LMFDB - Embedded newform 546.2.bn.e.173.1

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			173.1
Character	$\chi$	$=$	546.173
Dual form			546.2.bn.e.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-1.73183 + 0.0276700i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.84717 - 1.64381i) q^{5} +(0.889878 + 1.48597i) q^{6} +(-0.683149 - 2.55603i) q^{7} +1.00000 q^{8} +(2.99847 - 0.0958395i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.73183 + 0.0276700i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.84717 - 1.64381i) q^{5} +(0.889878 + 1.48597i) q^{6} +(-0.683149 - 2.55603i) q^{7} +1.00000 q^{8} +(2.99847 - 0.0958395i) q^{9} +3.28763i q^{10} -2.07020 q^{11} +(0.841952 - 1.51364i) q^{12} +(-3.53365 - 0.716460i) q^{13} +(-1.87202 + 1.86964i) q^{14} +(4.97629 + 2.76802i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.561810 + 0.973084i) q^{17} +(-1.58223 - 2.54883i) q^{18} -1.01086 q^{19} +(2.84717 - 1.64381i) q^{20} +(1.25382 + 4.40771i) q^{21} +(1.03510 + 1.79285i) q^{22} +(3.03183 - 1.75043i) q^{23} +(-1.73183 + 0.0276700i) q^{24} +(2.90424 + 5.03029i) q^{25} +(1.14635 + 3.41846i) q^{26} +(-5.19019 + 0.248945i) q^{27} +(2.55516 + 0.686393i) q^{28} +(7.97573 + 4.60479i) q^{29} +(-0.0909687 - 5.69361i) q^{30} +(1.86666 + 3.23315i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.58524 - 0.0572825i) q^{33} +1.12362 q^{34} +(-2.25660 + 8.40042i) q^{35} +(-1.41623 + 2.64467i) q^{36} +(-6.03816 + 3.48613i) q^{37} +(0.505430 + 0.875431i) q^{38} +(6.13951 + 1.14301i) q^{39} +(-2.84717 - 1.64381i) q^{40} +(8.52566 + 4.92229i) q^{41} +(3.19028 - 3.28970i) q^{42} +(3.35600 + 5.81276i) q^{43} +(1.03510 - 1.79285i) q^{44} +(-8.69468 - 4.65605i) q^{45} +(-3.03183 - 1.75043i) q^{46} +(-1.05515 - 0.609193i) q^{47} +(0.889878 + 1.48597i) q^{48} +(-6.06662 + 3.49230i) q^{49} +(2.90424 - 5.03029i) q^{50} +(0.946035 - 1.70076i) q^{51} +(2.38730 - 2.70200i) q^{52} +(-5.05843 + 2.92049i) q^{53} +(2.81069 + 4.37036i) q^{54} +(5.89421 + 3.40302i) q^{55} +(-0.683149 - 2.55603i) q^{56} +(1.75064 - 0.0279705i) q^{57} -9.20958i q^{58} +(-8.49492 - 4.90455i) q^{59} +(-4.88532 + 2.92558i) q^{60} -0.241991i q^{61} +(1.86666 - 3.23315i) q^{62} +(-2.29337 - 7.59871i) q^{63} +1.00000 q^{64} +(8.88317 + 7.84854i) q^{65} +(-1.84223 - 3.07626i) q^{66} -11.8144i q^{67} +(-0.561810 - 0.973084i) q^{68} +(-5.20218 + 3.11533i) q^{69} +(8.40328 - 2.24594i) q^{70} +(-3.94585 - 6.83441i) q^{71} +(2.99847 - 0.0958395i) q^{72} +(-0.878160 - 1.52102i) q^{73} +(6.03816 + 3.48613i) q^{74} +(-5.16884 - 8.63125i) q^{75} +(0.505430 - 0.875431i) q^{76} +(1.41426 + 5.29150i) q^{77} +(-2.07988 - 5.88847i) q^{78} +(-2.48977 + 4.31240i) q^{79} +3.28763i q^{80} +(8.98163 - 0.574744i) q^{81} -9.84458i q^{82} +0.999900i q^{83} +(-4.44410 - 1.11801i) q^{84} +(3.19914 - 1.84702i) q^{85} +(3.35600 - 5.81276i) q^{86} +(-13.9400 - 7.75403i) q^{87} -2.07020 q^{88} +(-6.59807 + 3.80940i) q^{89} +(0.315084 + 9.85784i) q^{90} +(0.582714 + 9.52158i) q^{91} +3.50085i q^{92} +(-3.32220 - 5.54762i) q^{93} +1.21839i q^{94} +(2.87809 + 1.66167i) q^{95} +(0.841952 - 1.51364i) q^{96} +(3.21628 + 5.57077i) q^{97} +(6.05773 + 3.50769i) q^{98} +(-6.20743 + 0.198407i) 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
$3$	−1.73183	+	0.0276700i	−0.999872	+	0.0159753i
$3$	−1.73183	+	0.0276700i	−0.999872	+	0.0159753i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−2.84717	−	1.64381i	−1.27329	−	0.735135i	−0.297686	−	0.954664i	$-0.596215\pi$
$5$	−2.84717	−	1.64381i	−1.27329	−	0.735135i	−0.975606	+	0.219529i	$0.929548\pi$
$6$	0.889878	+	1.48597i	0.363291	+	0.606646i
$7$	−0.683149	−	2.55603i	−0.258206	−	0.966090i
$7$	−0.683149	−	2.55603i	−0.258206	−	0.966090i
$8$	1.00000			0.353553
$9$	2.99847	−	0.0958395i	0.999490	−	0.0319465i
$10$			3.28763i			1.03964i
$11$	−2.07020			−0.624189			−0.312095	−	0.950051i	$-0.601031\pi$
$11$	−2.07020			−0.624189			−0.312095	+	0.950051i	$0.601031\pi$
$12$	0.841952	−	1.51364i	0.243051	−	0.436951i
$13$	−3.53365	−	0.716460i	−0.980058	−	0.198710i
$13$	−3.53365	−	0.716460i	−0.980058	−	0.198710i
$14$	−1.87202	+	1.86964i	−0.500317	+	0.499683i
$15$	4.97629	+	2.76802i	1.28487	+	0.714700i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.561810	+	0.973084i	−0.136259	+	0.236008i	−0.926078	−	0.377333i	$-0.876841\pi$
$17$	−0.561810	+	0.973084i	−0.136259	+	0.236008i	0.789819	+	0.613340i	$0.210175\pi$
$18$	−1.58223	−	2.54883i	−0.372936	−	0.600765i
$19$	−1.01086			−0.231907			−0.115954	−	0.993255i	$-0.536992\pi$
$19$	−1.01086			−0.231907			−0.115954	+	0.993255i	$0.536992\pi$
$20$	2.84717	−	1.64381i	0.636646	−	0.367568i
$21$	1.25382	+	4.40771i	0.273607	+	0.961842i
$22$	1.03510	+	1.79285i	0.220684	+	0.382236i
$23$	3.03183	−	1.75043i	0.632180	−	0.364989i	−0.149416	−	0.988774i	$-0.547739\pi$
$23$	3.03183	−	1.75043i	0.632180	−	0.364989i	0.781596	+	0.623785i	$0.214406\pi$
$24$	−1.73183	+	0.0276700i	−0.353508	+	0.00564812i
$25$	2.90424	+	5.03029i	0.580848	+	1.00606i
$26$	1.14635	+	3.41846i	0.224818	+	0.670415i
$27$	−5.19019	+	0.248945i	−0.998852	+	0.0479096i
$28$	2.55516	+	0.686393i	0.482881	+	0.129716i
$29$	7.97573	+	4.60479i	1.48106	+	0.855088i	0.999769	−	0.0214746i	$-0.00683611\pi$
$29$	7.97573	+	4.60479i	1.48106	+	0.855088i	0.481287	+	0.876563i	$0.340169\pi$
$30$	−0.0909687	−	5.69361i	−0.0166085	−	1.03951i
$31$	1.86666	+	3.23315i	0.335262	+	0.580691i	0.983535	−	0.180717i	$-0.0578418\pi$
$31$	1.86666	+	3.23315i	0.335262	+	0.580691i	−0.648273	+	0.761408i	$0.724508\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	3.58524	−	0.0572825i	0.624109	−	0.00997160i
$34$	1.12362			0.192699
$35$	−2.25660	+	8.40042i	−0.381435	+	1.41993i
$36$	−1.41623	+	2.64467i	−0.236039	+	0.440778i
$37$	−6.03816	+	3.48613i	−0.992667	+	0.573116i	−0.906070	−	0.423127i	$-0.860932\pi$
$37$	−6.03816	+	3.48613i	−0.992667	+	0.573116i	−0.0865963	+	0.996243i	$0.527599\pi$
$38$	0.505430	+	0.875431i	0.0819916	+	0.142014i
$39$	6.13951	+	1.14301i	0.983108	+	0.183028i
$40$	−2.84717	−	1.64381i	−0.450177	−	0.259910i
$41$	8.52566	+	4.92229i	1.33148	+	0.768733i	0.985527	−	0.169517i	$-0.0542209\pi$
$41$	8.52566	+	4.92229i	1.33148	+	0.768733i	0.345957	+	0.938250i	$0.387554\pi$
$42$	3.19028	−	3.28970i	0.492271	−	0.507612i
$43$	3.35600	+	5.81276i	0.511785	+	0.886438i	0.999907	+	0.0136621i	$0.00434890\pi$
$43$	3.35600	+	5.81276i	0.511785	+	0.886438i	−0.488122	+	0.872776i	$0.662318\pi$
$44$	1.03510	−	1.79285i	0.156047	−	0.270282i
$45$	−8.69468	−	4.65605i	−1.29613	−	0.694083i
$46$	−3.03183	−	1.75043i	−0.447019	−	0.258086i
$47$	−1.05515	−	0.609193i	−0.153910	−	0.0888599i	0.421067	−	0.907029i	$-0.361656\pi$
$47$	−1.05515	−	0.609193i	−0.153910	−	0.0888599i	−0.574977	+	0.818170i	$0.694989\pi$
$48$	0.889878	+	1.48597i	0.128443	+	0.214482i
$49$	−6.06662	+	3.49230i	−0.866659	+	0.498900i
$50$	2.90424	−	5.03029i	0.410722	−	0.711391i
$51$	0.946035	−	1.70076i	0.132471	−	0.238154i
$52$	2.38730	−	2.70200i	0.331059	−	0.374700i
$53$	−5.05843	+	2.92049i	−0.694829	+	0.401160i	−0.805419	−	0.592706i	$-0.798059\pi$
$53$	−5.05843	+	2.92049i	−0.694829	+	0.401160i	0.110589	+	0.993866i	$0.464726\pi$
$54$	2.81069	+	4.37036i	0.382486	+	0.594731i
$55$	5.89421	+	3.40302i	0.794775	+	0.458863i
$56$	−0.683149	−	2.55603i	−0.0912896	−	0.341564i
$57$	1.75064	−	0.0279705i	0.231878	−	0.00370479i
$58$		−	9.20958i		−	1.20928i
$59$	−8.49492	−	4.90455i	−1.10594	−	0.638517i	−0.168169	−	0.985758i	$-0.553785\pi$
$59$	−8.49492	−	4.90455i	−1.10594	−	0.638517i	−0.937776	+	0.347241i	$0.887119\pi$
$60$	−4.88532	+	2.92558i	−0.630693	+	0.377691i
$61$		−	0.241991i		−	0.0309838i	−0.999880	−	0.0154919i	$-0.995069\pi$
$61$		−	0.241991i		−	0.0309838i	0.999880	−	0.0154919i	$-0.00493142\pi$
$62$	1.86666	−	3.23315i	0.237066	−	0.410611i
$63$	−2.29337	−	7.59871i	−0.288937	−	0.957348i
$64$	1.00000			0.125000
$65$	8.88317	+	7.84854i	1.10182	+	0.973492i
$66$	−1.84223	−	3.07626i	−0.226762	−	0.378662i
$67$		−	11.8144i		−	1.44336i	−0.692226	−	0.721680i	$-0.743370\pi$
$67$		−	11.8144i		−	1.44336i	0.692226	−	0.721680i	$-0.256630\pi$
$68$	−0.561810	−	0.973084i	−0.0681295	−	0.118004i
$69$	−5.20218	+	3.11533i	−0.626268	+	0.375042i
$70$	8.40328	−	2.24594i	1.00438	−	0.268441i
$71$	−3.94585	−	6.83441i	−0.468286	−	0.811096i	0.531057	−	0.847336i	$-0.321795\pi$
$71$	−3.94585	−	6.83441i	−0.468286	−	0.811096i	−0.999343	+	0.0362405i	$0.988462\pi$
$72$	2.99847	−	0.0958395i	0.353373	−	0.0112948i
$73$	−0.878160	−	1.52102i	−0.102781	−	0.178022i	0.810049	−	0.586363i	$-0.199441\pi$
$73$	−0.878160	−	1.52102i	−0.102781	−	0.178022i	−0.912829	+	0.408341i	$0.866107\pi$
$74$	6.03816	+	3.48613i	0.701921	+	0.405254i
$75$	−5.16884	−	8.63125i	−0.596846	−	0.996651i
$76$	0.505430	−	0.875431i	0.0579768	−	0.100419i
$77$	1.41426	+	5.29150i	0.161169	+	0.603023i
$78$	−2.07988	−	5.88847i	−0.235500	−	0.666738i
