−3.22997			−0.135646
$568$	5.10162	−	8.83627i	0.214059	−	0.370762i
$569$	14.9816	+	25.9489i	0.628062	+	1.08784i	0.987940	+	0.154836i	$0.0494849\pi$
$569$	14.9816	+	25.9489i	0.628062	+	1.08784i	−0.359878	+	0.932999i	$0.617182\pi$
$570$	−0.847526	−	1.46796i	−0.0354989	−	0.0614860i
$571$	21.6865			0.907552			0.453776	−	0.891116i	$-0.350077\pi$
$571$	21.6865			0.907552			0.453776	+	0.891116i	$0.350077\pi$
$572$	4.45621	−	3.39866i	0.186323	−	0.142105i
$573$	−2.96870			−0.124019
$574$	4.02487	+	6.97128i	0.167995	+	0.290976i
$575$	−7.51347	−	13.0137i	−0.313333	−	0.542709i
$576$	−0.398912	+	0.690935i	−0.0166213	+	0.0287890i
$577$	−9.43193			−0.392656			−0.196328	−	0.980538i	$-0.562902\pi$
$577$	−9.43193			−0.392656			−0.196328	+	0.980538i	$0.562902\pi$
$578$	5.46657	−	9.46837i	0.227379	−	0.393832i
$579$	2.90711	−	5.03526i	0.120815	−	0.209258i
$580$	−1.52254			−0.0632200
$581$	26.8906	−	46.5759i	1.11561	−	1.93229i
$582$	−3.90457	−	6.76291i	−0.161850	−	0.280332i
$583$	0.418132	+	0.724226i	0.0173173	+	0.0299944i
$584$	−14.7056			−0.608522
$585$	0.390740	+	3.03672i	0.0161551	+	0.125553i
$586$	4.66211			0.192590
$587$	−12.7158	−	22.0245i	−0.524839	−	0.909048i	−0.999582	−	0.0289230i	$-0.990792\pi$
$587$	−12.7158	−	22.0245i	−0.524839	−	0.909048i	0.474743	−	0.880125i	$-0.342541\pi$
$588$	2.66785	+	4.62085i	0.110020	+	0.190561i
$589$	−0.0482275	+	0.0835324i	−0.00198718	+	0.00344189i
$590$	5.62163			0.231439
$591$	−4.22473	+	7.31745i	−0.173782	+	0.301000i
$592$	−3.86246	+	6.68997i	−0.158746	+	0.274956i
$593$	−2.11145			−0.0867069			−0.0433534	−	0.999060i	$-0.513804\pi$
$593$	−2.11145			−0.0867069			−0.0433534	+	0.999060i	$0.513804\pi$
$594$	0.333779	−	0.578123i	0.0136951	−	0.0237207i
$595$	−1.08177	−	1.87368i	−0.0443481	−	0.0768132i
$596$	−12.7684	−	22.1155i	−0.523014	−	0.905887i
$597$	14.5731			0.596436
$598$	−1.07874	−	8.38366i	−0.0441130	−	0.342833i
$599$	−30.7915			−1.25811			−0.629053	−	0.777362i	$-0.716557\pi$
$599$	−30.7915			−1.25811			−0.629053	+	0.777362i	$0.716557\pi$
$600$	−5.07637	−	8.79253i	−0.207242	−	0.358954i
$601$	−8.63565	−	14.9574i	−0.352255	−	0.610124i	0.634389	−	0.773014i	$-0.281252\pi$
$601$	−8.63565	−	14.9574i	−0.352255	−	0.610124i	−0.986644	+	0.162890i	$0.947918\pi$
$602$	−2.37285	+	4.10990i	−0.0967103	+	0.167507i
$603$	−9.94223			−0.404879
$604$	5.72298	−	9.91248i	0.232865	−	0.403333i
$605$	−0.424589	+	0.735409i	−0.0172620	+	0.0298986i
$606$	9.49169			0.385574
$607$	−8.44402	+	14.6255i	−0.342732	+	0.593630i	−0.984939	−	0.172902i	$-0.944686\pi$
$607$	−8.44402	+	14.6255i	−0.342732	+	0.593630i	0.642207	+	0.766531i	$0.278019\pi$
$608$	−8.61673	−	14.9246i	−0.349454	−	0.605273i
$609$	1.86288	+	3.22661i	0.0754879	+	0.130749i
$610$	−3.68737			−0.149297
$611$	4.48440	−	3.42017i	0.181419	−	0.138365i
$612$	1.22608			0.0495615
$613$	−11.0967	−	19.2201i	−0.448192	−	0.776291i	0.550077	−	0.835114i	$-0.314599\pi$
$613$	−11.0967	−	19.2201i	−0.448192	−	0.776291i	−0.998268	+	0.0588232i	$0.981265\pi$
$614$	6.29426	+	10.9020i	0.254016	+	0.439968i
$615$	−1.58512	+	2.74551i	−0.0639182	+	0.110710i
$616$	−7.66391			−0.308788
$617$	16.6239	−	28.7934i	0.669253	−	1.15918i	−0.308860	−	0.951107i	$-0.599948\pi$
$617$	16.6239	−	28.7934i	0.669253	−	1.15918i	0.978113	−	0.208073i	$-0.0667192\pi$
$618$	−3.91338	+	6.77818i	−0.157419	+	0.272658i
$619$	−26.2171			−1.05376			−0.526878	−	0.849941i	$-0.676637\pi$
$619$	−26.2171			−1.05376			−0.526878	+	0.849941i	$0.676637\pi$
$620$	0.0212888	−	0.0368732i	0.000854978	−	0.00148087i
$621$	1.75594	+	3.04137i	0.0704633	+	0.122046i
$622$	10.0924	+	17.4805i	0.404667	+	0.700903i
$623$	30.6952			1.22978
$624$	0.701613	+	5.45273i	0.0280870	+	0.218284i
$625$	14.7035			0.588138
$626$	−9.55840	−	16.5556i	−0.382030	−	0.661696i
$627$	1.49508	+	2.58956i	0.0597079	+	0.103417i
$628$	16.7663	−	29.0401i	0.669050	−	1.15883i
$629$	−3.99624			−0.159341
$630$	0.915496	−	1.58569i	0.0364742	−	0.0631752i
