LMFDB - Embedded newform 483.2.q.a.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(64,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("483.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.q (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:	$3.85677441763$
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			127.1
Root			$0.142315 + 0.989821i$ of defining polynomial
Character	$\chi$	$=$	483.127
Dual form			483.2.q.a.232.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.85380 - 1.19136i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(1.18639 - 2.59784i) q^{4} +(0.959493 - 0.281733i) q^{5} +(0.915415 + 2.00448i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.268423 - 1.86692i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(1.85380 - 1.19136i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(1.18639 - 2.59784i) q^{4} +(0.959493 - 0.281733i) q^{5} +(0.915415 + 2.00448i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.268423 - 1.86692i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(1.44306 - 1.66538i) q^{10} +(3.15455 + 2.02730i) q^{11} +(2.40255 + 1.54403i) q^{12} +(4.37102 - 5.04443i) q^{13} +(-2.11435 - 0.620830i) q^{14} +(0.142315 + 0.989821i) q^{15} +(1.01867 + 1.17561i) q^{16} +(-2.40287 - 5.26155i) q^{17} +(-2.11435 + 0.620830i) q^{18} +(-0.996114 + 2.18119i) q^{19} +(0.406440 - 2.82685i) q^{20} +(0.841254 - 0.540641i) q^{21} +8.26315 q^{22} +(-1.76381 + 4.45971i) q^{23} +1.88612 q^{24} +(-3.36501 + 2.16256i) q^{25} +(2.09325 - 14.5588i) q^{26} +(0.415415 - 0.909632i) q^{27} +(-2.74024 + 0.804606i) q^{28} +(0.707599 + 1.54943i) q^{29} +(1.44306 + 1.66538i) q^{30} +(0.417125 + 2.90117i) q^{31} +(6.90843 + 2.02850i) q^{32} +(-2.45561 + 2.83392i) q^{33} +(-10.7229 - 6.89116i) q^{34} +(-0.841254 - 0.540641i) q^{35} +(-1.87023 + 2.15836i) q^{36} +(-10.2274 - 3.00304i) q^{37} +(0.751992 + 5.23022i) q^{38} +(4.37102 + 5.04443i) q^{39} +(-0.783524 - 1.71568i) q^{40} +(-4.49005 + 1.31840i) q^{41} +(0.915415 - 2.00448i) q^{42} +(-0.301233 + 2.09512i) q^{43} +(9.00914 - 5.78982i) q^{44} -1.00000 q^{45} +(2.04338 + 10.3687i) q^{46} -11.5680 q^{47} +(-1.30862 + 0.840996i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(-3.66166 + 8.01792i) q^{50} +(5.54996 - 1.62961i) q^{51} +(-7.91886 - 17.3399i) q^{52} +(4.18330 + 4.82778i) q^{53} +(-0.313607 - 2.18119i) q^{54} +(3.59792 + 1.05645i) q^{55} +(-1.23515 + 1.42544i) q^{56} +(-2.01722 - 1.29639i) q^{57} +(3.15768 + 2.02932i) q^{58} +(8.87191 - 10.2387i) q^{59} +(2.74024 + 0.804606i) q^{60} +(-0.666994 - 4.63905i) q^{61} +(4.22962 + 4.88124i) q^{62} +(0.415415 + 0.909632i) q^{63} +(12.2384 - 3.59353i) q^{64} +(2.77279 - 6.07155i) q^{65} +(-1.17597 + 8.17905i) q^{66} +(-10.8071 + 6.94532i) q^{67} -16.5194 q^{68} +(-4.16330 - 2.38054i) q^{69} -2.20362 q^{70} +(4.44588 - 2.85719i) q^{71} +(-0.268423 + 1.86692i) q^{72} +(-3.17385 + 6.94976i) q^{73} +(-22.5373 + 6.61755i) q^{74} +(-1.66166 - 3.63853i) q^{75} +(4.48458 + 5.17549i) q^{76} +(-0.533654 - 3.71165i) q^{77} +(14.1128 + 4.14388i) q^{78} +(2.47187 - 2.85269i) q^{79} +(1.30862 + 0.840996i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-6.75296 + 7.79334i) q^{82} +(7.72882 + 2.26939i) q^{83} +(-0.406440 - 2.82685i) q^{84} +(-3.78789 - 4.37145i) q^{85} +(1.93763 + 4.24282i) q^{86} +(-1.63436 + 0.479890i) q^{87} +(2.93807 - 6.43348i) q^{88} +(-1.94277 + 13.5123i) q^{89} +(-1.85380 + 1.19136i) q^{90} -6.67474 q^{91} +(9.49302 + 9.87306i) q^{92} -2.93100 q^{93} +(-21.4448 + 13.7817i) q^{94} +(-0.341254 + 2.37347i) q^{95} +(-2.99103 + 6.54943i) q^{96} +(-8.69206 + 2.55222i) q^{97} +(0.915415 + 2.00448i) q^{98} +(-2.45561 - 2.83392i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} - q^{3} + 8 q^{4} + q^{5} + 4 q^{6} - q^{7} - 7 q^{8} - q^{9}+O(q^{10}) $ 10 * q + 4 * q^2 - q^3 + 8 * q^4 + q^5 + 4 * q^6 - q^7 - 7 * q^8 - q^9	\( 10 q + 4 q^{2} - q^{3} + 8 q^{4} + q^{5} + 4 q^{6} - q^{7} - 7 q^{8} - q^{9} - 4 q^{10} - q^{11} - 3 q^{12} + 15 q^{13} - 7 q^{14} + q^{15} - 10 q^{16} - 24 q^{17} - 7 q^{18} + 5 q^{19} - 8 q^{20} - q^{21} + 26 q^{22} + 21 q^{23} - 18 q^{24} + 4 q^{25} + 6 q^{26} - q^{27} - 3 q^{28} - 22 q^{29} - 4 q^{30} - 8 q^{31} + 10 q^{32} - q^{33} + 8 q^{34} + q^{35} - 14 q^{36} - 2 q^{37} + 2 q^{38} + 15 q^{39} - 4 q^{40} + 7 q^{41} + 4 q^{42} + q^{43} + 19 q^{44} - 10 q^{45} + 15 q^{46} - 6 q^{47} + q^{48} - q^{49} - 16 q^{50} + 20 q^{51} - 21 q^{52} - q^{53} - 7 q^{54} + 12 q^{55} + 4 q^{56} - 6 q^{57} + 22 q^{58} + 10 q^{59} + 3 q^{60} + 5 q^{61} - 34 q^{62} - q^{63} + 13 q^{64} - 4 q^{65} - 7 q^{66} + 29 q^{67} - 28 q^{68} - q^{69} - 4 q^{70} + 22 q^{71} - 7 q^{72} - 33 q^{73} - 36 q^{74} + 4 q^{75} + 26 q^{76} - q^{77} + 28 q^{78} + 27 q^{79} - q^{80} - q^{81} + 38 q^{82} + 25 q^{83} + 8 q^{84} + 2 q^{85} + 18 q^{86} - 7 q^{88} - 38 q^{89} - 4 q^{90} - 18 q^{91} + 41 q^{92} - 30 q^{93} - 42 q^{94} + 6 q^{95} - 23 q^{96} - q^{97} + 4 q^{98} - q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 - q^3 + 8 * q^4 + q^5 + 4 * q^6 - q^7 - 7 * q^8 - q^9 - 4 * q^10 - q^11 - 3 * q^12 + 15 * q^13 - 7 * q^14 + q^15 - 10 * q^16 - 24 * q^17 - 7 * q^18 + 5 * q^19 - 8 * q^20 - q^21 + 26 * q^22 + 21 * q^23 - 18 * q^24 + 4 * q^25 + 6 * q^26 - q^27 - 3 * q^28 - 22 * q^29 - 4 * q^30 - 8 * q^31 + 10 * q^32 - q^33 + 8 * q^34 + q^35 - 14 * q^36 - 2 * q^37 + 2 * q^38 + 15 * q^39 - 4 * q^40 + 7 * q^41 + 4 * q^42 + q^43 + 19 * q^44 - 10 * q^45 + 15 * q^46 - 6 * q^47 + q^48 - q^49 - 16 * q^50 + 20 * q^51 - 21 * q^52 - q^53 - 7 * q^54 + 12 * q^55 + 4 * q^56 - 6 * q^57 + 22 * q^58 + 10 * q^59 + 3 * q^60 + 5 * q^61 - 34 * q^62 - q^63 + 13 * q^64 - 4 * q^65 - 7 * q^66 + 29 * q^67 - 28 * q^68 - q^69 - 4 * q^70 + 22 * q^71 - 7 * q^72 - 33 * q^73 - 36 * q^74 + 4 * q^75 + 26 * q^76 - q^77 + 28 * q^78 + 27 * q^79 - q^80 - q^81 + 38 * q^82 + 25 * q^83 + 8 * q^84 + 2 * q^85 + 18 * q^86 - 7 * q^88 - 38 * q^89 - 4 * q^90 - 18 * q^91 + 41 * q^92 - 30 * q^93 - 42 * q^94 + 6 * q^95 - 23 * q^96 - q^97 + 4 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{10}{11}\right)$

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 $

$2$	1.85380	−	1.19136i	1.31083	−	0.842422i	0.316487	−	0.948597i	$-0.397497\pi$
$2$	1.85380	−	1.19136i	1.31083	−	0.842422i	0.994347	+	0.106175i	$0.0338604\pi$
$3$	−0.142315	+	0.989821i	−0.0821655	+	0.571474i
$3$	−0.142315	+	0.989821i	−0.0821655	+	0.571474i
$4$	1.18639	−	2.59784i	0.593196	−	1.29892i
$5$	0.959493	−	0.281733i	0.429098	−	0.125995i	−0.0600498	−	0.998195i	$-0.519126\pi$
$5$	0.959493	−	0.281733i	0.429098	−	0.125995i	0.489148	+	0.872201i	$0.337308\pi$
$6$	0.915415	+	2.00448i	0.373717	+	0.818325i
$7$	−0.654861	−	0.755750i	−0.247514	−	0.285646i
$7$	−0.654861	−	0.755750i	−0.247514	−	0.285646i
$8$	−0.268423	−	1.86692i	−0.0949019	−	0.660058i
$9$	−0.959493	−	0.281733i	−0.319831	−	0.0939109i
$10$	1.44306	−	1.66538i	0.456336	−	0.526640i
$11$	3.15455	+	2.02730i	0.951131	+	0.611255i	0.921530	−	0.388307i	$-0.126940\pi$
$11$	3.15455	+	2.02730i	0.951131	+	0.611255i	0.0296012	+	0.999562i	$0.490576\pi$
$12$	2.40255	+	1.54403i	0.693558	+	0.445722i
$13$	4.37102	−	5.04443i	1.21230	−	1.39907i	0.320134	−	0.947372i	$-0.396272\pi$
$13$	4.37102	−	5.04443i	1.21230	−	1.39907i	0.892170	−	0.451700i	$-0.149182\pi$
$14$	−2.11435	−	0.620830i	−0.565085	−	0.165924i
$15$	0.142315	+	0.989821i	0.0367455	+	0.255571i
$16$	1.01867	+	1.17561i	0.254668	+	0.293902i
$17$	−2.40287	−	5.26155i	−0.582781	−	1.27611i	−0.939707	−	0.341980i	$-0.888902\pi$
$17$	−2.40287	−	5.26155i	−0.582781	−	1.27611i	0.356926	−	0.934133i	$-0.383825\pi$
$18$	−2.11435	+	0.620830i	−0.498358	+	0.146331i
$19$	−0.996114	+	2.18119i	−0.228524	+	0.500398i	−0.988808	−	0.149193i	$-0.952333\pi$
$19$	−0.996114	+	2.18119i	−0.228524	+	0.500398i	0.760284	+	0.649591i	$0.225060\pi$
$20$	0.406440	−	2.82685i	0.0908828	−	0.632103i
$21$	0.841254	−	0.540641i	0.183577	−	0.117977i
$22$	8.26315			1.76171
$23$	−1.76381	+	4.45971i	−0.367780	+	0.929913i
$23$	−1.76381	+	4.45971i	−0.367780	+	0.929913i
$24$	1.88612			0.385003
$25$	−3.36501	+	2.16256i	−0.673003	+	0.432513i
$26$	2.09325	−	14.5588i	0.410519	−	2.85522i
$27$	0.415415	−	0.909632i	0.0799467	−	0.175059i
$28$	−2.74024	+	0.804606i	−0.517856	+	0.152056i
$29$	0.707599	+	1.54943i	0.131398	+	0.287721i	0.963883	−	0.266326i	$-0.0858099\pi$
$29$	0.707599	+	1.54943i	0.131398	+	0.287721i	−0.832485	+	0.554047i	$0.813083\pi$
$30$	1.44306	+	1.66538i	0.263466	+	0.304056i
$31$	0.417125	+	2.90117i	0.0749179	+	0.521065i	0.992377	+	0.123236i	$0.0393272\pi$
$31$	0.417125	+	2.90117i	0.0749179	+	0.521065i	−0.917459	+	0.397829i	$0.869764\pi$
$32$	6.90843	+	2.02850i	1.22125	+	0.358591i
$33$	−2.45561	+	2.83392i	−0.427466	+	0.493322i
$34$	−10.7229	−	6.89116i	−1.83896	−	1.18182i
$35$	−0.841254	−	0.540641i	−0.142198	−	0.0913850i
$36$	−1.87023	+	2.15836i	−0.311705	+	0.359727i
$37$	−10.2274	−	3.00304i	−1.68138	−	0.493697i	−0.704898	−	0.709308i	$-0.749007\pi$
$37$	−10.2274	−	3.00304i	−1.68138	−	0.493697i	−0.976479	+	0.215611i	$0.930826\pi$
$38$	0.751992	+	5.23022i	0.121989	+	0.848453i
$39$	4.37102	+	5.04443i	0.699924	+	0.807755i
$40$	−0.783524	−	1.71568i	−0.123886	−	0.271272i
$41$	−4.49005	+	1.31840i	−0.701228	+	0.205899i	−0.612863	−	0.790189i	$-0.709982\pi$
$41$	−4.49005	+	1.31840i	−0.701228	+	0.205899i	−0.0883651	+	0.996088i	$0.528164\pi$
$42$	0.915415	−	2.00448i	0.141252	−	0.309298i
$43$	−0.301233	+	2.09512i	−0.0459376	+	0.319503i	0.953876	+	0.300201i	$0.0970537\pi$
$43$	−0.301233	+	2.09512i	−0.0459376	+	0.319503i	−0.999814	+	0.0193026i	$0.993855\pi$
$44$	9.00914	−	5.78982i	1.35818	−	0.872848i
$45$	−1.00000			−0.149071
$46$	2.04338	+	10.3687i	0.301281	+	1.52879i
$47$	−11.5680			−1.68737			−0.843683	−	0.536841i	$-0.819617\pi$
