LMFDB - Embedded newform 799.2.g.d.189.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [799,2,Mod(189,799)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(799, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([7, 0]))

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

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

chi := DirichletCharacter("799.189");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 799 = 17 \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	799.g (of order $8$, 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:	$6.38004712150$
Analytic rank:	$0$
Dimension:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			189.2
Character	$\chi$	$=$	799.189
Dual form			799.2.g.d.706.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.79681 - 1.79681i) q^{2} +(2.48226 - 1.02819i) q^{3} +4.45704i q^{4} +(-1.34217 - 3.24029i) q^{5} +(-6.30760 - 2.61270i) q^{6} +(0.543897 - 1.31308i) q^{7} +(4.41484 - 4.41484i) q^{8} +(2.98314 - 2.98314i) q^{9} +O(q^{10})$	\(q+(-1.79681 - 1.79681i) q^{2} +(2.48226 - 1.02819i) q^{3} +4.45704i q^{4} +(-1.34217 - 3.24029i) q^{5} +(-6.30760 - 2.61270i) q^{6} +(0.543897 - 1.31308i) q^{7} +(4.41484 - 4.41484i) q^{8} +(2.98314 - 2.98314i) q^{9} +(-3.41055 + 8.23380i) q^{10} +(5.46605 + 2.26411i) q^{11} +(4.58267 + 11.0635i) q^{12} -6.14170i q^{13} +(-3.33664 + 1.38208i) q^{14} +(-6.66323 - 6.66323i) q^{15} -6.95115 q^{16} +(2.90042 - 2.93045i) q^{17} -10.7202 q^{18} +(0.836444 + 0.836444i) q^{19} +(14.4421 - 5.98211i) q^{20} -3.81864i q^{21} +(-5.75327 - 13.8896i) q^{22} +(6.27732 + 2.60015i) q^{23} +(6.41951 - 15.4981i) q^{24} +(-5.16249 + 5.16249i) q^{25} +(-11.0355 + 11.0355i) q^{26} +(1.25314 - 3.02536i) q^{27} +(5.85247 + 2.42417i) q^{28} +(1.13269 + 2.73457i) q^{29} +23.9451i q^{30} +(-2.87307 + 1.19006i) q^{31} +(3.66021 + 3.66021i) q^{32} +15.8961 q^{33} +(-10.4770 + 0.0539620i) q^{34} -4.98477 q^{35} +(13.2960 + 13.2960i) q^{36} +(-9.40668 + 3.89637i) q^{37} -3.00586i q^{38} +(-6.31482 - 15.2453i) q^{39} +(-20.2308 - 8.37987i) q^{40} +(-3.58829 + 8.66290i) q^{41} +(-6.86137 + 6.86137i) q^{42} +(1.32542 - 1.32542i) q^{43} +(-10.0912 + 24.3624i) q^{44} +(-13.6701 - 5.66233i) q^{45} +(-6.60716 - 15.9511i) q^{46} +1.00000i q^{47} +(-17.2546 + 7.14708i) q^{48} +(3.52138 + 3.52138i) q^{49} +18.5520 q^{50} +(4.18655 - 10.2563i) q^{51} +27.3738 q^{52} +(-2.01312 - 2.01312i) q^{53} +(-7.68764 + 3.18433i) q^{54} -20.7504i q^{55} +(-3.39583 - 8.19827i) q^{56} +(2.93629 + 1.21625i) q^{57} +(2.87826 - 6.94873i) q^{58} +(5.66981 - 5.66981i) q^{59} +(29.6983 - 29.6983i) q^{60} +(-2.91832 + 7.04544i) q^{61} +(7.30067 + 3.02404i) q^{62} +(-2.29459 - 5.53962i) q^{63} +0.748892i q^{64} +(-19.9009 + 8.24321i) q^{65} +(-28.5622 - 28.5622i) q^{66} -7.90276 q^{67} +(13.0612 + 12.9273i) q^{68} +18.2554 q^{69} +(8.95667 + 8.95667i) q^{70} +(-1.96989 + 0.815957i) q^{71} -26.3401i q^{72} +(-4.43241 - 10.7008i) q^{73} +(23.9030 + 9.90097i) q^{74} +(-7.50665 + 18.1227i) q^{75} +(-3.72807 + 3.72807i) q^{76} +(5.94594 - 5.94594i) q^{77} +(-16.0464 + 38.7394i) q^{78} +(-3.62804 - 1.50278i) q^{79} +(9.32963 + 22.5237i) q^{80} +3.85818i q^{81} +(22.0130 - 9.11810i) q^{82} +(-3.29615 - 3.29615i) q^{83} +17.0199 q^{84} +(-13.3884 - 5.46502i) q^{85} -4.76306 q^{86} +(5.62329 + 5.62329i) q^{87} +(34.1274 - 14.1360i) q^{88} +10.7114i q^{89} +(14.3884 + 34.7367i) q^{90} +(-8.06457 - 3.34045i) q^{91} +(-11.5890 + 27.9783i) q^{92} +(-5.90810 + 5.90810i) q^{93} +(1.79681 - 1.79681i) q^{94} +(1.58767 - 3.83297i) q^{95} +(12.8490 + 5.32223i) q^{96} +(1.26062 + 3.04341i) q^{97} -12.6545i q^{98} +(23.0601 - 9.55181i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q - 4 q^{2} + 4 q^{6} + 4 q^{7} + 4 q^{8} - 8 q^{9}+O(q^{10}) $ 152 * q - 4 * q^2 + 4 * q^6 + 4 * q^7 + 4 * q^8 - 8 * q^9	$ 152 q - 4 q^{2} + 4 q^{6} + 4 q^{7} + 4 q^{8} - 8 q^{9} - 8 q^{11} + 8 q^{12} - 12 q^{14} + 20 q^{15} - 160 q^{16} - 12 q^{17} + 96 q^{18} + 16 q^{19} + 96 q^{20} - 4 q^{22} - 16 q^{23} - 76 q^{24} - 12 q^{25} - 8 q^{26} + 8 q^{28} - 4 q^{29} - 4 q^{31} - 16 q^{32} - 72 q^{33} - 20 q^{34} + 48 q^{35} - 16 q^{36} + 16 q^{37} + 64 q^{40} - 68 q^{41} - 144 q^{42} + 4 q^{43} + 12 q^{44} - 4 q^{46} - 12 q^{48} - 4 q^{49} + 96 q^{50} - 52 q^{51} + 168 q^{52} - 16 q^{53} + 168 q^{54} + 108 q^{56} - 104 q^{58} - 84 q^{59} - 4 q^{60} + 4 q^{61} - 28 q^{62} + 60 q^{63} + 60 q^{65} - 44 q^{66} - 160 q^{67} - 96 q^{68} + 160 q^{69} + 36 q^{70} + 40 q^{71} + 4 q^{73} + 76 q^{74} - 116 q^{75} - 148 q^{76} - 4 q^{77} + 68 q^{78} - 76 q^{80} + 64 q^{82} - 124 q^{83} + 208 q^{84} - 68 q^{85} + 80 q^{86} - 72 q^{87} + 188 q^{88} + 236 q^{90} - 32 q^{91} - 196 q^{92} - 152 q^{93} + 4 q^{94} - 48 q^{95} - 56 q^{96} - 20 q^{97} + 244 q^{99}+O(q^{100}) $ 152 * q - 4 * q^2 + 4 * q^6 + 4 * q^7 + 4 * q^8 - 8 * q^9 - 8 * q^11 + 8 * q^12 - 12 * q^14 + 20 * q^15 - 160 * q^16 - 12 * q^17 + 96 * q^18 + 16 * q^19 + 96 * q^20 - 4 * q^22 - 16 * q^23 - 76 * q^24 - 12 * q^25 - 8 * q^26 + 8 * q^28 - 4 * q^29 - 4 * q^31 - 16 * q^32 - 72 * q^33 - 20 * q^34 + 48 * q^35 - 16 * q^36 + 16 * q^37 + 64 * q^40 - 68 * q^41 - 144 * q^42 + 4 * q^43 + 12 * q^44 - 4 * q^46 - 12 * q^48 - 4 * q^49 + 96 * q^50 - 52 * q^51 + 168 * q^52 - 16 * q^53 + 168 * q^54 + 108 * q^56 - 104 * q^58 - 84 * q^59 - 4 * q^60 + 4 * q^61 - 28 * q^62 + 60 * q^63 + 60 * q^65 - 44 * q^66 - 160 * q^67 - 96 * q^68 + 160 * q^69 + 36 * q^70 + 40 * q^71 + 4 * q^73 + 76 * q^74 - 116 * q^75 - 148 * q^76 - 4 * q^77 + 68 * q^78 - 76 * q^80 + 64 * q^82 - 124 * q^83 + 208 * q^84 - 68 * q^85 + 80 * q^86 - 72 * q^87 + 188 * q^88 + 236 * q^90 - 32 * q^91 - 196 * q^92 - 152 * q^93 + 4 * q^94 - 48 * q^95 - 56 * q^96 - 20 * q^97 + 244 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/799\mathbb{Z}\right)^\times$.

$n$	$52$	$377$
$\chi(n)$	$1$	$e\left(\frac{7}{8}\right)$

Coefficient data

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

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

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

$2$	−1.79681	−	1.79681i	−1.27054	−	1.27054i	−0.945807	−	0.324728i	$-0.894727\pi$
$2$	−1.79681	−	1.79681i	−1.27054	−	1.27054i	−0.324728	−	0.945807i	$-0.605273\pi$
$3$	2.48226	−	1.02819i	1.43313	−	0.593624i	0.475011	−	0.879980i	$-0.342444\pi$
$3$	2.48226	−	1.02819i	1.43313	−	0.593624i	0.958123	+	0.286356i	$0.0924440\pi$
$4$			4.45704i			2.22852i
$5$	−1.34217	−	3.24029i	−0.600237	−	1.44910i	−0.873338	−	0.487114i	$-0.838050\pi$
$5$	−1.34217	−	3.24029i	−0.600237	−	1.44910i	0.273102	−	0.961985i	$-0.411950\pi$
$6$	−6.30760	−	2.61270i	−2.57507	−	1.06663i
$7$	0.543897	−	1.31308i	0.205574	−	0.496299i	−0.787143	−	0.616770i	$-0.788441\pi$
$7$	0.543897	−	1.31308i	0.205574	−	0.496299i	0.992717	+	0.120472i	$0.0384407\pi$
$8$	4.41484	−	4.41484i	1.56088	−	1.56088i
$9$	2.98314	−	2.98314i	0.994378	−	0.994378i
$10$	−3.41055	+	8.23380i	−1.07851	+	2.60375i
$11$	5.46605	+	2.26411i	1.64808	+	0.682655i	0.997076	−	0.0764220i	$-0.0243496\pi$
$11$	5.46605	+	2.26411i	1.64808	+	0.682655i	0.651000	+	0.759077i	$0.274350\pi$
$12$	4.58267	+	11.0635i	1.32290	+	3.19377i
$13$		−	6.14170i		−	1.70340i	−0.524028	−	0.851701i	$-0.675571\pi$
$13$		−	6.14170i		−	1.70340i	0.524028	−	0.851701i	$-0.324429\pi$
$14$	−3.33664	+	1.38208i	−0.891754	+	0.369377i
$15$	−6.66323	−	6.66323i	−1.72044	−	1.72044i
$16$	−6.95115			−1.73779
$17$	2.90042	−	2.93045i	0.703455	−	0.710739i
$17$	2.90042	−	2.93045i	0.703455	−	0.710739i
$18$	−10.7202			−2.52679
$19$	0.836444	+	0.836444i	0.191893	+	0.191893i	0.796514	−	0.604620i	$-0.206675\pi$
$19$	0.836444	+	0.836444i	0.191893	+	0.191893i	−0.604620	+	0.796514i	$0.706675\pi$
$20$	14.4421	−	5.98211i	3.22935	−	1.33764i
$21$		−	3.81864i		−	0.833297i
$22$	−5.75327	−	13.8896i	−1.22660	−	2.96128i
$23$	6.27732	+	2.60015i	1.30891	+	0.542169i	0.924566	−	0.381021i	$-0.124428\pi$
$23$	6.27732	+	2.60015i	1.30891	+	0.542169i	0.384344	+	0.923190i	$0.374428\pi$
$24$	6.41951	−	15.4981i	1.31038	−	3.16353i
$25$	−5.16249	+	5.16249i	−1.03250	+	1.03250i
$26$	−11.0355	+	11.0355i	−2.16423	+	2.16423i
$27$	1.25314	−	3.02536i	0.241168	−	0.582230i
$28$	5.85247	+	2.42417i	1.10601	+	0.458126i
$29$	1.13269	+	2.73457i	0.210336	+	0.507796i	0.993475	−	0.114051i	$-0.0363826\pi$
$29$	1.13269	+	2.73457i	0.210336	+	0.507796i	−0.783139	+	0.621847i	$0.786383\pi$
$30$			23.9451i			4.37176i
$31$	−2.87307	+	1.19006i	−0.516018	+	0.213742i	−0.625467	−	0.780251i	$-0.715091\pi$
$31$	−2.87307	+	1.19006i	−0.516018	+	0.213742i	0.109449	+	0.993992i	$0.465091\pi$
$32$	3.66021	+	3.66021i	0.647041	+	0.647041i
$33$	15.8961			2.76715
$34$	−10.4770	+	0.0539620i	−1.79678	+	0.00925441i
$35$	−4.98477			−0.842579
$36$	13.2960	+	13.2960i	2.21599	+	2.21599i
$37$	−9.40668	+	3.89637i	−1.54645	+	0.640560i	−0.982670	−	0.185366i	$-0.940653\pi$
$37$	−9.40668	+	3.89637i	−1.54645	+	0.640560i	−0.563779	+	0.825926i	$0.690653\pi$
$38$		−	3.00586i		−	0.487615i
$39$	−6.31482	−	15.2453i	−1.01118	−	2.44120i
$40$	−20.2308	−	8.37987i	−3.19877	−	1.32497i
$41$	−3.58829	+	8.66290i	−0.560397	+	1.35292i	0.349053	+	0.937103i	$0.386503\pi$
$41$	−3.58829	+	8.66290i	−0.560397	+	1.35292i	−0.909450	+	0.415814i	$0.863497\pi$
