LMFDB - Embedded newform 169.2.h.a.12.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,2,Mod(12,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([21]))

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

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

chi := DirichletCharacter("169.12");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	169.h (of order $26$, degree $12$, 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:	$1.34947179416$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$14$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			12.9
Character	$\chi$	$=$	169.12
Dual form			169.2.h.a.155.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.323126 - 0.223038i) q^{2} +(-2.84614 - 1.49377i) q^{3} +(-0.654545 + 1.72589i) q^{4} +(1.31816 + 1.48790i) q^{5} +(-1.25283 + 0.152121i) q^{6} +(0.0500939 + 0.203239i) q^{7} +(0.361363 + 1.46611i) q^{8} +(4.16496 + 6.03399i) q^{9} +O(q^{10})$	\(q+(0.323126 - 0.223038i) q^{2} +(-2.84614 - 1.49377i) q^{3} +(-0.654545 + 1.72589i) q^{4} +(1.31816 + 1.48790i) q^{5} +(-1.25283 + 0.152121i) q^{6} +(0.0500939 + 0.203239i) q^{7} +(0.361363 + 1.46611i) q^{8} +(4.16496 + 6.03399i) q^{9} +(0.757790 + 0.186779i) q^{10} +(1.24884 + 0.862010i) q^{11} +(4.44101 - 3.93439i) q^{12} +(0.393277 + 3.58404i) q^{13} +(0.0615167 + 0.0544990i) q^{14} +(-1.52910 - 6.20379i) q^{15} +(-2.31950 - 2.05490i) q^{16} +(-3.65796 + 0.901606i) q^{17} +(2.69162 + 1.02080i) q^{18} +3.26624i q^{19} +(-3.43075 + 1.30111i) q^{20} +(0.161018 - 0.653275i) q^{21} +0.595793 q^{22} +3.39512 q^{23} +(1.16154 - 4.71253i) q^{24} +(0.126396 - 1.04096i) q^{25} +(0.926454 + 1.07038i) q^{26} +(-1.67834 - 13.8224i) q^{27} +(-0.383558 - 0.0465723i) q^{28} +(1.70372 + 2.46826i) q^{29} +(-1.87777 - 1.66356i) q^{30} +(-9.27335 + 1.12599i) q^{31} +(-4.20576 - 0.510672i) q^{32} +(-2.26672 - 4.31887i) q^{33} +(-0.980890 + 1.10720i) q^{34} +(-0.236367 + 0.342437i) q^{35} +(-13.1402 + 3.23876i) q^{36} +(7.09471 - 0.861454i) q^{37} +(0.728495 + 1.05541i) q^{38} +(4.23440 - 10.7881i) q^{39} +(-1.70508 + 2.47024i) q^{40} +(-3.94122 + 7.50936i) q^{41} +(-0.0936760 - 0.247003i) q^{42} +(1.45709 - 12.0002i) q^{43} +(-2.30516 + 1.59114i) q^{44} +(-3.48786 + 14.1508i) q^{45} +(1.09705 - 0.757241i) q^{46} +(5.47719 - 2.07722i) q^{47} +(3.53208 + 9.31333i) q^{48} +(6.15940 - 3.23270i) q^{49} +(-0.191332 - 0.364553i) q^{50} +(11.7578 + 2.89805i) q^{51} +(-6.44309 - 1.66716i) q^{52} +(0.355608 - 0.0876496i) q^{53} +(-3.62523 - 4.09204i) q^{54} +(0.363587 + 2.99441i) q^{55} +(-0.279868 + 0.146886i) q^{56} +(4.87900 - 9.29616i) q^{57} +(1.10103 + 0.417566i) q^{58} +(6.72780 + 7.59412i) q^{59} +(11.7079 + 1.42160i) q^{60} +(4.48931 + 1.10651i) q^{61} +(-2.74532 + 2.43214i) q^{62} +(-1.01770 + 1.14875i) q^{63} +(4.01486 - 2.10716i) q^{64} +(-4.81428 + 5.30950i) q^{65} +(-1.69571 - 0.889976i) q^{66} +(9.34877 - 3.54552i) q^{67} +(0.838224 - 6.90339i) q^{68} +(-9.66299 - 5.07153i) q^{69} +0.163369i q^{70} +(-4.41645 + 8.41484i) q^{71} +(-7.34141 + 8.28674i) q^{72} +(-7.22221 - 4.98513i) q^{73} +(2.10035 - 1.86075i) q^{74} +(-1.91470 + 2.77392i) q^{75} +(-5.63718 - 2.13790i) q^{76} +(-0.112635 + 0.296994i) q^{77} +(-1.03792 - 4.43036i) q^{78} +(-0.465951 - 1.22861i) q^{79} -6.15988i q^{80} +(-8.07094 + 21.2813i) q^{81} +(0.401362 + 3.30551i) q^{82} +(-3.68213 - 7.01571i) q^{83} +(1.02209 + 0.705498i) q^{84} +(-6.16328 - 4.25421i) q^{85} +(-2.20568 - 4.20257i) q^{86} +(-1.16200 - 9.56996i) q^{87} +(-0.812515 + 2.14243i) q^{88} -7.29445i q^{89} +(2.02915 + 5.35042i) q^{90} +(-0.708716 + 0.259468i) q^{91} +(-2.22226 + 5.85962i) q^{92} +(28.0752 + 10.6475i) q^{93} +(1.30652 - 1.89283i) q^{94} +(-4.85983 + 4.30543i) q^{95} +(11.2074 + 7.73588i) q^{96} +(5.84568 - 6.59840i) q^{97} +(1.26925 - 2.41835i) q^{98} +11.1257i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9}+O(q^{10}) $ 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9	\( 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9} - 9 q^{10} - 13 q^{11} - 9 q^{12} + 52 q^{13} - 15 q^{14} + 39 q^{15} - 31 q^{16} - 11 q^{17} + 26 q^{18} - 13 q^{20} - 13 q^{21} - 6 q^{22} - 102 q^{23} - 91 q^{24} + 3 q^{25} - 13 q^{26} - 19 q^{27} - 13 q^{28} - 17 q^{29} + 23 q^{30} + 39 q^{31} - 13 q^{33} + 52 q^{34} - 21 q^{35} + 11 q^{36} - 13 q^{37} - 40 q^{38} - 65 q^{39} + 53 q^{40} - 13 q^{41} + 101 q^{42} - 3 q^{43} - 39 q^{44} - 78 q^{45} - 39 q^{46} - 39 q^{47} + 8 q^{48} + 85 q^{49} - 13 q^{50} + 62 q^{51} - 78 q^{52} + 18 q^{53} + 65 q^{54} - 103 q^{55} + 3 q^{56} + 65 q^{57} + 39 q^{58} + 91 q^{59} - 117 q^{60} - 23 q^{61} - 64 q^{62} - 78 q^{63} + 15 q^{64} - 13 q^{65} + 134 q^{66} - 65 q^{67} + 40 q^{68} - 40 q^{69} + 26 q^{71} + 156 q^{72} - 13 q^{73} - 53 q^{74} + 35 q^{75} + 221 q^{76} + 3 q^{77} - 143 q^{78} - 23 q^{79} - 43 q^{81} - 129 q^{82} + 117 q^{83} + 234 q^{84} + 26 q^{85} - 91 q^{86} + 79 q^{87} + 95 q^{88} + 17 q^{90} + 39 q^{91} - 89 q^{92} + 52 q^{93} - 61 q^{94} + 122 q^{95} - 182 q^{96} - 91 q^{97} - 13 q^{98}+O(q^{100}) \) 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9 - 9 * q^10 - 13 * q^11 - 9 * q^12 + 52 * q^13 - 15 * q^14 + 39 * q^15 - 31 * q^16 - 11 * q^17 + 26 * q^18 - 13 * q^20 - 13 * q^21 - 6 * q^22 - 102 * q^23 - 91 * q^24 + 3 * q^25 - 13 * q^26 - 19 * q^27 - 13 * q^28 - 17 * q^29 + 23 * q^30 + 39 * q^31 - 13 * q^33 + 52 * q^34 - 21 * q^35 + 11 * q^36 - 13 * q^37 - 40 * q^38 - 65 * q^39 + 53 * q^40 - 13 * q^41 + 101 * q^42 - 3 * q^43 - 39 * q^44 - 78 * q^45 - 39 * q^46 - 39 * q^47 + 8 * q^48 + 85 * q^49 - 13 * q^50 + 62 * q^51 - 78 * q^52 + 18 * q^53 + 65 * q^54 - 103 * q^55 + 3 * q^56 + 65 * q^57 + 39 * q^58 + 91 * q^59 - 117 * q^60 - 23 * q^61 - 64 * q^62 - 78 * q^63 + 15 * q^64 - 13 * q^65 + 134 * q^66 - 65 * q^67 + 40 * q^68 - 40 * q^69 + 26 * q^71 + 156 * q^72 - 13 * q^73 - 53 * q^74 + 35 * q^75 + 221 * q^76 + 3 * q^77 - 143 * q^78 - 23 * q^79 - 43 * q^81 - 129 * q^82 + 117 * q^83 + 234 * q^84 + 26 * q^85 - 91 * q^86 + 79 * q^87 + 95 * q^88 + 17 * q^90 + 39 * q^91 - 89 * q^92 + 52 * q^93 - 61 * q^94 + 122 * q^95 - 182 * q^96 - 91 * q^97 - 13 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{21}{26}\right)$

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 $

$2$	0.323126	−	0.223038i	0.228485	−	0.157712i	−0.448323	−	0.893872i	$-0.647978\pi$
$2$	0.323126	−	0.223038i	0.228485	−	0.157712i	0.676807	+	0.736160i	$0.263363\pi$
$3$	−2.84614	−	1.49377i	−1.64322	−	0.862427i	−0.994879	−	0.101076i	$-0.967771\pi$
$3$	−2.84614	−	1.49377i	−1.64322	−	0.862427i	−0.648340	−	0.761351i	$-0.724536\pi$
$4$	−0.654545	+	1.72589i	−0.327273	+	0.862947i
$5$	1.31816	+	1.48790i	0.589500	+	0.665408i	0.965255	−	0.261311i	$-0.0841549\pi$
$5$	1.31816	+	1.48790i	0.589500	+	0.665408i	−0.375754	+	0.926719i	$0.622616\pi$
$6$	−1.25283	+	0.152121i	−0.511465	+	0.0621031i
$7$	0.0500939	+	0.203239i	0.0189337	+	0.0768171i	0.979649	−	0.200720i	$-0.0643281\pi$
$7$	0.0500939	+	0.203239i	0.0189337	+	0.0768171i	−0.960715	+	0.277537i	$0.910482\pi$
$8$	0.361363	+	1.46611i	0.127761	+	0.518347i
$9$	4.16496	+	6.03399i	1.38832	+	2.01133i
$10$	0.757790	+	0.186779i	0.239634	+	0.0590646i
$11$	1.24884	+	0.862010i	0.376539	+	0.259906i	0.741270	−	0.671207i	$-0.234224\pi$
$11$	1.24884	+	0.862010i	0.376539	+	0.259906i	−0.364731	+	0.931113i	$0.618839\pi$
$12$	4.44101	−	3.93439i	1.28201	−	1.13576i
$13$	0.393277	+	3.58404i	0.109075	+	0.994033i
$13$	0.393277	+	3.58404i	0.109075	+	0.994033i
$14$	0.0615167	+	0.0544990i	0.0164410	+	0.0145655i
$15$	−1.52910	−	6.20379i	−0.394811	−	1.60181i
$16$	−2.31950	−	2.05490i	−0.579876	−	0.513725i
$17$	−3.65796	+	0.901606i	−0.887186	+	0.218672i	−0.656472	−	0.754350i	$-0.727952\pi$
$17$	−3.65796	+	0.901606i	−0.887186	+	0.218672i	−0.230713	+	0.973022i	$0.574106\pi$
$18$	2.69162	+	1.02080i	0.634420	+	0.240604i
$19$			3.26624i			0.749326i	0.927161	+	0.374663i	$0.122242\pi$
$19$			3.26624i			0.749326i	−0.927161	+	0.374663i	$0.877758\pi$
$20$	−3.43075	+	1.30111i	−0.767139	+	0.290937i
$21$	0.161018	−	0.653275i	0.0351370	−	0.142556i
$22$	0.595793			0.127023
$23$	3.39512			0.707932			0.353966	−	0.935258i	$-0.384833\pi$
$23$	3.39512			0.707932			0.353966	+	0.935258i	$0.384833\pi$
$24$	1.16154	−	4.71253i	0.237097	−	0.961942i
$25$	0.126396	−	1.04096i	0.0252791	−	0.208192i
$26$	0.926454	+	1.07038i	0.181693	+	0.209919i
$27$	−1.67834	−	13.8224i	−0.322997	−	2.66012i
$28$	−0.383558	−	0.0465723i	−0.0724856	−	0.00880135i
$29$	1.70372	+	2.46826i	0.316372	+	0.458344i	0.948618	−	0.316424i	$-0.102482\pi$
$29$	1.70372	+	2.46826i	0.316372	+	0.458344i	−0.632246	+	0.774768i	$0.717867\pi$
$30$	−1.87777	−	1.66356i	−0.342833	−	0.303723i
$31$	−9.27335	+	1.12599i	−1.66554	+	0.202234i	−0.898380	−	0.439219i	$-0.855255\pi$
$31$	−9.27335	+	1.12599i	−1.66554	+	0.202234i	−0.767163	+	0.641452i	$0.778332\pi$
$32$	−4.20576	−	0.510672i	−0.743481	−	0.0902749i
$33$	−2.26672	−	4.31887i	−0.394585	−	0.751819i
$34$	−0.980890	+	1.10720i	−0.168221	+	0.189883i
$35$	−0.236367	+	0.342437i	−0.0399533	+	0.0578824i
$36$	−13.1402	+	3.23876i	−2.19003	+	0.539794i
$37$	7.09471	−	0.861454i	1.16636	−	0.141622i	0.485638	−	0.874160i	$-0.338587\pi$
$37$	7.09471	−	0.861454i	1.16636	−	0.141622i	0.680726	+	0.732538i	$0.261664\pi$
$38$	0.728495	+	1.05541i	0.118177	+	0.171210i
$39$	4.23440	−	10.7881i	0.678047	−	1.72748i
$40$	−1.70508	+	2.47024i	−0.269597	+	0.390579i
$41$	−3.94122	+	7.50936i	−0.615515	+	1.17277i	0.355709	+	0.934597i	$0.384239\pi$
$41$	−3.94122	+	7.50936i	−0.615515	+	1.17277i	−0.971224	+	0.238169i	$0.923453\pi$
$42$	−0.0936760	−	0.247003i	−0.0144545	−	0.0381134i
$43$	1.45709	−	12.0002i	0.222204	−	1.83002i	−0.273906	−	0.961756i	$-0.588316\pi$
$43$	1.45709	−	12.0002i	0.222204	−	1.83002i	0.496110	−	0.868260i	$-0.334761\pi$
$44$	−2.30516	+	1.59114i	−0.347516	+	0.239873i
$45$	−3.48786	+	14.1508i	−0.519940	+	2.10948i
