LMFDB - Embedded newform 546.2.bg.b.467.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(311,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 3]))

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

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

chi := DirichletCharacter("546.311");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bg (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			467.18
Character	$\chi$	$=$	546.467
Dual form			546.2.bg.b.311.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(1.73131 - 0.0505991i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(3.26421 + 1.88459i) q^{5} +(0.821836 - 1.52466i) q^{6} +(-0.385108 - 2.61757i) q^{7} -1.00000 q^{8} +(2.99488 - 0.175206i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(1.73131 - 0.0505991i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(3.26421 + 1.88459i) q^{5} +(0.821836 - 1.52466i) q^{6} +(-0.385108 - 2.61757i) q^{7} -1.00000 q^{8} +(2.99488 - 0.175206i) q^{9} +(3.26421 - 1.88459i) q^{10} +(-1.89239 - 3.27771i) q^{11} +(-0.909476 - 1.47406i) q^{12} +(-2.90274 + 2.13872i) q^{13} +(-2.45944 - 0.975274i) q^{14} +(5.74673 + 3.09765i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.16015 - 2.00944i) q^{17} +(1.34571 - 2.68124i) q^{18} +(-3.00909 + 5.21190i) q^{19} -3.76919i q^{20} +(-0.799188 - 4.51235i) q^{21} -3.78477 q^{22} +(5.79704 + 3.34692i) q^{23} +(-1.73131 + 0.0505991i) q^{24} +(4.60338 + 7.97329i) q^{25} +(0.400812 + 3.58320i) q^{26} +(5.17620 - 0.454874i) q^{27} +(-2.07433 + 1.64230i) q^{28} +3.07761i q^{29} +(5.55601 - 3.42798i) q^{30} +(-4.94611 - 8.56691i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.44216 - 5.57898i) q^{33} -2.32031 q^{34} +(3.67599 - 9.27009i) q^{35} +(-1.64917 - 2.50604i) q^{36} +(5.92523 + 3.42094i) q^{37} +(3.00909 + 5.21190i) q^{38} +(-4.91733 + 3.84966i) q^{39} +(-3.26421 - 1.88459i) q^{40} +6.69591i q^{41} +(-4.30740 - 1.56406i) q^{42} -3.47280 q^{43} +(-1.89239 + 3.27771i) q^{44} +(10.1061 + 5.07222i) q^{45} +(5.79704 - 3.34692i) q^{46} +(-6.71987 - 3.87972i) q^{47} +(-0.821836 + 1.52466i) q^{48} +(-6.70338 + 2.01610i) q^{49} +9.20677 q^{50} +(-2.11026 - 3.42027i) q^{51} +(3.30355 + 1.44449i) q^{52} +(-0.653696 + 0.377412i) q^{53} +(2.19417 - 4.71016i) q^{54} -14.2655i q^{55} +(0.385108 + 2.61757i) q^{56} +(-4.94596 + 9.17568i) q^{57} +(2.66529 + 1.53881i) q^{58} +(-3.68691 + 2.12864i) q^{59} +(-0.190718 - 6.52564i) q^{60} +(-8.37307 - 4.83419i) q^{61} -9.89221 q^{62} +(-1.61196 - 7.77184i) q^{63} +1.00000 q^{64} +(-13.5058 + 1.51074i) q^{65} +(-6.55262 + 0.191506i) q^{66} +(4.51984 - 2.60953i) q^{67} +(-1.16015 + 2.00944i) q^{68} +(10.2058 + 5.50124i) q^{69} +(-6.19013 - 7.81854i) q^{70} +6.23494 q^{71} +(-2.99488 + 0.175206i) q^{72} +(-2.53273 - 4.38682i) q^{73} +(5.92523 - 3.42094i) q^{74} +(8.37333 + 13.5713i) q^{75} +6.01818 q^{76} +(-7.85087 + 6.21573i) q^{77} +(0.875238 + 6.18336i) q^{78} +(-0.402095 + 0.696449i) q^{79} +(-3.26421 + 1.88459i) q^{80} +(8.93861 - 1.04944i) q^{81} +(5.79883 + 3.34796i) q^{82} +6.88779i q^{83} +(-3.50822 + 2.94829i) q^{84} -8.74567i q^{85} +(-1.73640 + 3.00754i) q^{86} +(0.155724 + 5.32830i) q^{87} +(1.89239 + 3.27771i) q^{88} +(13.5271 + 7.80988i) q^{89} +(9.44573 - 6.21604i) q^{90} +(6.71611 + 6.77450i) q^{91} -6.69384i q^{92} +(-8.99673 - 14.5817i) q^{93} +(-6.71987 + 3.87972i) q^{94} +(-19.6446 + 11.3418i) q^{95} +(0.909476 + 1.47406i) q^{96} -5.04512 q^{97} +(-1.60570 + 6.81335i) q^{98} +(-6.24174 - 9.48478i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 18 q^{2} - 18 q^{4} - 36 q^{8} + 4 q^{9}+O(q^{10}) $ 36 * q + 18 * q^2 - 18 * q^4 - 36 * q^8 + 4 * q^9	$ 36 q + 18 q^{2} - 18 q^{4} - 36 q^{8} + 4 q^{9} + 14 q^{15} - 18 q^{16} - 4 q^{18} - 23 q^{21} + 14 q^{25} + 6 q^{26} + 7 q^{30} + 18 q^{32} - 24 q^{33} - 8 q^{36} + 10 q^{39} - 16 q^{42} - 16 q^{43} + 9 q^{45} - 72 q^{47} + 12 q^{49} + 28 q^{50} - 3 q^{51} + 6 q^{52} - 9 q^{54} + 8 q^{57} - 24 q^{59} - 7 q^{60} - 36 q^{61} + 39 q^{63} + 36 q^{64} - 18 q^{65} - 24 q^{66} + 72 q^{71} - 4 q^{72} + 54 q^{75} + 20 q^{78} + 20 q^{79} - 20 q^{81} - 24 q^{82} + 7 q^{84} - 8 q^{86} - 24 q^{87} + 72 q^{89} - 2 q^{91} + 14 q^{93} - 72 q^{94} + 12 q^{98} - 72 q^{99}+O(q^{100}) $ 36 * q + 18 * q^2 - 18 * q^4 - 36 * q^8 + 4 * q^9 + 14 * q^15 - 18 * q^16 - 4 * q^18 - 23 * q^21 + 14 * q^25 + 6 * q^26 + 7 * q^30 + 18 * q^32 - 24 * q^33 - 8 * q^36 + 10 * q^39 - 16 * q^42 - 16 * q^43 + 9 * q^45 - 72 * q^47 + 12 * q^49 + 28 * q^50 - 3 * q^51 + 6 * q^52 - 9 * q^54 + 8 * q^57 - 24 * q^59 - 7 * q^60 - 36 * q^61 + 39 * q^63 + 36 * q^64 - 18 * q^65 - 24 * q^66 + 72 * q^71 - 4 * q^72 + 54 * q^75 + 20 * q^78 + 20 * q^79 - 20 * q^81 - 24 * q^82 + 7 * q^84 - 8 * q^86 - 24 * q^87 + 72 * q^89 - 2 * q^91 + 14 * q^93 - 72 * q^94 + 12 * q^98 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	1.73131	−	0.0505991i	0.999573	−	0.0292134i
$3$	1.73131	−	0.0505991i	0.999573	−	0.0292134i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	3.26421	+	1.88459i	1.45980	+	0.842816i	0.999001	−	0.0446889i	$-0.0142297\pi$
$5$	3.26421	+	1.88459i	1.45980	+	0.842816i	0.460799	+	0.887505i	$0.347563\pi$
$6$	0.821836	−	1.52466i	0.335513	−	0.622440i
$7$	−0.385108	−	2.61757i	−0.145557	−	0.989350i
$7$	−0.385108	−	2.61757i	−0.145557	−	0.989350i
$8$	−1.00000			−0.353553
$9$	2.99488	−	0.175206i	0.998293	−	0.0584019i
$10$	3.26421	−	1.88459i	1.03223	−	0.595961i
$11$	−1.89239	−	3.27771i	−0.570576	−	0.988266i	−0.996507	−	0.0835105i	$-0.973387\pi$
$11$	−1.89239	−	3.27771i	−0.570576	−	0.988266i	0.425931	−	0.904756i	$-0.359947\pi$
$12$	−0.909476	−	1.47406i	−0.262543	−	0.425525i
$13$	−2.90274	+	2.13872i	−0.805075	+	0.593173i
$13$	−2.90274	+	2.13872i	−0.805075	+	0.593173i
$14$	−2.45944	−	0.975274i	−0.657313	−	0.260653i
$15$	5.74673	+	3.09765i	1.48380	+	0.799810i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.16015	−	2.00944i	−0.281379	−	0.487362i	0.690346	−	0.723479i	$-0.257458\pi$
$17$	−1.16015	−	2.00944i	−0.281379	−	0.487362i	−0.971725	+	0.236117i	$0.924125\pi$
$18$	1.34571	−	2.68124i	0.317186	−	0.631975i
$19$	−3.00909	+	5.21190i	−0.690333	+	1.19569i	0.281396	+	0.959592i	$0.409202\pi$
$19$	−3.00909	+	5.21190i	−0.690333	+	1.19569i	−0.971729	+	0.236100i	$0.924131\pi$
$20$		−	3.76919i		−	0.842816i
$21$	−0.799188	−	4.51235i	−0.174397	−	0.984675i
$22$	−3.78477			−0.806916
$23$	5.79704	+	3.34692i	1.20877	+	0.697881i	0.962490	−	0.271319i	$-0.0874597\pi$
$23$	5.79704	+	3.34692i	1.20877	+	0.697881i	0.246276	+	0.969200i	$0.420793\pi$
$24$	−1.73131	+	0.0505991i	−0.353402	+	0.0103285i
$25$	4.60338	+	7.97329i	0.920677	+	1.59466i
$26$	0.400812	+	3.58320i	0.0786057	+	0.702724i
$27$	5.17620	−	0.454874i	0.996161	−	0.0875405i
$28$	−2.07433	+	1.64230i	−0.392012	+	0.310366i
$29$			3.07761i			0.571498i	0.958304	+	0.285749i	$0.0922424\pi$
$29$			3.07761i			0.571498i	−0.958304	+	0.285749i	$0.907758\pi$
$30$	5.55601	−	3.42798i	1.01438	−	0.625861i
$31$	−4.94611	−	8.56691i	−0.888347	−	1.53866i	−0.841829	−	0.539745i	$-0.818521\pi$
$31$	−4.94611	−	8.56691i	−0.888347	−	1.53866i	−0.0465184	−	0.998917i	$-0.514813\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−3.44216	−	5.57898i	−0.599203	−	0.971176i
$34$	−2.32031			−0.397929
$35$	3.67599	−	9.27009i	0.621356	−	1.56693i
$36$	−1.64917	−	2.50604i	−0.274862	−	0.417673i
$37$	5.92523	+	3.42094i	0.974102	+	0.562398i	0.900484	−	0.434888i	$-0.143212\pi$
$37$	5.92523	+	3.42094i	0.974102	+	0.562398i	0.0736180	+	0.997287i	$0.476545\pi$
$38$	3.00909	+	5.21190i	0.488139	+	0.845481i
$39$	−4.91733	+	3.84966i	−0.787403	+	0.616439i
$40$	−3.26421	−	1.88459i	−0.516117	−	0.297980i
$41$			6.69591i			1.04573i	0.852417	+	0.522863i	$0.175136\pi$
$41$			6.69591i			1.04573i	−0.852417	+	0.522863i	$0.824864\pi$
$42$	−4.30740	−	1.56406i	−0.664647	−	0.241339i
$43$	−3.47280			−0.529598			−0.264799	−	0.964304i	$-0.585306\pi$
$43$	−3.47280			−0.529598			−0.264799	+	0.964304i	$0.585306\pi$
$44$	−1.89239	+	3.27771i	−0.285288	+	0.494133i
$45$	10.1061	+	5.07222i	1.50653	+	0.756122i
$46$	5.79704	−	3.34692i	0.854726	−	0.493477i
$47$	−6.71987	−	3.87972i	−0.980194	−	0.565915i	−0.0778650	−	0.996964i	$-0.524810\pi$
$47$	−6.71987	−	3.87972i	−0.980194	−	0.565915i	−0.902329	+	0.431049i	$0.858144\pi$
$48$	−0.821836	+	1.52466i	−0.118622	+	0.220066i
$49$	−6.70338	+	2.01610i	−0.957626	+	0.288014i
$50$	9.20677			1.30203
$51$	−2.11026	−	3.42027i	−0.295496	−	0.478934i
$52$	3.30355	+	1.44449i	0.458120	+	0.200314i
$53$	−0.653696	+	0.377412i	−0.0897921	+	0.0518415i	−0.544224	−	0.838940i	$-0.683176\pi$
$53$	−0.653696	+	0.377412i	−0.0897921	+	0.0518415i	0.454432	+	0.890782i	$0.349842\pi$
$54$	2.19417	−	4.71016i	0.298589	−	0.640972i
$55$		−	14.2655i		−	1.92356i
$56$	0.385108	+	2.61757i	0.0514622	+	0.349788i
$57$	−4.94596	+	9.17568i	−0.655108	+	1.21535i
$58$	2.66529	+	1.53881i	0.349970	+	0.202055i
$59$	−3.68691	+	2.12864i	−0.479994	+	0.277125i	−0.720414	−	0.693544i	$-0.756048\pi$
$59$	−3.68691	+	2.12864i	−0.479994	+	0.277125i	0.240420	+	0.970669i	$0.422715\pi$
$60$	−0.190718	−	6.52564i	−0.0246215	−	0.842456i
$61$	−8.37307	−	4.83419i	−1.07206	−	0.618955i	−0.143317	−	0.989677i	$-0.545777\pi$
