LMFDB - Embedded newform 192.2.r.a.13.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,2,Mod(13,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

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

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

chi := DirichletCharacter("192.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.r (of order $16$, degree $8$, 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:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			13.13
Character	$\chi$	$=$	192.13
Dual form			192.2.r.a.133.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.929504 + 1.06584i) q^{2} +(-0.831470 + 0.555570i) q^{3} +(-0.272044 + 1.98141i) q^{4} +(-4.03340 + 0.802293i) q^{5} +(-1.36501 - 0.369811i) q^{6} +(-0.0612023 - 0.147755i) q^{7} +(-2.36474 + 1.55177i) q^{8} +(0.382683 - 0.923880i) q^{9} +O(q^{10})$	\(q+(0.929504 + 1.06584i) q^{2} +(-0.831470 + 0.555570i) q^{3} +(-0.272044 + 1.98141i) q^{4} +(-4.03340 + 0.802293i) q^{5} +(-1.36501 - 0.369811i) q^{6} +(-0.0612023 - 0.147755i) q^{7} +(-2.36474 + 1.55177i) q^{8} +(0.382683 - 0.923880i) q^{9} +(-4.60418 - 3.55324i) q^{10} +(-0.294415 + 0.440623i) q^{11} +(-0.874617 - 1.79862i) q^{12} +(4.43463 + 0.882103i) q^{13} +(0.100596 - 0.202571i) q^{14} +(2.90792 - 2.90792i) q^{15} +(-3.85198 - 1.07806i) q^{16} +(4.35026 + 4.35026i) q^{17} +(1.34042 - 0.450869i) q^{18} +(-1.57072 + 7.89653i) q^{19} +(-0.492413 - 8.21009i) q^{20} +(0.132976 + 0.0888519i) q^{21} +(-0.743295 + 0.0957609i) q^{22} +(-4.54457 - 1.88242i) q^{23} +(1.10409 - 2.60403i) q^{24} +(11.0053 - 4.55853i) q^{25} +(3.18182 + 5.54654i) q^{26} +(0.195090 + 0.980785i) q^{27} +(0.309414 - 0.0810710i) q^{28} +(-0.558645 - 0.836071i) q^{29} +(5.80231 + 0.396463i) q^{30} -0.971497i q^{31} +(-2.43139 - 5.10767i) q^{32} -0.529933i q^{33} +(-0.593110 + 8.68028i) q^{34} +(0.365397 + 0.546855i) q^{35} +(1.72648 + 1.00959i) q^{36} +(-0.153493 - 0.771661i) q^{37} +(-9.87646 + 5.66572i) q^{38} +(-4.17733 + 1.73031i) q^{39} +(8.29297 - 8.15615i) q^{40} +(4.03464 + 1.67120i) q^{41} +(0.0288998 + 0.224320i) q^{42} +(-5.11173 - 3.41555i) q^{43} +(-0.792962 - 0.703226i) q^{44} +(-0.802293 + 4.03340i) q^{45} +(-2.21783 - 6.59352i) q^{46} +(-0.409517 - 0.409517i) q^{47} +(3.80175 - 1.24367i) q^{48} +(4.93166 - 4.93166i) q^{49} +(15.0881 + 7.49271i) q^{50} +(-6.03398 - 1.20023i) q^{51} +(-2.95422 + 8.54686i) q^{52} +(-1.55137 + 2.32179i) q^{53} +(-0.864026 + 1.11958i) q^{54} +(0.833984 - 2.01342i) q^{55} +(0.374011 + 0.254431i) q^{56} +(-3.08107 - 7.43837i) q^{57} +(0.371858 - 1.37256i) q^{58} +(7.20772 - 1.43370i) q^{59} +(4.97071 + 6.55287i) q^{60} +(3.19336 - 2.13373i) q^{61} +(1.03546 - 0.903010i) q^{62} -0.159929 q^{63} +(3.18399 - 7.33909i) q^{64} -18.5943 q^{65} +(0.564825 - 0.492575i) q^{66} +(10.2146 - 6.82514i) q^{67} +(-9.80311 + 7.43619i) q^{68} +(4.82449 - 0.959650i) q^{69} +(-0.243224 + 0.897759i) q^{70} +(3.81060 + 9.19961i) q^{71} +(0.528706 + 2.77857i) q^{72} +(-5.05384 + 12.2011i) q^{73} +(0.679798 - 0.880862i) q^{74} +(-6.61795 + 9.90447i) q^{75} +(-15.2190 - 5.26044i) q^{76} +(0.0831233 + 0.0165342i) q^{77} +(-5.72708 - 2.84405i) q^{78} +(-1.43481 + 1.43481i) q^{79} +(16.4015 + 1.25783i) q^{80} +(-0.707107 - 0.707107i) q^{81} +(1.96897 + 5.85368i) q^{82} +(-1.31569 + 6.61440i) q^{83} +(-0.212228 + 0.239309i) q^{84} +(-21.0365 - 14.0562i) q^{85} +(-1.11094 - 8.62308i) q^{86} +(0.928992 + 0.384801i) q^{87} +(0.0124669 - 1.49882i) q^{88} +(8.40267 - 3.48050i) q^{89} +(-5.04471 + 2.89394i) q^{90} +(-0.141074 - 0.709227i) q^{91} +(4.96617 - 8.49256i) q^{92} +(0.539735 + 0.807770i) q^{93} +(0.0558331 - 0.817128i) q^{94} -33.1101i q^{95} +(4.85930 + 2.89607i) q^{96} -1.21732i q^{97} +(9.84038 + 0.672378i) q^{98} +(0.294415 + 0.440623i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 16 q^{22} - 80 q^{26} - 80 q^{28} - 80 q^{32} - 80 q^{34} - 80 q^{38} - 80 q^{40} - 16 q^{44} + 48 q^{50} - 32 q^{51} + 48 q^{52} + 16 q^{54} - 64 q^{55} + 112 q^{56} - 128 q^{59} + 96 q^{60} + 96 q^{62} - 32 q^{63} + 96 q^{64} + 96 q^{66} - 32 q^{67} + 96 q^{68} + 96 q^{70} - 128 q^{71} + 112 q^{74} - 64 q^{75} + 16 q^{76} + 48 q^{78} - 32 q^{79} + 48 q^{80} - 80 q^{82} - 80 q^{88} - 96 q^{94}+O(q^{100}) $ 128 * q - 16 * q^22 - 80 * q^26 - 80 * q^28 - 80 * q^32 - 80 * q^34 - 80 * q^38 - 80 * q^40 - 16 * q^44 + 48 * q^50 - 32 * q^51 + 48 * q^52 + 16 * q^54 - 64 * q^55 + 112 * q^56 - 128 * q^59 + 96 * q^60 + 96 * q^62 - 32 * q^63 + 96 * q^64 + 96 * q^66 - 32 * q^67 + 96 * q^68 + 96 * q^70 - 128 * q^71 + 112 * q^74 - 64 * q^75 + 16 * q^76 + 48 * q^78 - 32 * q^79 + 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$1$	$1$	$e\left(\frac{15}{16}\right)$

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 $

$2$	0.929504	+	1.06584i	0.657259	+	0.753665i
$2$	0.929504	+	1.06584i	0.657259	+	0.753665i
$3$	−0.831470	+	0.555570i	−0.480049	+	0.320759i
$3$	−0.831470	+	0.555570i	−0.480049	+	0.320759i
$4$	−0.272044	+	1.98141i	−0.136022	+	0.990706i
$5$	−4.03340	+	0.802293i	−1.80379	+	0.358797i	−0.978554	−	0.205989i	$-0.933959\pi$
$5$	−4.03340	+	0.802293i	−1.80379	+	0.358797i	−0.825238	+	0.564786i	$0.808959\pi$
$6$	−1.36501	−	0.369811i	−0.557261	−	0.150975i
$7$	−0.0612023	−	0.147755i	−0.0231323	−	0.0558463i	0.911891	−	0.410432i	$-0.134622\pi$
$7$	−0.0612023	−	0.147755i	−0.0231323	−	0.0558463i	−0.935024	+	0.354585i	$0.884622\pi$
$8$	−2.36474	+	1.55177i	−0.836062	+	0.548635i
$9$	0.382683	−	0.923880i	0.127561	−	0.307960i
$10$	−4.60418	−	3.55324i	−1.45597	−	1.12363i
$11$	−0.294415	+	0.440623i	−0.0887694	+	0.132853i	−0.873197	−	0.487368i	$-0.837957\pi$
$11$	−0.294415	+	0.440623i	−0.0887694	+	0.132853i	0.784427	+	0.620221i	$0.212957\pi$
$12$	−0.874617	−	1.79862i	−0.252480	−	0.519218i
$13$	4.43463	+	0.882103i	1.22995	+	0.244651i	0.766948	−	0.641709i	$-0.221774\pi$
$13$	4.43463	+	0.882103i	1.22995	+	0.244651i	0.462997	+	0.886360i	$0.346774\pi$
$14$	0.100596	−	0.202571i	0.0268855	−	0.0541395i
$15$	2.90792	−	2.90792i	0.750822	−	0.750822i
$16$	−3.85198	−	1.07806i	−0.962996	−	0.269515i
$17$	4.35026	+	4.35026i	1.05509	+	1.05509i	0.998391	+	0.0567015i	$0.0180583\pi$
$17$	4.35026	+	4.35026i	1.05509	+	1.05509i	0.0567015	+	0.998391i	$0.481942\pi$
$18$	1.34042	−	0.450869i	0.315939	−	0.106271i
$19$	−1.57072	+	7.89653i	−0.360347	+	1.81159i	0.195959	+	0.980612i	$0.437218\pi$
$19$	−1.57072	+	7.89653i	−0.360347	+	1.81159i	−0.556307	+	0.830977i	$0.687782\pi$
$20$	−0.492413	−	8.21009i	−0.110107	−	1.83583i
$21$	0.132976	+	0.0888519i	0.0290178	+	0.0193891i
$22$	−0.743295	+	0.0957609i	−0.158471	+	0.0204163i
$23$	−4.54457	−	1.88242i	−0.947608	−	0.392512i	−0.145277	−	0.989391i	$-0.546407\pi$
$23$	−4.54457	−	1.88242i	−0.947608	−	0.392512i	−0.802331	+	0.596879i	$0.796407\pi$
$24$	1.10409	−	2.60403i	0.225371	−	0.531546i
$25$	11.0053	−	4.55853i	2.20105	−	0.911705i
$26$	3.18182	+	5.54654i	0.624007	+	1.08777i
$27$	0.195090	+	0.980785i	0.0375451	+	0.188752i
$28$	0.309414	−	0.0810710i	0.0584737	−	0.0153210i
$29$	−0.558645	−	0.836071i	−0.103738	−	0.155254i	0.775969	−	0.630771i	$-0.217261\pi$
$29$	−0.558645	−	0.836071i	−0.103738	−	0.155254i	−0.879707	+	0.475516i	$0.842261\pi$
$30$	5.80231	+	0.396463i	1.05935	+	0.0723839i
$31$		−	0.971497i		−	0.174486i	−0.996187	−	0.0872430i	$-0.972194\pi$
$31$		−	0.971497i		−	0.174486i	0.996187	−	0.0872430i	$-0.0278057\pi$
$32$	−2.43139	−	5.10767i	−0.429814	−	0.902918i
$33$		−	0.529933i		−	0.0922495i
$34$	−0.593110	+	8.68028i	−0.101717	+	1.48866i
$35$	0.365397	+	0.546855i	0.0617633	+	0.0924353i
$36$	1.72648	+	1.00959i	0.287747	+	0.168265i
$37$	−0.153493	−	0.771661i	−0.0252341	−	0.126860i	0.966115	−	0.258112i	$-0.0831004\pi$
$37$	−0.153493	−	0.771661i	−0.0252341	−	0.126860i	−0.991349	+	0.131252i	$0.958100\pi$
$38$	−9.87646	+	5.66572i	−1.60217	+	0.919102i
$39$	−4.17733	+	1.73031i	−0.668908	+	0.277071i
$40$	8.29297	−	8.15615i	1.31123	−	1.28960i
$41$	4.03464	+	1.67120i	0.630104	+	0.260998i	0.674797	−	0.738003i	$-0.264231\pi$
$41$	4.03464	+	1.67120i	0.630104	+	0.260998i	−0.0446932	+	0.999001i	$0.514231\pi$
$42$	0.0288998	+	0.224320i	0.00445934	+	0.0346134i
$43$	−5.11173	−	3.41555i	−0.779532	−	0.520867i	0.100981	−	0.994888i	$-0.467802\pi$
$43$	−5.11173	−	3.41555i	−0.779532	−	0.520867i	−0.880513	+	0.474022i	$0.842802\pi$
$44$	−0.792962	−	0.703226i	−0.119543	−	0.106015i
$45$	−0.802293	+	4.03340i	−0.119599	+	0.601264i
$46$	−2.21783	−	6.59352i	−0.327001	−	0.972161i
$47$	−0.409517	−	0.409517i	−0.0597341	−	0.0597341i	0.676609	−	0.736343i	$-0.263449\pi$
$47$	−0.409517	−	0.409517i	−0.0597341	−	0.0597341i	−0.736343	+	0.676609i	$0.763449\pi$
$48$	3.80175	−	1.24367i	0.548735	−	0.179509i
$49$	4.93166	−	4.93166i	0.704523	−	0.704523i
$50$	15.0881	+	7.49271i	2.13378	+	1.05963i
$51$	−6.03398	−	1.20023i	−0.844926	−	0.168066i
$52$	−2.95422	+	8.54686i	−0.409677	+	1.18524i
$53$	−1.55137	+	2.32179i	−0.213098	+	0.318923i	−0.922584	−	0.385796i	$-0.873927\pi$
$53$	−1.55137	+	2.32179i	−0.213098	+	0.318923i	0.709487	+	0.704719i	$0.248927\pi$
$54$	−0.864026	+	1.11958i	−0.117579	+	0.152356i
$55$	0.833984	−	2.01342i	0.112454	−	0.271489i
$56$	0.374011	+	0.254431i	0.0499793	+	0.0339998i
$57$	−3.08107	−	7.43837i	−0.408098	−	0.985237i
$58$	0.371858	−	1.37256i	0.0488273	−	0.180226i
$59$	7.20772	−	1.43370i	0.938365	−	0.186652i	0.297863	−	0.954609i	$-0.403726\pi$
$59$	7.20772	−	1.43370i	0.938365	−	0.186652i	0.640502	+	0.767956i	$0.278726\pi$
$60$	4.97071	+	6.55287i	0.641715	+	0.845972i
$61$	3.19336	−	2.13373i	0.408868	−	0.273197i	−0.334082	−	0.942544i	$-0.608426\pi$
$61$	3.19336	−	2.13373i	0.408868	−	0.273197i	0.742950	+	0.669347i	$0.233426\pi$
