LMFDB - Embedded newform 165.2.s.a.4.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,2,Mod(4,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 2]))

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

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

chi := DirichletCharacter("165.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	165.s (of order $10$, degree $4$, 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:	$1.31753163335$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			4.4
Character	$\chi$	$=$	165.4
Dual form			165.2.s.a.124.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.472206 + 0.649936i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(0.418596 + 1.28830i) q^{4} +(-2.11660 + 0.721122i) q^{5} +(0.649936 - 0.472206i) q^{6} +(-0.483617 + 0.157137i) q^{7} +(-2.56307 - 0.832793i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.472206 + 0.649936i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(0.418596 + 1.28830i) q^{4} +(-2.11660 + 0.721122i) q^{5} +(0.649936 - 0.472206i) q^{6} +(-0.483617 + 0.157137i) q^{7} +(-2.56307 - 0.832793i) q^{8} +(0.809017 + 0.587785i) q^{9} +(0.530788 - 1.71617i) q^{10} +(-3.13337 - 1.08718i) q^{11} -1.35460i q^{12} +(-3.02003 + 4.15671i) q^{13} +(0.126238 - 0.388521i) q^{14} +(2.23584 - 0.0317629i) q^{15} +(-0.440233 + 0.319848i) q^{16} +(1.96639 + 2.70650i) q^{17} +(-0.764046 + 0.248254i) q^{18} +(0.362488 - 1.11562i) q^{19} +(-1.81502 - 2.42496i) q^{20} +0.508505 q^{21} +(2.18620 - 1.52312i) q^{22} +2.91459i q^{23} +(2.18028 + 1.58407i) q^{24} +(3.95997 - 3.05265i) q^{25} +(-1.27552 - 3.92565i) q^{26} +(-0.587785 - 0.809017i) q^{27} +(-0.404880 - 0.557269i) q^{28} +(0.121318 + 0.373379i) q^{29} +(-1.03514 + 1.46815i) q^{30} +(5.14154 + 3.73555i) q^{31} -5.82710i q^{32} +(2.64406 + 2.00224i) q^{33} -2.68759 q^{34} +(0.910308 - 0.681342i) q^{35} +(-0.418596 + 1.28830i) q^{36} +(4.23428 - 1.37580i) q^{37} +(0.553914 + 0.762398i) q^{38} +(4.15671 - 3.02003i) q^{39} +(6.02554 - 0.0856001i) q^{40} +(-0.864837 + 2.66170i) q^{41} +(-0.240119 + 0.330496i) q^{42} -3.05350i q^{43} +(0.0890077 - 4.49183i) q^{44} +(-2.13623 - 0.660705i) q^{45} +(-1.89430 - 1.37629i) q^{46} +(10.9298 + 3.55132i) q^{47} +(0.517525 - 0.168154i) q^{48} +(-5.45393 + 3.96251i) q^{49} +(0.114105 + 4.01521i) q^{50} +(-1.03379 - 3.18168i) q^{51} +(-6.61928 - 2.15074i) q^{52} +(-5.76469 + 7.93441i) q^{53} +0.803366 q^{54} +(7.41608 + 0.0415869i) q^{55} +1.37041 q^{56} +(-0.689492 + 0.949005i) q^{57} +(-0.299960 - 0.0974628i) q^{58} +(0.935871 + 2.88031i) q^{59} +(0.976834 + 2.86715i) q^{60} +(-0.853612 + 0.620185i) q^{61} +(-4.85573 + 1.57772i) q^{62} +(-0.483617 - 0.157137i) q^{63} +(2.90678 + 2.11190i) q^{64} +(3.39469 - 10.9759i) q^{65} +(-2.54987 + 0.772999i) q^{66} -5.31327i q^{67} +(-2.66367 + 3.66623i) q^{68} +(0.900658 - 2.77194i) q^{69} +(0.0129756 + 0.913376i) q^{70} +(-3.31678 + 2.40978i) q^{71} +(-1.58407 - 2.18028i) q^{72} +(-12.4668 + 4.05070i) q^{73} +(-1.10527 + 3.40167i) q^{74} +(-4.70947 + 1.67954i) q^{75} +1.58900 q^{76} +(1.68619 + 0.0334126i) q^{77} +4.12768i q^{78} +(-13.0578 - 9.48703i) q^{79} +(0.701147 - 0.994452i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-1.32155 - 1.81896i) q^{82} +(-9.02764 - 12.4255i) q^{83} +(0.212858 + 0.655110i) q^{84} +(-6.11376 - 4.31056i) q^{85} +(1.98458 + 1.44188i) q^{86} -0.392594i q^{87} +(7.12566 + 5.39598i) q^{88} +9.84603 q^{89} +(1.43816 - 1.07642i) q^{90} +(0.807365 - 2.48481i) q^{91} +(-3.75488 + 1.22004i) q^{92} +(-3.73555 - 5.14154i) q^{93} +(-7.46927 + 5.42674i) q^{94} +(0.0372589 + 2.62272i) q^{95} +(-1.80067 + 5.54191i) q^{96} +(-8.91621 + 12.2721i) q^{97} -5.41583i q^{98} +(-1.89592 - 2.72130i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 12 q^{4} - 4 q^{5} + 4 q^{6} + 12 q^{9}+O(q^{10}) $ 48 * q + 12 * q^4 - 4 * q^5 + 4 * q^6 + 12 * q^9	$ 48 q + 12 q^{4} - 4 q^{5} + 4 q^{6} + 12 q^{9} - 12 q^{10} - 4 q^{14} + 10 q^{15} - 44 q^{16} - 16 q^{19} + 46 q^{20} - 32 q^{21} - 12 q^{24} + 14 q^{25} - 76 q^{26} + 4 q^{30} - 20 q^{31} - 24 q^{34} - 40 q^{35} - 12 q^{36} - 8 q^{39} - 72 q^{40} + 60 q^{41} - 48 q^{44} + 4 q^{45} + 108 q^{46} - 28 q^{49} - 38 q^{50} + 28 q^{51} + 16 q^{54} - 20 q^{55} + 24 q^{56} + 60 q^{59} + 48 q^{60} + 40 q^{61} + 64 q^{64} + 20 q^{65} + 12 q^{66} + 20 q^{69} + 86 q^{70} - 32 q^{71} - 32 q^{74} - 40 q^{75} - 136 q^{76} - 52 q^{79} + 42 q^{80} - 12 q^{81} - 70 q^{85} - 104 q^{86} + 40 q^{89} - 8 q^{90} - 40 q^{91} + 72 q^{94} - 2 q^{95} + 28 q^{96}+O(q^{100}) $ 48 * q + 12 * q^4 - 4 * q^5 + 4 * q^6 + 12 * q^9 - 12 * q^10 - 4 * q^14 + 10 * q^15 - 44 * q^16 - 16 * q^19 + 46 * q^20 - 32 * q^21 - 12 * q^24 + 14 * q^25 - 76 * q^26 + 4 * q^30 - 20 * q^31 - 24 * q^34 - 40 * q^35 - 12 * q^36 - 8 * q^39 - 72 * q^40 + 60 * q^41 - 48 * q^44 + 4 * q^45 + 108 * q^46 - 28 * q^49 - 38 * q^50 + 28 * q^51 + 16 * q^54 - 20 * q^55 + 24 * q^56 + 60 * q^59 + 48 * q^60 + 40 * q^61 + 64 * q^64 + 20 * q^65 + 12 * q^66 + 20 * q^69 + 86 * q^70 - 32 * q^71 - 32 * q^74 - 40 * q^75 - 136 * q^76 - 52 * q^79 + 42 * q^80 - 12 * q^81 - 70 * q^85 - 104 * q^86 + 40 * q^89 - 8 * q^90 - 40 * q^91 + 72 * q^94 - 2 * q^95 + 28 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$-1$

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 $

$2$	−0.472206	+	0.649936i	−0.333900	+	0.459574i	−0.942648	−	0.333790i	$-0.891672\pi$
$2$	−0.472206	+	0.649936i	−0.333900	+	0.459574i	0.608747	+	0.793364i	$0.291672\pi$
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$4$	0.418596	+	1.28830i	0.209298	+	0.644152i
$5$	−2.11660	+	0.721122i	−0.946571	+	0.322495i
$5$	−2.11660	+	0.721122i	−0.946571	+	0.322495i
$6$	0.649936	−	0.472206i	0.265335	−	0.192777i
$7$	−0.483617	+	0.157137i	−0.182790	+	0.0593921i	−0.398982	−	0.916959i	$-0.630636\pi$
$7$	−0.483617	+	0.157137i	−0.182790	+	0.0593921i	0.216192	+	0.976351i	$0.430636\pi$
$8$	−2.56307	−	0.832793i	−0.906183	−	0.294437i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	0.530788	−	1.71617i	0.167850	−	0.542701i
$11$	−3.13337	−	1.08718i	−0.944748	−	0.327798i
$11$	−3.13337	−	1.08718i	−0.944748	−	0.327798i
$12$		−	1.35460i		−	0.391040i
$13$	−3.02003	+	4.15671i	−0.837605	+	1.15286i	0.148854	+	0.988859i	$0.452441\pi$
$13$	−3.02003	+	4.15671i	−0.837605	+	1.15286i	−0.986459	+	0.164005i	$0.947559\pi$
$14$	0.126238	−	0.388521i	0.0337386	−	0.103837i
$15$	2.23584	−	0.0317629i	0.577292	−	0.00820114i
$16$	−0.440233	+	0.319848i	−0.110058	+	0.0799621i
$17$	1.96639	+	2.70650i	0.476919	+	0.656422i	0.977909	−	0.209031i	$-0.0670308\pi$
$17$	1.96639	+	2.70650i	0.476919	+	0.656422i	−0.500990	+	0.865453i	$0.667031\pi$
$18$	−0.764046	+	0.248254i	−0.180087	+	0.0585139i
$19$	0.362488	−	1.11562i	0.0831603	−	0.255941i	−0.900827	−	0.434177i	$-0.857039\pi$
$19$	0.362488	−	1.11562i	0.0831603	−	0.255941i	0.983988	+	0.178236i	$0.0570391\pi$
$20$	−1.81502	−	2.42496i	−0.405851	−	0.542238i
$21$	0.508505			0.110965
$22$	2.18620	−	1.52312i	0.466099	−	0.324730i
$23$			2.91459i			0.607734i	0.952714	+	0.303867i	$0.0982779\pi$
$23$			2.91459i			0.607734i	−0.952714	+	0.303867i	$0.901722\pi$
$24$	2.18028	+	1.58407i	0.445048	+	0.323346i
$25$	3.95997	−	3.05265i	0.791993	−	0.610530i
$26$	−1.27552	−	3.92565i	−0.250150	−	0.769884i
$27$	−0.587785	−	0.809017i	−0.113119	−	0.155695i
$28$	−0.404880	−	0.557269i	−0.0765151	−	0.105314i
$29$	0.121318	+	0.373379i	0.0225282	+	0.0693347i	0.961689	−	0.274144i	$-0.0883946\pi$
$29$	0.121318	+	0.373379i	0.0225282	+	0.0693347i	−0.939160	+	0.343479i	$0.888395\pi$
$30$	−1.03514	+	1.46815i	−0.188989	+	0.268047i
$31$	5.14154	+	3.73555i	0.923447	+	0.670924i	0.944380	−	0.328857i	$-0.106663\pi$
$31$	5.14154	+	3.73555i	0.923447	+	0.670924i	−0.0209323	+	0.999781i	$0.506663\pi$
$32$		−	5.82710i		−	1.03010i
$33$	2.64406	+	2.00224i	0.460271	+	0.348545i
$34$	−2.68759			−0.460918
$35$	0.910308	−	0.681342i	0.153870	−	0.115168i
$36$	−0.418596	+	1.28830i	−0.0697659	+	0.214717i
$37$	4.23428	−	1.37580i	0.696111	−	0.226180i	0.0604757	−	0.998170i	$-0.480738\pi$
$37$	4.23428	−	1.37580i	0.696111	−	0.226180i	0.635635	+	0.771989i	$0.280738\pi$
$38$	0.553914	+	0.762398i	0.0898568	+	0.123677i
$39$	4.15671	−	3.02003i	0.665607	−	0.483592i
$40$	6.02554	−	0.0856001i	0.952721	−	0.0135346i
$41$	−0.864837	+	2.66170i	−0.135065	+	0.415687i	−0.995600	−	0.0937039i	$-0.970129\pi$
$41$	−0.864837	+	2.66170i	−0.135065	+	0.415687i	0.860535	+	0.509391i	$0.170129\pi$
$42$	−0.240119	+	0.330496i	−0.0370512	+	0.0509966i
$43$		−	3.05350i		−	0.465654i	−0.972518	−	0.232827i	$-0.925202\pi$
$43$		−	3.05350i		−	0.465654i	0.972518	−	0.232827i	$-0.0747976\pi$
$44$	0.0890077	−	4.49183i	0.0134184	−	0.677169i
$45$	−2.13623	−	0.660705i	−0.318450	−	0.0984921i
$46$	−1.89430	−	1.37629i	−0.279299	−	0.202923i
$47$	10.9298	+	3.55132i	1.59428	+	0.518013i	0.965684	−	0.259719i	$-0.0836300\pi$
$47$	10.9298	+	3.55132i	1.59428	+	0.518013i	0.628596	+	0.777732i	$0.283630\pi$
$48$	0.517525	−	0.168154i	0.0746984	−	0.0242710i
$49$	−5.45393	+	3.96251i	−0.779132	+	0.566073i
$50$	0.114105	+	4.01521i	0.0161369	+	0.567836i
$51$	−1.03379	−	3.18168i	−0.144760	−	0.445524i
$52$	−6.61928	−	2.15074i	−0.917929	−	0.298253i
$53$	−5.76469	+	7.93441i	−0.791841	+	1.08988i	0.202036	+	0.979378i	$0.435244\pi$
$53$	−5.76469	+	7.93441i	−0.791841	+	1.08988i	−0.993876	+	0.110497i	$0.964756\pi$
$54$	0.803366			0.109324
$55$	7.41608	+	0.0415869i	0.999984	+	0.00560758i
$56$	1.37041			0.183128
$57$	−0.689492	+	0.949005i	−0.0913255	+	0.125699i
$58$	−0.299960	−	0.0974628i	−0.0393866	−	0.0127975i
$59$	0.935871	+	2.88031i	0.121840	+	0.374985i	0.993312	−	0.115460i	$-0.0368342\pi$
