LMFDB - Embedded newform 546.2.bn.e.173.7

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			173.7
Character	$\chi$	$=$	546.173
Dual form			546.2.bn.e.101.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.786858 - 1.54300i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.98183 + 1.14421i) q^{5} +(-0.942850 + 1.45294i) q^{6} +(-2.60041 - 0.487738i) q^{7} +1.00000 q^{8} +(-1.76171 + 2.42825i) q^{9} +O(q^{10})$	\(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} +(-0.942850 + 1.45294i) 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} +(1.72971 + 0.0900624i) q^{12} +(-3.20028 + 1.66078i) q^{13} +(0.877809 + 2.49589i) q^{14} +(0.206101 - 3.95830i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.446664 + 0.773644i) q^{17} +(2.98378 + 0.311563i) q^{18} -7.89067 q^{19} +(-1.98183 + 1.14421i) q^{20} +(1.29357 + 4.39621i) 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} +(-1.22207 - 2.73981i) q^{36} +(4.32929 - 2.49951i) q^{37} +(3.94533 + 6.83352i) q^{38} +(5.08075 + 3.63124i) q^{39} +(1.98183 + 1.14421i) q^{40} +(6.52086 + 3.76482i) q^{41} +(3.16045 - 3.31837i) q^{42} +(-1.94207 - 3.36377i) q^{43} +(0.148570 - 0.257331i) q^{44} +(-6.26984 + 2.79660i) q^{45} +(6.76573 + 3.90620i) q^{46} +(-5.21062 - 3.00835i) q^{47} +(-0.942850 + 1.45294i) q^{48} +(6.52422 + 2.53663i) q^{49} +(0.118437 - 0.205138i) q^{50} +(1.54520 + 0.0804552i) q^{51} +(0.161862 - 3.60192i) q^{52} +(-6.28351 + 3.62779i) q^{53} +(-1.86707 - 4.84913i) 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} +(3.32494 + 2.15764i) q^{60} +8.44757i q^{61} +(0.839051 - 1.45328i) q^{62} +(5.76551 - 5.45517i) q^{63} +1.00000 q^{64} +(-8.24270 - 0.370410i) q^{65} +(0.280159 - 0.431727i) q^{66} +3.39883i q^{67} +(-0.446664 - 0.773644i) q^{68} +(11.3509 + 7.36592i) 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} +(0.223336 - 0.344163i) q^{75} +(3.94533 - 6.83352i) q^{76} +(0.772686 + 0.144927i) q^{77} +(0.604372 - 6.21568i) 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} +(-4.45402 - 1.07784i) q^{84} +(-1.77042 + 1.02215i) q^{85} +(-1.94207 + 3.36377i) q^{86} +(0.102014 - 1.95924i) 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} +(1.58220 - 2.43818i) q^{93} +6.01671i q^{94} +(-15.6380 - 9.02859i) q^{95} +(1.72971 + 0.0900624i) 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} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9}+O(q^{10}) $ 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9	$ 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9} - 18 q^{11} + 3 q^{12} - 8 q^{13} - 4 q^{14} - 17 q^{15} - 17 q^{16} + 6 q^{17} - 11 q^{18} - 10 q^{19} - 9 q^{20} - 4 q^{21} + 9 q^{22} + 6 q^{23} + 3 q^{24} + 16 q^{25} + 13 q^{26} + 18 q^{27} - q^{28} + 27 q^{29} + 13 q^{30} + q^{31} - 17 q^{32} + 21 q^{33} - 12 q^{34} - 3 q^{35} + 4 q^{36} + 6 q^{37} + 5 q^{38} + 20 q^{39} + 9 q^{40} + 3 q^{41} + 20 q^{42} - 3 q^{43} + 9 q^{44} - 6 q^{46} - 27 q^{47} - 6 q^{48} - 5 q^{49} + 16 q^{50} + 24 q^{51} - 5 q^{52} + 21 q^{53} - 18 q^{54} + 57 q^{55} + 5 q^{56} - 17 q^{57} - 6 q^{59} + 4 q^{60} + q^{62} - 21 q^{63} + 34 q^{64} + 33 q^{65} - 21 q^{66} + 6 q^{68} - 30 q^{69} + 3 q^{70} - 15 q^{71} + 7 q^{72} + 19 q^{73} - 6 q^{74} - 63 q^{75} + 5 q^{76} - 9 q^{77} - 10 q^{78} - 9 q^{79} - 5 q^{81} - 16 q^{84} - 42 q^{85} - 3 q^{86} - 75 q^{87} - 18 q^{88} - 18 q^{89} - 9 q^{90} - 27 q^{91} + 25 q^{93} - 3 q^{95} + 3 q^{96} - 19 q^{97} + 7 q^{98} - 27 q^{99}+O(q^{100}) $ 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9 - 18 * q^11 + 3 * q^12 - 8 * q^13 - 4 * q^14 - 17 * q^15 - 17 * q^16 + 6 * q^17 - 11 * q^18 - 10 * q^19 - 9 * q^20 - 4 * q^21 + 9 * q^22 + 6 * q^23 + 3 * q^24 + 16 * q^25 + 13 * q^26 + 18 * q^27 - q^28 + 27 * q^29 + 13 * q^30 + q^31 - 17 * q^32 + 21 * q^33 - 12 * q^34 - 3 * q^35 + 4 * q^36 + 6 * q^37 + 5 * q^38 + 20 * q^39 + 9 * q^40 + 3 * q^41 + 20 * q^42 - 3 * q^43 + 9 * q^44 - 6 * q^46 - 27 * q^47 - 6 * q^48 - 5 * q^49 + 16 * q^50 + 24 * q^51 - 5 * q^52 + 21 * q^53 - 18 * q^54 + 57 * q^55 + 5 * q^56 - 17 * q^57 - 6 * q^59 + 4 * q^60 + q^62 - 21 * q^63 + 34 * q^64 + 33 * q^65 - 21 * q^66 + 6 * q^68 - 30 * q^69 + 3 * q^70 - 15 * q^71 + 7 * q^72 + 19 * q^73 - 6 * q^74 - 63 * q^75 + 5 * q^76 - 9 * q^77 - 10 * q^78 - 9 * q^79 - 5 * q^81 - 16 * q^84 - 42 * q^85 - 3 * q^86 - 75 * q^87 - 18 * q^88 - 18 * q^89 - 9 * q^90 - 27 * q^91 + 25 * q^93 - 3 * q^95 + 3 * q^96 - 19 * q^97 + 7 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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	$-0.162347\pi$
$5$	1.98183	+	1.14421i	0.886302	+	0.511707i	0.0135708	+	0.999908i	$0.495680\pi$
$6$	−0.942850	+	1.45294i	−0.384917	+	0.593160i
$7$	−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	$-0.514264\pi$
$11$	−0.297141			−0.0895913			−0.0447956	+	0.998996i	$0.514264\pi$
$12$	1.72971	+	0.0900624i	0.499324	+	0.0259988i
$13$	−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
$15$	0.206101	−	3.95830i	0.0532150	−	1.02203i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.446664	+	0.773644i	−0.108332	+	0.187636i	−0.915095	−	0.403239i	$-0.867884\pi$
$17$	−0.446664	+	0.773644i	−0.108332	+	0.187636i	0.806763	+	0.590876i	$0.201218\pi$
$18$	2.98378	+	0.311563i	0.703283	+	0.0734362i
$19$	−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
$21$	1.29357	+	4.39621i	0.282280	+	0.959332i
$22$	0.148570	+	0.257331i	0.0316753	+	0.0548632i
$23$	−6.76573	+	3.90620i	−1.41075	+	0.814499i	−0.995459	−	0.0951887i	$-0.969655\pi$
$23$	−6.76573	+	3.90620i	−1.41075	+	0.814499i	−0.415294	+	0.909687i	$0.636321\pi$
$24$	−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	$-0.299795\pi$
$29$	0.980947	+	0.566350i	0.182157	+	0.105169i	−0.406149	+	0.913807i	$0.633128\pi$
$30$	−3.53104	+	1.80066i	−0.644677	+	0.328754i
$31$	0.839051	+	1.45328i	0.150698	+	0.261017i	0.931484	−	0.363782i	$-0.118515\pi$
$31$	0.839051	+	1.45328i	0.150698	+	0.261017i	−0.780786	+	0.624798i	$0.785181\pi$
$32$	−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
$36$	−1.22207	−	2.73981i	−0.203678	−	0.456635i
$37$	4.32929	−	2.49951i	0.711730	−	0.410918i	−0.0999712	−	0.994990i	$-0.531875\pi$
$37$	4.32929	−	2.49951i	0.711730	−	0.410918i	0.811701	+	0.584073i	$0.198542\pi$
$38$	3.94533	+	6.83352i	0.640018	+	1.10854i
$39$	5.08075	+	3.63124i	0.813572	+	0.581464i
$40$	1.98183	+	1.14421i	0.313355	+	0.180916i
$41$	6.52086	+	3.76482i	1.01839	+	0.587966i	0.913636	−	0.406532i	$-0.133262\pi$
$41$	6.52086	+	3.76482i	1.01839	+	0.587966i	0.104751	+	0.994498i	$0.466595\pi$
$42$	3.16045	−	3.31837i	0.487668	−	0.512035i
$43$	−1.94207	−	3.36377i	−0.296163	−	0.512970i	0.679092	−	0.734054i	$-0.262374\pi$
$43$	−1.94207	−	3.36377i	−0.296163	−	0.512970i	−0.975255	+	0.221084i	$0.929041\pi$
$44$	0.148570	−	0.257331i	0.0223978	−	0.0387942i
$45$	−6.26984	+	2.79660i	−0.934652	+	0.416893i
$46$	6.76573	+	3.90620i	0.997553	+	0.575938i
$47$	−5.21062	−	3.00835i	−0.760047	−	0.438813i	0.0692655	−	0.997598i	$-0.477934\pi$
$47$	−5.21062	−	3.00835i	−0.760047	−	0.438813i	−0.829313	+	0.558785i	$0.811268\pi$
$48$	−0.942850	+	1.45294i	−0.136089	+	0.209714i
$49$	6.52422	+	2.53663i	0.932032	+	0.362376i
$50$	0.118437	−	0.205138i	0.0167495	−	0.0290109i
$51$	1.54520	+	0.0804552i	0.216371	+	0.0112660i
$52$	0.161862	−	3.60192i	0.0224463	−	0.499496i
$53$	−6.28351	+	3.62779i	−0.863107	+	0.498315i	−0.865051	−	0.501683i	$-0.832714\pi$
$53$	−6.28351	+	3.62779i	−0.863107	+	0.498315i	0.00194455	+	0.999998i	$0.499381\pi$
$54$	−1.86707	−	4.84913i	−0.254075	−	0.659883i
$55$	−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	$-0.205068\pi$
