LMFDB - Embedded newform 354.2.e.d.25.2

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:	$84$
Relative dimension:	$3$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			25.2
Character	$\chi$	$=$	354.25
Dual form			354.2.e.d.85.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.796093 - 0.605174i) q^{2} +(0.468408 + 0.883512i) q^{3} +(0.267528 + 0.963550i) q^{4} +(-0.526198 - 0.498441i) q^{5} +(0.161782 - 0.986827i) q^{6} +(2.82058 - 3.32064i) q^{7} +(0.370138 - 0.928977i) q^{8} +(-0.561187 + 0.827689i) q^{9} +O(q^{10})$	\(q+(-0.796093 - 0.605174i) q^{2} +(0.468408 + 0.883512i) q^{3} +(0.267528 + 0.963550i) q^{4} +(-0.526198 - 0.498441i) q^{5} +(0.161782 - 0.986827i) q^{6} +(2.82058 - 3.32064i) q^{7} +(0.370138 - 0.928977i) q^{8} +(-0.561187 + 0.827689i) q^{9} +(0.117259 + 0.715246i) q^{10} +(-1.40341 - 0.844402i) q^{11} +(-0.725995 + 0.687699i) q^{12} +(-0.194957 - 0.287541i) q^{13} +(-4.25501 + 0.936599i) q^{14} +(0.193903 - 0.698376i) q^{15} +(-0.856857 + 0.515554i) q^{16} +(1.34586 + 1.58447i) q^{17} +(0.947653 - 0.319302i) q^{18} +(6.04018 - 2.79449i) q^{19} +(0.339500 - 0.640365i) q^{20} +(4.25501 + 0.936599i) q^{21} +(0.606232 + 1.52153i) q^{22} +(1.15158 + 0.388013i) q^{23} +(0.994138 - 0.108119i) q^{24} +(-0.242254 - 4.46811i) q^{25} +(-0.0188080 + 0.346892i) q^{26} +(-0.994138 - 0.108119i) q^{27} +(3.95419 + 1.82940i) q^{28} +(5.30487 - 4.03266i) q^{29} +(-0.577004 + 0.438627i) q^{30} +(2.64701 + 1.22464i) q^{31} +(0.994138 + 0.108119i) q^{32} +(0.0886716 - 1.63545i) q^{33} +(-0.112550 - 2.07586i) q^{34} +(-3.13933 + 0.341422i) q^{35} +(-0.947653 - 0.319302i) q^{36} +(2.54021 + 6.37546i) q^{37} +(-6.49970 - 1.43069i) q^{38} +(0.162726 - 0.306934i) q^{39} +(-0.657806 + 0.304333i) q^{40} +(-7.30089 + 2.45996i) q^{41} +(-2.82058 - 3.32064i) q^{42} +(-1.95491 + 1.17623i) q^{43} +(0.438172 - 1.57815i) q^{44} +(0.707849 - 0.155809i) q^{45} +(-0.681950 - 1.00580i) q^{46} +(-4.76013 + 4.50904i) q^{47} +(-0.856857 - 0.515554i) q^{48} +(-1.93853 - 11.8245i) q^{49} +(-2.51113 + 3.70364i) q^{50} +(-0.769484 + 1.93126i) q^{51} +(0.224903 - 0.264777i) q^{52} +(1.17353 - 7.15820i) q^{53} +(0.725995 + 0.687699i) q^{54} +(0.317585 + 1.14384i) q^{55} +(-2.04080 - 3.84935i) q^{56} +(5.29824 + 4.02761i) q^{57} -6.66363 q^{58} +(4.42632 - 6.27755i) q^{59} +0.724795 q^{60} +(0.340656 + 0.258960i) q^{61} +(-1.36615 - 2.57682i) q^{62} +(1.16559 + 4.19806i) q^{63} +(-0.725995 - 0.687699i) q^{64} +(-0.0407359 + 0.248478i) q^{65} +(-1.06032 + 1.24831i) q^{66} +(-3.87492 + 9.72533i) q^{67} +(-1.16666 + 1.72069i) q^{68} +(0.196596 + 1.19918i) q^{69} +(2.70582 + 1.62804i) q^{70} +(-9.37685 + 8.88222i) q^{71} +(0.561187 + 0.827689i) q^{72} +(0.773487 - 0.170257i) q^{73} +(1.83602 - 6.61273i) q^{74} +(3.83416 - 2.30693i) q^{75} +(4.30855 + 5.07241i) q^{76} +(-6.76237 + 2.27851i) q^{77} +(-0.315293 + 0.145870i) q^{78} +(-6.98767 + 13.1801i) q^{79} +(0.707849 + 0.155809i) q^{80} +(-0.370138 - 0.928977i) q^{81} +(7.30089 + 2.45996i) q^{82} +(6.07451 - 0.660643i) q^{83} +(0.235876 + 4.35048i) q^{84} +(0.0815755 - 1.50457i) q^{85} +(2.26812 + 0.246673i) q^{86} +(6.04775 + 2.79799i) q^{87} +(-1.30388 + 0.991187i) q^{88} +(-1.50440 + 1.14361i) q^{89} +(-0.657806 - 0.304333i) q^{90} +(-1.50471 - 0.163647i) q^{91} +(-0.0657892 + 1.21341i) q^{92} +(0.157900 + 2.91229i) q^{93} +(6.51826 - 0.708904i) q^{94} +(-4.57122 - 1.54022i) q^{95} +(0.370138 + 0.928977i) q^{96} +(-15.4646 - 3.40401i) q^{97} +(-5.61263 + 10.5865i) q^{98} +(1.48648 - 0.687717i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 3 q^{2} - 3 q^{3} - 3 q^{4} - 2 q^{5} + 3 q^{6} - 7 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 84 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 - 2 * q^5 + 3 * q^6 - 7 * q^7 + 3 * q^8 - 3 * q^9	\( 84 q + 3 q^{2} - 3 q^{3} - 3 q^{4} - 2 q^{5} + 3 q^{6} - 7 q^{7} + 3 q^{8} - 3 q^{9} + 2 q^{10} + 30 q^{11} - 3 q^{12} - 3 q^{13} + 7 q^{14} - 2 q^{15} - 3 q^{16} + 3 q^{17} + 3 q^{18} - 4 q^{19} - 2 q^{20} - 7 q^{21} - q^{22} + 2 q^{23} + 3 q^{24} - 67 q^{25} + 32 q^{26} - 3 q^{27} - 7 q^{28} + 4 q^{29} + 2 q^{30} - 6 q^{31} + 3 q^{32} + q^{33} + 26 q^{34} + 79 q^{35} - 3 q^{36} + 55 q^{37} + 4 q^{38} - 3 q^{39} + 2 q^{40} + q^{41} + 7 q^{42} + 51 q^{43} + q^{44} - 2 q^{45} - 31 q^{46} - 62 q^{47} - 3 q^{48} - 70 q^{49} + 9 q^{50} + 3 q^{51} - 32 q^{52} - 27 q^{53} + 3 q^{54} - 83 q^{55} + 7 q^{56} - 4 q^{57} - 120 q^{58} - 55 q^{59} + 56 q^{60} - 46 q^{61} - 23 q^{62} - 7 q^{63} - 3 q^{64} - 121 q^{65} - q^{66} + 8 q^{67} - 26 q^{68} - 27 q^{69} - 50 q^{70} - 61 q^{71} + 3 q^{72} + 49 q^{73} - 26 q^{74} - 9 q^{75} + 25 q^{76} + 77 q^{77} + 3 q^{78} - 5 q^{79} - 2 q^{80} - 3 q^{81} - q^{82} + 75 q^{83} - 7 q^{84} + 189 q^{85} + 65 q^{86} - 25 q^{87} - 30 q^{88} + 54 q^{89} + 2 q^{90} - 161 q^{91} + 2 q^{92} + 23 q^{93} + 33 q^{94} - 54 q^{95} + 3 q^{96} + 28 q^{97} + 12 q^{98} + q^{99}+O(q^{100}) \) 84 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 - 2 * q^5 + 3 * q^6 - 7 * q^7 + 3 * q^8 - 3 * q^9 + 2 * q^10 + 30 * q^11 - 3 * q^12 - 3 * q^13 + 7 * q^14 - 2 * q^15 - 3 * q^16 + 3 * q^17 + 3 * q^18 - 4 * q^19 - 2 * q^20 - 7 * q^21 - q^22 + 2 * q^23 + 3 * q^24 - 67 * q^25 + 32 * q^26 - 3 * q^27 - 7 * q^28 + 4 * q^29 + 2 * q^30 - 6 * q^31 + 3 * q^32 + q^33 + 26 * q^34 + 79 * q^35 - 3 * q^36 + 55 * q^37 + 4 * q^38 - 3 * q^39 + 2 * q^40 + q^41 + 7 * q^42 + 51 * q^43 + q^44 - 2 * q^45 - 31 * q^46 - 62 * q^47 - 3 * q^48 - 70 * q^49 + 9 * q^50 + 3 * q^51 - 32 * q^52 - 27 * q^53 + 3 * q^54 - 83 * q^55 + 7 * q^56 - 4 * q^57 - 120 * q^58 - 55 * q^59 + 56 * q^60 - 46 * q^61 - 23 * q^62 - 7 * q^63 - 3 * q^64 - 121 * q^65 - q^66 + 8 * q^67 - 26 * q^68 - 27 * q^69 - 50 * q^70 - 61 * q^71 + 3 * q^72 + 49 * q^73 - 26 * q^74 - 9 * q^75 + 25 * q^76 + 77 * q^77 + 3 * q^78 - 5 * q^79 - 2 * q^80 - 3 * q^81 - q^82 + 75 * q^83 - 7 * q^84 + 189 * q^85 + 65 * q^86 - 25 * q^87 - 30 * q^88 + 54 * q^89 + 2 * q^90 - 161 * q^91 + 2 * q^92 + 23 * q^93 + 33 * q^94 - 54 * q^95 + 3 * q^96 + 28 * q^97 + 12 * q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{6}{29}\right)$	$1$

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
$5$	−0.526198	−	0.498441i	−0.235323	−	0.222910i	0.560946	−	0.827852i	$-0.310437\pi$
$5$	−0.526198	−	0.498441i	−0.235323	−	0.222910i	−0.796269	+	0.604943i	$0.793196\pi$
$6$	0.161782	−	0.986827i	0.0660472	−	0.402870i
$7$	2.82058	−	3.32064i	1.06608	−	1.25509i	0.100510	−	0.994936i	$-0.467952\pi$
$7$	2.82058	−	3.32064i	1.06608	−	1.25509i	0.965568	−	0.260149i	$-0.0837717\pi$
$8$	0.370138	−	0.928977i	0.130864	−	0.328443i
$9$	−0.561187	+	0.827689i	−0.187062	+	0.275896i
$10$	0.117259	+	0.715246i	0.0370805	+	0.226181i
$11$	−1.40341	−	0.844402i	−0.423143	−	0.254597i	0.288019	−	0.957625i	$-0.407003\pi$
$11$	−1.40341	−	0.844402i	−0.423143	−	0.254597i	−0.711162	+	0.703028i	$0.751831\pi$
$12$	−0.725995	+	0.687699i	−0.209577	+	0.198522i
$13$	−0.194957	−	0.287541i	−0.0540715	−	0.0797495i	0.799692	−	0.600410i	$-0.204996\pi$
$13$	−0.194957	−	0.287541i	−0.0540715	−	0.0797495i	−0.853764	+	0.520661i	$0.825686\pi$
$14$	−4.25501	+	0.936599i	−1.13720	+	0.250317i
$15$	0.193903	−	0.698376i	0.0500656	−	0.180320i
$16$	−0.856857	+	0.515554i	−0.214214	+	0.128888i
$17$	1.34586	+	1.58447i	0.326418	+	0.384289i	0.900753	−	0.434331i	$-0.143015\pi$
$17$	1.34586	+	1.58447i	0.326418	+	0.384289i	−0.574335	+	0.818620i	$0.694739\pi$
$18$	0.947653	−	0.319302i	0.223364	−	0.0752601i
$19$	6.04018	−	2.79449i	1.38571	−	0.641099i	0.421647	−	0.906760i	$-0.361452\pi$
$19$	6.04018	−	2.79449i	1.38571	−	0.641099i	0.964066	+	0.265661i	$0.0855902\pi$
$20$	0.339500	−	0.640365i	0.0759145	−	0.143190i
$21$	4.25501	+	0.936599i	0.928520	+	0.204383i
$22$	0.606232	+	1.52153i	0.129249	+	0.324391i
$23$	1.15158	+	0.388013i	0.240121	+	0.0809063i	0.436789	−	0.899564i	$-0.356116\pi$
$23$	1.15158	+	0.388013i	0.240121	+	0.0809063i	−0.196668	+	0.980470i	$0.563012\pi$
$24$	0.994138	−	0.108119i	0.202928	−	0.0220697i
$25$	−0.242254	−	4.46811i	−0.0484508	−	0.893622i
$26$	−0.0188080	+	0.346892i	−0.00368854	+	0.0680312i
$27$	−0.994138	−	0.108119i	−0.191322	−	0.0208075i
$28$	3.95419	+	1.82940i	0.747272	+	0.345725i
$29$	5.30487	−	4.03266i	0.985090	−	0.748846i	0.0171049	−	0.999854i	$-0.494555\pi$
$29$	5.30487	−	4.03266i	0.985090	−	0.748846i	0.967985	+	0.251008i	$0.0807620\pi$
$30$	−0.577004	+	0.438627i	−0.105346	+	0.0800820i
$31$	2.64701	+	1.22464i	0.475416	+	0.219951i	0.642939	−	0.765917i	$-0.277715\pi$
$31$	2.64701	+	1.22464i	0.475416	+	0.219951i	−0.167523	+	0.985868i	$0.553577\pi$
$32$	0.994138	+	0.108119i	0.175740	+	0.0191129i
$33$	0.0886716	−	1.63545i	0.0154357	−	0.284696i
$34$	−0.112550	−	2.07586i	−0.0193021	−	0.356007i
$35$	−3.13933	+	0.341422i	−0.530643	+	0.0577109i
$36$	−0.947653	−	0.319302i	−0.157942	−	0.0532169i
$37$	2.54021	+	6.37546i	0.417609	+	1.04812i	0.975850	+	0.218440i	$0.0700969\pi$
$37$	2.54021	+	6.37546i	0.417609	+	1.04812i	−0.558242	+	0.829678i	$0.688524\pi$
$38$	−6.49970	−	1.43069i	−1.05439	−	0.232089i
$39$	0.162726	−	0.306934i	0.0260570	−	0.0491487i
$40$	−0.657806	+	0.304333i	−0.104008	+	0.0481193i
$41$	−7.30089	+	2.45996i	−1.14021	+	0.384180i	−0.825162	−	0.564896i	$-0.808916\pi$
$41$	−7.30089	+	2.45996i	−1.14021	+	0.384180i	−0.315045	+	0.949077i	$0.602020\pi$
$42$	−2.82058	−	3.32064i	−0.435225	−	0.512386i
$43$	−1.95491	+	1.17623i	−0.298121	+	0.179374i	−0.656754	−	0.754105i	$-0.728071\pi$
$43$	−1.95491	+	1.17623i	−0.298121	+	0.179374i	0.358632	+	0.933479i	$0.383243\pi$
$44$	0.438172	−	1.57815i	0.0660569	−	0.237916i
$45$	0.707849	−	0.155809i	0.105520	−	0.0232267i
$46$	−0.681950	−	1.00580i	−0.100548	−	0.148297i
$47$	−4.76013	+	4.50904i	−0.694337	+	0.657711i	−0.951142	−	0.308752i	$-0.900089\pi$
$47$	−4.76013	+	4.50904i	−0.694337	+	0.657711i	0.256806	+	0.966463i	$0.417330\pi$
$48$	−0.856857	−	0.515554i	−0.123677	−	0.0744138i
$49$	−1.93853	−	11.8245i	−0.276932	−	1.68921i
$50$	−2.51113	+	3.70364i	−0.355127	+	0.523773i
$51$	−0.769484	+	1.93126i	−0.107749	+	0.270430i
