LMFDB - Embedded newform 230.2.j.a.219.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,2,Mod(9,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("230.9"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([11, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.j (of order $22$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$12$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			219.12
Character	$\chi$	$=$	230.219
Dual form			230.2.j.a.209.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.540641 + 0.841254i) q^{2} +(2.80285 + 0.402989i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(0.225316 - 2.22469i) q^{5} +(1.17632 + 2.57578i) q^{6} +(-2.07707 + 1.79979i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(4.81510 + 1.41384i) q^{9} +(1.99334 - 1.01321i) q^{10} +(-2.81325 - 1.80797i) q^{11} +(-1.53092 + 2.38216i) q^{12} +(2.48449 + 2.15282i) q^{13} +(-2.63703 - 0.774302i) q^{14} +(1.52805 - 6.14467i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-3.09927 + 1.41539i) q^{17} +(1.41384 + 4.81510i) q^{18} +(3.40920 - 7.46511i) q^{19} +(1.93005 + 1.12912i) q^{20} +(-6.54702 + 4.20751i) q^{21} -3.34412i q^{22} +(-4.50034 + 1.65738i) q^{23} -2.83167 q^{24} +(-4.89847 - 1.00252i) q^{25} +(-0.467854 + 3.25399i) q^{26} +(5.19891 + 2.37426i) q^{27} +(-0.774302 - 2.63703i) q^{28} +(-0.0669710 - 0.146646i) q^{29} +(5.99535 - 2.03658i) q^{30} +(-0.0425932 - 0.296242i) q^{31} +(0.281733 - 0.959493i) q^{32} +(-7.15654 - 6.20117i) q^{33} +(-2.86629 - 1.84205i) q^{34} +(3.53598 + 5.02635i) q^{35} +(-3.28634 + 3.79264i) q^{36} +(-2.77482 + 9.45017i) q^{37} +(8.12320 - 1.16794i) q^{38} +(6.09610 + 7.03527i) q^{39} +(0.0935830 + 2.23411i) q^{40} +(3.66530 - 1.07623i) q^{41} +(-7.07917 - 3.23295i) q^{42} +(5.68070 + 0.816762i) q^{43} +(2.81325 - 1.80797i) q^{44} +(4.23028 - 10.3935i) q^{45} +(-3.82734 - 2.88988i) q^{46} -11.2246i q^{47} +(-1.53092 - 2.38216i) q^{48} +(0.0787672 - 0.547838i) q^{49} +(-1.80494 - 4.66285i) q^{50} +(-9.25717 + 2.71815i) q^{51} +(-2.99037 + 1.36566i) q^{52} +(-3.34604 + 2.89936i) q^{53} +(0.813387 + 5.65723i) q^{54} +(-4.65603 + 5.85124i) q^{55} +(1.79979 - 2.07707i) q^{56} +(12.5638 - 19.5497i) q^{57} +(0.0871592 - 0.135622i) q^{58} +(2.88140 - 3.32531i) q^{59} +(4.95461 + 3.94255i) q^{60} +(0.444817 + 3.09377i) q^{61} +(0.226187 - 0.195992i) q^{62} +(-12.5459 + 5.72953i) q^{63} +(0.959493 - 0.281733i) q^{64} +(5.34916 - 5.04215i) q^{65} +(1.34764 - 9.37307i) q^{66} +(3.45492 + 5.37595i) q^{67} -3.40717i q^{68} +(-13.2817 + 2.83179i) q^{69} +(-2.31675 + 5.69210i) q^{70} +(-7.55387 + 4.85458i) q^{71} +(-4.96730 - 0.714190i) q^{72} +(3.43446 + 1.56846i) q^{73} +(-9.45017 + 2.77482i) q^{74} +(-13.3257 - 4.78394i) q^{75} +(5.37427 + 6.20223i) q^{76} +(9.09729 - 1.30799i) q^{77} +(-2.62265 + 8.93192i) q^{78} +(4.12331 - 4.75855i) q^{79} +(-1.82886 + 1.28658i) q^{80} +(0.949791 + 0.610393i) q^{81} +(2.88699 + 2.50159i) q^{82} +(4.60162 - 15.6717i) q^{83} +(-1.10756 - 7.70324i) q^{84} +(2.45048 + 7.21381i) q^{85} +(2.38412 + 5.22049i) q^{86} +(-0.128613 - 0.438016i) q^{87} +(3.04192 + 1.38920i) q^{88} +(-1.04583 + 7.27394i) q^{89} +(11.0307 - 2.06043i) q^{90} -9.03510 q^{91} +(0.361907 - 4.78216i) q^{92} -0.847487i q^{93} +(9.44270 - 6.06846i) q^{94} +(-15.8394 - 9.26641i) q^{95} +(1.17632 - 2.57578i) q^{96} +(0.893213 + 3.04200i) q^{97} +(0.503456 - 0.229920i) q^{98} +(-10.9899 - 12.6830i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9} + 8 q^{11} - 6 q^{15} - 12 q^{16} - 16 q^{19} - 22 q^{20} + 4 q^{24} - 52 q^{25} - 4 q^{26} - 8 q^{29} - 44 q^{30} + 12 q^{31} + 16 q^{35} - 8 q^{36} - 36 q^{39} - 28 q^{41}+ \cdots + 188 q^{99}+O(q^{100}) $ 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9 + 8 * q^11 - 6 * q^15 - 12 * q^16 - 16 * q^19 - 22 * q^20 + 4 * q^24 - 52 * q^25 - 4 * q^26 - 8 * q^29 - 44 * q^30 + 12 * q^31 + 16 * q^35 - 8 * q^36 - 36 * q^39 - 28 * q^41 - 8 * q^44 + 16 * q^45 - 4 * q^46 - 58 * q^49 + 12 * q^50 - 24 * q^51 - 6 * q^54 - 36 * q^55 + 22 * q^56 - 102 * q^59 - 38 * q^60 + 72 * q^61 + 12 * q^64 - 138 * q^65 + 80 * q^66 - 212 * q^69 - 108 * q^70 + 176 * q^71 - 88 * q^74 - 100 * q^75 + 16 * q^76 - 104 * q^79 - 22 * q^80 - 28 * q^81 - 22 * q^84 + 2 * q^85 + 62 * q^86 + 48 * q^89 + 24 * q^90 - 56 * q^91 + 24 * q^94 + 18 * q^95 - 4 * q^96 + 188 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$e\left(\frac{10}{11}\right)$

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 $

$2$	0.540641	+	0.841254i	0.382291	+	0.594856i
$2$	0.540641	+	0.841254i	0.382291	+	0.594856i
$3$	2.80285	+	0.402989i	1.61823	+	0.232666i	0.891090	−	0.453826i	$-0.149941\pi$
$3$	2.80285	+	0.402989i	1.61823	+	0.232666i	0.727137	+	0.686492i	$0.240850\pi$
$4$	−0.415415	+	0.909632i	−0.207708	+	0.454816i
$5$	0.225316	−	2.22469i	0.100765	−	0.994910i
$5$	0.225316	−	2.22469i	0.100765	−	0.994910i
$6$	1.17632	+	2.57578i	0.480231	+	1.05156i
$7$	−2.07707	+	1.79979i	−0.785059	+	0.680257i	−0.952132	−	0.305687i	$-0.901114\pi$
$7$	−2.07707	+	1.79979i	−0.785059	+	0.680257i	0.167073	+	0.985944i	$0.446568\pi$
$8$	−0.989821	+	0.142315i	−0.349955	+	0.0503159i
$9$	4.81510	+	1.41384i	1.60503	+	0.471281i
$10$	1.99334	−	1.01321i	0.630350	−	0.320405i
$11$	−2.81325	−	1.80797i	−0.848227	−	0.545123i	0.0427941	−	0.999084i	$-0.486374\pi$
$11$	−2.81325	−	1.80797i	−0.848227	−	0.545123i	−0.891021	+	0.453961i	$0.850010\pi$
$12$	−1.53092	+	2.38216i	−0.441938	+	0.687669i
$13$	2.48449	+	2.15282i	0.689074	+	0.597086i	0.927388	−	0.374102i	$-0.122049\pi$
$13$	2.48449	+	2.15282i	0.689074	+	0.597086i	−0.238313	+	0.971188i	$0.576595\pi$
$14$	−2.63703	−	0.774302i	−0.704776	−	0.206941i
$15$	1.52805	−	6.14467i	0.394542	−	1.58655i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	−3.09927	+	1.41539i	−0.751683	+	0.343282i	−0.754139	−	0.656715i	$-0.771945\pi$
$17$	−3.09927	+	1.41539i	−0.751683	+	0.343282i	0.00245623	+	0.999997i	$0.499218\pi$
$18$	1.41384	+	4.81510i	0.333246	+	1.13493i
$19$	3.40920	−	7.46511i	0.782124	−	1.71261i	0.0841908	−	0.996450i	$-0.473169\pi$
$19$	3.40920	−	7.46511i	0.782124	−	1.71261i	0.697933	−	0.716163i	$-0.254103\pi$
$20$	1.93005	+	1.12912i	0.431572	+	0.252480i
$21$	−6.54702	+	4.20751i	−1.42868	+	0.918155i
$22$		−	3.34412i		−	0.712968i
$23$	−4.50034	+	1.65738i	−0.938387	+	0.345587i
$23$	−4.50034	+	1.65738i	−0.938387	+	0.345587i
$24$	−2.83167			−0.578013
$25$	−4.89847	−	1.00252i	−0.979693	−	0.200503i
$26$	−0.467854	+	3.25399i	−0.0917536	+	0.638161i
$27$	5.19891	+	2.37426i	1.00053	+	0.456927i
$28$	−0.774302	−	2.63703i	−0.146329	−	0.498352i
$29$	−0.0669710	−	0.146646i	−0.0124362	−	0.0272315i	0.903312	−	0.428984i	$-0.141128\pi$
$29$	−0.0669710	−	0.146646i	−0.0124362	−	0.0272315i	−0.915748	+	0.401753i	$0.868401\pi$
$30$	5.99535	−	2.03658i	1.09460	−	0.371827i
$31$	−0.0425932	−	0.296242i	−0.00764996	−	0.0532066i	0.985639	−	0.168867i	$-0.0540108\pi$
$31$	−0.0425932	−	0.296242i	−0.00764996	−	0.0532066i	−0.993289	+	0.115660i	$0.963102\pi$
$32$	0.281733	−	0.959493i	0.0498038	−	0.169616i
$33$	−7.15654	−	6.20117i	−1.24579	−	1.07949i
$34$	−2.86629	−	1.84205i	−0.491565	−	0.315909i
$35$	3.53598	+	5.02635i	0.597689	+	0.849609i
$36$	−3.28634	+	3.79264i	−0.547724	+	0.632107i
$37$	−2.77482	+	9.45017i	−0.456177	+	1.55360i	0.335126	+	0.942173i	$0.391221\pi$
$37$	−2.77482	+	9.45017i	−0.456177	+	1.55360i	−0.791303	+	0.611424i	$0.790597\pi$
$38$	8.12320	−	1.16794i	1.31776	−	0.189465i
$39$	6.09610	+	7.03527i	0.976157	+	1.12655i
$40$	0.0935830	+	2.23411i	0.0147968	+	0.353244i
$41$	3.66530	−	1.07623i	0.572424	−	0.168079i	0.0173057	−	0.999850i	$-0.494491\pi$
$41$	3.66530	−	1.07623i	0.572424	−	0.168079i	0.555118	+	0.831771i	$0.312673\pi$
$42$	−7.07917	−	3.23295i	−1.09234	−	0.498855i
$43$	5.68070	+	0.816762i	0.866299	+	0.124555i	0.561115	−	0.827738i	$-0.310373\pi$
$43$	5.68070	+	0.816762i	0.866299	+	0.124555i	0.305185	+	0.952293i	$0.401282\pi$
$44$	2.81325	−	1.80797i	0.424114	−	0.272561i
$45$	4.23028	−	10.3935i	0.630613	−	1.54938i
$46$	−3.82734	−	2.88988i	−0.564311	−	0.426090i
$47$		−	11.2246i		−	1.63727i	−0.574314	−	0.818635i	$-0.694731\pi$
$47$		−	11.2246i		−	1.63727i	0.574314	−	0.818635i	$-0.305269\pi$
$48$	−1.53092	−	2.38216i	−0.220969	−	0.343835i
$49$	0.0787672	−	0.547838i	0.0112525	−	0.0782626i
$50$	−1.80494	−	4.66285i	−0.255257	−	0.659427i
$51$	−9.25717	+	2.71815i	−1.29626	+	0.380617i
$52$	−2.99037	+	1.36566i	−0.414690	+	0.189383i
$53$	−3.34604	+	2.89936i	−0.459614	+	0.398258i	−0.853658	−	0.520833i	$-0.825621\pi$
$53$	−3.34604	+	2.89936i	−0.459614	+	0.398258i	0.394044	+	0.919092i	$0.371076\pi$
$54$	0.813387	+	5.65723i	0.110688	+	0.769851i
$55$	−4.65603	+	5.85124i	−0.627819	+	0.788981i
$56$	1.79979	−	2.07707i	0.240507	−	0.277560i
$57$	12.5638	−	19.5497i	1.66412	−	2.58942i
$58$	0.0871592	−	0.135622i	0.0114446	−	0.0178081i
$59$	2.88140	−	3.32531i	0.375126	−	0.432918i	−0.536525	−	0.843885i	$-0.680263\pi$
$59$	2.88140	−	3.32531i	0.375126	−	0.432918i	0.911651	+	0.410966i	$0.134809\pi$
$60$	4.95461	+	3.94255i	0.639638	+	0.508982i
$61$	0.444817	+	3.09377i	0.0569530	+	0.396117i	0.998280	+	0.0586218i	$0.0186706\pi$
$61$	0.444817	+	3.09377i	0.0569530	+	0.396117i	−0.941327	+	0.337495i	$0.890420\pi$
$62$	0.226187	−	0.195992i	0.0287258	−	0.0248910i
$63$	−12.5459	+	5.72953i	−1.58064	+	0.721853i
$64$	0.959493	−	0.281733i	0.119937	−	0.0352166i
$65$	5.34916	−	5.04215i	0.663481	−	0.625402i
$66$	1.34764	−	9.37307i	0.165884	−	1.15375i
