LMFDB - Embedded newform 354.2.e.a.85.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,2,Mod(7,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("354.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	354.e (of order $29$, degree $28$, 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:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$2$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			85.1
Character	$\chi$	$=$	354.85
Dual form			354.2.e.a.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.796093 - 0.605174i) q^{2} +(0.468408 - 0.883512i) q^{3} +(0.267528 - 0.963550i) q^{4} +(-0.300267 + 0.284428i) q^{5} +(-0.161782 - 0.986827i) q^{6} +(-2.60590 - 3.06790i) q^{7} +(-0.370138 - 0.928977i) q^{8} +(-0.561187 - 0.827689i) q^{9} +O(q^{10})$	\(q+(0.796093 - 0.605174i) q^{2} +(0.468408 - 0.883512i) q^{3} +(0.267528 - 0.963550i) q^{4} +(-0.300267 + 0.284428i) q^{5} +(-0.161782 - 0.986827i) q^{6} +(-2.60590 - 3.06790i) q^{7} +(-0.370138 - 0.928977i) q^{8} +(-0.561187 - 0.827689i) q^{9} +(-0.0669119 + 0.408144i) q^{10} +(0.728857 - 0.438539i) q^{11} +(-0.725995 - 0.687699i) q^{12} +(1.04714 - 1.54441i) q^{13} +(-3.93115 - 0.865312i) q^{14} +(0.110648 + 0.398517i) q^{15} +(-0.856857 - 0.515554i) q^{16} +(0.818430 - 0.963531i) q^{17} +(-0.947653 - 0.319302i) q^{18} +(1.01160 + 0.468018i) q^{19} +(0.193730 + 0.365414i) q^{20} +(-3.93115 + 0.865312i) q^{21} +(0.314846 - 0.790203i) q^{22} +(5.24431 - 1.76701i) q^{23} +(-0.994138 - 0.108119i) q^{24} +(-0.261434 + 4.82186i) q^{25} +(-0.101019 - 1.86319i) q^{26} +(-0.994138 + 0.108119i) q^{27} +(-3.65323 + 1.69016i) q^{28} +(4.33410 + 3.29470i) q^{29} +(0.329258 + 0.250296i) q^{30} +(1.77157 - 0.819615i) q^{31} +(-0.994138 + 0.108119i) q^{32} +(-0.0460515 - 0.849369i) q^{33} +(0.0684428 - 1.26235i) q^{34} +(1.65506 + 0.179999i) q^{35} +(-0.947653 + 0.319302i) q^{36} +(-3.21899 + 8.07906i) q^{37} +(1.08856 - 0.239611i) q^{38} +(-0.874017 - 1.64857i) q^{39} +(0.375367 + 0.173663i) q^{40} +(5.71752 + 1.92646i) q^{41} +(-2.60590 + 3.06790i) q^{42} +(-7.60002 - 4.57278i) q^{43} +(-0.227564 - 0.819612i) q^{44} +(0.403923 + 0.0889102i) q^{45} +(3.10561 - 4.58043i) q^{46} +(-1.54649 - 1.46491i) q^{47} +(-0.856857 + 0.515554i) q^{48} +(-1.48884 + 9.08149i) q^{49} +(2.70994 + 3.99686i) q^{50} +(-0.467931 - 1.17442i) q^{51} +(-1.20798 - 1.42214i) q^{52} +(-1.60696 - 9.80203i) q^{53} +(-0.725995 + 0.687699i) q^{54} +(-0.0941189 + 0.338986i) q^{55} +(-1.88547 + 3.55637i) q^{56} +(0.887343 - 0.674540i) q^{57} +5.44422 q^{58} +(6.53094 + 4.04313i) q^{59} +0.413593 q^{60} +(-1.00013 + 0.760279i) q^{61} +(0.914324 - 1.72460i) q^{62} +(-1.07687 + 3.87854i) q^{63} +(-0.725995 + 0.687699i) q^{64} +(0.124853 + 0.761569i) q^{65} +(-0.550678 - 0.648308i) q^{66} +(2.54671 + 6.39176i) q^{67} +(-0.709457 - 1.04637i) q^{68} +(0.895301 - 5.46109i) q^{69} +(1.42651 - 0.858304i) q^{70} +(4.07803 + 3.86291i) q^{71} +(-0.561187 + 0.827689i) q^{72} +(9.97519 + 2.19571i) q^{73} +(2.32662 + 8.37973i) q^{74} +(4.13771 + 2.48958i) q^{75} +(0.721591 - 0.849523i) q^{76} +(-3.24472 - 1.09327i) q^{77} +(-1.69347 - 0.783484i) q^{78} +(-2.73629 - 5.16119i) q^{79} +(0.403923 - 0.0889102i) q^{80} +(-0.370138 + 0.928977i) q^{81} +(5.71752 - 1.92646i) q^{82} +(10.4537 + 1.13691i) q^{83} +(-0.217923 + 4.01936i) q^{84} +(0.0283074 + 0.522100i) q^{85} +(-8.81765 + 0.958977i) q^{86} +(4.94104 - 2.28597i) q^{87} +(-0.677170 - 0.514771i) q^{88} +(3.93988 + 2.99502i) q^{89} +(0.375367 - 0.173663i) q^{90} +(-7.46682 + 0.812066i) q^{91} +(-0.299604 - 5.52588i) q^{92} +(0.105678 - 1.94912i) q^{93} +(-2.11767 - 0.230311i) q^{94} +(-0.436868 + 0.147198i) q^{95} +(-0.370138 + 0.928977i) q^{96} +(-12.6717 + 2.78924i) q^{97} +(4.31063 + 8.13072i) q^{98} +(-0.771999 - 0.357165i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 56 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9	\( 56 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} - 18 q^{11} - 2 q^{12} + 13 q^{13} - 20 q^{14} + 4 q^{15} - 2 q^{16} + 21 q^{17} - 2 q^{18} + 20 q^{19} + 4 q^{20} - 20 q^{21} + 11 q^{22} + 34 q^{23} - 2 q^{24} - 28 q^{25} - 16 q^{26} - 2 q^{27} + 9 q^{28} + 38 q^{29} + 4 q^{30} + 34 q^{31} - 2 q^{32} + 11 q^{33} - 8 q^{34} - 19 q^{35} - 2 q^{36} - 29 q^{37} + 20 q^{38} + 13 q^{39} + 4 q^{40} + 43 q^{41} + 9 q^{42} - 65 q^{43} + 11 q^{44} + 4 q^{45} + 5 q^{46} - 60 q^{47} - 2 q^{48} - 13 q^{49} - 86 q^{50} + 21 q^{51} - 16 q^{52} - 15 q^{53} - 2 q^{54} - 15 q^{55} + 9 q^{56} + 20 q^{57} - 78 q^{58} - 2 q^{59} - 54 q^{60} + 4 q^{61} + 5 q^{62} + 9 q^{63} - 2 q^{64} - 57 q^{65} + 11 q^{66} - 56 q^{67} - 8 q^{68} - 53 q^{69} + 10 q^{70} + 23 q^{71} - 2 q^{72} - 21 q^{73} + 30 q^{75} - 9 q^{76} - 57 q^{77} + 13 q^{78} + 99 q^{79} + 4 q^{80} - 2 q^{81} + 43 q^{82} + 33 q^{83} + 9 q^{84} - 45 q^{85} - 7 q^{86} + 9 q^{87} - 18 q^{88} + 32 q^{89} + 4 q^{90} - 75 q^{91} + 34 q^{92} + 5 q^{93} + 27 q^{94} + 82 q^{95} - 2 q^{96} + 70 q^{97} + 45 q^{98} + 11 q^{99}+O(q^{100}) \) 56 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9 + 4 * q^10 - 18 * q^11 - 2 * q^12 + 13 * q^13 - 20 * q^14 + 4 * q^15 - 2 * q^16 + 21 * q^17 - 2 * q^18 + 20 * q^19 + 4 * q^20 - 20 * q^21 + 11 * q^22 + 34 * q^23 - 2 * q^24 - 28 * q^25 - 16 * q^26 - 2 * q^27 + 9 * q^28 + 38 * q^29 + 4 * q^30 + 34 * q^31 - 2 * q^32 + 11 * q^33 - 8 * q^34 - 19 * q^35 - 2 * q^36 - 29 * q^37 + 20 * q^38 + 13 * q^39 + 4 * q^40 + 43 * q^41 + 9 * q^42 - 65 * q^43 + 11 * q^44 + 4 * q^45 + 5 * q^46 - 60 * q^47 - 2 * q^48 - 13 * q^49 - 86 * q^50 + 21 * q^51 - 16 * q^52 - 15 * q^53 - 2 * q^54 - 15 * q^55 + 9 * q^56 + 20 * q^57 - 78 * q^58 - 2 * q^59 - 54 * q^60 + 4 * q^61 + 5 * q^62 + 9 * q^63 - 2 * q^64 - 57 * q^65 + 11 * q^66 - 56 * q^67 - 8 * q^68 - 53 * q^69 + 10 * q^70 + 23 * q^71 - 2 * q^72 - 21 * q^73 + 30 * q^75 - 9 * q^76 - 57 * q^77 + 13 * q^78 + 99 * q^79 + 4 * q^80 - 2 * q^81 + 43 * q^82 + 33 * q^83 + 9 * q^84 - 45 * q^85 - 7 * q^86 + 9 * q^87 - 18 * q^88 + 32 * q^89 + 4 * q^90 - 75 * q^91 + 34 * q^92 + 5 * q^93 + 27 * q^94 + 82 * q^95 - 2 * q^96 + 70 * q^97 + 45 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{23}{29}\right)$	$1$

Coefficient data

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

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

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

$2$	0.796093	−	0.605174i	0.562923	−	0.427923i
$2$	0.796093	−	0.605174i	0.562923	−	0.427923i
$3$	0.468408	−	0.883512i	0.270436	−	0.510096i
$3$	0.468408	−	0.883512i	0.270436	−	0.510096i
$4$	0.267528	−	0.963550i	0.133764	−	0.481775i
$5$	−0.300267	+	0.284428i	−0.134283	+	0.127200i	−0.751894	−	0.659284i	$-0.770859\pi$
$5$	−0.300267	+	0.284428i	−0.134283	+	0.127200i	0.617611	+	0.786484i	$0.288101\pi$
$6$	−0.161782	−	0.986827i	−0.0660472	−	0.402870i
$7$	−2.60590	−	3.06790i	−0.984937	−	1.15956i	−0.987188	−	0.159560i	$-0.948992\pi$
$7$	−2.60590	−	3.06790i	−0.984937	−	1.15956i	0.00225106	−	0.999997i	$-0.499283\pi$
$8$	−0.370138	−	0.928977i	−0.130864	−	0.328443i
$9$	−0.561187	−	0.827689i	−0.187062	−	0.275896i
$10$	−0.0669119	+	0.408144i	−0.0211594	+	0.129067i
$11$	0.728857	−	0.438539i	0.219759	−	0.132224i	−0.401418	−	0.915895i	$-0.631483\pi$
$11$	0.728857	−	0.438539i	0.219759	−	0.132224i	0.621177	+	0.783671i	$0.286655\pi$
$12$	−0.725995	−	0.687699i	−0.209577	−	0.198522i
$13$	1.04714	−	1.54441i	0.290423	−	0.428342i	−0.654288	−	0.756245i	$-0.727032\pi$
$13$	1.04714	−	1.54441i	0.290423	−	0.428342i	0.944711	+	0.327903i	$0.106342\pi$
$14$	−3.93115	−	0.865312i	−1.05064	−	0.231264i
$15$	0.110648	+	0.398517i	0.0285691	+	0.102897i
$16$	−0.856857	−	0.515554i	−0.214214	−	0.128888i
$17$	0.818430	−	0.963531i	0.198498	−	0.233690i	−0.653903	−	0.756578i	$-0.726870\pi$
$17$	0.818430	−	0.963531i	0.198498	−	0.233690i	0.852401	+	0.522888i	$0.175145\pi$
$18$	−0.947653	−	0.319302i	−0.223364	−	0.0752601i
$19$	1.01160	+	0.468018i	0.232078	+	0.107371i	0.532482	−	0.846441i	$-0.321259\pi$
$19$	1.01160	+	0.468018i	0.232078	+	0.107371i	−0.300404	+	0.953812i	$0.597122\pi$
$20$	0.193730	+	0.365414i	0.0433194	+	0.0817091i
$21$	−3.93115	+	0.865312i	−0.857848	+	0.188827i
$22$	0.314846	−	0.790203i	0.0671254	−	0.168472i
$23$	5.24431	−	1.76701i	1.09351	−	0.368448i	0.285960	−	0.958242i	$-0.407688\pi$
$23$	5.24431	−	1.76701i	1.09351	−	0.368448i	0.807554	+	0.589794i	$0.200791\pi$
$24$	−0.994138	−	0.108119i	−0.202928	−	0.0220697i
$25$	−0.261434	+	4.82186i	−0.0522867	+	0.964372i
$26$	−0.101019	−	1.86319i	−0.0198115	−	0.365402i
$27$	−0.994138	+	0.108119i	−0.191322	+	0.0208075i
$28$	−3.65323	+	1.69016i	−0.690395	+	0.319411i
$29$	4.33410	+	3.29470i	0.804823	+	0.611810i	0.924578	−	0.380993i	$-0.124418\pi$
$29$	4.33410	+	3.29470i	0.804823	+	0.611810i	−0.119755	+	0.992803i	$0.538211\pi$
$30$	0.329258	+	0.250296i	0.0601141	+	0.0456975i
$31$	1.77157	−	0.819615i	0.318183	−	0.147207i	−0.254296	−	0.967126i	$-0.581844\pi$
$31$	1.77157	−	0.819615i	0.318183	−	0.147207i	0.572479	+	0.819919i	$0.305982\pi$
$32$	−0.994138	+	0.108119i	−0.175740	+	0.0191129i
$33$	−0.0460515	−	0.849369i	−0.00801653	−	0.147856i
$34$	0.0684428	−	1.26235i	0.0117378	−	0.216492i
$35$	1.65506	+	0.179999i	0.279756	+	0.0304253i
$36$	−0.947653	+	0.319302i	−0.157942	+	0.0532169i
$37$	−3.21899	+	8.07906i	−0.529199	+	1.32819i	0.384998	+	0.922918i	$0.374202\pi$
$37$	−3.21899	+	8.07906i	−0.529199	+	1.32819i	−0.914196	+	0.405271i	$0.867177\pi$
$38$	1.08856	−	0.239611i	0.176588	−	0.0388700i
$39$	−0.874017	−	1.64857i	−0.139955	−	0.263983i
$40$	0.375367	+	0.173663i	0.0593507	+	0.0274586i
$41$	5.71752	+	1.92646i	0.892926	+	0.300862i	0.728108	−	0.685462i	$-0.240400\pi$
$41$	5.71752	+	1.92646i	0.892926	+	0.300862i	0.164818	+	0.986324i	$0.447296\pi$
$42$	−2.60590	+	3.06790i	−0.402099	+	0.473387i
$43$	−7.60002	−	4.57278i	−1.15899	−	0.697342i	−0.199727	−	0.979852i	$-0.564006\pi$
$43$	−7.60002	−	4.57278i	−1.15899	−	0.697342i	−0.959264	+	0.282510i	$0.908833\pi$
$44$	−0.227564	−	0.819612i	−0.0343066	−	0.123561i
$45$	0.403923	+	0.0889102i	0.0602133	+	0.0132540i
$46$	3.10561	−	4.58043i	0.457897	−	0.675347i
