LMFDB - Embedded newform 546.2.bn.f.101.11

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			101.11
Character	$\chi$	$=$	546.101
Dual form			546.2.bn.f.173.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.786858 + 1.54300i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.98183 + 1.14421i) q^{5} +(1.72971 + 0.0900624i) q^{6} +(-2.60041 + 0.487738i) q^{7} -1.00000 q^{8} +(-1.76171 + 2.42825i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.786858 + 1.54300i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.98183 + 1.14421i) q^{5} +(1.72971 + 0.0900624i) q^{6} +(-2.60041 + 0.487738i) q^{7} -1.00000 q^{8} +(-1.76171 + 2.42825i) q^{9} +2.28842i q^{10} +0.297141 q^{11} +(0.942850 - 1.45294i) q^{12} +(-3.20028 - 1.66078i) q^{13} +(-0.877809 + 2.49589i) q^{14} +(-3.32494 - 2.15764i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.446664 + 0.773644i) q^{17} +(1.22207 + 2.73981i) q^{18} -7.89067 q^{19} +(1.98183 + 1.14421i) q^{20} +(-2.79873 - 3.62865i) q^{21} +(0.148570 - 0.257331i) q^{22} +(6.76573 + 3.90620i) q^{23} +(-0.786858 - 1.54300i) q^{24} +(0.118437 - 0.205138i) q^{25} +(-3.03842 + 1.94114i) q^{26} +(-5.13300 - 0.807639i) q^{27} +(1.72260 + 2.00815i) q^{28} +(-0.980947 + 0.566350i) q^{29} +(-3.53104 + 1.80066i) q^{30} +(0.839051 - 1.45328i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.233807 + 0.458489i) q^{33} +0.893327 q^{34} +(4.59549 - 3.94203i) q^{35} +(2.98378 + 0.311563i) q^{36} +(4.32929 + 2.49951i) q^{37} +(-3.94533 + 6.83352i) q^{38} +(0.0444224 - 6.24484i) q^{39} +(1.98183 - 1.14421i) q^{40} +(-6.52086 + 3.76482i) q^{41} +(-4.54187 + 0.609446i) q^{42} +(-1.94207 + 3.36377i) q^{43} +(-0.148570 - 0.257331i) q^{44} +(0.712988 - 6.82814i) q^{45} +(6.76573 - 3.90620i) q^{46} +(5.21062 - 3.00835i) q^{47} +(-1.72971 - 0.0900624i) q^{48} +(6.52422 - 2.53663i) q^{49} +(-0.118437 - 0.205138i) q^{50} +(-0.842274 + 1.29795i) q^{51} +(0.161862 + 3.60192i) q^{52} +(6.28351 + 3.62779i) q^{53} +(-3.26594 + 4.04149i) q^{54} +(-0.588883 + 0.339992i) q^{55} +(2.60041 - 0.487738i) q^{56} +(-6.20883 - 12.1753i) q^{57} +1.13270i q^{58} +(-5.21709 + 3.01209i) q^{59} +(-0.206101 + 3.95830i) q^{60} -8.44757i q^{61} +(-0.839051 - 1.45328i) q^{62} +(3.39681 - 7.17368i) q^{63} +1.00000 q^{64} +(8.24270 - 0.370410i) q^{65} +(0.513966 + 0.0267612i) q^{66} -3.39883i q^{67} +(0.446664 - 0.773644i) q^{68} +(-0.703603 + 13.5132i) q^{69} +(-1.11615 - 5.95083i) q^{70} +(-1.14995 + 1.99178i) q^{71} +(1.76171 - 2.42825i) q^{72} +(-6.16302 + 10.6747i) q^{73} +(4.32929 - 2.49951i) q^{74} +(0.409722 + 0.0213334i) q^{75} +(3.94533 + 6.83352i) q^{76} +(-0.772686 + 0.144927i) q^{77} +(-5.38598 - 3.16089i) q^{78} +(4.46469 + 7.73307i) q^{79} -2.28842i q^{80} +(-2.79275 - 8.55573i) q^{81} +7.52964i q^{82} -1.54870i q^{83} +(-1.74314 + 4.23810i) q^{84} +(-1.77042 - 1.02215i) q^{85} +(1.94207 + 3.36377i) q^{86} +(-1.64574 - 1.06797i) q^{87} -0.297141 q^{88} +(12.3933 + 7.15530i) q^{89} +(-5.55685 - 4.03154i) q^{90} +(9.13206 + 2.75781i) q^{91} -7.81240i q^{92} +(2.90263 + 0.151134i) q^{93} -6.01671i q^{94} +(15.6380 - 9.02859i) q^{95} +(-0.942850 + 1.45294i) q^{96} +(1.19346 - 2.06713i) q^{97} +(1.06532 - 6.91846i) q^{98} +(-0.523476 + 0.721530i) 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
$3$	0.786858	+	1.54300i	0.454292	+	0.890853i
$3$	0.786858	+	1.54300i	0.454292	+	0.890853i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.98183	+	1.14421i	−0.886302	+	0.511707i	−0.872731	−	0.488201i	$-0.837653\pi$
$5$	−1.98183	+	1.14421i	−0.886302	+	0.511707i	−0.0135708	+	0.999908i	$0.504320\pi$
$6$	1.72971	+	0.0900624i	0.706150	+	0.0367678i
$7$	−2.60041	+	0.487738i	−0.982861	+	0.184348i
$7$	−2.60041	+	0.487738i	−0.982861	+	0.184348i
$8$	−1.00000			−0.353553
$9$	−1.76171	+	2.42825i	−0.587237	+	0.809415i
$10$			2.28842i			0.723662i
$11$	0.297141			0.0895913			0.0447956	−	0.998996i	$-0.485736\pi$
$11$	0.297141			0.0895913			0.0447956	+	0.998996i	$0.485736\pi$
$12$	0.942850	−	1.45294i	0.272177	−	0.419428i
$13$	−3.20028	−	1.66078i	−0.887599	−	0.460618i
$13$	−3.20028	−	1.66078i	−0.887599	−	0.460618i
$14$	−0.877809	+	2.49589i	−0.234604	+	0.667054i
$15$	−3.32494	−	2.15764i	−0.858495	−	0.557100i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.446664	+	0.773644i	0.108332	+	0.187636i	0.915095	−	0.403239i	$-0.132116\pi$
$17$	0.446664	+	0.773644i	0.108332	+	0.187636i	−0.806763	+	0.590876i	$0.798782\pi$
$18$	1.22207	+	2.73981i	0.288044	+	0.645779i
$19$	−7.89067			−1.81024			−0.905122	−	0.425152i	$-0.860220\pi$
$19$	−7.89067			−1.81024			−0.905122	+	0.425152i	$0.860220\pi$
$20$	1.98183	+	1.14421i	0.443151	+	0.255853i
$21$	−2.79873	−	3.62865i	−0.610733	−	0.791837i
$22$	0.148570	−	0.257331i	0.0316753	−	0.0548632i
$23$	6.76573	+	3.90620i	1.41075	+	0.814499i	0.995459	−	0.0951887i	$-0.0303455\pi$
$23$	6.76573	+	3.90620i	1.41075	+	0.814499i	0.415294	+	0.909687i	$0.363679\pi$
$24$	−0.786858	−	1.54300i	−0.160617	−	0.314964i
$25$	0.118437	−	0.205138i	0.0236873	−	0.0410277i
$26$	−3.03842	+	1.94114i	−0.595883	+	0.380688i
$27$	−5.13300	−	0.807639i	−0.987847	−	0.155430i
$28$	1.72260	+	2.00815i	0.325540	+	0.379504i
$29$	−0.980947	+	0.566350i	−0.182157	+	0.105169i	−0.588306	−	0.808639i	$-0.700205\pi$
$29$	−0.980947	+	0.566350i	−0.182157	+	0.105169i	0.406149	+	0.913807i	$0.366872\pi$
$30$	−3.53104	+	1.80066i	−0.644677	+	0.328754i
$31$	0.839051	−	1.45328i	0.150698	−	0.261017i	−0.780786	−	0.624798i	$-0.785181\pi$
$31$	0.839051	−	1.45328i	0.150698	−	0.261017i	0.931484	+	0.363782i	$0.118515\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	0.233807	+	0.458489i	0.0407006	+	0.0798126i
$34$	0.893327			0.153204
$35$	4.59549	−	3.94203i	0.776780	−	0.666324i
$36$	2.98378	+	0.311563i	0.497296	+	0.0519272i
$37$	4.32929	+	2.49951i	0.711730	+	0.410918i	0.811701	−	0.584073i	$-0.198542\pi$
$37$	4.32929	+	2.49951i	0.711730	+	0.410918i	−0.0999712	+	0.994990i	$0.531875\pi$
$38$	−3.94533	+	6.83352i	−0.640018	+	1.10854i
$39$	0.0444224	−	6.24484i	0.00711328	−	0.999975i
$40$	1.98183	−	1.14421i	0.313355	−	0.180916i
$41$	−6.52086	+	3.76482i	−1.01839	+	0.587966i	−0.913636	−	0.406532i	$-0.866738\pi$
$41$	−6.52086	+	3.76482i	−1.01839	+	0.587966i	−0.104751	+	0.994498i	$0.533405\pi$
$42$	−4.54187	+	0.609446i	−0.700826	+	0.0940395i
$43$	−1.94207	+	3.36377i	−0.296163	+	0.512970i	−0.975255	−	0.221084i	$-0.929041\pi$
$43$	−1.94207	+	3.36377i	−0.296163	+	0.512970i	0.679092	+	0.734054i	$0.262374\pi$
$44$	−0.148570	−	0.257331i	−0.0223978	−	0.0387942i
$45$	0.712988	−	6.82814i	0.106286	−	1.01788i
$46$	6.76573	−	3.90620i	0.997553	−	0.575938i
$47$	5.21062	−	3.00835i	0.760047	−	0.438813i	−0.0692655	−	0.997598i	$-0.522066\pi$
$47$	5.21062	−	3.00835i	0.760047	−	0.438813i	0.829313	+	0.558785i	$0.188732\pi$
$48$	−1.72971	−	0.0900624i	−0.249662	−	0.0129994i
$49$	6.52422	−	2.53663i	0.932032	−	0.362376i
$50$	−0.118437	−	0.205138i	−0.0167495	−	0.0290109i
$51$	−0.842274	+	1.29795i	−0.117942	+	0.181749i
$52$	0.161862	+	3.60192i	0.0224463	+	0.499496i
$53$	6.28351	+	3.62779i	0.863107	+	0.498315i	0.865051	−	0.501683i	$-0.167286\pi$
$53$	6.28351	+	3.62779i	0.863107	+	0.498315i	−0.00194455	+	0.999998i	$0.500619\pi$
$54$	−3.26594	+	4.04149i	−0.444438	+	0.549977i
$55$	−0.588883	+	0.339992i	−0.0794049	+	0.0458444i
$56$	2.60041	−	0.487738i	0.347494	−	0.0651768i
$57$	−6.20883	−	12.1753i	−0.822380	−	1.61266i
$58$			1.13270i			0.148731i
$59$	−5.21709	+	3.01209i	−0.679207	+	0.392141i	−0.799556	−	0.600591i	$-0.794932\pi$
$59$	−5.21709	+	3.01209i	−0.679207	+	0.392141i	0.120349	+	0.992732i	$0.461599\pi$
$60$	−0.206101	+	3.95830i	−0.0266075	+	0.511014i
$61$		−	8.44757i		−	1.08160i	−0.841151	−	0.540800i	$-0.818121\pi$
$61$		−	8.44757i		−	1.08160i	0.841151	−	0.540800i	$-0.181879\pi$
$62$	−0.839051	−	1.45328i	−0.106560	−	0.184567i
$63$	3.39681	−	7.17368i	0.427958	−	0.903798i
$64$	1.00000			0.125000
$65$	8.24270	−	0.370410i	1.02238	−	0.0459437i
$66$	0.513966	+	0.0267612i	0.0632649	+	0.00329408i
$67$		−	3.39883i		−	0.415233i	−0.978210	−	0.207617i	$-0.933429\pi$
$67$		−	3.39883i		−	0.415233i	0.978210	−	0.207617i	$-0.0665706\pi$
$68$	0.446664	−	0.773644i	0.0541659	−	0.0938181i
$69$	−0.703603	+	13.5132i	−0.0847039	+	1.62679i
$70$	−1.11615	−	5.95083i	−0.133406	−	0.711260i
$71$	−1.14995	+	1.99178i	−0.136474	+	0.236381i	−0.926160	−	0.377131i	$-0.876910\pi$
$71$	−1.14995	+	1.99178i	−0.136474	+	0.236381i	0.789685	+	0.613512i	$0.210244\pi$
$72$	1.76171	−	2.42825i	0.207620	−	0.286171i
$73$	−6.16302	+	10.6747i	−0.721327	+	1.24937i	0.239141	+	0.970985i	$0.423134\pi$
$73$	−6.16302	+	10.6747i	−0.721327	+	1.24937i	−0.960468	+	0.278390i	$0.910199\pi$
$74$	4.32929	−	2.49951i	0.503269	−	0.290563i
$75$	0.409722	+	0.0213334i	0.0473106	+	0.00246337i
$76$	3.94533	+	6.83352i	0.452561	+	0.783858i
$77$	−0.772686	+	0.144927i	−0.0880558	+	0.0165159i
$78$	−5.38598	−	3.16089i	−0.609842	−	0.357900i
