LMFDB - Embedded newform 418.2.q.b.395.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(21,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 1]))

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

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

chi := DirichletCharacter("418.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.q (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			395.10
Character	$\chi$	$=$	418.395
Dual form			418.2.q.b.109.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 - 0.342020i) q^{2} +(2.84334 - 0.501357i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.382944 + 0.321328i) q^{5} +(-2.84334 - 0.501357i) q^{6} +(0.682188 + 0.393861i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(5.01412 - 1.82499i) q^{9} +O(q^{10})$	\(q+(-0.939693 - 0.342020i) q^{2} +(2.84334 - 0.501357i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.382944 + 0.321328i) q^{5} +(-2.84334 - 0.501357i) q^{6} +(0.682188 + 0.393861i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(5.01412 - 1.82499i) q^{9} +(0.469750 - 0.170975i) q^{10} +(-0.673402 - 3.24754i) q^{11} +(2.50039 + 1.44360i) q^{12} +(-0.636404 + 3.60923i) q^{13} +(-0.506338 - 0.603431i) q^{14} +(-0.927739 + 1.10564i) q^{15} +(0.173648 + 0.984808i) q^{16} +(2.66319 - 7.31706i) q^{17} -5.33592 q^{18} +(4.34422 + 0.357400i) q^{19} -0.499898 q^{20} +(2.13715 + 0.777861i) q^{21} +(-0.477934 + 3.28201i) q^{22} +(5.12411 + 4.29964i) q^{23} +(-1.85586 - 2.21172i) q^{24} +(-0.824847 + 4.67794i) q^{25} +(1.83245 - 3.17390i) q^{26} +(5.84070 - 3.37213i) q^{27} +(0.269417 + 0.740217i) q^{28} +(-3.72606 + 1.35618i) q^{29} +(1.24994 - 0.721652i) q^{30} +(-9.28076 - 5.35825i) q^{31} +(0.173648 - 0.984808i) q^{32} +(-3.54288 - 8.89624i) q^{33} +(-5.00517 + 5.96493i) q^{34} +(-0.387799 + 0.0683793i) q^{35} +(5.01412 + 1.82499i) q^{36} +5.42973i q^{37} +(-3.96000 - 1.82166i) q^{38} +10.5813i q^{39} +(0.469750 + 0.170975i) q^{40} +(1.78113 + 10.1013i) q^{41} +(-1.74222 - 1.46190i) q^{42} +(-3.84732 - 4.58506i) q^{43} +(1.57162 - 2.92062i) q^{44} +(-1.33371 + 2.31005i) q^{45} +(-3.34452 - 5.79289i) q^{46} +(-2.80828 + 1.02213i) q^{47} +(0.987480 + 2.71308i) q^{48} +(-3.18975 - 5.52480i) q^{49} +(2.37505 - 4.11371i) q^{50} +(3.90389 - 22.1401i) q^{51} +(-2.80748 + 2.35576i) q^{52} +(7.20424 - 8.58567i) q^{53} +(-6.64180 + 1.17113i) q^{54} +(1.30140 + 1.02724i) q^{55} -0.787723i q^{56} +(12.5313 - 1.16180i) q^{57} +3.96519 q^{58} +(-1.10701 + 3.04147i) q^{59} +(-1.42138 + 0.250627i) q^{60} +(-2.48206 + 2.95801i) q^{61} +(6.88843 + 8.20931i) q^{62} +(4.13937 + 0.729882i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.916039 - 1.58663i) q^{65} +(0.286529 + 9.57147i) q^{66} +(-0.303270 - 0.833227i) q^{67} +(6.74344 - 3.89333i) q^{68} +(16.7252 + 9.65631i) q^{69} +(0.387799 + 0.0683793i) q^{70} +(-2.57716 - 3.07134i) q^{71} +(-4.08755 - 3.42986i) q^{72} +(-7.20898 + 1.27114i) q^{73} +(1.85708 - 5.10227i) q^{74} +13.7145i q^{75} +(3.09814 + 3.06620i) q^{76} +(0.819695 - 2.48066i) q^{77} +(3.61902 - 9.94318i) q^{78} +(0.870146 + 4.93484i) q^{79} +(-0.382944 - 0.321328i) q^{80} +(2.65379 - 2.22679i) q^{81} +(1.78113 - 10.1013i) q^{82} +(-11.7879 - 6.80575i) q^{83} +(1.13716 + 1.96961i) q^{84} +(1.33133 + 3.65779i) q^{85} +(2.04712 + 5.62441i) q^{86} +(-9.91452 + 5.72415i) q^{87} +(-2.47575 + 2.20695i) q^{88} +(-1.93725 - 0.341589i) q^{89} +(2.04336 - 1.71458i) q^{90} +(-1.85568 + 2.21152i) q^{91} +(1.16154 + 6.58743i) q^{92} +(-29.0747 - 10.5823i) q^{93} +2.98851 q^{94} +(-1.77844 + 1.25906i) q^{95} -2.88720i q^{96} +(-5.10117 + 14.0153i) q^{97} +(1.10779 + 6.28257i) q^{98} +(-9.30326 - 15.0546i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 3 q^{3} + 3 q^{6} + 18 q^{7} - 30 q^{8} - 3 q^{9}+O(q^{10}) $ 60 * q - 3 * q^3 + 3 * q^6 + 18 * q^7 - 30 * q^8 - 3 * q^9	$ 60 q - 3 q^{3} + 3 q^{6} + 18 q^{7} - 30 q^{8} - 3 q^{9} + 3 q^{11} - 6 q^{13} - 12 q^{14} + 24 q^{15} + 6 q^{17} - 60 q^{18} + 30 q^{19} - 12 q^{20} - 12 q^{21} + 12 q^{22} - 3 q^{24} - 12 q^{25} + 6 q^{26} + 9 q^{27} - 6 q^{28} + 3 q^{29} - 9 q^{31} + 9 q^{33} - 6 q^{34} + 24 q^{35} - 3 q^{36} + 6 q^{38} - 15 q^{41} + 6 q^{42} + 3 q^{43} - 12 q^{44} - 48 q^{45} - 3 q^{46} + 54 q^{47} - 6 q^{48} + 6 q^{49} - 36 q^{50} + 45 q^{51} + 3 q^{52} + 24 q^{53} + 27 q^{54} - 48 q^{55} - 30 q^{57} + 24 q^{58} - 39 q^{59} + 12 q^{60} - 54 q^{61} + 66 q^{63} - 30 q^{64} - 30 q^{66} + 9 q^{67} + 27 q^{68} + 54 q^{69} - 24 q^{70} - 33 q^{71} + 6 q^{72} - 12 q^{74} + 18 q^{77} - 36 q^{79} - 93 q^{81} - 15 q^{82} + 36 q^{83} - 24 q^{84} + 60 q^{85} - 3 q^{86} - 54 q^{87} + 3 q^{88} - 3 q^{89} + 24 q^{90} - 12 q^{91} - 102 q^{93} + 12 q^{94} - 24 q^{95} - 6 q^{97} + 18 q^{98} + 75 q^{99}+O(q^{100}) $ 60 * q - 3 * q^3 + 3 * q^6 + 18 * q^7 - 30 * q^8 - 3 * q^9 + 3 * q^11 - 6 * q^13 - 12 * q^14 + 24 * q^15 + 6 * q^17 - 60 * q^18 + 30 * q^19 - 12 * q^20 - 12 * q^21 + 12 * q^22 - 3 * q^24 - 12 * q^25 + 6 * q^26 + 9 * q^27 - 6 * q^28 + 3 * q^29 - 9 * q^31 + 9 * q^33 - 6 * q^34 + 24 * q^35 - 3 * q^36 + 6 * q^38 - 15 * q^41 + 6 * q^42 + 3 * q^43 - 12 * q^44 - 48 * q^45 - 3 * q^46 + 54 * q^47 - 6 * q^48 + 6 * q^49 - 36 * q^50 + 45 * q^51 + 3 * q^52 + 24 * q^53 + 27 * q^54 - 48 * q^55 - 30 * q^57 + 24 * q^58 - 39 * q^59 + 12 * q^60 - 54 * q^61 + 66 * q^63 - 30 * q^64 - 30 * q^66 + 9 * q^67 + 27 * q^68 + 54 * q^69 - 24 * q^70 - 33 * q^71 + 6 * q^72 - 12 * q^74 + 18 * q^77 - 36 * q^79 - 93 * q^81 - 15 * q^82 + 36 * q^83 - 24 * q^84 + 60 * q^85 - 3 * q^86 - 54 * q^87 + 3 * q^88 - 3 * q^89 + 24 * q^90 - 12 * q^91 - 102 * q^93 + 12 * q^94 - 24 * q^95 - 6 * q^97 + 18 * q^98 + 75 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$-1$