$59$	0.935871	+	2.88031i	0.121840	+	0.374985i	−0.871472	+	0.490445i	$0.836834\pi$
$60$	0.976834	+	2.86715i	0.126109	+	0.370148i
$61$	−0.853612	+	0.620185i	−0.109294	+	0.0794066i	−0.641090	−	0.767466i	$-0.721517\pi$
$61$	−0.853612	+	0.620185i	−0.109294	+	0.0794066i	0.531796	+	0.846873i	$0.321517\pi$
$62$	−4.85573	+	1.57772i	−0.616679	+	0.200371i
$63$	−0.483617	−	0.157137i	−0.0609300	−	0.0197974i
$64$	2.90678	+	2.11190i	0.363348	+	0.263987i
$65$	3.39469	−	10.9759i	0.421059	−	1.36139i
$66$	−2.54987	+	0.772999i	−0.313867	+	0.0951496i
$67$		−	5.31327i		−	0.649120i	−0.945865	−	0.324560i	$-0.894784\pi$
$67$		−	5.31327i		−	0.649120i	0.945865	−	0.324560i	$-0.105216\pi$
$68$	−2.66367	+	3.66623i	−0.323018	+	0.444596i
$69$	0.900658	−	2.77194i	0.108427	−	0.333703i
$70$	0.0129756	+	0.913376i	0.00155088	+	0.109169i
$71$	−3.31678	+	2.40978i	−0.393629	+	0.285988i	−0.766941	−	0.641718i	$-0.778222\pi$
$71$	−3.31678	+	2.40978i	−0.393629	+	0.285988i	0.373312	+	0.927706i	$0.378222\pi$
$72$	−1.58407	−	2.18028i	−0.186684	−	0.256948i
$73$	−12.4668	+	4.05070i	−1.45913	+	0.474099i	−0.927803	−	0.373071i	$-0.878305\pi$
$73$	−12.4668	+	4.05070i	−1.45913	+	0.474099i	−0.531323	+	0.847169i	$0.678305\pi$
$74$	−1.10527	+	3.40167i	−0.128485	+	0.395437i
$75$	−4.70947	+	1.67954i	−0.543803	+	0.193937i
$76$	1.58900			0.182270
$77$	1.68619	+	0.0334126i	0.192159	+	0.00380772i
$78$			4.12768i			0.467367i
$79$	−13.0578	−	9.48703i	−1.46911	−	1.06737i	−0.980869	−	0.194668i	$-0.937637\pi$
$79$	−13.0578	−	9.48703i	−1.46911	−	1.06737i	−0.488246	−	0.872706i	$-0.662363\pi$
$80$	0.701147	−	0.994452i	0.0783907	−	0.111183i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	−1.32155	−	1.81896i	−0.145941	−	0.200870i
$83$	−9.02764	−	12.4255i	−0.990912	−	1.36387i	−0.930739	−	0.365685i	$-0.880835\pi$
$83$	−9.02764	−	12.4255i	−0.990912	−	1.36387i	−0.0601730	−	0.998188i	$-0.519165\pi$
$84$	0.212858	+	0.655110i	0.0232247	+	0.0714783i
$85$	−6.11376	−	4.31056i	−0.663131	−	0.467546i
$86$	1.98458	+	1.44188i	0.214003	+	0.155482i
$87$		−	0.392594i		−	0.0420905i
$88$	7.12566	+	5.39598i	0.759598	+	0.575213i
$89$	9.84603			1.04368			0.521838	−	0.853044i	$-0.325246\pi$
$89$	9.84603			1.04368			0.521838	+	0.853044i	$0.325246\pi$
$90$	1.43816	−	1.07642i	0.151595	−	0.113465i
$91$	0.807365	−	2.48481i	0.0846349	−	0.260479i
$92$	−3.75488	+	1.22004i	−0.391473	+	0.127197i
$93$	−3.73555	−	5.14154i	−0.387358	−	0.533153i
$94$	−7.46927	+	5.42674i	−0.770396	+	0.559726i
$95$	0.0372589	+	2.62272i	0.00382269	+	0.269085i
$96$	−1.80067	+	5.54191i	−0.183781	+	0.565618i
$97$	−8.91621	+	12.2721i	−0.905304	+	1.24604i	0.0634410	+	0.997986i	$0.479793\pi$
$97$	−8.91621	+	12.2721i	−0.905304	+	1.24604i	−0.968745	+	0.248059i	$0.920207\pi$
$98$		−	5.41583i		−	0.547081i
$99$	−1.89592	−	2.72130i	−0.190547	−	0.273501i
$100$	5.59037	+	3.82382i	0.559037	+	0.382382i
$101$	13.3869	+	9.72617i	1.33205	+	0.967790i	0.999697	+	0.0246350i	$0.00784235\pi$
$101$	13.3869	+	9.72617i	1.33205	+	0.967790i	0.332352	+	0.943155i	$0.392158\pi$
$102$	2.55605	+	0.830512i	0.253087	+	0.0822329i
$103$	13.6325	−	4.42946i	1.34325	−	0.436448i	0.452832	−	0.891596i	$-0.350414\pi$
$103$	13.6325	−	4.42946i	1.34325	−	0.436448i	0.890416	+	0.455148i	$0.150414\pi$
$104$	11.2022	−	8.13890i	1.09847	−	0.798084i
$105$	−1.07630	+	0.366694i	−0.105036	+	0.0357857i
$106$	−2.43474	−	7.49336i	−0.236483	−	0.727820i
$107$	6.53466	+	2.12324i	0.631729	+	0.205261i	0.607341	−	0.794441i	$-0.292236\pi$
$107$	6.53466	+	2.12324i	0.631729	+	0.205261i	0.0243883	+	0.999703i	$0.492236\pi$
$108$	0.796216	−	1.09590i	0.0766159	−	0.105453i
$109$	−16.9516			−1.62367			−0.811833	−	0.583890i	$-0.801530\pi$
$109$	−16.9516			−1.62367			−0.811833	+	0.583890i	$0.801530\pi$
$110$	−3.52895	+	4.80034i	−0.336472	+	0.457695i
$111$	−4.45218			−0.422583
$112$	0.162645	−	0.223861i	0.0153685	−	0.0211529i
$113$	4.28844	+	1.39340i	0.403422	+	0.131080i	0.503698	−	0.863880i	$-0.331972\pi$
$113$	4.28844	+	1.39340i	0.403422	+	0.131080i	−0.100276	+	0.994960i	$0.531972\pi$
$114$	−0.291210	−	0.896252i	−0.0272743	−	0.0839417i
$115$	−2.10177	−	6.16902i	−0.195992	−	0.575264i
$116$	−0.430243	+	0.312589i	−0.0399470	+	0.0290232i
$117$	−4.88651	+	1.58772i	−0.451758	+	0.146785i
$118$	−2.31395	−	0.751846i	−0.213016	−	0.0692131i
$119$	−1.37627	−	0.999917i	−0.126162	−	0.0916623i
$120$	−5.75708	−	1.78058i	−0.525547	−	0.162544i
$121$	8.63606	+	6.81311i	0.785097	+	0.619373i
$122$		−	0.847649i		−	0.0767425i
$123$	1.64502	−	2.26417i	0.148326	−	0.204154i
$124$	−2.66030	+	8.18755i	−0.238902	+	0.735264i
$125$	−6.18033	+	9.31684i	−0.552785	+	0.833324i
$126$	0.330496	−	0.240119i	0.0294429	−	0.0213915i
$127$	6.28611	+	8.65209i	0.557802	+	0.767749i	0.991045	−	0.133528i	$-0.0426308\pi$
$127$	6.28611	+	8.65209i	0.557802	+	0.767749i	−0.433243	+	0.901277i	$0.642631\pi$
$128$	8.33861	−	2.70938i	0.737036	−	0.239478i
$129$	−0.943583	+	2.90405i	−0.0830778	+	0.255687i
$130$	5.53064	+	7.38922i	0.485069	+	0.648077i
$131$	−7.00557			−0.612079			−0.306040	−	0.952019i	$-0.599004\pi$
$131$	−7.00557			−0.612079			−0.306040	+	0.952019i	$0.599004\pi$
$132$	−1.47270	+	4.24448i	−0.128182	+	0.369435i
$133$			0.596494i			0.0517226i
$134$	3.45329	+	2.50896i	0.298319	+	0.216741i
$135$	1.82750	+	1.28850i	0.157287	+	0.110896i
$136$	−2.78604	−	8.57454i	−0.238901	−	0.735261i
$137$	−6.47026	−	8.90555i	−0.552792	−	0.760852i	0.437596	−	0.899172i	$-0.355830\pi$
$137$	−6.47026	−	8.90555i	−0.552792	−	0.760852i	−0.990388	+	0.138319i	$0.955830\pi$
$138$	1.37629	+	1.89430i	0.117157	+	0.161253i
$139$	4.38892	+	13.5077i	0.372263	+	1.14571i	0.945307	+	0.326183i	$0.105763\pi$
$139$	4.38892	+	13.5077i	0.372263	+	1.14571i	−0.573043	+	0.819525i	$0.694237\pi$
$140$	1.25883	+	0.887547i	0.106390	+	0.0750114i
$141$	−9.29747	−	6.75501i	−0.782988	−	0.568874i
$142$		−	3.29361i		−	0.276393i
$143$	13.9820	−	9.74121i	1.16923	−	0.814601i
$144$	−0.544158			−0.0453465
$145$	−0.526033	−	0.702808i	−0.0436847	−	0.0583650i
$146$	3.25419	−	10.0154i	0.269319	−	0.828879i
$147$	6.41147	−	2.08321i	0.528809	−	0.171821i
$148$	3.54490	+	4.87914i	0.291389	+	0.401063i
$149$	10.5637	−	7.67498i	0.865412	−	0.628759i	−0.0639396	−	0.997954i	$-0.520367\pi$
$149$	10.5637	−	7.67498i	0.865412	−	0.628759i	0.929352	+	0.369195i	$0.120367\pi$
$150$	1.13225	−	3.85395i	0.0924476	−	0.314674i
$151$	5.67085	−	17.4531i	0.461487	−	1.42031i	−0.401859	−	0.915701i	$-0.631636\pi$
$151$	5.67085	−	17.4531i	0.461487	−	1.42031i	0.863347	−	0.504611i	$-0.168364\pi$
$152$	−1.85816	+	2.55754i	−0.150717	+	0.207444i
$153$			3.34542i			0.270461i
$154$	−0.817946	+	1.08014i	−0.0659119	+	0.0870400i
$155$	−13.5763	−	4.19897i	−1.09048	−	0.337270i
$156$	5.63070	+	4.09094i	0.450817	+	0.327537i
$157$	10.4048	+	3.38072i	0.830393	+	0.269811i	0.693211	−	0.720735i	$-0.256195\pi$
$157$	10.4048	+	3.38072i	0.830393	+	0.269811i	0.137182	+	0.990546i	$0.456195\pi$
$158$	12.3319	−	4.00689i	0.981076	−	0.318771i
$159$	7.93441	−	5.76469i	0.629240	−	0.457170i
$160$	4.20205	+	12.3336i	0.332201	+	0.975059i
$161$	−0.457989	−	1.40955i	−0.0360946	−	0.111088i
$162$	−0.764046	−	0.248254i	−0.0600291	−	0.0195046i
$163$	13.5674	−	18.6740i	1.06268	−	1.46266i	0.185416	−	0.982660i	$-0.440637\pi$
$163$	13.5674	−	18.6740i	1.06268	−	1.46266i	0.877269	−	0.479999i	$-0.159363\pi$
$164$	−3.79109			−0.296035
$165$	−7.04026	−	2.33125i	−0.548084	−	0.181487i
$166$	12.3387			0.957667
$167$	−2.45356	+	3.37704i	−0.189862	+	0.261323i	−0.893327	−	0.449407i	$-0.851635\pi$
$167$	−2.45356	+	3.37704i	−0.189862	+	0.261323i	0.703465	+	0.710730i	$0.251635\pi$
$168$	−1.30334	−	0.423479i	−0.100554	−	0.0326721i
$169$	−4.14047	−	12.7430i	−0.318497	−	0.980234i
$170$	5.68855	−	1.93808i	0.436292	−	0.148644i
$171$	0.949005	−	0.689492i	0.0725722	−	0.0527268i
$172$	3.93384	−	1.27818i	0.299952	−	0.0974604i
$173$	3.53501	+	1.14860i	0.268762	+	0.0873261i	0.440298	−	0.897852i	$-0.354873\pi$
$173$	3.53501	+	1.14860i	0.268762	+	0.0873261i	−0.171536	+	0.985178i	$0.554873\pi$
$174$	0.255161	+	0.185385i	0.0193437	+	0.0140540i
$175$	−1.43542	+	2.09857i	−0.108508	+	0.158637i
$176$	1.72715	−	0.523590i	0.130189	−	0.0394671i
$177$		−	3.02854i		−	0.227639i
$178$	−4.64936	+	6.39929i	−0.348484	+	0.479647i
$179$	−5.52898	+	17.0164i	−0.413255	+	1.27187i	0.500547	+	0.865709i	$0.333132\pi$
$179$	−5.52898	+	17.0164i	−0.413255	+	1.27187i	−0.913802	+	0.406159i	$0.866868\pi$
$180$	−0.0430261	−	3.02868i	−0.00320698	−	0.225745i
$181$	−12.2308	+	8.88618i	−0.909107	+	0.660505i	−0.940789	−	0.338993i	$-0.889914\pi$
$181$	−12.2308	+	8.88618i	−0.909107	+	0.660505i	0.0316820	+	0.999498i	$0.489914\pi$
$182$	1.23373	+	1.69808i	0.0914500	+	0.125870i
$183$	1.00348	−	0.326051i	0.0741794	−	0.0241024i
$184$	2.42725	−	7.47031i	0.178939	−	0.550718i
$185$	−7.97014	+	5.96544i	−0.585977	+	0.438588i
$186$	5.10562			0.374362
$187$	−3.21896	−	10.6183i	−0.235394	−	0.776487i
$188$			15.5675i			1.13538i
$189$	0.411389	+	0.298892i	0.0299242	+	0.0217412i
$190$	−1.72219	−	1.21425i	−0.124941	−	0.0880909i
$191$	0.230395	+	0.709082i	0.0166708	+	0.0513074i	0.959046	−	0.283251i	$-0.0914129\pi$
$191$	0.230395	+	0.709082i	0.0166708	+	0.0513074i	−0.942375	+	0.334558i	$0.891413\pi$
$192$	−2.11190	−	2.90678i	−0.152413	−	0.209779i
$193$	−5.21892	−	7.18323i	−0.375666	−	0.517060i	0.578764	−	0.815495i	$-0.303535\pi$
$193$	−5.21892	−	7.18323i	−0.375666	−	0.517060i	−0.954430	+	0.298435i	$0.903535\pi$
$194$	−3.76580	−	11.5899i	−0.270369	−	0.832109i
$195$	−6.62028	+	9.38968i	−0.474088	+	0.672409i
$196$	−7.38791	−	5.36763i	−0.527708	−	0.383402i
$197$		−	1.05280i		−	0.0750089i	−0.999296	−	0.0375044i	$-0.988059\pi$