$47$	−1.54649	−	1.46491i	−0.225578	−	0.213679i	0.566560	−	0.824020i	$-0.308274\pi$
$47$	−1.54649	−	1.46491i	−0.225578	−	0.213679i	−0.792139	+	0.610341i	$0.791032\pi$
$48$	−0.856857	+	0.515554i	−0.123677	+	0.0744138i
$49$	−1.48884	+	9.08149i	−0.212691	+	1.29736i
$50$	2.70994	+	3.99686i	0.383243	+	0.565242i
$51$	−0.467931	−	1.17442i	−0.0655235	−	0.164452i
$52$	−1.20798	−	1.42214i	−0.167516	−	0.197215i
$53$	−1.60696	−	9.80203i	−0.220733	−	1.34641i	−0.831907	−	0.554916i	$-0.812751\pi$
$53$	−1.60696	−	9.80203i	−0.220733	−	1.34641i	0.611173	−	0.791497i	$-0.290698\pi$
$54$	−0.725995	+	0.687699i	−0.0987955	+	0.0935840i
$55$	−0.0941189	+	0.338986i	−0.0126910	+	0.0457088i
$56$	−1.88547	+	3.55637i	−0.251956	+	0.475239i
$57$	0.887343	−	0.674540i	0.117531	−	0.0893451i
$58$	5.44422			0.714860
$59$	6.53094	+	4.04313i	0.850256	+	0.526370i
$59$	6.53094	+	4.04313i	0.850256	+	0.526370i
$60$	0.413593			0.0533946
$61$	−1.00013	+	0.760279i	−0.128054	+	0.0973438i	−0.667241	−	0.744842i	$-0.732525\pi$
$61$	−1.00013	+	0.760279i	−0.128054	+	0.0973438i	0.539187	+	0.842186i	$0.318732\pi$
$62$	0.914324	−	1.72460i	0.116119	−	0.219024i
$63$	−1.07687	+	3.87854i	−0.135673	+	0.488650i
$64$	−0.725995	+	0.687699i	−0.0907494	+	0.0859624i
$65$	0.124853	+	0.761569i	0.0154861	+	0.0944610i
$66$	−0.550678	−	0.648308i	−0.0677837	−	0.0798012i
$67$	2.54671	+	6.39176i	0.311130	+	0.780877i	0.998509	+	0.0545789i	$0.0173816\pi$
$67$	2.54671	+	6.39176i	0.311130	+	0.780877i	−0.687379	+	0.726298i	$0.741239\pi$
$68$	−0.709457	−	1.04637i	−0.0860342	−	0.126891i
$69$	0.895301	−	5.46109i	0.107782	−	0.657438i
$70$	1.42651	−	0.858304i	0.170501	−	0.102587i
$71$	4.07803	+	3.86291i	0.483973	+	0.458443i	0.890360	−	0.455258i	$-0.150453\pi$
$71$	4.07803	+	3.86291i	0.483973	+	0.458443i	−0.406387	+	0.913701i	$0.633211\pi$
$72$	−0.561187	+	0.827689i	−0.0661365	+	0.0975441i
$73$	9.97519	+	2.19571i	1.16751	+	0.256988i	0.756095	−	0.654461i	$-0.227105\pi$
$73$	9.97519	+	2.19571i	1.16751	+	0.256988i	0.411412	+	0.911449i	$0.365036\pi$
$74$	2.32662	+	8.37973i	0.270464	+	0.974124i
$75$	4.13771	+	2.48958i	0.477782	+	0.287472i
$76$	0.721591	−	0.849523i	0.0827722	−	0.0974469i
$77$	−3.24472	−	1.09327i	−0.369770	−	0.124590i
$78$	−1.69347	−	0.783484i	−0.191748	−	0.0887120i
$79$	−2.73629	−	5.16119i	−0.307856	−	0.580679i	0.680516	−	0.732734i	$-0.261756\pi$
$79$	−2.73629	−	5.16119i	−0.307856	−	0.580679i	−0.988372	+	0.152055i	$0.951411\pi$
$80$	0.403923	−	0.0889102i	0.0451600	−	0.00994047i
$81$	−0.370138	+	0.928977i	−0.0411265	+	0.103220i
$82$	5.71752	−	1.92646i	0.631394	−	0.212741i
$83$	10.4537	+	1.13691i	1.14744	+	0.124792i	0.662020	−	0.749486i	$-0.269699\pi$
$83$	10.4537	+	1.13691i	1.14744	+	0.124792i	0.485425	+	0.874278i	$0.338665\pi$
$84$	−0.217923	+	4.01936i	−0.0237774	+	0.438548i
$85$	0.0283074	+	0.522100i	0.00307037	+	0.0566297i
$86$	−8.81765	+	0.958977i	−0.950831	+	0.103409i
$87$	4.94104	−	2.28597i	0.529735	−	0.245081i
$88$	−0.677170	−	0.514771i	−0.0721866	−	0.0548748i
$89$	3.93988	+	2.99502i	0.417627	+	0.317472i	0.792799	−	0.609484i	$-0.208623\pi$
$89$	3.93988	+	2.99502i	0.417627	+	0.317472i	−0.375172	+	0.926955i	$0.622416\pi$
$90$	0.375367	−	0.173663i	0.0395671	−	0.0183057i
$91$	−7.46682	+	0.812066i	−0.782736	+	0.0851277i
$92$	−0.299604	−	5.52588i	−0.0312359	−	0.576113i
$93$	0.105678	−	1.94912i	0.0109583	−	0.202114i
$94$	−2.11767	−	0.230311i	−0.218421	−	0.0237548i
$95$	−0.436868	+	0.147198i	−0.0448217	+	0.0151022i
$96$	−0.370138	+	0.928977i	−0.0377771	+	0.0948133i
$97$	−12.6717	+	2.78924i	−1.28661	+	0.283205i	−0.805050	−	0.593207i	$-0.797862\pi$
$97$	−12.6717	+	2.78924i	−1.28661	+	0.283205i	−0.481562	+	0.876412i	$0.659931\pi$
$98$	4.31063	+	8.13072i	0.435440	+	0.821327i
$99$	−0.771999	−	0.357165i	−0.0775888	−	0.0358964i
$100$	4.57616	+	1.54189i	0.457616	+	0.154189i
$101$	−9.91116	+	11.6683i	−0.986197	+	1.16104i	0.000750481		1.00000i	$0.499761\pi$
$101$	−9.91116	+	11.6683i	−0.986197	+	1.16104i	−0.986948	+	0.161041i	$0.948515\pi$
$102$	−1.08324	−	0.651767i	−0.107257	−	0.0645345i
$103$	−2.25890	−	8.13581i	−0.222576	−	0.801645i	−0.987513	−	0.157540i	$-0.949644\pi$
$103$	−2.25890	−	8.13581i	−0.222576	−	0.801645i	0.764937	−	0.644105i	$-0.222770\pi$
$104$	−1.82231	−	0.401120i	−0.178692	−	0.0393330i
$105$	0.934275	−	1.37795i	0.0911759	−	0.134474i
$106$	−7.21123	−	6.83084i	−0.700416	−	0.663470i
$107$	6.60318	−	3.97300i	0.638354	−	0.384085i	−0.159274	−	0.987234i	$-0.550915\pi$
$107$	6.60318	−	3.97300i	0.638354	−	0.384085i	0.797628	+	0.603150i	$0.206088\pi$
$108$	−0.161782	+	0.986827i	−0.0155675	+	0.0949574i
$109$	−7.63260	−	11.2572i	−0.731071	−	1.07825i	−0.993559	−	0.113313i	$-0.963854\pi$
$109$	−7.63260	−	11.2572i	−0.731071	−	1.07825i	0.262489	−	0.964935i	$-0.415457\pi$
$110$	0.130218	+	0.326822i	0.0124158	+	0.0311613i
$111$	5.63014	+	6.62832i	0.534389	+	0.629132i
$112$	0.651215	+	3.97223i	0.0615340	+	0.375341i
$113$	0.160267	−	0.151813i	0.0150766	−	0.0142814i	−0.680124	−	0.733097i	$-0.738074\pi$
$113$	0.160267	−	0.151813i	0.0150766	−	0.0142814i	0.695201	+	0.718816i	$0.255315\pi$
$114$	0.298193	−	1.07399i	0.0279283	−	0.100589i
$115$	−1.07210	+	2.02220i	−0.0999741	+	0.188571i
$116$	4.33410	−	3.29470i	0.402411	−	0.305905i
$117$	−1.86593			−0.172505
$118$	7.64603	−	0.733651i	0.703874	−	0.0675380i
$119$	−5.08876			−0.466486
$120$	0.329258	−	0.250296i	0.0300570	−	0.0228488i
$121$	−4.81358	+	9.07937i	−0.437598	+	0.825397i
$122$	−0.336095	+	1.21051i	−0.0304286	+	0.109594i
$123$	4.38018	−	4.14913i	0.394948	−	0.374114i
$124$	−0.315795	−	1.92627i	−0.0283593	−	0.172984i
$125$	−2.63174	−	3.09833i	−0.235390	−	0.277123i
$126$	1.48990	+	3.73937i	0.132731	+	0.333130i
$127$	1.60043	+	2.36046i	0.142016	+	0.209457i	0.892044	−	0.451948i	$-0.149271\pi$
$127$	1.60043	+	2.36046i	0.142016	+	0.209457i	−0.750029	+	0.661405i	$0.769960\pi$
$128$	−0.161782	+	0.986827i	−0.0142996	+	0.0872240i
$129$	−7.60002	+	4.57278i	−0.669144	+	0.402611i
$130$	0.560276	+	0.530722i	0.0491395	+	0.0465474i
$131$	−1.25635	+	1.85297i	−0.109768	+	0.161895i	−0.878605	−	0.477549i	$-0.841525\pi$
$131$	−1.25635	+	1.85297i	−0.109768	+	0.161895i	0.768837	+	0.639444i	$0.220836\pi$
$132$	−0.830730	−	0.182858i	−0.0723058	−	0.0159157i
$133$	−1.20030	−	4.32311i	−0.104080	−	0.374861i
$134$	5.89554	+	3.54723i	0.509297	+	0.306434i
$135$	0.267754	−	0.315225i	0.0230446	−	0.0271302i
$136$	−1.19803	−	0.403663i	−0.102730	−	0.0346138i
$137$	−3.16027	−	1.46210i	−0.270000	−	0.124915i	0.280218	−	0.959936i	$-0.409593\pi$
$137$	−3.16027	−	1.46210i	−0.270000	−	0.124915i	−0.550218	+	0.835021i	$0.685455\pi$
$138$	−2.59217	−	4.88935i	−0.220660	−	0.416209i
$139$	4.92945	−	1.08505i	0.418110	−	0.0920330i	−0.000932420	−	1.00000i	$-0.500297\pi$
$139$	4.92945	−	1.08505i	0.418110	−	0.0920330i	0.419043	+	0.907967i	$0.362366\pi$
$140$	0.616213	−	1.54658i	0.0520795	−	0.130710i
$141$	−2.01865	+	0.680163i	−0.170001	+	0.0572801i
$142$	5.58423	+	0.607321i	0.468618	+	0.0509653i
$143$	0.0859288	−	1.58486i	0.00718573	−	0.132533i
$144$	0.0541389	+	0.998533i	0.00451158	+	0.0832111i
$145$	−2.23849	+	0.243450i	−0.185896	+	0.0202175i
$146$	9.26997	−	4.28874i	0.767188	−	0.354939i
$147$	7.32623	+	5.56925i	0.604257	+	0.459344i
$148$	6.92340	+	5.26303i	0.569100	+	0.432619i
$149$	11.8291	−	5.47272i	0.969077	−	0.448343i	0.129498	−	0.991580i	$-0.458663\pi$
$149$	11.8291	−	5.47272i	0.969077	−	0.448343i	0.839580	+	0.543237i	$0.182801\pi$
$150$	4.80063	−	0.522100i	0.391970	−	0.0426293i
$151$	−0.791146	−	14.5918i	−0.0643825	−	1.18747i	−0.835030	−	0.550204i	$-0.814550\pi$
$151$	−0.791146	−	14.5918i	−0.0643825	−	1.18747i	0.770648	−	0.637262i	$-0.219933\pi$
$152$	0.0603444	−	1.11299i	0.00489458	−	0.0902752i
$153$	−1.25680	−	0.136685i	−0.101606	−	0.0110503i
$154$	−3.24472	+	1.09327i	−0.261467	+	0.0880985i
$155$	−0.298822	+	0.749986i	−0.0240019	+	0.0602403i
$156$	−1.82231	+	0.401120i	−0.145901	+	0.0321153i
$157$	−0.718051	−	1.35439i	−0.0573067	−	0.108092i	0.853204	−	0.521577i	$-0.174656\pi$
$157$	−0.718051	−	1.35439i	−0.0573067	−	0.108092i	−0.910511	+	0.413485i	$0.864311\pi$
$158$	−5.30176	−	2.45285i	−0.421785	−	0.195139i
$159$	−9.41293	−	3.17158i	−0.746494	−	0.251523i
$160$	0.267754	−	0.315225i	0.0211678	−	0.0249207i
$161$	−19.0872	−	11.4844i	−1.50428	−	0.905094i
$162$	0.267528	+	0.963550i	0.0210190	+	0.0757036i
$163$	−16.4579	−	3.62266i	−1.28908	−	0.283749i	−0.483037	−	0.875600i	$-0.660466\pi$
$163$	−16.4579	−	3.62266i	−1.28908	−	0.283749i	−0.806047	+	0.591851i	$0.798397\pi$
$164$	3.38583	−	4.99373i	0.264389	−	0.389945i
$165$	0.255412	+	0.241939i	0.0198838	+	0.0188349i
$166$	9.01016	−	5.42123i	0.699324	−	0.420769i
$167$	1.67867	−	10.2394i	0.129899	−	0.792351i	−0.838860	−	0.544348i	$-0.816777\pi$
$167$	1.67867	−	10.2394i	0.129899	−	0.792351i	0.968759	−	0.248004i	$-0.0797745\pi$
$168$	2.25892	+	3.33166i	0.174280	+	0.257043i
$169$	3.52309	+	8.84229i	0.271007	+	0.680176i
$170$	0.338497	+	0.398509i	0.0259615	+	0.0305643i
$171$	−0.180326	−	1.09994i	−0.0137899	−	0.0841144i
$172$	−6.43932	+	6.09965i	−0.490993	+	0.465094i
$173$	−6.22970	+	22.4373i	−0.473635	+	1.70588i	0.211426	+	0.977394i	$0.432189\pi$
$173$	−6.22970	+	22.4373i	−0.473635	+	1.70588i	−0.685061	+	0.728486i	$0.740224\pi$
$174$	2.55012	−	4.81003i	0.193324	−	0.364647i
$175$	15.4743	−	11.7632i	1.16974	−	0.889216i
$176$	−0.850617			−0.0641177
$177$	6.63130	−	3.87633i	0.498439	−	0.291363i
$178$	4.94902			0.370945
$179$	−9.00815	+	6.84782i	−0.673301	+	0.511830i	−0.885051	−	0.465494i	$-0.845877\pi$
$179$	−9.00815	+	6.84782i	−0.673301	+	0.511830i	0.211750	+	0.977324i	$0.432084\pi$
$180$	0.193730	−	0.365414i	0.0144398	−	0.0272364i
$181$	−2.25253	+	8.11289i	−0.167429	+	0.603026i	0.831446	+	0.555606i	$0.187514\pi$
$181$	−2.25253	+	8.11289i	−0.167429	+	0.603026i	−0.998875	+	0.0474200i	$0.984900\pi$
$182$	−5.45285	+	5.16521i	−0.404192	+	0.382871i
$183$	0.203246	+	1.23975i	0.0150244	+	0.0916448i
$184$	−3.58263	−	4.21780i	−0.264115	−	0.310940i
$185$	−1.33135	−	3.34144i	−0.0978829	−	0.245668i
$186$	−1.09543	−	1.61563i	−0.0803205	−	0.118464i
$187$	0.173973	−	1.06119i	0.0127222	−	0.0776019i