$79$	4.46469	+	7.73307i	0.502317	+	0.870039i	0.999996	+	0.00267764i	$0.000852321\pi$
$79$	4.46469	+	7.73307i	0.502317	+	0.870039i	−0.497679	+	0.867361i	$0.665814\pi$
$80$		−	2.28842i		−	0.255853i
$81$	−2.79275	−	8.55573i	−0.310306	−	0.950637i
$82$			7.52964i			0.831510i
$83$		−	1.54870i		−	0.169992i	−0.996381	−	0.0849962i	$-0.972912\pi$
$83$		−	1.54870i		−	0.169992i	0.996381	−	0.0849962i	$-0.0270878\pi$
$84$	−1.74314	+	4.23810i	−0.190192	+	0.462414i
$85$	−1.77042	−	1.02215i	−0.192029	−	0.110868i
$86$	1.94207	+	3.36377i	0.209419	+	0.362725i
$87$	−1.64574	−	1.06797i	−0.176442	−	0.114498i
$88$	−0.297141			−0.0316753
$89$	12.3933	+	7.15530i	1.31369	+	0.758460i	0.982705	−	0.185176i	$-0.0592854\pi$
$89$	12.3933	+	7.15530i	1.31369	+	0.758460i	0.330986	+	0.943636i	$0.392619\pi$
$90$	−5.55685	−	4.03154i	−0.585743	−	0.424961i
$91$	9.13206	+	2.75781i	0.957300	+	0.289097i
$92$		−	7.81240i		−	0.814499i
$93$	2.90263	+	0.151134i	0.300988	+	0.0156719i
$94$		−	6.01671i		−	0.620576i
$95$	15.6380	−	9.02859i	1.60442	−	0.926314i
$96$	−0.942850	+	1.45294i	−0.0962292	+	0.148290i
$97$	1.19346	−	2.06713i	0.121178	−	0.209886i	−0.799055	−	0.601258i	$-0.794666\pi$
$97$	1.19346	−	2.06713i	0.121178	−	0.209886i	0.920232	+	0.391373i	$0.128000\pi$
$98$	1.06532	−	6.91846i	0.107614	−	0.698870i
$99$	−0.523476	+	0.721530i	−0.0526113	+	0.0725165i
$100$	−0.236873			−0.0236873
$101$	18.7772			1.86840			0.934200	−	0.356749i	$-0.116115\pi$
$101$	18.7772			1.86840			0.934200	+	0.356749i	$0.116115\pi$
$102$	0.702921	+	1.37841i	0.0695996	+	0.136483i
$103$	−12.3898	+	7.15323i	−1.22080	+	0.704828i	−0.965088	−	0.261925i	$-0.915643\pi$
$103$	−12.3898	+	7.15323i	−1.22080	+	0.704828i	−0.255710	+	0.966753i	$0.582309\pi$
$104$	3.20028	+	1.66078i	0.313813	+	0.162853i
$105$	9.69855	+	3.98904i	0.946482	+	0.389290i
$106$	6.28351	−	3.62779i	0.610309	−	0.352362i
$107$	−14.4499	−	8.34267i	−1.39693	−	0.806516i	−0.402858	−	0.915263i	$-0.631983\pi$
$107$	−14.4499	−	8.34267i	−1.39693	−	0.806516i	−0.994070	+	0.108746i	$0.965316\pi$
$108$	1.86707	+	4.84913i	0.179658	+	0.466608i
$109$	9.70354	+	5.60234i	0.929431	+	0.536607i	0.886632	−	0.462476i	$-0.153039\pi$
$109$	9.70354	+	5.60234i	0.929431	+	0.536607i	0.0427994	+	0.999084i	$0.486372\pi$
$110$			0.679983i			0.0648338i
$111$	−0.450224	+	8.64686i	−0.0427334	+	0.820723i
$112$	0.877809	−	2.49589i	0.0829452	−	0.235839i
$113$	−7.27033	−	4.19753i	−0.683935	−	0.394870i	0.117401	−	0.993085i	$-0.462544\pi$
$113$	−7.27033	−	4.19753i	−0.683935	−	0.394870i	−0.801336	+	0.598214i	$0.795877\pi$
$114$	−13.6485	−	0.710652i	−1.27830	−	0.0665587i
$115$	−17.8781			−1.66714
$116$	0.980947	+	0.566350i	0.0910786	+	0.0525843i
$117$	9.67075	−	4.84526i	0.894062	−	0.447944i
$118$			6.02418i			0.554571i
$119$	−1.53884	−	1.79393i	−0.141065	−	0.164450i
$120$	3.32494	+	2.15764i	0.303524	+	0.196965i
$121$	−10.9117			−0.991973
$122$	−7.31581	−	4.22379i	−0.662343	−	0.382404i
$123$	−10.9401	−	7.09932i	−0.986437	−	0.640124i
$124$	−1.67810			−0.150698
$125$		−	10.9000i		−	0.974929i
$126$	−4.51418	−	6.52857i	−0.402155	−	0.581611i
$127$	2.63228	+	4.55924i	0.233577	+	0.404567i	0.958858	−	0.283886i	$-0.0916236\pi$
$127$	2.63228	+	4.55924i	0.233577	+	0.404567i	−0.725281	+	0.688453i	$0.758290\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−6.71844	−	0.349815i	−0.591525	−	0.0307995i
$130$	3.80057	−	7.32359i	0.333332	−	0.642322i
$131$	−0.386257	−	0.669016i	−0.0337474	−	0.0584522i	0.848658	−	0.528941i	$-0.177411\pi$
$131$	−0.386257	−	0.669016i	−0.0337474	−	0.0584522i	−0.882406	+	0.470489i	$0.844078\pi$
$132$	0.280159	−	0.431727i	0.0243847	−	0.0375770i
$133$	20.5189	−	3.84858i	1.77922	−	0.333714i
$134$	−2.94347	−	1.69941i	−0.254277	−	0.146807i
$135$	11.0969	−	4.27263i	0.955065	−	0.367730i
$136$	−0.446664	−	0.773644i	−0.0383011	−	0.0663394i
$137$	−1.29342	−	2.24027i	−0.110505	−	0.191399i	0.805469	−	0.592638i	$-0.201913\pi$
$137$	−1.29342	−	2.24027i	−0.110505	−	0.191399i	−0.915974	+	0.401238i	$0.868580\pi$
$138$	11.3509	+	7.36592i	0.966256	+	0.627029i
$139$	−10.2034	−	5.89092i	−0.865438	−	0.499661i	0.000391380	−	1.00000i	$-0.499875\pi$
$139$	−10.2034	−	5.89092i	−0.865438	−	0.499661i	−0.865830	+	0.500339i	$0.833209\pi$
$140$	−5.71164	−	2.00880i	−0.482722	−	0.169774i
$141$	8.74191	+	5.67285i	0.736202	+	0.477740i
$142$	1.14995	+	1.99178i	0.0965020	+	0.167146i
$143$	−0.950934	−	0.493486i	−0.0795211	−	0.0412673i
$144$	−1.22207	−	2.73981i	−0.101839	−	0.228317i
$145$	1.29605	−	2.24482i	0.107631	−	0.186422i
$146$	6.16302	+	10.6747i	0.510055	+	0.883441i
$147$	9.04767	+	8.07092i	0.746239	+	0.665678i
$148$		−	4.99903i		−	0.410918i
$149$	−3.28750			−0.269322			−0.134661	−	0.990892i	$-0.542995\pi$
$149$	−3.28750			−0.269322			−0.134661	+	0.990892i	$0.542995\pi$
$150$	0.223336	−	0.344163i	0.0182353	−	0.0281008i
$151$	−10.5899	−	6.11409i	−0.861795	−	0.497557i	0.00281814	−	0.999996i	$-0.499103\pi$
$151$	−10.5899	−	6.11409i	−0.861795	−	0.497557i	−0.864613	+	0.502439i	$0.832436\pi$
$152$	7.89067			0.640018
$153$	−2.66549	−	0.278328i	−0.215492	−	0.0225015i
$154$	−0.260833	+	0.741629i	−0.0210185	+	0.0597622i
$155$			3.84021i			0.308453i
$156$	−5.43040	+	3.08395i	−0.434780	+	0.246914i
$157$	−15.4715	−	8.93248i	−1.23476	−	0.712889i	−0.266742	−	0.963768i	$-0.585947\pi$
$157$	−15.4715	−	8.93248i	−1.23476	−	0.712889i	−0.968019	+	0.250879i	$0.919280\pi$
$158$	8.92938			0.710384
$159$	−0.653455	+	12.5500i	−0.0518223	+	0.995282i
$160$	−1.98183	−	1.14421i	−0.156678	−	0.0904578i
$161$	−19.4989	−	6.85779i	−1.53673	−	0.540470i
$162$	−8.80586	−	1.85927i	−0.691853	−	0.146078i
$163$		−	2.31758i		−	0.181526i	−0.995872	−	0.0907632i	$-0.971069\pi$
$163$		−	2.31758i		−	0.181526i	0.995872	−	0.0907632i	$-0.0289307\pi$
$164$	6.52086	+	3.76482i	0.509194	+	0.293983i
$165$	−0.987974	−	0.641122i	−0.0769137	−	0.0499113i
$166$	−1.34122	−	0.774352i	−0.104099	−	0.0601014i
$167$	−11.5588	+	6.67349i	−0.894449	+	0.516410i	−0.875395	−	0.483408i	$-0.839399\pi$
$167$	−11.5588	+	6.67349i	−0.894449	+	0.516410i	−0.0190536	+	0.999818i	$0.506065\pi$
$168$	2.79873	+	3.62865i	0.215927	+	0.279957i
$169$	7.48361	+	10.6299i	0.575662	+	0.817687i
$170$	−1.77042	+	1.02215i	−0.135785	+	0.0783957i
$171$	13.9011	−	19.1605i	1.06304	−	1.46524i
$172$	3.88415			0.296163
$173$	18.3618			1.39602			0.698011	−	0.716087i	$-0.254069\pi$
$173$	18.3618			1.39602			0.698011	+	0.716087i	$0.254069\pi$
$174$	−1.74776	+	0.891273i	−0.132497	+	0.0675673i
$175$	−0.207930	+	0.591209i	−0.0157180	+	0.0446912i
$176$	−0.148570	+	0.257331i	−0.0111989	+	0.0193971i
$177$	−8.75277	−	5.67990i	−0.657898	−	0.426927i
$178$	12.3933	−	7.15530i	0.928920	−	0.536312i
$179$			10.3189i			0.771268i	0.922652	+	0.385634i	$0.126017\pi$
$179$			10.3189i			0.771268i	−0.922652	+	0.385634i	$0.873983\pi$
$180$	−6.26984	+	2.79660i	−0.467326	+	0.208447i
$181$		−	5.21743i		−	0.387809i	−0.981020	−	0.193904i	$-0.937885\pi$
$181$		−	5.21743i		−	0.387809i	0.981020	−	0.193904i	$-0.0621151\pi$
$182$	6.95436	−	6.52969i	0.515491	−	0.484013i
$183$	13.0346	−	6.64704i	0.963547	−	0.491363i
$184$	−6.76573	−	3.90620i	−0.498777	−	0.287969i
$185$	−11.4399			−0.841077
$186$	1.58220	−	2.43818i	0.116013	−	0.178776i
$187$	0.132722	+	0.229881i	0.00970559	+	0.0168106i
$188$	−5.21062	−	3.00835i	−0.380024	−	0.219407i
$189$	13.7418	−	0.403371i	0.999569	−	0.0293409i
$190$		−	18.0572i		−	1.31001i
$191$			26.3728i			1.90827i	0.299378	+	0.954135i	$0.403221\pi$
$191$			26.3728i			1.90827i	−0.299378	+	0.954135i	$0.596779\pi$
$192$	0.786858	+	1.54300i	0.0567866	+	0.111357i
$193$		−	3.20479i		−	0.230686i	−0.993326	−	0.115343i	$-0.963203\pi$
$193$		−	3.20479i		−	0.230686i	0.993326	−	0.115343i	$-0.0367967\pi$
$194$	−1.19346	−	2.06713i	−0.0856855	−	0.148412i
$195$	7.05738	+	12.4270i	0.505389	+	0.889919i
$196$	−5.45890	−	4.38183i	−0.389922	−	0.312988i
$197$	−12.9869	−	22.4940i	−0.925278	−	1.60263i	−0.791113	−	0.611670i	$-0.790498\pi$
$197$	−12.9869	−	22.4940i	−0.925278	−	1.60263i	−0.134165	−	0.990959i	$-0.542835\pi$
$198$	0.363126	+	0.814109i	0.0258062	+	0.0578562i
$199$	4.80414	−	2.77367i	0.340557	−	0.196621i	−0.319961	−	0.947431i	$-0.603670\pi$
$199$	4.80414	−	2.77367i	0.340557	−	0.196621i	0.660518	+	0.750810i	$0.270337\pi$
$200$	−0.118437	+	0.205138i	−0.00837474	+	0.0145055i
$201$	5.24440	−	2.67439i	0.369911	−	0.188637i
$202$	9.38860	−	16.2615i	0.660579	−	1.14416i
$203$	2.27463	−	1.95118i	0.159648	−	0.136946i
$204$	1.54520	+	0.0804552i	0.108185	+	0.00563299i
$205$	8.61550	−	14.9225i	0.601732	−	1.04223i
$206$			14.3065i			0.996778i
$207$	−21.4045	+	9.54727i	−1.48771	+	0.663581i
$208$	3.03842	−	1.94114i	0.210677	−	0.134594i
$209$	−2.34464			−0.162182
$210$	8.30388	−	6.40467i	0.573022	−	0.441965i
$211$	1.17040	+	2.02719i	0.0805736	+	0.139558i	0.903496	−	0.428596i	$-0.140991\pi$
$211$	1.17040	+	2.02719i	0.0805736	+	0.139558i	−0.822923	+	0.568153i	$0.807658\pi$
$212$		−	7.25558i		−	0.498315i