$59$	5.21709	+	3.01209i	0.679207	+	0.392141i	−0.120349	+	0.992732i	$0.538401\pi$
$60$	3.32494	+	2.15764i	0.429248	+	0.278550i
$61$			8.44757i			1.08160i	0.841151	+	0.540800i	$0.181879\pi$
$61$			8.44757i			1.08160i	−0.841151	+	0.540800i	$0.818121\pi$
$62$	0.839051	−	1.45328i	0.106560	−	0.184567i
$63$	5.76551	−	5.45517i	0.726386	−	0.687287i
$64$	1.00000			0.125000
$65$	−8.24270	−	0.370410i	−1.02238	−	0.0459437i
$66$	0.280159	−	0.431727i	0.0344852	−	0.0531420i
$67$			3.39883i			0.415233i	0.978210	+	0.207617i	$0.0665706\pi$
$67$			3.39883i			0.415233i	−0.978210	+	0.207617i	$0.933429\pi$
$68$	−0.446664	−	0.773644i	−0.0541659	−	0.0938181i
$69$	11.3509	+	7.36592i	1.36649	+	0.886752i
$70$	−1.11615	+	5.95083i	−0.133406	+	0.711260i
$71$	1.14995	+	1.99178i	0.136474	+	0.236381i	0.926160	−	0.377131i	$-0.123090\pi$
$71$	1.14995	+	1.99178i	0.136474	+	0.236381i	−0.789685	+	0.613512i	$0.789756\pi$
$72$	−1.76171	+	2.42825i	−0.207620	+	0.286171i
$73$	−6.16302	−	10.6747i	−0.721327	−	1.24937i	−0.960468	−	0.278390i	$-0.910199\pi$
$73$	−6.16302	−	10.6747i	−0.721327	−	1.24937i	0.239141	−	0.970985i	$-0.423134\pi$
$74$	−4.32929	−	2.49951i	−0.503269	−	0.290563i
$75$	0.223336	−	0.344163i	0.0257886	−	0.0397405i
$76$	3.94533	−	6.83352i	0.452561	−	0.783858i
$77$	0.772686	+	0.144927i	0.0880558	+	0.0165159i
$78$	0.604372	−	6.21568i	0.0684317	−	0.703788i
$79$	4.46469	−	7.73307i	0.502317	−	0.870039i	−0.497679	−	0.867361i	$-0.665814\pi$
$79$	4.46469	−	7.73307i	0.502317	−	0.870039i	0.999996	−	0.00267764i	$-0.000852321\pi$
$80$		−	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	$-0.0270878\pi$
$84$	−4.45402	−	1.07784i	−0.485973	−	0.117602i
$85$	−1.77042	+	1.02215i	−0.192029	+	0.110868i
$86$	−1.94207	+	3.36377i	−0.209419	+	0.362725i
$87$	0.102014	−	1.95924i	0.0109370	−	0.210053i
$88$	−0.297141			−0.0316753
$89$	−12.3933	+	7.15530i	−1.31369	+	0.758460i	−0.982705	−	0.185176i	$-0.940715\pi$
$89$	−12.3933	+	7.15530i	−1.31369	+	0.758460i	−0.330986	+	0.943636i	$0.607381\pi$
$90$	5.55685	+	4.03154i	0.585743	+	0.424961i
$91$	9.13206	−	2.75781i	0.957300	−	0.289097i
$92$		−	7.81240i		−	0.814499i
$93$	1.58220	−	2.43818i	0.164066	−	0.252828i
$94$			6.01671i			0.620576i
$95$	−15.6380	−	9.02859i	−1.60442	−	0.926314i
$96$	1.72971	+	0.0900624i	0.176538	+	0.00919195i
$97$	1.19346	+	2.06713i	0.121178	+	0.209886i	0.920232	−	0.391373i	$-0.128000\pi$
$97$	1.19346	+	2.06713i	0.121178	+	0.209886i	−0.799055	+	0.601258i	$0.794666\pi$
$98$	−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	$-0.883885\pi$
$101$	−18.7772			−1.86840			−0.934200	+	0.356749i	$0.883885\pi$
$102$	−0.702921	−	1.37841i	−0.0695996	−	0.136483i
$103$	−12.3898	−	7.15323i	−1.22080	−	0.704828i	−0.255710	−	0.966753i	$-0.582309\pi$
$103$	−12.3898	−	7.15323i	−1.22080	−	0.704828i	−0.965088	+	0.261925i	$0.915643\pi$
$104$	−3.20028	+	1.66078i	−0.313813	+	0.162853i
$105$	−2.46656	+	10.1927i	−0.240712	+	0.994702i
$106$	6.28351	+	3.62779i	0.610309	+	0.352362i
$107$	14.4499	−	8.34267i	1.39693	−	0.806516i	0.402858	−	0.915263i	$-0.368017\pi$
$107$	14.4499	−	8.34267i	1.39693	−	0.806516i	0.994070	+	0.108746i	$0.0346836\pi$
$108$	−3.26594	+	4.04149i	−0.314265	+	0.388893i
$109$	9.70354	−	5.60234i	0.929431	−	0.536607i	0.0427994	−	0.999084i	$-0.486372\pi$
$109$	9.70354	−	5.60234i	0.929431	−	0.536607i	0.886632	+	0.462476i	$0.153039\pi$
$110$			0.679983i			0.0648338i
$111$	−7.26329	−	4.71333i	−0.689401	−	0.447370i
$112$	0.877809	+	2.49589i	0.0829452	+	0.235839i
$113$	7.27033	−	4.19753i	0.683935	−	0.394870i	−0.117401	−	0.993085i	$-0.537456\pi$
$113$	7.27033	−	4.19753i	0.683935	−	0.394870i	0.801336	+	0.598214i	$0.204123\pi$
$114$	7.43972	−	11.4647i	0.696793	−	1.07376i
$115$	−17.8781			−1.66714
$116$	−0.980947	+	0.566350i	−0.0910786	+	0.0525843i
$117$	1.60519	−	10.6969i	0.148400	−	0.988927i
$118$		−	6.02418i		−	0.554571i
$119$	1.53884	−	1.79393i	0.141065	−	0.164450i
$120$	0.206101	−	3.95830i	0.0188143	−	0.361342i
$121$	−10.9117			−0.991973
$122$	7.31581	−	4.22379i	0.662343	−	0.382404i
$123$	0.678137	−	13.0241i	0.0611456	−	1.17434i
$124$	−1.67810			−0.150698
$125$		−	10.9000i		−	0.974929i
$126$	−7.60707	−	2.26549i	−0.677692	−	0.201826i
$127$	2.63228	−	4.55924i	0.233577	−	0.404567i	−0.725281	−	0.688453i	$-0.758290\pi$
$127$	2.63228	−	4.55924i	0.233577	−	0.404567i	0.958858	+	0.283886i	$0.0916236\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−3.66217	+	5.64343i	−0.322436	+	0.496876i
$130$	3.80057	+	7.32359i	0.333332	+	0.642322i
$131$	0.386257	−	0.669016i	0.0337474	−	0.0584522i	−0.848658	−	0.528941i	$-0.822589\pi$
$131$	0.386257	−	0.669016i	0.0337474	−	0.0584522i	0.882406	+	0.470489i	$0.155922\pi$
$132$	−0.513966	−	0.0267612i	−0.0447350	−	0.00232926i
$133$	20.5189	+	3.84858i	1.77922	+	0.333714i
$134$	2.94347	−	1.69941i	0.254277	−	0.146807i
$135$	9.24864	+	7.47384i	0.795996	+	0.643246i
$136$	−0.446664	+	0.773644i	−0.0383011	+	0.0663394i
$137$	1.29342	−	2.24027i	0.110505	−	0.191399i	−0.805469	−	0.592638i	$-0.798087\pi$
$137$	1.29342	−	2.24027i	0.110505	−	0.191399i	0.915974	+	0.401238i	$0.131420\pi$
$138$	0.703603	−	13.5132i	0.0598947	−	1.15032i
$139$	−10.2034	+	5.89092i	−0.865438	+	0.499661i	−0.865830	−	0.500339i	$-0.833209\pi$
$139$	−10.2034	+	5.89092i	−0.865438	+	0.499661i	0.000391380		1.00000i	$0.499875\pi$
$140$	5.71164	−	2.00880i	0.482722	−	0.169774i
$141$	−0.541879	+	10.4071i	−0.0456345	+	0.876440i
$142$	1.14995	−	1.99178i	0.0965020	−	0.167146i
$143$	0.950934	−	0.493486i	0.0795211	−	0.0412673i
$144$	2.98378	+	0.311563i	0.248648	+	0.0259636i
$145$	1.29605	+	2.24482i	0.107631	+	0.186422i
$146$	−6.16302	+	10.6747i	−0.510055	+	0.883441i
$147$	−1.21960	−	12.0629i	−0.100591	−	0.994928i
$148$			4.99903i			0.410918i
$149$	3.28750			0.269322			0.134661	−	0.990892i	$-0.457005\pi$
$149$	3.28750			0.269322			0.134661	+	0.990892i	$0.457005\pi$
$150$	−0.409722	−	0.0213334i	−0.0334536	−	0.00174186i
$151$	−10.5899	+	6.11409i	−0.861795	+	0.497557i	−0.864613	−	0.502439i	$-0.832436\pi$
$151$	−10.5899	+	6.11409i	−0.861795	+	0.497557i	0.00281814	+	0.999996i	$0.499103\pi$
$152$	−7.89067			−0.640018
$153$	−1.09171	−	2.44755i	−0.0882592	−	0.197872i
$154$	−0.260833	−	0.741629i	−0.0210185	−	0.0597622i
$155$			3.84021i			0.308453i
$156$	−5.68513	+	2.58444i	−0.455174	+	0.206921i
$157$	−15.4715	+	8.93248i	−1.23476	+	0.712889i	−0.968019	−	0.250879i	$-0.919280\pi$
$157$	−15.4715	+	8.93248i	−1.23476	+	0.712889i	−0.266742	+	0.963768i	$0.585947\pi$
$158$	−8.92938			−0.710384
$159$	10.5419	+	6.84092i	0.836028	+	0.542520i
$160$	−1.98183	+	1.14421i	−0.156678	+	0.0904578i
$161$	19.4989	−	6.85779i	1.53673	−	0.540470i
$162$	−6.01310	+	6.69646i	−0.472434	+	0.526124i
$163$			2.31758i			0.181526i	0.995872	+	0.0907632i	$0.0289307\pi$
$163$			2.31758i			0.181526i	−0.995872	+	0.0907632i	$0.971069\pi$
$164$	−6.52086	+	3.76482i	−0.509194	+	0.293983i
$165$	−0.0612409	+	1.17617i	−0.00476760	+	0.0915649i
$166$	−1.34122	+	0.774352i	−0.104099	+	0.0601014i
$167$	11.5588	+	6.67349i	0.894449	+	0.516410i	0.875395	−	0.483408i	$-0.160601\pi$
$167$	11.5588	+	6.67349i	0.894449	+	0.516410i	0.0190536	+	0.999818i	$0.493935\pi$
$168$	1.29357	+	4.39621i	0.0998009	+	0.339175i
$169$	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	$-0.745931\pi$
$173$	−18.3618			−1.39602			−0.698011	+	0.716087i	$0.745931\pi$
$174$	−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
$177$	0.542552	−	10.4201i	0.0407807	−	0.783220i
$178$	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	$0.873983\pi$
$180$	0.712988	−	6.82814i	0.0531430	−	0.508940i
$181$			5.21743i			0.387809i	0.981020	+	0.193904i	$0.0621151\pi$
