LMFDB - Embedded newform 546.2.bi.f.17.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(17,546)]

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, 1]))

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

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

chi := DirichletCharacter("546.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bi (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			17.16
Character	$\chi$	$=$	546.17
Dual form			546.2.bi.f.257.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(1.73046 - 0.0741172i) q^{3} +1.00000 q^{4} +(-1.09866 + 0.634311i) q^{5} +(1.73046 - 0.0741172i) q^{6} +(0.151485 + 2.64141i) q^{7} +1.00000 q^{8} +(2.98901 - 0.256514i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(1.73046 - 0.0741172i) q^{3} +1.00000 q^{4} +(-1.09866 + 0.634311i) q^{5} +(1.73046 - 0.0741172i) q^{6} +(0.151485 + 2.64141i) q^{7} +1.00000 q^{8} +(2.98901 - 0.256514i) q^{9} +(-1.09866 + 0.634311i) q^{10} +(2.57517 + 4.46032i) q^{11} +(1.73046 - 0.0741172i) q^{12} +(-2.55917 - 2.53981i) q^{13} +(0.151485 + 2.64141i) q^{14} +(-1.85418 + 1.17908i) q^{15} +1.00000 q^{16} -5.00288 q^{17} +(2.98901 - 0.256514i) q^{18} +(3.30166 - 5.71864i) q^{19} +(-1.09866 + 0.634311i) q^{20} +(0.457914 + 4.55964i) q^{21} +(2.57517 + 4.46032i) q^{22} -2.70000i q^{23} +(1.73046 - 0.0741172i) q^{24} +(-1.69530 + 2.93635i) q^{25} +(-2.55917 - 2.53981i) q^{26} +(5.15337 - 0.665427i) q^{27} +(0.151485 + 2.64141i) q^{28} +(-0.776779 - 0.448474i) q^{29} +(-1.85418 + 1.17908i) q^{30} +(4.25869 - 7.37627i) q^{31} +1.00000 q^{32} +(4.78682 + 7.52756i) q^{33} -5.00288 q^{34} +(-1.84191 - 2.80592i) q^{35} +(2.98901 - 0.256514i) q^{36} -5.53284i q^{37} +(3.30166 - 5.71864i) q^{38} +(-4.61679 - 4.20538i) q^{39} +(-1.09866 + 0.634311i) q^{40} +(4.54200 + 2.62233i) q^{41} +(0.457914 + 4.55964i) q^{42} +(1.72068 + 2.98031i) q^{43} +(2.57517 + 4.46032i) q^{44} +(-3.12119 + 2.17779i) q^{45} -2.70000i q^{46} +(-4.18472 + 2.41605i) q^{47} +(1.73046 - 0.0741172i) q^{48} +(-6.95410 + 0.800271i) q^{49} +(-1.69530 + 2.93635i) q^{50} +(-8.65730 + 0.370800i) q^{51} +(-2.55917 - 2.53981i) q^{52} +(-11.7150 - 6.76369i) q^{53} +(5.15337 - 0.665427i) q^{54} +(-5.65846 - 3.26691i) q^{55} +(0.151485 + 2.64141i) q^{56} +(5.28955 - 10.1406i) q^{57} +(-0.776779 - 0.448474i) q^{58} -11.8335i q^{59} +(-1.85418 + 1.17908i) q^{60} +(4.04224 + 2.33379i) q^{61} +(4.25869 - 7.37627i) q^{62} +(1.13035 + 7.85635i) q^{63} +1.00000 q^{64} +(4.42268 + 1.16708i) q^{65} +(4.78682 + 7.52756i) q^{66} +(-10.0157 + 5.78259i) q^{67} -5.00288 q^{68} +(-0.200117 - 4.67226i) q^{69} +(-1.84191 - 2.80592i) q^{70} +(3.79105 + 6.56628i) q^{71} +(2.98901 - 0.256514i) q^{72} +(0.210796 - 0.365109i) q^{73} -5.53284i q^{74} +(-2.71602 + 5.20689i) 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} +(-1.09866 + 0.634311i) q^{80} +(8.86840 - 1.53345i) q^{81} +(4.54200 + 2.62233i) q^{82} +9.22131i q^{83} +(0.457914 + 4.55964i) q^{84} +(5.49645 - 3.17338i) q^{85} +(1.72068 + 2.98031i) q^{86} +(-1.37743 - 0.718495i) q^{87} +(2.57517 + 4.46032i) q^{88} -8.30846i q^{89} +(-3.12119 + 2.17779i) q^{90} +(6.32102 - 7.14456i) q^{91} -2.70000i q^{92} +(6.82280 - 13.0800i) q^{93} +(-4.18472 + 2.41605i) q^{94} +8.37711i q^{95} +(1.73046 - 0.0741172i) q^{96} +(6.21010 + 10.7562i) q^{97} +(-6.95410 + 0.800271i) q^{98} +(8.84134 + 12.6714i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9}+O(q^{10}) $ 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9	$ 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9} + 9 q^{10} + 9 q^{11} + 6 q^{12} + 8 q^{13} + 4 q^{14} - 17 q^{15} + 34 q^{16} + 12 q^{17} + 4 q^{18} - 5 q^{19} + 9 q^{20} - 7 q^{21} + 9 q^{22} + 6 q^{24} + 16 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} + 27 q^{29} - 17 q^{30} - q^{31} + 34 q^{32} + 12 q^{34} - 3 q^{35} + 4 q^{36} - 5 q^{38} - 10 q^{39} + 9 q^{40} - 3 q^{41} - 7 q^{42} - 3 q^{43} + 9 q^{44} + 9 q^{45} - 27 q^{47} + 6 q^{48} - 2 q^{49} + 16 q^{50} - 36 q^{51} + 8 q^{52} - 21 q^{53} - 18 q^{54} - 57 q^{55} + 4 q^{56} - 17 q^{57} + 27 q^{58} - 17 q^{60} - 51 q^{61} - q^{62} - 24 q^{63} + 34 q^{64} - 21 q^{65} - 21 q^{67} + 12 q^{68} + 30 q^{69} - 3 q^{70} - 15 q^{71} + 4 q^{72} - 19 q^{73} - 54 q^{75} - 5 q^{76} + 9 q^{77} - 10 q^{78} - 9 q^{79} + 9 q^{80} + 28 q^{81} - 3 q^{82} - 7 q^{84} - 42 q^{85} - 3 q^{86} - 81 q^{87} + 9 q^{88} + 9 q^{90} - 72 q^{91} - 17 q^{93} - 27 q^{94} + 6 q^{96} + 19 q^{97} - 2 q^{98} - 27 q^{99}+O(q^{100}) $ 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9 + 9 * q^10 + 9 * q^11 + 6 * q^12 + 8 * q^13 + 4 * q^14 - 17 * q^15 + 34 * q^16 + 12 * q^17 + 4 * q^18 - 5 * q^19 + 9 * q^20 - 7 * q^21 + 9 * q^22 + 6 * q^24 + 16 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 + 27 * q^29 - 17 * q^30 - q^31 + 34 * q^32 + 12 * q^34 - 3 * q^35 + 4 * q^36 - 5 * q^38 - 10 * q^39 + 9 * q^40 - 3 * q^41 - 7 * q^42 - 3 * q^43 + 9 * q^44 + 9 * q^45 - 27 * q^47 + 6 * q^48 - 2 * q^49 + 16 * q^50 - 36 * q^51 + 8 * q^52 - 21 * q^53 - 18 * q^54 - 57 * q^55 + 4 * q^56 - 17 * q^57 + 27 * q^58 - 17 * q^60 - 51 * q^61 - q^62 - 24 * q^63 + 34 * q^64 - 21 * q^65 - 21 * q^67 + 12 * q^68 + 30 * q^69 - 3 * q^70 - 15 * q^71 + 4 * q^72 - 19 * q^73 - 54 * q^75 - 5 * q^76 + 9 * q^77 - 10 * q^78 - 9 * q^79 + 9 * q^80 + 28 * q^81 - 3 * q^82 - 7 * q^84 - 42 * q^85 - 3 * q^86 - 81 * q^87 + 9 * q^88 + 9 * q^90 - 72 * q^91 - 17 * q^93 - 27 * q^94 + 6 * q^96 + 19 * q^97 - 2 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	1.73046	−	0.0741172i	0.999084	−	0.0427916i
$3$	1.73046	−	0.0741172i	0.999084	−	0.0427916i
$4$	1.00000			0.500000
$5$	−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
$7$	0.151485	+	2.64141i	0.0572561	+	0.998360i
$7$	0.151485	+	2.64141i	0.0572561	+	0.998360i
$8$	1.00000			0.353553
$9$	2.98901	−	0.256514i	0.996338	−	0.0855048i
$10$	−1.09866	+	0.634311i	−0.347426	+	0.200587i
$11$	2.57517	+	4.46032i	0.776442	+	1.34484i	0.933981	+	0.357324i	$0.116311\pi$
$11$	2.57517	+	4.46032i	0.776442	+	1.34484i	−0.157539	+	0.987513i	$0.550356\pi$
$12$	1.73046	−	0.0741172i	0.499542	−	0.0213958i
$13$	−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
$16$	1.00000			0.250000
$17$	−5.00288			−1.21338			−0.606688	−	0.794940i	$-0.707502\pi$
$17$	−5.00288			−1.21338			−0.606688	+	0.794940i	$0.707502\pi$
$18$	2.98901	−	0.256514i	0.704517	−	0.0604610i
$19$	3.30166	−	5.71864i	0.757453	−	1.31195i	−0.186693	−	0.982418i	$-0.559777\pi$
$19$	3.30166	−	5.71864i	0.757453	−	1.31195i	0.944146	−	0.329528i	$-0.106890\pi$
$20$	−1.09866	+	0.634311i	−0.245668	+	0.141836i
$21$	0.457914	+	4.55964i	0.0999251	+	0.994995i
$22$	2.57517	+	4.46032i	0.549027	+	0.950943i
$23$		−	2.70000i		−	0.562990i	−0.959563	−	0.281495i	$-0.909170\pi$
$23$		−	2.70000i		−	0.562990i	0.959563	−	0.281495i	$-0.0908303\pi$
$24$	1.73046	−	0.0741172i	0.353230	−	0.0151291i
$25$	−1.69530	+	2.93635i	−0.339060	+	0.587269i
$26$	−2.55917	−	2.53981i	−0.501894	−	0.498099i
$27$	5.15337	−	0.665427i	0.991766	−	0.128061i
$28$	0.151485	+	2.64141i	0.0286281	+	0.499180i
$29$	−0.776779	−	0.448474i	−0.144244	−	0.0832794i	0.426141	−	0.904657i	$-0.359873\pi$
$29$	−0.776779	−	0.448474i	−0.144244	−	0.0832794i	−0.570385	+	0.821377i	$0.693206\pi$
$30$	−1.85418	+	1.17908i	−0.338525	+	0.215270i
$31$	4.25869	−	7.37627i	0.764883	−	1.32482i	−0.175425	−	0.984493i	$-0.556130\pi$
$31$	4.25869	−	7.37627i	0.764883	−	1.32482i	0.940308	−	0.340324i	$-0.110537\pi$
$32$	1.00000			0.176777
$33$	4.78682	+	7.52756i	0.833278	+	1.31038i
$34$	−5.00288			−0.857987
$35$	−1.84191	−	2.80592i	−0.311339	−	0.474287i
$36$	2.98901	−	0.256514i	0.498169	−	0.0427524i
$37$		−	5.53284i		−	0.909593i	−0.890595	−	0.454797i	$-0.849712\pi$
$37$		−	5.53284i		−	0.909593i	0.890595	−	0.454797i	$-0.150288\pi$
$38$	3.30166	−	5.71864i	0.535600	−	0.927686i
$39$	−4.61679	−	4.20538i	−0.739279	−	0.673400i
$40$	−1.09866	+	0.634311i	−0.173713	+	0.100293i
$41$	4.54200	+	2.62233i	0.709342	+	0.409539i	0.810817	−	0.585299i	$-0.199023\pi$
$41$	4.54200	+	2.62233i	0.709342	+	0.409539i	−0.101476	+	0.994838i	$0.532356\pi$
$42$	0.457914	+	4.55964i	0.0706577	+	0.703568i
$43$	1.72068	+	2.98031i	0.262402	+	0.454493i	0.966880	−	0.255233i	$-0.0821521\pi$
$43$	1.72068	+	2.98031i	0.262402	+	0.454493i	−0.704478	+	0.709726i	$0.748819\pi$
$44$	2.57517	+	4.46032i	0.388221	+	0.672418i
$45$	−3.12119	+	2.17779i	−0.465280	+	0.324645i
$46$		−	2.70000i		−	0.398094i
$47$	−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
$49$	−6.95410	+	0.800271i	−0.993443	+	0.114324i
$50$	−1.69530	+	2.93635i	−0.239752	+	0.415262i
$51$	−8.65730	+	0.370800i	−1.21226	+	0.0519223i
$52$	−2.55917	−	2.53981i	−0.354893	−	0.352209i
$53$	−11.7150	−	6.76369i	−1.60919	−	0.929064i	−0.989553	−	0.144172i	$-0.953948\pi$