$47$	−11.5680			−1.68737			−0.843683	+	0.536841i	$0.819617\pi$
$48$	−1.30862	+	0.840996i	−0.188882	+	0.121387i
$49$	−0.142315	+	0.989821i	−0.0203307	+	0.141403i
$50$	−3.66166	+	8.01792i	−0.517837	+	1.13390i
$51$	5.54996	−	1.62961i	0.777150	−	0.228192i
$52$	−7.91886	−	17.3399i	−1.09815	−	2.40461i
$53$	4.18330	+	4.82778i	0.574620	+	0.663147i	0.966439	−	0.256895i	$-0.0826995\pi$
$53$	4.18330	+	4.82778i	0.574620	+	0.663147i	−0.391819	+	0.920042i	$0.628154\pi$
$54$	−0.313607	−	2.18119i	−0.0426765	−	0.296822i
$55$	3.59792	+	1.05645i	0.485144	+	0.142451i
$56$	−1.23515	+	1.42544i	−0.165054	+	0.190482i
$57$	−2.01722	−	1.29639i	−0.267188	−	0.171711i
$58$	3.15768	+	2.02932i	0.414623	+	0.266462i
$59$	8.87191	−	10.2387i	1.15502	−	1.33297i	0.221204	−	0.975228i	$-0.429001\pi$
$59$	8.87191	−	10.2387i	1.15502	−	1.33297i	0.933821	−	0.357742i	$-0.116453\pi$
$60$	2.74024	+	0.804606i	0.353763	+	0.103874i
$61$	−0.666994	−	4.63905i	−0.0853999	−	0.593969i	−0.986917	−	0.161227i	$-0.948455\pi$
$61$	−0.666994	−	4.63905i	−0.0853999	−	0.593969i	0.901518	−	0.432743i	$-0.142454\pi$
$62$	4.22962	+	4.88124i	0.537162	+	0.619918i
$63$	0.415415	+	0.909632i	0.0523374	+	0.114603i
$64$	12.2384	−	3.59353i	1.52981	−	0.449192i
$65$	2.77279	−	6.07155i	0.343922	−	0.753083i
$66$	−1.17597	+	8.17905i	−0.144752	+	1.00677i
$67$	−10.8071	+	6.94532i	−1.32030	+	0.848506i	−0.995265	−	0.0971956i	$-0.969013\pi$
$67$	−10.8071	+	6.94532i	−1.32030	+	0.848506i	−0.325036	+	0.945702i	$0.605376\pi$
$68$	−16.5194			−2.00327
$69$	−4.16330	−	2.38054i	−0.501202	−	0.286583i
$70$	−2.20362			−0.263382
$71$	4.44588	−	2.85719i	0.527629	−	0.339086i	−0.249555	−	0.968361i	$-0.580284\pi$
$71$	4.44588	−	2.85719i	0.527629	−	0.339086i	0.777183	+	0.629274i	$0.216648\pi$
$72$	−0.268423	+	1.86692i	−0.0316340	+	0.220019i
$73$	−3.17385	+	6.94976i	−0.371471	+	0.813407i	0.627912	+	0.778284i	$0.283910\pi$
$73$	−3.17385	+	6.94976i	−0.371471	+	0.813407i	−0.999383	+	0.0351232i	$0.988818\pi$
$74$	−22.5373	+	6.61755i	−2.61991	+	0.769274i
$75$	−1.66166	−	3.63853i	−0.191872	−	0.420141i
$76$	4.48458	+	5.17549i	0.514417	+	0.593669i
$77$	−0.533654	−	3.71165i	−0.0608156	−	0.422982i
$78$	14.1128	+	4.14388i	1.59795	+	0.469202i
$79$	2.47187	−	2.85269i	0.278107	−	0.320953i	−0.599462	−	0.800404i	$-0.704619\pi$
$79$	2.47187	−	2.85269i	0.278107	−	0.320953i	0.877569	+	0.479451i	$0.159164\pi$
$80$	1.30862	+	0.840996i	0.146308	+	0.0940262i
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$	−6.75296	+	7.79334i	−0.745740	+	0.860630i
$83$	7.72882	+	2.26939i	0.848349	+	0.249098i	0.676881	−	0.736092i	$-0.263331\pi$
$83$	7.72882	+	2.26939i	0.848349	+	0.249098i	0.171467	+	0.985190i	$0.445149\pi$
$84$	−0.406440	−	2.82685i	−0.0443462	−	0.308435i
$85$	−3.78789	−	4.37145i	−0.410854	−	0.474151i
$86$	1.93763	+	4.24282i	0.208940	+	0.457515i
$87$	−1.63436	+	0.479890i	−0.175221	+	0.0514496i
$88$	2.93807	−	6.43348i	0.313199	−	0.685811i
$89$	−1.94277	+	13.5123i	−0.205933	+	1.43230i	0.580317	+	0.814391i	$0.302929\pi$
$89$	−1.94277	+	13.5123i	−0.205933	+	1.43230i	−0.786251	+	0.617908i	$0.787980\pi$
$90$	−1.85380	+	1.19136i	−0.195408	+	0.125581i
$91$	−6.67474			−0.699702
$92$	9.49302	+	9.87306i	0.989716	+	1.02934i
$93$	−2.93100			−0.303931
$94$	−21.4448	+	13.7817i	−2.21186	+	1.42147i
$95$	−0.341254	+	2.37347i	−0.0350119	+	0.243513i
$96$	−2.99103	+	6.54943i	−0.305270	+	0.668449i
$97$	−8.69206	+	2.55222i	−0.882545	+	0.259139i	−0.691443	−	0.722431i	$-0.743024\pi$
$97$	−8.69206	+	2.55222i	−0.882545	+	0.259139i	−0.191103	+	0.981570i	$0.561206\pi$
$98$	0.915415	+	2.00448i	0.0924709	+	0.202483i
$99$	−2.45561	−	2.83392i	−0.246798	−	0.284820i
$100$	1.62576	+	11.3074i	0.162576	+	1.13074i
$101$	15.5779	+	4.57408i	1.55006	+	0.455138i	0.941118	−	0.338079i	$-0.109777\pi$
$101$	15.5779	+	4.57408i	1.55006	+	0.455138i	0.608940	+	0.793217i	$0.291595\pi$
$102$	8.34704	−	9.63300i	0.826481	−	0.953809i
$103$	−9.56703	−	6.14836i	−0.942668	−	0.605816i	−0.0235176	−	0.999723i	$-0.507487\pi$
$103$	−9.56703	−	6.14836i	−0.942668	−	0.605816i	−0.919150	+	0.393908i	$0.871123\pi$
$104$	−10.5909	−	6.80633i	−1.03852	−	0.667415i
$105$	0.654861	−	0.755750i	0.0639079	−	0.0737536i
$106$	13.5066	+	3.96591i	1.31188	+	0.385203i
$107$	−2.35578	−	16.3848i	−0.227742	−	1.58398i	−0.707587	−	0.706626i	$-0.750216\pi$
$107$	−2.35578	−	16.3848i	−0.227742	−	1.58398i	0.479846	−	0.877353i	$-0.340693\pi$
$108$	−1.87023	−	2.15836i	−0.179963	−	0.207688i
$109$	−4.89051	−	10.7087i	−0.468426	−	1.02571i	−0.985485	−	0.169760i	$-0.945701\pi$
$109$	−4.89051	−	10.7087i	−0.468426	−	1.02571i	0.517059	−	0.855949i	$-0.327027\pi$
$110$	7.92844	−	2.32800i	0.755947	−	0.221966i
$111$	4.42799	−	9.69594i	0.420286	−	0.920298i
$112$	0.221378	−	1.53972i	0.0209183	−	0.145490i
$113$	−1.60340	+	1.03044i	−0.150835	+	0.0969359i	−0.613881	−	0.789398i	$-0.710393\pi$
$113$	−1.60340	+	1.03044i	−0.150835	+	0.0969359i	0.463046	+	0.886334i	$0.346756\pi$
$114$	−5.28400			−0.494892
$115$	−0.435919	+	4.77598i	−0.0406497	+	0.445362i
$116$	4.86465			0.451671
$117$	−5.61514	+	3.60863i	−0.519120	+	0.333618i
$118$	4.24868	−	29.5502i	0.391123	−	2.72032i
$119$	−2.40287	+	5.26155i	−0.220271	+	0.482325i
$120$	1.80972	−	0.531382i	0.165204	−	0.0485083i
$121$	1.27164	+	2.78449i	0.115603	+	0.253136i
$122$	−6.76327	−	7.80523i	−0.612318	−	0.706652i
$123$	−0.665978	−	4.63198i	−0.0600492	−	0.417651i
$124$	8.03164	+	2.35830i	0.721263	+	0.211782i
$125$	−5.89375	+	6.80175i	−0.527153	+	0.608367i
$126$	1.85380	+	1.19136i	0.165150	+	0.106135i
$127$	18.3858	+	11.8158i	1.63148	+	1.04849i	0.947881	+	0.318624i	$0.103221\pi$
$127$	18.3858	+	11.8158i	1.63148	+	1.04849i	0.683595	+	0.729862i	$0.260416\pi$
$128$	8.97631	−	10.3592i	0.793401	−	0.915634i
$129$	−2.03093	−	0.596334i	−0.178813	−	0.0525043i
$130$	−2.09325	−	14.5588i	−0.183590	−	1.27689i
$131$	−1.30493	−	1.50597i	−0.114012	−	0.131577i	0.695875	−	0.718163i	$-0.255017\pi$
$131$	−1.30493	−	1.50597i	−0.114012	−	0.131577i	−0.809887	+	0.586586i	$0.800471\pi$
$132$	4.44875	+	9.74141i	0.387214	+	0.847881i
$133$	2.30075	−	0.675560i	0.199500	−	0.0585785i
$134$	−11.7598	+	25.7505i	−1.01590	+	2.22450i
$135$	0.142315	−	0.989821i	0.0122485	−	0.0851903i
$136$	−9.17793	+	5.89830i	−0.787001	+	0.505775i
$137$	−3.90615			−0.333724			−0.166862	−	0.985980i	$-0.553364\pi$
$137$	−3.90615			−0.333724			−0.166862	+	0.985980i	$0.553364\pi$
$138$	−10.5540	+	0.546960i	−0.898417	+	0.0465603i
$139$	4.39994			0.373198			0.186599	−	0.982436i	$-0.440253\pi$
$139$	4.39994			0.373198			0.186599	+	0.982436i	$0.440253\pi$
$140$	−2.40255	+	1.54403i	−0.203053	+	0.130494i
$141$	1.64630	−	11.4503i	0.138643	−	0.964285i
$142$	4.83781	−	10.5933i	0.405980	−	0.888972i
$143$	24.0152	−	7.05149i	2.00825	−	0.589675i
$144$	−0.646201	−	1.41498i	−0.0538500	−	0.117915i
$145$	1.11546	+	1.28731i	0.0926339	+	0.106905i
$146$	2.39602	+	16.6647i	0.198296	+	1.37918i
$147$	−0.959493	−	0.281733i	−0.0791376	−	0.0232369i
$148$	−19.9352	+	23.0064i	−1.63866	+	1.89111i
$149$	13.8495	+	8.90054i	1.13460	+	0.729161i	0.966515	−	0.256612i	$-0.0826062\pi$
$149$	13.8495	+	8.90054i	1.13460	+	0.729161i	0.168082	+	0.985773i	$0.446243\pi$
$150$	−7.41520	−	4.76546i	−0.605448	−	0.389098i
$151$	5.62491	−	6.49149i	0.457749	−	0.528270i	−0.479215	−	0.877698i	$-0.659078\pi$
$151$	5.62491	−	6.49149i	0.457749	−	0.528270i	0.936963	+	0.349428i	$0.113624\pi$
$152$	4.33949	+	1.27419i	0.351979	+	0.103350i
$153$	0.823186	+	5.72539i	0.0665507	+	0.462870i
$154$	−5.41121	−	6.24487i	−0.436048	−	0.503226i
$155$	1.21758	+	2.66613i	0.0977986	+	0.214149i
$156$	18.2904	−	5.37053i	1.46440	−	0.429987i
$157$	4.84299	−	10.6047i	0.386512	−	0.846344i	−0.611949	−	0.790897i	$-0.709614\pi$
$157$	4.84299	−	10.6047i	0.386512	−	0.846344i	0.998462	−	0.0554471i	$-0.0176584\pi$
$158$	1.18376	−	8.23322i	0.0941747	−	0.655000i
$159$	−5.37399	+	3.45365i	−0.426185	+	0.273893i
$160$	7.20009			0.569217
$161$	4.52547	−	1.58749i	0.356657	−	0.125112i
$162$	2.20362			0.173132
$163$	−7.38436	+	4.74564i	−0.578388	+	0.371707i	−0.796886	−	0.604130i	$-0.793521\pi$
$163$	−7.38436	+	4.74564i	−0.578388	+	0.371707i	0.218498	+	0.975837i	$0.429884\pi$
$164$	−1.90198	+	13.2286i	−0.148520	+	1.03298i
$165$	−1.55773	+	3.41095i	−0.121269	+	0.265542i
$166$	17.0314	−	5.00086i	1.32189	−	0.388142i
$167$	0.0579386	+	0.126868i	0.00448342	+	0.00981732i	0.911860	−	0.410500i	$-0.134646\pi$
$167$	0.0579386	+	0.126868i	0.00448342	+	0.00981732i	−0.907377	+	0.420318i	$0.861919\pi$
$168$	−1.23515	−	1.42544i	−0.0952937	−	0.109975i
$169$	−4.49033	−	31.2309i	−0.345410	−	2.40238i
$170$	−12.2300	−	3.59104i	−0.937996	−	0.275421i
$171$	1.57028	−	1.81219i	0.120082	−	0.138582i
$172$	5.08541	+	3.26819i	0.387759	+	0.249197i
$173$	6.14014	+	3.94603i	0.466826	+	0.300011i	0.752827	−	0.658218i	$-0.228690\pi$
$173$	6.14014	+	3.94603i	0.466826	+	0.300011i	−0.286001	+	0.958229i	$0.592326\pi$
$174$	−2.45804	+	2.83673i	−0.186344	+	0.215052i
$175$	3.83797	+	1.12693i	0.290123	+	0.0851879i
$176$	0.830128	+	5.77367i	0.0625733	+	0.435207i
$177$	8.87191	+	10.2387i	0.666854	+	0.769590i
$178$	12.4965	+	27.3636i	0.936655	+	2.05099i
$179$	13.5950	−	3.99184i	1.01614	−	0.298364i	0.269075	−	0.963119i	$-0.413282\pi$
$179$	13.5950	−	3.99184i	1.01614	−	0.298364i	0.747062	+	0.664755i	$0.231464\pi$
$180$	−1.18639	+	2.59784i	−0.0884285	+	0.193631i
$181$	0.846107	−	5.88480i	0.0628906	−	0.437414i	−0.933911	−	0.357504i	$-0.883628\pi$
$181$	0.846107	−	5.88480i	0.0628906	−	0.437414i	0.996802	−	0.0799096i	$-0.0254632\pi$
$182$	−12.3736	+	7.95204i	−0.917194	+	0.589445i
$183$	4.68675			0.346455
$184$	8.79938	+	2.09581i	0.648699	+	0.154505i
$185$	−10.6592			−0.783679
$186$	−5.43349	+	3.49189i	−0.398403	+	0.256038i
$187$	3.08680	−	21.4691i	0.225729	−	1.56998i
$188$	−13.7242	+	30.0518i	−1.00094	+	2.19175i
