LMFDB - Embedded newform 546.2.bg.a.467.13

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			467.13
Character	$\chi$	$=$	546.467
Dual form			546.2.bg.a.311.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.909476 - 1.47406i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-3.26421 - 1.88459i) q^{5} +(0.821836 + 1.52466i) q^{6} +(-0.385108 - 2.61757i) q^{7} +1.00000 q^{8} +(-1.34571 - 2.68124i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.909476 - 1.47406i) 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} +(-1.34571 - 2.68124i) q^{9} +(3.26421 - 1.88459i) q^{10} +(1.89239 + 3.27771i) q^{11} +(-1.73131 - 0.0505991i) 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} +(2.99488 + 0.175206i) q^{18} +(-3.00909 + 5.21190i) q^{19} +3.76919i q^{20} +(-4.20871 - 1.81295i) q^{21} -3.78477 q^{22} +(-5.79704 - 3.34692i) q^{23} +(0.909476 - 1.47406i) 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} +(0.190718 - 6.52564i) q^{30} +(-4.94611 - 8.56691i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(6.55262 + 0.191506i) 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} +(0.512624 + 6.22392i) q^{39} +(-3.26421 - 1.88459i) q^{40} -6.69591i q^{41} +(3.67441 - 2.73837i) q^{42} -3.47280 q^{43} +(1.89239 - 3.27771i) q^{44} +(-0.660383 + 11.2883i) 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} +(4.01717 + 0.117406i) q^{51} +(3.30355 + 1.44449i) q^{52} +(0.653696 - 0.377412i) q^{53} +(2.98203 - 4.25529i) 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} +(5.55601 + 3.42798i) q^{60} +(-8.37307 - 4.83419i) q^{61} +9.89221 q^{62} +(-6.50011 + 4.55506i) q^{63} +1.00000 q^{64} +(13.5058 - 1.51074i) q^{65} +(-3.44216 + 5.57898i) 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} +(-1.34571 - 2.68124i) q^{72} +(-2.53273 - 4.38682i) q^{73} +(-5.92523 + 3.42094i) q^{74} +(15.9398 + 0.465854i) 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} +(-5.37814 + 7.21634i) q^{81} +(5.79883 + 3.34796i) q^{82} -6.88779i q^{83} +(0.534294 + 4.55132i) q^{84} -8.74567i q^{85} +(1.73640 - 3.00754i) q^{86} +(-4.53658 - 2.79901i) 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} +(-17.1265 - 0.500537i) q^{93} +(-6.71987 + 3.87972i) q^{94} +(19.6446 - 11.3418i) q^{95} +(-1.73131 - 0.0505991i) 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
$3$	0.909476	−	1.47406i	0.525086	−	0.851049i
$3$	0.909476	−	1.47406i	0.525086	−	0.851049i
$4$	−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
$9$	−1.34571	−	2.68124i	−0.448569	−	0.893748i
$10$	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	$0.640053\pi$
$12$	−1.73131	−	0.0505991i	−0.499787	−	0.0146067i
$13$	−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	0.971725	−	0.236117i	$-0.0758750\pi$
$17$	1.16015	+	2.00944i	0.281379	+	0.487362i	−0.690346	+	0.723479i	$0.742542\pi$
$18$	2.99488	+	0.175206i	0.705900	+	0.0412964i
$19$	−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
$21$	−4.20871	−	1.81295i	−0.918415	−	0.395618i
$22$	−3.78477			−0.806916
$23$	−5.79704	−	3.34692i	−1.20877	−	0.697881i	−0.246276	−	0.969200i	$-0.579207\pi$
$23$	−5.79704	−	3.34692i	−1.20877	−	0.697881i	−0.962490	+	0.271319i	$0.912540\pi$
$24$	0.909476	−	1.47406i	0.185646	−	0.300891i
$25$	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	$-0.907758\pi$
$29$		−	3.07761i		−	0.571498i	0.958304	−	0.285749i	$-0.0922424\pi$
$30$	0.190718	−	6.52564i	0.0348201	−	1.19141i
$31$	−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
$33$	6.55262	+	0.191506i	1.14066	+	0.0333369i
$34$	−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
$39$	0.512624	+	6.22392i	0.0820855	+	0.996625i
$40$	−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	$-0.175136\pi$
$42$	3.67441	−	2.73837i	0.566974	−	0.422540i
$43$	−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
$45$	−0.660383	+	11.2883i	−0.0984441	+	1.68275i
$46$	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
$51$	4.01717	+	0.117406i	0.562517	+	0.0164401i
$52$	3.30355	+	1.44449i	0.458120	+	0.200314i
$53$	0.653696	−	0.377412i	0.0897921	−	0.0518415i	−0.454432	−	0.890782i	$-0.650158\pi$
$53$	0.653696	−	0.377412i	0.0897921	−	0.0518415i	0.544224	+	0.838940i	$0.316824\pi$
$54$	2.98203	−	4.25529i	0.405803	−	0.579071i
$55$		−	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	$0.243952\pi$
$60$	5.55601	+	3.42798i	0.717278	+	0.442551i
$61$	−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
$63$	−6.50011	+	4.55506i	−0.818937	+	0.573883i
$64$	1.00000			0.125000
$65$	13.5058	−	1.51074i	1.67518	−	0.187384i
$66$	−3.44216	+	5.57898i	−0.423700	+	0.686725i
$67$	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	$-0.620634\pi$
$71$	−6.23494			−0.739951			−0.369976	+	0.929041i	$0.620634\pi$
$72$	−1.34571	−	2.68124i	−0.158593	−	0.315988i
$73$	−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
$75$	15.9398	+	0.465854i	1.84057	+	0.0537922i
$76$	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