$42$	−6.86137	+	6.86137i	−1.05873	+	1.05873i
$43$	1.32542	−	1.32542i	0.202125	−	0.202125i	−0.598785	−	0.800910i	$-0.704350\pi$
$43$	1.32542	−	1.32542i	0.202125	−	0.202125i	0.800910	+	0.598785i	$0.204350\pi$
$44$	−10.0912	+	24.3624i	−1.52131	+	3.67277i
$45$	−13.6701	−	5.66233i	−2.03782	−	0.844091i
$46$	−6.60716	−	15.9511i	−0.974173	−	2.35186i
$47$			1.00000i			0.145865i
$47$			1.00000i			0.145865i
$48$	−17.2546	+	7.14708i	−2.49048	+	1.03159i
$49$	3.52138	+	3.52138i	0.503055	+	0.503055i
$50$	18.5520			2.62365
$51$	4.18655	−	10.2563i	0.586235	−	1.43617i
$52$	27.3738			3.79607
$53$	−2.01312	−	2.01312i	−0.276523	−	0.276523i	0.555196	−	0.831719i	$-0.312643\pi$
$53$	−2.01312	−	2.01312i	−0.276523	−	0.276523i	−0.831719	+	0.555196i	$0.812643\pi$
$54$	−7.68764	+	3.18433i	−1.04616	+	0.433332i
$55$		−	20.7504i		−	2.79798i
$56$	−3.39583	−	8.19827i	−0.453787	−	1.09554i
$57$	2.93629	+	1.21625i	0.388922	+	0.161097i
$58$	2.87826	−	6.94873i	0.377934	−	0.912413i
$59$	5.66981	−	5.66981i	0.738146	−	0.738146i	−0.234073	−	0.972219i	$-0.575205\pi$
$59$	5.66981	−	5.66981i	0.738146	−	0.738146i	0.972219	+	0.234073i	$0.0752054\pi$
$60$	29.6983	−	29.6983i	3.83404	−	3.83404i
$61$	−2.91832	+	7.04544i	−0.373652	+	0.902076i	0.619473	+	0.785018i	$0.287346\pi$
$61$	−2.91832	+	7.04544i	−0.373652	+	0.902076i	−0.993125	+	0.117058i	$0.962654\pi$
$62$	7.30067	+	3.02404i	0.927186	+	0.384053i
$63$	−2.29459	−	5.53962i	−0.289091	−	0.697927i
$64$			0.748892i			0.0936115i
$65$	−19.9009	+	8.24321i	−2.46840	+	1.02244i
$66$	−28.5622	−	28.5622i	−3.51577	−	3.51577i
$67$	−7.90276			−0.965476			−0.482738	−	0.875765i	$-0.660358\pi$
$67$	−7.90276			−0.965476			−0.482738	+	0.875765i	$0.660358\pi$
$68$	13.0612	+	12.9273i	1.58390	+	1.56767i
$69$	18.2554			2.19769
$70$	8.95667	+	8.95667i	1.07053	+	1.07053i
$71$	−1.96989	+	0.815957i	−0.233783	+	0.0968363i	−0.496500	−	0.868037i	$-0.665382\pi$
$71$	−1.96989	+	0.815957i	−0.233783	+	0.0968363i	0.262716	+	0.964873i	$0.415382\pi$
$72$		−	26.3401i		−	3.10421i
$73$	−4.43241	−	10.7008i	−0.518774	−	1.25243i	−0.938657	−	0.344853i	$-0.887929\pi$
$73$	−4.43241	−	10.7008i	−0.518774	−	1.25243i	0.419882	−	0.907579i	$-0.362071\pi$
$74$	23.9030	+	9.90097i	2.77867	+	1.15096i
$75$	−7.50665	+	18.1227i	−0.866794	+	2.09262i
$76$	−3.72807	+	3.72807i	−0.427639	+	0.427639i
$77$	5.94594	−	5.94594i	0.677602	−	0.677602i
$78$	−16.0464	+	38.7394i	−1.81690	+	4.38638i
$79$	−3.62804	−	1.50278i	−0.408186	−	0.169076i	0.169136	−	0.985593i	$-0.445902\pi$
$79$	−3.62804	−	1.50278i	−0.408186	−	0.169076i	−0.577322	+	0.816516i	$0.695902\pi$
$80$	9.32963	+	22.5237i	1.04308	+	2.51823i
$81$			3.85818i			0.428687i
$82$	22.0130	−	9.11810i	2.43093	−	1.00693i
$83$	−3.29615	−	3.29615i	−0.361799	−	0.361799i	0.502676	−	0.864475i	$-0.332349\pi$
$83$	−3.29615	−	3.29615i	−0.361799	−	0.361799i	−0.864475	+	0.502676i	$0.832349\pi$
$84$	17.0199			1.85702
$85$	−13.3884	−	5.46502i	−1.45217	−	0.592765i
$86$	−4.76306			−0.513614
$87$	5.62329	+	5.62329i	0.602880	+	0.602880i
$88$	34.1274	−	14.1360i	3.63799	−	1.50691i
$89$			10.7114i			1.13541i	0.823232	+	0.567705i	$0.192168\pi$
$89$			10.7114i			1.13541i	−0.823232	+	0.567705i	$0.807832\pi$
$90$	14.3884	+	34.7367i	1.51667	+	3.66156i
$91$	−8.06457	−	3.34045i	−0.845396	−	0.350175i
$92$	−11.5890	+	27.9783i	−1.20823	+	2.91694i
$93$	−5.90810	+	5.90810i	−0.612641	+	0.612641i
$94$	1.79681	−	1.79681i	0.185327	−	0.185327i
$95$	1.58767	−	3.83297i	0.162891	−	0.393254i
$96$	12.8490	+	5.32223i	1.31139	+	0.543198i
$97$	1.26062	+	3.04341i	0.127997	+	0.309012i	0.974867	−	0.222788i	$-0.0715158\pi$
$97$	1.26062	+	3.04341i	0.127997	+	0.309012i	−0.846870	+	0.531800i	$0.821516\pi$
$98$		−	12.6545i		−	1.27830i
$99$	23.0601	−	9.55181i	2.31763	−	0.959993i
$100$	−23.0095	−	23.0095i	−2.30095	−	2.30095i
$101$	−1.16290			−0.115713			−0.0578567	−	0.998325i	$-0.518427\pi$
$101$	−1.16290			−0.115713			−0.0578567	+	0.998325i	$0.518427\pi$
$102$	−25.9511	+	10.9062i	−2.56954	+	1.07988i
$103$	8.69863			0.857101			0.428551	−	0.903518i	$-0.359024\pi$
$103$	8.69863			0.857101			0.428551	+	0.903518i	$0.359024\pi$
$104$	−27.1146	−	27.1146i	−2.65881	−	2.65881i
$105$	−12.3735	+	5.12527i	−1.20753	+	0.500175i
$106$			7.23438i			0.702665i
$107$	6.67770	+	16.1214i	0.645557	+	1.55851i	0.819078	+	0.573683i	$0.194486\pi$
$107$	6.67770	+	16.1214i	0.645557	+	1.55851i	−0.173520	+	0.984830i	$0.555514\pi$
$108$	13.4841	+	5.58531i	1.29751	+	0.537447i
$109$	−3.33905	+	8.06117i	−0.319823	+	0.772120i	0.679440	+	0.733731i	$0.262223\pi$
$109$	−3.33905	+	8.06117i	−0.319823	+	0.772120i	−0.999263	+	0.0383893i	$0.987777\pi$
$110$	−37.2845	+	37.2845i	−3.55493	+	3.55493i
$111$	−19.3436	+	19.3436i	−1.83602	+	1.83602i
$112$	−3.78071	+	9.12744i	−0.357244	+	0.862462i
$113$	2.02808	+	0.840058i	0.190786	+	0.0790260i	0.476031	−	0.879429i	$-0.342075\pi$
$113$	2.02808	+	0.840058i	0.190786	+	0.0790260i	−0.285245	+	0.958455i	$0.592075\pi$
$114$	−3.09059	−	7.46133i	−0.289460	−	0.698818i
$115$		−	23.8301i		−	2.22217i
$116$	−12.1881	+	5.04847i	−1.13164	+	0.468739i
$117$	−18.3215	−	18.3215i	−1.69383	−	1.69383i
$118$	−20.3751			−1.87568
$119$	−2.27040	−	5.40236i	−0.208127	−	0.495234i
$120$	−58.8342			−5.37080
$121$	16.9733	+	16.9733i	1.54303	+	1.54303i
$122$	17.9030	−	7.41565i	1.62086	−	0.671381i
$123$			25.1930i			2.27158i
$124$	−5.30416	−	12.8054i	−0.476328	−	1.14996i
$125$	7.45547	+	3.08816i	0.666837	+	0.276213i
$126$	−5.83071	+	14.0766i	−0.519441	+	1.25404i
$127$	−4.73396	+	4.73396i	−0.420071	+	0.420071i	−0.885228	−	0.465157i	$-0.845998\pi$
$127$	−4.73396	+	4.73396i	−0.420071	+	0.420071i	0.465157	+	0.885228i	$0.345998\pi$
$128$	8.66604	−	8.66604i	0.765977	−	0.765977i
$129$	1.92726	−	4.65282i	0.169686	−	0.409658i
$130$	50.5695	+	20.9466i	4.43524	+	1.83714i
$131$	3.80266	+	9.18044i	0.332240	+	0.802099i	0.998414	+	0.0563020i	$0.0179310\pi$
$131$	3.80266	+	9.18044i	0.332240	+	0.802099i	−0.666174	+	0.745797i	$0.732069\pi$
$132$			70.8496i			6.16667i
$133$	1.55326	−	0.643382i	0.134685	−	0.0557883i
$134$	14.1998	+	14.1998i	1.22667	+	1.22667i
$135$	−11.4849			−0.988467
$136$	−0.132587	−	25.7424i	−0.0113692	−	2.20739i
$137$	4.41024			0.376792			0.188396	−	0.982093i	$-0.439671\pi$
$137$	4.41024			0.376792			0.188396	+	0.982093i	$0.439671\pi$
$138$	−32.8014	−	32.8014i	−2.79224	−	2.79224i
$139$	8.56705	−	3.54859i	0.726648	−	0.300987i	0.0114742	−	0.999934i	$-0.496348\pi$
$139$	8.56705	−	3.54859i	0.726648	−	0.300987i	0.715174	+	0.698947i	$0.246348\pi$
$140$		−	22.2173i		−	1.87771i
$141$	1.02819	+	2.48226i	0.0865889	+	0.209044i
$142$	5.00564	+	2.07340i	0.420064	+	0.173996i
$143$	13.9055	−	33.5709i	1.16284	−	2.80734i
$144$	−20.7362	+	20.7362i	−1.72802	+	1.72802i
$145$	7.34051	−	7.34051i	0.609596	−	0.609596i
$146$	−11.2631	+	27.1915i	−0.932138	+	2.25038i
$147$	12.3616	+	5.12036i	1.01957	+	0.422320i
$148$	−17.3663	−	41.9260i	−1.42750	−	3.44629i
$149$		−	16.5630i		−	1.35689i	−0.734651	−	0.678445i	$-0.762654\pi$
$149$		−	16.5630i		−	1.35689i	0.734651	−	0.678445i	$-0.237346\pi$
$150$	46.0510	−	19.0749i	3.76005	−	1.55746i
$151$	3.63868	+	3.63868i	0.296111	+	0.296111i	0.839489	−	0.543377i	$-0.182855\pi$
$151$	3.63868	+	3.63868i	0.296111	+	0.296111i	−0.543377	+	0.839489i	$0.682855\pi$
$152$	7.38553			0.599046
$153$	−0.0895899	−	17.3943i	−0.00724292	−	1.40624i
$154$	−21.3674			−1.72184
$155$	7.71229	+	7.71229i	0.619466	+	0.619466i
$156$	67.9490	−	28.1454i	5.44028	−	2.25344i
$157$			6.08770i			0.485852i	0.970045	+	0.242926i	$0.0781071\pi$
$157$			6.08770i			0.485852i	−0.970045	+	0.242926i	$0.921893\pi$
$158$	3.81868	+	9.21910i	0.303798	+	0.733432i
$159$	−7.06695	−	2.92723i	−0.560446	−	0.232144i
$160$	6.94751	−	16.7728i	0.549249	−	1.32600i
$161$	6.82843	−	6.82843i	0.538155	−	0.538155i
$162$	6.93241	−	6.93241i	0.544662	−	0.544662i
$163$	−0.0123194	+	0.0297417i	−0.000964932	+	0.00232955i	−0.924361	−	0.381518i	$-0.875401\pi$
$163$	−0.0123194	+	0.0297417i	−0.000964932	+	0.00232955i	0.923396	+	0.383848i	$0.125401\pi$
$164$	−38.6109	−	15.9932i	−3.01501	−	1.24886i
$165$	−21.3353	−	51.5079i	−1.66095	−	4.00988i
$166$			11.8451i			0.919358i
$167$	6.05387	−	2.50759i	0.468462	−	0.194043i	−0.135949	−	0.990716i	$-0.543408\pi$
$167$	6.05387	−	2.50759i	0.468462	−	0.194043i	0.604411	+	0.796672i	$0.293408\pi$
$168$	−16.8587	−	16.8587i	−1.30068	−	1.30068i
$169$	−24.7205			−1.90158
$170$	14.2367	+	33.8759i	1.09191	+	2.59817i
$171$	4.99045			0.381629
$172$	5.90746	+	5.90746i	0.450440	+	0.450440i
$173$	2.93824	−	1.21706i	0.223390	−	0.0925312i	−0.268181	−	0.963368i	$-0.586423\pi$
$173$	2.93824	−	1.21706i	0.223390	−	0.0925312i	0.491571	+	0.870837i	$0.336423\pi$
$174$		−	20.2079i		−	1.53196i
$175$	3.97092	+	9.58665i	0.300173	+	0.724683i
$176$	−37.9953	−	15.7382i	−2.86401	−	1.18631i
$177$	8.24433	−	19.9036i	0.619682	−	1.49604i
$178$	19.2464	−	19.2464i	1.44258	−	1.44258i
$179$	−5.31912	+	5.31912i	−0.397570	+	0.397570i	−0.877375	−	0.479805i	$-0.840707\pi$
$179$	−5.31912	+	5.31912i	−0.397570	+	0.397570i	0.479805	+	0.877375i	$0.340707\pi$
$180$	25.2373	−	60.9282i	1.88107	−	4.54132i
$181$	−13.2784	−	5.50009i	−0.986976	−	0.408819i	−0.169971	−	0.985449i	$-0.554367\pi$
$181$	−13.2784	−	5.50009i	−0.986976	−	0.408819i	−0.817005	+	0.576630i	$0.804367\pi$