$52$	0.224903	−	0.264777i	0.0311885	−	0.0367179i
$53$	1.17353	−	7.15820i	0.161196	−	0.983254i	−0.775047	−	0.631903i	$-0.782274\pi$
$53$	1.17353	−	7.15820i	0.161196	−	0.983254i	0.936244	−	0.351351i	$-0.114278\pi$
$54$	0.725995	+	0.687699i	0.0987955	+	0.0935840i
$55$	0.317585	+	1.14384i	0.0428231	+	0.154235i
$56$	−2.04080	−	3.84935i	−0.272713	−	0.514391i
$57$	5.29824	+	4.02761i	0.701768	+	0.533470i
$58$	−6.66363			−0.874978
$59$	4.42632	−	6.27755i	0.576258	−	0.817268i
$59$	4.42632	−	6.27755i	0.576258	−	0.817268i
$60$	0.724795			0.0935706
$61$	0.340656	+	0.258960i	0.0436165	+	0.0331564i	0.626755	−	0.779216i	$-0.284383\pi$
$61$	0.340656	+	0.258960i	0.0436165	+	0.0331564i	−0.583139	+	0.812373i	$0.698176\pi$
$62$	−1.36615	−	2.57682i	−0.173501	−	0.327257i
$63$	1.16559	+	4.19806i	0.146850	+	0.528906i
$64$	−0.725995	−	0.687699i	−0.0907494	−	0.0859624i
$65$	−0.0407359	+	0.248478i	−0.00505267	+	0.0308199i
$66$	−1.06032	+	1.24831i	−0.130517	+	0.153656i
$67$	−3.87492	+	9.72533i	−0.473397	+	1.18814i	0.477500	+	0.878632i	$0.341543\pi$
$67$	−3.87492	+	9.72533i	−0.473397	+	1.18814i	−0.950897	+	0.309506i	$0.899836\pi$
$68$	−1.16666	+	1.72069i	−0.141478	+	0.208664i
$69$	0.196596	+	1.19918i	0.0236674	+	0.144365i
$70$	2.70582	+	1.62804i	0.323407	+	0.194587i
$71$	−9.37685	+	8.88222i	−1.11283	+	1.05413i	−0.114672	+	0.993403i	$0.536582\pi$
$71$	−9.37685	+	8.88222i	−1.11283	+	1.05413i	−0.998155	+	0.0607221i	$0.980660\pi$
$72$	0.561187	+	0.827689i	0.0661365	+	0.0975441i
$73$	0.773487	−	0.170257i	0.0905298	−	0.0199271i	−0.169474	−	0.985535i	$-0.554207\pi$
$73$	0.773487	−	0.170257i	0.0905298	−	0.0199271i	0.260004	+	0.965607i	$0.416276\pi$
$74$	1.83602	−	6.61273i	0.213432	−	0.768714i
$75$	3.83416	−	2.30693i	0.442730	−	0.266382i
$76$	4.30855	+	5.07241i	0.494224	+	0.581846i
$77$	−6.76237	+	2.27851i	−0.770644	+	0.259660i
$78$	−0.315293	+	0.145870i	−0.0357000	+	0.0165166i
$79$	−6.98767	+	13.1801i	−0.786174	+	1.48288i	0.0873913	+	0.996174i	$0.472147\pi$
$79$	−6.98767	+	13.1801i	−0.786174	+	1.48288i	−0.873565	+	0.486707i	$0.838198\pi$
$80$	0.707849	+	0.155809i	0.0791400	+	0.0174200i
$81$	−0.370138	−	0.928977i	−0.0411265	−	0.103220i
$82$	7.30089	+	2.45996i	0.806248	+	0.271657i
$83$	6.07451	−	0.660643i	0.666764	−	0.0725150i	0.231524	−	0.972829i	$-0.425629\pi$
$83$	6.07451	−	0.660643i	0.666764	−	0.0725150i	0.435240	+	0.900314i	$0.356663\pi$
$84$	0.235876	+	4.35048i	0.0257362	+	0.474677i
$85$	0.0815755	−	1.50457i	0.00884811	−	0.163194i
$86$	2.26812	+	0.246673i	0.244577	+	0.0265994i
$87$	6.04775	+	2.79799i	0.648387	+	0.299976i
$88$	−1.30388	+	0.991187i	−0.138994	+	0.105661i
$89$	−1.50440	+	1.14361i	−0.159466	+	0.121223i	−0.681864	−	0.731479i	$-0.738830\pi$
$89$	−1.50440	+	1.14361i	−0.159466	+	0.121223i	0.522398	+	0.852701i	$0.325037\pi$
$90$	−0.657806	−	0.304333i	−0.0693388	−	0.0320796i
$91$	−1.50471	−	0.163647i	−0.157737	−	0.0171549i
$92$	−0.0657892	+	1.21341i	−0.00685900	+	0.126507i
$93$	0.157900	+	2.91229i	0.0163735	+	0.301991i
$94$	6.51826	−	0.708904i	0.672307	−	0.0731178i
$95$	−4.57122	−	1.54022i	−0.468997	−	0.158023i
$96$	0.370138	+	0.928977i	0.0377771	+	0.0948133i
$97$	−15.4646	−	3.40401i	−1.57019	−	0.345625i	−0.657235	−	0.753686i	$-0.728274\pi$
$97$	−15.4646	−	3.40401i	−1.57019	−	0.345625i	−0.912955	+	0.408061i	$0.866205\pi$
$98$	−5.61263	+	10.5865i	−0.566961	+	1.06940i
$99$	1.48648	−	0.687717i	0.149396	−	0.0691181i
$100$	4.24044	−	1.42877i	0.424044	−	0.142877i
$101$	4.62730	+	5.44767i	0.460433	+	0.542064i	0.942560	−	0.334038i	$-0.108411\pi$
$101$	4.62730	+	5.44767i	0.460433	+	0.542064i	−0.482127	+	0.876102i	$0.660135\pi$
$102$	1.78133	−	1.07179i	0.176378	−	0.106123i
$103$	−3.32042	+	11.9591i	−0.327171	+	1.17836i	0.598841	+	0.800868i	$0.295628\pi$
$103$	−3.32042	+	11.9591i	−0.327171	+	1.17836i	−0.926012	+	0.377495i	$0.876786\pi$
$104$	−0.339280	+	0.0746811i	−0.0332691	+	0.00732309i
$105$	−1.77214	−	2.61371i	−0.172943	−	0.255072i
$106$	−5.26620	+	4.98841i	−0.511498	+	0.484517i
$107$	−3.25612	−	1.95914i	−0.314781	−	0.189397i	0.349392	−	0.936977i	$-0.386388\pi$
$107$	−3.25612	−	1.95914i	−0.314781	−	0.189397i	−0.664172	+	0.747579i	$0.731216\pi$
$108$	−0.161782	−	0.986827i	−0.0155675	−	0.0949574i
$109$	−1.91262	+	2.82090i	−0.183196	+	0.270193i	−0.908187	−	0.418565i	$-0.862533\pi$
$109$	−1.91262	+	2.82090i	−0.183196	+	0.270193i	0.724991	+	0.688758i	$0.241844\pi$
$110$	0.439394	−	1.10279i	0.0418945	−	0.105147i
$111$	−4.44293	+	5.23063i	−0.421705	+	0.496469i
$112$	−0.704864	+	4.29948i	−0.0666033	+	0.406262i
$113$	−9.93181	−	9.40791i	−0.934306	−	0.885022i	0.0592635	−	0.998242i	$-0.481125\pi$
$113$	−9.93181	−	9.40791i	−0.934306	−	0.885022i	−0.993570	+	0.113220i	$0.963883\pi$
$114$	−1.78048	−	6.41271i	−0.166757	−	0.600605i
$115$	−0.412558	−	0.778167i	−0.0384712	−	0.0725644i
$116$	5.30487	+	4.03266i	0.492545	+	0.374423i
$117$	0.347402			0.0321173
$118$	−7.32278	+	2.31882i	−0.674116	+	0.213465i
$119$	9.05754			0.830303
$120$	−0.577004	−	0.438627i	−0.0526730	−	0.0400410i
$121$	−3.89596	−	7.34856i	−0.354178	−	0.668051i
$122$	−0.114478	−	0.412312i	−0.0103643	−	0.0373290i
$123$	−5.59320	−	5.29816i	−0.504322	−	0.477719i
$124$	−0.471848	+	2.87815i	−0.0423732	+	0.258465i
$125$	−4.44573	+	5.23391i	−0.397638	+	0.468135i
$126$	1.61264	−	4.04743i	0.143666	−	0.360574i
$127$	1.89791	−	2.79921i	0.168413	−	0.248390i	−0.734112	−	0.679028i	$-0.762401\pi$
$127$	1.89791	−	2.79921i	0.168413	−	0.248390i	0.902524	+	0.430639i	$0.141712\pi$
$128$	0.161782	+	0.986827i	0.0142996	+	0.0872240i
$129$	−1.95491	−	1.17623i	−0.172120	−	0.103561i
$130$	0.182802	−	0.173159i	0.0160328	−	0.0151871i
$131$	11.3240	+	16.7017i	0.989386	+	1.45923i	0.885497	+	0.464646i	$0.153818\pi$
$131$	11.3240	+	16.7017i	0.989386	+	1.45923i	0.103889	+	0.994589i	$0.466871\pi$
$132$	1.59956	−	0.352090i	0.139224	−	0.0306455i
$133$	7.75733	−	27.9394i	0.672645	−	2.42265i
$134$	8.97032	−	5.39726i	0.774917	−	0.466252i
$135$	0.469222	+	0.552411i	0.0403842	+	0.0475440i
$136$	1.97008	−	0.663799i	0.168933	−	0.0569203i
$137$	−2.11702	+	0.979437i	−0.180869	+	0.0836790i	−0.508234	−	0.861219i	$-0.669701\pi$
$137$	−2.11702	+	0.979437i	−0.180869	+	0.0836790i	0.327365	+	0.944898i	$0.393839\pi$
$138$	0.569206	−	1.07364i	0.0484541	−	0.0913941i
$139$	5.15578	+	1.13487i	0.437308	+	0.0962587i	0.428167	−	0.903700i	$-0.359159\pi$
$139$	5.15578	+	1.13487i	0.437308	+	0.0962587i	0.00914048	+	0.999958i	$0.497090\pi$
$140$	−1.16884	−	2.93356i	−0.0987847	−	0.247931i
$141$	−6.21347	−	2.09356i	−0.523269	−	0.176310i
$142$	12.8401	−	1.39645i	1.07752	−	0.117187i
$143$	0.0308047	+	0.568159i	0.00257602	+	0.0475118i
$144$	0.0541389	−	0.998533i	0.00451158	−	0.0832111i
$145$	−4.80145	−	0.522189i	−0.398739	−	0.0433655i
$146$	−0.718803	−	0.332554i	−0.0594886	−	0.0275224i
$147$	9.53906	−	7.25140i	0.786768	−	0.598086i
$148$	−5.46349	+	4.15324i	−0.449096	+	0.341394i
$149$	16.8360	+	7.78915i	1.37926	+	0.638112i	0.962594	−	0.270949i	$-0.0873376\pi$
$149$	16.8360	+	7.78915i	1.37926	+	0.638112i	0.416663	+	0.909061i	$0.363200\pi$
$150$	−4.44844	−	0.483797i	−0.363214	−	0.0395019i
$151$	0.355443	−	6.55576i	0.0289255	−	0.533500i	−0.947781	−	0.318921i	$-0.896679\pi$
$151$	0.355443	−	6.55576i	0.0289255	−	0.533500i	0.976707	−	0.214579i	$-0.0688379\pi$
$152$	−0.360310	−	6.64554i	−0.0292250	−	0.539024i
$153$	−2.06672	+	0.224770i	−0.167085	+	0.0181715i
$154$	6.76237	+	2.27851i	0.544928	+	0.183608i
$155$	−0.782440	−	1.96378i	−0.0628471	−	0.157734i
$156$	0.339280	+	0.0746811i	0.0271641	+	0.00597928i
$157$	3.97397	−	7.49570i	0.317157	−	0.598222i	−0.672761	−	0.739860i	$-0.734892\pi$
$157$	3.97397	−	7.49570i	0.317157	−	0.598222i	0.989919	+	0.141638i	$0.0452368\pi$
$158$	13.5391	−	6.26386i	1.07711	−	0.498326i
$159$	6.87405	−	2.31614i	0.545147	−	0.183682i
$160$	−0.469222	−	0.552411i	−0.0370953	−	0.0436719i
$161$	4.53658	−	2.72957i	0.357532	−	0.215120i
$162$	−0.267528	+	0.963550i	−0.0210190	+	0.0757036i
$163$	−8.36799	+	1.84193i	−0.655432	+	0.144271i	−0.530222	−	0.847859i	$-0.677891\pi$
$163$	−8.36799	+	1.84193i	−0.655432	+	0.144271i	−0.125210	+	0.992130i	$0.539960\pi$
$164$	−4.32348	−	6.37666i	−0.337607	−	0.497934i
$165$	−0.861834	+	0.816373i	−0.0670937	+	0.0635545i
$166$	−5.23568	−	3.15020i	−0.406368	−	0.244503i
$167$	−0.751421	−	4.58347i	−0.0581467	−	0.354679i	−0.999835	−	0.0181914i	$-0.994209\pi$
$167$	−0.751421	−	4.58347i	−0.0581467	−	0.354679i	0.941688	−	0.336488i	$-0.109239\pi$
$168$	2.44502	−	3.60614i	0.188637	−	0.278219i
$169$	4.76712	−	11.9646i	0.366702	−	0.920352i
$170$	−0.975470	+	1.14841i	−0.0748151	+	0.0880792i
$171$	−1.07671	+	6.56762i	−0.0823379	+	0.502239i
$172$	−1.65635	−	1.56898i	−0.126296	−	0.119634i
$173$	−2.73662	−	9.85642i	−0.208062	−	0.749370i	−0.991747	−	0.128212i	$-0.959076\pi$
$173$	−2.73662	−	9.85642i	−0.208062	−	0.749370i	0.783685	−	0.621158i	$-0.213338\pi$
$174$	−3.12130	−	5.88740i	−0.236625	−	0.446323i
$175$	−15.5203	−	11.7982i	−1.17322	−	0.891862i
$176$	1.63785			0.123458
$177$	7.61962	+	0.970251i	0.572726	+	0.0729285i
$178$	1.88972			0.141641
$179$	16.7387	+	12.7244i	1.25111	+	0.951068i	0.999858	−	0.0168543i	$-0.00536513\pi$
$179$	16.7387	+	12.7244i	1.25111	+	0.951068i	0.251250	+	0.967922i	$0.419158\pi$
$180$	0.339500	+	0.640365i	0.0253048	+	0.0477300i
$181$	−1.27521	−	4.59289i	−0.0947856	−	0.341387i	0.900917	−	0.433991i	$-0.142895\pi$
$181$	−1.27521	−	4.59289i	−0.0947856	−	0.341387i	−0.995703	+	0.0926035i	$0.970481\pi$
$182$	1.09886	+	1.04089i	0.0814527	+	0.0771561i
$183$	−0.0692281	+	0.422273i	−0.00511749	+	0.0312153i
$184$	0.786699	−	0.926174i	0.0579962	−	0.0682784i
$185$	1.84113	−	4.62090i	0.135363	−	0.339735i
$186$	1.63674	−	2.41401i	0.120012	−	0.177004i
$187$	−0.550859	−	3.36009i	−0.0402828	−	0.245714i
$188$	−5.61815	−	3.38033i	−0.409746	−	0.246536i
$189$	−3.16307	+	2.99622i	−0.230079	+	0.217943i
$190$	2.70701	+	3.99254i	0.196387	+	0.289649i
$191$	8.17554	−	1.79957i	0.591561	−	0.130212i	0.0909063	−	0.995859i	$-0.471024\pi$
$191$	8.17554	−	1.79957i	0.591561	−	0.130212i	0.500655	+	0.865647i	$0.333093\pi$