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 $

$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$3$	2.84334	−	0.501357i	1.64160	−	0.289459i	0.724847	−	0.688910i	$-0.241911\pi$
$3$	2.84334	−	0.501357i	1.64160	−	0.289459i	0.916754	+	0.399452i	$0.130799\pi$
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	−0.382944	+	0.321328i	−0.171258	+	0.143702i	−0.724388	−	0.689392i	$-0.757878\pi$
$5$	−0.382944	+	0.321328i	−0.171258	+	0.143702i	0.553130	+	0.833095i	$0.313433\pi$
$6$	−2.84334	−	0.501357i	−1.16079	−	0.204678i
$7$	0.682188	+	0.393861i	0.257843	+	0.148866i	0.623350	−	0.781943i	$-0.285771\pi$
$7$	0.682188	+	0.393861i	0.257843	+	0.148866i	−0.365507	+	0.930808i	$0.619104\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	5.01412	−	1.82499i	1.67137	−	0.608331i
$10$	0.469750	−	0.170975i	0.148548	−	0.0540671i
$11$	−0.673402	−	3.24754i	−0.203038	−	0.979171i
$11$	−0.673402	−	3.24754i	−0.203038	−	0.979171i
$12$	2.50039	+	1.44360i	0.721800	+	0.416731i
$13$	−0.636404	+	3.60923i	−0.176507	+	1.00102i	0.759884	+	0.650059i	$0.225256\pi$
$13$	−0.636404	+	3.60923i	−0.176507	+	1.00102i	−0.936390	+	0.350960i	$0.885855\pi$
$14$	−0.506338	−	0.603431i	−0.135325	−	0.161274i
$15$	−0.927739	+	1.10564i	−0.239541	+	0.285474i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	2.66319	−	7.31706i	0.645919	−	1.77465i	0.0136416	−	0.999907i	$-0.495658\pi$
$17$	2.66319	−	7.31706i	0.645919	−	1.77465i	0.632278	−	0.774742i	$-0.282120\pi$
$18$	−5.33592			−1.25769
$19$	4.34422	+	0.357400i	0.996633	+	0.0819931i
$19$	4.34422	+	0.357400i	0.996633	+	0.0819931i
$20$	−0.499898			−0.111781
$21$	2.13715	+	0.777861i	0.466365	+	0.169743i
$22$	−0.477934	+	3.28201i	−0.101896	+	0.699727i
$23$	5.12411	+	4.29964i	1.06845	+	0.896536i	0.994911	−	0.100756i	$-0.0321262\pi$
$23$	5.12411	+	4.29964i	1.06845	+	0.896536i	0.0735392	+	0.997292i	$0.476571\pi$
$24$	−1.85586	−	2.21172i	−0.378825	−	0.451466i
$25$	−0.824847	+	4.67794i	−0.164969	+	0.935587i
$26$	1.83245	−	3.17390i	0.359373	−	0.622453i
$27$	5.84070	−	3.37213i	1.12404	−	0.648967i
$28$	0.269417	+	0.740217i	0.0509150	+	0.139888i
$29$	−3.72606	+	1.35618i	−0.691912	+	0.251836i	−0.663954	−	0.747774i	$-0.731123\pi$
$29$	−3.72606	+	1.35618i	−0.691912	+	0.251836i	−0.0279585	+	0.999609i	$0.508901\pi$
$30$	1.24994	−	0.721652i	0.228207	−	0.131755i
$31$	−9.28076	−	5.35825i	−1.66687	−	0.962370i	−0.969309	−	0.245847i	$-0.920934\pi$
$31$	−9.28076	−	5.35825i	−1.66687	−	0.962370i	−0.697564	−	0.716522i	$-0.745733\pi$
$32$	0.173648	−	0.984808i	0.0306970	−	0.174091i
$33$	−3.54288	−	8.89624i	−0.616737	−	1.54864i
$34$	−5.00517	+	5.96493i	−0.858379	+	1.02298i
$35$	−0.387799	+	0.0683793i	−0.0655499	+	0.0115582i
$36$	5.01412	+	1.82499i	0.835687	+	0.304165i
$37$			5.42973i			0.892641i	0.894873	+	0.446321i	$0.147266\pi$
$37$			5.42973i			0.892641i	−0.894873	+	0.446321i	$0.852734\pi$
$38$	−3.96000	−	1.82166i	−0.642396	−	0.295512i
$39$			10.5813i			1.69437i
$40$	0.469750	+	0.170975i	0.0742741	+	0.0270335i
$41$	1.78113	+	10.1013i	0.278166	+	1.57756i	0.728720	+	0.684811i	$0.240115\pi$
$41$	1.78113	+	10.1013i	0.278166	+	1.57756i	−0.450554	+	0.892749i	$0.648773\pi$
$42$	−1.74222	−	1.46190i	−0.268831	−	0.225576i
$43$	−3.84732	−	4.58506i	−0.586711	−	0.699215i	0.388259	−	0.921550i	$-0.373077\pi$
$43$	−3.84732	−	4.58506i	−0.586711	−	0.699215i	−0.974970	+	0.222335i	$0.928632\pi$
$44$	1.57162	−	2.92062i	0.236931	−	0.440299i
$45$	−1.33371	+	2.31005i	−0.198817	+	0.344362i
$46$	−3.34452	−	5.79289i	−0.493123	−	0.854114i
$47$	−2.80828	+	1.02213i	−0.409629	+	0.149093i	−0.538612	−	0.842554i	$-0.681051\pi$
$47$	−2.80828	+	1.02213i	−0.409629	+	0.149093i	0.128983	+	0.991647i	$0.458829\pi$
$48$	0.987480	+	2.71308i	0.142531	+	0.391599i
$49$	−3.18975	−	5.52480i	−0.455678	−	0.789258i
$50$	2.37505	−	4.11371i	0.335883	−	0.581766i
$51$	3.90389	−	22.1401i	0.546655	−	3.10023i
$52$	−2.80748	+	2.35576i	−0.389327	+	0.326684i
$53$	7.20424	−	8.58567i	0.989578	−	1.17933i	0.00579266	−	0.999983i	$-0.498156\pi$
$53$	7.20424	−	8.58567i	0.989578	−	1.17933i	0.983785	−	0.179350i	$-0.0573994\pi$
$54$	−6.64180	+	1.17113i	−0.903835	+	0.159370i
$55$	1.30140	+	1.02724i	0.175481	+	0.138514i
$56$		−	0.787723i		−	0.105264i
$57$	12.5313	−	1.16180i	1.65981	−	0.153884i
$58$	3.96519			0.520655
$59$	−1.10701	+	3.04147i	−0.144120	+	0.395966i	−0.990659	−	0.136360i	$-0.956460\pi$
$59$	−1.10701	+	3.04147i	−0.144120	+	0.395966i	0.846540	+	0.532326i	$0.178682\pi$
$60$	−1.42138	+	0.250627i	−0.183499	+	0.0323558i
$61$	−2.48206	+	2.95801i	−0.317796	+	0.378734i	−0.901167	−	0.433471i	$-0.857289\pi$
$61$	−2.48206	+	2.95801i	−0.317796	+	0.378734i	0.583372	+	0.812205i	$0.301733\pi$
$62$	6.88843	+	8.20931i	0.874831	+	1.04258i
$63$	4.13937	+	0.729882i	0.521511	+	0.0919565i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−0.916039	−	1.58663i	−0.113621	−	0.196797i
$66$	0.286529	+	9.57147i	0.0352693	+	1.17817i
$67$	−0.303270	−	0.833227i	−0.0370503	−	0.101795i	0.919788	−	0.392416i	$-0.128360\pi$
$67$	−0.303270	−	0.833227i	−0.0370503	−	0.101795i	−0.956838	+	0.290621i	$0.906138\pi$
$68$	6.74344	−	3.89333i	0.817763	−	0.472135i
$69$	16.7252	+	9.65631i	2.01348	+	1.16248i
$70$	0.387799	+	0.0683793i	0.0463508	+	0.00817289i
$71$	−2.57716	−	3.07134i	−0.305852	−	0.364500i	0.591123	−	0.806581i	$-0.298685\pi$
$71$	−2.57716	−	3.07134i	−0.305852	−	0.364500i	−0.896975	+	0.442081i	$0.854240\pi$
$72$	−4.08755	−	3.42986i	−0.481723	−	0.404213i
