LMFDB - Embedded newform 69.2.e.b.58.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,2,Mod(4,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("69.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	69.e (of order $11$, degree $10$, 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:	$0.550967773947$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			58.1
Root			$-0.841254 + 0.540641i$ of defining polynomial
Character	$\chi$	$=$	69.58
Dual form			69.2.e.b.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34125 - 0.861971i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.225136 - 0.492980i) q^{4} +(-2.43560 + 0.715158i) q^{5} +(-0.662317 - 1.45027i) q^{6} +(0.729022 + 0.841336i) q^{7} +(0.330830 + 2.30097i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(1.34125 - 0.861971i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.225136 - 0.492980i) q^{4} +(-2.43560 + 0.715158i) q^{5} +(-0.662317 - 1.45027i) q^{6} +(0.729022 + 0.841336i) q^{7} +(0.330830 + 2.30097i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(-2.65032 + 3.05863i) q^{10} +(-1.19537 - 0.768216i) q^{11} +(-0.455922 - 0.293003i) q^{12} +(2.76921 - 3.19584i) q^{13} +(1.70301 + 0.500049i) q^{14} +(0.361256 + 2.51259i) q^{15} +(3.13691 + 3.62019i) q^{16} +(-2.04342 - 4.47447i) q^{17} +(-1.52977 + 0.449181i) q^{18} +(-2.40533 + 5.26695i) q^{19} +(-0.195785 + 1.36171i) q^{20} +(0.936524 - 0.601867i) q^{21} -2.26547 q^{22} +(-2.44275 - 4.12710i) q^{23} +2.32463 q^{24} +(1.21445 - 0.780481i) q^{25} +(0.959493 - 6.67342i) q^{26} +(-0.415415 + 0.909632i) q^{27} +(0.578892 - 0.169978i) q^{28} +(2.66820 + 5.84254i) q^{29} +(2.65032 + 3.05863i) q^{30} +(-1.05906 - 7.36593i) q^{31} +(2.86695 + 0.841812i) q^{32} +(-0.930515 + 1.07387i) q^{33} +(-6.59761 - 4.24002i) q^{34} +(-2.37730 - 1.52780i) q^{35} +(-0.354905 + 0.409583i) q^{36} +(7.94159 + 2.33186i) q^{37} +(1.31379 + 9.13764i) q^{38} +(-2.76921 - 3.19584i) q^{39} +(-2.45133 - 5.36767i) q^{40} +(4.41546 - 1.29650i) q^{41} +(0.737323 - 1.61451i) q^{42} +(-0.288111 + 2.00386i) q^{43} +(-0.647836 + 0.416339i) q^{44} +2.53843 q^{45} +(-6.83379 - 3.42992i) q^{46} +2.61810 q^{47} +(4.02977 - 2.58978i) q^{48} +(0.819830 - 5.70204i) q^{49} +(0.956135 - 2.09364i) q^{50} +(-4.71973 + 1.38584i) q^{51} +(-0.952036 - 2.08467i) q^{52} +(6.82982 + 7.88203i) q^{53} +(0.226900 + 1.57812i) q^{54} +(3.46084 + 1.01619i) q^{55} +(-1.69471 + 1.95580i) q^{56} +(4.87102 + 3.13042i) q^{57} +(8.61483 + 5.53642i) q^{58} +(-7.84439 + 9.05291i) q^{59} +(1.31999 + 0.387584i) q^{60} +(-1.58058 - 10.9932i) q^{61} +(-7.76969 - 8.96670i) q^{62} +(-0.462460 - 1.01265i) q^{63} +(-4.62139 + 1.35696i) q^{64} +(-4.45918 + 9.76424i) q^{65} +(-0.322410 + 2.24241i) q^{66} +(-9.58188 + 6.15790i) q^{67} -2.66587 q^{68} +(-4.43274 + 1.83053i) q^{69} -4.50548 q^{70} +(3.26126 - 2.09588i) q^{71} +(0.330830 - 2.30097i) q^{72} +(-5.12376 + 11.2195i) q^{73} +(12.6617 - 3.71780i) q^{74} +(-0.599702 - 1.31316i) q^{75} +(2.05497 + 2.37156i) q^{76} +(-0.225121 - 1.56575i) q^{77} +(-6.46894 - 1.89945i) q^{78} +(-3.56932 + 4.11922i) q^{79} +(-10.2293 - 6.57396i) q^{80} +(0.841254 + 0.540641i) q^{81} +(4.80471 - 5.54493i) q^{82} +(1.50043 + 0.440567i) q^{83} +(-0.0858629 - 0.597190i) q^{84} +(8.17692 + 9.43666i) q^{85} +(1.34084 + 2.93602i) q^{86} +(6.16279 - 1.80956i) q^{87} +(1.37218 - 3.00466i) q^{88} +(0.324950 - 2.26007i) q^{89} +(3.40468 - 2.18805i) q^{90} +4.70760 q^{91} +(-2.58453 + 0.275064i) q^{92} -7.44168 q^{93} +(3.51153 - 2.25672i) q^{94} +(2.09174 - 14.5484i) q^{95} +(1.24125 - 2.71797i) q^{96} +(8.39691 - 2.46555i) q^{97} +(-3.81540 - 8.35456i) q^{98} +(0.930515 + 1.07387i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} + q^{3} - 14 q^{4} - 3 q^{5} - 4 q^{6} + 6 q^{7} - 7 q^{8} - q^{9}+O(q^{10}) $ 10 * q + 4 * q^2 + q^3 - 14 * q^4 - 3 * q^5 - 4 * q^6 + 6 * q^7 - 7 * q^8 - q^9	\( 10 q + 4 q^{2} + q^{3} - 14 q^{4} - 3 q^{5} - 4 q^{6} + 6 q^{7} - 7 q^{8} - q^{9} + 12 q^{10} - 15 q^{11} - 8 q^{12} + 8 q^{13} + 9 q^{14} - 8 q^{15} + 12 q^{16} + q^{17} + 4 q^{18} - 9 q^{19} - 9 q^{20} + 5 q^{21} - 28 q^{22} + 21 q^{23} + 18 q^{24} - 4 q^{25} + q^{26} + q^{27} + 29 q^{28} - 8 q^{29} - 12 q^{30} - 23 q^{31} - q^{32} + 4 q^{33} - 15 q^{34} + 18 q^{35} + 8 q^{36} + 3 q^{37} + 3 q^{38} - 8 q^{39} - 32 q^{40} - 15 q^{41} + 13 q^{42} + 22 q^{43} - q^{44} - 14 q^{45} + 26 q^{46} + 4 q^{47} + 21 q^{48} - 29 q^{49} + 49 q^{50} - 12 q^{51} + 2 q^{52} + 29 q^{53} + 7 q^{54} + 43 q^{55} - 2 q^{56} + 20 q^{57} + 21 q^{58} - 54 q^{59} - 2 q^{60} - 30 q^{61} - 7 q^{62} + 6 q^{63} - 31 q^{64} - 9 q^{65} - 27 q^{66} + q^{67} - 30 q^{68} + q^{69} - 94 q^{70} - 3 q^{71} - 7 q^{72} - 47 q^{73} - 12 q^{74} + 15 q^{75} + 50 q^{76} + 13 q^{77} - 12 q^{78} + 18 q^{79} + 3 q^{80} - q^{81} - 28 q^{82} + 18 q^{83} + 4 q^{84} + 58 q^{85} + 8 q^{87} + 16 q^{88} + 25 q^{89} + q^{90} + 18 q^{91} - 3 q^{92} - 10 q^{93} + 39 q^{94} - 16 q^{95} - 21 q^{96} + 21 q^{97} - 27 q^{98} - 4 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 + q^3 - 14 * q^4 - 3 * q^5 - 4 * q^6 + 6 * q^7 - 7 * q^8 - q^9 + 12 * q^10 - 15 * q^11 - 8 * q^12 + 8 * q^13 + 9 * q^14 - 8 * q^15 + 12 * q^16 + q^17 + 4 * q^18 - 9 * q^19 - 9 * q^20 + 5 * q^21 - 28 * q^22 + 21 * q^23 + 18 * q^24 - 4 * q^25 + q^26 + q^27 + 29 * q^28 - 8 * q^29 - 12 * q^30 - 23 * q^31 - q^32 + 4 * q^33 - 15 * q^34 + 18 * q^35 + 8 * q^36 + 3 * q^37 + 3 * q^38 - 8 * q^39 - 32 * q^40 - 15 * q^41 + 13 * q^42 + 22 * q^43 - q^44 - 14 * q^45 + 26 * q^46 + 4 * q^47 + 21 * q^48 - 29 * q^49 + 49 * q^50 - 12 * q^51 + 2 * q^52 + 29 * q^53 + 7 * q^54 + 43 * q^55 - 2 * q^56 + 20 * q^57 + 21 * q^58 - 54 * q^59 - 2 * q^60 - 30 * q^61 - 7 * q^62 + 6 * q^63 - 31 * q^64 - 9 * q^65 - 27 * q^66 + q^67 - 30 * q^68 + q^69 - 94 * q^70 - 3 * q^71 - 7 * q^72 - 47 * q^73 - 12 * q^74 + 15 * q^75 + 50 * q^76 + 13 * q^77 - 12 * q^78 + 18 * q^79 + 3 * q^80 - q^81 - 28 * q^82 + 18 * q^83 + 4 * q^84 + 58 * q^85 + 8 * q^87 + 16 * q^88 + 25 * q^89 + q^90 + 18 * q^91 - 3 * q^92 - 10 * q^93 + 39 * q^94 - 16 * q^95 - 21 * q^96 + 21 * q^97 - 27 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{10}{11}\right)$	$1$

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 $

$2$	1.34125	−	0.861971i	0.948409	−	0.609506i	0.0276421	−	0.999618i	$-0.491200\pi$
$2$	1.34125	−	0.861971i	0.948409	−	0.609506i	0.920767	+	0.390112i	$0.127564\pi$
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$4$	0.225136	−	0.492980i	0.112568	−	0.246490i
$5$	−2.43560	+	0.715158i	−1.08924	+	0.319828i	−0.776568	−	0.630034i	$-0.783041\pi$
$5$	−2.43560	+	0.715158i	−1.08924	+	0.319828i	−0.312668	+	0.949862i	$0.601223\pi$
$6$	−0.662317	−	1.45027i	−0.270390	−	0.592071i
$7$	0.729022	+	0.841336i	0.275544	+	0.317995i	0.876607	−	0.481207i	$-0.159801\pi$
$7$	0.729022	+	0.841336i	0.275544	+	0.317995i	−0.601063	+	0.799202i	$0.705256\pi$
$8$	0.330830	+	2.30097i	0.116966	+	0.813517i
$9$	−0.959493	−	0.281733i	−0.319831	−	0.0939109i
$10$	−2.65032	+	3.05863i	−0.838104	+	0.967224i
$11$	−1.19537	−	0.768216i	−0.360417	−	0.231626i	0.347882	−	0.937538i	$-0.386901\pi$
$11$	−1.19537	−	0.768216i	−0.360417	−	0.231626i	−0.708299	+	0.705912i	$0.750537\pi$
$12$	−0.455922	−	0.293003i	−0.131613	−	0.0845828i
$13$	2.76921	−	3.19584i	0.768042	−	0.886368i	−0.228144	−	0.973627i	$-0.573266\pi$
$13$	2.76921	−	3.19584i	0.768042	−	0.886368i	0.996186	+	0.0872599i	$0.0278111\pi$
$14$	1.70301	+	0.500049i	0.455149	+	0.133644i
$15$	0.361256	+	2.51259i	0.0932759	+	0.648748i
$16$	3.13691	+	3.62019i	0.784228	+	0.905047i
$17$	−2.04342	−	4.47447i	−0.495602	−	1.08522i	−0.977874	−	0.209196i	$-0.932915\pi$
$17$	−2.04342	−	4.47447i	−0.495602	−	1.08522i	0.482271	−	0.876022i	$-0.339812\pi$
$18$	−1.52977	+	0.449181i	−0.360570	+	0.105873i
$19$	−2.40533	+	5.26695i	−0.551821	+	1.20832i	0.404105	+	0.914713i	$0.367583\pi$
$19$	−2.40533	+	5.26695i	−0.551821	+	1.20832i	−0.955926	+	0.293608i	$0.905144\pi$
$20$	−0.195785	+	1.36171i	−0.0437788	+	0.304488i
$21$	0.936524	−	0.601867i	0.204366	−	0.131338i
$22$	−2.26547			−0.483000
$23$	−2.44275	−	4.12710i	−0.509348	−	0.860561i
$23$	−2.44275	−	4.12710i	−0.509348	−	0.860561i
$24$	2.32463			0.474514
$25$	1.21445	−	0.780481i	0.242890	−	0.156096i
$26$	0.959493	−	6.67342i	0.188172	−	1.30877i
$27$	−0.415415	+	0.909632i	−0.0799467	+	0.175059i
$28$	0.578892	−	0.169978i	0.109400	−	0.0321228i
$29$	2.66820	+	5.84254i	0.495472	+	1.08493i	0.977915	+	0.209005i	$0.0670224\pi$
$29$	2.66820	+	5.84254i	0.495472	+	1.08493i	−0.482443	+	0.875928i	$0.660250\pi$
$30$	2.65032	+	3.05863i	0.483880	+	0.558427i
$31$	−1.05906	−	7.36593i	−0.190213	−	1.32296i	−0.831442	−	0.555611i	$-0.812484\pi$
$31$	−1.05906	−	7.36593i	−0.190213	−	1.32296i	0.641229	−	0.767349i	$-0.278425\pi$
$32$	2.86695	+	0.841812i	0.506810	+	0.148813i
$33$	−0.930515	+	1.07387i	−0.161982	+	0.186937i
$34$	−6.59761	−	4.24002i	−1.13148	−	0.727158i
$35$	−2.37730	−	1.52780i	−0.401837	−	0.258245i
$36$	−0.354905	+	0.409583i	−0.0591509	+	0.0682638i
$37$	7.94159	+	2.33186i	1.30559	+	0.383355i	0.859272	−	0.511519i	$-0.170917\pi$
$37$	7.94159	+	2.33186i	1.30559	+	0.383355i	0.446317	+	0.894875i	$0.352735\pi$
$38$	1.31379	+	9.13764i	0.213126	+	1.48232i
$39$	−2.76921	−	3.19584i	−0.443429	−	0.511745i
$40$	−2.45133	−	5.36767i	−0.387589	−	0.848702i
$41$	4.41546	−	1.29650i	0.689579	−	0.202479i	0.0818753	−	0.996643i	$-0.473909\pi$
$41$	4.41546	−	1.29650i	0.689579	−	0.202479i	0.607704	+	0.794164i	$0.292091\pi$
$42$	0.737323	−	1.61451i	0.113771	−	0.249125i
$43$	−0.288111	+	2.00386i	−0.0439365	+	0.305585i	0.955989	+	0.293402i	$0.0947873\pi$
$43$	−0.288111	+	2.00386i	−0.0439365	+	0.305585i	−0.999926	+	0.0121835i	$0.996122\pi$
$44$	−0.647836	+	0.416339i	−0.0976650	+	0.0627655i
$45$	2.53843			0.378407
$46$	−6.83379	−	3.42992i	−1.00759	−	0.505713i