$62$	1.03546	−	0.903010i	0.131504	−	0.114682i
$63$	−0.159929			−0.0201492
$64$	3.18399	−	7.33909i	0.397999	−	0.917386i
$65$	−18.5943			−2.30634
$66$	0.564825	−	0.492575i	0.0695252	−	0.0606318i
$67$	10.2146	−	6.82514i	1.24791	−	0.833824i	0.256744	−	0.966480i	$-0.417350\pi$
$67$	10.2146	−	6.82514i	1.24791	−	0.833824i	0.991162	+	0.132655i	$0.0423504\pi$
$68$	−9.80311	+	7.43619i	−1.18880	+	0.901771i
$69$	4.82449	−	0.959650i	0.580800	−	0.115528i
$70$	−0.243224	+	0.897759i	−0.0290708	+	0.107303i
$71$	3.81060	+	9.19961i	0.452235	+	1.09179i	0.971470	+	0.237161i	$0.0762169\pi$
$71$	3.81060	+	9.19961i	0.452235	+	1.09179i	−0.519235	+	0.854632i	$0.673783\pi$
$72$	0.528706	+	2.77857i	0.0623086	+	0.327458i
$73$	−5.05384	+	12.2011i	−0.591507	+	1.42803i	0.290539	+	0.956863i	$0.406165\pi$
$73$	−5.05384	+	12.2011i	−0.591507	+	1.42803i	−0.882047	+	0.471162i	$0.843835\pi$
$74$	0.679798	−	0.880862i	0.0790249	−	0.102398i
$75$	−6.61795	+	9.90447i	−0.764175	+	1.14367i
$76$	−15.2190	−	5.26044i	−1.74574	−	0.603414i
$77$	0.0831233	+	0.0165342i	0.00947278	+	0.00188425i
$78$	−5.72708	−	2.84405i	−0.648464	−	0.322025i
$79$	−1.43481	+	1.43481i	−0.161429	+	0.161429i	−0.783199	−	0.621771i	$-0.786414\pi$
$79$	−1.43481	+	1.43481i	−0.161429	+	0.161429i	0.621771	+	0.783199i	$0.286414\pi$
$80$	16.4015	+	1.25783i	1.83375	+	0.140630i
$81$	−0.707107	−	0.707107i	−0.0785674	−	0.0785674i
$82$	1.96897	+	5.85368i	0.217437	+	0.646430i
$83$	−1.31569	+	6.61440i	−0.144415	+	0.726025i	0.838925	+	0.544248i	$0.183185\pi$
$83$	−1.31569	+	6.61440i	−0.144415	+	0.726025i	−0.983340	+	0.181777i	$0.941815\pi$
$84$	−0.212228	+	0.239309i	−0.0231559	+	0.0261108i
$85$	−21.0365	−	14.0562i	−2.28173	−	1.52460i
$86$	−1.11094	−	8.62308i	−0.119795	−	0.929850i
$87$	0.928992	+	0.384801i	0.0995984	+	0.0412550i
$88$	0.0124669	−	1.49882i	0.00132898	−	0.159775i
$89$	8.40267	−	3.48050i	0.890681	−	0.368932i	0.110052	−	0.993926i	$-0.464898\pi$
$89$	8.40267	−	3.48050i	0.890681	−	0.368932i	0.780630	+	0.624994i	$0.214898\pi$
$90$	−5.04471	+	2.89394i	−0.531759	+	0.305049i
$91$	−0.141074	−	0.709227i	−0.0147886	−	0.0743472i
$92$	4.96617	−	8.49256i	0.517759	−	0.885410i
$93$	0.539735	+	0.807770i	0.0559679	+	0.0837618i
$94$	0.0558331	−	0.817128i	0.00575874	−	0.0842803i
$95$		−	33.1101i		−	3.39702i
$96$	4.85930	+	2.89607i	0.495950	+	0.295579i
$97$		−	1.21732i		−	0.123600i	−0.998089	−	0.0617999i	$-0.980316\pi$
$97$		−	1.21732i		−	0.123600i	0.998089	−	0.0617999i	$-0.0196840\pi$
$98$	9.84038	+	0.672378i	0.994028	+	0.0679204i
$99$	0.294415	+	0.440623i	0.0295898	+	0.0442843i
$100$	6.03841	+	23.0461i	0.603841	+	2.30461i
$101$	−0.903088	−	4.54013i	−0.0898606	−	0.451760i	−0.999351	−	0.0360338i	$-0.988528\pi$
$101$	−0.903088	−	4.54013i	−0.0898606	−	0.451760i	0.909490	−	0.415726i	$-0.136472\pi$
$102$	−4.32935	−	7.54690i	−0.428670	−	0.747255i
$103$	−12.2443	+	5.07177i	−1.20647	+	0.499736i	−0.893084	−	0.449890i	$-0.851463\pi$
$103$	−12.2443	+	5.07177i	−1.20647	+	0.499736i	−0.313386	+	0.949626i	$0.601463\pi$
$104$	−11.8556	+	4.79560i	−1.16253	+	0.470248i
$105$	−0.607632	−	0.251690i	−0.0592988	−	0.0245624i
$106$	−3.91668	+	0.504597i	−0.380421	+	0.0490108i
$107$	−8.83634	−	5.90426i	−0.854242	−	0.570786i	0.0495438	−	0.998772i	$-0.484223\pi$
$107$	−8.83634	−	5.90426i	−0.854242	−	0.570786i	−0.903785	+	0.427986i	$0.859223\pi$
$108$	−1.99641	+	0.119738i	−0.192105	+	0.0115218i
$109$	−1.10574	+	5.55892i	−0.105910	+	0.532448i	0.891007	+	0.453990i	$0.150000\pi$
$109$	−1.10574	+	5.55892i	−0.105910	+	0.532448i	−0.996917	+	0.0784581i	$0.975000\pi$
$110$	2.92118	−	0.982583i	0.278523	−	0.0936856i
$111$	0.556337	+	0.556337i	0.0528052	+	0.0528052i
$112$	0.0764610	+	0.635131i	0.00722488	+	0.0600143i
$113$	−4.55586	+	4.55586i	−0.428579	+	0.428579i	−0.888144	−	0.459565i	$-0.848005\pi$
$113$	−4.55586	+	4.55586i	−0.428579	+	0.428579i	0.459565	+	0.888144i	$0.348005\pi$
$114$	5.06427	−	10.1979i	0.474312	−	0.955125i
$115$	19.8403	+	3.94648i	1.85012	+	0.368012i
$116$	1.80858	−	0.879457i	0.167922	−	0.0816556i
$117$	2.51202	−	3.75950i	0.232236	−	0.347566i
$118$	8.22771	+	6.34966i	0.757422	+	0.584534i
$119$	0.376528	−	0.909020i	0.0345163	−	0.0833297i
$120$	−2.36404	+	11.3889i	−0.215806	+	1.03966i
$121$	4.10205	+	9.90322i	0.372914	+	0.900293i
$122$	5.24247	+	1.42030i	0.474631	+	0.128588i
$123$	−4.28315	+	0.851971i	−0.386198	+	0.0768196i
$124$	1.92493	+	0.264289i	0.172864	+	0.0237339i
$125$	−23.6346	+	15.7921i	−2.11394	+	1.41249i
$126$	−0.148655	−	0.170460i	−0.0132432	−	0.0151857i
$127$	−7.96147			−0.706467			−0.353233	−	0.935535i	$-0.614918\pi$
$127$	−7.96147			−0.706467			−0.353233	+	0.935535i	$0.614918\pi$
$128$	10.7818	−	3.42808i	0.952990	−	0.303002i
$129$	6.14783			0.541286
$130$	−17.2835	−	19.8187i	−1.51587	−	1.73821i
$131$	−0.738840	+	0.493677i	−0.0645528	+	0.0431328i	−0.587428	−	0.809277i	$-0.699859\pi$
$131$	−0.738840	+	0.493677i	−0.0645528	+	0.0431328i	0.522875	+	0.852409i	$0.324859\pi$
$132$	1.05001	+	0.144165i	0.0913921	+	0.0125479i
$133$	1.26289	−	0.251204i	0.109506	−	0.0217821i
$134$	16.7690	+	4.54311i	1.44862	+	0.392465i
$135$	−1.57376	−	3.79938i	−0.135447	−	0.326999i
$136$	−17.0379	−	3.53661i	−1.46098	−	0.303262i
$137$	4.85900	−	11.7307i	0.415133	−	1.00222i	−0.568606	−	0.822610i	$-0.692517\pi$
$137$	4.85900	−	11.7307i	0.415133	−	1.00222i	0.983738	−	0.179608i	$-0.0574830\pi$
$138$	5.50722	+	4.25015i	0.468806	+	0.361797i
$139$	−4.39048	+	6.57082i	−0.372396	+	0.557330i	−0.969580	−	0.244774i	$-0.921286\pi$
$139$	−4.39048	+	6.57082i	−0.372396	+	0.557330i	0.597184	+	0.802104i	$0.296286\pi$
$140$	−1.18295	+	0.575233i	−0.0999773	+	0.0486160i
$141$	0.568016	+	0.112985i	0.0478356	+	0.00951509i
$142$	−6.26337	+	12.6126i	−0.525610	+	1.05842i
$143$	−1.69430	+	1.69430i	−0.141684	+	0.141684i
$144$	−2.47009	+	3.14621i	−0.205841	+	0.262184i
$145$	2.92401	+	2.92401i	0.242826	+	0.242826i
$146$	−17.7020	+	5.95433i	−1.46503	+	0.492784i
$147$	−1.36064	+	6.84041i	−0.112224	+	0.564188i
$148$	1.57074	−	0.0942073i	0.129114	−	0.00774379i
$149$	9.54742	+	6.37938i	0.782155	+	0.522620i	0.881359	−	0.472448i	$-0.156629\pi$
$149$	9.54742	+	6.37938i	0.782155	+	0.522620i	−0.0992033	+	0.995067i	$0.531629\pi$
$150$	−16.7080	+	2.15254i	−1.36420	+	0.175754i
$151$	12.7205	+	5.26900i	1.03518	+	0.428785i	0.834579	−	0.550888i	$-0.185711\pi$
$151$	12.7205	+	5.26900i	1.03518	+	0.428785i	0.200599	+	0.979673i	$0.435711\pi$
$152$	−8.53930	−	21.1107i	−0.692629	−	1.71230i
$153$	5.68389	−	2.35434i	0.459515	−	0.190337i
$154$	0.0596405	+	0.103965i	0.00480597	+	0.00837774i
$155$	0.779425	+	3.91844i	0.0626050	+	0.314736i
$156$	−2.29203	−	8.74773i	−0.183510	−	0.700379i
$157$	2.05329	+	3.07297i	0.163871	+	0.245250i	0.904313	−	0.426870i	$-0.140384\pi$
$157$	2.05329	+	3.07297i	0.163871	+	0.245250i	−0.740442	+	0.672120i	$0.765384\pi$
$158$	−2.86295	−	0.195621i	−0.227764	−	0.0155627i
$159$		−	2.79240i		−	0.221452i
$160$	13.9046	+	18.6506i	1.09926	+	1.47446i
$161$			0.786693i			0.0620001i
$162$	0.0964062	−	1.41092i	0.00757439	−	0.110853i
$163$	0.123694	+	0.185121i	0.00968844	+	0.0144998i	0.836282	−	0.548299i	$-0.184725\pi$
$163$	0.123694	+	0.185121i	0.00968844	+	0.0144998i	−0.826594	+	0.562799i	$0.809725\pi$
$164$	−4.40893	+	7.53963i	−0.344280	+	0.588747i
$165$	0.425162	+	2.13743i	0.0330988	+	0.166399i
$166$	−8.27285	+	4.74580i	−0.642097	+	0.368345i
$167$	15.5057	−	6.42268i	1.19987	−	0.497002i	0.308912	−	0.951091i	$-0.400035\pi$
$167$	15.5057	−	6.42268i	1.19987	−	0.497002i	0.890956	+	0.454089i	$0.150035\pi$
$168$	−0.452333	−	0.00376242i	−0.0348982	−	0.000290277i
$169$	6.87740	+	2.84871i	0.529031	+	0.219132i
$170$	−4.57188	−	35.4869i	−0.350647	−	2.72172i
$171$	6.69436	+	4.47303i	0.511930	+	0.342061i
$172$	8.15823	−	9.19927i	0.622059	−	0.701438i
$173$	2.78892	−	14.0208i	0.212037	−	1.06598i	−0.717304	−	0.696761i	$-0.754624\pi$
$173$	2.78892	−	14.0208i	0.212037	−	1.06598i	0.929341	−	0.369223i	$-0.120376\pi$
$174$	0.453364	+	1.34783i	0.0343695	+	0.102179i
$175$	−1.34709	−	1.34709i	−0.101831	−	0.101831i
$176$	1.60910	−	1.37988i	0.121290	−	0.104012i
$177$	−5.19647	+	5.19647i	−0.390591	+	0.390591i
$178$	11.5200	+	5.72079i	0.863460	+	0.428791i
$179$	14.6864	+	2.92130i	1.09771	+	0.218348i	0.710538	−	0.703659i	$-0.248452\pi$
$179$	14.6864	+	2.92130i	1.09771	+	0.218348i	0.387173	+	0.922007i	$0.373452\pi$
$180$	−7.77357	−	2.68693i	−0.579408	−	0.200272i
$181$	0.866110	−	1.29623i	0.0643775	−	0.0963477i	−0.797884	−	0.602811i	$-0.794047\pi$
$181$	0.866110	−	1.29623i	0.0643775	−	0.0963477i	0.862262	+	0.506463i	$0.169047\pi$
$182$	0.624796	−	0.809592i	0.0463130	−	0.0600110i
$183$	−1.46974	+	3.54827i	−0.108646	+	0.262296i
$184$	13.6678	−	2.60071i	1.00760	−	0.191727i
$185$	1.23820	+	2.98927i	0.0910341	+	0.219776i
$186$	−0.359270	+	1.32610i	−0.0263430	+	0.0972342i
$187$	−3.19760	+	0.636043i	−0.233832	+	0.0465121i
$188$	0.922828	−	0.700015i	0.0673041	−	0.0510538i
$189$	0.132976	−	0.0888519i	0.00967260	−	0.00646303i
$190$	35.2901	−	30.7760i	2.56022	−	2.23272i
$191$	26.1299			1.89069			0.945345	−	0.326072i	$-0.105725\pi$
$191$	26.1299			1.89069			0.945345	+	0.326072i	$0.105725\pi$
$192$	1.42999	+	7.87116i	0.103200	+	0.568052i
$193$	−3.00179			−0.216073			−0.108037	−	0.994147i	$-0.534456\pi$
$193$	−3.00179			−0.216073			−0.108037	+	0.994147i	$0.534456\pi$
$194$	1.29747	−	1.13150i	0.0931528	−	0.0812370i
$195$	15.4606	−	10.3305i	1.10716	−	0.739780i
$196$	8.43002	+	11.1133i	0.602145	+	0.793806i
$197$	15.5847	−	3.09998i	1.11036	−	0.220865i	0.394355	−	0.918958i	$-0.370968\pi$
$197$	15.5847	−	3.09998i	1.11036	−	0.220865i	0.716007	+	0.698093i	$0.245968\pi$
