LMFDB - Embedded newform 546.2.bg.b.311.13

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			311.13
Character	$\chi$	$=$	546.311
Dual form			546.2.bg.b.467.13

$q$-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} +(3.30355 + 1.44449i) 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} +(5.79257 + 2.33370i) 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} +(0.400812 + 3.58320i) 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} +(5.44455 - 12.4517i) 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} +(0.875238 + 6.18336i) 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} +(-4.48038 - 8.42177i) 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

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	$-0.347563\pi$
$5$	3.26421	−	1.88459i	1.45980	−	0.842816i	0.999001	+	0.0446889i	$0.0142297\pi$
$6$	−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	0.425931	+	0.904756i	$0.359947\pi$
$11$	−1.89239	+	3.27771i	−0.570576	+	0.988266i	−0.996507	+	0.0835105i	$0.973387\pi$
$12$	−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	−0.690346	−	0.723479i	$-0.742542\pi$
$17$	1.16015	−	2.00944i	0.281379	−	0.487362i	0.971725	+	0.236117i	$0.0758750\pi$
$18$	−2.99488	+	0.175206i	−0.705900	+	0.0412964i
$19$	3.00909	+	5.21190i	0.690333	+	1.19569i	0.971729	+	0.236100i	$0.0758691\pi$
$19$	3.00909	+	5.21190i	0.690333	+	1.19569i	−0.281396	+	0.959592i	$0.590798\pi$
$20$			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	−0.962490	−	0.271319i	$-0.912540\pi$
$23$	−5.79704	+	3.34692i	−1.20877	+	0.697881i	−0.246276	+	0.969200i	$0.579207\pi$
$24$	−0.909476	−	1.47406i	−0.185646	−	0.300891i
$25$	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	$0.907758\pi$
$30$	0.190718	+	6.52564i	0.0348201	+	1.19141i
$31$	4.94611	−	8.56691i	0.888347	−	1.53866i	0.0465184	−	0.998917i	$-0.485187\pi$
$31$	4.94611	−	8.56691i	0.888347	−	1.53866i	0.841829	−	0.539745i	$-0.181479\pi$
$32$	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	$-0.856788\pi$
$37$	−5.92523	+	3.42094i	−0.974102	+	0.562398i	−0.0736180	+	0.997287i	$0.523455\pi$
$38$	−3.00909	+	5.21190i	−0.488139	+	0.845481i
$39$	5.79257	+	2.33370i	0.927553	+	0.373691i
$40$	−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	$-0.858144\pi$
$47$	−6.71987	+	3.87972i	−0.980194	+	0.565915i	−0.0778650	+	0.996964i	$0.524810\pi$
$48$	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
$52$	0.400812	+	3.58320i	0.0555826	+	0.496901i
$53$	0.653696	+	0.377412i	0.0897921	+	0.0518415i	0.544224	−	0.838940i	$-0.316824\pi$
$53$	0.653696	+	0.377412i	0.0897921	+	0.0518415i	−0.454432	+	0.890782i	$0.650158\pi$
$54$	−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	$-0.422715\pi$
$59$	−3.68691	−	2.12864i	−0.479994	−	0.277125i	−0.720414	+	0.693544i	$0.756048\pi$
$60$	−5.55601	+	3.42798i	−0.717278	+	0.442551i
$61$	−8.37307	+	4.83419i	−1.07206	+	0.618955i	−0.928744	−	0.370722i	$-0.879110\pi$
$61$	−8.37307	+	4.83419i	−1.07206	+	0.618955i	−0.143317	+	0.989677i	$0.545777\pi$
$62$	9.89221			1.25631
$63$	6.50011	+	4.55506i	0.818937	+	0.573883i
$64$	1.00000			0.125000
$65$	5.44455	−	12.4517i	0.675313	−	1.54444i
$66$	−3.44216	−	5.57898i	−0.423700	−	0.686725i
$67$	−4.51984	−	2.60953i	−0.552187	−	0.318805i	0.197817	−	0.980239i	$-0.436615\pi$
$67$	−4.51984	−	2.60953i	−0.552187	−	0.318805i	−0.750004	+	0.661434i	$0.769948\pi$
$68$	1.16015	+	2.00944i	0.140689	+	0.243681i
$69$	−10.2058	−	5.50124i	−1.22864	−	0.662271i
$70$	6.19013	−	7.81854i	0.739863	−	0.934495i
$71$	6.23494			0.739951			0.369976	−	0.929041i	$-0.379366\pi$
$71$	6.23494			0.739951			0.369976	+	0.929041i	$0.379366\pi$
$72$	1.34571	−	2.68124i	0.158593	−	0.315988i
$73$	2.53273	−	4.38682i	0.296434	−	0.513438i	−0.678884	−	0.734246i	$-0.737536\pi$
$73$	2.53273	−	4.38682i	0.296434	−	0.513438i	0.975317	+	0.220808i	$0.0708693\pi$
$74$	−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
$78$	0.875238	+	6.18336i	0.0991012	+	0.700128i
$79$	−0.402095	−	0.696449i	−0.0452392	−	0.0783566i	0.842519	−	0.538666i	$-0.181072\pi$
$79$	−0.402095	−	0.696449i	−0.0452392	−	0.0783566i	−0.887758	+	0.460310i	$0.847738\pi$
