LMFDB - Embedded newform 177.2.e.b.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,2,Mod(4,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(58))

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

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

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

chi := DirichletCharacter("177.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	177.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:	$1.41335211578$
Analytic rank:	$0$
Dimension:	$140$
Relative dimension:	$5$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			121.1
Character	$\chi$	$=$	177.121
Dual form			177.2.e.b.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.13706 + 0.988707i) q^{2} +(0.947653 + 0.319302i) q^{3} +(2.29469 - 2.70152i) q^{4} +(2.84975 + 1.71464i) q^{5} +(-2.34088 + 0.254586i) q^{6} +(0.205959 - 3.79870i) q^{7} +(-0.972984 + 3.50437i) q^{8} +(0.796093 + 0.605174i) q^{9} +O(q^{10})$	\(q+(-2.13706 + 0.988707i) q^{2} +(0.947653 + 0.319302i) q^{3} +(2.29469 - 2.70152i) q^{4} +(2.84975 + 1.71464i) q^{5} +(-2.34088 + 0.254586i) q^{6} +(0.205959 - 3.79870i) q^{7} +(-0.972984 + 3.50437i) q^{8} +(0.796093 + 0.605174i) q^{9} +(-7.78535 - 0.846707i) q^{10} +(0.766914 - 4.67797i) q^{11} +(3.03717 - 1.82741i) q^{12} +(1.32729 - 1.00898i) q^{13} +(3.31565 + 8.32166i) q^{14} +(2.15309 + 2.53481i) q^{15} +(-0.238587 - 1.45532i) q^{16} +(0.334992 + 6.17856i) q^{17} +(-2.29964 - 0.506188i) q^{18} +(-0.760634 + 0.720510i) q^{19} +(11.1714 - 3.76409i) q^{20} +(1.40811 - 3.53408i) q^{21} +(2.98621 + 10.7553i) q^{22} +(-6.59327 + 1.45129i) q^{23} +(-2.04100 + 3.01025i) q^{24} +(2.83904 + 5.35500i) q^{25} +(-1.83890 + 3.46854i) q^{26} +(0.561187 + 0.827689i) q^{27} +(-9.78965 - 9.27325i) q^{28} +(1.47482 + 0.682323i) q^{29} +(-7.10745 - 3.28826i) q^{30} +(3.36504 + 3.18754i) q^{31} +(-2.13325 - 3.14630i) q^{32} +(2.22045 - 4.18822i) q^{33} +(-6.82468 - 12.8727i) q^{34} +(7.10032 - 10.4722i) q^{35} +(3.46168 - 0.761974i) q^{36} +(0.453724 + 1.63417i) q^{37} +(0.913143 - 2.29182i) q^{38} +(1.57998 - 0.532356i) q^{39} +(-8.78148 + 8.31826i) q^{40} +(-5.60800 - 1.23442i) q^{41} +(0.484970 + 8.94474i) q^{42} +(-0.677758 - 4.13414i) q^{43} +(-10.8778 - 12.8064i) q^{44} +(1.23101 + 3.08960i) q^{45} +(12.6553 - 9.62029i) q^{46} +(-11.1732 + 6.72270i) q^{47} +(0.238587 - 1.45532i) q^{48} +(-7.42872 - 0.807922i) q^{49} +(-11.3617 - 8.63696i) q^{50} +(-1.65537 + 5.96209i) q^{51} +(0.319942 - 5.90099i) q^{52} +(-3.87429 + 0.421354i) q^{53} +(-2.01763 - 1.21397i) q^{54} +(10.2065 - 12.0161i) q^{55} +(13.1116 + 4.41783i) q^{56} +(-0.950877 + 0.439922i) q^{57} -3.82638 q^{58} +(5.49712 - 5.36486i) q^{59} +11.7885 q^{60} +(-0.386501 + 0.178814i) q^{61} +(-10.3428 - 3.48490i) q^{62} +(2.46284 - 2.89948i) q^{63} +(10.1969 + 6.13529i) q^{64} +(5.51246 - 0.599516i) q^{65} +(-0.604310 + 11.1458i) q^{66} +(-4.22186 + 15.2058i) q^{67} +(17.4602 + 13.2729i) q^{68} +(-6.71153 - 0.729923i) q^{69} +(-4.81985 + 29.3998i) q^{70} +(9.90405 - 5.95907i) q^{71} +(-2.89534 + 2.20098i) q^{72} +(-1.94438 - 4.88001i) q^{73} +(-2.58535 - 3.04371i) q^{74} +(0.980567 + 5.98120i) q^{75} +(0.201054 + 3.70822i) q^{76} +(-17.6122 - 3.87675i) q^{77} +(-2.85015 + 2.69981i) q^{78} +(-5.10356 + 1.71959i) q^{79} +(1.81543 - 4.55637i) q^{80} +(0.267528 + 0.963550i) q^{81} +(13.2051 - 2.90666i) q^{82} +(3.34791 - 4.93779i) q^{83} +(-6.31623 - 11.9137i) q^{84} +(-9.63934 + 18.1817i) q^{85} +(5.53586 + 8.16479i) q^{86} +(1.17975 + 1.11752i) q^{87} +(15.6471 + 7.23914i) q^{88} +(9.08328 + 4.20237i) q^{89} +(-5.68545 - 5.38555i) q^{90} +(-3.55943 - 5.24977i) q^{91} +(-11.2088 + 21.1421i) q^{92} +(2.17111 + 4.09514i) q^{93} +(17.2310 - 25.4138i) q^{94} +(-3.40303 + 0.749063i) q^{95} +(-1.01696 - 3.66275i) q^{96} +(1.24418 - 3.12264i) q^{97} +(16.6744 - 5.61825i) q^{98} +(3.44152 - 3.25998i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q + q^{2} + 5 q^{3} - q^{4} + 2 q^{5} - q^{6} - 2 q^{7} - 3 q^{8} - 5 q^{9}+O(q^{10}) $ 140 * q + q^2 + 5 * q^3 - q^4 + 2 * q^5 - q^6 - 2 * q^7 - 3 * q^8 - 5 * q^9	\( 140 q + q^{2} + 5 q^{3} - q^{4} + 2 q^{5} - q^{6} - 2 q^{7} - 3 q^{8} - 5 q^{9} - 116 q^{10} + 2 q^{11} + q^{12} + 4 q^{13} - 43 q^{14} - 2 q^{15} + 7 q^{16} + q^{18} - 2 q^{19} + 4 q^{20} - 27 q^{21} + 6 q^{22} + 6 q^{23} + 3 q^{24} - 57 q^{25} + 12 q^{26} + 5 q^{27} - 10 q^{28} - 4 q^{29} - 12 q^{31} - 150 q^{32} - 2 q^{33} - 2 q^{34} + 6 q^{35} - q^{36} + 12 q^{37} - 12 q^{38} - 4 q^{39} - 66 q^{40} - 4 q^{41} + 14 q^{42} - 60 q^{43} + 20 q^{44} + 2 q^{45} + 76 q^{46} - 25 q^{47} - 7 q^{48} + 31 q^{49} + 137 q^{50} + 118 q^{52} + 48 q^{53} - q^{54} + 93 q^{55} + 228 q^{56} + 2 q^{57} - 120 q^{58} + 57 q^{59} - 4 q^{60} + 72 q^{61} - 179 q^{62} - 2 q^{63} + 249 q^{64} - 39 q^{65} - 6 q^{66} + 40 q^{67} + 94 q^{68} - 64 q^{69} + 94 q^{70} + 30 q^{71} - 3 q^{72} - 205 q^{73} + 66 q^{74} - q^{75} - 216 q^{76} - 46 q^{77} - 12 q^{78} + 4 q^{79} - 356 q^{80} - 5 q^{81} - 28 q^{82} + 4 q^{83} - 135 q^{84} + 50 q^{85} - 18 q^{86} - 54 q^{87} - 162 q^{88} + 26 q^{89} - 198 q^{91} + 10 q^{92} + 12 q^{93} - 4 q^{94} - 326 q^{95} + 5 q^{96} - 20 q^{97} - 143 q^{98} + 2 q^{99}+O(q^{100}) \) 140 * q + q^2 + 5 * q^3 - q^4 + 2 * q^5 - q^6 - 2 * q^7 - 3 * q^8 - 5 * q^9 - 116 * q^10 + 2 * q^11 + q^12 + 4 * q^13 - 43 * q^14 - 2 * q^15 + 7 * q^16 + q^18 - 2 * q^19 + 4 * q^20 - 27 * q^21 + 6 * q^22 + 6 * q^23 + 3 * q^24 - 57 * q^25 + 12 * q^26 + 5 * q^27 - 10 * q^28 - 4 * q^29 - 12 * q^31 - 150 * q^32 - 2 * q^33 - 2 * q^34 + 6 * q^35 - q^36 + 12 * q^37 - 12 * q^38 - 4 * q^39 - 66 * q^40 - 4 * q^41 + 14 * q^42 - 60 * q^43 + 20 * q^44 + 2 * q^45 + 76 * q^46 - 25 * q^47 - 7 * q^48 + 31 * q^49 + 137 * q^50 + 118 * q^52 + 48 * q^53 - q^54 + 93 * q^55 + 228 * q^56 + 2 * q^57 - 120 * q^58 + 57 * q^59 - 4 * q^60 + 72 * q^61 - 179 * q^62 - 2 * q^63 + 249 * q^64 - 39 * q^65 - 6 * q^66 + 40 * q^67 + 94 * q^68 - 64 * q^69 + 94 * q^70 + 30 * q^71 - 3 * q^72 - 205 * q^73 + 66 * q^74 - q^75 - 216 * q^76 - 46 * q^77 - 12 * q^78 + 4 * q^79 - 356 * q^80 - 5 * q^81 - 28 * q^82 + 4 * q^83 - 135 * q^84 + 50 * q^85 - 18 * q^86 - 54 * q^87 - 162 * q^88 + 26 * q^89 - 198 * q^91 + 10 * q^92 + 12 * q^93 - 4 * q^94 - 326 * q^95 + 5 * q^96 - 20 * q^97 - 143 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{25}{29}\right)$	$1$

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 $

$2$	−2.13706	+	0.988707i	−1.51113	+	0.699122i	−0.988188	−	0.153248i	$-0.951027\pi$
$2$	−2.13706	+	0.988707i	−1.51113	+	0.699122i	−0.522939	+	0.852370i	$0.675165\pi$
$3$	0.947653	+	0.319302i	0.547128	+	0.184349i
$3$	0.947653	+	0.319302i	0.547128	+	0.184349i
$4$	2.29469	−	2.70152i	1.14735	−	1.35076i
$5$	2.84975	+	1.71464i	1.27445	+	0.766809i	0.981892	−	0.189440i	$-0.0606673\pi$
$5$	2.84975	+	1.71464i	1.27445	+	0.766809i	0.292554	+	0.956249i	$0.405495\pi$
$6$	−2.34088	+	0.254586i	−0.955662	+	0.103934i
$7$	0.205959	−	3.79870i	0.0778453	−	1.43577i	−0.655129	−	0.755517i	$-0.727386\pi$
$7$	0.205959	−	3.79870i	0.0778453	−	1.43577i	0.732975	−	0.680256i	$-0.238131\pi$
$8$	−0.972984	+	3.50437i	−0.344002	+	1.23898i
$9$	0.796093	+	0.605174i	0.265364	+	0.201725i
$10$	−7.78535	−	0.846707i	−2.46194	−	0.267752i
$11$	0.766914	−	4.67797i	0.231233	−	1.41046i	−0.574656	−	0.818395i	$-0.694864\pi$
$11$	0.766914	−	4.67797i	0.231233	−	1.41046i	0.805889	−	0.592066i	$-0.201688\pi$
$12$	3.03717	−	1.82741i	0.876757	−	0.527527i
$13$	1.32729	−	1.00898i	0.368123	−	0.279840i	−0.404715	−	0.914443i	$-0.632629\pi$
$13$	1.32729	−	1.00898i	0.368123	−	0.279840i	0.772838	+	0.634603i	$0.218836\pi$
$14$	3.31565	+	8.32166i	0.886146	+	2.22406i
$15$	2.15309	+	2.53481i	0.555925	+	0.654485i
$16$	−0.238587	−	1.45532i	−0.0596467	−	0.363829i
$17$	0.334992	+	6.17856i	0.0812474	+	1.49852i	0.700683	+	0.713473i	$0.252879\pi$
$17$	0.334992	+	6.17856i	0.0812474	+	1.49852i	−0.619435	+	0.785048i	$0.712638\pi$
$18$	−2.29964	−	0.506188i	−0.542029	−	0.119310i
$19$	−0.760634	+	0.720510i	−0.174501	+	0.165296i	−0.769966	−	0.638085i	$-0.779727\pi$
$19$	−0.760634	+	0.720510i	−0.174501	+	0.165296i	0.595464	+	0.803382i	$0.296968\pi$
$20$	11.1714	−	3.76409i	2.49801	−	0.841677i
$21$	1.40811	−	3.53408i	0.307274	−	0.771200i
$22$	2.98621	+	10.7553i	0.636661	+	2.29305i
$23$	−6.59327	+	1.45129i	−1.37479	+	0.302614i	−0.840099	−	0.542433i	$-0.817503\pi$
$23$	−6.59327	+	1.45129i	−1.37479	+	0.302614i	−0.534692	+	0.845047i	$0.679572\pi$
$24$	−2.04100	+	3.01025i	−0.416618	+	0.614465i
$25$	2.83904	+	5.35500i	0.567809	+	1.07100i
$26$	−1.83890	+	3.46854i	−0.360639	+	0.680237i
$27$	0.561187	+	0.827689i	0.108001	+	0.159289i
$28$	−9.78965	−	9.27325i	−1.85007	−	1.75248i
$29$	1.47482	+	0.682323i	0.273867	+	0.126704i	0.552016	−	0.833834i	$-0.313859\pi$
$29$	1.47482	+	0.682323i	0.273867	+	0.126704i	−0.278149	+	0.960538i	$0.589721\pi$
$30$	−7.10745	−	3.28826i	−1.29764	−	0.600351i
$31$	3.36504	+	3.18754i	0.604379	+	0.572498i	0.927483	−	0.373865i	$-0.121968\pi$
$31$	3.36504	+	3.18754i	0.604379	+	0.572498i	−0.323104	+	0.946363i	$0.604726\pi$
$32$	−2.13325	−	3.14630i	−0.377108	−	0.556193i
$33$	2.22045	−	4.18822i	0.386531	−	0.729075i
$34$	−6.82468	−	12.8727i	−1.17042	−	2.20765i
$35$	7.10032	−	10.4722i	1.20017	−	1.77012i
$36$	3.46168	−	0.761974i	0.576947	−	0.126996i
$37$	0.453724	+	1.63417i	0.0745918	+	0.268655i	0.991437	−	0.130588i	$-0.0416866\pi$
$37$	0.453724	+	1.63417i	0.0745918	+	0.268655i	−0.916845	+	0.399244i	$0.869273\pi$
$38$	0.913143	−	2.29182i	0.148131	−	0.371782i
$39$	1.57998	−	0.532356i	0.252999	−	0.0852451i
$40$	−8.78148	+	8.31826i	−1.38847	+	1.31523i
$41$	−5.60800	−	1.23442i	−0.875823	−	0.192783i	−0.245763	−	0.969330i	$-0.579039\pi$
$41$	−5.60800	−	1.23442i	−0.875823	−	0.192783i	−0.630060	+	0.776547i	$0.716970\pi$
$42$	0.484970	+	8.94474i	0.0748325	+	1.38020i
$43$	−0.677758	−	4.13414i	−0.103357	−	0.630451i	−0.986804	−	0.161919i	$-0.948232\pi$
$43$	−0.677758	−	4.13414i	−0.103357	−	0.630451i	0.883447	−	0.468531i	$-0.155217\pi$
