LMFDB - Embedded newform 546.2.bi.e.257.13

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			257.13
Character	$\chi$	$=$	546.257
Dual form			546.2.bi.e.17.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(0.929420 + 1.46157i) q^{3} +1.00000 q^{4} +(1.09866 + 0.634311i) q^{5} +(-0.929420 - 1.46157i) q^{6} +(0.151485 - 2.64141i) q^{7} -1.00000 q^{8} +(-1.27236 + 2.71682i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(0.929420 + 1.46157i) q^{3} +1.00000 q^{4} +(1.09866 + 0.634311i) q^{5} +(-0.929420 - 1.46157i) q^{6} +(0.151485 - 2.64141i) q^{7} -1.00000 q^{8} +(-1.27236 + 2.71682i) q^{9} +(-1.09866 - 0.634311i) q^{10} +(-2.57517 + 4.46032i) q^{11} +(0.929420 + 1.46157i) q^{12} +(-2.55917 + 2.53981i) q^{13} +(-0.151485 + 2.64141i) q^{14} +(0.0940267 + 2.19530i) q^{15} +1.00000 q^{16} +5.00288 q^{17} +(1.27236 - 2.71682i) q^{18} +(3.30166 + 5.71864i) q^{19} +(1.09866 + 0.634311i) q^{20} +(4.00139 - 2.23357i) q^{21} +(2.57517 - 4.46032i) q^{22} -2.70000i q^{23} +(-0.929420 - 1.46157i) 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} +(-0.0940267 - 2.19530i) q^{30} +(4.25869 + 7.37627i) q^{31} -1.00000 q^{32} +(-8.91247 + 0.381728i) q^{33} -5.00288 q^{34} +(1.84191 - 2.80592i) q^{35} +(-1.27236 + 2.71682i) q^{36} +5.53284i q^{37} +(-3.30166 - 5.71864i) q^{38} +(-6.09065 - 1.37984i) q^{39} +(-1.09866 - 0.634311i) q^{40} +(-4.54200 + 2.62233i) q^{41} +(-4.00139 + 2.23357i) 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} +(0.929420 + 1.46157i) q^{48} +(-6.95410 - 0.800271i) q^{49} +(1.69530 + 2.93635i) q^{50} +(4.64977 + 7.31204i) 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} +(0.0940267 + 2.19530i) q^{60} +(4.04224 - 2.33379i) q^{61} +(-4.25869 - 7.37627i) q^{62} +(6.98349 + 3.77238i) q^{63} +1.00000 q^{64} +(-4.42268 + 1.16708i) q^{65} +(8.91247 - 0.381728i) q^{66} +(-10.0157 - 5.78259i) q^{67} +5.00288 q^{68} +(3.94624 - 2.50944i) q^{69} +(-1.84191 + 2.80592i) q^{70} +(-3.79105 + 6.56628i) q^{71} +(1.27236 - 2.71682i) 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} +(6.09065 + 1.37984i) q^{78} +(-2.95006 + 5.10965i) q^{79} +(1.09866 + 0.634311i) q^{80} +(-5.76221 - 6.91354i) q^{81} +(4.54200 - 2.62233i) q^{82} +9.22131i q^{83} +(4.00139 - 2.23357i) 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} +(-0.929420 - 1.46157i) 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} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9} + 9 q^{10} - 9 q^{11} + 3 q^{12} + 8 q^{13} - 4 q^{14} - 4 q^{15} + 34 q^{16} - 12 q^{17} + 11 q^{18} - 5 q^{19} - 9 q^{20} + 4 q^{21} + 9 q^{22} - 3 q^{24} + 16 q^{25} - 8 q^{26} + 18 q^{27} + 4 q^{28} - 27 q^{29} + 4 q^{30} - q^{31} - 34 q^{32} + 21 q^{33} + 12 q^{34} + 3 q^{35} - 11 q^{36} + 5 q^{38} + 7 q^{39} + 9 q^{40} + 3 q^{41} - 4 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} + 27 q^{47} + 3 q^{48} - 2 q^{49} - 16 q^{50} + 24 q^{51} + 8 q^{52} + 21 q^{53} - 18 q^{54} - 57 q^{55} - 4 q^{56} + 17 q^{57} + 27 q^{58} - 4 q^{60} - 51 q^{61} + q^{62} + 3 q^{63} + 34 q^{64} + 21 q^{65} - 21 q^{66} - 21 q^{67} - 12 q^{68} + 42 q^{69} - 3 q^{70} + 15 q^{71} + 11 q^{72} - 19 q^{73} + 54 q^{75} - 5 q^{76} - 9 q^{77} - 7 q^{78} - 9 q^{79} - 9 q^{80} - 23 q^{81} - 3 q^{82} + 4 q^{84} - 42 q^{85} + 3 q^{86} + 81 q^{87} + 9 q^{88} - 9 q^{90} - 72 q^{91} + 17 q^{93} - 27 q^{94} - 3 q^{96} + 19 q^{97} + 2 q^{98} + 27 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9 + 9 * q^10 - 9 * q^11 + 3 * q^12 + 8 * q^13 - 4 * q^14 - 4 * q^15 + 34 * q^16 - 12 * q^17 + 11 * q^18 - 5 * q^19 - 9 * q^20 + 4 * q^21 + 9 * q^22 - 3 * q^24 + 16 * q^25 - 8 * q^26 + 18 * q^27 + 4 * q^28 - 27 * q^29 + 4 * q^30 - q^31 - 34 * q^32 + 21 * q^33 + 12 * q^34 + 3 * q^35 - 11 * q^36 + 5 * q^38 + 7 * q^39 + 9 * q^40 + 3 * q^41 - 4 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 + 27 * q^47 + 3 * q^48 - 2 * q^49 - 16 * q^50 + 24 * q^51 + 8 * q^52 + 21 * q^53 - 18 * q^54 - 57 * q^55 - 4 * q^56 + 17 * q^57 + 27 * q^58 - 4 * q^60 - 51 * q^61 + q^62 + 3 * q^63 + 34 * q^64 + 21 * q^65 - 21 * q^66 - 21 * q^67 - 12 * q^68 + 42 * q^69 - 3 * q^70 + 15 * q^71 + 11 * q^72 - 19 * q^73 + 54 * q^75 - 5 * q^76 - 9 * q^77 - 7 * q^78 - 9 * q^79 - 9 * q^80 - 23 * q^81 - 3 * q^82 + 4 * 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 - 3 * 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	0.929420	+	1.46157i	0.536601	+	0.843836i
$3$	0.929420	+	1.46157i	0.536601	+	0.843836i
$4$	1.00000			0.500000
$5$	1.09866	+	0.634311i	0.491335	+	0.283672i	0.725128	−	0.688614i	$-0.241781\pi$
$5$	1.09866	+	0.634311i	0.491335	+	0.283672i	−0.233793	+	0.972286i	$0.575114\pi$
$6$	−0.929420	−	1.46157i	−0.379434	−	0.596682i
$7$	0.151485	−	2.64141i	0.0572561	−	0.998360i
$7$	0.151485	−	2.64141i	0.0572561	−	0.998360i
$8$	−1.00000			−0.353553
$9$	−1.27236	+	2.71682i	−0.424120	+	0.905606i
$10$	−1.09866	−	0.634311i	−0.347426	−	0.200587i
$11$	−2.57517	+	4.46032i	−0.776442	+	1.34484i	0.157539	+	0.987513i	$0.449644\pi$
$11$	−2.57517	+	4.46032i	−0.776442	+	1.34484i	−0.933981	+	0.357324i	$0.883689\pi$
$12$	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
$15$	0.0940267	+	2.19530i	0.0242776	+	0.566825i
$16$	1.00000			0.250000
$17$	5.00288			1.21338			0.606688	−	0.794940i	$-0.292498\pi$
$17$	5.00288			1.21338			0.606688	+	0.794940i	$0.292498\pi$
$18$	1.27236	−	2.71682i	0.299898	−	0.640360i
$19$	3.30166	+	5.71864i	0.757453	+	1.31195i	0.944146	+	0.329528i	$0.106890\pi$
$19$	3.30166	+	5.71864i	0.757453	+	1.31195i	−0.186693	+	0.982418i	$0.559777\pi$
$20$	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
$23$		−	2.70000i		−	0.562990i	−0.959563	−	0.281495i	$-0.909170\pi$
$23$		−	2.70000i		−	0.562990i	0.959563	−	0.281495i	$-0.0908303\pi$
$24$	−0.929420	−	1.46157i	−0.189717	−	0.298341i
$25$	−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	$-0.640127\pi$
$29$	0.776779	−	0.448474i	0.144244	−	0.0832794i	0.570385	+	0.821377i	$0.306794\pi$
$30$	−0.0940267	−	2.19530i	−0.0171669	−	0.400806i
$31$	4.25869	+	7.37627i	0.764883	+	1.32482i	0.940308	+	0.340324i	$0.110537\pi$
$31$	4.25869	+	7.37627i	0.764883	+	1.32482i	−0.175425	+	0.984493i	$0.556130\pi$
$32$	−1.00000			−0.176777
$33$	−8.91247	+	0.381728i	−1.55146	+	0.0664504i
$34$	−5.00288			−0.857987
$35$	1.84191	−	2.80592i	0.311339	−	0.474287i
$36$	−1.27236	+	2.71682i	−0.212060	+	0.452803i
$37$			5.53284i			0.909593i	0.890595	+	0.454797i	$0.150288\pi$
$37$			5.53284i			0.909593i	−0.890595	+	0.454797i	$0.849712\pi$
$38$	−3.30166	−	5.71864i	−0.535600	−	0.927686i
$39$	−6.09065	−	1.37984i	−0.975285	−	0.220952i
$40$	−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	$0.467644\pi$
$42$	−4.00139	+	2.23357i	−0.617428	+	0.344648i
$43$	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
$45$	−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	$-0.218693\pi$
$47$	4.18472	+	2.41605i	0.610404	+	0.352417i	−0.162719	+	0.986672i	$0.552027\pi$
$48$	0.929420	+	1.46157i	0.134150	+	0.210959i
$49$	−6.95410	−	0.800271i	−0.993443	−	0.114324i
