LMFDB - Embedded newform 805.2.u.d.71.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [805,2,Mod(36,805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(805, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

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

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

chi := DirichletCharacter("805.36");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 805 = 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	805.u (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:	$6.42795736271$
Analytic rank:	$0$
Dimension:	$130$
Relative dimension:	$13$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			71.2
Character	$\chi$	$=$	805.71
Dual form			805.2.u.d.771.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.90133 - 1.22191i) q^{2} +(-0.232141 - 1.61458i) q^{3} +(1.29116 + 2.82724i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(-1.53149 + 3.35350i) q^{6} +(0.654861 - 0.755750i) q^{7} +(0.356423 - 2.47898i) q^{8} +(0.325509 - 0.0955781i) q^{9} +O(q^{10})$	\(q+(-1.90133 - 1.22191i) q^{2} +(-0.232141 - 1.61458i) q^{3} +(1.29116 + 2.82724i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(-1.53149 + 3.35350i) q^{6} +(0.654861 - 0.755750i) q^{7} +(0.356423 - 2.47898i) q^{8} +(0.325509 - 0.0955781i) q^{9} +(1.48006 + 1.70808i) q^{10} +(1.27141 - 0.817087i) q^{11} +(4.26507 - 2.74099i) q^{12} +(-1.36340 - 1.57345i) q^{13} +(-2.16856 + 0.636748i) q^{14} +(-0.232141 + 1.61458i) q^{15} +(0.364001 - 0.420079i) q^{16} +(1.29428 - 2.83407i) q^{17} +(-0.735688 - 0.216018i) q^{18} +(1.24752 + 2.73168i) q^{19} +(-0.442331 - 3.07648i) q^{20} +(-1.37224 - 0.881883i) q^{21} -3.41578 q^{22} +(-0.715258 - 4.74219i) q^{23} -4.08524 q^{24} +(0.841254 + 0.540641i) q^{25} +(0.669661 + 4.65759i) q^{26} +(-2.26273 - 4.95469i) q^{27} +(2.98222 + 0.875658i) q^{28} +(2.73185 - 5.98191i) q^{29} +(2.41424 - 2.78619i) q^{30} +(-0.740559 + 5.15070i) q^{31} +(-6.01143 + 1.76511i) q^{32} +(-1.61440 - 1.86311i) q^{33} +(-5.92382 + 3.80701i) q^{34} +(-0.841254 + 0.540641i) q^{35} +(0.690507 + 0.796887i) q^{36} +(-4.09106 + 1.20124i) q^{37} +(0.965928 - 6.71818i) q^{38} +(-2.22395 + 2.56658i) q^{39} +(-1.04039 + 2.27815i) q^{40} +(-10.2876 - 3.02071i) q^{41} +(1.53149 + 3.35350i) q^{42} +(-1.11049 - 7.72364i) q^{43} +(3.95170 + 2.53960i) q^{44} -0.339251 q^{45} +(-4.43459 + 9.89045i) q^{46} +6.91140 q^{47} +(-0.762750 - 0.490190i) q^{48} +(-0.142315 - 0.989821i) q^{49} +(-0.938885 - 2.05587i) q^{50} +(-4.87628 - 1.43180i) q^{51} +(2.68815 - 5.88623i) q^{52} +(1.48539 - 1.71423i) q^{53} +(-1.75199 + 12.1854i) q^{54} +(-1.45011 + 0.425791i) q^{55} +(-1.64008 - 1.89275i) q^{56} +(4.12091 - 2.64835i) q^{57} +(-12.5035 + 8.03550i) q^{58} +(3.25682 + 3.75857i) q^{59} +(-4.86453 + 1.42836i) q^{60} +(-0.490604 + 3.41223i) q^{61} +(7.70174 - 8.88828i) q^{62} +(0.140930 - 0.308594i) q^{63} +(12.5199 + 3.67616i) q^{64} +(0.864881 + 1.89383i) q^{65} +(0.792943 + 5.51504i) q^{66} +(6.30430 + 4.05152i) q^{67} +9.68372 q^{68} +(-7.49060 + 2.25570i) q^{69} +2.26011 q^{70} +(-10.9861 - 7.06032i) q^{71} +(-0.120917 - 0.840997i) q^{72} +(6.00232 + 13.1433i) q^{73} +(9.24626 + 2.71495i) q^{74} +(0.677617 - 1.48377i) q^{75} +(-6.11238 + 7.05407i) q^{76} +(0.215085 - 1.49595i) q^{77} +(7.36459 - 2.16244i) q^{78} +(-2.99390 - 3.45514i) q^{79} +(-0.467606 + 0.300512i) q^{80} +(-6.61827 + 4.25330i) q^{81} +(15.8691 + 18.3139i) q^{82} +(-16.4742 + 4.83726i) q^{83} +(0.721522 - 5.01829i) q^{84} +(-2.04030 + 2.35463i) q^{85} +(-7.32619 + 16.0421i) q^{86} +(-10.2924 - 3.02213i) q^{87} +(-1.57238 - 3.44303i) q^{88} +(0.662830 + 4.61009i) q^{89} +(0.645028 + 0.414535i) q^{90} -2.08197 q^{91} +(12.4838 - 8.14513i) q^{92} +8.48812 q^{93} +(-13.1408 - 8.44511i) q^{94} +(-0.427380 - 2.97250i) q^{95} +(4.24541 + 9.29616i) q^{96} +(8.98192 + 2.63733i) q^{97} +(-0.938885 + 2.05587i) q^{98} +(0.335761 - 0.387489i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 130 q + 2 q^{2} + 2 q^{3} - 16 q^{4} - 13 q^{5} + 5 q^{6} + 13 q^{7} - 7 q^{8} - 39 q^{9}+O(q^{10}) $ 130 * q + 2 * q^2 + 2 * q^3 - 16 * q^4 - 13 * q^5 + 5 * q^6 + 13 * q^7 - 7 * q^8 - 39 * q^9	\( 130 q + 2 q^{2} + 2 q^{3} - 16 q^{4} - 13 q^{5} + 5 q^{6} + 13 q^{7} - 7 q^{8} - 39 q^{9} + 2 q^{10} + 2 q^{11} - 5 q^{12} + 13 q^{13} - 2 q^{14} + 2 q^{15} - 6 q^{16} - 51 q^{17} + q^{18} - 9 q^{19} - 16 q^{20} - 2 q^{21} + 34 q^{22} - 10 q^{23} - 76 q^{24} - 13 q^{25} - 31 q^{26} + 14 q^{27} + 27 q^{28} + 3 q^{29} + 5 q^{30} + 6 q^{31} + 22 q^{32} - 58 q^{33} + q^{34} + 13 q^{35} + 193 q^{36} - 36 q^{37} + 4 q^{38} - 2 q^{39} - 29 q^{40} - 34 q^{41} - 5 q^{42} - 22 q^{43} + 8 q^{44} + 170 q^{45} - 198 q^{46} - 14 q^{47} - 120 q^{48} - 13 q^{49} + 2 q^{50} - 6 q^{51} + 33 q^{52} - 18 q^{53} + 188 q^{54} - 31 q^{55} - 15 q^{56} - 9 q^{57} + 114 q^{58} + 46 q^{59} - 16 q^{60} - 56 q^{61} - 146 q^{62} + 17 q^{63} - 109 q^{64} + 2 q^{65} - 14 q^{66} - 10 q^{67} + 86 q^{68} - 6 q^{69} - 2 q^{70} - 25 q^{72} + 64 q^{73} + 79 q^{74} + 2 q^{75} + 32 q^{76} - 13 q^{77} - 64 q^{78} - 118 q^{79} - 17 q^{80} + 23 q^{81} + 129 q^{82} - 117 q^{83} - 72 q^{84} - 7 q^{85} + 74 q^{86} - 51 q^{87} - 40 q^{88} - 35 q^{89} + 100 q^{90} + 42 q^{91} + 76 q^{92} - 90 q^{93} - 7 q^{94} + 2 q^{95} + 393 q^{96} - 4 q^{97} + 2 q^{98} - 40 q^{99}+O(q^{100}) \) 130 * q + 2 * q^2 + 2 * q^3 - 16 * q^4 - 13 * q^5 + 5 * q^6 + 13 * q^7 - 7 * q^8 - 39 * q^9 + 2 * q^10 + 2 * q^11 - 5 * q^12 + 13 * q^13 - 2 * q^14 + 2 * q^15 - 6 * q^16 - 51 * q^17 + q^18 - 9 * q^19 - 16 * q^20 - 2 * q^21 + 34 * q^22 - 10 * q^23 - 76 * q^24 - 13 * q^25 - 31 * q^26 + 14 * q^27 + 27 * q^28 + 3 * q^29 + 5 * q^30 + 6 * q^31 + 22 * q^32 - 58 * q^33 + q^34 + 13 * q^35 + 193 * q^36 - 36 * q^37 + 4 * q^38 - 2 * q^39 - 29 * q^40 - 34 * q^41 - 5 * q^42 - 22 * q^43 + 8 * q^44 + 170 * q^45 - 198 * q^46 - 14 * q^47 - 120 * q^48 - 13 * q^49 + 2 * q^50 - 6 * q^51 + 33 * q^52 - 18 * q^53 + 188 * q^54 - 31 * q^55 - 15 * q^56 - 9 * q^57 + 114 * q^58 + 46 * q^59 - 16 * q^60 - 56 * q^61 - 146 * q^62 + 17 * q^63 - 109 * q^64 + 2 * q^65 - 14 * q^66 - 10 * q^67 + 86 * q^68 - 6 * q^69 - 2 * q^70 - 25 * q^72 + 64 * q^73 + 79 * q^74 + 2 * q^75 + 32 * q^76 - 13 * q^77 - 64 * q^78 - 118 * q^79 - 17 * q^80 + 23 * q^81 + 129 * q^82 - 117 * q^83 - 72 * q^84 - 7 * q^85 + 74 * q^86 - 51 * q^87 - 40 * q^88 - 35 * q^89 + 100 * q^90 + 42 * q^91 + 76 * q^92 - 90 * q^93 - 7 * q^94 + 2 * q^95 + 393 * q^96 - 4 * q^97 + 2 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/805\mathbb{Z}\right)^\times$.

$n$	$162$	$281$	$346$
$\chi(n)$	$1$	$e\left(\frac{1}{11}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.90133	−	1.22191i	−1.34444	−	0.864021i	−0.347168	−	0.937803i	$-0.612857\pi$
$2$	−1.90133	−	1.22191i	−1.34444	−	0.864021i	−0.997274	+	0.0737820i	$0.976493\pi$
$3$	−0.232141	−	1.61458i	−0.134027	−	0.932177i	−0.940231	−	0.340539i	$-0.889391\pi$
$3$	−0.232141	−	1.61458i	−0.134027	−	0.932177i	0.806204	−	0.591638i	$-0.201518\pi$
$4$	1.29116	+	2.82724i	0.645579	+	1.41362i
$5$	−0.959493	−	0.281733i	−0.429098	−	0.125995i
$5$	−0.959493	−	0.281733i	−0.429098	−	0.125995i
$6$	−1.53149	+	3.35350i	−0.625229	+	1.36906i
$7$	0.654861	−	0.755750i	0.247514	−	0.285646i
$7$	0.654861	−	0.755750i	0.247514	−	0.285646i
$8$	0.356423	−	2.47898i	0.126015	−	0.876451i
$9$	0.325509	−	0.0955781i	0.108503	−	0.0318594i
$10$	1.48006	+	1.70808i	0.468036	+	0.540142i
$11$	1.27141	−	0.817087i	0.383345	−	0.246361i	−0.334748	−	0.942308i	$-0.608651\pi$
$11$	1.27141	−	0.817087i	0.383345	−	0.246361i	0.718094	+	0.695946i	$0.245015\pi$
$12$	4.26507	−	2.74099i	1.23122	−	0.791257i
$13$	−1.36340	−	1.57345i	−0.378139	−	0.436396i	0.534496	−	0.845171i	$-0.320501\pi$
$13$	−1.36340	−	1.57345i	−0.378139	−	0.436396i	−0.912635	+	0.408775i	$0.865956\pi$
$14$	−2.16856	+	0.636748i	−0.579573	+	0.170178i
$15$	−0.232141	+	1.61458i	−0.0599386	+	0.416882i
$16$	0.364001	−	0.420079i	0.0910002	−	0.105020i
$17$	1.29428	−	2.83407i	0.313908	−	0.687363i	−0.685253	−	0.728305i	$-0.740309\pi$
$17$	1.29428	−	2.83407i	0.313908	−	0.687363i	0.999162	+	0.0409418i	$0.0130358\pi$
$18$	−0.735688	−	0.216018i	−0.173403	−	0.0509158i
$19$	1.24752	+	2.73168i	0.286200	+	0.626691i	0.997058	−	0.0766444i	$-0.0244206\pi$
$19$	1.24752	+	2.73168i	0.286200	+	0.626691i	−0.710858	+	0.703335i	$0.751693\pi$
$20$	−0.442331	−	3.07648i	−0.0989082	−	0.687922i
$21$	−1.37224	−	0.881883i	−0.299446	−	0.192443i
$22$	−3.41578			−0.728247
$23$	−0.715258	−	4.74219i	−0.149142	−	0.988816i
$23$	−0.715258	−	4.74219i	−0.149142	−	0.988816i
$24$	−4.08524			−0.833897
$25$	0.841254	+	0.540641i	0.168251	+	0.108128i
$26$	0.669661	+	4.65759i	0.131331	+	0.913429i
$27$	−2.26273	−	4.95469i	−0.435463	−	0.953531i
$28$	2.98222	+	0.875658i	0.563586	+	0.165484i
$29$	2.73185	−	5.98191i	0.507291	−	1.11081i	−0.466740	−	0.884395i	$-0.654571\pi$
$29$	2.73185	−	5.98191i	0.507291	−	1.11081i	0.974030	−	0.226417i	$-0.0727013\pi$
$30$	2.41424	−	2.78619i	0.440779	−	0.508686i
$31$	−0.740559	+	5.15070i	−0.133008	+	0.925093i	0.808594	+	0.588367i	$0.200229\pi$
$31$	−0.740559	+	5.15070i	−0.133008	+	0.925093i	−0.941603	+	0.336726i	$0.890680\pi$
$32$	−6.01143	+	1.76511i	−1.06268	+	0.312031i
$33$	−1.61440	−	1.86311i	−0.281031	−	0.324327i
$34$	−5.92382	+	3.80701i	−1.01593	+	0.652897i
$35$	−0.841254	+	0.540641i	−0.142198	+	0.0913850i
$36$	0.690507	+	0.796887i	0.115084	+	0.132815i
$37$	−4.09106	+	1.20124i	−0.672566	+	0.197483i	−0.600145	−	0.799891i	$-0.704891\pi$
$37$	−4.09106	+	1.20124i	−0.672566	+	0.197483i	−0.0724204	+	0.997374i	$0.523072\pi$
$38$	0.965928	−	6.71818i	0.156694	−	1.08983i
$39$	−2.22395	+	2.56658i	−0.356117	+	0.410981i
$40$	−1.04039	+	2.27815i	−0.164501	+	0.360207i
$41$	−10.2876	−	3.02071i	−1.60665	−	0.471756i	−0.649266	−	0.760561i	$-0.724924\pi$
$41$	−10.2876	−	3.02071i	−1.60665	−	0.471756i	−0.957388	+	0.288805i	$0.906742\pi$