$189$	−0.959493	+	0.281733i	−0.0697928	+	0.0204930i
$190$	2.19505	+	4.80650i	0.159246	+	0.348700i
$191$	7.21064	+	8.32152i	0.521744	+	0.602124i	0.954067	−	0.299595i	$-0.0968514\pi$
$191$	7.21064	+	8.32152i	0.521744	+	0.602124i	−0.432323	+	0.901719i	$0.642306\pi$
$192$	1.81524	+	12.6253i	0.131004	+	0.911152i
$193$	−9.60512	−	2.82032i	−0.691391	−	0.203011i	−0.0828842	−	0.996559i	$-0.526413\pi$
$193$	−9.60512	−	2.82032i	−0.691391	−	0.203011i	−0.608507	+	0.793548i	$0.708231\pi$
$194$	−13.0727	+	15.0867i	−0.938566	+	1.08316i
$195$	5.61514	+	3.60863i	0.402109	+	0.258420i
$196$	2.40255	+	1.54403i	0.171611	+	0.110288i
$197$	9.85377	−	11.3719i	0.702052	−	0.810211i	−0.286976	−	0.957938i	$-0.592650\pi$
$197$	9.85377	−	11.3719i	0.702052	−	0.810211i	0.989028	+	0.147726i	$0.0471955\pi$
$198$	−7.92844	−	2.32800i	−0.563450	−	0.165444i
$199$	0.0933070	+	0.648964i	0.00661436	+	0.0460039i	0.992861	−	0.119274i	$-0.0380568\pi$
$199$	0.0933070	+	0.648964i	0.00661436	+	0.0460039i	−0.986247	+	0.165278i	$0.947148\pi$
$200$	4.94059	+	5.70175i	0.349353	+	0.403174i
$201$	−5.33661	−	11.6856i	−0.376416	−	0.824235i
$202$	34.3277	−	10.0795i	2.41529	−	0.709192i
$203$	0.707599	−	1.54943i	0.0496637	−	0.108748i
$204$	2.35096	−	16.3513i	0.164600	−	1.14482i
$205$	−3.93674	+	2.52999i	−0.274954	+	0.176702i
$206$	−25.0603			−1.74603
$207$	2.94881	−	3.78213i	0.204956	−	0.262876i
$208$	10.3829			0.719925
$209$	−7.56421	+	4.86123i	−0.523228	+	0.336258i
$210$	0.313607	−	2.18119i	0.0216410	−	0.150516i
$211$	−3.44098	+	7.53470i	−0.236887	+	0.518710i	−0.990318	−	0.138817i	$-0.955670\pi$
$211$	−3.44098	+	7.53470i	−0.236887	+	0.518710i	0.753431	+	0.657527i	$0.228397\pi$
$212$	17.5048	−	5.13988i	1.20224	−	0.353009i
$213$	2.19540	+	4.80725i	0.150426	+	0.329387i
$214$	−23.8874	−	27.5675i	−1.63291	−	1.88448i
$215$	0.301233	+	2.09512i	0.0205439	+	0.142886i
$216$	−1.80972	−	0.531382i	−0.123136	−	0.0361560i
$217$	1.91940	−	2.21510i	0.130297	−	0.150371i
$218$	−21.8240	−	14.0254i	−1.47811	−	0.949923i
$219$	−6.42733	−	4.13060i	−0.434319	−	0.279120i
$220$	7.01302	−	8.09346i	0.472818	−	0.545661i
$221$	−37.0445	−	10.8772i	−2.49188	−	0.731683i
$222$	−3.34280	−	23.2497i	−0.224354	−	1.56042i
$223$	−3.43977	−	3.96971i	−0.230344	−	0.265831i	0.628798	−	0.777569i	$-0.283547\pi$
$223$	−3.43977	−	3.96971i	−0.230344	−	0.265831i	−0.859142	+	0.511738i	$0.829002\pi$
$224$	−2.99103	−	6.54943i	−0.199846	−	0.437602i
$225$	3.83797	−	1.12693i	0.255865	−	0.0751287i
$226$	−1.74475	+	3.82047i	−0.116059	+	0.254134i
$227$	1.80986	−	12.5878i	0.120125	−	0.835485i	−0.837288	−	0.546762i	$-0.815860\pi$
$227$	1.80986	−	12.5878i	0.120125	−	0.835485i	0.957413	−	0.288723i	$-0.0932306\pi$
$228$	−5.76103	+	3.70239i	−0.381534	+	0.245197i
$229$	−20.7623			−1.37201			−0.686004	−	0.727597i	$-0.740637\pi$
$229$	−20.7623			−1.37201			−0.686004	+	0.727597i	$0.740637\pi$
$230$	4.88182	+	9.37305i	0.321898	+	0.618040i
$231$	3.74982			0.246720
$232$	2.70272	−	1.73694i	0.177443	−	0.114035i
$233$	1.70699	−	11.8724i	0.111828	−	0.777784i	−0.854311	−	0.519762i	$-0.826020\pi$
$233$	1.70699	−	11.8724i	0.111828	−	0.777784i	0.966139	−	0.258021i	$-0.0830705\pi$
$234$	−6.11015	+	13.3794i	−0.399433	+	0.874637i
$235$	−11.0994	+	3.25908i	−0.724046	+	0.212599i
$236$	−16.0730	−	35.1949i	−1.04626	−	2.29100i
$237$	2.47187	+	2.85269i	0.160565	+	0.185302i
$238$	1.81399	+	12.6166i	0.117583	+	0.817809i
$239$	12.9766	+	3.81026i	0.839384	+	0.246465i	0.673043	−	0.739603i	$-0.264987\pi$
$239$	12.9766	+	3.81026i	0.839384	+	0.246465i	0.166341	+	0.986068i	$0.446805\pi$
$240$	−1.01867	+	1.17561i	−0.0657550	+	0.0758853i
$241$	−14.2793	−	9.17677i	−0.919813	−	0.591128i	−0.00720974	−	0.999974i	$-0.502295\pi$
$241$	−14.2793	−	9.17677i	−0.919813	−	0.591128i	−0.912603	+	0.408846i	$0.865931\pi$
$242$	5.67470	+	3.64691i	0.364784	+	0.234432i
$243$	−0.654861	+	0.755750i	−0.0420093	+	0.0484814i
$244$	−12.8428	−	3.77099i	−0.822177	−	0.241413i
$245$	0.142315	+	0.989821i	0.00909216	+	0.0632374i
$246$	−6.75296	−	7.79334i	−0.430553	−	0.496885i
$247$	6.64880	+	14.5588i	0.423053	+	0.926357i
$248$	5.30430	−	1.55748i	0.336823	−	0.0989002i
$249$	−3.34622	+	7.32719i	−0.212058	+	0.464342i
$250$	−2.82246	+	19.6307i	−0.178508	+	1.24155i
$251$	7.50086	−	4.82051i	0.473450	−	0.304268i	−0.282070	−	0.959394i	$-0.591021\pi$
$251$	7.50086	−	4.82051i	0.473450	−	0.304268i	0.755519	+	0.655126i	$0.227385\pi$
$252$	2.85592			0.179906
$253$	−14.6052	+	10.4926i	−0.918221	+	0.659662i
$254$	48.1606			3.02186
$255$	4.86603	−	3.12721i	0.304723	−	0.195833i
$256$	0.668192	−	4.64738i	0.0417620	−	0.290461i
$257$	7.95895	−	17.4277i	0.496466	−	1.08711i	−0.481136	−	0.876646i	$-0.659776\pi$
$257$	7.95895	−	17.4277i	0.496466	−	1.08711i	0.977602	−	0.210462i	$-0.0674969\pi$
$258$	−4.47538	+	1.31409i	−0.278625	+	0.0818118i
$259$	4.42799	+	9.69594i	0.275142	+	0.602477i
$260$	−12.4833	−	14.4065i	−0.774181	−	0.893453i
$261$	−0.242413	−	1.68602i	−0.0150050	−	0.104362i
$262$	−4.21323	−	1.23712i	−0.260294	−	0.0764292i
$263$	−14.9810	+	17.2889i	−0.923765	+	1.06608i	0.0738641	+	0.997268i	$0.476467\pi$
$263$	−14.9810	+	17.2889i	−0.923765	+	1.06608i	−0.997630	+	0.0688138i	$0.978079\pi$
$264$	5.94986	+	3.82374i	0.366189	+	0.235335i
$265$	5.37399	+	3.45365i	0.330122	+	0.212156i
$266$	3.46028	−	3.99338i	0.212164	−	0.244850i
$267$	−13.0983	−	3.84599i	−0.801600	−	0.235371i
$268$	5.22132	+	36.3151i	0.318943	+	2.21829i
$269$	−8.13362	−	9.38670i	−0.495915	−	0.572317i	0.451521	−	0.892260i	$-0.350882\pi$
$269$	−8.13362	−	9.38670i	−0.495915	−	0.572317i	−0.947437	+	0.319943i	$0.896336\pi$
$270$	−0.915415	−	2.00448i	−0.0557104	−	0.121989i
$271$	−16.7796	+	4.92693i	−1.01929	+	0.299289i	−0.748347	−	0.663307i	$-0.769152\pi$
$271$	−16.7796	+	4.92693i	−1.01929	+	0.299289i	−0.270939	+	0.962597i	$0.587334\pi$
$272$	3.73779	−	8.18463i	0.226637	−	0.496266i
$273$	0.949914	−	6.60680i	0.0574914	−	0.399862i
$274$	−7.24121	+	4.65364i	−0.437457	+	0.281137i
$275$	−14.9993			−0.904490
$276$	−11.1236	+	7.99131i	−0.669560	+	0.481020i
$277$	19.8074			1.19011			0.595056	−	0.803684i	$-0.297130\pi$
$277$	19.8074			1.19011			0.595056	+	0.803684i	$0.297130\pi$
$278$	8.15661	−	5.24193i	0.489201	−	0.314390i
$279$	0.417125	−	2.90117i	0.0249726	−	0.173688i
$280$	−0.783524	+	1.71568i	−0.0468245	+	0.102531i
$281$	−3.00488	+	0.882312i	−0.179256	+	0.0526343i	−0.370129	−	0.928980i	$-0.620686\pi$
$281$	−3.00488	+	0.882312i	−0.179256	+	0.0526343i	0.190873	+	0.981615i	$0.438868\pi$
$282$	−10.5895	−	23.1878i	−0.630597	−	1.38081i
$283$	−14.3402	−	16.5495i	−0.852437	−	0.983765i	0.147549	−	0.989055i	$-0.452862\pi$
$283$	−14.3402	−	16.5495i	−0.852437	−	0.983765i	−0.999986	+	0.00529011i	$0.998316\pi$
$284$	−2.14796	−	14.9394i	−0.127458	−	0.886492i
$285$	−2.30075	−	0.675560i	−0.136284	−	0.0400167i
$286$	36.1184	−	41.6829i	2.13573	−	2.46476i
$287$	3.93674	+	2.52999i	0.232378	+	0.149340i
$288$	−6.05710	−	3.89266i	−0.356918	−	0.229377i
$289$	−10.7775	+	12.4379i	−0.633970	+	0.731640i
$290$	3.60149	+	1.05749i	0.211487	+	0.0620982i
$291$	−1.28923	−	8.96681i	−0.0755761	−	0.525644i
$292$	14.2889	+	16.4903i	0.836195	+	0.965021i
$293$	−3.56664	−	7.80985i	−0.208365	−	0.456256i	0.776378	−	0.630267i	$-0.217055\pi$
$293$	−3.56664	−	7.80985i	−0.208365	−	0.456256i	−0.984744	+	0.174011i	$0.944327\pi$
$294$	−2.11435	+	0.620830i	−0.123312	+	0.0362076i
$295$	5.62795	−	12.3235i	0.327672	−	0.717502i
$296$	−2.86118	+	19.8999i	−0.166302	+	1.15666i
$297$	3.15455	−	2.02730i	0.183045	−	0.117636i
$298$	36.2780			2.10153
$299$	14.7870	+	28.3909i	0.855155	+	1.64189i
$300$	−11.4237			−0.659547
$301$	1.78065	−	1.14436i	0.102635	−	0.0659596i
$302$	2.69372	−	18.7352i	0.155006	−	1.07809i
$303$	−6.74449	+	14.7684i	−0.387461	+	0.848420i
$304$	−3.57894	+	1.05087i	−0.205266	+	0.0602716i
$305$	−1.94695	−	4.26322i	−0.111482	−	0.244111i
$306$	8.34704	+	9.63300i	0.477169	+	0.550682i
$307$	3.03322	+	21.0965i	0.173115	+	1.20404i	0.872253	+	0.489055i	$0.162658\pi$
$307$	3.03322	+	21.0965i	0.173115	+	1.20404i	−0.699138	+	0.714987i	$0.746433\pi$
$308$	−10.2754	−	3.01713i	−0.585494	−	0.171917i
$309$	7.44731	−	8.59465i	0.423662	−	0.488933i
$310$	5.43349	+	3.49189i	0.308602	+	0.198326i
$311$	15.6387	+	10.0504i	0.886791	+	0.569906i	0.902846	−	0.429965i	$-0.141474\pi$
$311$	15.6387	+	10.0504i	0.886791	+	0.569906i	−0.0160543	+	0.999871i	$0.505110\pi$
$312$	8.24428	−	9.51441i	0.466741	−	0.538647i
$313$	9.90726	+	2.90903i	0.559991	+	0.164428i	0.549466	−	0.835516i	$-0.314831\pi$
$313$	9.90726	+	2.90903i	0.559991	+	0.164428i	0.0105256	+	0.999945i	$0.496650\pi$
$314$	−3.65609	−	25.4287i	−0.206325	−	1.43502i
$315$	0.654861	+	0.755750i	0.0368972	+	0.0425817i
$316$	−4.47822	−	9.80593i	−0.251920	−	0.551627i
$317$	22.0613	−	6.47778i	1.23909	−	0.363828i	0.404414	−	0.914576i	$-0.367476\pi$
$317$	22.0613	−	6.47778i	1.23909	−	0.363828i	0.834672	+	0.550748i	$0.185657\pi$
$318$	−5.84774	+	12.8048i	−0.327925	+	0.718055i
$319$	−0.909002	+	6.32225i	−0.0508944	+	0.353978i
$320$	10.7303	−	6.89594i	0.599841	−	0.385495i
$321$	16.5533			0.923915
$322$	6.49804	−	8.33437i	0.362122	−	0.464456i
$323$	13.8700			0.771745
$324$	2.40255	−	1.54403i	0.133475	−	0.0857793i
$325$	−3.79966	+	26.4272i	−0.210767	+	1.46592i
$326$	−8.03533	+	17.5949i	−0.445036	+	0.974493i
$327$	11.2957	−	3.31672i	0.624655	−	0.183415i
$328$	3.66659	+	8.02870i	0.202453	+	0.443311i
$329$	7.57543	+	8.74251i	0.417647	+	0.481990i
$330$	1.17597	+	8.17905i	0.0647350	+	0.450242i
$331$	6.70231	+	1.96798i	0.368392	+	0.108170i	0.460689	−	0.887562i	$-0.347602\pi$
$331$	6.70231	+	1.96798i	0.368392	+	0.108170i	−0.0922962	+	0.995732i	$0.529421\pi$
$332$	15.0649	−	17.3858i	0.826795	−	0.954172i
$333$	8.96708	+	5.76279i	0.491393	+	0.315799i
$334$	0.258552	+	0.166161i	0.0141473	+	0.00909195i