$197$		−	1.05280i		−	0.0750089i	0.999296	−	0.0375044i	$-0.0119408\pi$
$198$	2.66394	+	0.0527872i	0.189318	+	0.00375142i
$199$	2.28171			0.161746			0.0808730	−	0.996724i	$-0.474229\pi$
$199$	2.28171			0.161746			0.0808730	+	0.996724i	$0.474229\pi$
$200$	−12.6919	+	4.52632i	−0.897453	+	0.320059i
$201$	−1.64189	+	5.05322i	−0.115810	+	0.356427i
$202$	−12.6428	+	4.10789i	−0.889543	+	0.289030i
$203$	−0.117343	−	0.161509i	−0.00823587	−	0.0113357i
$204$	3.66623	−	2.66367i	0.256688	−	0.186494i
$205$	−0.0888939	−	6.25739i	−0.00620862	−	0.437035i
$206$	−3.55848	+	10.9519i	−0.247931	+	0.763052i
$207$	−1.71315	+	2.35795i	−0.119072	+	0.163889i
$208$		−	2.79587i		−	0.193859i
$209$	−2.34869	+	3.10157i	−0.162463	+	0.214540i
$210$	0.269908	−	0.872682i	0.0186254	−	0.0602208i
$211$	7.74164	+	5.62463i	0.532957	+	0.387216i	0.821463	−	0.570263i	$-0.193159\pi$
$211$	7.74164	+	5.62463i	0.532957	+	0.387216i	−0.288506	+	0.957478i	$0.593159\pi$
$212$	−12.6350	−	4.10537i	−0.867776	−	0.281958i
$213$	3.89910	−	1.26690i	0.267162	−	0.0868063i
$214$	−4.46568	+	3.24451i	−0.305267	+	0.221790i
$215$	2.20194	+	6.46303i	0.150171	+	0.440775i
$216$	0.832793	+	2.56307i	0.0566644	+	0.174395i
$217$	−3.07353	−	0.998650i	−0.208645	−	0.0677927i
$218$	8.00464	−	11.0174i	0.542142	−	0.746195i
$219$	13.1083			0.885780
$220$	3.05076	+	9.57158i	0.205682	+	0.645316i
$221$	−17.1887			−1.15624
$222$	2.10235	−	2.89364i	0.141100	−	0.194208i
$223$	−8.38760	−	2.72530i	−0.561676	−	0.182499i	0.0143994	−	0.999896i	$-0.495416\pi$
$223$	−8.38760	−	2.72530i	−0.561676	−	0.182499i	−0.576075	+	0.817397i	$0.695416\pi$
$224$	0.915652	+	2.81809i	0.0611796	+	0.188291i
$225$	4.99798	−	0.142034i	0.333199	−	0.00946890i
$226$	−2.93065	+	2.12924i	−0.194944	+	0.141635i
$227$	−5.12395	+	1.66487i	−0.340088	+	0.110501i	−0.474082	−	0.880481i	$-0.657220\pi$
$227$	−5.12395	+	1.66487i	−0.340088	+	0.110501i	0.133993	+	0.990982i	$0.457220\pi$
$228$	−1.51123	−	0.491027i	−0.100083	−	0.0325191i
$229$	19.7252	+	14.3312i	1.30348	+	0.947034i	0.999983	−	0.00579853i	$-0.00184574\pi$
$229$	19.7252	+	14.3312i	1.30348	+	0.947034i	0.303497	+	0.952832i	$0.401846\pi$
$230$	5.00194	+	1.54703i	0.329818	+	0.102008i
$231$	−1.59334	−	0.552839i	−0.104834	−	0.0363741i
$232$		−	1.05803i		−	0.0694631i
$233$	2.71552	−	3.73760i	0.177900	−	0.244858i	−0.710750	−	0.703445i	$-0.751644\pi$
$233$	2.71552	−	3.73760i	0.177900	−	0.244858i	0.888650	+	0.458587i	$0.151644\pi$
$234$	1.27552	−	3.92565i	0.0833835	−	0.256628i
$235$	−25.6950	+	0.365029i	−1.67616	+	0.0238118i
$236$	−3.31897	+	2.41137i	−0.216047	+	0.156967i
$237$	9.48703	+	13.0578i	0.616249	+	0.848194i
$238$	1.29977	−	0.422319i	0.0842513	−	0.0273749i
$239$	−1.48904	+	4.58278i	−0.0963177	+	0.296435i	−0.987595	−	0.157024i	$-0.949810\pi$
$239$	−1.48904	+	4.58278i	−0.0963177	+	0.296435i	0.891277	+	0.453459i	$0.149810\pi$
$240$	−0.974133	+	0.729114i	−0.0628800	+	0.0470641i
$241$	0.424606			0.0273513			0.0136757	−	0.999906i	$-0.495647\pi$
$241$	0.424606			0.0273513			0.0136757	+	0.999906i	$0.495647\pi$
$242$	−8.50609	+	2.39570i	−0.546792	+	0.154001i
$243$		−	1.00000i		−	0.0641500i
$244$	−1.15631	−	0.840105i	−0.0740249	−	0.0537822i
$245$	8.68631	−	12.3200i	0.554948	−	0.787095i
$246$	0.694781	+	2.13831i	0.0442976	+	0.136334i
$247$	3.54260	+	4.87597i	0.225410	+	0.310250i
$248$	−10.0672	−	13.8563i	−0.639268	−	0.879876i
$249$	4.74611	+	14.6070i	0.300772	+	0.925682i
$250$	−3.13697	−	8.41629i	−0.198399	−	0.532293i
$251$	−12.4287	−	9.03000i	−0.784494	−	0.569968i	0.121830	−	0.992551i	$-0.461124\pi$
$251$	−12.4287	−	9.03000i	−0.784494	−	0.569968i	−0.906324	+	0.422583i	$0.861124\pi$
$252$		−	0.688823i		−	0.0433918i
$253$	3.16870	−	9.13250i	0.199214	−	0.574156i
$254$	−8.59165			−0.539088
$255$	4.48250	+	5.98885i	0.280705	+	0.375036i
$256$	−4.39720	+	13.5332i	−0.274825	+	0.845825i
$257$	−7.05184	+	2.29128i	−0.439882	+	0.142926i	−0.520581	−	0.853812i	$-0.674285\pi$
$257$	−7.05184	+	2.29128i	−0.439882	+	0.142926i	0.0806994	+	0.996738i	$0.474285\pi$
$258$	−1.44188	−	1.98458i	−0.0897676	−	0.123555i
$259$	−1.83158	+	1.33072i	−0.113809	+	0.0826870i
$260$	15.5613	−	0.221067i	0.965071	−	0.0137100i
$261$	−0.121318	+	0.373379i	−0.00750940	+	0.0231116i
$262$	3.30808	−	4.55317i	0.204374	−	0.281296i
$263$			30.6870i			1.89224i	0.323815	+	0.946120i	$0.395034\pi$
$263$			30.6870i			1.89224i	−0.323815	+	0.946120i	$0.604966\pi$
$264$	−5.10946	−	7.33383i	−0.314465	−	0.451366i
$265$	6.47985	−	20.9510i	0.398054	−	1.28701i
$266$	−0.387683	−	0.281668i	−0.0237704	−	0.0172702i
$267$	−9.36413	−	3.04259i	−0.573075	−	0.186203i
$268$	6.84511	−	2.22411i	0.418132	−	0.135859i
$269$	14.7575	−	10.7219i	0.899780	−	0.653729i	−0.0386292	−	0.999254i	$-0.512299\pi$
$269$	14.7575	−	10.7219i	0.899780	−	0.653729i	0.938410	+	0.345525i	$0.112299\pi$
$270$	−1.70040	+	0.579324i	−0.103483	+	0.0352566i
$271$	4.24624	+	13.0686i	0.257941	+	0.793860i	0.993236	+	0.116113i	$0.0370436\pi$
$271$	4.24624	+	13.0686i	0.257941	+	0.793860i	−0.735295	+	0.677747i	$0.762956\pi$
$272$	−1.73134	−	0.562546i	−0.104978	−	0.0341094i
$273$	−1.53570	+	2.11371i	−0.0929448	+	0.127928i
$274$	8.84334			0.534246
$275$	−15.7268	+	5.25987i	−0.948365	+	0.317182i
$276$	3.94812			0.237649
$277$	−0.809688	+	1.11444i	−0.0486495	+	0.0669602i	−0.832649	−	0.553802i	$-0.813177\pi$
$277$	−0.809688	+	1.11444i	−0.0486495	+	0.0669602i	0.783999	+	0.620762i	$0.213177\pi$
$278$	−10.8516	−	3.52591i	−0.650837	−	0.211470i
$279$	1.96389	+	6.04424i	0.117575	+	0.361859i
$280$	−2.90060	+	0.988231i	−0.173344	+	0.0590581i
$281$	15.6161	−	11.3457i	0.931576	−	0.676830i	−0.0148018	−	0.999890i	$-0.504712\pi$
$281$	15.6161	−	11.3457i	0.931576	−	0.676830i	0.946378	+	0.323061i	$0.104712\pi$
$282$	8.78065	−	2.85301i	0.522880	−	0.169894i
$283$	2.08871	+	0.678664i	0.124161	+	0.0403424i	0.370439	−	0.928857i	$-0.379207\pi$
$283$	2.08871	+	0.678664i	0.124161	+	0.0403424i	−0.246277	+	0.969199i	$0.579207\pi$
$284$	−4.49292	−	3.26430i	−0.266606	−	0.193700i
$285$	0.775030	−	2.50587i	0.0459088	−	0.148435i
$286$	−0.271219	+	13.6873i	−0.0160375	+	0.809345i
$287$		−	1.42314i		−	0.0840053i
$288$	3.42509	−	4.71423i	0.201825	−	0.277788i
$289$	1.79483	−	5.52392i	0.105578	−	0.324936i
$290$	0.705177	−	0.0100179i	0.0414094	−	0.000588271i
$291$	12.2721	−	8.91621i	0.719404	−	0.522678i
$292$	−10.4371	−	14.3654i	−0.610784	−	0.840672i
$293$	−25.9810	+	8.44173i	−1.51782	+	0.493171i	−0.945157	−	0.326617i	$-0.894091\pi$
$293$	−25.9810	+	8.44173i	−1.51782	+	0.493171i	−0.572668	+	0.819788i	$0.694091\pi$
$294$	−1.67358	+	5.15076i	−0.0976053	+	0.300398i
$295$	−4.05792	−	5.42159i	−0.236261	−	0.315657i
$296$	−11.9985			−0.697400
$297$	0.962201	+	3.17398i	0.0558325	+	0.184173i
$298$			10.4899i			0.607664i
$299$	−12.1151	−	8.80215i	−0.700635	−	0.509041i
$300$	−4.13513	−	5.36419i	−0.238742	−	0.309701i
$301$	0.479817	+	1.47672i	0.0276562	+	0.0851170i
$302$	8.66559	+	11.9272i	0.498648	+	0.686331i
$303$	−9.72617	−	13.3869i	−0.558754	−	0.769059i
$304$	0.197251	+	0.607075i	0.0113131	+	0.0348181i
$305$	1.35952	−	1.92824i	0.0778461	−	0.110411i
$306$	−2.17431	−	1.57973i	−0.124297	−	0.0903070i
$307$			26.9287i			1.53690i	0.639908	+	0.768451i	$0.278972\pi$
$307$			26.9287i			1.53690i	−0.639908	+	0.768451i	$0.721028\pi$
$308$	0.662786	+	2.18631i	0.0377657	+	0.124577i
$309$	−14.3340			−0.815434
$310$	9.13990	−	6.84098i	0.519112	−	0.388542i
$311$	3.68794	−	11.3503i	0.209124	−	0.643618i	−0.790395	−	0.612598i	$-0.790124\pi$
$311$	3.68794	−	11.3503i	0.209124	−	0.643618i	0.999519	−	0.0310199i	$-0.00987551\pi$
$312$	−13.1690	+	4.27887i	−0.745548	+	0.242243i
$313$	8.79398	+	12.1039i	0.497065	+	0.684152i	0.981672	−	0.190581i	$-0.0610371\pi$
$313$	8.79398	+	12.1039i	0.497065	+	0.684152i	−0.484606	+	0.874732i	$0.661037\pi$
$314$	−7.11047	+	5.16606i	−0.401267	+	0.291537i
$315$	1.13694	−	0.0161516i	0.0640592	−	0.000910038i
$316$	6.75626	−	20.7936i	0.380069	−	1.16973i
$317$	5.75168	−	7.91651i	0.323047	−	0.444635i	−0.616348	−	0.787474i	$-0.711388\pi$
$317$	5.75168	−	7.91651i	0.323047	−	0.444635i	0.939394	+	0.342839i	$0.111388\pi$
$318$			7.87899i			0.441832i
$319$	0.0257964	−	1.30183i	0.00144432	−	0.0728885i
$320$	−7.67542	−	2.37390i	−0.429069	−	0.132705i
$321$	−5.55871	−	4.03864i	−0.310257	−	0.225415i
$322$	1.13238	+	0.367933i	0.0631051	+	0.0205041i
$323$	3.73222	−	1.21267i	0.207666	−	0.0674748i
$324$	−1.09590	+	0.796216i	−0.0608832	+	0.0442342i
$325$	0.729765	+	25.6795i	0.0404801	+	1.42444i
$326$	5.73027	+	17.6360i	0.317370	+	0.976765i
$327$	16.1219	+	5.23832i	0.891543	+	0.289680i
$328$	4.43328	−	6.10189i	0.244787	−	0.336920i
$329$	−5.84390			−0.322184
$330$	4.83962	−	3.47489i	0.266412	−	0.191287i
$331$	5.14693			0.282901			0.141450	−	0.989945i	$-0.454823\pi$
$331$	5.14693			0.282901			0.141450	+	0.989945i	$0.454823\pi$
$332$	12.2289	−	16.8316i	0.671146	−	0.923754i
$333$	4.23428	+	1.37580i	0.232037	+	0.0753934i
$334$	−1.03627	−	3.18932i	−0.0567023	−	0.174512i
$335$	3.83152	+	11.2461i	0.209338	+	0.614438i
$336$	−0.223861	+	0.162645i	−0.0122126	+	0.00887299i
$337$	27.9149	−	9.07009i	1.52062	−	0.494079i	0.574668	−	0.818387i	$-0.305131\pi$
$337$	27.9149	−	9.07009i	1.52062	−	0.494079i	0.945952	+	0.324308i	$0.105131\pi$
$338$	10.2373	+	3.32631i	0.556837	+	0.180927i
$339$	−3.64796	−	2.65040i	−0.198130	−	0.143950i
$340$	2.99413	−	9.68077i	0.162379	−	0.525014i
$341$	−12.0491	−	17.2947i	−0.652497	−	0.936558i
$342$			0.942375i			0.0509578i
$343$	4.10720	−	5.65307i	0.221768	−	0.305237i
$344$	−2.54293	+	7.82634i	−0.137106	+	0.421968i
$345$	0.0925758	+	6.51657i	0.00498411	+	0.350840i
$346$	−2.41577	+	1.75516i	−0.129873	+	0.0943579i
