LMFDB - Embedded newform 950.2.h.d.381.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(191,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(10))

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("950.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.h (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			381.2
Character	$\chi$	$=$	950.381
Dual form			950.2.h.d.571.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(-2.00675 + 1.45799i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-2.21649 + 0.295244i) q^{5} +(2.00675 + 1.45799i) q^{6} +2.78117 q^{7} +(0.809017 + 0.587785i) q^{8} +(0.974256 - 2.99845i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(-2.00675 + 1.45799i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-2.21649 + 0.295244i) q^{5} +(2.00675 + 1.45799i) q^{6} +2.78117 q^{7} +(0.809017 + 0.587785i) q^{8} +(0.974256 - 2.99845i) q^{9} +(0.965727 + 2.01677i) q^{10} +(0.387035 + 1.19117i) q^{11} +(0.766509 - 2.35907i) q^{12} +(0.256872 - 0.790571i) q^{13} +(-0.859429 - 2.64505i) q^{14} +(4.01747 - 3.82410i) q^{15} +(0.309017 - 0.951057i) q^{16} +(3.13647 + 2.27878i) q^{17} -3.15276 q^{18} +(0.809017 + 0.587785i) q^{19} +(1.61964 - 1.54168i) q^{20} +(-5.58110 + 4.05491i) q^{21} +(1.01327 - 0.736184i) q^{22} +(-1.45242 - 4.47010i) q^{23} -2.48048 q^{24} +(4.82566 - 1.30881i) q^{25} -0.831255 q^{26} +(0.117091 + 0.360370i) q^{27} +(-2.25001 + 1.63473i) q^{28} +(-2.32377 + 1.68831i) q^{29} +(-4.87840 - 2.63913i) q^{30} +(4.29445 + 3.12010i) q^{31} -1.00000 q^{32} +(-2.51339 - 1.82609i) q^{33} +(1.19803 - 3.68715i) q^{34} +(-6.16444 + 0.821124i) q^{35} +(0.974256 + 2.99845i) q^{36} +(-1.24982 + 3.84655i) q^{37} +(0.309017 - 0.951057i) q^{38} +(0.637165 + 1.96099i) q^{39} +(-1.96672 - 1.06396i) q^{40} +(-2.52182 + 7.76135i) q^{41} +(5.58110 + 4.05491i) q^{42} -7.51267 q^{43} +(-1.01327 - 0.736184i) q^{44} +(-1.27415 + 6.93368i) q^{45} +(-3.80249 + 2.76267i) q^{46} +(-3.42647 + 2.48948i) q^{47} +(0.766509 + 2.35907i) q^{48} +0.734903 q^{49} +(-2.73597 - 4.18503i) q^{50} -9.61654 q^{51} +(0.256872 + 0.790571i) q^{52} +(0.232824 - 0.169157i) q^{53} +(0.306549 - 0.222721i) q^{54} +(-1.20955 - 2.52595i) q^{55} +(2.25001 + 1.63473i) q^{56} -2.48048 q^{57} +(2.32377 + 1.68831i) q^{58} +(-3.22369 + 9.92151i) q^{59} +(-1.00246 + 5.45517i) q^{60} +(2.37250 + 7.30179i) q^{61} +(1.64033 - 5.04843i) q^{62} +(2.70957 - 8.33920i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-0.335943 + 1.82813i) q^{65} +(-0.960031 + 2.95467i) q^{66} +(8.70631 + 6.32551i) q^{67} -3.87689 q^{68} +(9.43200 + 6.85275i) q^{69} +(2.68585 + 5.60899i) q^{70} +(-7.37920 + 5.36130i) q^{71} +(2.55064 - 1.85315i) q^{72} +(-1.33368 - 4.10464i) q^{73} +4.04450 q^{74} +(-7.77565 + 9.66221i) q^{75} -1.00000 q^{76} +(1.07641 + 3.31285i) q^{77} +(1.66812 - 1.21196i) q^{78} +(-10.6118 + 7.70991i) q^{79} +(-0.404139 + 2.19924i) q^{80} +(6.89152 + 5.00698i) q^{81} +8.16077 q^{82} +(-11.6618 - 8.47283i) q^{83} +(2.13179 - 6.56098i) q^{84} +(-7.62476 - 4.12487i) q^{85} +(2.32154 + 7.14498i) q^{86} +(2.20167 - 6.77604i) q^{87} +(-0.387035 + 1.19117i) q^{88} +(-1.45861 - 4.48915i) q^{89} +(6.98806 - 0.930834i) q^{90} +(0.714405 - 2.19871i) q^{91} +(3.80249 + 2.76267i) q^{92} -13.1669 q^{93} +(3.42647 + 2.48948i) q^{94} +(-1.96672 - 1.06396i) q^{95} +(2.00675 - 1.45799i) q^{96} +(-0.870458 + 0.632425i) q^{97} +(-0.227097 - 0.698934i) q^{98} +3.94874 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 11 q^{5} + q^{6} - 10 q^{7} + 11 q^{8}+O(q^{10}) $ 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 11 * q^5 + q^6 - 10 * q^7 + 11 * q^8	\( 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 11 q^{5} + q^{6} - 10 q^{7} + 11 q^{8} - 4 q^{10} + 7 q^{11} + 4 q^{12} + 10 q^{13} - 5 q^{14} - 20 q^{15} - 11 q^{16} + 11 q^{17} - 50 q^{18} + 11 q^{19} + 4 q^{20} + 9 q^{21} + 8 q^{22} - 7 q^{23} + 6 q^{24} - 3 q^{25} + 10 q^{26} + 5 q^{27} - 20 q^{29} - 10 q^{30} - 11 q^{31} - 44 q^{32} - 2 q^{33} - q^{34} + 5 q^{35} + 43 q^{37} - 11 q^{38} - 33 q^{39} - 4 q^{40} - 32 q^{41} - 9 q^{42} - 74 q^{43} - 8 q^{44} + 10 q^{45} - 8 q^{46} - 19 q^{47} + 4 q^{48} + 54 q^{49} + 18 q^{50} + 34 q^{51} + 10 q^{52} + 23 q^{53} - 40 q^{54} + 2 q^{55} + 6 q^{57} + 20 q^{58} + 24 q^{59} - 35 q^{60} - 12 q^{61} + q^{62} - 44 q^{63} - 11 q^{64} + 43 q^{65} - 8 q^{66} + 35 q^{67} - 24 q^{68} + 29 q^{69} - 5 q^{70} - 2 q^{71} + 25 q^{72} + 22 q^{73} + 72 q^{74} + 7 q^{75} - 44 q^{76} - 3 q^{77} - 22 q^{78} - 19 q^{79} - q^{80} - 26 q^{81} - 58 q^{82} - 24 q^{83} - 21 q^{84} - 18 q^{85} - 6 q^{86} + 83 q^{87} - 7 q^{88} - 8 q^{89} + 60 q^{90} - 30 q^{91} + 8 q^{92} - 72 q^{93} + 19 q^{94} - 4 q^{95} + q^{96} - 16 q^{97} + q^{98} + 84 q^{99}+O(q^{100}) \) 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 11 * q^5 + q^6 - 10 * q^7 + 11 * q^8 - 4 * q^10 + 7 * q^11 + 4 * q^12 + 10 * q^13 - 5 * q^14 - 20 * q^15 - 11 * q^16 + 11 * q^17 - 50 * q^18 + 11 * q^19 + 4 * q^20 + 9 * q^21 + 8 * q^22 - 7 * q^23 + 6 * q^24 - 3 * q^25 + 10 * q^26 + 5 * q^27 - 20 * q^29 - 10 * q^30 - 11 * q^31 - 44 * q^32 - 2 * q^33 - q^34 + 5 * q^35 + 43 * q^37 - 11 * q^38 - 33 * q^39 - 4 * q^40 - 32 * q^41 - 9 * q^42 - 74 * q^43 - 8 * q^44 + 10 * q^45 - 8 * q^46 - 19 * q^47 + 4 * q^48 + 54 * q^49 + 18 * q^50 + 34 * q^51 + 10 * q^52 + 23 * q^53 - 40 * q^54 + 2 * q^55 + 6 * q^57 + 20 * q^58 + 24 * q^59 - 35 * q^60 - 12 * q^61 + q^62 - 44 * q^63 - 11 * q^64 + 43 * q^65 - 8 * q^66 + 35 * q^67 - 24 * q^68 + 29 * q^69 - 5 * q^70 - 2 * q^71 + 25 * q^72 + 22 * q^73 + 72 * q^74 + 7 * q^75 - 44 * q^76 - 3 * q^77 - 22 * q^78 - 19 * q^79 - q^80 - 26 * q^81 - 58 * q^82 - 24 * q^83 - 21 * q^84 - 18 * q^85 - 6 * q^86 + 83 * q^87 - 7 * q^88 - 8 * q^89 + 60 * q^90 - 30 * q^91 + 8 * q^92 - 72 * q^93 + 19 * q^94 - 4 * q^95 + q^96 - 16 * q^97 + q^98 + 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$	−2.00675	+	1.45799i	−1.15860	+	0.841769i	−0.989600	−	0.143848i	$-0.954053\pi$
$3$	−2.00675	+	1.45799i	−1.15860	+	0.841769i	−0.168996	+	0.985617i	$0.554053\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	−2.21649	+	0.295244i	−0.991245	+	0.132037i
$5$	−2.21649	+	0.295244i	−0.991245	+	0.132037i
$6$	2.00675	+	1.45799i	0.819251	+	0.595221i
$7$	2.78117			1.05118			0.525592	−	0.850737i	$-0.323844\pi$
$7$	2.78117			1.05118			0.525592	+	0.850737i	$0.323844\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	0.974256	−	2.99845i	0.324752	−	0.999484i
$10$	0.965727	+	2.01677i	0.305390	+	0.637759i
$11$	0.387035	+	1.19117i	0.116695	+	0.359152i	0.992297	−	0.123883i	$-0.0395347\pi$
$11$	0.387035	+	1.19117i	0.116695	+	0.359152i	−0.875601	+	0.483034i	$0.839535\pi$
$12$	0.766509	−	2.35907i	0.221272	−	0.681006i
$13$	0.256872	−	0.790571i	0.0712435	−	0.219265i	−0.909095	−	0.416589i	$-0.863225\pi$
$13$	0.256872	−	0.790571i	0.0712435	−	0.219265i	0.980338	+	0.197325i	$0.0632253\pi$
$14$	−0.859429	−	2.64505i	−0.229692	−	0.706919i
$15$	4.01747	−	3.82410i	1.03731	−	0.987377i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	3.13647	+	2.27878i	0.760707	+	0.552686i	0.899127	−	0.437688i	$-0.144203\pi$
$17$	3.13647	+	2.27878i	0.760707	+	0.552686i	−0.138420	+	0.990374i	$0.544203\pi$
$18$	−3.15276			−0.743112
$19$	0.809017	+	0.587785i	0.185601	+	0.134847i
$19$	0.809017	+	0.587785i	0.185601	+	0.134847i
$20$	1.61964	−	1.54168i	0.362162	−	0.344730i
$21$	−5.58110	+	4.05491i	−1.21790	+	0.884854i
$22$	1.01327	−	0.736184i	0.216030	−	0.156955i
$23$	−1.45242	−	4.47010i	−0.302851	−	0.932080i	−0.980470	−	0.196667i	$-0.936988\pi$
$23$	−1.45242	−	4.47010i	−0.302851	−	0.932080i	0.677619	−	0.735413i	$-0.263012\pi$
$24$	−2.48048			−0.506325
$25$	4.82566	−	1.30881i	0.965132	−	0.261762i
$26$	−0.831255			−0.163023
$27$	0.117091	+	0.360370i	0.0225342	+	0.0693532i
$28$	−2.25001	+	1.63473i	−0.425213	+	0.308935i
$29$	−2.32377	+	1.68831i	−0.431512	+	0.313512i	−0.782253	−	0.622960i	$-0.785930\pi$
$29$	−2.32377	+	1.68831i	−0.431512	+	0.313512i	0.350741	+	0.936473i	$0.385930\pi$
$30$	−4.87840	−	2.63913i	−0.890670	−	0.481838i
$31$	4.29445	+	3.12010i	0.771306	+	0.560386i	0.902357	−	0.430989i	$-0.141835\pi$
$31$	4.29445	+	3.12010i	0.771306	+	0.560386i	−0.131052	+	0.991376i	$0.541835\pi$
$32$	−1.00000			−0.176777
$33$	−2.51339	−	1.82609i	−0.437525	−	0.317881i
$34$	1.19803	−	3.68715i	0.205460	−	0.632340i
$35$	−6.16444	+	0.821124i	−1.04198	+	0.138795i
$36$	0.974256	+	2.99845i	0.162376	+	0.499742i
$37$	−1.24982	+	3.84655i	−0.205469	+	0.632368i	0.794225	+	0.607624i	$0.207877\pi$
$37$	−1.24982	+	3.84655i	−0.205469	+	0.632368i	−0.999694	+	0.0247444i	$0.992123\pi$
$38$	0.309017	−	0.951057i	0.0501292	−	0.154282i
$39$	0.637165	+	1.96099i	0.102028	+	0.314010i
$40$	−1.96672	−	1.06396i	−0.310966	−	0.168227i
$41$	−2.52182	+	7.76135i	−0.393842	+	1.21212i	0.536018	+	0.844206i	$0.319928\pi$
$41$	−2.52182	+	7.76135i	−0.393842	+	1.21212i	−0.929860	+	0.367913i	$0.880072\pi$
$42$	5.58110	+	4.05491i	0.861183	+	0.625686i
$43$	−7.51267			−1.14567			−0.572836	−	0.819670i	$-0.694157\pi$
$43$	−7.51267			−1.14567			−0.572836	+	0.819670i	$0.694157\pi$
$44$	−1.01327	−	0.736184i	−0.152756	−	0.110984i
$45$	−1.27415	+	6.93368i	−0.189940	+	1.03361i
$46$	−3.80249	+	2.76267i	−0.560647	+	0.407334i
$47$	−3.42647	+	2.48948i	−0.499802	+	0.363128i	−0.808942	−	0.587889i	$-0.799959\pi$
$47$	−3.42647	+	2.48948i	−0.499802	+	0.363128i	0.309139	+	0.951017i	$0.399959\pi$
$48$	0.766509	+	2.35907i	0.110636	+	0.340503i
$49$	0.734903			0.104986