$213$	−3.97817	−	0.207135i	−0.272580	−	0.0141927i
$214$	−14.4499	+	8.34267i	−0.987777	+	0.570293i
$215$		−	8.88856i		−	0.606195i
$216$	5.13300	+	0.807639i	0.349257	+	0.0549529i
$217$	−1.47305	+	4.18835i	−0.0999975	+	0.284324i
$218$	9.70354	−	5.60234i	0.657207	−	0.379439i
$219$	−21.3204	−	1.11011i	−1.44070	−	0.0750144i
$220$	0.588883	+	0.339992i	0.0397025	+	0.0229222i
$221$	−0.144596	−	3.21769i	−0.00972659	−	0.216445i
$222$	7.26329	+	4.71333i	0.487480	+	0.316338i
$223$	−0.746837	−	1.29356i	−0.0500119	−	0.0866232i	0.839936	−	0.542686i	$-0.182593\pi$
$223$	−0.746837	−	1.29356i	−0.0500119	−	0.0866232i	−0.889948	+	0.456063i	$0.849259\pi$
$224$	−1.72260	−	2.00815i	−0.115096	−	0.134175i
$225$	0.289475	+	0.648988i	0.0192983	+	0.0432658i
$226$	−7.27033	+	4.19753i	−0.483615	+	0.279215i
$227$	5.51731	−	3.18542i	0.366197	−	0.211424i	−0.305599	−	0.952160i	$-0.598857\pi$
$227$	5.51731	−	3.18542i	0.366197	−	0.211424i	0.671796	+	0.740737i	$0.265523\pi$
$228$	−7.43972	+	11.4647i	−0.492707	+	0.759266i
$229$	3.93382	+	6.81358i	0.259954	+	0.450254i	0.966229	−	0.257684i	$-0.0829592\pi$
$229$	3.93382	+	6.81358i	0.259954	+	0.450254i	−0.706275	+	0.707937i	$0.749626\pi$
$230$	−8.93903	+	15.4829i	−0.589422	+	1.02091i
$231$	−0.831616	−	1.07822i	−0.0547163	−	0.0709417i
$232$	0.980947	−	0.566350i	0.0644023	−	0.0371827i
$233$	8.04627	−	4.64552i	0.527129	−	0.304338i	−0.212718	−	0.977114i	$-0.568231\pi$
$233$	8.04627	−	4.64552i	0.527129	−	0.304338i	0.739847	+	0.672776i	$0.234898\pi$
$234$	0.639263	−	10.7977i	0.0417899	−	0.705871i
$235$	−6.88438	+	11.9241i	−0.449088	+	0.777842i
$236$	5.21709	+	3.01209i	0.339604	+	0.196070i
$237$	−8.41907	+	12.9739i	−0.546877	+	0.842743i
$238$	−2.32301	+	0.435710i	−0.150579	+	0.0282429i
$239$	−22.6067			−1.46230			−0.731152	−	0.682215i	$-0.761017\pi$
$239$	−22.6067			−1.46230			−0.731152	+	0.682215i	$0.761017\pi$
$240$	3.53104	−	1.80066i	0.227928	−	0.116232i
$241$	14.5437	+	25.1904i	0.936842	+	1.62266i	0.771316	+	0.636453i	$0.219599\pi$
$241$	14.5437	+	25.1904i	0.936842	+	1.62266i	0.165526	+	0.986205i	$0.447068\pi$
$242$	−5.45585	+	9.44982i	−0.350716	+	0.607457i
$243$	11.0040	−	11.0414i	0.705908	−	0.708304i
$244$	−7.31581	+	4.22379i	−0.468347	+	0.270400i
$245$	−10.0275	+	12.4923i	−0.640631	+	0.798102i
$246$	−11.6183	+	5.92475i	−0.740753	+	0.377749i
$247$	25.2524	+	13.1047i	1.60677	+	0.833830i
$248$	−0.839051	+	1.45328i	−0.0532798	+	0.0922834i
$249$	2.38965	−	1.21861i	0.151438	−	0.0772263i
$250$	−9.43971	−	5.45002i	−0.597020	−	0.344690i
$251$	−6.89055	+	11.9348i	−0.434928	+	0.753317i	−0.997290	−	0.0735742i	$-0.976559\pi$
$251$	−6.89055	+	11.9348i	−0.434928	+	0.753317i	0.562362	+	0.826891i	$0.309893\pi$
$252$	−7.91099	+	0.645111i	−0.498346	+	0.0406382i
$253$	2.01037	+	1.16069i	0.126391	+	0.0729720i
$254$	5.26456			0.330328
$255$	0.184115	−	3.53606i	0.0115298	−	0.221437i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−2.81222	+	4.87090i	−0.175421	+	0.303839i	−0.940307	−	0.340327i	$-0.889462\pi$
$257$	−2.81222	+	4.87090i	−0.175421	+	0.303839i	0.764886	+	0.644166i	$0.222795\pi$
$258$	−3.66217	+	5.64343i	−0.227997	+	0.351345i
$259$	−12.4770	−	4.38819i	−0.775284	−	0.272669i
$260$	−4.44214	−	6.95319i	−0.275490	−	0.431218i
$261$	0.352908	−	3.37972i	0.0218444	−	0.209200i
$262$	−0.772513			−0.0477260
$263$			19.3817i			1.19513i	0.801821	+	0.597564i	$0.203865\pi$
$263$			19.3817i			1.19513i	−0.801821	+	0.597564i	$0.796135\pi$
$264$	−0.233807	−	0.458489i	−0.0143898	−	0.0282180i
$265$	−16.6038			−1.01996
$266$	6.92650	−	19.6942i	0.424691	−	1.20753i
$267$	−1.28885	+	24.7531i	−0.0788761	+	1.51487i
$268$	−2.94347	+	1.69941i	−0.179801	+	0.103808i
$269$	13.9773	+	24.2094i	0.852211	+	1.47607i	0.879209	+	0.476437i	$0.158072\pi$
$269$	13.9773	+	24.2094i	0.852211	+	1.47607i	−0.0269978	+	0.999635i	$0.508595\pi$
$270$	1.84822	−	11.7465i	0.112479	−	0.714868i
$271$	−10.2294	+	17.7179i	−0.621393	+	1.07628i	0.367834	+	0.929892i	$0.380100\pi$
$271$	−10.2294	+	17.7179i	−0.621393	+	1.07628i	−0.989227	+	0.146392i	$0.953234\pi$
$272$	−0.893327			−0.0541659
$273$	2.93033	+	16.2608i	0.177352	+	0.984148i
$274$	−2.58684			−0.156277
$275$	0.0351923	−	0.0609549i	0.00212218	−	0.00367572i
$276$	12.0545	−	6.14724i	0.725598	−	0.370021i
$277$	−3.25535	−	5.63843i	−0.195595	−	0.338780i	0.751501	−	0.659732i	$-0.229330\pi$
$277$	−3.25535	−	5.63843i	−0.195595	−	0.338780i	−0.947095	+	0.320952i	$0.895997\pi$
$278$	−10.2034	+	5.89092i	−0.611957	+	0.353314i
$279$	2.05075	+	4.59768i	0.122775	+	0.275256i
$280$	−4.59549	+	3.94203i	−0.274633	+	0.235581i
$281$	−10.0287			−0.598262			−0.299131	−	0.954212i	$-0.596697\pi$
$281$	−10.0287			−0.598262			−0.299131	+	0.954212i	$0.596697\pi$
$282$	9.28379	−	4.73429i	0.552842	−	0.281923i
$283$			22.8820i			1.36019i	0.733123	+	0.680097i	$0.238062\pi$
$283$			22.8820i			1.36019i	−0.733123	+	0.680097i	$0.761938\pi$
$284$	2.29991			0.136474
$285$	26.2360	+	17.0252i	1.55409	+	1.00849i
$286$	−0.902838	+	0.576790i	−0.0533859	+	0.0341063i
$287$	15.1206	−	12.9705i	0.892543	−	0.765626i
$288$	−2.98378	−	0.311563i	−0.175821	−	0.0183590i
$289$	8.10098	−	14.0313i	0.476528	−	0.825371i
$290$	−1.29605	−	2.24482i	−0.0761065	−	0.131820i
$291$	4.12868	+	0.214972i	0.242027	+	0.0126019i
$292$	12.3260			0.721327
$293$	17.4353	+	10.0663i	1.01858	+	0.588080i	0.913693	−	0.406404i	$-0.133217\pi$
$293$	17.4353	+	10.0663i	1.01858	+	0.588080i	0.104890	+	0.994484i	$0.466551\pi$
$294$	11.5135	−	3.80005i	0.671478	−	0.221623i
$295$	6.89293	−	11.9389i	0.401322	−	0.695110i
$296$	−4.32929	−	2.49951i	−0.251635	−	0.145281i
$297$	−1.52522	−	0.239983i	−0.0885025	−	0.0139252i
$298$	−1.64375	+	2.84705i	−0.0952198	+	0.164925i
$299$	−15.1649	−	23.7373i	−0.877010	−	1.37277i
$300$	−0.186386	−	0.365496i	−0.0107610	−	0.0211019i
$301$	3.40954	−	9.69439i	0.196523	−	0.558775i
$302$	−10.5899	+	6.11409i	−0.609381	+	0.351826i
$303$	14.7750	+	28.9732i	0.848800	+	1.66447i
$304$	3.94533	−	6.83352i	0.226280	−	0.391929i
$305$	9.66580	+	16.7417i	0.553462	+	0.958625i
$306$	−1.57378	+	2.16922i	−0.0899673	+	0.124006i
$307$	−3.07801			−0.175672			−0.0878358	−	0.996135i	$-0.527995\pi$
$307$	−3.07801			−0.175672			−0.0878358	+	0.996135i	$0.527995\pi$
$308$	0.511853	+	0.596703i	0.0291656	+	0.0340003i
$309$	−20.7864	−	13.4888i	−1.18250	−	0.767353i
$310$	3.32572	+	1.92010i	0.188888	+	0.109055i
$311$	−7.75963	+	13.4401i	−0.440008	+	0.762117i	−0.997690	−	0.0679384i	$-0.978358\pi$
$311$	−7.75963	+	13.4401i	−0.440008	+	0.762117i	0.557681	+	0.830055i	$0.311691\pi$
$312$	−0.0444224	+	6.24484i	−0.00251492	+	0.353544i
$313$	13.7068	−	7.91361i	0.774752	−	0.447303i	−0.0598149	−	0.998209i	$-0.519051\pi$
$313$	13.7068	−	7.91361i	0.774752	−	0.447303i	0.834567	+	0.550906i	$0.185718\pi$
$314$	−15.4715	+	8.93248i	−0.873108	+	0.504089i
$315$	1.47629	+	18.1037i	0.0831793	+	1.02003i
$316$	4.46469	−	7.73307i	0.251159	−	0.435019i
$317$	−6.47213	−	11.2101i	−0.363511	−	0.629619i	0.625025	−	0.780605i	$-0.285089\pi$
$317$	−6.47213	−	11.2101i	−0.363511	−	0.629619i	−0.988536	+	0.150985i	$0.951755\pi$
$318$	10.5419	+	6.84092i	0.591161	+	0.383620i
$319$	−0.291479	+	0.168286i	−0.0163197	+	0.00942218i
$320$	−1.98183	+	1.14421i	−0.110788	+	0.0639633i
$321$	1.50272	−	28.8608i	0.0838737	−	1.61085i
$322$	−15.6885	+	13.4576i	−0.874283	+	0.749963i
$323$	−3.52448	−	6.10457i	−0.196107	−	0.339667i
$324$	−6.01310	+	6.69646i	−0.334061	+	0.372026i
$325$	−0.719721	+	0.459803i	−0.0399229	+	0.0255053i
$326$	−2.00708	−	1.15879i	−0.111162	−	0.0641793i
$327$	−1.00912	+	19.3808i	−0.0558045	+	1.07176i
$328$	6.52086	−	3.76482i	0.360054	−	0.207877i
$329$	−12.0824	+	10.3644i	−0.666127	+	0.571406i
$330$	−1.04922	+	0.535050i	−0.0577574	+	0.0294535i
$331$			8.96310i			0.492656i	0.969186	+	0.246328i	$0.0792241\pi$
$331$			8.96310i			0.492656i	−0.969186	+	0.246328i	$0.920776\pi$
$332$	−1.34122	+	0.774352i	−0.0736089	+	0.0424981i
$333$	−13.6964	+	6.10915i	−0.750557	+	0.334779i
$334$			13.3470i			0.730314i
$335$	3.88898	+	6.73591i	0.212477	+	0.368022i
$336$	4.54187	−	0.609446i	0.247779	−	0.0332480i
$337$	−7.76837			−0.423170			−0.211585	−	0.977360i	$-0.567863\pi$
$337$	−7.76837			−0.423170			−0.211585	+	0.977360i	$0.567863\pi$
$338$	12.9476	−	1.16603i	0.704257	−	0.0634237i
$339$	0.756079	−	14.5210i	0.0410646	−	0.788672i
$340$			2.04431i			0.110868i
$341$	0.249316	−	0.431828i	0.0135012	−	0.0233848i
$342$	−9.64293	−	21.6189i	−0.521430	−	1.16902i
$343$	−15.7284	+	9.77839i	−0.849255	+	0.527984i
$344$	1.94207	−	3.36377i	0.104710	−	0.181362i
$345$	−14.0675	−	27.5859i	−0.757368	−	1.48517i
$346$	9.18090	−	15.9018i	0.493568	−	0.854886i
$347$	−8.40123	+	4.85045i	−0.451002	+	0.260386i	−0.708253	−	0.705959i	$-0.750516\pi$
$347$	−8.40123	+	4.85045i	−0.451002	+	0.260386i	0.257251	+	0.966344i	$0.417183\pi$
$348$	−0.102014	+	1.95924i	−0.00546851	+	0.105026i
$349$	−13.2526	−	22.9542i	−0.709396	−	1.22871i	−0.965081	−	0.261950i	$-0.915635\pi$