$182$	8.48833	+	20.4926i	0.629197	+	1.51902i
$183$			20.4892i			1.51460i
$184$	39.1926	−	16.2341i	2.88931	−	1.19679i
$185$	25.2507	+	25.2507i	1.85647	+	1.85647i
$186$	21.2314			1.55676
$187$	22.4887	−	9.45113i	1.64454	−	0.691135i
$188$	−4.45704			−0.325063
$189$	−3.29096	−	3.29096i	−0.239382	−	0.239382i
$190$	−9.73985	+	4.03438i	−0.706603	+	0.292684i
$191$		−	22.7703i		−	1.64760i	−0.566881	−	0.823799i	$-0.691850\pi$
$191$		−	22.7703i		−	1.64760i	0.566881	−	0.823799i	$-0.308150\pi$
$192$	0.770000	+	1.85895i	0.0555700	+	0.134158i
$193$	3.47195	+	1.43813i	0.249916	+	0.103519i	0.504125	−	0.863631i	$-0.331815\pi$
$193$	3.47195	+	1.43813i	0.249916	+	0.103519i	−0.254209	+	0.967149i	$0.581815\pi$
$194$	3.20333	−	7.73353i	0.229986	−	0.555235i
$195$	−40.9236	+	40.9236i	−2.93060	+	2.93060i
$196$	−15.6950	+	15.6950i	−1.12107	+	1.12107i
$197$	1.40750	−	3.39800i	0.100280	−	0.242097i	−0.865775	−	0.500433i	$-0.833174\pi$
$197$	1.40750	−	3.39800i	0.100280	−	0.242097i	0.966055	+	0.258336i	$0.0831741\pi$
$198$	−58.5974	−	24.2718i	−4.16434	−	1.72492i
$199$	−2.20575	−	5.32515i	−0.156361	−	0.377490i	0.826213	−	0.563357i	$-0.190490\pi$
$199$	−2.20575	−	5.32515i	−0.156361	−	0.377490i	−0.982575	+	0.185867i	$0.940490\pi$
$200$			45.5831i			3.22321i
$201$	−19.6167	+	8.12552i	−1.38366	+	0.573130i
$202$	2.08952	+	2.08952i	0.147018	+	0.147018i
$203$	4.20678			0.295258
$204$	45.7129	+	18.6596i	3.20054	+	1.30644i
$205$	32.8864			2.29688
$206$	−15.6298	−	15.6298i	−1.08898	−	1.08898i
$207$	26.4827	−	10.9695i	1.84067	−	0.762432i
$208$			42.6919i			2.96015i
$209$	2.67824	+	6.46585i	0.185258	+	0.447252i
$210$	31.4419	+	13.0237i	2.16970	+	0.898719i
$211$	−3.42975	+	8.28016i	−0.236114	+	0.570030i	−0.996874	−	0.0790032i	$-0.974826\pi$
$211$	−3.42975	+	8.28016i	−0.236114	+	0.570030i	0.760760	+	0.649033i	$0.224826\pi$
$212$	8.97256	−	8.97256i	0.616238	−	0.616238i
$213$	−4.05084	+	4.05084i	−0.277559	+	0.277559i
$214$	16.9685	−	40.9656i	1.15994	−	2.80035i
$215$	−6.07369	−	2.51580i	−0.414222	−	0.171576i
$216$	−7.82403	−	18.8889i	−0.532358	−	1.28523i
$217$			4.41985i			0.300039i
$218$	20.4840	−	8.48476i	1.38735	−	0.574660i
$219$	−22.0048	−	22.0048i	−1.48695	−	1.48695i
$220$	92.4854			6.23536
$221$	−17.9980	−	17.8135i	−1.21067	−	1.19827i
$222$	69.5137			4.66545
$223$	−17.7790	−	17.7790i	−1.19057	−	1.19057i	−0.976907	−	0.213666i	$-0.931460\pi$
$223$	−17.7790	−	17.7790i	−1.19057	−	1.19057i	−0.213666	−	0.976907i	$-0.568540\pi$
$224$	6.79695	−	2.81539i	0.454140	−	0.188111i
$225$			30.8008i			2.05339i
$226$	−2.13465	−	5.15350i	−0.141995	−	0.342805i
$227$	−1.58284	−	0.655634i	−0.105057	−	0.0435160i	0.329536	−	0.944143i	$-0.393108\pi$
$227$	−1.58284	−	0.655634i	−0.105057	−	0.0435160i	−0.434593	+	0.900627i	$0.643108\pi$
$228$	−5.42089	+	13.0872i	−0.359007	+	0.866720i
$229$	−20.0767	+	20.0767i	−1.32671	+	1.32671i	−0.418481	+	0.908226i	$0.637437\pi$
$229$	−20.0767	+	20.0767i	−1.32671	+	1.32671i	−0.908226	+	0.418481i	$0.862563\pi$
$230$	−42.8182	+	42.8182i	−2.82335	+	2.82335i
$231$	8.64584	−	20.8729i	0.568854	−	1.37334i
$232$	17.0733	+	7.07201i	1.12092	+	0.464300i
$233$	−5.62207	−	13.5729i	−0.368314	−	0.889188i	−0.994027	−	0.109135i	$-0.965192\pi$
$233$	−5.62207	−	13.5729i	−0.368314	−	0.889188i	0.625713	−	0.780053i	$-0.284808\pi$
$234$			65.8406i			4.30413i
$235$	3.24029	−	1.34217i	0.211373	−	0.0875535i
$236$	25.2706	+	25.2706i	1.64498	+	1.64498i
$237$	−10.5509			−0.685353
$238$	−5.62753	+	13.7865i	−0.364779	+	0.893645i
$239$	11.0859			0.717089			0.358544	−	0.933513i	$-0.383273\pi$
$239$	11.0859			0.717089			0.358544	+	0.933513i	$0.383273\pi$
$240$	46.3171	+	46.3171i	2.98976	+	2.98976i
$241$	12.1565	−	5.03539i	0.783070	−	0.324358i	0.0449163	−	0.998991i	$-0.485698\pi$
$241$	12.1565	−	5.03539i	0.783070	−	0.324358i	0.738154	+	0.674632i	$0.235698\pi$
$242$		−	60.9956i		−	3.92095i
$243$	7.72636	+	18.6531i	0.495646	+	1.19660i
$244$	−31.4018	−	13.0071i	−2.01030	−	0.832692i
$245$	6.68399	−	16.1366i	0.427024	−	1.03093i
$246$	45.2670	−	45.2670i	2.88612	−	2.88612i
$247$	5.13719	−	5.13719i	0.326872	−	0.326872i
$248$	−7.43019	+	17.9381i	−0.471817	+	1.13907i
$249$	−11.5710	−	4.79285i	−0.733280	−	0.303734i
$250$	−7.84722	−	18.9449i	−0.496302	−	1.19818i
$251$		−	8.50375i		−	0.536752i	−0.963314	−	0.268376i	$-0.913513\pi$
$251$		−	8.50375i		−	0.536752i	0.963314	−	0.268376i	$-0.0864869\pi$
$252$	24.6903	−	10.2271i	1.55535	−	0.644245i
$253$	28.4251	+	28.4251i	1.78707	+	1.78707i
$254$	17.0120			1.06743
$255$	−38.8525	+	0.200111i	−2.43304	+	0.0125314i
$256$	−29.6447			−1.85279
$257$	−10.5206	−	10.5206i	−0.656255	−	0.656255i	0.298237	−	0.954492i	$-0.403602\pi$
$257$	−10.5206	−	10.5206i	−0.656255	−	0.656255i	−0.954492	+	0.298237i	$0.903602\pi$
$258$	−11.8232	+	4.89731i	−0.736078	+	0.304893i
$259$			14.4710i			0.899183i
$260$	−36.7403	−	88.6990i	−2.27854	−	5.50088i
$261$	11.5366	+	4.77860i	0.714095	+	0.295788i
$262$	9.66284	−	23.3282i	0.596972	−	1.44122i
$263$	6.75362	−	6.75362i	0.416446	−	0.416446i	−0.467531	−	0.883977i	$-0.654856\pi$
$263$	6.75362	−	6.75362i	0.416446	−	0.416446i	0.883977	+	0.467531i	$0.154856\pi$
$264$	70.1787	−	70.1787i	4.31920	−	4.31920i
$265$	−3.82113	+	9.22503i	−0.234730	+	0.566689i
$266$	−3.94695	−	1.63488i	−0.242003	−	0.100241i
$267$	11.0133	+	26.5886i	0.674006	+	1.62719i
$268$		−	35.2230i		−	2.15159i
$269$	8.78158	−	3.63745i	0.535423	−	0.221779i	−0.0985537	−	0.995132i	$-0.531422\pi$
$269$	8.78158	−	3.63745i	0.535423	−	0.221779i	0.633976	+	0.773352i	$0.281422\pi$
$270$	20.6363	+	20.6363i	1.25588	+	1.25588i
$271$	16.2213			0.985372			0.492686	−	0.870207i	$-0.336015\pi$
$271$	16.2213			0.985372			0.492686	+	0.870207i	$0.336015\pi$
$272$	−20.1613	+	20.3700i	−1.22246	+	1.23511i
$273$	−23.4530			−1.41944
$274$	−7.92435	−	7.92435i	−0.478728	−	0.478728i
$275$	−39.9069	+	16.5300i	−2.40648	+	0.996795i
$276$			81.3650i			4.89760i
$277$	6.74005	+	16.2719i	0.404970	+	0.977685i	0.986441	+	0.164118i	$0.0524776\pi$
$277$	6.74005	+	16.2719i	0.404970	+	0.977685i	−0.581470	+	0.813568i	$0.697522\pi$
$278$	−21.7695	−	9.01722i	−1.30565	−	0.540817i
$279$	−5.02063	+	12.1209i	−0.300577	+	0.725657i
$280$	−22.0069	+	22.0069i	−1.31517	+	1.31517i
$281$	7.71917	−	7.71917i	0.460487	−	0.460487i	−0.438328	−	0.898815i	$-0.644429\pi$
$281$	7.71917	−	7.71917i	0.460487	−	0.460487i	0.898815	+	0.438328i	$0.144429\pi$
$282$	2.61270	−	6.30760i	0.155584	−	0.375612i
$283$	8.03935	+	3.33001i	0.477890	+	0.197948i	0.608608	−	0.793471i	$-0.291728\pi$
$283$	8.03935	+	3.33001i	0.477890	+	0.197948i	−0.130718	+	0.991420i	$0.541728\pi$
$284$	−3.63676	−	8.77990i	−0.215802	−	0.520991i
$285$		−	11.1468i		−	0.660282i
$286$	−85.3059	+	35.3349i	−5.04425	+	2.08939i
$287$	9.42345	+	9.42345i	0.556249	+	0.556249i
$288$	21.8378			1.28681
$289$	−0.175114	−	16.9991i	−0.0103008	−	0.999947i
$290$	−26.3790			−1.54903
$291$	6.25839	+	6.25839i	0.366874	+	0.366874i
$292$	47.6939	−	19.7554i	2.79107	−	1.15610i
$293$			14.9204i			0.871662i	0.900029	+	0.435831i	$0.143545\pi$
$293$			14.9204i			0.871662i	−0.900029	+	0.435831i	$0.856455\pi$
$294$	−13.0112	−	31.4118i	−0.758828	−	1.83197i
$295$	−25.9816	−	10.7619i	−1.51271	−	0.626585i
$296$	−24.3271	+	58.7308i	−1.41398	+	3.41366i
$297$	13.6995	−	13.6995i	0.794925	−	0.794925i
$298$	−29.7605	+	29.7605i	−1.72398	+	1.72398i
$299$	15.9693	−	38.5534i	0.923531	−	2.22960i
$300$	−80.7735	−	33.4575i	−4.66346	−	1.93167i
$301$	−1.01950	−	2.46128i	−0.0587628	−	0.141866i
$302$		−	13.0760i		−	0.752440i
$303$	−2.88663	+	1.19568i	−0.165833	+	0.0686902i
$304$	−5.81425	−	5.81425i	−0.333470	−	0.333470i
$305$	26.7461			1.53148
$306$	−31.0932	+	31.4152i	−1.77748	+	1.79589i
$307$	4.51017			0.257409			0.128705	−	0.991683i	$-0.458918\pi$
$307$	4.51017			0.257409			0.128705	+	0.991683i	$0.458918\pi$
$308$	26.5013	+	26.5013i	1.51005	+	1.51005i
$309$	21.5923	−	8.94381i	1.22834	−	0.508796i
$310$		−	27.7150i		−	1.57411i
$311$	2.90378	+	7.01035i	0.164658	+	0.397520i	0.984575	−	0.174962i	$-0.0559804\pi$
$311$	2.90378	+	7.01035i	0.164658	+	0.397520i	−0.819917	+	0.572483i	$0.805980\pi$
$312$	−95.1845	−	39.4267i	−5.38876	−	2.23210i
$313$	−0.820646	+	1.98121i	−0.0463856	+	0.111985i	−0.945374	−	0.325988i	$-0.894303\pi$
$313$	−0.820646	+	1.98121i	−0.0463856	+	0.111985i	0.898988	+	0.437972i	$0.144303\pi$
$314$	10.9384	−	10.9384i	0.617292	−	0.617292i
$315$	−14.8702	+	14.8702i	−0.837843	+	0.837843i
$316$	6.69797	−	16.1703i	0.376790	−	0.909652i
$317$	−30.8203	−	12.7662i	−1.73104	−	0.717020i	−0.999375	−	0.0353547i	$-0.988744\pi$
$317$	−30.8203	−	12.7662i	−1.73104	−	0.717020i	−0.731664	−	0.681665i	$-0.761256\pi$
$318$	7.43829	+	17.9576i	0.417119	+	1.00701i
$319$			17.5118i			0.980474i
$320$	2.42662	−	1.00514i	0.135652	−	0.0561890i
$321$	33.1516	+	33.1516i	1.85034	+	1.85034i
$322$	−24.5388			−1.36749
$323$	4.87720	−	0.0251202i	0.271375	−	0.00139773i
$324$	−17.1961			−0.955338
$325$	31.7065	+	31.7065i	1.75876	+	1.75876i
$326$	0.0755758	−	0.0313045i	0.00418576	−	0.00173380i
$327$			23.4431i			1.29641i
$328$	22.4036	+	54.0870i	1.23703	+	2.98646i
$329$	1.31308	+	0.543897i	0.0723926	+	0.0299860i
$330$	−54.2144	+	130.885i	−2.98441	+	7.20499i
