LMFDB - Embedded newform 546.2.bn.e.101.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(101,546)]

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, 5]))

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

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

chi := DirichletCharacter("546.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bn (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:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.13
Character	$\chi$	$=$	546.101
Dual form			546.2.bn.e.173.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(1.51226 + 0.844435i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.511132 - 0.295102i) q^{5} +(-1.48743 + 0.887438i) q^{6} +(1.57814 + 2.12355i) q^{7} +1.00000 q^{8} +(1.57386 + 2.55401i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(1.51226 + 0.844435i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.511132 - 0.295102i) q^{5} +(-1.48743 + 0.887438i) q^{6} +(1.57814 + 2.12355i) q^{7} +1.00000 q^{8} +(1.57386 + 2.55401i) q^{9} +0.590205i q^{10} +6.11042 q^{11} +(-0.0248275 - 1.73187i) q^{12} +(-1.86885 - 3.08341i) q^{13} +(-2.62812 + 0.304939i) q^{14} +(1.02216 - 0.0146533i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.82336 - 6.62225i) q^{17} +(-2.99877 + 0.0859963i) q^{18} -3.95103 q^{19} +(-0.511132 - 0.295102i) q^{20} +(0.593366 + 4.54400i) q^{21} +(-3.05521 + 5.29178i) q^{22} +(7.26252 + 4.19302i) q^{23} +(1.51226 + 0.844435i) q^{24} +(-2.32583 + 4.02845i) q^{25} +(3.60473 - 0.0767706i) q^{26} +(0.223387 + 5.19135i) q^{27} +(1.04997 - 2.42849i) q^{28} +(1.39183 - 0.803572i) q^{29} +(-0.498390 + 0.892543i) q^{30} +(-1.38966 + 2.40696i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(9.24054 + 5.15985i) q^{33} +7.64672 q^{34} +(1.43330 + 0.619700i) q^{35} +(1.42491 - 2.64001i) q^{36} +(-1.93040 - 1.11452i) q^{37} +(1.97552 - 3.42169i) q^{38} +(-0.222454 - 6.24103i) q^{39} +(0.511132 - 0.295102i) q^{40} +(1.36416 - 0.787598i) q^{41} +(-4.23190 - 1.75813i) q^{42} +(-2.90674 + 5.03462i) q^{43} +(-3.05521 - 5.29178i) q^{44} +(1.55814 + 0.840988i) q^{45} +(-7.26252 + 4.19302i) q^{46} +(-4.94554 + 2.85531i) q^{47} +(-1.48743 + 0.887438i) q^{48} +(-2.01892 + 6.70253i) q^{49} +(-2.32583 - 4.02845i) q^{50} +(-0.189849 - 13.2431i) q^{51} +(-1.73588 + 3.16018i) q^{52} +(-3.30431 - 1.90774i) q^{53} +(-4.60753 - 2.40222i) q^{54} +(3.12323 - 1.80320i) q^{55} +(1.57814 + 2.12355i) q^{56} +(-5.97499 - 3.33639i) q^{57} +1.60714i q^{58} +(3.88177 - 2.24114i) q^{59} +(-0.523770 - 0.877889i) q^{60} -0.100596i q^{61} +(-1.38966 - 2.40696i) q^{62} +(-2.93979 + 7.37276i) q^{63} +1.00000 q^{64} +(-1.86515 - 1.02453i) q^{65} +(-9.08883 + 5.42261i) q^{66} -10.3459i q^{67} +(-3.82336 + 6.62225i) q^{68} +(7.44209 + 12.4737i) q^{69} +(-1.25333 + 0.931429i) q^{70} +(-0.875991 + 1.51726i) q^{71} +(1.57386 + 2.55401i) q^{72} +(5.41081 - 9.37179i) q^{73} +(1.93040 - 1.11452i) q^{74} +(-6.91903 + 4.12806i) q^{75} +(1.97552 + 3.42169i) q^{76} +(9.64312 + 12.9758i) q^{77} +(5.51612 + 2.92787i) q^{78} +(-3.17751 - 5.50361i) q^{79} +0.590205i q^{80} +(-4.04594 + 8.03930i) q^{81} +1.57520i q^{82} -9.07449i q^{83} +(3.63853 - 2.78587i) q^{84} +(-3.90849 - 2.25657i) q^{85} +(-2.90674 - 5.03462i) q^{86} +(2.78337 - 0.0399014i) q^{87} +6.11042 q^{88} +(-3.56660 - 2.05918i) q^{89} +(-1.50739 + 0.928899i) q^{90} +(3.59844 - 8.83466i) q^{91} -8.38604i q^{92} +(-4.13405 + 2.46647i) q^{93} -5.71062i q^{94} +(-2.01950 + 1.16596i) q^{95} +(-0.0248275 - 1.73187i) q^{96} +(2.82580 - 4.89442i) q^{97} +(-4.79511 - 5.09970i) q^{98} +(9.61693 + 15.6061i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9}+O(q^{10}) $ 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9	$ 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9} - 18 q^{11} + 3 q^{12} - 8 q^{13} - 4 q^{14} - 17 q^{15} - 17 q^{16} + 6 q^{17} - 11 q^{18} - 10 q^{19} - 9 q^{20} - 4 q^{21} + 9 q^{22} + 6 q^{23} + 3 q^{24} + 16 q^{25} + 13 q^{26} + 18 q^{27} - q^{28} + 27 q^{29} + 13 q^{30} + q^{31} - 17 q^{32} + 21 q^{33} - 12 q^{34} - 3 q^{35} + 4 q^{36} + 6 q^{37} + 5 q^{38} + 20 q^{39} + 9 q^{40} + 3 q^{41} + 20 q^{42} - 3 q^{43} + 9 q^{44} - 6 q^{46} - 27 q^{47} - 6 q^{48} - 5 q^{49} + 16 q^{50} + 24 q^{51} - 5 q^{52} + 21 q^{53} - 18 q^{54} + 57 q^{55} + 5 q^{56} - 17 q^{57} - 6 q^{59} + 4 q^{60} + q^{62} - 21 q^{63} + 34 q^{64} + 33 q^{65} - 21 q^{66} + 6 q^{68} - 30 q^{69} + 3 q^{70} - 15 q^{71} + 7 q^{72} + 19 q^{73} - 6 q^{74} - 63 q^{75} + 5 q^{76} - 9 q^{77} - 10 q^{78} - 9 q^{79} - 5 q^{81} - 16 q^{84} - 42 q^{85} - 3 q^{86} - 75 q^{87} - 18 q^{88} - 18 q^{89} - 9 q^{90} - 27 q^{91} + 25 q^{93} - 3 q^{95} + 3 q^{96} - 19 q^{97} + 7 q^{98} - 27 q^{99}+O(q^{100}) $ 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9 - 18 * q^11 + 3 * q^12 - 8 * q^13 - 4 * q^14 - 17 * q^15 - 17 * q^16 + 6 * q^17 - 11 * q^18 - 10 * q^19 - 9 * q^20 - 4 * q^21 + 9 * q^22 + 6 * q^23 + 3 * q^24 + 16 * q^25 + 13 * q^26 + 18 * q^27 - q^28 + 27 * q^29 + 13 * q^30 + q^31 - 17 * q^32 + 21 * q^33 - 12 * q^34 - 3 * q^35 + 4 * q^36 + 6 * q^37 + 5 * q^38 + 20 * q^39 + 9 * q^40 + 3 * q^41 + 20 * q^42 - 3 * q^43 + 9 * q^44 - 6 * q^46 - 27 * q^47 - 6 * q^48 - 5 * q^49 + 16 * q^50 + 24 * q^51 - 5 * q^52 + 21 * q^53 - 18 * q^54 + 57 * q^55 + 5 * q^56 - 17 * q^57 - 6 * q^59 + 4 * q^60 + q^62 - 21 * q^63 + 34 * q^64 + 33 * q^65 - 21 * q^66 + 6 * q^68 - 30 * q^69 + 3 * q^70 - 15 * q^71 + 7 * q^72 + 19 * q^73 - 6 * q^74 - 63 * q^75 + 5 * q^76 - 9 * q^77 - 10 * q^78 - 9 * q^79 - 5 * q^81 - 16 * q^84 - 42 * q^85 - 3 * q^86 - 75 * q^87 - 18 * q^88 - 18 * q^89 - 9 * q^90 - 27 * q^91 + 25 * q^93 - 3 * q^95 + 3 * q^96 - 19 * q^97 + 7 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	1.51226	+	0.844435i	0.873104	+	0.487535i
$3$	1.51226	+	0.844435i	0.873104	+	0.487535i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.511132	−	0.295102i	0.228585	−	0.131974i	−0.381334	−	0.924437i	$-0.624535\pi$
$5$	0.511132	−	0.295102i	0.228585	−	0.131974i	0.609919	+	0.792464i	$0.291202\pi$
$6$	−1.48743	+	0.887438i	−0.607242	+	0.362295i
$7$	1.57814	+	2.12355i	0.596483	+	0.802626i
$7$	1.57814	+	2.12355i	0.596483	+	0.802626i
$8$	1.00000			0.353553
$9$	1.57386	+	2.55401i	0.524620	+	0.851337i
$10$			0.590205i			0.186639i
$11$	6.11042			1.84236			0.921180	−	0.389137i	$-0.127227\pi$
$11$	6.11042			1.84236			0.921180	+	0.389137i	$0.127227\pi$
$12$	−0.0248275	−	1.73187i	−0.00716709	−	0.499949i
$13$	−1.86885	−	3.08341i	−0.518326	−	0.855183i
$13$	−1.86885	−	3.08341i	−0.518326	−	0.855183i
$14$	−2.62812	+	0.304939i	−0.702394	+	0.0814984i
$15$	1.02216	−	0.0146533i	0.263920	−	0.00378347i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.82336	−	6.62225i	−0.927301	−	1.60613i	−0.787818	−	0.615908i	$-0.788789\pi$
$17$	−3.82336	−	6.62225i	−0.927301	−	1.60613i	−0.139483	−	0.990224i	$-0.544544\pi$
$18$	−2.99877	+	0.0859963i	−0.706816	+	0.0202695i
$19$	−3.95103			−0.906429			−0.453214	−	0.891401i	$-0.649723\pi$
$19$	−3.95103			−0.906429			−0.453214	+	0.891401i	$0.649723\pi$
$20$	−0.511132	−	0.295102i	−0.114293	−	0.0659869i
$21$	0.593366	+	4.54400i	0.129483	+	0.991582i
$22$	−3.05521	+	5.29178i	−0.651373	+	1.12821i
$23$	7.26252	+	4.19302i	1.51434	+	0.874305i	0.999859	+	0.0168038i	$0.00534907\pi$
$23$	7.26252	+	4.19302i	1.51434	+	0.874305i	0.514482	+	0.857501i	$0.327984\pi$
$24$	1.51226	+	0.844435i	0.308689	+	0.172370i
$25$	−2.32583	+	4.02845i	−0.465166	+	0.805691i
$26$	3.60473	−	0.0767706i	0.706946	−	0.0150560i
$27$	0.223387	+	5.19135i	0.0429908	+	0.999075i
$28$	1.04997	−	2.42849i	0.198427	−	0.458941i
$29$	1.39183	−	0.803572i	0.258456	−	0.149220i	−0.365174	−	0.930939i	$-0.618991\pi$
$29$	1.39183	−	0.803572i	0.258456	−	0.149220i	0.623630	+	0.781720i	$0.285657\pi$
$30$	−0.498390	+	0.892543i	−0.0909931	+	0.162955i
$31$	−1.38966	+	2.40696i	−0.249590	+	0.432303i	−0.963412	−	0.268024i	$-0.913629\pi$
$31$	−1.38966	+	2.40696i	−0.249590	+	0.432303i	0.713822	+	0.700327i	$0.246963\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	9.24054	+	5.15985i	1.60857	+	0.898215i
$34$	7.64672			1.31140
$35$	1.43330	+	0.619700i	0.242273	+	0.104748i
$36$	1.42491	−	2.64001i	0.237485	−	0.440001i
$37$	−1.93040	−	1.11452i	−0.317356	−	0.183226i	0.332857	−	0.942977i	$-0.391987\pi$
$37$	−1.93040	−	1.11452i	−0.317356	−	0.183226i	−0.650213	+	0.759752i	$0.725321\pi$
$38$	1.97552	−	3.42169i	0.320471	−	0.555072i
$39$	−0.222454	−	6.24103i	−0.0356211	−	0.999365i
$40$	0.511132	−	0.295102i	0.0808171	−	0.0466598i
$41$	1.36416	−	0.787598i	0.213046	−	0.123002i	−0.389680	−	0.920950i	$-0.627414\pi$
$41$	1.36416	−	0.787598i	0.213046	−	0.123002i	0.602726	+	0.797948i	$0.294081\pi$
$42$	−4.23190	−	1.75813i	−0.652996	−	0.271285i
$43$	−2.90674	+	5.03462i	−0.443274	+	0.767773i	−0.997930	−	0.0643067i	$-0.979516\pi$
$43$	−2.90674	+	5.03462i	−0.443274	+	0.767773i	0.554656	+	0.832080i	$0.312850\pi$
$44$	−3.05521	−	5.29178i	−0.460590	−	0.797765i
$45$	1.55814	+	0.840988i	0.232274	+	0.125367i
$46$	−7.26252	+	4.19302i	−1.07080	+	0.618227i
$47$	−4.94554	+	2.85531i	−0.721381	+	0.416489i	−0.815261	−	0.579094i	$-0.803406\pi$
$47$	−4.94554	+	2.85531i	−0.721381	+	0.416489i	0.0938798	+	0.995584i	$0.470073\pi$
$48$	−1.48743	+	0.887438i	−0.214692	+	0.128091i
$49$	−2.01892	+	6.70253i	−0.288417	+	0.957505i
$50$	−2.32583	−	4.02845i	−0.328922	−	0.569709i
$51$	−0.189849	−	13.2431i	−0.0265842	−	1.85441i