$335$	−8.41264	+	9.70871i	−0.459632	+	0.530443i
$336$	1.49254	+	0.438250i	0.0814249	+	0.0239085i
$337$	−1.52802	−	10.6276i	−0.0832368	−	0.578924i	−0.988169	−	0.153369i	$-0.950988\pi$
$337$	−1.52802	−	10.6276i	−0.0832368	−	0.578924i	0.904932	−	0.425556i	$-0.139921\pi$
$338$	−45.5316	−	52.5463i	−2.47659	−	2.85814i
$339$	−0.791767	−	1.73373i	−0.0430029	−	0.0941632i
$340$	−15.8502	+	4.65405i	−0.859600	+	0.252401i
$341$	−4.56571	+	9.99751i	−0.247247	+	0.541395i
$342$	0.751992	−	5.23022i	0.0406630	−	0.282818i
$343$	0.841254	−	0.540641i	0.0454234	−	0.0291919i
$344$	3.99230			0.215250
$345$	−4.66533	−	1.11118i	−0.251173	−	0.0598237i
$346$	16.0837			0.864667
$347$	−13.2721	+	8.52946i	−0.712483	+	0.457885i	−0.846015	−	0.533159i	$-0.821005\pi$
$347$	−13.2721	+	8.52946i	−0.712483	+	0.457885i	0.133532	+	0.991045i	$0.457368\pi$
$348$	−0.692311	+	4.81513i	−0.0371118	+	0.258118i
$349$	−2.77630	+	6.07925i	−0.148612	+	0.325415i	−0.969268	−	0.246008i	$-0.920881\pi$
$349$	−2.77630	+	6.07925i	−0.148612	+	0.325415i	0.820656	+	0.571423i	$0.193608\pi$
$350$	8.45741	−	2.48332i	0.452068	−	0.132739i
$351$	−2.77279	−	6.07155i	−0.148000	−	0.324076i
$352$	17.6806	+	20.4045i	0.942379	+	1.08756i
$353$	−1.99590	−	13.8818i	−0.106231	−	0.738852i	−0.971413	−	0.237395i	$-0.923706\pi$
$353$	−1.99590	−	13.8818i	−0.106231	−	0.738852i	0.865182	−	0.501457i	$-0.167203\pi$
$354$	28.6448	+	8.41087i	1.52245	+	0.447033i
$355$	3.46082	−	3.99400i	0.183681	−	0.211980i
$356$	32.7978	+	21.0779i	1.73828	+	1.11713i
$357$	−4.86603	−	3.12721i	−0.257538	−	0.165509i
$358$	20.4466	−	23.5966i	1.08064	−	1.24712i
$359$	9.55766	+	2.80638i	0.504434	+	0.148115i	0.524042	−	0.851693i	$-0.324424\pi$
$359$	9.55766	+	2.80638i	0.504434	+	0.148115i	−0.0196079	+	0.999808i	$0.506242\pi$
$360$	0.268423	+	1.86692i	0.0141471	+	0.0983956i
$361$	8.67703	+	10.0138i	0.456686	+	0.527043i
$362$	−5.44243	−	11.9173i	−0.286048	−	0.626357i
$363$	−2.93712	+	0.862417i	−0.154159	+	0.0452652i
$364$	−7.91886	+	17.3399i	−0.415061	+	0.908857i
$365$	−1.08731	+	7.56242i	−0.0569125	+	0.395835i
$366$	8.68830	−	5.58363i	0.454145	−	0.291861i
$367$	4.33747			0.226414			0.113207	−	0.993571i	$-0.463888\pi$
$367$	4.33747			0.226414			0.113207	+	0.993571i	$0.463888\pi$
$368$	−7.03961	+	2.46942i	−0.366965	+	0.128728i
$369$	4.67961			0.243611
$370$	−19.7600	+	12.6990i	−1.02727	+	0.660189i
$371$	0.909118	−	6.32305i	0.0471990	−	0.328276i
$372$	−3.47732	+	7.61427i	−0.180291	+	0.394781i
$373$	−25.2317	+	7.40871i	−1.30645	+	0.383608i	−0.859585	−	0.510993i	$-0.829278\pi$
$373$	−25.2317	+	7.40871i	−1.30645	+	0.383608i	−0.446865	+	0.894601i	$0.647460\pi$
$374$	−19.8553	−	43.4770i	−1.02669	−	2.24814i
$375$	−5.89375	−	6.80175i	−0.304352	−	0.351241i
$376$	3.10512	+	21.5966i	0.160134	+	1.11376i
$377$	10.9089	+	3.20314i	0.561837	+	0.164970i
$378$	−1.44306	+	1.66538i	−0.0742231	+	0.0856580i
$379$	18.4003	+	11.8251i	0.945159	+	0.607417i	0.919853	−	0.392263i	$-0.128308\pi$
$379$	18.4003	+	11.8251i	0.945159	+	0.607417i	0.0253062	+	0.999680i	$0.491944\pi$
$380$	5.76103	+	3.70239i	0.295535	+	0.189929i
$381$	−14.3121	+	16.5171i	−0.733233	+	0.846196i
$382$	23.2810	+	6.83593i	1.19116	+	0.349757i
$383$	0.296168	+	2.05989i	0.0151335	+	0.105256i	0.995988	−	0.0894857i	$-0.0285223\pi$
$383$	0.296168	+	2.05989i	0.0151335	+	0.105256i	−0.980855	+	0.194741i	$0.937613\pi$
$384$	8.97631	+	10.3592i	0.458070	+	0.528641i
$385$	−1.55773	−	3.41095i	−0.0793893	−	0.173838i
$386$	−21.1660	+	6.21489i	−1.07732	+	0.316330i
$387$	0.879296	−	1.92539i	0.0446971	−	0.0978730i
$388$	−3.68195	+	25.6085i	−0.186923	+	1.30007i
$389$	−15.8585	+	10.1917i	−0.804059	+	0.516737i	−0.876938	−	0.480603i	$-0.840418\pi$
$389$	−15.8585	+	10.1917i	−0.804059	+	0.516737i	0.0728790	+	0.997341i	$0.476781\pi$
$390$	14.7086			0.744796
$391$	27.7032	−	1.43571i	1.40101	−	0.0726071i
$392$	1.88612			0.0952636
$393$	1.67635	−	1.07732i	0.0845606	−	0.0543438i
$394$	4.71889	−	32.8206i	0.237734	−	1.65348i
$395$	1.56805	−	3.43354i	0.0788970	−	0.172760i
$396$	−10.2754	+	3.01713i	−0.516357	+	0.151616i
$397$	13.5818	+	29.7400i	0.681652	+	1.49261i	0.860883	+	0.508802i	$0.169912\pi$
$397$	13.5818	+	29.7400i	0.681652	+	1.49261i	−0.179232	+	0.983807i	$0.557361\pi$
$398$	0.946126	+	1.09189i	0.0474250	+	0.0547314i
$399$	0.341254	+	2.37347i	0.0170840	+	0.118822i
$400$	−5.97017	−	1.75300i	−0.298509	−	0.0876501i
$401$	1.90378	−	2.19708i	0.0950702	−	0.109717i	−0.706221	−	0.707992i	$-0.749601\pi$
$401$	1.90378	−	2.19708i	0.0950702	−	0.109717i	0.801291	+	0.598275i	$0.204147\pi$
$402$	−23.8148	−	15.3048i	−1.18777	−	0.763335i
$403$	16.4580	+	10.5769i	0.819831	+	0.526874i
$404$	30.3642	−	35.0422i	1.51068	−	1.74341i
$405$	0.959493	+	0.281733i	0.0476776	+	0.0139994i
$406$	−0.534184	−	3.71533i	−0.0265111	−	0.184389i
$407$	−26.1748	−	30.2073i	−1.29744	−	1.49732i
$408$	−4.53211	−	9.92393i	−0.224373	−	0.491308i
$409$	11.9047	−	3.49553i	0.588648	−	0.172843i	0.0261738	−	0.999657i	$-0.491668\pi$
$409$	11.9047	−	3.49553i	0.588648	−	0.172843i	0.562474	+	0.826815i	$0.309849\pi$
$410$	−4.28379	+	9.38018i	−0.211561	+	0.463254i
$411$	0.555902	−	3.86639i	0.0274206	−	0.190715i
$412$	−27.3227	+	17.5592i	−1.34609	+	0.865081i
$413$	−13.5478			−0.666643
$414$	0.960599	−	10.5244i	0.0472109	−	0.517247i
$415$	8.05511			0.395410
$416$	40.4295	−	25.9825i	1.98222	−	1.27390i
$417$	−0.626177	+	4.35516i	−0.0306640	+	0.213273i
$418$	−8.23104	+	18.0235i	−0.402594	+	0.881557i
$419$	8.72404	−	2.56161i	0.426197	−	0.125143i	−0.0615978	−	0.998101i	$-0.519620\pi$
$419$	8.72404	−	2.56161i	0.426197	−	0.125143i	0.487795	+	0.872958i	$0.337801\pi$
$420$	−1.18639	−	2.59784i	−0.0578900	−	0.126762i
$421$	9.86042	+	11.3795i	0.480568	+	0.554605i	0.943321	−	0.331883i	$-0.107684\pi$
$421$	9.86042	+	11.3795i	0.480568	+	0.554605i	−0.462753	+	0.886487i	$0.653138\pi$
$422$	2.59768	+	18.0673i	0.126453	+	0.879502i
$423$	11.0994	+	3.25908i	0.539672	+	0.158462i
$424$	7.89021	−	9.10579i	0.383183	−	0.442216i
$425$	19.4641	+	12.5088i	0.944149	+	0.606767i
$426$	9.79700	+	6.29615i	0.474666	+	0.305050i
$427$	−3.06917	+	3.54201i	−0.148528	+	0.171410i
$428$	−45.3599	−	13.3189i	−2.19256	−	0.643792i
$429$	3.56200	+	24.7743i	0.171975	+	1.19611i
$430$	3.05448	+	3.52506i	0.147300	+	0.169993i
$431$	−3.28710	−	7.19774i	−0.158334	−	0.346703i	0.813794	−	0.581153i	$-0.197398\pi$
$431$	−3.28710	−	7.19774i	−0.158334	−	0.346703i	−0.972128	+	0.234450i	$0.924671\pi$
$432$	1.49254	−	0.438250i	0.0718100	−	0.0210853i
$433$	6.09742	−	13.3515i	0.293023	−	0.641631i	−0.704669	−	0.709536i	$-0.748904\pi$
$433$	6.09742	−	13.3515i	0.293023	−	0.641631i	0.997692	+	0.0679055i	$0.0216316\pi$
$434$	0.919183	−	6.39306i	0.0441222	−	0.306877i
$435$	−1.43295	+	0.920903i	−0.0687048	+	0.0441539i
$436$	−33.6216			−1.61018
$437$	−7.97049	−	8.28957i	−0.381280	−	0.396544i
$438$	−16.8360			−0.804457
$439$	−11.2641	+	7.23897i	−0.537604	+	0.345497i	−0.781101	−	0.624404i	$-0.785342\pi$
$439$	−11.2641	+	7.23897i	−0.537604	+	0.345497i	0.243497	+	0.969902i	$0.421705\pi$
$440$	1.00654	−	7.00062i	0.0479848	−	0.333742i
$441$	0.415415	−	0.909632i	0.0197817	−	0.0433158i
$442$	−81.6318	+	23.9693i	−3.88283	+	1.14010i
$443$	−8.16971	−	17.8892i	−0.388155	−	0.849940i	−0.998335	−	0.0576778i	$-0.981630\pi$
$443$	−8.16971	−	17.8892i	−0.388155	−	0.849940i	0.610181	−	0.792262i	$-0.291097\pi$
$444$	−19.9352	−	23.0064i	−0.946081	−	1.09184i
$445$	1.94277	+	13.5123i	0.0920962	+	0.640543i
$446$	−11.1060	−	3.26102i	−0.525885	−	0.154414i
$447$	−10.7809	+	12.4419i	−0.509921	+	0.588480i
$448$	−10.7303	−	6.89594i	−0.506959	−	0.325802i
$449$	−19.4416	−	12.4944i	−0.917505	−	0.589645i	−0.00557255	−	0.999984i	$-0.501774\pi$
$449$	−19.4416	−	12.4944i	−0.917505	−	0.589645i	−0.911933	+	0.410340i	$0.865410\pi$
$450$	5.77225	−	6.66153i	0.272106	−	0.314027i
$451$	−16.8369	−	4.94375i	−0.792817	−	0.232792i
$452$	0.774661	+	5.38788i	0.0364370	+	0.253425i
$453$	5.62491	+	6.49149i	0.264281	+	0.304997i
$454$	−11.6416	−	25.4915i	−0.546367	−	1.19638i
$455$	−6.40436	+	1.88049i	−0.300241	+	0.0881587i
$456$	−1.87879	+	4.11398i	−0.0879826	+	0.192655i
$457$	−0.411780	+	2.86399i	−0.0192623	+	0.133972i	−0.997183	−	0.0750026i	$-0.976103\pi$
$457$	−0.411780	+	2.86399i	−0.0192623	+	0.133972i	0.977921	+	0.208975i	$0.0670126\pi$
$458$	−38.4891	+	24.7354i	−1.79848	+	1.15581i
$459$	−5.78426			−0.269986
$460$	11.8900	+	6.79864i	0.554376	+	0.316988i
$461$	9.74908			0.454060			0.227030	−	0.973888i	$-0.427098\pi$
$461$	9.74908			0.454060			0.227030	+	0.973888i	$0.427098\pi$
$462$	6.95141	−	4.46740i	0.323409	−	0.207842i
$463$	1.39876	−	9.72862i	0.0650061	−	0.452127i	−0.931158	−	0.364617i	$-0.881200\pi$
$463$	1.39876	−	9.72862i	0.0650061	−	0.452127i	0.996164	−	0.0875102i	$-0.0278910\pi$
$464$	−1.10071	+	2.41022i	−0.0510991	+	0.111891i
$465$	−2.81228	+	0.825759i	−0.130416	+	0.0382936i
$466$	−10.9799	−	24.0426i	−0.508634	−	1.11375i
$467$	7.02842	+	8.11123i	0.325237	+	0.375343i	0.894695	−	0.446677i	$-0.147393\pi$
$467$	7.02842	+	8.11123i	0.325237	+	0.375343i	−0.569459	+	0.822020i	$0.692847\pi$
$468$	2.71288	+	18.8685i	0.125403	+	0.872196i
$469$	12.3261	+	3.61927i	0.569166	+	0.167122i
$470$	−16.6933	+	19.2651i	−0.770006	+	0.888634i
$471$	9.80749	+	6.30289i	0.451905	+	0.290422i
$472$	−21.4964	−	13.8149i	−0.989450	−	0.635881i
$473$	−5.19771	+	5.99847i	−0.238991	+	0.275810i
$474$	7.98095	+	2.34342i	0.366577	+	0.107637i
$475$	−1.36501	−	9.49388i	−0.0626311	−	0.435609i
$476$	10.8179	+	12.4845i	0.495838	+	0.572227i
$477$	−2.65370	−	5.81080i	−0.121505	−	0.266058i
$478$	28.5954	−	8.39635i	1.30792	−	0.384040i
$479$	−0.888284	+	1.94507i	−0.0405867	+	0.0888726i	−0.928839	−	0.370483i	$-0.879192\pi$
$479$	−0.888284	+	1.94507i	−0.0405867	+	0.0888726i	0.888253	+	0.459355i	$0.151920\pi$