$79$	−2.48977	+	4.31240i	−0.280121	+	0.485183i	−0.971414	−	0.237391i	$-0.923708\pi$
$79$	−2.48977	+	4.31240i	−0.280121	+	0.485183i	0.691294	+	0.722574i	$0.257041\pi$
$80$			3.28763i			0.367568i
$81$	8.98163	−	0.574744i	0.997959	−	0.0638604i
$82$		−	9.84458i		−	1.08715i
$83$			0.999900i			0.109753i	0.998493	+	0.0548767i	$0.0174766\pi$
$83$			0.999900i			0.109753i	−0.998493	+	0.0548767i	$0.982523\pi$
$84$	−4.44410	−	1.11801i	−0.484891	−	0.121985i
$85$	3.19914	−	1.84702i	0.346995	−	0.200338i
$86$	3.35600	−	5.81276i	0.361887	−	0.626806i
$87$	−13.9400	−	7.75403i	−1.49453	−	0.831319i
$88$	−2.07020			−0.220684
$89$	−6.59807	+	3.80940i	−0.699394	+	0.403795i	−0.807122	−	0.590385i	$-0.798976\pi$
$89$	−6.59807	+	3.80940i	−0.699394	+	0.403795i	0.107728	+	0.994180i	$0.465642\pi$
$90$	0.315084	+	9.85784i	0.0332128	+	1.03911i
$91$	0.582714	+	9.52158i	0.0610850	+	0.998133i
$92$			3.50085i			0.364989i
$93$	−3.32220	−	5.54762i	−0.344496	−	0.575261i
$94$			1.21839i			0.125667i
$95$	2.87809	+	1.66167i	0.295286	+	0.170483i
$96$	0.841952	−	1.51364i	0.0859314	−	0.154486i
$97$	3.21628	+	5.57077i	0.326564	+	0.565626i	0.981828	−	0.189775i	$-0.0607757\pi$
$97$	3.21628	+	5.57077i	0.326564	+	0.565626i	−0.655264	+	0.755400i	$0.727442\pi$
$98$	6.05773	+	3.50769i	0.611923	+	0.354330i
$99$	−6.20743	+	0.198407i	−0.623870	+	0.0199407i
$100$	−5.80848			−0.580848
$101$	19.3241			1.92282			0.961409	−	0.275123i	$-0.0887185\pi$
$101$	19.3241			1.92282			0.961409	+	0.275123i	$0.0887185\pi$
$102$	−1.94592	+	0.0310906i	−0.192675	+	0.00307843i
$103$	−7.86720	−	4.54213i	−0.775178	−	0.447549i	0.0595405	−	0.998226i	$-0.481036\pi$
$103$	−7.86720	−	4.54213i	−0.775178	−	0.447549i	−0.834719	+	0.550677i	$0.814370\pi$
$104$	−3.53365	−	0.716460i	−0.346503	−	0.0702547i
$105$	3.67561	−	14.6105i	0.358703	−	1.42584i
$106$	5.05843	+	2.92049i	0.491318	+	0.283663i
$107$	−3.25929	+	1.88175i	−0.315088	+	0.181916i	−0.649201	−	0.760617i	$-0.724897\pi$
$107$	−3.25929	+	1.88175i	−0.315088	+	0.181916i	0.334113	+	0.942533i	$0.391563\pi$
$108$	2.37950	−	4.61931i	0.228967	−	0.444493i
$109$	2.43945	−	1.40841i	0.233657	−	0.134902i	−0.378601	−	0.925560i	$-0.623595\pi$
$109$	2.43945	−	1.40841i	0.233657	−	0.134902i	0.612258	+	0.790658i	$0.290261\pi$
$110$		−	6.80604i		−	0.648931i
$111$	10.3606	−	6.20446i	0.983384	−	0.588901i
$112$	−1.87202	+	1.86964i	−0.176889	+	0.176664i
$113$	−4.57774	+	2.64296i	−0.430637	+	0.248629i	−0.699618	−	0.714517i	$-0.746646\pi$
$113$	−4.57774	+	2.64296i	−0.430637	+	0.248629i	0.268981	+	0.963146i	$0.413313\pi$
$114$	−0.899542	−	1.50211i	−0.0842499	−	0.140686i
$115$	−11.5095			−1.07327
$116$	−7.97573	+	4.60479i	−0.740528	+	0.427544i
$117$	−10.6642	−	1.80962i	−0.985906	−	0.167299i
$118$			9.80909i			0.903000i
$119$	2.87104	+	0.771245i	0.263187	+	0.0706999i
$120$	4.97629	+	2.76802i	0.454271	+	0.252685i
$121$	−6.71427			−0.610388
$122$	−0.209571	+	0.120996i	−0.0189736	+	0.0109544i
$123$	−14.9012	−	8.28867i	−1.34360	−	0.747364i
$124$	−3.73332			−0.335262
$125$		−	2.65798i		−	0.237737i
$126$	−5.43399	+	5.78547i	−0.484099	+	0.515411i
$127$	9.40084	−	16.2827i	0.834190	−	1.44486i	−0.0604988	−	0.998168i	$-0.519269\pi$
$127$	9.40084	−	16.2827i	0.834190	−	1.44486i	0.894688	−	0.446691i	$-0.147398\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−5.97286	−	9.97385i	−0.525881	−	0.878149i
$130$	2.35545	−	11.6173i	0.206587	−	1.01891i
$131$	−1.45204	+	2.51500i	−0.126865	+	0.219737i	−0.922460	−	0.386092i	$-0.873825\pi$
$131$	−1.45204	+	2.51500i	−0.126865	+	0.219737i	0.795595	+	0.605828i	$0.207158\pi$
$132$	−1.74301	+	3.13355i	−0.151710	+	0.272740i
$133$	0.690568	+	2.58379i	0.0598799	+	0.224043i
$134$	−10.2316	+	5.90721i	−0.883874	+	0.510305i
$135$	15.1865	+	7.82290i	1.30705	+	0.673288i
$136$	−0.561810	+	0.973084i	−0.0481748	+	0.0834413i
$137$	−10.5895	+	18.3416i	−0.904724	+	1.56703i	−0.0834363	+	0.996513i	$0.526590\pi$
$137$	−10.5895	+	18.3416i	−0.904724	+	1.56703i	−0.821288	+	0.570515i	$0.806744\pi$
$138$	5.29905	+	2.94755i	0.451085	+	0.250912i
$139$	−17.6205	+	10.1732i	−1.49455	+	0.862878i	−0.999980	−	0.00626156i	$-0.998007\pi$
$139$	−17.6205	+	10.1732i	−1.49455	+	0.862878i	−0.494568	+	0.869139i	$0.664674\pi$
$140$	−6.14668	−	6.15449i	−0.519489	−	0.520149i
$141$	1.84420	+	1.02582i	0.155310	+	0.0863898i
$142$	−3.94585	+	6.83441i	−0.331128	+	0.573531i
$143$	7.31537	+	1.48322i	0.611742	+	0.124033i
$144$	−1.58223	−	2.54883i	−0.131853	−	0.212403i
$145$	−15.1388	−	26.2212i	−1.25721	−	2.17755i
$146$	−0.878160	+	1.52102i	−0.0726770	+	0.125880i
$147$	10.4097	−	6.21594i	0.858579	−	0.512682i
$148$		−	6.97226i		−	0.573116i
$149$	−13.2500			−1.08549			−0.542743	−	0.839899i	$-0.682614\pi$
$149$	−13.2500			−1.08549			−0.542743	+	0.839899i	$0.682614\pi$
$150$	−4.89046	+	8.79197i	−0.399304	+	0.717861i
$151$	15.0137	−	8.66818i	1.22180	−	0.705407i	0.256499	−	0.966545i	$-0.417431\pi$
$151$	15.0137	−	8.66818i	1.22180	−	0.705407i	0.965301	+	0.261138i	$0.0840978\pi$
$152$	−1.01086			−0.0819916
$153$	−1.59131	+	2.97161i	−0.128650	+	0.240240i
$154$	3.87545	−	3.87053i	0.312293	−	0.311896i
$155$		−	12.2738i		−	0.985852i
$156$	−4.05963	+	4.74546i	−0.325030	+	0.379941i
$157$	12.2223	−	7.05652i	0.975442	−	0.563172i	0.0745511	−	0.997217i	$-0.476248\pi$
$157$	12.2223	−	7.05652i	0.975442	−	0.563172i	0.900891	+	0.434045i	$0.142914\pi$
$158$	4.97953			0.396150
$159$	8.67953	−	5.19775i	0.688332	−	0.412209i
$160$	2.84717	−	1.64381i	0.225088	−	0.129955i
$161$	−6.54534	−	6.55365i	−0.515845	−	0.516500i
$162$	−4.98856	−	7.49095i	−0.391938	−	0.588544i
$163$			10.3152i			0.807947i	0.914771	+	0.403974i	$0.132371\pi$
$163$			10.3152i			0.807947i	−0.914771	+	0.403974i	$0.867629\pi$
$164$	−8.52566	+	4.92229i	−0.665742	+	0.384366i
$165$	−10.3019	−	5.73036i	−0.802004	−	0.446108i
$166$	0.865939	−	0.499950i	0.0672099	−	0.0388037i
$167$	−12.1099	−	6.99167i	−0.937094	−	0.541032i	−0.0480461	−	0.998845i	$-0.515299\pi$
$167$	−12.1099	−	6.99167i	−0.937094	−	0.541032i	−0.889048	+	0.457813i	$0.848633\pi$
$168$	1.25382	+	4.40771i	0.0967345	+	0.340062i
$169$	11.9734	+	5.06344i	0.921028	+	0.389495i
$170$	−3.19914	−	1.84702i	−0.245363	−	0.141660i
$171$	−3.03103	+	0.0968804i	−0.231789	+	0.00740863i
$172$	−6.71200			−0.511785
$173$	5.07795			0.386069			0.193035	−	0.981192i	$-0.438167\pi$
$173$	5.07795			0.386069			0.193035	+	0.981192i	$0.438167\pi$
$174$	0.254829	+	15.9494i	0.0193186	+	1.20912i
$175$	10.8736	−	10.8598i	0.821964	−	0.820922i
$176$	1.03510	+	1.79285i	0.0780236	+	0.135141i
$177$	14.8475	+	8.25878i	1.11600	+	0.620768i
$178$	6.59807	+	3.80940i	0.494546	+	0.285526i
$179$			11.7132i			0.875486i	0.899100	+	0.437743i	$0.144222\pi$
$179$			11.7132i			0.875486i	−0.899100	+	0.437743i	$0.855778\pi$
$180$	8.37960	−	5.20179i	0.624578	−	0.387719i
$181$			22.6731i			1.68528i	0.538480	+	0.842638i	$0.318999\pi$
$181$			22.6731i			1.68528i	−0.538480	+	0.842638i	$0.681001\pi$
$182$	7.95457	−	5.26543i	0.589632	−	0.390300i
$183$	0.00669590	+	0.419088i	0.000494975	+	0.0309798i
$184$	3.03183	−	1.75043i	0.223509	−	0.129043i
$185$	22.9222			1.68527
$186$	−3.14328	+	5.65092i	−0.230476	+	0.414345i
$187$	1.16306	−	2.01448i	0.0850514	−	0.147313i
$188$	1.05515	−	0.609193i	0.0769549	−	0.0444299i
$189$	4.18198	+	13.0962i	0.304194	+	0.952610i
$190$		−	3.32333i		−	0.241100i
$191$			25.8552i			1.87082i	0.353570	+	0.935408i	$0.384968\pi$
$191$			25.8552i			1.87082i	−0.353570	+	0.935408i	$0.615032\pi$
$192$	−1.73183	+	0.0276700i	−0.124984	+	0.00199691i
$193$			21.8098i			1.56990i	0.619558	+	0.784951i	$0.287312\pi$
$193$			21.8098i			1.56990i	−0.619558	+	0.784951i	$0.712688\pi$
$194$	3.21628	−	5.57077i	0.230916	−	0.399958i
$195$	−15.6013	−	13.3465i	−1.11723	−	0.955765i
$196$	0.00888497	−	6.99999i	0.000634641	−	0.500000i
$197$	3.51025	−	6.07993i	0.250095	−	0.433177i	−0.713457	−	0.700699i	$-0.752872\pi$
$197$	3.51025	−	6.07993i	0.250095	−	0.433177i	0.963552	+	0.267522i	$0.0862049\pi$
$198$	3.27554	+	5.27659i	0.232783	+	0.374991i
$199$	−13.0589	−	7.53954i	−0.925719	−	0.534464i	−0.0402638	−	0.999189i	$-0.512820\pi$
$199$	−13.0589	−	7.53954i	−0.925719	−	0.534464i	−0.885455	+	0.464725i	$0.846153\pi$
$200$	2.90424	+	5.03029i	0.205361	+	0.355695i
$201$	0.326905	+	20.4606i	0.0230581	+	1.44318i
$202$	−9.66204	−	16.7351i	−0.679819	−	1.17748i
$203$	6.32139	−	23.5320i	0.443675	−	1.65162i
$204$	0.999885	+	1.66967i	0.0700060	+	0.116900i
$205$	−16.1827	−	28.0292i	−1.13025	−	1.95764i
$206$			9.08426i			0.632930i
$207$	8.92308	−	5.53917i	0.620197	−	0.384999i
$208$	1.14635	+	3.41846i	0.0794853	+	0.237028i
$209$	2.09268			0.144754
$210$	−14.4909	+	4.12210i	−0.999968	+	0.284452i
$211$	−10.2101	+	17.6845i	−0.702895	+	1.21745i	0.264550	+	0.964372i	$0.414776\pi$
$211$	−10.2101	+	17.6845i	−0.702895	+	1.21745i	−0.967446	+	0.253079i	$0.918557\pi$
$212$		−	5.84097i		−	0.401160i
$213$	7.02265	+	11.7269i	0.481184	+	0.803511i