$80$	−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	$-0.356233\pi$
$89$	13.5271	−	7.80988i	1.43387	−	0.827845i	0.997413	+	0.0718798i	$0.0228998\pi$
$90$	−9.44573	+	6.21604i	−0.995667	+	0.655228i
$91$	−4.48038	−	8.42177i	−0.469671	−	0.882841i
$92$		−	6.69384i		−	0.697881i
$93$	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	$-0.417553\pi$
$97$	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	$-0.855858\pi$
$101$	−0.710555	+	1.23072i	−0.0707029	+	0.122461i	0.828507	+	0.559979i	$0.189191\pi$
$102$	2.11026	+	3.42027i	0.208947	+	0.338657i
$103$	−9.99478	+	5.77049i	−0.984814	+	0.568583i	−0.903720	−	0.428124i	$-0.859175\pi$
$103$	−9.99478	+	5.77049i	−0.984814	+	0.568583i	−0.0810943	+	0.996706i	$0.525841\pi$
$104$	−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	−0.711934	−	0.702247i	$-0.752180\pi$
$107$	−4.75556	+	2.74562i	−0.459737	+	0.265430i	0.252196	+	0.967676i	$0.418847\pi$
$108$	2.19417	−	4.71016i	0.211134	−	0.453235i
$109$	−0.280553	−	0.161977i	−0.0268721	−	0.0155146i	0.486504	−	0.873678i	$-0.338272\pi$
$109$	−0.280553	−	0.161977i	−0.0268721	−	0.0155146i	−0.513376	+	0.858164i	$0.671605\pi$
$110$	−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	$-0.185359\pi$
$114$	−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
$117$	1.82818	+	10.6610i	0.169015	+	0.985613i
$118$		−	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
$130$	13.5058	−	1.51074i	1.18453	−	0.132500i
$131$	−0.646676	−	1.12008i	−0.0565003	−	0.0978614i	0.836392	−	0.548132i	$-0.184661\pi$
$131$	−0.646676	−	1.12008i	−0.0565003	−	0.0978614i	−0.892892	+	0.450271i	$0.851328\pi$
$132$	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	$-0.872951\pi$
$137$	−1.45303	+	2.51672i	−0.124141	+	0.215018i	0.797256	+	0.603641i	$0.206284\pi$
$138$	−0.338702	−	11.5891i	−0.0288323	−	0.986532i
$139$			5.34738i			0.453558i	0.973946	+	0.226779i	$0.0728196\pi$
$139$			5.34738i			0.453558i	−0.973946	+	0.226779i	$0.927180\pi$
$140$	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
$144$	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	$-0.228381\pi$
$149$	−2.35181	−	4.07346i	−0.192668	−	0.333711i	−0.946134	+	0.323777i	$0.895047\pi$
$150$	8.37333	+	13.5713i	0.683680	+	1.10809i
$151$	5.51385	+	3.18342i	0.448711	+	0.259063i	0.707285	−	0.706928i	$-0.249920\pi$
$151$	5.51385	+	3.18342i	0.448711	+	0.259063i	−0.258575	+	0.965991i	$0.583253\pi$
$152$	−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
$156$	−4.91733	+	3.84966i	−0.393701	+	0.308219i
$157$	−9.82232	−	5.67092i	−0.783906	−	0.452588i	0.0539067	−	0.998546i	$-0.482833\pi$
$157$	−9.82232	−	5.67092i	−0.783906	−	0.452588i	−0.837813	+	0.545958i	$0.816166\pi$
$158$	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	$-0.783399\pi$
$163$	−7.92899	+	4.57780i	−0.621046	+	0.358561i	0.156230	+	0.987721i	$0.450066\pi$
$164$	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	0.992539	+	0.121928i	$0.0389077\pi$
$173$	7.91626	+	13.7114i	0.601862	+	1.04246i	−0.390677	+	0.920528i	$0.627759\pi$
$174$	−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	0.926369	−	0.376617i	$-0.122913\pi$
$179$	14.2272	+	8.21410i	1.06339	+	0.613950i	0.137024	+	0.990568i	$0.456246\pi$
$180$	−10.1061	−	5.07222i	−0.753265	−	0.378061i
$181$			10.7381i			0.798156i	0.916917	+	0.399078i	$0.130670\pi$
$181$			10.7381i			0.798156i	−0.916917	+	0.399078i	$0.869330\pi$
$182$	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
$186$	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	−0.129055	−	0.991637i	$-0.541194\pi$
$191$	9.19327	−	5.30774i	0.665201	−	0.384054i	0.794256	+	0.607583i	$0.207861\pi$
$192$	0.909476	+	1.47406i	0.0656358	+	0.106381i
$193$	−3.91178	−	2.25847i	−0.281576	−	0.162568i	0.352560	−	0.935789i	$-0.385311\pi$
$193$	−3.91178	−	2.25847i	−0.281576	−	0.162568i	−0.634137	+	0.773221i	$0.718644\pi$
$194$	2.52256	+	4.36920i	0.181109	+	0.313691i
$195$	23.3062	−	3.29893i	1.66899	−	0.236242i
$196$	5.09768	−	4.79725i	0.364120	−	0.342661i
$197$	−14.2398			−1.01454			−0.507271	−	0.861787i	$-0.669346\pi$
$197$	−14.2398			−1.01454			−0.507271	+	0.861787i	$0.669346\pi$