$73$	−7.20898	+	1.27114i	−0.843747	+	0.148775i	−0.578782	−	0.815483i	$-0.696472\pi$
$73$	−7.20898	+	1.27114i	−0.843747	+	0.148775i	−0.264965	+	0.964258i	$0.585360\pi$
$74$	1.85708	−	5.10227i	0.215881	−	0.593127i
$75$			13.7145i			1.58361i
$76$	3.09814	+	3.06620i	0.355380	+	0.351717i
$77$	0.819695	−	2.48066i	0.0934129	−	0.282698i
$78$	3.61902	−	9.94318i	0.409773	−	1.12584i
$79$	0.870146	+	4.93484i	0.0978990	+	0.555213i	0.993820	+	0.111000i	$0.0354055\pi$
$79$	0.870146	+	4.93484i	0.0978990	+	0.555213i	−0.895921	+	0.444213i	$0.853483\pi$
$80$	−0.382944	−	0.321328i	−0.0428144	−	0.0359256i
$81$	2.65379	−	2.22679i	0.294865	−	0.247421i
$82$	1.78113	−	10.1013i	0.196693	−	1.11550i
$83$	−11.7879	−	6.80575i	−1.29389	−	0.747029i	−0.314550	−	0.949241i	$-0.601854\pi$
$83$	−11.7879	−	6.80575i	−1.29389	−	0.747029i	−0.979342	+	0.202212i	$0.935187\pi$
$84$	1.13716	+	1.96961i	0.124074	+	0.214902i
$85$	1.33133	+	3.65779i	0.144402	+	0.396743i
$86$	2.04712	+	5.62441i	0.220746	+	0.606496i
$87$	−9.91452	+	5.72415i	−1.06295	+	0.613693i
$88$	−2.47575	+	2.20695i	−0.263916	+	0.235262i
$89$	−1.93725	−	0.341589i	−0.205348	−	0.0362084i	0.0700279	−	0.997545i	$-0.477691\pi$
$89$	−1.93725	−	0.341589i	−0.205348	−	0.0362084i	−0.275376	+	0.961337i	$0.588802\pi$
$90$	2.04336	−	1.71458i	0.215389	−	0.180733i
$91$	−1.85568	+	2.21152i	−0.194528	+	0.231830i
$92$	1.16154	+	6.58743i	0.121099	+	0.686787i
$93$	−29.0747	−	10.5823i	−3.01491	−	1.09734i
$94$	2.98851			0.308241
$95$	−1.77844	+	1.25906i	−0.182464	+	0.129177i
$96$		−	2.88720i		−	0.294674i
$97$	−5.10117	+	14.0153i	−0.517945	+	1.42304i	0.354835	+	0.934929i	$0.384537\pi$
$97$	−5.10117	+	14.0153i	−0.517945	+	1.42304i	−0.872780	+	0.488114i	$0.837685\pi$
$98$	1.10779	+	6.28257i	0.111903	+	0.634636i
$99$	−9.30326	−	15.0546i	−0.935012	−	1.51305i
$100$	−3.63879	+	3.05331i	−0.363879	+	0.305331i
$101$	−8.89868	−	1.56908i	−0.885452	−	0.156129i	−0.287614	−	0.957746i	$-0.592862\pi$
$101$	−8.89868	−	1.56908i	−0.885452	−	0.156129i	−0.597838	+	0.801617i	$0.703973\pi$
$102$	−11.2408	+	19.4697i	−1.11301	+	1.92778i
$103$	2.60616	−	1.50467i	0.256792	−	0.148259i	−0.366078	−	0.930584i	$-0.619300\pi$
$103$	2.60616	−	1.50467i	0.256792	−	0.148259i	0.622871	+	0.782325i	$0.285966\pi$
$104$	3.44388	−	1.25347i	0.337701	−	0.122913i
$105$	−1.06836	+	0.388851i	−0.104261	+	0.0379480i
$106$	−9.70624	+	5.60390i	−0.942754	+	0.544299i
$107$	−0.807929	+	1.39937i	−0.0781055	+	0.135283i	−0.902433	−	0.430831i	$-0.858220\pi$
$107$	−0.807929	+	1.39937i	−0.0781055	+	0.135283i	0.824327	+	0.566114i	$0.191554\pi$
$108$	6.64180	+	1.17113i	0.639108	+	0.112692i
$109$	4.52846	−	3.79983i	0.433748	−	0.363958i	−0.399616	−	0.916683i	$-0.630856\pi$
$109$	4.52846	−	3.79983i	0.433748	−	0.363958i	0.833364	+	0.552725i	$0.186412\pi$
$110$	−0.871580	−	1.41040i	−0.0831019	−	0.134476i
$111$	2.72223	+	15.4385i	0.258383	+	1.46536i
$112$	−0.269417	+	0.740217i	−0.0254575	+	0.0699439i
$113$		−	4.12316i		−	0.387874i	−0.981014	−	0.193937i	$-0.937874\pi$
$113$		−	4.12316i		−	0.387874i	0.981014	−	0.193937i	$-0.0621258\pi$
$114$	−12.1729	−	3.19421i	−1.14010	−	0.299165i
$115$	−3.34384			−0.311815
$116$	−3.72606	−	1.35618i	−0.345956	−	0.125918i
$117$	3.39580	+	19.2585i	0.313942	+	1.78045i
$118$	2.08049	−	2.47943i	0.191525	−	0.228250i
$119$	4.69871	−	3.94268i	0.430730	−	0.361425i
$120$	1.42138	+	0.250627i	0.129753	+	0.0228790i
$121$	−10.0931	+	4.37380i	−0.917551	+	0.397618i
$122$	3.34407	−	1.93070i	0.302758	−	0.174798i
$123$	10.1287	+	27.8285i	0.913277	+	2.50921i
$124$	−3.66526	−	10.0702i	−0.329150	−	0.904332i
$125$	−2.43703	−	4.22106i	−0.217974	−	0.377543i
$126$	−3.64010	−	2.10161i	−0.324286	−	0.187226i
$127$	−3.31403	+	18.7948i	−0.294073	+	1.66777i	0.376873	+	0.926265i	$0.376999\pi$
$127$	−3.31403	+	18.7948i	−0.294073	+	1.66777i	−0.670946	+	0.741506i	$0.734112\pi$
$128$	0.766044	−	0.642788i	0.0677094	−	0.0568149i
$129$	−13.2380	−	11.1080i	−1.16554	−	0.978004i
$130$	0.318137	+	1.80424i	0.0279025	+	0.158243i
$131$	1.10650	−	3.04008i	0.0966753	−	0.265613i	−0.881923	−	0.471394i	$-0.843751\pi$
$131$	1.10650	−	3.04008i	0.0966753	−	0.265613i	0.978598	+	0.205781i	$0.0659733\pi$
$132$	3.00439	−	9.09224i	0.261498	−	0.791378i
$133$	2.82281	+	1.95483i	0.244769	+	0.169506i
$134$			0.886702i			0.0765994i
$135$	−1.15310	+	3.16812i	−0.0992432	+	0.272668i
$136$	−7.66836	+	1.35214i	−0.657556	+	0.115945i
$137$	3.03730	+	2.54860i	0.259494	+	0.217741i	0.763248	−	0.646106i	$-0.223604\pi$
$137$	3.03730	+	2.54860i	0.259494	+	0.217741i	−0.503754	+	0.863847i	$0.668048\pi$
$138$	−12.4139	−	14.7943i	−1.05674	−	1.25938i
$139$	18.8682	+	3.32698i	1.60038	+	0.282191i	0.901413	−	0.432960i	$-0.142531\pi$
$139$	18.8682	+	3.32698i	1.60038	+	0.282191i	0.698971	+	0.715150i	$0.253642\pi$
$140$	−0.341024	−	0.196890i	−0.0288218	−	0.0166403i
$141$	−7.47243	+	4.31421i	−0.629292	+	0.363322i
$142$	1.37128	+	3.76755i	0.115075	+	0.316166i
$143$	12.1497	−	0.363710i	1.01601	−	0.0304150i
$144$	2.66796	+	4.62104i	0.222330	+	0.385087i
$145$	0.991096	−	1.71663i	0.0823060	−	0.142558i
$146$	7.20898	+	1.27114i	0.596619	+	0.105200i
$147$	−11.8394	−	14.1097i	−0.976499	−	1.16375i
$148$	−3.49016	+	4.15941i	−0.286889	+	0.341901i
$149$	−14.1060	+	2.48726i	−1.15561	+	0.203765i	−0.718422	−	0.695608i	$-0.755135\pi$
$149$	−14.1060	+	2.48726i	−1.15561	+	0.203765i	−0.437184	+	0.899372i	$0.644024\pi$
$150$	4.69063	−	12.8874i	0.382989	−	1.05225i
$151$	9.33219			0.759443			0.379722	−	0.925101i	$-0.376020\pi$
$151$	9.33219			0.759443			0.379722	+	0.925101i	$0.376020\pi$
$152$	−1.86259	−	3.94091i	−0.151076	−	0.319650i