$50$	1.69530	+	2.93635i	0.239752	+	0.415262i
$51$	4.64977	+	7.31204i	0.651098	+	1.02389i
$52$	−2.55917	+	2.53981i	−0.354893	+	0.352209i
$53$	11.7150	−	6.76369i	1.60919	−	0.929064i	0.619633	−	0.784891i	$-0.287281\pi$
$53$	11.7150	−	6.76369i	1.60919	−	0.929064i	0.989553	−	0.144172i	$-0.0460520\pi$
$54$	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	$-0.279891\pi$
$60$	0.0940267	+	2.19530i	0.0121388	+	0.283413i
$61$	4.04224	−	2.33379i	0.517556	−	0.298811i	−0.218378	−	0.975864i	$-0.570077\pi$
$61$	4.04224	−	2.33379i	0.517556	−	0.298811i	0.735934	+	0.677053i	$0.236743\pi$
$62$	−4.25869	−	7.37627i	−0.540854	−	0.936787i
$63$	6.98349	+	3.77238i	0.879837	+	0.475275i
$64$	1.00000			0.125000
$65$	−4.42268	+	1.16708i	−0.548566	+	0.144758i
$66$	8.91247	−	0.381728i	1.09705	−	0.0469875i
$67$	−10.0157	−	5.78259i	−1.22362	−	0.706456i	−0.257931	−	0.966163i	$-0.583041\pi$
$67$	−10.0157	−	5.78259i	−1.22362	−	0.706456i	−0.965687	+	0.259707i	$0.916374\pi$
$68$	5.00288			0.606688
$69$	3.94624	−	2.50944i	0.475071	−	0.302101i
$70$	−1.84191	+	2.80592i	−0.220150	+	0.335372i
$71$	−3.79105	+	6.56628i	−0.449914	+	0.779274i	−0.998380	−	0.0568986i	$-0.981879\pi$
$71$	−3.79105	+	6.56628i	−0.449914	+	0.779274i	0.548466	+	0.836173i	$0.315212\pi$
$72$	1.27236	−	2.71682i	0.149949	−	0.320180i
$73$	0.210796	+	0.365109i	0.0246718	+	0.0427328i	0.878098	−	0.478481i	$-0.158813\pi$
$73$	0.210796	+	0.365109i	0.0246718	+	0.0427328i	−0.853426	+	0.521214i	$0.825479\pi$
$74$		−	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
$78$	6.09065	+	1.37984i	0.689630	+	0.156237i
$79$	−2.95006	+	5.10965i	−0.331908	+	0.574881i	−0.982886	−	0.184216i	$-0.941026\pi$
$79$	−2.95006	+	5.10965i	−0.331908	+	0.574881i	0.650978	+	0.759096i	$0.274359\pi$
$80$	1.09866	+	0.634311i	0.122834	+	0.0709181i
$81$	−5.76221	−	6.91354i	−0.640245	−	0.768171i
$82$	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	$0.831092\pi$
$84$	4.00139	−	2.23357i	0.436588	−	0.243703i
$85$	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
$96$	−0.929420	−	1.46157i	−0.0948585	−	0.149171i
$97$	6.21010	−	10.7562i	0.630540	−	1.09213i	−0.356901	−	0.934142i	$-0.616167\pi$
$97$	6.21010	−	10.7562i	0.630540	−	1.09213i	0.987441	−	0.157985i	$-0.0504999\pi$
$98$	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	$-0.677455\pi$
$101$	4.72713	−	8.18763i	0.470367	−	0.814699i	0.999426	+	0.0338859i	$0.0107883\pi$
$102$	−4.64977	−	7.31204i	−0.460396	−	0.724000i
$103$	−15.4442	−	8.91672i	−1.52176	−	0.878590i	−0.999670	−	0.0257017i	$-0.991818\pi$
$103$	−15.4442	−	8.91672i	−1.52176	−	0.878590i	−0.522093	−	0.852888i	$-0.674849\pi$
$104$	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
$107$			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	0.00820581	−	0.999966i	$-0.497388\pi$
$109$	9.16977	−	5.29417i	0.878305	−	0.507090i	0.870099	+	0.492877i	$0.164055\pi$
$110$	5.65846	−	3.26691i	0.539513	−	0.311488i
$111$	−8.08662	+	5.14233i	−0.767548	+	0.488088i
$112$	0.151485	−	2.64141i	0.0143140	−	0.249590i
$113$	−2.68329	−	1.54920i	−0.252422	−	0.145736i	0.368451	−	0.929647i	$-0.379888\pi$
$113$	−2.68329	−	1.54920i	−0.252422	−	0.145736i	−0.620873	+	0.783911i	$0.713222\pi$
$114$	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
$117$	−3.64403	−	10.1844i	−0.336891	−	0.941544i
$118$			11.8335i			1.08936i
$119$	0.757863	−	13.2147i	0.0694732	−	1.21139i
$120$	−0.0940267	−	2.19530i	−0.00858343	−	0.200403i
$121$	−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
$126$	−6.98349	−	3.77238i	−0.622139	−	0.336070i
$127$	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	$0.658806\pi$
$128$	−1.00000			−0.0883883
$129$	5.95516	−	0.255065i	0.524323	−	0.0224572i
$130$	4.42268	−	1.16708i	0.387895	−	0.102360i
$131$	2.35882	−	4.08559i	0.206091	−	0.356960i	−0.744389	−	0.667746i	$-0.767259\pi$
$131$	2.35882	−	4.08559i	0.206091	−	0.356960i	0.950480	+	0.310787i	$0.100592\pi$
$132$	−8.91247	+	0.381728i	−0.775731	+	0.0332252i
$133$	15.6054	−	7.85475i	1.35316	−	0.681093i
$134$	10.0157	+	5.78259i	0.865229	+	0.499540i
$135$	−6.08388	−	2.53776i	−0.523617	−	0.218416i
$136$	−5.00288			−0.428993
$137$	9.61868			0.821779			0.410890	−	0.911685i	$-0.365218\pi$
$137$	9.61868			0.821779			0.410890	+	0.911685i	$0.365218\pi$
$138$	−3.94624	+	2.50944i	−0.335926	+	0.213617i
$139$	−1.81406	−	1.04735i	−0.153867	−	0.0888349i	0.421090	−	0.907019i	$-0.361648\pi$
$139$	−1.81406	−	1.04735i	−0.153867	−	0.0888349i	−0.574956	+	0.818184i	$0.694981\pi$
$140$	1.84191	−	2.80592i	0.155669	−	0.237143i
$141$	0.358142	+	8.36178i	0.0301610	+	0.704189i
$142$	3.79105	−	6.56628i	0.318137	−	0.551030i
$143$	−4.73810	−	17.9552i	−0.396220	−	1.50149i
$144$	−1.27236	+	2.71682i	−0.106030	+	0.226402i
$145$	1.13789			0.0944963
$146$	−0.210796	−	0.365109i	−0.0174456	−	0.0302166i
$147$	−5.29363	−	10.9077i	−0.436611	−	0.899650i
$148$			5.53284i			0.454797i
$149$	−3.85315	−	6.67385i	−0.315662	−	0.546743i	0.663916	−	0.747807i	$-0.268893\pi$
$149$	−3.85315	−	6.67385i	−0.315662	−	0.546743i	−0.979578	+	0.201064i	$0.935560\pi$
$150$	−2.71602	+	5.20689i	−0.221762	+	0.425141i
$151$	0.525736	−	0.303534i	0.0427838	−	0.0247012i	−0.478456	−	0.878112i	$-0.658803\pi$
$151$	0.525736	−	0.303534i	0.0427838	−	0.0247012i	0.521239	+	0.853411i	$0.325470\pi$
$152$	−3.30166	−	5.71864i	−0.267800	−	0.463843i
$153$	−6.36546	+	13.5919i	−0.514617	+	1.09884i
$154$	−11.3914	−	7.47775i	−0.917948	−	0.602574i
$155$			10.8053i			0.867905i
$156$	−6.09065	−	1.37984i	−0.487642	−	0.110476i
$157$	11.5582	−	6.67311i	0.922442	−	0.532572i	0.0380288	−	0.999277i	$-0.487892\pi$
$157$	11.5582	−	6.67311i	0.922442	−	0.532572i	0.884413	+	0.466704i	$0.154559\pi$
$158$	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
$162$	5.76221	+	6.91354i	0.452722	+	0.543179i
$163$	13.0162	−	7.51490i	1.01951	−	0.588612i	0.105545	−	0.994414i	$-0.466341\pi$
$163$	13.0162	−	7.51490i	1.01951	−	0.588612i	0.913961	+	0.405802i	$0.133008\pi$
$164$	−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	$-0.439915\pi$
$167$	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
$171$	−19.7374	+	1.69385i	−1.50936	+	0.129532i
$172$	1.72068	−	2.98031i	0.131201	−	0.227247i
$173$	0.256422	+	0.444137i	0.0194954	+	0.0337671i	0.875609	−	0.483021i	$-0.160461\pi$
$173$	0.256422	+	0.444137i	0.0194954	+	0.0337671i	−0.856113	+	0.516789i	$0.827127\pi$
$174$	−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
$177$	17.2955	−	10.9983i	1.30001	−	0.826682i
$178$			8.30846i			0.622746i
$179$	6.94512	+	4.00977i	0.519103	+	0.299704i	0.736567	−	0.676364i	$-0.236445\pi$
$179$	6.94512	+	4.00977i	0.519103	+	0.299704i	−0.217465	+	0.976068i	$0.569779\pi$
$180$	−3.12119	+	2.17779i	−0.232640	+	0.162323i
$181$			0.459074i			0.0341227i	0.999854	+	0.0170614i	$0.00543106\pi$
$181$			0.459074i			0.0341227i	−0.999854	+	0.0170614i	$0.994569\pi$
$182$	−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
$189$	0.977005	+	13.7130i	0.0710666	+	0.997472i
$190$		−	8.37711i		−	0.607740i