$198$	5.09319	−	10.1479i	0.361957	−	0.721180i
$199$	20.5340	+	11.8553i	1.45561	+	0.840399i	0.998791	−	0.0491586i	$-0.0156540\pi$
$199$	20.5340	+	11.8553i	1.45561	+	0.840399i	0.456823	+	0.889558i	$0.348987\pi$
$200$	−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
$208$	−3.30355	−	1.44449i	−0.229060	−	0.100157i
$209$	−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
$221$	−0.930007	−	8.31413i	−0.0625591	−	0.559269i
$222$	−0.346193	−	11.8454i	−0.0232349	−	0.795012i
$223$	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	$-0.515276\pi$
$227$	−14.1171	−	8.15053i	−0.936987	−	0.540970i	−0.889014	+	0.457879i	$0.848609\pi$
$228$	−5.47339	−	8.87116i	−0.362484	−	0.587507i
$229$	12.6694	+	21.9440i	0.837215	+	1.45010i	0.892214	+	0.451612i	$0.149151\pi$
$229$	12.6694	+	21.9440i	0.837215	+	1.45010i	−0.0549995	+	0.998486i	$0.517516\pi$
$230$	−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	−0.967681	−	0.252179i	$-0.918853\pi$
$233$	−18.8229	+	10.8674i	−1.23313	+	0.711947i	−0.265447	+	0.964125i	$0.585520\pi$
$234$	−8.31864	+	6.91377i	−0.543806	+	0.451967i
$235$	−14.6234	+	25.3284i	−0.953924	+	1.65225i
$236$	3.68691	−	2.12864i	0.239997	−	0.138562i
$237$	0.660912	−	1.22611i	0.0429308	−	0.0796447i
$238$	0.893568	−	6.07357i	0.0579214	−	0.393691i
$239$	22.1257			1.43119			0.715597	−	0.698514i	$-0.246155\pi$
$239$	22.1257			1.43119			0.715597	+	0.698514i	$0.246155\pi$
$240$	−0.190718	−	6.52564i	−0.0123108	−	0.421228i
$241$	6.28726	−	10.8899i	0.404998	−	0.701477i	−0.589323	−	0.807897i	$-0.700605\pi$
$241$	6.28726	−	10.8899i	0.404998	−	0.701477i	0.994321	+	0.106420i	$0.0339388\pi$
$242$	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
$247$	19.8814	+	8.69319i	1.26502	+	0.553135i
$248$	−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	−0.976506	−	0.215490i	$-0.930865\pi$
$257$	−10.8190	−	18.7391i	−0.674873	−	1.16891i	0.301633	−	0.953424i	$-0.402468\pi$
$258$	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	0.836360	−	0.548181i	$-0.184679\pi$
$263$	12.6463	+	7.30132i	0.779802	+	0.450219i	−0.0565583	+	0.998399i	$0.518013\pi$
$264$	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	−0.478308	−	0.878192i	$-0.658750\pi$
$269$	8.55131	−	14.8113i	0.521382	−	0.903061i	0.999691	−	0.0248689i	$-0.00791684\pi$
$270$	−17.7535	−	8.27024i	−1.08044	−	0.503310i
$271$	−14.9138	−	25.8315i	−0.905949	−	1.56915i	−0.819639	−	0.572881i	$-0.805826\pi$
$271$	−14.9138	−	25.8315i	−0.905949	−	1.56915i	−0.0863103	−	0.996268i	$-0.527508\pi$
$272$	−2.32031			−0.140689
$273$	8.33940	−	14.2637i	0.504723	−	0.863281i
$274$	−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	−0.999458	−	0.0329179i	$-0.989520\pi$
$277$	−7.84269	+	13.5839i	−0.471221	+	0.816179i	0.528237	+	0.849097i	$0.322853\pi$
$278$	−4.63096	+	2.67369i	−0.277747	+	0.160357i
$279$	16.3140	+	24.7903i	0.976692	+	1.48415i
$280$	3.67599	+	9.27009i	0.219682	+	0.553994i
$281$	21.2682			1.26875			0.634376	−	0.773025i	$-0.281257\pi$
$281$	21.2682			1.26875			0.634376	+	0.773025i	$0.281257\pi$
$282$	−0.392621	−	13.4340i	−0.0233802	−	0.799983i
$283$	28.1781	+	16.2686i	1.67501	+	0.967069i	0.964763	+	0.263119i	$0.0847512\pi$
$283$	28.1781	+	16.2686i	1.67501	+	0.967069i	0.710250	+	0.703950i	$0.248582\pi$
$284$	−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
$299$	−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
$303$	−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	$-0.724635\pi$
$307$	−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	$-0.775756\pi$
$311$	3.17259	−	5.49509i	0.179901	−	0.311598i	0.941847	+	0.336043i	$0.109089\pi$
$312$	−5.79257	−	2.33370i	−0.327940	−	0.132120i
$313$	9.83094	−	5.67590i	0.555678	−	0.320821i	−0.195731	−	0.980658i	$-0.562708\pi$
$313$	9.83094	−	5.67590i	0.555678	−	0.320821i	0.751409	+	0.659837i	$0.229375\pi$
$314$		−	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	$-0.161022\pi$
$317$	0.315688	+	0.546787i	0.0177308	+	0.0307106i	−0.857024	+	0.515277i	$0.827689\pi$
$318$	−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
$325$	−3.69018	−	32.9897i	−0.204695	−	1.82994i
