LMFDB - Embedded newform 546.2.bn.f.101.5

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			101.5
Character	$\chi$	$=$	546.101
Dual form			546.2.bn.f.173.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.51226 + 0.844435i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.511132 + 0.295102i) q^{5} +(-0.0248275 + 1.73187i) q^{6} +(1.57814 + 2.12355i) q^{7} -1.00000 q^{8} +(1.57386 - 2.55401i) q^{9} +O(q^{10})$	\(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} +(-0.0248275 + 1.73187i) 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} +(1.48743 + 0.887438i) q^{12} +(-1.86885 - 3.08341i) q^{13} +(2.62812 - 0.304939i) q^{14} +(0.523770 - 0.877889i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.82336 + 6.62225i) q^{17} +(-1.42491 - 2.64001i) q^{18} -3.95103 q^{19} +(0.511132 + 0.295102i) q^{20} +(-4.17976 - 1.87872i) 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} +(-2.99877 - 0.0859963i) q^{36} +(-1.93040 - 1.11452i) q^{37} +(-1.97552 + 3.42169i) q^{38} +(5.42993 + 3.08479i) q^{39} +(0.511132 - 0.295102i) q^{40} +(-1.36416 + 0.787598i) q^{41} +(-3.71690 + 2.68042i) q^{42} +(-2.90674 + 5.03462i) q^{43} +(3.05521 + 5.29178i) q^{44} +(-0.0507554 + 1.76989i) q^{45} +(-7.26252 + 4.19302i) q^{46} +(4.94554 - 2.85531i) q^{47} +(0.0248275 - 1.73187i) q^{48} +(-2.01892 + 6.70253i) q^{49} +(2.32583 + 4.02845i) q^{50} +(-11.3740 - 6.78599i) q^{51} +(-1.73588 + 3.16018i) q^{52} +(3.30431 + 1.90774i) q^{53} +(4.38415 + 2.78913i) 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} +(-1.02216 - 0.0146533i) q^{60} -0.100596i q^{61} +(1.38966 + 2.40696i) q^{62} +(7.90734 - 0.688433i) q^{63} +1.00000 q^{64} +(1.86515 + 1.02453i) q^{65} +(0.151707 - 10.5825i) q^{66} -10.3459i q^{67} +(3.82336 - 6.62225i) q^{68} +(14.5236 + 0.208205i) 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} +(0.115489 - 8.05608i) q^{75} +(1.97552 + 3.42169i) q^{76} +(-9.64312 - 12.9758i) q^{77} +(5.38647 - 3.16006i) 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} +(0.462866 + 4.55914i) q^{84} +(-3.90849 - 2.25657i) q^{85} +(2.90674 + 5.03462i) q^{86} +(1.42624 - 2.39052i) 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} +(0.0690037 - 4.81343i) q^{93} -5.71062i q^{94} +(2.01950 - 1.16596i) q^{95} +(-1.48743 - 0.887438i) 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} + 3 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 + 3 * 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} + 3 q^{6} + 5 q^{7} - 34 q^{8} + 7 q^{9} + 18 q^{11} + 6 q^{12} - 8 q^{13} + 4 q^{14} - 4 q^{15} - 17 q^{16} - 6 q^{17} - 4 q^{18} - 10 q^{19} + 9 q^{20} + 7 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} - 11 q^{36} + 6 q^{37} - 5 q^{38} - 2 q^{39} + 9 q^{40} - 3 q^{41} + 8 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} - 6 q^{46} + 27 q^{47} - 3 q^{48} - 5 q^{49} - 16 q^{50} - 36 q^{51} - 5 q^{52} - 21 q^{53} + 57 q^{55} - 5 q^{56} + 17 q^{57} + 6 q^{59} + 17 q^{60} - q^{62} + 34 q^{64} - 33 q^{65} - 6 q^{68} - 42 q^{69} + 3 q^{70} + 15 q^{71} - 7 q^{72} + 19 q^{73} + 6 q^{74} - 9 q^{75} + 5 q^{76} + 9 q^{77} - 7 q^{78} - 9 q^{79} - 5 q^{81} + q^{84} - 42 q^{85} + 3 q^{86} + 6 q^{87} - 18 q^{88} + 18 q^{89} + 9 q^{90} - 27 q^{91} + 8 q^{93} + 3 q^{95} - 6 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 + 3 * q^6 + 5 * q^7 - 34 * q^8 + 7 * q^9 + 18 * q^11 + 6 * q^12 - 8 * q^13 + 4 * q^14 - 4 * q^15 - 17 * q^16 - 6 * q^17 - 4 * q^18 - 10 * q^19 + 9 * q^20 + 7 * 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 - 11 * q^36 + 6 * q^37 - 5 * q^38 - 2 * q^39 + 9 * q^40 - 3 * q^41 + 8 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 - 6 * q^46 + 27 * q^47 - 3 * q^48 - 5 * q^49 - 16 * q^50 - 36 * q^51 - 5 * q^52 - 21 * q^53 + 57 * q^55 - 5 * q^56 + 17 * q^57 + 6 * q^59 + 17 * q^60 - q^62 + 34 * q^64 - 33 * q^65 - 6 * q^68 - 42 * q^69 + 3 * q^70 + 15 * q^71 - 7 * q^72 + 19 * q^73 + 6 * q^74 - 9 * q^75 + 5 * q^76 + 9 * q^77 - 7 * q^78 - 9 * q^79 - 5 * q^81 + q^84 - 42 * q^85 + 3 * q^86 + 6 * q^87 - 18 * q^88 + 18 * q^89 + 9 * q^90 - 27 * q^91 + 8 * q^93 + 3 * q^95 - 6 * 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	−0.609919	−	0.792464i	$-0.708798\pi$
$5$	−0.511132	+	0.295102i	−0.228585	+	0.131974i	0.381334	+	0.924437i	$0.375465\pi$
$6$	−0.0248275	+	1.73187i	−0.0101358	+	0.707034i
$7$	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	$-0.872773\pi$
$11$	−6.11042			−1.84236			−0.921180	+	0.389137i	$0.872773\pi$
$12$	1.48743	+	0.887438i	0.429385	+	0.256181i
$13$	−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
$15$	0.523770	−	0.877889i	0.135237	−	0.226670i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.82336	+	6.62225i	0.927301	+	1.60613i	0.787818	+	0.615908i	$0.211211\pi$
$17$	3.82336	+	6.62225i	0.927301	+	1.60613i	0.139483	+	0.990224i	$0.455456\pi$
$18$	−1.42491	−	2.64001i	−0.335854	−	0.622256i
$19$	−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
$21$	−4.17976	−	1.87872i	−0.912099	−	0.409969i
$22$	−3.05521	+	5.29178i	−0.651373	+	1.12821i
$23$	−7.26252	−	4.19302i	−1.51434	−	0.874305i	−0.999859	−	0.0168038i	$-0.994651\pi$
$23$	−7.26252	−	4.19302i	−1.51434	−	0.874305i	−0.514482	−	0.857501i	$-0.672016\pi$
$24$	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	−0.623630	−	0.781720i	$-0.714343\pi$
$29$	−1.39183	+	0.803572i	−0.258456	+	0.149220i	0.365174	+	0.930939i	$0.381009\pi$
$30$	−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
$36$	−2.99877	−	0.0859963i	−0.499795	−	0.0143327i
$37$	−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
$39$	5.42993	+	3.08479i	0.869484	+	0.493961i
$40$	0.511132	−	0.295102i	0.0808171	−	0.0466598i
$41$	−1.36416	+	0.787598i	−0.213046	+	0.123002i	−0.602726	−	0.797948i	$-0.705919\pi$
$41$	−1.36416	+	0.787598i	−0.213046	+	0.123002i	0.389680	+	0.920950i	$0.372586\pi$
$42$	−3.71690	+	2.68042i	−0.573530	+	0.413598i
$43$	−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
$45$	−0.0507554	+	1.76989i	−0.00756617	+	0.263839i
$46$	−7.26252	+	4.19302i	−1.07080	+	0.618227i
$47$	4.94554	−	2.85531i	0.721381	−	0.416489i	−0.0938798	−	0.995584i	$-0.529927\pi$
$47$	4.94554	−	2.85531i	0.721381	−	0.416489i	0.815261	+	0.579094i	$0.196594\pi$
$48$	0.0248275	−	1.73187i	0.00358355	−	0.249974i
$49$	−2.01892	+	6.70253i	−0.288417	+	0.957505i
$50$	2.32583	+	4.02845i	0.328922	+	0.569709i
$51$	−11.3740	−	6.78599i	−1.59268	−	0.950228i