$52$	−1.73588	+	3.16018i	−0.240723	+	0.438238i
$53$	−3.30431	−	1.90774i	−0.453881	−	0.262049i	0.255587	−	0.966786i	$-0.417731\pi$
$53$	−3.30431	−	1.90774i	−0.453881	−	0.262049i	−0.709468	+	0.704738i	$0.751065\pi$
$54$	−4.60753	−	2.40222i	−0.627006	−	0.326900i
$55$	3.12323	−	1.80320i	0.421136	−	0.243143i
$56$	1.57814	+	2.12355i	0.210888	+	0.283771i
$57$	−5.97499	−	3.33639i	−0.791406	−	0.441916i
$58$			1.60714i			0.211028i
$59$	3.88177	−	2.24114i	0.505363	−	0.291772i	−0.225562	−	0.974229i	$-0.572422\pi$
$59$	3.88177	−	2.24114i	0.505363	−	0.291772i	0.730926	+	0.682457i	$0.239089\pi$
$60$	−0.523770	−	0.877889i	−0.0676184	−	0.113335i
$61$		−	0.100596i		−	0.0128800i	−0.999979	−	0.00644002i	$-0.997950\pi$
$61$		−	0.100596i		−	0.0128800i	0.999979	−	0.00644002i	$-0.00204994\pi$
$62$	−1.38966	−	2.40696i	−0.176487	−	0.305684i
$63$	−2.93979	+	7.37276i	−0.370379	+	0.928881i
$64$	1.00000			0.125000
$65$	−1.86515	−	1.02453i	−0.231344	−	0.127077i
$66$	−9.08883	+	5.42261i	−1.11876	+	0.667478i
$67$		−	10.3459i		−	1.26396i	−0.774985	−	0.631979i	$-0.782243\pi$
$67$		−	10.3459i		−	1.26396i	0.774985	−	0.631979i	$-0.217757\pi$
$68$	−3.82336	+	6.62225i	−0.463651	+	0.803066i
$69$	7.44209	+	12.4737i	0.895922	+	1.50165i
$70$	−1.25333	+	0.931429i	−0.149801	+	0.111327i
$71$	−0.875991	+	1.51726i	−0.103961	+	0.180066i	−0.913313	−	0.407258i	$-0.866485\pi$
$71$	−0.875991	+	1.51726i	−0.103961	+	0.180066i	0.809352	+	0.587324i	$0.199818\pi$
$72$	1.57386	+	2.55401i	0.185481	+	0.300993i
$73$	5.41081	−	9.37179i	0.633287	−	1.09689i	−0.353588	−	0.935401i	$-0.615039\pi$
$73$	5.41081	−	9.37179i	0.633287	−	1.09689i	0.986875	−	0.161484i	$-0.0516280\pi$
$74$	1.93040	−	1.11452i	0.224405	−	0.129560i
$75$	−6.91903	+	4.12806i	−0.798940	+	0.476667i
$76$	1.97552	+	3.42169i	0.226607	+	0.392495i
$77$	9.64312	+	12.9758i	1.09894	+	1.47873i
$78$	5.51612	+	2.92787i	0.624578	+	0.331516i
$79$	−3.17751	−	5.50361i	−0.357498	−	0.619205i	0.630044	−	0.776559i	$-0.283037\pi$
$79$	−3.17751	−	5.50361i	−0.357498	−	0.619205i	−0.987542	+	0.157355i	$0.949703\pi$
$80$			0.590205i			0.0659869i
$81$	−4.04594	+	8.03930i	−0.449549	+	0.893256i
$82$			1.57520i			0.173951i
$83$		−	9.07449i		−	0.996055i	−0.867161	−	0.498027i	$-0.834058\pi$
$83$		−	9.07449i		−	0.996055i	0.867161	−	0.498027i	$-0.165942\pi$
$84$	3.63853	−	2.78587i	0.396997	−	0.303963i
$85$	−3.90849	−	2.25657i	−0.423935	−	0.244759i
$86$	−2.90674	−	5.03462i	−0.313442	−	0.542897i
$87$	2.78337	−	0.0399014i	0.298408	−	0.00427788i
$88$	6.11042			0.651373
$89$	−3.56660	−	2.05918i	−0.378059	−	0.218272i	0.298915	−	0.954280i	$-0.403375\pi$
$89$	−3.56660	−	2.05918i	−0.378059	−	0.218272i	−0.676973	+	0.736008i	$0.736709\pi$
$90$	−1.50739	+	0.928899i	−0.158893	+	0.0979145i
$91$	3.59844	−	8.83466i	0.377219	−	0.926124i
$92$		−	8.38604i		−	0.874305i
$93$	−4.13405	+	2.46647i	−0.428681	+	0.255761i
$94$		−	5.71062i		−	0.589005i
$95$	−2.01950	+	1.16596i	−0.207196	+	0.119625i
$96$	−0.0248275	−	1.73187i	−0.00253395	−	0.176759i
$97$	2.82580	−	4.89442i	0.286916	−	0.496953i	−0.686156	−	0.727455i	$-0.740703\pi$
$97$	2.82580	−	4.89442i	0.286916	−	0.496953i	0.973072	+	0.230501i	$0.0740365\pi$
$98$	−4.79511	−	5.09970i	−0.484379	−	0.515148i
$99$	9.61693	+	15.6061i	0.966538	+	1.56847i
$100$	4.65166			0.465166
$101$	−11.8216			−1.17629			−0.588144	−	0.808756i	$-0.700141\pi$
$101$	−11.8216			−1.17629			−0.588144	+	0.808756i	$0.700141\pi$
$102$	11.5638	+	6.45716i	1.14499	+	0.639354i
$103$	−3.76608	+	2.17435i	−0.371083	+	0.214245i	−0.673932	−	0.738794i	$-0.735396\pi$
$103$	−3.76608	+	2.17435i	−0.371083	+	0.214245i	0.302848	+	0.953039i	$0.402062\pi$
$104$	−1.86885	−	3.08341i	−0.183256	−	0.302353i
$105$	1.64423	+	2.14748i	0.160461	+	0.209573i
$106$	3.30431	−	1.90774i	0.320943	−	0.185296i
$107$	−7.65622	−	4.42032i	−0.740154	−	0.427328i	0.0819711	−	0.996635i	$-0.473878\pi$
$107$	−7.65622	−	4.42032i	−0.740154	−	0.427328i	−0.822125	+	0.569306i	$0.807212\pi$
$108$	4.38415	−	2.78913i	0.421865	−	0.268384i
$109$	−14.8949	−	8.59957i	−1.42667	−	0.823690i	−0.429816	−	0.902917i	$-0.641421\pi$
$109$	−14.8949	−	8.59957i	−1.42667	−	0.823690i	−0.996857	+	0.0792270i	$0.974755\pi$
$110$			3.60640i			0.343856i
$111$	−1.97813	−	3.31554i	−0.187756	−	0.314697i
$112$	−2.62812	+	0.304939i	−0.248334	+	0.0288141i
$113$	13.5393	+	7.81690i	1.27367	+	0.735353i	0.975676	−	0.219216i	$-0.0703499\pi$
$113$	13.5393	+	7.81690i	1.27367	+	0.735353i	0.297992	+	0.954568i	$0.403683\pi$
$114$	5.87689	−	3.50630i	0.550421	−	0.328395i
$115$	4.94948			0.461541
$116$	−1.39183	−	0.803572i	−0.129228	−	0.0746098i
$117$	4.93374	−	9.62591i	0.456125	−	0.889916i
$118$			4.48228i			0.412627i
$119$	8.02886	−	18.5700i	0.736005	−	1.70231i
$120$	1.02216	−	0.0146533i	0.0933100	−	0.00133766i
$121$	26.3372			2.39429
$122$	0.0871190	+	0.0502982i	0.00788738	+	0.00455378i
$123$	2.72804	−	0.0391082i	0.245979	−	0.00352627i
$124$	2.77932			0.249590
$125$			5.69645i			0.509506i
$126$	−4.91511	−	6.23231i	−0.437872	−	0.555219i
$127$	2.99064	+	5.17994i	0.265377	+	0.459646i	0.967662	−	0.252250i	$-0.0811704\pi$
$127$	2.99064	+	5.17994i	0.265377	+	0.459646i	−0.702286	+	0.711895i	$0.747837\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−8.64716	+	5.15910i	−0.761340	+	0.454234i
$130$	1.81984	−	1.10301i	0.159611	−	0.0967400i
$131$	−2.79856	−	4.84725i	−0.244511	−	0.423506i	0.717483	−	0.696576i	$-0.245294\pi$
$131$	−2.79856	−	4.84725i	−0.244511	−	0.423506i	−0.961994	+	0.273070i	$0.911961\pi$
$132$	−0.151707	−	10.5825i	−0.0132044	−	0.921085i
$133$	−6.23530	−	8.39021i	−0.540669	−	0.727523i
$134$	8.95985	+	5.17297i	0.774013	+	0.446877i
$135$	1.64616	+	2.58754i	0.141679	+	0.222700i
$136$	−3.82336	−	6.62225i	−0.327850	−	0.567854i
$137$	−10.5736	−	18.3140i	−0.903363	−	1.56467i	−0.823099	−	0.567898i	$-0.807757\pi$
$137$	−10.5736	−	18.3140i	−0.903363	−	1.56467i	−0.0802641	−	0.996774i	$-0.525576\pi$
$138$	−14.5236	+	0.208205i	−1.23633	+	0.0177236i
$139$	9.34314	+	5.39426i	0.792475	+	0.457535i	0.840833	−	0.541295i	$-0.182066\pi$
$139$	9.34314	+	5.39426i	0.792475	+	0.457535i	−0.0483583	+	0.998830i	$0.515399\pi$
$140$	−0.179977	−	1.55113i	−0.0152108	−	0.131094i
$141$	−9.89006	+	0.141781i	−0.832893	+	0.0119401i
$142$	−0.875991	−	1.51726i	−0.0735115	−	0.127326i
$143$	−11.4195	−	18.8409i	−0.954944	−	1.57555i
$144$	−2.99877	+	0.0859963i	−0.249897	+	0.00716636i
$145$	0.474272	−	0.821463i	0.0393861	−	0.0682188i
$146$	5.41081	+	9.37179i	0.447801	+	0.775615i
$147$	−8.71298	+	8.43113i	−0.718635	+	0.695388i
$148$			2.22904i			0.183226i
$149$	−8.02218			−0.657203			−0.328601	−	0.944469i	$-0.606577\pi$
$149$	−8.02218			−0.657203			−0.328601	+	0.944469i	$0.606577\pi$
$150$	−0.115489	−	8.05608i	−0.00942966	−	0.657776i
$151$	7.60834	+	4.39268i	0.619158	+	0.357471i	0.776541	−	0.630066i	$-0.216972\pi$
$151$	7.60834	+	4.39268i	0.619158	+	0.357471i	−0.157383	+	0.987538i	$0.550306\pi$
$152$	−3.95103			−0.320471
$153$	10.8959	−	20.1874i	0.880880	−	1.63205i
$154$	−16.0589	+	1.86331i	−1.29406	+	0.150149i
$155$			1.64037i			0.131758i
$156$	−5.29367	+	3.31317i	−0.423833	+	0.265266i
$157$	2.49489	+	1.44042i	0.199114	+	0.114958i	0.596242	−	0.802805i	$-0.296660\pi$
$157$	2.49489	+	1.44042i	0.199114	+	0.114958i	−0.397128	+	0.917763i	$0.629993\pi$
$158$	6.35503			0.505579
$159$	−3.38600	−	5.67527i	−0.268528	−	0.450078i
$160$	−0.511132	−	0.295102i	−0.0404086	−	0.0233299i
$161$	2.55723	+	22.0395i	0.201538	+	1.73696i
$162$	−4.93927	−	7.52354i	−0.388066	−	0.591105i
$163$		−	5.37931i		−	0.421340i	−0.977557	−	0.210670i	$-0.932435\pi$
$163$		−	5.37931i		−	0.421340i	0.977557	−	0.210670i	$-0.0675646\pi$
$164$	−1.36416	−	0.787598i	−0.106523	−	0.0615011i
$165$	6.24582	−	0.0895380i	0.486237	−	0.00697052i
$166$	7.85874	+	4.53725i	0.609957	+	0.352159i
$167$	14.1115	−	8.14728i	1.09198	−	0.630455i	0.157878	−	0.987459i	$-0.449535\pi$
$167$	14.1115	−	8.14728i	1.09198	−	0.630455i	0.934103	+	0.357003i	$0.116202\pi$
$168$	0.593366	+	4.54400i	0.0457792	+	0.350577i
$169$	−6.01478	+	11.5249i	−0.462676	+	0.886528i
$170$	3.90849	−	2.25657i	0.299767	−	0.173071i
$171$	−6.21837	−	10.0910i	−0.475530	−	0.771676i
$172$	5.81348			0.443274
$173$	14.4001			1.09482			0.547408	−	0.836866i	$-0.315615\pi$
$173$	14.4001			1.09482			0.547408	+	0.836866i	$0.315615\pi$
$174$	−1.35713	+	2.43042i	−0.102884	+	0.184250i
$175$	−12.2251	+	1.41847i	−0.924132	+	0.107227i
$176$	−3.05521	+	5.29178i	−0.230295	+	0.398883i
$177$	7.76274	−	0.111284i	0.583483	−	0.00836462i
$178$	3.56660	−	2.05918i	0.267328	−	0.154342i
$179$		−	11.4696i		−	0.857281i	−0.903475	−	0.428641i	$-0.858993\pi$
$179$		−	11.4696i		−	0.857281i	0.903475	−	0.428641i	$-0.141007\pi$
$180$	−0.0507554	−	1.76989i	−0.00378309	−	0.131920i
$181$			14.7039i			1.09293i	0.837482	+	0.546465i	$0.184027\pi$
$181$			14.7039i			1.09293i	−0.837482	+	0.546465i	$0.815973\pi$
$182$	5.85182	+	7.53367i	0.433766	+	0.558433i
$183$	0.0849471	−	0.152128i	0.00627947	−	0.0112456i
$184$	7.26252	+	4.19302i	0.535400	+	0.309114i
$185$	−1.31559			−0.0967239
$186$	−0.0690037	−	4.81343i	−0.00505960	−	0.352938i
$187$	−23.3623	−	40.4647i	−1.70842	−	2.95907i
$188$	4.94554	+	2.85531i	0.360690	+	0.208245i
$189$	−10.6715	+	8.66707i	−0.776241	+	0.630437i
$190$		−	2.33192i		−	0.169175i
$191$			10.8591i			0.785739i	0.919594	+	0.392870i	$0.128518\pi$
$191$			10.8591i			0.785739i	−0.919594	+	0.392870i	$0.871482\pi$
$192$	1.51226	+	0.844435i	0.109138	+	0.0609419i
$193$		−	19.2440i		−	1.38521i	−0.721315	−	0.692607i	$-0.756462\pi$