$50$	−2.73597	−	4.18503i	−0.386924	−	0.591853i
$51$	−9.61654			−1.34659
$52$	0.256872	+	0.790571i	0.0356217	+	0.109632i
$53$	0.232824	−	0.169157i	0.0319809	−	0.0232355i	−0.571680	−	0.820477i	$-0.693708\pi$
$53$	0.232824	−	0.169157i	0.0319809	−	0.0232355i	0.603661	+	0.797241i	$0.293708\pi$
$54$	0.306549	−	0.222721i	0.0417160	−	0.0303085i
$55$	−1.20955	−	2.52595i	−0.163095	−	0.340599i
$56$	2.25001	+	1.63473i	0.300671	+	0.218450i
$57$	−2.48048			−0.328547
$58$	2.32377	+	1.68831i	0.305125	+	0.221687i
$59$	−3.22369	+	9.92151i	−0.419689	+	1.29167i	0.488300	+	0.872676i	$0.337617\pi$
$59$	−3.22369	+	9.92151i	−0.419689	+	1.29167i	−0.907989	+	0.418994i	$0.862383\pi$
$60$	−1.00246	+	5.45517i	−0.129417	+	0.704259i
$61$	2.37250	+	7.30179i	0.303767	+	0.934899i	0.980134	+	0.198334i	$0.0635532\pi$
$61$	2.37250	+	7.30179i	0.303767	+	0.934899i	−0.676367	+	0.736564i	$0.736447\pi$
$62$	1.64033	−	5.04843i	0.208322	−	0.641151i
$63$	2.70957	−	8.33920i	0.341374	−	1.05064i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−0.335943	+	1.82813i	−0.0416686	+	0.226752i
$66$	−0.960031	+	2.95467i	−0.118172	+	0.363695i
$67$	8.70631	+	6.32551i	1.06365	+	0.772784i	0.974759	−	0.223258i	$-0.0716693\pi$
$67$	8.70631	+	6.32551i	1.06365	+	0.772784i	0.0888862	+	0.996042i	$0.471669\pi$
$68$	−3.87689			−0.470143
$69$	9.43200	+	6.85275i	1.13548	+	0.824974i
$70$	2.68585	+	5.60899i	0.321021	+	0.670402i
$71$	−7.37920	+	5.36130i	−0.875750	+	0.636270i	−0.932124	−	0.362140i	$-0.882046\pi$
$71$	−7.37920	+	5.36130i	−0.875750	+	0.636270i	0.0563737	+	0.998410i	$0.482046\pi$
$72$	2.55064	−	1.85315i	0.300595	−	0.218395i
$73$	−1.33368	−	4.10464i	−0.156095	−	0.480412i	0.842175	−	0.539205i	$-0.181275\pi$
$73$	−1.33368	−	4.10464i	−0.156095	−	0.480412i	−0.998270	+	0.0587923i	$0.981275\pi$
$74$	4.04450			0.470163
$75$	−7.77565	+	9.66221i	−0.897855	+	1.11570i
$76$	−1.00000			−0.114708
$77$	1.07641	+	3.31285i	0.122668	+	0.377534i
$78$	1.66812	−	1.21196i	0.188877	−	0.137227i
$79$	−10.6118	+	7.70991i	−1.19392	+	0.867432i	−0.993673	−	0.112313i	$-0.964174\pi$
$79$	−10.6118	+	7.70991i	−1.19392	+	0.867432i	−0.200245	+	0.979746i	$0.564174\pi$
$80$	−0.404139	+	2.19924i	−0.0451841	+	0.245883i
$81$	6.89152	+	5.00698i	0.765724	+	0.556331i
$82$	8.16077			0.901206
$83$	−11.6618	−	8.47283i	−1.28005	−	0.930013i	−0.280499	−	0.959854i	$-0.590500\pi$
$83$	−11.6618	−	8.47283i	−1.28005	−	0.930013i	−0.999555	+	0.0298409i	$0.990500\pi$
$84$	2.13179	−	6.56098i	0.232598	−	0.715862i
$85$	−7.62476	−	4.12487i	−0.827022	−	0.447405i
$86$	2.32154	+	7.14498i	0.250339	+	0.770463i
$87$	2.20167	−	6.77604i	0.236044	−	0.726468i
$88$	−0.387035	+	1.19117i	−0.0412581	+	0.126979i
$89$	−1.45861	−	4.48915i	−0.154613	−	0.475849i	0.843509	−	0.537115i	$-0.180486\pi$
$89$	−1.45861	−	4.48915i	−0.154613	−	0.475849i	−0.998121	+	0.0612666i	$0.980486\pi$
$90$	6.98806	−	0.930834i	0.736606	−	0.0981185i
$91$	0.714405	−	2.19871i	0.0748899	−	0.230488i
$92$	3.80249	+	2.76267i	0.396438	+	0.288029i
$93$	−13.1669			−1.36535
$94$	3.42647	+	2.48948i	0.353414	+	0.256770i
$95$	−1.96672	−	1.06396i	−0.201781	−	0.109160i
$96$	2.00675	−	1.45799i	0.204813	−	0.148805i
$97$	−0.870458	+	0.632425i	−0.0883816	+	0.0642130i	−0.631099	−	0.775703i	$-0.717396\pi$
$97$	−0.870458	+	0.632425i	−0.0883816	+	0.0642130i	0.542717	+	0.839916i	$0.317396\pi$
$98$	−0.227097	−	0.698934i	−0.0229403	−	0.0706030i
$99$	3.94874			0.396863
$100$	−3.13474	+	3.89530i	−0.313474	+	0.389530i
$101$	6.69977			0.666652			0.333326	−	0.942812i	$-0.391829\pi$
$101$	6.69977			0.666652			0.333326	+	0.942812i	$0.391829\pi$
$102$	2.97168	+	9.14588i	0.294240	+	0.905577i
$103$	9.45568	−	6.86995i	0.931696	−	0.676917i	−0.0147117	−	0.999892i	$-0.504683\pi$
$103$	9.45568	−	6.86995i	0.931696	−	0.676917i	0.946407	+	0.322975i	$0.104683\pi$
$104$	0.672500	−	0.488600i	0.0659440	−	0.0479111i
$105$	11.1733	−	10.6355i	1.09040	−	1.03791i
$106$	−0.232824	−	0.169157i	−0.0226139	−	0.0164300i
$107$	−18.7258			−1.81029			−0.905145	−	0.425104i	$-0.860238\pi$
$107$	−18.7258			−1.81029			−0.905145	+	0.425104i	$0.860238\pi$
$108$	−0.306549	−	0.222721i	−0.0294977	−	0.0214313i
$109$	−1.32909	+	4.09052i	−0.127304	+	0.391801i	−0.994314	−	0.106490i	$-0.966039\pi$
$109$	−1.32909	+	4.09052i	−0.127304	+	0.391801i	0.867010	+	0.498291i	$0.166039\pi$
$110$	−2.02855	+	1.93091i	−0.193415	+	0.184105i
$111$	−3.10014	−	9.54126i	−0.294253	−	0.905617i
$112$	0.859429	−	2.64505i	0.0812084	−	0.249934i
$113$	3.15374	−	9.70623i	0.296679	−	0.913085i	−0.685973	−	0.727627i	$-0.740623\pi$
$113$	3.15374	−	9.70623i	0.296679	−	0.913085i	0.982652	−	0.185458i	$-0.0593769\pi$
$114$	0.766509	+	2.35907i	0.0717902	+	0.220947i
$115$	4.53906	+	9.47912i	0.423269	+	0.883932i
$116$	0.887599	−	2.73175i	0.0824115	−	0.253637i
$117$	−2.12023	−	1.54044i	−0.196015	−	0.142413i
$118$	10.4321			0.960352
$119$	8.72306	+	6.33768i	0.799642	+	0.580974i
$120$	5.49795	−	0.732346i	0.501892	−	0.0668538i
$121$	7.63009	−	5.54359i	0.693645	−	0.503963i
$122$	6.21128	−	4.51276i	0.562342	−	0.408566i
$123$	−6.25530	−	19.2518i	−0.564022	−	1.73588i
$124$	−5.30823			−0.476693
$125$	−10.3096	+	4.32572i	−0.922120	+	0.386904i
$126$	−8.76836			−0.781147
$127$	−2.50998	−	7.72493i	−0.222725	−	0.685477i	−0.998515	−	0.0544854i	$-0.982648\pi$
$127$	−2.50998	−	7.72493i	−0.222725	−	0.685477i	0.775790	−	0.630992i	$-0.217352\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	15.0760	−	10.9534i	1.32737	−	0.964391i
$130$	1.84247	−	0.245423i	0.161595	−	0.0215251i
$131$	6.29829	+	4.57598i	0.550284	+	0.399805i	0.827890	−	0.560890i	$-0.189541\pi$
$131$	6.29829	+	4.57598i	0.550284	+	0.399805i	−0.277606	+	0.960695i	$0.589541\pi$
$132$	3.10672			0.270406
$133$	2.25001	+	1.63473i	0.195101	+	0.141749i
$134$	3.32552	−	10.2349i	0.287281	−	0.884159i
$135$	−0.365929	−	0.764186i	−0.0314942	−	0.0657707i
$136$	1.19803	+	3.68715i	0.102730	+	0.316170i
$137$	0.650266	−	2.00131i	0.0555560	−	0.170984i	−0.919428	−	0.393258i	$-0.871348\pi$
$137$	0.650266	−	2.00131i	0.0555560	−	0.170984i	0.974984	+	0.222274i	$0.0713480\pi$
$138$	3.60270	−	11.0880i	0.306682	−	0.943871i
$139$	0.0134190	+	0.0412995i	0.00113819	+	0.00350298i	0.951624	−	0.307265i	$-0.0994138\pi$
$139$	0.0134190	+	0.0412995i	0.00113819	+	0.00350298i	−0.950486	+	0.310768i	$0.899414\pi$
$140$	4.50449	−	4.28767i	0.380699	−	0.362374i
$141$	3.24644	−	9.99151i	0.273399	−	0.841437i
$142$	7.37920	+	5.36130i	0.619249	+	0.449911i
$143$	1.04112			0.0870631
$144$	−2.55064	−	1.85315i	−0.212553	−	0.154429i
$145$	4.65214	−	4.42821i	0.386339	−	0.367743i
$146$	−3.49162	+	2.53681i	−0.288968	+	0.209948i
$147$	−1.47476	+	1.07148i	−0.121636	+	0.0883741i
$148$	−1.24982	−	3.84655i	−0.102734	−	0.316184i
$149$	−11.9455			−0.978615			−0.489307	−	0.872111i	$-0.662750\pi$
$149$	−11.9455			−0.978615			−0.489307	+	0.872111i	$0.662750\pi$
$150$	11.5921	+	4.40930i	0.946492	+	0.360018i
$151$	−1.62732			−0.132429			−0.0662146	−	0.997805i	$-0.521092\pi$
$151$	−1.62732			−0.132429			−0.0662146	+	0.997805i	$0.521092\pi$
$152$	0.309017	+	0.951057i	0.0250646	+	0.0771409i
$153$	9.88855	−	7.18445i	0.799442	−	0.580828i
$154$	2.81808	−	2.04745i	0.227087	−	0.164988i
$155$	−10.4398	−	5.64776i	−0.838544	−	0.453639i
$156$	−1.66812	−	1.21196i	−0.133556	−	0.0970344i
$157$	12.6469			1.00933			0.504665	−	0.863316i	$-0.331616\pi$
$157$	12.6469			1.00933			0.504665	+	0.863316i	$0.331616\pi$
$158$	10.6118	+	7.70991i	0.844228	+	0.613367i
$159$	−0.220591	+	0.678910i	−0.0174940	+	0.0538410i
$160$	2.21649	−	0.295244i	0.175229	−	0.0233411i
$161$	−4.03944	−	12.4321i	−0.318352	−	0.979787i
$162$	2.63233	−	8.10147i	0.206815	−	0.636511i
$163$	−1.40726	+	4.33111i	−0.110225	+	0.339239i	−0.990921	−	0.134443i	$-0.957075\pi$
$163$	−1.40726	+	4.33111i	−0.110225	+	0.339239i	0.880696	+	0.473682i	$0.157075\pi$
$164$	−2.52182	−	7.76135i	−0.196921	−	0.606060i
$165$	6.11005	+	3.30544i	0.475667	+	0.257328i
$166$	−4.45443	+	13.7093i	−0.345731	+	1.06405i
$167$	4.93473	+	3.58529i	0.381861	+	0.277438i	0.762112	−	0.647445i	$-0.224163\pi$
$167$	4.93473	+	3.58529i	0.381861	+	0.277438i	−0.380251	+	0.924883i	$0.624163\pi$
$168$	−6.89862			−0.532240
$169$	9.95820	+	7.23506i	0.766016	+	0.556543i
$170$	−1.56681	+	8.52623i	−0.120168	+	0.653932i
$171$	2.55064	−	1.85315i	0.195052	−	0.141714i
$172$	6.07788	−	4.41584i	0.463434	−	0.336705i
$173$	4.69776	+	14.4582i	0.357164	+	1.09924i	0.954744	+	0.297429i	$0.0961291\pi$
$173$	4.69776	+	14.4582i	0.357164	+	1.09924i	−0.597580	+	0.801809i	$0.703871\pi$
$174$	−7.12475			−0.540126
$175$	13.4210	−	3.64003i	1.01453	−	0.275160i
$176$	1.25247			0.0944086
$177$	−7.99629	−	24.6101i	−0.601038	−	1.84981i
$178$	−3.81870	+	2.77445i	−0.286223	+	0.207953i
$179$	−17.6883	+	12.8513i	−1.32209	+	0.960553i	−0.322184	+	0.946677i	$0.604417\pi$
$179$	−17.6883	+	12.8513i	−1.32209	+	0.960553i	−0.999904	+	0.0138754i	$0.995583\pi$
$180$	−3.04471	−	6.35840i	−0.226939	−	0.473927i
$181$	5.49419	+	3.99177i	0.408380	+	0.296706i	0.772946	−	0.634472i	$-0.218782\pi$
$181$	5.49419	+	3.99177i	0.408380	+	0.296706i	−0.364566	+	0.931178i	$0.618782\pi$
$182$	−2.31186			−0.171367
$183$	−15.4069	−	11.1938i	−1.13891	−	0.827468i
$184$	1.45242	−	4.47010i	0.107074	−	0.329540i
$185$	1.63454	−	8.89484i	0.120174	−	0.653961i
$186$	4.06881	+	12.5225i	0.298339	+	0.918194i
$187$	−1.50049	+	4.61804i	−0.109727	+	0.337705i
$188$	1.30880	−	4.02806i	0.0954538	−	0.293777i
$189$	0.325651	+	1.00225i	0.0236876	+	0.0729030i
$190$	−0.404139	+	2.19924i	−0.0293193	+	0.159550i