$347$	4.31194	+	5.93488i	0.231477	+	0.318601i	0.908917	−	0.416977i	$-0.136911\pi$
$347$	4.31194	+	5.93488i	0.231477	+	0.318601i	−0.677440	+	0.735578i	$0.736911\pi$
$348$	0.505780	−	0.164338i	0.0271127	−	0.00880944i
$349$	8.81528	−	27.1306i	0.471871	−	1.45227i	−0.378261	−	0.925699i	$-0.623478\pi$
$349$	8.81528	−	27.1306i	0.471871	−	1.45227i	0.850132	−	0.526570i	$-0.176522\pi$
$350$	−0.686120	−	1.92389i	−0.0366746	−	0.102836i
$351$	5.13798			0.274245
$352$	−6.33513	+	18.2585i	−0.337664	+	0.973181i
$353$			16.1818i			0.861271i	0.902526	+	0.430636i	$0.141711\pi$
$353$			16.1818i			0.861271i	−0.902526	+	0.430636i	$0.858289\pi$
$354$	1.96836	+	1.43010i	0.104617	+	0.0760088i
$355$	5.28254	−	7.49233i	0.280368	−	0.397652i
$356$	4.12150	+	12.6847i	0.218439	+	0.672287i
$357$	0.999917	+	1.37627i	0.0529212	+	0.0728398i
$358$	−8.44878	−	11.6288i	−0.446532	−	0.614599i
$359$	−5.23240	−	16.1037i	−0.276156	−	0.849920i	−0.988911	−	0.148507i	$-0.952553\pi$
$359$	−5.23240	−	16.1037i	−0.276156	−	0.849920i	0.712756	−	0.701413i	$-0.247447\pi$
$360$	4.92508	+	3.47247i	0.259574	+	0.183015i
$361$	14.2581	+	10.3591i	0.750427	+	0.545217i
$362$		−	12.1453i		−	0.638345i
$363$	−6.10802	−	9.14834i	−0.320588	−	0.480163i
$364$	3.53916			0.185502
$365$	23.4661	−	17.5638i	1.22827	−	0.919330i
$366$	−0.261938	+	0.806162i	−0.0136917	+	0.0421388i
$367$	3.82592	−	1.24312i	0.199711	−	0.0648901i	−0.207453	−	0.978245i	$-0.566518\pi$
$367$	3.82592	−	1.24312i	0.199711	−	0.0648901i	0.407165	+	0.913355i	$0.366518\pi$
$368$	−0.932227	−	1.28310i	−0.0485957	−	0.0668862i
$369$	−2.26417	+	1.64502i	−0.117868	+	0.0856362i
$370$	−0.113607	−	7.99701i	−0.00590616	−	0.415745i
$371$	1.54111	−	4.74306i	0.0800107	−	0.246248i
$372$	5.06018	−	6.96475i	0.262358	−	0.361105i
$373$			36.2624i			1.87760i	0.344469	+	0.938798i	$0.388059\pi$
$373$			36.2624i			1.87760i	−0.344469	+	0.938798i	$0.611941\pi$
$374$	8.42123	+	2.92191i	0.435451	+	0.151088i
$375$	8.75690	−	6.95102i	0.452204	−	0.358949i
$376$	−25.0564	−	18.2046i	−1.29219	−	0.938829i
$377$	−1.91841	−	0.623330i	−0.0988033	−	0.0321031i
$378$	−0.388521	+	0.126238i	−0.0199834	+	0.00649299i
$379$	−16.0725	+	11.6774i	−0.825591	+	0.599827i	−0.918308	−	0.395866i	$-0.870445\pi$
$379$	−16.0725	+	11.6774i	−0.825591	+	0.599827i	0.0927176	+	0.995692i	$0.470445\pi$
$380$	−3.36327	+	1.14586i	−0.172532	+	0.0587814i
$381$	−3.30480	−	10.1711i	−0.169310	−	0.521083i
$382$	−0.569652	−	0.185091i	−0.0291460	−	0.00947010i
$383$	14.3708	−	19.7798i	0.734315	−	1.01070i	−0.264610	−	0.964355i	$-0.585243\pi$
$383$	14.3708	−	19.7798i	0.734315	−	1.01070i	0.998926	−	0.0463430i	$-0.0147567\pi$
$384$	−8.76773			−0.447427
$385$	−3.59308	+	1.14523i	−0.183120	+	0.0583662i
$386$	7.13305			0.363063
$387$	1.79480	−	2.47033i	0.0912349	−	0.125574i
$388$	−19.5425	−	6.34974i	−0.992120	−	0.322359i
$389$	3.73527	+	11.4960i	0.189386	+	0.582870i	0.999996	−	0.00271592i	$-0.000864505\pi$
$389$	3.73527	+	11.4960i	0.189386	+	0.582870i	−0.810610	+	0.585586i	$0.800865\pi$
$390$	−2.97656	−	8.73663i	−0.150724	−	0.442396i
$391$	−7.88834	+	5.73121i	−0.398930	+	0.289840i
$392$	17.2788	−	5.61421i	0.872709	−	0.283560i
$393$	6.66269	+	2.16484i	0.336088	+	0.109202i
$394$	0.684253	+	0.497139i	0.0344722	+	0.0250455i
$395$	34.4794	+	10.6640i	1.73484	+	0.536563i
$396$	2.71224	−	3.58165i	0.136295	−	0.179985i
$397$		−	22.7158i		−	1.14007i	−0.821619	−	0.570037i	$-0.806929\pi$
$397$		−	22.7158i		−	1.14007i	0.821619	−	0.570037i	$-0.193071\pi$
$398$	−1.07744	+	1.48297i	−0.0540071	+	0.0743343i
$399$	0.184327	−	0.567299i	0.00922788	−	0.0284005i
$400$	−0.766926	+	2.61047i	−0.0383463	+	0.130523i
$401$	1.90762	−	1.38597i	0.0952619	−	0.0692119i	−0.539135	−	0.842220i	$-0.681249\pi$
$401$	1.90762	−	1.38597i	0.0952619	−	0.0692119i	0.634397	+	0.773008i	$0.281249\pi$
$402$	−2.50896	−	3.45329i	−0.125136	−	0.172234i
$403$	−31.0552	+	10.0904i	−1.54697	+	0.502641i
$404$	−6.92656	+	21.3178i	−0.344609	+	1.06060i
$405$	−1.33989	−	1.79016i	−0.0665798	−	0.0889540i
$406$	0.160381			0.00795956
$407$	−14.7633	−	0.292542i	−0.731791	−	0.0145008i
$408$			9.01581i			0.446349i
$409$	−2.21976	−	1.61275i	−0.109760	−	0.0797452i	0.531551	−	0.847026i	$-0.321609\pi$
$409$	−2.21976	−	1.61275i	−0.109760	−	0.0797452i	−0.641311	+	0.767281i	$0.721609\pi$
$410$	4.10888	+	2.89700i	0.202923	+	0.143073i
$411$	3.40162	+	10.4691i	0.167789	+	0.516403i
$412$	11.4130	+	15.7086i	0.562277	+	0.773908i
$413$	−0.905206	−	1.24591i	−0.0445423	−	0.0613072i
$414$	−0.723558	−	2.22688i	−0.0355609	−	0.109445i
$415$	28.0681	+	19.7897i	1.37781	+	0.971438i
$416$	24.2216	+	17.5980i	1.18756	+	0.862814i
$417$		−	14.2028i		−	0.695516i
$418$	−0.906754	−	2.99108i	−0.0443508	−	0.146299i
$419$	13.9861			0.683266			0.341633	−	0.939833i	$-0.389020\pi$
$419$	13.9861			0.683266			0.341633	+	0.939833i	$0.389020\pi$
$420$	−0.922948	−	1.23311i	−0.0450353	−	0.0601694i
$421$	−5.49260	+	16.9045i	−0.267693	+	0.823875i	0.723368	+	0.690463i	$0.242593\pi$
$421$	−5.49260	+	16.9045i	−0.267693	+	0.823875i	−0.991061	+	0.133412i	$0.957407\pi$
$422$	−7.31131	+	2.37559i	−0.355909	+	0.115642i
$423$	6.75501	+	9.29747i	0.328440	+	0.452058i
$424$	21.3830	−	15.5357i	1.03845	−	0.754479i
$425$	16.0488	+	4.71496i	0.778482	+	0.228709i
$426$	−1.01778	+	3.13241i	−0.0493116	+	0.151766i
$427$	0.315367	−	0.434066i	0.0152617	−	0.0210059i
$428$			9.30741i			0.449891i
$429$	−16.3079	+	4.94377i	−0.787351	+	0.238687i
$430$	−5.24033	−	1.62076i	−0.252711	−	0.0781600i
$431$	−5.75712	−	4.18279i	−0.277311	−	0.201478i	0.440433	−	0.897786i	$-0.354825\pi$
$431$	−5.75712	−	4.18279i	−0.277311	−	0.201478i	−0.717744	+	0.696308i	$0.754825\pi$
$432$	0.517525	+	0.168154i	0.0248995	+	0.00809032i
$433$	−10.8247	+	3.51714i	−0.520200	+	0.169023i	−0.557336	−	0.830287i	$-0.688176\pi$
$433$	−10.8247	+	3.51714i	−0.520200	+	0.169023i	0.0371363	+	0.999310i	$0.488176\pi$
$434$	2.10040	−	1.52603i	0.100822	−	0.0732517i
$435$	0.283108	+	0.830963i	0.0135740	+	0.0398416i
$436$	−7.09585	−	21.8388i	−0.339830	−	1.04589i
$437$	3.25158	+	1.05650i	0.155544	+	0.0505394i
$438$	−6.18985	+	8.51959i	−0.295762	+	0.407082i
$439$	16.1917			0.772788			0.386394	−	0.922334i	$-0.373721\pi$
$439$	16.1917			0.772788			0.386394	+	0.922334i	$0.373721\pi$
$440$	−18.9733	−	6.28265i	−0.904517	−	0.299513i
$441$	−6.74142			−0.321020
$442$	8.11660	−	11.1715i	0.386068	−	0.531376i
$443$	−22.5896	−	7.33982i	−1.07327	−	0.348725i	−0.281508	−	0.959559i	$-0.590834\pi$
$443$	−22.5896	−	7.33982i	−1.07327	−	0.348725i	−0.791759	+	0.610834i	$0.790834\pi$
$444$	−1.86366	−	5.73577i	−0.0884456	−	0.272208i
$445$	−20.8401	+	7.10018i	−0.987914	+	0.336581i
$446$	5.73195	−	4.16451i	0.271416	−	0.197195i
$447$	−12.4184	+	4.03498i	−0.587369	+	0.190848i
$448$	−1.73763	−	0.564589i	−0.0820951	−	0.0266743i
$449$	−16.7134	−	12.1430i	−0.788755	−	0.573064i	0.118839	−	0.992914i	$-0.462083\pi$
$449$	−16.7134	−	12.1430i	−0.788755	−	0.573064i	−0.907594	+	0.419850i	$0.862083\pi$
$450$	−2.26777	+	3.31544i	−0.106904	+	0.156291i
$451$	5.60361	−	7.39985i	0.263864	−	0.348445i
$452$			6.10809i			0.287300i
$453$	−10.7866	+	14.8465i	−0.506799	+	0.697549i
$454$	1.33750	−	4.11640i	0.0627720	−	0.193192i
$455$	0.0829865	+	5.84156i	0.00389047	+	0.273857i
$456$	2.55754	−	1.85816i	0.119768	−	0.0870165i
$457$	4.53791	+	6.24590i	0.212274	+	0.292171i	0.901855	−	0.432038i	$-0.142205\pi$
$457$	4.53791	+	6.24590i	0.212274	+	0.292171i	−0.689581	+	0.724209i	$0.742205\pi$
$458$	−18.6288	+	6.05285i	−0.870465	+	0.282831i
$459$	1.03379	−	3.18168i	0.0482532	−	0.148508i
$460$	7.06778	−	5.29005i	0.329537	−	0.246650i
$461$	41.3034			1.92369			0.961845	−	0.273595i	$-0.0882128\pi$
$461$	41.3034			1.92369			0.961845	+	0.273595i	$0.0882128\pi$
$462$	1.11169	−	0.774514i	0.0517207	−	0.0360336i
$463$			19.5424i			0.908214i	0.890947	+	0.454107i	$0.150042\pi$
$463$			19.5424i			0.908214i	−0.890947	+	0.454107i	$0.849958\pi$
$464$	−0.172833	−	0.125570i	−0.00802357	−	0.00582946i
$465$	11.6143	+	8.18878i	0.538601	+	0.379746i
$466$	1.14691	+	3.52983i	0.0531297	+	0.163516i
$467$	−12.5559	−	17.2817i	−0.581016	−	0.799700i	0.412790	−	0.910826i	$-0.364554\pi$
$467$	−12.5559	−	17.2817i	−0.581016	−	0.799700i	−0.993806	+	0.111126i	$0.964554\pi$
$468$	−4.09094	−	5.63070i	−0.189104	−	0.260279i
$469$	0.834910	+	2.56959i	0.0385526	+	0.118653i
$470$	11.8961	−	16.8725i	0.548726	−	0.778269i
$471$	−8.85085	−	6.43052i	−0.407825	−	0.296303i
$472$		−	8.16184i		−	0.375679i
$473$	−3.31971	+	9.56775i	−0.152641	+	0.439926i
$474$	−12.9666			−0.595574
$475$	−1.97016	−	5.52437i	−0.0903972	−	0.253476i
$476$	0.712099	−	2.19161i	0.0326390	−	0.100452i
$477$	−9.32746	+	3.03068i	−0.427075	+	0.138765i
$478$	−2.27538	−	3.13180i	−0.104074	−	0.143245i
$479$	−12.4719	+	9.06140i	−0.569858	+	0.414026i	−0.835053	−	0.550169i	$-0.814563\pi$
$479$	−12.4719	+	9.06140i	−0.569858	+	0.414026i	0.265196	+	0.964195i	$0.414563\pi$
$480$	−0.185086	−	13.0285i	−0.00844796	−	0.594666i
$481$	−7.06883	+	21.7556i	−0.322311	+	0.991971i
$482$	−0.200502	+	0.275967i	−0.00913261	+	0.0125700i
$483$			1.48208i			0.0674372i
$484$	−5.16234	+	13.9778i	−0.234652	+	0.635355i
$485$	10.0223	−	32.4048i	0.455091	−	1.47143i
$486$	0.649936	+	0.472206i	0.0294817	+	0.0214197i
$487$	−23.8833	−	7.76017i	−1.08226	−	0.351647i	−0.287007	−	0.957928i	$-0.592660\pi$
$487$	−23.8833	−	7.76017i	−1.08226	−	0.351647i	−0.795250	+	0.606282i	$0.792660\pi$
$488$	2.70435	−	0.878698i	0.122420	−	0.0397768i
$489$	−18.6740	+	13.5674i	−0.844467	+	0.613541i
$490$	3.90547	+	11.4631i	0.176431	+	0.517851i
$491$	0.341112	+	1.04983i	0.0153942	+	0.0473784i	0.958459	−	0.285232i	$-0.0920706\pi$