$181$			5.21743i			0.387809i	−0.981020	+	0.193904i	$0.937885\pi$
$182$	−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
$186$	−2.90263	−	0.151134i	−0.212831	−	0.0110817i
$187$	0.132722	−	0.229881i	0.00970559	−	0.0168106i
$188$	5.21062	−	3.00835i	0.380024	−	0.219407i
$189$	−12.9540	−	4.60375i	−0.942263	−	0.334874i
$190$			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	$0.0367967\pi$
$193$			3.20479i			0.230686i	−0.993326	+	0.115343i	$0.963203\pi$
$194$	1.19346	−	2.06713i	0.0856855	−	0.148412i
$195$	5.91429	+	13.0100i	0.423531	+	0.931663i
$196$	−5.45890	+	4.38183i	−0.389922	+	0.312988i
$197$	12.9869	−	22.4940i	0.925278	−	1.60263i	0.134165	−	0.990959i	$-0.457165\pi$
$197$	12.9869	−	22.4940i	0.925278	−	1.60263i	0.791113	−	0.611670i	$-0.209502\pi$
$198$	−0.886602	−	0.0925781i	−0.0630080	−	0.00657924i
$199$	4.80414	+	2.77367i	0.340557	+	0.196621i	0.660518	−	0.750810i	$-0.270337\pi$
$199$	4.80414	+	2.77367i	0.340557	+	0.196621i	−0.319961	+	0.947431i	$0.603670\pi$
$200$	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
$204$	−0.842274	+	1.29795i	−0.0589710	+	0.0908747i
$205$	8.61550	+	14.9225i	0.601732	+	1.04223i
$206$			14.3065i			0.996778i
$207$	2.43406	−	23.3105i	0.169179	−	1.62019i
$208$	3.03842	+	1.94114i	0.210677	+	0.134594i
$209$	2.34464			0.162182
$210$	10.0604	−	2.96023i	0.694233	−	0.204275i
$211$	1.17040	−	2.02719i	0.0805736	−	0.139558i	−0.822923	−	0.568153i	$-0.807658\pi$
$211$	1.17040	−	2.02719i	0.0805736	−	0.139558i	0.903496	+	0.428596i	$0.140991\pi$
$212$		−	7.25558i		−	0.498315i
$213$	2.16847	−	3.34163i	0.148581	−	0.228965i
$214$	−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
$219$	−11.6216	+	17.9090i	−0.785315	+	1.21018i
$220$	0.588883	−	0.339992i	0.0397025	−	0.0229222i
$221$	0.144596	−	3.21769i	0.00972659	−	0.216445i
$222$	−0.450224	+	8.64686i	−0.0302171	+	0.580339i
$223$	−0.746837	+	1.29356i	−0.0500119	+	0.0866232i	−0.889948	−	0.456063i	$-0.849259\pi$
$223$	−0.746837	+	1.29356i	−0.0500119	+	0.0866232i	0.839936	+	0.542686i	$0.182593\pi$
$224$	1.72260	−	2.00815i	0.115096	−	0.134175i
$225$	−0.706777	−	0.0738010i	−0.0471185	−	0.00492007i
$226$	−7.27033	−	4.19753i	−0.483615	−	0.279215i
$227$	−5.51731	−	3.18542i	−0.366197	−	0.211424i	0.305599	−	0.952160i	$-0.401143\pi$
$227$	−5.51731	−	3.18542i	−0.366197	−	0.211424i	−0.671796	+	0.740737i	$0.734477\pi$
$228$	−13.6485	−	0.710652i	−0.903897	−	0.0470641i
$229$	3.93382	−	6.81358i	0.259954	−	0.450254i	−0.706275	−	0.707937i	$-0.749626\pi$
$229$	3.93382	−	6.81358i	0.259954	−	0.450254i	0.966229	+	0.257684i	$0.0829592\pi$
$230$	8.93903	+	15.4829i	0.589422	+	1.02091i
$231$	−0.384372	−	1.30629i	−0.0252898	−	0.0859478i
$232$	0.980947	+	0.566350i	0.0644023	+	0.0371827i
$233$	−8.04627	−	4.64552i	−0.527129	−	0.304338i	0.212718	−	0.977114i	$-0.431769\pi$
$233$	−8.04627	−	4.64552i	−0.527129	−	0.304338i	−0.739847	+	0.672776i	$0.765102\pi$
$234$	−10.0664	+	3.95831i	−0.658059	+	0.258763i
$235$	−6.88438	−	11.9241i	−0.449088	−	0.777842i
$236$	−5.21709	+	3.01209i	−0.339604	+	0.196070i
$237$	−15.4452	−	0.804202i	−1.00328	−	0.0522385i
$238$	−2.32301	−	0.435710i	−0.150579	−	0.0282429i
$239$	22.6067			1.46230			0.731152	−	0.682215i	$-0.238983\pi$
$239$	22.6067			1.46230			0.731152	+	0.682215i	$0.238983\pi$
$240$	−3.53104	+	1.80066i	−0.227928	+	0.116232i
$241$	14.5437	−	25.1904i	0.936842	−	1.62266i	0.165526	−	0.986205i	$-0.447068\pi$
$241$	14.5437	−	25.1904i	0.936842	−	1.62266i	0.771316	−	0.636453i	$-0.219599\pi$
$242$	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	$-0.0234406\pi$
$251$	6.89055	+	11.9348i	0.434928	+	0.753317i	−0.562362	+	0.826891i	$0.690107\pi$
$252$	1.84156	+	7.72066i	0.116007	+	0.486356i
$253$	2.01037	−	1.16069i	0.126391	−	0.0729720i
$254$	−5.26456			−0.330328
$255$	2.97026	+	1.92748i	0.186005	+	0.120703i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.81222	+	4.87090i	0.175421	+	0.303839i	0.940307	−	0.340327i	$-0.110538\pi$
$257$	2.81222	+	4.87090i	0.175421	+	0.303839i	−0.764886	+	0.644166i	$0.777205\pi$
$258$	6.71844	+	0.349815i	0.418272	+	0.0217786i
$259$	−12.4770	+	4.38819i	−0.775284	+	0.272669i
$260$	4.44214	−	6.95319i	0.275490	−	0.431218i
$261$	−3.10338	+	1.38424i	−0.192094	+	0.0856820i
$262$	−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
$267$	20.7924	+	13.4927i	1.27248	+	0.825743i
$268$	−2.94347	−	1.69941i	−0.179801	−	0.103808i
$269$	−13.9773	+	24.2094i	−0.852211	+	1.47607i	0.0269978	+	0.999635i	$0.491405\pi$
$269$	−13.9773	+	24.2094i	−0.852211	+	1.47607i	−0.879209	+	0.476437i	$0.841928\pi$
$270$	1.84822	−	11.7465i	0.112479	−	0.714868i
$271$	−10.2294	−	17.7179i	−0.621393	−	1.07628i	−0.989227	−	0.146392i	$-0.953234\pi$
$271$	−10.2294	−	17.7179i	−0.621393	−	1.07628i	0.367834	−	0.929892i	$-0.380100\pi$
$272$	0.893327			0.0541659
$273$	−11.4409	−	11.9208i	−0.692437	−	0.721479i
$274$	−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	−0.947095	−	0.320952i	$-0.895997\pi$
$277$	−3.25535	+	5.63843i	−0.195595	+	0.338780i	0.751501	+	0.659732i	$0.229330\pi$
$278$	10.2034	+	5.89092i	0.611957	+	0.353314i
$279$	−5.00709	−	0.522835i	−0.299766	−	0.0313013i
$280$	−4.59549	−	3.94203i	−0.274633	−	0.235581i
$281$	10.0287			0.598262			0.299131	−	0.954212i	$-0.403303\pi$
$281$	10.0287			0.598262			0.299131	+	0.954212i	$0.403303\pi$
$282$	9.28379	−	4.73429i	0.552842	−	0.281923i
$283$		−	22.8820i		−	1.36019i	−0.733123	−	0.680097i	$-0.761938\pi$
$283$		−	22.8820i		−	1.36019i	0.733123	−	0.680097i	$-0.238062\pi$
$284$	−2.29991			−0.136474
$285$	−1.62627	+	31.2336i	−0.0963321	+	1.85012i
$286$	−0.902838	−	0.576790i	−0.0533859	−	0.0341063i
$287$	−15.1206	−	12.9705i	−0.892543	−	0.765626i
$288$	−1.22207	−	2.73981i	−0.0720110	−	0.161445i
$289$	8.10098	+	14.0313i	0.476528	+	0.825371i
$290$	1.29605	−	2.24482i	0.0761065	−	0.131820i
$291$	2.25051	−	3.46805i	0.131927	−	0.203301i
$292$	12.3260			0.721327
$293$	−17.4353	+	10.0663i	−1.01858	+	0.588080i	−0.913693	−	0.406404i	$-0.866783\pi$
$293$	−17.4353	+	10.0663i	−1.01858	+	0.588080i	−0.104890	+	0.994484i	$0.533449\pi$
$294$	−9.83694	+	7.08764i	−0.573702	+	0.413359i
$295$	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
$309$	−1.28847	+	24.7460i	−0.0732987	+	1.40775i
$310$	3.32572	−	1.92010i	0.188888	−	0.109055i
$311$	7.75963	+	13.4401i	0.440008	+	0.762117i	0.997690	−	0.0679384i	$-0.0216421\pi$
$311$	7.75963	+	13.4401i	0.440008	+	0.762117i	−0.557681	+	0.830055i	$0.688309\pi$
$312$	5.08075	+	3.63124i	0.287641	+	0.205579i
$313$	13.7068	+	7.91361i	0.774752	+	0.447303i	0.834567	−	0.550906i	$-0.185718\pi$
$313$	13.7068	+	7.91361i	0.774752	+	0.447303i	−0.0598149	+	0.998209i	$0.519051\pi$
$314$	15.4715	+	8.93248i	0.873108	+	0.504089i
$315$	17.6681	−	4.21427i	0.995487	−	0.237447i
$316$	4.46469	+	7.73307i	0.251159	+	0.435019i
$317$	6.47213	−	11.2101i	0.363511	−	0.629619i	−0.625025	−	0.780605i	$-0.714911\pi$
$317$	6.47213	−	11.2101i	0.363511	−	0.629619i	0.988536	+	0.150985i	$0.0482446\pi$
$318$	0.653455	−	12.5500i	0.0366439	−	0.703771i
$319$	−0.291479	−	0.168286i	−0.0163197	−	0.00942218i
$320$	1.98183	+	1.14421i	0.110788	+	0.0639633i
$321$	−24.2428	−	15.7318i	−1.35310	−	0.878062i
$322$	−15.6885	−	13.4576i	−0.874283	−	0.749963i
$323$	3.52448	−	6.10457i	0.196107	−	0.339667i
$324$	8.80586	+	1.85927i	0.489214	+	0.103293i
$325$	−0.719721	−	0.459803i	−0.0399229	−	0.0255053i
$326$	2.00708	−	1.15879i	0.111162	−	0.0641793i
$327$	−16.2797	−	10.5643i	−0.900271	−	0.584209i
$328$	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	$-0.920776\pi$
$331$		−	8.96310i		−	0.492656i	0.969186	−	0.246328i	$-0.0792241\pi$