$53$	−11.7150	−	6.76369i	−1.60919	−	0.929064i	−0.619633	−	0.784891i	$-0.712719\pi$
$54$	5.15337	−	0.665427i	0.701285	−	0.0905531i
$55$	−5.65846	−	3.26691i	−0.762986	−	0.440510i
$56$	0.151485	+	2.64141i	0.0202431	+	0.352973i
$57$	5.28955	−	10.1406i	0.700618	−	1.34316i
$58$	−0.776779	−	0.448474i	−0.101996	−	0.0588875i
$59$		−	11.8335i		−	1.54059i	−0.637687	−	0.770296i	$-0.720109\pi$
$59$		−	11.8335i		−	1.54059i	0.637687	−	0.770296i	$-0.279891\pi$
$60$	−1.85418	+	1.17908i	−0.239373	+	0.152219i
$61$	4.04224	+	2.33379i	0.517556	+	0.298811i	0.735934	−	0.677053i	$-0.236743\pi$
$61$	4.04224	+	2.33379i	0.517556	+	0.298811i	−0.218378	+	0.975864i	$0.570077\pi$
$62$	4.25869	−	7.37627i	0.540854	−	0.936787i
$63$	1.13035	+	7.85635i	0.142411	+	0.989808i
$64$	1.00000			0.125000
$65$	4.42268	+	1.16708i	0.548566	+	0.144758i
$66$	4.78682	+	7.52756i	0.589217	+	0.926578i
$67$	−10.0157	+	5.78259i	−1.22362	+	0.706456i	−0.965687	−	0.259707i	$-0.916374\pi$
$67$	−10.0157	+	5.78259i	−1.22362	+	0.706456i	−0.257931	+	0.966163i	$0.583041\pi$
$68$	−5.00288			−0.606688
$69$	−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	0.998380	−	0.0568986i	$-0.0181212\pi$
$71$	3.79105	+	6.56628i	0.449914	+	0.779274i	−0.548466	+	0.836173i	$0.684788\pi$
$72$	2.98901	−	0.256514i	0.352259	−	0.0302305i
$73$	0.210796	−	0.365109i	0.0246718	−	0.0427328i	−0.853426	−	0.521214i	$-0.825479\pi$
$73$	0.210796	−	0.365109i	0.0246718	−	0.0427328i	0.878098	+	0.478481i	$0.158813\pi$
$74$		−	5.53284i		−	0.643180i
$75$	−2.71602	+	5.20689i	−0.313619	+	0.601240i
$76$	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	$0.941026\pi$
$80$	−1.09866	+	0.634311i	−0.122834	+	0.0709181i
$81$	8.86840	−	1.53345i	0.985378	−	0.170383i
$82$	4.54200	+	2.62233i	0.501580	+	0.289588i
$83$			9.22131i			1.01217i	0.862484	+	0.506085i	$0.168908\pi$
$83$			9.22131i			1.01217i	−0.862484	+	0.506085i	$0.831092\pi$
$84$	0.457914	+	4.55964i	0.0499625	+	0.497497i
$85$	5.49645	−	3.17338i	0.596174	−	0.344201i
$86$	1.72068	+	2.98031i	0.185546	+	0.321375i
$87$	−1.37743	−	0.718495i	−0.147676	−	0.0770307i
$88$	2.57517	+	4.46032i	0.274514	+	0.475472i
$89$		−	8.30846i		−	0.880695i	−0.897827	−	0.440348i	$-0.854855\pi$
$89$		−	8.30846i		−	0.880695i	0.897827	−	0.440348i	$-0.145145\pi$
$90$	−3.12119	+	2.17779i	−0.329003	+	0.229559i
$91$	6.32102	−	7.14456i	0.662623	−	0.748954i
$92$		−	2.70000i		−	0.281495i
$93$	6.82280	−	13.0800i	0.707492	−	1.35633i
$94$	−4.18472	+	2.41605i	−0.431621	+	0.249197i
$95$			8.37711i			0.859474i
$96$	1.73046	−	0.0741172i	0.176615	−	0.00756456i
$97$	6.21010	+	10.7562i	0.630540	+	1.09213i	0.987441	+	0.157985i	$0.0504999\pi$
$97$	6.21010	+	10.7562i	0.630540	+	1.09213i	−0.356901	+	0.934142i	$0.616167\pi$
$98$	−6.95410	+	0.800271i	−0.702471	+	0.0808396i
$99$	8.84134	+	12.6714i	0.888588	+	1.27352i
$100$	−1.69530	+	2.93635i	−0.169530	+	0.293635i
$101$	−4.72713	−	8.18763i	−0.470367	−	0.814699i	0.529059	−	0.848585i	$-0.322545\pi$
$101$	−4.72713	−	8.18763i	−0.470367	−	0.814699i	−0.999426	+	0.0338859i	$0.989212\pi$
$102$	−8.65730	+	0.370800i	−0.857201	+	0.0367146i
$103$	−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
$105$	−3.39532	−	4.71903i	−0.331349	−	0.460530i
$106$	−11.7150	−	6.76369i	−1.13787	−	0.656947i
$107$			9.73378i			0.941000i	0.882400	+	0.470500i	$0.155926\pi$
$107$			9.73378i			0.941000i	−0.882400	+	0.470500i	$0.844074\pi$
$108$	5.15337	−	0.665427i	0.495883	−	0.0640307i
$109$	9.16977	+	5.29417i	0.878305	+	0.507090i	0.870099	−	0.492877i	$-0.164055\pi$
$109$	9.16977	+	5.29417i	0.878305	+	0.507090i	0.00820581	+	0.999966i	$0.497388\pi$
$110$	−5.65846	−	3.26691i	−0.539513	−	0.311488i
$111$	−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	−0.368451	−	0.929647i	$-0.620112\pi$
$113$	2.68329	−	1.54920i	0.252422	−	0.145736i	0.620873	+	0.783911i	$0.286778\pi$
$114$	5.28955	−	10.1406i	0.495412	−	0.949756i
$115$	1.71264	+	2.96638i	0.159705	+	0.276617i
$116$	−0.776779	−	0.448474i	−0.0721221	−	0.0416397i
$117$	−8.30089	−	6.93507i	−0.767417	−	0.641148i
$118$		−	11.8335i		−	1.08936i
$119$	−0.757863	−	13.2147i	−0.0694732	−	1.21139i
$120$	−1.85418	+	1.17908i	−0.169262	+	0.107635i
$121$	−7.76296	+	13.4458i	−0.705724	+	1.22235i
$122$	4.04224	+	2.33379i	0.365967	+	0.211291i
$123$	8.05413	+	4.20120i	0.726217	+	0.378810i
$124$	4.25869	−	7.37627i	0.382442	−	0.662408i
$125$		−	10.6445i		−	0.952073i
$126$	1.13035	+	7.85635i	0.100700	+	0.699900i
$127$	5.87399	−	10.1740i	0.521232	−	0.902800i	−0.478463	−	0.878108i	$-0.658806\pi$
$127$	5.87399	−	10.1740i	0.521232	−	0.902800i	0.999695	−	0.0246926i	$-0.00786069\pi$
$128$	1.00000			0.0883883
$129$	3.19847	+	5.02979i	0.281610	+	0.442848i
$130$	4.42268	+	1.16708i	0.387895	+	0.102360i
$131$	−2.35882	−	4.08559i	−0.206091	−	0.356960i	0.744389	−	0.667746i	$-0.232741\pi$
$131$	−2.35882	−	4.08559i	−0.206091	−	0.356960i	−0.950480	+	0.310787i	$0.899408\pi$
$132$	4.78682	+	7.52756i	0.416639	+	0.655190i
$133$	15.6054	+	7.85475i	1.35316	+	0.681093i
$134$	−10.0157	+	5.78259i	−0.865229	+	0.499540i
$135$	−5.23970	+	3.99991i	−0.450962	+	0.344258i
$136$	−5.00288			−0.428993
$137$	−9.61868			−0.821779			−0.410890	−	0.911685i	$-0.634782\pi$
$137$	−9.61868			−0.821779			−0.410890	+	0.911685i	$0.634782\pi$
$138$	−0.200117	−	4.67226i	−0.0170351	−	0.397729i
$139$	−1.81406	+	1.04735i	−0.153867	+	0.0888349i	−0.574956	−	0.818184i	$-0.694981\pi$
$139$	−1.81406	+	1.04735i	−0.153867	+	0.0888349i	0.421090	+	0.907019i	$0.361648\pi$
$140$	−1.84191	−	2.80592i	−0.155669	−	0.237143i
$141$	−7.06244	+	4.49105i	−0.594765	+	0.378215i
$142$	3.79105	+	6.56628i	0.318137	+	0.551030i
$143$	4.73810	−	17.9552i	0.396220	−	1.50149i
$144$	2.98901	−	0.256514i	0.249084	−	0.0213762i
$145$	1.13789			0.0944963
$146$	0.210796	−	0.365109i	0.0174456	−	0.0302166i
$147$	−11.9745	+	1.90026i	−0.987641	+	0.156731i
$148$		−	5.53284i		−	0.454797i
$149$	3.85315	−	6.67385i	0.315662	−	0.546743i	−0.663916	−	0.747807i	$-0.731107\pi$
$149$	3.85315	−	6.67385i	0.315662	−	0.546743i	0.979578	+	0.201064i	$0.0644400\pi$
$150$	−2.71602	+	5.20689i	−0.221762	+	0.425141i
$151$	0.525736	+	0.303534i	0.0427838	+	0.0247012i	0.521239	−	0.853411i	$-0.325470\pi$
$151$	0.525736	+	0.303534i	0.0427838	+	0.0247012i	−0.478456	+	0.878112i	$0.658803\pi$
$152$	3.30166	−	5.71864i	0.267800	−	0.463843i
$153$	−14.9537	+	1.28331i	−1.20893	+	0.103750i
$154$	−11.3914	+	7.47775i	−0.917948	+	0.602574i
$155$			10.8053i			0.867905i
$156$	−4.61679	−	4.20538i	−0.369639	−	0.336700i
$157$	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	$0.487892\pi$
$158$	−2.95006	−	5.10965i	−0.234694	−	0.406502i
$159$	−20.7738	−	10.8360i	−1.64747	−	0.859353i
$160$	−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
$163$	13.0162	+	7.51490i	1.01951	+	0.588612i	0.913961	−	0.405802i	$-0.133008\pi$
$163$	13.0162	+	7.51490i	1.01951	+	0.588612i	0.105545	+	0.994414i	$0.466341\pi$
$164$	4.54200	+	2.62233i	0.354671	+	0.204769i
$165$	−10.0339	−	5.23388i	−0.781137	−	0.407457i
$166$			9.22131i			0.715712i
$167$	−14.6300	−	8.44665i	−1.13211	−	0.653622i	−0.187642	−	0.982237i	$-0.560085\pi$
$167$	−14.6300	−	8.44665i	−1.13211	−	0.653622i	−0.944464	+	0.328616i	$0.893418\pi$
$168$	0.457914	+	4.55964i	0.0353289	+	0.351784i
$169$	0.0986879	+	12.9996i	0.00759138	+	0.999971i
$170$	5.49645	−	3.17338i	0.421559	−	0.243387i
$171$	8.40179	−	17.9400i	0.642501	−	1.37191i
$172$	1.72068	+	2.98031i	0.131201	+	0.227247i
$173$	−0.256422	+	0.444137i	−0.0194954	+	0.0337671i	−0.875609	−	0.483021i	$-0.839539\pi$
$173$	−0.256422	+	0.444137i	−0.0194954	+	0.0337671i	0.856113	+	0.516789i	$0.172873\pi$
$174$	−1.37743	−	0.718495i	−0.104423	−	0.0544689i
$175$	−8.01291	−	4.03317i	−0.605719	−	0.304879i
$176$	2.57517	+	4.46032i	0.194110	+	0.336209i
$177$	−0.877067	−	20.4775i	−0.0659244	−	1.53918i
$178$		−	8.30846i		−	0.622746i
$179$	−6.94512	+	4.00977i	−0.519103	+	0.299704i	−0.736567	−	0.676364i	$-0.763555\pi$
$179$	−6.94512	+	4.00977i	−0.519103	+	0.299704i	0.217465	+	0.976068i	$0.430221\pi$
$180$	−3.12119	+	2.17779i	−0.232640	+	0.162323i
$181$		−	0.459074i		−	0.0341227i	−0.999854	−	0.0170614i	$-0.994569\pi$
$181$		−	0.459074i		−	0.0341227i	0.999854	−	0.0170614i	$-0.00543106\pi$
$182$	6.32102	−	7.14456i	0.468545	−	0.529590i
$183$	7.16793	+	3.73894i	0.529869	+	0.276390i
$184$		−	2.70000i		−	0.199047i
$185$	3.50954	+	6.07870i	0.258026	+	0.446915i
$186$	6.82280	−	13.0800i	0.500272	−	0.959073i
$187$	−12.8832	−	22.3144i	−0.942116	−	1.63179i
$188$	−4.18472	+	2.41605i	−0.305202	+	0.176209i
$189$	2.53833	+	13.5114i	0.184636	+	0.982807i
$190$			8.37711i			0.607740i
$191$	−8.74352	−	5.04808i	−0.632659	−	0.365266i	0.149122	−	0.988819i	$-0.452355\pi$
$191$	−8.74352	−	5.04808i	−0.632659	−	0.365266i	−0.781781	+	0.623553i	$0.785689\pi$
$192$	1.73046	−	0.0741172i	0.124886	−	0.00534895i