$480$	−1.02468	+	7.12680i	−0.0467700	+	0.325293i
$481$	−59.8529	+	38.4651i	−2.72906	+	1.75386i
$482$	−37.4039			−1.70370
$483$	0.927287	+	4.70533i	0.0421930	+	0.214100i
$484$	8.74232			0.397378
$485$	−7.62093	+	4.89767i	−0.346049	+	0.222392i
$486$	−0.313607	+	2.18119i	−0.0142255	+	0.0989406i
$487$	2.12851	−	4.66079i	0.0964521	−	0.211201i	−0.855256	−	0.518206i	$-0.826600\pi$
$487$	2.12851	−	4.66079i	0.0964521	−	0.211201i	0.951708	+	0.307006i	$0.0993271\pi$
$488$	−8.48172	+	2.49046i	−0.383949	+	0.112738i
$489$	−3.64643	−	7.98457i	−0.164897	−	0.361075i
$490$	1.44306	+	1.66538i	0.0651909	+	0.0752343i
$491$	−2.81968	−	19.6113i	−0.127250	−	0.885046i	−0.949018	−	0.315223i	$-0.897921\pi$
$491$	−2.81968	−	19.6113i	−0.127250	−	0.885046i	0.821767	−	0.569823i	$-0.192988\pi$
$492$	−12.8232	−	3.76524i	−0.578116	−	0.169750i
$493$	6.45211	−	7.44613i	0.290588	−	0.335357i
$494$	29.6704	+	19.0680i	1.33494	+	0.857911i
$495$	−3.15455	−	2.02730i	−0.141786	−	0.0911205i
$496$	−2.98573	+	3.44571i	−0.134063	+	0.154717i
$497$	−5.07075	−	1.48891i	−0.227454	−	0.0667866i
$498$	2.52614	+	17.5697i	0.113199	+	0.787317i
$499$	10.4824	+	12.0973i	0.469255	+	0.541550i	0.940204	−	0.340611i	$-0.110634\pi$
$499$	10.4824	+	12.0973i	0.469255	+	0.541550i	−0.470949	+	0.882160i	$0.656088\pi$
$500$	10.6775	+	23.3805i	0.477514	+	1.04561i
$501$	−0.133822	+	0.0392937i	−0.00597872	+	0.00175551i
$502$	8.16210	−	17.8725i	0.364292	−	0.797689i
$503$	0.363329	−	2.52701i	0.0162000	−	0.112674i	−0.980117	−	0.198421i	$-0.936419\pi$
$503$	0.363329	−	2.52701i	0.0162000	−	0.112674i	0.996317	+	0.0857473i	$0.0273278\pi$
$504$	1.58671	−	1.01971i	0.0706776	−	0.0454217i
$505$	16.2355			0.722472
$506$	−14.5746	+	36.8512i	−0.647922	+	1.63824i
$507$	31.5521			1.40128
$508$	52.5084	−	33.7451i	2.32968	−	1.49720i
$509$	−5.15072	+	35.8240i	−0.228302	+	1.58787i	0.476960	+	0.878925i	$0.341739\pi$
$509$	−5.15072	+	35.8240i	−0.228302	+	1.58787i	−0.705261	+	0.708947i	$0.749170\pi$
$510$	5.29500	−	11.5944i	0.234467	−	0.513410i
$511$	7.33070	−	2.15249i	0.324291	−	0.0952205i
$512$	7.09033	+	15.5257i	0.313351	+	0.686143i
$513$	1.57028	+	1.81219i	0.0693294	+	0.0800104i
$514$	−6.00841	−	41.7894i	−0.265020	−	1.84325i
$515$	−10.9117	−	3.20396i	−0.480827	−	0.141183i
$516$	−3.95866	+	4.56853i	−0.174270	+	0.201119i
$517$	−36.4918	−	23.4518i	−1.60491	−	1.03141i
$518$	19.7600	+	12.6990i	0.868205	+	0.557961i
$519$	−4.77970	+	5.51606i	−0.209805	+	0.242128i
$520$	−12.0794	−	3.54684i	−0.529717	−	0.155539i
$521$	0.401521	+	2.79264i	0.0175909	+	0.122348i	0.996725	−	0.0808690i	$-0.0257695\pi$
$521$	0.401521	+	2.79264i	0.0175909	+	0.122348i	−0.979134	+	0.203217i	$0.934860\pi$
$522$	−2.45804	−	2.83673i	−0.107586	−	0.124160i
$523$	16.0766	+	35.2028i	0.702979	+	1.53931i	0.836322	+	0.548239i	$0.184702\pi$
$523$	16.0766	+	35.2028i	0.702979	+	1.53931i	−0.133343	+	0.991070i	$0.542571\pi$
$524$	−5.46041	+	1.60332i	−0.238539	+	0.0700414i
$525$	−1.66166	+	3.63853i	−0.0725208	+	0.158798i
$526$	−7.17425	+	49.8980i	−0.312812	+	2.17566i
$527$	14.2623	−	9.16585i	0.621278	−	0.399271i
$528$	−5.83304			−0.253851
$529$	−16.7779	−	15.7321i	−0.729476	−	0.684007i
$530$	14.0769			0.611460
$531$	−11.3971	+	7.32448i	−0.494593	+	0.317856i
$532$	0.974593	−	6.77845i	0.0422540	−	0.293883i
$533$	−12.9756	+	28.4125i	−0.562034	+	1.23068i
$534$	−28.8635	+	8.47509i	−1.24905	+	0.366753i
$535$	−6.87649	−	15.0574i	−0.297296	−	0.650988i
$536$	15.8673	+	18.3118i	0.685362	+	0.790950i
$537$	2.01645	+	14.0247i	0.0870161	+	0.605210i
$538$	−26.2611	−	7.71095i	−1.13220	−	0.332443i
$539$	−2.45561	+	2.83392i	−0.105770	+	0.122066i
$540$	−2.40255	−	1.54403i	−0.103389	−	0.0664444i
$541$	6.16074	+	3.95927i	0.264871	+	0.170222i	0.666335	−	0.745653i	$-0.267862\pi$
$541$	6.16074	+	3.95927i	0.264871	+	0.170222i	−0.401464	+	0.915875i	$0.631498\pi$
$542$	−25.2362	+	29.1241i	−1.08399	+	1.25099i
$543$	5.70449	+	1.67499i	0.244803	+	0.0718807i
$544$	−5.92701	−	41.2233i	−0.254119	−	1.76743i
$545$	−7.70941	−	8.89713i	−0.330235	−	0.381111i
$546$	−6.11015	−	13.3794i	−0.261490	−	0.572584i
$547$	−23.1985	+	6.81170i	−0.991897	+	0.291247i	−0.737127	−	0.675754i	$-0.763818\pi$
$547$	−23.1985	+	6.81170i	−0.991897	+	0.291247i	−0.254770	+	0.967002i	$0.582000\pi$
$548$	−4.63422	+	10.1475i	−0.197964	+	0.433481i
$549$	−0.666994	+	4.63905i	−0.0284666	+	0.197990i
$550$	−27.8056	+	17.8696i	−1.18564	+	0.761962i
$551$	−4.08443			−0.174003
$552$	−3.32676	+	8.41155i	−0.141596	+	0.358019i
$553$	−3.77465			−0.160515
$554$	36.7189	−	23.5978i	1.56004	−	1.00258i
$555$	1.51696	−	10.5507i	0.0643914	−	0.447852i
$556$	5.22006	−	11.4303i	0.221380	−	0.484754i
$557$	24.5894	−	7.22010i	1.04189	−	0.305926i	0.284352	−	0.958720i	$-0.408222\pi$
$557$	24.5894	−	7.22010i	1.04189	−	0.305926i	0.757535	+	0.652794i	$0.226403\pi$
$558$	−2.68308	−	5.87513i	−0.113584	−	0.248714i
$559$	9.25200	+	10.6774i	0.391318	+	0.451605i
$560$	−0.221378	−	1.53972i	−0.00935495	−	0.0650651i
$561$	20.8113	+	6.11076i	0.878655	+	0.257996i
$562$	−4.51929	+	5.21554i	−0.190635	+	0.220004i
$563$	−3.56296	−	2.28978i	−0.150161	−	0.0965026i	0.463403	−	0.886148i	$-0.346628\pi$
$563$	−3.56296	−	2.28978i	−0.150161	−	0.0965026i	−0.613564	+	0.789645i	$0.710265\pi$
$564$	−27.7927	−	17.8613i	−1.17029	−	0.752097i
$565$	−1.24814	+	1.44043i	−0.0525097	+	0.0605995i
$566$	−46.3003	−	13.5950i	−1.94615	−	0.571441i
$567$	−0.142315	−	0.989821i	−0.00597666	−	0.0415686i
$568$	−6.52754	−	7.53318i	−0.273889	−	0.316085i
$569$	−1.35587	−	2.96895i	−0.0568412	−	0.124465i	0.879080	−	0.476674i	$-0.158158\pi$
$569$	−1.35587	−	2.96895i	−0.0568412	−	0.124465i	−0.935921	+	0.352209i	$0.885431\pi$
$570$	−5.06996	+	1.48867i	−0.212357	+	0.0623537i
$571$	−0.935381	+	2.04820i	−0.0391445	+	0.0857144i	−0.928194	−	0.372096i	$-0.878639\pi$
$571$	−0.935381	+	2.04820i	−0.0391445	+	0.0857144i	0.889050	+	0.457811i	$0.151366\pi$
$572$	10.1728	−	70.7534i	0.425346	−	2.95835i
$573$	−9.26300	+	5.95297i	−0.386967	+	0.248689i
$574$	10.3121			0.430417
$575$	−3.70915	−	18.8213i	−0.154682	−	0.784903i
$576$	−12.7551			−0.531463
$577$	26.1897	−	16.8311i	1.09029	−	0.700687i	0.133379	−	0.991065i	$-0.457417\pi$
$577$	26.1897	−	16.8311i	1.09029	−	0.700687i	0.956912	+	0.290378i	$0.0937810\pi$
$578$	−5.16125	+	35.8973i	−0.214680	+	1.49313i
$579$	4.15856	−	9.10598i	0.172824	−	0.378432i
$580$	4.66759	−	1.37053i	0.193811	−	0.0569081i
$581$	−3.34622	−	7.32719i	−0.138824	−	0.303983i
$582$	−13.0727	−	15.0867i	−0.541881	−	0.625364i
$583$	3.40902	+	23.7103i	0.141187	+	0.981979i
$584$	13.8266	+	4.05986i	0.572149	+	0.167998i
$585$	−4.37102	+	5.04443i	−0.180720	+	0.208561i
$586$	−15.9162	−	10.2287i	−0.657493	−	0.422545i
$587$	−3.18263	−	2.04535i	−0.131361	−	0.0844206i	0.473310	−	0.880896i	$-0.343059\pi$
$587$	−3.18263	−	2.04535i	−0.131361	−	0.0844206i	−0.604671	+	0.796475i	$0.706695\pi$
$588$	−1.87023	+	2.15836i	−0.0771270	+	0.0890093i
$589$	−6.74349	−	1.98007i	−0.277861	−	0.0815873i
$590$	−4.24868	−	29.5502i	−0.174915	−	1.21656i
$591$	9.85377	+	11.3719i	0.405330	+	0.467776i
$592$	−6.88798	−	15.0826i	−0.283094	−	0.619890i
$593$	−2.11791	+	0.621874i	−0.0869720	+	0.0255373i	−0.324929	−	0.945738i	$-0.605340\pi$
$593$	−2.11791	+	0.621874i	−0.0869720	+	0.0255373i	0.237957	+	0.971276i	$0.423522\pi$
$594$	3.43264	−	7.51643i	0.140843	−	0.308403i
$595$	−0.823186	+	5.72539i	−0.0337473	+	0.234718i
$596$	39.5531	−	25.4193i	1.62016	−	1.04121i
$597$	−0.655638			−0.0268335
$598$	61.2360	+	35.0143i	2.50413	+	1.43184i
$599$	24.2766			0.991917			0.495958	−	0.868346i	$-0.334817\pi$
$599$	24.2766			0.991917			0.495958	+	0.868346i	$0.334817\pi$
$600$	−6.34683	+	4.07886i	−0.259108	+	0.166519i
$601$	1.35406	−	9.41768i	0.0552332	−	0.384155i	−0.943389	−	0.331687i	$-0.892382\pi$
$601$	1.35406	−	9.41768i	0.0552332	−	0.384155i	0.998623	−	0.0524679i	$-0.0167087\pi$
$602$	1.93763	−	4.24282i	0.0789719	−	0.172924i
$603$	12.3261	−	3.61927i	0.501957	−	0.147388i
$604$	−10.1905	−	22.3141i	−0.414645	−	0.907947i
$605$	2.00461	+	2.31344i	0.0814989	+	0.0940547i
$606$	5.09158	+	35.4127i	0.206831	+	1.43854i
$607$	−33.8804	−	9.94819i	−1.37516	−	0.403785i	−0.491081	−	0.871114i	$-0.663398\pi$
$607$	−33.8804	−	9.94819i	−1.37516	−	0.403785i	−0.884083	+	0.467329i	$0.845216\pi$
$608$	−11.3061	+	13.0480i	−0.458524	+	0.529165i
$609$	1.43295	+	0.920903i	0.0580662	+	0.0373169i
$610$	−8.68830	−	5.58363i	−0.351779	−	0.226075i
$611$	−50.5640	+	58.3540i	−2.04560	+	2.36075i
$612$	15.8502	+	4.65405i	0.640708	+	0.188129i
$613$	4.64957	+	32.3385i	0.187794	+	1.30614i	0.837703	+	0.546126i	$0.183898\pi$
$613$	4.64957	+	32.3385i	0.187794	+	1.30614i	−0.649908	+	0.760013i	$0.725193\pi$
$614$	30.7566	+	35.4950i	1.24124	+	1.43246i
$615$	−1.94398	−	4.25672i	−0.0783888	−	0.171648i
$616$	−6.78612	+	1.99259i	−0.273421	+	0.0802836i
$617$	0.201114	−	0.440378i	0.00809654	−	0.0177290i	−0.905541	−	0.424260i	$-0.860534\pi$
$617$	0.201114	−	0.440378i	0.00809654	−	0.0177290i	0.913637	+	0.406531i	$0.133262\pi$
$618$	3.56645	−	24.8052i	0.143464	−	0.997812i
$619$	−4.42442	+	2.84340i	−0.177833	+	0.114286i	−0.626529	−	0.779398i	$-0.715525\pi$
$619$	−4.42442	+	2.84340i	−0.177833	+	0.114286i	0.448696	+	0.893684i	$0.351889\pi$
$620$	8.37071			0.336176
$621$	3.32398	+	3.45705i	0.133387	+	0.138727i
$622$	40.9648			1.64254
$623$	11.4841	−	7.38041i	0.460102	−	0.295690i
$624$	−1.47764	+	10.2772i	−0.0591530	+	0.411418i
$625$	4.56957	−	10.0060i	0.182783	−	0.400238i
$626$	21.8318	−	6.41039i	0.872574	−	0.256211i
$627$	−3.73525	−	8.17905i	−0.149171	−	0.326640i
$628$	−21.8035	−	25.1626i	−0.870055	−	1.00410i
$629$	8.77450	+	61.0280i	0.349862	+	2.43335i
$630$	2.11435	+	0.620830i	0.0842379	+	0.0247345i
$631$	27.5768	−	31.8253i	1.09782	−	1.26695i	0.136756	−	0.990605i	$-0.456332\pi$
$631$	27.5768	−	31.8253i	1.09782	−	1.26695i	0.961059	−	0.276342i	$-0.0891223\pi$