$349$	−13.2526	−	22.9542i	−0.709396	−	1.22871i	0.255686	−	0.966760i	$-0.417699\pi$
$350$	0.408037	+	0.475677i	0.0218105	+	0.0254260i
$351$	15.0857	+	11.1095i	0.805218	+	0.592980i
$352$	0.148570	+	0.257331i	0.00791882	+	0.0137158i
$353$			25.6157i			1.36339i	0.731639	+	0.681693i	$0.238756\pi$
$353$			25.6157i			1.36339i	−0.731639	+	0.681693i	$0.761244\pi$
$354$	−9.29532	+	4.74017i	−0.494041	+	0.251937i
$355$		−	5.26316i		−	0.279340i
$356$		−	14.3106i		−	0.758460i
$357$	1.55719	−	3.78601i	0.0824154	−	0.200377i
$358$	8.93640	+	5.15943i	0.472303	+	0.272684i
$359$	6.41408	+	11.1095i	0.338522	+	0.586338i	0.984155	−	0.177310i	$-0.0567396\pi$
$359$	6.41408	+	11.1095i	0.338522	+	0.586338i	−0.645633	+	0.763648i	$0.723406\pi$
$360$	−0.712988	+	6.82814i	−0.0375778	+	0.359875i
$361$	43.2626			2.27698
$362$	−4.51843	−	2.60872i	−0.237483	−	0.137111i
$363$	−8.58596	−	16.8368i	−0.450646	−	0.883702i
$364$	−2.17770	−	9.28750i	−0.114143	−	0.486797i
$365$		−	28.2072i		−	1.47643i
$366$	0.760809	−	14.6118i	0.0397681	−	0.763773i
$367$		−	24.5596i		−	1.28200i	−0.767541	−	0.641000i	$-0.778520\pi$
$367$		−	24.5596i		−	1.28200i	0.767541	−	0.641000i	$-0.221480\pi$
$368$	−6.76573	+	3.90620i	−0.352688	+	0.203625i
$369$	2.34596	−	22.4668i	0.122126	−	1.16957i
$370$	−5.71994	+	9.90723i	−0.297366	+	0.515052i
$371$	−18.1091	−	6.36901i	−0.940177	−	0.330663i
$372$	−1.32043	−	2.58932i	−0.0684610	−	0.134250i
$373$	−21.4766			−1.11202			−0.556009	−	0.831176i	$-0.687668\pi$
$373$	−21.4766			−1.11202			−0.556009	+	0.831176i	$0.687668\pi$
$374$	0.265444			0.0137258
$375$	16.8188	−	8.57678i	0.868518	−	0.442903i
$376$	−5.21062	+	3.00835i	−0.268717	+	0.155144i
$377$	4.07989	−	0.183342i	0.210125	−	0.00944257i
$378$	6.52157	−	12.1024i	0.335434	−	0.622482i
$379$	−13.9171	+	8.03505i	−0.714874	+	0.412733i	−0.812863	−	0.582455i	$-0.802092\pi$
$379$	−13.9171	+	8.03505i	−0.714874	+	0.412733i	0.0979889	+	0.995188i	$0.468759\pi$
$380$	−15.6380	−	9.02859i	−0.802211	−	0.463157i
$381$	−4.96369	+	7.64908i	−0.254297	+	0.391874i
$382$	22.8395	+	13.1864i	1.16857	+	0.674675i
$383$		−	26.7854i		−	1.36867i	−0.729168	−	0.684335i	$-0.760093\pi$
$383$		−	26.7854i		−	1.36867i	0.729168	−	0.684335i	$-0.239907\pi$
$384$	1.72971	+	0.0900624i	0.0882688	+	0.00459598i
$385$	1.36551	−	1.17134i	0.0695927	−	0.0596968i
$386$	−2.77543	−	1.60239i	−0.141266	−	0.0815597i
$387$	−4.74669	−	10.6418i	−0.241288	−	0.540954i
$388$	−2.38692			−0.121178
$389$	3.67405	+	2.12122i	0.186282	+	0.107550i	0.590241	−	0.807227i	$-0.299033\pi$
$389$	3.67405	+	2.12122i	0.186282	+	0.107550i	−0.403959	+	0.914777i	$0.632366\pi$
$390$	14.2908	+	0.101657i	0.723644	+	0.00514761i
$391$			6.97903i			0.352945i
$392$	−6.52422	+	2.53663i	−0.329523	+	0.128119i
$393$	0.728364	−	1.12242i	0.0367411	−	0.0566184i
$394$	−25.9738			−1.30854
$395$	−17.6965	−	10.2171i	−0.890409	−	0.514078i
$396$	0.886602	+	0.0925781i	0.0445534	+	0.00465222i
$397$	−0.710146			−0.0356412			−0.0178206	−	0.999841i	$-0.505673\pi$
$397$	−0.710146			−0.0356412			−0.0178206	+	0.999841i	$0.505673\pi$
$398$		−	5.54735i		−	0.278063i
$399$	22.0839	+	28.6325i	1.10558	+	1.43342i
$400$	0.118437	+	0.205138i	0.00592183	+	0.0102569i
$401$	7.61652	−	13.1922i	0.380351	−	0.658787i	−0.610762	−	0.791815i	$-0.709137\pi$
$401$	7.61652	−	13.1922i	0.380351	−	0.658787i	0.991112	+	0.133028i	$0.0424700\pi$
$402$	0.306107	−	5.87898i	0.0152672	−	0.293217i
$403$	−5.09878	+	3.25742i	−0.253988	+	0.162264i
$404$	−9.38860	−	16.2615i	−0.467100	−	0.809041i
$405$	15.3243	+	13.7605i	0.761472	+	0.683766i
$406$	−0.552461	−	2.94548i	−0.0274182	−	0.146182i
$407$	1.28641	+	0.742707i	0.0637648	+	0.0368146i
$408$	0.842274	−	1.29795i	0.0416988	−	0.0642581i
$409$	13.0031	+	22.5221i	0.642964	+	1.11365i	0.984768	+	0.173875i	$0.0556289\pi$
$409$	13.0031	+	22.5221i	0.642964	+	1.11365i	−0.341804	+	0.939771i	$0.611038\pi$
$410$	−8.61550	−	14.9225i	−0.425489	−	0.736969i
$411$	2.43901	−	3.75853i	0.120307	−	0.185395i
$412$	12.3898	+	7.15323i	0.610399	+	0.352414i
$413$	12.0974	−	10.3772i	0.595276	−	0.510630i
$414$	−2.43406	+	23.3105i	−0.119627	+	1.14565i
$415$	1.77204	+	3.06927i	0.0869863	+	0.150665i
$416$	−0.161862	−	3.60192i	−0.00793596	−	0.176598i
$417$	1.06110	−	20.3791i	0.0519623	−	0.997970i
$418$	−1.17232	+	2.03052i	−0.0573400	+	0.0993158i
$419$	4.44170	+	7.69326i	0.216991	+	0.375840i	0.953887	−	0.300167i	$-0.0970423\pi$
$419$	4.44170	+	7.69326i	0.216991	+	0.375840i	−0.736895	+	0.676007i	$0.763709\pi$
$420$	−1.39467	−	10.3937i	−0.0680529	−	0.507161i
$421$		−	11.9274i		−	0.581308i	−0.956828	−	0.290654i	$-0.906127\pi$
$421$		−	11.9274i		−	0.581308i	0.956828	−	0.290654i	$-0.0938729\pi$
$422$	2.34080			0.113948
$423$	−1.87458	+	17.9525i	−0.0911454	+	0.872881i
$424$	−6.28351	−	3.62779i	−0.305154	−	0.176181i
$425$	0.211605			0.0102644
$426$	−2.16847	+	3.34163i	−0.105063	+	0.161902i
$427$	4.12020	+	21.9671i	0.199391	+	1.06306i
$428$			16.6853i			0.806516i
$429$	0.0131997	−	1.85560i	0.000637287	−	0.0895890i
$430$	−7.69772	−	4.44428i	−0.371217	−	0.214322i
$431$	−19.4830			−0.938462			−0.469231	−	0.883075i	$-0.655469\pi$
$431$	−19.4830			−0.938462			−0.469231	+	0.883075i	$0.655469\pi$
$432$	3.26594	−	4.04149i	0.157133	−	0.194446i
$433$	15.8703	+	9.16273i	0.762679	+	0.440333i	0.830257	−	0.557381i	$-0.188194\pi$
$433$	15.8703	+	9.16273i	0.762679	+	0.440333i	−0.0675780	+	0.997714i	$0.521527\pi$
$434$	2.89069	+	3.36988i	0.138758	+	0.161759i
$435$	4.48357	+	0.233450i	0.214971	+	0.0111931i
$436$		−	11.2047i		−	0.536607i
$437$	−53.3862	−	30.8225i	−2.55381	−	1.47444i
$438$	−11.6216	+	17.9090i	−0.555302	+	0.855724i
$439$	−2.15827	−	1.24608i	−0.103009	−	0.0594720i	0.447611	−	0.894229i	$-0.352275\pi$
$439$	−2.15827	−	1.24608i	−0.103009	−	0.0594720i	−0.550619	+	0.834757i	$0.685608\pi$
$440$	0.588883	−	0.339992i	0.0280739	−	0.0162085i
$441$	−5.33422	+	20.3112i	−0.254011	+	0.967201i
$442$	−2.85890	−	1.48362i	−0.135984	−	0.0705687i
$443$	14.4424	−	8.33832i	0.686179	−	0.396166i	−0.116000	−	0.993249i	$-0.537007\pi$
$443$	14.4424	−	8.33832i	0.686179	−	0.396166i	0.802179	+	0.597083i	$0.203674\pi$
$444$	7.71351	−	3.93352i	0.366067	−	0.186677i
$445$	−32.7487			−1.55244
$446$	−1.49367			−0.0707276
$447$	−2.58679	−	5.07261i	−0.122351	−	0.239926i
$448$	−2.60041	+	0.487738i	−0.122858	+	0.0230435i
$449$	18.5701	−	32.1643i	0.876375	−	1.51793i	0.0210850	−	0.999778i	$-0.493288\pi$
$449$	18.5701	−	32.1643i	0.876375	−	1.51793i	0.855290	−	0.518149i	$-0.173379\pi$
$450$	0.706777	+	0.0738010i	0.0333178	+	0.00347901i
$451$	−1.93761	+	1.11868i	−0.0912386	+	0.0526766i
$452$			8.39506i			0.394870i
$453$	1.10130	−	21.1512i	0.0517435	−	0.993769i
$454$		−	6.37084i		−	0.298998i
$455$	−21.2537	+	4.98350i	−0.996389	+	0.233630i
$456$	6.20883	+	12.1753i	0.290755	+	0.570161i
$457$	13.9495	+	8.05374i	0.652529	+	0.376738i	0.789425	−	0.613848i	$-0.210379\pi$
$457$	13.9495	+	8.05374i	0.652529	+	0.376738i	−0.136895	+	0.990586i	$0.543712\pi$
$458$	7.86764			0.367631
$459$	−1.66790	−	4.33186i	−0.0778509	−	0.202194i
$460$	8.93903	+	15.4829i	0.416784	+	0.721892i
$461$	−12.1978	−	7.04240i	−0.568108	−	0.327997i	0.188285	−	0.982114i	$-0.439707\pi$
$461$	−12.1978	−	7.04240i	−0.568108	−	0.327997i	−0.756393	+	0.654117i	$0.773040\pi$
$462$	−1.34957	+	0.181091i	−0.0627879	+	0.00842512i
$463$		−	20.5027i		−	0.952843i	−0.879217	−	0.476421i	$-0.841934\pi$
$463$		−	20.5027i		−	0.952843i	0.879217	−	0.476421i	$-0.158066\pi$
$464$		−	1.13270i		−	0.0525843i
$465$	−5.92545	+	3.02170i	−0.274786	+	0.140128i
$466$		−	9.29104i		−	0.430399i
$467$	2.86923	+	4.96965i	0.132772	+	0.229968i	0.924744	−	0.380589i	$-0.124279\pi$
$467$	2.86923	+	4.96965i	0.132772	+	0.229968i	−0.791972	+	0.610557i	$0.790946\pi$
$468$	−9.03149	−	5.95249i	−0.417481	−	0.275154i
$469$	1.65774	+	8.83834i	0.0765473	+	0.408116i
$470$	6.88438	+	11.9241i	0.317553	+	0.550018i
$471$	1.60896	−	30.9012i	0.0741370	−	1.42385i
$472$	5.21709	−	3.01209i	0.240136	−	0.138643i
$473$	−0.577069	+	0.999512i	−0.0265336	+	0.0459576i
$474$	7.02615	+	13.7781i	0.322722	+	0.632847i
$475$	−0.934544	+	1.61868i	−0.0428798	+	0.0742701i
$476$	−0.784171	+	2.22964i	−0.0359424	+	0.102196i
$477$	−19.8789	+	8.86680i	−0.910192	+	0.405983i
$478$	−11.3033	+	19.5780i	−0.517003	+	0.895475i
$479$			28.1682i			1.28704i	0.765430	+	0.643519i	$0.222526\pi$
$479$			28.1682i			1.28704i	−0.765430	+	0.643519i	$0.777474\pi$
$480$	0.206101	−	3.95830i	0.00940717	−	0.180671i
$481$	−9.70379	−	15.1891i	−0.442455	−	0.692565i
$482$	29.0874			1.32489
$483$	−4.76123	−	35.4829i	−0.216644	−	1.61453i
$484$	5.45585	+	9.44982i	0.247993	+	0.429537i
$485$			5.46228i			0.248029i
$486$	−4.06010	−	15.0504i	−0.184170	−	0.682702i
$487$	25.7292	−	14.8548i	1.16590	−	0.673133i	0.213190	−	0.977011i	$-0.431615\pi$
$487$	25.7292	−	14.8548i	1.16590	−	0.673133i	0.952711	+	0.303877i	$0.0982813\pi$
$488$			8.44757i			0.382404i