$191$	−5.12768	+	15.7814i	−0.371026	+	1.14190i	0.575095	+	0.818087i	$0.304965\pi$
$191$	−5.12768	+	15.7814i	−0.371026	+	1.14190i	−0.946121	+	0.323814i	$0.895035\pi$
$192$	−2.00675	−	1.45799i	−0.144824	−	0.105221i
$193$	−18.3648			−1.32193			−0.660965	−	0.750417i	$-0.729853\pi$
$193$	−18.3648			−1.32193			−0.660965	+	0.750417i	$0.729853\pi$
$194$	0.870458	+	0.632425i	0.0624953	+	0.0454055i
$195$	−1.99124	−	4.15840i	−0.142596	−	0.297789i
$196$	−0.594549	+	0.431965i	−0.0424678	+	0.0308546i
$197$	−4.70158	+	3.41590i	−0.334974	+	0.243373i	−0.742538	−	0.669804i	$-0.766378\pi$
$197$	−4.70158	+	3.41590i	−0.334974	+	0.243373i	0.407564	+	0.913176i	$0.366378\pi$
$198$	−1.22023	−	3.75547i	−0.0867178	−	0.266890i
$199$	4.56562			0.323648			0.161824	−	0.986820i	$-0.448262\pi$
$199$	4.56562			0.323648			0.161824	+	0.986820i	$0.448262\pi$
$200$	4.67334	+	1.77760i	0.330455	+	0.125695i
$201$	−26.6939			−1.88284
$202$	−2.07034	−	6.37186i	−0.145669	−	0.448323i
$203$	−6.46279	+	4.69549i	−0.453599	+	0.329559i
$204$	7.77995	−	5.65246i	0.544705	−	0.395751i
$205$	3.29809	−	17.9475i	0.230348	−	1.25351i
$206$	−9.45568	−	6.86995i	−0.658808	−	0.478652i
$207$	−14.8184			−1.02995
$208$	−0.672500	−	0.488600i	−0.0466295	−	0.0338783i
$209$	−0.387035	+	1.19117i	−0.0267718	+	0.0823950i
$210$	−13.5677	−	7.33988i	−0.936257	−	0.506500i
$211$	−2.95066	−	9.08119i	−0.203132	−	0.625175i	−0.999785	−	0.0207384i	$-0.993398\pi$
$211$	−2.95066	−	9.08119i	−0.203132	−	0.625175i	0.796653	−	0.604437i	$-0.206602\pi$
$212$	−0.0889310	+	0.273701i	−0.00610781	+	0.0187979i
$213$	6.99148	−	21.5176i	0.479048	−	1.47436i
$214$	5.78658	+	17.8093i	0.395563	+	1.21742i
$215$	16.6518	−	2.21807i	1.13564	−	0.151271i
$216$	−0.117091	+	0.360370i	−0.00796706	+	0.0245201i
$217$	11.9436	+	8.67752i	0.810783	+	0.589069i
$218$	4.30103			0.291303
$219$	8.66088	+	6.29249i	0.585248	+	0.425207i
$220$	2.46326	+	1.33258i	0.166073	+	0.0898427i
$221$	2.60721	−	1.89425i	0.175380	−	0.127421i
$222$	−8.11628	+	5.89683i	−0.544729	+	0.395769i
$223$	6.07111	+	18.6850i	0.406552	+	1.25124i	0.919593	+	0.392873i	$0.128519\pi$
$223$	6.07111	+	18.6850i	0.406552	+	1.25124i	−0.513041	+	0.858364i	$0.671481\pi$
$224$	−2.78117			−0.185825
$225$	0.777019	−	15.7446i	0.0518013	−	1.04964i
$226$	−10.2057			−0.678875
$227$	5.23785	+	16.1205i	0.347649	+	1.06995i	0.960151	+	0.279483i	$0.0901631\pi$
$227$	5.23785	+	16.1205i	0.347649	+	1.06995i	−0.612502	+	0.790469i	$0.709837\pi$
$228$	2.00675	−	1.45799i	0.132900	−	0.0965575i
$229$	8.05282	−	5.85072i	0.532145	−	0.386626i	−0.289014	−	0.957325i	$-0.593327\pi$
$229$	8.05282	−	5.85072i	0.532145	−	0.386626i	0.821160	+	0.570699i	$0.193327\pi$
$230$	7.61253	−	7.24611i	0.501955	−	0.477794i
$231$	−6.99017	−	5.07866i	−0.459919	−	0.334151i
$232$	−2.87233			−0.188578
$233$	13.8637	+	10.0725i	0.908239	+	0.659874i	0.940569	−	0.339603i	$-0.110293\pi$
$233$	13.8637	+	10.0725i	0.908239	+	0.659874i	−0.0323300	+	0.999477i	$0.510293\pi$
$234$	−0.809856	+	2.49248i	−0.0529419	+	0.162938i
$235$	6.85974	−	6.52955i	0.447480	−	0.425941i
$236$	−3.22369	−	9.92151i	−0.209845	−	0.645835i
$237$	10.0542	−	30.9437i	0.653091	−	2.01001i
$238$	3.33191	−	10.2546i	0.215976	−	0.664706i
$239$	0.210700	+	0.648469i	0.0136291	+	0.0419460i	0.957640	−	0.287969i	$-0.0929800\pi$
$239$	0.210700	+	0.648469i	0.0136291	+	0.0419460i	−0.944011	+	0.329915i	$0.892980\pi$
$240$	−2.39546	−	5.00255i	−0.154626	−	0.322914i
$241$	−4.54973	+	14.0026i	−0.293074	+	0.901989i	0.690788	+	0.723058i	$0.257264\pi$
$241$	−4.54973	+	14.0026i	−0.293074	+	0.901989i	−0.983862	+	0.178931i	$0.942736\pi$
$242$	−7.63009	−	5.54359i	−0.490481	−	0.356355i
$243$	−22.2664			−1.42839
$244$	−6.21128	−	4.51276i	−0.397636	−	0.288900i
$245$	−1.62890	+	0.216976i	−0.104067	+	0.0138621i
$246$	−16.3766	+	11.8983i	−1.04413	+	0.758608i
$247$	0.672500	−	0.488600i	0.0427901	−	0.0310888i
$248$	1.64033	+	5.04843i	0.104161	+	0.320575i
$249$	35.7556			2.26592
$250$	7.29985	+	8.46831i	0.461683	+	0.535583i
$251$	0.917258			0.0578968			0.0289484	−	0.999581i	$-0.490784\pi$
$251$	0.917258			0.0578968			0.0289484	+	0.999581i	$0.490784\pi$
$252$	2.70957	+	8.33920i	0.170687	+	0.525320i
$253$	4.76252	−	3.46017i	0.299417	−	0.217539i
$254$	−6.57122	+	4.77427i	−0.412315	+	0.299564i
$255$	21.3150	−	2.83923i	1.33480	−	0.177799i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	2.74613			0.171299			0.0856494	−	0.996325i	$-0.472704\pi$
$257$	2.74613			0.171299			0.0856494	+	0.996325i	$0.472704\pi$
$258$	−15.0760	−	10.9534i	−0.938593	−	0.681928i
$259$	−3.47596	+	10.6979i	−0.215985	+	0.664735i
$260$	−0.802766	−	1.67645i	−0.0497854	−	0.103969i
$261$	2.79839	+	8.61255i	0.173216	+	0.533103i
$262$	2.40573	−	7.40409i	0.148627	−	0.457426i
$263$	−4.77251	+	14.6883i	−0.294286	+	0.905719i	0.689175	+	0.724595i	$0.257973\pi$
$263$	−4.77251	+	14.6883i	−0.294286	+	0.905719i	−0.983460	+	0.181123i	$0.942027\pi$
$264$	−0.960031	−	2.95467i	−0.0590858	−	0.181847i
$265$	−0.466110	+	0.443675i	−0.0286329	+	0.0272547i
$266$	0.859429	−	2.64505i	0.0526949	−	0.162178i
$267$	9.47218	+	6.88194i	0.579688	+	0.421168i
$268$	−10.7616			−0.657369
$269$	−15.3049	−	11.1196i	−0.933154	−	0.677976i	0.0136090	−	0.999907i	$-0.495668\pi$
$269$	−15.3049	−	11.1196i	−0.933154	−	0.677976i	−0.946763	+	0.321931i	$0.895668\pi$
$270$	−0.613706	+	0.584166i	−0.0373490	+	0.0355512i
$271$	5.95914	−	4.32957i	0.361992	−	0.263003i	−0.391890	−	0.920012i	$-0.628179\pi$
$271$	5.95914	−	4.32957i	0.361992	−	0.263003i	0.753883	+	0.657009i	$0.228179\pi$
$272$	3.13647	−	2.27878i	0.190177	−	0.138171i
$273$	1.77206	+	5.45385i	0.107250	+	0.330082i
$274$	−2.10431			−0.127126
$275$	3.42672	+	5.24163i	0.206639	+	0.316082i
$276$	−11.6586			−0.701765
$277$	−6.91219	−	21.2735i	−0.415313	−	1.27820i	−0.911971	−	0.410256i	$-0.865439\pi$
$277$	−6.91219	−	21.2735i	−0.415313	−	1.27820i	0.496657	−	0.867947i	$-0.334561\pi$
$278$	0.0351315	−	0.0255245i	0.00210705	−	0.00153086i
$279$	13.5394	−	9.83692i	0.810580	−	0.588921i
$280$	−5.46978	−	2.95906i	−0.326882	−	0.176838i
$281$	12.4111	+	9.01721i	0.740385	+	0.537921i	0.892832	−	0.450390i	$-0.148715\pi$
$281$	12.4111	+	9.01721i	0.740385	+	0.537921i	−0.152446	+	0.988312i	$0.548715\pi$
$282$	−10.5057			−0.625605
$283$	−11.3069	−	8.21496i	−0.672127	−	0.488329i	0.198610	−	0.980079i	$-0.436357\pi$
$283$	−11.3069	−	8.21496i	−0.672127	−	0.488329i	−0.870737	+	0.491750i	$0.836357\pi$
$284$	2.81860	−	8.67477i	0.167253	−	0.514753i
$285$	5.49795	−	0.732346i	0.325671	−	0.0433804i
$286$	−0.321725	−	0.990167i	−0.0190240	−	0.0585498i
$287$	−7.01360	+	21.5856i	−0.414000	+	1.27416i
$288$	−0.974256	+	2.99845i	−0.0574086	+	0.176685i
$289$	−0.608667	−	1.87328i	−0.0358039	−	0.110193i
$290$	−5.64907	−	3.05605i	−0.331725	−	0.179458i
$291$	0.824722	−	2.53823i	0.0483461	−	0.148794i
$292$	3.49162	+	2.53681i	0.204332	+	0.148456i
$293$	25.7972			1.50709			0.753543	−	0.657399i	$-0.228343\pi$
$293$	25.7972			1.50709			0.753543	+	0.657399i	$0.228343\pi$
$294$	1.47476	+	1.07148i	0.0860100	+	0.0624899i
$295$	4.21602	−	22.9427i	0.245466	−	1.33578i
$296$	−3.27207	+	2.37730i	−0.190185	+	0.138178i
$297$	−0.383944	+	0.278952i	−0.0222787	+	0.0161864i
$298$	3.69137	+	11.3609i	0.213835	+	0.658117i
$299$	−3.90702			−0.225949
$300$	0.611330	−	12.3873i	0.0352952	−	0.715181i
$301$	−20.8940			−1.20431
$302$	0.502869	+	1.54767i	0.0289368	+	0.0890584i
$303$	−13.4447	+	9.76818i	−0.772381	+	0.561167i
$304$	0.809017	−	0.587785i	0.0464003	−	0.0337118i
$305$	−7.41443	−	15.4839i	−0.424549	−	0.886605i
$306$	−9.88855	−	7.18445i	−0.565291	−	0.410708i
$307$	−31.6097			−1.80406			−0.902031	−	0.431670i	$-0.857924\pi$
$307$	−31.6097			−1.80406			−0.902031	+	0.431670i	$0.857924\pi$
$308$	−2.81808	−	2.04745i	−0.160575	−	0.116664i
$309$	−8.95885	+	27.5725i	−0.509651	+	1.56855i
$310$	−2.14526	+	11.6741i	−0.121843	+	0.663044i
$311$	−4.42257	−	13.6113i	−0.250781	−	0.771825i	−0.994632	−	0.103479i	$-0.967003\pi$
$311$	−4.42257	−	13.6113i	−0.250781	−	0.771825i	0.743851	−	0.668346i	$-0.232997\pi$
$312$	−0.637165	+	1.96099i	−0.0360724	+	0.111019i
$313$	−5.73821	+	17.6604i	−0.324343	+	0.998225i	0.647394	+	0.762156i	$0.275859\pi$
$313$	−5.73821	+	17.6604i	−0.324343	+	0.998225i	−0.971736	+	0.236069i	$0.924141\pi$
$314$	−3.90809	−	12.0279i	−0.220547	−	0.678772i
$315$	−3.54364	+	19.2838i	−0.199661	+	1.08652i
$316$	4.05334	−	12.4749i	0.228018	−	0.701768i
$317$	3.33869	+	2.42570i	0.187519	+	0.136241i	0.677584	−	0.735445i	$-0.263027\pi$
$317$	3.33869	+	2.42570i	0.187519	+	0.136241i	−0.490065	+	0.871686i	$0.663027\pi$
$318$	0.713848			0.0400306
$319$	−2.91045	−	2.11457i	−0.162954	−	0.118393i
$320$	−0.965727	−	2.01677i	−0.0539858	−	0.112741i
$321$	37.5779	−	27.3019i	2.09739	−	1.52385i
$322$	−10.5754	+	7.68346i	−0.589343	+	0.428183i
$323$	1.19803	+	3.68715i	0.0666600	+	0.205158i
$324$	−8.51839			−0.473244
$325$	0.204869	−	4.15122i	0.0113641	−	0.230268i
$326$	4.55400			0.252223
$327$	−3.29678	−	10.1464i	−0.182312	−	0.561100i
$328$	−6.60220	+	4.79678i	−0.364546	+	0.264858i
$329$	−9.52960	+	6.92366i	−0.525384	+	0.381714i
$330$	1.25555	−	6.83244i	0.0691157	−	0.376114i
$331$	−9.54552	−	6.93523i	−0.524669	−	0.381195i	0.293691	−	0.955901i	$-0.405116\pi$
$331$	−9.54552	−	6.93523i	−0.524669	−	0.381195i	−0.818360	+	0.574706i	$0.805116\pi$
$332$	14.4148			0.791117
$333$	10.3160	+	7.49504i	0.565316	+	0.410726i
$334$	1.88490	−	5.80112i	0.103137	−	0.317423i
$335$	−21.1650	−	11.4499i	−1.15637	−	0.625577i
$336$	2.13179	+	6.56098i	0.116299	+	0.357931i