$491$	0.341112	+	1.04983i	0.0153942	+	0.0473784i	−0.943064	+	0.332610i	$0.892071\pi$
$492$	3.60554	+	1.17151i	0.162550	+	0.0528158i
$493$	−0.771991	+	1.06255i	−0.0347687	+	0.0478550i
$494$	−4.84190			−0.217848
$495$	5.97529	+	4.39271i	0.268569	+	0.197438i
$496$	−3.45829			−0.155282
$497$	1.22539	−	1.68660i	0.0549660	−	0.0756543i
$498$	−11.7348	−	3.81286i	−0.525848	−	0.170858i
$499$	−0.709867	−	2.18475i	−0.0317780	−	0.0978026i	0.933909	−	0.357510i	$-0.116374\pi$
$499$	−0.709867	−	2.18475i	−0.0317780	−	0.0978026i	−0.965687	+	0.259707i	$0.916374\pi$
$500$	−14.5900	−	4.06215i	−0.652484	−	0.181665i
$501$	3.37704	−	2.45356i	0.150875	−	0.109617i
$502$	11.7378	−	3.81386i	0.523886	−	0.170221i
$503$	6.52108	+	2.11883i	0.290761	+	0.0944739i	0.450766	−	0.892642i	$-0.351151\pi$
$503$	6.52108	+	2.11883i	0.290761	+	0.0944739i	−0.160005	+	0.987116i	$0.551151\pi$
$504$	1.10868	+	0.805505i	0.0493847	+	0.0358801i
$505$	−35.3485	−	10.9328i	−1.57299	−	0.486503i
$506$	4.43927	+	6.37188i	0.197350	+	0.283265i
$507$			13.3988i			0.595063i
$508$	−8.51519	+	11.7202i	−0.377800	+	0.519998i
$509$	−7.99840	+	24.6166i	−0.354523	+	1.09111i	0.601762	+	0.798675i	$0.294465\pi$
$509$	−7.99840	+	24.6166i	−0.354523	+	1.09111i	−0.956286	+	0.292435i	$0.905535\pi$
$510$	−6.00903	+	0.0853656i	−0.266084	+	0.00378005i
$511$	5.39263	−	3.91798i	0.238556	−	0.173321i
$512$	3.58776	+	4.93812i	0.158558	+	0.218236i
$513$	−1.11562	+	0.362488i	−0.0492559	+	0.0160042i
$514$	1.84074	−	5.66521i	0.0811914	−	0.249881i
$515$	−25.6603	+	19.2061i	−1.13073	+	0.846320i
$516$	−4.13628			−0.182090
$517$	−30.3863	−	23.0103i	−1.33639	−	1.01199i
$518$		−	1.81879i		−	0.0799129i
$519$	−3.00706	−	2.18476i	−0.131995	−	0.0959002i
$520$	−17.8415	+	25.3049i	−0.782400	+	1.10969i
$521$	−8.89377	−	27.3722i	−0.389643	−	1.19920i	−0.933055	−	0.359733i	$-0.882868\pi$
$521$	−8.89377	−	27.3722i	−0.389643	−	1.19920i	0.543412	−	0.839466i	$-0.317132\pi$
$522$	−0.185385	−	0.255161i	−0.00811410	−	0.0111681i
$523$	−17.6295	−	24.2649i	−0.770883	−	1.06103i	−0.996230	−	0.0867506i	$-0.972352\pi$
$523$	−17.6295	−	24.2649i	−0.770883	−	1.06103i	0.225347	−	0.974279i	$-0.427648\pi$
$524$	−2.93250	−	9.02531i	−0.128107	−	0.394272i
$525$	2.01366	−	1.55229i	0.0878835	−	0.0677474i
$526$	−19.9446	−	14.4906i	−0.869626	−	0.631820i
$527$			21.2611i			0.926148i
$528$	−1.80442	−	0.0357553i	−0.0785271	−	0.00155605i
$529$	14.5052			0.630659
$530$	10.5570	+	14.1047i	0.458566	+	0.612668i
$531$	−0.935871	+	2.88031i	−0.0406133	+	0.124995i
$532$	−0.768466	+	0.249690i	−0.0333172	+	0.0108254i
$533$	−8.45207	−	11.6333i	−0.366100	−	0.503893i
$534$	6.39929	−	4.64936i	0.276924	−	0.201197i
$535$	−15.3624	+	0.218241i	−0.664172	+	0.00943538i
$536$	−4.42485	+	13.6183i	−0.191125	+	0.588221i
$537$	10.5167	−	14.4750i	0.453831	−	0.624644i
$538$			14.6544i			0.631796i
$539$	21.3972	−	6.48660i	0.921641	−	0.279398i
$540$	−0.894993	+	2.89374i	−0.0385144	+	0.124527i
$541$	−2.14753	−	1.56027i	−0.0923295	−	0.0670813i	0.540663	−	0.841239i	$-0.318174\pi$
$541$	−2.14753	−	1.56027i	−0.0923295	−	0.0670813i	−0.632992	+	0.774158i	$0.718174\pi$
$542$	−10.4989	−	3.41129i	−0.450964	−	0.146527i
$543$	14.3781	−	4.67174i	0.617025	−	0.200484i
$544$	15.7710	−	11.4583i	0.676178	−	0.491272i
$545$	35.8796	−	12.2241i	1.53691	−	0.523625i
$546$	−0.648609	−	1.99621i	−0.0277579	−	0.0854301i
$547$	−3.19797	−	1.03908i	−0.136735	−	0.0444281i	0.239850	−	0.970810i	$-0.422902\pi$
$547$	−3.19797	−	1.03908i	−0.136735	−	0.0444281i	−0.376585	+	0.926382i	$0.622902\pi$
$548$	8.76464	−	12.0635i	0.374407	−	0.515327i
$549$	−1.05512			−0.0450315
$550$	4.00774	−	12.7052i	0.170890	−	0.541751i
$551$	0.460526			0.0196191
$552$	−4.61690	+	6.35462i	−0.196508	+	0.270471i
$553$	7.80573	+	2.53623i	0.331933	+	0.107852i
$554$	−0.341975	−	1.05249i	−0.0145291	−	0.0447161i
$555$	9.42348	−	3.21057i	0.400004	−	0.136281i
$556$	−15.5649	+	11.3085i	−0.660097	+	0.479588i
$557$	23.3079	−	7.57320i	0.987588	−	0.320887i	0.229693	−	0.973263i	$-0.426228\pi$
$557$	23.3079	−	7.57320i	0.987588	−	0.320887i	0.757895	+	0.652376i	$0.226228\pi$
$558$	−4.85573	−	1.57772i	−0.205560	−	0.0667904i
$559$	12.6925	+	9.22165i	0.536836	+	0.390034i
$560$	−0.182822	+	0.591110i	−0.00772564	+	0.0249790i
$561$	−0.219819	+	11.0933i	−0.00928077	+	0.468360i
$562$			15.5070i			0.654123i
$563$	−4.71301	+	6.48691i	−0.198630	+	0.273390i	−0.896700	−	0.442639i	$-0.854042\pi$
$563$	−4.71301	+	6.48691i	−0.198630	+	0.273390i	0.698070	+	0.716029i	$0.254042\pi$
$564$	4.81063	−	14.8056i	0.202564	−	0.623428i
$565$	−10.0817	+	0.143223i	−0.424141	+	0.00602544i
$566$	−1.42739	+	1.03706i	−0.0599978	+	0.0435909i
$567$	−0.298892	−	0.411389i	−0.0125523	−	0.0172767i
$568$	10.5080	−	3.41425i	0.440905	−	0.143259i
$569$	−2.93903	+	9.04541i	−0.123211	+	0.379203i	−0.993571	−	0.113212i	$-0.963886\pi$
$569$	−2.93903	+	9.04541i	−0.123211	+	0.379203i	0.870360	+	0.492416i	$0.163886\pi$
$570$	1.26268	+	1.68701i	0.0528879	+	0.0706610i
$571$	−11.6232			−0.486415			−0.243208	−	0.969974i	$-0.578200\pi$
$571$	−11.6232			−0.486415			−0.243208	+	0.969974i	$0.578200\pi$
$572$	18.4024	+	13.9354i	0.769445	+	0.582670i
$573$		−	0.745573i		−	0.0311468i
$574$	0.924950	+	0.672016i	0.0386067	+	0.0280494i
$575$	8.89722	+	11.5417i	0.371040	+	0.481322i
$576$	1.11029	+	3.41713i	0.0462621	+	0.142380i
$577$	5.72262	+	7.87651i	0.238236	+	0.327903i	0.911348	−	0.411637i	$-0.135043\pi$
$577$	5.72262	+	7.87651i	0.238236	+	0.327903i	−0.673112	+	0.739540i	$0.735043\pi$
$578$	2.74267	+	3.77496i	0.114080	+	0.157017i
$579$	2.74375	+	8.44439i	0.114026	+	0.350937i
$580$	0.685235	−	0.971883i	0.0284528	−	0.0403553i
$581$	6.31842	+	4.59060i	0.262132	+	0.190450i
$582$			12.1864i			0.505142i
$583$	26.6891	−	18.5942i	1.10535	−	0.770093i
$584$	35.3266			1.46183
$585$	9.19783	−	6.88434i	0.380283	−	0.284632i
$586$	6.78179	−	20.8722i	0.280153	−	0.862223i
$587$	6.04377	−	1.96374i	0.249453	−	0.0810523i	−0.181621	−	0.983369i	$-0.558135\pi$
$587$	6.04377	−	1.96374i	0.249453	−	0.0810523i	0.431075	+	0.902316i	$0.358135\pi$
$588$	5.36763	+	7.38791i	0.221357	+	0.304672i
$589$	6.03120	−	4.38192i	0.248511	−	0.180554i
$590$	5.43986	−	0.0772799i	0.223956	−	0.00318156i
$591$	−0.325333	+	1.00127i	−0.0133824	+	0.0411868i
$592$	−1.42402	+	1.96000i	−0.0585270	+	0.0805555i
$593$			4.58134i			0.188133i	0.995566	+	0.0940666i	$0.0299867\pi$
$593$			4.58134i			0.188133i	−0.995566	+	0.0940666i	$0.970013\pi$
$594$	−2.51724	−	0.873406i	−0.103284	−	0.0358363i
$595$	3.63407	+	1.12397i	0.148982	+	0.0460781i
$596$	14.3096	+	10.3966i	0.586145	+	0.425860i
$597$	−2.17003	−	0.705087i	−0.0888136	−	0.0288573i
$598$	11.4417	−	3.71763i	0.467885	−	0.152025i
$599$	−7.49415	+	5.44482i	−0.306202	+	0.222469i	−0.730265	−	0.683164i	$-0.760604\pi$
$599$	−7.49415	+	5.44482i	−0.306202	+	0.222469i	0.424063	+	0.905633i	$0.360604\pi$
$600$	13.4694	−	0.382777i	0.549887	−	0.0156268i
$601$	−3.24279	−	9.98027i	−0.132276	−	0.407104i	0.862880	−	0.505408i	$-0.168658\pi$
$601$	−3.24279	−	9.98027i	−0.132276	−	0.407104i	−0.995156	+	0.0983045i	$0.968658\pi$
$602$	−1.18635	−	0.385468i	−0.0483520	−	0.0157105i
$603$	3.12306	−	4.29853i	0.127181	−	0.175050i
$604$	24.8587			1.01149
$605$	−23.1921	−	8.19295i	−0.942895	−	0.333091i
$606$	13.2934			0.540008
$607$	−12.2259	+	16.8275i	−0.496234	+	0.683008i	−0.981523	−	0.191346i	$-0.938715\pi$
$607$	−12.2259	+	16.8275i	−0.496234	+	0.683008i	0.485288	+	0.874354i	$0.338715\pi$
$608$	−6.50085	−	2.11225i	−0.263644	−	0.0856632i
$609$	0.0616909	+	0.189865i	0.00249984	+	0.00769372i
$610$	0.611258	+	1.79413i	0.0247491	+	0.0726422i
$611$	−47.7702	+	34.7071i	−1.93258	+	1.40410i
$612$	−4.30992	+	1.40038i	−0.174218	+	0.0566069i
$613$	23.5458	+	7.65048i	0.951004	+	0.309000i	0.743124	−	0.669154i	$-0.233343\pi$
$613$	23.5458	+	7.65048i	0.951004	+	0.309000i	0.207881	+	0.978154i	$0.433343\pi$
$614$	−17.5020	−	12.7159i	−0.706321	−	0.513172i
$615$	−1.84910	+	5.97860i	−0.0745628	+	0.241080i
$616$	−4.29400	−	1.48989i	−0.173010	−	0.0600292i
$617$		−	28.2943i		−	1.13909i	−0.821962	−	0.569543i	$-0.807120\pi$
$617$		−	28.2943i		−	1.13909i	0.821962	−	0.569543i	$-0.192880\pi$
$618$	6.76862	−	9.31621i	0.272274	−	0.374753i
$619$	8.22111	−	25.3020i	0.330434	−	1.01697i	−0.638493	−	0.769627i	$-0.720442\pi$
$619$	8.22111	−	25.3020i	0.330434	−	1.01697i	0.968928	−	0.247345i	$-0.0795581\pi$
$620$	−0.273443	−	19.2481i	−0.0109817	−	0.773024i
$621$	2.35795	−	1.71315i	0.0946214	−	0.0687465i
$622$	5.63552	+	7.75663i	0.225964	+	0.311012i
$623$	−4.76171	+	1.54717i	−0.190774	+	0.0619861i
$624$	−0.863973	+	2.65903i	−0.0345866	+	0.106447i
$625$	6.36268	−	24.1768i	0.254507	−	0.967071i
$626$	−12.0193			−0.480389
$627$	3.19218	−	2.22398i	0.127483	−	0.0888173i
$628$			14.8197i			0.591370i
$629$	12.0498	+	8.75471i	0.480458	+	0.349073i
$630$	−0.526372	+	0.746564i	−0.0209711	+	0.0297438i
$631$	5.09026	+	15.6662i	0.202640	+	0.623662i	0.999802	+	0.0198965i	$0.00633368\pi$
$631$	5.09026	+	15.6662i	0.202640	+	0.623662i	−0.797162	+	0.603766i	$0.793666\pi$
$632$	25.5673	+	35.1904i	1.01701	+	1.39980i
$633$	−5.62463	−	7.74164i	−0.223559	−	0.307703i
$634$	2.42925	+	7.47645i	0.0964777	+	0.296928i
$635$	−19.5444	−	13.7799i	−0.775595	−	0.546840i
$636$	10.7480	+	7.80887i	0.426185	+	0.309642i
$637$		−	34.6373i		−	1.37238i
$638$	0.833926	+	0.631499i	0.0330154	+	0.0250013i
$639$	−4.09976			−0.162184
$640$	−15.6957	+	11.7478i	−0.620427	+	0.464373i
$641$	2.21008	−	6.80193i	0.0872930	−	0.268660i	−0.897876	−	0.440249i	$-0.854890\pi$
$641$	2.21008	−	6.80193i	0.0872930	−	0.268660i	0.985169	+	0.171589i	$0.0548901\pi$
$642$	5.24972	−	1.70574i	0.207190	−	0.0673201i