$193$	7.17088	−	4.14011i	0.516171	−	0.298011i	−0.219196	−	0.975681i	$-0.570343\pi$
$193$	7.17088	−	4.14011i	0.516171	−	0.298011i	0.735367	+	0.677669i	$0.237010\pi$
$194$	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	0.496023	+	0.868309i	$0.334793\pi$
$197$	−7.07350	+	12.2517i	−0.503966	+	0.872895i	−0.999989	+	0.00458596i	$0.998540\pi$
$198$	8.84134	+	12.6714i	0.628327	+	0.900516i
$199$			15.3246i			1.08633i	0.839626	+	0.543164i	$0.182774\pi$
$199$			15.3246i			1.08633i	−0.839626	+	0.543164i	$0.817226\pi$
$200$	−1.69530	+	2.93635i	−0.119876	+	0.207631i
$201$	−16.9033	+	10.7489i	−1.19227	+	0.758170i
$202$	−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
$205$	−6.65348			−0.464699
$206$	−15.4442	+	8.91672i	−1.07605	+	0.621257i
$207$	−0.692590	−	8.07035i	−0.0481384	−	0.560928i
$208$	−2.55917	−	2.53981i	−0.177446	−	0.176104i
$209$	34.0093			2.35247
$210$	−3.39532	−	4.71903i	−0.234299	−	0.325644i
$211$	4.63016	−	8.01968i	0.318754	−	0.552097i	−0.661475	−	0.749967i	$-0.730069\pi$
$211$	4.63016	−	8.01968i	0.318754	−	0.552097i	0.980228	+	0.197870i	$0.0634025\pi$
$212$	−11.7150	−	6.76369i	−0.804593	−	0.464532i
$213$	7.04694	+	11.0817i	0.482849	+	0.759308i
$214$			9.73378i			0.665388i
$215$	−3.78089	−	2.18290i	−0.257854	−	0.148872i
$216$	5.15337	−	0.665427i	0.350642	−	0.0452765i
$217$	20.1289	+	10.1316i	1.36644	+	0.687775i
$218$	9.16977	+	5.29417i	0.621055	+	0.358567i
$219$	0.337714	−	0.647432i	0.0228206	−	0.0437494i
$220$	−5.65846	−	3.26691i	−0.381493	−	0.220255i
$221$	12.8032	+	12.7064i	0.861237	+	0.854724i
$222$	−0.410079	−	9.57438i	−0.0275227	−	0.642590i
$223$	6.58695	−	11.4089i	0.441095	−	0.763998i	−0.556676	−	0.830729i	$-0.687924\pi$
$223$	6.58695	−	11.4089i	0.441095	−	0.763998i	0.997771	+	0.0667312i	$0.0212570\pi$
$224$	0.151485	+	2.64141i	0.0101215	+	0.176487i
$225$	−4.31406	+	9.21164i	−0.287604	+	0.614110i
$226$	2.68329	−	1.54920i	0.178490	−	0.103051i
$227$		−	2.37069i		−	0.157348i	−0.996900	−	0.0786742i	$-0.974931\pi$
$227$		−	2.37069i		−	0.157348i	0.996900	−	0.0786742i	$-0.0250687\pi$
$228$	5.28955	−	10.1406i	0.350309	−	0.671579i
$229$	5.91454	+	10.2443i	0.390844	+	0.676961i	0.992561	−	0.121748i	$-0.0388500\pi$
$229$	5.91454	+	10.2443i	0.390844	+	0.676961i	−0.601717	+	0.798709i	$0.705517\pi$
$230$	1.71264	+	2.96638i	0.112928	+	0.195598i
$231$	−19.1582	+	13.7843i	−1.26052	+	0.906939i
$232$	−0.776779	−	0.448474i	−0.0509980	−	0.0294437i
$233$	6.84440	−	3.95162i	0.448392	−	0.258879i	−0.258759	−	0.965942i	$-0.583314\pi$
$233$	6.84440	−	3.95162i	0.448392	−	0.258879i	0.707151	+	0.707063i	$0.249980\pi$
$234$	−8.30089	−	6.93507i	−0.542646	−	0.453360i
$235$	3.06505	−	5.30883i	0.199942	−	0.346310i
$236$		−	11.8335i		−	0.770296i
$237$	−5.48369	−	8.62342i	−0.356204	−	0.560151i
$238$	−0.757863	−	13.2147i	−0.0491250	−	0.856579i
$239$	27.3019			1.76601			0.883007	−	0.469360i	$-0.155515\pi$
$239$	27.3019			1.76601			0.883007	+	0.469360i	$0.155515\pi$
$240$	−1.85418	+	1.17908i	−0.119687	+	0.0761094i
$241$	−11.2815			−0.726707			−0.363353	−	0.931651i	$-0.618368\pi$
$241$	−11.2815			−0.726707			−0.363353	+	0.931651i	$0.618368\pi$
$242$	−7.76296	+	13.4458i	−0.499022	+	0.864332i
$243$	15.2328	−	3.31088i	0.977184	−	0.212393i
$244$	4.04224	+	2.33379i	0.258778	+	0.149406i
$245$	7.13257	−	5.29029i	0.455683	−	0.337984i
$246$	8.05413	+	4.20120i	0.513513	+	0.267859i
$247$	−22.9738	+	6.24937i	−1.46179	+	0.397638i
$248$	4.25869	−	7.37627i	0.270427	−	0.468393i
$249$	0.683458	+	15.9571i	0.0433124	+	1.01124i
$250$		−	10.6445i		−	0.673217i
$251$	11.3067	+	19.5838i	0.713675	+	1.23612i	0.963469	+	0.267822i	$0.0863038\pi$
$251$	11.3067	+	19.5838i	0.713675	+	1.23612i	−0.249794	+	0.968299i	$0.580363\pi$
$252$	1.13035	+	7.85635i	0.0712055	+	0.494904i
$253$	12.0429	−	6.95296i	0.757130	−	0.437129i
$254$	5.87399	−	10.1740i	0.368567	−	0.638376i
$255$	9.27622	−	5.89880i	0.580899	−	0.369397i
$256$	1.00000			0.0625000
$257$	−1.36558			−0.0851824			−0.0425912	−	0.999093i	$-0.513561\pi$
$257$	−1.36558			−0.0851824			−0.0425912	+	0.999093i	$0.513561\pi$
$258$	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
$261$	−2.43684	−	1.14124i	−0.150837	−	0.0706409i
$262$	−2.35882	−	4.08559i	−0.145728	−	0.252409i
$263$	−9.36276	+	5.40559i	−0.577333	+	0.333323i	−0.760073	−	0.649838i	$-0.774837\pi$
$263$	−9.36276	+	5.40559i	−0.577333	+	0.333323i	0.182740	+	0.983161i	$0.441503\pi$
$264$	4.78682	+	7.52756i	0.294608	+	0.463289i
$265$	17.1611			1.05420
$266$	15.6054	+	7.85475i	0.956831	+	0.481605i
$267$	−0.615800	−	14.3775i	−0.0376864	−	0.879889i
$268$	−10.0157	+	5.78259i	−0.611809	+	0.353228i
$269$	−22.9534			−1.39949			−0.699747	−	0.714391i	$-0.746704\pi$
$269$	−22.9534			−1.39949			−0.699747	+	0.714391i	$0.746704\pi$
$270$	−5.23970	+	3.99991i	−0.318878	+	0.243427i
$271$	−15.5927			−0.947192			−0.473596	−	0.880742i	$-0.657044\pi$
$271$	−15.5927			−0.947192			−0.473596	+	0.880742i	$0.657044\pi$
$272$	−5.00288			−0.303344
$273$	10.4088	−	12.8319i	0.629967	−	0.776622i
$274$	−9.61868			−0.581086
$275$	−17.4627			−1.05304
$276$	−0.200117	−	4.67226i	−0.0120456	−	0.281237i
$277$	22.3309			1.34173			0.670867	−	0.741577i	$-0.265922\pi$
$277$	22.3309			1.34173			0.670867	+	0.741577i	$0.265922\pi$
$278$	−1.81406	+	1.04735i	−0.108800	+	0.0628158i
$279$	10.8372	−	23.1402i	0.648804	−	1.38537i
$280$	−1.84191	−	2.80592i	−0.110075	−	0.167686i
$281$	21.7986			1.30040			0.650199	−	0.759764i	$-0.274686\pi$
$281$	21.7986			1.30040			0.650199	+	0.759764i	$0.274686\pi$
$282$	−7.06244	+	4.49105i	−0.420562	+	0.267438i
$283$	3.89678	−	2.24981i	0.231639	−	0.133737i	−0.379689	−	0.925114i	$-0.623969\pi$
$283$	3.89678	−	2.24981i	0.231639	−	0.133737i	0.611328	+	0.791377i	$0.290636\pi$
$284$	3.79105	+	6.56628i	0.224957	+	0.389637i
$285$	0.620888	+	14.4963i	0.0367783	+	0.858686i
$286$	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
$289$	8.02879			0.472282
$290$	1.13789			0.0668190
$291$	11.5436	+	18.1530i	0.676696	+	1.06415i
$292$	0.210796	−	0.365109i	0.0123359	−	0.0213664i
$293$	11.6501	−	6.72621i	0.680608	−	0.392949i	−0.119476	−	0.992837i	$-0.538121\pi$
$293$	11.6501	−	6.72621i	0.680608	−	0.392949i	0.800084	+	0.599888i	$0.204788\pi$
$294$	−11.9745	+	1.90026i	−0.698368	+	0.110825i
$295$	7.50612	+	13.0010i	0.437023	+	0.756946i
$296$		−	5.53284i		−	0.321590i
$297$	16.2388	+	21.2721i	0.942270	+	1.23433i
$298$	3.85315	−	6.67385i	0.223207	−	0.386606i
$299$	−6.85751	+	6.90977i	−0.396580	+	0.399602i
$300$	−2.71602	+	5.20689i	−0.156810	+	0.300620i
$301$	−7.61157	+	4.99651i	−0.438723	+	0.287994i
$302$	0.525736	+	0.303534i	0.0302527	+	0.0174664i
$303$	−8.78697	−	13.8180i	−0.504798	−	0.793825i
$304$	3.30166	−	5.71864i	0.189363	−	0.327987i
$305$	−5.92139			−0.339058
$306$	−14.9537	+	1.28331i	−0.854844	+	0.0733620i
$307$	15.8067			0.902135			0.451068	−	0.892490i	$-0.351043\pi$
$307$	15.8067			0.902135			0.451068	+	0.892490i	$0.351043\pi$
$308$	−11.3914	+	7.47775i	−0.649087	+	0.426084i
$309$	−26.0648	+	16.5747i	−1.48277	+	0.942904i
$310$			10.8053i			0.613702i
$311$	−13.1198	+	22.7241i	−0.743954	+	1.28857i	0.206727	+	0.978399i	$0.433719\pi$
$311$	−13.1198	+	22.7241i	−0.743954	+	1.28857i	−0.950682	+	0.310168i	$0.899615\pi$
$312$	−4.61679	−	4.20538i	−0.261374	−	0.238083i
$313$	−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
$315$	−6.22524	−	7.91446i	−0.350753	−	0.445929i
$316$	−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	$0.520039\pi$
$318$	−20.7738	−	10.8360i	−1.16494	−	0.607654i
$319$		−	4.61958i		−	0.258647i
$320$	−1.09866	+	0.634311i	−0.0614169	+	0.0354590i
$321$	0.721441	+	16.8440i	0.0402669	+	0.940138i
$322$	7.13182	−	0.409011i	0.397441	−	0.0227933i
$323$	−16.5178	+	28.6097i	−0.919075	+	1.59188i
$324$	8.86840	−	1.53345i	0.492689	−	0.0851917i
$325$	11.7963	−	3.20886i	0.654343	−	0.177995i
$326$	13.0162	+	7.51490i	0.720900	+	0.416212i
$327$	16.2604	+	8.48174i	0.899200	+	0.469041i
$328$	4.54200	+	2.62233i	0.250790	+	0.144794i
$329$	−7.01571	−	10.6876i	−0.386788	−	0.589225i
$330$	−10.0339	−	5.23388i	−0.552348	−	0.288116i
$331$	−27.3462	−	15.7883i	−1.50308	−	0.867806i	−0.999994	−	0.00357128i	$-0.998863\pi$
$331$	−27.3462	−	15.7883i	−1.50308	−	0.867806i	−0.503090	−	0.864234i	$-0.667803\pi$
$332$			9.22131i			0.506085i
$333$	−1.41925	−	16.5377i	−0.0777746	−	0.906262i
$334$	−14.6300	−	8.44665i	−0.800520	−	0.462180i
$335$	7.33592	−	12.7062i	0.400804	−	0.694214i
$336$	0.457914	+	4.55964i	0.0249813	+	0.248749i
$337$	18.8701			1.02792			0.513961	−	0.857814i	$-0.328178\pi$
$337$	18.8701			1.02792			0.513961	+	0.857814i	$0.328178\pi$
$338$	0.0986879	+	12.9996i	0.00536792	+	0.707086i
$339$	4.52851	−	2.87971i	0.245955	−	0.156404i
$340$	5.49645	−	3.17338i	0.298087	−	0.172101i
$341$	43.8673			2.37555
$342$	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