$337$	7.21184	−	22.1957i	0.392854	−	1.20908i	−0.537767	−	0.843094i	$-0.680732\pi$
$337$	7.21184	−	22.1957i	0.392854	−	1.20908i	0.930620	−	0.365986i	$-0.119268\pi$
$338$	3.80369	−	11.7066i	0.206894	−	0.636753i
$339$	7.82279	+	24.0761i	0.424875	+	1.30763i
$340$	8.59310	−	1.14463i	0.466026	−	0.0620763i
$341$	−2.05447	+	6.32301i	−0.111256	+	0.342410i
$342$	−2.55064	−	1.85315i	−0.137923	−	0.100207i
$343$	−17.4243			−0.940824
$344$	−6.07788	−	4.41584i	−0.327697	−	0.238086i
$345$	−22.9292	−	12.4043i	−1.23446	−	0.667825i
$346$	12.2989	−	8.93567i	0.661193	−	0.480385i
$347$	7.23990	−	5.26010i	0.388658	−	0.282377i	−0.376247	−	0.926519i	$-0.622786\pi$
$347$	7.23990	−	5.26010i	0.388658	−	0.282377i	0.764906	+	0.644142i	$0.222786\pi$
$348$	2.20167	+	6.77604i	0.118022	+	0.363234i
$349$	16.7729			0.897831			0.448915	−	0.893574i	$-0.351811\pi$
$349$	16.7729			0.897831			0.448915	+	0.893574i	$0.351811\pi$
$350$	−7.60918	−	11.6393i	−0.406728	−	0.622146i
$351$	0.314975			0.0168121
$352$	−0.387035	−	1.19117i	−0.0206290	−	0.0634896i
$353$	−2.55543	+	1.85663i	−0.136012	+	0.0988182i	−0.653711	−	0.756745i	$-0.726789\pi$
$353$	−2.55543	+	1.85663i	−0.136012	+	0.0988182i	0.517699	+	0.855563i	$0.326789\pi$
$354$	−20.9346	+	15.2099i	−1.11266	+	0.808394i
$355$	14.7730	−	14.0619i	0.784071	−	0.746330i
$356$	3.81870	+	2.77445i	0.202391	+	0.147045i
$357$	−26.7452			−1.41551
$358$	17.6883	+	12.8513i	0.934857	+	0.679213i
$359$	4.79940	−	14.7710i	0.253303	−	0.779585i	−0.740857	−	0.671663i	$-0.765580\pi$
$359$	4.79940	−	14.7710i	0.253303	−	0.779585i	0.994159	−	0.107922i	$-0.0344197\pi$
$360$	−5.10633	+	4.86054i	−0.269127	+	0.256173i
$361$	0.309017	+	0.951057i	0.0162641	+	0.0500556i
$362$	2.09860	−	6.45881i	0.110300	−	0.339468i
$363$	−7.22919	+	22.2492i	−0.379434	+	1.16778i
$364$	0.714405	+	2.19871i	0.0374450	+	0.115244i
$365$	4.16796	+	8.70414i	0.218161	+	0.455596i
$366$	−5.88492	+	18.1119i	−0.307610	+	0.946725i
$367$	17.7763	+	12.9152i	0.927916	+	0.674170i	0.945482	−	0.325675i	$-0.105592\pi$
$367$	17.7763	+	12.9152i	0.927916	+	0.674170i	−0.0175658	+	0.999846i	$0.505592\pi$
$368$	−4.70014			−0.245012
$369$	20.8152	+	15.1231i	1.08359	+	0.787277i
$370$	−8.96459	+	1.19412i	−0.466047	+	0.0620791i
$371$	0.647524	−	0.470454i	0.0336178	−	0.0244247i
$372$	10.6523	−	7.73933i	0.552295	−	0.401266i
$373$	10.6932	+	32.9103i	0.553672	+	1.70403i	0.699424	+	0.714707i	$0.253440\pi$
$373$	10.6932	+	32.9103i	0.553672	+	1.70403i	−0.145752	+	0.989321i	$0.546560\pi$
$374$	4.85570			0.251082
$375$	14.3819	−	23.7119i	0.742680	−	1.22448i
$376$	−4.23535			−0.218422
$377$	0.737822	+	2.27078i	0.0379998	+	0.116951i
$378$	0.852565	−	0.619425i	0.0438512	−	0.0318598i
$379$	−13.8108	+	10.0342i	−0.709415	+	0.515420i	−0.882985	−	0.469402i	$-0.844470\pi$
$379$	−13.8108	+	10.0342i	−0.709415	+	0.515420i	0.173570	+	0.984822i	$0.444470\pi$
$380$	2.21649	−	0.295244i	0.113704	−	0.0151457i
$381$	16.2998	+	11.8425i	0.835062	+	0.606708i
$382$	16.5935			0.848999
$383$	−27.3956	−	19.9041i	−1.39985	−	1.01705i	−0.994702	−	0.102798i	$-0.967221\pi$
$383$	−27.3956	−	19.9041i	−1.39985	−	1.01705i	−0.405146	−	0.914252i	$-0.632779\pi$
$384$	−0.766509	+	2.35907i	−0.0391158	+	0.120386i
$385$	−3.36395	−	7.02509i	−0.171443	−	0.358032i
$386$	5.67504	+	17.4660i	0.288852	+	0.888995i
$387$	−7.31927	+	22.5264i	−0.372059	+	1.14508i
$388$	0.332485	−	1.02329i	0.0168794	−	0.0519494i
$389$	4.46038	+	13.7276i	0.226150	+	0.696019i	0.998173	+	0.0604239i	$0.0192452\pi$
$389$	4.46038	+	13.7276i	0.226150	+	0.696019i	−0.772022	+	0.635595i	$0.780755\pi$
$390$	−3.33955	+	3.17880i	−0.169104	+	0.160965i
$391$	5.63089	−	17.3301i	0.284767	−	0.876421i
$392$	0.594549	+	0.431965i	0.0300292	+	0.0218175i
$393$	−19.3108			−0.974101
$394$	4.70158	+	3.41590i	0.236862	+	0.172091i
$395$	21.2446	−	20.2220i	1.06893	−	1.01748i
$396$	−3.19460	+	2.32101i	−0.160535	+	0.116635i
$397$	23.7276	−	17.2391i	1.19085	−	0.865206i	0.197499	−	0.980303i	$-0.436718\pi$
$397$	23.7276	−	17.2391i	1.19085	−	0.865206i	0.993354	+	0.115097i	$0.0367180\pi$
$398$	−1.41085	−	4.34216i	−0.0707197	−	0.217653i
$399$	−6.89862			−0.345363
$400$	0.246457	−	4.99392i	0.0123228	−	0.249696i
$401$	−18.1828			−0.908004			−0.454002	−	0.891001i	$-0.650004\pi$
$401$	−18.1828			−0.908004			−0.454002	+	0.891001i	$0.650004\pi$
$402$	8.24886	+	25.3874i	0.411416	+	1.26621i
$403$	3.56978	−	2.59360i	0.177824	−	0.129196i
$404$	−5.42023	+	3.93803i	−0.269667	+	0.195924i
$405$	−16.7533	−	9.06325i	−0.832477	−	0.450356i
$406$	6.46279	+	4.69549i	0.320743	+	0.233033i
$407$	−5.06562			−0.251093
$408$	−7.77995	−	5.65246i	−0.385165	−	0.279839i
$409$	−3.63463	+	11.1862i	−0.179721	+	0.553124i	−0.999818	−	0.0191009i	$-0.993920\pi$
$409$	−3.63463	+	11.1862i	−0.179721	+	0.553124i	0.820097	+	0.572225i	$0.193920\pi$
$410$	−18.0883	+	2.40942i	−0.893316	+	0.118993i
$411$	1.61297	+	4.96421i	0.0795619	+	0.244866i
$412$	−3.61175	+	11.1158i	−0.177938	+	0.547637i
$413$	−8.96564	+	27.5934i	−0.441170	+	1.35778i
$414$	4.57914	+	14.0932i	0.225053	+	0.692641i
$415$	28.3499	+	15.3368i	1.39164	+	0.752856i
$416$	−0.256872	+	0.790571i	−0.0125942	+	0.0387609i
$417$	−0.0871428	−	0.0633130i	−0.00426740	−	0.00310045i
$418$	1.25247			0.0612604
$419$	6.85191	+	4.97820i	0.334737	+	0.243201i	0.742438	−	0.669915i	$-0.233669\pi$
$419$	6.85191	+	4.97820i	0.334737	+	0.243201i	−0.407701	+	0.913116i	$0.633669\pi$
$420$	−2.78800	+	15.1718i	−0.136041	+	0.740306i
$421$	2.69760	−	1.95992i	0.131473	−	0.0955207i	−0.520105	−	0.854102i	$-0.674107\pi$
$421$	2.69760	−	1.95992i	0.131473	−	0.0955207i	0.651578	+	0.758582i	$0.274107\pi$
$422$	−7.72492	+	5.61248i	−0.376043	+	0.273211i
$423$	4.12632	+	12.6995i	0.200629	+	0.617471i
$424$	0.287787			0.0139762
$425$	18.1181	+	6.89157i	0.878855	+	0.334290i
$426$	−22.6249			−1.09618
$427$	6.59831	+	20.3075i	0.319315	+	0.982750i
$428$	15.1495	−	11.0067i	0.732277	−	0.532031i
$429$	−2.08927	+	1.51794i	−0.100871	+	0.0732870i
$430$	−7.25519	−	15.1514i	−0.349877	−	0.730663i
$431$	1.06612	+	0.774584i	0.0513534	+	0.0373104i	0.613166	−	0.789954i	$-0.289896\pi$
$431$	1.06612	+	0.774584i	0.0513534	+	0.0373104i	−0.561812	+	0.827265i	$0.689896\pi$
$432$	0.378915			0.0182306
$433$	30.0758	+	21.8514i	1.44535	+	1.05011i	0.986890	+	0.161395i	$0.0515992\pi$
$433$	30.0758	+	21.8514i	1.44535	+	1.05011i	0.458461	+	0.888714i	$0.348401\pi$
$434$	4.56204	−	14.0405i	0.218985	−	0.673967i
$435$	−2.87939	+	15.6691i	−0.138056	+	0.751274i
$436$	−1.32909	−	4.09052i	−0.0636520	−	0.195901i
$437$	1.45242	−	4.47010i	0.0694789	−	0.213834i
$438$	3.30816	−	10.1815i	0.158070	−	0.486489i
$439$	10.3006	+	31.7020i	0.491621	+	1.51305i	0.822157	+	0.569260i	$0.192770\pi$
$439$	10.3006	+	31.7020i	0.491621	+	1.51305i	−0.330536	+	0.943793i	$0.607230\pi$
$440$	0.506173	−	2.75449i	0.0241308	−	0.131315i
$441$	0.715983	−	2.20357i	0.0340945	−	0.104932i
$442$	−2.60721	−	1.89425i	−0.124012	−	0.0901002i
$443$	−21.9171			−1.04131			−0.520656	−	0.853767i	$-0.674313\pi$
$443$	−21.9171			−1.04131			−0.520656	+	0.853767i	$0.674313\pi$
$444$	8.11628	+	5.89683i	0.385182	+	0.279851i
$445$	4.55840	+	9.51951i	0.216089	+	0.451268i
$446$	15.8944	−	11.5479i	0.752620	−	0.546811i
$447$	23.9716	−	17.4164i	1.13382	−	0.823768i
$448$	0.859429	+	2.64505i	0.0406042	+	0.124967i
$449$	30.6631			1.44708			0.723540	−	0.690282i	$-0.242514\pi$
$449$	30.6631			1.44708			0.723540	+	0.690282i	$0.242514\pi$
$450$	−15.2141	+	4.12637i	−0.717202	+	0.194519i
$451$	−10.2211			−0.481294
$452$	3.15374	+	9.70623i	0.148340	+	0.456543i
$453$	3.26561	−	2.37261i	0.153432	−	0.111475i
$454$	13.7129	−	9.96299i	0.643577	−	0.467586i
$455$	−0.934314	+	5.08435i	−0.0438013	+	0.238358i
$456$	−2.00675	−	1.45799i	−0.0939745	−	0.0682765i
$457$	8.65960			0.405079			0.202539	−	0.979274i	$-0.435081\pi$
$457$	8.65960			0.405079			0.202539	+	0.979274i	$0.435081\pi$
$458$	−8.05282	−	5.85072i	−0.376284	−	0.273386i
$459$	−0.453951	+	1.39712i	−0.0211886	+	0.0652118i
$460$	−9.24386	−	5.00078i	−0.430997	−	0.233162i
$461$	−1.70030	−	5.23297i	−0.0791907	−	0.243724i	0.903622	−	0.428332i	$-0.140899\pi$
$461$	−1.70030	−	5.23297i	−0.0791907	−	0.243724i	−0.982812	+	0.184608i	$0.940899\pi$
$462$	−2.67001	+	8.21744i	−0.124220	+	0.382310i
$463$	−2.83209	+	8.71627i	−0.131618	+	0.405080i	−0.995049	−	0.0993885i	$-0.968311\pi$
$463$	−2.83209	+	8.71627i	−0.131618	+	0.405080i	0.863430	+	0.504468i	$0.168311\pi$
$464$	0.887599	+	2.73175i	0.0412058	+	0.126818i
$465$	29.1844	−	3.88746i	1.35339	−	0.180277i
$466$	5.29545	−	16.2977i	0.245307	−	0.754977i
$467$	32.2720	+	23.4470i	1.49337	+	1.08500i	0.972931	+	0.231097i	$0.0742313\pi$
$467$	32.2720	+	23.4470i	1.49337	+	1.08500i	0.520438	+	0.853899i	$0.325769\pi$
$468$	2.62075			0.121144
$469$	24.2137	+	17.5923i	1.11809	+	0.812337i
$470$	−8.32975	−	4.50626i	−0.384223	−	0.207858i
$471$	−25.3790	+	18.4390i	−1.16940	+	0.849622i
$472$	−8.43974	+	6.13183i	−0.388470	+	0.282240i
$473$	−2.90767	−	8.94888i	−0.133695	−	0.411470i
$474$	−32.5361			−1.49443
$475$	4.67334	+	1.77760i	0.214428	+	0.0815619i
$476$	−10.7823			−0.494206
$477$	−0.280378	−	0.862915i	−0.0128376	−	0.0395102i
$478$	0.551621	−	0.400776i	0.0252306	−	0.0183311i
$479$	−21.6321	+	15.7167i	−0.988397	+	0.718112i	−0.959569	−	0.281472i	$-0.909177\pi$
$479$	−21.6321	+	15.7167i	−0.988397	+	0.718112i	−0.0288275	+	0.999584i	$0.509177\pi$
$480$	−4.01747	+	3.82410i	−0.183372	+	0.174545i
$481$	2.71992	+	1.97614i	0.124018	+	0.0901042i
$482$	14.7232			0.670625
$483$	26.2320	+	19.0586i	1.19360	+	0.867198i