$193$		−	19.2440i		−	1.38521i	0.721315	−	0.692607i	$-0.243538\pi$
$194$	2.82580	+	4.89442i	0.202880	+	0.351399i
$195$	−1.95545	−	3.12435i	−0.140032	−	0.223739i
$196$	6.81402	−	1.60283i	0.486716	−	0.114488i
$197$	3.97307	+	6.88156i	0.283070	+	0.490291i	0.972139	−	0.234404i	$-0.0753139\pi$
$197$	3.97307	+	6.88156i	0.283070	+	0.490291i	−0.689070	+	0.724695i	$0.741981\pi$
$198$	−18.3237	+	0.525473i	−1.30221	+	0.0373438i
$199$	−16.2970	+	9.40910i	−1.15527	+	0.666993i	−0.950165	−	0.311748i	$-0.899086\pi$
$199$	−16.2970	+	9.40910i	−1.15527	+	0.666993i	−0.205101	+	0.978741i	$0.565752\pi$
$200$	−2.32583	+	4.02845i	−0.164461	+	0.284855i
$201$	8.73648	−	15.6458i	0.616224	−	1.10357i
$202$	5.91078	−	10.2378i	0.415881	−	0.720327i
$203$	3.90293	+	1.68746i	0.273932	+	0.118436i
$204$	−11.3740	+	6.78599i	−0.796338	+	0.475114i
$205$	0.464844	−	0.805133i	0.0324661	−	0.0562330i
$206$		−	4.34870i		−	0.302988i
$207$	0.721168	+	25.1478i	0.0501247	+	1.74789i
$208$	3.60473	−	0.0767706i	0.249943	−	0.00532309i
$209$	−24.1425			−1.66997
$210$	−2.68189	+	0.350207i	−0.185068	+	0.0241666i
$211$	1.28361	+	2.22329i	0.0883677	+	0.153057i	0.906821	−	0.421515i	$-0.138502\pi$
$211$	1.28361	+	2.22329i	0.0883677	+	0.153057i	−0.818454	+	0.574573i	$0.805168\pi$
$212$			3.81548i			0.262049i
$213$	−2.60595	+	1.55477i	−0.178557	+	0.106531i
$214$	7.65622	−	4.42032i	0.523368	−	0.302167i
$215$			3.43114i			0.234002i
$216$	0.223387	+	5.19135i	0.0151995	+	0.353227i
$217$	−7.30439	+	0.847524i	−0.495854	+	0.0575337i
$218$	14.8949	−	8.59957i	1.00881	−	0.582437i
$219$	16.0964	−	9.60351i	1.08769	−	0.648945i
$220$	−3.12323	−	1.80320i	−0.210568	−	0.121572i
$221$	−13.2738	+	24.1650i	−0.892893	+	1.62551i
$222$	3.86041	−	0.0553415i	0.259093	−	0.00371428i
$223$	−1.78923	−	3.09905i	−0.119816	−	0.207527i	0.799879	−	0.600162i	$-0.204897\pi$
$223$	−1.78923	−	3.09905i	−0.119816	−	0.207527i	−0.919695	+	0.392634i	$0.871564\pi$
$224$	1.04997	−	2.42849i	0.0701544	−	0.162260i
$225$	−13.9492	+	0.400025i	−0.929949	+	0.0266684i
$226$	−13.5393	+	7.81690i	−0.900619	+	0.519973i
$227$	10.3697	−	5.98695i	0.688261	−	0.397368i	−0.114699	−	0.993400i	$-0.536590\pi$
$227$	10.3697	−	5.98695i	0.688261	−	0.397368i	0.802960	+	0.596033i	$0.203257\pi$
$228$	0.0980944	+	6.84269i	0.00649646	+	0.453168i
$229$	−5.57509	−	9.65634i	−0.368412	−	0.638109i	0.620905	−	0.783886i	$-0.286765\pi$
$229$	−5.57509	−	9.65634i	−0.368412	−	0.638109i	−0.989318	+	0.145777i	$0.953432\pi$
$230$	−2.47474	+	4.28638i	−0.163180	+	0.282635i
$231$	3.62571	+	27.7657i	0.238554	+	1.82685i
$232$	1.39183	−	0.803572i	0.0913779	−	0.0527571i
$233$	13.8355	−	7.98795i	0.906396	−	0.523308i	0.0271263	−	0.999632i	$-0.491364\pi$
$233$	13.8355	−	7.98795i	0.906396	−	0.523308i	0.879270	+	0.476324i	$0.158031\pi$
$234$	5.86941	+	9.08570i	0.383696	+	0.593951i
$235$	−1.68522	+	2.91888i	−0.109931	+	0.190407i
$236$	−3.88177	−	2.24114i	−0.252682	−	0.145886i
$237$	−0.157780	−	11.0061i	−0.0102489	−	0.714923i
$238$	12.0676	+	16.2382i	0.782229	+	1.05257i
$239$	−17.6869			−1.14407			−0.572034	−	0.820230i	$-0.693846\pi$
$239$	−17.6869			−1.14407			−0.572034	+	0.820230i	$0.693846\pi$
$240$	−0.498390	+	0.892543i	−0.0321709	+	0.0576134i
$241$	12.0836	+	20.9293i	0.778370	+	1.34818i	0.932881	+	0.360186i	$0.117287\pi$
$241$	12.0836	+	20.9293i	0.778370	+	1.34818i	−0.154510	+	0.987991i	$0.549380\pi$
$242$	−13.1686	+	22.8087i	−0.846510	+	1.46620i
$243$	−12.9072	+	8.74098i	−0.827996	+	0.560734i
$244$	−0.0871190	+	0.0502982i	−0.00557722	+	0.00322001i
$245$	0.946000	+	4.02167i	0.0604377	+	0.256935i
$246$	−1.33015	+	2.38210i	−0.0848073	+	0.151877i
$247$	7.38390	+	12.1826i	0.469826	+	0.775163i
$248$	−1.38966	+	2.40696i	−0.0882435	+	0.152842i
$249$	7.66282	−	13.7230i	0.485612	−	0.869659i
$250$	−4.93327	−	2.84823i	−0.312008	−	0.180138i
$251$	1.60381	−	2.77787i	0.101231	−	0.175338i	−0.810961	−	0.585100i	$-0.801055\pi$
$251$	1.60381	−	2.77787i	0.101231	−	0.175338i	0.912192	+	0.409763i	$0.134388\pi$
$252$	7.85489	−	1.14045i	0.494812	−	0.0718416i
$253$	44.3770	+	25.6211i	2.78996	+	1.61078i
$254$	−5.98128			−0.375299
$255$	−4.00512	−	6.71298i	−0.250811	−	0.420383i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.591663	+	1.02479i	−0.0369069	+	0.0639246i	−0.883889	−	0.467697i	$-0.845084\pi$
$257$	−0.591663	+	1.02479i	−0.0369069	+	0.0639246i	0.846982	+	0.531622i	$0.178417\pi$
$258$	−0.144334	−	10.0682i	−0.00898587	−	0.626819i
$259$	−0.679720	−	5.85817i	−0.0422358	−	0.364009i
$260$	0.0453104	+	2.12753i	0.00281003	+	0.131944i
$261$	4.24287	+	2.29003i	0.262627	+	0.141749i
$262$	5.59712			0.345791
$263$		−	1.34212i		−	0.0827589i	−0.999144	−	0.0413794i	$-0.986825\pi$
$263$		−	1.34212i		−	0.0827589i	0.999144	−	0.0413794i	$-0.0131752\pi$
$264$	9.24054	+	5.15985i	0.568716	+	0.317567i
$265$	−2.25192			−0.138334
$266$	10.3838	−	1.20482i	0.636671	−	0.0738726i
$267$	−3.65478	−	6.12577i	−0.223669	−	0.374891i
$268$	−8.95985	+	5.17297i	−0.547310	+	0.315990i
$269$	3.23296	+	5.59965i	0.197117	+	0.341417i	0.947592	−	0.319482i	$-0.103509\pi$
$269$	3.23296	+	5.59965i	0.197117	+	0.341417i	−0.750476	+	0.660898i	$0.770175\pi$
$270$	−3.06396	+	0.131844i	−0.186467	+	0.00802376i
$271$	−9.61794	+	16.6588i	−0.584249	+	1.01195i	0.410720	+	0.911761i	$0.365277\pi$
$271$	−9.61794	+	16.6588i	−0.584249	+	1.01195i	−0.994969	+	0.100187i	$0.968056\pi$
$272$	7.64672			0.463651
$273$	12.9021	−	10.3216i	0.780869	−	0.624695i
$274$	21.1472			1.27755
$275$	−14.2118	+	24.6155i	−0.857003	+	1.48437i
$276$	7.08147	−	12.6819i	0.426254	−	0.763359i
$277$	5.88112	+	10.1864i	0.353362	+	0.612042i	0.986836	−	0.161722i	$-0.0517049\pi$
$277$	5.88112	+	10.1864i	0.353362	+	0.612042i	−0.633474	+	0.773764i	$0.718372\pi$
$278$	−9.34314	+	5.39426i	−0.560364	+	0.323526i
$279$	−8.33453	+	0.239011i	−0.498976	+	0.0143092i
$280$	1.43330	+	0.619700i	0.0856564	+	0.0370342i
$281$	21.9950			1.31211			0.656057	−	0.754711i	$-0.272223\pi$
$281$	21.9950			1.31211			0.656057	+	0.754711i	$0.272223\pi$
$282$	4.82224	−	8.63593i	0.287160	−	0.514262i
$283$		−	12.8485i		−	0.763761i	−0.924212	−	0.381881i	$-0.875277\pi$
$283$		−	12.8485i		−	0.763761i	0.924212	−	0.381881i	$-0.124723\pi$
$284$	1.75198			0.103961
$285$	−4.03859	+	0.0578958i	−0.239225	+	0.00342945i
$286$	22.0264	−	0.469101i	1.30245	−	0.0277385i
$287$	3.82534	+	1.65392i	0.225803	+	0.0976275i
$288$	1.42491	−	2.64001i	0.0839635	−	0.155564i
$289$	−20.7362	+	35.9161i	−1.21977	+	2.11271i
$290$	0.474272	+	0.821463i	0.0278502	+	0.0482380i
$291$	8.40636	−	5.01544i	0.492790	−	0.294010i
$292$	−10.8216			−0.633287
$293$	0.344829	+	0.199087i	0.0201451	+	0.0116308i	0.510039	−	0.860151i	$-0.329631\pi$
$293$	0.344829	+	0.199087i	0.0201451	+	0.0116308i	−0.489894	+	0.871782i	$0.662964\pi$
$294$	−2.94508	−	11.7612i	−0.171761	−	0.685929i
$295$	1.32273	−	2.29104i	0.0770124	−	0.133389i
$296$	−1.93040	−	1.11452i	−0.112202	−	0.0647800i
$297$	1.36499	+	31.7213i	0.0792045	+	1.84066i
$298$	4.01109	−	6.94741i	0.232356	−	0.402453i
$299$	−0.643802	−	30.2294i	−0.0372320	−	1.74821i
$300$	7.03452	+	3.92802i	0.406138	+	0.226785i
$301$	−15.2785	+	1.77276i	−0.880640	+	0.102180i
$302$	−7.60834	+	4.39268i	−0.437811	+	0.252770i
$303$	−17.8773	−	9.98254i	−1.02702	−	0.573482i
$304$	1.97552	−	3.42169i	0.113304	−	0.196248i
$305$	−0.0296862	−	0.0514180i	−0.00169983	−	0.00294419i
$306$	12.0349	+	19.5298i	0.687987	+	1.11644i
$307$	−10.2738			−0.586356			−0.293178	−	0.956058i	$-0.594713\pi$
$307$	−10.2738			−0.586356			−0.293178	+	0.956058i	$0.594713\pi$
$308$	6.41578	−	14.8391i	0.365573	−	0.845535i
$309$	−7.53139	+	0.107968i	−0.428446	+	0.00614206i
$310$	−1.42060	−	0.820184i	−0.0806847	−	0.0465833i
$311$	1.05163	−	1.82148i	0.0596325	−	0.103287i	−0.834668	−	0.550754i	$-0.814340\pi$
$311$	1.05163	−	1.82148i	0.0596325	−	0.103287i	0.894300	+	0.447467i	$0.147674\pi$
$312$	−0.222454	−	6.24103i	−0.0125940	−	0.353329i
$313$	−9.44084	+	5.45067i	−0.533628	+	0.308090i	−0.742492	−	0.669854i	$-0.766356\pi$
$313$	−9.44084	+	5.45067i	−0.533628	+	0.308090i	0.208865	+	0.977945i	$0.433023\pi$
$314$	−2.49489	+	1.44042i	−0.140795	+	0.0812878i
$315$	0.673099	+	4.63600i	0.0379248	+	0.261209i
$316$	−3.17751	+	5.50361i	−0.178749	+	0.309602i
$317$	5.27267	+	9.13253i	0.296143	+	0.512934i	0.975250	−	0.221105i	$-0.0709663\pi$
$317$	5.27267	+	9.13253i	0.296143	+	0.512934i	−0.679107	+	0.734039i	$0.737633\pi$
$318$	6.60793	−	0.0947291i	0.370555	−	0.00531214i
$319$	8.50465	−	4.91016i	0.476169	−	0.274916i
$320$	0.511132	−	0.295102i	0.0285732	−	0.0164967i
$321$	−7.84551	−	13.1498i	−0.437894	−	0.733953i
$322$	−20.3654	−	8.80513i	−1.13492	−	0.490691i
$323$	15.1062	+	26.1647i	0.840533	+	1.45585i
$324$	8.98521	−	0.515766i	0.499178	−	0.0286537i
$325$	16.7680	−	0.357111i	0.930121	−	0.0198089i
$326$	4.65862	+	2.68966i	0.258017	+	0.148966i
$327$	−15.2632	−	25.5826i	−0.844055	−	1.41472i
$328$	1.36416	−	0.787598i	0.0753231	−	0.0434878i
$329$	−13.8682	−	5.99600i	−0.764576	−	0.330570i
$330$	−3.04537	+	5.45381i	−0.167642	+	0.300222i
$331$		−	14.5681i		−	0.800733i	−0.916355	−	0.400366i	$-0.868883\pi$
$331$		−	14.5681i		−	0.800733i	0.916355	−	0.400366i	$-0.131117\pi$
$332$	−7.85874	+	4.53725i	−0.431304	+	0.249014i
$333$	−0.191689	−	6.68436i	−0.0105045	−	0.366301i
$334$			16.2946i			0.891599i
$335$	−3.05311	−	5.28815i	−0.166809	−	0.288922i
$336$	−4.23190	−	1.75813i	−0.230869	−	0.0959138i
$337$	−31.0830			−1.69320			−0.846599	−	0.532231i	$-0.821354\pi$