$46$	1.09705	−	0.757241i	0.161752	−	0.111649i
$47$	5.47719	−	2.07722i	0.798930	−	0.302994i	0.0788510	−	0.996886i	$-0.474875\pi$
$47$	5.47719	−	2.07722i	0.798930	−	0.302994i	0.720079	+	0.693892i	$0.244106\pi$
$48$	3.53208	+	9.31333i	0.509812	+	1.34426i
$49$	6.15940	−	3.23270i	0.879914	−	0.461814i
$50$	−0.191332	−	0.364553i	−0.0270585	−	0.0515556i
$51$	11.7578	+	2.89805i	1.64643	+	0.405808i
$52$	−6.44309	−	1.66716i	−0.893496	−	0.231194i
$53$	0.355608	−	0.0876496i	0.0488466	−	0.0120396i	−0.214817	−	0.976654i	$-0.568915\pi$
$53$	0.355608	−	0.0876496i	0.0488466	−	0.0120396i	0.263663	+	0.964615i	$0.415069\pi$
$54$	−3.62523	−	4.09204i	−0.493332	−	0.556857i
$55$	0.363587	+	2.99441i	0.0490261	+	0.403766i
$56$	−0.279868	+	0.146886i	−0.0373989	+	0.0196285i
$57$	4.87900	−	9.29616i	0.646240	−	1.23131i
$58$	1.10103	+	0.417566i	0.144572	+	0.0548290i
$59$	6.72780	+	7.59412i	0.875885	+	0.988670i	0.999994	−	0.00359893i	$-0.00114558\pi$
$59$	6.72780	+	7.59412i	0.875885	+	0.988670i	−0.124109	+	0.992269i	$0.539607\pi$
$60$	11.7079	+	1.42160i	1.51149	+	0.183528i
$61$	4.48931	+	1.10651i	0.574797	+	0.141675i	0.515990	−	0.856595i	$-0.327424\pi$
$61$	4.48931	+	1.10651i	0.574797	+	0.141675i	0.0588069	+	0.998269i	$0.481270\pi$
$62$	−2.74532	+	2.43214i	−0.348656	+	0.308883i
$63$	−1.01770	+	1.14875i	−0.128218	+	0.144729i
$64$	4.01486	−	2.10716i	0.501857	−	0.263395i
$65$	−4.81428	+	5.30950i	−0.597138	+	0.658563i
$66$	−1.69571	−	0.889976i	−0.208727	−	0.109549i
$67$	9.34877	−	3.54552i	1.14213	−	0.433154i	0.290284	−	0.956941i	$-0.406250\pi$
$67$	9.34877	−	3.54552i	1.14213	−	0.433154i	0.851850	+	0.523786i	$0.175481\pi$
$68$	0.838224	−	6.90339i	0.101650	−	0.837159i
$69$	−9.66299	−	5.07153i	−1.16329	−	0.610540i
$70$			0.163369i			0.0195263i
$71$	−4.41645	+	8.41484i	−0.524136	+	0.998657i	0.469166	+	0.883110i	$0.344555\pi$
$71$	−4.41645	+	8.41484i	−0.524136	+	0.998657i	−0.993302	+	0.115547i	$0.963138\pi$
$72$	−7.34141	+	8.28674i	−0.865193	+	0.976601i
$73$	−7.22221	−	4.98513i	−0.845296	−	0.583466i	0.0647835	−	0.997899i	$-0.479364\pi$
$73$	−7.22221	−	4.98513i	−0.845296	−	0.583466i	−0.910080	+	0.414434i	$0.863980\pi$
$74$	2.10035	−	1.86075i	0.244161	−	0.216308i
$75$	−1.91470	+	2.77392i	−0.221090	+	0.320304i
$76$	−5.63718	−	2.13790i	−0.646629	−	0.245234i
$77$	−0.112635	+	0.296994i	−0.0128359	+	0.0338456i
$78$	−1.03792	−	4.43036i	−0.117521	−	0.501639i
$79$	−0.465951	−	1.22861i	−0.0524236	−	0.138230i	0.906246	−	0.422750i	$-0.138935\pi$
$79$	−0.465951	−	1.22861i	−0.0524236	−	0.138230i	−0.958670	+	0.284520i	$0.908166\pi$
$80$		−	6.15988i		−	0.688696i
$81$	−8.07094	+	21.2813i	−0.896771	+	2.36459i
$82$	0.401362	+	3.30551i	0.0443230	+	0.365033i
$83$	−3.68213	−	7.01571i	−0.404166	−	0.770074i	0.595274	−	0.803522i	$-0.297043\pi$
$83$	−3.68213	−	7.01571i	−0.404166	−	0.770074i	−0.999440	+	0.0334485i	$0.989351\pi$
$84$	1.02209	+	0.705498i	0.111519	+	0.0769761i
$85$	−6.16328	−	4.25421i	−0.668502	−	0.461434i
$86$	−2.20568	−	4.20257i	−0.237844	−	0.453175i
$87$	−1.16200	−	9.56996i	−0.124580	−	1.02601i
$88$	−0.812515	+	2.14243i	−0.0866144	+	0.228383i
$89$		−	7.29445i		−	0.773210i	−0.922245	−	0.386605i	$-0.873648\pi$
$89$		−	7.29445i		−	0.773210i	0.922245	−	0.386605i	$-0.126352\pi$
$90$	2.02915	+	5.35042i	0.213891	+	0.563984i
$91$	−0.708716	+	0.259468i	−0.0742936	+	0.0271996i
$92$	−2.22226	+	5.85962i	−0.231687	+	0.610908i
$93$	28.0752	+	10.6475i	2.91126	+	1.10410i
$94$	1.30652	−	1.89283i	0.134758	−	0.195230i
$95$	−4.85983	+	4.30543i	−0.498608	+	0.441728i
$96$	11.2074	+	7.73588i	1.14385	+	0.789540i
$97$	5.84568	−	6.59840i	0.593538	−	0.669966i	−0.372600	−	0.927992i	$-0.621533\pi$
$97$	5.84568	−	6.59840i	0.593538	−	0.669966i	0.966138	+	0.258026i	$0.0830720\pi$
$98$	1.26925	−	2.41835i	0.128213	−	0.244290i
$99$			11.1257i			1.11818i
$100$	1.71386	+	0.899502i	0.171386	+	0.0899502i
$101$	0.403392	−	3.32223i	0.0401390	−	0.330574i	−0.958782	−	0.284141i	$-0.908291\pi$
$101$	0.403392	−	3.32223i	0.0401390	−	0.330574i	0.998921	−	0.0464331i	$-0.0147854\pi$
$102$	4.44564	−	1.68601i	0.440184	−	0.166940i
$103$	−0.281201	−	0.147586i	−0.0277076	−	0.0145421i	0.450813	−	0.892619i	$-0.351134\pi$
$103$	−0.281201	−	0.147586i	−0.0277076	−	0.0145421i	−0.478520	+	0.878077i	$0.658827\pi$
$104$	−5.11247	+	1.87172i	−0.501319	+	0.183538i
$105$	1.18425	−	0.621545i	0.115571	−	0.0606565i
$106$	0.0953572	−	0.107636i	0.00926191	−	0.0104545i
$107$	−14.2068	+	12.5861i	−1.37342	+	1.21675i	−0.422866	+	0.906192i	$0.638976\pi$
$107$	−14.2068	+	12.5861i	−1.37342	+	1.21675i	−0.950556	+	0.310553i	$0.899486\pi$
$108$	24.9545	+	6.15074i	2.40125	+	0.591855i
$109$	8.22580	+	0.998792i	0.787888	+	0.0956670i	0.504583	−	0.863363i	$-0.331646\pi$
$109$	8.22580	+	0.998792i	0.787888	+	0.0956670i	0.283305	+	0.959030i	$0.408569\pi$
$110$	0.785352	+	0.886479i	0.0748803	+	0.0845224i
$111$	−21.4793	−	8.14604i	−2.03873	−	0.773188i
$112$	0.301443	−	0.574352i	0.0284837	−	0.0542712i
$113$	−10.9406	+	5.74208i	−1.02921	+	0.540170i	−0.892786	−	0.450481i	$-0.851253\pi$
$113$	−10.9406	+	5.74208i	−1.02921	+	0.540170i	−0.136422	+	0.990651i	$0.543560\pi$
$114$	−0.496863	−	4.09204i	−0.0465355	−	0.383254i
$115$	4.47532	+	5.05160i	0.417326	+	0.471064i
$116$	−5.37511	+	1.32485i	−0.499066	+	0.123009i
$117$	−19.9881	+	17.3004i	−1.84790	+	1.59942i
$118$	3.86770	+	0.953303i	0.356051	+	0.0877587i
$119$	−0.366483	−	0.698275i	−0.0335955	−	0.0640108i
$120$	8.54286	−	4.48364i	0.779853	−	0.409298i
$121$	−3.08412	−	8.13216i	−0.280375	−	0.739287i
$122$	1.69741	−	0.643742i	0.153676	−	0.0582816i
$123$	22.4345	−	15.4854i	2.02285	−	1.39627i
$124$	4.12649	−	16.7418i	0.370570	−	1.50346i
$125$	9.89514	−	6.83012i	0.885048	−	0.610905i
$126$	−0.0726318	+	0.598177i	−0.00647056	+	0.0532898i
$127$	1.88731	+	4.97642i	0.167471	+	0.441586i	0.992309	−	0.123784i	$-0.0395029\pi$
$127$	1.88731	+	4.97642i	0.167471	+	0.441586i	−0.824838	+	0.565369i	$0.808734\pi$
$128$	4.76507	−	9.07908i	0.421177	−	0.802485i
$129$	−22.0726	+	31.9777i	−1.94339	+	2.81548i
$130$	−0.371400	+	2.78941i	−0.0325739	+	0.244647i
$131$	6.94959	+	10.0682i	0.607189	+	0.879665i	0.999188	−	0.0403009i	$-0.0128316\pi$
$131$	6.94959	+	10.0682i	0.607189	+	0.879665i	−0.391999	+	0.919966i	$0.628216\pi$
$132$	8.93759	−	1.08522i	0.777917	−	0.0944562i
$133$	−0.663827	+	0.163619i	−0.0575611	+	0.0141875i
$134$	2.23005	−	3.23078i	0.192647	−	0.279097i
$135$	18.3540	−	20.7174i	1.57966	−	1.78307i
$136$	−2.64370	−	5.03715i	−0.226696	−	0.431932i
$137$	7.25202	+	0.880555i	0.619582	+	0.0752309i	0.424308	−	0.905518i	$-0.360517\pi$
$137$	7.25202	+	0.880555i	0.619582	+	0.0752309i	0.195274	+	0.980749i	$0.437440\pi$
$138$	−4.25351	+	0.516469i	−0.362082	+	0.0439648i
$139$	−2.39677	−	2.12335i	−0.203291	−	0.180100i	0.555334	−	0.831627i	$-0.312590\pi$
$139$	−2.39677	−	2.12335i	−0.203291	−	0.180100i	−0.758626	+	0.651527i	$0.774129\pi$
$140$	−0.436297	−	0.632085i	−0.0368738	−	0.0534209i
$141$	−18.6917	−	2.26959i	−1.57413	−	0.191134i
$142$	0.449758	+	3.70409i	0.0377428	+	0.310840i
$143$	−2.59834	+	4.81489i	−0.217284	+	0.402641i
$144$	2.73861	−	22.5544i	0.228217	−	1.87954i
$145$	−1.42674	+	5.78852i	−0.118484	+	0.480710i
$146$	−3.44556			−0.285156
$147$	−22.3594			−1.84417
$148$	−3.15703	+	12.8086i	−0.259506	+	1.05286i
$149$	18.2037	−	6.90376i	1.49131	−	0.565578i	0.531703	−	0.846931i	$-0.321552\pi$
$149$	18.2037	−	6.90376i	1.49131	−	0.565578i	0.959604	+	0.281353i	$0.0907831\pi$
$150$			1.32337i			0.108053i
$151$	−3.68078	−	1.39594i	−0.299538	−	0.113600i	0.200258	−	0.979743i	$-0.435822\pi$
$151$	−3.68078	−	1.39594i	−0.299538	−	0.113600i	−0.499795	+	0.866144i	$0.666591\pi$
$152$	−4.78865	+	1.18030i	−0.388411	+	0.0957347i
$153$	−20.6755	−	18.3169i	−1.67152	−	1.48084i
$154$	0.0298456	+	0.121088i	0.00240503	+	0.00975758i
$155$	−13.8991	−	12.3136i	−1.11641	−	0.989049i
$156$	15.8476	+	14.3694i	1.26882	+	1.15048i
$157$	−0.302946	+	0.268387i	−0.0241777	+	0.0214196i	−0.675125	−	0.737703i	$-0.735910\pi$
$157$	−0.302946	+	0.268387i	−0.0241777	+	0.0214196i	0.650947	+	0.759123i	$0.274372\pi$
$158$	−0.424588	−	0.293072i	−0.0337784	−	0.0233156i
$159$	−1.14304	−	0.281734i	−0.0906488	−	0.0223429i
$160$	−4.78405	−	6.93089i	−0.378212	−	0.547935i
$161$	0.170075	+	0.690022i	0.0134038	+	0.0543813i
$162$	2.13861	+	8.67668i	0.168025	+	0.681704i
$163$	−5.50679	+	0.668645i	−0.431325	+	0.0523723i	−0.333320	−	0.942814i	$-0.608169\pi$
$163$	−5.50679	+	0.668645i	−0.431325	+	0.0523723i	−0.0980045	+	0.995186i	$0.531246\pi$
$164$	−10.3807	−	11.7173i	−0.810593	−	0.914971i
$165$	3.43814	−	9.06562i	0.267659	−	0.705758i
$166$	−2.75456	−	1.44570i	−0.213795	−	0.112208i
$167$	1.99217	−	1.37510i	0.154159	−	0.106408i	−0.488488	−	0.872570i	$-0.662451\pi$
$167$	1.99217	−	1.37510i	0.154159	−	0.106408i	0.642647	+	0.766162i	$0.277836\pi$
$168$	1.01596			0.0783828
$169$	−12.6907	+	2.81904i	−0.976205	+	0.216849i
$170$	−2.94037			−0.225516
$171$	−19.7084	+	13.6038i	−1.50714	+	1.04031i
$172$	19.7574	+	10.3695i	1.50649	+	0.790664i
$173$	−0.475932	+	1.25493i	−0.0361845	+	0.0954106i	−0.951891	−	0.306438i	$-0.900863\pi$
$173$	−0.475932	+	1.25493i	−0.0361845	+	0.0954106i	0.915706	+	0.401848i	$0.131632\pi$
$174$	−2.50994	−	2.83313i	−0.190278	−	0.214779i
$175$	0.217896	−	0.0264573i	0.0164714	−	0.00199999i
$176$	−1.12534	−	4.56567i	−0.0848255	−	0.344151i
$177$	−7.80439	−	31.6637i	−0.586614	−	2.37999i
$178$	−1.62694	−	2.35703i	−0.121944	−	0.176667i
$179$	16.2347	+	4.00151i	1.21344	+	0.299087i	0.793560	−	0.608492i	$-0.208225\pi$
$179$	16.2347	+	4.00151i	1.21344	+	0.299087i	0.419882	+	0.907579i	$0.362071\pi$
$180$	−22.1398	−	15.2820i	−1.65021	−	1.13905i
$181$	18.4989	−	16.3886i	1.37501	−	1.21815i	0.425292	−	0.905056i	$-0.360171\pi$
$181$	18.4989	−	16.3886i	1.37501	−	1.21815i	0.949721	−	0.313098i	$-0.101367\pi$
$182$	−0.171133	+	0.241911i	−0.0126853	+	0.0179317i
$183$	−11.1243	−	9.85528i	−0.822332	−	0.728523i
$184$	1.22687	+	4.97761i	0.0904462	+	0.366954i
