LMFDB - Embedded newform 49.2.e.b.29.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,2,Mod(8,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([12]))

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

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

chi := DirichletCharacter("49.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	49.e (of order $7$, degree $6$, 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:	$0.391266969904$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{7})$
Coefficient field:	$\Q(\zeta_{21})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + x^{9} - x^{8} + x^{6} - x^{4} + x^{3} - x + 1 $ x^12 - x^11 + x^9 - x^8 + x^6 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			29.1
Root			$0.0747301 + 0.997204i$ of defining polynomial
Character	$\chi$	$=$	49.29
Dual form			49.2.e.b.22.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.78181 - 0.858075i) q^{2} +(0.590232 + 2.58597i) q^{3} +(1.19158 + 1.49419i) q^{4} +(0.359497 + 1.57506i) q^{5} +(1.16728 - 5.11418i) q^{6} +(1.95991 - 1.77729i) q^{7} +(0.0391023 + 0.171318i) q^{8} +(-3.63598 + 1.75100i) q^{9} +O(q^{10})$	\(q+(-1.78181 - 0.858075i) q^{2} +(0.590232 + 2.58597i) q^{3} +(1.19158 + 1.49419i) q^{4} +(0.359497 + 1.57506i) q^{5} +(1.16728 - 5.11418i) q^{6} +(1.95991 - 1.77729i) q^{7} +(0.0391023 + 0.171318i) q^{8} +(-3.63598 + 1.75100i) q^{9} +(0.710963 - 3.11493i) q^{10} +(-3.98899 - 1.92100i) q^{11} +(-3.16064 + 3.96332i) q^{12} +(1.03563 + 0.498732i) q^{13} +(-5.01723 + 1.48506i) q^{14} +(-3.86087 + 1.85930i) q^{15} +(0.927871 - 4.06527i) q^{16} +(4.05008 - 5.07864i) q^{17} +7.98112 q^{18} -1.87680 q^{19} +(-1.92507 + 2.41397i) q^{20} +(5.75283 + 4.01925i) q^{21} +(5.45927 + 6.84570i) q^{22} +(-0.184292 - 0.231095i) q^{23} +(-0.419945 + 0.202235i) q^{24} +(2.15327 - 1.03696i) q^{25} +(-1.41734 - 1.77729i) q^{26} +(-1.71273 - 2.14769i) q^{27} +(4.99100 + 0.810692i) q^{28} +(1.70387 - 2.13658i) q^{29} +8.47477 q^{30} -5.93520 q^{31} +(-4.92247 + 6.17259i) q^{32} +(2.61322 - 11.4493i) q^{33} +(-11.5743 + 5.57391i) q^{34} +(3.50392 + 2.44803i) q^{35} +(-6.94889 - 3.34641i) q^{36} +(-5.66584 + 7.10474i) q^{37} +(3.34411 + 1.61044i) q^{38} +(-0.678448 + 2.97247i) q^{39} +(-0.255779 + 0.123177i) q^{40} +(0.655181 + 2.87054i) q^{41} +(-6.80165 - 12.0979i) q^{42} +(-0.200509 + 0.878488i) q^{43} +(-1.88286 - 8.24934i) q^{44} +(-4.06505 - 5.09741i) q^{45} +(0.130077 + 0.569904i) q^{46} +(1.53276 + 0.738138i) q^{47} +11.0603 q^{48} +(0.682458 - 6.96665i) q^{49} -4.72652 q^{50} +(15.5237 + 7.47584i) q^{51} +(0.488831 + 2.14171i) q^{52} +(-1.35041 - 1.69336i) q^{53} +(1.20888 + 5.29644i) q^{54} +(1.59165 - 6.97348i) q^{55} +(0.381119 + 0.266271i) q^{56} +(-1.10775 - 4.85337i) q^{57} +(-4.86932 + 2.34494i) q^{58} +(-0.611266 + 2.67813i) q^{59} +(-7.37869 - 3.55339i) q^{60} +(-2.01709 + 2.52936i) q^{61} +(10.5754 + 5.09285i) q^{62} +(-4.01415 + 9.89400i) q^{63} +(6.55372 - 3.15610i) q^{64} +(-0.413227 + 1.81047i) q^{65} +(-14.4806 + 18.1581i) q^{66} -3.33572 q^{67} +12.4145 q^{68} +(0.488831 - 0.612974i) q^{69} +(-4.14273 - 7.36856i) q^{70} +(-7.37877 - 9.25269i) q^{71} +(-0.442153 - 0.554442i) q^{72} +(5.15719 - 2.48357i) q^{73} +(16.1919 - 7.79760i) q^{74} +(3.95249 + 4.95626i) q^{75} +(-2.23636 - 2.80431i) q^{76} +(-11.2322 + 3.32463i) q^{77} +(3.75947 - 4.71423i) q^{78} -10.5153 q^{79} +6.73660 q^{80} +(-3.00556 + 3.76885i) q^{81} +(1.29573 - 5.67695i) q^{82} +(-6.48731 + 3.12412i) q^{83} +(0.849421 + 13.3851i) q^{84} +(9.45515 + 4.55336i) q^{85} +(1.11108 - 1.39325i) q^{86} +(6.53082 + 3.14508i) q^{87} +(0.173123 - 0.758501i) q^{88} +(12.2554 - 5.90189i) q^{89} +(2.86919 + 12.5707i) q^{90} +(2.91613 - 0.863147i) q^{91} +(0.125702 - 0.550736i) q^{92} +(-3.50314 - 15.3483i) q^{93} +(-2.09771 - 2.63045i) q^{94} +(-0.674705 - 2.95608i) q^{95} +(-18.8675 - 9.08613i) q^{96} +3.26934 q^{97} +(-7.19392 + 11.8277i) q^{98} +17.8676 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + 2 q^{4} - 7 q^{5} - 7 q^{6} - 7 q^{7} + 6 q^{8} - 8 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 + 2 * q^4 - 7 * q^5 - 7 * q^6 - 7 * q^7 + 6 * q^8 - 8 * q^9	\( 12 q - 2 q^{2} + 2 q^{4} - 7 q^{5} - 7 q^{6} - 7 q^{7} + 6 q^{8} - 8 q^{9} + 14 q^{10} - 8 q^{11} - 14 q^{12} + 7 q^{13} - 28 q^{14} - 7 q^{15} + 16 q^{16} + 20 q^{18} - 14 q^{19} + 7 q^{20} + 21 q^{21} + 13 q^{22} - 2 q^{23} + 3 q^{25} - 7 q^{26} + 21 q^{27} + 14 q^{28} - 11 q^{29} + 42 q^{30} - 14 q^{31} - 24 q^{32} + 35 q^{33} - 42 q^{34} + 21 q^{35} - 13 q^{36} - 30 q^{37} + 21 q^{38} + 21 q^{41} - 35 q^{42} + 17 q^{43} - 6 q^{44} - 49 q^{45} - 16 q^{46} - 21 q^{47} + 7 q^{49} - 46 q^{50} + 7 q^{51} - 7 q^{52} + 6 q^{53} + 42 q^{54} - 28 q^{55} - 14 q^{56} + 7 q^{57} - 32 q^{58} + 14 q^{59} - 28 q^{60} - 7 q^{61} + 56 q^{62} + 14 q^{63} + 14 q^{64} + 14 q^{65} - 28 q^{66} + 48 q^{67} + 56 q^{68} - 7 q^{69} + 21 q^{70} - 39 q^{71} - 4 q^{72} + 42 q^{73} + 61 q^{74} + 7 q^{75} - 28 q^{76} + 21 q^{77} - 16 q^{79} + 42 q^{80} - 25 q^{81} + 28 q^{82} - 7 q^{83} + 42 q^{84} + 28 q^{85} + 17 q^{86} + 7 q^{87} - 11 q^{88} - 14 q^{89} - 14 q^{90} - 21 q^{91} + 16 q^{92} - 70 q^{93} - 49 q^{94} - 7 q^{95} - 70 q^{96} - 28 q^{97} - 28 q^{98} - 18 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 + 2 * q^4 - 7 * q^5 - 7 * q^6 - 7 * q^7 + 6 * q^8 - 8 * q^9 + 14 * q^10 - 8 * q^11 - 14 * q^12 + 7 * q^13 - 28 * q^14 - 7 * q^15 + 16 * q^16 + 20 * q^18 - 14 * q^19 + 7 * q^20 + 21 * q^21 + 13 * q^22 - 2 * q^23 + 3 * q^25 - 7 * q^26 + 21 * q^27 + 14 * q^28 - 11 * q^29 + 42 * q^30 - 14 * q^31 - 24 * q^32 + 35 * q^33 - 42 * q^34 + 21 * q^35 - 13 * q^36 - 30 * q^37 + 21 * q^38 + 21 * q^41 - 35 * q^42 + 17 * q^43 - 6 * q^44 - 49 * q^45 - 16 * q^46 - 21 * q^47 + 7 * q^49 - 46 * q^50 + 7 * q^51 - 7 * q^52 + 6 * q^53 + 42 * q^54 - 28 * q^55 - 14 * q^56 + 7 * q^57 - 32 * q^58 + 14 * q^59 - 28 * q^60 - 7 * q^61 + 56 * q^62 + 14 * q^63 + 14 * q^64 + 14 * q^65 - 28 * q^66 + 48 * q^67 + 56 * q^68 - 7 * q^69 + 21 * q^70 - 39 * q^71 - 4 * q^72 + 42 * q^73 + 61 * q^74 + 7 * q^75 - 28 * q^76 + 21 * q^77 - 16 * q^79 + 42 * q^80 - 25 * q^81 + 28 * q^82 - 7 * q^83 + 42 * q^84 + 28 * q^85 + 17 * q^86 + 7 * q^87 - 11 * q^88 - 14 * q^89 - 14 * q^90 - 21 * q^91 + 16 * q^92 - 70 * q^93 - 49 * q^94 - 7 * q^95 - 70 * q^96 - 28 * q^97 - 28 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{3}{7}\right)$

Coefficient data

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

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

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

$2$	−1.78181	−	0.858075i	−1.25993	−	0.606751i	−0.319775	−	0.947494i	$-0.603607\pi$
$2$	−1.78181	−	0.858075i	−1.25993	−	0.606751i	−0.940157	+	0.340743i	$0.889321\pi$
$3$	0.590232	+	2.58597i	0.340770	+	1.49301i	0.797452	+	0.603383i	$0.206181\pi$
$3$	0.590232	+	2.58597i	0.340770	+	1.49301i	−0.456681	+	0.889630i	$0.650962\pi$
$4$	1.19158	+	1.49419i	0.595790	+	0.747097i
$5$	0.359497	+	1.57506i	0.160772	+	0.704388i	0.989476	+	0.144700i	$0.0462217\pi$
$5$	0.359497	+	1.57506i	0.160772	+	0.704388i	−0.828704	+	0.559688i	$0.810921\pi$
$6$	1.16728	−	5.11418i	0.476540	−	2.08786i
$7$	1.95991	−	1.77729i	0.740775	−	0.671754i
$7$	1.95991	−	1.77729i	0.740775	−	0.671754i
$8$	0.0391023	+	0.171318i	0.0138247	+	0.0605701i
$9$	−3.63598	+	1.75100i	−1.21199	+	0.583666i
$10$	0.710963	−	3.11493i	0.224826	−	0.985028i
$11$	−3.98899	−	1.92100i	−1.20273	−	0.579202i	−0.278274	−	0.960502i	$-0.589762\pi$
$11$	−3.98899	−	1.92100i	−1.20273	−	0.579202i	−0.924451	+	0.381300i	$0.875477\pi$
$12$	−3.16064	+	3.96332i	−0.912398	+	1.14411i
$13$	1.03563	+	0.498732i	0.287231	+	0.138323i	0.571952	−	0.820287i	$-0.306186\pi$
$13$	1.03563	+	0.498732i	0.287231	+	0.138323i	−0.284720	+	0.958611i	$0.591901\pi$
$14$	−5.01723	+	1.48506i	−1.34091	+	0.396898i
$15$	−3.86087	+	1.85930i	−0.996873	+	0.480069i
$16$	0.927871	−	4.06527i	0.231968	−	1.01632i
$17$	4.05008	−	5.07864i	0.982290	−	1.23175i	0.00952568	−	0.999955i	$-0.496968\pi$
$17$	4.05008	−	5.07864i	0.982290	−	1.23175i	0.972764	−	0.231798i	$-0.0744607\pi$
$18$	7.98112			1.88117
$19$	−1.87680			−0.430568			−0.215284	−	0.976551i	$-0.569068\pi$
$19$	−1.87680			−0.430568			−0.215284	+	0.976551i	$0.569068\pi$
$20$	−1.92507	+	2.41397i	−0.430459	+	0.539779i
$21$	5.75283	+	4.01925i	1.25537	+	0.877072i
$22$	5.45927	+	6.84570i	1.16392	+	1.45951i
$23$	−0.184292	−	0.231095i	−0.0384276	−	0.0481867i	0.762246	−	0.647287i	$-0.224096\pi$
$23$	−0.184292	−	0.231095i	−0.0384276	−	0.0481867i	−0.800674	+	0.599100i	$0.795525\pi$
$24$	−0.419945	+	0.202235i	−0.0857209	+	0.0412810i
$25$	2.15327	−	1.03696i	0.430655	−	0.207392i
$26$	−1.41734	−	1.77729i	−0.277964	−	0.348556i
$27$	−1.71273	−	2.14769i	−0.329615	−	0.413324i
$28$	4.99100	+	0.810692i	0.943211	+	0.153206i
$29$	1.70387	−	2.13658i	0.316400	−	0.396753i	−0.598045	−	0.801462i	$-0.704056\pi$
$29$	1.70387	−	2.13658i	0.316400	−	0.396753i	0.914446	+	0.404709i	$0.132627\pi$
$30$	8.47477			1.54727
$31$	−5.93520			−1.06599			−0.532997	−	0.846117i	$-0.678934\pi$
$31$	−5.93520			−1.06599			−0.532997	+	0.846117i	$0.678934\pi$
$32$	−4.92247	+	6.17259i	−0.870178	+	1.09117i
$33$	2.61322	−	11.4493i	0.454903	−	1.99306i
$34$	−11.5743	+	5.57391i	−1.98498	+	0.955918i
$35$	3.50392	+	2.44803i	0.592271	+	0.413793i
$36$	−6.94889	−	3.34641i	−1.15815	−	0.557735i
$37$	−5.66584	+	7.10474i	−0.931459	+	1.16801i	0.0540752	+	0.998537i	$0.482779\pi$
$37$	−5.66584	+	7.10474i	−0.931459	+	1.16801i	−0.985534	+	0.169476i	$0.945792\pi$
$38$	3.34411	+	1.61044i	0.542486	+	0.261248i
$39$	−0.678448	+	2.97247i	−0.108639	+	0.475977i
$40$	−0.255779	+	0.123177i	−0.0404422	+	0.0194759i
$41$	0.655181	+	2.87054i	0.102322	+	0.448303i	0.999971	+	0.00759156i	$0.00241649\pi$
$41$	0.655181	+	2.87054i	0.102322	+	0.448303i	−0.897649	+	0.440711i	$0.854726\pi$