$42$	1.53149	+	3.35350i	0.236314	+	0.517456i
$43$	−1.11049	−	7.72364i	−0.169349	−	1.17784i	−0.880235	−	0.474538i	$-0.842615\pi$
$43$	−1.11049	−	7.72364i	−0.169349	−	1.17784i	0.710886	−	0.703307i	$-0.248294\pi$
$44$	3.95170	+	2.53960i	0.595741	+	0.382859i
$45$	−0.339251			−0.0505726
$46$	−4.43459	+	9.89045i	−0.653845	+	1.45827i
$47$	6.91140			1.00813			0.504066	−	0.863665i	$-0.331837\pi$
$47$	6.91140			1.00813			0.504066	+	0.863665i	$0.331837\pi$
$48$	−0.762750	−	0.490190i	−0.110093	−	0.0707528i
$49$	−0.142315	−	0.989821i	−0.0203307	−	0.141403i
$50$	−0.938885	−	2.05587i	−0.132778	−	0.290744i
$51$	−4.87628	−	1.43180i	−0.682816	−	0.200493i
$52$	2.68815	−	5.88623i	0.372780	−	0.816273i
$53$	1.48539	−	1.71423i	0.204034	−	0.235468i	−0.644506	−	0.764600i	$-0.722937\pi$
$53$	1.48539	−	1.71423i	0.204034	−	0.235468i	0.848540	+	0.529132i	$0.177482\pi$
$54$	−1.75199	+	12.1854i	−0.238416	+	1.65822i
$55$	−1.45011	+	0.425791i	−0.195533	+	0.0574137i
$56$	−1.64008	−	1.89275i	−0.219165	−	0.252930i
$57$	4.12091	−	2.64835i	0.545828	−	0.350782i
$58$	−12.5035	+	8.03550i	−1.64179	+	1.05511i
$59$	3.25682	+	3.75857i	0.424002	+	0.489324i	0.927052	−	0.374933i	$-0.122334\pi$
$59$	3.25682	+	3.75857i	0.424002	+	0.489324i	−0.503050	+	0.864257i	$0.667789\pi$
$60$	−4.86453	+	1.42836i	−0.628008	+	0.184400i
$61$	−0.490604	+	3.41223i	−0.0628154	+	0.436891i	0.934008	+	0.357251i	$0.116286\pi$
$61$	−0.490604	+	3.41223i	−0.0628154	+	0.436891i	−0.996824	+	0.0796396i	$0.974623\pi$
$62$	7.70174	−	8.88828i	0.978122	−	1.12881i
$63$	0.140930	−	0.308594i	0.0177555	−	0.0388792i
$64$	12.5199	+	3.67616i	1.56498	+	0.459520i
$65$	0.864881	+	1.89383i	0.107275	+	0.234900i
$66$	0.792943	+	5.51504i	0.0976046	+	0.678855i
$67$	6.30430	+	4.05152i	0.770192	+	0.494973i	0.865766	−	0.500450i	$-0.166832\pi$
$67$	6.30430	+	4.05152i	0.770192	+	0.494973i	−0.0955732	+	0.995422i	$0.530468\pi$
$68$	9.68372			1.17432
$69$	−7.49060	+	2.25570i	−0.901762	+	0.271554i
$70$	2.26011			0.270135
$71$	−10.9861	−	7.06032i	−1.30381	−	0.837906i	−0.310186	−	0.950676i	$-0.600391\pi$
$71$	−10.9861	−	7.06032i	−1.30381	−	0.837906i	−0.993621	+	0.112769i	$0.964028\pi$
$72$	−0.120917	−	0.840997i	−0.0142502	−	0.0991124i
$73$	6.00232	+	13.1433i	0.702519	+	1.53830i	0.836891	+	0.547370i	$0.184371\pi$
$73$	6.00232	+	13.1433i	0.702519	+	1.53830i	−0.134372	+	0.990931i	$0.542902\pi$
$74$	9.24626	+	2.71495i	1.07486	+	0.315606i
$75$	0.677617	−	1.48377i	0.0782444	−	0.171331i
$76$	−6.11238	+	7.05407i	−0.701138	+	0.809157i
$77$	0.215085	−	1.49595i	0.0245112	−	0.170479i
$78$	7.36459	−	2.16244i	0.833875	−	0.244848i
$79$	−2.99390	−	3.45514i	−0.336840	−	0.388734i	0.561908	−	0.827200i	$-0.310067\pi$
$79$	−2.99390	−	3.45514i	−0.336840	−	0.388734i	−0.898748	+	0.438466i	$0.855522\pi$
$80$	−0.467606	+	0.300512i	−0.0522800	+	0.0335983i
$81$	−6.61827	+	4.25330i	−0.735364	+	0.472589i
$82$	15.8691	+	18.3139i	1.75245	+	2.02243i
$83$	−16.4742	+	4.83726i	−1.80828	+	0.530958i	−0.998447	−	0.0557049i	$-0.982259\pi$
$83$	−16.4742	+	4.83726i	−1.80828	+	0.530958i	−0.809831	+	0.586663i	$0.800441\pi$
$84$	0.721522	−	5.01829i	0.0787245	−	0.547541i
$85$	−2.04030	+	2.35463i	−0.221302	+	0.255396i
$86$	−7.32619	+	16.0421i	−0.790003	+	1.72987i
$87$	−10.2924	−	3.02213i	−1.10346	−	0.324006i
$88$	−1.57238	−	3.44303i	−0.167616	−	0.367029i
$89$	0.662830	+	4.61009i	0.0702599	+	0.488668i	0.994321	+	0.106423i	$0.0339399\pi$
$89$	0.662830	+	4.61009i	0.0702599	+	0.488668i	−0.924061	+	0.382245i	$0.875151\pi$
$90$	0.645028	+	0.414535i	0.0679920	+	0.0436958i
$91$	−2.08197			−0.218250
$92$	12.4838	−	8.14513i	1.30153	−	0.849188i
$93$	8.48812			0.880177
$94$	−13.1408	−	8.44511i	−1.35537	−	0.871047i
$95$	−0.427380	−	2.97250i	−0.0438483	−	0.304972i
$96$	4.24541	+	9.29616i	0.433296	+	0.948785i
$97$	8.98192	+	2.63733i	0.911975	+	0.267780i	0.703872	−	0.710327i	$-0.251453\pi$
$97$	8.98192	+	2.63733i	0.911975	+	0.267780i	0.208103	+	0.978107i	$0.433271\pi$
$98$	−0.938885	+	2.05587i	−0.0948417	+	0.207674i
$99$	0.335761	−	0.387489i	0.0337452	−	0.0389441i
$100$	−0.442331	+	3.07648i	−0.0442331	+	0.307648i
$101$	−1.39102	+	0.408439i	−0.138411	+	0.0406412i	−0.350204	−	0.936673i	$-0.613888\pi$
$101$	−1.39102	+	0.408439i	−0.138411	+	0.0406412i	0.211793	+	0.977315i	$0.432070\pi$
$102$	7.52188	+	8.68071i	0.744777	+	0.859518i
$103$	−11.4942	+	7.38687i	−1.13256	+	0.727850i	−0.966092	−	0.258197i	$-0.916872\pi$
$103$	−11.4942	+	7.38687i	−1.13256	+	0.727850i	−0.166465	+	0.986047i	$0.553235\pi$
$104$	−4.38649	+	2.81902i	−0.430131	+	0.276428i
$105$	1.06820	+	1.23276i	0.104245	+	0.120305i
$106$	−4.91885	+	1.44431i	−0.477761	+	0.140283i
$107$	1.82711	−	12.7078i	0.176633	−	1.22851i	−0.687851	−	0.725852i	$-0.741446\pi$
$107$	1.82711	−	12.7078i	0.176633	−	1.22851i	0.864484	−	0.502660i	$-0.167645\pi$
$108$	11.0866	−	12.7946i	1.06681	−	1.23116i
$109$	1.76374	−	3.86206i	0.168936	−	0.369918i	−0.806161	−	0.591696i	$-0.798459\pi$
$109$	1.76374	−	3.86206i	0.168936	−	0.369918i	0.975097	+	0.221778i	$0.0711859\pi$
$110$	3.27742	+	0.962337i	0.312490	+	0.0917552i
$111$	2.88920	+	6.32647i	0.274231	+	0.600482i
$112$	−0.0791049	−	0.550187i	−0.00747471	−	0.0519878i
$113$	−6.74374	−	4.33394i	−0.634397	−	0.407702i	0.183538	−	0.983013i	$-0.441245\pi$
$113$	−6.74374	−	4.33394i	−0.634397	−	0.407702i	−0.817935	+	0.575310i	$0.804881\pi$
$114$	−11.0713			−1.03692
$115$	−0.649746	+	4.75161i	−0.0605891	+	0.443090i
$116$	20.4395			1.89776
$117$	−0.594186	−	0.381860i	−0.0549325	−	0.0353030i
$118$	−1.59965	−	11.1258i	−0.147260	−	1.02421i
$119$	−1.29428	−	2.83407i	−0.118646	−	0.259799i
$120$	3.91976	+	1.15095i	0.357824	+	0.105066i
$121$	−3.62071	+	7.92824i	−0.329155	+	0.720749i
$122$	5.10223	−	5.88829i	0.461935	−	0.533101i
$123$	−2.48900	+	17.3114i	−0.224425	+	1.56091i
$124$	−15.5185	+	4.55663i	−1.39360	+	0.409197i
$125$	−0.654861	−	0.755750i	−0.0585725	−	0.0675963i
$126$	−0.645028	+	0.414535i	−0.0574637	+	0.0369297i
$127$	−14.4893	+	9.31170i	−1.28572	+	0.826280i	−0.991582	−	0.129484i	$-0.958668\pi$
$127$	−14.4893	+	9.31170i	−1.28572	+	0.826280i	−0.294135	+	0.955764i	$0.595032\pi$
$128$	−11.1067	−	12.8179i	−0.981707	−	1.13295i
$129$	−12.2126	+	3.58595i	−1.07526	+	0.315725i
$130$	0.669661	−	4.65759i	0.0587331	−	0.408498i
$131$	−0.365794	+	0.422149i	−0.0319596	+	0.0368833i	−0.771504	−	0.636224i	$-0.780495\pi$
$131$	−0.365794	+	0.422149i	−0.0319596	+	0.0368833i	0.739545	+	0.673107i	$0.235041\pi$
$132$	3.18303	−	6.96987i	0.277047	−	0.606649i
$133$	2.88142	+	0.846060i	0.249851	+	0.0733627i
$134$	−7.03594	−	15.4066i	−0.607813	−	1.33092i
$135$	0.775178	+	5.39148i	0.0667167	+	0.464025i
$136$	−6.56429	−	4.21861i	−0.562883	−	0.361743i
$137$	1.21725			0.103997			0.0519983	−	0.998647i	$-0.483441\pi$
$137$	1.21725			0.103997			0.0519983	+	0.998647i	$0.483441\pi$
$138$	16.9983	+	4.86401i	1.44700	+	0.414052i
$139$	19.9037			1.68821			0.844104	−	0.536179i	$-0.180133\pi$
$139$	19.9037			1.68821			0.844104	+	0.536179i	$0.180133\pi$
$140$	−2.61471	−	1.68037i	−0.220984	−	0.142018i
$141$	−1.60442	−	11.1590i	−0.135117	−	0.939756i
$142$	12.2611	+	26.8480i	1.02893	+	2.25303i
$143$	−3.01909	−	0.886484i	−0.252469	−	0.0741315i
$144$	0.0783352	−	0.171530i	0.00652794	−	0.0142942i
$145$	−4.30648	+	4.96995i	−0.357634	+	0.412732i
$146$	4.64748	−	32.3239i	0.384628	−	2.67515i
$147$	−1.56511	+	0.459557i	−0.129088	+	0.0379036i
$148$	−8.67841	−	10.0154i	−0.713361	−	0.823262i
$149$	8.97781	−	5.76969i	0.735491	−	0.472671i	−0.118503	−	0.992954i	$-0.537810\pi$
$149$	8.97781	−	5.76969i	0.735491	−	0.472671i	0.853994	+	0.520282i	$0.174173\pi$
$150$	−3.10141	+	1.99316i	−0.253229	+	0.162740i
$151$	−4.46303	−	5.15061i	−0.363196	−	0.419151i	0.544512	−	0.838753i	$-0.316715\pi$
$151$	−4.46303	−	5.15061i	−0.363196	−	0.419151i	−0.907708	+	0.419602i	$0.862170\pi$
$152$	7.21642	−	2.11893i	0.585329	−	0.171868i
$153$	0.150424	−	1.04622i	0.0121610	−	0.0845819i
$154$	−2.23686	+	2.58148i	−0.180251	+	0.208021i
$155$	2.16168	−	4.73342i	0.173630	−	0.380198i
$156$	−10.1278	−	2.97379i	−0.810873	−	0.238094i
$157$	−5.98675	−	13.1091i	−0.477794	−	1.04622i	−0.983064	−	0.183262i	$-0.941334\pi$
$157$	−5.98675	−	13.1091i	−0.477794	−	1.04622i	0.505270	−	0.862962i	$-0.331393\pi$
$158$	1.47051	+	10.2276i	0.116988	+	0.813667i
$159$	−3.11258	−	2.00033i	−0.246844	−	0.158637i
$160$	6.26521			0.495309
$161$	−4.05231	−	2.56492i	−0.319366	−	0.202144i
$162$	17.7807			1.39698
$163$	−16.1735	−	10.3941i	−1.26680	−	0.814126i	−0.277604	−	0.960696i	$-0.589540\pi$
$163$	−16.1735	−	10.3941i	−1.26680	−	0.814126i	−0.989200	+	0.146570i	$0.953177\pi$
$164$	−4.74264	−	32.9858i	−0.370338	−	2.57576i
$165$	1.02410	+	2.24247i	0.0797263	+	0.174576i
$166$	37.2336	+	10.9328i	2.88989	+	0.848547i
$167$	8.62129	−	18.8780i	0.667135	−	1.46082i	−0.208585	−	0.978004i	$-0.566886\pi$
$167$	8.62129	−	18.8780i	0.667135	−	1.46082i	0.875720	−	0.482818i	$-0.160387\pi$
$168$	−2.67526	+	3.08742i	−0.206401	+	0.238200i
$169$	1.23322	−	8.57720i	0.0948628	−	0.659785i
$170$	6.75643	−	1.98387i	0.518194	−	0.152156i
$171$	0.667167	+	0.769952i	0.0510196	+	0.0588797i
$172$	20.4028	−	13.1121i	1.55570	−	0.999787i
$173$	−1.66958	+	1.07297i	−0.126935	+	0.0815765i	−0.602568	−	0.798068i	$-0.705856\pi$
$173$	−1.66958	+	1.07297i	−0.126935	+	0.0815765i	0.475632	+	0.879644i	$0.342219\pi$
$174$	15.8765	+	18.3225i	1.20360	+	1.38902i
$175$	0.959493	−	0.281733i	0.0725309	−	0.0212970i
$176$	0.119554	−	0.831514i	0.00901170	−	0.0626778i
$177$	5.31246	−	6.13091i	0.399309	−	0.460827i
$178$	4.37285	−	9.57521i	0.327759	−	0.717692i
$179$	−4.80698	−	1.41146i	−0.359290	−	0.105497i	0.0971053	−	0.995274i	$-0.469042\pi$
$179$	−4.80698	−	1.41146i	−0.359290	−	0.105497i	−0.456396	+	0.889777i	$0.650860\pi$
$180$	−0.438027	−	0.959146i	−0.0326486	−	0.0714905i
$181$	0.358673	+	2.49462i	0.0266599	+	0.185424i	0.998800	−	0.0489773i	$-0.0155962\pi$