$185$	10.6337	+	9.42067i	0.781808	+	0.692622i
$186$	11.4466	−	2.82134i	0.839308	−	0.206871i
$187$	−5.34539	−	2.02724i	−0.390894	−	0.148246i
$188$			10.8127i			0.788596i
$189$	2.72518	−	1.03352i	0.198227	−	0.0751777i
$190$	−0.610063	+	2.47512i	−0.0442586	+	0.179564i
$191$	−0.930117			−0.0673009			−0.0336504	−	0.999434i	$-0.510713\pi$
$191$	−0.930117			−0.0673009			−0.0336504	+	0.999434i	$0.510713\pi$
$192$	−14.5744			−1.05182
$193$	−2.29324	+	9.30403i	−0.165071	+	0.669719i	0.828836	+	0.559492i	$0.189004\pi$
$193$	−2.29324	+	9.30403i	−0.165071	+	0.669719i	−0.993906	+	0.110226i	$0.964842\pi$
$194$	0.417197	−	3.43592i	0.0299530	−	0.246685i
$195$	21.6333	−	7.92015i	1.54919	−	0.567174i
$196$	1.54769	+	12.7464i	0.110550	+	0.910458i
$197$	23.1011	+	2.80498i	1.64589	+	0.199847i	0.890355	−	0.455266i	$-0.150456\pi$
$197$	23.1011	+	2.80498i	1.64589	+	0.199847i	0.755531	+	0.655113i	$0.227379\pi$
$198$	2.48145	+	3.59501i	0.176349	+	0.255486i
$199$	11.4745	+	10.1655i	0.813403	+	0.720612i	0.963398	−	0.268075i	$-0.0863873\pi$
$199$	11.4745	+	10.1655i	0.813403	+	0.720612i	−0.149995	+	0.988687i	$0.547926\pi$
$200$	1.57184	−	0.190856i	0.111146	−	0.0134955i
$201$	−31.9041	−	3.87385i	−2.25034	−	0.273241i
$202$	−0.610637	−	1.16347i	−0.0429643	−	0.0818616i
$203$	−0.416301	+	0.469906i	−0.0292186	+	0.0329810i
$204$	−12.6978	+	18.3959i	−0.889022	+	1.28797i
$205$	−16.3683	+	4.03443i	−1.14321	+	0.281777i
$206$	−0.123781	+	0.0150297i	−0.00862421	+	0.00104717i
$207$	14.1406	+	20.4861i	0.982836	+	1.42388i
$208$	6.45264	−	9.12134i	0.447410	−	0.632451i
$209$	−2.81553	+	4.07900i	−0.194754	+	0.282150i
$210$	0.244035	−	0.464971i	0.0168400	−	0.0320860i
$211$	−6.37005	−	16.7964i	−0.438532	−	1.15631i	−0.954106	−	0.299469i	$-0.903190\pi$
$211$	−6.37005	−	16.7964i	−0.438532	−	1.15631i	0.515574	−	0.856845i	$-0.327579\pi$
$212$	−0.0814878	+	0.671113i	−0.00559661	+	0.0460922i
$213$	25.1396	−	17.3526i	1.72254	−	1.18898i
$214$	−1.78340	+	7.23555i	−0.121911	+	0.494612i
$215$	19.7758	−	13.6502i	1.34870	−	0.930938i
$216$	19.6586	−	7.45553i	1.33760	−	0.507285i
$217$	−0.693383	−	1.82830i	−0.0470699	−	0.124113i
$218$	2.88074	−	1.51193i	0.195108	−	0.102401i
$219$	13.1088	+	24.9767i	0.885809	+	1.68777i
$220$	−5.40602	−	1.33246i	−0.364474	−	0.0898347i
$221$	−4.66998	−	12.7557i	−0.314137	−	0.858041i
$222$	−8.75741	+	2.15851i	−0.587759	+	0.144870i
$223$	−6.70716	−	7.57082i	−0.449145	−	0.506980i	0.479708	−	0.877428i	$-0.340743\pi$
$223$	−6.70716	−	7.57082i	−0.449145	−	0.506980i	−0.928853	+	0.370448i	$0.879204\pi$
$224$	−0.106895	−	0.880357i	−0.00714220	−	0.0588213i
$225$	6.80759	−	3.57290i	0.453839	−	0.238193i
$226$	−2.25450	+	4.29559i	−0.149967	+	0.285739i
$227$	5.84152	+	2.21540i	0.387716	+	0.147041i	0.540757	−	0.841179i	$-0.318138\pi$
$227$	5.84152	+	2.21540i	0.387716	+	0.147041i	−0.153042	+	0.988220i	$0.548907\pi$
$228$	12.8507	+	14.5054i	0.851056	+	0.960643i
$229$	3.15770	+	0.383414i	0.208666	+	0.0253367i	0.224202	−	0.974543i	$-0.428022\pi$
$229$	3.15770	+	0.383414i	0.208666	+	0.0253367i	−0.0155359	+	0.999879i	$0.504945\pi$
$230$	2.57279	+	0.634136i	0.169645	+	0.0418137i
$231$	0.764215	−	0.677035i	0.0502816	−	0.0445456i
$232$	−3.00307	+	3.38977i	−0.197161	+	0.222549i
$233$	−9.71744	+	5.10010i	−0.636610	+	0.334119i	−0.751963	−	0.659206i	$-0.770893\pi$
$233$	−9.71744	+	5.10010i	−0.636610	+	0.334119i	0.115352	+	0.993325i	$0.463200\pi$
$234$	−2.60002	+	10.0483i	−0.169968	+	0.656878i
$235$	10.3105	+	5.41138i	0.672584	+	0.352999i
$236$	−17.5103	+	6.64078i	−1.13982	+	0.432278i
$237$	−0.509101	+	4.19282i	−0.0330697	+	0.272353i
$238$	−0.274162	−	0.143891i	−0.0177713	−	0.00932709i
$239$			19.7769i			1.27926i	0.768683	+	0.639630i	$0.220913\pi$
$239$			19.7769i			1.27926i	−0.768683	+	0.639630i	$0.779087\pi$
$240$	−9.20143	+	17.5319i	−0.593950	+	1.13168i
$241$	0.880831	−	0.994253i	0.0567393	−	0.0640454i	−0.719456	−	0.694538i	$-0.755609\pi$
$241$	0.880831	−	0.994253i	0.0567393	−	0.0640454i	0.776195	+	0.630493i	$0.217147\pi$
$242$	−2.81034	−	1.93984i	−0.180655	−	0.124697i
$243$	23.4938	−	20.8137i	1.50713	−	1.33520i
$244$	−4.84818	+	7.02380i	−0.310373	+	0.449653i
$245$	12.9290	+	4.90333i	0.826004	+	0.313262i
$246$	3.79534	−	10.0075i	0.241982	−	0.638054i
$247$	−11.7063	+	1.28454i	−0.744856	+	0.0817332i
$248$	−5.00186	−	13.1888i	−0.317619	−	0.837492i
$249$			25.4679i			1.61396i
$250$	1.67400	−	4.41398i	0.105873	−	0.279165i
$251$	1.54400	+	12.7160i	0.0974565	+	0.802626i	0.956703	+	0.291065i	$0.0940096\pi$
$251$	1.54400	+	12.7160i	0.0974565	+	0.802626i	−0.859247	+	0.511561i	$0.829067\pi$
$252$	−1.31649	−	2.50835i	−0.0829308	−	0.158012i
$253$	4.23996	+	2.92663i	0.266564	+	0.183996i
$254$	1.71977	+	1.18707i	0.107908	+	0.0744834i
$255$	11.1868	+	21.3146i	0.700542	+	1.33477i
$256$	0.607820	+	5.00585i	0.0379888	+	0.312866i
$257$	−2.83077	+	7.46412i	−0.176578	+	0.465599i	−0.993861	−	0.110638i	$-0.964710\pi$
$257$	−2.83077	+	7.46412i	−0.176578	+	0.465599i	0.817282	+	0.576238i	$0.195480\pi$
$258$			15.2559i			0.949789i
$259$	0.530483	+	1.39877i	0.0329626	+	0.0869153i
$260$	−6.01247	−	11.7842i	−0.372878	−	0.730828i
$261$	−7.79753	+	20.5604i	−0.482655	+	1.27266i
$262$	4.49119	+	1.70328i	0.277467	+	0.105229i
$263$	8.53798	−	12.3694i	0.526474	−	0.762730i	−0.466052	−	0.884757i	$-0.654324\pi$
$263$	8.53798	−	12.3694i	0.526474	−	0.762730i	0.992527	+	0.122027i	$0.0389396\pi$
$264$	5.51282	−	4.88393i	0.339291	−	0.300585i
$265$	0.599163	+	0.413572i	0.0368063	+	0.0254056i
$266$	−0.178007	+	0.200928i	−0.0109143	+	0.0123197i
$267$	−10.8962	+	20.7610i	−0.666838	+	1.27055i
$268$			18.4557i			1.12736i
$269$	−23.8238	−	12.5037i	−1.45256	−	0.762365i	−0.460449	−	0.887686i	$-0.652311\pi$
$269$	−23.8238	−	12.5037i	−1.45256	−	0.762365i	−0.992116	+	0.125322i	$0.960004\pi$
$270$	1.30990	−	10.7880i	0.0797177	−	0.656534i
$271$	13.0763	−	4.95919i	0.794329	−	0.301249i	0.0761399	−	0.997097i	$-0.475740\pi$
$271$	13.0763	−	4.95919i	0.794329	−	0.301249i	0.718189	+	0.695848i	$0.244971\pi$
$272$	10.3374	+	5.42547i	0.626795	+	0.328967i
$273$	2.40469	+	0.320176i	0.145538	+	0.0193779i
$274$	2.53971	−	1.33294i	0.153430	−	0.0805261i
$275$	1.05517	−	1.19104i	0.0636290	−	0.0718223i
$276$	15.0778	−	13.3577i	0.907576	−	0.804042i
$277$	−16.4933	−	4.06524i	−0.990989	−	0.244257i	−0.289687	−	0.957121i	$-0.593551\pi$
$277$	−16.4933	−	4.06524i	−0.990989	−	0.244257i	−0.701302	+	0.712864i	$0.747397\pi$
$278$	−1.24805	−	0.151540i	−0.0748529	−	0.00908878i
$279$	−45.4173	−	51.2656i	−2.71907	−	3.06919i
$280$	−0.587463	−	0.222795i	−0.0351076	−	0.0133146i
$281$	12.0289	−	22.9192i	0.717586	−	1.36725i	−0.203960	−	0.978979i	$-0.565381\pi$
$281$	12.0289	−	22.9192i	0.717586	−	1.36725i	0.921547	−	0.388268i	$-0.126926\pi$
$282$	−6.54599	+	3.43560i	−0.389808	+	0.204587i
$283$	1.54086	+	12.6901i	0.0915944	+	0.754347i	0.964062	+	0.265676i	$0.0855952\pi$
$283$	1.54086	+	12.6901i	0.0915944	+	0.754347i	−0.872468	+	0.488671i	$0.837482\pi$
$284$	−11.6323	−	13.1302i	−0.690253	−	0.779134i
$285$	20.2631	−	4.99440i	1.20028	−	0.295842i
$286$	0.234312	+	2.13534i	0.0138551	+	0.126266i
$287$	−1.72363	−	0.424836i	−0.101742	−	0.0250773i
$288$	−14.4354	−	27.5044i	−0.850617	−	1.62072i
$289$	−2.48497	+	1.30421i	−0.146175	+	0.0767185i
$290$	0.830041	+	2.18864i	0.0487417	+	0.128521i
$291$	−26.4941	+	10.0479i	−1.55311	+	0.589017i
$292$	13.3311	−	9.20178i	0.780142	−	0.538493i
$293$	−2.53577	+	10.2880i	−0.148141	+	0.601032i	0.849194	+	0.528080i	$0.177088\pi$
$293$	−2.53577	+	10.2880i	−0.148141	+	0.601032i	−0.997335	+	0.0729516i	$0.976758\pi$
$294$	−7.22490	+	4.98699i	−0.421365	+	0.290847i
$295$	−2.43094	+	20.0206i	−0.141535	+	1.16564i
$296$	3.82675	+	10.0903i	0.222425	+	0.586487i
$297$	9.81907	−	18.7087i	0.569760	−	1.08559i
$298$	4.34230	−	6.29091i	0.251543	−	0.364422i
$299$	1.33522	+	12.1683i	0.0772180	+	0.703708i
$300$	−3.53423	−	5.12022i	−0.204049	−	0.295616i
$301$	2.51190	−	0.305000i	0.144784	−	0.0175799i
$302$	−1.50070	+	0.369890i	−0.0863557	+	0.0212848i
$303$	−6.11075	+	8.85295i	−0.351054	+	0.508589i
$304$	6.71180	−	7.57605i	0.384948	−	0.434516i
$305$	4.27125	+	8.13820i	0.244571	+	0.465992i
$306$	−10.7662	−	1.30725i	−0.615461	−	0.0747305i
$307$	−32.7597	+	3.97775i	−1.86970	+	0.227022i	−0.975398	−	0.220451i	$-0.929247\pi$
$307$	−32.7597	+	3.97775i	−1.86970	+	0.227022i	−0.894297	+	0.447473i	$0.852324\pi$
$308$	−0.438855	−	0.388792i	−0.0250061	−	0.0221535i
$309$	0.579878	+	0.840099i	0.0329881	+	0.0477915i
$310$	−7.23757	−	0.878800i	−0.411066	−	0.0499125i
$311$	−3.17718	−	26.1664i	−0.180161	−	1.48376i	−0.749689	−	0.661790i	$-0.769797\pi$
$311$	−3.17718	−	26.1664i	−0.180161	−	1.48376i	0.569528	−	0.821972i	$-0.307126\pi$
$312$	17.3467	+	2.30965i	0.982064	+	0.130758i
$313$	−0.708839	+	5.83781i	−0.0400659	+	0.329973i	0.958870	+	0.283847i	$0.0916106\pi$
$313$	−0.708839	+	5.83781i	−0.0400659	+	0.329973i	−0.998936	+	0.0461260i	$0.985312\pi$
$314$	−0.0380294	+	0.154291i	−0.00214612	+	0.00870716i
$315$	−3.05072			−0.171889
$316$	2.42544			0.136442
$317$	−5.10231	+	20.7009i	−0.286574	+	1.16268i	0.634385	+	0.773017i	$0.281253\pi$
$317$	−5.10231	+	20.7009i	−0.286574	+	1.16268i	−0.920959	+	0.389659i	$0.872593\pi$
$318$	−0.432183	+	0.163905i	−0.0242356	+	0.00919135i
$319$			4.55107i			0.254811i
$320$	8.42747	+	3.19612i	0.471110	+	0.178668i
$321$	59.2352	−	14.6002i	3.30619	−	0.814902i
$322$	0.208857	+	0.185031i	0.0116391	+	0.0103114i
$323$	−2.94486	−	11.9478i	−0.163856	−	0.664792i
$324$	−31.4465	−	27.8592i	−1.74703	−	1.54773i
$325$	3.78056	+	0.0436203i	0.209708	+	0.00241962i
$326$	−1.63025	+	1.44428i	−0.0902914	+	0.0799912i
$327$	−21.9198	−	15.1301i	−1.21217	−	0.836698i
$328$	−12.4337	−	3.06464i	−0.686538	−	0.169217i
$329$	0.696547	+	1.00912i	0.0384019	+	0.0556347i
$330$	−0.911025	−	3.69617i	−0.0501503	−	0.203468i
$331$	1.82914	+	7.42113i	0.100539	+	0.407902i	0.999549	−	0.0300254i	$-0.00955880\pi$