$42$	−6.80165	−	12.0979i	−1.04952	−	1.86675i
$43$	−0.200509	+	0.878488i	−0.0305773	+	0.133968i	−0.987913	−	0.155011i	$-0.950459\pi$
$43$	−0.200509	+	0.878488i	−0.0305773	+	0.133968i	0.957335	+	0.288979i	$0.0933158\pi$
$44$	−1.88286	−	8.24934i	−0.283852	−	1.24364i
$45$	−4.06505	−	5.09741i	−0.605981	−	0.759877i
$46$	0.130077	+	0.569904i	0.0191788	+	0.0840278i
$47$	1.53276	+	0.738138i	0.223576	+	0.107669i	0.542319	−	0.840173i	$-0.317546\pi$
$47$	1.53276	+	0.738138i	0.223576	+	0.107669i	−0.318743	+	0.947841i	$0.603261\pi$
$48$	11.0603			1.59642
$49$	0.682458	−	6.96665i	0.0974940	−	0.995236i
$50$	−4.72652			−0.668431
$51$	15.5237	+	7.47584i	2.17376	+	1.04683i
$52$	0.488831	+	2.14171i	0.0677886	+	0.297001i
$53$	−1.35041	−	1.69336i	−0.185493	−	0.232601i	0.680387	−	0.732853i	$-0.261812\pi$
$53$	−1.35041	−	1.69336i	−0.185493	−	0.232601i	−0.865880	+	0.500253i	$0.833240\pi$
$54$	1.20888	+	5.29644i	0.164507	+	0.720754i
$55$	1.59165	−	6.97348i	0.214618	−	0.940304i
$56$	0.381119	+	0.266271i	0.0509292	+	0.0355820i
$57$	−1.10775	−	4.85337i	−0.146725	−	0.642844i
$58$	−4.86932	+	2.34494i	−0.639373	+	0.307906i
$59$	−0.611266	+	2.67813i	−0.0795800	+	0.348663i	−0.999005	−	0.0446030i	$-0.985798\pi$
$59$	−0.611266	+	2.67813i	−0.0795800	+	0.348663i	0.919425	+	0.393266i	$0.128655\pi$
$60$	−7.37869	−	3.55339i	−0.952585	−	0.458741i
$61$	−2.01709	+	2.52936i	−0.258262	+	0.323851i	−0.894011	−	0.448046i	$-0.852120\pi$
$61$	−2.01709	+	2.52936i	−0.258262	+	0.323851i	0.635748	+	0.771896i	$0.280692\pi$
$62$	10.5754	+	5.09285i	1.34308	+	0.646792i
$63$	−4.01415	+	9.89400i	−0.505735	+	1.24653i
$64$	6.55372	−	3.15610i	0.819215	−	0.394513i
$65$	−0.413227	+	1.81047i	−0.0512545	+	0.224561i
$66$	−14.4806	+	18.1581i	−1.78244	+	2.23510i
$67$	−3.33572			−0.407523			−0.203762	−	0.979021i	$-0.565317\pi$
$67$	−3.33572			−0.407523			−0.203762	+	0.979021i	$0.565317\pi$
$68$	12.4145			1.50548
$69$	0.488831	−	0.612974i	0.0588483	−	0.0737935i
$70$	−4.14273	−	7.36856i	−0.495151	−	0.880712i
$71$	−7.37877	−	9.25269i	−0.875699	−	1.09809i	−0.994454	−	0.105168i	$-0.966462\pi$
$71$	−7.37877	−	9.25269i	−0.875699	−	1.09809i	0.118756	−	0.992924i	$-0.462110\pi$
$72$	−0.442153	−	0.554442i	−0.0521082	−	0.0653416i
$73$	5.15719	−	2.48357i	0.603603	−	0.290680i	−0.107015	−	0.994257i	$-0.534129\pi$
$73$	5.15719	−	2.48357i	0.603603	−	0.290680i	0.710619	+	0.703577i	$0.248415\pi$
$74$	16.1919	−	7.79760i	1.88227	−	0.906452i
$75$	3.95249	+	4.95626i	0.456394	+	0.572300i
$76$	−2.23636	−	2.80431i	−0.256528	−	0.321676i
$77$	−11.2322	+	3.32463i	−1.28003	+	0.378877i
$78$	3.75947	−	4.71423i	0.425677	−	0.533781i
$79$	−10.5153			−1.18307			−0.591534	−	0.806280i	$-0.701477\pi$
$79$	−10.5153			−1.18307			−0.591534	+	0.806280i	$0.701477\pi$
$80$	6.73660			0.753175
$81$	−3.00556	+	3.76885i	−0.333951	+	0.418761i
$82$	1.29573	−	5.67695i	0.143089	−	0.626914i
$83$	−6.48731	+	3.12412i	−0.712075	+	0.342917i	−0.754606	−	0.656178i	$-0.772172\pi$
$83$	−6.48731	+	3.12412i	−0.712075	+	0.342917i	0.0425312	+	0.999095i	$0.486458\pi$
$84$	0.849421	+	13.3851i	0.0926795	+	1.46043i
$85$	9.45515	+	4.55336i	1.02556	+	0.493881i
$86$	1.11108	−	1.39325i	0.119811	−	0.150238i
$87$	6.53082	+	3.14508i	0.700178	+	0.337188i
$88$	0.173123	−	0.758501i	0.0184550	−	0.0808565i
$89$	12.2554	−	5.90189i	1.29907	−	0.625599i	0.348850	−	0.937178i	$-0.386572\pi$
$89$	12.2554	−	5.90189i	1.29907	−	0.625599i	0.950220	+	0.311579i	$0.100858\pi$
$90$	2.86919	+	12.5707i	0.302439	+	1.32507i
$91$	2.91613	−	0.863147i	0.305693	−	0.0904824i
$92$	0.125702	−	0.550736i	0.0131053	−	0.0574182i
$93$	−3.50314	−	15.3483i	−0.363259	−	1.59154i
$94$	−2.09771	−	2.63045i	−0.216362	−	0.271310i
$95$	−0.674705	−	2.95608i	−0.0692233	−	0.303287i
$96$	−18.8675	−	9.08613i	−1.92566	−	0.927349i
$97$	3.26934			0.331951			0.165975	−	0.986130i	$-0.446923\pi$
$97$	3.26934			0.331951			0.165975	+	0.986130i	$0.446923\pi$
$98$	−7.19392	+	11.8277i	−0.726696	+	1.19477i
$99$	17.8676			1.79576
$100$	4.11522	+	1.98179i	0.411522	+	0.198179i
$101$	0.681086	+	2.98403i	0.0677706	+	0.296923i	0.997443	−	0.0714645i	$-0.0227673\pi$
$101$	0.681086	+	2.98403i	0.0677706	+	0.296923i	−0.929673	+	0.368387i	$0.879910\pi$
$102$	−21.2455	−	26.6411i	−2.10362	−	2.63786i
$103$	3.03826	+	13.3115i	0.299369	+	1.31162i	0.871070	+	0.491159i	$0.163427\pi$
$103$	3.03826	+	13.3115i	0.299369	+	1.31162i	−0.571701	+	0.820462i	$0.693716\pi$
$104$	−0.0449465	+	0.196923i	−0.00440736	+	0.0193099i
$105$	−4.26243	+	10.5060i	−0.415970	+	1.02528i
$106$	0.953145	+	4.17600i	0.0925776	+	0.405609i
$107$	10.8604	−	5.23009i	1.04991	−	0.505612i	0.172333	−	0.985039i	$-0.444870\pi$
$107$	10.8604	−	5.23009i	1.04991	−	0.505612i	0.877582	+	0.479426i	$0.159155\pi$
$108$	1.16822	−	5.11830i	0.112412	−	0.492509i
$109$	0.638550	+	0.307509i	0.0611620	+	0.0294541i	0.464215	−	0.885723i	$-0.346337\pi$
$109$	0.638550	+	0.307509i	0.0611620	+	0.0294541i	−0.403053	+	0.915177i	$0.632051\pi$
$110$	−8.81979	+	11.0597i	−0.840934	+	1.05450i
$111$	−21.7168	−	10.4583i	−2.06127	−	0.992656i
$112$	−5.40663	−	9.61664i	−0.510879	−	0.908687i
$113$	−9.95317	+	4.79320i	−0.936316	+	0.450906i	−0.838868	−	0.544335i	$-0.816782\pi$
$113$	−9.95317	+	4.79320i	−0.936316	+	0.450906i	−0.0974477	+	0.995241i	$0.531068\pi$
$114$	−2.19075	+	9.59832i	−0.205183	+	0.898965i
$115$	0.297736	−	0.373349i	0.0277640	−	0.0348150i
$116$	5.22276			0.484921
$117$	−4.63880			−0.428858
$118$	3.38720	−	4.24741i	0.311817	−	0.391006i
$119$	−1.08846	−	17.1519i	−0.0997789	−	1.57231i
$120$	−0.469501	−	0.588735i	−0.0428593	−	0.0537439i
$121$	5.36342	+	6.72551i	0.487583	+	0.611410i
$122$	5.76446	−	2.77602i	0.521889	−	0.251329i
$123$	−7.03643	+	3.38856i	−0.634453	+	0.305537i
$124$	−7.07226	−	8.86834i	−0.635108	−	0.796400i
$125$	7.44381	+	9.33424i	0.665794	+	0.834880i
$126$	15.6422	−	14.1848i	1.39352	−	1.26368i
$127$	−5.62898	+	7.05852i	−0.499492	+	0.626343i	−0.966115	−	0.258114i	$-0.916899\pi$
$127$	−5.62898	+	7.05852i	−0.499492	+	0.626343i	0.466623	+	0.884456i	$0.345471\pi$
$128$	1.40440			0.124133
$129$	−2.39009			−0.210436
$130$	2.28981	−	2.87133i	0.200830	−	0.251832i
$131$	0.760791	−	3.33324i	0.0664707	−	0.291227i	−0.930757	−	0.365638i	$-0.880851\pi$
$131$	0.760791	−	3.33324i	0.0664707	−	0.291227i	0.997228	+	0.0744115i	$0.0237078\pi$
$132$	20.2213	−	9.73805i	1.76004	−	0.847588i
$133$	−3.67836	+	3.33563i	−0.318954	+	0.289236i
$134$	5.94363	+	2.86230i	0.513451	+	0.247265i
$135$	2.76702	−	3.46974i	0.238147	−	0.298627i
$136$	1.02843	+	0.495266i	0.0881873	+	0.0424688i
$137$	−4.16860	+	18.2638i	−0.356148	+	1.56039i	0.406548	+	0.913629i	$0.366732\pi$
$137$	−4.16860	+	18.2638i	−0.356148	+	1.56039i	−0.762696	+	0.646757i	$0.776125\pi$
$138$	−1.39698	+	0.672751i	−0.118919	+	0.0572684i
$139$	−2.26639	−	9.92968i	−0.192232	−	0.842225i	−0.975405	−	0.220420i	$-0.929257\pi$
$139$	−2.26639	−	9.92968i	−0.192232	−	0.842225i	0.783173	−	0.621804i	$-0.213600\pi$
$140$	0.517363	+	8.15256i	0.0437252	+	0.689017i
$141$	−1.00412	+	4.39935i	−0.0845624	+	0.370492i
$142$	5.20808	+	22.8181i	0.437052	+	1.91485i
$143$	−3.17305	−	3.97887i	−0.265343	−	0.332730i
$144$	3.74455	+	16.4059i	0.312046	+	1.36716i
$145$	3.97778	+	1.91560i	0.330336	+	0.159082i
$146$	−11.3202			−0.936869
$147$	18.4184	−	2.34712i	1.51912	−	0.193587i
$148$	−17.3672			−1.42757
$149$	−8.98610	−	4.32748i	−0.736170	−	0.354521i	0.0279376	−	0.999610i	$-0.491106\pi$
$149$	−8.98610	−	4.32748i	−0.736170	−	0.354521i	−0.764107	+	0.645089i	$0.776820\pi$
$150$	−2.78974	−	12.2227i	−0.227781	−	0.997976i
$151$	9.00660	+	11.2939i	0.732947	+	0.919086i	0.998993	−	0.0448741i	$-0.0142887\pi$
$151$	9.00660	+	11.2939i	0.732947	+	0.919086i	−0.266046	+	0.963960i	$0.585717\pi$
$152$	−0.0733872	−	0.321531i	−0.00595249	−	0.0260796i
$153$	−5.83335	+	25.5576i	−0.471598	+	2.06621i
$154$	22.8665	+	3.71421i	1.84263	+	0.299300i
$155$	−2.13369	−	9.34829i	−0.171382	−	0.750872i
$156$	−5.24988	+	2.52821i	−0.420327	+	0.202419i
$157$	0.930217	−	4.07555i	0.0742394	−	0.325264i	−0.924148	−	0.382035i	$-0.875223\pi$
$157$	0.930217	−	4.07555i	0.0742394	−	0.325264i	0.998387	+	0.0567710i	$0.0180805\pi$
$158$	18.7363	+	9.02295i	1.49058	+	0.717827i
$159$	3.58193	−	4.49160i	0.284066	−	0.356207i
$160$	−11.4918	−	5.53416i	−0.908506	−	0.437514i
$161$	−0.771919	−	0.125383i	−0.0608357	−	0.00988158i
$162$	8.58930	−	4.13639i	0.674839	−	0.324985i
$163$	3.63591	−	15.9300i	0.284787	−	1.24773i	−0.606790	−	0.794862i	$-0.707543\pi$
$163$	3.63591	−	15.9300i	0.284787	−	1.24773i	0.891576	−	0.452870i	$-0.149600\pi$
$164$	−3.50844	+	4.39944i	−0.273963	+	0.343539i
$165$	18.9727			1.47702
$166$	14.2399			1.10523
$167$	3.38609	−	4.24602i	0.262024	−	0.328567i	−0.633365	−	0.773854i	$-0.718327\pi$
$167$	3.38609	−	4.24602i	0.262024	−	0.328567i	0.895388	+	0.445286i	$0.146898\pi$
$168$	−0.463622	+	1.14273i	−0.0357692	+	0.0881633i
$169$	−7.28158	−	9.13081i	−0.560121	−	0.702370i
$170$	−12.9402	−	16.2265i	−0.992466	−	1.24451i
$171$	6.82403	−	3.28628i	0.521846	−	0.251308i
$172$	−1.55155	+	0.747189i	−0.118305	+	0.0569726i
$173$	1.93989	+	2.43254i	0.147487	+	0.184943i	0.850087	−	0.526642i	$-0.176549\pi$
$173$	1.93989	+	2.43254i	0.147487	+	0.184943i	−0.702600	+	0.711585i	$0.747978\pi$
$174$	−8.93798	−	11.2079i	−0.677587	−	0.849667i
$175$	2.37723	−	5.85935i	0.179701	−	0.442925i
$176$	−11.5106	+	14.4339i	−0.867646	+	1.08799i
$177$	−7.28637			−0.547677
$178$	−26.9011			−2.01632
$179$	7.93974	−	9.95612i	0.593444	−	0.744155i	−0.390896	−	0.920435i	$-0.627835\pi$
$179$	7.93974	−	9.95612i	0.593444	−	0.744155i	0.984340	+	0.176280i	$0.0564063\pi$
$180$	2.77269	−	12.1479i	0.206664	−	0.905454i
$181$	11.5681	−	5.57092i	0.859852	−	0.414083i	0.0486273	−	0.998817i	$-0.484515\pi$
$181$	11.5681	−	5.57092i	0.859852	−	0.414083i	0.811225	+	0.584734i	$0.198801\pi$
$182$	−5.93663	−	0.964290i	−0.440052	−	0.0714780i