$345$	3.18353	+	5.00628i	0.171395	+	0.269529i
$346$	−0.256422	+	0.444137i	−0.0137854	+	0.0238769i
$347$		−	5.84190i		−	0.313610i	−0.987630	−	0.156805i	$-0.949881\pi$
$347$		−	5.84190i		−	0.313610i	0.987630	−	0.156805i	$-0.0501194\pi$
$348$	−1.37743	−	0.718495i	−0.0738379	−	0.0385154i
$349$	−4.14640	+	7.18177i	−0.221952	+	0.384431i	−0.955400	−	0.295313i	$-0.904576\pi$
$349$	−4.14640	+	7.18177i	−0.221952	+	0.384431i	0.733449	+	0.679745i	$0.237909\pi$
$350$	−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
$353$	18.9199	−	10.9234i	1.00700	−	0.581393i	0.0966897	−	0.995315i	$-0.469175\pi$
$353$	18.9199	−	10.9234i	1.00700	−	0.581393i	0.910313	+	0.413922i	$0.135841\pi$
$354$	−0.877067	−	20.4775i	−0.0466156	−	1.08836i
$355$	−8.33013	−	4.80940i	−0.442117	−	0.255257i
$356$		−	8.30846i		−	0.440348i
$357$	−2.29089	−	22.8113i	−0.121247	−	1.20730i
$358$	−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	$0.652467\pi$
$360$	−3.12119	+	2.17779i	−0.164501	+	0.114779i
$361$	−12.3019	−	21.3075i	−0.647469	−	1.12145i
$362$		−	0.459074i		−	0.0241284i
$363$	−12.4370	+	23.8429i	−0.652771	+	1.25143i
$364$	6.32102	−	7.14456i	0.331311	−	0.374477i
$365$			0.534840i			0.0279948i
$366$	7.16793	+	3.73894i	0.374674	+	0.195437i
$367$	−14.1857	+	8.19011i	−0.740486	+	0.427520i	−0.822246	−	0.569132i	$-0.807279\pi$
$367$	−14.1857	+	8.19011i	−0.740486	+	0.427520i	0.0817597	+	0.996652i	$0.473946\pi$
$368$		−	2.70000i		−	0.140747i
$369$	14.2488	+	6.67308i	0.741761	+	0.347387i
$370$	3.50954	+	6.07870i	0.182452	+	0.316017i
$371$	16.0910	−	31.9689i	0.835404	−	1.65974i
$372$	6.82280	−	13.0800i	0.353746	−	0.678167i
$373$	7.06962	−	12.2449i	0.366051	−	0.634019i	−0.622893	−	0.782307i	$-0.714043\pi$
$373$	7.06962	−	12.2449i	0.366051	−	0.634019i	0.988944	+	0.148288i	$0.0473762\pi$
$374$	−12.8832	−	22.3144i	−0.666177	−	1.15385i
$375$	−0.788941	−	18.4199i	−0.0407407	−	0.951200i
$376$	−4.18472	+	2.41605i	−0.215811	+	0.124598i
$377$	0.848869	+	3.12059i	0.0437190	+	0.160719i
$378$	2.53833	+	13.5114i	0.130557	+	0.694949i
$379$	9.57195	+	5.52637i	0.491678	+	0.283871i	0.725270	−	0.688464i	$-0.241715\pi$
$379$	9.57195	+	5.52637i	0.491678	+	0.283871i	−0.233592	+	0.972335i	$0.575048\pi$
$380$			8.37711i			0.429737i
$381$	9.41065	−	18.0412i	0.482122	−	0.924278i
$382$	−8.74352	−	5.04808i	−0.447358	−	0.258282i
$383$	−0.828157	−	0.478136i	−0.0423168	−	0.0244316i	0.478692	−	0.877983i	$-0.341111\pi$
$383$	−0.828157	−	0.478136i	−0.0423168	−	0.0244316i	−0.521009	+	0.853551i	$0.674444\pi$
$384$	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
$387$	5.90764	+	8.46681i	0.300302	+	0.430392i
$388$	6.21010	+	10.7562i	0.315270	+	0.546064i
$389$	−2.35900	−	1.36197i	−0.119606	−	0.0690546i	0.439003	−	0.898485i	$-0.355332\pi$
$389$	−2.35900	−	1.36197i	−0.119606	−	0.0690546i	−0.558609	+	0.829431i	$0.688665\pi$
$390$	7.73980	+	1.69179i	0.391920	+	0.0856673i
$391$			13.5078i			0.683119i
$392$	−6.95410	+	0.800271i	−0.351235	+	0.0404198i
$393$	−4.38466	−	6.89514i	−0.221177	−	0.347814i
$394$	−7.07350	+	12.2517i	−0.356358	+	0.617230i
$395$	6.48222	+	3.74251i	0.326156	+	0.188306i
$396$	8.84134	+	12.6714i	0.444294	+	0.636761i
$397$	−12.1261	+	21.0031i	−0.608593	+	1.05411i	0.382879	+	0.923798i	$0.374932\pi$
$397$	−12.1261	+	21.0031i	−0.608593	+	1.05411i	−0.991473	+	0.130316i	$0.958401\pi$
$398$			15.3246i			0.768150i
$399$	27.5868	+	12.4357i	1.38107	+	0.622565i
$400$	−1.69530	+	2.93635i	−0.0847650	+	0.146817i
$401$	−32.8317			−1.63954			−0.819768	−	0.572696i	$-0.805898\pi$
$401$	−32.8317			−1.63954			−0.819768	+	0.572696i	$0.805898\pi$
$402$	−16.9033	+	10.7489i	−0.843060	+	0.536107i
$403$	−29.6331	+	8.06083i	−1.47613	+	0.401539i
$404$	−4.72713	−	8.18763i	−0.235183	−	0.407350i
$405$	−8.77066	+	7.31006i	−0.435818	+	0.363240i
$406$	1.06693	−	2.11973i	0.0529510	−	0.105200i
$407$	24.6782	−	14.2480i	1.22325	−	0.706246i
$408$	−8.65730	+	0.370800i	−0.428600	+	0.0183573i
$409$	−19.9476			−0.986347			−0.493173	−	0.869931i	$-0.664163\pi$
$409$	−19.9476			−0.986347			−0.493173	+	0.869931i	$0.664163\pi$
$410$	−6.65348			−0.328592
$411$	−16.6448	+	0.712910i	−0.821027	+	0.0351653i
$412$	−15.4442	+	8.91672i	−0.760881	+	0.439295i
$413$	31.2572	−	1.79260i	1.53806	−	0.0882083i
$414$	−0.692590	−	8.07035i	−0.0340390	−	0.396636i
$415$	−5.84918	−	10.1311i	−0.287125	−	0.497315i
$416$	−2.55917	−	2.53981i	−0.125474	−	0.124525i
$417$	−3.06154	+	1.94685i	−0.149924	+	0.0953377i
$418$	34.0093			1.66345
$419$	2.15496	−	3.73250i	0.105277	−	0.182345i	−0.808574	−	0.588394i	$-0.799760\pi$
$419$	2.15496	−	3.73250i	0.105277	−	0.182345i	0.913851	+	0.406049i	$0.133094\pi$
$420$	−3.39532	−	4.71903i	−0.165675	−	0.230265i
$421$			9.35440i			0.455905i	0.973672	+	0.227953i	$0.0732032\pi$
$421$			9.35440i			0.455905i	−0.973672	+	0.227953i	$0.926797\pi$
$422$	4.63016	−	8.01968i	0.225393	−	0.390392i
$423$	−11.8884	+	8.29505i	−0.578036	+	0.403319i
$424$	−11.7150	−	6.76369i	−0.568933	−	0.328474i
$425$	8.48138	−	14.6902i	0.411407	−	0.712578i
$426$	7.04694	+	11.0817i	0.341426	+	0.536912i
$427$	−5.55216	+	11.0308i	−0.268688	+	0.533816i
$428$			9.73378i			0.470500i
$429$	6.86832	−	31.4219i	0.331606	−	1.51706i
$430$	−3.78089	−	2.18290i	−0.182331	−	0.105269i
$431$	0.433968	+	0.751655i	0.0209035	+	0.0362060i	0.876288	−	0.481788i	$-0.160012\pi$
$431$	0.433968	+	0.751655i	0.0209035	+	0.0362060i	−0.855384	+	0.517994i	$0.826679\pi$
$432$	5.15337	−	0.665427i	0.247942	−	0.0320154i
$433$	−20.7610	+	11.9864i	−0.997710	+	0.576028i	−0.907570	−	0.419901i	$-0.862065\pi$
$433$	−20.7610	+	11.9864i	−0.997710	+	0.576028i	−0.0901401	+	0.995929i	$0.528731\pi$
$434$	20.1289	+	10.1316i	0.966217	+	0.486330i
$435$	1.96907	−	0.0843370i	0.0944098	−	0.00404365i
$436$	9.16977	+	5.29417i	0.439152	+	0.253545i
$437$	−15.4404	−	8.91450i	−0.738613	−	0.426438i
$438$	0.337714	−	0.647432i	0.0161366	−	0.0309355i
$439$		−	18.1387i		−	0.865711i	−0.901463	−	0.432855i	$-0.857506\pi$
$439$		−	18.1387i		−	0.865711i	0.901463	−	0.432855i	$-0.142494\pi$
$440$	−5.65846	−	3.26691i	−0.269756	−	0.155744i
$441$	−20.5806	+	4.17585i	−0.980030	+	0.198850i
$442$	12.8032	+	12.7064i	0.608987	+	0.604381i
$443$	25.1388	−	14.5139i	1.19438	−	0.689575i	0.235082	−	0.971975i	$-0.424464\pi$
$443$	25.1388	−	14.5139i	1.19438	−	0.689575i	0.959297	+	0.282401i	$0.0911307\pi$
$444$	−0.410079	−	9.57438i	−0.0194615	−	0.454380i
$445$	5.27015	+	9.12816i	0.249829	+	0.432716i
$446$	6.58695	−	11.4089i	0.311901	−	0.540228i
$447$	6.17309	−	11.8344i	0.291977	−	0.559750i
$448$	0.151485	+	2.64141i	0.00715702	+	0.124795i
$449$	1.47303	+	2.55136i	0.0695165	+	0.120406i	0.898689	−	0.438587i	$-0.144521\pi$
$449$	1.47303	+	2.55136i	0.0695165	+	0.120406i	−0.829172	+	0.558993i	$0.811188\pi$
$450$	−4.31406	+	9.21164i	−0.203367	+	0.434241i
$451$			27.0117i			1.27193i
$452$	2.68329	−	1.54920i	0.126211	−	0.0728680i
$453$	0.932265	+	0.486289i	0.0438016	+	0.0228478i
$454$		−	2.37069i		−	0.111262i
$455$	−2.41277	+	11.8589i	−0.113112	+	0.555955i
$456$	5.28955	−	10.1406i	0.247706	−	0.474878i
$457$			19.3905i			0.907049i	0.891244	+	0.453524i	$0.149833\pi$
$457$			19.3905i			0.907049i	−0.891244	+	0.453524i	$0.850167\pi$
$458$	5.91454	+	10.2443i	0.276368	+	0.478684i
$459$	−25.7817	+	3.32905i	−1.20339	+	0.155387i
$460$	1.71264	+	2.96638i	0.0798523	+	0.138308i
$461$	−18.5093	+	10.6864i	−0.862066	+	0.497714i	−0.864704	−	0.502283i	$-0.832494\pi$
$461$	−18.5093	+	10.6864i	−0.862066	+	0.497714i	0.00263775	+	0.999997i	$0.499160\pi$
$462$	−19.1582	+	13.7843i	−0.891322	+	0.641302i
$463$		−	7.17045i		−	0.333239i	−0.986021	−	0.166620i	$-0.946715\pi$
$463$		−	7.17045i		−	0.333239i	0.986021	−	0.166620i	$-0.0532852\pi$
$464$	−0.776779	−	0.448474i	−0.0360611	−	0.0208199i
$465$	0.800861	+	18.6982i	0.0371391	+	0.867110i
$466$	6.84440	−	3.95162i	0.317061	−	0.183055i
$467$	4.50077	+	7.79557i	0.208271	+	0.360736i	0.951170	−	0.308668i	$-0.0998831\pi$
$467$	4.50077	+	7.79557i	0.208271	+	0.360736i	−0.742899	+	0.669404i	$0.766550\pi$
$468$	−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
$471$	20.4956	+	10.6909i	0.944387	+	0.492612i
$472$		−	11.8335i		−	0.544681i
$473$	−8.86209	+	15.3496i	−0.407479	+	0.705775i
$474$	−5.48369	−	8.62342i	−0.251874	−	0.396087i
$475$	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
$478$	27.3019			1.24876
$479$	3.50004	−	2.02075i	0.159921	−	0.0923303i	−0.417904	−	0.908491i	$-0.637235\pi$
$479$	3.50004	−	2.02075i	0.159921	−	0.0923303i	0.577825	+	0.816161i	$0.303902\pi$
$480$	−1.85418	+	1.17908i	−0.0846312	+	0.0538175i
$481$	−14.0524	+	14.1595i	−0.640734	+	0.645616i
$482$	−11.2815			−0.513859
$483$	12.3110	−	1.23637i	0.560172	−	0.0562568i
$484$	−7.76296	+	13.4458i	−0.352862	+	0.611175i
$485$	−13.6456	−	7.87827i	−0.619613	−	0.357734i
$486$	15.2328	−	3.31088i	0.690974	−	0.150185i