$484$	−2.91444	+	8.96971i	−0.132474	+	0.407714i
$485$	1.74264	−	1.65876i	0.0791293	−	0.0753205i
$486$	6.88070	+	21.1766i	0.312115	+	0.960590i
$487$	7.95351	−	24.4784i	0.360408	−	1.10922i	−0.592399	−	0.805645i	$-0.701819\pi$
$487$	7.95351	−	24.4784i	0.360408	−	1.10922i	0.952807	−	0.303577i	$-0.0981810\pi$
$488$	−2.37250	+	7.30179i	−0.107398	+	0.330537i
$489$	−3.49068	−	10.7432i	−0.157854	−	0.485825i
$490$	0.709716	+	1.48213i	0.0320617	+	0.0669559i
$491$	9.97113	−	30.6880i	0.449991	−	1.38493i	−0.426926	−	0.904286i	$-0.640404\pi$
$491$	9.97113	−	30.6880i	0.449991	−	1.38493i	0.876917	−	0.480642i	$-0.159596\pi$
$492$	16.3766	+	11.8983i	0.738314	+	0.536417i
$493$	−11.1357			−0.501528
$494$	−0.672500	−	0.488600i	−0.0302572	−	0.0219831i
$495$	−8.75235	+	1.16584i	−0.393389	+	0.0524007i
$496$	4.29445	−	3.12010i	0.192826	−	0.140097i
$497$	−20.5228	+	14.9107i	−0.920574	+	0.668836i
$498$	−11.0491	−	34.0056i	−0.495122	−	1.52383i
$499$	6.82428			0.305497			0.152748	−	0.988265i	$-0.451188\pi$
$499$	6.82428			0.305497			0.152748	+	0.988265i	$0.451188\pi$
$500$	5.79806	−	9.55942i	0.259297	−	0.427510i
$501$	−15.1301			−0.675961
$502$	−0.283448	−	0.872364i	−0.0126509	−	0.0389355i
$503$	22.4426	−	16.3055i	1.00067	−	0.727028i	0.0384365	−	0.999261i	$-0.487762\pi$
$503$	22.4426	−	16.3055i	1.00067	−	0.727028i	0.962231	+	0.272233i	$0.0877623\pi$
$504$	7.09375	−	5.15391i	0.315981	−	0.229573i
$505$	−14.8500	+	1.97807i	−0.660816	+	0.0880229i
$506$	−4.76252	−	3.46017i	−0.211720	−	0.153823i
$507$	−30.5322			−1.35598
$508$	6.57122	+	4.77427i	0.291551	+	0.211824i
$509$	−1.78523	+	5.49437i	−0.0791289	+	0.243534i	−0.982794	−	0.184707i	$-0.940866\pi$
$509$	−1.78523	+	5.49437i	−0.0791289	+	0.243534i	0.903665	+	0.428241i	$0.140866\pi$
$510$	−9.28696	−	19.3944i	−0.411233	−	0.858797i
$511$	−3.70919	−	11.4157i	−0.164085	−	0.505001i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	−0.117091	+	0.360370i	−0.00516971	+	0.0159107i
$514$	−0.848600	−	2.61172i	−0.0374301	−	0.115198i
$515$	−18.9301	+	18.0189i	−0.834160	+	0.794009i
$516$	−5.75853	+	17.7229i	−0.253505	+	0.780209i
$517$	−4.29156	−	3.11800i	−0.188743	−	0.137129i
$518$	11.2484			0.494228
$519$	−30.5071	−	22.1647i	−1.33911	−	0.972923i
$520$	−1.34633	+	1.28153i	−0.0590406	+	0.0561987i
$521$	18.8052	−	13.6628i	0.823872	−	0.598578i	−0.0939468	−	0.995577i	$-0.529948\pi$
$521$	18.8052	−	13.6628i	0.823872	−	0.598578i	0.917819	+	0.396999i	$0.129948\pi$
$522$	7.32627	−	5.32285i	0.320662	−	0.232975i
$523$	1.24479	+	3.83107i	0.0544309	+	0.167521i	0.974576	−	0.224056i	$-0.0719297\pi$
$523$	1.24479	+	3.83107i	0.0544309	+	0.167521i	−0.920145	+	0.391577i	$0.871930\pi$
$524$	−7.78512			−0.340094
$525$	−21.6254	+	26.8722i	−0.943810	+	1.17280i
$526$	15.4442			0.673398
$527$	6.35940	+	19.5722i	0.277020	+	0.852579i
$528$	−2.51339	+	1.82609i	−0.109381	+	0.0794702i
$529$	0.735124	−	0.534099i	0.0319619	−	0.0232217i
$530$	0.565996	+	0.306194i	0.0245853	+	0.0133002i
$531$	26.6085	+	19.3322i	1.15471	+	0.838945i
$532$	−2.78117			−0.120579
$533$	5.48811	+	3.98735i	0.237717	+	0.172711i
$534$	3.61805	−	11.1352i	0.156568	−	0.481868i
$535$	41.5055	−	5.52868i	1.79444	−	0.239026i
$536$	3.32552	+	10.2349i	0.143640	+	0.442080i
$537$	16.7589	−	51.5787i	0.723201	−	2.22578i
$538$	−5.84594	+	17.9919i	−0.252036	+	0.775688i
$539$	0.284433	+	0.875395i	0.0122514	+	0.0377059i
$540$	0.745220	+	0.403152i	0.0320692	+	0.0173489i
$541$	4.27648	−	13.1616i	0.183860	−	0.565863i	−0.816067	−	0.577958i	$-0.803850\pi$
$541$	4.27648	−	13.1616i	0.183860	−	0.565863i	0.999927	+	0.0120945i	$0.00384989\pi$
$542$	−5.95914	−	4.32957i	−0.255967	−	0.185971i
$543$	−16.8454			−0.722905
$544$	−3.13647	−	2.27878i	−0.134475	−	0.0977020i
$545$	1.73822	−	9.45902i	0.0744570	−	0.405180i
$546$	4.63932	−	3.37066i	0.198545	−	0.144251i
$547$	−35.0265	+	25.4483i	−1.49763	+	1.08809i	−0.526310	+	0.850292i	$0.676425\pi$
$547$	−35.0265	+	25.4483i	−1.49763	+	1.08809i	−0.971315	+	0.237796i	$0.923575\pi$
$548$	0.650266	+	2.00131i	0.0277780	+	0.0854919i
$549$	24.2055			1.03307
$550$	3.92617	−	4.87876i	0.167413	−	0.208031i
$551$	−2.87233			−0.122365
$552$	3.60270	+	11.0880i	0.153341	+	0.471936i
$553$	−29.5132	+	21.4426i	−1.25503	+	0.911830i
$554$	−18.0963	+	13.1478i	−0.768840	+	0.558595i
$555$	9.68845	+	20.2328i	0.411252	+	0.858836i
$556$	−0.0351315	−	0.0255245i	−0.00148991	−	0.00108248i
$557$	−6.15821			−0.260932			−0.130466	−	0.991453i	$-0.541647\pi$
$557$	−6.15821			−0.260932			−0.130466	+	0.991453i	$0.541647\pi$
$558$	−13.5394	−	9.83692i	−0.573167	−	0.416430i
$559$	−1.92980	+	5.93930i	−0.0816217	+	0.251206i
$560$	−1.12398	+	6.11647i	−0.0474968	+	0.258468i
$561$	−3.72194	−	11.4549i	−0.157140	−	0.483628i
$562$	4.74063	−	14.5901i	0.199971	−	0.615448i
$563$	5.66997	−	17.4504i	0.238961	−	0.735445i	−0.757611	−	0.652707i	$-0.773633\pi$
$563$	5.66997	−	17.4504i	0.238961	−	0.735445i	0.996571	−	0.0827385i	$-0.0263666\pi$
$564$	3.24644	+	9.99151i	0.136700	+	0.420718i
$565$	−4.12454	+	22.4449i	−0.173521	+	0.944264i
$566$	−4.31886	+	13.2921i	−0.181535	+	0.558708i
$567$	19.1665	+	13.9253i	0.804917	+	0.584806i
$568$	−9.12119			−0.382717
$569$	−18.2607	−	13.2672i	−0.765530	−	0.556190i	0.135072	−	0.990836i	$-0.456874\pi$
$569$	−18.2607	−	13.2672i	−0.765530	−	0.556190i	−0.900601	+	0.434646i	$0.856874\pi$
$570$	−2.39546	−	5.00255i	−0.100335	−	0.209534i
$571$	14.2329	−	10.3408i	0.595630	−	0.432750i	−0.248695	−	0.968582i	$-0.580002\pi$
$571$	14.2329	−	10.3408i	0.595630	−	0.432750i	0.844325	+	0.535831i	$0.180002\pi$
$572$	−0.842286	+	0.611957i	−0.0352178	+	0.0255872i
$573$	−12.7191	−	39.1453i	−0.531347	−	1.63532i
$574$	22.6965			0.947333
$575$	−12.8594	−	19.6702i	−0.536275	−	0.820306i
$576$	3.15276			0.131365
$577$	0.786683	+	2.42116i	0.0327500	+	0.100794i	0.966095	−	0.258186i	$-0.0831246\pi$
$577$	0.786683	+	2.42116i	0.0327500	+	0.100794i	−0.933345	+	0.358980i	$0.883125\pi$
$578$	−1.59351	+	1.15775i	−0.0662813	+	0.0481562i
$579$	36.8536	−	26.7757i	1.53158	−	1.11276i
$580$	−1.16082	+	6.31696i	−0.0482005	+	0.262297i
$581$	−32.4336	−	23.5644i	−1.34557	−	0.977614i
$582$	−2.66886			−0.110628
$583$	0.291606	+	0.211864i	0.0120771	+	0.00877451i
$584$	1.33368	−	4.10464i	0.0551881	−	0.169851i
$585$	5.15427	+	2.78838i	0.213103	+	0.115285i
$586$	−7.97176	−	24.5346i	−0.329310	−	1.01351i
$587$	11.6277	−	35.7862i	0.479925	−	1.47706i	−0.359274	−	0.933232i	$-0.616976\pi$
$587$	11.6277	−	35.7862i	0.479925	−	1.47706i	0.839199	−	0.543824i	$-0.183024\pi$
$588$	0.563310	−	1.73369i	0.0232305	−	0.0714961i
$589$	1.64033	+	5.04843i	0.0675887	+	0.208017i
$590$	−23.1226	+	3.08002i	−0.951944	+	0.126802i
$591$	4.45455	−	13.7097i	0.183236	−	0.563941i
$592$	3.27207	+	2.37730i	0.134481	+	0.0977063i
$593$	−31.0113			−1.27348			−0.636740	−	0.771078i	$-0.719718\pi$
$593$	−31.0113			−1.27348			−0.636740	+	0.771078i	$0.719718\pi$
$594$	0.383944	+	0.278952i	0.0157534	+	0.0114455i
$595$	−21.2058	−	11.4720i	−0.869351	−	0.470305i
$596$	9.66413	−	7.02140i	0.395858	−	0.287608i
$597$	−9.16204	+	6.65661i	−0.374977	+	0.272437i
$598$	1.20733	+	3.71579i	0.0493716	+	0.151950i
$599$	30.5352			1.24764			0.623818	−	0.781570i	$-0.285581\pi$
$599$	30.5352			1.24764			0.623818	+	0.781570i	$0.285581\pi$
$600$	−11.9699	+	3.24648i	−0.488671	+	0.132537i
$601$	−20.6265			−0.841372			−0.420686	−	0.907206i	$-0.638211\pi$
$601$	−20.6265			−0.841372			−0.420686	+	0.907206i	$0.638211\pi$
$602$	6.45661	+	19.8714i	0.263152	+	0.809897i
$603$	27.4489	−	19.9428i	1.11781	−	0.812134i
$604$	1.31653	−	0.956513i	0.0535687	−	0.0389200i
$605$	−15.2753	+	14.5401i	−0.621030	+	0.591137i
$606$	13.4447	+	9.76818i	0.546156	+	0.396805i
$607$	18.6639			0.757546			0.378773	−	0.925490i	$-0.376346\pi$
$607$	18.6639			0.757546			0.378773	+	0.925490i	$0.376346\pi$
$608$	−0.809017	−	0.587785i	−0.0328100	−	0.0238378i
$609$	6.12321	−	18.8453i	0.248125	−	0.763651i
$610$	−12.4349	+	11.8363i	−0.503473	+	0.479239i
$611$	1.08794	+	3.34835i	0.0440135	+	0.135460i
$612$	−3.77709	+	11.6247i	−0.152680	+	0.469900i
$613$	−7.15694	+	22.0268i	−0.289066	+	0.889654i	0.696084	+	0.717960i	$0.254924\pi$
$613$	−7.15694	+	22.0268i	−0.289066	+	0.889654i	−0.985150	+	0.171694i	$0.945076\pi$
$614$	9.76795	+	30.0626i	0.394202	+	1.21323i
$615$	19.5488	+	40.8247i	0.788285	+	1.64621i
$616$	−1.07641	+	3.31285i	−0.0433698	+	0.133478i
$617$	−36.2302	−	26.3228i	−1.45857	−	1.05972i	−0.983732	−	0.179644i	$-0.942506\pi$
$617$	−36.2302	−	26.3228i	−1.45857	−	1.05972i	−0.474841	−	0.880072i	$-0.657494\pi$
$618$	28.9915			1.16621
$619$	−31.8178	−	23.1169i	−1.27886	−	0.929149i	−0.279345	−	0.960191i	$-0.590117\pi$
$619$	−31.8178	−	23.1169i	−1.27886	−	0.929149i	−0.999518	+	0.0310421i	$0.990117\pi$
$620$	11.7656	−	1.56722i	0.472519	−	0.0629412i
$621$	1.44082	−	1.04682i	0.0578183	−	0.0420074i
$622$	−11.5784	+	8.41223i	−0.464253	+	0.337300i
$623$	−4.05665	−	12.4851i	−0.162526	−	0.500204i
$624$	2.06191			0.0825424
$625$	21.5740	−	12.6318i	0.862961	−	0.505271i
$626$	18.5692			0.742176
$627$	−0.960031	−	2.95467i	−0.0383399	−	0.117998i
$628$	−10.2315	+	7.43364i	−0.408282	+	0.296634i
$629$	−12.6855	+	9.21653i	−0.505803	+	0.367487i
$630$	19.4350	−	2.58881i	0.774308	−	0.103141i
$631$	9.77191	+	7.09971i	0.389014	+	0.282635i	0.765051	−	0.643970i	$-0.222714\pi$
$631$	9.77191	+	7.09971i	0.389014	+	0.282635i	−0.376038	+	0.926604i	$0.622714\pi$
$632$	−13.1169			−0.521761
$633$	19.1615	+	13.9216i	0.761600	+	0.553335i
$634$	1.27527	−	3.92486i	0.0506473	−	0.155876i