$67$	3.45492	+	5.37595i	0.422085	+	0.656777i	0.985554	−	0.169360i	$-0.0541700\pi$
$67$	3.45492	+	5.37595i	0.422085	+	0.656777i	−0.563469	+	0.826137i	$0.690534\pi$
$68$		−	3.40717i		−	0.413179i
$69$	−13.2817	+	2.83179i	−1.59893	+	0.340908i
$70$	−2.31675	+	5.69210i	−0.276904	+	0.680337i
$71$	−7.55387	+	4.85458i	−0.896480	+	0.576133i	−0.905744	−	0.423824i	$-0.860687\pi$
$71$	−7.55387	+	4.85458i	−0.896480	+	0.576133i	0.00926440	+	0.999957i	$0.497051\pi$
$72$	−4.96730	−	0.714190i	−0.585402	−	0.0841681i
$73$	3.43446	+	1.56846i	0.401973	+	0.183575i	0.606134	−	0.795363i	$-0.292719\pi$
$73$	3.43446	+	1.56846i	0.401973	+	0.183575i	−0.204161	+	0.978937i	$0.565447\pi$
$74$	−9.45017	+	2.77482i	−1.09856	+	0.322566i
$75$	−13.3257	−	4.78394i	−1.53872	−	0.552401i
$76$	5.37427	+	6.20223i	0.616471	+	0.711445i
$77$	9.09729	−	1.30799i	1.03673	−	0.149060i
$78$	−2.62265	+	8.93192i	−0.296957	+	1.01134i
$79$	4.12331	−	4.75855i	0.463909	−	0.535379i	−0.474799	−	0.880095i	$-0.657479\pi$
$79$	4.12331	−	4.75855i	0.463909	−	0.535379i	0.938707	+	0.344715i	$0.112025\pi$
$80$	−1.82886	+	1.28658i	−0.204472	+	0.143844i
$81$	0.949791	+	0.610393i	0.105532	+	0.0678215i
$82$	2.88699	+	2.50159i	0.318815	+	0.276255i
$83$	4.60162	−	15.6717i	0.505094	−	1.72019i	−0.172733	−	0.984969i	$-0.555260\pi$
$83$	4.60162	−	15.6717i	0.505094	−	1.72019i	0.677826	−	0.735222i	$-0.262922\pi$
$84$	−1.10756	−	7.70324i	−0.120845	−	0.840493i
$85$	2.45048	+	7.21381i	0.265792	+	0.782447i
$86$	2.38412	+	5.22049i	0.257086	+	0.562940i
$87$	−0.128613	−	0.438016i	−0.0137888	−	0.0469602i
$88$	3.04192	+	1.38920i	0.324269	+	0.148089i
$89$	−1.04583	+	7.27394i	−0.110858	+	0.771036i	0.856230	+	0.516595i	$0.172801\pi$
$89$	−1.04583	+	7.27394i	−0.110858	+	0.771036i	−0.967088	+	0.254441i	$0.918108\pi$
$90$	11.0307	−	2.06043i	1.16273	−	0.217189i
$91$	−9.03510			−0.947136
$92$	0.361907	−	4.78216i	0.0377314	−	0.498574i
$93$		−	0.847487i		−	0.0878803i
$94$	9.44270	−	6.06846i	0.973940	−	0.625913i
$95$	−15.8394	−	9.26641i	−1.62509	−	0.950714i
$96$	1.17632	−	2.57578i	0.120058	−	0.262890i
$97$	0.893213	+	3.04200i	0.0906920	+	0.308869i	0.992329	−	0.123625i	$-0.0394520\pi$
$97$	0.893213	+	3.04200i	0.0906920	+	0.308869i	−0.901637	+	0.432494i	$0.857634\pi$
$98$	0.503456	−	0.229920i	0.0508567	−	0.0232255i
$99$	−10.9899	−	12.6830i	−1.10453	−	1.27469i
$100$	2.94682	−	4.03934i	0.294682	−	0.403934i
$101$	17.6790	+	5.19103i	1.75913	+	0.516527i	0.992140	−	0.125134i	$-0.0399362\pi$
$101$	17.6790	+	5.19103i	1.75913	+	0.516527i	0.766988	+	0.641661i	$0.221754\pi$
$102$	−7.29146	−	6.31809i	−0.721962	−	0.625584i
$103$	0.0229293	−	0.0356787i	0.00225929	−	0.00351553i	−0.840122	−	0.542397i	$-0.817517\pi$
$103$	0.0229293	−	0.0356787i	0.00225929	−	0.00351553i	0.842381	+	0.538882i	$0.181153\pi$
$104$	−2.76558	−	1.77733i	−0.271188	−	0.174282i
$105$	7.88525	+	15.5131i	0.769522	+	1.51392i
$106$	−4.24811	−	1.24736i	−0.412613	−	0.121154i
$107$	12.7985	−	1.84014i	1.23728	−	0.177894i	0.507544	−	0.861626i	$-0.330554\pi$
$107$	12.7985	−	1.84014i	1.23728	−	0.177894i	0.729733	+	0.683732i	$0.239644\pi$
$108$	−4.31941	+	3.74279i	−0.415636	+	0.360151i
$109$	4.06144	+	8.89332i	0.389016	+	0.851826i	0.998267	+	0.0588484i	$0.0187429\pi$
$109$	4.06144	+	8.89332i	0.389016	+	0.851826i	−0.609251	+	0.792977i	$0.708530\pi$
$110$	−7.43962	−	0.753485i	−0.709340	−	0.0718419i
$111$	−11.5857	+	25.3692i	−1.09967	+	2.40794i
$112$	2.72038	+	0.391132i	0.257052	+	0.0369585i
$113$	1.45272	+	2.26048i	0.136661	+	0.212648i	0.902838	−	0.429981i	$-0.141480\pi$
$113$	1.45272	+	2.26048i	0.136661	+	0.212648i	−0.766177	+	0.642629i	$0.777844\pi$
$114$	23.2388			2.17651
$115$	2.67315	+	10.3853i	0.249272	+	0.968433i
$116$	0.161215			0.0149684
$117$	8.91933	+	13.8788i	0.824593	+	1.28309i
$118$	4.35523	+	0.626187i	0.400931	+	0.0576452i
$119$	3.88999	−	8.51789i	0.356595	−	0.780834i
$120$	−0.638023	+	6.29959i	−0.0582432	+	0.575071i
$121$	0.0760740	+	0.166579i	0.00691582	+	0.0151435i
$122$	−2.36216	+	2.04682i	−0.213860	+	0.185311i
$123$	10.7070	−	1.53944i	0.965419	−	0.138806i
$124$	0.287165	+	0.0843192i	0.0257882	+	0.00757209i
$125$	−3.33399	+	10.6717i	−0.298201	+	0.954503i
$126$	−11.6028	−	7.45669i	−1.03366	−	0.664295i
$127$	−10.8431	+	16.8722i	−0.962169	+	1.49716i	−0.0972463	+	0.995260i	$0.531003\pi$
$127$	−10.8431	+	16.8722i	−0.962169	+	1.49716i	−0.864923	+	0.501904i	$0.832633\pi$
$128$	0.755750	+	0.654861i	0.0667995	+	0.0578821i
$129$	15.5930	+	4.57853i	1.37289	+	0.403117i
$130$	7.13370	+	1.77401i	0.625667	+	0.155591i
$131$	7.02144	+	8.10317i	0.613466	+	0.707977i	0.974453	−	0.224594i	$-0.0721055\pi$
$131$	7.02144	+	8.10317i	0.613466	+	0.707977i	−0.360987	+	0.932571i	$0.617560\pi$
$132$	8.61372	−	3.93375i	0.749728	−	0.342389i
$133$	6.35449	+	21.6414i	0.551004	+	1.87655i
$134$	−2.65467	+	5.81292i	−0.229329	+	0.502160i
$135$	6.45340	−	11.0310i	0.555420	−	0.949397i
$136$	2.86629	−	1.84205i	0.245782	−	0.157955i
$137$			11.0352i			0.942803i	0.881919	+	0.471401i	$0.156252\pi$
$137$			11.0352i			0.942803i	−0.881919	+	0.471401i	$0.843748\pi$
$138$	−9.56289	−	9.64230i	−0.814047	−	0.820807i
$139$	−3.35347			−0.284438			−0.142219	−	0.989835i	$-0.545424\pi$
$139$	−3.35347			−0.284438			−0.142219	+	0.989835i	$0.545424\pi$
$140$	−6.04103	+	1.12841i	−0.510560	+	0.0953683i
$141$	4.52338	−	31.4608i	0.380937	−	2.64948i
$142$	−8.16787	−	3.73014i	−0.685432	−	0.313026i
$143$	−3.09727	−	10.5483i	−0.259006	−	0.882095i
$144$	−2.08471	−	4.56488i	−0.173726	−	0.380407i
$145$	−0.341331	+	0.115948i	−0.0283460	+	0.00962894i
$146$	0.537331	+	3.73722i	0.0444699	+	0.309295i
$147$	0.441546	−	1.50377i	0.0364181	−	0.124029i
$148$	−7.44347	−	6.44981i	−0.611850	−	0.530171i
$149$	−6.76376	−	4.34681i	−0.554109	−	0.356104i	0.233426	−	0.972375i	$-0.425006\pi$
$149$	−6.76376	−	4.34681i	−0.554109	−	0.356104i	−0.787535	+	0.616270i	$0.788643\pi$
$150$	−3.17990	−	13.7967i	−0.259638	−	1.12649i
$151$	−4.33014	+	4.99725i	−0.352382	+	0.406671i	−0.904073	−	0.427378i	$-0.859437\pi$
$151$	−4.33014	+	4.99725i	−0.352382	+	0.406671i	0.551691	+	0.834049i	$0.313983\pi$
$152$	−2.31210	+	7.87430i	−0.187536	+	0.638690i
$153$	−16.9244	+	2.43336i	−1.36826	+	0.196726i
$154$	6.01872	+	6.94597i	0.485002	+	0.559722i
$155$	−0.668642	+	0.0280083i	−0.0537067	+	0.00224968i
$156$	−8.93192	+	2.62265i	−0.715126	+	0.209980i
$157$	−14.0364	−	6.41020i	−1.12023	−	0.511590i	−0.232793	−	0.972526i	$-0.574786\pi$
$157$	−14.0364	−	6.41020i	−1.12023	−	0.511590i	−0.887433	+	0.460936i	$0.847514\pi$
$158$	6.23238	+	0.896081i	0.495822	+	0.0712884i
$159$	−10.5469	+	6.77807i	−0.836422	+	0.537536i
$160$	−2.07109	−	0.842956i	−0.163734	−	0.0666415i
$161$	6.36460	−	11.5422i	0.501601	−	0.909651i
$162$			1.12902i			0.0887040i
$163$	−6.73127	−	10.4741i	−0.527234	−	0.820392i	0.470853	−	0.882211i	$-0.343946\pi$
$163$	−6.73127	−	10.4741i	−0.527234	−	0.820392i	−0.998087	+	0.0618194i	$0.980310\pi$
$164$	−0.543649	+	3.78116i	−0.0424518	+	0.295259i
$165$	−15.4082	+	14.5238i	−1.19952	+	1.13068i
$166$	15.6717	−	4.60162i	1.21636	−	0.357155i
$167$	−6.88378	+	3.14372i	−0.532683	+	0.243268i	−0.663550	−	0.748132i	$-0.730951\pi$
$167$	−6.88378	+	3.14372i	−0.532683	+	0.243268i	0.130867	+	0.991400i	$0.458224\pi$
$168$	5.88159	−	5.09643i	0.453774	−	0.393198i
$169$	−0.312045	−	2.17032i	−0.0240035	−	0.166948i
$170$	−4.74381	+	5.96155i	−0.363834	+	0.457230i
$171$	26.9701	−	31.1252i	2.06246	−	2.38020i
$172$	−3.10280	+	4.82806i	−0.236587	+	0.368136i
$173$	6.61108	−	10.2870i	0.502631	−	0.782109i	−0.493523	−	0.869733i	$-0.664291\pi$
$173$	6.61108	−	10.2870i	0.502631	−	0.782109i	0.996154	+	0.0876240i	$0.0279274\pi$
$174$	0.298949	−	0.345005i	0.0226633	−	0.0261548i
$175$	11.9788	−	6.73392i	0.905511	−	0.509036i
$176$	0.475918	+	3.31008i	0.0358736	+	0.249507i
$177$	9.41619	−	8.15918i	0.707764	−	0.613281i
$178$	−6.68465	+	3.05278i	−0.501035	+	0.228815i
$179$	−11.8320	+	3.47419i	−0.884366	+	0.259673i	−0.692214	−	0.721692i	$-0.743365\pi$
$179$	−11.8320	+	3.47419i	−0.884366	+	0.259673i	−0.192152	+	0.981365i	$0.561547\pi$
$180$	7.69697	+	8.16563i	0.573698	+	0.608630i
$181$	1.83805	−	12.7839i	0.136621	−	0.950222i	−0.800030	−	0.599960i	$-0.795183\pi$
$181$	1.83805	−	12.7839i	0.136621	−	0.950222i	0.936652	−	0.350262i	$-0.113908\pi$
$182$	−4.88475	−	7.60081i	−0.362081	−	0.563410i
$183$			8.85065i			0.654259i
$184$	4.21867	−	2.28097i	0.311004	−	0.168156i
$185$	20.3984	+	8.30238i	1.49972	+	0.610403i
$186$	0.712951	−	0.458186i	0.0522761	−	0.0335958i
$187$	11.2780	+	1.62153i	0.824728	+	0.118578i
$188$	10.2102	+	4.66285i	0.744657	+	0.340073i
$189$	−15.0717	+	4.42545i	−1.09630	+	0.321904i
$190$	−0.768010	−	18.3347i	−0.0557173	−	1.33014i
$191$	−14.6474	−	16.9039i	−1.05985	−	1.22313i	−0.973936	−	0.226824i	$-0.927166\pi$
$191$	−14.6474	−	16.9039i	−1.05985	−	1.22313i	−0.0859095	−	0.996303i	$-0.527380\pi$
$192$	2.80285	−	0.402989i	0.202278	−	0.0290833i
$193$	5.79260	−	19.7278i	0.416961	−	1.42004i	−0.436888	−	0.899516i	$-0.643919\pi$
$193$	5.79260	−	19.7278i	0.416961	−	1.42004i	0.853848	−	0.520522i	$-0.174263\pi$
$194$	−2.07619	+	2.39605i	−0.149062	+	0.172026i
$195$	17.0248	−	11.9768i	1.21917	−	0.857673i
$196$	0.465610	+	0.299229i	0.0332579	+	0.0213735i
$197$	0.247709	+	0.214641i	0.0176485	+	0.0152925i	0.663640	−	0.748052i	$-0.269011\pi$
$197$	0.247709	+	0.214641i	0.0176485	+	0.0152925i	−0.645992	+	0.763344i	$0.723556\pi$
$198$	4.72805	−	16.1023i	0.336008	−	1.14434i
$199$	2.15145	+	14.9637i	0.152512	+	1.06075i	0.911990	+	0.410213i	$0.134546\pi$