$191$	8.74352	−	5.04808i	0.632659	−	0.365266i	−0.149122	−	0.988819i	$-0.547645\pi$
$191$	8.74352	−	5.04808i	0.632659	−	0.365266i	0.781781	+	0.623553i	$0.214311\pi$
$192$	0.929420	+	1.46157i	0.0670751	+	0.105480i
$193$	7.17088	+	4.14011i	0.516171	+	0.298011i	0.735367	−	0.677669i	$-0.237010\pi$
$193$	7.17088	+	4.14011i	0.516171	+	0.298011i	−0.219196	+	0.975681i	$0.570343\pi$
$194$	−6.21010	+	10.7562i	−0.445859	+	0.772251i
$195$	−5.81630	−	5.37934i	−0.416514	−	0.385223i
$196$	−6.95410	−	0.800271i	−0.496722	−	0.0571622i
$197$	7.07350	+	12.2517i	0.503966	+	0.872895i	0.999989	+	0.00458596i	$0.00145976\pi$
$197$	7.07350	+	12.2517i	0.503966	+	0.872895i	−0.496023	+	0.868309i	$0.665207\pi$
$198$	8.84134	+	12.6714i	0.628327	+	0.900516i
$199$		−	15.3246i		−	1.08633i	−0.839626	−	0.543164i	$-0.817226\pi$
$199$		−	15.3246i		−	1.08633i	0.839626	−	0.543164i	$-0.182774\pi$
$200$	1.69530	+	2.93635i	0.119876	+	0.207631i
$201$	−0.857180	−	20.0131i	−0.0604608	−	1.41162i
$202$	−4.72713	+	8.18763i	−0.332600	+	0.576079i
$203$	−1.06693	−	2.11973i	−0.0748840	−	0.148776i
$204$	4.64977	+	7.31204i	0.325549	+	0.511945i
$205$	−6.65348			−0.464699
$206$	15.4442	+	8.91672i	1.07605	+	0.621257i
$207$	7.33542	+	3.43537i	0.509847	+	0.238775i
$208$	−2.55917	+	2.53981i	−0.177446	+	0.176104i
$209$	−34.0093			−2.35247
$210$	−5.81294	−	0.0841934i	−0.401131	−	0.00580990i
$211$	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	$0.730069\pi$
$212$	11.7150	−	6.76369i	0.804593	−	0.464532i
$213$	−13.1205	+	0.561964i	−0.899004	+	0.0385051i
$214$		−	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
$222$	8.08662	−	5.14233i	0.542738	−	0.345131i
$223$	6.58695	+	11.4089i	0.441095	+	0.763998i	0.997771	−	0.0667312i	$-0.0212570\pi$
$223$	6.58695	+	11.4089i	0.441095	+	0.763998i	−0.556676	+	0.830729i	$0.687924\pi$
$224$	−0.151485	+	2.64141i	−0.0101215	+	0.176487i
$225$	10.1345	−	0.869738i	0.675636	−	0.0579825i
$226$	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	−0.601717	−	0.798709i	$-0.705517\pi$
$229$	5.91454	−	10.2443i	0.390844	−	0.676961i	0.992561	+	0.121748i	$0.0388500\pi$
$230$	−1.71264	+	2.96638i	−0.112928	+	0.195598i
$231$	−0.341807	+	23.5993i	−0.0224893	+	1.55272i
$232$	−0.776779	+	0.448474i	−0.0509980	+	0.0294437i
$233$	−6.84440	−	3.95162i	−0.448392	−	0.258879i	0.258759	−	0.965942i	$-0.416686\pi$
$233$	−6.84440	−	3.95162i	−0.448392	−	0.258879i	−0.707151	+	0.707063i	$0.750020\pi$
$234$	3.64403	+	10.1844i	0.238218	+	0.665772i
$235$	3.06505	+	5.30883i	0.199942	+	0.346310i
$236$		−	11.8335i		−	0.770296i
$237$	−10.2099	+	0.437301i	−0.663207	+	0.0284057i
$238$	−0.757863	+	13.2147i	−0.0491250	+	0.856579i
$239$	−27.3019			−1.76601			−0.883007	−	0.469360i	$-0.844485\pi$
$239$	−27.3019			−1.76601			−0.883007	+	0.469360i	$0.844485\pi$
$240$	0.0940267	+	2.19530i	0.00606940	+	0.141706i
$241$	−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
$243$	4.74909	−	14.8474i	0.304654	−	0.952463i
$244$	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
$249$	−13.4776	+	8.57046i	−0.854106	+	0.543131i
$250$			10.6445i			0.673217i
$251$	−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
$254$	−5.87399	−	10.1740i	−0.368567	−	0.638376i
$255$	0.470404	+	10.9828i	0.0294579	+	0.687772i
$256$	1.00000			0.0625000
$257$	1.36558			0.0851824			0.0425912	−	0.999093i	$-0.486439\pi$
$257$	1.36558			0.0851824			0.0425912	+	0.999093i	$0.486439\pi$
$258$	−5.95516	+	0.255065i	−0.370752	+	0.0158796i
$259$	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
$262$	−2.35882	+	4.08559i	−0.145728	+	0.252409i
$263$	9.36276	+	5.40559i	0.577333	+	0.333323i	0.760073	−	0.649838i	$-0.225163\pi$
$263$	9.36276	+	5.40559i	0.577333	+	0.333323i	−0.182740	+	0.983161i	$0.558497\pi$
$264$	8.91247	−	0.381728i	0.548524	−	0.0234938i
$265$	17.1611			1.05420
$266$	−15.6054	+	7.85475i	−0.956831	+	0.481605i
$267$	12.1434	−	7.72205i	0.743163	−	0.472582i
$268$	−10.0157	−	5.78259i	−0.611809	−	0.353228i
$269$	22.9534			1.39949			0.699747	−	0.714391i	$-0.253296\pi$
$269$	22.9534			1.39949			0.699747	+	0.714391i	$0.253296\pi$
$270$	6.08388	+	2.53776i	0.370253	+	0.154443i
$271$	−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
$273$	−4.56738	+	15.8789i	−0.276430	+	0.961034i
$274$	−9.61868			−0.581086
$275$	17.4627			1.05304
$276$	3.94624	−	2.50944i	0.237536	−	0.151050i
$277$	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
$279$	−25.4586	+	2.18483i	−1.52416	+	0.130802i
$280$	−1.84191	+	2.80592i	−0.110075	+	0.167686i
$281$	−21.7986			−1.30040			−0.650199	−	0.759764i	$-0.725314\pi$
$281$	−21.7986			−1.30040			−0.650199	+	0.759764i	$0.725314\pi$
$282$	−0.358142	−	8.36178i	−0.0213270	−	0.497937i
$283$	3.89678	+	2.24981i	0.231639	+	0.133737i	0.611328	−	0.791377i	$-0.290636\pi$
$283$	3.89678	+	2.24981i	0.231639	+	0.133737i	−0.379689	+	0.925114i	$0.623969\pi$
$284$	−3.79105	+	6.56628i	−0.224957	+	0.389637i
$285$	−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
$288$	1.27236	−	2.71682i	0.0749744	−	0.160090i
$289$	8.02879			0.472282
$290$	−1.13789			−0.0668190
$291$	21.4927	−	0.920551i	1.25992	−	0.0539636i
$292$	0.210796	+	0.365109i	0.0123359	+	0.0213664i
$293$	−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
$296$		−	5.53284i		−	0.321590i
$297$	10.3028	−	24.6993i	0.597827	−	1.43320i
$298$	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
$303$	16.3603	−	0.700723i	0.939872	−	0.0402555i
$304$	3.30166	+	5.71864i	0.189363	+	0.327987i
$305$	5.92139			0.339058
$306$	6.36546	−	13.5919i	0.363889	−	0.776998i
$307$	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
$309$	−1.32176	−	30.8601i	−0.0751926	−	1.75557i
$310$		−	10.8053i		−	0.613702i
$311$	13.1198	+	22.7241i	0.743954	+	1.28857i	0.950682	+	0.310168i	$0.100385\pi$
$311$	13.1198	+	22.7241i	0.743954	+	1.28857i	−0.206727	+	0.978399i	$0.566281\pi$
$312$	6.09065	+	1.37984i	0.344815	+	0.0781183i
$313$	−14.2929	−	8.25201i	−0.807883	−	0.466431i	0.0383374	−	0.999265i	$-0.487794\pi$
$313$	−14.2929	−	8.25201i	−0.807883	−	0.466431i	−0.846220	+	0.532834i	$0.821127\pi$
$314$	−11.5582	+	6.67311i	−0.652265	+	0.376585i
$315$	5.27961	+	8.57426i	0.297472	+	0.483105i
$316$	−2.95006	+	5.10965i	−0.165954	+	0.287440i
$317$	−14.8285	+	25.6838i	−0.832854	+	1.44255i	0.0629121	+	0.998019i	$0.479961\pi$
$317$	−14.8285	+	25.6838i	−0.832854	+	1.44255i	−0.895766	+	0.444526i	$0.853372\pi$
$318$	−20.7738	−	10.8360i	−1.16494	−	0.607654i
$319$			4.61958i			0.258647i
$320$	1.09866	+	0.634311i	0.0614169	+	0.0354590i
$321$	−14.2266	+	9.04677i	−0.794050	+	0.504941i
$322$	7.13182	+	0.409011i	0.397441	+	0.0227933i
$323$	16.5178	+	28.6097i	0.919075	+	1.59188i
$324$	−5.76221	−	6.91354i	−0.320123	−	0.384085i
$325$	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	−0.503090	+	0.864234i	$0.667803\pi$
$331$	−27.3462	+	15.7883i	−1.50308	+	0.867806i	−0.999994	+	0.00357128i	$0.998863\pi$
$332$			9.22131i			0.506085i
$333$	−15.0317	−	7.03976i	−0.823733	−	0.385776i
$334$	−14.6300	+	8.44665i	−0.800520	+	0.462180i
$335$	−7.33592	−	12.7062i	−0.400804	−	0.694214i