$44$	−10.8778	−	12.8064i	−1.63989	−	1.93063i
$45$	1.23101	+	3.08960i	0.183508	+	0.460571i
$46$	12.6553	−	9.62029i	1.86592	−	1.41843i
$47$	−11.1732	+	6.72270i	−1.62978	+	0.980606i	−0.655520	+	0.755178i	$0.727550\pi$
$47$	−11.1732	+	6.72270i	−1.62978	+	0.980606i	−0.974260	+	0.225428i	$0.927622\pi$
$48$	0.238587	−	1.45532i	0.0344371	−	0.210057i
$49$	−7.42872	−	0.807922i	−1.06125	−	0.115417i
$50$	−11.3617	−	8.63696i	−1.60679	−	1.22145i
$51$	−1.65537	+	5.96209i	−0.231798	+	0.834860i
$52$	0.319942	−	5.90099i	0.0443680	−	0.818320i
$53$	−3.87429	+	0.421354i	−0.532174	+	0.0578774i	−0.370261	−	0.928928i	$-0.620732\pi$
$53$	−3.87429	+	0.421354i	−0.532174	+	0.0578774i	−0.161913	+	0.986805i	$0.551766\pi$
$54$	−2.01763	−	1.21397i	−0.274565	−	0.165200i
$55$	10.2065	−	12.0161i	1.37625	−	1.62025i
$56$	13.1116	+	4.41783i	1.75212	+	0.590357i
$57$	−0.950877	+	0.439922i	−0.125947	+	0.0582692i
$58$	−3.82638			−0.502429
$59$	5.49712	−	5.36486i	0.715664	−	0.698445i
$59$	5.49712	−	5.36486i	0.715664	−	0.698445i
$60$	11.7885			1.52189
$61$	−0.386501	+	0.178814i	−0.0494864	+	0.0228948i	−0.444476	−	0.895791i	$-0.646610\pi$
$61$	−0.386501	+	0.178814i	−0.0494864	+	0.0228948i	0.394990	+	0.918685i	$0.370748\pi$
$62$	−10.3428	−	3.48490i	−1.31354	−	0.442583i
$63$	2.46284	−	2.89948i	0.310288	−	0.365300i
$64$	10.1969	+	6.13529i	1.27462	+	0.766911i
$65$	5.51246	−	0.599516i	0.683737	−	0.0743609i
$66$	−0.604310	+	11.1458i	−0.0743854	+	1.37196i
$67$	−4.22186	+	15.2058i	−0.515783	+	1.85768i	−0.00160430	+	0.999999i	$0.500511\pi$
$67$	−4.22186	+	15.2058i	−0.515783	+	1.85768i	−0.514179	+	0.857683i	$0.671903\pi$
$68$	17.4602	+	13.2729i	2.11736	+	1.60958i
$69$	−6.71153	−	0.729923i	−0.807973	−	0.0878724i
$70$	−4.81985	+	29.3998i	−0.576082	+	3.51395i
$71$	9.90405	−	5.95907i	1.17539	−	0.707211i	0.212519	−	0.977157i	$-0.431833\pi$
$71$	9.90405	−	5.95907i	1.17539	−	0.707211i	0.962876	+	0.269945i	$0.0870057\pi$
$72$	−2.89534	+	2.20098i	−0.341219	+	0.259388i
$73$	−1.94438	−	4.88001i	−0.227572	−	0.571162i	0.770206	−	0.637796i	$-0.220154\pi$
$73$	−1.94438	−	4.88001i	−0.227572	−	0.571162i	−0.997778	+	0.0666332i	$0.978774\pi$
$74$	−2.58535	−	3.04371i	−0.300541	−	0.353824i
$75$	0.980567	+	5.98120i	0.113226	+	0.690649i
$76$	0.201054	+	3.70822i	0.0230625	+	0.425362i
$77$	−17.6122	−	3.87675i	−2.00710	−	0.441796i
$78$	−2.85015	+	2.69981i	−0.322716	+	0.305693i
$79$	−5.10356	+	1.71959i	−0.574195	+	0.193469i	−0.591393	−	0.806383i	$-0.701422\pi$
$79$	−5.10356	+	1.71959i	−0.574195	+	0.193469i	0.0171983	+	0.999852i	$0.494525\pi$
$80$	1.81543	−	4.55637i	0.202971	−	0.509418i
$81$	0.267528	+	0.963550i	0.0297254	+	0.107061i
$82$	13.2051	−	2.90666i	1.45826	−	0.320987i
$83$	3.34791	−	4.93779i	0.367480	−	0.541993i	−0.598328	−	0.801252i	$-0.704168\pi$
$83$	3.34791	−	4.93779i	0.367480	−	0.541993i	0.965808	+	0.259259i	$0.0834782\pi$
$84$	−6.31623	−	11.9137i	−0.689158	−	1.29989i
$85$	−9.63934	+	18.1817i	−1.04553	+	1.97208i
$86$	5.53586	+	8.16479i	0.596948	+	0.880432i
$87$	1.17975	+	1.11752i	0.126482	+	0.119810i
$88$	15.6471	+	7.23914i	1.66799	+	0.771695i
$89$	9.08328	+	4.20237i	0.962825	+	0.445450i	0.837363	−	0.546648i	$-0.184096\pi$
$89$	9.08328	+	4.20237i	0.962825	+	0.445450i	0.125463	+	0.992098i	$0.459958\pi$
$90$	−5.68545	−	5.38555i	−0.599299	−	0.567687i
$91$	−3.55943	−	5.24977i	−0.373130	−	0.550325i
$92$	−11.2088	+	21.1421i	−1.16860	+	2.20422i
$93$	2.17111	+	4.09514i	0.225133	+	0.424646i
$94$	17.2310	−	25.4138i	1.77724	−	2.62123i
$95$	−3.40303	+	0.749063i	−0.349143	+	0.0768522i
$96$	−1.01696	−	3.66275i	−0.103793	−	0.373828i
$97$	1.24418	−	3.12264i	0.126327	−	0.317056i	−0.852187	−	0.523237i	$-0.824724\pi$
$97$	1.24418	−	3.12264i	0.126327	−	0.317056i	0.978514	+	0.206181i	$0.0661035\pi$
$98$	16.6744	−	5.61825i	1.68437	−	0.567529i
$99$	3.44152	−	3.25998i	0.345886	−	0.327641i
$100$	20.9814	+	4.61836i	2.09814	+	0.461836i
$101$	−1.02296	−	18.8674i	−0.101789	−	1.87738i	−0.391380	−	0.920229i	$-0.628002\pi$
$101$	−1.02296	−	18.8674i	−0.101789	−	1.87738i	0.289591	−	0.957151i	$-0.406481\pi$
$102$	−2.35715	−	14.3780i	−0.233393	−	1.42363i
$103$	3.11334	+	3.66530i	0.306766	+	0.361153i	0.893845	−	0.448377i	$-0.147998\pi$
$103$	3.11334	+	3.66530i	0.306766	+	0.361153i	−0.587078	+	0.809530i	$0.699722\pi$
$104$	2.24440	+	5.63302i	0.220082	+	0.552363i
$105$	10.0724	−	7.65686i	0.982968	−	0.747233i
$106$	7.86297	−	4.73099i	0.763719	−	0.459515i
$107$	−1.19637	+	7.29751i	−0.115657	+	0.705477i	0.863802	+	0.503832i	$0.168077\pi$
$107$	−1.19637	+	7.29751i	−0.115657	+	0.705477i	−0.979459	+	0.201645i	$0.935371\pi$
$108$	3.52377	+	0.383233i	0.339075	+	0.0368767i
$109$	−4.92227	−	3.74181i	−0.471468	−	0.358401i	0.342300	−	0.939591i	$-0.388794\pi$
$109$	−4.92227	−	3.74181i	−0.471468	−	0.358401i	−0.813768	+	0.581190i	$0.802587\pi$
$110$	−9.93157	+	35.7703i	−0.946938	+	3.41056i
$111$	−0.0918188	+	1.69350i	−0.00871506	+	0.160740i
$112$	−5.57745	+	0.606584i	−0.527019	+	0.0573168i
$113$	−2.14903	−	1.29303i	−0.202163	−	0.121638i	0.410872	−	0.911693i	$-0.365224\pi$
$113$	−2.14903	−	1.29303i	−0.202163	−	0.121638i	−0.613036	+	0.790055i	$0.710052\pi$
$114$	1.59712	−	1.88028i	0.149584	−	0.176104i
$115$	−21.2776	−	7.16925i	−1.98414	−	0.668536i
$116$	5.22756	−	2.41853i	0.485367	−	0.224555i
$117$	1.66725			0.154137
$118$	−6.44338	+	16.9000i	−0.593161	+	1.55578i
$119$	23.5395			2.15786
$120$	−10.9778	+	5.07888i	−1.00213	+	0.463637i
$121$	−10.8711	−	3.66289i	−0.988279	−	0.332990i
$122$	0.649180	−	0.764273i	0.0587740	−	0.0691940i
$123$	−4.92029	−	2.96044i	−0.443648	−	0.266934i
$124$	16.3329	−	1.77631i	1.46674	−	0.159518i
$125$	−0.191047	+	3.52365i	−0.0170878	+	0.315165i
$126$	−2.39649	+	8.63137i	−0.213496	+	0.768943i
$127$	1.02572	+	0.779729i	0.0910176	+	0.0691898i	0.649693	−	0.760196i	$-0.274897\pi$
$127$	1.02572	+	0.779729i	0.0910176	+	0.0691898i	−0.558676	+	0.829386i	$0.688690\pi$
$128$	−20.2994	−	2.20769i	−1.79423	−	0.195134i
$129$	0.677758	−	4.13414i	0.0596733	−	0.363991i
$130$	−11.1877	+	6.73141i	−0.981226	+	0.590384i
$131$	−12.9785	+	9.86599i	−1.13394	+	0.861996i	−0.991793	−	0.127851i	$-0.959192\pi$
$131$	−12.9785	+	9.86599i	−1.13394	+	0.861996i	−0.142142	+	0.989846i	$0.545399\pi$
$132$	−6.21931	−	15.6093i	−0.541321	−	1.35861i
$133$	2.58034	+	3.03781i	0.223744	+	0.263412i
$134$	−6.01171	−	36.6698i	−0.519333	−	3.16779i
$135$	0.180056	+	3.32094i	0.0154968	+	0.285821i
$136$	−21.9779	−	4.83770i	−1.88459	−	0.414829i
$137$	−5.84699	+	5.53856i	−0.499542	+	0.473191i	−0.895490	−	0.445082i	$-0.853175\pi$
$137$	−5.84699	+	5.53856i	−0.499542	+	0.473191i	0.395948	+	0.918273i	$0.370416\pi$
$138$	15.0646	−	5.07585i	1.28238	−	0.432085i
$139$	1.04622	−	2.62581i	0.0887390	−	0.222718i	−0.877909	−	0.478828i	$-0.841062\pi$
$139$	1.04622	−	2.62581i	0.0887390	−	0.222718i	0.966648	+	0.256110i	$0.0824410\pi$
$140$	−11.9978	−	43.2121i	−1.01400	−	3.65209i
$141$	−12.7349	+	2.80316i	−1.07247	+	0.236069i
$142$	−15.2737	+	22.5271i	−1.28174	+	1.89043i
$143$	−3.70205	−	6.98281i	−0.309581	−	0.583932i
$144$	0.690782	−	1.30295i	0.0575652	−	0.108579i
$145$	3.03292	+	4.47322i	0.251870	+	0.371481i
$146$	8.98015	+	8.50645i	0.743202	+	0.703998i
$147$	−6.78188	−	3.13763i	−0.559360	−	0.258787i
$148$	5.45590	+	2.52417i	0.448472	+	0.207485i
$149$	8.27751	+	7.84088i	0.678120	+	0.642350i	0.947153	−	0.320781i	$-0.103945\pi$
$149$	8.27751	+	7.84088i	0.678120	+	0.642350i	−0.269033	+	0.963131i	$0.586704\pi$
$150$	−8.00918	−	11.8127i	−0.653947	−	0.964500i
$151$	0.729332	−	1.37567i	0.0593522	−	0.111950i	−0.852061	−	0.523442i	$-0.824647\pi$
$151$	0.729332	−	1.37567i	0.0593522	−	0.111950i	0.911413	+	0.411492i	$0.134992\pi$
$152$	−1.78485	−	3.36659i	−0.144771	−	0.273066i
$153$	−3.47242	+	5.12144i	−0.280728	+	0.414044i
$154$	41.4713	−	9.12853i	3.34185	−	0.735598i
$155$	4.12405	+	14.8535i	0.331252	+	1.19306i
$156$	2.18739	−	5.48993i	0.175131	−	0.439546i
$157$	−4.60010	+	1.54996i	−0.367128	+	0.123700i	−0.496818	−	0.867855i	$-0.665498\pi$
$157$	−4.60010	+	1.54996i	−0.367128	+	0.123700i	0.129690	+	0.991555i	$0.458602\pi$
$158$	9.20642	−	8.72078i	0.732423	−	0.693788i
$159$	−3.80602	−	0.837768i	−0.301837	−	0.0664393i
$160$	−0.684449	−	12.6239i	−0.0541104	−	0.998008i
$161$	4.15506	+	25.3447i	0.327464	+	1.99744i
$162$	−1.52439	−	1.79465i	−0.119768	−	0.141001i
$163$	−6.55741	−	16.4579i	−0.513616	−	1.28908i	−0.925812	−	0.377984i	$-0.876617\pi$
$163$	−6.55741	−	16.4579i	−0.513616	−	1.28908i	0.412196	−	0.911095i	$-0.364762\pi$
$164$	−16.2035	+	12.3175i	−1.26528	+	0.961839i
$165$	13.5090	−	8.12810i	1.05167	−	0.632771i
$166$	−2.27263	+	13.8624i	−0.176390	+	1.07593i
$167$	1.64935	+	0.179378i	0.127631	+	0.0138807i	0.171711	−	0.985147i	$-0.445070\pi$
$167$	1.64935	+	0.179378i	0.127631	+	0.0138807i	−0.0440807	+	0.999028i	$0.514036\pi$
$168$	11.0147	+	8.37314i	0.849801	+	0.646002i
$169$	−2.73421	+	9.84775i	−0.210324	+	0.757519i
$170$	2.62340	−	48.3859i	0.201206	−	3.71103i
$171$	−1.04157	+	0.113277i	−0.0796508	+	0.00866255i
$172$	−12.7237	−	7.65561i	−0.970175	−	0.583735i
$173$	−0.571245	+	0.672522i	−0.0434310	+	0.0511309i	−0.783449	−	0.621457i	$-0.786541\pi$
$173$	−0.571245	+	0.672522i	−0.0434310	+	0.0511309i	0.740018	+	0.672587i	$0.234817\pi$
$174$	−3.62608	−	1.22177i	−0.274893	−	0.0926222i
$175$	20.9268	−	9.68175i	1.58191	−	0.731872i
$176$	−6.99090			−0.526959
$177$	6.92237	−	3.32879i	0.520317	−	0.250207i
$178$	−23.5664			−1.76638
$179$	−4.64838	+	2.15057i	−0.347436	+	0.160741i	−0.585844	−	0.810424i	$-0.699237\pi$
$179$	−4.64838	+	2.15057i	−0.347436	+	0.160741i	0.238407	+	0.971165i	$0.423375\pi$
$180$	11.1714	+	3.76409i	0.832669	+	0.280559i
$181$	−2.18869	+	2.57672i	−0.162684	+	0.191526i	−0.837464	−	0.546493i	$-0.815963\pi$
$181$	−2.18869	+	2.57672i	−0.162684	+	0.191526i	0.674780	+	0.738019i	$0.264239\pi$
$182$	12.7972	+	7.69982i	0.948591	+	0.570748i
$183$	−0.423365	+	0.0460437i	−0.0312960	+	0.00340365i
$184$	1.32929	−	24.5173i	0.0979966	−	1.80744i
$185$	−1.50900	+	5.43494i	−0.110944	+	0.399585i