$192$	0.267528	−	0.963550i	0.0193072	−	0.0695382i
$193$	−17.0558	+	10.2621i	−1.22770	+	0.738683i	−0.973548	−	0.228481i	$-0.926624\pi$
$193$	−17.0558	+	10.2621i	−1.22770	+	0.738683i	−0.254152	+	0.967164i	$0.581796\pi$
$194$	10.2512	+	12.0687i	0.735995	+	0.866480i
$195$	−0.238614	+	0.0803985i	−0.0170875	+	0.00575746i
$196$	10.8749	−	5.03125i	0.776777	−	0.359375i
$197$	−9.51333	+	17.9441i	−0.677797	+	1.27846i	0.271002	+	0.962579i	$0.412645\pi$
$197$	−9.51333	+	17.9441i	−0.677797	+	1.27846i	−0.948799	+	0.315882i	$0.897700\pi$
$198$	−1.59956	−	0.352090i	−0.113676	−	0.0250219i
$199$	1.17244	+	2.94261i	0.0831123	+	0.208596i	0.964659	−	0.263500i	$-0.0848769\pi$
$199$	1.17244	+	2.94261i	0.0831123	+	0.208596i	−0.881547	+	0.472096i	$0.843498\pi$
$200$	−4.24044	−	1.42877i	−0.299844	−	0.101029i
$201$	−10.4075	+	1.13188i	−0.734088	+	0.0798369i
$202$	−0.386966	−	7.13718i	−0.0272269	−	0.502170i
$203$	1.57179	−	28.9900i	0.110318	−	2.03470i
$204$	−2.06672	−	0.224770i	−0.144700	−	0.0157370i
$205$	5.06785	+	2.34464i	0.353954	+	0.163757i
$206$	9.88069	−	7.51110i	0.688420	−	0.523323i
$207$	−0.967406	+	0.735403i	−0.0672394	+	0.0511141i
$208$	0.315293	+	0.145870i	0.0218617	+	0.0101143i
$209$	−10.8365	−	1.17854i	−0.749576	−	0.0815213i
$210$	−0.170962	+	3.15321i	−0.0117975	+	0.217592i
$211$	0.172405	+	3.17982i	0.0118688	+	0.218908i	0.998451	+	0.0556412i	$0.0177203\pi$
$211$	0.172405	+	3.17982i	0.0118688	+	0.218908i	−0.986582	+	0.163267i	$0.947797\pi$
$212$	7.21124	−	0.784269i	0.495270	−	0.0538638i
$213$	−12.2397	−	4.12405i	−0.838653	−	0.282575i
$214$	1.40655	+	3.53018i	0.0961499	+	0.241318i
$215$	1.61495	+	0.355478i	0.110139	+	0.0242434i
$216$	−0.468408	+	0.883512i	−0.0318712	+	0.0601154i
$217$	11.5327	−	5.33558i	0.782889	−	0.362203i
$218$	3.22976	−	1.08823i	0.218747	−	0.0737044i
$219$	0.512732	+	0.603635i	0.0346473	+	0.0407899i
$220$	−1.01718	+	0.612018i	−0.0685783	+	0.0412622i
$221$	0.193214	−	0.695892i	0.0129969	−	0.0468108i
$222$	6.70243	−	1.47532i	0.449838	−	0.0990168i
$223$	−0.664473	−	0.980024i	−0.0444964	−	0.0656273i	0.804790	−	0.593560i	$-0.202278\pi$
$223$	−0.664473	−	0.980024i	−0.0444964	−	0.0656273i	−0.849286	+	0.527932i	$0.822967\pi$
$224$	3.16307	−	2.99622i	0.211341	−	0.200193i
$225$	3.83416	+	2.30693i	0.255610	+	0.153796i
$226$	2.21322	+	13.5001i	0.147221	+	0.898010i
$227$	11.3150	−	16.6884i	0.751003	−	1.10765i	−0.239599	−	0.970872i	$-0.577016\pi$
$227$	11.3150	−	16.6884i	0.751003	−	1.10765i	0.990602	−	0.136775i	$-0.0436737\pi$
$228$	−2.46338	+	6.18262i	−0.163141	+	0.409454i
$229$	−16.7548	+	19.7253i	−1.10719	+	1.30348i	−0.158470	+	0.987364i	$0.550656\pi$
$229$	−16.7548	+	19.7253i	−1.10719	+	1.30348i	−0.948719	+	0.316120i	$0.897620\pi$
$230$	−0.142492	+	0.869162i	−0.00939564	+	0.0573109i
$231$	−5.18064	−	4.90737i	−0.340861	−	0.322881i
$232$	−1.78271	−	6.42074i	−0.117041	−	0.421542i
$233$	−3.13049	−	5.90473i	−0.205085	−	0.386831i	0.759539	−	0.650462i	$-0.225425\pi$
$233$	−3.13049	−	5.90473i	−0.205085	−	0.386831i	−0.964624	+	0.263631i	$0.915080\pi$
$234$	−0.276564	−	0.210239i	−0.0180796	−	0.0137437i
$235$	4.75226			0.310003
$236$	7.23290	+	2.58556i	0.470822	+	0.168306i
$237$	−14.9179			−0.969021
$238$	−7.21065	−	5.48139i	−0.467397	−	0.355306i
$239$	11.3077	+	21.3286i	0.731436	+	1.37964i	0.917755	+	0.397146i	$0.129999\pi$
$239$	11.3077	+	21.3286i	0.731436	+	1.37964i	−0.186319	+	0.982489i	$0.559656\pi$
$240$	0.193903	+	0.698376i	0.0125164	+	0.0450800i
$241$	16.3007	+	15.4409i	1.05002	+	0.994634i	0.999992	−	0.00411332i	$-0.00130931\pi$
$241$	16.3007	+	15.4409i	1.05002	+	0.994634i	0.0500312	+	0.998748i	$0.484068\pi$
$242$	−1.34561	+	8.20787i	−0.0864992	+	0.527622i
$243$	0.647386	−	0.762162i	0.0415298	−	0.0488927i
$244$	−0.158386	+	0.397518i	−0.0101396	+	0.0254485i
$245$	−4.87376	+	7.18826i	−0.311373	+	0.459241i
$246$	1.24640	+	7.60268i	0.0794674	+	0.484729i
$247$	−1.98111	−	1.19199i	−0.126055	−	0.0758447i
$248$	2.11742	−	2.00572i	0.134456	−	0.127364i
$249$	3.42904	+	5.05745i	0.217307	+	0.320503i
$250$	6.70664	−	1.47624i	0.424165	−	0.0933658i
$251$	3.78913	−	13.6472i	0.239168	−	0.861404i	−0.742347	−	0.670016i	$-0.766287\pi$
$251$	3.78913	−	13.6472i	0.239168	−	0.861404i	0.981514	−	0.191388i	$-0.0612989\pi$
$252$	−3.73322	+	2.24620i	−0.235171	+	0.141497i
$253$	−1.28850	−	1.51694i	−0.0810071	−	0.0953690i
$254$	−3.20493	+	1.07987i	−0.201095	+	0.0677568i
$255$	1.36752	−	0.632681i	0.0856373	−	0.0396200i
$256$	0.468408	−	0.883512i	0.0292755	−	0.0552195i
$257$	9.74632	+	2.14533i	0.607959	+	0.133822i	0.508271	−	0.861197i	$-0.330285\pi$
$257$	9.74632	+	2.14533i	0.607959	+	0.133822i	0.0996874	+	0.995019i	$0.468216\pi$
$258$	0.844467	+	2.11945i	0.0525742	+	0.131951i
$259$	28.3355	+	9.54734i	1.76068	+	0.593243i
$260$	−0.250319	+	0.0272238i	−0.0155241	+	0.00168835i
$261$	0.360762	+	6.65386i	0.0223306	+	0.411864i
$262$	1.09245	−	20.1491i	0.0674920	−	1.24482i
$263$	4.59041	+	0.499237i	0.283057	+	0.0307843i	0.248546	−	0.968620i	$-0.420047\pi$
$263$	4.59041	+	0.499237i	0.283057	+	0.0307843i	0.0345107	+	0.999404i	$0.489013\pi$
$264$	−1.48648	−	0.687717i	−0.0914862	−	0.0423260i
$265$	−4.18545	+	3.18169i	−0.257110	+	0.195450i
$266$	−23.0837	+	17.5478i	−1.41535	+	1.07592i
$267$	−1.71507	−	0.793474i	−0.104960	−	0.0485598i
$268$	−10.4075	−	1.13188i	−0.635739	−	0.0691407i
$269$	−0.00439390	+	0.0810407i	−0.000267901	+	0.00494114i	−0.998664	−	0.0516682i	$-0.983546\pi$
$269$	−0.00439390	+	0.0810407i	−0.000267901	+	0.00494114i	0.998396	+	0.0566093i	$0.0180289\pi$
$270$	−0.0392396	−	0.723732i	−0.00238805	−	0.0440449i
$271$	−23.4981	+	2.55558i	−1.42741	+	0.155240i	−0.788970	−	0.614432i	$-0.789385\pi$
$271$	−23.4981	+	2.55558i	−1.42741	+	0.155240i	−0.638440	+	0.769672i	$0.720420\pi$
$272$	−1.97008	−	0.663799i	−0.119454	−	0.0402487i
$273$	−0.560236	−	1.40609i	−0.0339070	−	0.0851002i
$274$	2.27807	+	0.501442i	0.137624	+	0.0302932i
$275$	−3.43290	+	6.47513i	−0.207012	+	0.390465i
$276$	−1.10288	+	0.510246i	−0.0663855	+	0.0307132i
$277$	26.3384	−	8.87443i	1.58252	−	0.533213i	0.615548	−	0.788100i	$-0.288935\pi$
$277$	26.3384	−	8.87443i	1.58252	−	0.533213i	0.966971	+	0.254887i	$0.0820382\pi$
$278$	−3.41769	−	4.02361i	−0.204979	−	0.241320i
$279$	−2.49908	+	1.50365i	−0.149616	+	0.0900211i
$280$	−0.844811	+	3.04273i	−0.0504871	+	0.181838i
$281$	15.2447	−	3.35561i	0.909421	−	0.200179i	0.264462	−	0.964396i	$-0.414805\pi$
$281$	15.2447	−	3.35561i	0.909421	−	0.200179i	0.644959	+	0.764217i	$0.276874\pi$
$282$	3.67953	+	5.42691i	0.219113	+	0.323168i
$283$	−19.8253	+	18.7795i	−1.17849	+	1.11633i	−0.187520	+	0.982261i	$0.560045\pi$
$283$	−19.8253	+	18.7795i	−1.17849	+	1.11633i	−0.990972	+	0.134066i	$0.957196\pi$
$284$	−11.0670	−	6.65881i	−0.656708	−	0.395128i
$285$	−0.780391	−	4.76018i	−0.0462264	−	0.281969i
$286$	0.319312	−	0.470950i	0.0188813	−	0.0278478i
$287$	−12.4241	+	31.1821i	−0.733371	+	1.84062i
$288$	−0.647386	+	0.762162i	−0.0381476	+	0.0449108i
$289$	2.05109	−	12.5111i	0.120653	−	0.735948i
$290$	3.50639	+	3.32143i	0.205902	+	0.195041i
$291$	−4.23625	−	15.2576i	−0.248334	−	0.894417i
$292$	0.370981	+	0.699745i	0.0217100	+	0.0409495i
$293$	−15.4793	−	11.7671i	−0.904312	−	0.687440i	0.0459327	−	0.998945i	$-0.485374\pi$
$293$	−15.4793	−	11.7671i	−0.904312	−	0.687440i	−0.950245	+	0.311504i	$0.899167\pi$
$294$	−11.9823			−0.698824
$295$	−5.45811	+	1.09697i	−0.317783	+	0.0638682i
$296$	6.86288			0.398897
$297$	1.30388	+	0.991187i	0.0756590	+	0.0575145i
$298$	−8.68921	−	16.3896i	−0.503352	−	0.949423i
$299$	−0.112940	−	0.406773i	−0.00653148	−	0.0235243i
$300$	3.24859	+	3.07723i	0.187558	+	0.177664i
$301$	−1.60814	+	9.80922i	−0.0926917	+	0.565394i
$302$	−4.25034	+	5.00389i	−0.244580	+	0.287942i
$303$	−2.64562	+	6.64001i	−0.151987	+	0.381459i
$304$	−3.73487	+	5.50852i	−0.214209	+	0.315935i
$305$	−0.0501761	−	0.306061i	−0.00287308	−	0.0175250i
$306$	1.78133	+	1.07179i	0.101832	+	0.0612701i
$307$	−17.5400	+	16.6148i	−1.00106	+	0.948254i	−0.998660	−	0.0517427i	$-0.983522\pi$
$307$	−17.5400	+	16.6148i	−1.00106	+	0.948254i	−0.00239954	+	0.999997i	$0.500764\pi$
$308$	−4.00458	−	5.90632i	−0.228182	−	0.336544i
$309$	−12.1213	+	2.66810i	−0.689557	+	0.151783i
$310$	−0.565532	+	2.03686i	−0.0321200	+	0.115686i
$311$	8.69493	−	5.23156i	0.493044	−	0.296655i	−0.247234	−	0.968956i	$-0.579522\pi$
$311$	8.69493	−	5.23156i	0.493044	−	0.296655i	0.740278	+	0.672301i	$0.234694\pi$
$312$	−0.224903	−	0.264777i	−0.0127326	−	0.0149900i
$313$	31.8079	−	10.7173i	1.79789	−	0.605780i	0.797894	−	0.602798i	$-0.205947\pi$
$313$	31.8079	−	10.7173i	1.79789	−	0.605780i	0.999996	−	0.00298200i	$-0.000949202\pi$
$314$	−7.69985	+	3.56233i	−0.434528	+	0.201034i
$315$	1.47916	−	2.78999i	0.0833411	−	0.157198i
$316$	−14.5691	−	3.20691i	−0.819577	−	0.180403i
$317$	5.18799	+	13.0209i	0.291387	+	0.731325i	0.999677	+	0.0254044i	$0.00808735\pi$
$317$	5.18799	+	13.0209i	0.291387	+	0.731325i	−0.708291	+	0.705921i	$0.750533\pi$
$318$	−6.87405	−	2.31614i	−0.385477	−	0.129882i
$319$	−10.8501	+	1.18002i	−0.607488	+	0.0660682i
$320$	0.0392396	+	0.723732i	0.00219356	+	0.0404578i
$321$	0.205732	−	3.79450i	0.0114828	−	0.211788i
$322$	−5.26340	−	0.572430i	−0.293318	−	0.0319003i
$323$	12.5570	+	5.80948i	0.698690	+	0.323248i
$324$	0.796093	−	0.605174i	0.0442274	−	0.0336208i
$325$	−1.23753	+	0.940749i	−0.0686461	+	0.0521834i
$326$	7.77639	+	3.59774i	0.430694	+	0.199260i
$327$	−3.38819	−	0.368487i	−0.187367	−	0.0203774i
$328$	−0.417096	+	7.69288i	−0.0230303	+	0.424768i
$329$	1.54657	+	28.5248i	0.0852651	+	1.57262i
$330$	1.18015	−	0.128349i	0.0649650	−	0.00706537i
$331$	21.1912	+	7.14015i	1.16477	+	0.392458i	0.834275	−	0.551348i	$-0.185886\pi$
$331$	21.1912	+	7.14015i	1.16477	+	0.392458i	0.330499	+	0.943806i	$0.392783\pi$
$332$	2.26167	+	5.67636i	0.124125	+	0.311530i
$333$	−6.70243	−	1.47532i	−0.367291	−	0.0808468i
$334$	−2.17559	+	4.10361i	−0.119043	+	0.224539i
$335$	6.88648	−	3.18602i	0.376248	−	0.174071i
$336$	−4.12880	+	1.39116i	−0.225245	+	0.0758938i
$337$	−6.22358	−	7.32697i	−0.339020	−	0.399126i	0.566062	−	0.824363i	$-0.308466\pi$