$199$	2.15145	+	14.9637i	0.152512	+	1.06075i	−0.759477	+	0.650534i	$0.774545\pi$
$200$	4.99128	+	0.295188i	0.352937	+	0.0208730i
$201$	7.51717	+	16.4603i	0.530220	+	1.16102i
$202$	5.19103	+	17.6790i	0.365239	+	1.24389i
$203$	0.403036	+	0.184060i	0.0282876	+	0.0129185i
$204$	1.37305	−	9.54978i	0.0961328	−	0.668618i
$205$	−1.56842	−	8.39664i	−0.109543	−	0.586447i
$206$	0.0424114			0.00295494
$207$	−24.0129	+	1.61767i	−1.66901	+	0.112436i
$208$		−	3.28745i		−	0.227944i
$209$	−23.0876	+	14.8375i	−1.59700	+	1.02633i
$210$	−8.78735	+	15.0205i	−0.606385	+	1.03651i
$211$	−8.40701	+	18.4088i	−0.578763	+	1.26731i	0.363236	+	0.931697i	$0.381672\pi$
$211$	−8.40701	+	18.4088i	−0.578763	+	1.26731i	−0.941999	+	0.335616i	$0.891056\pi$
$212$	−1.24736	−	4.24811i	−0.0856688	−	0.291761i
$213$	−23.1287	+	10.5625i	−1.58476	+	0.723733i
$214$	8.46741	+	9.77192i	0.578821	+	0.667994i
$215$	3.09700	−	12.4538i	0.211213	−	0.849339i
$216$	−5.48389	−	1.61022i	−0.373131	−	0.109561i
$217$	0.621643	+	0.538656i	0.0421999	+	0.0365664i
$218$	−5.28576	+	8.22480i	−0.357997	+	0.557054i
$219$	8.99420	+	5.78022i	0.607772	+	0.390591i
$220$	−3.38829	−	6.66597i	−0.228438	−	0.449420i
$221$	−10.7472	−	3.15566i	−0.722934	−	0.212273i
$222$	−27.6056	+	3.96909i	−1.85277	+	0.266388i
$223$	16.8428	−	14.5943i	1.12788	−	0.977310i	0.127980	−	0.991777i	$-0.459151\pi$
$223$	16.8428	−	14.5943i	1.12788	−	0.977310i	0.999895	+	0.0144670i	$0.00460514\pi$
$224$	1.14171	+	2.49999i	0.0762837	+	0.167038i
$225$	−22.1692	−	11.7529i	−1.47795	−	0.783525i
$226$	−1.11624	+	2.44421i	−0.0742509	+	0.162587i
$227$	−22.0396	−	3.16882i	−1.46282	−	0.210322i	−0.635522	−	0.772083i	$-0.719215\pi$
$227$	−22.0396	−	3.16882i	−1.46282	−	0.210322i	−0.827300	+	0.561761i	$0.810124\pi$
$228$	12.5638	+	19.5497i	0.832061	+	1.29471i
$229$	9.90071			0.654258			0.327129	−	0.944980i	$-0.393919\pi$
$229$	9.90071			0.654258			0.327129	+	0.944980i	$0.393919\pi$
$230$	−7.29145	+	7.86351i	−0.480784	+	0.518504i
$231$	26.0255			1.71235
$232$	0.0871592	+	0.135622i	0.00572228	+	0.00890405i
$233$	−4.82388	−	0.693569i	−0.316023	−	0.0454372i	−0.0175216	−	0.999846i	$-0.505578\pi$
$233$	−4.82388	−	0.693569i	−0.316023	−	0.0454372i	−0.298501	+	0.954409i	$0.596487\pi$
$234$	−6.85339	+	15.0068i	−0.448020	+	0.981028i
$235$	−24.9711	−	2.52908i	−1.62894	−	0.164979i
$236$	1.82783	+	4.00239i	0.118982	+	0.260534i
$237$	13.4747	−	11.6759i	0.875275	−	0.758430i
$238$	9.26880	−	1.33265i	0.600807	−	0.0863830i
$239$	3.94894	+	1.15951i	0.255436	+	0.0750027i	0.406943	−	0.913453i	$-0.366595\pi$
$239$	3.94894	+	1.15951i	0.255436	+	0.0750027i	−0.151508	+	0.988456i	$0.548413\pi$
$240$	−5.64449	+	2.86908i	−0.364351	+	0.185198i
$241$	−5.06881	−	3.25753i	−0.326511	−	0.209836i	0.367107	−	0.930179i	$-0.380348\pi$
$241$	−5.06881	−	3.25753i	−0.326511	−	0.209836i	−0.693618	+	0.720343i	$0.743985\pi$
$242$	−0.0990063	+	0.154057i	−0.00636437	+	0.00990315i
$243$	−10.5421	−	9.13478i	−0.676276	−	0.585997i
$244$	−2.99898	−	0.880580i	−0.191990	−	0.0563733i
$245$	−1.20102	−	0.298669i	−0.0767304	−	0.0190813i
$246$	7.08370	+	8.17503i	0.451640	+	0.521221i
$247$	24.5412	−	11.2076i	1.56152	−	0.713122i
$248$	0.0843192	+	0.287165i	0.00535428	+	0.0182350i
$249$	19.2132	−	42.0710i	1.21759	−	2.66614i
$250$	−10.7801	+	2.96481i	−0.681792	+	0.187511i
$251$	7.26915	−	4.67160i	0.458824	−	0.294869i	−0.290737	−	0.956803i	$-0.593901\pi$
$251$	7.26915	−	4.67160i	0.458824	−	0.294869i	0.749562	+	0.661934i	$0.230264\pi$
$252$		−	13.7923i		−	0.868834i
$253$	15.6571	+	3.47385i	0.984352	+	0.218399i
$254$	−20.0560			−1.25843
$255$	3.96124	+	21.2068i	0.248063	+	1.32802i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	−3.55239	−	1.62232i	−0.221592	−	0.101198i	0.301526	−	0.953458i	$-0.402504\pi$
$257$	−3.55239	−	1.62232i	−0.221592	−	0.101198i	−0.523118	+	0.852260i	$0.675231\pi$
$258$	4.57853	+	15.5930i	0.285047	+	0.970780i
$259$	−11.2448	−	24.6228i	−0.698720	−	1.52998i
$260$	2.36438	+	6.96035i	0.146633	+	0.431663i
$261$	−0.115138	−	0.800802i	−0.00712686	−	0.0495684i
$262$	−3.02075	+	10.2877i	−0.186622	+	0.635577i
$263$	3.69651	+	3.20304i	0.227937	+	0.197508i	0.761340	−	0.648353i	$-0.224542\pi$
$263$	3.69651	+	3.20304i	0.227937	+	0.197508i	−0.533403	+	0.845861i	$0.679087\pi$
$264$	7.96621	+	5.11957i	0.490287	+	0.315088i
$265$	5.69626	+	8.09717i	0.349918	+	0.497405i
$266$	−14.7704	+	17.0460i	−0.905632	+	1.04515i
$267$	−5.86264	+	19.9663i	−0.358788	+	1.22192i
$268$	−6.32536	+	0.909450i	−0.386383	+	0.0555535i
$269$	−6.17800	−	7.12979i	−0.376679	−	0.434711i	0.535479	−	0.844548i	$-0.320131\pi$
$269$	−6.17800	−	7.12979i	−0.376679	−	0.434711i	−0.912159	+	0.409837i	$0.865586\pi$
$270$	12.7688	−	0.534865i	0.777087	−	0.0325508i
$271$	14.5233	−	4.26442i	0.882227	−	0.259045i	0.190920	−	0.981606i	$-0.438853\pi$
$271$	14.5233	−	4.26442i	0.882227	−	0.259045i	0.691308	+	0.722560i	$0.257035\pi$
$272$	3.09927	+	1.41539i	0.187921	+	0.0858205i
$273$	−25.3241	−	3.64105i	−1.53268	−	0.220366i
$274$	−9.28342	+	5.96609i	−0.560832	+	0.360425i
$275$	11.9681	+	11.6766i	0.721703	+	0.704125i
$276$	2.94153	−	13.2578i	0.177059	−	0.798028i
$277$			5.28445i			0.317512i	0.987318	+	0.158756i	$0.0507483\pi$
$277$			5.28445i			0.317512i	−0.987318	+	0.158756i	$0.949252\pi$
$278$	−1.81302	−	2.82112i	−0.108738	−	0.169199i
$279$	0.213749	−	1.48666i	0.0127968	−	0.0890037i
$280$	−4.21531	−	4.47197i	−0.251913	−	0.267251i
$281$	24.0643	−	7.06591i	1.43555	−	0.421517i	0.530817	−	0.847487i	$-0.321885\pi$
$281$	24.0643	−	7.06591i	1.43555	−	0.421517i	0.904737	+	0.425970i	$0.140067\pi$
$282$	28.9120	−	13.2037i	1.72169	−	0.786268i
$283$	−0.0575560	+	0.0498726i	−0.00342135	+	0.00296462i	−0.656570	−	0.754265i	$-0.727993\pi$
$283$	−0.0575560	+	0.0498726i	−0.00342135	+	0.00296462i	0.653148	+	0.757230i	$0.273448\pi$
$284$	−1.27789	−	8.88791i	−0.0758287	−	0.527401i
$285$	−40.6612	−	32.3555i	−2.40856	−	1.91657i
$286$	7.19930	−	8.30844i	0.425704	−	0.491288i
$287$	−5.67610	+	8.83219i	−0.335050	+	0.521347i
$288$	2.71314	−	4.22173i	0.159873	−	0.248768i
$289$	−3.53050	+	4.07442i	−0.207677	+	0.239671i
$290$	−0.282079	−	0.224460i	−0.0165642	−	0.0131807i
$291$	1.27765	+	8.88624i	0.0748971	+	0.520921i
$292$	−2.85345	+	2.47253i	−0.166985	+	0.144694i
$293$	12.7832	−	5.83788i	0.746802	−	0.341053i	−0.00540043	−	0.999985i	$-0.501719\pi$
$293$	12.7832	−	5.83788i	0.746802	−	0.341053i	0.752202	+	0.658933i	$0.228992\pi$
$294$	1.50377	−	0.441546i	0.0877015	−	0.0257515i
$295$	−6.74855	−	7.15945i	−0.392915	−	0.416839i
$296$	1.40168	−	9.74887i	0.0814708	−	0.566642i
$297$	−10.3333	−	16.0789i	−0.599597	−	0.932991i
$298$		−	8.04010i		−	0.465750i
$299$	−14.7491	−	5.57071i	−0.852963	−	0.322163i
$300$	9.88731	−	10.1341i	0.570844	−	0.585095i
$301$	−13.2692	+	8.52761i	−0.764825	+	0.491523i
$302$	−6.54501	−	0.941030i	−0.376623	−	0.0541502i
$303$	47.4598	+	21.6741i	2.72649	+	1.24515i
$304$	−7.87430	+	2.31210i	−0.451622	+	0.132608i
$305$	6.98290	−	0.292502i	0.399840	−	0.0167486i
$306$	−11.1971	−	12.9222i	−0.640096	−	0.738710i
$307$	−5.87650	+	0.844913i	−0.335390	+	0.0482218i	−0.307952	−	0.951402i	$-0.599644\pi$
$307$	−5.87650	+	0.844913i	−0.335390	+	0.0482218i	−0.0274373	+	0.999624i	$0.508735\pi$
$308$	−2.58936	+	8.81854i	−0.147542	+	0.502483i
$309$	0.0786457	−	0.0907620i	0.00447400	−	0.00516327i
$310$	−0.385057	−	0.547355i	−0.0218698	−	0.0310877i
$311$	−15.8294	−	10.1730i	−0.897604	−	0.576855i	0.00847459	−	0.999964i	$-0.497302\pi$
$311$	−15.8294	−	10.1730i	−0.897604	−	0.576855i	−0.906079	+	0.423109i	$0.860939\pi$
$312$	−7.03527	−	6.09610i	−0.398294	−	0.345124i
$313$	−7.23848	+	24.6520i	−0.409143	+	1.39341i	0.455146	+	0.890417i	$0.349587\pi$
$313$	−7.23848	+	24.6520i	−0.409143	+	1.39341i	−0.864289	+	0.502996i	$0.832231\pi$
$314$	−2.19604	−	15.2738i	−0.123930	−	0.861949i
$315$	9.91962	+	29.2017i	0.558907	+	1.64533i
$316$	2.61565	+	5.72747i	0.147142	+	0.322195i
$317$	−6.06543	−	20.6570i	−0.340669	−	1.16021i	−0.934602	−	0.355696i	$-0.884244\pi$
$317$	−6.06543	−	20.6570i	−0.340669	−	1.16021i	0.593933	−	0.804514i	$-0.297574\pi$
$318$	−11.4041	−	5.20810i	−0.639513	−	0.292056i
$319$	−0.0767249	+	0.533633i	−0.00429577	+	0.0298777i
$320$	−0.410577	−	2.19805i	−0.0229520	−	0.122875i
$321$	36.6138			2.04359
$322$	13.1509	−	0.885930i	0.732868	−	0.0493709i
$323$			27.9617i			1.55583i
$324$	−0.949791	+	0.610393i	−0.0527661	+	0.0339107i
$325$	−10.0120	−	13.0363i	−0.555363	−	0.723123i
$326$	5.17214	−	11.3254i	0.286459	−	0.627257i
$327$	7.79972	+	26.5634i	0.431325	+	1.46896i
$328$	−3.47483	+	1.58690i	−0.191865	+	0.0876220i
$329$	20.2019	+	23.3142i	1.11377	+	1.28535i
$330$	−20.5485	−	5.10999i	−1.13116	−	0.281296i
$331$	17.2876	+	5.07609i	0.950212	+	0.279007i	0.719875	−	0.694104i	$-0.244199\pi$
$331$	17.2876	+	5.07609i	0.950212	+	0.279007i	0.230337	+	0.973111i	$0.426017\pi$
$332$	12.3439	+	10.6960i	0.677458	+	0.587021i
$333$	−26.7221	+	41.5804i	−1.46436	+	2.27859i
$334$	−6.36632	−	4.09138i	−0.348349	−	0.223871i
$335$	12.7383	−	6.47482i	0.695966	−	0.353757i
$336$	7.46721	+	2.19257i	0.407370	+	0.119615i
$337$	−3.47807	+	0.500071i	−0.189462	+	0.0272406i	−0.236393	−	0.971658i	$-0.575965\pi$
$337$	−3.47807	+	0.500071i	−0.189462	+	0.0272406i	0.0469304	+	0.998898i	$0.485056\pi$
$338$	1.65709	−	1.43588i	0.0901337	−	0.0781013i
$339$	3.16081	+	6.92122i	0.171672	+	0.375909i
$340$	−7.57988	−	0.767690i	−0.411077	−	0.0416338i
$341$	−0.415770	+	0.910410i	−0.0225152	+	0.0493015i
$342$	40.7653	+	5.86117i	2.20434	+	0.316936i
$343$	−9.57873	−	14.9048i	−0.517203	−	0.804783i