$326$	−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	$-0.776634\pi$
$331$	−10.6712	+	6.16103i	−0.586543	+	0.338641i	0.177186	+	0.984177i	$0.443300\pi$
$332$	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	$0.561974\pi$
$338$	12.6787	−	2.87238i	0.689630	−	0.156237i
$339$	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	0.527291	−	0.849685i	$-0.323208\pi$
$347$	1.02619	+	0.592469i	0.0550886	+	0.0318054i	−0.472203	+	0.881490i	$0.656541\pi$
$348$	−0.155724	−	5.32830i	−0.00834770	−	0.285627i
$349$	−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
$351$	−14.0523	+	12.3908i	−0.750058	+	0.661372i
$352$	1.89239	+	3.27771i	0.100864	+	0.174702i
$353$	0.0869477	+	0.0501993i	0.00462776	+	0.00267184i	0.502312	−	0.864686i	$-0.332483\pi$
$353$	0.0869477	+	0.0501993i	0.00462776	+	0.00267184i	−0.497684	+	0.867358i	$0.665816\pi$
$354$	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	$-0.0967178\pi$
$359$	4.13025	+	7.15381i	0.217987	+	0.377564i	−0.736206	+	0.676758i	$0.763384\pi$
$360$	−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
$364$	9.53366	+	0.330764i	0.499699	+	0.0173367i
$365$		−	19.0927i		−	0.999356i
$366$	−0.489212	−	16.7390i	−0.0255715	−	0.874961i
$367$	−24.5980	−	14.2017i	−1.28400	−	0.741320i	−0.306427	−	0.951894i	$-0.599133\pi$
$367$	−24.5980	−	14.2017i	−1.28400	−	0.741320i	−0.977578	+	0.210574i	$0.932467\pi$
$368$	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	0.976536	−	0.215354i	$-0.0690905\pi$
$373$	5.82807	+	10.0945i	0.301766	+	0.522674i	−0.674770	+	0.738028i	$0.735757\pi$
$374$	−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	$-0.496323\pi$
$383$	17.2864	−	9.98032i	0.883295	−	0.509971i	0.871743	+	0.489963i	$0.162990\pi$
$384$	−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	−0.0533140	−	0.998578i	$-0.516978\pi$
$389$	−18.6337	−	10.7582i	−0.944765	−	0.545460i	−0.891451	+	0.453118i	$0.850312\pi$
$390$	14.5101	+	18.5343i	0.734747	+	0.938522i
$391$			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	0.980891	+	0.194558i	$0.0623273\pi$
$397$	13.1292	+	22.7405i	0.658938	+	1.14131i	−0.321953	+	0.946756i	$0.604339\pi$
$398$			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	$-0.105839\pi$
$401$	3.80346	+	6.58778i	0.189936	+	0.328978i	−0.755293	+	0.655387i	$0.772505\pi$
$402$	7.69322	−	4.74662i	0.383703	−	0.236740i
$403$	−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
$408$	−4.01717	+	0.117406i	−0.198880	+	0.00581244i
$409$	6.08464	−	10.5389i	0.300866	−	0.521115i	−0.675466	−	0.737391i	$-0.736058\pi$
$409$	6.08464	−	10.5389i	0.300866	−	0.521115i	0.976332	+	0.216276i	$0.0693910\pi$
$410$	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
$416$	−0.400812	−	3.58320i	−0.0196514	−	0.175681i
$417$	−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
$429$	−18.6110	+	14.5701i	−0.898546	+	0.703450i
$430$	−11.3360	−	6.54482i	−0.546669	−	0.315619i
$431$	−6.87264	+	11.9038i	−0.331043	+	0.573384i	−0.982717	−	0.185116i	$-0.940734\pi$
$431$	−6.87264	+	11.9038i	−0.331043	+	0.573384i	0.651673	+	0.758500i	$0.274067\pi$
$432$	2.98203	+	4.25529i	0.143473	+	0.204733i
$433$		−	31.5338i		−	1.51542i	−0.652592	−	0.757709i	$-0.726319\pi$
$433$		−	31.5338i		−	1.51542i	0.652592	−	0.757709i	$-0.273681\pi$
$434$	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	−0.960420	−	0.278557i	$-0.910144\pi$
$439$	−25.1301	+	14.5088i	−1.19939	+	0.692469i	−0.238973	+	0.971026i	$0.576811\pi$
$440$		−	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	−0.614475	−	0.788937i	$-0.710632\pi$
$443$	−5.01928	+	2.89788i	−0.238473	+	0.137682i	0.376002	+	0.926619i	$0.377299\pi$
$444$	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	$-0.380095\pi$
$449$	15.5891			0.735696			0.367848	+	0.929886i	$0.380095\pi$
$450$	−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
$455$	−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	−0.430080	−	0.902791i	$-0.641515\pi$
$457$	2.92274	−	1.68744i	0.136720	−	0.0789353i	0.566800	+	0.823856i	$0.308181\pi$
$458$	−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	−0.878949	−	0.476916i	$-0.841755\pi$