$337$	−6.22358	−	7.32697i	−0.339020	−	0.399126i	−0.905082	+	0.425237i	$0.860191\pi$
$338$	−11.0357	+	6.63998i	−0.600265	+	0.361167i
$339$	3.65986	−	13.1816i	0.198776	−	0.715927i
$340$	1.47155	−	0.323914i	0.0798062	−	0.0175667i
$341$	−2.68074	−	3.95380i	−0.145170	−	0.214110i
$342$	4.83172	−	4.57684i	0.261269	−	0.247487i
$343$	−18.6002	−	11.1913i	−1.00431	−	0.604276i
$344$	0.369104	+	2.25144i	0.0199008	+	0.121389i
$345$	0.494274	−	0.729000i	0.0266108	−	0.0392480i
$346$	−3.78625	+	9.50276i	−0.203550	+	0.510872i
$347$	−1.89495	+	2.23091i	−0.101726	+	0.119762i	−0.810669	−	0.585504i	$-0.800897\pi$
$347$	−1.89495	+	2.23091i	−0.101726	+	0.119762i	0.708943	+	0.705266i	$0.249172\pi$
$348$	−1.07806	+	6.57585i	−0.0577899	+	0.352503i
$349$	−6.94359	−	6.57732i	−0.371682	−	0.352076i	0.478946	−	0.877845i	$-0.341019\pi$
$349$	−6.94359	−	6.57732i	−0.371682	−	0.352076i	−0.850627	+	0.525769i	$0.823778\pi$
$350$	5.21562	+	18.7850i	0.278787	+	1.00410i
$351$	0.162726	+	0.306934i	0.00868567	+	0.0163829i
$352$	−1.30388	−	0.991187i	−0.0694972	−	0.0528304i
$353$	4.51463			0.240290			0.120145	−	0.992756i	$-0.461664\pi$
$353$	4.51463			0.240290			0.120145	+	0.992756i	$0.461664\pi$
$354$	−5.47876	−	5.38361i	−0.291193	−	0.286136i
$355$	9.36133			0.496848
$356$	−1.50440	−	1.14361i	−0.0797328	−	0.0606113i
$357$	4.24263	+	8.00245i	0.224544	+	0.423534i
$358$	−5.62506	−	20.2596i	−0.297294	−	1.07076i
$359$	−1.13723	−	1.07724i	−0.0600209	−	0.0568548i	0.657101	−	0.753802i	$-0.271782\pi$
$359$	−1.13723	−	1.07724i	−0.0600209	−	0.0568548i	−0.717122	+	0.696948i	$0.754541\pi$
$360$	0.117259	−	0.715246i	0.00618008	−	0.0376968i
$361$	16.3743	−	19.2773i	0.861806	−	1.01460i
$362$	−1.76431	+	4.42809i	−0.0927303	+	0.232735i
$363$	4.66764	−	6.88425i	0.244987	−	0.361329i
$364$	−0.244871	−	1.49365i	−0.0128347	−	0.0782884i
$365$	−0.491870	−	0.295949i	−0.0257457	−	0.0154907i
$366$	0.310660	−	0.294273i	0.0162385	−	0.0153819i
$367$	7.69553	+	11.3501i	0.401704	+	0.592468i	0.973713	−	0.227779i	$-0.0731463\pi$
$367$	7.69553	+	11.3501i	0.401704	+	0.592468i	−0.572009	+	0.820247i	$0.693836\pi$
$368$	−1.18678	+	0.261231i	−0.0618653	+	0.0136176i
$369$	2.06109	−	7.42336i	0.107296	−	0.386445i
$370$	−4.26216	+	2.56446i	−0.221579	+	0.133320i
$371$	−20.4598	−	24.0871i	−1.06222	−	1.25054i
$372$	−2.76390	+	0.931265i	−0.143301	+	0.0482838i
$373$	−0.997529	+	0.461506i	−0.0516501	+	0.0238959i	−0.445544	−	0.895260i	$-0.646990\pi$
$373$	−0.997529	+	0.461506i	−0.0516501	+	0.0238959i	0.393894	+	0.919156i	$0.371128\pi$
$374$	−1.59491	+	3.00831i	−0.0824706	+	0.155556i
$375$	−6.70664	−	1.47624i	−0.346329	−	0.0762329i
$376$	2.42688	+	6.09102i	0.125157	+	0.314120i
$377$	−2.19378	−	0.739170i	−0.112985	−	0.0380692i
$378$	4.33133	−	0.471061i	0.222780	−	0.0242288i
$379$	0.433785	+	8.00070i	0.0222820	+	0.410968i	0.988303	+	0.152504i	$0.0487337\pi$
$379$	0.433785	+	8.00070i	0.0222820	+	0.410968i	−0.966021	+	0.258464i	$0.916784\pi$
$380$	0.261151	−	4.81665i	0.0133968	−	0.247089i
$381$	3.36214	+	0.365654i	0.172247	+	0.0187330i
$382$	−7.59754	−	3.51500i	−0.388724	−	0.179843i
$383$	−17.9095	+	13.6145i	−0.915135	+	0.695667i	−0.952792	−	0.303623i	$-0.901804\pi$
$383$	−17.9095	+	13.6145i	−0.915135	+	0.695667i	0.0376573	+	0.999291i	$0.488010\pi$
$384$	−0.796093	+	0.605174i	−0.0406255	+	0.0308827i
$385$	4.69405	+	2.17170i	0.239231	+	0.110680i
$386$	19.7883	+	2.15211i	1.00720	+	0.109540i
$387$	0.123517	−	2.27815i	0.00627875	−	0.115805i
$388$	−0.857278	−	15.8116i	−0.0435217	−	0.802710i
$389$	−31.0292	+	3.37463i	−1.57324	+	0.171100i	−0.852734	−	0.522345i	$-0.825057\pi$
$389$	−31.0292	+	3.37463i	−1.57324	+	0.171100i	−0.720509	+	0.693446i	$0.756092\pi$
$390$	0.238614	+	0.0803985i	0.0120827	+	0.00407114i
$391$	0.935071	+	2.34685i	0.0472886	+	0.118685i
$392$	−11.7022	−	2.57585i	−0.591050	−	0.130100i
$393$	−9.45188	+	17.8281i	−0.476784	+	0.899311i
$394$	18.4328	−	8.52791i	0.928630	−	0.429630i
$395$	10.2464	−	3.45242i	0.515553	−	0.173710i
$396$	1.06032	+	1.24831i	0.0532833	+	0.0627299i
$397$	31.2195	−	18.7842i	1.56686	−	0.942750i	0.574621	−	0.818419i	$-0.305149\pi$
$397$	31.2195	−	18.7842i	1.56686	−	0.942750i	0.992241	−	0.124330i	$-0.0396783\pi$
$398$	0.847418	−	3.05212i	0.0424772	−	0.152989i
$399$	28.3184	−	6.23334i	1.41769	−	0.312057i
$400$	2.51113	+	3.70364i	0.125556	+	0.185182i
$401$	22.3493	−	21.1703i	1.11607	−	1.05720i	0.118131	−	0.992998i	$-0.462310\pi$
$401$	22.3493	−	21.1703i	1.11607	−	1.05720i	0.997937	−	0.0641981i	$-0.0204490\pi$
$402$	8.97032	+	5.39726i	0.447399	+	0.269191i
$403$	−0.163921	−	0.999874i	−0.00816549	−	0.0498073i
$404$	−4.01117	+	5.91604i	−0.199563	+	0.294334i
$405$	−0.268274	+	0.673317i	−0.0133306	+	0.0334574i
$406$	−18.7953	+	22.1275i	−0.932795	+	1.09817i
$407$	1.81849	−	11.0923i	0.0901393	−	0.549826i
$408$	1.50928	+	1.42966i	0.0747204	+	0.0707789i
$409$	2.19324	+	7.89935i	0.108449	+	0.390598i	0.997775	−	0.0666766i	$-0.0212396\pi$
$409$	2.19324	+	7.89935i	0.108449	+	0.390598i	−0.889326	+	0.457274i	$0.848826\pi$
$410$	−2.61557	−	4.93348i	−0.129174	−	0.243647i
$411$	−1.85697	−	1.41164i	−0.0915978	−	0.0696308i
$412$	−12.4115			−0.611470
$413$	−8.36072	−	32.4046i	−0.411404	−	1.59452i
$414$	1.21519			0.0597235
$415$	−3.52569	−	2.68016i	−0.173069	−	0.131564i
$416$	−0.162726	−	0.306934i	−0.00797830	−	0.0150487i
$417$	1.41234	+	5.08678i	0.0691625	+	0.249101i
$418$	7.91364	+	7.49620i	0.387069	+	0.366651i
$419$	1.01895	−	6.21533i	0.0497790	−	0.303639i	−0.950189	−	0.311675i	$-0.899110\pi$
$419$	1.01895	−	6.21533i	0.0497790	−	0.303639i	0.999968	+	0.00803670i	$0.00255819\pi$
$420$	2.04434	−	2.40678i	0.0997536	−	0.117439i
$421$	−7.03295	+	17.6514i	−0.342765	+	0.860275i	0.652013	+	0.758208i	$0.273925\pi$
$421$	−7.03295	+	17.6514i	−0.342765	+	0.860275i	−0.994778	+	0.102067i	$0.967454\pi$
$422$	1.78709	−	2.63577i	0.0869944	−	0.128307i
$423$	−1.06076	−	6.47032i	−0.0515757	−	0.314598i
$424$	−6.21543	−	3.73970i	−0.301848	−	0.181616i
$425$	6.75353	−	6.39728i	0.327594	−	0.310314i
$426$	7.24821	+	10.6903i	0.351177	+	0.517947i
$427$	1.82076	−	0.400780i	0.0881128	−	0.0193951i
$428$	1.01663	−	3.66156i	0.0491405	−	0.176988i
$429$	−0.487546	+	0.293347i	−0.0235389	+	0.0141629i
$430$	−1.07053	−	1.26032i	−0.0516254	−	0.0607781i
$431$	−36.6204	+	12.3389i	−1.76394	+	0.594342i	−0.998775	−	0.0494858i	$-0.984242\pi$
$431$	−36.6204	+	12.3389i	−1.76394	+	0.594342i	−0.765170	+	0.643828i	$0.777345\pi$
$432$	0.907575	−	0.419889i	0.0436657	−	0.0202019i
$433$	−3.82129	+	7.20772i	−0.183640	+	0.346381i	−0.958191	−	0.286130i	$-0.907631\pi$
$433$	−3.82129	+	7.20772i	−0.183640	+	0.346381i	0.774551	+	0.632511i	$0.217976\pi$
$434$	−12.4100	−	2.73165i	−0.595701	−	0.131124i
$435$	−1.78768	−	4.48674i	−0.0857127	−	0.215123i
$436$	−3.22976	−	1.08823i	−0.154677	−	0.0521169i
$437$	8.04006	−	0.874409i	0.384608	−	0.0418287i
$438$	−0.0428782	−	0.790842i	−0.00204880	−	0.0377879i
$439$	1.42892	−	26.3549i	0.0681988	−	1.25785i	−0.741479	−	0.670977i	$-0.765875\pi$
$439$	1.42892	−	26.3549i	0.0681988	−	1.25785i	0.809677	−	0.586875i	$-0.199642\pi$
$440$	1.18015	+	0.128349i	0.0562614	+	0.00611879i
$441$	10.8749	+	5.03125i	0.517851	+	0.239583i
$442$	−0.574952	+	0.437067i	−0.0273477	+	0.0207892i
$443$	−11.9767	+	9.10446i	−0.569031	+	0.432566i	−0.849721	−	0.527233i	$-0.823230\pi$
$443$	−11.9767	+	9.10446i	−0.569031	+	0.432566i	0.280690	+	0.959798i	$0.409437\pi$
$444$	−6.22858	−	2.88165i	−0.295595	−	0.136757i
$445$	1.36163	+	0.148086i	0.0645476	+	0.00701997i
$446$	−0.0641031	+	1.18231i	−0.00303537	+	0.0559841i
$447$	1.00430	+	18.5233i	0.0475019	+	0.876121i
$448$	−4.33133	+	0.471061i	−0.204636	+	0.0222555i
$449$	−8.30329	−	2.79771i	−0.391857	−	0.132032i	0.116474	−	0.993194i	$-0.462841\pi$
$449$	−8.30329	−	2.79771i	−0.391857	−	0.132032i	−0.508331	+	0.861162i	$0.669737\pi$
$450$	−1.65625	−	4.15687i	−0.0780762	−	0.195957i
$451$	12.3233	+	2.71256i	0.580282	+	0.127730i
$452$	6.40795	−	12.0867i	0.301405	−	0.568510i
$453$	5.95859	−	2.75674i	0.279959	−	0.129523i
$454$	−19.1072	+	6.43796i	−0.896744	+	0.302148i
$455$	0.710208	+	0.836121i	0.0332951	+	0.0391980i
$456$	5.70264	−	3.43116i	0.267051	−	0.160679i
$457$	−0.448734	+	1.61619i	−0.0209909	+	0.0756024i	−0.973304	−	0.229521i	$-0.926284\pi$
$457$	−0.448734	+	1.61619i	−0.0209909	+	0.0756024i	0.952313	+	0.305124i	$0.0986978\pi$
$458$	25.2756	−	5.56359i	1.18105	−	0.259969i
$459$	−1.16666	−	1.72069i	−0.0544549	−	0.0803149i
$460$	0.639431	−	0.605702i	0.0298136	−	0.0282410i
$461$	−10.3404	−	6.22159i	−0.481599	−	0.289768i	0.253978	−	0.967210i	$-0.418261\pi$
$461$	−10.3404	−	6.22159i	−0.481599	−	0.289768i	−0.735577	+	0.677442i	$0.763089\pi$
$462$	1.15446	+	7.04191i	0.0537105	+	0.327619i
$463$	−23.4595	+	34.6002i	−1.09026	+	1.60801i	−0.348540	+	0.937294i	$0.613322\pi$
$463$	−23.4595	+	34.6002i	−1.09026	+	1.60801i	−0.741716	+	0.670714i	$0.765988\pi$
$464$	−2.46646	+	6.19036i	−0.114503	+	0.287380i
$465$	1.36852	−	1.61114i	0.0634635	−	0.0747150i
$466$	−1.08123	+	6.59520i	−0.0500869	+	0.305517i
$467$	−12.2458	−	11.5999i	−0.566670	−	0.536778i	0.349830	−	0.936813i	$-0.386239\pi$
$467$	−12.2458	−	11.5999i	−0.566670	−	0.536778i	−0.916500	+	0.400035i	$0.868998\pi$
$468$	0.0929399	+	0.334739i	0.00429615	+	0.0154733i
$469$	21.3648	+	40.2983i	0.986535	+	1.86080i
$470$	−3.78324	−	2.87594i	−0.174508	−	0.132657i
$471$	8.48398			0.390921
$472$	−4.19335	−	6.43551i	−0.193015	−	0.296218i
$473$	3.73675			0.171816
$474$	11.8760	+	9.02792i	0.545484	+	0.414666i
$475$	−13.9493	−	26.3112i	−0.640039	−	1.20724i
$476$	2.42315	+	8.72739i	0.111065	+	0.400019i
$477$	5.26620	+	4.98841i	0.241123	+	0.228403i
$478$	3.90554	−	23.8227i	0.178635	−	1.08963i
$479$	20.7910	−	24.4771i	0.949966	−	1.11839i	−0.0428919	−	0.999080i	$-0.513657\pi$
$479$	20.7910	−	24.4771i	0.949966	−	1.11839i	0.992858	−	0.119306i	$-0.0380670\pi$
$480$	0.268274	−	0.673317i	0.0122450	−	0.0307326i
$481$	1.33797	−	1.97336i	0.0610062	−	0.0899774i
$482$	−3.63248	−	22.1572i	−0.165455	−	1.00923i
$483$	4.53658	+	2.72957i	0.206421	+	0.124200i
$484$	6.03842	−	5.71990i	0.274474	−	0.259995i