$337$	−31.0830			−1.69320			−0.846599	+	0.532231i	$0.821354\pi$
$338$	−6.97343	−	10.9714i	−0.379305	−	0.596765i
$339$	13.8740	+	23.2542i	0.753534	+	1.26300i
$340$			4.51313i			0.244759i
$341$	−8.49140	+	14.7075i	−0.459835	+	0.796458i
$342$	11.8482	−	0.339774i	0.640679	−	0.0183729i
$343$	−17.4193	+	6.29030i	−0.940554	+	0.339644i
$344$	−2.90674	+	5.03462i	−0.156721	+	0.271449i
$345$	7.48490	+	4.17951i	0.402973	+	0.225018i
$346$	−7.20003	+	12.4708i	−0.387076	+	0.670435i
$347$	−21.3630	+	12.3339i	−1.14682	+	0.662119i	−0.948111	−	0.317938i	$-0.897009\pi$
$347$	−21.3630	+	12.3339i	−1.14682	+	0.662119i	−0.198713	+	0.980058i	$0.563676\pi$
$348$	−1.42624	−	2.39052i	−0.0764545	−	0.128145i
$349$	16.5800	+	28.7175i	0.887509	+	1.53721i	0.842811	+	0.538210i	$0.180899\pi$
$349$	16.5800	+	28.7175i	0.887509	+	1.53721i	0.0446981	+	0.999001i	$0.485767\pi$
$350$	4.88412	−	11.2965i	0.261067	−	0.603823i
$351$	15.5896	−	10.3907i	0.832109	−	0.554612i
$352$	−3.05521	−	5.29178i	−0.162843	−	0.282053i
$353$			14.4690i			0.770108i	0.922894	+	0.385054i	$0.125817\pi$
$353$			14.4690i			0.770108i	−0.922894	+	0.385054i	$0.874183\pi$
$354$	−3.78499	+	6.77837i	−0.201170	+	0.360266i
$355$			1.03403i			0.0548805i
$356$			4.11835i			0.218272i
$357$	27.8229	−	21.3028i	1.47254	−	1.12746i
$358$	9.93300	+	5.73482i	0.524975	+	0.303095i
$359$	7.00098	+	12.1261i	0.369498	+	0.639989i	0.989487	−	0.144621i	$-0.0461964\pi$
$359$	7.00098	+	12.1261i	0.369498	+	0.639989i	−0.619989	+	0.784610i	$0.712863\pi$
$360$	1.55814	+	0.840988i	0.0821214	+	0.0443239i
$361$	−3.38934			−0.178386
$362$	−12.7339	−	7.35194i	−0.669281	−	0.386409i
$363$	39.8287	+	22.2401i	2.09046	+	1.16730i
$364$	−9.45026	+	1.30099i	−0.495328	+	0.0681903i
$365$		−	6.38697i		−	0.334309i
$366$	0.0892730	+	0.149630i	0.00466637	+	0.00782130i
$367$		−	14.7332i		−	0.769065i	−0.923111	−	0.384533i	$-0.874363\pi$
$367$		−	14.7332i		−	0.769065i	0.923111	−	0.384533i	$-0.125637\pi$
$368$	−7.26252	+	4.19302i	−0.378585	+	0.218576i
$369$	4.15853	+	2.24451i	0.216484	+	0.116845i
$370$	0.657794	−	1.13933i	0.0341971	−	0.0592310i
$371$	−1.16349	−	10.0275i	−0.0604054	−	0.520604i
$372$	4.20305	+	2.34696i	0.217918	+	0.121684i
$373$	15.8300			0.819645			0.409822	−	0.912165i	$-0.365591\pi$
$373$	15.8300			0.819645			0.409822	+	0.912165i	$0.365591\pi$
$374$	46.7247			2.41607
$375$	−4.81029	+	8.61452i	−0.248402	+	0.444852i
$376$	−4.94554	+	2.85531i	−0.255047	+	0.147251i
$377$	−5.07886	−	2.78981i	−0.261575	−	0.143683i
$378$	−2.17013	−	13.5754i	−0.111620	−	0.698241i
$379$	−11.2444	+	6.49193i	−0.577584	+	0.333468i	−0.760173	−	0.649721i	$-0.774886\pi$
$379$	−11.2444	+	6.49193i	−0.577584	+	0.333468i	0.182589	+	0.983189i	$0.441552\pi$
$380$	2.01950	+	1.16596i	0.103598	+	0.0598124i
$381$	0.148501	+	10.3588i	0.00760791	+	0.530698i
$382$	−9.40428	−	5.42957i	−0.481165	−	0.277801i
$383$		−	4.18573i		−	0.213881i	−0.994265	−	0.106940i	$-0.965895\pi$
$383$		−	4.18573i		−	0.213881i	0.994265	−	0.106940i	$-0.0341054\pi$
$384$	−1.48743	+	0.887438i	−0.0759052	+	0.0452869i
$385$	8.75809	+	3.78663i	0.446354	+	0.192984i
$386$	16.6658	+	9.62200i	0.848267	+	0.489747i
$387$	−17.4333	+	0.499938i	−0.886183	+	0.0254133i
$388$	−5.65159			−0.286916
$389$	−19.0201	−	10.9812i	−0.964356	−	0.556771i	−0.0668451	−	0.997763i	$-0.521293\pi$
$389$	−19.0201	−	10.9812i	−0.964356	−	0.556771i	−0.897511	+	0.440992i	$0.854627\pi$
$390$	3.68349	−	0.131293i	0.186521	−	0.00664829i
$391$		−	64.1257i		−	3.24298i
$392$	−2.01892	+	6.70253i	−0.101971	+	0.338529i
$393$	−0.138963	−	9.69349i	−0.00700974	−	0.488972i
$394$	−7.94614			−0.400321
$395$	−3.24826	−	1.87538i	−0.163438	−	0.0943608i
$396$	8.70679	−	16.1315i	0.437532	−	0.810641i
$397$	−33.1213			−1.66231			−0.831156	−	0.556039i	$-0.812320\pi$
$397$	−33.1213			−1.66231			−0.831156	+	0.556039i	$0.812320\pi$
$398$		−	18.8182i		−	0.943271i
$399$	−2.34441	−	17.9535i	−0.117367	−	0.898798i
$400$	−2.32583	−	4.02845i	−0.116291	−	0.201423i
$401$	−3.47187	+	6.01346i	−0.173377	+	0.300298i	−0.939598	−	0.342279i	$-0.888801\pi$
$401$	−3.47187	+	6.01346i	−0.173377	+	0.300298i	0.766221	+	0.642577i	$0.222135\pi$
$402$	9.18138	+	15.3889i	0.457926	+	0.767528i
$403$	10.0187	−	0.213370i	0.499067	−	0.0106287i
$404$	5.91078	+	10.2378i	0.294072	+	0.509348i
$405$	0.304407	+	5.30311i	0.0151261	+	0.263514i
$406$	−3.41285	+	2.53631i	−0.169377	+	0.125875i
$407$	−11.7956	−	6.81017i	−0.584684	−	0.337568i
$408$	−0.189849	−	13.2431i	−0.00939894	−	0.655634i
$409$	−0.151773	−	0.262878i	−0.00750467	−	0.0129985i	0.862249	−	0.506485i	$-0.169056\pi$
$409$	−0.151773	−	0.262878i	−0.00750467	−	0.0129985i	−0.869753	+	0.493487i	$0.835722\pi$
$410$	0.464844	+	0.805133i	0.0229570	+	0.0397627i
$411$	−0.525033	−	36.6243i	−0.0258980	−	1.80654i
$412$	3.76608	+	2.17435i	0.185542	+	0.107123i
$413$	10.8852	+	4.70628i	0.535624	+	0.231581i
$414$	−22.1392	−	11.9493i	−1.08808	−	0.587278i
$415$	−2.67790	−	4.63827i	−0.131453	−	0.227684i
$416$	−1.73588	+	3.16018i	−0.0851086	+	0.154940i
$417$	9.57415	+	16.0472i	0.468848	+	0.785835i
$418$	12.0712	−	20.9080i	0.590423	−	1.02264i
$419$	2.85725	+	4.94891i	0.139586	+	0.241770i	0.927340	−	0.374220i	$-0.122089\pi$
$419$	2.85725	+	4.94891i	0.139586	+	0.241770i	−0.787754	+	0.615990i	$0.788756\pi$
$420$	1.03766	−	2.49769i	0.0506324	−	0.121875i
$421$		−	9.25537i		−	0.451079i	−0.974234	−	0.225540i	$-0.927585\pi$
$421$		−	9.25537i		−	0.451079i	0.974234	−	0.225540i	$-0.0724145\pi$
$422$	−2.56723			−0.124971
$423$	−15.0761	−	8.13711i	−0.733023	−	0.395640i
$424$	−3.30431	−	1.90774i	−0.160471	−	0.0926481i
$425$	35.5699			1.72540
$426$	−0.0434974	−	3.03421i	−0.00210746	−	0.147008i
$427$	0.213621	−	0.158756i	0.0103379	−	0.00768272i
$428$			8.84064i			0.427328i
$429$	−1.35928	−	38.1353i	−0.0656269	−	1.84119i
$430$	−2.97146	−	1.71557i	−0.143296	−	0.0827322i
$431$	−10.1057			−0.486773			−0.243386	−	0.969929i	$-0.578258\pi$
$431$	−10.1057			−0.486773			−0.243386	+	0.969929i	$0.578258\pi$
$432$	−4.60753	−	2.40222i	−0.221680	−	0.115577i
$433$	−32.8655	−	18.9749i	−1.57942	−	0.911877i	−0.994941	−	0.100466i	$-0.967967\pi$
$433$	−32.8655	−	18.9749i	−1.57942	−	0.911877i	−0.584476	−	0.811411i	$-0.698700\pi$
$434$	2.91822	−	6.74955i	0.140079	−	0.323989i
$435$	1.41089	−	0.841774i	0.0676472	−	0.0403600i
$436$			17.1991i			0.823690i
$437$	−28.6945	−	16.5668i	−1.37264	−	0.792495i
$438$	0.268674	+	18.7417i	0.0128377	+	0.895511i
$439$	24.6369	+	14.2241i	1.17586	+	0.678881i	0.955052	−	0.296437i	$-0.0957984\pi$
$439$	24.6369	+	14.2241i	1.17586	+	0.678881i	0.220805	+	0.975318i	$0.429132\pi$
$440$	3.12323	−	1.80320i	0.148894	−	0.0859641i
$441$	−20.2958	+	5.39251i	−0.966468	+	0.256786i
$442$	−14.2906	−	23.5779i	−0.679734	−	1.12149i
$443$	18.7651	−	10.8340i	0.891555	−	0.514740i	0.0171043	−	0.999854i	$-0.494555\pi$
$443$	18.7651	−	10.8340i	0.891555	−	0.514740i	0.874451	+	0.485114i	$0.161222\pi$
$444$	−1.88228	+	3.37088i	−0.0893289	+	0.159975i
$445$	−2.43067			−0.115225
$446$	3.57847			0.169445
$447$	−12.1316	−	6.77421i	−0.573806	−	0.320409i
$448$	1.57814	+	2.12355i	0.0745603	+	0.100328i
$449$	6.23704	−	10.8029i	0.294344	−	0.509819i	−0.680488	−	0.732759i	$-0.738232\pi$
$449$	6.23704	−	10.8029i	0.294344	−	0.509819i	0.974832	+	0.222940i	$0.0715656\pi$
$450$	6.62819	−	12.2804i	0.312456	−	0.578904i
$451$	8.33558	−	4.81255i	0.392507	−	0.226614i
$452$		−	15.6338i		−	0.735353i
$453$	7.79646	+	13.0676i	0.366310	+	0.613971i
$454$			11.9739i			0.561963i
$455$	−0.767849	−	5.57759i	−0.0359973	−	0.261481i
$456$	−5.97499	−	3.33639i	−0.279804	−	0.156241i
$457$	8.30703	+	4.79607i	0.388587	+	0.224351i	0.681548	−	0.731774i	$-0.261307\pi$
$457$	8.30703	+	4.79607i	0.388587	+	0.224351i	−0.292961	+	0.956124i	$0.594641\pi$
$458$	11.1502			0.521014
$459$	33.5243	−	21.3277i	1.56478	−	0.995493i
$460$	−2.47474	−	4.28638i	−0.115385	−	0.199853i
$461$	−4.17780	−	2.41206i	−0.194580	−	0.112341i	0.399545	−	0.916714i	$-0.369168\pi$
$461$	−4.17780	−	2.41206i	−0.194580	−	0.112341i	−0.594125	+	0.804373i	$0.702501\pi$
$462$	−25.8587	−	10.7429i	−1.20305	−	0.499805i
$463$		−	3.08747i		−	0.143487i	−0.997423	−	0.0717434i	$-0.977144\pi$
$463$		−	3.08747i		−	0.143487i	0.997423	−	0.0717434i	$-0.0228563\pi$
$464$			1.60714i			0.0746098i
$465$	−1.38518	+	2.48066i	−0.0642364	+	0.115038i
$466$			15.9759i			0.740069i
$467$	4.16237	+	7.20943i	0.192611	+	0.333613i	0.946115	−	0.323831i	$-0.104971\pi$
$467$	4.16237	+	7.20943i	0.192611	+	0.333613i	−0.753504	+	0.657444i	$0.771638\pi$
$468$	−10.8032	+	0.540211i	−0.499376	+	0.0249713i
$469$	21.9701	−	16.3274i	1.01449	−	0.753929i
$470$	−1.68522	−	2.91888i	−0.0777332	−	0.134638i
$471$	2.55657	+	4.28506i	0.117801	+	0.197445i
$472$	3.88177	−	2.24114i	0.178673	−	0.103157i
$473$	−17.7614	+	30.7636i	−0.816670	+	1.41451i
$474$	9.61045	+	5.36641i	0.441422	+	0.246487i
$475$	9.18943	−	15.9166i	0.421640	−	0.730302i
$476$	−20.0965	+	2.33179i	−0.921121	+	0.106877i
$477$	−0.328118	−	11.4417i	−0.0150235	−	0.523882i
$478$	8.84344	−	15.3173i	0.404489	−	0.700596i
$479$			12.0776i			0.551839i	0.961181	+	0.275920i	$0.0889824\pi$
$479$			12.0776i			0.551839i	−0.961181	+	0.275920i	$0.911018\pi$
$480$	−0.523770	−	0.877889i	−0.0239067	−	0.0400700i
$481$	0.171124	+	8.03508i	0.00780260	+	0.366368i
$482$	−24.1671			−1.10078
$483$	−14.7437	+	35.4889i	−0.670863	+	1.61480i
$484$	−13.1686	−	22.8087i	−0.598573	−	1.03676i
$485$		−	3.33560i		−	0.151462i
$486$	−1.11632	−	15.5484i	−0.0506374	−	0.705291i