$61$	−8.37307	−	4.83419i	−1.07206	−	0.618955i	−0.928744	+	0.370722i	$0.879110\pi$
$62$	−9.89221			−1.25631
$63$	−1.61196	−	7.77184i	−0.203088	−	0.979160i
$64$	1.00000			0.125000
$65$	−13.5058	+	1.51074i	−1.67518	+	0.187384i
$66$	−6.55262	+	0.191506i	−0.806571	+	0.0235728i
$67$	4.51984	−	2.60953i	0.552187	−	0.318805i	−0.197817	−	0.980239i	$-0.563385\pi$
$67$	4.51984	−	2.60953i	0.552187	−	0.318805i	0.750004	+	0.661434i	$0.230052\pi$
$68$	−1.16015	+	2.00944i	−0.140689	+	0.243681i
$69$	10.2058	+	5.50124i	1.22864	+	0.662271i
$70$	−6.19013	−	7.81854i	−0.739863	−	0.934495i
$71$	6.23494			0.739951			0.369976	−	0.929041i	$-0.379366\pi$
$71$	6.23494			0.739951			0.369976	+	0.929041i	$0.379366\pi$
$72$	−2.99488	+	0.175206i	−0.352950	+	0.0206482i
$73$	−2.53273	−	4.38682i	−0.296434	−	0.513438i	0.678884	−	0.734246i	$-0.262464\pi$
$73$	−2.53273	−	4.38682i	−0.296434	−	0.513438i	−0.975317	+	0.220808i	$0.929131\pi$
$74$	5.92523	−	3.42094i	0.688794	−	0.397676i
$75$	8.37333	+	13.5713i	0.966869	+	1.56708i
$76$	6.01818			0.690333
$77$	−7.85087	+	6.21573i	−0.894690	+	0.708348i
$78$	0.875238	+	6.18336i	0.0991012	+	0.700128i
$79$	−0.402095	+	0.696449i	−0.0452392	+	0.0783566i	−0.887758	−	0.460310i	$-0.847738\pi$
$79$	−0.402095	+	0.696449i	−0.0452392	+	0.0783566i	0.842519	+	0.538666i	$0.181072\pi$
$80$	−3.26421	+	1.88459i	−0.364950	+	0.210704i
$81$	8.93861	−	1.04944i	0.993178	−	0.116604i
$82$	5.79883	+	3.34796i	0.640374	+	0.369720i
$83$			6.88779i			0.756033i	0.925799	+	0.378017i	$0.123394\pi$
$83$			6.88779i			0.756033i	−0.925799	+	0.378017i	$0.876606\pi$
$84$	−3.50822	+	2.94829i	−0.382778	+	0.321685i
$85$		−	8.74567i		−	0.948601i
$86$	−1.73640	+	3.00754i	−0.187241	+	0.324311i
$87$	0.155724	+	5.32830i	0.0166954	+	0.571254i
$88$	1.89239	+	3.27771i	0.201729	+	0.349405i
$89$	13.5271	+	7.80988i	1.43387	+	0.827845i	0.997413	−	0.0718798i	$-0.0228998\pi$
$89$	13.5271	+	7.80988i	1.43387	+	0.827845i	0.436457	+	0.899725i	$0.356233\pi$
$90$	9.44573	−	6.21604i	0.995667	−	0.655228i
$91$	6.71611	+	6.77450i	0.704040	+	0.710160i
$92$		−	6.69384i		−	0.697881i
$93$	−8.99673	−	14.5817i	−0.932917	−	1.51205i
$94$	−6.71987	+	3.87972i	−0.693102	+	0.400162i
$95$	−19.6446	+	11.3418i	−2.01549	+	1.16365i
$96$	0.909476	+	1.47406i	0.0928230	+	0.150446i
$97$	−5.04512			−0.512255			−0.256127	−	0.966643i	$-0.582447\pi$
$97$	−5.04512			−0.512255			−0.256127	+	0.966643i	$0.582447\pi$
$98$	−1.60570	+	6.81335i	−0.162200	+	0.688252i
$99$	−6.24174	−	9.48478i	−0.627318	−	0.953257i
$100$	4.60338	−	7.97329i	0.460338	−	0.797329i
$101$	0.710555	+	1.23072i	0.0707029	+	0.122461i	0.899210	−	0.437518i	$-0.144142\pi$
$101$	0.710555	+	1.23072i	0.0707029	+	0.122461i	−0.828507	+	0.559979i	$0.810809\pi$
$102$	−4.01717	+	0.117406i	−0.397760	+	0.0116249i
$103$	−9.99478	−	5.77049i	−0.984814	−	0.568583i	−0.0810943	−	0.996706i	$-0.525841\pi$
$103$	−9.99478	−	5.77049i	−0.984814	−	0.568583i	−0.903720	+	0.428124i	$0.859175\pi$
$104$	2.90274	−	2.13872i	0.284637	−	0.209718i
$105$	5.89522	−	16.2354i	0.575315	−	1.58441i
$106$			0.754823i			0.0733149i
$107$	4.75556	+	2.74562i	0.459737	+	0.265430i	0.711934	−	0.702247i	$-0.247820\pi$
$107$	4.75556	+	2.74562i	0.459737	+	0.265430i	−0.252196	+	0.967676i	$0.581153\pi$
$108$	−2.98203	−	4.25529i	−0.286946	−	0.409465i
$109$	0.280553	−	0.161977i	0.0268721	−	0.0155146i	−0.486504	−	0.873678i	$-0.661728\pi$
$109$	0.280553	−	0.161977i	0.0268721	−	0.0155146i	0.513376	+	0.858164i	$0.328395\pi$
$110$	−12.3543	−	7.13275i	−1.17794	−	0.680081i
$111$	10.4315	+	5.62289i	0.990116	+	0.533701i
$112$	2.45944	+	0.975274i	0.232395	+	0.0921547i
$113$		−	11.6924i		−	1.09993i	−0.835187	−	0.549965i	$-0.814641\pi$
$113$		−	11.6924i		−	1.09993i	0.835187	−	0.549965i	$-0.185359\pi$
$114$	5.47339	+	8.87116i	0.512630	+	0.830860i
$115$	12.6152	+	21.8501i	1.17637	+	2.03753i
$116$	2.66529	−	1.53881i	0.247466	−	0.142875i
$117$	−8.31864	+	6.91377i	−0.769059	+	0.639178i
$118$			4.25727i			0.391914i
$119$	−4.81309	+	3.81064i	−0.441215	+	0.349321i
$120$	−5.74673	−	3.09765i	−0.524602	−	0.282776i
$121$	−1.66224	+	2.87909i	−0.151113	+	0.261736i
$122$	−8.37307	+	4.83419i	−0.758062	+	0.437667i
$123$	0.338807	+	11.5927i	0.0305492	+	1.04528i
$124$	−4.94611	+	8.56691i	−0.444174	+	0.769331i
$125$			15.8561i			1.41821i
$126$	−7.53660	−	2.48992i	−0.671413	−	0.221820i
$127$	12.1818			1.08096			0.540482	−	0.841356i	$-0.318242\pi$
$127$	12.1818			1.08096			0.540482	+	0.841356i	$0.318242\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−6.01251	+	0.175721i	−0.529372	+	0.0154714i
$130$	−5.44455	+	12.4517i	−0.477518	+	1.09209i
$131$	0.646676	−	1.12008i	0.0565003	−	0.0978614i	−0.836392	−	0.548132i	$-0.815339\pi$
$131$	0.646676	−	1.12008i	0.0565003	−	0.0978614i	0.892892	+	0.450271i	$0.148672\pi$
$132$	−3.11046	+	5.77049i	−0.270731	+	0.502256i
$133$	14.8013	+	5.86937i	1.28344	+	0.508939i
$134$		−	5.21907i		−	0.450859i
$135$	17.7535	+	8.27024i	1.52798	+	0.711789i
$136$	1.16015	+	2.00944i	0.0994823	+	0.172308i
$137$	−1.45303	−	2.51672i	−0.124141	−	0.215018i	0.797256	−	0.603641i	$-0.206284\pi$
$137$	−1.45303	−	2.51672i	−0.124141	−	0.215018i	−0.921397	+	0.388623i	$0.872951\pi$
$138$	9.86713	−	6.08789i	0.839945	−	0.518235i
$139$		−	5.34738i		−	0.453558i	−0.973946	−	0.226779i	$-0.927180\pi$
$139$		−	5.34738i		−	0.453558i	0.973946	−	0.226779i	$-0.0728196\pi$
$140$	−9.86612	+	1.45154i	−0.833840	+	0.122678i
$141$	−11.8305	−	6.37698i	−0.996308	−	0.537039i
$142$	3.11747	−	5.39962i	0.261612	−	0.453126i
$143$	12.5032	+	5.46706i	1.04557	+	0.457178i
$144$	−1.34571	+	2.68124i	−0.112142	+	0.223437i
$145$	−5.80004	+	10.0460i	−0.481668	+	0.834273i
$146$	−5.06546			−0.419220
$147$	−11.5036	+	3.82967i	−0.948804	+	0.315866i
$148$		−	6.84187i		−	0.562398i
$149$	−2.35181	+	4.07346i	−0.192668	+	0.333711i	−0.946134	−	0.323777i	$-0.895047\pi$
$149$	−2.35181	+	4.07346i	−0.192668	+	0.333711i	0.753465	+	0.657487i	$0.228381\pi$
$150$	15.9398	−	0.465854i	1.30148	−	0.0380368i
$151$	−5.51385	+	3.18342i	−0.448711	+	0.259063i	−0.707285	−	0.706928i	$-0.750080\pi$
$151$	−5.51385	+	3.18342i	−0.448711	+	0.259063i	0.258575	+	0.965991i	$0.416747\pi$
$152$	3.00909	−	5.21190i	0.244069	−	0.422741i
$153$	−3.82659	−	5.81478i	−0.309361	−	0.470097i
$154$	1.45754	+	9.90692i	0.117452	+	0.798322i
$155$		−	37.2856i		−	2.99485i
$156$	5.79257	+	2.33370i	0.463777	+	0.186846i
$157$	−9.82232	+	5.67092i	−0.783906	+	0.452588i	−0.837813	−	0.545958i	$-0.816166\pi$
$157$	−9.82232	+	5.67092i	−0.783906	+	0.452588i	0.0539067	+	0.998546i	$0.482833\pi$
$158$	0.402095	+	0.696449i	0.0319889	+	0.0554065i
$159$	−1.11266	+	0.686494i	−0.0882393	+	0.0544425i
$160$			3.76919i			0.297980i
$161$	6.52833	−	16.4631i	0.514504	−	1.29747i
$162$	3.56046	−	8.26578i	0.279736	−	0.649421i
$163$	7.92899	+	4.57780i	0.621046	+	0.358561i	0.777276	−	0.629159i	$-0.216601\pi$
$163$	7.92899	+	4.57780i	0.621046	+	0.358561i	−0.156230	+	0.987721i	$0.549934\pi$
$164$	5.79883	−	3.34796i	0.452813	−	0.261431i
$165$	−0.721822	−	24.6980i	−0.0561938	−	1.92274i
$166$	5.96500	+	3.44389i	0.462974	+	0.267298i
$167$		−	6.31465i		−	0.488642i	−0.969694	−	0.244321i	$-0.921435\pi$
$167$		−	6.31465i		−	0.488642i	0.969694	−	0.244321i	$-0.0785651\pi$
$168$	0.799188	+	4.51235i	0.0616587	+	0.348135i
$169$	3.85179	−	12.4163i	0.296292	−	0.955097i
$170$	−7.57397	−	4.37284i	−0.580897	−	0.335381i
$171$	−8.09871	+	16.1362i	−0.619324	+	1.23397i
$172$	1.73640	+	3.00754i	0.132399	+	0.229323i
$173$	−7.91626	+	13.7114i	−0.601862	+	1.04246i	0.390677	+	0.920528i	$0.372241\pi$
$173$	−7.91626	+	13.7114i	−0.601862	+	1.04246i	−0.992539	+	0.121928i	$0.961092\pi$
$174$	4.69231	+	2.52929i	0.355723	+	0.191745i
$175$	19.0979	−	15.1203i	1.44366	−	1.14299i
$176$	3.78477			0.285288
$177$	−6.27548	+	3.87189i	−0.471694	+	0.291029i
$178$	13.5271	−	7.80988i	1.01390	−	0.585375i
$179$	−14.2272	+	8.21410i	−1.06339	+	0.613950i	−0.926369	−	0.376617i	$-0.877087\pi$
$179$	−14.2272	+	8.21410i	−1.06339	+	0.613950i	−0.137024	+	0.990568i	$0.543754\pi$
$180$	−0.660383	−	11.2883i	−0.0492220	−	0.841377i
$181$		−	10.7381i		−	0.798156i	−0.916917	−	0.399078i	$-0.869330\pi$
$181$		−	10.7381i		−	0.798156i	0.916917	−	0.399078i	$-0.130670\pi$
$182$	9.22494	−	2.42907i	0.683798	−	0.180055i
$183$	−14.7410	−	7.94582i	−1.08969	−	0.587372i
$184$	−5.79704	−	3.34692i	−0.427363	−	0.246738i
$185$	12.8941	+	22.3333i	0.947996	+	1.64198i
$186$	−17.1265	+	0.500537i	−1.25578	+	0.0367012i
$187$	−4.39092	+	7.60529i	−0.321096	+	0.556154i
$188$			7.75944i			0.565915i
$189$	−3.18406	−	13.3739i	−0.231606	−	0.972810i
$190$			22.6836i			1.64564i
$191$	−9.19327	−	5.30774i	−0.665201	−	0.384054i	0.129055	−	0.991637i	$-0.458806\pi$
$191$	−9.19327	−	5.30774i	−0.665201	−	0.384054i	−0.794256	+	0.607583i	$0.792139\pi$
$192$	1.73131	−	0.0505991i	0.124947	−	0.00365168i
$193$	3.91178	−	2.25847i	0.281576	−	0.162568i	−0.352560	−	0.935789i	$-0.614689\pi$
$193$	3.91178	−	2.25847i	0.281576	−	0.162568i	0.634137	+	0.773221i	$0.281356\pi$
$194$	−2.52256	+	4.36920i	−0.181109	+	0.313691i
$195$	−23.3062	+	3.29893i	−1.66899	+	0.236242i
$196$	5.09768	+	4.79725i	0.364120	+	0.342661i
$197$	−14.2398			−1.01454			−0.507271	−	0.861787i	$-0.669346\pi$
$197$	−14.2398			−1.01454			−0.507271	+	0.861787i	$0.669346\pi$