$52$	−1.73588	+	3.16018i	−0.240723	+	0.438238i
$53$	3.30431	+	1.90774i	0.453881	+	0.262049i	0.709468	−	0.704738i	$-0.248935\pi$
$53$	3.30431	+	1.90774i	0.453881	+	0.262049i	−0.255587	+	0.966786i	$0.582269\pi$
$54$	4.38415	+	2.78913i	0.596607	+	0.379553i
$55$	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	−0.730926	−	0.682457i	$-0.760911\pi$
$59$	−3.88177	+	2.24114i	−0.505363	+	0.291772i	0.225562	+	0.974229i	$0.427578\pi$
$60$	−1.02216	−	0.0146533i	−0.131960	−	0.00189174i
$61$		−	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
$63$	7.90734	−	0.688433i	0.996231	−	0.0867344i
$64$	1.00000			0.125000
$65$	1.86515	+	1.02453i	0.231344	+	0.127077i
$66$	0.151707	−	10.5825i	0.0186738	−	1.30261i
$67$		−	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
$69$	14.5236	+	0.208205i	1.74843	+	0.0250649i
$70$	−1.25333	+	0.931429i	−0.149801	+	0.111327i
$71$	0.875991	−	1.51726i	0.103961	−	0.180066i	−0.809352	−	0.587324i	$-0.800182\pi$
$71$	0.875991	−	1.51726i	0.103961	−	0.180066i	0.913313	+	0.407258i	$0.133515\pi$
$72$	−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
$75$	0.115489	−	8.05608i	0.0133356	−	0.930236i
$76$	1.97552	+	3.42169i	0.226607	+	0.392495i
$77$	−9.64312	−	12.9758i	−1.09894	−	1.47873i
$78$	5.38647	−	3.16006i	0.609897	−	0.357806i
$79$	−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	$0.165942\pi$
$83$			9.07449i			0.996055i	−0.867161	+	0.498027i	$0.834058\pi$
$84$	0.462866	+	4.55914i	0.0505029	+	0.497443i
$85$	−3.90849	−	2.25657i	−0.423935	−	0.244759i
$86$	2.90674	+	5.03462i	0.313442	+	0.542897i
$87$	1.42624	−	2.39052i	0.152909	−	0.256290i
$88$	6.11042			0.651373
$89$	3.56660	+	2.05918i	0.378059	+	0.218272i	0.676973	−	0.736008i	$-0.263291\pi$
$89$	3.56660	+	2.05918i	0.378059	+	0.218272i	−0.298915	+	0.954280i	$0.596625\pi$
$90$	1.50739	+	0.928899i	0.158893	+	0.0979145i
$91$	3.59844	−	8.83466i	0.377219	−	0.926124i
$92$			8.38604i			0.874305i
$93$	0.0690037	−	4.81343i	0.00715535	−	0.499129i
$94$		−	5.71062i		−	0.589005i
$95$	2.01950	−	1.16596i	0.207196	−	0.119625i
$96$	−1.48743	−	0.887438i	−0.151810	−	0.0905737i
$97$	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	$-0.299859\pi$
$101$	11.8216			1.17629			0.588144	+	0.808756i	$0.299859\pi$
$102$	−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
$105$	2.69083	−	0.273186i	0.262598	−	0.0266602i
$106$	3.30431	−	1.90774i	0.320943	−	0.185296i
$107$	7.65622	+	4.42032i	0.740154	+	0.427328i	0.822125	−	0.569306i	$-0.192788\pi$
$107$	7.65622	+	4.42032i	0.740154	+	0.427328i	−0.0819711	+	0.996635i	$0.526122\pi$
$108$	4.60753	−	2.40222i	0.443360	−	0.231153i
$109$	−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
$111$	3.86041	+	0.0553415i	0.366414	+	0.00525278i
$112$	−2.62812	+	0.304939i	−0.248334	+	0.0288141i
$113$	−13.5393	−	7.81690i	−1.27367	−	0.735353i	−0.297992	−	0.954568i	$-0.596317\pi$
$113$	−13.5393	−	7.81690i	−1.27367	−	0.735353i	−0.975676	+	0.219216i	$0.929650\pi$
$114$	0.0980944	−	6.84269i	0.00918739	−	0.640876i
$115$	4.94948			0.461541
$116$	1.39183	+	0.803572i	0.129228	+	0.0746098i
$117$	−10.8164	−	0.0797765i	−0.999973	−	0.00737534i
$118$			4.48228i			0.412627i
$119$	−8.02886	+	18.5700i	−0.736005	+	1.70231i
$120$	−0.523770	+	0.877889i	−0.0478134	+	0.0801400i
$121$	26.3372			2.39429
$122$	−0.0871190	−	0.0502982i	−0.00788738	−	0.00455378i
$123$	1.39789	−	2.34300i	0.126043	−	0.211261i
$124$	2.77932			0.249590
$125$		−	5.69645i		−	0.509506i
$126$	3.35747	−	7.19218i	0.299107	−	0.640730i
$127$	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
$129$	0.144334	−	10.0682i	0.0127079	−	0.886457i
$130$	1.81984	−	1.10301i	0.159611	−	0.0967400i
$131$	2.79856	+	4.84725i	0.244511	+	0.423506i	0.961994	−	0.273070i	$-0.0880392\pi$
$131$	2.79856	+	4.84725i	0.244511	+	0.423506i	−0.717483	+	0.696576i	$0.754706\pi$
$132$	−9.08883	−	5.42261i	−0.791081	−	0.471978i
$133$	−6.23530	−	8.39021i	−0.540669	−	0.727523i
$134$	−8.95985	−	5.17297i	−0.774013	−	0.446877i
$135$	−1.41780	−	2.71939i	−0.122025	−	0.234048i
$136$	−3.82336	−	6.62225i	−0.327850	−	0.567854i
$137$	10.5736	+	18.3140i	0.903363	+	1.56467i	0.823099	+	0.567898i	$0.192243\pi$
$137$	10.5736	+	18.3140i	0.903363	+	1.56467i	0.0802641	+	0.996774i	$0.474424\pi$
$138$	7.44209	−	12.4737i	0.633513	−	1.06183i
$139$	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
$141$	−5.06782	+	8.49415i	−0.426787	+	0.715337i
$142$	−0.875991	−	1.51726i	−0.0735115	−	0.127326i
$143$	11.4195	+	18.8409i	0.954944	+	1.57555i
$144$	1.42491	+	2.64001i	0.118742	+	0.220001i
$145$	0.474272	−	0.821463i	0.0393861	−	0.0682188i
$146$	−5.41081	−	9.37179i	−0.447801	−	0.775615i
$147$	−2.60673	−	11.8408i	−0.214999	−	0.976614i
$148$			2.22904i			0.183226i
$149$	8.02218			0.657203			0.328601	−	0.944469i	$-0.393423\pi$
$149$	8.02218			0.657203			0.328601	+	0.944469i	$0.393423\pi$
$150$	−6.91903	−	4.12806i	−0.564936	−	0.337054i
$151$	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
$153$	22.9307	+	0.657590i	1.85384	+	0.0531630i
$154$	−16.0589	+	1.86331i	−1.29406	+	0.150149i
$155$		−	1.64037i		−	0.131758i
$156$	−0.0434603	−	6.24485i	−0.00347961	−	0.499988i
$157$	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
$159$	−6.60793	−	0.0947291i	−0.524043	−	0.00751251i
$160$	−0.511132	−	0.295102i	−0.0404086	−	0.0233299i
$161$	−2.55723	−	22.0395i	−0.201538	−	1.73696i
$162$	−8.98521	−	0.515766i	−0.705945	−	0.0405224i
$163$		−	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
$165$	−3.20045	+	5.36427i	−0.249155	+	0.417608i
$166$	7.85874	+	4.53725i	0.609957	+	0.352159i
$167$	−14.1115	+	8.14728i	−1.09198	+	0.630455i	−0.934103	−	0.357003i	$-0.883798\pi$
$167$	−14.1115	+	8.14728i	−1.09198	+	0.630455i	−0.157878	+	0.987459i	$0.550465\pi$
$168$	4.17976	+	1.87872i	0.322476	+	0.144946i
$169$	−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	$-0.684385\pi$
$173$	−14.4001			−1.09482			−0.547408	+	0.836866i	$0.684385\pi$
$174$	−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
$177$	3.97774	−	6.66709i	0.298986	−	0.501129i
$178$	3.56660	−	2.05918i	0.267328	−	0.154342i
$179$			11.4696i			0.857281i	0.903475	+	0.428641i	$0.141007\pi$
$179$			11.4696i			0.857281i	−0.903475	+	0.428641i	$0.858993\pi$
$180$	1.55814	−	0.840988i	0.116137	−	0.0626835i
$181$			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
$186$	−4.13405	−	2.46647i	−0.303123	−	0.180851i
$187$	−23.3623	−	40.4647i	−1.70842	−	2.95907i
$188$	−4.94554	−	2.85531i	−0.360690	−	0.208245i