$332$	1.34122	+	0.774352i	0.0736089	+	0.0424981i
$333$	−1.55751	+	14.9160i	−0.0853512	+	0.817391i
$334$		−	13.3470i		−	0.730314i
$335$	−3.88898	+	6.73591i	−0.212477	+	0.368022i
$336$	3.16045	−	3.31837i	0.172417	−	0.181032i
$337$	−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
$339$	−12.1975	−	7.91528i	−0.662478	−	0.429899i
$340$		−	2.04431i		−	0.110868i
$341$	−0.249316	−	0.431828i	−0.0135012	−	0.0233848i
$342$	−23.5440	−	2.45844i	−1.27311	−	0.132937i
$343$	−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	$-0.249484\pi$
$347$	8.40123	+	4.85045i	0.451002	+	0.260386i	−0.257251	+	0.966344i	$0.582817\pi$
$348$	1.64574	+	1.06797i	0.0882212	+	0.0572490i
$349$	−13.2526	+	22.9542i	−0.709396	+	1.22871i	0.255686	+	0.966760i	$0.417699\pi$
$349$	−13.2526	+	22.9542i	−0.709396	+	1.22871i	−0.965081	+	0.261950i	$0.915635\pi$
$350$	−0.408037	+	0.475677i	−0.0218105	+	0.0254260i
$351$	−17.7684	+	5.94012i	−0.948405	+	0.317060i
$352$	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
$357$	−3.97889	−	0.962867i	−0.210585	−	0.0509603i
$358$	8.93640	−	5.15943i	0.472303	−	0.272684i
$359$	−6.41408	+	11.1095i	−0.338522	+	0.586338i	−0.984155	−	0.177310i	$-0.943260\pi$
$359$	−6.41408	+	11.1095i	−0.338522	+	0.586338i	0.645633	+	0.763648i	$0.276594\pi$
$360$	−6.26984	+	2.79660i	−0.330449	+	0.147394i
$361$	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
$366$	−12.2738	−	7.96480i	−0.641562	−	0.416327i
$367$			24.5596i			1.28200i	0.767541	+	0.641000i	$0.221480\pi$
$367$			24.5596i			1.28200i	−0.767541	+	0.641000i	$0.778520\pi$
$368$	6.76573	+	3.90620i	0.352688	+	0.203625i
$369$	−20.6298	+	9.20173i	−1.07394	+	0.479023i
$370$	−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
$378$	2.49002	+	13.5203i	0.128073	+	0.695412i
$379$	−13.9171	−	8.03505i	−0.714874	−	0.412733i	0.0979889	−	0.995188i	$-0.468759\pi$
$379$	−13.9171	−	8.03505i	−0.714874	−	0.412733i	−0.812863	+	0.582455i	$0.802092\pi$
$380$	15.6380	−	9.02859i	0.802211	−	0.463157i
$381$	−9.10615	−	0.474139i	−0.466522	−	0.0242909i
$382$	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	$-0.239907\pi$
$384$	−0.942850	+	1.45294i	−0.0481146	+	0.0741450i
$385$	1.36551	+	1.17134i	0.0695927	+	0.0596968i
$386$	2.77543	−	1.60239i	0.141266	−	0.0815597i
$387$	11.5894	+	1.21016i	0.589124	+	0.0615157i
$388$	−2.38692			−0.121178
$389$	−3.67405	+	2.12122i	−0.186282	+	0.107550i	−0.590241	−	0.807227i	$-0.700967\pi$
$389$	−3.67405	+	2.12122i	−0.186282	+	0.107550i	0.403959	+	0.914777i	$0.367634\pi$
$390$	8.30982	−	11.6269i	0.420784	−	0.588751i
$391$		−	6.97903i		−	0.352945i
$392$	6.52422	+	2.53663i	0.329523	+	0.128119i
$393$	−1.33622	−	0.0695744i	−0.0674035	−	0.00350956i
$394$	−25.9738			−1.30854
$395$	17.6965	−	10.2171i	0.890409	−	0.514078i
$396$	0.363126	+	0.814109i	0.0182478	+	0.0409105i
$397$	−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
$399$	−10.2071	−	34.6891i	−0.510995	−	1.73662i
$400$	0.118437	−	0.205138i	0.00592183	−	0.0102569i
$401$	−7.61652	−	13.1922i	−0.380351	−	0.658787i	0.610762	−	0.791815i	$-0.290863\pi$
$401$	−7.61652	−	13.1922i	−0.380351	−	0.658787i	−0.991112	+	0.133028i	$0.957530\pi$
$402$	−4.93829	−	3.20459i	−0.246300	−	0.159830i
$403$	−5.09878	−	3.25742i	−0.253988	−	0.162264i
$404$	9.38860	−	16.2615i	0.467100	−	0.809041i
$405$	4.25480	−	20.1515i	0.211422	−	1.00134i
$406$	−0.552461	+	2.94548i	−0.0274182	+	0.146182i
$407$	−1.28641	+	0.742707i	−0.0637648	+	0.0368146i
$408$	1.54520	+	0.0804552i	0.0764986	+	0.00398313i
$409$	13.0031	−	22.5221i	0.642964	−	1.11365i	−0.341804	−	0.939771i	$-0.611038\pi$
$409$	13.0031	−	22.5221i	0.642964	−	1.11365i	0.984768	−	0.173875i	$-0.0556289\pi$
$410$	8.61550	−	14.9225i	0.425489	−	0.736969i
$411$	−4.47448	−	0.232977i	−0.220710	−	0.0114919i
$412$	12.3898	−	7.15323i	0.610399	−	0.352414i
$413$	−12.0974	−	10.3772i	−0.595276	−	0.510630i
$414$	−21.4045	+	9.54727i	−1.05197	+	0.469223i
$415$	1.77204	−	3.06927i	0.0869863	−	0.150665i
$416$	0.161862	−	3.60192i	0.00793596	−	0.176598i
$417$	17.1183	+	11.1085i	0.838286	+	0.543986i
$418$	−1.17232	−	2.03052i	−0.0573400	−	0.0993158i
$419$	−4.44170	+	7.69326i	−0.216991	+	0.375840i	−0.953887	−	0.300167i	$-0.902958\pi$
$419$	−4.44170	+	7.69326i	−0.216991	+	0.375840i	0.736895	+	0.676007i	$0.236291\pi$
$420$	−7.59383	−	7.23244i	−0.370541	−	0.352907i
$421$			11.9274i			0.581308i	0.956828	+	0.290654i	$0.0938729\pi$
$421$			11.9274i			0.581308i	−0.956828	+	0.290654i	$0.906127\pi$
$422$	−2.34080			−0.113948
$423$	16.4846	−	7.35282i	0.801510	−	0.357506i
$424$	−6.28351	+	3.62779i	−0.305154	+	0.176181i
$425$	−0.211605			−0.0102644
$426$	−3.97817	−	0.207135i	−0.192743	−	0.0100357i
$427$	4.12020	−	21.9671i	0.199391	−	1.06306i
$428$			16.6853i			0.806516i
$429$	−1.50970	−	1.07899i	−0.0728889	−	0.0520941i
$430$	−7.69772	+	4.44428i	−0.371217	+	0.214322i
$431$	19.4830			0.938462			0.469231	−	0.883075i	$-0.344531\pi$
$431$	19.4830			0.938462			0.469231	+	0.883075i	$0.344531\pi$
$432$	−1.86707	−	4.84913i	−0.0898292	−	0.233304i
$433$	15.8703	−	9.16273i	0.762679	−	0.440333i	−0.0675780	−	0.997714i	$-0.521527\pi$
$433$	15.8703	−	9.16273i	0.762679	−	0.440333i	0.830257	+	0.557381i	$0.188194\pi$
$434$	−2.89069	+	3.36988i	−0.138758	+	0.161759i
$435$	2.44396	−	3.76616i	0.117179	−	0.180573i
$436$			11.2047i			0.536607i
$437$	53.3862	−	30.8225i	2.55381	−	1.47444i
$438$	21.3204	+	1.11011i	1.01873	+	0.0530432i
$439$	−2.15827	+	1.24608i	−0.103009	+	0.0594720i	−0.550619	−	0.834757i	$-0.685608\pi$
$439$	−2.15827	+	1.24608i	−0.103009	+	0.0594720i	0.447611	+	0.894229i	$0.352275\pi$
$440$	−0.588883	−	0.339992i	−0.0280739	−	0.0162085i
$441$	−17.6534	+	11.3736i	−0.840636	+	0.541600i
$442$	−2.85890	+	1.48362i	−0.135984	+	0.0705687i
$443$	−14.4424	−	8.33832i	−0.686179	−	0.396166i	0.116000	−	0.993249i	$-0.462993\pi$
$443$	−14.4424	−	8.33832i	−0.686179	−	0.396166i	−0.802179	+	0.597083i	$0.796326\pi$
$444$	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	−0.855290	−	0.518149i	$-0.826621\pi$
$449$	−18.5701	−	32.1643i	−0.876375	−	1.51793i	−0.0210850	−	0.999778i	$-0.506712\pi$
$450$	0.289475	+	0.648988i	0.0136460	+	0.0305936i
$451$	−1.93761	−	1.11868i	−0.0912386	−	0.0526766i
$452$			8.39506i			0.394870i
$453$	17.7668	+	11.5293i	0.834757	+	0.541696i
$454$			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	−0.136895	−	0.990586i	$-0.543712\pi$
$457$	13.9495	−	8.05374i	0.652529	−	0.376738i	0.789425	+	0.613848i	$0.210379\pi$
$458$	−7.86764			−0.367631
$459$	−2.91755	+	3.61037i	−0.136180	+	0.168518i
$460$	8.93903	−	15.4829i	0.416784	−	0.721892i
$461$	12.1978	−	7.04240i	0.568108	−	0.327997i	−0.188285	−	0.982114i	$-0.560293\pi$
$461$	12.1978	−	7.04240i	0.568108	−	0.327997i	0.756393	+	0.654117i	$0.226960\pi$
$462$	−0.939097	+	0.986022i	−0.0436908	+	0.0458739i
$463$			20.5027i			0.952843i	0.879217	+	0.476421i	$0.158066\pi$
$463$			20.5027i			0.952843i	−0.879217	+	0.476421i	$0.841934\pi$
$464$		−	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	$-0.875721\pi$
$467$	−2.86923	+	4.96965i	−0.132772	+	0.229968i	0.791972	+	0.610557i	$0.209054\pi$
$468$	8.46118	+	6.73858i	0.391118	+	0.311491i
$469$	1.65774	−	8.83834i	0.0765473	−	0.408116i
$470$	−6.88438	+	11.9241i	−0.317553	+	0.550018i
$471$	25.9567	+	16.8440i	1.19602	+	0.776129i
$472$	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
$477$	2.26057	−	21.6490i	0.103504	−	0.991241i
$478$	−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	$0.777474\pi$
$480$	3.32494	+	2.15764i	0.151762	+	0.0984823i
$481$	−9.70379	+	15.1891i	−0.442455	+	0.692565i
$482$	−29.0874			−1.32489
$483$	−25.9244	−	24.6907i	−1.17960	−	1.12346i