$344$	−5.73912			−0.309433
$345$	3.30727	+	30.1857i	0.178057	+	1.62514i
$346$	12.2282			0.657393
$347$	−8.45709	−	13.1595i	−0.454001	−	0.706439i	0.536507	−	0.843896i	$-0.319743\pi$
$347$	−8.45709	−	13.1595i	−0.454001	−	0.706439i	−0.990508	+	0.137457i	$0.956107\pi$
$348$	0.451861	+	0.0649678i	0.0242223	+	0.00348264i
$349$	−3.89175	+	8.52174i	−0.208321	+	0.456158i	−0.984734	−	0.174065i	$-0.944310\pi$
$349$	−3.89175	+	8.52174i	−0.208321	+	0.456158i	0.776414	+	0.630224i	$0.217037\pi$
$350$	12.1411	+	6.43656i	0.648972	+	0.344049i
$351$	7.80529	+	17.0912i	0.416615	+	0.912261i
$352$	−2.52732	+	2.18993i	−0.134706	+	0.116724i
$353$	−9.57224	+	1.37628i	−0.509479	+	0.0732520i	−0.392260	−	0.919854i	$-0.628307\pi$
$353$	−9.57224	+	1.37628i	−0.509479	+	0.0732520i	−0.117218	+	0.993106i	$0.537398\pi$
$354$	11.9547	+	3.51022i	0.635386	+	0.186566i
$355$	9.09791	+	17.8988i	0.482867	+	0.949971i
$356$	−6.18215	−	3.97303i	−0.327653	−	0.210570i
$357$	14.3357	−	22.3068i	0.758725	−	1.18060i
$358$	−9.31954	−	8.07543i	−0.492553	−	0.426800i
$359$	22.5166	+	6.61146i	1.18838	+	0.348939i	0.815398	−	0.578900i	$-0.196518\pi$
$359$	22.5166	+	6.61146i	1.18838	+	0.348939i	0.372980	+	0.927839i	$0.378336\pi$
$360$	−2.70806	+	10.8898i	−0.142728	+	0.573942i
$361$	−31.6628	−	36.5408i	−1.66646	−	1.92320i
$362$	11.7483	−	5.36525i	0.617474	−	0.281991i
$363$	0.146095	+	0.497553i	0.00766798	+	0.0261147i
$364$	3.75332	−	8.21862i	0.196727	−	0.430773i
$365$	4.26318	−	7.28719i	0.223145	−	0.381429i
$366$	−7.44564	+	4.78502i	−0.389190	+	0.250117i
$367$		−	15.6121i		−	0.814943i	−0.913218	−	0.407472i	$-0.866411\pi$
$367$		−	15.6121i		−	0.814943i	0.913218	−	0.407472i	$-0.133589\pi$
$368$	4.19966	+	2.31578i	0.218922	+	0.120718i
$369$	19.1704			0.997973
$370$	4.04383	+	21.6489i	0.210229	+	1.12547i
$371$	1.73172	−	12.0444i	0.0899063	−	0.625312i
$372$	0.770901	+	0.352059i	0.0399694	+	0.0182534i
$373$	−3.71194	−	12.6417i	−0.192197	−	0.654563i	−0.998048	−	0.0624450i	$-0.980110\pi$
$373$	−3.71194	−	12.6417i	−0.192197	−	0.654563i	0.805851	−	0.592118i	$-0.201708\pi$
$374$	4.73322	+	10.3643i	0.244749	+	0.535926i
$375$	−13.6453	+	28.5676i	−0.704638	+	1.47522i
$376$	1.59742	+	11.1103i	0.0823807	+	0.572970i
$377$	0.149314	−	0.508518i	0.00769008	−	0.0261900i
$378$	−11.8713	−	10.2865i	−0.610594	−	0.529082i
$379$	2.82564	+	1.81593i	0.145143	+	0.0932780i	0.611197	−	0.791478i	$-0.290688\pi$
$379$	2.82564	+	1.81593i	0.145143	+	0.0932780i	−0.466054	+	0.884756i	$0.654325\pi$
$380$	15.0089	−	10.5586i	0.769942	−	0.541644i
$381$	−37.1909	+	42.9206i	−1.90535	+	2.19889i
$382$	6.30155	−	21.4611i	0.322415	−	1.09805i
$383$	10.5072	−	1.51070i	0.536891	−	0.0771932i	0.131464	−	0.991321i	$-0.458032\pi$
$383$	10.5072	−	1.51070i	0.536891	−	0.0771932i	0.405426	+	0.914128i	$0.367123\pi$
$384$	1.85435	+	2.14004i	0.0946295	+	0.109208i
$385$	−0.860106	−	20.5333i	−0.0438350	−	1.04648i
$386$	19.7278	−	5.79260i	1.00412	−	0.294836i
$387$	26.1984	+	11.9644i	1.33174	+	0.608185i
$388$	−3.13816	−	0.451199i	−0.159316	−	0.0229062i
$389$	−9.49042	+	6.09912i	−0.481184	+	0.309238i	−0.758651	−	0.651497i	$-0.774141\pi$
$389$	−9.49042	+	6.09912i	−0.481184	+	0.309238i	0.277468	+	0.960735i	$0.410505\pi$
$390$	19.2798	+	7.84708i	0.976271	+	0.397352i
$391$	11.6019	−	11.5064i	0.586735	−	0.581903i
$392$			0.553472i			0.0279545i
$393$	16.4146	+	25.5416i	0.828005	+	1.28840i
$394$	−0.0466459	+	0.324430i	−0.00234999	+	0.0163445i
$395$	−9.65725	−	10.2453i	−0.485909	−	0.515495i
$396$	16.1023	−	4.72805i	0.809170	−	0.237594i
$397$	12.4018	−	5.66370i	0.622428	−	0.284253i	−0.0791318	−	0.996864i	$-0.525215\pi$
$397$	12.4018	−	5.66370i	0.622428	−	0.284253i	0.701559	+	0.712611i	$0.252488\pi$
$398$	−11.4251	+	9.89989i	−0.572688	+	0.496237i
$399$	9.08944	+	63.2184i	0.455041	+	3.16488i
$400$	2.45016	+	4.35852i	0.122508	+	0.217926i
$401$	16.7941	−	19.3814i	0.838657	−	0.967862i	−0.161161	−	0.986928i	$-0.551524\pi$
$401$	16.7941	−	19.3814i	0.838657	−	0.967862i	0.999818	+	0.0190660i	$0.00606926\pi$
$402$	−9.78320	+	15.2230i	−0.487942	+	0.759252i
$403$	0.531935	−	0.827706i	0.0264976	−	0.0412310i
$404$	−12.0661	+	13.9250i	−0.600309	+	0.692793i
$405$	1.57194	−	1.97546i	0.0781102	−	0.0981612i
$406$	0.0630562	+	0.438566i	0.00312943	+	0.0217657i
$407$	24.8919	−	21.5689i	1.23384	−	1.06913i
$408$	8.77612	−	4.00792i	0.434482	−	0.198421i
$409$	15.3476	−	4.50645i	0.758888	−	0.222830i	0.120678	−	0.992692i	$-0.461493\pi$
$409$	15.3476	−	4.50645i	0.758888	−	0.222830i	0.638210	+	0.769862i	$0.279675\pi$
$410$	6.21575	−	5.85901i	0.306974	−	0.289356i
$411$	−4.44708	+	30.9301i	−0.219358	+	1.52567i
$412$	0.0229293	+	0.0356787i	0.00112965	+	0.00175777i
$413$			12.0928i			0.595048i
$414$	−14.3432	−	19.3264i	−0.704931	−	0.949838i
$415$	−33.8278	−	13.7683i	−1.66054	−	0.675857i
$416$	2.76558	−	1.77733i	0.135594	−	0.0871409i
$417$	−9.39928	−	1.35141i	−0.460285	−	0.0661790i
$418$	−24.9642	−	11.4008i	−1.22104	−	0.557630i
$419$	−14.7543	+	4.33224i	−0.720793	+	0.211644i	−0.621500	−	0.783414i	$-0.713476\pi$
$419$	−14.7543	+	4.33224i	−0.720793	+	0.211644i	−0.0992931	+	0.995058i	$0.531658\pi$
$420$	−17.3869	+	0.728306i	−0.848392	+	0.0355377i
$421$	−13.1265	−	15.1487i	−0.639745	−	0.738305i	0.339585	−	0.940575i	$-0.389713\pi$
$421$	−13.1265	−	15.1487i	−0.639745	−	0.738305i	−0.979330	+	0.202271i	$0.935168\pi$
$422$	−20.0316	+	2.88011i	−0.975125	+	0.140202i
$423$	15.8698	−	54.0474i	0.771614	−	2.62788i
$424$	2.89936	−	3.34604i	0.140806	−	0.162498i
$425$	16.6006	−	3.82616i	0.805247	−	0.185596i
$426$	−21.3901	−	13.7466i	−1.03635	−	0.666025i
$427$	−6.49206	−	5.62540i	−0.314173	−	0.272232i
$428$	−3.64283	+	12.4063i	−0.176083	+	0.599683i
$429$	−4.43032	−	30.8135i	−0.213898	−	1.48769i
$430$	12.1511	−	4.12765i	0.585980	−	0.199053i
$431$	0.984516	+	2.15579i	0.0474225	+	0.103841i	0.931860	−	0.362817i	$-0.118185\pi$
$431$	0.984516	+	2.15579i	0.0474225	+	0.103841i	−0.884438	+	0.466658i	$0.845458\pi$
$432$	−1.61022	−	5.48389i	−0.0774715	−	0.263844i
$433$	−0.278198	−	0.127049i	−0.0133694	−	0.00610558i	0.408719	−	0.912660i	$-0.365976\pi$
$433$	−0.278198	−	0.127049i	−0.0133694	−	0.00610558i	−0.422088	+	0.906555i	$0.638703\pi$
$434$	−0.117061	+	0.814179i	−0.00561912	+	0.0390818i
$435$	−1.00343	+	0.187432i	−0.0481106	+	0.00898666i
$436$	−9.77684			−0.468226
$437$	−2.97007	+	39.2459i	−0.142078	+	1.87738i
$438$			10.6914i			0.510856i
$439$	26.5399	−	17.0561i	1.26668	−	0.814045i	0.277495	−	0.960727i	$-0.410496\pi$
$439$	26.5399	−	17.0561i	1.26668	−	0.814045i	0.989184	+	0.146682i	$0.0468595\pi$
$440$	3.77592	−	6.45430i	0.180010	−	0.307697i
$441$	1.15383	−	2.52653i	0.0549442	−	0.120311i
$442$	−3.15566	−	10.7472i	−0.150099	−	0.511192i
$443$	19.2284	−	8.78131i	0.913568	−	0.417213i	0.0975447	−	0.995231i	$-0.468901\pi$
$443$	19.2284	−	8.78131i	0.913568	−	0.417213i	0.816024	+	0.578018i	$0.196174\pi$
$444$	−18.2638	−	21.0775i	−0.866759	−	1.00029i
$445$	15.9466	+	3.96559i	0.755941	+	0.187987i
$446$	21.3834	+	6.27874i	1.01254	+	0.297307i
$447$	−17.2061	−	14.9092i	−0.813821	−	0.705180i
$448$	−1.48587	+	2.31207i	−0.0702010	+	0.109235i
$449$	−10.0427	−	6.45408i	−0.473946	−	0.304587i	0.281774	−	0.959481i	$-0.409077\pi$
$449$	−10.0427	−	6.45408i	−0.473946	−	0.304587i	−0.755721	+	0.654894i	$0.772713\pi$
$450$	−2.09843	−	25.0040i	−0.0989211	−	1.17870i
$451$	−12.2572	−	3.59904i	−0.577169	−	0.169472i
$452$	−2.65969	+	0.382405i	−0.125101	+	0.0179868i
$453$	−14.1506	+	12.2616i	−0.664853	+	0.576098i
$454$	−9.24974	−	20.2541i	−0.434112	−	0.950572i
$455$	−2.03576	+	20.1003i	−0.0954377	+	0.942315i
$456$	−9.65374	+	21.1388i	−0.452078	+	0.989913i
$457$	−14.4114	−	2.07205i	−0.674138	−	0.0969265i	−0.203260	−	0.979125i	$-0.565154\pi$
$457$	−14.4114	−	2.07205i	−0.674138	−	0.0969265i	−0.470878	+	0.882198i	$0.656063\pi$
$458$	5.35273	+	8.32901i	0.250117	+	0.389189i
$459$	−19.4733			−0.908937
$460$	−10.5573	−	1.88263i	−0.492235	−	0.0877780i
$461$	−34.8073			−1.62114			−0.810568	−	0.585644i	$-0.800842\pi$
$461$	−34.8073			−1.62114			−0.810568	+	0.585644i	$0.800842\pi$
$462$	14.0704	+	21.8940i	0.654615	+	1.01860i
$463$	9.62926	+	1.38448i	0.447510	+	0.0643422i	0.362386	−	0.932028i	$-0.381962\pi$
$463$	9.62926	+	1.38448i	0.447510	+	0.0643422i	0.0851240	+	0.996370i	$0.472871\pi$
$464$	−0.0669710	+	0.146646i	−0.00310905	+	0.00680787i
$465$	−1.88539	−	0.190953i	−0.0874330	−	0.00885522i
$466$	−2.02452	−	4.43308i	−0.0937840	−	0.205358i
$467$	−12.0372	+	10.4303i	−0.557015	+	0.482657i	−0.887280	−	0.461232i	$-0.847408\pi$
$467$	−12.0372	+	10.4303i	−0.557015	+	0.482657i	0.330264	+	0.943889i	$0.392862\pi$
$468$	−16.3298	+	2.34787i	−0.754845	+	0.108530i
$469$	−16.8517	−	4.94811i	−0.778139	−	0.228482i
$470$	−11.3728	−	22.3744i	−0.524589	−	1.03205i
$471$	−36.7587	−	23.6234i	−1.69375	−	1.08851i
$472$	−2.37883	+	3.70153i	−0.109494	+	0.170377i
$473$	−14.5046	−	12.5683i	−0.666921	−	0.577890i
$474$	17.1073	+	5.02317i	0.785766	+	0.230722i
$475$	−24.1837	+	33.1498i	−1.10963	+	1.52102i
$476$	6.13219	+	7.07692i	0.281068	+	0.324370i
$477$	−20.2108	+	9.22996i	−0.925388	+	0.422611i
$478$	1.15951	+	3.94894i	0.0530349	+	0.180620i
$479$	−0.950164	+	2.08057i	−0.0434141	+	0.0950636i	−0.930096	−	0.367316i	$-0.880277\pi$
$479$	−0.950164	+	2.08057i	−0.0434141	+	0.0950636i	0.886682	+	0.462379i	$0.153004\pi$
$480$	−5.46526	−	3.19731i	−0.249454	−	0.145937i
$481$	−27.2386	+	17.5052i	−1.24197	+	0.798167i
$482$		−	6.02531i		−	0.274445i
$483$	22.4904	−	29.7861i	1.02335	−	1.35532i