$632$	−5.98927	−	3.84907i	−0.238240	−	0.153108i
$633$	−6.96831	−	4.47826i	−0.276965	−	0.177995i
$634$	33.1798	−	38.2915i	1.31774	−	1.52075i
$635$	20.9700	+	6.15733i	0.832167	+	0.244346i
$636$	2.59637	+	18.0581i	0.102953	+	0.716052i
$637$	4.37102	+	5.04443i	0.173186	+	0.199868i
$638$	5.84700	+	12.8031i	0.231485	+	0.506881i
$639$	−5.07075	+	1.48891i	−0.200596	+	0.0589003i
$640$	5.69418	−	12.4685i	0.225082	−	0.492861i
$641$	0.0376155	−	0.261622i	0.00148572	−	0.0103334i	−0.989065	−	0.147480i	$-0.952884\pi$
$641$	0.0376155	−	0.261622i	0.00148572	−	0.0103334i	0.990551	+	0.137146i	$0.0437930\pi$
$642$	30.6865	−	19.7210i	1.21110	−	0.778326i
$643$	14.7010			0.579753			0.289876	−	0.957064i	$-0.406386\pi$
$643$	14.7010			0.579753			0.289876	+	0.957064i	$0.406386\pi$
$644$	1.24495	−	13.6398i	0.0490580	−	0.537484i
$645$	−2.11667			−0.0833437
$646$	25.7121	−	16.5242i	1.01163	−	0.650135i
$647$	−5.36766	+	37.3329i	−0.211024	+	1.46771i	0.558721	+	0.829356i	$0.311292\pi$
$647$	−5.36766	+	37.3329i	−0.211024	+	1.46771i	−0.769745	+	0.638351i	$0.779617\pi$
$648$	0.783524	−	1.71568i	0.0307797	−	0.0673982i
$649$	48.7439	−	14.3125i	1.91336	−	0.561814i
$650$	24.4406	+	53.5175i	0.958640	+	2.09913i
$651$	1.91940	+	2.21510i	0.0752271	+	0.0868168i
$652$	3.56765	+	24.8136i	0.139720	+	0.971774i
$653$	−44.0399	−	12.9313i	−1.72342	−	0.506040i	−0.737796	−	0.675024i	$-0.764133\pi$
$653$	−44.0399	−	12.9313i	−1.72342	−	0.506040i	−0.985619	+	0.168983i	$0.945952\pi$
$654$	16.9886	−	19.6059i	0.664306	−	0.766650i
$655$	−1.67635	−	1.07732i	−0.0655003	−	0.0420945i
$656$	−6.12381	−	3.93553i	−0.239095	−	0.153657i
$657$	5.00326	−	5.77407i	0.195196	−	0.225268i
$658$	24.4588	+	7.18176i	0.953505	+	0.279974i
$659$	4.22287	+	29.3707i	0.164500	+	1.14412i	0.890021	+	0.455920i	$0.150690\pi$
$659$	4.22287	+	29.3707i	0.164500	+	1.14412i	−0.725521	+	0.688200i	$0.758401\pi$
$660$	7.01302	+	8.09346i	0.272982	+	0.315037i
$661$	−18.1278	−	39.6944i	−0.705090	−	1.54393i	−0.833688	−	0.552236i	$-0.813775\pi$
$661$	−18.1278	−	39.6944i	−0.705090	−	1.54393i	0.128598	−	0.991697i	$-0.458952\pi$
$662$	14.7693	−	4.33666i	0.574026	−	0.168549i
$663$	16.0385	−	35.1195i	0.622884	−	1.36393i
$664$	2.16218	−	15.0383i	0.0839088	−	0.583599i
$665$	2.01722	−	1.29639i	0.0782245	−	0.0502719i
$666$	23.4888			0.910171
$667$	−8.15805	+	0.422790i	−0.315881	+	0.0163705i
$668$	0.398320			0.0154115
$669$	4.41884	−	2.83981i	0.170842	−	0.109794i
$670$	−4.02874	+	28.0205i	−0.155644	+	1.08253i
$671$	7.30069	−	15.9863i	0.281840	−	0.617144i
$672$	6.90843	−	2.02850i	0.266499	−	0.0782511i
$673$	−16.9908	−	37.2047i	−0.654948	−	1.43414i	−0.887156	−	0.461470i	$-0.847322\pi$
$673$	−16.9908	−	37.2047i	−0.654948	−	1.43414i	0.232208	−	0.972666i	$-0.425405\pi$
$674$	−15.4940	−	17.8811i	−0.596808	−	0.688753i
$675$	0.569259	+	3.95929i	0.0219108	+	0.152393i
$676$	−86.4602	−	25.3870i	−3.32539	−	0.976423i
$677$	4.67914	−	5.40002i	0.179834	−	0.207540i	−0.658675	−	0.752428i	$-0.728883\pi$
$677$	4.67914	−	5.40002i	0.179834	−	0.207540i	0.838509	+	0.544888i	$0.183428\pi$
$678$	−3.53328	−	2.27070i	−0.135695	−	0.0872057i
$679$	7.62093	+	4.89767i	0.292464	+	0.187955i
$680$	−7.14442	+	8.24510i	−0.273976	+	0.316185i
$681$	12.2021	+	3.58287i	0.467587	+	0.137296i
$682$	3.44677	+	23.9728i	0.131984	+	0.917966i
$683$	0.144292	+	0.166521i	0.00552116	+	0.00637176i	0.758503	−	0.651669i	$-0.225931\pi$
$683$	0.144292	+	0.166521i	0.00552116	+	0.00637176i	−0.752982	+	0.658041i	$0.771385\pi$
$684$	−2.84482	−	6.22930i	−0.108775	−	0.238183i
$685$	−3.74792	+	1.10049i	−0.143201	+	0.0420475i
$686$	0.915415	−	2.00448i	0.0349507	−	0.0765314i
$687$	2.95478	−	20.5509i	0.112732	−	0.784067i
$688$	−2.76990	+	1.78011i	−0.105602	+	0.0678660i
$689$	42.6387			1.62441
$690$	−9.97240	+	3.49821i	−0.379643	+	0.133175i
$691$	−35.7049			−1.35828			−0.679139	−	0.734010i	$-0.737647\pi$
$691$	−35.7049			−1.35828			−0.679139	+	0.734010i	$0.737647\pi$
$692$	17.5358	−	11.2695i	0.666609	−	0.428404i
$693$	−0.533654	+	3.71165i	−0.0202719	+	0.140994i
$694$	−14.4421	+	31.6238i	−0.548215	+	1.20042i
$695$	4.22171	−	1.23961i	0.160139	−	0.0470210i
$696$	1.33462	+	2.92241i	0.0505886	+	0.110774i
$697$	17.7258	+	20.4567i	0.671414	+	0.774853i
$698$	2.09590	+	14.5773i	0.0793310	+	0.551759i
$699$	11.5086	+	3.37922i	0.435295	+	0.127814i
$700$	7.48092	−	8.63345i	0.282752	−	0.326314i
$701$	30.7724	+	19.7762i	1.16226	+	0.746937i	0.972042	−	0.234806i	$-0.0754455\pi$
$701$	30.7724	+	19.7762i	1.16226	+	0.746937i	0.190214	+	0.981743i	$0.439082\pi$
$702$	−12.3736	−	7.95204i	−0.467012	−	0.300131i
$703$	16.7379	−	19.3165i	0.631281	−	0.728537i
$704$	45.8919	+	13.4751i	1.72962	+	0.507861i
$705$	−1.64630	−	11.4503i	−0.0620032	−	0.431242i
$706$	−20.2383	−	23.3562i	−0.761677	−	0.879022i
$707$	−6.74449	−	14.7684i	−0.253653	−	0.555422i
$708$	37.1241	−	10.9006i	1.39521	−	0.409671i
$709$	16.0226	−	35.0847i	0.601742	−	1.31763i	−0.326338	−	0.945253i	$-0.605815\pi$
$709$	16.0226	−	35.0847i	0.601742	−	1.31763i	0.928081	−	0.372379i	$-0.121458\pi$
$710$	1.65736	−	11.5272i	0.0621996	−	0.432608i
$711$	−3.17544	+	2.04073i	−0.119088	+	0.0765334i
$712$	25.7479			0.964943
$713$	−13.6741	−	3.25686i	−0.512099	−	0.121970i
$714$	−12.7463			−0.477018
$715$	21.0558	−	13.5317i	0.787441	−	0.506057i
$716$	5.75881	−	40.0534i	0.215217	−	1.49687i
$717$	−5.61824	+	12.3022i	−0.209817	+	0.459435i
$718$	21.0614	−	6.18418i	0.786004	−	0.230792i
$719$	−6.81146	−	14.9150i	−0.254025	−	0.556237i	0.739060	−	0.673640i	$-0.235270\pi$
$719$	−6.81146	−	14.9150i	−0.254025	−	0.556237i	−0.993084	+	0.117404i	$0.962543\pi$
$720$	−1.01867	−	1.17561i	−0.0379636	−	0.0438124i
$721$	1.61845	+	11.2566i	0.0602744	+	0.419218i
$722$	28.0156	+	8.22612i	1.04263	+	0.306144i
$723$	11.1155	−	12.8280i	0.413391	−	0.477079i
$724$	−14.2839	−	9.17973i	−0.530859	−	0.341162i
$725$	−5.73181	−	3.68361i	−0.212874	−	0.136806i
$726$	−4.41738	+	5.09793i	−0.163944	+	0.189202i
$727$	−26.9596	−	7.91605i	−0.999876	−	0.293590i	−0.259471	−	0.965751i	$-0.583548\pi$
$727$	−26.9596	−	7.91605i	−0.999876	−	0.293590i	−0.740405	+	0.672161i	$0.765366\pi$
$728$	1.79165	+	12.4612i	0.0664031	+	0.461844i
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$	6.99394	+	15.3146i	0.258857	+	0.566818i
$731$	11.7474	−	3.44935i	0.434494	−	0.127579i
$732$	5.56033	−	12.1754i	0.205516	−	0.450017i
$733$	3.59512	−	25.0046i	0.132789	−	0.923566i	−0.809107	−	0.587661i	$-0.800049\pi$
$733$	3.59512	−	25.0046i	0.132789	−	0.923566i	0.941896	−	0.335905i	$-0.109042\pi$
$734$	8.04080	−	5.16751i	0.296791	−	0.190736i
$735$	−1.00000			−0.0368856
$736$	−21.2317	+	27.2317i	−0.782610	+	1.00377i
$737$	−48.1719			−1.77443
$738$	8.67506	−	5.57512i	0.319333	−	0.205223i
$739$	6.79036	−	47.2280i	0.249787	−	1.73731i	−0.349644	−	0.936883i	$-0.613698\pi$
$739$	6.79036	−	47.2280i	0.249787	−	1.73731i	0.599432	−	0.800426i	$-0.295393\pi$
$740$	−12.6460	+	27.6909i	−0.464876	+	1.01794i
$741$	−15.3569	+	4.50919i	−0.564149	+	0.165649i
$742$	−5.84774	−	12.8048i	−0.214677	−	0.470078i
$743$	10.7106	+	12.3607i	0.392934	+	0.453470i	0.917403	−	0.397959i	$-0.130281\pi$
$743$	10.7106	+	12.3607i	0.392934	+	0.453470i	−0.524469	+	0.851430i	$0.675736\pi$
$744$	0.786749	+	5.47196i	0.0288436	+	0.200612i
$745$	15.7961	+	4.63815i	0.578724	+	0.169929i
$746$	−37.9481	+	43.7945i	−1.38938	+	1.60343i
$747$	−6.77639	−	4.35492i	−0.247935	−	0.159338i
$748$	−52.1112	−	33.4898i	−1.90537	−	1.22451i
$749$	−10.8401	+	12.5101i	−0.396089	+	0.457111i
$750$	−19.0292	−	5.58747i	−0.694848	−	0.204026i
$751$	3.34153	+	23.2408i	0.121934	+	0.848070i	0.955361	+	0.295440i	$0.0954663\pi$
$751$	3.34153	+	23.2408i	0.121934	+	0.848070i	−0.833427	+	0.552629i	$0.813625\pi$
$752$	−11.7840	−	13.5995i	−0.429718	−	0.495921i
$753$	3.70396	+	8.11054i	0.134980	+	0.295564i
$754$	24.0390	−	7.05849i	0.875449	−	0.257055i
$755$	3.56820	−	7.81326i	0.129860	−	0.284354i
$756$	−0.406440	+	2.82685i	−0.0147821	+	0.102812i
$757$	−24.8416	+	15.9647i	−0.902884	+	0.580249i	−0.907644	−	0.419740i	$-0.862121\pi$
$757$	−24.8416	+	15.9647i	−0.902884	+	0.580249i	0.00475999	+	0.999989i	$0.498485\pi$
$758$	48.1985			1.75065
$759$	−8.30723	−	15.9498i	−0.301533	−	0.578941i
$760$	4.52269			0.164055
$761$	−24.5226	+	15.7597i	−0.888943	+	0.571289i	−0.903492	−	0.428605i	$-0.859005\pi$
$761$	−24.5226	+	15.7597i	−0.888943	+	0.571289i	0.0145488	+	0.999894i	$0.495369\pi$
$762$	−6.85396	+	47.6703i	−0.248293	+	1.72691i
$763$	−4.89051	+	10.7087i	−0.177048	+	0.387682i
$764$	30.1726	−	8.85948i	1.09161	−	0.320525i
$765$	2.40287	+	5.26155i	0.0868759	+	0.190232i
$766$	3.00312	+	3.46579i	0.108507	+	0.125224i
$767$	−12.8692	−	89.5074i	−0.464681	−	3.23193i
$768$	4.50498	+	1.32278i	0.162560	+	0.0477318i
$769$	14.1837	−	16.3688i	0.511477	−	0.590276i	−0.439999	−	0.897998i	$-0.645021\pi$
$769$	14.1837	−	16.3688i	0.511477	−	0.590276i	0.951476	+	0.307722i	$0.0995668\pi$
$770$	−6.95141	−	4.46740i	−0.250511	−	0.160994i
$771$	16.1176	+	10.3582i	0.580461	+	0.373040i
$772$	−18.7222	+	21.6065i	−0.673826	+	0.777636i
$773$	−42.3356	−	12.4308i	−1.52271	−	0.447107i	−0.589897	−	0.807479i	$-0.700832\pi$
$773$	−42.3356	−	12.4308i	−1.52271	−	0.447107i	−0.932809	+	0.360372i	$0.882650\pi$
$774$	−0.663802	−	4.61685i	−0.0238599	−	0.165949i
$775$	−7.67759	−	8.86041i	−0.275787	−	0.318275i
$776$	7.09795	+	15.5423i	0.254802	+	0.557938i
$777$	−10.2274	+	3.00304i	−0.366907	+	0.107734i
$778$	−17.2565	+	37.7866i	−0.618677	+	1.35471i
$779$	1.59693	−	11.1069i	0.0572161	−	0.397947i
$780$	16.0364	−	10.3060i	0.574196	−	0.369013i
$781$	19.8171			0.709112
$782$	49.6457	−	35.6661i	1.77533	−	1.27542i
$783$	1.70335			0.0608729
$784$	−1.30862	+	0.840996i	−0.0467363	+	0.0300356i
$785$	1.65913	−	11.5395i	0.0592170	−	0.411863i