$489$	3.57602	−	1.82360i	0.161713	−	0.0824661i
$490$	5.80489	+	14.9302i	0.262238	+	0.674476i
$491$	35.4120	−	20.4451i	1.59812	−	0.922676i	0.606272	−	0.795258i	$-0.292664\pi$
$491$	35.4120	−	20.4451i	1.59812	−	0.922676i	0.991849	−	0.127418i	$-0.0406690\pi$
$492$	−0.678137	+	13.0241i	−0.0305728	+	0.587171i
$493$	−0.876307	−	0.505936i	−0.0394669	−	0.0227862i
$494$	23.9752	−	15.3169i	1.07869	−	0.689138i
$495$	0.211858	−	2.02892i	0.00952230	−	0.0911931i
$496$	0.839051	+	1.45328i	0.0376745	+	0.0652542i
$497$	2.01888	−	5.74031i	0.0905592	−	0.257488i
$498$	0.139480	−	2.67881i	0.00625025	−	0.120040i
$499$	−11.0351	+	6.37111i	−0.493998	+	0.285210i	−0.726232	−	0.687450i	$-0.758730\pi$
$499$	−11.0351	+	6.37111i	−0.493998	+	0.285210i	0.232233	+	0.972660i	$0.425397\pi$
$500$	−9.43971	+	5.45002i	−0.422157	+	0.243732i
$501$	−19.3924	−	12.5842i	−0.866386	−	0.562221i
$502$	6.89055	+	11.9348i	0.307540	+	0.532675i
$503$	20.5763	−	35.6392i	0.917453	−	1.58908i	0.114183	−	0.993460i	$-0.463575\pi$
$503$	20.5763	−	35.6392i	0.917453	−	1.58908i	0.803270	−	0.595615i	$-0.203092\pi$
$504$	−3.39681	+	7.17368i	−0.151306	+	0.319541i
$505$	−37.2132	+	21.4851i	−1.65597	+	0.956073i
$506$	2.01037	−	1.16069i	0.0893720	−	0.0515990i
$507$	−10.5135	+	19.9115i	−0.466920	+	0.884300i
$508$	2.63228	−	4.55924i	0.116788	−	0.202284i
$509$	15.5770	+	8.99339i	0.690439	+	0.398625i	0.803776	−	0.594932i	$-0.202821\pi$
$509$	15.5770	+	8.99339i	0.690439	+	0.398625i	−0.113338	+	0.993557i	$0.536154\pi$
$510$	−2.97026	−	1.92748i	−0.131525	−	0.0853502i
$511$	10.8199	−	30.7644i	0.478645	−	1.36094i
$512$	−1.00000			−0.0441942
$513$	40.5028	+	6.37282i	1.78824	+	0.281367i
$514$	2.81222	+	4.87090i	0.124042	+	0.214846i
$515$	16.3696	−	28.3530i	0.721331	−	1.24938i
$516$	3.05627	+	5.99324i	0.134545	+	0.263838i
$517$	1.54829	−	0.893904i	0.0680936	−	0.0393139i
$518$	−10.0388	+	8.61131i	−0.441079	+	0.378359i
$519$	14.4481	+	28.3323i	0.634202	+	1.24365i
$520$	−8.24270	+	0.370410i	−0.361466	+	0.0162435i
$521$	−12.5794	+	21.7881i	−0.551113	+	0.954555i	0.447082	+	0.894493i	$0.352463\pi$
$521$	−12.5794	+	21.7881i	−0.551113	+	0.954555i	−0.998195	+	0.0600622i	$0.980870\pi$
$522$	−2.75047	−	1.99549i	−0.120385	−	0.0873402i
$523$	−36.4677	−	21.0547i	−1.59462	−	0.920656i	−0.992499	−	0.122253i	$-0.960988\pi$
$523$	−36.4677	−	21.0547i	−1.59462	−	0.920656i	−0.602124	−	0.798403i	$-0.705679\pi$
$524$	−0.386257	+	0.669016i	−0.0168737	+	0.0292261i
$525$	−1.07585	+	0.144361i	−0.0469538	+	0.00630045i
$526$	16.7851	+	9.69087i	0.731864	+	0.422542i
$527$	1.49910			0.0653016
$528$	−0.513966	−	0.0267612i	−0.0223675	−	0.00116463i
$529$	19.0168	+	32.9380i	0.826816	+	1.43209i
$530$	−8.30191	+	14.3793i	−0.360612	+	0.624598i
$531$	1.87691	−	17.9748i	0.0814511	−	0.780040i
$532$	−13.5924	−	15.8456i	−0.589307	−	0.686995i
$533$	27.1211	−	1.21877i	1.17475	−	0.0527906i
$534$	20.7924	+	13.4927i	0.899776	+	0.583888i
$535$	38.1831			1.65080
$536$			3.39883i			0.146807i
$537$	−15.9220	+	8.11947i	−0.687086	+	0.350381i
$538$	27.9546			1.20521
$539$	1.93861	−	0.753737i	0.0835019	−	0.0324658i
$540$	−9.24864	−	7.47384i	−0.397998	−	0.321623i
$541$	15.7491	−	9.09276i	0.677107	−	0.390928i	−0.121657	−	0.992572i	$-0.538821\pi$
$541$	15.7491	−	9.09276i	0.677107	−	0.390928i	0.798764	+	0.601644i	$0.205487\pi$
$542$	10.2294	+	17.7179i	0.439391	+	0.761048i
$543$	8.05051	−	4.10538i	0.345480	−	0.176179i
$544$	−0.446664	+	0.773644i	−0.0191505	+	0.0331697i
$545$	−25.6410			−1.09834
$546$	15.5474	+	5.59265i	0.665368	+	0.239343i
$547$	7.61792			0.325719			0.162859	−	0.986649i	$-0.447928\pi$
$547$	7.61792			0.325719			0.162859	+	0.986649i	$0.447928\pi$
$548$	−1.29342	+	2.24027i	−0.0552523	+	0.0956997i
$549$	20.5128	+	14.8822i	0.875464	+	0.635156i
$550$	−0.0351923	−	0.0609549i	−0.00150061	−	0.00259913i
$551$	7.74033	−	4.46888i	0.329749	−	0.190381i
$552$	0.703603	−	13.5132i	0.0299473	−	0.575158i
$553$	−15.3817	−	17.9315i	−0.654098	−	0.762526i
$554$	−6.51069			−0.276613
$555$	−9.00156	−	17.6518i	−0.382095	−	0.749276i
$556$			11.7818i			0.499661i
$557$	31.7201			1.34402			0.672011	−	0.740541i	$-0.265431\pi$
$557$	31.7201			1.34402			0.672011	+	0.740541i	$0.265431\pi$
$558$	5.00709	+	0.522835i	0.211967	+	0.0221334i
$559$	11.8017	−	7.53965i	0.499157	−	0.318893i
$560$	1.11615	+	5.95083i	0.0471660	+	0.251468i
$561$	−0.250274	+	0.385674i	−0.0105666	+	0.0162832i
$562$	−5.01435	+	8.68510i	−0.211517	+	0.366359i
$563$	1.44913	+	2.50997i	0.0610737	+	0.105783i	0.894946	−	0.446175i	$-0.147214\pi$
$563$	1.44913	+	2.50997i	0.0610737	+	0.105783i	−0.833872	+	0.551958i	$0.813881\pi$
$564$	0.541879	−	10.4071i	0.0228172	−	0.438220i
$565$	19.2114			0.808231
$566$	19.8164	+	11.4410i	0.832945	+	0.480901i
$567$	11.4352	+	20.8862i	0.480235	+	0.877140i
$568$	1.14995	−	1.99178i	0.0482510	−	0.0835732i
$569$	32.8060	+	18.9406i	1.37530	+	0.794030i	0.991589	−	0.129423i	$-0.0413125\pi$
$569$	32.8060	+	18.9406i	1.37530	+	0.794030i	0.383711	+	0.923453i	$0.374646\pi$
$570$	27.8623	−	14.2084i	1.16702	−	0.595125i
$571$	−13.5869	+	23.5332i	−0.568594	+	0.984834i	0.428111	+	0.903726i	$0.359179\pi$
$571$	−13.5869	+	23.5332i	−0.568594	+	0.984834i	−0.996705	+	0.0811082i	$0.974154\pi$
$572$	0.0480959	+	1.07028i	0.00201099	+	0.0447505i
$573$	−40.6933	+	20.7516i	−1.69999	+	0.866912i
$574$	−3.67249	−	19.5801i	−0.153287	−	0.817259i
$575$	1.60262	−	0.925274i	0.0668340	−	0.0385866i
$576$	−1.76171	+	2.42825i	−0.0734046	+	0.101177i
$577$	19.0478	−	32.9918i	0.792972	−	1.37347i	−0.131147	−	0.991363i	$-0.541866\pi$
$577$	19.0478	−	32.9918i	0.792972	−	1.37347i	0.924119	−	0.382105i	$-0.124801\pi$
$578$	−8.10098	−	14.0313i	−0.336956	−	0.583626i
$579$	4.94500	−	2.52171i	0.205507	−	0.104799i
$580$	−2.59209			−0.107631
$581$	0.755362	+	4.02726i	0.0313377	+	0.167079i
$582$	2.25051	−	3.46805i	0.0932866	−	0.143755i
$583$	1.86709	+	1.07796i	0.0773268	+	0.0446447i
$584$	6.16302	−	10.6747i	0.255028	−	0.441721i
$585$	−13.6218	+	20.6679i	−0.563193	+	0.854511i
$586$	17.4353	−	10.0663i	0.720248	−	0.415835i
$587$	19.1503	−	11.0565i	0.790419	−	0.456349i	−0.0496910	−	0.998765i	$-0.515824\pi$
$587$	19.1503	−	11.0565i	0.790419	−	0.456349i	0.840110	+	0.542416i	$0.182490\pi$
$588$	2.46579	−	11.8710i	0.101687	−	0.489550i
$589$	−6.62068	+	11.4673i	−0.272800	+	0.472504i
$590$	−6.89293	−	11.9389i	−0.283777	−	0.491517i
$591$	24.4894	−	37.7384i	1.00736	−	1.55235i
$592$	−4.32929	+	2.49951i	−0.177933	+	0.102729i
$593$	−22.7957	+	13.1611i	−0.936109	+	0.540463i	−0.888738	−	0.458415i	$-0.848417\pi$
$593$	−22.7957	+	13.1611i	−0.936109	+	0.540463i	−0.0473705	+	0.998877i	$0.515084\pi$
$594$	−0.970443	+	1.20089i	−0.0398178	+	0.0492732i
$595$	5.10237	+	1.79451i	0.209177	+	0.0735679i
$596$	1.64375	+	2.84705i	0.0673305	+	0.116620i
$597$	8.05996	+	5.23032i	0.329872	+	0.214063i
$598$	−28.1396	+	1.26453i	−1.15071	+	0.0517106i
$599$	−5.69118	−	3.28581i	−0.232536	−	0.134254i	0.379206	−	0.925312i	$-0.376197\pi$
$599$	−5.69118	−	3.28581i	−0.232536	−	0.134254i	−0.611741	+	0.791058i	$0.709531\pi$
$600$	−0.409722	−	0.0213334i	−0.0167268	−	0.000870932i
$601$	−22.1774	+	12.8041i	−0.904634	+	0.522291i	−0.878701	−	0.477373i	$-0.841589\pi$
$601$	−22.1774	+	12.8041i	−0.904634	+	0.522291i	−0.0259335	+	0.999664i	$0.508256\pi$
$602$	−6.69082	−	7.79994i	−0.272697	−	0.317902i
$603$	8.25319	+	5.98775i	0.336096	+	0.243840i
$604$			12.2282i			0.497557i
$605$	21.6252	−	12.4853i	0.879188	−	0.507599i
$606$	32.4791	+	1.69112i	1.31937	+	0.0686970i
$607$		−	42.6384i		−	1.73064i	−0.501220	−	0.865320i	$-0.667115\pi$
$607$		−	42.6384i		−	1.73064i	0.501220	−	0.865320i	$-0.332885\pi$
$608$	−3.94533	−	6.83352i	−0.160004	−	0.277136i
$609$	4.80049	+	1.97445i	0.194526	+	0.0800089i
$610$	19.3316			0.782714
$611$	−21.6717	+	0.973879i	−0.876742	+	0.0393989i
$612$	1.09171	+	2.44755i	0.0441296	+	0.0989362i
$613$			4.01879i			0.162318i	0.996701	+	0.0811588i	$0.0258621\pi$
$613$			4.01879i			0.162318i	−0.996701	+	0.0811588i	$0.974138\pi$
$614$	−1.53901	+	2.66564i	−0.0621093	+	0.107576i
$615$	29.8046	+	1.55186i	1.20184	+	0.0625772i
$616$	0.772686	−	0.144927i	0.0311324	−	0.00583927i
$617$	−12.9809	+	22.4837i	−0.522593	+	0.905158i	0.477061	+	0.878870i	$0.341702\pi$
$617$	−12.9809	+	22.4837i	−0.522593	+	0.905158i	−0.999654	+	0.0262879i	$0.991631\pi$
$618$	−22.0749	+	11.2571i	−0.887982	+	0.452829i
$619$	−2.84282	+	4.92392i	−0.114263	+	0.197909i	−0.917485	−	0.397771i	$-0.869784\pi$
$619$	−2.84282	+	4.92392i	−0.114263	+	0.197909i	0.803222	+	0.595680i	$0.203117\pi$
$620$	3.32572	−	1.92010i	0.133564	−	0.0771132i
$621$	−31.5737	−	25.5148i	−1.26701	−	1.02387i
$622$	7.75963	+	13.4401i	0.311133	+	0.538898i
$623$	−35.7176	−	12.5620i	−1.43100	−	0.503285i
$624$	5.38598	+	3.16089i	0.215612	+	0.126537i
$625$	13.0641	+	22.6277i	0.522565	+	0.905109i
$626$		−	15.8272i		−	0.632583i
$627$	−1.84490	−	3.61778i	−0.0736781	−	0.144480i
$628$			17.8650i			0.712889i
$629$			4.46577i			0.178062i
