LMFDB - Embedded newform 546.2.bn.e.101.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 5]))

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

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

chi := DirichletCharacter("546.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.11
Character	$\chi$	$=$	546.101
Dual form			546.2.bn.e.173.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.801045 + 1.53568i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.09866 + 0.634311i) q^{5} +(-1.73046 - 0.0741172i) q^{6} +(-2.21179 + 1.45190i) q^{7} +1.00000 q^{8} +(-1.71665 + 2.46030i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.801045 + 1.53568i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.09866 + 0.634311i) q^{5} +(-1.73046 - 0.0741172i) q^{6} +(-2.21179 + 1.45190i) q^{7} +1.00000 q^{8} +(-1.71665 + 2.46030i) q^{9} -1.26862i q^{10} -5.15033 q^{11} +(0.929420 - 1.46157i) q^{12} +(2.55917 - 2.53981i) q^{13} +(-0.151485 - 2.64141i) q^{14} +(-1.85418 - 1.17908i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.50144 - 4.33262i) q^{17} +(-1.27236 - 2.71682i) q^{18} +6.60332 q^{19} +(1.09866 + 0.634311i) q^{20} +(-4.00139 - 2.23357i) q^{21} +(2.57517 - 4.46032i) q^{22} +(-2.33827 - 1.35000i) q^{23} +(0.801045 + 1.53568i) q^{24} +(-1.69530 + 2.93635i) q^{25} +(0.919959 + 3.48621i) q^{26} +(-5.15337 - 0.665427i) q^{27} +(2.36327 + 1.18952i) q^{28} +(-0.776779 + 0.448474i) q^{29} +(1.94820 - 1.01622i) q^{30} +(-4.25869 + 7.37627i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-4.12565 - 7.90929i) q^{33} +5.00288 q^{34} +(1.50904 - 2.99810i) q^{35} +(2.98901 + 0.256514i) q^{36} +(-4.79158 - 2.76642i) q^{37} +(-3.30166 + 5.71864i) q^{38} +(5.95036 + 1.89557i) q^{39} +(-1.09866 + 0.634311i) q^{40} +(-4.54200 + 2.62233i) q^{41} +(3.93503 - 2.34852i) q^{42} +(1.72068 - 2.98031i) q^{43} +(2.57517 + 4.46032i) q^{44} +(0.325420 - 3.79193i) q^{45} +(2.33827 - 1.35000i) q^{46} +(-4.18472 + 2.41605i) q^{47} +(-1.73046 - 0.0741172i) q^{48} +(2.78400 - 6.42257i) q^{49} +(-1.69530 - 2.93635i) q^{50} +(4.64977 - 7.31204i) q^{51} +(-3.47913 - 0.946398i) q^{52} +(11.7150 + 6.76369i) q^{53} +(3.15296 - 4.13023i) q^{54} +(5.65846 - 3.26691i) q^{55} +(-2.21179 + 1.45190i) q^{56} +(5.28955 + 10.1406i) q^{57} -0.896947i q^{58} +(-10.2481 + 5.91675i) q^{59} +(-0.0940267 + 2.19530i) q^{60} -4.66758i q^{61} +(-4.25869 - 7.37627i) q^{62} +(0.224768 - 7.93407i) q^{63} +1.00000 q^{64} +(-1.20062 + 4.41370i) q^{65} +(8.91247 + 0.381728i) q^{66} +11.5652i q^{67} +(-2.50144 + 4.33262i) q^{68} +(0.200117 - 4.67226i) q^{69} +(1.84191 + 2.80592i) q^{70} +(3.79105 - 6.56628i) q^{71} +(-1.71665 + 2.46030i) q^{72} +(-0.210796 + 0.365109i) q^{73} +(4.79158 - 2.76642i) q^{74} +(-5.86731 - 0.251302i) q^{75} +(-3.30166 - 5.71864i) q^{76} +(11.3914 - 7.47775i) q^{77} +(-4.61679 + 4.20538i) q^{78} +(-2.95006 - 5.10965i) q^{79} -1.26862i q^{80} +(-3.10619 - 8.44699i) q^{81} -5.24465i q^{82} +9.22131i q^{83} +(0.0663661 + 4.58210i) q^{84} +(5.49645 + 3.17338i) q^{85} +(1.72068 + 2.98031i) q^{86} +(-1.31095 - 0.833640i) q^{87} -5.15033 q^{88} +(7.19534 + 4.15423i) q^{89} +(3.12119 + 2.17779i) q^{90} +(-1.97279 + 9.33317i) q^{91} +2.70000i q^{92} +(-14.7390 - 0.631285i) q^{93} -4.83210i q^{94} +(-7.25479 + 4.18856i) q^{95} +(0.929420 - 1.46157i) q^{96} +(-6.21010 + 10.7562i) q^{97} +(4.17011 + 5.62230i) q^{98} +(8.84134 - 12.6714i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9}+O(q^{10}) $ 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9	$ 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9} - 18 q^{11} + 3 q^{12} - 8 q^{13} - 4 q^{14} - 17 q^{15} - 17 q^{16} + 6 q^{17} - 11 q^{18} - 10 q^{19} - 9 q^{20} - 4 q^{21} + 9 q^{22} + 6 q^{23} + 3 q^{24} + 16 q^{25} + 13 q^{26} + 18 q^{27} - q^{28} + 27 q^{29} + 13 q^{30} + q^{31} - 17 q^{32} + 21 q^{33} - 12 q^{34} - 3 q^{35} + 4 q^{36} + 6 q^{37} + 5 q^{38} + 20 q^{39} + 9 q^{40} + 3 q^{41} + 20 q^{42} - 3 q^{43} + 9 q^{44} - 6 q^{46} - 27 q^{47} - 6 q^{48} - 5 q^{49} + 16 q^{50} + 24 q^{51} - 5 q^{52} + 21 q^{53} - 18 q^{54} + 57 q^{55} + 5 q^{56} - 17 q^{57} - 6 q^{59} + 4 q^{60} + q^{62} - 21 q^{63} + 34 q^{64} + 33 q^{65} - 21 q^{66} + 6 q^{68} - 30 q^{69} + 3 q^{70} - 15 q^{71} + 7 q^{72} + 19 q^{73} - 6 q^{74} - 63 q^{75} + 5 q^{76} - 9 q^{77} - 10 q^{78} - 9 q^{79} - 5 q^{81} - 16 q^{84} - 42 q^{85} - 3 q^{86} - 75 q^{87} - 18 q^{88} - 18 q^{89} - 9 q^{90} - 27 q^{91} + 25 q^{93} - 3 q^{95} + 3 q^{96} - 19 q^{97} + 7 q^{98} - 27 q^{99}+O(q^{100}) $ 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9 - 18 * q^11 + 3 * q^12 - 8 * q^13 - 4 * q^14 - 17 * q^15 - 17 * q^16 + 6 * q^17 - 11 * q^18 - 10 * q^19 - 9 * q^20 - 4 * q^21 + 9 * q^22 + 6 * q^23 + 3 * q^24 + 16 * q^25 + 13 * q^26 + 18 * q^27 - q^28 + 27 * q^29 + 13 * q^30 + q^31 - 17 * q^32 + 21 * q^33 - 12 * q^34 - 3 * q^35 + 4 * q^36 + 6 * q^37 + 5 * q^38 + 20 * q^39 + 9 * q^40 + 3 * q^41 + 20 * q^42 - 3 * q^43 + 9 * q^44 - 6 * q^46 - 27 * q^47 - 6 * q^48 - 5 * q^49 + 16 * q^50 + 24 * q^51 - 5 * q^52 + 21 * q^53 - 18 * q^54 + 57 * q^55 + 5 * q^56 - 17 * q^57 - 6 * q^59 + 4 * q^60 + q^62 - 21 * q^63 + 34 * q^64 + 33 * q^65 - 21 * q^66 + 6 * q^68 - 30 * q^69 + 3 * q^70 - 15 * q^71 + 7 * q^72 + 19 * q^73 - 6 * q^74 - 63 * q^75 + 5 * q^76 - 9 * q^77 - 10 * q^78 - 9 * q^79 - 5 * q^81 - 16 * q^84 - 42 * q^85 - 3 * q^86 - 75 * q^87 - 18 * q^88 - 18 * q^89 - 9 * q^90 - 27 * q^91 + 25 * q^93 - 3 * q^95 + 3 * q^96 - 19 * q^97 + 7 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.801045	+	1.53568i	0.462483	+	0.886628i
$3$	0.801045	+	1.53568i	0.462483	+	0.886628i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.09866	+	0.634311i	−0.491335	+	0.283672i	−0.725128	−	0.688614i	$-0.758219\pi$
$5$	−1.09866	+	0.634311i	−0.491335	+	0.283672i	0.233793	+	0.972286i	$0.424886\pi$
$6$	−1.73046	−	0.0741172i	−0.706459	−	0.0302582i
$7$	−2.21179	+	1.45190i	−0.835977	+	0.548765i
$7$	−2.21179	+	1.45190i	−0.835977	+	0.548765i
$8$	1.00000			0.353553
$9$	−1.71665	+	2.46030i	−0.572218	+	0.820101i
$10$		−	1.26862i		−	0.401173i
$11$	−5.15033			−1.55288			−0.776442	−	0.630189i	$-0.782977\pi$
$11$	−5.15033			−1.55288			−0.776442	+	0.630189i	$0.782977\pi$
$12$	0.929420	−	1.46157i	0.268300	−	0.421918i
$13$	2.55917	−	2.53981i	0.709786	−	0.704418i
$13$	2.55917	−	2.53981i	0.709786	−	0.704418i
$14$	−0.151485	−	2.64141i	−0.0404862	−	0.705947i
$15$	−1.85418	−	1.17908i	−0.478746	−	0.304438i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.50144	−	4.33262i	−0.606688	−	1.05081i	−0.991782	−	0.127937i	$-0.959164\pi$
$17$	−2.50144	−	4.33262i	−0.606688	−	1.05081i	0.385094	−	0.922877i	$-0.374169\pi$
$18$	−1.27236	−	2.71682i	−0.299898	−	0.640360i
$19$	6.60332			1.51491			0.757453	−	0.652890i	$-0.226444\pi$
$19$	6.60332			1.51491			0.757453	+	0.652890i	$0.226444\pi$
$20$	1.09866	+	0.634311i	0.245668	+	0.141836i
$21$	−4.00139	−	2.23357i	−0.873176	−	0.487406i
$22$	2.57517	−	4.46032i	0.549027	−	0.950943i
$23$	−2.33827	−	1.35000i	−0.487564	−	0.281495i	0.236000	−	0.971753i	$-0.424164\pi$
$23$	−2.33827	−	1.35000i	−0.487564	−	0.281495i	−0.723563	+	0.690258i	$0.757497\pi$
$24$	0.801045	+	1.53568i	0.163513	+	0.313470i
$25$	−1.69530	+	2.93635i	−0.339060	+	0.587269i
$26$	0.919959	+	3.48621i	0.180419	+	0.683702i
$27$	−5.15337	−	0.665427i	−0.991766	−	0.128061i
$28$	2.36327	+	1.18952i	0.446616	+	0.224797i
$29$	−0.776779	+	0.448474i	−0.144244	+	0.0832794i	−0.570385	−	0.821377i	$-0.693206\pi$
$29$	−0.776779	+	0.448474i	−0.144244	+	0.0832794i	0.426141	+	0.904657i	$0.359873\pi$
$30$	1.94820	−	1.01622i	0.355692	−	0.185536i
$31$	−4.25869	+	7.37627i	−0.764883	+	1.32482i	0.175425	+	0.984493i	$0.443870\pi$
$31$	−4.25869	+	7.37627i	−0.764883	+	1.32482i	−0.940308	+	0.340324i	$0.889463\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−4.12565	−	7.90929i	−0.718183	−	1.37683i
$34$	5.00288			0.857987
$35$	1.50904	−	2.99810i	0.255075	−	0.506771i
$36$	2.98901	+	0.256514i	0.498169	+	0.0427524i
$37$	−4.79158	−	2.76642i	−0.787731	−	0.454797i	0.0514322	−	0.998676i	$-0.483621\pi$
$37$	−4.79158	−	2.76642i	−0.787731	−	0.454797i	−0.839163	+	0.543880i	$0.816955\pi$
$38$	−3.30166	+	5.71864i	−0.535600	+	0.927686i
$39$	5.95036	+	1.89557i	0.952821	+	0.303534i
$40$	−1.09866	+	0.634311i	−0.173713	+	0.100293i
$41$	−4.54200	+	2.62233i	−0.709342	+	0.409539i	−0.810817	−	0.585299i	$-0.800977\pi$
$41$	−4.54200	+	2.62233i	−0.709342	+	0.409539i	0.101476	+	0.994838i	$0.467644\pi$
$42$	3.93503	−	2.34852i	0.607188	−	0.362385i
$43$	1.72068	−	2.98031i	0.262402	−	0.454493i	−0.704478	−	0.709726i	$-0.748819\pi$
$43$	1.72068	−	2.98031i	0.262402	−	0.454493i	0.966880	+	0.255233i	$0.0821521\pi$
$44$	2.57517	+	4.46032i	0.388221	+	0.672418i
$45$	0.325420	−	3.79193i	0.0485107	−	0.565267i
$46$	2.33827	−	1.35000i	0.344760	−	0.199047i
$47$	−4.18472	+	2.41605i	−0.610404	+	0.352417i	−0.773124	−	0.634255i	$-0.781307\pi$
$47$	−4.18472	+	2.41605i	−0.610404	+	0.352417i	0.162719	+	0.986672i	$0.447973\pi$
$48$	−1.73046	−	0.0741172i	−0.249771	−	0.0106979i
$49$	2.78400	−	6.42257i	0.397714	−	0.917509i