$484$	−0.183128			−0.00832398
$485$	6.96876	−	1.30171i	0.316435	−	0.0591074i
$486$	1.98518	−	13.8072i	0.0900495	−	0.626308i
$487$	−0.235141	−	0.107385i	−0.0106553	−	0.00486610i	0.410080	−	0.912049i	$-0.365501\pi$
$487$	−0.235141	−	0.107385i	−0.0106553	−	0.00486610i	−0.420736	+	0.907183i	$0.638228\pi$
$488$	−0.880580	−	2.99898i	−0.0398620	−	0.135757i
$489$	−14.6458	−	32.0699i	−0.662307	−	1.45025i
$490$	−0.398064	−	1.17184i	−0.0179827	−	0.0529382i
$491$	0.355861	+	2.47507i	0.0160598	+	0.111698i	0.996274	−	0.0862389i	$-0.0274848\pi$
$491$	0.355861	+	2.47507i	0.0160598	+	0.111698i	−0.980215	+	0.197937i	$0.936576\pi$
$492$	−3.04753	+	10.3789i	−0.137393	+	0.467919i
$493$	0.415122	+	0.359705i	0.0186962	+	0.0162003i
$494$	22.6964	+	14.5861i	1.02116	+	0.656259i
$495$	−30.6920	+	21.5914i	−1.37950	+	0.970463i
$496$	−0.195992	+	0.226187i	−0.00880031	+	0.0101561i
$497$	6.95270	−	23.6787i	0.311871	−	1.06214i
$498$	45.7798	−	6.58214i	2.05144	−	0.294953i
$499$	29.0552	+	33.5315i	1.30069	+	1.50107i	0.738951	+	0.673759i	$0.235321\pi$
$499$	29.0552	+	33.5315i	1.30069	+	1.50107i	0.561737	+	0.827316i	$0.310133\pi$
$500$	−8.32230	−	7.46588i	−0.372185	−	0.333884i
$501$	−20.5611	+	6.03729i	−0.918603	+	0.269726i
$502$	7.85999	+	3.58954i	0.350809	+	0.160209i
$503$	−33.4440	−	4.80852i	−1.49119	−	0.214401i	−0.651994	−	0.758224i	$-0.726067\pi$
$503$	−33.4440	−	4.80852i	−1.49119	−	0.214401i	−0.839200	+	0.543823i	$0.816976\pi$
$504$	11.6028	−	7.45669i	0.516831	−	0.332147i
$505$	15.5318	−	38.1607i	0.691155	−	1.69813i
$506$	5.54247	+	15.0497i	0.246393	+	0.669040i
$507$		−	6.20885i		−	0.275745i
$508$	−10.8431	−	16.8722i	−0.481085	−	0.748582i
$509$	−1.60351	+	11.1527i	−0.0710745	+	0.494334i	0.922928	+	0.384974i	$0.125789\pi$
$509$	−1.60351	+	11.1527i	−0.0710745	+	0.494334i	−0.994002	+	0.109361i	$0.965120\pi$
$510$	−15.6987	+	14.7976i	−0.695148	+	0.655251i
$511$	−9.95651	+	2.92350i	−0.440450	+	0.129328i
$512$	−0.909632	+	0.415415i	−0.0402004	+	0.0183589i
$513$	35.4483	−	30.7161i	1.56508	−	1.35615i
$514$	−0.555783	−	3.86556i	−0.0245145	−	0.170502i
$515$	−0.0742077	−	0.0590496i	−0.00326998	−	0.00260204i
$516$	−10.6424	+	12.2819i	−0.468504	+	0.540682i
$517$	−20.2936	+	31.5775i	−0.892513	+	1.38878i
$518$	14.6346	−	22.7718i	0.643006	−	1.00054i
$519$	22.6754	−	26.1689i	0.995341	−	1.14869i
$520$	−4.57714	+	5.75209i	−0.200721	+	0.252246i
$521$	4.25300	+	29.5803i	0.186327	+	1.29594i	0.841418	+	0.540385i	$0.181721\pi$
$521$	4.25300	+	29.5803i	0.186327	+	1.29594i	−0.655091	+	0.755550i	$0.727370\pi$
$522$	0.611429	−	0.529806i	0.0267615	−	0.0231890i
$523$	−21.9179	+	10.0096i	−0.958404	+	0.437688i	−0.832298	−	0.554328i	$-0.812975\pi$
$523$	−21.9179	+	10.0096i	−0.958404	+	0.437688i	−0.126106	+	0.992017i	$0.540248\pi$
$524$	−10.2877	+	3.02075i	−0.449421	+	0.131962i
$525$	36.2884	−	14.0469i	1.58376	−	0.613055i
$526$	−0.696088	+	4.84140i	−0.0303509	+	0.211095i
$527$	0.551305	+	0.857847i	0.0240152	+	0.0373684i
$528$			9.46946i			0.412105i
$529$	17.5062	−	14.9175i	0.761139	−	0.648589i
$530$	−3.73215	+	9.16966i	−0.162114	+	0.398304i
$531$	18.5757	−	11.9379i	0.806116	−	0.518059i
$532$	−22.3255	−	3.20992i	−0.967931	−	0.139168i
$533$	11.4234	+	5.21687i	0.494800	+	0.225968i
$534$	−19.9663	+	5.86264i	−0.864027	+	0.253701i
$535$	−1.21004	−	28.8872i	−0.0523145	−	1.24890i
$536$	−4.18483	−	4.82955i	−0.180757	−	0.208605i
$537$	−34.5634	+	4.96947i	−1.49152	+	0.214449i
$538$	2.65788	−	9.05192i	0.114590	−	0.390256i
$539$	−1.21207	+	1.39880i	−0.0522074	+	0.0602505i
$540$	7.35331	+	10.4527i	0.316436	+	0.449811i
$541$	18.8522	+	12.1156i	0.810519	+	0.520889i	0.879033	−	0.476761i	$-0.158189\pi$
$541$	18.8522	+	12.1156i	0.810519	+	0.520889i	−0.0685136	+	0.997650i	$0.521826\pi$
$542$	11.4393	+	9.91225i	0.491362	+	0.425768i
$543$	10.3036	−	35.0908i	0.442169	−	1.50589i
$544$	0.484890	+	3.37249i	0.0207895	+	0.144594i
$545$	20.7000	−	7.03163i	0.886689	−	0.301202i
$546$	−10.6282	−	23.2725i	−0.454844	−	0.995969i
$547$	−10.5310	−	35.8653i	−0.450273	−	1.53349i	−0.801963	−	0.597374i	$-0.796211\pi$
$547$	−10.5310	−	35.8653i	−0.450273	−	1.53349i	0.351689	−	0.936117i	$-0.385607\pi$
$548$	−10.0380	−	4.58420i	−0.428802	−	0.195827i
$549$	−2.23226	+	15.5257i	−0.0952707	+	0.662622i
$550$	−3.35254	+	16.3810i	−0.142953	+	0.698490i
$551$	−1.32305			−0.0563636
$552$	12.7435	−	4.69315i	0.542400	−	0.199754i
$553$			17.3050i			0.735882i
$554$	−4.44557	+	2.85699i	−0.188874	+	0.121382i
$555$	53.8281	+	31.4907i	2.28487	+	1.33671i
$556$	1.39308	−	3.05042i	0.0590798	−	0.129367i
$557$	0.983523	+	3.34957i	0.0416732	+	0.141926i	0.977702	−	0.209998i	$-0.0673458\pi$
$557$	0.983523	+	3.34957i	0.0416732	+	0.141926i	−0.936029	+	0.351924i	$0.885528\pi$
$558$	1.36622	−	0.623930i	0.0578365	−	0.0264130i
$559$	12.3553	+	14.2588i	0.522574	+	0.603083i
$560$	1.48309	−	5.96387i	0.0626721	−	0.252020i
$561$	30.9571	+	9.08982i	1.30701	+	0.383773i
$562$	18.9543	+	16.4240i	0.799541	+	0.692806i
$563$	−9.70330	+	15.0986i	−0.408945	+	0.636331i	−0.983240	−	0.182317i	$-0.941640\pi$
$563$	−9.70330	+	15.0986i	−0.408945	+	0.636331i	0.574294	+	0.818649i	$0.305276\pi$
$564$	26.7387	+	17.1839i	1.12590	+	0.723572i
$565$	5.35618	−	2.72253i	0.225336	−	0.114538i
$566$	−0.0730726	−	0.0214561i	−0.00307147	−	0.000901866i
$567$	−3.07136	+	0.441595i	−0.128985	+	0.0185453i
$568$	6.78611	−	5.88020i	0.284739	−	0.246728i
$569$	14.8264	+	32.4654i	0.621557	+	1.36102i	0.914382	+	0.404853i	$0.132677\pi$
$569$	14.8264	+	32.4654i	0.621557	+	1.36102i	−0.292825	+	0.956166i	$0.594595\pi$
$570$	5.23608	−	51.6990i	0.219315	−	2.16543i
$571$	−16.9254	+	37.0614i	−0.708305	+	1.55097i	0.121297	+	0.992616i	$0.461295\pi$
$571$	−16.9254	+	37.0614i	−0.708305	+	1.55097i	−0.829602	+	0.558355i	$0.811433\pi$
$572$	10.8817	+	1.56456i	0.454988	+	0.0654174i
$573$	−34.2423	−	53.2820i	−1.43049	−	2.22589i
$574$	−10.4988			−0.438213
$575$	23.7063	−	3.60694i	0.988622	−	0.150420i
$576$	5.01838			0.209099
$577$	−13.3491	−	20.7716i	−0.555731	−	0.864734i	0.443776	−	0.896138i	$-0.353639\pi$
$577$	−13.3491	−	20.7716i	−0.555731	−	0.864734i	−0.999507	+	0.0314037i	$0.990002\pi$
$578$	−5.33635	−	0.767251i	−0.221963	−	0.0319134i
$579$	24.1859	−	52.9597i	1.00513	−	2.20093i
$580$	0.0363243	−	0.358652i	0.00150828	−	0.0148922i
$581$	18.6479	+	40.8331i	0.773644	+	1.69404i
$582$	−6.78484	+	5.87909i	−0.281240	+	0.243696i
$583$	14.6552	−	2.10710i	0.606957	−	0.0872672i
$584$	−3.62271	−	1.06372i	−0.149909	−	0.0440172i
$585$	32.8856	−	16.7156i	1.35965	−	0.691106i
$586$	11.8223	+	7.59770i	0.488373	+	0.313858i
$587$	3.46136	−	5.38598i	0.142866	−	0.222303i	−0.762445	−	0.647053i	$-0.776001\pi$
$587$	3.46136	−	5.38598i	0.142866	−	0.222303i	0.905311	+	0.424749i	$0.139638\pi$
$588$	1.18445	+	1.02633i	0.0488459	+	0.0423252i
$589$	−2.35669	−	0.691985i	−0.0971055	−	0.0285128i
$590$	2.37437	−	9.54793i	0.0977515	−	0.393082i
$591$	0.607794	+	0.701431i	0.0250013	+	0.0288530i
$592$	8.95908	−	4.09147i	0.368216	−	0.168159i
$593$	6.84883	+	23.3250i	0.281248	+	0.957842i	0.972045	+	0.234794i	$0.0754415\pi$
$593$	6.84883	+	23.3250i	0.281248	+	0.957842i	−0.690797	+	0.723048i	$0.742740\pi$
$594$	7.93982	−	17.3858i	0.325775	−	0.713347i
$595$	−18.0732	−	10.5732i	−0.740928	−	0.433460i
$596$	6.76376	−	4.34681i	0.277054	−	0.178052i
$597$			42.8080i			1.75201i
$598$	−3.28759	−	15.4195i	−0.134440	−	0.630550i
$599$	−47.2059			−1.92878			−0.964390	−	0.264486i	$-0.914798\pi$
$599$	−47.2059			−1.92878			−0.964390	+	0.264486i	$0.914798\pi$
$600$	13.8709	+	2.83880i	0.566276	+	0.115894i
$601$	−2.47396	+	17.2068i	−0.100915	+	0.701878i	0.875063	+	0.484009i	$0.160820\pi$
$601$	−2.47396	+	17.2068i	−0.100915	+	0.701878i	−0.975978	+	0.217869i	$0.930089\pi$
$602$	−14.3478	−	6.55241i	−0.584771	−	0.267056i
$603$	9.03503	+	30.7705i	0.367935	+	1.25307i
$604$	−2.74685	−	6.01477i	−0.111768	−	0.244738i
$605$	0.387726	−	0.131708i	0.0157633	−	0.00535469i
$606$	7.42523	+	51.6436i	0.301629	+	2.09788i
$607$	−8.56441	+	29.1677i	−0.347619	+	1.18388i	0.581329	+	0.813669i	$0.302533\pi$
$607$	−8.56441	+	29.1677i	−0.347619	+	1.18388i	−0.928947	+	0.370212i	$0.879285\pi$
$608$	−6.20223	−	5.37427i	−0.251534	−	0.217955i
$609$	1.05548	+	0.678313i	0.0427700	+	0.0274866i
$610$	4.02131	+	5.71625i	0.162818	+	0.231444i
$611$	24.1645	−	27.8873i	0.977592	−	1.12820i
$612$	4.81719	−	16.4059i	0.194723	−	0.663167i
$613$	−0.864212	+	0.124255i	−0.0349052	+	0.00501861i	−0.159745	−	0.987158i	$-0.551067\pi$
$613$	−0.864212	+	0.124255i	−0.0349052	+	0.00501861i	0.124840	+	0.992177i	$0.460158\pi$
$614$	−3.88786	−	4.48683i	−0.156901	−	0.181074i
$615$	−1.01230	−	24.1666i	−0.0408198	−	0.974492i
$616$	−8.81854	+	2.58936i	−0.355309	+	0.104328i
$617$	18.4315	+	8.41738i	0.742024	+	0.338871i	0.750303	−	0.661095i	$-0.229908\pi$
$617$	18.4315	+	8.41738i	0.742024	+	0.338871i	−0.00827833	+	0.999966i	$0.502635\pi$
$618$	0.118873	+	0.0170913i	0.00478177	+	0.000687515i
$619$	−14.7503	+	9.47944i	−0.592865	+	0.381011i	−0.802397	−	0.596791i	$-0.796442\pi$
$619$	−14.7503	+	9.47944i	−0.592865	+	0.381011i	0.209532	+	0.977802i	$0.432806\pi$
$620$	0.252287	−	0.619854i	0.0101321	−	0.0248939i
$621$	−27.3320	−	2.06844i	−1.09679	−	0.0830038i
$622$		−	18.8165i		−	0.754472i
$623$	−10.9193	−	16.9908i	−0.437473	−	0.680721i
$624$	1.32481	−	9.21425i	0.0530348	−	0.368865i
$625$	22.9899	+	9.82159i	0.919597	+	0.392864i
$626$	−24.6520	+	7.23848i	−0.985292	+	0.289308i
$627$	−70.6905	+	32.2833i	−2.82311	+	1.28927i
$628$	11.6619	−	10.1051i	0.465359	−	0.403236i