$631$	4.19122	−	7.25940i	0.166850	−	0.288992i	−0.770461	−	0.637487i	$-0.779974\pi$
$631$	4.19122	−	7.25940i	0.166850	−	0.288992i	0.937311	+	0.348495i	$0.113307\pi$
$632$	−29.6769			−1.18048
$633$	−4.79309	+	8.30187i	−0.190508	+	0.329970i
$634$	−6.56956	−	11.3788i	−0.260911	−	0.451910i
$635$	−3.67100	−	6.35836i	−0.145679	−	0.252324i
$636$	−1.29986			−0.0515428
$637$	−11.4208	−	4.76991i	−0.452508	−	0.188991i
$638$	−0.770028			−0.0304857
$639$	−2.15009	−	3.72407i	−0.0850563	−	0.147322i
$640$	4.66799	+	8.08520i	0.184519	+	0.319596i
$641$	−10.5327	+	18.2432i	−0.416017	+	0.720563i	−0.995535	−	0.0943971i	$-0.969908\pi$
$641$	−10.5327	+	18.2432i	−0.416017	+	0.720563i	0.579518	+	0.814960i	$0.303241\pi$
$642$	−7.80230			−0.307932
$643$	22.2642	−	38.5627i	0.878015	−	1.52077i	0.0244987	−	0.999700i	$-0.492201\pi$
$643$	22.2642	−	38.5627i	0.878015	−	1.52077i	0.853516	−	0.521066i	$-0.174466\pi$
$644$	8.81577	−	15.2694i	0.347390	−	0.601697i
$645$	−1.86901			−0.0735921
$646$	0.787266	−	1.36358i	0.0309745	−	0.0536495i
$647$	9.16480	+	15.8739i	0.360306	+	0.624068i	0.988011	−	0.154383i	$-0.0493391\pi$
$647$	9.16480	+	15.8739i	0.360306	+	0.624068i	−0.627705	+	0.778451i	$0.716006\pi$
$648$	1.18637	+	2.05486i	0.0466052	+	0.0807225i
$649$	−9.91687			−0.389271
$650$	9.50340	+	3.96911i	0.372754	+	0.155681i
$651$	−0.104190			−0.00408355
$652$	10.6892	+	18.5142i	0.418621	+	0.725074i
$653$	7.09516	+	12.2892i	0.277655	+	0.480913i	0.970802	−	0.239884i	$-0.0771094\pi$
$653$	7.09516	+	12.2892i	0.277655	+	0.480913i	−0.693147	+	0.720797i	$0.743776\pi$
$654$	−2.28511	+	3.95793i	−0.0893549	+	0.154767i
$655$	−8.58403			−0.335406
$656$	−2.84624	+	4.92984i	−0.111127	+	0.192478i
$657$	−3.09886	+	5.36738i	−0.120898	+	0.209401i
$658$	−3.37272			−0.131482
$659$	9.07017	−	15.7100i	0.353324	−	0.611974i	−0.633506	−	0.773738i	$-0.718385\pi$
$659$	9.07017	−	15.7100i	0.353324	−	0.611974i	0.986830	+	0.161763i	$0.0517181\pi$
$660$	−0.659966	−	1.14309i	−0.0256891	−	0.0444949i
$661$	0.628382	+	1.08839i	0.0244412	+	0.0423335i	0.877987	−	0.478684i	$-0.158886\pi$
$661$	0.628382	+	1.08839i	0.0244412	+	0.0423335i	−0.853546	+	0.521017i	$0.825553\pi$
$662$	14.3957			0.559505
$663$	−2.26141	+	1.72473i	−0.0878258	+	0.0669830i
$664$	−39.5078			−1.53320
$665$	4.10074	+	7.10269i	0.159020	+	0.275431i
$666$	−1.69100	−	2.92891i	−0.0655251	−	0.113493i
$667$	2.02547	−	3.50821i	0.0784265	−	0.135839i
$668$	−16.4716			−0.637304
$669$	4.60905	−	7.98311i	0.178196	−	0.308645i
$670$	2.81800	−	4.88093i	0.108869	−	0.188567i
$671$	6.50473			0.251112
$672$	9.30777	−	16.1215i	0.359055	−	0.621902i
$673$	−9.68580	−	16.7763i	−0.373360	−	0.646679i	0.616720	−	0.787183i	$-0.288461\pi$
$673$	−9.68580	−	16.7763i	−0.373360	−	0.646679i	−0.990080	+	0.140504i	$0.955128\pi$
$674$	11.3780	+	19.7072i	0.438263	+	0.759093i
$675$	−4.27890			−0.164695
$676$	−14.2043	−	14.3718i	−0.546320	−	0.552763i
$677$	26.3139			1.01132			0.505662	−	0.862732i	$-0.331248\pi$
$677$	26.3139			1.01132			0.505662	+	0.862732i	$0.331248\pi$
$678$	3.45434	+	5.98309i	0.132663	+	0.229779i
$679$	18.8922	+	32.7222i	0.725016	+	1.25576i
$680$	−0.794669	+	1.37641i	−0.0304742	+	0.0527828i
$681$	20.5599			0.787857
$682$	0.0107668	−	0.0186487i	0.000412284	−	0.000714097i
$683$	−0.939059	+	1.62650i	−0.0359321	+	0.0622362i	−0.883432	−	0.468559i	$-0.844773\pi$
$683$	−0.939059	+	1.62650i	−0.0359321	+	0.0622362i	0.847500	+	0.530795i	$0.178107\pi$
$684$	−4.64781			−0.177713
$685$	−5.87589	+	10.1773i	−0.224506	+	0.388856i
$686$	−3.84588	−	6.66125i	−0.146836	−	0.254328i
$687$	3.46369	+	5.99928i	0.132148	+	0.228887i
$688$	−3.35599			−0.127946
$689$	2.39748	−	1.82851i	0.0913368	−	0.0696608i
$690$	−1.99079			−0.0757882
$691$	−19.0598	−	33.0126i	−0.725070	−	1.25586i	−0.958945	−	0.283592i	$-0.908474\pi$
$691$	−19.0598	−	33.0126i	−0.725070	−	1.25586i	0.233875	−	0.972267i	$-0.424859\pi$
$692$	−3.38870	−	5.86940i	−0.128819	−	0.223121i
$693$	−1.61499	+	2.79724i	−0.0613483	+	0.106258i