$198$	−11.3349	+	0.663113i	−0.805539	+	0.0471254i
$199$	20.5340	−	11.8553i	1.45561	−	0.840399i	0.456823	−	0.889558i	$-0.348987\pi$
$199$	20.5340	−	11.8553i	1.45561	−	0.840399i	0.998791	+	0.0491586i	$0.0156540\pi$
$200$	−4.60338	−	7.97329i	−0.325508	−	0.563797i
$201$	7.69322	−	4.74662i	0.542638	−	0.334800i
$202$	1.42111			0.0999890
$203$	8.05587	−	1.18521i	0.565411	−	0.0831855i
$204$	−1.90691	+	3.53768i	−0.133510	+	0.247687i
$205$	−12.6191	+	21.8569i	−0.881354	+	1.52655i
$206$	−9.99478	+	5.77049i	−0.696369	+	0.402049i
$207$	17.9478	+	9.00795i	1.24746	+	0.626096i
$208$	−0.400812	−	3.58320i	−0.0277913	−	0.248450i
$209$	22.7774			1.57555
$210$	−11.1127	−	13.2231i	−0.766847	−	0.912482i
$211$	−13.0673			−0.899588			−0.449794	−	0.893132i	$-0.648503\pi$
$211$	−13.0673			−0.899588			−0.449794	+	0.893132i	$0.648503\pi$
$212$	0.653696	+	0.377412i	0.0448960	+	0.0259207i
$213$	10.7946	−	0.315483i	0.739636	−	0.0216165i
$214$	4.75556	−	2.74562i	0.325083	−	0.187687i
$215$	−11.3360	−	6.54482i	−0.773107	−	0.446353i
$216$	−5.17620	+	0.454874i	−0.352196	+	0.0309502i
$217$	−20.5197	+	16.2460i	−1.39297	+	1.10285i
$218$		−	0.323955i		−	0.0219410i
$219$	−4.60691	−	7.46679i	−0.311306	−	0.504559i
$220$	−12.3543	+	7.13275i	−0.832926	+	0.480890i
$221$	7.66525	+	3.35166i	0.515621	+	0.225457i
$222$	10.0853	−	6.22252i	0.676883	−	0.417628i
$223$	−2.14629			−0.143726			−0.0718632	−	0.997414i	$-0.522894\pi$
$223$	−2.14629			−0.143726			−0.0718632	+	0.997414i	$0.522894\pi$
$224$	2.07433	−	1.64230i	0.138597	−	0.109731i
$225$	15.1835	+	23.0725i	1.01224	+	1.53817i
$226$	−10.1259	−	5.84621i	−0.673567	−	0.388884i
$227$	−14.1171	+	8.15053i	−0.936987	+	0.540970i	−0.889014	−	0.457879i	$-0.848609\pi$
$227$	−14.1171	+	8.15053i	−0.936987	+	0.540970i	−0.0479723	+	0.998849i	$0.515276\pi$
$228$	10.4193	−	0.304515i	0.690038	−	0.0201670i
$229$	−12.6694	+	21.9440i	−0.837215	+	1.45010i	0.0549995	+	0.998486i	$0.482484\pi$
$229$	−12.6694	+	21.9440i	−0.837215	+	1.45010i	−0.892214	+	0.451612i	$0.850849\pi$
$230$	25.2303			1.66364
$231$	−13.2778	+	11.1586i	−0.873614	+	0.734183i
$232$		−	3.07761i		−	0.202055i
$233$	18.8229	+	10.8674i	1.23313	+	0.711947i	0.967681	−	0.252179i	$-0.0811471\pi$
$233$	18.8229	+	10.8674i	1.23313	+	0.711947i	0.265447	+	0.964125i	$0.414480\pi$
$234$	1.82818	+	10.6610i	0.119512	+	0.696934i
$235$	−14.6234	−	25.3284i	−0.953924	−	1.65225i
$236$	3.68691	+	2.12864i	0.239997	+	0.138562i
$237$	−0.660912	+	1.22611i	−0.0429308	+	0.0796447i
$238$	0.893568	+	6.07357i	0.0579214	+	0.393691i
$239$	22.1257			1.43119			0.715597	−	0.698514i	$-0.246155\pi$
$239$	22.1257			1.43119			0.715597	+	0.698514i	$0.246155\pi$
$240$	−5.55601	+	3.42798i	−0.358639	+	0.221275i
$241$	−6.28726	−	10.8899i	−0.404998	−	0.701477i	0.589323	−	0.807897i	$-0.299395\pi$
$241$	−6.28726	−	10.8899i	−0.404998	−	0.701477i	−0.994321	+	0.106420i	$0.966061\pi$
$242$	1.66224	+	2.87909i	0.106853	+	0.185075i
$243$	15.4224	−	2.26919i	0.989348	−	0.145569i
$244$			9.66839i			0.618955i
$245$	−25.6808	−	6.05219i	−1.64069	−	0.386660i
$246$	10.2090	+	5.50294i	0.650901	+	0.350855i
$247$	−2.41216	−	21.5644i	−0.153482	−	1.37211i
$248$	4.94611	+	8.56691i	0.314078	+	0.543999i
$249$	0.348516	+	11.9249i	0.0220863	+	0.755710i
$250$	13.7318	+	7.92805i	0.868474	+	0.501414i
$251$	8.59657			0.542611			0.271305	−	0.962493i	$-0.412545\pi$
$251$	8.59657			0.542611			0.271305	+	0.962493i	$0.412545\pi$
$252$	−5.92463	+	5.28192i	−0.373217	+	0.332730i
$253$		−	25.3347i		−	1.59278i
$254$	6.09092	−	10.5498i	0.382178	−	0.661952i
$255$	−0.442523	−	15.1415i	−0.0277119	−	0.948196i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	10.8190	−	18.7391i	0.674873	−	1.16891i	−0.301633	−	0.953424i	$-0.597532\pi$
$257$	10.8190	−	18.7391i	0.674873	−	1.16891i	0.976506	−	0.215490i	$-0.0691349\pi$
$258$	−2.85407	+	5.29484i	−0.177687	+	0.329643i
$259$	6.67270	−	16.8272i	0.414621	−	1.04559i
$260$	8.06122	+	10.9410i	0.499935	+	0.678530i
$261$	0.539215	+	9.21707i	0.0333766	+	0.570523i
$262$	−0.646676	−	1.12008i	−0.0399518	−	0.0691985i
$263$	−12.6463	+	7.30132i	−0.779802	+	0.450219i	−0.836360	−	0.548181i	$-0.815321\pi$
$263$	−12.6463	+	7.30132i	−0.779802	+	0.450219i	0.0565583	+	0.998399i	$0.481987\pi$
$264$	3.44216	+	5.57898i	0.211850	+	0.343362i
$265$	−2.84507			−0.174771
$266$	12.4837	−	9.88366i	0.765425	−	0.606006i
$267$	23.8148	+	12.8369i	1.45744	+	0.785604i
$268$	−4.51984	−	2.60953i	−0.276093	−	0.159403i
$269$	−8.55131	−	14.8113i	−0.521382	−	0.903061i	−0.999691	−	0.0248689i	$-0.992083\pi$
$269$	−8.55131	−	14.8113i	−0.521382	−	0.903061i	0.478308	−	0.878192i	$-0.341250\pi$
$270$	16.0390	−	11.2398i	0.976101	−	0.684035i
$271$	14.9138	−	25.8315i	0.905949	−	1.56915i	0.0863103	−	0.996268i	$-0.472492\pi$
$271$	14.9138	−	25.8315i	0.905949	−	1.56915i	0.819639	−	0.572881i	$-0.194174\pi$
$272$	2.32031			0.140689
$273$	11.9705	+	11.3889i	0.724486	+	0.689290i
$274$	−2.90606			−0.175561
$275$	17.4228	−	30.1771i	1.05063	−	1.81975i
$276$	−0.338702	−	11.5891i	−0.0203875	−	0.697583i
$277$	−7.84269	−	13.5839i	−0.471221	−	0.816179i	0.528237	−	0.849097i	$-0.322853\pi$
$277$	−7.84269	−	13.5839i	−0.471221	−	0.816179i	−0.999458	+	0.0329179i	$0.989520\pi$
$278$	−4.63096	−	2.67369i	−0.277747	−	0.160357i
$279$	−16.3140	−	24.7903i	−0.976692	−	1.48415i
$280$	−3.67599	+	9.27009i	−0.219682	+	0.553994i
$281$	21.2682			1.26875			0.634376	−	0.773025i	$-0.281257\pi$
$281$	21.2682			1.26875			0.634376	+	0.773025i	$0.281257\pi$
$282$	−11.4379	+	7.05702i	−0.681116	+	0.420239i
$283$	28.1781	−	16.2686i	1.67501	−	0.967069i	0.710250	−	0.703950i	$-0.248582\pi$
$283$	28.1781	−	16.2686i	1.67501	−	0.967069i	0.964763	−	0.263119i	$-0.0847512\pi$
$284$	−3.11747	−	5.39962i	−0.184988	−	0.320408i
$285$	−33.4371	+	20.6302i	−1.98064	+	1.22203i
$286$	10.9862	−	8.09455i	0.649628	−	0.478641i
$287$	17.5270	−	2.57865i	1.03459	−	0.152213i
$288$	1.64917	+	2.50604i	0.0971784	+	0.147670i
$289$	5.80809	−	10.0599i	0.341652	−	0.591759i
$290$	5.80004	+	10.0460i	0.340590	+	0.589920i
$291$	−8.73468	+	0.255279i	−0.512036	+	0.0149647i
$292$	−2.53273	+	4.38682i	−0.148217	+	0.256719i
$293$		−	15.1575i		−	0.885509i	−0.896643	−	0.442755i	$-0.854001\pi$
$293$		−	15.1575i		−	0.885509i	0.896643	−	0.442755i	$-0.145999\pi$
$294$	−2.43522	+	11.8773i	−0.142025	+	0.692697i
$295$	−16.0465			−0.934261
$296$	−5.92523	−	3.42094i	−0.344397	−	0.198838i
$297$	−11.2863	−	16.1053i	−0.654899	−	0.934524i
$298$	2.35181	+	4.07346i	0.136237	+	0.235969i
$299$	−23.9854	+	2.68297i	−1.38711	+	0.155160i
$300$	7.56645	−	14.0372i	0.436849	−	0.810437i
$301$	1.33740	+	9.09032i	0.0770867	+	0.523958i
$302$			6.36684i			0.366371i
$303$	1.29247	+	2.09480i	0.0742502	+	0.120343i
$304$	−3.00909	−	5.21190i	−0.172583	−	0.298923i
$305$	−18.2210	−	31.5597i	−1.04333	−	1.80710i
$306$	−6.94904	+	0.406531i	−0.397250	+	0.0232398i
$307$	22.7279			1.29715			0.648576	−	0.761150i	$-0.275365\pi$
$307$	22.7279			1.29715			0.648576	+	0.761150i	$0.275365\pi$
$308$	9.30841	+	3.69119i	0.530396	+	0.210325i
$309$	−17.5961	−	9.48478i	−1.00100	−	0.539570i
$310$	−32.2903	−	18.6428i	−1.83396	−	1.05884i
$311$	−3.17259	−	5.49509i	−0.179901	−	0.311598i	0.761945	−	0.647641i	$-0.224244\pi$
$311$	−3.17259	−	5.49509i	−0.179901	−	0.311598i	−0.941847	+	0.336043i	$0.890911\pi$
$312$	4.91733	−	3.84966i	0.278389	−	0.217944i
$313$	9.83094	+	5.67590i	0.555678	+	0.320821i	0.751409	−	0.659837i	$-0.229375\pi$
$313$	9.83094	+	5.67590i	0.555678	+	0.320821i	−0.195731	+	0.980658i	$0.562708\pi$
$314$			11.3418i			0.640057i
$315$	9.38497	−	28.4068i	0.528783	−	1.60054i
$316$	0.804189			0.0452392
$317$	0.315688	−	0.546787i	0.0177308	−	0.0307106i	−0.857024	−	0.515277i	$-0.827689\pi$
$317$	0.315688	−	0.546787i	0.0177308	−	0.0307106i	0.874755	+	0.484566i	$0.161022\pi$
$318$	0.0381934	+	1.30683i	0.00214178	+	0.0732836i
$319$	10.0875	−	5.82403i	0.564792	−	0.326083i
$320$	3.26421	+	1.88459i	0.182475	+	0.105352i
$321$	8.37228	+	4.51290i	0.467295	+	0.251886i
$322$	−10.9933	−	13.8852i	−0.612632	−	0.773794i
$323$	13.9640			0.776979
$324$	−5.37814	−	7.21634i	−0.298786	−	0.400908i
$325$	−30.4150	−	13.2991i	−1.68712	−	0.737700i
$326$	7.92899	−	4.57780i	0.439146	−	0.253541i
$327$	0.477529	−	0.294629i	0.0264074	−	0.0162930i
$328$		−	6.69591i		−	0.369720i
$329$	−7.56757	+	19.0839i	−0.417214	+	1.05213i
$330$	−21.7500	−	11.7239i	−1.19730	−	0.645380i
$331$	10.6712	+	6.16103i	0.586543	+	0.338641i	0.763729	−	0.645536i	$-0.223366\pi$
$331$	10.6712	+	6.16103i	0.586543	+	0.338641i	−0.177186	+	0.984177i	$0.556700\pi$
$332$	5.96500	−	3.44389i	0.327372	−	0.189008i
$333$	18.3447	+	9.20715i	1.00528	+	0.504549i
$334$	−5.46865	−	3.15733i	−0.299231	−	0.172761i
$335$	19.6716			1.07478
$336$	4.30740	+	1.56406i	0.234988	+	0.0853263i
$337$	−7.10322			−0.386937			−0.193469	−	0.981106i	$-0.561974\pi$
$337$	−7.10322			−0.386937			−0.193469	+	0.981106i	$0.561974\pi$
$338$	−8.82691	−	9.54388i	−0.480120	−	0.519119i
$339$	−0.591626	−	20.2432i	−0.0321327	−	1.09946i
$340$	−7.57397	+	4.37284i	−0.410756	+	0.237150i
$341$	−18.7199	+	32.4238i	−1.01374	+	1.75585i
$342$	9.92502	+	15.0818i	0.536683	+	0.815530i
$343$	7.85880	+	16.7702i	0.424335	+	0.905505i
$344$	3.47280			0.187241