$467$	−18.4226	−	31.9089i	−0.852496	−	1.47657i	0.0264534	−	0.999650i	$-0.491579\pi$
$468$	−10.1468	−	3.74727i	−0.469037	−	0.173218i
$469$	−8.57127	+	10.8261i	−0.395785	+	0.499902i
$470$	−29.2468			−1.34905
$471$	−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	$-0.377511\pi$
$479$	−5.24426	−	3.02777i	−0.239616	−	0.138343i	−0.615000	+	0.788527i	$0.710844\pi$
$480$	5.55601	−	3.42798i	0.253596	−	0.156465i
$481$	−9.88300	+	22.6025i	−0.450626	+	1.03058i
$482$	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	$-0.140872\pi$
$487$	21.7283	+	12.5449i	0.984605	+	0.568462i	0.0809478	+	0.996718i	$0.474205\pi$
$488$	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	$0.827411\pi$
$492$	0.338807	+	11.5927i	0.0152746	+	0.522640i
$493$	6.18429	+	3.57050i	0.278526	+	0.160807i
$494$	2.41216	+	21.5644i	0.108528	+	0.970227i
$495$	−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	$-0.946845\pi$
$499$	−29.8258	+	17.2200i	−1.33519	+	0.770871i	−0.349098	+	0.937086i	$0.613512\pi$
$500$	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
$507$	21.8054	−	5.61452i	0.968414	−	0.249350i
$508$	−6.09092	+	10.5498i	−0.270241	+	0.468071i
$509$	22.1861	−	12.8091i	0.983380	−	0.567755i	0.0800909	−	0.996788i	$-0.474479\pi$
$509$	22.1861	−	12.8091i	0.983380	−	0.567755i	0.903289	+	0.429033i	$0.141146\pi$
$510$	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
$520$	−5.44455	+	12.4517i	−0.238759	+	0.546043i
$521$	−10.2805	+	17.8063i	−0.450396	+	0.780109i	−0.998411	−	0.0563599i	$-0.982051\pi$
$521$	−10.2805	+	17.8063i	−0.450396	+	0.780109i	0.548014	+	0.836469i	$0.315384\pi$
$522$	−0.539215	−	9.21707i	−0.0236008	−	0.403420i
$523$	2.64380	−	1.52640i	0.115605	−	0.0667448i	−0.441082	−	0.897467i	$-0.645405\pi$
$523$	2.64380	−	1.52640i	0.115605	−	0.0667448i	0.556688	+	0.830722i	$0.312072\pi$
$524$	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	$-0.502611\pi$
$541$	19.8564	−	11.4641i	0.853694	−	0.492881i	0.861896	+	0.507086i	$0.169277\pi$
$542$	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
$546$	16.5225	+	0.0902606i	0.707096	+	0.00386280i
$547$	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	$-0.696033\pi$
$557$	9.86728	−	17.0906i	0.418090	−	0.724154i	0.995747	+	0.0921260i	$0.0293662\pi$
$558$	−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	−0.959054	−	0.283222i	$-0.908597\pi$
$563$	−5.55820	+	9.62708i	−0.234250	+	0.405733i	0.724804	+	0.688955i	$0.241930\pi$
$564$	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	−0.819551	−	0.573007i	$-0.805777\pi$
$569$	−17.4869	+	10.0960i	−0.733088	+	0.423248i	0.0864631	+	0.996255i	$0.472444\pi$
$570$	−33.4371	+	20.6302i	−1.40052	+	0.864105i
$571$	−2.34574	+	4.06294i	−0.0981661	+	0.170029i	−0.910926	−	0.412571i	$-0.864631\pi$
$571$	−2.34574	+	4.06294i	−0.0981661	+	0.170029i	0.812759	+	0.582599i	$0.197964\pi$
$572$	−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
$576$	−1.34571	+	2.68124i	−0.0560711	+	0.111719i
$577$	−10.4339	+	18.0720i	−0.434368	+	0.752347i	−0.997244	−	0.0741941i	$-0.976362\pi$
$577$	−10.4339	+	18.0720i	−0.434368	+	0.752347i	0.562876	+	0.826541i	$0.309695\pi$
$578$	−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
$585$	26.0593	+	31.3545i	1.07742	+	1.29635i
$586$	−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	$-0.640597\pi$
$593$	3.45052	−	1.99216i	0.141696	−	0.0818081i	0.569172	+	0.822219i	$0.307264\pi$
$594$	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
$598$	−23.9854	+	2.68297i	−0.980836	+	0.109715i
$599$	1.61182	+	0.930583i	0.0658571	+	0.0380226i	0.532567	−	0.846388i	$-0.321227\pi$
$599$	1.61182	+	0.930583i	0.0658571	+	0.0380226i	−0.466710	+	0.884410i	$0.654561\pi$
$600$	−15.9398	+	0.465854i	−0.650739	+	0.0190184i
$601$			4.01388i			0.163729i	0.996643	+	0.0818647i	$0.0260875\pi$
$601$			4.01388i			0.163729i	−0.996643	+	0.0818647i	$0.973912\pi$
$602$	−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	−0.250919	−	0.968008i	$-0.580733\pi$
$607$	11.3810	−	6.57082i	0.461941	−	0.266701i	0.712860	+	0.701307i	$0.247400\pi$
$608$	6.01818			0.244069
$609$	5.57955	+	12.9528i	0.226095	+	0.524872i