$188$	−1.82524	+	1.09821i	−0.133120	+	0.0800954i
$189$	2.92232	+	2.76817i	0.212568	+	0.201355i
$190$	−0.258707	+	0.381564i	−0.0187686	+	0.0276816i
$191$	−14.2506	−	3.13680i	−1.03114	−	0.226971i	−0.332995	−	0.942929i	$-0.608059\pi$
$191$	−14.2506	−	3.13680i	−1.03114	−	0.226971i	−0.698143	+	0.715958i	$0.745990\pi$
$192$	0.267528	+	0.963550i	0.0193072	+	0.0695382i
$193$	−10.0875	−	6.06942i	−0.726111	−	0.436887i	0.103933	−	0.994584i	$-0.466857\pi$
$193$	−10.0875	−	6.06942i	−0.726111	−	0.436887i	−0.830044	+	0.557698i	$0.811685\pi$
$194$	−8.39984	+	9.88906i	−0.603074	+	0.709993i
$195$	0.731337	+	0.246416i	0.0523722	+	0.0176462i
$196$	8.35217	+	3.86412i	0.596583	+	0.276009i
$197$	−10.4458	−	19.7028i	−0.744232	−	1.40377i	−0.908727	−	0.417392i	$-0.862944\pi$
$197$	−10.4458	−	19.7028i	−0.744232	−	1.40377i	0.164495	−	0.986378i	$-0.447401\pi$
$198$	−0.830730	+	0.182858i	−0.0590374	+	0.0129951i
$199$	8.21083	−	20.6076i	0.582050	−	1.46084i	−0.282985	−	0.959124i	$-0.591325\pi$
$199$	8.21083	−	20.6076i	0.582050	−	1.46084i	0.865035	−	0.501711i	$-0.167296\pi$
$200$	4.57616	−	1.54189i	0.323583	−	0.109028i
$201$	6.84009	+	0.743905i	0.482463	+	0.0524710i
$202$	−0.828840	+	15.2870i	−0.0583169	+	1.07559i
$203$	−1.18642	−	21.8822i	−0.0832704	−	1.53583i
$204$	−1.25680	+	0.136685i	−0.0879933	+	0.00956985i
$205$	−2.26472	+	1.04777i	−0.158175	+	0.0731794i
$206$	−6.72187	−	5.10983i	−0.468335	−	0.356019i
$207$	−4.40558	−	3.34903i	−0.306209	−	0.232774i
$208$	−1.69347	+	0.783484i	−0.117421	+	0.0543248i
$209$	0.942558	−	0.102509i	0.0651981	−	0.00709072i
$210$	−0.0901315	−	1.66238i	−0.00621966	−	0.114715i
$211$	−1.31992	+	24.3444i	−0.0908668	+	1.67594i	0.497592	+	0.867411i	$0.334218\pi$
$211$	−1.31992	+	24.3444i	−0.0908668	+	1.67594i	−0.588458	+	0.808528i	$0.700265\pi$
$212$	−9.87465	−	1.07393i	−0.678194	−	0.0737580i
$213$	5.32311	−	1.79357i	0.364734	−	0.122893i
$214$	2.85239	−	7.15895i	0.194985	−	0.489376i
$215$	3.58265	−	0.788602i	0.244335	−	0.0537822i
$216$	0.468408	+	0.883512i	0.0318712	+	0.0601154i
$217$	−7.13103	−	3.29917i	−0.484086	−	0.223962i
$218$	−12.8889	−	4.34276i	−0.872943	−	0.294129i
$219$	6.61240	−	7.78471i	0.446824	−	0.526042i
$220$	0.301450	+	0.181377i	0.0203238	+	0.0122284i
$221$	−0.631078	−	2.27294i	−0.0424509	−	0.152894i
$222$	8.49340	+	1.86954i	0.570040	+	0.125475i
$223$	6.74134	−	9.94273i	0.451434	−	0.665815i	−0.532071	−	0.846700i	$-0.678586\pi$
$223$	6.74134	−	9.94273i	0.451434	−	0.665815i	0.983504	+	0.180885i	$0.0578963\pi$
$224$	2.92232	+	2.76817i	0.195256	+	0.184956i
$225$	4.13771	−	2.48958i	0.275848	−	0.165972i
$226$	0.0357141	−	0.217847i	0.00237567	−	0.0144909i
$227$	−2.74319	−	4.04591i	−0.182072	−	0.268536i	0.725690	−	0.688022i	$-0.241521\pi$
$227$	−2.74319	−	4.04591i	−0.182072	−	0.268536i	−0.907762	+	0.419486i	$0.862210\pi$
$228$	−0.412564	−	1.03546i	−0.0273227	−	0.0685749i
$229$	10.2185	+	12.0302i	0.675258	+	0.794975i	0.987932	−	0.154885i	$-0.0495008\pi$
$229$	10.2185	+	12.0302i	0.675258	+	0.794975i	−0.312674	+	0.949860i	$0.601225\pi$
$230$	0.370290	+	2.25867i	0.0244162	+	0.148932i
$231$	−2.48578	+	2.35465i	−0.163552	+	0.154925i
$232$	1.45648	−	5.24577i	0.0956227	−	0.344402i
$233$	−4.22893	+	7.97661i	−0.277047	+	0.522565i	−0.982517	−	0.186174i	$-0.940391\pi$
$233$	−4.22893	+	7.97661i	−0.277047	+	0.522565i	0.705470	+	0.708740i	$0.250736\pi$
$234$	−1.48545	+	1.12921i	−0.0971071	+	0.0738189i
$235$	0.881019			0.0574714
$236$	5.64296	−	5.21123i	0.367326	−	0.339222i
$237$	−5.84167			−0.379457
$238$	−4.05113	+	3.07959i	−0.262596	+	0.199620i
$239$	−6.38081	+	12.0355i	−0.412740	+	0.778510i	−0.999512	−	0.0312420i	$-0.990054\pi$
$239$	−6.38081	+	12.0355i	−0.412740	+	0.778510i	0.586772	+	0.809752i	$0.300399\pi$
$240$	0.110648	−	0.398517i	0.00714229	−	0.0257242i
$241$	2.47830	−	2.34757i	0.159641	−	0.151220i	−0.603710	−	0.797204i	$-0.706311\pi$
$241$	2.47830	−	2.34757i	0.159641	−	0.151220i	0.763351	+	0.645984i	$0.223553\pi$
$242$	1.66254	+	10.1411i	0.106872	+	0.651893i
$243$	0.647386	+	0.762162i	0.0415298	+	0.0488927i
$244$	0.465004	+	1.16707i	0.0297688	+	0.0747141i
$245$	−2.13598	−	3.15033i	−0.136463	−	0.201268i
$246$	0.976086	−	5.95386i	0.0622330	−	0.379604i
$247$	1.78210	−	1.07225i	0.113392	−	0.0682258i
$248$	−1.41713	−	1.34238i	−0.0899878	−	0.0852409i
$249$	5.90108	−	8.70345i	0.373966	−	0.551558i
$250$	−3.97014	−	0.873894i	−0.251094	−	0.0552699i
$251$	3.81908	+	13.7551i	0.241058	+	0.868214i	0.980750	+	0.195268i	$0.0625577\pi$
$251$	3.81908	+	13.7551i	0.241058	+	0.868214i	−0.739691	+	0.672946i	$0.765029\pi$
$252$	3.44907	+	2.07524i	0.217271	+	0.130728i
$253$	3.04745	−	3.58773i	0.191591	−	0.225559i
$254$	2.70259	+	0.910608i	0.169575	+	0.0571366i
$255$	0.474541	+	0.219546i	0.0297169	+	0.0137485i
$256$	0.468408	+	0.883512i	0.0292755	+	0.0552195i
$257$	−15.1388	+	3.33229i	−0.944330	+	0.207863i	−0.660342	−	0.750965i	$-0.729589\pi$
$257$	−15.1388	+	3.33229i	−0.944330	+	0.207863i	−0.283988	+	0.958828i	$0.591658\pi$
$258$	−3.28299	+	8.23969i	−0.204390	+	0.512981i
$259$	33.1741	−	11.1777i	2.06134	−	0.694546i
$260$	0.767211	+	0.0834393i	0.0475804	+	0.00517468i
$261$	0.294744	−	5.43623i	0.0182442	−	0.336494i
$262$	0.121203	+	2.23545i	0.00748792	+	0.138107i
$263$	0.699383	−	0.0760625i	0.0431258	−	0.00469021i	−0.0865307	−	0.996249i	$-0.527578\pi$
$263$	0.699383	−	0.0760625i	0.0431258	−	0.00469021i	0.129656	+	0.991559i	$0.458613\pi$
$264$	−0.771999	+	0.357165i	−0.0475133	+	0.0219820i
$265$	3.27048	+	2.48616i	0.200904	+	0.152723i
$266$	−3.57179	−	2.71520i	−0.219000	−	0.166480i
$267$	4.49161	−	2.07804i	0.274882	−	0.127174i
$268$	6.84009	−	0.743905i	0.417825	−	0.0454412i
$269$	−0.169690	−	3.12975i	−0.0103462	−	0.190824i	−0.999138	−	0.0415208i	$-0.986780\pi$
$269$	−0.169690	−	3.12975i	−0.0103462	−	0.190824i	0.988791	−	0.149303i	$-0.0477031\pi$
$270$	0.0223915	−	0.412986i	0.00136270	−	0.0251335i
$271$	−11.4948	−	1.25014i	−0.698261	−	0.0759405i	−0.247898	−	0.968786i	$-0.579740\pi$
$271$	−11.4948	−	1.25014i	−0.698261	−	0.0759405i	−0.450363	+	0.892846i	$0.648705\pi$
$272$	−1.19803	+	0.403663i	−0.0726412	+	0.0244757i
$273$	−2.78005	+	6.97741i	−0.168256	+	0.422292i
$274$	−3.40069	+	0.748548i	−0.205443	+	0.0452215i
$275$	1.92402	+	3.62910i	0.116023	+	0.218843i
$276$	−5.02252	−	2.32366i	−0.302320	−	0.139868i
$277$	8.60422	+	2.89910i	0.516978	+	0.174190i	0.565682	−	0.824623i	$-0.308613\pi$
$277$	8.60422	+	2.89910i	0.516978	+	0.174190i	−0.0487048	+	0.998813i	$0.515509\pi$
$278$	3.26765	−	3.84698i	0.195981	−	0.230726i
$279$	−1.67257	−	1.00635i	−0.100134	−	0.0602487i
$280$	−0.445386	−	1.60414i	−0.0266169	−	0.0958655i
$281$	−13.2303	−	2.91220i	−0.789252	−	0.173727i	−0.197987	−	0.980205i	$-0.563440\pi$
$281$	−13.2303	−	2.91220i	−0.789252	−	0.173727i	−0.591265	+	0.806477i	$0.701371\pi$
$282$	−1.19542	+	1.76311i	−0.0711861	+	0.104992i
$283$	11.3391	+	10.7409i	0.674038	+	0.638483i	0.946129	−	0.323789i	$-0.104957\pi$
$283$	11.3391	+	10.7409i	0.674038	+	0.638483i	−0.272091	+	0.962271i	$0.587715\pi$
$284$	4.81310	−	2.89595i	0.285605	−	0.171843i
$285$	−0.0745815	+	0.454927i	−0.00441782	+	0.0269475i
$286$	−0.890711	−	1.31370i	−0.0526689	−	0.0776808i
$287$	−8.98909	−	22.5609i	−0.530609	−	1.33173i
$288$	0.647386	+	0.762162i	0.0381476	+	0.0449108i
$289$	2.49173	+	15.1989i	0.146572	+	0.894052i
$290$	−1.63472	+	1.54849i	−0.0959938	+	0.0909302i
$291$	−3.47118	+	12.5021i	−0.203484	+	0.732884i
$292$	4.78432	−	9.02418i	0.279981	−	0.528100i
$293$	14.4017	−	10.9479i	0.841359	−	0.639584i	−0.0930994	−	0.995657i	$-0.529677\pi$
$293$	14.4017	−	10.9479i	0.841359	−	0.639584i	0.934458	+	0.356072i	$0.115884\pi$
$294$	9.20273			0.536714
$295$	−3.11100	+	0.643563i	−0.181129	+	0.0374697i
$296$	8.69673			0.505487
$297$	−0.677170	+	0.514771i	−0.0392934	+	0.0298701i
$298$	6.10511	−	11.5155i	0.353660	−	0.667073i
$299$	2.76251	−	9.94966i	0.159760	−	0.575404i
$300$	3.50579	−	3.32086i	0.202407	−	0.191730i
$301$	5.77604	+	35.2323i	0.332925	+	2.03076i
$302$	−9.46042	−	11.1377i	−0.544386	−	0.640901i
$303$	5.66663	+	14.2222i	0.325539	+	0.817042i
$304$	−0.625511	−	0.922560i	−0.0358755	−	0.0529125i
$305$	0.0840613	−	0.512751i	0.00481334	−	0.0293600i
$306$	−1.08324	+	0.651767i	−0.0619250	+	0.0372590i
$307$	15.5547	+	14.7342i	0.887755	+	0.840926i	0.988066	−	0.154030i	$-0.0492253\pi$
$307$	15.5547	+	14.7342i	0.887755	+	0.840926i	−0.100311	+	0.994956i	$0.531984\pi$
$308$	−1.92148	+	2.83397i	−0.109486	+	0.161480i
$309$	−8.24617	−	1.81512i	−0.469108	−	0.103259i
$310$	0.215982	+	0.777898i	0.0122670	+	0.0441816i
$311$	3.66985	+	2.20807i	0.208098	+	0.125208i	0.615788	−	0.787912i	$-0.288838\pi$
$311$	3.66985	+	2.20807i	0.208098	+	0.125208i	−0.407690	+	0.913121i	$0.633665\pi$
$312$	−1.20798	+	1.42214i	−0.0683882	+	0.0805129i
$313$	−9.19339	−	3.09761i	−0.519641	−	0.175088i	0.0472454	−	0.998883i	$-0.484956\pi$
$313$	−9.19339	−	3.09761i	−0.519641	−	0.175088i	−0.566887	+	0.823796i	$0.691852\pi$
$314$	−1.39128	−	0.643673i	−0.0785143	−	0.0363246i
$315$	−0.779815	−	1.47089i	−0.0439376	−	0.0828751i
$316$	−5.70510	+	1.25579i	−0.320937	+	0.0706435i
$317$	−6.77983	+	17.0161i	−0.380793	+	0.955719i	0.606251	+	0.795273i	$0.292673\pi$
$317$	−6.77983	+	17.0161i	−0.380793	+	0.955719i	−0.987045	+	0.160446i	$0.948707\pi$
$318$	−9.41293	+	3.17158i	−0.527851	+	0.177854i
$319$	4.60380	+	0.500693i	0.257763	+	0.0280334i
$320$	0.0223915	−	0.412986i	0.00125172	−	0.0230866i
$321$	−0.417210	−	7.69498i	−0.0232864	−	0.429492i
$322$	−22.1452	+	2.40843i	−1.23410	+	0.134217i
$323$	1.27888	−	0.591671i	0.0711586	−	0.0329215i
$324$	0.796093	+	0.605174i	0.0442274	+	0.0336208i
$325$	7.17317	+	5.45290i	0.397896	+	0.302473i
$326$	−15.2944	+	7.07593i	−0.847077	+	0.391900i
$327$	−13.5211	+	1.47051i	−0.747718	+	0.0813192i
$328$	−0.326639	−	6.02449i	−0.0180356	−	0.332647i
$329$	−0.464211	+	8.56188i	−0.0255928	+	0.472032i
$330$	0.349747	+	0.0380373i	0.0192529	+	0.00209388i
$331$	−9.64395	+	3.24943i	−0.530080	+	0.178605i	−0.571599	−	0.820533i	$-0.693677\pi$
$331$	−9.64395	+	3.24943i	−0.530080	+	0.178605i	0.0415195	+	0.999138i	$0.486780\pi$
$332$	3.89214	−	9.76852i	0.213609	−	0.536117i