$81$	−5.37814	+	7.21634i	−0.597572	+	0.801816i
$82$	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	$-0.123394\pi$
$84$	0.534294	+	4.55132i	0.0582963	+	0.496590i
$85$		−	8.74567i		−	0.948601i
$86$	1.73640	−	3.00754i	0.187241	−	0.324311i
$87$	−4.53658	−	2.79901i	−0.486373	−	0.300086i
$88$	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
$91$	6.71611	+	6.77450i	0.704040	+	0.710160i
$92$			6.69384i			0.697881i
$93$	−17.1265	−	0.500537i	−1.77594	−	0.0519033i
$94$	−6.71987	+	3.87972i	−0.693102	+	0.400162i
$95$	19.6446	−	11.3418i	2.01549	−	1.16365i
$96$	−1.73131	−	0.0505991i	−0.176701	−	0.00516425i
$97$	−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	0.828507	−	0.559979i	$-0.189191\pi$
$101$	−0.710555	−	1.23072i	−0.0707029	−	0.122461i	−0.899210	+	0.437518i	$0.855858\pi$
$102$	−2.11026	+	3.42027i	−0.208947	+	0.338657i
$103$	−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
$105$	10.3214	+	13.8495i	1.00727	+	1.35158i
$106$			0.754823i			0.0733149i
$107$	−4.75556	−	2.74562i	−0.459737	−	0.265430i	0.252196	−	0.967676i	$-0.418847\pi$
$107$	−4.75556	−	2.74562i	−0.459737	−	0.265430i	−0.711934	+	0.702247i	$0.752180\pi$
$108$	2.19417	+	4.71016i	0.211134	+	0.453235i
$109$	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	$0.185359\pi$
$113$			11.6924i			1.09993i	−0.835187	+	0.549965i	$0.814641\pi$
$114$	−10.4193	−	0.304515i	−0.975861	−	0.0285204i
$115$	12.6152	+	21.8501i	1.17637	+	2.03753i
$116$	−2.66529	+	1.53881i	−0.247466	+	0.142875i
$117$	9.64066	+	4.90487i	0.891279	+	0.453455i
$118$			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
$123$	−9.87018	−	6.08977i	−0.889964	−	0.549096i
$124$	−4.94611	+	8.56691i	−0.444174	+	0.769331i
$125$		−	15.8561i		−	1.41821i
$126$	−0.694737	−	7.90679i	−0.0618921	−	0.704393i
$127$	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
$129$	−3.15843	+	5.11912i	−0.278084	+	0.450714i
$130$	−5.44455	+	12.4517i	−0.477518	+	1.09209i
$131$	−0.646676	+	1.12008i	−0.0565003	+	0.0978614i	−0.892892	−	0.450271i	$-0.851328\pi$
$131$	−0.646676	+	1.12008i	−0.0565003	+	0.0978614i	0.836392	+	0.548132i	$0.184661\pi$
$132$	−3.11046	−	5.77049i	−0.270731	−	0.502256i
$133$	14.8013	+	5.86937i	1.28344	+	0.508939i
$134$			5.21907i			0.450859i
$135$	16.0390	+	11.2398i	1.38041	+	0.967372i
$136$	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	$0.793716\pi$
$138$	0.338702	−	11.5891i	0.0288323	−	0.986532i
$139$		−	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
$144$	2.99488	+	0.175206i	0.249573	+	0.0146005i
$145$	−5.80004	+	10.0460i	−0.481668	+	0.834273i
$146$	5.06546			0.419220
$147$	−3.12472	+	11.7148i	−0.257723	+	0.966219i
$148$		−	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	$0.104953\pi$
$150$	−8.37333	+	13.5713i	−0.683680	+	1.10809i
$151$	−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
$156$	5.13376	−	3.55591i	0.411030	−	0.284700i
$157$	−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
$159$	0.0381934	−	1.30683i	0.00302893	−	0.103639i
$160$			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
$165$	−21.0282	−	12.9741i	−1.63704	−	1.01004i
$166$	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	$0.921435\pi$
$168$	−4.20871	−	1.81295i	−0.324709	−	0.139872i
$169$	3.85179	−	12.4163i	0.296292	−	0.955097i
$170$	7.57397	+	4.37284i	0.580897	+	0.335381i
$171$	18.0237	+	1.05442i	1.37831	+	0.0806335i
$172$	1.73640	+	3.00754i	0.132399	+	0.229323i
$173$	7.91626	−	13.7114i	0.601862	−	1.04246i	−0.390677	−	0.920528i	$-0.627759\pi$
$173$	7.91626	−	13.7114i	0.601862	−	1.04246i	0.992539	−	0.121928i	$-0.0389077\pi$
$174$	4.69231	−	2.52929i	0.355723	−	0.191745i
$175$	19.0979	−	15.1203i	1.44366	−	1.14299i
$176$	−3.78477			−0.285288
$177$	0.215414	−	7.37067i	0.0161915	−	0.554013i
$178$	13.5271	−	7.80988i	1.01390	−	0.585375i
$179$	14.2272	−	8.21410i	1.06339	−	0.613950i	0.137024	−	0.990568i	$-0.456246\pi$
$179$	14.2272	−	8.21410i	1.06339	−	0.613950i	0.926369	+	0.376617i	$0.122913\pi$
$180$	10.1061	−	5.07222i	0.753265	−	0.378061i
$181$		−	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
$186$	8.99673	−	14.5817i	0.659672	−	1.06918i
$187$	−4.39092	+	7.60529i	−0.321096	+	0.556154i
$188$		−	7.75944i		−	0.565915i
$189$	0.802730	+	13.7243i	0.0583900	+	0.998294i
$190$			22.6836i			1.64564i
$191$	9.19327	+	5.30774i	0.665201	+	0.384054i	0.794256	−	0.607583i	$-0.207861\pi$
$191$	9.19327	+	5.30774i	0.665201	+	0.384054i	−0.129055	+	0.991637i	$0.541194\pi$
$192$	0.909476	−	1.47406i	0.0656358	−	0.106381i
$193$	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
$195$	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	$0.330654\pi$
$198$	5.09319	+	10.1479i	0.361957	+	0.721180i
$199$	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
$201$	0.264080	−	9.03583i	0.0186268	−	0.637338i
$202$	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
$207$	−1.17280	+	20.0472i	−0.0815152	+	1.39338i
$208$	−0.400812	−	3.58320i	−0.0277913	−	0.248450i
$209$	−22.7774			−1.57555