$198$	−0.195975	+	0.723361i	−0.0139273	+	0.0514070i
$199$	−7.11704	−	17.1820i	−0.504513	−	1.21800i	−0.947002	−	0.321229i	$-0.895904\pi$
$199$	−7.11704	−	17.1820i	−0.504513	−	1.21800i	0.442488	−	0.896774i	$-0.354096\pi$
$200$	−18.9508	+	27.8574i	−1.34002	+	1.96982i
$201$	−4.70124	+	11.3498i	−0.331600	+	0.800553i
$202$	3.99964	−	5.18262i	0.281414	−	0.364648i
$203$	−0.0893436	+	0.133712i	−0.00627069	+	0.00938476i
$204$	4.01966	−	11.6293i	0.281433	−	0.814213i
$205$	−17.6141	−	3.50366i	−1.23022	−	0.244706i
$206$	−16.7869	−	8.33631i	−1.16960	−	0.580818i
$207$	−3.47826	+	3.47826i	−0.241756	+	0.241756i
$208$	−16.1312	−	8.17865i	−1.11850	−	0.567087i
$209$	−3.01695	−	3.01695i	−0.208687	−	0.208687i
$210$	−0.296535	−	0.881587i	−0.0204629	−	0.0608353i
$211$	2.63480	−	13.2460i	0.181387	−	0.911895i	−0.777668	−	0.628675i	$-0.783597\pi$
$211$	2.63480	−	13.2460i	0.181387	−	0.911895i	0.959055	−	0.283220i	$-0.0914025\pi$
$212$	−4.17839	−	3.70554i	−0.286973	−	0.254497i
$213$	−8.27943	−	5.53214i	−0.567297	−	0.379056i
$214$	−1.92041	−	14.9062i	−0.131276	−	1.01897i
$215$	23.3580	+	9.67518i	1.59300	+	0.659842i
$216$	−1.98330	−	2.01657i	−0.134946	−	0.137210i
$217$	−0.143544	+	0.0594578i	−0.00974439	+	0.00403626i
$218$	−6.95272	+	3.98849i	−0.470898	+	0.270135i
$219$	−2.57643	−	12.9526i	−0.174099	−	0.875253i
$220$	3.76253	+	2.20020i	0.253670	+	0.148338i
$221$	15.4544	+	23.1292i	1.03958	+	1.55584i
$222$	−0.0758504	+	1.11009i	−0.00509075	+	0.0745041i
$223$			15.5839i			1.04358i	0.853075	+	0.521788i	$0.174735\pi$
$223$			15.5839i			1.04358i	−0.853075	+	0.521788i	$0.825265\pi$
$224$	−0.605880	+	0.671853i	−0.0404820	+	0.0448900i
$225$		−	11.9120i		−	0.794133i
$226$	−9.09053	−	0.621141i	−0.604693	−	0.0413177i
$227$	−2.68903	−	4.02442i	−0.178477	−	0.267110i	0.731435	−	0.681912i	$-0.238851\pi$
$227$	−2.68903	−	4.02442i	−0.178477	−	0.267110i	−0.909912	+	0.414801i	$0.863851\pi$
$228$	15.5767	−	4.08132i	1.03159	−	0.270292i
$229$	−4.60850	−	23.1685i	−0.304538	−	1.53102i	−0.765406	−	0.643548i	$-0.777462\pi$
$229$	−4.60850	−	23.1685i	−0.304538	−	1.53102i	0.460868	−	0.887469i	$-0.347538\pi$
$230$	14.2353	+	24.8149i	0.938650	+	1.63625i
$231$	−0.0783004	+	0.0324331i	−0.00515179	+	0.00213394i
$232$	2.61844	+	1.11020i	0.171909	+	0.0728882i
$233$	−24.5900	−	10.1855i	−1.61095	−	0.667276i	−0.618037	−	0.786149i	$-0.712072\pi$
$233$	−24.5900	−	10.1855i	−1.61095	−	0.667276i	−0.992910	+	0.118873i	$0.962072\pi$
$234$	6.34196	−	0.817054i	0.414587	−	0.0534125i
$235$	1.98030	+	1.32319i	0.129180	+	0.0863156i
$236$	0.879945	+	14.6715i	0.0572795	+	0.955032i
$237$	0.395864	−	1.99014i	0.0257141	−	0.129274i
$238$	1.31886	−	0.443618i	0.0854888	−	0.0287555i
$239$	−3.60679	−	3.60679i	−0.233304	−	0.233304i	0.580766	−	0.814070i	$-0.302753\pi$
$239$	−3.60679	−	3.60679i	−0.233304	−	0.233304i	−0.814070	+	0.580766i	$0.802753\pi$
$240$	−14.3362	+	8.06635i	−0.925396	+	0.520681i
$241$	−7.86137	+	7.86137i	−0.506396	+	0.506396i	−0.913418	−	0.407023i	$-0.866567\pi$
$241$	−7.86137	+	7.86137i	−0.506396	+	0.506396i	0.407023	+	0.913418i	$0.366567\pi$
$242$	−6.74241	+	13.5772i	−0.433419	+	0.872777i
$243$	0.980785	+	0.195090i	0.0629174	+	0.0125150i
$244$	3.35907	+	6.90783i	0.215043	+	0.442228i
$245$	−15.9347	+	23.8480i	−1.01803	+	1.52359i
$246$	−4.88927	−	3.77325i	−0.311728	−	0.240574i
$247$	−13.9311	+	33.6327i	−0.886415	+	2.14000i
$248$	1.50754	+	2.29734i	0.0957291	+	0.145881i
$249$	−2.58081	−	6.23063i	−0.163552	−	0.394850i
$250$	−38.8004	−	10.5119i	−2.45395	−	0.664831i
$251$	7.60256	−	1.51224i	0.479870	−	0.0954520i	0.0507723	−	0.998710i	$-0.483832\pi$
$251$	7.60256	−	1.51224i	0.479870	−	0.0954520i	0.429097	+	0.903258i	$0.358832\pi$
$252$	0.0435077	−	0.316886i	0.00274073	−	0.0199619i
$253$	2.16743	−	1.44823i	0.136265	−	0.0910493i
$254$	−7.40022	−	8.48568i	−0.464331	−	0.532439i
$255$	25.3004			1.58437
$256$	13.6756	+	8.30535i	0.854723	+	0.519084i
$257$	−21.5954			−1.34708			−0.673541	−	0.739150i	$-0.735227\pi$
$257$	−21.5954			−1.34708			−0.673541	+	0.739150i	$0.735227\pi$
$258$	5.71444	+	6.55262i	0.355765	+	0.407949i
$259$	−0.104623	+	0.0699069i	−0.00650096	+	0.00434380i
$260$	5.05847	−	36.8431i	0.313713	−	2.28491i
$261$	−0.986213	+	0.196170i	−0.0610450	+	0.0121426i
$262$	−1.21294	−	0.328613i	−0.0749355	−	0.0203018i
$263$	1.07217	+	2.58844i	0.0661127	+	0.159610i	0.953483	−	0.301448i	$-0.0974699\pi$
$263$	1.07217	+	2.58844i	0.0661127	+	0.159610i	−0.887370	+	0.461058i	$0.847470\pi$
$264$	0.822336	+	1.25315i	0.0506113	+	0.0771262i
$265$	4.39455	−	10.6094i	0.269955	−	0.651729i
$266$	1.44160	+	1.11254i	0.0883903	+	0.0682145i
$267$	−5.05290	+	7.56220i	−0.309233	+	0.462799i
$268$	10.7446	+	22.0960i	0.656332	+	1.34973i
$269$	14.3901	+	2.86237i	0.877380	+	0.174522i	0.613177	−	0.789946i	$-0.289891\pi$
$269$	14.3901	+	2.86237i	0.877380	+	0.174522i	0.264203	+	0.964467i	$0.414891\pi$
$270$	2.58673	−	5.20892i	0.157424	−	0.317005i
$271$	−3.75306	+	3.75306i	−0.227982	+	0.227982i	−0.811849	−	0.583867i	$-0.801539\pi$
$271$	−3.75306	+	3.75306i	−0.227982	+	0.227982i	0.583867	+	0.811849i	$0.301539\pi$
$272$	−12.0673	−	21.4470i	−0.731687	−	1.30041i
$273$	0.511324	+	0.511324i	0.0309468	+	0.0309468i
$274$	17.0195	−	5.72477i	1.02819	−	0.345846i
$275$	−1.23152	+	6.19127i	−0.0742634	+	0.373347i
$276$	0.588991	+	9.82036i	0.0354531	+	0.591116i
$277$	−14.9569	−	9.99386i	−0.898671	−	0.600473i	0.0181216	−	0.999836i	$-0.494231\pi$
$277$	−14.9569	−	9.99386i	−0.898671	−	0.600473i	−0.916793	+	0.399363i	$0.869231\pi$
$278$	−11.0844	+	1.42804i	−0.664800	+	0.0856481i
$279$	−0.897546	−	0.371776i	−0.0537347	−	0.0222576i
$280$	−1.71266	−	0.726156i	−0.102351	−	0.0433961i
$281$	11.1334	−	4.61158i	0.664160	−	0.275104i	−0.0250279	−	0.999687i	$-0.507967\pi$
$281$	11.1334	−	4.61158i	0.664160	−	0.275104i	0.689188	+	0.724583i	$0.257967\pi$
$282$	0.407549	+	0.710436i	0.0242692	+	0.0423059i
$283$	−5.73960	−	28.8549i	−0.341184	−	1.71525i	−0.646430	−	0.762973i	$-0.723739\pi$
$283$	−5.73960	−	28.8549i	−0.341184	−	1.71525i	0.305246	−	0.952273i	$-0.401261\pi$
$284$	−19.2649	+	5.04768i	−1.14316	+	0.299525i
$285$	18.3950	+	27.5300i	1.08962	+	1.63074i
$286$	−3.38071	−	0.230999i	−0.199905	−	0.0136592i
$287$		−	0.698420i		−	0.0412265i
$288$	−5.64933	+	0.291692i	−0.332890	+	0.0171881i
$289$			20.8495i			1.22644i
$290$	−0.398657	+	5.83442i	−0.0234099	+	0.342609i
$291$	0.676305	+	1.01216i	0.0396457	+	0.0593339i
$292$	−22.8004	−	13.3330i	−1.33429	−	0.780252i
$293$	3.28132	+	16.4963i	0.191697	+	0.963724i	0.950102	+	0.311940i	$0.100979\pi$
$293$	3.28132	+	16.4963i	0.191697	+	0.963724i	−0.758405	+	0.651783i	$0.774021\pi$
$294$	−8.55553	+	4.90796i	−0.498969	+	0.286238i
$295$	−27.9214	+	11.5654i	−1.62564	+	0.673364i
$296$	1.56042	+	1.58659i	0.0906973	+	0.0922188i
$297$	−0.489594	−	0.202796i	−0.0284091	−	0.0117674i
$298$	2.07495	+	16.1057i	0.120198	+	0.932979i
$299$	−18.4930	−	12.3566i	−1.06948	−	0.714602i
$300$	−17.8245	−	15.8073i	−1.02910	−	0.912637i
$301$	−0.191816	+	0.964326i	−0.0110561	+	0.0555828i
$302$	6.20782	+	18.4556i	0.357220	+	1.06200i
$303$	3.27325	+	3.27325i	0.188043	+	0.188043i
$304$	14.5633	−	28.7240i	0.835264	−	1.64743i
$305$	−11.1682	+	11.1682i	−0.639490	+	0.639490i
$306$	7.79256	+	3.86976i	0.445471	+	0.221219i
$307$	1.03994	+	0.206857i	0.0593525	+	0.0118059i	0.224677	−	0.974433i	$-0.427867\pi$
$307$	1.03994	+	0.206857i	0.0593525	+	0.0118059i	−0.165325	+	0.986239i	$0.552867\pi$
$308$	−0.0553743	+	0.160203i	−0.00315524	+	0.00912844i
$309$	7.36307	−	11.0196i	0.418870	−	0.626884i
$310$	−3.45196	+	4.47295i	−0.196058	+	0.254046i
$311$	0.00613582	−	0.0148132i	0.000347931	−	0.000839979i	−0.923705	−	0.383103i	$-0.874855\pi$
$311$	0.00613582	−	0.0148132i	0.000347931	−	0.000839979i	0.924053	+	0.382263i	$0.124855\pi$
$312$	7.19325	−	10.5740i	0.407238	−	0.598635i
$313$	−5.70335	−	13.7691i	−0.322372	−	0.778275i	−0.999115	−	0.0420560i	$-0.986609\pi$
$313$	−5.70335	−	13.7691i	−0.322372	−	0.778275i	0.676743	−	0.736219i	$-0.263391\pi$
$314$	−1.36676	+	5.04482i	−0.0771307	+	0.284696i
$315$	0.645059	−	0.128310i	0.0363450	−	0.00722946i
$316$	−2.45262	−	3.23328i	−0.137971	−	0.181886i
$317$	19.9834	−	13.3525i	1.12238	−	0.749949i	0.151248	−	0.988496i	$-0.451671\pi$
$317$	19.9834	−	13.3525i	1.12238	−	0.749949i	0.971131	+	0.238546i	$0.0766709\pi$
$318$	2.97626	−	2.59555i	0.166900	−	0.145551i
$319$	0.532865			0.0298347
$320$	−6.95421	+	32.1560i	−0.388752	+	1.79757i
$321$	10.6274			0.593162
$322$	−0.838491	+	0.731234i	−0.0467273	+	0.0407501i
$323$	−41.1850	+	27.5189i	−2.29159	+	1.53119i
$324$	1.59343	−	1.20871i	0.0885241	−	0.0671503i
$325$	52.8253	−	10.5076i	2.93022	−	0.582857i
$326$	−0.0823359	+	0.303909i	−0.00456016	+	0.0168319i
$327$	−2.16898	−	5.23639i	−0.119945	−	0.289573i
$328$	−12.1342	+	2.30889i	−0.669999	+	0.127487i
$329$	−0.0354449	+	0.0855716i	−0.00195414	+	0.00471772i
$330$	−1.88298	+	2.43991i	−0.103654	+	0.134312i
$331$	5.73640	−	8.58513i	0.315301	−	0.471881i	−0.639641	−	0.768674i	$-0.720917\pi$
$331$	5.73640	−	8.58513i	0.315301	−	0.471881i	0.954942	+	0.296793i	$0.0959170\pi$
$332$	−12.7479	−	4.40632i	−0.699633	−	0.241828i
$333$	−0.771661	−	0.153493i	−0.0422868	−	0.00841137i
$334$	21.2582	+	10.5568i	1.16320	+	0.577640i
$335$	−35.7236	+	35.7236i	−1.95179	+	1.95179i
$336$	−0.416435	−	0.485613i	−0.0227184	−	0.0264924i
$337$	18.1565	+	18.1565i	0.989049	+	0.989049i	0.999941	−	0.0108916i	$-0.00346698\pi$
$337$	18.1565	+	18.1565i	0.989049	+	0.989049i	−0.0108916	+	0.999941i	$0.503467\pi$
$338$	3.35629	+	9.97813i	0.182558	+	0.542738i
$339$	1.25696	−	6.31916i	0.0682687	−	0.343210i
$340$	33.5739	−	37.8581i	1.82080	−	2.05315i