$336$	4.00139	−	2.23357i	0.218294	−	0.121851i
$337$	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
$339$	−0.229644	−	5.36166i	−0.0124726	−	0.291205i
$340$	5.49645	+	3.17338i	0.298087	+	0.172101i
$341$	−43.8673			−2.37555
$342$	19.7374	−	1.69385i	1.06728	−	0.0915927i
$343$	−3.16729	+	18.2474i	−0.171018	+	0.985268i
$344$	−1.72068	+	2.98031i	−0.0927730	+	0.160688i
$345$	5.92733	−	0.253873i	0.319117	−	0.0136680i
$346$	−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	0.733449	−	0.679745i	$-0.237909\pi$
$349$	−4.14640	−	7.18177i	−0.221952	−	0.384431i	−0.955400	+	0.295313i	$0.904576\pi$
$350$	8.01291	−	4.03317i	0.428308	−	0.215582i
$351$	11.4983	−	14.7915i	0.613733	−	0.789514i
$352$	2.57517	−	4.46032i	0.137257	−	0.237736i
$353$	−18.9199	−	10.9234i	−1.00700	−	0.581393i	−0.0966897	−	0.995315i	$-0.530825\pi$
$353$	−18.9199	−	10.9234i	−1.00700	−	0.581393i	−0.910313	+	0.413922i	$0.864159\pi$
$354$	−17.2955	+	10.9983i	−0.919244	+	0.584553i
$355$	−8.33013	+	4.80940i	−0.442117	+	0.255257i
$356$		−	8.30846i		−	0.440348i
$357$	20.0185	−	11.1743i	1.05949	−	0.591406i
$358$	−6.94512	−	4.00977i	−0.367061	−	0.211923i
$359$	−10.1960	+	17.6599i	−0.538122	+	0.932055i	0.460883	+	0.887461i	$0.347533\pi$
$359$	−10.1960	+	17.6599i	−0.538122	+	0.932055i	−0.999005	+	0.0445941i	$0.985801\pi$
$360$	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	0.0817597	−	0.996652i	$-0.473946\pi$
$367$	−14.1857	−	8.19011i	−0.740486	−	0.427520i	−0.822246	+	0.569132i	$0.807279\pi$
$368$		−	2.70000i		−	0.140747i
$369$	−1.34533	−	15.6763i	−0.0700351	−	0.816078i
$370$	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	0.988944	−	0.148288i	$-0.0473762\pi$
$373$	7.06962	+	12.2449i	0.366051	+	0.634019i	−0.622893	+	0.782307i	$0.714043\pi$
$374$	12.8832	−	22.3144i	0.666177	−	1.15385i
$375$	15.5576	−	9.89320i	0.803393	−	0.510883i
$376$	−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	$0.241715\pi$
$380$			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	$-0.658889\pi$
$383$	0.828157	−	0.478136i	0.0423168	−	0.0244316i	0.521009	+	0.853551i	$0.325556\pi$
$384$	−0.929420	−	1.46157i	−0.0474292	−	0.0745853i
$385$	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	$-0.644668\pi$
$389$	2.35900	−	1.36197i	0.119606	−	0.0690546i	0.558609	+	0.829431i	$0.311335\pi$
$390$	5.81630	+	5.37934i	0.294520	+	0.272394i
$391$		−	13.5078i		−	0.683119i
$392$	6.95410	+	0.800271i	0.351235	+	0.0404198i
$393$	8.16370	−	0.349658i	0.411804	−	0.0176379i
$394$	−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	−0.991473	−	0.130316i	$-0.958401\pi$
$397$	−12.1261	−	21.0031i	−0.608593	−	1.05411i	0.382879	−	0.923798i	$-0.374932\pi$
$398$			15.3246i			0.768150i
$399$	25.9842	+	15.5080i	1.30084	+	0.776373i
$400$	−1.69530	−	2.93635i	−0.0847650	−	0.146817i
$401$	32.8317			1.63954			0.819768	−	0.572696i	$-0.194102\pi$
$401$	32.8317			1.63954			0.819768	+	0.572696i	$0.194102\pi$
$402$	0.857180	+	20.0131i	0.0427523	+	0.998165i
$403$	−29.6331	−	8.06083i	−1.47613	−	0.401539i
$404$	4.72713	−	8.18763i	0.235183	−	0.407350i
$405$	−1.94537	−	11.2506i	−0.0966661	−	0.559049i
$406$	1.06693	+	2.11973i	0.0529510	+	0.105200i
$407$	−24.6782	−	14.2480i	−1.22325	−	0.706246i
$408$	−4.64977	−	7.31204i	−0.230198	−	0.362000i
$409$	−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
$411$	8.93979	+	14.0583i	0.440967	+	0.693447i
$412$	−15.4442	−	8.91672i	−0.760881	−	0.439295i
$413$	−31.2572	−	1.79260i	−1.53806	−	0.0882083i
$414$	−7.33542	−	3.43537i	−0.360516	−	0.168839i
$415$	−5.84918	+	10.1311i	−0.287125	+	0.497315i
$416$	2.55917	−	2.53981i	0.125474	−	0.124525i
$417$	−0.155253	−	3.62480i	−0.00760278	−	0.177507i
$418$	34.0093			1.66345
$419$	−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	$0.866906\pi$
$420$	5.81294	+	0.0841934i	0.283643	+	0.00410822i
$421$		−	9.35440i		−	0.455905i	−0.973672	−	0.227953i	$-0.926797\pi$
$421$		−	9.35440i		−	0.455905i	0.973672	−	0.227953i	$-0.0732032\pi$
$422$	−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
$426$	13.1205	−	0.561964i	0.635692	−	0.0272272i
$427$	−5.55216	−	11.0308i	−0.268688	−	0.533816i
$428$			9.73378i			0.470500i
$429$	21.8390	−	23.6129i	1.05440	−	1.14004i
$430$	−3.78089	+	2.18290i	−0.182331	+	0.105269i
$431$	−0.433968	+	0.751655i	−0.0209035	+	0.0362060i	−0.876288	−	0.481788i	$-0.839988\pi$
$431$	−0.433968	+	0.751655i	−0.0209035	+	0.0362060i	0.855384	+	0.517994i	$0.173321\pi$
$432$	−5.15337	+	0.665427i	−0.247942	+	0.0320154i
$433$	−20.7610	−	11.9864i	−0.997710	−	0.576028i	−0.0901401	−	0.995929i	$-0.528731\pi$
$433$	−20.7610	−	11.9864i	−0.997710	−	0.576028i	−0.907570	+	0.419901i	$0.862065\pi$
$434$	−20.1289	+	10.1316i	−0.966217	+	0.486330i
$435$	1.05757	+	1.66310i	0.0507068	+	0.0797394i
$436$	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	$0.142494\pi$
$439$			18.1387i			0.865711i	−0.901463	+	0.432855i	$0.857506\pi$
$440$	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	−0.235082	−	0.971975i	$-0.575536\pi$
$443$	−25.1388	−	14.5139i	−1.19438	−	0.689575i	−0.959297	+	0.282401i	$0.908869\pi$
$444$	−8.08662	+	5.14233i	−0.383774	+	0.244044i
$445$	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	$-0.855479\pi$
$449$	−1.47303	+	2.55136i	−0.0695165	+	0.120406i	0.829172	+	0.558993i	$0.188812\pi$
$450$	−10.1345	+	0.869738i	−0.477747	+	0.0409998i
$451$		−	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	$-0.850167\pi$
$457$		−	19.3905i		−	0.907049i	0.891244	−	0.453524i	$-0.149833\pi$
$458$	−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	$-0.167506\pi$
$461$	18.5093	+	10.6864i	0.862066	+	0.497714i	−0.00263775	+	0.999997i	$0.500840\pi$
$462$	0.341807	−	23.5993i	0.0159023	−	1.09794i
$463$			7.17045i			0.333239i	0.986021	+	0.166620i	$0.0532852\pi$
$463$			7.17045i			0.333239i	−0.986021	+	0.166620i	$0.946715\pi$
$464$	0.776779	−	0.448474i	0.0360611	−	0.0208199i
$465$	−15.7927	+	10.0427i	−0.732370	+	0.465718i
$466$	6.84440	+	3.95162i	0.317061	+	0.183055i
$467$	−4.50077	+	7.79557i	−0.208271	+	0.360736i	−0.951170	−	0.308668i	$-0.900117\pi$
$467$	−4.50077	+	7.79557i	−0.208271	+	0.360736i	0.742899	+	0.669404i	$0.233450\pi$
$468$	−3.64403	−	10.1844i	−0.168446	−	0.470772i
$469$	−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
$474$	10.2099	−	0.437301i	0.468958	−	0.0200859i
$475$	11.1946	−	19.3896i	0.513644	−	0.889657i
$476$	0.757863	−	13.2147i	0.0347366	−	0.605693i
$477$	3.46997	+	40.4335i	0.158879	+	1.85132i
$478$	27.3019			1.24876
$479$	−3.50004	−	2.02075i	−0.159921	−	0.0923303i	0.417904	−	0.908491i	$-0.362765\pi$
$479$	−3.50004	−	2.02075i	−0.159921	−	0.0923303i	−0.577825	+	0.816161i	$0.696098\pi$
$480$	−0.0940267	−	2.19530i	−0.00429171	−	0.100201i
$481$	−14.0524	−	14.1595i	−0.640734	−	0.645616i
$482$	11.2815			0.513859
$483$	−6.03066	−	10.8038i	−0.274404	−	0.491589i
$484$	−7.76296	−	13.4458i	−0.352862	−	0.611175i
$485$	13.6456	−	7.87827i	0.619613	−	0.357734i
$486$	−4.74909	+	14.8474i	−0.215423	+	0.673493i
$487$			13.7020i			0.620897i	0.950590	+	0.310449i	$0.100479\pi$