$153$		−	41.5490i		−	3.35904i
$154$	−1.61870	+	2.05071i	−0.130438	+	0.165251i
$155$	5.27577	−	0.930260i	0.423760	−	0.0747203i
$156$	−6.80153	+	8.10575i	−0.544559	+	0.648980i
$157$	−0.931253	+	0.781414i	−0.0743221	+	0.0623636i	−0.679192	−	0.733961i	$-0.737670\pi$
$157$	−0.931253	+	0.781414i	−0.0743221	+	0.0623636i	0.604870	+	0.796324i	$0.293225\pi$
$158$	0.870146	−	4.93484i	0.0692251	−	0.392595i
$159$	16.1796	−	28.0239i	1.28312	−	2.22244i
$160$	0.249949	+	0.432924i	0.0197602	+	0.0342257i
$161$	1.80214	+	4.95135i	0.142029	+	0.390221i
$162$	−3.25535	+	1.18485i	−0.255765	+	0.0930907i
$163$	3.78849	+	6.56186i	0.296738	+	0.513965i	0.975388	−	0.220497i	$-0.0707680\pi$
$163$	3.78849	+	6.56186i	0.296738	+	0.513965i	−0.678650	+	0.734462i	$0.737435\pi$
$164$	−5.12857	+	8.88295i	−0.400474	+	0.693642i
$165$	4.21534	+	2.26833i	0.328164	+	0.176589i
$166$	8.74931	+	10.4270i	0.679078	+	0.809294i
$167$	2.85558	+	2.39611i	0.220971	+	0.185417i	0.746553	−	0.665326i	$-0.231708\pi$
$167$	2.85558	+	2.39611i	0.220971	+	0.185417i	−0.525581	+	0.850743i	$0.676152\pi$
$168$	−0.394930	−	2.23976i	−0.0304695	−	0.172801i
$169$	−0.405499	−	0.147590i	−0.0311922	−	0.0113530i
$170$		−	3.89253i		−	0.298544i
$171$	22.4347	−	6.13612i	1.71563	−	0.469241i
$172$		−	5.98537i		−	0.456380i
$173$	−4.05261	−	1.47503i	−0.308114	−	0.112144i	0.183335	−	0.983050i	$-0.441311\pi$
$173$	−4.05261	−	1.47503i	−0.308114	−	0.112144i	−0.491450	+	0.870906i	$0.663533\pi$
$174$	11.2744	−	1.98798i	0.854708	−	0.150708i
$175$	−2.40516	+	2.86636i	−0.181813	+	0.216676i
$176$	3.08127	−	1.22710i	0.232259	−	0.0924962i
$177$	−1.62273	+	9.20293i	−0.121972	+	0.691735i
$178$	1.70359	+	0.983567i	0.127689	+	0.0737214i
$179$	1.27390	−	0.735487i	0.0952158	−	0.0549729i	−0.451636	−	0.892202i	$-0.649159\pi$
$179$	1.27390	−	0.735487i	0.0952158	−	0.0549729i	0.546852	+	0.837229i	$0.315826\pi$
$180$	−2.50655	+	0.912310i	−0.186827	+	0.0679995i
$181$	0.848847	+	2.33219i	0.0630943	+	0.173350i	0.967234	−	0.253887i	$-0.0817091\pi$
$181$	0.848847	+	2.33219i	0.0630943	+	0.173350i	−0.904140	+	0.427237i	$0.859487\pi$
$182$	2.50015	−	1.44346i	0.185324	−	0.106997i
$183$	−5.57432	+	9.65501i	−0.412066	+	0.713719i
$184$	1.16154	−	6.58743i	0.0856299	−	0.485631i
$185$	−1.74472	−	2.07928i	−0.128275	−	0.152872i
$186$	23.7019	+	19.8883i	1.73791	+	1.45828i
$187$	−25.5559	−	3.72151i	−1.86883	−	0.272144i
$188$	−2.80828	−	1.02213i	−0.204815	−	0.0745465i
$189$	5.31261			0.386435
$190$	2.10181	−	0.574865i	0.152481	−	0.0417051i
$191$	13.1283			0.949931			0.474966	−	0.880004i	$-0.342461\pi$
$191$	13.1283			0.949931			0.474966	+	0.880004i	$0.342461\pi$
$192$	−0.987480	+	2.71308i	−0.0712653	+	0.195800i
$193$	−2.59866	−	14.7377i	−0.187056	−	1.06085i	−0.923286	−	0.384114i	$-0.874507\pi$
$193$	−2.59866	−	14.7377i	−0.187056	−	1.06085i	0.736230	−	0.676731i	$-0.236604\pi$
$194$	9.58706	−	11.4254i	0.688311	−	0.820297i
$195$	−3.40007	−	4.05205i	−0.243484	−	0.290173i
$196$	1.10779	−	6.28257i	0.0791277	−	0.448755i
$197$	−18.3821	−	10.6129i	−1.30967	−	0.756140i	−0.327631	−	0.944806i	$-0.606250\pi$
$197$	−18.3821	−	10.6129i	−1.30967	−	0.756140i	−0.982041	+	0.188666i	$0.939584\pi$
$198$	3.59322	+	17.3286i	0.255359	+	1.23149i
$199$	20.0003	−	7.27952i	1.41778	−	0.516031i	0.484380	−	0.874858i	$-0.339045\pi$
$199$	20.0003	−	7.27952i	1.41778	−	0.516031i	0.933404	+	0.358826i	$0.116823\pi$
$200$	4.46364	−	1.62463i	0.315627	−	0.114879i
$201$	−1.28004	−	2.21710i	−0.0902872	−	0.156382i
$202$	7.82537	+	4.51798i	0.550591	+	0.317884i
$203$	−3.07602	−	0.542385i	−0.215894	−	0.0380680i
$204$	17.2219	−	14.4509i	1.20578	−	1.01177i
$205$	−3.92791	−	3.29591i	−0.274337	−	0.230196i
$206$	−2.96361	+	0.522565i	−0.206485	+	0.0364088i
$207$	33.5397	+	12.2075i	2.33117	+	0.848477i
$208$	−3.66490			−0.254115
$209$	−1.76474	−	14.3487i	−0.122069	−	0.992522i
$210$	1.13692			0.0784552
$211$	8.90448	+	3.24097i	0.613010	+	0.223117i	0.629820	−	0.776741i	$-0.283129\pi$
$211$	8.90448	+	3.24097i	0.613010	+	0.223117i	−0.0168099	+	0.999859i	$0.505351\pi$
$212$	11.0375	−	1.94621i	0.758061	−	0.133667i
$213$	−8.86756	−	7.44076i	−0.607595	−	0.509833i
$214$	1.23782	−	1.03865i	0.0846156	−	0.0710009i
$215$	2.94662	+	0.519568i	0.200958	+	0.0354343i
$216$	−5.84070	−	3.37213i	−0.397410	−	0.229444i
$217$	−4.22081	−	7.31066i	−0.286527	−	0.496280i
$218$	−5.55498	+	2.02185i	−0.376231	+	0.136937i
$219$	−19.8602	+	7.22854i	−1.34203	+	0.488459i
$220$	0.336632	+	1.62344i	0.0226957	+	0.109452i
$221$	24.7141	+	14.2687i	1.66245	+	0.959815i
$222$	2.72223	−	15.4385i	0.182704	−	1.03617i
$223$	−6.30946	−	7.51932i	−0.422512	−	0.503531i	0.512234	−	0.858846i	$-0.328818\pi$
$223$	−6.30946	−	7.51932i	−0.422512	−	0.503531i	−0.934747	+	0.355315i	$0.884374\pi$
$224$	0.506338	−	0.603431i	0.0338312	−	0.0403184i
$225$	4.40131	+	24.9611i	0.293421	+	1.66407i
$226$	−1.41020	+	3.87450i	−0.0938054	+	0.257728i
$227$	18.8139			1.24872			0.624360	−	0.781137i	$-0.285360\pi$
$227$	18.8139			1.24872			0.624360	+	0.781137i	$0.285360\pi$
$228$	10.3463	+	7.16495i	0.685200	+	0.474511i
$229$	10.1958			0.673756			0.336878	−	0.941548i	$-0.390629\pi$
$229$	10.1958			0.673756			0.336878	+	0.941548i	$0.390629\pi$
$230$	3.14218	+	1.14366i	0.207189	+	0.0754108i
$231$	1.08697	−	7.46431i	0.0715175	−	0.491116i
$232$	3.03751	+	2.54878i	0.199423	+	0.167335i
$233$	−8.25297	−	9.83551i	−0.540670	−	0.644346i	0.424668	−	0.905349i	$-0.360391\pi$
$233$	−8.25297	−	9.83551i	−0.540670	−	0.644346i	−0.965338	+	0.261004i	$0.915947\pi$
$234$	3.39580	−	19.2585i	0.221990	−	1.25897i
$235$	0.746974	−	1.29380i	0.0487272	−	0.0843980i
