LMFDB - Embedded newform 546.2.bg.a.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.a.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} +(-3.30355 + 1.44449i) 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} +(5.13376 + 3.55591i) 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} +(0.400812 - 3.58320i) 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} +(-5.44455 - 12.4517i) 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} +(-5.64639 + 2.66802i) 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} +(-4.48038 + 8.42177i) 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	−0.460799	−	0.887505i	$-0.652437\pi$
$5$	−3.26421	−	1.88459i	−1.45980	−	0.842816i	−0.999001	+	0.0446889i	$0.985770\pi$
$6$	−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	$0.0266132\pi$
$11$	1.89239	+	3.27771i	0.570576	+	0.988266i	−0.425931	+	0.904756i	$0.640053\pi$
$12$	−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	$-0.590798\pi$
$19$	3.00909	−	5.21190i	0.690333	−	1.19569i	0.971729	−	0.236100i	$-0.0758691\pi$
$20$			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
$26$	−3.30355	+	1.44449i	−0.647880	+	0.283287i
$27$	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	$0.181479\pi$
$31$	4.94611	+	8.56691i	0.888347	+	1.53866i	0.0465184	+	0.998917i	$0.485187\pi$
$32$	−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	−0.0736180	−	0.997287i	$-0.523455\pi$
$37$	−5.92523	−	3.42094i	−0.974102	−	0.562398i	−0.900484	+	0.434888i	$0.856788\pi$
$38$	3.00909	+	5.21190i	0.488139	+	0.845481i
$39$	5.13376	+	3.55591i	0.822060	+	0.569401i
$40$	−3.26421	−	1.88459i	−0.516117	−	0.297980i
$41$		−	6.69591i		−	1.04573i	−0.852417	−	0.522863i	$-0.824864\pi$
$41$		−	6.69591i		−	1.04573i	0.852417	−	0.522863i	$-0.175136\pi$
$42$	−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	0.902329	−	0.431049i	$-0.141856\pi$
$47$	6.71987	+	3.87972i	0.980194	+	0.565915i	0.0778650	+	0.996964i	$0.475190\pi$
$48$	−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
$52$	0.400812	−	3.58320i	0.0555826	−	0.496901i
$53$	−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	−0.240420	−	0.970669i	$-0.577285\pi$
$59$	3.68691	−	2.12864i	0.479994	−	0.277125i	0.720414	+	0.693544i	$0.243952\pi$
$60$	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
$65$	−5.44455	−	12.4517i	−0.675313	−	1.54444i
$66$	−6.55262	+	0.191506i	−0.806571	+	0.0235728i
$67$	−4.51984	+	2.60953i	−0.552187	+	0.318805i	−0.750004	−	0.661434i	$-0.769948\pi$
$67$	−4.51984	+	2.60953i	−0.552187	+	0.318805i	0.197817	+	0.980239i	$0.436615\pi$
$68$	−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	$-0.620634\pi$
$71$	−6.23494			−0.739951			−0.369976	+	0.929041i	$0.620634\pi$
$72$	2.99488	−	0.175206i	0.352950	−	0.0206482i
$73$	2.53273	+	4.38682i	0.296434	+	0.513438i	0.975317	−	0.220808i	$-0.0708693\pi$
$73$	2.53273	+	4.38682i	0.296434	+	0.513438i	−0.678884	+	0.734246i	$0.737536\pi$
$74$	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
$78$	−5.64639	+	2.66802i	−0.639327	+	0.302093i
$79$	−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	$-0.876606\pi$
$83$		−	6.88779i		−	0.756033i	0.925799	−	0.378017i	$-0.123394\pi$
$84$	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	−0.436457	−	0.899725i	$-0.643767\pi$
$89$	−13.5271	−	7.80988i	−1.43387	−	0.827845i	−0.997413	+	0.0718798i	$0.977100\pi$
$90$	9.44573	−	6.21604i	0.995667	−	0.655228i
$91$	−4.48038	+	8.42177i	−0.469671	+	0.882841i
$92$		−	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	$-0.417553\pi$
$97$	5.04512			0.512255			0.256127	+	0.966643i	$0.417553\pi$
$98$	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	−0.513376	−	0.858164i	$-0.671605\pi$
$109$	−0.280553	+	0.161977i	−0.0268721	+	0.0155146i	0.486504	+	0.873678i	$0.338272\pi$
$110$	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