$50$	−1.69530	−	2.93635i	−0.239752	−	0.415262i
$51$	4.64977	−	7.31204i	0.651098	−	1.02389i
$52$	−3.47913	−	0.946398i	−0.482468	−	0.131242i
$53$	11.7150	+	6.76369i	1.60919	+	0.929064i	0.989553	+	0.144172i	$0.0460520\pi$
$53$	11.7150	+	6.76369i	1.60919	+	0.929064i	0.619633	+	0.784891i	$0.287281\pi$
$54$	3.15296	−	4.13023i	0.429064	−	0.562054i
$55$	5.65846	−	3.26691i	0.762986	−	0.440510i
$56$	−2.21179	+	1.45190i	−0.295562	+	0.194018i
$57$	5.28955	+	10.1406i	0.700618	+	1.34316i
$58$		−	0.896947i		−	0.117775i
$59$	−10.2481	+	5.91675i	−1.33419	+	0.770296i	−0.985939	−	0.167105i	$-0.946558\pi$
$59$	−10.2481	+	5.91675i	−1.33419	+	0.770296i	−0.348252	+	0.937401i	$0.613225\pi$
$60$	−0.0940267	+	2.19530i	−0.0121388	+	0.283413i
$61$		−	4.66758i		−	0.597622i	−0.954312	−	0.298811i	$-0.903410\pi$
$61$		−	4.66758i		−	0.597622i	0.954312	−	0.298811i	$-0.0965901\pi$
$62$	−4.25869	−	7.37627i	−0.540854	−	0.936787i
$63$	0.224768	−	7.93407i	0.0283181	−	0.999599i
$64$	1.00000			0.125000
$65$	−1.20062	+	4.41370i	−0.148919	+	0.547452i
$66$	8.91247	+	0.381728i	1.09705	+	0.0469875i
$67$			11.5652i			1.41291i	0.707757	+	0.706456i	$0.249707\pi$
$67$			11.5652i			1.41291i	−0.707757	+	0.706456i	$0.750293\pi$
$68$	−2.50144	+	4.33262i	−0.303344	+	0.525407i
$69$	0.200117	−	4.67226i	0.0240912	−	0.562474i
$70$	1.84191	+	2.80592i	0.220150	+	0.335372i
$71$	3.79105	−	6.56628i	0.449914	−	0.779274i	−0.548466	−	0.836173i	$-0.684788\pi$
$71$	3.79105	−	6.56628i	0.449914	−	0.779274i	0.998380	+	0.0568986i	$0.0181212\pi$
$72$	−1.71665	+	2.46030i	−0.202310	+	0.289950i
$73$	−0.210796	+	0.365109i	−0.0246718	+	0.0427328i	−0.878098	−	0.478481i	$-0.841187\pi$
$73$	−0.210796	+	0.365109i	−0.0246718	+	0.0427328i	0.853426	+	0.521214i	$0.174521\pi$
$74$	4.79158	−	2.76642i	0.557010	−	0.321590i
$75$	−5.86731	−	0.251302i	−0.677499	−	0.0290178i
$76$	−3.30166	−	5.71864i	−0.378726	−	0.655973i
$77$	11.3914	−	7.47775i	1.29817	−	0.852168i
$78$	−4.61679	+	4.20538i	−0.522749	+	0.476165i
$79$	−2.95006	−	5.10965i	−0.331908	−	0.574881i	0.650978	−	0.759096i	$-0.274359\pi$
$79$	−2.95006	−	5.10965i	−0.331908	−	0.574881i	−0.982886	+	0.184216i	$0.941026\pi$
$80$		−	1.26862i		−	0.141836i
$81$	−3.10619	−	8.44699i	−0.345133	−	0.938554i
$82$		−	5.24465i		−	0.579175i
$83$			9.22131i			1.01217i	0.862484	+	0.506085i	$0.168908\pi$
$83$			9.22131i			1.01217i	−0.862484	+	0.506085i	$0.831092\pi$
$84$	0.0663661	+	4.58210i	0.00724113	+	0.499948i
$85$	5.49645	+	3.17338i	0.596174	+	0.344201i
$86$	1.72068	+	2.98031i	0.185546	+	0.321375i
$87$	−1.31095	−	0.833640i	−0.140548	−	0.0893756i
$88$	−5.15033			−0.549027
$89$	7.19534	+	4.15423i	0.762705	+	0.440348i	0.830266	−	0.557367i	$-0.188189\pi$
$89$	7.19534	+	4.15423i	0.762705	+	0.440348i	−0.0675614	+	0.997715i	$0.521522\pi$
$90$	3.12119	+	2.17779i	0.329003	+	0.229559i
$91$	−1.97279	+	9.33317i	−0.206804	+	0.978382i
$92$			2.70000i			0.281495i
$93$	−14.7390	−	0.631285i	−1.52837	−	0.0654612i
$94$		−	4.83210i		−	0.498393i
$95$	−7.25479	+	4.18856i	−0.744326	+	0.429737i
$96$	0.929420	−	1.46157i	0.0948585	−	0.149171i
$97$	−6.21010	+	10.7562i	−0.630540	+	1.09213i	0.356901	+	0.934142i	$0.383833\pi$
$97$	−6.21010	+	10.7562i	−0.630540	+	1.09213i	−0.987441	+	0.157985i	$0.949500\pi$
$98$	4.17011	+	5.62230i	0.421244	+	0.567938i
$99$	8.84134	−	12.6714i	0.888588	−	1.27352i
$100$	3.39060			0.339060
$101$	−9.45426			−0.940734			−0.470367	−	0.882471i	$-0.655878\pi$
$101$	−9.45426			−0.940734			−0.470367	+	0.882471i	$0.655878\pi$
$102$	4.00753	+	7.68284i	0.396805	+	0.760715i
$103$	−15.4442	+	8.91672i	−1.52176	+	0.878590i	−0.522093	+	0.852888i	$0.674849\pi$
$103$	−15.4442	+	8.91672i	−1.52176	+	0.878590i	−0.999670	+	0.0257017i	$0.991818\pi$
$104$	2.55917	−	2.53981i	0.250947	−	0.249049i
$105$	5.81294	−	0.0841934i	0.567285	−	0.00821644i
$106$	−11.7150	+	6.76369i	−1.13787	+	0.656947i
$107$	8.42970	+	4.86689i	0.814930	+	0.470500i	0.848665	−	0.528931i	$-0.177407\pi$
$107$	8.42970	+	4.86689i	0.814930	+	0.470500i	−0.0337349	+	0.999431i	$0.510740\pi$
$108$	2.00041	+	4.79566i	0.192489	+	0.461463i
$109$	−9.16977	−	5.29417i	−0.878305	−	0.507090i	−0.00820581	−	0.999966i	$-0.502612\pi$
$109$	−9.16977	−	5.29417i	−0.878305	−	0.507090i	−0.870099	+	0.492877i	$0.835945\pi$
$110$			6.53382i			0.622976i
$111$	0.410079	−	9.57438i	0.0389230	−	0.908760i
$112$	−0.151485	−	2.64141i	−0.0143140	−	0.249590i
$113$	2.68329	+	1.54920i	0.252422	+	0.145736i	0.620873	−	0.783911i	$-0.286778\pi$
$113$	2.68329	+	1.54920i	0.252422	+	0.145736i	−0.368451	+	0.929647i	$0.620112\pi$
$114$	−11.4268	−	0.489420i	−1.07022	−	0.0458384i
$115$	3.42528			0.319409
$116$	0.776779	+	0.448474i	0.0721221	+	0.0416397i
$117$	1.85551	+	10.6563i	0.171542	+	0.985177i
$118$		−	11.8335i		−	1.08936i
$119$	11.8232	+	5.95100i	1.08383	+	0.545527i
$120$	−1.85418	−	1.17908i	−0.169262	−	0.107635i
$121$	15.5259			1.41145
$122$	4.04224	+	2.33379i	0.365967	+	0.211291i
$123$	−7.66541	−	4.87448i	−0.691167	−	0.439517i
$124$	8.51738			0.764883
$125$		−	10.6445i		−	0.952073i
$126$	6.75872	+	4.16169i	0.602115	+	0.370753i
$127$	5.87399	+	10.1740i	0.521232	+	0.902800i	0.999695	+	0.0246926i	$0.00786069\pi$
$127$	5.87399	+	10.1740i	0.521232	+	0.902800i	−0.478463	+	0.878108i	$0.658806\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	5.95516	+	0.255065i	0.524323	+	0.0224572i
$130$	−3.22206	−	3.24662i	−0.282594	−	0.284747i
$131$	2.35882	+	4.08559i	0.206091	+	0.356960i	0.950480	−	0.310787i	$-0.100592\pi$
$131$	2.35882	+	4.08559i	0.206091	+	0.356960i	−0.744389	+	0.667746i	$0.767259\pi$
$132$	−4.78682	+	7.52756i	−0.416639	+	0.655190i
$133$	−14.6051	+	9.58733i	−1.26643	+	0.831327i
$134$	−10.0157	−	5.78259i	−0.865229	−	0.499540i
$135$	6.08388	−	2.53776i	0.523617	−	0.218416i
$136$	−2.50144	−	4.33262i	−0.214497	−	0.371519i
$137$	4.80934	+	8.33002i	0.410890	+	0.711682i	0.994987	−	0.100002i	$-0.0318848\pi$
$137$	4.80934	+	8.33002i	0.410890	+	0.711682i	−0.584098	+	0.811683i	$0.698551\pi$
$138$	3.94624	+	2.50944i	0.335926	+	0.213617i
$139$	1.81406	+	1.04735i	0.153867	+	0.0888349i	0.574956	−	0.818184i	$-0.305019\pi$
$139$	1.81406	+	1.04735i	0.153867	+	0.0888349i	−0.421090	+	0.907019i	$0.638352\pi$
$140$	−3.35095	+	0.192178i	−0.283207	+	0.0162420i
$141$	−7.06244	−	4.49105i	−0.594765	−	0.378215i
$142$	3.79105	+	6.56628i	0.318137	+	0.551030i
$143$	−13.1806	+	13.0809i	−1.10221	+	1.09388i
$144$	−1.27236	−	2.71682i	−0.106030	−	0.226402i
$145$	0.568943	−	0.985438i	0.0472482	−	0.0818362i
$146$	−0.210796	−	0.365109i	−0.0174456	−	0.0302166i
$147$	12.0931	−	0.869421i	0.997426	−	0.0717086i
$148$			5.53284i			0.454797i
$149$	−7.70630			−0.631324			−0.315662	−	0.948872i	$-0.602227\pi$
$149$	−7.70630			−0.631324			−0.315662	+	0.948872i	$0.602227\pi$
$150$	3.15129	−	4.95559i	0.257302	−	0.404622i
$151$	−0.525736	−	0.303534i	−0.0427838	−	0.0247012i	0.478456	−	0.878112i	$-0.341197\pi$
$151$	−0.525736	−	0.303534i	−0.0427838	−	0.0247012i	−0.521239	+	0.853411i	$0.674530\pi$
$152$	6.60332			0.535600
$153$	14.9537	+	1.28331i	1.20893	+	0.103750i
$154$	0.780200	+	13.6041i	0.0628703	+	1.09625i
$155$		−	10.8053i		−	0.867905i
$156$	−1.33357	−	6.10095i	−0.106771	−	0.488467i
$157$	11.5582	+	6.67311i	0.922442	+	0.532572i	0.884413	−	0.466704i	$-0.154559\pi$
$157$	11.5582	+	6.67311i	0.922442	+	0.532572i	0.0380288	+	0.999277i	$0.487892\pi$
$158$	5.90012			0.469388
$159$	−1.00261	+	23.4086i	−0.0795123	+	1.85643i
$160$	1.09866	+	0.634311i	0.0868566	+	0.0501467i
$161$	7.13182	−	0.409011i	0.562066	−	0.0322346i
$162$	8.86840	+	1.53345i	0.696767	+	0.120479i
$163$			15.0298i			1.17722i	0.808416	+	0.588612i	$0.200325\pi$
$163$			15.0298i			1.17722i	−0.808416	+	0.588612i	$0.799675\pi$
$164$	4.54200	+	2.62233i	0.354671	+	0.204769i
$165$	9.54962	+	6.07266i	0.743437	+	0.472756i
$166$	−7.98589	−	4.61065i	−0.619825	−	0.357856i
$167$	14.6300	−	8.44665i	1.13211	−	0.653622i	0.187642	−	0.982237i	$-0.439915\pi$
$167$	14.6300	−	8.44665i	1.13211	−	0.653622i	0.944464	+	0.328616i	$0.106582\pi$
$168$	−4.00139	−	2.23357i	−0.308714	−	0.172324i
$169$	0.0986879	−	12.9996i	0.00759138	−	0.999971i
$170$	−5.49645	+	3.17338i	−0.421559	+	0.243387i
$171$	−11.3356	+	16.2462i	−0.866856	+	1.24238i
$172$	−3.44137			−0.262402
$173$	−0.512845			−0.0389909			−0.0194954	−	0.999810i	$-0.506206\pi$
$173$	−0.512845			−0.0389909			−0.0194954	+	0.999810i	$0.506206\pi$
$174$	1.37743	−	0.718495i	0.104423	−	0.0544689i
$175$	−0.513627	−	8.95597i	−0.0388265	−	0.677007i
$176$	2.57517	−	4.46032i	0.194110	−	0.336209i
$177$	−17.2955	−	10.9983i	−1.30001	−	0.826682i
$178$	−7.19534	+	4.15423i	−0.539314	+	0.311373i
$179$			8.01953i			0.599408i	0.954032	+	0.299704i	$0.0968879\pi$
$179$			8.01953i			0.599408i	−0.954032	+	0.299704i	$0.903112\pi$
$180$	−3.44661	+	1.61414i	−0.256895	+	0.120311i
$181$		−	0.459074i		−	0.0341227i	−0.999854	−	0.0170614i	$-0.994569\pi$
$181$		−	0.459074i		−	0.0341227i	0.999854	−	0.0170614i	$-0.00543106\pi$
$182$	−7.09637	−	6.37507i	−0.526018	−	0.472552i
$183$	7.16793	−	3.73894i	0.529869	−	0.276390i
$184$	−2.33827	−	1.35000i	−0.172380	−	0.0995235i
$185$	7.01908			0.516053
$186$	7.91622	−	12.4487i	0.580445	−	0.912785i
$187$	12.8832	+	22.3144i	0.942116	+	1.63179i