$485$	6.44072	+	9.49936i	0.292458	+	0.431344i
$486$	−0.976621	+	0.214970i	−0.0443004	+	0.00975126i
$487$	−5.57095	+	20.0648i	−0.252444	+	0.909221i	0.723341	+	0.690491i	$0.242605\pi$
$487$	−5.57095	+	20.0648i	−0.252444	+	0.909221i	−0.975785	+	0.218731i	$0.929808\pi$
$488$	0.366657	−	0.220610i	0.0165978	−	0.00998657i
$489$	−5.54701	−	6.53044i	−0.250844	−	0.295317i
$490$	8.23012	−	2.77305i	0.371799	−	0.125274i
$491$	37.4055	−	17.3056i	1.68808	−	0.780991i	0.689705	−	0.724090i	$-0.257740\pi$
$491$	37.4055	−	17.3056i	1.68808	−	0.780991i	0.998380	−	0.0569007i	$-0.0181218\pi$
$492$	3.60870	−	6.80673i	0.162693	−	0.306871i
$493$	13.5292	+	2.97800i	0.609325	+	0.134123i
$494$	0.855783	+	2.14785i	0.0385035	+	0.0966365i
$495$	−1.12497	−	0.379045i	−0.0505635	−	0.0170368i
$496$	−2.89947	+	0.315337i	−0.130190	+	0.0141590i
$497$	3.04654	+	56.1902i	0.136656	+	2.52047i
$498$	0.330807	−	6.10137i	0.0148238	−	0.273409i
$499$	34.9979	+	3.80626i	1.56672	+	0.170391i	0.849930	−	0.526895i	$-0.176644\pi$
$499$	34.9979	+	3.80626i	1.56672	+	0.170391i	0.716793	+	0.697286i	$0.245609\pi$
$500$	−6.23249	−	2.88346i	−0.278726	−	0.128952i
$501$	3.69758	−	2.81082i	0.165195	−	0.125578i
$502$	−11.2754	+	8.57136i	−0.503247	+	0.382559i
$503$	−31.0929	−	14.3851i	−1.38636	−	0.641399i	−0.422148	−	0.906527i	$-0.638724\pi$
$503$	−31.0929	−	14.3851i	−1.38636	−	0.641399i	−0.964213	+	0.265127i	$0.914586\pi$
$504$	4.33133	+	0.471061i	0.192933	+	0.0209827i
$505$	0.280471	−	5.17299i	0.0124808	−	0.230195i
$506$	0.107753	+	1.98739i	0.00479021	+	0.0883502i
$507$	12.8038	−	1.39250i	0.568637	−	0.0618430i
$508$	3.20493	+	1.07987i	0.142196	+	0.0479113i
$509$	0.649429	+	1.62994i	0.0287854	+	0.0722460i	0.942667	−	0.333735i	$-0.108309\pi$
$509$	0.649429	+	1.62994i	0.0287854	+	0.0722460i	−0.913881	+	0.405981i	$0.866930\pi$
$510$	−1.47155	−	0.323914i	−0.0651615	−	0.0143431i
$511$	1.61632	−	3.04870i	0.0715017	−	0.134867i
$512$	−0.907575	+	0.419889i	−0.0401095	+	0.0185567i
$513$	−6.30691	+	2.12505i	−0.278457	+	0.0938231i
$514$	−6.46068	−	7.60610i	−0.284968	−	0.335491i
$515$	7.70809	−	4.63780i	0.339659	−	0.204366i
$516$	0.610364	−	2.19833i	0.0268698	−	0.0967762i
$517$	10.4878	−	2.30855i	0.461255	−	0.101530i
$518$	−16.7799	−	24.7485i	−0.737266	−	1.08739i
$519$	7.42641	−	7.03467i	0.325983	−	0.308788i
$520$	0.215752	+	0.129814i	0.00946137	+	0.00569272i
$521$	4.85225	+	29.5974i	0.212581	+	1.29669i	0.850252	+	0.526376i	$0.176450\pi$
$521$	4.85225	+	29.5974i	0.212581	+	1.29669i	−0.637671	+	0.770309i	$0.720102\pi$
$522$	3.73954	−	5.51542i	0.163675	−	0.241403i
$523$	8.85985	−	22.2365i	0.387414	−	0.972336i	−0.597898	−	0.801572i	$-0.703997\pi$
$523$	8.85985	−	22.2365i	0.387414	−	0.972336i	0.985312	−	0.170764i	$-0.0546234\pi$
$524$	−13.0634	+	15.3795i	−0.570678	+	0.671855i
$525$	3.15403	−	19.2388i	0.137653	−	0.839648i
$526$	−3.35227	−	3.17544i	−0.146166	−	0.138456i
$527$	1.62210	+	5.84227i	0.0706598	+	0.254493i
$528$	0.767184	+	1.44706i	0.0333874	+	0.0629753i
$529$	−17.1346	−	13.0254i	−0.744981	−	0.566320i
$530$	5.25748			0.228371
$531$	2.71187	+	7.18650i	0.117685	+	0.311868i
$532$	28.9963			1.25715
$533$	2.13070	+	1.61972i	0.0922908	+	0.0701577i
$534$	0.885162	+	1.66959i	0.0383047	+	0.0722504i
$535$	0.736845	+	2.65388i	0.0318566	+	0.114737i
$536$	7.60034	+	7.19943i	0.328285	+	0.310968i
$537$	−3.40164	+	20.7491i	−0.146791	+	0.895388i
$538$	0.0525417	−	0.0618569i	0.00226523	−	0.00266684i
$539$	−7.26408	+	18.2315i	−0.312886	+	0.785284i
$540$	−0.406745	+	0.599904i	−0.0175035	+	0.0258158i
$541$	−1.83930	−	11.2192i	−0.0790777	−	0.482352i	−0.996440	−	0.0843002i	$-0.973135\pi$
$541$	−1.83930	−	11.2192i	−0.0790777	−	0.482352i	0.917363	−	0.398052i	$-0.130314\pi$
$542$	20.2533	+	12.1860i	0.869952	+	0.523433i
$543$	3.46056	−	3.27801i	0.148507	−	0.140673i
$544$	1.16666	+	1.72069i	0.0500200	+	0.0737740i
$545$	2.41247	−	0.531024i	0.103339	−	0.0227466i
$546$	−0.404927	+	1.45842i	−0.0173293	+	0.0624144i
$547$	2.02569	−	1.21882i	0.0866124	−	0.0521130i	−0.471589	−	0.881819i	$-0.656319\pi$
$547$	2.02569	−	1.21882i	0.0866124	−	0.0521130i	0.558201	+	0.829706i	$0.311492\pi$
$548$	−1.51010	−	1.77783i	−0.0645083	−	0.0759450i
$549$	−0.405510	+	0.136632i	−0.0173067	+	0.00583132i
$550$	6.65149	−	3.07731i	0.283621	−	0.131217i
$551$	20.7732	−	39.1824i	0.884968	−	1.66923i
$552$	1.18678	+	0.261231i	0.0505128	+	0.0111187i
$553$	24.0573	+	60.3792i	1.02302	+	2.56758i
$554$	−26.3384	−	8.87443i	−1.11901	−	0.377038i
$555$	4.94502	−	0.537803i	0.209904	−	0.0228285i
$556$	0.285810	+	5.27146i	0.0121211	+	0.223560i
$557$	0.598462	−	11.0380i	0.0253576	−	0.467694i	−0.958086	−	0.286480i	$-0.907515\pi$
$557$	0.598462	−	11.0380i	0.0253576	−	0.467694i	0.983444	−	0.181214i	$-0.0580026\pi$
$558$	2.89947	+	0.315337i	0.122744	+	0.0133493i
$559$	0.719340	+	0.332802i	0.0304248	+	0.0140760i
$560$	2.51393	−	1.91104i	0.106233	−	0.0807563i
$561$	2.71066	−	2.06059i	0.114444	−	0.0869980i
$562$	−14.1669	−	6.55431i	−0.597595	−	0.276477i
$563$	−29.1949	−	3.17514i	−1.23042	−	0.133816i	−0.530279	−	0.847823i	$-0.677913\pi$
$563$	−29.1949	−	3.17514i	−1.23042	−	0.133816i	−0.700139	+	0.714007i	$0.746878\pi$
$564$	0.354972	−	6.54708i	0.0149470	−	0.275682i
$565$	0.536808	+	9.90084i	0.0225837	+	0.416532i
$566$	27.1477	−	2.95249i	1.14110	−	0.124102i
$567$	−4.12880	−	1.39116i	−0.173393	−	0.0584231i
$568$	4.78065	+	11.9985i	0.200591	+	0.503447i
$569$	−29.8120	−	6.56211i	−1.24978	−	0.275098i	−0.459687	−	0.888081i	$-0.652038\pi$
$569$	−29.8120	−	6.56211i	−1.24978	−	0.275098i	−0.790096	+	0.612983i	$0.789969\pi$
$570$	−2.25947	+	4.26182i	−0.0946389	+	0.178508i
$571$	−25.8019	+	11.9372i	−1.07978	+	0.499558i	−0.877405	−	0.479750i	$-0.840727\pi$
$571$	−25.8019	+	11.9372i	−1.07978	+	0.499558i	−0.202372	+	0.979309i	$0.564865\pi$
$572$	−0.539208	+	0.181680i	−0.0225454	+	0.00759644i
$573$	5.41943	+	6.38025i	0.226400	+	0.266539i
$574$	28.7614	−	17.3051i	1.20048	−	0.722303i
$575$	1.45471	−	5.23939i	0.0606656	−	0.218498i
$576$	0.976621	−	0.214970i	0.0406925	−	0.00895710i
$577$	−16.0096	−	23.6124i	−0.666488	−	0.982997i	−0.999201	−	0.0399685i	$-0.987274\pi$
$577$	−16.0096	−	23.6124i	−0.666488	−	0.982997i	0.332713	−	0.943028i	$-0.392036\pi$
$578$	−9.20427	+	8.71875i	−0.382847	+	0.362652i
$579$	−17.0558	−	10.2621i	−0.708813	−	0.426479i
$580$	−0.781369	−	4.76614i	−0.0324446	−	0.197903i
$581$	14.9399	−	22.0347i	0.619811	−	0.914153i
$582$	−5.86106	+	14.7101i	−0.242949	+	0.609755i
$583$	−7.69133	+	9.05494i	−0.318542	+	0.375017i
$584$	0.128132	−	0.781570i	0.00530214	−	0.0323416i
$585$	−0.182802	−	0.173159i	−0.00755793	−	0.00715926i
$586$	5.20185	+	18.7354i	0.214887	+	0.773951i
$587$	−15.7411	−	29.6908i	−0.649703	−	1.22547i	−0.961365	−	0.275277i	$-0.911230\pi$
$587$	−15.7411	−	29.6908i	−0.649703	−	1.22547i	0.311662	−	0.950193i	$-0.399114\pi$
$588$	9.53906	+	7.25140i	0.393384	+	0.299043i
$589$	19.4106			0.799801
$590$	5.00902	+	2.42981i	0.206218	+	0.100034i
$591$	−20.3099			−0.835438
$592$	−5.46349	−	4.15324i	−0.224548	−	0.170697i
$593$	−15.7774	−	29.7594i	−0.647901	−	1.22207i	−0.962096	−	0.272712i	$-0.912079\pi$
$593$	−15.7774	−	29.7594i	−0.647901	−	1.22207i	0.314195	−	0.949358i	$-0.398265\pi$
$594$	−0.438172	−	1.57815i	−0.0179784	−	0.0647524i
$595$	−4.76606	−	4.51465i	−0.195389	−	0.185083i
$596$	−3.00114	+	18.3061i	−0.122931	+	0.749848i
$597$	−2.05065	+	2.41421i	−0.0839275	+	0.0988071i
$598$	−0.156258	+	0.392177i	−0.00638985	+	0.0160373i
$599$	−10.5212	+	15.5176i	−0.429883	+	0.634030i	−0.979514	−	0.201378i	$-0.935458\pi$
$599$	−10.5212	+	15.5176i	−0.429883	+	0.634030i	0.549631	+	0.835408i	$0.314768\pi$
$600$	−0.723922	−	4.41573i	−0.0295540	−	0.180271i
$601$	−4.17672	−	2.51305i	−0.170372	−	0.102509i	0.427814	−	0.903867i	$-0.359284\pi$
$601$	−4.17672	−	2.51305i	−0.170372	−	0.102509i	−0.598186	+	0.801358i	$0.704111\pi$
$602$	7.21652	−	6.83585i	0.294123	−	0.278608i
$603$	−5.87499	−	8.66496i	−0.239248	−	0.352864i
$604$	6.41189	−	1.41136i	0.260896	−	0.0574276i
$605$	−1.61278	+	5.80870i	−0.0655687	+	0.236157i
$606$	6.12452	−	3.68500i	0.248792	−	0.149693i
$607$	−0.228345	−	0.268828i	−0.00926823	−	0.0109114i	0.757508	−	0.652825i	$-0.226416\pi$
$607$	−0.228345	−	0.268828i	−0.00926823	−	0.0109114i	−0.766777	+	0.641914i	$0.778141\pi$
$608$	6.30691	−	2.12505i	0.255779	−	0.0861820i
$609$	26.3493	−	12.1905i	1.06773	−	0.493983i
$610$	−0.145275	+	0.274018i	−0.00588202	+	0.0110947i
$611$	2.22456	+	0.489662i	0.0899959	+	0.0198096i
$612$	−0.769484	−	1.93126i	−0.0311045	−	0.0780665i
$613$	−22.9004	−	7.71604i	−0.924938	−	0.311648i	−0.183772	−	0.982969i	$-0.558831\pi$
$613$	−22.9004	−	7.71604i	−0.924938	−	0.311648i	−0.741167	+	0.671321i	$0.765727\pi$
$614$	24.0183	−	2.61215i	0.969299	−	0.105418i
$615$	0.302309	+	5.57576i	0.0121903	+	0.224836i
$616$	−0.386331	+	7.12545i	−0.0155657	+	0.287093i
$617$	26.1816	+	2.84742i	1.05403	+	0.114633i	0.618693	−	0.785633i	$-0.287663\pi$
$617$	26.1816	+	2.84742i	1.05403	+	0.114633i	0.435340	+	0.900266i	$0.356628\pi$
$618$	11.2643	+	5.21144i	0.453119	+	0.209635i
$619$	8.92077	−	6.78140i	0.358556	−	0.272567i	−0.410351	−	0.911928i	$-0.634594\pi$
$619$	8.92077	−	6.78140i	0.358556	−	0.272567i	0.768907	+	0.639360i	$0.220801\pi$
$620$	1.68287	−	1.27929i	0.0675858	−	0.0513774i
$621$	−1.10288	−	0.510246i	−0.0442570	−	0.0204755i
$622$	−10.0880	−	1.09713i	−0.404491	−	0.0439911i
$623$	−0.445741	+	8.22121i	−0.0178582	+	0.329376i
$624$	0.0188080	+	0.346892i	0.000752921	+	0.0138868i
$625$	−17.2941	+	1.88085i	−0.691763	+	0.0752338i
$626$	−31.8079	−	10.7173i	−1.27130	−	0.428351i
$627$	−4.03465	−	10.1262i	−0.161129	−	0.404402i
$628$	8.28563	+	1.82381i	0.330633	+	0.0727778i
$629$	−6.68293	+	12.6053i	−0.266466	+	0.502608i
$630$	−2.86598	+	1.32594i	−0.114183	+	0.0528268i
$631$	33.6418	−	11.3352i	1.33926	−	0.451249i	0.443693	−	0.896179i	$-0.353668\pi$
$631$	33.6418	−	11.3352i	1.33926	−	0.451249i	0.895565	+	0.444930i	$0.146772\pi$
$632$	9.65764	+	11.3699i	0.384160	+	0.452268i
$633$	−2.72865	+	1.64178i	−0.108454	+	0.0652547i
$634$	3.74978	−	13.5055i	0.148923	−	0.536371i
$635$	−2.39392	+	0.526941i	−0.0949998	+	0.0209110i