$181$	0.358673	+	2.49462i	0.0266599	+	0.185424i	−0.972140	+	0.234401i	$0.924687\pi$
$182$	3.95851	+	2.54398i	0.293424	+	0.188572i
$183$	5.62319			0.415678
$184$	−12.0107	+	0.0828794i	−0.885443	+	0.00610995i
$185$	4.26377			0.313479
$186$	−16.1387	−	10.3717i	−1.18335	−	0.760491i
$187$	−0.670123	−	4.66081i	−0.0490043	−	0.340832i
$188$	8.92371	+	19.5402i	0.650829	+	1.42512i
$189$	−5.22628	−	1.53457i	−0.380156	−	0.111624i
$190$	−2.81953	+	6.17391i	−0.204550	+	0.447903i
$191$	4.06783	−	4.69453i	0.294338	−	0.339684i	−0.589249	−	0.807952i	$-0.700576\pi$
$191$	4.06783	−	4.69453i	0.294338	−	0.339684i	0.883587	+	0.468268i	$0.155122\pi$
$192$	3.02907	−	21.0677i	0.218604	−	1.52043i
$193$	8.82942	−	2.59255i	0.635555	−	0.186616i	0.0519453	−	0.998650i	$-0.483458\pi$
$193$	8.82942	−	2.59255i	0.635555	−	0.186616i	0.583610	+	0.812034i	$0.301640\pi$
$194$	−13.8550	−	15.9895i	−0.994731	−	1.14798i
$195$	2.85695	−	1.83605i	0.204591	−	0.131482i
$196$	2.61471	−	1.68037i	0.186765	−	0.120027i
$197$	9.24847	+	10.6733i	0.658926	+	0.760442i	0.982601	−	0.185727i	$-0.0594639\pi$
$197$	9.24847	+	10.6733i	0.658926	+	0.760442i	−0.323675	+	0.946168i	$0.604918\pi$
$198$	−1.11187	+	0.326474i	−0.0790170	+	0.0232015i
$199$	2.05406	−	14.2863i	0.145608	−	1.01273i	−0.777690	−	0.628647i	$-0.783609\pi$
$199$	2.05406	−	14.2863i	0.145608	−	1.01273i	0.923299	−	0.384082i	$-0.125482\pi$
$200$	1.64008	−	1.89275i	0.115971	−	0.133838i
$201$	5.07801	−	11.1193i	0.358175	−	0.784295i
$202$	3.14386	+	0.923120i	0.221201	+	0.0649505i
$203$	−2.73185	−	5.98191i	−0.191738	−	0.419848i
$204$	−2.24799	−	15.6351i	−0.157391	−	1.09468i
$205$	9.01985	+	5.79671i	0.629974	+	0.404860i
$206$	30.8803			2.15154
$207$	−0.686073	−	1.47527i	−0.0476854	−	0.102538i
$208$	−1.15725			−0.0802409
$209$	3.81813	+	2.45376i	0.264106	+	0.169730i
$210$	−0.524666	−	3.64913i	−0.0362054	−	0.251814i
$211$	−8.36077	−	18.3075i	−0.575579	−	1.26034i	−0.943773	−	0.330593i	$-0.892751\pi$
$211$	−8.36077	−	18.3075i	−0.575579	−	1.26034i	0.368194	−	0.929749i	$-0.379976\pi$
$212$	6.76442	+	1.98621i	0.464582	+	0.136414i
$213$	−8.84912	+	19.3769i	−0.606331	+	1.32768i
$214$	−19.0018	+	21.9292i	−1.29893	+	1.49905i
$215$	−1.11049	+	7.72364i	−0.0757350	+	0.526748i
$216$	−13.0891	+	3.84330i	−0.890598	+	0.261503i
$217$	3.40768	+	3.93267i	0.231328	+	0.266967i
$218$	−8.07254	+	5.18791i	−0.546742	+	0.351370i
$219$	19.8274	−	12.7423i	1.33981	−	0.861045i
$220$	−3.07614	−	3.55005i	−0.207393	−	0.239345i
$221$	−6.22388	+	1.82749i	−0.418663	+	0.122931i
$222$	2.23705	−	15.5590i	0.150141	−	1.04425i
$223$	−4.09160	+	4.72196i	−0.273994	+	0.316206i	−0.876024	−	0.482268i	$-0.839813\pi$
$223$	−4.09160	+	4.72196i	−0.273994	+	0.316206i	0.602030	+	0.798474i	$0.294359\pi$
$224$	−2.60266	+	5.69904i	−0.173898	+	0.380783i
$225$	0.325509	+	0.0955781i	0.0217006	+	0.00637188i
$226$	7.52638	+	16.4805i	0.500648	+	1.09627i
$227$	−0.481936	−	3.35194i	−0.0319872	−	0.222476i	0.967557	−	0.252651i	$-0.0813026\pi$
$227$	−0.481936	−	3.35194i	−0.0319872	−	0.222476i	−0.999545	+	0.0301753i	$0.990393\pi$
$228$	12.8083	+	8.23138i	0.848248	+	0.545136i
$229$	5.63489			0.372364			0.186182	−	0.982515i	$-0.440389\pi$
$229$	5.63489			0.372364			0.186182	+	0.982515i	$0.440389\pi$
$230$	7.04143	−	8.24045i	0.464298	−	0.543359i
$231$	−2.46525			−0.162202
$232$	−13.8553	−	8.90427i	−0.909646	−	0.584594i
$233$	1.65549	+	11.5142i	0.108455	+	0.754319i	0.969376	+	0.245581i	$0.0789788\pi$
$233$	1.65549	+	11.5142i	0.108455	+	0.754319i	−0.860921	+	0.508738i	$0.830112\pi$
$234$	0.663145	+	1.45208i	0.0433511	+	0.0949257i
$235$	−6.63144	−	1.94717i	−0.432587	−	0.127019i
$236$	−6.42132	+	14.0607i	−0.417992	+	0.915275i
$237$	−4.88358	+	5.63596i	−0.317223	+	0.366095i
$238$	−1.00213	+	6.96999i	−0.0649586	+	0.451797i
$239$	−8.96928	+	2.63362i	−0.580174	+	0.170355i	−0.558635	−	0.829413i	$-0.688675\pi$
$239$	−8.96928	+	2.63362i	−0.580174	+	0.170355i	−0.0215391	+	0.999768i	$0.506857\pi$
$240$	0.593751	+	0.685225i	0.0383264	+	0.0442311i
$241$	15.5389	−	9.98624i	1.00095	−	0.643270i	0.0659132	−	0.997825i	$-0.479004\pi$
$241$	15.5389	−	9.98624i	1.00095	−	0.643270i	0.935035	+	0.354555i	$0.115368\pi$
$242$	16.5718	−	10.6500i	1.06527	−	0.684609i
$243$	−2.29726	−	2.65118i	−0.147369	−	0.170073i
$244$	−10.2806	+	3.01867i	−0.658150	+	0.193250i
$245$	−0.142315	+	0.989821i	−0.00909216	+	0.0632374i
$246$	25.8853	−	29.8733i	1.65039	−	1.90465i
$247$	2.59729	−	5.68728i	0.165262	−	0.361873i
$248$	12.5045	+	3.67166i	0.794038	+	0.233151i
$249$	11.6345	+	25.4759i	0.737305	+	1.61447i
$250$	0.321648	+	2.23711i	0.0203428	+	0.141487i
$251$	−1.64651	−	1.05815i	−0.103927	−	0.0667896i	0.487645	−	0.873042i	$-0.337856\pi$
$251$	−1.64651	−	1.05815i	−0.103927	−	0.0667896i	−0.591572	+	0.806252i	$0.701492\pi$
$252$	1.05443			0.0664230
$253$	−4.78417	−	5.44486i	−0.300778	−	0.342315i
$254$	38.9270			2.44250
$255$	4.27537	+	2.74761i	0.267734	+	0.172062i
$256$	1.74133	+	12.1112i	0.108833	+	0.756952i
$257$	1.79985	+	3.94112i	0.112272	+	0.245840i	0.957424	−	0.288685i	$-0.0932179\pi$
$257$	1.79985	+	3.94112i	0.112272	+	0.245840i	−0.845153	+	0.534525i	$0.820491\pi$
$258$	27.6019	+	8.10466i	1.71842	+	0.504574i
$259$	−1.77123	+	3.87846i	−0.110059	+	0.240996i
$260$	−4.23760	+	4.89046i	−0.262805	+	0.303293i
$261$	0.317501	−	2.20827i	0.0196528	−	0.136689i
$262$	1.21132	−	0.355677i	0.0748358	−	0.0219738i
$263$	4.73403	+	5.46336i	0.291913	+	0.336885i	0.882695	−	0.469945i	$-0.155726\pi$
$263$	4.73403	+	5.46336i	0.291913	+	0.336885i	−0.590783	+	0.806831i	$0.701181\pi$
$264$	−5.19403	+	3.33800i	−0.319670	+	0.205440i
$265$	−1.90818	+	1.22631i	−0.117218	+	0.0753316i
$266$	−4.44471	−	5.12947i	−0.272523	−	0.314508i
$267$	7.28947	−	2.14038i	0.446108	−	0.130989i
$268$	−3.31480	+	23.0549i	−0.202484	+	1.40830i
$269$	−4.41213	+	5.09187i	−0.269012	+	0.310457i	−0.874142	−	0.485670i	$-0.838576\pi$
$269$	−4.41213	+	5.09187i	−0.269012	+	0.310457i	0.605130	+	0.796127i	$0.293121\pi$
$270$	5.11403	−	11.1982i	0.311230	−	0.681499i
$271$	−6.11388	−	1.79520i	−0.371392	−	0.109051i	0.0907100	−	0.995877i	$-0.471086\pi$
$271$	−6.11388	−	1.79520i	−0.371392	−	0.109051i	−0.462102	+	0.886827i	$0.652905\pi$
$272$	−0.719416	−	1.57530i	−0.0436210	−	0.0955167i
$273$	0.483311	+	3.36150i	0.0292513	+	0.203447i
$274$	−2.31439	−	1.48737i	−0.139818	−	0.0898553i
$275$	1.51133			0.0911367
$276$	−16.0489	−	18.2653i	−0.966033	−	1.09944i
$277$	−7.93595			−0.476825			−0.238413	−	0.971164i	$-0.576627\pi$
$277$	−7.93595			−0.476825			−0.238413	+	0.971164i	$0.576627\pi$
$278$	−37.8435	−	24.3205i	−2.26970	−	1.45865i
$279$	0.251236	+	1.74738i	0.0150411	+	0.104613i
$280$	1.04039	+	2.27815i	0.0621755	+	0.136145i
$281$	−6.68187	−	1.96197i	−0.398607	−	0.117042i	0.0762842	−	0.997086i	$-0.475694\pi$
$281$	−6.68187	−	1.96197i	−0.398607	−	0.117042i	−0.474891	+	0.880045i	$0.657513\pi$
$282$	−10.5847	+	23.1774i	−0.630313	+	1.38019i
$283$	10.1457	−	11.7088i	0.603101	−	0.696016i	−0.369305	−	0.929308i	$-0.620404\pi$
$283$	10.1457	−	11.7088i	0.603101	−	0.696016i	0.972407	+	0.233292i	$0.0749498\pi$
$284$	5.77648	−	40.1763i	0.342771	−	2.38402i
$285$	−4.70011	+	1.38008i	−0.278411	+	0.0817487i
$286$	4.65707	+	5.37455i	0.275379	+	0.317804i
$287$	−9.01985	+	5.79671i	−0.532425	+	0.342169i
$288$	−1.78807	+	1.14912i	−0.105363	+	0.0677127i
$289$	4.77583	+	5.51160i	0.280931	+	0.324212i
$290$	14.2609	−	4.18737i	0.837427	−	0.245891i
$291$	2.17310	−	15.1142i	0.127389	−	0.886012i
$292$	−29.4092	+	33.9400i	−1.72104	+	1.98619i
$293$	−0.110358	+	0.241651i	−0.00644719	+	0.0141174i	−0.912828	−	0.408344i	$-0.866106\pi$
$293$	−0.110358	+	0.241651i	−0.00644719	+	0.0141174i	0.906381	+	0.422461i	$0.138834\pi$
$294$	3.53732	+	1.03865i	0.206301	+	0.0605753i
$295$	−2.06598	−	4.52387i	−0.120286	−	0.263390i
$296$	1.51971	+	10.5698i	0.0883311	+	0.614357i
$297$	−6.92528	−	4.45061i	−0.401846	−	0.258251i
$298$	−24.1198			−1.39722
$299$	−6.48641	+	7.59093i	−0.375119	+	0.438995i
$300$	5.06990			0.292711
$301$	−6.56436	−	4.21866i	−0.378363	−	0.243159i
$302$	2.19211	+	15.2464i	0.126142	+	0.877334i
$303$	0.982369	+	2.15109i	0.0564356	+	0.123577i
$304$	1.60162	+	0.470278i	0.0918592	+	0.0269723i
$305$	1.43207	−	3.13579i	0.0819999	−	0.179555i
$306$	−1.56439	+	1.80541i	−0.0894304	+	0.103208i
$307$	2.06680	−	14.3749i	0.117958	−	0.820418i	−0.841840	−	0.539727i	$-0.818527\pi$
$307$	2.06680	−	14.3749i	0.117958	−	0.820418i	0.959798	−	0.280691i	$-0.0905635\pi$
$308$	4.50712	−	1.32341i	0.256817	−	0.0754082i
$309$	14.5950	+	16.8435i	0.830278	+	0.958192i
$310$	−9.89388	+	6.35841i	−0.561935	+	0.361134i
$311$	−20.0072	+	12.8578i	−1.13450	+	0.729100i	−0.966495	−	0.256685i	$-0.917370\pi$
$311$	−20.0072	+	12.8578i	−1.13450	+	0.729100i	−0.168007	+	0.985786i	$0.553733\pi$
$312$	5.56982	+	6.42791i	0.315329	+	0.363909i
$313$	−2.13985	+	0.628316i	−0.120951	+	0.0355145i	−0.341648	−	0.939828i	$-0.610985\pi$
$313$	−2.13985	+	0.628316i	−0.120951	+	0.0355145i	0.220697	+	0.975342i	$0.429167\pi$
$314$	−4.63542	+	32.2401i	−0.261592	+	1.81941i
$315$	−0.222162	+	0.256389i	−0.0125174	+	0.0144459i
$316$	5.90293	−	12.9256i	0.332066	−	0.727122i
$317$	11.6834	+	3.43056i	0.656206	+	0.192680i	0.592852	−	0.805312i	$-0.298002\pi$
$317$	11.6834	+	3.43056i	0.656206	+	0.192680i	0.0633544	+	0.997991i	$0.479820\pi$
$318$	3.47381	+	7.60658i	0.194802	+	0.426556i
$319$	−1.41444	−	9.83763i	−0.0791933	−	0.550801i
$320$	−10.9770	−	7.05450i	−0.613634	−	0.394359i
$321$	−20.9419			−1.16886
$322$	4.57066	+	9.82831i	0.254713	+	0.547710i
$323$	9.35641			0.520605
$324$	−20.5704	−	13.2198i	−1.14280	−	0.734432i
$325$	−0.296295	−	2.06078i	−0.0164355	−	0.114311i
$326$	18.0505	+	39.5251i	0.999724	+	2.18909i
$327$	−6.64503	−	1.95116i	−0.367471	−	0.107899i
$328$	−11.1550	+	24.4261i	−0.615933	+	1.34871i
$329$	4.52600	−	5.22329i	0.249527	−	0.287969i
$330$	0.792943	−	5.51504i	0.0436501	−	0.303593i
$331$	28.6293	−	8.40632i	1.57361	−	0.462053i	0.625559	−	0.780177i	$-0.284871\pi$