$188$	4.18472	+	2.41605i	0.305202	+	0.176209i
$189$	12.3643	−	6.01037i	0.899369	−	0.437190i
$190$		−	8.37711i		−	0.607740i
$191$		−	10.0962i		−	0.730532i	−0.930903	−	0.365266i	$-0.880978\pi$
$191$		−	10.0962i		−	0.730532i	0.930903	−	0.365266i	$-0.119022\pi$
$192$	0.801045	+	1.53568i	0.0578104	+	0.110828i
$193$		−	8.28022i		−	0.596023i	−0.954562	−	0.298011i	$-0.903677\pi$
$193$		−	8.28022i		−	0.596023i	0.954562	−	0.298011i	$-0.0963234\pi$
$194$	−6.21010	−	10.7562i	−0.445859	−	0.772251i
$195$	−7.73980	+	1.69179i	−0.554258	+	0.121152i
$196$	−6.95410	+	0.800271i	−0.496722	+	0.0571622i
$197$	−7.07350	−	12.2517i	−0.503966	−	0.872895i	−0.999989	−	0.00458596i	$-0.998540\pi$
$197$	−7.07350	−	12.2517i	−0.503966	−	0.872895i	0.496023	−	0.868309i	$-0.334793\pi$
$198$	6.55307	+	13.9925i	0.465706	+	0.994405i
$199$	13.2715	−	7.66228i	0.940788	−	0.543164i	0.0505810	−	0.998720i	$-0.483893\pi$
$199$	13.2715	−	7.66228i	0.940788	−	0.543164i	0.890207	+	0.455556i	$0.150559\pi$
$200$	−1.69530	+	2.93635i	−0.119876	+	0.207631i
$201$	−17.7605	+	9.26423i	−1.25273	+	0.653449i
$202$	4.72713	−	8.18763i	0.332600	−	0.576079i
$203$	1.06693	−	2.11973i	0.0748840	−	0.148776i
$204$	−8.65730	−	0.370800i	−0.606132	−	0.0259612i
$205$	3.32674	−	5.76208i	0.232350	−	0.402441i
$206$		−	17.8334i		−	1.24251i
$207$	7.33542	−	3.43537i	0.509847	−	0.238775i
$208$	0.919959	+	3.48621i	0.0637877	+	0.241725i
$209$	−34.0093			−2.35247
$210$	−2.83356	+	5.07625i	−0.195534	+	0.350295i
$211$	4.63016	+	8.01968i	0.318754	+	0.552097i	0.980228	−	0.197870i	$-0.0634025\pi$
$211$	4.63016	+	8.01968i	0.318754	+	0.552097i	−0.661475	+	0.749967i	$0.730069\pi$
$212$		−	13.5274i		−	0.929064i
$213$	13.1205	+	0.561964i	0.899004	+	0.0385051i
$214$	−8.42970	+	4.86689i	−0.576243	+	0.332694i
$215$			4.36579i			0.297745i
$216$	−5.15337	−	0.665427i	−0.350642	−	0.0452765i
$217$	−1.29026	−	22.4979i	−0.0875885	−	1.52726i
$218$	9.16977	−	5.29417i	0.621055	−	0.358567i
$219$	−0.729549	−	0.0312472i	−0.0492984	−	0.00211149i
$220$	−5.65846	−	3.26691i	−0.381493	−	0.220255i
$221$	−17.4057	−	4.73471i	−1.17083	−	0.318491i
$222$	8.08662	+	5.14233i	0.542738	+	0.345131i
$223$	−6.58695	−	11.4089i	−0.441095	−	0.763998i	0.556676	−	0.830729i	$-0.312076\pi$
$223$	−6.58695	−	11.4089i	−0.441095	−	0.763998i	−0.997771	+	0.0667312i	$0.978743\pi$
$224$	2.36327	+	1.18952i	0.157903	+	0.0794778i
$225$	−4.31406	−	9.21164i	−0.287604	−	0.614110i
$226$	−2.68329	+	1.54920i	−0.178490	+	0.103051i
$227$	−2.05308	+	1.18535i	−0.136268	+	0.0786742i	−0.566584	−	0.824004i	$-0.691735\pi$
$227$	−2.05308	+	1.18535i	−0.136268	+	0.0786742i	0.430316	+	0.902678i	$0.358402\pi$
$228$	6.13725	−	9.65119i	0.406450	−	0.639166i
$229$	−5.91454	−	10.2443i	−0.390844	−	0.676961i	0.601717	−	0.798709i	$-0.294483\pi$
$229$	−5.91454	−	10.2443i	−0.390844	−	0.676961i	−0.992561	+	0.121748i	$0.961150\pi$
$230$	−1.71264	+	2.96638i	−0.112928	+	0.195598i
$231$	20.6085	+	11.5036i	1.35594	+	0.756884i
$232$	−0.776779	+	0.448474i	−0.0509980	+	0.0294437i
$233$	−6.84440	+	3.95162i	−0.448392	+	0.258879i	−0.707151	−	0.707063i	$-0.750020\pi$
$233$	−6.84440	+	3.95162i	−0.448392	+	0.258879i	0.258759	+	0.965942i	$0.416686\pi$
$234$	−10.1564	−	3.72124i	−0.663944	−	0.243265i
$235$	3.06505	−	5.30883i	0.199942	−	0.346310i
$236$	10.2481	+	5.91675i	0.667096	+	0.385148i
$237$	5.48369	−	8.62342i	0.356204	−	0.560151i
$238$	−11.0653	+	7.26366i	−0.717257	+	0.470833i
$239$	27.3019			1.76601			0.883007	−	0.469360i	$-0.155515\pi$
$239$	27.3019			1.76601			0.883007	+	0.469360i	$0.155515\pi$
$240$	1.94820	−	1.01622i	0.125756	−	0.0655969i
$241$	−5.64076	−	9.77009i	−0.363353	−	0.629347i	0.625157	−	0.780499i	$-0.285035\pi$
$241$	−5.64076	−	9.77009i	−0.363353	−	0.629347i	−0.988510	+	0.151152i	$0.951702\pi$
$242$	−7.76296	+	13.4458i	−0.499022	+	0.864332i
$243$	10.4837	−	11.5365i	0.672530	−	0.740070i
$244$	−4.04224	+	2.33379i	−0.258778	+	0.149406i
$245$	1.01524	+	8.82213i	0.0648613	+	0.563625i
$246$	8.05413	−	4.20120i	0.513513	−	0.267859i
$247$	16.8990	−	16.7712i	1.07526	−	1.06713i
$248$	−4.25869	+	7.37627i	−0.270427	+	0.468393i
$249$	−14.1610	+	7.38668i	−0.897418	+	0.468112i
$250$	9.21840	+	5.32225i	0.583023	+	0.336608i
$251$	−11.3067	+	19.5838i	−0.713675	+	1.23612i	0.249794	+	0.968299i	$0.419637\pi$
$251$	−11.3067	+	19.5838i	−0.713675	+	1.23612i	−0.963469	+	0.267822i	$0.913696\pi$
$252$	−6.98349	+	3.77238i	−0.439919	+	0.237638i
$253$	12.0429	+	6.95296i	0.757130	+	0.437129i
$254$	−11.7480			−0.737133
$255$	−0.470404	+	10.9828i	−0.0294579	+	0.687772i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.682789	+	1.18262i	−0.0425912	+	0.0737701i	−0.886535	−	0.462661i	$-0.846895\pi$
$257$	−0.682789	+	1.18262i	−0.0425912	+	0.0737701i	0.843944	+	0.536431i	$0.180228\pi$
$258$	−3.19847	+	5.02979i	−0.199128	+	0.313141i
$259$	14.6145	−	0.838145i	0.908101	−	0.0520798i
$260$	4.42268	−	1.16708i	0.274283	−	0.0723792i
$261$	0.230080	−	2.68099i	0.0142416	−	0.165949i
$262$	−4.71763			−0.291456
$263$			10.8112i			0.666646i	0.942813	+	0.333323i	$0.108170\pi$
$263$			10.8112i			0.666646i	−0.942813	+	0.333323i	$0.891830\pi$
$264$	−4.12565	−	7.90929i	−0.253916	−	0.486783i
$265$	−17.1611			−1.05420
$266$	−1.00031	−	17.4421i	−0.0613327	−	1.06944i
$267$	−0.615800	+	14.3775i	−0.0376864	+	0.879889i
$268$	10.0157	−	5.78259i	0.611809	−	0.353228i
$269$	−11.4767	−	19.8782i	−0.699747	−	1.21200i	−0.968554	−	0.248803i	$-0.919963\pi$
$269$	−11.4767	−	19.8782i	−0.699747	−	1.21200i	0.268807	−	0.963194i	$-0.413371\pi$
$270$	−0.844174	+	6.53767i	−0.0513748	+	0.397870i
$271$	−7.79637	+	13.5037i	−0.473596	+	0.820292i	−0.999543	−	0.0302249i	$-0.990378\pi$
$271$	−7.79637	+	13.5037i	−0.473596	+	0.820292i	0.525947	+	0.850517i	$0.323711\pi$
$272$	5.00288			0.303344
$273$	−15.9131	+	4.44671i	−0.963105	+	0.269127i
$274$	−9.61868			−0.581086
$275$	8.73136	−	15.1232i	0.526521	−	0.911961i
$276$	−4.14636	+	2.16282i	−0.249581	+	0.130187i
$277$	−11.1655	−	19.3391i	−0.670867	−	1.16198i	−0.977658	−	0.210200i	$-0.932589\pi$
$277$	−11.1655	−	19.3391i	−0.670867	−	1.16198i	0.306791	−	0.951777i	$-0.400745\pi$
$278$	−1.81406	+	1.04735i	−0.108800	+	0.0628158i
$279$	−10.8372	−	23.1402i	−0.648804	−	1.38537i
$280$	1.50904	−	2.99810i	0.0901827	−	0.179171i
$281$	21.7986			1.30040			0.650199	−	0.759764i	$-0.274686\pi$
$281$	21.7986			1.30040			0.650199	+	0.759764i	$0.274686\pi$
$282$	7.42058	−	3.87073i	0.441889	−	0.230499i
$283$			4.49961i			0.267474i	0.991017	+	0.133737i	$0.0426978\pi$
$283$			4.49961i			0.267474i	−0.991017	+	0.133737i	$0.957302\pi$
$284$	−7.58209			−0.449914
$285$	−12.2437	−	7.78585i	−0.725255	−	0.461194i
$286$	−4.73810	−	17.9552i	−0.280170	−	1.06171i
$287$	6.23859	−	12.3945i	0.368253	−	0.731627i
$288$	2.98901	+	0.256514i	0.176129	+	0.0151153i
$289$	−4.01440	+	6.95314i	−0.236141	+	0.409008i
$290$	0.568943	+	0.985438i	0.0334095	+	0.0578669i
$291$	−21.4927	−	0.920551i	−1.25992	−	0.0539636i
$292$	0.421592			0.0246718
$293$	−11.6501	−	6.72621i	−0.680608	−	0.392949i	0.119476	−	0.992837i	$-0.461879\pi$
$293$	−11.6501	−	6.72621i	−0.680608	−	0.392949i	−0.800084	+	0.599888i	$0.795212\pi$
$294$	−5.29363	+	10.9077i	−0.308731	+	0.636149i
$295$	7.50612	−	13.0010i	0.437023	−	0.756946i
$296$	−4.79158	−	2.76642i	−0.278505	−	0.160795i
$297$	26.5416	+	3.42717i	1.54010	+	0.198864i
$298$	3.85315	−	6.67385i	0.223207	−	0.386606i
$299$	−9.41279	+	2.48389i	−0.544356	+	0.143647i
$300$	2.71602	+	5.20689i	0.156810	+	0.300620i
$301$	0.521317	+	9.09006i	0.0300482	+	0.523943i
$302$	0.525736	−	0.303534i	0.0302527	−	0.0174664i
$303$	−7.57328	−	14.5188i	−0.435074	−	0.834081i
$304$	−3.30166	+	5.71864i	−0.189363	+	0.327987i
$305$	2.96070	+	5.12808i	0.169529	+	0.293633i
$306$	−8.58821	+	12.3086i	−0.490956	+	0.703636i
$307$	−15.8067			−0.902135			−0.451068	−	0.892490i	$-0.648957\pi$
$307$	−15.8067			−0.902135			−0.451068	+	0.892490i	$0.648957\pi$
$308$	−12.1716	−	6.12640i	−0.693543	−	0.349084i
$309$	−26.0648	−	16.5747i	−1.48277	−	0.942904i
$310$	9.35769	+	5.40267i	0.531481	+	0.306851i
$311$	13.1198	−	22.7241i	0.743954	−	1.28857i	−0.206727	−	0.978399i	$-0.566281\pi$
$311$	13.1198	−	22.7241i	0.743954	−	1.28857i	0.950682	−	0.310168i	$-0.100385\pi$
$312$	5.95036	+	1.89557i	0.336873	+	0.107316i
$313$	−14.2929	+	8.25201i	−0.807883	+	0.466431i	−0.846220	−	0.532834i	$-0.821127\pi$
$313$	−14.2929	+	8.25201i	−0.807883	+	0.466431i	0.0383374	+	0.999265i	$0.487794\pi$
$314$	−11.5582	+	6.67311i	−0.652265	+	0.376585i
$315$	4.78572	+	8.85941i	0.269645	+	0.499171i
$316$	−2.95006	+	5.10965i	−0.165954	+	0.287440i
$317$	14.8285	+	25.6838i	0.832854	+	1.44255i	0.895766	+	0.444526i	$0.146628\pi$
$317$	14.8285	+	25.6838i	0.832854	+	1.44255i	−0.0629121	+	0.998019i	$0.520039\pi$
$318$	−19.7712	−	12.5726i	−1.10871	−	0.705037i
$319$	4.00067	−	2.30979i	0.223994	−	0.129323i
$320$	−1.09866	+	0.634311i	−0.0614169	+	0.0354590i
$321$	−0.721441	+	16.8440i	−0.0402669	+	0.940138i
$322$	−3.21170	+	6.38085i	−0.178981	+	0.355591i
$323$	−16.5178	−	28.6097i	−0.919075	−	1.59188i
$324$	−5.76221	+	6.91354i	−0.320123	+	0.384085i
$325$	3.11921	+	11.8203i	0.173023	+	0.655675i
$326$	−13.0162	−	7.51490i	−0.720900	−	0.416212i