$487$		−	13.7020i		−	0.620897i	−0.950590	−	0.310449i	$-0.899521\pi$
$487$		−	13.7020i		−	0.620897i	0.950590	−	0.310449i	$-0.100479\pi$
$488$	4.04224	+	2.33379i	0.182984	+	0.105646i
$489$	23.0810	+	12.0395i	1.04376	+	0.544447i
$490$	7.13257	−	5.29029i	0.322216	−	0.238991i
$491$	−19.4095	−	11.2061i	−0.875940	−	0.505724i	−0.00662258	−	0.999978i	$-0.502108\pi$
$491$	−19.4095	−	11.2061i	−0.875940	−	0.505724i	−0.869318	+	0.494254i	$0.835441\pi$
$492$	8.05413	+	4.20120i	0.363108	+	0.189405i
$493$	3.88613	+	2.24366i	0.175023	+	0.101049i
$494$	−22.9738	+	6.24937i	−1.03364	+	0.281172i
$495$	−17.7512	−	8.31337i	−0.797858	−	0.373658i
$496$	4.25869	−	7.37627i	0.191221	−	0.331204i
$497$	−16.7700	+	11.0084i	−0.752236	+	0.493794i
$498$	0.683458	+	15.9571i	0.0306265	+	0.715057i
$499$	17.1062	−	9.87625i	0.765777	−	0.442122i	−0.0655891	−	0.997847i	$-0.520893\pi$
$499$	17.1062	−	9.87625i	0.765777	−	0.442122i	0.831366	+	0.555725i	$0.187559\pi$
$500$		−	10.6445i		−	0.476036i
$501$	−25.9428	−	13.5323i	−1.15904	−	0.604578i
$502$	11.3067	+	19.5838i	0.504644	+	0.874069i
$503$	−3.11599	−	5.39705i	−0.138935	−	0.240643i	0.788159	−	0.615472i	$-0.211035\pi$
$503$	−3.11599	−	5.39705i	−0.138935	−	0.240643i	−0.927094	+	0.374829i	$0.877701\pi$
$504$	1.13035	+	7.85635i	0.0503499	+	0.349950i
$505$	10.3870	+	5.99694i	0.462215	+	0.266860i
$506$	12.0429	−	6.95296i	0.535371	−	0.309097i
$507$	1.13427	+	22.4881i	0.0503748	+	0.998730i
$508$	5.87399	−	10.1740i	0.260616	−	0.451400i
$509$			16.1726i			0.716839i	0.933561	+	0.358419i	$0.116684\pi$
$509$			16.1726i			0.716839i	−0.933561	+	0.358419i	$0.883316\pi$
$510$	9.27622	−	5.89880i	0.410758	−	0.261203i
$511$	0.996336	+	0.501490i	0.0440753	+	0.0221846i
$512$	1.00000			0.0441942
$513$	13.2093	−	31.6673i	0.583206	−	1.39814i
$514$	−1.36558			−0.0602330
$515$	11.3119	−	19.5929i	0.498464	−	0.863364i
$516$	3.19847	+	5.02979i	0.140805	+	0.221424i
$517$	−21.5527	−	12.4435i	−0.947887	−	0.547263i
$518$	14.6145	−	0.838145i	0.642124	−	0.0368260i
$519$	−0.410812	+	0.787568i	−0.0180326	+	0.0345704i
$520$	4.42268	+	1.16708i	0.193948	+	0.0511799i
$521$	8.95460	−	15.5098i	0.392308	−	0.679498i	−0.600445	−	0.799666i	$-0.705010\pi$
$521$	8.95460	−	15.5098i	0.392308	−	0.679498i	0.992754	+	0.120168i	$0.0383433\pi$
$522$	−2.43684	−	1.14124i	−0.106658	−	0.0499506i
$523$		−	15.3139i		−	0.669630i	−0.942284	−	0.334815i	$-0.891326\pi$
$523$		−	15.3139i		−	0.669630i	0.942284	−	0.334815i	$-0.108674\pi$
$524$	−2.35882	−	4.08559i	−0.103045	−	0.178480i
$525$	−14.1650	−	6.38536i	−0.618210	−	0.278680i
$526$	−9.36276	+	5.40559i	−0.408236	+	0.235695i
$527$	−21.3057	+	36.9026i	−0.928091	+	1.60750i
$528$	4.78682	+	7.52756i	0.208320	+	0.327595i
$529$	15.7100			0.683042
$530$	17.1611			0.745431
$531$	−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
$534$	−0.615800	−	14.3775i	−0.0266483	−	0.622175i
$535$	−6.17424	−	10.6941i	−0.266936	−	0.462346i
$536$	−10.0157	+	5.78259i	−0.432614	+	0.249770i
$537$	−11.7211	+	7.45351i	−0.505802	+	0.321643i
$538$	−22.9534			−0.989592
$539$	−21.4774	−	28.9567i	−0.925099	−	1.24725i
$540$	−5.23970	+	3.99991i	−0.225481	+	0.172129i
$541$	−3.16570	+	1.82772i	−0.136104	+	0.0785797i	−0.566506	−	0.824058i	$-0.691705\pi$
$541$	−3.16570	+	1.82772i	−0.136104	+	0.0785797i	0.430402	+	0.902637i	$0.358372\pi$
$542$	−15.5927			−0.669766
$543$	−0.0340253	−	0.794412i	−0.00146017	−	0.0340915i
$544$	−5.00288			−0.214497
$545$	−13.4326			−0.575389
$546$	10.4088	−	12.8319i	0.445454	−	0.549155i
$547$	−44.4370			−1.89999			−0.949995	−	0.312265i	$-0.898912\pi$
$547$	−44.4370			−1.89999			−0.949995	+	0.312265i	$0.898912\pi$
$548$	−9.61868			−0.410890
$549$	12.6810	+	5.93883i	0.541210	+	0.253463i
$550$	−17.4627			−0.744613
$551$	−5.12932	+	2.96141i	−0.218516	+	0.126160i
$552$	−0.200117	−	4.67226i	−0.00851754	−	0.198865i
$553$	13.0498	−	8.56636i	0.554934	−	0.364279i
$554$	22.3309			0.948750
$555$	6.52367	+	10.2589i	0.276914	+	0.435464i
$556$	−1.81406	+	1.04735i	−0.0769333	+	0.0444175i
$557$	−0.938911	−	1.62624i	−0.0397830	−	0.0689061i	0.845448	−	0.534057i	$-0.179333\pi$
$557$	−0.938911	−	1.62624i	−0.0397830	−	0.0689061i	−0.885231	+	0.465151i	$0.846000\pi$
$558$	10.8372	−	23.1402i	0.458774	−	0.979602i
$559$	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
$562$	21.7986			0.919520
$563$	−6.19768			−0.261201			−0.130601	−	0.991435i	$-0.541691\pi$
$563$	−6.19768			−0.261201			−0.130601	+	0.991435i	$0.541691\pi$
$564$	−7.06244	+	4.49105i	−0.297382	+	0.189107i
$565$	−1.96534	+	3.40407i	−0.0826826	+	0.143210i
$566$	3.89678	−	2.24981i	0.163794	−	0.0945664i
$567$	5.39391	+	23.1928i	0.226523	+	0.974006i
$568$	3.79105	+	6.56628i	0.159069	+	0.275515i
$569$		−	6.56295i		−	0.275133i	−0.990493	−	0.137567i	$-0.956072\pi$
$569$		−	6.56295i		−	0.275133i	0.990493	−	0.137567i	$-0.0439281\pi$
$570$	0.620888	+	14.4963i	0.0260062	+	0.607183i
$571$	−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	$0.288231\pi$
$572$	4.73810	−	17.9552i	0.198110	−	0.750743i
$573$	−15.5045	−	8.08747i	−0.647710	−	0.337859i
$574$	−6.23859	+	12.3945i	−0.260394	+	0.517338i
$575$	7.92815	+	4.57732i	0.330627	+	0.190887i
$576$	2.98901	−	0.256514i	0.124542	−	0.0106881i
$577$	−1.86181	+	3.22475i	−0.0775082	+	0.134248i	−0.902174	−	0.431372i	$-0.858030\pi$
$577$	−1.86181	+	3.22475i	−0.0775082	+	0.134248i	0.824666	+	0.565620i	$0.191363\pi$
$578$	8.02879			0.333954
$579$	12.1021	−	7.69579i	0.502946	−	0.319826i
$580$	1.13789			0.0472482
$581$	−24.3573	+	1.39689i	−1.01051	+	0.0579529i
$582$	11.5436	+	18.1530i	0.478497	+	0.752464i
$583$		−	69.6705i		−	2.88546i
$584$	0.210796	−	0.365109i	0.00872279	−	0.0151083i
$585$	13.5188	+	2.35394i	0.558935	+	0.0973233i
$586$	11.6501	−	6.72621i	0.481263	−	0.277857i
$587$	−36.8272	−	21.2622i	−1.52002	−	0.877585i	−0.999721	−	0.0236021i	$-0.992487\pi$
$587$	−36.8272	−	21.2622i	−1.52002	−	0.877585i	−0.520301	−	0.853983i	$-0.674180\pi$
$588$	−11.9745	+	1.90026i	−0.493821	+	0.0783654i
$589$	−28.1215	−	48.7078i	−1.15873	−	2.00697i
$590$	7.50612	+	13.0010i	0.309022	+	0.535242i
$591$	−11.3324	+	21.7253i	−0.466152	+	0.893661i
$592$		−	5.53284i		−	0.227398i
$593$	−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
$595$	9.21483	+	14.0377i	0.377771	+	0.575489i
$596$	3.85315	−	6.67385i	0.157831	−	0.273371i
$597$	1.13581	+	26.5186i	0.0464858	+	1.08533i
$598$	−6.85751	+	6.90977i	−0.280424	+	0.282561i
$599$	−7.32482	−	4.22899i	−0.299284	−	0.172792i	0.342837	−	0.939395i	$-0.388612\pi$
$599$	−7.32482	−	4.22899i	−0.299284	−	0.172792i	−0.642121	+	0.766603i	$0.721945\pi$
$600$	−2.71602	+	5.20689i	−0.110881	+	0.212570i
$601$	−12.8550	−	7.42186i	−0.524368	−	0.302744i	0.214352	−	0.976756i	$-0.431236\pi$
$601$	−12.8550	−	7.42186i	−0.524368	−	0.302744i	−0.738720	+	0.674013i	$0.764569\pi$
$602$	−7.61157	+	4.99651i	−0.310224	+	0.203642i
$603$	−28.4539	+	19.8534i	−1.15873	+	0.808494i
$604$	0.525736	+	0.303534i	0.0213919	+	0.0123506i
$605$		−	19.6965i		−	0.800778i
$606$	−8.78697	−	13.8180i	−0.356946	−	0.561319i
$607$	−23.5350	−	13.5879i	−0.955256	−	0.551517i	−0.0605460	−	0.998165i	$-0.519284\pi$
$607$	−23.5350	−	13.5879i	−0.955256	−	0.551517i	−0.894710	+	0.446648i	$0.852618\pi$
$608$	3.30166	−	5.71864i	0.133900	−	0.231922i
$609$	1.68918	−	3.74719i	0.0684490	−	0.151844i
$610$	−5.92139			−0.239750
$611$	16.8457	+	4.44534i	0.681505	+	0.179839i
$612$	−14.9537	+	1.28331i	−0.604466	+	0.0518748i
$613$	12.8149	−	7.39869i	0.517590	−	0.298830i	−0.218358	−	0.975869i	$-0.570070\pi$
$613$	12.8149	−	7.39869i	0.517590	−	0.298830i	0.735948	+	0.677038i	$0.236737\pi$
$614$	15.8067			0.637906
$615$	−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	0.576594	−	0.817031i	$-0.304381\pi$
$617$	−10.4145	−	18.0385i	−0.419272	−	0.726201i	−0.995866	+	0.0908296i	$0.971048\pi$
$618$	−26.0648	+	16.5747i	−1.04848	+	0.666734i
$619$	13.6057	−	23.5658i	0.546860	−	0.947189i	−0.451627	−	0.892207i	$-0.649156\pi$
$619$	13.6057	−	23.5658i	0.546860	−	0.947189i	0.998487	−	0.0549827i	$-0.0175104\pi$
$620$			10.8053i			0.433953i
$621$	−1.79665	−	13.9141i	−0.0720973	−	0.558354i
$622$	−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
$626$	−14.2929	+	8.25201i	−0.571259	+	0.329817i
$627$	58.8519	−	2.52067i	2.35032	−	0.100666i
$628$	11.5582	+	6.67311i	0.461221	+	0.266286i
$629$			27.6801i			1.10368i
$630$	−6.22524	−	7.91446i	−0.248020	−	0.315319i
$631$	−23.4710	+	13.5510i	−0.934365	+	0.539456i	−0.888189	−	0.459478i	$-0.848037\pi$
$631$	−23.4710	+	13.5510i	−0.934365	+	0.539456i	−0.0461755	+	0.998933i	$0.514703\pi$
$632$	−2.95006	−	5.10965i	−0.117347	−	0.203251i
$633$	7.41793	−	14.2209i	0.294836	−	0.565232i
$634$	14.8285	+	25.6838i	0.588917	+	1.02003i
$635$			14.9037i			0.591436i
$636$	−20.7738	−	10.8360i	−0.823734	−	0.429677i
$637$	19.8293	+	15.6141i	0.785664	+	0.618653i