$487$	4.84833	−	2.79918i	0.219699	−	0.126843i	−0.386112	−	0.922452i	$-0.626182\pi$
$487$	4.84833	−	2.79918i	0.219699	−	0.126843i	0.605811	+	0.795609i	$0.292849\pi$
$488$		−	0.100596i		−	0.00455378i
$489$	4.54248	−	8.13492i	0.205418	−	0.367874i
$490$	−3.95587	−	1.19157i	−0.178708	−	0.0538299i
$491$	0.451495	−	0.260671i	0.0203757	−	0.0117639i	−0.489778	−	0.871847i	$-0.662922\pi$
$491$	0.451495	−	0.260671i	0.0203757	−	0.0117639i	0.510153	+	0.860084i	$0.329589\pi$
$492$	−1.39789	−	2.34300i	−0.0630217	−	0.105630i
$493$	−10.6429	−	6.14469i	−0.479333	−	0.276743i
$494$	−14.2424	+	0.303323i	−0.640797	+	0.0136472i
$495$	9.52091	+	5.13879i	0.427933	+	0.230971i
$496$	−1.38966	−	2.40696i	−0.0623976	−	0.108076i
$497$	−4.60442	+	0.534248i	−0.206536	+	0.0239643i
$498$	8.05305	+	13.4977i	0.360866	+	0.604846i
$499$	28.9603	−	16.7202i	1.29644	−	0.748501i	0.316654	−	0.948541i	$-0.397441\pi$
$499$	28.9603	−	16.7202i	1.29644	−	0.748501i	0.979788	+	0.200041i	$0.0641074\pi$
$500$	4.93327	−	2.84823i	0.220623	−	0.127377i
$501$	28.2201	−	0.404554i	1.26078	−	0.0180741i
$502$	1.60381	+	2.77787i	0.0715814	+	0.123983i
$503$	−9.16509	+	15.8744i	−0.408651	+	0.707805i	−0.994739	−	0.102443i	$-0.967334\pi$
$503$	−9.16509	+	15.8744i	−0.408651	+	0.707805i	0.586088	+	0.810248i	$0.300667\pi$
$504$	−2.93979	+	7.37276i	−0.130949	+	0.328409i
$505$	−6.04238	+	3.48857i	−0.268882	+	0.155239i
$506$	−44.3770	+	25.6211i	−1.97280	+	1.13900i
$507$	−18.8279	+	12.3495i	−0.836177	+	0.548460i
$508$	2.99064	−	5.17994i	0.132688	−	0.229823i
$509$	30.2332	+	17.4552i	1.34006	+	0.773686i	0.986816	−	0.161843i	$-0.0517439\pi$
$509$	30.2332	+	17.4552i	1.34006	+	0.773686i	0.353248	+	0.935530i	$0.385077\pi$
$510$	7.81617	−	0.112050i	0.346106	−	0.00496166i
$511$	28.4405	−	3.29993i	1.25813	−	0.145980i
$512$	1.00000			0.0441942
$513$	−0.882608	−	20.5112i	−0.0389681	−	0.905591i
$514$	−0.591663	−	1.02479i	−0.0260971	−	0.0452015i
$515$	−1.28331	+	2.22276i	−0.0565495	+	0.0979465i
$516$	8.79149	+	4.90911i	0.387024	+	0.216111i
$517$	−30.2193	+	17.4471i	−1.32904	+	0.767324i
$518$	5.41319	+	2.34043i	0.237842	+	0.102833i
$519$	21.7766	+	12.1599i	0.955888	+	0.533761i
$520$	−1.86515	−	1.02453i	−0.0817923	−	0.0449284i
$521$	15.3561	−	26.5976i	0.672763	−	1.16526i	−0.304354	−	0.952559i	$-0.598441\pi$
$521$	15.3561	−	26.5976i	0.672763	−	1.16526i	0.977117	−	0.212701i	$-0.0682260\pi$
$522$	−4.10466	+	2.52942i	−0.179656	+	0.110710i
$523$	27.1317	+	15.6645i	1.18639	+	0.684960i	0.957483	−	0.288490i	$-0.0931531\pi$
$523$	27.1317	+	15.6645i	1.18639	+	0.684960i	0.228902	+	0.973449i	$0.426486\pi$
$524$	−2.79856	+	4.84725i	−0.122256	+	0.211753i
$525$	−19.6854	−	8.17822i	−0.859139	−	0.356927i
$526$	1.16231	+	0.671062i	0.0506793	+	0.0292597i
$527$	21.2527			0.925782
$528$	−9.08883	+	5.42261i	−0.395541	+	0.235989i
$529$	23.6628	+	40.9852i	1.02882	+	1.78197i
$530$	1.12596	−	1.95022i	0.0489085	−	0.0847120i
$531$	11.8332	+	6.38684i	0.513519	+	0.277165i
$532$	−4.14848	+	9.59503i	−0.179860	+	0.415997i
$533$	−4.97790	−	2.73435i	−0.215617	−	0.118438i
$534$	7.13246	−	0.102249i	0.308652	−	0.00442473i
$535$	−5.21779			−0.225585
$536$		−	10.3459i		−	0.446877i
$537$	9.68537	−	17.3451i	0.417954	−	0.748495i
$538$	−6.46592			−0.278765
$539$	−12.3364	+	40.9553i	−0.531368	+	1.76407i
$540$	1.41780	−	2.71939i	0.0610124	−	0.117024i
$541$	18.3221	−	10.5782i	0.787726	−	0.454794i	−0.0514351	−	0.998676i	$-0.516380\pi$
$541$	18.3221	−	10.5782i	0.787726	−	0.454794i	0.839162	+	0.543882i	$0.183046\pi$
$542$	−9.61794	−	16.6588i	−0.413126	−	0.715555i
$543$	−12.4165	+	22.2361i	−0.532842	+	0.954241i
$544$	−3.82336	+	6.62225i	−0.163925	+	0.283927i
$545$	−10.1510			−0.434822
$546$	2.48777	+	16.3344i	0.106467	+	0.699046i
$547$	−2.57133			−0.109942			−0.0549710	−	0.998488i	$-0.517507\pi$
$547$	−2.57133			−0.109942			−0.0549710	+	0.998488i	$0.517507\pi$
$548$	−10.5736	+	18.3140i	−0.451682	+	0.782336i
$549$	0.256924	−	0.158324i	0.0109653	−	0.00675712i
$550$	−14.2118	−	24.6155i	−0.605993	−	1.04961i
$551$	−5.49916	+	3.17494i	−0.234272	+	0.135257i
$552$	7.44209	+	12.4737i	0.316756	+	0.530914i
$553$	6.67261	−	15.4331i	0.283748	−	0.656282i
$554$	−11.7622			−0.499730
$555$	−1.98951	−	1.11093i	−0.0844500	−	0.0471563i
$556$		−	10.7885i		−	0.457535i
$557$	15.1289			0.641031			0.320515	−	0.947243i	$-0.396144\pi$
$557$	15.1289			0.641031			0.320515	+	0.947243i	$0.396144\pi$
$558$	3.96028	−	7.33742i	0.167652	−	0.310618i
$559$	20.9561	−	0.446305i	0.886347	−	0.0188767i
$560$	−1.25333	+	0.931429i	−0.0529628	+	0.0393600i
$561$	−1.16006	−	80.9212i	−0.0489777	−	3.41649i
$562$	−10.9975	+	19.0483i	−0.463902	+	0.803503i
$563$	−2.91404	−	5.04726i	−0.122812	−	0.212717i	0.798064	−	0.602573i	$-0.205858\pi$
$563$	−2.91404	−	5.04726i	−0.122812	−	0.212717i	−0.920876	+	0.389857i	$0.872525\pi$
$564$	5.06782	+	8.49415i	0.213394	+	0.357668i
$565$	9.22715			0.388189
$566$	11.1271	+	6.42423i	0.467706	+	0.270030i
$567$	−23.4569	+	4.09544i	−0.985098	+	0.171992i
$568$	−0.875991	+	1.51726i	−0.0367558	+	0.0636628i
$569$	−20.0259	−	11.5620i	−0.839530	−	0.484703i	0.0175747	−	0.999846i	$-0.494406\pi$
$569$	−20.0259	−	11.5620i	−0.839530	−	0.484703i	−0.857104	+	0.515143i	$0.827739\pi$
$570$	1.96915	−	3.52647i	0.0824788	−	0.147707i
$571$	−17.1315	+	29.6727i	−0.716933	+	1.24176i	0.245277	+	0.969453i	$0.421121\pi$
$571$	−17.1315	+	29.6727i	−0.716933	+	1.24176i	−0.962209	+	0.272311i	$0.912212\pi$
$572$	−10.6070	+	19.3100i	−0.443499	+	0.807392i
$573$	−9.16983	+	16.4218i	−0.383075	+	0.686032i
$574$	−3.34500	+	2.48589i	−0.139618	+	0.103759i
$575$	−33.7828	+	19.5045i	−1.40884	+	0.813394i
$576$	1.57386	+	2.55401i	0.0655774	+	0.106417i
$577$	7.81628	−	13.5382i	0.325396	−	0.563602i	−0.656196	−	0.754590i	$-0.727836\pi$
$577$	7.81628	−	13.5382i	0.325396	−	0.563602i	0.981592	+	0.190988i	$0.0611691\pi$
$578$	−20.7362	−	35.9161i	−0.862511	−	1.49391i
$579$	16.2503	−	29.1019i	0.675340	−	1.20944i
$580$	−0.948544			−0.0393861
$581$	19.2701	−	14.3209i	0.799460	−	0.594130i
$582$	0.140315	+	9.78784i	0.00581625	+	0.405719i
$583$	−20.1907	−	11.6571i	−0.836213	−	0.482788i
$584$	5.41081	−	9.37179i	0.223901	−	0.387807i
$585$	−0.318835	−	6.37607i	−0.0131822	−	0.263618i
$586$	−0.344829	+	0.199087i	−0.0142448	+	0.00822421i
$587$	25.9699	−	14.9937i	1.07189	−	0.618856i	0.143193	−	0.989695i	$-0.454263\pi$
$587$	25.9699	−	14.9937i	1.07189	−	0.618856i	0.928697	+	0.370838i	$0.120930\pi$
$588$	11.6581	+	3.33010i	0.480770	+	0.137331i
$589$	5.49059	−	9.50998i	0.226236	−	0.391852i
$590$	1.32273	+	2.29104i	0.0544560	+	0.0943205i
$591$	0.197283	+	13.7617i	0.00811514	+	0.566081i
$592$	1.93040	−	1.11452i	0.0793390	−	0.0458064i
$593$	12.0409	−	6.95181i	0.494460	−	0.285477i	−0.231963	−	0.972725i	$-0.574515\pi$
$593$	12.0409	−	6.95181i	0.494460	−	0.285477i	0.726423	+	0.687248i	$0.241181\pi$
$594$	−28.1539	−	14.6785i	−1.15517	−	0.602268i
$595$	−1.37623	−	11.8610i	−0.0564200	−	0.486256i
$596$	4.01109	+	6.94741i	0.164301	+	0.284577i
$597$	−32.5907	+	0.467210i	−1.33385	+	0.0191216i
$598$	26.5014	+	14.5572i	1.08372	+	0.595287i
$599$	5.85303	+	3.37925i	0.239148	+	0.138072i	0.614785	−	0.788695i	$-0.289243\pi$
$599$	5.85303	+	3.37925i	0.239148	+	0.138072i	−0.375637	+	0.926767i	$0.622576\pi$
$600$	−6.91903	+	4.12806i	−0.282468	+	0.168527i
$601$	−11.3845	+	6.57283i	−0.464382	+	0.268111i	−0.713885	−	0.700263i	$-0.753066\pi$
$601$	−11.3845	+	6.57283i	−0.464382	+	0.268111i	0.249503	+	0.968374i	$0.419733\pi$
$602$	6.10401	−	14.1180i	0.248781	−	0.575405i
$603$	26.4236	−	16.2831i	1.07605	−	0.663097i
$604$		−	8.78536i		−	0.357471i
$605$	13.4618	−	7.77217i	0.547300	−	0.315984i
$606$	17.5838	−	10.4909i	0.714291	−	0.426163i
$607$			30.5177i			1.23867i	0.785125	+	0.619337i	$0.212599\pi$
$607$			30.5177i			1.23867i	−0.785125	+	0.619337i	$0.787401\pi$
$608$	1.97552	+	3.42169i	0.0801178	+	0.138768i
$609$	4.47729	+	5.84765i	0.181429	+	0.236959i
$610$	0.0593724			0.00240392
$611$	18.0466	+	9.91295i	0.730085	+	0.401035i
$612$	−22.9307	+	0.657590i	−0.926920	+	0.0265815i
$613$		−	3.63396i		−	0.146774i	−0.997304	−	0.0733872i	$-0.976619\pi$
$613$		−	3.63396i		−	0.146774i	0.997304	−	0.0733872i	$-0.0233809\pi$
$614$	5.13689	−	8.89736i	0.207308	−	0.359068i
$615$	1.38285	−	0.825040i	0.0557618	−	0.0332688i
$616$	9.64312	+	12.9758i	0.388533	+	0.522809i
$617$	−17.7255	+	30.7015i	−0.713603	+	1.23600i	0.249893	+	0.968273i	$0.419605\pi$
$617$	−17.7255	+	30.7015i	−0.713603	+	1.23600i	−0.963496	+	0.267723i	$0.913729\pi$
$618$	3.67219	−	6.57636i	0.147717	−	0.264540i
$619$	−21.7709	+	37.7083i	−0.875046	+	1.51562i	−0.0183329	+	0.999832i	$0.505836\pi$
$619$	−21.7709	+	37.7083i	−0.875046	+	1.51562i	−0.856713	+	0.515793i	$0.827497\pi$
$620$	1.42060	−	0.820184i	0.0570527	−	0.0329394i
$621$	−20.1451	+	38.6390i	−0.808394	+	1.55053i
$622$	1.05163	+	1.82148i	0.0421666	+	0.0730347i
$623$	−1.25585	−	10.8235i	−0.0503144	−	0.433635i
$624$	5.51612	+	2.92787i	0.220822	+	0.117208i
$625$	−9.94811	−	17.2306i	−0.397924	−	0.689225i
$626$		−	10.9013i		−	0.435705i
$627$	−36.5097	−	20.3867i	−1.45806	−	0.814168i
$628$		−	2.88085i		−	0.114958i
$629$			17.0448i			0.679621i
$630$	−4.35144	−	1.73508i	−0.173366	−	0.0691271i
$631$	−21.1471	−	12.2093i	−0.841854	−	0.486045i	0.0160399	−	0.999871i	$-0.494894\pi$
$631$	−21.1471	−	12.2093i	−0.841854	−	0.486045i	−0.857894	+	0.513827i	$0.828227\pi$
$632$	−3.17751	−	5.50361i	−0.126395	−	0.218922i
$633$	0.0637380	+	4.44611i	0.00253336	+	0.176717i
$634$	−10.5453			−0.418809