$484$	5.45585	−	9.44982i	0.247993	−	0.429537i
$485$			5.46228i			0.248029i
$486$	15.0641	+	4.00907i	0.683322	+	0.181855i
$487$	25.7292	+	14.8548i	1.16590	+	0.673133i	0.952711	−	0.303877i	$-0.0982813\pi$
$487$	25.7292	+	14.8548i	1.16590	+	0.673133i	0.213190	+	0.977011i	$0.431615\pi$
$488$			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	−0.991849	−	0.127418i	$-0.959331\pi$
$491$	−35.4120	−	20.4451i	−1.59812	−	0.922676i	−0.606272	−	0.795258i	$-0.707336\pi$
$492$	10.9401	+	7.09932i	0.493218	+	0.320062i
$493$	−0.876307	+	0.505936i	−0.0394669	+	0.0227862i
$494$	−23.9752	−	15.3169i	−1.07869	−	0.689138i
$495$	1.86302	−	0.830985i	0.0837367	−	0.0373500i
$496$	0.839051	−	1.45328i	0.0376745	−	0.0652542i
$497$	−2.01888	−	5.74031i	−0.0905592	−	0.257488i
$498$	2.25017	+	1.46020i	0.100833	+	0.0654330i
$499$	−11.0351	−	6.37111i	−0.493998	−	0.285210i	0.232233	−	0.972660i	$-0.425397\pi$
$499$	−11.0351	−	6.37111i	−0.493998	−	0.285210i	−0.726232	+	0.687450i	$0.758730\pi$
$500$	9.43971	+	5.45002i	0.422157	+	0.243732i
$501$	1.20206	−	23.0864i	0.0537041	−	1.03142i
$502$	6.89055	−	11.9348i	0.307540	−	0.532675i
$503$	−20.5763	−	35.6392i	−0.917453	−	1.58908i	−0.803270	−	0.595615i	$-0.796908\pi$
$503$	−20.5763	−	35.6392i	−0.917453	−	1.58908i	−0.114183	−	0.993460i	$-0.536425\pi$
$504$	5.76551	−	5.45517i	0.256816	−	0.242993i
$505$	−37.2132	−	21.4851i	−1.65597	−	0.956073i
$506$	−2.01037	−	1.16069i	−0.0893720	−	0.0515990i
$507$	−22.2905	−	3.18298i	−0.989958	−	0.141361i
$508$	2.63228	+	4.55924i	0.116788	+	0.202284i
$509$	−15.5770	+	8.99339i	−0.690439	+	0.398625i	−0.803776	−	0.594932i	$-0.797179\pi$
$509$	−15.5770	+	8.99339i	−0.690439	+	0.398625i	0.113338	+	0.993557i	$0.463846\pi$
$510$	0.184115	−	3.53606i	0.00815277	−	0.156579i
$511$	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	0.998195	+	0.0600622i	$0.0191299\pi$
$521$	12.5794	+	21.7881i	0.551113	+	0.954555i	−0.447082	+	0.894493i	$0.647537\pi$
$522$	2.75047	+	1.99549i	0.120385	+	0.0873402i
$523$	−36.4677	+	21.0547i	−1.59462	+	0.920656i	−0.602124	+	0.798403i	$0.705679\pi$
$523$	−36.4677	+	21.0547i	−1.59462	+	0.920656i	−0.992499	+	0.122253i	$0.960988\pi$
$524$	0.386257	+	0.669016i	0.0168737	+	0.0292261i
$525$	−0.748626	+	0.786033i	−0.0326727	+	0.0343053i
$526$	16.7851	−	9.69087i	0.731864	−	0.422542i
$527$	−1.49910			−0.0653016
$528$	0.280159	−	0.431727i	0.0121924	−	0.0187885i
$529$	19.0168	−	32.9380i	0.826816	−	1.43209i
$530$	8.30191	+	14.3793i	0.360612	+	0.624598i
$531$	−16.5051	+	7.36195i	−0.716260	+	0.319481i
$532$	−13.5924	+	15.8456i	−0.589307	+	0.686995i
$533$	−27.1211	−	1.21877i	−1.17475	−	0.0527906i
$534$	1.28885	−	24.7531i	0.0557738	−	1.07117i
$535$	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
$540$	−11.0969	+	4.27263i	−0.477533	+	0.183865i
$541$	15.7491	+	9.09276i	0.677107	+	0.390928i	0.798764	−	0.601644i	$-0.205487\pi$
$541$	15.7491	+	9.09276i	0.677107	+	0.390928i	−0.121657	+	0.992572i	$0.538821\pi$
$542$	−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
$546$	−4.60324	+	15.8685i	−0.197000	+	0.679110i
$547$	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
$552$	11.3509	+	7.36592i	0.483128	+	0.313514i
$553$	−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	$-0.734569\pi$
$557$	−31.7201			−1.34402			−0.672011	+	0.740541i	$0.734569\pi$
$558$	2.05075	+	4.59768i	0.0868154	+	0.194635i
$559$	11.8017	+	7.53965i	0.499157	+	0.318893i
$560$	−1.11615	+	5.95083i	−0.0471660	+	0.251468i
$561$	−0.459140	−	0.0239065i	−0.0193849	−	0.00100933i
$562$	−5.01435	−	8.68510i	−0.211517	−	0.366359i
$563$	−1.44913	+	2.50997i	−0.0610737	+	0.105783i	−0.894946	−	0.446175i	$-0.852786\pi$
$563$	−1.44913	+	2.50997i	−0.0610737	+	0.105783i	0.833872	+	0.551958i	$0.186119\pi$
$564$	−8.74191	−	5.67285i	−0.368101	−	0.238870i
$565$	19.2114			0.808231
$566$	−19.8164	+	11.4410i	−0.832945	+	0.480901i
$567$	3.08933	+	23.6105i	0.129740	+	0.991548i
$568$	1.14995	+	1.99178i	0.0482510	+	0.0835732i
$569$	−32.8060	+	18.9406i	−1.37530	+	0.794030i	−0.991589	−	0.129423i	$-0.958688\pi$
$569$	−32.8060	+	18.9406i	−1.37530	+	0.794030i	−0.383711	+	0.923453i	$0.625354\pi$
$570$	27.8623	−	14.2084i	1.16702	−	0.595125i
$571$	−13.5869	−	23.5332i	−0.568594	−	0.984834i	−0.996705	−	0.0811082i	$-0.974154\pi$
$571$	−13.5869	−	23.5332i	−0.568594	−	0.984834i	0.428111	−	0.903726i	$-0.359179\pi$
$572$	−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	0.924119	+	0.382105i	$0.124801\pi$
$577$	19.0478	+	32.9918i	0.792972	+	1.37347i	−0.131147	+	0.991363i	$0.541866\pi$
$578$	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
$582$	−4.12868	−	0.214972i	−0.171139	−	0.00891087i
$583$	1.86709	−	1.07796i	0.0773268	−	0.0446447i
$584$	−6.16302	−	10.6747i	−0.255028	−	0.441721i
$585$	15.4207	−	19.3628i	0.637568	−	0.800551i
$586$	17.4353	+	10.0663i	0.720248	+	0.415835i
$587$	−19.1503	−	11.0565i	−0.790419	−	0.456349i	0.0496910	−	0.998765i	$-0.484176\pi$
$587$	−19.1503	−	11.0565i	−0.790419	−	0.456349i	−0.840110	+	0.542416i	$0.817510\pi$
$588$	11.0565	+	4.97522i	0.455964	+	0.205175i
$589$	−6.62068	−	11.4673i	−0.272800	−	0.472504i
$590$	6.89293	−	11.9389i	0.283777	−	0.491517i
$591$	−44.9271	−	2.33926i	−1.84805	−	0.0962244i
$592$	−4.32929	−	2.49951i	−0.177933	−	0.102729i
$593$	22.7957	+	13.1611i	0.936109	+	0.540463i	0.888738	−	0.458415i	$-0.151583\pi$
$593$	22.7957	+	13.1611i	0.936109	+	0.540463i	0.0473705	+	0.998877i	$0.484916\pi$
$594$	0.554781	+	1.44087i	0.0227629	+	0.0591198i
$595$	5.10237	−	1.79451i	0.209177	−	0.0735679i
$596$	−1.64375	+	2.84705i	−0.0673305	+	0.116620i
$597$	0.499607	−	9.59529i	0.0204476	−	0.392709i
$598$	−28.1396	−	1.26453i	−1.15071	−	0.0517106i
$599$	5.69118	−	3.28581i	0.232536	−	0.134254i	−0.379206	−	0.925312i	$-0.623803\pi$
$599$	5.69118	−	3.28581i	0.232536	−	0.134254i	0.611741	+	0.791058i	$0.290469\pi$
$600$	0.223336	−	0.344163i	0.00911766	−	0.0140504i
$601$	−22.1774	−	12.8041i	−0.904634	−	0.522291i	−0.0259335	−	0.999664i	$-0.508256\pi$
$601$	−22.1774	−	12.8041i	−0.904634	−	0.522291i	−0.878701	+	0.477373i	$0.841589\pi$
$602$	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
$606$	17.7041	−	27.2821i	0.719179	−	1.10826i
$607$			42.6384i			1.73064i	0.501220	+	0.865320i	$0.332885\pi$
$607$			42.6384i			1.73064i	−0.501220	+	0.865320i	$0.667115\pi$
$608$	3.94533	−	6.83352i	0.160004	−	0.277136i
$609$	−1.22087	+	5.04506i	−0.0494723	+	0.204436i
$610$	19.3316			0.782714
$611$	21.6717	+	0.973879i	0.876742	+	0.0393989i
$612$	2.66549	+	0.278328i	0.107746	+	0.0112507i
$613$		−	4.01879i		−	0.162318i	−0.996701	−	0.0811588i	$-0.974138\pi$
$613$		−	4.01879i		−	0.162318i	0.996701	−	0.0811588i	$-0.0258621\pi$
$614$	1.53901	+	2.66564i	0.0621093	+	0.107576i
$615$	16.2462	−	25.0356i	0.655112	−	1.00953i
$616$	0.772686	+	0.144927i	0.0311324	+	0.00583927i
$617$	12.9809	+	22.4837i	0.522593	+	0.905158i	0.999654	+	0.0262879i	$0.00836868\pi$
$617$	12.9809	+	22.4837i	0.522593	+	0.905158i	−0.477061	+	0.878870i	$0.658298\pi$
$618$	22.0749	−	11.2571i	0.887982	−	0.452829i
$619$	−2.84282	−	4.92392i	−0.114263	−	0.197909i	0.803222	−	0.595680i	$-0.203117\pi$
$619$	−2.84282	−	4.92392i	−0.114263	−	0.197909i	−0.917485	+	0.397771i	$0.869784\pi$
$620$	−3.32572	−	1.92010i	−0.133564	−	0.0771132i
$621$	−37.8833	+	14.5863i	−1.52021	+	0.585326i
$622$	7.75963	−	13.4401i	0.311133	−	0.538898i
$623$	35.7176	−	12.5620i	1.43100	−	0.503285i
$624$	0.604372	−	6.21568i	0.0241942	−	0.248827i
$625$	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
$630$	−12.4837	−	13.1939i	−0.497364	−	0.525658i
$631$	11.9099	−	6.87621i	0.474128	−	0.273738i	−0.243838	−	0.969816i	$-0.578407\pi$