$189$	−11.3766	+	7.71833i	−0.827527	+	0.561426i
$190$		−	2.33192i		−	0.169175i
$191$		−	10.8591i		−	0.785739i	−0.919594	−	0.392870i	$-0.871482\pi$
$191$		−	10.8591i		−	0.785739i	0.919594	−	0.392870i	$-0.128518\pi$
$192$	−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
$195$	−3.68574	+	0.0256505i	−0.263941	+	0.00183687i
$196$	6.81402	−	1.60283i	0.486716	−	0.114488i
$197$	−3.97307	−	6.88156i	−0.283070	−	0.490291i	0.689070	−	0.724695i	$-0.258019\pi$
$197$	−3.97307	−	6.88156i	−0.283070	−	0.490291i	−0.972139	+	0.234404i	$0.924686\pi$
$198$	8.70679	+	16.1315i	0.618764	+	1.14642i
$199$	−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
$204$	−0.189849	+	13.2431i	−0.0132921	+	0.927206i
$205$	0.464844	−	0.805133i	0.0324661	−	0.0562330i
$206$			4.34870i			0.302988i
$207$	−22.1392	+	11.9493i	−1.53878	+	0.830537i
$208$	3.60473	−	0.0767706i	0.249943	−	0.00532309i
$209$	24.1425			1.66997
$210$	1.10883	−	2.46692i	0.0765163	−	0.170233i
$211$	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
$213$	−0.0434974	+	3.03421i	−0.00298039	+	0.207901i
$214$	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
$219$	−0.268674	+	18.7417i	−0.0181553	+	1.26644i
$220$	−3.12323	−	1.80320i	−0.210568	−	0.121572i
$221$	13.2738	−	24.1650i	0.892893	−	1.62551i
$222$	1.97813	−	3.31554i	0.132763	−	0.222524i
$223$	−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
$225$	6.62819	+	12.2804i	0.441879	+	0.818694i
$226$	−13.5393	+	7.81690i	−0.900619	+	0.519973i
$227$	−10.3697	+	5.98695i	−0.688261	+	0.397368i	−0.802960	−	0.596033i	$-0.796743\pi$
$227$	−10.3697	+	5.98695i	−0.688261	+	0.397368i	0.114699	+	0.993400i	$0.463410\pi$
$228$	−5.87689	−	3.50630i	−0.389207	−	0.232210i
$229$	−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
$231$	25.5401	+	11.4797i	1.68042	+	0.755311i
$232$	1.39183	−	0.803572i	0.0913779	−	0.0527571i
$233$	−13.8355	+	7.98795i	−0.906396	+	0.523308i	−0.879270	−	0.476324i	$-0.841969\pi$
$233$	−13.8355	+	7.98795i	−0.906396	+	0.523308i	−0.0271263	+	0.999632i	$0.508636\pi$
$234$	−5.47727	+	9.32735i	−0.358060	+	0.609748i
$235$	−1.68522	+	2.91888i	−0.109931	+	0.190407i
$236$	3.88177	+	2.24114i	0.252682	+	0.145886i
$237$	9.45267	+	5.63969i	0.614017	+	0.366337i
$238$	12.0676	+	16.2382i	0.782229	+	1.05257i
$239$	17.6869			1.14407			0.572034	−	0.820230i	$-0.306154\pi$
$239$	17.6869			1.14407			0.572034	+	0.820230i	$0.306154\pi$
$240$	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	−0.912192	−	0.409763i	$-0.865612\pi$
$251$	−1.60381	+	2.77787i	−0.101231	+	0.175338i	0.810961	+	0.585100i	$0.198945\pi$
$252$	−4.54987	−	6.50374i	−0.286615	−	0.409697i
$253$	44.3770	+	25.6211i	2.78996	+	1.61078i
$254$	5.98128			0.375299
$255$	7.81617	+	0.112050i	0.489467	+	0.00701684i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.591663	−	1.02479i	0.0369069	−	0.0639246i	−0.846982	−	0.531622i	$-0.821583\pi$
$257$	0.591663	−	1.02479i	0.0369069	−	0.0639246i	0.883889	+	0.467697i	$0.154916\pi$
$258$	−8.64716	−	5.15910i	−0.538349	−	0.321192i
$259$	−0.679720	−	5.85817i	−0.0422358	−	0.364009i
$260$	−0.0453104	−	2.12753i	−0.00281003	−	0.131944i
$261$	−0.138208	+	4.81945i	−0.00855489	+	0.298316i
$262$	5.59712			0.345791
$263$			1.34212i			0.0827589i	0.999144	+	0.0413794i	$0.0131752\pi$
$263$			1.34212i			0.0827589i	−0.999144	+	0.0413794i	$0.986825\pi$
$264$	−9.24054	+	5.15985i	−0.568716	+	0.317567i
$265$	−2.25192			−0.138334
$266$	−10.3838	+	1.20482i	−0.636671	+	0.0738726i
$267$	−7.13246	−	0.102249i	−0.436500	−	0.00625751i
$268$	−8.95985	+	5.17297i	−0.547310	+	0.315990i
$269$	−3.23296	−	5.59965i	−0.197117	−	0.341417i	0.750476	−	0.660898i	$-0.229825\pi$
$269$	−3.23296	−	5.59965i	−0.197117	−	0.341417i	−0.947592	+	0.319482i	$0.896491\pi$
$270$	−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
$273$	2.01852	+	16.3990i	0.122166	+	0.992510i
$274$	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
$279$	3.96028	+	7.33742i	0.237096	+	0.439280i
$280$	1.43330	+	0.619700i	0.0856564	+	0.0370342i
$281$	−21.9950			−1.31211			−0.656057	−	0.754711i	$-0.727777\pi$
$281$	−21.9950			−1.31211			−0.656057	+	0.754711i	$0.727777\pi$
$282$	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
$285$	−2.06943	+	3.46857i	−0.122583	+	0.205460i
$286$	22.0264	−	0.469101i	1.30245	−	0.0277385i
$287$	−3.82534	−	1.65392i	−0.225803	−	0.0976275i
$288$	2.99877	+	0.0859963i	0.176704	+	0.00506738i
$289$	−20.7362	+	35.9161i	−1.21977	+	2.11271i
$290$	−0.474272	−	0.821463i	−0.0278502	−	0.0482380i
$291$	−0.140315	+	9.78784i	−0.00822542	+	0.573773i
$292$	−10.8216			−0.633287
$293$	−0.344829	−	0.199087i	−0.0201451	−	0.0116308i	0.489894	−	0.871782i	$-0.337036\pi$
$293$	−0.344829	−	0.199087i	−0.0201451	−	0.0116308i	−0.510039	+	0.860151i	$0.670369\pi$
$294$	−11.5578	−	3.66292i	−0.674065	−	0.213626i
$295$	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
$309$	3.85920	−	6.46839i	0.219542	−	0.367974i
$310$	−1.42060	−	0.820184i	−0.0806847	−	0.0465833i
$311$	−1.05163	+	1.82148i	−0.0596325	+	0.103287i	−0.894300	−	0.447467i	$-0.852326\pi$
$311$	−1.05163	+	1.82148i	−0.0596325	+	0.103287i	0.834668	+	0.550754i	$0.185660\pi$
$312$	−5.42993	−	3.08479i	−0.307409	−	0.174642i
$313$	−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
$315$	−3.83854	+	2.68536i	−0.216277	+	0.151303i
$316$	−3.17751	+	5.50361i	−0.178749	+	0.309602i
$317$	−5.27267	−	9.13253i	−0.296143	−	0.512934i	0.679107	−	0.734039i	$-0.262367\pi$
$317$	−5.27267	−	9.13253i	−0.296143	−	0.512934i	−0.975250	+	0.221105i	$0.929034\pi$
$318$	−3.38600	+	5.67527i	−0.189878	+	0.318254i
$319$	8.50465	−	4.91016i	0.476169	−	0.274916i
$320$	−0.511132	+	0.295102i	−0.0285732	+	0.0164967i
$321$	−15.3109	−	0.219491i	−0.854569	−	0.0122508i
$322$	−20.3654	−	8.80513i	−1.13492	−	0.490691i
$323$	−15.1062	−	26.1647i	−0.840533	−	1.45585i
$324$	−4.93927	+	7.52354i	−0.274404	+	0.417974i
$325$	16.7680	−	0.357111i	0.930121	−	0.0198089i
$326$	−4.65862	−	2.68966i	−0.258017	−	0.148966i
$327$	29.7867	+	0.427013i	1.64721	+	0.0236138i
$328$	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
$333$	−5.88467	+	3.17617i	−0.322478	+	0.174053i
$334$			16.2946i			0.891599i
$335$	3.05311	+	5.28815i	0.166809	+	0.288922i
$336$	3.71690	−	2.68042i	0.202773	−	0.146229i
$337$	−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
$339$	27.0758	+	0.388149i	1.47055	+	0.0210814i
$340$			4.51313i			0.244759i
$341$	8.49140	−	14.7075i	0.459835	−	0.796458i
$342$	5.62986	+	10.4308i	0.304428	+	0.564030i