$331$	−15.7262	+	15.7262i	−0.864391	+	0.864391i	−0.991845	−	0.127453i	$-0.959320\pi$
$331$	−15.7262	+	15.7262i	−0.864391	+	0.864391i	0.127453	+	0.991845i	$0.459320\pi$
$332$	14.6911	−	14.6911i	0.806278	−	0.806278i
$333$	−16.4380	+	39.6848i	−0.900796	+	2.17471i
$334$	−15.3833	−	6.37198i	−0.841737	−	0.348659i
$335$	10.6069	+	25.6072i	0.579514	+	1.39907i
$336$			26.5440i			1.44809i
$337$	8.48465	−	3.51446i	0.462188	−	0.191445i	−0.139424	−	0.990233i	$-0.544525\pi$
$337$	8.48465	−	3.51446i	0.462188	−	0.191445i	0.601612	+	0.798788i	$0.294525\pi$
$338$	44.4180	+	44.4180i	2.41602	+	2.41602i
$339$	5.89796			0.320333
$340$	24.3579	−	59.6725i	1.32099	−	3.23620i
$341$	−18.3988			−0.996349
$342$	−8.96689	−	8.96689i	−0.484874	−	0.484874i
$343$	15.7307	−	6.51588i	0.849379	−	0.351824i
$344$		−	11.7030i		−	0.630986i
$345$	−24.5018	−	59.1526i	−1.31913	−	3.18467i
$346$	−7.46627	−	3.09263i	−0.401389	−	0.166261i
$347$	7.05474	−	17.0316i	0.378718	−	0.914306i	−0.613489	−	0.789704i	$-0.710234\pi$
$347$	7.05474	−	17.0316i	0.378718	−	0.914306i	0.992207	−	0.124603i	$-0.0397657\pi$
$348$	−25.0632	+	25.0632i	−1.34353	+	1.34353i
$349$	15.9587	−	15.9587i	0.854251	−	0.854251i	−0.136402	−	0.990654i	$-0.543554\pi$
$349$	15.9587	−	15.9587i	0.854251	−	0.854251i	0.990654	+	0.136402i	$0.0435540\pi$
$350$	10.0904	−	24.3604i	0.539354	−	1.30212i
$351$	−18.5808	−	7.69643i	−0.991772	−	0.410805i
$352$	11.7198	+	28.2940i	0.624666	+	1.50808i
$353$			0.399123i			0.0212432i	0.999944	+	0.0106216i	$0.00338102\pi$
$353$			0.399123i			0.0212432i	−0.999944	+	0.0106216i	$0.996619\pi$
$354$	−50.5764	+	20.9494i	−2.68810	+	1.11345i
$355$	5.28787	+	5.28787i	0.280651	+	0.280651i
$356$	−47.7413			−2.53028
$357$	−11.1904	−	11.0757i	−0.592257	−	0.586187i
$358$	19.1149			1.01025
$359$	10.3916	+	10.3916i	0.548450	+	0.548450i	0.925992	−	0.377543i	$-0.123231\pi$
$359$	10.3916	+	10.3916i	0.548450	+	0.548450i	−0.377543	+	0.925992i	$0.623231\pi$
$360$	−85.3495	+	35.3529i	−4.49831	+	1.86326i
$361$		−	17.6007i		−	0.926354i
$362$	13.9761	+	33.7414i	0.734569	+	1.77341i
$363$	59.5840	+	24.6805i	3.12735	+	1.29539i
$364$	14.8885	−	35.9441i	0.780372	−	1.88398i
$365$	−28.7245	+	28.7245i	−1.50351	+	1.50351i
$366$	36.8152	−	36.8152i	1.92436	−	1.92436i
$367$	−4.49162	+	10.8437i	−0.234461	+	0.566038i	−0.996692	−	0.0812659i	$-0.974104\pi$
$367$	−4.49162	+	10.8437i	−0.234461	+	0.566038i	0.762232	+	0.647304i	$0.224104\pi$
$368$	−43.6346	−	18.0740i	−2.27461	−	0.942174i
$369$	15.1382	+	36.5470i	0.788065	+	1.90256i
$370$		−	90.7415i		−	4.71742i
$371$	−3.73832	+	1.54846i	−0.194084	+	0.0803922i
$372$	−26.3326	−	26.3326i	−1.36528	−	1.36528i
$373$	−25.9721			−1.34478			−0.672391	−	0.740196i	$-0.734733\pi$
$373$	−25.9721			−1.34478			−0.672391	+	0.740196i	$0.734733\pi$
$374$	−57.3898	−	23.4261i	−2.96756	−	1.21133i
$375$	21.6816			1.11963
$376$	4.41484	+	4.41484i	0.227678	+	0.227678i
$377$	16.7949	−	6.95667i	0.864981	−	0.358287i
$378$			11.8265i			0.608288i
$379$	−4.83226	−	11.6661i	−0.248217	−	0.599248i	0.749836	−	0.661624i	$-0.230132\pi$
$379$	−4.83226	−	11.6661i	−0.248217	−	0.599248i	−0.998053	+	0.0623755i	$0.980132\pi$
$380$	17.0837	+	7.07630i	0.876376	+	0.363007i
$381$	−6.88353	+	16.6183i	−0.352654	+	0.851382i
$382$	−40.9138	+	40.9138i	−2.09333	+	2.09333i
$383$	7.03000	−	7.03000i	0.359216	−	0.359216i	−0.504308	−	0.863524i	$-0.668252\pi$
$383$	7.03000	−	7.03000i	0.359216	−	0.359216i	0.863524	+	0.504308i	$0.168252\pi$
$384$	12.6011	−	30.4217i	0.643046	−	1.55245i
$385$	−27.2470	−	11.2861i	−1.38863	−	0.575191i
$386$	−3.65439	−	8.82247i	−0.186003	−	0.449052i
$387$		−	7.90782i		−	0.401977i
$388$	−13.5646	+	5.61865i	−0.688640	+	0.285244i
$389$	8.86773	+	8.86773i	0.449612	+	0.449612i	0.895225	−	0.445614i	$-0.147014\pi$
$389$	8.86773	+	8.86773i	0.449612	+	0.449612i	−0.445614	+	0.895225i	$0.647014\pi$
$390$	147.064			7.44686
$391$	25.8265	−	10.8539i	1.30610	−	0.548903i
$392$	31.0927			1.57042
$393$	18.8784	+	18.8784i	0.952290	+	0.952290i
$394$	−8.63456	+	3.57655i	−0.435003	+	0.180184i
$395$			13.7729i			0.692988i
$396$	42.5728	+	102.780i	2.13937	+	5.16489i
$397$	16.0845	+	6.66243i	0.807259	+	0.334378i	0.747860	−	0.663857i	$-0.231082\pi$
$397$	16.0845	+	6.66243i	0.807259	+	0.334378i	0.0593991	+	0.998234i	$0.481082\pi$
$398$	−5.60496	+	13.5316i	−0.280951	+	0.678277i
$399$	3.19408	−	3.19408i	0.159904	−	0.159904i
$400$	35.8853	−	35.8853i	1.79426	−	1.79426i
$401$	−7.76033	+	18.7351i	−0.387533	+	0.935587i	0.602929	+	0.797795i	$0.294000\pi$
$401$	−7.76033	+	18.7351i	−0.387533	+	0.935587i	−0.990461	+	0.137791i	$0.956000\pi$
$402$	49.8475	+	20.6475i	2.48617	+	1.02980i
$403$	7.30902	+	17.6455i	0.364088	+	0.878986i
$404$		−	5.18312i		−	0.257870i
$405$	12.5016	−	5.17833i	0.621210	−	0.257314i
$406$	−7.55879	−	7.55879i	−0.375136	−	0.375136i
$407$	−60.2392			−2.98595
$408$	−26.7971	−	63.7630i	−1.32665	−	3.15674i
$409$	−24.6246			−1.21761			−0.608805	−	0.793320i	$-0.708351\pi$
$409$	−24.6246			−1.21761			−0.608805	+	0.793320i	$0.708351\pi$
$410$	−59.0905	−	59.0905i	−2.91827	−	2.91827i
$411$	10.9474	−	4.53455i	0.539994	−	0.223673i
$412$			38.7702i			1.91007i
$413$	−4.36114	−	10.5287i	−0.214598	−	0.518085i
$414$	−67.2944	−	27.8742i	−3.30734	−	1.36994i
$415$	−6.25647	+	15.1045i	−0.307118	+	0.741448i
$416$	22.4799	−	22.4799i	1.10217	−	1.10217i
$417$	17.6171	−	17.6171i	0.862711	−	0.862711i
$418$	6.80561	−	16.4302i	0.332873	−	0.803627i
$419$	20.1097	+	8.32972i	0.982425	+	0.406934i	0.815323	−	0.579006i	$-0.196559\pi$
$419$	20.1097	+	8.32972i	0.982425	+	0.406934i	0.167101	+	0.985940i	$0.446559\pi$
$420$	−22.8436	−	55.1492i	−1.11465	−	2.69101i
$421$			1.79941i			0.0876978i	0.999038	+	0.0438489i	$0.0139620\pi$
$421$			1.79941i			0.0876978i	−0.999038	+	0.0438489i	$0.986038\pi$
$422$	21.0405	−	8.71525i	1.02423	−	0.424252i
$423$	2.98314	+	2.98314i	0.145045	+	0.145045i
$424$	−17.7752			−0.863239
$425$	0.155041	+	30.1018i	0.00752058	+	1.46015i
$426$	14.5572			0.705297
$427$	7.66398	+	7.66398i	0.370886	+	0.370886i
$428$	−71.8537	+	29.7628i	−3.47318	+	1.43864i
$429$		−	97.6291i		−	4.71358i
$430$	6.39284	+	15.4337i	0.308290	+	0.744278i
$431$	−1.73427	−	0.718359i	−0.0835369	−	0.0346021i	0.340524	−	0.940236i	$-0.389396\pi$
$431$	−1.73427	−	0.718359i	−0.0835369	−	0.0346021i	−0.424061	+	0.905634i	$0.639396\pi$
$432$	−8.71079	+	21.0297i	−0.419098	+	1.01179i
$433$	−1.48413	+	1.48413i	−0.0713230	+	0.0713230i	−0.741868	−	0.670545i	$-0.766060\pi$
$433$	−1.48413	+	1.48413i	−0.0713230	+	0.0713230i	0.670545	+	0.741868i	$0.266060\pi$
$434$	7.94162	−	7.94162i	0.381210	−	0.381210i
$435$	10.6736	−	25.7685i	0.511762	−	1.23550i
$436$	−35.9290	−	14.8823i	−1.72069	−	0.712732i
$437$	3.07574	+	7.42550i	0.147133	+	0.355210i
$438$			79.0768i			3.77844i
$439$	5.26144	−	2.17936i	0.251115	−	0.104015i	−0.253576	−	0.967316i	$-0.581607\pi$
$439$	5.26144	−	2.17936i	0.251115	−	0.104015i	0.504690	+	0.863300i	$0.331607\pi$
$440$	−91.6096	−	91.6096i	−4.36731	−	4.36731i
$441$	21.0095			1.00045
$442$	0.331419	+	64.3464i	0.0157640	+	3.06065i
$443$	−34.2097			−1.62535			−0.812676	−	0.582716i	$-0.801990\pi$
$443$	−34.2097			−1.62535			−0.812676	+	0.582716i	$0.801990\pi$
$444$	−86.2155	−	86.2155i	−4.09160	−	4.09160i
$445$	34.7081	−	14.3766i	1.64532	−	0.681514i
$446$			63.8911i			3.02533i
$447$	−17.0298	−	41.1136i	−0.805482	−	1.94461i
$448$	0.983357	+	0.407320i	0.0464593	+	0.0192441i
$449$	8.53042	−	20.5943i	0.402576	−	0.971903i	−0.584463	−	0.811420i	$-0.698695\pi$
$449$	8.53042	−	20.5943i	0.402576	−	0.971903i	0.987039	−	0.160483i	$-0.0513052\pi$
$450$	55.3432	−	55.3432i	2.60890	−	2.60890i
$451$	−39.2275	+	39.2275i	−1.84715	+	1.84715i
$452$	−3.74418	+	9.03924i	−0.176111	+	0.425170i
$453$	12.7734	+	5.29091i	0.600146	+	0.248589i
$454$	1.66601	+	4.02211i	0.0781899	+	0.188767i
$455$			30.6150i			1.43525i
$456$	18.3328	−	7.59370i	0.858513	−	0.355608i
$457$	−25.4755	−	25.4755i	−1.19169	−	1.19169i	−0.976592	−	0.215101i	$-0.930992\pi$
$457$	−25.4755	−	25.4755i	−1.19169	−	1.19169i	−0.215101	−	0.976592i	$-0.569008\pi$
$458$	72.1480			3.37126
$459$	−5.23102	−	12.4471i	−0.244163	−	0.580980i
$460$	106.212			4.95216
$461$	−7.52732	−	7.52732i	−0.350582	−	0.350582i	0.509744	−	0.860326i	$-0.329740\pi$
$461$	−7.52732	−	7.52732i	−0.350582	−	0.350582i	−0.860326	+	0.509744i	$0.829740\pi$
$462$	−53.0395	+	21.9697i	−2.46762	+	1.02212i
$463$		−	8.91714i		−	0.414414i	−0.978297	−	0.207207i	$-0.933563\pi$
$463$		−	8.91714i		−	0.414414i	0.978297	−	0.207207i	$-0.0664374\pi$
$464$	−7.87353	−	19.0084i	−0.365520	−	0.882442i
$465$	27.0736	+	11.2142i	1.25551	+	0.520048i
$466$	−14.2861	+	34.4896i	−0.661790	+	1.59770i
$467$	−18.7671	+	18.7671i	−0.868438	+	0.868438i	−0.992299	−	0.123862i	$-0.960472\pi$
$467$	−18.7671	+	18.7671i	−0.868438	+	0.868438i	0.123862	+	0.992299i	$0.460472\pi$
$468$	81.6599	−	81.6599i	3.77473	−	3.77473i
$469$	−4.29829	+	10.3770i	−0.198477	+	0.479165i
$470$	−8.23380	−	3.41055i	−0.379797	−	0.157317i
$471$	6.25929	+	15.1113i	0.288413	+	0.696291i
$472$		−	50.0626i		−	2.30432i
$473$	10.2457	−	4.24392i	0.471099	−	0.195136i
$474$	18.9579	+	18.9579i	0.870766	+	0.870766i
$475$	−8.63627			−0.396259
$476$	24.0786	−	10.1193i	1.10364	−	0.463816i
$477$	−12.0108			−0.549937
$478$	−19.9193	−	19.9193i	−0.911087	−	0.911087i
