LMFDB - Embedded newform 49.2.e.b.36.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [49,2,Mod(8,49)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("49.8"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(49, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([12])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	49.e (of order $7$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$0.391266969904$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{7})$
Coefficient field:	$\Q(\zeta_{21})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + x^{9} - x^{8} + x^{6} - x^{4} + x^{3} - x + 1 $ x^12 - x^11 + x^9 - x^8 + x^6 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			36.1
Root			$-0.733052 + 0.680173i$ of defining polynomial
Character	$\chi$	$=$	49.36
Dual form			49.2.e.b.15.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0332580 + 0.145713i) q^{2} +(-1.81507 - 2.27603i) q^{3} +(1.78181 - 0.858075i) q^{4} +(1.36967 + 1.71752i) q^{5} +(0.271281 - 0.340175i) q^{6} +(-2.64558 - 0.0302261i) q^{7} +(0.370666 + 0.464800i) q^{8} +(-1.21825 + 5.33750i) q^{9} +(-0.204712 + 0.256700i) q^{10} +(0.763709 + 3.34603i) q^{11} +(-5.18711 - 2.49798i) q^{12} +(-0.103718 - 0.454418i) q^{13} +(-0.0835824 - 0.386500i) q^{14} +(1.42306 - 6.23482i) q^{15} +(2.41070 - 3.02293i) q^{16} +(1.37657 + 0.662922i) q^{17} -0.818260 q^{18} -4.33771 q^{19} +(3.91426 + 1.88501i) q^{20} +(4.73311 + 6.07627i) q^{21} +(-0.462160 + 0.222565i) q^{22} +(0.197424 - 0.0950744i) q^{23} +(0.385113 - 1.68729i) q^{24} +(0.0387481 - 0.169766i) q^{25} +(0.0627651 - 0.0302261i) q^{26} +(6.49095 - 3.12588i) q^{27} +(-4.73986 + 2.21625i) q^{28} +(-7.82477 - 3.76821i) q^{29} +0.955822 q^{30} +4.09046 q^{31} +(1.59191 + 0.766624i) q^{32} +(6.22946 - 7.81149i) q^{33} +(-0.0508143 + 0.222632i) q^{34} +(-3.57167 - 4.58522i) q^{35} +(2.40929 + 10.5558i) q^{36} +(-5.82710 - 2.80618i) q^{37} +(-0.144263 - 0.632060i) q^{38} +(-0.846011 + 1.06086i) q^{39} +(-0.290611 + 1.27325i) q^{40} +(-1.77240 - 2.22252i) q^{41} +(-0.727976 + 0.891760i) q^{42} +(2.00772 - 2.51761i) q^{43} +(4.23193 + 5.30667i) q^{44} +(-10.8359 + 5.21827i) q^{45} +(0.0204195 + 0.0256052i) q^{46} +(2.50791 + 10.9879i) q^{47} -11.2559 q^{48} +(6.99817 + 0.159931i) q^{49} +0.0260258 q^{50} +(-0.989747 - 4.33636i) q^{51} +(-0.574730 - 0.720689i) q^{52} +(-4.13420 + 1.99092i) q^{53} +(0.671357 + 0.841855i) q^{54} +(-4.70082 + 5.89465i) q^{55} +(-0.966577 - 1.24087i) q^{56} +(7.87324 + 9.87273i) q^{57} +(0.288840 - 1.26549i) q^{58} +(4.49188 - 5.63264i) q^{59} +(-2.81433 - 12.3304i) q^{60} +(4.32681 + 2.08368i) q^{61} +(0.136041 + 0.596034i) q^{62} +(3.38431 - 14.0840i) q^{63} +(1.66198 - 7.28160i) q^{64} +(0.638410 - 0.800541i) q^{65} +(1.34541 + 0.647918i) q^{66} +6.29811 q^{67} +3.02163 q^{68} +(-0.574730 - 0.276775i) q^{69} +(0.549340 - 0.672933i) q^{70} +(-5.98346 + 2.88148i) q^{71} +(-2.93244 + 1.41219i) q^{72} +(-0.817597 + 3.58213i) q^{73} +(0.215099 - 0.942411i) q^{74} +(-0.456723 + 0.219946i) q^{75} +(-7.72897 + 3.72208i) q^{76} +(-1.91931 - 8.87526i) q^{77} +(-0.182718 - 0.0879925i) q^{78} +3.46554 q^{79} +8.49380 q^{80} +(-4.09832 - 1.97364i) q^{81} +(0.264903 - 0.332178i) q^{82} +(0.948934 - 4.15755i) q^{83} +(13.6474 + 6.76539i) q^{84} +(0.746875 + 3.27227i) q^{85} +(0.433621 + 0.208821i) q^{86} +(5.62596 + 24.6489i) q^{87} +(-1.27215 + 1.59523i) q^{88} +(0.937643 - 4.10808i) q^{89} +(-1.12075 - 1.40537i) q^{90} +(0.260658 + 1.20533i) q^{91} +(0.270191 - 0.338809i) q^{92} +(-7.42448 - 9.31000i) q^{93} +(-1.51767 + 0.730871i) q^{94} +(-5.94124 - 7.45008i) q^{95} +(-1.14457 - 5.01470i) q^{96} +7.50450 q^{97} +(0.209441 + 1.02504i) q^{98} -18.7898 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + 2 q^{4} - 7 q^{5} - 7 q^{6} - 7 q^{7} + 6 q^{8} - 8 q^{9} + 14 q^{10} - 8 q^{11} - 14 q^{12} + 7 q^{13} - 28 q^{14} - 7 q^{15} + 16 q^{16} + 20 q^{18} - 14 q^{19} + 7 q^{20} + 21 q^{21}+ \cdots - 18 q^{99}+O(q^{100}) $ 12 * q - 2 * q^2 + 2 * q^4 - 7 * q^5 - 7 * q^6 - 7 * q^7 + 6 * q^8 - 8 * q^9 + 14 * q^10 - 8 * q^11 - 14 * q^12 + 7 * q^13 - 28 * q^14 - 7 * q^15 + 16 * q^16 + 20 * q^18 - 14 * q^19 + 7 * q^20 + 21 * q^21 + 13 * q^22 - 2 * q^23 + 3 * q^25 - 7 * q^26 + 21 * q^27 + 14 * q^28 - 11 * q^29 + 42 * q^30 - 14 * q^31 - 24 * q^32 + 35 * q^33 - 42 * q^34 + 21 * q^35 - 13 * q^36 - 30 * q^37 + 21 * q^38 + 21 * q^41 - 35 * q^42 + 17 * q^43 - 6 * q^44 - 49 * q^45 - 16 * q^46 - 21 * q^47 + 7 * q^49 - 46 * q^50 + 7 * q^51 - 7 * q^52 + 6 * q^53 + 42 * q^54 - 28 * q^55 - 14 * q^56 + 7 * q^57 - 32 * q^58 + 14 * q^59 - 28 * q^60 - 7 * q^61 + 56 * q^62 + 14 * q^63 + 14 * q^64 + 14 * q^65 - 28 * q^66 + 48 * q^67 + 56 * q^68 - 7 * q^69 + 21 * q^70 - 39 * q^71 - 4 * q^72 + 42 * q^73 + 61 * q^74 + 7 * q^75 - 28 * q^76 + 21 * q^77 - 16 * q^79 + 42 * q^80 - 25 * q^81 + 28 * q^82 - 7 * q^83 + 42 * q^84 + 28 * q^85 + 17 * q^86 + 7 * q^87 - 11 * q^88 - 14 * q^89 - 14 * q^90 - 21 * q^91 + 16 * q^92 - 70 * q^93 - 49 * q^94 - 7 * q^95 - 70 * q^96 - 28 * q^97 - 28 * q^98 - 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{7}\right)$

Coefficient data

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

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

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

$2$	0.0332580	+	0.145713i	0.0235170	+	0.103035i	0.985324	−	0.170693i	$-0.0546006\pi$
$2$	0.0332580	+	0.145713i	0.0235170	+	0.103035i	−0.961807	+	0.273727i	$0.911743\pi$
$3$	−1.81507	−	2.27603i	−1.04793	−	1.31406i	−0.947722	−	0.319097i	$-0.896620\pi$
$3$	−1.81507	−	2.27603i	−1.04793	−	1.31406i	−0.100209	−	0.994966i	$-0.531951\pi$
$4$	1.78181	−	0.858075i	0.890906	−	0.429038i
$5$	1.36967	+	1.71752i	0.612537	+	0.768097i	0.987273	−	0.159035i	$-0.0508382\pi$
$5$	1.36967	+	1.71752i	0.612537	+	0.768097i	−0.374736	+	0.927131i	$0.622267\pi$
$6$	0.271281	−	0.340175i	0.110750	−	0.138876i
$7$	−2.64558	−	0.0302261i	−0.999935	−	0.0114244i
$7$	−2.64558	−	0.0302261i	−0.999935	−	0.0114244i
$8$	0.370666	+	0.464800i	0.131050	+	0.164332i
$9$	−1.21825	+	5.33750i	−0.406084	+	1.77917i
$10$	−0.204712	+	0.256700i	−0.0647355	+	0.0811758i
$11$	0.763709	+	3.34603i	0.230267	+	1.00887i	0.949419	+	0.314012i	$0.101673\pi$
$11$	0.763709	+	3.34603i	0.230267	+	1.00887i	−0.719152	+	0.694853i	$0.755469\pi$
$12$	−5.18711	−	2.49798i	−1.49739	−	0.721105i
$13$	−0.103718	−	0.454418i	−0.0287662	−	0.126033i	0.958506	−	0.285072i	$-0.0920175\pi$
$13$	−0.103718	−	0.454418i	−0.0287662	−	0.126033i	−0.987272	+	0.159039i	$0.949160\pi$
$14$	−0.0835824	−	0.386500i	−0.0223383	−	0.103297i
$15$	1.42306	−	6.23482i	0.367432	−	1.60982i
$16$	2.41070	−	3.02293i	0.602676	−	0.755732i
$17$	1.37657	+	0.662922i	0.333868	+	0.160782i	0.593305	−	0.804978i	$-0.297823\pi$
$17$	1.37657	+	0.662922i	0.333868	+	0.160782i	−0.259437	+	0.965760i	$0.583537\pi$
$18$	−0.818260			−0.192866
$19$	−4.33771			−0.995138			−0.497569	−	0.867424i	$-0.665774\pi$
$19$	−4.33771			−0.995138			−0.497569	+	0.867424i	$0.665774\pi$
$20$	3.91426	+	1.88501i	0.875255	+	0.421500i
$21$	4.73311	+	6.07627i	1.03285	+	1.32595i
$22$	−0.462160	+	0.222565i	−0.0985328	+	0.0474509i
$23$	0.197424	−	0.0950744i	0.0411658	−	0.0198244i	−0.413188	−	0.910646i	$-0.635585\pi$
$23$	0.197424	−	0.0950744i	0.0411658	−	0.0198244i	0.454353	+	0.890822i	$0.349870\pi$
$24$	0.385113	−	1.68729i	0.0786109	−	0.344417i
$25$	0.0387481	−	0.169766i	0.00774961	−	0.0339533i
$26$	0.0627651	−	0.0302261i	0.0123092	−	0.00592782i
$27$	6.49095	−	3.12588i	1.24918	−	0.601575i
$28$	−4.73986	+	2.21625i	−0.895749	+	0.418832i
$29$	−7.82477	−	3.76821i	−1.45302	−	0.699739i	−0.469906	−	0.882717i	$-0.655712\pi$
$29$	−7.82477	−	3.76821i	−1.45302	−	0.699739i	−0.983117	+	0.182978i	$0.941426\pi$
$30$	0.955822			0.174508
$31$	4.09046			0.734669			0.367335	−	0.930089i	$-0.380270\pi$
$31$	4.09046			0.734669			0.367335	+	0.930089i	$0.380270\pi$
$32$	1.59191	+	0.766624i	0.281413	+	0.135521i
$33$	6.22946	−	7.81149i	1.08441	−	1.35981i
$34$	−0.0508143	+	0.222632i	−0.00871458	+	0.0381810i
$35$	−3.57167	−	4.58522i	−0.603722	−	0.775044i
$36$	2.40929	+	10.5558i	0.401548	+	1.75930i
$37$	−5.82710	−	2.80618i	−0.957969	−	0.461333i	−0.111496	−	0.993765i	$-0.535564\pi$
$37$	−5.82710	−	2.80618i	−0.957969	−	0.461333i	−0.846473	+	0.532431i	$0.821278\pi$
$38$	−0.144263	−	0.632060i	−0.0234026	−	0.102534i
$39$	−0.846011	+	1.06086i	−0.135470	+	0.169874i
$40$	−0.290611	+	1.27325i	−0.0459496	+	0.201318i
$41$	−1.77240	−	2.22252i	−0.276802	−	0.347099i	0.623925	−	0.781484i	$-0.285537\pi$
$41$	−1.77240	−	2.22252i	−0.276802	−	0.347099i	−0.900727	+	0.434385i	$0.856966\pi$
$42$	−0.727976	+	0.891760i	−0.112329	+	0.137602i
$43$	2.00772	−	2.51761i	0.306175	−	0.383931i	−0.604811	−	0.796369i	$-0.706751\pi$
$43$	2.00772	−	2.51761i	0.306175	−	0.383931i	0.910986	+	0.412438i	$0.135323\pi$
$44$	4.23193	+	5.30667i	0.637987	+	0.800011i
$45$	−10.8359	+	5.21827i	−1.61531	+	0.777894i
$46$	0.0204195	+	0.0256052i	0.00301069	+	0.00377529i
$47$	2.50791	+	10.9879i	0.365817	+	1.60275i	0.738141	+	0.674646i	$0.235704\pi$
$47$	2.50791	+	10.9879i	0.365817	+	1.60275i	−0.372324	+	0.928103i	$0.621439\pi$
$48$	−11.2559			−1.62464
$49$	6.99817	+	0.159931i	0.999739	+	0.0228473i
$50$	0.0260258			0.00368061
$51$	−0.989747	−	4.33636i	−0.138592	−	0.607212i
$52$	−0.574730	−	0.720689i	−0.0797007	−	0.0999415i
$53$	−4.13420	+	1.99092i	−0.567875	+	0.273474i	−0.695712	−	0.718321i	$-0.744911\pi$
$53$	−4.13420	+	1.99092i	−0.567875	+	0.273474i	0.127837	+	0.991795i	$0.459197\pi$
$54$	0.671357	+	0.841855i	0.0913601	+	0.114562i
$55$	−4.70082	+	5.89465i	−0.633859	+	0.794834i