$117$	9.06807	+	5.89662i	0.838343	+	0.545143i
$118$			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
$130$	13.5058	+	1.51074i	1.18453	+	0.132500i
$131$	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	0.921397	−	0.388623i	$-0.127049\pi$
$137$	1.45303	+	2.51672i	0.124141	+	0.215018i	−0.797256	+	0.603641i	$0.793716\pi$
$138$	−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
$143$	−1.51698	+	13.5616i	−0.126856	+	1.13408i
$144$	−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	−0.753465	−	0.657487i	$-0.771619\pi$
$149$	2.35181	−	4.07346i	0.192668	−	0.333711i	0.946134	+	0.323777i	$0.104953\pi$
$150$	−15.9398	+	0.465854i	−1.30148	+	0.0380368i
$151$	5.51385	−	3.18342i	0.448711	−	0.259063i	−0.258575	−	0.965991i	$-0.583253\pi$
$151$	5.51385	−	3.18342i	0.448711	−	0.259063i	0.707285	+	0.706928i	$0.249920\pi$
$152$	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
$156$	0.512624	−	6.22392i	0.0410427	−	0.498313i
$157$	−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	0.156230	−	0.987721i	$-0.450066\pi$
$163$	−7.92899	−	4.57780i	−0.621046	−	0.358561i	−0.777276	+	0.629159i	$0.783399\pi$
$164$	−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	$0.0785651\pi$
$167$			6.31465i			0.488642i	−0.969694	+	0.244321i	$0.921435\pi$
$168$	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	$-0.130670\pi$
$182$	−5.05328	−	8.09101i	−0.374574	−	0.599745i
$183$	−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	−0.634137	−	0.773221i	$-0.718644\pi$
$193$	−3.91178	+	2.25847i	−0.281576	+	0.162568i	0.352560	+	0.935789i	$0.385311\pi$
$194$	−2.52256	+	4.36920i	−0.181109	+	0.313691i
$195$	−10.0563	−	21.2823i	−0.720143	−	1.52406i
$196$	5.09768	+	4.79725i	0.364120	+	0.342661i
$197$	14.2398			1.01454			0.507271	−	0.861787i	$-0.330654\pi$
$197$	14.2398			1.01454			0.507271	+	0.861787i	$0.330654\pi$
$198$	−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
$208$	−3.30355	+	1.44449i	−0.229060	+	0.100157i
$209$	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
$221$	0.930007	−	8.31413i	0.0625591	−	0.559269i
$222$	10.0853	−	6.22252i	0.676883	−	0.417628i
$223$	2.14629			0.143726			0.0718632	−	0.997414i	$-0.477106\pi$
$223$	2.14629			0.143726			0.0718632	+	0.997414i	$0.477106\pi$
$224$	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	0.0479723	−	0.998849i	$-0.484724\pi$
$227$	14.1171	−	8.15053i	0.936987	−	0.540970i	0.889014	+	0.457879i	$0.151391\pi$
$228$	−10.4193	+	0.304515i	−0.690038	+	0.0201670i
$229$	12.6694	−	21.9440i	0.837215	−	1.45010i	−0.0549995	−	0.998486i	$-0.517516\pi$
$229$	12.6694	−	21.9440i	0.837215	−	1.45010i	0.892214	−	0.451612i	$-0.149151\pi$
$230$	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	$0.414480\pi$
$234$	−9.64066	+	4.90487i	−0.630229	+	0.320641i
$235$	−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	$-0.753845\pi$
$239$	−22.1257			−1.43119			−0.715597	+	0.698514i	$0.753845\pi$
$240$	5.55601	−	3.42798i	0.358639	−	0.221275i
$241$	6.28726	+	10.8899i	0.404998	+	0.701477i	0.994321	−	0.106420i	$-0.0339388\pi$
$241$	6.28726	+	10.8899i	0.404998	+	0.701477i	−0.589323	+	0.807897i	$0.700605\pi$
$242$	−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
$247$	19.8814	−	8.69319i	1.26502	−	0.553135i
$248$	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	$0.527508\pi$
$271$	−14.9138	+	25.8315i	−0.905949	+	1.56915i	−0.819639	+	0.572881i	$0.805826\pi$
$272$	2.32031			0.140689
$273$	−7.33080	+	14.8074i	−0.443680	+	0.896185i
$274$	−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	$-0.718743\pi$
$281$	−21.2682			−1.26875			−0.634376	+	0.773025i	$0.718743\pi$
$282$	−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	$0.145999\pi$
$293$			15.1575i			0.885509i	−0.896643	+	0.442755i	$0.854001\pi$
$294$	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
$299$	9.66918	+	22.1135i	0.559183	+	1.27885i