$333$	8.49340	−	1.86954i	0.465436	−	0.102450i
$334$	−4.86026	−	9.16743i	−0.265942	−	0.501619i
$335$	−2.58268	−	1.19488i	−0.141107	−	0.0652831i
$336$	3.81455	+	1.28527i	0.208101	+	0.0701173i
$337$	−14.3321	+	16.8731i	−0.780720	+	0.919135i	−0.998380	−	0.0568895i	$-0.981882\pi$
$337$	−14.3321	+	16.8731i	−0.780720	+	0.919135i	0.217660	+	0.976025i	$0.430158\pi$
$338$	8.15583	+	4.90720i	0.443619	+	0.266916i
$339$	−0.0590581	−	0.212708i	−0.00320760	−	0.0115527i
$340$	0.510643	+	0.112401i	0.0276935	+	0.00609580i
$341$	0.931788	−	1.37428i	0.0504592	−	0.0744217i
$342$	−0.809211	−	0.766525i	−0.0437571	−	0.0414489i
$343$	7.59736	−	4.57118i	0.410219	−	0.246821i
$344$	−1.43495	+	8.75280i	−0.0773672	+	0.471919i
$345$	1.28446	+	1.89443i	0.0691528	+	0.101993i
$346$	8.61908	+	21.6323i	0.463365	+	1.16296i
$347$	22.3900	+	26.3595i	1.20196	+	1.41505i	0.884347	+	0.466831i	$0.154604\pi$
$347$	22.3900	+	26.3595i	1.20196	+	1.41505i	0.317609	+	0.948222i	$0.397120\pi$
$348$	−0.880776	−	5.37250i	−0.0472145	−	0.287996i
$349$	22.2792	−	21.1040i	1.19258	−	1.12967i	0.203998	−	0.978971i	$-0.434606\pi$
$349$	22.2792	−	21.1040i	1.19258	−	1.12967i	0.988580	−	0.150698i	$-0.0481521\pi$
$350$	5.20015	−	18.7292i	0.277960	−	1.00112i
$351$	−0.874017	+	1.64857i	−0.0466516	+	0.0879942i
$352$	−0.677170	+	0.514771i	−0.0360933	+	0.0274374i
$353$	33.9775			1.80844			0.904219	−	0.427070i	$-0.140454\pi$
$353$	33.9775			1.80844			0.904219	+	0.427070i	$0.140454\pi$
$354$	2.93328	−	7.09901i	0.155902	−	0.377308i
$355$	−2.32321			−0.123303
$356$	3.93988	−	2.99502i	0.208813	−	0.158736i
$357$	−2.38362	+	4.49598i	−0.126155	+	0.237953i
$358$	−3.02720	+	10.9030i	−0.159993	+	0.576241i
$359$	−14.3999	+	13.6404i	−0.760000	+	0.719910i	−0.965972	−	0.258648i	$-0.916723\pi$
$359$	−14.3999	+	13.6404i	−0.760000	+	0.719910i	0.205972	+	0.978558i	$0.433964\pi$
$360$	−0.0669119	−	0.408144i	−0.00352657	−	0.0215111i
$361$	−11.4960	−	13.5342i	−0.605055	−	0.712325i
$362$	3.11648	+	7.82179i	0.163799	+	0.411104i
$363$	5.76701	+	8.50571i	0.302690	+	0.446434i
$364$	−1.21512	+	7.41191i	−0.0636896	+	0.388490i
$365$	−3.61974	+	2.17792i	−0.189466	+	0.113998i
$366$	0.912067	+	0.863956i	0.0476745	+	0.0451597i
$367$	−11.2550	+	16.5999i	−0.587507	+	0.866509i	−0.998991	−	0.0449085i	$-0.985700\pi$
$367$	−11.2550	+	16.5999i	−0.587507	+	0.866509i	0.411484	+	0.911417i	$0.365011\pi$
$368$	−5.40461	−	1.18965i	−0.281735	−	0.0620145i
$369$	−1.61409	−	5.81343i	−0.0840262	−	0.302635i
$370$	−3.08203	−	1.85440i	−0.160227	−	0.0964056i
$371$	−25.8841	+	30.4731i	−1.34383	+	1.58208i
$372$	−1.84980	−	0.623270i	−0.0959077	−	0.0323151i
$373$	34.5530	+	15.9859i	1.78909	+	0.827719i	0.965445	+	0.260608i	$0.0839229\pi$
$373$	34.5530	+	15.9859i	1.78909	+	0.827719i	0.823641	+	0.567112i	$0.191939\pi$
$374$	−0.503706	−	0.950090i	−0.0260460	−	0.0491280i
$375$	−3.97014	+	0.873894i	−0.205017	+	0.0451277i
$376$	−0.788454	+	1.97887i	−0.0406614	+	0.102052i
$377$	9.62676	−	3.24363i	0.495803	−	0.167056i
$378$	4.00166	+	0.435207i	0.205823	+	0.0223846i
$379$	0.111914	−	2.06414i	0.00574866	−	0.106028i	−0.994251	−	0.107076i	$-0.965851\pi$
$379$	0.111914	−	2.06414i	0.00574866	−	0.106028i	0.999999	+	0.00104864i	$0.000333794\pi$
$380$	0.0249580	+	0.460324i	0.00128032	+	0.0236141i
$381$	2.83516	−	0.308342i	0.145249	−	0.0157968i
$382$	−13.2431	+	6.12692i	−0.677577	+	0.313481i
$383$	8.93288	+	6.79060i	0.456449	+	0.346983i	0.807997	−	0.589186i	$-0.200552\pi$
$383$	8.93288	+	6.79060i	0.456449	+	0.346983i	−0.351548	+	0.936170i	$0.614345\pi$
$384$	0.796093	+	0.605174i	0.0406255	+	0.0308827i
$385$	1.28524	−	0.594615i	0.0655018	−	0.0303044i
$386$	−11.7036	+	1.27284i	−0.595698	+	0.0647861i
$387$	0.480193	+	8.85663i	0.0244096	+	0.450208i
$388$	−0.702453	+	12.9560i	−0.0356616	+	0.657740i
$389$	29.1893	+	3.17453i	1.47996	+	0.160955i	0.812181	−	0.583406i	$-0.198280\pi$
$389$	29.1893	+	3.17453i	1.47996	+	0.160955i	0.667777	+	0.744361i	$0.267246\pi$
$390$	0.731337	−	0.246416i	0.0370327	−	0.0124778i
$391$	2.58953	−	6.49923i	0.130958	−	0.328680i
$392$	8.98757	−	1.97831i	0.453941	−	0.0999199i
$393$	1.04864	+	1.97795i	0.0528970	+	0.0997742i
$394$	−20.2395	−	9.36378i	−1.01965	−	0.471740i
$395$	2.28960	+	0.771456i	0.115202	+	0.0388162i
$396$	−0.550678	+	0.648308i	−0.0276726	+	0.0325787i
$397$	−10.3895	−	6.25115i	−0.521433	−	0.313736i	0.230392	−	0.973098i	$-0.425999\pi$
$397$	−10.3895	−	6.25115i	−0.521433	−	0.313736i	−0.751826	+	0.659362i	$0.770827\pi$
$398$	−5.93462	−	21.3746i	−0.297476	−	1.07141i
$399$	−4.38175	−	0.964496i	−0.219362	−	0.0482852i
$400$	2.70994	−	3.99686i	0.135497	−	0.199843i
$401$	7.06334	+	6.69075i	0.352727	+	0.334120i	0.843463	−	0.537188i	$-0.180513\pi$
$401$	7.06334	+	6.69075i	0.352727	+	0.334120i	−0.490736	+	0.871308i	$0.663272\pi$
$402$	5.89554	−	3.54723i	0.294043	−	0.176920i
$403$	0.589252	−	3.59428i	0.0293527	−	0.179044i
$404$	8.59149	+	12.6715i	0.427443	+	0.630431i
$405$	−0.153087	−	0.384218i	−0.00760693	−	0.0190920i
$406$	−14.1871	−	16.7023i	−0.704093	−	0.828922i
$407$	1.19680	+	7.30013i	0.0593230	+	0.361854i
$408$	−0.917809	+	0.869394i	−0.0454383	+	0.0430414i
$409$	7.54862	−	27.1877i	0.373255	−	1.34434i	−0.503744	−	0.863853i	$-0.668044\pi$
$409$	7.54862	−	27.1877i	0.373255	−	1.34434i	0.876999	−	0.480492i	$-0.159542\pi$
$410$	−1.16884	+	2.20467i	−0.0577250	+	0.108881i
$411$	−2.77208	+	2.10728i	−0.136736	+	0.103944i
$412$	−8.44357			−0.415985
$413$	−4.61505	−	30.5722i	−0.227092	−	1.50436i
$414$	−5.53399			−0.271981
$415$	−3.46227	+	2.63195i	−0.169956	+	0.129197i
$416$	−0.874017	+	1.64857i	−0.0428522	+	0.0808279i
$417$	1.35034	−	4.86347i	0.0661263	−	0.238165i
$418$	0.688328	−	0.652019i	0.0336672	−	0.0318913i
$419$	4.14290	+	25.2706i	0.202394	+	1.23455i	0.871132	+	0.491050i	$0.163387\pi$
$419$	4.14290	+	25.2706i	0.202394	+	1.23455i	−0.668738	+	0.743498i	$0.733165\pi$
$420$	−1.07778	−	1.26886i	−0.0525903	−	0.0619141i
$421$	−1.49931	−	3.76298i	−0.0730719	−	0.183397i	0.887904	−	0.460029i	$-0.152161\pi$
$421$	−1.49931	−	3.76298i	−0.0730719	−	0.183397i	−0.960976	+	0.276632i	$0.910782\pi$
$422$	13.6818	+	20.1792i	0.666021	+	0.982308i
$423$	−0.344622	+	2.10210i	−0.0167561	+	0.102208i
$424$	−8.51106	+	5.12093i	−0.413334	+	0.248695i
$425$	4.43204	+	4.19825i	0.214986	+	0.203645i
$426$	3.15227	−	4.64926i	0.152728	−	0.225257i
$427$	4.93870	+	1.08709i	0.239000	+	0.0526080i
$428$	−2.06165	−	7.42539i	−0.0996535	−	0.358920i
$429$	−1.36000	−	0.818283i	−0.0656612	−	0.0395071i
$430$	2.37489	−	2.79593i	0.114527	−	0.134832i
$431$	−13.5788	−	4.57522i	−0.654066	−	0.220381i	−0.0273475	−	0.999626i	$-0.508706\pi$
$431$	−13.5788	−	4.57522i	−0.654066	−	0.220381i	−0.626719	+	0.779245i	$0.715603\pi$
$432$	0.907575	+	0.419889i	0.0436657	+	0.0202019i
$433$	13.8331	+	26.0919i	0.664774	+	1.25390i	0.954905	+	0.296910i	$0.0959561\pi$
$433$	13.8331	+	26.0919i	0.664774	+	1.25390i	−0.290131	+	0.956987i	$0.593699\pi$
$434$	−7.67353	+	1.68907i	−0.368341	+	0.0810781i
$435$	−0.833436	+	2.09177i	−0.0399602	+	0.100293i
$436$	−12.8889	+	4.34276i	−0.617264	+	0.207981i
$437$	6.13215	+	0.666912i	0.293341	+	0.0319027i
$438$	0.552974	−	10.1990i	0.0264221	−	0.487328i
$439$	0.417682	+	7.70368i	0.0199349	+	0.367677i	0.991432	+	0.130625i	$0.0416984\pi$
$439$	0.417682	+	7.70368i	0.0199349	+	0.367677i	−0.971497	+	0.237052i	$0.923819\pi$
$440$	0.349747	−	0.0380373i	0.0166735	−	0.00181336i
$441$	8.35217	−	3.86412i	0.397722	−	0.184006i
$442$	−1.87792	−	1.42756i	−0.0893236	−	0.0679020i
$443$	1.13669	+	0.864087i	0.0540056	+	0.0410540i	0.631829	−	0.775108i	$-0.282305\pi$
$443$	1.13669	+	0.864087i	0.0540056	+	0.0410540i	−0.577823	+	0.816162i	$0.696098\pi$
$444$	7.89294	−	3.65166i	0.374582	−	0.173300i
$445$	−2.03488	+	0.221307i	−0.0964627	+	0.0104909i
$446$	−0.650351	−	11.9950i	−0.0307950	−	0.567981i
$447$	0.705632	−	13.0146i	0.0333753	−	0.615570i
$448$	4.00166	+	0.435207i	0.189061	+	0.0205616i
$449$	−35.6660	+	12.0173i	−1.68318	+	0.567130i	−0.988371	−	0.152061i	$-0.951409\pi$
$449$	−35.6660	+	12.0173i	−1.68318	+	0.567130i	−0.694812	+	0.719192i	$0.744512\pi$
$450$	1.78738	−	4.48597i	0.0842577	−	0.211471i
$451$	5.01208	−	1.10324i	0.236010	−	0.0519496i
$452$	−0.103403	−	0.195039i	−0.00486368	−	0.00917388i
$453$	−13.2626	−	6.13595i	−0.623133	−	0.288292i
$454$	−4.63231	−	1.56081i	−0.217405	−	0.0732524i
$455$	2.01106	−	2.36761i	0.0942801	−	0.110995i
$456$	−0.955072	−	0.574648i	−0.0447253	−	0.0269103i
$457$	−10.0520	−	36.2042i	−0.470214	−	1.69356i	−0.694882	−	0.719124i	$-0.744544\pi$
$457$	−10.0520	−	36.2042i	−0.470214	−	1.69356i	0.224668	−	0.974435i	$-0.427870\pi$
$458$	15.4152	+	3.39315i	0.720306	+	0.158551i
$459$	−0.709457	+	1.04637i	−0.0331146	+	0.0488404i
$460$	1.66167	+	1.57402i	0.0774759	+	0.0733891i
$461$	9.54742	−	5.74449i	0.444668	−	0.267548i	−0.275562	−	0.961283i	$-0.588864\pi$
$461$	9.54742	−	5.74449i	0.444668	−	0.267548i	0.720230	+	0.693736i	$0.244036\pi$
$462$	−0.553934	+	3.37885i	−0.0257714	+	0.157198i
$463$	−17.1829	−	25.3429i	−0.798557	−	1.17778i	−0.980893	−	0.194547i	$-0.937676\pi$
$463$	−17.1829	−	25.3429i	−0.798557	−	1.17778i	0.182336	−	0.983236i	$-0.441634\pi$
$464$	−2.01511	−	5.05755i	−0.0935492	−	0.234791i
$465$	0.522651	+	0.615313i	0.0242374	+	0.0285344i
$466$	1.46062	+	8.90937i	0.0676618	+	0.412719i
$467$	−0.394195	+	0.373401i	−0.0182412	+	0.0172790i	−0.696766	−	0.717299i	$-0.745378\pi$
$467$	−0.394195	+	0.373401i	−0.0182412	+	0.0172790i	0.678525	+	0.734578i	$0.262620\pi$
$468$	−0.499189	+	1.79792i	−0.0230750	+	0.0831087i
$469$	12.9728	−	24.4693i	0.599029	−	1.12989i
$470$	0.701373	−	0.533170i	0.0323519	−	0.0245933i
$471$	−1.53296			−0.0706351
$472$	1.33862	−	7.56360i	0.0616150	−	0.348143i
$473$	−7.54467			−0.346904
$474$	−4.65051	+	3.53523i	−0.213605	+	0.162378i
$475$	−2.52118	+	4.75545i	−0.115680	+	0.218195i
$476$	−1.36139	+	4.90328i	−0.0623991	+	0.224741i
$477$	−7.21123	+	6.83084i	−0.330179	+	0.312763i
$478$	2.20384	+	13.4429i	0.100802	+	0.614862i
$479$	8.45589	+	9.95504i	0.386359	+	0.454858i	0.920618	−	0.390463i	$-0.127685\pi$
$479$	8.45589	+	9.95504i	0.386359	+	0.454858i	−0.534259	+	0.845321i	$0.679409\pi$