$327$	0.784779	−	18.3227i	0.0433984	−	1.01325i
$328$	−4.54200	+	2.62233i	−0.250790	+	0.144794i
$329$	5.74786	−	11.4196i	0.316890	−	0.629581i
$330$	−10.0339	+	5.23388i	−0.552348	+	0.288116i
$331$		−	31.5767i		−	1.73561i	−0.496904	−	0.867806i	$-0.665530\pi$
$331$		−	31.5767i		−	1.73561i	0.496904	−	0.867806i	$-0.334470\pi$
$332$	7.98589	−	4.61065i	0.438283	−	0.253043i
$333$	15.0317	−	7.03976i	0.823733	−	0.385776i
$334$			16.8933i			0.924361i
$335$	−7.33592	−	12.7062i	−0.400804	−	0.694214i
$336$	3.93503	−	2.34852i	0.214673	−	0.128122i
$337$	18.8701			1.02792			0.513961	−	0.857814i	$-0.328178\pi$
$337$	18.8701			1.02792			0.513961	+	0.857814i	$0.328178\pi$
$338$	11.2087	+	6.58528i	0.609671	+	0.358192i
$339$	−0.229644	+	5.36166i	−0.0124726	+	0.291205i
$340$		−	6.34676i		−	0.344201i
$341$	21.9337	−	37.9902i	1.18777	−	2.05729i
$342$	−8.40179	−	17.9400i	−0.454317	−	0.970085i
$343$	3.16729	+	18.2474i	0.171018	+	0.985268i
$344$	1.72068	−	2.98031i	0.0927730	−	0.160688i
$345$	2.74381	+	5.26016i	0.147722	+	0.283197i
$346$	0.256422	−	0.444137i	0.0137854	−	0.0238769i
$347$	5.05923	−	2.92095i	0.271594	−	0.156805i	−0.358018	−	0.933715i	$-0.616547\pi$
$347$	5.05923	−	2.92095i	0.271594	−	0.156805i	0.629612	+	0.776910i	$0.283214\pi$
$348$	−0.0664792	+	1.55213i	−0.00356366	+	0.0832032i
$349$	4.14640	+	7.18177i	0.221952	+	0.384431i	0.955400	−	0.295313i	$-0.0954240\pi$
$349$	4.14640	+	7.18177i	0.221952	+	0.384431i	−0.733449	+	0.679745i	$0.762091\pi$
$350$	8.01291	+	4.03317i	0.428308	+	0.215582i
$351$	−14.8784	+	11.3857i	−0.794150	+	0.607722i
$352$	2.57517	+	4.46032i	0.137257	+	0.237736i
$353$			21.8468i			1.16279i	0.813623	+	0.581393i	$0.197492\pi$
$353$			21.8468i			1.16279i	−0.813623	+	0.581393i	$0.802508\pi$
$354$	18.1725	−	9.47917i	0.965859	−	0.503812i
$355$			9.61880i			0.510513i
$356$		−	8.30846i		−	0.440348i
$357$	0.332021	+	22.9237i	0.0175724	+	1.21325i
$358$	−6.94512	−	4.00977i	−0.367061	−	0.211923i
$359$	10.1960	+	17.6599i	0.538122	+	0.932055i	0.999005	+	0.0445941i	$0.0141995\pi$
$359$	10.1960	+	17.6599i	0.538122	+	0.932055i	−0.460883	+	0.887461i	$0.652467\pi$
$360$	0.325420	−	3.79193i	0.0171511	−	0.199852i
$361$	24.6038			1.29494
$362$	0.397570	+	0.229537i	0.0208958	+	0.0120642i
$363$	12.4370	+	23.8429i	0.652771	+	1.25143i
$364$	9.06916	−	2.95810i	0.475353	−	0.155047i
$365$		−	0.534840i		−	0.0279948i
$366$	−0.345948	+	8.07708i	−0.0180830	+	0.422196i
$367$		−	16.3802i		−	0.855040i	−0.904006	−	0.427520i	$-0.859387\pi$
$367$		−	16.3802i		−	0.855040i	0.904006	−	0.427520i	$-0.140613\pi$
$368$	2.33827	−	1.35000i	0.121891	−	0.0703737i
$369$	1.34533	−	15.6763i	0.0700351	−	0.816078i
$370$	−3.50954	+	6.07870i	−0.182452	+	0.316017i
$371$	−35.7314	+	2.04920i	−1.85508	+	0.106389i
$372$	6.82280	+	13.0800i	0.353746	+	0.678167i
$373$	−14.1392			−0.732102			−0.366051	−	0.930595i	$-0.619290\pi$
$373$	−14.1392			−0.732102			−0.366051	+	0.930595i	$0.619290\pi$
$374$	−25.7665			−1.33235
$375$	16.3466	−	8.52672i	0.844134	−	0.440318i
$376$	−4.18472	+	2.41605i	−0.215811	+	0.124598i
$377$	−0.848869	+	3.12059i	−0.0437190	+	0.160719i
$378$	−0.977005	+	13.7130i	−0.0502517	+	0.705319i
$379$	9.57195	−	5.52637i	0.491678	−	0.283871i	−0.233592	−	0.972335i	$-0.575048\pi$
$379$	9.57195	−	5.52637i	0.491678	−	0.283871i	0.725270	+	0.688464i	$0.241715\pi$
$380$	7.25479	+	4.18856i	0.372163	+	0.214868i
$381$	−10.9188	+	17.1705i	−0.559387	+	0.879669i
$382$	8.74352	+	5.04808i	0.447358	+	0.258282i
$383$			0.956273i			0.0488633i	0.999702	+	0.0244316i	$0.00777760\pi$
$383$			0.956273i			0.0488633i	−0.999702	+	0.0244316i	$0.992222\pi$
$384$	−1.73046	−	0.0741172i	−0.0883074	−	0.00378228i
$385$	−7.77208	+	15.4412i	−0.396102	+	0.786956i
$386$	7.17088	+	4.14011i	0.364988	+	0.210726i
$387$	4.37865	+	9.34957i	0.222579	+	0.475265i
$388$	12.4202			0.630540
$389$	2.35900	+	1.36197i	0.119606	+	0.0690546i	0.558609	−	0.829431i	$-0.311335\pi$
$389$	2.35900	+	1.36197i	0.119606	+	0.0690546i	−0.439003	+	0.898485i	$0.644668\pi$
$390$	2.40476	−	7.54876i	0.121770	−	0.382246i
$391$			13.5078i			0.683119i
$392$	2.78400	−	6.42257i	0.140613	−	0.324389i
$393$	−4.38466	+	6.89514i	−0.221177	+	0.347814i
$394$	14.1470			0.712716
$395$	6.48222	+	3.74251i	0.326156	+	0.188306i
$396$	−15.3944	−	1.32113i	−0.773598	−	0.0663895i
$397$	−24.2523			−1.21719			−0.608593	−	0.793482i	$-0.708266\pi$
$397$	−24.2523			−1.21719			−0.608593	+	0.793482i	$0.708266\pi$
$398$			15.3246i			0.768150i
$399$	−26.4225	−	14.7490i	−1.32278	−	0.738373i
$400$	−1.69530	−	2.93635i	−0.0847650	−	0.146817i
$401$	16.4158	−	28.4331i	0.819768	−	1.41988i	−0.0860853	−	0.996288i	$-0.527436\pi$
$401$	16.4158	−	28.4331i	0.819768	−	1.41988i	0.905853	−	0.423592i	$-0.139231\pi$
$402$	0.857180	−	20.0131i	0.0427523	−	0.998165i
$403$	7.83564	+	29.6934i	0.390321	+	1.47913i
$404$	4.72713	+	8.18763i	0.235183	+	0.407350i
$405$	8.77066	+	7.31006i	0.435818	+	0.363240i
$406$	1.30227	+	1.98386i	0.0646308	+	0.0984571i
$407$	24.6782	+	14.2480i	1.22325	+	0.706246i
$408$	4.64977	−	7.31204i	0.230198	−	0.362000i
$409$	−9.97381	−	17.2752i	−0.493173	−	0.854201i	0.506796	−	0.862066i	$-0.330830\pi$
$409$	−9.97381	−	17.2752i	−0.493173	−	0.854201i	−0.999969	+	0.00786485i	$0.997497\pi$
$410$	3.32674	+	5.76208i	0.164296	+	0.284569i
$411$	−8.93979	+	14.0583i	−0.440967	+	0.693447i
$412$	15.4442	+	8.91672i	0.760881	+	0.439295i
$413$	14.0761	−	27.9658i	0.692641	−	1.37611i
$414$	−0.692590	+	8.07035i	−0.0340390	+	0.396636i
$415$	−5.84918	−	10.1311i	−0.287125	−	0.497315i
$416$	−3.47913	−	0.946398i	−0.170578	−	0.0464010i
$417$	−0.155253	+	3.62480i	−0.00760278	+	0.177507i
$418$	17.0046	−	29.4529i	0.831724	−	1.44059i
$419$	−2.15496	−	3.73250i	−0.105277	−	0.182345i	0.808574	−	0.588394i	$-0.200240\pi$
$419$	−2.15496	−	3.73250i	−0.105277	−	0.182345i	−0.913851	+	0.406049i	$0.866906\pi$
$420$	−2.97939	−	4.99206i	−0.145379	−	0.243588i
$421$		−	9.35440i		−	0.455905i	−0.973672	−	0.227953i	$-0.926797\pi$
$421$		−	9.35440i		−	0.455905i	0.973672	−	0.227953i	$-0.0732032\pi$
$422$	−9.26032			−0.450786
$423$	1.23950	−	14.4432i	0.0602667	−	0.702253i
$424$	11.7150	+	6.76369i	0.568933	+	0.328474i
$425$	16.9628			0.822815
$426$	−7.04694	+	11.0817i	−0.341426	+	0.536912i
$427$	6.77684	+	10.3237i	0.327954	+	0.499598i
$428$		−	9.73378i		−	0.470500i
$429$	−30.6463	−	9.76282i	−1.47962	−	0.471353i
$430$	−3.78089	−	2.18290i	−0.182331	−	0.105269i
$431$	−0.867937			−0.0418070			−0.0209035	−	0.999781i	$-0.506654\pi$
$431$	−0.867937			−0.0418070			−0.0209035	+	0.999781i	$0.506654\pi$
$432$	3.15296	−	4.13023i	0.151697	−	0.198716i
$433$	20.7610	+	11.9864i	0.997710	+	0.576028i	0.907570	−	0.419901i	$-0.137935\pi$
$433$	20.7610	+	11.9864i	0.997710	+	0.576028i	0.0901401	+	0.995929i	$0.471269\pi$
$434$	20.1289	+	10.1316i	0.966217	+	0.486330i
$435$	1.96907	+	0.0843370i	0.0944098	+	0.00404365i
$436$			10.5883i			0.507090i
$437$	−15.4404	−	8.91450i	−0.738613	−	0.426438i
$438$	0.391836	−	0.616185i	0.0187226	−	0.0294424i
$439$	15.7085	+	9.06933i	0.749727	+	0.432855i	0.825595	−	0.564263i	$-0.190839\pi$
$439$	15.7085	+	9.06933i	0.749727	+	0.432855i	−0.0758680	+	0.997118i	$0.524173\pi$
$440$	5.65846	−	3.26691i	0.269756	−	0.155744i
$441$	11.0223	+	17.8748i	0.524872	+	0.851181i
$442$	12.8032	−	12.7064i	0.608987	−	0.604381i
$443$	−25.1388	+	14.5139i	−1.19438	+	0.689575i	−0.959297	−	0.282401i	$-0.908869\pi$
$443$	−25.1388	+	14.5139i	−1.19438	+	0.689575i	−0.235082	+	0.971975i	$0.575536\pi$
$444$	−8.49670	+	4.43205i	−0.403235	+	0.210336i
$445$	−10.5403			−0.499658
$446$	13.1739			0.623802
$447$	−6.17309	−	11.8344i	−0.291977	−	0.559750i
$448$	−2.21179	+	1.45190i	−0.104497	+	0.0685956i
$449$	1.47303	−	2.55136i	0.0695165	−	0.120406i	−0.829172	−	0.558993i	$-0.811188\pi$
$449$	1.47303	−	2.55136i	0.0695165	−	0.120406i	0.898689	+	0.438587i	$0.144521\pi$
$450$	10.1345	+	0.869738i	0.477747	+	0.0409998i
$451$	23.3928	−	13.5059i	1.10153	−	0.635966i
$452$		−	3.09839i		−	0.145736i
$453$	0.0449942	−	1.05051i	0.00211401	−	0.0493572i
$454$		−	2.37069i		−	0.111262i
$455$	−3.75271	−	11.5053i	−0.175930	−	0.539378i
$456$	5.28955	+	10.1406i	0.247706	+	0.474878i
$457$	16.7927	+	9.69524i	0.785527	+	0.453524i	0.838386	−	0.545078i	$-0.183500\pi$
$457$	16.7927	+	9.69524i	0.785527	+	0.453524i	−0.0528584	+	0.998602i	$0.516833\pi$
$458$	11.8291			0.552736
$459$	10.0078	+	23.9921i	0.467124	+	1.11986i
$460$	−1.71264	−	2.96638i	−0.0798523	−	0.138308i
$461$	18.5093	+	10.6864i	0.862066	+	0.497714i	0.864704	−	0.502283i	$-0.167506\pi$
$461$	18.5093	+	10.6864i	0.862066	+	0.497714i	−0.00263775	+	0.999997i	$0.500840\pi$
$462$	−20.2667	+	12.0957i	−0.942892	+	0.562742i
$463$			7.17045i			0.333239i	0.986021	+	0.166620i	$0.0532852\pi$
$463$			7.17045i			0.333239i	−0.986021	+	0.166620i	$0.946715\pi$
$464$		−	0.896947i		−	0.0416397i
$465$	16.5936	−	8.65555i	0.769509	−	0.401392i
$466$		−	7.90323i		−	0.366110i
$467$	−4.50077	−	7.79557i	−0.208271	−	0.360736i	0.742899	−	0.669404i	$-0.233450\pi$
$467$	−4.50077	−	7.79557i	−0.208271	−	0.360736i	−0.951170	+	0.308668i	$0.900117\pi$
$468$	8.30089	−	6.93507i	0.383709	−	0.320574i
$469$	−16.7915	−	25.5797i	−0.775357	−	1.18116i