$345$	22.9464	+	37.1910i	1.23539	+	2.00230i
$346$	7.91626	+	13.7114i	0.425581	+	0.737128i
$347$	−1.02619	+	0.592469i	−0.0550886	+	0.0318054i	−0.527291	−	0.849685i	$-0.676792\pi$
$347$	−1.02619	+	0.592469i	−0.0550886	+	0.0318054i	0.472203	+	0.881490i	$0.343459\pi$
$348$	4.53658	−	2.79901i	0.243186	−	0.150043i
$349$	19.2573			1.03082			0.515411	−	0.856943i	$-0.327639\pi$
$349$	19.2573			1.03082			0.515411	+	0.856943i	$0.327639\pi$
$350$	−3.54560	−	24.0994i	−0.189520	−	1.28817i
$351$	−14.0523	+	12.3908i	−0.750058	+	0.661372i
$352$	1.89239	−	3.27771i	0.100864	−	0.174702i
$353$	0.0869477	−	0.0501993i	0.00462776	−	0.00267184i	−0.497684	−	0.867358i	$-0.665816\pi$
$353$	0.0869477	−	0.0501993i	0.00462776	−	0.00267184i	0.502312	+	0.864686i	$0.332483\pi$
$354$	0.215414	+	7.37067i	0.0114491	+	0.391746i
$355$	20.3522	+	11.7503i	1.08018	+	0.623643i
$356$		−	15.6198i		−	0.827845i
$357$	−8.14014	+	6.84094i	−0.430822	+	0.362061i
$358$			16.4282i			0.868257i
$359$	4.13025	−	7.15381i	0.217987	−	0.377564i	−0.736206	−	0.676758i	$-0.763384\pi$
$359$	4.13025	−	7.15381i	0.217987	−	0.377564i	0.954192	+	0.299194i	$0.0967178\pi$
$360$	−10.1061	−	5.07222i	−0.532639	−	0.267330i
$361$	−8.60925	−	14.9117i	−0.453118	−	0.784824i
$362$	−9.29946	−	5.36904i	−0.488769	−	0.282191i
$363$	−2.73218	+	5.06871i	−0.143402	+	0.266039i
$364$	2.50883	−	9.20357i	0.131499	−	0.482398i
$365$		−	19.0927i		−	0.999356i
$366$	−14.2518	+	8.79316i	−0.744953	+	0.459626i
$367$	−24.5980	+	14.2017i	−1.28400	+	0.741320i	−0.977578	−	0.210574i	$-0.932467\pi$
$367$	−24.5980	+	14.2017i	−1.28400	+	0.741320i	−0.306427	+	0.951894i	$0.599133\pi$
$368$	−5.79704	+	3.34692i	−0.302191	+	0.174470i
$369$	1.17316	+	20.0534i	0.0610724	+	1.04394i
$370$	25.7883			1.34067
$371$	1.23965	+	1.56575i	0.0643592	+	0.0812899i
$372$	−8.12977	+	15.0823i	−0.421509	+	0.781979i
$373$	5.82807	−	10.0945i	0.301766	−	0.522674i	−0.674770	−	0.738028i	$-0.735757\pi$
$373$	5.82807	−	10.0945i	0.301766	−	0.522674i	0.976536	+	0.215354i	$0.0690905\pi$
$374$	4.39092	+	7.60529i	0.227049	+	0.393260i
$375$	0.802304	+	27.4518i	0.0414308	+	1.41761i
$376$	6.71987	+	3.87972i	0.346551	+	0.200081i
$377$	−6.58213	−	8.93350i	−0.338997	−	0.460099i
$378$	−13.1742	−	3.92948i	−0.677607	−	0.202111i
$379$		−	5.72601i		−	0.294125i	−0.989127	−	0.147063i	$-0.953018\pi$
$379$		−	5.72601i		−	0.294125i	0.989127	−	0.147063i	$-0.0469819\pi$
$380$	19.6446	+	11.3418i	1.00775	+	0.581823i
$381$	21.0906	−	0.616390i	1.08050	−	0.0315786i
$382$	−9.19327	+	5.30774i	−0.470368	+	0.271567i
$383$	17.2864	+	9.98032i	0.883295	+	0.509971i	0.871743	−	0.489963i	$-0.162990\pi$
$383$	17.2864	+	9.98032i	0.883295	+	0.509971i	0.0115516	+	0.999933i	$0.496323\pi$
$384$	0.821836	−	1.52466i	0.0419391	−	0.0778049i
$385$	−37.3410	+	5.49376i	−1.90307	+	0.279988i
$386$		−	4.51694i		−	0.229906i
$387$	−10.4006	+	0.608455i	−0.528694	+	0.0309295i
$388$	2.52256	+	4.36920i	0.128064	+	0.221813i
$389$	18.6337	−	10.7582i	0.944765	−	0.545460i	0.0533140	−	0.998578i	$-0.483022\pi$
$389$	18.6337	−	10.7582i	0.944765	−	0.545460i	0.891451	+	0.453118i	$0.149688\pi$
$390$	−8.79616	+	21.8333i	−0.445411	+	1.10557i
$391$		−	15.5318i		−	0.785475i
$392$	6.70338	−	2.01610i	0.338572	−	0.101828i
$393$	1.06292	−	1.97192i	0.0536173	−	0.0994702i
$394$	−7.11989	+	12.3320i	−0.358695	+	0.621278i
$395$	−2.62504	+	1.51557i	−0.132080	+	0.0762566i
$396$	−5.09319	+	10.1479i	−0.255943	+	0.509951i
$397$	−13.1292	+	22.7405i	−0.658938	+	1.14131i	0.321953	+	0.946756i	$0.395661\pi$
$397$	−13.1292	+	22.7405i	−0.658938	+	1.14131i	−0.980891	+	0.194558i	$0.937673\pi$
$398$		−	23.7106i		−	1.18850i
$399$	25.9227	+	9.41278i	1.29776	+	0.471228i
$400$	−9.20677			−0.460338
$401$	3.80346	−	6.58778i	0.189936	−	0.328978i	−0.755293	−	0.655387i	$-0.772505\pi$
$401$	3.80346	−	6.58778i	0.189936	−	0.328978i	0.945229	+	0.326409i	$0.105839\pi$
$402$	−0.264080	−	9.03583i	−0.0131711	−	0.450666i
$403$	32.6794	+	14.2892i	1.62788	+	0.711795i
$404$	0.710555	−	1.23072i	0.0353515	−	0.0612305i
$405$	31.1553	+	13.4200i	1.54812	+	0.666847i
$406$	3.00151	−	7.56920i	0.148963	−	0.375653i
$407$		−	25.8949i		−	1.28356i
$408$	2.11026	+	3.42027i	0.104474	+	0.169329i
$409$	−6.08464	−	10.5389i	−0.300866	−	0.521115i	0.675466	−	0.737391i	$-0.263942\pi$
$409$	−6.08464	−	10.5389i	−0.300866	−	0.521115i	−0.976332	+	0.216276i	$0.930609\pi$
$410$	12.6191	+	21.8569i	0.623211	+	1.07943i
$411$	−2.64299	−	4.28371i	−0.130369	−	0.211300i
$412$			11.5410i			0.568583i
$413$	6.99172	+	8.83099i	0.344040	+	0.434545i
$414$	16.7750	−	11.0393i	0.824448	−	0.542552i
$415$	−12.9807	+	22.4832i	−0.637197	+	1.10366i
$416$	−3.30355	−	1.44449i	−0.161970	−	0.0708219i
$417$	−0.270572	−	9.25797i	−0.0132500	−	0.453365i
$418$	11.3887	−	19.7258i	0.557040	−	0.964822i
$419$	−26.6532			−1.30209			−0.651047	−	0.759037i	$-0.725670\pi$
$419$	−26.6532			−1.30209			−0.651047	+	0.759037i	$0.725670\pi$
$420$	−17.0079	+	3.01229i	−0.829900	+	0.146985i
$421$			5.46674i			0.266433i	0.991087	+	0.133216i	$0.0425305\pi$
$421$			5.46674i			0.266433i	−0.991087	+	0.133216i	$0.957469\pi$
$422$	−6.53364	+	11.3166i	−0.318053	+	0.550883i
$423$	−20.8049	−	10.4419i	−1.01157	−	0.507704i
$424$	0.653696	−	0.377412i	0.0317463	−	0.0183287i
$425$	10.6813	−	18.5005i	0.518117	−	0.897406i
$426$	5.12410	−	9.50616i	0.248263	−	0.460575i
$427$	−9.42932	+	23.7788i	−0.456317	+	1.15074i
$428$		−	5.49125i		−	0.265430i
$429$	21.9235	+	8.83253i	1.05848	+	0.426439i
$430$	−11.3360	+	6.54482i	−0.546669	+	0.315619i
$431$	−6.87264	−	11.9038i	−0.331043	−	0.573384i	0.651673	−	0.758500i	$-0.274067\pi$
$431$	−6.87264	−	11.9038i	−0.331043	−	0.573384i	−0.982717	+	0.185116i	$0.940734\pi$
$432$	−2.19417	+	4.71016i	−0.105567	+	0.226618i
$433$			31.5338i			1.51542i	0.652592	+	0.757709i	$0.273681\pi$
$433$			31.5338i			1.51542i	−0.652592	+	0.757709i	$0.726319\pi$
$434$	3.80957	+	25.8936i	0.182865	+	1.24293i
$435$	−9.53337	+	17.6862i	−0.457090	+	0.847988i
$436$	−0.280553	−	0.161977i	−0.0134361	−	0.00775731i
$437$	−34.8876	+	20.1424i	−1.66890	+	0.963540i
$438$	−8.76989	+	0.256308i	−0.419041	+	0.0122469i
$439$	−25.1301	−	14.5088i	−1.19939	−	0.692469i	−0.238973	−	0.971026i	$-0.576811\pi$
$439$	−25.1301	−	14.5088i	−1.19939	−	0.692469i	−0.960420	+	0.278557i	$0.910144\pi$
$440$			14.2655i			0.680081i
$441$	−19.7226	+	7.21243i	−0.939171	+	0.343449i
$442$	6.73525	−	4.96248i	0.320363	−	0.236041i
$443$	5.01928	+	2.89788i	0.238473	+	0.137682i	0.614475	−	0.788937i	$-0.289368\pi$
$443$	5.01928	+	2.89788i	0.238473	+	0.137682i	−0.376002	+	0.926619i	$0.622701\pi$
$444$	−0.346193	−	11.8454i	−0.0164296	−	0.562158i
$445$	29.4369	+	50.9862i	1.39544	+	2.41698i
$446$	−1.07315	+	1.85874i	−0.0508149	+	0.0880141i
$447$	−3.86561	+	7.17143i	−0.182837	+	0.339197i
$448$	−0.385108	−	2.61757i	−0.0181946	−	0.123669i
$449$	15.5891			0.735696			0.367848	−	0.929886i	$-0.380095\pi$
$449$	15.5891			0.735696			0.367848	+	0.929886i	$0.380095\pi$
$450$	27.5732	−	1.61308i	1.29981	−	0.0760412i
$451$	21.9472	−	12.6712i	1.03346	−	0.596666i
$452$	−10.1259	+	5.84621i	−0.476284	+	0.274983i
$453$	−9.38511	+	5.79049i	−0.440951	+	0.272061i
$454$			16.3011i			0.765047i
$455$	9.15564	+	34.7705i	0.429223	+	1.63007i
$456$	4.94596	−	9.17568i	0.231616	−	0.429690i
$457$	−2.92274	−	1.68744i	−0.136720	−	0.0789353i	0.430080	−	0.902791i	$-0.358485\pi$
$457$	−2.92274	−	1.68744i	−0.136720	−	0.0789353i	−0.566800	+	0.823856i	$0.691819\pi$
$458$	12.6694	+	21.9440i	0.592000	+	1.02537i
$459$	−6.91924	−	9.87357i	−0.322962	−	0.460859i
$460$	12.6152	−	21.8501i	0.588185	−	1.01877i
$461$			3.58098i			0.166783i	0.996517	+	0.0833914i	$0.0265752\pi$
$461$			3.58098i			0.166783i	−0.996517	+	0.0833914i	$0.973425\pi$
$462$	3.02474	+	17.0782i	0.140724	+	0.794550i
$463$			8.12604i			0.377649i	0.982011	+	0.188825i	$0.0604677\pi$
$463$			8.12604i			0.377649i	−0.982011	+	0.188825i	$0.939532\pi$
$464$	−2.66529	−	1.53881i	−0.123733	−	0.0714373i
$465$	−1.88662	−	64.5530i	−0.0874898	−	2.99357i
$466$	18.8229	−	10.8674i	0.871953	−	0.503422i
$467$	18.4226	−	31.9089i	0.852496	−	1.47657i	−0.0264534	−	0.999650i	$-0.508421\pi$
$467$	18.4226	−	31.9089i	0.852496	−	1.47657i	0.878949	−	0.476916i	$-0.158245\pi$
$468$	10.1468	+	3.74727i	0.469037	+	0.173218i
$469$	−8.57127	−	10.8261i	−0.395785	−	0.499902i
$470$	−29.2468			−1.34905
$471$	−16.7185	+	10.3151i	−0.770350	+	0.475296i
$472$	3.68691	−	2.12864i	0.169704	−	0.0979784i
$473$	6.57189	+	11.3828i	0.302176	+	0.523384i
$474$	0.731391	+	1.18542i	0.0335939	+	0.0544483i
$475$	−55.4080			−2.54229
$476$	5.70665	+	2.26293i	0.261564	+	0.103721i
$477$	−1.89162	+	1.24483i	−0.0866112	+	0.0569970i
$478$	11.0629	−	19.1614i	0.506003	−	0.876424i
$479$	−5.24426	+	3.02777i	−0.239616	+	0.138343i	−0.615000	−	0.788527i	$-0.710844\pi$
$479$	−5.24426	+	3.02777i	−0.239616	+	0.138343i	0.375384	+	0.926869i	$0.377511\pi$
$480$	0.190718	+	6.52564i	0.00870502	+	0.297853i
$481$	−24.5158	+	2.74230i	−1.11782	+	0.125038i
$482$	−12.5745			−0.572754
$483$	10.4696	−	28.8331i	0.476381	−	1.31195i
$484$	3.32449			0.151113
$485$	−16.4683	−	9.50800i	−0.747789	−	0.431736i
$486$	5.74603	−	14.4908i	0.260645	−	0.657316i
$487$	−21.7283	+	12.5449i	−0.984605	+	0.568462i	−0.903657	−	0.428256i	$-0.859128\pi$