$480$	−0.153087	−	0.384218i	−0.00698741	−	0.0175371i
$481$	9.10665	+	13.4313i	0.415228	+	0.612415i
$482$	0.552268	−	3.36869i	0.0251551	−	0.153439i
$483$	−19.0872	+	11.4844i	−0.868496	+	0.522557i
$484$	7.46066	+	7.06711i	0.339121	+	0.321232i
$485$	3.01154	−	4.44169i	0.136747	−	0.201687i
$486$	0.976621	+	0.214970i	0.0443004	+	0.00975126i
$487$	−10.7348	−	38.6634i	−0.486441	−	1.75200i	−0.644530	−	0.764579i	$-0.722947\pi$
$487$	−10.7348	−	38.6634i	−0.486441	−	1.75200i	0.158089	−	0.987425i	$-0.449467\pi$
$488$	1.07647	+	0.647689i	0.0487294	+	0.0293195i
$489$	−10.9097	+	12.8439i	−0.493354	+	0.580821i
$490$	−3.60694	−	1.21532i	−0.162945	−	0.0549025i
$491$	−25.3013	−	11.7056i	−1.14183	−	0.528267i	−0.244510	−	0.969647i	$-0.578627\pi$
$491$	−25.3013	−	11.7056i	−1.14183	−	0.528267i	−0.897321	+	0.441379i	$0.854489\pi$
$492$	−2.82607	−	5.33053i	−0.127409	−	0.240319i
$493$	6.72170	−	1.47956i	0.302730	−	0.0666360i
$494$	0.769816	−	1.93209i	0.0346356	−	0.0869289i
$495$	0.333393	−	0.112333i	0.0149849	−	0.00504900i
$496$	−1.94054	−	0.211046i	−0.0871327	−	0.00947625i
$497$	1.22411	−	22.5773i	0.0549088	−	1.01273i
$498$	−0.569290	−	10.4999i	−0.0255105	−	0.470513i
$499$	−5.90421	+	0.642121i	−0.264309	+	0.0287453i	−0.239314	−	0.970942i	$-0.576922\pi$
$499$	−5.90421	+	0.642121i	−0.264309	+	0.0287453i	−0.0249948	+	0.999688i	$0.507957\pi$
$500$	−3.68946	+	1.70692i	−0.164998	+	0.0763360i
$501$	−8.26036	−	6.27936i	−0.369046	−	0.280541i
$502$	11.3646	+	8.63913i	0.507226	+	0.385583i
$503$	28.9153	−	13.3776i	1.28927	−	0.596480i	0.349068	−	0.937097i	$-0.386498\pi$
$503$	28.9153	−	13.3776i	1.28927	−	0.596480i	0.940202	+	0.340618i	$0.110636\pi$
$504$	4.00166	−	0.435207i	0.178248	−	0.0193857i
$505$	−0.342802	−	6.32261i	−0.0152545	−	0.281353i
$506$	0.254849	−	4.70041i	0.0113294	−	0.208959i
$507$	9.46251	+	1.02911i	0.420245	+	0.0457044i
$508$	2.70259	−	0.910608i	0.119908	−	0.0404017i
$509$	−12.2228	+	30.6768i	−0.541764	+	1.35973i	0.362193	+	0.932103i	$0.382028\pi$
$509$	−12.2228	+	30.6768i	−0.541764	+	1.35973i	−0.903957	+	0.427623i	$0.859351\pi$
$510$	0.510643	−	0.112401i	0.0226116	−	0.00497720i
$511$	−19.2581	−	36.3247i	−0.851930	−	1.60691i
$512$	0.907575	+	0.419889i	0.0401095	+	0.0185567i
$513$	−1.05628	−	0.355900i	−0.0466357	−	0.0157134i
$514$	−10.0352	+	11.8144i	−0.442636	+	0.521111i
$515$	2.99232	+	1.80042i	0.131857	+	0.0793359i
$516$	2.37288	+	8.54634i	0.104460	+	0.376232i
$517$	−1.76959	−	0.389516i	−0.0778264	−	0.0171309i
$518$	19.6452	−	28.9746i	0.863163	−	1.27307i
$519$	16.9056	+	16.0139i	0.742074	+	0.702930i
$520$	0.661267	−	0.397871i	0.0289985	−	0.0174478i
$521$	2.82240	−	17.2159i	0.123652	−	0.754243i	−0.850099	−	0.526624i	$-0.823458\pi$
$521$	2.82240	−	17.2159i	0.123652	−	0.754243i	0.973750	−	0.227619i	$-0.0730940\pi$
$522$	−3.05522	−	4.50612i	−0.133723	−	0.197227i
$523$	−9.83631	−	24.6873i	−0.430112	−	1.07950i	−0.971143	−	0.238497i	$-0.923345\pi$
$523$	−9.83631	−	24.6873i	−0.430112	−	1.07950i	0.541032	−	0.841002i	$-0.318034\pi$
$524$	1.44932	+	1.70628i	0.0633140	+	0.0745391i
$525$	−3.14468	−	19.1817i	−0.137245	−	0.837157i
$526$	0.510743	−	0.483801i	0.0222694	−	0.0210947i
$527$	0.660182	−	2.37776i	0.0287580	−	0.103577i
$528$	−0.398436	+	0.751530i	−0.0173397	+	0.0327062i
$529$	6.07029	−	4.61451i	0.263926	−	0.200631i
$530$	4.10817			0.178447
$531$	−0.318627	−	7.67453i	−0.0138272	−	0.333046i
$532$	−4.48664			−0.194521
$533$	8.96225	−	6.81293i	0.388198	−	0.295101i
$534$	2.31816	−	4.37252i	0.100317	−	0.189218i
$535$	−0.852683	+	3.07109i	−0.0368647	+	0.132775i
$536$	4.99516	−	4.73167i	0.215758	−	0.204377i
$537$	1.83064	+	11.1664i	0.0789978	+	0.481865i
$538$	−2.02913	−	2.38888i	−0.0874821	−	0.102992i
$539$	2.89744	+	7.27203i	0.124802	+	0.313228i
$540$	−0.232103	−	0.342326i	−0.00998812	−	0.0147314i
$541$	−3.36042	+	20.4977i	−0.144476	+	0.881264i	0.810751	+	0.585391i	$0.199059\pi$
$541$	−3.36042	+	20.4977i	−0.144476	+	0.881264i	−0.955227	+	0.295873i	$0.904389\pi$
$542$	−9.90751	+	5.96115i	−0.425564	+	0.256053i
$543$	6.11273	+	5.79028i	0.262322	+	0.248485i
$544$	−0.709457	+	1.04637i	−0.0304177	+	0.0448628i
$545$	5.49369	+	1.20925i	0.235324	+	0.0517987i
$546$	2.00937	+	7.23708i	0.0859929	+	0.309719i
$547$	−34.3229	−	20.6514i	−1.46754	−	0.882991i	−0.467543	−	0.883970i	$-0.654861\pi$
$547$	−34.3229	−	20.6514i	−1.46754	−	0.882991i	−1.00000		0.000979359i	$0.999688\pi$
$548$	−2.25426	+	2.65392i	−0.0962974	+	0.113370i
$549$	1.19054	+	0.401138i	0.0508108	+	0.0171202i
$550$	3.72794	+	1.72473i	0.158960	+	0.0735426i
$551$	2.84242	+	5.36136i	0.121091	+	0.228402i
$552$	−5.40461	+	1.18965i	−0.230036	+	0.0506347i
$553$	−8.70352	+	21.8442i	−0.370111	+	0.928909i
$554$	8.60422	−	2.89910i	0.365558	−	0.123171i
$555$	−3.57582	−	0.388894i	−0.151785	−	0.0165076i
$556$	0.273264	−	5.04005i	0.0115890	−	0.213746i
$557$	−0.477371	−	8.80459i	−0.0202269	−	0.373063i	−0.991070	−	0.133345i	$-0.957428\pi$
$557$	−0.477371	−	8.80459i	−0.0202269	−	0.373063i	0.970843	−	0.239717i	$-0.0770547\pi$
$558$	−1.94054	+	0.211046i	−0.0821495	+	0.00893430i
$559$	−15.0205	+	6.94922i	−0.635299	+	0.293921i
$560$	−1.32535	−	1.00751i	−0.0560063	−	0.0425749i
$561$	−0.856083	−	0.650778i	−0.0361439	−	0.0274759i
$562$	−12.2949	+	5.68823i	−0.518630	+	0.239944i
$563$	18.4326	−	2.00467i	0.776843	−	0.0844868i	0.288897	−	0.957360i	$-0.406712\pi$
$563$	18.4326	−	2.00467i	0.776843	−	0.0844868i	0.487947	+	0.872873i	$0.337746\pi$
$564$	0.115325	+	2.12704i	0.00485604	+	0.0895644i
$565$	−0.00494302	+	0.0911687i	−0.000207954	+	0.00383549i
$566$	15.5271	+	1.68867i	0.652653	+	0.0709803i
$567$	3.81455	−	1.28527i	0.160196	−	0.0539763i
$568$	2.07912	−	5.21821i	0.0872381	−	0.218951i
$569$	38.2991	−	8.43026i	1.60558	−	0.353415i	0.680370	−	0.732869i	$-0.261819\pi$
$569$	38.2991	−	8.43026i	1.60558	−	0.353415i	0.925211	+	0.379454i	$0.123888\pi$
$570$	0.215936	+	0.407299i	0.00904457	+	0.0170599i
$571$	1.80877	+	0.836828i	0.0756948	+	0.0350202i	0.457371	−	0.889276i	$-0.348791\pi$
$571$	1.80877	+	0.836828i	0.0756948	+	0.0350202i	−0.381676	+	0.924296i	$0.624653\pi$
$572$	−1.50411	−	0.506793i	−0.0628899	−	0.0211901i
$573$	−9.44651	+	11.1213i	−0.394633	+	0.464598i
$574$	−20.8094	−	12.5206i	−0.868569	−	0.522601i
$575$	7.14925	+	25.7493i	0.298144	+	1.07382i
$576$	0.976621	+	0.214970i	0.0406925	+	0.00895710i
$577$	11.7342	−	17.3066i	0.488500	−	0.720484i	−0.500931	−	0.865487i	$-0.667009\pi$
$577$	11.7342	−	17.3066i	0.488500	−	0.720484i	0.989431	+	0.145003i	$0.0463193\pi$
$578$	11.1816	+	10.5918i	0.465094	+	0.440561i
$579$	−10.0875	+	6.06942i	−0.419220	+	0.252237i
$580$	−0.364283	+	2.22203i	−0.0151260	+	0.0922646i
$581$	−23.7534	−	35.0336i	−0.985457	−	1.45344i
$582$	4.80255	+	12.0535i	0.199072	+	0.499633i
$583$	−5.46982	−	6.43957i	−0.226537	−	0.266700i
$584$	−1.65244	−	10.0794i	−0.0683784	−	0.417090i
$585$	0.560276	−	0.530722i	0.0231646	−	0.0219427i
$586$	4.83973	−	17.4311i	0.199927	−	0.720073i
$587$	12.9888	−	24.4996i	0.536107	−	1.01121i	−0.456487	−	0.889730i	$-0.650893\pi$
$587$	12.9888	−	24.4996i	0.536107	−	1.01121i	0.992594	−	0.121475i	$-0.0387625\pi$
$588$	7.32623	−	5.56925i	0.302128	−	0.229672i
$589$	2.17572			0.0896490
$590$	−2.08718	+	2.39503i	−0.0859277	+	0.0986019i
$591$	−22.3006			−0.917324
$592$	6.92340	−	5.26303i	0.284550	−	0.216309i
$593$	13.0577	−	24.6294i	0.536216	−	1.01141i	−0.456362	−	0.889794i	$-0.650848\pi$
$593$	13.0577	−	24.6294i	0.536216	−	1.01141i	0.992577	−	0.121615i	$-0.0388075\pi$
$594$	−0.227564	+	0.819612i	−0.00933707	+	0.0336291i
$595$	1.52799	−	1.44738i	0.0626413	−	0.0593370i
$596$	−2.10862	−	12.8620i	−0.0863726	−	0.526849i
$597$	−14.3611	−	16.9071i	−0.587759	−	0.691964i
$598$	−3.82206	−	9.59266i	−0.156296	−	0.392273i
$599$	−23.6713	−	34.9126i	−0.967185	−	1.42649i	−0.903533	−	0.428518i	$-0.859036\pi$
$599$	−23.6713	−	34.9126i	−0.967185	−	1.42649i	−0.0636516	−	0.997972i	$-0.520275\pi$
$600$	0.781236	−	4.76533i	0.0318938	−	0.194544i
$601$	−11.9610	+	7.19670i	−0.487900	+	0.293559i	−0.738168	−	0.674617i	$-0.764309\pi$
$601$	−11.9610	+	7.19670i	−0.487900	+	0.293559i	0.250268	+	0.968177i	$0.419481\pi$
$602$	25.9199	+	24.5527i	1.05642	+	1.00069i
$603$	3.86121	−	5.69485i	0.157240	−	0.231912i
$604$	−14.2716	−	3.14142i	−0.580703	−	0.127823i
$605$	−1.13707	−	4.09534i	−0.0462283	−	0.166499i
$606$	13.1181	+	7.89287i	0.532884	+	0.320626i
$607$	−26.1963	+	30.8406i	−1.06327	+	1.25178i	−0.0967226	+	0.995311i	$0.530836\pi$
$607$	−26.1963	+	30.8406i	−1.06327	+	1.25178i	−0.966552	+	0.256472i	$0.917440\pi$
$608$	−1.05628	−	0.355900i	−0.0428376	−	0.0144337i
$609$	−19.8890	−	9.20161i	−0.805941	−	0.372868i
$610$	−0.243383	−	0.459069i	−0.00985430	−	0.0185872i
$611$	−3.88180	+	0.854449i	−0.157041	+	0.0345673i
$612$	−0.467931	+	1.17442i	−0.0189150	+	0.0474731i
$613$	38.7693	−	13.0629i	1.56588	−	0.527605i	0.603045	−	0.797707i	$-0.293954\pi$
$613$	38.7693	−	13.0629i	1.56588	−	0.527605i	0.962832	+	0.270102i	$0.0870573\pi$
$614$	21.2998	+	2.31649i	0.859589	+	0.0934859i
$615$	−0.135095	+	2.49169i	−0.00544757	+	0.100475i
$616$	0.185369	+	3.41893i	0.00746874	+	0.137753i
$617$	44.1439	−	4.80094i	1.77717	−	0.193279i	0.840101	−	0.542430i	$-0.182496\pi$
$617$	44.1439	−	4.80094i	1.77717	−	0.193279i	0.937066	+	0.349152i	$0.113530\pi$
$618$	−7.66318	+	3.54536i	−0.308258	+	0.142615i
$619$	−31.6676	−	24.0731i	−1.27283	−	0.967578i	−0.999985	−	0.00551931i	$-0.998243\pi$
$619$	−31.6676	−	24.0731i	−1.27283	−	0.967578i	−0.272842	−	0.962059i	$-0.587964\pi$
$620$	0.642706	+	0.488572i	0.0258117	+	0.0196215i
$621$	−5.02252	+	2.32366i	−0.201547	+	0.0932454i
$622$	4.25781	−	0.463065i	0.170723	−	0.0185672i
$623$	−1.07851	−	19.8919i	−0.0432095	−	0.796952i
$624$	−0.101019	+	1.86319i	−0.00404401	+	0.0745874i
$625$	−22.3317	−	2.42872i	−0.893268	−	0.0971487i
$626$	−9.19339	+	3.09761i	−0.367442	+	0.123806i
$627$	0.350934	−	0.880778i	0.0140150	−	0.0351749i
$628$	−1.49712	+	0.329541i	−0.0597416	+	0.0131501i
$629$	5.14990	+	9.71374i	0.205340	+	0.387312i
$630$	−1.51095	−	0.699039i	−0.0601977	−	0.0278504i
$631$	−8.05372	−	2.71361i	−0.320614	−	0.108027i	0.154393	−	0.988010i	$-0.450658\pi$