$183$	−7.73140	−	3.72325i	−0.571522	−	0.275230i
$184$	0.0323845	−	0.0406089i	0.00238742	−	0.00299373i
$185$	−13.2272	−	6.36990i	−0.972486	−	0.468325i
$186$	−6.92803	+	30.3537i	−0.507988	+	2.22564i
$187$	−25.9118	+	12.4785i	−1.89486	+	0.912516i
$188$	0.723484	+	3.16979i	0.0527655	+	0.231181i
$189$	−7.17387	−	1.16526i	−0.521822	−	0.0847599i
$190$	−1.33434	+	5.84612i	−0.0968030	+	0.424122i
$191$	2.88904	+	12.6577i	0.209044	+	0.915881i	0.965205	+	0.261495i	$0.0842155\pi$
$191$	2.88904	+	12.6577i	0.209044	+	0.915881i	−0.756161	+	0.654386i	$0.772927\pi$
$192$	12.0298	+	15.0849i	0.868177	+	1.08866i
$193$	−3.72384	−	16.3152i	−0.268048	−	1.17439i	−0.912281	−	0.409565i	$-0.865680\pi$
$193$	−3.72384	−	16.3152i	−0.268048	−	1.17439i	0.644233	−	0.764829i	$-0.277177\pi$
$194$	−5.82534	−	2.80534i	−0.418235	−	0.201411i
$195$	−4.92572			−0.352738
$196$	11.2227	−	7.28160i	0.801624	−	0.520114i
$197$	−12.3172			−0.877566			−0.438783	−	0.898593i	$-0.644590\pi$
$197$	−12.3172			−0.877566			−0.438783	+	0.898593i	$0.644590\pi$
$198$	−31.8366	−	15.3317i	−2.26253	−	1.08958i
$199$	4.70744	+	20.6246i	0.333701	+	1.46204i	0.811904	+	0.583791i	$0.198431\pi$
$199$	4.70744	+	20.6246i	0.333701	+	1.46204i	−0.478203	+	0.878250i	$0.658712\pi$
$200$	0.261848	+	0.328347i	0.0185155	+	0.0232177i
$201$	−1.96885	−	8.62609i	−0.138872	−	0.608437i
$202$	1.34696	−	5.90141i	0.0947717	−	0.415222i
$203$	−0.457914	−	7.21577i	−0.0321393	−	0.506448i
$204$	7.32742	+	32.1035i	0.513022	+	2.24770i
$205$	−4.28573	+	2.06390i	−0.299328	+	0.144149i
$206$	6.00866	−	26.3256i	0.418643	−	1.83419i
$207$	1.07473	+	0.517563i	0.0746989	+	0.0359731i
$208$	2.98841	−	3.74735i	0.207209	−	0.259832i
$209$	7.48655	+	3.60533i	0.517855	+	0.249386i
$210$	16.6097	−	15.0621i	1.14618	−	1.03939i
$211$	22.4586	−	10.8155i	1.54611	−	0.744568i	0.550210	−	0.835026i	$-0.314548\pi$
$211$	22.4586	−	10.8155i	1.54611	−	0.744568i	0.995900	+	0.0904585i	$0.0288333\pi$
$212$	0.921087	−	4.03555i	0.0632605	−	0.277162i
$213$	19.5720	−	24.5425i	1.34105	−	1.68163i
$214$	−23.8390			−1.62960
$215$	−1.45575			−0.0992814
$216$	0.300967	−	0.377401i	0.0204782	−	0.0256789i
$217$	−11.6324	+	10.5486i	−0.789661	+	0.716085i
$218$	−0.873909	−	1.09585i	−0.0591886	−	0.0742202i
$219$	9.46639	+	11.8705i	0.639679	+	0.802133i
$220$	12.3163	−	5.93122i	0.830366	−	0.399883i
$221$	6.72726	−	3.23968i	0.452525	−	0.217924i
$222$	29.7213	+	37.2694i	1.99477	+	2.50136i
$223$	8.82826	+	11.0703i	0.591184	+	0.741321i	0.983975	−	0.178306i	$-0.0570618\pi$
$223$	8.82826	+	11.0703i	0.591184	+	0.741321i	−0.392791	+	0.919628i	$0.628490\pi$
$224$	1.32291	+	20.8464i	0.0883909	+	1.39286i
$225$	−6.01355	+	7.54075i	−0.400903	+	0.502717i
$226$	21.8476			1.45328
$227$	6.79783			0.451188			0.225594	−	0.974221i	$-0.427568\pi$
$227$	6.79783			0.451188			0.225594	+	0.974221i	$0.427568\pi$
$228$	5.93190	−	7.43836i	0.392850	−	0.492618i
$229$	−3.52314	+	15.4359i	−0.232816	+	1.02003i	0.714476	+	0.699660i	$0.246665\pi$
$229$	−3.52314	+	15.4359i	−0.232816	+	1.02003i	−0.947292	+	0.320373i	$0.896192\pi$
$230$	−0.850870	+	0.409758i	−0.0561047	+	0.0270186i
$231$	−15.2270	−	27.0839i	−1.00186	−	1.78199i
$232$	0.432660	+	0.208358i	0.0284055	+	0.0136794i
$233$	4.44933	−	5.57928i	0.291485	−	0.365511i	−0.614429	−	0.788972i	$-0.710614\pi$
$233$	4.44933	−	5.57928i	0.291485	−	0.365511i	0.905914	+	0.423461i	$0.139185\pi$
$234$	8.26548	+	3.98044i	0.540331	+	0.260210i
$235$	−0.611588	+	2.67954i	−0.0398956	+	0.174794i
$236$	−4.73002	+	2.27786i	−0.307898	+	0.148276i
$237$	−6.20649	−	27.1924i	−0.403155	−	1.76634i
$238$	−12.7781	+	31.4953i	−0.828284	+	2.04154i
$239$	3.49764	−	15.3242i	0.226244	−	0.991238i	−0.726429	−	0.687241i	$-0.758822\pi$
$239$	3.49764	−	15.3242i	0.226244	−	0.991238i	0.952673	−	0.303997i	$-0.0983213\pi$
$240$	3.97616	+	17.4207i	0.256660	+	1.12450i
$241$	0.530225	+	0.664881i	0.0341548	+	0.0428287i	0.798616	−	0.601842i	$-0.205566\pi$
$241$	0.530225	+	0.664881i	0.0341548	+	0.0428287i	−0.764461	+	0.644670i	$0.776995\pi$
$242$	−3.78560	−	16.5858i	−0.243348	−	1.06618i
$243$	−18.9450	−	9.12345i	−1.21532	−	0.585269i
$244$	−6.18287			−0.395818
$245$	11.2182	−	1.42958i	0.716706	−	0.0913324i
$246$	15.4452			0.984752
$247$	−1.94367	−	0.936022i	−0.123673	−	0.0595577i
$248$	−0.232080	−	1.01681i	−0.0147371	−	0.0645673i
$249$	−11.9079	−	14.9321i	−0.754634	−	0.946281i
$250$	−5.25398	−	23.0192i	−0.332291	−	1.45586i
$251$	−3.91274	+	17.1428i	−0.246970	+	1.08205i	0.687550	+	0.726137i	$0.258686\pi$
$251$	−3.91274	+	17.1428i	−0.246970	+	1.08205i	−0.934520	+	0.355910i	$0.884171\pi$
$252$	−19.5667	+	5.79157i	−1.23259	+	0.364835i
$253$	0.291207	+	1.27586i	0.0183080	+	0.0802126i
$254$	16.0865	−	7.74687i	1.00936	−	0.486082i
$255$	−6.19415	+	27.1383i	−0.387892	+	1.69947i
$256$	−15.6098	−	7.51729i	−0.975613	−	0.469831i
$257$	−14.2385	+	17.8545i	−0.888175	+	1.11374i	0.104692	+	0.994505i	$0.466614\pi$
$257$	−14.2385	+	17.8545i	−0.888175	+	1.11374i	−0.992867	+	0.119231i	$0.961957\pi$
$258$	4.25870	+	2.05088i	0.265135	+	0.127682i
$259$	1.52270	+	23.9945i	0.0946157	+	1.49095i
$260$	−3.19758	+	1.53987i	−0.198306	+	0.0954989i
$261$	−2.45408	+	10.7520i	−0.151904	+	0.665535i
$262$	−4.21576	+	5.28640i	−0.260451	+	0.326595i
$263$	6.92239			0.426853			0.213427	−	0.976959i	$-0.431538\pi$
$263$	6.92239			0.426853			0.213427	+	0.976959i	$0.431538\pi$
$264$	2.06365			0.127009
$265$	2.18167	−	2.73573i	0.134019	−	0.168055i
$266$	9.41636	−	2.78716i	0.577354	−	0.170892i
$267$	22.4957	+	28.2087i	1.37671	+	1.72634i
$268$	−3.97478	−	4.98421i	−0.242798	−	0.304459i
$269$	−25.9782	+	12.5105i	−1.58392	+	0.762776i	−0.998838	−	0.0481964i	$-0.984653\pi$
$269$	−25.9782	+	12.5105i	−1.58392	+	0.762776i	−0.585084	+	0.810973i	$0.698938\pi$
$270$	−7.90761	+	3.80810i	−0.481242	+	0.231754i
$271$	−20.1486	−	25.2656i	−1.22394	−	1.53478i	−0.761559	−	0.648095i	$-0.775566\pi$
$271$	−20.1486	−	25.2656i	−1.22394	−	1.53478i	−0.462383	−	0.886680i	$-0.653006\pi$
$272$	−16.8881	−	21.1770i	−1.02399	−	1.28404i
$273$	3.95327	+	7.03157i	0.239262	+	0.425570i
$274$	23.0994	−	28.9658i	1.39549	−	1.74989i
$275$	−10.5814			−0.638081
$276$	1.49838			0.0901921
$277$	9.44399	−	11.8424i	0.567435	−	0.711541i	−0.412478	−	0.910968i	$-0.635337\pi$
$277$	9.44399	−	11.8424i	0.567435	−	0.711541i	0.979913	+	0.199427i	$0.0639081\pi$
$278$	−4.48214	+	19.6376i	−0.268821	+	1.17778i
$279$	21.5803	−	10.3925i	1.29198	−	0.622184i
$280$	−0.282382	+	0.696009i	−0.0168755	+	0.0415945i
$281$	20.6304	+	9.93508i	1.23071	+	0.592677i	0.932274	−	0.361753i	$-0.117822\pi$
$281$	20.6304	+	9.93508i	1.23071	+	0.592677i	0.298433	+	0.954431i	$0.403536\pi$
$282$	5.56413	−	6.97720i	0.331339	−	0.415486i
$283$	17.3388	+	8.34990i	1.03068	+	0.496350i	0.871240	−	0.490857i	$-0.163316\pi$
$283$	17.3388	+	8.34990i	1.03068	+	0.496350i	0.159442	+	0.987207i	$0.449031\pi$
$284$	5.03291	−	22.0506i	0.298648	−	1.30846i
$285$	7.24610	−	3.48954i	0.429222	−	0.206702i
$286$	2.23960	+	9.81231i	0.132430	+	0.580214i
$287$	6.38588	+	4.46153i	0.376947	+	0.263356i
$288$	7.08985	−	31.0627i	0.417773	−	1.83038i
$289$	−5.60660	−	24.5641i	−0.329800	−	1.44495i
$290$	−5.44392	−	6.82646i	−0.319678	−	0.400864i
$291$	1.92967	+	8.45442i	0.113119	+	0.495607i
$292$	9.85614	+	4.74647i	0.576787	+	0.277766i
$293$	−17.9938			−1.05121			−0.525604	−	0.850729i	$-0.676161\pi$
$293$	−17.9938			−1.05121			−0.525604	+	0.850729i	$0.676161\pi$
$294$	−34.8321	−	11.6222i	−2.03145	−	0.677823i
$295$	−4.43796			−0.258388
$296$	−1.43872	−	0.692851i	−0.0836238	−	0.0402711i
$297$	2.70635	+	11.8573i	0.157038	+	0.688029i
$298$	12.2982	+	15.4215i	0.712418	+	0.893343i
$299$	−0.0756036	−	0.331241i	−0.00437227	−	0.0191562i
$300$	−2.69591	+	11.8116i	−0.155649	+	0.681941i
$301$	1.16835	+	2.07812i	0.0673427	+	0.119781i
$302$	−6.35703	−	27.8520i	−0.365806	−	1.60270i
$303$	−7.31464	+	3.52254i	−0.420215	+	0.202365i
$304$	−1.74143	+	7.62971i	−0.0998779	+	0.437594i
$305$	−4.70902	−	2.26774i	−0.269638	−	0.129851i
$306$	32.3242	−	40.5333i	1.84785	−	2.31713i
$307$	22.9404	+	11.0475i	1.30928	+	0.630514i	0.952746	−	0.303769i	$-0.0982452\pi$
$307$	22.9404	+	11.0475i	1.30928	+	0.630514i	0.356531	+	0.934284i	$0.383959\pi$
$308$	−18.3517	−	12.8215i	−1.04569	−	0.730575i
$309$	−32.6299	+	15.7137i	−1.85625	+	0.893924i
$310$	−4.21971	+	18.4877i	−0.239663	+	1.05003i
$311$	−2.46498	+	3.09098i	−0.139776	+	0.175274i	−0.846792	−	0.531924i	$-0.821469\pi$
$311$	−2.46498	+	3.09098i	−0.139776	+	0.175274i	0.707016	+	0.707197i	$0.250041\pi$
$312$	−0.535768			−0.0303319
$313$	35.2353			1.99161			0.995807	−	0.0914762i	$-0.0291585\pi$
$313$	35.2353			1.99161			0.995807	+	0.0914762i	$0.0291585\pi$
$314$	−5.15460	+	6.46366i	−0.290891	+	0.364766i
$315$	−17.0267	−	2.76566i	−0.959346	−	0.155827i
$316$	−12.5299	−	15.7120i	−0.704860	−	0.883866i
$317$	5.24093	+	6.57192i	0.294360	+	0.369116i	0.906916	−	0.421311i	$-0.138430\pi$
$317$	5.24093	+	6.57192i	0.294360	+	0.369116i	−0.612556	+	0.790427i	$0.709859\pi$
$318$	−10.2365	+	4.92962i	−0.574032	+	0.276439i
$319$	−10.9011	+	5.24968i	−0.610343	+	0.293926i
$320$	7.32709	+	9.18788i	0.409597	+	0.513618i
$321$	19.9350	+	24.9978i	1.11267	+	1.39524i
$322$	1.26783	+	0.885774i	0.0706532	+	0.0493622i
$323$	−7.60121	+	9.53162i	−0.422943	+	0.530353i
$324$	−9.21276			−0.511820
$325$	2.74716			0.152385
$326$	−20.1476	+	25.2643i	−1.11587	+	1.39926i
$327$	−0.418319	+	1.83278i	−0.0231331	+	0.101353i
$328$	−0.466156	+	0.224489i	−0.0257392	+	0.0123953i
$329$	4.31595	−	1.27748i	0.237946	−	0.0704299i
$330$	−33.8058	−	16.2800i	−1.86095	−	0.896184i
$331$	9.97628	−	12.5099i	0.548346	−	0.687604i	−0.428010	−	0.903774i	$-0.640785\pi$
$331$	9.97628	−	12.5099i	0.548346	−	0.687604i	0.976356	+	0.216170i	$0.0693566\pi$
$332$	−12.3982	−	5.97066i	−0.680440	−	0.327682i
$333$	8.16053	−	35.7536i	0.447194	−	1.95929i
$334$	−9.67679	+	4.66009i	−0.529490	+	0.254989i