$487$	−21.7283	+	12.5449i	−0.984605	+	0.568462i	−0.0809478	+	0.996718i	$0.525795\pi$
$488$	8.37307	+	4.83419i	0.379031	+	0.218834i
$489$	13.9592	+	7.52441i	0.631256	+	0.340265i
$490$	−18.0817	+	19.2141i	−0.816850	+	0.868005i
$491$			22.8687i			1.03205i	0.856574	+	0.516024i	$0.172589\pi$
$491$			22.8687i			1.03205i	−0.856574	+	0.516024i	$0.827411\pi$
$492$	9.87018	−	6.08977i	0.444982	−	0.274548i
$493$	6.18429	−	3.57050i	0.278526	−	0.160807i
$494$	−19.8814	−	8.69319i	−0.894505	−	0.391125i
$495$	−2.49940	−	42.7235i	−0.112340	−	1.92028i
$496$	9.89221			0.444174
$497$	−2.40112	−	16.3204i	−0.107705	−	0.732071i
$498$	10.5015	+	5.66063i	0.470585	+	0.253659i
$499$	29.8258	+	17.2200i	1.33519	+	0.770871i	0.986090	−	0.166215i	$-0.0531546\pi$
$499$	29.8258	+	17.2200i	1.33519	+	0.770871i	0.349098	+	0.937086i	$0.386488\pi$
$500$	13.7318	−	7.92805i	0.614104	−	0.354553i
$501$	−0.319516	−	10.9326i	−0.0142749	−	0.488434i
$502$	4.29829	−	7.44485i	0.191842	−	0.332280i
$503$	−27.5477			−1.22829			−0.614145	−	0.789193i	$-0.710499\pi$
$503$	−27.5477			−1.22829			−0.614145	+	0.789193i	$0.710499\pi$
$504$	1.61196	+	7.77184i	0.0718026	+	0.346185i
$505$			5.35643i			0.238358i
$506$	−21.9405	−	12.6673i	−0.975372	−	0.563131i
$507$	6.04040	−	21.6913i	0.268264	−	0.963346i
$508$	−6.09092	−	10.5498i	−0.270241	−	0.468071i
$509$	22.1861	+	12.8091i	0.983380	+	0.567755i	0.903289	−	0.429033i	$-0.141146\pi$
$509$	22.1861	+	12.8091i	0.983380	+	0.567755i	0.0800909	+	0.996788i	$0.474479\pi$
$510$	−13.3342	−	7.18750i	−0.590447	−	0.318268i
$511$	−10.5074	+	8.31900i	−0.464822	+	0.368011i
$512$	−1.00000			−0.0441942
$513$	−13.2049	+	28.3466i	−0.583011	+	1.25153i
$514$	−10.8190	−	18.7391i	−0.477207	−	0.826547i
$515$	−21.7500	−	37.6722i	−0.958421	−	1.66003i
$516$	3.15843	+	5.11912i	0.139042	+	0.225357i
$517$			29.3677i			1.29159i
$518$	−11.2364	−	14.1923i	−0.493699	−	0.623574i
$519$	−13.0117	+	24.1392i	−0.571152	+	1.05959i
$520$	13.5058	−	1.51074i	0.592267	−	0.0662502i
$521$	10.2805	+	17.8063i	0.450396	+	0.780109i	0.998411	−	0.0563599i	$-0.0179494\pi$
$521$	10.2805	+	17.8063i	0.450396	+	0.780109i	−0.548014	+	0.836469i	$0.684616\pi$
$522$	8.25183	+	4.14156i	0.361173	+	0.181271i
$523$	2.64380	+	1.52640i	0.115605	+	0.0667448i	0.556688	−	0.830722i	$-0.312072\pi$
$523$	2.64380	+	1.52640i	0.115605	+	0.0667448i	−0.441082	+	0.897467i	$0.645405\pi$
$524$	−1.29335			−0.0565003
$525$	32.2993	−	27.1442i	1.40966	−	1.18467i
$526$			14.6026i			0.636705i
$527$	−11.4765	+	19.8779i	−0.499924	+	0.865893i
$528$	6.55262	−	0.191506i	0.285166	−	0.00833423i
$529$	10.9038	+	18.8859i	0.474076	+	0.821124i
$530$	−1.42254	+	2.46390i	−0.0617910	+	0.107025i
$531$	−10.6689	+	7.02098i	−0.462990	+	0.304684i
$532$	−2.31765	−	15.7530i	−0.100483	−	0.682981i
$533$	−14.3207	−	19.4365i	−0.620296	−	0.841888i
$534$	23.0245	−	14.2058i	0.996366	−	0.614745i
$535$	10.3488	+	17.9246i	0.447416	+	0.774948i
$536$	−4.51984	+	2.60953i	−0.195228	+	0.112715i
$537$	−24.2161	+	14.9410i	−1.04500	+	0.644754i
$538$	−17.1026			−0.737346
$539$	19.2936	+	18.1565i	0.831032	+	0.782056i
$540$	−1.71450	−	19.5101i	−0.0737805	−	0.839580i
$541$	−19.8564	−	11.4641i	−0.853694	−	0.492881i	0.00820130	−	0.999966i	$-0.497389\pi$
$541$	−19.8564	−	11.4641i	−0.853694	−	0.492881i	−0.861896	+	0.507086i	$0.830723\pi$
$542$	−14.9138	−	25.8315i	−0.640603	−	1.10956i
$543$	−0.543338	−	18.5910i	−0.0233169	−	0.797815i
$544$	1.16015	−	2.00944i	0.0497412	−	0.0861542i
$545$	1.22105			0.0523039
$546$	15.8483	−	4.67226i	0.678246	−	0.199954i
$547$	18.9906			0.811981			0.405991	−	0.913877i	$-0.366927\pi$
$547$	18.9906			0.811981			0.405991	+	0.913877i	$0.366927\pi$
$548$	−1.45303	+	2.51672i	−0.0620704	+	0.107509i
$549$	−25.9233	−	13.0108i	−1.10638	−	0.555288i
$550$	−17.4228	−	30.1771i	−0.742909	−	1.28676i
$551$	−16.0402	−	9.26081i	−0.683335	−	0.394524i
$552$	−10.2058	−	5.50124i	−0.434389	−	0.234148i
$553$	1.97786	+	0.784305i	0.0841070	+	0.0333520i
$554$	−15.6854			−0.666408
$555$	23.4538	+	38.0135i	0.995559	+	1.61358i
$556$	−4.63096	+	2.67369i	−0.196397	+	0.113390i
$557$	9.86728	+	17.0906i	0.418090	+	0.724154i	0.995747	−	0.0921260i	$-0.0293662\pi$
$557$	9.86728	+	17.0906i	0.418090	+	0.724154i	−0.577657	+	0.816280i	$0.696033\pi$
$558$	−29.6260	+	1.73317i	−1.25417	+	0.0733710i
$559$	10.0806	−	7.42734i	0.426366	−	0.314143i
$560$	6.19013	+	7.81854i	0.261581	+	0.330394i
$561$	−7.21722	+	13.3893i	−0.304711	+	0.565297i
$562$	10.6341	−	18.4188i	0.448571	−	0.776949i
$563$	5.55820	+	9.62708i	0.234250	+	0.405733i	0.959054	−	0.283222i	$-0.0914032\pi$
$563$	5.55820	+	9.62708i	0.234250	+	0.405733i	−0.724804	+	0.688955i	$0.758070\pi$
$564$	0.392621	+	13.4340i	0.0165323	+	0.565673i
$565$	22.0355	−	38.1665i	0.927039	−	1.60568i
$566$		−	32.5372i		−	1.36764i
$567$	−6.18931	−	22.9933i	−0.259927	−	0.965628i
$568$	−6.23494			−0.261612
$569$	17.4869	+	10.0960i	0.733088	+	0.423248i	0.819551	−	0.573007i	$-0.194223\pi$
$569$	17.4869	+	10.0960i	0.733088	+	0.423248i	−0.0864631	+	0.996255i	$0.527556\pi$
$570$	1.14777	+	39.2725i	0.0480749	+	1.64494i
$571$	−2.34574	−	4.06294i	−0.0981661	−	0.170029i	0.812759	−	0.582599i	$-0.197964\pi$
$571$	−2.34574	−	4.06294i	−0.0981661	−	0.170029i	−0.910926	+	0.412571i	$0.864631\pi$
$572$	−1.51698	−	13.5616i	−0.0634282	−	0.567039i
$573$	−16.1850	−	8.72417i	−0.676137	−	0.364458i
$574$	6.53035	−	16.4682i	0.272571	−	0.687369i
$575$			61.6286i			2.57009i
$576$	2.99488	−	0.175206i	0.124787	−	0.00730024i
$577$	10.4339	+	18.0720i	0.434368	+	0.752347i	0.997244	−	0.0741941i	$-0.0236384\pi$
$577$	10.4339	+	18.0720i	0.434368	+	0.752347i	−0.562876	+	0.826541i	$0.690305\pi$
$578$	−5.80809	−	10.0599i	−0.241585	−	0.418437i
$579$	6.65824	−	4.10805i	0.276707	−	0.170725i
$580$	11.6001			0.481668
$581$	18.0293	−	2.65254i	0.747981	−	0.110046i
$582$	−4.14626	+	7.69209i	−0.171868	+	0.318848i
$583$	2.47409	+	1.42842i	0.102466	+	0.0591590i
$584$	2.53273	+	4.38682i	0.104805	+	0.181528i
$585$	−40.1834	+	6.89076i	−1.66138	+	0.284898i
$586$	−13.1268	−	7.57874i	−0.542261	−	0.313075i
$587$			7.52079i			0.310416i	0.987882	+	0.155208i	$0.0496048\pi$
$587$			7.52079i			0.310416i	−0.987882	+	0.155208i	$0.950395\pi$
$588$	9.06841	+	8.04760i	0.373975	+	0.331878i
$589$	59.5331			2.45302
$590$	−8.02323	+	13.8966i	−0.330311	+	0.572116i
$591$	−24.6535	+	0.720520i	−1.01411	+	0.0296382i
$592$	−5.92523	+	3.42094i	−0.243526	+	0.140600i
$593$	3.45052	+	1.99216i	0.141696	+	0.0818081i	0.569172	−	0.822219i	$-0.307264\pi$
$593$	3.45052	+	1.99216i	0.141696	+	0.0818081i	−0.427476	+	0.904027i	$0.640597\pi$
$594$	−19.5907	+	1.72159i	−0.803818	+	0.0706378i
$595$	−22.8924	+	3.36802i	−0.938498	+	0.138076i
$596$	4.70363			0.192668
$597$	34.9508	−	21.5642i	1.43044	−	0.882564i
$598$	−9.66918	+	22.1135i	−0.395402	+	0.904286i
$599$	−1.61182	+	0.930583i	−0.0658571	+	0.0380226i	−0.532567	−	0.846388i	$-0.678773\pi$
$599$	−1.61182	+	0.930583i	−0.0658571	+	0.0380226i	0.466710	+	0.884410i	$0.345439\pi$
$600$	−8.37333	−	13.5713i	−0.341840	−	0.554047i
$601$		−	4.01388i		−	0.163729i	−0.996643	−	0.0818647i	$-0.973912\pi$
$601$		−	4.01388i		−	0.163729i	0.996643	−	0.0818647i	$-0.0260875\pi$
$602$	8.54115	+	3.38694i	0.348111	+	0.138041i
$603$	13.0792	−	8.60714i	0.532626	−	0.350510i
$604$	5.51385	+	3.18342i	0.224355	+	0.129532i
$605$	−10.8518	+	6.26531i	−0.441190	+	0.254721i
$606$	2.46039	−	0.0719070i	0.0999463	−	0.00292102i
$607$	11.3810	+	6.57082i	0.461941	+	0.266701i	0.712860	−	0.701307i	$-0.247400\pi$
$607$	11.3810	+	6.57082i	0.461941	+	0.266701i	−0.250919	+	0.968008i	$0.580733\pi$
$608$	−6.01818			−0.244069
$609$	13.8873	−	2.45959i	0.562740	−	0.0996676i
$610$	−36.4419			−1.47549
$611$	27.8036	−	3.11008i	1.12481	−	0.125820i
$612$	−3.12245	+	6.22131i	−0.126218	+	0.251482i
$613$	−9.33110	+	5.38731i	−0.376880	+	0.217592i	−0.676460	−	0.736480i	$-0.736487\pi$
$613$	−9.33110	+	5.38731i	−0.376880	+	0.217592i	0.299580	+	0.954071i	$0.403153\pi$
$614$	11.3640	−	19.6830i	0.458613	−	0.794340i
$615$	−20.7416	+	38.4796i	−0.836382	+	1.55165i
$616$	7.85087	−	6.21573i	0.316321	−	0.250439i
$617$	−22.7546			−0.916066			−0.458033	−	0.888935i	$-0.651446\pi$
$617$	−22.7546			−0.916066			−0.458033	+	0.888935i	$0.651446\pi$
$618$	−17.0121	+	10.4962i	−0.684327	+	0.422221i
$619$	−11.7673	−	20.3816i	−0.472969	−	0.819207i	0.526552	−	0.850143i	$-0.323484\pi$
$619$	−11.7673	−	20.3816i	−0.472969	−	0.819207i	−0.999521	+	0.0309362i	$0.990151\pi$
$620$	−32.2903	+	18.6428i	−1.29681	+	0.748713i
$621$	31.5291	+	14.6874i	1.26522	+	0.589386i
$622$	−6.34519			−0.254419
$623$	15.2335	−	38.4158i	0.610319	−	1.53910i
$624$	−0.875238	−	6.18336i	−0.0350375	−	0.247533i
$625$	−6.86537	+	11.8912i	−0.274615	+	0.475647i
$626$	9.83094	−	5.67590i	0.392924	−	0.226854i
$627$	39.4348	−	1.15252i	1.57488	−	0.0460271i
$628$	9.82232	+	5.67092i	0.391953	+	0.226294i
$629$		−	15.8752i		−	0.632987i
$630$	−19.9086	−	22.3310i	−0.793176	−	0.889690i
$631$		−	40.3755i		−	1.60733i	−0.595085	−	0.803663i	$-0.702882\pi$
$631$		−	40.3755i		−	1.60733i	0.595085	−	0.803663i	$-0.297118\pi$
$632$	0.402095	−	0.696449i	0.0159945	−	0.0277032i
$633$	−22.6235	+	0.661193i	−0.899204	+	0.0262801i
$634$	−0.315688	−	0.546787i	−0.0125376	−	0.0217157i