$210$	−17.1548	+	2.01386i	−1.18379	+	0.138969i
$211$	−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
$213$	−5.67053	+	9.19068i	−0.388538	+	0.629735i
$214$	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
$219$	−8.76989	−	0.256308i	−0.592614	−	0.0173197i
$220$	−12.3543	+	7.13275i	−0.832926	+	0.480890i
$221$	−7.66525	−	3.35166i	−0.515621	−	0.225457i
$222$	−0.346193	+	11.8454i	−0.0232349	+	0.795012i
$223$	−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	0.0479723	−	0.998849i	$-0.484724\pi$
$227$	14.1171	−	8.15053i	0.936987	−	0.540970i	0.889014	+	0.457879i	$0.151391\pi$
$228$	5.47339	−	8.87116i	0.362484	−	0.587507i
$229$	−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
$231$	−2.02218	−	17.2257i	−0.133050	−	1.13337i
$232$		−	3.07761i		−	0.202055i
$233$	−18.8229	−	10.8674i	−1.23313	−	0.711947i	−0.265447	−	0.964125i	$-0.585520\pi$
$233$	−18.8229	−	10.8674i	−1.23313	−	0.711947i	−0.967681	+	0.252179i	$0.918853\pi$
$234$	−9.06807	+	5.89662i	−0.592798	+	0.385474i
$235$	−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	$0.753845\pi$
$240$	0.190718	−	6.52564i	0.0123108	−	0.421228i
$241$	−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
$243$	5.74603	+	14.4908i	0.368608	+	0.929585i
$244$			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
$249$	−10.1530	−	6.26428i	−0.643421	−	0.396983i
$250$	13.7318	+	7.92805i	0.868474	+	0.501414i
$251$	−8.59657			−0.542611			−0.271305	−	0.962493i	$-0.587455\pi$
$251$	−8.59657			−0.542611			−0.271305	+	0.962493i	$0.587455\pi$
$252$	7.19485	+	3.35174i	0.453233	+	0.211139i
$253$		−	25.3347i		−	1.59278i
$254$	−6.09092	+	10.5498i	−0.382178	+	0.661952i
$255$	−12.8916	−	7.95398i	−0.807306	−	0.498097i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−10.8190	+	18.7391i	−0.674873	+	1.16891i	0.301633	+	0.953424i	$0.402468\pi$
$257$	−10.8190	+	18.7391i	−0.674873	+	1.16891i	−0.976506	+	0.215490i	$0.930865\pi$
$258$	−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
$261$	−8.25183	+	4.14156i	−0.510775	+	0.256356i
$262$	−0.646676	−	1.12008i	−0.0399518	−	0.0691985i
$263$	12.6463	−	7.30132i	0.779802	−	0.450219i	−0.0565583	−	0.998399i	$-0.518013\pi$
$263$	12.6463	−	7.30132i	0.779802	−	0.450219i	0.836360	+	0.548181i	$0.184679\pi$
$264$	6.55262	+	0.191506i	0.403286	+	0.0117864i
$265$	−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	$0.00791684\pi$
$269$	8.55131	+	14.8113i	0.521382	+	0.903061i	−0.478308	+	0.878192i	$0.658750\pi$
$270$	−17.7535	+	8.27024i	−1.08044	+	0.503310i
$271$	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
$273$	16.0942	−	3.73871i	0.974063	−	0.226277i
$274$	−2.90606			−0.175561
$275$	−17.4228	+	30.1771i	−1.05063	+	1.81975i
$276$	9.86713	+	6.08789i	0.593931	+	0.366448i
$277$	−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	$0.718743\pi$
$282$	−0.392621	+	13.4340i	−0.0233802	+	0.799983i
$283$	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
$285$	1.14777	−	39.2725i	0.0679882	−	2.32630i
$286$	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
$291$	−4.58842	+	7.43681i	−0.268978	+	0.435954i
$292$	−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	$0.854001\pi$
$294$	−8.58294	−	8.56348i	−0.500567	−	0.499432i
$295$	−16.0465			−0.934261
$296$	5.92523	+	3.42094i	0.344397	+	0.198838i
$297$	−8.30443	−	17.8269i	−0.481872	−	1.03442i
$298$	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
$303$	−2.46039	−	0.0719070i	−0.141345	−	0.00413095i
$304$	−3.00909	−	5.21190i	−0.172583	−	0.298923i
$305$	18.2210	+	31.5597i	1.04333	+	1.80710i
$306$	3.12245	+	6.22131i	0.178499	+	0.355649i
$307$	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	0.941847	−	0.336043i	$-0.109089\pi$
$311$	3.17259	+	5.49509i	0.179901	+	0.311598i	−0.761945	+	0.647641i	$0.775756\pi$
$312$	0.512624	+	6.22392i	0.0290216	+	0.352360i
$313$	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
$315$	29.8022	−	2.61859i	1.67916	−	0.147541i
$316$	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	$0.172311\pi$
$318$	1.11266	+	0.686494i	0.0623946	+	0.0384967i
$319$	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
$324$	8.93861	+	1.04944i	0.496589	+	0.0583022i
$325$	−30.4150	−	13.2991i	−1.68712	−	0.737700i
$326$	−7.92899	+	4.57780i	−0.439146	+	0.253541i
$327$	0.0163918	−	0.560867i	0.000906470	−	0.0310160i
$328$		−	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
$333$	1.19873	−	20.4906i	0.0656903	−	1.12288i
$334$	−5.46865	−	3.15733i	−0.299231	−	0.172761i
$335$	−19.6716			−1.07478
$336$	3.67441	−	2.73837i	0.200456	−	0.149391i
$337$	−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
$339$	17.2353	+	10.6340i	0.936095	+	0.577558i
$340$	−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
$345$	43.6816	+	1.27663i	2.35174	+	0.0687316i
$346$	7.91626	+	13.7114i	0.425581	+	0.737128i
$347$	1.02619	−	0.592469i	0.0550886	−	0.0318054i	−0.472203	−	0.881490i	$-0.656541\pi$
$347$	1.02619	−	0.592469i	0.0550886	−	0.0318054i	0.527291	+	0.849685i	$0.323208\pi$