$635$	7.84410	+	16.3812i	0.311284	+	0.650068i
$636$	−0.220591	−	0.678910i	−0.00874701	−	0.0269205i
$637$	0.188776	−	0.580993i	0.00747957	−	0.0230198i
$638$	−1.11169	+	3.42144i	−0.0440123	+	0.135456i
$639$	8.88638	+	27.3495i	0.351540	+	1.08193i
$640$	−1.61964	+	1.54168i	−0.0640218	+	0.0609402i
$641$	−1.30279	+	4.00957i	−0.0514570	+	0.158368i	−0.973483	−	0.228760i	$-0.926533\pi$
$641$	−1.30279	+	4.00957i	−0.0514570	+	0.158368i	0.922026	+	0.387128i	$0.126533\pi$
$642$	−37.5779	−	27.3019i	−1.48308	−	1.07752i
$643$	15.5249			0.612244			0.306122	−	0.951992i	$-0.400968\pi$
$643$	15.5249			0.612244			0.306122	+	0.951992i	$0.400968\pi$
$644$	10.5754	+	7.68346i	0.416728	+	0.302771i
$645$	−30.1820	+	28.7292i	−1.18841	+	1.13121i
$646$	3.13647	−	2.27878i	0.123403	−	0.0896575i
$647$	0.504752	−	0.366724i	0.0198438	−	0.0144174i	−0.577819	−	0.816165i	$-0.696096\pi$
$647$	0.504752	−	0.366724i	0.0198438	−	0.0144174i	0.597663	+	0.801747i	$0.296096\pi$
$648$	2.63233	+	8.10147i	0.103408	+	0.318256i
$649$	−13.0659			−0.512881
$650$	−4.01136	+	1.08796i	−0.157338	+	0.0426732i
$651$	−36.6195			−1.43523
$652$	−1.40726	−	4.33111i	−0.0551127	−	0.169619i
$653$	3.76297	−	2.73396i	0.147256	−	0.106988i	−0.511718	−	0.859154i	$-0.670991\pi$
$653$	3.76297	−	2.73396i	0.147256	−	0.106988i	0.658974	+	0.752166i	$0.270991\pi$
$654$	−8.63108	+	6.27085i	−0.337502	+	0.245210i
$655$	−15.3111	−	8.28307i	−0.598256	−	0.323646i
$656$	6.60220	+	4.79678i	0.257773	+	0.187283i
$657$	−13.6069			−0.530857
$658$	9.52960	+	6.92366i	0.371503	+	0.269912i
$659$	12.2403	−	37.6717i	0.476814	−	1.46748i	−0.366683	−	0.930346i	$-0.619506\pi$
$659$	12.2403	−	37.6717i	0.476814	−	1.46748i	0.843496	−	0.537135i	$-0.180494\pi$
$660$	−6.88603	+	0.917243i	−0.268038	+	0.0357036i
$661$	12.9106	+	39.7349i	0.502166	+	1.54551i	0.805484	+	0.592618i	$0.201906\pi$
$661$	12.9106	+	39.7349i	0.502166	+	1.54551i	−0.303318	+	0.952889i	$0.598094\pi$
$662$	−3.64607	+	11.2214i	−0.141708	+	0.436133i
$663$	−2.47022	+	7.60256i	−0.0959354	+	0.295259i
$664$	−4.45443	−	13.7093i	−0.172865	−	0.532025i
$665$	−5.46978	−	2.95906i	−0.212109	−	0.114747i
$666$	3.94038	−	12.1272i	0.152687	−	0.469921i
$667$	10.9220	+	7.93532i	0.422903	+	0.307257i
$668$	−6.09966			−0.236003
$669$	−39.4256	−	28.6444i	−1.52428	−	1.10746i
$670$	−4.34918	+	23.6674i	−0.168024	+	0.914350i
$671$	−7.77944	+	5.65210i	−0.300322	+	0.218197i
$672$	5.58110	−	4.05491i	0.215296	−	0.156421i
$673$	−0.0990184	−	0.304747i	−0.00381688	−	0.0117471i	0.949130	−	0.314885i	$-0.101966\pi$
$673$	−0.0990184	−	0.304747i	−0.00381688	−	0.0117471i	−0.952947	+	0.303138i	$0.901966\pi$
$674$	−23.3380			−0.898946
$675$	1.03670	+	1.58577i	0.0399026	+	0.0610364i
$676$	−12.3090			−0.473424
$677$	−5.43370	−	16.7232i	−0.208834	−	0.642725i	−0.999534	−	0.0305213i	$-0.990283\pi$
$677$	−5.43370	−	16.7232i	−0.208834	−	0.642725i	0.790700	−	0.612204i	$-0.209717\pi$
$678$	20.4803	−	14.8798i	0.786542	−	0.571456i
$679$	−2.42089	+	1.75888i	−0.0929053	+	0.0674996i
$680$	−3.74402	−	7.81881i	−0.143577	−	0.299838i
$681$	−34.0145	−	24.7129i	−1.30344	−	0.947002i
$682$	6.64840			0.254581
$683$	29.0224	+	21.0860i	1.11051	+	0.806832i	0.982744	−	0.184972i	$-0.0592195\pi$
$683$	29.0224	+	21.0860i	1.11051	+	0.806832i	0.127766	+	0.991804i	$0.459219\pi$
$684$	−0.974256	+	2.99845i	−0.0372516	+	0.114649i
$685$	−0.850433	+	4.62788i	−0.0324934	+	0.176822i
$686$	5.38440	+	16.5715i	0.205577	+	0.632702i
$687$	−7.62971	+	23.4818i	−0.291091	+	0.895887i
$688$	−2.32154	+	7.14498i	−0.0885080	+	0.272400i
$689$	−0.0739244	−	0.227516i	−0.00281629	−	0.00866766i
$690$	−4.71169	+	25.6401i	−0.179371	+	0.976101i
$691$	3.32356	−	10.2289i	0.126434	−	0.389124i	−0.867726	−	0.497044i	$-0.834419\pi$
$691$	3.32356	−	10.2289i	0.126434	−	0.389124i	0.994160	+	0.107920i	$0.0344189\pi$
$692$	−12.2989	−	8.93567i	−0.467534	−	0.339683i
$693$	10.9821			0.417176
$694$	−7.23990	−	5.26010i	−0.274823	−	0.199671i
$695$	−0.0419366	−	0.0875782i	−0.00159075	−	0.00332203i
$696$	5.76404	−	4.18782i	0.218486	−	0.158739i
$697$	−25.5960	+	18.5966i	−0.969519	+	0.704397i
$698$	−5.18310	−	15.9519i	−0.196183	−	0.603790i
$699$	−42.5065			−1.60774
$700$	−8.71825	+	10.8335i	−0.329519	+	0.409468i
$701$	25.0810			0.947294			0.473647	−	0.880715i	$-0.342937\pi$
$701$	25.0810			0.947294			0.473647	+	0.880715i	$0.342937\pi$
$702$	−0.0973328	−	0.299559i	−0.00367359	−	0.0113061i
$703$	−3.27207	+	2.37730i	−0.123408	+	0.0896614i
$704$	−1.01327	+	0.736184i	−0.0381891	+	0.0277460i
$705$	−4.24576	+	23.1046i	−0.159905	+	0.870168i
$706$	2.55543	+	1.85663i	0.0961747	+	0.0698750i
$707$	18.6332			0.700774
$708$	20.9346	+	15.2099i	0.786769	+	0.571621i
$709$	−8.99935	+	27.6971i	−0.337978	+	1.04019i	0.627259	+	0.778811i	$0.284177\pi$
$709$	−8.99935	+	27.6971i	−0.337978	+	1.04019i	−0.965237	+	0.261377i	$0.915823\pi$
$710$	−17.9388	−	9.70461i	−0.673232	−	0.364208i
$711$	12.7792	+	39.3303i	0.479257	+	1.47500i
$712$	1.45861	−	4.48915i	0.0546638	−	0.168238i
$713$	7.70980	−	23.7283i	0.288734	−	0.888633i
$714$	8.26473	+	25.4362i	0.309300	+	0.951927i
$715$	−2.30764	+	0.307386i	−0.0863008	+	0.0114956i
$716$	6.75634	−	20.7939i	0.252496	−	0.777103i
$717$	−1.36828	−	0.994115i	−0.0510994	−	0.0371259i
$718$	−15.5312			−0.579618
$719$	0.458803	+	0.333340i	0.0171105	+	0.0124315i	0.596308	−	0.802756i	$-0.296634\pi$
$719$	0.458803	+	0.333340i	0.0171105	+	0.0124315i	−0.579197	+	0.815187i	$0.696634\pi$
$720$	6.20059	+	3.35442i	0.231082	+	0.125012i
$721$	26.2978	−	19.1065i	0.979383	−	0.711563i
$722$	0.809017	−	0.587785i	0.0301085	−	0.0218751i
$723$	−11.2855	−	34.7332i	−0.419712	−	1.29174i
$724$	−6.79120			−0.252393
$725$	−9.00402	+	11.1886i	−0.334401	+	0.415534i
$726$	23.3941			0.868238
$727$	−15.7818	−	48.5715i	−0.585316	−	1.80142i	−0.597996	−	0.801499i	$-0.704036\pi$
$727$	−15.7818	−	48.5715i	−0.585316	−	1.80142i	0.0126798	−	0.999920i	$-0.495964\pi$
$728$	1.87034	−	1.35888i	0.0693192	−	0.0503634i
$729$	24.0085	−	17.4432i	0.889202	−	0.646043i
$730$	6.99016	−	6.65370i	0.258718	−	0.246264i
$731$	−23.5633	−	17.1197i	−0.871520	−	0.633197i
$732$	19.0440			0.703886
$733$	25.1587	+	18.2789i	0.929258	+	0.675145i	0.945811	−	0.324718i	$-0.105269\pi$
$733$	25.1587	+	18.2789i	0.929258	+	0.675145i	−0.0165534	+	0.999863i	$0.505269\pi$
$734$	6.78995	−	20.8973i	0.250621	−	0.771334i
$735$	2.95245	−	2.81034i	0.108903	−	0.103661i
$736$	1.45242	+	4.47010i	0.0535371	+	0.164770i
$737$	−4.16511	+	12.8189i	−0.153424	+	0.472190i
$738$	7.95068	−	24.4697i	0.292669	−	0.900741i
$739$	−13.3336	−	41.0366i	−0.490484	−	1.50955i	−0.823878	−	0.566767i	$-0.808194\pi$
$739$	−13.3336	−	41.0366i	−0.490484	−	1.50955i	0.333394	−	0.942787i	$-0.391806\pi$
$740$	3.90588	+	8.15683i	0.143583	+	0.299851i
$741$	−0.637165	+	1.96099i	−0.0234068	+	0.0720388i
$742$	−0.647524	−	0.470454i	−0.0237714	−	0.0172709i
$743$	9.52476			0.349430			0.174715	−	0.984619i	$-0.444100\pi$
$743$	9.52476			0.349430			0.174715	+	0.984619i	$0.444100\pi$
$744$	−10.6523	−	7.73933i	−0.390531	−	0.283738i
$745$	26.4771	−	3.52685i	0.970047	−	0.129214i
$746$	27.9951	−	20.3397i	1.02497	−	0.744688i
$747$	−36.7670	+	26.7128i	−1.34523	+	0.977369i
$748$	−1.50049	−	4.61804i	−0.0548635	−	0.168852i
$749$	−52.0796			−1.90295
$750$	−26.9956	−	6.35066i	−0.985741	−	0.231893i
$751$	−28.2607			−1.03125			−0.515625	−	0.856815i	$-0.672440\pi$
$751$	−28.2607			−1.03125			−0.515625	+	0.856815i	$0.672440\pi$
$752$	1.30880	+	4.02806i	0.0477269	+	0.146888i
$753$	−1.84070	+	1.33735i	−0.0670790	+	0.0487357i
$754$	1.93164	−	1.40342i	0.0703463	−	0.0511096i
$755$	3.60693	−	0.480456i	0.131270	−	0.0174856i
$756$	−0.852565	−	0.619425i	−0.0310075	−	0.0225283i
$757$	26.1599			0.950797			0.475398	−	0.879771i	$-0.342304\pi$
$757$	26.1599			0.950797			0.475398	+	0.879771i	$0.342304\pi$
$758$	13.8108	+	10.0342i	0.501632	+	0.364457i
$759$	−4.51228	+	13.8874i	−0.163785	+	0.504080i
$760$	−0.965727	−	2.01677i	−0.0350306	−	0.0731560i
$761$	13.9688	+	42.9916i	0.506369	+	1.55844i	0.798456	+	0.602053i	$0.205650\pi$
$761$	13.9688	+	42.9916i	0.506369	+	1.55844i	−0.292087	+	0.956392i	$0.594350\pi$
$762$	6.22595	−	19.1615i	0.225542	−	0.694148i
$763$	−3.69643	+	11.3764i	−0.133820	+	0.411855i
$764$	−5.12768	−	15.7814i	−0.185513	−	0.570950i
$765$	−19.7967	+	18.8438i	−0.715751	+	0.681299i
$766$	−10.4642	+	32.2054i	−0.378086	+	1.16363i
$767$	7.01558	+	5.09711i	0.253318	+	0.184046i
$768$	2.48048			0.0895065
$769$	−20.0468	−	14.5648i	−0.722906	−	0.525222i	0.164406	−	0.986393i	$-0.447429\pi$
$769$	−20.0468	−	14.5648i	−0.722906	−	0.525222i	−0.887311	+	0.461171i	$0.847429\pi$
$770$	−5.64174	+	5.37018i	−0.203314	+	0.193528i
$771$	−5.51078	+	4.00382i	−0.198466	+	0.144194i
$772$	14.8575	−	10.7946i	0.534732	−	0.388505i
$773$	−11.4129	−	35.1254i	−0.410495	−	1.26337i	−0.916219	−	0.400678i	$-0.868775\pi$
$773$	−11.4129	−	35.1254i	−0.410495	−	1.26337i	0.505724	−	0.862695i	$-0.331225\pi$
$774$	23.6857			0.851363
$775$	24.8072	+	9.43591i	0.891100	+	0.338948i
$776$	−1.07595			−0.0386242
$777$	−8.62203	−	26.5359i	−0.309314	−	0.951969i
$778$	11.6774	−	8.48415i	0.418656	−	0.304171i
$779$	−6.60220	+	4.79678i	−0.236548	+	0.171862i
$780$	4.05519	+	2.19379i	0.145199	+	0.0785504i
$781$	−9.24224	−	6.71488i	−0.330713	−	0.240277i
$782$	−18.2220			−0.651616
$783$	−0.880511	−	0.639728i	−0.0314669	−	0.0228620i
$784$	0.227097	−	0.698934i	0.00811062	−	0.0249619i
$785$	−28.0316	+	3.73391i	−1.00049	+	0.133269i
$786$	5.96736	+	18.3657i	0.212849	+	0.655081i
$787$	−8.16972	+	25.1438i	−0.291219	+	0.896280i	0.693246	+	0.720701i	$0.256180\pi$