$300$	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	$-0.724635\pi$
$307$	−22.7279			−1.29715			−0.648576	+	0.761150i	$0.724635\pi$
$308$	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	$0.890911\pi$
$312$	5.13376	+	3.55591i	0.290642	+	0.201314i
$313$	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	−0.874755	−	0.484566i	$-0.838978\pi$
$317$	−0.315688	+	0.546787i	−0.0177308	+	0.0307106i	0.857024	+	0.515277i	$0.172311\pi$
$318$	−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
$325$	−3.69018	+	32.9897i	−0.204695	+	1.82994i
$326$	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	0.177186	−	0.984177i	$-0.443300\pi$
$331$	−10.6712	−	6.16103i	−0.586543	−	0.338641i	−0.763729	+	0.645536i	$0.776634\pi$
$332$	−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	$0.561974\pi$
$338$	−12.6787	−	2.87238i	−0.689630	−	0.156237i
$339$	−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	$-0.672361\pi$
$349$	−19.2573			−1.03082			−0.515411	+	0.856943i	$0.672361\pi$
$350$	−3.54560	−	24.0994i	−0.189520	−	1.28817i
$351$	15.9980	+	9.75005i	0.853911	+	0.520419i
$352$	1.89239	−	3.27771i	0.100864	−	0.174702i
$353$	−0.0869477	+	0.0501993i	−0.00462776	+	0.00267184i	−0.502312	−	0.864686i	$-0.667517\pi$
$353$	−0.0869477	+	0.0501993i	−0.00462776	+	0.00267184i	0.497684	+	0.867358i	$0.334184\pi$
$354$	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	−0.954192	−	0.299194i	$-0.903282\pi$
$359$	−4.13025	+	7.15381i	−0.217987	+	0.377564i	0.736206	+	0.676758i	$0.236616\pi$
$360$	−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
$364$	9.53366	−	0.330764i	0.499699	−	0.0173367i
$365$		−	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	$0.0469819\pi$
$379$			5.72601i			0.294125i	−0.989127	+	0.147063i	$0.953018\pi$
$380$	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	−0.0115516	−	0.999933i	$-0.503677\pi$
$383$	−17.2864	−	9.98032i	−0.883295	−	0.509971i	−0.871743	+	0.489963i	$0.837010\pi$
$384$	−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	$0.149688\pi$
$390$	23.4591	+	1.93217i	1.18790	+	0.0978395i
$391$		−	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	$-0.604339\pi$
$397$	13.1292	−	22.7405i	0.658938	−	1.14131i	0.980891	−	0.194558i	$-0.0623273\pi$
$398$			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	−0.945229	−	0.326409i	$-0.894161\pi$
$401$	−3.80346	+	6.58778i	−0.189936	+	0.328978i	0.755293	+	0.655387i	$0.227495\pi$
$402$	−0.264080	−	9.03583i	−0.0131711	−	0.450666i
$403$	−3.96492	+	35.4458i	−0.197507	+	1.76568i
$404$	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	0.976332	−	0.216276i	$-0.0693910\pi$
$409$	6.08464	+	10.5389i	0.300866	+	0.521115i	−0.675466	+	0.737391i	$0.736058\pi$
$410$	−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
$416$	0.400812	−	3.58320i	0.0196514	−	0.175681i
$417$	−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	$-0.957469\pi$
$421$		−	5.46674i		−	0.266433i	0.991087	−	0.133216i	$-0.0425305\pi$
$422$	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
$429$	−1.94016	+	23.5561i	−0.0936720	+	1.13730i
$430$	−11.3360	+	6.54482i	−0.546669	+	0.315619i
$431$	6.87264	+	11.9038i	0.331043	+	0.573384i	0.982717	−	0.185116i	$-0.0592661\pi$
$431$	6.87264	+	11.9038i	0.331043	+	0.573384i	−0.651673	+	0.758500i	$0.725933\pi$
$432$	−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	$-0.619905\pi$
$449$	−15.5891			−0.735696			−0.367848	+	0.929886i	$0.619905\pi$
$450$	−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
$455$	30.4965	−	19.0467i	1.42970	−	0.892925i
$456$	4.94596	−	9.17568i	0.231616	−	0.429690i
$457$	2.92274	+	1.68744i	0.136720	+	0.0789353i	0.566800	−	0.823856i	$-0.308181\pi$
$457$	2.92274	+	1.68744i	0.136720	+	0.0789353i	−0.430080	+	0.902791i	$0.641515\pi$
$458$	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	$-0.973425\pi$