$694$	−17.6021			−0.668167
$695$	−2.91201	+	5.04376i	−0.110459	+	0.191321i
$696$	1.36848	−	2.37028i	0.0518721	−	0.0898451i
$697$	−2.94483			−0.111543
$698$	3.35041	−	5.80309i	0.126815	−	0.219650i
$699$	4.97224	+	8.61218i	0.188068	+	0.325743i
$700$	10.7412	+	18.6044i	0.405980	+	0.703178i
$701$	22.4490			0.847886			0.423943	−	0.905689i	$-0.360646\pi$
$701$	22.4490			0.847886			0.423943	+	0.905689i	$0.360646\pi$
$702$	−2.22099	−	0.927601i	−0.0838259	−	0.0350100i
$703$	15.1489			0.571351
$704$	0.398912	+	0.690935i	0.0150346	+	0.0260406i
$705$	−0.664141	−	1.15033i	−0.0250130	−	0.0433238i
$706$	6.82387	−	11.8193i	0.256820	−	0.444825i
$707$	−45.9254			−1.72720
$708$	7.70722	−	13.3493i	0.289655	−	0.501698i
$709$	−10.1426	+	17.5675i	−0.380914	+	0.659762i	−0.991193	−	0.132424i	$-0.957724\pi$
$709$	−10.1426	+	17.5675i	−0.380914	+	0.659762i	0.610279	+	0.792186i	$0.291057\pi$
$710$	2.43767			0.0914841
$711$	−6.25370	+	10.8317i	−0.234532	+	0.406222i
$712$	−11.2744	−	19.5278i	−0.422526	−	0.731837i
$713$	0.0566419	+	0.0981066i	0.00212126	+	0.00367412i
$714$	1.70081			0.0636511
$715$	2.82524	+	1.17997i	0.105658	+	0.0441283i
$716$	−21.3612			−0.798307
$717$	5.35086	+	9.26796i	0.199832	+	0.346118i
$718$	−9.33715	−	16.1724i	−0.348459	−	0.603549i
$719$	−16.8621	+	29.2060i	−0.628849	+	1.08920i	0.358934	+	0.933363i	$0.383140\pi$
$719$	−16.8621	+	29.2060i	−0.628849	+	1.08920i	−0.987783	+	0.155836i	$0.950193\pi$
$720$	1.29481			0.0482548
$721$	18.9349	−	32.7961i	0.705171	−	1.22139i
$722$	3.35746	−	5.81528i	0.124952	−	0.216422i
$723$	24.4248			0.908368
$724$	−11.7828	+	20.4085i	−0.437906	+	0.758476i
$725$	2.46785	+	4.27444i	0.0916537	+	0.158749i
$726$	−0.333779	−	0.578123i	−0.0123877	−	0.0214561i
$727$	28.7674			1.06692			0.533461	−	0.845825i	$-0.320891\pi$
$727$	28.7674			1.06692			0.533461	+	0.845825i	$0.320891\pi$
$728$	3.52646	+	27.4067i	0.130699	+	1.01576i
$729$	1.00000			0.0370370
$730$	−1.75667	−	3.04263i	−0.0650171	−	0.112613i
$731$	−0.868059	−	1.50352i	−0.0321063	−	0.0556098i
$732$	−5.05537	+	8.75615i	−0.186852	+	0.323637i
$733$	−46.7802			−1.72787			−0.863933	−	0.503607i	$-0.832006\pi$
$733$	−46.7802			−1.72787			−0.863933	+	0.503607i	$0.832006\pi$
$734$	8.92637	−	15.4609i	0.329478	−	0.570673i
$735$	−1.45749	+	2.52445i	−0.0537605	+	0.0931159i
$736$	−20.2402			−0.746065
$737$	−4.97112	+	8.61023i	−0.183113	+	0.317162i
$738$	−1.24610	−	2.15831i	−0.0458696	−	0.0794485i
$739$	1.24801	+	2.16162i	0.0459089	+	0.0795166i	0.888067	−	0.459715i	$-0.152048\pi$
$739$	1.24801	+	2.16162i	0.0459089	+	0.0795166i	−0.842158	+	0.539231i	$0.818715\pi$
$740$	−6.68709			−0.245822
$741$	8.57250	−	6.53808i	0.314919	−	0.240182i
$742$	−1.80315			−0.0661957
$743$	−8.36060	−	14.4810i	−0.306721	−	0.531256i	0.670922	−	0.741528i	$-0.265898\pi$
$743$	−8.36060	−	14.4810i	−0.306721	−	0.531256i	−0.977643	+	0.210272i	$0.932565\pi$
$744$	0.0382693	+	0.0662844i	0.00140302	+	0.00243010i
$745$	6.97560	−	12.0821i	0.255566	−	0.442654i
$746$	15.7943			0.578272
$747$	−8.32533	+	14.4199i	−0.304608	+	0.527597i
$748$	0.613041	−	1.06182i	0.0224150	−	0.0388239i
$749$	37.7513			1.37940
$750$	2.62999	−	4.55528i	0.0960336	−	0.166335i
$751$	13.7170	+	23.7585i	0.500539	+	0.866959i	1.00000		0.000622786i	$0.000198239\pi$
$751$	13.7170	+	23.7585i	0.500539	+	0.866959i	−0.499461	+	0.866337i	$0.666468\pi$
$752$	−1.19253	−	2.06553i	−0.0434872	−	0.0753221i
$753$	4.88517			0.178025
$754$	0.354320	+	2.75367i	0.0129036	+	0.100283i
$755$	6.25312			0.227574
$756$	−2.51028	−	4.34793i	−0.0912980	−	0.158133i
$757$	−15.5355	−	26.9083i	−0.564648	−	0.977999i	−0.997082	−	0.0763338i	$-0.975679\pi$
$757$	−15.5355	−	26.9083i	−0.564648	−	0.977999i	0.432434	−	0.901666i	$-0.357655\pi$
$758$	8.90982	−	15.4323i	0.323619	−	0.560525i
$759$	3.51187			0.127473
$760$	3.01242	−	5.21766i	0.109272	−	0.189264i
$761$	−7.72426	+	13.3788i	−0.280004	+	0.484982i	−0.971385	−	0.237509i	$-0.923669\pi$