$331$	1.82914	+	7.42113i	0.100539	+	0.407902i	−0.899010	+	0.437928i	$0.855713\pi$
$332$	14.5185	−	1.76286i	0.796805	−	0.0967497i
$333$	34.7472	+	39.2215i	1.90414	+	2.14932i
$334$	0.337025	−	0.888661i	0.0184412	−	0.0486253i
$335$	17.5986	+	9.23644i	0.961512	+	0.504641i
$336$	−1.71590	+	1.18440i	−0.0936099	+	0.0646142i
$337$	−5.61311			−0.305765			−0.152883	−	0.988244i	$-0.548856\pi$
$337$	−5.61311			−0.305765			−0.152883	+	0.988244i	$0.548856\pi$
$338$	−3.47193	+	3.74141i	−0.188848	+	0.203506i
$339$	39.7159			2.15707
$340$	11.3765	−	7.85260i	0.616975	−	0.425867i
$341$	−12.5515	−	6.58755i	−0.679703	−	0.356736i
$342$	−3.33416	+	8.79146i	−0.180291	+	0.475388i
$343$	1.93720	+	2.18665i	0.104599	+	0.118068i
$344$	18.1201	−	2.20018i	0.976972	−	0.118626i
$345$	−5.19147	−	21.0626i	−0.279499	−	1.13397i
$346$	0.126111	+	0.511652i	0.00677976	+	0.0275066i
$347$	5.54461	+	8.03275i	0.297650	+	0.431221i	0.943063	−	0.332613i	$-0.107930\pi$
$347$	5.54461	+	8.03275i	0.297650	+	0.431221i	−0.645413	+	0.763834i	$0.723315\pi$
$348$	17.2773	+	4.25848i	0.926161	+	0.228278i
$349$	14.7699	+	10.1949i	0.790612	+	0.545720i	0.893548	−	0.448968i	$-0.148208\pi$
$349$	14.7699	+	10.1949i	0.790612	+	0.545720i	−0.102936	+	0.994688i	$0.532824\pi$
$350$	0.0645069	−	0.0571481i	0.00344804	−	0.00305469i
$351$	48.8800	−	11.4513i	2.60902	−	0.611224i
$352$	−4.81211	−	4.26316i	−0.256486	−	0.227227i
$353$	−6.40287	−	25.9775i	−0.340790	−	1.38264i	−0.852161	−	0.523280i	$-0.824708\pi$
$353$	−6.40287	−	25.9775i	−0.340790	−	1.38264i	0.511370	−	0.859361i	$-0.329138\pi$
$354$	−9.58400	−	8.49068i	−0.509384	−	0.451275i
$355$	−18.3420	+	4.52090i	−0.973493	+	0.239944i
$356$	12.5894	+	4.77455i	0.667239	+	0.253050i
$357$			2.53483i			0.134157i
$358$	6.13836	−	2.32797i	0.324422	−	0.123037i
$359$	3.12831	−	12.6921i	0.165106	−	0.669862i	−0.828792	−	0.559557i	$-0.810971\pi$
$359$	3.12831	−	12.6921i	0.165106	−	0.669862i	0.993898	−	0.110305i	$-0.0351827\pi$
$360$	−22.0070			−1.15987
$361$	8.33169			0.438510
$362$	2.32220	−	9.42154i	0.122052	−	0.495185i
$363$	−3.36973	+	27.7522i	−0.176865	+	1.45661i
$364$	0.0160725	−	1.39300i	0.000842429	−	0.0730131i
$365$	−2.10268	−	17.3171i	−0.110059	−	0.906420i
$366$	−5.79265	−	0.703356i	−0.302787	−	0.0367650i
$367$	−4.46497	−	6.46863i	−0.233070	−	0.337660i	0.688946	−	0.724813i	$-0.258074\pi$
$367$	−4.46497	−	6.46863i	−0.233070	−	0.337660i	−0.922015	+	0.387153i	$0.873458\pi$
$368$	−7.87500	−	6.97664i	−0.410513	−	0.363683i
$369$	−61.7264	+	7.49495i	−3.21335	+	0.390171i
$370$	5.53721	+	0.672338i	0.287866	+	0.0349532i
$371$	0.0356276	+	0.0678828i	0.00184969	+	0.00352430i
$372$	−36.7530	+	41.4855i	−1.90555	+	2.15092i
$373$	−15.2421	+	22.0821i	−0.789208	+	1.14337i	0.197410	+	0.980321i	$0.436747\pi$
$373$	−15.2421	+	22.0821i	−0.789208	+	1.14337i	−0.986619	+	0.163045i	$0.947868\pi$
$374$	−2.17939	+	0.537170i	−0.112693	+	0.0277764i
$375$	−38.3655	+	4.65842i	−1.98119	+	0.240560i
$376$	5.02468	+	7.27951i	0.259128	+	0.375412i
$377$	−8.17630	+	7.07689i	−0.421101	+	0.364478i
$378$	0.650061	−	0.941776i	0.0334355	−	0.0484397i
$379$	6.16450	−	11.7455i	0.316649	−	0.603325i	−0.674161	−	0.738584i	$-0.735495\pi$
$379$	6.16450	−	11.7455i	0.316649	−	0.603325i	0.990810	+	0.135260i	$0.0431869\pi$
$380$	−4.24974	−	11.2056i	−0.218007	−	0.574838i
$381$	2.06208	−	16.9828i	0.105644	−	0.870053i
$382$	−0.300545	+	0.207451i	−0.0153772	+	0.0106141i
$383$	−2.63958	+	10.7092i	−0.134876	+	0.547215i	0.864156	+	0.503225i	$0.167853\pi$
$383$	−2.63958	+	10.7092i	−0.134876	+	0.547215i	−0.999032	+	0.0439902i	$0.985993\pi$
$384$	−27.1241	+	18.7224i	−1.38417	+	0.955424i
$385$	−0.590368	+	0.223897i	−0.0300879	+	0.0114108i
$386$	1.33415	+	3.51785i	0.0679062	+	0.179054i
$387$	78.4779	−	41.1884i	3.98925	−	2.09372i
$388$	7.56189	+	14.4080i	0.383897	+	0.731454i
$389$	−23.8812	−	5.88619i	−1.21082	−	0.298442i	−0.418316	−	0.908302i	$-0.637379\pi$
$389$	−23.8812	−	5.88619i	−1.21082	−	0.298442i	−0.792509	+	0.609860i	$0.791226\pi$
$390$	5.22378	−	7.38425i	0.264516	−	0.373916i
$391$	−12.4192	+	3.06106i	−0.628067	+	0.154805i
$392$	6.96526	+	7.86215i	0.351799	+	0.397099i
$393$	−4.73991	−	39.0366i	−0.239097	−	1.96914i
$394$	8.09019	−	4.24606i	0.407578	−	0.213913i
$395$	1.21385	−	2.31280i	0.0610755	−	0.116370i
$396$	−19.2018	−	7.28228i	−0.964926	−	0.365948i
$397$	−12.8056	−	14.4545i	−0.642692	−	0.725450i	0.333405	−	0.942784i	$-0.391802\pi$
$397$	−12.8056	−	14.4545i	−0.642692	−	0.725450i	−0.976097	+	0.217334i	$0.930264\pi$
$398$	5.97499	+	0.725495i	0.299499	+	0.0363658i
$399$	2.13375	+	0.525923i	0.106821	+	0.0263291i
$400$	−2.43225	+	2.15479i	−0.121613	+	0.107739i
$401$	23.0071	−	25.9696i	1.14892	−	1.29686i	0.200554	−	0.979683i	$-0.435726\pi$
$401$	23.0071	−	25.9696i	1.14892	−	1.29686i	0.948366	−	0.317179i	$-0.102736\pi$
$402$	−11.1731	+	5.86407i	−0.557261	+	0.292473i
$403$	−7.68258	−	32.7932i	−0.382697	−	1.63355i
$404$	5.46978	+	2.87076i	0.272132	+	0.142826i
$405$	−42.3032	+	16.0435i	−2.10207	+	0.797208i
$406$	−0.0297107	+	0.244690i	−0.00147452	+	0.0121438i
$407$	9.60272	+	5.03990i	0.475989	+	0.249818i
$408$			18.2855i			0.905267i
$409$	−5.14244	+	9.79810i	−0.254277	+	0.484485i	−0.978814	−	0.204751i	$-0.934361\pi$
$409$	−5.14244	+	9.79810i	−0.254277	+	0.484485i	0.724537	+	0.689236i	$0.242054\pi$
$410$	−4.38920	+	4.95439i	−0.216767	+	0.244680i
$411$	−19.3249	−	13.3390i	−0.953227	−	0.657965i
$412$	0.438776	−	0.388722i	0.0216170	−	0.0191509i
$413$	−1.20640	+	1.74777i	−0.0593630	+	0.0860022i
$414$	9.13836	+	3.46572i	0.449126	+	0.170331i
$415$	5.58501	−	14.7265i	0.274158	−	0.722894i
$416$	0.176237	−	15.2745i	0.00864075	−	0.748892i
$417$	3.64974	+	9.62357i	0.178728	+	0.471268i
$418$			1.94600i			0.0951820i
$419$	−2.08918	+	5.50872i	−0.102063	+	0.269119i	−0.976315	−	0.216354i	$-0.930583\pi$
$419$	−2.08918	+	5.50872i	−0.102063	+	0.269119i	0.874252	+	0.485473i	$0.161353\pi$
$420$	0.297572	+	2.45073i	0.0145200	+	0.119583i
$421$	1.60490	+	3.05788i	0.0782180	+	0.149032i	0.921424	−	0.388559i	$-0.127027\pi$
$421$	1.60490	+	3.05788i	0.0782180	+	0.149032i	−0.843206	+	0.537591i	$0.819335\pi$
$422$	−5.80457	−	4.00660i	−0.282562	−	0.195038i
$423$	35.3462	+	24.3977i	1.71859	+	1.18626i
$424$	0.257007	+	0.489686i	0.0124814	+	0.0237813i
$425$	0.476188	+	3.92176i	0.0230985	+	0.190233i
$426$	4.25298	−	11.2142i	0.206057	−	0.543329i
$427$			0.967832i			0.0468367i
$428$	−12.4233	−	32.7576i	−0.600504	−	1.58340i
$429$	14.5876	−	9.82252i	0.704294	−	0.474236i
$430$	3.34555	−	8.82149i	0.161337	−	0.425410i
$431$	−31.7052	−	12.0242i	−1.52718	−	0.579185i	−0.558944	−	0.829205i	$-0.688793\pi$
$431$	−31.7052	−	12.0242i	−1.52718	−	0.579185i	−0.968241	+	0.250020i	$0.919563\pi$
$432$	−24.5107	+	35.5099i	−1.17927	+	1.70847i
$433$	12.5638	−	11.1305i	0.603776	−	0.534898i	−0.304909	−	0.952381i	$-0.598626\pi$
$433$	12.5638	−	11.1305i	0.603776	−	0.534898i	0.908685	+	0.417483i	$0.137088\pi$
$434$	−0.631831	−	0.436121i	−0.0303289	−	0.0209345i
$435$	12.7074	−	14.3437i	0.609274	−	0.687728i
$436$	−7.10796	+	13.5431i	−0.340410	+	0.648597i
$437$			11.0893i			0.530472i
$438$	9.80653	+	5.14687i	0.468574	+	0.245927i
$439$	0.244760	−	2.01578i	0.0116818	−	0.0962079i	−0.985702	−	0.168499i	$-0.946108\pi$
$439$	0.244760	−	2.01578i	0.0116818	−	0.0962079i	0.997384	+	0.0722911i	$0.0230311\pi$
$440$	−4.25874	+	1.61513i	−0.203027	+	0.0769982i
$441$	45.1597	+	23.7016i	2.15046	+	1.12865i
$442$	−4.35400	−	3.08011i	−0.207098	−	0.146506i
$443$	−12.6577	+	6.64325i	−0.601383	+	0.315630i	−0.737798	−	0.675022i	$-0.764134\pi$
$443$	−12.6577	+	6.64325i	−0.601383	+	0.315630i	0.136415	+	0.990652i	$0.456442\pi$
$444$	28.1184	−	31.7391i	1.33444	−	1.50627i
$445$	10.8534	−	9.61527i	0.514500	−	0.455807i
$446$	−3.85584	−	0.950379i	−0.182579	−	0.0450018i
$447$	−62.1229	−	7.54309i	−2.93831	−	0.356776i
$448$	0.629377	+	0.710420i	0.0297353	+	0.0335642i
$449$	18.6841	+	7.08595i	0.881758	+	0.334407i	0.753589	−	0.657346i	$-0.228321\pi$
$449$	18.6841	+	7.08595i	0.881758	+	0.334407i	0.128169	+	0.991752i	$0.459090\pi$
$450$	1.40282	−	2.67285i	0.0661295	−	0.125999i
$451$	−11.3951	+	5.98060i	−0.536574	+	0.281616i
$452$	−2.74909	−	22.6408i	−0.129306	−	1.06493i
$453$	8.39080	+	9.47125i	0.394234	+	0.444998i
$454$	2.38167	−	0.587028i	0.111777	−	0.0275506i
$455$	−1.32026	−	0.712476i	−0.0618949	−	0.0334014i
$456$	15.3923	+	3.79385i	0.720808	+	0.177663i
$457$	3.90466	+	7.43970i	0.182652	+	0.348015i	0.959516	−	0.281654i	$-0.0908830\pi$
$457$	3.90466	+	7.43970i	0.182652	+	0.348015i	−0.776864	+	0.629669i	$0.783191\pi$
$458$	1.10585	−	0.580395i	0.0516730	−	0.0271201i
$459$	18.6017	+	49.0486i	0.868252	+	2.28939i
$460$	−11.6478	+	4.41744i	−0.543082	+	0.205964i
$461$	−11.1718	+	7.71133i	−0.520322	+	0.359153i	−0.799095	−	0.601204i	$-0.794688\pi$
$461$	−11.1718	+	7.71133i	−0.520322	+	0.359153i	0.278773	+	0.960357i	$0.410072\pi$
$462$	0.0959333	−	0.389217i	0.00446322	−	0.0181080i
$463$	−20.7745	+	14.3396i	−0.965475	+	0.666419i	−0.942812	−	0.333324i	$-0.891830\pi$
$463$	−20.7745	+	14.3396i	−0.965475	+	0.666419i	−0.0226623	+	0.999743i	$0.507214\pi$
$464$	1.12025	−	9.22610i	0.0520064	−	0.428311i
$465$	21.1653	+	55.8082i	0.981515	+	2.58804i
$466$	−2.00244	+	3.81533i	−0.0927613	+	0.176742i
$467$	5.78084	−	8.37499i	0.267505	−	0.387548i	−0.666094	−	0.745868i	$-0.732035\pi$
$467$	5.78084	−	8.37499i	0.267505	−	0.387548i	0.933599	+	0.358320i	$0.116650\pi$
$468$	−16.7756	−	45.8212i	−0.775452	−	2.11808i
$469$	1.18890	+	1.72243i	0.0548985	+	0.0795342i
$470$	4.53854	−	0.551078i	0.209347	−	0.0254194i
$471$	1.26313	−	0.311335i	0.0582022	−	0.0143455i
$472$	−8.70261	+	12.6079i	−0.400570	+	0.580326i
$473$	12.1640	−	13.7303i	0.559300	−	0.631319i
$474$	0.770655	+	1.46836i	0.0353973	+	0.0674440i
$475$	3.40003	+	0.412838i	0.156004	+	0.0189423i
$476$	1.44503	−	0.175458i	0.0662328	−	0.00804212i
$477$	2.00997	+	1.78068i	0.0920303	+	0.0815317i
$478$	4.41100	+	6.39043i	0.201754	+	0.292292i