$214$	3.25929	+	1.88175i	0.222801	+	0.128634i
$215$		−	22.0665i		−	1.50493i
$216$	−5.19019	+	0.248945i	−0.353147	+	0.0169386i
$217$	6.98884	−	6.97997i	0.474433	−	0.473831i
$218$	−2.43945	−	1.40841i	−0.165220	−	0.0953899i
$219$	1.56291	+	2.60985i	0.105612	+	0.176357i
$220$	−5.89421	+	3.40302i	−0.397387	+	0.229432i
$221$	2.68242	−	3.03602i	0.180439	−	0.204225i
$222$	−10.5535	−	5.87031i	−0.708306	−	0.393989i
$223$	−1.37326	+	2.37855i	−0.0919602	+	0.159280i	−0.908336	−	0.418241i	$-0.862647\pi$
$223$	−1.37326	+	2.37855i	−0.0919602	+	0.159280i	0.816376	+	0.577521i	$0.195980\pi$
$224$	2.55516	+	0.686393i	0.170724	+	0.0458615i
$225$	9.19037	+	14.8048i	0.612692	+	0.986989i
$226$	4.57774	+	2.64296i	0.304507	+	0.175807i
$227$	−7.77691	−	4.49000i	−0.516172	−	0.298012i	0.219195	−	0.975681i	$-0.429657\pi$
$227$	−7.77691	−	4.49000i	−0.516172	−	0.298012i	−0.735367	+	0.677669i	$0.762990\pi$
$228$	−0.851096	+	1.53008i	−0.0563652	+	0.101332i
$229$	−8.23500	+	14.2634i	−0.544184	+	0.942554i	0.454474	+	0.890760i	$0.349827\pi$
$229$	−8.23500	+	14.2634i	−0.544184	+	0.942554i	−0.998658	+	0.0517940i	$0.983506\pi$
$230$	5.75475	+	9.96752i	0.379457	+	0.657239i
$231$	−2.59567	−	9.12485i	−0.170782	−	0.600371i
$232$	7.97573	+	4.60479i	0.523633	+	0.302319i
$233$	4.79194	+	2.76663i	0.313931	+	0.181248i	0.648684	−	0.761058i	$-0.275320\pi$
$233$	4.79194	+	2.76663i	0.313931	+	0.181248i	−0.334753	+	0.942306i	$0.608653\pi$
$234$	3.76493	+	10.1403i	0.246121	+	0.662891i
$235$	2.00280	+	3.46895i	0.130648	+	0.226289i
$236$	8.49492	−	4.90455i	0.552972	−	0.319259i
$237$	4.19253	−	7.53724i	0.272334	−	0.489596i
$238$	−0.767600	−	2.87201i	−0.0497561	−	0.186165i
$239$	4.33497			0.280406			0.140203	−	0.990123i	$-0.455224\pi$
$239$	4.33497			0.280406			0.140203	+	0.990123i	$0.455224\pi$
$240$	−0.0909687	−	5.69361i	−0.00587200	−	0.367521i
$241$	2.10349	−	3.64335i	0.135498	−	0.234689i	−0.790290	−	0.612733i	$-0.790070\pi$
$241$	2.10349	−	3.64335i	0.135498	−	0.234689i	0.925787	+	0.378044i	$0.123403\pi$
$242$	3.35713	+	5.81473i	0.215805	+	0.373785i
$243$	−15.5388	+	1.24388i	−0.996811	+	0.0797949i
$244$	0.209571	+	0.120996i	0.0134164	+	0.00774595i
$245$	23.0134	+	0.0292105i	1.47027	+	0.00186619i
$246$	0.272400	+	17.0491i	0.0173676	+	1.08701i
$247$	3.57203	+	0.724241i	0.227283	+	0.0460824i
$248$	1.86666	+	3.23315i	0.118533	+	0.205305i
$249$	−0.0276673	−	1.73166i	−0.00175334	−	0.109739i
$250$	−2.30188	+	1.32899i	−0.145583	+	0.0840526i
$251$	−9.79168	−	16.9597i	−0.618045	−	1.07049i	−0.989842	−	0.142172i	$-0.954591\pi$
$251$	−9.79168	−	16.9597i	−0.618045	−	1.07049i	0.371797	−	0.928314i	$-0.378742\pi$
$252$	7.72736	+	1.81324i	0.486778	+	0.114223i
$253$	−6.27649	+	3.62374i	−0.394600	+	0.227822i
$254$	−18.8017			−1.17972
$255$	−5.48925	+	3.28725i	−0.343750	+	0.205855i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	8.97486	+	15.5449i	0.559837	+	0.969665i	0.997510	+	0.0705311i	$0.0224694\pi$
$257$	8.97486	+	15.5449i	0.559837	+	0.969665i	−0.437673	+	0.899134i	$0.644197\pi$
$258$	−5.65118	+	10.1596i	−0.351827	+	0.632507i
$259$	13.0356	+	13.0522i	0.809994	+	0.811023i
$260$	−11.2386	+	3.76878i	−0.696990	+	0.233730i
$261$	24.3563	+	13.0429i	1.50762	+	0.807337i
$262$	2.90408			0.179414
$263$		−	27.8469i		−	1.71711i	−0.512717	−	0.858557i	$-0.671361\pi$
$263$		−	27.8469i		−	1.71711i	0.512717	−	0.858557i	$-0.328639\pi$
$264$	3.58524	−	0.0572825i	0.220656	−	0.00352549i
$265$	19.2029			1.17963
$266$	1.89235	−	1.88995i	0.116027	−	0.115880i
$267$	11.3213	−	6.77979i	0.692854	−	0.414917i
$268$	10.2316	+	5.90721i	0.624994	+	0.360840i
$269$	14.1534	−	24.5145i	0.862951	−	1.49467i	−0.00611690	−	0.999981i	$-0.501947\pi$
$269$	14.1534	−	24.5145i	0.862951	−	1.49467i	0.869068	−	0.494693i	$-0.164720\pi$
$270$	−0.818439	−	17.0634i	−0.0498086	−	1.03844i
$271$	12.6519	+	21.9137i	0.768546	+	1.33116i	0.938352	+	0.345682i	$0.112353\pi$
$271$	12.6519	+	21.9137i	0.768546	+	1.33116i	−0.169806	+	0.985478i	$0.554314\pi$
$272$	1.12362			0.0681295
$273$	−1.27262	−	16.4736i	−0.0770226	−	0.997029i
$274$	21.1790			1.27947
$275$	−6.01236	−	10.4137i	−0.362559	−	0.627970i
$276$	−0.0968687	−	6.06288i	−0.00583081	−	0.364943i
$277$	6.54676	−	11.3393i	0.393356	−	0.681313i	−0.599533	−	0.800350i	$-0.704647\pi$
$277$	6.54676	−	11.3393i	0.393356	−	0.681313i	0.992890	+	0.119036i	$0.0379805\pi$
$278$	17.6205	+	10.1732i	1.05680	+	0.610147i
$279$	5.90699	+	9.51560i	0.353642	+	0.569684i
$280$	−2.25660	+	8.40042i	−0.134858	+	0.502021i
$281$	−16.5616			−0.987980			−0.493990	−	0.869468i	$-0.664462\pi$
$281$	−16.5616			−0.987980			−0.493990	+	0.869468i	$0.664462\pi$
$282$	−0.0337127	−	2.11004i	−0.00200756	−	0.125651i
$283$			18.3919i			1.09328i	0.837367	+	0.546642i	$0.184094\pi$
$283$			18.3919i			1.09328i	−0.837367	+	0.546642i	$0.815906\pi$
$284$	7.89170			0.468286
$285$	−5.03034	−	2.79808i	−0.297971	−	0.165744i
$286$	−2.37318	−	7.07690i	−0.140329	−	0.418466i
$287$	6.75725	−	25.1545i	0.398868	−	1.48483i
$288$	−1.41623	+	2.64467i	−0.0834524	+	0.155839i
$289$	7.86874	+	13.6291i	0.462867	+	0.801709i
$290$	−15.1388	+	26.2212i	−0.888983	+	1.53976i
$291$	−5.72420	−	9.55863i	−0.335559	−	0.560337i
$292$	1.75632			0.102781
$293$	7.37759	−	4.25945i	0.431003	−	0.248840i	−0.268771	−	0.963204i	$-0.586617\pi$
$293$	7.37759	−	4.25945i	0.431003	−	0.248840i	0.699774	+	0.714364i	$0.253284\pi$
$294$	−10.5880	−	5.90711i	−0.617506	−	0.344510i
$295$	16.1243	+	27.9281i	0.938793	+	1.62604i
$296$	−6.03816	+	3.48613i	−0.350961	+	0.202627i
$297$	10.7447	−	0.515367i	0.623472	−	0.0299046i
$298$	6.62502	+	11.4749i	0.383777	+	0.664721i
$299$	−11.9675	+	4.01321i	−0.692100	+	0.232090i
$300$	10.0593	−	0.160721i	0.580774	−	0.00927922i
$301$	12.5650	−	12.5490i	0.724233	−	0.723314i
$302$	−15.0137	−	8.66818i	−0.863943	−	0.498798i
$303$	−33.4660	+	0.534698i	−1.92257	+	0.0307176i
$304$	0.505430	+	0.875431i	0.0289884	+	0.0502094i
$305$	−0.397788	+	0.688989i	−0.0227773	+	0.0394514i
$306$	3.36914	−	0.107687i	0.192601	−	0.00615607i
$307$	21.3161			1.21658			0.608288	−	0.793716i	$-0.291857\pi$
$307$	21.3161			1.21658			0.608288	+	0.793716i	$0.291857\pi$
$308$	−5.28970	−	1.42097i	−0.301409	−	0.0809673i
$309$	13.7503	+	7.64851i	0.782229	+	0.435109i
$310$	−10.6294	+	6.13688i	−0.603709	+	0.348551i
$311$	−7.40693	−	12.8292i	−0.420008	−	0.727476i	0.575931	−	0.817498i	$-0.304639\pi$
$311$	−7.40693	−	12.8292i	−0.420008	−	0.727476i	−0.995940	+	0.0900223i	$0.971306\pi$
$312$	6.13951	+	1.14301i	0.347581	+	0.0647102i
$313$	−22.7031	−	13.1077i	−1.28326	−	0.740889i	−0.305814	−	0.952091i	$-0.598929\pi$
$313$	−22.7031	−	13.1077i	−1.28326	−	0.740889i	−0.977442	+	0.211203i	$0.932262\pi$
$314$	−12.2223	−	7.05652i	−0.689742	−	0.398223i
$315$	−5.96126	+	25.4047i	−0.335879	+	1.43139i
$316$	−2.48977	−	4.31240i	−0.140060	−	0.242592i
$317$	−9.80532	+	16.9833i	−0.550722	+	0.953878i	0.447501	+	0.894283i	$0.352314\pi$
$317$	−9.80532	+	16.9833i	−0.550722	+	0.953878i	−0.998223	+	0.0595945i	$0.981019\pi$
$318$	−8.84115	−	4.91782i	−0.495787	−	0.275778i
$319$	−16.5114	−	9.53284i	−0.924459	−	0.533737i
$320$	−2.84717	−	1.64381i	−0.159161	−	0.0918919i
$321$	5.59247	−	3.34906i	0.312141	−	0.186926i
$322$	−2.40296	+	8.94526i	−0.133912	+	0.498500i
$323$	0.567912	−	0.983652i	0.0315995	−	0.0547319i
$324$	−3.99307	+	8.06569i	−0.221837	+	0.448094i
$325$	−6.65857	−	19.8561i	−0.369351	−	1.10142i
$326$	8.93321	−	5.15759i	0.494765	−	0.285652i
$327$	−4.18573	+	2.50663i	−0.231472	+	0.138617i
$328$	8.52566	+	4.92229i	0.470751	+	0.271788i
$329$	−0.836291	+	3.11317i	−0.0461062	+	0.171635i
$330$	0.188323	+	11.7869i	0.0103669	+	0.648848i
$331$		−	26.0774i		−	1.43334i	−0.697412	−	0.716671i	$-0.745665\pi$
$331$		−	26.0774i		−	1.43334i	0.697412	−	0.716671i	$-0.254335\pi$
$332$	−0.865939	−	0.499950i	−0.0475246	−	0.0274383i
$333$	−17.7711	+	11.0317i	−0.973851	+	0.604536i
$334$			13.9833i			0.765134i
$335$	−19.4207	+	33.6376i	−1.06107	+	1.83782i
$336$	3.19028	−	3.28970i	0.174044	−	0.179468i
$337$	−13.5184			−0.736394			−0.368197	−	0.929748i	$-0.620025\pi$
$337$	−13.5184			−0.736394			−0.368197	+	0.929748i	$0.620025\pi$
$338$	−1.60162	−	12.9010i	−0.0871166	−	0.701720i
$339$	7.85473	−	4.70382i	0.426610	−	0.255476i
$340$			3.69404i			0.200338i
$341$	−3.86436	−	6.69327i	−0.209267	−	0.362461i
$342$	1.59942	+	2.57651i	0.0864866	+	0.139322i
$343$	13.0708	+	13.1207i	0.705759	+	0.708452i
$344$	3.35600	+	5.81276i	0.180943	+	0.313403i
$345$	19.9325	−	0.318468i	1.07313	−	0.0171457i
$346$	−2.53897	−	4.39763i	−0.136496	−	0.236418i
$347$	−29.0781	−	16.7882i	−1.56099	−	0.901239i	−0.997157	−	0.0753519i	$-0.975992\pi$
$347$	−29.0781	−	16.7882i	−1.56099	−	0.901239i	−0.563835	−	0.825887i	$-0.690675\pi$
$348$	13.6852	−	8.19540i	0.733604	−	0.439320i
$349$	−11.8845	+	20.5845i	−0.636161	+	1.10186i	0.350107	+	0.936710i	$0.386145\pi$