$487$			13.7020i			0.620897i	−0.950590	+	0.310449i	$0.899521\pi$
$488$	−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	$-0.497892\pi$
$491$	19.4095	−	11.2061i	0.875940	−	0.505724i	0.869318	+	0.494254i	$0.164559\pi$
$492$	−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
$495$	−1.67602	−	19.5297i	−0.0753315	−	0.877794i
$496$	4.25869	+	7.37627i	0.191221	+	0.331204i
$497$	16.7700	+	11.0084i	0.752236	+	0.493794i
$498$	13.4776	−	8.57046i	0.603944	−	0.384052i
$499$	17.1062	+	9.87625i	0.765777	+	0.442122i	0.831366	−	0.555725i	$-0.187559\pi$
$499$	17.1062	+	9.87625i	0.765777	+	0.442122i	−0.0655891	+	0.997847i	$0.520893\pi$
$500$		−	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	$-0.788965\pi$
$503$	3.11599	−	5.39705i	0.138935	−	0.240643i	0.927094	+	0.374829i	$0.122299\pi$
$504$	−6.98349	−	3.77238i	−0.311069	−	0.168035i
$505$	10.3870	−	5.99694i	0.462215	−	0.266860i
$506$	−12.0429	−	6.95296i	−0.535371	−	0.309097i
$507$	19.0916	−	11.9379i	0.847886	−	0.530179i
$508$	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	$0.883316\pi$
$510$	−0.470404	−	10.9828i	−0.0208299	−	0.486328i
$511$	0.996336	−	0.501490i	0.0440753	−	0.0221846i
$512$	−1.00000			−0.0441942
$513$	−20.8200	−	27.2733i	−0.919226	−	1.20414i
$514$	−1.36558			−0.0602330
$515$	−11.3119	−	19.5929i	−0.498464	−	0.863364i
$516$	5.95516	−	0.255065i	0.262161	−	0.0112286i
$517$	−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	$-0.294990\pi$
$521$	−8.95460	−	15.5098i	−0.392308	−	0.679498i	−0.992754	+	0.120168i	$0.961657\pi$
$522$	−0.230080	−	2.68099i	−0.0100703	−	0.117344i
$523$			15.3139i			0.669630i	0.942284	+	0.334815i	$0.108674\pi$
$523$			15.3139i			0.669630i	−0.942284	+	0.334815i	$0.891326\pi$
$524$	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
$527$	21.3057	+	36.9026i	0.928091	+	1.60750i
$528$	−8.91247	+	0.381728i	−0.387865	+	0.0166126i
$529$	15.7100			0.683042
$530$	−17.1611			−0.745431
$531$	32.1495	+	15.0565i	1.39517	+	0.653395i
$532$	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
$535$	−6.17424	+	10.6941i	−0.266936	+	0.462346i
$536$	10.0157	+	5.78259i	0.432614	+	0.249770i
$537$	0.594386	+	13.8775i	0.0256496	+	0.598859i
$538$	−22.9534			−0.989592
$539$	21.4774	−	28.9567i	0.925099	−	1.24725i
$540$	−6.08388	−	2.53776i	−0.261808	−	0.109208i
$541$	−3.16570	−	1.82772i	−0.136104	−	0.0785797i	0.430402	−	0.902637i	$-0.358372\pi$
$541$	−3.16570	−	1.82772i	−0.136104	−	0.0785797i	−0.566506	+	0.824058i	$0.691705\pi$
$542$	15.5927			0.669766
$543$	−0.670968	+	0.426673i	−0.0287940	+	0.0183103i
$544$	−5.00288			−0.214497
$545$	13.4326			0.575389
$546$	4.56738	−	15.8789i	0.195466	−	0.679554i
$547$	−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
$549$	1.19730	+	13.9515i	0.0510996	+	0.595434i
$550$	−17.4627			−0.744613
$551$	5.12932	+	2.96141i	0.218516	+	0.126160i
$552$	−3.94624	+	2.50944i	−0.167963	+	0.106809i
$553$	13.0498	+	8.56636i	0.554934	+	0.364279i
$554$	−22.3309			−0.948750
$555$	−12.1463	+	0.520235i	−0.515580	+	0.0220827i
$556$	−1.81406	−	1.04735i	−0.0769333	−	0.0444175i
$557$	0.938911	−	1.62624i	0.0397830	−	0.0689061i	−0.845448	−	0.534057i	$-0.820667\pi$
$557$	0.938911	−	1.62624i	0.0397830	−	0.0689061i	0.885231	+	0.465151i	$0.154000\pi$
$558$	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
$561$	−44.5880	+	1.90974i	−1.88251	+	0.0806293i
$562$	21.7986			0.919520
$563$	6.19768			0.261201			0.130601	−	0.991435i	$-0.458309\pi$
$563$	6.19768			0.261201			0.130601	+	0.991435i	$0.458309\pi$
$564$	0.358142	+	8.36178i	0.0150805	+	0.352094i
$565$	−1.96534	−	3.40407i	−0.0826826	−	0.143210i
$566$	−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
$569$		−	6.56295i		−	0.275133i	−0.990493	−	0.137567i	$-0.956072\pi$
$569$		−	6.56295i		−	0.275133i	0.990493	−	0.137567i	$-0.0439281\pi$
$570$	12.2437	−	7.78585i	0.512833	−	0.326113i
$571$	−8.90567	−	15.4251i	−0.372691	−	0.645519i	0.617288	−	0.786737i	$-0.288231\pi$
$571$	−8.90567	−	15.4251i	−0.372691	−	0.645519i	−0.989978	+	0.141218i	$0.954898\pi$
$572$	−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
$576$	−1.27236	+	2.71682i	−0.0530149	+	0.113201i
$577$	−1.86181	−	3.22475i	−0.0775082	−	0.134248i	0.824666	−	0.565620i	$-0.191363\pi$
$577$	−1.86181	−	3.22475i	−0.0775082	−	0.134248i	−0.902174	+	0.431372i	$0.858030\pi$
$578$	−8.02879			−0.333954
$579$	0.613707	+	14.3286i	0.0255048	+	0.595477i
$580$	1.13789			0.0472482
$581$	24.3573	+	1.39689i	1.01051	+	0.0579529i
$582$	−21.4927	+	0.920551i	−0.890901	+	0.0381581i
$583$			69.6705i			2.88546i
$584$	−0.210796	−	0.365109i	−0.00872279	−	0.0151083i
$585$	2.45649	−	13.5006i	0.101564	−	0.558180i
$586$	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	$-0.00751349\pi$
$588$	−5.29363	−	10.9077i	−0.218306	−	0.449825i
$589$	−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	$-0.141786\pi$
$593$	23.8770	+	13.7854i	0.980509	+	0.566097i	0.0780852	+	0.996947i	$0.475119\pi$
$594$	−10.3028	+	24.6993i	−0.422728	+	1.01342i
$595$	9.21483	−	14.0377i	0.377771	−	0.575489i
$596$	−3.85315	−	6.67385i	−0.157831	−	0.273371i
$597$	22.3979	−	14.2429i	0.916684	−	0.582925i
$598$	−6.85751	−	6.90977i	−0.280424	−	0.282561i
$599$	7.32482	−	4.22899i	0.299284	−	0.172792i	−0.342837	−	0.939395i	$-0.611388\pi$
$599$	7.32482	−	4.22899i	0.299284	−	0.172792i	0.642121	+	0.766603i	$0.278055\pi$
$600$	−2.71602	+	5.20689i	−0.110881	+	0.212570i
$601$	−12.8550	+	7.42186i	−0.524368	+	0.302744i	−0.738720	−	0.674013i	$-0.764569\pi$
$601$	−12.8550	+	7.42186i	−0.524368	+	0.302744i	0.214352	+	0.976756i	$0.431236\pi$
$602$	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
$606$	−16.3603	+	0.700723i	−0.664590	+	0.0284649i
$607$	−23.5350	+	13.5879i	−0.955256	+	0.551517i	−0.894710	−	0.446648i	$-0.852618\pi$
$607$	−23.5350	+	13.5879i	−0.955256	+	0.551517i	−0.0605460	+	0.998165i	$0.519284\pi$
$608$	−3.30166	−	5.71864i	−0.133900	−	0.231922i
$609$	2.10650	−	3.52951i	0.0853597	−	0.143023i
$610$	−5.92139			−0.239750
$611$	−16.8457	+	4.44534i	−0.681505	+	0.179839i
$612$	−6.36546	+	13.5919i	−0.257308	+	0.549421i
$613$	12.8149	+	7.39869i	0.517590	+	0.298830i	0.735948	−	0.677038i	$-0.236737\pi$
$613$	12.8149	+	7.39869i	0.517590	+	0.298830i	−0.218358	+	0.975869i	$0.570070\pi$
$614$	−15.8067			−0.637906
$615$	−6.18387	−	9.72451i	−0.249358	−	0.392130i
$616$	−11.3914	−	7.47775i	−0.458974	−	0.301287i
$617$	10.4145	−	18.0385i	0.419272	−	0.726201i	−0.576594	−	0.817031i	$-0.695619\pi$
$617$	10.4145	−	18.0385i	0.419272	−	0.726201i	0.995866	+	0.0908296i	$0.0289519\pi$
$618$	1.32176	+	30.8601i	0.0531692	+	1.24138i
$619$	13.6057	+	23.5658i	0.546860	+	0.947189i	0.998487	+	0.0549827i	$0.0175104\pi$
$619$	13.6057	+	23.5658i	0.546860	+	0.947189i	−0.451627	+	0.892207i	$0.649156\pi$
$620$			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
$624$	−6.09065	−	1.37984i	−0.243821	−	0.0552380i
$625$	−1.72458	+	2.98706i	−0.0689832	+	0.119482i
$626$	14.2929	+	8.25201i	0.571259	+	0.329817i
$627$	−31.6089	−	49.7069i	−1.26234	−	1.98510i
$628$	11.5582	−	6.67311i	0.461221	−	0.266286i