$236$	−2.80304	+	1.61833i	−0.182462	+	0.105345i
$237$	4.94823	+	13.5952i	0.321422	+	0.883101i
$238$	−5.76382	+	2.09786i	−0.373613	+	0.135984i
$239$	−11.1548	+	6.44024i	−0.721545	+	0.416584i	−0.815321	−	0.579009i	$-0.803440\pi$
$239$	−11.1548	+	6.44024i	−0.721545	+	0.416584i	0.0937758	+	0.995593i	$0.470106\pi$
$240$	−1.24994	−	0.721652i	−0.0806832	−	0.0465825i
$241$	4.42633	−	25.1030i	0.285125	−	1.61702i	−0.419714	−	0.907657i	$-0.637869\pi$
$241$	4.42633	−	25.1030i	0.285125	−	1.61702i	0.704839	−	0.709368i	$-0.251019\pi$
$242$	10.9803	−	0.657998i	0.705841	−	0.0422977i
$243$	−6.57619	+	7.83720i	−0.421863	+	0.502757i
$244$	−3.80274	+	0.670526i	−0.243446	+	0.0429260i
$245$	2.99677	+	1.09073i	0.191457	+	0.0696845i
$246$		−	29.6144i		−	1.88815i
$247$	−4.05462	+	15.4518i	−0.257989	+	0.983176i
$248$			10.7165i			0.680498i
$249$	−36.9291	−	13.4411i	−2.34029	−	0.851795i
$250$	0.846371	+	4.80001i	0.0535292	+	0.303579i
$251$	6.76166	+	5.67370i	0.426792	+	0.358121i	0.830740	−	0.556661i	$-0.187918\pi$
$251$	6.76166	+	5.67370i	0.426792	+	0.358121i	−0.403948	+	0.914782i	$0.632362\pi$
$252$	2.70178	+	3.21986i	0.170196	+	0.202832i
$253$	10.5127	−	19.5361i	0.660926	−	1.22823i
$254$	9.54238	−	16.5279i	0.598742	−	1.03705i
$255$	5.61926	+	9.73284i	0.351892	+	0.609494i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−4.59712	−	12.6305i	−0.286761	−	0.787868i	−0.996515	−	0.0834185i	$-0.973416\pi$
$257$	−4.59712	−	12.6305i	−0.286761	−	0.787868i	0.709754	−	0.704450i	$-0.248806\pi$
$258$	8.64048	+	14.9657i	0.537933	+	0.931727i
$259$	−2.13856	+	3.70409i	−0.132884	+	0.230161i
$260$	0.318137	−	1.80424i	0.0197300	−	0.111895i
$261$	−16.2079	+	13.6001i	−1.00325	+	0.841823i
$262$	−2.07954	+	2.47830i	−0.128474	+	0.153110i
$263$	12.9705	−	2.28704i	0.799793	−	0.141025i	0.241209	−	0.970473i	$-0.422456\pi$
$263$	12.9705	−	2.28704i	0.799793	−	0.141025i	0.558584	+	0.829448i	$0.311345\pi$
$264$	−5.93293	+	7.51635i	−0.365146	+	0.462599i
$265$			5.60276i			0.344175i
$266$	−1.98398	−	2.80240i	−0.121646	−	0.171826i
$267$	−5.67951			−0.347580
$268$	0.303270	−	0.833227i	0.0185252	−	0.0508974i
$269$	13.4114	−	2.36479i	0.817708	−	0.144184i	0.250878	−	0.968019i	$-0.419281\pi$
$269$	13.4114	−	2.36479i	0.817708	−	0.144184i	0.566830	+	0.823835i	$0.308170\pi$
$270$	2.16712	−	2.58268i	0.131887	−	0.157177i
$271$	10.5461	+	12.5683i	0.640628	+	0.763471i	0.984469	−	0.175557i	$-0.0561726\pi$
$271$	10.5461	+	12.5683i	0.640628	+	0.763471i	−0.343841	+	0.939028i	$0.611728\pi$
$272$	7.66836	+	1.35214i	0.464963	+	0.0819855i
$273$	−4.16757	+	7.21844i	−0.252233	+	0.436880i
$274$	−1.98246	−	3.43372i	−0.119765	−	0.207438i
$275$	15.7473	−	0.471406i	0.949595	−	0.0284269i
$276$	6.60530	+	18.1479i	0.397592	+	1.09238i
$277$	21.2057	−	12.2431i	1.27413	−	0.735618i	0.298366	−	0.954452i	$-0.403558\pi$
$277$	21.2057	−	12.2431i	1.27413	−	0.735618i	0.975762	+	0.218833i	$0.0702251\pi$
$278$	−16.5925	−	9.57966i	−0.995150	−	0.574550i
$279$	−56.3136	−	9.92961i	−3.37141	−	0.594470i
$280$	0.253118	+	0.301654i	0.0151267	+	0.0180273i
$281$	17.3918	+	14.5934i	1.03751	+	0.870571i	0.991725	−	0.128380i	$-0.0409777\pi$
$281$	17.3918	+	14.5934i	1.03751	+	0.870571i	0.0457816	+	0.998951i	$0.485422\pi$
$282$	8.49733	−	1.49831i	0.506009	−	0.0892230i
$283$	3.14369	−	8.63721i	0.186873	−	0.513429i	−0.810511	−	0.585724i	$-0.800810\pi$
$283$	3.14369	−	8.63721i	0.186873	−	0.513429i	0.997383	+	0.0722955i	$0.0230325\pi$
$284$		−	4.00934i		−	0.237911i
$285$	−4.42546	+	4.47155i	−0.262141	+	0.264872i
$286$	−11.5414	−	3.81366i	−0.682454	−	0.225506i
$287$	−2.76345	+	7.59252i	−0.163121	+	0.448172i
$288$	−0.926573	−	5.25485i	−0.0545988	−	0.309645i
$289$	−33.4241	−	28.0461i	−1.96612	−	1.64977i
$290$	−1.51845	+	1.27413i	−0.0891663	+	0.0748194i
$291$	−7.47765	+	42.4079i	−0.438348	+	2.48599i
$292$	−6.33947	−	3.66009i	−0.370989	−	0.214191i
$293$	−5.77029	−	9.99443i	−0.337104	−	0.583881i	0.646783	−	0.762674i	$-0.276114\pi$
$293$	−5.77029	−	9.99443i	−0.337104	−	0.583881i	−0.983887	+	0.178793i	$0.942781\pi$
$294$	6.29962	+	17.3081i	0.367402	+	1.00943i
$295$	−0.553390	−	1.52043i	−0.0322196	−	0.0885226i
$296$	4.70228	−	2.71486i	0.273314	−	0.157798i
$297$	−14.8843	−	16.6971i	−0.863673	−	0.968866i
$298$	14.1060	+	2.48726i	0.817137	+	0.144083i
$299$	−18.7794	+	15.7578i	−1.08604	+	0.911295i
$300$	−8.81550	+	10.5059i	−0.508963	+	0.606559i
$301$	−0.818719	−	4.64318i	−0.0471902	−	0.267629i
$302$	−8.76939	−	3.19180i	−0.504622	−	0.183667i
$303$	−26.0886			−1.49875
$304$	0.402396	+	4.34029i	0.0230790	+	0.248932i
$305$		−	1.93031i		−	0.110529i
$306$	−14.2106	+	39.0433i	−0.812365	+	2.23195i
$307$	3.53775	+	20.0636i	0.201910	+	1.14509i	0.902228	+	0.431259i	$0.141930\pi$
$307$	3.53775	+	20.0636i	0.201910	+	1.14509i	−0.700318	+	0.713831i	$0.746958\pi$
$308$	2.22246	−	1.37341i	0.126636	−	0.0782571i
$309$	6.65581	−	5.58489i	0.378636	−	0.317713i
$310$	−5.27577	−	0.930260i	−0.299643	−	0.0528352i
$311$	6.53120	−	11.3124i	0.370350	−	0.641465i	−0.619269	−	0.785179i	$-0.712571\pi$
$311$	6.53120	−	11.3124i	0.370350	−	0.641465i	0.989619	+	0.143713i	$0.0459044\pi$
$312$	9.16368	−	5.29065i	0.518791	−	0.299524i
$313$	0.0546296	−	0.0198835i	0.00308785	−	0.00112388i	−0.340476	−	0.940253i	$-0.610588\pi$
$313$	0.0546296	−	0.0198835i	0.00308785	−	0.00112388i	0.343564	+	0.939129i	$0.388366\pi$
$314$	1.14235	−	0.415782i	0.0644666	−	0.0234639i
$315$	−1.81968	+	1.05059i	−0.102527	+	0.0591941i
$316$	−2.50548	+	4.33963i	−0.140945	+	0.244123i
$317$	−14.2013	−	2.50406i	−0.797622	−	0.140642i	−0.240039	−	0.970763i	$-0.577160\pi$