$56$	−0.966577	−	1.24087i	−0.129164	−	0.165818i
$57$	7.87324	+	9.87273i	1.04284	+	1.30767i
$58$	0.288840	−	1.26549i	0.0379266	−	0.166167i
$59$	4.49188	−	5.63264i	0.584793	−	0.733307i	−0.398129	−	0.917329i	$-0.630340\pi$
$59$	4.49188	−	5.63264i	0.584793	−	0.733307i	0.982922	+	0.184022i	$0.0589119\pi$
$60$	−2.81433	−	12.3304i	−0.363328	−	1.59184i
$61$	4.32681	+	2.08368i	0.553992	+	0.266788i	0.689865	−	0.723938i	$-0.257670\pi$
$61$	4.32681	+	2.08368i	0.553992	+	0.266788i	−0.135874	+	0.990726i	$0.543384\pi$
$62$	0.136041	+	0.596034i	0.0172772	+	0.0756963i
$63$	3.38431	−	14.0840i	0.426383	−	1.77441i
$64$	1.66198	−	7.28160i	0.207747	−	0.910200i
$65$	0.638410	−	0.800541i	0.0791850	−	0.0992949i
$66$	1.34541	+	0.647918i	0.165609	+	0.0797532i
$67$	6.29811			0.769436			0.384718	−	0.923034i	$-0.374299\pi$
$67$	6.29811			0.769436			0.384718	+	0.923034i	$0.374299\pi$
$68$	3.02163			0.366426
$69$	−0.574730	−	0.276775i	−0.0691894	−	0.0333198i
$70$	0.549340	−	0.672933i	0.0656587	−	0.0804309i
$71$	−5.98346	+	2.88148i	−0.710106	+	0.341969i	−0.753825	−	0.657075i	$-0.771793\pi$
$71$	−5.98346	+	2.88148i	−0.710106	+	0.341969i	0.0437196	+	0.999044i	$0.486079\pi$
$72$	−2.93244	+	1.41219i	−0.345591	+	0.166428i
$73$	−0.817597	+	3.58213i	−0.0956925	+	0.419256i	−0.999970	−	0.00768802i	$-0.997553\pi$
$73$	−0.817597	+	3.58213i	−0.0956925	+	0.419256i	0.904278	+	0.426944i	$0.140410\pi$
$74$	0.215099	−	0.942411i	0.0250048	−	0.109553i
$75$	−0.456723	+	0.219946i	−0.0527378	+	0.0253972i
$76$	−7.72897	+	3.72208i	−0.886574	+	0.426952i
$77$	−1.91931	−	8.87526i	−0.218726	−	1.01143i
$78$	−0.182718	−	0.0879925i	−0.0206888	−	0.00996318i
$79$	3.46554			0.389903			0.194952	−	0.980813i	$-0.437545\pi$
$79$	3.46554			0.389903			0.194952	+	0.980813i	$0.437545\pi$
$80$	8.49380			0.949636
$81$	−4.09832	−	1.97364i	−0.455368	−	0.219294i
$82$	0.264903	−	0.332178i	0.0292537	−	0.0366829i
$83$	0.948934	−	4.15755i	0.104159	−	0.456351i	−0.895771	−	0.444516i	$-0.853376\pi$
$83$	0.948934	−	4.15755i	0.104159	−	0.456351i	0.999930	−	0.0118347i	$-0.00376719\pi$
$84$	13.6474	+	6.76539i	1.48905	+	0.738165i
$85$	0.746875	+	3.27227i	0.0810100	+	0.354928i
$86$	0.433621	+	0.208821i	0.0467585	+	0.0225177i
$87$	5.62596	+	24.6489i	0.603166	+	2.64264i
$88$	−1.27215	+	1.59523i	−0.135612	+	0.170052i
$89$	0.937643	−	4.10808i	0.0993900	−	0.435456i	−0.900610	−	0.434629i	$-0.856880\pi$
$89$	0.937643	−	4.10808i	0.0993900	−	0.435456i	1.00000		0.000827205i	$-0.000263308\pi$
$90$	−1.12075	−	1.40537i	−0.118137	−	0.148140i
$91$	0.260658	+	1.20533i	0.0273244	+	0.126353i
$92$	0.270191	−	0.338809i	0.0281694	−	0.0353233i
$93$	−7.42448	−	9.31000i	−0.769883	−	0.965402i
$94$	−1.51767	+	0.730871i	−0.156536	+	0.0753836i
$95$	−5.94124	−	7.45008i	−0.609558	−	0.764362i
$96$	−1.14457	−	5.01470i	−0.116818	−	0.511811i
$97$	7.50450			0.761966			0.380983	−	0.924582i	$-0.375586\pi$
$97$	7.50450			0.761966			0.380983	+	0.924582i	$0.375586\pi$
$98$	0.209441	+	1.02504i	0.0211568	+	0.103545i
$99$	−18.7898			−1.88845
$100$	−0.0766305	−	0.335740i	−0.00766305	−	0.0335740i
$101$	−7.74142	−	9.70744i	−0.770300	−	0.965926i	0.229673	−	0.973268i	$-0.426234\pi$
$101$	−7.74142	−	9.70744i	−0.770300	−	0.965926i	−0.999973	+	0.00734198i	$0.997663\pi$
$102$	0.598947	−	0.288438i	0.0593046	−	0.0285596i
$103$	−1.37791	−	1.72784i	−0.135769	−	0.170249i	0.709299	−	0.704908i	$-0.249012\pi$
$103$	−1.37791	−	1.72784i	−0.135769	−	0.170249i	−0.845068	+	0.534659i	$0.820440\pi$
$104$	0.172769	−	0.216645i	0.0169414	−	0.0212438i
$105$	−3.95327	+	16.4517i	−0.385799	+	1.60552i
$106$	−0.427598	−	0.536191i	−0.0415320	−	0.0520795i
$107$	3.14987	−	13.8005i	0.304509	−	1.33414i	−0.558731	−	0.829349i	$-0.688712\pi$
$107$	3.14987	−	13.8005i	0.304509	−	1.33414i	0.863240	−	0.504793i	$-0.168431\pi$
$108$	8.88341	−	11.1394i	0.854807	−	1.07189i
$109$	2.84774	+	12.4768i	0.272764	+	1.19506i	0.906735	+	0.421701i	$0.138567\pi$
$109$	2.84774	+	12.4768i	0.272764	+	1.19506i	−0.633971	+	0.773357i	$0.718576\pi$
$110$	−1.01527	−	0.488927i	−0.0968019	−	0.0466173i
$111$	4.18965	+	18.3560i	0.397664	+	1.74228i
$112$	−6.46908	+	7.92453i	−0.611270	+	0.748797i
$113$	−2.27119	+	9.95071i	−0.213655	+	0.936084i	0.748404	+	0.663243i	$0.230820\pi$
$113$	−2.27119	+	9.95071i	−0.213655	+	0.936084i	−0.962059	+	0.272841i	$0.912037\pi$
$114$	−1.17674	+	1.47558i	−0.110211	+	0.138201i
$115$	0.433698	+	0.208858i	0.0404426	+	0.0194761i
$116$	−17.1757			−1.59472
$117$	2.55181			0.235915
$118$	0.970139	+	0.467194i	0.0893085	+	0.0430087i
$119$	−3.62179	−	1.79542i	−0.332009	−	0.164586i
$120$	3.42543	−	1.64960i	0.312697	−	0.150587i
$121$	−0.701992	+	0.338061i	−0.0638174	+	0.0307329i
$122$	−0.159718	+	0.699772i	−0.0144602	+	0.0633543i
$123$	−1.84148	+	8.06805i	−0.166041	+	0.727472i
$124$	7.28844	−	3.50993i	0.654521	−	0.315201i
$125$	10.2408	−	4.93172i	0.915967	−	0.441107i
$126$	2.16477	+	0.0247328i	0.192853	+	0.00220337i
$127$	2.61806	+	1.26079i	0.232315	+	0.111877i	0.546420	−	0.837511i	$-0.315990\pi$
$127$	2.61806	+	1.26079i	0.232315	+	0.111877i	−0.314105	+	0.949388i	$0.601704\pi$
$128$	4.65007			0.411012
$129$	−9.37430			−0.825361
$130$	0.137881	+	0.0664002i	0.0120930	+	0.00582368i
$131$	−13.0300	+	16.3391i	−1.13843	+	1.42755i	−0.250177	+	0.968200i	$0.580489\pi$
$131$	−13.0300	+	16.3391i	−1.13843	+	1.42755i	−0.888256	+	0.459350i	$0.848083\pi$
$132$	4.39687	−	19.2640i	0.382699	−	1.67671i
$133$	11.4757	+	0.131112i	0.995073	+	0.0113688i
$134$	0.209463	+	0.917715i	0.0180948	+	0.0792785i
$135$	14.2592	+	6.86688i	1.22724	+	0.591007i
$136$	0.202122	+	0.885554i	0.0173318	+	0.0759356i
$137$	8.00691	−	10.0404i	0.684077	−	0.857805i	−0.311646	−	0.950198i	$-0.600880\pi$
$137$	8.00691	−	10.0404i	0.684077	−	0.857805i	0.995723	+	0.0923932i	$0.0294517\pi$
$138$	0.0212154	−	0.0929506i	0.00180597	−	0.00791248i
$139$	−12.4426	−	15.6026i	−1.05537	−	1.32339i	−0.944120	−	0.329602i	$-0.893085\pi$
$139$	−12.4426	−	15.6026i	−1.05537	−	1.32339i	−0.111252	−	0.993792i	$-0.535486\pi$
$140$	−10.2985	−	5.10525i	−0.870382	−	0.431472i
$141$	20.4567	−	25.6519i	1.72276	−	2.16028i
$142$	−0.618867	−	0.776034i	−0.0519341	−	0.0651234i
$143$	1.44128	−	0.694086i	0.120526	−	0.0580423i
$144$	13.1980	+	16.5498i	1.09984	+	1.37915i
$145$	−4.24541	−	18.6004i	−0.352563	−	1.54468i
$146$	−0.549154			−0.0454483
$147$	−12.3382	−	16.2183i	−1.01763	−	1.33766i
$148$	−12.7907			−1.05139
$149$	2.84083	+	12.4465i	0.232730	+	1.01966i	0.947364	+	0.320158i	$0.103736\pi$
$149$	2.84083	+	12.4465i	0.232730	+	1.01966i	−0.714634	+	0.699498i	$0.753407\pi$
$150$	−0.0472387	−	0.0592354i	−0.00385702	−	0.00483655i
$151$	6.00423	−	2.89148i	0.488617	−	0.235306i	−0.173319	−	0.984866i	$-0.555449\pi$
$151$	6.00423	−	2.89148i	0.488617	−	0.235306i	0.661936	+	0.749560i	$0.269735\pi$
$152$	−1.60784	−	2.01617i	−0.130413	−	0.163533i
$153$	−5.21536	+	6.53986i	−0.421637	+	0.528716i
$154$	1.22941	−	0.574843i	0.0990685	−	0.0463221i
$155$	5.60260	+	7.02544i	0.450012	+	0.564297i
$156$	−0.597131	+	2.61620i	−0.0478087	+	0.209464i
$157$	−5.01554	+	6.28929i	−0.400284	+	0.501940i	−0.940597	−	0.339524i	$-0.889734\pi$
$157$	−5.01554	+	6.28929i	−0.400284	+	0.501940i	0.540314	+	0.841464i	$0.318306\pi$
$158$	0.115257	+	0.504973i	0.00916934	+	0.0401735i
$159$	12.0352	+	5.79587i	0.954457	+	0.459642i
$160$	0.863709	+	3.78416i	0.0682822	+	0.299164i
$161$	−0.525175	+	0.245559i	−0.0413896	+	0.0193528i
$162$	0.151284	−	0.662817i	0.0118860	−	0.0520758i
$163$	−15.3206	+	19.2114i	−1.20000	+	1.50475i	−0.387421	+	0.921903i	$0.626634\pi$
$163$	−15.3206	+	19.2114i	−1.20000	+	1.50475i	−0.812579	+	0.582850i	$0.801937\pi$
$164$	−5.06517	−	2.43926i	−0.395523	−	0.190474i
$165$	21.9487			1.70870
$166$	0.637369			0.0494694
$167$	7.50517	+	3.61430i	0.580768	+	0.279683i	0.701114	−	0.713049i	$-0.252686\pi$
$167$	7.50517	+	3.61430i	0.580768	+	0.279683i	−0.120346	+	0.992732i	$0.538401\pi$
$168$	−1.06985	+	4.45222i	−0.0825405	+	0.343496i
$169$	11.5169	−	5.54623i	0.885912	−	0.426633i
$170$	−0.451973	+	0.217659i	−0.0346647	+	0.0166937i
$171$	5.28441	−	23.1525i	0.404109	−	1.77052i
$172$	1.41709	−	6.20868i	0.108052	−	0.473407i
$173$	−9.70040	+	4.67146i	−0.737507	+	0.355165i	−0.764632	−	0.644467i	$-0.777079\pi$
$173$	−9.70040	+	4.67146i	−0.737507	+	0.355165i	0.0271245	+	0.999632i	$0.491365\pi$
$174$	−3.40456	+	1.63955i	−0.258099	+	0.124294i
$175$	−0.107642	+	0.447959i	−0.00813700	+	0.0338625i
$176$	11.9559	+	5.75765i	0.901208	+	0.433999i
$177$	−20.9731			−1.57643
$178$	0.629785			0.0472044
$179$	−7.46017	−	3.59263i	−0.557599	−	0.268526i	0.133788	−	0.991010i	$-0.457286\pi$
$179$	−7.46017	−	3.59263i	−0.557599	−	0.268526i	−0.691387	+	0.722484i	$0.743000\pi$
$180$	−14.8298	+	18.5960i	−1.10535	+	1.38606i
$181$	−1.41369	+	6.19379i	−0.105079	+	0.460381i	0.894824	+	0.446420i	$0.147301\pi$
$181$	−1.41369	+	6.19379i	−0.105079	+	0.460381i	−0.999903	+	0.0139610i	$0.995556\pi$
$182$	−0.166963	+	0.0780683i	−0.0123762	+	0.00578681i
$183$	−3.11095	−	13.6300i	−0.229968	−	1.00756i
$184$	0.117369	+	0.0565219i	0.00865256	+	0.00416685i
$185$	−3.16156	−	13.8517i	−0.232442	−	1.01840i
$186$	1.10966	−	1.39147i	0.0813645	−	0.102028i
$187$	−1.16686	+	5.11233i	−0.0853289	+	0.373851i
$188$	13.8971	+	17.4264i	1.01355	+	1.27095i
$189$	−17.2668	+	8.07356i	−1.25598	+	0.587265i
$190$	0.887979	−	1.11349i	0.0644208	−	0.0807811i
$191$	13.8565	+	17.3755i	1.00262	+	1.25725i	0.966169	+	0.257910i	$0.0830337\pi$
$191$	13.8565	+	17.3755i	1.00262	+	1.25725i	0.0364505	+	0.999335i	$0.488395\pi$
$192$	−19.5897	+	9.43391i	−1.41377	+	0.680834i
$193$	−4.13632	−	5.18678i	−0.297739	−	0.373353i	0.610349	−	0.792133i	$-0.291029\pi$