$348$	−0.155724	+	5.32830i	−0.00834770	+	0.285627i
$349$	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
$351$	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	$0.334184\pi$
$354$	6.27548	+	3.87189i	0.333538	+	0.205788i
$355$	20.3522	+	11.7503i	1.08018	+	0.623643i
$356$			15.6198i			0.827845i
$357$	−1.23973	−	10.5605i	−0.0656133	−	0.558919i
$358$			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	$0.236616\pi$
$360$	−0.660383	+	11.2883i	−0.0348052	+	0.594944i
$361$	−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
$366$	0.489212	−	16.7390i	0.0255715	−	0.874961i
$367$	−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
$369$	−17.9534	+	9.01074i	−0.934616	+	0.469080i
$370$	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
$375$	−23.3728	−	14.4207i	−1.20697	−	0.744684i
$376$	6.71987	+	3.87972i	0.346551	+	0.200081i
$377$	6.58213	+	8.93350i	0.338997	+	0.460099i
$378$	−12.2869	−	6.16695i	−0.631972	−	0.317194i
$379$		−	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
$381$	11.0791	−	17.9568i	0.567599	−	0.919953i
$382$	−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
$387$	4.67338	+	9.31144i	0.237561	+	0.473327i
$388$	2.52256	+	4.36920i	0.128064	+	0.221813i
$389$	−18.6337	+	10.7582i	−0.944765	+	0.545460i	−0.891451	−	0.453118i	$-0.850312\pi$
$389$	−18.6337	+	10.7582i	−0.944765	+	0.545460i	−0.0533140	+	0.998578i	$0.516978\pi$
$390$	13.4029	+	19.3501i	0.678681	+	0.979831i
$391$		−	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
$396$	−11.3349	−	0.663113i	−0.569602	−	0.0333227i
$397$	−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
$399$	22.1133	−	16.4800i	1.10705	−	0.825033i
$400$	−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	$0.227495\pi$
$402$	7.69322	+	4.74662i	0.383703	+	0.236740i
$403$	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
$408$	4.01717	+	0.117406i	0.198880	+	0.00581244i
$409$	−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
$411$	5.03129	+	0.147044i	0.248175	+	0.00725315i
$412$			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
$417$	−7.88235	−	4.86331i	−0.386001	−	0.238157i
$418$	11.3887	−	19.7258i	0.557040	−	0.964822i
$419$	26.6532			1.30209			0.651047	−	0.759037i	$-0.274330\pi$
$419$	26.6532			1.30209			0.651047	+	0.759037i	$0.274330\pi$
$420$	6.83334	−	15.8634i	0.333433	−	0.774055i
$421$			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
$423$	1.35950	−	23.2386i	0.0661010	−	1.12990i
$424$	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
$429$	−19.4301	+	13.4583i	−0.938095	+	0.649772i
$430$	−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	$0.725933\pi$
$432$	2.98203	−	4.25529i	0.143473	−	0.204733i
$433$			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
$438$	4.60691	−	7.46679i	0.220127	−	0.356777i
$439$	−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
$441$	14.4264	+	15.2603i	0.686973	+	0.726683i
$442$	6.73525	−	4.96248i	0.320363	−	0.236041i
$443$	−5.01928	−	2.89788i	−0.238473	−	0.137682i	0.376002	−	0.926619i	$-0.377299\pi$
$443$	−5.01928	−	2.89788i	−0.238473	−	0.137682i	−0.614475	+	0.788937i	$0.710632\pi$
$444$	−10.0853	−	6.22252i	−0.478629	−	0.295308i
$445$	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	$0.619905\pi$
$450$	12.3896	+	24.6856i	0.584052	+	1.16369i
$451$	21.9472	−	12.6712i	1.03346	−	0.596666i
$452$	10.1259	−	5.84621i	0.476284	−	0.274983i
$453$	−0.322157	+	11.0230i	−0.0151362	+	0.517905i
$454$			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
$459$	−5.09115	−	10.9290i	−0.237634	−	0.510123i
$460$	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	$-0.0265752\pi$
$462$	15.9290	+	6.86159i	0.741084	+	0.319230i
$463$			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
$465$	54.9612	+	33.9104i	2.54877	+	1.57256i
$466$	18.8229	−	10.8674i	0.871953	−	0.503422i
$467$	−18.4226	+	31.9089i	−0.852496	+	1.47657i	0.0264534	+	0.999650i	$0.491579\pi$
$467$	−18.4226	+	31.9089i	−0.852496	+	1.47657i	−0.878949	+	0.476916i	$0.841755\pi$
$468$	−0.572586	−	10.8015i	−0.0264678	−	0.499299i
$469$	−8.57127	−	10.8261i	−0.395785	−	0.499902i
$470$	29.2468			1.34905
$471$	−0.573887	+	19.6362i	−0.0264433	+	0.904790i
$472$	3.68691	−	2.12864i	0.169704	−	0.0979784i
$473$	−6.57189	−	11.3828i	−0.302176	−	0.523384i
$474$	−1.39230	−	0.0406913i	−0.0639506	−	0.00186901i
$475$	−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	$0.289156\pi$
$480$	5.55601	+	3.42798i	0.253596	+	0.156465i
$481$	−24.5158	+	2.74230i	−1.11782	+	0.125038i
$482$	12.5745			0.572754
$483$	18.3302	+	24.5959i	0.834055	+	1.11915i
$484$	3.32449			0.151113
$485$	16.4683	+	9.50800i	0.747789	+	0.431736i
$486$	−15.4224	−	2.26919i	−0.699575	−	0.102933i
$487$	−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	$-0.827411\pi$
$491$		−	22.8687i		−	1.03205i	0.856574	−	0.516024i	$-0.172589\pi$
$492$	−0.338807	+	11.5927i	−0.0152746	+	0.522640i
$493$	6.18429	−	3.57050i	0.278526	−	0.160807i
$494$	19.8814	+	8.69319i	0.894505	+	0.391125i