$629$	−4.77574	−	33.2160i	−0.190421	−	1.32441i
$630$	−19.2031	+	24.1326i	−0.765070	+	0.961464i
$631$	−1.81500	+	2.09462i	−0.0722539	+	0.0833855i	−0.790726	−	0.612171i	$-0.790297\pi$
$631$	−1.81500	+	2.09462i	−0.0722539	+	0.0833855i	0.718472	+	0.695556i	$0.244842\pi$
$632$	−3.40413	+	5.29693i	−0.135409	+	0.210700i
$633$	−30.9822	+	48.2092i	−1.23143	+	1.91614i
$634$	14.0985	−	16.2706i	0.559924	−	0.646187i
$635$	35.0922	+	27.9241i	1.39259	+	1.10813i
$636$	−1.78422	−	12.4095i	−0.0707487	−	0.492068i
$637$	1.37510	−	1.19153i	0.0544833	−	0.0472101i
$638$	−0.490402	+	0.223959i	−0.0194152	+	0.00886662i
$639$	−43.2363	+	12.6953i	−1.71040	+	0.502219i
$640$	1.62714	−	1.53376i	0.0643185	−	0.0606270i
$641$	−0.337696	+	2.34873i	−0.0133382	+	0.0927692i	−0.995403	−	0.0957739i	$-0.969467\pi$
$641$	−0.337696	+	2.34873i	−0.0133382	+	0.0927692i	0.982065	+	0.188543i	$0.0603765\pi$
$642$	19.7949	+	30.8015i	0.781244	+	1.21564i
$643$		−	22.5624i		−	0.889773i	−0.895587	−	0.444886i	$-0.853244\pi$
$643$		−	22.5624i		−	0.889773i	0.895587	−	0.444886i	$-0.146756\pi$
$644$	7.85518	+	10.5842i	0.309537	+	0.417077i
$645$	13.6992	−	33.6580i	0.539404	−	1.32528i
$646$	−23.5229	+	15.1172i	−0.925495	+	0.594780i
$647$	12.2111	+	1.75569i	0.480068	+	0.0690234i	0.378101	−	0.925764i	$-0.376577\pi$
$647$	12.2111	+	1.75569i	0.480068	+	0.0690234i	0.101967	+	0.994788i	$0.467486\pi$
$648$	−1.02699	−	0.469011i	−0.0403440	−	0.0184245i
$649$	−14.1181	+	4.14546i	−0.554185	+	0.162724i
$650$	5.55395	−	15.4705i	0.217844	−	0.606805i
$651$	1.52530	+	1.76029i	0.0597812	+	0.0689912i
$652$	12.3238	−	1.77190i	0.482638	−	0.0693929i
$653$	−0.254643	+	0.867233i	−0.00996493	+	0.0339374i	−0.964325	−	0.264720i	$-0.914721\pi$
$653$	−0.254643	+	0.867233i	−0.00996493	+	0.0339374i	0.954360	+	0.298657i	$0.0965387\pi$
$654$	−18.1297	+	20.9228i	−0.708927	+	0.818146i
$655$	19.6091	−	13.7947i	0.766190	−	0.539004i
$656$	−3.21362	−	2.06527i	−0.125471	−	0.0806353i
$657$	14.3197	+	12.4081i	0.558665	+	0.484086i
$658$	−8.69120	+	29.5995i	−0.338818	+	1.15391i
$659$	−1.87069	−	13.0109i	−0.0728718	−	0.506834i	−0.993267	−	0.115846i	$-0.963042\pi$
$659$	−1.87069	−	13.0109i	−0.0728718	−	0.506834i	0.920395	−	0.390989i	$-0.127867\pi$
$660$	−6.81056	−	20.0492i	−0.265101	−	0.780413i
$661$	−6.72908	−	14.7346i	−0.261731	−	0.573111i	0.732452	−	0.680819i	$-0.238376\pi$
$661$	−6.72908	−	14.7346i	−0.261731	−	0.573111i	−0.994183	+	0.107708i	$0.965649\pi$
$662$	5.07609	+	17.2876i	0.197288	+	0.671901i
$663$	−28.8511	−	13.1758i	−1.12048	−	0.511708i
$664$	−2.32447	+	16.1670i	−0.0902069	+	0.627403i
$665$	49.5771	−	9.26058i	1.92252	−	0.359110i
$666$	−49.4267			−1.91524
$667$	0.544440	+	0.548961i	0.0210808	+	0.0212559i
$668$		−	7.56766i		−	0.292801i
$669$	53.0892	−	34.1183i	2.05255	−	1.31909i
$670$	12.3338	+	7.21556i	0.476496	+	0.278761i
$671$	4.34206	−	9.50778i	0.167623	−	0.367044i
$672$	2.19257	+	7.46721i	0.0845803	+	0.288054i
$673$	35.8081	−	16.3530i	1.38030	−	0.630363i	0.419540	−	0.907737i	$-0.362191\pi$
$673$	35.8081	−	16.3530i	1.38030	−	0.630363i	0.960762	+	0.277374i	$0.0894641\pi$
$674$	−2.30107	−	2.65558i	−0.0886339	−	0.102289i
$675$	−23.0865	−	16.8423i	−0.888598	−	0.648259i
$676$	2.10382	+	0.617739i	0.0809163	+	0.0237592i
$677$	25.3637	+	21.9778i	0.974806	+	0.844674i	0.987877	−	0.155241i	$-0.0496153\pi$
$677$	25.3637	+	21.9778i	0.974806	+	0.844674i	−0.0130709	+	0.999915i	$0.504161\pi$
$678$	−4.11363	+	6.40094i	−0.157983	+	0.245827i
$679$	−7.33024	−	4.71086i	−0.281309	−	0.180786i
$680$	−3.45217	−	6.79164i	−0.132385	−	0.260448i
$681$	−60.4968	−	17.7635i	−2.31824	−	0.680698i
$682$	−0.990668	+	0.142437i	−0.0379346	+	0.00545418i
$683$	−21.7743	+	18.8675i	−0.833171	+	0.721947i	−0.962974	−	0.269593i	$-0.913111\pi$
$683$	−21.7743	+	18.8675i	−0.833171	+	0.721947i	0.129803	+	0.991540i	$0.458565\pi$
$684$	17.1087	+	37.4628i	0.654166	+	1.43242i
$685$	24.5499	+	2.48642i	0.938004	+	0.0950011i
$686$	7.36006	−	16.1163i	0.281008	−	0.615323i
$687$	27.7502	+	3.98988i	1.05874	+	0.152224i
$688$	−3.10280	−	4.82806i	−0.118293	−	0.184068i
$689$	−14.5550			−0.554503
$690$	−23.6058	+	19.1019i	−0.898656	+	0.727196i
$691$	24.0956			0.916638			0.458319	−	0.888788i	$-0.348452\pi$
$691$	24.0956			0.916638			0.458319	+	0.888788i	$0.348452\pi$
$692$	6.61108	+	10.2870i	0.251315	+	0.391054i
$693$	45.6537	+	6.56401i	1.73424	+	0.249346i
$694$	6.49822	−	14.2291i	0.246669	−	0.540130i
$695$	−0.755592	+	7.46042i	−0.0286612	+	0.282990i
$696$	0.189640	+	0.415254i	0.00718829	+	0.0157402i
$697$	−9.83647	+	8.52335i	−0.372583	+	0.322845i
$698$	−9.27299	+	1.33325i	−0.350988	+	0.0504644i
$699$	−13.2411	−	3.88794i	−0.500825	−	0.147056i
$700$	1.14922	+	13.6937i	0.0434366	+	0.517571i
$701$	−0.0462398	−	0.0297165i	−0.00174645	−	0.00112238i	0.539767	−	0.841814i	$-0.318512\pi$
$701$	−0.0462398	−	0.0297165i	−0.00174645	−	0.00112238i	−0.541514	+	0.840692i	$0.682149\pi$
$702$	−10.1582	+	15.8064i	−0.383395	+	0.596575i
$703$	61.0866	+	52.9318i	2.30392	+	1.99636i
$704$	−3.20866	−	0.942147i	−0.120931	−	0.0355085i
$705$	−68.9712	−	17.1517i	−2.59761	−	0.645972i
$706$	−6.33294	−	7.30861i	−0.238343	−	0.275063i
$707$	−46.0633	+	21.0364i	−1.73239	+	0.791156i
$708$	3.51022	+	11.9547i	0.131922	+	0.449286i
$709$	−0.186762	+	0.408952i	−0.00701400	+	0.0153585i	−0.913107	−	0.407721i	$-0.866324\pi$
$709$	−0.186762	+	0.408952i	−0.00701400	+	0.0153585i	0.906093	+	0.423079i	$0.139051\pi$
$710$	−10.1387	+	17.3305i	−0.380500	+	0.650401i
$711$	26.5820	−	17.0832i	0.996903	−	0.640671i
$712$		−	7.34874i		−	0.275406i
$713$	0.682669	+	1.26260i	0.0255661	+	0.0472847i
$714$	26.5161			0.992341
$715$	−24.1646	+	4.51374i	−0.903704	+	0.168804i
$716$	1.75496	−	12.2060i	0.0655859	−	0.456160i
$717$	10.6010	+	4.84133i	0.395903	+	0.180803i
$718$	6.61146	+	22.5166i	0.246737	+	0.840310i
$719$	9.92835	+	21.7401i	0.370265	+	0.810767i	0.999439	+	0.0335026i	$0.0106662\pi$
$719$	9.92835	+	21.7401i	0.370265	+	0.810767i	−0.629174	+	0.777265i	$0.716607\pi$
$720$	−10.6252	+	3.60929i	−0.395976	+	0.134510i
$721$	0.0165885	+	0.115375i	0.000617787	+	0.00429680i
$722$	13.6219	−	46.3919i	0.506954	−	1.72653i
$723$	−12.8944	−	11.1731i	−0.479547	−	0.415530i
$724$	10.8651	+	6.98259i	0.403799	+	0.259506i
$725$	0.181040	+	0.785480i	0.00672365	+	0.0291720i
$726$	−0.339583	+	0.391900i	−0.0126031	+	0.0145448i
$727$	1.13196	−	3.85512i	0.0419822	−	0.142978i	−0.935835	−	0.352439i	$-0.885353\pi$
$727$	1.13196	−	3.85512i	0.0419822	−	0.142978i	0.977817	+	0.209460i	$0.0671707\pi$
$728$	8.94314	−	1.28583i	0.331455	−	0.0476560i
$729$	−28.0848	−	32.4116i	−1.04018	−	1.20043i
$730$	8.43522	−	0.353337i	0.312202	−	0.0130776i
$731$	−18.7621	+	5.50904i	−0.693940	+	0.203759i
$732$	−8.05083	−	3.67669i	−0.297567	−	0.135894i
$733$	−39.4106	−	5.66639i	−1.45566	−	0.209293i	−0.631382	−	0.775472i	$-0.717512\pi$
$733$	−39.4106	−	5.66639i	−1.45566	−	0.209293i	−0.824282	+	0.566179i	$0.808421\pi$
$734$	13.1337	−	8.44052i	0.484774	−	0.311545i
$735$	−3.24592	−	1.32112i	−0.119728	−	0.0487304i
$736$	0.322349	+	4.78499i	0.0118819	+	0.176377i
$737$		−	21.3703i		−	0.787185i
$738$	10.3643	+	16.1272i	0.381516	+	0.593650i
$739$	5.91259	−	41.1230i	0.217498	−	1.51273i	−0.529731	−	0.848166i	$-0.677707\pi$
$739$	5.91259	−	41.1230i	0.217498	−	1.51273i	0.747229	−	0.664567i	$-0.231384\pi$
$740$	−16.0259	+	15.1061i	−0.589125	+	0.555313i
$741$	73.3019	−	21.5234i	2.69281	−	0.790681i
$742$	11.0686	−	5.05486i	0.406341	−	0.185570i
$743$	6.63246	−	5.74706i	0.243321	−	0.210839i	−0.524659	−	0.851312i	$-0.675807\pi$
$743$	6.63246	−	5.74706i	0.243321	−	0.210839i	0.767981	+	0.640473i	$0.221262\pi$
$744$	0.120610	+	0.838861i	0.00442178	+	0.0307541i
$745$	−11.1943	+	14.0678i	−0.410126	+	0.515406i
$746$	8.62805	−	9.95731i	0.315896	−	0.364563i
$747$	44.3146	−	68.9548i	1.62138	−	2.52292i
$748$	−6.16004	+	9.58521i	−0.225233	+	0.350470i
$749$	−23.2715	+	26.8567i	−0.850322	+	0.981323i
$750$	−31.4097	+	3.96567i	−1.14692	+	0.144806i
$751$	−3.66433	−	25.4860i	−0.133713	−	0.929998i	−0.940655	−	0.339366i	$-0.889788\pi$
$751$	−3.66433	−	25.4860i	−0.133713	−	0.929998i	0.806941	−	0.590632i	$-0.201121\pi$
$752$	−8.48296	+	7.35052i	−0.309342	+	0.268046i
$753$	22.2569	−	10.1644i	0.811088	−	0.370412i
$754$	0.508518	−	0.149314i	0.0185191	−	0.00543771i
$755$	10.1417	+	10.7592i	0.369093	+	0.391567i
$756$	2.23548	−	15.5481i	0.0813036	−	0.565479i
$757$	0.612230	+	0.952649i	0.0222519	+	0.0346246i	0.852201	−	0.523214i	$-0.175267\pi$
$757$	0.612230	+	0.952649i	0.0222519	+	0.0346246i	−0.829949	+	0.557839i	$0.811631\pi$
$758$			3.35884i			0.121999i
$759$	42.4846	+	16.0463i	1.54209	+	0.582445i
$760$	16.9969	+	6.91792i	0.616542	+	0.250939i
$761$	−39.7789	+	25.5643i	−1.44198	+	0.926707i	−0.442431	+	0.896803i	$0.645884\pi$
$761$	−39.7789	+	25.5643i	−1.44198	+	0.926707i	−0.999553	+	0.0299041i	$0.990480\pi$
$762$	−56.2140	−	8.08236i	−2.03642	−	0.292793i
$763$	−24.4420	−	11.1623i	−0.884861	−	0.404102i
$764$	21.4611	−	6.30155i	0.776435	−	0.227982i
$765$	1.60013	+	38.1998i	0.0578526	+	1.38112i
$766$	6.95148	+	8.02244i	0.251167	+	0.289862i
$767$	14.3176	−	2.05856i	0.516979	−	0.0743304i
$768$	−0.797775	+	2.71697i	−0.0287872	+	0.0980403i
$769$	−14.1931	+	16.3797i	−0.511816	+	0.590667i	−0.951563	−	0.307455i	$-0.900523\pi$
$769$	−14.1931	+	16.3797i	−0.511816	+	0.590667i	0.439747	+	0.898122i	$0.355068\pi$
$770$	16.8087	−	11.8247i	0.605744	−	0.426133i
$771$	−9.30305	−	5.97871i	−0.335041	−	0.215318i
$772$	15.5387	+	13.4644i	0.559250	+	0.484593i