$636$	4.07072	+	6.00386i	0.161414	+	0.238068i
$637$	−3.02209	+	2.86268i	−0.119740	+	0.113423i
$638$	9.35178	+	5.62678i	0.370241	+	0.222766i
$639$	−2.08955	−	12.7457i	−0.0826614	−	0.504212i
$640$	0.406745	−	0.599904i	0.0160780	−	0.0237133i
$641$	−10.7197	+	26.9045i	−0.423403	+	1.06266i	0.550325	+	0.834950i	$0.314504\pi$
$641$	−10.7197	+	26.9045i	−0.423403	+	1.06266i	−0.973729	+	0.227712i	$0.926876\pi$
$642$	−2.46011	+	2.89627i	−0.0970929	+	0.114307i
$643$	6.16176	−	37.5850i	0.242996	−	1.48221i	−0.530108	−	0.847930i	$-0.677849\pi$
$643$	6.16176	−	37.5850i	0.242996	−	1.48221i	0.773104	−	0.634279i	$-0.218703\pi$
$644$	3.84374	+	3.64098i	0.151465	+	0.143475i
$645$	0.442388	+	1.59334i	0.0174190	+	0.0627377i
$646$	−6.48078	−	12.2241i	−0.254983	−	0.480949i
$647$	−27.9837	−	21.2726i	−1.10015	−	0.836313i	−0.112605	−	0.993640i	$-0.535919\pi$
$647$	−27.9837	−	21.2726i	−1.10015	−	0.836313i	−0.987547	+	0.157327i	$0.949712\pi$
$648$	−1.00000			−0.0392837
$649$	−11.5127	+	5.07236i	−0.451913	+	0.199108i
$650$	1.55451			0.0609729
$651$	10.1160	+	7.69002i	0.396479	+	0.301396i
$652$	−4.01347	−	7.57021i	−0.157180	−	0.296472i
$653$	4.91558	+	17.7043i	0.192362	+	0.692824i	0.995307	+	0.0967708i	$0.0308514\pi$
$653$	4.91558	+	17.7043i	0.192362	+	0.692824i	−0.802945	+	0.596053i	$0.796735\pi$
$654$	2.47431	+	2.34379i	0.0967533	+	0.0916496i
$655$	2.36613	−	14.4328i	0.0924524	−	0.563935i
$656$	4.98758	−	5.87183i	0.194732	−	0.229256i
$657$	−0.293151	+	0.735753i	−0.0114369	+	0.0287045i
$658$	16.0313	−	23.6443i	0.624963	−	0.921752i
$659$	−4.58867	−	27.9896i	−0.178749	−	1.09032i	−0.911948	−	0.410307i	$-0.865422\pi$
$659$	−4.58867	−	27.9896i	−0.178749	−	1.09032i	0.733199	−	0.680015i	$-0.238027\pi$
$660$	−1.01718	−	0.612018i	−0.0395937	−	0.0238228i
$661$	16.3659	−	15.5026i	0.636559	−	0.602980i	−0.299810	−	0.953999i	$-0.596923\pi$
$661$	16.3659	−	15.5026i	0.636559	−	0.602980i	0.936368	+	0.351019i	$0.114165\pi$
$662$	−12.5491	−	18.5086i	−0.487736	−	0.719357i
$663$	0.705332	−	0.155255i	0.0273928	−	0.00602962i
$664$	1.63469	−	5.88761i	0.0634382	−	0.228484i
$665$	−18.0080	+	10.8351i	−0.698321	+	0.420166i
$666$	4.44293	+	5.23063i	0.172160	+	0.202683i
$667$	7.67371	−	2.58558i	0.297127	−	0.100114i
$668$	4.21537	−	1.95024i	0.163098	−	0.0754570i
$669$	0.554619	−	1.04612i	0.0214428	−	0.0404454i
$670$	−7.41037	−	1.63115i	−0.286288	−	0.0630167i
$671$	−0.259412	−	0.651076i	−0.0100145	−	0.0251345i
$672$	4.12880	+	1.39116i	0.159272	+	0.0536650i
$673$	−49.2113	+	5.35205i	−1.89696	+	0.206306i	−0.980868	−	0.194673i	$-0.937636\pi$
$673$	−49.2113	+	5.35205i	−1.89696	+	0.206306i	−0.916087	+	0.400979i	$0.868670\pi$
$674$	0.520459	+	9.59930i	0.0200473	+	0.369751i
$675$	−0.242254	+	4.46811i	−0.00932436	+	0.171978i
$676$	12.8038	+	1.39250i	0.492454	+	0.0535576i
$677$	5.01665	+	2.32095i	0.192805	+	0.0892013i	0.513916	−	0.857840i	$-0.328194\pi$
$677$	5.01665	+	2.32095i	0.192805	+	0.0892013i	−0.321111	+	0.947042i	$0.604056\pi$
$678$	−10.8908	+	8.27895i	−0.418257	+	0.317951i
$679$	−54.9226	+	41.7511i	−2.10773	+	1.60226i
$680$	−1.36752	−	0.632681i	−0.0524419	−	0.0242622i
$681$	20.0444	+	2.17996i	0.768104	+	0.0835364i
$682$	−0.258617	+	4.76991i	−0.00990295	+	0.182649i
$683$	0.283605	+	5.23078i	0.0108518	+	0.200150i	0.998932	+	0.0462089i	$0.0147140\pi$
$683$	0.283605	+	5.23078i	0.0108518	+	0.200150i	−0.988080	+	0.153941i	$0.950803\pi$
$684$	−6.61628	+	0.719564i	−0.252980	+	0.0275132i
$685$	1.60216	+	0.539831i	0.0612155	+	0.0206259i
$686$	8.03474	+	20.1657i	0.306768	+	0.769929i
$687$	−25.2756	−	5.56359i	−0.964325	−	0.212264i
$688$	1.06867	−	2.01573i	0.0407427	−	0.0768488i
$689$	−2.28706	+	1.05811i	−0.0871301	+	0.0403107i
$690$	−0.834660	+	0.281230i	−0.0317750	+	0.0107062i
$691$	9.77692	+	11.5103i	0.371931	+	0.437871i	0.916006	−	0.401166i	$-0.131395\pi$
$691$	9.77692	+	11.5103i	0.371931	+	0.437871i	−0.544074	+	0.839037i	$0.683119\pi$
$692$	8.76503	−	5.27374i	0.333196	−	0.200478i
$693$	1.90906	−	6.87581i	0.0725192	−	0.261191i
$694$	2.85865	−	0.629236i	0.108513	−	0.0238855i
$695$	−2.14729	−	3.16702i	−0.0814515	−	0.120132i
$696$	4.83777	−	4.58258i	0.183375	−	0.173702i
$697$	−13.7237	−	8.25725i	−0.519821	−	0.312766i
$698$	1.54732	+	9.43824i	0.0585669	+	0.357243i
$699$	3.75055	−	5.53165i	0.141859	−	0.209226i
$700$	7.21606	−	18.1109i	0.272741	−	0.684529i
$701$	−14.5741	+	17.1579i	−0.550454	+	0.648045i	−0.965083	−	0.261946i	$-0.915636\pi$
$701$	−14.5741	+	17.1579i	−0.550454	+	0.648045i	0.414628	+	0.909991i	$0.363912\pi$
$702$	0.0562034	−	0.342825i	0.00212126	−	0.0129391i
$703$	33.1595	+	31.4103i	1.25063	+	1.18466i
$704$	0.438172	+	1.57815i	0.0165142	+	0.0594789i
$705$	2.22600	+	4.19868i	0.0838359	+	0.158131i
$706$	−3.59407	−	2.73214i	−0.135265	−	0.102825i
$707$	31.1414			1.17119
$708$	1.10358	+	7.60145i	0.0414751	+	0.285680i
$709$	13.1358			0.493327			0.246663	−	0.969101i	$-0.420666\pi$
$709$	13.1358			0.493327			0.246663	+	0.969101i	$0.420666\pi$
$710$	−7.45249	−	5.66524i	−0.279687	−	0.212613i
$711$	−6.98767	−	13.1801i	−0.262058	−	0.494294i
$712$	0.505555	+	1.82084i	0.0189465	+	0.0682390i
$713$	2.57307	+	2.43734i	0.0963622	+	0.0912791i
$714$	1.46535	−	8.93822i	0.0548392	−	0.334505i
$715$	0.266984	−	0.314318i	0.00998464	−	0.0117548i
$716$	−7.78254	+	19.5327i	−0.290847	+	0.729972i
$717$	−13.5475	+	19.9810i	−0.505940	+	0.746205i
$718$	0.253423	+	1.54581i	0.00945766	+	0.0576892i
$719$	−30.5113	−	18.3581i	−1.13788	−	0.684640i	−0.183437	−	0.983031i	$-0.558722\pi$
$719$	−30.5113	−	18.3581i	−1.13788	−	0.684640i	−0.954444	+	0.298391i	$0.903550\pi$
$720$	−0.526198	+	0.498441i	−0.0196102	+	0.0185758i
$721$	30.3463	+	44.7575i	1.13016	+	1.66685i
$722$	−24.7016	+	5.43724i	−0.919300	+	0.202353i
$723$	−6.00680	+	21.6345i	−0.223395	+	0.804597i
$724$	4.08433	−	2.45746i	0.151793	−	0.0913307i
$725$	−19.3035	−	22.7258i	−0.716914	−	0.844016i
$726$	−7.88205	+	2.65577i	−0.292530	+	0.0985649i
$727$	4.27835	−	1.97937i	0.158675	−	0.0734109i	−0.338944	−	0.940807i	$-0.610070\pi$
$727$	4.27835	−	1.97937i	0.158675	−	0.0734109i	0.497619	+	0.867396i	$0.334208\pi$
$728$	−0.708976	+	1.33727i	−0.0262764	+	0.0495626i
$729$	0.976621	+	0.214970i	0.0361711	+	0.00796187i
$730$	0.212474	+	0.533270i	0.00786402	+	0.0197372i
$731$	−4.49473	−	1.51445i	−0.166244	−	0.0560140i
$732$	−0.425401	+	0.0462652i	−0.0157233	+	0.00171001i
$733$	0.848539	+	15.6504i	0.0313415	+	0.578060i	0.971459	+	0.237209i	$0.0762325\pi$
$733$	0.848539	+	15.6504i	0.0313415	+	0.578060i	−0.940117	+	0.340851i	$0.889285\pi$
$734$	0.742404	−	13.6928i	0.0274026	−	0.505412i
$735$	−8.63382	−	0.938985i	−0.318463	−	0.0346350i
$736$	1.10288	+	0.510246i	0.0406527	+	0.0188079i
$737$	13.6502	−	10.3766i	0.502811	−	0.382227i
$738$	−6.13324	+	4.66237i	−0.225768	+	0.171624i
$739$	1.86569	+	0.863162i	0.0686307	+	0.0317519i	0.453904	−	0.891050i	$-0.350031\pi$
$739$	1.86569	+	0.863162i	0.0686307	+	0.0317519i	−0.385274	+	0.922802i	$0.625893\pi$
$740$	4.94502	+	0.537803i	0.181783	+	0.0197700i
$741$	0.125173	−	2.30867i	0.00459833	−	0.0848112i
$742$	1.71099	+	31.5573i	0.0628124	+	1.15851i
$743$	29.9082	−	3.25271i	1.09722	−	0.119330i	0.458447	−	0.888722i	$-0.348406\pi$
$743$	29.9082	−	3.25271i	1.09722	−	0.119330i	0.638778	+	0.769391i	$0.279440\pi$
$744$	2.76390	+	0.931265i	0.101329	+	0.0341418i
$745$	−4.97662	−	12.4904i	−0.182329	−	0.457612i
$746$	1.07342	+	0.236277i	0.0393006	+	0.00865071i
$747$	−2.86213	+	5.39855i	−0.104720	+	0.197523i
$748$	3.09025	−	1.42970i	0.112991	−	0.0522750i
$749$	−15.6897	+	5.28649i	−0.573291	+	0.193164i
$750$	4.44573	+	5.23391i	0.162335	+	0.191115i
$751$	30.0688	−	18.0918i	1.09723	−	0.660178i	0.152586	−	0.988290i	$-0.451240\pi$
$751$	30.0688	−	18.0918i	1.09723	−	0.660178i	0.944639	+	0.328112i	$0.106412\pi$
$752$	1.75410	−	6.31770i	0.0639655	−	0.230383i
$753$	13.8323	−	3.04473i	0.504078	−	0.110956i
$754$	1.29913	+	1.91607i	0.0473113	+	0.0697790i
$755$	−3.45469	+	3.27246i	−0.125729	+	0.119097i
$756$	−3.73322	−	2.24620i	−0.135776	−	0.0816936i
$757$	4.29538	+	26.2006i	0.156118	+	0.952278i	0.942419	+	0.334435i	$0.108545\pi$
$757$	4.29538	+	26.2006i	0.156118	+	0.952278i	−0.786301	+	0.617844i	$0.788006\pi$
$758$	4.49648	−	6.63181i	0.163320	−	0.240878i
$759$	0.736689	−	1.84895i	0.0267401	−	0.0671126i
$760$	−3.12281	+	3.67646i	−0.113276	+	0.133359i
$761$	−2.97807	+	18.1655i	−0.107955	+	0.658497i	0.876303	+	0.481760i	$0.160002\pi$
$761$	−2.97807	+	18.1655i	−0.107955	+	0.658497i	−0.984258	+	0.176737i	$0.943446\pi$
$762$	−2.45529	−	2.32577i	−0.0889457	−	0.0842539i
$763$	3.97251	+	14.3077i	0.143815	+	0.517973i
$764$	3.92117	+	7.39610i	0.141863	+	0.267582i
$765$	1.19954	+	0.911866i	0.0433694	+	0.0329686i
$766$	22.4968			0.812842
$767$	−2.66800	−	0.0488924i	−0.0963358	−	0.00176540i
$768$	1.00000			0.0360844
$769$	−38.7665	−	29.4695i	−1.39796	−	1.06270i	−0.988640	−	0.150305i	$-0.951974\pi$
$769$	−38.7665	−	29.4695i	−1.39796	−	1.06270i	−0.409316	−	0.912393i	$-0.634233\pi$
$770$	−2.42264	−	4.56959i	−0.0873060	−	0.164677i
$771$	2.66984	+	9.61588i	0.0961518	+	0.346308i
$772$	−14.4510	−	13.6887i	−0.520101	−	0.492666i
$773$	4.70826	−	28.7191i	0.169344	−	1.03295i	−0.756207	−	0.654332i	$-0.772950\pi$
$773$	4.70826	−	28.7191i	0.169344	−	1.03295i	0.925551	−	0.378622i	$-0.123602\pi$
$774$	−1.47701	+	1.73887i	−0.0530899	+	0.0625023i
$775$	4.83056	−	12.1238i	0.173519	−	0.435499i
$776$	−8.88628	+	13.1063i	−0.318999	+	0.470488i
$777$	4.83739	+	29.5068i	0.173541	+	1.05855i
$778$	26.7444	+	16.0916i	0.958832	+	0.576910i
$779$	−37.2244	+	35.2608i	−1.33370	+	1.26335i
$780$	−0.141304	−	0.208408i	−0.00505950	−	0.00746220i
$781$	20.6597	−	4.54754i	0.739262	−	0.162724i
$782$	0.675850	−	2.43419i	0.0241684	−	0.0870465i
$783$	−5.70978	+	3.43546i	−0.204051	+	0.122773i
$784$	7.75720	+	9.13248i	0.277043	+	0.326160i
$785$	−5.82726	+	1.96343i	−0.207984	+	0.0700779i
$786$	18.3137	−	8.47282i	0.653228	−	0.302216i
$787$	−20.1925	+	38.0871i	−0.719784	+	1.35766i	0.205604	+	0.978635i	$0.434084\pi$
$787$	−20.1925	+	38.0871i	−0.719784	+	1.35766i	−0.925388	+	0.379022i	$0.876261\pi$