$335$	−1.19918	−	5.25395i	−0.0655182	−	0.287054i
$336$	21.6772	−	19.6575i	1.18259	−	1.07240i
$337$	−1.82919	+	8.01419i	−0.0996422	+	0.436561i	0.900357	+	0.435152i	$0.143305\pi$
$337$	−1.82919	+	8.01419i	−0.0996422	+	0.436561i	−0.999999	+	0.00140852i	$0.999552\pi$
$338$	5.13948	+	22.5175i	0.279551	+	1.22479i
$339$	−18.2698	−	22.9096i	−0.992277	−	1.24428i
$340$	4.46297	+	19.5535i	0.242038	+	1.06044i
$341$	23.6754	+	11.4015i	1.28210	+	0.617425i
$342$	−14.9790			−0.809972
$343$	−11.0442	−	14.8669i	−0.596332	−	0.802738i
$344$	−0.158341			−0.00853719
$345$	1.14120	+	0.549575i	0.0614403	+	0.0295881i
$346$	−1.36921	−	5.99890i	−0.0736091	−	0.322503i
$347$	−3.25455	−	4.08108i	−0.174714	−	0.219084i	0.686763	−	0.726882i	$-0.259031\pi$
$347$	−3.25455	−	4.08108i	−0.174714	−	0.219084i	−0.861476	+	0.507798i	$0.830460\pi$
$348$	3.08264	+	13.5059i	0.165247	+	0.723994i
$349$	1.55731	−	6.82300i	0.0833607	−	0.365227i	−0.915992	−	0.401196i	$-0.868595\pi$
$349$	1.55731	−	6.82300i	0.0833607	−	0.365227i	0.999353	+	0.0359690i	$0.0114518\pi$
$350$	−9.26353	+	8.40041i	−0.495156	+	0.449021i
$351$	−0.702626	−	3.07841i	−0.0375034	−	0.164313i
$352$	31.4932	−	15.1663i	1.67859	−	0.808368i
$353$	−0.901903	+	3.95149i	−0.0480034	+	0.210317i	−0.993242	−	0.116064i	$-0.962972\pi$
$353$	−0.901903	+	3.95149i	−0.0480034	+	0.210317i	0.945238	+	0.326381i	$0.105829\pi$
$354$	12.9829	+	6.25225i	0.690035	+	0.332303i
$355$	11.9209	−	14.9483i	0.632694	−	0.793374i
$356$	23.4219	+	11.2794i	1.24136	+	0.597806i
$357$	43.7118	−	12.9383i	2.31347	−	0.684767i
$358$	−22.6902	+	10.9270i	−1.19922	+	0.577512i
$359$	−3.79295	+	16.6180i	−0.200184	+	0.877065i	0.770639	+	0.637272i	$0.219937\pi$
$359$	−3.79295	+	16.6180i	−0.200184	+	0.877065i	−0.970824	+	0.239794i	$0.922920\pi$
$360$	0.714326	−	0.895737i	0.0376483	−	0.0472095i
$361$	−15.4776			−0.814611
$362$	−25.3925			−1.33460
$363$	−14.2263	+	17.8393i	−0.746689	+	0.936319i
$364$	4.76450	+	3.32875i	0.249728	+	0.174474i
$365$	5.76576	+	7.23004i	0.301794	+	0.378438i
$366$	10.5811	+	13.2682i	0.553082	+	0.693542i
$367$	−17.8724	+	8.60688i	−0.932930	+	0.449275i	−0.837670	−	0.546177i	$-0.816083\pi$
$367$	−17.8724	+	8.60688i	−0.932930	+	0.449275i	−0.0952601	+	0.995452i	$0.530368\pi$
$368$	−1.11046	+	0.534771i	−0.0578869	+	0.0278768i
$369$	−7.40853	−	9.29000i	−0.385673	−	0.483618i
$370$	18.1026	+	22.6999i	0.941109	+	1.18011i
$371$	−5.65627	−	0.918751i	−0.293659	−	0.0476992i
$372$	18.7590	−	23.5231i	0.972610	−	1.21961i
$373$	3.76648			0.195021			0.0975106	−	0.995234i	$-0.468912\pi$
$373$	3.76648			0.195021			0.0975106	+	0.995234i	$0.468912\pi$
$374$	56.8774			2.94106
$375$	−19.7445	+	24.7589i	−1.01960	+	1.27854i
$376$	−0.0665221	+	0.291452i	−0.00343062	+	0.0150305i
$377$	2.83015	−	1.36293i	0.145760	−	0.0701945i
$378$	11.7826	+	8.23199i	0.606032	+	0.423408i
$379$	−12.3578	−	5.95118i	−0.634775	−	0.305692i	0.0886829	−	0.996060i	$-0.471734\pi$
$379$	−12.3578	−	5.95118i	−0.634775	−	0.305692i	−0.723458	+	0.690368i	$0.757449\pi$
$380$	3.61298	−	4.53054i	0.185342	−	0.232412i
$381$	−21.5756	−	10.3902i	−1.10535	−	0.532308i
$382$	5.71355	−	25.0327i	0.292331	−	1.28078i
$383$	34.0166	−	16.3815i	1.73817	−	0.837057i	0.754677	−	0.656096i	$-0.227793\pi$
$383$	34.0166	−	16.3815i	1.73817	−	0.837057i	0.983490	−	0.180961i	$-0.0579208\pi$
$384$	0.828924	+	3.63175i	0.0423008	+	0.185332i
$385$	−9.27443	−	16.4962i	−0.472669	−	0.840724i
$386$	−7.36450	+	32.2660i	−0.374843	+	1.64229i
$387$	−0.809182	−	3.54526i	−0.0411330	−	0.180216i
$388$	3.89568	+	4.88502i	0.197773	+	0.247999i
$389$	3.06385	+	13.4236i	0.155343	+	0.680603i	0.991279	+	0.131776i	$0.0420681\pi$
$389$	3.06385	+	13.4236i	0.155343	+	0.680603i	−0.835936	+	0.548827i	$0.815075\pi$
$390$	8.77671	+	4.22664i	0.444426	+	0.214024i
$391$	−1.92005			−0.0971010
$392$	1.22020	−	0.155494i	0.0616294	−	0.00785365i
$393$	9.06873			0.457457
$394$	21.9470	+	10.5691i	1.10567	+	0.532464i
$395$	−3.78023	−	16.5623i	−0.190204	−	0.833338i
$396$	21.2906	+	26.6976i	1.06989	+	1.34160i
$397$	−4.04953	−	17.7422i	−0.203240	−	0.890453i	−0.968948	−	0.247265i	$-0.920468\pi$
$397$	−4.04953	−	17.7422i	−0.203240	−	0.890453i	0.765708	−	0.643189i	$-0.222389\pi$
$398$	9.30971	−	40.7885i	0.466654	−	2.04454i
$399$	−10.7969	−	7.54334i	−0.540523	−	0.377639i
$400$	−2.21757	−	9.71580i	−0.110878	−	0.485790i
$401$	1.09371	−	0.526701i	0.0546170	−	0.0263022i	−0.406376	−	0.913706i	$-0.633208\pi$
$401$	1.09371	−	0.526701i	0.0546170	−	0.0263022i	0.460993	+	0.887404i	$0.347493\pi$
$402$	−3.89372	+	17.0595i	−0.194201	+	0.850850i
$403$	−6.14666	−	2.96007i	−0.306187	−	0.147452i
$404$	−3.64716	+	4.57339i	−0.181453	+	0.227535i
$405$	−7.01665	−	3.37904i	−0.348660	−	0.167906i
$406$	−5.37576	+	13.2501i	−0.266794	+	0.657590i
$407$	36.2492	−	17.4567i	1.79680	−	0.865296i
$408$	−0.673734	+	2.95182i	−0.0333548	+	0.146137i
$409$	−22.6552	+	28.4087i	−1.12023	+	1.40472i	−0.216676	+	0.976244i	$0.569522\pi$
$409$	−22.6552	+	28.4087i	−1.12023	+	1.40472i	−0.903552	+	0.428478i	$0.859050\pi$
$410$	9.40734			0.464595
$411$	−49.6903			−2.45104
$412$	−16.2696	+	20.4015i	−0.801547	+	1.00511i
$413$	3.56180	+	6.33528i	0.175265	+	0.311739i
$414$	−1.47086	−	1.84440i	−0.0722888	−	0.0906472i
$415$	−7.25285	−	9.09478i	−0.356028	−	0.446445i
$416$	−8.17632	+	3.93751i	−0.400877	+	0.193052i
$417$	24.3402	−	11.7216i	1.19195	−	0.574011i
$418$	−10.2460	−	12.8480i	−0.501147	−	0.628418i
$419$	−4.23852	−	5.31494i	−0.207065	−	0.259652i	0.667444	−	0.744660i	$-0.267388\pi$
$419$	−4.23852	−	5.31494i	−0.207065	−	0.259652i	−0.874510	+	0.485008i	$0.838817\pi$
$420$	−20.7770	+	6.14979i	−1.01381	+	0.300079i
$421$	−5.75315	+	7.21422i	−0.280391	+	0.351600i	−0.902006	−	0.431724i	$-0.857906\pi$
$421$	−5.75315	+	7.21422i	−0.280391	+	0.351600i	0.621615	+	0.783323i	$0.286477\pi$
$422$	−49.2974			−2.39976
$423$	−6.86557			−0.333815
$424$	0.237299	−	0.297564i	0.0115243	−	0.0144510i
$425$	3.45458	−	15.1355i	0.167572	−	0.734179i
$426$	−55.9330	+	26.9359i	−2.70996	+	1.30505i
$427$	0.542094	+	8.54226i	0.0262337	+	0.413389i
$428$	20.7558	+	9.99547i	1.00327	+	0.483149i
$429$	8.41643	−	10.5539i	0.406349	−	0.509546i
$430$	2.59388	+	1.24914i	0.125088	+	0.0602391i
$431$	0.475512	−	2.08335i	0.0229046	−	0.100352i	−0.962184	−	0.272402i	$-0.912182\pi$
$431$	0.475512	−	2.08335i	0.0229046	−	0.100352i	0.985088	+	0.172050i	$0.0550391\pi$
$432$	−10.3201	+	4.96992i	−0.496528	+	0.239115i
$433$	−6.40692	−	28.0705i	−0.307897	−	1.34898i	−0.857898	−	0.513820i	$-0.828230\pi$
$433$	−6.40692	−	28.0705i	−0.307897	−	1.34898i	0.550001	−	0.835164i	$-0.314627\pi$
$434$	29.7783	−	8.81410i	1.42940	−	0.423090i
$435$	−2.60587	+	11.4171i	−0.124942	+	0.547407i
$436$	0.301404	+	1.32054i	0.0144347	+	0.0632424i
$437$	0.345880	+	0.433720i	0.0165457	+	0.0207476i
$438$	−6.68156	−	29.2738i	−0.319257	−	1.39876i
$439$	−5.55487	−	2.67509i	−0.265120	−	0.127675i	0.296602	−	0.955001i	$-0.404147\pi$
$439$	−5.55487	−	2.67509i	−0.265120	−	0.127675i	−0.561722	+	0.827326i	$0.689861\pi$
$440$	1.25692			0.0599214
$441$	9.71719	+	26.5256i	0.462723	+	1.26312i
$442$	−14.7666			−0.702376
$443$	14.9908	+	7.21921i	0.712236	+	0.342995i	0.754670	−	0.656104i	$-0.227797\pi$
$443$	14.9908	+	7.21921i	0.712236	+	0.342995i	−0.0424338	+	0.999099i	$0.513511\pi$
$444$	−10.2507	−	44.9111i	−0.486475	−	2.13138i
$445$	13.7016	+	17.1813i	0.649518	+	0.814470i
$446$	−6.23116	−	27.3005i	−0.295054	−	1.29272i
$447$	5.88686	−	25.7920i	0.278439	−	1.21992i
$448$	7.23534	−	17.8335i	0.341838	−	0.842556i
$449$	−2.46333	−	10.7925i	−0.116252	−	0.509332i	−0.999205	−	0.0398708i	$-0.987305\pi$
$449$	−2.46333	−	10.7925i	−0.116252	−	0.509332i	0.882953	−	0.469461i	$-0.155552\pi$
$450$	17.1855	−	8.27612i	0.810134	−	0.390140i
$451$	2.90078	−	12.7091i	0.136592	−	0.598450i
$452$	−19.0220	−	9.16049i	−0.894718	−	0.430873i
$453$	−23.8898	+	29.9569i	−1.12244	+	1.40750i
$454$	−12.1124	−	5.83305i	−0.568465	−	0.273758i
$455$	2.40784	+	4.28277i	0.112881	+	0.200779i
$456$	0.788154	−	0.379555i	0.0369087	−	0.0177743i
$457$	6.87577	−	30.1247i	0.321635	−	1.40918i	−0.513008	−	0.858384i	$-0.671469\pi$
$457$	6.87577	−	30.1247i	0.321635	−	1.40918i	0.834643	−	0.550791i	$-0.185674\pi$
$458$	19.5227	−	24.4807i	0.912238	−	1.14391i
$459$	−17.8441			−0.832890
$460$	0.912631			0.0425517
$461$	2.87936	−	3.61060i	0.134105	−	0.168163i	−0.710245	−	0.703955i	$-0.751416\pi$
$461$	2.87936	−	3.61060i	0.134105	−	0.168163i	0.844350	+	0.535792i	$0.179987\pi$
$462$	3.89165	+	61.3244i	0.181056	+	2.85307i
$463$	9.74412	+	12.2187i	0.452848	+	0.567853i	0.954879	−	0.296997i	$-0.0959850\pi$
$463$	9.74412	+	12.2187i	0.452848	+	0.567853i	−0.502031	+	0.864850i	$0.667414\pi$
$464$	−7.10481	−	8.90915i	−0.329833	−	0.413597i
$465$	22.9151	−	11.0353i	1.06266	−	0.511750i
$466$	−12.7153	+	6.12337i	−0.589026	+	0.283660i
$467$	6.80785	+	8.53677i	0.315030	+	0.395035i	0.913985	−	0.405748i	$-0.132989\pi$
$467$	6.80785	+	8.53677i	0.315030	+	0.395035i	−0.598956	+	0.800782i	$0.704417\pi$
$468$	−5.52751	−	6.93127i	−0.255509	−	0.320398i
$469$	−6.53770	+	5.92855i	−0.301883	+	0.273755i
$470$	3.38899	−	4.24965i	0.156322	−	0.196022i
$471$	11.0883			0.510922
$472$	−0.482714			−0.0222187
$473$	2.48740	−	3.11910i	0.114371	−	0.143416i
$474$	−12.2743	+	53.7773i	−0.563779	+	2.47008i
$475$	−4.04127	+	1.94617i	−0.185426	+	0.0892966i
$476$	24.3312	−	22.0642i	1.11522	−	1.01131i
$477$	7.87513	+	3.79246i	0.360578	+	0.173645i
$478$	−19.3814	+	24.3035i	−0.886486	+	1.11162i
$479$	35.3576	+	17.0273i	1.61553	+	0.777997i	0.999949	−	0.0100780i	$-0.00320797\pi$
$479$	35.3576	+	17.0273i	1.61553	+	0.777997i	0.615579	+	0.788075i	$0.288922\pi$
$480$	7.52837	−	32.9839i	0.343621	−	1.50550i
$481$	−9.41107	+	4.53213i	−0.429108	+	0.206647i
$482$	−0.374243	−	1.63966i	−0.0170463	−	0.0746847i
$483$	−0.131373	−	2.07017i	−0.00597769	−	0.0941959i
$484$	−3.65828	+	16.0280i	−0.166285	+	0.728544i