$341$	0.428064	+	0.286023i	0.0231810	+	0.0154890i
$342$	1.45489	+	11.2928i	0.0786714	+	0.610647i
$343$	−2.06480	−	0.855267i	−0.111489	−	0.0461801i
$344$	17.3881	+	0.144631i	0.937503	+	0.00779797i
$345$	−18.6892	+	7.74131i	−1.00619	+	0.416778i
$346$	17.5363	−	10.0599i	0.942758	−	0.540822i
$347$	−6.03964	−	30.3633i	−0.324225	−	1.62999i	−0.707754	−	0.706459i	$-0.750291\pi$
$347$	−6.03964	−	30.3633i	−0.324225	−	1.62999i	0.383529	−	0.923529i	$-0.374709\pi$
$348$	−1.01518	+	1.73603i	−0.0544191	+	0.0930611i
$349$	−2.58857	−	3.87407i	−0.138563	−	0.207374i	0.755698	−	0.654920i	$-0.227298\pi$
$349$	−2.58857	−	3.87407i	−0.138563	−	0.207374i	−0.894261	+	0.447547i	$0.852298\pi$
$350$	0.183661	−	2.68792i	0.00981711	−	0.143675i
$351$			4.52151i			0.241340i
$352$	2.96640	+	0.432448i	0.158109	+	0.0230495i
$353$		−	23.4512i		−	1.24818i	−0.781352	−	0.624090i	$-0.785470\pi$
$353$		−	23.4512i		−	1.24818i	0.781352	−	0.624090i	$-0.214530\pi$
$354$	−10.3688	−	0.708482i	−0.551094	−	0.0376554i
$355$	−22.7505	−	34.0485i	−1.20747	−	1.80711i
$356$	4.61041	+	17.5960i	0.244351	+	0.932586i
$357$	0.191952	+	0.965010i	0.0101592	+	0.0510738i
$358$	10.5374	+	18.3687i	0.556919	+	0.970817i
$359$	−17.3271	+	7.17713i	−0.914490	+	0.378794i	−0.789774	−	0.613398i	$-0.789802\pi$
$359$	−17.3271	+	7.17713i	−0.914490	+	0.378794i	−0.124716	+	0.992192i	$0.539802\pi$
$360$	−4.36172	−	10.7829i	−0.229883	−	0.568310i
$361$	−42.3344	−	17.5355i	−2.22813	−	0.922920i
$362$	2.18663	−	0.281710i	0.114927	−	0.0148063i
$363$	−8.91267	−	5.95525i	−0.467794	−	0.312570i
$364$	1.44365	−	0.0865851i	0.0756678	−	0.00453829i
$365$	10.5953	−	53.2664i	0.554586	−	2.78809i
$366$	−5.14803	+	1.73162i	−0.269092	+	0.0905131i
$367$	26.2985	+	26.2985i	1.37277	+	1.37277i	0.856313	+	0.516458i	$0.172750\pi$
$367$	26.2985	+	26.2985i	1.37277	+	1.37277i	0.516458	+	0.856313i	$0.327250\pi$
$368$	15.4762	+	12.1504i	0.806755	+	0.633382i
$369$	3.08798	−	3.08798i	0.160754	−	0.160754i
$370$	−2.03519	+	4.09827i	−0.105804	+	0.213059i
$371$	0.438005	+	0.0871247i	0.0227401	+	0.00452329i
$372$	−1.74736	+	0.849688i	−0.0905962	+	0.0440543i
$373$	−15.8345	+	23.6980i	−0.819879	+	1.22704i	0.151253	+	0.988495i	$0.451669\pi$
$373$	−15.8345	+	23.6980i	−0.819879	+	1.22704i	−0.971132	+	0.238541i	$0.923331\pi$
$374$	−3.65011	−	2.81694i	−0.188743	−	0.145661i
$375$	10.8778	−	26.2613i	0.561727	−	1.35613i
$376$	1.60388	+	0.332923i	0.0827137	+	0.0171692i
$377$	−1.73988	−	4.20045i	−0.0896085	−	0.216334i
$378$	0.218304	+	0.0591437i	0.0112284	+	0.00304202i
$379$	16.5739	−	3.29675i	0.851343	−	0.169343i	0.249913	−	0.968268i	$-0.419598\pi$
$379$	16.5739	−	3.29675i	0.851343	−	0.169343i	0.601430	+	0.798926i	$0.294598\pi$
$380$	65.6047	+	9.00738i	3.36545	+	0.462069i
$381$	6.61972	−	4.42316i	0.339139	−	0.226605i
$382$	24.2878	+	27.8503i	1.24267	+	1.42495i
$383$	−17.4182			−0.890029			−0.445014	−	0.895523i	$-0.646801\pi$
$383$	−17.4182			−0.890029			−0.445014	+	0.895523i	$0.646801\pi$
$384$	−7.06024	+	8.84042i	−0.360291	+	0.451136i
$385$	−0.348535			−0.0177630
$386$	−2.79018	−	3.19944i	−0.142016	−	0.162847i
$387$	−5.11173	+	3.41555i	−0.259844	+	0.173622i
$388$	2.41200	+	0.331163i	0.122451	+	0.0168123i
$389$	−12.4269	+	2.47187i	−0.630070	+	0.125329i	−0.499787	−	0.866148i	$-0.666588\pi$
$389$	−12.4269	+	2.47187i	−0.630070	+	0.125329i	−0.130283	+	0.991477i	$0.541588\pi$
$390$	25.3814	+	6.87640i	1.28524	+	0.348200i
$391$	−11.5810	−	27.9591i	−0.585678	−	1.41395i
$392$	−4.00927	+	19.3149i	−0.202499	+	0.975551i
$393$	0.340051	−	0.820955i	0.0171533	−	0.0414117i
$394$	17.7901	+	13.7294i	0.896253	+	0.691676i
$395$	4.63603	−	6.93831i	0.233264	−	0.349104i
$396$	−0.953149	+	0.463488i	−0.0478975	+	0.0232912i
$397$	17.2612	+	3.43346i	0.866314	+	0.172321i	0.608190	−	0.793791i	$-0.291896\pi$
$397$	17.2612	+	3.43346i	0.866314	+	0.172321i	0.258124	+	0.966112i	$0.416896\pi$
$398$	11.6981	−	23.5564i	0.586370	−	1.18078i
$399$	−0.910491	+	0.910491i	−0.0455816	+	0.0455816i
$400$	−47.3064	+	5.69504i	−2.36532	+	0.284752i
$401$	−0.360223	−	0.360223i	−0.0179887	−	0.0179887i	0.698055	−	0.716044i	$-0.254049\pi$
$401$	−0.360223	−	0.360223i	−0.0179887	−	0.0179887i	−0.716044	+	0.698055i	$0.754049\pi$
$402$	−16.4669	+	5.53890i	−0.821296	+	0.276255i
$403$	0.856960	−	4.30823i	0.0426882	−	0.214608i
$404$	9.24154	−	0.554276i	0.459784	−	0.0275762i
$405$	3.41935	+	2.28474i	0.169909	+	0.113530i
$406$	−0.225562	+	0.0290598i	−0.0111944	+	0.00144221i
$407$	0.385202	+	0.159556i	0.0190938	+	0.00790890i
$408$	16.1313	−	6.52514i	0.798618	−	0.323043i
$409$	4.87452	−	2.01909i	0.241029	−	0.0998376i	−0.258899	−	0.965904i	$-0.583360\pi$
$409$	4.87452	−	2.01909i	0.241029	−	0.0998376i	0.499928	+	0.866067i	$0.333360\pi$
$410$	−12.6380	−	22.0305i	−0.624148	−	1.08801i
$411$	2.47710	+	12.4532i	0.122186	+	0.614272i
$412$	−6.71827	−	25.6408i	−0.330985	−	1.26323i
$413$	−0.652966	−	0.977233i	−0.0321304	−	0.0480865i
$414$	−6.94034	−	0.474223i	−0.341099	−	0.0233068i
$415$		−	27.7341i		−	1.36141i
$416$	−6.27683	−	24.7954i	−0.307747	−	1.21569i
$417$		−	7.90266i		−	0.386995i
$418$	0.411328	−	6.01987i	0.0201187	−	0.294441i
$419$	4.63467	+	6.93628i	0.226419	+	0.338859i	0.927233	−	0.374484i	$-0.122180\pi$
$419$	4.63467	+	6.93628i	0.226419	+	0.338859i	−0.700815	+	0.713343i	$0.747180\pi$
$420$	0.664003	−	1.13550i	0.0324000	−	0.0554067i
$421$	3.45295	+	17.3591i	0.168286	+	0.846033i	0.969014	+	0.247005i	$0.0794463\pi$
$421$	3.45295	+	17.3591i	0.168286	+	0.846033i	−0.800728	+	0.599028i	$0.795554\pi$
$422$	16.5673	−	9.50397i	0.806482	−	0.462646i
$423$	−0.535059	+	0.221629i	−0.0260155	+	0.0107760i
$424$	0.0656926	−	7.89782i	0.00319031	−	0.383552i
$425$	67.7065	+	28.0449i	3.28425	+	1.36038i
$426$	−1.79937	−	13.9667i	−0.0871799	−	0.676690i
$427$	−0.510711	−	0.341246i	−0.0247151	−	0.0165141i
$428$	14.1026	−	15.9022i	0.681676	−	0.768663i
$429$	0.467455	−	2.35006i	0.0225689	−	0.113462i
$430$	11.3991	+	33.8890i	0.549713	+	1.63427i
$431$	−8.86022	−	8.86022i	−0.426782	−	0.426782i	0.460749	−	0.887531i	$-0.347581\pi$
$431$	−8.86022	−	8.86022i	−0.426782	−	0.426782i	−0.887531	+	0.460749i	$0.847581\pi$
$432$	0.305861	−	3.98829i	0.0147158	−	0.191887i
$433$	6.64880	−	6.64880i	0.319521	−	0.319521i	−0.529062	−	0.848583i	$-0.677456\pi$
$433$	6.64880	−	6.64880i	0.319521	−	0.319521i	0.848583	+	0.529062i	$0.177456\pi$
$434$	−0.196797	−	0.0977290i	−0.00944657	−	0.00469114i
$435$	−4.05572	−	0.806733i	−0.194457	−	0.0386799i
$436$	−10.7137	−	3.70319i	−0.513093	−	0.177351i
$437$	22.0028	−	32.9296i	1.05254	−	1.57524i
$438$	11.4106	−	14.7855i	0.545220	−	0.706480i
$439$	−5.18915	+	12.5277i	−0.247664	+	0.597915i	−0.998005	−	0.0631368i	$-0.979890\pi$
$439$	−5.18915	+	12.5277i	−0.247664	+	0.597915i	0.750340	+	0.661052i	$0.229890\pi$
$440$	1.15221	+	6.05536i	0.0549296	+	0.288678i
$441$	−2.66900	−	6.44353i	−0.127095	−	0.306835i
$442$	−10.2871	+	37.9706i	−0.489308	+	1.80608i
$443$	3.79768	−	0.755406i	0.180433	−	0.0358904i	−0.104047	−	0.994572i	$-0.533179\pi$
$443$	3.79768	−	0.755406i	0.180433	−	0.0358904i	0.284480	+	0.958682i	$0.408179\pi$
$444$	−1.25368	+	0.950985i	−0.0594970	+	0.0451317i
$445$	−31.0990	+	20.7797i	−1.47423	+	0.985051i
$446$	−16.6100	+	14.4853i	−0.786506	+	0.685899i
$447$	−11.4826			−0.543108
$448$	−1.27926	−	0.0212827i	−0.0604392	−	0.00100551i
$449$	14.9436			0.705231			0.352615	−	0.935768i	$-0.385292\pi$
$449$	14.9436			0.705231			0.352615	+	0.935768i	$0.385292\pi$
$450$	12.6963	−	11.0723i	0.598511	−	0.521951i
$451$	−1.92423	+	1.28573i	−0.0906083	+	0.0605425i
$452$	−7.78764	−	10.2664i	−0.366300	−	0.482892i
$453$	−13.5040	+	2.68611i	−0.634473	+	0.126205i
$454$	1.78994	−	6.60681i	0.0840058	−	0.310073i
$455$	1.13802	+	2.74741i	0.0533510	+	0.128801i
$456$	18.8286	+	12.8087i	0.881731	+	0.599822i
$457$	−9.64011	+	23.2733i	−0.450945	+	1.08868i	0.521018	+	0.853546i	$0.325552\pi$
$457$	−9.64011	+	23.2733i	−0.450945	+	1.08868i	−0.971963	+	0.235132i	$0.924448\pi$
$458$	20.4104	−	26.4471i	0.953713	−	1.23579i
$459$	−3.41798	+	5.11536i	−0.159537	+	0.238765i
$460$	−13.2170	+	38.2382i	−0.616248	+	1.78287i
$461$	−26.5707	−	5.28525i	−1.23752	−	0.246158i	−0.467395	−	0.884049i	$-0.654807\pi$
$461$	−26.5707	−	5.28525i	−1.23752	−	0.246158i	−0.770127	+	0.637890i	$0.779807\pi$
$462$	−0.107349	−	0.0533093i	−0.00499434	−	0.00248017i
$463$	25.5671	−	25.5671i	1.18820	−	1.18820i	0.210640	−	0.977564i	$-0.432445\pi$
$463$	25.5671	−	25.5671i	1.18820	−	1.18820i	0.977564	−	0.210640i	$-0.0675548\pi$
$464$	1.25056	+	3.82278i	0.0580556	+	0.177468i
$465$	−2.82503	−	2.82503i	−0.131008	−	0.131008i
$466$	−12.0004	−	35.6766i	−0.555906	−	1.65269i
$467$	−4.80271	+	24.1448i	−0.222243	+	1.11729i	0.695015	+	0.718995i	$0.255398\pi$
$467$	−4.80271	+	24.1448i	−0.222243	+	1.11729i	−0.917258	+	0.398294i	$0.869602\pi$
$468$	6.76573	+	6.00009i	0.312746	+	0.277354i
$469$	−1.63361	−	1.09154i	−0.0754329	−	0.0504027i
$470$	0.430379	+	3.34060i	0.0198519	+	0.154090i
$471$	−3.41450	−	1.41433i	−0.157332	−	0.0651690i
$472$	−14.8196	+	14.5751i	−0.682127	+	0.670873i
$473$	3.00994	−	1.24676i	0.138397	−	0.0573260i
$474$	2.48914	−	1.42792i	0.114330	−	0.0655864i
$475$	18.7104	+	94.0635i	0.858492	+	4.31593i
$476$	1.69871	+	0.993351i	0.0778603	+	0.0455302i
$477$	1.55137	+	2.32179i	0.0710325	+	0.106308i
$478$	0.491746	−	7.19680i	0.0224919	−	0.329174i
$479$			13.7288i			0.627286i	0.949541	+	0.313643i	$0.101550\pi$
$479$			13.7288i			0.627286i	−0.949541	+	0.313643i	$0.898450\pi$
$480$	−21.9230	−	7.78241i	−1.00064	−	0.355217i
$481$		−	3.55743i		−	0.162205i
$482$	−15.6862	−	1.07181i	−0.714486	−	0.0488197i
$483$	−0.437063	−	0.654111i	−0.0198871	−	0.0297631i