$470$	3.06505	+	5.30883i	0.141380	+	0.244878i
$471$	−0.989185	+	23.0952i	−0.0455792	+	1.06417i
$472$	−10.2481	+	5.91675i	−0.471708	+	0.272341i
$473$	−8.86209	+	15.3496i	−0.407479	+	0.705775i
$474$	4.72626	+	9.06072i	0.217084	+	0.416173i
$475$	−11.1946	+	19.3896i	−0.513644	+	0.889657i
$476$	−0.757863	−	13.2147i	−0.0347366	−	0.605693i
$477$	−36.7514	+	17.2117i	−1.68273	+	0.788068i
$478$	−13.6510	+	23.6441i	−0.624380	+	1.08146i
$479$			4.04149i			0.184661i	0.995728	+	0.0923303i	$0.0294316\pi$
$479$			4.04149i			0.184661i	−0.995728	+	0.0923303i	$0.970568\pi$
$480$	−0.0940267	+	2.19530i	−0.00429171	+	0.100201i
$481$	−19.2887	+	5.08999i	−0.879487	+	0.232083i
$482$	11.2815			0.513859
$483$	6.34102	+	10.6246i	0.288526	+	0.483436i
$484$	−7.76296	−	13.4458i	−0.352862	−	0.611175i
$485$		−	15.7565i		−	0.715467i
$486$	4.74909	+	14.8474i	0.215423	+	0.673493i
$487$	11.8663	−	6.85100i	0.537713	−	0.310449i	−0.206439	−	0.978460i	$-0.566187\pi$
$487$	11.8663	−	6.85100i	0.537713	−	0.310449i	0.744151	+	0.668011i	$0.232854\pi$
$488$		−	4.66758i		−	0.211291i
$489$	−23.0810	+	12.0395i	−1.04376	+	0.544447i
$490$	−8.14781	−	3.53184i	−0.368080	−	0.159552i
$491$	−19.4095	+	11.2061i	−0.875940	+	0.505724i	−0.869318	−	0.494254i	$-0.835441\pi$
$491$	−19.4095	+	11.2061i	−0.875940	+	0.505724i	−0.00662258	+	0.999978i	$0.502108\pi$
$492$	−0.388719	+	9.07568i	−0.0175248	+	0.409163i
$493$	3.88613	+	2.24366i	0.175023	+	0.101049i
$494$	6.07478	+	23.0206i	0.273317	+	1.03574i
$495$	−1.67602	+	19.5297i	−0.0753315	+	0.877794i
$496$	−4.25869	−	7.37627i	−0.191221	−	0.331204i
$497$	1.14858	+	20.0274i	0.0515207	+	0.898352i
$498$	0.683458	−	15.9571i	0.0306265	−	0.715057i
$499$	−17.1062	+	9.87625i	−0.765777	+	0.442122i	−0.831366	−	0.555725i	$-0.812441\pi$
$499$	−17.1062	+	9.87625i	−0.765777	+	0.442122i	0.0655891	+	0.997847i	$0.479107\pi$
$500$	−9.21840	+	5.32225i	−0.412260	+	0.238018i
$501$	24.6907	+	15.7010i	1.10310	+	0.701468i
$502$	−11.3067	−	19.5838i	−0.504644	−	0.874069i
$503$	3.11599	−	5.39705i	0.138935	−	0.240643i	−0.788159	−	0.615472i	$-0.788965\pi$
$503$	3.11599	−	5.39705i	0.138935	−	0.240643i	0.927094	+	0.374829i	$0.122299\pi$
$504$	0.224768	−	7.93407i	0.0100120	−	0.353412i
$505$	10.3870	−	5.99694i	0.462215	−	0.266860i
$506$	−12.0429	+	6.95296i	−0.535371	+	0.309097i
$507$	20.0424	−	10.2617i	0.890113	−	0.455739i
$508$	5.87399	−	10.1740i	0.260616	−	0.451400i
$509$	−14.0059	−	8.08631i	−0.620800	−	0.358419i	0.156380	−	0.987697i	$-0.450018\pi$
$509$	−14.0059	−	8.08631i	−0.620800	−	0.358419i	−0.777181	+	0.629278i	$0.783351\pi$
$510$	−9.27622	−	5.89880i	−0.410758	−	0.261203i
$511$	−0.0638650	−	1.11360i	−0.00282522	−	0.0492626i
$512$	1.00000			0.0441942
$513$	−34.0293	−	4.39402i	−1.50243	−	0.194001i
$514$	−0.682789	−	1.18262i	−0.0301165	−	0.0521633i
$515$	11.3119	−	19.5929i	0.498464	−	0.863364i
$516$	−2.75669	−	5.28485i	−0.121356	−	0.232653i
$517$	21.5527	−	12.4435i	0.947887	−	0.547263i
$518$	−6.58140	+	13.0756i	−0.289170	+	0.574509i
$519$	−0.410812	−	0.787568i	−0.0180326	−	0.0345704i
$520$	−1.20062	+	4.41370i	−0.0526507	+	0.193553i
$521$	−8.95460	+	15.5098i	−0.392308	+	0.679498i	−0.992754	−	0.120168i	$-0.961657\pi$
$521$	−8.95460	+	15.5098i	−0.392308	+	0.679498i	0.600445	+	0.799666i	$0.294990\pi$
$522$	2.20676	+	1.53975i	0.0965874	+	0.0673930i
$523$	13.2622	+	7.65695i	0.579917	+	0.334815i	0.761100	−	0.648634i	$-0.224660\pi$
$523$	13.2622	+	7.65695i	0.579917	+	0.334815i	−0.181184	+	0.983449i	$0.557993\pi$
$524$	2.35882	−	4.08559i	0.103045	−	0.178480i
$525$	13.3421	−	7.96290i	0.582297	−	0.347529i
$526$	−9.36276	−	5.40559i	−0.408236	−	0.235695i
$527$	42.6114			1.85618
$528$	8.91247	+	0.381728i	0.387865	+	0.0166126i
$529$	−7.85499	−	13.6052i	−0.341521	−	0.591532i
$530$	8.58056	−	14.8620i	0.372716	−	0.645562i
$531$	3.03547	−	35.3705i	0.131728	−	1.53495i
$532$	15.6054	+	7.85475i	0.676581	+	0.340547i
$533$	−4.96353	+	18.2468i	−0.214994	+	0.790357i
$534$	−12.1434	−	7.72205i	−0.525495	−	0.334166i
$535$	−12.3485			−0.533872
$536$			11.5652i			0.499540i
$537$	−12.3155	+	6.42400i	−0.531452	+	0.277216i
$538$	22.9534			0.989592
$539$	−14.3385	+	33.0784i	−0.617603	+	1.42479i
$540$	−5.23970	−	3.99991i	−0.225481	−	0.172129i
$541$	3.16570	−	1.82772i	0.136104	−	0.0785797i	−0.430402	−	0.902637i	$-0.641628\pi$
$541$	3.16570	−	1.82772i	0.136104	−	0.0785797i	0.566506	+	0.824058i	$0.308295\pi$
$542$	−7.79637	−	13.5037i	−0.334883	−	0.580034i
$543$	0.704993	−	0.367739i	0.0302542	−	0.0157812i
$544$	−2.50144	+	4.33262i	−0.107248	+	0.185760i
$545$	13.4326			0.575389
$546$	4.10559	−	16.0045i	0.175703	−	0.684930i
$547$	−44.4370			−1.89999			−0.949995	−	0.312265i	$-0.898912\pi$
$547$	−44.4370			−1.89999			−0.949995	+	0.312265i	$0.898912\pi$
$548$	4.80934	−	8.33002i	0.205445	−	0.355841i
$549$	11.4837	+	8.01262i	0.490111	+	0.341970i
$550$	8.73136	+	15.1232i	0.372306	+	0.644853i
$551$	−5.12932	+	2.96141i	−0.218516	+	0.126160i
$552$	0.200117	−	4.67226i	0.00851754	−	0.198865i
$553$	13.9436	+	7.01828i	0.592942	+	0.298448i
$554$	22.3309			0.948750
$555$	5.62260	+	10.7791i	0.238666	+	0.457547i
$556$		−	2.09470i		−	0.0888349i
$557$	1.87782			0.0795659			0.0397830	−	0.999208i	$-0.487333\pi$
$557$	1.87782			0.0795659			0.0397830	+	0.999208i	$0.487333\pi$
$558$	25.4586	+	2.18483i	1.07775	+	0.0924913i
$559$	−3.16592	−	11.9973i	−0.133904	−	0.507433i
$560$	1.84191	+	2.80592i	0.0778347	+	0.118572i
$561$	−23.9479	+	37.6595i	−1.01108	+	1.58998i
$562$	−10.8993	+	18.8782i	−0.459760	+	0.796328i
$563$	−3.09884	−	5.36735i	−0.130601	−	0.226207i	0.793308	−	0.608821i	$-0.208357\pi$
$563$	−3.09884	−	5.36735i	−0.130601	−	0.226207i	−0.923908	+	0.382614i	$0.875024\pi$
$564$	−0.358142	+	8.36178i	−0.0150805	+	0.352094i
$565$	−3.93069			−0.165365
$566$	−3.89678	−	2.24981i	−0.163794	−	0.0945664i
$567$	19.1344	+	14.1731i	0.803568	+	0.595212i
$568$	3.79105	−	6.56628i	0.159069	−	0.275515i
$569$	−5.68369	−	3.28148i	−0.238272	−	0.137567i	0.376110	−	0.926575i	$-0.377261\pi$
$569$	−5.68369	−	3.28148i	−0.238272	−	0.137567i	−0.614383	+	0.789008i	$0.710595\pi$
$570$	12.8646	−	6.71044i	0.538839	−	0.281069i
$571$	−8.90567	+	15.4251i	−0.372691	+	0.645519i	−0.989978	−	0.141218i	$-0.954898\pi$
$571$	−8.90567	+	15.4251i	−0.372691	+	0.645519i	0.617288	+	0.786737i	$0.288231\pi$
$572$	17.9187	+	4.87426i	0.749217	+	0.203803i
$573$	15.5045	−	8.08747i	0.647710	−	0.337859i
$574$	7.61469	+	11.6001i	0.317831	+	0.484177i
$575$	7.92815	−	4.57732i	0.330627	−	0.190887i
$576$	−1.71665	+	2.46030i	−0.0715273	+	0.102513i
$577$	1.86181	−	3.22475i	0.0775082	−	0.134248i	−0.824666	−	0.565620i	$-0.808637\pi$
$577$	1.86181	−	3.22475i	0.0775082	−	0.134248i	0.902174	+	0.431372i	$0.141970\pi$
$578$	−4.01440	−	6.95314i	−0.166977	−	0.289212i
$579$	12.7158	−	6.63282i	0.528451	−	0.275651i
$580$	−1.13789			−0.0472482
$581$	−13.3884	−	20.3956i	−0.555444	−	0.846151i
$582$	11.5436	−	18.1530i	0.478497	−	0.752464i
$583$	−60.3364	−	34.8352i	−2.49888	−	1.44273i
$584$	−0.210796	+	0.365109i	−0.00872279	+	0.0151083i
$585$	−8.79798	−	10.5307i	−0.363752	−	0.435390i
$586$	11.6501	−	6.72621i	0.481263	−	0.277857i
$587$	36.8272	−	21.2622i	1.52002	−	0.877585i	0.520301	−	0.853983i	$-0.325820\pi$
$587$	36.8272	−	21.2622i	1.52002	−	0.877585i	0.999721	−	0.0236021i	$-0.00751349\pi$
$588$	−6.79951	−	10.0383i	−0.280407	−	0.413971i
$589$	−28.1215	+	48.7078i	−1.15873	+	2.00697i
$590$	7.50612	+	13.0010i	0.309022	+	0.535242i
$591$	13.1485	−	20.6768i	0.540857	−	0.850530i
$592$	4.79158	−	2.76642i	0.196933	−	0.113699i
$593$	−23.8770	+	13.7854i	−0.980509	+	0.566097i	−0.902424	−	0.430850i	$-0.858214\pi$
$593$	−23.8770	+	13.7854i	−0.980509	+	0.566097i	−0.0780852	+	0.996947i	$0.524881\pi$
$594$	−16.2388	+	21.2721i	−0.666286	+	0.872804i
$595$	−16.7644	+	0.961442i	−0.687273	+	0.0394153i
$596$	3.85315	+	6.67385i	0.157831	+	0.273371i
$597$	22.3979	+	14.2429i	0.916684	+	0.582925i
$598$	2.55528	−	9.39366i	0.104493	−	0.384135i
$599$	7.32482	+	4.22899i	0.299284	+	0.172792i	0.642121	−	0.766603i	$-0.278055\pi$
$599$	7.32482	+	4.22899i	0.299284	+	0.172792i	−0.342837	+	0.939395i	$0.611388\pi$
$600$	−5.86731	−	0.251302i	−0.239532	−	0.0102594i
$601$	12.8550	−	7.42186i	0.524368	−	0.302744i	−0.214352	−	0.976756i	$-0.568764\pi$
$601$	12.8550	−	7.42186i	0.524368	−	0.302744i	0.738720	+	0.674013i	$0.235431\pi$
$602$	−8.13288	−	4.09356i	−0.331472	−	0.166841i
$603$	−28.4539	−	19.8534i	−1.15873	−	0.808494i
$604$			0.607068i			0.0247012i
$605$	−17.0577	+	9.84826i	−0.693494	+	0.400389i
$606$	16.3603	+	0.700723i	0.664590	+	0.0284649i
$607$			27.1759i			1.10303i	0.834164	+	0.551517i	$0.185951\pi$
$607$			27.1759i			1.10303i	−0.834164	+	0.551517i	$0.814049\pi$
$608$	−3.30166	−	5.71864i	−0.133900	−	0.231922i
$609$	4.10990	−	0.0595268i	0.166541	−	0.00241215i
$610$	−5.92139			−0.239750
$611$	−4.57309	+	16.8115i	−0.185007	+	0.680120i
$612$	−6.36546	−	13.5919i	−0.257308	−	0.549421i
$613$		−	14.7974i		−	0.597661i	−0.954306	−	0.298830i	$-0.903403\pi$
$613$		−	14.7974i		−	0.597661i	0.954306	−	0.298830i	$-0.0965965\pi$
$614$	7.90334	−	13.6890i	0.318953	−	0.552443i
$615$	11.5136	+	0.493138i	0.464274	+	0.0198852i