$643$	−10.4404	−	14.3700i	−0.411730	−	0.566698i	0.551909	−	0.833904i	$-0.313899\pi$
$643$	−10.4404	−	14.3700i	−0.411730	−	0.566698i	−0.963639	+	0.267206i	$0.913899\pi$
$644$	1.62421	−	1.18006i	0.0640029	−	0.0465009i
$645$	−0.0969879	−	6.82714i	−0.00381889	−	0.268818i
$646$	−0.974219	+	2.99834i	−0.0383301	+	0.117968i
$647$	−0.841497	+	1.15822i	−0.0330827	+	0.0455344i	−0.825238	−	0.564785i	$-0.808959\pi$
$647$	−0.841497	+	1.15822i	−0.0330827	+	0.0455344i	0.792155	+	0.610320i	$0.208959\pi$
$648$		−	2.69497i		−	0.105869i
$649$	0.198998	−	10.0426i	0.00781136	−	0.394205i
$650$	−17.0347	−	11.6517i	−0.668154	−	0.457019i
$651$	2.61450	+	1.89954i	0.102470	+	0.0744490i
$652$	29.7371	+	9.66216i	1.16459	+	0.378399i
$653$	27.8540	−	9.05032i	1.09001	−	0.354166i	0.291761	−	0.956491i	$-0.405759\pi$
$653$	27.8540	−	9.05032i	1.09001	−	0.354166i	0.798251	+	0.602325i	$0.205759\pi$
$654$	−11.0174	+	8.00464i	−0.430816	+	0.313006i
$655$	14.8280	−	5.05187i	0.579377	−	0.197393i
$656$	−0.470609	−	1.44838i	−0.0183742	−	0.0565499i
$657$	−12.4668	−	4.05070i	−0.486375	−	0.158033i
$658$	2.75953	−	3.79816i	0.107578	−	0.148068i
$659$	−21.2056			−0.826054			−0.413027	−	0.910719i	$-0.635529\pi$
$659$	−21.2056			−0.826054			−0.413027	+	0.910719i	$0.635529\pi$
$660$	0.0563338	−	10.0459i	0.00219279	−	0.391034i
$661$	−16.5453			−0.643537			−0.321768	−	0.946818i	$-0.604277\pi$
$661$	−16.5453			−0.643537			−0.321768	+	0.946818i	$0.604277\pi$
$662$	−2.43041	+	3.34517i	−0.0944606	+	0.130014i
$663$	16.3474	+	5.31159i	0.634881	+	0.206285i
$664$	12.7906	+	39.3655i	0.496373	+	1.52768i
$665$	−0.430145	−	1.26254i	−0.0166803	−	0.0489591i
$666$	−2.89364	+	2.10235i	−0.112126	+	0.0814644i
$667$	−1.08825	+	0.353593i	−0.0421371	+	0.0136912i
$668$	−5.37770	−	1.74732i	−0.208070	−	0.0676059i
$669$	7.13492	+	5.18382i	0.275852	+	0.200418i
$670$	−9.11849	−	2.82022i	−0.352278	−	0.108955i
$671$	3.34894	−	1.01524i	0.129284	−	0.0391929i
$672$		−	2.96311i		−	0.114305i
$673$	11.1405	−	15.3336i	0.429434	−	0.591066i	−0.538389	−	0.842696i	$-0.680967\pi$
$673$	11.1405	−	15.3336i	0.429434	−	0.591066i	0.967823	+	0.251631i	$0.0809669\pi$
$674$	−7.28660	+	22.4258i	−0.280669	+	0.863811i
$675$	−4.79725	−	1.40938i	−0.184646	−	0.0542470i
$676$	14.6837	−	10.6684i	0.564759	−	0.410322i
$677$	19.4233	+	26.7338i	0.746496	+	1.02746i	0.998218	+	0.0596644i	$0.0190031\pi$
$677$	19.4233	+	26.7338i	0.746496	+	1.02746i	−0.251722	+	0.967800i	$0.580997\pi$
$678$	3.44519	−	1.11941i	0.132312	−	0.0429906i
$679$	2.38363	−	7.33607i	0.0914754	−	0.281532i
$680$	12.0802	+	16.1398i	0.463255	+	0.618932i
$681$	5.38764			0.206455
$682$	16.9301	+	0.335478i	0.648287	+	0.0128461i
$683$		−	26.1102i		−	0.999079i	−0.866291	−	0.499540i	$-0.833503\pi$
$683$		−	26.1102i		−	0.999079i	0.866291	−	0.499540i	$-0.166497\pi$
$684$	1.28553	+	0.933989i	0.0491533	+	0.0357119i
$685$	20.1169	+	14.1836i	0.768628	+	0.541928i
$686$	1.73469	+	5.33884i	0.0662309	+	0.203838i
$687$	−14.3312	−	19.7252i	−0.546770	−	0.752565i
$688$	0.976656	+	1.34425i	0.0372347	+	0.0512491i
$689$	−15.5716	−	47.9243i	−0.593229	−	1.82577i
$690$	−4.27907	−	3.01700i	−0.162901	−	0.114855i
$691$	19.2821	+	14.0093i	0.733527	+	0.532939i	0.890677	−	0.454636i	$-0.150231\pi$
$691$	19.2821	+	14.0093i	0.733527	+	0.532939i	−0.157150	+	0.987575i	$0.550231\pi$
$692$			5.03497i			0.191401i
$693$	1.34452	+	1.01815i	0.0510740	+	0.0386763i
$694$	−5.89342			−0.223711
$695$	−19.0303	−	25.4254i	−0.721859	−	0.964441i
$696$	−0.326949	+	1.00625i	−0.0123930	+	0.0381417i
$697$	−8.90448	+	2.89324i	−0.337281	+	0.109589i
$698$	13.4706	+	18.5406i	0.509868	+	0.701773i
$699$	−3.73760	+	2.71552i	−0.141369	+	0.102710i
$700$	−3.30446	−	0.970813i	−0.124897	−	0.0366933i
$701$	5.05431	−	15.5556i	0.190899	−	0.587525i	−0.809101	−	0.587669i	$-0.800046\pi$
$701$	5.05431	−	15.5556i	0.190899	−	0.587525i	1.00000		0.000143622i	$4.57162e-5\pi$
$702$	−2.42619	+	3.33936i	−0.0915705	+	0.126036i
$703$		−	5.22256i		−	0.196973i
$704$	−6.81201	−	9.77758i	−0.256737	−	0.368506i
$705$	24.5502	+	7.59302i	0.924613	+	0.285970i
$706$	−10.5172	−	7.64116i	−0.395818	−	0.287579i
$707$	−8.00249	−	2.60017i	−0.300964	−	0.0977893i
$708$	3.90168	−	1.26773i	0.146634	−	0.0476444i
$709$	12.2026	−	8.86573i	0.458279	−	0.332959i	−0.334577	−	0.942369i	$-0.608593\pi$
$709$	12.2026	−	8.86573i	0.458279	−	0.332959i	0.792856	+	0.609409i	$0.208593\pi$
$710$	2.37509	+	6.97124i	0.0891356	+	0.261626i
$711$	−4.98763	−	15.3503i	−0.187051	−	0.575683i
$712$	−25.2361	−	8.19970i	−0.945762	−	0.307297i
$713$	−10.8876	+	14.9855i	−0.407743	+	0.561211i
$714$	−1.36665			−0.0511458
$715$	−22.5696	+	30.7009i	−0.844057	+	1.14815i
$716$	−24.2368			−0.905770
$717$	2.83231	−	3.89834i	0.105775	−	0.145586i
$718$	12.9371	+	4.20353i	0.482810	+	0.156874i
$719$	−6.99094	−	21.5159i	−0.260718	−	0.802408i	−0.992649	−	0.121029i	$-0.961381\pi$
$719$	−6.99094	−	21.5159i	−0.260718	−	0.802408i	0.731931	−	0.681379i	$-0.238619\pi$
$720$	1.15176	−	0.392404i	0.0429237	−	0.0146240i
$721$	−5.89687	+	4.28432i	−0.219611	+	0.159557i
$722$	−13.4655	+	4.37522i	−0.501136	+	0.162829i
$723$	−0.403825	−	0.131211i	−0.0150184	−	0.00487977i
$724$	−16.5679	−	12.0373i	−0.615740	−	0.447361i
$725$	1.62021	+	1.10823i	0.0601731	+	0.0411585i
$726$	8.83008	+	0.350082i	0.327715	+	0.0129928i
$727$			20.2062i			0.749408i	0.927144	+	0.374704i	$0.122256\pi$
$727$			20.2062i			0.749408i	−0.927144	+	0.374704i	$0.877744\pi$
$728$	−4.13867	+	5.69639i	−0.153389	+	0.211122i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	0.334488	+	23.5452i	0.0123800	+	0.871447i
$731$	8.26429	−	6.00436i	0.305666	−	0.222079i
$732$	0.840105	+	1.15631i	0.0310512	+	0.0427383i
$733$	1.43150	−	0.465123i	0.0528737	−	0.0171797i	−0.282461	−	0.959279i	$-0.591151\pi$
$733$	1.43150	−	0.465123i	0.0528737	−	0.0171797i	0.335334	+	0.942099i	$0.391151\pi$
$734$	−0.998676	+	3.07361i	−0.0368618	+	0.113449i
$735$	−12.0683	+	9.03278i	−0.445144	+	0.333179i
$736$	16.9836			0.626025
$737$	−5.77650	+	16.6485i	−0.212780	+	0.613254i
$738$		−	2.24836i		−	0.0827632i
$739$	31.3766	+	22.7965i	1.15421	+	0.838581i	0.989035	−	0.147683i	$-0.0471816\pi$
$739$	31.3766	+	22.7965i	1.15421	+	0.838581i	0.165174	+	0.986265i	$0.447182\pi$
$740$	−11.0216	−	7.77086i	−0.405161	−	0.285663i
$741$	−1.86245	−	5.73204i	−0.0684189	−	0.210572i
$742$	2.35496	+	3.24133i	0.0864535	+	0.118993i
$743$	−15.7883	−	21.7307i	−0.579215	−	0.797221i	0.414394	−	0.910098i	$-0.363993\pi$
$743$	−15.7883	−	21.7307i	−0.579215	−	0.797221i	−0.993609	+	0.112877i	$0.963993\pi$
$744$	5.29264	+	16.2891i	0.194038	+	0.597186i
$745$	−16.8245	+	23.8626i	−0.616402	+	0.874256i
$746$	−23.5682	−	17.1233i	−0.862895	−	0.626930i
$747$		−	15.3587i		−	0.561947i
$748$	12.3322	−	8.59177i	0.450908	−	0.314146i
$749$	−3.49391			−0.127665
$750$	0.382655	+	8.97375i	0.0139726	+	0.327675i
$751$	8.03522	−	24.7299i	0.293209	−	0.902405i	−0.690608	−	0.723229i	$-0.742657\pi$
$751$	8.03522	−	24.7299i	0.293209	−	0.902405i	0.983817	−	0.179176i	$-0.0573431\pi$
$752$	−5.94756	+	1.93248i	−0.216885	+	0.0704703i
$753$	9.03000	+	12.4287i	0.329071	+	0.452928i
$754$	1.31101	−	0.952506i	0.0477442	−	0.0346882i
$755$	0.582889	+	41.0305i	0.0212135	+	1.49325i
$756$	−0.212858	+	0.655110i	−0.00774157	+	0.0238261i
$757$	−17.3931	+	23.9395i	−0.632162	+	0.870096i	−0.998167	−	0.0605164i	$-0.980725\pi$
$757$	−17.3931	+	23.9395i	−0.632162	+	0.870096i	0.366005	+	0.930613i	$0.380725\pi$
$758$		−	15.9603i		−	0.579703i
$759$	−5.83571	+	7.70635i	−0.211823	+	0.279723i
$760$	2.08868	−	6.75325i	0.0757645	−	0.244966i
$761$	−26.7546	−	19.4383i	−0.969852	−	0.704639i	−0.0144341	−	0.999896i	$-0.504595\pi$
$761$	−26.7546	−	19.4383i	−0.969852	−	0.704639i	−0.955418	+	0.295257i	$0.904595\pi$
$762$	8.17115	+	2.65497i	0.296009	+	0.0961793i
$763$	8.19807	−	2.66371i	0.296790	−	0.0964329i
$764$	−0.817072	+	0.593638i	−0.0295606	+	0.0214771i
$765$	−2.41245	−	7.08090i	−0.0872224	−	0.256010i
$766$	6.06958	+	18.6803i	0.219303	+	0.674945i
$767$	−14.7990	−	4.80848i	−0.534361	−	0.173624i
$768$	8.36398	−	11.5120i	0.301809	−	0.415405i
$769$	−3.37489			−0.121702			−0.0608508	−	0.998147i	$-0.519381\pi$
$769$	−3.37489			−0.121702			−0.0608508	+	0.998147i	$0.519381\pi$
$770$	0.952351	−	2.87606i	0.0343203	−	0.103646i
$771$	7.41474			0.267035
$772$	7.06957	−	9.73043i	0.254439	−	0.350206i
$773$	22.0538	+	7.16571i	0.793220	+	0.257733i	0.677475	−	0.735546i	$-0.263074\pi$
$773$	22.0538	+	7.16571i	0.793220	+	0.257733i	0.115745	+	0.993279i	$0.463074\pi$
$774$	0.758042	+	2.33301i	0.0272473	+	0.0838584i
$775$	31.7636	−	0.902664i	1.14098	−	0.0324247i
$776$	33.0730	−	24.0290i	1.18725	−	0.862589i
$777$	2.15315	−	0.699602i	0.0772439	−	0.0250981i
$778$	−9.23548	−	3.00079i	−0.331108	−	0.107584i
$779$	2.65595	+	1.92966i	0.0951594	+	0.0691373i
$780$	−14.8680	−	4.59846i	−0.532359	−	0.164651i
$781$	13.0126	−	3.94479i	0.465626	−	0.141156i
$782$		−	7.83323i		−	0.280116i
$783$	0.230761	−	0.317615i	0.00824672	−	0.0113506i
$784$	1.13360	−	3.48886i	0.0404857	−	0.124602i
$785$	−24.4607	+	0.347494i	−0.873039	+	0.0124026i
$786$	−4.55317	+	3.30808i	−0.162406	+	0.117995i
$787$	−24.1392	−	33.2248i	−0.860470	−	1.18434i	−0.981457	−	0.191681i	$-0.938606\pi$
$787$	−24.1392	−	33.2248i	−0.860470	−	1.18434i	0.120987	−	0.992654i	$-0.461394\pi$
$788$	1.35633	−	0.440697i	0.0483171	−	0.0156992i
$789$	9.48280	−	29.1851i	0.337597	−	1.03902i
$790$	−23.2123	+	17.3738i	−0.825856	+	0.618132i
$791$	−2.29292			−0.0815267
$792$	2.59311	+	8.55380i	0.0921420	+	0.303946i
$793$		−	5.42119i		−	0.192512i
$794$	14.7638	+	10.7266i	0.523949	+	0.380671i
$795$	−12.6369	+	17.9232i	−0.448185	+	0.635670i