$331$	28.6293	−	8.40632i	1.57361	−	0.462053i	0.948049	+	0.318123i	$0.103053\pi$
$332$	−34.9469	−	40.3309i	−1.91796	−	2.21344i
$333$	−1.21686	+	0.782031i	−0.0666838	+	0.0428550i
$334$	−39.4591	+	25.3588i	−2.15911	+	1.38757i
$335$	−4.90748	−	5.66354i	−0.268124	−	0.309432i
$336$	−0.869956	+	0.255442i	−0.0474600	+	0.0139355i
$337$	−1.56898	+	10.9125i	−0.0854680	+	0.594443i	0.901409	+	0.432969i	$0.142534\pi$
$337$	−1.56898	+	10.9125i	−0.0854680	+	0.594443i	−0.986877	+	0.161474i	$0.948375\pi$
$338$	−12.8253	+	14.8012i	−0.697606	+	0.805080i
$339$	−5.43198	+	11.8944i	−0.295024	+	0.646013i
$340$	−9.29146	−	2.72822i	−0.503900	−	0.147958i
$341$	3.26702	+	7.15377i	0.176919	+	0.387398i
$342$	−0.327693	−	2.27915i	−0.0177196	−	0.123242i
$343$	−0.841254	−	0.540641i	−0.0454234	−	0.0291919i
$344$	−19.5426			−1.05366
$345$	7.82268	−	0.0539800i	0.421159	−	0.00290619i
$346$	4.48549			0.241141
$347$	12.3574	+	7.94159i	0.663378	+	0.426327i	0.828533	−	0.559941i	$-0.189176\pi$
$347$	12.3574	+	7.94159i	0.663378	+	0.426327i	−0.165155	+	0.986268i	$0.552812\pi$
$348$	−4.74486	−	33.0012i	−0.254351	−	1.76905i
$349$	−0.934507	−	2.04628i	−0.0500230	−	0.109535i	0.882970	−	0.469429i	$-0.155540\pi$
$349$	−0.934507	−	2.04628i	−0.0500230	−	0.109535i	−0.932993	+	0.359894i	$0.882813\pi$
$350$	−2.16856	−	0.636748i	−0.115915	−	0.0340356i
$351$	−4.71094	+	10.3155i	−0.251451	+	0.550602i
$352$	−6.20075	+	7.15605i	−0.330501	+	0.381419i
$353$	−1.91726	+	13.3348i	−0.102045	+	0.709741i	0.872997	+	0.487725i	$0.162173\pi$
$353$	−1.91726	+	13.3348i	−0.102045	+	0.709741i	−0.975043	+	0.222017i	$0.928736\pi$
$354$	−17.5921	+	5.16552i	−0.935012	+	0.274544i
$355$	8.55194	+	9.86947i	0.453890	+	0.523817i
$356$	−12.1780	+	7.82633i	−0.645433	+	0.414795i
$357$	−4.27537	+	2.74761i	−0.226277	+	0.145419i
$358$	7.41497	+	8.55734i	0.391894	+	0.452269i
$359$	11.5539	−	3.39254i	0.609793	−	0.179051i	0.0377668	−	0.999287i	$-0.487976\pi$
$359$	11.5539	−	3.39254i	0.609793	−	0.179051i	0.572027	+	0.820235i	$0.306157\pi$
$360$	−0.120917	+	0.840997i	−0.00637289	+	0.0443244i
$361$	6.53657	−	7.54360i	0.344030	−	0.397032i
$362$	2.36625	−	5.18136i	0.124367	−	0.272326i
$363$	13.6413	+	4.00544i	0.715981	+	0.210231i
$364$	−2.68815	−	5.88623i	−0.140897	−	0.308522i
$365$	−2.05630	−	14.3019i	−0.107632	−	0.748596i
$366$	−10.6915	−	6.87104i	−0.558856	−	0.359155i
$367$	1.54562			0.0806809			0.0403405	−	0.999186i	$-0.487156\pi$
$367$	1.54562			0.0806809			0.0403405	+	0.999186i	$0.487156\pi$
$368$	−2.25245	−	1.42570i	−0.117417	−	0.0743196i
$369$	−3.63743			−0.189357
$370$	−8.10683	−	5.20994i	−0.421454	−	0.270852i
$371$	−0.322806	−	2.24517i	−0.0167593	−	0.116563i
$372$	10.9595	+	23.9980i	0.568224	+	1.24424i
$373$	−18.8784	−	5.54321i	−0.977488	−	0.287016i	−0.246301	−	0.969193i	$-0.579215\pi$
$373$	−18.8784	−	5.54321i	−0.977488	−	0.287016i	−0.731187	+	0.682177i	$0.761033\pi$
$374$	−4.42097	+	9.68056i	−0.228603	+	0.500570i
$375$	−1.06820	+	1.23276i	−0.0551614	+	0.0636596i
$376$	2.46338	−	17.1332i	0.127039	−	0.883578i
$377$	−13.1368	+	3.85732i	−0.676580	+	0.198662i
$378$	8.06177	+	9.30378i	0.414653	+	0.478535i
$379$	16.0870	−	10.3385i	0.826336	−	0.531054i	−0.0577758	−	0.998330i	$-0.518401\pi$
$379$	16.0870	−	10.3385i	0.826336	−	0.531054i	0.884112	+	0.467276i	$0.154764\pi$
$380$	7.85215	−	5.04627i	0.402807	−	0.258868i
$381$	18.3980	+	21.2324i	0.942559	+	1.08777i
$382$	−13.4706	+	3.95532i	−0.689215	+	0.202372i
$383$	0.946755	−	6.58483i	0.0483769	−	0.336469i	−0.951231	−	0.308479i	$-0.900180\pi$
$383$	0.946755	−	6.58483i	0.0483769	−	0.336469i	0.999608	−	0.0279903i	$-0.00891075\pi$
$384$	−18.1171	+	20.9082i	−0.924534	+	1.06697i
$385$	−0.627830	+	1.37476i	−0.0319972	+	0.0700640i
$386$	−19.9555	−	5.85946i	−1.01571	−	0.298239i
$387$	−1.09969	−	2.40798i	−0.0559002	−	0.122404i
$388$	4.14071	+	28.7993i	0.210213	+	1.46206i
$389$	28.6921	+	18.4393i	1.45475	+	0.934910i	0.998996	+	0.0448043i	$0.0142664\pi$
$389$	28.6921	+	18.4393i	1.45475	+	0.934910i	0.455753	+	0.890106i	$0.349370\pi$
$390$	−7.67550			−0.388664
$391$	−14.3655	−	4.11062i	−0.726492	−	0.207883i
$392$	−2.50447			−0.126495
$393$	0.766508	+	0.492605i	0.0386652	+	0.0248486i
$394$	−4.54257	−	31.5943i	−0.228851	−	1.59170i
$395$	1.89920	+	4.15866i	0.0955590	+	0.209245i
$396$	1.52905	+	0.448968i	0.0768374	+	0.0225615i
$397$	−7.18198	+	15.7263i	−0.360453	+	0.789283i	0.639339	+	0.768925i	$0.279208\pi$
$397$	−7.18198	+	15.7263i	−0.360453	+	0.789283i	−0.999793	+	0.0203581i	$0.993519\pi$
$398$	−21.3620	+	24.6531i	−1.07078	+	1.23575i
$399$	0.697134	−	4.84868i	0.0349004	−	0.242737i
$400$	0.533329	−	0.156599i	0.0266664	−	0.00782997i
$401$	19.3189	+	22.2952i	0.964739	+	1.11337i	0.993506	+	0.113782i	$0.0362965\pi$
$401$	19.3189	+	22.2952i	0.964739	+	1.11337i	−0.0287670	+	0.999586i	$0.509158\pi$
$402$	−23.2418	+	14.9366i	−1.15919	+	0.744968i
$403$	9.11403	−	5.85723i	0.454002	−	0.291770i
$404$	−2.95078	−	3.40538i	−0.146807	−	0.169424i
$405$	7.54848	−	2.21643i	0.375087	−	0.110135i
$406$	−2.11521	+	14.7116i	−0.104976	+	0.730127i
$407$	−4.21990	+	4.87003i	−0.209173	+	0.241398i
$408$	−5.28743	+	11.5779i	−0.261767	+	0.573190i
$409$	−7.54326	−	2.21490i	−0.372990	−	0.109520i	0.0898643	−	0.995954i	$-0.471357\pi$
$409$	−7.54326	−	2.21490i	−0.372990	−	0.109520i	−0.462855	+	0.886434i	$0.653175\pi$
$410$	−10.0667	−	22.0429i	−0.497157	−	1.08862i
$411$	−0.282574	−	1.96534i	−0.0139383	−	0.0969432i
$412$	−35.7253	−	22.9593i	−1.76006	−	1.13112i
$413$	4.97330			0.244720
$414$	−0.498191	+	3.64328i	−0.0244847	+	0.179058i
$415$	17.1697			0.842827
$416$	10.9733	+	7.05211i	0.538010	+	0.345758i
$417$	−4.62046	−	32.1360i	−0.226265	−	1.57371i
$418$	−4.26125	−	9.33083i	−0.208424	−	0.456386i
$419$	35.2537	+	10.3514i	1.72226	+	0.505700i	0.985386	−	0.170335i	$-0.0544850\pi$
$419$	35.2537	+	10.3514i	1.72226	+	0.505700i	0.736869	+	0.676035i	$0.236303\pi$
$420$	−2.10611	+	4.61174i	−0.102768	+	0.225030i
$421$	−8.35939	+	9.64725i	−0.407412	+	0.470178i	−0.921961	−	0.387283i	$-0.873414\pi$
$421$	−8.35939	+	9.64725i	−0.407412	+	0.470178i	0.514549	+	0.857461i	$0.327959\pi$
$422$	−6.47358	+	45.0247i	−0.315129	+	2.19177i
$423$	2.24973	−	0.660579i	0.109385	−	0.0321184i
$424$	−3.72011	−	4.29324i	−0.180665	−	0.208498i
$425$	2.62103	−	1.68443i	0.127139	−	0.0817070i
$426$	40.5019	−	26.0290i	1.96232	−	1.26111i
$427$	2.25751	+	2.60531i	0.109249	+	0.126080i
$428$	38.2872	−	11.2421i	1.85068	−	0.543409i
$429$	−0.730442	+	5.08034i	−0.0352661	+	0.245281i
$430$	11.5490	−	13.3283i	0.556943	−	0.642746i
$431$	5.53683	−	12.1240i	0.266699	−	0.583990i	−0.728143	−	0.685426i	$-0.759616\pi$
$431$	5.53683	−	12.1240i	0.266699	−	0.583990i	0.994842	+	0.101435i	$0.0323434\pi$
$432$	−2.90500	−	0.852985i	−0.139767	−	0.0410393i
$433$	15.9988	+	35.0326i	0.768855	+	1.68356i	0.729157	+	0.684347i	$0.239913\pi$
$433$	15.9988	+	35.0326i	0.768855	+	1.68356i	0.0396986	+	0.999212i	$0.487360\pi$
$434$	−1.67375	−	11.6412i	−0.0803425	−	0.558794i
$435$	9.02408	+	5.79942i	0.432671	+	0.278061i
$436$	13.1962			0.631986
$437$	12.0619	−	7.86982i	0.576997	−	0.376465i
$438$	−53.2684			−2.54526
$439$	4.33137	+	2.78360i	0.206725	+	0.132854i	0.639907	−	0.768452i	$-0.278973\pi$
$439$	4.33137	+	2.78360i	0.206725	+	0.132854i	−0.433182	+	0.901306i	$0.642609\pi$
$440$	0.538674	+	3.74656i	0.0256803	+	0.178610i
$441$	−0.140930	−	0.308594i	−0.00671096	−	0.0146949i
$442$	14.0667	+	4.13035i	0.669083	+	0.196461i
$443$	1.20645	−	2.64177i	0.0573204	−	0.125514i	−0.878804	−	0.477182i	$-0.841658\pi$
$443$	1.20645	−	2.64177i	0.0573204	−	0.125514i	0.936125	+	0.351668i	$0.114385\pi$
$444$	−14.1560	+	16.3369i	−0.671816	+	0.775317i
$445$	0.662830	−	4.61009i	0.0314212	−	0.218539i
$446$	13.5493	−	3.97843i	0.641578	−	0.188384i
$447$	−11.3997	−	13.1560i	−0.539189	−	0.622257i
$448$	10.9770	−	7.05450i	0.518615	−	0.333294i
$449$	−2.66028	+	1.70966i	−0.125546	+	0.0806838i	−0.601907	−	0.798566i	$-0.705592\pi$
$449$	−2.66028	+	1.70966i	−0.125546	+	0.0806838i	0.476360	+	0.879250i	$0.341956\pi$
$450$	−0.502112	−	0.579469i	−0.0236698	−	0.0273164i
$451$	−15.5480	+	4.56530i	−0.732126	+	0.214972i
$452$	3.54586	−	24.6620i	0.166783	−	1.16000i
$453$	−7.28001	+	8.40158i	−0.342045	+	0.394741i
$454$	−3.17945	+	6.96202i	−0.149219	+	0.326744i
$455$	1.99763	+	0.586558i	0.0936505	+	0.0274983i
$456$	−5.09641	−	11.1596i	−0.238661	−	0.522595i
$457$	−3.66128	−	25.4647i	−0.171267	−	1.19119i	−0.876211	−	0.481927i	$-0.839937\pi$
$457$	−3.66128	−	25.4647i	−0.171267	−	1.19119i	0.704944	−	0.709263i	$-0.250972\pi$
$458$	−10.7138	−	6.88533i	−0.500622	−	0.321730i
$459$	−16.9705			−0.792117
$460$	−14.2729	+	4.29810i	−0.665477	+	0.200400i
$461$	7.83707			0.365009			0.182504	−	0.983205i	$-0.441580\pi$
$461$	7.83707			0.365009			0.182504	+	0.983205i	$0.441580\pi$
$462$	4.68726	+	3.01232i	0.218071	+	0.140146i
$463$	−4.02427	−	27.9894i	−0.187024	−	1.30078i	−0.839662	−	0.543109i	$-0.817247\pi$
$463$	−4.02427	−	27.9894i	−0.187024	−	1.30078i	0.652639	−	0.757669i	$-0.273662\pi$
$464$	−1.51848	−	3.32501i	−0.0704937	−	0.154360i
$465$	−8.14429	−	2.39138i	−0.377682	−	0.110898i
$466$	10.9217	−	23.9151i	0.505936	−	1.10785i
$467$	−13.3389	+	15.3939i	−0.617251	+	0.712345i	−0.975183	−	0.221402i	$-0.928937\pi$
$467$	−13.3389	+	15.3939i	−0.617251	+	0.712345i	0.357932	+	0.933748i	$0.383482\pi$
$468$	0.312423	−	2.17295i	0.0144418	−	0.100445i
$469$	7.19037	−	2.11128i	0.332021	−	0.0974901i
$470$	10.2293	+	11.8052i	0.471842	+	0.544535i
$471$	−19.7760	+	12.7092i	−0.911228	+	0.585611i
$472$	10.4782	−	6.73394i	0.482299	−	0.309955i
$473$	−7.72279	−	8.91257i	−0.355094	−	0.409800i
$474$	16.1719	−	4.74851i	0.742802	−	0.218106i
$475$	−0.427380	+	2.97250i	−0.0196096	+	0.136387i
$476$	6.34149	−	7.31847i	0.290662	−	0.335441i
$477$	0.319665	−	0.699969i	0.0146365	−	0.0320494i
$478$	20.2716	+	5.95228i	0.927201	+	0.272251i
$479$	−6.16897	−	13.5082i	−0.281867	−	0.617203i	0.714751	−	0.699380i	$-0.246540\pi$