$343$	−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	0.198713	−	0.980058i	$-0.436324\pi$
$347$	21.3630	−	12.3339i	1.14682	−	0.662119i	0.948111	+	0.317938i	$0.102991\pi$
$348$	−2.78337	−	0.0399014i	−0.149204	−	0.00213894i
$349$	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
$351$	16.4245	−	9.01307i	0.876676	−	0.481082i
$352$	−3.05521	−	5.29178i	−0.162843	−	0.282053i
$353$		−	14.4690i		−	0.770108i	−0.922894	−	0.385054i	$-0.874183\pi$
$353$		−	14.4690i		−	0.770108i	0.922894	−	0.385054i	$-0.125817\pi$
$354$	−3.78499	−	6.77837i	−0.201170	−	0.360266i
$355$			1.03403i			0.0548805i
$356$		−	4.11835i		−	0.218272i
$357$	−3.53941	−	34.8625i	−0.187325	−	1.84512i
$358$	9.93300	+	5.73482i	0.524975	+	0.303095i
$359$	−7.00098	−	12.1261i	−0.369498	−	0.639989i	0.619989	−	0.784610i	$-0.287137\pi$
$359$	−7.00098	−	12.1261i	−0.369498	−	0.639989i	−0.989487	+	0.144621i	$0.953804\pi$
$360$	0.0507554	−	1.76989i	0.00267505	−	0.0932812i
$361$	−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
$366$	0.174220	+	0.00249756i	0.00910663	+	0.000130550i
$367$		−	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
$369$	−0.135461	+	4.72364i	−0.00705182	+	0.245903i
$370$	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
$378$	0.995959	+	13.7116i	0.0512266	+	0.705249i
$379$	−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
$381$	−8.89675	−	5.30802i	−0.455794	−	0.271938i
$382$	−9.40428	−	5.42957i	−0.481165	−	0.277801i
$383$			4.18573i			0.213881i	0.994265	+	0.106940i	$0.0341054\pi$
$383$			4.18573i			0.213881i	−0.994265	+	0.106940i	$0.965895\pi$
$384$	−0.0248275	+	1.73187i	−0.00126698	+	0.0883793i
$385$	8.75809	+	3.78663i	0.446354	+	0.192984i
$386$	−16.6658	−	9.62200i	−0.848267	−	0.489747i
$387$	8.28368	+	15.3476i	0.421083	+	0.780164i
$388$	−5.65159			−0.286916
$389$	19.0201	+	10.9812i	0.964356	+	0.556771i	0.897511	−	0.440992i	$-0.145373\pi$
$389$	19.0201	+	10.9812i	0.964356	+	0.556771i	0.0668451	+	0.997763i	$0.478707\pi$
$390$	−1.82066	+	3.20477i	−0.0921925	+	0.162280i
$391$		−	64.1257i		−	3.24298i
$392$	2.01892	−	6.70253i	0.101971	−	0.338529i
$393$	−8.32533	−	4.96709i	−0.419957	−	0.250557i
$394$	−7.94614			−0.400321
$395$	3.24826	+	1.87538i	0.163438	+	0.0943608i
$396$	18.3237	+	0.525473i	0.920802	+	0.0264060i
$397$	−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
$399$	16.5144	+	7.42287i	0.826753	+	0.371608i
$400$	−2.32583	−	4.02845i	−0.116291	−	0.201423i
$401$	3.47187	−	6.01346i	0.173377	−	0.300298i	−0.766221	−	0.642577i	$-0.777865\pi$
$401$	3.47187	−	6.01346i	0.173377	−	0.300298i	0.939598	+	0.342279i	$0.111199\pi$
$402$	17.9179	+	0.256864i	0.893662	+	0.0128112i
$403$	10.0187	−	0.213370i	0.499067	−	0.0106287i
$404$	−5.91078	−	10.2378i	−0.294072	−	0.509348i
$405$	4.44043	+	2.91518i	0.220647	+	0.144857i
$406$	−3.41285	+	2.53631i	−0.169377	+	0.125875i
$407$	11.7956	+	6.81017i	0.584684	+	0.337568i
$408$	11.3740	+	6.78599i	0.563096	+	0.335957i
$409$	−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
$411$	−31.4550	−	18.7668i	−1.55156	−	0.925699i
$412$	3.76608	+	2.17435i	0.185542	+	0.107123i
$413$	−10.8852	−	4.70628i	−0.535624	−	0.231581i
$414$	−0.721168	+	25.1478i	−0.0354435	+	1.23595i
$415$	−2.67790	−	4.63827i	−0.131453	−	0.227684i
$416$	1.73588	−	3.16018i	0.0851086	−	0.154940i
$417$	−18.6844	−	0.267853i	−0.914977	−	0.0131168i
$418$	12.0712	−	20.9080i	0.590423	−	1.02264i
$419$	−2.85725	−	4.94891i	−0.139586	−	0.241770i	0.787754	−	0.615990i	$-0.211244\pi$
$419$	−2.85725	−	4.94891i	−0.139586	−	0.241770i	−0.927340	+	0.374220i	$0.877911\pi$
$420$	−1.58200	−	2.19373i	−0.0771936	−	0.107043i
$421$		−	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
$423$	0.491092	−	17.1248i	0.0238777	−	0.832637i
$424$	−3.30431	−	1.90774i	−0.160471	−	0.0926481i
$425$	−35.5699			−1.72540
$426$	2.60595	+	1.55477i	0.126259	+	0.0753291i
$427$	0.213621	−	0.158756i	0.0103379	−	0.00768272i
$428$		−	8.84064i		−	0.427328i
$429$	−33.1791	−	18.8493i	−1.60190	−	0.910054i
$430$	−2.97146	−	1.71557i	−0.143296	−	0.0827322i
$431$	10.1057			0.486773			0.243386	−	0.969929i	$-0.421742\pi$
$431$	10.1057			0.486773			0.243386	+	0.969929i	$0.421742\pi$
$432$	−4.38415	−	2.78913i	−0.210932	−	0.134192i
$433$	−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
$435$	−0.0235500	+	1.64276i	−0.00112914	+	0.0787642i
$436$			17.1991i			0.823690i
$437$	28.6945	+	16.5668i	1.37264	+	0.792495i
$438$	16.0964	+	9.60351i	0.769116	+	0.458873i
$439$	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
$441$	13.9409	+	15.7052i	0.663850	+	0.747866i
$442$	−14.2906	−	23.5779i	−0.679734	−	1.12149i
$443$	−18.7651	+	10.8340i	−0.891555	+	0.514740i	−0.874451	−	0.485114i	$-0.838778\pi$
$443$	−18.7651	+	10.8340i	−0.891555	+	0.514740i	−0.0171043	+	0.999854i	$0.505445\pi$
$444$	−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	−0.974832	−	0.222940i	$-0.928434\pi$
$449$	−6.23704	+	10.8029i	−0.294344	+	0.509819i	0.680488	+	0.732759i	$0.261768\pi$
$450$	13.9492	+	0.400025i	0.657574	+	0.0188574i
$451$	8.33558	−	4.81255i	0.392507	−	0.226614i
$452$			15.6338i			0.735353i
$453$	−15.2151	−	0.218119i	−0.714869	−	0.0102481i
$454$			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
$459$	−35.2325	+	18.3691i	−1.64451	+	0.857395i
$460$	−2.47474	−	4.28638i	−0.115385	−	0.199853i
$461$	4.17780	+	2.41206i	0.194580	+	0.112341i	0.594125	−	0.804373i	$-0.297499\pi$
$461$	4.17780	+	2.41206i	0.194580	+	0.112341i	−0.399545	+	0.916714i	$0.630832\pi$
$462$	22.7118	−	16.3785i	1.05665	−	0.761997i
$463$		−	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	0.753504	−	0.657444i	$-0.228362\pi$
$467$	−4.16237	−	7.20943i	−0.192611	−	0.333613i	−0.946115	+	0.323831i	$0.895029\pi$
$468$	5.33909	+	9.40713i	0.246800	+	0.434845i
$469$	21.9701	−	16.3274i	1.01449	−	0.753929i
$470$	1.68522	+	2.91888i	0.0777332	+	0.134638i
$471$	−4.98926	−	0.0715243i	−0.229893	−	0.00329567i
$472$	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
$477$	10.0729	−	5.43672i	0.461207	−	0.248930i
$478$	8.84344	−	15.3173i	0.404489	−	0.700596i
$479$		−	12.0776i		−	0.551839i	−0.961181	−	0.275920i	$-0.911018\pi$
$479$		−	12.0776i		−	0.551839i	0.961181	−	0.275920i	$-0.0889824\pi$
$480$	1.02216	+	0.0146533i	0.0466550	+	0.000668830i
$481$	0.171124	+	8.03508i	0.00780260	+	0.366368i
$482$	24.1671			1.10078
$483$	22.4781	+	31.1700i	1.02279	+	1.41829i
$484$	−13.1686	−	22.8087i	−0.598573	−	1.03676i
$485$			3.33560i			0.151462i