$193$	−4.13632	−	5.18678i	−0.297739	−	0.373353i	−0.908088	+	0.418780i	$0.862458\pi$
$194$	0.249585	+	1.09350i	0.0179191	+	0.0785089i
$195$	−2.98081			−0.213460
$196$	12.6067	−	5.71999i	0.900476	−	0.408571i
$197$	−10.0402			−0.715332			−0.357666	−	0.933850i	$-0.616427\pi$
$197$	−10.0402			−0.715332			−0.357666	+	0.933850i	$0.616427\pi$
$198$	−0.624912	−	2.73792i	−0.0444106	−	0.194576i
$199$	−10.8453	−	13.5996i	−0.768805	−	0.964050i	0.231156	−	0.972917i	$-0.425749\pi$
$199$	−10.8453	−	13.5996i	−0.768805	−	0.964050i	−0.999961	+	0.00886619i	$0.997178\pi$
$200$	0.0932700	−	0.0449165i	0.00659519	−	0.00317608i
$201$	−11.4315	−	14.3346i	−0.806316	−	1.01109i
$202$	1.15703	−	1.45088i	0.0814086	−	0.102083i
$203$	20.5871	+	10.2056i	1.44493	+	0.716293i
$204$	−5.48447	−	6.87731i	−0.383990	−	0.481508i
$205$	1.38960	−	6.08825i	0.0970541	−	0.425222i
$206$	0.205942	−	0.258243i	0.0143487	−	0.0179926i
$207$	0.266948	+	1.16958i	0.0185542	+	0.0812912i
$208$	−1.62370	−	0.781935i	−0.112584	−	0.0542174i
$209$	−3.31274	−	14.5141i	−0.229147	−	1.00396i
$210$	−2.52870	−	0.0288907i	−0.174497	−	0.00199365i
$211$	−1.44188	+	6.31729i	−0.0992632	+	0.434900i	0.900737	+	0.434366i	$0.143027\pi$
$211$	−1.44188	+	6.31729i	−0.0992632	+	0.434900i	−1.00000		0.000534816i	$0.999830\pi$
$212$	−5.65799	+	7.09490i	−0.388593	+	0.487280i
$213$	17.4187	+	8.38841i	1.19351	+	0.574764i
$214$	2.11567			0.144624
$215$	7.07396			0.482440
$216$	3.85888	+	1.85834i	0.262564	+	0.126444i
$217$	−10.8216	−	0.123639i	−0.734621	−	0.00839314i
$218$	−1.72332	+	0.829906i	−0.116718	+	0.0562083i
$219$	9.63701	−	4.64094i	0.651209	−	0.313606i
$220$	−3.31793	+	14.5368i	−0.223695	+	0.980072i
$221$	0.158468	−	0.694296i	0.0106597	−	0.0467034i
$222$	−2.53537	+	1.22097i	−0.170163	+	0.0819462i
$223$	13.7827	−	6.63738i	0.922956	−	0.444472i	0.0888303	−	0.996047i	$-0.471687\pi$
$223$	13.7827	−	6.63738i	0.922956	−	0.444472i	0.834125	+	0.551575i	$0.185973\pi$
$224$	−4.18835	−	2.07628i	−0.279846	−	0.138727i
$225$	0.858924	+	0.413636i	0.0572616	+	0.0275757i
$226$	−1.52548			−0.101474
$227$	18.6023			1.23468			0.617338	−	0.786698i	$-0.288211\pi$
$227$	18.6023			1.23468			0.617338	+	0.786698i	$0.288211\pi$
$228$	22.5002	+	10.8355i	1.49011	+	0.717599i
$229$	11.6479	−	14.6060i	0.769715	−	0.965192i	−0.230254	−	0.973131i	$-0.573956\pi$
$229$	11.6479	−	14.6060i	0.769715	−	0.965192i	0.999968	+	0.00793873i	$0.00252700\pi$
$230$	−0.0160094	+	0.0701416i	−0.00105563	+	0.00462500i
$231$	−16.7166	+	20.4776i	−1.09987	+	1.34733i
$232$	−1.14891	−	5.03370i	−0.0754296	−	0.330479i
$233$	7.01198	+	3.37679i	0.459370	+	0.221221i	0.649233	−	0.760590i	$-0.275090\pi$
$233$	7.01198	+	3.37679i	0.459370	+	0.221221i	−0.189863	+	0.981811i	$0.560804\pi$
$234$	0.0848682	+	0.371832i	0.00554800	+	0.0243074i
$235$	−15.4369	+	19.3572i	−1.00699	+	1.26273i
$236$	3.17045	−	13.8907i	0.206379	−	0.904205i
$237$	−6.29019	−	7.88765i	−0.408592	−	0.512358i
$238$	0.141162	−	0.587454i	0.00915020	−	0.0380790i
$239$	−3.84245	+	4.81828i	−0.248547	+	0.311668i	−0.890417	−	0.455145i	$-0.849587\pi$
$239$	−3.84245	+	4.81828i	−0.248547	+	0.311668i	0.641870	+	0.766813i	$0.278159\pi$
$240$	−15.4168	−	19.3321i	−0.995153	−	1.24788i
$241$	3.10331	−	1.49448i	0.199902	−	0.0962676i	−0.331255	−	0.943541i	$-0.607472\pi$
$241$	3.10331	−	1.49448i	0.199902	−	0.0962676i	0.531156	+	0.847274i	$0.321758\pi$
$242$	−0.0726068	−	0.0910460i	−0.00466734	−	0.00585266i
$243$	−1.86274	−	8.16118i	−0.119495	−	0.523540i
$244$	9.49752			0.608017
$245$	9.31053	+	12.2385i	0.594828	+	0.781891i
$246$	−1.23686			−0.0788595
$247$	0.449897	+	1.97113i	0.0286263	+	0.125420i
$248$	1.51620	+	1.90125i	0.0962785	+	0.120729i
$249$	−11.1851	+	5.38645i	−0.708826	+	0.341352i
$250$	1.05921	+	1.32820i	0.0669900	+	0.0840028i
$251$	5.83985	−	7.32294i	0.368608	−	0.462220i	−0.562589	−	0.826737i	$-0.690194\pi$
$251$	5.83985	−	7.32294i	0.368608	−	0.462220i	0.931197	+	0.364517i	$0.118766\pi$
$252$	−6.05490	−	27.9990i	−0.381423	−	1.76377i
$253$	0.468896	+	0.587977i	0.0294792	+	0.0369658i
$254$	−0.0966419	+	0.423416i	−0.00606385	+	0.0265675i
$255$	6.09215	−	7.63931i	0.381505	−	0.478392i
$256$	−3.16930	−	13.8856i	−0.198081	−	0.867851i
$257$	5.57366	+	2.68413i	0.347675	+	0.167432i	0.599569	−	0.800323i	$-0.295339\pi$
$257$	5.57366	+	2.68413i	0.347675	+	0.167432i	−0.251893	+	0.967755i	$0.581053\pi$
$258$	−0.311770	−	1.36596i	−0.0194100	−	0.0850407i
$259$	15.3312	+	7.60011i	0.952636	+	0.472248i
$260$	0.450602	−	1.97422i	0.0279452	−	0.122436i
$261$	29.6454	−	37.1741i	1.83500	−	2.30102i
$262$	−2.81416	−	1.35523i	−0.173859	−	0.0837263i
$263$	−22.1760			−1.36743			−0.683715	−	0.729749i	$-0.739637\pi$
$263$	−22.1760			−1.36743			−0.683715	+	0.729749i	$0.739637\pi$
$264$	5.93983			0.365572
$265$	−9.08194	−	4.37363i	−0.557899	−	0.268670i
$266$	0.362556	+	1.67652i	0.0222297	+	0.102794i
$267$	−11.0520	+	5.32236i	−0.676371	+	0.325723i
$268$	11.2220	−	5.40425i	0.685495	−	0.330117i
$269$	−2.65587	+	11.6361i	−0.161931	+	0.709466i	0.827136	+	0.562001i	$0.189968\pi$
$269$	−2.65587	+	11.6361i	−0.161931	+	0.709466i	−0.989067	+	0.147465i	$0.952889\pi$
$270$	−0.526360	+	2.30613i	−0.0320332	+	0.140347i
$271$	−13.3776	+	6.44231i	−0.812631	+	0.391343i	−0.793573	−	0.608476i	$-0.791781\pi$
$271$	−13.3776	+	6.44231i	−0.812631	+	0.391343i	−0.0190589	+	0.999818i	$0.506067\pi$
$272$	5.32247	−	2.56317i	0.322722	−	0.155415i
$273$	2.27025	−	2.78103i	0.137402	−	0.168315i
$274$	1.72930	+	0.832788i	0.104471	+	0.0503106i
$275$	0.597635			0.0360387
$276$	−1.26155			−0.0759367
$277$	2.25063	+	1.08385i	0.135227	+	0.0651221i	0.500274	−	0.865867i	$-0.333233\pi$
$277$	2.25063	+	1.08385i	0.135227	+	0.0651221i	−0.365047	+	0.930989i	$0.618947\pi$
$278$	1.85968	−	2.33197i	0.111536	−	0.139862i
$279$	−4.98321	+	21.8329i	−0.298337	+	1.30710i
$280$	0.807319	−	3.35970i	0.0482466	−	0.200780i
$281$	2.47839	+	10.8585i	0.147848	+	0.647766i	0.993481	+	0.114000i	$0.0363665\pi$
$281$	2.47839	+	10.8585i	0.147848	+	0.647766i	−0.845632	+	0.533766i	$0.820776\pi$
$282$	4.41816	+	2.12767i	0.263097	+	0.126701i
$283$	1.01300	+	4.43823i	0.0602164	+	0.263825i	0.996071	−	0.0885620i	$-0.0282271\pi$
$283$	1.01300	+	4.43823i	0.0602164	+	0.263825i	−0.935854	+	0.352387i	$0.885370\pi$
$284$	−8.18886	+	10.2685i	−0.485920	+	0.609324i
$285$	−6.17281	+	27.0448i	−0.365645	+	1.60200i
$286$	0.149071	+	0.186930i	0.00881478	+	0.0110534i
$287$	4.62184	+	5.93342i	0.272819	+	0.350239i
$288$	−6.03120	+	7.56289i	−0.355392	+	0.445648i
$289$	−9.14384	−	11.4660i	−0.537873	−	0.674471i
$290$	2.56912	−	1.23722i	0.150864	−	0.0726523i
$291$	−13.6212	−	17.0804i	−0.798488	−	1.00127i
$292$	1.61693	+	7.08423i	0.0946237	+	0.414573i
$293$	−26.1249			−1.52623			−0.763116	−	0.646262i	$-0.776331\pi$
$293$	−26.1249			−1.52623			−0.763116	+	0.646262i	$0.776331\pi$
$294$	1.95287	−	2.33722i	0.113894	−	0.136309i
$295$	15.8266			0.921457
$296$	−0.855592	−	3.74859i	−0.0497303	−	0.217883i
$297$	15.4165	+	19.3316i	0.894554	+	1.12174i
$298$	−1.71913	+	0.827892i	−0.0995868	+	0.0479585i
$299$	−0.0636799	−	0.0798520i	−0.00368270	−	0.00461796i
$300$	−0.625064	+	0.783805i	−0.0360881	+	0.0452530i
$301$	−5.38769	+	6.59984i	−0.310541	+	0.380408i
$302$	0.621015	+	0.778728i	0.0357354	+	0.0448108i
$303$	−8.04315	+	35.2393i	−0.462067	+	2.02445i
$304$	−10.4569	+	13.1126i	−0.599746	+	0.752057i
$305$	2.34756	+	10.2853i	0.134421	+	0.588937i
$306$	−1.12639	−	0.542443i	−0.0643917	−	0.0310094i
$307$	−0.488612	−	2.14075i	−0.0278866	−	0.122179i	0.959069	−	0.283173i	$-0.0913871\pi$
$307$	−0.488612	−	2.14075i	−0.0278866	−	0.122179i	−0.986955	+	0.160994i	$0.948530\pi$
$308$	−11.0355	−	14.1671i	−0.628806	−	0.807247i
$309$	−1.43161	+	6.27229i	−0.0814415	+	0.356818i
$310$	−0.837366	+	1.05002i	−0.0475592	+	0.0596373i
$311$	−14.4145	−	6.94165i	−0.817371	−	0.393625i	−0.0220074	−	0.999758i	$-0.507006\pi$
$311$	−14.4145	−	6.94165i	−0.817371	−	0.393625i	−0.795364	+	0.606133i	$0.792720\pi$
$312$	−0.806677			−0.0456691
$313$	0.916124			0.0517824			0.0258912	−	0.999665i	$-0.491758\pi$
$313$	0.916124			0.0517824			0.0258912	+	0.999665i	$0.491758\pi$
$314$	−1.08324	−	0.521660i	−0.0611306	−	0.0294390i
$315$	28.8248	−	13.4778i	1.62410	−	0.759390i
$316$	6.17493	−	2.97369i	0.347367	−	0.167283i
$317$	−9.69962	+	4.67109i	−0.544785	+	0.262355i	−0.685971	−	0.727628i	$-0.740623\pi$
$317$	−9.69962	+	4.67109i	−0.544785	+	0.262355i	0.141187	+	0.989983i	$0.454908\pi$
$318$	−0.444264	+	1.94645i	−0.0249131	+	0.109151i
$319$	6.63269	−	29.0597i	0.371359	−	1.62703i
$320$	14.7826	−	7.11894i	0.826374	−	0.397961i
$321$	−37.1275	+	17.8796i	−2.07225	+	0.997944i
$322$	−0.0532474	−	0.0683579i	−0.00296736	−	0.00380944i
$323$	−5.97117	−	2.87556i	−0.332245	−	0.160001i
$324$	−8.99596			−0.499776
$325$	−0.0811637			−0.00450215
$326$	−3.30888	−	1.59347i	−0.183262	−	0.0882543i
$327$	23.2286	−	29.1277i	1.28454	−	1.61077i
$328$	0.376059	−	1.64762i	0.0207644	−	0.0909748i
$329$	−6.30276	−	29.1451i	−0.347483	−	1.60682i
$330$	0.729970	+	3.19821i	0.0401835	+	0.176056i
$331$	−29.7332	−	14.3188i	−1.63428	−	0.787030i	−0.999902	−	0.0140113i	$-0.995540\pi$
$331$	−29.7332	−	14.3188i	−1.63428	−	0.787030i	−0.634383	−	0.773019i	$-0.718746\pi$
$332$	−1.87667	−	8.22223i	−0.102996	−	0.451254i
$333$	22.0769	−	27.6835i	1.20981	−	1.51705i
$334$	−0.277043	+	1.21381i	−0.0151591	+	0.0664165i
$335$	8.62635	+	10.8171i	0.471308	+	0.591001i
$336$	29.7782	+	0.340220i	1.62454	+	0.0185605i
$337$	−11.7365	+	14.7171i	−0.639328	+	0.801692i	−0.990919	−	0.134462i	$-0.957069\pi$
$337$	−11.7365	+	14.7171i	−0.639328	+	0.801692i	0.351591	+	0.936154i	$0.385641\pi$
$338$	1.19118	+	1.49370i	0.0647919	+	0.0812465i