$349$	−11.8845	+	20.5845i	−0.636161	+	1.10186i	−0.986268	+	0.165153i	$0.947188\pi$
$350$	−14.8416	−	3.98690i	−0.793318	−	0.213109i
$351$	18.5187	+	2.83887i	0.988453	+	0.151528i
$352$	1.03510	−	1.79285i	0.0551710	−	0.0955590i
$353$			10.7207i			0.570608i	0.958437	+	0.285304i	$0.0920945\pi$
$353$			10.7207i			0.570608i	−0.958437	+	0.285304i	$0.907905\pi$
$354$	−0.271418	−	16.9877i	−0.0144257	−	0.902885i
$355$			25.9450i			1.37702i
$356$		−	7.61879i		−	0.403795i
$357$	−4.99349	−	1.25622i	−0.264283	−	0.0664864i
$358$	10.1439	−	5.85660i	0.536123	−	0.309531i
$359$	−7.26878	+	12.5899i	−0.383632	+	0.664469i	−0.991578	−	0.129508i	$-0.958660\pi$
$359$	−7.26878	+	12.5899i	−0.383632	+	0.664469i	0.607947	+	0.793978i	$0.291993\pi$
$360$	−8.69468	−	4.65605i	−0.458250	−	0.245395i
$361$	−17.9782			−0.946219
$362$	19.6355	−	11.3365i	1.03202	−	0.595835i
$363$	11.6280	−	0.185784i	0.610310	−	0.00975113i
$364$	−8.53729	−	4.25614i	−0.447475	−	0.223083i
$365$			5.77412i			0.302231i
$366$	0.359592	−	0.215343i	0.0187962	−	0.0112561i
$367$			17.4965i			0.913308i	0.889644	+	0.456654i	$0.150952\pi$
$367$			17.4965i			0.913308i	−0.889644	+	0.456654i	$0.849048\pi$
$368$	−3.03183	−	1.75043i	−0.158045	−	0.0912473i
$369$	26.0357	+	13.9422i	1.35536	+	0.725804i
$370$	−11.4611	−	19.8512i	−0.595834	−	1.03201i
$371$	10.9205	+	10.9344i	0.566965	+	0.567686i
$372$	6.46548	−	0.103301i	0.335219	−	0.00535591i
$373$	−11.8665			−0.614423			−0.307211	−	0.951641i	$-0.599396\pi$
$373$	−11.8665			−0.614423			−0.307211	+	0.951641i	$0.599396\pi$
$374$	−2.32612			−0.120281
$375$	0.0735463	+	4.60316i	0.00379791	+	0.237706i
$376$	−1.05515	−	0.609193i	−0.0544153	−	0.0314167i
$377$	−24.8843	−	21.9860i	−1.28161	−	1.13234i
$378$	9.25067	−	10.1698i	0.475803	−	0.523079i
$379$	10.9141	+	6.30127i	0.560620	+	0.323674i	0.753394	−	0.657569i	$-0.228415\pi$
$379$	10.9141	+	6.30127i	0.560620	+	0.323674i	−0.192774	+	0.981243i	$0.561748\pi$
$380$	−2.87809	+	1.66167i	−0.147643	+	0.0852416i
$381$	−15.8301	+	28.4590i	−0.811001	+	1.45800i
$382$	22.3913	−	12.9276i	1.14564	−	0.661433i
$383$			1.06335i			0.0543345i	0.999631	+	0.0271672i	$0.00864866\pi$
$383$			1.06335i			0.0543345i	−0.999631	+	0.0271672i	$0.991351\pi$
$384$	0.889878	+	1.48597i	0.0454114	+	0.0758308i
$385$	4.67162	−	17.3906i	0.238088	−	0.886305i
$386$	18.8878	−	10.9049i	0.961364	−	0.555044i
$387$	10.6199	+	17.1077i	0.539842	+	0.869635i
$388$	−6.43257			−0.326564
$389$	−2.28039	+	1.31658i	−0.115620	+	0.0667534i	−0.556695	−	0.830717i	$-0.687931\pi$
$389$	−2.28039	+	1.31658i	−0.115620	+	0.0667534i	0.441075	+	0.897470i	$0.354597\pi$
$390$	−3.75779	+	20.1844i	−0.190283	+	1.02208i
$391$			3.93363i			0.198932i
$392$	−6.06662	+	3.49230i	−0.306410	+	0.176388i
$393$	2.44509	−	4.39574i	0.123339	−	0.221736i
$394$	−7.02050			−0.353688
$395$	14.1776	−	8.18542i	0.713351	−	0.411853i
$396$	2.93189	−	5.47500i	0.147333	−	0.275129i
$397$	−8.54714			−0.428969			−0.214484	−	0.976727i	$-0.568807\pi$
$397$	−8.54714			−0.428969			−0.214484	+	0.976727i	$0.568807\pi$
$398$			15.0791i			0.755846i
$399$	−1.26744	−	4.45558i	−0.0634514	−	0.223058i
$400$	2.90424	−	5.03029i	0.145212	−	0.251515i
$401$	−7.78768	−	13.4887i	−0.388898	−	0.673592i	0.603403	−	0.797436i	$-0.293811\pi$
$401$	−7.78768	−	13.4887i	−0.388898	−	0.673592i	−0.992302	+	0.123845i	$0.960478\pi$
$402$	17.5559	−	10.5134i	0.875609	−	0.524360i
$403$	−4.27970	−	12.7622i	−0.213187	−	0.635731i
$404$	−9.66204	+	16.7351i	−0.480705	+	0.832605i
$405$	−26.5170	−	13.1277i	−1.31764	−	0.652322i
$406$	−23.5400	+	6.29152i	−1.16827	+	0.312243i
$407$	12.5002	−	7.21699i	0.619612	−	0.357733i
$408$	0.946035	−	1.70076i	0.0468357	−	0.0842002i
$409$	5.40484	−	9.36145i	0.267252	−	0.462894i	−0.700899	−	0.713260i	$-0.747218\pi$
$409$	5.40484	−	9.36145i	0.267252	−	0.462894i	0.968151	+	0.250366i	$0.0805511\pi$
$410$	−16.1827	+	28.0292i	−0.799204	+	1.38426i
$411$	17.8317	−	32.0575i	0.879575	−	1.58128i
$412$	7.86720	−	4.54213i	0.387589	−	0.223775i
$413$	−6.73289	+	25.0638i	−0.331304	+	1.23331i
$414$	−9.25860	−	4.95803i	−0.455036	−	0.243674i
$415$	1.64365	−	2.84688i	0.0806836	−	0.139748i
$416$	2.38730	−	2.70200i	0.117047	−	0.132477i
$417$	30.2341	−	18.1058i	1.48057	−	0.886643i
$418$	−1.04634	−	1.81232i	−0.0511783	−	0.0886434i
$419$	−7.13932	+	12.3657i	−0.348779	+	0.604102i	−0.986033	−	0.166551i	$-0.946737\pi$
$419$	−7.13932	+	12.3657i	−0.348779	+	0.604102i	0.637254	+	0.770654i	$0.280070\pi$
$420$	10.8153	+	10.4884i	0.527732	+	0.511784i
$421$		−	31.1553i		−	1.51842i	−0.650848	−	0.759208i	$-0.725586\pi$
$421$		−	31.1553i		−	1.51842i	0.650848	−	0.759208i	$-0.274414\pi$
$422$	20.4203			0.994044
$423$	−3.22223	−	1.72552i	−0.156670	−	0.0838976i
$424$	−5.05843	+	2.92049i	−0.245659	+	0.141831i
$425$	−6.52653			−0.316583
$426$	6.64443	−	11.9452i	0.321924	−	0.578748i
$427$	−0.618538	+	0.165316i	−0.0299331	+	0.00800020i
$428$		−	3.76351i		−	0.181916i
$429$	−12.7100	−	2.36626i	−0.613645	−	0.114244i
$430$	−19.1102	+	11.0333i	−0.921575	+	0.532071i
$431$	21.5902			1.03996			0.519981	−	0.854178i	$-0.325939\pi$
$431$	21.5902			1.03996			0.519981	+	0.854178i	$0.325939\pi$
$432$	2.81069	+	4.37036i	0.135229	+	0.210269i
$433$	−16.2009	+	9.35358i	−0.778565	+	0.449505i	−0.835921	−	0.548849i	$-0.815066\pi$
$433$	−16.2009	+	9.35358i	−0.778565	+	0.449505i	0.0573567	+	0.998354i	$0.481733\pi$
$434$	−9.53925	−	2.56252i	−0.457899	−	0.123005i
$435$	26.9434	+	44.9918i	1.29184	+	2.15719i
$436$			2.81683i			0.134902i
$437$	−3.06476	+	1.76944i	−0.146607	+	0.0846437i
$438$	1.47874	−	2.65844i	0.0706568	−	0.127025i
$439$	−12.4456	+	7.18545i	−0.593994	+	0.342943i	−0.766675	−	0.642035i	$-0.778090\pi$
$439$	−12.4456	+	7.18545i	−0.593994	+	0.342943i	0.172681	+	0.984978i	$0.444757\pi$
$440$	5.89421	+	3.40302i	0.280995	+	0.162233i
$441$	−17.8559	+	11.0530i	−0.850279	+	0.526332i
$442$	−3.97048	−	0.805029i	−0.188857	−	0.0382913i
$443$	1.21594	+	0.702023i	0.0577711	+	0.0333541i	0.528607	−	0.848866i	$-0.322714\pi$
$443$	1.21594	+	0.702023i	0.0577711	+	0.0333541i	−0.470836	+	0.882221i	$0.656048\pi$
$444$	0.192923	+	12.0748i	0.00915570	+	0.573043i
$445$	25.0477			1.18738
$446$	2.74652			0.130051
$447$	22.9468	−	0.366629i	1.08535	−	0.0173409i
$448$	−0.683149	−	2.55603i	−0.0322757	−	0.120761i
$449$	−11.0266	−	19.0987i	−0.520379	−	0.901323i	−0.999719	−	0.0236937i	$-0.992457\pi$
$449$	−11.0266	−	19.0987i	−0.520379	−	0.901323i	0.479340	−	0.877629i	$-0.340876\pi$
$450$	8.22617	−	15.3615i	0.387785	−	0.724149i
$451$	−17.6498	−	10.1901i	−0.831098	−	0.479835i
$452$		−	5.28591i		−	0.248629i
$453$	−25.7614	+	15.4272i	−1.21038	+	0.724835i
$454$			8.98000i			0.421453i
$455$	13.9926	−	28.0674i	0.655984	−	1.31582i
$456$	1.75064	−	0.0279705i	0.0819812	−	0.00130984i
$457$	36.6548	−	21.1627i	1.71464	−	0.989948i	0.786604	−	0.617457i	$-0.211837\pi$
$457$	36.6548	−	21.1627i	1.71464	−	0.989948i	0.928036	−	0.372491i	$-0.121496\pi$
$458$	16.4700			0.769592
$459$	2.67366	−	5.19035i	0.124796	−	0.242265i
$460$	5.75475	−	9.96752i	0.268317	−	0.464738i
$461$	10.2913	−	5.94166i	0.479312	−	0.276731i	−0.240818	−	0.970570i	$-0.577416\pi$
$461$	10.2913	−	5.94166i	0.479312	−	0.276731i	0.720130	+	0.693839i	$0.244082\pi$
$462$	−6.60452	+	6.81034i	−0.307270	+	0.316846i
$463$		−	3.56440i		−	0.165652i	−0.996564	−	0.0828258i	$-0.973605\pi$
$463$		−	3.56440i		−	0.165652i	0.996564	−	0.0828258i	$-0.0263945\pi$
$464$		−	9.20958i		−	0.427544i
$465$	0.339615	+	21.2561i	0.0157493	+	0.985727i
$466$		−	5.53326i		−	0.256323i
$467$	−3.56143	+	6.16858i	−0.164803	+	0.285448i	−0.936585	−	0.350439i	$-0.886032\pi$
$467$	−3.56143	+	6.16858i	−0.164803	+	0.285448i	0.771782	+	0.635887i	$0.219366\pi$
$468$	6.89928	−	8.33066i	0.318919	−	0.385085i
$469$	−30.1981	+	8.07101i	−1.39442	+	0.372684i
$470$	2.00280	−	3.46895i	0.0923821	−	0.160011i
$471$	−20.9716	+	12.5589i	−0.966321	+	0.578683i
$472$	−8.49492	−	4.90455i	−0.391010	−	0.225750i
$473$	−6.94759	−	12.0336i	−0.319451	−	0.553305i
$474$	−8.62370	+	0.137784i	−0.396100	+	0.00632862i
$475$	−2.93578	−	5.08492i	−0.134703	−	0.233312i
$476$	−2.10344	+	2.10077i	−0.0964108	+	0.0962885i
$477$	−14.8877	+	9.24179i	−0.681659	+	0.423152i
$478$	−2.16749	−	3.75420i	−0.0991386	−	0.171713i
$479$			30.5472i			1.39574i	0.716225	+	0.697870i	$0.245868\pi$
$479$			30.5472i			1.39574i	−0.716225	+	0.697870i	$0.754132\pi$
$480$	−4.88532	+	2.92558i	−0.222984	+	0.133534i
$481$	23.8344	−	7.99267i	1.08676	−	0.364434i
$482$	−4.20698			−0.191623
$483$	11.5168	+	11.1687i	0.524031	+	0.508194i
$484$	3.35713	−	5.81473i	0.152597	−	0.264306i
$485$		−	21.1479i		−	0.960275i
$486$	8.84661	+	12.8350i	0.401290	+	0.582208i
$487$	−27.7303	−	16.0101i	−1.25658	−	0.725488i	−0.284173	−	0.958773i	$-0.591719\pi$
$487$	−27.7303	−	16.0101i	−1.25658	−	0.725488i	−0.972408	+	0.233285i	$0.925052\pi$
$488$		−	0.241991i		−	0.0109544i
$489$	−0.285421	−	17.8641i	−0.0129072	−	0.807844i