$486$	14.0235	−	6.80745i	0.636119	−	0.308792i
$487$	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	−0.510153	−	0.860084i	$-0.670411\pi$
$491$	−0.451495	+	0.260671i	−0.0203757	+	0.0117639i	0.489778	+	0.871847i	$0.337078\pi$
$492$	−2.72804	−	0.0391082i	−0.122989	−	0.00176314i
$493$	−10.6429	−	6.14469i	−0.479333	−	0.276743i
$494$	14.2424	−	0.303323i	0.640797	−	0.0136472i
$495$	0.310137	−	10.8147i	0.0139396	−	0.486087i
$496$	−1.38966	−	2.40696i	−0.0623976	−	0.108076i
$497$	4.60442	−	0.534248i	0.206536	−	0.0239643i
$498$	−15.7159	−	0.225297i	−0.704245	−	0.0100958i
$499$	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
$501$	14.4604	−	24.2370i	0.646043	−	1.08283i
$502$	1.60381	+	2.77787i	0.0715814	+	0.123983i
$503$	9.16509	−	15.8744i	0.408651	−	0.707805i	−0.586088	−	0.810248i	$-0.699333\pi$
$503$	9.16509	−	15.8744i	0.408651	−	0.707805i	0.994739	+	0.102443i	$0.0326659\pi$
$504$	−7.90734	+	0.688433i	−0.352221	+	0.0306653i
$505$	−6.04238	+	3.48857i	−0.268882	+	0.155239i
$506$	44.3770	−	25.6211i	1.97280	−	1.13900i
$507$	−0.636084	−	22.5077i	−0.0282495	−	0.999601i
$508$	2.99064	−	5.17994i	0.132688	−	0.229823i
$509$	−30.2332	−	17.4552i	−1.34006	−	0.773686i	−0.353248	−	0.935530i	$-0.614923\pi$
$509$	−30.2332	−	17.4552i	−1.34006	−	0.773686i	−0.986816	+	0.161843i	$0.948256\pi$
$510$	4.00512	−	6.71298i	0.177350	−	0.297256i
$511$	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	$0.401559\pi$
$521$	−15.3561	+	26.5976i	−0.672763	+	1.16526i	−0.977117	+	0.212701i	$0.931774\pi$
$522$	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
$525$	17.2897	−	12.4684i	0.754586	−	0.544166i
$526$	1.16231	+	0.671062i	0.0506793	+	0.0292597i
$527$	−21.2527			−0.925782
$528$	−0.151707	+	10.5825i	−0.00660219	+	0.460543i
$529$	23.6628	+	40.9852i	1.02882	+	1.78197i
$530$	−1.12596	+	1.95022i	−0.0489085	+	0.0847120i
$531$	−0.385459	+	13.4413i	−0.0167275	+	0.583303i
$532$	−4.14848	+	9.59503i	−0.179860	+	0.415997i
$533$	4.97790	+	2.73435i	0.215617	+	0.118438i
$534$	−3.65478	+	6.12577i	−0.158158	+	0.265088i
$535$	−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
$540$	−1.64616	+	2.58754i	−0.0708394	+	0.111350i
$541$	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
$546$	15.2112	+	6.45139i	0.650978	+	0.276094i
$547$	−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
$552$	−14.5236	−	0.208205i	−0.618164	−	0.00886178i
$553$	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	$-0.603856\pi$
$557$	−15.1289			−0.641031			−0.320515	+	0.947243i	$0.603856\pi$
$558$	8.33453	+	0.239011i	0.352829	+	0.0101182i
$559$	20.9561	−	0.446305i	0.886347	−	0.0188767i
$560$	1.25333	−	0.931429i	0.0529628	−	0.0393600i
$561$	69.4998	+	41.4652i	2.93428	+	1.75066i
$562$	−10.9975	+	19.0483i	−0.463902	+	0.803503i
$563$	2.91404	+	5.04726i	0.122812	+	0.212717i	0.920876	−	0.389857i	$-0.127475\pi$
$563$	2.91404	+	5.04726i	0.122812	+	0.212717i	−0.798064	+	0.602573i	$0.794142\pi$
$564$	9.89006	+	0.141781i	0.416447	+	0.00597004i
$565$	9.22715			0.388189
$566$	−11.1271	−	6.42423i	−0.467706	−	0.270030i
$567$	10.6868	−	21.2789i	0.448802	−	0.893631i
$568$	−0.875991	+	1.51726i	−0.0367558	+	0.0636628i
$569$	20.0259	+	11.5620i	0.839530	+	0.484703i	0.857104	−	0.515143i	$-0.172261\pi$
$569$	20.0259	+	11.5620i	0.839530	+	0.484703i	−0.0175747	+	0.999846i	$0.505594\pi$
$570$	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
$582$	8.40636	+	5.01544i	0.348455	+	0.207897i
$583$	−20.1907	−	11.6571i	−0.836213	−	0.482788i
$584$	−5.41081	+	9.37179i	−0.223901	+	0.387807i
$585$	5.55213	−	3.15116i	0.229552	−	0.130284i
$586$	−0.344829	+	0.199087i	−0.0142448	+	0.00822421i
$587$	−25.9699	+	14.9937i	−1.07189	+	0.618856i	−0.928697	−	0.370838i	$-0.879070\pi$
$587$	−25.9699	+	14.9937i	−1.07189	+	0.618856i	−0.143193	+	0.989695i	$0.545737\pi$
$588$	−8.95108	+	8.17790i	−0.369137	+	0.337251i
$589$	5.49059	−	9.50998i	0.226236	−	0.391852i
$590$	−1.32273	−	2.29104i	−0.0544560	−	0.0943205i
$591$	11.8193	+	7.05170i	0.486183	+	0.290068i
$592$	1.93040	−	1.11452i	0.0793390	−	0.0458064i
$593$	−12.0409	+	6.95181i	−0.494460	+	0.285477i	−0.726423	−	0.687248i	$-0.758819\pi$
$593$	−12.0409	+	6.95181i	−0.494460	+	0.285477i	0.231963	+	0.972725i	$0.425485\pi$
$594$	−26.7890	−	17.0428i	−1.09916	−	0.699273i
$595$	−1.37623	−	11.8610i	−0.0564200	−	0.486256i
$596$	−4.01109	−	6.94741i	−0.164301	−	0.284577i
$597$	16.7000	−	27.9908i	0.683484	−	1.14559i
$598$	26.5014	+	14.5572i	1.08372	+	0.595287i
$599$	−5.85303	−	3.37925i	−0.239148	−	0.138072i	0.375637	−	0.926767i	$-0.377424\pi$
$599$	−5.85303	−	3.37925i	−0.239148	−	0.138072i	−0.614785	+	0.788695i	$0.710757\pi$
$600$	−0.115489	+	8.05608i	−0.00471483	+	0.328888i
$601$	−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
$606$	−0.293500	+	20.4734i	−0.0119226	+	0.831676i
$607$			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
$609$	7.32719	−	0.743893i	0.296913	−	0.0301441i
$610$	0.0593724			0.00240392
$611$	−18.0466	−	9.91295i	−0.730085	−	0.401035i
$612$	−10.8959	−	20.1874i	−0.440440	−	0.816027i
$613$		−	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
$615$	−0.0230819	+	1.61010i	−0.000930751	+	0.0649255i
$616$	9.64312	+	12.9758i	0.388533	+	0.522809i
$617$	17.7255	−	30.7015i	0.713603	−	1.23600i	−0.249893	−	0.968273i	$-0.580395\pi$
$617$	17.7255	−	30.7015i	0.713603	−	1.23600i	0.963496	−	0.267723i	$-0.0862712\pi$
$618$	−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
$621$	23.3898	−	36.7656i	0.938599	−	1.47535i
$622$	1.05163	+	1.82148i	0.0421666	+	0.0730347i
$623$	1.25585	+	10.8235i	0.0503144	+	0.433635i
$624$	−5.38647	+	3.16006i	−0.215631	+	0.126504i
$625$	−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
$630$	0.406317	+	4.66695i	0.0161880	+	0.185936i
$631$	−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
$633$	−3.81858	−	2.27826i	−0.151775	−	0.0905525i
$634$	−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
$639$	−2.49641	−	4.62524i	−0.0987566	−	0.182972i
$640$			0.590205i			0.0233299i
$641$	−16.6886	+	9.63517i	−0.659160	+	0.380566i	−0.791957	−	0.610577i	$-0.790938\pi$
$641$	−16.6886	+	9.63517i	−0.659160	+	0.380566i	0.132797	+	0.991143i	$0.457604\pi$
$642$	−7.84551	+	13.1498i	−0.309638	+	0.518983i
$643$	−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	$-0.309423\pi$
$647$	28.6708			1.12716			0.563582	+	0.826060i	$0.309423\pi$
$648$	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
$651$	10.3304	−	7.44976i	0.404882	−	0.291979i