$47$	2.61810			0.381888			0.190944	−	0.981601i	$-0.438845\pi$
$47$	2.61810			0.381888			0.190944	+	0.981601i	$0.438845\pi$
$48$	4.02977	−	2.58978i	0.581647	−	0.373802i
$49$	0.819830	−	5.70204i	0.117119	−	0.814578i
$50$	0.956135	−	2.09364i	0.135218	−	0.296086i
$51$	−4.71973	+	1.38584i	−0.660895	+	0.194056i
$52$	−0.952036	−	2.08467i	−0.132024	−	0.289092i
$53$	6.82982	+	7.88203i	0.938148	+	1.08268i	0.996434	+	0.0843807i	$0.0268912\pi$
$53$	6.82982	+	7.88203i	0.938148	+	1.08268i	−0.0582855	+	0.998300i	$0.518563\pi$
$54$	0.226900	+	1.57812i	0.0308772	+	0.214755i
$55$	3.46084	+	1.01619i	0.466659	+	0.137024i
$56$	−1.69471	+	1.95580i	−0.226465	+	0.261355i
$57$	4.87102	+	3.13042i	0.645183	+	0.414634i
$58$	8.61483	+	5.53642i	1.13118	+	0.726967i
$59$	−7.84439	+	9.05291i	−1.02125	+	1.17859i	−0.0374567	+	0.999298i	$0.511926\pi$
$59$	−7.84439	+	9.05291i	−1.02125	+	1.17859i	−0.983796	+	0.179290i	$0.942620\pi$
$60$	1.31999	+	0.387584i	0.170410	+	0.0500369i
$61$	−1.58058	−	10.9932i	−0.202373	−	1.40753i	−0.797217	−	0.603693i	$-0.793695\pi$
$61$	−1.58058	−	10.9932i	−0.202373	−	1.40753i	0.594844	−	0.803841i	$-0.297214\pi$
$62$	−7.76969	−	8.96670i	−0.986752	−	1.13877i
$63$	−0.462460	−	1.01265i	−0.0582645	−	0.127581i
$64$	−4.62139	+	1.35696i	−0.577674	+	0.169620i
$65$	−4.45918	+	9.76424i	−0.553093	+	1.21110i
$66$	−0.322410	+	2.24241i	−0.0396860	+	0.276022i
$67$	−9.58188	+	6.15790i	−1.17061	+	0.752307i	−0.973637	−	0.228101i	$-0.926748\pi$
$67$	−9.58188	+	6.15790i	−1.17061	+	0.752307i	−0.196975	+	0.980408i	$0.563112\pi$
$68$	−2.66587			−0.323284
$69$	−4.43274	+	1.83053i	−0.533639	+	0.220370i
$70$	−4.50548			−0.538508
$71$	3.26126	−	2.09588i	0.387040	−	0.248735i	−0.332622	−	0.943060i	$-0.607933\pi$
$71$	3.26126	−	2.09588i	0.387040	−	0.248735i	0.719662	+	0.694325i	$0.244297\pi$
$72$	0.330830	−	2.30097i	0.0389887	−	0.271172i
$73$	−5.12376	+	11.2195i	−0.599691	+	1.31314i	0.329715	+	0.944081i	$0.393047\pi$
$73$	−5.12376	+	11.2195i	−0.599691	+	1.31314i	−0.929406	+	0.369059i	$0.879680\pi$
$74$	12.6617	−	3.71780i	1.47189	−	0.432186i
$75$	−0.599702	−	1.31316i	−0.0692476	−	0.151631i
$76$	2.05497	+	2.37156i	0.235721	+	0.272037i
$77$	−0.225121	−	1.56575i	−0.0256550	−	0.178434i
$78$	−6.46894	−	1.89945i	−0.732464	−	0.215071i
$79$	−3.56932	+	4.11922i	−0.401580	+	0.463448i	−0.920138	−	0.391594i	$-0.871924\pi$
$79$	−3.56932	+	4.11922i	−0.401580	+	0.463448i	0.518558	+	0.855043i	$0.326469\pi$
$80$	−10.2293	−	6.57396i	−1.14367	−	0.734991i
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$	4.80471	−	5.54493i	0.530591	−	0.612335i
$83$	1.50043	+	0.440567i	0.164694	+	0.0483585i	0.363040	−	0.931774i	$-0.381739\pi$
$83$	1.50043	+	0.440567i	0.164694	+	0.0483585i	−0.198346	+	0.980132i	$0.563557\pi$
$84$	−0.0858629	−	0.597190i	−0.00936841	−	0.0651587i
$85$	8.17692	+	9.43666i	0.886911	+	1.02355i
$86$	1.34084	+	2.93602i	0.144586	+	0.316599i
$87$	6.16279	−	1.80956i	0.660721	−	0.194005i
$88$	1.37218	−	3.00466i	0.146275	−	0.320298i
$89$	0.324950	−	2.26007i	0.0344446	−	0.239567i	−0.965325	−	0.261053i	$-0.915930\pi$
$89$	0.324950	−	2.26007i	0.0344446	−	0.239567i	0.999769	+	0.0214852i	$0.00683949\pi$
$90$	3.40468	−	2.18805i	0.358884	−	0.230641i
$91$	4.70760			0.493490
$92$	−2.58453	+	0.275064i	−0.269456	+	0.0286774i
$93$	−7.44168			−0.771666
$94$	3.51153	−	2.25672i	0.362187	−	0.232763i
$95$	2.09174	−	14.5484i	0.214608	−	1.49263i
$96$	1.24125	−	2.71797i	0.126685	−	0.277401i
$97$	8.39691	−	2.46555i	0.852577	−	0.250339i	0.173888	−	0.984765i	$-0.444367\pi$
$97$	8.39691	−	2.46555i	0.852577	−	0.250339i	0.678688	+	0.734426i	$0.262549\pi$
$98$	−3.81540	−	8.35456i	−0.385413	−	0.843938i
$99$	0.930515	+	1.07387i	0.0935203	+	0.107928i
$100$	−0.111344	−	0.774415i	−0.0111344	−	0.0774415i
$101$	−2.49380	−	0.732247i	−0.248143	−	0.0728613i	0.155296	−	0.987868i	$-0.450367\pi$
$101$	−2.49380	−	0.732247i	−0.248143	−	0.0728613i	−0.403439	+	0.915007i	$0.632185\pi$
$102$	−5.13580	+	5.92703i	−0.508520	+	0.586864i
$103$	0.196789	+	0.126468i	0.0193902	+	0.0124613i	0.550300	−	0.834967i	$-0.314513\pi$
$103$	0.196789	+	0.126468i	0.0193902	+	0.0124613i	−0.530910	+	0.847428i	$0.678150\pi$
$104$	8.26969	+	5.31461i	0.810910	+	0.521140i
$105$	−1.85057	+	2.13567i	−0.180597	+	0.208420i
$106$	15.9546	+	4.68470i	1.54965	+	0.455018i
$107$	−0.204273	−	1.42075i	−0.0197478	−	0.137349i	0.977562	−	0.210646i	$-0.0675569\pi$
$107$	−0.204273	−	1.42075i	−0.0197478	−	0.137349i	−0.997310	+	0.0732974i	$0.976648\pi$
$108$	0.354905	+	0.409583i	0.0341508	+	0.0394121i
$109$	−5.92310	−	12.9698i	−0.567330	−	1.24228i	−0.948207	−	0.317654i	$-0.897105\pi$
$109$	−5.92310	−	12.9698i	−0.567330	−	1.24228i	0.380876	−	0.924626i	$-0.375622\pi$
$110$	5.51779	−	1.62017i	0.526101	−	0.154477i
$111$	3.43833	−	7.52890i	0.326352	−	0.714611i
$112$	−0.758919	+	5.27840i	−0.0717111	+	0.498761i
$113$	3.86768	−	2.48560i	0.363840	−	0.233826i	−0.345928	−	0.938261i	$-0.612436\pi$
$113$	3.86768	−	2.48560i	0.363840	−	0.233826i	0.709769	+	0.704435i	$0.248800\pi$
$114$	9.23160			0.864619
$115$	8.90110	+	8.30504i	0.830032	+	0.774449i
$116$	3.48096			0.323199
$117$	−3.55742	+	2.28621i	−0.328883	+	0.211360i
$118$	−2.71797	+	18.9039i	−0.250209	+	1.74024i
$119$	2.27483	−	4.98119i	0.208534	−	0.456625i
$120$	−5.66189	+	1.66248i	−0.516858	+	0.151763i
$121$	−3.73082	−	8.16935i	−0.339165	−	0.742668i
$122$	−11.5958	−	13.3822i	−1.04983	−	1.21157i
$123$	−0.654914	−	4.55503i	−0.0590516	−	0.410713i
$124$	−3.86969	−	1.13624i	−0.347509	−	0.102038i
$125$	5.91183	−	6.82262i	0.528770	−	0.610233i
$126$	−1.49315	−	0.959588i	−0.133020	−	0.0854869i
$127$	2.27279	+	1.46063i	0.201677	+	0.129610i	0.637581	−	0.770383i	$-0.279935\pi$
$127$	2.27279	+	1.46063i	0.201677	+	0.129610i	−0.435904	+	0.899993i	$0.643571\pi$
$128$	−8.94222	+	10.3199i	−0.790388	+	0.912157i
$129$	1.94246	+	0.570357i	0.171024	+	0.0502171i
$130$	2.43560	+	16.9400i	0.213617	+	1.48574i
$131$	−4.63411	−	5.34805i	−0.404884	−	0.467261i	0.516289	−	0.856415i	$-0.327313\pi$
$131$	−4.63411	−	5.34805i	−0.404884	−	0.467261i	−0.921173	+	0.389153i	$0.872768\pi$
$132$	0.319905	+	0.700493i	0.0278441	+	0.0609701i
$133$	−6.18482	+	1.81603i	−0.536292	+	0.157469i
$134$	−7.54379	+	16.5186i	−0.651685	+	1.42699i
$135$	0.361256	−	2.51259i	0.0310920	−	0.216249i
$136$	9.61960	−	6.18214i	0.824874	−	0.530115i
$137$	−4.85066			−0.414420			−0.207210	−	0.978296i	$-0.566438\pi$
$137$	−4.85066			−0.414420			−0.207210	+	0.978296i	$0.566438\pi$
$138$	−4.36755	+	6.27610i	−0.371791	+	0.534257i
$139$	−20.0995			−1.70482			−0.852410	−	0.522875i	$-0.824860\pi$
$139$	−20.0995			−1.70482			−0.852410	+	0.522875i	$0.824860\pi$
$140$	−1.28839	+	0.827998i	−0.108889	+	0.0699786i
$141$	0.372594	−	2.59145i	0.0313781	−	0.218239i
$142$	2.56758	−	5.62222i	0.215467	−	0.471806i
$143$	−5.76533	+	1.69285i	−0.482121	+	0.141564i
$144$	−1.98992	−	4.35731i	−0.165827	−	0.363110i
$145$	−10.6770	−	12.3219i	−0.886678	−	1.02328i
$146$	2.79860	+	19.4647i	0.231614	+	1.61091i
$147$	−5.52733	−	1.62297i	−0.455887	−	0.133860i
$148$	2.93750	−	3.39006i	0.241461	−	0.278661i
$149$	6.39324	+	4.10868i	0.523754	+	0.336596i	0.775656	−	0.631156i	$-0.217419\pi$
$149$	6.39324	+	4.10868i	0.523754	+	0.336596i	−0.251901	+	0.967753i	$0.581056\pi$
$150$	−1.93626	−	1.24436i	−0.158095	−	0.101602i
$151$	−7.84815	+	9.05725i	−0.638673	+	0.737068i	−0.979140	−	0.203188i	$-0.934870\pi$
$151$	−7.84815	+	9.05725i	−0.638673	+	0.737068i	0.340466	+	0.940257i	$0.389415\pi$
$152$	−12.9149	−	3.79215i	−1.04753	−	0.307584i
$153$	0.700045	+	4.86892i	0.0565953	+	0.393629i
$154$	−1.65158	−	1.90602i	−0.133088	−	0.153592i
$155$	7.84726	+	17.1831i	0.630307	+	1.38018i
$156$	−2.19894	+	0.645667i	−0.176056	+	0.0516947i
$157$	2.51857	−	5.51489i	0.201003	−	0.440136i	−0.782108	−	0.623143i	$-0.785856\pi$
$157$	2.51857	−	5.51489i	0.201003	−	0.440136i	0.983112	+	0.183006i	$0.0585829\pi$
$158$	−1.23672	+	8.60157i	−0.0983881	+	0.684304i
$159$	8.77379	−	5.63857i	0.695807	−	0.447168i
$160$	−7.58478			−0.599630
$161$	1.69147	−	5.06392i	0.133306	−	0.399093i
$162$	1.59435			0.125264
$163$	14.0504	−	9.02963i	1.10051	−	0.707255i	0.141306	−	0.989966i	$-0.454870\pi$
$163$	14.0504	−	9.02963i	1.10051	−	0.707255i	0.959205	+	0.282711i	$0.0912336\pi$
$164$	0.354934	−	2.46862i	0.0277157	−	0.192767i
$165$	1.49838	−	3.28099i	0.116649	−	0.255425i
$166$	2.39222	−	0.702418i	0.185672	−	0.0545182i
$167$	8.44065	+	18.4825i	0.653157	+	1.43022i	0.888763	+	0.458367i	$0.151565\pi$
$167$	8.44065	+	18.4825i	0.653157	+	1.43022i	−0.235606	+	0.971849i	$0.575707\pi$
$168$	1.69471	+	1.95580i	0.130750	+	0.150893i
$169$	−0.694776	−	4.83228i	−0.0534443	−	0.371713i
$170$	19.1015	+	5.60869i	1.46501	+	0.430167i
$171$	3.79177	−	4.37594i	0.289964	−	0.334636i
$172$	0.922997	+	0.593174i	0.0703779	+	0.0452291i
$173$	−1.63360	−	1.04985i	−0.124200	−	0.0798188i	0.477066	−	0.878868i	$-0.341700\pi$
$173$	−1.63360	−	1.04985i	−0.124200	−	0.0798188i	−0.601266	+	0.799049i	$0.705337\pi$
$174$	6.70608	−	7.73923i	0.508387	−	0.586709i
$175$	1.54201	+	0.452775i	0.116565	+	0.0342265i
$176$	−0.968675	−	6.73728i	−0.0730166	−	0.507842i
$177$	7.84439	+	9.05291i	0.589621	+	0.680458i
$178$	−1.51228	−	3.31143i	−0.113350	−	0.248202i
$179$	16.8179	−	4.93817i	1.25703	−	0.369096i	0.415639	−	0.909530i	$-0.363558\pi$
$179$	16.8179	−	4.93817i	1.25703	−	0.369096i	0.841387	+	0.540434i	$0.181740\pi$
$180$	0.571493	−	1.25139i	0.0425966	−	0.0932735i
$181$	−1.85460	+	12.8990i	−0.137851	+	0.958777i	0.797061	+	0.603899i	$0.206387\pi$
$181$	−1.85460	+	12.8990i	−0.137851	+	0.958777i	−0.934912	+	0.354878i	$0.884522\pi$
$182$	6.31408	−	4.05782i	0.468031	−	0.300785i
$183$	−11.1062			−0.820996
$184$	8.68822	−	6.98606i	0.640504	−	0.515020i
$185$	−21.0102			−1.54470
$186$	−9.98118	+	6.41451i	−0.731855	+	0.470335i
$187$	−0.994719	+	6.91842i	−0.0727411	+	0.505925i
$188$	0.589429	−	1.29067i	0.0429885	−	0.0941317i
$189$	−1.06815	+	0.313638i	−0.0776967	+	0.0228138i