$635$	39.7641	+	22.9578i	1.57799	+	0.911053i
$636$	1.15085	+	0.620341i	0.0456341	+	0.0245981i
$637$	15.1463	−	20.1888i	0.600119	−	0.799911i
$638$		−	11.6481i		−	0.461151i
$639$	18.6729	−	1.09240i	0.738688	−	0.0432146i
$640$	3.26421	−	1.88459i	0.129029	−	0.0744951i
$641$	−17.5159	+	10.1128i	−0.691835	+	0.399431i	−0.804299	−	0.594225i	$-0.797459\pi$
$641$	−17.5159	+	10.1128i	−0.691835	+	0.399431i	0.112464	+	0.993656i	$0.464126\pi$
$642$	8.09443	−	4.99416i	0.319462	−	0.197104i
$643$	−40.2432			−1.58704			−0.793519	−	0.608545i	$-0.791753\pi$
$643$	−40.2432			−1.58704			−0.793519	+	0.608545i	$0.791753\pi$
$644$	−17.5216	+	2.57785i	−0.690449	+	0.101581i
$645$	−19.9573	−	10.7575i	−0.785816	−	0.423578i
$646$	6.98201	−	12.0932i	0.274704	−	0.475801i
$647$	−18.5795	−	32.1806i	−0.730435	−	1.26515i	−0.956697	−	0.291084i	$-0.905984\pi$
$647$	−18.5795	−	32.1806i	−0.730435	−	1.26515i	0.226262	−	0.974066i	$-0.427349\pi$
$648$	−8.93861	+	1.04944i	−0.351142	+	0.0412259i
$649$	13.9541	+	8.05640i	0.547746	+	0.316241i
$650$	−26.7248	+	19.6907i	−1.04823	+	0.772331i
$651$	−34.7040	+	29.1651i	−1.36016	+	1.14307i
$652$		−	9.15561i		−	0.358561i
$653$	−35.2713	−	20.3639i	−1.38027	−	0.796900i	−0.388081	−	0.921625i	$-0.626862\pi$
$653$	−35.2713	−	20.3639i	−1.38027	−	0.796900i	−0.992191	+	0.124725i	$0.960195\pi$
$654$	−0.0163918	−	0.560867i	−0.000640971	−	0.0219316i
$655$	4.22177	−	2.43744i	0.164958	−	0.0952387i
$656$	−5.79883	−	3.34796i	−0.226406	−	0.130716i
$657$	−8.35381	−	12.6942i	−0.325913	−	0.495249i
$658$	12.7433	+	16.0956i	0.496786	+	0.627473i
$659$			8.49218i			0.330808i	0.986226	+	0.165404i	$0.0528929\pi$
$659$			8.49218i			0.330808i	−0.986226	+	0.165404i	$0.947107\pi$
$660$	−21.0282	+	12.9741i	−0.818522	+	0.505018i
$661$	9.22875	+	15.9847i	0.358957	+	0.621731i	0.987787	−	0.155811i	$-0.0497992\pi$
$661$	9.22875	+	15.9847i	0.358957	+	0.621731i	−0.628830	+	0.777543i	$0.716466\pi$
$662$	10.6712	−	6.16103i	0.414749	−	0.239455i
$663$	13.4405	+	5.41491i	0.521987	+	0.210298i
$664$		−	6.88779i		−	0.267298i
$665$	37.2533	+	47.0534i	1.44462	+	1.82465i
$666$	17.1460	−	11.2834i	0.664394	−	0.437224i
$667$	−10.3005	+	17.8410i	−0.398838	+	0.690807i
$668$	−5.46865	+	3.15733i	−0.211588	+	0.122161i
$669$	−3.71590	+	0.108601i	−0.143665	+	0.00419874i
$670$	9.83582	−	17.0361i	0.379991	−	0.658163i
$671$			36.5926i			1.41264i
$672$	3.50822	−	2.94829i	0.135332	−	0.113733i
$673$	6.98712			0.269334			0.134667	−	0.990891i	$-0.457004\pi$
$673$	6.98712			0.269334			0.134667	+	0.990891i	$0.457004\pi$
$674$	−3.55161	+	6.15157i	−0.136803	+	0.236950i
$675$	27.4549	+	39.1774i	1.05674	+	1.50794i
$676$	−12.6787	+	2.87238i	−0.487642	+	0.110476i
$677$	6.77872	−	11.7411i	0.260527	−	0.451247i	−0.705855	−	0.708357i	$-0.749437\pi$
$677$	6.77872	−	11.7411i	0.260527	−	0.451247i	0.966382	+	0.257110i	$0.0827703\pi$
$678$	−17.8270	−	9.60925i	−0.684641	−	0.369041i
$679$	1.94292	+	13.2060i	0.0745622	+	0.506799i
$680$			8.74567i			0.335381i
$681$	−24.0287	+	14.8254i	−0.920783	+	0.568111i
$682$	18.7199	+	32.4238i	0.716821	+	1.24157i
$683$	13.4864	+	23.3591i	0.516042	+	0.893811i	0.999827	+	0.0186238i	$0.00592847\pi$
$683$	13.4864	+	23.3591i	0.516042	+	0.893811i	−0.483785	+	0.875187i	$0.660738\pi$
$684$	18.0237	−	1.05442i	0.689154	−	0.0403167i
$685$		−	10.9535i		−	0.418511i
$686$	18.4528	+	1.57917i	0.704532	+	0.0602931i
$687$	−20.8243	+	38.6329i	−0.794495	+	1.47394i
$688$	1.73640	−	3.00754i	0.0661997	−	0.114661i
$689$	1.09033	−	2.49360i	0.0415384	−	0.0949985i
$690$	43.6816	−	1.27663i	1.66293	−	0.0486006i
$691$	−0.543955	+	0.942158i	−0.0206930	+	0.0358414i	−0.876186	−	0.481972i	$-0.839921\pi$
$691$	−0.543955	+	0.942158i	−0.0206930	+	0.0358414i	0.855493	+	0.517814i	$0.173254\pi$
$692$	15.8325			0.601862
$693$	−22.4234	+	19.9909i	−0.851794	+	0.759391i
$694$			1.18494i			0.0449797i
$695$	10.0776	−	17.4550i	0.382266	−	0.662104i
$696$	−0.155724	−	5.32830i	−0.00590272	−	0.201969i
$697$	13.4551	−	7.76829i	0.509647	−	0.294245i
$698$	9.62867	−	16.6773i	0.364450	−	0.631247i
$699$	33.1381	+	17.8624i	1.25340	+	0.675619i
$700$	−22.6435	−	8.97912i	−0.855843	−	0.339379i
$701$			28.8352i			1.08909i	0.838731	+	0.544546i	$0.183298\pi$
$701$			28.8352i			1.08909i	−0.838731	+	0.544546i	$0.816702\pi$
$702$	3.70459	+	18.3651i	0.139821	+	0.693145i
$703$	−35.6591	+	20.5878i	−1.34491	+	0.776484i
$704$	−1.89239	−	3.27771i	−0.0713220	−	0.123533i
$705$	−26.5992	−	43.1115i	−1.00178	−	1.62367i
$706$		−	0.100399i		−	0.00377855i
$707$	2.94786	−	2.33389i	0.110866	−	0.0877750i
$708$	6.49089	+	3.49878i	0.243943	+	0.131492i
$709$	−0.432082	−	0.249463i	−0.0162272	−	0.00936877i	0.491864	−	0.870672i	$-0.336316\pi$
$709$	−0.432082	−	0.249463i	−0.0162272	−	0.00936877i	−0.508092	+	0.861303i	$0.669649\pi$
$710$	20.3522	−	11.7503i	0.763803	−	0.440982i
$711$	−1.08220	+	2.15623i	−0.0405858	+	0.0808649i
$712$	−13.5271	−	7.80988i	−0.506950	−	0.292688i
$713$		−	66.2169i		−	2.47984i
$714$	1.85436	+	10.4700i	0.0693978	+	0.391831i
$715$	30.5099	+	41.4091i	1.14100	+	1.54861i
$716$	14.2272	+	8.21410i	0.531697	+	0.306975i
$717$	38.3065	−	1.11954i	1.43058	−	0.0418101i
$718$	−4.13025	−	7.15381i	−0.154140	−	0.266978i
$719$	−3.21317	+	5.56538i	−0.119831	+	0.207554i	−0.919701	−	0.392620i	$-0.871569\pi$
$719$	−3.21317	+	5.56538i	−0.119831	+	0.207554i	0.799869	+	0.600174i	$0.204902\pi$
$720$	−9.44573	+	6.21604i	−0.352022	+	0.231658i
$721$	−11.2556	+	28.3843i	−0.419181	+	1.05709i
$722$	−17.2185			−0.640806
$723$	−11.4362	−	18.5356i	−0.425318	−	0.689347i
$724$	−9.29946	+	5.36904i	−0.345612	+	0.199539i
$725$	−24.5387	+	14.1674i	−0.911344	+	0.526165i
$726$	3.02354	+	4.90050i	0.112214	+	0.181875i
$727$		−	12.3057i		−	0.456392i	−0.973615	−	0.228196i	$-0.926717\pi$
$727$		−	12.3057i		−	0.456392i	0.973615	−	0.228196i	$-0.0732827\pi$
$728$	−6.71611	−	6.77450i	−0.248916	−	0.251080i
$729$	26.5862	−	4.70904i	0.984673	−	0.174409i
$730$	−16.5347	−	9.54633i	−0.611978	−	0.353326i
$731$	4.02899	+	6.97841i	0.149017	+	0.258106i
$732$	0.489212	+	16.7390i	0.0180818	+	0.618691i
$733$	−24.4841	+	42.4077i	−0.904341	+	1.56636i	−0.0825411	+	0.996588i	$0.526304\pi$
$733$	−24.4841	+	42.4077i	−0.904341	+	1.56636i	−0.821800	+	0.569777i	$0.807030\pi$
$734$			28.4033i			1.04839i
$735$	−44.7677	−	9.17880i	−1.65128	−	0.338565i
$736$			6.69384i			0.246738i
$737$	−17.1066	−	9.87649i	−0.630129	−	0.363805i
$738$	17.9534	+	9.01074i	0.660873	+	0.331690i
$739$	−1.87629	+	1.08328i	−0.0690204	+	0.0398489i	−0.534113	−	0.845413i	$-0.679354\pi$
$739$	−1.87629	+	1.08328i	−0.0690204	+	0.0398489i	0.465093	+	0.885262i	$0.346021\pi$
$740$	12.8941	−	22.3333i	0.473998	−	0.820989i
$741$	−5.26734	−	37.2126i	−0.193501	−	1.36704i
$742$	1.97581	−	0.290688i	0.0725341	−	0.0106715i
$743$	−9.34291			−0.342758			−0.171379	−	0.985205i	$-0.554822\pi$
$743$	−9.34291			−0.342758			−0.171379	+	0.985205i	$0.554822\pi$
$744$	8.99673	+	14.5817i	0.329836	+	0.534592i
$745$	−15.3536	+	8.86443i	−0.562514	+	0.324767i
$746$	−5.82807	−	10.0945i	−0.213381	−	0.369586i
$747$	1.20678	+	20.6281i	0.0441538	+	0.754743i
$748$	8.78183			0.321096
$749$	5.35547	−	13.5054i	0.195685	−	0.493476i
$750$	24.1751	+	13.0311i	0.882751	+	0.475829i
$751$	13.9317	−	24.1305i	0.508377	−	0.880534i	−0.491576	−	0.870834i	$-0.663579\pi$
$751$	13.9317	−	24.1305i	0.508377	−	0.880534i	0.999953	−	0.00969962i	$-0.00308753\pi$
$752$	6.71987	−	3.87972i	0.245048	−	0.141479i
$753$	14.8833	−	0.434979i	0.542379	−	0.0158515i
$754$	−11.0277	+	1.23354i	−0.401605	+	0.0449230i
$755$	−23.9978			−0.873370
$756$	−9.99012	+	9.44444i	−0.363337	+	0.343491i
$757$	−5.47162			−0.198869			−0.0994347	−	0.995044i	$-0.531703\pi$
$757$	−5.47162			−0.198869			−0.0994347	+	0.995044i	$0.531703\pi$
$758$	−4.95887	−	2.86301i	−0.180114	−	0.103989i
$759$	−1.28191	−	43.8622i	−0.0465304	−	1.59210i
$760$	19.6446	−	11.3418i	0.712585	−	0.411411i
$761$	−11.9787	−	6.91589i	−0.434227	−	0.250701i	0.266919	−	0.963719i	$-0.413994\pi$
$761$	−11.9787	−	6.91589i	−0.434227	−	0.250701i	−0.701146	+	0.713018i	$0.747328\pi$
$762$	10.0115	−	18.5732i	0.362677	−	0.672834i
$763$	−0.532031	−	0.671990i	−0.0192608	−	0.0243277i
$764$			10.6155i			0.384054i
$765$	−1.53229	−	26.1922i	−0.0554001	−	0.946982i
$766$	17.2864	−	9.98032i	0.624584	−	0.360604i
$767$	6.14958	−	14.0641i	0.222048	−	0.507826i
$768$	−0.909476	−	1.47406i	−0.0328179	−	0.0531906i
$769$	34.5029			1.24421			0.622104	−	0.782935i	$-0.286278\pi$
$769$	34.5029			1.24421			0.622104	+	0.782935i	$0.286278\pi$
$770$	−13.9128	+	35.0851i	−0.501382	+	1.26438i
$771$	17.7829	−	32.9907i	0.640437	−	1.18813i
$772$	−3.91178	−	2.25847i	−0.140788	−	0.0812841i
$773$	22.7475	−	13.1333i	0.818170	−	0.472371i	−0.0316148	−	0.999500i	$-0.510065\pi$
$773$	22.7475	−	13.1333i	0.818170	−	0.472371i	0.849785	+	0.527129i	$0.176732\pi$
$774$	−4.67338	+	9.31144i	−0.167981	+	0.334693i
$775$	45.5377	−	78.8735i	1.63576	−	2.83322i
$776$	5.04512			0.181109
$777$	10.7011	−	29.4707i	0.383899	−	1.05726i
$778$		−	21.5163i		−	0.771397i
$779$	−34.8984	−	20.1486i	−1.25037	−	0.721899i
$780$	14.5101	+	18.5343i	0.519544	+	0.663636i
$781$	−11.7989	−	20.4363i	−0.422198	−	0.731269i
$782$	−13.4509	−	7.76588i	−0.481003	−	0.277707i
$783$	1.39992	+	15.9303i	0.0500292	+	0.569304i