$631$	11.9099	−	6.87621i	0.474128	−	0.273738i	0.717966	+	0.696078i	$0.245073\pi$
$632$	4.46469	−	7.73307i	0.177596	−	0.307605i
$633$	−4.04890	−	0.210818i	−0.160929	−	0.00837926i
$634$	−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
$639$	−6.86241	−	0.716567i	−0.271473	−	0.0283469i
$640$		−	2.28842i		−	0.0904578i
$641$	5.44576	+	3.14411i	0.215094	+	0.124185i	0.603677	−	0.797229i	$-0.293702\pi$
$641$	5.44576	+	3.14411i	0.215094	+	0.124185i	−0.388582	+	0.921414i	$0.627035\pi$
$642$	−1.50272	+	28.8608i	−0.0593077	+	1.13904i
$643$	17.3160	+	29.9922i	0.682877	+	1.18278i	0.974099	+	0.226122i	$0.0726049\pi$
$643$	17.3160	+	29.9922i	0.682877	+	1.18278i	−0.291222	+	0.956656i	$0.594062\pi$
$644$	−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	$-0.384031\pi$
$647$	18.1269			0.712643			0.356322	+	0.934363i	$0.384031\pi$
$648$	−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
$651$	−5.30356	+	5.56856i	−0.207863	+	0.218249i
$652$	−2.00708	−	1.15879i	−0.0786033	−	0.0453816i
$653$	34.7749	−	20.0773i	1.36085	−	0.785685i	0.371110	−	0.928589i	$-0.378977\pi$
$653$	34.7749	−	20.0773i	1.36085	−	0.785685i	0.989737	+	0.142904i	$0.0456440\pi$
$654$	−1.00912	+	19.3808i	−0.0394598	+	0.757851i
$655$	1.53099	−	0.883918i	0.0598208	−	0.0345375i
$656$		−	7.52964i		−	0.293983i
$657$	36.7782	+	3.84034i	1.43485	+	0.149826i
$658$	2.93458	−	15.6459i	0.114402	−	0.609940i
$659$	−15.7627	+	9.10062i	−0.614029	+	0.354510i	−0.774541	−	0.632524i	$-0.782019\pi$
$659$	−15.7627	+	9.10062i	−0.614029	+	0.354510i	0.160512	+	0.987034i	$0.448686\pi$
$660$	−0.987974	−	0.641122i	−0.0384568	−	0.0249556i
$661$	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
$663$	−5.07868	+	2.30875i	−0.197240	+	0.0896645i
$664$		−	1.54870i		−	0.0601014i
$665$	36.2615	+	31.1052i	1.40616	+	1.20621i
$666$	13.6964	−	6.10915i	0.530724	−	0.236725i
$667$	−8.84910			−0.342639
$668$	−11.5588	+	6.67349i	−0.447224	+	0.258205i
$669$	2.58362	+	0.134524i	0.0998886	+	0.00520100i
$670$	7.77795			0.300489
$671$		−	2.51012i		−	0.0969020i
$672$	−4.45402	−	1.07784i	−0.171817	−	0.0415787i
$673$	−18.1450	+	31.4281i	−0.699438	+	1.21146i	0.269223	+	0.963078i	$0.413233\pi$
$673$	−18.1450	+	31.4281i	−0.699438	+	1.21146i	−0.968661	+	0.248385i	$0.920100\pi$
$674$	3.88418	+	6.72760i	0.149613	+	0.259138i
$675$	0.442258	+	1.14863i	0.0170225	+	0.0442108i
$676$	5.46399	+	11.7960i	0.210153	+	0.453691i
$677$	−2.13681	+	3.70106i	−0.0821243	+	0.142243i	−0.904162	−	0.427189i	$-0.859504\pi$
$677$	−2.13681	+	3.70106i	−0.0821243	+	0.142243i	0.822038	+	0.569433i	$0.192837\pi$
$678$	−0.756079	+	14.5210i	−0.0290370	+	0.557675i
$679$	−2.09526	−	5.95749i	−0.0804088	−	0.228627i
$680$	−1.77042	+	1.02215i	−0.0678927	+	0.0391978i
$681$	−0.573773	+	11.0197i	−0.0219870	+	0.422276i
$682$	−0.249316	+	0.431828i	−0.00954681	+	0.0165356i
$683$	−15.0386	+	26.0477i	−0.575438	+	0.996688i	0.420556	+	0.907267i	$0.361835\pi$
$683$	−15.0386	+	26.0477i	−0.575438	+	0.996688i	−0.995994	+	0.0894210i	$0.971498\pi$
$684$	9.64293	+	21.6189i	0.368706	+	0.826620i
$685$	5.12669	−	2.95989i	0.195881	−	0.113092i
$686$	−0.604128	+	18.5104i	−0.0230657	+	0.706730i
$687$	−13.6087	−	0.708579i	−0.519205	−	0.0270340i
$688$	−1.94207	+	3.36377i	−0.0740408	+	0.128242i
$689$	14.0841	−	22.0455i	0.536560	−	0.839866i
$690$	16.8563	−	25.9757i	0.641709	−	0.988879i
$691$	−8.59159	−	14.8811i	−0.326840	−	0.566103i	0.655043	−	0.755591i	$-0.272650\pi$
$691$	−8.59159	−	14.8811i	−0.326840	−	0.566103i	−0.981883	+	0.189489i	$0.939317\pi$
$692$	9.18090	−	15.9018i	0.349006	−	0.604495i
$693$	−1.71317	+	1.62095i	−0.0650778	+	0.0615749i
$694$		−	9.70091i		−	0.368241i
$695$	−26.9618			−1.02272
$696$	0.102014	−	1.95924i	0.00386682	−	0.0742648i
$697$	−5.82526	+	3.36322i	−0.220648	+	0.127391i
$698$	26.5052			1.00324
$699$	−0.836773	+	16.0708i	−0.0316497	+	0.607853i
$700$	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	$0.779827\pi$
$702$	14.0285	+	12.4178i	0.529471	+	0.468680i
$703$	−34.1610	+	19.7228i	−1.28840	+	0.743861i
$704$	−0.297141			−0.0111989
$705$	−12.9819	+	20.0052i	−0.488926	+	0.753439i
$706$	22.1838	−	12.8078i	0.834900	−	0.482030i
$707$	48.8283	+	9.15835i	1.83638	+	0.344435i
$708$	8.75277	+	5.67990i	0.328949	+	0.213464i
$709$			1.22167i			0.0458807i	0.999737	+	0.0229403i	$0.00730278\pi$
$709$			1.22167i			0.0458807i	−0.999737	+	0.0229403i	$0.992697\pi$
$710$	4.55803	−	2.63158i	0.171060	−	0.0987614i
$711$	10.9123	+	24.4648i	0.409243	+	0.917502i
$712$	−12.3933	+	7.15530i	−0.464460	+	0.268156i
$713$	−11.3536	−	6.55500i	−0.425196	−	0.245487i
$714$	1.15558	+	3.92726i	0.0432465	+	0.146974i
$715$	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	$-0.303545\pi$
$719$	31.0368			1.15748			0.578738	+	0.815514i	$0.303545\pi$
$720$	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
$723$	−50.3127	−	2.61968i	−1.87115	−	0.0974270i
$724$	−4.51843	−	2.60872i	−0.167926	−	0.0969522i
$725$			0.268306i			0.00996465i
$726$	10.2881	−	15.8541i	0.381827	−	0.588399i
$727$			33.4726i			1.24143i	0.784036	+	0.620716i	$0.213158\pi$
$727$			33.4726i			1.24143i	−0.784036	+	0.620716i	$0.786842\pi$
$728$	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
$732$	−0.760809	+	14.6118i	−0.0281203	+	0.540069i
$733$	12.3342	−	21.3634i	0.455573	−	0.789076i	−0.543148	−	0.839637i	$-0.682768\pi$
$733$	12.3342	−	21.3634i	0.455573	−	0.789076i	0.998721	+	0.0505610i	$0.0161009\pi$
$734$	21.2692	−	12.2798i	0.785061	−	0.453255i
$735$	11.3854	−	25.3020i	0.419957	−	0.933280i
$736$		−	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	$0.305451\pi$
$739$			44.5264i			1.63793i	−0.573845	+	0.818964i	$0.694549\pi$
$740$	−5.71994	+	9.90723i	−0.210269	+	0.364197i
$741$	−40.0906	−	28.6529i	−1.47276	−	1.05259i
$742$	−14.5703	−	12.4984i	−0.534892	−	0.458832i
$743$	−19.9258	+	34.5124i	−0.731006	+	1.26614i	0.225448	+	0.974255i	$0.427615\pi$
$743$	−19.9258	+	34.5124i	−0.731006	+	1.26614i	−0.956454	+	0.291884i	$0.905718\pi$
$744$	1.58220	−	2.43818i	0.0580063	−	0.0893881i
$745$	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
$750$	15.8371	+	10.2771i	0.578289	+	0.375267i
$751$	8.99264	+	15.5757i	0.328146	+	0.568366i	0.982144	−	0.188130i	$-0.0602428\pi$
$751$	8.99264	+	15.5757i	0.328146	+	0.568366i	−0.653998	+	0.756496i	$0.726909\pi$
$752$			6.01671i			0.219407i
$753$	12.9935	−	20.0231i	0.473510	−	0.729683i
$754$	1.88117	+	3.62496i	0.0685080	+	0.132013i
$755$	−27.9832			−1.01841
$756$	10.4640	−	8.91660i	0.380570	−	0.324293i
$757$	20.2665	−	35.1027i	0.736600	−	1.27583i	−0.217417	−	0.976079i	$-0.569763\pi$
$757$	20.2665	−	35.1027i	0.736600	−	1.27583i	0.954018	−	0.299750i	$-0.0969034\pi$
$758$			16.0701i			0.583692i
$759$	−3.37283	−	2.18871i	−0.122426	−	0.0794453i
$760$	−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
$765$	0.636932	−	6.09977i	0.0230283	−	0.220537i
$766$	−23.1968	+	13.3927i	−0.838136	+	0.483898i
$767$	−21.6986	−	0.975089i	−0.783491	−	0.0352084i
$768$	1.72971	+	0.0900624i	0.0624155	+	0.00324985i
$769$	3.70242	−	6.41278i	0.133513	−	0.231251i	−0.791516	−	0.611149i	$-0.790708\pi$
$769$	3.70242	−	6.41278i	0.133513	−	0.231251i	0.925028	+	0.379898i	$0.124041\pi$
$770$	0.331654	−	1.76823i	0.0119520	−	0.0637227i
$771$	5.30300	−	8.17196i	0.190983	−	0.294306i
$772$	−2.77543	−	1.60239i	−0.0998899	−	0.0576714i
$773$	4.71590	+	2.72273i	0.169619	+	0.0979297i	0.582406	−	0.812898i	$-0.302111\pi$
$773$	4.71590	+	2.72273i	0.169619	+	0.0979297i	−0.412787	+	0.910828i	$0.635445\pi$
$774$	−4.74669	−	10.6418i	−0.170616	−	0.382512i
$775$	−0.198749	+	0.344243i	−0.00713927	+	0.0123656i
$776$	1.19346	+	2.06713i	0.0428427	+	0.0742058i