$610$	−36.4419			−1.47549
$611$	−11.2084	+	25.6337i	−0.453444	+	1.03703i
$612$	−6.94904	+	0.406531i	−0.280898	+	0.0164330i
$613$	9.33110	+	5.38731i	0.376880	+	0.217592i	0.676460	−	0.736480i	$-0.263513\pi$
$613$	9.33110	+	5.38731i	0.376880	+	0.217592i	−0.299580	+	0.954071i	$0.596847\pi$
$614$	−11.3640	−	19.6830i	−0.458613	−	0.794340i
$615$	20.7416	−	38.4796i	0.836382	−	1.55165i
$616$	−7.85087	−	6.21573i	−0.316321	−	0.250439i
$617$	−22.7546			−0.916066			−0.458033	−	0.888935i	$-0.651446\pi$
$617$	−22.7546			−0.916066			−0.458033	+	0.888935i	$0.651446\pi$
$618$	−0.583963	−	19.9810i	−0.0234904	−	0.803754i
$619$	11.7673	−	20.3816i	0.472969	−	0.819207i	−0.526552	−	0.850143i	$-0.676516\pi$
$619$	11.7673	−	20.3816i	0.472969	−	0.819207i	0.999521	+	0.0309362i	$0.00984888\pi$
$620$	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
$624$	−0.875238	−	6.18336i	−0.0350375	−	0.247533i
$625$	−6.86537	−	11.8912i	−0.274615	−	0.475647i
$626$	9.83094	+	5.67590i	0.392924	+	0.226854i
$627$	−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
$637$	−23.7700	+	8.48443i	−0.941803	+	0.336165i
$638$		−	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	0.804299	−	0.594225i	$-0.202541\pi$
$641$	17.5159	+	10.1128i	0.691835	+	0.399431i	−0.112464	+	0.993656i	$0.535874\pi$
$642$	−0.277852	−	9.50706i	−0.0109660	−	0.375214i
$643$	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	−0.226262	−	0.974066i	$-0.572651\pi$
$647$	18.5795	−	32.1806i	0.730435	−	1.26515i	0.956697	−	0.291084i	$-0.0940160\pi$
$648$	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	0.388081	−	0.921625i	$-0.373138\pi$
$653$	35.2713	−	20.3639i	1.38027	−	0.796900i	0.992191	+	0.124725i	$0.0398049\pi$
$654$	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	$0.0528929\pi$
$659$			8.49218i			0.330808i	−0.986226	+	0.165404i	$0.947107\pi$
$660$	−0.721822	−	24.6980i	−0.0280969	−	0.961370i
$661$	−9.22875	+	15.9847i	−0.358957	+	0.621731i	−0.987787	−	0.155811i	$-0.950201\pi$
$661$	−9.22875	+	15.9847i	−0.358957	+	0.621731i	0.628830	+	0.777543i	$0.283534\pi$
$662$	−10.6712	−	6.16103i	−0.414749	−	0.239455i
$663$	11.4097	−	8.93239i	0.443117	−	0.346905i
$664$			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
$676$	8.82691	+	9.54388i	0.339496	+	0.367072i
$677$	−6.77872	−	11.7411i	−0.260527	−	0.451247i	0.705855	−	0.708357i	$-0.250563\pi$
$677$	−6.77872	−	11.7411i	−0.260527	−	0.451247i	−0.966382	+	0.257110i	$0.917230\pi$
$678$	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	−0.483785	−	0.875187i	$-0.660738\pi$
$683$	13.4864	−	23.3591i	0.516042	−	0.893811i	0.999827	−	0.0186238i	$-0.00592847\pi$
$684$	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
$689$	2.70469	−	0.302542i	0.103040	−	0.0115259i
$690$	−22.9464	−	37.1910i	−0.873554	−	1.41584i
$691$	0.543955	+	0.942158i	0.0206930	+	0.0358414i	0.876186	−	0.481972i	$-0.160079\pi$
$691$	0.543955	+	0.942158i	0.0206930	+	0.0358414i	−0.855493	+	0.517814i	$0.826746\pi$
$692$	−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	$0.183298\pi$
$701$			28.8352i			1.08909i	−0.838731	+	0.544546i	$0.816702\pi$
$702$	−17.7569	−	5.97427i	−0.670192	−	0.225484i
$703$	−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	$-0.663684\pi$
$709$	0.432082	−	0.249463i	0.0162272	−	0.00936877i	0.508092	+	0.861303i	$0.330351\pi$
$710$	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	0.919701	−	0.392620i	$-0.128431\pi$
$719$	3.21317	+	5.56538i	0.119831	+	0.207554i	−0.799869	+	0.600174i	$0.795098\pi$
$720$	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	$0.0732827\pi$
$727$			12.3057i			0.456392i	−0.973615	+	0.228196i	$0.926717\pi$
$728$	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
$732$	14.2518	−	8.79316i	0.526761	−	0.325005i
$733$	24.4841	+	42.4077i	0.904341	+	1.56636i	0.821800	+	0.569777i	$0.192970\pi$
$733$	24.4841	+	42.4077i	0.904341	+	1.56636i	0.0825411	+	0.996588i	$0.473696\pi$
$734$		−	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	$-0.320646\pi$
$739$	1.87629	+	1.08328i	0.0690204	+	0.0398489i	−0.465093	+	0.885262i	$0.653979\pi$
$740$	−12.8941	−	22.3333i	−0.473998	−	0.820989i