$787$	−8.16972	+	25.1438i	−0.291219	+	0.896280i	−0.984465	+	0.175579i	$0.943820\pi$
$788$	1.79584	−	5.52704i	0.0639743	−	0.196893i
$789$	−11.8381	−	36.4339i	−0.421448	−	1.29708i
$790$	−25.7972	−	13.9559i	−0.917824	−	0.496528i
$791$	8.77110	−	26.9947i	0.311864	−	0.959820i
$792$	3.19460	+	2.32101i	0.113515	+	0.0824735i
$793$	6.38201			0.226632
$794$	−23.7276	−	17.2391i	−0.842061	−	0.611793i
$795$	0.288494	−	1.56993i	0.0102318	−	0.0556795i
$796$	−3.69366	+	2.68360i	−0.130918	+	0.0951178i
$797$	29.3705	−	21.3389i	1.04036	−	0.755863i	0.0700011	−	0.997547i	$-0.477700\pi$
$797$	29.3705	−	21.3389i	1.04036	−	0.755863i	0.970355	+	0.241684i	$0.0776997\pi$
$798$	2.13179	+	6.56098i	0.0754646	+	0.232256i
$799$	−16.4200			−0.580899
$800$	−4.82566	+	1.30881i	−0.170613	+	0.0462735i
$801$	−14.8816			−0.525814
$802$	5.61879	+	17.2928i	0.198406	+	0.610631i
$803$	4.37315	−	3.17728i	0.154325	−	0.112124i
$804$	21.5958	−	15.6903i	0.761625	−	0.553353i
$805$	12.6239	+	26.3630i	0.444933	+	0.929175i
$806$	−3.56978	−	2.59360i	−0.125740	−	0.0913556i
$807$	46.9253			1.65185
$808$	5.42023	+	3.93803i	0.190683	+	0.138539i
$809$	−3.64922	+	11.2312i	−0.128300	+	0.394866i	−0.994488	−	0.104852i	$-0.966563\pi$
$809$	−3.64922	+	11.2312i	−0.128300	+	0.394866i	0.866188	+	0.499718i	$0.166563\pi$
$810$	−3.44261	+	18.7340i	−0.120961	+	0.658246i
$811$	−11.8345	−	36.4229i	−0.415566	−	1.27898i	−0.911744	−	0.410759i	$-0.865264\pi$
$811$	−11.8345	−	36.4229i	−0.415566	−	1.27898i	0.496178	−	0.868221i	$-0.334736\pi$
$812$	2.46856	−	7.59746i	0.0866296	−	0.266619i
$813$	−5.64603	+	17.3767i	−0.198015	+	0.609428i
$814$	1.56536	+	4.81769i	0.0548659	+	0.168860i
$815$	1.84045	−	10.0154i	0.0644682	−	0.350823i
$816$	−2.97168	+	9.14588i	−0.104029	+	0.320170i
$817$	−6.07788	−	4.41584i	−0.212638	−	0.154491i
$818$	11.7619			0.411246
$819$	−5.89672	−	4.28422i	−0.206048	−	0.149703i
$820$	7.88108	+	16.4584i	0.275219	+	0.574753i
$821$	5.33867	−	3.87877i	0.186321	−	0.135370i	−0.490715	−	0.871320i	$-0.663264\pi$
$821$	5.33867	−	3.87877i	0.186321	−	0.135370i	0.677036	+	0.735950i	$0.263264\pi$
$822$	4.22281	−	3.06805i	0.147287	−	0.107011i
$823$	1.70627	+	5.25135i	0.0594767	+	0.183050i	0.976381	−	0.216058i	$-0.0693199\pi$
$823$	1.70627	+	5.25135i	0.0594767	+	0.183050i	−0.916904	+	0.399108i	$0.869320\pi$
$824$	11.6879			0.407166
$825$	−14.5188	−	5.52252i	−0.505479	−	0.192269i
$826$	29.0134			1.00951
$827$	8.85791	+	27.2618i	0.308020	+	0.947987i	0.978533	+	0.206090i	$0.0660738\pi$
$827$	8.85791	+	27.2618i	0.308020	+	0.947987i	−0.670514	+	0.741897i	$0.733926\pi$
$828$	11.9884	−	8.71005i	0.416624	−	0.302695i
$829$	−39.8481	+	28.9513i	−1.38398	+	1.00552i	−0.387484	+	0.921876i	$0.626656\pi$
$829$	−39.8481	+	28.9513i	−1.38398	+	1.00552i	−0.996496	+	0.0836442i	$0.973344\pi$
$830$	5.82560	−	31.7017i	0.202210	−	1.10038i
$831$	44.8875	+	32.6127i	1.55713	+	1.13132i
$832$	0.831255			0.0288186
$833$	2.30500	+	1.67468i	0.0798636	+	0.0580243i
$834$	−0.0332856	+	0.102443i	−0.00115259	+	0.00354729i
$835$	−11.9963	−	6.48981i	−0.415149	−	0.224589i
$836$	−0.387035	−	1.19117i	−0.0133859	−	0.0411975i
$837$	−0.621548	+	1.91293i	−0.0214838	+	0.0661204i
$838$	2.61720	−	8.05490i	0.0904095	−	0.278252i
$839$	3.76504	+	11.5876i	0.129984	+	0.400048i	0.994776	−	0.102081i	$-0.0325502\pi$
$839$	3.76504	+	11.5876i	0.129984	+	0.400048i	−0.864793	+	0.502129i	$0.832550\pi$
$840$	15.2907	−	2.03678i	0.527580	−	0.0702756i
$841$	−6.41201	+	19.7341i	−0.221104	+	0.680488i
$842$	−2.69760	−	1.95992i	−0.0929655	−	0.0675434i
$843$	−38.0529			−1.31061
$844$	7.72492	+	5.61248i	0.265903	+	0.193190i
$845$	−24.2084	−	13.0963i	−0.832793	−	0.450528i
$846$	10.8028	−	7.84873i	0.371409	−	0.269845i
$847$	21.2206	−	15.4177i	0.729148	−	0.529757i
$848$	−0.0889310	−	0.273701i	−0.00305390	−	0.00939895i
$849$	34.6674			1.18978
$850$	0.955487	−	19.3609i	0.0327729	−	0.664074i
$851$	19.0097			0.651645
$852$	6.99148	+	21.5176i	0.239524	+	0.737179i
$853$	−7.13116	+	5.18109i	−0.244166	+	0.177397i	−0.703137	−	0.711054i	$-0.748218\pi$
$853$	−7.13116	+	5.18109i	−0.244166	+	0.177397i	0.458971	+	0.888451i	$0.348218\pi$
$854$	17.2746	−	12.5507i	0.591125	−	0.429477i
$855$	−5.10633	+	4.86054i	−0.174633	+	0.166227i
$856$	−15.1495	−	11.0067i	−0.517798	−	0.376203i
$857$	8.51626			0.290910			0.145455	−	0.989365i	$-0.453535\pi$
$857$	8.51626			0.290910			0.145455	+	0.989365i	$0.453535\pi$
$858$	2.08927	+	1.51794i	0.0713265	+	0.0518218i
$859$	16.7875	−	51.6667i	0.572783	−	1.76284i	−0.0708251	−	0.997489i	$-0.522563\pi$
$859$	16.7875	−	51.6667i	0.572783	−	1.76284i	0.643608	−	0.765355i	$-0.277437\pi$
$860$	−12.1678	+	11.5821i	−0.414919	+	0.394947i
$861$	−17.3971	−	53.5426i	−0.592890	−	1.82473i
$862$	0.407223	−	1.25330i	0.0138701	−	0.0426877i
$863$	13.4344	−	41.3469i	0.457313	−	1.40747i	−0.411084	−	0.911597i	$-0.634850\pi$
$863$	13.4344	−	41.3469i	0.457313	−	1.40747i	0.868398	−	0.495868i	$-0.165150\pi$
$864$	−0.117091	−	0.360370i	−0.00398353	−	0.0122600i
$865$	−14.6812	−	30.6595i	−0.499177	−	1.04245i
$866$	11.4879	−	35.3562i	0.390376	−	1.20145i
$867$	3.95267	+	2.87178i	0.134240	+	0.0975307i
$868$	−14.7631			−0.501092
$869$	−13.2909	−	9.65644i	−0.450864	−	0.327572i
$870$	15.7919	−	2.10354i	0.535397	−	0.0713167i
$871$	7.23717	−	5.25811i	0.245222	−	0.178164i
$872$	−3.47961	+	2.52808i	−0.117834	+	0.0856117i
$873$	1.04825	+	3.22617i	0.0354778	+	0.109189i
$874$	−4.70014			−0.158985
$875$	−28.6728	+	12.0306i	−0.969317	+	0.406707i
$876$	−10.7054			−0.361703
$877$	−2.76850	−	8.52057i	−0.0934857	−	0.287719i	0.893370	−	0.449321i	$-0.148334\pi$
$877$	−2.76850	−	8.52057i	−0.0934857	−	0.287719i	−0.986856	+	0.161602i	$0.948334\pi$
$878$	26.9673	−	19.5929i	0.910103	−	0.661229i
$879$	−51.7684	+	37.6119i	−1.74610	+	1.26862i
$880$	−2.77609	+	0.369785i	−0.0935820	+	0.0124654i
$881$	−25.2068	−	18.3138i	−0.849237	−	0.617007i	0.0756984	−	0.997131i	$-0.475881\pi$
$881$	−25.2068	−	18.3138i	−0.849237	−	0.617007i	−0.924936	+	0.380124i	$0.875881\pi$
$882$	−2.31697			−0.0780165
$883$	32.4805	+	23.5985i	1.09306	+	0.794152i	0.979913	−	0.199426i	$-0.0639079\pi$
$883$	32.4805	+	23.5985i	1.09306	+	0.794152i	0.113144	+	0.993579i	$0.463908\pi$
$884$	−0.995866	+	3.06496i	−0.0334946	+	0.103086i
$885$	24.9897	+	52.1871i	0.840019	+	1.75425i
$886$	6.77275	+	20.8444i	0.227535	+	0.700281i
$887$	−7.61409	+	23.4338i	−0.255656	+	0.786828i	0.738044	+	0.674753i	$0.235750\pi$
$887$	−7.61409	+	23.4338i	−0.255656	+	0.786828i	−0.993700	+	0.112075i	$0.964250\pi$
$888$	3.10014	−	9.54126i	0.104034	−	0.320184i
$889$	−6.98069	−	21.4844i	−0.234125	−	0.720562i
$890$	7.64497	−	7.27698i	0.256260	−	0.243925i
$891$	−3.29691	+	10.1469i	−0.110451	+	0.339932i
$892$	−15.8944	−	11.5479i	−0.532183	−	0.386654i
$893$	−4.23535			−0.141731
$894$	−23.9716	−	17.4164i	−0.801731	−	0.582492i
$895$	35.4117	−	33.7072i	1.18368	−	1.12671i
$896$	2.25001	−	1.63473i	0.0751677	−	0.0546125i
$897$	7.84040	−	5.69638i	0.261783	−	0.190197i
$898$	−9.47541	−	29.1623i	−0.316199	−	0.973159i
$899$	−15.2470			−0.508516
$900$	8.62584	+	13.1944i	0.287528	+	0.439813i
$901$	1.11572			0.0371700
$902$	3.15850	+	9.72087i	0.105167	+	0.323670i
$903$	41.9290	−	30.4632i	1.39531	−	1.01375i
$904$	8.25661	−	5.99878i	0.274611	−	0.199516i
$905$	−13.3564	−	7.22558i	−0.443981	−	0.240186i
$906$	−3.26561	−	2.37261i	−0.108493	−	0.0788246i
$907$	3.68213			0.122263			0.0611316	−	0.998130i	$-0.480529\pi$
$907$	3.68213			0.122263			0.0611316	+	0.998130i	$0.480529\pi$
$908$	−13.7129	−	9.96299i	−0.455078	−	0.330633i
$909$	6.52729	−	20.0889i	0.216497	−	0.666308i
$910$	5.12422	−	0.682564i	0.169866	−	0.0226268i
$911$	7.57850	+	23.3242i	0.251087	+	0.772766i	0.994575	+	0.104017i	$0.0331698\pi$
$911$	7.57850	+	23.3242i	0.251087	+	0.772766i	−0.743489	+	0.668749i	$0.766830\pi$
$912$	−0.766509	+	2.35907i	−0.0253817	+	0.0781167i
$913$	5.57904	−	17.1705i	0.184639	−	0.568262i
$914$	−2.67596	−	8.23577i	−0.0885130	−	0.272415i
$915$	37.4542	+	20.2621i	1.23820	+	0.669845i
$916$	−3.07590	+	9.46666i	−0.101631	+	0.312787i
$917$	17.5166	+	12.7266i	0.578450	+	0.420268i
$918$	1.46902			0.0484847
$919$	−20.6590	−	15.0096i	−0.681476	−	0.495121i	0.192371	−	0.981322i	$-0.438382\pi$
$919$	−20.6590	−	15.0096i	−0.681476	−	0.495121i	−0.873847	+	0.486201i	$0.838382\pi$
$920$	−1.89951	+	10.3368i	−0.0626251	+	0.340793i
$921$	63.4327	−	46.0866i	2.09018	−	1.51860i
$922$	−4.45143	+	3.23416i	−0.146600	+	0.106511i
$923$	2.34298	+	7.21095i	0.0771201	+	0.237351i
$924$	8.64033			0.284246
$925$	−0.996794	+	20.1979i	−0.0327744	+	0.664103i
$926$	9.16483			0.301175
$927$	−11.3870	−	35.0455i	−0.373997	−	1.15105i
$928$	2.32377	−	1.68831i	0.0762813	−	0.0554216i
$929$	−4.69025	+	3.40766i	−0.153882	+	0.111802i	−0.662062	−	0.749449i	$-0.730318\pi$
$929$	−4.69025	+	3.40766i	−0.153882	+	0.111802i	0.508180	+	0.861251i	$0.330318\pi$
$930$	−12.7157	−	26.5547i	−0.416963	−	0.870763i
$931$	0.594549	+	0.431965i	0.0194855	+	0.0141571i
$932$	−17.1364			−0.561322
$933$	28.7201	+	20.8663i	0.940252	+	0.683133i
$934$	12.3268	−	37.9380i	0.403345	−	1.24137i
$935$	1.96238	−	10.6789i	0.0641766	−	0.349236i
$936$	−0.809856	−	2.49248i	−0.0264710	−	0.0814692i
$937$	−9.31826	+	28.6786i	−0.304414	+	0.936891i	0.675481	+	0.737377i	$0.263936\pi$
$937$	−9.31826	+	28.6786i	−0.304414	+	0.936891i	−0.979895	+	0.199513i	$0.936064\pi$
$938$	9.24882	−	28.4650i	0.301985	−	0.929414i
$939$	−14.2335	−	43.8062i	−0.464492	−	1.42956i
$940$	−1.71167	+	9.31457i	−0.0558286	+	0.303808i