$485$	1.17532	+	5.14940i	0.0533684	+	0.233822i
$486$	25.9279	+	32.5125i	1.17611	+	1.47480i
$487$	4.08504	+	17.8977i	0.185111	+	0.811023i	0.979147	+	0.203153i	$0.0651187\pi$
$487$	4.08504	+	17.8977i	0.185111	+	0.811023i	−0.794036	+	0.607870i	$0.792024\pi$
$488$	−0.512197	−	0.246661i	−0.0231861	−	0.0111658i
$489$	43.3406			1.95993
$490$	−21.2155	−	7.07884i	−0.958416	−	0.319789i
$491$	14.6136			0.659501			0.329750	−	0.944068i	$-0.393035\pi$
$491$	14.6136			0.659501			0.329750	+	0.944068i	$0.393035\pi$
$492$	−13.4476	−	6.47604i	−0.606266	−	0.291962i
$493$	−3.95014	−	17.3067i	−0.177905	−	0.779454i
$494$	2.66008	+	3.33563i	0.119682	+	0.150077i
$495$	6.42333	+	28.1424i	0.288707	+	1.26491i
$496$	−5.50710	+	24.1282i	−0.247276	+	1.08339i
$497$	−30.9064	−	5.02015i	−1.38634	−	0.225184i
$498$	8.40484	+	36.8240i	0.376630	+	1.65012i
$499$	−38.8912	+	18.7290i	−1.74101	+	0.838425i	−0.758630	+	0.651522i	$0.774131\pi$
$499$	−38.8912	+	18.7290i	−1.74101	+	0.838425i	−0.982378	+	0.186903i	$0.940155\pi$
$500$	−5.07727	+	22.2450i	−0.227063	+	0.994826i
$501$	12.9787	+	6.25021i	0.579845	+	0.279239i
$502$	21.6816	−	27.1879i	0.967698	−	1.21346i
$503$	0.661740	+	0.318677i	0.0295055	+	0.0142091i	0.448578	−	0.893744i	$-0.351931\pi$
$503$	0.661740	+	0.318677i	0.0295055	+	0.0142091i	−0.419073	+	0.907953i	$0.637645\pi$
$504$	−1.85198	−	0.300819i	−0.0824939	−	0.0133995i
$505$	−4.45518	+	2.14550i	−0.198253	+	0.0954736i
$506$	0.575908	−	2.52322i	0.0256022	−	0.112171i
$507$	19.3142	−	24.2193i	0.857774	−	1.07562i
$508$	−17.2542			−0.765531
$509$	3.87205			0.171626			0.0858128	−	0.996311i	$-0.472651\pi$
$509$	3.87205			0.171626			0.0858128	+	0.996311i	$0.472651\pi$
$510$	34.3235	−	43.0403i	1.51987	−	1.90586i
$511$	5.69357	−	14.0334i	0.251869	−	0.620801i
$512$	19.6121	+	24.5928i	0.866740	+	1.08686i
$513$	3.21446	+	4.03080i	0.141922	+	0.177964i
$514$	40.6909	−	19.5957i	1.79480	−	0.864330i
$515$	−19.8741	+	9.57088i	−0.875759	+	0.421744i
$516$	−2.84799	−	3.57126i	−0.125376	−	0.157216i
$517$	−4.69620	−	5.88885i	−0.206539	−	0.258991i
$518$	17.8759	−	44.0603i	0.785423	−	1.93590i
$519$	−5.14550	+	6.45226i	−0.225863	+	0.283223i
$520$	−0.326324			−0.0143103
$521$	−22.1762			−0.971557			−0.485779	−	0.874082i	$-0.661464\pi$
$521$	−22.1762			−0.971557			−0.485779	+	0.874082i	$0.661464\pi$
$522$	13.5988	−	17.0523i	0.595202	−	0.746360i
$523$	−4.73248	+	20.7343i	−0.206937	+	0.906649i	0.759654	+	0.650327i	$0.225368\pi$
$523$	−4.73248	+	20.7343i	−0.206937	+	0.906649i	−0.966591	+	0.256323i	$0.917489\pi$
$524$	5.88706	−	2.83506i	0.257177	−	0.123850i
$525$	16.5552	+	2.68908i	0.722530	+	0.117361i
$526$	−12.3344	−	5.93993i	−0.537805	−	0.258993i
$527$	−24.0381	+	30.1428i	−1.04711	+	1.31304i
$528$	−44.1196	−	21.2469i	−1.92006	−	0.924651i
$529$	5.09854	−	22.3382i	0.221676	−	0.971225i
$530$	−6.23479	+	3.00252i	−0.270822	+	0.130421i
$531$	−2.46685	−	10.8080i	−0.107052	−	0.469026i
$532$	−9.36713	−	1.52151i	−0.406117	−	0.0659658i
$533$	−0.753105	+	3.29957i	−0.0326206	+	0.142920i
$534$	−15.8779	−	69.5656i	−0.687103	−	3.01040i
$535$	12.1420	+	15.2256i	0.524944	+	0.658259i
$536$	−0.130434	−	0.571469i	−0.00563390	−	0.0246837i
$537$	30.4326	+	14.6555i	1.31326	+	0.632434i
$538$	57.0233			2.45845
$539$	−16.1052	+	26.4789i	−0.693701	+	1.14053i
$540$	8.48159			0.364990
$541$	−15.7002	−	7.56083i	−0.675005	−	0.325065i	0.0647885	−	0.997899i	$-0.479363\pi$
$541$	−15.7002	−	7.56083i	−0.675005	−	0.325065i	−0.739794	+	0.672834i	$0.765077\pi$
$542$	14.2213	+	62.3076i	0.610857	+	2.67634i
$543$	21.2341	+	26.6268i	0.911244	+	1.14266i
$544$	11.4119	+	49.9990i	0.489283	+	2.14369i
$545$	−0.254789	+	1.11630i	−0.0109139	+	0.0478171i
$546$	−1.01036	−	15.9211i	−0.0432393	−	0.681362i
$547$	−0.0205374	−	0.0899802i	−0.000878115	−	0.00384727i	0.974487	−	0.224444i	$-0.0720566\pi$
$547$	−0.0205374	−	0.0899802i	−0.000878115	−	0.00384727i	−0.975365	+	0.220597i	$0.929199\pi$
$548$	−32.2570	+	15.5341i	−1.37795	+	0.663585i
$549$	2.90522	−	12.7286i	0.123992	−	0.543244i
$550$	18.8540	+	9.07962i	0.803938	+	0.387156i
$551$	−3.19782	+	4.00995i	−0.136232	+	0.170829i
$552$	0.124128	+	0.0597769i	0.00528324	+	0.00254427i
$553$	−20.6091	+	18.6888i	−0.876387	+	0.794730i
$554$	−26.9891	+	12.9973i	−1.14666	+	0.552201i
$555$	8.66527	−	37.9650i	0.367820	−	1.61153i
$556$	12.1363	−	15.2184i	0.514693	−	0.645405i
$557$	7.23417			0.306522			0.153261	−	0.988186i	$-0.451023\pi$
$557$	7.23417			0.306522			0.153261	+	0.988186i	$0.451023\pi$
$558$	−47.3696			−2.00531
$559$	−0.645783	+	0.809786i	−0.0273137	+	0.0342503i
$560$	13.2031	−	11.9729i	0.557933	−	0.505948i
$561$	−47.5629	−	59.6420i	−2.00811	−	2.51809i
$562$	−28.2345	−	35.4049i	−1.19100	−	1.49346i
$563$	−23.3115	+	11.2262i	−0.982461	+	0.473128i	−0.854951	−	0.518709i	$-0.826413\pi$
$563$	−23.3115	+	11.2262i	−0.982461	+	0.473128i	−0.127510	+	0.991837i	$0.540698\pi$
$564$	−7.76997	+	3.74182i	−0.327175	+	0.157559i
$565$	−11.1277	−	13.9537i	−0.468146	−	0.587036i
$566$	−23.7295	−	29.7559i	−0.997427	−	1.25073i
$567$	0.807744	+	12.7284i	0.0339221	+	0.534541i
$568$	1.29663	−	1.62592i	0.0544052	−	0.0682220i
$569$	41.4431			1.73738			0.868692	−	0.495352i	$-0.164961\pi$
$569$	41.4431			1.73738			0.868692	+	0.495352i	$0.164961\pi$
$570$	−15.9055			−0.666207
$571$	20.9437	−	26.2626i	0.876466	−	1.09905i	−0.117897	−	0.993026i	$-0.537615\pi$
$571$	20.9437	−	26.2626i	0.876466	−	1.09905i	0.994363	−	0.106028i	$-0.0338132\pi$
$572$	2.16427	−	9.48229i	0.0904927	−	0.396474i
$573$	−31.0273	+	14.9420i	−1.29619	+	0.624210i
$574$	−7.55010	−	13.4292i	−0.315135	−	0.560523i
$575$	−0.636468	−	0.306507i	−0.0265426	−	0.0127822i
$576$	−18.3029	+	22.9511i	−0.762620	+	0.956295i
$577$	9.17297	+	4.41747i	0.381876	+	0.183902i	0.614966	−	0.788553i	$-0.289170\pi$
$577$	9.17297	+	4.41747i	0.381876	+	0.183902i	−0.233091	+	0.972455i	$0.574884\pi$
$578$	−11.0880	+	48.5795i	−0.461198	+	2.02064i
$579$	39.9928	−	19.2595i	1.66204	−	0.800398i
$580$	1.87757	+	8.22616i	0.0779617	+	0.341573i
$581$	−7.16203	+	17.6528i	−0.297131	+	0.732363i
$582$	3.81623	−	16.7200i	0.158188	−	0.693066i
$583$	2.13383	+	9.34892i	0.0883742	+	0.387193i
$584$	0.627139	+	0.786407i	0.0259512	+	0.0325418i
$585$	−1.66764	−	7.30639i	−0.0689482	−	0.302082i
$586$	32.0615	+	15.4400i	1.32445	+	0.637821i
$587$	−29.2267			−1.20632			−0.603158	−	0.797622i	$-0.706091\pi$
$587$	−29.2267			−1.20632			−0.603158	+	0.797622i	$0.706091\pi$
$588$	25.4540	+	24.7239i	1.04971	+	1.01960i
$589$	11.1392			0.458983
$590$	7.90761	+	3.80810i	0.325551	+	0.156777i
$591$	−7.27002	−	31.8520i	−0.299049	−	1.31022i
$592$	23.6255	+	29.6255i	0.971003	+	1.21760i
$593$	−4.93986	−	21.6429i	−0.202856	−	0.888769i	−0.969188	−	0.246324i	$-0.920777\pi$
$593$	−4.93986	−	21.6429i	−0.202856	−	0.888769i	0.766332	−	0.642445i	$-0.222080\pi$
$594$	5.35224	−	23.4497i	0.219605	−	0.962152i
$595$	26.6239	−	7.88042i	1.09147	−	0.323066i
$596$	−4.24156	−	18.5835i	−0.173741	−	0.761210i
$597$	−50.5563	+	24.3466i	−2.06913	+	0.996441i
$598$	−0.149518	+	0.655082i	−0.00611426	+	0.0267883i
$599$	3.98096	+	1.91713i	0.162657	+	0.0783317i	0.513441	−	0.858125i	$-0.328370\pi$
$599$	3.98096	+	1.91713i	0.162657	+	0.0783317i	−0.350784	+	0.936457i	$0.614085\pi$
$600$	−0.694547	+	0.870934i	−0.0283547	+	0.0355557i
$601$	−23.5465	−	11.3394i	−0.960483	−	0.462544i	−0.113134	−	0.993580i	$-0.536089\pi$
$601$	−23.5465	−	11.3394i	−0.960483	−	0.462544i	−0.847350	+	0.531035i	$0.821803\pi$
$602$	−0.298602	−	4.70534i	−0.0121701	−	0.191776i
$603$	12.1286	−	5.84084i	0.493916	−	0.237857i
$604$	−6.14322	+	26.9152i	−0.249964	+	1.09516i
$605$	−8.66494	+	10.8655i	−0.352280	+	0.441745i
$606$	16.0559			0.652227
$607$	−10.2582			−0.416368			−0.208184	−	0.978090i	$-0.566755\pi$
$607$	−10.2582			−0.416368			−0.208184	+	0.978090i	$0.566755\pi$
$608$	9.23851	−	11.5847i	0.374671	−	0.469823i
$609$	18.3895	−	5.44313i	0.745181	−	0.220567i
$610$	6.44469	+	8.08139i	0.260938	+	0.327206i
$611$	1.21924	+	1.52887i	0.0493250	+	0.0618516i
$612$	−45.1388	+	21.7377i	−1.82463	+	0.878695i
$613$	−36.3601	+	17.5101i	−1.46857	+	0.707226i	−0.985707	−	0.168470i	$-0.946117\pi$
$613$	−36.3601	+	17.5101i	−1.46857	+	0.707226i	−0.482863	+	0.875696i	$0.660403\pi$
$614$	−31.3958	−	39.3691i	−1.26703	−	1.58881i
$615$	−7.86676	−	9.86460i	−0.317218	−	0.397779i
$616$	−1.00877	−	1.79428i	−0.0406447	−	0.0722936i
$617$	1.36605	−	1.71298i	0.0549952	−	0.0689618i	−0.753573	−	0.657364i	$-0.771671\pi$
$617$	1.36605	−	1.71298i	0.0549952	−	0.0689618i	0.808568	+	0.588402i	$0.200243\pi$
$618$	71.6239			2.88114
$619$	7.10982			0.285768			0.142884	−	0.989739i	$-0.454362\pi$
$619$	7.10982			0.285768			0.142884	+	0.989739i	$0.454362\pi$
$620$	11.4257	−	14.3274i	0.458867	−	0.575401i
$621$	−0.180679	+	0.791607i	−0.00725040	+	0.0317661i
$622$	7.04442	−	3.39241i	0.282455	−	0.136023i
$623$	13.5300	−	33.3486i	0.542070	−	1.33608i
$624$	11.4544	+	5.51614i	0.458543	+	0.220823i
$625$	−4.57539	+	5.73736i	−0.183016	+	0.229494i
$626$	−62.7826	−	30.2345i	−2.50930	−	1.20841i
$627$	−4.90450	+	21.4880i	−0.195867	+	0.858148i
$628$	7.19809	−	3.46642i	0.287235	−	0.138325i
$629$	13.1353	+	57.5496i	0.523740	+	2.29465i
$630$	27.9652	+	19.5381i	1.11416	+	0.778415i
$631$	−1.89785	+	8.31501i	−0.0755521	+	0.331015i	−0.998553	−	0.0537834i	$-0.982872\pi$
$631$	−1.89785	+	8.31501i	−0.0755521	+	0.331015i	0.923001	+	0.384799i	$0.125729\pi$
$632$	−0.411173	−	1.80147i	−0.0163556	−	0.0716585i
$633$	41.2243	+	51.6936i	1.63852	+	2.05464i
$634$	−3.69915	−	16.2070i	−0.146912	−	0.643664i
$635$	−13.1412	−	6.32846i	−0.521492	−	0.251137i
$636$	10.9795			0.435364
$637$	4.18127	−	6.87450i	0.165668	−	0.272377i
$638$	23.9283			0.947330
$639$	43.0305	+	20.7224i	1.70226	+	0.819766i
$640$	0.504879	+	2.21202i	0.0199571	+	0.0874377i
$641$	−19.6532	−	24.6443i	−0.776254	−	0.973392i	0.223745	−	0.974648i	$-0.428172\pi$