$461$		−	3.58098i		−	0.166783i	0.996517	−	0.0833914i	$-0.0265752\pi$
$462$	−3.02474	−	17.0782i	−0.140724	−	0.794550i
$463$		−	8.12604i		−	0.377649i	−0.982011	−	0.188825i	$-0.939532\pi$
$463$		−	8.12604i		−	0.377649i	0.982011	−	0.188825i	$-0.0604677\pi$
$464$	−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	$-0.158245\pi$
$468$	0.572586	−	10.8015i	0.0264678	−	0.499299i
$469$	−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	−0.375384	−	0.926869i	$-0.622489\pi$
$479$	5.24426	−	3.02777i	0.239616	−	0.138343i	0.615000	+	0.788527i	$0.289156\pi$
$480$	0.190718	+	6.52564i	0.00870502	+	0.297853i
$481$	−9.88300	−	22.6025i	−0.450626	−	1.03058i
$482$	−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	0.0809478	−	0.996718i	$-0.474205\pi$
$487$	21.7283	−	12.5449i	0.984605	−	0.568462i	0.903657	+	0.428256i	$0.140872\pi$
$488$	−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
$494$	−2.41216	+	21.5644i	−0.108528	+	0.970227i
$495$	−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	−0.349098	−	0.937086i	$-0.613512\pi$
$499$	−29.8258	−	17.2200i	−1.33519	−	0.770871i	−0.986090	+	0.166215i	$0.946845\pi$
$500$	−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
$507$	7.29691	+	21.3015i	0.324067	+	0.946034i
$508$	−6.09092	−	10.5498i	−0.270241	−	0.468071i
$509$	−22.1861	−	12.8091i	−0.983380	−	0.567755i	−0.0800909	−	0.996788i	$-0.525521\pi$
$509$	−22.1861	−	12.8091i	−0.983380	−	0.567755i	−0.903289	+	0.429033i	$0.858854\pi$
$510$	−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
$520$	−5.44455	−	12.4517i	−0.238759	−	0.546043i
$521$	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	0.861896	−	0.507086i	$-0.169277\pi$
$541$	19.8564	+	11.4641i	0.853694	+	0.492881i	−0.00820130	+	0.999966i	$0.502611\pi$
$542$	−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
$546$	−9.15820	−	13.7524i	−0.391935	−	0.588547i
$547$	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	0.577657	−	0.816280i	$-0.303967\pi$
$557$	−9.86728	−	17.0906i	−0.418090	−	0.724154i	−0.995747	+	0.0921260i	$0.970634\pi$
$558$	−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	$0.864631\pi$
$572$	12.5032	−	5.46706i	0.522784	−	0.228589i
$573$	−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	0.562876	−	0.826541i	$-0.309695\pi$
$577$	−10.4339	−	18.0720i	−0.434368	−	0.752347i	−0.997244	+	0.0741941i	$0.976362\pi$
$578$	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
$585$	−18.4874	−	36.3374i	−0.764359	−	1.50237i
$586$	−13.1268	−	7.57874i	−0.542261	−	0.313075i
$587$		−	7.52079i		−	0.310416i	−0.987882	−	0.155208i	$-0.950395\pi$
$587$		−	7.52079i		−	0.310416i	0.987882	−	0.155208i	$-0.0496048\pi$
$588$	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	0.427476	−	0.904027i	$-0.359403\pi$
$593$	−3.45052	−	1.99216i	−0.141696	−	0.0818081i	−0.569172	+	0.822219i	$0.692736\pi$
$594$	−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
$598$	−23.9854	−	2.68297i	−0.980836	−	0.109715i
$599$	−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
$611$	11.2084	+	25.6337i	0.453444	+	1.03703i
$612$	−3.12245	+	6.22131i	−0.126218	+	0.251482i
$613$	9.33110	−	5.38731i	0.376880	−	0.217592i	−0.299580	−	0.954071i	$-0.596847\pi$
$613$	9.33110	−	5.38731i	0.376880	−	0.217592i	0.676460	+	0.736480i	$0.263513\pi$
$614$	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	$-0.348554\pi$
$617$	22.7546			0.916066			0.458033	+	0.888935i	$0.348554\pi$
$618$	17.0121	−	10.4962i	0.684327	−	0.422221i
$619$	11.7673	+	20.3816i	0.472969	+	0.819207i	0.999521	−	0.0309362i	$-0.00984888\pi$
$619$	11.7673	+	20.3816i	0.472969	+	0.819207i	−0.526552	+	0.850143i	$0.676516\pi$
$620$	−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
$624$	−5.64639	+	2.66802i	−0.226036	+	0.106806i
$625$	−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	$0.297118\pi$
$631$			40.3755i			1.60733i	−0.595085	+	0.803663i	$0.702882\pi$