$484$	−20.7383	+	5.43374i	−0.942650	+	0.246988i
$485$	0.976645	+	4.90992i	0.0443471	+	0.222948i
$486$	0.703708	+	1.22670i	0.0319209	+	0.0556443i
$487$	12.5172	−	5.18479i	0.567209	−	0.234945i	−0.0806028	−	0.996746i	$-0.525685\pi$
$487$	12.5172	−	5.18479i	0.567209	−	0.234945i	0.647811	+	0.761801i	$0.275685\pi$
$488$	−4.24039	+	10.0011i	−0.191953	+	0.452728i
$489$	−0.205695	−	0.0852017i	−0.00930186	−	0.00385296i
$490$	−40.2296	+	5.18290i	−1.81739	+	0.234140i
$491$	15.3604	+	10.2635i	0.693205	+	0.463185i	0.851601	−	0.524191i	$-0.175632\pi$
$491$	15.3604	+	10.2635i	0.693205	+	0.463185i	−0.158396	+	0.987376i	$0.550632\pi$
$492$	−0.522902	−	8.71845i	−0.0235743	−	0.393058i
$493$	1.20688	−	6.06737i	0.0543549	−	0.273261i
$494$	−48.7962	+	16.4133i	−2.19544	+	0.738471i
$495$	−1.54100	−	1.54100i	−0.0692629	−	0.0692629i
$496$	−1.04733	+	3.74219i	−0.0470266	+	0.168029i
$497$	1.12607	−	1.12607i	0.0505113	−	0.0505113i
$498$	4.24200	−	8.54213i	0.190088	−	0.382782i
$499$	−0.995163	−	0.197950i	−0.0445496	−	0.00886147i	0.172765	−	0.984963i	$-0.444730\pi$
$499$	−0.995163	−	0.197950i	−0.0445496	−	0.00886147i	−0.217315	+	0.976102i	$0.569730\pi$
$500$	−24.8610	−	51.1260i	−1.11182	−	2.28642i
$501$	−9.32429	+	13.9548i	−0.416578	+	0.623454i
$502$	8.67843	+	6.69750i	0.387337	+	0.298924i
$503$	−2.06266	+	4.97969i	−0.0919693	+	0.222033i	−0.963170	−	0.268894i	$-0.913342\pi$
$503$	−2.06266	+	4.97969i	−0.0919693	+	0.222033i	0.871201	+	0.490927i	$0.163342\pi$
$504$	0.378191	−	0.248174i	0.0168460	−	0.0110546i
$505$	7.28503	+	17.5876i	0.324180	+	0.782639i
$506$	3.55822	+	0.964003i	0.158182	+	0.0428551i
$507$	−7.30101	+	1.45226i	−0.324249	+	0.0644972i
$508$	2.16587	−	15.7750i	0.0960949	−	0.699901i
$509$	18.9878	−	12.6872i	0.841618	−	0.562351i	−0.0583555	−	0.998296i	$-0.518586\pi$
$509$	18.9878	−	12.6872i	0.841618	−	0.562351i	0.899973	+	0.435945i	$0.143586\pi$
$510$	23.5168	+	26.9663i	1.04134	+	1.19409i
$511$	2.11208			0.0934328
$512$	3.85930	+	22.2959i	0.170559	+	0.985348i
$513$	−8.05124			−0.355471
$514$	−20.0730	−	23.0173i	−0.885381	−	1.01525i
$515$	45.3173	−	30.2800i	1.99692	−	1.33430i
$516$	−1.67248	+	12.1814i	−0.0736267	+	0.536256i
$517$	0.301010	−	0.0598747i	0.0132384	−	0.00263328i
$518$	−0.171757	−	0.0465330i	−0.00754658	−	0.00204454i
$519$	5.47065	+	13.2073i	0.240135	+	0.579737i
$520$	43.9708	−	28.8542i	1.92825	−	1.26534i
$521$	−10.9734	+	26.4922i	−0.480755	+	1.16064i	0.478496	+	0.878089i	$0.341182\pi$
$521$	−10.9734	+	26.4922i	−0.480755	+	1.16064i	−0.959251	+	0.282555i	$0.908818\pi$
$522$	−1.12578	−	0.868807i	−0.0492739	−	0.0380267i
$523$	5.85945	−	8.76928i	0.256216	−	0.383454i	−0.680955	−	0.732325i	$-0.738435\pi$
$523$	5.85945	−	8.76928i	0.256216	−	0.383454i	0.937171	+	0.348871i	$0.113435\pi$
$524$	−0.777181	−	1.59825i	−0.0339513	−	0.0698198i
$525$	1.86847	+	0.371662i	0.0815468	+	0.0162207i
$526$	−1.76229	+	3.54873i	−0.0768395	+	0.154732i
$527$	4.22626	−	4.22626i	0.184099	−	0.184099i
$528$	−0.571300	+	2.04129i	−0.0248626	+	0.0888359i
$529$	0.846126	+	0.846126i	0.0367881	+	0.0367881i
$530$	15.3927	−	5.17757i	0.668616	−	0.224899i
$531$	1.43370	−	7.20772i	0.0622174	−	0.312788i
$532$	0.154178	+	2.57064i	0.00668446	+	0.111451i
$533$	16.4179	+	10.9701i	0.711140	+	0.475169i
$534$	−12.7568	+	1.64350i	−0.552042	+	0.0711211i
$535$	40.3775	+	16.7249i	1.74567	+	0.723080i
$536$	−13.5637	+	31.9904i	−0.585861	+	1.38177i
$537$	−13.8343	+	5.73034i	−0.596992	+	0.247282i
$538$	10.3248	+	17.9982i	0.445135	+	0.775956i
$539$	0.721049	+	3.62496i	0.0310578	+	0.156138i
$540$	7.95627	−	2.08466i	0.342383	−	0.0897095i
$541$	−6.02666	−	9.01954i	−0.259107	−	0.387780i	0.678994	−	0.734144i	$-0.262416\pi$
$541$	−6.02666	−	9.01954i	−0.259107	−	0.387780i	−0.938100	+	0.346364i	$0.887416\pi$
$542$	−7.48867	−	0.511689i	−0.321666	−	0.0219789i
$543$			1.55896i			0.0669013i
$544$	11.6425	−	32.7969i	0.499169	−	1.40615i
$545$		−	23.3085i		−	0.998425i
$546$	−0.0697134	+	1.02027i	−0.00298346	+	0.0436635i
$547$	−19.8942	−	29.7737i	−0.850612	−	1.27303i	−0.960273	−	0.279062i	$-0.909976\pi$
$547$	−19.8942	−	29.7737i	−0.850612	−	1.27303i	0.109661	−	0.993969i	$-0.465024\pi$
$548$	21.9214	+	12.8189i	0.936437	+	0.547598i
$549$	−0.749268	−	3.76682i	−0.0319780	−	0.160764i
$550$	−7.74362	+	4.44220i	−0.330189	+	0.189416i
$551$	7.47954	−	3.09813i	0.318639	−	0.131985i
$552$	−9.91950	+	9.75584i	−0.422202	+	0.415236i
$553$	0.299815	+	0.124187i	0.0127494	+	0.00528099i
$554$	−3.25059	−	25.2310i	−0.138104	−	1.07196i
$555$	−2.69028	−	1.79758i	−0.114196	−	0.0763032i
$556$	−11.8251	−	10.4869i	−0.501496	−	0.444744i
$557$	−1.70870	+	8.59023i	−0.0724001	+	0.363980i	−0.999953	−	0.00971252i	$-0.996908\pi$
$557$	−1.70870	+	8.59023i	−0.0724001	+	0.363980i	0.927553	+	0.373692i	$0.121908\pi$
$558$	−0.438018	−	1.30221i	−0.0185428	−	0.0551270i
$559$	−19.6558	−	19.6558i	−0.831351	−	0.831351i
$560$	−0.817959	−	2.50040i	−0.0345651	−	0.105661i
$561$	2.30534	−	2.30534i	0.0973317	−	0.0973317i
$562$	15.2637	+	7.57992i	0.643861	+	0.319740i
$563$	−41.7534	−	8.30527i	−1.75970	−	0.350025i	−0.793646	−	0.608380i	$-0.791820\pi$
$563$	−41.7534	−	8.30527i	−1.75970	−	0.350025i	−0.966050	+	0.258355i	$0.916820\pi$
$564$	−0.378396	+	1.09474i	−0.0159333	+	0.0460967i
$565$	14.7205	−	22.0308i	0.619295	−	0.926841i
$566$	25.4198	−	32.9383i	1.06848	−	1.38450i
$567$	−0.0612023	+	0.147755i	−0.00257025	+	0.00620514i
$568$	−23.2868	−	15.8415i	−0.977093	−	0.664694i
$569$	−5.94155	−	14.3442i	−0.249083	−	0.601339i	0.749044	−	0.662520i	$-0.230513\pi$
$569$	−5.94155	−	14.3442i	−0.249083	−	0.601339i	−0.998127	+	0.0611815i	$0.980513\pi$
$570$	−12.2445	+	45.1954i	−0.512865	+	1.89303i
$571$	9.57768	−	1.90512i	0.400813	−	0.0797267i	0.00943242	−	0.999956i	$-0.496998\pi$
$571$	9.57768	−	1.90512i	0.400813	−	0.0797267i	0.391381	+	0.920229i	$0.371998\pi$
$572$	−2.89617	−	3.81802i	−0.121095	−	0.159639i
$573$	−21.7262	+	14.5170i	−0.907624	+	0.606455i
$574$	0.744407	−	0.649185i	0.0310709	−	0.0270964i
$575$	−58.5952			−2.44359
$576$	−5.56197	−	5.75017i	−0.231749	−	0.239590i
$577$	−16.1734			−0.673309			−0.336654	−	0.941628i	$-0.609295\pi$
$577$	−16.1734			−0.673309			−0.336654	+	0.941628i	$0.609295\pi$
$578$	−22.2223	+	19.3797i	−0.924326	+	0.806089i
$579$	2.49590	−	1.66770i	0.103726	−	0.0693074i
$580$	−6.58913	+	4.99821i	−0.273599	+	0.207540i
$581$	1.05784	−	0.210417i	0.0438864	−	0.00872955i
$582$	−0.450177	+	1.66164i	−0.0186604	+	0.0688773i
$583$	−0.566289	−	1.36714i	−0.0234533	−	0.0566212i
$584$	−6.98227	−	36.6947i	−0.288928	−	1.51844i
$585$	−7.11575	+	17.1789i	−0.294200	+	0.710262i
$586$	−14.5325	+	18.8307i	−0.600331	+	0.777891i
$587$	−9.20074	+	13.7699i	−0.379755	+	0.568344i	−0.971279	−	0.237944i	$-0.923527\pi$
$587$	−9.20074	+	13.7699i	−0.379755	+	0.568344i	0.591524	+	0.806288i	$0.298527\pi$
$588$	−13.1835	−	4.55688i	−0.543679	−	0.187923i
$589$	7.67146	+	1.52595i	0.316097	+	0.0628756i
$590$	−38.2799	−	19.0097i	−1.57596	−	0.782617i
$591$	−11.2359	+	11.2359i	−0.462184	+	0.462184i
$592$	−0.240645	+	3.13790i	−0.00989046	+	0.128967i
$593$	11.5062	+	11.5062i	0.472505	+	0.472505i	0.902724	−	0.430219i	$-0.141564\pi$
$593$	11.5062	+	11.5062i	0.472505	+	0.472505i	−0.430219	+	0.902724i	$0.641564\pi$
$594$	−0.238930	−	0.710331i	−0.00980344	−	0.0291452i
$595$	−0.789389	+	3.96853i	−0.0323618	+	0.162694i
$596$	−15.2375	+	17.1819i	−0.624152	+	0.703798i
$597$	15.4634	+	10.3323i	0.632876	+	0.422874i
$598$	−4.01909	−	31.1962i	−0.164353	−	1.27571i
$599$	7.56518	+	3.13360i	0.309105	+	0.128035i	0.531843	−	0.846843i	$-0.321500\pi$
$599$	7.56518	+	3.13360i	0.309105	+	0.128035i	−0.222738	+	0.974878i	$0.571500\pi$
$600$	0.280236	−	33.6911i	0.0114406	−	1.37543i
$601$	−0.465404	+	0.192777i	−0.0189842	+	0.00786352i	−0.392155	−	0.919899i	$-0.628270\pi$
$601$	−0.465404	+	0.192777i	−0.0189842	+	0.00786352i	0.373171	+	0.927763i	$0.378270\pi$
$602$	−1.20611	+	0.691899i	−0.0491576	+	0.0281997i
$603$	−2.39667	−	12.0489i	−0.0976000	−	0.490668i
$604$	−13.9006	+	23.7711i	−0.565607	+	0.967233i
$605$	−24.4905	−	36.6526i	−0.995680	−	1.49014i
$606$	−0.446271	+	6.53127i	−0.0181285	+	0.265315i
$607$			42.7312i			1.73441i	0.497955	+	0.867203i	$0.334084\pi$
$607$			42.7312i			1.73441i	−0.497955	+	0.867203i	$0.665916\pi$
$608$	44.1520	−	11.1769i	1.79060	−	0.453281i
$609$		−	0.160814i		−	0.00651652i
$610$	−22.2845	−	1.52266i	−0.902272	−	0.0616508i
$611$	−1.45482	−	2.17729i	−0.0588557	−	0.0880838i
$612$	3.11866	+	11.9026i	0.126064	+	0.481134i
$613$	4.44223	+	22.3326i	0.179420	+	0.902005i	0.960650	+	0.277762i	$0.0895926\pi$
$613$	4.44223	+	22.3326i	0.179420	+	0.902005i	−0.781230	+	0.624243i	$0.785407\pi$
$614$	0.746152	+	1.30069i	0.0301122	+	0.0524915i
$615$	16.5921	−	6.87268i	0.669059	−	0.277133i
$616$	−0.222222	+	0.0898894i	−0.00895359	+	0.00362175i
$617$	−21.5245	−	8.91575i	−0.866545	−	0.358935i	−0.0952812	−	0.995450i	$-0.530375\pi$
$617$	−21.5245	−	8.91575i	−0.866545	−	0.358935i	−0.771264	+	0.636516i	$0.780375\pi$
$618$	18.5892	−	2.39490i	0.747766	−	0.0963369i
$619$	−12.7526	−	8.52103i	−0.512571	−	0.342489i	0.272235	−	0.962231i	$-0.412237\pi$
$619$	−12.7526	−	8.52103i	−0.512571	−	0.342489i	−0.784806	+	0.619742i	$0.787237\pi$
$620$	−7.97607	+	0.478377i	−0.320327	+	0.0192121i
$621$	0.959650	−	4.82449i	0.0385094	−	0.193600i
$622$	0.0214918	−	0.00722909i	0.000861743	−	0.000289860i
$623$	−1.02853	−	1.02853i	−0.0412070	−	0.0412070i
$624$	17.9564	−	2.16170i	0.718831	−	0.0865372i
$625$	40.5425	−	40.5425i	1.62170	−	1.62170i
$626$	9.37441	−	18.8773i	0.374677	−	0.754489i
$627$	4.18463	+	0.832375i	0.167118	+	0.0332419i
$628$	−6.64740	+	3.23244i	−0.265260	+	0.128988i