$796$	0.955113	+	2.93954i	0.0338531	+	0.104189i
$797$	−28.3677	−	39.0448i	−1.00484	−	1.38304i	−0.922311	−	0.386449i	$-0.873701\pi$
$797$	−28.3677	−	39.0448i	−1.00484	−	1.38304i	−0.0825256	−	0.996589i	$-0.526299\pi$
$798$	0.281668	+	0.387683i	0.00997095	+	0.0137238i
$799$	11.8806	+	36.5648i	0.420307	+	1.29357i
$800$	−17.7881	−	23.0751i	−0.628904	−	0.815830i
$801$	7.96560	+	5.78735i	0.281451	+	0.204486i
$802$			1.89429i			0.0668898i
$803$	43.4669	+	0.861317i	1.53391	+	0.0303952i
$804$	−7.19738			−0.253832
$805$	1.98583	+	2.65318i	0.0699914	+	0.0935122i
$806$	8.10631	−	24.9487i	0.285533	−	0.878779i
$807$	−17.3485	+	5.63686i	−0.610695	+	0.198427i
$808$	−26.2118	−	36.0774i	−0.922127	−	1.26920i
$809$	−35.4699	+	25.7704i	−1.24706	+	0.906040i	−0.998047	−	0.0624612i	$-0.980105\pi$
$809$	−35.4699	+	25.7704i	−1.24706	+	0.906040i	−0.249009	+	0.968501i	$0.580105\pi$
$810$	1.79620	−	0.0255172i	0.0631120	−	0.000896583i
$811$	−12.7912	+	39.3673i	−0.449161	+	1.38237i	0.428695	+	0.903449i	$0.358973\pi$
$811$	−12.7912	+	39.3673i	−0.449161	+	1.38237i	−0.877856	+	0.478925i	$0.841027\pi$
$812$	0.158953	−	0.218781i	0.00557817	−	0.00767769i
$813$		−	13.7411i		−	0.481922i
$814$	7.16147	−	9.45708i	0.251009	−	0.331471i
$815$	−15.2506	+	49.3091i	−0.534205	+	1.72722i
$816$	1.47276	+	1.07003i	0.0515571	+	0.0374584i
$817$	−3.40655	−	1.10686i	−0.119180	−	0.0387240i
$818$	2.09637	−	0.681150i	0.0732977	−	0.0238159i
$819$	2.11371	−	1.53570i	0.0738590	−	0.0536617i
$820$	8.02421	−	2.73384i	0.280218	−	0.0954698i
$821$	13.2750	+	40.8564i	0.463302	+	1.42590i	0.861105	+	0.508427i	$0.169773\pi$
$821$	13.2750	+	40.8564i	0.463302	+	1.42590i	−0.397803	+	0.917471i	$0.630227\pi$
$822$	−8.41052	−	2.73274i	−0.293350	−	0.0953153i
$823$	8.24443	−	11.3475i	0.287383	−	0.395548i	−0.640779	−	0.767725i	$-0.721389\pi$
$823$	8.24443	−	11.3475i	0.287383	−	0.395548i	0.928162	+	0.372177i	$0.121389\pi$
$824$	−38.6298			−1.34573
$825$	16.5825	−	0.142574i	0.577329	−	0.00496380i
$826$	1.23721			0.0430479
$827$	−18.1652	+	25.0022i	−0.631666	+	0.869413i	−0.998137	−	0.0610161i	$-0.980566\pi$
$827$	−18.1652	+	25.0022i	−0.631666	+	0.869413i	0.366471	+	0.930429i	$0.380566\pi$
$828$	−3.75488	−	1.22004i	−0.130491	−	0.0423991i
$829$	−11.4274	−	35.1699i	−0.396890	−	1.22150i	−0.927480	−	0.373872i	$-0.878030\pi$
$829$	−11.4274	−	35.1699i	−0.396890	−	1.22150i	0.530591	−	0.847628i	$-0.321970\pi$
$830$	−26.1160	+	8.89769i	−0.906500	+	0.308843i
$831$	1.11444	−	0.809688i	0.0386595	−	0.0280878i
$832$	−17.5571	+	5.70465i	−0.608684	+	0.197773i
$833$	−21.4490	−	6.96922i	−0.743165	−	0.241469i
$834$	9.23094	+	6.70667i	0.319641	+	0.232233i
$835$	2.75795	−	8.91715i	0.0954427	−	0.308591i
$836$	−4.97892	−	1.72753i	−0.172200	−	0.0597479i
$837$		−	6.35529i		−	0.219671i
$838$	−6.60433	+	9.09008i	−0.228143	+	0.314012i
$839$	−0.679929	+	2.09261i	−0.0234737	+	0.0722447i	−0.962107	−	0.272672i	$-0.912093\pi$
$839$	−0.679929	+	2.09261i	−0.0234737	+	0.0722447i	0.938633	+	0.344916i	$0.112093\pi$
$840$	3.06402	−	0.0435281i	0.105719	−	0.00150186i
$841$	23.3368	−	16.9552i	0.804717	−	0.584661i
$842$	−8.39320	−	11.5523i	−0.289249	−	0.398117i
$843$	−18.3578	+	5.96481i	−0.632276	+	0.205439i
$844$	−4.00562	+	12.3280i	−0.137879	+	0.424349i
$845$	17.9530	+	23.9861i	0.617601	+	0.825147i
$846$	−9.23252			−0.317421
$847$	−5.24714	−	1.93789i	−0.180294	−	0.0665868i
$848$		−	5.33682i		−	0.183267i
$849$	−1.77677	−	1.29090i	−0.0609784	−	0.0443034i
$850$	−10.6428	+	8.20427i	−0.365044	+	0.281404i
$851$	4.00990	+	12.3412i	0.137457	+	0.423051i
$852$	3.26430	+	4.49292i	0.111833	+	0.153925i
$853$	19.4985	+	26.8374i	0.667617	+	0.918896i	0.999703	−	0.0243532i	$-0.00775264\pi$
$853$	19.4985	+	26.8374i	0.667617	+	0.918896i	−0.332087	+	0.943249i	$0.607753\pi$
$854$	0.133197	+	0.409937i	0.00455790	+	0.0140278i
$855$	−1.51145	+	2.14372i	−0.0516906	+	0.0733138i
$856$	−14.9806	−	10.8840i	−0.512026	−	0.372008i
$857$		−	28.5419i		−	0.974972i	−0.873131	−	0.487486i	$-0.837914\pi$
$857$		−	28.5419i		−	0.974972i	0.873131	−	0.487486i	$-0.162086\pi$
$858$	4.48754	−	12.9336i	0.153202	−	0.441544i
$859$	−53.6600			−1.83085			−0.915427	−	0.402484i	$-0.868147\pi$
$859$	−53.6600			−1.83085			−0.915427	+	0.402484i	$0.868147\pi$
$860$	−7.40462	+	5.54217i	−0.252496	+	0.188986i
$861$	−0.439774	+	1.35349i	−0.0149875	+	0.0461267i
$862$	5.43710	−	1.76662i	0.185188	−	0.0601713i
$863$	11.2233	+	15.4475i	0.382045	+	0.525840i	0.956125	−	0.292960i	$-0.0946401\pi$
$863$	11.2233	+	15.4475i	0.382045	+	0.525840i	−0.574080	+	0.818799i	$0.694640\pi$
$864$	−4.71423	+	3.42509i	−0.160381	+	0.116524i
$865$	−8.31047	+	0.118060i	−0.282565	+	0.00401417i
$866$	2.82555	−	8.69615i	0.0960162	−	0.295507i
$867$	−3.41397	+	4.69893i	−0.115944	+	0.159584i
$868$		−	4.37767i		−	0.148588i
$869$	30.6008	+	43.9226i	1.03806	+	1.48997i
$870$	−0.673758	−	0.208384i	−0.0228425	−	0.00706488i
$871$	22.0857	+	16.0462i	0.748347	+	0.543706i
$872$	43.4481	+	14.1171i	1.47134	+	0.478067i
$873$	−14.4267	+	4.68753i	−0.488271	+	0.158649i
$874$	−2.22208	+	1.61443i	−0.0751629	+	0.0546090i
$875$	1.52489	−	5.47694i	0.0515508	−	0.185154i
$876$	5.48710	+	16.8875i	0.185392	+	0.570577i
$877$	13.1387	+	4.26902i	0.443662	+	0.144155i	0.522325	−	0.852747i	$-0.325065\pi$
$877$	13.1387	+	4.26902i	0.443662	+	0.144155i	−0.0786625	+	0.996901i	$0.525065\pi$
$878$	−7.64582	+	10.5236i	−0.258034	+	0.355153i
$879$	27.3180			0.921414
$880$	−3.27811	+	2.35371i	−0.110505	+	0.0793437i
$881$	−14.7416			−0.496658			−0.248329	−	0.968676i	$-0.579881\pi$
$881$	−14.7416			−0.496658			−0.248329	+	0.968676i	$0.579881\pi$
$882$	3.18334	−	4.38150i	0.107189	−	0.147533i
$883$	0.157386	+	0.0511379i	0.00529647	+	0.00172093i	0.311664	−	0.950192i	$-0.399114\pi$
$883$	0.157386	+	0.0511379i	0.00529647	+	0.00172093i	−0.306368	+	0.951913i	$0.599114\pi$
$884$	−7.19510	−	22.1443i	−0.241998	−	0.744792i
$885$	2.18395	+	6.41020i	0.0734126	+	0.215477i
$886$	15.4374	−	11.2159i	0.518629	−	0.376806i
$887$	−13.1958	+	4.28759i	−0.443073	+	0.143963i	−0.522053	−	0.852913i	$-0.674834\pi$
$887$	−13.1958	+	4.28759i	−0.443073	+	0.143963i	0.0789801	+	0.996876i	$0.474834\pi$
$888$	11.4113	+	3.70775i	0.382937	+	0.124424i
$889$	−4.39963	−	3.19652i	−0.147559	−	0.107208i
$890$	5.22615	−	16.8975i	0.175181	−	0.566405i
$891$	0.0657076	−	3.31597i	0.00220129	−	0.111089i
$892$		−	11.9466i		−	0.400001i
$893$	7.92386	−	10.9063i	0.265162	−	0.364964i
$894$	3.24156	−	9.97650i	0.108414	−	0.333664i
$895$	−0.568306	−	40.0040i	−0.0189964	−	1.33719i
$896$	−3.60695	+	2.62060i	−0.120500	+	0.0875482i
$897$	8.80215	+	12.1151i	0.293895	+	0.404512i
$898$	15.7844	−	5.12865i	0.526731	−	0.171145i
$899$	−0.771012	+	2.37293i	−0.0257147	+	0.0791417i
$900$	2.27512	+	6.37947i	0.0758372	+	0.212649i
$901$	−32.8101			−1.09306
$902$	2.16337	+	7.13625i	0.0720324	+	0.237611i
$903$		−	1.55272i		−	0.0516713i
$904$	−9.83117	−	7.14276i	−0.326980	−	0.237565i
$905$	19.4796	−	27.6284i	0.647524	−	0.918397i
$906$	−4.55577	−	14.0212i	−0.151355	−	0.465824i
$907$	−5.35122	−	7.36533i	−0.177684	−	0.244562i	0.710880	−	0.703313i	$-0.248297\pi$
$907$	−5.35122	−	7.36533i	−0.177684	−	0.244562i	−0.888565	+	0.458752i	$0.848297\pi$
$908$	−4.28972	−	5.90430i	−0.142359	−	0.195941i
$909$	5.11335	+	15.7373i	0.169599	+	0.521972i
$910$	−3.83583	−	2.70449i	−0.127157	−	0.0896529i
$911$	36.6306	+	26.6137i	1.21363	+	0.881751i	0.995555	−	0.0941815i	$-0.0300234\pi$
$911$	36.6306	+	26.6137i	1.21363	+	0.881751i	0.218072	+	0.975933i	$0.430023\pi$
$912$		−	0.638317i		−	0.0211368i
$913$	14.7782	+	48.7484i	0.489086	+	1.61334i
$914$	−6.20227			−0.205153
$915$	−1.88884	+	1.41375i	−0.0624432	+	0.0467371i
$916$	−10.2061	+	31.4111i	−0.337219	+	1.03785i
$917$	3.38801	−	1.10083i	0.111882	−	0.0363527i
$918$	1.57973	+	2.17431i	0.0521388	+	0.0717629i
$919$	−12.0247	+	8.73644i	−0.396658	+	0.288189i	−0.768178	−	0.640236i	$-0.778837\pi$
$919$	−12.0247	+	8.73644i	−0.396658	+	0.288189i	0.371521	+	0.928425i	$0.378837\pi$
$920$	0.249489	+	17.5620i	0.00822542	+	0.579001i
$921$	8.32143	−	25.6107i	0.274200	−	0.843902i
$922$	−19.5037	+	26.8446i	−0.642321	+	0.884079i
$923$		−	21.0645i		−	0.693346i
$924$	0.0452609	−	2.28412i	0.00148897	−	0.0751420i
$925$	12.5678	−	18.3739i	0.413226	−	0.604130i
$926$	−12.7013	−	9.22806i	−0.417392	−	0.303253i
$927$	13.6325	+	4.42946i	0.447749	+	0.145483i
$928$	2.17572	−	0.706934i	0.0714214	−	0.0232062i
$929$	2.66467	−	1.93600i	0.0874251	−	0.0635181i	−0.543214	−	0.839594i	$-0.682793\pi$
$929$	2.66467	−	1.93600i	0.0874251	−	0.0635181i	0.630639	+	0.776076i	$0.282793\pi$
$930$	−10.8065	+	3.68177i	−0.354361	+	0.120730i
$931$	2.44368	+	7.52088i	0.0800884	+	0.246487i
$932$	5.95187	+	1.93388i	0.194960	+	0.0633463i
$933$	−7.01489	+	9.65516i	−0.229657	+	0.316096i
$934$	17.1609			0.561523
$935$	14.4703	+	20.1534i	0.473230	+	0.659086i
$936$	13.8467			0.452594
$937$	0.469231	−	0.645840i	0.0153291	−	0.0210987i	−0.801284	−	0.598285i	$-0.795849\pi$
$937$	0.469231	−	0.645840i	0.0153291	−	0.0210987i	0.816613	+	0.577186i	$0.195849\pi$
$938$	−2.06432	−	0.670738i	−0.0674024	−	0.0219004i
$939$	−4.62327	−	14.2290i	−0.150875	−	0.464345i
$940$	−11.2261	−	32.9502i	−0.366154	−	1.07472i
$941$	20.4562	−	14.8623i	0.666853	−	0.484497i	−0.202117	−	0.979361i	$-0.564782\pi$
$941$	20.4562	−	14.8623i	0.666853	−	0.484497i	0.868970	+	0.494864i	$0.164782\pi$
$942$	8.35885	−	2.71596i	0.272346	−	0.0884906i
$943$	−7.75776	−	2.52065i	−0.252627	−	0.0820836i
$944$	−1.33327	−	0.968674i	−0.0433941	−	0.0315276i
$945$	−1.08628	−	0.335972i	−0.0353368	−	0.0109292i
$946$	−4.65084	−	6.67556i	−0.151212	−	0.217041i
$947$			49.6668i			1.61396i	0.590582	+	0.806978i	$0.298898\pi$