$652$	−4.65862	+	2.68966i	−0.182446	+	0.105335i
$653$	−23.9099	−	13.8044i	−0.935666	−	0.540207i	−0.0470671	−	0.998892i	$-0.514987\pi$
$653$	−23.9099	−	13.8044i	−0.935666	−	0.540207i	−0.888599	+	0.458685i	$0.848321\pi$
$654$	15.2632	−	25.5826i	0.596837	−	1.00036i
$655$	−2.86087	−	1.65172i	−0.111783	−	0.0645381i
$656$		−	1.57520i		−	0.0615011i
$657$	−15.4198	−	28.5691i	−0.601584	−	1.11459i
$658$	12.1268	−	9.01218i	0.472751	−	0.351331i
$659$	−28.9405	−	16.7088i	−1.12736	−	0.650884i	−0.184093	−	0.982909i	$-0.558935\pi$
$659$	−28.9405	−	16.7088i	−1.12736	−	0.650884i	−0.943270	+	0.332025i	$0.892268\pi$
$660$	6.24582	+	0.0895380i	0.243118	+	0.00348526i
$661$	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
$663$	0.332329	+	47.7526i	0.0129066	+	1.85456i
$664$		−	9.07449i		−	0.352159i
$665$	5.66303	+	2.44845i	0.219603	+	0.0949470i
$666$	−0.191689	+	6.68436i	−0.00742779	+	0.259014i
$667$	13.4776			0.521854
$668$	14.1115	+	8.14728i	0.545990	+	0.315228i
$669$	5.32273	+	3.17567i	0.205789	+	0.122778i
$670$	6.10622			0.235904
$671$			0.614686i			0.0237297i
$672$	−0.462866	−	4.55914i	−0.0178555	−	0.175873i
$673$	−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
$675$	−20.3936	−	12.9741i	−0.784948	−	0.499373i
$676$	12.9882	−	0.553475i	0.499547	−	0.0212875i
$677$	11.7820	+	20.4071i	0.452820	+	0.784307i	0.998560	−	0.0536474i	$-0.0170847\pi$
$677$	11.7820	+	20.4071i	0.452820	+	0.784307i	−0.545740	+	0.837955i	$0.683751\pi$
$678$	13.8740	−	23.2542i	0.532829	−	0.893073i
$679$	14.8531	−	1.72339i	0.570008	−	0.0661377i
$680$	3.90849	+	2.25657i	0.149884	+	0.0865353i
$681$	10.6261	−	17.8104i	0.407193	−	0.682495i
$682$	−8.49140	−	14.7075i	−0.325153	−	0.563181i
$683$	0.694198	+	1.20239i	0.0265627	+	0.0460080i	0.879001	−	0.476820i	$-0.158210\pi$
$683$	0.694198	+	1.20239i	0.0265627	+	0.0460080i	−0.852438	+	0.522828i	$0.824877\pi$
$684$	11.8482	+	0.339774i	0.453028	+	0.0129916i
$685$	−10.8090	−	6.24059i	−0.412991	−	0.238441i
$686$	−3.26209	+	18.2307i	−0.124547	+	0.696052i
$687$	16.5851	+	9.89509i	0.632763	+	0.377521i
$688$	−2.90674	−	5.03462i	−0.110818	−	0.191943i
$689$	−0.292917	−	13.7538i	−0.0111593	−	0.523978i
$690$	−0.122883	+	8.57187i	−0.00467809	+	0.326326i
$691$	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
$693$	−48.3172	+	4.20661i	−1.83542	+	0.159796i
$694$		−	24.6678i		−	0.936378i
$695$	−6.36744			−0.241531
$696$	−1.42624	+	2.39052i	−0.0540615	+	0.0906123i
$697$	−10.4313	−	6.02254i	−0.395115	−	0.228120i
$698$	33.1601			1.25513
$699$	14.1776	−	23.7631i	0.536247	−	0.898802i
$700$	7.34099	+	9.87802i	0.277463	+	0.373354i
$701$			35.5148i			1.34137i	0.741740	+	0.670687i	$0.234001\pi$
$701$			35.5148i			1.34137i	−0.741740	+	0.670687i	$0.765999\pi$
$702$	0.406706	−	18.7306i	0.0153501	−	0.706940i
$703$	7.62708	+	4.40350i	0.287661	+	0.166081i
$704$	−6.11042			−0.230295
$705$	0.0836796	−	5.83716i	0.00315155	−	0.219840i
$706$	−12.5305	−	7.23450i	−0.471593	−	0.272274i
$707$	18.6561	+	25.1036i	0.701636	+	0.944120i
$708$	−7.76274	−	0.111284i	−0.291742	−	0.00418231i
$709$			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
$711$	−19.0572	−	0.546509i	−0.714702	−	0.0204957i
$712$	−3.56660	−	2.05918i	−0.133664	−	0.0771709i
$713$	20.1849	−	11.6537i	0.755930	−	0.436436i
$714$	−31.9615	−	14.3660i	−1.19613	−	0.537635i
$715$	−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	$-0.314710\pi$
$719$	29.4841			1.09957			0.549785	+	0.835306i	$0.314710\pi$
$720$	−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
$723$	−35.9469	−	21.4468i	−1.33688	−	0.797615i
$724$	12.7339	−	7.35194i	0.473253	−	0.273233i
$725$		−	7.47588i		−	0.277647i
$726$	−0.653888	+	45.6127i	−0.0242681	+	1.69285i
$727$			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
$732$	0.0892730	−	0.149630i	0.00329962	−	0.00553049i
$733$	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
$735$	4.82664	+	5.28297i	0.178033	+	0.194865i
$736$		−	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
$741$	−21.4538	−	12.1881i	−0.788126	−	0.447741i
$742$	9.26586	+	4.00616i	0.340160	+	0.147071i
$743$	−5.23639	−	9.06969i	−0.192104	−	0.332735i	0.753843	−	0.657055i	$-0.228198\pi$
$743$	−5.23639	−	9.06969i	−0.192104	−	0.332735i	−0.945947	+	0.324320i	$0.894865\pi$
$744$	−0.0690037	+	4.81343i	−0.00252980	+	0.176469i
$745$	−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
$750$	9.86553	+	0.141429i	0.360238	+	0.00516426i
$751$	−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
$753$	0.0796371	−	5.55518i	0.00290214	−	0.202442i
$754$	4.95548	−	3.00351i	0.180468	−	0.109382i
$755$	−5.18516			−0.188707
$756$	12.3726	+	5.99328i	0.449986	+	0.217973i
$757$	−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
$759$	−88.7450	−	1.27222i	−3.22124	−	0.0461786i
$760$	−2.01950	+	1.16596i	−0.0732550	+	0.0422938i
$761$		−	6.69934i		−	0.242851i	−0.992601	−	0.121426i	$-0.961253\pi$
$761$		−	6.69934i		−	0.242851i	0.992601	−	0.121426i	$-0.0387466\pi$
$762$	−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
$765$	−11.9147	+	6.43080i	−0.430777	+	0.232506i
$766$	3.62494	+	2.09286i	0.130975	+	0.0756182i
$767$	14.1648	+	7.78071i	0.511461	+	0.280945i
$768$	1.48743	+	0.887438i	0.0536731	+	0.0320227i
$769$	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
$771$	−0.0293791	+	2.04937i	−0.00105806	+	0.0738062i
$772$	−16.6658	+	9.62200i	−0.599815	+	0.346304i
$773$	12.9640	−	7.48477i	0.466283	−	0.269208i	−0.248400	−	0.968658i	$-0.579905\pi$
$773$	12.9640	−	7.48477i	0.466283	−	0.269208i	0.714682	+	0.699449i	$0.246571\pi$
$774$	17.4333	+	0.499938i	0.626626	+	0.0179699i
$775$	−6.46422	−	11.1964i	−0.232202	−	0.402185i
$776$	−2.82580	+	4.89442i	−0.101440	+	0.175700i
$777$	5.97476	+	8.28510i	0.214343	+	0.297226i
$778$	19.0201	−	10.9812i	0.681903	−	0.393697i
$779$	5.38984	−	3.11182i	0.193111	−	0.111493i
$780$	1.86508	+	3.17912i	0.0667807	+	0.113831i
$781$	−5.35267	+	9.27110i	−0.191534	+	0.331746i
$782$	−55.5345	−	32.0629i	−1.98591	−	1.14657i
$783$	−3.86071	−	7.40497i	−0.137970	−	0.264632i
$784$	−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	−0.865852	−	0.500300i	$-0.833223\pi$
$797$	0.00976904	−	0.0169205i	0.000346037	−	0.000599354i	0.866198	+	0.499700i	$0.166557\pi$
$798$	14.6856	−	10.5904i	0.519864	−	0.374898i
$799$	37.8172	+	21.8337i	1.33787	+	0.772422i
$800$	−4.65166			−0.164461
$801$	10.8725	−	5.86827i	0.384160	−	0.207345i
$802$	−3.47187	−	6.01346i	−0.122596	−	0.212343i