$638$		−	4.61958i		−	0.182891i
$639$	13.0158	+	18.6542i	0.514898	+	0.737951i
$640$	−1.09866	+	0.634311i	−0.0434283	+	0.0250733i
$641$		−	6.37483i		−	0.251791i	−0.992044	−	0.125895i	$-0.959820\pi$
$641$		−	6.37483i		−	0.251791i	0.992044	−	0.125895i	$-0.0401804\pi$
$642$	0.721441	+	16.8440i	0.0284730	+	0.664778i
$643$	21.5821	+	37.3812i	0.851113	+	1.47417i	0.880204	+	0.474595i	$0.157405\pi$
$643$	21.5821	+	37.3812i	0.851113	+	1.47417i	−0.0290911	+	0.999577i	$0.509261\pi$
$644$	7.13182	−	0.409011i	0.281033	−	0.0161173i
$645$	−6.70448	−	3.49719i	−0.263989	−	0.137702i
$646$	−16.5178	+	28.6097i	−0.649884	+	1.12563i
$647$	−10.6092	−	18.3756i	−0.417089	−	0.722419i	0.578556	−	0.815642i	$-0.303616\pi$
$647$	−10.6092	−	18.3756i	−0.417089	−	0.722419i	−0.995645	+	0.0932232i	$0.970283\pi$
$648$	8.86840	−	1.53345i	0.348384	−	0.0602396i
$649$	52.7812	−	30.4732i	2.07184	−	1.19618i
$650$	11.7963	−	3.20886i	0.462690	−	0.125862i
$651$	35.5832	+	16.0404i	1.39462	+	0.628673i
$652$	13.0162	+	7.51490i	0.509753	+	0.294306i
$653$			39.8572i			1.55973i	0.625946	+	0.779867i	$0.284713\pi$
$653$			39.8572i			1.55973i	−0.625946	+	0.779867i	$0.715287\pi$
$654$	16.2604	+	8.48174i	0.635830	+	0.331662i
$655$	5.18307	+	2.99245i	0.202519	+	0.116925i
$656$	4.54200	+	2.62233i	0.177335	+	0.102385i
$657$	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	0.214431	−	0.976739i	$-0.431210\pi$
$659$	29.9716	−	17.3041i	1.16753	−	0.674072i	0.953096	+	0.302667i	$0.0978769\pi$
$660$	−10.0339	−	5.23388i	−0.390569	−	0.203729i
$661$	9.59801	+	16.6242i	0.373319	+	0.646608i	0.990074	−	0.140547i	$-0.0448862\pi$
$661$	9.59801	+	16.6242i	0.373319	+	0.646608i	−0.616755	+	0.787155i	$0.711553\pi$
$662$	−27.3462	−	15.7883i	−1.06284	−	0.613631i
$663$	23.0973	+	21.0390i	0.897023	+	0.817087i
$664$			9.22131i			0.357856i
$665$	−22.1274	+	1.26901i	−0.858064	+	0.0492101i
$666$	−1.41925	−	16.5377i	−0.0549950	−	0.640824i
$667$	−1.21088	+	2.09731i	−0.0468855	+	0.0812080i
$668$	−14.6300	−	8.44665i	−0.566053	−	0.326811i
$669$	10.5529	−	20.2309i	0.407998	−	0.782174i
$670$	7.33592	−	12.7062i	0.283411	−	0.490883i
$671$			24.0396i			0.928038i
$672$	0.457914	+	4.55964i	0.0176644	+	0.175892i
$673$	10.3779	−	17.9751i	0.400039	−	0.692888i	−0.593691	−	0.804693i	$-0.702330\pi$
$673$	10.3779	−	17.9751i	0.400039	−	0.692888i	0.993730	+	0.111805i	$0.0356632\pi$
$674$	18.8701			0.726850
$675$	−6.78258	+	16.2602i	−0.261062	+	0.625854i
$676$	0.0986879	+	12.9996i	0.00379569	+	0.499986i
$677$	3.91466	+	6.78038i	0.150452	+	0.260591i	0.931394	−	0.364013i	$-0.118594\pi$
$677$	3.91466	+	6.78038i	0.150452	+	0.260591i	−0.780941	+	0.624604i	$0.785260\pi$
$678$	4.52851	−	2.87971i	0.173916	−	0.110594i
$679$	−27.4708	+	18.0328i	−1.05423	+	0.692037i
$680$	5.49645	−	3.17338i	0.210779	−	0.121694i
$681$	−0.175709	−	4.10240i	−0.00673319	−	0.157204i
$682$	43.8673			1.67977
$683$	25.4681			0.974511			0.487255	−	0.873260i	$-0.337998\pi$
$683$	25.4681			0.974511			0.487255	+	0.873260i	$0.337998\pi$
$684$	8.40179	−	17.9400i	0.321250	−	0.685954i
$685$	10.5676	−	6.10123i	0.403769	−	0.233116i
$686$	−3.16729	−	18.2474i	−0.120928	−	0.696690i
$687$	10.9942	+	17.2890i	0.419454	+	0.659616i
$688$	1.72068	+	2.98031i	0.0656004	+	0.113623i
$689$	12.8023	+	47.0635i	0.487728	+	1.79298i
$690$	3.18353	+	5.00628i	0.121195	+	0.190586i
$691$	−18.3430			−0.697801			−0.348901	−	0.937160i	$-0.613445\pi$
$691$	−18.3430			−0.697801			−0.348901	+	0.937160i	$0.613445\pi$
$692$	−0.256422	+	0.444137i	−0.00974772	+	0.0168835i
$693$	−32.1310	+	25.2731i	−1.22056	+	0.960048i
$694$		−	5.84190i		−	0.221755i
$695$	1.32869	−	2.30136i	0.0504000	−	0.0872954i
$696$	−1.37743	−	0.718495i	−0.0522113	−	0.0272345i
$697$	−22.7231	−	13.1192i	−0.860698	−	0.496924i
$698$	−4.14640	+	7.18177i	−0.156943	+	0.271834i
$699$	11.5511	−	7.34542i	0.436903	−	0.277829i
$700$	−8.01291	−	4.03317i	−0.302859	−	0.152439i
$701$		−	4.16816i		−	0.157429i	−0.996897	−	0.0787147i	$-0.974918\pi$
$701$		−	4.16816i		−	0.157429i	0.996897	−	0.0787147i	$-0.0250816\pi$
$702$	−14.8784	−	11.3857i	−0.561549	−	0.429724i
$703$	−31.6403	−	18.2676i	−1.19334	−	0.688974i
$704$	2.57517	+	4.46032i	0.0970552	+	0.168105i
$705$	4.91049	−	9.41391i	0.184940	−	0.354548i
$706$	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
$709$	−16.0287	−	9.25420i	−0.601972	−	0.347549i	0.167845	−	0.985813i	$-0.446319\pi$
$709$	−16.0287	−	9.25420i	−0.601972	−	0.347549i	−0.769817	+	0.638265i	$0.779653\pi$
$710$	−8.33013	−	4.80940i	−0.312624	−	0.180494i
$711$	−10.1285	−	14.5161i	−0.379847	−	0.544396i
$712$		−	8.30846i		−	0.311373i
$713$	−19.9160	−	11.4985i	−0.745859	−	0.430622i
$714$	−2.29089	−	22.8113i	−0.0857344	−	0.853692i
$715$	6.18360	+	22.7320i	0.231253	+	0.850129i
$716$	−6.94512	+	4.00977i	−0.259551	+	0.149852i
$717$	47.2450	−	2.02354i	1.76440	−	0.0755706i
$718$	10.1960	+	17.6599i	0.380510	+	0.659062i
$719$	−5.00141	+	8.66270i	−0.186521	+	0.323064i	−0.944088	−	0.329693i	$-0.893055\pi$
$719$	−5.00141	+	8.66270i	−0.186521	+	0.323064i	0.757567	+	0.652758i	$0.226388\pi$
$720$	−3.12119	+	2.17779i	−0.116320	+	0.0811613i
$721$	−25.8923	−	39.4437i	−0.964279	−	1.46896i
$722$	−12.3019	−	21.3075i	−0.457830	−	0.792984i
$723$	−19.5223	+	0.836156i	−0.726041	+	0.0310970i
$724$		−	0.459074i		−	0.0170614i
$725$	2.63375	−	1.52059i	0.0978149	−	0.0564734i
$726$	−12.4370	+	23.8429i	−0.461579	+	0.884894i
$727$			27.8818i			1.03408i	0.855961	+	0.517040i	$0.172966\pi$
$727$			27.8818i			1.03408i	−0.855961	+	0.517040i	$0.827034\pi$
$728$	6.32102	−	7.14456i	0.234272	−	0.264795i
$729$	26.1144	−	6.85838i	0.967201	−	0.254014i
$730$			0.534840i			0.0197953i
$731$	−8.60837	−	14.9101i	−0.318392	−	0.551471i
$732$	7.16793	+	3.73894i	0.264934	+	0.138195i
$733$	9.38772	+	16.2600i	0.346743	+	0.600577i	0.985669	−	0.168691i	$-0.0539541\pi$
$733$	9.38772	+	16.2600i	0.346743	+	0.600577i	−0.638925	+	0.769269i	$0.720621\pi$
$734$	−14.1857	+	8.19011i	−0.523603	+	0.302302i
$735$	11.9505	−	9.68330i	0.440803	−	0.357174i
$736$		−	2.70000i		−	0.0995235i
$737$	−51.5844	−	29.7823i	−1.90014	−	1.09704i
$738$	14.2488	+	6.67308i	0.524505	+	0.245639i
$739$	4.75988	−	2.74812i	0.175095	−	0.101091i	−0.409891	−	0.912135i	$-0.634433\pi$
$739$	4.75988	−	2.74812i	0.175095	−	0.101091i	0.584986	+	0.811043i	$0.301100\pi$
$740$	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	−0.983412	−	0.181386i	$-0.941942\pi$
$743$	−9.12112	+	15.7982i	−0.334621	+	0.579581i	0.648791	+	0.760967i	$0.275275\pi$
$744$	6.82280	−	13.0800i	0.250136	−	0.479536i
$745$			9.77637i			0.358179i
$746$	7.06962	−	12.2449i	0.258837	−	0.448319i
$747$	2.36540	+	27.5626i	0.0865454	+	1.00846i
$748$	−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
$751$	−20.5779			−0.750898			−0.375449	−	0.926843i	$-0.622511\pi$
$751$	−20.5779			−0.750898			−0.375449	+	0.926843i	$0.622511\pi$
$752$	−4.18472	+	2.41605i	−0.152601	+	0.0881043i
$753$	21.0174	+	33.0511i	0.765916	+	1.20445i
$754$	0.848869	+	3.12059i	0.0309140	+	0.113645i
$755$	−0.770139			−0.0280282
$756$	2.53833	+	13.5114i	0.0923180	+	0.491403i
$757$	1.82325	−	3.15796i	0.0662672	−	0.114778i	−0.830988	−	0.556290i	$-0.812224\pi$
$757$	1.82325	−	3.15796i	0.0662672	−	0.114778i	0.897255	+	0.441512i	$0.145558\pi$
$758$	9.57195	+	5.52637i	0.347669	+	0.200727i
$759$	20.3244	−	12.9244i	0.737731	−	0.469127i
$760$			8.37711i			0.303870i
$761$	39.7985	+	22.9777i	1.44269	+	0.832940i	0.998029	−	0.0627562i	$-0.0199890\pi$
$761$	39.7985	+	22.9777i	1.44269	+	0.832940i	0.444666	+	0.895696i	$0.353322\pi$
$762$	9.41065	−	18.0412i	0.340912	−	0.653563i
$763$	−12.5950	+	25.0231i	−0.455969	+	0.905898i
$764$	−8.74352	−	5.04808i	−0.316330	−	0.182633i
$765$	15.6150	−	10.8952i	0.564560	−	0.393917i
$766$	−0.828157	−	0.478136i	−0.0299225	−	0.0172758i
$767$	−30.0549	+	30.2839i	−1.08522	+	1.09349i
$768$	1.73046	−	0.0741172i	0.0624428	−	0.00267448i
$769$	−3.19274	+	5.52999i	−0.115133	+	0.199417i	−0.917833	−	0.396967i	$-0.870063\pi$
$769$	−3.19274	+	5.52999i	−0.115133	+	0.199417i	0.802700	+	0.596383i	$0.203396\pi$
$770$	7.77208	−	15.4412i	0.280086	−	0.556462i
$771$	−2.36308	+	0.101213i	−0.0851043	+	0.00364509i
$772$	7.17088	−	4.14011i	0.258086	−	0.149006i
$773$			8.98086i			0.323019i	0.986871	+	0.161510i	$0.0516363\pi$
$773$			8.98086i			0.323019i	−0.986871	+	0.161510i	$0.948364\pi$
$774$	5.90764	+	8.46681i	0.212346	+	0.304333i
$775$	14.4395	+	25.0100i	0.518683	+	0.898385i
$776$	6.21010	+	10.7562i	0.222930	+	0.386125i
$777$	25.2278	−	2.53357i	0.905041	−	0.0908912i
$778$	−2.35900	−	1.36197i	−0.0845742	−	0.0488289i
$779$	29.9923	−	17.3161i	1.07459	−	0.620412i
$780$	7.73980	+	1.69179i	0.277129	+	0.0605759i
$781$	−19.5251	+	33.8185i	−0.698665	+	1.21012i
$782$			13.5078i			0.483038i
$783$	−4.30145	−	1.79426i	−0.153721	−	0.0641216i
$784$	−6.95410	+	0.800271i	−0.248361	+	0.0285811i