$641$	−19.6532	−	24.6443i	−0.776254	−	0.973392i	−0.999999	+	0.00125596i	$0.999600\pi$
$642$	−14.0705	−	61.6471i	−0.555320	−	2.43302i
$643$	−3.27632	+	14.3545i	−0.129206	+	0.566087i	0.868334	+	0.495980i	$0.165191\pi$
$643$	−3.27632	+	14.3545i	−0.129206	+	0.566087i	−0.997539	+	0.0701067i	$0.977666\pi$
$644$	−0.732456	−	1.30280i	−0.0288628	−	0.0513375i
$645$	−0.859231	−	3.76454i	−0.0338322	−	0.148228i
$646$	21.7228	−	10.4611i	0.854671	−	0.411588i
$647$	3.15319	−	13.8150i	0.123965	−	0.543124i	−0.874361	−	0.485276i	$-0.838719\pi$
$647$	3.15319	−	13.8150i	0.123965	−	0.543124i	0.998325	−	0.0578479i	$-0.0184238\pi$
$648$	−0.763197	−	0.367536i	−0.0299812	−	0.0144382i
$649$	7.58301	−	9.50880i	0.297659	−	0.373253i
$650$	−4.89491	−	2.35727i	−0.191994	−	0.0924596i
$651$	−34.1442	−	23.8551i	−1.33822	−	0.934953i
$652$	28.1350	−	13.5491i	1.10185	−	0.530623i
$653$	7.94549	−	34.8115i	0.310931	−	1.36228i	−0.542055	−	0.840343i	$-0.682353\pi$
$653$	7.94549	−	34.8115i	0.310931	−	1.36228i	0.852986	−	0.521934i	$-0.174789\pi$
$654$	2.31802	−	2.90671i	0.0906419	−	0.113661i
$655$	5.52356			0.215823
$656$	12.2774			0.479353
$657$	−14.4027	+	18.0605i	−0.561904	+	0.704605i
$658$	−8.78639	−	1.42718i	−0.342529	−	0.0556372i
$659$	−10.8723	−	13.6334i	−0.423523	−	0.531082i	0.523594	−	0.851968i	$-0.324591\pi$
$659$	−10.8723	−	13.6334i	−0.423523	−	0.531082i	−0.947118	+	0.320886i	$0.896019\pi$
$660$	22.6075	+	28.3489i	0.879995	+	1.10348i
$661$	37.4022	−	18.0120i	1.45478	−	0.700584i	0.471360	−	0.881941i	$-0.343763\pi$
$661$	37.4022	−	18.0120i	1.45478	−	0.700584i	0.983417	+	0.181357i	$0.0580490\pi$
$662$	−28.5102	+	13.7298i	−1.10808	+	0.533624i
$663$	12.3484	+	15.4844i	0.479571	+	0.601363i
$664$	−0.788888	−	0.989234i	−0.0306148	−	0.0383897i
$665$	−6.57617	−	4.59448i	−0.255013	−	0.178166i
$666$	−45.2198	+	56.7039i	−1.75223	+	2.19723i
$667$	−0.807763			−0.0312767
$668$	10.3792			0.401583
$669$	−23.4168	+	29.3637i	−0.905344	+	1.13527i
$670$	−2.37157	+	10.3905i	−0.0916219	+	0.401422i
$671$	12.9050	−	6.21474i	0.498194	−	0.239917i
$672$	−53.1273	+	15.7252i	−2.04943	+	0.606613i
$673$	0.949748	+	0.457375i	0.0366101	+	0.0176305i	0.452099	−	0.891968i	$-0.350675\pi$
$673$	0.949748	+	0.457375i	0.0366101	+	0.0176305i	−0.415489	+	0.909598i	$0.636390\pi$
$674$	10.1360	−	12.7102i	0.390426	−	0.489579i
$675$	−5.91505	−	2.84854i	−0.227670	−	0.109640i
$676$	4.96662	−	21.7602i	0.191024	−	0.836930i
$677$	−32.3065	+	15.5580i	−1.24164	+	0.597942i	−0.935258	−	0.353967i	$-0.884832\pi$
$677$	−32.3065	+	15.5580i	−1.24164	+	0.597942i	−0.306381	+	0.951909i	$0.599118\pi$
$678$	12.8951	+	56.4973i	0.495235	+	2.16977i
$679$	6.40759	−	5.81057i	0.245901	−	0.222989i
$680$	−0.410356	+	1.79789i	−0.0157364	+	0.0689458i
$681$	4.01229	+	17.5790i	0.153751	+	0.673629i
$682$	−32.4018	−	40.6306i	−1.24073	−	1.55583i
$683$	−3.05496	−	13.3846i	−0.116895	−	0.512149i	−0.999144	−	0.0413667i	$-0.986829\pi$
$683$	−3.05496	−	13.3846i	−0.116895	−	0.512149i	0.882249	−	0.470782i	$-0.156028\pi$
$684$	13.0417	+	6.28056i	0.498662	+	0.240143i
$685$	−30.2652			−1.15637
$686$	6.92182	+	35.9668i	0.264276	+	1.37322i
$687$	−41.9963			−1.60226
$688$	3.38524	+	1.63025i	0.129061	+	0.0621526i
$689$	−0.553989	−	2.42718i	−0.0211053	−	0.0924683i
$690$	−1.56183	−	1.95848i	−0.0594580	−	0.0745580i
$691$	8.38901	+	36.7547i	0.319133	+	1.39821i	0.839077	+	0.544013i	$0.183096\pi$
$691$	8.38901	+	36.7547i	0.319133	+	1.39821i	−0.519944	+	0.854200i	$0.674047\pi$
$692$	−1.32316	+	5.79713i	−0.0502989	+	0.220374i
$693$	35.0187	−	31.7559i	1.33025	−	1.20631i
$694$	2.29713	+	10.0644i	0.0871978	+	0.382038i
$695$	14.8251	−	7.13938i	0.562347	−	0.270812i
$696$	−0.283439	+	1.24183i	−0.0107437	+	0.0470714i
$697$	17.2320	+	8.29848i	0.652708	+	0.314327i
$698$	−8.62948	+	10.8210i	−0.326630	+	0.409582i
$699$	17.0540	+	8.21278i	0.645042	+	0.310636i
$700$	11.5877	−	3.42984i	0.437972	−	0.129636i
$701$	−32.8460	+	15.8178i	−1.24058	+	0.597431i	−0.934970	−	0.354727i	$-0.884574\pi$
$701$	−32.8460	+	15.8178i	−1.24058	+	0.597431i	−0.305608	+	0.952158i	$0.598860\pi$
$702$	−1.38956	+	6.08804i	−0.0524454	+	0.229778i
$703$	10.6337	−	13.3342i	0.401057	−	0.502909i
$704$	−32.2056			−1.21379
$705$	−7.29021			−0.274565
$706$	4.99770	−	6.26692i	0.188091	−	0.235859i
$707$	6.63837	+	4.63794i	0.249662	+	0.174427i
$708$	−8.68229	−	10.8872i	−0.326300	−	0.409168i
$709$	24.5539	+	30.7896i	0.922142	+	1.15633i	0.987366	+	0.158459i	$0.0506525\pi$
$709$	24.5539	+	30.7896i	0.922142	+	1.15633i	−0.0652235	+	0.997871i	$0.520776\pi$
$710$	−34.0675	+	16.4061i	−1.27853	+	0.615708i
$711$	38.2336	−	18.4123i	1.43387	−	0.690516i
$712$	1.49032	+	1.86880i	0.0558519	+	0.0700361i
$713$	1.09381	+	1.37160i	0.0409635	+	0.0513667i
$714$	−88.9882	−	14.4544i	−3.33030	−	0.540943i
$715$	5.12626	−	6.42812i	0.191711	−	0.240398i
$716$	24.3372			0.909524
$717$	41.6923			1.55703
$718$	21.0178	−	26.3555i	0.784379	−	0.983580i
$719$	10.0112	−	43.8621i	0.373357	−	1.63578i	−0.343924	−	0.938998i	$-0.611756\pi$
$719$	10.0112	−	43.8621i	0.373357	−	1.63578i	0.717280	−	0.696785i	$-0.245387\pi$
$720$	−24.4942	+	11.7958i	−0.912844	+	0.439602i
$721$	29.6131	+	20.6894i	1.10285	+	0.770513i
$722$	27.5782	+	13.2810i	1.02635	+	0.494266i
$723$	−1.40641	+	1.76358i	−0.0523049	+	0.0655883i
$724$	22.1084	+	10.6468i	0.821652	+	0.395687i
$725$	1.45334	−	6.36749i	0.0539756	−	0.236483i
$726$	40.6561	−	19.5789i	1.50889	−	0.726643i
$727$	7.46500	+	32.7063i	0.276861	+	1.21301i	0.901737	+	0.432285i	$0.142293\pi$
$727$	7.46500	+	32.7063i	0.276861	+	1.21301i	−0.624876	+	0.780724i	$0.714850\pi$
$728$	0.261900	+	0.465834i	0.00970665	+	0.0172650i
$729$	9.19302	−	40.2773i	0.340482	−	1.49175i
$730$	−4.06959	−	17.8300i	−0.150622	−	0.659919i
$731$	3.64945	+	4.57626i	0.134980	+	0.169259i
$732$	−3.64933	−	15.9888i	−0.134883	−	0.590961i
$733$	27.9829	+	13.4759i	1.03357	+	0.497743i	0.872199	−	0.489151i	$-0.162693\pi$
$733$	27.9829	+	13.4759i	1.03357	+	0.497743i	0.161374	+	0.986893i	$0.448407\pi$
$734$	39.2305			1.44803
$735$	10.3182	+	28.1663i	0.380593	+	1.03893i
$736$	2.33363			0.0860186
$737$	13.3062	+	6.40790i	0.490138	+	0.236038i
$738$	5.22908	+	22.9101i	0.192485	+	0.843333i
$739$	−26.0048	−	32.6090i	−0.956601	−	1.19954i	−0.979835	−	0.199810i	$-0.935968\pi$
$739$	−26.0048	−	32.6090i	−0.956601	−	1.19954i	0.0232334	−	0.999730i	$-0.492604\pi$
$740$	−6.24344	−	27.3543i	−0.229514	−	1.00556i
$741$	1.27331	−	5.57875i	0.0467763	−	0.204941i
$742$	9.29005	+	6.49055i	0.341049	+	0.238276i
$743$	−0.802263	−	3.51494i	−0.0294322	−	0.128951i	0.958078	−	0.286509i	$-0.0924949\pi$
$743$	−0.802263	−	3.51494i	−0.0294322	−	0.128951i	−0.987510	+	0.157558i	$0.949638\pi$
$744$	2.49246	−	1.20030i	0.0913779	−	0.0440053i
$745$	3.58556	−	15.7093i	0.131365	−	0.575546i
$746$	−6.71116	−	3.23193i	−0.245713	−	0.118329i
$747$	18.1174	−	22.7185i	0.662882	−	0.831228i
$748$	−49.5212	−	23.8482i	−1.81067	−	0.871975i
$749$	11.9900	−	29.5526i	0.438103	−	1.07983i
$750$	56.4260	−	27.1733i	2.06039	−	0.992230i
$751$	3.57703	−	15.6720i	0.130528	−	0.571879i	−0.866789	−	0.498675i	$-0.833820\pi$
$751$	3.57703	−	15.6720i	0.130528	−	0.571879i	0.997317	−	0.0732046i	$-0.0233226\pi$
$752$	4.42293	−	5.54618i	0.161288	−	0.202248i
$753$	−46.6404			−1.69967
$754$	−6.21230			−0.226239
$755$	−14.5507	+	18.2461i	−0.529556	+	0.664042i
$756$	−6.80712	−	12.1076i	−0.247573	−	0.440351i
$757$	19.1415	+	24.0027i	0.695710	+	0.872392i	0.996695	−	0.0812365i	$-0.0258869\pi$
$757$	19.1415	+	24.0027i	0.695710	+	0.872392i	−0.300985	+	0.953629i	$0.597315\pi$
$758$	16.9126	+	21.2078i	0.614294	+	0.770301i
$759$	−3.12746	+	1.50611i	−0.113520	+	0.0546682i
$760$	0.480047	−	0.231178i	0.0174131	−	0.00838572i
$761$	−1.42327	−	1.78472i	−0.0515935	−	0.0646962i	0.755365	−	0.655304i	$-0.227459\pi$
$761$	−1.42327	−	1.78472i	−0.0515935	−	0.0646962i	−0.806959	+	0.590608i	$0.798888\pi$
$762$	29.5280	+	37.0269i	1.06969	+	1.34134i
$763$	1.79803	−	0.532201i	0.0650931	−	0.0192670i
$764$	−15.4706	+	19.3995i	−0.559705	+	0.701848i
$765$	−42.3517			−1.53123
$766$	−74.6678			−2.69786
$767$	−1.96871	+	2.46869i	−0.0710861	+	0.0891392i
$768$	10.2261	−	44.8035i	0.369003	−	1.61671i
$769$	−2.62722	+	1.26520i	−0.0947400	+	0.0456244i	−0.480654	−	0.876911i	$-0.659601\pi$
$769$	−2.62722	+	1.26520i	−0.0947400	+	0.0456244i	0.385914	+	0.922535i	$0.373886\pi$
$770$	2.37032	+	37.3513i	0.0854204	+	1.34605i
$771$	−54.5754	−	26.2821i	−1.96549	−	0.946528i
$772$	19.9408	−	25.0050i	0.717686	−	0.899950i
$773$	−5.41854	−	2.60943i	−0.194891	−	0.0938548i	0.333893	−	0.942611i	$-0.391638\pi$
$773$	−5.41854	−	2.60943i	−0.194891	−	0.0938548i	−0.528784	+	0.848756i	$0.677352\pi$
$774$	−1.60029	+	7.01132i	−0.0575212	+	0.252017i
$775$	−12.7801	+	6.15458i	−0.459075	+	0.221079i
$776$	0.127838	+	0.560097i	0.00458913	+	0.0201063i
$777$	−61.1504	+	18.1000i	−2.19376	+	0.649333i
$778$	6.05925	−	26.5473i	0.217235	−	0.951767i
$779$	−1.22965	−	5.38743i	−0.0440567	−	0.193025i
$780$	−5.86939	−	7.35998i	−0.210158	−	0.263530i
$781$	11.6595	+	51.0834i	0.417208	+	1.82791i
$782$	3.42116	+	1.64755i	0.122341	+	0.0589161i
$783$	−7.50699			−0.268278
$784$	−27.6881	−	9.23853i	−0.988860	−	0.329947i
$785$	6.75364			0.241048
$786$	−16.1588	−	7.78165i	−0.576364	−	0.277562i
$787$	−6.33689	−	27.7637i	−0.225886	−	0.989669i	−0.952957	−	0.303107i	$-0.901976\pi$
$787$	−6.33689	−	27.7637i	−0.225886	−	0.989669i	0.727071	−	0.686562i	$-0.240881\pi$
$788$	−14.6770	−	18.4043i	−0.522845	−	0.655627i
$789$	4.08582	+	17.9011i	0.145459	+	0.637297i
$790$	−7.47602	+	32.7546i	−0.265985	+	1.16536i
$791$	−10.9884	+	27.0839i	−0.390701	+	0.962993i
$792$	0.698662	+	3.06104i	0.0248259	+	0.108769i
$793$	−3.35043	+	1.61348i	−0.118977	+	0.0572964i
$794$	−8.00860	+	35.0880i	−0.284215	+	1.24523i
$795$	8.36222	+	4.02703i	0.296577	+	0.142824i
$796$	−25.2079	+	31.6097i	−0.893470	+	1.12038i
$797$	−43.0000	−	20.7077i	−1.52314	−	0.733504i	−0.529732	−	0.848165i	$-0.677708\pi$