$317$	−14.2013	−	2.50406i	−0.797622	−	0.140642i	−0.557583	+	0.830121i	$0.688271\pi$
$318$	−24.7886	+	20.8001i	−1.39007	+	1.16641i
$319$	6.91337	+	11.1873i	0.387075	+	0.626368i
$320$	−0.0868064	−	0.492303i	−0.00485262	−	0.0275206i
$321$	−1.59563	+	4.38395i	−0.0890593	+	0.244688i
$322$		−	5.26911i		−	0.293636i
$323$	14.1846	−	30.8351i	0.789253	−	1.71571i
$324$	3.46427			0.192460
$325$	−16.3588	−	5.95412i	−0.907423	−	0.330275i
$326$	−1.31573	−	7.46188i	−0.0728715	−	0.413275i
$327$	10.9709	−	13.0746i	0.606690	−	0.723025i
$328$	7.85743	−	6.59317i	0.433854	−	0.364047i
$329$	−2.31835	−	0.408788i	−0.127815	−	0.0225372i
$330$	−3.18531	−	3.57327i	−0.175345	−	0.196702i
$331$	6.18025	−	3.56817i	0.339697	−	0.196124i	−0.320441	−	0.947269i	$-0.603831\pi$
$331$	6.18025	−	3.56817i	0.339697	−	0.196124i	0.660138	+	0.751144i	$0.270498\pi$
$332$	−4.65541	−	12.7906i	−0.255499	−	0.701977i
$333$	9.90920	+	27.2253i	0.543021	+	1.49194i
$334$	−1.86385	−	3.22828i	−0.101985	−	0.176643i
$335$	0.383875	+	0.221630i	0.0209733	+	0.0121090i
$336$	−0.394930	+	2.23976i	−0.0215452	+	0.122189i
$337$	−6.15116	+	5.16144i	−0.335075	+	0.281161i	−0.794764	−	0.606919i	$-0.792405\pi$
$337$	−6.15116	+	5.16144i	−0.335075	+	0.281161i	0.459689	+	0.888080i	$0.347961\pi$
$338$	0.330566	+	0.277378i	0.0179804	+	0.0150874i
$339$	−2.06717	−	11.7235i	−0.112274	−	0.636735i
$340$	−1.33133	+	3.65779i	−0.0722012	+	0.198371i
$341$	−11.1515	+	33.7479i	−0.603885	+	1.82755i
$342$	−23.1804	−	1.90706i	−1.25345	−	0.103122i
$343$		−	10.5393i		−	0.569070i
$344$	−2.04712	+	5.62441i	−0.110373	+	0.303248i
$345$	−9.50766	+	1.67646i	−0.511875	+	0.0902575i
$346$	3.30372	+	2.77215i	0.177609	+	0.149032i
$347$	−12.2160	−	14.5585i	−0.655792	−	0.781542i	0.330983	−	0.943637i	$-0.392620\pi$
$347$	−12.2160	−	14.5585i	−0.655792	−	0.781542i	−0.986775	+	0.162094i	$0.948175\pi$
$348$	−11.2744	−	1.98798i	−0.604370	−	0.106567i
$349$	12.7057	+	7.33565i	0.680122	+	0.392669i	0.799901	−	0.600132i	$-0.204885\pi$
$349$	12.7057	+	7.33565i	0.680122	+	0.392669i	−0.119779	+	0.992801i	$0.538219\pi$
$350$	3.24046	−	1.87088i	0.173210	−	0.100003i
$351$	8.45374	+	23.2265i	0.451227	+	1.23974i
$352$	−3.31514	+	0.0992413i	−0.176698	+	0.00528958i
$353$	11.3850	+	19.7194i	0.605962	+	1.04956i	0.991899	+	0.127032i	$0.0405452\pi$
$353$	11.3850	+	19.7194i	0.605962	+	1.04956i	−0.385936	+	0.922525i	$0.626122\pi$
$354$	4.67245	−	8.09292i	0.248338	−	0.430134i
$355$	1.97381	+	0.348037i	0.104759	+	0.0184719i
$356$	−1.26445	−	1.50691i	−0.0670157	−	0.0798661i
$357$	11.3833	−	13.5661i	0.602469	−	0.717994i
$358$	−1.44863	+	0.255432i	−0.0765623	+	0.0135000i
$359$	2.51111	−	6.89921i	0.132531	−	0.364126i	−0.855621	−	0.517602i	$-0.826825\pi$
$359$	2.51111	−	6.89921i	0.132531	−	0.364126i	0.988152	+	0.153476i	$0.0490468\pi$
$360$	2.66741			0.140585
$361$	18.7445	+	3.10525i	0.986554	+	0.163434i
$362$		−	2.48186i		−	0.130444i
$363$	−26.5051	+	17.4964i	−1.39116	+	0.918323i
$364$	−2.84307	+	0.501310i	−0.149017	+	0.0262758i
$365$	2.35218	−	2.80322i	0.123119	−	0.146727i
$366$	8.54036	−	7.16621i	0.446412	−	0.374584i
$367$	−0.260646	+	1.47820i	−0.0136056	+	0.0771613i	−0.990855	−	0.134934i	$-0.956918\pi$
$367$	−0.260646	+	1.47820i	−0.0136056	+	0.0771613i	0.977249	+	0.212096i	$0.0680288\pi$
$368$	−3.34452	+	5.79289i	−0.174345	+	0.301975i
$369$	27.3656	+	47.3987i	1.42460	+	2.46748i
$370$	0.928348	+	2.55062i	0.0482625	+	0.132600i
$371$	8.29621	−	3.01957i	0.430718	−	0.156768i
$372$	−15.4703	−	26.7954i	−0.802099	−	1.38928i
$373$	5.10142	−	8.83591i	0.264141	−	0.457506i	−0.703197	−	0.710995i	$-0.748245\pi$
$373$	5.10142	−	8.83591i	0.264141	−	0.457506i	0.967338	+	0.253489i	$0.0815782\pi$
$374$	22.7418	+	12.2377i	1.17595	+	0.632796i
$375$	−9.04555	−	10.7801i	−0.467110	−	0.556680i
$376$	2.28933	+	1.92098i	0.118063	+	0.0990667i
$377$	−2.52346	−	14.3113i	−0.129965	−	0.737068i
$378$	−4.99222	−	1.81702i	−0.256772	−	0.0934574i
$379$		−	8.58017i		−	0.440734i	−0.975417	−	0.220367i	$-0.929275\pi$
$379$		−	8.58017i		−	0.440734i	0.975417	−	0.220367i	$-0.0707255\pi$
$380$	−2.17167	−	0.178663i	−0.111404	−	0.00916524i
$381$			55.1015i			2.82294i
$382$	−12.3366	−	4.49015i	−0.631194	−	0.229736i
$383$	−20.4717	+	3.60971i	−1.04605	+	0.184448i	−0.670161	−	0.742215i	$-0.733775\pi$
$383$	−20.4717	+	3.60971i	−1.04605	+	0.184448i	−0.375893	+	0.926663i	$0.622664\pi$
$384$	1.85586	−	2.21172i	0.0947062	−	0.112867i
$385$	0.483209	+	1.21335i	0.0246266	+	0.0618378i
$386$	−2.59866	+	14.7377i	−0.132268	+	0.750131i
$387$	−27.6586	−	15.9687i	−1.40597	−	0.811736i
$388$	−12.9166	+	7.45741i	−0.655742	+	0.378593i
$389$	−27.6889	+	10.0779i	−1.40388	+	0.510971i	−0.929328	−	0.369255i	$-0.879613\pi$
$389$	−27.6889	+	10.0779i	−1.40388	+	0.510971i	−0.474554	+	0.880226i	$0.657391\pi$
$390$	1.80914	+	4.97057i	0.0916094	+	0.251695i
$391$	45.1072	−	26.0427i	2.28117	−	1.31703i
$392$	−3.18975	+	5.52480i	−0.161107	+	0.279045i
$393$	1.62198	−	9.19873i	0.0818183	−	0.464014i
$394$	13.6437	+	16.2599i	0.687360	+	0.819164i
$395$	−1.91892	−	1.61017i	−0.0965514	−	0.0810162i
$396$	2.55022	−	17.5125i	0.128153	−	0.880038i
$397$	−15.8506	−	5.76913i	−0.795517	−	0.289544i	−0.0878895	−	0.996130i	$-0.528012\pi$
$397$	−15.8506	−	5.76913i	−0.795517	−	0.289544i	−0.707627	+	0.706586i	$0.750234\pi$
$398$	−21.2839			−1.06686
$399$	9.00627	+	4.14302i	0.450877	+	0.207410i
$400$	−4.75010			−0.237505
$401$	5.61554	−	15.4286i	0.280427	−	0.770466i	−0.716885	−	0.697191i	$-0.754433\pi$
$401$	5.61554	−	15.4286i	0.280427	−	0.770466i	0.997312	−	0.0732747i	$-0.0233450\pi$
$402$	0.444554	+	2.52119i	0.0221723	+	0.125746i
$403$	25.2454	−	30.0863i	1.25756	−	1.49871i