$785$	−16.9313			−0.604304
$786$	−4.38466	−	6.89514i	−0.156396	−	0.245941i
$787$	25.2874			0.901400			0.450700	−	0.892676i	$-0.351174\pi$
$787$	25.2874			0.901400			0.450700	+	0.892676i	$0.351174\pi$
$788$	−7.07350	+	12.2517i	−0.251983	+	0.436448i
$789$	−15.8013	+	10.0481i	−0.562540	+	0.357723i
$790$	6.48222	+	3.74251i	0.230627	+	0.133152i
$791$	4.49854	+	6.85298i	0.159950	+	0.243664i
$792$	8.84134	+	12.6714i	0.314163	+	0.450258i
$793$	−4.41739	−	16.2391i	−0.156866	−	0.576667i
$794$	−12.1261	+	21.0031i	−0.430340	+	0.745371i
$795$	29.6967	−	1.27193i	1.05323	−	0.0451109i
$796$			15.3246i			0.543164i
$797$	17.4459	+	30.2171i	0.617964	+	1.07034i	0.989857	+	0.142069i	$0.0453756\pi$
$797$	17.4459	+	30.2171i	0.617964	+	1.07034i	−0.371893	+	0.928276i	$0.621291\pi$
$798$	27.5868	+	12.4357i	0.976563	+	0.440220i
$799$	20.9357	−	12.0872i	0.740650	−	0.427615i
$800$	−1.69530	+	2.93635i	−0.0599379	+	0.103815i
$801$	−2.13124	−	24.8341i	−0.0753037	−	0.877470i
$802$	−32.8317			−1.15933
$803$	2.17134			0.0766248
$804$	−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
$807$	−39.7201	+	1.70124i	−1.39821	+	0.0598866i
$808$	−4.72713	−	8.18763i	−0.166300	−	0.288040i
$809$	−9.85463	+	5.68957i	−0.346470	+	0.200035i	−0.663130	−	0.748505i	$-0.730772\pi$
$809$	−9.85463	+	5.68957i	−0.346470	+	0.200035i	0.316659	+	0.948539i	$0.397439\pi$
$810$	−8.77066	+	7.31006i	−0.308170	+	0.256849i
$811$	41.1437			1.44475			0.722376	−	0.691501i	$-0.243050\pi$
$811$	41.1437			1.44475			0.722376	+	0.691501i	$0.243050\pi$
$812$	1.06693	−	2.11973i	0.0374420	−	0.0743879i
$813$	−26.9827	+	1.15569i	−0.946324	+	0.0405319i
$814$	24.6782	−	14.2480i	0.864971	−	0.499392i
$815$	−19.0671			−0.667892
$816$	−8.65730	+	0.370800i	−0.303066	+	0.0129806i
$817$	22.7244			0.795027
$818$	−19.9476			−0.697452
$819$	17.0609	−	22.9766i	0.596157	−	0.802868i
$820$	−6.65348			−0.232350
$821$	45.6193			1.59213			0.796063	−	0.605214i	$-0.206912\pi$
$821$	45.6193			1.59213			0.796063	+	0.605214i	$0.206912\pi$
$822$	−16.6448	+	0.712910i	−0.580553	+	0.0248656i
$823$	27.2208			0.948856			0.474428	−	0.880294i	$-0.342655\pi$
$823$	27.2208			0.948856			0.474428	+	0.880294i	$0.342655\pi$
$824$	−15.4442	+	8.91672i	−0.538024	+	0.310629i
$825$	−30.2186	+	1.29429i	−1.05208	+	0.0450613i
$826$	31.2572	−	1.79260i	1.08758	−	0.0623727i
$827$	36.7827			1.27906			0.639530	−	0.768766i	$-0.279129\pi$
$827$	36.7827			1.27906			0.639530	+	0.768766i	$0.279129\pi$
$828$	−0.692590	−	8.07035i	−0.0240692	−	0.280464i
$829$	−2.19111	+	1.26504i	−0.0761003	+	0.0439365i	−0.537567	−	0.843221i	$-0.680657\pi$
$829$	−2.19111	+	1.26504i	−0.0761003	+	0.0439365i	0.461467	+	0.887157i	$0.347323\pi$
$830$	−5.84918	−	10.1311i	−0.203028	−	0.351655i
$831$	38.6429	−	1.65511i	1.34051	−	0.0574150i
$832$	−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
$835$	21.4312			0.741658
$836$	34.0093			1.17624
$837$	17.0382	−	40.8465i	0.588928	−	1.41186i
$838$	2.15496	−	3.73250i	0.0744419	−	0.128937i
$839$	38.7140	−	22.3515i	1.33656	−	0.771661i	0.350261	−	0.936652i	$-0.386093\pi$
$839$	38.7140	−	22.3515i	1.33656	−	0.771661i	0.986295	+	0.164991i	$0.0527596\pi$
$840$	−3.39532	−	4.71903i	−0.117150	−	0.162822i
$841$	−14.0977	−	24.4180i	−0.486129	−	0.842000i
$842$			9.35440i			0.322374i
$843$	37.7218	−	1.61566i	1.29921	−	0.0556461i
$844$	4.63016	−	8.01968i	0.159377	−	0.276049i
$845$	−8.35423	−	14.2195i	−0.287394	−	0.489167i
$846$	−11.8884	+	8.29505i	−0.408733	+	0.285190i
$847$	−36.6920	−	18.4683i	−1.26075	−	0.634579i
$848$	−11.7150	−	6.76369i	−0.402296	−	0.232266i
$849$	6.57648	−	4.18203i	0.225704	−	0.143527i
$850$	8.48138	−	14.6902i	0.290909	−	0.503869i
$851$	−14.9387			−0.512092
$852$	7.04694	+	11.0817i	0.241424	+	0.379654i
$853$	−18.5205			−0.634130			−0.317065	−	0.948404i	$-0.602697\pi$
$853$	−18.5205			−0.634130			−0.317065	+	0.948404i	$0.602697\pi$
$854$	−5.55216	+	11.0308i	−0.189991	+	0.377465i
$855$	2.14885	+	25.0393i	0.0734891	+	0.856326i
$856$			9.73378i			0.332694i
$857$	18.8542	−	32.6564i	0.644047	−	1.11552i	−0.340474	−	0.940254i	$-0.610587\pi$
$857$	18.8542	−	32.6564i	0.644047	−	1.11552i	0.984521	−	0.175268i	$-0.0560792\pi$
$858$	6.86832	−	31.4219i	0.234481	−	1.07273i
$859$	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
$861$	−9.87702	+	21.9107i	−0.336608	+	0.746715i
$862$	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	$-0.499422\pi$
$864$	5.15337	−	0.665427i	0.175321	−	0.0226383i
$865$		−	0.650606i		−	0.0221213i
$866$	−20.7610	+	11.9864i	−0.705488	+	0.407313i
$867$	13.8935	−	0.595072i	0.471849	−	0.0202097i
$868$	20.1289	+	10.1316i	0.683219	+	0.343887i
$869$	15.1938	−	26.3164i	0.515414	−	0.892723i
$870$	1.96907	−	0.0843370i	0.0667578	−	0.00285929i
$871$	40.3187	+	10.6395i	1.36615	+	0.360506i
$872$	9.16977	+	5.29417i	0.310528	+	0.179283i
$873$	21.3212	+	30.5575i	0.721613	+	1.03421i
$874$	−15.4404	−	8.91450i	−0.522278	−	0.301537i
$875$	28.1165	−	1.61249i	0.950511	−	0.0545120i
$876$	0.337714	−	0.647432i	0.0114103	−	0.0218747i
$877$	27.3721	+	15.8033i	0.924289	+	0.533638i	0.885001	−	0.465590i	$-0.154158\pi$
$877$	27.3721	+	15.8033i	0.924289	+	0.533638i	0.0392879	+	0.999228i	$0.487491\pi$
$878$		−	18.1387i		−	0.612150i
$879$	19.6616	−	12.5029i	0.663170	−	0.421714i
$880$	−5.65846	−	3.26691i	−0.190747	−	0.110128i
$881$	−20.2411	+	35.0585i	−0.681939	+	1.18115i	0.292450	+	0.956281i	$0.405530\pi$
$881$	−20.2411	+	35.0585i	−0.681939	+	1.18115i	−0.974388	+	0.224872i	$0.927804\pi$
$882$	−20.5806	+	4.17585i	−0.692986	+	0.140608i
$883$	0.239886			0.00807282			0.00403641	−	0.999992i	$-0.498715\pi$
$883$	0.239886			0.00807282			0.00403641	+	0.999992i	$0.498715\pi$
$884$	12.8032	+	12.7064i	0.430619	+	0.427362i
$885$	13.9527	+	21.9414i	0.469014	+	0.737552i
$886$	25.1388	−	14.5139i	0.844553	−	0.487603i
$887$	−40.9299			−1.37429			−0.687146	−	0.726519i	$-0.741137\pi$
$887$	−40.9299			−1.37429			−0.687146	+	0.726519i	$0.741137\pi$
$888$	−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
$891$	29.6773	+	35.6070i	0.994226	+	1.19288i
$892$	6.58695	−	11.4089i	0.220547	−	0.381999i
$893$			31.9079i			1.06776i
$894$	6.17309	−	11.8344i	0.206459	−	0.395803i
$895$	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
$899$	−6.61612	+	3.81982i	−0.220660	+	0.127398i
$900$	−4.31406	+	9.21164i	−0.143802	+	0.307055i
$901$	58.6090	+	33.8379i	1.95255	+	1.12730i
$902$			27.0117i			0.899391i
$903$	−12.8012	+	9.21042i	−0.425998	+	0.306504i
$904$	2.68329	−	1.54920i	0.0892448	−	0.0515255i
$905$	0.291196	+	0.504366i	0.00967968	+	0.0167657i
$906$	0.932265	+	0.486289i	0.0309724	+	0.0161559i
$907$	−11.6405	−	20.1619i	−0.386515	−	0.669464i	0.605463	−	0.795874i	$-0.292988\pi$
$907$	−11.6405	−	20.1619i	−0.386515	−	0.669464i	−0.991978	+	0.126409i	$0.959655\pi$
$908$		−	2.37069i		−	0.0786742i
$909$	−16.2297	−	23.2603i	−0.538305	−	0.771497i
$910$	−2.41277	+	11.8589i	−0.0799824	+	0.393119i
$911$		−	28.7163i		−	0.951415i	−0.879604	−	0.475708i	$-0.842192\pi$
$911$		−	28.7163i		−	0.951415i	0.879604	−	0.475708i	$-0.157808\pi$
$912$	5.28955	−	10.1406i	0.175155	−	0.335789i
$913$	−41.1300	+	23.7464i	−1.36120	+	0.785891i
$914$			19.3905i			0.641380i
$915$	−10.2468	+	0.438877i	−0.338747	+	0.0145088i
$916$	5.91454	+	10.2443i	0.195422	+	0.338480i
$917$	10.4344	−	6.84951i	0.344574	−	0.226191i
$918$	−25.7817	+	3.32905i	−0.850922	+	0.109875i
$919$	7.63269	−	13.2202i	0.251779	−	0.436094i	−0.712237	−	0.701940i	$-0.752318\pi$
$919$	7.63269	−	13.2202i	0.251779	−	0.436094i	0.964016	+	0.265845i	$0.0856510\pi$
$920$	1.71264	+	2.96638i	0.0564641	+	0.0977988i
$921$	27.3529	−	1.17155i	0.901309	−	0.0386038i
$922$	−18.5093	+	10.6864i	−0.609573	+	0.351937i
$923$	6.97521	−	26.4328i	0.229592	−	0.870045i
$924$	−19.1582	+	13.7843i	−0.630260	+	0.453469i
$925$	16.2463	+	9.37982i	0.534176	+	0.308407i
$926$		−	7.17045i		−	0.235636i
$927$	−43.8757	+	30.6138i	−1.44107	+	1.00549i
$928$	−0.776779	−	0.448474i	−0.0254990	−	0.0147219i
$929$	9.48735	+	5.47752i	0.311270	+	0.179712i	0.647495	−	0.762070i	$-0.275817\pi$
$929$	9.48735	+	5.47752i	0.311270	+	0.179712i	−0.336225	+	0.941782i	$0.609150\pi$
$930$	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
$933$	−21.0191	+	40.2957i	−0.688133	+	1.31922i
$934$	4.50077	+	7.79557i	0.147270	+	0.255079i
$935$	28.3086	+	16.3440i	0.925789	+	0.534505i
$936$	−8.30089	−	6.93507i	−0.271323	−	0.226680i
$937$			24.6465i			0.805165i	0.915384	+	0.402583i	$0.131887\pi$
$937$			24.6465i			0.805165i	−0.915384	+	0.402583i	$0.868113\pi$
$938$	−16.7915	−	25.5797i	−0.548260	−	0.835208i
$939$	−24.1217	+	15.3392i	−0.787183	+	0.500575i
$940$	3.06505	−	5.30883i	0.0999710	−	0.173155i
$941$	−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	$0.711833\pi$
$942$	20.4956	+	10.6909i	0.667782	+	0.348329i