$941$	3.54134	−	10.8991i	0.115444	−	0.355302i	−0.876595	−	0.481229i	$-0.840191\pi$
$941$	3.54134	−	10.8991i	0.115444	−	0.355302i	0.992039	+	0.125927i	$0.0401906\pi$
$942$	25.3790	+	18.4390i	0.826894	+	0.600774i
$943$	38.3568			1.24907
$944$	8.43974	+	6.13183i	0.274690	+	0.199574i
$945$	−1.01771	−	2.12533i	−0.0331061	−	0.0691370i
$946$	−7.61237	+	5.53071i	−0.247500	+	0.179819i
$947$	21.3769	−	15.5312i	0.694655	−	0.504696i	−0.183532	−	0.983014i	$-0.558753\pi$
$947$	21.3769	−	15.5312i	0.694655	−	0.504696i	0.878187	+	0.478318i	$0.158753\pi$
$948$	10.0542	+	30.9437i	0.326545	+	1.00500i
$949$	−3.58760			−0.116458
$950$	0.246457	−	4.99392i	0.00799612	−	0.162024i
$951$	−10.2365			−0.331943
$952$	3.33191	+	10.2546i	0.107988	+	0.332353i
$953$	25.1296	−	18.2577i	0.814029	−	0.591426i	−0.100967	−	0.994890i	$-0.532194\pi$
$953$	25.1296	−	18.2577i	0.814029	−	0.591426i	0.914996	+	0.403463i	$0.132194\pi$
$954$	−0.734039	+	0.533311i	−0.0237654	+	0.0172666i
$955$	6.70609	−	36.4932i	0.217004	−	1.18089i
$956$	−0.551621	−	0.400776i	−0.0178407	−	0.0129620i
$957$	8.92354			0.288457
$958$	21.6321	+	15.7167i	0.698902	+	0.507782i
$959$	1.80850	−	5.56599i	0.0583995	−	0.179735i
$960$	4.87840	+	2.63913i	0.157450	+	0.0851777i
$961$	−0.872264	−	2.68455i	−0.0281375	−	0.0865984i
$962$	1.03892	−	3.19746i	0.0334961	−	0.103090i
$963$	−18.2437	+	56.1484i	−0.587895	+	1.80936i
$964$	−4.54973	−	14.0026i	−0.146537	−	0.450994i
$965$	40.7055	−	5.42211i	1.31036	−	0.174544i
$966$	10.0197	−	30.8375i	0.322379	−	0.992182i
$967$	−13.4956	−	9.80513i	−0.433989	−	0.315312i	0.349253	−	0.937029i	$-0.386435\pi$
$967$	−13.4956	−	9.80513i	−0.433989	−	0.315312i	−0.783242	+	0.621717i	$0.786435\pi$
$968$	9.43132			0.303134
$969$	−7.77995	−	5.65246i	−0.249928	−	0.181583i
$970$	−2.11608	−	1.14477i	−0.0679433	−	0.0367562i
$971$	42.7439	−	31.0553i	1.37172	−	0.996611i	0.374117	−	0.927381i	$-0.377946\pi$
$971$	42.7439	−	31.0553i	1.37172	−	0.996611i	0.997601	−	0.0692299i	$-0.0220542\pi$
$972$	18.0139	−	13.0879i	0.577796	−	0.419793i
$973$	0.0373206	+	0.114861i	0.00119644	+	0.00368228i
$974$	−25.7381			−0.824702
$975$	5.64131	+	8.62915i	0.180667	+	0.276354i
$976$	7.67756			0.245753
$977$	−17.1400	−	52.7514i	−0.548356	−	1.68767i	−0.712873	−	0.701293i	$-0.752606\pi$
$977$	−17.1400	−	52.7514i	−0.548356	−	1.68767i	0.164517	−	0.986374i	$-0.447394\pi$
$978$	−9.13873	+	6.63968i	−0.292224	+	0.212313i
$979$	4.78281	−	3.47491i	0.152859	−	0.111059i
$980$	1.19028	−	1.13298i	0.0380220	−	0.0361918i
$981$	10.9704	+	7.97044i	0.350257	+	0.254476i
$982$	−32.2672			−1.02969
$983$	14.3975	+	10.4604i	0.459208	+	0.333634i	0.793220	−	0.608935i	$-0.208403\pi$
$983$	14.3975	+	10.4604i	0.459208	+	0.333634i	−0.334013	+	0.942569i	$0.608403\pi$
$984$	6.25530	−	19.2518i	0.199412	−	0.613726i
$985$	9.41249	−	8.95942i	0.299907	−	0.285471i
$986$	3.44113	+	10.5907i	0.109588	+	0.337277i
$987$	9.02889	−	27.7881i	0.287393	−	0.884504i
$988$	−0.256872	+	0.790571i	−0.00817219	+	0.0251514i
$989$	10.9116	+	33.5824i	0.346968	+	1.06786i
$990$	3.81341	+	7.96371i	0.121198	+	0.253103i
$991$	−15.0748	+	46.3954i	−0.478866	+	1.47380i	0.361806	+	0.932253i	$0.382160\pi$
$991$	−15.0748	+	46.3954i	−0.478866	+	1.47380i	−0.840672	+	0.541545i	$0.817840\pi$
$992$	−4.29445	−	3.12010i	−0.136349	−	0.0990632i
$993$	29.2669			0.928758
$994$	20.5228	+	14.9107i	0.650944	+	0.472938i
$995$	−10.1196	+	1.34797i	−0.320814	+	0.0427336i
$996$	−28.9269	+	21.0166i	−0.916585	+	0.665938i
$997$	1.50318	−	1.09212i	0.0476061	−	0.0345879i	−0.563728	−	0.825961i	$-0.690633\pi$
$997$	1.50318	−	1.09212i	0.0476061	−	0.0345879i	0.611334	+	0.791373i	$0.290633\pi$
$998$	−2.10882	−	6.49028i	−0.0667535	−	0.205446i
$999$	−1.53252			−0.0484869

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.h.d.381.2	✓	44
25.21	even	5	inner	950.2.h.d.571.2	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.h.d.381.2	✓	44	1.1	even	1	trivial
950.2.h.d.571.2	yes	44	25.21	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-2.00675 + 1.45799i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-2.21649 + 0.295244i) q^{5} +(2.00675 + 1.45799i) q^{6} +2.78117 q^{7} +(0.809017 + 0.587785i) q^{8} +(0.974256 - 2.99845i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-2.00675 + 1.45799i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-2.21649 + 0.295244i) q^{5} +(2.00675 + 1.45799i) q^{6} +2.78117 q^{7} +(0.809017 + 0.587785i) q^{8} +(0.974256 - 2.99845i) q^{9} +(0.965727 + 2.01677i) q^{10} +(0.387035 + 1.19117i) q^{11} +(0.766509 - 2.35907i) q^{12} +(0.256872 - 0.790571i) q^{13} +(-0.859429 - 2.64505i) q^{14} +(4.01747 - 3.82410i) q^{15} +(0.309017 - 0.951057i) q^{16} +(3.13647 + 2.27878i) q^{17} -3.15276 q^{18} +(0.809017 + 0.587785i) q^{19} +(1.61964 - 1.54168i) q^{20} +(-5.58110 + 4.05491i) q^{21} +(1.01327 - 0.736184i) q^{22} +(-1.45242 - 4.47010i) q^{23} -2.48048 q^{24} +(4.82566 - 1.30881i) q^{25} -0.831255 q^{26} +(0.117091 + 0.360370i) q^{27} +(-2.25001 + 1.63473i) q^{28} +(-2.32377 + 1.68831i) q^{29} +(-4.87840 - 2.63913i) q^{30} +(4.29445 + 3.12010i) q^{31} -1.00000 q^{32} +(-2.51339 - 1.82609i) q^{33} +(1.19803 - 3.68715i) q^{34} +(-6.16444 + 0.821124i) q^{35} +(0.974256 + 2.99845i) q^{36} +(-1.24982 + 3.84655i) q^{37} +(0.309017 - 0.951057i) q^{38} +(0.637165 + 1.96099i) q^{39} +(-1.96672 - 1.06396i) q^{40} +(-2.52182 + 7.76135i) q^{41} +(5.58110 + 4.05491i) q^{42} -7.51267 q^{43} +(-1.01327 - 0.736184i) q^{44} +(-1.27415 + 6.93368i) q^{45} +(-3.80249 + 2.76267i) q^{46} +(-3.42647 + 2.48948i) q^{47} +(0.766509 + 2.35907i) q^{48} +0.734903 q^{49} +(-2.73597 - 4.18503i) q^{50} -9.61654 q^{51} +(0.256872 + 0.790571i) q^{52} +(0.232824 - 0.169157i) q^{53} +(0.306549 - 0.222721i) q^{54} +(-1.20955 - 2.52595i) q^{55} +(2.25001 + 1.63473i) q^{56} -2.48048 q^{57} +(2.32377 + 1.68831i) q^{58} +(-3.22369 + 9.92151i) q^{59} +(-1.00246 + 5.45517i) q^{60} +(2.37250 + 7.30179i) q^{61} +(1.64033 - 5.04843i) q^{62} +(2.70957 - 8.33920i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-0.335943 + 1.82813i) q^{65} +(-0.960031 + 2.95467i) q^{66} +(8.70631 + 6.32551i) q^{67} -3.87689 q^{68} +(9.43200 + 6.85275i) q^{69} +(2.68585 + 5.60899i) q^{70} +(-7.37920 + 5.36130i) q^{71} +(2.55064 - 1.85315i) q^{72} +(-1.33368 - 4.10464i) q^{73} +4.04450 q^{74} +(-7.77565 + 9.66221i) q^{75} -1.00000 q^{76} +(1.07641 + 3.31285i) q^{77} +(1.66812 - 1.21196i) q^{78} +(-10.6118 + 7.70991i) q^{79} +(-0.404139 + 2.19924i) q^{80} +(6.89152 + 5.00698i) q^{81} +8.16077 q^{82} +(-11.6618 - 8.47283i) q^{83} +(2.13179 - 6.56098i) q^{84} +(-7.62476 - 4.12487i) q^{85} +(2.32154 + 7.14498i) q^{86} +(2.20167 - 6.77604i) q^{87} +(-0.387035 + 1.19117i) q^{88} +(-1.45861 - 4.48915i) q^{89} +(6.98806 - 0.930834i) q^{90} +(0.714405 - 2.19871i) q^{91} +(3.80249 + 2.76267i) q^{92} -13.1669 q^{93} +(3.42647 + 2.48948i) q^{94} +(-1.96672 - 1.06396i) q^{95} +(2.00675 - 1.45799i) q^{96} +(-0.870458 + 0.632425i) q^{97} +(-0.227097 - 0.698934i) q^{98} +3.94874 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 11 q^{5} + q^{6} - 10 q^{7} + 11 q^{8}+O(q^{10}) \) 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 11 * q^5 + q^6 - 10 * q^7 + 11 * q^8	\( 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 11 q^{5} + q^{6} - 10 q^{7} + 11 q^{8} - 4 q^{10} + 7 q^{11} + 4 q^{12} + 10 q^{13} - 5 q^{14} - 20 q^{15} - 11 q^{16} + 11 q^{17} - 50 q^{18} + 11 q^{19} + 4 q^{20} + 9 q^{21} + 8 q^{22} - 7 q^{23} + 6 q^{24} - 3 q^{25} + 10 q^{26} + 5 q^{27} - 20 q^{29} - 10 q^{30} - 11 q^{31} - 44 q^{32} - 2 q^{33} - q^{34} + 5 q^{35} + 43 q^{37} - 11 q^{38} - 33 q^{39} - 4 q^{40} - 32 q^{41} - 9 q^{42} - 74 q^{43} - 8 q^{44} + 10 q^{45} - 8 q^{46} - 19 q^{47} + 4 q^{48} + 54 q^{49} + 18 q^{50} + 34 q^{51} + 10 q^{52} + 23 q^{53} - 40 q^{54} + 2 q^{55} + 6 q^{57} + 20 q^{58} + 24 q^{59} - 35 q^{60} - 12 q^{61} + q^{62} - 44 q^{63} - 11 q^{64} + 43 q^{65} - 8 q^{66} + 35 q^{67} - 24 q^{68} + 29 q^{69} - 5 q^{70} - 2 q^{71} + 25 q^{72} + 22 q^{73} + 72 q^{74} + 7 q^{75} - 44 q^{76} - 3 q^{77} - 22 q^{78} - 19 q^{79} - q^{80} - 26 q^{81} - 58 q^{82} - 24 q^{83} - 21 q^{84} - 18 q^{85} - 6 q^{86} + 83 q^{87} - 7 q^{88} - 8 q^{89} + 60 q^{90} - 30 q^{91} + 8 q^{92} - 72 q^{93} + 19 q^{94} - 4 q^{95} + q^{96} - 16 q^{97} + q^{98} + 84 q^{99}+O(q^{100}) \) 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 11 * q^5 + q^6 - 10 * q^7 + 11 * q^8 - 4 * q^10 + 7 * q^11 + 4 * q^12 + 10 * q^13 - 5 * q^14 - 20 * q^15 - 11 * q^16 + 11 * q^17 - 50 * q^18 + 11 * q^19 + 4 * q^20 + 9 * q^21 + 8 * q^22 - 7 * q^23 + 6 * q^24 - 3 * q^25 + 10 * q^26 + 5 * q^27 - 20 * q^29 - 10 * q^30 - 11 * q^31 - 44 * q^32 - 2 * q^33 - q^34 + 5 * q^35 + 43 * q^37 - 11 * q^38 - 33 * q^39 - 4 * q^40 - 32 * q^41 - 9 * q^42 - 74 * q^43 - 8 * q^44 + 10 * q^45 - 8 * q^46 - 19 * q^47 + 4 * q^48 + 54 * q^49 + 18 * q^50 + 34 * q^51 + 10 * q^52 + 23 * q^53 - 40 * q^54 + 2 * q^55 + 6 * q^57 + 20 * q^58 + 24 * q^59 - 35 * q^60 - 12 * q^61 + q^62 - 44 * q^63 - 11 * q^64 + 43 * q^65 - 8 * q^66 + 35 * q^67 - 24 * q^68 + 29 * q^69 - 5 * q^70 - 2 * q^71 + 25 * q^72 + 22 * q^73 + 72 * q^74 + 7 * q^75 - 44 * q^76 - 3 * q^77 - 22 * q^78 - 19 * q^79 - q^80 - 26 * q^81 - 58 * q^82 - 24 * q^83 - 21 * q^84 - 18 * q^85 - 6 * q^86 + 83 * q^87 - 7 * q^88 - 8 * q^89 + 60 * q^90 - 30 * q^91 + 8 * q^92 - 72 * q^93 + 19 * q^94 - 4 * q^95 + q^96 - 16 * q^97 + q^98 + 84 * q^99

Introduction

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