$635$	3.05723	+	1.76509i	0.121322	+	0.0700455i
$636$	−3.22193	+	5.77000i	−0.127758	+	0.228795i
$637$	24.4397	−	6.30091i	0.968336	−	0.249651i
$638$			9.82032i			0.388790i
$639$	−5.25379	+	0.150664i	−0.207837	+	0.00596017i
$640$			0.590205i			0.0233299i
$641$	16.6886	−	9.63517i	0.659160	−	0.380566i	−0.132797	−	0.991143i	$-0.542396\pi$
$641$	16.6886	−	9.63517i	0.659160	−	0.380566i	0.791957	+	0.610577i	$0.209062\pi$
$642$	15.3109	−	0.219491i	0.604271	−	0.00866263i
$643$	−15.0498	+	26.0670i	−0.593505	+	1.02798i	0.400251	+	0.916405i	$0.368923\pi$
$643$	−15.0498	+	26.0670i	−0.593505	+	1.02798i	−0.993756	+	0.111575i	$0.964410\pi$
$644$	17.8082	−	13.2344i	0.701740	−	0.521508i
$645$	−2.89738	+	5.18878i	−0.114084	+	0.204308i
$646$	−30.2124			−1.18869
$647$	−28.6708			−1.12716			−0.563582	−	0.826060i	$-0.690577\pi$
$647$	−28.6708			−1.12716			−0.563582	+	0.826060i	$0.690577\pi$
$648$	−4.04594	+	8.03930i	−0.158939	+	0.315814i
$649$	23.7192	−	13.6943i	0.931061	−	0.537548i
$650$	−8.07473	+	14.7001i	−0.316717	+	0.576584i
$651$	−11.7618	−	4.88640i	−0.460982	−	0.191513i
$652$	−4.65862	+	2.68966i	−0.182446	+	0.105335i
$653$	23.9099	+	13.8044i	0.935666	+	0.540207i	0.888599	−	0.458685i	$-0.151679\pi$
$653$	23.9099	+	13.8044i	0.935666	+	0.540207i	0.0470671	+	0.998892i	$0.485013\pi$
$654$	29.7867	−	0.427013i	1.16475	−	0.0166975i
$655$	−2.86087	−	1.65172i	−0.111783	−	0.0645381i
$656$			1.57520i			0.0615011i
$657$	32.4515	−	0.930619i	1.26605	−	0.0363069i
$658$	12.1268	−	9.01218i	0.472751	−	0.351331i
$659$	28.9405	+	16.7088i	1.12736	+	0.650884i	0.943270	−	0.332025i	$-0.107732\pi$
$659$	28.9405	+	16.7088i	1.12736	+	0.650884i	0.184093	+	0.982909i	$0.441065\pi$
$660$	−3.20045	−	5.36427i	−0.124577	−	0.208804i
$661$	10.4140			0.405058			0.202529	−	0.979276i	$-0.435084\pi$
$661$	10.4140			0.405058			0.202529	+	0.979276i	$0.435084\pi$
$662$	12.6163	+	7.28403i	0.490347	+	0.283102i
$663$	−40.4792	+	25.3349i	−1.57208	+	0.983925i
$664$		−	9.07449i		−	0.352159i
$665$	−5.66303	−	2.44845i	−0.219603	−	0.0949470i
$666$	5.88467	+	3.17617i	0.228026	+	0.123074i
$667$	13.4776			0.521854
$668$	−14.1115	−	8.14728i	−0.545990	−	0.315228i
$669$	−0.0888446	−	6.19745i	−0.00343493	−	0.239607i
$670$	6.10622			0.235904
$671$		−	0.614686i		−	0.0237297i
$672$	3.63853	−	2.78587i	0.140360	−	0.107467i
$673$	−0.105584	−	0.182877i	−0.00406998	−	0.00704941i	0.863983	−	0.503521i	$-0.167962\pi$
$673$	−0.105584	−	0.182877i	−0.00406998	−	0.00704941i	−0.868053	+	0.496471i	$0.834629\pi$
$674$	15.5415	−	26.9187i	0.598636	−	1.03687i
$675$	−21.4327	−	11.1743i	−0.824944	−	0.430098i
$676$	12.9882	−	0.553475i	0.499547	−	0.0212875i
$677$	−11.7820	−	20.4071i	−0.452820	−	0.784307i	0.545740	−	0.837955i	$-0.316249\pi$
$677$	−11.7820	−	20.4071i	−0.452820	−	0.784307i	−0.998560	+	0.0536474i	$0.982915\pi$
$678$	−27.0758	+	0.388149i	−1.03984	+	0.0149068i
$679$	14.8531	−	1.72339i	0.570008	−	0.0661377i
$680$	−3.90849	−	2.25657i	−0.149884	−	0.0865353i
$681$	20.7373	−	0.297282i	0.794654	−	0.0113919i
$682$	−8.49140	−	14.7075i	−0.325153	−	0.563181i
$683$	−0.694198	−	1.20239i	−0.0265627	−	0.0460080i	0.852438	−	0.522828i	$-0.175123\pi$
$683$	−0.694198	−	1.20239i	−0.0265627	−	0.0460080i	−0.879001	+	0.476820i	$0.841790\pi$
$684$	−5.62986	+	10.4308i	−0.215263	+	0.398830i
$685$	−10.8090	−	6.24059i	−0.412991	−	0.238441i
$686$	3.26209	−	18.2307i	0.124547	−	0.696052i
$687$	−0.276832	−	19.3107i	−0.0105618	−	0.736749i
$688$	−2.90674	−	5.03462i	−0.110818	−	0.191943i
$689$	0.292917	+	13.7538i	0.0111593	+	0.523978i
$690$	−7.36202	+	4.39236i	−0.280267	+	0.167214i
$691$	13.1244	−	22.7321i	0.499276	−	0.864771i	−0.500724	−	0.865607i	$-0.666933\pi$
$691$	13.1244	−	22.7321i	0.499276	−	0.864771i	1.00000		0.000835740i	$0.000266024\pi$
$692$	−7.20003	−	12.4708i	−0.273704	−	0.474069i
$693$	−17.9633	+	45.0507i	−0.682371	+	1.71133i
$694$		−	24.6678i		−	0.936378i
$695$	6.36744			0.241531
$696$	2.78337	−	0.0399014i	0.105503	−	0.00151246i
$697$	−10.4313	−	6.02254i	−0.395115	−	0.228120i
$698$	−33.1601			−1.25513
$699$	27.6682	−	0.396642i	1.04651	−	0.0150024i
$700$	7.34099	+	9.87802i	0.277463	+	0.373354i
$701$		−	35.5148i		−	1.34137i	−0.741740	−	0.670687i	$-0.765999\pi$
$701$		−	35.5148i		−	1.34137i	0.741740	−	0.670687i	$-0.234001\pi$
$702$	1.20379	+	18.6963i	0.0454342	+	0.705646i
$703$	7.62708	+	4.40350i	0.287661	+	0.166081i
$704$	6.11042			0.230295
$705$	−5.01329	+	2.99105i	−0.188811	+	0.112649i
$706$	−12.5305	−	7.23450i	−0.471593	−	0.272274i
$707$	−18.6561	−	25.1036i	−0.701636	−	0.944120i
$708$	−3.97774	−	6.66709i	−0.149493	−	0.250564i
$709$			21.6989i			0.814918i	0.913224	+	0.407459i	$0.133585\pi$
$709$			21.6989i			0.814918i	−0.913224	+	0.407459i	$0.866415\pi$
$710$	−0.895494	−	0.517014i	−0.0336073	−	0.0194032i
$711$	9.05533	−	16.7773i	0.339601	−	0.629198i
$712$	−3.56660	−	2.05918i	−0.133664	−	0.0771709i
$713$	−20.1849	+	11.6537i	−0.755930	+	0.436436i
$714$	4.53730	+	34.7467i	0.169804	+	1.30036i
$715$	−11.3969	−	6.26028i	−0.426218	−	0.234121i
$716$	−9.93300	+	5.73482i	−0.371214	+	0.214320i
$717$	−26.7471	−	14.9354i	−0.998890	−	0.557773i
$718$	−14.0020			−0.522549
$719$	−29.4841			−1.09957			−0.549785	−	0.835306i	$-0.685290\pi$
$719$	−29.4841			−1.09957			−0.549785	+	0.835306i	$0.685290\pi$
$720$	−1.50739	+	0.928899i	−0.0561771	+	0.0346180i
$721$	−10.5608	−	4.56602i	−0.393303	−	0.170048i
$722$	1.69467	−	2.93526i	0.0630691	−	0.109239i
$723$	0.600010	+	41.8544i	0.0223146	+	1.55658i
$724$	12.7339	−	7.35194i	0.473253	−	0.273233i
$725$			7.47588i			0.277647i
$726$	−39.1748	+	23.3726i	−1.45391	+	0.867439i
$727$			7.96128i			0.295268i	0.989042	+	0.147634i	$0.0471657\pi$
$727$			7.96128i			0.295268i	−0.989042	+	0.147634i	$0.952834\pi$
$728$	3.59844	−	8.83466i	0.133367	−	0.327434i
$729$	−26.9002	+	2.31936i	−0.996304	+	0.0859021i
$730$	5.53127	+	3.19348i	0.204722	+	0.118196i
$731$	44.4541			1.64419
$732$	−0.174220	+	0.00249756i	−0.00643936	+	9.23125e-5i
$733$	23.6265	+	40.9223i	0.872665	+	1.51150i	0.859230	+	0.511590i	$0.170943\pi$
$733$	23.6265	+	40.9223i	0.872665	+	1.51150i	0.0134348	+	0.999910i	$0.495723\pi$
$734$	12.7593	+	7.36659i	0.470954	+	0.271906i
$735$	−1.96544	+	6.88064i	−0.0724964	+	0.253796i
$736$		−	8.38604i		−	0.309114i
$737$		−	63.2180i		−	2.32867i
$738$	−4.02307	+	2.47914i	−0.148091	+	0.0912582i
$739$		−	21.8654i		−	0.804332i	−0.915567	−	0.402166i	$-0.868258\pi$
$739$		−	21.8654i		−	0.804332i	0.915567	−	0.402166i	$-0.131742\pi$
$740$	0.657794	+	1.13933i	0.0241810	+	0.0418827i
$741$	0.878922	+	24.6585i	0.0322880	+	0.905854i
$742$	9.26586	+	4.00616i	0.340160	+	0.147071i
$743$	5.23639	+	9.06969i	0.192104	+	0.332735i	0.945947	−	0.324320i	$-0.105135\pi$
$743$	5.23639	+	9.06969i	0.192104	+	0.332735i	−0.753843	+	0.657055i	$0.771802\pi$
$744$	−4.13405	+	2.46647i	−0.151562	+	0.0904253i
$745$	−4.10040	+	2.36736i	−0.150227	+	0.0867335i
$746$	−7.91499	+	13.7092i	−0.289788	+	0.501928i
$747$	23.1763	−	14.2820i	0.847978	−	0.522550i
$748$	−23.3623	+	40.4647i	−0.854211	+	1.47954i
$749$	−2.69586	−	23.2342i	−0.0985045	−	0.848961i
$750$	−5.05525	−	8.47309i	−0.184592	−	0.309393i
$751$	−17.3269	+	30.0111i	−0.632268	+	1.09512i	0.354819	+	0.934935i	$0.384542\pi$
$751$	−17.3269	+	30.0111i	−0.632268	+	1.09512i	−0.987087	+	0.160185i	$0.948791\pi$
$752$		−	5.71062i		−	0.208245i
$753$	4.77111	−	2.84656i	0.173869	−	0.103734i
$754$	4.95548	−	3.00351i	0.180468	−	0.109382i
$755$	5.18516			0.188707
$756$	12.8417	+	4.90829i	0.467047	+	0.178513i
$757$	−12.1846	−	21.1043i	−0.442856	−	0.767050i	0.555044	−	0.831821i	$-0.312701\pi$
$757$	−12.1846	−	21.1043i	−0.442856	−	0.767050i	−0.997900	+	0.0647715i	$0.979368\pi$
$758$		−	12.9839i		−	0.471595i
$759$	45.4743	+	76.2193i	1.65061	+	2.76659i
$760$	−2.01950	+	1.16596i	−0.0732550	+	0.0422938i
$761$			6.69934i			0.242851i	0.992601	+	0.121426i	$0.0387466\pi$
$761$			6.69934i			0.242851i	−0.992601	+	0.121426i	$0.961253\pi$
$762$	−9.04525	−	5.05081i	−0.327675	−	0.182971i
$763$	−5.24469	−	45.2014i	−0.189871	−	1.63640i
$764$	9.40428	−	5.42957i	0.340235	−	0.196435i
$765$	−0.388113	−	13.5338i	−0.0140322	−	0.489317i
$766$	3.62494	+	2.09286i	0.130975	+	0.0756182i
$767$	−14.1648	−	7.78071i	−0.511461	−	0.280945i
$768$	−0.0248275	−	1.73187i	−0.000895887	−	0.0624936i
$769$	3.97005	+	6.87633i	0.143164	+	0.247967i	0.928686	−	0.370866i	$-0.120939\pi$
$769$	3.97005	+	6.87633i	0.143164	+	0.247967i	−0.785523	+	0.618833i	$0.787606\pi$
$770$	−7.65836	+	5.69142i	−0.275988	+	0.205104i
$771$	−1.76012	+	1.05013i	−0.0633890	+	0.0378194i
$772$	−16.6658	+	9.62200i	−0.599815	+	0.346304i
$773$	−12.9640	+	7.48477i	−0.466283	+	0.269208i	−0.714682	−	0.699449i	$-0.753429\pi$
$773$	−12.9640	+	7.48477i	−0.466283	+	0.269208i	0.248400	+	0.968658i	$0.420095\pi$
$774$	8.28368	−	15.3476i	0.297751	−	0.551659i
$775$	−6.46422	−	11.1964i	−0.232202	−	0.402185i
$776$	2.82580	−	4.89442i	0.101440	−	0.175700i
$777$	3.91893	−	9.43306i	0.140591	−	0.338409i
$778$	19.0201	−	10.9812i	0.681903	−	0.393697i
$779$	−5.38984	+	3.11182i	−0.193111	+	0.111493i
$780$	−1.72804	+	3.25564i	−0.0618738	+	0.116571i
$781$	−5.35267	+	9.27110i	−0.191534	+	0.331746i
$782$	55.5345	+	32.0629i	1.98591	+	1.14657i
$783$	4.48254	+	7.04595i	0.160193	+	0.251802i
$784$	−4.79511	−	5.09970i	−0.171254	−	0.182132i
$785$	1.70029			0.0606859
$786$	8.46429	+	4.72640i	0.301911	+	0.168585i
$787$	−8.80556	−	15.2517i	−0.313884	−	0.543664i	0.665315	−	0.746562i	$-0.268297\pi$