$186$	−8.68867	−	6.60496i	−0.637084	−	0.484299i
$187$	29.1600	+	3.17134i	2.13239	+	0.231912i
$188$	−7.47758	+	45.6112i	−0.545358	+	3.32654i
$189$	3.25972	−	1.96131i	0.237110	−	0.142664i
$190$	6.53186	−	4.96539i	0.473871	−	0.360227i
$191$	−1.94261	−	4.87558i	−0.140562	−	0.352785i	0.841795	−	0.539797i	$-0.181499\pi$
$191$	−1.94261	−	4.87558i	−0.140562	−	0.352785i	−0.982358	+	0.187012i	$0.940120\pi$
$192$	7.70415	+	9.07002i	0.555999	+	0.654573i
$193$	0.894760	+	5.45779i	0.0644062	+	0.392861i	0.999282	+	0.0378858i	$0.0120623\pi$
$193$	0.894760	+	5.45779i	0.0644062	+	0.392861i	−0.934876	+	0.354975i	$0.884489\pi$
$194$	0.428509	+	7.90339i	0.0307652	+	0.567430i
$195$	5.41533	+	1.19200i	0.387800	+	0.0853612i
$196$	−19.2293	+	18.2149i	−1.37352	+	1.30107i
$197$	−0.177460	+	0.0597931i	−0.0126435	+	0.00426008i	−0.325616	−	0.945502i	$-0.605572\pi$
$197$	−0.177460	+	0.0597931i	−0.0126435	+	0.00426008i	0.312973	+	0.949762i	$0.398675\pi$
$198$	−4.13156	+	10.3694i	−0.293617	+	0.736923i
$199$	−5.04258	−	18.1617i	−0.357459	−	1.28745i	−0.895699	−	0.444661i	$-0.853324\pi$
$199$	−5.04258	−	18.1617i	−0.357459	−	1.28745i	0.538240	−	0.842792i	$-0.319089\pi$
$200$	−21.5283	+	4.73873i	−1.52228	+	0.335079i
$201$	−8.85609	+	13.0618i	−0.624661	+	0.921305i
$202$	20.8405	+	39.3094i	1.46633	+	2.76580i
$203$	2.89569	−	5.46185i	0.203238	−	0.383347i
$204$	12.3082	+	18.1532i	0.861744	+	1.27098i
$205$	−13.8648	−	13.1335i	−0.968361	−	0.917281i
$206$	−10.2773	−	4.75478i	−0.716053	−	0.331281i
$207$	−6.12713	−	2.83471i	−0.425865	−	0.197026i
$208$	−1.78505	−	1.69089i	−0.123771	−	0.117242i
$209$	2.78719	+	4.11079i	0.192794	+	0.284349i
$210$	−13.9549	+	26.3218i	−0.962983	+	1.81638i
$211$	5.14494	+	9.70439i	0.354192	+	0.668078i	0.995027	−	0.0996008i	$-0.0317566\pi$
$211$	5.14494	+	9.70439i	0.354192	+	0.668078i	−0.640835	+	0.767679i	$0.721412\pi$
$212$	−7.75200	+	11.4333i	−0.532410	+	0.785246i
$213$	11.2883	−	2.48475i	0.773465	−	0.170252i
$214$	−4.65840	−	16.7780i	−0.318442	−	1.14692i
$215$	5.15711	−	12.9434i	0.351712	−	0.882731i
$216$	−3.44655	+	1.16128i	−0.234508	+	0.0790151i
$217$	12.8015	−	12.1263i	0.869026	−	0.823185i
$218$	14.2187	+	3.12978i	0.963014	+	0.211975i
$219$	−0.284397	−	5.24540i	−0.0192178	−	0.354451i
$220$	−9.04079	−	55.1464i	−0.609530	−	3.71797i
$221$	6.67865	+	7.86272i	0.449255	+	0.528904i
$222$	−1.47815	−	3.70988i	−0.0992071	−	0.248991i
$223$	16.7225	−	12.7121i	1.11982	−	0.851267i	0.129711	−	0.991552i	$-0.458595\pi$
$223$	16.7225	−	12.7121i	1.11982	−	0.851267i	0.990111	+	0.140285i	$0.0448018\pi$
$224$	−12.3912	+	7.45555i	−0.827923	+	0.498145i
$225$	−0.980567	+	5.98120i	−0.0653712	+	0.398746i
$226$	5.87102	+	0.638511i	0.390534	+	0.0424731i
$227$	17.6706	+	13.4328i	1.17284	+	0.891567i	0.995702	−	0.0926196i	$-0.0295241\pi$
$227$	17.6706	+	13.4328i	1.17284	+	0.891567i	0.177135	+	0.984187i	$0.443317\pi$
$228$	−0.993511	+	3.57830i	−0.0657969	+	0.236979i
$229$	−0.554801	+	10.2327i	−0.0366623	+	0.676196i	0.921221	+	0.389039i	$0.127193\pi$
$229$	−0.554801	+	10.2327i	−0.0366623	+	0.676196i	−0.957884	+	0.287157i	$0.907290\pi$
$230$	52.5597	−	5.71621i	3.46568	−	0.376916i
$231$	−15.4524	−	9.29743i	−1.01670	−	0.611726i
$232$	−3.82608	+	4.50441i	−0.251195	+	0.295729i
$233$	9.99437	+	3.36749i	0.654753	+	0.220612i	0.627020	−	0.779003i	$-0.284275\pi$
$233$	9.99437	+	3.36749i	0.654753	+	0.220612i	0.0277332	+	0.999615i	$0.491171\pi$
$234$	−3.56301	+	1.64842i	−0.232921	+	0.107761i
$235$	−43.3678			−2.82900
$236$	−1.87908	−	27.1613i	−0.122318	−	1.76805i
$237$	−5.38547			−0.349824
$238$	−50.3052	+	23.2736i	−3.26080	+	1.50861i
$239$	−21.6919	−	7.30884i	−1.40313	−	0.472769i	−0.486912	−	0.873451i	$-0.661877\pi$
$239$	−21.6919	−	7.30884i	−1.40313	−	0.472769i	−0.916217	+	0.400682i	$0.868773\pi$
$240$	3.17525	−	3.73819i	0.204962	−	0.241299i
$241$	16.8020	+	10.1094i	1.08231	+	0.651204i	0.940879	−	0.338744i	$-0.110002\pi$
$241$	16.8020	+	10.1094i	1.08231	+	0.651204i	0.141431	+	0.989948i	$0.454830\pi$
$242$	26.8536	−	2.92051i	1.72622	−	0.187737i
$243$	−0.0541389	+	0.998533i	−0.00347301	+	0.0640559i
$244$	−0.403831	+	1.45447i	−0.0258526	+	0.0931127i
$245$	−19.7847	−	15.0399i	−1.26400	−	0.960865i
$246$	13.4420	+	1.46190i	0.857028	+	0.0932074i
$247$	−0.282600	+	1.72379i	−0.0179814	+	0.109682i
$248$	−14.4444	+	8.69093i	−0.917222	+	0.551874i
$249$	4.74930	−	3.61032i	0.300975	−	0.228795i
$250$	−3.07559	−	7.71914i	−0.194517	−	0.488201i
$251$	3.03354	+	3.57136i	0.191475	+	0.225422i	0.849520	−	0.527557i	$-0.176892\pi$
$251$	3.03354	+	3.57136i	0.191475	+	0.225422i	−0.658044	+	0.752979i	$0.728616\pi$
$252$	−2.18154	−	13.3068i	−0.137424	−	0.838251i
$253$	1.73261	+	31.9561i	0.108928	+	2.00906i
$254$	−2.96294	−	0.652192i	−0.185911	−	0.0409222i
$255$	−14.9402	+	14.1521i	−0.935592	+	0.886240i
$256$	23.0088	−	7.75256i	1.43805	−	0.484535i
$257$	11.3145	−	28.3973i	0.705781	−	1.77138i	0.0726179	−	0.997360i	$-0.476865\pi$
$257$	11.3145	−	28.3973i	0.705781	−	1.77138i	0.633164	−	0.774018i	$-0.281756\pi$
$258$	2.63905	+	9.50500i	0.164300	+	0.591755i
$259$	6.30116	−	1.38699i	0.391535	−	0.0861833i
$260$	11.0298	−	16.2677i	0.684040	−	1.00888i
$261$	0.761167	+	1.43571i	0.0471151	+	0.0888684i
$262$	17.9812	−	33.9161i	1.11088	−	2.09534i
$263$	−15.2076	−	22.4296i	−0.937742	−	1.38307i	−0.923680	−	0.383165i	$-0.874834\pi$
$263$	−15.2076	−	22.4296i	−0.937742	−	1.38307i	−0.0140623	−	0.999901i	$-0.504476\pi$
$264$	12.5166	+	11.8564i	0.770343	+	0.729708i
$265$	−11.7632	−	5.44224i	−0.722608	−	0.334314i
$266$	−8.51784	−	3.94077i	−0.522262	−	0.241624i
$267$	7.26597	+	6.88269i	0.444670	+	0.421214i
$268$	31.3909	+	46.2981i	1.91750	+	2.82811i
$269$	−3.89015	+	7.33761i	−0.237187	+	0.447382i	−0.973319	−	0.229456i	$-0.926305\pi$
$269$	−3.89015	+	7.33761i	−0.237187	+	0.447382i	0.736132	+	0.676838i	$0.236650\pi$
$270$	−3.66822	−	6.91901i	−0.223241	−	0.421077i
$271$	−14.4699	+	21.3415i	−0.878983	+	1.29640i	0.0751963	+	0.997169i	$0.476042\pi$
$271$	−14.4699	+	21.3415i	−0.878983	+	1.29640i	−0.954180	+	0.299235i	$0.903269\pi$
$272$	8.91183	−	1.96164i	0.540359	−	0.118942i
$273$	−1.69685	−	6.11149i	−0.102698	−	0.369884i
$274$	7.01932	−	17.6172i	0.424053	−	1.06429i
$275$	27.2279	−	9.17413i	1.64190	−	0.553221i
$276$	−17.3728	+	16.4564i	−1.04572	+	0.990559i
$277$	−15.1875	−	3.34303i	−0.912531	−	0.200863i	−0.266198	−	0.963919i	$-0.585767\pi$
$277$	−15.1875	−	3.34303i	−0.912531	−	0.200863i	−0.646333	+	0.763055i	$0.723698\pi$
$278$	0.360330	+	6.64590i	0.0216112	+	0.398595i
$279$	0.749871	+	4.57401i	0.0448936	+	0.273839i
$280$	29.7899	+	35.0714i	1.78029	+	2.09592i
$281$	−2.77237	−	6.95813i	−0.165386	−	0.415087i	0.822803	−	0.568326i	$-0.192409\pi$
$281$	−2.77237	−	6.95813i	−0.165386	−	0.415087i	−0.988189	+	0.153239i	$0.951030\pi$
$282$	24.4437	−	18.5816i	1.45560	−	1.10652i
$283$	8.57030	−	5.15658i	0.509451	−	0.306527i	−0.237520	−	0.971383i	$-0.576335\pi$
$283$	8.57030	−	5.15658i	0.509451	−	0.306527i	0.746972	+	0.664856i	$0.231507\pi$
$284$	6.62821	−	40.4303i	0.393312	−	2.39909i
$285$	−3.46407	−	0.376740i	−0.205194	−	0.0223161i
$286$	14.8154	+	11.2624i	0.876056	+	0.665960i
$287$	−5.84419	+	21.0489i	−0.344972	+	1.24248i
$288$	0.205799	−	3.79574i	0.0121268	−	0.223666i
$289$	−21.1620	+	2.30151i	−1.24482	+	0.135383i
$290$	−10.9042	−	6.56086i	−0.640318	−	0.385267i
$291$	2.17611	−	2.56192i	0.127566	−	0.150182i
$292$	−17.6452	−	5.94537i	−1.03261	−	0.347926i
$293$	6.85758	−	3.17266i	0.400624	−	0.185349i	−0.209222	−	0.977868i	$-0.567093\pi$
$293$	6.85758	−	3.17266i	0.400624	−	0.185349i	0.609846	+	0.792520i	$0.291231\pi$
$294$	17.5954			1.02619
$295$	24.8642	−	5.86293i	1.44765	−	0.341353i
$296$	−6.16819			−0.358519
$297$	4.30229	−	1.99045i	0.249644	−	0.115498i
$298$	−25.4418	−	8.57235i	−1.47381	−	0.496583i
$299$	−7.28684	+	8.57873i	−0.421409	+	0.496121i
$300$	18.4084	+	11.0760i	1.06281	+	0.639473i
$301$	−15.8439	+	1.72313i	−0.913230	+	0.0993197i
$302$	−0.198492	+	3.66097i	−0.0114219	+	0.210665i
$303$	5.05499	−	18.2064i	0.290401	−	1.04593i
$304$	1.23005	+	0.935058i	0.0705481	+	0.0536293i
$305$	−1.40803	−	0.153133i	−0.0806237	−	0.00876836i
$306$	2.35715	−	14.3780i	0.134750	−	0.821936i
$307$	−1.80508	+	1.08608i	−0.103021	+	0.0619859i	−0.566132	−	0.824315i	$-0.691561\pi$
$307$	−1.80508	+	1.08608i	−0.103021	+	0.0619859i	0.463111	+	0.886300i	$0.346733\pi$
$308$	−50.8878	+	38.6839i	−2.89960	+	2.20422i
$309$	1.78003	+	4.46753i	0.101262	+	0.254149i
$310$	−23.4991	−	27.6653i	−1.33466	−	1.57128i
$311$	−3.02566	−	18.4557i	−0.171570	−	1.04653i	−0.922458	−	0.386098i	$-0.873823\pi$
$311$	−3.02566	−	18.4557i	−0.171570	−	1.04653i	0.750888	−	0.660429i	$-0.229626\pi$
$312$	0.328281	+	6.05479i	0.0185853	+	0.342785i
$313$	−24.4742	−	5.38718i	−1.38336	−	0.304502i	−0.539919	−	0.841717i	$-0.681545\pi$
$313$	−24.4742	−	5.38718i	−1.38336	−	0.304502i	−0.843445	+	0.537215i	$0.819476\pi$
$314$	8.29823	−	7.86050i	0.468296	−	0.443594i
$315$	11.9900	−	4.03990i	0.675561	−	0.227623i
$316$	−7.06559	+	17.7333i	−0.397471	+	0.997576i
$317$	0.360954	+	1.30004i	0.0202732	+	0.0730174i	0.972995	−	0.230828i	$-0.0741433\pi$
$317$	0.360954	+	1.30004i	0.0202732	+	0.0730174i	−0.952722	+	0.303845i	$0.901730\pi$
$318$	8.96198	−	1.97268i	0.502563	−	0.110622i
$319$	4.32294	−	6.37587i	0.242038	−	0.356980i
$320$	18.5389	+	34.9681i	1.03636	+	1.95477i
$321$	−3.46385	+	6.53351i	−0.193333	+	0.364665i
$322$	−33.9381	−	50.0550i	−1.89130	−	2.78945i
$323$	−4.70652	−	4.45825i	−0.261878	−	0.248064i
$324$	3.21695	+	1.48832i	0.178719	+	0.0826844i
$325$	9.17130	+	4.24310i	0.508732	+	0.235365i
$326$	30.2856	+	28.6880i	1.67736	+	1.58888i
$327$	−3.46984	−	5.11763i	−0.191882	−	0.283006i
$328$	9.78234	−	18.4515i	0.540140	−	1.01881i
$329$	23.2363	+	43.8282i	1.28106	+	2.41633i
$330$	−20.8332	+	30.7266i	−1.14683	+	1.69145i
$331$	20.7446	−	4.56622i	1.14022	−	0.250982i	0.395572	−	0.918435i	$-0.370546\pi$
$331$	20.7446	−	4.56622i	1.14022	−	0.250982i	0.744652	+	0.667453i	$0.232615\pi$
$332$	−5.65714	−	20.3752i	−0.310476	−	1.11823i
$333$	−0.627749	+	1.57553i	−0.0344004	+	0.0863386i