$495$	−38.2493	+	19.1972i	−1.71918	+	0.862850i
$496$	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
$501$	9.30818	+	5.74302i	0.415859	+	0.256579i
$502$	4.29829	−	7.44485i	0.191842	−	0.332280i
$503$	27.5477			1.22829			0.614145	−	0.789193i	$-0.289501\pi$
$503$	27.5477			1.22829			0.614145	+	0.789193i	$0.289501\pi$
$504$	−6.50011	+	4.55506i	−0.289538	+	0.202898i
$505$			5.35643i			0.238358i
$506$	21.9405	+	12.6673i	0.975372	+	0.563131i
$507$	−14.7992	−	16.9701i	−0.657256	−	0.753667i
$508$	−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
$513$	17.9464	−	25.6091i	0.792354	−	1.13067i
$514$	−10.8190	−	18.7391i	−0.477207	−	0.826547i
$515$	21.7500	+	37.6722i	0.958421	+	1.66003i
$516$	6.01251	+	0.175721i	0.264686	+	0.00773568i
$517$			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	0.548014	−	0.836469i	$-0.315384\pi$
$521$	−10.2805	−	17.8063i	−0.450396	−	0.780109i	−0.998411	+	0.0563599i	$0.982051\pi$
$522$	0.539215	−	9.21707i	0.0236008	−	0.403420i
$523$	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
$525$	−4.91912	−	41.9030i	−0.214688	−	1.82880i
$526$			14.6026i			0.636705i
$527$	11.4765	−	19.8779i	0.499924	−	0.865893i
$528$	−3.44216	+	5.57898i	−0.149801	+	0.242794i
$529$	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
$534$	0.790346	−	27.0427i	0.0342016	−	1.17025i
$535$	10.3488	+	17.9246i	0.447416	+	0.774948i
$536$	4.51984	−	2.60953i	0.195228	−	0.112715i
$537$	0.831252	−	28.4423i	0.0358712	−	1.22738i
$538$	−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
$543$	−15.8286	−	9.76603i	−0.679270	−	0.419101i
$544$	1.16015	−	2.00944i	0.0497412	−	0.0861542i
$545$	−1.22105			−0.0523039
$546$	−4.80926	+	15.8073i	−0.205817	+	0.676490i
$547$	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
$549$	−1.69396	+	28.9556i	−0.0722963	+	1.23580i
$550$	−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
$555$	−44.6476	−	1.30486i	−1.89518	−	0.0553884i
$556$	−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	$0.970634\pi$
$558$	−13.3120	−	26.5234i	−0.563543	−	1.12283i
$559$	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	0.724804	−	0.688955i	$-0.241930\pi$
$563$	−5.55820	−	9.62708i	−0.234250	−	0.405733i	−0.959054	+	0.283222i	$0.908597\pi$
$564$	−11.4379	−	7.05702i	−0.481621	−	0.297154i
$565$	22.0355	−	38.1665i	0.927039	−	1.60568i
$566$			32.5372i			1.36764i
$567$	20.9605	+	11.2986i	0.880257	+	0.474498i
$568$	−6.23494			−0.261612
$569$	−17.4869	−	10.0960i	−0.733088	−	0.423248i	0.0864631	−	0.996255i	$-0.472444\pi$
$569$	−17.4869	−	10.0960i	−0.733088	−	0.423248i	−0.819551	+	0.573007i	$0.805777\pi$
$570$	33.4371	+	20.6302i	1.40052	+	0.864105i
$571$	−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
$576$	−1.34571	−	2.68124i	−0.0560711	−	0.111719i
$577$	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
$579$	0.228553	−	7.82023i	0.00949834	−	0.324998i
$580$	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
$585$	−22.2255	−	34.1792i	−0.918909	−	1.41314i
$586$	−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	$-0.0496048\pi$
$588$	11.7077	−	3.15130i	0.482816	−	0.129958i
$589$	59.5331			2.45302
$590$	8.02323	−	13.8966i	0.330311	−	0.572116i
$591$	12.9507	−	20.9903i	0.532722	−	0.863425i
$592$	−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
$597$	1.19973	−	41.0504i	0.0491019	−	1.68008i
$598$	−9.66918	+	22.1135i	−0.395402	+	0.904286i
$599$	1.61182	−	0.930583i	0.0658571	−	0.0380226i	−0.466710	−	0.884410i	$-0.654561\pi$
$599$	1.61182	−	0.930583i	0.0658571	−	0.0380226i	0.532567	+	0.846388i	$0.321227\pi$
$600$	15.9398	+	0.465854i	0.650739	+	0.0190184i
$601$		−	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
$606$	1.29247	−	2.09480i	0.0525028	−	0.0850956i
$607$	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
$609$	−5.57955	+	12.9528i	−0.226095	+	0.524872i
$610$	−36.4419			−1.47549
$611$	−27.8036	+	3.11008i	−1.12481	+	0.125820i
$612$	−6.94904	−	0.406531i	−0.280898	−	0.0164330i
$613$	−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	$-0.348554\pi$
$617$	22.7546			0.916066			0.458033	+	0.888935i	$0.348554\pi$
$618$	0.583963	−	19.9810i	0.0234904	−	0.803754i
$619$	−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
$621$	28.4842	+	19.9613i	1.14303	+	0.801018i
$622$	−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
$627$	−20.7155	+	33.5753i	−0.827298	+	1.34087i
$628$	9.82232	+	5.67092i	0.391953	+	0.226294i
$629$			15.8752i			0.632987i
$630$	−12.6333	+	27.1187i	−0.503323	+	1.08044i
$631$		−	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
$633$	−11.8844	+	19.2620i	−0.472361	+	0.765594i
$634$	−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
$639$	8.39041	+	16.7174i	0.331919	+	0.661330i
$640$	3.26421	−	1.88459i	0.129029	−	0.0744951i
$641$	17.5159	−	10.1128i	0.691835	−	0.399431i	−0.112464	−	0.993656i	$-0.535874\pi$
$641$	17.5159	−	10.1128i	0.691835	−	0.399431i	0.804299	+	0.594225i	$0.202541\pi$