$784$	1.60570	−	6.81335i	0.0573465	−	0.243334i
$785$	−42.7495			−1.52579
$786$	−1.17627	−	1.90648i	−0.0419562	−	0.0680018i
$787$	12.3223	+	21.3429i	0.439243	+	0.760791i	0.997631	−	0.0687887i	$-0.0219134\pi$
$787$	12.3223	+	21.3429i	0.439243	+	0.760791i	−0.558388	+	0.829580i	$0.688580\pi$
$788$	7.11989	+	12.3320i	0.253636	+	0.439310i
$789$	−21.5252	+	13.2807i	−0.766316	+	0.472807i
$790$			3.03114i			0.107843i
$791$	−30.6058	+	4.50284i	−1.08822	+	0.160103i
$792$	6.24174	+	9.48478i	0.221791	+	0.337027i
$793$	34.6438	−	3.87521i	1.23024	−	0.137613i
$794$	13.1292	+	22.7405i	0.465939	+	0.807031i
$795$	−4.92570	+	0.143958i	−0.174697	+	0.00510567i
$796$	−20.5340	−	11.8553i	−0.727807	−	0.420200i
$797$	−13.0997			−0.464014			−0.232007	−	0.972714i	$-0.574529\pi$
$797$	−13.0997			−0.464014			−0.232007	+	0.972714i	$0.574529\pi$
$798$	21.1131	−	17.7434i	0.747395	−	0.628108i
$799$			18.0043i			0.636945i
$800$	−4.60338	+	7.97329i	−0.162754	+	0.281899i
$801$	41.8804	+	21.0196i	1.47977	+	0.742692i
$802$	−3.80346	−	6.58778i	−0.134305	−	0.232623i
$803$	−9.58580	+	16.6031i	−0.338276	+	0.585910i
$804$	−7.95730	−	4.28921i	−0.280632	−	0.151269i
$805$	52.3361	−	41.4358i	1.84460	−	1.46042i
$806$	28.7145	−	21.1566i	1.01143	−	0.745211i
$807$	−15.5544	−	25.2103i	−0.547541	−	0.887444i
$808$	−0.710555	−	1.23072i	−0.0249973	−	0.0432965i
$809$	−4.66926	+	2.69580i	−0.164163	+	0.0947793i	−0.579830	−	0.814737i	$-0.696881\pi$
$809$	−4.66926	+	2.69580i	−0.164163	+	0.0947793i	0.415668	+	0.909516i	$0.363548\pi$
$810$	27.1997	−	20.2712i	0.955701	−	0.712258i
$811$	9.84596			0.345739			0.172869	−	0.984945i	$-0.444696\pi$
$811$	9.84596			0.345739			0.172869	+	0.984945i	$0.444696\pi$
$812$	−5.05436	−	6.38399i	−0.177373	−	0.224034i
$813$	24.5134	−	45.4769i	0.859722	−	1.59495i
$814$	−22.4257	−	12.9475i	−0.786019	−	0.453808i
$815$	17.2546	+	29.8858i	0.604402	+	1.04686i
$816$	4.01717	−	0.117406i	0.140629	−	0.00411001i
$817$	10.4500	−	18.0999i	0.365599	−	0.633235i
$818$	−12.1693			−0.425489
$819$	21.3009	+	19.1121i	0.744313	+	0.667831i
$820$	25.2381			0.881354
$821$	27.5211	−	47.6680i	0.960494	−	1.66362i	0.239232	−	0.970963i	$-0.423104\pi$
$821$	27.5211	−	47.6680i	0.960494	−	1.66362i	0.721262	−	0.692662i	$-0.243562\pi$
$822$	−5.03129	+	0.147044i	−0.175487	+	0.00512875i
$823$	−23.0974	−	40.0059i	−0.805125	−	1.39452i	−0.916206	−	0.400707i	$-0.868765\pi$
$823$	−23.0974	−	40.0059i	−0.805125	−	1.39452i	0.111081	−	0.993811i	$-0.464569\pi$
$824$	9.99478	+	5.77049i	0.348184	+	0.201024i
$825$	28.6373	−	53.1275i	0.997022	−	1.84966i
$826$	11.1437	−	1.63951i	0.387740	−	0.0570458i
$827$	−36.9395			−1.28451			−0.642256	−	0.766491i	$-0.722001\pi$
$827$	−36.9395			−1.28451			−0.642256	+	0.766491i	$0.722001\pi$
$828$	−1.17280	−	20.0472i	−0.0407576	−	0.696690i
$829$	34.3756	−	19.8468i	1.19391	−	0.689307i	0.234723	−	0.972062i	$-0.424582\pi$
$829$	34.3756	−	19.8468i	1.19391	−	0.689307i	0.959192	+	0.282755i	$0.0912485\pi$
$830$	12.9807	+	22.4832i	0.450566	+	0.780403i
$831$	−14.2655	−	23.1212i	−0.494864	−	0.802065i
$832$	−2.90274	+	2.13872i	−0.100634	+	0.0741466i
$833$	11.8282	+	11.1311i	0.409822	+	0.385670i
$834$	−8.15293	−	4.39466i	−0.282313	−	0.152175i
$835$	11.9006	−	20.6124i	0.411836	−	0.713320i
$836$	−11.3887	−	19.7258i	−0.393887	−	0.682232i
$837$	−29.4989	−	42.0942i	−1.01963	−	1.45499i
$838$	−13.3266	+	23.0824i	−0.460360	+	0.797367i
$839$			10.9609i			0.378412i	0.981937	+	0.189206i	$0.0605914\pi$
$839$			10.9609i			0.378412i	−0.981937	+	0.189206i	$0.939409\pi$
$840$	−5.89522	+	16.2354i	−0.203405	+	0.560175i
$841$	19.5283			0.673390
$842$	4.73434	+	2.73337i	0.163156	+	0.0941982i
$843$	36.8218	−	1.07615i	1.26821	−	0.0370646i
$844$	6.53364	+	11.3166i	0.224897	+	0.389533i
$845$	35.9727	−	33.2703i	1.23750	−	1.14453i
$846$	−19.4454	+	12.7966i	−0.668548	+	0.439958i
$847$	8.17638	+	3.24229i	0.280944	+	0.111406i
$848$		−	0.754823i		−	0.0259207i
$849$	47.9619	−	29.5918i	1.64605	−	1.01559i
$850$	−10.6813	−	18.5005i	−0.366364	−	0.634562i
$851$	22.8992	+	39.6626i	0.784974	+	1.35962i
$852$	−5.67053	−	9.19068i	−0.194269	−	0.314867i
$853$	−49.5106			−1.69521			−0.847605	−	0.530628i	$-0.821956\pi$
$853$	−49.5106			−1.69521			−0.847605	+	0.530628i	$0.821956\pi$
$854$	15.8784	+	20.0554i	0.543347	+	0.686283i
$855$	−56.8461	+	37.4092i	−1.94410	+	1.27937i
$856$	−4.75556	−	2.74562i	−0.162542	−	0.0938435i
$857$	−2.81201	−	4.87055i	−0.0960565	−	0.166375i	0.813993	−	0.580875i	$-0.197290\pi$
$857$	−2.81201	−	4.87055i	−0.0960565	−	0.166375i	−0.910049	+	0.414501i	$0.863956\pi$
$858$	18.6110	−	14.5701i	0.635368	−	0.497414i
$859$	21.3946	+	12.3522i	0.729975	+	0.421451i	0.818413	−	0.574631i	$-0.194854\pi$
$859$	21.3946	+	12.3522i	0.729975	+	0.421451i	−0.0884382	+	0.996082i	$0.528188\pi$
$860$			13.0896i			0.446353i
$861$	30.2143	−	5.35129i	1.02970	−	0.182372i
$862$	−13.7453			−0.468166
$863$	−20.4709	+	35.4566i	−0.696836	+	1.20696i	0.272722	+	0.962093i	$0.412076\pi$
$863$	−20.4709	+	35.4566i	−0.696836	+	1.20696i	−0.969558	+	0.244862i	$0.921257\pi$
$864$	2.98203	+	4.25529i	0.101451	+	0.144768i
$865$	−51.6807	+	29.8379i	−1.75720	+	1.01452i
$866$	27.3091	+	15.7669i	0.928000	+	0.535781i
$867$	9.54659	−	17.7107i	0.324219	−	0.601487i
$868$	24.3293	+	9.64762i	0.825790	+	0.327461i
$869$	3.04367			0.103250
$870$	10.5500	+	17.0992i	0.357679	+	0.579718i
$871$	−7.53888	+	17.2415i	−0.255445	+	0.584204i
$872$	−0.280553	+	0.161977i	−0.00950073	+	0.00548525i
$873$	−15.1095	+	0.883934i	−0.511380	+	0.0299166i
$874$			40.2847i			1.36265i
$875$	41.5045	−	6.10630i	1.40311	−	0.206431i
$876$	−4.16297	+	7.72310i	−0.140654	+	0.260939i
$877$	−17.0997	−	9.87250i	−0.577415	−	0.333371i	0.182690	−	0.983170i	$-0.441519\pi$
$877$	−17.0997	−	9.87250i	−0.577415	−	0.333371i	−0.760105	+	0.649800i	$0.774853\pi$
$878$	−25.1301	+	14.5088i	−0.848098	+	0.489650i
$879$	−0.766955	−	26.2423i	−0.0258688	−	0.885131i
$880$	12.3543	+	7.13275i	0.416463	+	0.240445i
$881$	9.97339			0.336012			0.168006	−	0.985786i	$-0.446267\pi$
$881$	9.97339			0.336012			0.168006	+	0.985786i	$0.446267\pi$
$882$	−3.61515	+	20.6865i	−0.121728	+	0.696550i
$883$	−10.4363			−0.351210			−0.175605	−	0.984461i	$-0.556188\pi$
$883$	−10.4363			−0.351210			−0.175605	+	0.984461i	$0.556188\pi$
$884$	−0.930007	−	8.31413i	−0.0312795	−	0.279635i
$885$	−27.7814	+	0.811937i	−0.933862	+	0.0272929i
$886$	5.01928	−	2.89788i	0.168626	−	0.0973562i
$887$	−14.2694	+	24.7152i	−0.479118	+	0.829857i	−0.999713	−	0.0239468i	$-0.992377\pi$
$887$	−14.2694	+	24.7152i	−0.479118	+	0.829857i	0.520595	+	0.853804i	$0.325710\pi$
$888$	−10.4315	−	5.62289i	−0.350059	−	0.188692i
$889$	−4.69132	−	31.8869i	−0.157342	−	1.06945i
$890$	58.8738			1.97345
$891$	−20.3550	−	27.3122i	−0.681920	−	0.914993i
$892$	1.07315	+	1.85874i	0.0359316	+	0.0622353i
$893$	40.4414	−	23.3488i	1.35332	−	0.781339i
$894$	4.27784	+	6.93343i	0.143072	+	0.231889i
$895$	−61.9209			−2.06979
$896$	−2.45944	−	0.975274i	−0.0821641	−	0.0325816i
$897$	−41.3904	+	5.85870i	−1.38199	+	0.195616i
$898$	7.79456	−	13.5006i	0.260108	−	0.450520i
$899$	26.3656	−	15.2222i	0.879342	−	0.507689i
$900$	12.3896	−	24.6856i	0.412987	−	0.822853i
$901$	1.51678	+	0.875711i	0.0505311	+	0.0291742i
$902$		−	25.3425i		−	0.843813i
$903$	2.77542	+	15.6705i	0.0923604	+	0.521482i
$904$			11.6924i			0.388884i
$905$	20.2369	−	35.0514i	0.672698	−	1.16515i
$906$	0.322157	+	11.0230i	0.0107029	+	0.366214i
$907$	27.0286	+	46.8148i	0.897468	+	1.55446i	0.830720	+	0.556691i	$0.187929\pi$
$907$	27.0286	+	46.8148i	0.897468	+	1.55446i	0.0667488	+	0.997770i	$0.478737\pi$
$908$	14.1171	+	8.15053i	0.468493	+	0.270485i
$909$	2.34366	+	3.56136i	0.0777342	+	0.118123i
$910$	34.6900	+	9.45626i	1.14996	+	0.313472i
$911$			26.6150i			0.881795i	0.897557	+	0.440898i	$0.145340\pi$
$911$			26.6150i			0.881795i	−0.897557	+	0.440898i	$0.854660\pi$
$912$	−5.47339	−	8.87116i	−0.181242	−	0.293753i
$913$	22.5762	−	13.0344i	0.747162	−	0.431374i
$914$	−2.92274	+	1.68744i	−0.0966756	+	0.0558157i
$915$	−33.1431	−	53.7176i	−1.09568	−	1.77585i
$916$	25.3387			0.837215
$917$	−3.18092	−	1.26137i	−0.105043	−	0.0416542i
$918$	−12.0104	+	1.05545i	−0.396402	+	0.0348349i
$919$	−11.2395	+	19.4674i	−0.370758	+	0.642171i	−0.989682	−	0.143279i	$-0.954235\pi$
$919$	−11.2395	+	19.4674i	−0.370758	+	0.642171i	0.618925	+	0.785450i	$0.287569\pi$
$920$	−12.6152	−	21.8501i	−0.415910	−	0.720377i
$921$	39.3492	−	1.15001i	1.29660	−	0.0378943i
$922$	3.10122	+	1.79049i	0.102133	+	0.0589666i
$923$	−18.0984	+	13.3348i	−0.595716	+	0.438919i
$924$	16.3025	+	5.91960i	0.536314	+	0.194741i
$925$			62.9915i			2.07115i
$926$	7.03736	+	4.06302i	0.231262	+	0.133519i
$927$	−30.9442	−	15.5308i	−1.01634	−	0.510097i
$928$	−2.66529	+	1.53881i	−0.0874924	+	0.0505138i
$929$	40.6262	+	23.4556i	1.33290	+	0.769552i	0.985744	−	0.168253i	$-0.0538127\pi$
$929$	40.6262	+	23.4556i	1.33290	+	0.769552i	0.347160	+	0.937806i	$0.387146\pi$
$930$	−56.8478	−	30.6426i	−1.86411	−	1.00481i
$931$	9.66341	−	41.0040i	0.316705	−	1.34385i
$932$		−	21.7348i		−	0.711947i
$933$	−5.77079	−	9.35319i	−0.188927	−	0.306210i
$934$	−18.4226	−	31.9089i	−0.602805	−	1.04409i
$935$	−28.6658	+	16.5502i	−0.937470	+	0.541249i