$616$	11.3914	−	7.47775i	0.458974	−	0.301287i
$617$	−10.4145	+	18.0385i	−0.419272	+	0.726201i	−0.995866	−	0.0908296i	$-0.971048\pi$
$617$	−10.4145	+	18.0385i	−0.419272	+	0.726201i	0.576594	+	0.817031i	$0.304381\pi$
$618$	27.3865	−	14.2854i	1.10165	−	0.574642i
$619$	−13.6057	+	23.5658i	−0.546860	+	0.947189i	0.451627	+	0.892207i	$0.350844\pi$
$619$	−13.6057	+	23.5658i	−0.546860	+	0.947189i	−0.998487	+	0.0549827i	$0.982490\pi$
$620$	−9.35769	+	5.40267i	−0.375814	+	0.216976i
$621$	11.1517	+	8.51301i	0.447500	+	0.341615i
$622$	13.1198	+	22.7241i	0.526055	+	0.911154i
$623$	−21.9461	+	1.25861i	−0.879251	+	0.0504252i
$624$	−4.61679	+	4.20538i	−0.184820	+	0.168350i
$625$	−1.72458	−	2.98706i	−0.0689832	−	0.119482i
$626$		−	16.5040i		−	0.659633i
$627$	−27.2430	−	52.2275i	−1.08798	−	2.08577i
$628$		−	13.3462i		−	0.532572i
$629$			27.6801i			1.10368i
$630$	−10.0653	−	0.285146i	−0.401012	−	0.0113605i
$631$	−23.4710	−	13.5510i	−0.934365	−	0.539456i	−0.0461755	−	0.998933i	$-0.514703\pi$
$631$	−23.4710	−	13.5510i	−0.934365	−	0.539456i	−0.888189	+	0.459478i	$0.848037\pi$
$632$	−2.95006	−	5.10965i	−0.117347	−	0.203251i
$633$	−8.60673	+	13.5346i	−0.342087	+	0.537952i
$634$	−29.6571			−1.17783
$635$	−12.9070	−	7.45186i	−0.512199	−	0.295718i
$636$	20.7738	−	10.8360i	0.823734	−	0.429677i
$637$	−9.18741	−	23.5073i	−0.364018	−	0.931392i
$638$			4.61958i			0.182891i
$639$	9.64714	+	20.5992i	0.381635	+	0.814890i
$640$		−	1.26862i		−	0.0501467i
$641$	5.52077	−	3.18742i	0.218057	−	0.125895i	−0.386993	−	0.922083i	$-0.626486\pi$
$641$	5.52077	−	3.18742i	0.218057	−	0.125895i	0.605050	+	0.796187i	$0.293153\pi$
$642$	−14.2266	−	9.04677i	−0.561478	−	0.357047i
$643$	−21.5821	+	37.3812i	−0.851113	+	1.47417i	0.0290911	+	0.999577i	$0.490739\pi$
$643$	−21.5821	+	37.3812i	−0.851113	+	1.47417i	−0.880204	+	0.474595i	$0.842595\pi$
$644$	−3.92013	−	5.97183i	−0.154475	−	0.235323i
$645$	−6.70448	+	3.49719i	−0.263989	+	0.137702i
$646$	33.0356			1.29977
$647$	−21.2183			−0.834178			−0.417089	−	0.908866i	$-0.636950\pi$
$647$	−21.2183			−0.834178			−0.417089	+	0.908866i	$0.636950\pi$
$648$	−3.10619	−	8.44699i	−0.122023	−	0.331829i
$649$	52.7812	−	30.4732i	2.07184	−	1.19618i
$650$	−11.7963	−	3.20886i	−0.462690	−	0.125862i
$651$	33.5161	−	20.0033i	1.31360	−	0.783989i
$652$	13.0162	−	7.51490i	0.509753	−	0.294306i
$653$	34.5174	+	19.9286i	1.35077	+	0.779867i	0.988357	−	0.152152i	$-0.0486202\pi$
$653$	34.5174	+	19.9286i	1.35077	+	0.779867i	0.362411	+	0.932018i	$0.381954\pi$
$654$	15.4756	+	9.84101i	0.605143	+	0.384814i
$655$	−5.18307	−	2.99245i	−0.202519	−	0.116925i
$656$		−	5.24465i		−	0.204769i
$657$	−0.536416	−	1.14539i	−0.0209276	−	0.0446859i
$658$	7.01571	+	10.6876i	0.273501	+	0.416645i
$659$	29.9716	+	17.3041i	1.16753	+	0.674072i	0.953096	−	0.302667i	$-0.0978769\pi$
$659$	29.9716	+	17.3041i	1.16753	+	0.674072i	0.214431	+	0.976739i	$0.431210\pi$
$660$	0.484269	−	11.3065i	0.0188501	−	0.440107i
$661$	19.1960			0.746639			0.373319	−	0.927703i	$-0.378220\pi$
$661$	19.1960			0.746639			0.373319	+	0.927703i	$0.378220\pi$
$662$	27.3462	+	15.7883i	1.06284	+	0.613631i
$663$	−6.67168	−	30.5223i	−0.259107	−	1.18539i
$664$			9.22131i			0.357856i
$665$	9.96470	−	19.7974i	0.386415	−	0.767710i
$666$	−1.41925	+	16.5377i	−0.0549950	+	0.640824i
$667$	2.42176			0.0937710
$668$	−14.6300	−	8.44665i	−0.566053	−	0.326811i
$669$	12.2441	−	19.2545i	0.473383	−	0.744423i
$670$	14.6718			0.566823
$671$			24.0396i			0.928038i
$672$	0.0663661	+	4.58210i	0.00256013	+	0.176758i
$673$	10.3779	+	17.9751i	0.400039	+	0.692888i	0.993730	−	0.111805i	$-0.0356632\pi$
$673$	10.3779	+	17.9751i	0.400039	+	0.692888i	−0.593691	+	0.804693i	$0.702330\pi$
$674$	−9.43507	+	16.3420i	−0.363425	+	0.629471i
$675$	10.6904	−	14.0040i	0.411475	−	0.539013i
$676$	−11.3073	+	6.41435i	−0.434898	+	0.246706i
$677$	−3.91466	−	6.78038i	−0.150452	−	0.260591i	0.780941	−	0.624604i	$-0.214740\pi$
$677$	−3.91466	−	6.78038i	−0.150452	−	0.260591i	−0.931394	+	0.364013i	$0.881406\pi$
$678$	−4.52851	−	2.87971i	−0.173916	−	0.110594i
$679$	−1.88148	−	32.8068i	−0.0722046	−	1.25901i
$680$	5.49645	+	3.17338i	0.210779	+	0.121694i
$681$	−3.46493	−	2.20337i	−0.132776	−	0.0844333i
$682$	21.9337	+	37.9902i	0.839884	+	1.45472i
$683$	−12.7341	−	22.0560i	−0.487255	−	0.843951i	0.512637	−	0.858605i	$-0.328669\pi$
$683$	−12.7341	−	22.0560i	−0.487255	−	0.843951i	−0.999893	+	0.0146544i	$0.995335\pi$
$684$	19.7374	+	1.69385i	0.754679	+	0.0647659i
$685$	−10.5676	−	6.10123i	−0.403769	−	0.233116i
$686$	−17.3864	−	6.38076i	−0.663815	−	0.243618i
$687$	10.9942	−	17.2890i	0.419454	−	0.659616i
$688$	1.72068	+	2.98031i	0.0656004	+	0.113623i
$689$	47.1593	−	12.4446i	1.79663	−	0.474103i
$690$	−5.92733	−	0.253873i	−0.225650	−	0.00966477i
$691$	−9.17151	+	15.8855i	−0.348901	+	0.604314i	−0.986054	−	0.166423i	$-0.946778\pi$
$691$	−9.17151	+	15.8855i	−0.348901	+	0.604314i	0.637154	+	0.770737i	$0.280112\pi$
$692$	0.256422	+	0.444137i	0.00974772	+	0.0168835i
$693$	−1.15763	+	40.8631i	−0.0439748	+	1.55226i
$694$			5.84190i			0.221755i
$695$	−2.65738			−0.100800
$696$	−1.31095	−	0.833640i	−0.0496914	−	0.0315990i
$697$	22.7231	+	13.1192i	0.860698	+	0.496924i
$698$	−8.29279			−0.313887
$699$	−11.5511	−	7.34542i	−0.436903	−	0.277829i
$700$	−7.49928	+	4.92280i	−0.283446	+	0.186064i
$701$			4.16816i			0.157429i	0.996897	+	0.0787147i	$0.0250816\pi$
$701$			4.16816i			0.157429i	−0.996897	+	0.0787147i	$0.974918\pi$
$702$	−2.42107	−	18.5779i	−0.0913774	−	0.701178i
$703$	−31.6403	−	18.2676i	−1.19334	−	0.688974i
$704$	−5.15033			−0.194110
$705$	10.6079	+	0.454347i	0.399518	+	0.0171117i
$706$	−18.9199	−	10.9234i	−0.712058	−	0.411107i
$707$	20.9108	−	13.7266i	0.786431	−	0.516242i
$708$	−0.877067	+	20.4775i	−0.0329622	+	0.769590i
$709$		−	18.5084i		−	0.695097i	−0.937662	−	0.347549i	$-0.887014\pi$
$709$		−	18.5084i		−	0.695097i	0.937662	−	0.347549i	$-0.112986\pi$
$710$	−8.33013	−	4.80940i	−0.312624	−	0.180494i
$711$	17.6355	+	1.51347i	0.661384	+	0.0567594i
$712$	7.19534	+	4.15423i	0.269657	+	0.155686i
$713$	19.9160	−	11.4985i	0.745859	−	0.430622i
$714$	−20.0185	−	11.1743i	−0.749173	−	0.418187i
$715$	6.18360	−	22.7320i	0.231253	−	0.850129i
$716$	6.94512	−	4.00977i	0.259551	−	0.149852i
$717$	21.8701	+	41.9271i	0.816752	+	1.56580i
$718$	−20.3919			−0.761020
$719$	−10.0028			−0.373042			−0.186521	−	0.982451i	$-0.559721\pi$
$719$	−10.0028			−0.373042			−0.186521	+	0.982451i	$0.559721\pi$
$720$	3.12119	+	2.17779i	0.116320	+	0.0811613i
$721$	21.2131	−	42.1452i	0.790019	−	1.56957i
$722$	−12.3019	+	21.3075i	−0.457830	+	0.792984i
$723$	10.4853	−	16.4887i	0.389951	−	0.613222i
$724$	−0.397570	+	0.229537i	−0.0147756	+	0.00853068i
$725$		−	3.04119i		−	0.112947i
$726$	−26.8671	−	1.15074i	−0.997130	−	0.0427079i
$727$			27.8818i			1.03408i	0.855961	+	0.517040i	$0.172966\pi$
$727$			27.8818i			1.03408i	−0.855961	+	0.517040i	$0.827034\pi$
$728$	−1.97279	+	9.33317i	−0.0731164	+	0.345910i
$729$	26.1144	+	6.85838i	0.967201	+	0.254014i
$730$	0.463185	+	0.267420i	0.0171433	+	0.00989766i
$731$	−17.2167			−0.636784
$732$	−6.82198	−	4.33814i	−0.252148	−	0.160342i
$733$	−9.38772	−	16.2600i	−0.346743	−	0.600577i	0.638925	−	0.769269i	$-0.279379\pi$
$733$	−9.38772	−	16.2600i	−0.346743	−	0.600577i	−0.985669	+	0.168691i	$0.946046\pi$
$734$	14.1857	+	8.19011i	0.523603	+	0.302302i
$735$	−12.7348	+	8.62601i	−0.469728	+	0.318175i
$736$			2.70000i			0.0995235i
$737$		−	59.5646i		−	2.19409i
$738$	12.9034	+	9.00326i	0.474982	+	0.331415i
$739$		−	5.49624i		−	0.202183i	−0.994877	−	0.101091i	$-0.967767\pi$
$739$		−	5.49624i		−	0.202183i	0.994877	−	0.101091i	$-0.0322334\pi$
$740$	−3.50954	−	6.07870i	−0.129013	−	0.223458i
$741$	39.2921	+	12.5171i	1.44343	+	0.459826i
$742$	16.0910	−	31.9689i	0.590720	−	1.17361i
$743$	−9.12112	−	15.7982i	−0.334621	−	0.579581i	0.648791	−	0.760967i	$-0.275275\pi$
$743$	−9.12112	−	15.7982i	−0.334621	−	0.579581i	−0.983412	+	0.181386i	$0.941942\pi$
$744$	−14.7390	−	0.631285i	−0.540359	−	0.0231440i
$745$	8.46659	−	4.88819i	0.310192	−	0.179089i
$746$	7.06962	−	12.2449i	0.258837	−	0.448319i
$747$	−22.6872	−	15.8298i	−0.830082	−	0.579182i
$748$	12.8832	−	22.3144i	0.471058	−	0.815896i
$749$	−25.7109	+	1.47453i	−0.939457	+	0.0538780i
$750$	−0.788941	+	18.4199i	−0.0288080	+	0.672600i
$751$	10.2889	−	17.8210i	0.375449	−	0.650297i	−0.614945	−	0.788570i	$-0.710822\pi$
$751$	10.2889	−	17.8210i	0.375449	−	0.650297i	0.990394	+	0.138273i	$0.0441552\pi$
$752$		−	4.83210i		−	0.176209i
$753$	−39.1318	−	1.67605i	−1.42604	−	0.0610786i
$754$	−2.27808	−	2.29544i	−0.0829627	−	0.0835949i
$755$	0.770139			0.0280282
$756$	−11.3873	−	7.70259i	−0.414151	−	0.280141i
$757$	1.82325	+	3.15796i	0.0662672	+	0.114778i	0.897255	−	0.441512i	$-0.145558\pi$
$757$	1.82325	+	3.15796i	0.0662672	+	0.114778i	−0.830988	+	0.556290i	$0.812224\pi$
$758$			11.0527i			0.401454i
$759$	−1.03067	+	24.0637i	−0.0374109	+	0.873457i
$760$	−7.25479	+	4.18856i	−0.263159	+	0.151935i
$761$		−	45.9554i		−	1.66588i	−0.553363	−	0.832940i	$-0.686656\pi$
$761$		−	45.9554i		−	1.66588i	0.553363	−	0.832940i	$-0.313344\pi$
$762$	−9.41065	−	18.0412i	−0.340912	−	0.653563i