$339$	26.7704	−	12.8920i	1.45397	−	0.700195i
$340$	4.13865	+	5.18970i	0.224450	+	0.281451i
$341$	3.12392	+	13.6868i	0.169170	+	0.741182i
$342$	3.54937			0.191928
$343$	−18.5094	−	0.634637i	−0.999413	−	0.0342672i
$344$	1.91438			0.103216
$345$	−0.311826	−	1.36620i	−0.0167882	−	0.0735538i
$346$	−1.00331	−	1.25811i	−0.0539382	−	0.0676364i
$347$	28.9730	−	13.9527i	1.55535	−	0.749018i	0.558591	−	0.829443i	$-0.311342\pi$
$347$	28.9730	−	13.9527i	1.55535	−	0.749018i	0.996761	+	0.0804255i	$0.0256279\pi$
$348$	31.1750	+	39.0922i	1.67116	+	2.09556i
$349$	−6.40434	+	8.03078i	−0.342816	+	0.429878i	−0.923114	−	0.384526i	$-0.874365\pi$
$349$	−6.40434	+	8.03078i	−0.342816	+	0.429878i	0.580298	+	0.814404i	$0.302936\pi$
$350$	−0.0688534		0.000786658i	−0.00368037		4.20486e-5i
$351$	−2.09368	−	2.62539i	−0.111752	−	0.140133i
$352$	−1.34939	+	5.91205i	−0.0719226	+	0.315114i
$353$	−17.0775	+	21.4145i	−0.908945	+	1.13978i	0.0807709	+	0.996733i	$0.474262\pi$
$353$	−17.0775	+	21.4145i	−0.908945	+	1.13978i	−0.989716	+	0.143048i	$0.954310\pi$
$354$	−0.697524	−	3.05605i	−0.0370730	−	0.162427i
$355$	−13.1444	−	6.33000i	−0.697631	−	0.335961i
$356$	−1.85434	−	8.12440i	−0.0982799	−	0.430592i
$357$	2.48738	+	11.5021i	0.131646	+	0.608756i
$358$	0.275382	−	1.20653i	0.0145544	−	0.0637669i
$359$	−2.94629	+	3.69453i	−0.155499	+	0.194990i	−0.853478	−	0.521128i	$-0.825511\pi$
$359$	−2.94629	+	3.69453i	−0.155499	+	0.194990i	0.697979	+	0.716118i	$0.254083\pi$
$360$	−6.44194	−	3.10227i	−0.339520	−	0.163504i
$361$	−0.184312			−0.00970061
$362$	−0.949532			−0.0499063
$363$	2.04360	+	0.984146i	0.107261	+	0.0516543i
$364$	1.49871	+	1.92401i	0.0785538	+	0.100846i
$365$	−7.27220	+	3.50211i	−0.380644	+	0.183309i
$366$	1.88260	−	0.906611i	0.0984050	−	0.0473893i
$367$	0.721934	−	3.16300i	0.0376847	−	0.165107i	−0.952584	−	0.304275i	$-0.901586\pi$
$367$	0.721934	−	3.16300i	0.0376847	−	0.165107i	0.990269	+	0.139168i	$0.0444428\pi$
$368$	0.188528	−	0.825995i	0.00982770	−	0.0430579i
$369$	14.0219	−	6.75261i	0.729952	−	0.351527i
$370$	1.91322	−	0.921359i	0.0994637	−	0.0478992i
$371$	10.9975	−	5.14218i	0.570963	−	0.266969i
$372$	−21.2177	−	10.2179i	−1.10009	−	0.529774i
$373$	35.4368			1.83485			0.917424	−	0.397911i	$-0.130265\pi$
$373$	35.4368			1.83485			0.917424	+	0.397911i	$0.130265\pi$
$374$	−0.783740			−0.0405262
$375$	−29.8125	−	14.3570i	−1.53951	−	0.741390i
$376$	−4.17758	+	5.23852i	−0.215442	+	0.270156i
$377$	−0.900772	+	3.94654i	−0.0463921	+	0.203257i
$378$	−1.75068	−	2.24749i	−0.0900453	−	0.115598i
$379$	5.47579	+	23.9910i	0.281272	+	1.23233i	0.896164	+	0.443723i	$0.146343\pi$
$379$	5.47579	+	23.9910i	0.281272	+	1.23233i	−0.614892	+	0.788611i	$0.710800\pi$
$380$	−16.9789	−	8.17661i	−0.870999	−	0.419451i
$381$	−1.88236	−	8.24718i	−0.0964365	−	0.422516i
$382$	−2.07099	+	2.59694i	−0.105961	+	0.132871i
$383$	1.13240	−	4.96135i	0.0578628	−	0.253513i	−0.937721	−	0.347389i	$-0.887068\pi$
$383$	1.13240	−	4.96135i	0.0578628	−	0.253513i	0.995584	+	0.0938755i	$0.0299256\pi$
$384$	−8.44020	−	10.5837i	−0.430712	−	0.540096i
$385$	12.6146	−	15.4527i	0.642898	−	0.787541i
$386$	0.618215	−	0.775217i	0.0314663	−	0.0394575i
$387$	10.9918	+	13.7833i	0.558746	+	0.700645i
$388$	13.3716	−	6.43942i	0.678840	−	0.326912i
$389$	9.43816	+	11.8351i	0.478534	+	0.600062i	0.961238	−	0.275721i	$-0.0889167\pi$
$389$	9.43816	+	11.8351i	0.478534	+	0.600062i	−0.482704	+	0.875784i	$0.660345\pi$
$390$	−0.0991358	−	0.434342i	−0.00501994	−	0.0219938i
$391$	0.334795			0.0169313
$392$	2.51965	+	3.31203i	0.127261	+	0.167283i
$393$	60.8384			3.06889
$394$	−0.333916	−	1.46298i	−0.0168224	−	0.0737039i
$395$	4.74665	+	5.95211i	0.238830	+	0.299483i
$396$	−33.4799	+	16.1231i	−1.68243	+	0.810216i
$397$	4.44874	+	5.57854i	0.223276	+	0.279979i	0.880835	−	0.473424i	$-0.156982\pi$
$397$	4.44874	+	5.57854i	0.223276	+	0.279979i	−0.657559	+	0.753403i	$0.728411\pi$
$398$	1.62094	−	2.03260i	0.0812506	−	0.101885i
$399$	−20.5309	−	26.3571i	−1.02783	−	1.31950i
$400$	−0.419781	−	0.526389i	−0.0209891	−	0.0263194i
$401$	6.40622	−	28.0675i	0.319912	−	1.40162i	−0.517796	−	0.855504i	$-0.673247\pi$
$401$	6.40622	−	28.0675i	0.319912	−	1.40162i	0.837707	−	0.546120i	$-0.183896\pi$
$402$	1.70855	−	2.14246i	0.0852149	−	0.106856i
$403$	−0.424254	−	1.85878i	−0.0211336	−	0.0925924i
$404$	−22.1235	−	10.6541i	−1.10068	−	0.530061i
$405$	−2.22359	−	9.74217i	−0.110491	−	0.484092i
$406$	−0.802401	+	3.33923i	−0.0398225	+	0.165723i
$407$	4.93936	−	21.6407i	0.244835	−	1.07269i
$408$	1.64868	−	2.06738i	0.0816217	−	0.102350i
$409$	26.3938	+	12.7106i	1.30509	+	0.628497i	0.951714	−	0.306986i	$-0.0993203\pi$
$409$	26.3938	+	12.7106i	1.30509	+	0.628497i	0.353373	+	0.935482i	$0.385035\pi$
$410$	0.933352			0.0460950
$411$	−37.3852			−1.84408
$412$	−3.93778	−	1.89634i	−0.194001	−	0.0934258i
$413$	−12.0539	+	14.7658i	−0.593132	+	0.726578i
$414$	−0.161544	+	0.0777956i	−0.00793946	+	0.00382344i
$415$	8.44040	−	4.06468i	0.414323	−	0.199527i
$416$	0.183258	−	0.802905i	0.00898495	−	0.0393656i
$417$	−12.9276	+	56.6396i	−0.633068	+	2.77365i
$418$	2.00471	−	0.965419i	0.0980538	−	0.0472202i
$419$	19.5831	−	9.43072i	0.956697	−	0.460721i	0.110668	−	0.993857i	$-0.464701\pi$
$419$	19.5831	−	9.43072i	0.956697	−	0.460721i	0.846029	+	0.533136i	$0.178987\pi$
$420$	7.07282	+	32.7060i	0.345118	+	1.59589i
$421$	−3.60206	−	1.73466i	−0.175554	−	0.0845423i	0.344043	−	0.938954i	$-0.388203\pi$
$421$	−3.60206	−	1.73466i	−0.175554	−	0.0845423i	−0.519597	+	0.854412i	$0.673918\pi$
$422$	−0.968465			−0.0471441
$423$	−61.7032			−3.00011
$424$	−2.45779	−	1.18361i	−0.119361	−	0.0574811i
$425$	0.165881	−	0.208009i	0.00804643	−	0.0100899i
$426$	−0.642988	+	2.81711i	−0.0311529	+	0.136490i
$427$	−11.3839	−	5.64333i	−0.550908	−	0.273100i
$428$	−6.22937	−	27.2927i	−0.301108	−	1.31924i
$429$	−4.19579	−	2.02058i	−0.202574	−	0.0975547i
$430$	0.235266	+	1.03077i	0.0113455	+	0.0497080i
$431$	5.32648	−	6.67920i	0.256568	−	0.321726i	−0.636820	−	0.771013i	$-0.719751\pi$
$431$	5.32648	−	6.67920i	0.256568	−	0.321726i	0.893387	+	0.449287i	$0.148322\pi$
$432$	6.19846	−	27.1572i	0.298224	−	1.30660i
$433$	15.9991	+	20.0623i	0.768868	+	0.964131i	0.999961	−	0.00880118i	$-0.00280154\pi$
$433$	15.9991	+	20.0623i	0.768868	+	0.964131i	−0.231093	+	0.972932i	$0.574230\pi$
$434$	−0.341891	−	1.58097i	−0.0164113	−	0.0758888i
$435$	−34.6292	+	43.4237i	−1.66034	+	2.08200i
$436$	15.7802	+	19.7877i	0.755732	+	0.947658i
$437$	−0.856367	+	0.412405i	−0.0409656	+	0.0197280i
$438$	0.996752	+	1.24989i	0.0476267	+	0.0597220i
$439$	3.64981	+	15.9909i	0.174196	+	0.763203i	0.984241	+	0.176835i	$0.0565858\pi$
$439$	3.64981	+	15.9909i	0.174196	+	0.763203i	−0.810044	+	0.586368i	$0.800557\pi$
$440$	−4.48227			−0.213684
$441$	−9.37916	+	37.1579i	−0.446627	+	1.76943i
$442$	0.106438			0.00506275
$443$	−5.33901	−	23.3917i	−0.253664	−	1.11137i	−0.927891	−	0.372851i	$-0.878380\pi$
$443$	−5.33901	−	23.3917i	−0.253664	−	1.11137i	0.674227	−	0.738524i	$-0.264477\pi$
$444$	23.2160	+	29.1120i	1.10178	+	1.38159i
$445$	8.33997	−	4.01632i	0.395352	−	0.190392i
$446$	1.42554	+	1.78757i	0.0675011	+	0.0846437i
$447$	23.1722	−	29.0571i	1.09601	−	1.37435i
$448$	−4.61699	+	19.2138i	−0.218132	+	0.907767i
$449$	−18.0813	−	22.6732i	−0.853309	−	1.07002i	−0.996766	−	0.0803595i	$-0.974393\pi$
$449$	−18.0813	−	22.6732i	−0.853309	−	1.07002i	0.143457	−	0.989657i	$-0.454178\pi$
$450$	−0.0317060	+	0.138913i	−0.00149463	+	0.00654842i
$451$	6.08301	−	7.62785i	0.286438	−	0.359182i
$452$	4.49164	+	19.6791i	0.211269	+	0.925629i
$453$	−17.4792	−	8.41753i	−0.821243	−	0.395490i
$454$	0.618675	+	2.71059i	0.0290358	+	0.127214i
$455$	−1.71316	+	2.09860i	−0.0803142	+	0.0983837i
$456$	−1.67051	+	7.31897i	−0.0782286	+	0.342742i
$457$	0.604757	−	0.758341i	0.0282893	−	0.0354737i	−0.767486	−	0.641066i	$-0.778492\pi$
$457$	0.604757	−	0.758341i	0.0282893	−	0.0354737i	0.795775	+	0.605592i	$0.207064\pi$
$458$	2.51567	+	1.21148i	0.117550	+	0.0566089i
$459$	11.0075			0.513785
$460$	0.951985			0.0443865
$461$	−18.6091	−	8.96165i	−0.866710	−	0.417386i	−0.0529575	−	0.998597i	$-0.516865\pi$
$461$	−18.6091	−	8.96165i	−0.866710	−	0.417386i	−0.813753	+	0.581211i	$0.802579\pi$
$462$	−3.53982	−	1.75478i	−0.164687	−	0.0816399i
$463$	−11.6576	+	5.61401i	−0.541776	+	0.260905i	−0.684696	−	0.728829i	$-0.740065\pi$
$463$	−11.6576	+	5.61401i	−0.541776	+	0.260905i	0.142920	+	0.989734i	$0.454351\pi$
$464$	−30.2542	+	14.5697i	−1.40452	+	0.676380i
$465$	5.82097	−	25.5033i	0.269941	−	1.18269i
$466$	−0.258838	+	1.13404i	−0.0119904	+	0.0525335i
$467$	16.1614	−	7.78294i	0.747862	−	0.360151i	−0.0208192	−	0.999783i	$-0.506627\pi$
$467$	16.1614	−	7.78294i	0.747862	−	0.360151i	0.768681	+	0.639632i	$0.220913\pi$
$468$	4.54685	−	2.18965i	0.210178	−	0.101216i
$469$	−16.6621	−	0.190367i	−0.769386	−	0.00879033i
$470$	−3.33399	−	1.60557i	−0.153786	−	0.0740593i
$471$	23.4181			1.07905
$472$	4.28304			0.197143
$473$	9.95730	+	4.79518i	0.457837	+	0.220483i
$474$	0.940133	−	1.17889i	0.0431817	−	0.0541482i
$475$	−0.168078	+	0.736396i	−0.00771193	+	0.0337882i
$476$	−7.99396	−	0.0913320i	−0.366403	−	0.00418619i
$477$	−5.59008	−	24.4917i	−0.255952	−	1.12140i
$478$	−0.829877	−	0.399648i	−0.0379577	−	0.0182795i
$479$	2.07454	+	9.08917i	0.0947883	+	0.415295i	0.999952	−	0.00976781i	$-0.00310924\pi$
$479$	2.07454	+	9.08917i	0.0947883	+	0.415295i	−0.905164	+	0.425063i	$0.860252\pi$
$480$	7.04514	−	8.83433i	0.321565	−	0.403230i
$481$	−0.670804	+	2.93899i	−0.0305860	+	0.134006i
$482$	0.320974	+	0.402489i	0.0146200	+	0.0183329i
$483$	1.51213	+	0.749603i	0.0688042	+	0.0341081i
$484$	−0.960735	+	1.20472i	−0.0436698	+	0.0547602i