$334$	−3.70211	+	1.24739i	−0.202570	+	0.0682539i
$335$	−38.1036	+	36.0937i	−2.08182	+	1.97201i
$336$	−5.47917	−	1.20606i	−0.298913	−	0.0657957i
$337$	1.09202	+	20.1411i	0.0594861	+	1.09716i	0.864087	+	0.503342i	$0.167896\pi$
$337$	1.09202	+	20.1411i	0.0594861	+	1.09716i	−0.804601	+	0.593816i	$0.797621\pi$
$338$	−3.89337	−	23.7485i	−0.211772	−	1.29175i
$339$	−1.62367	−	1.91153i	−0.0881855	−	0.103820i
$340$	26.9990	+	67.7624i	1.46423	+	3.67493i
$341$	17.4919	−	13.2970i	0.947239	−	0.720073i
$342$	2.11389	−	1.27189i	0.114306	−	0.0687758i
$343$	−0.290819	+	1.77392i	−0.0157028	+	0.0957826i
$344$	15.1470	+	1.64734i	0.816672	+	0.0888184i
$345$	−17.8746	−	13.5879i	−0.962337	−	0.731549i
$346$	0.555856	−	2.00201i	0.0298830	−	0.107629i
$347$	−0.617675	+	11.3923i	−0.0331585	+	0.611573i	0.933980	+	0.357325i	$0.116311\pi$
$347$	−0.617675	+	11.3923i	−0.0331585	+	0.611573i	−0.967139	+	0.254249i	$0.918172\pi$
$348$	5.72616	−	0.622757i	0.306954	−	0.0333833i
$349$	4.00298	+	2.40851i	0.214275	+	0.128925i	0.618645	−	0.785670i	$-0.287682\pi$
$349$	4.00298	+	2.40851i	0.214275	+	0.128925i	−0.404371	+	0.914595i	$0.632509\pi$
$350$	−35.1493	+	41.3809i	−1.87881	+	2.21190i
$351$	1.57998	+	0.532356i	0.0843329	+	0.0284150i
$352$	−16.3543	+	7.56632i	−0.871689	+	0.403286i
$353$	27.9534			1.48781			0.743905	−	0.668285i	$-0.232971\pi$
$353$	27.9534			1.48781			0.743905	+	0.668285i	$0.232971\pi$
$354$	−11.5023	+	13.9580i	−0.611340	+	0.741859i
$355$	38.4417			2.04027
$356$	32.1961	−	14.8955i	1.70639	−	0.789461i
$357$	22.3073	+	7.51619i	1.18062	+	0.397799i
$358$	7.80757	−	9.19178i	0.412643	−	0.485801i
$359$	−16.6282	−	10.0048i	−0.877601	−	0.528035i	0.00402060	−	0.999992i	$-0.498720\pi$
$359$	−16.6282	−	10.0048i	−0.877601	−	0.528035i	−0.881622	+	0.471957i	$0.843548\pi$
$360$	−12.0249	+	1.30778i	−0.633766	+	0.0689262i
$361$	−0.969211	+	17.8760i	−0.0510111	+	0.940845i
$362$	2.12973	−	7.67058i	0.111936	−	0.403157i
$363$	−9.13244	−	6.94230i	−0.479329	−	0.364376i
$364$	−22.3502	−	2.43073i	−1.17147	−	0.127405i
$365$	2.82647	−	17.2407i	0.147944	−	0.902420i
$366$	0.859231	−	0.516982i	0.0449127	−	0.0270231i
$367$	12.5940	−	9.57368i	0.657399	−	0.499742i	−0.222481	−	0.974937i	$-0.571416\pi$
$367$	12.5940	−	9.57368i	0.657399	−	0.499742i	0.879881	+	0.475195i	$0.157622\pi$
$368$	3.68515	+	9.24903i	0.192102	+	0.482139i
$369$	−3.71746	−	4.37653i	−0.193523	−	0.227833i
$370$	−2.14874	−	13.1067i	−0.111708	−	0.681386i
$371$	0.802651	+	14.8040i	0.0416715	+	0.768586i
$372$	16.0451	+	3.53180i	0.831902	+	0.183115i
$373$	12.4545	−	11.7975i	0.644870	−	0.610853i	−0.293719	−	0.955892i	$-0.594893\pi$
$373$	12.4545	−	11.7975i	0.644870	−	0.610853i	0.938588	+	0.345039i	$0.112134\pi$
$374$	−65.4522	+	22.0534i	−3.38445	+	1.14035i
$375$	−1.30615	+	3.27820i	−0.0674495	+	0.169286i
$376$	−12.6875	−	45.6961i	−0.654306	−	2.35660i
$377$	2.64595	−	0.582418i	0.136274	−	0.0299961i
$378$	−5.02705	+	7.41434i	−0.258563	+	0.381352i
$379$	9.03713	+	17.0458i	0.464206	+	0.875586i	0.999521	+	0.0309336i	$0.00984804\pi$
$379$	9.03713	+	17.0458i	0.464206	+	0.875586i	−0.535315	+	0.844652i	$0.679807\pi$
$380$	−5.78530	+	10.9122i	−0.296779	+	0.559785i
$381$	0.723055	+	1.06643i	0.0370432	+	0.0546346i
$382$	8.97199	+	8.49872i	0.459047	+	0.434832i
$383$	12.9720	+	6.00151i	0.662840	+	0.306663i	0.722312	−	0.691567i	$-0.243079\pi$
$383$	12.9720	+	6.00151i	0.662840	+	0.306663i	−0.0594715	+	0.998230i	$0.518942\pi$
$384$	−18.5318	−	8.57374i	−0.945699	−	0.437527i
$385$	−43.5432	−	41.2464i	−2.21917	−	2.10211i
$386$	−7.30831	−	10.7790i	−0.371983	−	0.548634i
$387$	1.96232	−	3.70132i	0.0997502	−	0.188149i
$388$	−5.58089	−	10.5267i	−0.283327	−	0.534411i
$389$	16.9987	−	25.0713i	0.861870	−	1.27116i	−0.0992584	−	0.995062i	$-0.531647\pi$
$389$	16.9987	−	25.0713i	0.861870	−	1.27116i	0.961128	−	0.276102i	$-0.0890426\pi$
$390$	−12.7514	+	2.80680i	−0.645693	+	0.142128i
$391$	−11.1756	−	40.2507i	−0.565172	−	2.03557i
$392$	10.0593	−	25.2469i	0.508070	−	1.27516i
$393$	−15.4493	+	5.20549i	−0.779316	+	0.262582i
$394$	0.320123	−	0.303237i	0.0161276	−	0.0152768i
$395$	−17.4923	−	3.85035i	−0.880134	−	0.193732i
$396$	−0.909678	−	16.7780i	−0.0457130	−	0.843127i
$397$	−2.06255	−	12.5810i	−0.103516	−	0.631421i	−0.986720	−	0.162431i	$-0.948066\pi$
$397$	−2.06255	−	12.5810i	−0.103516	−	0.631421i	0.883204	−	0.468990i	$-0.155382\pi$
$398$	28.7329	+	33.8270i	1.44025	+	1.69560i
$399$	1.47529	+	3.70270i	0.0738569	+	0.185367i
$400$	7.11587	−	5.40934i	0.355793	−	0.270467i
$401$	20.7544	−	12.4875i	1.03643	−	0.623596i	0.107631	−	0.994191i	$-0.465674\pi$
$401$	20.7544	−	12.4875i	1.03643	−	0.623596i	0.928795	+	0.370595i	$0.120846\pi$
$402$	6.01171	−	36.6698i	0.299837	−	1.82892i
$403$	7.68253	+	0.835525i	0.382694	+	0.0416205i
$404$	−53.3182	−	40.5314i	−2.65268	−	2.01651i
$405$	−0.889750	+	3.20459i	−0.0442120	+	0.159237i
$406$	−0.788080	+	14.5353i	−0.0391117	+	0.721374i
$407$	7.99256	−	0.869243i	0.396176	−	0.0430868i
$408$	−19.2827	−	11.6020i	−0.954638	−	0.574386i
$409$	15.6809	−	18.4610i	0.775371	−	0.912837i	−0.222702	−	0.974886i	$-0.571488\pi$
$409$	15.6809	−	18.4610i	0.775371	−	0.912837i	0.998073	+	0.0620495i	$0.0197637\pi$
$410$	42.6151	+	14.3587i	2.10461	+	0.709125i
$411$	−7.30939	+	3.38168i	−0.360545	+	0.166806i
$412$	17.0461			0.839799
$413$	−19.2473	−	21.9868i	−0.947097	−	1.08190i
$414$	15.8967			0.781282
$415$	18.0072	−	8.33102i	0.883939	−	0.408954i
$416$	−6.00598	−	2.02365i	−0.294467	−	0.0992176i
$417$	1.82987	−	2.15430i	0.0896094	−	0.105496i
$418$	−10.0207	−	6.02928i	−0.490131	−	0.294902i
$419$	−23.1060	+	2.51293i	−1.12880	+	0.122765i	−0.653407	−	0.757007i	$-0.726661\pi$
$419$	−23.1060	+	2.51293i	−1.12880	+	0.122765i	−0.475396	+	0.879772i	$0.657695\pi$
$420$	2.42796	−	44.7810i	0.118472	−	2.18509i
$421$	6.23008	−	22.4387i	0.303636	−	1.09360i	−0.641555	−	0.767077i	$-0.721710\pi$
$421$	6.23008	−	22.4387i	0.303636	−	1.09360i	0.945190	−	0.326520i	$-0.105876\pi$
$422$	−20.5898	−	15.6520i	−1.00230	−	0.761927i
$423$	−12.9633	−	1.40985i	−0.630298	−	0.0685490i
$424$	2.29304	−	13.9869i	0.111360	−	0.679264i
$425$	−32.1351	+	19.3351i	−1.55878	+	0.937889i
$426$	−21.6671	+	16.4709i	−1.04978	+	0.798019i
$427$	0.599659	+	1.50503i	0.0290195	+	0.0728335i
$428$	16.9691	+	19.9776i	0.820232	+	0.965652i
$429$	−1.27864	−	7.79935i	−0.0617333	−	0.376556i
$430$	1.77617	+	32.7596i	0.0856547	+	1.57981i
$431$	3.01325	+	0.663266i	0.145143	+	0.0319484i	0.286948	−	0.957946i	$-0.407359\pi$
$431$	3.01325	+	0.663266i	0.145143	+	0.0319484i	−0.141805	+	0.989895i	$0.545290\pi$
$432$	1.07066	−	1.01418i	0.0515120	−	0.0487948i
$433$	−15.9265	+	5.36626i	−0.765378	+	0.257886i	−0.674797	−	0.738003i	$-0.735769\pi$
$433$	−15.9265	+	5.36626i	−0.765378	+	0.257886i	−0.0905807	+	0.995889i	$0.528872\pi$
$434$	−15.3683	+	38.5715i	−0.737702	+	1.85149i
$435$	1.44585	+	5.20748i	0.0693232	+	0.249680i
$436$	−21.4037	+	4.71131i	−1.02505	+	0.225631i
$437$	3.96939	−	5.85441i	0.189882	−	0.280055i
$438$	5.79394	+	10.9285i	0.276845	+	0.522186i
$439$	−6.98287	+	13.1711i	−0.333274	+	0.628622i	−0.992350	−	0.123454i	$-0.960603\pi$
$439$	−6.98287	+	13.1711i	−0.333274	+	0.628622i	0.659076	+	0.752076i	$0.270948\pi$
$440$	32.1779	+	47.4589i	1.53402	+	2.26251i
$441$	−5.42502	−	5.13885i	−0.258334	−	0.244707i
$442$	−22.0466	−	10.1998i	−1.04865	−	0.485157i
$443$	19.5675	+	9.05290i	0.929682	+	0.430116i	0.825475	−	0.564439i	$-0.190908\pi$
$443$	19.5675	+	9.05290i	0.929682	+	0.430116i	0.104207	+	0.994556i	$0.466770\pi$
$444$	4.36433	+	4.13411i	0.207122	+	0.196196i
$445$	18.6795	+	27.5502i	0.885494	+	1.30601i
$446$	−23.1684	+	43.7002i	−1.09705	+	2.06926i
$447$	5.34061	+	10.0735i	0.252602	+	0.476458i
$448$	25.4063	−	37.4714i	1.20033	−	1.77036i
$449$	−6.61161	+	1.45533i	−0.312021	+	0.0686810i	−0.368220	−	0.929739i	$-0.620033\pi$
$449$	−6.61161	+	1.45533i	−0.312021	+	0.0686810i	0.0561993	+	0.998420i	$0.482102\pi$
$450$	−3.81813	−	13.7516i	−0.179988	−	0.648259i
$451$	−10.0754	+	25.2874i	−0.474433	+	1.19074i
$452$	−8.42450	+	2.83854i	−0.396255	+	0.133514i
$453$	1.13041	−	1.07078i	0.0531111	−	0.0503095i
$454$	−51.0441	−	11.2357i	−2.39562	−	0.527316i
$455$	−1.14204	−	21.0637i	−0.0535396	−	0.987479i
$456$	−0.616464	−	3.76026i	−0.0288686	−	0.176090i
$457$	6.94378	+	8.17485i	0.324816	+	0.382403i	0.900197	−	0.435482i	$-0.143422\pi$
$457$	6.94378	+	8.17485i	0.324816	+	0.382403i	−0.575381	+	0.817885i	$0.695146\pi$
$458$	−8.93150	−	22.4164i	−0.417342	−	1.04745i
$459$	−4.92593	+	3.74460i	−0.229923	+	0.174783i
$460$	−68.1934	+	41.0306i	−3.17953	+	1.91306i
$461$	0.321945	−	1.96378i	0.0149945	−	0.0914621i	−0.978269	−	0.207339i	$-0.933520\pi$
$461$	0.321945	−	1.96378i	0.0149945	−	0.0914621i	0.993264	+	0.115877i	$0.0369679\pi$
$462$	42.2152	+	4.59118i	1.96403	+	0.213601i
$463$	1.25437	+	0.953551i	0.0582957	+	0.0443153i	0.633916	−	0.773402i	$-0.281446\pi$
$463$	1.25437	+	0.953551i	0.0582957	+	0.0443153i	−0.575621	+	0.817717i	$0.695239\pi$
$464$	0.641123	−	2.30912i	0.0297634	−	0.107198i
$465$	−0.834572	+	15.3928i	−0.0387024	+	0.713823i
$466$	−24.6880	+	2.68498i	−1.14365	+	0.124379i
$467$	30.3058	+	18.2344i	1.40239	+	0.843788i	0.997506	−	0.0705810i	$-0.0224853\pi$
$467$	30.3058	+	18.2344i	1.40239	+	0.843788i	0.404881	+	0.914369i	$0.367313\pi$
$468$	3.82583	−	4.50412i	0.176849	−	0.208203i
$469$	56.8926	+	19.1694i	2.62706	+	0.885159i
$470$	92.6794	−	42.8781i	4.27498	−	1.97782i
$471$	−4.85421			−0.223670
$472$	13.4518	+	24.4839i	0.619171	+	1.12696i
$473$	−19.8592			−0.913126
$474$	11.5091	−	5.32465i	0.528628	−	0.244569i
$475$	−6.01781	−	2.02764i	−0.276116	−	0.0930343i
$476$	54.0159	−	63.5924i	2.47581	−	2.91475i
$477$	−3.33928	−	2.00918i	−0.152895	−	0.0919941i
$478$	53.5830	−	5.82750i	2.45083	−	0.266544i
$479$	−0.702861	+	12.9635i	−0.0321146	+	0.592318i	0.937546	+	0.347862i	$0.113092\pi$
$479$	−0.702861	+	12.9635i	−0.0321146	+	0.592318i	−0.969660	+	0.244456i	$0.921391\pi$
$480$	3.38222	−	12.1816i	0.154376	−	0.556013i
$481$	2.25106	+	1.71121i	0.102640	+	0.0780245i