$777$	16.5886	+	15.7992i	0.595113	+	0.566792i
$778$	3.67405	+	2.12122i	0.131721	+	0.0760493i
$779$	−51.4539	−	29.7069i	−1.84353	−	1.06436i
$780$	−14.2241	−	1.38306i	−0.509305	−	0.0495214i
$781$	−0.341698	−	0.591838i	−0.0122269	−	0.0211776i
$782$	−6.04402	+	3.48951i	−0.216134	+	0.124785i
$783$	4.57780	+	3.69933i	0.163597	+	0.132203i
$784$	−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	−0.395170	−	0.918608i	$-0.629314\pi$
$787$	16.7747	−	29.0546i	0.597953	−	1.03568i	0.993123	−	0.117076i	$-0.0373522\pi$
$788$	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	−0.992622	−	0.121248i	$-0.961310\pi$
$797$	−16.9758	−	29.4030i	−0.601315	−	1.04151i	0.391308	−	0.920260i	$-0.372023\pi$
$798$	−24.9380	+	26.1841i	−0.882797	+	0.926909i
$799$	4.65479	−	2.68744i	0.164675	−	0.0950750i
$800$	−0.236873			−0.00837474
$801$	4.45865	−	42.6996i	0.157539	−	1.50872i
$802$	−7.61652	+	13.1922i	−0.268949	+	0.465833i
$803$	1.83128	+	3.17188i	0.0646246	+	0.111933i
$804$	−0.306107	+	5.87898i	−0.0107955	+	0.207336i
$805$	46.4902	+	8.71981i	1.63856	+	0.307333i
$806$	−0.271622	+	6.04439i	−0.00956747	+	0.212904i
$807$	48.3533	+	2.51766i	1.70212	+	0.0886257i
$808$	−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
$813$	−19.2896	+	29.7255i	−0.676516	+	1.04252i
$814$	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
$819$	−9.39142	+	27.0333i	−0.328163	+	0.944621i
$820$	−17.2310			−0.601732
$821$	16.2192	+	28.0926i	0.566056	+	0.980437i	0.996951	+	0.0780351i	$0.0248646\pi$
$821$	16.2192	+	28.0926i	0.566056	+	0.980437i	−0.430895	+	0.902402i	$0.641802\pi$
$822$	2.03548	+	3.99151i	0.0709954	+	0.139220i
$823$	−11.7933	+	20.4265i	−0.411087	+	0.712024i	−0.995009	−	0.0997858i	$-0.968184\pi$
$823$	−11.7933	+	20.4265i	−0.411087	+	0.712024i	0.583921	+	0.811810i	$0.301518\pi$
$824$	−12.3898	−	7.15323i	−0.431618	−	0.249194i
$825$	−0.0663622	+	0.102265i	−0.00231044	+	0.00356040i
$826$	−2.93822	+	15.6653i	−0.102234	+	0.545066i
$827$	11.5185			0.400539			0.200269	−	0.979741i	$-0.435818\pi$
$827$	11.5185			0.400539			0.200269	+	0.979741i	$0.435818\pi$
$828$	18.9704	+	13.7632i	0.659268	+	0.478304i
$829$			36.4890i			1.26731i	0.773614	+	0.633657i	$0.218447\pi$
$829$			36.4890i			1.26731i	−0.773614	+	0.633657i	$0.781553\pi$
$830$	−3.54409			−0.123017
$831$	11.2616	+	0.586369i	0.390660	+	0.0203409i
$832$	−3.20028	+	1.66078i	−0.110950	+	0.0575772i
$833$	−4.87659	+	3.91440i	−0.168964	+	0.135626i
$834$	1.06110	−	20.3791i	0.0367429	−	0.705671i
$835$	15.2718	+	26.4515i	0.528501	+	0.915390i
$836$	−1.17232	+	2.03052i	−0.0405455	+	0.0702269i
$837$	3.13313	+	8.13734i	0.108297	+	0.281268i
$838$	8.88341			0.306872
$839$	−27.0771	+	15.6330i	−0.934807	+	0.539711i	−0.888329	−	0.459209i	$-0.848133\pi$
$839$	−27.0771	+	15.6330i	−0.934807	+	0.539711i	−0.0464780	+	0.998919i	$0.514800\pi$
$840$	−2.46656	+	10.1927i	−0.0851044	+	0.351680i
$841$	−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
$855$	49.4732	−	22.0671i	1.69195	−	0.754678i
$856$	14.4499	−	8.34267i	0.493888	−	0.285147i
$857$	−3.94184	−	6.82747i	−0.134651	−	0.233222i	0.790813	−	0.612058i	$-0.209658\pi$
$857$	−3.94184	−	6.82747i	−0.134651	−	0.233222i	−0.925464	+	0.378836i	$0.876325\pi$
$858$	−0.179583	+	1.84693i	−0.00613088	+	0.0630532i
$859$	−16.8815	−	9.74653i	−0.575989	−	0.332547i	0.183549	−	0.983011i	$-0.441241\pi$
$859$	−16.8815	−	9.74653i	−0.575989	−	0.332547i	−0.759538	+	0.650463i	$0.774575\pi$
$860$	7.69772	+	4.44428i	0.262490	+	0.151549i
$861$	−8.11577	+	33.5371i	−0.276585	+	1.14294i
$862$	−9.74149	−	16.8728i	−0.331796	−	0.574688i
$863$	5.07880	−	8.79674i	0.172884	−	0.299445i	−0.766543	−	0.642193i	$-0.778025\pi$
$863$	5.07880	−	8.79674i	0.172884	−	0.299445i	0.939427	+	0.342749i	$0.111358\pi$
$864$	−3.26594	+	4.04149i	−0.111109	+	0.137494i
$865$	−36.3900	−	21.0098i	−1.23730	−	0.714354i
$866$	−15.8703	−	9.16273i	−0.539295	−	0.311362i
$867$	15.2760	−	23.5405i	0.518801	−	0.799477i
$868$	4.36375	+	0.818475i	0.148115	+	0.0277808i
$869$	−1.32664	+	2.29781i	−0.0450032	+	0.0779479i
$870$	−4.48357	−	0.233450i	−0.152007	−	0.00791470i
$871$	−5.64471	−	10.8772i	−0.191264	−	0.368560i
$872$	9.70354	−	5.60234i	0.328603	−	0.189719i
$873$	−7.12204	−	0.743677i	−0.241045	−	0.0251696i
$874$	−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	$-0.954628\pi$
$877$		−	8.41388i		−	0.284117i	0.989858	−	0.142058i	$-0.0453720\pi$
$878$	2.15827	+	1.24608i	0.0728381	+	0.0420531i
$879$	29.2515	+	18.9820i	0.986627	+	0.640248i
$880$			0.679983i			0.0229222i
$881$	−3.40189	+	5.89224i	−0.114612	+	0.198515i	−0.917625	−	0.397448i	$-0.869896\pi$
$881$	−3.40189	+	5.89224i	−0.114612	+	0.198515i	0.803012	+	0.595962i	$0.203229\pi$
$882$	18.6765	+	9.60146i	0.628871	+	0.323298i
$883$	−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
$885$	12.9980	−	20.0300i	0.436923	−	0.673302i
$886$			16.6766i			0.560263i
$887$	9.70164	+	16.8037i	0.325749	+	0.564214i	0.981664	−	0.190621i	$-0.0610501\pi$
$887$	9.70164	+	16.8037i	0.325749	+	0.564214i	−0.655914	+	0.754835i	$0.727717\pi$
$888$	−7.26329	−	4.71333i	−0.243740	−	0.158169i
$889$	−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
$894$	−3.09962	+	4.77653i	−0.103667	+	0.159751i
$895$	−11.8070	+	20.4502i	−0.394663	+	0.683576i
$896$	0.877809	+	2.49589i	0.0293256	+	0.0833817i
$897$	−48.5594	−	4.72159i	−1.62135	−	0.157649i
$898$	−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
$903$	12.2756	−	12.8890i	0.408508	−	0.428920i
$904$	7.27033	−	4.19753i	0.241808	−	0.139608i
$905$	−5.96984	+	10.3401i	−0.198444	+	0.343716i
$906$	1.10130	−	21.1512i	0.0365882	−	0.702701i
$907$	−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	$-0.0933439\pi$
$912$	7.43972	−	11.4647i	0.246354	−	0.379633i
$913$			0.460183i			0.0152298i
$914$	−13.9495	−	8.05374i	−0.461408	−	0.266394i
$915$	33.4380	+	1.74105i	1.10543	+	0.0575574i
$916$	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
$924$	1.32347	+	0.320271i	0.0435389	+	0.0105361i
$925$	1.02549	+	0.592068i	0.0337180	+	0.0194671i
$926$	17.7559	−	10.2514i	0.583495	−	0.336881i
$927$	39.1969	−	17.4834i	1.28740	−	0.574232i
$928$	−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	$0.898165\pi$
$930$	−5.57959	−	3.62074i	−0.182962	−	0.118729i
$931$	−51.4805	−	20.0157i	−1.68720	−	0.655989i
$932$	8.04627	−	4.64552i	0.263564	−	0.152169i
$933$	14.6323	−	22.5486i	0.479041	−	0.738207i
$934$	5.73845			0.187768
$935$	0.526065	−	0.303724i	0.0172042	−	0.00993283i
$936$	1.60519	−	10.6969i	0.0524672	−	0.349639i
$937$		−	38.4000i		−	1.25447i	−0.778828	−	0.627237i	$-0.784186\pi$
$937$		−	38.4000i		−	1.25447i	0.778828	−	0.627237i	$-0.215814\pi$
$938$	−8.48309	+	2.98352i	−0.276983	+	0.0974155i
$939$	1.42544	−	27.3765i	0.0465174	−	0.893397i
$940$	13.7688			0.449088
$941$	−6.21610	+	3.58887i	−0.202639	+	0.116994i	−0.597886	−	0.801581i	$-0.703992\pi$
$941$	−6.21610	+	3.58887i	−0.202639	+	0.116994i	0.395247	+	0.918575i	$0.370659\pi$
$942$	1.60896	−	30.9012i	0.0524228	−	1.00681i
$943$	−58.8245			−1.91559
$944$		−	6.02418i		−	0.196070i
$945$	−20.4049	−	23.9459i	−0.663772	−	0.778961i
$946$	0.577069	−	0.999512i	0.0187621	−	0.0324970i
$947$	−12.3986	−	21.4750i	−0.402899	−	0.697842i	0.591175	−	0.806543i	$-0.298664\pi$
$947$	−12.3986	−	21.4750i	−0.402899	−	0.697842i	−0.994074	+	0.108701i	$0.965331\pi$
$948$	8.41907	−	12.9739i	0.273439	−	0.421371i
$949$	37.4517	+	23.9265i	1.21573	+	0.776687i
$950$	−0.934544	+	1.61868i	−0.0303206	+	0.0525169i
$951$	−22.3898	−	1.16579i	−0.726038	−	0.0378033i
$952$	1.53884	−	1.79393i	0.0498742	−	0.0581417i
$953$	17.1692	−	9.91265i	0.556165	−	0.321102i	−0.195440	−	0.980716i	$-0.562613\pi$