$485$	10.2787	+	12.8891i	0.466732	+	0.585264i
$486$	1.12724	−	0.542849i	0.0511325	−	0.0246241i
$487$	0.245180	+	0.307446i	0.0111102	+	0.0139317i	0.787356	−	0.616499i	$-0.211450\pi$
$487$	0.245180	+	0.307446i	0.0111102	+	0.0139317i	−0.776245	+	0.630431i	$0.782878\pi$
$488$	0.635305	+	2.78345i	0.0287589	+	0.126001i
$489$	71.5336			3.23486
$490$	−1.47366	+	1.76369i	−0.0665733	+	0.0796755i
$491$	25.1698			1.13590			0.567948	−	0.823065i	$-0.307738\pi$
$491$	25.1698			1.13590			0.567948	+	0.823065i	$0.307738\pi$
$492$	3.64182	+	15.9559i	0.164186	+	0.719346i
$493$	−8.27333	−	10.3744i	−0.372612	−	0.467241i
$494$	−0.272256	+	0.131112i	−0.0122494	+	0.00589900i
$495$	−25.7359	−	32.2718i	−1.15674	−	1.45051i
$496$	9.86090	−	12.3652i	0.442767	−	0.555213i
$497$	15.9168	−	7.44233i	0.713966	−	0.333834i
$498$	−1.15687	−	1.45067i	−0.0518405	−	0.0650060i
$499$	−0.539812	+	2.36507i	−0.0241653	+	0.105875i	−0.985572	−	0.169255i	$-0.945864\pi$
$499$	−0.539812	+	2.36507i	−0.0241653	+	0.105875i	0.961407	+	0.275130i	$0.0887210\pi$
$500$	14.0154	−	17.5748i	0.626789	−	0.785969i
$501$	−5.39617	−	23.6422i	−0.241083	−	1.05625i
$502$	1.26127	+	0.607395i	0.0562932	+	0.0271094i
$503$	−3.94989	−	17.3056i	−0.176117	−	0.771618i	−0.983400	−	0.181453i	$-0.941920\pi$
$503$	−3.94989	−	17.3056i	−0.176117	−	0.771618i	0.807283	−	0.590165i	$-0.200937\pi$
$504$	7.80068	−	3.64742i	0.347470	−	0.162469i
$505$	6.06946	−	26.5920i	0.270087	−	1.18333i
$506$	−0.0700813	+	0.0878792i	−0.00311549	+	0.00390671i
$507$	−33.5272	−	16.1459i	−1.48900	−	0.717063i
$508$	5.74673			0.254970
$509$	−26.2218			−1.16226			−0.581130	−	0.813811i	$-0.697389\pi$
$509$	−26.2218			−1.16226			−0.581130	+	0.813811i	$0.697389\pi$
$510$	1.31576	+	0.633636i	0.0582628	+	0.0280579i
$511$	2.27129	−	9.45209i	0.100476	−	0.418136i
$512$	10.2970	−	4.95880i	0.455070	−	0.219150i
$513$	−28.1558	+	13.5591i	−1.24311	+	0.598650i
$514$	−0.205744	+	0.901423i	−0.00907498	+	0.0397601i
$515$	1.08031	−	4.73315i	0.0476042	−	0.208568i
$516$	−16.7032	+	8.04385i	−0.735319	+	0.354111i
$517$	−34.8505	+	16.7831i	−1.53272	+	0.738120i
$518$	−0.597547	+	2.48672i	−0.0262547	+	0.109260i
$519$	28.2393	+	13.5993i	1.23957	+	0.596944i
$520$	0.608729			0.0266945
$521$	4.75489			0.208316			0.104158	−	0.994561i	$-0.466785\pi$
$521$	4.75489			0.208316			0.104158	+	0.994561i	$0.466785\pi$
$522$	6.40269	+	3.08337i	0.280238	+	0.134956i
$523$	−0.245787	+	0.308208i	−0.0107475	+	0.0134770i	−0.787176	−	0.616728i	$-0.788458\pi$
$523$	−0.245787	+	0.308208i	−0.0107475	+	0.0134770i	0.776429	+	0.630205i	$0.217029\pi$
$524$	−9.19680	+	40.2938i	−0.401764	+	1.76024i
$525$	1.21494	−	0.568080i	0.0530245	−	0.0247930i
$526$	−0.737530	−	3.23133i	−0.0321578	−	0.140893i
$527$	5.63082	+	2.71166i	0.245282	+	0.118122i
$528$	−8.59620	−	37.6624i	−0.374101	−	1.63905i
$529$	−14.3103	+	17.9446i	−0.622188	+	0.780199i
$530$	0.335247	−	1.46881i	0.0145622	−	0.0638012i
$531$	24.5920	+	30.8374i	1.06720	+	1.33823i
$532$	20.5601	−	9.61343i	0.891394	−	0.416795i
$533$	−0.826122	+	1.03592i	−0.0357833	+	0.0448709i
$534$	−1.14310	−	1.43341i	−0.0494669	−	0.0620296i
$535$	28.0168	−	13.4922i	1.21127	−	0.583319i
$536$	2.33449	+	2.92736i	0.100835	+	0.126443i
$537$	5.36381	+	23.5004i	0.231466	+	1.01412i
$538$	−1.78386			−0.0769077
$539$	4.80943	+	23.5382i	0.207157	+	1.01386i
$540$	31.2996			1.34692
$541$	3.53368	+	15.4821i	0.151925	+	0.665626i	0.992325	+	0.123660i	$0.0394631\pi$
$541$	3.53368	+	15.4821i	0.151925	+	0.665626i	−0.840400	+	0.541967i	$0.817680\pi$
$542$	−1.38364	−	1.73503i	−0.0594325	−	0.0745259i
$543$	16.6632	−	8.02456i	0.715085	−	0.344367i
$544$	1.68317	+	2.11063i	0.0721652	+	0.0904923i
$545$	−17.5286	+	21.9802i	−0.750842	+	0.941526i
$546$	0.480736	+	0.238314i	0.0205736	+	0.0101989i
$547$	−21.5460	−	27.0178i	−0.921239	−	1.15520i	−0.987535	−	0.157397i	$-0.949690\pi$
$547$	−21.5460	−	27.0178i	−0.921239	−	1.15520i	0.0662966	−	0.997800i	$-0.478882\pi$
$548$	5.65143	−	24.7605i	0.241417	−	1.05772i
$549$	−16.3928	+	20.5559i	−0.699628	+	0.877306i
$550$	0.0198762	+	0.0870831i	0.000847522	+	0.00371324i
$551$	33.9415	+	16.3454i	1.44596	+	0.696337i
$552$	−0.0843876	−	0.369726i	−0.00359177	−	0.0157366i
$553$	−9.16835	−	0.104749i	−0.389878	−	0.00445440i
$554$	−0.0830789	+	0.363993i	−0.00352969	+	0.0154646i
$555$	−25.7883	+	32.3376i	−1.09465	+	1.37265i
$556$	−35.5586	−	17.1241i	−1.50802	−	0.726225i
$557$	26.4369			1.12017			0.560084	−	0.828436i	$-0.310769\pi$
$557$	26.4369			1.12017			0.560084	+	0.828436i	$0.310769\pi$
$558$	−3.34706			−0.141692
$559$	−1.35228	−	0.651224i	−0.0571954	−	0.0275439i
$560$	−22.4710	−	0.256734i	−0.949574	−	0.0108490i
$561$	13.7537	−	6.62344i	0.580682	−	0.279642i
$562$	−1.49980	+	0.722267i	−0.0632654	+	0.0304670i
$563$	−9.21737	+	40.3840i	−0.388466	+	1.70198i	0.281477	+	0.959568i	$0.409176\pi$
$563$	−9.21737	+	40.3840i	−0.388466	+	1.70198i	−0.669943	+	0.742413i	$0.733681\pi$
$564$	14.4387	−	63.2602i	0.607980	−	2.66373i
$565$	−20.2013	+	9.72843i	−0.849875	+	0.409278i
$566$	−0.613017	+	0.295213i	−0.0257670	+	0.0124087i
$567$	10.7828	+	5.34531i	0.452833	+	0.224482i
$568$	−3.55718	−	1.71305i	−0.149256	−	0.0718778i
$569$	−28.4967			−1.19464			−0.597321	−	0.802002i	$-0.703768\pi$
$569$	−28.4967			−1.19464			−0.597321	+	0.802002i	$0.703768\pi$
$570$	−4.14608			−0.173660
$571$	26.2178	+	12.6258i	1.09718	+	0.528375i	0.892771	−	0.450510i	$-0.148758\pi$
$571$	26.2178	+	12.6258i	1.09718	+	0.528375i	0.204411	+	0.978885i	$0.434472\pi$
$572$	1.97252	−	2.47346i	0.0824751	−	0.103421i
$573$	14.3965	−	63.0754i	0.601424	−	2.63501i
$574$	−0.710862	+	0.870796i	−0.0296708	+	0.0363463i
$575$	−0.00849063	−	0.0371999i	−0.000354084	−	0.00155134i
$576$	36.8409	+	17.7416i	1.53504	+	0.739234i
$577$	−8.93329	−	39.1393i	−0.371898	−	1.62939i	−0.721445	−	0.692472i	$-0.756522\pi$
$577$	−8.93329	−	39.1393i	−0.371898	−	1.62939i	0.349547	−	0.936919i	$-0.386335\pi$
$578$	1.36664	−	1.71371i	0.0568447	−	0.0712810i
$579$	−4.29754	+	18.8287i	−0.178600	+	0.782496i
$580$	−23.5251	−	29.4995i	−0.976825	−	1.22490i
$581$	−2.63615	+	10.9705i	−0.109366	+	0.455131i
$582$	2.03582	−	2.55284i	0.0843876	−	0.105819i
$583$	−9.81901	−	12.3126i	−0.406662	−	0.509938i
$584$	−1.96803	+	0.947753i	−0.0814376	+	0.0392183i
$585$	3.49515	+	4.38278i	0.144507	+	0.181205i
$586$	−0.868861	−	3.80673i	−0.0358923	−	0.157255i
$587$	−23.9240			−0.987449			−0.493724	−	0.869618i	$-0.664365\pi$
$587$	−23.9240			−0.987449			−0.493724	+	0.869618i	$0.664365\pi$
$588$	−35.9008	−	18.3109i	−1.48052	−	0.755128i
$589$	−17.7432			−0.731097
$590$	0.526360	+	2.30613i	0.0216699	+	0.0949420i
$591$	18.2236	+	22.8517i	0.749618	+	0.939991i
$592$	−22.5303	+	10.8500i	−0.925989	+	0.445933i
$593$	−17.6191	−	22.0936i	−0.723529	−	0.907276i	0.275003	−	0.961443i	$-0.411321\pi$
$593$	−17.6191	−	22.0936i	−0.723529	−	0.907276i	−0.998532	+	0.0541670i	$0.982750\pi$
$594$	−2.30415	+	2.88931i	−0.0945404	+	0.118550i
$595$	−1.87701	−	8.67963i	−0.0769498	−	0.355830i
$596$	15.7419	+	19.7397i	0.644811	+	0.808568i
$597$	−11.2680	+	49.3685i	−0.461170	+	2.02052i
$598$	0.00951761	−	0.0119347i	0.000389204	−	0.000488046i
$599$	1.05041	+	4.60215i	0.0429187	+	0.188039i	0.991843	−	0.127464i	$-0.0406838\pi$
$599$	1.05041	+	4.60215i	0.0429187	+	0.188039i	−0.948925	+	0.315503i	$0.897827\pi$
$600$	−0.271523	−	0.130758i	−0.0110849	−	0.00533819i
$601$	7.41533	+	32.4887i	0.302478	+	1.32524i	0.866374	+	0.499396i	$0.166445\pi$
$601$	7.41533	+	32.4887i	0.302478	+	1.32524i	−0.563896	+	0.825846i	$0.690698\pi$
$602$	−1.14087	−	0.565558i	−0.0464982	−	0.0230504i
$603$	−7.67267	+	33.6162i	−0.312455	+	1.36896i
$604$	8.21729	−	10.3042i	0.334357	−	0.419270i
$605$	−1.54213	−	0.742649i	−0.0626963	−	0.0301930i
$606$	−5.40233			−0.219454
$607$	33.7153			1.36846			0.684230	−	0.729266i	$-0.260138\pi$
$607$	33.7153			1.36846			0.684230	+	0.729266i	$0.260138\pi$
$608$	−6.90524	−	3.32539i	−0.280044	−	0.134862i
$609$	−14.1389	−	65.3807i	−0.572936	−	2.64936i
$610$	−1.42063	+	0.684140i	−0.0575197	+	0.0277000i
$611$	4.73298	−	2.27928i	0.191476	−	0.0922098i
$612$	−3.68110	+	16.1280i	−0.148800	+	0.651934i
$613$	−8.03182	+	35.1897i	−0.324402	+	1.42130i	0.505229	+	0.862986i	$0.331408\pi$
$613$	−8.03182	+	35.1897i	−0.324402	+	1.42130i	−0.829631	+	0.558313i	$0.811449\pi$
$614$	0.295685	−	0.142394i	0.0119329	−	0.00574656i
$615$	−16.3792	+	7.88782i	−0.660475	+	0.318068i
$616$	3.41380	−	4.18186i	0.137546	−	0.168492i
$617$	2.28017	+	1.09807i	0.0917961	+	0.0442067i	0.479218	−	0.877696i	$-0.340920\pi$
$617$	2.28017	+	1.09807i	0.0917961	+	0.0442067i	−0.387422	+	0.921902i	$0.626634\pi$
$618$	−0.961567			−0.0386799
$619$	2.68266			0.107825			0.0539126	−	0.998546i	$-0.482831\pi$
$619$	2.68266			0.107825			0.0539126	+	0.998546i	$0.482831\pi$
$620$	16.0111	+	7.71056i	0.643023	+	0.309663i
$621$	0.984279	−	1.23425i	0.0394977	−	0.0495286i
$622$	0.532091	−	2.33124i	0.0213349	−	0.0934743i
$623$	−2.60478	+	10.8399i	−0.104358	+	0.434292i
$624$	1.16743	+	5.11486i	0.0467347	+	0.204758i
$625$	21.7125	+	10.4562i	0.868499	+	0.418247i
$626$	0.0304685	+	0.133491i	0.00121777	+	0.00533538i
$627$	−27.0216	+	33.8840i	−1.07914	+	1.35319i
$628$	−3.54007	+	15.5100i	−0.141264	+	0.618918i
$629$	−6.16114	−	7.72583i	−0.245661	−	0.308049i
$630$	2.92255	+	3.75191i	0.116437	+	0.149479i
$631$	10.5445	−	13.2224i	0.419772	−	0.526377i	−0.526315	−	0.850289i	$-0.676427\pi$
$631$	10.5445	−	13.2224i	0.419772	−	0.526377i	0.946087	+	0.323912i	$0.104998\pi$
$632$	1.28456	+	1.61078i	0.0510969	+	0.0640735i
$633$	16.9954	−	8.18457i	0.675508	−	0.325307i
$634$	−1.00323	−	1.25801i	−0.0398433	−	0.0499619i