$630$	16.4164	+	7.77334i	0.654045	+	0.309697i
$631$	11.9099	+	6.87621i	0.474128	+	0.273738i	0.717966	−	0.696078i	$-0.245073\pi$
$631$	11.9099	+	6.87621i	0.474128	+	0.273738i	−0.243838	+	0.969816i	$0.578407\pi$
$632$	−4.46469	−	7.73307i	−0.177596	−	0.307605i
$633$	−2.20702	+	3.40104i	−0.0877213	+	0.135179i
$634$	−12.9443			−0.514082
$635$	−10.4335	−	6.02376i	−0.414039	−	0.239046i
$636$	11.1954	−	5.70910i	0.443925	−	0.226381i
$637$	−25.0921	−	2.71736i	−0.994187	−	0.107666i
$638$			0.336571i			0.0133250i
$639$	−2.81064	−	6.30131i	−0.111187	−	0.249276i
$640$			2.28842i			0.0904578i
$641$	−5.44576	+	3.14411i	−0.215094	+	0.124185i	−0.603677	−	0.797229i	$-0.706298\pi$
$641$	−5.44576	+	3.14411i	−0.215094	+	0.124185i	0.388582	+	0.921414i	$0.372965\pi$
$642$	−24.2428	−	15.7318i	−0.956787	−	0.620884i
$643$	17.3160	−	29.9922i	0.682877	−	1.18278i	−0.291222	−	0.956656i	$-0.594062\pi$
$643$	17.3160	−	29.9922i	0.682877	−	1.18278i	0.974099	−	0.226122i	$-0.0726049\pi$
$644$	3.81040	+	20.3154i	0.150151	+	0.800539i
$645$	13.7151	−	6.99403i	0.540030	−	0.275390i
$646$	−7.04895			−0.277337
$647$	−18.1269			−0.712643			−0.356322	−	0.934363i	$-0.615969\pi$
$647$	−18.1269			−0.712643			−0.356322	+	0.934363i	$0.615969\pi$
$648$	2.79275	+	8.55573i	0.109710	+	0.336101i
$649$	−1.55021	+	0.895014i	−0.0608511	+	0.0351324i
$650$	0.0383409	+	0.853198i	0.00150385	+	0.0334652i
$651$	−7.62172	+	1.02271i	−0.298719	+	0.0400833i
$652$	−2.00708	+	1.15879i	−0.0786033	+	0.0453816i
$653$	−34.7749	−	20.0773i	−1.36085	−	0.785685i	−0.371110	−	0.928589i	$-0.621023\pi$
$653$	−34.7749	−	20.0773i	−1.36085	−	0.785685i	−0.989737	+	0.142904i	$0.954356\pi$
$654$	16.2797	+	10.5643i	0.636588	+	0.413098i
$655$	1.53099	+	0.883918i	0.0598208	+	0.0345375i
$656$		−	7.52964i		−	0.293983i
$657$	−15.0632	−	33.7710i	−0.587673	−	1.31753i
$658$	2.93458	+	15.6459i	0.114402	+	0.609940i
$659$	15.7627	+	9.10062i	0.614029	+	0.354510i	0.774541	−	0.632524i	$-0.217981\pi$
$659$	15.7627	+	9.10062i	0.614029	+	0.354510i	−0.160512	+	0.987034i	$0.551314\pi$
$660$	−0.0612409	+	1.17617i	−0.00238380	+	0.0457824i
$661$	23.1137			0.899020			0.449510	−	0.893275i	$-0.351599\pi$
$661$	23.1137			0.899020			0.449510	+	0.893275i	$0.351599\pi$
$662$	7.76227	+	4.48155i	0.301689	+	0.174180i
$663$	4.85113	−	2.75498i	0.188402	−	0.106994i
$664$			1.54870i			0.0601014i
$665$	−36.2615	+	31.1052i	−1.40616	+	1.20621i
$666$	−1.55751	+	14.9160i	−0.0603524	+	0.577983i
$667$	−8.84910			−0.342639
$668$	11.5588	+	6.67349i	0.447224	+	0.258205i
$669$	1.40831	−	2.17022i	0.0544485	−	0.0839055i
$670$	7.77795			0.300489
$671$		−	2.51012i		−	0.0969020i
$672$	1.74314	−	4.23810i	0.0672431	−	0.163488i
$673$	−18.1450	−	31.4281i	−0.699438	−	1.21146i	−0.968661	−	0.248385i	$-0.920100\pi$
$673$	−18.1450	−	31.4281i	−0.699438	−	1.21146i	0.269223	−	0.963078i	$-0.413233\pi$
$674$	−3.88418	+	6.72760i	−0.149613	+	0.259138i
$675$	−0.773614	+	0.957321i	−0.0297764	+	0.0368473i
$676$	5.46399	−	11.7960i	0.210153	−	0.453691i
$677$	2.13681	+	3.70106i	0.0821243	+	0.142243i	0.904162	−	0.427189i	$-0.140496\pi$
$677$	2.13681	+	3.70106i	0.0821243	+	0.142243i	−0.822038	+	0.569433i	$0.807163\pi$
$678$	−12.1975	−	7.91528i	−0.468443	−	0.303985i
$679$	−2.09526	+	5.95749i	−0.0804088	+	0.228627i
$680$	1.77042	+	1.02215i	0.0678927	+	0.0391978i
$681$	9.25645	+	6.00675i	0.354708	+	0.230179i
$682$	−0.249316	−	0.431828i	−0.00954681	−	0.0165356i
$683$	15.0386	+	26.0477i	0.575438	+	0.996688i	0.995994	+	0.0894210i	$0.0285017\pi$
$683$	15.0386	+	26.0477i	0.575438	+	0.996688i	−0.420556	+	0.907267i	$0.638165\pi$
$684$	−23.5440	−	2.45844i	−0.900227	−	0.0940009i
$685$	5.12669	+	2.95989i	0.195881	+	0.113092i
$686$	0.604128	+	18.5104i	0.0230657	+	0.706730i
$687$	−7.41801	+	11.4312i	−0.283015	+	0.436128i
$688$	−1.94207	−	3.36377i	−0.0740408	−	0.128242i
$689$	−14.0841	−	22.0455i	−0.536560	−	0.839866i
$690$	−30.9238	−	1.61014i	−1.17725	−	0.0612970i
$691$	−8.59159	+	14.8811i	−0.326840	+	0.566103i	−0.981883	−	0.189489i	$-0.939317\pi$
$691$	−8.59159	+	14.8811i	−0.326840	+	0.566103i	0.655043	+	0.755591i	$0.272650\pi$
$692$	−9.18090	−	15.9018i	−0.349006	−	0.604495i
$693$	1.00933	−	2.13159i	0.0383413	−	0.0809725i
$694$			9.70091i			0.368241i
$695$	26.9618			1.02272
$696$	1.64574	+	1.06797i	0.0623818	+	0.0404812i
$697$	−5.82526	−	3.36322i	−0.220648	−	0.127391i
$698$	−26.5052			−1.00324
$699$	13.4993	+	8.76006i	0.510591	+	0.331336i
$700$	0.615967	−	0.115532i	0.0232814	−	0.00436671i
$701$			33.7755i			1.27568i	0.770167	+	0.637842i	$0.220173\pi$
$701$			33.7755i			1.27568i	−0.770167	+	0.637842i	$0.779827\pi$
$702$	17.1640	−	7.50990i	0.647812	−	0.283443i
$703$	−34.1610	−	19.7228i	−1.28840	−	0.743861i
$704$	0.297141			0.0111989
$705$	−23.8159	−	1.24005i	−0.896960	−	0.0467029i
$706$	22.1838	+	12.8078i	0.834900	+	0.482030i
$707$	−48.8283	+	9.15835i	−1.83638	+	0.344435i
$708$	−0.542552	+	10.4201i	−0.0203904	+	0.391610i
$709$		−	1.22167i		−	0.0458807i	−0.999737	−	0.0229403i	$-0.992697\pi$
$709$		−	1.22167i		−	0.0458807i	0.999737	−	0.0229403i	$-0.00730278\pi$
$710$	−4.55803	−	2.63158i	−0.171060	−	0.0987614i
$711$	−26.6433	−	2.78207i	−0.999202	−	0.104336i
$712$	−12.3933	−	7.15530i	−0.464460	−	0.268156i
$713$	11.3536	−	6.55500i	0.425196	−	0.245487i
$714$	−2.50018	−	3.24157i	−0.0935670	−	0.121313i
$715$	2.44924	−	0.110064i	0.0915965	−	0.00411615i
$716$	8.93640	−	5.15943i	0.333969	−	0.192817i
$717$	−17.7882	−	34.8821i	−0.664314	−	1.30270i
$718$	12.8282			0.478743
$719$	−31.0368			−1.15748			−0.578738	−	0.815514i	$-0.696455\pi$
$719$	−31.0368			−1.15748			−0.578738	+	0.815514i	$0.696455\pi$
$720$	5.55685	+	4.03154i	0.207092	+	0.150246i
$721$	28.7295	−	24.6443i	1.06994	−	0.917800i
$722$	21.6313	−	37.4666i	0.805035	−	1.39436i
$723$	−27.4251	+	42.2622i	−1.01995	+	1.57175i
$724$	−4.51843	+	2.60872i	−0.167926	+	0.0969522i
$725$			0.268306i			0.00996465i
$726$	−18.8741	−	0.982734i	−0.700482	−	0.0364727i
$727$		−	33.4726i		−	1.24143i	−0.784036	−	0.620716i	$-0.786842\pi$
$727$		−	33.4726i		−	1.24143i	0.784036	−	0.620716i	$-0.213158\pi$
$728$	−9.13206	−	2.75781i	−0.338457	−	0.102211i
$729$	25.6954	+	8.29123i	0.951683	+	0.307083i
$730$	−24.4281	−	14.1036i	−0.904125	−	0.521997i
$731$	−3.46981			−0.128336
$732$	−12.2738	−	7.96480i	−0.453653	−	0.294387i
$733$	12.3342	+	21.3634i	0.455573	+	0.789076i	0.998721	−	0.0505610i	$-0.0161009\pi$
$733$	12.3342	+	21.3634i	0.455573	+	0.789076i	−0.543148	+	0.839637i	$0.682768\pi$
$734$	−21.2692	−	12.2798i	−0.785061	−	0.453255i
$735$	−27.1658	−	5.64276i	−1.00202	−	0.208136i
$736$			7.81240i			0.287969i
$737$		−	1.00993i		−	0.0372013i
$738$	−18.2838	−	13.2650i	−0.673037	−	0.488293i
$739$		−	44.5264i		−	1.63793i	−0.573845	−	0.818964i	$-0.694549\pi$
$739$		−	44.5264i		−	1.63793i	0.573845	−	0.818964i	$-0.305451\pi$
$740$	5.71994	+	9.90723i	0.210269	+	0.364197i
$741$	−0.350522	+	49.2760i	−0.0128768	+	1.81020i
$742$	−14.5703	+	12.4984i	−0.534892	+	0.458832i
$743$	19.9258	+	34.5124i	0.731006	+	1.26614i	0.956454	+	0.291884i	$0.0942820\pi$
$743$	19.9258	+	34.5124i	0.731006	+	1.26614i	−0.225448	+	0.974255i	$0.572385\pi$
$744$	−2.90263	−	0.151134i	−0.106415	−	0.00554084i
$745$	6.51526	−	3.76159i	0.238701	−	0.137814i
$746$	−10.7383	+	18.5993i	−0.393158	+	0.680969i
$747$	3.76064	+	2.72837i	0.137594	+	0.0998258i
$748$	0.132722	−	0.229881i	0.00485279	−	0.00840529i
$749$	41.6447	+	14.6465i	1.52166	+	0.535173i
$750$	0.981684	−	18.8539i	0.0358460	−	0.688447i
$751$	8.99264	−	15.5757i	0.328146	−	0.568366i	−0.653998	−	0.756496i	$-0.726909\pi$
$751$	8.99264	−	15.5757i	0.328146	−	0.568366i	0.982144	+	0.188130i	$0.0602428\pi$
$752$			6.01671i			0.219407i
$753$	−23.8373	−	1.24116i	−0.868679	−	0.0452303i
$754$	1.88117	−	3.62496i	0.0685080	−	0.132013i
$755$	27.9832			1.01841
$756$	−7.22023	−	11.6991i	−0.262597	−	0.425491i
$757$	20.2665	+	35.1027i	0.736600	+	1.27583i	0.954018	+	0.299750i	$0.0969034\pi$
$757$	20.2665	+	35.1027i	0.736600	+	1.27583i	−0.217417	+	0.976079i	$0.569763\pi$
$758$			16.0701i			0.583692i
$759$	−0.209069	+	4.01531i	−0.00758873	+	0.145747i
$760$	−15.6380	+	9.02859i	−0.567249	+	0.327501i
$761$			1.38144i			0.0500770i	0.999686	+	0.0250385i	$0.00797084\pi$
$761$			1.38144i			0.0500770i	−0.999686	+	0.0250385i	$0.992029\pi$
$762$	4.14246	+	8.12322i	0.150065	+	0.294273i
$763$	−27.9656	−	9.83558i	−1.01242	−	0.356072i
$764$	22.8395	−	13.1864i	0.826305	−	0.477067i
$765$	5.60102	−	2.49828i	0.202505	−	0.0903256i
$766$	−23.1968	−	13.3927i	−0.838136	−	0.483898i
$767$	21.6986	−	0.975089i	0.783491	−	0.0352084i
$768$	0.942850	−	1.45294i	0.0340222	−	0.0524284i
$769$	3.70242	+	6.41278i	0.133513	+	0.231251i	0.925028	−	0.379898i	$-0.124041\pi$
$769$	3.70242	+	6.41278i	0.133513	+	0.231251i	−0.791516	+	0.611149i	$0.790708\pi$
$770$	−0.331654	−	1.76823i	−0.0119520	−	0.0637227i
$771$	−9.72863	−	0.506550i	−0.350368	−	0.0182430i