$479$	−2.24401	−	0.272472i	−0.102532	−	0.0124496i	0.0691101	−	0.997609i	$-0.477984\pi$
$479$	−2.24401	−	0.272472i	−0.102532	−	0.0124496i	−0.171642	+	0.985159i	$0.554907\pi$
$480$	3.26292	+	26.8725i	0.148931	+	1.22656i
$481$	5.87767	+	25.0889i	0.267999	+	1.14396i
$482$	0.0628635	−	0.517728i	0.00286335	−	0.0235818i
$483$	0.546675	−	2.21795i	0.0248746	−	0.100920i
$484$	16.0539			0.729724
$485$	17.5233			0.795692
$486$	2.94922	−	11.9654i	0.133779	−	0.542763i
$487$	15.9393	−	6.04499i	0.722279	−	0.273924i	0.0340526	−	0.999420i	$-0.489159\pi$
$487$	15.9393	−	6.04499i	0.722279	−	0.273924i	0.688227	+	0.725496i	$0.258389\pi$
$488$			6.98166i			0.316045i
$489$	16.6719	+	6.32281i	0.753928	+	0.285927i
$490$	5.27133	−	1.29927i	0.238134	−	0.0586948i
$491$	−12.6521	−	11.2087i	−0.570980	−	0.505844i	0.327505	−	0.944850i	$-0.393792\pi$
$491$	−12.6521	−	11.2087i	−0.570980	−	0.505844i	−0.898484	+	0.439006i	$0.855331\pi$
$492$	12.0418	+	48.8555i	0.542886	+	2.20257i
$493$	−8.45752	−	7.49271i	−0.380908	−	0.337455i
$494$	−3.49612	+	3.02602i	−0.157298	+	0.136147i
$495$	−16.5539	+	14.6655i	−0.744043	+	0.659165i
$496$	23.8234	+	16.4441i	1.06970	+	0.738361i
$497$	−1.93146	−	0.476062i	−0.0866378	−	0.0213543i
$498$	5.68031	+	8.22935i	0.254541	+	0.368766i
$499$	−6.42599	−	26.0713i	−0.287667	−	1.16711i	−0.919844	−	0.392285i	$-0.871685\pi$
$499$	−6.42599	−	26.0713i	−0.287667	−	1.16711i	0.632177	−	0.774824i	$-0.282162\pi$
$500$	5.31125	+	21.5486i	0.237526	+	0.963682i
$501$	−7.72408	+	0.937873i	−0.345086	+	0.0419011i
$502$	3.33505	+	3.76450i	0.148851	+	0.168018i
$503$	9.80765	−	25.8607i	0.437302	−	1.15307i	−0.517463	−	0.855706i	$-0.673123\pi$
$503$	9.80765	−	25.8607i	0.437302	−	1.15307i	0.954764	−	0.297364i	$-0.0961074\pi$
$504$	−2.05195	−	1.07695i	−0.0914010	−	0.0479710i
$505$	5.47488	−	3.77904i	0.243629	−	0.168165i
$506$	2.02279			0.0899240
$507$	40.3304	+	10.9335i	1.79113	+	0.485575i
$508$	−9.82409			−0.435874
$509$	8.28644	−	5.71971i	0.367290	−	0.253522i	−0.370096	−	0.928993i	$-0.620675\pi$
$509$	8.28644	−	5.71971i	0.367290	−	0.253522i	0.737386	+	0.675472i	$0.236060\pi$
$510$	8.36869	+	4.39223i	0.370572	+	0.194491i
$511$	0.651385	−	1.71756i	0.0288156	−	0.0759804i
$512$	14.9116	+	16.8318i	0.659008	+	0.743866i
$513$	45.1472	−	5.48187i	1.99330	−	0.242030i
$514$	0.750087	+	3.04322i	0.0330849	+	0.134231i
$515$	−0.151076	−	0.612941i	−0.00665722	−	0.0270094i
$516$	−40.7426	−	59.0259i	−1.79359	−	2.59847i
$517$	8.63070	+	2.12728i	0.379578	+	0.0935575i
$518$	0.483391	+	0.333661i	0.0212390	+	0.0146602i
$519$	3.22914	−	2.86077i	0.141744	−	0.125574i
$520$	−9.52400	−	5.13959i	−0.417655	−	0.225386i
$521$	3.90352	+	3.45822i	0.171016	+	0.151507i	0.744290	−	0.667857i	$-0.232788\pi$
$521$	3.90352	+	3.45822i	0.171016	+	0.151507i	−0.573273	+	0.819364i	$0.694327\pi$
$522$	2.06616	+	8.38274i	0.0904334	+	0.366903i
$523$	8.39082	+	7.43362i	0.366905	+	0.325050i	0.826350	−	0.563157i	$-0.190413\pi$
$523$	8.39082	+	7.43362i	0.366905	+	0.325050i	−0.459445	+	0.888206i	$0.651952\pi$
$524$	−21.9255	+	5.40415i	−0.957820	+	0.236082i
$525$	−0.659683	−	0.250185i	−0.0287909	−	0.0109190i
$526$		−	5.90117i		−	0.257303i
$527$	32.9063	−	12.4797i	1.43342	−	0.543626i
$528$	−3.61719	+	14.6755i	−0.157418	+	0.638670i
$529$	−11.4731			−0.498832
$530$	0.285848			0.0124164
$531$	−17.8018	+	72.2247i	−0.772531	+	3.13428i
$532$	0.152116	−	1.25279i	0.00659508	−	0.0543154i
$533$	−28.4638	−	11.1722i	−1.23291	−	0.483922i
$534$	1.10964	+	9.13869i	0.0480187	+	0.395470i
$535$	−37.4537	−	4.54770i	−1.61926	−	0.196614i
$536$	8.57641	+	12.4251i	0.370444	+	0.536681i
$537$	−40.2290	−	35.6398i	−1.73601	−	1.53797i
$538$	−10.4869	+	1.27334i	−0.452123	+	0.0548976i
$539$	10.4787	+	1.27234i	0.451350	+	0.0548038i
$540$	23.7425	+	45.2375i	1.02171	+	1.94671i
$541$	11.9065	−	13.4397i	0.511900	−	0.577816i	−0.434557	−	0.900644i	$-0.643095\pi$
$541$	11.9065	−	13.4397i	0.511900	−	0.577816i	0.946458	+	0.322828i	$0.104634\pi$
$542$	3.11921	−	4.51896i	0.133982	−	0.194106i
$543$	−77.1312	+	19.0111i	−3.31002	+	0.815846i
$544$	15.8449	−	1.92392i	0.679346	−	0.0824875i
$545$	9.35683	+	13.5557i	0.400803	+	0.580663i
$546$	0.848429	−	0.432879i	0.0363094	−	0.0185255i
$547$	1.03614	−	1.50111i	0.0443022	−	0.0641829i	−0.800207	−	0.599724i	$-0.795277\pi$
$547$	1.03614	−	1.50111i	0.0443022	−	0.0641829i	0.844509	+	0.535541i	$0.179892\pi$
$548$	−6.26652	+	11.9399i	−0.267692	+	0.510045i
$549$	12.0211	+	31.6970i	0.513048	+	1.35280i
$550$	0.0753057	−	0.620198i	0.00321104	−	0.0264453i
$551$	−8.06192	+	5.56474i	−0.343449	+	0.237066i
$552$	3.94355	−	15.9996i	0.167849	−	0.680989i
$553$	0.226361	−	0.156246i	0.00962584	−	0.00664424i
$554$	−6.23613	+	2.36505i	−0.264948	+	0.100482i
$555$	−16.1928	−	42.6969i	−0.687345	−	1.81238i
$556$	5.23347	−	2.74674i	0.221949	−	0.116488i
$557$	−8.56025	−	16.3102i	−0.362709	−	0.691085i	0.633896	−	0.773419i	$-0.281455\pi$
$557$	−8.56025	−	16.3102i	−0.362709	−	0.691085i	−0.996605	+	0.0823339i	$0.973763\pi$
$558$	−26.1097	−	6.43546i	−1.10531	−	0.272435i
$559$	43.5823	+	0.502854i	1.84333	+	0.0212685i
$560$	1.25193	−	0.308573i	0.0529036	−	0.0130396i
$561$	12.1855	+	13.7546i	0.514472	+	0.580719i
$562$	−1.22499	−	10.0887i	−0.0516731	−	0.425567i
$563$	18.9021	−	9.92058i	0.796628	−	0.418103i	−0.0167344	−	0.999860i	$-0.505327\pi$
$563$	18.9021	−	9.92058i	0.796628	−	0.418103i	0.813362	+	0.581757i	$0.197635\pi$
$564$	16.1516	−	30.7744i	0.680107	−	1.29583i
$565$	−22.9652	−	8.70954i	−0.966152	−	0.366413i
$566$	3.32826	+	3.75683i	0.139897	+	0.157911i
$567$	−4.72950	−	0.574265i	−0.198620	−	0.0241169i
$568$	−13.9330	−	3.43417i	−0.584615	−	0.144095i
$569$	5.39313	−	4.77790i	0.226092	−	0.200300i	−0.542470	−	0.840075i	$-0.682511\pi$
$569$	5.39313	−	4.77790i	0.226092	−	0.200300i	0.768562	+	0.639775i	$0.220972\pi$
$570$	5.43358	−	6.13325i	0.227588	−	0.256894i
$571$	−20.8456	+	10.9406i	−0.872363	+	0.457852i	−0.840608	−	0.541644i	$-0.817802\pi$
$571$	−20.8456	+	10.9406i	−0.872363	+	0.457852i	−0.0317553	+	0.999496i	$0.510110\pi$
$572$	−6.60926	−	7.63602i	−0.276347	−	0.319278i
$573$	2.64724	+	1.38938i	0.110590	+	0.0580421i
$574$	−0.651703	+	0.247159i	−0.0272016	+	0.0103162i
$575$	0.429129	−	3.53420i	0.0178959	−	0.147386i
$576$	29.4363	+	15.4494i	1.22651	+	0.643723i
$577$		−	10.2244i		−	0.425645i	−0.977091	−	0.212823i	$-0.931734\pi$
$577$		−	10.2244i		−	0.425645i	0.977091	−	0.212823i	$-0.0682657\pi$
$578$	−0.512071	+	0.975669i	−0.0212993	+	0.0405825i
$579$	20.4249	−	23.0550i	0.848831	−	0.958132i
$580$	−9.05650	−	6.25125i	−0.376051	−	0.259569i
$581$	1.24141	−	1.09980i	0.0515025	−	0.0456272i
$582$	−6.31987	+	9.15592i	−0.261967	+	0.379525i
$583$	0.519652	+	0.197078i	0.0215218	+	0.00816213i
$584$	4.69890	−	12.3900i	0.194442	−	0.512701i
$585$	−52.0888	−	6.93544i	−2.15360	−	0.286745i
$586$	1.47524	+	3.88990i	0.0609417	+	0.160690i
$587$			45.5303i			1.87924i	0.342222	+	0.939619i	$0.388821\pi$
$587$			45.5303i			1.87924i	−0.342222	+	0.939619i	$0.611179\pi$
$588$	14.6352	−	38.5899i	0.603547	−	1.59142i
$589$	−3.67775	−	30.2890i	−0.151539	−	1.24804i
$590$	3.67984	+	7.01136i	0.151497	+	0.288653i
$591$	−61.5590	−	42.4911i	−2.53220	−	1.74785i
$592$	−18.2264	−	12.5808i	−0.749101	−	0.517067i
$593$	−2.72990	−	5.20139i	−0.112104	−	0.213596i	0.822940	−	0.568128i	$-0.192332\pi$
$593$	−2.72990	−	5.20139i	−0.112104	−	0.213596i	−0.935044	+	0.354533i	$0.884640\pi$
$594$	−0.999945	−	8.23528i	−0.0410282	−	0.337898i
$595$	0.555878	−	1.46573i	0.0227888	−	0.0600891i
$596$			35.9365i			1.47202i
$597$	−17.4730	−	46.0726i	−0.715123	−	1.88562i
$598$	3.14543	+	3.63407i	0.128626	+	0.148608i
$599$	−10.3888	+	27.3929i	−0.424473	+	1.11924i	0.536816	+	0.843700i	$0.319627\pi$
$599$	−10.3888	+	27.3929i	−0.424473	+	1.11924i	−0.961289	+	0.275544i	$0.911142\pi$
$600$	−4.75876	−	1.80476i	−0.194275	−	0.0736790i
$601$	−5.31275	+	7.69685i	−0.216712	+	0.313961i	−0.916229	−	0.400654i	$-0.868783\pi$
$601$	−5.31275	+	7.69685i	−0.216712	+	0.313961i	0.699518	+	0.714615i	$0.253398\pi$
$602$	0.743635	−	0.658803i	0.0303083	−	0.0268508i
$603$	60.3309	+	41.6434i	2.45686	+	1.69585i
$604$	4.81847	−	5.43893i	0.196061	−	0.221307i
$605$	8.03445	−	15.3084i	0.326647	−	0.622373i
$606$			4.22355i			0.171570i
$607$	−19.2553	−	10.1060i	−0.781549	−	0.410188i	0.0262436	−	0.999656i	$-0.491645\pi$
$607$	−19.2553	−	10.1060i	−0.781549	−	0.410188i	−0.807792	+	0.589467i	$0.799338\pi$
$608$	1.66798	−	13.7370i	0.0676454	−	0.557110i
$609$	1.88678	−	0.715561i	0.0764562	−	0.0289960i
$610$	3.19528	+	1.67701i	0.129373	+	0.0679002i
$611$	9.59890	+	18.8135i	0.388330	+	0.761114i
$612$	45.1462	−	23.6945i	1.82493	−	0.957795i
$613$	16.8625	−	19.0338i	0.681071	−	0.768770i	−0.301739	−	0.953391i	$-0.597567\pi$
$613$	16.8625	−	19.0338i	0.681071	−	0.768770i	0.982810	+	0.184621i	$0.0591056\pi$
$614$	−9.69833	+	8.59197i	−0.391393	+	0.346744i
$615$	52.6130	+	12.9679i	2.12156	+	0.522918i
$616$	−0.476127	−	0.0578123i	−0.0191837	−	0.00232932i
$617$	1.80745	+	2.04019i	0.0727652	+	0.0821349i	0.783766	−	0.621056i	$-0.213296\pi$
$617$	1.80745	+	2.04019i	0.0727652	+	0.0821349i	−0.711001	+	0.703191i	$0.751758\pi$
$618$	0.374748	+	0.142123i	0.0150746	+	0.00571703i
$619$	12.0880	−	23.0318i	0.485858	−	0.925726i	−0.511915	−	0.859036i	$-0.671064\pi$
$619$	12.0880	−	23.0318i	0.485858	−	0.925726i	0.997774	−	0.0666899i	$-0.0212438\pi$
$620$	30.3495	−	15.9287i	1.21887	−	0.639710i
$621$	−5.69818	−	46.9287i	−0.228660	−	1.88319i
$622$	−6.86274	−	7.74643i	−0.275171	−	0.310603i
$623$	1.48252	−	0.365408i	0.0593958	−	0.0146397i
$624$	−31.9903	+	16.3218i	−1.28064	+	0.653397i
$625$	18.1152	+	4.46500i	0.724609	+	0.178600i
$626$	1.07301	+	2.04445i	0.0428860	+	0.0817125i
$627$	14.1065	−	7.40364i	0.563358	−	0.295673i
$628$	−0.264915	−	0.698525i	−0.0105713	−	0.0278742i
$629$	−25.1755	+	9.54780i	−1.00381	+	0.380696i
$630$	−0.985767	+	0.680426i	−0.0392739	+	0.0271088i
$631$	−2.09727	+	8.50898i	−0.0834912	+	0.338737i	−0.997801	−	0.0662781i	$-0.978888\pi$