$803$	−33.0623	+	57.2656i	−1.16674	+	2.02086i
$804$	9.18138	−	15.3889i	0.323802	−	0.542724i
$805$	7.81100	+	10.5105i	0.275301	+	0.370445i
$806$	4.82457	−	8.78314i	0.169938	−	0.309373i
$807$	9.61761	+	5.73810i	0.338556	+	0.201991i
$808$	−11.8216			−0.415881
$809$			6.51658i			0.229111i	0.993417	+	0.114555i	$0.0365443\pi$
$809$			6.51658i			0.229111i	−0.993417	+	0.114555i	$0.963456\pi$
$810$	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
$813$	0.477580	−	33.3141i	0.0167495	−	1.16838i
$814$	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
$819$	−16.9004	−	23.0950i	−0.590547	−	0.807003i
$820$	−0.929688			−0.0324661
$821$	−6.32403	+	10.9535i	−0.220710	+	0.382281i	−0.955024	−	0.296529i	$-0.904171\pi$
$821$	−6.32403	+	10.9535i	−0.220710	+	0.382281i	0.734314	+	0.678810i	$0.237504\pi$
$822$	−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
$825$	−0.705688	+	49.2260i	−0.0245689	+	1.71383i
$826$	−9.51834	+	7.07369i	−0.331185	+	0.246125i
$827$	−25.1546			−0.874712			−0.437356	−	0.899288i	$-0.644085\pi$
$827$	−25.1546			−0.874712			−0.437356	+	0.899288i	$0.644085\pi$
$828$	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
$831$	−17.4955	−	10.4383i	−0.606914	−	0.362099i
$832$	−1.86885	−	3.08341i	−0.0647908	−	0.106898i
$833$	−52.1049	+	12.2564i	−1.80533	+	0.424660i
$834$	−9.57415	+	16.0472i	−0.331526	+	0.555669i
$835$	4.80856	−	8.32867i	0.166407	−	0.288226i
$836$	−12.0712	−	20.9080i	−0.417492	−	0.723118i
$837$	−12.1849	−	7.75189i	−0.421173	−	0.267945i
$838$	−5.71451			−0.197404
$839$	18.3244	+	10.5796i	0.632630	+	0.365249i	0.781770	−	0.623567i	$-0.214317\pi$
$839$	18.3244	+	10.5796i	0.632630	+	0.365249i	−0.149140	+	0.988816i	$0.547650\pi$
$840$	−2.69083	+	0.273186i	−0.0928423	+	0.00942581i
$841$	−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
$855$	0.200536	−	6.99288i	0.00685820	−	0.239151i
$856$	−7.65622	−	4.42032i	−0.261684	−	0.151083i
$857$	−12.3135	+	21.3277i	−0.420623	+	0.728540i	−0.996000	−	0.0893479i	$-0.971522\pi$
$857$	−12.3135	+	21.3277i	−0.420623	+	0.728540i	0.575378	+	0.817888i	$0.304855\pi$
$858$	−32.9136	+	19.3093i	−1.12365	+	0.659208i
$859$	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
$861$	7.18154	−	0.729105i	0.244746	−	0.0248478i
$862$	5.05283	−	8.75176i	0.172100	−	0.298086i
$863$	−13.1821	−	22.8320i	−0.448723	−	0.777210i	0.549581	−	0.835441i	$-0.314788\pi$
$863$	−13.1821	−	22.8320i	−0.448723	−	0.777210i	−0.998303	+	0.0582303i	$0.981454\pi$
$864$	−4.60753	+	2.40222i	−0.156751	+	0.0817250i
$865$	7.36033	−	4.24949i	0.250259	−	0.144487i
$866$	−32.8655	+	18.9749i	−1.11682	+	0.644794i
$867$	1.02966	−	71.8248i	0.0349690	−	2.43930i
$868$	4.38617	+	5.90202i	0.148876	+	0.200328i
$869$	19.4159	+	33.6294i	0.658640	+	1.14080i
$870$	1.41089	+	0.841774i	0.0478338	+	0.0285388i
$871$	−31.9007	+	19.3350i	−1.08092	+	0.655143i
$872$	14.8949	+	8.59957i	0.504405	+	0.291218i
$873$	−8.05300	−	14.9202i	−0.272553	−	0.504974i
$874$	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
$879$	0.689587	+	0.00988569i	0.0232592	+	0.000333436i
$880$			3.60640i			0.121572i
$881$	−7.67467	−	13.2929i	−0.258566	−	0.447850i	0.707292	−	0.706922i	$-0.249917\pi$
$881$	−7.67467	−	13.2929i	−0.258566	−	0.447850i	−0.965858	+	0.259072i	$0.916583\pi$
$882$	20.5715	−	4.22054i	0.692679	−	0.142113i
$883$	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
$885$	−0.0656803	+	4.58160i	−0.00220782	+	0.154009i
$886$			21.6680i			0.727952i
$887$	21.8340	−	37.8177i	0.733116	−	1.26979i	−0.222430	−	0.974949i	$-0.571399\pi$
$887$	21.8340	−	37.8177i	0.733116	−	1.26979i	0.955545	−	0.294845i	$-0.0952679\pi$
$888$	−3.86041	−	0.0553415i	−0.129547	−	0.00185714i
$889$	−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
$894$	−0.199171	+	13.8934i	−0.00666128	+	0.464665i
$895$	−3.38472	−	5.86250i	−0.113139	−	0.195962i
$896$	2.62812	−	0.304939i	0.0877993	−	0.0101873i
$897$	−26.5004	−	45.1711i	−0.884822	−	1.50822i
$898$	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
$903$	21.6081	−	15.5826i	0.719073	−	0.518556i
$904$	13.5393	+	7.81690i	0.450310	+	0.259986i
$905$	−4.33915	−	7.51563i	−0.144238	−	0.249828i
$906$	−7.79646	+	13.0676i	−0.259020	+	0.434143i
$907$	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	$-0.703163\pi$
$911$		−	48.4817i		−	1.60627i	0.595796	−	0.803136i	$-0.296837\pi$
$912$	−0.0980944	+	6.84269i	−0.00324823	+	0.226584i
$913$		−	55.4489i		−	1.83509i
$914$	8.30703	−	4.79607i	0.274772	−	0.158640i
$915$	−0.0883124	−	0.0526893i	−0.00291952	−	0.00174186i
$916$	−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
$924$	−2.82831	−	27.8582i	−0.0930444	−	0.916469i
$925$	8.97957	−	5.18436i	0.295246	−	0.170461i
$926$	−2.67382	−	1.54373i	−0.0878673	−	0.0507302i
$927$	−0.373972	+	13.0407i	−0.0122829	+	0.428314i
$928$	−1.39183	−	0.803572i	−0.0456890	−	0.0263785i
$929$		−	29.5977i		−	0.971069i	−0.874217	−	0.485535i	$-0.838625\pi$
$929$		−	29.5977i		−	0.971069i	0.874217	−	0.485535i	$-0.161375\pi$
$930$	2.84091	+	0.0407263i	0.0931571	+	0.00133547i
$931$	7.97681	−	26.4819i	0.261429	−	0.867910i
$932$	13.8355	+	7.98795i	0.453198	+	0.261654i
$933$	0.0522189	−	3.64258i	0.00170957	−	0.119253i
$934$	−8.32473			−0.272394
$935$	23.8825	+	13.7886i	0.781041	+	0.450934i
$936$	10.8164	+	0.0797765i	0.353544	+	0.00260758i
$937$			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
$939$	9.67426	−	16.2150i	0.315708	−	0.529157i
$940$	3.37043			0.109931
$941$	32.5113	+	18.7704i	1.05984	+	0.611898i	0.925387	−	0.379022i	$-0.123740\pi$
$941$	32.5113	+	18.7704i	1.05984	+	0.611898i	0.134451	+	0.990920i	$0.457073\pi$
$942$	−2.55657	+	4.28506i	−0.0832976	+	0.139615i
$943$	13.2097			0.430165
$944$		−	4.48228i		−	0.145886i
$945$	3.53726	−	7.30235i	0.115067	−	0.237546i
$946$	−17.7614	−	30.7636i	−0.577473	−	1.00021i
$947$	15.7164	−	27.2216i	0.510714	−	0.884583i	−0.489209	−	0.872167i	$-0.662714\pi$
$947$	15.7164	−	27.2216i	0.510714	−	0.884583i	0.999923	−	0.0124164i	$-0.00395236\pi$
$948$	0.157780	−	11.0061i	0.00512445	−	0.357461i
$949$	−39.0090	+	0.830782i	−1.26629	+	0.0269683i
$950$	−9.18943	−	15.9166i	−0.298144	−	0.516401i
$951$	15.6855	+	9.35833i	0.508636	+	0.303465i
$952$	8.02886	−	18.5700i	0.260217	−	0.601856i
$953$	47.5409	+	27.4478i	1.54000	+	0.889120i	0.998838	+	0.0482023i	$0.0153492\pi$
$953$	47.5409	+	27.4478i	1.54000	+	0.889120i	0.541163	+	0.840918i	$0.317984\pi$
$954$	0.328118	−	11.4417i	0.0106232	−	0.370440i
$955$	3.20456	+	5.55045i	0.103697	+	0.179608i