$761$	−7.72426	+	13.3788i	−0.280004	+	0.484982i	0.691381	+	0.722490i	$0.257003\pi$
$762$	5.77173			0.209088
$763$	11.0565	−	19.1504i	0.400271	−	0.693291i
$764$	−2.30722	−	3.99622i	−0.0834723	−	0.144578i
$765$	0.334915	+	0.580090i	0.0121089	+	0.0209732i
$766$	19.2916			0.697034
$767$	4.56314	+	35.4634i	0.164766	+	1.28051i
$768$	−8.93489			−0.322410
$769$	8.45407	+	14.6429i	0.304861	+	0.528035i	0.977230	−	0.212181i	$-0.0680565\pi$
$769$	8.45407	+	14.6429i	0.304861	+	0.528035i	−0.672369	+	0.740216i	$0.734723\pi$
$770$	−0.915496	−	1.58569i	−0.0329922	−	0.0571441i
$771$	−11.6952	+	20.2567i	−0.421192	+	0.729526i
$772$	9.03743			0.325264
$773$	−26.3558	+	45.6496i	−0.947952	+	1.64190i	−0.198223	+	0.980157i	$0.563517\pi$
$773$	−26.3558	+	45.6496i	−0.947952	+	1.64190i	−0.749729	+	0.661745i	$0.769816\pi$
$774$	0.734636	−	1.27243i	0.0264059	−	0.0457364i
$775$	−0.138026			−0.00495804
$776$	13.8783	−	24.0378i	0.498200	−	0.862908i
$777$	8.18190	+	14.1715i	0.293524	+	0.508399i
$778$	8.26941	+	14.3230i	0.296473	+	0.513506i
$779$	11.1632			0.399964
$780$	−3.78411	+	2.88607i	−0.135493	+	0.103338i
$781$	−4.30018			−0.153873
$782$	−0.924623	−	1.60149i	−0.0330644	−	0.0572693i
$783$	−0.576749	−	0.998959i	−0.0206113	−	0.0356999i
$784$	−2.61708	+	4.53291i	−0.0934671	+	0.161890i
$785$	18.3195			0.653850
$786$	3.37406	−	5.84404i	0.120349	−	0.208450i
$787$	−3.38669	+	5.86591i	−0.120722	+	0.209097i	−0.920053	−	0.391795i	$-0.871854\pi$
$787$	−3.38669	+	5.86591i	−0.120722	+	0.209097i	0.799330	+	0.600892i	$0.205188\pi$
$788$	−13.1335			−0.467863
$789$	2.67363	−	4.63086i	0.0951837	−	0.164863i
$790$	−3.54507	−	6.14024i	−0.126128	−	0.218460i
$791$	−16.7138	−	28.9491i	−0.594274	−	1.02931i
$792$	2.37275			0.0843119
$793$	−2.99308	−	23.2614i	−0.106287	−	0.826036i
$794$	3.42474			0.121539
$795$	−0.355068	−	0.614996i	−0.0125930	−	0.0218117i
$796$	11.3259	+	19.6171i	0.401437	+	0.695310i
$797$	14.3568	−	24.8667i	0.508543	−	0.880823i	−0.491408	−	0.870930i	$-0.663518\pi$
$797$	14.3568	−	24.8667i	0.508543	−	0.880823i	0.999951	−	0.00989301i	$-0.00314909\pi$
$798$	−6.44738			−0.228235
$799$	0.616920	−	1.06854i	0.0218251	−	0.0378021i
$800$	12.3305	−	21.3570i	0.435947	−	0.755083i
$801$	−9.50325			−0.335781
$802$	−2.58829	+	4.48305i	−0.0913957	+	0.158302i
$803$	3.09886	+	5.36738i	0.109356	+	0.189411i
$804$	−7.72693	−	13.3834i	−0.272508	−	0.471998i
$805$	9.63242			0.339498
$806$	−0.0716434	−	0.0299220i	−0.00252353	−	0.00105396i
$807$	−11.3400			−0.399186
$808$	16.8685	+	29.2171i	0.593431	+	1.02785i
$809$	21.5142	+	37.2637i	0.756400	+	1.31012i	0.944676	+	0.328006i	$0.106377\pi$
$809$	21.5142	+	37.2637i	0.756400	+	1.31012i	−0.188276	+	0.982116i	$0.560290\pi$
$810$	−0.283438	+	0.490929i	−0.00995899	+	0.0172495i
$811$	8.68276			0.304893			0.152446	−	0.988312i	$-0.451285\pi$
$811$	8.68276			0.304893			0.152446	+	0.988312i	$0.451285\pi$
$812$	−2.89560	+	5.01533i	−0.101616	+	0.176004i
$813$	−6.23570	+	10.8005i	−0.218695	+	0.378792i
$814$	−3.38201			−0.118539
$815$	−5.83970	+	10.1147i	−0.204556	+	0.354301i
$816$	0.601374	+	1.04161i	0.0210523	+	0.0364637i
$817$	3.29062	+	5.69952i	0.115124	+	0.199401i
$818$	3.65382			0.127753
$819$	10.7462	+	4.48818i	0.375504	+	0.156830i
$820$	−4.92771			−0.172083
$821$	−5.92189	−	10.2570i	−0.206675	−	0.357972i	0.743990	−	0.668191i	$-0.232931\pi$
$821$	−5.92189	−	10.2570i	−0.206675	−	0.357972i	−0.950665	+	0.310219i	$0.899598\pi$
$822$	−4.61918	−	8.00065i	−0.161112	−	0.279055i
$823$	8.34044	−	14.4461i	0.290730	−	0.503558i	−0.683253	−	0.730182i	$-0.739435\pi$
$823$	8.34044	−	14.4461i	0.290730	−	0.503558i	0.973982	+	0.226623i	$0.0727687\pi$
$824$	−27.8192			−0.969128
$825$	−2.13945	+	3.70563i	−0.0744861	+	0.129014i
$826$	10.6914	−	18.5180i	0.372000	−	0.644323i
$827$	−43.0588			−1.49730			−0.748651	−	0.662965i	$-0.769298\pi$
$827$	−43.0588			−1.49730			−0.748651	+	0.662965i	$0.769298\pi$
$828$	−2.72937	+	4.72740i	−0.0948520	+	0.164288i