$741$	5.26734	+	37.2126i	0.193501	+	1.36704i
$742$	1.97581	+	0.290688i	0.0725341	+	0.0106715i
$743$	−9.34291			−0.342758			−0.171379	−	0.985205i	$-0.554822\pi$
$743$	−9.34291			−0.342758			−0.171379	+	0.985205i	$0.554822\pi$
$744$	−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	0.999953	+	0.00969962i	$0.00308753\pi$
$751$	13.9317	+	24.1305i	0.508377	+	0.880534i	−0.491576	+	0.870834i	$0.663579\pi$
$752$	6.71987	+	3.87972i	0.245048	+	0.141479i
$753$	−7.81837	−	12.6719i	−0.284917	−	0.461788i
$754$	−4.44557	+	10.1670i	−0.161898	+	0.370262i
$755$	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	$-0.747328\pi$
$761$	−11.9787	+	6.91589i	−0.434227	+	0.250701i	0.266919	+	0.963719i	$0.413994\pi$
$762$	−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
$767$	−15.2547	+	1.70637i	−0.550814	+	0.0616133i
$768$	−1.73131	+	0.0505991i	−0.0624733	+	0.00182584i
$769$	−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	$-0.176732\pi$
$773$	22.7475	+	13.1333i	0.818170	+	0.472371i	−0.0316148	+	0.999500i	$0.510065\pi$
$774$	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
$780$	−8.79616	+	21.8333i	−0.314953	+	0.781756i
$781$	−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	$-0.978087\pi$
$787$	−12.3223	+	21.3429i	−0.439243	+	0.760791i	0.558388	+	0.829580i	$0.311420\pi$
$788$	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
$793$	−13.9659	+	31.9400i	−0.495943	+	1.13422i
$794$	−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	0.579830	−	0.814737i	$-0.303119\pi$
$809$	4.66926	+	2.69580i	0.164163	+	0.0947793i	−0.415668	+	0.909516i	$0.636452\pi$
$810$	−3.95553	−	33.6913i	−0.138983	−	1.18379i
$811$	−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
$816$	−2.11026	−	3.42027i	−0.0738740	−	0.119733i
$817$	−10.4500	−	18.0999i	−0.365599	−	0.633235i
$818$	12.1693			0.425489
$819$	28.6101	−	0.679753i	0.999718	−	0.0237525i
$820$	25.2381			0.881354
$821$	27.5211	+	47.6680i	0.960494	+	1.66362i	0.721262	+	0.692662i	$0.243562\pi$
$821$	27.5211	+	47.6680i	0.960494	+	1.66362i	0.239232	+	0.970963i	$0.423104\pi$
$822$	−2.64299	−	4.28371i	−0.0921849	−	0.149411i
$823$	−23.0974	+	40.0059i	−0.805125	+	1.39452i	0.111081	+	0.993811i	$0.464569\pi$
$823$	−23.0974	+	40.0059i	−0.805125	+	1.39452i	−0.916206	+	0.400707i	$0.868765\pi$
$824$	9.99478	−	5.77049i	0.348184	−	0.201024i
$825$	−28.6373	+	53.1275i	−0.997022	+	1.84966i
$826$	−11.1437	−	1.63951i	−0.387740	−	0.0570458i
$827$	−36.9395			−1.28451			−0.642256	−	0.766491i	$-0.722001\pi$
$827$	−36.9395			−1.28451			−0.642256	+	0.766491i	$0.722001\pi$
$828$	17.9478	+	9.00795i	0.623730	+	0.313048i
$829$	34.3756	+	19.8468i	1.19391	+	0.689307i	0.959192	−	0.282755i	$-0.0912485\pi$
$829$	34.3756	+	19.8468i	1.19391	+	0.689307i	0.234723	+	0.972062i	$0.424582\pi$
$830$	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
$845$	−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
$849$	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	$-0.178044\pi$
$853$	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	$-0.802710\pi$
$857$	2.81201	−	4.87055i	0.0960565	−	0.166375i	0.910049	+	0.414501i	$0.136044\pi$
$858$	−21.9235	−	8.83253i	−0.748457	−	0.301538i
$859$	21.3946	−	12.3522i	0.729975	−	0.421451i	−0.0884382	−	0.996082i	$-0.528188\pi$
$859$	21.3946	−	12.3522i	0.729975	−	0.421451i	0.818413	+	0.574631i	$0.194854\pi$
$860$		−	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	−0.969558	−	0.244862i	$-0.921257\pi$
$863$	−20.4709	−	35.4566i	−0.696836	−	1.20696i	0.272722	−	0.962093i	$-0.412076\pi$
$864$	−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
$871$	−18.7010	+	2.09187i	−0.633658	+	0.0708802i
$872$	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	$-0.558481\pi$
$877$	17.0997	−	9.87250i	0.577415	−	0.333371i	0.760105	+	0.649800i	$0.225147\pi$
$878$	−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	$0.556188\pi$
$884$	7.66525	+	3.35166i	0.257810	+	0.112728i
$885$	−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	0.999713	−	0.0239468i	$-0.00762323\pi$
$887$	14.2694	+	24.7152i	0.479118	+	0.829857i	−0.520595	+	0.853804i	$0.674290\pi$