$786$	1.82413	−	3.99428i	0.0650645	−	0.142471i
$787$	29.5530	−	8.67753i	1.05345	−	0.309321i	0.291239	−	0.956650i	$-0.405932\pi$
$787$	29.5530	−	8.67753i	1.05345	−	0.309321i	0.762210	+	0.647330i	$0.224114\pi$
$788$	−17.8518	−	39.0900i	−0.635944	−	1.39252i
$789$	−14.9810	−	17.2889i	−0.533336	−	0.615503i
$790$	−1.18376	−	8.23322i	−0.0421162	−	0.292925i
$791$	1.82876	+	0.536973i	0.0650233	+	0.0190925i
$792$	−4.63158	+	5.34512i	−0.164576	+	0.189931i
$793$	−26.3168	−	16.9128i	−0.934537	−	0.600590i
$794$	60.6092	+	38.9512i	2.15094	+	1.38232i
$795$	−4.18330	+	4.82778i	−0.148366	+	0.171224i
$796$	1.79660	+	0.527530i	0.0636789	+	0.0186978i
$797$	0.835393	+	5.81028i	0.0295911	+	0.205811i	0.999253	−	0.0386383i	$-0.0123020\pi$
$797$	0.835393	+	5.81028i	0.0295911	+	0.205811i	−0.969662	+	0.244449i	$0.921393\pi$
$798$	3.46028	+	3.99338i	0.122493	+	0.141364i
$799$	27.7964	+	60.8656i	0.983366	+	2.15327i
$800$	−27.6337	+	8.11400i	−0.977000	+	0.286873i
$801$	5.67092	−	12.4176i	0.200372	−	0.438754i
$802$	0.911704	−	6.34104i	0.0321934	−	0.223910i
$803$	−24.1013	+	15.4890i	−0.850517	+	0.546594i
$804$	−36.6885			−1.29390
$805$	3.89491	−	2.79816i	0.137278	−	0.0986220i
$806$	43.1108			1.51851
$807$	10.4487	−	6.71496i	0.367811	−	0.236378i
$808$	4.35800	−	30.3105i	0.153314	−	1.06632i
$809$	−9.88548	+	21.6462i	−0.347555	+	0.761039i	0.652440	+	0.757841i	$0.273746\pi$
$809$	−9.88548	+	21.6462i	−0.347555	+	0.761039i	−0.999995	+	0.00319889i	$0.998982\pi$
$810$	2.11435	−	0.620830i	0.0742908	−	0.0218138i
$811$	5.08886	+	11.1431i	0.178694	+	0.391286i	0.977691	−	0.210050i	$-0.0673627\pi$
$811$	5.08886	+	11.1431i	0.178694	+	0.391286i	−0.798996	+	0.601336i	$0.794635\pi$
$812$	−3.18567	−	3.67645i	−0.111795	−	0.129018i
$813$	−2.48880	−	17.3100i	−0.0872859	−	0.607087i
$814$	−84.5107	−	24.8146i	−2.96210	−	0.869751i
$815$	−5.74824	+	6.63382i	−0.201352	+	0.232373i
$816$	7.56937	+	4.86454i	0.264981	+	0.170293i
$817$	−4.26979	−	2.74403i	−0.149381	−	0.0960014i
$818$	17.9044	−	20.6628i	0.626014	−	0.722458i
$819$	6.40436	+	1.88049i	0.223787	+	0.0657096i
$820$	1.90198	+	13.2286i	0.0664201	+	0.461962i
$821$	−2.38125	−	2.74811i	−0.0831062	−	0.0959097i	0.712673	−	0.701496i	$-0.247484\pi$
$821$	−2.38125	−	2.74811i	−0.0831062	−	0.0959097i	−0.795780	+	0.605586i	$0.792939\pi$
$822$	−3.57574	−	7.82979i	−0.124718	−	0.273095i
$823$	1.76684	−	0.518792i	0.0615883	−	0.0180840i	−0.250793	−	0.968041i	$-0.580691\pi$
$823$	1.76684	−	0.518792i	0.0615883	−	0.0180840i	0.312382	+	0.949957i	$0.398873\pi$
$824$	−8.91051	+	19.5113i	−0.310412	+	0.679708i
$825$	2.13462	−	14.8466i	0.0743179	−	0.516892i
$826$	−25.1149	+	16.1403i	−0.873858	+	0.561595i
$827$	39.6256			1.37792			0.688958	−	0.724802i	$-0.258069\pi$
$827$	39.6256			1.37792			0.688958	+	0.724802i	$0.258069\pi$
$828$	−6.32692	−	12.1476i	−0.219876	−	0.422159i
$829$	−45.1928			−1.56961			−0.784806	−	0.619742i	$-0.787237\pi$
$829$	−45.1928			−1.56961			−0.784806	+	0.619742i	$0.787237\pi$
$830$	14.9326	−	9.59658i	0.518317	−	0.333102i
$831$	−2.81889	+	19.6058i	−0.0977861	+	0.680117i
$832$	35.3672	−	77.4434i	1.22614	−	2.68487i
$833$	5.54996	−	1.62961i	0.192295	−	0.0564628i
$834$	4.02777	+	8.81959i	0.139470	+	0.305397i
$835$	0.0913344	+	0.105406i	0.00316076	+	0.00364771i
$836$	3.65455	+	25.4179i	0.126395	+	0.879097i
$837$	2.81228	+	0.825759i	0.0972065	+	0.0285424i
$838$	13.1208	−	15.1422i	0.453251	−	0.523079i
$839$	0.0266990	+	0.0171584i	0.000921752	+	0.000592374i	0.541102	−	0.840957i	$-0.318007\pi$
$839$	0.0266990	+	0.0171584i	0.000921752	+	0.000592374i	−0.540180	+	0.841550i	$0.681644\pi$
$840$	−1.58671	−	1.01971i	−0.0547466	−	0.0351835i
$841$	17.0909	−	19.7240i	0.589343	−	0.680138i
$842$	31.8364	+	9.34802i	1.09716	+	0.322154i
$843$	−0.445693	−	3.09986i	−0.0153505	−	0.106765i
$844$	15.4916	+	17.8782i	0.533242	+	0.615394i
$845$	−13.1072	−	28.7008i	−0.450902	−	0.987337i
$846$	24.4588	−	7.18176i	0.840912	−	0.246914i
$847$	1.27164	−	2.78449i	0.0436939	−	0.0956763i
$848$	−1.41418	+	9.83585i	−0.0485632	+	0.337764i
$849$	18.4219	−	11.8390i	0.632236	−	0.406314i
$850$	50.9852			1.74878
$851$	31.4319	−	40.3145i	1.07747	−	1.38196i
$852$	15.0930			0.517079
$853$	−46.0695	+	29.6071i	−1.57739	+	1.01373i	−0.600595	+	0.799553i	$0.705070\pi$
$853$	−46.0695	+	29.6071i	−1.57739	+	1.01373i	−0.976795	+	0.214174i	$0.931294\pi$
$854$	−1.46980	+	10.2227i	−0.0502955	+	0.349813i
$855$	0.996114	−	2.18119i	0.0340664	−	0.0745950i
$856$	−29.9568	+	8.79612i	−1.02390	+	0.300645i
$857$	0.630072	+	1.37967i	0.0215229	+	0.0471285i	0.920088	−	0.391711i	$-0.128117\pi$
$857$	0.630072	+	1.37967i	0.0215229	+	0.0471285i	−0.898565	+	0.438840i	$0.855390\pi$
$858$	36.1184	+	41.6829i	1.23306	+	1.42303i
$859$	−1.64473	−	11.4394i	−0.0561176	−	0.390306i	−0.998451	−	0.0556318i	$-0.982283\pi$
$859$	−1.64473	−	11.4394i	−0.0561176	−	0.390306i	0.942334	−	0.334675i	$-0.108626\pi$
$860$	5.80017	+	1.70308i	0.197784	+	0.0580747i
$861$	−3.06449	+	3.53661i	−0.104438	+	0.120527i
$862$	−14.6687	−	9.42703i	−0.499619	−	0.321086i
$863$	−20.4586	−	13.1480i	−0.696420	−	0.447562i	0.143943	−	0.989586i	$-0.454022\pi$
$863$	−20.4586	−	13.1480i	−0.696420	−	0.447562i	−0.840363	+	0.542024i	$0.817658\pi$
$864$	4.71506	−	5.44146i	0.160409	−	0.185122i
$865$	7.00314	+	2.05631i	0.238114	+	0.0699166i
$866$	−4.60309	−	32.0152i	−0.156419	−	1.08792i
$867$	−10.7775	−	12.4379i	−0.366023	−	0.422413i
$868$	−3.47732	−	7.61427i	−0.118028	−	0.258445i
$869$	13.5809	−	3.98771i	0.460701	−	0.135274i
$870$	−1.55928	+	3.41434i	−0.0528644	+	0.115757i
$871$	−12.2030	+	84.8740i	−0.413484	+	2.87584i
$872$	−18.6797	+	12.0047i	−0.632573	+	0.406530i
$873$	9.05901			0.306601
$874$	−24.6516	−	5.87145i	−0.833853	−	0.198605i
$875$	9.00000			0.304256
$876$	−18.3560	+	11.7967i	−0.620190	+	0.398572i
$877$	4.75852	−	33.0963i	0.160684	−	1.11758i	−0.736664	−	0.676259i	$-0.763600\pi$
$877$	4.75852	−	33.0963i	0.160684	−	1.11758i	0.897348	−	0.441323i	$-0.145491\pi$
$878$	−12.2570	+	26.8392i	−0.413655	+	0.905779i
$879$	8.23794	−	2.41888i	0.277859	−	0.0815867i
$880$	2.42313	+	5.30592i	0.0816838	+	0.178863i
$881$	23.1450	+	26.7107i	0.779774	+	0.899908i	0.997093	−	0.0761931i	$-0.0242765\pi$
$881$	23.1450	+	26.7107i	0.779774	+	0.899908i	−0.217319	+	0.976101i	$0.569731\pi$
$882$	−0.313607	−	2.18119i	−0.0105597	−	0.0734444i
$883$	17.3144	+	5.08396i	0.582675	+	0.171089i	0.559769	−	0.828649i	$-0.310890\pi$
$883$	17.3144	+	5.08396i	0.582675	+	0.171089i	0.0229062	+	0.999738i	$0.492708\pi$
$884$	−72.2067	+	83.3309i	−2.42857	+	2.80272i
$885$	11.3971	+	7.32448i	0.383110	+	0.246210i
$886$	−36.4575	−	23.4298i	−1.22481	−	0.787141i
$887$	−10.2405	+	11.8181i	−0.343842	+	0.396815i	−0.901162	−	0.433483i	$-0.857284\pi$
$887$	−10.2405	+	11.8181i	−0.343842	+	0.396815i	0.557320	+	0.830298i	$0.311830\pi$
$888$	−19.2902	−	5.66410i	−0.647336	−	0.190075i
$889$	−3.11033	−	21.6328i	−0.104317	−	0.725540i
$890$	19.6996	+	22.7345i	0.660331	+	0.762062i
$891$	1.55773	+	3.41095i	0.0521859	+	0.114271i
$892$	−14.3936	+	4.22634i	−0.481933	+	0.141508i
$893$	11.5230	−	25.2320i	0.385604	−	0.844355i
$894$	−5.16290	+	35.9088i	−0.172673	+	1.20097i
$895$	11.9196	−	7.66029i	0.398430	−	0.256055i
$896$	−13.7072			−0.457926
$897$	−30.2063	+	10.5961i	−1.00856	+	0.353792i
$898$	−50.9261			−1.69943
$899$	−4.19999	+	2.69917i	−0.140077	+	0.0900223i
$900$	1.62576	−	11.3074i	0.0541920	−	0.376914i
$901$	15.3497	−	33.6112i	0.511373	−	1.11975i
$902$	−37.1020	+	10.8941i	−1.23536	+	0.362735i
$903$	0.879296	+	1.92539i	0.0292611	+	0.0640729i
$904$	2.35415	+	2.71683i	0.0782978	+	0.0903605i
$905$	−0.846107	−	5.88480i	−0.0281255	−	0.195617i
$906$	18.1612	+	5.33261i	0.603365	+	0.177164i
$907$	−26.8774	+	31.0182i	−0.892449	+	1.02994i	0.106914	+	0.994268i	$0.465903\pi$
$907$	−26.8774	+	31.0182i	−0.892449	+	1.02994i	−0.999364	+	0.0356731i	$0.988643\pi$
$908$	−30.5540	−	19.6358i	−1.01397	−	0.651638i
$909$	−13.6582	−	8.77759i	−0.453014	−	0.291134i
$910$	−9.63205	+	11.1160i	−0.319299	+	0.368491i
$911$	−47.3146	−	13.8928i	−1.56760	−	0.460290i	−0.621301	−	0.783572i	$-0.713396\pi$
$911$	−47.3146	−	13.8928i	−1.56760	−	0.460290i	−0.946303	+	0.323282i	$0.895214\pi$
$912$	−0.530838	−	3.69206i	−0.0175778	−	0.122256i
$913$	19.7802	+	22.8276i	0.654629	+	0.755482i
$914$	2.64870	+	5.79985i	0.0876113	+	0.191842i
$915$	4.49691	−	1.32041i	0.148663	−	0.0436514i
$916$	−24.6322	+	53.9370i	−0.813871	+	1.78213i
$917$	−0.283588	+	1.97240i	−0.00936489	+	0.0651343i
$918$	−10.7229	+	6.89116i	−0.353907	+	0.227442i
$919$	36.7801			1.21326			0.606631	−	0.794983i	$-0.292521\pi$
$919$	36.7801			1.21326			0.606631	+	0.794983i	$0.292521\pi$
$920$	9.03340	−	0.468155i	0.297823	−	0.0154346i
$921$	−21.3134			−0.702302
$922$	18.0728	−	11.6147i	0.595197	−	0.382510i
$923$	5.02013	−	34.9158i	0.165240	−	1.14927i
$924$	4.44875	−	9.74141i	0.146353	−	0.320469i
$925$	40.9097	−	12.0122i	1.34510	−	0.394958i
$926$	−8.99730	−	19.7013i	−0.295670	−	0.647426i
$927$	7.44731	+	8.59465i	0.244602	+	0.282285i
$928$	1.74539	+	12.1395i	0.0572953	+	0.398498i
$929$	10.7823	+	3.16597i	0.353756	+	0.103872i	0.453782	−	0.891113i	$-0.350074\pi$
$929$	10.7823	+	3.16597i	0.353756	+	0.103872i	−0.100026	+	0.994985i	$0.531893\pi$
$930$	−4.22962	+	4.88124i	−0.138695	+	0.160062i
$931$	−2.01722	−	1.29639i	−0.0661118	−	0.0424875i
$932$	−28.8173	−	18.5198i	−0.943942	−	0.606635i
$933$	−12.1737	+	14.0492i	−0.398550	+	0.459951i
$934$	22.6927	+	6.66318i	0.742529	+	0.218026i
$935$	−3.08680	−	21.4691i	−0.100949	−	0.702116i
$936$	8.24428	+	9.51441i	0.269473	+	0.310988i
$937$	7.93348	+	17.3719i	0.259175	+	0.567515i	0.993828	−	0.110928i	$-0.0353823\pi$
$937$	7.93348	+	17.3719i	0.259175	+	0.567515i	−0.734653	+	0.678443i	$0.762655\pi$
$938$	27.1620	−	7.97547i	0.886870	−	0.260408i
$939$	−4.28937	+	9.39242i	−0.139978	+	0.306510i