$490$	−11.4814	−	19.9448i	−0.518676	−	0.901012i
$491$	−13.0865	−	7.55549i	−0.590585	−	0.340975i	0.174744	−	0.984614i	$-0.444090\pi$
$491$	−13.0865	−	7.55549i	−0.590585	−	0.340975i	−0.765329	+	0.643639i	$0.777424\pi$
$492$	14.6288	−	8.76048i	0.659517	−	0.394953i
$493$	−8.96170	+	5.17404i	−0.403615	+	0.233027i
$494$	−1.15880	−	3.45559i	−0.0521370	−	0.155474i
$495$	17.9997	+	9.63896i	0.809028	+	0.433239i
$496$	1.86666	−	3.23315i	0.0838156	−	0.145173i
$497$	−14.7734	+	14.7546i	−0.662677	+	0.661836i
$498$	−1.48583	+	0.889789i	−0.0665814	+	0.0398724i
$499$	4.18606	+	2.41682i	0.187394	+	0.108192i	0.590762	−	0.806846i	$-0.298827\pi$
$499$	4.18606	+	2.41682i	0.187394	+	0.108192i	−0.403368	+	0.915038i	$0.632161\pi$
$500$	2.30188	+	1.32899i	0.102943	+	0.0594342i
$501$	21.1658	+	11.7733i	0.945618	+	0.525992i
$502$	−9.79168	+	16.9597i	−0.437024	+	0.756948i
$503$	13.7946	+	23.8930i	0.615073	+	1.06534i	0.990372	+	0.138433i	$0.0442066\pi$
$503$	13.7946	+	23.8930i	0.615073	+	1.06534i	−0.375299	+	0.926904i	$0.622460\pi$
$504$	−2.29337	−	7.59871i	−0.102155	−	0.338474i
$505$	−55.0189	−	31.7652i	−2.44831	−	1.41353i
$506$	6.27649	+	3.62374i	0.279024	+	0.161095i
$507$	−20.8759	−	8.43771i	−0.927133	−	0.374732i
$508$	9.40084	+	16.2827i	0.417095	+	0.722429i
$509$	27.1836	−	15.6945i	1.20489	−	0.695645i	0.243253	−	0.969963i	$-0.421786\pi$
$509$	27.1836	−	15.6945i	1.20489	−	0.695645i	0.961639	+	0.274318i	$0.0884522\pi$
$510$	5.59147	+	3.11021i	0.247594	+	0.137722i
$511$	−3.28786	+	3.28369i	−0.145446	+	0.145262i
$512$	1.00000			0.0441942
$513$	5.24655	−	0.251649i	0.231641	−	0.0111106i
$514$	8.97486	−	15.5449i	0.395864	−	0.685657i
$515$	14.9328	+	25.8644i	0.658019	+	1.13972i
$516$	11.6240	−	0.185721i	0.511720	−	0.00817592i
$517$	2.18438	+	1.26115i	0.0960688	+	0.0554654i
$518$	4.78571	−	17.8153i	0.210272	−	0.782758i
$519$	−8.79414	+	0.140507i	−0.386020	+	0.00616757i
$520$	8.88317	+	7.84854i	0.389553	+	0.344181i
$521$	0.178115	+	0.308505i	0.00780338	+	0.0135159i	0.869901	−	0.493227i	$-0.164183\pi$
$521$	0.178115	+	0.308505i	0.00780338	+	0.0135159i	−0.862097	+	0.506743i	$0.830849\pi$
$522$	−0.882642	−	27.6146i	−0.0386322	−	1.20866i
$523$	21.5730	−	12.4552i	0.943320	−	0.544626i	0.0523207	−	0.998630i	$-0.483338\pi$
$523$	21.5730	−	12.4552i	0.943320	−	0.544626i	0.891000	+	0.454004i	$0.150005\pi$
$524$	−1.45204	−	2.51500i	−0.0634326	−	0.109868i
$525$	−18.5307	+	19.1081i	−0.808745	+	0.833948i
$526$	−24.1161	+	13.9235i	−1.05151	+	0.607092i
$527$	−4.19484			−0.182730
$528$	−1.84223	−	3.07626i	−0.0801726	−	0.133877i
$529$	−5.37201	+	9.30459i	−0.233566	+	0.404548i
$530$	−9.60147	−	16.6302i	−0.417061	−	0.722371i
$531$	−25.9418	−	13.8920i	−1.12578	−	0.602860i
$532$	−2.58291	−	0.693847i	−0.111984	−	0.0300821i
$533$	−26.6001	−	23.5020i	−1.15218	−	1.01798i
$534$	−11.5321	−	6.41466i	−0.499044	−	0.277589i
$535$	12.3730			0.534931
$536$		−	11.8144i		−	0.510305i
$537$	−0.324105	−	20.2853i	−0.0139861	−	0.875374i
$538$	−28.3069			−1.22040
$539$	12.5591	−	7.22977i	0.540959	−	0.311408i
$540$	−14.3681	+	9.24048i	−0.618305	+	0.397647i
$541$	−17.5713	−	10.1448i	−0.755447	−	0.436158i	0.0722115	−	0.997389i	$-0.476994\pi$
$541$	−17.5713	−	10.1448i	−0.755447	−	0.436158i	−0.827659	+	0.561232i	$0.810328\pi$
$542$	12.6519	−	21.9137i	0.543444	−	0.941272i
$543$	−0.627364	−	39.2659i	−0.0269228	−	1.68506i
$544$	−0.561810	−	0.973084i	−0.0240874	−	0.0417206i
$545$	−9.26068			−0.396684
$546$	−13.6303	+	9.33894i	−0.583322	+	0.399670i
$547$	−18.3443			−0.784344			−0.392172	−	0.919892i	$-0.628276\pi$
$547$	−18.3443			−0.784344			−0.392172	+	0.919892i	$0.628276\pi$
$548$	−10.5895	−	18.3416i	−0.452362	−	0.783514i
$549$	−0.0231923	−	0.725603i	−0.000989824	−	0.0309680i
$550$	−6.01236	+	10.4137i	−0.256368	+	0.444042i
$551$	−8.06235	−	4.65480i	−0.343468	−	0.198301i
$552$	−5.20218	+	3.11533i	−0.221419	+	0.132597i
$553$	12.7235	+	3.41791i	0.541059	+	0.145345i
$554$	−13.0935			−0.556290
$555$	−39.6973	+	0.634257i	−1.68506	+	0.0269227i
$556$		−	20.3464i		−	0.862878i
$557$	−12.1781			−0.516004			−0.258002	−	0.966144i	$-0.583064\pi$
$557$	−12.1781			−0.516004			−0.258002	+	0.966144i	$0.583064\pi$
$558$	5.28726	−	9.87340i	0.223828	−	0.417975i
$559$	−7.69432	−	22.9447i	−0.325435	−	0.970457i
$560$	8.40328	−	2.24594i	0.355103	−	0.0949082i
$561$	−1.95848	+	3.52092i	−0.0826872	+	0.148653i
$562$	8.28078	+	14.3427i	0.349304	+	0.605012i
$563$	−5.68587	+	9.84822i	−0.239631	+	0.415053i	−0.960608	−	0.277906i	$-0.910360\pi$
$563$	−5.68587	+	9.84822i	−0.239631	+	0.415053i	0.720978	+	0.692958i	$0.243693\pi$
$564$	−1.81049	+	1.08421i	−0.0762353	+	0.0456536i
$565$	17.3781			0.731102
$566$	15.9278	−	9.19594i	0.669497	−	0.386534i
$567$	−7.60485	−	22.5647i	−0.319374	−	0.947629i
$568$	−3.94585	−	6.83441i	−0.165564	−	0.286766i
$569$	−20.8276	+	12.0248i	−0.873140	+	0.504108i	−0.868391	−	0.495881i	$-0.834845\pi$
$569$	−20.8276	+	12.0248i	−0.873140	+	0.504108i	−0.00474984	+	0.999989i	$0.501512\pi$
$570$	0.0919566	+	5.75544i	0.00385164	+	0.241069i
$571$	3.64194	+	6.30802i	0.152410	+	0.263983i	0.932113	−	0.362167i	$-0.117963\pi$
$571$	3.64194	+	6.30802i	0.152410	+	0.263983i	−0.779703	+	0.626150i	$0.784630\pi$
$572$	−4.94219	+	5.59369i	−0.206643	+	0.233884i
$573$	−0.715414	−	44.7768i	−0.0298868	−	1.87058i
$574$	−25.1631	+	6.72532i	−1.05029	+	0.280709i
$575$	17.6103	+	10.1673i	0.734401	+	0.424007i
$576$	2.99847	−	0.0958395i	0.124936	−	0.00399331i
$577$	2.11186	+	3.65785i	0.0879179	+	0.152278i	0.906631	−	0.421925i	$-0.138645\pi$
$577$	2.11186	+	3.65785i	0.0879179	+	0.152278i	−0.818713	+	0.574203i	$0.805312\pi$
$578$	7.86874	−	13.6291i	0.327296	−	0.566894i
$579$	−0.603477	−	37.7708i	−0.0250796	−	1.56970i
$580$	30.2777			1.25721
$581$	2.55578	−	0.683081i	0.106032	−	0.0283390i
$582$	−5.41591	+	9.73662i	−0.224497	+	0.403596i
$583$	10.4720	−	6.04600i	0.433705	−	0.250400i
$584$	−0.878160	−	1.52102i	−0.0363385	−	0.0629402i
$585$	27.3881	+	22.6822i	1.13236	+	0.937795i
$586$	−7.37759	−	4.25945i	−0.304765	−	0.175956i
$587$	39.5103	+	22.8113i	1.63077	+	0.941523i	0.983857	+	0.178954i	$0.0572714\pi$
$587$	39.5103	+	22.8113i	1.63077	+	0.941523i	0.646908	+	0.762568i	$0.276062\pi$
$588$	0.178303	+	12.1230i	0.00735308	+	0.499946i
$589$	−1.88693	−	3.26827i	−0.0777498	−	0.134667i
$590$	16.1243	−	27.9281i	0.663827	−	1.14978i
$591$	−5.91092	+	10.6265i	−0.243143	+	0.437117i
$592$	6.03816	+	3.48613i	0.248167	+	0.143279i
$593$	−21.1653	−	12.2198i	−0.869154	−	0.501807i	−0.00208732	−	0.999998i	$-0.500664\pi$
$593$	−21.1653	−	12.2198i	−0.869154	−	0.501807i	−0.867067	+	0.498191i	$0.833998\pi$
$594$	−5.81868	−	9.04752i	−0.238744	−	0.371224i
$595$	−6.90654	−	6.91531i	−0.283140	−	0.283500i
$596$	6.62502	−	11.4749i	0.271371	−	0.470029i
$597$	22.8244	+	12.6959i	0.934139	+	0.519607i
$598$	9.45931	+	8.35758i	0.386820	+	0.341767i
$599$	−11.4214	+	6.59416i	−0.466667	+	0.269430i	−0.714843	−	0.699285i	$-0.753502\pi$
$599$	−11.4214	+	6.59416i	−0.466667	+	0.269430i	0.248177	+	0.968715i	$0.420169\pi$
$600$	−5.16884	−	8.63125i	−0.211017	−	0.352369i
$601$	−34.6176	−	19.9865i	−1.41208	−	0.815266i	−0.416497	−	0.909137i	$-0.636742\pi$
$601$	−34.6176	−	19.9865i	−1.41208	−	0.815266i	−0.995584	+	0.0938714i	$0.970076\pi$
$602$	−17.1503	−	4.60707i	−0.698992	−	0.187770i
$603$	−1.13229	−	35.4252i	−0.0461103	−	1.44262i
$604$			17.3364i			0.705407i
$605$	19.1166	+	11.0370i	0.777202	+	0.448718i
$606$	17.1961	+	28.7151i	0.698543	+	1.16647i
$607$		−	20.1780i		−	0.819000i	−0.912310	−	0.409500i	$-0.865703\pi$
$607$		−	20.1780i		−	0.819000i	0.912310	−	0.409500i	$-0.134297\pi$
$608$	0.505430	−	0.875431i	0.0204979	−	0.0355034i
$609$	−10.2964	+	40.9283i	−0.417233	+	1.65850i
$610$	0.795576			0.0322119
$611$	3.29208	+	2.90865i	0.133183	+	0.117671i
$612$	−1.77783	−	2.86392i	−0.0718646	−	0.115767i
$613$			24.9422i			1.00741i	0.863877	+	0.503703i	$0.168030\pi$
$613$			24.9422i			1.00741i	−0.863877	+	0.503703i	$0.831970\pi$
$614$	−10.6581	−	18.4603i	−0.430124	−	0.744997i
$615$	28.8012	+	48.0940i	1.16138	+	1.93934i
$616$	1.41426	+	5.29150i	0.0569820	+	0.213201i
$617$	1.22499	+	2.12175i	0.0493164	+	0.0854185i	0.889630	−	0.456682i	$-0.150962\pi$
$617$	1.22499	+	2.12175i	0.0493164	+	0.0854185i	−0.840313	+	0.542101i	$0.817629\pi$
$618$	−0.251362	−	15.7324i	−0.0101112	−	0.632850i
$619$	11.9145	+	20.6365i	0.478883	+	0.829449i	0.999707	−	0.0242147i	$-0.00770853\pi$
$619$	11.9145	+	20.6365i	0.478883	+	0.829449i	−0.520824	+	0.853664i	$0.674375\pi$
$620$	10.6294	+	6.13688i	0.426887	+	0.246463i
$621$	−15.3000	+	9.83980i	−0.613968	+	0.394858i
$622$	−7.40693	+	12.8292i	−0.296991	+	0.514403i
$623$	14.2444	+	14.2625i	0.570690	+	0.571415i
$624$	−2.07988	−	5.88847i	−0.0832617	−	0.235728i
$625$	10.1520	−	17.5837i	0.406079	−	0.703350i
$626$			26.2153i			1.04777i
$627$	−3.62417	+	0.0579046i	−0.144736	+	0.00231249i
$628$			14.1130i			0.563172i