$190$	−9.73474	−	21.3161i	−0.706232	−	1.54643i
$191$	−9.24532	−	10.6697i	−0.668968	−	0.772030i	0.315247	−	0.949010i	$-0.397913\pi$
$191$	−9.24532	−	10.6697i	−0.668968	−	0.772030i	−0.984215	+	0.176980i	$0.943367\pi$
$192$	0.685459	+	4.76747i	0.0494687	+	0.344063i
$193$	−11.6561	−	3.42253i	−0.839021	−	0.246359i	−0.166133	−	0.986103i	$-0.553128\pi$
$193$	−11.6561	−	3.42253i	−0.839021	−	0.246359i	−0.672888	+	0.739744i	$0.734946\pi$
$194$	9.13714	−	10.5448i	0.656009	−	0.757074i
$195$	9.03025	+	5.80339i	0.646669	+	0.415589i
$196$	−2.62642	−	1.68790i	−0.187601	−	0.120564i
$197$	2.87078	−	3.31305i	0.204534	−	0.236045i	−0.644210	−	0.764849i	$-0.722814\pi$
$197$	2.87078	−	3.31305i	0.204534	−	0.236045i	0.848744	+	0.528803i	$0.177359\pi$
$198$	2.17370	+	0.638257i	0.154478	+	0.0453590i
$199$	−2.41756	−	16.8145i	−0.171376	−	1.19195i	−0.875980	−	0.482347i	$-0.839785\pi$
$199$	−2.41756	−	16.8145i	−0.171376	−	1.19195i	0.704604	−	0.709600i	$-0.251124\pi$
$200$	2.19764	+	2.53621i	0.155397	+	0.179337i
$201$	4.73158	+	10.3607i	0.333740	+	0.730788i
$202$	−3.97600	+	1.16746i	−0.279750	+	0.0821421i
$203$	−2.97037	+	6.50419i	−0.208479	+	0.456505i
$204$	−0.379393	+	2.63874i	−0.0265628	+	0.184749i
$205$	−9.82711	+	6.31550i	−0.686355	+	0.441094i
$206$	0.372955			0.0259850
$207$	1.18106	+	4.64813i	0.0820892	+	0.323067i
$208$	20.2563			1.40452
$209$	6.92141	−	4.44812i	0.478764	−	0.307683i
$210$	−0.641196	+	4.45962i	−0.0442467	+	0.307743i
$211$	−2.95148	+	6.46284i	−0.203188	+	0.444920i	−0.983604	−	0.180340i	$-0.942280\pi$
$211$	−2.95148	+	6.46284i	−0.203188	+	0.444920i	0.780416	+	0.625261i	$0.215007\pi$
$212$	5.42333	−	1.59243i	0.372476	−	0.109369i
$213$	−1.61042	−	3.52634i	−0.110344	−	0.241621i
$214$	−1.49863	−	1.72951i	−0.102444	−	0.118227i
$215$	−0.731349	−	5.08665i	−0.0498776	−	0.346906i
$216$	−2.23047	−	0.654925i	−0.151764	−	0.0445620i
$217$	5.42515	−	6.26095i	0.368283	−	0.425021i
$218$	−19.1240	−	12.2902i	−1.29524	−	0.832399i
$219$	10.3761	+	6.66831i	0.701151	+	0.450602i
$220$	1.28012	−	1.47734i	0.0863060	−	0.0996024i
$221$	−19.9584	−	5.86031i	−1.34255	−	0.394207i
$222$	−1.87802	−	13.0619i	−0.126044	−	0.876657i
$223$	3.34045	+	3.85508i	0.223693	+	0.258155i	0.856492	−	0.516161i	$-0.172639\pi$
$223$	3.34045	+	3.85508i	0.223693	+	0.258155i	−0.632799	+	0.774316i	$0.718094\pi$
$224$	1.38182	+	3.02577i	0.0923269	+	0.202168i
$225$	−1.38514	+	0.406715i	−0.0923430	+	0.0271143i
$226$	3.04501	−	6.66765i	0.202551	−	0.443526i
$227$	1.98911	−	13.8345i	0.132022	−	0.918231i	−0.810892	−	0.585195i	$-0.801018\pi$
$227$	1.98911	−	13.8345i	0.132022	−	0.918231i	0.942914	−	0.333036i	$-0.108073\pi$
$228$	2.63988	−	1.69655i	0.174830	−	0.112357i
$229$	2.53723			0.167665			0.0838324	−	0.996480i	$-0.473284\pi$
$229$	2.53723			0.167665			0.0838324	+	0.996480i	$0.473284\pi$
$230$	19.0973	+	3.46668i	1.25924	+	0.228586i
$231$	−1.58185			−0.104078
$232$	−12.5608	+	8.07234i	−0.824657	+	0.529975i
$233$	−0.174982	+	1.21703i	−0.0114635	+	0.0797301i	−0.994750	−	0.102334i	$-0.967369\pi$
$233$	−0.174982	+	1.21703i	−0.0114635	+	0.0797301i	0.983287	+	0.182064i	$0.0582779\pi$
$234$	−2.80075	+	6.13278i	−0.183091	+	0.400912i
$235$	−6.37665	+	1.87235i	−0.415966	+	0.122139i
$236$	2.69685	+	5.90527i	0.175550	+	0.384400i
$237$	3.56932	+	4.11922i	0.231852	+	0.267572i
$238$	−1.24251	−	8.64188i	−0.0805403	−	0.560170i
$239$	9.71455	+	2.85245i	0.628382	+	0.184510i	0.580391	−	0.814338i	$-0.302900\pi$
$239$	9.71455	+	2.85245i	0.628382	+	0.184510i	0.0479912	+	0.998848i	$0.484718\pi$
$240$	−7.96283	+	9.18959i	−0.513998	+	0.593185i
$241$	16.9700	+	10.9060i	1.09314	+	0.702516i	0.957555	−	0.288250i	$-0.0930733\pi$
$241$	16.9700	+	10.9060i	1.09314	+	0.702516i	0.135582	+	0.990766i	$0.456710\pi$
$242$	−12.0457	−	7.74131i	−0.774328	−	0.497630i
$243$	0.654861	−	0.755750i	0.0420093	−	0.0484814i
$244$	−5.77527	−	1.69577i	−0.369724	−	0.108561i
$245$	2.08108	+	14.4742i	0.132955	+	0.924725i
$246$	−4.80471	−	5.54493i	−0.306337	−	0.353532i
$247$	10.1715	+	22.2724i	0.647194	+	1.41716i
$248$	16.5984	−	4.87374i	1.05400	−	0.309483i
$249$	0.649616	−	1.42246i	0.0411677	−	0.0901448i
$250$	2.04836	−	14.2467i	0.129550	−	0.901040i
$251$	−13.4477	+	8.64231i	−0.848811	+	0.545498i	−0.891204	−	0.453603i	$-0.850138\pi$
$251$	−13.4477	+	8.64231i	−0.848811	+	0.545498i	0.0423928	+	0.999101i	$0.486502\pi$
$252$	−0.603331			−0.0380063
$253$	−0.250528	+	6.80996i	−0.0157506	+	0.428139i
$254$	4.30740			0.270270
$255$	10.5043	−	6.75071i	0.657805	−	0.422746i
$256$	−1.72743	+	12.0146i	−0.107965	+	0.750911i
$257$	−9.02114	+	19.7535i	−0.562723	+	1.23219i	0.387859	+	0.921719i	$0.373215\pi$
$257$	−9.02114	+	19.7535i	−0.562723	+	1.23219i	−0.950582	+	0.310473i	$0.899513\pi$
$258$	3.09696	−	0.909349i	0.192808	−	0.0566136i
$259$	3.82771	+	8.38153i	0.237843	+	0.520803i
$260$	3.80965	+	4.39657i	0.236265	+	0.272664i
$261$	−0.914084	−	6.35759i	−0.0565804	−	0.393525i
$262$	−10.8254	−	3.17862i	−0.668794	−	0.196376i
$263$	10.5941	−	12.2263i	0.653262	−	0.753904i	−0.328399	−	0.944539i	$-0.606509\pi$
$263$	10.5941	−	12.2263i	0.653262	−	0.753904i	0.981661	+	0.190635i	$0.0610546\pi$
$264$	−2.77879	−	1.78582i	−0.171023	−	0.109910i
$265$	−22.2716	−	14.3131i	−1.36814	−	0.879248i
$266$	−6.73004	+	7.76689i	−0.412646	+	0.476218i
$267$	−2.19082	−	0.643284i	−0.134076	−	0.0393684i
$268$	0.878492	+	6.11004i	0.0536624	+	0.373230i
$269$	−1.27244	−	1.46847i	−0.0775818	−	0.0895342i	0.715632	−	0.698478i	$-0.246139\pi$
$269$	−1.27244	−	1.46847i	−0.0775818	−	0.0895342i	−0.793213	+	0.608944i	$0.791594\pi$
$270$	−1.68125	−	3.68141i	−0.102317	−	0.224044i
$271$	−4.74854	+	1.39430i	−0.288453	+	0.0846975i	−0.422758	−	0.906243i	$-0.638938\pi$
$271$	−4.74854	+	1.39430i	−0.288453	+	0.0846975i	0.134305	+	0.990940i	$0.457120\pi$
$272$	9.78838	−	21.4336i	0.593508	−	1.29960i
$273$	0.669961	−	4.65968i	0.0405479	−	0.282017i
$274$	−6.50597	+	4.18113i	−0.393040	+	0.252591i
$275$	−2.05129			−0.123698
$276$	−0.0955532	+	2.59737i	−0.00575163	+	0.156343i
$277$	20.3847			1.22480			0.612400	−	0.790548i	$-0.290204\pi$
$277$	20.3847			1.22480			0.612400	+	0.790548i	$0.290204\pi$
$278$	−26.9586	+	17.3252i	−1.61687	+	1.03910i
$279$	−1.05906	+	7.36593i	−0.0634043	+	0.440987i
$280$	2.72894	−	5.97554i	0.163085	−	0.357107i
$281$	19.8152	−	5.81826i	1.18207	−	0.347088i	0.369101	−	0.929389i	$-0.379666\pi$
$281$	19.8152	−	5.81826i	1.18207	−	0.347088i	0.812973	+	0.582301i	$0.197848\pi$
$282$	−1.73401	−	3.79695i	−0.103259	−	0.226105i
$283$	11.0558	+	12.7591i	0.657200	+	0.758449i	0.982317	−	0.187225i	$-0.0599493\pi$
$283$	11.0558	+	12.7591i	0.657200	+	0.758449i	−0.325117	+	0.945674i	$0.605404\pi$
$284$	−0.299000	−	2.07959i	−0.0177424	−	0.123401i
$285$	−14.1026	−	4.14090i	−0.835368	−	0.245286i
$286$	−6.27358	+	7.24009i	−0.370964	+	0.428116i
$287$	4.30976	+	2.76971i	0.254397	+	0.163491i
$288$	−2.51365	−	1.61543i	−0.148118	−	0.0951899i
$289$	−4.71265	+	5.43869i	−0.277215	+	0.319923i
$290$	−24.9417	−	7.32355i	−1.46463	−	0.430054i
$291$	−1.24545	−	8.66232i	−0.0730098	−	0.507794i
$292$	4.37743	+	5.05182i	0.256170	+	0.295636i
$293$	−7.75250	−	16.9756i	−0.452906	−	0.991726i	−0.989048	−	0.147597i	$-0.952846\pi$
$293$	−7.75250	−	16.9756i	−0.452906	−	0.991726i	0.536142	−	0.844128i	$-0.319881\pi$
$294$	−8.81251	+	2.58759i	−0.513956	+	0.150911i
$295$	12.6316	−	27.6593i	0.735439	−	1.61039i
$296$	−2.73823	+	19.0448i	−0.159157	+	1.10696i
$297$	1.19537	−	0.768216i	0.0693623	−	0.0445764i
$298$	12.1165			0.701891
$299$	−19.9541	−	3.62220i	−1.15397	−	0.209477i
$300$	−0.782379			−0.0451706
$301$	−1.89596	+	1.21846i	−0.109281	+	0.0702307i
$302$	−2.71927	+	18.9129i	−0.156476	+	1.08832i
$303$	−1.07970	+	2.36421i	−0.0620271	+	0.135820i
$304$	−26.6127	+	7.81418i	−1.52634	+	0.448174i
$305$	11.7115	+	25.6447i	0.670601	+	1.46841i
$306$	5.13580	+	5.92703i	0.293594	+	0.338826i
$307$	1.58202	+	11.0032i	0.0902906	+	0.627985i	0.983844	+	0.179028i	$0.0572953\pi$
$307$	1.58202	+	11.0032i	0.0902906	+	0.627985i	−0.893553	+	0.448957i	$0.851796\pi$
$308$	−0.822568	−	0.241528i	−0.0468702	−	0.0137623i
$309$	0.153187	−	0.176787i	0.00871450	−	0.0100571i
$310$	25.3365	+	16.2828i	1.43902	+	0.924800i
$311$	−4.67177	−	3.00236i	−0.264912	−	0.170248i	0.401441	−	0.915885i	$-0.368509\pi$
$311$	−4.67177	−	3.00236i	−0.264912	−	0.170248i	−0.666353	+	0.745636i	$0.732146\pi$
$312$	6.43741	−	7.42917i	0.364447	−	0.420594i
$313$	−11.3436	−	3.33078i	−0.641178	−	0.188267i	−0.0550479	−	0.998484i	$-0.517531\pi$
$313$	−11.3436	−	3.33078i	−0.641178	−	0.188267i	−0.586130	+	0.810217i	$0.699349\pi$
$314$	−1.37564	−	9.56779i	−0.0776319	−	0.539942i
$315$	1.85057	+	2.13567i	0.104268	+	0.120332i
$316$	1.22711	+	2.68699i	0.0690302	+	0.151155i
$317$	−32.6171	+	9.57726i	−1.83196	+	0.537912i	−0.999860	−	0.0167114i	$-0.994680\pi$
$317$	−32.6171	+	9.57726i	−1.83196	+	0.537912i	−0.832101	+	0.554624i	$0.812862\pi$
$318$	6.90759	−	15.1255i	0.387358	−	0.848197i
$319$	1.29885	−	9.03373i	0.0727219	−	0.505792i
$320$	10.2854	−	6.61005i	0.574974	−	0.369513i
$321$	−1.43536			−0.0801140
$322$	−2.09627	−	8.25000i	−0.116821	−	0.459755i
$323$	28.4819			1.58477
$324$	0.455922	−	0.293003i	0.0253290	−	0.0162780i
$325$	0.868783	−	6.04252i	0.0481914	−	0.335178i
$326$	11.0618	−	24.2221i	0.612659	−	1.34154i
$327$	−13.6807	+	4.01702i	−0.756545	+	0.222142i
$328$	4.44397	+	9.73093i	0.245377	+	0.537301i
$329$	1.90865	+	2.20270i	0.105227	+	0.121439i
$330$	−0.818415	−	5.69220i	−0.0450523	−	0.313346i
$331$	6.36568	+	1.86913i	0.349889	+	0.102737i	0.451955	−	0.892041i	$-0.350727\pi$
$331$	6.36568	+	1.86913i	0.349889	+	0.102737i	−0.102065	+	0.994778i	$0.532545\pi$
$332$	0.554993	−	0.640496i	0.0304592	−	0.0351518i
$333$	−6.96294	−	4.47481i	−0.381567	−	0.245218i
$334$	27.2524	+	17.5141i	1.49119	+	0.958327i
$335$	18.9338	−	21.8508i	1.03446	−	1.19383i
$336$	5.11666	+	1.50239i	0.279137	+	0.0819620i