$763$	27.9682	−	1.60398i	1.01252	−	0.0580680i
$764$	−8.74352	+	5.04808i	−0.316330	+	0.182633i
$765$	−17.2430	+	8.07535i	−0.623422	+	0.291965i
$766$	−0.828157	−	0.478136i	−0.0299225	−	0.0172758i
$767$	−11.1992	+	41.1703i	−0.404380	+	1.48657i
$768$	0.929420	−	1.46157i	0.0335375	−	0.0527398i
$769$	3.19274	+	5.52999i	0.115133	+	0.199417i	0.917833	−	0.396967i	$-0.129937\pi$
$769$	3.19274	+	5.52999i	0.115133	+	0.199417i	−0.802700	+	0.596383i	$0.796604\pi$
$770$	−9.48643	−	14.4514i	−0.341867	−	0.520793i
$771$	−2.36308	−	0.101213i	−0.0851043	−	0.00364509i
$772$	−7.17088	+	4.14011i	−0.258086	+	0.149006i
$773$	7.77765	−	4.49043i	0.279743	−	0.161510i	−0.353564	−	0.935410i	$-0.615030\pi$
$773$	7.77765	−	4.49043i	0.279743	−	0.161510i	0.633307	+	0.773901i	$0.281697\pi$
$774$	−10.2863	−	0.882760i	−0.369733	−	0.0317302i
$775$	−14.4395	−	25.0100i	−0.518683	−	0.898385i
$776$	−6.21010	+	10.7562i	−0.222930	+	0.386125i
$777$	12.9940	+	21.7719i	0.466157	+	0.781062i
$778$	−2.35900	+	1.36197i	−0.0845742	+	0.0488289i
$779$	−29.9923	+	17.3161i	−1.07459	+	0.620412i
$780$	5.33503	+	5.85696i	0.191025	+	0.209713i
$781$	−19.5251	+	33.8185i	−0.698665	+	1.21012i
$782$	−11.6981	−	6.75390i	−0.418323	−	0.241519i
$783$	4.30145	−	1.79426i	0.153721	−	0.0641216i
$784$	4.17011	+	5.62230i	0.148932	+	0.200796i
$785$	−16.9313			−0.604304
$786$	−3.77904	−	7.24480i	−0.134794	−	0.258413i
$787$	12.6437	+	21.8996i	0.450700	+	0.780635i	0.998430	−	0.0560203i	$-0.0178411\pi$
$787$	12.6437	+	21.8996i	0.450700	+	0.780635i	−0.547730	+	0.836655i	$0.684508\pi$
$788$	−7.07350	+	12.2517i	−0.251983	+	0.436448i
$789$	−16.6026	+	8.66024i	−0.591067	+	0.308313i
$790$	−6.48222	+	3.74251i	−0.230627	+	0.133152i
$791$	−8.18413	+	0.469361i	−0.290994	+	0.0166886i
$792$	8.84134	−	12.6714i	0.314163	−	0.450258i
$793$	−11.8548	−	11.9451i	−0.420976	−	0.424184i
$794$	12.1261	−	21.0031i	0.430340	−	0.745371i
$795$	−13.7468	−	26.3541i	−0.487550	−	0.934682i
$796$	−13.2715	−	7.66228i	−0.470394	−	0.271582i
$797$	−17.4459	+	30.2171i	−0.617964	+	1.07034i	0.371893	+	0.928276i	$0.378709\pi$
$797$	−17.4459	+	30.2171i	−0.617964	+	1.07034i	−0.989857	+	0.142069i	$0.954624\pi$
$798$	25.9842	−	15.5080i	0.919832	−	0.548979i
$799$	20.9357	+	12.0872i	0.740650	+	0.427615i
$800$	3.39060			0.119876
$801$	−22.5726	+	10.5713i	−0.797563	+	0.373520i
$802$	16.4158	+	28.4331i	0.579663	+	1.00401i
$803$	1.08567	−	1.88043i	0.0383124	−	0.0663591i
$804$	16.9033	+	10.7489i	0.596134	+	0.379085i
$805$	−7.57600	+	4.97316i	−0.267019	+	0.175281i
$806$	−29.6331	−	8.06083i	−1.04378	−	0.283931i
$807$	21.3333	−	33.5480i	0.750969	−	1.18094i
$808$	−9.45426			−0.332600
$809$			11.3791i			0.400069i	0.979789	+	0.200035i	$0.0641055\pi$
$809$			11.3791i			0.400069i	−0.979789	+	0.200035i	$0.935894\pi$
$810$	−10.7160	+	3.94058i	−0.376523	+	0.138458i
$811$	−41.1437			−1.44475			−0.722376	−	0.691501i	$-0.756950\pi$
$811$	−41.1437			−1.44475			−0.722376	+	0.691501i	$0.756950\pi$
$812$	−2.36921	+	0.135874i	−0.0831428	+	0.00476826i
$813$	−26.9827	−	1.15569i	−0.946324	−	0.0405319i
$814$	−24.6782	+	14.2480i	−0.864971	+	0.499392i
$815$	−9.53356	−	16.5126i	−0.333946	−	0.578412i
$816$	4.00753	+	7.68284i	0.140292	+	0.268953i
$817$	11.3622	−	19.6799i	0.397514	−	0.688514i
$818$	19.9476			0.697452
$819$	−19.5758	−	20.8755i	−0.684035	−	0.729449i
$820$	−6.65348			−0.232350
$821$	−22.8097	+	39.5075i	−0.796063	+	1.37882i	0.126099	+	0.992018i	$0.459754\pi$
$821$	−22.8097	+	39.5075i	−0.796063	+	1.37882i	−0.922162	+	0.386804i	$0.873579\pi$
$822$	−7.70499	−	14.7713i	−0.268742	−	0.515207i
$823$	−13.6104	−	23.5739i	−0.474428	−	0.821733i	0.525143	−	0.851014i	$-0.324012\pi$
$823$	−13.6104	−	23.5739i	−0.474428	−	0.821733i	−0.999571	+	0.0292806i	$0.990678\pi$
$824$	−15.4442	+	8.91672i	−0.538024	+	0.310629i
$825$	30.2186	+	1.29429i	1.05208	+	0.0450613i
$826$	17.1810	+	26.1732i	0.597804	+	0.910682i
$827$	36.7827			1.27906			0.639530	−	0.768766i	$-0.279129\pi$
$827$	36.7827			1.27906			0.639530	+	0.768766i	$0.279129\pi$
$828$	−6.64283	−	4.63498i	−0.230854	−	0.161077i
$829$		−	2.53007i		−	0.0878730i	−0.999034	−	0.0439365i	$-0.986010\pi$
$829$		−	2.53007i		−	0.0878730i	0.999034	−	0.0439365i	$-0.0139899\pi$
$830$	11.6984			0.406056
$831$	20.7548	−	32.6381i	0.719976	−	1.13220i
$832$	2.55917	−	2.53981i	0.0887232	−	0.0880522i
$833$	−34.7905	+	4.00366i	−1.20542	+	0.138719i
$834$	−3.06154	−	1.94685i	−0.106012	−	0.0674140i
$835$	−10.7156	+	18.5600i	−0.370829	+	0.642294i
$836$	17.0046	+	29.4529i	0.588118	+	1.01865i
$837$	26.8550	−	35.1788i	0.928243	−	1.21596i
$838$	4.30992			0.148884
$839$	−38.7140	−	22.3515i	−1.33656	−	0.771661i	−0.350261	−	0.936652i	$-0.613907\pi$
$839$	−38.7140	−	22.3515i	−1.33656	−	0.771661i	−0.986295	+	0.164991i	$0.947240\pi$
$840$	5.81294	−	0.0841934i	0.200566	−	0.00290495i
$841$	−14.0977	+	24.4180i	−0.486129	+	0.842000i
$842$	8.10114	+	4.67720i	0.279184	+	0.161187i
$843$	17.4617	+	33.4758i	0.601412	+	1.15297i
$844$	4.63016	−	8.01968i	0.159377	−	0.276049i
$845$	8.13738	+	14.3447i	0.279934	+	0.493474i
$846$	11.8884	+	8.29505i	0.408733	+	0.285190i
$847$	−34.3400	+	22.5420i	−1.17994	+	0.774553i
$848$	−11.7150	+	6.76369i	−0.402296	+	0.232266i
$849$	−6.90998	+	3.60439i	−0.237150	+	0.123702i
$850$	−8.48138	+	14.6902i	−0.290909	+	0.503869i
$851$	7.46935	+	12.9373i	0.256046	+	0.443485i
$852$	−6.07359	−	11.6437i	−0.208078	−	0.398907i
$853$	18.5205			0.634130			0.317065	−	0.948404i	$-0.397303\pi$
$853$	18.5205			0.634130			0.317065	+	0.948404i	$0.397303\pi$
$854$	−12.3290	+	0.707070i	−0.421889	+	0.0241954i
$855$	2.14885	−	25.0393i	0.0734891	−	0.856326i
$856$	8.42970	+	4.86689i	0.288121	+	0.166347i
$857$	−18.8542	+	32.6564i	−0.644047	+	1.11552i	0.340474	+	0.940254i	$0.389413\pi$
$857$	−18.8542	+	32.6564i	−0.644047	+	1.11552i	−0.984521	+	0.175268i	$0.943921\pi$
$858$	23.7780	−	21.6591i	0.811768	−	0.739430i
$859$	2.88055	−	1.66308i	0.0982830	−	0.0567437i	−0.450053	−	0.893002i	$-0.648595\pi$
$859$	2.88055	−	1.66308i	0.0982830	−	0.0567437i	0.548336	+	0.836258i	$0.315262\pi$
$860$	3.78089	−	2.18290i	0.128927	−	0.0744361i
$861$	24.0315	−	0.348067i	0.818991	−	0.0118621i
$862$	0.433968	−	0.751655i	0.0147810	−	0.0256015i
$863$	−25.4144	−	44.0190i	−0.865116	−	1.49842i	−0.866932	−	0.498426i	$-0.833911\pi$
$863$	−25.4144	−	44.0190i	−0.865116	−	1.49842i	0.00181612	−	0.999998i	$-0.499422\pi$
$864$	2.00041	+	4.79566i	0.0680553	+	0.163152i
$865$	0.563441	−	0.325303i	0.0191576	−	0.0110606i
$866$	−20.7610	+	11.9864i	−0.705488	+	0.407313i
$867$	−13.8935	−	0.595072i	−0.471849	−	0.0202097i
$868$	−18.8386	+	12.3663i	−0.639425	+	0.419741i
$869$	15.1938	+	26.3164i	0.515414	+	0.892723i
$870$	−1.05757	+	1.66310i	−0.0358551	+	0.0563843i
$871$	29.3734	+	29.5973i	0.995281	+	1.00287i
$872$	−9.16977	−	5.29417i	−0.310528	−	0.179283i
$873$	−15.8029	−	33.7434i	−0.534849	−	1.14204i
$874$	15.4404	−	8.91450i	0.522278	−	0.301537i
$875$	15.4547	+	23.5433i	0.522464	+	0.795910i
$876$	0.337714	+	0.647432i	0.0114103	+	0.0218747i
$877$			31.6065i			1.06728i	0.845713	+	0.533638i	$0.179176\pi$
$877$			31.6065i			1.06728i	−0.845713	+	0.533638i	$0.820824\pi$
$878$	−15.7085	+	9.06933i	−0.530137	+	0.306075i
$879$	0.997056	−	23.2789i	0.0336299	−	0.785179i
$880$			6.53382i			0.220255i
$881$	20.2411	+	35.0585i	0.681939	+	1.18115i	0.974388	+	0.224872i	$0.0721963\pi$
$881$	20.2411	+	35.0585i	0.681939	+	1.18115i	−0.292450	+	0.956281i	$0.594470\pi$
$882$	−20.9912	+	0.608191i	−0.706810	+	0.0204789i
$883$	0.239886			0.00807282			0.00403641	−	0.999992i	$-0.498715\pi$
$883$	0.239886			0.00807282			0.00403641	+	0.999992i	$0.498715\pi$
$884$	4.60244	+	17.4411i	0.154797	+	0.586608i
$885$	25.9781	+	1.11267i	0.873246	+	0.0374019i
$886$		−	29.0277i		−	0.975206i
$887$	−20.4650	+	35.4464i	−0.687146	+	1.19017i	0.285611	+	0.958346i	$0.407804\pi$
$887$	−20.4650	+	35.4464i	−0.687146	+	1.19017i	−0.972757	+	0.231827i	$0.925530\pi$
$888$	0.410079	−	9.57438i	0.0137613	−	0.321295i
$889$	−27.7636	−	13.9744i	−0.931163	−	0.468686i
$890$	5.27015	−	9.12816i	0.176656	−	0.305977i
$891$	15.9979	+	43.5048i	0.535951	+	1.45747i
$892$	−6.58695	+	11.4089i	−0.220547	+	0.381999i
$893$	−27.6330	+	15.9539i	−0.924705	+	0.533879i
$894$	13.3355	+	0.571169i	0.446005	+	0.0191028i
$895$	−5.08688	−	8.81073i	−0.170036	−	0.294510i
$896$	−0.151485	−	2.64141i	−0.00506077	−	0.0882433i
$897$	−11.3545	−	12.4654i	−0.379117	−	0.416206i
$898$	1.47303	+	2.55136i	0.0491556	+	0.0851400i
$899$		−	7.63964i		−	0.254796i
$900$	−5.82049	+	8.34191i	−0.194016	+	0.278064i
$901$		−	67.6758i		−	2.25461i
$902$			27.0117i			0.899391i
$903$	−13.5419	+	8.08213i	−0.450645	+	0.268956i
$904$	2.68329	+	1.54920i	0.0892448	+	0.0515255i
$905$	0.291196	+	0.504366i	0.00967968	+	0.0167657i
$906$	0.887271	+	0.564221i	0.0294776	+	0.0187450i
$907$	23.2809			0.773031			0.386515	−	0.922283i	$-0.373679\pi$
$907$	23.2809			0.773031			0.386515	+	0.922283i	$0.373679\pi$
$908$	2.05308	+	1.18535i	0.0681339	+	0.0393371i
$909$	16.2297	−	23.2603i	0.538305	−	0.771497i
$910$	11.8403	+	2.50272i	0.392501	+	0.0829644i
$911$			28.7163i			0.951415i	0.879604	+	0.475708i	$0.157808\pi$