$629$			27.6801i			1.10368i
$630$	−5.27961	−	8.57426i	−0.210345	−	0.341607i
$631$	−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
$633$	−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	$-0.0401804\pi$
$642$	14.2266	−	9.04677i	0.561478	−	0.357047i
$643$	21.5821	−	37.3812i	0.851113	−	1.47417i	−0.0290911	−	0.999577i	$-0.509261\pi$
$643$	21.5821	−	37.3812i	0.851113	−	1.47417i	0.880204	−	0.474595i	$-0.157405\pi$
$644$	−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	$-0.696384\pi$
$647$	10.6092	−	18.3756i	0.417089	−	0.722419i	0.995645	+	0.0932232i	$0.0297170\pi$
$648$	5.76221	+	6.91354i	0.226361	+	0.271589i
$649$	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
$653$			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
$657$	−1.26014	+	0.108144i	−0.0491629	+	0.00421911i
$658$	−7.01571	+	10.6876i	−0.273501	+	0.416645i
$659$	−29.9716	−	17.3041i	−1.16753	−	0.674072i	−0.214431	−	0.976739i	$-0.568790\pi$
$659$	−29.9716	−	17.3041i	−1.16753	−	0.674072i	−0.953096	+	0.302667i	$0.902123\pi$
$660$	−10.0339	−	5.23388i	−0.390569	−	0.203729i
$661$	9.59801	−	16.6242i	0.373319	−	0.646608i	−0.616755	−	0.787155i	$-0.711553\pi$
$661$	9.59801	−	16.6242i	0.373319	−	0.646608i	0.990074	+	0.140547i	$0.0448862\pi$
$662$	27.3462	−	15.7883i	1.06284	−	0.613631i
$663$	−30.4708	−	6.90319i	−1.18339	−	0.268098i
$664$		−	9.22131i		−	0.357856i
$665$	22.1274	+	1.26901i	0.858064	+	0.0492101i
$666$	15.0317	+	7.03976i	0.582467	+	0.272785i
$667$	−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
$672$	−4.00139	+	2.23357i	−0.154357	+	0.0861619i
$673$	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	$0.702330\pi$
$674$	−18.8701			−0.726850
$675$	10.6904	+	14.0040i	0.411475	+	0.539013i
$676$	0.0986879	−	12.9996i	0.00379569	−	0.499986i
$677$	−3.91466	+	6.78038i	−0.150452	+	0.260591i	−0.931394	−	0.364013i	$-0.881406\pi$
$677$	−3.91466	+	6.78038i	−0.150452	+	0.260591i	0.780941	+	0.624604i	$0.214740\pi$
$678$	0.229644	+	5.36166i	0.00881943	+	0.205913i
$679$	−27.4708	−	18.0328i	−1.05423	−	0.692037i
$680$	−5.49645	−	3.17338i	−0.210779	−	0.121694i
$681$	3.46493	−	2.20337i	0.132776	−	0.0844333i
$682$	43.8673			1.67977
$683$	−25.4681			−0.974511			−0.487255	−	0.873260i	$-0.662002\pi$
$683$	−25.4681			−0.974511			−0.487255	+	0.873260i	$0.662002\pi$
$684$	−19.7374	+	1.69385i	−0.754679	+	0.0647659i
$685$	10.5676	+	6.10123i	0.403769	+	0.233116i
$686$	3.16729	−	18.2474i	0.120928	−	0.696690i
$687$	20.4698	−	0.876738i	0.780971	−	0.0334496i
$688$	1.72068	−	2.98031i	0.0656004	−	0.113623i
$689$	−12.8023	+	47.0635i	−0.487728	+	1.79298i
$690$	−5.92733	+	0.253873i	−0.225650	+	0.00966477i
$691$	−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
$693$	−34.8097	+	21.4341i	−1.32231	+	0.814214i
$694$			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
$699$	−0.585766	−	13.6763i	−0.0221557	−	0.517284i
$700$	−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	$-0.0250816\pi$
$702$	−11.4983	+	14.7915i	−0.433975	+	0.558271i
$703$	−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
$708$	17.2955	−	10.9983i	0.650003	−	0.413341i
$709$	−16.0287	+	9.25420i	−0.601972	+	0.347549i	−0.769817	−	0.638265i	$-0.779653\pi$
$709$	−16.0287	+	9.25420i	−0.601972	+	0.347549i	0.167845	+	0.985813i	$0.446319\pi$
$710$	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
$714$	−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
$717$	−25.3749	−	39.9036i	−0.947644	−	1.49023i
$718$	10.1960	−	17.6599i	0.380510	−	0.659062i
$719$	5.00141	+	8.66270i	0.186521	+	0.323064i	0.944088	−	0.329693i	$-0.106945\pi$
$719$	5.00141	+	8.66270i	0.186521	+	0.323064i	−0.757567	+	0.652758i	$0.773612\pi$
$720$	−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
$723$	−10.4853	−	16.4887i	−0.389951	−	0.613222i
$724$			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	$-0.827034\pi$
$727$		−	27.8818i		−	1.03408i	0.855961	−	0.517040i	$-0.172966\pi$
$728$	−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	−0.638925	−	0.769269i	$-0.720621\pi$
$733$	9.38772	−	16.2600i	0.346743	−	0.600577i	0.985669	+	0.168691i	$0.0539541\pi$
$734$	14.1857	+	8.19011i	0.523603	+	0.302302i
$735$	1.10297	−	15.3416i	0.0406835	−	0.565884i
$736$			2.70000i			0.0995235i
$737$	51.5844	−	29.7823i	1.90014	−	1.09704i
$738$	1.34533	+	15.6763i	0.0495223	+	0.577054i
$739$	4.75988	+	2.74812i	0.175095	+	0.101091i	0.584986	−	0.811043i	$-0.301100\pi$
$739$	4.75988	+	2.74812i	0.175095	+	0.101091i	−0.409891	+	0.912135i	$0.634433\pi$
$740$	−3.50954	+	6.07870i	−0.129013	+	0.223458i
$741$	−12.2184	−	39.3860i	−0.448855	−	1.44688i
$742$	16.0910	+	31.9689i	0.590720	+	1.17361i
$743$	9.12112	+	15.7982i	0.334621	+	0.579581i	0.983412	−	0.181386i	$-0.0580583\pi$
$743$	9.12112	+	15.7982i	0.334621	+	0.579581i	−0.648791	+	0.760967i	$0.724725\pi$
$744$	6.82280	−	13.0800i	0.250136	−	0.479536i
$745$		−	9.77637i		−	0.358179i
$746$	−7.06962	−	12.2449i	−0.258837	−	0.448319i
$747$	−25.0526	−	11.7328i	−0.916628	−	0.429281i
$748$	−12.8832	+	22.3144i	−0.471058	+	0.815896i
$749$	25.7109	+	1.47453i	0.939457	+	0.0538780i
$750$	−15.5576	+	9.89320i	−0.568085	+	0.361249i
$751$	−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
$753$	−39.1318	+	1.67605i	−1.42604	+	0.0610786i
$754$	0.848869	−	3.12059i	0.0309140	−	0.113645i
$755$	0.770139			0.0280282
$756$	0.977005	+	13.7130i	0.0355333	+	0.498736i
$757$	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	$0.812224\pi$
$758$	−9.57195	+	5.52637i	−0.347669	+	0.200727i
$759$	1.03067	+	24.0637i	0.0374109	+	0.873457i
$760$		−	8.37711i		−	0.303870i
$761$	−39.7985	+	22.9777i	−1.44269	+	0.832940i	−0.998029	−	0.0627562i	$-0.980011\pi$
$761$	−39.7985	+	22.9777i	−1.44269	+	0.832940i	−0.444666	+	0.895696i	$0.646678\pi$
$762$	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
$768$	0.929420	+	1.46157i	0.0335375	+	0.0527398i
$769$	−3.19274	−	5.52999i	−0.115133	−	0.199417i	0.802700	−	0.596383i	$-0.203396\pi$
$769$	−3.19274	−	5.52999i	−0.115133	−	0.199417i	−0.917833	+	0.396967i	$0.870063\pi$
$770$	−7.77208	−	15.4412i	−0.280086	−	0.556462i
$771$	1.26919	+	1.99588i	0.0457089	+	0.0718800i
$772$	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
$777$	12.3580	+	22.1391i	0.443341	+	0.794235i
$778$	−2.35900	+	1.36197i	−0.0845742	+	0.0488289i
$779$	−29.9923	−	17.3161i	−1.07459	−	0.620412i
$780$	−5.81630	−	5.37934i	−0.208257	−	0.192611i
$781$	−19.5251	−	33.8185i	−0.698665	−	1.21012i
$782$			13.5078i			0.483038i
$783$	−3.70460	+	2.82804i	−0.132392	+	0.101066i
$784$	−6.95410	−	0.800271i	−0.248361	−	0.0285811i
$785$	16.9313			0.604304
$786$	−8.16370	+	0.349658i	−0.291189	+	0.0124719i
$787$	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
$789$	0.801295	+	18.7084i	0.0285269	+	0.666036i
$790$	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
$795$	15.9499	+	25.0821i	0.565684	+	0.889572i
$796$		−	15.3246i		−	0.543164i
$797$	−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
$800$	1.69530	+	2.93635i	0.0599379	+	0.103815i
$801$	22.5726	+	10.5713i	0.797563	+	0.373520i