$772$	−2.77543	+	1.60239i	−0.0998899	+	0.0576714i
$773$	−4.71590	+	2.72273i	−0.169619	+	0.0979297i	−0.582406	−	0.812898i	$-0.697889\pi$
$773$	−4.71590	+	2.72273i	−0.169619	+	0.0979297i	0.412787	+	0.910828i	$0.364555\pi$
$774$	−11.5894	−	1.21016i	−0.416573	−	0.0434982i
$775$	−0.198749	−	0.344243i	−0.00713927	−	0.0123656i
$776$	−1.19346	+	2.06713i	−0.0428427	+	0.0742058i
$777$	−3.04664	−	22.7049i	−0.109297	−	0.814535i
$778$	3.67405	−	2.12122i	0.131721	−	0.0760493i
$779$	51.4539	−	29.7069i	1.84353	−	1.06436i
$780$	7.23345	−	12.3254i	0.258999	−	0.441320i
$781$	−0.341698	+	0.591838i	−0.0122269	+	0.0211776i
$782$	6.04402	+	3.48951i	0.216134	+	0.124785i
$783$	5.49261	−	2.11482i	0.196290	−	0.0755777i
$784$	−1.06532	+	6.91846i	−0.0380472	+	0.247088i
$785$	40.8825			1.45916
$786$	−0.607858	−	1.19199i	−0.0216816	−	0.0425169i
$787$	16.7747	+	29.0546i	0.597953	+	1.03568i	0.993123	+	0.117076i	$0.0373522\pi$
$787$	16.7747	+	29.0546i	0.597953	+	1.03568i	−0.395170	+	0.918608i	$0.629314\pi$
$788$	−12.9869	+	22.4940i	−0.462639	+	0.801314i
$789$	−29.9061	+	15.2507i	−1.06468	+	0.542938i
$790$	−17.6965	+	10.2171i	−0.629614	+	0.363508i
$791$	20.9531	+	7.36926i	0.745007	+	0.262021i
$792$	0.523476	−	0.721530i	0.0186009	−	0.0256385i
$793$	−14.0296	+	27.0346i	−0.498205	+	0.960027i
$794$	−0.355073	+	0.615005i	−0.0126011	+	0.0218257i
$795$	−13.0648	−	25.6197i	−0.463362	−	0.908638i
$796$	−4.80414	−	2.77367i	−0.170278	−	0.0983103i
$797$	16.9758	−	29.4030i	0.601315	−	1.04151i	−0.391308	−	0.920260i	$-0.627977\pi$
$797$	16.9758	−	29.4030i	0.601315	−	1.04151i	0.992622	−	0.121248i	$-0.0386895\pi$
$798$	35.8384	−	4.80893i	1.26867	−	0.170234i
$799$	4.65479	+	2.68744i	0.164675	+	0.0950750i
$800$	0.236873			0.00837474
$801$	−39.2083	+	17.4885i	−1.38536	+	0.617926i
$802$	−7.61652	−	13.1922i	−0.268949	−	0.465833i
$803$	−1.83128	+	3.17188i	−0.0646246	+	0.111933i
$804$	−4.93829	−	3.20459i	−0.174160	−	0.113017i
$805$	46.4902	−	8.71981i	1.63856	−	0.307333i
$806$	0.271622	+	6.04439i	0.00956747	+	0.212904i
$807$	−26.3570	+	40.6163i	−0.927810	+	1.42976i
$808$	−18.7772			−0.660579
$809$		−	24.7142i		−	0.868905i	−0.900695	−	0.434453i	$-0.856942\pi$
$809$		−	24.7142i		−	0.868905i	0.900695	−	0.434453i	$-0.143058\pi$
$810$	19.5791	−	6.39100i	0.687940	−	0.224557i
$811$	−17.8537			−0.626927			−0.313464	−	0.949600i	$-0.601489\pi$
$811$	−17.8537			−0.626927			−0.313464	+	0.949600i	$0.601489\pi$
$812$	−2.82709	−	0.994295i	−0.0992114	−	0.0348929i
$813$	−35.3878	−	1.84257i	−1.24110	−	0.0646218i
$814$	1.28641	−	0.742707i	0.0450885	−	0.0260319i
$815$	2.65179	+	4.59304i	0.0928883	+	0.160887i
$816$	−0.702921	−	1.37841i	−0.0246072	−	0.0482539i
$817$	15.3243	−	26.5424i	0.536128	−	0.928600i
$818$	26.0063			0.909289
$819$	−22.7847	+	17.3164i	−0.796161	+	0.605085i
$820$	−17.2310			−0.601732
$821$	−16.2192	+	28.0926i	−0.566056	+	0.980437i	0.430895	+	0.902402i	$0.358198\pi$
$821$	−16.2192	+	28.0926i	−0.566056	+	0.980437i	−0.996951	+	0.0780351i	$0.975135\pi$
$822$	−2.03548	−	3.99151i	−0.0709954	−	0.139220i
$823$	−11.7933	−	20.4265i	−0.411087	−	0.712024i	0.583921	−	0.811810i	$-0.301518\pi$
$823$	−11.7933	−	20.4265i	−0.411087	−	0.712024i	−0.995009	+	0.0997858i	$0.968184\pi$
$824$	12.3898	−	7.15323i	0.431618	−	0.249194i
$825$	0.121745	+	0.00633901i	0.00423861	+	0.000220696i
$826$	−2.93822	−	15.6653i	−0.102234	−	0.545066i
$827$	−11.5185			−0.400539			−0.200269	−	0.979741i	$-0.564182\pi$
$827$	−11.5185			−0.400539			−0.200269	+	0.979741i	$0.564182\pi$
$828$	18.9704	+	13.7632i	0.659268	+	0.478304i
$829$		−	36.4890i		−	1.26731i	−0.773614	−	0.633657i	$-0.781553\pi$
$829$		−	36.4890i		−	1.26731i	0.773614	−	0.633657i	$-0.218447\pi$
$830$	3.54409			0.123017
$831$	6.13861	−	9.45964i	0.212946	−	0.328151i
$832$	−3.20028	−	1.66078i	−0.110950	−	0.0575772i
$833$	4.87659	+	3.91440i	0.168964	+	0.135626i
$834$	−17.1183	−	11.1085i	−0.592758	−	0.384656i
$835$	15.2718	−	26.4515i	0.528501	−	0.915390i
$836$	1.17232	+	2.03052i	0.0405455	+	0.0702269i
$837$	−5.48058	+	6.78204i	−0.189437	+	0.234422i
$838$	8.88341			0.306872
$839$	27.0771	+	15.6330i	0.934807	+	0.539711i	0.888329	−	0.459209i	$-0.151867\pi$
$839$	27.0771	+	15.6330i	0.934807	+	0.539711i	0.0464780	+	0.998919i	$0.485200\pi$
$840$	−9.69855	−	3.98904i	−0.334632	−	0.137635i
$841$	−13.8585	+	24.0036i	−0.477879	+	0.827711i
$842$	−10.3295	−	5.96372i	−0.355977	−	0.205523i
$843$	−7.89115	−	15.4743i	−0.271786	−	0.532963i
$844$	1.17040	−	2.02719i	0.0402868	−	0.0697788i
$845$	−26.9941	−	12.5039i	−0.928627	−	0.430148i
$846$	14.6100	+	10.5997i	0.502304	+	0.364425i
$847$	28.3749	−	5.32206i	0.974972	−	0.182868i
$848$	−6.28351	+	3.62779i	−0.215777	+	0.124579i
$849$	−35.3070	+	18.0049i	−1.21173	+	0.617925i
$850$	0.105803	−	0.183256i	0.00362900	−	0.00628562i
$851$	19.5272	+	33.8221i	0.669384	+	1.15941i
$852$	1.80970	+	3.54876i	0.0619993	+	0.121579i
$853$	33.1802			1.13607			0.568034	−	0.823005i	$-0.307704\pi$
$853$	33.1802			1.13607			0.568034	+	0.823005i	$0.307704\pi$
$854$	21.0842	+	7.41536i	0.721486	+	0.253748i
$855$	−5.62595	+	53.8786i	−0.192403	+	1.84261i
$856$	14.4499	+	8.34267i	0.493888	+	0.285147i
$857$	3.94184	−	6.82747i	0.134651	−	0.233222i	−0.790813	−	0.612058i	$-0.790342\pi$
$857$	3.94184	−	6.82747i	0.134651	−	0.233222i	0.925464	+	0.378836i	$0.123675\pi$
$858$	−1.60039	−	0.939229i	−0.0546365	−	0.0320648i
$859$	−16.8815	+	9.74653i	−0.575989	+	0.332547i	−0.759538	−	0.650463i	$-0.774575\pi$
$859$	−16.8815	+	9.74653i	−0.575989	+	0.332547i	0.183549	+	0.983011i	$0.441241\pi$
$860$	−7.69772	+	4.44428i	−0.262490	+	0.151549i
$861$	31.9113	+	13.1252i	1.08754	+	0.447306i
$862$	−9.74149	+	16.8728i	−0.331796	+	0.574688i
$863$	−5.07880	−	8.79674i	−0.172884	−	0.299445i	0.766543	−	0.642193i	$-0.221975\pi$
$863$	−5.07880	−	8.79674i	−0.172884	−	0.299445i	−0.939427	+	0.342749i	$0.888642\pi$
$864$	−1.86707	−	4.84913i	−0.0635188	−	0.164971i
$865$	−36.3900	+	21.0098i	−1.23730	+	0.714354i
$866$	15.8703	−	9.16273i	0.539295	−	0.311362i
$867$	28.0247	+	1.45919i	0.951768	+	0.0495566i
$868$	4.36375	−	0.818475i	0.148115	−	0.0277808i
$869$	1.32664	+	2.29781i	0.0450032	+	0.0779479i
$870$	2.44396	−	3.76616i	0.0828579	−	0.127685i
$871$	−5.64471	+	10.8772i	−0.191264	+	0.368560i
$872$	−9.70354	−	5.60234i	−0.328603	−	0.189719i
$873$	2.91698	+	6.53971i	0.0987247	+	0.221336i
$874$	−53.3862	+	30.8225i	−1.80581	+	1.04259i
$875$	5.31637	+	28.3445i	0.179726	+	0.958220i
$876$	9.69883	+	19.0191i	0.327693	+	0.642596i
$877$			8.41388i			0.284117i	0.989858	+	0.142058i	$0.0453720\pi$
$877$			8.41388i			0.284117i	−0.989858	+	0.142058i	$0.954628\pi$
$878$	−2.15827	+	1.24608i	−0.0728381	+	0.0420531i
$879$	−1.81319	+	34.8235i	−0.0611574	+	1.17457i
$880$		−	0.679983i		−	0.0229222i
$881$	3.40189	+	5.89224i	0.114612	+	0.198515i	0.917625	−	0.397448i	$-0.130104\pi$
$881$	3.40189	+	5.89224i	0.114612	+	0.198515i	−0.803012	+	0.595962i	$0.796771\pi$
$882$	14.9229	+	14.7752i	0.502481	+	0.497506i
$883$	−8.76402			−0.294933			−0.147466	−	0.989067i	$-0.547112\pi$
$883$	−8.76402			−0.294933			−0.147466	+	0.989067i	$0.547112\pi$
$884$	−2.71430	+	1.73407i	−0.0912919	+	0.0583231i
$885$	23.8455	+	1.24159i	0.801558	+	0.0417355i
$886$		−	16.6766i		−	0.560263i
$887$	−9.70164	+	16.8037i	−0.325749	+	0.564214i	−0.981664	−	0.190621i	$-0.938950\pi$
$887$	−9.70164	+	16.8037i	−0.325749	+	0.564214i	0.655914	+	0.754835i	$0.272283\pi$
$888$	0.450224	−	8.64686i	0.0151085	−	0.290170i
$889$	−9.06871	−	10.5720i	−0.304155	−	0.354574i
$890$	−16.3743	+	28.3612i	−0.548869	+	0.950669i
$891$	−0.829840	−	2.54226i	−0.0278007	−	0.0851688i
$892$	−0.746837	+	1.29356i	−0.0250060	+	0.0433116i
$893$	−41.1153	+	23.7379i	−1.37587	+	0.794359i
$894$	−5.68641	−	0.296080i	−0.190182	−	0.00990239i
$895$	−11.8070	−	20.4502i	−0.394663	−	0.683576i
$896$	−0.877809	+	2.49589i	−0.0293256	+	0.0833817i
$897$	24.6941	−	42.0774i	0.824513	−	1.40492i
$898$	−18.5701	−	32.1643i	−0.619691	−	1.07334i
$899$			1.90079i			0.0633948i
$900$	0.417302	−	0.575187i	0.0139101	−	0.0191729i
$901$			6.48161i			0.215934i
$902$			2.23736i			0.0744960i
$903$	17.6413	−	2.36718i	0.587065	−	0.0787747i
$904$	7.27033	+	4.19753i	0.241808	+	0.139608i
$905$	5.96984	+	10.3401i	0.198444	+	0.343716i
$906$	−17.7668	−	11.5293i	−0.590262	−	0.383037i
$907$	−16.6204			−0.551872			−0.275936	−	0.961176i	$-0.588988\pi$
$907$	−16.6204			−0.551872			−0.275936	+	0.961176i	$0.588988\pi$
$908$	−5.51731	−	3.18542i	−0.183098	−	0.105712i
$909$	−33.0800	+	45.5956i	−1.09719	+	1.51231i
$910$	−6.31102	+	20.8980i	−0.209208	+	0.692762i
$911$		−	17.4495i		−	0.578127i	−0.957310	−	0.289063i	$-0.906656\pi$
$911$		−	17.4495i		−	0.578127i	0.957310	−	0.289063i	$-0.0933439\pi$
$912$	13.6485	+	0.710652i	0.451949	+	0.0235321i
$913$		−	0.460183i		−	0.0152298i
$914$	13.9495	−	8.05374i	0.461408	−	0.266394i
$915$	−18.2268	+	28.0877i	−0.602560	+	0.928549i
$916$	3.93382	−	6.81358i	0.129977	−	0.225127i