$773$	−4.21642	+	14.3598i	−0.151654	+	0.516487i	−0.999914	−	0.0130932i	$-0.995832\pi$
$773$	−4.21642	+	14.3598i	−0.151654	+	0.516487i	0.848260	+	0.529580i	$0.177650\pi$
$774$	4.09882	+	28.5080i	0.147329	+	1.02470i
$775$	−0.0883464	+	1.49383i	−0.00317350	+	0.0536600i
$776$	−1.31704	−	2.88392i	−0.0472791	−	0.103527i
$777$	−21.5949	−	73.5455i	−0.774713	−	2.63843i
$778$	−10.2618	−	4.68642i	−0.367904	−	0.168016i
$779$	4.46158	−	31.0310i	0.159853	−	1.11180i
$780$	3.82207	+	20.4617i	0.136852	+	0.732645i
$781$	30.0279			1.07448
$782$	15.9523	+	3.53935i	0.570452	+	0.126567i
$783$		−	0.921407i		−	0.0329284i
$784$	−0.465610	+	0.299229i	−0.0166289	+	0.0106868i
$785$	−17.4233	+	29.7823i	−0.621865	+	1.06297i
$786$	−12.6125	+	27.6176i	−0.449875	+	0.985088i
$787$	−11.3366	−	38.6087i	−0.404104	−	1.37625i	−0.870714	−	0.491790i	$-0.836343\pi$
$787$	−11.3366	−	38.6087i	−0.404104	−	1.37625i	0.466610	−	0.884463i	$-0.345475\pi$
$788$	−0.298146	+	0.136159i	−0.0106210	+	0.00485046i
$789$	9.06998	+	10.4673i	0.322900	+	0.372646i
$790$	3.39776	−	13.6632i	0.120887	−	0.486115i
$791$	−7.08580	−	2.08058i	−0.251942	−	0.0739768i
$792$	12.6830	+	10.9899i	0.450672	+	0.390510i
$793$	−5.55521	+	8.64407i	−0.197271	+	0.306960i
$794$	11.4695	+	7.37101i	0.407038	+	0.261587i
$795$	12.7027	+	24.9907i	0.450518	+	0.886329i
$796$	−14.5052	−	4.25911i	−0.514122	−	0.150960i
$797$	45.5070	−	6.54292i	1.61194	−	0.231762i	0.723357	−	0.690475i	$-0.242598\pi$
$797$	45.5070	−	6.54292i	1.61194	−	0.231762i	0.888585	+	0.458713i	$0.151689\pi$
$798$	−48.2686	+	41.8250i	−1.70869	+	1.48059i
$799$	15.8871	+	34.7879i	0.562045	+	1.23071i
$800$	−2.34197	+	4.41760i	−0.0828010	+	0.156186i
$801$	−15.3200	+	33.5461i	−0.541306	+	1.18529i
$802$	25.3843	+	3.64971i	0.896350	+	0.128876i
$803$	−6.82626	−	10.6219i	−0.240893	−	0.374837i
$804$	−18.0956			−0.638181
$805$	−24.2437	−	16.7599i	−0.854477	−	0.590708i
$806$	0.983896			0.0346563
$807$	−14.4428	−	22.4734i	−0.508410	−	0.791102i
$808$	−18.2378	−	2.62220i	−0.641605	−	0.0922488i
$809$	−7.44990	+	16.3130i	−0.261925	+	0.573535i	−0.994209	−	0.107464i	$-0.965727\pi$
$809$	−7.44990	+	16.3130i	−0.261925	+	0.573535i	0.732284	+	0.680999i	$0.238454\pi$
$810$	2.51171	+	0.254386i	0.0882526	+	0.00893822i
$811$	11.7161	+	25.6546i	0.411407	+	0.900855i	0.995985	+	0.0895179i	$0.0285326\pi$
$811$	11.7161	+	25.6546i	0.411407	+	0.900855i	−0.584579	+	0.811337i	$0.698740\pi$
$812$	−0.334854	+	0.290153i	−0.0117511	+	0.0101824i
$813$	42.4252	−	6.09982i	1.48792	−	0.213930i
$814$	31.6025	+	9.27932i	1.10767	+	0.325240i
$815$	−24.8182	+	12.6150i	−0.869343	+	0.441884i
$816$	8.11640	+	5.21609i	0.284131	+	0.182600i
$817$	25.4639	−	39.6226i	0.890868	−	1.38622i
$818$	12.0886	+	10.4748i	0.422668	+	0.366243i
$819$	−43.5049	−	12.7742i	−1.52019	−	0.446367i
$820$	8.28940	+	2.06140i	0.289478	+	0.0719874i
$821$	−6.10169	−	7.04172i	−0.212950	−	0.245758i	0.639218	−	0.769026i	$-0.279258\pi$
$821$	−6.10169	−	7.04172i	−0.212950	−	0.245758i	−0.852168	+	0.523268i	$0.824713\pi$
$822$	−28.4243	+	12.9810i	−0.991412	+	0.452763i
$823$	13.7753	+	46.9143i	0.480176	+	1.63533i	0.742134	+	0.670251i	$0.233814\pi$
$823$	13.7753	+	46.9143i	0.480176	+	1.63533i	−0.261958	+	0.965079i	$0.584368\pi$
$824$	−0.0176183	+	0.0385788i	−0.000613764	+	0.00134396i
$825$	28.8393	+	37.5508i	1.00405	+	1.30735i
$826$	−10.1731	+	6.53787i	−0.353968	+	0.227482i
$827$			41.2938i			1.43592i	0.696082	+	0.717962i	$0.254925\pi$
$827$			41.2938i			1.43592i	−0.696082	+	0.717962i	$0.745075\pi$
$828$	8.50383	−	22.5149i	0.295529	−	0.782447i
$829$	17.9512			0.623472			0.311736	−	0.950169i	$-0.399090\pi$
$829$	17.9512			0.623472			0.311736	+	0.950169i	$0.399090\pi$
$830$	−6.70608	−	35.9014i	−0.232771	−	1.24616i
$831$	−2.12958	+	14.8115i	−0.0738743	+	0.513807i
$832$	2.99037	+	1.36566i	0.103673	+	0.0473457i
$833$	0.531283	+	1.80938i	0.0184079	+	0.0626914i
$834$	−3.94475	−	8.63781i	−0.136596	−	0.299103i
$835$	5.44276	+	16.0226i	0.188354	+	0.554485i
$836$	−3.90573	−	27.1649i	−0.135082	−	0.939519i
$837$	0.481919	−	1.64126i	0.0166575	−	0.0567304i
$838$	−11.6213	−	10.0699i	−0.401450	−	0.347858i
$839$	7.73269	+	4.96950i	0.266962	+	0.171566i	0.667273	−	0.744813i	$-0.267461\pi$
$839$	7.73269	+	4.96950i	0.266962	+	0.171566i	−0.400311	+	0.916379i	$0.631098\pi$
$840$	−10.0127	−	14.2330i	−0.345472	−	0.491085i
$841$	18.9739	−	21.8971i	0.654274	−	0.755072i
$842$	5.64723	−	19.2327i	0.194617	−	0.662803i
$843$	70.2961	−	10.1071i	2.42113	−	0.348105i
$844$	−13.2528	−	15.2946i	−0.456181	−	0.526461i
$845$	−4.89860	+	0.205194i	−0.168517	+	0.00705889i
$846$	54.0474	−	15.8698i	1.85819	−	0.545613i
$847$	−0.457818	−	0.209079i	−0.0157308	−	0.00718402i
$848$	4.38238	+	0.630092i	0.150492	+	0.0216374i
$849$	−0.181419	+	0.116591i	−0.00622629	+	0.00400140i
$850$	12.1937	+	11.8967i	0.418242	+	0.408055i
$851$	−3.17485	−	47.1279i	−0.108833	−	1.61552i
$852$		−	25.4265i		−	0.871097i
$853$	−9.20245	−	14.3193i	−0.315086	−	0.490283i	0.647201	−	0.762319i	$-0.275939\pi$
$853$	−9.20245	−	14.3193i	−0.315086	−	0.490283i	−0.962287	+	0.272036i	$0.912303\pi$
$854$	1.22252	−	8.50279i	0.0418337	−	0.290960i
$855$	−63.1670	−	67.0131i	−2.16027	−	2.29180i
$856$	−12.4063	+	3.64283i	−0.424040	+	0.124509i
$857$	10.4435	−	4.76940i	0.356744	−	0.162919i	−0.228978	−	0.973432i	$-0.573538\pi$
$857$	10.4435	−	4.76940i	0.356744	−	0.162919i	0.585722	+	0.810512i	$0.300811\pi$
$858$	23.5268	−	20.3861i	0.803191	−	0.695969i
$859$	−3.36457	−	23.4011i	−0.114798	−	0.798435i	−0.963143	−	0.268991i	$-0.913310\pi$
$859$	−3.36457	−	23.4011i	−0.114798	−	0.798435i	0.848345	−	0.529444i	$-0.177599\pi$
$860$	10.0418	+	7.99061i	0.342423	+	0.272477i
$861$	−19.4686	+	22.4679i	−0.663487	+	0.765704i
$862$	−1.28130	+	1.99373i	−0.0436411	+	0.0679069i
$863$	0.270670	−	0.421171i	0.00921372	−	0.0143368i	−0.836616	−	0.547790i	$-0.815469\pi$
$863$	0.270670	−	0.421171i	0.00921372	−	0.0143368i	0.845830	+	0.533453i	$0.179106\pi$
$864$	3.74279	−	4.31941i	0.127332	−	0.146949i
$865$	−21.3959	−	17.0254i	−0.727481	−	0.578881i
$866$	−0.0435250	−	0.302723i	−0.00147904	−	0.0102869i
$867$	−11.5374	+	9.99723i	−0.391831	+	0.339524i
$868$	−0.748219	+	0.341700i	−0.0253962	+	0.0115981i
$869$	−20.2032	+	5.93220i	−0.685347	+	0.201236i
$870$	−0.700171	−	0.742803i	−0.0237380	−	0.0251834i
$871$	−2.98978	+	20.7943i	−0.101305	+	0.704590i
$872$	−5.28576	−	8.22480i	−0.178998	−	0.278527i
$873$			15.9104i			0.538486i
$874$	−34.6215	+	18.7193i	−1.17109	+	0.633191i
$875$	−12.2818	−	28.1663i	−0.415202	−	0.952195i
$876$	−8.99420	+	5.78022i	−0.303886	+	0.195296i
$877$	41.4975	+	5.96645i	1.40127	+	0.201473i	0.801163	−	0.598446i	$-0.204215\pi$
$877$	41.4975	+	5.96645i	1.40127	+	0.201473i	0.600109	+	0.799918i	$0.295124\pi$
$878$	28.6971	+	13.1055i	0.968479	+	0.442290i
$879$	38.1820	−	11.2112i	1.28785	−	0.378146i
$880$	7.47112	−	0.312953i	0.251852	−	0.0105496i
$881$	27.7082	+	31.9770i	0.933513	+	1.07733i	0.996848	+	0.0793392i	$0.0252810\pi$
$881$	27.7082	+	31.9770i	0.933513	+	1.07733i	−0.0633346	+	0.997992i	$0.520174\pi$
$882$	2.74926	−	0.395284i	0.0925725	−	0.0133099i
$883$	−9.19064	+	31.3004i	−0.309290	+	1.05334i	0.647380	+	0.762167i	$0.275865\pi$
$883$	−9.19064	+	31.3004i	−0.309290	+	1.05334i	−0.956669	+	0.291176i	$0.905953\pi$
$884$	7.33503	−	8.46508i	0.246704	−	0.284711i
$885$	−16.0300	−	22.7865i	−0.538842	−	0.765959i
$886$	17.7830	+	11.4284i	0.597430	+	0.383945i
$887$	20.2984	+	17.5887i	0.681554	+	0.590570i	0.925285	−	0.379273i	$-0.123826\pi$
$887$	20.2984	+	17.5887i	0.681554	+	0.590570i	−0.243731	+	0.969843i	$0.578371\pi$
$888$	7.85739	−	26.7598i	0.263677	−	0.898000i
$889$	−7.84455	−	54.5600i	−0.263098	−	1.82989i
$890$	5.28531	+	15.5591i	0.177164	+	0.521542i
$891$	−1.56843	−	3.43438i	−0.0525443	−	0.115056i
$892$	6.27874	+	21.3834i	0.210228	+	0.715970i
$893$	−83.7925	−	38.2668i	−2.80401	−	1.28055i
$894$	3.24007	−	22.5352i	0.108364	−	0.753690i
$895$	5.06304	+	27.1053i	0.169239	+	0.906031i
$896$	−2.74836			−0.0918162
$897$	−39.0947	−	21.5576i	−1.30533	−	0.719788i
$898$		−	11.9378i		−	0.398371i
$899$	−0.0405902	+	0.0260857i	−0.00135376	+	0.000870008i
$900$	19.9002	−	15.2835i	0.663341	−	0.509450i
$901$	6.26656	−	13.7218i	0.208769	−	0.457141i
$902$	−3.59904	−	12.2572i	−0.119835	−	0.408120i
$903$	−40.6282	+	18.5543i	−1.35202	+	0.617448i
$904$	−1.75963	−	2.03073i	−0.0585246	−	0.0675410i
$905$	−28.0261	−	6.96952i	−0.931619	−	0.231675i
$906$	−17.9655	−	5.27514i	−0.596863	−	0.175255i
$907$	6.27011	+	5.43308i	0.208196	+	0.180403i	0.752717	−	0.658345i	$-0.228743\pi$
$907$	6.27011	+	5.43308i	0.208196	+	0.180403i	−0.544521	+	0.838747i	$0.683289\pi$
$908$	12.0381	−	18.7316i	0.399497	−	0.621629i
$909$	77.7870	+	49.9907i	2.58003	+	1.65809i
$910$	−18.0100	+	9.15444i	−0.597027	+	0.303467i
$911$	1.00860	+	0.296151i	0.0334163	+	0.00981192i	0.298398	−	0.954442i	$-0.403548\pi$
$911$	1.00860	+	0.296151i	0.0334163	+	0.00981192i	−0.264982	+	0.964253i	$0.585366\pi$
$912$	−23.0023	+	3.30723i	−0.761681	+	0.109513i
$913$	−41.2794	+	35.7688i	−1.36615	+	1.18377i
$914$	−6.04829	−	13.2439i	−0.200060	−	0.438069i
$915$	19.6899	+	1.99420i	0.650929	+	0.0659261i
$916$	−4.11291	+	9.00601i	−0.135894	+	0.297567i
$917$	−29.1680	−	4.19373i	−0.963214	−	0.138489i
$918$	−10.5281	−	16.3820i	−0.347478	−	0.540687i
$919$	−28.1556			−0.928767			−0.464383	−	0.885634i	$-0.653724\pi$
$919$	−28.1556			−0.928767			−0.464383	+	0.885634i	$0.653724\pi$
$920$	−4.12392	−	9.89916i	−0.135962	−	0.326366i
$921$	−16.8115			−0.553956