$802$	−32.8317			−1.15933
$803$	−2.17134			−0.0766248
$804$	−0.857180	−	20.0131i	−0.0302304	−	0.705809i
$805$	−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
$808$	−4.72713	+	8.18763i	−0.166300	+	0.288040i
$809$	9.85463	+	5.68957i	0.346470	+	0.200035i	0.663130	−	0.748505i	$-0.269228\pi$
$809$	9.85463	+	5.68957i	0.346470	+	0.200035i	−0.316659	+	0.948539i	$0.602561\pi$
$810$	1.94537	+	11.2506i	0.0683533	+	0.395307i
$811$	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
$813$	−14.4922	−	22.7899i	−0.508264	−	0.799275i
$814$	24.6782	+	14.2480i	0.864971	+	0.499392i
$815$	19.0671			0.667892
$816$	4.64977	+	7.31204i	0.162775	+	0.255973i
$817$	22.7244			0.795027
$818$	19.9476			0.697452
$819$	−27.4531	+	8.08261i	−0.959288	+	0.282429i
$820$	−6.65348			−0.232350
$821$	−45.6193			−1.59213			−0.796063	−	0.605214i	$-0.793088\pi$
$821$	−45.6193			−1.59213			−0.796063	+	0.605214i	$0.793088\pi$
$822$	−8.93979	−	14.0583i	−0.311811	−	0.490341i
$823$	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
$825$	16.2302	+	25.5229i	0.565063	+	0.888595i
$826$	31.2572	+	1.79260i	1.08758	+	0.0623727i
$827$	−36.7827			−1.27906			−0.639530	−	0.768766i	$-0.720871\pi$
$827$	−36.7827			−1.27906			−0.639530	+	0.768766i	$0.720871\pi$
$828$	7.33542	+	3.43537i	0.254924	+	0.119388i
$829$	−2.19111	−	1.26504i	−0.0761003	−	0.0439365i	0.461467	−	0.887157i	$-0.347323\pi$
$829$	−2.19111	−	1.26504i	−0.0761003	−	0.0439365i	−0.537567	+	0.843221i	$0.680657\pi$
$830$	5.84918	−	10.1311i	0.203028	−	0.351655i
$831$	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
$834$	0.155253	+	3.62480i	0.00537598	+	0.125516i
$835$	21.4312			0.741658
$836$	−34.0093			−1.17624
$837$	−26.8550	−	35.1788i	−0.928243	−	1.21596i
$838$	2.15496	+	3.73250i	0.0744419	+	0.128937i
$839$	−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
$842$			9.35440i			0.322374i
$843$	−20.2601	−	31.8602i	−0.697794	−	1.09732i
$844$	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
$849$	0.333499	+	7.78642i	0.0114456	+	0.267229i
$850$	8.48138	+	14.6902i	0.290909	+	0.503869i
$851$	14.9387			0.512092
$852$	−13.1205	+	0.561964i	−0.449502	+	0.0192526i
$853$	−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
$855$	−22.7591	−	10.6587i	−0.778345	−	0.364519i
$856$		−	9.73378i		−	0.332694i
$857$	−18.8542	−	32.6564i	−0.644047	−	1.11552i	−0.984521	−	0.175268i	$-0.943921\pi$
$857$	−18.8542	−	32.6564i	−0.644047	−	1.11552i	0.340474	−	0.940254i	$-0.389413\pi$
$858$	−21.8390	+	23.6129i	−0.745571	+	0.806132i
$859$	2.88055	+	1.66308i	0.0982830	+	0.0567437i	0.548336	−	0.836258i	$-0.315262\pi$
$859$	2.88055	+	1.66308i	0.0982830	+	0.0567437i	−0.450053	+	0.893002i	$0.648595\pi$
$860$	3.78089	−	2.18290i	0.128927	−	0.0744361i
$861$	−12.3172	+	20.6379i	−0.419769	+	0.703336i
$862$	0.433968	−	0.751655i	0.0147810	−	0.0256015i
$863$	25.4144	−	44.0190i	0.865116	−	1.49842i	−0.00181612	−	0.999998i	$-0.500578\pi$
$863$	25.4144	−	44.0190i	0.865116	−	1.49842i	0.866932	−	0.498426i	$-0.166089\pi$
$864$	5.15337	−	0.665427i	0.175321	−	0.0226383i
$865$			0.650606i			0.0221213i
$866$	20.7610	+	11.9864i	0.705488	+	0.407313i
$867$	7.46212	+	11.7346i	0.253427	+	0.398529i
$868$	20.1289	−	10.1316i	0.683219	−	0.343887i
$869$	−15.1938	−	26.3164i	−0.515414	−	0.892723i
$870$	−1.05757	−	1.66310i	−0.0358551	−	0.0563843i
$871$	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	0.0392879	−	0.999228i	$-0.487491\pi$
$877$	27.3721	−	15.8033i	0.924289	−	0.533638i	0.885001	+	0.465590i	$0.154158\pi$
$878$		−	18.1387i		−	0.612150i
$879$	−0.997056	−	23.2789i	−0.0336299	−	0.785179i
$880$	−5.65846	+	3.26691i	−0.190747	+	0.110128i
$881$	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	$0.594470\pi$
$882$	−11.0223	+	17.8748i	−0.371140	+	0.601876i
$883$	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
$885$	25.9781	−	1.11267i	0.873246	−	0.0374019i
$886$	25.1388	+	14.5139i	0.844553	+	0.487603i
$887$	40.9299			1.37429			0.687146	−	0.726519i	$-0.258863\pi$
$887$	40.9299			1.37429			0.687146	+	0.726519i	$0.258863\pi$
$888$	8.08662	−	5.14233i	0.271369	−	0.172565i
$889$	27.7636	−	13.9744i	0.931163	−	0.468686i
$890$	−5.27015	+	9.12816i	−0.176656	+	0.305977i
$891$	45.6752	−	7.89778i	1.53018	−	0.264586i
$892$	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
$897$	−3.72559	+	16.4448i	−0.124394	+	0.549075i
$898$	1.47303	−	2.55136i	0.0491556	−	0.0851400i
$899$	6.61612	+	3.81982i	0.220660	+	0.127398i
$900$	10.1345	−	0.869738i	0.337818	−	0.0289913i
$901$	58.6090	−	33.8379i	1.95255	−	1.12730i
$902$			27.0117i			0.899391i
$903$	0.228390	−	15.7687i	0.00760034	−	0.524748i
$904$	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	−0.991978	−	0.126409i	$-0.959655\pi$
$907$	−11.6405	+	20.1619i	−0.386515	+	0.669464i	0.605463	+	0.795874i	$0.292988\pi$
$908$		−	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
$915$	5.50346	+	8.65451i	0.181939	+	0.286109i
$916$	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	0.964016	−	0.265845i	$-0.0856510\pi$
$919$	7.63269	+	13.2202i	0.251779	+	0.436094i	−0.712237	+	0.701940i	$0.752318\pi$
$920$	−1.71264	+	2.96638i	−0.0564641	+	0.0977988i
$921$	14.6910	+	23.1025i	0.484086	+	0.761255i
$922$	−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
$926$		−	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	$-0.724183\pi$
$929$	−9.48735	+	5.47752i	−0.311270	+	0.179712i	0.336225	+	0.941782i	$0.390850\pi$
$930$	15.7927	−	10.0427i	0.517864	−	0.329313i
$931$	−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
$936$	3.64403	+	10.1844i	0.119109	+	0.332886i
$937$		−	24.6465i		−	0.805165i	−0.915384	−	0.402583i	$-0.868113\pi$
$937$		−	24.6465i		−	0.805165i	0.915384	−	0.402583i	$-0.131887\pi$
$938$	16.7915	−	25.5797i	0.548260	−	0.835208i
$939$	−1.22323	−	28.5596i	−0.0399187	−	0.932008i
$940$	3.06505	+	5.30883i	0.0999710	+	0.173155i
$941$	7.51387	−	4.33814i	0.244945	−	0.141419i	−0.372502	−	0.928031i	$-0.621500\pi$
$941$	7.51387	−	4.33814i	0.244945	−	0.141419i	0.617448	+	0.786612i	$0.288167\pi$
$942$	−20.4956	−	10.6909i	−0.667782	−	0.348329i
$943$	7.08029	+	12.2634i	0.230566	+	0.399352i
$944$		−	11.8335i		−	0.385148i
$945$	−7.62489	+	15.6856i	−0.248038	+	0.510252i
$946$	−8.86209	−	15.3496i	−0.288131	−	0.499058i
$947$	−5.19193			−0.168715			−0.0843575	−	0.996436i	$-0.526884\pi$
$947$	−5.19193			−0.168715			−0.0843575	+	0.996436i	$0.526884\pi$
$948$	−10.2099	+	0.437301i	−0.331604	+	0.0142029i
$949$	−1.46677	−	0.398994i	−0.0476134	−	0.0129519i
$950$	−11.1946	+	19.3896i	−0.363201	+	0.629082i
$951$	−51.3205	+	2.19810i	−1.66418	+	0.0712783i
$952$	−0.757863	+	13.2147i	−0.0245625	+	0.428290i
$953$	12.1003	+	6.98613i	0.391968	+	0.226303i	0.683013	−	0.730406i	$-0.260669\pi$
$953$	12.1003	+	6.98613i	0.391968	+	0.226303i	−0.291044	+	0.956710i	$0.594003\pi$
$954$	−3.46997	−	40.4335i	−0.112344	−	1.30908i
$955$	12.8082			0.414463
$956$	−27.3019			−0.883007
$957$	−6.75182	+	4.29352i	−0.218255	+	0.138790i
$958$	3.50004	+	2.02075i	0.113081	+	0.0652874i
$959$	1.45709	−	25.4069i	0.0470519	−	0.820431i