$629$		−	7.83418i		−	0.312369i
$630$	24.9817	−	7.53974i	0.995296	−	0.300390i
$631$	−17.5516	+	10.1334i	−0.698718	+	0.403405i	−0.806870	−	0.590729i	$-0.798840\pi$
$631$	−17.5516	+	10.1334i	−0.698718	+	0.403405i	0.108152	+	0.994134i	$0.465507\pi$
$632$	−2.48977	+	4.31240i	−0.0990376	+	0.171538i
$633$	17.1929	−	30.9090i	0.683357	−	1.22852i
$634$	19.6106			0.778838
$635$	−53.5315	+	30.9064i	−2.12433	+	1.22648i
$636$	0.161620	+	10.1156i	0.00640865	+	0.401109i
$637$	23.9394	−	7.99409i	0.948513	−	0.316737i
$638$			19.0657i			0.754818i
$639$	−12.4865	−	20.1146i	−0.493959	−	0.795722i
$640$			3.28763i			0.129955i
$641$	28.8080	+	16.6323i	1.13785	+	0.656938i	0.945897	−	0.324467i	$-0.105185\pi$
$641$	28.8080	+	16.6323i	1.13785	+	0.656938i	0.191952	+	0.981404i	$0.438518\pi$
$642$	−5.69661	−	3.16869i	−0.224827	−	0.125058i
$643$	3.65734	+	6.33469i	0.144231	+	0.249816i	0.929086	−	0.369864i	$-0.120596\pi$
$643$	3.65734	+	6.33469i	0.144231	+	0.249816i	−0.784855	+	0.619680i	$0.787262\pi$
$644$	8.94830	−	2.39160i	0.352612	−	0.0942424i
$645$	0.610581	+	38.2155i	0.0240416	+	1.50473i
$646$	−1.13582			−0.0446884
$647$	32.0372			1.25951			0.629757	−	0.776792i	$-0.283154\pi$
$647$	32.0372			1.25951			0.629757	+	0.776792i	$0.283154\pi$
$648$	8.98163	−	0.574744i	0.352832	−	0.0225781i
$649$	17.5862	+	10.1534i	0.690319	+	0.398556i
$650$	−13.8666	+	15.6945i	−0.543892	+	0.615590i
$651$	−11.9103	+	12.2815i	−0.466803	+	0.481350i
$652$	−8.93321	−	5.15759i	−0.349851	−	0.201987i
$653$	−29.1377	+	16.8227i	−1.14025	+	0.658321i	−0.946491	−	0.322729i	$-0.895400\pi$
$653$	−29.1377	+	16.8227i	−1.14025	+	0.658321i	−0.193754	+	0.981050i	$0.562066\pi$
$654$	4.26368	+	2.37163i	0.166723	+	0.0927383i
$655$	8.26839	−	4.77376i	0.323073	−	0.186526i
$656$		−	9.84458i		−	0.384366i
$657$	−2.77891	−	4.47656i	−0.108416	−	0.174647i
$658$	3.11423	−	0.832338i	0.121405	−	0.0324479i
$659$	21.1966	−	12.2379i	0.825704	−	0.476720i	−0.0266755	−	0.999644i	$-0.508492\pi$
$659$	21.1966	−	12.2379i	0.825704	−	0.476720i	0.852379	+	0.522924i	$0.175159\pi$
$660$	10.1136	−	6.05655i	0.393671	−	0.235751i
$661$	5.55570			0.216092			0.108046	−	0.994146i	$-0.465541\pi$
$661$	5.55570			0.216092			0.108046	+	0.994146i	$0.465541\pi$
$662$	−22.5837	+	13.0387i	−0.877739	+	0.506763i
$663$	−4.56148	+	5.33210i	−0.177153	+	0.207082i
$664$			0.999900i			0.0388037i
$665$	2.28111	−	8.49166i	0.0884576	−	0.329292i
$666$	18.4393	+	9.87436i	0.714510	+	0.382624i
$667$	32.2414			1.24839
$668$	12.1099	−	6.99167i	0.468547	−	0.270516i
$669$	2.31244	−	4.15725i	0.0894039	−	0.160729i
$670$	38.8414			1.50057
$671$			0.500970i			0.0193397i
$672$	−4.44410	−	1.11801i	−0.171435	−	0.0431283i
$673$	9.31475	−	16.1336i	0.359057	−	0.621905i	−0.628746	−	0.777610i	$-0.716432\pi$
$673$	9.31475	−	16.1336i	0.359057	−	0.621905i	0.987804	+	0.155705i	$0.0497649\pi$
$674$	6.75920	+	11.7073i	0.260355	+	0.450947i
$675$	−16.3258	−	25.3851i	−0.628381	−	0.977075i
$676$	−10.3718	+	7.83752i	−0.398913	+	0.301443i
$677$	−13.4512	+	23.2982i	−0.516972	+	0.895422i	0.482833	+	0.875712i	$0.339608\pi$
$677$	−13.4512	+	23.2982i	−0.516972	+	0.895422i	−0.999806	+	0.0197102i	$0.993726\pi$
$678$	−8.00099	−	4.45049i	−0.307276	−	0.170920i
$679$	12.0419	−	12.0266i	0.462124	−	0.461538i
$680$	3.19914	−	1.84702i	0.122681	−	0.0708301i
$681$	13.5925	+	7.56073i	0.520867	+	0.289728i
$682$	−3.86436	+	6.69327i	−0.147974	+	0.256299i
$683$	−20.3836	+	35.3055i	−0.779958	+	1.35093i	0.152007	+	0.988379i	$0.451426\pi$
$683$	−20.3836	+	35.3055i	−0.779958	+	1.35093i	−0.931965	+	0.362548i	$0.881907\pi$
$684$	1.43162	−	2.67339i	0.0547392	−	0.102220i
$685$	60.3003	−	34.8144i	2.30395	−	1.33019i
$686$	4.82745	−	17.8800i	0.184313	−	0.682663i
$687$	13.8669	−	24.9297i	0.529057	−	0.951127i
$688$	3.35600	−	5.81276i	0.127946	−	0.221609i
$689$	19.9671	−	6.69582i	0.760688	−	0.255090i
$690$	−10.2420	−	17.1028i	−0.389908	−	0.651093i
$691$	6.89853	+	11.9486i	0.262432	+	0.454546i	0.966888	−	0.255202i	$-0.0821420\pi$
$691$	6.89853	+	11.9486i	0.262432	+	0.454546i	−0.704455	+	0.709748i	$0.748809\pi$
$692$	−2.53897	+	4.39763i	−0.0965173	+	0.167173i
$693$	4.74774	+	15.7309i	0.180352	+	0.597566i
$694$			33.5765i			1.27454i
$695$	66.8912			2.53733
$696$	−13.9400	−	7.75403i	−0.528395	−	0.293916i
$697$	−9.57961	+	5.53079i	−0.362854	+	0.209494i
$698$	23.7689			0.899667
$699$	−8.37538	−	4.65874i	−0.316786	−	0.176210i
$700$	3.96806	+	14.8467i	0.149978	+	0.561151i
$701$		−	9.30649i		−	0.351501i	−0.984435	−	0.175751i	$-0.943765\pi$
$701$		−	9.30649i		−	0.351501i	0.984435	−	0.175751i	$-0.0562352\pi$
$702$	−6.80079	−	17.4571i	−0.256679	−	0.658875i
$703$	6.10373	−	3.52399i	0.230207	−	0.132910i
$704$	−2.07020			−0.0780236
$705$	−3.56449	−	5.95221i	−0.134246	−	0.224173i
$706$	9.28444	−	5.36037i	0.349425	−	0.201740i
$707$	−13.2012	−	49.3930i	−0.496483	−	1.85762i
$708$	−14.5760	+	8.72889i	−0.547801	+	0.328052i
$709$			3.09917i			0.116392i	0.998305	+	0.0581958i	$0.0185348\pi$
$709$			3.09917i			0.116392i	−0.998305	+	0.0581958i	$0.981465\pi$
$710$	22.4690	−	12.9725i	0.843246	−	0.486848i
$711$	−7.05219	+	13.1692i	−0.264478	+	0.493884i
$712$	−6.59807	+	3.80940i	−0.247273	+	0.142763i
$713$	11.3188	+	6.53491i	0.423892	+	0.244734i
$714$	1.40882	+	4.95260i	0.0527238	+	0.185346i
$715$	−18.3899	−	16.2481i	−0.687745	−	0.607643i
$716$	−10.1439	−	5.85660i	−0.379097	−	0.218871i
$717$	−7.50744	+	0.119949i	−0.280370	+	0.00447957i
$718$	14.5376			0.542537
$719$	11.7740			0.439098			0.219549	−	0.975602i	$-0.429541\pi$
$719$	11.7740			0.439098			0.219549	+	0.975602i	$0.429541\pi$
$720$	0.315084	+	9.85784i	0.0117425	+	0.367380i
$721$	−6.23537	+	23.2118i	−0.232217	+	0.864452i
$722$	8.98908	+	15.5695i	0.334539	+	0.579438i
$723$	−3.54207	+	6.36786i	−0.131731	+	0.236823i
$724$	−19.6355	−	11.3365i	−0.729746	−	0.421319i
$725$			53.4937i			1.98671i
$726$	−5.97488	−	9.97723i	−0.221749	−	0.370290i
$727$		−	13.8729i		−	0.514518i	−0.966342	−	0.257259i	$-0.917181\pi$
$727$		−	13.8729i		−	0.514518i	0.966342	−	0.257259i	$-0.0828194\pi$
$728$	0.582714	+	9.52158i	0.0215968	+	0.352893i
$729$	26.8761	−	2.58415i	0.995409	−	0.0957091i
$730$	5.00054	−	2.88706i	0.185078	−	0.106855i
$731$	−7.54174			−0.278941
$732$	−0.366288	−	0.203745i	−0.0135384	−	0.00753063i
$733$	−21.6003	+	37.4129i	−0.797827	+	1.38188i	0.123202	+	0.992382i	$0.460684\pi$
$733$	−21.6003	+	37.4129i	−0.797827	+	1.38188i	−0.921029	+	0.389495i	$0.872650\pi$
$734$	15.1524	−	8.74823i	0.559284	−	0.322903i
$735$	−39.8560	+	0.586193i	−1.47011	+	0.0216220i
$736$			3.50085i			0.129043i
$737$			24.4582i			0.900930i
$738$	−0.943500	−	29.5187i	−0.0347307	−	1.08660i
$739$		−	34.1756i		−	1.25717i	−0.777741	−	0.628585i	$-0.783635\pi$
$739$		−	34.1756i		−	1.25717i	0.777741	−	0.628585i	$-0.216365\pi$
$740$	−11.4611	+	19.8512i	−0.421318	+	0.729744i
$741$	−6.20618	−	1.15542i	−0.227990	−	0.0424456i
$742$	4.00920	−	14.9247i	0.147182	−	0.547901i
$743$	−15.6321	+	27.0755i	−0.573484	+	0.993304i	0.422720	+	0.906260i	$0.361075\pi$
$743$	−15.6321	+	27.0755i	−0.573484	+	0.993304i	−0.996204	+	0.0870439i	$0.972258\pi$
$744$	−3.32220	−	5.54762i	−0.121798	−	0.203386i
$745$	37.7251	+	21.7806i	1.38214	+	0.797978i
$746$	5.93324	+	10.2767i	0.217231	+	0.376256i
$747$	0.0958300	+	2.99817i	0.00350624	+	0.109697i
$748$	1.16306	+	2.01448i	0.0425257	+	0.0736567i
$749$	7.03641	+	7.04534i	0.257105	+	0.257431i
$750$	3.94968	−	2.36528i	0.144222	−	0.0863676i
$751$	−1.05163	−	1.82147i	−0.0383744	−	0.0664664i	0.846200	−	0.532865i	$-0.178885\pi$
$751$	−1.05163	−	1.82147i	−0.0383744	−	0.0664664i	−0.884575	+	0.466398i	$0.845551\pi$
$752$			1.21839i			0.0444299i
$753$	17.4268	+	29.1004i	0.635068	+	1.06048i
$754$	−6.59830	+	32.5434i	−0.240296	+	1.18516i
$755$	−56.9955			−2.07428
$756$	−13.4327	−	2.92641i	−0.488541	−	0.106432i
$757$	16.8638	−	29.2089i	0.612924	−	1.06162i	−0.377821	−	0.925879i	$-0.623326\pi$
$757$	16.8638	−	29.2089i	0.612924	−	1.06162i	0.990745	−	0.135737i	$-0.0433402\pi$
$758$		−	12.6025i		−	0.457745i
$759$	10.7696	−	6.44936i	0.390910	−	0.234097i
$760$	2.87809	+	1.66167i	0.104399	+	0.0602749i
$761$		−	19.2154i		−	0.696556i	−0.937391	−	0.348278i	$-0.886767\pi$
$761$		−	19.2154i		−	0.696556i	0.937391	−	0.348278i	$-0.113233\pi$
$762$	32.5613	−	0.520243i	1.17957	−	0.0188464i
$763$	−5.26646	−	5.27315i	−0.190659	−	0.190901i
$764$	−22.3913	−	12.9276i	−0.810087	−	0.467704i
$765$	9.41549	−	5.84484i	0.340418	−	0.211321i
$766$	0.920885	−	0.531673i	0.0332729	−	0.0192101i
$767$	26.5042	+	23.4172i	0.957010	+	0.845547i
$768$	0.841952	−	1.51364i	0.0303813	−	0.0546189i
$769$	−19.1381	+	33.1482i	−0.690139	+	1.19536i	0.281653	+	0.959516i	$0.409117\pi$
$769$	−19.1381	+	33.1482i	−0.690139	+	1.19536i	−0.971792	+	0.235840i	$0.924216\pi$
$770$	−17.3965	+	4.64954i	−0.626926	+	0.167558i
$771$	−15.9731	−	26.6728i	−0.575256	−	0.960598i
$772$	−18.8878	−	10.9049i	−0.679787	−	0.392475i