$635$	1.42046	+	6.22342i	0.0563691	+	0.246969i
$636$	26.4178			1.04754
$637$	−0.653160	−	3.19668i	−0.0258791	−	0.126657i
$638$	4.45496			0.176374
$639$	−8.09057	−	35.4471i	−0.320058	−	1.40227i
$640$	6.36908	+	7.98657i	0.251760	+	0.315697i
$641$	8.21118	−	3.95430i	0.324322	−	0.156185i	−0.264637	−	0.964348i	$-0.585252\pi$
$641$	8.21118	−	3.95430i	0.324322	−	0.156185i	0.588959	+	0.808163i	$0.299538\pi$
$642$	−3.84008	−	4.81531i	−0.151556	−	0.190045i
$643$	23.7264	−	29.7520i	0.935679	−	1.17330i	−0.0489769	−	0.998800i	$-0.515596\pi$
$643$	23.7264	−	29.7520i	0.935679	−	1.17330i	0.984656	−	0.174505i	$-0.0558325\pi$
$644$	−0.725054	+	0.888180i	−0.0285711	+	0.0349992i
$645$	−12.8397	−	16.1005i	−0.505564	−	0.633957i
$646$	0.220417	−	0.965711i	0.00867220	−	0.0379954i
$647$	−15.1147	+	18.9532i	−0.594220	+	0.745129i	−0.984465	−	0.175583i	$-0.943819\pi$
$647$	−15.1147	+	18.9532i	−0.594220	+	0.745129i	0.390244	+	0.920711i	$0.372391\pi$
$648$	−0.601755	−	2.63646i	−0.0236392	−	0.103570i
$649$	22.2774	+	10.7283i	0.874466	+	0.421121i
$650$	−0.00269934	−	0.0118266i	−0.000105877	−	0.000463877i
$651$	19.3606	+	24.8548i	0.758803	+	0.974135i
$652$	−10.8136	+	47.3773i	−0.423492	+	1.85544i
$653$	16.2712	−	20.4035i	0.636742	−	0.798450i	−0.353849	−	0.935303i	$-0.615127\pi$
$653$	16.2712	−	20.4035i	0.636742	−	0.798450i	0.990591	+	0.136853i	$0.0436987\pi$
$654$	5.01683	+	2.41598i	0.196173	+	0.0944721i
$655$	−45.9094			−1.79383
$656$	−10.9912			−0.429136
$657$	−18.1236	−	8.72786i	−0.707068	−	0.340506i
$658$	4.03721	−	1.88770i	0.157387	−	0.0735904i
$659$	35.4630	−	17.0781i	1.38144	−	0.665268i	0.412136	−	0.911122i	$-0.364783\pi$
$659$	35.4630	−	17.0781i	1.38144	−	0.665268i	0.969307	+	0.245855i	$0.0790687\pi$
$660$	39.1084	−	18.8336i	1.52229	−	0.733098i
$661$	4.11935	−	18.0481i	0.160224	−	0.701989i	−0.829441	−	0.558594i	$-0.811341\pi$
$661$	4.11935	−	18.0481i	0.160224	−	0.701989i	0.989666	−	0.143395i	$-0.0458018\pi$
$662$	1.09756	−	4.80873i	0.0426579	−	0.186896i
$663$	−1.86787	+	0.899517i	−0.0725419	+	0.0349343i
$664$	2.28417	−	1.10000i	0.0886430	−	0.0426882i
$665$	15.4928	+	19.8894i	0.600786	+	0.771276i
$666$	4.76808	+	2.29619i	0.184759	+	0.0889754i
$667$	−1.90306			−0.0736867
$668$	16.4741			0.637404
$669$	−40.1234	−	19.3224i	−1.55126	−	0.747047i
$670$	−1.28930	+	1.61673i	−0.0498098	+	0.0624596i
$671$	−3.66764	+	16.0690i	−0.141588	+	0.620335i
$672$	2.87648	+	13.3014i	0.110963	+	0.513112i
$673$	−7.07769	−	31.0094i	−0.272825	−	1.19532i	−0.906662	−	0.421857i	$-0.861378\pi$
$673$	−7.07769	−	31.0094i	−0.272825	−	1.19532i	0.633838	−	0.773466i	$-0.281479\pi$
$674$	−2.53481	−	1.22070i	−0.0976371	−	0.0470195i
$675$	−0.279157	−	1.22307i	−0.0107448	−	0.0470759i
$676$	15.7618	−	19.7647i	0.606223	−	0.760179i
$677$	8.37075	−	36.6746i	0.321714	−	1.40952i	−0.512788	−	0.858516i	$-0.671387\pi$
$677$	8.37075	−	36.6746i	0.321714	−	1.40952i	0.834502	−	0.551006i	$-0.185756\pi$
$678$	2.76886	+	3.47204i	0.106337	+	0.133343i
$679$	−19.8537	−	0.226831i	−0.761916	−	0.00870499i
$680$	−1.24411	+	1.56007i	−0.0477095	+	0.0598259i
$681$	−33.7644	−	42.3392i	−1.29386	−	1.62244i
$682$	−1.89045	+	0.910392i	−0.0723890	+	0.0348607i
$683$	−9.06997	−	11.3734i	−0.347053	−	0.435191i	0.577415	−	0.816451i	$-0.304062\pi$
$683$	−9.06997	−	11.3734i	−0.347053	−	0.435191i	−0.924468	+	0.381260i	$0.875490\pi$
$684$	−10.4508	−	45.7879i	−0.399596	−	1.75074i
$685$	28.2113			1.07790
$686$	−0.523111	−	2.71816i	−0.0199725	−	0.103780i
$687$	−54.3854			−2.07493
$688$	−2.77051	−	12.1384i	−0.105625	−	0.462772i
$689$	1.33350	+	1.67216i	0.0508023	+	0.0637041i
$690$	0.188702	−	0.0908742i	0.00718377	−	0.00345952i
$691$	11.8844	+	14.9025i	0.452103	+	0.566919i	0.954688	−	0.297609i	$-0.0961891\pi$
$691$	11.8844	+	14.9025i	0.452103	+	0.566919i	−0.502585	+	0.864528i	$0.667618\pi$
$692$	−13.2758	+	16.6473i	−0.504671	+	0.632837i
$693$	49.7100	+	0.567942i	1.88833	+	0.0215743i
$694$	2.99667	+	3.75770i	0.113752	+	0.142640i
$695$	9.75533	−	42.7409i	0.370041	−	1.62125i
$696$	−9.37148	+	11.7515i	−0.355225	+	0.445438i
$697$	−0.966479	−	4.23442i	−0.0366080	−	0.160390i
$698$	−1.38318	−	0.666106i	−0.0523543	−	0.0252125i
$699$	−5.04157	−	22.0886i	−0.190690	−	0.835466i
$700$	0.192584	+	0.890544i	0.00727899	+	0.0336594i
$701$	−3.63929	+	15.9448i	−0.137454	+	0.602225i	0.858535	+	0.512754i	$0.171375\pi$
$701$	−3.63929	+	15.9448i	−0.137454	+	0.602225i	−0.995989	+	0.0894711i	$0.971482\pi$
$702$	0.312922	−	0.392392i	0.0118105	−	0.0148099i
$703$	25.2762	+	12.1724i	0.953311	+	0.459090i
$704$	25.6337			0.966106
$705$	72.0765			2.71456
$706$	−3.68834	−	1.77621i	−0.138812	−	0.0668486i
$707$	20.1871	+	25.9158i	0.759215	+	0.974663i
$708$	−37.3701	+	17.9965i	−1.40445	+	0.676350i
$709$	8.16901	−	3.93399i	0.306793	−	0.147744i	−0.274152	−	0.961686i	$-0.588397\pi$
$709$	8.16901	−	3.93399i	0.306793	−	0.147744i	0.580946	+	0.813942i	$0.302683\pi$
$710$	0.485206	−	2.12583i	0.0182095	−	0.0797809i
$711$	−4.22189	+	18.4973i	−0.158333	+	0.693703i
$712$	2.25699	−	1.08691i	0.0845843	−	0.0407337i
$713$	0.807556	−	0.388898i	0.0302432	−	0.0145644i
$714$	−1.59328	+	0.744981i	−0.0596270	+	0.0278802i
$715$	3.16619	+	1.52476i	0.118409	+	0.0570227i
$716$	−16.3754			−0.611976
$717$	17.9408			0.670012
$718$	−0.636329	−	0.306440i	−0.0237476	−	0.0114362i
$719$	−23.6927	+	29.7097i	−0.883587	+	1.10798i	0.109889	+	0.993944i	$0.464950\pi$
$719$	−23.6927	+	29.7097i	−0.883587	+	1.10798i	−0.993476	+	0.114039i	$0.963621\pi$
$720$	−10.3476	+	45.3357i	−0.385632	+	1.68956i
$721$	3.59313	+	4.61278i	0.133815	+	0.171789i
$722$	−0.00612984	−	0.0268566i	−0.000228129	−	0.000999498i
$723$	−9.03419	−	4.35064i	−0.335985	−	0.161802i
$724$	2.79581	+	12.2492i	0.103905	+	0.455239i
$725$	−0.942909	+	1.18237i	−0.0350188	+	0.0439122i
$726$	−0.0754367	+	0.330510i	−0.00279972	+	0.0122664i
$727$	9.93554	+	12.4588i	0.368489	+	0.462070i	0.931160	−	0.364610i	$-0.118798\pi$
$727$	9.93554	+	12.4588i	0.368489	+	0.462070i	−0.562671	+	0.826681i	$0.690226\pi$
$728$	−0.463622	+	0.567930i	−0.0171830	+	0.0210489i
$729$	−23.7024	+	29.7219i	−0.877867	+	1.10081i
$730$	−0.752161	−	0.943181i	−0.0278387	−	0.0349087i
$731$	4.43276	−	2.13470i	0.163951	−	0.0789548i
$732$	−17.2387	−	21.6166i	−0.637159	−	0.798973i
$733$	−8.76567	−	38.4049i	−0.323767	−	1.41852i	−0.830791	−	0.556585i	$-0.812111\pi$
$733$	−8.76567	−	38.4049i	−0.323767	−	1.41852i	0.507023	−	0.861932i	$-0.330746\pi$
$734$	0.484900			0.0178980
$735$	10.9559	−	43.4048i	0.404116	−	1.60101i
$736$	0.387168			0.0142712
$737$	4.80992	+	21.0736i	0.177176	+	0.776257i
$738$	1.45028	+	1.81860i	0.0533857	+	0.0669435i
$739$	15.4957	−	7.46234i	0.570019	−	0.274506i	−0.126593	−	0.991955i	$-0.540404\pi$
$739$	15.4957	−	7.46234i	0.570019	−	0.274506i	0.696612	+	0.717448i	$0.254690\pi$
$740$	−17.5191	−	21.9682i	−0.644015	−	0.807569i
$741$	3.66975	−	4.60172i	0.134811	−	0.169048i
$742$	1.11504	+	1.43146i	0.0409343	+	0.0525506i
$743$	−12.1490	−	15.2344i	−0.445704	−	0.558896i	0.507332	−	0.861750i	$-0.330632\pi$
$743$	−12.1490	−	15.2344i	−0.445704	−	0.558896i	−0.953037	+	0.302855i	$0.902060\pi$
$744$	1.57529	−	6.90180i	0.0577530	−	0.253032i
$745$	−17.4860	+	21.9268i	−0.640639	+	0.803336i
$746$	1.17856	+	5.16360i	0.0431501	+	0.189053i
$747$	21.0349	+	10.1299i	0.769627	+	0.370633i
$748$	2.30765	+	10.1105i	0.0843759	+	0.369675i
$749$	−8.75036	+	36.4150i	−0.319731	+	1.33058i
$750$	1.10049	−	4.82156i	0.0401842	−	0.176058i
$751$	−22.0590	+	27.6611i	−0.804943	+	1.00937i	0.194651	+	0.980873i	$0.437642\pi$
$751$	−22.0590	+	27.6611i	−0.804943	+	1.00937i	−0.999594	+	0.0284937i	$0.990929\pi$
$752$	39.2614	+	18.9073i	1.43172	+	0.689479i
$753$	−27.2669			−0.993663
$754$	−0.605020			−0.0220335
$755$	13.1900	+	6.35197i	0.480033	+	0.231172i
$756$	−23.8385	+	29.2018i	−0.866997	+	1.06206i
$757$	−19.5973	+	9.43757i	−0.712276	+	0.343014i	−0.754686	−	0.656086i	$-0.772211\pi$
$757$	−19.5973	+	9.43757i	−0.712276	+	0.343014i	0.0424098	+	0.999100i	$0.486497\pi$
$758$	−3.31368	+	1.59579i	−0.120358	+	0.0579615i
$759$	0.487172	−	2.13444i	0.0176832	−	0.0774752i
$760$	1.26058	−	5.52298i	0.0457262	−	0.200340i
$761$	11.2446	−	5.41513i	0.407618	−	0.196298i	−0.218828	−	0.975763i	$-0.570223\pi$
$761$	11.2446	−	5.41513i	0.407618	−	0.196298i	0.626446	+	0.779465i	$0.284509\pi$
$762$	1.13912	−	0.548570i	0.0412658	−	0.0198726i
$763$	−7.15680	−	33.0944i	−0.259094	−	1.19810i
$764$	39.5991	+	19.0699i	1.43264	+	0.689925i
$765$	−18.3757			−0.664373
$766$	0.760595			0.0274814
$767$	−3.02546	−	1.45698i	−0.109243	−	0.0526086i
$768$	−25.8515	+	32.4168i	−0.932836	+	1.16974i
$769$	4.89228	−	21.4345i	0.176420	−	0.772947i	−0.806844	−	0.590764i	$-0.798826\pi$
$769$	4.89228	−	21.4345i	0.176420	−	0.772947i	0.983265	−	0.182183i	$-0.0583164\pi$
$770$	2.67119	+	1.32418i	0.0962630	+	0.0477202i
$771$	−4.00743	−	17.5577i	−0.144324	−	0.632324i
$772$	−11.8208	−	5.69259i	−0.425440	−	0.204881i
$773$	4.38850	+	19.2273i	0.157843	+	0.691557i	0.990471	+	0.137723i	$0.0439785\pi$
$773$	4.38850	+	19.2273i	0.157843	+	0.691557i	−0.832627	+	0.553834i	$0.813164\pi$
$774$	−1.64284	+	2.06006i	−0.0590507	+	0.0740472i
$775$	0.158498	−	0.694423i	0.00569340	−	0.0249444i
$776$	2.78166	+	3.48809i	0.0998558	+	0.125215i
$777$	−10.5292	−	48.6890i	−0.377733	−	1.74671i
$778$	−1.41063	+	1.76887i	−0.0505735	+	0.0634172i
$779$	7.68815	+	9.64063i	0.275456	+	0.345411i
$780$	−5.31124	+	2.55776i	−0.190173	+	0.0915825i
$781$	−14.2111	−	17.8202i	−0.508514	−	0.637657i
$782$	0.0111346	+	0.0487840i	0.000398174	+	0.00174451i
$783$	−62.5691			−2.23604
$784$	17.3540	−	20.7694i	0.619785	−	0.741765i
$785$	−17.6716			−0.630727
$786$	2.02336	+	8.86494i	0.0721710	+	0.316202i