$788$	−19.8351	−	4.36603i	−0.706595	−	0.155533i
$789$	1.70911	+	4.28953i	0.0608458	+	0.152711i
$790$	−10.2464	−	3.45242i	−0.364551	−	0.122832i
$791$	−59.2538	+	6.44424i	−2.10682	+	0.229131i
$792$	−0.0886716	−	1.63545i	−0.00315081	−	0.0581132i
$793$	0.00804811	−	0.148439i	0.000285797	−	0.00527121i
$794$	−36.2213	−	3.93931i	−1.28545	−	0.139801i
$795$	−4.77156	−	2.20756i	−0.169230	−	0.0782941i
$796$	−2.52169	+	1.91694i	−0.0893790	+	0.0679441i
$797$	−19.6329	+	14.9246i	−0.695435	+	0.528656i	−0.892113	−	0.451812i	$-0.850778\pi$
$797$	−19.6329	+	14.9246i	−0.695435	+	0.528656i	0.196678	+	0.980468i	$0.436985\pi$
$798$	−26.3163	−	12.1752i	−0.931587	−	0.430998i
$799$	−13.5509	−	1.47375i	−0.479395	−	0.0521374i
$800$	0.242254	−	4.46811i	0.00856497	−	0.157972i
$801$	−0.102308	−	1.88695i	−0.00361486	−	0.0666722i
$802$	−30.6038	+	3.32837i	−1.08066	+	0.117529i
$803$	−1.22928	−	0.414194i	−0.0433804	−	0.0146166i
$804$	−3.87492	−	9.72533i	−0.136658	−	0.342986i
$805$	−3.74767	−	0.824923i	−0.132088	−	0.0290747i
$806$	−0.474602	+	0.895193i	−0.0167171	+	0.0315318i
$807$	−0.0736586	+	0.0340781i	−0.00259290	+	0.00119961i
$808$	6.77350	−	2.28226i	0.238291	−	0.0802896i
$809$	27.2131	+	32.0377i	0.956760	+	1.12639i	0.991902	+	0.127003i	$0.0405358\pi$
$809$	27.2131	+	32.0377i	0.956760	+	1.12639i	−0.0351420	+	0.999382i	$0.511188\pi$
$810$	0.621045	−	0.373671i	0.0218213	−	0.0131294i
$811$	10.7016	−	38.5436i	0.375783	−	1.35345i	−0.498019	−	0.867166i	$-0.665939\pi$
$811$	10.7016	−	38.5436i	0.375783	−	1.35345i	0.873802	−	0.486282i	$-0.161647\pi$
$812$	28.3538	−	6.24115i	0.995025	−	0.219021i
$813$	−13.2646	−	19.5638i	−0.465210	−	0.686134i
$814$	−8.16047	+	7.73001i	−0.286024	+	0.270937i
$815$	5.32131	+	3.20173i	0.186397	+	0.112152i
$816$	−0.336330	−	2.05152i	−0.0117739	−	0.0718177i
$817$	−8.52107	+	12.5676i	−0.298114	+	0.439686i
$818$	3.03446	−	7.61591i	0.106097	−	0.266284i
$819$	0.979875	−	1.15360i	0.0342396	−	0.0403100i
$820$	−0.903382	+	5.51038i	−0.0315475	+	0.192431i
$821$	32.8628	+	31.1293i	1.14692	+	1.08642i	0.995187	+	0.0979984i	$0.0312440\pi$
$821$	32.8628	+	31.1293i	1.14692	+	1.08642i	0.151733	+	0.988422i	$0.451515\pi$
$822$	0.624039	+	2.24759i	0.0217659	+	0.0783936i
$823$	10.0018	+	18.8654i	0.348640	+	0.657605i	0.994370	−	0.105961i	$-0.0337917\pi$
$823$	10.0018	+	18.8654i	0.348640	+	0.657605i	−0.645730	+	0.763566i	$0.723447\pi$
$824$	9.88069	+	7.51110i	0.344210	+	0.261662i
$825$	−7.32886			−0.255158
$826$	−12.9545	+	30.8567i	−0.450745	+	1.07364i
$827$	7.85324			0.273084			0.136542	−	0.990634i	$-0.456401\pi$
$827$	7.85324			0.273084			0.136542	+	0.990634i	$0.456401\pi$
$828$	−0.967406	−	0.735403i	−0.0336197	−	0.0255570i
$829$	−9.34250	−	17.6218i	−0.324478	−	0.612031i	0.666584	−	0.745430i	$-0.267756\pi$
$829$	−9.34250	−	17.6218i	−0.324478	−	0.612031i	−0.991062	+	0.133399i	$0.957411\pi$
$830$	1.18481	+	4.26731i	0.0411254	+	0.148120i
$831$	20.1778	+	19.1134i	0.699959	+	0.663037i
$832$	−0.0562034	+	0.342825i	−0.00194850	+	0.0118853i
$833$	16.1265	−	18.9856i	0.558751	−	0.657812i
$834$	1.95404	−	4.90426i	0.0676627	−	0.169821i
$835$	−1.88919	+	2.78635i	−0.0653781	+	0.0964255i
$836$	−1.76349	−	10.7568i	−0.0609915	−	0.372032i
$837$	−2.49908	−	1.50365i	−0.0863809	−	0.0519737i
$838$	−4.57253	+	4.33133i	−0.157956	+	0.149623i
$839$	4.30528	+	6.34982i	0.148635	+	0.219220i	0.894717	−	0.446634i	$-0.147378\pi$
$839$	4.30528	+	6.34982i	0.148635	+	0.219220i	−0.746082	+	0.665854i	$0.768067\pi$
$840$	−3.08401	+	0.678842i	−0.106408	+	0.0234223i
$841$	4.12101	−	14.8425i	0.142104	−	0.511811i
$842$	16.2810	−	9.79597i	0.561081	−	0.337592i
$843$	10.1055	+	11.8971i	0.348050	+	0.409757i
$844$	−3.01779	+	1.01681i	−0.103877	+	0.0350001i
$845$	−8.47209	+	3.91960i	−0.291449	+	0.134838i
$846$	−3.07121	+	5.79292i	−0.105590	+	0.199165i
$847$	−35.3908	−	7.79010i	−1.21604	−	0.267671i
$848$	2.68489	+	6.73857i	0.0921996	+	0.231404i
$849$	−25.8783	−	8.71941i	−0.888140	−	0.299249i
$850$	−9.24791	+	1.00577i	−0.317201	+	0.0344976i
$851$	0.451503	+	8.32749i	0.0154773	+	0.285463i
$852$	0.699250	−	12.8969i	0.0239559	−	0.441841i
$853$	−7.35610	−	0.800024i	−0.251868	−	0.0273923i	−0.0186861	−	0.999825i	$-0.505948\pi$
$853$	−7.35610	−	0.800024i	−0.251868	−	0.0273923i	−0.233182	+	0.972433i	$0.574914\pi$
$854$	−1.69204	−	0.782819i	−0.0579003	−	0.0267875i
$855$	3.84013	−	2.91919i	0.131330	−	0.0998343i
$856$	−3.02521	+	2.29970i	−0.103400	+	0.0786023i
$857$	−8.80523	−	4.07373i	−0.300781	−	0.139156i	0.263694	−	0.964606i	$-0.415059\pi$
$857$	−8.80523	−	4.07373i	−0.300781	−	0.139156i	−0.564475	+	0.825450i	$0.690921\pi$
$858$	0.565658	+	0.0615190i	0.0193112	+	0.00210022i
$859$	0.918701	−	16.9444i	0.0313457	−	0.578137i	−0.940103	−	0.340889i	$-0.889272\pi$
$859$	0.918701	−	16.9444i	0.0313457	−	0.578137i	0.971449	−	0.237248i	$-0.0762453\pi$
$860$	0.0895248	+	1.65119i	0.00305277	+	0.0563050i
$861$	−33.3693	+	3.62913i	−1.13722	+	0.123681i
$862$	36.6204	+	12.3389i	1.24730	+	0.420263i
$863$	3.59828	+	9.03099i	0.122487	+	0.307418i	0.977415	−	0.211327i	$-0.0677785\pi$
$863$	3.59828	+	9.03099i	0.122487	+	0.307418i	−0.854929	+	0.518746i	$0.826399\pi$
$864$	−0.976621	−	0.214970i	−0.0332253	−	0.00731344i
$865$	−3.47284	+	6.55047i	−0.118080	+	0.222723i
$866$	7.40403	−	3.42547i	0.251599	−	0.116402i
$867$	12.0145	−	4.04815i	0.408033	−	0.137482i
$868$	8.22641	+	9.68488i	0.279223	+	0.328726i
$869$	20.9359	−	12.5967i	0.710200	−	0.427313i
$870$	−1.29210	+	4.65372i	−0.0438063	+	0.157776i
$871$	3.55187	−	0.781826i	0.120351	−	0.0264912i
$872$	1.91262	+	2.82090i	0.0647694	+	0.0955277i
$873$	11.4960	−	10.8896i	0.389080	−	0.368556i
$874$	−6.92980	−	4.16953i	−0.234404	−	0.141036i
$875$	4.84043	+	29.5253i	0.163636	+	0.998138i
$876$	−0.444462	+	0.655533i	−0.0150170	+	0.0221484i
$877$	−4.57144	+	11.4735i	−0.154367	+	0.387431i	−0.985738	−	0.168286i	$-0.946177\pi$
$877$	−4.57144	+	11.4735i	−0.154367	+	0.387431i	0.831372	+	0.555717i	$0.187556\pi$
$878$	−17.0869	+	20.1162i	−0.576654	+	0.678890i
$879$	3.14571	−	19.1880i	0.106102	−	0.647194i
$880$	−0.861834	−	0.816373i	−0.0290524	−	0.0275199i
$881$	−14.0256	−	50.5158i	−0.472536	−	1.70192i	−0.688259	−	0.725465i	$-0.741625\pi$
$881$	−14.0256	−	50.5158i	−0.472536	−	1.70192i	0.215724	−	0.976454i	$-0.430789\pi$
$882$	−5.61263	−	10.5865i	−0.188987	−	0.356467i
$883$	−26.6363	−	20.2484i	−0.896384	−	0.681413i	0.0519630	−	0.998649i	$-0.483452\pi$
$883$	−26.6363	−	20.2484i	−0.896384	−	0.681413i	−0.948347	+	0.317236i	$0.897245\pi$
$884$	0.722217			0.0242908
$885$	−3.52581	−	4.30847i	−0.118519	−	0.144828i
$886$	15.0444			0.505425
$887$	39.1631	+	29.7710i	1.31497	+	0.999613i	0.998702	+	0.0509425i	$0.0162225\pi$
$887$	39.1631	+	29.7710i	1.31497	+	0.999613i	0.316267	+	0.948670i	$0.397571\pi$
$888$	3.21463	+	6.06344i	0.107876	+	0.203476i
$889$	−3.94197	−	14.1977i	−0.132209	−	0.476175i
$890$	−0.994368	−	0.941915i	−0.0333313	−	0.0315731i
$891$	−0.264975	+	1.61628i	−0.00887700	+	0.0541473i
$892$	0.766537	−	0.902437i	0.0256656	−	0.0302158i
$893$	−16.1516	+	40.5375i	−0.540494	+	1.35654i
$894$	10.4103	−	15.3540i	0.348172	−	0.513516i
$895$	−2.46549	−	15.0388i	−0.0824121	−	0.502692i
$896$	3.73322	+	2.24620i	0.124718	+	0.0750404i
$897$	0.306486	−	0.290319i	0.0102333	−	0.00969348i
$898$	4.91710	+	7.25217i	0.164086	+	0.242008i
$899$	18.9806	−	4.17794i	0.633037	−	0.139342i
$900$	−1.19710	+	4.31157i	−0.0399034	+	0.143719i
$901$	12.9213	−	7.77450i	0.430472	−	0.259006i
$902$	−8.16892	−	9.61720i	−0.271995	−	0.320218i
$903$	−9.41983	+	3.17391i	−0.313472	+	0.105621i
$904$	−12.4159	+	5.74420i	−0.412946	+	0.191049i
$905$	−1.61827	+	3.05239i	−0.0537932	+	0.101465i
$906$	−6.41189	−	1.41136i	−0.213021	−	0.0468894i
$907$	−8.46492	−	21.2453i	−0.281073	−	0.705440i	−0.999947	−	0.0102994i	$-0.996722\pi$
$907$	−8.46492	−	21.2453i	−0.281073	−	0.705440i	0.718874	−	0.695140i	$-0.244658\pi$
$908$	19.1072	+	6.43796i	0.634094	+	0.213651i
$909$	−7.10576	+	0.772798i	−0.235683	+	0.0256321i
$910$	−0.0593925	−	1.09543i	−0.00196884	−	0.0363131i
$911$	−1.06373	+	19.6193i	−0.0352428	+	0.650015i	0.926539	+	0.376198i	$0.122769\pi$
$911$	−1.06373	+	19.6193i	−0.0352428	+	0.650015i	−0.961782	+	0.273817i	$0.911714\pi$
$912$	−6.61628	−	0.719564i	−0.219087	−	0.0238271i
$913$	−9.08286	−	4.20218i	−0.300599	−	0.139072i
$914$	1.33531	−	1.01508i	0.0441682	−	0.0335758i
$915$	0.246906	−	0.187693i	0.00816245	−	0.00620493i
$916$	−23.4887	−	10.8670i	−0.776088	−	0.359057i
$917$	87.4007	+	9.50540i	2.88623	+	0.313896i
$918$	−0.112550	+	2.07586i	−0.00371470	+	0.0685136i
$919$	1.59875	+	29.4872i	0.0527380	+	0.972694i	0.898456	+	0.439064i	$0.144690\pi$
$919$	1.59875	+	29.4872i	0.0527380	+	0.972694i	−0.845718	+	0.533630i	$0.820827\pi$
$920$	−0.875602	+	0.0952275i	−0.0288677	+	0.00313956i
$921$	−22.8952	−	7.71430i	−0.754423	−	0.254195i
$922$	4.46675	+	11.2107i	0.147104	+	0.369204i
$923$	4.38209	+	0.964570i	0.144238	+	0.0317492i
$924$	3.34252	−	6.30467i	0.109961	−	0.207408i
$925$	27.8709	−	12.8944i	0.916388	−	0.423966i
$926$	39.6151	−	13.3479i	1.30183	−	0.438639i
$927$	−8.03502	−	9.45956i	−0.263905	−	0.310693i
$928$	5.70978	−	3.43546i	0.187433	−	0.112775i
$929$	−11.3362	+	40.8293i	−0.371928	+	1.33956i	0.506727	+	0.862107i	$0.330855\pi$
$929$	−11.3362	+	40.8293i	−0.371928	+	1.33956i	−0.878655	+	0.477458i	$0.841558\pi$
$930$	−2.06449	+	0.454429i	−0.0676973	+	0.0149013i
$931$	−44.7524	−	66.0049i	−1.46670	−	2.16322i
$932$	4.85200	−	4.59606i	0.158933	−	0.150549i
$933$	8.69493	+	5.23156i	0.284659	+	0.171274i
$934$	2.72888	+	16.6455i	0.0892918	+	0.544656i
$935$	−1.38495	+	2.04264i	−0.0452926	+	0.0668016i
$936$	0.128587	−	0.322728i	0.00420299	−	0.0105487i
$937$	29.6869	−	34.9501i	0.969827	−	1.14177i	−0.0200438	−	0.999799i	$-0.506381\pi$
$937$	29.6869	−	34.9501i	0.969827	−	1.14177i	0.989871	−	0.141970i	$-0.0453436\pi$
$938$	7.37912	−	45.0106i	0.240937	−	1.46965i
$939$	24.3680	+	23.0826i	0.795219	+	0.753272i
$940$	1.27136	+	4.57904i	0.0414673	+	0.149352i
$941$	−14.1136	−	26.6211i	−0.460091	−	0.867823i	−0.999665	−	0.0258851i	$-0.991760\pi$