$629$	2.68919	−	4.02466i	0.107225	−	0.160474i
$630$	0.736344	+	0.568267i	0.0293366	+	0.0226403i
$631$	18.3438	−	44.2859i	0.730257	−	1.76300i	0.0885150	−	0.996075i	$-0.471788\pi$
$631$	18.3438	−	44.2859i	0.730257	−	1.76300i	0.641742	−	0.766921i	$-0.278212\pi$
$632$	1.16645	−	5.61946i	0.0463990	−	0.223530i
$633$	5.16835	+	12.4775i	0.205423	+	0.495936i
$634$	32.8063	+	8.88798i	1.30290	+	0.352987i
$635$	32.1118	−	6.38744i	1.27432	−	0.253478i
$636$	5.53289	+	0.759654i	0.219393	+	0.0301222i
$637$	26.2203	−	17.5199i	1.03889	−	0.694162i
$638$	0.495301	+	0.567951i	0.0196091	+	0.0224854i
$639$	9.95758			0.393916
$640$	−40.7372	+	22.4770i	−1.61028	+	0.888483i
$641$	6.36951			0.251580			0.125790	−	0.992057i	$-0.459853\pi$
$641$	6.36951			0.251580			0.125790	+	0.992057i	$0.459853\pi$
$642$	9.87820	+	11.3271i	0.389861	+	0.447046i
$643$	−9.44521	+	6.31108i	−0.372483	+	0.248885i	−0.727695	−	0.685901i	$-0.759408\pi$
$643$	−9.44521	+	6.31108i	−0.372483	+	0.248885i	0.355213	+	0.934786i	$0.384408\pi$
$644$	−1.55876	−	0.214015i	−0.0614238	−	0.00843336i
$645$	−24.7967	+	4.93236i	−0.976368	+	0.194212i
$646$	−67.6125	−	18.3178i	−2.66018	−	0.720703i
$647$	10.9484	+	26.4317i	0.430425	+	1.03914i	0.979151	+	0.203136i	$0.0651134\pi$
$647$	10.9484	+	26.4317i	0.430425	+	1.03914i	−0.548725	+	0.836003i	$0.684887\pi$
$648$	2.76939	+	0.574853i	0.108792	+	0.0225824i
$649$	−1.49034	+	3.59799i	−0.0585008	+	0.141233i
$650$	60.3008	+	46.5366i	2.36519	+	1.82532i
$651$	0.0863194	−	0.129186i	0.00338312	−	0.00506320i
$652$	−0.400451	+	0.194727i	−0.0156829	+	0.00762611i
$653$	−17.9473	−	3.56994i	−0.702332	−	0.139702i	−0.169009	−	0.985614i	$-0.554057\pi$
$653$	−17.9473	−	3.56994i	−0.702332	−	0.139702i	−0.533323	+	0.845912i	$0.679057\pi$
$654$	3.56509	−	7.17904i	0.139406	−	0.280723i
$655$	2.58396	−	2.58396i	0.100964	−	0.100964i
$656$	−13.7397	−	10.7870i	−0.536445	−	0.421162i
$657$	9.33828	+	9.33828i	0.364321	+	0.364321i
$658$	−0.124152	+	0.0417605i	−0.00483996	+	0.00162799i
$659$	−4.08656	+	20.5445i	−0.159190	+	0.800301i	0.815849	+	0.578265i	$0.196270\pi$
$659$	−4.08656	+	20.5445i	−0.159190	+	0.800301i	−0.975039	+	0.222036i	$0.928730\pi$
$660$	−4.35079	+	0.260946i	−0.169354	+	0.0101573i
$661$	28.6557	+	19.1471i	1.11458	+	0.744737i	0.969599	−	0.244698i	$-0.0786889\pi$
$661$	28.6557	+	19.1471i	1.11458	+	0.744737i	0.144978	+	0.989435i	$0.453689\pi$
$662$	14.4824	−	1.86581i	0.562875	−	0.0725168i
$663$	−25.6997	−	10.6452i	−0.998095	−	0.413425i
$664$	−7.15280	−	17.6830i	−0.277583	−	0.686233i
$665$	−4.89219	+	2.02641i	−0.189711	+	0.0785809i
$666$	−0.553663	−	0.965143i	−0.0214540	−	0.0373985i
$667$	0.964961	+	4.85119i	0.0373634	+	0.187839i
$668$	8.50774	+	32.4705i	0.329174	+	1.25632i
$669$	−8.65795	−	12.9575i	−0.334736	−	0.500968i
$670$	−71.2810	−	4.87052i	−2.75383	−	0.188165i
$671$			2.03527i			0.0785707i
$672$	0.130509	−	0.895234i	0.00503450	−	0.0345344i
$673$		−	25.9788i		−	1.00141i	−0.865618	−	0.500704i	$-0.833074\pi$
$673$		−	25.9788i		−	1.00141i	0.865618	−	0.500704i	$-0.166926\pi$
$674$	−2.47544	+	36.2286i	−0.0953505	+	1.39547i
$675$	6.61795	+	9.90447i	0.254725	+	0.381223i
$676$	−7.51543	+	12.8520i	−0.289055	+	0.494307i
$677$	8.91804	+	44.8340i	0.342748	+	1.72311i	0.640055	+	0.768329i	$0.278911\pi$
$677$	8.91804	+	44.8340i	0.342748	+	1.72311i	−0.297307	+	0.954782i	$0.596089\pi$
$678$	7.90358	−	4.53397i	0.303535	−	0.174126i
$679$	−0.179865	+	0.0745025i	−0.00690258	+	0.00285914i
$680$	71.5579	+	0.595205i	2.74412	+	0.0228251i
$681$	4.47170	+	1.85224i	0.171356	+	0.0709779i
$682$	0.0930314	+	0.722108i	0.00356235	+	0.0276510i
$683$	38.6849	+	25.8484i	1.48024	+	0.989063i	0.993292	+	0.115630i	$0.0368886\pi$
$683$	38.6849	+	25.8484i	1.48024	+	0.989063i	0.486944	+	0.873433i	$0.338111\pi$
$684$	−10.6841	+	12.0474i	−0.408515	+	0.460645i
$685$	−10.1869	+	51.2128i	−0.389220	+	1.95674i
$686$	−1.00766	−	2.99572i	−0.0384725	−	0.114377i
$687$	16.7035	+	16.7035i	0.637280	+	0.637280i
$688$	16.0082	+	18.6674i	0.610305	+	0.711688i
$689$	−8.92783	+	8.92783i	−0.340123	+	0.340123i
$690$	−25.6227	−	12.7241i	−0.975439	−	0.484400i
$691$	49.8201	+	9.90983i	1.89525	+	0.376988i	0.997925	−	0.0643920i	$-0.0205108\pi$
$691$	49.8201	+	9.90983i	1.89525	+	0.376988i	0.897320	+	0.441380i	$0.145511\pi$
$692$	27.0223	+	9.34026i	1.02723	+	0.355064i
$693$	0.0470856	−	0.0704685i	0.00178863	−	0.00267688i
$694$	26.7487	−	34.6601i	1.01537	−	1.31568i
$695$	12.4368	−	30.0252i	0.471756	−	1.13892i
$696$	−2.79395	+	0.531632i	−0.105904	+	0.0201515i
$697$	10.2816	+	24.8219i	0.389442	+	0.940195i
$698$	1.72306	−	6.35997i	0.0652188	−	0.240728i
$699$	26.1046	−	5.19254i	0.987368	−	0.196400i
$700$	3.03561	−	2.30268i	0.114735	−	0.0870331i
$701$	−13.5081	+	9.02580i	−0.510193	+	0.340900i	−0.783873	−	0.620921i	$-0.786759\pi$
$701$	−13.5081	+	9.02580i	−0.510193	+	0.340900i	0.273681	+	0.961821i	$0.411759\pi$
$702$	−4.81922	+	4.20276i	−0.181890	+	0.158623i
$703$	6.33455			0.238912
$704$	2.29636	+	3.56368i	0.0865472	+	0.134311i
$705$	−2.38168			−0.0896994
$706$	24.9953	−	21.7980i	0.940710	−	0.820377i
$707$	−0.615557	+	0.411302i	−0.0231504	+	0.0154686i
$708$	−8.88269	−	11.7100i	−0.333832	−	0.440090i
$709$	−23.8585	+	4.74575i	−0.896025	+	0.178231i	−0.621560	−	0.783366i	$-0.713501\pi$
$709$	−23.8585	+	4.74575i	−0.896025	+	0.178231i	−0.274465	+	0.961597i	$0.588501\pi$
$710$	15.1437	−	55.8967i	0.568333	−	2.09776i
$711$	0.776515	+	1.87467i	0.0291216	+	0.0703057i
$712$	−14.4692	+	21.2695i	−0.542255	+	0.797109i
$713$	−1.82877	+	4.41503i	−0.0684878	+	0.165344i
$714$	−0.850129	+	1.10157i	−0.0318153	+	0.0412253i
$715$	5.47445	−	8.19310i	0.204733	−	0.306404i
$716$	−9.78363	+	28.3050i	−0.365631	+	1.05781i
$717$	5.00276	+	0.995112i	0.186832	+	0.0371631i
$718$	−23.7553	−	11.7968i	−0.886541	−	0.440253i
$719$	12.2682	−	12.2682i	0.457528	−	0.457528i	−0.440315	−	0.897843i	$-0.645133\pi$
$719$	12.2682	−	12.2682i	0.457528	−	0.457528i	0.897843	+	0.440315i	$0.145133\pi$
$720$	7.43867	−	14.6717i	0.277223	−	0.546781i
$721$	1.49876	+	1.49876i	0.0558168	+	0.0558168i
$722$	−20.6599	−	61.4211i	−0.768883	−	2.28586i
$723$	2.16895	−	10.9040i	0.0806640	−	0.405526i
$724$	2.33274	+	2.06875i	0.0866955	+	0.0768845i
$725$	−9.95928	−	6.65458i	−0.369878	−	0.247145i
$726$	−1.93699	−	15.0349i	−0.0718886	−	0.557999i
$727$	−18.6584	−	7.72858i	−0.692003	−	0.286637i	0.00883141	−	0.999961i	$-0.497189\pi$
$727$	−18.6584	−	7.72858i	−0.692003	−	0.286637i	−0.700834	+	0.713324i	$0.747189\pi$
$728$	1.43416	+	1.45822i	0.0531537	+	0.0540453i
$729$	−0.923880	+	0.382683i	−0.0342178	+	0.0141735i
$730$	66.6221	−	38.2184i	2.46579	−	1.41453i
$731$	−7.37883	−	37.0959i	−0.272916	−	1.37204i
$732$	−6.63075	−	3.87745i	−0.245080	−	0.143315i
$733$	−14.1805	−	21.2227i	−0.523770	−	0.783877i	0.471413	−	0.881913i	$-0.343744\pi$
$733$	−14.1805	−	21.2227i	−0.523770	−	0.783877i	−0.995183	+	0.0980356i	$0.968744\pi$
$734$	−3.58551	+	52.4746i	−0.132344	+	1.93687i
$735$		−	28.6818i		−	1.05794i
$736$	1.43483	+	27.7891i	0.0528886	+	1.02432i
$737$			6.51019i			0.239806i
$738$	6.16159	+	0.421011i	0.226811	+	0.0154976i
$739$	0.668624	+	1.00067i	0.0245957	+	0.0368101i	0.843564	−	0.537029i	$-0.180453\pi$
$739$	0.668624	+	1.00067i	0.0245957	+	0.0368101i	−0.818968	+	0.573839i	$0.805453\pi$
$740$	−6.25983	+	1.64017i	−0.230116	+	0.0602937i
$741$	−7.10202	−	35.7043i	−0.260899	−	1.31163i
$742$	0.314266	+	0.547828i	0.0115371	+	0.0201114i
$743$	−1.17547	+	0.486897i	−0.0431239	+	0.0178625i	−0.404141	−	0.914697i	$-0.632430\pi$
$743$	−1.17547	+	0.486897i	−0.0431239	+	0.0178625i	0.361017	+	0.932559i	$0.382430\pi$
$744$	−2.52981	−	1.07262i	−0.0927473	−	0.0393241i
$745$	−43.6267	−	18.0708i	−1.59836	−	0.662062i
$746$	−39.9766	+	5.15030i	−1.46365	+	0.188566i
$747$	5.60742	+	3.74676i	0.205165	+	0.137087i
$748$	−0.390375	−	6.50880i	−0.0142735	−	0.237985i
$749$	−0.331581	+	1.66697i	−0.0121157	+	0.0609098i
$750$	38.1014	−	12.8160i	1.39127	−	0.467974i
$751$	28.6332	+	28.6332i	1.04484	+	1.04484i	0.998946	+	0.0458937i	$0.0146135\pi$
$751$	28.6332	+	28.6332i	1.04484	+	1.04484i	0.0458937	+	0.998946i	$0.485386\pi$
$752$	1.13597	+	2.01894i	0.0414245	+	0.0736230i
$753$	−5.48114	+	5.48114i	−0.199744	+	0.199744i
$754$	2.85979	−	5.75877i	0.104147	−	0.209722i
$755$	−55.5341	−	11.0464i	−2.02109	−	0.402020i
$756$	0.139877	+	0.287652i	0.00508727	+	0.0104618i
$757$	−7.84971	+	11.7479i	−0.285303	+	0.426986i	−0.946245	−	0.323451i	$-0.895157\pi$
$757$	−7.84971	+	11.7479i	−0.285303	+	0.426986i	0.660942	+	0.750437i	$0.270157\pi$
$758$	18.9193	+	14.6008i	0.687180	+	0.530325i
$759$	−0.997557	+	2.40832i	−0.0362090	+	0.0874163i
$760$	51.3794	+	78.2967i	1.86373	+	2.84012i
$761$	−13.8423	−	33.4182i	−0.501783	−	1.21141i	−0.948512	−	0.316741i	$-0.897411\pi$
$761$	−13.8423	−	33.4182i	−0.501783	−	1.21141i	0.446729	−	0.894669i	$-0.352589\pi$
$762$	10.8675	+	2.94424i	0.393686	+	0.106659i
$763$	0.889034	−	0.176840i	0.0321852	−	0.00640203i
$764$	−7.10846	+	51.7740i	−0.257175	+	1.87312i
$765$	−21.0365	+	14.0562i	−0.760577	+	0.508201i
$766$	−16.1903	−	18.5651i	−0.584979	−	0.670784i
$767$	33.2282			1.19980
$768$	−15.9850	+	0.692097i	−0.576810	+	0.0249739i
$769$	−22.7030			−0.818690			−0.409345	−	0.912380i	$-0.634243\pi$
$769$	−22.7030			−0.818690			−0.409345	+	0.912380i	$0.634243\pi$
$770$	−0.323965	−	0.371484i	−0.0116749	−	0.0133873i
$771$	17.9559	−	11.9977i	0.646665	−	0.432088i
$772$	0.816617	−	5.94778i	0.0293907	−	0.214065i
$773$	−22.3417	+	4.44404i	−0.803576	+	0.159841i	−0.579757	−	0.814790i	$-0.696852\pi$
$773$	−22.3417	+	4.44404i	−0.803576	+	0.159841i	−0.223819	+	0.974631i	$0.571852\pi$
$774$	−8.39182	−	2.27354i	−0.301638	−	0.0817206i