$479$	31.1443	−	12.9004i	1.42302	−	0.589433i	0.467401	−	0.884046i	$-0.345191\pi$
$479$	31.1443	−	12.9004i	1.42302	−	0.589433i	0.955617	+	0.294613i	$0.0951906\pi$
$480$		−	48.7777i		−	2.22639i
$481$	23.9304	+	57.7730i	1.09113	+	2.63422i
$482$	−30.8906	−	12.7953i	−1.40703	−	0.582810i
$483$	9.92904	−	23.9708i	0.451787	−	1.09071i
$484$	−75.6508	+	75.6508i	−3.43867	+	3.43867i
$485$	8.16956	−	8.16956i	0.370961	−	0.370961i
$486$	19.6332	−	47.3988i	0.890581	−	2.15005i
$487$	−20.2050	−	8.36919i	−0.915577	−	0.379244i	−0.125388	−	0.992108i	$-0.540018\pi$
$487$	−20.2050	−	8.36919i	−0.915577	−	0.379244i	−0.790189	+	0.612863i	$0.790018\pi$
$488$	18.2206	+	43.9883i	0.824806	+	1.99126i
$489$			0.0864934i			0.00391137i
$490$	−41.0042	+	16.9845i	−1.85238	+	0.767281i
$491$	−14.2897	−	14.2897i	−0.644884	−	0.644884i	0.306868	−	0.951752i	$-0.400719\pi$
$491$	−14.2897	−	14.2897i	−0.644884	−	0.644884i	−0.951752	+	0.306868i	$0.900719\pi$
$492$	−112.286			−5.06226
$493$	11.2988	+	4.61209i	0.508873	+	0.207718i
$494$	−18.4611			−0.830604
$495$	−61.9012	−	61.9012i	−2.78225	−	2.78225i
$496$	19.9711	−	8.27231i	0.896730	−	0.371438i
$497$			3.03043i			0.135933i
$498$	12.1790	+	29.4026i	0.545753	+	1.31756i
$499$	−9.19305	−	3.80789i	−0.411538	−	0.170464i	0.167302	−	0.985906i	$-0.446494\pi$
$499$	−9.19305	−	3.80789i	−0.411538	−	0.170464i	−0.578840	+	0.815441i	$0.696494\pi$
$500$	−13.7640	+	33.2293i	−0.615547	+	1.48606i
$501$	12.4490	−	12.4490i	0.556181	−	0.556181i
$502$	−15.2796	+	15.2796i	−0.681962	+	0.681962i
$503$	−10.1998	+	24.6244i	−0.454784	+	1.09795i	0.515697	+	0.856771i	$0.327533\pi$
$503$	−10.1998	+	24.6244i	−0.454784	+	1.09795i	−0.970481	+	0.241176i	$0.922467\pi$
$504$	−34.5868	−	14.3263i	−1.54062	−	0.638145i
$505$	1.56082	+	3.76814i	0.0694554	+	0.167680i
$506$		−	102.149i		−	4.54107i
$507$	−61.3628	+	25.4173i	−2.72522	+	1.12882i
$508$	−21.0995	−	21.0995i	−0.936137	−	0.936137i
$509$	31.3989			1.39173			0.695865	−	0.718172i	$-0.255021\pi$
$509$	31.3989			1.39173			0.695865	+	0.718172i	$0.255021\pi$
$510$	70.1700	+	69.4509i	3.10718	+	3.07534i
$511$	−16.4618			−0.728227
$512$	35.9337	+	35.9337i	1.58806	+	1.58806i
$513$	3.57873	−	1.48236i	0.158005	−	0.0654477i
$514$			37.8069i			1.66759i
$515$	−11.6750	−	28.1860i	−0.514464	−	1.24203i
$516$	20.7378	+	8.58990i	0.912933	+	0.378149i
$517$	−2.26411	+	5.46605i	−0.0995755	+	0.240397i
$518$	26.0016	−	26.0016i	1.14244	−	1.14244i
$519$	6.04211	−	6.04211i	0.265219	−	0.265219i
$520$	−51.4667	+	124.252i	−2.25696	+	5.44879i
$521$	−17.2782	−	7.15684i	−0.756970	−	0.313547i	−0.0293878	−	0.999568i	$-0.509356\pi$
$521$	−17.2782	−	7.15684i	−0.756970	−	0.313547i	−0.727582	+	0.686021i	$0.759356\pi$
$522$	−12.1428	−	29.3152i	−0.531474	−	1.28309i
$523$		−	20.2482i		−	0.885391i	−0.896672	−	0.442695i	$-0.854022\pi$
$523$		−	20.2482i		−	0.885391i	0.896672	−	0.442695i	$-0.145978\pi$
$524$	−40.9176	+	16.9486i	−1.78749	+	0.740404i
$525$	19.7137	+	19.7137i	0.860377	+	0.860377i
$526$	−24.2699			−1.05822
$527$	−4.84568	+	11.8711i	−0.211081	+	0.517112i
$528$	−110.496			−4.80873
$529$	16.3805	+	16.3805i	0.712194	+	0.712194i
$530$	23.4415	−	9.70977i	1.01823	−	0.421765i
$531$		−	33.8276i		−	1.46799i
$532$	2.86758	+	6.92295i	0.124325	+	0.300148i
$533$	53.2049	+	22.0382i	2.30456	+	0.954581i
$534$	27.9857	−	67.5634i	1.21106	−	2.92376i
$535$	43.2753	−	43.2753i	1.87095	−	1.87095i
$536$	−34.8894	+	34.8894i	−1.50699	+	1.50699i
$537$	−7.73440	+	18.6725i	−0.333764	+	0.805777i
$538$	−22.3146	−	9.24302i	−0.962052	−	0.398495i
$539$	11.2752	+	27.2209i	0.485659	+	1.17249i
$540$		−	51.1889i		−	2.20282i
$541$	−8.60543	+	3.56449i	−0.369976	+	0.153249i	−0.559922	−	0.828545i	$-0.689169\pi$
$541$	−8.60543	+	3.56449i	−0.369976	+	0.153249i	0.189945	+	0.981795i	$0.439169\pi$
$542$	−29.1465	−	29.1465i	−1.25195	−	1.25195i
$543$	−38.6156			−1.65715
$544$	21.3423	−	0.109924i	0.915041	−	0.00471296i
$545$	30.6021			1.31085
$546$	42.1405	+	42.1405i	1.80345	+	1.80345i
$547$	−27.6986	+	11.4731i	−1.18430	+	0.490555i	−0.885896	−	0.463883i	$-0.846456\pi$
$547$	−27.6986	+	11.4731i	−1.18430	+	0.490555i	−0.298408	+	0.954438i	$0.596456\pi$
$548$			19.6566i			0.839689i
$549$	12.3118	+	29.7232i	0.525453	+	1.26856i
$550$	101.406	+	42.0039i	4.32398	+	1.79105i
$551$	−1.33988	+	3.23475i	−0.0570807	+	0.137805i
$552$	80.5945	−	80.5945i	3.43033	−	3.43033i
$553$	−3.94656	+	3.94656i	−0.167825	+	0.167825i
$554$	17.1270	−	41.3481i	0.727654	−	1.75671i
$555$	88.6414	+	36.7165i	3.76262	+	1.55853i
$556$	15.8162	+	38.1837i	0.670757	+	1.61935i
$557$		−	12.5701i		−	0.532612i	−0.963889	−	0.266306i	$-0.914197\pi$
$557$		−	12.5701i		−	0.532612i	0.963889	−	0.266306i	$-0.0858031\pi$
$558$	30.8000	−	12.7578i	1.30387	−	0.540080i
$559$	−8.14035	−	8.14035i	−0.344300	−	0.344300i
$560$	34.6499			1.46422
$561$	46.1054	−	46.5828i	1.94657	−	1.96673i
$562$	−27.7397			−1.17013
$563$	10.7161	+	10.7161i	0.451628	+	0.451628i	0.895895	−	0.444267i	$-0.146536\pi$
$563$	10.7161	+	10.7161i	0.451628	+	0.451628i	−0.444267	+	0.895895i	$0.646536\pi$
$564$	−11.0635	+	4.58267i	−0.465859	+	0.192965i
$565$		−	7.69906i		−	0.323902i
$566$	−8.46178	−	20.4286i	−0.355675	−	0.858676i
$567$	5.06611	+	2.09845i	0.212757	+	0.0881267i
$568$	−5.09445	+	12.2991i	−0.213758	+	0.516058i
$569$	9.87105	−	9.87105i	0.413816	−	0.413816i	−0.469250	−	0.883066i	$-0.655476\pi$
$569$	9.87105	−	9.87105i	0.413816	−	0.413816i	0.883066	+	0.469250i	$0.155476\pi$
$570$	−20.0288	+	20.0288i	−0.838912	+	0.838912i
$571$	0.499568	−	1.20606i	0.0209063	−	0.0504722i	−0.913082	−	0.407777i	$-0.866304\pi$
$571$	0.499568	−	1.20606i	0.0209063	−	0.0504722i	0.933988	+	0.357305i	$0.116304\pi$
$572$	149.627	+	61.9774i	6.25621	+	2.59141i
$573$	−23.4121	−	56.5218i	−0.978054	−	2.36123i
$574$		−	33.8643i		−	1.41347i
$575$	−45.8298	+	18.9833i	−1.91124	+	0.791660i
$576$	2.23405	+	2.23405i	0.0930852	+	0.0930852i
$577$	19.7316			0.821437			0.410718	−	0.911762i	$-0.365278\pi$
$577$	19.7316			0.821437			0.410718	+	0.911762i	$0.365278\pi$
$578$	−30.2295	+	30.8588i	−1.25738	+	1.28356i
$579$	10.0970			0.419615
$580$	32.7170	+	32.7170i	1.35850	+	1.35850i
$581$	−6.12088	+	2.53535i	−0.253937	+	0.105184i
$582$		−	22.4903i		−	0.932252i
$583$	−6.44588	−	15.5617i	−0.266961	−	0.644501i
$584$	−66.8106	−	27.6739i	−2.76464	−	1.14515i
$585$	−34.7764	+	83.9576i	−1.43783	+	3.47122i
$586$	26.8092	−	26.8092i	1.10748	−	1.10748i
$587$	−29.8614	+	29.8614i	−1.23251	+	1.23251i	−0.269514	+	0.962996i	$0.586863\pi$
$587$	−29.8614	+	29.8614i	−1.23251	+	1.23251i	−0.962996	+	0.269514i	$0.913137\pi$
$588$	−22.8216	+	55.0963i	−0.941149	+	2.27213i
$589$	−3.39858	−	1.40774i	−0.140036	−	0.0580049i
$590$	27.3469	+	66.0212i	1.12585	+	2.71805i
$591$		−	9.88189i		−	0.406487i
$592$	65.3873	−	27.0843i	2.68740	−	1.11316i
$593$	13.6541	+	13.6541i	0.560706	+	0.560706i	0.929508	−	0.368802i	$-0.120232\pi$
$593$	13.6541	+	13.6541i	0.560706	+	0.560706i	−0.368802	+	0.929508i	$0.620232\pi$
$594$	−49.2307			−2.01996
$595$	−14.4579	+	14.6076i	−0.592717	+	0.598854i
$596$	73.8218			3.02386
$597$	−10.9505	−	10.9505i	−0.448174	−	0.448174i
$598$	−97.9669	+	40.5792i	−4.00617	+	1.65941i
$599$			21.6874i			0.886124i	0.896491	+	0.443062i	$0.146108\pi$
$599$			21.6874i			0.886124i	−0.896491	+	0.443062i	$0.853892\pi$
$600$	46.8680	+	113.149i	1.91338	+	4.61930i
$601$	19.7601	+	8.18489i	0.806030	+	0.333869i	0.747369	−	0.664409i	$-0.231317\pi$
$601$	19.7601	+	8.18489i	0.806030	+	0.333869i	0.0586614	+	0.998278i	$0.481317\pi$
$602$	−2.59061	+	6.25429i	−0.105586	+	0.254906i
$603$	−23.5750	+	23.5750i	−0.960049	+	0.960049i
$604$	−16.2177	+	16.2177i	−0.659891	+	0.659891i
$605$	32.2173	−	77.7795i	1.30982	−	3.16219i
$606$	7.33514	+	3.03831i	0.297970	+	0.123423i
$607$	−2.52519	−	6.09634i	−0.102494	−	0.247443i	0.864311	−	0.502958i	$-0.167755\pi$
$607$	−2.52519	−	6.09634i	−0.102494	−	0.247443i	−0.966805	+	0.255515i	$0.917755\pi$
$608$			6.12313i			0.248326i
$609$	10.4423	−	4.32536i	0.423145	−	0.175272i
$610$	−48.0576	−	48.0576i	−1.94580	−	1.94580i
$611$	6.14170			0.248467
$612$	77.5271	−	0.399306i	3.13385	−	0.0161410i
$613$	−1.34228			−0.0542143			−0.0271072	−	0.999633i	$-0.508630\pi$
$613$	−1.34228			−0.0542143			−0.0271072	+	0.999633i	$0.508630\pi$
$614$	−8.10391	−	8.10391i	−0.327047	−	0.327047i
$615$	81.6325	−	33.8133i	3.29174	−	1.36348i
$616$		−	52.5007i		−	2.11531i
$617$	9.14911	+	22.0879i	0.368329	+	0.889225i	0.994024	+	0.109158i	$0.0348154\pi$
$617$	9.14911	+	22.0879i	0.368329	+	0.889225i	−0.625695	+	0.780068i	$0.715185\pi$
$618$	−54.8675	−	22.7269i	−2.20709	−	0.914209i
$619$	1.32965	−	3.21005i	0.0534430	−	0.129023i	−0.894903	−	0.446261i	$-0.852755\pi$
$619$	1.32965	−	3.21005i	0.0534430	−	0.129023i	0.948346	+	0.317238i	$0.102755\pi$
$620$	−34.3740	+	34.3740i	−1.38049	+	1.38049i
$621$	15.7328	−	15.7328i	0.631334	−	0.631334i
$622$	7.37872	−	17.8138i	0.295860	−	0.714268i
$623$	14.0650	+	5.82591i	0.563502	+	0.233410i
$624$	43.8952	+	105.972i	1.75722	+	4.24229i
$625$			8.20167i			0.328067i
$626$	5.03441	−	2.08532i	0.201215	−	0.0833461i
$627$	13.2962	+	13.2962i	0.530999	+	0.530999i
$628$	−27.1332			−1.08273
$629$	−15.8652	+	38.8670i	−0.632587	+	1.54973i
$630$	53.4379			2.12902