$960$	0.0940267	+	2.19530i	0.00303470	+	0.0708531i
$961$	−20.7729	+	35.9797i	−0.670093	+	1.16064i
$962$	14.0524	+	14.1595i	0.453067	+	0.456520i
$963$	−26.4449	−	12.3849i	−0.852176	−	0.399097i
$964$	−11.2815			−0.363353
$965$	5.25223	+	9.09713i	0.169075	+	0.292847i
$966$	6.03066	+	10.8038i	0.194033	+	0.347606i
$967$		−	17.0679i		−	0.548866i	−0.961606	−	0.274433i	$-0.911510\pi$
$967$		−	17.0679i		−	0.548866i	0.961606	−	0.274433i	$-0.0884902\pi$
$968$	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	$-0.208678\pi$
$971$	−4.10072	−	7.10265i	−0.131598	−	0.227935i	−0.924293	+	0.381684i	$0.875344\pi$
$972$	4.74909	−	14.8474i	0.152327	−	0.476232i
$973$	−3.04128	+	4.63302i	−0.0974990	+	0.148528i
$974$		−	13.7020i		−	0.439040i
$975$	6.27378	+	20.2235i	0.200922	+	0.647670i
$976$	4.04224	−	2.33379i	0.129389	−	0.0747028i
$977$	18.7166	−	32.4182i	0.598798	−	1.03715i	−0.394201	−	0.919024i	$-0.628979\pi$
$977$	18.7166	−	32.4182i	0.598798	−	1.03715i	0.992999	−	0.118124i	$-0.0376881\pi$
$978$	−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
$981$	2.71606	+	31.6487i	0.0867172	+	1.01047i
$982$	−19.4095	+	11.2061i	−0.619383	+	0.357601i
$983$	−6.77655	+	3.91244i	−0.216138	+	0.124787i	−0.604161	−	0.796862i	$-0.706492\pi$
$983$	−6.77655	+	3.91244i	−0.216138	+	0.124787i	0.388023	+	0.921650i	$0.373158\pi$
$984$	8.05413	+	4.20120i	0.256756	+	0.133929i
$985$			17.9472i			0.571845i
$986$	−3.88613	+	2.24366i	−0.123760	+	0.0714526i
$987$	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
$990$	1.67602	+	19.5297i	0.0532674	+	0.620694i
$991$	2.06784	−	3.58160i	0.0656870	−	0.113773i	−0.831312	−	0.555807i	$-0.812409\pi$
$991$	2.06784	−	3.58160i	0.0656870	−	0.113773i	0.896999	+	0.442034i	$0.145743\pi$
$992$	−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
$996$	−13.4776	+	8.57046i	−0.427053	+	0.271566i
$997$			20.2952i			0.642755i	0.946951	+	0.321378i	$0.104146\pi$
$997$			20.2952i			0.642755i	−0.946951	+	0.321378i	$0.895854\pi$
$998$	−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.e.257.13	yes	34
3.2	odd	2		546.2.bi.f.257.16	yes	34
7.3	odd	6		546.2.bn.f.101.7	yes	34
13.4	even	6		546.2.bn.e.173.11	yes	34
21.17	even	6		546.2.bn.e.101.11	yes	34
39.17	odd	6		546.2.bn.f.173.7	yes	34
91.17	odd	6		546.2.bi.f.17.16	yes	34
273.17	even	6	inner	546.2.bi.e.17.13	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.13	✓	34	273.17	even	6	inner
546.2.bi.e.257.13	yes	34	1.1	even	1	trivial
546.2.bi.f.17.16	yes	34	91.17	odd	6
546.2.bi.f.257.16	yes	34	3.2	odd	2
546.2.bn.e.101.11	yes	34	21.17	even	6
546.2.bn.e.173.11	yes	34	13.4	even	6
546.2.bn.f.101.7	yes	34	7.3	odd	6
546.2.bn.f.173.7	yes	34	39.17	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.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(0.929420 + 1.46157i) q^{3} +1.00000 q^{4} +(1.09866 + 0.634311i) q^{5} +(-0.929420 - 1.46157i) q^{6} +(0.151485 - 2.64141i) q^{7} -1.00000 q^{8} +(-1.27236 + 2.71682i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(0.929420 + 1.46157i) q^{3} +1.00000 q^{4} +(1.09866 + 0.634311i) q^{5} +(-0.929420 - 1.46157i) q^{6} +(0.151485 - 2.64141i) q^{7} -1.00000 q^{8} +(-1.27236 + 2.71682i) q^{9} +(-1.09866 - 0.634311i) q^{10} +(-2.57517 + 4.46032i) q^{11} +(0.929420 + 1.46157i) q^{12} +(-2.55917 + 2.53981i) q^{13} +(-0.151485 + 2.64141i) q^{14} +(0.0940267 + 2.19530i) q^{15} +1.00000 q^{16} +5.00288 q^{17} +(1.27236 - 2.71682i) q^{18} +(3.30166 + 5.71864i) q^{19} +(1.09866 + 0.634311i) q^{20} +(4.00139 - 2.23357i) q^{21} +(2.57517 - 4.46032i) q^{22} -2.70000i q^{23} +(-0.929420 - 1.46157i) 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} +(-0.0940267 - 2.19530i) q^{30} +(4.25869 + 7.37627i) q^{31} -1.00000 q^{32} +(-8.91247 + 0.381728i) q^{33} -5.00288 q^{34} +(1.84191 - 2.80592i) q^{35} +(-1.27236 + 2.71682i) q^{36} +5.53284i q^{37} +(-3.30166 - 5.71864i) q^{38} +(-6.09065 - 1.37984i) q^{39} +(-1.09866 - 0.634311i) q^{40} +(-4.54200 + 2.62233i) q^{41} +(-4.00139 + 2.23357i) 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} +(0.929420 + 1.46157i) q^{48} +(-6.95410 - 0.800271i) q^{49} +(1.69530 + 2.93635i) q^{50} +(4.64977 + 7.31204i) 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} +(0.0940267 + 2.19530i) q^{60} +(4.04224 - 2.33379i) q^{61} +(-4.25869 - 7.37627i) q^{62} +(6.98349 + 3.77238i) q^{63} +1.00000 q^{64} +(-4.42268 + 1.16708i) q^{65} +(8.91247 - 0.381728i) q^{66} +(-10.0157 - 5.78259i) q^{67} +5.00288 q^{68} +(3.94624 - 2.50944i) q^{69} +(-1.84191 + 2.80592i) q^{70} +(-3.79105 + 6.56628i) q^{71} +(1.27236 - 2.71682i) 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} +(6.09065 + 1.37984i) q^{78} +(-2.95006 + 5.10965i) q^{79} +(1.09866 + 0.634311i) q^{80} +(-5.76221 - 6.91354i) q^{81} +(4.54200 - 2.62233i) q^{82} +9.22131i q^{83} +(4.00139 - 2.23357i) 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} +(-0.929420 - 1.46157i) q^{96} +(6.21010 - 10.7562i) q^{97} +(6.95410 + 0.800271i) q^{98} +(-8.84134 - 12.6714i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9} + 9 q^{10} - 9 q^{11} + 3 q^{12} + 8 q^{13} - 4 q^{14} - 4 q^{15} + 34 q^{16} - 12 q^{17} + 11 q^{18} - 5 q^{19} - 9 q^{20} + 4 q^{21} + 9 q^{22} - 3 q^{24} + 16 q^{25} - 8 q^{26} + 18 q^{27} + 4 q^{28} - 27 q^{29} + 4 q^{30} - q^{31} - 34 q^{32} + 21 q^{33} + 12 q^{34} + 3 q^{35} - 11 q^{36} + 5 q^{38} + 7 q^{39} + 9 q^{40} + 3 q^{41} - 4 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} + 27 q^{47} + 3 q^{48} - 2 q^{49} - 16 q^{50} + 24 q^{51} + 8 q^{52} + 21 q^{53} - 18 q^{54} - 57 q^{55} - 4 q^{56} + 17 q^{57} + 27 q^{58} - 4 q^{60} - 51 q^{61} + q^{62} + 3 q^{63} + 34 q^{64} + 21 q^{65} - 21 q^{66} - 21 q^{67} - 12 q^{68} + 42 q^{69} - 3 q^{70} + 15 q^{71} + 11 q^{72} - 19 q^{73} + 54 q^{75} - 5 q^{76} - 9 q^{77} - 7 q^{78} - 9 q^{79} - 9 q^{80} - 23 q^{81} - 3 q^{82} + 4 q^{84} - 42 q^{85} + 3 q^{86} + 81 q^{87} + 9 q^{88} - 9 q^{90} - 72 q^{91} + 17 q^{93} - 27 q^{94} - 3 q^{96} + 19 q^{97} + 2 q^{98} + 27 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9 + 9 * q^10 - 9 * q^11 + 3 * q^12 + 8 * q^13 - 4 * q^14 - 4 * q^15 + 34 * q^16 - 12 * q^17 + 11 * q^18 - 5 * q^19 - 9 * q^20 + 4 * q^21 + 9 * q^22 - 3 * q^24 + 16 * q^25 - 8 * q^26 + 18 * q^27 + 4 * q^28 - 27 * q^29 + 4 * q^30 - q^31 - 34 * q^32 + 21 * q^33 + 12 * q^34 + 3 * q^35 - 11 * q^36 + 5 * q^38 + 7 * q^39 + 9 * q^40 + 3 * q^41 - 4 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 + 27 * q^47 + 3 * q^48 - 2 * q^49 - 16 * q^50 + 24 * q^51 + 8 * q^52 + 21 * q^53 - 18 * q^54 - 57 * q^55 - 4 * q^56 + 17 * q^57 + 27 * q^58 - 4 * q^60 - 51 * q^61 + q^62 + 3 * q^63 + 34 * q^64 + 21 * q^65 - 21 * q^66 - 21 * q^67 - 12 * q^68 + 42 * q^69 - 3 * q^70 + 15 * q^71 + 11 * q^72 - 19 * q^73 + 54 * q^75 - 5 * q^76 - 9 * q^77 - 7 * q^78 - 9 * q^79 - 9 * q^80 - 23 * q^81 - 3 * q^82 + 4 * 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 - 3 * q^96 + 19 * q^97 + 2 * q^98 + 27 * q^99

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