$404$	−5.80820	−	6.92195i	−0.288969	−	0.344380i
$405$	−0.300721	+	1.70547i	−0.0149430	+	0.0847457i
$406$	2.70501	+	1.56174i	0.134247	+	0.0775077i
$407$	17.6333	−	3.65639i	0.874048	−	0.181240i
$408$	−21.1258	+	7.68917i	−1.04588	+	0.380671i
$409$	−25.1036	+	9.13696i	−1.24129	+	0.451794i	−0.877451	−	0.479667i	$-0.840758\pi$
$409$	−25.1036	+	9.13696i	−1.24129	+	0.451794i	−0.363843	+	0.931460i	$0.618535\pi$
$410$	2.56376	+	4.44057i	0.126615	+	0.219304i
$411$	9.91383	+	5.72375i	0.489013	+	0.282332i
$412$	2.96361	+	0.522565i	0.146007	+	0.0257449i
$413$	−1.95310	+	1.63885i	−0.0961060	+	0.0806425i
$414$	−27.3418	−	22.9425i	−1.34378	−	1.12756i
$415$	6.70099	−	1.18157i	0.328939	−	0.0580008i
$416$	3.44388	+	1.25347i	0.168850	+	0.0614565i
$417$	55.3168			2.70887
$418$	−3.24924	+	14.0870i	−0.158926	+	0.689016i
$419$	−1.46621			−0.0716290			−0.0358145	−	0.999358i	$-0.511403\pi$
$419$	−1.46621			−0.0716290			−0.0358145	+	0.999358i	$0.511403\pi$
$420$	−1.06836	−	0.388851i	−0.0521306	−	0.0189740i
$421$	−33.7064	+	5.94335i	−1.64275	+	0.289661i	−0.917175	−	0.398484i	$-0.869537\pi$
$421$	−33.7064	+	5.94335i	−1.64275	+	0.289661i	−0.725574	+	0.688145i	$0.758425\pi$
$422$	−7.25900	−	6.09102i	−0.353363	−	0.296506i
$423$	−12.2157	+	10.2502i	−0.593946	+	0.498380i
$424$	−11.0375	−	1.94621i	−0.536030	−	0.0945165i
$425$	32.0320	+	18.4937i	1.55378	+	0.897077i
$426$	5.78789	+	10.0249i	0.280424	+	0.485709i
$427$	−2.85828	+	1.04033i	−0.138322	+	0.0503450i
$428$	−1.51841	+	0.552656i	−0.0733951	+	0.0267136i
$429$	34.3632	−	7.12547i	1.65907	−	0.344021i
$430$	−2.59121	−	1.49604i	−0.124959	−	0.0721453i
$431$	−4.83822	+	27.4389i	−0.233049	+	1.32169i	0.613635	+	0.789590i	$0.289707\pi$
$431$	−4.83822	+	27.4389i	−0.233049	+	1.32169i	−0.846684	+	0.532096i	$0.821404\pi$
$432$	4.33513	+	5.16641i	0.208574	+	0.248569i
$433$	11.9003	−	14.1822i	0.571890	−	0.681552i	−0.400128	−	0.916459i	$-0.631034\pi$
$433$	11.9003	−	14.1822i	0.571890	−	0.681552i	0.972018	+	0.234908i	$0.0754788\pi$
$434$	1.46587	+	8.31338i	0.0703641	+	0.399055i
$435$	1.95738	−	5.37784i	0.0938490	−	0.257848i
$436$	5.91149			0.283109
$437$	20.7236	+	20.5099i	0.991343	+	0.981123i
$438$	21.1348			1.00986
$439$	27.3289	+	9.94689i	1.30434	+	0.474739i	0.898406	−	0.439166i	$-0.144726\pi$
$439$	27.3289	+	9.94689i	1.30434	+	0.474739i	0.405929	+	0.913905i	$0.366948\pi$
$440$	0.238918	−	1.64067i	0.0113900	−	0.0782158i
$441$	−26.0765	−	21.8808i	−1.24174	−	1.04194i
$442$	−18.3435	−	21.8609i	−0.872509	−	1.03982i
$443$	3.87426	−	21.9720i	0.184072	−	1.04392i	−0.743070	−	0.669213i	$-0.766631\pi$
$443$	3.87426	−	21.9720i	0.184072	−	1.04392i	0.927142	−	0.374710i	$-0.122258\pi$
$444$	−7.83835	+	13.5764i	−0.371992	+	0.644308i
$445$	0.851620	−	0.491683i	0.0403706	−	0.0233080i
$446$	3.35719	+	9.22381i	0.158968	+	0.436760i
$447$	−38.8610	+	14.1442i	−1.83806	+	0.669000i
$448$	−0.682188	+	0.393861i	−0.0322303	+	0.0186082i
$449$	27.4647	+	15.8568i	1.29614	+	0.748327i	0.979735	−	0.200297i	$-0.0641908\pi$
$449$	27.4647	+	15.8568i	1.29614	+	0.748327i	0.316405	+	0.948624i	$0.397524\pi$
$450$	4.40131	−	24.9611i	0.207480	−	1.17668i
$451$	31.6050	−	12.5866i	1.48822	−	0.592678i
$452$	2.65032	−	3.15852i	0.124660	−	0.148564i
$453$	26.5346	−	4.67876i	1.24670	−	0.219827i
$454$	−17.6793	−	6.43472i	−0.829728	−	0.301996i
$455$		−	1.44317i		−	0.0676568i
$456$	−7.27178	−	10.2715i	−0.340532	−	0.481007i
$457$		−	9.59857i		−	0.449002i	−0.974474	−	0.224501i	$-0.927925\pi$
$457$		−	9.59857i		−	0.449002i	0.974474	−	0.224501i	$-0.0720752\pi$
$458$	−9.58090	−	3.48716i	−0.447686	−	0.162944i
$459$	−9.11918	−	51.7174i	−0.425647	−	2.41396i
$460$	−2.56153	−	2.14938i	−0.119432	−	0.100215i
$461$	−15.9711	−	19.0336i	−0.743847	−	0.886483i	0.252865	−	0.967502i	$-0.418627\pi$
$461$	−15.9711	−	19.0336i	−0.743847	−	0.886483i	−0.996713	+	0.0810186i	$0.974183\pi$
$462$	−3.57436	+	6.64239i	−0.166294	+	0.309032i
$463$	7.51676	−	13.0194i	0.349334	−	0.605063i	−0.636798	−	0.771031i	$-0.719741\pi$
$463$	7.51676	−	13.0194i	0.349334	−	0.605063i	0.986131	+	0.165967i	$0.0530747\pi$
$464$	−1.98260	−	3.43396i	−0.0920397	−	0.159417i
$465$	14.5344	−	5.29008i	0.674016	−	0.245322i
$466$	4.39132	+	12.0650i	0.203424	+	0.558902i
$467$	−15.5919	−	27.0060i	−0.721508	−	1.24969i	−0.960395	−	0.278641i	$-0.910116\pi$
$467$	−15.5919	−	27.0060i	−0.721508	−	1.24969i	0.238888	−	0.971047i	$-0.423217\pi$
$468$	−9.77782	+	16.9357i	−0.451980	+	0.782852i
$469$	0.121289	−	0.687864i	0.00560060	−	0.0317626i
$470$	−1.14443	+	0.960292i	−0.0527887	+	0.0442949i
$471$	−2.25610	+	2.68871i	−0.103956	+	0.123889i
$472$	3.18750	−	0.562041i	0.146716	−	0.0258701i
$473$	−12.2994	+	15.5819i	−0.565526	+	0.716458i
$474$		−	14.4677i		−	0.664522i
$475$	−5.25521	+	20.0272i	−0.241126	+	0.918911i
$476$	6.13373			0.281139
$477$	20.4541	−	56.1973i	0.936531	−	2.57310i
$478$	12.6848	−	2.23667i	0.580189	−	0.102303i
$479$	10.5411	−	12.5624i	0.481637	−	0.573993i	−0.469433	−	0.882968i	$-0.655542\pi$
$479$	10.5411	−	12.5624i	0.481637	−	0.573993i	0.951070	+	0.308975i	$0.0999861\pi$
$480$	0.927739	+	1.10564i	0.0423453	+	0.0504651i
$481$	−19.5971	−	3.45550i	−0.893551	−	0.157557i
$482$	−12.7451	+	22.0752i	−0.580524	+	1.00550i
$483$	7.60649	+	13.1748i	0.346107	+	0.599476i
$484$	−10.5432	−	3.13717i	−0.479234	−	0.142599i
$485$	−2.55006	−	7.00624i	−0.115792	−	0.318137i
$486$	8.86008	−	5.11537i	0.401901	−	0.232038i
$487$	1.39554	+	0.805713i	0.0632378	+	0.0365104i	0.531286	−	0.847193i	$-0.321709\pi$
$487$	1.39554	+	0.805713i	0.0632378	+	0.0365104i	−0.468048	+	0.883703i	$0.655042\pi$
$488$	3.80274	+	0.670526i	0.172142	+	0.0303533i