$337$	−2.50295	−	17.4084i	−0.136345	−	0.948297i	−0.937039	−	0.349225i	$-0.886445\pi$
$337$	−2.50295	−	17.4084i	−0.136345	−	0.948297i	0.800694	−	0.599073i	$-0.204464\pi$
$338$	−5.09715	−	5.88243i	−0.277249	−	0.319962i
$339$	−1.90988	−	4.18205i	−0.103730	−	0.227138i
$340$	6.49301	−	1.90652i	0.352133	−	0.103396i
$341$	−4.39266	+	9.61858i	−0.237876	+	0.520876i
$342$	1.31379	−	9.13764i	0.0710419	−	0.494107i
$343$	11.9507	−	7.68023i	0.645276	−	0.414694i
$344$	−4.70614			−0.253738
$345$	9.48727	−	7.62857i	0.510777	−	0.410708i
$346$	−3.09602			−0.166443
$347$	−2.45596	+	1.57835i	−0.131843	+	0.0847302i	−0.604900	−	0.796302i	$-0.706787\pi$
$347$	−2.45596	+	1.57835i	−0.131843	+	0.0847302i	0.473057	+	0.881032i	$0.343150\pi$
$348$	0.495393	−	3.44553i	0.0265558	−	0.184700i
$349$	−0.978953	+	2.14361i	−0.0524022	+	0.114745i	−0.934022	−	0.357216i	$-0.883726\pi$
$349$	−0.978953	+	2.14361i	−0.0524022	+	0.114745i	0.881620	+	0.471960i	$0.156453\pi$
$350$	2.45850	−	0.721882i	0.131413	−	0.0385862i
$351$	1.75667	+	3.84657i	0.0937640	+	0.205315i
$352$	−2.78037	−	3.20871i	−0.148194	−	0.171025i
$353$	−0.304479	−	2.11770i	−0.0162058	−	0.112714i	0.980113	−	0.198441i	$-0.0635878\pi$
$353$	−0.304479	−	2.11770i	−0.0162058	−	0.112714i	−0.996319	+	0.0857271i	$0.972679\pi$
$354$	18.3247	+	5.38061i	0.973945	+	0.285976i
$355$	−6.44424	+	7.43705i	−0.342025	+	0.394718i
$356$	−1.04101	−	0.669019i	−0.0551736	−	0.0354579i
$357$	−4.60675	−	2.96058i	−0.243815	−	0.156690i
$358$	18.3004	−	21.1198i	0.967209	−	1.11622i
$359$	18.1631	+	5.33317i	0.958612	+	0.281474i	0.723368	−	0.690463i	$-0.242593\pi$
$359$	18.1631	+	5.33317i	0.958612	+	0.281474i	0.235244	+	0.971936i	$0.424411\pi$
$360$	0.839788	+	5.84086i	0.0442607	+	0.307840i
$361$	−9.51274	−	10.9783i	−0.500671	−	0.577805i
$362$	8.63110	+	18.8995i	0.453641	+	0.993334i
$363$	−8.61715	+	2.53022i	−0.452283	+	0.132802i
$364$	1.05985	−	2.32075i	0.0555514	−	0.121640i
$365$	4.45576	−	30.9905i	0.233225	−	1.62212i
$366$	−14.8963	+	9.57326i	−0.778641	+	0.500402i
$367$	7.75649			0.404885			0.202443	−	0.979294i	$-0.435112\pi$
$367$	7.75649			0.404885			0.202443	+	0.979294i	$0.435112\pi$
$368$	7.27822	−	21.7896i	0.379403	−	1.13586i
$369$	−4.60187			−0.239564
$370$	−28.1800	+	18.1102i	−1.46501	+	0.941505i
$371$	−1.65235	+	11.4924i	−0.0857858	+	0.596653i
$372$	−1.67539	+	3.66860i	−0.0868651	+	0.190208i
$373$	18.8535	−	5.53589i	0.976198	−	0.286638i	0.245544	−	0.969385i	$-0.421033\pi$
$373$	18.8535	−	5.53589i	0.976198	−	0.286638i	0.730654	+	0.682748i	$0.239215\pi$
$374$	4.62931	+	10.1368i	0.239376	+	0.524160i
$375$	−5.91183	−	6.82262i	−0.305286	−	0.352318i
$376$	0.866145	+	6.02417i	0.0446680	+	0.310673i
$377$	26.0607	+	7.65210i	1.34219	+	0.394103i
$378$	−1.16232	+	1.34139i	−0.0597832	+	0.0689934i
$379$	−8.08602	−	5.19657i	−0.415351	−	0.266930i	0.316232	−	0.948682i	$-0.397582\pi$
$379$	−8.08602	−	5.19657i	−0.415351	−	0.266930i	−0.731584	+	0.681752i	$0.761218\pi$
$380$	−6.70114	−	4.30656i	−0.343761	−	0.220922i
$381$	1.76921	−	2.04178i	0.0906396	−	0.104604i
$382$	−21.5973	−	6.34153i	−1.10501	−	0.324461i
$383$	0.303176	+	2.10863i	0.0154916	+	0.107746i	0.996100	−	0.0882308i	$-0.0281213\pi$
$383$	0.303176	+	2.10863i	0.0154916	+	0.107746i	−0.980608	+	0.195977i	$0.937212\pi$
$384$	8.94222	+	10.3199i	0.456331	+	0.526634i
$385$	1.66807	+	3.65256i	0.0850126	+	0.186152i
$386$	−18.5838	+	5.45671i	−0.945893	+	0.277739i
$387$	0.840992	−	1.84152i	0.0427500	−	0.0936095i
$388$	0.674981	−	4.69459i	0.0342670	−	0.238332i
$389$	−28.1831	+	18.1121i	−1.42894	+	0.918322i	−0.429051	+	0.903280i	$0.641152\pi$
$389$	−28.1831	+	18.1121i	−1.42894	+	0.918322i	−0.999887	+	0.0150420i	$0.995212\pi$
$390$	17.1142			0.866611
$391$	−13.4750	+	19.3634i	−0.681462	+	0.979249i
$392$	13.3915			0.676372
$393$	−5.95312	+	3.82584i	−0.300295	+	0.192988i
$394$	0.994683	−	6.91817i	0.0501114	−	0.348532i
$395$	5.74757	−	12.5854i	0.289192	−	0.633241i
$396$	0.738891	−	0.216958i	0.0371306	−	0.0109025i
$397$	9.10121	+	19.9289i	0.456777	+	1.00020i	0.988210	+	0.153102i	$0.0489262\pi$
$397$	9.10121	+	19.9289i	0.456777	+	1.00020i	−0.531434	+	0.847100i	$0.678347\pi$
$398$	−17.7362	−	20.4686i	−0.889033	−	1.02600i
$399$	0.917350	+	6.38031i	0.0459250	+	0.319415i
$400$	6.63511	+	1.94824i	0.331756	+	0.0974122i
$401$	4.02898	−	4.64969i	0.201198	−	0.232194i	−0.646180	−	0.763185i	$-0.723635\pi$
$401$	4.02898	−	4.64969i	0.201198	−	0.232194i	0.847378	+	0.530991i	$0.178180\pi$
$402$	15.2769	+	9.81785i	0.761941	+	0.489670i
$403$	−26.4731	−	17.0132i	−1.31872	−	0.847490i
$404$	−0.922430	+	1.06454i	−0.0458926	+	0.0529629i
$405$	−2.43560	−	0.715158i	−0.121026	−	0.0355365i
$406$	1.62241	+	11.2841i	0.0805191	+	0.560022i
$407$	−7.70174	−	8.88829i	−0.381761	−	0.440576i
$408$	−4.75021	−	10.4015i	−0.235170	−	0.514951i
$409$	−3.53362	+	1.03757i	−0.174726	+	0.0513043i	−0.367925	−	0.929855i	$-0.619932\pi$
$409$	−3.53362	+	1.03757i	−0.174726	+	0.0513043i	0.193199	+	0.981160i	$0.438114\pi$
$410$	−7.73687	+	16.9414i	−0.382097	+	0.836675i
$411$	−0.690321	+	4.80129i	−0.0340510	+	0.236830i
$412$	0.106651	−	0.0685402i	0.00525430	−	0.00337673i
$413$	−13.3353			−0.656186
$414$	5.59065	+	5.21628i	0.274766	+	0.256366i
$415$	−3.96953			−0.194857
$416$	10.6295	−	6.83116i	0.521154	−	0.334925i
$417$	−2.86046	+	19.8949i	−0.140077	+	0.974259i
$418$	5.44922	−	11.9321i	0.266530	−	0.583619i
$419$	−34.6476	+	10.1734i	−1.69264	+	0.497005i	−0.979061	−	0.203565i	$-0.934747\pi$
$419$	−34.6476	+	10.1734i	−1.69264	+	0.497005i	−0.713583	+	0.700571i	$0.752929\pi$
$420$	0.636213	+	1.39311i	0.0310440	+	0.0679769i
$421$	12.7180	+	14.6773i	0.619836	+	0.715329i	0.975676	−	0.219218i	$-0.0703506\pi$
$421$	12.7180	+	14.6773i	0.619836	+	0.715329i	−0.355840	+	0.934547i	$0.615805\pi$
$422$	1.61210	+	11.2124i	0.0784758	+	0.545811i
$423$	−2.51204	−	0.737603i	−0.122140	−	0.0358635i
$424$	−15.8768	+	18.3229i	−0.771048	+	0.889836i
$425$	−5.97387	−	3.83917i	−0.289775	−	0.186227i
$426$	−5.19959	−	3.34157i	−0.251921	−	0.161900i
$427$	8.09669	−	9.34408i	0.391826	−	0.452192i
$428$	−0.746391	−	0.219160i	−0.0360782	−	0.0105935i
$429$	0.855131	+	5.94756i	0.0412861	+	0.287151i
$430$	−5.36547	−	6.19208i	−0.258746	−	0.298609i
$431$	2.13218	+	4.66883i	0.102704	+	0.224890i	0.954007	−	0.299784i	$-0.0969146\pi$
$431$	2.13218	+	4.66883i	0.102704	+	0.224890i	−0.851303	+	0.524674i	$0.824187\pi$
$432$	−4.59616	+	1.34955i	−0.221133	+	0.0649304i
$433$	−6.88613	+	15.0785i	−0.330926	+	0.724628i	−0.999825	−	0.0187264i	$-0.994039\pi$
$433$	−6.88613	+	15.0785i	−0.330926	+	0.724628i	0.668898	+	0.743354i	$0.266766\pi$
$434$	1.87974	−	13.0738i	0.0902302	−	0.627565i
$435$	−13.7160	+	8.81474i	−0.657632	+	0.422635i
$436$	−7.72735			−0.370073
$437$	27.6129	−	2.93875i	1.32090	−	0.140580i
$438$	19.6649			0.939623
$439$	1.05400	−	0.677363i	0.0503045	−	0.0323288i	−0.515247	−	0.857042i	$-0.672300\pi$
$439$	1.05400	−	0.677363i	0.0503045	−	0.0323288i	0.565551	+	0.824713i	$0.308663\pi$
$440$	−1.19329	+	8.29949i	−0.0568877	+	0.395663i
$441$	−2.39307	+	5.24010i	−0.113956	+	0.249528i
$442$	−31.8206	+	9.34338i	−1.51355	+	0.444419i
$443$	−8.84700	−	19.3722i	−0.420333	−	0.920402i	−0.994798	−	0.101872i	$-0.967517\pi$
$443$	−8.84700	−	19.3722i	−0.420333	−	0.920402i	0.574464	−	0.818530i	$-0.305211\pi$
$444$	−2.93750	−	3.39006i	−0.139408	−	0.160885i
$445$	0.824861	+	5.73704i	0.0391022	+	0.271962i
$446$	7.80336	+	2.29127i	0.369500	+	0.108495i
$447$	4.97672	−	5.74344i	0.235391	−	0.271655i
$448$	−4.51076	−	2.89889i	−0.213113	−	0.136960i
$449$	−6.95511	−	4.46978i	−0.328232	−	0.210942i	0.366137	−	0.930561i	$-0.380680\pi$
$449$	−6.95511	−	4.46978i	−0.328232	−	0.210942i	−0.694369	+	0.719619i	$0.744316\pi$
$450$	−1.50725	+	1.73946i	−0.0710526	+	0.0819991i
$451$	−6.27409	−	1.84224i	−0.295435	−	0.0867476i
$452$	−0.354599	−	2.46629i	−0.0166789	−	0.116004i
$453$	7.84815	+	9.05725i	0.368738	+	0.425547i
$454$	−9.25709	−	20.2702i	−0.434457	−	0.951327i
$455$	−11.4658	+	3.36668i	−0.537527	+	0.157832i
$456$	−5.59152	+	12.2437i	−0.261847	+	0.573365i
$457$	2.17916	−	15.1564i	0.101937	−	0.708987i	−0.873196	−	0.487369i	$-0.837957\pi$
$457$	2.17916	−	15.1564i	0.101937	−	0.708987i	0.975133	−	0.221619i	$-0.0711341\pi$
$458$	3.40307	−	2.18702i	0.159015	−	0.102193i
$459$	4.91899			0.229599
$460$	6.09818	−	2.51830i	0.284329	−	0.117416i
$461$	28.6751			1.33553			0.667767	−	0.744370i	$-0.267250\pi$
$461$	28.6751			1.33553			0.667767	+	0.744370i	$0.267250\pi$
$462$	−2.12167	+	1.36351i	−0.0987089	+	0.0634364i
$463$	4.22090	−	29.3570i	0.196162	−	1.36433i	−0.619132	−	0.785287i	$-0.712516\pi$
$463$	4.22090	−	29.3570i	0.196162	−	1.36433i	0.815294	−	0.579047i	$-0.196575\pi$
$464$	−12.7812	+	27.9869i	−0.593352	+	1.29926i
$465$	18.1250	−	5.32198i	0.840526	−	0.246801i
$466$	0.814347	+	1.78317i	0.0377239	+	0.0826038i
$467$	19.4399	+	22.4348i	0.899569	+	1.03816i	0.999070	+	0.0431206i	$0.0137300\pi$
$467$	19.4399	+	22.4348i	0.899569	+	1.03816i	−0.0995008	+	0.995037i	$0.531725\pi$
$468$	0.326153	+	2.26844i	0.0150764	+	0.104859i
$469$	−12.1663	−	3.57234i	−0.561786	−	0.164955i
$470$	−6.93878	+	8.00778i	−0.320062	+	0.369372i
$471$	−5.10033	−	3.27778i	−0.235011	−	0.151032i
$472$	−23.4257	−	15.0548i	−1.07825	−	0.692952i
$473$	1.88379	−	2.17401i	0.0866169	−	0.0999612i
$474$	8.33802	+	2.44826i	0.382978	+	0.112452i
$475$	1.18959	+	8.27377i	0.0545820	+	0.379626i
$476$	−1.94348	−	2.24290i	−0.0890793	−	0.102803i
$477$	−4.33254	−	9.48694i	−0.198373	−	0.434377i
$478$	15.4884	−	4.54780i	0.708423	−	0.208012i
$479$	−1.06180	+	2.32502i	−0.0485150	+	0.106233i	−0.932337	−	0.361590i	$-0.882234\pi$
$479$	−1.06180	+	2.32502i	−0.0485150	+	0.106233i	0.883822	+	0.467823i	$0.154961\pi$
$480$	−1.07943	+	7.50758i	−0.0492689	+	0.342673i
$481$	29.4442	−	18.9227i	1.34254	−	0.862799i
$482$	32.1618			1.46493
$483$	−4.77166	−	2.39492i	−0.217118	−	0.108973i
$484$	−4.86727			−0.221240