$631$	−2.09727	+	8.50898i	−0.0834912	+	0.338737i	0.914310	+	0.405015i	$0.132734\pi$
$632$	1.63290	−	1.12711i	0.0649533	−	0.0448340i
$633$	−6.95995	+	57.3203i	−0.276633	+	2.27828i
$634$	2.96839	+	7.82700i	0.117890	+	0.310850i
$635$	−4.91662	+	9.36784i	−0.195110	+	0.371752i
$636$	1.23441	−	1.78836i	0.0489476	−	0.0709129i
$637$	14.0085	+	20.8042i	0.555036	+	0.824291i
$638$	1.01506	+	1.47057i	0.0401867	+	0.0582204i
$639$	−69.1693	+	8.39868i	−2.73630	+	0.332247i
$640$	19.7899	−	4.87777i	0.782264	−	0.192811i
$641$	−27.2313	+	39.4514i	−1.07557	+	1.55824i	−0.272687	+	0.962103i	$0.587912\pi$
$641$	−27.2313	+	39.4514i	−1.07557	+	1.55824i	−0.802886	+	0.596133i	$0.796703\pi$
$642$	15.8841	−	17.9294i	0.626894	−	0.707617i
$643$	−6.10743	−	11.6367i	−0.240854	−	0.458908i	0.734783	−	0.678303i	$-0.237284\pi$
$643$	−6.10743	−	11.6367i	−0.240854	−	0.458908i	−0.975636	+	0.219395i	$0.929592\pi$
$644$	−1.30223	−	0.158119i	−0.0513149	−	0.00623076i
$645$	−76.6749	+	9.31001i	−3.01907	+	0.366581i
$646$	−3.61637	−	3.20382i	−0.142284	−	0.126053i
$647$	−23.2651	−	33.7053i	−0.914645	−	1.32509i	−0.945519	−	0.325568i	$-0.894444\pi$
$647$	−23.2651	−	33.7053i	−0.914645	−	1.32509i	0.0308738	−	0.999523i	$-0.490171\pi$
$648$	−34.1172	−	4.14258i	−1.34025	−	0.162736i
$649$	1.85572	+	15.2832i	0.0728435	+	0.599920i
$650$	1.23133	−	0.829113i	0.0482966	−	0.0325205i
$651$	−0.757595	+	6.23935i	−0.0296925	+	0.244540i
$652$	2.45043	−	9.94179i	0.0959662	−	0.389350i
$653$	−12.5130			−0.489671			−0.244835	−	0.969565i	$-0.578734\pi$
$653$	−12.5130			−0.489671			−0.244835	+	0.969565i	$0.578734\pi$
$654$	−10.4574			−0.408919
$655$	−5.81980	+	23.6118i	−0.227398	+	0.922591i
$656$	24.5727	−	9.31919i	0.959402	−	0.363853i
$657$		−	64.3416i		−	2.51021i
$658$	0.450145	+	0.170717i	0.0175485	+	0.00665526i
$659$	22.4142	−	5.52460i	0.873133	−	0.215208i	0.222806	−	0.974863i	$-0.428478\pi$
$659$	22.4142	−	5.52460i	0.873133	−	0.215208i	0.650326	+	0.759655i	$0.274632\pi$
$660$	13.3959	+	11.8677i	0.521434	+	0.461950i
$661$	−9.36591	−	37.9990i	−0.364292	−	1.47799i	−0.811920	−	0.583769i	$-0.801577\pi$
$661$	−9.36591	−	37.9990i	−0.364292	−	1.47799i	0.447628	−	0.894220i	$-0.352269\pi$
$662$	2.24624	+	1.98999i	0.0873025	+	0.0773433i
$663$	−5.76263	+	43.2803i	−0.223802	+	1.68087i
$664$	8.95519	−	7.93361i	0.347529	−	0.307884i
$665$	−1.11848	−	0.772031i	−0.0433728	−	0.0299381i
$666$	19.9756	+	4.92354i	0.774039	+	0.190783i
$667$	5.78432	+	8.38004i	0.223970	+	0.324476i
$668$	1.06931	+	4.33835i	0.0413727	+	0.167856i
$669$	7.78046	+	31.5666i	0.300810	+	1.22043i
$670$	7.74663	−	0.940611i	0.299278	−	0.0363390i
$671$	4.65259	+	5.25168i	0.179611	+	0.202739i
$672$	−1.01081	+	2.66529i	−0.0389929	+	0.102816i
$673$	1.72560	+	0.905665i	0.0665170	+	0.0349108i	0.497654	−	0.867376i	$-0.334195\pi$
$673$	1.72560	+	0.905665i	0.0665170	+	0.0349108i	−0.431137	+	0.902287i	$0.641887\pi$
$674$	−1.81374	+	1.25193i	−0.0698627	+	0.0482227i
$675$	−14.6007			−0.561982
$676$	3.44125	−	23.7479i	0.132356	−	0.913382i
$677$	−7.04764			−0.270863			−0.135431	−	0.990787i	$-0.543242\pi$
$677$	−7.04764			−0.270863			−0.135431	+	0.990787i	$0.543242\pi$
$678$	12.8332	−	8.85814i	0.492858	−	0.340195i
$679$	1.63389	+	0.857530i	0.0627028	+	0.0329090i
$680$	4.00994	−	10.5733i	0.153774	−	0.405469i
$681$	−13.3165	−	15.0312i	−0.510289	−	0.575997i
$682$	−5.52500	+	0.670856i	−0.211563	+	0.0256884i
$683$	1.33404	+	5.41243i	0.0510458	+	0.207101i	0.990927	−	0.134400i	$-0.0429108\pi$
$683$	1.33404	+	5.41243i	0.0510458	+	0.207101i	−0.939881	+	0.341501i	$0.889065\pi$
$684$	−10.5786	−	42.9189i	−0.404482	−	1.64105i
$685$	8.24916	+	11.9510i	0.315184	+	0.456623i
$686$	1.11367	+	0.274494i	0.0425199	+	0.0104802i
$687$	−8.41451	−	5.80811i	−0.321033	−	0.221593i
$688$	−28.0390	+	24.8404i	−1.06898	+	0.947031i
$689$	0.453992	+	1.24004i	0.0172957	+	0.0472419i
$690$	−6.37526	−	5.64799i	−0.242702	−	0.215015i
$691$	10.8782	+	44.1347i	0.413827	+	1.67896i	0.694765	+	0.719237i	$0.255509\pi$
$691$	10.8782	+	44.1347i	0.413827	+	1.67896i	−0.280937	+	0.959726i	$0.590645\pi$
$692$	−1.85436	−	1.64282i	−0.0704921	−	0.0624505i
$693$	−2.26118	+	0.557330i	−0.0858951	+	0.0211712i
$694$	3.58322	+	1.35893i	0.136017	+	0.0515845i
$695$		−	6.36507i		−	0.241441i
$696$	13.6107	−	5.16185i	0.515911	−	0.195659i
$697$	7.64633	−	31.0224i	0.289625	−	1.17506i
$698$	7.04637			0.266709
$699$	35.2755			1.33424
$700$	−0.0969601	+	0.393383i	−0.00366475	+	0.0148685i
$701$	−3.29255	+	27.1166i	−0.124358	+	1.02418i	0.788253	+	0.615352i	$0.210986\pi$
$701$	−3.29255	+	27.1166i	−0.124358	+	1.02418i	−0.912611	+	0.408829i	$0.865937\pi$
$702$	13.2403	−	14.6023i	0.499724	−	0.551128i
$703$	2.81371	+	23.1730i	0.106121	+	0.873987i
$704$	6.83030	+	0.829348i	0.257426	+	0.0312572i
$705$	−21.2618	−	30.8030i	−0.800766	−	1.16011i
$706$	−7.86289	−	6.96592i	−0.295924	−	0.262166i
$707$	0.695415	−	0.0844386i	0.0261538	−	0.00317564i
$708$	59.7565	+	7.25575i	2.24579	+	0.272688i
$709$	5.41246	+	10.3126i	0.203269	+	0.387297i	0.965656	−	0.259825i	$-0.0836648\pi$
$709$	5.41246	+	10.3126i	0.203269	+	0.387297i	−0.762387	+	0.647122i	$0.775973\pi$
$710$	−4.91845	+	5.55178i	−0.184586	+	0.208355i
$711$	5.47277	−	7.92867i	0.205245	−	0.297348i
$712$	10.6944	−	2.63594i	0.400791	−	0.0987861i
$713$	−31.4842	+	3.82287i	−1.17909	+	0.143168i
$714$	0.565363	+	0.819069i	0.0211582	+	0.0306529i
$715$	−10.5891	+	2.48075i	−0.396010	+	0.0927746i
$716$	−17.5326	+	25.4003i	−0.655222	+	0.949253i
$717$	29.5421	−	56.2878i	1.10327	−	2.10210i
$718$	−1.81997	−	4.79887i	−0.0679208	−	0.179092i
$719$	−3.63029	+	29.8981i	−0.135387	+	1.11501i	0.753682	+	0.657239i	$0.228276\pi$
$719$	−3.63029	+	29.8981i	−0.135387	+	1.11501i	−0.889069	+	0.457773i	$0.848647\pi$
$720$	37.1686	−	25.6557i	1.38519	−	0.956130i
$721$	0.0159087	−	0.0645442i	0.000592472	−	0.00240375i
$722$	2.69219	−	1.85828i	0.100193	−	0.0691581i
$723$	−3.99215	+	1.51402i	−0.148470	+	0.0563071i
$724$	16.1766	+	42.6542i	0.601199	+	1.58523i
$725$	2.78471	−	1.46153i	0.103421	−	0.0542797i
$726$	5.10094	+	9.71904i	0.189314	+	0.360707i
$727$	−18.3976	−	4.53459i	−0.682328	−	0.168179i	−0.117108	−	0.993119i	$-0.537362\pi$
$727$	−18.3976	−	4.53459i	−0.682328	−	0.168179i	−0.565219	+	0.824941i	$0.691209\pi$
$728$	−0.636511	−	0.945291i	−0.0235907	−	0.0350348i
$729$	−31.6603	+	7.80355i	−1.17260	+	0.289020i
$730$	−4.54181	−	5.12664i	−0.168100	−	0.189745i
$731$	5.48949	+	45.2100i	0.203036	+	1.67215i
$732$	24.2905	−	12.7486i	0.897803	−	0.471204i
$733$	19.0101	−	36.2207i	0.702155	−	1.33784i	−0.229074	−	0.973409i	$-0.573570\pi$
$733$	19.0101	−	36.2207i	0.702155	−	1.33784i	0.931229	−	0.364435i	$-0.118738\pi$
$734$	−2.88550	−	1.09433i	−0.106506	−	0.0403923i
$735$	−29.4733	−	33.2685i	−1.08714	−	1.22713i
$736$	−14.2791	−	1.73379i	−0.526334	−	0.0639085i
$737$	14.7314	+	3.63095i	0.542637	+	0.133748i
$738$	−18.2738	+	16.1891i	−0.672667	+	0.595931i
$739$	−6.38719	+	7.20964i	−0.234956	+	0.265211i	−0.854149	−	0.520028i	$-0.825921\pi$
$739$	−6.38719	+	7.20964i	−0.234956	+	0.265211i	0.619193	+	0.785239i	$0.287460\pi$
$740$	−23.2193	+	12.1865i	−0.853560	+	0.447983i
$741$	35.2366	+	13.8306i	1.29445	+	0.508078i
$742$	0.0266527	+	0.0139884i	0.000978450	+	0.000513530i
$743$	−5.96460	+	2.26207i	−0.218820	+	0.0829875i	−0.461579	−	0.887099i	$-0.652717\pi$
$743$	−5.96460	+	2.26207i	−0.218820	+	0.0829875i	0.242759	+	0.970087i	$0.421948\pi$
$744$	−5.46506	+	45.0088i	−0.200359	+	1.65010i
$745$	34.2676	+	17.9850i	1.25547	+	0.658920i
$746$			10.5349i			0.385709i
$747$	26.9968	−	51.4381i	0.987760	−	1.88202i
$748$	6.99760	−	7.89866i	0.255858	−	0.288803i
$749$	−3.26966	−	2.25689i	−0.119471	−	0.0824648i
$750$	−11.3579	+	10.0622i	−0.414732	+	0.367420i
$751$	−6.94446	+	10.0608i	−0.253407	+	0.367124i	−0.928955	−	0.370192i	$-0.879292\pi$
$751$	−6.94446	+	10.0608i	−0.253407	+	0.367124i	0.675548	+	0.737316i	$0.263907\pi$
$752$	−16.9728	−	6.43695i	−0.618936	−	0.234732i
$753$	14.6003	−	38.4978i	0.532065	−	1.40294i
$754$	−1.06356	+	4.11035i	−0.0387326	+	0.149690i
$755$	−2.77486	−	7.31669i	−0.100987	−	0.266282i
$756$			5.37985i			0.195663i
$757$	16.1743	−	42.6482i	0.587866	−	1.55007i	−0.229109	−	0.973401i	$-0.573581\pi$
$757$	16.1743	−	42.6482i	0.587866	−	1.55007i	0.816974	−	0.576674i	$-0.195650\pi$
$758$	−0.627774	−	5.17019i	−0.0228018	−	0.187790i
$759$	−7.69579	−	14.6631i	−0.279339	−	0.532237i
$760$	−8.06838	−	5.56920i	−0.292671	−	0.202016i
$761$	−20.6785	−	14.2733i	−0.749595	−	0.517408i	0.130940	−	0.991390i	$-0.458201\pi$
$761$	−20.6785	−	14.2733i	−0.749595	−	0.517408i	−0.880534	+	0.473983i	$0.842816\pi$
$762$	−3.12149	−	5.94750i	−0.113080	−	0.215455i
$763$	0.209069	+	1.72184i	0.00756880	+	0.0623347i
$764$	0.608803	−	1.60528i	0.0220257	−	0.0580771i
$765$		−	54.9078i		−	1.98520i
$766$	1.53564	+	4.04915i	0.0554849	+	0.146302i
$767$	−24.5717	+	27.0993i	−0.887233	+	0.978499i
$768$	5.74764	−	15.1553i	0.207400	−	0.546869i
$769$	8.80025	+	3.33750i	0.317345	+	0.120353i	0.508134	−	0.861278i	$-0.330335\pi$
$769$	8.80025	+	3.33750i	0.317345	+	0.120353i	−0.190789	+	0.981631i	$0.561105\pi$
$770$	−0.140826	+	0.204021i	−0.00507501	+	0.00735242i
$771$	19.2064	−	17.0154i	0.691702	−	0.612795i
$772$	−14.5567	−	10.0478i	−0.523908	−	0.361628i
$773$	−15.7161	+	17.7398i	−0.565269	+	0.638056i	−0.959753	−	0.280846i	$-0.909385\pi$
$773$	−15.7161	+	17.7398i	−0.565269	+	0.638056i	0.394484	+	0.918903i	$0.370923\pi$
$774$	16.1717	−	30.8126i	0.581279	−	1.10754i
$775$			9.79553i			0.351866i
$776$	11.7864	+	6.18597i	0.423106	+	0.222063i
$777$	0.579609	−	4.77351i	0.0207934	−	0.171249i
$778$	−9.02948	+	3.42443i	−0.323723	+	0.122772i
$779$	−24.5274	−	12.8730i	−0.878784	−	0.461222i
$780$	−0.490607	+	42.5208i	−0.0175666	+	1.52249i
$781$	−12.7691	+	6.70174i	−0.456914	+	0.239807i
$782$	−3.33024	+	3.75907i	−0.119089	+	0.134424i
$783$	31.2578	−	27.6920i	1.11706	−	0.989632i