$943$	7.08029	−	12.2634i	0.230566	−	0.399352i
$944$		−	11.8335i		−	0.385148i
$945$	−11.3592	−	13.2343i	−0.369513	−	0.430511i
$946$	−8.86209	+	15.3496i	−0.288131	+	0.499058i
$947$	5.19193			0.168715			0.0843575	−	0.996436i	$-0.473116\pi$
$947$	5.19193			0.168715			0.0843575	+	0.996436i	$0.473116\pi$
$948$	−5.48369	−	8.62342i	−0.178102	−	0.280076i
$949$	−1.46677	+	0.398994i	−0.0476134	+	0.0129519i
$950$	11.1946	+	19.3896i	0.363201	+	0.629082i
$951$	27.5639	+	43.3458i	0.893820	+	1.40558i
$952$	−0.757863	−	13.2147i	−0.0245625	−	0.428290i
$953$	−12.1003	+	6.98613i	−0.391968	+	0.226303i	−0.683013	−	0.730406i	$-0.739331\pi$
$953$	−12.1003	+	6.98613i	−0.391968	+	0.226303i	0.291044	+	0.956710i	$0.405997\pi$
$954$	−36.7514	−	17.2117i	−1.18987	−	0.557248i
$955$	12.8082			0.414463
$956$	27.3019			0.883007
$957$	−0.342390	−	7.99401i	−0.0110679	−	0.258410i
$958$	3.50004	−	2.02075i	0.113081	−	0.0652874i
$959$	−1.45709	−	25.4069i	−0.0470519	−	0.820431i
$960$	−1.85418	+	1.17908i	−0.0598433	+	0.0380547i
$961$	−20.7729	−	35.9797i	−0.670093	−	1.16064i
$962$	−14.0524	+	14.1595i	−0.453067	+	0.456520i
$963$	2.49686	+	29.0944i	0.0804601	+	0.937554i
$964$	−11.2815			−0.363353
$965$	−5.25223	+	9.09713i	−0.169075	+	0.292847i
$966$	12.3110	−	1.23637i	0.396102	−	0.0397796i
$967$			17.0679i			0.548866i	0.961606	+	0.274433i	$0.0884902\pi$
$967$			17.0679i			0.548866i	−0.961606	+	0.274433i	$0.911510\pi$
$968$	−7.76296	+	13.4458i	−0.249511	+	0.432166i
$969$	−26.4630	+	50.7323i	−0.850114	+	1.62976i
$970$	−13.6456	−	7.87827i	−0.438132	−	0.252956i
$971$	4.10072	−	7.10265i	0.131598	−	0.227935i	−0.792695	−	0.609619i	$-0.791322\pi$
$971$	4.10072	−	7.10265i	0.131598	−	0.227935i	0.924293	+	0.381684i	$0.124656\pi$
$972$	15.2328	−	3.31088i	0.488592	−	0.106197i
$973$	−3.04128	−	4.63302i	−0.0974990	−	0.148528i
$974$		−	13.7020i		−	0.439040i
$975$	20.1753	−	6.42712i	0.646127	−	0.205833i
$976$	4.04224	+	2.33379i	0.129389	+	0.0747028i
$977$	−18.7166	−	32.4182i	−0.598798	−	1.03715i	−0.992999	−	0.118124i	$-0.962312\pi$
$977$	−18.7166	−	32.4182i	−0.598798	−	1.03715i	0.394201	−	0.919024i	$-0.371021\pi$
$978$	23.0810	+	12.0395i	0.738050	+	0.384982i
$979$	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
$982$	−19.4095	−	11.2061i	−0.619383	−	0.357601i
$983$	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	$0.626842\pi$
$984$	8.05413	+	4.20120i	0.256756	+	0.133929i
$985$		−	17.9472i		−	0.571845i
$986$	3.88613	+	2.24366i	0.123760	+	0.0714526i
$987$	−12.9326	−	17.9745i	−0.411648	−	0.572134i
$988$	−22.9738	+	6.24937i	−0.730894	+	0.198819i
$989$	8.04685	−	4.64585i	0.255875	−	0.147730i
$990$	−17.7512	−	8.31337i	−0.564171	−	0.264216i
$991$	2.06784	+	3.58160i	0.0656870	+	0.113773i	0.896999	−	0.442034i	$-0.145743\pi$
$991$	2.06784	+	3.58160i	0.0656870	+	0.113773i	−0.831312	+	0.555807i	$0.812409\pi$
$992$	4.25869	−	7.37627i	0.135214	−	0.234197i
$993$	−48.4918	−	25.2943i	−1.53884	−	0.802691i
$994$	−16.7700	+	11.0084i	−0.531911	+	0.349165i
$995$	−9.72053	−	16.8365i	−0.308162	−	0.533751i
$996$	0.683458	+	15.9571i	0.0216562	+	0.505621i
$997$		−	20.2952i		−	0.642755i	−0.946951	−	0.321378i	$-0.895854\pi$
$997$		−	20.2952i		−	0.642755i	0.946951	−	0.321378i	$-0.104146\pi$
$998$	17.1062	−	9.87625i	0.541486	−	0.312627i
$999$	−3.68170	−	28.5128i	−0.116484	−	0.902104i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.13	✓	34	3.2	odd	2
546.2.bi.e.257.13	yes	34	91.75	odd	6
546.2.bi.f.17.16	yes	34	1.1	even	1	trivial
546.2.bi.f.257.16	yes	34	273.257	even	6	inner
546.2.bn.e.101.11	yes	34	39.23	odd	6
546.2.bn.e.173.11	yes	34	7.5	odd	6
546.2.bn.f.101.7	yes	34	13.10	even	6
546.2.bn.f.173.7	yes	34	21.5	even	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.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.73046 - 0.0741172i) q^{3} +1.00000 q^{4} +(-1.09866 + 0.634311i) q^{5} +(1.73046 - 0.0741172i) q^{6} +(0.151485 + 2.64141i) q^{7} +1.00000 q^{8} +(2.98901 - 0.256514i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(1.73046 - 0.0741172i) q^{3} +1.00000 q^{4} +(-1.09866 + 0.634311i) q^{5} +(1.73046 - 0.0741172i) q^{6} +(0.151485 + 2.64141i) q^{7} +1.00000 q^{8} +(2.98901 - 0.256514i) q^{9} +(-1.09866 + 0.634311i) q^{10} +(2.57517 + 4.46032i) q^{11} +(1.73046 - 0.0741172i) q^{12} +(-2.55917 - 2.53981i) q^{13} +(0.151485 + 2.64141i) q^{14} +(-1.85418 + 1.17908i) q^{15} +1.00000 q^{16} -5.00288 q^{17} +(2.98901 - 0.256514i) q^{18} +(3.30166 - 5.71864i) q^{19} +(-1.09866 + 0.634311i) q^{20} +(0.457914 + 4.55964i) q^{21} +(2.57517 + 4.46032i) q^{22} -2.70000i q^{23} +(1.73046 - 0.0741172i) q^{24} +(-1.69530 + 2.93635i) q^{25} +(-2.55917 - 2.53981i) q^{26} +(5.15337 - 0.665427i) q^{27} +(0.151485 + 2.64141i) q^{28} +(-0.776779 - 0.448474i) q^{29} +(-1.85418 + 1.17908i) q^{30} +(4.25869 - 7.37627i) q^{31} +1.00000 q^{32} +(4.78682 + 7.52756i) q^{33} -5.00288 q^{34} +(-1.84191 - 2.80592i) q^{35} +(2.98901 - 0.256514i) q^{36} -5.53284i q^{37} +(3.30166 - 5.71864i) q^{38} +(-4.61679 - 4.20538i) q^{39} +(-1.09866 + 0.634311i) q^{40} +(4.54200 + 2.62233i) q^{41} +(0.457914 + 4.55964i) q^{42} +(1.72068 + 2.98031i) q^{43} +(2.57517 + 4.46032i) q^{44} +(-3.12119 + 2.17779i) q^{45} -2.70000i q^{46} +(-4.18472 + 2.41605i) q^{47} +(1.73046 - 0.0741172i) q^{48} +(-6.95410 + 0.800271i) q^{49} +(-1.69530 + 2.93635i) q^{50} +(-8.65730 + 0.370800i) q^{51} +(-2.55917 - 2.53981i) q^{52} +(-11.7150 - 6.76369i) q^{53} +(5.15337 - 0.665427i) q^{54} +(-5.65846 - 3.26691i) q^{55} +(0.151485 + 2.64141i) q^{56} +(5.28955 - 10.1406i) q^{57} +(-0.776779 - 0.448474i) q^{58} -11.8335i q^{59} +(-1.85418 + 1.17908i) q^{60} +(4.04224 + 2.33379i) q^{61} +(4.25869 - 7.37627i) q^{62} +(1.13035 + 7.85635i) q^{63} +1.00000 q^{64} +(4.42268 + 1.16708i) q^{65} +(4.78682 + 7.52756i) q^{66} +(-10.0157 + 5.78259i) q^{67} -5.00288 q^{68} +(-0.200117 - 4.67226i) q^{69} +(-1.84191 - 2.80592i) q^{70} +(3.79105 + 6.56628i) q^{71} +(2.98901 - 0.256514i) q^{72} +(0.210796 - 0.365109i) q^{73} -5.53284i q^{74} +(-2.71602 + 5.20689i) 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} +(-1.09866 + 0.634311i) q^{80} +(8.86840 - 1.53345i) q^{81} +(4.54200 + 2.62233i) q^{82} +9.22131i q^{83} +(0.457914 + 4.55964i) q^{84} +(5.49645 - 3.17338i) q^{85} +(1.72068 + 2.98031i) q^{86} +(-1.37743 - 0.718495i) q^{87} +(2.57517 + 4.46032i) q^{88} -8.30846i q^{89} +(-3.12119 + 2.17779i) q^{90} +(6.32102 - 7.14456i) q^{91} -2.70000i q^{92} +(6.82280 - 13.0800i) q^{93} +(-4.18472 + 2.41605i) q^{94} +8.37711i q^{95} +(1.73046 - 0.0741172i) q^{96} +(6.21010 + 10.7562i) q^{97} +(-6.95410 + 0.800271i) q^{98} +(8.84134 + 12.6714i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9}+O(q^{10}) \) 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9	\( 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9} + 9 q^{10} + 9 q^{11} + 6 q^{12} + 8 q^{13} + 4 q^{14} - 17 q^{15} + 34 q^{16} + 12 q^{17} + 4 q^{18} - 5 q^{19} + 9 q^{20} - 7 q^{21} + 9 q^{22} + 6 q^{24} + 16 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} + 27 q^{29} - 17 q^{30} - q^{31} + 34 q^{32} + 12 q^{34} - 3 q^{35} + 4 q^{36} - 5 q^{38} - 10 q^{39} + 9 q^{40} - 3 q^{41} - 7 q^{42} - 3 q^{43} + 9 q^{44} + 9 q^{45} - 27 q^{47} + 6 q^{48} - 2 q^{49} + 16 q^{50} - 36 q^{51} + 8 q^{52} - 21 q^{53} - 18 q^{54} - 57 q^{55} + 4 q^{56} - 17 q^{57} + 27 q^{58} - 17 q^{60} - 51 q^{61} - q^{62} - 24 q^{63} + 34 q^{64} - 21 q^{65} - 21 q^{67} + 12 q^{68} + 30 q^{69} - 3 q^{70} - 15 q^{71} + 4 q^{72} - 19 q^{73} - 54 q^{75} - 5 q^{76} + 9 q^{77} - 10 q^{78} - 9 q^{79} + 9 q^{80} + 28 q^{81} - 3 q^{82} - 7 q^{84} - 42 q^{85} - 3 q^{86} - 81 q^{87} + 9 q^{88} + 9 q^{90} - 72 q^{91} - 17 q^{93} - 27 q^{94} + 6 q^{96} + 19 q^{97} - 2 q^{98} - 27 q^{99}+O(q^{100}) \) 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9 + 9 * q^10 + 9 * q^11 + 6 * q^12 + 8 * q^13 + 4 * q^14 - 17 * q^15 + 34 * q^16 + 12 * q^17 + 4 * q^18 - 5 * q^19 + 9 * q^20 - 7 * q^21 + 9 * q^22 + 6 * q^24 + 16 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 + 27 * q^29 - 17 * q^30 - q^31 + 34 * q^32 + 12 * q^34 - 3 * q^35 + 4 * q^36 - 5 * q^38 - 10 * q^39 + 9 * q^40 - 3 * q^41 - 7 * q^42 - 3 * q^43 + 9 * q^44 + 9 * q^45 - 27 * q^47 + 6 * q^48 - 2 * q^49 + 16 * q^50 - 36 * q^51 + 8 * q^52 - 21 * q^53 - 18 * q^54 - 57 * q^55 + 4 * q^56 - 17 * q^57 + 27 * q^58 - 17 * q^60 - 51 * q^61 - q^62 - 24 * q^63 + 34 * q^64 - 21 * q^65 - 21 * q^67 + 12 * q^68 + 30 * q^69 - 3 * q^70 - 15 * q^71 + 4 * q^72 - 19 * q^73 - 54 * q^75 - 5 * q^76 + 9 * q^77 - 10 * q^78 - 9 * q^79 + 9 * q^80 + 28 * q^81 - 3 * q^82 - 7 * q^84 - 42 * q^85 - 3 * q^86 - 81 * q^87 + 9 * q^88 + 9 * q^90 - 72 * q^91 - 17 * q^93 - 27 * q^94 + 6 * q^96 + 19 * q^97 - 2 * q^98 - 27 * q^99

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