$485$	−18.6883	+	12.0102i	−0.848591	+	0.545356i
$486$	0.226900	−	1.57812i	0.0102924	−	0.0715851i
$487$	13.4728	−	29.5012i	0.610509	−	1.33683i	−0.311716	−	0.950175i	$-0.600904\pi$
$487$	13.4728	−	29.5012i	0.610509	−	1.33683i	0.922225	−	0.386654i	$-0.126369\pi$
$488$	24.7721	−	7.27375i	1.12138	−	0.329267i
$489$	−6.93815	−	15.1924i	−0.313754	−	0.687025i
$490$	15.2676	+	17.6198i	0.689721	+	0.795981i
$491$	0.866630	+	6.02754i	0.0391105	+	0.272019i	0.999988	−	0.00495530i	$-0.00157733\pi$
$491$	0.866630	+	6.02754i	0.0391105	+	0.272019i	−0.960877	+	0.276975i	$0.910668\pi$
$492$	−2.39298	−	0.702643i	−0.107884	−	0.0316776i
$493$	20.6900	−	23.8775i	0.931830	−	1.07539i
$494$	32.8406	+	21.1054i	1.47757	+	0.949577i
$495$	−3.03436	−	1.95006i	−0.136384	−	0.0876488i
$496$	23.3439	−	26.9403i	1.04817	−	1.20965i
$497$	4.14087	+	1.21587i	0.185743	+	0.0545392i
$498$	−0.354821	−	2.46783i	−0.0158999	−	0.110586i
$499$	−13.3850	−	15.4471i	−0.599194	−	0.691507i	0.372424	−	0.928063i	$-0.378527\pi$
$499$	−13.3850	−	15.4471i	−0.599194	−	0.691507i	−0.971618	+	0.236556i	$0.923981\pi$
$500$	−2.03245	−	4.45043i	−0.0908937	−	0.199029i
$501$	19.4956	−	5.72441i	0.870997	−	0.255748i
$502$	−10.5873	+	23.1831i	−0.472536	+	1.03471i
$503$	−0.403200	+	2.80432i	−0.0179778	+	0.125038i	−0.996834	−	0.0795115i	$-0.974664\pi$
$503$	−0.403200	+	2.80432i	−0.0179778	+	0.125038i	0.978856	+	0.204550i	$0.0655730\pi$
$504$	2.17708	−	1.39912i	0.0969746	−	0.0623218i
$505$	6.59760			0.293589
$506$	5.53397	+	9.34984i	0.246015	+	0.415651i
$507$	−4.88197			−0.216816
$508$	1.23175	−	0.791597i	0.0546500	−	0.0351214i
$509$	4.91880	−	34.2110i	0.218022	−	1.51638i	−0.527305	−	0.849676i	$-0.676798\pi$
$509$	4.91880	−	34.2110i	0.218022	−	1.51638i	0.745327	−	0.666699i	$-0.232293\pi$
$510$	8.27002	−	18.1088i	0.366203	−	0.801872i
$511$	−13.1747	+	3.86844i	−0.582814	+	0.171130i
$512$	−3.30582	−	7.23875i	−0.146098	−	0.319910i
$513$	−3.79177	−	4.37594i	−0.167411	−	0.193202i
$514$	4.92735	+	34.2705i	0.217336	+	1.51161i
$515$	−0.569744	−	0.167292i	−0.0251059	−	0.00737176i
$516$	0.718493	−	0.829185i	0.0316299	−	0.0365028i
$517$	−3.12959	−	2.01126i	−0.137639	−	0.0884553i
$518$	12.3586	+	7.94237i	0.543004	+	0.348968i
$519$	−1.27165	+	1.46756i	−0.0558193	+	0.0644189i
$520$	−23.9425	−	7.03015i	−1.04995	−	0.308292i
$521$	2.39911	+	16.6862i	0.105107	+	0.731034i	0.972414	+	0.233261i	$0.0749397\pi$
$521$	2.39911	+	16.6862i	0.105107	+	0.731034i	−0.867307	+	0.497773i	$0.834151\pi$
$522$	−6.70608	−	7.73923i	−0.293517	−	0.338737i
$523$	10.8623	+	23.7852i	0.474977	+	1.04005i	0.983814	+	0.179192i	$0.0573482\pi$
$523$	10.8623	+	23.7852i	0.474977	+	1.04005i	−0.508837	+	0.860863i	$0.669924\pi$
$524$	−3.67979	+	1.08048i	−0.160752	+	0.0472012i
$525$	0.667617	−	1.46188i	0.0291372	−	0.0638015i
$526$	3.67071	−	25.5304i	0.160051	−	1.11318i
$527$	−30.7945	+	19.7904i	−1.34143	+	0.862085i
$528$	−6.80656			−0.296218
$529$	−11.0660	+	20.1629i	−0.481130	+	0.876650i
$530$	−42.2094			−1.83346
$531$	10.0771	−	6.47618i	0.437311	−	0.281042i
$532$	−0.497163	+	3.45785i	−0.0215548	+	0.149917i
$533$	8.08396	−	17.7014i	0.350155	−	0.766732i
$534$	−3.49294	+	1.02562i	−0.151154	+	0.0443830i
$535$	1.51359	+	3.31430i	0.0654382	+	0.143290i
$536$	−17.3391	−	20.0104i	−0.748936	−	0.864319i
$537$	−2.49447	−	17.3494i	−0.107644	−	0.748684i
$538$	−2.97244	−	0.872787i	−0.128151	−	0.0376285i
$539$	−5.36040	+	6.18623i	−0.230889	+	0.266460i
$540$	−1.15733	−	0.743768i	−0.0498034	−	0.0320067i
$541$	12.4240	+	7.98441i	0.534149	+	0.343277i	0.779747	−	0.626095i	$-0.215348\pi$
$541$	12.4240	+	7.98441i	0.534149	+	0.343277i	−0.245598	+	0.969372i	$0.578984\pi$
$542$	−5.16715	+	5.96321i	−0.221948	+	0.256142i
$543$	12.5038	+	3.67144i	0.536589	+	0.157557i
$544$	−2.09172	−	14.5482i	−0.0896818	−	0.623751i
$545$	23.7018	+	27.3533i	1.01527	+	1.17169i
$546$	−3.11792	−	6.82730i	−0.133435	−	0.292182i
$547$	−3.61642	+	1.06188i	−0.154627	+	0.0454026i	−0.358130	−	0.933672i	$-0.616586\pi$
$547$	−3.61642	+	1.06188i	−0.154627	+	0.0454026i	0.203503	+	0.979074i	$0.434767\pi$
$548$	−1.09206	+	2.39128i	−0.0466506	+	0.102150i
$549$	−1.58058	+	10.9932i	−0.0674576	+	0.469178i
$550$	−2.75131	+	1.76816i	−0.117316	+	0.0753944i
$551$	−37.1902			−1.58436
$552$	−5.67849	−	9.59401i	−0.241693	−	0.408348i
$553$	−6.06777			−0.258028
$554$	27.3411	−	17.5711i	1.16161	−	0.746523i
$555$	−2.99007	+	20.7964i	−0.126921	+	0.882756i
$556$	−4.52514	+	9.90866i	−0.191908	+	0.420221i
$557$	0.734010	−	0.215525i	0.0311010	−	0.00913208i	−0.266145	−	0.963933i	$-0.585750\pi$
$557$	0.734010	−	0.215525i	0.0311010	−	0.00913208i	0.297246	+	0.954801i	$0.403932\pi$
$558$	4.92875	+	10.7925i	0.208651	+	0.456881i
$559$	5.60617	+	6.46987i	0.237116	+	0.273646i
$560$	−1.92646	−	13.3988i	−0.0814078	−	0.566204i
$561$	6.70644	+	1.96919i	0.283146	+	0.0831392i
$562$	21.5620	−	24.8839i	0.909538	−	1.04966i
$563$	12.9451	+	8.31933i	0.545572	+	0.350618i	0.784215	−	0.620490i	$-0.213066\pi$
$563$	12.9451	+	8.31933i	0.545572	+	0.350618i	−0.238643	+	0.971107i	$0.576702\pi$
$564$	−1.19365	−	0.767111i	−0.0502616	−	0.0323012i
$565$	−7.64253	+	8.81995i	−0.321524	+	0.371058i
$566$	25.8266	+	7.58338i	1.08557	+	0.318753i
$567$	0.158432	+	1.10192i	0.00665350	+	0.0462761i
$568$	5.90149	+	6.81068i	0.247621	+	0.285770i
$569$	−17.0473	−	37.3284i	−0.714660	−	1.56489i	−0.821240	−	0.570583i	$-0.806717\pi$
$569$	−17.0473	−	37.3284i	−0.714660	−	1.56489i	0.106580	−	0.994304i	$-0.466010\pi$
$570$	−22.4845	+	6.60206i	−0.941774	+	0.276530i
$571$	8.99000	−	19.6854i	0.376220	−	0.823807i	−0.622918	−	0.782287i	$-0.714053\pi$
$571$	8.99000	−	19.6854i	0.376220	−	0.823807i	0.999138	−	0.0415195i	$-0.0132199\pi$
$572$	−0.463443	+	3.22332i	−0.0193775	+	0.134774i
$573$	−11.8768	+	7.63276i	−0.496161	+	0.318863i
$574$	8.16789			0.340921
$575$	−6.18772	−	3.10565i	−0.258046	−	0.129515i
$576$	4.81650			0.200687
$577$	−27.6437	+	17.7655i	−1.15082	+	0.739588i	−0.969803	−	0.243891i	$-0.921576\pi$
$577$	−27.6437	+	17.7655i	−1.15082	+	0.739588i	−0.181019	+	0.983480i	$0.557940\pi$
$578$	−1.63287	+	11.3568i	−0.0679183	+	0.472382i
$579$	−5.04652	+	11.0503i	−0.209726	+	0.459236i
$580$	−8.47825	+	2.48944i	−0.352040	+	0.103368i
$581$	0.723184	+	1.58355i	0.0300027	+	0.0656968i
$582$	−9.13714	−	10.5448i	−0.378747	−	0.437097i
$583$	−2.10904	−	14.6687i	−0.0873476	−	0.607516i
$584$	−27.5108	−	8.07790i	−1.13840	−	0.334266i
$585$	7.02945	−	8.11242i	0.290632	−	0.335407i
$586$	−25.0306	−	16.0862i	−1.03400	−	0.664513i
$587$	−8.80071	−	5.65587i	−0.363244	−	0.233443i	0.346269	−	0.938135i	$-0.387449\pi$
$587$	−8.80071	−	5.65587i	−0.363244	−	0.233443i	−0.709513	+	0.704693i	$0.751085\pi$
$588$	−2.04450	+	2.35947i	−0.0843136	+	0.0973031i
$589$	41.3434	+	12.1395i	1.70352	+	0.500200i
$590$	−6.89937	−	47.9862i	−0.284043	−	1.97556i
$591$	−2.87078	−	3.31305i	−0.118088	−	0.136281i
$592$	16.4703	+	36.0649i	0.676924	+	1.48226i
$593$	22.2328	−	6.52814i	0.912992	−	0.268079i	0.208692	−	0.977981i	$-0.433079\pi$
$593$	22.2328	−	6.52814i	0.912992	−	0.268079i	0.704300	+	0.709903i	$0.251261\pi$
$594$	0.941111	−	2.06075i	0.0386142	−	0.0845534i
$595$	−1.97826	+	13.7591i	−0.0811006	+	0.564067i
$596$	3.46485	−	2.22672i	0.141926	−	0.0912102i
$597$	−16.9874			−0.695247
$598$	−29.8857	+	12.3415i	−1.22212	+	0.504683i
$599$	−24.4836			−1.00037			−0.500187	−	0.865917i	$-0.666735\pi$
$599$	−24.4836			−1.00037			−0.500187	+	0.865917i	$0.666735\pi$
$600$	2.82316	−	1.81433i	0.115255	−	0.0740698i
$601$	−3.79167	+	26.3716i	−0.154665	+	1.07572i	0.753602	+	0.657331i	$0.228315\pi$
$601$	−3.79167	+	26.3716i	−0.154665	+	1.07572i	−0.908267	+	0.418390i	$0.862595\pi$
$602$	−1.49268	+	3.26852i	−0.0608372	+	0.133215i
$603$	10.9286	−	3.20893i	0.445048	−	0.130678i
$604$	2.69814	+	5.90810i	0.109786	+	0.240397i
$605$	14.9292	+	17.2292i	0.606957	+	0.700466i
$606$	0.589732	+	4.10168i	0.0239562	+	0.166619i
$607$	21.7054	+	6.37329i	0.880996	+	0.258684i	0.690786	−	0.723059i	$-0.257265\pi$
$607$	21.7054	+	6.37329i	0.880996	+	0.258684i	0.190210	+	0.981743i	$0.439083\pi$
$608$	−11.3298	+	13.0752i	−0.459482	+	0.530271i
$609$	6.01526	+	3.86577i	0.243751	+	0.156649i
$610$	37.8131	+	24.3010i	1.53101	+	0.983920i
$611$	7.25007	−	8.36702i	0.293306	−	0.338494i
$612$	2.55789	+	0.751063i	0.103396	+	0.0303599i
$613$	4.71172	+	32.7707i	0.190304	+	1.32360i	0.831202	+	0.555970i	$0.187653\pi$
$613$	4.71172	+	32.7707i	0.190304	+	1.32360i	−0.640898	+	0.767626i	$0.721438\pi$
$614$	11.6063	+	13.3944i	0.468393	+	0.540554i
$615$	4.85268	+	10.6259i	0.195679	+	0.428477i
$616$	3.52828	−	1.03600i	0.142158	−	0.0417415i
$617$	5.18384	−	11.3510i	0.208693	−	0.456975i	−0.776121	−	0.630584i	$-0.782816\pi$
$617$	5.18384	−	11.3510i	0.208693	−	0.456975i	0.984815	+	0.173609i	$0.0555429\pi$
$618$	0.0530771	−	0.369159i	0.00213507	−	0.0148498i
$619$	29.4730	−	18.9412i	1.18462	−	0.761310i	0.208391	−	0.978046i	$-0.433177\pi$
$619$	29.4730	−	18.9412i	1.18462	−	0.761310i	0.976230	+	0.216736i	$0.0695411\pi$
$620$	10.2376			0.411153
$621$	4.76890	−	0.507539i	0.191369	−	0.0203669i
$622$	−8.85398			−0.355012
$623$	2.13838	−	1.37425i	0.0856723	−	0.0550583i
$624$	2.88278	−	20.0502i	0.115403	−	0.802649i
$625$	−12.5181	+	27.4109i	−0.500726	+	1.09644i
$626$	−18.0857	+	5.31044i	−0.722849	+	0.212248i
$627$	−3.41783	−	7.48400i	−0.136495	−	0.298882i
$628$	−2.15171	−	2.48321i	−0.0858626	−	0.0990907i
$629$	−5.79417	−	40.2993i	−0.231029	−	1.60684i
$630$	4.32297	+	1.26934i	0.172231	+	0.0505717i
$631$	−19.9919	+	23.0718i	−0.795864	+	0.918476i	−0.998147	−	0.0608514i	$-0.980618\pi$
$631$	−19.9919	+	23.0718i	−0.795864	+	0.918476i	0.202283	+	0.979327i	$0.435164\pi$
$632$	−10.6591	−	6.85016i	−0.423994	−	0.272485i
$633$	5.97702	+	3.84120i	0.237565	+	0.152674i
$634$	−35.4925	+	40.9606i	−1.40959	+	1.62675i
$635$	−6.58019	−	1.93212i	−0.261127	−	0.0766737i
$636$	−0.804404	−	5.59475i	−0.0318967	−	0.221846i