$632$	−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
$637$	−23.7700	−	8.48443i	−0.941803	−	0.336165i
$638$		−	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	$-0.208247\pi$
$643$	40.2432			1.58704			0.793519	+	0.608545i	$0.208247\pi$
$644$	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	0.628830	−	0.777543i	$-0.283534\pi$
$661$	−9.22875	−	15.9847i	−0.358957	−	0.621731i	−0.987787	+	0.155811i	$0.950201\pi$
$662$	10.6712	−	6.16103i	0.414749	−	0.239455i
$663$	1.18944	−	14.4414i	0.0461942	−	0.560858i
$664$		−	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
$676$	8.82691	−	9.54388i	0.339496	−	0.367072i
$677$	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	$-0.994072\pi$
$683$	−13.4864	−	23.3591i	−0.516042	−	0.893811i	0.483785	−	0.875187i	$-0.339262\pi$
$684$	−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
$689$	−2.70469	−	0.302542i	−0.103040	−	0.0115259i
$690$	43.6816	−	1.27663i	1.66293	−	0.0486006i
$691$	0.543955	−	0.942158i	0.0206930	−	0.0358414i	−0.855493	−	0.517814i	$-0.826746\pi$
$691$	0.543955	−	0.942158i	0.0206930	−	0.0358414i	0.876186	+	0.481972i	$0.160079\pi$
$692$	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	$0.816702\pi$
$702$	−16.4428	+	8.97967i	−0.620593	+	0.338916i
$703$	−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	0.508092	−	0.861303i	$-0.330351\pi$
$709$	0.432082	+	0.249463i	0.0162272	+	0.00936877i	−0.491864	+	0.870672i	$0.663684\pi$
$710$	−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	$-0.0732827\pi$
$728$	−4.48038	+	8.42177i	−0.166054	+	0.312132i
$729$	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	$-0.473696\pi$
$733$	24.4841	−	42.4077i	0.904341	−	1.56636i	0.821800	−	0.569777i	$-0.192970\pi$
$734$		−	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	−0.465093	−	0.885262i	$-0.653979\pi$
$739$	1.87629	−	1.08328i	0.0690204	−	0.0398489i	0.534113	+	0.845413i	$0.320646\pi$
$740$	12.8941	−	22.3333i	0.473998	−	0.820989i
$741$	33.9810	−	16.0566i	1.24832	−	0.589854i
$742$	1.97581	−	0.290688i	0.0725341	−	0.0106715i
$743$	9.34291			0.342758			0.171379	−	0.985205i	$-0.445178\pi$
$743$	9.34291			0.342758			0.171379	+	0.985205i	$0.445178\pi$
$744$	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
$754$	−4.44557	−	10.1670i	−0.161898	−	0.370262i
$755$	−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	0.701146	−	0.713018i	$-0.252672\pi$
$761$	11.9787	+	6.91589i	0.434227	+	0.250701i	−0.266919	+	0.963719i	$0.586006\pi$
$762$	−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
$767$	15.2547	+	1.70637i	0.550814	+	0.0616133i
$768$	−0.909476	−	1.47406i	−0.0328179	−	0.0531906i
$769$	−34.5029			−1.24421			−0.622104	−	0.782935i	$-0.713722\pi$
$769$	−34.5029			−1.24421			−0.622104	+	0.782935i	$0.713722\pi$
$770$	−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	−0.849785	−	0.527129i	$-0.823268\pi$
$773$	−22.7475	+	13.1333i	−0.818170	+	0.472371i	0.0316148	+	0.999500i	$0.489935\pi$
$774$	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
$780$	−13.4029	+	19.3501i	−0.479900	+	0.692845i
$781$	−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	0.558388	−	0.829580i	$-0.311420\pi$
$787$	−12.3223	−	21.3429i	−0.439243	−	0.760791i	−0.997631	+	0.0687887i	$0.978087\pi$
$788$	−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
$793$	−13.9659	−	31.9400i	−0.495943	−	1.13422i
$794$	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	$-0.555304\pi$
$811$	−9.84596			−0.345739			−0.172869	+	0.984945i	$0.555304\pi$
$812$	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
$819$	−11.9427	+	26.0072i	−0.417310	+	0.908764i
$820$	25.2381			0.881354
$821$	−27.5211	+	47.6680i	−0.960494	+	1.66362i	−0.239232	+	0.970963i	$0.576896\pi$
$821$	−27.5211	+	47.6680i	−0.960494	+	1.66362i	−0.721262	+	0.692662i	$0.756438\pi$
$822$	−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	$-0.277999\pi$