$773$	−2.18604	−	1.26211i	−0.0786263	−	0.0453949i	0.460171	−	0.887830i	$-0.347788\pi$
$773$	−2.18604	−	1.26211i	−0.0786263	−	0.0453949i	−0.538798	+	0.842435i	$0.681121\pi$
$774$	9.50577	−	17.7510i	0.341678	−	0.638047i
$775$	−10.8425	+	18.7797i	−0.389473	+	0.674587i
$776$	3.21628	+	5.57077i	0.115458	+	0.199979i
$777$	−22.9366	−	22.2435i	−0.822847	−	0.797980i
$778$	2.28039	+	1.31658i	0.0817558	+	0.0472018i
$779$	−8.61825	−	4.97575i	−0.308781	−	0.178275i
$780$	19.3591	−	6.83786i	0.693167	−	0.244834i
$781$	8.16870	+	14.1486i	0.292299	+	0.506277i
$782$	3.40663	−	1.96682i	0.121821	−	0.0703332i
$783$	−42.5419	−	21.9142i	−1.52032	−	0.783150i
$784$	6.05773	+	3.50769i	0.216348	+	0.125275i
$785$	−46.3984			−1.65603
$786$	−5.02937	+	0.0803559i	−0.179392	+	0.00286620i
$787$	−0.882459	+	1.52846i	−0.0314563	+	0.0544839i	−0.881325	−	0.472511i	$-0.843348\pi$
$787$	−0.882459	+	1.52846i	−0.0314563	+	0.0544839i	0.849869	+	0.526995i	$0.176681\pi$
$788$	3.51025	+	6.07993i	0.125047	+	0.216588i
$789$	0.770525	+	48.2261i	0.0274314	+	1.71690i
$790$	−14.1776	−	8.18542i	−0.504415	−	0.291224i
$791$	9.88276	+	9.89532i	0.351391	+	0.351837i
$792$	−6.20743	+	0.198407i	−0.220572	+	0.00705009i
$793$	−0.173377	+	0.855112i	−0.00615680	+	0.0303659i
$794$	4.27357	+	7.40204i	0.151663	+	0.262689i
$795$	−33.2562	+	0.531346i	−1.17948	+	0.0188449i
$796$	13.0589	−	7.53954i	0.462859	−	0.267232i
$797$	−5.40206	−	9.35664i	−0.191351	−	0.331429i	0.754347	−	0.656476i	$-0.227953\pi$
$797$	−5.40206	−	9.35664i	−0.191351	−	0.331429i	−0.945698	+	0.325046i	$0.894620\pi$
$798$	−3.22493	+	3.32543i	−0.114161	+	0.117719i
$799$	1.18559	−	0.684502i	0.0419432	−	0.0242159i
$800$	−5.80848			−0.205361
$801$	−19.4190	+	12.0547i	−0.686137	+	0.425932i
$802$	−7.78768	+	13.4887i	−0.274993	+	0.476301i
$803$	1.81797	+	3.14881i	0.0641547	+	0.111119i
$804$	−17.8828	−	9.94717i	−0.630678	−	0.350810i
$805$	7.86270	+	29.4187i	0.277124	+	1.03687i
$806$	−8.91255	+	10.0874i	−0.313931	+	0.355315i
$807$	−23.8330	+	42.8465i	−0.838963	+	1.50827i
$808$	19.3241			0.679819
$809$		−	16.6138i		−	0.584110i	−0.956402	−	0.292055i	$-0.905661\pi$
$809$		−	16.6138i		−	0.584110i	0.956402	−	0.292055i	$-0.0943390\pi$
$810$	1.88954	+	29.5282i	0.0663917	+	1.03752i
$811$	7.44633			0.261476			0.130738	−	0.991417i	$-0.458265\pi$
$811$	7.44633			0.261476			0.130738	+	0.991417i	$0.458265\pi$
$812$	17.2186	+	17.2405i	0.604255	+	0.605022i
$813$	−22.5172	−	37.6006i	−0.789713	−	1.31871i
$814$	−12.5002	−	7.21699i	−0.438132	−	0.252955i
$815$	16.9562	−	29.3690i	0.593951	−	1.02875i
$816$	−1.94592	+	0.0310906i	−0.0681208	+	0.00108839i
$817$	−3.39245	−	5.87589i	−0.118687	−	0.205571i
$818$	−10.8097			−0.377951
$819$	2.65979	+	28.4943i	0.0929406	+	0.995672i
$820$	32.3653			1.13025
$821$	1.71387	+	2.96850i	0.0598143	+	0.103601i	0.894382	−	0.447304i	$-0.147616\pi$
$821$	1.71387	+	2.96850i	0.0598143	+	0.103601i	−0.834568	+	0.550905i	$0.814282\pi$
$822$	−36.6785	+	0.586025i	−1.27931	+	0.0204400i
$823$	−19.8190	+	34.3275i	−0.690847	+	1.19658i	0.280713	+	0.959792i	$0.409429\pi$
$823$	−19.8190	+	34.3275i	−0.690847	+	1.19658i	−0.971561	+	0.236791i	$0.923904\pi$
$824$	−7.86720	−	4.54213i	−0.274067	−	0.158233i
$825$	10.7005	+	17.8684i	0.372545	+	0.622098i
$826$	25.0724	−	6.70107i	0.872379	−	0.233160i
$827$	0.211856			0.00736695			0.00368347	−	0.999993i	$-0.498828\pi$
$827$	0.211856			0.00736695			0.00368347	+	0.999993i	$0.498828\pi$
$828$	0.335520	+	10.4972i	0.0116601	+	0.364803i
$829$		−	31.5116i		−	1.09444i	−0.836988	−	0.547221i	$-0.815686\pi$
$829$		−	31.5116i		−	1.09444i	0.836988	−	0.547221i	$-0.184314\pi$
$830$	−3.28730			−0.114104
$831$	−11.0241	+	19.8189i	−0.382422	+	0.687510i
$832$	−3.53365	−	0.716460i	−0.122507	−	0.0248388i
$833$	0.00998334	−	7.86534i	0.000345902	−	0.272518i
$834$	−30.7971	−	17.1307i	−1.06642	−	0.593186i
$835$	22.9860	+	39.8129i	0.795463	+	1.37778i
$836$	−1.04634	+	1.81232i	−0.0361885	+	0.0626803i
$837$	−10.4932	−	16.3160i	−0.362698	−	0.563962i
$838$	14.2786			0.493248
$839$	13.7645	−	7.94694i	0.475204	−	0.274359i	−0.243212	−	0.969973i	$-0.578201\pi$
$839$	13.7645	−	7.94694i	0.475204	−	0.274359i	0.718416	+	0.695614i	$0.244868\pi$
$840$	3.67561	−	14.6105i	0.126821	−	0.504112i
$841$	27.9082	+	48.3384i	0.962352	+	1.66684i
$842$	−26.9813	+	15.5776i	−0.929836	+	0.536841i
$843$	28.6818	−	0.458259i	0.987854	−	0.0157833i
$844$	−10.2101	−	17.6845i	−0.351448	−	0.608725i
$845$	−25.7668	−	34.0984i	−0.886406	−	1.17302i
$846$	0.116769	+	3.65329i	0.00401462	+	0.125603i
$847$	4.58684	+	17.1619i	0.157606	+	0.589690i
$848$	5.05843	+	2.92049i	0.173707	+	0.100290i
$849$	−0.508904	−	31.8516i	−0.0174655	−	1.09314i
$850$	3.26326	+	5.65214i	0.111929	+	0.193867i
$851$	−12.2044	+	21.1387i	−0.418363	+	0.724625i
$852$	−13.6671	+	0.218364i	−0.468227	+	0.00748101i
$853$	8.80214			0.301379			0.150690	−	0.988581i	$-0.451851\pi$
$853$	8.80214			0.301379			0.150690	+	0.988581i	$0.451851\pi$
$854$	0.452437	+	0.453011i	0.0154821	+	0.0155017i
$855$	8.78911	+	4.70662i	0.300581	+	0.160963i
$856$	−3.25929	+	1.88175i	−0.111400	+	0.0643170i
$857$	2.96296	+	5.13199i	0.101213	+	0.175305i	0.912185	−	0.409780i	$-0.134394\pi$
$857$	2.96296	+	5.13199i	0.101213	+	0.175305i	−0.810972	+	0.585085i	$0.801061\pi$
$858$	4.30576	+	12.1903i	0.146996	+	0.416171i
$859$	21.0079	+	12.1289i	0.716781	+	0.413834i	0.813567	−	0.581472i	$-0.197523\pi$
$859$	21.0079	+	12.1289i	0.716781	+	0.413834i	−0.0967860	+	0.995305i	$0.530856\pi$
$860$	19.1102	+	11.0333i	0.651652	+	0.376231i
$861$	−11.0064	+	43.7503i	−0.375096	+	1.49101i
$862$	−10.7951	−	18.6976i	−0.367682	−	0.636844i
$863$	9.92236	−	17.1860i	0.337761	−	0.585019i	−0.646250	−	0.763126i	$-0.723664\pi$
$863$	9.92236	−	17.1860i	0.337761	−	0.585019i	0.984011	+	0.178106i	$0.0569971\pi$
$864$	2.37950	−	4.61931i	0.0809522	−	0.157152i
$865$	−14.4578	−	8.34719i	−0.491579	−	0.283813i
$866$	16.2009	+	9.35358i	0.550528	+	0.317848i
$867$	−14.0044	−	23.3855i	−0.475615	−	0.794212i
$868$	2.55041	+	9.54250i	0.0865667	+	0.323893i
$869$	5.15432	−	8.92754i	0.174848	−	0.302846i
$870$	25.4923	−	45.8296i	0.864271	−	1.55377i
$871$	−8.46456	+	41.7480i	−0.286811	+	1.41458i
$872$	2.43945	−	1.40841i	0.0826101	−	0.0476949i
$873$	10.1778	+	16.3955i	0.344467	+	0.554904i
$874$	3.06476	+	1.76944i	0.103667	+	0.0598521i
$875$	−6.79388	+	1.81579i	−0.229675	+	0.0613850i
$876$	−3.04165	+	0.0485974i	−0.102768	+	0.00164195i
$877$			8.82826i			0.298109i	0.988829	+	0.149055i	$0.0476230\pi$
$877$			8.82826i			0.298109i	−0.988829	+	0.149055i	$0.952377\pi$
$878$	12.4456	+	7.18545i	0.420017	+	0.242497i
$879$	−12.6589	+	7.58078i	−0.426973	+	0.255693i
$880$		−	6.80604i		−	0.229432i
$881$	9.51336	−	16.4776i	0.320513	−	0.555145i	−0.660081	−	0.751195i	$-0.729478\pi$
$881$	9.51336	−	16.4776i	0.320513	−	0.555145i	0.980594	+	0.196049i	$0.0628113\pi$
$882$	18.5001	+	9.93713i	0.622930	+	0.334601i
$883$	−30.8587			−1.03848			−0.519239	−	0.854629i	$-0.673785\pi$
$883$	−30.8587			−1.03848			−0.519239	+	0.854629i	$0.673785\pi$
$884$	1.28807	+	3.84105i	0.0433223	+	0.129189i
$885$	−28.6973	−	47.9206i	−0.964650	−	1.61083i
$886$		−	1.40405i		−	0.0471699i
$887$	−6.57095	−	11.3812i	−0.220631	−	0.382144i	0.734369	−	0.678751i	$-0.237478\pi$
$887$	−6.57095	−	11.3812i	−0.220631	−	0.382144i	−0.955000	+	0.296607i	$0.904145\pi$
$888$	10.3606	−	6.20446i	0.347679	−	0.208208i
$889$	−48.0414	−	12.9053i	−1.61126	−	0.432831i
$890$	−12.5239	−	21.6920i	−0.419801	−	0.727116i
$891$	−18.5938	+	1.18983i	−0.622915	+	0.0398610i
$892$	−1.37326	−	2.37855i	−0.0459801	−	0.0796399i
$893$	1.06661	+	0.615809i	0.0356928	+	0.0206073i
$894$	−11.7909	−	19.6892i	−0.394347	−	0.658505i
$895$	19.2543	−	33.3494i	0.643601	−	1.11475i
$896$	−1.87202	+	1.86964i	−0.0625397	+	0.0624603i
$897$	20.6147	−	7.28135i	0.688304	−	0.243117i
$898$	−11.0266	+	19.0987i	−0.367963	+	0.637331i
$899$			34.3823i			1.14672i
$900$	−17.4165	+	0.556682i	−0.580551	+	0.0185561i
$901$		−	6.56304i		−	0.218647i
$902$			20.3803i			0.678589i
$903$	−21.4131	+	22.0804i	−0.712585	+	0.734791i
$904$	−4.57774	+	2.64296i	−0.152253	+	0.0879035i
$905$	37.2703	−	64.5540i	1.23891	−	2.14585i
$906$	26.2411	+	14.5964i	0.871801	+	0.484932i
$907$	48.7067			1.61728			0.808640	−	0.588303i	$-0.200204\pi$
$907$	48.7067			1.61728			0.808640	+	0.588303i	$0.200204\pi$
$908$	7.77691	−	4.49000i	0.258086	−	0.149006i
$909$	57.9427	−	1.85201i	1.92184	−	0.0614273i
$910$	−31.3034	+	1.91574i	−1.03770	+	0.0635063i
$911$		−	7.94598i		−	0.263262i	−0.991299	−	0.131631i	$-0.957979\pi$
$911$		−	7.94598i		−	0.263262i	0.991299	−	0.131631i	$-0.0420214\pi$
$912$	−0.899542	−	1.50211i	−0.0297868	−	0.0497399i
$913$		−	2.06999i		−	0.0685068i
$914$	−36.6548	−	21.1627i	−1.21243	−	0.699999i
$915$	0.669837	−	1.20422i	0.0221441	−	0.0398103i
$916$	−8.23500	−	14.2634i	−0.272092	−	0.471277i
$917$	7.42039	+	1.99334i	0.245043	+	0.0658258i