$922$	−18.8182	−	29.2817i	−0.619746	−	0.964343i
$923$	−29.2186	−	4.20100i	−0.961742	−	0.138278i
$924$	−10.8114	+	23.6736i	−0.355668	+	0.778804i
$925$	23.0663	−	43.5095i	0.758415	−	1.43058i
$926$	4.04128	+	8.84916i	0.132805	+	0.290801i
$927$	0.160851	−	0.139378i	0.00528305	−	0.00457779i
$928$	−0.159574	+	0.0229432i	−0.00523826	+	0.000753149i
$929$	−14.0385	−	4.12207i	−0.460587	−	0.135241i	0.0432035	−	0.999066i	$-0.486244\pi$
$929$	−14.0385	−	4.12207i	−0.460587	−	0.135241i	−0.503791	+	0.863826i	$0.668062\pi$
$930$	−0.858681	−	1.68933i	−0.0281573	−	0.0553953i
$931$	−3.82114	−	2.45570i	−0.125233	−	0.0804822i
$932$	2.63480	−	4.09983i	0.0863059	−	0.134295i
$933$	−40.2679	−	34.8924i	−1.31831	−	1.14233i
$934$	−15.2823	−	4.48730i	−0.500053	−	0.146829i
$935$	6.14851	−	24.7246i	0.201078	−	0.808582i
$936$	−10.8037	−	12.4681i	−0.353130	−	0.407534i
$937$	26.0194	−	11.8827i	0.850016	−	0.388189i	0.0577248	−	0.998333i	$-0.481615\pi$
$937$	26.0194	−	11.8827i	0.850016	−	0.388189i	0.792291	+	0.610143i	$0.208888\pi$
$938$	−4.94811	−	16.8517i	−0.161561	−	0.550228i
$939$	−30.2229	+	66.1789i	−0.986286	+	2.15967i
$940$	12.6739	−	21.6639i	0.413377	−	0.706599i
$941$	1.27474	−	0.819225i	0.0415553	−	0.0267060i	−0.519698	−	0.854350i	$-0.673956\pi$
$941$	1.27474	−	0.819225i	0.0415553	−	0.0267060i	0.561254	+	0.827644i	$0.310319\pi$
$942$		−	43.6951i		−	1.42366i
$943$	−14.7114	+	10.9182i	−0.479069	+	0.355545i
$944$	−4.40001			−0.143208
$945$	6.44934	+	34.5269i	0.209797	+	1.12316i
$946$	2.73135	−	18.9969i	0.0888038	−	0.617644i
$947$	−10.0927	−	4.60918i	−0.327969	−	0.149778i	0.244625	−	0.969618i	$-0.421335\pi$
$947$	−10.0927	−	4.60918i	−0.327969	−	0.149778i	−0.572593	+	0.819840i	$0.694063\pi$
$948$	5.02317	+	17.1073i	0.163145	+	0.555620i
$949$	5.15625	+	11.2906i	0.167379	+	0.366509i
$950$	−40.9621	−	2.42253i	−1.32899	−	0.0785973i
$951$	−8.67597	−	60.3427i	−0.281338	−	1.95675i
$952$	−2.63817	+	8.98480i	−0.0855037	+	0.291199i
$953$	1.34488	+	1.16534i	0.0435649	+	0.0377492i	0.676371	−	0.736561i	$-0.263552\pi$
$953$	1.34488	+	1.16534i	0.0435649	+	0.0377492i	−0.632806	+	0.774310i	$0.718097\pi$
$954$	−18.6915	−	12.0123i	−0.605160	−	0.388913i
$955$	−40.9063	+	28.7770i	−1.32370	+	0.931203i
$956$	−2.69518	+	3.11040i	−0.0871684	+	0.100598i
$957$	−0.430097	+	1.46478i	−0.0139031	+	0.0473495i
$958$	−2.26398	+	0.325512i	−0.0731460	+	0.0105168i
$959$	−19.8611	−	22.9209i	−0.641348	−	0.740156i
$960$	−0.264997	−	6.32627i	−0.00855273	−	0.204179i
$961$	29.6583	−	8.70847i	0.956721	−	0.280919i
$962$	−29.4526	−	13.4505i	−0.949589	−	0.433663i
$963$	64.2277	+	9.23455i	2.06971	+	0.297579i
$964$	5.06881	−	3.25753i	0.163256	−	0.104918i
$965$	−42.5830	−	17.3317i	−1.37080	−	0.557928i
$966$	37.2169	+	2.81652i	1.19743	+	0.0906202i
$967$			10.6153i			0.341365i	0.985326	+	0.170683i	$0.0545972\pi$
$967$			10.6153i			0.341365i	−0.985326	+	0.170683i	$0.945403\pi$
$968$	−0.0990063	−	0.154057i	−0.00318218	−	0.00495157i
$969$	−11.2683	+	78.3725i	−0.361989	+	2.51769i
$970$	4.86266	+	5.15874i	0.156131	+	0.165637i
$971$	−23.9811	+	7.04149i	−0.769591	+	0.225972i	−0.642880	−	0.765967i	$-0.722260\pi$
$971$	−23.9811	+	7.04149i	−0.769591	+	0.225972i	−0.126711	+	0.991940i	$0.540442\pi$
$972$	12.6886	−	5.79471i	0.406988	−	0.185865i
$973$	6.96539	−	6.03555i	0.223300	−	0.193491i
$974$	−0.0367886	−	0.255870i	−0.00117878	−	0.00819861i
$975$	−22.8086	−	40.5735i	−0.730458	−	1.29939i
$976$	2.04682	−	2.36216i	0.0655172	−	0.0756109i
$977$	14.3577	−	22.3411i	0.459345	−	0.714754i	−0.531898	−	0.846808i	$-0.678521\pi$
$977$	14.3577	−	22.3411i	0.459345	−	0.714754i	0.991242	+	0.132054i	$0.0421574\pi$
$978$	19.0608	−	29.6591i	0.609496	−	0.948395i
$979$	16.0932	−	18.5726i	0.514342	−	0.593582i
$980$	0.770601	−	0.968415i	0.0246160	−	0.0309349i
$981$	6.98252	+	48.5645i	0.222935	+	1.55055i
$982$	−1.88977	+	1.63749i	−0.0603049	+	0.0522545i
$983$	−8.10293	+	3.70048i	−0.258443	+	0.118027i	−0.540424	−	0.841393i	$-0.681736\pi$
$983$	−8.10293	+	3.70048i	−0.258443	+	0.118027i	0.281980	+	0.959420i	$0.409009\pi$
$984$	−10.3789	+	3.04753i	−0.330869	+	0.0971518i
$985$	0.533322	−	0.502713i	0.0169931	−	0.0160178i
$986$	−0.0781714	+	0.543694i	−0.00248948	+	0.0173147i
$987$	47.2275	+	73.4874i	1.50327	+	2.33913i
$988$			26.9793i			0.858324i
$989$	−26.9188	+	5.73936i	−0.855968	+	0.182501i
$990$	−34.7572	−	14.1465i	−1.10466	−	0.449607i
$991$	52.2461	−	33.5765i	1.65965	−	1.06659i	0.741017	−	0.671487i	$-0.234344\pi$
$991$	52.2461	−	33.5765i	1.65965	−	1.06659i	0.918635	−	0.395107i	$-0.129292\pi$
$992$	−0.296242	−	0.0425932i	−0.00940569	−	0.00135233i
$993$	46.4090	+	21.1943i	1.47274	+	0.672580i
$994$	23.6787	−	6.95270i	0.751043	−	0.220526i
$995$	33.7742	−	1.41475i	1.07072	−	0.0448504i
$996$	30.2877	+	34.9539i	0.959702	+	1.10756i
$997$	−43.0536	+	6.19017i	−1.36352	+	0.196045i	−0.784935	−	0.619578i	$-0.787304\pi$
$997$	−43.0536	+	6.19017i	−1.36352	+	0.196045i	−0.578585	+	0.815622i	$0.696395\pi$
$998$	−12.5000	+	42.5713i	−0.395682	+	1.34757i
$999$	−36.8632	+	42.5425i	−1.16630	+	1.34598i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.j.a.219.12	yes	120
5.4	even	2	inner	230.2.j.a.219.1	yes	120
23.2	even	11	inner	230.2.j.a.209.1	✓	120
115.94	even	22	inner	230.2.j.a.209.12	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.j.a.209.1	✓	120	23.2	even	11	inner
230.2.j.a.209.12	yes	120	115.94	even	22	inner
230.2.j.a.219.1	yes	120	5.4	even	2	inner
230.2.j.a.219.12	yes	120	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.j (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.540641 + 0.841254i) q^{2} +(2.80285 + 0.402989i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(0.225316 - 2.22469i) q^{5} +(1.17632 + 2.57578i) q^{6} +(-2.07707 + 1.79979i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(4.81510 + 1.41384i) q^{9} +(1.99334 - 1.01321i) q^{10} +(-2.81325 - 1.80797i) q^{11} +(-1.53092 + 2.38216i) q^{12} +(2.48449 + 2.15282i) q^{13} +(-2.63703 - 0.774302i) q^{14} +(1.52805 - 6.14467i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-3.09927 + 1.41539i) q^{17} +(1.41384 + 4.81510i) q^{18} +(3.40920 - 7.46511i) q^{19} +(1.93005 + 1.12912i) q^{20} +(-6.54702 + 4.20751i) q^{21} -3.34412i q^{22} +(-4.50034 + 1.65738i) q^{23} -2.83167 q^{24} +(-4.89847 - 1.00252i) q^{25} +(-0.467854 + 3.25399i) q^{26} +(5.19891 + 2.37426i) q^{27} +(-0.774302 - 2.63703i) q^{28} +(-0.0669710 - 0.146646i) q^{29} +(5.99535 - 2.03658i) q^{30} +(-0.0425932 - 0.296242i) q^{31} +(0.281733 - 0.959493i) q^{32} +(-7.15654 - 6.20117i) q^{33} +(-2.86629 - 1.84205i) q^{34} +(3.53598 + 5.02635i) q^{35} +(-3.28634 + 3.79264i) q^{36} +(-2.77482 + 9.45017i) q^{37} +(8.12320 - 1.16794i) q^{38} +(6.09610 + 7.03527i) q^{39} +(0.0935830 + 2.23411i) q^{40} +(3.66530 - 1.07623i) q^{41} +(-7.07917 - 3.23295i) q^{42} +(5.68070 + 0.816762i) q^{43} +(2.81325 - 1.80797i) q^{44} +(4.23028 - 10.3935i) q^{45} +(-3.82734 - 2.88988i) q^{46} -11.2246i q^{47} +(-1.53092 - 2.38216i) q^{48} +(0.0787672 - 0.547838i) q^{49} +(-1.80494 - 4.66285i) q^{50} +(-9.25717 + 2.71815i) q^{51} +(-2.99037 + 1.36566i) q^{52} +(-3.34604 + 2.89936i) q^{53} +(0.813387 + 5.65723i) q^{54} +(-4.65603 + 5.85124i) q^{55} +(1.79979 - 2.07707i) q^{56} +(12.5638 - 19.5497i) q^{57} +(0.0871592 - 0.135622i) q^{58} +(2.88140 - 3.32531i) q^{59} +(4.95461 + 3.94255i) q^{60} +(0.444817 + 3.09377i) q^{61} +(0.226187 - 0.195992i) q^{62} +(-12.5459 + 5.72953i) q^{63} +(0.959493 - 0.281733i) q^{64} +(5.34916 - 5.04215i) q^{65} +(1.34764 - 9.37307i) q^{66} +(3.45492 + 5.37595i) q^{67} -3.40717i q^{68} +(-13.2817 + 2.83179i) q^{69} +(-2.31675 + 5.69210i) q^{70} +(-7.55387 + 4.85458i) q^{71} +(-4.96730 - 0.714190i) q^{72} +(3.43446 + 1.56846i) q^{73} +(-9.45017 + 2.77482i) q^{74} +(-13.3257 - 4.78394i) q^{75} +(5.37427 + 6.20223i) q^{76} +(9.09729 - 1.30799i) q^{77} +(-2.62265 + 8.93192i) q^{78} +(4.12331 - 4.75855i) q^{79} +(-1.82886 + 1.28658i) q^{80} +(0.949791 + 0.610393i) q^{81} +(2.88699 + 2.50159i) q^{82} +(4.60162 - 15.6717i) q^{83} +(-1.10756 - 7.70324i) q^{84} +(2.45048 + 7.21381i) q^{85} +(2.38412 + 5.22049i) q^{86} +(-0.128613 - 0.438016i) q^{87} +(3.04192 + 1.38920i) q^{88} +(-1.04583 + 7.27394i) q^{89} +(11.0307 - 2.06043i) q^{90} -9.03510 q^{91} +(0.361907 - 4.78216i) q^{92} -0.847487i q^{93} +(9.44270 - 6.06846i) q^{94} +(-15.8394 - 9.26641i) q^{95} +(1.17632 - 2.57578i) q^{96} +(0.893213 + 3.04200i) q^{97} +(0.503456 - 0.229920i) q^{98} +(-10.9899 - 12.6830i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9} + 8 q^{11} - 6 q^{15} - 12 q^{16} - 16 q^{19} - 22 q^{20} + 4 q^{24} - 52 q^{25} - 4 q^{26} - 8 q^{29} - 44 q^{30} + 12 q^{31} + 16 q^{35} - 8 q^{36} - 36 q^{39} - 28 q^{41}+ \cdots + 188 q^{99}+O(q^{100}) \) 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9 + 8 * q^11 - 6 * q^15 - 12 * q^16 - 16 * q^19 - 22 * q^20 + 4 * q^24 - 52 * q^25 - 4 * q^26 - 8 * q^29 - 44 * q^30 + 12 * q^31 + 16 * q^35 - 8 * q^36 - 36 * q^39 - 28 * q^41 - 8 * q^44 + 16 * q^45 - 4 * q^46 - 58 * q^49 + 12 * q^50 - 24 * q^51 - 6 * q^54 - 36 * q^55 + 22 * q^56 - 102 * q^59 - 38 * q^60 + 72 * q^61 + 12 * q^64 - 138 * q^65 + 80 * q^66 - 212 * q^69 - 108 * q^70 + 176 * q^71 - 88 * q^74 - 100 * q^75 + 16 * q^76 - 104 * q^79 - 22 * q^80 - 28 * q^81 - 22 * q^84 + 2 * q^85 + 62 * q^86 + 48 * q^89 + 24 * q^90 - 56 * q^91 + 24 * q^94 + 18 * q^95 - 4 * q^96 + 188 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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