$787$	9.59591	+	12.0329i	0.342057	+	0.428926i	0.922870	−	0.385111i	$-0.125837\pi$
$787$	9.59591	+	12.0329i	0.342057	+	0.428926i	−0.580813	+	0.814037i	$0.697265\pi$
$788$	−17.8897	+	8.61521i	−0.637293	+	0.306904i
$789$	40.2510	+	50.4731i	1.43297	+	1.79689i
$790$	−0.709436	+	0.889604i	−0.0252406	+	0.0316507i
$791$	6.30937	−	26.2567i	0.224335	−	0.933582i
$792$	−6.96475	−	8.73352i	−0.247482	−	0.310332i
$793$	0.498095	−	2.18229i	0.0176879	−	0.0774956i
$794$	−0.664910	+	0.833770i	−0.0235968	+	0.0295894i
$795$	6.52986	+	28.6092i	0.231590	+	1.01466i
$796$	−30.9938	−	14.9258i	−1.09855	−	0.529032i
$797$	−4.92695	−	21.5864i	−0.174522	−	0.764629i	−0.984100	−	0.177617i	$-0.943161\pi$
$797$	−4.92695	−	21.5864i	−0.174522	−	0.764629i	0.809578	−	0.587012i	$-0.199696\pi$
$798$	3.15775	−	3.86819i	0.111783	−	0.136933i
$799$	−3.83179	+	16.7882i	−0.135559	+	0.593923i
$800$	0.191830	−	0.240548i	0.00678223	−	0.00850464i
$801$	20.7846	+	10.0094i	0.734389	+	0.353663i
$802$	4.30285			0.151939
$803$	−12.6103			−0.445008
$804$	−32.6690	−	15.7326i	−1.15215	−	0.554844i
$805$	−1.14107	−	0.565660i	−0.0402174	−	0.0199369i
$806$	0.256738	−	0.123639i	0.00904322	−	0.00435498i
$807$	31.3047	−	15.0755i	1.10198	−	0.530684i
$808$	1.64254	−	7.19643i	0.0577843	−	0.253170i
$809$	4.14143	−	18.1448i	0.145605	−	0.637936i	−0.848470	−	0.529243i	$-0.822476\pi$
$809$	4.14143	−	18.1448i	0.145605	−	0.637936i	0.994075	−	0.108694i	$-0.0346668\pi$
$810$	1.34561	−	0.648011i	0.0472798	−	0.0227688i
$811$	−28.7892	+	13.8641i	−1.01092	+	0.486835i	−0.864632	−	0.502406i	$-0.832448\pi$
$811$	−28.7892	+	13.8641i	−1.01092	+	0.486835i	−0.146292	+	0.989241i	$0.546734\pi$
$812$	45.4396	+	0.519153i	1.59462	+	0.0182187i
$813$	38.9441	+	18.7545i	1.36583	+	0.657749i
$814$	3.31761			0.116282
$815$	−53.9801			−1.89084
$816$	−15.4945	−	7.46176i	−0.542416	−	0.261214i
$817$	−8.70892	+	10.9206i	−0.304686	+	0.382065i
$818$	−0.974289	+	4.26864i	−0.0340652	+	0.149249i
$819$	−6.75101	−	0.0771312i	−0.235900	−	0.00269518i
$820$	−2.74816	−	12.0405i	−0.0959701	−	0.420472i
$821$	15.1074	+	7.27534i	0.527252	+	0.253911i	0.678520	−	0.734582i	$-0.262622\pi$
$821$	15.1074	+	7.27534i	0.527252	+	0.253911i	−0.151269	+	0.988493i	$0.548336\pi$
$822$	−1.24336	−	5.44751i	−0.0433671	−	0.190004i
$823$	30.2784	−	37.9679i	1.05544	−	1.32348i	0.111353	−	0.993781i	$-0.464482\pi$
$823$	30.2784	−	37.9679i	1.05544	−	1.32348i	0.944086	−	0.329698i	$-0.106947\pi$
$824$	0.292358	−	1.28090i	0.0101848	−	0.0446223i
$825$	−1.08475	−	1.36023i	−0.0377661	−	0.0473572i
$826$	−2.55246	−	1.26532i	−0.0888113	−	0.0440262i
$827$	27.7978	−	34.8574i	0.966625	−	1.21211i	−0.0106085	−	0.999944i	$-0.503377\pi$
$827$	27.7978	−	34.8574i	0.966625	−	1.21211i	0.977234	−	0.212166i	$-0.0680517\pi$
$828$	1.47924	+	1.85490i	0.0514070	+	0.0644623i
$829$	−37.8714	+	18.2379i	−1.31533	+	0.633429i	−0.954223	−	0.299097i	$-0.903315\pi$
$829$	−37.8714	+	18.2379i	−1.31533	+	0.633429i	−0.361105	+	0.932525i	$0.617600\pi$
$830$	0.872987	+	1.09469i	0.0303018	+	0.0379973i
$831$	−1.61819	−	7.08975i	−0.0561344	−	0.245941i
$832$	−3.48126			−0.120691
$833$	9.52747	+	4.85940i	0.330107	+	0.168368i
$834$	−8.68306			−0.300670
$835$	4.07202	+	17.8407i	0.140918	+	0.617402i
$836$	−18.3569	−	23.0188i	−0.634885	−	0.796121i
$837$	26.5510	−	12.7863i	0.917737	−	0.441959i
$838$	2.02547	+	2.53986i	0.0699688	+	0.0877381i
$839$	−14.7280	+	18.4683i	−0.508466	+	0.637596i	−0.968116	−	0.250504i	$-0.919404\pi$
$839$	−14.7280	+	18.4683i	−0.508466	+	0.637596i	0.459650	+	0.888100i	$0.347975\pi$
$840$	−9.11210	+	4.26061i	−0.314397	+	0.147005i
$841$	28.9464	+	36.2976i	0.998150	+	1.25164i
$842$	0.132965	−	0.582559i	0.00458229	−	0.0200763i
$843$	20.2159	−	25.3499i	0.696271	−	0.873096i
$844$	2.85155	+	12.4935i	0.0981545	+	0.430043i
$845$	25.3001	+	12.1839i	0.870349	+	0.419138i
$846$	−2.05213	−	8.99095i	−0.0705536	−	0.309115i
$847$	1.86739	−	0.873150i	0.0641644	−	0.0300018i
$848$	−3.94790	+	17.2969i	−0.135572	+	0.593978i
$849$	8.26286	−	10.3613i	0.283581	−	0.355599i
$850$	0.0358264	+	0.0172531i	0.00122884	+	0.000591777i
$851$	−1.41721			−0.0485812
$852$	38.2347			1.30990
$853$	41.7615	+	20.1113i	1.42989	+	0.688597i	0.978976	−	0.203973i	$-0.0653855\pi$
$853$	41.7615	+	20.1113i	1.42989	+	0.688597i	0.450909	+	0.892570i	$0.351100\pi$
$854$	0.443699	−	1.84647i	0.0151831	−	0.0631850i
$855$	47.0028	−	22.6353i	1.60746	−	0.774112i
$856$	7.58202	−	3.65131i	0.259148	−	0.124799i
$857$	4.08960	−	17.9177i	0.139698	−	0.612057i	−0.855803	−	0.517302i	$-0.826936\pi$
$857$	4.08960	−	17.9177i	0.139698	−	0.612057i	0.995501	−	0.0947546i	$-0.0302066\pi$
$858$	0.154882	−	0.678581i	0.00528757	−	0.0231664i
$859$	−1.87398	+	0.902463i	−0.0639395	+	0.0307916i	−0.465580	−	0.885006i	$-0.654154\pi$
$859$	−1.87398	+	0.902463i	−0.0639395	+	0.0307916i	0.401641	+	0.915797i	$0.368440\pi$
$860$	12.6045	−	6.06999i	0.429808	−	0.206985i
$861$	5.11565	−	21.2890i	0.174341	−	0.725527i
$862$	1.15039	+	0.554000i	0.0391826	+	0.0188693i
$863$	−50.2081			−1.70910			−0.854552	−	0.519366i	$-0.826168\pi$
$863$	−50.2081			−1.70910			−0.854552	+	0.519366i	$0.826168\pi$
$864$	12.7294			0.433062
$865$	−21.3097	−	10.2622i	−0.724551	−	0.348925i
$866$	−2.39123	+	2.99851i	−0.0812573	+	0.101893i
$867$	−9.50023	+	41.6232i	−0.322645	+	1.41360i
$868$	−19.3882	+	9.06549i	−0.658079	+	0.307703i
$869$	2.64666	+	11.5958i	0.0897818	+	0.393360i
$870$	−7.47909	−	3.60174i	−0.253565	−	0.122110i
$871$	−0.653226	−	2.86197i	−0.0221337	−	0.0969742i
$872$	−4.74365	+	5.94835i	−0.160640	+	0.201436i
$873$	−9.14236	+	40.0553i	−0.309422	+	1.35567i
$874$	−0.0885738	−	0.111068i	−0.00299605	−	0.00375693i
$875$	−27.2420	+	12.7377i	−0.920947	+	0.430614i
$876$	13.1891	−	16.5386i	0.445617	−	0.558786i
$877$	−2.02102	−	2.53428i	−0.0682451	−	0.0855766i	0.746537	−	0.665344i	$-0.231715\pi$
$877$	−2.02102	−	2.53428i	−0.0682451	−	0.0855766i	−0.814782	+	0.579767i	$0.803144\pi$
$878$	−2.20869	+	1.06365i	−0.0745397	+	0.0358964i
$879$	47.4185	+	59.4609i	1.59938	+	2.00557i
$880$	6.48679	+	28.4205i	0.218670	+	0.958055i
$881$	−47.0450			−1.58499			−0.792494	−	0.609880i	$-0.791218\pi$
$881$	−47.0450			−1.58499			−0.792494	+	0.609880i	$0.791218\pi$
$882$	−5.72632	−	0.130865i	−0.192815	−	0.00440645i
$883$	20.9572			0.705266			0.352633	−	0.935762i	$-0.385286\pi$
$883$	20.9572			0.705266			0.352633	+	0.935762i	$0.385286\pi$
$884$	−0.313397	−	1.37308i	−0.0105407	−	0.0461817i
$885$	−28.7263	−	36.0216i	−0.965624	−	1.21085i
$886$	3.23091	−	1.55592i	0.108545	−	0.0522723i
$887$	−22.2588	−	27.9116i	−0.747377	−	0.937181i	0.252158	−	0.967686i	$-0.418860\pi$
$887$	−22.2588	−	27.9116i	−0.747377	−	0.937181i	−0.999535	+	0.0305051i	$0.990288\pi$
$888$	−6.97893	+	8.75131i	−0.234198	+	0.293675i
$889$	−6.88816	−	3.41465i	−0.231022	−	0.114524i
$890$	0.862600	+	1.08167i	0.0289144	+	0.0362575i
$891$	3.47395	−	15.2204i	0.116382	−	0.509901i
$892$	18.8627	−	23.6531i	0.631571	−	0.791965i
$893$	−10.8786	−	47.6622i	−0.364038	−	1.59496i
$894$	5.00465	+	2.41011i	0.167381	+	0.0806062i
$895$	−4.04760	−	17.7337i	−0.135296	−	0.592772i
$896$	−12.3021	−	0.140553i	−0.410985	−	0.00469556i
$897$	−0.0661618	+	0.289874i	−0.00220908	+	0.00967861i
$898$	2.70243	−	3.38875i	0.0901814	−	0.113084i
$899$	−32.0069	−	15.4137i	−1.06749	−	0.514076i
$900$	1.88537			0.0628457
$901$	−7.01085			−0.233565
$902$	1.31379	+	0.632686i	0.0437443	+	0.0210661i
$903$	24.8004	+	0.283348i	0.825307	+	0.00942923i
$904$	−5.46695	+	2.63274i	−0.181828	+	0.0875637i
$905$	−12.5742	+	6.05543i	−0.417982	+	0.201289i
$906$	0.645220	−	2.82689i	0.0214360	−	0.0939172i
$907$	−6.14465	+	26.9215i	−0.204030	+	0.893913i	0.764423	+	0.644715i	$0.223024\pi$
$907$	−6.14465	+	26.9215i	−0.204030	+	0.893913i	−0.968453	+	0.249198i	$0.919833\pi$
$908$	33.1457	−	15.9621i	1.09998	−	0.529722i
$909$	61.2445	−	29.4938i	2.03135	−	0.978247i
$910$	−0.362769	−	0.179834i	−0.0120257	−	0.00596146i
$911$	−32.8752	−	15.8319i	−1.08920	−	0.524533i	−0.198955	−	0.980009i	$-0.563755\pi$
$911$	−32.8752	−	15.8319i	−1.08920	−	0.524533i	−0.890248	+	0.455476i	$0.849469\pi$
$912$	48.8246			1.61674
$913$	14.6360			0.484381
$914$	0.130613	+	0.0628999i	0.00432030	+	0.00208055i
$915$	19.1487	−	24.0117i	0.633037	−	0.793803i
$916$	8.22131	−	36.0199i	0.271640	−	1.19013i
$917$	34.9656	−	42.8324i	1.15467	−	1.41445i
$918$	0.366087	+	1.60393i	0.0120827	+	0.0529376i
$919$	2.93525	+	1.41354i	0.0968249	+	0.0466284i	0.481669	−	0.876353i	$-0.340031\pi$
$919$	2.93525	+	1.41354i	0.0968249	+	0.0466284i	−0.384844	+	0.922981i	$0.625745\pi$
$920$	0.0636799	+	0.279000i	0.00209946	+	0.00919835i
$921$	−3.98554	+	4.99770i	−0.131328	+	0.164680i
$922$	0.686928	−	3.00963i	0.0226228	−	0.0991168i
$923$	1.92999	+	2.42013i	0.0635263	+	0.0796594i
$924$	−12.2145	+	50.8314i	−0.401829	+	1.67223i
$925$	−0.702184	+	0.880511i	−0.0230877	+	0.0289510i
$926$	−1.20574	−	1.51195i	−0.0396232	−	0.0496859i
$927$	10.9010	−	5.24964i	0.358035	−	0.172421i
$928$	−9.56753	−	11.9973i	−0.314070	−	0.393831i
$929$	−10.9330	−	47.9007i	−0.358701	−	1.57157i	−0.756435	−	0.654069i	$-0.773061\pi$
$929$	−10.9330	−	47.9007i	−0.358701	−	1.57157i	0.397734	−	0.917501i	$-0.369797\pi$
$930$	3.90976			0.128206
$931$	−30.3560	−	0.693733i	−0.994878	−	0.0227362i
$932$	15.3916			0.504168
$933$	10.3639	+	45.4073i	0.339300	+	1.48657i
$934$	1.67157	+	2.09609i	0.0546955	+	0.0685860i
$935$	−10.3787	+	4.99813i	−0.339420	+	0.163456i
$936$	0.945869	+	1.18608i	0.0309167	+	0.0387683i
$937$	20.6062	−	25.8394i	0.673177	−	0.844137i	−0.321529	−	0.946900i	$-0.604197\pi$
$937$	20.6062	−	25.8394i	0.673177	−	0.844137i	0.994706	+	0.102763i	$0.0327682\pi$