$888$	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
$897$	−41.3904	+	5.85870i	−1.38199	+	0.195616i
$898$	7.79456	+	13.5006i	0.260108	+	0.450520i
$899$	26.3656	+	15.2222i	0.879342	+	0.507689i
$900$	−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	0.0667488	−	0.997770i	$-0.478737\pi$
$907$	27.0286	−	46.8148i	0.897468	−	1.55446i	0.830720	−	0.556691i	$-0.187929\pi$
$908$	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	$0.854660\pi$
$912$	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	0.618925	−	0.785450i	$-0.287569\pi$
$919$	−11.2395	−	19.4674i	−0.370758	−	0.642171i	−0.989682	+	0.143279i	$0.954235\pi$
$920$	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	$-0.387146\pi$
$929$	40.6262	−	23.4556i	1.33290	−	0.769552i	0.985744	+	0.168253i	$0.0538127\pi$
$930$	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
$936$	−1.82818	−	10.6610i	−0.0597560	−	0.348467i
$937$		−	18.9682i		−	0.619665i	−0.950791	−	0.309832i	$-0.899727\pi$
$937$		−	18.9682i		−	0.619665i	0.950791	−	0.309832i	$-0.100273\pi$
$938$	−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	$-0.215101\pi$
$941$	19.2846	+	11.1340i	0.628660	+	0.362957i	−0.151573	+	0.988446i	$0.548434\pi$
$942$	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	−0.876109	−	0.482112i	$-0.839870\pi$
$947$	−26.3290	−	45.6031i	−0.855576	−	1.48190i	0.0205332	−	0.999789i	$-0.493464\pi$
$948$	0.731391	+	1.18542i	0.0237545	+	0.0385008i
$949$	−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	$-0.00658932\pi$
$954$	−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
$962$	−24.5158	+	2.74230i	−0.790422	+	0.0884155i
$963$	−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	−0.989310	−	0.145826i	$-0.953416\pi$
$971$	−19.3492	−	33.5137i	−0.620944	−	1.07551i	0.368366	−	0.929681i	$-0.379917\pi$
$972$	9.67638	+	12.2216i	0.310370	+	0.392008i
$973$	13.9971	+	2.05932i	0.448728	+	0.0660186i
$974$			25.0897i			0.803927i
$975$	45.2727	−	35.4429i	1.44989	−	1.13508i
$976$	8.37307	+	4.83419i	0.268015	+	0.154739i
$977$	−22.8365	+	39.5540i	−0.730605	+	1.26544i	0.226020	+	0.974123i	$0.427428\pi$
$977$	−22.8365	+	39.5540i	−0.730605	+	1.26544i	−0.956625	+	0.291322i	$0.905905\pi$
$978$	−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	−0.981798	−	0.189927i	$-0.939175\pi$
$983$	−51.3302	−	29.6355i	−1.63718	−	0.945226i	−0.655381	−	0.755298i	$-0.727492\pi$
$984$	−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	−0.582155	−	0.813078i	$-0.697790\pi$
$991$	13.0035	−	22.5226i	0.413068	−	0.715455i	0.995224	+	0.0976225i	$0.0311238\pi$
$992$	−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	0.301221	−	0.953554i	$-0.402606\pi$
$997$	−11.8082	−	6.81749i	−0.373971	−	0.215912i	−0.675192	+	0.737642i	$0.735939\pi$
$998$	−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.b.311.13	yes	36
3.2	odd	2		546.2.bg.a.311.18	yes	36
7.5	odd	6	inner	546.2.bg.b.467.18	yes	36
13.12	even	2		546.2.bg.a.311.13	✓	36
21.5	even	6		546.2.bg.a.467.13	yes	36
39.38	odd	2	inner	546.2.bg.b.311.18	yes	36
91.12	odd	6		546.2.bg.a.467.18	yes	36
273.194	even	6	inner	546.2.bg.b.467.13	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bg.a.311.13	✓	36	13.12	even	2
546.2.bg.a.311.18	yes	36	3.2	odd	2
546.2.bg.a.467.13	yes	36	21.5	even	6
546.2.bg.a.467.18	yes	36	91.12	odd	6
546.2.bg.b.311.13	yes	36	1.1	even	1	trivial
546.2.bg.b.311.18	yes	36	39.38	odd	2	inner
546.2.bg.b.467.13	yes	36	273.194	even	6	inner
546.2.bg.b.467.18	yes	36	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
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} +(3.30355 + 1.44449i) 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} +(5.79257 + 2.33370i) 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} +(0.400812 + 3.58320i) 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} +(5.44455 - 12.4517i) 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} +(0.875238 + 6.18336i) 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} +(-4.48038 - 8.42177i) 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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