$940$	−4.70170	+	32.7010i	−0.153352	+	1.06659i
$941$	−11.4596	+	7.36466i	−0.373574	+	0.240081i	−0.713933	−	0.700214i	$-0.753088\pi$
$941$	−11.4596	+	7.36466i	−0.373574	+	0.240081i	0.340359	+	0.940296i	$0.389451\pi$
$942$	25.6902			0.837031
$943$	2.03993	−	22.3497i	0.0664294	−	0.727807i
$944$	21.0743			0.685910
$945$	−0.841254	+	0.540641i	−0.0273660	+	0.0175870i
$946$	−2.48914	+	17.3123i	−0.0809288	+	0.562872i
$947$	1.86960	−	4.09385i	0.0607538	−	0.133032i	−0.876820	−	0.480819i	$-0.840339\pi$
$947$	1.86960	−	4.09385i	0.0607538	−	0.133032i	0.937574	+	0.347787i	$0.113067\pi$
$948$	10.3434	−	3.03711i	0.335939	−	0.0986407i
$949$	21.1846	+	46.3878i	0.687681	+	1.50581i
$950$	−13.8411	−	15.9735i	−0.449066	−	0.518250i
$951$	3.27220	+	22.7586i	0.106108	+	0.737999i
$952$	10.4679	+	3.07365i	0.339267	+	0.0996177i
$953$	15.4620	−	17.8441i	0.500864	−	0.578028i	−0.447872	−	0.894098i	$-0.647818\pi$
$953$	15.4620	−	17.8441i	0.500864	−	0.578028i	0.948736	+	0.316070i	$0.102363\pi$
$954$	−11.8422	−	7.61052i	−0.383406	−	0.246400i
$955$	9.26300	+	5.95297i	0.299744	+	0.192634i
$956$	25.2937	−	29.1905i	0.818058	−	0.944089i
$957$	−6.12854	−	1.79950i	−0.198107	−	0.0581696i
$958$	0.670588	+	4.66404i	0.0216657	+	0.150688i
$959$	2.55798	+	2.95207i	0.0826015	+	0.0953272i
$960$	5.29867	+	11.6025i	0.171014	+	0.374468i
$961$	21.5015	−	6.31341i	0.693597	−	0.203658i
$962$	−65.1293	+	142.613i	−2.09985	+	4.59804i
$963$	−2.35578	+	16.3848i	−0.0759139	+	0.527993i
$964$	−40.7807	+	26.2082i	−1.31346	+	0.844108i
$965$	−10.0106			−0.322253
$966$	7.32477	+	7.61800i	0.235671	+	0.245105i
$967$	−47.2627			−1.51987			−0.759933	−	0.650001i	$-0.774768\pi$
$967$	−47.2627			−1.51987			−0.759933	+	0.650001i	$0.774768\pi$
$968$	4.85710	−	3.12147i	0.156113	−	0.100328i
$969$	−1.97390	+	13.7288i	−0.0634108	+	0.441032i
$970$	−8.29276	+	18.1586i	−0.266264	+	0.583038i
$971$	5.59250	−	1.64211i	0.179472	−	0.0526977i	−0.190762	−	0.981636i	$-0.561096\pi$
$971$	5.59250	−	1.64211i	0.179472	−	0.0526977i	0.370234	+	0.928939i	$0.379278\pi$
$972$	1.18639	+	2.59784i	0.0380536	+	0.0833257i
$973$	−2.88135	−	3.32525i	−0.0923718	−	0.106603i
$974$	−1.60687	−	11.1760i	−0.0514873	−	0.358102i
$975$	−25.6174	−	7.52196i	−0.820415	−	0.240896i
$976$	4.77426	−	5.50979i	0.152820	−	0.176364i
$977$	−9.59991	−	6.16948i	−0.307128	−	0.197379i	0.377993	−	0.925808i	$-0.376614\pi$
$977$	−9.59991	−	6.16948i	−0.307128	−	0.197379i	−0.685121	+	0.728429i	$0.740251\pi$
$978$	−16.2723	−	10.4576i	−0.520330	−	0.334396i
$979$	−33.5220	+	38.6865i	−1.07137	+	1.23643i
$980$	2.74024	+	0.804606i	0.0875337	+	0.0257022i
$981$	1.67541	+	11.6528i	0.0534919	+	0.372044i
$982$	−28.5913	−	32.9962i	−0.912386	−	1.05295i
$983$	8.84083	+	19.3587i	0.281979	+	0.617447i	0.996630	−	0.0820342i	$-0.0261417\pi$
$983$	8.84083	+	19.3587i	0.281979	+	0.617447i	−0.714651	+	0.699481i	$0.753414\pi$
$984$	−8.46879	+	2.48666i	−0.269975	+	0.0792719i
$985$	6.25080	−	13.6873i	0.199167	−	0.436115i
$986$	3.08986	−	21.4905i	0.0984012	−	0.684395i
$987$	−9.73162	+	6.25413i	−0.309761	+	0.199071i
$988$	45.7096			1.45422
$989$	−8.81231	−	5.03881i	−0.280215	−	0.160225i
$990$	−8.26315			−0.262620
$991$	−47.0775	+	30.2549i	−1.49547	+	0.961078i	−0.499994	+	0.866029i	$0.666664\pi$
$991$	−47.0775	+	30.2549i	−1.49547	+	0.961078i	−0.995473	+	0.0950486i	$0.969699\pi$
$992$	−3.00334	+	20.8887i	−0.0953561	+	0.663216i
$993$	−2.90178	+	6.35402i	−0.0920853	+	0.201639i
$994$	−11.1740	+	3.28098i	−0.354417	+	0.104066i
$995$	0.272362	+	0.596389i	0.00863445	+	0.0189068i
$996$	15.0649	+	17.3858i	0.477350	+	0.550892i
$997$	−6.62507	−	46.0784i	−0.209818	−	1.45932i	−0.773747	−	0.633494i	$-0.781620\pi$
$997$	−6.62507	−	46.0784i	−0.209818	−	1.45932i	0.563929	−	0.825823i	$-0.309289\pi$
$998$	33.8445	+	9.93765i	1.07133	+	0.314571i
$999$	−6.98029	+	8.05568i	−0.220846	+	0.254870i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.q.a.127.1	✓	10
23.2	even	11	inner	483.2.q.a.232.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.a.127.1	✓	10	1.1	even	1	trivial
483.2.q.a.232.1	yes	10	23.2	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.85380 - 1.19136i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(1.18639 - 2.59784i) q^{4} +(0.959493 - 0.281733i) q^{5} +(0.915415 + 2.00448i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.268423 - 1.86692i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(1.85380 - 1.19136i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(1.18639 - 2.59784i) q^{4} +(0.959493 - 0.281733i) q^{5} +(0.915415 + 2.00448i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.268423 - 1.86692i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(1.44306 - 1.66538i) q^{10} +(3.15455 + 2.02730i) q^{11} +(2.40255 + 1.54403i) q^{12} +(4.37102 - 5.04443i) q^{13} +(-2.11435 - 0.620830i) q^{14} +(0.142315 + 0.989821i) q^{15} +(1.01867 + 1.17561i) q^{16} +(-2.40287 - 5.26155i) q^{17} +(-2.11435 + 0.620830i) q^{18} +(-0.996114 + 2.18119i) q^{19} +(0.406440 - 2.82685i) q^{20} +(0.841254 - 0.540641i) q^{21} +8.26315 q^{22} +(-1.76381 + 4.45971i) q^{23} +1.88612 q^{24} +(-3.36501 + 2.16256i) q^{25} +(2.09325 - 14.5588i) q^{26} +(0.415415 - 0.909632i) q^{27} +(-2.74024 + 0.804606i) q^{28} +(0.707599 + 1.54943i) q^{29} +(1.44306 + 1.66538i) q^{30} +(0.417125 + 2.90117i) q^{31} +(6.90843 + 2.02850i) q^{32} +(-2.45561 + 2.83392i) q^{33} +(-10.7229 - 6.89116i) q^{34} +(-0.841254 - 0.540641i) q^{35} +(-1.87023 + 2.15836i) q^{36} +(-10.2274 - 3.00304i) q^{37} +(0.751992 + 5.23022i) q^{38} +(4.37102 + 5.04443i) q^{39} +(-0.783524 - 1.71568i) q^{40} +(-4.49005 + 1.31840i) q^{41} +(0.915415 - 2.00448i) q^{42} +(-0.301233 + 2.09512i) q^{43} +(9.00914 - 5.78982i) q^{44} -1.00000 q^{45} +(2.04338 + 10.3687i) q^{46} -11.5680 q^{47} +(-1.30862 + 0.840996i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(-3.66166 + 8.01792i) q^{50} +(5.54996 - 1.62961i) q^{51} +(-7.91886 - 17.3399i) q^{52} +(4.18330 + 4.82778i) q^{53} +(-0.313607 - 2.18119i) q^{54} +(3.59792 + 1.05645i) q^{55} +(-1.23515 + 1.42544i) q^{56} +(-2.01722 - 1.29639i) q^{57} +(3.15768 + 2.02932i) q^{58} +(8.87191 - 10.2387i) q^{59} +(2.74024 + 0.804606i) q^{60} +(-0.666994 - 4.63905i) q^{61} +(4.22962 + 4.88124i) q^{62} +(0.415415 + 0.909632i) q^{63} +(12.2384 - 3.59353i) q^{64} +(2.77279 - 6.07155i) q^{65} +(-1.17597 + 8.17905i) q^{66} +(-10.8071 + 6.94532i) q^{67} -16.5194 q^{68} +(-4.16330 - 2.38054i) q^{69} -2.20362 q^{70} +(4.44588 - 2.85719i) q^{71} +(-0.268423 + 1.86692i) q^{72} +(-3.17385 + 6.94976i) q^{73} +(-22.5373 + 6.61755i) q^{74} +(-1.66166 - 3.63853i) q^{75} +(4.48458 + 5.17549i) q^{76} +(-0.533654 - 3.71165i) q^{77} +(14.1128 + 4.14388i) q^{78} +(2.47187 - 2.85269i) q^{79} +(1.30862 + 0.840996i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-6.75296 + 7.79334i) q^{82} +(7.72882 + 2.26939i) q^{83} +(-0.406440 - 2.82685i) q^{84} +(-3.78789 - 4.37145i) q^{85} +(1.93763 + 4.24282i) q^{86} +(-1.63436 + 0.479890i) q^{87} +(2.93807 - 6.43348i) q^{88} +(-1.94277 + 13.5123i) q^{89} +(-1.85380 + 1.19136i) q^{90} -6.67474 q^{91} +(9.49302 + 9.87306i) q^{92} -2.93100 q^{93} +(-21.4448 + 13.7817i) q^{94} +(-0.341254 + 2.37347i) q^{95} +(-2.99103 + 6.54943i) q^{96} +(-8.69206 + 2.55222i) q^{97} +(0.915415 + 2.00448i) q^{98} +(-2.45561 - 2.83392i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} - q^{3} + 8 q^{4} + q^{5} + 4 q^{6} - q^{7} - 7 q^{8} - q^{9}+O(q^{10}) \) 10 * q + 4 * q^2 - q^3 + 8 * q^4 + q^5 + 4 * q^6 - q^7 - 7 * q^8 - q^9	\( 10 q + 4 q^{2} - q^{3} + 8 q^{4} + q^{5} + 4 q^{6} - q^{7} - 7 q^{8} - q^{9} - 4 q^{10} - q^{11} - 3 q^{12} + 15 q^{13} - 7 q^{14} + q^{15} - 10 q^{16} - 24 q^{17} - 7 q^{18} + 5 q^{19} - 8 q^{20} - q^{21} + 26 q^{22} + 21 q^{23} - 18 q^{24} + 4 q^{25} + 6 q^{26} - q^{27} - 3 q^{28} - 22 q^{29} - 4 q^{30} - 8 q^{31} + 10 q^{32} - q^{33} + 8 q^{34} + q^{35} - 14 q^{36} - 2 q^{37} + 2 q^{38} + 15 q^{39} - 4 q^{40} + 7 q^{41} + 4 q^{42} + q^{43} + 19 q^{44} - 10 q^{45} + 15 q^{46} - 6 q^{47} + q^{48} - q^{49} - 16 q^{50} + 20 q^{51} - 21 q^{52} - q^{53} - 7 q^{54} + 12 q^{55} + 4 q^{56} - 6 q^{57} + 22 q^{58} + 10 q^{59} + 3 q^{60} + 5 q^{61} - 34 q^{62} - q^{63} + 13 q^{64} - 4 q^{65} - 7 q^{66} + 29 q^{67} - 28 q^{68} - q^{69} - 4 q^{70} + 22 q^{71} - 7 q^{72} - 33 q^{73} - 36 q^{74} + 4 q^{75} + 26 q^{76} - q^{77} + 28 q^{78} + 27 q^{79} - q^{80} - q^{81} + 38 q^{82} + 25 q^{83} + 8 q^{84} + 2 q^{85} + 18 q^{86} - 7 q^{88} - 38 q^{89} - 4 q^{90} - 18 q^{91} + 41 q^{92} - 30 q^{93} - 42 q^{94} + 6 q^{95} - 23 q^{96} - q^{97} + 4 q^{98} - q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 - q^3 + 8 * q^4 + q^5 + 4 * q^6 - q^7 - 7 * q^8 - q^9 - 4 * q^10 - q^11 - 3 * q^12 + 15 * q^13 - 7 * q^14 + q^15 - 10 * q^16 - 24 * q^17 - 7 * q^18 + 5 * q^19 - 8 * q^20 - q^21 + 26 * q^22 + 21 * q^23 - 18 * q^24 + 4 * q^25 + 6 * q^26 - q^27 - 3 * q^28 - 22 * q^29 - 4 * q^30 - 8 * q^31 + 10 * q^32 - q^33 + 8 * q^34 + q^35 - 14 * q^36 - 2 * q^37 + 2 * q^38 + 15 * q^39 - 4 * q^40 + 7 * q^41 + 4 * q^42 + q^43 + 19 * q^44 - 10 * q^45 + 15 * q^46 - 6 * q^47 + q^48 - q^49 - 16 * q^50 + 20 * q^51 - 21 * q^52 - q^53 - 7 * q^54 + 12 * q^55 + 4 * q^56 - 6 * q^57 + 22 * q^58 + 10 * q^59 + 3 * q^60 + 5 * q^61 - 34 * q^62 - q^63 + 13 * q^64 - 4 * q^65 - 7 * q^66 + 29 * q^67 - 28 * q^68 - q^69 - 4 * q^70 + 22 * q^71 - 7 * q^72 - 33 * q^73 - 36 * q^74 + 4 * q^75 + 26 * q^76 - q^77 + 28 * q^78 + 27 * q^79 - q^80 - q^81 + 38 * q^82 + 25 * q^83 + 8 * q^84 + 2 * q^85 + 18 * q^86 - 7 * q^88 - 38 * q^89 - 4 * q^90 - 18 * q^91 + 41 * q^92 - 30 * q^93 - 42 * q^94 + 6 * q^95 - 23 * q^96 - q^97 + 4 * q^98 - q^99

Introduction

L-functions

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