$631$	−8.05372	−	2.71361i	−0.320614	−	0.108027i	−0.475007	+	0.879982i	$0.657554\pi$
$632$	−3.78182	+	4.45230i	−0.150433	+	0.177103i
$633$	20.8903	+	12.5693i	0.830316	+	0.499585i
$634$	4.90033	+	17.6494i	0.194617	+	0.700946i
$635$	−1.15194	−	0.253561i	−0.0457133	−	0.0100623i
$636$	−5.57420	+	8.22134i	−0.221032	+	0.325997i
$637$	12.4665	+	11.8089i	0.493942	+	0.467887i
$638$	3.96806	−	2.38750i	0.157097	−	0.0945220i
$639$	0.908754	−	5.54316i	0.0359498	−	0.219284i
$640$	−0.232103	−	0.342326i	−0.00917468	−	0.0135316i
$641$	0.549439	+	1.37899i	0.0217015	+	0.0544667i	0.939428	−	0.342746i	$-0.111357\pi$
$641$	0.549439	+	1.37899i	0.0217015	+	0.0544667i	−0.917727	+	0.397212i	$0.869978\pi$
$642$	−4.98894	−	5.87343i	−0.196898	−	0.231806i
$643$	1.93891	+	11.8268i	0.0764630	+	0.466404i	0.997108	+	0.0760021i	$0.0242156\pi$
$643$	1.93891	+	11.8268i	0.0764630	+	0.466404i	−0.920645	+	0.390402i	$0.872336\pi$
$644$	−16.1721	+	15.3190i	−0.637270	+	0.603655i
$645$	0.981406	−	3.53471i	0.0386428	−	0.139179i
$646$	0.660040	−	1.24497i	0.0259689	−	0.0489826i
$647$	−18.3243	+	13.9298i	−0.720402	+	0.547636i	−0.899886	−	0.436125i	$-0.856350\pi$
$647$	−18.3243	+	13.9298i	−0.720402	+	0.547636i	0.179484	+	0.983761i	$0.442557\pi$
$648$	1.00000			0.0392837
$649$	6.53319	+	0.0827914i	0.256450	+	0.00324985i
$650$	9.01046			0.353419
$651$	−6.25509	+	4.75499i	−0.245156	+	0.186363i
$652$	−7.89358	+	14.8889i	−0.309136	+	0.583093i
$653$	−4.48344	+	16.1479i	−0.175451	+	0.631916i	0.822549	+	0.568694i	$0.192551\pi$
$653$	−4.48344	+	16.1479i	−0.175451	+	0.631916i	−0.998000	+	0.0632214i	$0.979863\pi$
$654$	−9.87413	+	9.35327i	−0.386109	+	0.365742i
$655$	−0.149798	−	0.913726i	−0.00585308	−	0.0357022i
$656$	−3.90590	−	4.59839i	−0.152500	−	0.179537i
$657$	−3.78059	−	9.48856i	−0.147495	−	0.370184i
$658$	4.81187	+	7.09698i	0.187586	+	0.276669i
$659$	−0.631520	+	3.85210i	−0.0246005	+	0.150057i	−0.996270	−	0.0862854i	$-0.972500\pi$
$659$	−0.631520	+	3.85210i	−0.0246005	+	0.150057i	0.971670	+	0.236342i	$0.0759486\pi$
$660$	0.301450	−	0.181377i	0.0117339	−	0.00706007i
$661$	32.2738	+	30.5713i	1.25530	+	1.18909i	0.973265	+	0.229684i	$0.0737691\pi$
$661$	32.2738	+	30.5713i	1.25530	+	1.18909i	0.282038	+	0.959403i	$0.408990\pi$
$662$	−5.71101	+	8.42312i	−0.221965	+	0.327374i
$663$	−2.30377	−	0.507098i	−0.0894711	−	0.0196941i
$664$	−2.81316	−	10.1321i	−0.109172	−	0.393201i
$665$	1.59002	+	0.956684i	0.0616584	+	0.0370986i
$666$	5.63014	−	6.62832i	0.218164	−	0.256842i
$667$	28.5511	+	9.62000i	1.10550	+	0.372488i
$668$	−9.41712	−	4.35682i	−0.364359	−	0.168570i
$669$	−5.62682	−	10.6133i	−0.217546	−	0.410335i
$670$	−2.77917	+	0.611740i	−0.107369	+	0.0236336i
$671$	−0.395540	+	0.992731i	−0.0152697	+	0.0383240i
$672$	3.81455	−	1.28527i	0.147150	−	0.0495804i
$673$	−1.16030	−	0.126190i	−0.0447263	−	0.00486427i	0.0857285	−	0.996319i	$-0.472678\pi$
$673$	−1.16030	−	0.126190i	−0.0447263	−	0.00486427i	−0.130455	+	0.991454i	$0.541644\pi$
$674$	−1.19855	+	22.1060i	−0.0461665	+	0.851490i
$675$	−0.261434	−	4.82186i	−0.0100626	−	0.185593i
$676$	9.46251	−	1.02911i	0.363943	−	0.0395812i
$677$	−43.9969	+	20.3551i	−1.69094	+	0.782311i	−0.692811	+	0.721119i	$0.743628\pi$
$677$	−43.9969	+	20.3551i	−1.69094	+	0.782311i	−0.998126	+	0.0611917i	$0.980510\pi$
$678$	−0.175741	−	0.133595i	−0.00674930	−	0.00513069i
$679$	41.5782	+	31.6069i	1.59562	+	1.21296i
$680$	0.474541	−	0.219546i	0.0181978	−	0.00841921i
$681$	−4.85954	+	0.528507i	−0.186218	+	0.0202524i
$682$	−0.0898916	−	1.65795i	−0.00344213	−	0.0634863i
$683$	−2.44950	+	45.1783i	−0.0937274	+	1.72870i	0.453104	+	0.891458i	$0.350317\pi$
$683$	−2.44950	+	45.1783i	−0.0937274	+	1.72870i	−0.546831	+	0.837243i	$0.684166\pi$
$684$	−1.10809	−	0.120512i	−0.0423688	−	0.00460789i
$685$	1.36478	−	0.459849i	0.0521457	−	0.0175699i
$686$	3.28185	−	8.23682i	0.125302	−	0.314483i
$687$	15.4152	−	3.39315i	0.588127	−	0.129457i
$688$	4.15461	+	7.83643i	0.158393	+	0.298761i
$689$	−16.8211	−	7.78225i	−0.640831	−	0.296480i
$690$	2.16901	+	0.730824i	0.0825727	+	0.0278220i
$691$	−0.185199	+	0.218033i	−0.00704530	+	0.00829437i	−0.765673	−	0.643230i	$-0.777594\pi$
$691$	−0.185199	+	0.218033i	−0.00704530	+	0.00829437i	0.758628	+	0.651524i	$0.225870\pi$
$692$	19.9529	+	12.0053i	0.758495	+	0.456371i
$693$	0.916005	+	3.29915i	0.0347962	+	0.125324i
$694$	33.7766	+	7.43479i	1.28214	+	0.282221i
$695$	−1.17153	+	1.72788i	−0.0444386	+	0.0655421i
$696$	−3.95248	−	3.74398i	−0.149818	−	0.141915i
$697$	6.53559	−	3.93233i	0.247553	−	0.148948i
$698$	4.96473	−	30.2835i	0.187918	−	1.14625i
$699$	5.06657	+	7.47263i	0.191635	+	0.282641i
$700$	−7.19465	−	18.0572i	−0.271932	−	0.682499i
$701$	7.86803	+	9.26297i	0.297172	+	0.349857i	0.890402	−	0.455175i	$-0.150423\pi$
$701$	7.86803	+	9.26297i	0.297172	+	0.349857i	−0.593230	+	0.805033i	$0.702148\pi$
$702$	0.301874	+	1.84135i	0.0113935	+	0.0694972i
$703$	−7.03748	+	6.66626i	−0.265424	+	0.251423i
$704$	−0.227564	+	0.819612i	−0.00857665	+	0.0308903i
$705$	0.412677	−	0.778391i	0.0155423	−	0.0293159i
$706$	27.0492	−	20.5623i	1.01801	−	0.773872i
$707$	61.6247			2.31764
$708$	−1.96098	−	7.42661i	−0.0736980	−	0.279109i
$709$	−33.2252			−1.24780			−0.623898	−	0.781505i	$-0.714452\pi$
$709$	−33.2252			−1.24780			−0.623898	+	0.781505i	$0.714452\pi$
$710$	−1.84950	+	1.40595i	−0.0694103	+	0.0527644i
$711$	−2.73629	+	5.16119i	−0.102619	+	0.193560i
$712$	1.32400	−	4.76863i	0.0496192	−	0.178712i
$713$	7.84238	−	7.42870i	0.293700	−	0.278207i
$714$	0.823270	+	5.02173i	0.0308101	+	0.187933i
$715$	0.424977	+	0.500322i	0.0158933	+	0.0187110i
$716$	4.18828	+	10.5118i	0.156523	+	0.392844i
$717$	7.64467	+	11.2750i	0.285495	+	0.421074i
$718$	−3.20891	+	19.5735i	−0.119755	+	0.730475i
$719$	−38.8880	+	23.3981i	−1.45028	+	0.872602i	−0.999796	−	0.0201847i	$-0.993575\pi$
$719$	−38.8880	+	23.3981i	−1.45028	+	0.872602i	−0.450480	+	0.892787i	$0.648747\pi$
$720$	−0.300267	−	0.284428i	−0.0111903	−	0.0106000i
$721$	−19.0734	+	28.1312i	−0.710330	+	1.04766i
$722$	−17.3425	−	3.81736i	−0.645419	−	0.142068i
$723$	−0.913250	−	3.28923i	−0.0339641	−	0.122328i
$724$	7.21456	+	4.34085i	0.268127	+	0.161327i
$725$	−17.0197	+	20.0371i	−0.632094	+	0.744159i
$726$	9.73851	+	3.28129i	0.361430	+	0.121780i
$727$	−8.86814	−	4.10284i	−0.328901	−	0.152166i	0.248488	−	0.968635i	$-0.420066\pi$
$727$	−8.86814	−	4.10284i	−0.328901	−	0.152166i	−0.577389	+	0.816469i	$0.695928\pi$
$728$	3.51815	+	6.63593i	0.130391	+	0.245944i
$729$	0.976621	−	0.214970i	0.0361711	−	0.00796187i
$730$	−1.56362	+	3.92440i	−0.0578723	+	0.145249i
$731$	−10.6261	+	3.58035i	−0.393020	+	0.132424i
$732$	1.24893	+	0.135830i	0.0461619	+	0.00502041i
$733$	0.761364	−	14.0425i	0.0281216	−	0.518673i	−0.950208	−	0.311617i	$-0.899129\pi$
$733$	0.761364	−	14.0425i	0.0281216	−	0.518673i	0.978329	−	0.207055i	$-0.0663880\pi$
$734$	1.08580	+	20.0263i	0.0400775	+	0.739185i
$735$	−3.78387	+	0.411521i	−0.139570	+	0.0151792i
$736$	−5.02252	+	2.32366i	−0.185132	+	0.0856514i
$737$	4.65922	+	3.54185i	0.171625	+	0.130466i
$738$	−4.80310	−	3.65122i	−0.176805	−	0.134403i
$739$	−7.36706	+	3.40837i	−0.271002	+	0.125379i	−0.550684	−	0.834714i	$-0.685633\pi$
$739$	−7.36706	+	3.40837i	−0.271002	+	0.125379i	0.279682	+	0.960093i	$0.409771\pi$
$740$	−3.57582	+	0.388894i	−0.131450	+	0.0142960i
$741$	−0.112598	−	2.07676i	−0.00413641	−	0.0762915i
$742$	−2.16461	+	39.9238i	−0.0794652	+	1.46565i
$743$	−25.1435	−	2.73452i	−0.922424	−	0.100320i	−0.365433	−	0.930838i	$-0.619079\pi$
$743$	−25.1435	−	2.73452i	−0.922424	−	0.100320i	−0.556992	+	0.830518i	$0.688044\pi$
$744$	−1.84980	+	0.623270i	−0.0678170	+	0.0228502i
$745$	−1.99529	+	5.00780i	−0.0731017	+	0.183471i
$746$	37.1817	−	8.18430i	1.36132	−	0.299649i
$747$	−4.92548	−	9.29045i	−0.180214	−	0.339920i
$748$	−0.975967	−	0.451530i	−0.0356849	−	0.0165096i
$749$	−29.3960	−	9.90467i	−1.07411	−	0.361909i
$750$	−2.63174	+	3.09833i	−0.0960976	+	0.113135i
$751$	−40.9065	−	24.6126i	−1.49270	−	0.898128i	−0.999604	−	0.0281529i	$-0.991037\pi$
$751$	−40.9065	−	24.6126i	−1.49270	−	0.898128i	−0.493096	−	0.869975i	$-0.664135\pi$
$752$	0.569878	+	2.05252i	0.0207813	+	0.0748476i
$753$	13.9417	+	3.06880i	0.508063	+	0.111833i
$754$	5.70083	−	8.40810i	0.207612	−	0.306205i
$755$	4.38787	+	4.15641i	0.159691	+	0.151267i
$756$	3.44907	−	2.07524i	0.125442	−	0.0754757i
$757$	−4.64324	+	28.3225i	−0.168761	+	1.02940i	0.757588	+	0.652733i	$0.226378\pi$
$757$	−4.64324	+	28.3225i	−0.168761	+	1.02940i	−0.926349	+	0.376666i	$0.877070\pi$
$758$	−1.16007	−	1.71098i	−0.0421357	−	0.0621455i
$759$	−1.74236	−	4.37298i	−0.0632435	−	0.158729i
$760$	0.298445	+	0.351356i	0.0108257	+	0.0127450i
$761$	4.03867	+	24.6348i	0.146402	+	0.893010i	0.953235	+	0.302231i	$0.0977313\pi$
$761$	4.03867	+	24.6348i	0.146402	+	0.893010i	−0.806833	+	0.590779i	$0.798820\pi$
$762$	2.07045	−	1.96123i	0.0750044	−	0.0710479i
$763$	−14.6463	+	52.7513i	−0.530233	+	1.90973i
$764$	−6.83490	+	12.8920i	−0.247278	+	0.466416i
$765$	0.416251	−	0.316426i	0.0150496	−	0.0114404i
$766$	11.2209			0.405428
$767$	13.0830	−	5.85274i	0.472400	−	0.211330i
$768$	1.00000			0.0360844
$769$	26.2746	−	19.9735i	0.947488	−	0.720262i	−0.0126115	−	0.999920i	$-0.504014\pi$
$769$	26.2746	−	19.9735i	0.947488	−	0.720262i	0.960099	+	0.279659i	$0.0902214\pi$
$770$	0.663324	−	1.25116i	0.0239045	−	0.0450888i
$771$	−4.14700	+	14.9361i	−0.149351	+	0.537912i
$772$	−8.54687	+	8.09603i	−0.307609	+	0.291382i
$773$	0.865560	+	5.27969i	0.0311320	+	0.189897i	0.997814	−	0.0660829i	$-0.0210502\pi$
$773$	0.865560	+	5.27969i	0.0311320	+	0.189897i	−0.966682	+	0.255980i	$0.917602\pi$
$774$	5.74208	+	6.76010i	0.206395	+	0.242987i
$775$	3.48892	+	8.75653i	0.125326	+	0.314544i
$776$	7.28141	+	10.7393i	0.261387	+	0.385517i
$777$	5.66344	−	34.5454i	0.203175	−	1.23931i
$778$	25.1586	−	15.1374i	0.901979	−	0.542702i
$779$	4.88224	+	4.62471i	0.174925	+	0.165697i
$780$	0.433088	−	0.638757i	0.0155070	−	0.0228712i
$781$	4.66634	+	1.02714i	0.166975	+	0.0367539i
$782$	−1.87166	−	6.74111i	−0.0669304	−	0.241061i
$783$	−4.66491	−	2.80679i	−0.166710	−	0.100306i