$479$	−6.16897	−	13.5082i	−0.281867	−	0.617203i	−0.996618	+	0.0821762i	$0.973813\pi$
$480$	−1.45441	−	10.1157i	−0.0663846	−	0.461715i
$481$	7.46784	+	4.79929i	0.340504	+	0.218829i
$482$	−41.7468			−1.90152
$483$	−3.20056	+	7.13818i	−0.145630	+	0.324799i
$484$	−27.0900			−1.23136
$485$	−7.87506	−	5.06100i	−0.357588	−	0.229808i
$486$	1.12835	+	7.84781i	0.0511828	+	0.355984i
$487$	17.0344	+	37.3001i	0.771901	+	1.69023i	0.722423	+	0.691452i	$0.243028\pi$
$487$	17.0344	+	37.3001i	0.771901	+	1.69023i	0.0494778	+	0.998775i	$0.484244\pi$
$488$	8.28397	+	2.43239i	0.374998	+	0.110109i
$489$	−13.0275	+	28.5262i	−0.589123	+	1.29000i
$490$	1.48006	−	1.70808i	0.0668623	−	0.0771632i
$491$	3.63115	−	25.2552i	0.163872	−	1.13975i	−0.727377	−	0.686238i	$-0.759261\pi$
$491$	3.63115	−	25.2552i	0.163872	−	1.13975i	0.891249	−	0.453515i	$-0.149830\pi$
$492$	−52.1571	+	15.3147i	−2.35142	+	0.690441i
$493$	−13.4174	−	15.4845i	−0.604288	−	0.697386i
$494$	−11.8876	+	7.63973i	−0.534850	+	0.343728i
$495$	−0.431328	+	0.277198i	−0.0193868	+	0.0124591i
$496$	1.89414	+	2.18595i	0.0850493	+	0.0981522i
$497$	−12.5302	+	3.67920i	−0.562056	+	0.165034i
$498$	9.00834	−	62.6544i	0.403674	−	2.80761i
$499$	−1.02491	+	1.18280i	−0.0458811	+	0.0529496i	−0.778226	−	0.627984i	$-0.783880\pi$
$499$	−1.02491	+	1.18280i	−0.0458811	+	0.0529496i	0.732345	+	0.680934i	$0.238426\pi$
$500$	1.29116	−	2.82724i	0.0577424	−	0.126438i
$501$	−32.4813	−	9.53738i	−1.45116	−	0.426099i
$502$	1.83759	+	4.02377i	0.0820158	+	0.179590i
$503$	−1.58354	−	11.0138i	−0.0706065	−	0.491079i	−0.994186	−	0.107673i	$-0.965660\pi$
$503$	−1.58354	−	11.0138i	−0.0706065	−	0.491079i	0.923580	−	0.383406i	$-0.125249\pi$
$504$	−0.714767	−	0.459353i	−0.0318382	−	0.0204612i
$505$	1.44974			0.0645126
$506$	2.44316	+	16.1983i	0.108612	+	0.720102i
$507$	−14.1348			−0.627750
$508$	−45.0344	−	28.9419i	−1.99808	−	1.28409i
$509$	−4.26384	−	29.6557i	−0.188992	−	1.31447i	−0.834625	−	0.550818i	$-0.814316\pi$
$509$	−4.26384	−	29.6557i	−0.188992	−	1.31447i	0.645634	−	0.763647i	$-0.276593\pi$
$510$	−4.77155	−	10.4482i	−0.211288	−	0.462656i
$511$	13.8637	+	4.07075i	0.613294	+	0.180079i
$512$	−2.60327	+	5.70037i	−0.115049	+	0.251923i
$513$	10.7118	−	12.3621i	0.472940	−	0.545801i
$514$	1.39359	−	9.69262i	0.0614685	−	0.427523i
$515$	13.1097	−	3.84936i	0.577683	−	0.169623i
$516$	−25.9068	−	29.8980i	−1.14048	−	1.31619i
$517$	8.78724	−	5.64722i	0.386462	−	0.248364i
$518$	8.10683	−	5.20994i	0.356194	−	0.228912i
$519$	2.11997	+	2.44658i	0.0930564	+	0.107393i
$520$	5.00302	−	1.46902i	0.219397	−	0.0644207i
$521$	−2.68788	+	18.6946i	−0.117758	+	0.819027i	0.842256	+	0.539077i	$0.181227\pi$
$521$	−2.68788	+	18.6946i	−0.117758	+	0.819027i	−0.960015	+	0.279950i	$0.909682\pi$
$522$	−3.30198	+	3.81069i	−0.144524	+	0.166789i
$523$	16.5095	−	36.1508i	0.721911	−	1.58076i	−0.0892961	−	0.996005i	$-0.528462\pi$
$523$	16.5095	−	36.1508i	0.721911	−	1.58076i	0.811207	−	0.584759i	$-0.198811\pi$
$524$	−1.66582	−	0.489128i	−0.0727715	−	0.0213676i
$525$	−0.677617	−	1.48377i	−0.0295736	−	0.0647572i
$526$	−2.32521	−	16.1722i	−0.101384	−	0.705141i
$527$	13.6390	+	8.76523i	0.594122	+	0.381819i
$528$	−1.37030			−0.0596345
$529$	−21.9768	+	6.78378i	−0.955514	+	0.294947i
$530$	5.12651			0.222681
$531$	1.41936	+	0.912169i	0.0615951	+	0.0395848i
$532$	1.32835	+	9.23886i	0.0575912	+	0.400555i
$533$	9.27319	+	20.3054i	0.401666	+	0.879527i
$534$	−16.4750	−	4.83751i	−0.712945	−	0.209339i
$535$	−5.33331	+	11.6783i	−0.230579	+	0.504898i
$536$	12.2906	−	14.1842i	0.530875	−	0.612662i
$537$	−1.16301	+	8.08889i	−0.0501875	+	0.349061i
$538$	14.6107	−	4.29010i	0.629913	−	0.184959i
$539$	−0.989711	−	1.14219i	−0.0426299	−	0.0491975i
$540$	−14.2421	+	9.15287i	−0.612884	+	0.393877i
$541$	35.6665	−	22.9215i	1.53342	−	0.985471i	0.544217	−	0.838945i	$-0.316827\pi$
$541$	35.6665	−	22.9215i	1.53342	−	0.985471i	0.989207	−	0.146527i	$-0.0468094\pi$
$542$	9.43093	+	10.8839i	0.405093	+	0.467503i
$543$	3.94450	−	1.15821i	0.169275	−	0.0497035i
$544$	−2.77799	+	19.3214i	−0.119105	+	0.828396i
$545$	−2.78037	+	3.20871i	−0.119098	+	0.137446i
$546$	3.18852	−	6.98188i	0.136456	−	0.298797i
$547$	42.0340	+	12.3423i	1.79725	+	0.527719i	0.997372	−	0.0724500i	$-0.0230818\pi$
$547$	42.0340	+	12.3423i	1.79725	+	0.527719i	0.799873	+	0.600169i	$0.204900\pi$
$548$	1.57166	+	3.44146i	0.0671381	+	0.147012i
$549$	0.166438	+	1.15760i	0.00710341	+	0.0494053i
$550$	−2.87354	−	1.84671i	−0.122528	−	0.0787440i
$551$	19.7487			0.841322
$552$	2.92200	+	19.3730i	0.124369	+	0.824570i
$553$	−4.57181			−0.194413
$554$	15.0889	+	9.69702i	0.641064	+	0.411987i
$555$	−0.989796	−	6.88418i	−0.0420145	−	0.292217i
$556$	25.6988	+	56.2725i	1.08987	+	2.38649i
$557$	10.6372	+	3.12336i	0.450712	+	0.132341i	0.499208	−	0.866482i	$-0.333624\pi$
$557$	10.6372	+	3.12336i	0.450712	+	0.132341i	−0.0484955	+	0.998823i	$0.515443\pi$
$558$	1.65746	−	3.62934i	0.0701660	−	0.153642i
$559$	−10.6387	+	12.2777i	−0.449969	+	0.519292i
$560$	−0.0791049	+	0.550187i	−0.00334279	+	0.0232496i
$561$	−7.36967	+	2.16393i	−0.311148	+	0.0913612i
$562$	10.3071	+	11.8950i	0.434778	+	0.501760i
$563$	−32.4217	+	20.8361i	−1.36641	+	0.878138i	−0.998658	−	0.0517859i	$-0.983509\pi$
$563$	−32.4217	+	20.8361i	−1.36641	+	0.878138i	−0.367751	+	0.929924i	$0.619872\pi$
$564$	29.4776	−	18.9441i	1.24123	−	0.797691i
$565$	5.24956	+	6.05831i	0.220851	+	0.254875i
$566$	−33.5975	+	9.86511i	−1.41221	+	0.414661i
$567$	−1.11961	+	7.78708i	−0.0470193	+	0.327027i
$568$	−21.4181	+	24.7178i	−0.898683	+	1.03714i
$569$	8.78793	−	19.2429i	0.368409	−	0.806704i	−0.631110	−	0.775694i	$-0.717400\pi$
$569$	8.78793	−	19.2429i	0.368409	−	0.806704i	0.999519	−	0.0310104i	$-0.00987251\pi$
$570$	10.6228	+	3.11913i	0.444940	+	0.130646i
$571$	2.72925	+	5.97622i	0.114215	+	0.250097i	0.958103	−	0.286422i	$-0.0924661\pi$
$571$	2.72925	+	5.97622i	0.114215	+	0.250097i	−0.843888	+	0.536519i	$0.819739\pi$
$572$	−1.39181	−	9.68028i	−0.0581947	−	0.404753i
$573$	−8.52399	−	5.47804i	−0.356095	−	0.228848i
$574$	24.2328			1.01146
$575$	1.96211	−	4.37609i	0.0818257	−	0.182495i
$576$	4.42669			0.184445
$577$	25.8510	+	16.6134i	1.07619	+	0.691626i	0.953674	−	0.300841i	$-0.0972674\pi$
$577$	25.8510	+	16.6134i	1.07619	+	0.691626i	0.122516	+	0.992467i	$0.460904\pi$
$578$	−2.34574	−	16.3150i	−0.0975701	−	0.678615i
$579$	−6.23555	−	13.6539i	−0.259140	−	0.567438i
$580$	−19.6116	−	5.75848i	−0.814327	−	0.239108i
$581$	−7.13255	+	15.6181i	−0.295908	+	0.647948i
$582$	−22.6000	+	26.0818i	−0.936800	+	1.08113i
$583$	0.487867	−	3.39319i	0.0202054	−	0.140532i
$584$	34.7212	−	10.1951i	1.43677	−	0.421875i
$585$	0.462535	+	0.533794i	0.0191235	+	0.0220697i
$586$	0.505102	−	0.324610i	0.0208656	−	0.0134095i
$587$	−11.2373	+	7.22177i	−0.463812	+	0.298074i	−0.751599	−	0.659620i	$-0.770717\pi$
$587$	−11.2373	+	7.22177i	−0.463812	+	0.298074i	0.287786	+	0.957695i	$0.407081\pi$
$588$	−3.32008	−	3.83157i	−0.136918	−	0.158011i
$589$	−14.9939	+	4.40262i	−0.617814	+	0.181407i
$590$	−1.59965	+	11.1258i	−0.0658566	+	0.458043i
$591$	15.0859	−	17.4101i	0.620552	−	0.716155i
$592$	−0.984531	+	2.15582i	−0.0404640	+	0.0886037i
$593$	42.3628	+	12.4388i	1.73963	+	0.510802i	0.988742	−	0.149628i	$-0.0478076\pi$
$593$	42.3628	+	12.4388i	1.73963	+	0.510802i	0.750888	+	0.660430i	$0.229626\pi$
$594$	7.72900	+	16.9241i	0.317125	+	0.694406i
$595$	0.443399	+	3.08391i	0.0181776	+	0.126428i
$596$	27.9041	+	17.9329i	1.14300	+	0.734559i
$597$	−23.5432			−0.963558
$598$	21.6082	−	6.50704i	0.883626	−	0.266093i
$599$	45.4511			1.85708			0.928541	−	0.371231i	$-0.121064\pi$
$599$	45.4511			1.85708			0.928541	+	0.371231i	$0.121064\pi$
$600$	−3.43672	−	2.20865i	−0.140304	−	0.0901677i
$601$	4.40132	+	30.6118i	0.179533	+	1.24868i	0.857845	+	0.513908i	$0.171803\pi$
$601$	4.40132	+	30.6118i	0.179533	+	1.24868i	−0.678312	+	0.734774i	$0.737288\pi$
$602$	7.32619	+	16.0421i	0.298593	+	0.653828i
$603$	2.43934	+	0.716256i	0.0993378	+	0.0291682i
$604$	8.79955	−	19.2683i	0.358049	−	0.784017i
$605$	5.70769	−	6.58702i	0.232050	−	0.267801i
$606$	0.760629	−	5.29029i	0.0308984	−	0.214903i
$607$	−5.62698	+	1.65223i	−0.228392	+	0.0670620i	−0.393926	−	0.919142i	$-0.628883\pi$
$607$	−5.62698	+	1.65223i	−0.228392	+	0.0670620i	0.165534	+	0.986204i	$0.447065\pi$
$608$	−12.3211	−	14.2193i	−0.499686	−	0.576669i
$609$	−9.02408	+	5.79942i	−0.365674	+	0.235004i
$610$	−6.55448	+	4.21231i	−0.265383	+	0.170551i
$611$	−9.42300	−	10.8747i	−0.381214	−	0.439944i
$612$	3.15214	−	0.925552i	0.127418	−	0.0374132i
$613$	3.04853	−	21.2030i	0.123129	−	0.856382i	−0.830847	−	0.556500i	$-0.812144\pi$
$613$	3.04853	−	21.2030i	0.123129	−	0.856382i	0.953976	−	0.299882i	$-0.0969472\pi$
$614$	−21.4945	+	24.8059i	−0.867447	+	1.00109i
$615$	7.26535	−	15.9089i	0.292967	−	0.641509i
$616$	−3.63176	−	1.06638i	−0.146328	−	0.0429657i
$617$	1.84420	+	4.03823i	0.0742447	+	0.162573i	0.943115	−	0.332466i	$-0.107881\pi$
$617$	1.84420	+	4.03823i	0.0742447	+	0.162573i	−0.868870	+	0.495040i	$0.835154\pi$
$618$	−7.16860	−	49.8587i	−0.288363	−	2.00561i
$619$	15.8718	+	10.2002i	0.637941	+	0.409980i	0.819242	−	0.573448i	$-0.194394\pi$
$619$	15.8718	+	10.2002i	0.637941	+	0.409980i	−0.181301	+	0.983428i	$0.558031\pi$
$620$	16.1736			0.649547
$621$	−21.8777	+	14.2742i	−0.877921	+	0.572804i
$622$	53.7513			2.15523
$623$	3.91813	+	2.51803i	0.156977	+	0.100883i
$624$	0.268646	+	1.86847i	0.0107544	+	0.0747987i
$625$	0.415415	+	0.909632i	0.0166166	+	0.0363853i
$626$	4.83630	+	1.42007i	0.193298	+	0.0567573i
$627$	3.07545	−	6.73429i	0.122821	−	0.268942i
$628$	29.3329	−	33.8520i	1.17051	−	1.35084i
$629$	−1.89055	+	13.1491i	−0.0753813	+	0.524288i
$630$	0.735688	−	0.216018i	0.0293105	−	0.00860634i
$631$	−29.6992	−	34.2747i	−1.18231	−	1.36445i	−0.916305	−	0.400481i	$-0.868843\pi$
$631$	−29.6992	−	34.2747i	−1.18231	−	1.36445i	−0.266001	−	0.963973i	$-0.585702\pi$