$637$	−15.9526	−	18.4102i	−0.632063	−	0.729440i
$638$	−6.04473	−	13.2361i	−0.239313	−	0.524022i
$639$	−3.71963	+	1.09218i	−0.147146	+	0.0432061i
$640$	14.3994	−	31.5302i	0.569185	−	1.24634i
$641$	−2.24966	+	15.6467i	−0.0888563	+	0.618009i	0.895924	+	0.444207i	$0.146514\pi$
$641$	−2.24966	+	15.6467i	−0.0888563	+	0.618009i	−0.984781	+	0.173802i	$0.944395\pi$
$642$	−1.92518	+	1.23724i	−0.0759808	+	0.0488299i
$643$	−21.2193			−0.836809			−0.418404	−	0.908261i	$-0.637411\pi$
$643$	−21.2193			−0.836809			−0.418404	+	0.908261i	$0.637411\pi$
$644$	−2.11560	−	1.97393i	−0.0833664	−	0.0777839i
$645$	−5.13895			−0.202346
$646$	38.2014	−	24.5506i	1.50302	−	0.965929i
$647$	−4.95569	+	34.4676i	−0.194828	+	1.35506i	0.624180	+	0.781280i	$0.285433\pi$
$647$	−4.95569	+	34.4676i	−0.194828	+	1.35506i	−0.819009	+	0.573781i	$0.805476\pi$
$648$	−0.965688	+	2.11456i	−0.0379358	+	0.0830678i
$649$	16.3315	−	4.79537i	0.641069	−	0.188235i
$650$	−4.04322	−	8.85341i	−0.158588	−	0.347259i
$651$	−5.42515	−	6.26095i	−0.212628	−	0.245386i
$652$	−1.28818	−	8.95946i	−0.0504489	−	0.350879i
$653$	−27.2447	−	7.99978i	−1.06617	−	0.313056i	−0.298836	−	0.954304i	$-0.596598\pi$
$653$	−27.2447	−	7.99978i	−1.06617	−	0.313056i	−0.767333	+	0.641249i	$0.778417\pi$
$654$	−14.8868	+	17.1802i	−0.582118	+	0.671800i
$655$	15.1116	+	9.71161i	0.590458	+	0.379464i
$656$	18.5445	+	11.9178i	0.724040	+	0.465312i
$657$	8.07710	−	9.32147i	0.315118	−	0.363665i
$658$	4.45865	+	1.30918i	0.173816	+	0.0510370i
$659$	2.80223	+	19.4899i	0.109159	+	0.759220i	0.968715	+	0.248177i	$0.0798315\pi$
$659$	2.80223	+	19.4899i	0.109159	+	0.759220i	−0.859555	+	0.511043i	$0.829259\pi$
$660$	−1.28012	−	1.47734i	−0.0498288	−	0.0575055i
$661$	12.3026	+	26.9390i	0.478517	+	1.04781i	0.982869	+	0.184308i	$0.0590044\pi$
$661$	12.3026	+	26.9390i	0.478517	+	1.04781i	−0.504351	+	0.863499i	$0.668268\pi$
$662$	10.1491	−	2.98005i	0.394457	−	0.115823i
$663$	−8.64103	+	18.9212i	−0.335590	+	0.734839i
$664$	−0.517344	+	3.59821i	−0.0200768	+	0.139638i
$665$	13.7650	−	8.84624i	0.533785	−	0.343043i
$666$	−13.1962			−0.511343
$667$	17.5950	−	25.2838i	0.681282	−	0.978992i
$668$	11.0118			0.426059
$669$	4.29124	−	2.75781i	0.165909	−	0.106623i
$670$	6.56029	−	45.6278i	0.253446	−	1.76276i
$671$	−6.55577	+	14.3551i	−0.253083	+	0.554174i
$672$	3.19162	−	0.937146i	0.123120	−	0.0361512i
$673$	−11.3169	−	24.7806i	−0.436236	−	0.955224i	−0.992274	−	0.124067i	$-0.960406\pi$
$673$	−11.3169	−	24.7806i	−0.436236	−	0.955224i	0.556038	−	0.831157i	$-0.312321\pi$
$674$	−18.3627	−	21.1916i	−0.707303	−	0.816271i
$675$	0.205449	+	1.42893i	0.00790772	+	0.0549994i
$676$	−2.53864	−	0.745411i	−0.0976398	−	0.0286696i
$677$	1.41937	−	1.63804i	0.0545510	−	0.0629552i	−0.727818	−	0.685770i	$-0.759466\pi$
$677$	1.41937	−	1.63804i	0.0545510	−	0.0629552i	0.782369	+	0.622815i	$0.214011\pi$
$678$	−6.16643	−	3.96293i	−0.236820	−	0.152195i
$679$	8.19589	+	5.26718i	0.314529	+	0.202136i
$680$	−19.0083	+	21.9368i	−0.728937	+	0.841238i
$681$	−13.4107	−	3.93772i	−0.513897	−	0.150894i
$682$	2.39927	+	16.6873i	0.0918729	+	0.638990i
$683$	−6.60252	−	7.61971i	−0.252638	−	0.291560i	0.615237	−	0.788342i	$-0.289060\pi$
$683$	−6.60252	−	7.61971i	−0.252638	−	0.291560i	−0.867875	+	0.496782i	$0.834515\pi$
$684$	−1.30358	−	2.85445i	−0.0498438	−	0.109143i
$685$	11.8143	−	3.46899i	0.451401	−	0.132543i
$686$	9.40875	−	20.6023i	0.359228	−	0.786599i
$687$	0.361085	−	2.51140i	0.0137763	−	0.0958161i
$688$	−8.15811	+	5.24290i	−0.311025	+	0.199884i
$689$	44.1030			1.68019
$690$	6.14923	−	18.4096i	0.234097	−	0.700841i
$691$	−31.1667			−1.18564			−0.592819	−	0.805336i	$-0.701985\pi$
$691$	−31.1667			−1.18564			−0.592819	+	0.805336i	$0.701985\pi$
$692$	−0.885339	+	0.568973i	−0.0336556	+	0.0216291i
$693$	−0.225121	+	1.56575i	−0.00855165	+	0.0594780i
$694$	−1.93357	+	4.23393i	−0.0733974	+	0.160718i
$695$	48.9545	−	14.3743i	1.85695	−	0.545250i
$696$	6.20259	+	13.5818i	0.235108	+	0.514816i
$697$	−14.8238	−	17.1075i	−0.561490	−	0.647994i
$698$	0.534705	+	3.71895i	0.0202389	+	0.140764i
$699$	1.17974	+	0.346402i	0.0446217	+	0.0131021i
$700$	0.570371	−	0.658244i	0.0215580	−	0.0248793i
$701$	−38.9312	−	25.0196i	−1.47041	−	0.944976i	−0.997975	−	0.0636110i	$-0.979738\pi$
$701$	−38.9312	−	25.0196i	−1.47041	−	0.944976i	−0.472436	−	0.881365i	$-0.656625\pi$
$702$	5.67177	+	3.64502i	0.214067	+	0.137573i
$703$	−31.3840	+	36.2190i	−1.18367	+	1.36603i
$704$	6.56671	+	1.92816i	0.247492	+	0.0726702i
$705$	0.945803	+	6.57820i	0.0356210	+	0.247749i
$706$	−2.23378	−	2.57792i	−0.0840694	−	0.0970212i
$707$	−1.20197	−	2.63195i	−0.0452048	−	0.0989848i
$708$	6.22896	−	1.82899i	0.234099	−	0.0687376i
$709$	−12.0747	+	26.4398i	−0.453474	+	0.992969i	0.535453	+	0.844565i	$0.320141\pi$
$709$	−12.0747	+	26.4398i	−0.453474	+	0.992969i	−0.988927	+	0.148404i	$0.952586\pi$
$710$	−2.23284	+	15.5297i	−0.0837969	+	0.582820i
$711$	4.58526	−	2.94677i	0.171961	−	0.110512i
$712$	5.30787			0.198921
$713$	−27.8129	+	22.3640i	−1.04160	+	0.837537i
$714$	−8.73075			−0.326740
$715$	12.8314	−	8.24624i	0.479867	−	0.308392i
$716$	1.35189	−	9.40263i	0.0505227	−	0.351393i
$717$	4.20594	−	9.20972i	0.157074	−	0.343943i
$718$	28.9584	−	8.50294i	1.08072	−	0.317327i
$719$	−15.2511	−	33.3953i	−0.568771	−	1.24543i	−0.947449	−	0.319906i	$-0.896349\pi$
$719$	−15.2511	−	33.3953i	−0.568771	−	1.24543i	0.378678	−	0.925528i	$-0.376379\pi$
$720$	7.96283	+	9.18959i	0.296757	+	0.342476i
$721$	0.0370608	+	0.257764i	0.00138022	+	0.00959962i
$722$	−22.2220	−	6.52496i	−0.827016	−	0.242834i
$723$	13.2101	−	15.2452i	0.491288	−	0.566976i
$724$	5.94142	+	3.81832i	0.220811	+	0.141907i
$725$	7.80038	+	5.01300i	0.289699	+	0.186178i
$726$	−9.37680	+	10.8214i	−0.348006	+	0.401620i
$727$	−32.4087	−	9.51604i	−1.20197	−	0.352930i	−0.381365	−	0.924425i	$-0.624546\pi$
$727$	−32.4087	−	9.51604i	−1.20197	−	0.352930i	−0.820606	+	0.571494i	$0.806364\pi$
$728$	1.55742	+	10.8321i	0.0577216	+	0.401463i
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$	−20.7366	−	45.4068i	−0.767496	−	1.68058i
$731$	9.55492	−	2.80558i	0.353401	−	0.103768i
$732$	−2.50042	+	5.47515i	−0.0924181	+	0.202367i
$733$	−6.86590	+	47.7534i	−0.253598	+	1.76381i	0.322633	+	0.946524i	$0.395432\pi$
$733$	−6.86590	+	47.7534i	−0.253598	+	1.76381i	−0.576231	+	0.817287i	$0.695477\pi$
$734$	10.4034	−	6.68587i	0.383997	−	0.246780i
$735$	14.6231			0.539380
$736$	−3.52898	−	13.8885i	−0.130080	−	0.511938i
$737$	16.1845			0.596162
$738$	−6.17227	+	3.96668i	−0.227204	+	0.146015i
$739$	6.09629	−	42.4006i	0.224256	−	1.55973i	−0.497426	−	0.867507i	$-0.665721\pi$
$739$	6.09629	−	42.4006i	0.224256	−	1.55973i	0.721681	−	0.692226i	$-0.243370\pi$
$740$	−4.73017	+	10.3576i	−0.173884	+	0.380754i
$741$	23.4932	−	6.89823i	0.863045	−	0.253413i
$742$	7.68986	+	16.8384i	0.282304	+	0.618159i
$743$	19.8927	+	22.9574i	0.729791	+	0.842224i	0.992448	−	0.122665i	$-0.0391442\pi$
$743$	19.8927	+	22.9574i	0.729791	+	0.842224i	−0.262657	+	0.964889i	$0.584599\pi$
$744$	−2.46193	−	17.1231i	−0.0902587	−	0.627763i
$745$	−18.5098	−	5.43495i	−0.678145	−	0.199121i
$746$	20.5156	−	23.6762i	0.751128	−	0.866848i
$747$	−1.31553	−	0.845441i	−0.0481328	−	0.0309331i
$748$	3.18670	+	2.04797i	0.116517	+	0.0748811i
$749$	1.04641	−	1.20762i	0.0382350	−	0.0441255i
$750$	−13.8102	−	4.05503i	−0.504276	−	0.148069i
$751$	−2.45871	−	17.1007i	−0.0897196	−	0.624014i	−0.984220	−	0.176947i	$-0.943378\pi$
$751$	−2.45871	−	17.1007i	−0.0897196	−	0.624014i	0.894501	−	0.447067i	$-0.147531\pi$
$752$	8.21273	+	9.47800i	0.299487	+	0.345627i
$753$	6.64053	+	14.5407i	0.241995	+	0.529894i
$754$	41.5498	−	12.2001i	1.51316	−	0.444303i
$755$	12.6376	−	27.6725i	0.459930	−	1.00711i
$756$	−0.0858629	+	0.597190i	−0.00312280	+	0.0217196i
$757$	24.9051	−	16.0055i	0.905190	−	0.581730i	−0.00313505	−	0.999995i	$-0.500998\pi$
$757$	24.9051	−	16.0055i	0.905190	−	0.581730i	0.908325	+	0.418265i	$0.137362\pi$
$758$	−15.3247			−0.556618
$759$	6.70500	+	1.21714i	0.243376	+	0.0441793i
$760$	34.1675			1.23938
$761$	9.58484	−	6.15980i	0.347450	−	0.223293i	−0.355262	−	0.934767i	$-0.615608\pi$
$761$	9.58484	−	6.15980i	0.347450	−	0.223293i	0.702712	+	0.711474i	$0.251972\pi$
$762$	0.613007	−	4.26356i	0.0222069	−	0.154452i
$763$	6.59388	−	14.4386i	0.238715	−	0.522712i
$764$	−7.34139	+	2.15563i	−0.265602	+	0.0779879i
$765$	−5.18708	−	11.3581i	−0.187539	−	0.410654i
$766$	2.22422	+	2.56688i	0.0803642	+	0.0927453i
$767$	7.20889	+	50.1389i	0.260298	+	1.81041i
$768$	11.6464	+	3.41970i	0.420255	+	0.123398i
$769$	9.41495	−	10.8654i	0.339512	−	0.391818i	−0.560160	−	0.828384i	$-0.689260\pi$
$769$	9.41495	−	10.8654i	0.339512	−	0.391818i	0.899672	+	0.436567i	$0.143806\pi$
$770$	5.38570	+	3.46118i	0.194087	+	0.124732i
$771$	18.2686	+	11.7405i	0.657929	+	0.422825i
$772$	−4.31144	+	4.97567i	−0.155172	+	0.179078i
$773$	18.8601	+	5.53781i	0.678349	+	0.199181i	0.602718	−	0.797955i	$-0.294085\pi$
$773$	18.8601	+	5.53781i	0.678349	+	0.199181i	0.0756315	+	0.997136i	$0.475903\pi$
$774$	−0.459350	−	3.19485i	−0.0165110	−	0.114837i
$775$	−7.03514	−	8.11899i	−0.252710	−	0.291643i
$776$	8.45112	+	18.5054i	0.303378	+	0.664304i
$777$	8.84095	−	2.59594i	0.317167	−	0.0931288i
$778$	−22.1885	+	48.5860i	−0.795495	+	1.74189i
$779$	−3.79208	+	26.3745i	−0.135865	+	0.944964i
$780$	4.89399	−	3.14518i	0.175233	−	0.112615i
$781$	−5.50849			−0.197109
$782$	−1.38274	+	37.5863i	−0.0494467	+	1.34408i
$783$	−6.42297			−0.229538
$784$	23.2142	−	14.9189i	0.829079	−	0.532817i
$785$	−2.19021	+	15.2333i	−0.0781720	+	0.543698i
$786$	−4.68688	+	10.2628i	−0.167175	+	0.366063i
$787$	3.23609	−	0.950203i	0.115354	−	0.0338711i	−0.223546	−	0.974693i	$-0.571763\pi$
$787$	3.23609	−	0.950203i	0.115354	−	0.0338711i	0.338900	+	0.940822i	$0.389945\pi$
$788$	−0.986953	−	2.16113i	−0.0351587	−	0.0769869i
$789$	−10.5941	−	12.2263i	−0.377161	−	0.435267i
$790$	−3.13932	−	21.8345i	−0.111692	−	0.776836i