$917$	1.33073	+	1.55132i	0.0439445	+	0.0512292i
$918$	−4.58545	−	0.721486i	−0.151342	−	0.0238126i
$919$	16.1766			0.533616			0.266808	−	0.963750i	$-0.414031\pi$
$919$	16.1766			0.533616			0.266808	+	0.963750i	$0.414031\pi$
$920$	17.8781			0.589422
$921$	−2.42196	−	4.74938i	−0.0798062	−	0.156497i
$922$	−12.1978	+	7.04240i	−0.401713	+	0.231929i
$923$	6.98809	−	4.46443i	0.230016	−	0.146949i
$924$	−0.517957	+	1.25931i	−0.0170396	+	0.0414283i
$925$	1.02549	−	0.592068i	0.0337180	−	0.0194671i
$926$	−17.7559	−	10.2514i	−0.583495	−	0.336881i
$927$	4.45737	−	42.6873i	0.146399	−	1.40203i
$928$	−0.980947	−	0.566350i	−0.0322012	−	0.0185913i
$929$			19.1713i			0.628990i	0.949259	+	0.314495i	$0.101835\pi$
$929$			19.1713i			0.628990i	−0.949259	+	0.314495i	$0.898165\pi$
$930$	−0.345858	+	6.64244i	−0.0113411	+	0.217814i
$931$	−51.4805	+	20.0157i	−1.68720	+	0.655989i
$932$	−8.04627	−	4.64552i	−0.263564	−	0.152169i
$933$	−26.8438	−	1.39770i	−0.878826	−	0.0457587i
$934$	5.73845			0.187768
$935$	−0.526065	−	0.303724i	−0.0172042	−	0.00993283i
$936$	−9.67075	+	4.84526i	−0.316099	+	0.158372i
$937$			38.4000i			1.25447i	0.778828	+	0.627237i	$0.215814\pi$
$937$			38.4000i			1.25447i	−0.778828	+	0.627237i	$0.784186\pi$
$938$	8.48309	+	2.98352i	0.276983	+	0.0974155i
$939$	22.9960	+	14.9227i	0.750446	+	0.486984i
$940$	13.7688			0.449088
$941$	6.21610	+	3.58887i	0.202639	+	0.116994i	0.597886	−	0.801581i	$-0.296008\pi$
$941$	6.21610	+	3.58887i	0.202639	+	0.116994i	−0.395247	+	0.918575i	$0.629341\pi$
$942$	−25.9567	−	16.8440i	−0.845715	−	0.548806i
$943$	−58.8245			−1.91559
$944$		−	6.02418i		−	0.196070i
$945$	−26.7724	+	16.5229i	−0.870906	+	0.537491i
$946$	0.577069	+	0.999512i	0.0187621	+	0.0324970i
$947$	12.3986	−	21.4750i	0.402899	−	0.697842i	−0.591175	−	0.806543i	$-0.701336\pi$
$947$	12.3986	−	21.4750i	0.402899	−	0.697842i	0.994074	+	0.108701i	$0.0346691\pi$
$948$	15.4452	+	0.804202i	0.501638	+	0.0261193i
$949$	37.4517	−	23.9265i	1.21573	−	0.776687i
$950$	0.934544	+	1.61868i	0.0303206	+	0.0525169i
$951$	12.2045	−	18.8072i	0.395758	−	0.609866i
$952$	1.53884	+	1.79393i	0.0498742	+	0.0581417i
$953$	−17.1692	−	9.91265i	−0.556165	−	0.321102i	0.195440	−	0.980716i	$-0.437387\pi$
$953$	−17.1692	−	9.91265i	−0.556165	−	0.321102i	−0.751605	+	0.659614i	$0.770720\pi$
$954$	−2.26057	+	21.6490i	−0.0731887	+	0.700913i
$955$	−30.1761	−	52.2665i	−0.976474	−	1.69130i
$956$	11.3033	+	19.5780i	0.365576	+	0.633196i
$957$	−0.489018	−	0.317336i	−0.0158077	−	0.0102580i
$958$	24.3944	+	14.0841i	0.788147	+	0.455037i
$959$	4.45609	+	5.19477i	0.143895	+	0.167748i
$960$	−3.32494	−	2.15764i	−0.107312	−	0.0696375i
$961$	14.0920	+	24.4080i	0.454580	+	0.787356i
$962$	−18.0061	+	0.809155i	−0.580539	+	0.0260882i
$963$	45.7146	−	20.3906i	1.47313	−	0.657078i
$964$	14.5437	−	25.1904i	0.468421	−	0.811329i
$965$	3.66695	+	6.35135i	0.118043	+	0.204457i
$966$	−33.1097	−	13.6181i	−1.06529	−	0.438155i
$967$			4.47698i			0.143970i	0.997406	+	0.0719849i	$0.0229333\pi$
$967$			4.47698i			0.143970i	−0.997406	+	0.0719849i	$0.977067\pi$
$968$	10.9117			0.350716
$969$	6.64610	−	10.2417i	0.213504	−	0.329011i
$970$	4.73047	+	2.73114i	0.151886	+	0.0876917i
$971$	−12.5415			−0.402477			−0.201239	−	0.979542i	$-0.564497\pi$
$971$	−12.5415			−0.402477			−0.201239	+	0.979542i	$0.564497\pi$
$972$	−15.0641	−	4.00907i	−0.483181	−	0.128591i
$973$	29.4061	+	10.3422i	0.942717	+	0.331556i
$974$		−	29.7095i		−	0.951954i
$975$	−1.27579	−	0.748731i	−0.0408581	−	0.0239786i
$976$	7.31581	+	4.22379i	0.234173	+	0.135200i
$977$	54.6021			1.74687			0.873437	−	0.486937i	$-0.161886\pi$
$977$	54.6021			1.74687			0.873437	+	0.486937i	$0.161886\pi$
$978$	0.208726	−	4.00873i	0.00667433	−	0.128185i
$979$	3.68256	+	2.12613i	0.117695	+	0.0679514i
$980$	15.8324	+	2.43790i	0.505746	+	0.0778760i
$981$	−30.6987	+	13.6929i	−0.980134	+	0.437180i
$982$		−	40.8902i		−	1.30486i
$983$	40.1578	+	23.1851i	1.28083	+	0.739490i	0.977001	−	0.213236i	$-0.0684002\pi$
$983$	40.1578	+	23.1851i	1.28083	+	0.739490i	0.303833	+	0.952725i	$0.401734\pi$
$984$	10.9401	+	7.09932i	0.348758	+	0.226318i
$985$	51.4757	+	29.7195i	1.64015	+	0.946942i
$986$	−0.876307	+	0.505936i	−0.0279073	+	0.0161123i
$987$	−25.4994	−	10.4880i	−0.811655	−	0.333835i
$988$	−1.27720	−	28.4215i	−0.0406332	−	0.904209i
$989$	−26.2791	+	15.1722i	−0.835627	+	0.482449i
$990$	−1.65117	−	1.19793i	−0.0524775	−	0.0380728i
$991$	8.41250			0.267232			0.133616	−	0.991033i	$-0.457341\pi$
$991$	8.41250			0.267232			0.133616	+	0.991033i	$0.457341\pi$
$992$	1.67810			0.0532798
$993$	−13.8301	+	7.05268i	−0.438884	+	0.223810i
$994$	−3.96181	−	4.61856i	−0.125661	−	0.146492i
$995$	−6.34734	+	10.9939i	−0.201224	+	0.348530i
$996$	−2.25017	−	1.46020i	−0.0712995	−	0.0462681i
$997$	−53.5194	+	30.8994i	−1.69498	+	0.978595i	−0.744590	+	0.667522i	$0.767355\pi$
$997$	−53.5194	+	30.8994i	−1.69498	+	0.978595i	−0.950386	+	0.311073i	$0.899312\pi$
$998$			12.7422i			0.403348i
$999$	−20.2035	−	16.3265i	−0.639211	−	0.516548i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bn.f.101.11	yes	34
3.2	odd	2		546.2.bn.e.101.7	yes	34
7.5	odd	6		546.2.bi.e.257.17	yes	34
13.4	even	6		546.2.bi.f.17.11	yes	34
21.5	even	6		546.2.bi.f.257.11	yes	34
39.17	odd	6		546.2.bi.e.17.17	✓	34
91.82	odd	6		546.2.bn.e.173.7	yes	34
273.173	even	6	inner	546.2.bn.f.173.11	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.17	✓	34	39.17	odd	6
546.2.bi.e.257.17	yes	34	7.5	odd	6
546.2.bi.f.17.11	yes	34	13.4	even	6
546.2.bi.f.257.11	yes	34	21.5	even	6
546.2.bn.e.101.7	yes	34	3.2	odd	2
546.2.bn.e.173.7	yes	34	91.82	odd	6
546.2.bn.f.101.11	yes	34	1.1	even	1	trivial
546.2.bn.f.173.11	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)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.786858 + 1.54300i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.98183 + 1.14421i) q^{5} +(1.72971 + 0.0900624i) q^{6} +(-2.60041 + 0.487738i) q^{7} -1.00000 q^{8} +(-1.76171 + 2.42825i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.786858 + 1.54300i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.98183 + 1.14421i) q^{5} +(1.72971 + 0.0900624i) q^{6} +(-2.60041 + 0.487738i) q^{7} -1.00000 q^{8} +(-1.76171 + 2.42825i) q^{9} +2.28842i q^{10} +0.297141 q^{11} +(0.942850 - 1.45294i) q^{12} +(-3.20028 - 1.66078i) q^{13} +(-0.877809 + 2.49589i) q^{14} +(-3.32494 - 2.15764i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.446664 + 0.773644i) q^{17} +(1.22207 + 2.73981i) q^{18} -7.89067 q^{19} +(1.98183 + 1.14421i) q^{20} +(-2.79873 - 3.62865i) q^{21} +(0.148570 - 0.257331i) q^{22} +(6.76573 + 3.90620i) q^{23} +(-0.786858 - 1.54300i) q^{24} +(0.118437 - 0.205138i) q^{25} +(-3.03842 + 1.94114i) q^{26} +(-5.13300 - 0.807639i) q^{27} +(1.72260 + 2.00815i) q^{28} +(-0.980947 + 0.566350i) q^{29} +(-3.53104 + 1.80066i) q^{30} +(0.839051 - 1.45328i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.233807 + 0.458489i) q^{33} +0.893327 q^{34} +(4.59549 - 3.94203i) q^{35} +(2.98378 + 0.311563i) q^{36} +(4.32929 + 2.49951i) q^{37} +(-3.94533 + 6.83352i) q^{38} +(0.0444224 - 6.24484i) q^{39} +(1.98183 - 1.14421i) q^{40} +(-6.52086 + 3.76482i) q^{41} +(-4.54187 + 0.609446i) q^{42} +(-1.94207 + 3.36377i) q^{43} +(-0.148570 - 0.257331i) q^{44} +(0.712988 - 6.82814i) q^{45} +(6.76573 - 3.90620i) q^{46} +(5.21062 - 3.00835i) q^{47} +(-1.72971 - 0.0900624i) q^{48} +(6.52422 - 2.53663i) q^{49} +(-0.118437 - 0.205138i) q^{50} +(-0.842274 + 1.29795i) q^{51} +(0.161862 + 3.60192i) q^{52} +(6.28351 + 3.62779i) q^{53} +(-3.26594 + 4.04149i) q^{54} +(-0.588883 + 0.339992i) q^{55} +(2.60041 - 0.487738i) q^{56} +(-6.20883 - 12.1753i) q^{57} +1.13270i q^{58} +(-5.21709 + 3.01209i) q^{59} +(-0.206101 + 3.95830i) q^{60} -8.44757i q^{61} +(-0.839051 - 1.45328i) q^{62} +(3.39681 - 7.17368i) q^{63} +1.00000 q^{64} +(8.24270 - 0.370410i) q^{65} +(0.513966 + 0.0267612i) q^{66} -3.39883i q^{67} +(0.446664 - 0.773644i) q^{68} +(-0.703603 + 13.5132i) q^{69} +(-1.11615 - 5.95083i) q^{70} +(-1.14995 + 1.99178i) q^{71} +(1.76171 - 2.42825i) q^{72} +(-6.16302 + 10.6747i) q^{73} +(4.32929 - 2.49951i) q^{74} +(0.409722 + 0.0213334i) q^{75} +(3.94533 + 6.83352i) q^{76} +(-0.772686 + 0.144927i) q^{77} +(-5.38598 - 3.16089i) q^{78} +(4.46469 + 7.73307i) q^{79} -2.28842i q^{80} +(-2.79275 - 8.55573i) q^{81} +7.52964i q^{82} -1.54870i q^{83} +(-1.74314 + 4.23810i) q^{84} +(-1.77042 - 1.02215i) q^{85} +(1.94207 + 3.36377i) q^{86} +(-1.64574 - 1.06797i) q^{87} -0.297141 q^{88} +(12.3933 + 7.15530i) q^{89} +(-5.55685 - 4.03154i) q^{90} +(9.13206 + 2.75781i) q^{91} -7.81240i q^{92} +(2.90263 + 0.151134i) q^{93} -6.01671i q^{94} +(15.6380 - 9.02859i) q^{95} +(-0.942850 + 1.45294i) q^{96} +(1.19346 - 2.06713i) q^{97} +(1.06532 - 6.91846i) q^{98} +(-0.523476 + 0.721530i) 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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