$784$	5.95772	−	7.01397i	0.212776	−	0.250499i
$785$	0.600832	+	0.202444i	0.0214446	+	0.00722554i
$786$	2.03182	+	0.940019i	0.0724726	+	0.0335294i
$787$	12.4671	+	23.5155i	0.444405	+	0.838237i	0.999977	+	0.00676842i	$0.00215447\pi$
$787$	12.4671	+	23.5155i	0.444405	+	0.838237i	−0.555572	+	0.831468i	$0.687501\pi$
$788$	−21.7792	+	4.79397i	−0.775853	+	0.170778i
$789$	0.260395	−	0.653541i	0.00927030	−	0.0232667i
$790$	2.28960	−	0.771456i	0.0814603	−	0.0274472i
$791$	−0.883386	−	0.0960740i	−0.0314096	−	0.00341600i
$792$	−0.0460515	+	0.849369i	−0.00163637	+	0.0301810i
$793$	0.126910	+	2.34073i	0.00450672	+	0.0831216i
$794$	−12.0540	+	1.31096i	−0.427782	+	0.0465241i
$795$	3.72847	−	1.72498i	0.132235	−	0.0611786i
$796$	−17.6598	−	13.4247i	−0.625937	−	0.475825i
$797$	−16.0046	−	12.1664i	−0.566913	−	0.430956i	0.282057	−	0.959398i	$-0.408983\pi$
$797$	−16.0046	−	12.1664i	−0.566913	−	0.430956i	−0.848969	+	0.528442i	$0.822776\pi$
$798$	−4.07197	+	1.88389i	−0.144146	+	0.0666891i
$799$	−2.67718	+	0.291161i	−0.0947117	+	0.0103005i
$800$	−0.261434	−	4.82186i	−0.00924307	−	0.170478i
$801$	0.267935	−	4.94177i	0.00946701	−	0.174609i
$802$	9.67215	+	1.05191i	0.341536	+	0.0371442i
$803$	8.23339	−	2.77415i	0.290550	−	0.0978977i
$804$	2.54671	−	6.39176i	0.0898155	−	0.225420i
$805$	8.99770	−	1.98054i	0.317127	−	0.0698050i
$806$	−1.70606	−	3.21798i	−0.0600936	−	0.113348i
$807$	−2.84465	−	1.31608i	−0.100137	−	0.0463281i
$808$	14.5081	+	4.88835i	0.510393	+	0.171971i
$809$	−16.0857	+	18.9376i	−0.565545	+	0.665811i	−0.968385	−	0.249459i	$-0.919747\pi$
$809$	−16.0857	+	18.9376i	−0.565545	+	0.665811i	0.402840	+	0.915270i	$0.368023\pi$
$810$	−0.354390	−	0.213229i	−0.0124520	−	0.00749212i
$811$	−3.24790	−	11.6979i	−0.114049	−	0.410768i	0.884382	−	0.466764i	$-0.154580\pi$
$811$	−3.24790	−	11.6979i	−0.114049	−	0.410768i	−0.998431	+	0.0559960i	$0.982167\pi$
$812$	−21.4020	−	4.71095i	−0.751064	−	0.165322i
$813$	−6.48879	+	9.57025i	−0.227572	+	0.335643i
$814$	5.37061	+	5.08731i	0.188240	+	0.178310i
$815$	5.97215	−	3.59332i	0.209195	−	0.125869i
$816$	−0.204526	+	1.24755i	−0.00715984	+	0.0436731i
$817$	−5.54806	−	8.18278i	−0.194102	−	0.286279i
$818$	−10.4439	−	26.2122i	−0.365162	−	0.916487i
$819$	4.86242	+	5.72449i	0.169907	+	0.200030i
$820$	0.403702	+	2.46248i	0.0140979	+	0.0859934i
$821$	10.0392	−	9.50967i	0.350372	−	0.331890i	−0.492192	−	0.870487i	$-0.663804\pi$
$821$	10.0392	−	9.50967i	0.350372	−	0.331890i	0.842564	+	0.538597i	$0.181045\pi$
$822$	−0.931560	+	3.35518i	−0.0324919	+	0.117025i
$823$	8.78168	−	16.5640i	0.306110	−	0.577385i	−0.681960	−	0.731389i	$-0.738872\pi$
$823$	8.78168	−	16.5640i	0.306110	−	0.577385i	0.988070	+	0.154005i	$0.0492171\pi$
$824$	−6.72187	+	5.10983i	−0.234167	+	0.178009i
$825$	4.10758			0.143008
$826$	−22.1755	−	21.5454i	−0.771586	−	0.749662i
$827$	−46.2287			−1.60753			−0.803765	−	0.594947i	$-0.797173\pi$
$827$	−46.2287			−1.60753			−0.803765	+	0.594947i	$0.797173\pi$
$828$	−4.40558	+	3.34903i	−0.153104	+	0.116387i
$829$	12.7872	−	24.1192i	0.444117	−	0.837694i	−0.555862	−	0.831274i	$-0.687612\pi$
$829$	12.7872	−	24.1192i	0.444117	−	0.837694i	0.999979	−	0.00641927i	$-0.00204333\pi$
$830$	−1.16350	+	4.19055i	−0.0403857	+	0.145456i
$831$	6.59168	−	6.24397i	0.228663	−	0.216601i
$832$	0.301874	+	1.84135i	0.0104656	+	0.0638373i
$833$	7.53179	+	8.86711i	0.260961	+	0.307227i
$834$	−1.86826	−	4.68897i	−0.0646924	−	0.162366i
$835$	2.40833	+	3.55202i	0.0833437	+	0.122923i
$836$	0.153388	−	0.935626i	0.00530504	−	0.0323593i
$837$	−1.67257	+	1.00635i	−0.0578124	+	0.0347846i
$838$	18.5912	+	17.6105i	0.642223	+	0.608346i
$839$	−4.20418	+	6.20070i	−0.145144	+	0.214072i	−0.893311	−	0.449439i	$-0.851624\pi$
$839$	−4.20418	+	6.20070i	−0.145144	+	0.214072i	0.748167	+	0.663511i	$0.230934\pi$
$840$	−1.62590	−	0.357887i	−0.0560988	−	0.0123483i
$841$	0.171079	+	0.616170i	0.00589926	+	0.0212472i
$842$	−3.47085	−	2.08834i	−0.119613	−	0.0719690i
$843$	−8.77014	+	10.3250i	−0.302060	+	0.355612i
$844$	23.1039	+	7.78463i	0.795271	+	0.267958i
$845$	−3.57286	−	1.65298i	−0.122910	−	0.0568642i
$846$	0.997785	+	1.88202i	0.0343046	+	0.0647053i
$847$	40.3983	−	8.89234i	1.38810	−	0.305544i
$848$	−3.67654	+	9.22741i	−0.126253	+	0.316871i
$849$	14.8011	−	4.98706i	0.507972	−	0.171156i
$850$	6.06899	+	0.660043i	0.208165	+	0.0226393i
$851$	−2.60558	+	48.0571i	−0.0893181	+	1.64737i
$852$	−0.304107	−	5.60892i	−0.0104185	−	0.192158i
$853$	26.9279	−	2.92859i	0.921995	−	0.100273i	0.365206	−	0.930927i	$-0.380999\pi$
$853$	26.9279	−	2.92859i	0.921995	−	0.100273i	0.556789	+	0.830654i	$0.312033\pi$
$854$	4.58954	−	2.12335i	0.157051	−	0.0726595i
$855$	0.366999	+	0.278985i	0.0125511	+	0.00954109i
$856$	−6.13492	−	4.66364i	−0.209687	−	0.159400i
$857$	49.3372	−	22.8258i	1.68533	−	0.779715i	0.686721	−	0.726921i	$-0.259049\pi$
$857$	49.3372	−	22.8258i	1.68533	−	0.779715i	0.998605	−	0.0527937i	$-0.0168126\pi$
$858$	−1.57789	+	0.171606i	−0.0538682	+	0.00585852i
$859$	1.82979	+	33.7485i	0.0624316	+	1.15148i	0.847053	+	0.531509i	$0.178375\pi$
$859$	1.82979	+	33.7485i	0.0624316	+	1.15148i	−0.784621	+	0.619975i	$0.787143\pi$
$860$	0.198604	−	3.66304i	0.00677235	−	0.124909i
$861$	−24.1434	−	2.62575i	−0.822805	−	0.0894855i
$862$	−13.5788	+	4.57522i	−0.462495	+	0.155833i
$863$	18.5604	−	46.5831i	0.631803	−	1.58571i	−0.168228	−	0.985748i	$-0.553804\pi$
$863$	18.5604	−	46.5831i	0.631803	−	1.58571i	0.800031	−	0.599959i	$-0.204816\pi$
$864$	0.976621	−	0.214970i	0.0332253	−	0.00731344i
$865$	−4.51123	−	8.50908i	−0.153386	−	0.289318i
$866$	26.8025	+	12.4002i	0.910787	+	0.421375i
$867$	14.5955	+	4.91781i	0.495691	+	0.167018i
$868$	−5.08666	+	5.98848i	−0.172653	+	0.203262i
$869$	−4.25774	−	2.56180i	−0.144434	−	0.0869031i
$870$	0.602391	+	2.16961i	0.0204230	+	0.0735568i
$871$	12.5382	+	2.75988i	0.424842	+	0.0935148i
$872$	−7.63260	+	11.2572i	−0.258472	+	0.381218i
$873$	9.41980	+	8.92291i	0.318812	+	0.301995i
$874$	5.28536	−	3.18010i	0.178780	−	0.107568i
$875$	−2.64731	+	16.1478i	−0.0894953	+	0.545897i
$876$	−5.73196	−	8.45401i	−0.193665	−	0.285634i
$877$	−2.08341	−	5.22896i	−0.0703517	−	0.176570i	0.889596	−	0.456748i	$-0.150986\pi$
$877$	−2.08341	−	5.22896i	−0.0703517	−	0.176570i	−0.959948	+	0.280178i	$0.909606\pi$
$878$	4.99458	+	5.88008i	0.168559	+	0.198443i
$879$	−2.92672	−	17.8522i	−0.0987159	−	0.602140i
$880$	0.255412	−	0.241939i	0.00860993	−	0.00815576i
$881$	12.9305	−	46.5713i	0.435638	−	1.56903i	−0.341616	−	0.939840i	$-0.610974\pi$
$881$	12.9305	−	46.5713i	0.435638	−	1.56903i	0.777254	−	0.629187i	$-0.216612\pi$
$882$	4.31063	−	8.13072i	0.145147	−	0.273776i
$883$	16.0217	−	12.1794i	0.539174	−	0.409869i	−0.299832	−	0.953992i	$-0.596930\pi$
$883$	16.0217	−	12.1794i	0.539174	−	0.409869i	0.839006	+	0.544123i	$0.183137\pi$
$884$	−2.35892			−0.0793391
$885$	−0.888622	+	3.05006i	−0.0298707	+	0.102526i
$886$	1.42783			0.0479690
$887$	−5.17767	+	3.93596i	−0.173849	+	0.132157i	−0.688480	−	0.725255i	$-0.741722\pi$
$887$	−5.17767	+	3.93596i	−0.173849	+	0.132157i	0.514631	+	0.857412i	$0.327929\pi$
$888$	4.07362	−	7.68366i	0.136702	−	0.257847i
$889$	3.07110	−	11.0611i	0.103001	−	0.370978i
$890$	−1.48603	+	1.40764i	−0.0498117	+	0.0471842i
$891$	0.137615	+	0.839411i	0.00461026	+	0.0281213i
$892$	−7.77682	−	9.15558i	−0.260387	−	0.306552i
$893$	−0.878828	−	2.20569i	−0.0294088	−	0.0738106i
$894$	−7.31436	−	10.7879i	−0.244629	−	0.360801i
$895$	0.757138	−	4.61834i	0.0253083	−	0.154374i
$896$	3.44907	−	2.07524i	0.115225	−	0.0693289i
$897$	−7.49666	−	7.10122i	−0.250306	−	0.237103i
$898$	−21.1209	+	31.1510i	−0.704814	+	1.03952i
$899$	10.3785	+	2.28449i	0.346144	+	0.0761920i
$900$	−1.29188	−	4.65293i	−0.0430626	−	0.155098i
$901$	−10.7597	−	6.47392i	−0.358459	−	0.215678i
$902$	3.32243	−	3.91146i	0.110625	−	0.130238i
$903$	33.8337	+	11.3999i	1.12592	+	0.379365i
$904$	−0.200352	−	0.0926925i	−0.00666359	−	0.00308291i
$905$	−1.63117	−	3.07671i	−0.0542219	−	0.102273i
$906$	−14.2716	+	3.14142i	−0.474142	+	0.104367i
$907$	10.6796	−	26.8038i	0.354611	−	0.890006i	−0.638151	−	0.769911i	$-0.720301\pi$
$907$	10.6796	−	26.8038i	0.354611	−	0.890006i	0.992762	−	0.120096i	$-0.0383201\pi$
$908$	−4.63231	+	1.56081i	−0.153729	+	0.0517972i
$909$	15.2198	+	1.65525i	0.504807	+	0.0549011i
$910$	0.168179	−	3.10188i	0.00557508	−	0.102826i
$911$	−2.42718	−	44.7666i	−0.0804159	−	1.48318i	−0.708871	−	0.705338i	$-0.750795\pi$
$911$	−2.42718	−	44.7666i	−0.0804159	−	1.48318i	0.628455	−	0.777846i	$-0.283688\pi$
$912$	−1.10809	+	0.120512i	−0.0366925	+	0.00399055i
$913$	8.11785	−	3.75572i	0.268661	−	0.124296i
$914$	−29.9122	−	22.7386i	−0.989407	−	0.752128i
$915$	−0.413647	−	0.314446i	−0.0136747	−	0.0103953i
$916$	14.3254	−	6.62763i	0.473324	−	0.218983i
$917$	8.95866	−	0.974313i	0.295841	−	0.0321746i
$918$	0.0684428	+	1.26235i	0.00225895	+	0.0416639i
$919$	−1.54977	+	28.5838i	−0.0511222	+	0.942894i	0.854670	+	0.519172i	$0.173759\pi$
$919$	−1.54977	+	28.5838i	−0.0511222	+	0.942894i	−0.905792	+	0.423722i	$0.860723\pi$
$920$	2.27540	+	0.247465i	0.0750178	+	0.00815868i
$921$	20.3038	−	6.84115i	0.669034	−	0.225424i
$922$	4.12422	−	10.3510i	0.135824	−	0.340892i
$923$	10.2362	−	2.25315i	0.336928	−	0.0741634i
$924$	1.60381	+	3.02511i	0.0527615	+	0.0995187i
$925$	−38.1145	−	17.6337i	−1.25320	−	0.579791i
$926$	−29.0160	−	9.77664i	−0.953526	−	0.321280i
$927$	−5.46625	+	6.43537i	−0.179535	+	0.211365i
$928$	−4.66491	−	2.80679i	−0.153133	−	0.0921373i
$929$	−7.99758	−	28.8047i	−0.262392	−	0.945051i	−0.970927	−	0.239376i	$-0.923057\pi$
$929$	−7.99758	−	28.8047i	−0.262392	−	0.945051i	0.708535	−	0.705676i	$-0.249357\pi$
$930$	0.788450	+	0.173551i	0.0258543	+	0.00569096i
$931$	−5.75641	+	8.49007i	−0.188659	+	0.278251i
$932$	6.55451	+	6.20876i	0.214700	+	0.203375i
$933$	3.66985	−	2.20807i	0.120145	−	0.0722891i
$934$	−0.0878431	+	0.535819i	−0.00287431	+	0.0175325i
$935$	0.249593	+	0.368123i	0.00816257	+	0.0120389i
$936$	0.690652	+	1.73341i	0.0225747	+	0.0566581i
$937$	11.5013	+	13.5403i	0.375730	+	0.442343i	0.917230	−	0.398357i	$-0.130420\pi$
$937$	11.5013	+	13.5403i	0.375730	+	0.442343i	−0.541501	+	0.840700i	$0.682144\pi$