$482$	−45.9020	−	4.99214i	−2.09078	−	0.227386i
$483$	−4.15506	+	25.3447i	−0.189062	+	1.15323i
$484$	−34.8412	+	20.9632i	−1.58369	+	0.952874i
$485$	8.89978	−	6.76544i	0.404118	−	0.307203i
$486$	−0.871560	−	2.18745i	−0.0395347	−	0.0992247i
$487$	−20.5953	−	24.2466i	−0.933261	−	1.09872i	−0.994925	−	0.100623i	$-0.967916\pi$
$487$	−20.5953	−	24.2466i	−0.933261	−	1.09872i	0.0616636	−	0.998097i	$-0.480359\pi$
$488$	−0.250573	−	1.52843i	−0.0113429	−	0.0691886i
$489$	−0.959131	−	17.6901i	−0.0433734	−	0.799976i
$490$	57.1511	+	12.5799i	2.58182	+	0.568302i
$491$	−14.7650	+	13.9861i	−0.666335	+	0.631186i	−0.944176	−	0.329441i	$-0.893140\pi$
$491$	−14.7650	+	13.9861i	−0.666335	+	0.631186i	0.277841	+	0.960627i	$0.410381\pi$
$492$	−19.2883	+	6.49897i	−0.869582	+	0.292996i
$493$	−3.72172	+	9.34081i	−0.167618	+	0.420689i
$494$	−1.10039	−	3.96324i	−0.0495088	−	0.178314i
$495$	15.3972	−	3.38917i	0.692051	−	0.152332i
$496$	3.83602	−	5.65770i	0.172242	−	0.254038i
$497$	−20.5969	−	38.8498i	−0.923896	−	1.74265i
$498$	−6.57996	+	12.4111i	−0.294855	+	0.556156i
$499$	23.0285	+	33.9644i	1.03090	+	1.52046i	0.842742	+	0.538317i	$0.180940\pi$
$499$	23.0285	+	33.9644i	1.03090	+	1.52046i	0.188153	+	0.982140i	$0.439750\pi$
$500$	9.08084	+	8.60183i	0.406107	+	0.384685i
$501$	1.50574	+	0.696628i	0.0672714	+	0.0311231i
$502$	−10.0139	−	4.63291i	−0.446941	−	0.206777i
$503$	2.42627	+	2.29828i	0.108182	+	0.102475i	0.739879	−	0.672740i	$-0.234883\pi$
$503$	2.42627	+	2.29828i	0.108182	+	0.102475i	−0.631697	+	0.775215i	$0.717641\pi$
$504$	7.76453	+	11.4518i	0.345860	+	0.510105i
$505$	29.4356	−	55.5214i	1.30987	−	2.47067i
$506$	−35.2979	−	66.5790i	−1.56918	−	2.95980i
$507$	−5.73549	+	8.45921i	−0.254722	+	0.375687i
$508$	4.46016	−	0.981756i	0.197888	−	0.0435584i
$509$	−7.17037	−	25.8253i	−0.317821	−	1.14469i	−0.934056	−	0.357126i	$-0.883757\pi$
$509$	−7.17037	−	25.8253i	−0.317821	−	1.14469i	0.616235	−	0.787562i	$-0.288657\pi$
$510$	17.9358	−	45.0154i	0.794209	−	1.99331i
$511$	−18.9382	+	6.38101i	−0.837775	+	0.282279i
$512$	−11.8577	+	11.2322i	−0.524043	+	0.496399i
$513$	−1.02322	−	0.225227i	−0.0451761	−	0.00994401i
$514$	3.89687	+	71.8735i	0.171883	+	3.17020i
$515$	2.58756	+	15.7834i	0.114022	+	0.695501i
$516$	−9.61323	−	11.3176i	−0.423199	−	0.498228i
$517$	22.8797	+	57.4237i	1.00625	+	2.52549i
$518$	−12.0946	+	9.19407i	−0.531406	+	0.403964i
$519$	−0.756079	+	0.454918i	−0.0331882	+	0.0199687i
$520$	−3.26261	+	19.9010i	−0.143075	+	0.872718i
$521$	27.1298	+	2.95054i	1.18858	+	0.129266i	0.680962	−	0.732318i	$-0.261562\pi$
$521$	27.1298	+	2.95054i	1.18858	+	0.129266i	0.507615	+	0.861584i	$0.330527\pi$
$522$	−3.04616	−	2.31563i	−0.133327	−	0.101352i
$523$	5.10952	−	18.4028i	0.223424	−	0.804700i	−0.763812	−	0.645438i	$-0.776675\pi$
$523$	5.10952	−	18.4028i	0.223424	−	0.804700i	0.987236	−	0.159262i	$-0.0509114\pi$
$524$	−3.12846	+	57.7011i	−0.136668	+	2.52068i
$525$	22.9227	−	2.49300i	1.00043	−	0.108803i
$526$	54.6758	+	32.8974i	2.38398	+	1.43439i
$527$	−18.5671	+	21.8589i	−0.808796	+	0.952189i
$528$	−6.62495	−	2.23221i	−0.288314	−	0.0971443i
$529$	20.4907	−	9.48000i	0.890899	−	0.412174i
$530$	30.5194			1.32568
$531$	7.62289	−	0.944211i	0.330805	−	0.0409753i
$532$	14.1278			0.612518
$533$	−8.68893	+	4.01993i	−0.376359	+	0.174122i
$534$	−22.3328	−	7.52478i	−0.966433	−	0.325629i
$535$	−15.9219	+	18.7447i	−0.688364	+	0.810405i
$536$	−49.1789	−	29.5900i	−2.12420	−	1.27809i
$537$	−5.09173	+	0.553759i	−0.219725	+	0.0238965i
$538$	1.05873	−	19.5271i	0.0456450	−	0.841873i
$539$	−9.47662	+	34.1317i	−0.408187	+	1.47016i
$540$	9.38476	+	7.13411i	0.403856	+	0.307003i
$541$	8.93585	+	0.971832i	0.384182	+	0.0417823i	0.298173	−	0.954512i	$-0.403623\pi$
$541$	8.93585	+	0.971832i	0.384182	+	0.0417823i	0.0860096	+	0.996294i	$0.472588\pi$
$542$	9.82248	−	59.9145i	0.421912	−	2.57355i
$543$	−2.89687	+	1.74299i	−0.124317	+	0.0747988i
$544$	18.7250	−	14.2344i	0.802828	−	0.610294i
$545$	−7.61138	−	19.1031i	−0.326036	−	0.818288i
$546$	9.66874	+	11.3829i	0.413784	+	0.487144i
$547$	1.33143	+	8.12138i	0.0569280	+	0.347245i	0.999897	+	0.0143643i	$0.00457247\pi$
$547$	1.33143	+	8.12138i	0.0569280	+	0.347245i	−0.942969	+	0.332881i	$0.891979\pi$
$548$	1.54550	+	28.5051i	0.0660205	+	1.21768i
$549$	−0.415905	−	0.0915476i	−0.0177504	−	0.00390716i
$550$	−49.1169	+	46.5260i	−2.09435	+	1.98388i
$551$	−1.61342	+	0.543623i	−0.0687338	+	0.0231591i
$552$	9.08812	−	22.8095i	0.386816	−	0.970836i
$553$	5.48107	+	19.7410i	0.233079	+	0.839474i
$554$	35.7619	−	7.87179i	1.51938	−	0.334440i
$555$	−3.16540	+	4.66861i	−0.134364	+	0.198171i
$556$	−4.69293	−	8.85180i	−0.199025	−	0.375400i
$557$	17.9944	−	33.9411i	0.762447	−	1.43813i	−0.132138	−	0.991231i	$-0.542184\pi$
$557$	17.9944	−	33.9411i	0.762447	−	1.43813i	0.894585	−	0.446897i	$-0.147471\pi$
$558$	−6.12488	−	9.03352i	−0.259287	−	0.382419i
$559$	−5.07083	−	4.80335i	−0.214473	−	0.203160i
$560$	−16.9344	−	7.83468i	−0.715608	−	0.331076i
$561$	26.6210	+	12.3162i	1.12394	+	0.519989i
$562$	12.8043	+	12.1288i	0.540115	+	0.511624i
$563$	−7.19528	−	10.6122i	−0.303245	−	0.447253i	0.645284	−	0.763942i	$-0.276739\pi$
$563$	−7.19528	−	10.6122i	−0.303245	−	0.447253i	−0.948529	+	0.316690i	$0.897429\pi$
$564$	−21.6499	+	40.8360i	−0.911624	+	1.71951i
$565$	−3.90711	−	7.36960i	−0.164374	−	0.310041i
$566$	−13.2169	+	19.4934i	−0.555546	+	0.819369i
$567$	3.71533	−	0.817807i	0.156029	−	0.0343447i
$568$	11.2463	+	40.5055i	0.471885	+	1.69957i
$569$	−11.7335	+	29.4489i	−0.491895	+	1.23456i	0.448287	+	0.893890i	$0.352034\pi$
$569$	−11.7335	+	29.4489i	−0.491895	+	1.23456i	−0.940182	+	0.340674i	$0.889345\pi$
$570$	7.77539	−	2.61983i	0.325675	−	0.109733i
$571$	−2.64080	+	2.50150i	−0.110514	+	0.104684i	−0.740962	−	0.671547i	$-0.765630\pi$
$571$	−2.64080	+	2.50150i	−0.110514	+	0.104684i	0.630448	+	0.776232i	$0.282871\pi$
$572$	−27.3593	−	6.02224i	−1.14395	−	0.251802i
$573$	−0.284139	−	5.24064i	−0.0118701	−	0.218931i
$574$	−8.32181	−	50.7608i	−0.347346	−	2.11872i
$575$	−26.4902	−	31.1867i	−1.10472	−	1.30058i
$576$	4.40479	+	11.0552i	0.183533	+	0.460633i
$577$	−22.5611	+	17.1505i	−0.939232	+	0.713985i	−0.958279	−	0.285833i	$-0.907730\pi$
$577$	−22.5611	+	17.1505i	−0.939232	+	0.713985i	0.0190478	+	0.999819i	$0.493937\pi$
$578$	42.9489	−	25.8415i	1.78644	−	1.07486i
$579$	−0.894760	+	5.45779i	−0.0371850	+	0.226818i
$580$	19.0441	+	2.07117i	0.790765	+	0.0860008i
$581$	−18.0676	−	13.7347i	−0.749572	−	0.569810i
$582$	−2.11749	+	7.62650i	−0.0877726	+	0.316128i
$583$	−1.00016	+	18.4469i	−0.0414226	+	0.763994i
$584$	18.9932	−	2.06564i	0.785945	−	0.0854767i
$585$	4.75124	+	2.85873i	0.196440	+	0.118194i
$586$	−11.5182	+	13.5603i	−0.475813	+	0.560170i
$587$	−5.15750	−	1.73776i	−0.212873	−	0.0717252i	0.210845	−	0.977520i	$-0.432379\pi$
$587$	−5.15750	−	1.73776i	−0.212873	−	0.0717252i	−0.423718	+	0.905794i	$0.639275\pi$
$588$	−24.0387	+	11.1215i	−0.991340	+	0.458643i
$589$	−4.85622			−0.200097
$590$	−47.3394	+	37.1128i	−1.94893	+	1.52791i
$591$	−0.187262			−0.00770293
$592$	2.26998	−	1.05020i	0.0932955	−	0.0431631i
$593$	−13.3363	−	4.49353i	−0.547658	−	0.184527i	0.0318522	−	0.999493i	$-0.489859\pi$
$593$	−13.3363	−	4.49353i	−0.547658	−	0.184527i	−0.579510	+	0.814965i	$0.696756\pi$
$594$	−7.22626	+	8.50741i	−0.296497	+	0.349063i
$595$	67.0816	+	40.3616i	2.75008	+	1.65467i
$596$	40.1767	−	4.36948i	1.64570	−	0.178981i
$597$	1.02045	−	18.8211i	0.0417644	−	0.770298i
$598$	7.09053	−	25.5378i	0.289953	−	1.04432i
$599$	24.7511	+	18.8153i	1.01130	+	0.768771i	0.973073	−	0.230498i	$-0.0740356\pi$
$599$	24.7511	+	18.8153i	1.01130	+	0.768771i	0.0382280	+	0.999269i	$0.487829\pi$
$600$	−21.9144	−	2.38334i	−0.894652	−	0.0972992i
$601$	−2.55391	+	15.5782i	−0.104176	+	0.635448i	0.882191	+	0.470891i	$0.156068\pi$
$601$	−2.55391	+	15.5782i	−0.104176	+	0.635448i	−0.986368	+	0.164556i	$0.947381\pi$
$602$	32.1557	−	19.3475i	1.31057	−	0.788543i
$603$	−12.5631	+	9.55025i	−0.511611	+	0.388916i
$604$	−2.04280	−	5.12704i	−0.0831203	−	0.208616i
$605$	−24.6993	−	29.0783i	−1.00417	−	1.18220i
$606$	7.19803	+	43.9060i	0.292400	+	1.78356i
$607$	−2.20880	−	40.7388i	−0.0896523	−	1.65354i	−0.604756	−	0.796411i	$-0.706729\pi$
$607$	−2.20880	−	40.7388i	−0.0896523	−	1.65354i	0.515104	−	0.857128i	$-0.327753\pi$
$608$	3.88956	+	0.856158i	0.157743	+	0.0347218i
$609$	4.48809	−	4.25134i	0.181866	−	0.172273i
$610$	3.16045	−	1.06488i	0.127963	−	0.0431157i
$611$	−8.04700	+	20.1965i	−0.325547	+	0.817061i
$612$	5.86753	+	21.1330i	0.237181	+	0.854249i
$613$	−5.55769	+	1.22334i	−0.224473	+	0.0494102i	−0.325783	−	0.945445i	$-0.605628\pi$
$613$	−5.55769	+	1.22334i	−0.224473	+	0.0494102i	0.101310	+	0.994855i	$0.467697\pi$
$614$	2.78374	−	4.10571i	0.112343	−	0.165693i
$615$	−8.94551	−	16.8730i	−0.360718	−	0.680386i
$616$	30.7220	−	57.9478i	1.23782	−	2.33478i
$617$	−7.42901	−	10.9570i	−0.299081	−	0.441111i	0.648222	−	0.761452i	$-0.275513\pi$
$617$	−7.42901	−	10.9570i	−0.299081	−	0.441111i	−0.947302	+	0.320341i	$0.896203\pi$
$618$	−8.22110	−	7.78744i	−0.330701	−	0.313257i
$619$	−26.2239	−	12.1325i	−1.05403	−	0.487645i	−0.185169	−	0.982707i	$-0.559283\pi$
$619$	−26.2239	−	12.1325i	−1.05403	−	0.487645i	−0.868858	+	0.495062i	$0.835145\pi$
$620$	49.5905	+	22.9430i	1.99160	+	0.921413i
$621$	−4.90127	−	4.64273i	−0.196681	−	0.186306i
$622$	24.7133	+	36.4494i	0.990914	+	1.46149i
$623$	17.8343	−	33.6391i	0.714517	−	1.34772i
$624$	−1.15171	−	2.17235i	−0.0461052	−	0.0869636i
$625$	10.4207	−	15.3693i	0.416827	−	0.614774i
$626$	57.6291	−	12.6851i	2.30332	−	0.507000i
$627$	1.32870	+	4.78556i	0.0530633	+	0.191117i
$628$	−6.36859	+	15.9840i	−0.254134	+	0.637829i
$629$	−9.94481	+	3.35080i	−0.396525	+	0.133605i
$630$	−21.6290	+	20.4881i	−0.861722	+	0.816266i
$631$	18.1590	+	3.99711i	0.722900	+	0.159122i	0.561155	−	0.827710i	$-0.310357\pi$
$631$	18.1590	+	3.99711i	0.722900	+	0.159122i	0.161744	+	0.986833i	$0.448288\pi$
$632$	−1.06040	−	19.5579i	−0.0421804	−	0.777971i
$633$	1.77699	+	10.8392i	0.0706292	+	0.430819i