$829$	1.74789	+	3.02743i	0.0607066	+	0.105147i	0.894781	−	0.446504i	$-0.147331\pi$
$829$	1.74789	+	3.02743i	0.0607066	+	0.105147i	−0.834075	+	0.551651i	$0.813998\pi$
$830$	−4.71943	−	8.17429i	−0.163814	−	0.283734i
$831$	−19.8913			−0.690021
$832$	2.28728	−	1.74446i	0.0792971	−	0.0604784i
$833$	−2.70773			−0.0938172
$834$	−2.28920	−	3.96502i	−0.0792687	−	0.137297i
$835$	−4.49935	−	7.79310i	−0.155706	−	0.269691i
$836$	−2.32391	+	4.02512i	−0.0803740	+	0.139212i
$837$	0.0322574			0.00111498
$838$	−11.2194	+	19.4327i	−0.387569	+	0.671290i
$839$	0.538989	−	0.933557i	0.0186080	−	0.0322300i	−0.856571	−	0.516028i	$-0.827410\pi$
$839$	0.538989	−	0.933557i	0.0186080	−	0.0322300i	0.875179	+	0.483798i	$0.160743\pi$
$840$	6.50801			0.224548
$841$	13.8347	−	23.9624i	0.477059	−	0.826291i
$842$	10.5186	+	18.2187i	0.362493	+	0.627857i
$843$	−9.89022	−	17.1304i	−0.340637	−	0.590001i
$844$	−14.9004			−0.512894
$845$	2.91964	−	10.6462i	0.100439	−	0.366241i
$846$	1.04419			0.0359002
$847$	1.61499	+	2.79724i	0.0554916	+	0.0961142i
$848$	−0.637561	−	1.10429i	−0.0218939	−	0.0379214i
$849$	−2.55376	+	4.42324i	−0.0876448	+	0.151805i
$850$	2.25314			0.0772820
$851$	8.89598	−	15.4083i	0.304950	−	0.528190i
$852$	3.34203	−	5.78856i	0.114496	−	0.198313i
$853$	−2.87104			−0.0983025			−0.0491513	−	0.998791i	$-0.515652\pi$
$853$	−2.87104			−0.0983025			−0.0491513	+	0.998791i	$0.515652\pi$
$854$	−7.01274	+	12.1464i	−0.239971	+	0.415642i
$855$	−1.26959	−	2.19899i	−0.0434191	−	0.0752040i
$856$	−13.8661	−	24.0168i	−0.473934	−	0.820878i
$857$	12.4441			0.425082			0.212541	−	0.977152i	$-0.431826\pi$
$857$	12.4441			0.425082			0.212541	+	0.977152i	$0.431826\pi$
$858$	−1.91382	+	1.45963i	−0.0653368	+	0.0498311i
$859$	−20.3537			−0.694460			−0.347230	−	0.937780i	$-0.612878\pi$
$859$	−20.3537			−0.694460			−0.347230	+	0.937780i	$0.612878\pi$
$860$	−1.45256	−	2.51591i	−0.0495319	−	0.0857918i
$861$	6.02924	+	10.4430i	0.205476	+	0.355895i
$862$	9.76963	−	16.9215i	0.332755	−	0.576348i
$863$	−2.44402			−0.0831953			−0.0415977	−	0.999134i	$-0.513245\pi$
$863$	−2.44402			−0.0831953			−0.0415977	+	0.999134i	$0.513245\pi$
$864$	−2.88169	+	4.99123i	−0.0980370	+	0.169805i
$865$	1.85131	−	3.20656i	0.0629463	−	0.109026i
$866$	−14.3305			−0.486970
$867$	8.18890	−	14.1836i	0.278110	−	0.481700i
$868$	−0.0809751	−	0.140253i	−0.00274847	−	0.00476049i
$869$	6.25370	+	10.8317i	0.212142	+	0.367441i
$870$	0.653890			0.0221689
$871$	33.0782	+	13.8152i	1.12081	+	0.468109i
$872$	−16.2442			−0.550100
$873$	−5.84903	−	10.1308i	−0.197960	−	0.342876i
$874$	3.50504	+	6.07091i	0.118560	+	0.205352i
$875$	−12.7252	+	22.0406i	−0.430189	+	0.745109i
$876$	−9.63352			−0.325486
$877$	−11.6174	+	20.1219i	−0.392292	+	0.679469i	−0.992751	−	0.120186i	$-0.961651\pi$
$877$	−11.6174	+	20.1219i	−0.392292	+	0.679469i	0.600460	+	0.799655i	$0.294984\pi$
$878$	0.777186	−	1.34613i	0.0262288	−	0.0454296i
$879$	6.98382			0.235558
$880$	0.647406	−	1.12134i	0.0218240	−	0.0378004i
$881$	23.8079	+	41.2365i	0.802109	+	1.38929i	0.918226	+	0.396057i	$0.129622\pi$
$881$	23.8079	+	41.2365i	0.802109	+	1.38929i	−0.116117	+	0.993236i	$0.537045\pi$
$882$	−1.14577	−	1.98453i	−0.0385801	−	0.0668227i
$883$	14.6456			0.492864			0.246432	−	0.969160i	$-0.420742\pi$
$883$	14.6456			0.492864			0.246432	+	0.969160i	$0.420742\pi$
$884$	−4.07922	−	1.70369i	−0.137199	−	0.0573014i
$885$	8.42118			0.283075
$886$	−4.16983	−	7.22236i	−0.140088	−	0.242640i
$887$	−20.9277	−	36.2479i	−0.702684	−	1.21708i	−0.967521	−	0.252791i	$-0.918651\pi$
$887$	−20.9277	−	36.2479i	−0.702684	−	1.21708i	0.264837	−	0.964293i	$-0.414682\pi$
$888$	6.01045	−	10.4104i	0.201697	−	0.349350i
$889$	−27.9264			−0.936622
$890$	2.69358	−	4.66542i	0.0902890	−	0.156385i
$891$	0.500000	−	0.866025i	0.0167506	−	0.0290129i
$892$	14.3283			0.479747
$893$	−2.33861	+	4.05059i	−0.0782585	+	0.135548i
$894$	5.48369	+	9.49803i	0.183402	+	0.317661i
$895$	−5.83501	−	10.1065i	−0.195043	−	0.337824i