$631$	27.9255	+	27.9255i	1.11170	+	1.11170i	0.992921	+	0.118775i	$0.0378967\pi$
$631$	27.9255	+	27.9255i	1.11170	+	1.11170i	0.118775	+	0.992921i	$0.462103\pi$
$632$	−22.6517	+	9.38266i	−0.901038	+	0.373222i
$633$			24.0799i			0.957092i
$634$	32.4398	+	78.3165i	1.28835	+	3.11035i
$635$	21.6931	+	8.98559i	0.860866	+	0.356582i
$636$	13.0468	−	31.4977i	0.517338	−	1.24897i
$637$	21.6273	−	21.6273i	0.856904	−	0.856904i
$638$	31.4654	−	31.4654i	1.24573	−	1.24573i
$639$	−3.44235	+	8.31057i	−0.136177	+	0.328761i
$640$	−39.7118	−	16.4491i	−1.56975	−	0.650210i
$641$	−12.8938	−	31.1284i	−0.509275	−	1.22950i	−0.944302	−	0.329080i	$-0.893261\pi$
$641$	−12.8938	−	31.1284i	−0.509275	−	1.22950i	0.435027	−	0.900417i	$-0.356739\pi$
$642$		−	119.134i		−	4.70185i
$643$	−9.11331	+	3.77486i	−0.359394	+	0.148866i	−0.555072	−	0.831802i	$-0.687309\pi$
$643$	−9.11331	+	3.77486i	−0.359394	+	0.148866i	0.195678	+	0.980668i	$0.437309\pi$
$644$	30.4346	+	30.4346i	1.19929	+	1.19929i
$645$	−17.6632			−0.695488
$646$	−8.80853	−	8.71826i	−0.346567	−	0.343015i
$647$	7.56640			0.297466			0.148733	−	0.988877i	$-0.452481\pi$
$647$	7.56640			0.297466			0.148733	+	0.988877i	$0.452481\pi$
$648$	17.0332	+	17.0332i	0.669129	+	0.669129i
$649$	43.8285	−	18.1544i	1.72042	−	0.712622i
$650$		−	113.941i		−	4.46913i
$651$	4.54443	+	10.9712i	0.178110	+	0.429996i
$652$	−0.132560	−	0.0549082i	−0.00519146	−	0.00215037i
$653$	−15.7597	+	38.0473i	−0.616724	+	1.48890i	0.238762	+	0.971078i	$0.423258\pi$
$653$	−15.7597	+	38.0473i	−0.616724	+	1.48890i	−0.855486	+	0.517826i	$0.826742\pi$
$654$	42.1228	−	42.1228i	1.64713	−	1.64713i
$655$	24.6434	−	24.6434i	0.962898	−	0.962898i
$656$	24.9427	−	60.2171i	0.973851	−	2.35108i
$657$	−45.1444	−	18.6994i	−1.76125	−	0.729533i
$658$	−1.38208	−	3.33664i	−0.0538791	−	0.130076i
$659$		−	6.27749i		−	0.244536i	−0.992497	−	0.122268i	$-0.960983\pi$
$659$		−	6.27749i		−	0.244536i	0.992497	−	0.122268i	$-0.0390168\pi$
$660$	229.573	−	95.0922i	8.93611	−	3.70146i
$661$	9.33070	+	9.33070i	0.362922	+	0.362922i	0.864888	−	0.501965i	$-0.167390\pi$
$661$	9.33070	+	9.33070i	0.362922	+	0.362922i	−0.501965	+	0.864888i	$0.667390\pi$
$662$	56.5140			2.19648
$663$	−62.9913	−	25.7126i	−2.44638	−	0.998593i
$664$	−29.1039			−1.12945
$665$	−4.16948	−	4.16948i	−0.161685	−	0.161685i
$666$	100.842	−	41.7701i	3.90755	−	1.61856i
$667$			20.1109i			0.778698i
$668$	11.1765	+	26.9824i	0.432430	+	1.04398i
$669$	−62.4124	−	25.8521i	−2.41300	−	0.999498i
$670$	26.9528	−	65.0698i	1.04128	−	2.51386i
$671$	−31.9033	+	31.9033i	−1.23161	+	1.23161i
$672$	13.9771	−	13.9771i	0.539177	−	0.539177i
$673$	−18.5514	+	44.7870i	−0.715103	+	1.72641i	−0.0282643	+	0.999600i	$0.508998\pi$
$673$	−18.5514	+	44.7870i	−0.715103	+	1.72641i	−0.686838	+	0.726810i	$0.741002\pi$
$674$	−21.5601	−	8.93048i	−0.830464	−	0.343989i
$675$	9.14903	+	22.0877i	0.352146	+	0.850157i
$676$		−	110.180i		−	4.23771i
$677$	−3.53671	+	1.46495i	−0.135927	+	0.0563027i	−0.449610	−	0.893225i	$-0.648437\pi$
$677$	−3.53671	+	1.46495i	−0.135927	+	0.0563027i	0.313683	+	0.949528i	$0.398437\pi$
$678$	−10.5975	−	10.5975i	−0.406995	−	0.406995i
$679$	4.68191			0.179675
$680$	−83.2346	+	34.9803i	−3.19190	+	1.34143i
$681$	−4.60314			−0.176393
$682$	33.0591	+	33.0591i	1.26590	+	1.26590i
$683$	−20.3936	+	8.44729i	−0.780338	+	0.323227i	−0.737052	−	0.675836i	$-0.763783\pi$
$683$	−20.3936	+	8.44729i	−0.780338	+	0.323227i	−0.0432861	+	0.999063i	$0.513783\pi$
$684$			22.2427i			0.850470i
$685$	−5.91929	−	14.2904i	−0.226164	−	0.546009i
$686$	−39.9729	−	16.5573i	−1.52617	−	0.632161i
$687$	−29.1931	+	70.4783i	−1.11378	+	2.68891i
$688$	−9.21321	+	9.21321i	−0.351250	+	0.351250i
$689$	−12.3640	+	12.3640i	−0.471030	+	0.471030i
$690$	−62.2609	+	150.311i	−2.37023	+	5.72224i
$691$	−42.6570	−	17.6691i	−1.62275	−	0.672164i	−0.628357	−	0.777925i	$-0.716272\pi$
$691$	−42.6570	−	17.6691i	−1.62275	−	0.672164i	−0.994392	+	0.105761i	$0.966272\pi$
$692$	5.42448	+	13.0959i	0.206208	+	0.497830i
$693$		−	35.4751i		−	1.34759i
$694$	−43.2786	+	17.9266i	−1.64283	+	0.680484i
$695$	−22.9969	−	22.9969i	−0.872322	−	0.872322i
$696$	49.6518			1.88205
$697$	14.9787	+	35.6414i	0.567357	+	1.35001i
$698$	−57.3496			−2.17071
$699$	−27.9109	−	27.9109i	−1.05569	−	1.05569i
$700$	−42.7281	+	17.6986i	−1.61497	+	0.668943i
$701$		−	37.9848i		−	1.43466i	−0.696731	−	0.717332i	$-0.745363\pi$
$701$		−	37.9848i		−	1.43466i	0.696731	−	0.717332i	$-0.254637\pi$
$702$	19.5572	+	47.2152i	0.738138	+	1.78202i
$703$	−11.1273	−	4.60906i	−0.419673	−	0.173834i
$704$	−1.69557	+	4.09348i	−0.0639044	+	0.154279i
$705$	6.66323	−	6.66323i	0.250952	−	0.250952i
$706$	0.717149	−	0.717149i	0.0269902	−	0.0269902i
$707$	−0.632500	+	1.52699i	−0.0237876	+	0.0574284i
$708$	88.7111	+	36.7453i	3.33397	+	1.38097i
$709$	−17.2472	−	41.6384i	−0.647731	−	1.56376i	−0.816020	−	0.578024i	$-0.803824\pi$
$709$	−17.2472	−	41.6384i	−0.647731	−	1.56376i	0.168288	−	0.985738i	$-0.446176\pi$
$710$		−	19.0026i		−	0.713154i
$711$	−15.3059	+	6.33992i	−0.574017	+	0.237766i
$712$	47.2892	+	47.2892i	1.77224	+	1.77224i
$713$	−21.1295			−0.791306
$714$	0.206062	+	40.0078i	0.00771167	+	1.49725i
$715$	−127.443			−4.76609
$716$	−23.7075	−	23.7075i	−0.885993	−	0.885993i
$717$	27.5182	−	11.3984i	1.02768	−	0.425681i
$718$		−	37.3436i		−	1.39365i
$719$	13.0667	+	31.5457i	0.487305	+	1.17646i	0.956071	+	0.293135i	$0.0946987\pi$
$719$	13.0667	+	31.5457i	0.487305	+	1.17646i	−0.468766	+	0.883322i	$0.655301\pi$
$720$	95.0228	+	39.3597i	3.54129	+	1.46685i
$721$	4.73116	−	11.4220i	0.176198	−	0.425379i
$722$	−31.6251	+	31.6251i	−1.17697	+	1.17697i
$723$	24.9983	−	24.9983i	0.929698	−	0.929698i
$724$	24.5142	−	59.1824i	0.911062	−	2.19950i
$725$	−19.9647	−	8.26965i	−0.741471	−	0.307127i
$726$	−62.7149	−	151.407i	−2.32757	−	5.61924i
$727$		−	20.2312i		−	0.750334i	−0.926957	−	0.375167i	$-0.877585\pi$
$727$		−	20.2312i		−	0.750334i	0.926957	−	0.375167i	$-0.122415\pi$
$728$	−50.3513	+	20.8562i	−1.86614	+	0.772982i
$729$	30.1733	+	30.1733i	1.11753	+	1.11753i
$730$	103.225			3.82053
$731$	−0.0398053	−	7.72837i	−0.00147225	−	0.285844i
$732$	−91.3212			−3.37533
$733$	−5.21111	−	5.21111i	−0.192477	−	0.192477i	0.604289	−	0.796765i	$-0.293457\pi$
$733$	−5.21111	−	5.21111i	−0.192477	−	0.192477i	−0.796765	+	0.604289i	$0.793457\pi$
$734$	27.5547	−	11.4135i	1.01706	−	0.421281i
$735$		−	46.9276i		−	1.73095i
$736$	13.4592	+	32.4934i	0.496113	+	1.19772i
$737$	−43.1969	−	17.8927i	−1.59118	−	0.659088i
$738$	38.4674	−	92.8684i	1.41600	−	3.41853i
$739$	32.2179	−	32.2179i	1.18516	−	1.18516i	0.206766	−	0.978391i	$-0.433706\pi$
$739$	32.2179	−	32.2179i	1.18516	−	1.18516i	0.978391	−	0.206766i	$-0.0662937\pi$
$740$	−112.544	+	112.544i	−4.13719	+	4.13719i
$741$	7.46986	−	18.0338i	0.274412	−	0.662490i
$742$	9.49934	+	3.93476i	0.348732	+	0.144449i
$743$	1.89065	+	4.56442i	0.0693610	+	0.167452i	0.954758	−	0.297383i	$-0.0961137\pi$
$743$	1.89065	+	4.56442i	0.0693610	+	0.167452i	−0.885397	+	0.464835i	$0.846114\pi$
$744$			52.1666i			1.91252i
$745$	−53.6687	+	22.2303i	−1.96627	+	0.814455i
$746$	46.6668	+	46.6668i	1.70859	+	1.70859i
$747$	−19.6657			−0.719531
$748$	42.1241	+	100.233i	1.54021	+	3.66489i
$749$	24.8007			0.906198
$750$	−38.9577	−	38.9577i	−1.42253	−	1.42253i
$751$	38.8421	−	16.0889i	1.41737	−	0.587092i	0.463169	−	0.886270i	$-0.346712\pi$
$751$	38.8421	−	16.0889i	1.41737	−	0.587092i	0.954197	+	0.299177i	$0.0967123\pi$
$752$		−	6.95115i		−	0.253482i
$753$	−8.74344	−	21.1085i	−0.318629	−	0.769237i
$754$	−42.6770	−	17.6774i	−1.55421	−	0.643773i
$755$	6.90663	−	16.6741i	0.251358	−	0.606832i
$756$	14.6680	−	14.6680i	0.533469	−	0.533469i
$757$	−0.239646	+	0.239646i	−0.00871007	+	0.00871007i	−0.711448	−	0.702738i	$-0.751960\pi$
$757$	−0.239646	+	0.239646i	−0.00871007	+	0.00871007i	0.702738	+	0.711448i	$0.251960\pi$
$758$	−12.2791	+	29.6444i	−0.445998	+	1.07673i
$759$	99.7848	+	41.3322i	3.62196	+	1.50026i
$760$	−9.91264	−	23.9312i	−0.359569	−	0.868077i
$761$		−	4.46507i		−	0.161859i	−0.996720	−	0.0809293i	$-0.974211\pi$
$761$		−	4.46507i		−	0.161859i	0.996720	−	0.0809293i	$-0.0257888\pi$
$762$	42.2283	−	17.4915i	1.52977	−	0.633652i
$763$	8.76889	+	8.76889i	0.317455	+	0.317455i
$764$	101.488			3.67171
$765$	−56.2422	+	23.6364i	−2.03344	+	0.854575i
$766$	−25.2631			−0.912794
$767$	−34.8223	−	34.8223i	−1.25736	−	1.25736i
$768$	−73.5858	+	30.4802i	−2.65530	+	1.09986i
$769$			19.6704i			0.709332i	0.934993	+	0.354666i	$0.115405\pi$
$769$			19.6704i			0.709332i	−0.934993	+	0.354666i	$0.884595\pi$
$770$	28.6787	+	69.2365i	1.03351	+	2.49511i
$771$	−36.9319	−	15.2977i	−1.33007	−	0.550933i
$772$	−6.40980	+	15.4746i	−0.230694	+	0.556944i
$773$	−9.53799	+	9.53799i	−0.343058	+	0.343058i	−0.857516	−	0.514458i	$-0.827993\pi$
$773$	−9.53799	+	9.53799i	−0.343058	+	0.343058i	0.514458	+	0.857516i	$0.327993\pi$
$774$	−14.2088	+	14.2088i	−0.510727	+	0.510727i
$775$	8.68850	−	20.9759i	0.312100	−	0.753476i
$776$	19.0016	+	7.87073i	0.682119	+	0.282543i
$777$	14.8789	+	35.9208i	0.533776	+	1.28865i
$778$		−	31.8672i		−	1.14250i
$779$	−10.2474	+	4.24463i	−0.367153	+	0.152080i
$780$	−182.398	−	182.398i	−6.53091	−	6.53091i
$781$	−12.6150			−0.451399
$782$	−65.9075	−	26.9029i	−2.35685	−	0.962047i