$632$	−9.63231	+	6.19031i	−0.383153	+	0.246237i
$633$	−27.6180	+	17.7490i	−1.09772	+	0.705461i
$634$	−18.0222	−	20.7987i	−0.715753	−	0.826023i
$635$	16.5258	−	4.85241i	0.655806	−	0.192562i
$636$	1.63659	−	11.3828i	0.0648952	−	0.451356i
$637$	−1.36340	+	1.57345i	−0.0540199	+	0.0623422i
$638$	−9.33138	+	20.4329i	−0.369433	+	0.808946i
$639$	−4.25088	−	1.24817i	−0.168162	−	0.0493769i
$640$	7.04563	+	15.4278i	0.278503	+	0.609837i
$641$	0.201153	+	1.39905i	0.00794506	+	0.0552591i	0.993408	−	0.114630i	$-0.0365682\pi$
$641$	0.201153	+	1.39905i	0.00794506	+	0.0552591i	−0.985463	+	0.169889i	$0.945659\pi$
$642$	39.8175	+	25.5891i	1.57147	+	1.00992i
$643$	39.8671			1.57220			0.786102	−	0.618097i	$-0.212096\pi$
$643$	39.8671			1.57220			0.786102	+	0.618097i	$0.212096\pi$
$644$	2.01949	−	14.7686i	0.0795789	−	0.581963i
$645$	12.7282			0.501173
$646$	−17.7896	−	11.4327i	−0.699923	−	0.449813i
$647$	3.41106	+	23.7245i	0.134103	+	0.932705i	0.940127	+	0.340823i	$0.110706\pi$
$647$	3.41106	+	23.7245i	0.134103	+	0.932705i	−0.806025	+	0.591882i	$0.798385\pi$
$648$	8.18494	+	17.9225i	0.321535	+	0.704063i
$649$	7.21184	+	2.11759i	0.283090	+	0.0831226i
$650$	−1.95473	+	4.28026i	−0.0766708	+	0.167886i
$651$	5.55853	−	6.41489i	0.217856	−	0.251419i
$652$	8.50401	−	59.1467i	0.333043	−	2.31636i
$653$	38.0298	−	11.1666i	1.48822	−	0.436981i	0.566248	−	0.824235i	$-0.308394\pi$
$653$	38.0298	−	11.1666i	1.48822	−	0.436981i	0.921973	+	0.387254i	$0.126576\pi$
$654$	10.2502	+	11.8294i	0.400816	+	0.462567i
$655$	0.469910	−	0.301993i	0.0183609	−	0.0117998i
$656$	−5.01364	+	3.22207i	−0.195750	+	0.125801i
$657$	3.21002	+	3.70456i	0.125235	+	0.144529i
$658$	−14.9878	+	4.40082i	−0.584286	+	0.171562i
$659$	−3.21791	+	22.3811i	−0.125352	+	0.871842i	0.825986	+	0.563691i	$0.190619\pi$
$659$	−3.21791	+	22.3811i	−0.125352	+	0.871842i	−0.951337	+	0.308151i	$0.900290\pi$
$660$	−5.01774	+	5.79078i	−0.195315	+	0.225406i
$661$	15.4181	−	33.7609i	0.599694	−	1.31315i	−0.329710	−	0.944082i	$-0.606951\pi$
$661$	15.4181	−	33.7609i	0.599694	−	1.31315i	0.929404	−	0.369065i	$-0.120322\pi$
$662$	−64.7055	−	18.9992i	−2.51485	−	0.738427i
$663$	4.39545	+	9.62469i	0.170705	+	0.373792i
$664$	6.11968	+	42.5633i	0.237490	+	1.65178i
$665$	−2.52634	−	1.62358i	−0.0979671	−	0.0629597i
$666$	3.26923			0.126680
$667$	−30.3213	−	8.67634i	−1.17405	−	0.335949i
$668$	64.5041			2.49574
$669$	8.57380	+	5.51005i	0.331482	+	0.213031i
$670$	2.41041	+	16.7647i	0.0931221	+	0.647679i
$671$	2.16433	+	4.73921i	0.0835529	+	0.182955i
$672$	9.80572	+	2.87922i	0.378264	+	0.111068i
$673$	−15.7120	+	34.4046i	−0.605654	+	1.32620i	0.319852	+	0.947467i	$0.396367\pi$
$673$	−15.7120	+	34.4046i	−0.605654	+	1.32620i	−0.925507	+	0.378731i	$0.876361\pi$
$674$	16.3173	−	18.8311i	0.628518	−	0.725349i
$675$	0.775178	−	5.39148i	0.0298366	−	0.207518i
$676$	25.8421	−	7.58793i	0.993927	−	0.291843i
$677$	−26.2967	−	30.3480i	−1.01066	−	1.16637i	−0.986012	−	0.166672i	$-0.946698\pi$
$677$	−26.2967	−	30.3480i	−1.01066	−	1.16637i	−0.0246515	−	0.999696i	$-0.507848\pi$
$678$	24.8618	−	15.9777i	0.954812	−	0.613621i
$679$	7.87506	−	5.06100i	0.302217	−	0.194223i
$680$	5.10987	+	5.89710i	0.195954	+	0.226144i
$681$	−5.30009	+	1.55625i	−0.203100	+	0.0596355i
$682$	2.52959	−	17.5937i	0.0968629	−	0.673696i
$683$	11.1475	−	12.8649i	0.426546	−	0.492260i	−0.501274	−	0.865288i	$-0.667135\pi$
$683$	11.1475	−	12.8649i	0.426546	−	0.492260i	0.927820	+	0.373029i	$0.121681\pi$
$684$	−1.31542	+	2.88037i	−0.0502965	+	0.110134i
$685$	−1.16794	−	0.342939i	−0.0446248	−	0.0131030i
$686$	0.938885	+	2.05587i	0.0358468	+	0.0784936i
$687$	−1.30809	−	9.09797i	−0.0499067	−	0.347109i
$688$	−3.64876	−	2.34492i	−0.139108	−	0.0893991i
$689$	−4.72243			−0.179910
$690$	−14.9394	−	9.45598i	−0.568735	−	0.359983i
$691$	−4.93260			−0.187645			−0.0938224	−	0.995589i	$-0.529909\pi$
$691$	−4.93260			−0.187645			−0.0938224	+	0.995589i	$0.529909\pi$
$692$	−5.18924	−	3.33492i	−0.197265	−	0.126775i
$693$	−0.0729678	−	0.507502i	−0.00277182	−	0.0192784i
$694$	−13.7915	−	30.1992i	−0.523518	−	1.14634i
$695$	−19.0974	−	5.60752i	−0.724407	−	0.212705i
$696$	−11.1602	+	24.4375i	−0.423028	+	0.926302i
$697$	−21.8759	+	25.2462i	−0.828610	+	0.956267i
$698$	−0.723571	+	5.03254i	−0.0273875	+	0.190485i
$699$	18.2062	−	5.34583i	0.688623	−	0.202198i
$700$	2.03538	+	2.34896i	0.0769303	+	0.0887823i
$701$	−20.4698	+	13.1551i	−0.773133	+	0.496862i	−0.866748	−	0.498746i	$-0.833794\pi$
$701$	−20.4698	+	13.1551i	−0.773133	+	0.496862i	0.0936154	+	0.995608i	$0.470158\pi$
$702$	21.5617	−	13.8568i	0.813793	−	0.522993i
$703$	−8.38508	−	9.67689i	−0.316249	−	0.364971i
$704$	18.9216	−	5.55590i	0.713136	−	0.209396i
$705$	−1.60442	+	11.1590i	−0.0604260	+	0.420272i
$706$	19.9393	−	23.0112i	0.750425	−	0.866037i
$707$	−0.602244	+	1.31873i	−0.0226497	+	0.0495960i
$708$	24.1928	+	7.10364i	0.909220	+	0.266971i
$709$	−2.29014	−	5.01470i	−0.0860079	−	0.188331i	0.861741	−	0.507349i	$-0.169374\pi$
$709$	−2.29014	−	5.01470i	−0.0860079	−	0.188331i	−0.947749	+	0.319018i	$0.896647\pi$
$710$	−4.20046	−	29.2148i	−0.157640	−	1.09641i
$711$	−1.30478	−	0.838529i	−0.0489330	−	0.0314473i
$712$	11.6646			0.437148
$713$	24.9553	−	0.172203i	0.934584	−	0.00644905i
$714$	11.4862			0.429861
$715$	2.64704	+	1.70115i	0.0989937	+	0.0636194i
$716$	−2.21604	−	15.4129i	−0.0828173	−	0.576007i
$717$	6.33432	+	13.8702i	0.236559	+	0.517993i
$718$	−26.1132	−	7.66753i	−0.974536	−	0.286150i
$719$	19.2067	−	42.0568i	0.716289	−	1.56846i	−0.102743	−	0.994708i	$-0.532762\pi$
$719$	19.2067	−	42.0568i	0.716289	−	1.56846i	0.819032	−	0.573747i	$-0.194511\pi$
$720$	−0.123488	+	0.142512i	−0.00460212	+	0.00531113i
$721$	−1.94447	+	13.5241i	−0.0724160	+	0.503664i
$722$	−21.6458	+	6.35577i	−0.805572	+	0.236537i
$723$	−19.7308	−	22.7705i	−0.733795	−	0.846845i
$724$	−6.58980	+	4.23501i	−0.244908	+	0.157393i
$725$	5.53224	−	3.55535i	0.205462	−	0.132042i
$726$	−21.0423	−	24.2841i	−0.780952	−	0.901266i
$727$	−17.0856	+	5.01678i	−0.633670	+	0.186062i	−0.582764	−	0.812641i	$-0.698029\pi$
$727$	−17.0856	+	5.01678i	−0.633670	+	0.186062i	−0.0509054	+	0.998703i	$0.516211\pi$
$728$	−0.742062	+	5.16116i	−0.0275027	+	0.191285i
$729$	−19.2029	+	22.1613i	−0.711219	+	0.820791i
$730$	−13.5659	+	29.7052i	−0.502098	+	1.09944i
$731$	−23.3266	−	6.84932i	−0.862767	−	0.253331i
$732$	7.26043	+	15.8981i	0.268353	+	0.587612i
$733$	−5.16530	−	35.9255i	−0.190785	−	1.32694i	−0.829937	−	0.557857i	$-0.811624\pi$
$733$	−5.16530	−	35.9255i	−0.190785	−	1.32694i	0.639152	−	0.769080i	$-0.279285\pi$
$734$	−2.93874	−	1.88861i	−0.108471	−	0.0697100i
$735$	1.63118			0.0601670
$736$	12.6702	+	27.2448i	0.467031	+	1.00426i
$737$	11.3258			0.417192
$738$	6.91594	+	4.44461i	0.254579	+	0.163608i
$739$	−1.84392	−	12.8247i	−0.0678296	−	0.471765i	−0.995219	−	0.0976678i	$-0.968862\pi$
$739$	−1.84392	−	12.8247i	−0.0678296	−	0.471765i	0.927390	−	0.374097i	$-0.122047\pi$
$740$	5.50520	+	12.0547i	0.202375	+	0.443140i
$741$	−9.78548	−	2.87328i	−0.359479	−	0.105552i
$742$	−2.12963	+	4.66324i	−0.0781812	+	0.171193i
$743$	12.9399	−	14.9335i	0.474720	−	0.547856i	−0.466998	−	0.884258i	$-0.654665\pi$
$743$	12.9399	−	14.9335i	0.474720	−	0.547856i	0.941719	+	0.336402i	$0.109210\pi$
$744$	3.02536	−	21.0419i	0.110915	−	0.771432i
$745$	−10.2397	+	3.00663i	−0.375152	+	0.110155i
$746$	29.1208	+	33.6072i	1.06619	+	1.23045i
$747$	−4.90017	+	3.14915i	−0.179288	+	0.115221i
$748$	12.3120	−	7.91244i	0.450171	−	0.289308i
$749$	−8.40743	−	9.70270i	−0.307201	−	0.354529i
$750$	3.53732	−	1.03865i	0.129165	−	0.0379261i
$751$	6.17884	−	42.9748i	0.225469	−	1.56817i	−0.491382	−	0.870944i	$-0.663508\pi$
$751$	6.17884	−	42.9748i	0.225469	−	1.56817i	0.716851	−	0.697227i	$-0.245583\pi$
$752$	2.51575	−	2.90334i	0.0917401	−	0.105874i
$753$	−1.32624	+	2.90405i	−0.0483307	+	0.105830i
$754$	29.6907	+	8.71797i	1.08127	+	0.317490i
$755$	2.83115	+	6.19936i	0.103036	+	0.225618i
$756$	−2.40934	−	16.7573i	−0.0876269	−	0.609459i
$757$	5.21154	+	3.34926i	0.189417	+	0.121731i	0.631912	−	0.775040i	$-0.282270\pi$
$757$	5.21154	+	3.34926i	0.189417	+	0.121731i	−0.442495	+	0.896771i	$0.645907\pi$
$758$	−43.2195			−1.56980
$759$	−7.68054	+	8.98839i	−0.278786	+	0.326258i
$760$	−7.52108			−0.272818
$761$	−5.76086	−	3.70228i	−0.208831	−	0.134208i	0.432045	−	0.901852i	$-0.357792\pi$
$761$	−5.76086	−	3.70228i	−0.208831	−	0.134208i	−0.640876	+	0.767645i	$0.721429\pi$
$762$	−9.03655	−	62.8506i	−0.327360	−	2.27684i
$763$	−1.76374	−	3.86206i	−0.0638518	−	0.139816i
$764$	18.5248	+	5.43937i	0.670203	+	0.196789i
$765$	−0.439085	+	0.961462i	−0.0158752	+	0.0347617i
$766$	−9.84616	+	11.3631i	−0.355756	+	0.410565i
$767$	1.47356	−	10.2489i	0.0532073	−	0.370065i
$768$	19.1503	−	5.62303i	0.691026	−	0.202904i
$769$	−5.57083	−	6.42908i	−0.200889	−	0.231839i	0.646362	−	0.763031i	$-0.276290\pi$
$769$	−5.57083	−	6.42908i	−0.200889	−	0.231839i	−0.847251	+	0.531192i	$0.821744\pi$
$770$	2.87354	−	1.84671i	0.103555	−	0.0665508i
$771$	5.94542	−	3.82089i	0.214119	−	0.137606i
$772$	18.7299	+	21.6155i	0.674106	+	0.777959i
$773$	−24.4859	+	7.18972i	−0.880698	+	0.258596i	−0.690659	−	0.723180i	$-0.742680\pi$
$773$	−24.4859	+	7.18972i	−0.880698	+	0.258596i	−0.190039	+	0.981777i	$0.560861\pi$
$774$	−0.851467	+	5.92208i	−0.0306053	+	0.212865i
$775$	−3.40768	+	3.93267i	−0.122407	+	0.141266i
$776$	9.73924	−	21.3260i	0.349618	−	0.765558i
$777$	6.67325	+	1.95944i	0.239402	+	0.0702946i
$778$	−32.0220	−	70.1184i	−1.14804	−	2.51387i
$779$	−4.58234	−	31.8709i	−0.164179	−	1.14189i
$780$	8.87974	+	5.70666i	0.317946	+	0.204331i
$781$	−19.7367			−0.706236
$782$	22.2906	+	25.3689i	0.797112	+	0.907191i
$783$	−35.8199			−1.28010
$784$	−0.467606	−	0.300512i	−0.0167002	−	0.0107326i
$785$	2.05097	+	14.2648i	0.0732022	+	0.509132i
$786$	−0.855465	−	1.87321i	−0.0305134	−	0.0668151i
$787$	−24.8371	−	7.29282i	−0.885346	−	0.259961i	−0.192716	−	0.981255i	$-0.561730\pi$