$896$	35.5108			1.18633
$897$	−1.61595	−	12.5587i	−0.0539550	−	0.419323i
$898$	−18.4249			−0.614848
$899$	−0.0186044	−	0.0322238i	−0.000620492	−	0.00107472i
$900$	−3.32549	−	5.75991i	−0.110850	−	0.191997i
$901$	0.329822	−	0.571269i	0.0109880	−	0.0190317i
$902$	−2.49220			−0.0829812
$903$	−3.55452	+	6.15662i	−0.118287	+	0.204879i
$904$	−12.2780	+	21.2661i	−0.408360	+	0.707300i
$905$	−12.8744			−0.427958
$906$	−2.45787	+	4.25715i	−0.0816571	+	0.141434i
$907$	−1.63040	−	2.82394i	−0.0541367	−	0.0937674i	0.837687	−	0.546150i	$-0.183907\pi$
$907$	−1.63040	−	2.82394i	−0.0541367	−	0.0937674i	−0.891824	+	0.452383i	$0.850574\pi$
$908$	15.9788	+	27.6761i	0.530275	+	0.918463i
$909$	14.2185			0.471599
$910$	−5.24927	+	4.00351i	−0.174011	+	0.132715i
$911$	34.8710			1.15533			0.577664	−	0.816275i	$-0.303965\pi$
$911$	34.8710			1.15533			0.577664	+	0.816275i	$0.303965\pi$
$912$	−2.27968	−	3.94852i	−0.0754877	−	0.130749i
$913$	8.32533	+	14.4199i	0.275528	+	0.477229i
$914$	−3.58274	+	6.20550i	−0.118507	+	0.205260i
$915$	−5.52367			−0.182607
$916$	−5.38383	+	9.32508i	−0.177887	+	0.308109i
$917$	−16.3253	+	28.2763i	−0.539110	+	0.933765i
$918$	−0.526570			−0.0173794
$919$	−15.4941	+	26.8366i	−0.511103	+	0.885257i	0.488814	+	0.872388i	$0.337430\pi$
$919$	−15.4941	+	26.8366i	−0.511103	+	0.885257i	−0.999917	+	0.0128686i	$0.995904\pi$
$920$	−3.53800	−	6.12800i	−0.116645	−	0.202034i
$921$	9.42878	+	16.3311i	0.310689	+	0.538129i
$922$	22.7971			0.750782
$923$	1.97868	+	15.3778i	0.0651292	+	0.506165i
$924$	−5.02056			−0.165164
$925$	10.8390	+	18.7736i	0.356383	+	0.617273i
$926$	−8.85451	−	15.3365i	−0.290977	−	0.503987i
$927$	−5.86223	+	10.1537i	−0.192541	+	0.333491i
$928$	6.64805			0.218233
$929$	9.76291	−	16.9099i	0.320311	−	0.554794i	−0.660241	−	0.751053i	$-0.729546\pi$
$929$	9.76291	−	16.9099i	0.320311	−	0.554794i	0.980552	+	0.196259i	$0.0628794\pi$
$930$	−0.00914296	+	0.0158361i	−0.000299810	+	0.000519285i
$931$	10.2644			0.336402
$932$	−7.72868	+	13.3865i	−0.253161	+	0.438489i
$933$	15.1183	+	26.1857i	0.494951	+	0.857281i
$934$	12.2410	+	21.2021i	0.400539	+	0.693753i
$935$	0.669831			0.0219058
$936$	−1.09179	−	8.48511i	−0.0356864	−	0.277344i
$937$	28.0493			0.916329			0.458165	−	0.888867i	$-0.348507\pi$
$937$	28.0493			0.916329			0.458165	+	0.888867i	$0.348507\pi$
$938$	−10.7187	−	18.5653i	−0.349978	−	0.606180i
$939$	−14.3184	−	24.8003i	−0.467265	−	0.809326i
$940$	1.03232	−	1.78803i	0.0336705	−	0.0583190i
$941$	−18.6286			−0.607274			−0.303637	−	0.952788i	$-0.598201\pi$
$941$	−18.6286			−0.607274			−0.303637	+	0.952788i	$0.598201\pi$
$942$	−7.20069	+	12.4720i	−0.234611	+	0.406359i
$943$	6.55545	−	11.3544i	0.213475	−	0.369749i
$944$	15.1211			0.492150
$945$	1.37141	−	2.37535i	0.0446119	−	0.0772702i
$946$	−0.734636	−	1.27243i	−0.0238851	−	0.0413701i
$947$	−6.92545	−	11.9952i	−0.225047	−	0.389793i	0.731287	−	0.682070i	$-0.238920\pi$
$947$	−6.92545	−	11.9952i	−0.225047	−	0.389793i	−0.956333	+	0.292278i	$0.905587\pi$
$948$	−19.4411			−0.631417
$949$	17.7682	−	13.5515i	0.576781	−	0.439899i
$950$	−8.54115			−0.277112
$951$	−9.84118	−	17.0454i	−0.319122	−	0.552736i
$952$	3.02264	+	5.23537i	0.0979644	+	0.169679i
$953$	4.05889	−	7.03020i	0.131480	−	0.227731i	−0.792767	−	0.609525i	$-0.791360\pi$
$953$	4.05889	−	7.03020i	0.131480	−	0.227731i	0.924247	+	0.381794i	$0.124694\pi$
$954$	0.558255			0.0180742
$955$	1.26047	−	2.18321i	0.0407880	−	0.0706469i
$956$	−8.31719	+	14.4058i	−0.268997	+	0.465917i
$957$	−1.15350			−0.0372873
$958$	1.72420	−	2.98641i	0.0557064	−	0.0964864i
$959$	22.3498	+	38.7110i	0.721713	+	1.25004i
$960$	−0.338747	−	0.586727i	−0.0109330	−	0.0189365i
$961$	−30.9990			−0.999966
$962$	1.55619	+	12.0943i	0.0501737	+	0.389936i
$963$	−11.6878			−0.376635
$964$	18.9825	+	32.8787i	0.611386	+	1.05895i
$965$	2.46865	+	4.27583i	0.0794687	+	0.137644i
$966$	−3.78614	+	6.55779i	−0.121817	+	0.210993i