$775$	−4.42859	−	10.6916i	−0.159080	−	0.384052i
$776$	1.88900	+	2.87864i	0.0678112	+	0.103337i
$777$	0.0481527	−	0.116251i	0.00172747	−	0.00417048i
$778$	−14.1855	−	10.9475i	−0.508575	−	0.392488i
$779$	−19.5340	+	29.2346i	−0.699877	+	1.04744i
$780$	16.2629	+	33.4442i	0.582307	+	1.19750i
$781$	−5.17546	−	1.02946i	−0.185192	−	0.0368371i
$782$	19.0354	−	38.3316i	0.680703	−	1.37074i
$783$	0.711020	−	0.711020i	0.0254098	−	0.0254098i
$784$	−24.3133	+	13.6801i	−0.868333	+	0.488573i
$785$	−10.7472	−	10.7472i	−0.383583	−	0.383583i
$786$	1.19109	−	0.400641i	0.0424847	−	0.0142904i
$787$	−1.46181	+	7.34903i	−0.0521080	+	0.261965i	−0.998054	−	0.0623605i	$-0.980137\pi$
$787$	−1.46181	+	7.34903i	−0.0521080	+	0.261965i	0.945946	+	0.324325i	$0.105137\pi$
$788$	1.90263	+	31.7230i	0.0677786	+	1.13008i
$789$	−2.32954	−	1.55655i	−0.0829337	−	0.0554146i
$790$	11.7044	−	1.50791i	0.416423	−	0.0536489i
$791$	0.951982	+	0.394324i	0.0338486	+	0.0140205i
$792$	−1.37996	−	0.585093i	−0.0490348	−	0.0207904i
$793$	16.0435	−	6.64545i	0.569723	−	0.235987i
$794$	12.3848	+	21.5891i	0.439521	+	0.766170i
$795$	2.24032	+	11.2629i	0.0794561	+	0.399453i
$796$	35.9808	−	9.42751i	1.27531	−	0.334149i
$797$	−11.9523	−	17.8879i	−0.423373	−	0.633623i	0.557061	−	0.830472i	$-0.311929\pi$
$797$	−11.9523	−	17.8879i	−0.423373	−	0.633623i	−0.980434	+	0.196849i	$0.936929\pi$
$798$	−1.81675	−	0.124135i	−0.0643121	−	0.00439434i
$799$		−	3.56301i		−	0.126050i
$800$	−50.0416	−	45.1277i	−1.76924	−	1.59550i
$801$		−	9.09499i		−	0.321356i
$802$	0.0491125	−	0.718771i	0.00173422	−	0.0253807i
$803$	−3.88814	−	5.81901i	−0.137209	−	0.205348i
$804$	−21.2097	−	12.4027i	−0.748008	−	0.437411i
$805$	−0.631158	−	3.17305i	−0.0222454	−	0.111835i
$806$	5.38844	−	3.09113i	0.189800	−	0.108880i
$807$	−13.5552	+	5.61474i	−0.477165	+	0.197648i
$808$	9.18082	+	9.33483i	0.322980	+	0.328398i
$809$	25.4887	+	10.5578i	0.896136	+	0.371192i	0.782733	−	0.622357i	$-0.213825\pi$
$809$	25.4887	+	10.5578i	0.896136	+	0.371192i	0.113403	+	0.993549i	$0.463825\pi$
$810$	0.743130	+	5.76817i	0.0261109	+	0.202673i
$811$	−22.3281	−	14.9192i	−0.784047	−	0.523883i	0.0979205	−	0.995194i	$-0.468781\pi$
$811$	−22.3281	−	14.9192i	−0.784047	−	0.523883i	−0.881967	+	0.471311i	$0.843781\pi$
$812$	−0.240634	−	0.213402i	−0.00844458	−	0.00748894i
$813$	1.03547	−	5.20565i	0.0363155	−	0.182570i
$814$	0.187986	+	0.558873i	0.00658889	+	0.0195885i
$815$	−0.647428	−	0.647428i	−0.0226784	−	0.0226784i
$816$	21.9489	+	11.1283i	0.768365	+	0.389568i
$817$	35.0001	−	35.0001i	1.22450	−	1.22450i
$818$	6.68292	+	3.31872i	0.233663	+	0.116036i
$819$	−0.709227	−	0.141074i	−0.0247824	−	0.00492953i
$820$	11.7340	−	33.9476i	0.409769	−	1.18550i
$821$	−28.1391	+	42.1131i	−0.982061	+	1.46976i	−0.102065	+	0.994778i	$0.532545\pi$
$821$	−28.1391	+	42.1131i	−0.982061	+	1.46976i	−0.879996	+	0.474981i	$0.842455\pi$
$822$	−10.9707	+	14.2155i	−0.382647	+	0.495823i
$823$	13.8604	−	33.4619i	0.483143	−	1.16641i	−0.474966	−	0.880004i	$-0.657540\pi$
$823$	13.8604	−	33.4619i	0.483143	−	1.16641i	0.958109	−	0.286405i	$-0.0924604\pi$
$824$	21.0844	−	30.9939i	0.734511	−	1.07972i
$825$	−2.41571	−	5.83204i	−0.0841043	−	0.203046i
$826$	0.434642	−	1.60430i	0.0151231	−	0.0558208i
$827$	19.7636	−	3.93122i	0.687247	−	0.136702i	0.160899	−	0.986971i	$-0.448561\pi$
$827$	19.7636	−	3.93122i	0.687247	−	0.136702i	0.526348	+	0.850269i	$0.323561\pi$
$828$	−5.94563	−	7.83811i	−0.206625	−	0.272393i
$829$	13.1032	−	8.75528i	0.455093	−	0.304083i	−0.306814	−	0.951769i	$-0.599263\pi$
$829$	13.1032	−	8.75528i	0.455093	−	0.304083i	0.761907	+	0.647686i	$0.224263\pi$
$830$	29.5602	−	25.7790i	1.02605	−	0.894801i
$831$	17.9885			0.624013
$832$	20.5936	−	29.7375i	0.713956	−	1.03096i
$833$	42.9080			1.48667
$834$	8.42299	−	7.34555i	0.291664	−	0.254356i
$835$	−57.3879	+	38.3454i	−1.98599	+	1.32700i
$836$	6.79857	−	5.15708i	0.235133	−	0.178361i
$837$	0.952830	−	0.189530i	0.0329346	−	0.00655110i
$838$	−3.08504	+	11.3871i	−0.106571	+	0.393362i
$839$	−9.65125	−	23.3002i	−0.333198	−	0.804412i	−0.998335	−	0.0576897i	$-0.981627\pi$
$839$	−9.65125	−	23.3002i	−0.333198	−	0.804412i	0.665136	−	0.746722i	$-0.268373\pi$
$840$	1.82746	−	0.347728i	0.0630533	−	0.0119978i
$841$	10.7109	−	25.8584i	0.369341	−	0.891668i
$842$	−15.2926	+	19.8157i	−0.527018	+	0.682894i
$843$	−6.69498	+	10.0198i	−0.230587	+	0.345099i
$844$	25.5291	+	8.82413i	0.878747	+	0.303739i
$845$	−30.0248	−	5.97231i	−1.03289	−	0.205454i
$846$	−0.733562	−	0.364284i	−0.0252204	−	0.0125244i
$847$	1.21220	−	1.21220i	0.0416517	−	0.0416517i
$848$	8.47890	−	7.27104i	0.291167	−	0.249689i
$849$	20.8032	+	20.8032i	0.713965	+	0.713965i
$850$	33.0419	+	98.2324i	1.13333	+	3.36934i
$851$	−0.755033	+	3.79581i	−0.0258822	+	0.130119i
$852$	13.2138	−	14.9000i	0.452698	−	0.510465i
$853$	−31.9309	−	21.3356i	−1.09329	−	0.730515i	−0.128024	−	0.991771i	$-0.540863\pi$
$853$	−31.9309	−	21.3356i	−1.09329	−	0.730515i	−0.965270	+	0.261256i	$0.915863\pi$
$854$	−0.110993	−	0.861528i	−0.00379811	−	0.0294809i
$855$	−30.5897	−	12.6707i	−1.04615	−	0.433328i
$856$	30.0577	+	0.250014i	1.02735	+	0.00854532i
$857$	5.72004	−	2.36932i	0.195393	−	0.0809343i	−0.282841	−	0.959167i	$-0.591277\pi$
$857$	5.72004	−	2.36932i	0.195393	−	0.0809343i	0.478234	+	0.878232i	$0.341277\pi$
$858$	2.93929	−	1.68615i	0.100346	−	0.0575643i
$859$	4.46439	+	22.4440i	0.152323	+	0.765779i	0.979121	+	0.203280i	$0.0651601\pi$
$859$	4.46439	+	22.4440i	0.152323	+	0.765779i	−0.826798	+	0.562499i	$0.809840\pi$
$860$	−25.5249	+	43.6497i	−0.870392	+	1.48844i
$861$	0.388022	+	0.580715i	0.0132237	+	0.0197907i
$862$	1.20799	−	17.6792i	0.0411444	−	0.602156i
$863$		−	0.983709i		−	0.0334858i	−0.999860	−	0.0167429i	$-0.994670\pi$
$863$		−	0.983709i		−	0.0334858i	0.999860	−	0.0167429i	$-0.00532968\pi$
$864$	4.53519	−	3.38113i	0.154290	−	0.115028i
$865$			58.7891i			1.99889i
$866$	13.2667	+	0.906491i	0.450820	+	0.0308038i
$867$	−11.5834	−	17.3357i	−0.393392	−	0.588752i
$868$	−0.0787602	−	0.300595i	−0.00267330	−	0.0102028i
$869$	−0.209781	−	1.05464i	−0.00711634	−	0.0357762i
$870$	−2.90996	−	5.07263i	−0.0986569	−	0.171978i
$871$	51.3182	−	21.2567i	1.73885	−	0.720256i
$872$	−6.01141	−	14.8612i	−0.203572	−	0.503265i
$873$	−1.12465	−	0.465847i	−0.0380637	−	0.0157665i
$874$	55.5495	−	7.15660i	1.87899	−	0.242076i
$875$	3.77986	+	2.52562i	0.127783	+	0.0853816i
$876$	26.3653	−	1.58130i	0.890800	−	0.0534271i
$877$	4.03552	−	20.2879i	0.136270	−	0.685074i	−0.850891	−	0.525343i	$-0.823937\pi$
$877$	4.03552	−	20.2879i	0.136270	−	0.685074i	0.987160	−	0.159732i	$-0.0510629\pi$
$878$	−18.1759	+	6.11374i	−0.613407	+	0.206329i
$879$	−11.8932	−	11.8932i	−0.401147	−	0.401147i
$880$	−5.38308	+	6.85656i	−0.181464	+	0.231135i
$881$	−18.2942	+	18.2942i	−0.616347	+	0.616347i	−0.944592	−	0.328245i	$-0.893543\pi$
$881$	−18.2942	+	18.2942i	−0.616347	+	0.616347i	0.328245	+	0.944592i	$0.393543\pi$
$882$	4.38695	−	8.83402i	0.147716	−	0.297457i
$883$	31.5867	+	6.28298i	1.06298	+	0.211439i	0.695450	−	0.718574i	$-0.255205\pi$
$883$	31.5867	+	6.28298i	1.06298	+	0.211439i	0.367526	+	0.930013i	$0.380205\pi$
$884$	−50.0327	+	24.3294i	−1.68278	+	0.818287i
$885$	16.7904	−	25.1286i	0.564402	−	0.844687i
$886$	4.33510	+	3.34558i	0.145641	+	0.112397i
$887$	2.95376	−	7.13100i	0.0991775	−	0.239436i	−0.866501	−	0.499175i	$-0.833637\pi$
$887$	2.95376	−	7.13100i	0.0991775	−	0.239436i	0.965679	+	0.259739i	$0.0836366\pi$
$888$	−2.17890	−	0.452283i	−0.0731192	−	0.0151776i
$889$	0.487260	+	1.17635i	0.0163422	+	0.0394535i
$890$	−51.0545	−	13.8318i	−1.71135	−	0.463644i
$891$	0.519750	−	0.103385i	0.0174123	−	0.00346352i
$892$	−30.8781	−	4.23950i	−1.03388	−	0.141949i
$893$	3.87700	−	2.59053i	0.129739	−	0.0866887i
$894$	−10.6731	−	12.2386i	−0.356962	−	0.409321i
$895$	−61.5798			−2.05838
$896$	−1.16639	−	1.38327i	−0.0389664	−	0.0462118i
$897$	22.2413			0.742616
$898$	13.8901	+	15.9275i	0.463519	+	0.531508i
$899$	−0.812240	+	0.542721i	−0.0270897	+	0.0181008i
$900$	23.6026	+	3.24058i	0.786753	+	0.108019i
$901$	−16.8493	+	3.35153i	−0.561331	+	0.111656i
$902$	−3.15896	−	0.855835i	−0.105182	−	0.0284962i
$903$	−0.376261	−	0.908375i	−0.0125212	−	0.0302288i
$904$	3.70376	−	17.8431i	0.123185	−	0.593453i
$905$	−2.45342	+	5.92307i	−0.0815544	+	0.196890i
$906$	−15.4150	−	11.8964i	−0.512129	−	0.395231i
$907$	23.8710	−	35.7254i	0.792623	−	1.18624i	−0.186396	−	0.982475i	$-0.559681\pi$
$907$	23.8710	−	35.7254i	0.792623	−	1.18624i	0.979019	−	0.203769i	$-0.0653192\pi$
$908$	8.70557	−	4.23326i	0.288905	−	0.140486i
$909$	−4.54013	−	0.903088i	−0.150587	−	0.0299535i
$910$	−1.87052	+	3.76668i	−0.0620072	+	0.124864i
$911$	20.0142	−	20.0142i	0.663099	−	0.663099i	−0.293011	−	0.956109i	$-0.594657\pi$
$911$	20.0142	−	20.0142i	0.663099	−	0.663099i	0.956109	+	0.293011i	$0.0946571\pi$
$912$	3.84924	+	31.9741i	0.127461	+	1.05877i
$913$	−2.52710	−	2.52710i	−0.0836347	−	0.0836347i
$914$	−33.7662	+	11.3578i	−1.11689	+	0.375682i
$915$	3.08130	−	15.4908i	0.101865	−	0.512109i
$916$	47.1600	−	2.82849i	1.55821	−	0.0934561i
$917$	0.118162	+	0.0789534i	0.00390206	+	0.00260727i
$918$	−8.62920	+	1.11172i	−0.284806	+	0.0366924i
$919$	−34.2127	−	14.1714i	−1.12857	−	0.467471i	−0.261278	−	0.965264i	$-0.584144\pi$
$919$	−34.2127	−	14.1714i	−1.12857	−	0.467471i	−0.867296	+	0.497793i	$0.834144\pi$
$920$	−53.0412	+	21.4553i	−1.74872	+	0.707360i
$921$	−0.979602	+	0.405764i	−0.0322790	+	0.0133704i
$922$	−19.0644	−	33.2329i	−0.627851	−	1.09447i
$923$	8.78361	+	44.1582i	0.289116	+	1.45348i
$924$	−0.0429622	−	0.163969i	−0.00141335	−	0.00539417i
$925$	−5.20687	−	7.79263i	−0.171201	−	0.256220i