$783$	9.69247			0.346380
$784$	−24.4777	−	24.4777i	−0.874202	−	0.874202i
$785$	19.7259	−	8.17073i	0.704047	−	0.291626i
$786$		−	67.8418i		−	2.41984i
$787$	−3.89900	−	9.41302i	−0.138984	−	0.335538i	0.839027	−	0.544090i	$-0.183125\pi$
$787$	−3.89900	−	9.41302i	−0.138984	−	0.335538i	−0.978011	+	0.208552i	$0.933125\pi$
$788$	15.1450	+	6.27328i	0.539520	+	0.223476i
$789$	9.82027	−	23.7082i	0.349611	−	0.844036i
$790$	24.7472	−	24.7472i	0.880466	−	0.880466i
$791$	2.20613	−	2.20613i	0.0784411	−	0.0784411i
$792$	59.6370	−	143.976i	2.11911	−	5.11598i
$793$	43.2710	+	17.9234i	1.53660	+	0.636479i
$794$	−16.9297	−	40.8719i	−0.600813	−	1.45049i
$795$			26.8278i			0.951483i
$796$	23.7344	−	9.83112i	0.841244	−	0.348455i
$797$	−32.9064	−	32.9064i	−1.16561	−	1.16561i	−0.983229	−	0.182377i	$-0.941621\pi$
$797$	−32.9064	−	32.9064i	−1.16561	−	1.16561i	−0.182377	−	0.983229i	$-0.558379\pi$
$798$	−11.4783			−0.406328
$799$	2.93045	+	2.90042i	0.103672	+	0.102610i
$800$	−37.7917			−1.33614
$801$	31.9536	+	31.9536i	1.12903	+	1.12903i
$802$	47.6072	−	19.7196i	1.68107	−	0.696322i
$803$		−	68.5265i		−	2.41825i
$804$	−36.2158	−	87.4326i	−1.27723	−	3.08351i
$805$	−31.2910	−	12.9611i	−1.10286	−	0.456820i
$806$	18.5727	−	44.8385i	0.654197	−	1.57937i
$807$	18.0582	−	18.0582i	0.635679	−	0.635679i
$808$	−5.13403	+	5.13403i	−0.180615	+	0.180615i
$809$	4.52232	−	10.9178i	0.158996	−	0.383851i	−0.824226	−	0.566260i	$-0.808390\pi$
$809$	4.52232	−	10.9178i	0.158996	−	0.383851i	0.983223	+	0.182409i	$0.0583897\pi$
$810$	−31.7675	−	13.1585i	−1.11620	−	0.462343i
$811$	−0.892018	−	2.15352i	−0.0313230	−	0.0756204i	0.907444	−	0.420173i	$-0.138031\pi$
$811$	−0.892018	−	2.15352i	−0.0313230	−	0.0756204i	−0.938767	+	0.344553i	$0.888031\pi$
$812$			18.7498i			0.657990i
$813$	40.2654	−	16.6785i	1.41217	−	0.584940i
$814$	108.238	+	108.238i	3.79375	+	3.79375i
$815$	0.112906			0.00395494
$816$	−29.1014	+	71.2933i	−1.01875	+	2.49576i
$817$	2.21728			0.0775729
$818$	44.2458	+	44.2458i	1.54702	+	1.54702i
$819$	−34.0227	+	14.0927i	−1.18885	+	0.492438i
$820$			146.576i			5.11865i
$821$	−4.20013	−	10.1400i	−0.146586	−	0.353889i	0.833484	−	0.552544i	$-0.186343\pi$
$821$	−4.20013	−	10.1400i	−0.146586	−	0.353889i	−0.980070	+	0.198655i	$0.936343\pi$
$822$	−27.8180	−	11.5226i	−0.970265	−	0.401897i
$823$	19.4458	−	46.9462i	0.677837	−	1.63644i	−0.0901115	−	0.995932i	$-0.528722\pi$
$823$	19.4458	−	46.9462i	0.677837	−	1.63644i	0.767949	−	0.640512i	$-0.221278\pi$
$824$	38.4030	−	38.4030i	1.33783	−	1.33783i
$825$	−82.0635	+	82.0635i	−2.85708	+	2.85708i
$826$	−11.0820	+	26.7542i	−0.385591	+	0.930899i
$827$	−34.0896	−	14.1204i	−1.18541	−	0.491013i	−0.299153	−	0.954205i	$-0.596704\pi$
$827$	−34.0896	−	14.1204i	−1.18541	−	0.491013i	−0.886258	+	0.463192i	$0.846704\pi$
$828$	48.8915	+	118.034i	1.69910	+	4.10198i
$829$			50.9775i			1.77052i	0.465094	+	0.885261i	$0.346021\pi$
$829$			50.9775i			1.77052i	−0.465094	+	0.885261i	$0.653979\pi$
$830$	38.3815	−	15.8981i	1.33224	−	0.551832i
$831$	33.4611	+	33.4611i	1.16075	+	1.16075i
$832$	4.59947			0.159458
$833$	20.5327	−	0.105755i	0.711417	−	0.00366418i
$834$	−63.3090			−2.19221
$835$	−16.2506	−	16.2506i	−0.562377	−	0.562377i
$836$	−28.8186	+	11.9370i	−0.996711	+	0.412851i
$837$			10.1834i			0.351989i
$838$	−21.1664	−	51.1003i	−0.731182	−	1.76523i
$839$	−1.35296	−	0.560414i	−0.0467093	−	0.0193476i	0.359206	−	0.933258i	$-0.383047\pi$
$839$	−1.35296	−	0.560414i	−0.0467093	−	0.0193476i	−0.405916	+	0.913910i	$0.633047\pi$
$840$	−31.9997	+	77.2542i	−1.10410	+	2.66552i
$841$	14.3112	−	14.3112i	0.493491	−	0.493491i
$842$	3.23319	−	3.23319i	0.111423	−	0.111423i
$843$	11.2243	−	27.0977i	0.386584	−	0.933296i
$844$	−36.9050	−	15.2866i	−1.27032	−	0.526185i
$845$	33.1791	+	80.1015i	1.14140	+	2.75558i
$846$		−	10.7202i		−	0.368570i
$847$	31.5191	−	13.0557i	1.08301	−	0.448597i
$848$	13.9935	+	13.9935i	0.480539	+	0.480539i
$849$	23.3796			0.802387
$850$	53.8087	−	54.3658i	1.84562	−	1.86473i
$851$	−69.1799			−2.37145
$852$	−18.0548	−	18.0548i	−0.618546	−	0.618546i
$853$	12.8116	−	5.30675i	0.438662	−	0.181700i	−0.152412	−	0.988317i	$-0.548704\pi$
$853$	12.8116	−	5.30675i	0.438662	−	0.181700i	0.591074	+	0.806617i	$0.298704\pi$
$854$		−	27.5414i		−	0.942448i
$855$	−6.69804	−	16.1705i	−0.229068	−	0.553019i
$856$	100.654	+	41.6924i	3.44029	+	1.42502i
$857$	0.244956	−	0.591377i	0.00836755	−	0.0202011i	−0.919641	−	0.392761i	$-0.871520\pi$
$857$	0.244956	−	0.591377i	0.00836755	−	0.0202011i	0.928008	+	0.372560i	$0.121520\pi$
$858$	−175.421	+	175.421i	−5.98877	+	5.98877i
$859$	39.4587	−	39.4587i	1.34631	−	1.34631i	0.456688	−	0.889627i	$-0.349036\pi$
$859$	39.4587	−	39.4587i	1.34631	−	1.34631i	0.889627	−	0.456688i	$-0.150964\pi$
$860$	11.2130	−	27.0707i	0.382362	−	0.923103i
$861$	33.0805	+	13.7024i	1.12738	+	0.466977i
$862$	1.82540	+	4.40691i	0.0621734	+	0.150100i
$863$			36.7522i			1.25106i	0.780201	+	0.625529i	$0.215117\pi$
$863$			36.7522i			1.25106i	−0.780201	+	0.625529i	$0.784883\pi$
$864$	15.6602	−	6.48668i	0.532772	−	0.220681i
$865$	−7.88723	−	7.88723i	−0.268174	−	0.268174i
$866$	5.33341			0.181237
$867$	−17.9129	−	42.0162i	−0.608355	−	1.42694i
$868$	−19.6995			−0.668643
$869$	−16.4286	−	16.4286i	−0.557301	−	0.557301i
$870$	−65.4795	+	27.1225i	−2.21996	+	0.919539i
$871$			48.5364i			1.64459i
$872$	20.8474	+	50.3301i	0.705983	+	1.70439i
$873$	12.8395	+	5.31831i	0.434552	+	0.179997i
$874$	7.81569	−	18.8687i	0.264370	−	0.638245i
$875$	8.11001	−	8.11001i	0.274168	−	0.274168i
$876$	98.0764	−	98.0764i	3.31369	−	3.31369i
$877$	−11.1009	+	26.7999i	−0.374850	+	0.904969i	0.618063	+	0.786129i	$0.287918\pi$
$877$	−11.1009	+	26.7999i	−0.374850	+	0.904969i	−0.992913	+	0.118840i	$0.962082\pi$
$878$	−13.3697	−	5.53791i	−0.451205	−	0.186895i
$879$	15.3410	+	37.0364i	0.517439	+	1.24921i
$880$			144.239i			4.86230i
$881$	−23.9902	+	9.93709i	−0.808252	+	0.334789i	−0.748256	−	0.663410i	$-0.769109\pi$
$881$	−23.9902	+	9.93709i	−0.808252	+	0.334789i	−0.0599956	+	0.998199i	$0.519109\pi$
$882$	−37.7501	−	37.7501i	−1.27111	−	1.27111i
$883$	−6.87977			−0.231523			−0.115761	−	0.993277i	$-0.536931\pi$
$883$	−6.87977			−0.231523			−0.115761	+	0.993277i	$0.536931\pi$
$884$	79.3957	−	80.2178i	2.67036	−	2.69801i
$885$	−75.5585			−2.53987
$886$	61.4683	+	61.4683i	2.06507	+	2.06507i
$887$	−44.1321	+	18.2801i	−1.48181	+	0.613786i	−0.969517	−	0.245024i	$-0.921204\pi$
$887$	−44.1321	+	18.2801i	−1.48181	+	0.613786i	−0.512294	+	0.858810i	$0.671204\pi$
$888$			170.798i			5.73161i
$889$	3.64130	+	8.79087i	0.122125	+	0.294836i
$890$	−88.1957	−	36.5319i	−2.95633	−	1.22455i
$891$	−8.73535	+	21.0890i	−0.292645	+	0.706508i
$892$	79.2420	−	79.2420i	2.65322	−	2.65322i
$893$	−0.836444	+	0.836444i	−0.0279905	+	0.0279905i
$894$	−43.2739	+	104.473i	−1.44730	+	3.49408i
$895$	24.3746	+	10.0963i	0.814754	+	0.337482i
$896$	−6.66580	−	16.0927i	−0.222689	−	0.537619i
$897$		−	112.119i		−	3.74355i
$898$	−52.3315	+	21.6764i	−1.74632	+	0.723351i
$899$	−6.50862	−	6.50862i	−0.217074	−	0.217074i
$900$	−137.281			−4.57602
$901$	−11.7382	+	0.0604583i	−0.391058	+	0.00201416i
$902$	140.969			4.69375
$903$	−5.06131	−	5.06131i	−0.168430	−	0.168430i
$904$	12.6624	−	5.24492i	0.421144	−	0.174444i
$905$			50.4079i			1.67561i
$906$	−13.4446	−	32.4581i	−0.446666	−	1.07835i
$907$	−7.37903	−	3.05650i	−0.245017	−	0.101489i	0.256796	−	0.966466i	$-0.417333\pi$
$907$	−7.37903	−	3.05650i	−0.245017	−	0.101489i	−0.501812	+	0.864976i	$0.667333\pi$
$908$	2.92219	−	7.05479i	0.0969763	−	0.234121i
$909$	−3.46910	+	3.46910i	−0.115063	+	0.115063i
$910$	55.0092	−	55.0092i	1.82354	−	1.82354i
$911$	−6.74179	+	16.2761i	−0.223366	+	0.539252i	−0.995343	−	0.0963980i	$-0.969268\pi$
$911$	−6.74179	+	16.2761i	−0.223366	+	0.539252i	0.771977	+	0.635650i	$0.219268\pi$
$912$	−20.4106	−	8.45436i	−0.675863	−	0.279952i
$913$	−10.5541	−	25.4798i	−0.349289	−	0.843257i
$914$			91.5492i			3.02818i
$915$	66.3908	−	27.5000i	2.19481	−	0.909121i
$916$	−89.4828	−	89.4828i	−2.95659	−	2.95659i
$917$	14.1229			0.466381
$918$	−12.9659	+	31.7642i	−0.427938	+	1.04837i
$919$	2.33585			0.0770526			0.0385263	−	0.999258i	$-0.487734\pi$
$919$	2.33585			0.0770526			0.0385263	+	0.999258i	$0.487734\pi$
$920$	−105.206	−	105.206i	−3.46854	−	3.46854i
$921$	11.1954	−	4.63730i	0.368902	−	0.152804i
$922$			27.0503i			0.890854i
$923$	5.01136	+	12.0985i	0.164951	+	0.398227i
$924$	93.0314	+	38.5349i	3.06051	+	1.26770i
$925$	28.4469	−	68.6769i	0.935329	−	2.25808i
$926$	−16.0224	+	16.0224i	−0.526528	+	0.526528i
$927$	25.9492	−	25.9492i	0.852283	−	0.852283i
$928$	−5.86320	+	14.1550i	−0.192469	+	0.464661i
$929$	1.84307	+	0.763425i	0.0604692	+	0.0250471i	0.412713	−	0.910861i	$-0.364581\pi$
$929$	1.84307	+	0.763425i	0.0604692	+	0.0250471i	−0.352244	+	0.935908i	$0.614581\pi$
$930$	−28.4962	−	68.7959i	−0.934427	−	2.25591i
$931$			5.89088i			0.193066i
$932$	60.4949	−	25.0578i	1.98158	−	0.820795i
$933$	14.4159	+	14.4159i	0.471955	+	0.471955i
$934$	67.4418			2.20676
$935$	−60.8080	−	60.1848i	−1.98864	−	1.96825i
$936$	−161.773			−5.28772
$937$	−7.73737	−	7.73737i	−0.252769	−	0.252769i	0.569336	−	0.822105i	$-0.307200\pi$
$937$	−7.73737	−	7.73737i	−0.252769	−	0.252769i	−0.822105	+	0.569336i	$0.807200\pi$