$787$	−24.8371	−	7.29282i	−0.885346	−	0.259961i	−0.692630	+	0.721294i	$0.743548\pi$
$788$	−18.2348	+	39.9286i	−0.649587	+	1.42240i
$789$	7.72205	−	8.91172i	0.274912	−	0.317266i
$790$	1.47051	−	10.2276i	0.0523185	−	0.363883i
$791$	−7.69158	+	2.25845i	−0.273481	+	0.0803013i
$792$	−0.840903	−	0.970454i	−0.0298802	−	0.0344836i
$793$	6.03785	−	3.88029i	0.214410	−	0.137793i
$794$	32.8715	−	21.1252i	1.16657	−	0.749706i
$795$	2.42294	+	2.79622i	0.0859328	+	0.0991717i
$796$	43.0430	−	12.6386i	1.52562	−	0.447962i
$797$	6.11302	−	42.5170i	0.216534	−	1.50603i	−0.534162	−	0.845382i	$-0.679373\pi$
$797$	6.11302	−	42.5170i	0.216534	−	1.50603i	0.750697	−	0.660647i	$-0.229718\pi$
$798$	−7.25013	+	8.36709i	−0.256652	+	0.296192i
$799$	8.94526	−	19.5874i	0.316461	−	0.692952i
$800$	−6.01143	−	1.76511i	−0.212536	−	0.0624062i
$801$	0.656381	+	1.43727i	0.0231921	+	0.0507836i
$802$	−9.48885	−	65.9964i	−0.335063	−	2.33041i
$803$	18.3706	+	11.8061i	0.648285	+	0.416627i
$804$	37.9935			1.33993
$805$	3.16554	+	3.60269i	0.111571	+	0.126978i
$806$	−24.4858			−0.862475
$807$	9.24546	+	5.94169i	0.325456	+	0.209158i
$808$	0.516721	+	3.59388i	0.0181782	+	0.126432i
$809$	9.46127	+	20.7173i	0.332640	+	0.728381i	0.999864	−	0.0164764i	$-0.00524484\pi$
$809$	9.46127	+	20.7173i	0.332640	+	0.728381i	−0.667224	+	0.744857i	$0.732518\pi$
$810$	−17.0604	−	5.00939i	−0.599442	−	0.176012i
$811$	−4.16401	+	9.11791i	−0.146218	+	0.320173i	−0.968543	−	0.248845i	$-0.919949\pi$
$811$	−4.16401	+	9.11791i	−0.146218	+	0.320173i	0.822325	+	0.569018i	$0.192676\pi$
$812$	13.3851	−	15.4472i	0.469723	−	0.542090i
$813$	−1.47920	+	10.2881i	−0.0518779	+	0.360819i
$814$	13.9742	−	4.10318i	0.489794	−	0.143816i
$815$	12.5900	+	14.5296i	0.441008	+	0.508950i
$816$	−2.37644	+	1.52725i	−0.0831921	+	0.0534643i
$817$	19.7132	−	12.6689i	0.689677	−	0.443228i
$818$	11.6358	+	13.4284i	0.406837	+	0.469515i
$819$	−0.677700	+	0.198991i	−0.0236808	+	0.00695330i
$820$	−4.74264	+	32.9858i	−0.165620	+	1.15191i
$821$	9.07283	−	10.4706i	0.316644	−	0.365427i	−0.575008	−	0.818148i	$-0.695001\pi$
$821$	9.07283	−	10.4706i	0.316644	−	0.365427i	0.891652	+	0.452721i	$0.149547\pi$
$822$	−1.86421	+	4.08204i	−0.0650217	+	0.142378i
$823$	4.86927	+	1.42975i	0.169732	+	0.0498378i	0.365494	−	0.930814i	$-0.380900\pi$
$823$	4.86927	+	1.42975i	0.169732	+	0.0498378i	−0.195762	+	0.980651i	$0.562718\pi$
$824$	14.2151	+	31.1267i	0.495206	+	1.08435i
$825$	−0.350842	−	2.44016i	−0.0122148	−	0.0849555i
$826$	−9.45588	−	6.07693i	−0.329012	−	0.211443i
$827$	−32.9279			−1.14501			−0.572507	−	0.819900i	$-0.694029\pi$
$827$	−32.9279			−1.14501			−0.572507	+	0.819900i	$0.694029\pi$
$828$	3.28510	−	3.84450i	0.114165	−	0.133605i
$829$	50.1566			1.74201			0.871005	−	0.491274i	$-0.163469\pi$
$829$	50.1566			1.74201			0.871005	+	0.491274i	$0.163469\pi$
$830$	−32.6452	−	20.9798i	−1.13313	−	0.728220i
$831$	1.84226	+	12.8132i	0.0639073	+	0.444485i
$832$	−11.2853	−	24.7114i	−0.391248	−	0.856714i
$833$	−2.98942	−	0.877772i	−0.103577	−	0.0304130i
$834$	−30.4823	+	66.7470i	−1.05552	+	2.31126i
$835$	−13.5906	+	15.6844i	−0.470322	+	0.542781i
$836$	−2.00757	+	13.9630i	−0.0694334	+	0.482920i
$837$	27.1958	−	7.98542i	0.940025	−	0.276016i
$838$	−54.3804	−	62.7583i	−1.87854	−	2.16795i
$839$	−21.0119	+	13.5036i	−0.725413	+	0.466195i	−0.850516	−	0.525949i	$-0.823710\pi$
$839$	−21.0119	+	13.5036i	−0.725413	+	0.466195i	0.125103	+	0.992144i	$0.460074\pi$
$840$	3.43672	−	2.20865i	0.118578	−	0.0762056i
$841$	−9.32926	−	10.7665i	−0.321699	−	0.371260i
$842$	27.6820	−	8.12817i	0.953985	−	0.280115i
$843$	−1.61662	+	11.2438i	−0.0556794	+	0.387259i
$844$	40.9647	−	47.2758i	1.41006	−	1.62730i
$845$	−3.59974	+	7.88233i	−0.123835	+	0.271160i
$846$	−5.08464	−	1.49298i	−0.174813	−	0.0513298i
$847$	3.62071	+	7.92824i	0.124409	+	0.272418i
$848$	−0.179430	−	1.24796i	−0.00616165	−	0.0428552i
$849$	−21.2600	−	13.6630i	−0.729641	−	0.468912i
$850$	−7.04166			−0.241527
$851$	8.62268	+	18.5414i	0.295582	+	0.635591i
$852$	−66.2087			−2.26827
$853$	18.9698	+	12.1912i	0.649514	+	0.417418i	0.823489	−	0.567333i	$-0.192025\pi$
$853$	18.9698	+	12.1912i	0.649514	+	0.417418i	−0.173974	+	0.984750i	$0.555661\pi$
$854$	−1.10882	−	7.71202i	−0.0379431	−	0.263900i
$855$	−0.423222	−	0.926727i	−0.0144739	−	0.0316934i
$856$	−30.8512	−	9.05873i	−1.05447	−	0.309621i
$857$	−2.63992	+	5.78061i	−0.0901778	+	0.197462i	−0.949347	−	0.314230i	$-0.898254\pi$
$857$	−2.63992	+	5.78061i	−0.0901778	+	0.197462i	0.859169	+	0.511692i	$0.170981\pi$
$858$	7.59653	−	8.76686i	0.259341	−	0.299296i
$859$	−2.72598	+	18.9596i	−0.0930094	+	0.646895i	0.888978	+	0.457949i	$0.151416\pi$
$859$	−2.72598	+	18.9596i	−0.0930094	+	0.646895i	−0.981988	+	0.188945i	$0.939493\pi$
$860$	−23.2704	+	6.83282i	−0.793515	+	0.232997i
$861$	11.4531	+	13.2176i	0.390321	+	0.450454i
$862$	−25.3417	+	16.2861i	−0.863142	+	0.554708i
$863$	−35.0974	+	22.5557i	−1.19473	+	0.767806i	−0.978036	−	0.208434i	$-0.933163\pi$
$863$	−35.0974	+	22.5557i	−1.19473	+	0.767806i	−0.216693	+	0.976240i	$0.569527\pi$
$864$	22.3479	+	25.7908i	0.760289	+	0.877421i
$865$	1.90424	−	0.559134i	0.0647460	−	0.0190111i
$866$	12.3876	−	86.1576i	0.420948	−	2.92775i
$867$	7.79024	−	8.99042i	0.264570	−	0.305331i
$868$	−6.71876	+	14.7120i	−0.228049	+	0.499359i
$869$	−6.62963	−	1.94663i	−0.224895	−	0.0660351i
$870$	−10.0714	−	22.0532i	−0.341451	−	0.747674i
$871$	−2.22041	−	15.4433i	−0.0752359	−	0.523277i
$872$	−8.94532	−	5.74881i	−0.302927	−	0.194679i
$873$	3.17577			0.107483
$874$	−32.5498	+	0.224608i	−1.10101	+	0.00759749i
$875$	−1.00000			−0.0338062
$876$	61.6259	+	39.6046i	2.08215	+	1.33811i
$877$	4.50621	+	31.3414i	0.152164	+	1.05832i	0.912583	+	0.408891i	$0.134084\pi$
$877$	4.50621	+	31.3414i	0.152164	+	1.05832i	−0.760420	+	0.649432i	$0.775007\pi$
$878$	−4.83405	−	10.5851i	−0.163141	−	0.357229i
$879$	0.415782	+	0.122085i	0.0140240	+	0.00411781i
$880$	−0.348976	+	0.764150i	−0.0117640	+	0.0257595i
$881$	2.08415	−	2.40524i	0.0702168	−	0.0810345i	−0.719554	−	0.694436i	$-0.755654\pi$
$881$	2.08415	−	2.40524i	0.0702168	−	0.0810345i	0.789771	+	0.613402i	$0.210199\pi$
$882$	−0.109119	+	0.758942i	−0.00367424	+	0.0255549i
$883$	40.8117	−	11.9834i	1.37342	−	0.403274i	0.489949	−	0.871751i	$-0.337015\pi$
$883$	40.8117	−	11.9834i	1.37342	−	0.403274i	0.883476	+	0.468477i	$0.155197\pi$
$884$	−13.2028	−	15.2368i	−0.444058	−	0.512470i
$885$	−6.82454	+	4.38587i	−0.229405	+	0.147429i
$886$	−5.52187	+	3.54869i	−0.185511	+	0.119221i
$887$	−5.21173	−	6.01466i	−0.174993	−	0.201952i	0.661477	−	0.749965i	$-0.269930\pi$
$887$	−5.21173	−	6.01466i	−0.174993	−	0.201952i	−0.836470	+	0.548013i	$0.815384\pi$
$888$	16.7130	−	4.90737i	0.560850	−	0.164680i
$889$	−2.45115	+	17.0481i	−0.0822090	+	0.571776i
$890$	−6.89337	+	7.95537i	−0.231066	+	0.266665i
$891$	−4.93923	+	10.8154i	−0.165471	+	0.362330i
$892$	−18.6330	−	5.47115i	−0.623880	−	0.183188i
$893$	8.62209	+	18.8797i	0.288527	+	0.631787i
$894$	5.59920	+	38.9433i	0.187265	+	1.30246i
$895$	4.21461	+	2.70856i	0.140879	+	0.0905373i
$896$	−16.9605			−0.566609
$897$	13.7619	+	8.71064i	0.459496	+	0.290840i
$898$	7.14712			0.238502
$899$	28.7879	+	18.5009i	0.960131	+	0.617039i
$900$	0.150061	+	1.04370i	0.00500205	+	0.0347900i
$901$	−2.93575	−	6.42839i	−0.0978039	−	0.214161i
$902$	35.1402	+	10.3181i	1.17004	+	0.343555i
$903$	−5.28749	+	11.5780i	−0.175957	+	0.385291i
$904$	−13.1474	+	15.1729i	−0.437275	+	0.504642i
$905$	0.358673	−	2.49462i	0.0119227	−	0.0829240i
$906$	24.1077	−	7.07865i	0.800924	−	0.235172i
$907$	−28.9911	−	33.4575i	−0.962633	−	1.11094i	−0.993773	−	0.111423i	$-0.964459\pi$
$907$	−28.9911	−	33.4575i	−0.962633	−	1.11094i	0.0311398	−	0.999515i	$-0.490086\pi$
$908$	8.85449	−	5.69044i	0.293847	−	0.188844i
$909$	−0.413751	+	0.265902i	−0.0137233	+	0.00881940i
$910$	−3.08144	−	3.55617i	−0.102149	−	0.117886i
$911$	−8.82521	+	2.59132i	−0.292392	+	0.0858541i	−0.424639	−	0.905363i	$-0.639599\pi$
$911$	−8.82521	+	2.59132i	−0.292392	+	0.0858541i	0.132247	+	0.991217i	$0.457781\pi$
$912$	0.387498	−	2.69511i	0.0128314	−	0.0892440i
$913$	−16.9930	+	19.6110i	−0.562388	+	0.649030i
$914$	−24.1543	+	52.8906i	−0.798954	+	1.74947i
$915$	−5.39541	−	1.58424i	−0.178367	−	0.0523732i
$916$	7.27554	+	15.9312i	0.240390	+	0.526382i
$917$	0.0794947	+	0.552897i	0.00262514	+	0.0182583i
$918$	32.2666	+	20.7365i	1.06496	+	0.684406i
$919$	−45.3195			−1.49495			−0.747476	−	0.664289i	$-0.768734\pi$
$919$	−45.3195			−1.49495			−0.747476	+	0.664289i	$0.768734\pi$
$920$	11.5476	+	3.30429i	0.380712	+	0.108939i
$921$	−23.6891			−0.780584
$922$	−14.9009	−	9.57620i	−0.490733	−	0.315375i
$923$	3.86937	+	26.9121i	0.127362	+	0.885821i
$924$	−3.18303	−	6.96987i	−0.104714	−	0.229292i
$925$	−4.09106	−	1.20124i	−0.134513	−	0.0394966i
$926$	−26.5491	+	58.1344i	−0.872457	+	1.91041i
$927$	−3.03544	+	3.50309i	−0.0996971	+	0.115057i
$928$	−5.86354	+	40.7818i	−0.192480	+	1.33873i
$929$	−23.3613	+	6.85951i	−0.766461	+	0.225053i	−0.641515	−	0.767110i	$-0.721694\pi$
$929$	−23.3613	+	6.85951i	−0.766461	+	0.225053i	−0.124946	+	0.992164i	$0.539876\pi$
$930$	12.5629	+	14.4984i	0.411954	+	0.475421i
$931$	2.52634	−	1.62358i	0.0827973	−	0.0532106i
$932$	−30.4159	+	19.5471i	−0.996305	+	0.640287i
$933$	25.4044	+	29.3183i	0.831704	+	0.959837i
$934$	44.1716	−	12.9700i	1.44534	−	0.424390i
$935$	−0.670123	+	4.66081i	−0.0219154	+	0.152425i
$936$	−1.15841	+	1.33687i	−0.0378637	+	0.0436970i
$937$	7.91036	−	17.3213i	0.258420	−	0.565862i	−0.735302	−	0.677740i	$-0.762959\pi$
$937$	7.91036	−	17.3213i	0.258420	−	0.565862i	0.993722	+	0.111879i	$0.0356867\pi$
$938$	−16.2511	−	4.77174i	−0.530616	−	0.155803i
$939$	1.51121	+	3.30909i	0.0493165	+	0.107988i
$940$	−3.05713	−	21.2628i	−0.0997125	−	0.693516i
$941$	−30.7494	−	19.7614i	−1.00240	−	0.644204i	−0.0669852	−	0.997754i	$-0.521338\pi$
$941$	−30.7494	−	19.7614i	−1.00240	−	0.644204i	−0.935416	+	0.353550i	$0.884974\pi$