$911$			28.7163i			0.951415i	−0.879604	+	0.475708i	$0.842192\pi$
$912$	−11.4268	−	0.489420i	−0.378379	−	0.0162063i
$913$		−	47.4928i		−	1.57178i
$914$	−16.7927	+	9.69524i	−0.555452	+	0.320690i
$915$	−5.50346	+	8.65451i	−0.181939	+	0.286109i
$916$	−5.91454	+	10.2443i	−0.195422	+	0.338480i
$917$	−11.1490	−	5.61170i	−0.368174	−	0.185315i
$918$	−25.7817	−	3.32905i	−0.850922	−	0.109875i
$919$	−15.2654			−0.503558			−0.251779	−	0.967785i	$-0.581016\pi$
$919$	−15.2654			−0.503558			−0.251779	+	0.967785i	$0.581016\pi$
$920$	3.42528			0.112928
$921$	−12.6619	−	24.2741i	−0.417223	−	0.799858i
$922$	−18.5093	+	10.6864i	−0.609573	+	0.351937i
$923$	−6.97521	−	26.4328i	−0.229592	−	0.870045i
$924$	−0.341807	−	23.5993i	−0.0112446	−	0.776360i
$925$	16.2463	−	9.37982i	0.534176	−	0.308407i
$926$	−6.20980	−	3.58523i	−0.204067	−	0.117818i
$927$	4.57453	−	53.3044i	0.150247	−	1.75075i
$928$	0.776779	+	0.448474i	0.0254990	+	0.0147219i
$929$		−	10.9550i		−	0.359423i	−0.983719	−	0.179712i	$-0.942484\pi$
$929$		−	10.9550i		−	0.359423i	0.983719	−	0.179712i	$-0.0575165\pi$
$930$	−0.800861	+	18.6982i	−0.0262613	+	0.613140i
$931$	18.3836	−	42.4102i	0.602499	−	1.38994i
$932$	6.84440	+	3.95162i	0.224196	+	0.129440i
$933$	45.4066	+	1.94480i	1.48655	+	0.0636700i
$934$	9.00155			0.294540
$935$	−28.3086	−	16.3440i	−0.925789	−	0.534505i
$936$	1.85551	+	10.6563i	0.0606491	+	0.348313i
$937$			24.6465i			0.805165i	0.915384	+	0.402583i	$0.131887\pi$
$937$			24.6465i			0.805165i	−0.915384	+	0.402583i	$0.868113\pi$
$938$	30.5484	−	1.75196i	0.997441	−	0.0572035i
$939$	−24.1217	−	15.3392i	−0.787183	−	0.500575i
$940$	−6.13011			−0.199942
$941$	−7.51387	−	4.33814i	−0.244945	−	0.141419i	0.372502	−	0.928031i	$-0.378500\pi$
$941$	−7.51387	−	4.33814i	−0.244945	−	0.141419i	−0.617448	+	0.786612i	$0.711833\pi$
$942$	−19.5064	−	12.4042i	−0.635553	−	0.404152i
$943$	14.1606			0.461132
$944$		−	11.8335i		−	0.385148i
$945$	−9.77168	+	14.4461i	−0.317873	+	0.469933i
$946$	−8.86209	−	15.3496i	−0.288131	−	0.499058i
$947$	−2.59596	+	4.49634i	−0.0843575	+	0.146112i	−0.905117	−	0.425162i	$-0.860217\pi$
$947$	−2.59596	+	4.49634i	−0.0843575	+	0.146112i	0.820760	+	0.571274i	$0.193550\pi$
$948$	−10.2099	−	0.437301i	−0.331604	−	0.0142029i
$949$	0.387847	+	1.46976i	0.0125901	+	0.0477104i
$950$	−11.1946	−	19.3896i	−0.363201	−	0.629082i
$951$	−27.5639	+	43.3458i	−0.893820	+	1.40558i
$952$	11.8232	+	5.95100i	0.383191	+	0.192873i
$953$	−12.1003	−	6.98613i	−0.391968	−	0.226303i	0.291044	−	0.956710i	$-0.405997\pi$
$953$	−12.1003	−	6.98613i	−0.391968	−	0.226303i	−0.683013	+	0.730406i	$0.739331\pi$
$954$	3.46997	−	40.4335i	0.112344	−	1.30908i
$955$	6.40410	+	11.0922i	0.207232	+	0.358936i
$956$	−13.6510	−	23.6441i	−0.441503	−	0.764706i
$957$	6.75182	+	4.29352i	0.218255	+	0.138790i
$958$	−3.50004	−	2.02075i	−0.113081	−	0.0652874i
$959$	−22.7316	−	11.4416i	−0.734040	−	0.369467i
$960$	−1.85418	−	1.17908i	−0.0598433	−	0.0380547i
$961$	−20.7729	−	35.9797i	−0.670093	−	1.16064i
$962$	5.23627	−	19.2495i	0.168824	−	0.620627i
$963$	−26.4449	+	12.3849i	−0.852176	+	0.399097i
$964$	−5.64076	+	9.77009i	−0.181677	+	0.314673i
$965$	5.25223	+	9.09713i	0.169075	+	0.292847i
$966$	−12.3717	+	0.179189i	−0.398052	+	0.00576530i
$967$		−	17.0679i		−	0.548866i	−0.961606	−	0.274433i	$-0.911510\pi$
$967$		−	17.0679i		−	0.548866i	0.961606	−	0.274433i	$-0.0884902\pi$
$968$	15.5259			0.499022
$969$	30.7039	−	48.2838i	0.986352	−	1.55110i
$970$	13.6456	+	7.87827i	0.438132	+	0.252956i
$971$	8.20143			0.263196			0.131598	−	0.991303i	$-0.457989\pi$
$971$	8.20143			0.263196			0.131598	+	0.991303i	$0.457989\pi$
$972$	−15.2328	−	3.31088i	−0.488592	−	0.106197i
$973$	−5.53295	+	0.317316i	−0.177378	+	0.0101727i
$974$			13.7020i			0.439040i
$975$	−15.6537	+	14.2588i	−0.501320	+	0.456646i
$976$	4.04224	+	2.33379i	0.129389	+	0.0747028i
$977$	37.4333			1.19760			0.598798	−	0.800900i	$-0.295645\pi$
$977$	37.4333			1.19760			0.598798	+	0.800900i	$0.295645\pi$
$978$	1.11397	−	26.0085i	0.0356207	−	0.831661i
$979$	−37.0584	−	21.3957i	−1.18439	−	0.683809i
$980$	7.13257	−	5.29029i	0.227841	−	0.168992i
$981$	28.7666	−	13.4722i	0.918447	−	0.430133i
$982$		−	22.4122i		−	0.715202i
$983$	6.77655	+	3.91244i	0.216138	+	0.124787i	0.604161	−	0.796862i	$-0.293508\pi$
$983$	6.77655	+	3.91244i	0.216138	+	0.124787i	−0.388023	+	0.921650i	$0.626842\pi$
$984$	−7.66541	−	4.87448i	−0.244364	−	0.155393i
$985$	15.5427	+	8.97360i	0.495233	+	0.285923i
$986$	−3.88613	+	2.24366i	−0.123760	+	0.0714526i
$987$	22.1411	−	0.320688i	0.704760	−	0.0102076i
$988$	−22.9738	−	6.24937i	−0.730894	−	0.198819i
$989$	−8.04685	+	4.64585i	−0.255875	+	0.147730i
$990$	−16.0752	−	11.2163i	−0.510903	−	0.356478i
$991$	−4.13567			−0.131374			−0.0656870	−	0.997840i	$-0.520924\pi$
$991$	−4.13567			−0.131374			−0.0656870	+	0.997840i	$0.520924\pi$
$992$	8.51738			0.270427
$993$	48.4918	−	25.2943i	1.53884	−	0.802691i
$994$	−17.9185	−	9.01901i	−0.568342	−	0.286066i
$995$	−9.72053	+	16.8365i	−0.308162	+	0.533751i
$996$	13.4776	+	8.57046i	0.427053	+	0.271566i
$997$	−17.5761	+	10.1476i	−0.556642	+	0.321378i	−0.751797	−	0.659395i	$-0.770813\pi$
$997$	−17.5761	+	10.1476i	−0.556642	+	0.321378i	0.195154	+	0.980773i	$0.437479\pi$
$998$		−	19.7525i		−	0.625254i
$999$	22.8519	+	17.4448i	0.723003	+	0.551930i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bn.e.101.11	yes	34
3.2	odd	2		546.2.bn.f.101.7	yes	34
7.5	odd	6		546.2.bi.f.257.16	yes	34
13.4	even	6		546.2.bi.e.17.13	✓	34
21.5	even	6		546.2.bi.e.257.13	yes	34
39.17	odd	6		546.2.bi.f.17.16	yes	34
91.82	odd	6		546.2.bn.f.173.7	yes	34
273.173	even	6	inner	546.2.bn.e.173.11	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.13	✓	34	13.4	even	6
546.2.bi.e.257.13	yes	34	21.5	even	6
546.2.bi.f.17.16	yes	34	39.17	odd	6
546.2.bi.f.257.16	yes	34	7.5	odd	6
546.2.bn.e.101.11	yes	34	1.1	even	1	trivial
546.2.bn.e.173.11	yes	34	273.173	even	6	inner
546.2.bn.f.101.7	yes	34	3.2	odd	2
546.2.bn.f.173.7	yes	34	91.82	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.801045 + 1.53568i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.09866 + 0.634311i) q^{5} +(-1.73046 - 0.0741172i) q^{6} +(-2.21179 + 1.45190i) q^{7} +1.00000 q^{8} +(-1.71665 + 2.46030i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.801045 + 1.53568i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.09866 + 0.634311i) q^{5} +(-1.73046 - 0.0741172i) q^{6} +(-2.21179 + 1.45190i) q^{7} +1.00000 q^{8} +(-1.71665 + 2.46030i) q^{9} -1.26862i q^{10} -5.15033 q^{11} +(0.929420 - 1.46157i) q^{12} +(2.55917 - 2.53981i) q^{13} +(-0.151485 - 2.64141i) q^{14} +(-1.85418 - 1.17908i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.50144 - 4.33262i) q^{17} +(-1.27236 - 2.71682i) q^{18} +6.60332 q^{19} +(1.09866 + 0.634311i) q^{20} +(-4.00139 - 2.23357i) q^{21} +(2.57517 - 4.46032i) q^{22} +(-2.33827 - 1.35000i) q^{23} +(0.801045 + 1.53568i) q^{24} +(-1.69530 + 2.93635i) q^{25} +(0.919959 + 3.48621i) q^{26} +(-5.15337 - 0.665427i) q^{27} +(2.36327 + 1.18952i) q^{28} +(-0.776779 + 0.448474i) q^{29} +(1.94820 - 1.01622i) q^{30} +(-4.25869 + 7.37627i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-4.12565 - 7.90929i) q^{33} +5.00288 q^{34} +(1.50904 - 2.99810i) q^{35} +(2.98901 + 0.256514i) q^{36} +(-4.79158 - 2.76642i) q^{37} +(-3.30166 + 5.71864i) q^{38} +(5.95036 + 1.89557i) q^{39} +(-1.09866 + 0.634311i) q^{40} +(-4.54200 + 2.62233i) q^{41} +(3.93503 - 2.34852i) q^{42} +(1.72068 - 2.98031i) q^{43} +(2.57517 + 4.46032i) q^{44} +(0.325420 - 3.79193i) q^{45} +(2.33827 - 1.35000i) q^{46} +(-4.18472 + 2.41605i) q^{47} +(-1.73046 - 0.0741172i) q^{48} +(2.78400 - 6.42257i) q^{49} +(-1.69530 - 2.93635i) q^{50} +(4.64977 - 7.31204i) q^{51} +(-3.47913 - 0.946398i) q^{52} +(11.7150 + 6.76369i) q^{53} +(3.15296 - 4.13023i) q^{54} +(5.65846 - 3.26691i) q^{55} +(-2.21179 + 1.45190i) q^{56} +(5.28955 + 10.1406i) q^{57} -0.896947i q^{58} +(-10.2481 + 5.91675i) q^{59} +(-0.0940267 + 2.19530i) q^{60} -4.66758i q^{61} +(-4.25869 - 7.37627i) q^{62} +(0.224768 - 7.93407i) q^{63} +1.00000 q^{64} +(-1.20062 + 4.41370i) q^{65} +(8.91247 + 0.381728i) q^{66} +11.5652i q^{67} +(-2.50144 + 4.33262i) q^{68} +(0.200117 - 4.67226i) q^{69} +(1.84191 + 2.80592i) q^{70} +(3.79105 - 6.56628i) q^{71} +(-1.71665 + 2.46030i) q^{72} +(-0.210796 + 0.365109i) q^{73} +(4.79158 - 2.76642i) q^{74} +(-5.86731 - 0.251302i) q^{75} +(-3.30166 - 5.71864i) q^{76} +(11.3914 - 7.47775i) q^{77} +(-4.61679 + 4.20538i) q^{78} +(-2.95006 - 5.10965i) q^{79} -1.26862i q^{80} +(-3.10619 - 8.44699i) q^{81} -5.24465i q^{82} +9.22131i q^{83} +(0.0663661 + 4.58210i) q^{84} +(5.49645 + 3.17338i) q^{85} +(1.72068 + 2.98031i) q^{86} +(-1.31095 - 0.833640i) q^{87} -5.15033 q^{88} +(7.19534 + 4.15423i) q^{89} +(3.12119 + 2.17779i) q^{90} +(-1.97279 + 9.33317i) q^{91} +2.70000i q^{92} +(-14.7390 - 0.631285i) q^{93} -4.83210i q^{94} +(-7.25479 + 4.18856i) q^{95} +(0.929420 - 1.46157i) q^{96} +(-6.21010 + 10.7562i) q^{97} +(4.17011 + 5.62230i) q^{98} +(8.84134 - 12.6714i) 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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