$642$	0.277852	−	9.50706i	0.0109660	−	0.375214i
$643$	−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	$0.0940160\pi$
$647$	18.5795	+	32.1806i	0.730435	+	1.26515i	−0.226262	+	0.974066i	$0.572651\pi$
$648$	−5.37814	+	7.21634i	−0.211273	+	0.283485i
$649$	13.9541	+	8.05640i	0.547746	+	0.316241i
$650$	26.7248	−	19.6907i	1.04823	−	0.772331i
$651$	5.28535	+	45.0226i	0.207149	+	1.76458i
$652$		−	9.15561i		−	0.358561i
$653$	35.2713	+	20.3639i	1.38027	+	0.796900i	0.992191	−	0.124725i	$-0.0398049\pi$
$653$	35.2713	+	20.3639i	1.38027	+	0.796900i	0.388081	+	0.921625i	$0.373138\pi$
$654$	0.477529	+	0.294629i	0.0186729	+	0.0115209i
$655$	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	$-0.947107\pi$
$659$		−	8.49218i		−	0.330808i	0.986226	−	0.165404i	$-0.0528929\pi$
$660$	−0.721822	+	24.6980i	−0.0280969	+	0.961370i
$661$	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
$663$	−11.9119	+	8.25080i	−0.462620	+	0.320434i
$664$		−	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
$669$	−1.95200	+	3.16376i	−0.0754687	+	0.122318i
$670$	9.83582	−	17.0361i	0.379991	−	0.658163i
$671$		−	36.5926i		−	1.41264i
$672$	0.534294	+	4.55132i	0.0206109	+	0.175571i
$673$	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
$675$	−20.2012	−	43.3654i	−0.777545	−	1.66913i
$676$	−12.6787	+	2.87238i	−0.487642	+	0.110476i
$677$	−6.77872	+	11.7411i	−0.260527	+	0.451247i	−0.966382	−	0.257110i	$-0.917230\pi$
$677$	−6.77872	+	11.7411i	−0.260527	+	0.451247i	0.705855	+	0.708357i	$0.250563\pi$
$678$	−17.8270	+	9.60925i	−0.684641	+	0.369041i
$679$	1.94292	+	13.2060i	0.0745622	+	0.506799i
$680$		−	8.74567i		−	0.335381i
$681$	0.824819	−	28.2222i	0.0316071	−	1.08148i
$682$	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	$-0.339262\pi$
$684$	−8.09871	−	16.1362i	−0.309662	−	0.616984i
$685$		−	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
$690$	−22.9464	+	37.1910i	−0.873554	+	1.41584i
$691$	−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
$693$	−27.2309	−	12.6856i	−1.03441	−	0.481884i
$694$			1.18494i			0.0449797i
$695$	−10.0776	+	17.4550i	−0.382266	+	0.662104i
$696$	−4.53658	−	2.79901i	−0.171959	−	0.106096i
$697$	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	$-0.816702\pi$
$701$		−	28.8352i		−	1.08909i	0.838731	−	0.544546i	$-0.183298\pi$
$702$	0.444780	+	18.7297i	0.0167871	+	0.706907i
$703$	−35.6591	+	20.5878i	−1.34491	+	0.776484i
$704$	1.89239	+	3.27771i	0.0713220	+	0.123533i
$705$	−50.6353	−	1.47986i	−1.90703	−	0.0557348i
$706$		−	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
$711$	2.40845	+	0.140899i	0.0903240	+	0.00528411i
$712$	−13.5271	−	7.80988i	−0.506950	−	0.292688i
$713$			66.2169i			2.47984i
$714$	9.76549	+	4.20660i	0.365464	+	0.157428i
$715$	30.5099	+	41.4091i	1.14100	+	1.54861i
$716$	−14.2272	−	8.21410i	−0.531697	−	0.306975i
$717$	−20.1228	+	32.6146i	−0.751500	+	1.21802i
$718$	−4.13025	−	7.15381i	−0.154140	−	0.266978i
$719$	3.21317	−	5.56538i	0.119831	−	0.207554i	−0.799869	−	0.600174i	$-0.795098\pi$
$719$	3.21317	−	5.56538i	0.119831	−	0.207554i	0.919701	+	0.392620i	$0.128431\pi$
$720$	−9.44573	−	6.21604i	−0.352022	−	0.231658i
$721$	−11.2556	+	28.3843i	−0.419181	+	1.05709i
$722$	17.2185			0.640806
$723$	−21.7704	−	0.636260i	−0.809651	−	0.0236628i
$724$	−9.29946	+	5.36904i	−0.345612	+	0.199539i
$725$	24.5387	−	14.1674i	0.911344	−	0.526165i
$726$	−5.75573	−	0.168216i	−0.213615	−	0.00624309i
$727$		−	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
$732$	14.2518	+	8.79316i	0.526761	+	0.325005i
$733$	−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
$735$	32.2773	−	32.3507i	1.19057	−	1.19327i
$736$			6.69384i			0.246738i
$737$	17.1066	+	9.87649i	0.630129	+	0.363805i
$738$	1.17316	−	20.0534i	0.0431847	−	0.738178i
$739$	−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
$741$	−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	$0.445178\pi$
$744$	−17.1265	−	0.500537i	−0.627888	−	0.0183506i
$745$	−15.3536	+	8.86443i	−0.562514	+	0.324767i
$746$	5.82807	+	10.0945i	0.213381	+	0.369586i
$747$	−18.4678	+	9.26895i	−0.675703	+	0.339133i
$748$	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
$753$	−7.81837	+	12.6719i	−0.284917	+	0.461788i
$754$	−11.0277	+	1.23354i	−0.401605	+	0.0449230i
$755$	23.9978			0.873370
$756$	11.4842	−	7.55732i	0.417676	−	0.274857i
$757$	−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
$759$	−37.3448	−	23.0413i	−1.35553	−	0.836345i
$760$	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
$765$	−23.4493	+	11.7691i	−0.847811	+	0.425513i
$766$	17.2864	−	9.98032i	0.624584	−	0.360604i
$767$	−6.14958	+	14.0641i	−0.222048	+	0.507826i
$768$	−1.73131	−	0.0505991i	−0.0624733	−	0.00182584i
$769$	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	−0.849785	−	0.527129i	$-0.823268\pi$
$773$	−22.7475	+	13.1333i	−0.818170	+	0.472371i	0.0316148	+	0.999500i	$0.489935\pi$
$774$	−10.4006	−	0.608455i	−0.373843	−	0.0218705i
$775$	45.5377	−	78.8735i	1.63576	−	2.83322i