$787$	−8.80556	−	15.2517i	−0.313884	−	0.543664i	−0.979200	+	0.202899i	$0.934964\pi$
$788$	3.97307	−	6.88156i	0.141535	−	0.245145i
$789$	1.13334	−	2.02964i	0.0403478	−	0.0722571i
$790$	3.24826	−	1.87538i	0.115568	−	0.0667231i
$791$	4.76736	+	41.0875i	0.169508	+	1.46090i
$792$	9.61693	+	15.6061i	0.341723	+	0.554538i
$793$	−0.310179	+	0.188000i	−0.0110148	+	0.00667606i
$794$	16.5607	−	28.6839i	0.587716	−	1.01795i
$795$	−3.40548	−	1.90160i	−0.120780	−	0.0674427i
$796$	16.2970	+	9.40910i	0.577633	+	0.333497i
$797$	−0.00976904	+	0.0169205i	−0.000346037	+	0.000599354i	−0.866198	−	0.499700i	$-0.833443\pi$
$797$	−0.00976904	+	0.0169205i	−0.000346037	+	0.000599354i	0.865852	+	0.500300i	$0.166777\pi$
$798$	16.7204	+	6.94642i	0.591895	+	0.245901i
$799$	37.8172	+	21.8337i	1.33787	+	0.772422i
$800$	4.65166			0.164461
$801$	−0.354163	−	12.3500i	−0.0125137	−	0.436365i
$802$	−3.47187	−	6.01346i	−0.122596	−	0.212343i
$803$	33.0623	−	57.2656i	1.16674	−	2.02086i
$804$	−17.9179	+	0.256864i	−0.631914	+	0.00905891i
$805$	7.81100	+	10.5105i	0.275301	+	0.370445i
$806$	−4.82457	+	8.78314i	−0.169938	+	0.309373i
$807$	0.160533	+	11.1981i	0.00565102	+	0.394193i
$808$	−11.8216			−0.415881
$809$		−	6.51658i		−	0.229111i	−0.993417	−	0.114555i	$-0.963456\pi$
$809$		−	6.51658i		−	0.229111i	0.993417	−	0.114555i	$-0.0365443\pi$
$810$	−4.74483	−	2.38793i	−0.166716	−	0.0839034i
$811$	−7.01415			−0.246300			−0.123150	−	0.992388i	$-0.539300\pi$
$811$	−7.01415			−0.246300			−0.123150	+	0.992388i	$0.539300\pi$
$812$	−0.490081	−	4.22377i	−0.0171985	−	0.148225i
$813$	−28.6121	+	17.0707i	−1.00347	+	0.598694i
$814$	11.7956	−	6.81017i	0.413434	−	0.238696i
$815$	−1.58745	−	2.74954i	−0.0556059	−	0.0963122i
$816$	11.5638	+	6.45716i	0.404815	+	0.226046i
$817$	11.4846	−	19.8920i	0.401796	−	0.695932i
$818$	0.303545			0.0106132
$819$	28.2273	−	4.71405i	0.986340	−	0.164722i
$820$	−0.929688			−0.0324661
$821$	6.32403	−	10.9535i	0.220710	−	0.382281i	−0.734314	−	0.678810i	$-0.762496\pi$
$821$	6.32403	−	10.9535i	0.220710	−	0.382281i	0.955024	+	0.296529i	$0.0958292\pi$
$822$	31.9800	+	17.8574i	1.11543	+	0.622850i
$823$	21.7868	+	37.7359i	0.759441	+	1.31539i	0.943136	+	0.332408i	$0.107861\pi$
$823$	21.7868	+	37.7359i	0.759441	+	1.31539i	−0.183694	+	0.982983i	$0.558806\pi$
$824$	−3.76608	+	2.17435i	−0.131198	+	0.0757471i
$825$	−42.2781	+	25.2242i	−1.47194	+	0.878192i
$826$	−9.51834	+	7.07369i	−0.331185	+	0.246125i
$827$	25.1546			0.874712			0.437356	−	0.899288i	$-0.355915\pi$
$827$	25.1546			0.874712			0.437356	+	0.899288i	$0.355915\pi$
$828$	21.4180	−	13.1984i	0.744328	−	0.458677i
$829$			48.6579i			1.68996i	0.534799	+	0.844979i	$0.320387\pi$
$829$			48.6579i			1.68996i	−0.534799	+	0.844979i	$0.679613\pi$
$830$	5.35581			0.185903
$831$	0.292028	+	20.3707i	0.0101303	+	0.706652i
$832$	−1.86885	−	3.08341i	−0.0647908	−	0.106898i
$833$	52.1049	−	12.2564i	1.80533	−	0.424660i
$834$	−18.6844	+	0.267853i	−0.646986	+	0.00927498i
$835$	4.80856	−	8.32867i	0.166407	−	0.288226i
$836$	12.0712	+	20.9080i	0.417492	+	0.723118i
$837$	−12.8058	−	6.67653i	−0.442634	−	0.230775i
$838$	−5.71451			−0.197404
$839$	−18.3244	−	10.5796i	−0.632630	−	0.365249i	0.149140	−	0.988816i	$-0.452350\pi$
$839$	−18.3244	−	10.5796i	−0.632630	−	0.365249i	−0.781770	+	0.623567i	$0.785683\pi$
$840$	1.64423	+	2.14748i	0.0567314	+	0.0740951i
$841$	−13.2085	+	22.8779i	−0.455467	+	0.788892i
$842$	8.01539	+	4.62769i	0.276229	+	0.159481i
$843$	33.2622	+	18.5734i	1.14561	+	0.639701i
$844$	1.28361	−	2.22329i	0.0441838	−	0.0765286i
$845$	0.326664	+	7.66570i	0.0112376	+	0.263708i
$846$	14.5850	−	8.98770i	0.501442	−	0.309004i
$847$	41.5639	+	55.9283i	1.42815	+	1.92172i
$848$	3.30431	−	1.90774i	0.113470	−	0.0655121i
$849$	10.8497	−	19.4302i	0.372360	−	0.666843i
$850$	−17.7850	+	30.8045i	−0.610019	+	1.05658i
$851$	−9.34639	−	16.1884i	−0.320390	−	0.554932i
$852$	2.64945	+	1.47944i	0.0907687	+	0.0506846i
$853$	−53.6426			−1.83669			−0.918344	−	0.395782i	$-0.870473\pi$
$853$	−53.6426			−1.83669			−0.918344	+	0.395782i	$0.870473\pi$
$854$	0.0306758	+	0.264379i	0.00104970	+	0.00904687i
$855$	−6.15628	−	3.32277i	−0.210540	−	0.113636i
$856$	−7.65622	−	4.42032i	−0.261684	−	0.151083i
$857$	12.3135	−	21.3277i	0.420623	−	0.728540i	−0.575378	−	0.817888i	$-0.695145\pi$
$857$	12.3135	−	21.3277i	0.420623	−	0.728540i	0.996000	+	0.0893479i	$0.0284783\pi$
$858$	33.7058	+	17.8905i	1.15070	+	0.610771i
$859$	1.35293	−	0.781117i	0.0461615	−	0.0266514i	−0.476742	−	0.879043i	$-0.658182\pi$
$859$	1.35293	−	0.781117i	0.0461615	−	0.0266514i	0.522903	+	0.852392i	$0.324849\pi$
$860$	2.97146	−	1.71557i	0.101326	−	0.0585005i
$861$	4.38829	+	5.73140i	0.149552	+	0.195326i
$862$	5.05283	−	8.75176i	0.172100	−	0.298086i
$863$	13.1821	+	22.8320i	0.448723	+	0.777210i	0.998303	−	0.0582303i	$-0.0185458\pi$
$863$	13.1821	+	22.8320i	0.448723	+	0.777210i	−0.549581	+	0.835441i	$0.685212\pi$
$864$	4.38415	−	2.78913i	0.149152	−	0.0948882i
$865$	7.36033	−	4.24949i	0.250259	−	0.144487i
$866$	32.8655	−	18.9749i	1.11682	−	0.644794i
$867$	−61.6873	+	36.8041i	−2.09501	+	1.24993i
$868$	4.38617	+	5.90202i	0.148876	+	0.200328i
$869$	−19.4159	−	33.6294i	−0.658640	−	1.14080i
$870$	0.0235500	+	1.64276i	0.000798420	+	0.0556947i
$871$	−31.9007	+	19.3350i	−1.08092	+	0.655143i
$872$	−14.8949	−	8.59957i	−0.504405	−	0.291218i
$873$	16.9478	−	0.486016i	0.573597	−	0.0164492i
$874$	28.6945	−	16.5668i	0.970605	−	0.560379i
$875$	−12.0967	+	8.98983i	−0.408943	+	0.303912i
$876$	−16.3651	−	9.13815i	−0.552925	−	0.308749i
$877$		−	23.3161i		−	0.787328i	−0.919254	−	0.393664i	$-0.871207\pi$
$877$		−	23.3161i		−	0.787328i	0.919254	−	0.393664i	$-0.128793\pi$
$878$	−24.6369	+	14.2241i	−0.831456	+	0.480042i
$879$	0.353355	+	0.592257i	0.0119184	+	0.0199763i
$880$			3.60640i			0.121572i
$881$	7.67467	+	13.2929i	0.258566	+	0.447850i	0.965858	−	0.259072i	$-0.0834167\pi$
$881$	7.67467	+	13.2929i	0.258566	+	0.447850i	−0.707292	+	0.706922i	$0.750083\pi$
$882$	5.47787	−	20.2730i	0.184449	−	0.682626i
$883$	34.2457			1.15246			0.576230	−	0.817287i	$-0.304523\pi$
$883$	34.2457			1.15246			0.576230	+	0.817287i	$0.304523\pi$
$884$	27.5644	−	0.587044i	0.927091	−	0.0197444i
$885$	3.93495	−	2.34768i	0.132272	−	0.0789165i
$886$			21.6680i			0.727952i
$887$	−21.8340	+	37.8177i	−0.733116	+	1.26979i	0.222430	+	0.974949i	$0.428601\pi$
$887$	−21.8340	+	37.8177i	−0.733116	+	1.26979i	−0.955545	+	0.294845i	$0.904732\pi$
$888$	−1.97813	−	3.31554i	−0.0663817	−	0.111262i
$889$	−6.28019	+	14.5255i	−0.210631	+	0.487169i
$890$	1.21534	−	2.10502i	0.0407381	−	0.0705605i
$891$	−24.7224	+	49.1235i	−0.828231	+	1.64570i
$892$	−1.78923	+	3.09905i	−0.0599080	+	0.103764i
$893$	19.5400	−	11.2814i	0.653881	−	0.377518i
$894$	11.9324	−	7.11919i	0.399081	−	0.238101i
$895$	−3.38472	−	5.86250i	−0.113139	−	0.195962i
$896$	−2.62812	+	0.304939i	−0.0877993	+	0.0101873i
$897$	24.5532	−	46.2584i	0.819808	−	1.54452i
$898$	6.23704	+	10.8029i	0.208133	+	0.360496i
$899$			4.46677i			0.148975i
$900$	7.32105	+	11.8804i	0.244035	+	0.396013i
$901$			29.1759i			0.971992i
$902$			9.62510i			0.320481i
$903$	−24.6021	−	10.2209i	−0.818706	−	0.340129i
$904$	13.5393	+	7.81690i	0.450310	+	0.259986i
$905$	4.33915	+	7.51563i	0.144238	+	0.249828i
$906$	−15.2151	+	0.218119i	−0.505489	+	0.00724651i
$907$	23.3018			0.773723			0.386861	−	0.922138i	$-0.373559\pi$
$907$	23.3018			0.773723			0.386861	+	0.922138i	$0.373559\pi$
$908$	−10.3697	−	5.98695i	−0.344131	−	0.198684i
$909$	−18.6055	−	30.1924i	−0.617104	−	1.00142i
$910$	5.21426	+	2.12382i	0.172851	+	0.0704039i
$911$			48.4817i			1.60627i	0.595796	+	0.803136i	$0.296837\pi$
$911$			48.4817i			1.60627i	−0.595796	+	0.803136i	$0.703163\pi$
$912$	5.87689	−	3.50630i	0.194603	−	0.116105i
$913$		−	55.4489i		−	1.83509i
$914$	−8.30703	+	4.79607i	−0.274772	+	0.158640i
$915$	−0.00147407	−	0.102825i	−4.87313e−5	−	0.00339931i
$916$	−5.57509	+	9.65634i	−0.184206	+	0.319054i
$917$	5.87683	−	13.5925i	0.194070	−	0.448865i
$918$	1.70818	+	39.6968i	0.0563782	+	1.31019i
$919$	2.50142			0.0825141			0.0412570	−	0.999149i	$-0.486864\pi$
$919$	2.50142			0.0825141			0.0412570	+	0.999149i	$0.486864\pi$
$920$	4.94948			0.163180
$921$	−15.5366	−	8.67554i	−0.511949	−	0.285869i
$922$	4.17780	−	2.41206i	0.137589	−	0.0794368i
$923$	6.31543	−	0.134501i	0.207875	−	0.00442715i
$924$	22.2330	−	17.0228i	0.731411	−	0.560010i
$925$	8.97957	−	5.18436i	0.295246	−	0.170461i
$926$	2.67382	+	1.54373i	0.0878673	+	0.0507302i
$927$	−11.4806	−	6.19650i	−0.377072	−	0.203520i
$928$	−1.39183	−	0.803572i	−0.0456890	−	0.0263785i
$929$			29.5977i			0.971069i	0.874217	+	0.485535i	$0.161375\pi$
$929$			29.5977i			0.971069i	−0.874217	+	0.485535i	$0.838625\pi$
$930$	−1.45572	−	2.43994i	−0.0477351	−	0.0800086i
$931$	7.97681	−	26.4819i	0.261429	−	0.867910i
$932$	−13.8355	−	7.98795i	−0.453198	−	0.261654i
$933$	3.12846	−	1.86651i	0.102421	−	0.0611070i
$934$	−8.32473			−0.272394
$935$	−23.8825	−	13.7886i	−0.781041	−	0.450934i
$936$	4.93374	−	9.62591i	0.161264	−	0.314633i
$937$			27.0251i			0.882873i	0.897293	+	0.441436i	$0.145531\pi$
$937$			27.0251i			0.882873i	−0.897293	+	0.441436i	$0.854469\pi$
$938$	3.15488	+	27.1904i	0.103011	+	0.887797i
$939$	−18.8797	+	0.270654i	−0.616117	+	0.00883244i
$940$	3.37043			0.109931
$941$	−32.5113	−	18.7704i	−1.05984	−	0.611898i	−0.134451	−	0.990920i	$-0.542927\pi$
$941$	−32.5113	−	18.7704i	−1.05984	−	0.611898i	−0.925387	+	0.379022i	$0.876260\pi$
$942$	−4.98926	+	0.0715243i	−0.162559	+	0.00233039i