$947$			49.6668i			1.61396i	−0.590582	+	0.806978i	$0.701102\pi$
$948$	−12.8512	+	17.6881i	−0.417387	+	0.574483i
$949$	20.8124	−	64.0540i	0.675600	−	2.07928i
$950$	4.52081	+	1.32816i	0.146675	+	0.0430913i
$951$	−7.91651	+	5.75168i	−0.256710	+	0.186511i
$952$	2.69475	+	3.70901i	0.0873374	+	0.120210i
$953$	26.4148	−	8.58269i	0.855660	−	0.278021i	0.151845	−	0.988404i	$-0.451479\pi$
$953$	26.4148	−	8.58269i	0.855660	−	0.278021i	0.703815	+	0.710384i	$0.251479\pi$
$954$	2.43474	−	7.49336i	0.0788277	−	0.242607i
$955$	−0.998988	−	1.33470i	−0.0323265	−	0.0431899i
$956$	−6.52732			−0.211109
$957$	−0.426822	+	1.23014i	−0.0137972	+	0.0397649i
$958$		−	12.3848i		−	0.400135i
$959$	4.52852	+	3.29016i	0.146233	+	0.106245i
$960$	6.56618	+	4.62955i	0.211923	+	0.149418i
$961$	2.90158	+	8.93015i	0.0935994	+	0.288069i
$962$	−10.8018	−	14.8674i	−0.348265	−	0.479346i
$963$	4.03864	+	5.55871i	0.130143	+	0.179127i
$964$	0.177738	+	0.547022i	0.00572457	+	0.0176184i
$965$	16.2263	+	11.4405i	0.522344	+	0.368283i
$966$	−0.963261	−	0.699850i	−0.0309924	−	0.0225173i
$967$		−	11.0951i		−	0.356793i	−0.983959	−	0.178396i	$-0.942909\pi$
$967$		−	11.0951i		−	0.356793i	0.983959	−	0.178396i	$-0.0570909\pi$
$968$	−16.4609	−	24.6545i	−0.529075	−	0.792427i
$969$	−3.92429			−0.126066
$970$	16.3284	+	21.8156i	0.524275	+	0.700458i
$971$	−9.86435	+	30.3594i	−0.316562	+	0.974278i	0.658544	+	0.752542i	$0.271172\pi$
$971$	−9.86435	+	30.3594i	−0.316562	+	0.974278i	−0.975107	+	0.221736i	$0.928828\pi$
$972$	1.28830	−	0.418596i	0.0413224	−	0.0134265i
$973$	−4.24511	−	5.84289i	−0.136092	−	0.187315i
$974$	16.3215	−	11.8583i	0.522974	−	0.379963i
$975$	7.24136	−	24.6482i	0.231909	−	0.789374i
$976$	0.177423	−	0.546052i	0.00567918	−	0.0174787i
$977$	−6.11624	+	8.41829i	−0.195676	+	0.269325i	−0.895569	−	0.444923i	$-0.853231\pi$
$977$	−6.11624	+	8.41829i	−0.195676	+	0.269325i	0.699893	+	0.714248i	$0.253231\pi$
$978$		−	18.5435i		−	0.592957i
$979$	−30.8513	−	10.7044i	−0.986011	−	0.342115i
$980$	19.5079	+	6.03353i	0.623158	+	0.192734i
$981$	−13.7141	−	9.96388i	−0.437858	−	0.318122i
$982$	−0.843401	−	0.274037i	−0.0269140	−	0.00874489i
$983$	39.4055	−	12.8036i	1.25684	−	0.408372i	0.396472	−	0.918047i	$-0.370234\pi$
$983$	39.4055	−	12.8036i	1.25684	−	0.408372i	0.860367	+	0.509675i	$0.170234\pi$
$984$	−6.10189	+	4.43328i	−0.194521	+	0.141328i
$985$	0.759196	+	2.22835i	0.0241900	+	0.0710012i
$986$	−0.326054	−	1.00349i	−0.0103837	−	0.0319576i
$987$	5.55788	+	1.80586i	0.176909	+	0.0574813i
$988$	−4.79881	+	6.60500i	−0.152671	+	0.210133i
$989$	8.89970			0.282994
$990$	−5.67655	+	1.80929i	−0.180413	+	0.0575032i
$991$	−2.17000			−0.0689322			−0.0344661	−	0.999406i	$-0.510973\pi$
$991$	−2.17000			−0.0689322			−0.0344661	+	0.999406i	$0.510973\pi$
$992$	21.7674	−	29.9603i	0.691116	−	0.951240i
$993$	−4.89502	−	1.59049i	−0.155339	−	0.0504726i
$994$	0.517547	+	1.59284i	0.0164156	+	0.0505220i
$995$	−4.82946	+	1.64539i	−0.153104	+	0.0521623i
$996$	−16.8316	+	12.2289i	−0.533329	+	0.387487i
$997$	−0.769399	+	0.249993i	−0.0243671	+	0.00791735i	−0.321175	−	0.947020i	$-0.604078\pi$
$997$	−0.769399	+	0.249993i	−0.0243671	+	0.00791735i	0.296808	+	0.954937i	$0.404078\pi$
$998$	1.75515	+	0.570283i	0.0555583	+	0.0180520i
$999$	−3.60189	−	2.61693i	−0.113959	−	0.0827959i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.2.s.a.4.4	✓	48
3.2	odd	2		495.2.ba.c.334.9		48
5.2	odd	4		825.2.n.o.301.3		24
5.3	odd	4		825.2.n.p.301.4		24
5.4	even	2	inner	165.2.s.a.4.9	yes	48
11.3	even	5	inner	165.2.s.a.124.9	yes	48
11.5	even	5		1815.2.c.j.364.8		24
11.6	odd	10		1815.2.c.k.364.17		24
15.14	odd	2		495.2.ba.c.334.4		48
33.14	odd	10		495.2.ba.c.289.4		48
55.3	odd	20		825.2.n.p.751.4		24
55.14	even	10	inner	165.2.s.a.124.4	yes	48
55.17	even	20		9075.2.a.dx.1.5		12
55.27	odd	20		9075.2.a.dz.1.8		12
55.28	even	20		9075.2.a.ea.1.8		12
55.38	odd	20		9075.2.a.dy.1.5		12
55.39	odd	10		1815.2.c.k.364.8		24
55.47	odd	20		825.2.n.o.751.3		24
55.49	even	10		1815.2.c.j.364.17		24
165.14	odd	10		495.2.ba.c.289.9		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.s.a.4.4	✓	48	1.1	even	1	trivial
165.2.s.a.4.9	yes	48	5.4	even	2	inner
165.2.s.a.124.4	yes	48	55.14	even	10	inner
165.2.s.a.124.9	yes	48	11.3	even	5	inner
495.2.ba.c.289.4		48	33.14	odd	10
495.2.ba.c.289.9		48	165.14	odd	10
495.2.ba.c.334.4		48	15.14	odd	2
495.2.ba.c.334.9		48	3.2	odd	2
825.2.n.o.301.3		24	5.2	odd	4
825.2.n.o.751.3		24	55.47	odd	20
825.2.n.p.301.4		24	5.3	odd	4
825.2.n.p.751.4		24	55.3	odd	20
1815.2.c.j.364.8		24	11.5	even	5
1815.2.c.j.364.17		24	55.49	even	10
1815.2.c.k.364.8		24	55.39	odd	10
1815.2.c.k.364.17		24	11.6	odd	10
9075.2.a.dx.1.5		12	55.17	even	20
9075.2.a.dy.1.5		12	55.38	odd	20
9075.2.a.dz.1.8		12	55.27	odd	20
9075.2.a.ea.1.8		12	55.28	even	20

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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	165.s (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.472206 + 0.649936i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(0.418596 + 1.28830i) q^{4} +(-2.11660 + 0.721122i) q^{5} +(0.649936 - 0.472206i) q^{6} +(-0.483617 + 0.157137i) q^{7} +(-2.56307 - 0.832793i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.472206 + 0.649936i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(0.418596 + 1.28830i) q^{4} +(-2.11660 + 0.721122i) q^{5} +(0.649936 - 0.472206i) q^{6} +(-0.483617 + 0.157137i) q^{7} +(-2.56307 - 0.832793i) q^{8} +(0.809017 + 0.587785i) q^{9} +(0.530788 - 1.71617i) q^{10} +(-3.13337 - 1.08718i) q^{11} -1.35460i q^{12} +(-3.02003 + 4.15671i) q^{13} +(0.126238 - 0.388521i) q^{14} +(2.23584 - 0.0317629i) q^{15} +(-0.440233 + 0.319848i) q^{16} +(1.96639 + 2.70650i) q^{17} +(-0.764046 + 0.248254i) q^{18} +(0.362488 - 1.11562i) q^{19} +(-1.81502 - 2.42496i) q^{20} +0.508505 q^{21} +(2.18620 - 1.52312i) q^{22} +2.91459i q^{23} +(2.18028 + 1.58407i) q^{24} +(3.95997 - 3.05265i) q^{25} +(-1.27552 - 3.92565i) q^{26} +(-0.587785 - 0.809017i) q^{27} +(-0.404880 - 0.557269i) q^{28} +(0.121318 + 0.373379i) q^{29} +(-1.03514 + 1.46815i) q^{30} +(5.14154 + 3.73555i) q^{31} -5.82710i q^{32} +(2.64406 + 2.00224i) q^{33} -2.68759 q^{34} +(0.910308 - 0.681342i) q^{35} +(-0.418596 + 1.28830i) q^{36} +(4.23428 - 1.37580i) q^{37} +(0.553914 + 0.762398i) q^{38} +(4.15671 - 3.02003i) q^{39} +(6.02554 - 0.0856001i) q^{40} +(-0.864837 + 2.66170i) q^{41} +(-0.240119 + 0.330496i) q^{42} -3.05350i q^{43} +(0.0890077 - 4.49183i) q^{44} +(-2.13623 - 0.660705i) q^{45} +(-1.89430 - 1.37629i) q^{46} +(10.9298 + 3.55132i) q^{47} +(0.517525 - 0.168154i) q^{48} +(-5.45393 + 3.96251i) q^{49} +(0.114105 + 4.01521i) q^{50} +(-1.03379 - 3.18168i) q^{51} +(-6.61928 - 2.15074i) q^{52} +(-5.76469 + 7.93441i) q^{53} +0.803366 q^{54} +(7.41608 + 0.0415869i) q^{55} +1.37041 q^{56} +(-0.689492 + 0.949005i) q^{57} +(-0.299960 - 0.0974628i) q^{58} +(0.935871 + 2.88031i) q^{59} +(0.976834 + 2.86715i) q^{60} +(-0.853612 + 0.620185i) q^{61} +(-4.85573 + 1.57772i) q^{62} +(-0.483617 - 0.157137i) q^{63} +(2.90678 + 2.11190i) q^{64} +(3.39469 - 10.9759i) q^{65} +(-2.54987 + 0.772999i) q^{66} -5.31327i q^{67} +(-2.66367 + 3.66623i) q^{68} +(0.900658 - 2.77194i) q^{69} +(0.0129756 + 0.913376i) q^{70} +(-3.31678 + 2.40978i) q^{71} +(-1.58407 - 2.18028i) q^{72} +(-12.4668 + 4.05070i) q^{73} +(-1.10527 + 3.40167i) q^{74} +(-4.70947 + 1.67954i) q^{75} +1.58900 q^{76} +(1.68619 + 0.0334126i) q^{77} +4.12768i q^{78} +(-13.0578 - 9.48703i) q^{79} +(0.701147 - 0.994452i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-1.32155 - 1.81896i) q^{82} +(-9.02764 - 12.4255i) q^{83} +(0.212858 + 0.655110i) q^{84} +(-6.11376 - 4.31056i) q^{85} +(1.98458 + 1.44188i) q^{86} -0.392594i q^{87} +(7.12566 + 5.39598i) q^{88} +9.84603 q^{89} +(1.43816 - 1.07642i) q^{90} +(0.807365 - 2.48481i) q^{91} +(-3.75488 + 1.22004i) q^{92} +(-3.73555 - 5.14154i) q^{93} +(-7.46927 + 5.42674i) q^{94} +(0.0372589 + 2.62272i) q^{95} +(-1.80067 + 5.54191i) q^{96} +(-8.91621 + 12.2721i) q^{97} -5.41583i q^{98} +(-1.89592 - 2.72130i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{4} - 4 q^{5} + 4 q^{6} + 12 q^{9}+O(q^{10}) \) 48 * q + 12 * q^4 - 4 * q^5 + 4 * q^6 + 12 * q^9	\( 48 q + 12 q^{4} - 4 q^{5} + 4 q^{6} + 12 q^{9} - 12 q^{10} - 4 q^{14} + 10 q^{15} - 44 q^{16} - 16 q^{19} + 46 q^{20} - 32 q^{21} - 12 q^{24} + 14 q^{25} - 76 q^{26} + 4 q^{30} - 20 q^{31} - 24 q^{34} - 40 q^{35} - 12 q^{36} - 8 q^{39} - 72 q^{40} + 60 q^{41} - 48 q^{44} + 4 q^{45} + 108 q^{46} - 28 q^{49} - 38 q^{50} + 28 q^{51} + 16 q^{54} - 20 q^{55} + 24 q^{56} + 60 q^{59} + 48 q^{60} + 40 q^{61} + 64 q^{64} + 20 q^{65} + 12 q^{66} + 20 q^{69} + 86 q^{70} - 32 q^{71} - 32 q^{74} - 40 q^{75} - 136 q^{76} - 52 q^{79} + 42 q^{80} - 12 q^{81} - 70 q^{85} - 104 q^{86} + 40 q^{89} - 8 q^{90} - 40 q^{91} + 72 q^{94} - 2 q^{95} + 28 q^{96}+O(q^{100}) \) 48 * q + 12 * q^4 - 4 * q^5 + 4 * q^6 + 12 * q^9 - 12 * q^10 - 4 * q^14 + 10 * q^15 - 44 * q^16 - 16 * q^19 + 46 * q^20 - 32 * q^21 - 12 * q^24 + 14 * q^25 - 76 * q^26 + 4 * q^30 - 20 * q^31 - 24 * q^34 - 40 * q^35 - 12 * q^36 - 8 * q^39 - 72 * q^40 + 60 * q^41 - 48 * q^44 + 4 * q^45 + 108 * q^46 - 28 * q^49 - 38 * q^50 + 28 * q^51 + 16 * q^54 - 20 * q^55 + 24 * q^56 + 60 * q^59 + 48 * q^60 + 40 * q^61 + 64 * q^64 + 20 * q^65 + 12 * q^66 + 20 * q^69 + 86 * q^70 - 32 * q^71 - 32 * q^74 - 40 * q^75 - 136 * q^76 - 52 * q^79 + 42 * q^80 - 12 * q^81 - 70 * q^85 - 104 * q^86 + 40 * q^89 - 8 * q^90 - 40 * q^91 + 72 * q^94 - 2 * q^95 + 28 * q^96

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