$776$	−5.04512			−0.181109
$777$	−18.7356	−	25.1399i	−0.672136	−	0.901887i
$778$		−	21.5163i		−	0.771397i
$779$	34.8984	+	20.1486i	1.25037	+	0.721899i
$780$	−23.4591	+	1.93217i	−0.839971	+	0.0691830i
$781$	−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
$786$	−2.23919	−	0.0654425i	−0.0798694	−	0.00233425i
$787$	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
$789$	0.738881	−	25.2817i	0.0263049	−	0.900053i
$790$			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
$795$	−2.58752	+	4.19381i	−0.0917700	+	0.148739i
$796$	−20.5340	−	11.8553i	−0.727807	−	0.420200i
$797$	13.0997			0.464014			0.232007	−	0.972714i	$-0.425471\pi$
$797$	13.0997			0.464014			0.232007	+	0.972714i	$0.425471\pi$
$798$	3.21548	+	27.3907i	0.113827	+	0.969619i
$799$			18.0043i			0.636945i
$800$	4.60338	−	7.97329i	0.162754	−	0.281899i
$801$	−2.73667	+	46.7793i	−0.0966955	+	1.65286i
$802$	−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
$807$	29.6100	+	0.865377i	1.04232	+	0.0304627i
$808$	−0.710555	−	1.23072i	−0.0249973	−	0.0432965i
$809$	4.66926	−	2.69580i	0.164163	−	0.0947793i	−0.415668	−	0.909516i	$-0.636452\pi$
$809$	4.66926	−	2.69580i	0.164163	−	0.0947793i	0.579830	+	0.814737i	$0.303119\pi$
$810$	−3.95553	+	33.6913i	−0.138983	+	1.18379i
$811$	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
$816$	−2.11026	+	3.42027i	−0.0738740	+	0.119733i
$817$	10.4500	−	18.0999i	0.365599	−	0.633235i
$818$	12.1693			0.425489
$819$	9.12617	−	27.1240i	0.318894	−	0.947790i
$820$	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	$0.756438\pi$
$822$	−2.64299	+	4.28371i	−0.0921849	+	0.149411i
$823$	−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	$0.277999\pi$
$828$	17.9478	−	9.00795i	0.623730	−	0.313048i
$829$	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
$831$	−27.1563	−	0.793666i	−0.942040	−	0.0275320i
$832$	−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
$837$	21.7052	+	46.5939i	0.750241	+	1.61052i
$838$	−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	$-0.0605914\pi$
$840$	10.3214	+	13.8495i	0.356124	+	0.477855i
$841$	19.5283			0.673390
$842$	−4.73434	−	2.73337i	−0.163156	−	0.0941982i
$843$	−19.3429	+	31.3505i	−0.666204	+	1.07977i
$844$	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
$849$	1.64636	−	56.3321i	0.0565028	−	1.93331i
$850$	−10.6813	−	18.5005i	−0.366364	−	0.634562i
$851$	−22.8992	−	39.6626i	−0.784974	−	1.35962i
$852$	10.7946	+	0.315483i	0.369818	+	0.0108083i
$853$	−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	0.910049	−	0.414501i	$-0.136044\pi$
$857$	2.81201	+	4.87055i	0.0960565	+	0.166375i	−0.813993	+	0.580875i	$0.802710\pi$
$858$	−1.94016	−	23.5561i	−0.0662361	−	0.804193i
$859$	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
$861$	−12.1393	+	28.1811i	−0.413708	+	0.960411i
$862$	−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	$-0.0787428\pi$
$864$	2.19417	+	4.71016i	0.0746472	+	0.160243i
$865$	−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
$870$	−20.0834	−	0.586954i	−0.680890	−	0.0198996i
$871$	−7.53888	+	17.2415i	−0.255445	+	0.584204i
$872$	0.280553	−	0.161977i	0.00950073	−	0.00548525i
$873$	6.78926	+	13.5272i	0.229782	+	0.457827i
$874$			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
$879$	22.3430	+	13.7854i	0.753612	+	0.464969i
$880$	12.3543	+	7.13275i	0.416463	+	0.240445i
$881$	−9.97339			−0.336012			−0.168006	−	0.985786i	$-0.553733\pi$
$881$	−9.97339			−0.336012			−0.168006	+	0.985786i	$0.553733\pi$
$882$	−20.4291	+	4.86349i	−0.687882	+	0.163762i
$883$	−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
$885$	−14.5939	+	23.6534i	−0.490567	+	0.795102i
$886$	5.01928	−	2.89788i	0.168626	−	0.0973562i
$887$	14.2694	−	24.7152i	0.479118	−	0.829857i	−0.520595	−	0.853804i	$-0.674290\pi$
$887$	14.2694	−	24.7152i	0.479118	−	0.829857i	0.999713	+	0.0239468i	$0.00762323\pi$
$888$	10.4315	−	5.62289i	0.350059	−	0.188692i
$889$	−4.69132	−	31.8869i	−0.157342	−	1.06945i
$890$	−58.8738			−1.97345
$891$	−33.8306	−	3.97189i	−1.13337	−	0.133063i
$892$	1.07315	+	1.85874i	0.0359316	+	0.0622353i
$893$	−40.4414	+	23.3488i	−1.35332	+	0.781339i
$894$	8.14345	+	0.237999i	0.272358	+	0.00795989i
$895$	−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
$900$	−27.5732	−	1.61308i	−0.919105	−	0.0537693i
$901$	1.51678	+	0.875711i	0.0505311	+	0.0291742i
$902$			25.3425i			0.843813i
$903$	14.6160	+	6.29602i	0.486391	+	0.209518i
$904$			11.6924i			0.388884i
$905$	−20.2369	+	35.0514i	−0.672698	+	1.16515i
$906$	−9.38511	−	5.79049i	−0.311799	−	0.192376i
$907$	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	$-0.854660\pi$
$911$		−	26.6150i		−	0.881795i	0.897557	−	0.440898i	$-0.145340\pi$
$912$	−10.4193	−	0.304515i	−0.345019	−	0.0100835i
$913$	22.5762	−	13.0344i	0.747162	−	0.431374i
$914$	2.92274	−	1.68744i	0.0966756	−	0.0558157i
$915$	63.0924	+	1.84393i	2.08577	+	0.0609585i
$916$	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
$921$	20.6705	−	33.5024i	0.681117	−	1.10394i