$827$	36.9395			1.28451			0.642256	+	0.766491i	$0.277999\pi$
$828$	−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	$-0.939409\pi$
$839$		−	10.9609i		−	0.378412i	0.981937	−	0.189206i	$-0.0605914\pi$
$840$	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
$845$	10.8265	−	47.7884i	0.372445	−	1.64397i
$846$	−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	$-0.178044\pi$
$853$	49.5106			1.69521			0.847605	+	0.530628i	$0.178044\pi$
$854$	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	$0.863956\pi$
$858$	−19.4301	−	13.4583i	−0.663333	−	0.459459i
$859$	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	$-0.587924\pi$
$863$	20.4709	−	35.4566i	0.696836	−	1.20696i	0.969558	−	0.244862i	$-0.0787428\pi$
$864$	−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
$871$	−18.7010	−	2.09187i	−0.633658	−	0.0708802i
$872$	−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	0.760105	−	0.649800i	$-0.225147\pi$
$877$	17.0997	+	9.87250i	0.577415	+	0.333371i	−0.182690	+	0.983170i	$0.558481\pi$
$878$	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	$0.556188\pi$
$884$	−7.66525	+	3.35166i	−0.257810	+	0.112728i
$885$	−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
$897$	17.8593	+	37.7960i	0.596304	+	1.26197i
$898$	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
$910$	1.24671	+	35.9341i	0.0413280	+	1.19120i
$911$			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	−0.347160	−	0.937806i	$-0.612854\pi$
$929$	−40.6262	−	23.4556i	−1.33290	−	0.769552i	−0.985744	+	0.168253i	$0.946187\pi$
$930$	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
$936$	9.06807	+	5.89662i	0.296399	+	0.192737i
$937$			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	−0.780233	−	0.625489i	$-0.784899\pi$
$941$	−19.2846	+	11.1340i	−0.628660	+	0.362957i	0.151573	+	0.988446i	$0.451566\pi$
$942$	−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	$-0.506536\pi$
$947$	26.3290	−	45.6031i	0.855576	−	1.48190i	0.876109	−	0.482112i	$-0.160130\pi$
$948$	1.39230	−	0.0406913i	0.0452199	−	0.00132159i
$949$	−2.03030	+	18.1506i	−0.0659062	+	0.589192i
$950$	−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
$962$	24.5158	+	2.74230i	0.790422	+	0.0884155i
$963$	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	$0.0145819\pi$
$967$			2.84809i			0.0915884i	−0.998951	+	0.0457942i	$0.985418\pi$
$968$	−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
$975$	−4.71961	+	57.3022i	−0.151148	+	1.83514i
$976$	8.37307	−	4.83419i	0.268015	−	0.154739i
$977$	22.8365	+	39.5540i	0.730605	+	1.26544i	0.956625	+	0.291322i	$0.0940950\pi$
$977$	22.8365	+	39.5540i	0.730605	+	1.26544i	−0.226020	+	0.974123i	$0.572572\pi$
$978$	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	$-0.272508\pi$
$983$	51.3302	−	29.6355i	1.63718	−	0.945226i	0.981798	−	0.189927i	$-0.0608253\pi$
$984$	−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.a.467.18	yes	36
3.2	odd	2		546.2.bg.b.467.13	yes	36
7.3	odd	6	inner	546.2.bg.a.311.13	✓	36
13.12	even	2		546.2.bg.b.467.18	yes	36
21.17	even	6		546.2.bg.b.311.18	yes	36
39.38	odd	2	inner	546.2.bg.a.467.13	yes	36
91.38	odd	6		546.2.bg.b.311.13	yes	36
273.38	even	6	inner	546.2.bg.a.311.18	yes	36

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

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} +(-3.30355 + 1.44449i) 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} +(5.13376 + 3.55591i) 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} +(0.400812 - 3.58320i) 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} +(-5.44455 - 12.4517i) 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} +(-5.64639 + 2.66802i) 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} +(-4.48038 + 8.42177i) 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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