$938$	26.3687	−	10.9223i	0.860968	−	0.356624i
$939$			5.76167i			0.188025i
$940$	5.98211	+	14.4421i	0.195115	+	0.471049i
$941$	32.6113	+	13.5081i	1.06310	+	0.440350i	0.844550	−	0.535476i	$-0.179868\pi$
$941$	32.6113	+	13.5081i	1.06310	+	0.440350i	0.218549	+	0.975826i	$0.429868\pi$
$942$	15.9053	−	38.3988i	0.518223	−	1.25110i
$943$	−45.0497	+	45.0497i	−1.46702	+	1.46702i
$944$	−39.4117	+	39.4117i	−1.28274	+	1.28274i
$945$	−6.24663	+	15.0807i	−0.203203	+	0.490575i
$946$	−26.0351	−	10.7841i	−0.846475	−	0.350621i
$947$	15.9448	+	38.4943i	0.518138	+	1.25090i	0.939046	+	0.343792i	$0.111712\pi$
$947$	15.9448	+	38.4943i	0.518138	+	1.25090i	−0.420908	+	0.907103i	$0.638288\pi$
$948$		−	47.0257i		−	1.52732i
$949$	−65.7210	+	27.2225i	−2.13339	+	0.883681i
$950$	15.5177	+	15.5177i	0.503462	+	0.503462i
$951$	−89.6300			−2.90645
$952$	−33.8740	−	13.8271i	−1.09786	−	0.448139i
$953$	37.1022			1.20186			0.600929	−	0.799302i	$-0.294797\pi$
$953$	37.1022			1.20186			0.600929	+	0.799302i	$0.294797\pi$
$954$	21.5811	+	21.5811i	0.698715	+	0.698715i
$955$	−73.7822	+	30.5616i	−2.38753	+	0.988949i
$956$			49.4104i			1.59805i
$957$	18.0054	+	43.4689i	0.582033	+	1.40515i
$958$	−79.1398	−	32.7808i	−2.55689	−	1.05910i
$959$	2.39871	−	5.79101i	0.0774585	−	0.187001i
$960$	4.99004	−	4.99004i	0.161053	−	0.161053i
$961$	−15.0820	+	15.0820i	−0.486518	+	0.486518i
$962$	60.8088	−	146.805i	1.96055	−	4.73320i
$963$	68.0127	+	28.1718i	2.19168	+	0.907824i
$964$	22.4430	+	54.1821i	0.722840	+	1.74509i
$965$		−	13.1803i		−	0.424289i
$966$	−60.9116	+	25.2304i	−1.95980	+	0.811775i
$967$	−1.16264	−	1.16264i	−0.0373879	−	0.0373879i	0.688166	−	0.725554i	$-0.258416\pi$
$967$	−1.16264	−	1.16264i	−0.0373879	−	0.0373879i	−0.725554	+	0.688166i	$0.758416\pi$
$968$	149.869			4.81697
$969$	12.0807	−	5.07703i	0.388087	−	0.163098i
$970$	−29.3583			−0.942637
$971$	3.37250	+	3.37250i	0.108229	+	0.108229i	0.759147	−	0.650919i	$-0.225616\pi$
$971$	3.37250	+	3.37250i	0.108229	+	0.108229i	−0.650919	+	0.759147i	$0.725616\pi$
$972$	−83.1376	+	34.4367i	−2.66664	+	1.10456i
$973$		−	13.1793i		−	0.422510i
$974$	21.2667	+	51.3424i	0.681430	+	1.64512i
$975$	111.304	+	46.1036i	3.56458	+	1.47650i
$976$	20.2857	−	48.9739i	0.649328	−	1.56762i
$977$	40.0747	−	40.0747i	1.28210	−	1.28210i	0.342635	−	0.939469i	$-0.388681\pi$
$977$	40.0747	−	40.0747i	1.28210	−	1.28210i	0.939469	−	0.342635i	$-0.111319\pi$
$978$	0.155412	−	0.155412i	0.00496953	−	0.00496953i
$979$	−24.2519	+	58.5492i	−0.775093	+	1.87124i
$980$	71.9214	+	29.7908i	2.29745	+	0.951633i
$981$	14.0867	+	34.0084i	0.449755	+	1.08580i
$982$			51.3516i			1.63870i
$983$	51.7861	−	21.4505i	1.65172	−	0.684165i	0.654319	−	0.756219i	$-0.272956\pi$
$983$	51.7861	−	21.4505i	1.65172	−	0.684165i	0.997401	+	0.0720543i	$0.0229555\pi$
$984$	111.223	+	111.223i	3.54566	+	3.54566i
$985$	−12.8996			−0.411015
$986$	−12.0148	−	28.5888i	−0.382628	−	0.910454i
$987$	3.81864			0.121549
$988$	22.8967	+	22.8967i	0.728441	+	0.728441i
$989$	11.7664	−	4.87380i	0.374149	−	0.154978i
$990$			222.449i			7.06990i
$991$	−17.8416	−	43.0735i	−0.566758	−	1.36828i	−0.904273	−	0.426955i	$-0.859586\pi$
$991$	−17.8416	−	43.0735i	−0.566758	−	1.36828i	0.337515	−	0.941320i	$-0.390414\pi$
$992$	−14.8719	−	6.16016i	−0.472184	−	0.195585i
$993$	−22.8671	+	55.2061i	−0.725666	+	1.75191i
$994$	5.44511	−	5.44511i	0.172708	−	0.172708i
$995$	−14.2945	+	14.2945i	−0.453166	+	0.453166i
$996$	21.3619	−	51.5723i	0.676879	−	1.63413i
$997$	−48.5605	−	20.1144i	−1.53793	−	0.637031i	−0.556845	−	0.830617i	$-0.687988\pi$
$997$	−48.5605	−	20.1144i	−1.53793	−	0.637031i	−0.981083	+	0.193586i	$0.937988\pi$
$998$	9.67611	+	23.3602i	0.306292	+	0.739454i
$999$			33.3413i			1.05487i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	799.2.g.d.189.2	✓	152
17.9	even	8	inner	799.2.g.d.706.2	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
799.2.g.d.189.2	✓	152	1.1	even	1	trivial
799.2.g.d.706.2	yes	152	17.9	even	8	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:	\( N \)	\(=\)	\( 799 = 17 \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	799.g (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.79681 - 1.79681i) q^{2} +(2.48226 - 1.02819i) q^{3} +4.45704i q^{4} +(-1.34217 - 3.24029i) q^{5} +(-6.30760 - 2.61270i) q^{6} +(0.543897 - 1.31308i) q^{7} +(4.41484 - 4.41484i) q^{8} +(2.98314 - 2.98314i) q^{9} +O(q^{10})\)	\(q+(-1.79681 - 1.79681i) q^{2} +(2.48226 - 1.02819i) q^{3} +4.45704i q^{4} +(-1.34217 - 3.24029i) q^{5} +(-6.30760 - 2.61270i) q^{6} +(0.543897 - 1.31308i) q^{7} +(4.41484 - 4.41484i) q^{8} +(2.98314 - 2.98314i) q^{9} +(-3.41055 + 8.23380i) q^{10} +(5.46605 + 2.26411i) q^{11} +(4.58267 + 11.0635i) q^{12} -6.14170i q^{13} +(-3.33664 + 1.38208i) q^{14} +(-6.66323 - 6.66323i) q^{15} -6.95115 q^{16} +(2.90042 - 2.93045i) q^{17} -10.7202 q^{18} +(0.836444 + 0.836444i) q^{19} +(14.4421 - 5.98211i) q^{20} -3.81864i q^{21} +(-5.75327 - 13.8896i) q^{22} +(6.27732 + 2.60015i) q^{23} +(6.41951 - 15.4981i) q^{24} +(-5.16249 + 5.16249i) q^{25} +(-11.0355 + 11.0355i) q^{26} +(1.25314 - 3.02536i) q^{27} +(5.85247 + 2.42417i) q^{28} +(1.13269 + 2.73457i) q^{29} +23.9451i q^{30} +(-2.87307 + 1.19006i) q^{31} +(3.66021 + 3.66021i) q^{32} +15.8961 q^{33} +(-10.4770 + 0.0539620i) q^{34} -4.98477 q^{35} +(13.2960 + 13.2960i) q^{36} +(-9.40668 + 3.89637i) q^{37} -3.00586i q^{38} +(-6.31482 - 15.2453i) q^{39} +(-20.2308 - 8.37987i) q^{40} +(-3.58829 + 8.66290i) q^{41} +(-6.86137 + 6.86137i) q^{42} +(1.32542 - 1.32542i) q^{43} +(-10.0912 + 24.3624i) q^{44} +(-13.6701 - 5.66233i) q^{45} +(-6.60716 - 15.9511i) q^{46} +1.00000i q^{47} +(-17.2546 + 7.14708i) q^{48} +(3.52138 + 3.52138i) q^{49} +18.5520 q^{50} +(4.18655 - 10.2563i) q^{51} +27.3738 q^{52} +(-2.01312 - 2.01312i) q^{53} +(-7.68764 + 3.18433i) q^{54} -20.7504i q^{55} +(-3.39583 - 8.19827i) q^{56} +(2.93629 + 1.21625i) q^{57} +(2.87826 - 6.94873i) q^{58} +(5.66981 - 5.66981i) q^{59} +(29.6983 - 29.6983i) q^{60} +(-2.91832 + 7.04544i) q^{61} +(7.30067 + 3.02404i) q^{62} +(-2.29459 - 5.53962i) q^{63} +0.748892i q^{64} +(-19.9009 + 8.24321i) q^{65} +(-28.5622 - 28.5622i) q^{66} -7.90276 q^{67} +(13.0612 + 12.9273i) q^{68} +18.2554 q^{69} +(8.95667 + 8.95667i) q^{70} +(-1.96989 + 0.815957i) q^{71} -26.3401i q^{72} +(-4.43241 - 10.7008i) q^{73} +(23.9030 + 9.90097i) q^{74} +(-7.50665 + 18.1227i) q^{75} +(-3.72807 + 3.72807i) q^{76} +(5.94594 - 5.94594i) q^{77} +(-16.0464 + 38.7394i) q^{78} +(-3.62804 - 1.50278i) q^{79} +(9.32963 + 22.5237i) q^{80} +3.85818i q^{81} +(22.0130 - 9.11810i) q^{82} +(-3.29615 - 3.29615i) q^{83} +17.0199 q^{84} +(-13.3884 - 5.46502i) q^{85} -4.76306 q^{86} +(5.62329 + 5.62329i) q^{87} +(34.1274 - 14.1360i) q^{88} +10.7114i q^{89} +(14.3884 + 34.7367i) q^{90} +(-8.06457 - 3.34045i) q^{91} +(-11.5890 + 27.9783i) q^{92} +(-5.90810 + 5.90810i) q^{93} +(1.79681 - 1.79681i) q^{94} +(1.58767 - 3.83297i) q^{95} +(12.8490 + 5.32223i) q^{96} +(1.26062 + 3.04341i) q^{97} -12.6545i q^{98} +(23.0601 - 9.55181i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q - 4 q^{2} + 4 q^{6} + 4 q^{7} + 4 q^{8} - 8 q^{9}+O(q^{10}) \) 152 * q - 4 * q^2 + 4 * q^6 + 4 * q^7 + 4 * q^8 - 8 * q^9	\( 152 q - 4 q^{2} + 4 q^{6} + 4 q^{7} + 4 q^{8} - 8 q^{9} - 8 q^{11} + 8 q^{12} - 12 q^{14} + 20 q^{15} - 160 q^{16} - 12 q^{17} + 96 q^{18} + 16 q^{19} + 96 q^{20} - 4 q^{22} - 16 q^{23} - 76 q^{24} - 12 q^{25} - 8 q^{26} + 8 q^{28} - 4 q^{29} - 4 q^{31} - 16 q^{32} - 72 q^{33} - 20 q^{34} + 48 q^{35} - 16 q^{36} + 16 q^{37} + 64 q^{40} - 68 q^{41} - 144 q^{42} + 4 q^{43} + 12 q^{44} - 4 q^{46} - 12 q^{48} - 4 q^{49} + 96 q^{50} - 52 q^{51} + 168 q^{52} - 16 q^{53} + 168 q^{54} + 108 q^{56} - 104 q^{58} - 84 q^{59} - 4 q^{60} + 4 q^{61} - 28 q^{62} + 60 q^{63} + 60 q^{65} - 44 q^{66} - 160 q^{67} - 96 q^{68} + 160 q^{69} + 36 q^{70} + 40 q^{71} + 4 q^{73} + 76 q^{74} - 116 q^{75} - 148 q^{76} - 4 q^{77} + 68 q^{78} - 76 q^{80} + 64 q^{82} - 124 q^{83} + 208 q^{84} - 68 q^{85} + 80 q^{86} - 72 q^{87} + 188 q^{88} + 236 q^{90} - 32 q^{91} - 196 q^{92} - 152 q^{93} + 4 q^{94} - 48 q^{95} - 56 q^{96} - 20 q^{97} + 244 q^{99}+O(q^{100}) \) 152 * q - 4 * q^2 + 4 * q^6 + 4 * q^7 + 4 * q^8 - 8 * q^9 - 8 * q^11 + 8 * q^12 - 12 * q^14 + 20 * q^15 - 160 * q^16 - 12 * q^17 + 96 * q^18 + 16 * q^19 + 96 * q^20 - 4 * q^22 - 16 * q^23 - 76 * q^24 - 12 * q^25 - 8 * q^26 + 8 * q^28 - 4 * q^29 - 4 * q^31 - 16 * q^32 - 72 * q^33 - 20 * q^34 + 48 * q^35 - 16 * q^36 + 16 * q^37 + 64 * q^40 - 68 * q^41 - 144 * q^42 + 4 * q^43 + 12 * q^44 - 4 * q^46 - 12 * q^48 - 4 * q^49 + 96 * q^50 - 52 * q^51 + 168 * q^52 - 16 * q^53 + 168 * q^54 + 108 * q^56 - 104 * q^58 - 84 * q^59 - 4 * q^60 + 4 * q^61 - 28 * q^62 + 60 * q^63 + 60 * q^65 - 44 * q^66 - 160 * q^67 - 96 * q^68 + 160 * q^69 + 36 * q^70 + 40 * q^71 + 4 * q^73 + 76 * q^74 - 116 * q^75 - 148 * q^76 - 4 * q^77 + 68 * q^78 - 76 * q^80 + 64 * q^82 - 124 * q^83 + 208 * q^84 - 68 * q^85 + 80 * q^86 - 72 * q^87 + 188 * q^88 + 236 * q^90 - 32 * q^91 - 196 * q^92 - 152 * q^93 + 4 * q^94 - 48 * q^95 - 56 * q^96 - 20 * q^97 + 244 * q^99

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