$634$	−2.05674	−	2.42138i	−0.0816834	−	0.0961651i
$635$	1.58608	+	3.98076i	0.0629417	+	0.157972i
$636$	−10.9969	+	8.35962i	−0.436055	+	0.331481i
$637$	−10.6752	+	6.42306i	−0.422967	+	0.254491i
$638$	−2.93451	+	17.8997i	−0.116178	+	0.708656i
$639$	11.4908	+	1.24970i	0.454570	+	0.0494375i
$640$	−54.0627	−	41.0974i	−2.13702	−	1.62452i
$641$	5.55876	−	20.0209i	0.219558	−	0.790776i	−0.768911	−	0.639355i	$-0.779201\pi$
$641$	5.55876	−	20.0209i	0.219558	−	0.790776i	0.988469	−	0.151421i	$-0.0483849\pi$
$642$	0.942706	−	17.3872i	0.0372057	−	0.686218i
$643$	3.50865	−	0.381588i	0.138368	−	0.0150484i	−0.0386731	−	0.999252i	$-0.512313\pi$
$643$	3.50865	−	0.381588i	0.138368	−	0.0150484i	0.177041	+	0.984204i	$0.443348\pi$
$644$	78.0039	+	46.9334i	3.07379	+	1.84944i
$645$	9.01999	−	10.6192i	0.355162	−	0.418129i
$646$	14.4660	+	4.87417i	0.569158	+	0.191771i
$647$	−8.32838	+	3.85312i	−0.327422	+	0.151482i	−0.576713	−	0.816947i	$-0.695665\pi$
$647$	−8.32838	+	3.85312i	−0.327422	+	0.151482i	0.249290	+	0.968429i	$0.419803\pi$
$648$	−3.63694			−0.142872
$649$	−20.8808	−	29.8297i	−0.819644	−	1.17092i
$650$	−23.7948			−0.933308
$651$	16.0034	−	7.40394i	0.627221	−	0.290183i
$652$	−59.5085	−	20.0508i	−2.33053	−	0.785248i
$653$	−19.8841	+	23.4094i	−0.778125	+	0.916080i	−0.998235	−	0.0593956i	$-0.981083\pi$
$653$	−19.8841	+	23.4094i	−0.778125	+	0.916080i	0.220110	+	0.975475i	$0.429359\pi$
$654$	12.4751	+	7.50600i	0.487814	+	0.293508i
$655$	−53.9020	+	5.86220i	−2.10613	+	0.229055i
$656$	−0.458468	+	8.45594i	−0.0179001	+	0.330149i
$657$	1.40535	−	5.06163i	0.0548281	−	0.197473i
$658$	−92.9905	−	70.6895i	−3.62515	−	2.75577i
$659$	−19.3986	−	2.10973i	−0.755663	−	0.0821833i	−0.277825	−	0.960632i	$-0.589614\pi$
$659$	−19.3986	−	2.10973i	−0.755663	−	0.0821833i	−0.477837	+	0.878448i	$0.658579\pi$
$660$	9.04079	−	55.1464i	0.351912	−	2.14657i
$661$	−11.0966	+	6.67660i	−0.431608	+	0.259690i	−0.714739	−	0.699391i	$-0.753454\pi$
$661$	−11.0966	+	6.67660i	−0.431608	+	0.259690i	0.283131	+	0.959081i	$0.408627\pi$
$662$	−39.8176	+	30.2686i	−1.54756	+	1.17642i
$663$	3.81847	+	9.58364i	0.148297	+	0.372198i
$664$	14.0464	+	16.5367i	0.545106	+	0.641748i
$665$	2.14458	+	13.0813i	0.0831632	+	0.507273i
$666$	−0.216205	−	3.98766i	−0.00837776	−	0.154519i
$667$	−10.7141	−	2.35835i	−0.414852	−	0.0913158i
$668$	4.26935	−	4.04414i	0.165186	−	0.156473i
$669$	19.9061	−	6.70716i	0.769616	−	0.259314i
$670$	45.7435	−	114.808i	1.76723	−	4.43540i
$671$	0.540076	+	1.94518i	0.0208494	+	0.0750927i
$672$	−14.1231	+	3.10874i	−0.544812	+	0.119922i
$673$	11.5553	−	17.0427i	0.445423	−	0.656949i	−0.537008	−	0.843577i	$-0.680446\pi$
$673$	11.5553	−	17.0427i	0.445423	−	0.656949i	0.982431	+	0.186628i	$0.0597559\pi$
$674$	−22.2474	−	41.9630i	−0.856938	−	1.61636i
$675$	−2.83904	+	5.35500i	−0.109275	+	0.206114i
$676$	20.3297	+	29.9841i	0.781913	+	1.15323i
$677$	21.0943	+	19.9815i	0.810718	+	0.767953i	0.975879	−	0.218314i	$-0.0700556\pi$
$677$	21.0943	+	19.9815i	0.810718	+	0.767953i	−0.165161	+	0.986267i	$0.552814\pi$
$678$	5.35981	+	2.47971i	0.205842	+	0.0952328i
$679$	−11.6057	−	5.36938i	−0.445387	−	0.206058i
$680$	−54.3366	−	51.4703i	−2.08371	−	1.97380i
$681$	12.4564	+	18.3719i	0.477332	+	0.704012i
$682$	−24.2343	+	45.7108i	−0.927981	+	1.75036i
$683$	4.10014	+	7.73368i	0.156887	+	0.295921i	0.949478	−	0.313833i	$-0.101613\pi$
$683$	4.10014	+	7.73368i	0.156887	+	0.295921i	−0.792591	+	0.609754i	$0.791268\pi$
$684$	−2.08406	+	3.07376i	−0.0796861	+	0.117528i
$685$	−26.1591	+	5.75804i	−0.999486	+	0.220004i
$686$	−1.13239	−	4.07850i	−0.0432349	−	0.155718i
$687$	−3.79307	+	9.51990i	−0.144715	+	0.363207i
$688$	−5.85478	+	1.97270i	−0.223211	+	0.0752087i
$689$	−4.71715	+	4.46832i	−0.179709	+	0.170230i
$690$	51.6335	+	11.3654i	1.96565	+	0.432673i
$691$	−0.177624	−	3.27608i	−0.00675713	−	0.124628i	−0.999966	−	0.00828062i	$-0.997364\pi$
$691$	−0.177624	−	3.27608i	−0.00675713	−	0.124628i	0.993209	−	0.116347i	$-0.0371186\pi$
$692$	0.506000	+	3.08646i	0.0192352	+	0.117330i
$693$	−11.6749	−	13.7447i	−0.443492	−	0.522119i
$694$	−9.94369	−	24.9568i	−0.377457	−	0.947347i
$695$	7.48376	−	5.68901i	0.283875	−	0.215796i
$696$	−5.06407	+	3.04695i	−0.191953	+	0.115494i
$697$	5.74827	−	35.0629i	0.217731	−	1.32810i
$698$	−10.9359	−	1.18935i	−0.413930	−	0.0450176i
$699$	8.39595	+	6.38243i	0.317564	+	0.241406i
$700$	21.8651	−	78.7508i	0.826421	−	2.97650i
$701$	0.0659512	−	1.21640i	0.00249094	−	0.0459428i	−0.997024	−	0.0770960i	$-0.975435\pi$
$701$	0.0659512	−	1.21640i	0.00249094	−	0.0459428i	0.999515	+	0.0311532i	$0.00991798\pi$
$702$	−3.90284	+	0.424460i	−0.147303	+	0.0160202i
$703$	−1.52255	−	0.916089i	−0.0574242	−	0.0345510i
$704$	36.5209	−	42.9957i	1.37643	−	1.62046i
$705$	−41.0976	−	13.8474i	−1.54783	−	0.521523i
$706$	−59.7380	+	27.6378i	−2.24827	+	1.04016i
$707$	−71.8824			−2.70341
$708$	6.89193	−	26.3395i	0.259015	−	0.989898i
$709$	1.57273			0.0590651			0.0295326	−	0.999564i	$-0.490598\pi$
$709$	1.57273			0.0590651			0.0295326	+	0.999564i	$0.490598\pi$
$710$	−82.1521	+	38.0076i	−3.08311	+	1.42640i
$711$	−5.10356	−	1.71959i	−0.191398	−	0.0644896i
$712$	−23.5645	+	27.7423i	−0.883118	+	1.03969i
$713$	−26.8126	−	16.1326i	−1.00414	−	0.604172i
$714$	−55.1032	+	5.99283i	−2.06218	+	0.224276i
$715$	1.42307	−	26.2469i	0.0532197	−	0.981579i
$716$	−4.85680	+	17.4926i	−0.181507	+	0.653730i
$717$	−18.2226	−	13.8525i	−0.680537	−	0.517331i
$718$	45.4272	+	4.94050i	1.69533	+	0.184378i
$719$	3.89482	−	23.7574i	0.145252	−	0.886000i	−0.809177	−	0.587564i	$-0.800087\pi$
$719$	3.89482	−	23.7574i	0.145252	−	0.886000i	0.954430	−	0.298436i	$-0.0964648\pi$
$720$	4.20265	−	2.52865i	0.156623	−	0.0942372i
$721$	14.5646	−	11.0717i	0.542414	−	0.412333i
$722$	−15.6029	−	39.1604i	−0.580681	−	1.45740i
$723$	12.6945	+	14.9451i	0.472113	+	0.555814i
$724$	1.93871	+	11.8256i	0.0720515	+	0.439494i
$725$	0.533227	+	9.83479i	0.0198036	+	0.365255i
$726$	26.3804	+	5.80677i	0.979070	+	0.215510i
$727$	3.09573	−	2.93243i	0.114814	−	0.108758i	−0.628139	−	0.778101i	$-0.716183\pi$
$727$	3.09573	−	2.93243i	0.114814	−	0.108758i	0.742953	+	0.669343i	$0.233424\pi$
$728$	21.8604	−	7.36563i	0.810200	−	0.272988i
$729$	−0.370138	+	0.928977i	−0.0137088	+	0.0344065i
$730$	11.0057	+	39.6389i	0.407339	+	1.46710i
$731$	25.3160	−	5.57247i	0.936346	−	0.206105i
$732$	−0.847105	+	1.24939i	−0.0313099	+	0.0461786i
$733$	4.17678	+	7.87824i	0.154273	+	0.290989i	0.948586	−	0.316519i	$-0.102514\pi$
$733$	4.17678	+	7.87824i	0.154273	+	0.290989i	−0.794313	+	0.607508i	$0.792169\pi$
$734$	−17.4484	+	32.9112i	−0.644033	+	1.21478i
$735$	−13.9467	−	20.5699i	−0.514433	−	0.758732i
$736$	18.6313	+	17.6485i	0.686757	+	0.650531i
$737$	67.8944	+	31.4113i	2.50092	+	1.15705i
$738$	12.2715	+	5.67741i	0.451721	+	0.208988i
$739$	24.8901	+	23.5771i	0.915597	+	0.867299i	0.991539	−	0.129813i	$-0.0414377\pi$
$739$	24.8901	+	23.5771i	0.915597	+	0.867299i	−0.0759417	+	0.997112i	$0.524196\pi$
$740$	11.2199	+	16.5481i	0.412452	+	0.608321i
$741$	−0.818215	+	1.54332i	−0.0300579	+	0.0566951i
$742$	−16.3522	−	30.8434i	−0.600306	−	1.13230i
$743$	−29.6446	+	43.7226i	−1.08756	+	1.60403i	−0.339219	+	0.940707i	$0.610163\pi$
$743$	−29.6446	+	43.7226i	−1.08756	+	1.60403i	−0.748337	+	0.663318i	$0.769148\pi$
$744$	−16.4633	+	3.62386i	−0.603575	+	0.132857i
$745$	10.1446	+	36.5374i	0.371668	+	1.33863i
$746$	−14.9517	+	37.5259i	−0.547420	+	1.37392i
$747$	5.65347	−	1.90488i	0.206850	−	0.0696958i
$748$	75.4808	−	71.4992i	2.75985	−	2.61427i
$749$	27.4746	+	6.04762i	1.00390	+	0.220975i
$750$	−0.449856	−	8.29710i	−0.0164264	−	0.302967i
$751$	−1.42155	−	8.67106i	−0.0518730	−	0.316411i	0.948126	−	0.317895i	$-0.102976\pi$
$751$	−1.42155	−	8.67106i	−0.0518730	−	0.316411i	−0.999999	+	0.00148369i	$0.999528\pi$
$752$	12.4494	+	14.6566i	0.453984	+	0.534471i
$753$	1.73440	+	4.35302i	0.0632051	+	0.158633i
$754$	−5.07871	+	3.86073i	−0.184956	+	0.140600i
$755$	4.43718	−	2.66976i	0.161485	−	0.0971626i
$756$	2.18154	−	13.3068i	0.0793419	−	0.483964i
$757$	42.6800	+	4.64173i	1.55123	+	0.168707i	0.843249	−	0.537523i	$-0.180640\pi$
$757$	42.6800	+	4.64173i	1.55123	+	0.168707i	0.707983	+	0.706229i	$0.249605\pi$
$758$	−36.1662	−	27.4928i	−1.31362	−	0.998585i
$759$	−8.56172	+	30.8365i	−0.310771	+	1.11930i
$760$	0.686096	−	12.6543i	0.0248873	−	0.459019i
$761$	38.8621	−	4.22650i	1.40875	−	0.153211i	0.628077	−	0.778151i	$-0.283842\pi$
$761$	38.8621	−	4.22650i	1.40875	−	0.153211i	0.780672	+	0.624941i	$0.214877\pi$
$762$	−2.59959	−	1.56412i	−0.0941733	−	0.0566622i
$763$	−15.2278	+	17.9276i	−0.551283	+	0.649021i
$764$	−17.6292	−	5.93997i	−0.637802	−	0.214900i
$765$	−18.6769	+	8.64086i	−0.675266	+	0.312411i
$766$	−33.6557			−1.21603
$767$	1.88323	−	12.6672i	0.0679997	−	0.457385i
$768$	24.2797			0.876120
$769$	3.14864	−	1.45672i	0.113543	−	0.0525306i	−0.362295	−	0.932063i	$-0.618007\pi$
$769$	3.14864	−	1.45672i	0.113543	−	0.0525306i	0.475838	+	0.879533i	$0.342145\pi$
$770$	133.835	+	45.0942i	4.82308	+	1.62508i
$771$	19.7896	−	23.2981i	0.712704	−	0.839060i
$772$	16.7976	+	10.1068i	0.604557	+	0.363750i
$773$	−32.3255	+	3.51561i	−1.16267	+	0.126448i	−0.669040	−	0.743226i	$-0.733295\pi$
$773$	−32.3255	+	3.51561i	−1.16267	+	0.126448i	−0.493627	+	0.869674i	$0.664329\pi$
$774$	−0.534057	+	9.85009i	−0.0191963	+	0.354054i
$775$	−7.51577	+	27.0694i	−0.269974	+	0.972360i
$776$	9.73234	+	7.39833i	0.349371	+	0.265585i
$777$	6.41418	+	0.697584i	0.230107	+	0.0250257i
$778$	−11.5391	+	70.3855i	−0.413697	+	2.52344i
$779$	5.15504	−	3.10169i	0.184699	−	0.111129i
$780$	15.6467	−	11.8943i	0.560244	−	0.425886i
$781$	−20.2808	−	50.9010i	−0.725704	−	1.82138i
$782$	63.6790	+	74.9687i	2.27716	+	2.68087i
$783$	0.262897	+	1.60360i	0.00939517	+	0.0573080i
$784$	0.596614	+	11.0039i	0.0213076	+	0.392996i
$785$	−15.7667	−	3.47052i	−0.562739	−	0.123868i
$786$	27.8694	−	26.3993i	0.994068	−	0.941631i
$787$	−14.6475	+	4.93533i	−0.522128	+	0.175926i	−0.568010	−	0.823021i	$-0.692287\pi$