$791$	4.91085	+	1.44196i	0.174610	+	0.0512701i
$792$	−2.16311	+	2.49636i	−0.0768627	+	0.0887043i
$793$	−39.5095	−	25.3912i	−1.40302	−	0.901668i
$794$	29.3852	+	18.8847i	1.04284	+	0.670193i
$795$	−17.3370	+	20.0080i	−0.614881	+	0.709610i
$796$	−8.83348	−	2.59375i	−0.313095	−	0.0919329i
$797$	−5.63539	−	39.1950i	−0.199616	−	1.38836i	−0.805401	−	0.592731i	$-0.798050\pi$
$797$	−5.63539	−	39.1950i	−0.199616	−	1.38836i	0.605785	−	0.795629i	$-0.292859\pi$
$798$	6.73004	+	7.76689i	0.238241	+	0.274945i
$799$	−5.34987	−	11.7146i	−0.189265	−	0.414432i
$800$	4.13879	−	1.21526i	0.146328	−	0.0429659i
$801$	−0.948523	+	2.07698i	−0.0335144	+	0.0733864i
$802$	1.39598	−	9.70927i	0.0492939	−	0.342846i
$803$	14.7438	−	9.47524i	0.520296	−	0.334374i
$804$	6.17287			0.217700
$805$	−0.498240	+	13.5434i	−0.0175606	+	0.477341i
$806$	−50.1721			−1.76724
$807$	−1.63461	+	1.05050i	−0.0575410	+	0.0369794i
$808$	0.859856	−	5.98043i	0.0302496	−	0.210391i
$809$	−11.4426	+	25.0557i	−0.402299	+	0.880911i	0.594733	+	0.803923i	$0.297258\pi$
$809$	−11.4426	+	25.0557i	−0.402299	+	0.880911i	−0.997032	+	0.0769883i	$0.975470\pi$
$810$	−3.88321	+	1.14021i	−0.136442	+	0.0400630i
$811$	−21.5220	−	47.1265i	−0.755738	−	1.65484i	−0.755772	−	0.654835i	$-0.772738\pi$
$811$	−21.5220	−	47.1265i	−0.755738	−	1.65484i	3.37537e−5	−	1.00000i	$-0.499989\pi$
$812$	2.53770	+	2.92866i	0.0890558	+	0.102776i
$813$	0.704317	+	4.89863i	0.0247015	+	0.171803i
$814$	−17.9914	−	5.28276i	−0.630600	−	0.185161i
$815$	−27.7636	+	32.0409i	−0.972515	+	1.12234i
$816$	−19.8224	−	12.7391i	−0.693922	−	0.445957i
$817$	−9.86120	−	6.33741i	−0.345000	−	0.221718i
$818$	−3.84513	+	4.43752i	−0.134442	+	0.155154i
$819$	−4.51691	−	1.32628i	−0.157834	−	0.0463441i
$820$	0.900975	+	6.26642i	0.0314634	+	0.218833i
$821$	18.2431	+	21.0537i	0.636690	+	0.734779i	0.978786	−	0.204886i	$-0.0656823\pi$
$821$	18.2431	+	21.0537i	0.636690	+	0.734779i	−0.342096	+	0.939665i	$0.611137\pi$
$822$	3.21268	+	7.03479i	0.112055	+	0.245366i
$823$	2.61020	−	0.766425i	0.0909860	−	0.0267159i	−0.235923	−	0.971772i	$-0.575811\pi$
$823$	2.61020	−	0.766425i	0.0909860	−	0.0267159i	0.326909	+	0.945056i	$0.393993\pi$
$824$	−0.225897	+	0.494645i	−0.00786948	+	0.0172318i
$825$	−0.291930	+	2.03041i	−0.0101637	+	0.0706900i
$826$	−17.8860	+	11.4946i	−0.622333	+	0.399949i
$827$	−24.9432			−0.867361			−0.433680	−	0.901067i	$-0.642785\pi$
$827$	−24.9432			−0.867361			−0.433680	+	0.901067i	$0.642785\pi$
$828$	2.55733	+	0.464225i	0.0888735	+	0.0161329i
$829$	12.8583			0.446587			0.223294	−	0.974751i	$-0.428319\pi$
$829$	12.8583			0.446587			0.223294	+	0.974751i	$0.428319\pi$
$830$	−5.32415	+	3.42162i	−0.184804	+	0.118766i
$831$	2.90105	−	20.1773i	0.100636	−	0.699941i
$832$	−8.46099	+	18.5270i	−0.293332	+	0.642307i
$833$	−27.1889	+	7.98337i	−0.942038	+	0.276607i
$834$	13.3123	+	29.1498i	0.460966	+	1.00937i
$835$	−33.7760	−	38.9796i	−1.16887	−	1.34894i
$836$	−0.634573	−	4.41355i	−0.0219472	−	0.152646i
$837$	7.14024	+	2.09656i	0.246803	+	0.0724678i
$838$	−37.7020	+	43.5104i	−1.30239	+	1.50304i
$839$	−18.8338	−	12.1037i	−0.650215	−	0.417868i	0.173530	−	0.984829i	$-0.444483\pi$
$839$	−18.8338	−	12.1037i	−0.650215	−	0.417868i	−0.823745	+	0.566961i	$0.808119\pi$
$840$	−5.52635	−	3.55157i	−0.190677	−	0.122541i
$841$	−8.02501	+	9.26136i	−0.276725	+	0.319357i
$842$	29.7094	+	8.72348i	1.02386	+	0.300631i
$843$	−2.93904	−	20.4415i	−0.101226	−	0.704043i
$844$	2.52157	+	2.91004i	0.0867959	+	0.100168i
$845$	5.14804	+	11.2726i	0.177098	+	0.387790i
$846$	−4.00508	+	1.17600i	−0.137697	+	0.0404316i
$847$	4.15332	−	9.09451i	0.142710	−	0.312491i
$848$	−7.10991	+	49.4505i	−0.244155	+	1.69814i
$849$	14.2026	−	9.12747i	0.487433	−	0.313254i
$850$	−11.3217			−0.388332
$851$	−9.77545	−	38.4719i	−0.335098	−	1.31880i
$852$	−2.10098			−0.0719783
$853$	−14.5528	+	9.35253i	−0.498279	+	0.320225i	−0.765528	−	0.643403i	$-0.777522\pi$
$853$	−14.5528	+	9.35253i	−0.498279	+	0.320225i	0.267248	+	0.963628i	$0.413886\pi$
$854$	2.80539	−	19.5119i	0.0959984	−	0.667683i
$855$	−6.10577	+	13.3698i	−0.208813	+	0.457236i
$856$	3.20153	−	0.940053i	0.109426	−	0.0321304i
$857$	−16.9466	−	37.1078i	−0.578884	−	1.26758i	−0.941931	−	0.335808i	$-0.890991\pi$
$857$	−16.9466	−	37.1078i	−0.578884	−	1.26758i	0.363047	−	0.931771i	$-0.381737\pi$
$858$	6.27358	+	7.24009i	0.214176	+	0.247173i
$859$	0.928129	+	6.45528i	0.0316674	+	0.220251i	0.999510	−	0.0313056i	$-0.00996651\pi$
$859$	0.928129	+	6.45528i	0.0316674	+	0.220251i	−0.967842	+	0.251557i	$0.919057\pi$
$860$	−2.67227	−	0.784649i	−0.0911236	−	0.0267563i
$861$	3.35486	−	3.87172i	0.114333	−	0.131948i
$862$	6.88419	+	4.42420i	0.234477	+	0.150689i
$863$	−5.31084	−	3.41307i	−0.180783	−	0.116182i	0.447119	−	0.894474i	$-0.352450\pi$
$863$	−5.31084	−	3.41307i	−0.180783	−	0.116182i	−0.627902	+	0.778292i	$0.716086\pi$
$864$	−1.95671	+	2.25817i	−0.0665687	+	0.0768244i
$865$	4.72962	+	1.38874i	0.160812	+	0.0472186i
$866$	3.76121	+	26.1598i	0.127811	+	0.888945i
$867$	4.71265	+	5.43869i	0.160050	+	0.184708i
$868$	−1.86513	−	4.08406i	−0.0633065	−	0.138622i
$869$	7.43110	−	2.18197i	0.252083	−	0.0740182i
$870$	−10.7986	+	23.6456i	−0.366106	+	0.801661i
$871$	−6.85459	+	47.6747i	−0.232259	+	1.61540i
$872$	27.8836	−	17.9197i	0.944258	−	0.606838i
$873$	−8.75140			−0.296190
$874$	34.5027	−	27.7431i	1.16707	−	0.938425i
$875$	10.0500			0.339751
$876$	5.62338	−	3.61393i	0.189996	−	0.122103i
$877$	−5.81597	+	40.4510i	−0.196391	+	1.36593i	0.618256	+	0.785977i	$0.287839\pi$
$877$	−5.81597	+	40.4510i	−0.196391	+	1.36593i	−0.814648	+	0.579956i	$0.803070\pi$
$878$	0.829810	−	1.81703i	0.0280047	−	0.0613218i
$879$	−17.9061	+	5.25771i	−0.603958	+	0.177338i
$880$	7.17753	+	15.7166i	0.241955	+	0.529806i
$881$	−1.52108	−	1.75542i	−0.0512464	−	0.0591415i	0.729548	−	0.683930i	$-0.239731\pi$
$881$	−1.52108	−	1.75542i	−0.0512464	−	0.0591415i	−0.780794	+	0.624789i	$0.785185\pi$
$882$	1.30710	+	9.09106i	0.0440123	+	0.306112i
$883$	29.7689	+	8.74095i	1.00180	+	0.294156i	0.741196	−	0.671288i	$-0.234259\pi$
$883$	29.7689	+	8.74095i	1.00180	+	0.294156i	0.260608	+	0.965445i	$0.416077\pi$
$884$	−7.38237	+	8.51971i	−0.248296	+	0.286549i
$885$	−25.5801	−	16.4393i	−0.859866	−	0.552602i
$886$	−28.5644	−	18.3572i	−0.959638	−	0.616722i
$887$	26.3245	−	30.3800i	0.883889	−	1.02006i	−0.115752	−	0.993278i	$-0.536928\pi$
$887$	26.3245	−	30.3800i	0.883889	−	1.02006i	0.999641	−	0.0267839i	$-0.00852660\pi$
$888$	18.4613	+	5.42072i	0.619520	+	0.181908i
$889$	0.428029	+	2.97701i	0.0143556	+	0.0998457i
$890$	6.05151	+	6.98381i	0.202847	+	0.234098i
$891$	−0.590278	−	1.29253i	−0.0197751	−	0.0433014i
$892$	2.65254	−	0.778855i	0.0888135	−	0.0260780i
$893$	−6.29739	+	13.7894i	−0.210734	+	0.461444i
$894$	1.72436	−	11.9932i	0.0576712	−	0.401112i
$895$	−37.4301	+	24.0548i	−1.25115	+	0.804065i
$896$	−15.2016			−0.507849
$897$	−6.42509	+	19.2355i	−0.214528	+	0.642254i
$898$	−13.1814			−0.439869
$899$	40.2100	−	25.8414i	1.34108	−	0.861858i
$900$	−0.111344	+	0.774415i	−0.00371147	+	0.0258138i
$901$	21.3117	−	46.6661i	0.709996	−	1.55467i
$902$	−10.0031	+	2.93717i	−0.333067	+	0.0977972i
$903$	0.936232	+	2.05006i	0.0311559	+	0.0682218i
$904$	6.99885	+	8.07711i	0.232778	+	0.268641i
$905$	−4.70777	−	32.7433i	−0.156492	−	1.08842i
$906$	18.3334	+	5.38319i	0.609088	+	0.178844i
$907$	22.4383	−	25.8952i	0.745052	−	0.859836i	−0.249027	−	0.968497i	$-0.580111\pi$
$907$	22.4383	−	25.8952i	0.745052	−	0.859836i	0.994079	+	0.108661i	$0.0346562\pi$
$908$	−6.37234	−	4.09525i	−0.211473	−	0.135906i
$909$	2.18649	+	1.40517i	0.0725213	+	0.0466066i
$910$	−12.4766	+	14.3988i	−0.413596	+	0.477316i
$911$	45.0429	+	13.2258i	1.49234	+	0.438190i	0.923287	−	0.384112i	$-0.125492\pi$
$911$	45.0429	+	13.2258i	1.49234	+	0.438190i	0.569052	+	0.822302i	$0.307310\pi$
$912$	3.94727	+	27.4539i	0.130707	+	0.909088i
$913$	−1.45512	−	1.67930i	−0.0481574	−	0.0555766i
$914$	−10.1416	−	22.2070i	−0.335454	−	0.734542i
$915$	27.0504	−	7.94271i	0.894258	−	0.262578i
$916$	0.571223	−	1.25080i	0.0188737	−	0.0413277i
$917$	1.12114	−	7.79769i	0.0370233	−	0.257503i
$918$	6.59761	−	4.24002i	0.217753	−	0.139942i
$919$	4.61902			0.152367			0.0761837	−	0.997094i	$-0.475726\pi$
$919$	4.61902			0.152367			0.0761837	+	0.997094i	$0.475726\pi$
$920$	−16.1649	+	23.2287i	−0.532942	+	0.765829i
$921$	11.1163			0.366296
$922$	38.4606	−	24.7171i	1.26663	−	0.814016i
$923$	2.33301	−	16.2264i	0.0767918	−	0.534099i
$924$	−0.356133	+	0.779823i	−0.0117159	+	0.0256543i
$925$	11.4646	−	3.36632i	0.376955	−	0.110684i
$926$	−19.6436	−	43.0134i	−0.645528	−	1.41351i
$927$	−0.153187	−	0.176787i	−0.00503132	−	0.00580645i
$928$	2.73127	+	18.9964i	0.0896583	+	0.623587i
$929$	−9.97941	−	2.93022i	−0.327414	−	0.0961374i	0.113895	−	0.993493i	$-0.463667\pi$
$929$	−9.97941	−	2.93022i	−0.327414	−	0.0961374i	−0.441309	+	0.897355i	$0.645486\pi$
$930$	19.7228	−	22.7613i	0.646736	−	0.746374i
$931$	28.0604	+	18.0333i	0.919642	+	0.591018i
$932$	0.560575	+	0.360260i	0.0183622	+	0.0118007i
$933$	−3.63667	+	4.19694i	−0.119059	+	0.137402i
$934$	45.4119	+	13.3341i	1.48592	+	0.436306i
$935$	−2.52502	−	17.5619i	−0.0825771	−	0.574336i
$936$	−6.43741	−	7.42917i	−0.210413	−	0.242830i
$937$	−17.1835	−	37.6266i	−0.561360	−	1.22921i	−0.951272	−	0.308354i	$-0.900222\pi$
$937$	−17.1835	−	37.6266i	−0.561360	−	1.22921i	0.389912	−	0.920852i	$-0.372506\pi$
$938$	−19.3973	+	5.69556i	−0.633344	+	0.185967i
$939$	−4.91124	+	10.7541i	−0.160272	+	0.350947i
$940$	−0.512583	+	3.56509i	−0.0167186	+	0.116281i
$941$	14.8142	−	9.52049i	0.482928	−	0.310359i	−0.276428	−	0.961035i	$-0.589151\pi$
$941$	14.8142	−	9.52049i	0.482928	−	0.310359i	0.759356	+	0.650676i	$0.225514\pi$
$942$	−9.66618			−0.314941
$943$	−16.1366	−	15.0560i	−0.525481	−	0.490292i
$944$	−57.3804			−1.86757
$945$	2.37730	−	1.52780i	0.0773335	−	0.0496992i
$946$	0.652707	−	4.53968i	0.0212213	−	0.147598i