$967$	19.8745			0.639122			0.319561	−	0.947566i	$-0.396465\pi$
$967$	19.8745			0.639122			0.319561	+	0.947566i	$0.396465\pi$
$968$	1.18637	−	2.05486i	0.0381315	−	0.0660457i
$969$	1.17932	−	2.04264i	0.0378852	−	0.0656192i
$970$	6.63134			0.212919
$971$	−18.3152	+	31.7229i	−0.587764	+	1.01804i	0.406761	+	0.913535i	$0.366658\pi$
$971$	−18.3152	+	31.7229i	−0.587764	+	1.01804i	−0.994525	+	0.104502i	$0.966675\pi$
$972$	0.777183	+	1.34612i	0.0249282	+	0.0431768i
$973$	11.0763	+	19.1847i	0.355089	+	0.615033i
$974$	−13.5596			−0.434478
$975$	14.2361	+	5.94571i	0.455918	+	0.190415i
$976$	−9.91831			−0.317477
$977$	0.562945	+	0.975049i	0.0180102	+	0.0311946i	0.874890	−	0.484322i	$-0.160934\pi$
$977$	0.562945	+	0.975049i	0.0180102	+	0.0311946i	−0.856880	+	0.515516i	$0.827600\pi$
$978$	−4.59073	−	7.95137i	−0.146795	−	0.254257i
$979$	−4.75163	+	8.23006i	−0.151863	+	0.263034i
$980$	−4.53096			−0.144736
$981$	−3.42309	+	5.92896i	−0.109291	+	0.189297i
$982$	−10.3384	+	17.9066i	−0.329910	+	0.571421i
$983$	53.9539			1.72086			0.860432	−	0.509566i	$-0.170194\pi$
$983$	53.9539			1.72086			0.860432	+	0.509566i	$0.170194\pi$
$984$	4.42910	−	7.67142i	0.141195	−	0.244556i
$985$	−3.58754	−	6.21381i	−0.114309	−	0.197988i
$986$	0.303699	+	0.526022i	0.00967174	+	0.0167519i
$987$	−5.05232			−0.160817
$988$	15.4634	+	6.45833i	0.491957	+	0.205467i
$989$	7.72950			0.245784
$990$	0.283438	+	0.490929i	0.00900824	+	0.0156027i
$991$	15.5233	+	26.8872i	0.493114	+	0.854098i	0.999969	−	0.00793312i	$-0.00252522\pi$
$991$	15.5233	+	26.8872i	0.493114	+	0.854098i	−0.506855	+	0.862032i	$0.669192\pi$
$992$	−0.0929558	+	0.161004i	−0.00295135	+	0.00511189i
$993$	21.5647			0.684335
$994$	4.63602	−	8.02982i	0.147046	−	0.254690i
$995$	−6.18756	+	10.7172i	−0.196159	+	0.339757i
$996$	−25.8812			−0.820078
$997$	−23.2190	+	40.2165i	−0.735352	+	1.27367i	0.219216	+	0.975676i	$0.429650\pi$
$997$	−23.2190	+	40.2165i	−0.735352	+	1.27367i	−0.954569	+	0.297992i	$0.903683\pi$
$998$	8.28406	+	14.3484i	0.262227	+	0.454191i
$999$	−2.53312	−	4.38749i	−0.0801443	−	0.138814i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.i.c.133.3	yes	10
13.3	even	3		5577.2.a.v.1.3		5
13.9	even	3	inner	429.2.i.c.100.3	✓	10
13.10	even	6		5577.2.a.p.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.i.c.100.3	✓	10	13.9	even	3	inner
429.2.i.c.133.3	yes	10	1.1	even	1	trivial
5577.2.a.p.1.3		5	13.10	even	6
5577.2.a.v.1.3		5	13.3	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.333779 - 0.578123i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.777183 - 1.34612i) q^{4} +0.849177 q^{5} +(-0.333779 + 0.578123i) q^{6} +(1.61499 - 2.79724i) q^{7} -2.37275 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.333779 - 0.578123i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.777183 - 1.34612i) q^{4} +0.849177 q^{5} +(-0.333779 + 0.578123i) q^{6} +(1.61499 - 2.79724i) q^{7} -2.37275 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.283438 - 0.490929i) q^{10} +(0.500000 + 0.866025i) q^{11} -1.55437 q^{12} +(2.86690 - 2.18653i) q^{13} -2.15620 q^{14} +(-0.424589 - 0.735409i) q^{15} +(-0.762392 - 1.32050i) q^{16} +(0.394400 - 0.683120i) q^{17} +0.667559 q^{18} +(-1.49508 + 2.58956i) q^{19} +(0.659966 - 1.14309i) q^{20} -3.22997 q^{21} +(0.333779 - 0.578123i) q^{22} +(1.75594 + 3.04137i) q^{23} +(1.18637 + 2.05486i) q^{24} -4.27890 q^{25} +(-2.22099 - 0.927601i) q^{26} +1.00000 q^{27} +(-2.51028 - 4.34793i) q^{28} +(-0.576749 - 0.998959i) q^{29} +(-0.283438 + 0.490929i) q^{30} +0.0322574 q^{31} +(-2.88169 + 4.99123i) q^{32} +(0.500000 - 0.866025i) q^{33} -0.526570 q^{34} +(1.37141 - 2.37535i) q^{35} +(0.777183 + 1.34612i) q^{36} +(-2.53312 - 4.38749i) q^{37} +1.99611 q^{38} +(-3.32704 - 1.38954i) q^{39} -2.01488 q^{40} +(-1.86665 - 3.23314i) q^{41} +(1.07810 + 1.86732i) q^{42} +(1.10048 - 1.90609i) q^{43} +1.55437 q^{44} +(-0.424589 + 0.735409i) q^{45} +(1.17219 - 2.03029i) q^{46} +1.56420 q^{47} +(-0.762392 + 1.32050i) q^{48} +(-1.71636 - 2.97282i) q^{49} +(1.42821 + 2.47373i) q^{50} -0.788800 q^{51} +(-0.715225 - 5.55852i) q^{52} +0.836264 q^{53} +(-0.333779 - 0.578123i) q^{54} +(0.424589 + 0.735409i) q^{55} +(-3.83195 + 6.63714i) q^{56} +2.99017 q^{57} +(-0.385014 + 0.666864i) q^{58} +(-4.95844 + 8.58827i) q^{59} -1.31993 q^{60} +(3.25237 - 5.63326i) q^{61} +(-0.0107668 - 0.0186487i) q^{62} +(1.61499 + 2.79724i) q^{63} +0.797823 q^{64} +(2.43450 - 1.85675i) q^{65} -0.667559 q^{66} +(4.97112 + 8.61023i) q^{67} +(-0.613041 - 1.06182i) q^{68} +(1.75594 - 3.04137i) q^{69} -1.83099 q^{70} +(-2.15009 + 3.72407i) q^{71} +(1.18637 - 2.05486i) q^{72} +6.19771 q^{73} +(-1.69100 + 2.92891i) q^{74} +(2.13945 + 3.70563i) q^{75} +(2.32391 + 4.02512i) q^{76} +3.22997 q^{77} +(0.307170 + 2.38724i) q^{78} +12.5074 q^{79} +(-0.647406 - 1.12134i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.24610 + 2.15831i) q^{82} +16.6507 q^{83} +(-2.51028 + 4.34793i) q^{84} +(0.334915 - 0.580090i) q^{85} -1.46927 q^{86} +(-0.576749 + 0.998959i) q^{87} +(-1.18637 - 2.05486i) q^{88} +(4.75163 + 8.23006i) q^{89} +0.566875 q^{90} +(-1.48624 - 11.5506i) q^{91} +5.45873 q^{92} +(-0.0161287 - 0.0279357i) q^{93} +(-0.522097 - 0.904299i) q^{94} +(-1.26959 + 2.19899i) q^{95} +5.76338 q^{96} +(-5.84903 + 10.1308i) q^{97} +(-1.14577 + 1.98453i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 5 q^{3} - 2 q^{4} + 16 q^{5} - 2 q^{6} - 9 q^{7} + 6 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q - 2 * q^2 - 5 * q^3 - 2 * q^4 + 16 * q^5 - 2 * q^6 - 9 * q^7 + 6 * q^8 - 5 * q^9	\( 10 q - 2 q^{2} - 5 q^{3} - 2 q^{4} + 16 q^{5} - 2 q^{6} - 9 q^{7} + 6 q^{8} - 5 q^{9} - 7 q^{10} + 5 q^{11} + 4 q^{12} + q^{13} + 6 q^{14} - 8 q^{15} + 4 q^{16} - 3 q^{17} + 4 q^{18} + 3 q^{19} - 6 q^{20} + 18 q^{21} + 2 q^{22} + q^{23} - 3 q^{24} + 18 q^{25} - 20 q^{26} + 10 q^{27} - 25 q^{28} + 2 q^{29} - 7 q^{30} - 4 q^{31} - 3 q^{32} + 5 q^{33} - 46 q^{34} - 12 q^{35} - 2 q^{36} + q^{37} + 14 q^{38} - 2 q^{39} + 50 q^{40} - 18 q^{41} - 3 q^{42} + 9 q^{43} - 4 q^{44} - 8 q^{45} + 2 q^{46} + 32 q^{47} + 4 q^{48} - 22 q^{49} - 12 q^{50} + 6 q^{51} - 7 q^{52} + 6 q^{53} - 2 q^{54} + 8 q^{55} - 25 q^{56} - 6 q^{57} - 29 q^{58} - 16 q^{59} + 12 q^{60} - 8 q^{61} - 16 q^{62} - 9 q^{63} - 2 q^{64} - 6 q^{65} - 4 q^{66} - 19 q^{67} + 22 q^{68} + q^{69} + 72 q^{70} - 25 q^{71} - 3 q^{72} + 16 q^{73} + 5 q^{74} - 9 q^{75} + 38 q^{76} - 18 q^{77} + 13 q^{78} + 36 q^{79} - 20 q^{80} - 5 q^{81} + 40 q^{82} + 44 q^{83} - 25 q^{84} + 7 q^{85} - 8 q^{86} + 2 q^{87} + 3 q^{88} + 20 q^{89} + 14 q^{90} - 25 q^{91} - 60 q^{92} + 2 q^{93} + 8 q^{94} + 7 q^{95} + 6 q^{96} - 21 q^{97} - 6 q^{98} - 10 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 - 5 * q^3 - 2 * q^4 + 16 * q^5 - 2 * q^6 - 9 * q^7 + 6 * q^8 - 5 * q^9 - 7 * q^10 + 5 * q^11 + 4 * q^12 + q^13 + 6 * q^14 - 8 * q^15 + 4 * q^16 - 3 * q^17 + 4 * q^18 + 3 * q^19 - 6 * q^20 + 18 * q^21 + 2 * q^22 + q^23 - 3 * q^24 + 18 * q^25 - 20 * q^26 + 10 * q^27 - 25 * q^28 + 2 * q^29 - 7 * q^30 - 4 * q^31 - 3 * q^32 + 5 * q^33 - 46 * q^34 - 12 * q^35 - 2 * q^36 + q^37 + 14 * q^38 - 2 * q^39 + 50 * q^40 - 18 * q^41 - 3 * q^42 + 9 * q^43 - 4 * q^44 - 8 * q^45 + 2 * q^46 + 32 * q^47 + 4 * q^48 - 22 * q^49 - 12 * q^50 + 6 * q^51 - 7 * q^52 + 6 * q^53 - 2 * q^54 + 8 * q^55 - 25 * q^56 - 6 * q^57 - 29 * q^58 - 16 * q^59 + 12 * q^60 - 8 * q^61 - 16 * q^62 - 9 * q^63 - 2 * q^64 - 6 * q^65 - 4 * q^66 - 19 * q^67 + 22 * q^68 + q^69 + 72 * q^70 - 25 * q^71 - 3 * q^72 + 16 * q^73 + 5 * q^74 - 9 * q^75 + 38 * q^76 - 18 * q^77 + 13 * q^78 + 36 * q^79 - 20 * q^80 - 5 * q^81 + 40 * q^82 + 44 * q^83 - 25 * q^84 + 7 * q^85 - 8 * q^86 + 2 * q^87 + 3 * q^88 + 20 * q^89 + 14 * q^90 - 25 * q^91 - 60 * q^92 + 2 * q^93 + 8 * q^94 + 7 * q^95 + 6 * q^96 - 21 * q^97 - 6 * q^98 - 10 * q^99

Introduction

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