$787$	−14.6475	+	4.93533i	−0.522128	+	0.175926i	0.0458821	+	0.998947i	$0.485390\pi$
$788$	−0.245683	+	0.616618i	−0.00875209	+	0.0219661i
$789$	−7.24976	−	26.1113i	−0.258098	−	0.929586i
$790$	41.1889	−	9.06637i	1.46544	−	0.322567i
$791$	−5.35443	+	7.89719i	−0.190382	+	0.280792i
$792$	8.07564	+	15.2323i	0.286956	+	0.541256i
$793$	−0.332578	+	0.627309i	−0.0118102	+	0.0222764i
$794$	16.8467	+	24.8470i	0.597867	+	0.881787i
$795$	−9.40972	−	8.91336i	−0.333729	−	0.316124i
$796$	−60.6356	−	28.0530i	−2.14917	−	0.994312i
$797$	−19.2604	−	8.91083i	−0.682240	−	0.315638i	0.0479817	−	0.998848i	$-0.484721\pi$
$797$	−19.2604	−	8.91083i	−0.682240	−	0.315638i	−0.730222	+	0.683210i	$0.760583\pi$
$798$	−6.81366	−	6.45425i	−0.241201	−	0.228478i
$799$	−45.2795	−	66.7823i	−1.60187	−	2.36259i
$800$	10.7921	−	20.3560i	0.381558	−	0.719695i
$801$	4.68797	+	8.84244i	0.165641	+	0.312432i
$802$	−32.0068	+	47.2065i	−1.13020	+	1.66692i
$803$	−24.3197	+	5.35318i	−0.858225	+	0.188910i
$804$	14.9646	+	53.8977i	0.527761	+	1.90082i
$805$	−31.6161	+	79.3505i	−1.11432	+	2.79674i
$806$	−17.2441	+	5.81021i	−0.607397	+	0.204656i
$807$	−6.02942	+	5.71137i	−0.212246	+	0.201050i
$808$	67.1138	+	14.7729i	2.36106	+	0.519708i
$809$	2.67490	+	49.3357i	0.0940446	+	1.73455i	0.541898	+	0.840444i	$0.317706\pi$
$809$	2.67490	+	49.3357i	0.0940446	+	1.73455i	−0.447854	+	0.894107i	$0.647811\pi$
$810$	−1.26696	−	7.72809i	−0.0445163	−	0.271537i
$811$	−25.6988	−	30.2549i	−0.902406	−	1.06239i	−0.997756	−	0.0669511i	$-0.978673\pi$
$811$	−25.6988	−	30.2549i	−0.902406	−	1.06239i	0.0953499	−	0.995444i	$-0.469603\pi$
$812$	−8.11059	−	20.3561i	−0.284626	−	0.714357i
$813$	−20.5268	+	15.6041i	−0.719907	+	0.547259i
$814$	−16.2211	+	9.75992i	−0.568550	+	0.342085i
$815$	9.53228	−	58.1443i	0.333901	−	2.03671i
$816$	9.07168	+	0.986605i	0.317572	+	0.0345381i
$817$	3.49422	+	2.65623i	0.122247	+	0.0929299i
$818$	−15.2585	+	54.9560i	−0.533499	+	1.92149i
$819$	0.343386	−	6.33338i	0.0119989	−	0.221306i
$820$	−67.2959	+	7.31887i	−2.35007	+	0.255586i
$821$	11.7551	+	7.07281i	0.410256	+	0.246843i	0.705691	−	0.708520i	$-0.250637\pi$
$821$	11.7551	+	7.07281i	0.410256	+	0.246843i	−0.295435	+	0.955363i	$0.595464\pi$
$822$	12.2771	−	14.4537i	0.428212	−	0.504130i
$823$	31.8110	+	10.7184i	1.10886	+	0.373619i	0.813382	−	0.581730i	$-0.197624\pi$
$823$	31.8110	+	10.7184i	1.10886	+	0.373619i	0.295480	+	0.955349i	$0.404520\pi$
$824$	−15.8738	+	7.34401i	−0.552990	+	0.255841i
$825$	28.7319			1.00032
$826$	62.8711	+	27.9572i	2.18756	+	0.972754i
$827$	27.7869			0.966245			0.483122	−	0.875553i	$-0.339503\pi$
$827$	27.7869			0.966245			0.483122	+	0.875553i	$0.339503\pi$
$828$	−21.7179	+	10.0478i	−0.754751	+	0.349185i
$829$	13.4687	+	4.53814i	0.467788	+	0.157616i	0.543317	−	0.839528i	$-0.317168\pi$
$829$	13.4687	+	4.53814i	0.467788	+	0.157616i	−0.0755295	+	0.997144i	$0.524065\pi$
$830$	−30.2455	+	35.6077i	−1.04984	+	1.23596i
$831$	−13.3251	−	8.01744i	−0.462242	−	0.278122i
$832$	19.7246	−	2.14518i	0.683828	−	0.0743708i
$833$	2.50323	−	46.1694i	0.0867319	−	1.59968i
$834$	−1.78058	+	6.41306i	−0.0616564	+	0.222066i
$835$	4.39267	+	3.33922i	0.152015	+	0.115558i
$836$	17.5011	+	1.90336i	0.605289	+	0.0658292i
$837$	−0.749871	+	4.57401i	−0.0259193	+	0.158101i
$838$	46.8943	−	28.2154i	1.61994	−	0.974684i
$839$	−5.69323	+	4.32788i	−0.196552	+	0.149415i	−0.698821	−	0.715296i	$-0.746292\pi$
$839$	−5.69323	+	4.32788i	−0.196552	+	0.149415i	0.502269	+	0.864711i	$0.332499\pi$
$840$	17.0322	+	42.7475i	0.587665	+	1.47493i
$841$	−17.0647	−	20.0901i	−0.588437	−	0.692762i
$842$	8.87130	+	54.1126i	0.305725	+	1.86484i
$843$	−0.405506	−	7.47911i	−0.0139664	−	0.257594i
$844$	38.0227	+	8.36943i	1.30880	+	0.288088i
$845$	−24.6771	+	23.3754i	−0.848919	+	0.804139i
$846$	29.0973	−	9.80401i	1.00038	−	0.337069i
$847$	−16.1532	+	40.5415i	−0.555031	+	1.39302i
$848$	1.53756	+	5.53778i	0.0527999	+	0.190168i
$849$	9.76817	−	2.15014i	0.335243	−	0.0737925i
$850$	49.5579	−	73.0924i	1.69982	−	2.50705i
$851$	−5.36317	−	10.1160i	−0.183847	−	0.346773i
$852$	19.1907	−	36.1975i	0.657462	−	1.24010i
$853$	−8.95520	−	13.2079i	−0.306620	−	0.452231i	0.642894	−	0.765955i	$-0.277734\pi$
$853$	−8.95520	−	13.2079i	−0.306620	−	0.452231i	−0.949514	+	0.313724i	$0.898423\pi$
$854$	−2.76954	−	2.62345i	−0.0947716	−	0.0897725i
$855$	−3.16244	−	1.46310i	−0.108153	−	0.0500370i
$856$	−24.4091	−	11.2929i	−0.834287	−	0.385982i
$857$	30.7990	+	29.1743i	1.05207	+	0.996576i	0.999998	−	0.00206735i	$-0.000658057\pi$
$857$	30.7990	+	29.1743i	1.05207	+	0.996576i	0.0520745	+	0.998643i	$0.483417\pi$
$858$	10.4438	+	15.4035i	0.356545	+	0.525865i
$859$	−5.68994	+	10.7324i	−0.194138	+	0.366183i	−0.961402	−	0.275148i	$-0.911273\pi$
$859$	−5.68994	+	10.7324i	−0.194138	+	0.366183i	0.767264	+	0.641332i	$0.221618\pi$
$860$	−23.1328	−	43.6331i	−0.788823	−	1.48788i
$861$	−12.2592	+	18.0810i	−0.417793	+	0.616198i
$862$	−7.09525	+	1.56178i	−0.241665	+	0.0531945i
$863$	−11.5678	−	41.6636i	−0.393774	−	1.41825i	−0.849247	−	0.527996i	$-0.822944\pi$
$863$	−11.5678	−	41.6636i	−0.393774	−	1.41825i	0.455473	−	0.890250i	$-0.349470\pi$
$864$	1.40701	−	3.53133i	0.0478675	−	0.120138i
$865$	−2.78103	+	0.937040i	−0.0945580	+	0.0318603i
$866$	28.7301	−	27.2146i	0.976289	−	0.924791i
$867$	−20.7891	−	4.57603i	−0.706036	−	0.155410i
$868$	−3.38376	−	62.4097i	−0.114852	−	2.11832i
$869$	4.13019	+	25.1931i	0.140107	+	0.854616i
$870$	−8.23854	−	9.69915i	−0.279313	−	0.328832i
$871$	9.73866	+	24.4422i	0.329982	+	0.828192i
$872$	17.9020	−	13.6087i	0.606238	−	0.460850i
$873$	2.88022	−	1.73297i	0.0974808	−	0.0586522i
$874$	−2.69451	+	16.4358i	−0.0911431	+	0.555948i
$875$	13.3459	+	1.45146i	0.451175	+	0.0490683i
$876$	−14.8232	−	11.2683i	−0.500829	−	0.380720i
$877$	−5.11536	+	18.4239i	−0.172733	+	0.622130i	0.825591	+	0.564269i	$0.190842\pi$
$877$	−5.11536	+	18.4239i	−0.172733	+	0.622130i	−0.998325	+	0.0578610i	$0.981572\pi$
$878$	1.90043	−	35.0514i	0.0641364	−	1.18293i
$879$	7.51164	−	0.816941i	0.253361	−	0.0275547i
$880$	−19.9223	−	11.9869i	−0.671581	−	0.404077i
$881$	−18.7006	+	22.0161i	−0.630040	+	0.741740i	−0.980862	−	0.194702i	$-0.937626\pi$
$881$	−18.7006	+	22.0161i	−0.630040	+	0.741740i	0.350823	+	0.936442i	$0.385902\pi$
$882$	16.6744	+	5.61825i	0.561456	+	0.189176i
$883$	−6.55731	+	3.03373i	−0.220671	+	0.102093i	−0.527110	−	0.849797i	$-0.676724\pi$
$883$	−6.55731	+	3.03373i	−0.220671	+	0.102093i	0.306439	+	0.951890i	$0.400862\pi$
$884$	36.5668			1.22987
$885$	25.4347	+	2.38315i	0.854977	+	0.0801086i
$886$	−50.7676			−1.70557
$887$	18.3318	−	8.48118i	0.615521	−	0.284770i	−0.0872501	−	0.996186i	$-0.527808\pi$
$887$	18.3318	−	8.48118i	0.615521	−	0.284770i	0.702771	+	0.711416i	$0.251946\pi$
$888$	−5.84531	−	1.96951i	−0.196156	−	0.0660926i
$889$	3.17321	−	3.73579i	0.106426	−	0.125294i
$890$	−67.1583	−	40.4078i	−2.25115	−	1.35447i
$891$	4.71263	−	0.512529i	0.157879	−	0.0171704i
$892$	4.03096	−	74.3467i	0.134967	−	2.48931i
$893$	3.65494	−	13.1639i	0.122308	−	0.440514i
$894$	−21.3729	−	16.2472i	−0.714816	−	0.543389i
$895$	−16.9342	−	1.84170i	−0.566047	−	0.0615613i
$896$	−12.5672	+	76.6565i	−0.419840	+	2.56091i
$897$	−9.64460	+	5.80296i	−0.322024	+	0.193755i
$898$	12.6905	−	9.64706i	0.423487	−	0.321927i
$899$	2.78789	+	6.99707i	0.0929813	+	0.233366i
$900$	13.9082	+	16.3740i	0.463608	+	0.545801i
$901$	−3.90121	−	23.7963i	−0.129968	−	0.792771i
$902$	−3.47010	−	64.0022i	−0.115542	−	2.13104i
$903$	−15.5648	−	3.42606i	−0.517963	−	0.114012i
$904$	6.62221	−	6.27289i	0.220251	−	0.208633i
$905$	−10.6554	+	3.59021i	−0.354196	+	0.119343i
$906$	−1.35706	+	3.40595i	−0.0450851	+	0.113155i
$907$	0.206134	+	0.742426i	0.00684455	+	0.0246519i	0.966893	−	0.255181i	$-0.0821349\pi$
$907$	0.206134	+	0.742426i	0.00684455	+	0.0246519i	−0.960049	+	0.279832i	$0.909721\pi$
$908$	76.8376	−	16.9132i	2.54994	−	0.561285i
$909$	10.6037	−	15.6393i	0.351703	−	0.518723i
$910$	23.2664	+	43.8851i	0.771273	+	1.45478i
$911$	−0.0511404	+	0.0964610i	−0.00169436	+	0.00319590i	−0.884358	−	0.466810i	$-0.845403\pi$
$911$	−0.0511404	+	0.0964610i	−0.00169436	+	0.00319590i	0.882663	+	0.470006i	$0.155748\pi$
$912$	0.867093	+	1.27887i	0.0287123	+	0.0423475i
$913$	−20.5313	−	19.4483i	−0.679487	−	0.643644i
$914$	−22.9218	−	10.6047i	−0.758185	−	0.350774i
$915$	−1.28543	−	0.594704i	−0.0424950	−	0.0196603i
$916$	26.3708	+	24.9797i	0.871315	+	0.825353i
$917$	34.8049	+	51.3333i	1.14936	+	1.69518i
$918$	6.82468	−	12.8727i	0.225248	−	0.424863i
$919$	−18.4446	−	34.7903i	−0.608433	−	1.14763i	−0.976029	−	0.217640i	$-0.930164\pi$
$919$	−18.4446	−	34.7903i	−0.608433	−	1.14763i	0.367596	−	0.929985i	$-0.380181\pi$
$920$	45.8264	−	67.5889i	1.51085	−	2.22834i
$921$	−2.05738	+	0.452863i	−0.0677929	+	0.0149223i
$922$	1.25359	+	4.51501i	0.0412846	+	0.148694i
$923$	7.13295	−	17.9024i	0.234784	−	0.589263i
$924$	−60.5759	+	20.4104i	−1.99280	+	0.671452i
$925$	−7.46283	+	7.06917i	−0.245376	+	0.232433i
$926$	−3.62345	−	0.797582i	−0.119074	−	0.0262102i
$927$	0.260359	+	4.80204i	0.00855131	+	0.157720i
$928$	−0.999353	−	6.09579i	−0.0328054	−	0.200104i
$929$	−9.22843	−	10.8645i	−0.302775	−	0.356454i	0.589643	−	0.807664i	$-0.299268\pi$
$929$	−9.22843	−	10.8645i	−0.302775	−	0.356454i	−0.892418	+	0.451210i	$0.850993\pi$
$930$	−13.4354	−	33.7204i	−0.440565	−	1.10573i
$931$	6.23265	−	4.73793i	0.204267	−	0.155280i
$932$	32.0314	−	19.2726i	1.04922	−	0.631296i
$933$	3.02566	−	18.4557i	0.0990557	−	0.604213i
$934$	−82.7938	−	9.00437i	−2.70910	−	0.294632i
$935$	77.6610	+	59.0364i	2.53979	+	1.93070i
$936$	−1.62221	+	5.84266i	−0.0530235	+	0.190973i
$937$	2.55972	−	47.2112i	0.0836223	−	1.54232i	−0.592523	−	0.805554i	$-0.701868\pi$
$937$	2.55972	−	47.2112i	0.0836223	−	1.54232i	0.676145	−	0.736768i	$-0.263649\pi$
$938$	−140.536	+	15.2842i	−4.58865	+	0.499046i
$939$	−21.4729	−	12.9198i	−0.700743	−	0.421623i
$940$	−99.5159	+	117.159i	−3.24585	+	3.82131i
$941$	−28.5112	−	9.60656i	−0.929440	−	0.313165i	−0.186448	−	0.982465i	$-0.559698\pi$
$941$	−28.5112	−	9.60656i	−0.929440	−	0.313165i	−0.742992	+	0.669300i	$0.766594\pi$