$918$	−5.83180	+	0.279720i	−0.192478	+	0.00923215i
$919$	−27.1660			−0.896124			−0.448062	−	0.894002i	$-0.647886\pi$
$919$	−27.1660			−0.896124			−0.448062	+	0.894002i	$0.647886\pi$
$920$	−11.5095			−0.379457
$921$	−36.9159	+	0.589818i	−1.21642	+	0.0194352i
$922$	−10.2913	−	5.94166i	−0.338925	−	0.195678i
$923$	9.04667	+	26.9775i	0.297775	+	0.887974i
$924$	9.20018	+	2.31451i	0.302664	+	0.0761419i
$925$	−35.0725	−	20.2491i	−1.15318	−	0.665787i
$926$	−3.08686	+	1.78220i	−0.101441	+	0.0585667i
$927$	−24.0249	−	12.8654i	−0.789080	−	0.422557i
$928$	−7.97573	+	4.60479i	−0.261816	+	0.151160i
$929$			23.7500i			0.779211i	0.920982	+	0.389605i	$0.127389\pi$
$929$			23.7500i			0.779211i	−0.920982	+	0.389605i	$0.872611\pi$
$930$	18.2385	−	10.9221i	0.598064	−	0.358151i
$931$	6.13250	−	3.53023i	0.200985	−	0.115699i
$932$	−4.79194	+	2.76663i	−0.156965	+	0.0906240i
$933$	13.1825	+	22.0130i	0.431576	+	0.720673i
$934$	7.12287			0.233067
$935$	−6.62285	+	3.82371i	−0.216591	+	0.125049i
$936$	−10.6642	−	1.80962i	−0.348570	−	0.0591493i
$937$		−	44.8244i		−	1.46435i	−0.681116	−	0.732175i	$-0.738505\pi$
$937$		−	44.8244i		−	1.46435i	0.681116	−	0.732175i	$-0.261495\pi$
$938$	22.0887	+	22.1168i	0.721222	+	0.722138i
$939$	39.6806	+	22.0720i	1.29493	+	0.720294i
$940$	−4.00559			−0.130648
$941$	−26.3318	+	15.2027i	−0.858393	+	0.495593i	−0.863474	−	0.504394i	$-0.831716\pi$
$941$	−26.3318	+	15.2027i	−0.858393	+	0.495593i	0.00508113	+	0.999987i	$0.498383\pi$
$942$	21.3621	+	11.8825i	0.696015	+	0.387153i
$943$	34.4645			1.12232
$944$			9.80909i			0.319259i
$945$	9.62093	−	44.1615i	0.312969	−	1.43657i
$946$	−6.94759	+	12.0336i	−0.225886	+	0.391245i
$947$	−4.00703	−	6.94038i	−0.130211	−	0.225532i	0.793547	−	0.608509i	$-0.208232\pi$
$947$	−4.00703	−	6.94038i	−0.130211	−	0.225532i	−0.923758	+	0.382977i	$0.874899\pi$
$948$	4.43118	+	7.39946i	0.143918	+	0.240323i
$949$	2.01336	+	6.00391i	0.0653565	+	0.194895i
$950$	−2.93578	+	5.08492i	−0.0952493	+	0.164977i
$951$	16.5112	−	29.6835i	0.535413	−	0.962554i
$952$	2.87104	+	0.771245i	0.0930508	+	0.0249962i
$953$	4.48194	−	2.58765i	0.145184	−	0.0838222i	−0.425648	−	0.904889i	$-0.639954\pi$
$953$	4.48194	−	2.58765i	0.145184	−	0.0838222i	0.570833	+	0.821067i	$0.306621\pi$
$954$	15.4474	+	8.27219i	0.500130	+	0.267822i
$955$	42.5011	−	73.6140i	1.37530	−	2.38209i
$956$	−2.16749	+	3.75420i	−0.0701016	+	0.121419i
$957$	28.8587	+	16.0524i	0.932868	+	0.518900i
$958$	26.4547	−	15.2736i	0.854712	−	0.493468i
$959$	54.1159	+	14.5371i	1.74749	+	0.469429i
$960$	4.97629	+	2.76802i	0.160609	+	0.0893375i
$961$	8.53115	−	14.7764i	0.275199	−	0.476658i
$962$	−18.8391	−	16.6449i	−0.607396	−	0.536652i
$963$	−9.59254	+	5.95475i	−0.309115	+	0.191889i
$964$	2.10349	+	3.64335i	0.0677488	+	0.117344i
$965$	35.8512	−	62.0960i	1.15409	−	1.99894i
$966$	3.91400	−	15.5582i	0.125931	−	0.500575i
$967$			14.4231i			0.463816i	0.972738	+	0.231908i	$0.0744968\pi$
$967$			14.4231i			0.463816i	−0.972738	+	0.231908i	$0.925503\pi$
$968$	−6.71427			−0.215805
$969$	−0.956309	+	1.71923i	−0.0307211	+	0.0552297i
$970$	−18.3146	+	10.5739i	−0.588046	+	0.339509i
$971$	1.42967			0.0458802			0.0229401	−	0.999737i	$-0.492697\pi$
$971$	1.42967			0.0458802			0.0229401	+	0.999737i	$0.492697\pi$
$972$	6.69214	−	14.0789i	0.214651	−	0.451581i
$973$	38.0404	+	38.0887i	1.21952	+	1.22107i
$974$			32.0202i			1.02599i
$975$	12.0809	+	34.2031i	0.386899	+	1.09538i
$976$	−0.209571	+	0.120996i	−0.00670819	+	0.00387297i
$977$	14.9269			0.477552			0.238776	−	0.971075i	$-0.423254\pi$
$977$	14.9269			0.477552			0.238776	+	0.971075i	$0.423254\pi$
$978$	−15.3281	+	9.17925i	−0.490138	+	0.293520i
$979$	13.6593	−	7.88621i	0.436554	−	0.252044i
$980$	−11.5320	+	19.9155i	−0.368375	+	0.636179i
$981$	7.17962	−	4.45688i	0.229228	−	0.142297i
$982$			15.1110i			0.482211i
$983$	2.34938	−	1.35641i	0.0749334	−	0.0432628i	−0.462065	−	0.886846i	$-0.652891\pi$
$983$	2.34938	−	1.35641i	0.0749334	−	0.0432628i	0.536999	+	0.843583i	$0.319558\pi$
$984$	−14.9012	−	8.28867i	−0.475033	−	0.264233i
$985$	−19.9885	+	11.5404i	−0.636887	+	0.367707i
$986$	8.96170	+	5.17404i	0.285399	+	0.164775i
$987$	1.36217	−	5.41463i	0.0433584	−	0.172350i
$988$	−2.41322	+	2.73135i	−0.0767749	+	0.0868957i
$989$	20.3496	+	11.7489i	0.647080	+	0.373592i
$990$	−0.652288	−	20.4077i	−0.0207311	−	0.648600i
$991$	−6.57676			−0.208918			−0.104459	−	0.994529i	$-0.533311\pi$
$991$	−6.57676			−0.208918			−0.104459	+	0.994529i	$0.533311\pi$
$992$	−3.73332			−0.118533
$993$	0.721561	+	45.1615i	0.0228980	+	1.43316i
$994$	20.1646	+	5.41681i	0.639582	+	0.171811i
$995$	24.7872	+	42.9327i	0.785807	+	1.36106i
$996$	1.51349	+	0.841868i	0.0479569	+	0.0266756i
$997$	19.9103	+	11.4952i	0.630565	+	0.364057i	0.780971	−	0.624568i	$-0.214725\pi$
$997$	19.9103	+	11.4952i	0.630565	+	0.364057i	−0.150406	+	0.988624i	$0.548058\pi$
$998$		−	4.83365i		−	0.153007i
$999$	30.4713	−	19.5968i	0.964069	−	0.620016i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bn.e.173.1	yes	34
3.2	odd	2		546.2.bn.f.173.17	yes	34
7.3	odd	6		546.2.bi.f.17.6	yes	34
13.10	even	6		546.2.bi.e.257.12	yes	34
21.17	even	6		546.2.bi.e.17.12	✓	34
39.23	odd	6		546.2.bi.f.257.6	yes	34
91.10	odd	6		546.2.bn.f.101.17	yes	34
273.101	even	6	inner	546.2.bn.e.101.1	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.12	✓	34	21.17	even	6
546.2.bi.e.257.12	yes	34	13.10	even	6
546.2.bi.f.17.6	yes	34	7.3	odd	6
546.2.bi.f.257.6	yes	34	39.23	odd	6
546.2.bn.e.101.1	yes	34	273.101	even	6	inner
546.2.bn.e.173.1	yes	34	1.1	even	1	trivial
546.2.bn.f.101.17	yes	34	91.10	odd	6
546.2.bn.f.173.17	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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.73183 + 0.0276700i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.84717 - 1.64381i) q^{5} +(0.889878 + 1.48597i) q^{6} +(-0.683149 - 2.55603i) q^{7} +1.00000 q^{8} +(2.99847 - 0.0958395i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.73183 + 0.0276700i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.84717 - 1.64381i) q^{5} +(0.889878 + 1.48597i) q^{6} +(-0.683149 - 2.55603i) q^{7} +1.00000 q^{8} +(2.99847 - 0.0958395i) q^{9} +3.28763i q^{10} -2.07020 q^{11} +(0.841952 - 1.51364i) q^{12} +(-3.53365 - 0.716460i) q^{13} +(-1.87202 + 1.86964i) q^{14} +(4.97629 + 2.76802i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.561810 + 0.973084i) q^{17} +(-1.58223 - 2.54883i) q^{18} -1.01086 q^{19} +(2.84717 - 1.64381i) q^{20} +(1.25382 + 4.40771i) q^{21} +(1.03510 + 1.79285i) q^{22} +(3.03183 - 1.75043i) q^{23} +(-1.73183 + 0.0276700i) q^{24} +(2.90424 + 5.03029i) q^{25} +(1.14635 + 3.41846i) q^{26} +(-5.19019 + 0.248945i) q^{27} +(2.55516 + 0.686393i) q^{28} +(7.97573 + 4.60479i) q^{29} +(-0.0909687 - 5.69361i) q^{30} +(1.86666 + 3.23315i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.58524 - 0.0572825i) q^{33} +1.12362 q^{34} +(-2.25660 + 8.40042i) q^{35} +(-1.41623 + 2.64467i) q^{36} +(-6.03816 + 3.48613i) q^{37} +(0.505430 + 0.875431i) q^{38} +(6.13951 + 1.14301i) q^{39} +(-2.84717 - 1.64381i) q^{40} +(8.52566 + 4.92229i) q^{41} +(3.19028 - 3.28970i) q^{42} +(3.35600 + 5.81276i) q^{43} +(1.03510 - 1.79285i) q^{44} +(-8.69468 - 4.65605i) q^{45} +(-3.03183 - 1.75043i) q^{46} +(-1.05515 - 0.609193i) q^{47} +(0.889878 + 1.48597i) q^{48} +(-6.06662 + 3.49230i) q^{49} +(2.90424 - 5.03029i) q^{50} +(0.946035 - 1.70076i) q^{51} +(2.38730 - 2.70200i) q^{52} +(-5.05843 + 2.92049i) q^{53} +(2.81069 + 4.37036i) q^{54} +(5.89421 + 3.40302i) q^{55} +(-0.683149 - 2.55603i) q^{56} +(1.75064 - 0.0279705i) q^{57} -9.20958i q^{58} +(-8.49492 - 4.90455i) q^{59} +(-4.88532 + 2.92558i) q^{60} -0.241991i q^{61} +(1.86666 - 3.23315i) q^{62} +(-2.29337 - 7.59871i) q^{63} +1.00000 q^{64} +(8.88317 + 7.84854i) q^{65} +(-1.84223 - 3.07626i) q^{66} -11.8144i q^{67} +(-0.561810 - 0.973084i) q^{68} +(-5.20218 + 3.11533i) q^{69} +(8.40328 - 2.24594i) q^{70} +(-3.94585 - 6.83441i) q^{71} +(2.99847 - 0.0958395i) q^{72} +(-0.878160 - 1.52102i) q^{73} +(6.03816 + 3.48613i) q^{74} +(-5.16884 - 8.63125i) q^{75} +(0.505430 - 0.875431i) q^{76} +(1.41426 + 5.29150i) q^{77} +(-2.07988 - 5.88847i) q^{78} +(-2.48977 + 4.31240i) q^{79} +3.28763i q^{80} +(8.98163 - 0.574744i) q^{81} -9.84458i q^{82} +0.999900i q^{83} +(-4.44410 - 1.11801i) q^{84} +(3.19914 - 1.84702i) q^{85} +(3.35600 - 5.81276i) q^{86} +(-13.9400 - 7.75403i) q^{87} -2.07020 q^{88} +(-6.59807 + 3.80940i) q^{89} +(0.315084 + 9.85784i) q^{90} +(0.582714 + 9.52158i) q^{91} +3.50085i q^{92} +(-3.32220 - 5.54762i) q^{93} +1.21839i q^{94} +(2.87809 + 1.66167i) q^{95} +(0.841952 - 1.51364i) q^{96} +(3.21628 + 5.57077i) q^{97} +(6.05773 + 3.50769i) q^{98} +(-6.20743 + 0.198407i) 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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