$953$	17.1692	−	9.91265i	0.556165	−	0.321102i	0.751605	+	0.659614i	$0.229280\pi$
$954$	−19.8789	+	8.86680i	−0.643603	+	0.287073i
$955$	−30.1761	+	52.2665i	−0.976474	+	1.69130i
$956$	−11.3033	+	19.5780i	−0.365576	+	0.633196i
$957$	−0.0303124	+	0.582170i	−0.000979861	+	0.0188189i
$958$	24.3944	−	14.0841i	0.788147	−	0.455037i
$959$	−4.45609	+	5.19477i	−0.143895	+	0.167748i
$960$	0.206101	−	3.95830i	0.00665187	−	0.127754i
$961$	14.0920	−	24.4080i	0.454580	−	0.787356i
$962$	18.0061	+	0.809155i	0.580539	+	0.0260882i
$963$	−5.19854	+	49.7853i	−0.167521	+	1.60431i
$964$	14.5437	+	25.1904i	0.468421	+	0.811329i
$965$	−3.66695	+	6.35135i	−0.118043	+	0.204457i
$966$	−8.42054	+	34.7965i	−0.270926	+	1.11956i
$967$		−	4.47698i		−	0.143970i	−0.997406	−	0.0719849i	$-0.977067\pi$
$967$		−	4.47698i		−	0.143970i	0.997406	−	0.0719849i	$-0.0229333\pi$
$968$	−10.9117			−0.350716
$969$	−12.1926	−	0.634845i	−0.391684	−	0.0203942i
$970$	4.73047	−	2.73114i	0.151886	−	0.0876917i
$971$	12.5415			0.402477			0.201239	−	0.979542i	$-0.435503\pi$
$971$	12.5415			0.402477			0.201239	+	0.979542i	$0.435503\pi$
$972$	−4.06010	−	15.0504i	−0.130228	−	0.482743i
$973$	29.4061	−	10.3422i	0.942717	−	0.331556i
$974$		−	29.7095i		−	0.951954i
$975$	−0.143160	+	1.47233i	−0.00458478	+	0.0471523i
$976$	7.31581	−	4.22379i	0.234173	−	0.135200i
$977$	−54.6021			−1.74687			−0.873437	−	0.486937i	$-0.838114\pi$
$977$	−54.6021			−1.74687			−0.873437	+	0.486937i	$0.838114\pi$
$978$	−3.36730	−	2.18513i	−0.107674	−	0.0698726i
$979$	3.68256	−	2.12613i	0.117695	−	0.0679514i
$980$	−15.8324	+	2.43790i	−0.505746	+	0.0778760i
$981$	−3.49097	+	33.4323i	−0.111458	+	1.06741i
$982$			40.8902i			1.30486i
$983$	−40.1578	+	23.1851i	−1.28083	+	0.739490i	−0.977001	−	0.213236i	$-0.931600\pi$
$983$	−40.1578	+	23.1851i	−1.28083	+	0.739490i	−0.303833	+	0.952725i	$0.598266\pi$
$984$	0.678137	−	13.0241i	0.0216182	−	0.415192i
$985$	51.4757	−	29.7195i	1.64015	−	0.946942i
$986$	0.876307	+	0.505936i	0.0279073	+	0.0161123i
$987$	6.48507	−	26.7985i	0.206422	−	0.853006i
$988$	−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
$996$	0.139480	−	2.67881i	0.00441959	−	0.0848812i
$997$	−53.5194	−	30.8994i	−1.69498	−	0.978595i	−0.950386	−	0.311073i	$-0.899312\pi$
$997$	−53.5194	−	30.8994i	−1.69498	−	0.978595i	−0.744590	−	0.667522i	$-0.767355\pi$
$998$			12.7422i			0.403348i
$999$	24.2409	−	9.33351i	0.766949	−	0.295299i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bn.e.173.7	yes	34
3.2	odd	2		546.2.bn.f.173.11	yes	34
7.3	odd	6		546.2.bi.f.17.11	yes	34
13.10	even	6		546.2.bi.e.257.17	yes	34
21.17	even	6		546.2.bi.e.17.17	✓	34
39.23	odd	6		546.2.bi.f.257.11	yes	34
91.10	odd	6		546.2.bn.f.101.11	yes	34
273.101	even	6	inner	546.2.bn.e.101.7	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.17	✓	34	21.17	even	6
546.2.bi.e.257.17	yes	34	13.10	even	6
546.2.bi.f.17.11	yes	34	7.3	odd	6
546.2.bi.f.257.11	yes	34	39.23	odd	6
546.2.bn.e.101.7	yes	34	273.101	even	6	inner
546.2.bn.e.173.7	yes	34	1.1	even	1	trivial
546.2.bn.f.101.11	yes	34	91.10	odd	6
546.2.bn.f.173.11	yes	34	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bn (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.786858 - 1.54300i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.98183 + 1.14421i) q^{5} +(-0.942850 + 1.45294i) q^{6} +(-2.60041 - 0.487738i) q^{7} +1.00000 q^{8} +(-1.76171 + 2.42825i) q^{9} +O(q^{10})\)	\(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} +(-0.942850 + 1.45294i) 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} +(1.72971 + 0.0900624i) q^{12} +(-3.20028 + 1.66078i) q^{13} +(0.877809 + 2.49589i) q^{14} +(0.206101 - 3.95830i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.446664 + 0.773644i) q^{17} +(2.98378 + 0.311563i) q^{18} -7.89067 q^{19} +(-1.98183 + 1.14421i) q^{20} +(1.29357 + 4.39621i) 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} +(-1.22207 - 2.73981i) q^{36} +(4.32929 - 2.49951i) q^{37} +(3.94533 + 6.83352i) q^{38} +(5.08075 + 3.63124i) q^{39} +(1.98183 + 1.14421i) q^{40} +(6.52086 + 3.76482i) q^{41} +(3.16045 - 3.31837i) q^{42} +(-1.94207 - 3.36377i) q^{43} +(0.148570 - 0.257331i) q^{44} +(-6.26984 + 2.79660i) q^{45} +(6.76573 + 3.90620i) q^{46} +(-5.21062 - 3.00835i) q^{47} +(-0.942850 + 1.45294i) q^{48} +(6.52422 + 2.53663i) q^{49} +(0.118437 - 0.205138i) q^{50} +(1.54520 + 0.0804552i) q^{51} +(0.161862 - 3.60192i) q^{52} +(-6.28351 + 3.62779i) q^{53} +(-1.86707 - 4.84913i) 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} +(3.32494 + 2.15764i) q^{60} +8.44757i q^{61} +(0.839051 - 1.45328i) q^{62} +(5.76551 - 5.45517i) q^{63} +1.00000 q^{64} +(-8.24270 - 0.370410i) q^{65} +(0.280159 - 0.431727i) q^{66} +3.39883i q^{67} +(-0.446664 - 0.773644i) q^{68} +(11.3509 + 7.36592i) 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} +(0.223336 - 0.344163i) q^{75} +(3.94533 - 6.83352i) q^{76} +(0.772686 + 0.144927i) q^{77} +(0.604372 - 6.21568i) 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} +(-4.45402 - 1.07784i) q^{84} +(-1.77042 + 1.02215i) q^{85} +(-1.94207 + 3.36377i) q^{86} +(0.102014 - 1.95924i) 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} +(1.58220 - 2.43818i) q^{93} +6.01671i q^{94} +(-15.6380 - 9.02859i) q^{95} +(1.72971 + 0.0900624i) q^{96} +(1.19346 + 2.06713i) q^{97} +(-1.06532 - 6.91846i) q^{98} +(0.523476 - 0.721530i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9}+O(q^{10}) \) 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9	\( 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9} - 18 q^{11} + 3 q^{12} - 8 q^{13} - 4 q^{14} - 17 q^{15} - 17 q^{16} + 6 q^{17} - 11 q^{18} - 10 q^{19} - 9 q^{20} - 4 q^{21} + 9 q^{22} + 6 q^{23} + 3 q^{24} + 16 q^{25} + 13 q^{26} + 18 q^{27} - q^{28} + 27 q^{29} + 13 q^{30} + q^{31} - 17 q^{32} + 21 q^{33} - 12 q^{34} - 3 q^{35} + 4 q^{36} + 6 q^{37} + 5 q^{38} + 20 q^{39} + 9 q^{40} + 3 q^{41} + 20 q^{42} - 3 q^{43} + 9 q^{44} - 6 q^{46} - 27 q^{47} - 6 q^{48} - 5 q^{49} + 16 q^{50} + 24 q^{51} - 5 q^{52} + 21 q^{53} - 18 q^{54} + 57 q^{55} + 5 q^{56} - 17 q^{57} - 6 q^{59} + 4 q^{60} + q^{62} - 21 q^{63} + 34 q^{64} + 33 q^{65} - 21 q^{66} + 6 q^{68} - 30 q^{69} + 3 q^{70} - 15 q^{71} + 7 q^{72} + 19 q^{73} - 6 q^{74} - 63 q^{75} + 5 q^{76} - 9 q^{77} - 10 q^{78} - 9 q^{79} - 5 q^{81} - 16 q^{84} - 42 q^{85} - 3 q^{86} - 75 q^{87} - 18 q^{88} - 18 q^{89} - 9 q^{90} - 27 q^{91} + 25 q^{93} - 3 q^{95} + 3 q^{96} - 19 q^{97} + 7 q^{98} - 27 q^{99}+O(q^{100}) \) 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9 - 18 * q^11 + 3 * q^12 - 8 * q^13 - 4 * q^14 - 17 * q^15 - 17 * q^16 + 6 * q^17 - 11 * q^18 - 10 * q^19 - 9 * q^20 - 4 * q^21 + 9 * q^22 + 6 * q^23 + 3 * q^24 + 16 * q^25 + 13 * q^26 + 18 * q^27 - q^28 + 27 * q^29 + 13 * q^30 + q^31 - 17 * q^32 + 21 * q^33 - 12 * q^34 - 3 * q^35 + 4 * q^36 + 6 * q^37 + 5 * q^38 + 20 * q^39 + 9 * q^40 + 3 * q^41 + 20 * q^42 - 3 * q^43 + 9 * q^44 - 6 * q^46 - 27 * q^47 - 6 * q^48 - 5 * q^49 + 16 * q^50 + 24 * q^51 - 5 * q^52 + 21 * q^53 - 18 * q^54 + 57 * q^55 + 5 * q^56 - 17 * q^57 - 6 * q^59 + 4 * q^60 + q^62 - 21 * q^63 + 34 * q^64 + 33 * q^65 - 21 * q^66 + 6 * q^68 - 30 * q^69 + 3 * q^70 - 15 * q^71 + 7 * q^72 + 19 * q^73 - 6 * q^74 - 63 * q^75 + 5 * q^76 - 9 * q^77 - 10 * q^78 - 9 * q^79 - 5 * q^81 - 16 * q^84 - 42 * q^85 - 3 * q^86 - 75 * q^87 - 18 * q^88 - 18 * q^89 - 9 * q^90 - 27 * q^91 + 25 * q^93 - 3 * q^95 + 3 * q^96 - 19 * q^97 + 7 * q^98 - 27 * q^99

Introduction

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