$797$	−43.0000	−	20.7077i	−1.52314	−	0.733504i	−0.993405	+	0.114661i	$0.963422\pi$
$798$	12.7654	+	22.7054i	0.451889	+	0.803762i
$799$	9.95655	−	4.79482i	0.352237	−	0.169629i
$800$	−4.19869	+	18.3957i	−0.148446	+	0.650385i
$801$	−34.2263	+	42.9184i	−1.20933	+	1.51645i
$802$	−2.40073			−0.0847726
$803$	−25.3429			−0.894331
$804$	10.5430	−	13.2205i	0.371823	−	0.466252i
$805$	−0.0800164	−	1.26089i	−0.00282021	−	0.0444406i
$806$	8.41222	+	10.5486i	0.296308	+	0.371558i
$807$	−47.6849	−	59.7950i	−1.67859	−	2.10488i
$808$	−0.484587	+	0.233365i	−0.0170477	+	0.00820975i
$809$	−3.49925	+	1.68515i	−0.123027	+	0.0592467i	−0.494385	−	0.869243i	$-0.664607\pi$
$809$	−3.49925	+	1.68515i	−0.123027	+	0.0592467i	0.371358	+	0.928490i	$0.378892\pi$
$810$	9.60288	+	12.0416i	0.337411	+	0.423100i
$811$	−9.40897	−	11.7985i	−0.330394	−	0.414301i	0.588692	−	0.808357i	$-0.299643\pi$
$811$	−9.40897	−	11.7985i	−0.330394	−	0.414301i	−0.919086	+	0.394056i	$0.871071\pi$
$812$	10.2361	−	9.28238i	0.359217	−	0.325748i
$813$	53.4438	−	67.0164i	1.87436	−	2.35037i
$814$	−79.5683			−2.78887
$815$	26.3978			0.924673
$816$	44.7953	−	56.1715i	1.56815	−	1.96640i
$817$	0.376316	−	1.64875i	0.0131656	−	0.0576824i
$818$	64.7442	−	31.1791i	2.26373	−	1.09015i
$819$	−9.09162	+	8.24452i	−0.317687	+	0.288087i
$820$	−8.19065	−	3.94441i	−0.286030	−	0.137745i
$821$	−6.76132	+	8.47843i	−0.235972	+	0.295899i	−0.885691	−	0.464275i	$-0.846315\pi$
$821$	−6.76132	+	8.47843i	−0.235972	+	0.295899i	0.649719	+	0.760174i	$0.274886\pi$
$822$	88.5387	+	42.6380i	3.08814	+	1.48717i
$823$	3.91073	−	17.1340i	0.136320	−	0.597255i	−0.859906	−	0.510453i	$-0.829478\pi$
$823$	3.91073	−	17.1340i	0.136320	−	0.597255i	0.996226	−	0.0868027i	$-0.0276650\pi$
$824$	−2.16170	+	1.04102i	−0.0753063	+	0.0362656i
$825$	−6.24547	−	27.3632i	−0.217439	−	0.952664i
$826$	−0.910309	−	14.3446i	−0.0316737	−	0.499112i
$827$	8.53809	−	37.4078i	0.296898	−	1.30080i	−0.577819	−	0.816165i	$-0.696096\pi$
$827$	8.53809	−	37.4078i	0.296898	−	1.30080i	0.874718	−	0.484632i	$-0.161047\pi$
$828$	0.507288	+	2.22257i	0.0176295	+	0.0772397i
$829$	−26.5808	−	33.3312i	−0.923189	−	1.15764i	−0.987167	−	0.159691i	$-0.948950\pi$
$829$	−26.5808	−	33.3312i	−0.923189	−	1.15764i	0.0639786	−	0.997951i	$-0.479621\pi$
$830$	5.11920	+	22.4287i	0.177690	+	0.778511i
$831$	36.1983	+	17.4322i	1.25570	+	0.604715i
$832$	8.36126			0.289875
$833$	−32.6171	−	31.6815i	−1.13012	−	1.09770i
$834$	−53.4277			−1.85005
$835$	7.90503	+	3.80686i	0.273565	+	0.131742i
$836$	3.53376	+	15.4824i	0.122217	+	0.535470i
$837$	10.1654	+	12.7470i	0.351367	+	0.440601i
$838$	2.99163	+	13.1072i	0.103344	+	0.452780i
$839$	5.64405	−	24.7282i	0.194854	−	0.853712i	−0.779088	−	0.626915i	$-0.784317\pi$
$839$	5.64405	−	24.7282i	0.194854	−	0.853712i	0.973942	−	0.226797i	$-0.0728255\pi$
$840$	−1.96653	−	0.319425i	−0.0678518	−	0.0110212i
$841$	4.79129	+	20.9920i	0.165217	+	0.723862i
$842$	16.4414	−	7.91775i	0.566607	−	0.272864i
$843$	−13.5151	+	59.2137i	−0.465486	+	2.03943i
$844$	42.9216	+	20.6699i	1.47742	+	0.711489i
$845$	11.7639	−	14.7514i	0.404689	−	0.507464i
$846$	12.2331	+	5.89117i	0.420584	+	0.202543i
$847$	22.4650	+	3.64900i	0.771906	+	0.125381i
$848$	−8.13697	+	3.91856i	−0.279425	+	0.134564i
$849$	−11.3588	+	49.7660i	−0.389831	+	1.70796i
$850$	−19.1428	+	24.0043i	−0.656593	+	0.823341i
$851$	2.68604			0.0920763
$852$	59.9929			2.05532
$853$	27.1557	−	34.0521i	0.929792	−	1.16592i	−0.0560803	−	0.998426i	$-0.517860\pi$
$853$	27.1557	−	34.0521i	0.929792	−	1.16592i	0.985873	−	0.167496i	$-0.0535683\pi$
$854$	6.36400	−	15.6859i	0.217771	−	0.536759i
$855$	7.62930	+	9.56683i	0.260916	+	0.327179i
$856$	1.32068	+	1.65608i	0.0451398	+	0.0566035i
$857$	−16.8675	+	8.12294i	−0.576182	+	0.277474i	−0.699196	−	0.714931i	$-0.746458\pi$
$857$	−16.8675	+	8.12294i	−0.576182	+	0.277474i	0.123014	+	0.992405i	$0.460744\pi$
$858$	−24.0525	+	11.5831i	−0.821139	+	0.395440i
$859$	9.77163	+	12.2532i	0.333404	+	0.418075i	0.920070	−	0.391754i	$-0.128131\pi$
$859$	9.77163	+	12.2532i	0.333404	+	0.418075i	−0.586666	+	0.809829i	$0.699560\pi$
$860$	−1.73464	−	2.17518i	−0.0591509	−	0.0741729i
$861$	−7.76826	+	19.1471i	−0.264741	+	0.652530i
$862$	−2.63495	+	3.30412i	−0.0897466	+	0.112539i
$863$	10.6617			0.362929			0.181465	−	0.983397i	$-0.441916\pi$
$863$	10.6617			0.362929			0.181465	+	0.983397i	$0.441916\pi$
$864$	21.6877			0.737830
$865$	−3.13401	+	3.92992i	−0.106560	+	0.133621i
$866$	−12.6707	+	55.5140i	−0.430568	+	1.88644i
$867$	60.2130	−	28.9970i	2.04494	−	0.984791i
$868$	−29.6226	−	4.81162i	−1.00546	−	0.163317i
$869$	41.9456	+	20.1999i	1.42291	+	0.685235i
$870$	14.4399	−	18.1070i	0.489558	−	0.613886i
$871$	−3.45457	−	1.66363i	−0.117053	−	0.0563700i
$872$	−0.0277132	+	0.121419i	−0.000938488	+	0.00411178i
$873$	−11.8873	+	5.72460i	−0.402323	+	0.193748i
$874$	−0.244129	−	1.06960i	−0.00825778	−	0.0361797i
$875$	31.1788	+	5.06440i	1.05404	+	0.171208i
$876$	−6.45683	+	28.2892i	−0.218156	+	0.955805i
$877$	1.37698	+	6.03293i	0.0464972	+	0.203717i	0.992841	−	0.119444i	$-0.0381113\pi$
$877$	1.37698	+	6.03293i	0.0464972	+	0.203717i	−0.946344	+	0.323162i	$0.895254\pi$
$878$	7.60231	+	9.53300i	0.256566	+	0.321723i
$879$	−10.6205	−	46.5314i	−0.358221	−	1.56947i
$880$	−26.8722	−	12.9410i	−0.905862	−	0.436240i
$881$	46.9328			1.58120			0.790602	−	0.612330i	$-0.209768\pi$
$881$	46.9328			1.58120			0.790602	+	0.612330i	$0.209768\pi$
$882$	5.44678	−	55.6017i	0.183403	−	1.87221i
$883$	−20.8366			−0.701207			−0.350604	−	0.936524i	$-0.614024\pi$
$883$	−20.8366			−0.701207			−0.350604	+	0.936524i	$0.614024\pi$
$884$	12.8568	+	6.19150i	0.432420	+	0.208243i
$885$	−2.61943	−	11.4765i	−0.0880510	−	0.385777i
$886$	−20.5162	−	25.7265i	−0.689256	−	0.864300i
$887$	4.74419	+	20.7857i	0.159294	+	0.697914i	0.989984	+	0.141179i	$0.0450892\pi$
$887$	4.74419	+	20.7857i	0.159294	+	0.697914i	−0.830690	+	0.556736i	$0.812054\pi$
$888$	0.942516	−	4.12943i	0.0316288	−	0.138575i
$889$	1.51279	+	23.8384i	0.0507373	+	0.799514i
$890$	−9.67086	−	42.3708i	−0.324168	−	1.42027i
$891$	19.2291	−	9.26024i	0.644199	−	0.310230i
$892$	−6.02158	+	26.3823i	−0.201617	+	0.883344i
$893$	−2.87669	−	1.38534i	−0.0962647	−	0.0463586i
$894$	−32.6208	+	40.9052i	−1.09100	+	1.36807i
$895$	18.5358	+	8.92636i	0.619583	+	0.298375i
$896$	2.75250	−	2.49604i	0.0919545	−	0.0833868i
$897$	0.811957	−	0.391018i	0.0271105	−	0.0130557i
$898$	−4.87163	+	21.3440i	−0.162568	+	0.712259i
$899$	−10.1128	+	12.6810i	−0.337281	+	0.422936i
$900$	−18.4330			−0.614432
$901$	−14.0692			−0.468714
$902$	−16.0740	+	20.1562i	−0.535207	+	0.671128i
$903$	−4.68436	+	4.24790i	−0.155886	+	0.141361i
$904$	−1.21035	−	1.51773i	−0.0402557	−	0.0504791i
$905$	12.9332	+	16.2178i	0.429915	+	0.539096i
$906$	68.2724	−	32.8783i	2.26820	−	1.09231i
$907$	27.0337	−	13.0187i	0.897638	−	0.432280i	0.0726029	−	0.997361i	$-0.476869\pi$
$907$	27.0337	−	13.0187i	0.897638	−	0.432280i	0.825035	+	0.565081i	$0.191155\pi$
$908$	8.10015	+	10.1573i	0.268813	+	0.337081i
$909$	−7.70146	−	9.65732i	−0.255441	−	0.320313i
$910$	−0.615386	−	9.69720i	−0.0203999	−	0.321459i
$911$	8.27568	−	10.3774i	0.274186	−	0.343818i	−0.625605	−	0.780140i	$-0.715148\pi$
$911$	8.27568	−	10.3774i	0.274186	−	0.343818i	0.899791	+	0.436322i	$0.143719\pi$
$912$	−20.7581			−0.687369
$913$	31.8792			1.05505
$914$	−38.1006	+	47.7767i	−1.26026	+	1.58031i
$915$	3.08492	−	13.5159i	0.101984	−	0.446822i
$916$	−27.2623	+	13.1288i	−0.900773	+	0.433789i
$917$	−4.43307	−	7.88499i	−0.146393	−	0.260385i
$918$	31.7948	+	15.3116i	1.04938	+	0.505357i
$919$	−11.5759	+	14.5157i	−0.381853	+	0.478828i	−0.935199	−	0.354123i	$-0.884779\pi$
$919$	−11.5759	+	14.5157i	−0.381853	+	0.478828i	0.553346	+	0.832952i	$0.313351\pi$
$920$	0.0756036	+	0.0364088i	0.00249258	+	0.00120036i
$921$	−15.0284	+	65.8438i	−0.495203	+	2.16963i
$922$	−8.22865	+	3.96271i	−0.270996	+	0.130505i
$923$	−3.02705	−	13.2624i	−0.0996365	−	0.436536i
$924$	22.3244	−	55.0248i	0.734419	−	1.81018i
$925$	−4.83276	+	21.1737i	−0.158900	+	0.696188i
$926$	−6.87759	−	30.1327i	−0.226012	−	0.990221i
$927$	−34.3555	−	43.0804i	−1.12838	−	1.41495i
$928$	4.80100	+	21.0345i	0.157600	+	0.690492i
$929$	−34.9086	−	16.8111i	−1.14531	−	0.551554i	−0.237691	−	0.971341i	$-0.576391\pi$
$929$	−34.9086	−	16.8111i	−1.14531	−	0.551554i	−0.907623	+	0.419786i	$0.862105\pi$
$930$	−50.2994			−1.64938
$931$	−1.28084	+	13.0750i	−0.0419778	+	0.428517i
$932$	13.6383			0.446736
$933$	−9.44811	−	4.54997i	−0.309317	−	0.148959i
$934$	−4.80511	−	21.0526i	−0.157228	−	0.688861i
$935$	−28.9695	−	36.3266i	−0.947404	−	1.18801i
$936$	−0.181388	−	0.794711i	−0.00592884	−	0.0259760i
$937$	−6.68239	+	29.2775i	−0.218304	+	0.956454i	0.740426	+	0.672138i	$0.234624\pi$
$937$	−6.68239	+	29.2775i	−0.218304	+	0.956454i	−0.958731	+	0.284316i	$0.908233\pi$
$938$	16.7361	−	4.95373i	0.546453	−	0.161745i
$939$	20.7970	+	91.1175i	0.678683	+	2.97351i
$940$	−4.73251	+	2.27906i	−0.154358	+	0.0743347i
$941$	11.1374	−	48.7961i	0.363068	−	1.59071i	−0.382290	−	0.924042i	$-0.624865\pi$
$941$	11.1374	−	48.7961i	0.363068	−	1.59071i	0.745358	−	0.666664i	$-0.232278\pi$
$942$	−19.7573	−	9.51460i	−0.643727	−	0.310002i
$943$	0.542622	−	0.680427i	0.0176702	−	0.0221577i
$944$	10.3201	+	4.96992i	0.335892	+	0.161757i
$945$	−0.743637	−	11.7182i	−0.0241905	−	0.381192i
$946$	−7.10850	+	3.42327i	−0.231117	+	0.111300i
$947$	−2.82316	+	12.3691i	−0.0917403	+	0.401941i	−0.999859	−	0.0167715i	$-0.994661\pi$
$947$	−2.82316	+	12.3691i	−0.0917403	+	0.401941i	0.908119	+	0.418712i	$0.137518\pi$
$948$	33.2352	−	41.6756i	1.07943	−	1.35356i
$949$	6.57957			0.213582
$950$	8.87075			0.287805
$951$	−13.9015	+	17.4319i	−0.450786	+	0.565267i
$952$	2.89586	−	0.857149i	0.0938554	−	0.0277804i
$953$	3.32832	+	4.17358i	0.107815	+	0.135195i	0.832811	−	0.553557i	$-0.186730\pi$