$926$	51.0152	+	3.48579i	1.67646	+	0.114550i
$927$			13.2532i			0.435291i
$928$	−2.91209	+	4.88619i	−0.0955941	+	0.160397i
$929$			20.5329i			0.673662i	0.941565	+	0.336831i	$0.109355\pi$
$929$			20.5329i			0.673662i	−0.941565	+	0.336831i	$0.890645\pi$
$930$	0.385162	−	5.63693i	0.0126300	−	0.184842i
$931$	31.1968	+	46.6893i	1.02243	+	1.53018i
$932$	26.8713	−	45.9521i	0.880198	−	1.50521i
$933$	0.00312801	+	0.0157256i	0.000102407	+	0.000514833i
$934$	−30.1987	+	17.3238i	−0.988133	+	0.566852i
$935$	12.3869	−	5.13083i	0.405096	−	0.167796i
$936$	−0.106371	+	12.7883i	−0.00347684	+	0.417999i
$937$	12.0887	+	5.00729i	0.394919	+	0.163581i	0.571301	−	0.820741i	$-0.306439\pi$
$937$	12.0887	+	5.00729i	0.394919	+	0.163581i	−0.176381	+	0.984322i	$0.556439\pi$
$938$	−0.355032	−	2.75576i	−0.0115922	−	0.0899787i
$939$	12.3919	+	8.27997i	0.404393	+	0.270207i
$940$	−3.16052	+	3.56382i	−0.103085	+	0.116239i
$941$	−7.73824	+	38.9028i	−0.252260	+	1.26819i	0.622109	+	0.782931i	$0.286276\pi$
$941$	−7.73824	+	38.9028i	−0.252260	+	1.26819i	−0.874368	+	0.485263i	$0.838724\pi$
$942$	−1.66634	−	4.95395i	−0.0542922	−	0.161408i
$943$	−15.1898	−	15.1898i	−0.494647	−	0.494647i
$944$	−29.3096	−	2.24775i	−0.953947	−	0.0731580i
$945$	−0.465062	+	0.465062i	−0.0151285	+	0.0151285i
$946$	4.12660	+	2.04926i	0.134167	+	0.0666271i
$947$	−26.5144	−	5.27405i	−0.861604	−	0.171384i	−0.255539	−	0.966799i	$-0.582253\pi$
$947$	−26.5144	−	5.27405i	−0.861604	−	0.171384i	−0.606065	+	0.795415i	$0.707253\pi$
$948$	3.83560	+	1.32577i	0.124574	+	0.0430591i
$949$	−33.1745	+	49.6491i	−1.07689	+	1.61168i
$950$	−82.8656	+	107.375i	−2.68851	+	3.48370i
$951$	−9.19734	+	22.2043i	−0.298244	+	0.720025i
$952$	0.520202	+	2.73388i	0.0168599	+	0.0886056i
$953$	−13.7257	−	33.1368i	−0.444619	−	1.07341i	−0.974309	−	0.225214i	$-0.927692\pi$
$953$	−13.7257	−	33.1368i	−0.444619	−	1.07341i	0.529690	−	0.848191i	$-0.322308\pi$
$954$	−1.03266	+	3.81164i	−0.0334336	+	0.123406i
$955$	−105.392	+	20.9638i	−3.41041	+	0.678373i
$956$	8.12774	−	6.16533i	0.262870	−	0.199401i
$957$	−0.443061	+	0.296044i	−0.0143221	+	0.00956975i
$958$	−14.6328	+	12.7610i	−0.472764	+	0.412289i
$959$	−2.03065			−0.0655732
$960$	−12.0827	−	30.6003i	−0.389967	−	0.987620i
$961$	30.0562			0.969555
$962$	3.79166	−	3.30665i	0.122248	−	0.106611i
$963$	−8.83634	+	5.90426i	−0.284747	+	0.190262i
$964$	−13.4380	−	17.7153i	−0.432808	−	0.570570i
$965$	12.1074	−	2.40831i	0.389752	−	0.0775264i
$966$	0.290928	−	1.07384i	0.00936045	−	0.0345502i
$967$	−10.5094	−	25.3719i	−0.337959	−	0.815905i	−0.997911	−	0.0645976i	$-0.979424\pi$
$967$	−10.5094	−	25.3719i	−0.337959	−	0.815905i	0.659953	−	0.751307i	$-0.270576\pi$
$968$	−25.0679	−	17.0531i	−0.805711	−	0.548107i
$969$	18.9554	−	45.7623i	0.608934	−	1.47010i
$970$	−4.32541	+	5.60475i	−0.138881	+	0.179958i
$971$	21.7675	−	32.5773i	0.698551	−	1.04546i	−0.297329	−	0.954775i	$-0.596096\pi$
$971$	21.7675	−	32.5773i	0.698551	−	1.04546i	0.995880	−	0.0906809i	$-0.0289043\pi$
$972$	−0.653371	+	1.89027i	−0.0209569	+	0.0606303i
$973$	1.23958	+	0.246568i	0.0397391	+	0.00790461i
$974$	17.1610	+	8.52209i	0.549873	+	0.273065i
$975$	−38.0849	+	38.0849i	−1.21969	+	1.21969i
$976$	−14.6011	+	4.77648i	−0.467369	+	0.152891i
$977$	−20.7541	−	20.7541i	−0.663981	−	0.663981i	0.292335	−	0.956316i	$-0.405568\pi$
$977$	−20.7541	−	20.7541i	−0.663981	−	0.663981i	−0.956316	+	0.292335i	$0.905568\pi$
$978$	−0.100383	−	0.298434i	−0.00320989	−	0.00954287i
$979$	−0.940283	+	4.72712i	−0.0300516	+	0.151079i
$980$	−42.9178	−	38.0610i	−1.37096	−	1.21581i
$981$	4.71262	+	3.14887i	0.150462	+	0.100536i
$982$	3.33828	+	25.9117i	0.106529	+	0.826877i
$983$	−12.2377	−	5.06903i	−0.390322	−	0.161677i	0.178887	−	0.983870i	$-0.442750\pi$
$983$	−12.2377	−	5.06903i	−0.390322	−	0.161677i	−0.569209	+	0.822193i	$0.692750\pi$
$984$	8.80646	−	8.66117i	0.280740	−	0.276108i
$985$	−60.3721	+	25.0070i	−1.92362	+	0.796788i
$986$	7.58866	−	4.35331i	0.241672	−	0.138638i
$987$	−0.0180697	−	0.0908424i	−0.000575164	−	0.00289154i
$988$	−62.8503	−	36.7528i	−1.99953	−	1.16926i
$989$	16.8011	+	25.1446i	0.534244	+	0.799553i
$990$	0.210099	−	3.07483i	0.00667737	−	0.0977247i
$991$			10.4419i			0.331697i	0.986151	+	0.165848i	$0.0530362\pi$
$991$			10.4419i			0.331697i	−0.986151	+	0.165848i	$0.946964\pi$
$992$	−4.96209	+	2.36209i	−0.157546	+	0.0749964i
$993$			10.3252i			0.327662i
$994$	2.24691	+	0.153528i	0.0712676	+	0.00486960i
$995$	42.4909	+	63.5921i	1.34705	+	2.01601i
$996$	13.0475	−	3.41865i	0.413427	−	0.108324i
$997$	−5.17776	−	26.0304i	−0.163981	−	0.824390i	−0.971954	−	0.235170i	$-0.924435\pi$
$997$	−5.17776	−	26.0304i	−0.163981	−	0.824390i	0.807973	−	0.589220i	$-0.200565\pi$
$998$	−0.714025	−	1.24468i	−0.0226021	−	0.0393998i
$999$	0.726889	−	0.301087i	0.0229978	−	0.00952598i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.r.a.13.13	✓	128
3.2	odd	2		576.2.bd.b.397.4		128
4.3	odd	2		768.2.r.a.145.9		128
64.5	even	16	inner	192.2.r.a.133.13	yes	128
64.59	odd	16		768.2.r.a.625.9		128
192.5	odd	16		576.2.bd.b.325.4		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.r.a.13.13	✓	128	1.1	even	1	trivial
192.2.r.a.133.13	yes	128	64.5	even	16	inner
576.2.bd.b.325.4		128	192.5	odd	16
576.2.bd.b.397.4		128	3.2	odd	2
768.2.r.a.145.9		128	4.3	odd	2
768.2.r.a.625.9		128	64.59	odd	16

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:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.r (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.929504 + 1.06584i) q^{2} +(-0.831470 + 0.555570i) q^{3} +(-0.272044 + 1.98141i) q^{4} +(-4.03340 + 0.802293i) q^{5} +(-1.36501 - 0.369811i) q^{6} +(-0.0612023 - 0.147755i) q^{7} +(-2.36474 + 1.55177i) q^{8} +(0.382683 - 0.923880i) q^{9} +O(q^{10})\)	\(q+(0.929504 + 1.06584i) q^{2} +(-0.831470 + 0.555570i) q^{3} +(-0.272044 + 1.98141i) q^{4} +(-4.03340 + 0.802293i) q^{5} +(-1.36501 - 0.369811i) q^{6} +(-0.0612023 - 0.147755i) q^{7} +(-2.36474 + 1.55177i) q^{8} +(0.382683 - 0.923880i) q^{9} +(-4.60418 - 3.55324i) q^{10} +(-0.294415 + 0.440623i) q^{11} +(-0.874617 - 1.79862i) q^{12} +(4.43463 + 0.882103i) q^{13} +(0.100596 - 0.202571i) q^{14} +(2.90792 - 2.90792i) q^{15} +(-3.85198 - 1.07806i) q^{16} +(4.35026 + 4.35026i) q^{17} +(1.34042 - 0.450869i) q^{18} +(-1.57072 + 7.89653i) q^{19} +(-0.492413 - 8.21009i) q^{20} +(0.132976 + 0.0888519i) q^{21} +(-0.743295 + 0.0957609i) q^{22} +(-4.54457 - 1.88242i) q^{23} +(1.10409 - 2.60403i) q^{24} +(11.0053 - 4.55853i) q^{25} +(3.18182 + 5.54654i) q^{26} +(0.195090 + 0.980785i) q^{27} +(0.309414 - 0.0810710i) q^{28} +(-0.558645 - 0.836071i) q^{29} +(5.80231 + 0.396463i) q^{30} -0.971497i q^{31} +(-2.43139 - 5.10767i) q^{32} -0.529933i q^{33} +(-0.593110 + 8.68028i) q^{34} +(0.365397 + 0.546855i) q^{35} +(1.72648 + 1.00959i) q^{36} +(-0.153493 - 0.771661i) q^{37} +(-9.87646 + 5.66572i) q^{38} +(-4.17733 + 1.73031i) q^{39} +(8.29297 - 8.15615i) q^{40} +(4.03464 + 1.67120i) q^{41} +(0.0288998 + 0.224320i) q^{42} +(-5.11173 - 3.41555i) q^{43} +(-0.792962 - 0.703226i) q^{44} +(-0.802293 + 4.03340i) q^{45} +(-2.21783 - 6.59352i) q^{46} +(-0.409517 - 0.409517i) q^{47} +(3.80175 - 1.24367i) q^{48} +(4.93166 - 4.93166i) q^{49} +(15.0881 + 7.49271i) q^{50} +(-6.03398 - 1.20023i) q^{51} +(-2.95422 + 8.54686i) q^{52} +(-1.55137 + 2.32179i) q^{53} +(-0.864026 + 1.11958i) q^{54} +(0.833984 - 2.01342i) q^{55} +(0.374011 + 0.254431i) q^{56} +(-3.08107 - 7.43837i) q^{57} +(0.371858 - 1.37256i) q^{58} +(7.20772 - 1.43370i) q^{59} +(4.97071 + 6.55287i) q^{60} +(3.19336 - 2.13373i) q^{61} +(1.03546 - 0.903010i) q^{62} -0.159929 q^{63} +(3.18399 - 7.33909i) q^{64} -18.5943 q^{65} +(0.564825 - 0.492575i) q^{66} +(10.2146 - 6.82514i) q^{67} +(-9.80311 + 7.43619i) q^{68} +(4.82449 - 0.959650i) q^{69} +(-0.243224 + 0.897759i) q^{70} +(3.81060 + 9.19961i) q^{71} +(0.528706 + 2.77857i) q^{72} +(-5.05384 + 12.2011i) q^{73} +(0.679798 - 0.880862i) q^{74} +(-6.61795 + 9.90447i) q^{75} +(-15.2190 - 5.26044i) q^{76} +(0.0831233 + 0.0165342i) q^{77} +(-5.72708 - 2.84405i) q^{78} +(-1.43481 + 1.43481i) q^{79} +(16.4015 + 1.25783i) q^{80} +(-0.707107 - 0.707107i) q^{81} +(1.96897 + 5.85368i) q^{82} +(-1.31569 + 6.61440i) q^{83} +(-0.212228 + 0.239309i) q^{84} +(-21.0365 - 14.0562i) q^{85} +(-1.11094 - 8.62308i) q^{86} +(0.928992 + 0.384801i) q^{87} +(0.0124669 - 1.49882i) q^{88} +(8.40267 - 3.48050i) q^{89} +(-5.04471 + 2.89394i) q^{90} +(-0.141074 - 0.709227i) q^{91} +(4.96617 - 8.49256i) q^{92} +(0.539735 + 0.807770i) q^{93} +(0.0558331 - 0.817128i) q^{94} -33.1101i q^{95} +(4.85930 + 2.89607i) q^{96} -1.21732i q^{97} +(9.84038 + 0.672378i) q^{98} +(0.294415 + 0.440623i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 16 q^{22} - 80 q^{26} - 80 q^{28} - 80 q^{32} - 80 q^{34} - 80 q^{38} - 80 q^{40} - 16 q^{44} + 48 q^{50} - 32 q^{51} + 48 q^{52} + 16 q^{54} - 64 q^{55} + 112 q^{56} - 128 q^{59} + 96 q^{60} + 96 q^{62} - 32 q^{63} + 96 q^{64} + 96 q^{66} - 32 q^{67} + 96 q^{68} + 96 q^{70} - 128 q^{71} + 112 q^{74} - 64 q^{75} + 16 q^{76} + 48 q^{78} - 32 q^{79} + 48 q^{80} - 80 q^{82} - 80 q^{88} - 96 q^{94}+O(q^{100}) \) 128 * q - 16 * q^22 - 80 * q^26 - 80 * q^28 - 80 * q^32 - 80 * q^34 - 80 * q^38 - 80 * q^40 - 16 * q^44 + 48 * q^50 - 32 * q^51 + 48 * q^52 + 16 * q^54 - 64 * q^55 + 112 * q^56 - 128 * q^59 + 96 * q^60 + 96 * q^62 - 32 * q^63 + 96 * q^64 + 96 * q^66 - 32 * q^67 + 96 * q^68 + 96 * q^70 - 128 * q^71 + 112 * q^74 - 64 * q^75 + 16 * q^76 + 48 * q^78 - 32 * q^79 + 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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