$956$	−8.84344	−	15.3173i	−0.286017	−	0.495396i
$957$	−8.71492	+	14.6071i	−0.281713	+	0.472179i
$958$	−10.4595	−	6.03880i	−0.337931	−	0.195105i
$959$	−22.2040	+	51.3557i	−0.717005	+	1.65836i
$960$	0.523770	−	0.877889i	0.0169046	−	0.0283338i
$961$	11.6377	+	20.1571i	0.375409	+	0.650228i
$962$	7.04415	+	3.86934i	0.227112	+	0.124753i
$963$	23.3393	−	12.5971i	0.752100	−	0.405936i
$964$	12.0836	−	20.9293i	0.389185	−	0.674088i
$965$	5.67895	+	9.83623i	0.182812	+	0.316640i
$966$	38.2331	−	3.88161i	1.23013	−	0.124889i
$967$		−	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
$969$	44.9390	+	26.8117i	1.44365	+	0.861315i
$970$	2.88871	+	1.66780i	0.0927509	+	0.0535498i
$971$	−49.9796			−1.60392			−0.801962	−	0.597376i	$-0.796210\pi$
$971$	−49.9796			−1.60392			−0.801962	+	0.597376i	$0.796210\pi$
$972$	1.11632	−	15.5484i	0.0358060	−	0.498716i
$973$	3.28985	+	28.3535i	0.105468	+	0.908973i
$974$		−	5.59837i		−	0.179383i
$975$	−25.0560	+	14.6995i	−0.802434	+	0.470762i
$976$	0.0871190	+	0.0502982i	0.00278861	+	0.00161000i
$977$	4.37679			0.140026			0.0700129	−	0.997546i	$-0.477696\pi$
$977$	4.37679			0.140026			0.0700129	+	0.997546i	$0.477696\pi$
$978$	9.31629	+	0.133555i	0.297902	+	0.00427062i
$979$	−21.7934	−	12.5824i	−0.696520	−	0.402136i
$980$	−3.00987	+	2.83009i	−0.0961467	+	0.0904041i
$981$	−45.4059	+	24.5072i	−1.44970	+	0.782455i
$982$			0.521341i			0.0166367i
$983$	22.4448	+	12.9585i	0.715879	+	0.413313i	0.813234	−	0.581937i	$-0.197705\pi$
$983$	22.4448	+	12.9585i	0.715879	+	0.413313i	−0.0973553	+	0.995250i	$0.531038\pi$
$984$	−1.39789	+	2.34300i	−0.0445630	+	0.0746920i
$985$	4.06153	+	2.34492i	0.129411	+	0.0747155i
$986$	−10.6429	+	6.14469i	−0.338940	+	0.195687i
$987$	−26.0355	+	2.64325i	−0.828719	+	0.0841356i
$988$	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
$996$	−8.05305	+	13.4977i	−0.255171	+	0.427691i
$997$	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
$999$	6.21708	−	9.77242i	0.196700	−	0.309186i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.51226 + 0.844435i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.511132 + 0.295102i) q^{5} +(-0.0248275 + 1.73187i) q^{6} +(1.57814 + 2.12355i) q^{7} -1.00000 q^{8} +(1.57386 - 2.55401i) q^{9} +O(q^{10})\)	\(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} +(-0.0248275 + 1.73187i) 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} +(1.48743 + 0.887438i) q^{12} +(-1.86885 - 3.08341i) q^{13} +(2.62812 - 0.304939i) q^{14} +(0.523770 - 0.877889i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.82336 + 6.62225i) q^{17} +(-1.42491 - 2.64001i) q^{18} -3.95103 q^{19} +(0.511132 + 0.295102i) q^{20} +(-4.17976 - 1.87872i) 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} +(-2.99877 - 0.0859963i) q^{36} +(-1.93040 - 1.11452i) q^{37} +(-1.97552 + 3.42169i) q^{38} +(5.42993 + 3.08479i) q^{39} +(0.511132 - 0.295102i) q^{40} +(-1.36416 + 0.787598i) q^{41} +(-3.71690 + 2.68042i) q^{42} +(-2.90674 + 5.03462i) q^{43} +(3.05521 + 5.29178i) q^{44} +(-0.0507554 + 1.76989i) q^{45} +(-7.26252 + 4.19302i) q^{46} +(4.94554 - 2.85531i) q^{47} +(0.0248275 - 1.73187i) q^{48} +(-2.01892 + 6.70253i) q^{49} +(2.32583 + 4.02845i) q^{50} +(-11.3740 - 6.78599i) q^{51} +(-1.73588 + 3.16018i) q^{52} +(3.30431 + 1.90774i) q^{53} +(4.38415 + 2.78913i) 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} +(-1.02216 - 0.0146533i) q^{60} -0.100596i q^{61} +(1.38966 + 2.40696i) q^{62} +(7.90734 - 0.688433i) q^{63} +1.00000 q^{64} +(1.86515 + 1.02453i) q^{65} +(0.151707 - 10.5825i) q^{66} -10.3459i q^{67} +(3.82336 - 6.62225i) q^{68} +(14.5236 + 0.208205i) 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} +(0.115489 - 8.05608i) q^{75} +(1.97552 + 3.42169i) q^{76} +(-9.64312 - 12.9758i) q^{77} +(5.38647 - 3.16006i) 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} +(0.462866 + 4.55914i) q^{84} +(-3.90849 - 2.25657i) q^{85} +(2.90674 + 5.03462i) q^{86} +(1.42624 - 2.39052i) 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} +(0.0690037 - 4.81343i) q^{93} -5.71062i q^{94} +(2.01950 - 1.16596i) q^{95} +(-1.48743 - 0.887438i) q^{96} +(2.82580 - 4.89442i) q^{97} +(4.79511 + 5.09970i) q^{98} +(-9.61693 + 15.6061i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 17 q^{2} - 3 q^{3} - 17 q^{4} - 9 q^{5} + 3 q^{6} + 5 q^{7} - 34 q^{8} + 7 q^{9}+O(q^{10}) \) 34 * q + 17 * q^2 - 3 * q^3 - 17 * q^4 - 9 * q^5 + 3 * q^6 + 5 * q^7 - 34 * q^8 + 7 * q^9	\( 34 q + 17 q^{2} - 3 q^{3} - 17 q^{4} - 9 q^{5} + 3 q^{6} + 5 q^{7} - 34 q^{8} + 7 q^{9} + 18 q^{11} + 6 q^{12} - 8 q^{13} + 4 q^{14} - 4 q^{15} - 17 q^{16} - 6 q^{17} - 4 q^{18} - 10 q^{19} + 9 q^{20} + 7 q^{21} + 9 q^{22} - 6 q^{23} + 3 q^{24} + 16 q^{25} - 13 q^{26} - 18 q^{27} - q^{28} - 27 q^{29} + 13 q^{30} + q^{31} + 17 q^{32} + 21 q^{33} - 12 q^{34} + 3 q^{35} - 11 q^{36} + 6 q^{37} - 5 q^{38} - 2 q^{39} + 9 q^{40} - 3 q^{41} + 8 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} - 6 q^{46} + 27 q^{47} - 3 q^{48} - 5 q^{49} - 16 q^{50} - 36 q^{51} - 5 q^{52} - 21 q^{53} + 57 q^{55} - 5 q^{56} + 17 q^{57} + 6 q^{59} + 17 q^{60} - q^{62} + 34 q^{64} - 33 q^{65} - 6 q^{68} - 42 q^{69} + 3 q^{70} + 15 q^{71} - 7 q^{72} + 19 q^{73} + 6 q^{74} - 9 q^{75} + 5 q^{76} + 9 q^{77} - 7 q^{78} - 9 q^{79} - 5 q^{81} + q^{84} - 42 q^{85} + 3 q^{86} + 6 q^{87} - 18 q^{88} + 18 q^{89} + 9 q^{90} - 27 q^{91} + 8 q^{93} + 3 q^{95} - 6 q^{96} - 19 q^{97} - 7 q^{98} + 27 q^{99}+O(q^{100}) \) 34 * q + 17 * q^2 - 3 * q^3 - 17 * q^4 - 9 * q^5 + 3 * q^6 + 5 * q^7 - 34 * q^8 + 7 * q^9 + 18 * q^11 + 6 * q^12 - 8 * q^13 + 4 * q^14 - 4 * q^15 - 17 * q^16 - 6 * q^17 - 4 * q^18 - 10 * q^19 + 9 * q^20 + 7 * 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 - 11 * q^36 + 6 * q^37 - 5 * q^38 - 2 * q^39 + 9 * q^40 - 3 * q^41 + 8 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 - 6 * q^46 + 27 * q^47 - 3 * q^48 - 5 * q^49 - 16 * q^50 - 36 * q^51 - 5 * q^52 - 21 * q^53 + 57 * q^55 - 5 * q^56 + 17 * q^57 + 6 * q^59 + 17 * q^60 - q^62 + 34 * q^64 - 33 * q^65 - 6 * q^68 - 42 * q^69 + 3 * q^70 + 15 * q^71 - 7 * q^72 + 19 * q^73 + 6 * q^74 - 9 * q^75 + 5 * q^76 + 9 * q^77 - 7 * q^78 - 9 * q^79 - 5 * q^81 + q^84 - 42 * q^85 + 3 * q^86 + 6 * q^87 - 18 * q^88 + 18 * q^89 + 9 * q^90 - 27 * q^91 + 8 * q^93 + 3 * q^95 - 6 * q^96 - 19 * q^97 - 7 * q^98 + 27 * q^99

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