$941$	−14.1136	−	26.6211i	−0.460091	−	0.867823i	0.539574	−	0.841938i	$-0.318585\pi$
$942$	−6.75404	−	5.13429i	−0.220058	−	0.167284i
$943$	−9.36206			−0.304871
$944$	−0.556310	+	7.66097i	−0.0181063	+	0.249343i
$945$	3.15784			0.102724
$946$	−2.97480	−	2.26138i	−0.0967191	−	0.0735239i
$947$	−0.357786	−	0.674856i	−0.0116265	−	0.0219299i	0.877631	−	0.479337i	$-0.159123\pi$
$947$	−0.357786	−	0.674856i	−0.0116265	−	0.0219299i	−0.889257	+	0.457407i	$0.848778\pi$
$948$	−3.99096	−	14.3741i	−0.129620	−	0.466850i
$949$	−0.199753	−	0.189216i	−0.00648426	−	0.00614222i
$950$	−4.81791	+	29.3880i	−0.156314	+	0.953471i
$951$	−9.07400	+	10.6827i	−0.294245	+	0.346412i
$952$	3.35254	−	8.41425i	0.108657	−	0.272707i
$953$	13.1662	−	19.4187i	0.426496	−	0.629034i	−0.552355	−	0.833609i	$-0.686271\pi$
$953$	13.1662	−	19.4187i	0.426496	−	0.629034i	0.978851	+	0.204575i	$0.0655812\pi$
$954$	−1.17353	−	7.15820i	−0.0379944	−	0.231755i
$955$	−5.19893	−	3.12809i	−0.168233	−	0.101223i
$956$	−17.5261	+	16.6016i	−0.566834	+	0.536934i
$957$	−6.12483	−	9.03344i	−0.197987	−	0.292010i
$958$	−31.3645	+	6.90384i	−1.01334	+	0.223053i
$959$	−2.71886	+	9.79245i	−0.0877966	+	0.316215i
$960$	−0.621045	+	0.373671i	−0.0200442	+	0.0120602i
$961$	−14.5621	−	17.1438i	−0.469744	−	0.553025i
$962$	−2.25937	+	0.761272i	−0.0728451	+	0.0245444i
$963$	3.44885	−	1.59561i	0.111138	−	0.0514178i
$964$	−10.5171	+	19.8374i	−0.338735	+	0.638921i
$965$	14.0898	+	3.10139i	0.453565	+	0.0998373i
$966$	−1.95967	−	4.91841i	−0.0630515	−	0.158247i
$967$	31.9155	+	10.7536i	1.02633	+	0.345812i	0.781601	−	0.623778i	$-0.214403\pi$
$967$	31.9155	+	10.7536i	1.02633	+	0.345812i	0.244733	+	0.969590i	$0.421300\pi$
$968$	−8.26868	+	0.899273i	−0.265765	+	0.0289037i
$969$	0.749053	+	13.8155i	0.0240630	+	0.443817i
$970$	0.621350	−	11.4601i	0.0199504	−	0.367963i
$971$	52.2395	+	5.68139i	1.67644	+	0.182324i	0.896353	−	0.443341i	$-0.146207\pi$
$971$	52.2395	+	5.68139i	1.67644	+	0.182324i	0.780092	+	0.625665i	$0.215172\pi$
$972$	0.907575	+	0.419889i	0.0291105	+	0.0134679i
$973$	18.3108	−	13.9195i	0.587017	−	0.446239i
$974$	16.5777	−	12.6020i	0.531183	−	0.403795i
$975$	−1.41084	−	0.652722i	−0.0451829	−	0.0209038i
$976$	−0.425401	−	0.0462652i	−0.0136168	−	0.00148091i
$977$	−1.18423	+	21.8418i	−0.0378868	+	0.698781i	0.916468	+	0.400107i	$0.131027\pi$
$977$	−1.18423	+	21.8418i	−0.0378868	+	0.698781i	−0.954355	+	0.298674i	$0.903456\pi$
$978$	0.463879	+	8.55575i	0.0148332	+	0.273583i
$979$	3.07695	−	0.334638i	0.0983396	−	0.0106951i
$980$	−8.23012	−	2.77305i	−0.262901	−	0.0885818i
$981$	−1.26149	−	3.16611i	−0.0402763	−	0.101086i
$982$	−40.2511	−	8.85995i	−1.28447	−	0.282732i
$983$	9.99621	−	18.8548i	0.318830	−	0.601376i	−0.671356	−	0.741135i	$-0.734288\pi$
$983$	9.99621	−	18.8548i	0.318830	−	0.601376i	0.990186	+	0.139759i	$0.0446327\pi$
$984$	−6.99212	+	3.23490i	−0.222901	+	0.103125i
$985$	13.9499	−	4.70028i	0.444482	−	0.149763i
$986$	−8.96830	−	10.5583i	−0.285609	−	0.336245i
$987$	−24.4776	+	14.7277i	−0.779130	+	0.468787i
$988$	0.618542	−	2.22779i	0.0196785	−	0.0708754i
$989$	−2.70763	+	0.595995i	−0.0860978	+	0.0189515i
$990$	0.666189	+	0.982555i	0.0211729	+	0.0312277i
$991$	−24.7991	+	23.4910i	−0.787770	+	0.746216i	−0.971571	−	0.236748i	$-0.923919\pi$
$991$	−24.7991	+	23.4910i	−0.787770	+	0.746216i	0.183801	+	0.982964i	$0.441160\pi$
$992$	2.49908	+	1.50365i	0.0793460	+	0.0477409i
$993$	3.61773	+	22.0672i	0.114805	+	0.700281i
$994$	31.5795	−	46.5763i	1.00164	−	1.47731i
$995$	0.849781	−	2.13279i	0.0269399	−	0.0676139i
$996$	−3.95574	+	4.65706i	−0.125343	+	0.147565i
$997$	−3.88077	+	23.6716i	−0.122905	+	0.749688i	0.851410	+	0.524500i	$0.175748\pi$
$997$	−3.88077	+	23.6716i	−0.122905	+	0.749688i	−0.974315	+	0.225188i	$0.927700\pi$
$998$	−25.5582	−	24.2100i	−0.809030	−	0.766354i
$999$	−1.83602	−	6.61273i	−0.0580889	−	0.209217i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.e.d.25.2	✓	84
59.26	even	29	inner	354.2.e.d.85.2	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.e.d.25.2	✓	84	1.1	even	1	trivial
354.2.e.d.85.2	yes	84	59.26	even	29	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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.796093 - 0.605174i) q^{2} +(0.468408 + 0.883512i) q^{3} +(0.267528 + 0.963550i) q^{4} +(-0.526198 - 0.498441i) q^{5} +(0.161782 - 0.986827i) q^{6} +(2.82058 - 3.32064i) q^{7} +(0.370138 - 0.928977i) q^{8} +(-0.561187 + 0.827689i) q^{9} +O(q^{10})\)	\(q+(-0.796093 - 0.605174i) q^{2} +(0.468408 + 0.883512i) q^{3} +(0.267528 + 0.963550i) q^{4} +(-0.526198 - 0.498441i) q^{5} +(0.161782 - 0.986827i) q^{6} +(2.82058 - 3.32064i) q^{7} +(0.370138 - 0.928977i) q^{8} +(-0.561187 + 0.827689i) q^{9} +(0.117259 + 0.715246i) q^{10} +(-1.40341 - 0.844402i) q^{11} +(-0.725995 + 0.687699i) q^{12} +(-0.194957 - 0.287541i) q^{13} +(-4.25501 + 0.936599i) q^{14} +(0.193903 - 0.698376i) q^{15} +(-0.856857 + 0.515554i) q^{16} +(1.34586 + 1.58447i) q^{17} +(0.947653 - 0.319302i) q^{18} +(6.04018 - 2.79449i) q^{19} +(0.339500 - 0.640365i) q^{20} +(4.25501 + 0.936599i) q^{21} +(0.606232 + 1.52153i) q^{22} +(1.15158 + 0.388013i) q^{23} +(0.994138 - 0.108119i) q^{24} +(-0.242254 - 4.46811i) q^{25} +(-0.0188080 + 0.346892i) q^{26} +(-0.994138 - 0.108119i) q^{27} +(3.95419 + 1.82940i) q^{28} +(5.30487 - 4.03266i) q^{29} +(-0.577004 + 0.438627i) q^{30} +(2.64701 + 1.22464i) q^{31} +(0.994138 + 0.108119i) q^{32} +(0.0886716 - 1.63545i) q^{33} +(-0.112550 - 2.07586i) q^{34} +(-3.13933 + 0.341422i) q^{35} +(-0.947653 - 0.319302i) q^{36} +(2.54021 + 6.37546i) q^{37} +(-6.49970 - 1.43069i) q^{38} +(0.162726 - 0.306934i) q^{39} +(-0.657806 + 0.304333i) q^{40} +(-7.30089 + 2.45996i) q^{41} +(-2.82058 - 3.32064i) q^{42} +(-1.95491 + 1.17623i) q^{43} +(0.438172 - 1.57815i) q^{44} +(0.707849 - 0.155809i) q^{45} +(-0.681950 - 1.00580i) q^{46} +(-4.76013 + 4.50904i) q^{47} +(-0.856857 - 0.515554i) q^{48} +(-1.93853 - 11.8245i) q^{49} +(-2.51113 + 3.70364i) q^{50} +(-0.769484 + 1.93126i) q^{51} +(0.224903 - 0.264777i) q^{52} +(1.17353 - 7.15820i) q^{53} +(0.725995 + 0.687699i) q^{54} +(0.317585 + 1.14384i) q^{55} +(-2.04080 - 3.84935i) q^{56} +(5.29824 + 4.02761i) q^{57} -6.66363 q^{58} +(4.42632 - 6.27755i) q^{59} +0.724795 q^{60} +(0.340656 + 0.258960i) q^{61} +(-1.36615 - 2.57682i) q^{62} +(1.16559 + 4.19806i) q^{63} +(-0.725995 - 0.687699i) q^{64} +(-0.0407359 + 0.248478i) q^{65} +(-1.06032 + 1.24831i) q^{66} +(-3.87492 + 9.72533i) q^{67} +(-1.16666 + 1.72069i) q^{68} +(0.196596 + 1.19918i) q^{69} +(2.70582 + 1.62804i) q^{70} +(-9.37685 + 8.88222i) q^{71} +(0.561187 + 0.827689i) q^{72} +(0.773487 - 0.170257i) q^{73} +(1.83602 - 6.61273i) q^{74} +(3.83416 - 2.30693i) q^{75} +(4.30855 + 5.07241i) q^{76} +(-6.76237 + 2.27851i) q^{77} +(-0.315293 + 0.145870i) q^{78} +(-6.98767 + 13.1801i) q^{79} +(0.707849 + 0.155809i) q^{80} +(-0.370138 - 0.928977i) q^{81} +(7.30089 + 2.45996i) q^{82} +(6.07451 - 0.660643i) q^{83} +(0.235876 + 4.35048i) q^{84} +(0.0815755 - 1.50457i) q^{85} +(2.26812 + 0.246673i) q^{86} +(6.04775 + 2.79799i) q^{87} +(-1.30388 + 0.991187i) q^{88} +(-1.50440 + 1.14361i) q^{89} +(-0.657806 - 0.304333i) q^{90} +(-1.50471 - 0.163647i) q^{91} +(-0.0657892 + 1.21341i) q^{92} +(0.157900 + 2.91229i) q^{93} +(6.51826 - 0.708904i) q^{94} +(-4.57122 - 1.54022i) q^{95} +(0.370138 + 0.928977i) q^{96} +(-15.4646 - 3.40401i) q^{97} +(-5.61263 + 10.5865i) q^{98} +(1.48648 - 0.687717i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 3 q^{2} - 3 q^{3} - 3 q^{4} - 2 q^{5} + 3 q^{6} - 7 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 84 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 - 2 * q^5 + 3 * q^6 - 7 * q^7 + 3 * q^8 - 3 * q^9	\( 84 q + 3 q^{2} - 3 q^{3} - 3 q^{4} - 2 q^{5} + 3 q^{6} - 7 q^{7} + 3 q^{8} - 3 q^{9} + 2 q^{10} + 30 q^{11} - 3 q^{12} - 3 q^{13} + 7 q^{14} - 2 q^{15} - 3 q^{16} + 3 q^{17} + 3 q^{18} - 4 q^{19} - 2 q^{20} - 7 q^{21} - q^{22} + 2 q^{23} + 3 q^{24} - 67 q^{25} + 32 q^{26} - 3 q^{27} - 7 q^{28} + 4 q^{29} + 2 q^{30} - 6 q^{31} + 3 q^{32} + q^{33} + 26 q^{34} + 79 q^{35} - 3 q^{36} + 55 q^{37} + 4 q^{38} - 3 q^{39} + 2 q^{40} + q^{41} + 7 q^{42} + 51 q^{43} + q^{44} - 2 q^{45} - 31 q^{46} - 62 q^{47} - 3 q^{48} - 70 q^{49} + 9 q^{50} + 3 q^{51} - 32 q^{52} - 27 q^{53} + 3 q^{54} - 83 q^{55} + 7 q^{56} - 4 q^{57} - 120 q^{58} - 55 q^{59} + 56 q^{60} - 46 q^{61} - 23 q^{62} - 7 q^{63} - 3 q^{64} - 121 q^{65} - q^{66} + 8 q^{67} - 26 q^{68} - 27 q^{69} - 50 q^{70} - 61 q^{71} + 3 q^{72} + 49 q^{73} - 26 q^{74} - 9 q^{75} + 25 q^{76} + 77 q^{77} + 3 q^{78} - 5 q^{79} - 2 q^{80} - 3 q^{81} - q^{82} + 75 q^{83} - 7 q^{84} + 189 q^{85} + 65 q^{86} - 25 q^{87} - 30 q^{88} + 54 q^{89} + 2 q^{90} - 161 q^{91} + 2 q^{92} + 23 q^{93} + 33 q^{94} - 54 q^{95} + 3 q^{96} + 28 q^{97} + 12 q^{98} + q^{99}+O(q^{100}) \) 84 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 - 2 * q^5 + 3 * q^6 - 7 * q^7 + 3 * q^8 - 3 * q^9 + 2 * q^10 + 30 * q^11 - 3 * q^12 - 3 * q^13 + 7 * q^14 - 2 * q^15 - 3 * q^16 + 3 * q^17 + 3 * q^18 - 4 * q^19 - 2 * q^20 - 7 * q^21 - q^22 + 2 * q^23 + 3 * q^24 - 67 * q^25 + 32 * q^26 - 3 * q^27 - 7 * q^28 + 4 * q^29 + 2 * q^30 - 6 * q^31 + 3 * q^32 + q^33 + 26 * q^34 + 79 * q^35 - 3 * q^36 + 55 * q^37 + 4 * q^38 - 3 * q^39 + 2 * q^40 + q^41 + 7 * q^42 + 51 * q^43 + q^44 - 2 * q^45 - 31 * q^46 - 62 * q^47 - 3 * q^48 - 70 * q^49 + 9 * q^50 + 3 * q^51 - 32 * q^52 - 27 * q^53 + 3 * q^54 - 83 * q^55 + 7 * q^56 - 4 * q^57 - 120 * q^58 - 55 * q^59 + 56 * q^60 - 46 * q^61 - 23 * q^62 - 7 * q^63 - 3 * q^64 - 121 * q^65 - q^66 + 8 * q^67 - 26 * q^68 - 27 * q^69 - 50 * q^70 - 61 * q^71 + 3 * q^72 + 49 * q^73 - 26 * q^74 - 9 * q^75 + 25 * q^76 + 77 * q^77 + 3 * q^78 - 5 * q^79 - 2 * q^80 - 3 * q^81 - q^82 + 75 * q^83 - 7 * q^84 + 189 * q^85 + 65 * q^86 - 25 * q^87 - 30 * q^88 + 54 * q^89 + 2 * q^90 - 161 * q^91 + 2 * q^92 + 23 * q^93 + 33 * q^94 - 54 * q^95 + 3 * q^96 + 28 * q^97 + 12 * q^98 + q^99

Introduction

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