$936$	8.31864	−	6.91377i	0.271903	−	0.225984i
$937$			18.9682i			0.619665i	0.950791	+	0.309832i	$0.100273\pi$
$937$			18.9682i			0.619665i	−0.950791	+	0.309832i	$0.899727\pi$
$938$	−13.6613	+	2.00990i	−0.446057	+	0.0656256i
$939$	17.3076	+	9.32931i	0.564813	+	0.304451i
$940$	−14.6234	+	25.3284i	−0.476962	+	0.826123i
$941$	19.2846	−	11.1340i	0.628660	−	0.362957i	−0.151573	−	0.988446i	$-0.548434\pi$
$941$	19.2846	−	11.1340i	0.628660	−	0.362957i	0.780233	+	0.625489i	$0.215101\pi$
$942$	0.573887	+	19.6362i	0.0186982	+	0.639783i
$943$	−22.4107	+	38.8164i	−0.729792	+	1.26404i
$944$		−	4.25727i		−	0.138562i
$945$	14.8110	−	49.6560i	0.481800	−	1.61531i
$946$	13.1438			0.427341
$947$	−26.3290	+	45.6031i	−0.855576	+	1.48190i	0.0205332	+	0.999789i	$0.493464\pi$
$947$	−26.3290	+	45.6031i	−0.855576	+	1.48190i	−0.876109	+	0.482112i	$0.839870\pi$
$948$	1.39230	−	0.0406913i	0.0452199	−	0.00132159i
$949$	16.7340	+	7.31700i	0.543209	+	0.237520i
$950$	−27.7040	+	47.9847i	−0.898836	+	1.55683i
$951$	0.518887	−	0.962633i	0.0168261	−	0.0312155i
$952$	4.81309	−	3.81064i	0.155993	−	0.123504i
$953$		−	1.27801i		−	0.0413990i	−0.999786	−	0.0206995i	$-0.993411\pi$
$953$		−	1.27801i		−	0.0413990i	0.999786	−	0.0206995i	$-0.00658932\pi$
$954$	0.132249	+	2.26061i	0.00428173	+	0.0731898i
$955$	−20.0058	−	34.6511i	−0.647374	−	1.12128i
$956$	−11.0629	−	19.1614i	−0.357798	−	0.619725i
$957$	17.1699	−	10.5936i	0.555025	−	0.342443i
$958$			6.05555i			0.195646i
$959$	−6.02813	+	4.77262i	−0.194659	+	0.154116i
$960$	5.74673	+	3.09765i	0.185475	+	0.0999763i
$961$	−33.4280	+	57.8989i	−1.07832	+	1.86771i
$962$	−9.88300	+	22.6025i	−0.318641	+	0.728733i
$963$	14.7234	+	7.38961i	0.474454	+	0.238127i
$964$	−6.28726	+	10.8899i	−0.202499	+	0.350739i
$965$	17.0252			0.548060
$966$	−19.7354	−	23.4834i	−0.634976	−	0.755567i
$967$		−	2.84809i		−	0.0915884i	−0.998951	−	0.0457942i	$-0.985418\pi$
$967$		−	2.84809i		−	0.0915884i	0.998951	−	0.0457942i	$-0.0145819\pi$
$968$	1.66224	−	2.87909i	0.0534266	−	0.0925375i
$969$	24.1761	−	0.706567i	0.776648	−	0.0226982i
$970$	−16.4683	+	9.50800i	−0.528767	+	0.305284i
$971$	19.3492	−	33.5137i	0.620944	−	1.07551i	−0.368366	−	0.929681i	$-0.620083\pi$
$971$	19.3492	−	33.5137i	0.620944	−	1.07551i	0.989310	−	0.145826i	$-0.0465838\pi$
$972$	−9.67638	−	12.2216i	−0.310370	−	0.392008i
$973$	−13.9971	+	2.05932i	−0.448728	+	0.0660186i
$974$			25.0897i			0.803927i
$975$	−53.3308	−	21.4859i	−1.70795	−	0.688098i
$976$	8.37307	−	4.83419i	0.268015	−	0.154739i
$977$	−22.8365	−	39.5540i	−0.730605	−	1.26544i	−0.956625	−	0.291322i	$-0.905905\pi$
$977$	−22.8365	−	39.5540i	−0.730605	−	1.26544i	0.226020	−	0.974123i	$-0.427428\pi$
$978$	13.4959	−	8.32681i	0.431552	−	0.266262i
$979$		−	59.1172i		−	1.88939i
$980$	7.59904	+	25.2663i	0.242742	+	0.807103i
$981$	0.811843	−	0.534257i	0.0259202	−	0.0170575i
$982$	19.8049	+	11.4343i	0.631998	+	0.364884i
$983$	−51.3302	+	29.6355i	−1.63718	+	0.945226i	−0.655381	+	0.755298i	$0.727492\pi$
$983$	−51.3302	+	29.6355i	−1.63718	+	0.945226i	−0.981798	+	0.189927i	$0.939175\pi$
$984$	−0.338807	−	11.5927i	−0.0108008	−	0.369562i
$985$	−46.4817	−	26.8362i	−1.48103	−	0.855072i
$986$		−	7.14100i		−	0.227416i
$987$	−12.1362	+	33.4230i	−0.386300	+	1.06387i
$988$	−17.4692	+	12.8712i	−0.555770	+	0.409487i
$989$	−20.1320	−	11.6232i	−0.640160	−	0.369596i
$990$	−38.2493	−	19.1972i	−1.21564	−	0.610127i
$991$	13.0035	+	22.5226i	0.413068	+	0.715455i	0.995224	−	0.0976225i	$-0.0311238\pi$
$991$	13.0035	+	22.5226i	0.413068	+	0.715455i	−0.582155	+	0.813078i	$0.697790\pi$
$992$	4.94611	−	8.56691i	0.157039	−	0.272000i
$993$	18.7869	+	10.1267i	0.596186	+	0.321361i
$994$	−15.3345	−	6.08078i	−0.486380	−	0.192870i
$995$	89.3696			2.83321
$996$	10.1530	−	6.26428i	0.321711	−	0.198491i
$997$	−11.8082	+	6.81749i	−0.373971	+	0.215912i	−0.675192	−	0.737642i	$-0.735939\pi$
$997$	−11.8082	+	6.81749i	−0.373971	+	0.215912i	0.301221	+	0.953554i	$0.402606\pi$
$998$	29.8258	−	17.2200i	0.944120	−	0.545088i
$999$	32.2263	+	15.0122i	1.01960	+	0.474966i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bg.b.467.18	yes	36
3.2	odd	2		546.2.bg.a.467.13	yes	36
7.3	odd	6	inner	546.2.bg.b.311.13	yes	36
13.12	even	2		546.2.bg.a.467.18	yes	36
21.17	even	6		546.2.bg.a.311.18	yes	36
39.38	odd	2	inner	546.2.bg.b.467.13	yes	36
91.38	odd	6		546.2.bg.a.311.13	✓	36
273.38	even	6	inner	546.2.bg.b.311.18	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bg.a.311.13	✓	36	91.38	odd	6
546.2.bg.a.311.18	yes	36	21.17	even	6
546.2.bg.a.467.13	yes	36	3.2	odd	2
546.2.bg.a.467.18	yes	36	13.12	even	2
546.2.bg.b.311.13	yes	36	7.3	odd	6	inner
546.2.bg.b.311.18	yes	36	273.38	even	6	inner
546.2.bg.b.467.13	yes	36	39.38	odd	2	inner
546.2.bg.b.467.18	yes	36	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bg (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.73131 - 0.0505991i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(3.26421 + 1.88459i) q^{5} +(0.821836 - 1.52466i) q^{6} +(-0.385108 - 2.61757i) q^{7} -1.00000 q^{8} +(2.99488 - 0.175206i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.73131 - 0.0505991i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(3.26421 + 1.88459i) q^{5} +(0.821836 - 1.52466i) q^{6} +(-0.385108 - 2.61757i) q^{7} -1.00000 q^{8} +(2.99488 - 0.175206i) q^{9} +(3.26421 - 1.88459i) q^{10} +(-1.89239 - 3.27771i) q^{11} +(-0.909476 - 1.47406i) q^{12} +(-2.90274 + 2.13872i) q^{13} +(-2.45944 - 0.975274i) q^{14} +(5.74673 + 3.09765i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.16015 - 2.00944i) q^{17} +(1.34571 - 2.68124i) q^{18} +(-3.00909 + 5.21190i) q^{19} -3.76919i q^{20} +(-0.799188 - 4.51235i) q^{21} -3.78477 q^{22} +(5.79704 + 3.34692i) q^{23} +(-1.73131 + 0.0505991i) q^{24} +(4.60338 + 7.97329i) q^{25} +(0.400812 + 3.58320i) q^{26} +(5.17620 - 0.454874i) q^{27} +(-2.07433 + 1.64230i) q^{28} +3.07761i q^{29} +(5.55601 - 3.42798i) q^{30} +(-4.94611 - 8.56691i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.44216 - 5.57898i) q^{33} -2.32031 q^{34} +(3.67599 - 9.27009i) q^{35} +(-1.64917 - 2.50604i) q^{36} +(5.92523 + 3.42094i) q^{37} +(3.00909 + 5.21190i) q^{38} +(-4.91733 + 3.84966i) q^{39} +(-3.26421 - 1.88459i) q^{40} +6.69591i q^{41} +(-4.30740 - 1.56406i) q^{42} -3.47280 q^{43} +(-1.89239 + 3.27771i) q^{44} +(10.1061 + 5.07222i) q^{45} +(5.79704 - 3.34692i) q^{46} +(-6.71987 - 3.87972i) q^{47} +(-0.821836 + 1.52466i) q^{48} +(-6.70338 + 2.01610i) q^{49} +9.20677 q^{50} +(-2.11026 - 3.42027i) q^{51} +(3.30355 + 1.44449i) q^{52} +(-0.653696 + 0.377412i) q^{53} +(2.19417 - 4.71016i) q^{54} -14.2655i q^{55} +(0.385108 + 2.61757i) q^{56} +(-4.94596 + 9.17568i) q^{57} +(2.66529 + 1.53881i) q^{58} +(-3.68691 + 2.12864i) q^{59} +(-0.190718 - 6.52564i) q^{60} +(-8.37307 - 4.83419i) q^{61} -9.89221 q^{62} +(-1.61196 - 7.77184i) q^{63} +1.00000 q^{64} +(-13.5058 + 1.51074i) q^{65} +(-6.55262 + 0.191506i) q^{66} +(4.51984 - 2.60953i) q^{67} +(-1.16015 + 2.00944i) q^{68} +(10.2058 + 5.50124i) q^{69} +(-6.19013 - 7.81854i) q^{70} +6.23494 q^{71} +(-2.99488 + 0.175206i) q^{72} +(-2.53273 - 4.38682i) q^{73} +(5.92523 - 3.42094i) q^{74} +(8.37333 + 13.5713i) q^{75} +6.01818 q^{76} +(-7.85087 + 6.21573i) q^{77} +(0.875238 + 6.18336i) q^{78} +(-0.402095 + 0.696449i) q^{79} +(-3.26421 + 1.88459i) q^{80} +(8.93861 - 1.04944i) q^{81} +(5.79883 + 3.34796i) q^{82} +6.88779i q^{83} +(-3.50822 + 2.94829i) q^{84} -8.74567i q^{85} +(-1.73640 + 3.00754i) q^{86} +(0.155724 + 5.32830i) q^{87} +(1.89239 + 3.27771i) q^{88} +(13.5271 + 7.80988i) q^{89} +(9.44573 - 6.21604i) q^{90} +(6.71611 + 6.77450i) q^{91} -6.69384i q^{92} +(-8.99673 - 14.5817i) q^{93} +(-6.71987 + 3.87972i) q^{94} +(-19.6446 + 11.3418i) q^{95} +(0.909476 + 1.47406i) q^{96} -5.04512 q^{97} +(-1.60570 + 6.81335i) q^{98} +(-6.24174 - 9.48478i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 18 q^{2} - 18 q^{4} - 36 q^{8} + 4 q^{9}+O(q^{10}) \) 36 * q + 18 * q^2 - 18 * q^4 - 36 * q^8 + 4 * q^9	\( 36 q + 18 q^{2} - 18 q^{4} - 36 q^{8} + 4 q^{9} + 14 q^{15} - 18 q^{16} - 4 q^{18} - 23 q^{21} + 14 q^{25} + 6 q^{26} + 7 q^{30} + 18 q^{32} - 24 q^{33} - 8 q^{36} + 10 q^{39} - 16 q^{42} - 16 q^{43} + 9 q^{45} - 72 q^{47} + 12 q^{49} + 28 q^{50} - 3 q^{51} + 6 q^{52} - 9 q^{54} + 8 q^{57} - 24 q^{59} - 7 q^{60} - 36 q^{61} + 39 q^{63} + 36 q^{64} - 18 q^{65} - 24 q^{66} + 72 q^{71} - 4 q^{72} + 54 q^{75} + 20 q^{78} + 20 q^{79} - 20 q^{81} - 24 q^{82} + 7 q^{84} - 8 q^{86} - 24 q^{87} + 72 q^{89} - 2 q^{91} + 14 q^{93} - 72 q^{94} + 12 q^{98} - 72 q^{99}+O(q^{100}) \) 36 * q + 18 * q^2 - 18 * q^4 - 36 * q^8 + 4 * q^9 + 14 * q^15 - 18 * q^16 - 4 * q^18 - 23 * q^21 + 14 * q^25 + 6 * q^26 + 7 * q^30 + 18 * q^32 - 24 * q^33 - 8 * q^36 + 10 * q^39 - 16 * q^42 - 16 * q^43 + 9 * q^45 - 72 * q^47 + 12 * q^49 + 28 * q^50 - 3 * q^51 + 6 * q^52 - 9 * q^54 + 8 * q^57 - 24 * q^59 - 7 * q^60 - 36 * q^61 + 39 * q^63 + 36 * q^64 - 18 * q^65 - 24 * q^66 + 72 * q^71 - 4 * q^72 + 54 * q^75 + 20 * q^78 + 20 * q^79 - 20 * q^81 - 24 * q^82 + 7 * q^84 - 8 * q^86 - 24 * q^87 + 72 * q^89 - 2 * q^91 + 14 * q^93 - 72 * q^94 + 12 * q^98 - 72 * q^99

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