$922$	3.10122	+	1.79049i	0.102133	+	0.0589666i
$923$	18.0984	−	13.3348i	0.595716	−	0.438919i
$924$	−13.9068	+	10.3641i	−0.457500	+	0.340954i
$925$			62.9915i			2.07115i
$926$	−7.03736	−	4.06302i	−0.231262	−	0.133519i
$927$	−2.02204	+	34.5638i	−0.0664126	+	1.13522i
$928$	−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
$933$	10.9855	+	0.321061i	0.359649	+	0.0105111i
$934$	−18.4226	−	31.9089i	−0.602805	−	1.04409i
$935$	28.6658	−	16.5502i	0.937470	−	0.541249i
$936$	9.64066	+	4.90487i	0.315115	+	0.160321i
$937$			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	$0.451566\pi$
$942$	−16.7185	−	10.3151i	−0.544720	−	0.336085i
$943$	−22.4107	+	38.8164i	−0.729792	+	1.26404i
$944$			4.25727i			0.138562i
$945$	23.2444	−	46.3117i	0.756140	−	1.50652i
$946$	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	$-0.160130\pi$
$948$	0.731391	−	1.18542i	0.0237545	−	0.0385008i
$949$	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	$0.00658932\pi$
$953$			1.27801i			0.0413990i	−0.999786	+	0.0206995i	$0.993411\pi$
$954$	2.02387	−	1.01577i	0.0655251	−	0.0328868i
$955$	−20.0058	−	34.6511i	−0.647374	−	1.12128i
$956$	11.0629	+	19.1614i	0.357798	+	0.619725i
$957$	0.589381	−	20.1664i	0.0190520	−	0.651887i
$958$			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
$963$	−0.962098	+	16.4456i	−0.0310032	+	0.529953i
$964$	−6.28726	+	10.8899i	−0.202499	+	0.350739i
$965$	−17.0252			−0.548060
$966$	−30.4658	+	3.57648i	−0.980222	+	0.115071i
$967$		−	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
$969$	−12.6999	+	20.5838i	−0.407981	+	0.661247i
$970$	−16.4683	+	9.50800i	−0.528767	+	0.305284i
$971$	−19.3492	+	33.5137i	−0.620944	+	1.07551i	0.368366	+	0.929681i	$0.379917\pi$
$971$	−19.3492	+	33.5137i	−0.620944	+	1.07551i	−0.989310	+	0.145826i	$0.953416\pi$
$972$	9.67638	−	12.2216i	0.310370	−	0.392008i
$973$	−13.9971	+	2.05932i	−0.448728	+	0.0660186i
$974$		−	25.0897i		−	0.803927i
$975$	−47.2654	+	32.7384i	−1.51370	+	1.04847i
$976$	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	$0.572572\pi$
$978$	−0.463266	+	15.8512i	−0.0148136	+	0.506866i
$979$		−	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	$-0.0608253\pi$
$984$	−9.87018	−	6.08977i	−0.314650	−	0.194135i
$985$	−46.4817	−	26.8362i	−1.48103	−	0.855072i
$986$			7.14100i			0.227416i
$987$	−21.2482	−	28.5114i	−0.676339	−	0.907527i
$988$	−17.4692	+	12.8712i	−0.555770	+	0.409487i
$989$	20.1320	+	11.6232i	0.640160	+	0.369596i
$990$	2.49940	−	42.7235i	0.0794361	−	1.35784i
$991$	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
$996$	−0.348516	+	11.9249i	−0.0110432	+	0.377855i
$997$	−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
$999$	−29.1141	−	20.4027i	−0.921130	−	0.645513i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.909476 - 1.47406i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-3.26421 - 1.88459i) q^{5} +(0.821836 + 1.52466i) q^{6} +(-0.385108 - 2.61757i) q^{7} +1.00000 q^{8} +(-1.34571 - 2.68124i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.909476 - 1.47406i) 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} +(-1.34571 - 2.68124i) q^{9} +(3.26421 - 1.88459i) q^{10} +(1.89239 + 3.27771i) q^{11} +(-1.73131 - 0.0505991i) 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} +(2.99488 + 0.175206i) q^{18} +(-3.00909 + 5.21190i) q^{19} +3.76919i q^{20} +(-4.20871 - 1.81295i) q^{21} -3.78477 q^{22} +(-5.79704 - 3.34692i) q^{23} +(0.909476 - 1.47406i) 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} +(0.190718 - 6.52564i) q^{30} +(-4.94611 - 8.56691i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(6.55262 + 0.191506i) 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} +(0.512624 + 6.22392i) q^{39} +(-3.26421 - 1.88459i) q^{40} -6.69591i q^{41} +(3.67441 - 2.73837i) q^{42} -3.47280 q^{43} +(1.89239 - 3.27771i) q^{44} +(-0.660383 + 11.2883i) 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} +(4.01717 + 0.117406i) q^{51} +(3.30355 + 1.44449i) q^{52} +(0.653696 - 0.377412i) q^{53} +(2.98203 - 4.25529i) 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} +(5.55601 + 3.42798i) q^{60} +(-8.37307 - 4.83419i) q^{61} +9.89221 q^{62} +(-6.50011 + 4.55506i) q^{63} +1.00000 q^{64} +(13.5058 - 1.51074i) q^{65} +(-3.44216 + 5.57898i) 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} +(-1.34571 - 2.68124i) q^{72} +(-2.53273 - 4.38682i) q^{73} +(-5.92523 + 3.42094i) q^{74} +(15.9398 + 0.465854i) 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} +(-5.37814 + 7.21634i) q^{81} +(5.79883 + 3.34796i) q^{82} -6.88779i q^{83} +(0.534294 + 4.55132i) q^{84} -8.74567i q^{85} +(1.73640 - 3.00754i) q^{86} +(-4.53658 - 2.79901i) 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} +(-17.1265 - 0.500537i) q^{93} +(-6.71987 + 3.87972i) q^{94} +(19.6446 - 11.3418i) q^{95} +(-1.73131 - 0.0505991i) 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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