$938$	−4.48064	−	27.3307i	−0.146298	−	0.892378i
$939$	−7.04304	+	6.67153i	−0.229841	+	0.217717i
$940$	0.235698	−	0.848906i	0.00768761	−	0.0276883i
$941$	5.96205	−	11.2456i	0.194357	−	0.366597i	−0.767110	−	0.641515i	$-0.778306\pi$
$941$	5.96205	−	11.2456i	0.194357	−	0.366597i	0.961467	+	0.274919i	$0.0886509\pi$
$942$	−1.22038	+	0.927708i	−0.0397621	+	0.0302264i
$943$	33.3885			1.08728
$944$	−3.51163	−	6.83143i	−0.114294	−	0.222344i
$945$	−1.66482			−0.0541566
$946$	−6.00626	+	4.56584i	−0.195280	+	0.148448i
$947$	4.64366	−	8.75887i	0.150899	−	0.284625i	−0.796526	−	0.604604i	$-0.793331\pi$
$947$	4.64366	−	8.75887i	0.150899	−	0.284625i	0.947424	+	0.319979i	$0.103676\pi$
$948$	−1.56281	+	5.62874i	−0.0507578	+	0.182813i
$949$	13.8364	−	13.1066i	0.449150	−	0.425458i
$950$	0.870782	+	5.31154i	0.0282519	+	0.172329i
$951$	11.8582	+	13.9605i	0.384528	+	0.452702i
$952$	1.88355	+	4.72734i	0.0610461	+	0.153214i
$953$	−7.09806	−	10.4689i	−0.229929	−	0.339119i	0.695171	−	0.718845i	$-0.255329\pi$
$953$	−7.09806	−	10.4689i	−0.229929	−	0.339119i	−0.925099	+	0.379725i	$0.876018\pi$
$954$	−1.60696	+	9.80203i	−0.0520273	+	0.317352i
$955$	5.17117	−	3.11139i	0.167335	−	0.100682i
$956$	9.88974	+	9.36806i	0.319857	+	0.302985i
$957$	2.59882	−	3.83298i	0.0840081	−	0.123903i
$958$	12.7562	+	2.80785i	0.412134	+	0.0907177i
$959$	3.74977	+	13.5055i	0.121086	+	0.436114i
$960$	−0.354390	−	0.213229i	−0.0114379	−	0.00688195i
$961$	−17.6023	+	20.7230i	−0.567816	+	0.668484i
$962$	15.3780	+	5.18146i	0.495807	+	0.167057i
$963$	−6.99403	−	3.23578i	−0.225379	−	0.104272i
$964$	−1.59899	−	3.01601i	−0.0514999	−	0.0971390i
$965$	4.75524	−	1.04671i	0.153077	−	0.0336947i
$966$	−8.24511	+	20.6937i	−0.265282	+	0.665808i
$967$	−21.3241	+	7.18494i	−0.685738	+	0.231052i	−0.640539	−	0.767926i	$-0.721289\pi$
$967$	−21.3241	+	7.18494i	−0.685738	+	0.231052i	−0.0451992	+	0.998978i	$0.514392\pi$
$968$	10.2162	+	1.11108i	0.328361	+	0.0357115i
$969$	0.0762878	−	1.40705i	0.00245072	−	0.0452008i
$970$	−0.290530	−	5.35850i	−0.00932834	−	0.172051i
$971$	−56.7490	+	6.17183i	−1.82116	+	0.198063i	−0.953969	−	0.299906i	$-0.903045\pi$
$971$	−56.7490	+	6.17183i	−1.82116	+	0.198063i	−0.867194	+	0.497970i	$0.834079\pi$
$972$	0.907575	−	0.419889i	0.0291105	−	0.0134679i
$973$	−16.1745	−	12.2955i	−0.518530	−	0.394176i
$974$	−31.9440	−	24.2832i	−1.02355	−	0.778084i
$975$	8.17768	−	3.78340i	0.261895	−	0.121166i
$976$	1.24893	−	0.135830i	0.0399774	−	0.00434780i
$977$	0.813169	+	14.9980i	0.0260156	+	0.479829i	0.982291	+	0.187362i	$0.0599936\pi$
$977$	0.813169	+	14.9980i	0.0260156	+	0.479829i	−0.956275	+	0.292468i	$0.905524\pi$
$978$	−0.912344	+	16.8272i	−0.0291735	+	0.538074i
$979$	4.18505	+	0.455151i	0.133755	+	0.0145467i
$980$	−3.60694	+	1.21532i	−0.115219	+	0.0388220i
$981$	−5.03418	+	12.6348i	−0.160729	+	0.403399i
$982$	−27.2261	+	5.99292i	−0.868820	+	0.191242i
$983$	−12.5695	−	23.7085i	−0.400904	−	0.756185i	0.598072	−	0.801443i	$-0.295934\pi$
$983$	−12.5695	−	23.7085i	−0.400904	−	0.756185i	−0.998975	+	0.0452579i	$0.985589\pi$
$984$	−5.47571	−	2.53333i	−0.174559	−	0.0807598i
$985$	8.74055	+	2.94504i	0.278497	+	0.0938366i
$986$	4.45571	−	5.24567i	0.141899	−	0.167056i
$987$	7.34708	+	4.42059i	0.233860	+	0.140709i
$988$	−0.556407	−	2.00400i	−0.0177017	−	0.0637556i
$989$	−47.9370	−	10.5517i	−1.52431	−	0.335525i
$990$	0.197431	−	0.291189i	0.00627476	−	0.00925458i
$991$	14.5482	+	13.7808i	0.462140	+	0.437762i	0.883007	−	0.469360i	$-0.155516\pi$
$991$	14.5482	+	13.7808i	0.462140	+	0.437762i	−0.420867	+	0.907122i	$0.638274\pi$
$992$	−1.67257	+	1.00635i	−0.0531041	+	0.0319517i
$993$	−1.64640	+	10.0426i	−0.0522470	+	0.318692i
$994$	−12.6887	−	18.7145i	−0.402462	−	0.593587i
$995$	3.39594	+	8.52317i	0.107659	+	0.270203i
$996$	−6.80750	−	8.01441i	−0.215704	−	0.253946i
$997$	0.586698	+	3.57870i	0.0185809	+	0.113338i	0.994488	−	0.104846i	$-0.0334349\pi$
$997$	0.586698	+	3.57870i	0.0185809	+	0.113338i	−0.975908	+	0.218184i	$0.929987\pi$
$998$	−4.31170	+	4.08426i	−0.136485	+	0.129285i
$999$	2.32662	−	8.37973i	0.0736110	−	0.265123i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.e.a.85.1	yes	56
59.25	even	29	inner	354.2.e.a.25.1	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.e.a.25.1	✓	56	59.25	even	29	inner
354.2.e.a.85.1	yes	56	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(0.796093 - 0.605174i) q^{2} +(0.468408 - 0.883512i) q^{3} +(0.267528 - 0.963550i) q^{4} +(-0.300267 + 0.284428i) q^{5} +(-0.161782 - 0.986827i) q^{6} +(-2.60590 - 3.06790i) q^{7} +(-0.370138 - 0.928977i) q^{8} +(-0.561187 - 0.827689i) q^{9} +O(q^{10})\)	\(q+(0.796093 - 0.605174i) q^{2} +(0.468408 - 0.883512i) q^{3} +(0.267528 - 0.963550i) q^{4} +(-0.300267 + 0.284428i) q^{5} +(-0.161782 - 0.986827i) q^{6} +(-2.60590 - 3.06790i) q^{7} +(-0.370138 - 0.928977i) q^{8} +(-0.561187 - 0.827689i) q^{9} +(-0.0669119 + 0.408144i) q^{10} +(0.728857 - 0.438539i) q^{11} +(-0.725995 - 0.687699i) q^{12} +(1.04714 - 1.54441i) q^{13} +(-3.93115 - 0.865312i) q^{14} +(0.110648 + 0.398517i) q^{15} +(-0.856857 - 0.515554i) q^{16} +(0.818430 - 0.963531i) q^{17} +(-0.947653 - 0.319302i) q^{18} +(1.01160 + 0.468018i) q^{19} +(0.193730 + 0.365414i) q^{20} +(-3.93115 + 0.865312i) q^{21} +(0.314846 - 0.790203i) q^{22} +(5.24431 - 1.76701i) q^{23} +(-0.994138 - 0.108119i) q^{24} +(-0.261434 + 4.82186i) q^{25} +(-0.101019 - 1.86319i) q^{26} +(-0.994138 + 0.108119i) q^{27} +(-3.65323 + 1.69016i) q^{28} +(4.33410 + 3.29470i) q^{29} +(0.329258 + 0.250296i) q^{30} +(1.77157 - 0.819615i) q^{31} +(-0.994138 + 0.108119i) q^{32} +(-0.0460515 - 0.849369i) q^{33} +(0.0684428 - 1.26235i) q^{34} +(1.65506 + 0.179999i) q^{35} +(-0.947653 + 0.319302i) q^{36} +(-3.21899 + 8.07906i) q^{37} +(1.08856 - 0.239611i) q^{38} +(-0.874017 - 1.64857i) q^{39} +(0.375367 + 0.173663i) q^{40} +(5.71752 + 1.92646i) q^{41} +(-2.60590 + 3.06790i) q^{42} +(-7.60002 - 4.57278i) q^{43} +(-0.227564 - 0.819612i) q^{44} +(0.403923 + 0.0889102i) q^{45} +(3.10561 - 4.58043i) q^{46} +(-1.54649 - 1.46491i) q^{47} +(-0.856857 + 0.515554i) q^{48} +(-1.48884 + 9.08149i) q^{49} +(2.70994 + 3.99686i) q^{50} +(-0.467931 - 1.17442i) q^{51} +(-1.20798 - 1.42214i) q^{52} +(-1.60696 - 9.80203i) q^{53} +(-0.725995 + 0.687699i) q^{54} +(-0.0941189 + 0.338986i) q^{55} +(-1.88547 + 3.55637i) q^{56} +(0.887343 - 0.674540i) q^{57} +5.44422 q^{58} +(6.53094 + 4.04313i) q^{59} +0.413593 q^{60} +(-1.00013 + 0.760279i) q^{61} +(0.914324 - 1.72460i) q^{62} +(-1.07687 + 3.87854i) q^{63} +(-0.725995 + 0.687699i) q^{64} +(0.124853 + 0.761569i) q^{65} +(-0.550678 - 0.648308i) q^{66} +(2.54671 + 6.39176i) q^{67} +(-0.709457 - 1.04637i) q^{68} +(0.895301 - 5.46109i) q^{69} +(1.42651 - 0.858304i) q^{70} +(4.07803 + 3.86291i) q^{71} +(-0.561187 + 0.827689i) q^{72} +(9.97519 + 2.19571i) q^{73} +(2.32662 + 8.37973i) q^{74} +(4.13771 + 2.48958i) q^{75} +(0.721591 - 0.849523i) q^{76} +(-3.24472 - 1.09327i) q^{77} +(-1.69347 - 0.783484i) q^{78} +(-2.73629 - 5.16119i) q^{79} +(0.403923 - 0.0889102i) q^{80} +(-0.370138 + 0.928977i) q^{81} +(5.71752 - 1.92646i) q^{82} +(10.4537 + 1.13691i) q^{83} +(-0.217923 + 4.01936i) q^{84} +(0.0283074 + 0.522100i) q^{85} +(-8.81765 + 0.958977i) q^{86} +(4.94104 - 2.28597i) q^{87} +(-0.677170 - 0.514771i) q^{88} +(3.93988 + 2.99502i) q^{89} +(0.375367 - 0.173663i) q^{90} +(-7.46682 + 0.812066i) q^{91} +(-0.299604 - 5.52588i) q^{92} +(0.105678 - 1.94912i) q^{93} +(-2.11767 - 0.230311i) q^{94} +(-0.436868 + 0.147198i) q^{95} +(-0.370138 + 0.928977i) q^{96} +(-12.6717 + 2.78924i) q^{97} +(4.31063 + 8.13072i) q^{98} +(-0.771999 - 0.357165i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 56 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9	\( 56 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} - 18 q^{11} - 2 q^{12} + 13 q^{13} - 20 q^{14} + 4 q^{15} - 2 q^{16} + 21 q^{17} - 2 q^{18} + 20 q^{19} + 4 q^{20} - 20 q^{21} + 11 q^{22} + 34 q^{23} - 2 q^{24} - 28 q^{25} - 16 q^{26} - 2 q^{27} + 9 q^{28} + 38 q^{29} + 4 q^{30} + 34 q^{31} - 2 q^{32} + 11 q^{33} - 8 q^{34} - 19 q^{35} - 2 q^{36} - 29 q^{37} + 20 q^{38} + 13 q^{39} + 4 q^{40} + 43 q^{41} + 9 q^{42} - 65 q^{43} + 11 q^{44} + 4 q^{45} + 5 q^{46} - 60 q^{47} - 2 q^{48} - 13 q^{49} - 86 q^{50} + 21 q^{51} - 16 q^{52} - 15 q^{53} - 2 q^{54} - 15 q^{55} + 9 q^{56} + 20 q^{57} - 78 q^{58} - 2 q^{59} - 54 q^{60} + 4 q^{61} + 5 q^{62} + 9 q^{63} - 2 q^{64} - 57 q^{65} + 11 q^{66} - 56 q^{67} - 8 q^{68} - 53 q^{69} + 10 q^{70} + 23 q^{71} - 2 q^{72} - 21 q^{73} + 30 q^{75} - 9 q^{76} - 57 q^{77} + 13 q^{78} + 99 q^{79} + 4 q^{80} - 2 q^{81} + 43 q^{82} + 33 q^{83} + 9 q^{84} - 45 q^{85} - 7 q^{86} + 9 q^{87} - 18 q^{88} + 32 q^{89} + 4 q^{90} - 75 q^{91} + 34 q^{92} + 5 q^{93} + 27 q^{94} + 82 q^{95} - 2 q^{96} + 70 q^{97} + 45 q^{98} + 11 q^{99}+O(q^{100}) \) 56 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9 + 4 * q^10 - 18 * q^11 - 2 * q^12 + 13 * q^13 - 20 * q^14 + 4 * q^15 - 2 * q^16 + 21 * q^17 - 2 * q^18 + 20 * q^19 + 4 * q^20 - 20 * q^21 + 11 * q^22 + 34 * q^23 - 2 * q^24 - 28 * q^25 - 16 * q^26 - 2 * q^27 + 9 * q^28 + 38 * q^29 + 4 * q^30 + 34 * q^31 - 2 * q^32 + 11 * q^33 - 8 * q^34 - 19 * q^35 - 2 * q^36 - 29 * q^37 + 20 * q^38 + 13 * q^39 + 4 * q^40 + 43 * q^41 + 9 * q^42 - 65 * q^43 + 11 * q^44 + 4 * q^45 + 5 * q^46 - 60 * q^47 - 2 * q^48 - 13 * q^49 - 86 * q^50 + 21 * q^51 - 16 * q^52 - 15 * q^53 - 2 * q^54 - 15 * q^55 + 9 * q^56 + 20 * q^57 - 78 * q^58 - 2 * q^59 - 54 * q^60 + 4 * q^61 + 5 * q^62 + 9 * q^63 - 2 * q^64 - 57 * q^65 + 11 * q^66 - 56 * q^67 - 8 * q^68 - 53 * q^69 + 10 * q^70 + 23 * q^71 - 2 * q^72 - 21 * q^73 + 30 * q^75 - 9 * q^76 - 57 * q^77 + 13 * q^78 + 99 * q^79 + 4 * q^80 - 2 * q^81 + 43 * q^82 + 33 * q^83 + 9 * q^84 - 45 * q^85 - 7 * q^86 + 9 * q^87 - 18 * q^88 + 32 * q^89 + 4 * q^90 - 75 * q^91 + 34 * q^92 + 5 * q^93 + 27 * q^94 + 82 * q^95 - 2 * q^96 + 70 * q^97 + 45 * q^98 + 11 * q^99

Introduction

L-functions

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