$942$	10.3737	−	4.79939i	0.337994	−	0.156373i
$943$	38.7666			1.26241
$944$	−9.11910	−	6.72006i	−0.296802	−	0.218719i
$945$	12.6523			0.411580
$946$	42.4402	−	19.6349i	1.37985	−	0.638386i
$947$	19.0381	+	6.41469i	0.618655	+	0.208449i	0.611140	−	0.791522i	$-0.290711\pi$
$947$	19.0381	+	6.41469i	0.618655	+	0.208449i	0.00751540	+	0.999972i	$0.497608\pi$
$948$	−12.3580	+	14.5490i	−0.401369	+	0.472529i
$949$	−7.50457	−	4.51535i	−0.243609	−	0.146574i
$950$	14.8651	−	1.61668i	0.482289	−	0.0524520i
$951$	−0.0730451	+	1.34724i	−0.00236865	+	0.0436872i
$952$	−22.9035	+	82.4910i	−0.742307	+	2.67355i
$953$	−24.6364	−	18.7281i	−0.798051	−	0.606663i	0.124640	−	0.992202i	$-0.460222\pi$
$953$	−24.6364	−	18.7281i	−0.798051	−	0.606663i	−0.922691	+	0.385539i	$0.874015\pi$
$954$	9.12273	+	0.992157i	0.295359	+	0.0321223i
$955$	2.82390	−	17.2251i	0.0913794	−	0.557390i
$956$	−69.5212	+	41.8295i	−2.24848	+	1.35286i
$957$	6.13248	−	4.66179i	0.198235	−	0.150694i
$958$	−11.3151	−	28.3987i	−0.365573	−	0.917520i
$959$	19.8351	+	23.3516i	0.640508	+	0.754064i
$960$	6.40309	+	39.0571i	0.206659	+	1.26056i
$961$	−0.515192	−	9.50216i	−0.0166191	−	0.306521i
$962$	−6.50253	−	1.43132i	−0.209650	−	0.0461474i
$963$	−5.36868	+	5.08549i	−0.173003	+	0.163877i
$964$	65.8662	−	22.1929i	2.12141	−	0.714785i
$965$	−6.80829	+	17.0875i	−0.219167	+	0.550067i
$966$	−16.1789	−	58.2712i	−0.520549	−	1.87485i
$967$	15.4660	−	3.40433i	0.497354	−	0.109476i	0.0407922	−	0.999168i	$-0.487012\pi$
$967$	15.4660	−	3.40433i	0.497354	−	0.109476i	0.456562	+	0.889692i	$0.349081\pi$
$968$	23.4135	−	34.5323i	0.752538	−	1.10991i
$969$	−3.03662	−	5.72768i	−0.0975504	−	0.184000i
$970$	−12.3303	+	23.2574i	−0.395902	+	0.746750i
$971$	9.59128	+	14.1461i	0.307799	+	0.453969i	0.949856	−	0.312687i	$-0.101229\pi$
$971$	9.59128	+	14.1461i	0.307799	+	0.453969i	−0.642057	+	0.766657i	$0.721919\pi$
$972$	2.57333	+	2.43759i	0.0825396	+	0.0781856i
$973$	−9.75917	−	4.51507i	−0.312865	−	0.144747i
$974$	67.9861	+	31.4537i	2.17841	+	1.00784i
$975$	7.33639	+	6.94939i	0.234952	+	0.222559i
$976$	0.352446	+	0.519819i	0.0112815	+	0.0166390i
$977$	2.49704	−	4.70992i	0.0798875	−	0.150684i	−0.840350	−	0.542044i	$-0.817651\pi$
$977$	2.49704	−	4.70992i	0.0798875	−	0.150684i	0.920238	+	0.391360i	$0.127995\pi$
$978$	19.5401	+	36.8565i	0.624823	+	1.17854i
$979$	26.6247	−	39.2684i	0.850928	−	1.25502i
$980$	−86.0305	+	18.9367i	−2.74814	+	0.604912i
$981$	−1.65414	−	5.95766i	−0.0528125	−	0.190213i
$982$	17.7254	−	44.4874i	0.565641	−	1.41965i
$983$	55.8954	−	18.8333i	1.78279	−	0.600690i	0.783013	−	0.622005i	$-0.213682\pi$
$983$	55.8954	−	18.8333i	1.78279	−	0.600690i	0.999773	+	0.0213150i	$0.00678530\pi$
$984$	15.1618	−	14.3621i	0.483342	−	0.457846i
$985$	−0.608238	−	0.133883i	−0.0193801	−	0.00426588i
$986$	−1.28181	−	23.6415i	−0.0408210	−	0.752900i
$987$	8.02549	+	48.9533i	0.255454	+	1.55820i
$988$	4.00837	+	4.71901i	0.127523	+	0.150132i
$989$	10.4685	+	26.2739i	0.332878	+	0.835461i
$990$	−29.5537	+	22.4661i	−0.939278	+	0.714021i
$991$	10.0264	−	6.03267i	0.318498	−	0.191634i	−0.347322	−	0.937746i	$-0.612909\pi$
$991$	10.0264	−	6.03267i	0.318498	−	0.191634i	0.665821	+	0.746112i	$0.268081\pi$
$992$	2.85049	−	17.3872i	0.0905033	−	0.552046i
$993$	21.1167	+	2.29657i	0.670117	+	0.0728796i
$994$	82.4278	+	62.6600i	2.61445	+	1.98745i
$995$	16.7707	−	60.4026i	0.531667	−	1.91489i
$996$	1.14482	−	21.1149i	0.0362749	−	0.669052i
$997$	−5.06903	+	0.551290i	−0.160538	+	0.0174595i	−0.188035	−	0.982162i	$-0.560212\pi$
$997$	−5.06903	+	0.551290i	−0.160538	+	0.0174595i	0.0274971	+	0.999622i	$0.491246\pi$
$998$	−82.7940	−	49.8155i	−2.62080	−	1.57688i
$999$	−1.09796	+	1.29262i	−0.0347379	+	0.0408966i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.2.e.b.121.1	yes	140
3.2	odd	2		531.2.i.b.298.5		140
59.20	even	29	inner	177.2.e.b.79.1	✓	140
177.20	odd	58		531.2.i.b.433.5		140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.2.e.b.79.1	✓	140	59.20	even	29	inner
177.2.e.b.121.1	yes	140	1.1	even	1	trivial
531.2.i.b.298.5		140	3.2	odd	2
531.2.i.b.433.5		140	177.20	odd	58

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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	177.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.13706 + 0.988707i) q^{2} +(0.947653 + 0.319302i) q^{3} +(2.29469 - 2.70152i) q^{4} +(2.84975 + 1.71464i) q^{5} +(-2.34088 + 0.254586i) q^{6} +(0.205959 - 3.79870i) q^{7} +(-0.972984 + 3.50437i) q^{8} +(0.796093 + 0.605174i) q^{9} +O(q^{10})\)	\(q+(-2.13706 + 0.988707i) q^{2} +(0.947653 + 0.319302i) q^{3} +(2.29469 - 2.70152i) q^{4} +(2.84975 + 1.71464i) q^{5} +(-2.34088 + 0.254586i) q^{6} +(0.205959 - 3.79870i) q^{7} +(-0.972984 + 3.50437i) q^{8} +(0.796093 + 0.605174i) q^{9} +(-7.78535 - 0.846707i) q^{10} +(0.766914 - 4.67797i) q^{11} +(3.03717 - 1.82741i) q^{12} +(1.32729 - 1.00898i) q^{13} +(3.31565 + 8.32166i) q^{14} +(2.15309 + 2.53481i) q^{15} +(-0.238587 - 1.45532i) q^{16} +(0.334992 + 6.17856i) q^{17} +(-2.29964 - 0.506188i) q^{18} +(-0.760634 + 0.720510i) q^{19} +(11.1714 - 3.76409i) q^{20} +(1.40811 - 3.53408i) q^{21} +(2.98621 + 10.7553i) q^{22} +(-6.59327 + 1.45129i) q^{23} +(-2.04100 + 3.01025i) q^{24} +(2.83904 + 5.35500i) q^{25} +(-1.83890 + 3.46854i) q^{26} +(0.561187 + 0.827689i) q^{27} +(-9.78965 - 9.27325i) q^{28} +(1.47482 + 0.682323i) q^{29} +(-7.10745 - 3.28826i) q^{30} +(3.36504 + 3.18754i) q^{31} +(-2.13325 - 3.14630i) q^{32} +(2.22045 - 4.18822i) q^{33} +(-6.82468 - 12.8727i) q^{34} +(7.10032 - 10.4722i) q^{35} +(3.46168 - 0.761974i) q^{36} +(0.453724 + 1.63417i) q^{37} +(0.913143 - 2.29182i) q^{38} +(1.57998 - 0.532356i) q^{39} +(-8.78148 + 8.31826i) q^{40} +(-5.60800 - 1.23442i) q^{41} +(0.484970 + 8.94474i) q^{42} +(-0.677758 - 4.13414i) q^{43} +(-10.8778 - 12.8064i) q^{44} +(1.23101 + 3.08960i) q^{45} +(12.6553 - 9.62029i) q^{46} +(-11.1732 + 6.72270i) q^{47} +(0.238587 - 1.45532i) q^{48} +(-7.42872 - 0.807922i) q^{49} +(-11.3617 - 8.63696i) q^{50} +(-1.65537 + 5.96209i) q^{51} +(0.319942 - 5.90099i) q^{52} +(-3.87429 + 0.421354i) q^{53} +(-2.01763 - 1.21397i) q^{54} +(10.2065 - 12.0161i) q^{55} +(13.1116 + 4.41783i) q^{56} +(-0.950877 + 0.439922i) q^{57} -3.82638 q^{58} +(5.49712 - 5.36486i) q^{59} +11.7885 q^{60} +(-0.386501 + 0.178814i) q^{61} +(-10.3428 - 3.48490i) q^{62} +(2.46284 - 2.89948i) q^{63} +(10.1969 + 6.13529i) q^{64} +(5.51246 - 0.599516i) q^{65} +(-0.604310 + 11.1458i) q^{66} +(-4.22186 + 15.2058i) q^{67} +(17.4602 + 13.2729i) q^{68} +(-6.71153 - 0.729923i) q^{69} +(-4.81985 + 29.3998i) q^{70} +(9.90405 - 5.95907i) q^{71} +(-2.89534 + 2.20098i) q^{72} +(-1.94438 - 4.88001i) q^{73} +(-2.58535 - 3.04371i) q^{74} +(0.980567 + 5.98120i) q^{75} +(0.201054 + 3.70822i) q^{76} +(-17.6122 - 3.87675i) q^{77} +(-2.85015 + 2.69981i) q^{78} +(-5.10356 + 1.71959i) q^{79} +(1.81543 - 4.55637i) q^{80} +(0.267528 + 0.963550i) q^{81} +(13.2051 - 2.90666i) q^{82} +(3.34791 - 4.93779i) q^{83} +(-6.31623 - 11.9137i) q^{84} +(-9.63934 + 18.1817i) q^{85} +(5.53586 + 8.16479i) q^{86} +(1.17975 + 1.11752i) q^{87} +(15.6471 + 7.23914i) q^{88} +(9.08328 + 4.20237i) q^{89} +(-5.68545 - 5.38555i) q^{90} +(-3.55943 - 5.24977i) q^{91} +(-11.2088 + 21.1421i) q^{92} +(2.17111 + 4.09514i) q^{93} +(17.2310 - 25.4138i) q^{94} +(-3.40303 + 0.749063i) q^{95} +(-1.01696 - 3.66275i) q^{96} +(1.24418 - 3.12264i) q^{97} +(16.6744 - 5.61825i) q^{98} +(3.44152 - 3.25998i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q + q^{2} + 5 q^{3} - q^{4} + 2 q^{5} - q^{6} - 2 q^{7} - 3 q^{8} - 5 q^{9}+O(q^{10}) \) 140 * q + q^2 + 5 * q^3 - q^4 + 2 * q^5 - q^6 - 2 * q^7 - 3 * q^8 - 5 * q^9	\( 140 q + q^{2} + 5 q^{3} - q^{4} + 2 q^{5} - q^{6} - 2 q^{7} - 3 q^{8} - 5 q^{9} - 116 q^{10} + 2 q^{11} + q^{12} + 4 q^{13} - 43 q^{14} - 2 q^{15} + 7 q^{16} + q^{18} - 2 q^{19} + 4 q^{20} - 27 q^{21} + 6 q^{22} + 6 q^{23} + 3 q^{24} - 57 q^{25} + 12 q^{26} + 5 q^{27} - 10 q^{28} - 4 q^{29} - 12 q^{31} - 150 q^{32} - 2 q^{33} - 2 q^{34} + 6 q^{35} - q^{36} + 12 q^{37} - 12 q^{38} - 4 q^{39} - 66 q^{40} - 4 q^{41} + 14 q^{42} - 60 q^{43} + 20 q^{44} + 2 q^{45} + 76 q^{46} - 25 q^{47} - 7 q^{48} + 31 q^{49} + 137 q^{50} + 118 q^{52} + 48 q^{53} - q^{54} + 93 q^{55} + 228 q^{56} + 2 q^{57} - 120 q^{58} + 57 q^{59} - 4 q^{60} + 72 q^{61} - 179 q^{62} - 2 q^{63} + 249 q^{64} - 39 q^{65} - 6 q^{66} + 40 q^{67} + 94 q^{68} - 64 q^{69} + 94 q^{70} + 30 q^{71} - 3 q^{72} - 205 q^{73} + 66 q^{74} - q^{75} - 216 q^{76} - 46 q^{77} - 12 q^{78} + 4 q^{79} - 356 q^{80} - 5 q^{81} - 28 q^{82} + 4 q^{83} - 135 q^{84} + 50 q^{85} - 18 q^{86} - 54 q^{87} - 162 q^{88} + 26 q^{89} - 198 q^{91} + 10 q^{92} + 12 q^{93} - 4 q^{94} - 326 q^{95} + 5 q^{96} - 20 q^{97} - 143 q^{98} + 2 q^{99}+O(q^{100}) \) 140 * q + q^2 + 5 * q^3 - q^4 + 2 * q^5 - q^6 - 2 * q^7 - 3 * q^8 - 5 * q^9 - 116 * q^10 + 2 * q^11 + q^12 + 4 * q^13 - 43 * q^14 - 2 * q^15 + 7 * q^16 + q^18 - 2 * q^19 + 4 * q^20 - 27 * q^21 + 6 * q^22 + 6 * q^23 + 3 * q^24 - 57 * q^25 + 12 * q^26 + 5 * q^27 - 10 * q^28 - 4 * q^29 - 12 * q^31 - 150 * q^32 - 2 * q^33 - 2 * q^34 + 6 * q^35 - q^36 + 12 * q^37 - 12 * q^38 - 4 * q^39 - 66 * q^40 - 4 * q^41 + 14 * q^42 - 60 * q^43 + 20 * q^44 + 2 * q^45 + 76 * q^46 - 25 * q^47 - 7 * q^48 + 31 * q^49 + 137 * q^50 + 118 * q^52 + 48 * q^53 - q^54 + 93 * q^55 + 228 * q^56 + 2 * q^57 - 120 * q^58 + 57 * q^59 - 4 * q^60 + 72 * q^61 - 179 * q^62 - 2 * q^63 + 249 * q^64 - 39 * q^65 - 6 * q^66 + 40 * q^67 + 94 * q^68 - 64 * q^69 + 94 * q^70 + 30 * q^71 - 3 * q^72 - 205 * q^73 + 66 * q^74 - q^75 - 216 * q^76 - 46 * q^77 - 12 * q^78 + 4 * q^79 - 356 * q^80 - 5 * q^81 - 28 * q^82 + 4 * q^83 - 135 * q^84 + 50 * q^85 - 18 * q^86 - 54 * q^87 - 162 * q^88 + 26 * q^89 - 198 * q^91 + 10 * q^92 + 12 * q^93 - 4 * q^94 - 326 * q^95 + 5 * q^96 - 20 * q^97 - 143 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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