$784$	−20.9296	−	5.15869i	−0.747487	−	0.184239i
$785$	−0.798665	−	0.0969755i	−0.0285056	−	0.00346120i
$786$	−10.2382	−	11.5566i	−0.365186	−	0.412209i
$787$	4.67537	+	1.77313i	0.166659	+	0.0632054i	0.436523	−	0.899693i	$-0.356210\pi$
$787$	4.67537	+	1.77313i	0.166659	+	0.0632054i	−0.269864	+	0.962898i	$0.586979\pi$
$788$	−19.9618	+	38.0341i	−0.711111	+	1.35491i
$789$	−42.7773	+	22.4512i	−1.52291	+	0.799285i
$790$	−0.123615	−	1.01806i	−0.00439802	−	0.0362210i
$791$	−1.71508	−	1.93592i	−0.0609811	−	0.0688334i
$792$	−16.3115	+	4.02042i	−0.579603	+	0.142859i
$793$	−2.20025	+	16.5250i	−0.0781331	+	0.586820i
$794$	−7.36171	−	1.81450i	−0.261257	−	0.0643941i
$795$	−1.08752	−	2.07209i	−0.0385703	−	0.0734896i
$796$	−25.0551	+	13.1499i	−0.888055	+	0.466087i
$797$	10.3448	+	27.2770i	0.366432	+	0.966202i	0.983759	+	0.179495i	$0.0574464\pi$
$797$	10.3448	+	27.2770i	0.366432	+	0.966202i	−0.617327	+	0.786707i	$0.711784\pi$
$798$	0.806772	−	0.305968i	0.0285594	−	0.0108312i
$799$	−18.1625	+	12.5367i	−0.642543	+	0.443515i
$800$	−1.06318	+	4.31349i	−0.0375891	+	0.152505i
$801$	44.0146	−	30.3811i	1.55518	−	1.07346i
$802$	1.64198	−	13.5229i	0.0579803	−	0.477511i
$803$	−4.72213	−	12.4512i	−0.166640	−	0.439395i
$804$	27.5685	−	52.5274i	0.972266	−	1.85250i
$805$	−0.802495	+	1.16261i	−0.0282842	+	0.0409768i
$806$	−9.79657	−	8.88284i	−0.345070	−	0.312885i
$807$	49.1283	+	71.1746i	1.72940	+	2.50546i
$808$	5.01652	−	0.609115i	0.176480	−	0.0214286i
$809$	0.0554845	−	0.0136757i	0.00195073	−	0.000480812i	−0.238340	−	0.971182i	$-0.576603\pi$
$809$	0.0554845	−	0.0136757i	0.00195073	−	0.000480812i	0.240291	+	0.970701i	$0.422757\pi$
$810$	−10.0910	+	14.6193i	−0.354561	+	0.513670i
$811$	14.6521	−	16.5388i	0.514506	−	0.580757i	−0.432638	−	0.901568i	$-0.642417\pi$
$811$	14.6521	−	16.5388i	0.514506	−	0.580757i	0.947143	+	0.320811i	$0.103955\pi$
$812$	−0.538521	−	1.02607i	−0.0188984	−	0.0360078i
$813$	−44.6249	−	5.41844i	−1.56506	−	0.190033i
$814$	4.22698	−	0.513248i	0.148156	−	0.0179893i
$815$	−8.25371	−	7.31215i	−0.289115	−	0.256134i
$816$	−21.3172	−	30.8833i	−0.746250	−	1.08113i
$817$	39.1956	+	4.75920i	1.37128	+	0.166503i
$818$	0.523691	+	4.31298i	0.0183104	+	0.150800i
$819$	−4.51740	−	3.19571i	−0.157851	−	0.111667i
$820$	3.75081	−	30.8907i	0.130984	−	1.07875i
$821$	−5.90447	+	23.9554i	−0.206067	+	0.836048i	0.773313	+	0.634024i	$0.218598\pi$
$821$	−5.90447	+	23.9554i	−0.206067	+	0.836048i	−0.979381	+	0.202024i	$0.935248\pi$
$822$	−9.21949			−0.321567
$823$	15.2073			0.530092			0.265046	−	0.964236i	$-0.414613\pi$
$823$	15.2073			0.530092			0.265046	+	0.964236i	$0.414613\pi$
$824$	0.114761	−	0.465603i	0.00399788	−	0.0162200i
$825$	−4.78229	+	1.81368i	−0.166498	+	0.0631443i
$826$			0.833823i			0.0290124i
$827$	34.8203	+	13.2056i	1.21082	+	0.459203i	0.875646	−	0.482953i	$-0.160436\pi$
$827$	34.8203	+	13.2056i	1.21082	+	0.459203i	0.335174	+	0.942156i	$0.391205\pi$
$828$	−44.6125	+	10.9960i	−1.55039	+	0.382137i
$829$	2.20630	+	1.95461i	0.0766280	+	0.0678865i	0.700567	−	0.713586i	$-0.252930\pi$
$829$	2.20630	+	1.95461i	0.0766280	+	0.0678865i	−0.623939	+	0.781473i	$0.714469\pi$
$830$	−1.47990	−	6.00418i	−0.0513680	−	0.208408i
$831$	40.8698	+	36.2075i	1.41776	+	1.25602i
$832$	9.13109	+	13.5607i	0.316564	+	0.470133i
$833$	−19.6162	+	17.3784i	−0.679661	+	0.602127i
$834$	3.32575	+	2.29560i	0.115161	+	0.0794900i
$835$	4.67202	+	1.15155i	0.161682	+	0.0398510i
$836$	−5.19703	−	7.52920i	−0.179743	−	0.260403i
$837$	31.1277	+	126.290i	1.07593	+	4.36523i
$838$	0.553584	+	2.24598i	0.0191232	+	0.0775860i
$839$	1.40956	−	0.171151i	0.0486633	−	0.00590879i	−0.0961688	−	0.995365i	$-0.530659\pi$
$839$	1.40956	−	0.171151i	0.0486633	−	0.00590879i	0.144832	+	0.989456i	$0.453736\pi$
$840$	1.33920	+	1.51164i	0.0462067	+	0.0521565i
$841$	7.09389	−	18.7051i	0.244617	−	0.645002i
$842$	1.20061	+	0.630128i	0.0413757	+	0.0217156i
$843$	−68.4720	+	47.2628i	−2.35830	+	1.62782i
$844$	33.1583			1.14136
$845$	−20.9228	−	15.1665i	−0.719766	−	0.521742i
$846$	16.8629			0.579758
$847$	1.49828	−	1.03419i	0.0514814	−	0.0355350i
$848$	−1.00495	−	0.527437i	−0.0345100	−	0.0181122i
$849$	14.5706	−	38.4194i	0.500060	−	1.31855i
$850$	1.02857	+	1.16101i	0.0352796	+	0.0398225i
$851$	24.0874	−	2.92474i	0.825706	−	0.100259i
$852$	13.4938	+	54.7464i	0.462289	+	1.87558i
$853$	3.48076	+	14.1220i	0.119179	+	0.483527i	0.999950	+	0.00998564i	$0.00317858\pi$
$853$	3.48076	+	14.1220i	0.119179	+	0.483527i	−0.880771	+	0.473542i	$0.842975\pi$
$854$	0.215863	+	0.312732i	0.00738669	+	0.0107015i
$855$	−46.2199	−	11.3922i	−1.58069	−	0.389605i
$856$	−23.5864	−	16.2805i	−0.806166	−	0.556456i
$857$	15.0647	−	13.3461i	0.514599	−	0.455895i	−0.365414	−	0.930845i	$-0.619072\pi$
$857$	15.0647	−	13.3461i	0.514599	−	0.455895i	0.880013	+	0.474950i	$0.157534\pi$
$858$	2.52283	−	6.42749i	0.0861279	−	0.219431i
$859$	6.67350	+	5.91220i	0.227697	+	0.201722i	0.769256	−	0.638941i	$-0.220627\pi$
$859$	6.67350	+	5.91220i	0.227697	+	0.201722i	−0.541559	+	0.840663i	$0.682166\pi$
$860$	10.6147	+	43.0656i	0.361959	+	1.46852i
$861$	4.27107	+	3.78384i	0.145558	+	0.128953i
$862$	−12.9266	+	3.18613i	−0.440282	+	0.108520i
$863$	18.2022	+	6.90320i	0.619611	+	0.234988i	0.644380	−	0.764706i	$-0.277116\pi$
$863$	18.2022	+	6.90320i	0.619611	+	0.234988i	−0.0247685	+	0.999693i	$0.507885\pi$
$864$			58.9908i			2.00691i
$865$	−2.49456	+	0.946063i	−0.0848177	+	0.0321671i
$866$	1.57715	−	6.39875i	0.0535938	−	0.217438i
$867$	9.02077			0.306361
$868$	3.60931			0.122508
$869$	0.477179	−	1.93599i	0.0161872	−	0.0656740i
$870$	0.906908	−	7.46906i	0.0307471	−	0.253225i
$871$	16.3839	+	32.1120i	0.555149	+	1.08807i
$872$	1.50816	+	12.4208i	0.0510728	+	0.420622i
$873$	64.1617	+	7.79064i	2.17154	+	0.263673i
$874$	2.47333	+	3.58324i	0.0836616	+	0.121205i
$875$	1.88383	+	1.66893i	0.0636852	+	0.0564202i
$876$	−51.6874	+	6.27599i	−1.74636	+	0.212046i
$877$	−51.5125	−	6.25475i	−1.73945	−	0.211208i	−0.811615	−	0.584192i	$-0.801411\pi$
$877$	−51.5125	−	6.25475i	−1.73945	−	0.211208i	−0.927838	+	0.372985i	$0.878334\pi$
$878$	−0.370507	−	0.705942i	−0.0125040	−	0.0238244i
$879$	22.5850	−	25.4932i	0.761775	−	0.859866i
$880$	5.30988	−	7.69269i	0.178996	−	0.259320i
$881$	3.39245	−	0.836165i	0.114295	−	0.0281711i	−0.181753	−	0.983344i	$-0.558177\pi$
$881$	3.39245	−	0.836165i	0.114295	−	0.0281711i	0.296048	+	0.955173i	$0.404331\pi$
$882$	19.8786	−	2.41370i	0.669349	−	0.0812737i
$883$	1.58430	+	2.29526i	0.0533161	+	0.0772417i	0.848735	−	0.528818i	$-0.177365\pi$
$883$	1.58430	+	2.29526i	0.0533161	+	0.0772417i	−0.795419	+	0.606060i	$0.792749\pi$
$884$	25.0717	+	0.289278i	0.843252	+	0.00972948i
$885$	36.8248	−	53.3500i	1.23785	−	1.79334i
$886$	−2.60832	+	4.96974i	−0.0876283	+	0.166962i
$887$	7.88866	+	20.8007i	0.264875	+	0.698419i	0.999795	+	0.0202642i	$0.00645075\pi$
$887$	7.88866	+	20.8007i	0.264875	+	0.698419i	−0.734919	+	0.678154i	$0.762780\pi$
$888$	4.18113	−	34.4347i	0.140309	−	1.15555i
$889$	−0.916860	+	0.632863i	−0.0307505	+	0.0212255i
$890$	1.36245	−	5.52766i	0.0456693	−	0.185288i
$891$	−28.4240	+	19.6197i	−0.952240	+	0.657284i
$892$	17.4566	−	6.62041i	0.584489	−	0.221668i
$893$	6.78470	+	17.8898i	0.227041	+	0.598659i
$894$	−21.7559	+	11.4184i	−0.727627	+	0.381888i
$895$	15.4462	+	29.4303i	0.516310	+	0.983746i
$896$	2.08393	+	0.513641i	0.0696191	+	0.0171596i
$897$	14.3763	−	36.6270i	0.480011	−	1.22294i
$898$	7.61776	−	1.87761i	0.254208	−	0.0626567i
$899$	−18.5784	−	20.9707i	−0.619624	−	0.699411i
$900$	1.71057	+	14.0878i	0.0570189	+	0.469593i
$901$	−1.22178	+	0.641237i	−0.0407032	+	0.0213627i
$902$	−2.34815	+	4.47403i	−0.0781848	+	0.148969i
$903$	−7.60482	−	2.88413i	−0.253073	−	0.0959778i
$904$	−12.3720	−	13.9652i	−0.411488	−	0.464474i
$905$	48.7691	+	5.92164i	1.62114	+	0.196842i
$906$	4.82373	+	1.18894i	0.160258	+	0.0395000i
$907$	−10.7200	+	9.49708i	−0.355951	+	0.315345i	−0.822080	−	0.569371i	$-0.807187\pi$
$907$	−10.7200	+	9.49708i	−0.355951	+	0.315345i	0.466129	+	0.884717i	$0.345648\pi$
$908$	−7.64708	+	8.63177i	−0.253777	+	0.286455i
$909$	21.7264	−	11.4029i	0.720620	−	0.378210i
$910$	−0.585521	+	0.0642493i	−0.0194098	+	0.00212984i
$911$	−34.8185	−	18.2742i	−1.15359	−	0.605450i	−0.224197	−	0.974544i	$-0.571976\pi$
$911$	−34.8185	−	18.2742i	−1.15359	−	0.605450i	−0.929392	+	0.369094i	$0.879668\pi$
$912$	−30.4196	+	11.5366i	−1.00729	+	0.382016i
$913$	1.44923	−	11.9355i	0.0479626	−	0.395008i
$914$	2.92103	+	1.53308i	0.0966192	+	0.0507097i
$915$		−	29.5427i		−	0.976651i
$916$	−2.72859	+	5.19889i	−0.0901550	+	0.171776i
$917$	−1.69812	+	1.91679i	−0.0560770	+	0.0632978i
$918$	16.9504	+	11.7000i	0.559446	+	0.386157i
$919$	21.4129	−	18.9702i	0.706348	−	0.625770i	−0.231492	−	0.972837i	$-0.574361\pi$
$919$	21.4129	−	18.9702i	0.706348	−	0.625770i	0.937840	+	0.347067i	$0.112822\pi$
$920$	−5.78896	+	8.38676i	−0.190856	+	0.276503i
$921$	99.1805	+	37.6142i	3.26811	+	1.23943i
$922$	−1.88998	+	4.98347i	−0.0622432	+	0.164122i
$923$	−31.8960	−	12.5194i	−1.04987	−	0.412079i
$924$	0.668278	+	1.76210i	0.0219847	+	0.0579690i
$925$		−	7.49421i		−	0.246408i
$926$	−3.51452	+	9.26702i	−0.115494	+	0.304533i
$927$	−0.280661	−	2.31145i	−0.00921812	−	0.0759181i
$928$	−5.90495	−	11.2509i	−0.193840	−	0.369330i
$929$	−0.841219	−	0.580651i	−0.0275995	−	0.0190505i	0.554185	−	0.832393i	$-0.313030\pi$
$929$	−0.841219	−	0.580651i	−0.0275995	−	0.0190505i	−0.581785	+	0.813343i	$0.697645\pi$
$930$	19.2864	+	13.3124i	0.632425	+	0.436532i
$931$	10.5588	+	20.1181i	0.346050	+	0.659343i
$932$	−2.44174	−	20.1095i	−0.0799817	−	0.658709i
$933$	−30.0439	+	79.2192i	−0.983593	+	2.59352i
$934$		−	3.99553i		−	0.130738i
$935$	−4.02977	−	10.6256i	−0.131788	−	0.347495i
$936$	−32.5872	−	23.0529i	−1.06515	−	0.753508i
$937$	−8.90615	+	23.4836i	−0.290951	+	0.767175i	0.707235	+	0.706978i	$0.249942\pi$
$937$	−8.90615	+	23.4836i	−0.290951	+	0.767175i	−0.998187	+	0.0601971i	$0.980827\pi$