$943$	13.2097			0.430165
$944$			4.48228i			0.145886i
$945$	−2.89690	+	7.57922i	−0.0942361	+	0.246552i
$946$	−17.7614	−	30.7636i	−0.577473	−	1.00021i
$947$	−15.7164	+	27.2216i	−0.510714	+	0.884583i	0.489209	+	0.872167i	$0.337286\pi$
$947$	−15.7164	+	27.2216i	−0.510714	+	0.884583i	−0.999923	+	0.0124164i	$0.996048\pi$
$948$	−9.45267	+	5.63969i	−0.307008	+	0.183169i
$949$	−39.0090	+	0.830782i	−1.26629	+	0.0269683i
$950$	9.18943	+	15.9166i	0.298144	+	0.516401i
$951$	0.261815	+	18.2632i	0.00848993	+	0.592224i
$952$	8.02886	−	18.5700i	0.260217	−	0.601856i
$953$	−47.5409	−	27.4478i	−1.54000	−	0.889120i	−0.998838	−	0.0482023i	$-0.984651\pi$
$953$	−47.5409	−	27.4478i	−1.54000	−	0.889120i	−0.541163	−	0.840918i	$-0.682016\pi$
$954$	10.0729	+	5.43672i	0.326122	+	0.176020i
$955$	3.20456	+	5.55045i	0.103697	+	0.179608i
$956$	8.84344	+	15.3173i	0.286017	+	0.495396i
$957$	17.0075	−	0.243814i	0.549776	−	0.00788140i
$958$	−10.4595	−	6.03880i	−0.337931	−	0.195105i
$959$	22.2040	−	51.3557i	0.717005	−	1.65836i
$960$	1.02216	−	0.0146533i	0.0329901	−	0.000472934i
$961$	11.6377	+	20.1571i	0.375409	+	0.650228i
$962$	−7.04415	−	3.86934i	−0.227112	−	0.124753i
$963$	−0.760262	−	26.5110i	−0.0244991	−	0.854305i
$964$	12.0836	−	20.9293i	0.389185	−	0.674088i
$965$	−5.67895	−	9.83623i	−0.182812	−	0.316640i
$966$	−23.3624	−	30.5129i	−0.751673	−	0.981736i
$967$		−	11.5256i		−	0.370639i	−0.982678	−	0.185320i	$-0.940668\pi$
$967$		−	11.5256i		−	0.370639i	0.982678	−	0.185320i	$-0.0593321\pi$
$968$	26.3372			0.846510
$969$	0.750101	+	52.3241i	0.0240967	+	1.68089i
$970$	2.88871	+	1.66780i	0.0927509	+	0.0535498i
$971$	49.9796			1.60392			0.801962	−	0.597376i	$-0.203790\pi$
$971$	49.9796			1.60392			0.801962	+	0.597376i	$0.203790\pi$
$972$	14.0235	+	6.80745i	0.449804	+	0.218349i
$973$	3.28985	+	28.3535i	0.105468	+	0.908973i
$974$			5.59837i			0.179383i
$975$	25.6591	+	13.6194i	0.821749	+	0.436171i
$976$	0.0871190	+	0.0502982i	0.00278861	+	0.00161000i
$977$	−4.37679			−0.140026			−0.0700129	−	0.997546i	$-0.522304\pi$
$977$	−4.37679			−0.140026			−0.0700129	+	0.997546i	$0.522304\pi$
$978$	4.77381	+	8.00136i	0.152649	+	0.255855i
$979$	−21.7934	−	12.5824i	−0.696520	−	0.402136i
$980$	3.00987	−	2.83009i	0.0961467	−	0.0904041i
$981$	−1.47906	−	51.5762i	−0.0472228	−	1.64670i
$982$			0.521341i			0.0166367i
$983$	−22.4448	−	12.9585i	−0.715879	−	0.413313i	0.0973553	−	0.995250i	$-0.468962\pi$
$983$	−22.4448	−	12.9585i	−0.715879	−	0.413313i	−0.813234	+	0.581937i	$0.802295\pi$
$984$	2.72804	−	0.0391082i	0.0869667	−	0.00124673i
$985$	4.06153	+	2.34492i	0.129411	+	0.0747155i
$986$	10.6429	−	6.14469i	0.338940	−	0.195687i
$987$	−15.9090	−	20.7783i	−0.506390	−	0.661380i
$988$	6.85852	−	12.4860i	0.218199	−	0.397231i
$989$	−42.2205	+	24.3760i	−1.34254	+	0.775113i
$990$	−9.21078	+	5.67596i	−0.292738	+	0.180394i
$991$	23.1574			0.735620			0.367810	−	0.929901i	$-0.380108\pi$
$991$	23.1574			0.735620			0.367810	+	0.929901i	$0.380108\pi$
$992$	2.77932			0.0882435
$993$	12.3018	−	22.0307i	0.390385	−	0.699123i
$994$	1.83954	−	4.25467i	0.0583466	−	0.134950i
$995$	−5.55329	+	9.61859i	−0.176051	+	0.304930i
$996$	−15.7159	+	0.225297i	−0.497976	+	0.00713882i
$997$	8.34585	−	4.81848i	0.264316	−	0.152603i	−0.361986	−	0.932184i	$-0.617901\pi$
$997$	8.34585	−	4.81848i	0.264316	−	0.152603i	0.626302	+	0.779581i	$0.284568\pi$
$998$			33.4405i			1.05854i
$999$	5.35462	−	10.2704i	0.169413	−	0.324940i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bn.e.101.13	yes	34
3.2	odd	2		546.2.bn.f.101.5	yes	34
7.5	odd	6		546.2.bi.f.257.14	yes	34
13.4	even	6		546.2.bi.e.17.9	✓	34
21.5	even	6		546.2.bi.e.257.9	yes	34
39.17	odd	6		546.2.bi.f.17.14	yes	34
91.82	odd	6		546.2.bn.f.173.5	yes	34
273.173	even	6	inner	546.2.bn.e.173.13	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.9	✓	34	13.4	even	6
546.2.bi.e.257.9	yes	34	21.5	even	6
546.2.bi.f.17.14	yes	34	39.17	odd	6
546.2.bi.f.257.14	yes	34	7.5	odd	6
546.2.bn.e.101.13	yes	34	1.1	even	1	trivial
546.2.bn.e.173.13	yes	34	273.173	even	6	inner
546.2.bn.f.101.5	yes	34	3.2	odd	2
546.2.bn.f.173.5	yes	34	91.82	odd	6

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.bn (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.51226 + 0.844435i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.511132 - 0.295102i) q^{5} +(-1.48743 + 0.887438i) q^{6} +(1.57814 + 2.12355i) q^{7} +1.00000 q^{8} +(1.57386 + 2.55401i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.51226 + 0.844435i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.511132 - 0.295102i) q^{5} +(-1.48743 + 0.887438i) q^{6} +(1.57814 + 2.12355i) q^{7} +1.00000 q^{8} +(1.57386 + 2.55401i) q^{9} +0.590205i q^{10} +6.11042 q^{11} +(-0.0248275 - 1.73187i) q^{12} +(-1.86885 - 3.08341i) q^{13} +(-2.62812 + 0.304939i) q^{14} +(1.02216 - 0.0146533i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.82336 - 6.62225i) q^{17} +(-2.99877 + 0.0859963i) q^{18} -3.95103 q^{19} +(-0.511132 - 0.295102i) q^{20} +(0.593366 + 4.54400i) q^{21} +(-3.05521 + 5.29178i) q^{22} +(7.26252 + 4.19302i) q^{23} +(1.51226 + 0.844435i) q^{24} +(-2.32583 + 4.02845i) q^{25} +(3.60473 - 0.0767706i) q^{26} +(0.223387 + 5.19135i) q^{27} +(1.04997 - 2.42849i) q^{28} +(1.39183 - 0.803572i) q^{29} +(-0.498390 + 0.892543i) q^{30} +(-1.38966 + 2.40696i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(9.24054 + 5.15985i) q^{33} +7.64672 q^{34} +(1.43330 + 0.619700i) q^{35} +(1.42491 - 2.64001i) q^{36} +(-1.93040 - 1.11452i) q^{37} +(1.97552 - 3.42169i) q^{38} +(-0.222454 - 6.24103i) q^{39} +(0.511132 - 0.295102i) q^{40} +(1.36416 - 0.787598i) q^{41} +(-4.23190 - 1.75813i) q^{42} +(-2.90674 + 5.03462i) q^{43} +(-3.05521 - 5.29178i) q^{44} +(1.55814 + 0.840988i) q^{45} +(-7.26252 + 4.19302i) q^{46} +(-4.94554 + 2.85531i) q^{47} +(-1.48743 + 0.887438i) q^{48} +(-2.01892 + 6.70253i) q^{49} +(-2.32583 - 4.02845i) q^{50} +(-0.189849 - 13.2431i) q^{51} +(-1.73588 + 3.16018i) q^{52} +(-3.30431 - 1.90774i) q^{53} +(-4.60753 - 2.40222i) q^{54} +(3.12323 - 1.80320i) q^{55} +(1.57814 + 2.12355i) q^{56} +(-5.97499 - 3.33639i) q^{57} +1.60714i q^{58} +(3.88177 - 2.24114i) q^{59} +(-0.523770 - 0.877889i) q^{60} -0.100596i q^{61} +(-1.38966 - 2.40696i) q^{62} +(-2.93979 + 7.37276i) q^{63} +1.00000 q^{64} +(-1.86515 - 1.02453i) q^{65} +(-9.08883 + 5.42261i) q^{66} -10.3459i q^{67} +(-3.82336 + 6.62225i) q^{68} +(7.44209 + 12.4737i) q^{69} +(-1.25333 + 0.931429i) q^{70} +(-0.875991 + 1.51726i) q^{71} +(1.57386 + 2.55401i) q^{72} +(5.41081 - 9.37179i) q^{73} +(1.93040 - 1.11452i) q^{74} +(-6.91903 + 4.12806i) q^{75} +(1.97552 + 3.42169i) q^{76} +(9.64312 + 12.9758i) q^{77} +(5.51612 + 2.92787i) q^{78} +(-3.17751 - 5.50361i) q^{79} +0.590205i q^{80} +(-4.04594 + 8.03930i) q^{81} +1.57520i q^{82} -9.07449i q^{83} +(3.63853 - 2.78587i) q^{84} +(-3.90849 - 2.25657i) q^{85} +(-2.90674 - 5.03462i) q^{86} +(2.78337 - 0.0399014i) q^{87} +6.11042 q^{88} +(-3.56660 - 2.05918i) q^{89} +(-1.50739 + 0.928899i) q^{90} +(3.59844 - 8.83466i) q^{91} -8.38604i q^{92} +(-4.13405 + 2.46647i) q^{93} -5.71062i q^{94} +(-2.01950 + 1.16596i) q^{95} +(-0.0248275 - 1.73187i) q^{96} +(2.82580 - 4.89442i) q^{97} +(-4.79511 - 5.09970i) q^{98} +(9.61693 + 15.6061i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9}+O(q^{10}) \) 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9	\( 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9} - 18 q^{11} + 3 q^{12} - 8 q^{13} - 4 q^{14} - 17 q^{15} - 17 q^{16} + 6 q^{17} - 11 q^{18} - 10 q^{19} - 9 q^{20} - 4 q^{21} + 9 q^{22} + 6 q^{23} + 3 q^{24} + 16 q^{25} + 13 q^{26} + 18 q^{27} - q^{28} + 27 q^{29} + 13 q^{30} + q^{31} - 17 q^{32} + 21 q^{33} - 12 q^{34} - 3 q^{35} + 4 q^{36} + 6 q^{37} + 5 q^{38} + 20 q^{39} + 9 q^{40} + 3 q^{41} + 20 q^{42} - 3 q^{43} + 9 q^{44} - 6 q^{46} - 27 q^{47} - 6 q^{48} - 5 q^{49} + 16 q^{50} + 24 q^{51} - 5 q^{52} + 21 q^{53} - 18 q^{54} + 57 q^{55} + 5 q^{56} - 17 q^{57} - 6 q^{59} + 4 q^{60} + q^{62} - 21 q^{63} + 34 q^{64} + 33 q^{65} - 21 q^{66} + 6 q^{68} - 30 q^{69} + 3 q^{70} - 15 q^{71} + 7 q^{72} + 19 q^{73} - 6 q^{74} - 63 q^{75} + 5 q^{76} - 9 q^{77} - 10 q^{78} - 9 q^{79} - 5 q^{81} - 16 q^{84} - 42 q^{85} - 3 q^{86} - 75 q^{87} - 18 q^{88} - 18 q^{89} - 9 q^{90} - 27 q^{91} + 25 q^{93} - 3 q^{95} + 3 q^{96} - 19 q^{97} + 7 q^{98} - 27 q^{99}+O(q^{100}) \) 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9 - 18 * q^11 + 3 * q^12 - 8 * q^13 - 4 * q^14 - 17 * q^15 - 17 * q^16 + 6 * q^17 - 11 * q^18 - 10 * q^19 - 9 * q^20 - 4 * q^21 + 9 * q^22 + 6 * q^23 + 3 * q^24 + 16 * q^25 + 13 * q^26 + 18 * q^27 - q^28 + 27 * q^29 + 13 * q^30 + q^31 - 17 * q^32 + 21 * q^33 - 12 * q^34 - 3 * q^35 + 4 * q^36 + 6 * q^37 + 5 * q^38 + 20 * q^39 + 9 * q^40 + 3 * q^41 + 20 * q^42 - 3 * q^43 + 9 * q^44 - 6 * q^46 - 27 * q^47 - 6 * q^48 - 5 * q^49 + 16 * q^50 + 24 * q^51 - 5 * q^52 + 21 * q^53 - 18 * q^54 + 57 * q^55 + 5 * q^56 - 17 * q^57 - 6 * q^59 + 4 * q^60 + q^62 - 21 * q^63 + 34 * q^64 + 33 * q^65 - 21 * q^66 + 6 * q^68 - 30 * q^69 + 3 * q^70 - 15 * q^71 + 7 * q^72 + 19 * q^73 - 6 * q^74 - 63 * q^75 + 5 * q^76 - 9 * q^77 - 10 * q^78 - 9 * q^79 - 5 * q^81 - 16 * q^84 - 42 * q^85 - 3 * q^86 - 75 * q^87 - 18 * q^88 - 18 * q^89 - 9 * q^90 - 27 * q^91 + 25 * q^93 - 3 * q^95 + 3 * q^96 - 19 * q^97 + 7 * q^98 - 27 * q^99

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