$942$	53.1302			1.73107
$943$	−6.96653	+	50.9464i	−0.226861	+	1.65904i
$944$	2.76438			0.0899730
$945$	4.58224	+	2.94483i	0.149060	+	0.0957952i
$946$	3.79320	+	26.3823i	0.123328	+	0.857762i
$947$	−14.8524	−	32.5223i	−0.482639	−	1.05683i	−0.981730	−	0.190282i	$-0.939060\pi$
$947$	−14.8524	−	32.5223i	−0.482639	−	1.05683i	0.499091	−	0.866550i	$-0.333667\pi$
$948$	−22.2397	−	6.53016i	−0.722312	−	0.212090i
$949$	12.4966	−	27.3638i	0.405658	−	0.888268i
$950$	4.44471	−	5.12947i	0.144206	−	0.166422i
$951$	2.82670	−	19.6602i	0.0916622	−	0.637524i
$952$	−7.48691	+	2.19835i	−0.242652	+	0.0712491i
$953$	14.8730	+	17.1644i	0.481785	+	0.556010i	0.943652	−	0.330939i	$-0.107366\pi$
$953$	14.8730	+	17.1644i	0.481785	+	0.556010i	−0.461867	+	0.886949i	$0.652820\pi$
$954$	−1.46309	+	0.940270i	−0.0473692	+	0.0304423i
$955$	−5.22566	+	3.35833i	−0.169098	+	0.108673i
$956$	−19.0266	−	21.9579i	−0.615365	−	0.710169i
$957$	−15.5553	+	4.56744i	−0.502830	+	0.147644i
$958$	−4.77651	+	33.2214i	−0.154322	+	1.07333i
$959$	0.797129	−	0.919936i	0.0257406	−	0.0297063i
$960$	−8.84182	+	19.3609i	−0.285368	+	0.624870i
$961$	3.76299	+	1.10491i	0.121387	+	0.0356424i
$962$	−8.33452	−	18.2500i	−0.268716	−	0.588405i
$963$	−0.619850	−	4.31115i	−0.0199744	−	0.138925i
$964$	48.2967	+	31.0384i	1.55553	+	0.999680i
$965$	−9.20217			−0.296228
$966$	14.8075	−	9.66124i	0.476424	−	0.310845i
$967$	−30.2610			−0.973129			−0.486565	−	0.873645i	$-0.661750\pi$
$967$	−30.2610			−0.973129			−0.486565	+	0.873645i	$0.661750\pi$
$968$	18.3634	+	11.8015i	0.590223	+	0.379313i
$969$	−2.17201	−	15.1066i	−0.0697749	−	0.485295i
$970$	8.78901	+	19.2452i	0.282198	+	0.617927i
$971$	17.2576	+	5.06728i	0.553822	+	0.162617i	0.546656	−	0.837357i	$-0.315901\pi$
$971$	17.2576	+	5.06728i	0.553822	+	0.162617i	0.00716644	+	0.999974i	$0.497719\pi$
$972$	4.52940	−	9.91801i	0.145281	−	0.318120i
$973$	13.0341	−	15.0422i	0.417855	−	0.482231i
$974$	13.1894	−	91.7341i	0.422615	−	2.93935i
$975$	−3.25850	+	0.956782i	−0.104356	+	0.0306416i
$976$	1.25483	+	1.44815i	0.0401660	+	0.0463540i
$977$	−14.3361	+	9.21327i	−0.458653	+	0.294759i	−0.749492	−	0.662014i	$-0.769702\pi$
$977$	−14.3361	+	9.21327i	−0.458653	+	0.294759i	0.290839	+	0.956772i	$0.406066\pi$
$978$	59.6260	−	38.3193i	1.90663	−	1.22532i
$979$	4.60957	+	5.31973i	0.147323	+	0.170019i
$980$	−2.98222	+	0.875658i	−0.0952634	+	0.0279719i
$981$	0.204986	−	1.42571i	0.00654471	−	0.0455195i
$982$	−37.7636	+	43.5816i	−1.20509	+	1.39074i
$983$	−20.2906	+	44.4301i	−0.647168	+	1.41710i	0.246843	+	0.969055i	$0.420607\pi$
$983$	−20.2906	+	44.4301i	−0.647168	+	1.41710i	−0.894011	+	0.448045i	$0.852120\pi$
$984$	42.0274	+	12.3403i	1.33978	+	0.393396i
$985$	−5.86683	−	12.8466i	−0.186933	−	0.409325i
$986$	6.59021	+	45.8359i	0.209875	+	1.45971i
$987$	−9.48407	−	6.09504i	−0.301881	−	0.194007i
$988$	19.4328			0.618240
$989$	−35.8327	+	10.7906i	−1.13941	+	0.343120i
$990$	1.15881			0.0368293
$991$	43.8849	+	28.2031i	1.39405	+	0.895902i	0.999734	−	0.0230721i	$-0.00734472\pi$
$991$	43.8849	+	28.2031i	1.39405	+	0.895902i	0.394317	+	0.918974i	$0.370981\pi$
$992$	−4.63976	−	32.2702i	−0.147312	−	1.02458i
$993$	−20.2187	−	44.2728i	−0.641621	−	1.40495i
$994$	28.3197	+	8.31540i	0.898245	+	0.263749i
$995$	−5.99577	+	13.1289i	−0.190079	+	0.416215i
$996$	−57.0047	+	65.7869i	−1.80626	+	2.08454i
$997$	−1.67656	+	11.6608i	−0.0530973	+	0.369300i	0.945897	+	0.324467i	$0.105185\pi$
$997$	−1.67656	+	11.6608i	−0.0530973	+	0.369300i	−0.998994	+	0.0448334i	$0.985724\pi$
$998$	3.39396	−	0.996557i	0.107434	−	0.0315455i
$999$	15.2088	+	17.5518i	0.481184	+	0.555316i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	805.2.u.d.71.2	✓	130
23.12	even	11	inner	805.2.u.d.771.2	yes	130

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.u.d.71.2	✓	130	1.1	even	1	trivial
805.2.u.d.771.2	yes	130	23.12	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:	\( N \)	\(=\)	\( 805 = 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	805.u (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.90133 - 1.22191i) q^{2} +(-0.232141 - 1.61458i) q^{3} +(1.29116 + 2.82724i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(-1.53149 + 3.35350i) q^{6} +(0.654861 - 0.755750i) q^{7} +(0.356423 - 2.47898i) q^{8} +(0.325509 - 0.0955781i) q^{9} +O(q^{10})\)	\(q+(-1.90133 - 1.22191i) q^{2} +(-0.232141 - 1.61458i) q^{3} +(1.29116 + 2.82724i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(-1.53149 + 3.35350i) q^{6} +(0.654861 - 0.755750i) q^{7} +(0.356423 - 2.47898i) q^{8} +(0.325509 - 0.0955781i) q^{9} +(1.48006 + 1.70808i) q^{10} +(1.27141 - 0.817087i) q^{11} +(4.26507 - 2.74099i) q^{12} +(-1.36340 - 1.57345i) q^{13} +(-2.16856 + 0.636748i) q^{14} +(-0.232141 + 1.61458i) q^{15} +(0.364001 - 0.420079i) q^{16} +(1.29428 - 2.83407i) q^{17} +(-0.735688 - 0.216018i) q^{18} +(1.24752 + 2.73168i) q^{19} +(-0.442331 - 3.07648i) q^{20} +(-1.37224 - 0.881883i) q^{21} -3.41578 q^{22} +(-0.715258 - 4.74219i) q^{23} -4.08524 q^{24} +(0.841254 + 0.540641i) q^{25} +(0.669661 + 4.65759i) q^{26} +(-2.26273 - 4.95469i) q^{27} +(2.98222 + 0.875658i) q^{28} +(2.73185 - 5.98191i) q^{29} +(2.41424 - 2.78619i) q^{30} +(-0.740559 + 5.15070i) q^{31} +(-6.01143 + 1.76511i) q^{32} +(-1.61440 - 1.86311i) q^{33} +(-5.92382 + 3.80701i) q^{34} +(-0.841254 + 0.540641i) q^{35} +(0.690507 + 0.796887i) q^{36} +(-4.09106 + 1.20124i) q^{37} +(0.965928 - 6.71818i) q^{38} +(-2.22395 + 2.56658i) q^{39} +(-1.04039 + 2.27815i) q^{40} +(-10.2876 - 3.02071i) q^{41} +(1.53149 + 3.35350i) q^{42} +(-1.11049 - 7.72364i) q^{43} +(3.95170 + 2.53960i) q^{44} -0.339251 q^{45} +(-4.43459 + 9.89045i) q^{46} +6.91140 q^{47} +(-0.762750 - 0.490190i) q^{48} +(-0.142315 - 0.989821i) q^{49} +(-0.938885 - 2.05587i) q^{50} +(-4.87628 - 1.43180i) q^{51} +(2.68815 - 5.88623i) q^{52} +(1.48539 - 1.71423i) q^{53} +(-1.75199 + 12.1854i) q^{54} +(-1.45011 + 0.425791i) q^{55} +(-1.64008 - 1.89275i) q^{56} +(4.12091 - 2.64835i) q^{57} +(-12.5035 + 8.03550i) q^{58} +(3.25682 + 3.75857i) q^{59} +(-4.86453 + 1.42836i) q^{60} +(-0.490604 + 3.41223i) q^{61} +(7.70174 - 8.88828i) q^{62} +(0.140930 - 0.308594i) q^{63} +(12.5199 + 3.67616i) q^{64} +(0.864881 + 1.89383i) q^{65} +(0.792943 + 5.51504i) q^{66} +(6.30430 + 4.05152i) q^{67} +9.68372 q^{68} +(-7.49060 + 2.25570i) q^{69} +2.26011 q^{70} +(-10.9861 - 7.06032i) q^{71} +(-0.120917 - 0.840997i) q^{72} +(6.00232 + 13.1433i) q^{73} +(9.24626 + 2.71495i) q^{74} +(0.677617 - 1.48377i) q^{75} +(-6.11238 + 7.05407i) q^{76} +(0.215085 - 1.49595i) q^{77} +(7.36459 - 2.16244i) q^{78} +(-2.99390 - 3.45514i) q^{79} +(-0.467606 + 0.300512i) q^{80} +(-6.61827 + 4.25330i) q^{81} +(15.8691 + 18.3139i) q^{82} +(-16.4742 + 4.83726i) q^{83} +(0.721522 - 5.01829i) q^{84} +(-2.04030 + 2.35463i) q^{85} +(-7.32619 + 16.0421i) q^{86} +(-10.2924 - 3.02213i) q^{87} +(-1.57238 - 3.44303i) q^{88} +(0.662830 + 4.61009i) q^{89} +(0.645028 + 0.414535i) q^{90} -2.08197 q^{91} +(12.4838 - 8.14513i) q^{92} +8.48812 q^{93} +(-13.1408 - 8.44511i) q^{94} +(-0.427380 - 2.97250i) q^{95} +(4.24541 + 9.29616i) q^{96} +(8.98192 + 2.63733i) q^{97} +(-0.938885 + 2.05587i) q^{98} +(0.335761 - 0.387489i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 130 q + 2 q^{2} + 2 q^{3} - 16 q^{4} - 13 q^{5} + 5 q^{6} + 13 q^{7} - 7 q^{8} - 39 q^{9}+O(q^{10}) \) 130 * q + 2 * q^2 + 2 * q^3 - 16 * q^4 - 13 * q^5 + 5 * q^6 + 13 * q^7 - 7 * q^8 - 39 * q^9	\( 130 q + 2 q^{2} + 2 q^{3} - 16 q^{4} - 13 q^{5} + 5 q^{6} + 13 q^{7} - 7 q^{8} - 39 q^{9} + 2 q^{10} + 2 q^{11} - 5 q^{12} + 13 q^{13} - 2 q^{14} + 2 q^{15} - 6 q^{16} - 51 q^{17} + q^{18} - 9 q^{19} - 16 q^{20} - 2 q^{21} + 34 q^{22} - 10 q^{23} - 76 q^{24} - 13 q^{25} - 31 q^{26} + 14 q^{27} + 27 q^{28} + 3 q^{29} + 5 q^{30} + 6 q^{31} + 22 q^{32} - 58 q^{33} + q^{34} + 13 q^{35} + 193 q^{36} - 36 q^{37} + 4 q^{38} - 2 q^{39} - 29 q^{40} - 34 q^{41} - 5 q^{42} - 22 q^{43} + 8 q^{44} + 170 q^{45} - 198 q^{46} - 14 q^{47} - 120 q^{48} - 13 q^{49} + 2 q^{50} - 6 q^{51} + 33 q^{52} - 18 q^{53} + 188 q^{54} - 31 q^{55} - 15 q^{56} - 9 q^{57} + 114 q^{58} + 46 q^{59} - 16 q^{60} - 56 q^{61} - 146 q^{62} + 17 q^{63} - 109 q^{64} + 2 q^{65} - 14 q^{66} - 10 q^{67} + 86 q^{68} - 6 q^{69} - 2 q^{70} - 25 q^{72} + 64 q^{73} + 79 q^{74} + 2 q^{75} + 32 q^{76} - 13 q^{77} - 64 q^{78} - 118 q^{79} - 17 q^{80} + 23 q^{81} + 129 q^{82} - 117 q^{83} - 72 q^{84} - 7 q^{85} + 74 q^{86} - 51 q^{87} - 40 q^{88} - 35 q^{89} + 100 q^{90} + 42 q^{91} + 76 q^{92} - 90 q^{93} - 7 q^{94} + 2 q^{95} + 393 q^{96} - 4 q^{97} + 2 q^{98} - 40 q^{99}+O(q^{100}) \) 130 * q + 2 * q^2 + 2 * q^3 - 16 * q^4 - 13 * q^5 + 5 * q^6 + 13 * q^7 - 7 * q^8 - 39 * q^9 + 2 * q^10 + 2 * q^11 - 5 * q^12 + 13 * q^13 - 2 * q^14 + 2 * q^15 - 6 * q^16 - 51 * q^17 + q^18 - 9 * q^19 - 16 * q^20 - 2 * q^21 + 34 * q^22 - 10 * q^23 - 76 * q^24 - 13 * q^25 - 31 * q^26 + 14 * q^27 + 27 * q^28 + 3 * q^29 + 5 * q^30 + 6 * q^31 + 22 * q^32 - 58 * q^33 + q^34 + 13 * q^35 + 193 * q^36 - 36 * q^37 + 4 * q^38 - 2 * q^39 - 29 * q^40 - 34 * q^41 - 5 * q^42 - 22 * q^43 + 8 * q^44 + 170 * q^45 - 198 * q^46 - 14 * q^47 - 120 * q^48 - 13 * q^49 + 2 * q^50 - 6 * q^51 + 33 * q^52 - 18 * q^53 + 188 * q^54 - 31 * q^55 - 15 * q^56 - 9 * q^57 + 114 * q^58 + 46 * q^59 - 16 * q^60 - 56 * q^61 - 146 * q^62 + 17 * q^63 - 109 * q^64 + 2 * q^65 - 14 * q^66 - 10 * q^67 + 86 * q^68 - 6 * q^69 - 2 * q^70 - 25 * q^72 + 64 * q^73 + 79 * q^74 + 2 * q^75 + 32 * q^76 - 13 * q^77 - 64 * q^78 - 118 * q^79 - 17 * q^80 + 23 * q^81 + 129 * q^82 - 117 * q^83 - 72 * q^84 - 7 * q^85 + 74 * q^86 - 51 * q^87 - 40 * q^88 - 35 * q^89 + 100 * q^90 + 42 * q^91 + 76 * q^92 - 90 * q^93 - 7 * q^94 + 2 * q^95 + 393 * q^96 - 4 * q^97 + 2 * q^98 - 40 * q^99

Introduction

L-functions

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