$938$	0.768332	+	0.291390i	0.0250869	+	0.00951422i
$939$	10.7378	−	15.5564i	0.350414	−	0.507663i
$940$	−16.0882	+	14.2529i	−0.524738	+	0.464877i
$941$	−21.0563	−	14.5341i	−0.686416	−	0.473799i	0.173102	−	0.984904i	$-0.444621\pi$
$941$	−21.0563	−	14.5341i	−0.686416	−	0.473799i	−0.859518	+	0.511105i	$0.829236\pi$
$942$	0.338712	−	0.382327i	0.0110358	−	0.0124569i
$943$	−13.3809	+	25.4952i	−0.435743	+	0.830238i
$944$		−	31.4396i		−	1.02327i
$945$	5.13000	+	2.69243i	0.166879	+	0.0875848i
$946$	0.868124	−	7.14964i	0.0282251	−	0.232455i
$947$	41.8287	−	15.8635i	1.35925	−	0.515495i	0.436086	−	0.899905i	$-0.356364\pi$
$947$	41.8287	−	15.8635i	1.35925	−	0.515495i	0.923163	+	0.384410i	$0.125595\pi$
$948$	−6.90314	−	3.62305i	−0.224204	−	0.117671i
$949$	15.0266	−	27.8452i	0.487783	−	0.903894i
$950$	1.19072	−	0.624937i	0.0386320	−	0.0202756i
$951$	45.4442	−	51.2959i	1.47363	−	1.66338i
$952$	0.891313	−	0.789634i	0.0288876	−	0.0255922i
$953$	−52.4931	−	12.9384i	−1.70042	−	0.419115i	−0.734634	−	0.678464i	$-0.762646\pi$
$953$	−52.4931	−	12.9384i	−1.70042	−	0.419115i	−0.965784	+	0.259349i	$0.916492\pi$
$954$	1.04663	+	0.127084i	0.0338860	+	0.00411450i
$955$	−1.22604	−	1.38392i	−0.0396739	−	0.0447825i
$956$	−34.1328	−	12.9449i	−1.10393	−	0.418667i
$957$	6.79825	−	12.9530i	0.219756	−	0.418710i
$958$	−0.785871	+	0.412457i	−0.0253903	+	0.0133259i
$959$	0.184319	+	1.51800i	0.00595197	+	0.0490189i
$960$	−19.2115	−	21.6853i	−0.620048	−	0.699889i
$961$	54.6280	−	13.4646i	1.76219	−	0.434342i
$962$	7.49501	+	6.79595i	0.241649	+	0.219110i
$963$	−135.115	−	33.3029i	−4.35403	−	1.07317i
$964$	1.13943	+	2.17100i	0.0366986	+	0.0699233i
$965$	−16.8663	+	8.85212i	−0.542945	+	0.284960i
$966$	−0.318042	−	0.838607i	−0.0102328	−	0.0269817i
$967$	50.2651	−	19.0631i	1.61642	−	0.613026i	0.629899	−	0.776677i	$-0.283096\pi$
$967$	50.2651	−	19.0631i	1.61642	−	0.613026i	0.986518	+	0.163650i	$0.0523269\pi$
$968$	10.8081	−	7.46031i	0.347386	−	0.239783i
$969$	−9.46572	+	38.4039i	−0.304083	+	1.23371i
$970$	5.66224	−	3.90836i	0.181803	−	0.125490i
$971$	5.77919	−	47.5959i	0.185463	−	1.52743i	−0.541472	−	0.840719i	$-0.682133\pi$
$971$	5.77919	−	47.5959i	0.185463	−	1.52743i	0.726935	−	0.686706i	$-0.240944\pi$
$972$	20.5444	+	54.1712i	0.658963	+	1.73754i
$973$	0.311485	−	0.593484i	0.00998574	−	0.0190262i
$974$	3.80215	−	5.50836i	0.121829	−	0.176499i
$975$	−10.6948	−	5.77143i	−0.342509	−	0.184834i
$976$	−8.13919	−	11.7916i	−0.260529	−	0.377441i
$977$	−39.3694	+	4.78031i	−1.25954	+	0.152936i	−0.722946	−	0.690905i	$-0.757212\pi$
$977$	−39.3694	+	4.78031i	−1.25954	+	0.152936i	−0.536594	+	0.843841i	$0.680289\pi$
$978$	6.79734	−	1.67539i	0.217355	−	0.0535732i
$979$	6.28789	−	9.10958i	0.200962	−	0.291143i
$980$	−16.9252	+	19.1047i	−0.540657	+	0.610276i
$981$	28.2334	+	53.7943i	0.901424	+	1.71752i
$982$	−6.58819	−	0.799951i	−0.210238	−	0.0255275i
$983$	57.2871	−	6.95591i	1.82717	−	0.221859i	0.866431	−	0.499298i	$-0.166409\pi$
$983$	57.2871	−	6.95591i	1.82717	−	0.221859i	0.960743	+	0.277438i	$0.0894855\pi$
$984$	30.8103	+	27.2955i	0.982195	+	0.870149i
$985$	26.2775	+	38.0695i	0.837271	+	1.21300i
$986$	−4.40400	−	0.534743i	−0.140252	−	0.0170297i
$987$	−0.475073	−	3.91258i	−0.0151217	−	0.124539i
$988$	5.44534	−	21.0447i	0.173239	−	0.669520i
$989$	4.94700	−	40.7422i	0.157305	−	1.29553i
$990$	−2.07804	+	8.43095i	−0.0660445	+	0.267953i
$991$	−9.26828			−0.294417			−0.147208	−	0.989106i	$-0.547029\pi$
$991$	−9.26828			−0.294417			−0.147208	+	0.989106i	$0.547029\pi$
$992$	39.5765			1.25656
$993$	5.87945	−	23.8539i	0.186579	−	0.756980i
$994$	−0.730285	+	0.276961i	−0.0231632	+	0.00878466i
$995$			30.4726i			0.966046i
$996$	−43.9549	−	16.6699i	−1.39276	−	0.528206i
$997$	−32.6389	+	8.04476i	−1.03368	+	0.254780i	−0.719434	−	0.694561i	$-0.755599\pi$
$997$	−32.6389	+	8.04476i	−1.03368	+	0.254780i	−0.314249	+	0.949341i	$0.601753\pi$
$998$	−7.89128	−	6.99106i	−0.249794	−	0.221298i
$999$	−23.8147	−	96.6201i	−0.753464	−	3.05693i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.2.h.a.12.9	✓	168
169.155	even	26	inner	169.2.h.a.155.9	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
169.2.h.a.12.9	✓	168	1.1	even	1	trivial
169.2.h.a.155.9	yes	168	169.155	even	26	inner

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	169.h (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.323126 - 0.223038i) q^{2} +(-2.84614 - 1.49377i) q^{3} +(-0.654545 + 1.72589i) q^{4} +(1.31816 + 1.48790i) q^{5} +(-1.25283 + 0.152121i) q^{6} +(0.0500939 + 0.203239i) q^{7} +(0.361363 + 1.46611i) q^{8} +(4.16496 + 6.03399i) q^{9} +O(q^{10})\)	\(q+(0.323126 - 0.223038i) q^{2} +(-2.84614 - 1.49377i) q^{3} +(-0.654545 + 1.72589i) q^{4} +(1.31816 + 1.48790i) q^{5} +(-1.25283 + 0.152121i) q^{6} +(0.0500939 + 0.203239i) q^{7} +(0.361363 + 1.46611i) q^{8} +(4.16496 + 6.03399i) q^{9} +(0.757790 + 0.186779i) q^{10} +(1.24884 + 0.862010i) q^{11} +(4.44101 - 3.93439i) q^{12} +(0.393277 + 3.58404i) q^{13} +(0.0615167 + 0.0544990i) q^{14} +(-1.52910 - 6.20379i) q^{15} +(-2.31950 - 2.05490i) q^{16} +(-3.65796 + 0.901606i) q^{17} +(2.69162 + 1.02080i) q^{18} +3.26624i q^{19} +(-3.43075 + 1.30111i) q^{20} +(0.161018 - 0.653275i) q^{21} +0.595793 q^{22} +3.39512 q^{23} +(1.16154 - 4.71253i) q^{24} +(0.126396 - 1.04096i) q^{25} +(0.926454 + 1.07038i) q^{26} +(-1.67834 - 13.8224i) q^{27} +(-0.383558 - 0.0465723i) q^{28} +(1.70372 + 2.46826i) q^{29} +(-1.87777 - 1.66356i) q^{30} +(-9.27335 + 1.12599i) q^{31} +(-4.20576 - 0.510672i) q^{32} +(-2.26672 - 4.31887i) q^{33} +(-0.980890 + 1.10720i) q^{34} +(-0.236367 + 0.342437i) q^{35} +(-13.1402 + 3.23876i) q^{36} +(7.09471 - 0.861454i) q^{37} +(0.728495 + 1.05541i) q^{38} +(4.23440 - 10.7881i) q^{39} +(-1.70508 + 2.47024i) q^{40} +(-3.94122 + 7.50936i) q^{41} +(-0.0936760 - 0.247003i) q^{42} +(1.45709 - 12.0002i) q^{43} +(-2.30516 + 1.59114i) q^{44} +(-3.48786 + 14.1508i) q^{45} +(1.09705 - 0.757241i) q^{46} +(5.47719 - 2.07722i) q^{47} +(3.53208 + 9.31333i) q^{48} +(6.15940 - 3.23270i) q^{49} +(-0.191332 - 0.364553i) q^{50} +(11.7578 + 2.89805i) q^{51} +(-6.44309 - 1.66716i) q^{52} +(0.355608 - 0.0876496i) q^{53} +(-3.62523 - 4.09204i) q^{54} +(0.363587 + 2.99441i) q^{55} +(-0.279868 + 0.146886i) q^{56} +(4.87900 - 9.29616i) q^{57} +(1.10103 + 0.417566i) q^{58} +(6.72780 + 7.59412i) q^{59} +(11.7079 + 1.42160i) q^{60} +(4.48931 + 1.10651i) q^{61} +(-2.74532 + 2.43214i) q^{62} +(-1.01770 + 1.14875i) q^{63} +(4.01486 - 2.10716i) q^{64} +(-4.81428 + 5.30950i) q^{65} +(-1.69571 - 0.889976i) q^{66} +(9.34877 - 3.54552i) q^{67} +(0.838224 - 6.90339i) q^{68} +(-9.66299 - 5.07153i) q^{69} +0.163369i q^{70} +(-4.41645 + 8.41484i) q^{71} +(-7.34141 + 8.28674i) q^{72} +(-7.22221 - 4.98513i) q^{73} +(2.10035 - 1.86075i) q^{74} +(-1.91470 + 2.77392i) q^{75} +(-5.63718 - 2.13790i) q^{76} +(-0.112635 + 0.296994i) q^{77} +(-1.03792 - 4.43036i) q^{78} +(-0.465951 - 1.22861i) q^{79} -6.15988i q^{80} +(-8.07094 + 21.2813i) q^{81} +(0.401362 + 3.30551i) q^{82} +(-3.68213 - 7.01571i) q^{83} +(1.02209 + 0.705498i) q^{84} +(-6.16328 - 4.25421i) q^{85} +(-2.20568 - 4.20257i) q^{86} +(-1.16200 - 9.56996i) q^{87} +(-0.812515 + 2.14243i) q^{88} -7.29445i q^{89} +(2.02915 + 5.35042i) q^{90} +(-0.708716 + 0.259468i) q^{91} +(-2.22226 + 5.85962i) q^{92} +(28.0752 + 10.6475i) q^{93} +(1.30652 - 1.89283i) q^{94} +(-4.85983 + 4.30543i) q^{95} +(11.2074 + 7.73588i) q^{96} +(5.84568 - 6.59840i) q^{97} +(1.26925 - 2.41835i) q^{98} +11.1257i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9}+O(q^{10}) \) 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9	\( 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9} - 9 q^{10} - 13 q^{11} - 9 q^{12} + 52 q^{13} - 15 q^{14} + 39 q^{15} - 31 q^{16} - 11 q^{17} + 26 q^{18} - 13 q^{20} - 13 q^{21} - 6 q^{22} - 102 q^{23} - 91 q^{24} + 3 q^{25} - 13 q^{26} - 19 q^{27} - 13 q^{28} - 17 q^{29} + 23 q^{30} + 39 q^{31} - 13 q^{33} + 52 q^{34} - 21 q^{35} + 11 q^{36} - 13 q^{37} - 40 q^{38} - 65 q^{39} + 53 q^{40} - 13 q^{41} + 101 q^{42} - 3 q^{43} - 39 q^{44} - 78 q^{45} - 39 q^{46} - 39 q^{47} + 8 q^{48} + 85 q^{49} - 13 q^{50} + 62 q^{51} - 78 q^{52} + 18 q^{53} + 65 q^{54} - 103 q^{55} + 3 q^{56} + 65 q^{57} + 39 q^{58} + 91 q^{59} - 117 q^{60} - 23 q^{61} - 64 q^{62} - 78 q^{63} + 15 q^{64} - 13 q^{65} + 134 q^{66} - 65 q^{67} + 40 q^{68} - 40 q^{69} + 26 q^{71} + 156 q^{72} - 13 q^{73} - 53 q^{74} + 35 q^{75} + 221 q^{76} + 3 q^{77} - 143 q^{78} - 23 q^{79} - 43 q^{81} - 129 q^{82} + 117 q^{83} + 234 q^{84} + 26 q^{85} - 91 q^{86} + 79 q^{87} + 95 q^{88} + 17 q^{90} + 39 q^{91} - 89 q^{92} + 52 q^{93} - 61 q^{94} + 122 q^{95} - 182 q^{96} - 91 q^{97} - 13 q^{98}+O(q^{100}) \) 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9 - 9 * q^10 - 13 * q^11 - 9 * q^12 + 52 * q^13 - 15 * q^14 + 39 * q^15 - 31 * q^16 - 11 * q^17 + 26 * q^18 - 13 * q^20 - 13 * q^21 - 6 * q^22 - 102 * q^23 - 91 * q^24 + 3 * q^25 - 13 * q^26 - 19 * q^27 - 13 * q^28 - 17 * q^29 + 23 * q^30 + 39 * q^31 - 13 * q^33 + 52 * q^34 - 21 * q^35 + 11 * q^36 - 13 * q^37 - 40 * q^38 - 65 * q^39 + 53 * q^40 - 13 * q^41 + 101 * q^42 - 3 * q^43 - 39 * q^44 - 78 * q^45 - 39 * q^46 - 39 * q^47 + 8 * q^48 + 85 * q^49 - 13 * q^50 + 62 * q^51 - 78 * q^52 + 18 * q^53 + 65 * q^54 - 103 * q^55 + 3 * q^56 + 65 * q^57 + 39 * q^58 + 91 * q^59 - 117 * q^60 - 23 * q^61 - 64 * q^62 - 78 * q^63 + 15 * q^64 - 13 * q^65 + 134 * q^66 - 65 * q^67 + 40 * q^68 - 40 * q^69 + 26 * q^71 + 156 * q^72 - 13 * q^73 - 53 * q^74 + 35 * q^75 + 221 * q^76 + 3 * q^77 - 143 * q^78 - 23 * q^79 - 43 * q^81 - 129 * q^82 + 117 * q^83 + 234 * q^84 + 26 * q^85 - 91 * q^86 + 79 * q^87 + 95 * q^88 + 17 * q^90 + 39 * q^91 - 89 * q^92 + 52 * q^93 - 61 * q^94 + 122 * q^95 - 182 * q^96 - 91 * q^97 - 13 * q^98

Introduction

L-functions

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