$953$	3.32832	+	4.17358i	0.107815	+	0.135195i	−0.724996	+	0.688753i	$0.758159\pi$
$954$	−10.7778	−	13.5149i	−0.348944	−	0.437562i
$955$	−18.8981	+	9.10082i	−0.611527	+	0.294496i
$956$	27.0650	−	13.0338i	0.875344	−	0.421544i
$957$	−20.0097	−	25.0914i	−0.646822	−	0.811089i
$958$	−48.3898	−	60.6789i	−1.56340	−	1.96045i
$959$	24.2901	+	43.2042i	0.784370	+	1.39514i
$960$	−19.4349	+	24.3706i	−0.627260	+	0.786559i
$961$	4.22660			0.136342
$962$	20.6577			0.666030
$963$	−30.3304	+	38.0331i	−0.977382	+	1.22560i
$964$	−0.361656	+	1.58452i	−0.0116481	+	0.0510338i
$965$	24.3587	−	11.7305i	0.784134	−	0.377619i
$966$	−1.54228	+	3.80138i	−0.0496220	+	0.122307i
$967$	−35.2929	−	16.9962i	−1.13494	−	0.546560i	−0.230466	−	0.973080i	$-0.574025\pi$
$967$	−35.2929	−	16.9962i	−1.13494	−	0.546560i	−0.904478	+	0.426520i	$0.859739\pi$
$968$	−0.942481	+	1.18183i	−0.0302925	+	0.0379856i
$969$	−29.1350	−	14.0307i	−0.935951	−	0.450730i
$970$	2.32438	−	10.1838i	0.0746313	−	0.326981i
$971$	32.4926	−	15.6476i	1.04274	−	0.502155i	0.167511	−	0.985870i	$-0.446427\pi$
$971$	32.4926	−	15.6476i	1.04274	−	0.502155i	0.875226	+	0.483715i	$0.160713\pi$
$972$	−8.94232	−	39.1789i	−0.286825	−	1.25666i
$973$	−22.0899	−	15.4332i	−0.708168	−	0.494766i
$974$	8.07882	−	35.3956i	0.258862	−	1.13415i
$975$	1.62146	+	7.10408i	0.0519282	+	0.227512i
$976$	8.41090	+	10.5469i	0.269226	+	0.337599i
$977$	−1.26084	−	5.52410i	−0.0403379	−	0.176732i	0.950746	−	0.309971i	$-0.100319\pi$
$977$	−1.26084	−	5.52410i	−0.0403379	−	0.176732i	−0.991084	+	0.133239i	$0.957462\pi$
$978$	−77.2247	−	37.1895i	−2.46937	−	1.18919i
$979$	−60.2242			−1.92477
$980$	15.5035	+	15.0587i	0.495240	+	0.481034i
$981$	−2.86020			−0.0913193
$982$	−26.0386	−	12.5395i	−0.830925	−	0.400153i
$983$	7.40242	+	32.4321i	0.236101	+	1.03442i	0.944474	+	0.328586i	$0.106572\pi$
$983$	7.40242	+	32.4321i	0.236101	+	1.03442i	−0.708374	+	0.705838i	$0.750571\pi$
$984$	−0.855663	−	1.07297i	−0.0272775	−	0.0342049i
$985$	−4.42800	−	19.4003i	−0.141088	−	0.618146i
$986$	−7.81203	+	34.2268i	−0.248786	+	1.09000i
$987$	5.85095	+	10.4069i	0.186238	+	0.331256i
$988$	−0.917439	−	4.01956i	−0.0291876	−	0.127879i
$989$	0.239966	−	0.115562i	0.00763049	−	0.00367465i
$990$	12.7032	−	55.6562i	0.403733	−	1.76887i
$991$	18.1215	+	8.72684i	0.575647	+	0.277217i	0.698972	−	0.715149i	$-0.253641\pi$
$991$	18.1215	+	8.72684i	0.575647	+	0.277217i	−0.123324	+	0.992366i	$0.539356\pi$
$992$	29.2159	−	36.6355i	0.927604	−	1.16318i
$993$	38.2385	+	18.4147i	1.21346	+	0.584372i
$994$	50.7618	+	35.4650i	1.61007	+	1.12488i
$995$	−30.7927	+	14.8290i	−0.976193	+	0.470110i
$996$	8.12216	−	35.5855i	0.257360	−	1.12757i
$997$	1.45233	−	1.82117i	0.0459959	−	0.0576770i	−0.758301	−	0.651904i	$-0.773970\pi$
$997$	1.45233	−	1.82117i	0.0459959	−	0.0576770i	0.804297	+	0.594227i	$0.202542\pi$
$998$	85.3676			2.70227
$999$	24.9629			0.789790

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.2.e.b.29.1	yes	12
3.2	odd	2		441.2.u.b.127.2		12
4.3	odd	2		784.2.u.b.225.1		12
7.2	even	3		343.2.g.d.116.1		12
7.3	odd	6		343.2.g.c.30.1		12
7.4	even	3		343.2.g.b.30.1		12
7.5	odd	6		343.2.g.a.116.1		12
7.6	odd	2		343.2.e.b.197.1		12
49.4	even	21		343.2.g.d.275.1		12
49.13	odd	14		2401.2.a.d.1.6		6
49.22	even	7	inner	49.2.e.b.22.1	✓	12
49.23	even	21		343.2.g.b.263.1		12
49.26	odd	42		343.2.g.c.263.1		12
49.27	odd	14		343.2.e.b.148.1		12
49.36	even	7		2401.2.a.c.1.6		6
49.45	odd	42		343.2.g.a.275.1		12
147.71	odd	14		441.2.u.b.316.2		12
196.71	odd	14		784.2.u.b.561.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.e.b.22.1	✓	12	49.22	even	7	inner
49.2.e.b.29.1	yes	12	1.1	even	1	trivial
343.2.e.b.148.1		12	49.27	odd	14
343.2.e.b.197.1		12	7.6	odd	2
343.2.g.a.116.1		12	7.5	odd	6
343.2.g.a.275.1		12	49.45	odd	42
343.2.g.b.30.1		12	7.4	even	3
343.2.g.b.263.1		12	49.23	even	21
343.2.g.c.30.1		12	7.3	odd	6
343.2.g.c.263.1		12	49.26	odd	42
343.2.g.d.116.1		12	7.2	even	3
343.2.g.d.275.1		12	49.4	even	21
441.2.u.b.127.2		12	3.2	odd	2
441.2.u.b.316.2		12	147.71	odd	14
784.2.u.b.225.1		12	4.3	odd	2
784.2.u.b.561.1		12	196.71	odd	14
2401.2.a.c.1.6		6	49.36	even	7
2401.2.a.d.1.6		6	49.13	odd	14

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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	49.e (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.78181 - 0.858075i) q^{2} +(0.590232 + 2.58597i) q^{3} +(1.19158 + 1.49419i) q^{4} +(0.359497 + 1.57506i) q^{5} +(1.16728 - 5.11418i) q^{6} +(1.95991 - 1.77729i) q^{7} +(0.0391023 + 0.171318i) q^{8} +(-3.63598 + 1.75100i) q^{9} +O(q^{10})\)	\(q+(-1.78181 - 0.858075i) q^{2} +(0.590232 + 2.58597i) q^{3} +(1.19158 + 1.49419i) q^{4} +(0.359497 + 1.57506i) q^{5} +(1.16728 - 5.11418i) q^{6} +(1.95991 - 1.77729i) q^{7} +(0.0391023 + 0.171318i) q^{8} +(-3.63598 + 1.75100i) q^{9} +(0.710963 - 3.11493i) q^{10} +(-3.98899 - 1.92100i) q^{11} +(-3.16064 + 3.96332i) q^{12} +(1.03563 + 0.498732i) q^{13} +(-5.01723 + 1.48506i) q^{14} +(-3.86087 + 1.85930i) q^{15} +(0.927871 - 4.06527i) q^{16} +(4.05008 - 5.07864i) q^{17} +7.98112 q^{18} -1.87680 q^{19} +(-1.92507 + 2.41397i) q^{20} +(5.75283 + 4.01925i) q^{21} +(5.45927 + 6.84570i) q^{22} +(-0.184292 - 0.231095i) q^{23} +(-0.419945 + 0.202235i) q^{24} +(2.15327 - 1.03696i) q^{25} +(-1.41734 - 1.77729i) q^{26} +(-1.71273 - 2.14769i) q^{27} +(4.99100 + 0.810692i) q^{28} +(1.70387 - 2.13658i) q^{29} +8.47477 q^{30} -5.93520 q^{31} +(-4.92247 + 6.17259i) q^{32} +(2.61322 - 11.4493i) q^{33} +(-11.5743 + 5.57391i) q^{34} +(3.50392 + 2.44803i) q^{35} +(-6.94889 - 3.34641i) q^{36} +(-5.66584 + 7.10474i) q^{37} +(3.34411 + 1.61044i) q^{38} +(-0.678448 + 2.97247i) q^{39} +(-0.255779 + 0.123177i) q^{40} +(0.655181 + 2.87054i) q^{41} +(-6.80165 - 12.0979i) q^{42} +(-0.200509 + 0.878488i) q^{43} +(-1.88286 - 8.24934i) q^{44} +(-4.06505 - 5.09741i) q^{45} +(0.130077 + 0.569904i) q^{46} +(1.53276 + 0.738138i) q^{47} +11.0603 q^{48} +(0.682458 - 6.96665i) q^{49} -4.72652 q^{50} +(15.5237 + 7.47584i) q^{51} +(0.488831 + 2.14171i) q^{52} +(-1.35041 - 1.69336i) q^{53} +(1.20888 + 5.29644i) q^{54} +(1.59165 - 6.97348i) q^{55} +(0.381119 + 0.266271i) q^{56} +(-1.10775 - 4.85337i) q^{57} +(-4.86932 + 2.34494i) q^{58} +(-0.611266 + 2.67813i) q^{59} +(-7.37869 - 3.55339i) q^{60} +(-2.01709 + 2.52936i) q^{61} +(10.5754 + 5.09285i) q^{62} +(-4.01415 + 9.89400i) q^{63} +(6.55372 - 3.15610i) q^{64} +(-0.413227 + 1.81047i) q^{65} +(-14.4806 + 18.1581i) q^{66} -3.33572 q^{67} +12.4145 q^{68} +(0.488831 - 0.612974i) q^{69} +(-4.14273 - 7.36856i) q^{70} +(-7.37877 - 9.25269i) q^{71} +(-0.442153 - 0.554442i) q^{72} +(5.15719 - 2.48357i) q^{73} +(16.1919 - 7.79760i) q^{74} +(3.95249 + 4.95626i) q^{75} +(-2.23636 - 2.80431i) q^{76} +(-11.2322 + 3.32463i) q^{77} +(3.75947 - 4.71423i) q^{78} -10.5153 q^{79} +6.73660 q^{80} +(-3.00556 + 3.76885i) q^{81} +(1.29573 - 5.67695i) q^{82} +(-6.48731 + 3.12412i) q^{83} +(0.849421 + 13.3851i) q^{84} +(9.45515 + 4.55336i) q^{85} +(1.11108 - 1.39325i) q^{86} +(6.53082 + 3.14508i) q^{87} +(0.173123 - 0.758501i) q^{88} +(12.2554 - 5.90189i) q^{89} +(2.86919 + 12.5707i) q^{90} +(2.91613 - 0.863147i) q^{91} +(0.125702 - 0.550736i) q^{92} +(-3.50314 - 15.3483i) q^{93} +(-2.09771 - 2.63045i) q^{94} +(-0.674705 - 2.95608i) q^{95} +(-18.8675 - 9.08613i) q^{96} +3.26934 q^{97} +(-7.19392 + 11.8277i) q^{98} +17.8676 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + 2 q^{4} - 7 q^{5} - 7 q^{6} - 7 q^{7} + 6 q^{8} - 8 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 + 2 * q^4 - 7 * q^5 - 7 * q^6 - 7 * q^7 + 6 * q^8 - 8 * q^9	\( 12 q - 2 q^{2} + 2 q^{4} - 7 q^{5} - 7 q^{6} - 7 q^{7} + 6 q^{8} - 8 q^{9} + 14 q^{10} - 8 q^{11} - 14 q^{12} + 7 q^{13} - 28 q^{14} - 7 q^{15} + 16 q^{16} + 20 q^{18} - 14 q^{19} + 7 q^{20} + 21 q^{21} + 13 q^{22} - 2 q^{23} + 3 q^{25} - 7 q^{26} + 21 q^{27} + 14 q^{28} - 11 q^{29} + 42 q^{30} - 14 q^{31} - 24 q^{32} + 35 q^{33} - 42 q^{34} + 21 q^{35} - 13 q^{36} - 30 q^{37} + 21 q^{38} + 21 q^{41} - 35 q^{42} + 17 q^{43} - 6 q^{44} - 49 q^{45} - 16 q^{46} - 21 q^{47} + 7 q^{49} - 46 q^{50} + 7 q^{51} - 7 q^{52} + 6 q^{53} + 42 q^{54} - 28 q^{55} - 14 q^{56} + 7 q^{57} - 32 q^{58} + 14 q^{59} - 28 q^{60} - 7 q^{61} + 56 q^{62} + 14 q^{63} + 14 q^{64} + 14 q^{65} - 28 q^{66} + 48 q^{67} + 56 q^{68} - 7 q^{69} + 21 q^{70} - 39 q^{71} - 4 q^{72} + 42 q^{73} + 61 q^{74} + 7 q^{75} - 28 q^{76} + 21 q^{77} - 16 q^{79} + 42 q^{80} - 25 q^{81} + 28 q^{82} - 7 q^{83} + 42 q^{84} + 28 q^{85} + 17 q^{86} + 7 q^{87} - 11 q^{88} - 14 q^{89} - 14 q^{90} - 21 q^{91} + 16 q^{92} - 70 q^{93} - 49 q^{94} - 7 q^{95} - 70 q^{96} - 28 q^{97} - 28 q^{98} - 18 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 + 2 * q^4 - 7 * q^5 - 7 * q^6 - 7 * q^7 + 6 * q^8 - 8 * q^9 + 14 * q^10 - 8 * q^11 - 14 * q^12 + 7 * q^13 - 28 * q^14 - 7 * q^15 + 16 * q^16 + 20 * q^18 - 14 * q^19 + 7 * q^20 + 21 * q^21 + 13 * q^22 - 2 * q^23 + 3 * q^25 - 7 * q^26 + 21 * q^27 + 14 * q^28 - 11 * q^29 + 42 * q^30 - 14 * q^31 - 24 * q^32 + 35 * q^33 - 42 * q^34 + 21 * q^35 - 13 * q^36 - 30 * q^37 + 21 * q^38 + 21 * q^41 - 35 * q^42 + 17 * q^43 - 6 * q^44 - 49 * q^45 - 16 * q^46 - 21 * q^47 + 7 * q^49 - 46 * q^50 + 7 * q^51 - 7 * q^52 + 6 * q^53 + 42 * q^54 - 28 * q^55 - 14 * q^56 + 7 * q^57 - 32 * q^58 + 14 * q^59 - 28 * q^60 - 7 * q^61 + 56 * q^62 + 14 * q^63 + 14 * q^64 + 14 * q^65 - 28 * q^66 + 48 * q^67 + 56 * q^68 - 7 * q^69 + 21 * q^70 - 39 * q^71 - 4 * q^72 + 42 * q^73 + 61 * q^74 + 7 * q^75 - 28 * q^76 + 21 * q^77 - 16 * q^79 + 42 * q^80 - 25 * q^81 + 28 * q^82 - 7 * q^83 + 42 * q^84 + 28 * q^85 + 17 * q^86 + 7 * q^87 - 11 * q^88 - 14 * q^89 - 14 * q^90 - 21 * q^91 + 16 * q^92 - 70 * q^93 - 49 * q^94 - 7 * q^95 - 70 * q^96 - 28 * q^97 - 28 * q^98 - 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more