$938$	−0.526411	−	2.43422i	−0.0171879	−	0.0794801i
$939$	−1.66283	−	2.08512i	−0.0542644	−	0.0680454i
$940$	−10.8956	+	47.7369i	−0.355376	+	1.55701i
$941$	−11.7674	+	14.7559i	−0.383607	+	0.481028i	−0.935721	−	0.352740i	$-0.885250\pi$
$941$	−11.7674	+	14.7559i	−0.383607	+	0.481028i	0.552114	+	0.833769i	$0.313821\pi$
$942$	0.778841	+	3.41232i	0.0253760	+	0.111180i
$943$	−0.561219	−	0.270269i	−0.0182758	−	0.00880116i
$944$	−6.19846	−	27.1572i	−0.201743	−	0.883893i
$945$	−37.5164	−	18.5979i	−1.22041	−	0.604989i
$946$	−0.367560	+	1.61039i	−0.0119504	+	0.0523581i
$947$	3.43219	−	4.30383i	0.111531	−	0.139856i	−0.722932	−	0.690919i	$-0.757206\pi$
$947$	3.43219	−	4.30383i	0.111531	−	0.139856i	0.834464	+	0.551063i	$0.185778\pi$
$948$	−17.9761	−	8.65685i	−0.583837	−	0.281161i
$949$	1.71258			0.0555927
$950$	−0.112892			−0.00366271
$951$	28.2370	+	13.5982i	0.915648	+	0.440953i
$952$	−0.507963	−	2.34891i	−0.0164632	−	0.0761287i
$953$	−22.6943	+	10.9290i	−0.735140	+	0.354025i	−0.763703	−	0.645567i	$-0.776621\pi$
$953$	−22.6943	+	10.9290i	−0.735140	+	0.354025i	0.0285637	+	0.999592i	$0.490907\pi$
$954$	3.38285	−	1.62909i	0.109524	−	0.0527438i
$955$	−10.8638	+	47.5975i	−0.351545	+	1.54022i
$956$	−2.71207	+	11.8824i	−0.0877147	+	0.384303i
$957$	−78.1794	+	37.6492i	−2.52718	+	1.21703i
$958$	−1.25541	+	0.604576i	−0.0405606	+	0.0195329i
$959$	−21.4864	+	26.3205i	−0.693832	+	0.849934i
$960$	−43.0344	−	20.7243i	−1.38893	−	0.668873i
$961$	−14.2681			−0.460261
$962$	−0.450558			−0.0145266
$963$	69.8228	+	33.6249i	2.25001	+	1.08355i
$964$	4.24714	−	5.32575i	0.136791	−	0.171531i
$965$	3.24297	−	14.2084i	0.104395	−	0.457384i
$966$	−0.0589365	+	0.245267i	−0.00189625	+	0.00789133i
$967$	4.88076	+	21.3840i	0.156955	+	0.687664i	0.990762	+	0.135609i	$0.0432990\pi$
$967$	4.88076	+	21.3840i	0.156955	+	0.687664i	−0.833808	+	0.552055i	$0.813844\pi$
$968$	−0.417336	−	0.200978i	−0.0134137	−	0.00645968i
$969$	4.29323	+	18.8099i	0.137918	+	0.604260i
$970$	−1.53626	+	1.92641i	−0.0493263	+	0.0618532i
$971$	−1.25723	+	5.50829i	−0.0403465	+	0.176769i	−0.991087	−	0.133220i	$-0.957468\pi$
$971$	−1.25723	+	5.50829i	−0.0403465	+	0.176769i	0.950740	+	0.309989i	$0.100325\pi$
$972$	−10.3219	−	12.9433i	−0.331077	−	0.415157i
$973$	32.4464	+	41.6540i	1.04018	+	1.33536i
$974$	−0.0366446	+	0.0459509i	−0.00117417	+	0.00147236i
$975$	0.147318	+	0.184731i	0.00471794	+	0.00591611i
$976$	16.7295	−	8.05650i	0.535498	−	0.257882i
$977$	−2.58619	−	3.24298i	−0.0827395	−	0.103752i	0.738739	−	0.673992i	$-0.235422\pi$
$977$	−2.58619	−	3.24298i	−0.0827395	−	0.103752i	−0.821478	+	0.570240i	$0.806850\pi$
$978$	2.37906	+	10.4234i	0.0760741	+	0.333302i
$979$	14.4619			0.462203
$980$	27.0912	+	13.8176i	0.865396	+	0.441388i
$981$	−70.0641			−2.23697
$982$	0.837097	+	3.66756i	0.0267128	+	0.117037i
$983$	12.2736	+	15.3906i	0.391468	+	0.490885i	0.938040	−	0.346527i	$-0.112639\pi$
$983$	12.2736	+	15.3906i	0.391468	+	0.490885i	−0.546572	+	0.837412i	$0.684068\pi$
$984$	−4.43261	+	2.13463i	−0.141306	+	0.0680496i
$985$	−13.7517	−	17.2441i	−0.438167	−	0.549444i
$986$	1.23653	−	1.55056i	0.0393792	−	0.0493800i
$987$	−54.8951	+	67.2457i	−1.74733	+	2.14045i
$988$	2.49301	+	3.12614i	0.0793132	+	0.0994556i
$989$	0.157013	−	0.687919i	0.00499272	−	0.0218746i
$990$	3.84650	−	4.82335i	0.122250	−	0.153296i
$991$	2.96958	+	13.0106i	0.0943317	+	0.413294i	0.999941	−	0.0108178i	$-0.00344347\pi$
$991$	2.96958	+	13.0106i	0.0943317	+	0.413294i	−0.905610	+	0.424112i	$0.860586\pi$
$992$	6.51165	+	3.13585i	0.206745	+	0.0995632i
$993$	21.3780	+	93.6631i	0.678410	+	2.97231i
$994$	1.61380	+	2.07177i	0.0511868	+	0.0657124i
$995$	8.50299	−	37.2540i	0.269563	−	1.18103i
$996$	−15.3077	+	19.1953i	−0.485044	+	0.608226i
$997$	−44.0102	−	21.1942i	−1.39382	−	0.671226i	−0.421919	−	0.906633i	$-0.638643\pi$
$997$	−44.0102	−	21.1942i	−1.39382	−	0.671226i	−0.971897	+	0.235407i	$0.924358\pi$
$998$	−0.362575			−0.0114771
$999$	−46.5952			−1.47421

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.2.e.b.36.1	yes	12
3.2	odd	2		441.2.u.b.379.2		12
4.3	odd	2		784.2.u.b.673.2		12
7.2	even	3		343.2.g.d.312.1		12
7.3	odd	6		343.2.g.c.128.1		12
7.4	even	3		343.2.g.b.128.1		12
7.5	odd	6		343.2.g.a.312.1		12
7.6	odd	2		343.2.e.b.246.1		12
49.8	even	7		2401.2.a.c.1.4		6
49.9	even	21		343.2.g.b.67.1		12
49.15	even	7	inner	49.2.e.b.15.1	✓	12
49.24	odd	42		343.2.g.a.177.1		12
49.25	even	21		343.2.g.d.177.1		12
49.34	odd	14		343.2.e.b.99.1		12
49.40	odd	42		343.2.g.c.67.1		12
49.41	odd	14		2401.2.a.d.1.4		6
147.113	odd	14		441.2.u.b.64.2		12
196.15	odd	14		784.2.u.b.113.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.e.b.15.1	✓	12	49.15	even	7	inner
49.2.e.b.36.1	yes	12	1.1	even	1	trivial
343.2.e.b.99.1		12	49.34	odd	14
343.2.e.b.246.1		12	7.6	odd	2
343.2.g.a.177.1		12	49.24	odd	42
343.2.g.a.312.1		12	7.5	odd	6
343.2.g.b.67.1		12	49.9	even	21
343.2.g.b.128.1		12	7.4	even	3
343.2.g.c.67.1		12	49.40	odd	42
343.2.g.c.128.1		12	7.3	odd	6
343.2.g.d.177.1		12	49.25	even	21
343.2.g.d.312.1		12	7.2	even	3
441.2.u.b.64.2		12	147.113	odd	14
441.2.u.b.379.2		12	3.2	odd	2
784.2.u.b.113.2		12	196.15	odd	14
784.2.u.b.673.2		12	4.3	odd	2
2401.2.a.c.1.4		6	49.8	even	7
2401.2.a.d.1.4		6	49.41	odd	14

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	49.e (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0332580 + 0.145713i) q^{2} +(-1.81507 - 2.27603i) q^{3} +(1.78181 - 0.858075i) q^{4} +(1.36967 + 1.71752i) q^{5} +(0.271281 - 0.340175i) q^{6} +(-2.64558 - 0.0302261i) q^{7} +(0.370666 + 0.464800i) q^{8} +(-1.21825 + 5.33750i) q^{9} +(-0.204712 + 0.256700i) q^{10} +(0.763709 + 3.34603i) q^{11} +(-5.18711 - 2.49798i) q^{12} +(-0.103718 - 0.454418i) q^{13} +(-0.0835824 - 0.386500i) q^{14} +(1.42306 - 6.23482i) q^{15} +(2.41070 - 3.02293i) q^{16} +(1.37657 + 0.662922i) q^{17} -0.818260 q^{18} -4.33771 q^{19} +(3.91426 + 1.88501i) q^{20} +(4.73311 + 6.07627i) q^{21} +(-0.462160 + 0.222565i) q^{22} +(0.197424 - 0.0950744i) q^{23} +(0.385113 - 1.68729i) q^{24} +(0.0387481 - 0.169766i) q^{25} +(0.0627651 - 0.0302261i) q^{26} +(6.49095 - 3.12588i) q^{27} +(-4.73986 + 2.21625i) q^{28} +(-7.82477 - 3.76821i) q^{29} +0.955822 q^{30} +4.09046 q^{31} +(1.59191 + 0.766624i) q^{32} +(6.22946 - 7.81149i) q^{33} +(-0.0508143 + 0.222632i) q^{34} +(-3.57167 - 4.58522i) q^{35} +(2.40929 + 10.5558i) q^{36} +(-5.82710 - 2.80618i) q^{37} +(-0.144263 - 0.632060i) q^{38} +(-0.846011 + 1.06086i) q^{39} +(-0.290611 + 1.27325i) q^{40} +(-1.77240 - 2.22252i) q^{41} +(-0.727976 + 0.891760i) q^{42} +(2.00772 - 2.51761i) q^{43} +(4.23193 + 5.30667i) q^{44} +(-10.8359 + 5.21827i) q^{45} +(0.0204195 + 0.0256052i) q^{46} +(2.50791 + 10.9879i) q^{47} -11.2559 q^{48} +(6.99817 + 0.159931i) q^{49} +0.0260258 q^{50} +(-0.989747 - 4.33636i) q^{51} +(-0.574730 - 0.720689i) q^{52} +(-4.13420 + 1.99092i) q^{53} +(0.671357 + 0.841855i) q^{54} +(-4.70082 + 5.89465i) q^{55} +(-0.966577 - 1.24087i) q^{56} +(7.87324 + 9.87273i) q^{57} +(0.288840 - 1.26549i) q^{58} +(4.49188 - 5.63264i) q^{59} +(-2.81433 - 12.3304i) q^{60} +(4.32681 + 2.08368i) q^{61} +(0.136041 + 0.596034i) q^{62} +(3.38431 - 14.0840i) q^{63} +(1.66198 - 7.28160i) q^{64} +(0.638410 - 0.800541i) q^{65} +(1.34541 + 0.647918i) q^{66} +6.29811 q^{67} +3.02163 q^{68} +(-0.574730 - 0.276775i) q^{69} +(0.549340 - 0.672933i) q^{70} +(-5.98346 + 2.88148i) q^{71} +(-2.93244 + 1.41219i) q^{72} +(-0.817597 + 3.58213i) q^{73} +(0.215099 - 0.942411i) q^{74} +(-0.456723 + 0.219946i) q^{75} +(-7.72897 + 3.72208i) q^{76} +(-1.91931 - 8.87526i) q^{77} +(-0.182718 - 0.0879925i) q^{78} +3.46554 q^{79} +8.49380 q^{80} +(-4.09832 - 1.97364i) q^{81} +(0.264903 - 0.332178i) q^{82} +(0.948934 - 4.15755i) q^{83} +(13.6474 + 6.76539i) q^{84} +(0.746875 + 3.27227i) q^{85} +(0.433621 + 0.208821i) q^{86} +(5.62596 + 24.6489i) q^{87} +(-1.27215 + 1.59523i) q^{88} +(0.937643 - 4.10808i) q^{89} +(-1.12075 - 1.40537i) q^{90} +(0.260658 + 1.20533i) q^{91} +(0.270191 - 0.338809i) q^{92} +(-7.42448 - 9.31000i) q^{93} +(-1.51767 + 0.730871i) q^{94} +(-5.94124 - 7.45008i) q^{95} +(-1.14457 - 5.01470i) q^{96} +7.50450 q^{97} +(0.209441 + 1.02504i) q^{98} -18.7898 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + 2 q^{4} - 7 q^{5} - 7 q^{6} - 7 q^{7} + 6 q^{8} - 8 q^{9} + 14 q^{10} - 8 q^{11} - 14 q^{12} + 7 q^{13} - 28 q^{14} - 7 q^{15} + 16 q^{16} + 20 q^{18} - 14 q^{19} + 7 q^{20} + 21 q^{21}+ \cdots - 18 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 + 2 * q^4 - 7 * q^5 - 7 * q^6 - 7 * q^7 + 6 * q^8 - 8 * q^9 + 14 * q^10 - 8 * q^11 - 14 * q^12 + 7 * q^13 - 28 * q^14 - 7 * q^15 + 16 * q^16 + 20 * q^18 - 14 * q^19 + 7 * q^20 + 21 * q^21 + 13 * q^22 - 2 * q^23 + 3 * q^25 - 7 * q^26 + 21 * q^27 + 14 * q^28 - 11 * q^29 + 42 * q^30 - 14 * q^31 - 24 * q^32 + 35 * q^33 - 42 * q^34 + 21 * q^35 - 13 * q^36 - 30 * q^37 + 21 * q^38 + 21 * q^41 - 35 * q^42 + 17 * q^43 - 6 * q^44 - 49 * q^45 - 16 * q^46 - 21 * q^47 + 7 * q^49 - 46 * q^50 + 7 * q^51 - 7 * q^52 + 6 * q^53 + 42 * q^54 - 28 * q^55 - 14 * q^56 + 7 * q^57 - 32 * q^58 + 14 * q^59 - 28 * q^60 - 7 * q^61 + 56 * q^62 + 14 * q^63 + 14 * q^64 + 14 * q^65 - 28 * q^66 + 48 * q^67 + 56 * q^68 - 7 * q^69 + 21 * q^70 - 39 * q^71 - 4 * q^72 + 42 * q^73 + 61 * q^74 + 7 * q^75 - 28 * q^76 + 21 * q^77 - 16 * q^79 + 42 * q^80 - 25 * q^81 + 28 * q^82 - 7 * q^83 + 42 * q^84 + 28 * q^85 + 17 * q^86 + 7 * q^87 - 11 * q^88 - 14 * q^89 - 14 * q^90 - 21 * q^91 + 16 * q^92 - 70 * q^93 - 49 * q^94 - 7 * q^95 - 70 * q^96 - 28 * q^97 - 28 * q^98 - 18 * q^99

Introduction

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