$947$	21.7975	−	47.7299i	0.708324	−	1.55101i	−0.121254	−	0.992622i	$-0.538691\pi$
$947$	21.7975	−	47.7299i	0.708324	−	1.55101i	0.829578	−	0.558391i	$-0.188581\pi$
$948$	2.83428	−	0.832219i	0.0920531	−	0.0270292i
$949$	21.6669	+	47.4439i	0.703337	+	1.54009i
$950$	8.72729	+	10.0718i	0.283151	+	0.326773i
$951$	4.83787	+	33.6481i	0.156879	+	1.09112i
$952$	12.2142	+	3.58640i	0.395863	+	0.116236i
$953$	−30.7502	+	35.4876i	−0.996095	+	1.14956i	−0.00734579	+	0.999973i	$0.502338\pi$
$953$	−30.7502	+	35.4876i	−0.996095	+	1.14956i	−0.988749	+	0.149582i	$0.952207\pi$
$954$	−13.9885	−	8.98987i	−0.452895	−	0.291058i
$955$	30.1484	+	19.3752i	0.975581	+	0.626968i
$956$	3.59330	−	4.14689i	0.116216	−	0.134120i
$957$	−8.75694	−	2.57127i	−0.283072	−	0.0831173i
$958$	0.579956	+	4.03369i	0.0187375	+	0.130322i
$959$	−3.53624	−	4.08104i	−0.114191	−	0.131784i
$960$	−5.07900	−	11.1215i	−0.163924	−	0.358944i
$961$	−23.3911	+	6.86823i	−0.754550	+	0.221556i
$962$	23.1814	−	50.7601i	0.747398	−	1.63657i
$963$	−0.204273	+	1.42075i	−0.00658260	+	0.0457830i
$964$	9.19701	−	5.91056i	0.296216	−	0.190366i
$965$	30.8372			0.992684
$966$	−8.46436	+	0.900836i	−0.272336	+	0.0289839i
$967$	−15.7485			−0.506439			−0.253220	−	0.967409i	$-0.581490\pi$
$967$	−15.7485			−0.506439			−0.253220	+	0.967409i	$0.581490\pi$
$968$	17.5632	−	11.2872i	0.564502	−	0.362784i
$969$	4.05340	−	28.1920i	0.130214	−	0.905657i
$970$	−14.7133	+	32.2175i	−0.472414	+	1.03444i
$971$	−12.6784	+	3.72271i	−0.406868	+	0.119467i	−0.478761	−	0.877945i	$-0.658914\pi$
$971$	−12.6784	+	3.72271i	−0.406868	+	0.119467i	0.0718932	+	0.997412i	$0.477096\pi$
$972$	−0.225136	−	0.492980i	−0.00722126	−	0.0158123i
$973$	−14.6530	−	16.9105i	−0.469754	−	0.542124i
$974$	−7.35883	−	51.1818i	−0.235792	−	1.63997i
$975$	−5.85737	−	1.71988i	−0.187586	−	0.0550802i
$976$	34.8393	−	40.2067i	1.11518	−	1.28698i
$977$	50.0734	+	32.1802i	1.60199	+	1.02954i	0.966241	+	0.257638i	$0.0829443\pi$
$977$	50.0734	+	32.1802i	1.60199	+	1.02954i	0.635747	+	0.771897i	$0.280692\pi$
$978$	−22.4012	−	14.3964i	−0.716313	−	0.460346i
$979$	−2.12466	+	2.45199i	−0.0679044	+	0.0783659i
$980$	7.60404	+	2.23275i	0.242902	+	0.0713225i
$981$	2.02916	+	14.1131i	0.0647862	+	0.450598i
$982$	6.35794	+	7.33745i	0.202890	+	0.234148i
$983$	16.7585	+	36.6960i	0.534513	+	1.17042i	0.963647	+	0.267180i	$0.0860917\pi$
$983$	16.7585	+	36.6960i	0.534513	+	1.17042i	−0.429133	+	0.903241i	$0.641181\pi$
$984$	10.2643	−	3.01388i	0.327215	−	0.0960790i
$985$	−4.62272	+	10.1223i	−0.147292	+	0.322525i
$986$	7.16879	−	49.8600i	0.228301	−	1.58787i
$987$	2.45191	−	1.57575i	0.0780451	−	0.0501565i
$988$	13.2698			0.422169
$989$	8.97391	−	3.70585i	0.285354	−	0.117839i
$990$	−5.75074			−0.182770
$991$	−8.33633	+	5.35743i	−0.264812	+	0.170184i	−0.666309	−	0.745676i	$-0.732127\pi$
$991$	−8.33633	+	5.35743i	−0.264812	+	0.170184i	0.401496	+	0.915861i	$0.368490\pi$
$992$	3.16446	−	22.0093i	0.100472	−	0.698795i
$993$	2.75604	−	6.03488i	0.0874602	−	0.191511i
$994$	6.60200	−	1.93852i	0.209403	−	0.0614862i
$995$	17.9132	+	39.2245i	0.567887	+	1.24350i
$996$	−0.554993	−	0.640496i	−0.0175856	−	0.0202949i
$997$	2.26237	+	15.7351i	0.0716499	+	0.498336i	0.993772	+	0.111436i	$0.0355450\pi$
$997$	2.26237	+	15.7351i	0.0716499	+	0.498336i	−0.922122	+	0.386900i	$0.873546\pi$
$998$	−31.2676	−	9.18100i	−0.989759	−	0.290619i
$999$	−5.42019	+	6.25523i	−0.171487	+	0.197907i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.2.e.b.58.1	yes	10
3.2	odd	2		207.2.i.a.127.1		10
23.2	even	11	inner	69.2.e.b.25.1	✓	10
23.5	odd	22		1587.2.a.r.1.4		5
23.18	even	11		1587.2.a.q.1.4		5
69.2	odd	22		207.2.i.a.163.1		10
69.5	even	22		4761.2.a.bm.1.2		5
69.41	odd	22		4761.2.a.bp.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.b.25.1	✓	10	23.2	even	11	inner
69.2.e.b.58.1	yes	10	1.1	even	1	trivial
207.2.i.a.127.1		10	3.2	odd	2
207.2.i.a.163.1		10	69.2	odd	22
1587.2.a.q.1.4		5	23.18	even	11
1587.2.a.r.1.4		5	23.5	odd	22
4761.2.a.bm.1.2		5	69.5	even	22
4761.2.a.bp.1.2		5	69.41	odd	22

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:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	69.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34125 - 0.861971i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.225136 - 0.492980i) q^{4} +(-2.43560 + 0.715158i) q^{5} +(-0.662317 - 1.45027i) q^{6} +(0.729022 + 0.841336i) q^{7} +(0.330830 + 2.30097i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(1.34125 - 0.861971i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.225136 - 0.492980i) q^{4} +(-2.43560 + 0.715158i) q^{5} +(-0.662317 - 1.45027i) q^{6} +(0.729022 + 0.841336i) q^{7} +(0.330830 + 2.30097i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(-2.65032 + 3.05863i) q^{10} +(-1.19537 - 0.768216i) q^{11} +(-0.455922 - 0.293003i) q^{12} +(2.76921 - 3.19584i) q^{13} +(1.70301 + 0.500049i) q^{14} +(0.361256 + 2.51259i) q^{15} +(3.13691 + 3.62019i) q^{16} +(-2.04342 - 4.47447i) q^{17} +(-1.52977 + 0.449181i) q^{18} +(-2.40533 + 5.26695i) q^{19} +(-0.195785 + 1.36171i) q^{20} +(0.936524 - 0.601867i) q^{21} -2.26547 q^{22} +(-2.44275 - 4.12710i) q^{23} +2.32463 q^{24} +(1.21445 - 0.780481i) q^{25} +(0.959493 - 6.67342i) q^{26} +(-0.415415 + 0.909632i) q^{27} +(0.578892 - 0.169978i) q^{28} +(2.66820 + 5.84254i) q^{29} +(2.65032 + 3.05863i) q^{30} +(-1.05906 - 7.36593i) q^{31} +(2.86695 + 0.841812i) q^{32} +(-0.930515 + 1.07387i) q^{33} +(-6.59761 - 4.24002i) q^{34} +(-2.37730 - 1.52780i) q^{35} +(-0.354905 + 0.409583i) q^{36} +(7.94159 + 2.33186i) q^{37} +(1.31379 + 9.13764i) q^{38} +(-2.76921 - 3.19584i) q^{39} +(-2.45133 - 5.36767i) q^{40} +(4.41546 - 1.29650i) q^{41} +(0.737323 - 1.61451i) q^{42} +(-0.288111 + 2.00386i) q^{43} +(-0.647836 + 0.416339i) q^{44} +2.53843 q^{45} +(-6.83379 - 3.42992i) q^{46} +2.61810 q^{47} +(4.02977 - 2.58978i) q^{48} +(0.819830 - 5.70204i) q^{49} +(0.956135 - 2.09364i) q^{50} +(-4.71973 + 1.38584i) q^{51} +(-0.952036 - 2.08467i) q^{52} +(6.82982 + 7.88203i) q^{53} +(0.226900 + 1.57812i) q^{54} +(3.46084 + 1.01619i) q^{55} +(-1.69471 + 1.95580i) q^{56} +(4.87102 + 3.13042i) q^{57} +(8.61483 + 5.53642i) q^{58} +(-7.84439 + 9.05291i) q^{59} +(1.31999 + 0.387584i) q^{60} +(-1.58058 - 10.9932i) q^{61} +(-7.76969 - 8.96670i) q^{62} +(-0.462460 - 1.01265i) q^{63} +(-4.62139 + 1.35696i) q^{64} +(-4.45918 + 9.76424i) q^{65} +(-0.322410 + 2.24241i) q^{66} +(-9.58188 + 6.15790i) q^{67} -2.66587 q^{68} +(-4.43274 + 1.83053i) q^{69} -4.50548 q^{70} +(3.26126 - 2.09588i) q^{71} +(0.330830 - 2.30097i) q^{72} +(-5.12376 + 11.2195i) q^{73} +(12.6617 - 3.71780i) q^{74} +(-0.599702 - 1.31316i) q^{75} +(2.05497 + 2.37156i) q^{76} +(-0.225121 - 1.56575i) q^{77} +(-6.46894 - 1.89945i) q^{78} +(-3.56932 + 4.11922i) q^{79} +(-10.2293 - 6.57396i) q^{80} +(0.841254 + 0.540641i) q^{81} +(4.80471 - 5.54493i) q^{82} +(1.50043 + 0.440567i) q^{83} +(-0.0858629 - 0.597190i) q^{84} +(8.17692 + 9.43666i) q^{85} +(1.34084 + 2.93602i) q^{86} +(6.16279 - 1.80956i) q^{87} +(1.37218 - 3.00466i) q^{88} +(0.324950 - 2.26007i) q^{89} +(3.40468 - 2.18805i) q^{90} +4.70760 q^{91} +(-2.58453 + 0.275064i) q^{92} -7.44168 q^{93} +(3.51153 - 2.25672i) q^{94} +(2.09174 - 14.5484i) q^{95} +(1.24125 - 2.71797i) q^{96} +(8.39691 - 2.46555i) q^{97} +(-3.81540 - 8.35456i) q^{98} +(0.930515 + 1.07387i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} + q^{3} - 14 q^{4} - 3 q^{5} - 4 q^{6} + 6 q^{7} - 7 q^{8} - q^{9}+O(q^{10}) \) 10 * q + 4 * q^2 + q^3 - 14 * q^4 - 3 * q^5 - 4 * q^6 + 6 * q^7 - 7 * q^8 - q^9	\( 10 q + 4 q^{2} + q^{3} - 14 q^{4} - 3 q^{5} - 4 q^{6} + 6 q^{7} - 7 q^{8} - q^{9} + 12 q^{10} - 15 q^{11} - 8 q^{12} + 8 q^{13} + 9 q^{14} - 8 q^{15} + 12 q^{16} + q^{17} + 4 q^{18} - 9 q^{19} - 9 q^{20} + 5 q^{21} - 28 q^{22} + 21 q^{23} + 18 q^{24} - 4 q^{25} + q^{26} + q^{27} + 29 q^{28} - 8 q^{29} - 12 q^{30} - 23 q^{31} - q^{32} + 4 q^{33} - 15 q^{34} + 18 q^{35} + 8 q^{36} + 3 q^{37} + 3 q^{38} - 8 q^{39} - 32 q^{40} - 15 q^{41} + 13 q^{42} + 22 q^{43} - q^{44} - 14 q^{45} + 26 q^{46} + 4 q^{47} + 21 q^{48} - 29 q^{49} + 49 q^{50} - 12 q^{51} + 2 q^{52} + 29 q^{53} + 7 q^{54} + 43 q^{55} - 2 q^{56} + 20 q^{57} + 21 q^{58} - 54 q^{59} - 2 q^{60} - 30 q^{61} - 7 q^{62} + 6 q^{63} - 31 q^{64} - 9 q^{65} - 27 q^{66} + q^{67} - 30 q^{68} + q^{69} - 94 q^{70} - 3 q^{71} - 7 q^{72} - 47 q^{73} - 12 q^{74} + 15 q^{75} + 50 q^{76} + 13 q^{77} - 12 q^{78} + 18 q^{79} + 3 q^{80} - q^{81} - 28 q^{82} + 18 q^{83} + 4 q^{84} + 58 q^{85} + 8 q^{87} + 16 q^{88} + 25 q^{89} + q^{90} + 18 q^{91} - 3 q^{92} - 10 q^{93} + 39 q^{94} - 16 q^{95} - 21 q^{96} + 21 q^{97} - 27 q^{98} - 4 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 + q^3 - 14 * q^4 - 3 * q^5 - 4 * q^6 + 6 * q^7 - 7 * q^8 - q^9 + 12 * q^10 - 15 * q^11 - 8 * q^12 + 8 * q^13 + 9 * q^14 - 8 * q^15 + 12 * q^16 + q^17 + 4 * q^18 - 9 * q^19 - 9 * q^20 + 5 * q^21 - 28 * q^22 + 21 * q^23 + 18 * q^24 - 4 * q^25 + q^26 + q^27 + 29 * q^28 - 8 * q^29 - 12 * q^30 - 23 * q^31 - q^32 + 4 * q^33 - 15 * q^34 + 18 * q^35 + 8 * q^36 + 3 * q^37 + 3 * q^38 - 8 * q^39 - 32 * q^40 - 15 * q^41 + 13 * q^42 + 22 * q^43 - q^44 - 14 * q^45 + 26 * q^46 + 4 * q^47 + 21 * q^48 - 29 * q^49 + 49 * q^50 - 12 * q^51 + 2 * q^52 + 29 * q^53 + 7 * q^54 + 43 * q^55 - 2 * q^56 + 20 * q^57 + 21 * q^58 - 54 * q^59 - 2 * q^60 - 30 * q^61 - 7 * q^62 + 6 * q^63 - 31 * q^64 - 9 * q^65 - 27 * q^66 + q^67 - 30 * q^68 + q^69 - 94 * q^70 - 3 * q^71 - 7 * q^72 - 47 * q^73 - 12 * q^74 + 15 * q^75 + 50 * q^76 + 13 * q^77 - 12 * q^78 + 18 * q^79 + 3 * q^80 - q^81 - 28 * q^82 + 18 * q^83 + 4 * q^84 + 58 * q^85 + 8 * q^87 + 16 * q^88 + 25 * q^89 + q^90 + 18 * q^91 - 3 * q^92 - 10 * q^93 + 39 * q^94 - 16 * q^95 - 21 * q^96 + 21 * q^97 - 27 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more