$489$	14.0618	+	16.7582i	0.635896	+	0.757832i
$490$	−2.44299	−	2.04991i	−0.110363	−	0.0926055i
$491$	6.34089	−	1.11807i	0.286160	−	0.0504578i	−0.0287255	−	0.999587i	$-0.509145\pi$
$491$	6.34089	−	1.11807i	0.286160	−	0.0504578i	0.314886	+	0.949130i	$0.398034\pi$
$492$	−10.1287	+	27.8285i	−0.456638	+	1.25460i
$493$			30.8756i			1.39057i
$494$	9.09493	−	13.1332i	0.409200	−	0.590891i
$495$	8.40010	+	2.77568i	0.377557	+	0.124758i
$496$	3.66526	−	10.0702i	0.164575	−	0.452166i
$497$	−0.548424	−	3.11027i	−0.0246002	−	0.139515i
$498$	30.1049	+	25.2610i	1.34903	+	1.13197i
$499$	−14.0844	+	11.8182i	−0.630505	+	0.529057i	−0.901086	−	0.433641i	$-0.857229\pi$
$499$	−14.0844	+	11.8182i	−0.630505	+	0.529057i	0.270581	+	0.962697i	$0.412784\pi$
$500$	0.846371	−	4.80001i	0.0378509	−	0.214663i
$501$	9.32068	+	5.38130i	0.416417	+	0.240419i
$502$	−4.41336	−	7.64416i	−0.196978	−	0.341176i
$503$	−8.26632	−	22.7115i	−0.368577	−	1.01266i	−0.975903	−	0.218204i	$-0.929980\pi$
$503$	−8.26632	−	22.7115i	−0.368577	−	1.01266i	0.607326	−	0.794453i	$-0.292242\pi$
$504$	−1.43759	−	3.94974i	−0.0640352	−	0.175935i
$505$	3.91189	−	2.25853i	0.174077	−	0.100503i
$506$	−16.5604	+	14.7624i	−0.736201	+	0.656270i
$507$	−1.22697	−	0.216347i	−0.0544914	−	0.00960831i
$508$	−14.6198	+	12.2675i	−0.648648	+	0.544280i
$509$	0.242071	−	0.288489i	0.0107296	−	0.0127871i	−0.760653	−	0.649159i	$-0.775121\pi$
$509$	0.242071	−	0.288489i	0.0107296	−	0.0127871i	0.771383	+	0.636372i	$0.219566\pi$
$510$	−1.95155	−	11.0678i	−0.0864160	−	0.490090i
$511$	−5.41853	−	1.97218i	−0.239702	−	0.0872442i
$512$	1.00000			0.0441942
$513$	26.5785	−	12.5618i	1.17347	−	0.554618i
$514$			13.4411i			0.592861i
$515$	−0.514521	+	1.41364i	−0.0226725	+	0.0622922i
$516$	−3.00081	−	17.0184i	−0.132103	−	0.749194i
$517$	5.21051	+	8.43170i	0.229158	+	0.370826i
$518$	3.27646	−	2.74928i	0.143959	−	0.120796i
$519$	−12.2625	−	2.16220i	−0.538262	−	0.0949101i
$520$	−0.916039	+	1.58663i	−0.0401710	+	0.0695782i
$521$	−19.4949	+	11.2554i	−0.854087	+	0.493107i	−0.862028	−	0.506861i	$-0.830806\pi$
$521$	−19.4949	+	11.2554i	−0.854087	+	0.493107i	0.00794059	+	0.999968i	$0.497472\pi$
$522$	19.8820	−	7.23644i	0.870210	−	0.316731i
$523$	15.0650	−	5.48321i	0.658746	−	0.239764i	0.00905134	−	0.999959i	$-0.497119\pi$
$523$	15.0650	−	5.48321i	0.658746	−	0.239764i	0.649695	+	0.760195i	$0.274897\pi$
$524$	2.80176	−	1.61759i	0.122395	−	0.0706649i
$525$	−5.40161	+	9.35586i	−0.235745	+	0.408323i
$526$	−12.9705	−	2.28704i	−0.565539	−	0.0997198i
$527$	−63.9231	+	53.6378i	−2.78453	+	2.33650i
$528$	8.14587	−	5.03388i	0.354503	−	0.219071i
$529$	3.77569	+	21.4130i	0.164161	+	0.931001i
$530$	1.91626	−	5.26487i	0.0832368	−	0.228691i
$531$			17.2706i			0.749480i
$532$	0.905854	+	3.31196i	0.0392738	+	0.143592i
$533$	−37.5915			−1.62827
$534$	5.33699	+	1.94251i	0.230954	+	0.0840604i
$535$	−0.140267	−	0.795493i	−0.00606426	−	0.0343921i
$536$	−0.569961	+	0.679253i	−0.0246186	+	0.0293393i
$537$	3.25339	−	2.72991i	0.140394	−	0.117805i
$538$	−13.4114	−	2.36479i	−0.578207	−	0.101954i
$539$	−15.7941	+	14.0792i	−0.680298	+	0.606436i
$540$	−2.91976	+	1.68572i	−0.125646	+	0.0725419i
$541$	1.33857	+	3.67770i	0.0575497	+	0.158117i	0.965136	−	0.261749i	$-0.0842993\pi$
$541$	1.33857	+	3.67770i	0.0575497	+	0.158117i	−0.907586	+	0.419866i	$0.862077\pi$
$542$	−5.61145	−	15.4173i	−0.241032	−	0.662231i
$543$	3.58282	+	6.20562i	0.153753	+	0.266309i
$544$	−6.74344	−	3.89333i	−0.289123	−	0.166925i
$545$	−0.513155	+	2.91024i	−0.0219811	+	0.124661i
$546$	6.38509	−	5.35772i	0.273256	−	0.229289i
$547$	16.8396	+	14.1301i	0.720008	+	0.604159i	0.927388	−	0.374102i	$-0.122049\pi$
$547$	16.8396	+	14.1301i	0.720008	+	0.604159i	−0.207379	+	0.978261i	$0.566493\pi$
$548$	0.688500	+	3.90468i	0.0294113	+	0.166800i
$549$	−7.04703	+	19.3616i	−0.300760	+	0.826331i
$550$	−14.9588	−	4.94290i	−0.637846	−	0.210766i
$551$	−16.6715	+	4.55984i	−0.710231	+	0.194256i
$552$		−	19.3126i		−	0.821999i
$553$	−1.35004	+	3.70921i	−0.0574096	+	0.157731i
$554$	−24.1143	+	4.25199i	−1.02452	+	0.180650i
$555$	−6.00330	−	5.03737i	−0.254826	−	0.213824i
$556$	12.3154	+	14.6769i	0.522288	+	0.622439i
$557$	12.5220	+	2.20797i	0.530575	+	0.0935546i	0.432516	−	0.901626i	$-0.357626\pi$
$557$	12.5220	+	2.20797i	0.530575	+	0.0935546i	0.0980582	+	0.995181i	$0.468737\pi$
$558$	49.5214	+	28.5912i	2.09641	+	1.21036i
$559$	18.9970	−	10.9679i	0.803486	−	0.463893i
$560$	−0.134681	−	0.370033i	−0.00569131	−	0.0156368i
$561$	−74.5297	+	2.23111i	−3.14665	+	0.0941974i
$562$	−11.3517	−	19.6617i	−0.478842	−	0.829378i
$563$	6.18515	−	10.7130i	0.260673	−	0.451499i	−0.705748	−	0.708463i	$-0.749389\pi$
$563$	6.18515	−	10.7130i	0.260673	−	0.451499i	0.966421	+	0.256964i	$0.0827222\pi$
$564$	−8.49733	−	1.49831i	−0.357802	−	0.0630902i
$565$	1.32489	+	1.57894i	0.0557384	+	0.0664265i
$566$	−5.90820	+	7.04112i	−0.248340	+	0.295960i
$567$	2.68743	−	0.473866i	0.112861	−	0.0199005i
$568$	−1.37128	+	3.76755i	−0.0575375	+	0.158083i
$569$	7.91935			0.331996			0.165998	−	0.986126i	$-0.446915\pi$
$569$	7.91935			0.331996			0.165998	+	0.986126i	$0.446915\pi$
$570$	5.68793	−	2.68829i	0.238241	−	0.112600i
$571$			21.6809i			0.907317i	0.891175	+	0.453659i	$0.149881\pi$
$571$			21.6809i			0.907317i	−0.891175	+	0.453659i	$0.850119\pi$
$572$	9.54098	+	7.53104i	0.398928	+	0.314889i
$573$	37.3282	−	6.58197i	1.55941	−	0.274966i
$574$	5.19359	−	6.18948i	0.216776	−	0.258344i
$575$	−24.3400	+	20.4237i	−1.01505	+	0.851728i
$576$	−0.926573	+	5.25485i	−0.0386072	+	0.218952i
$577$	12.8630	−	22.2793i	0.535492	−	0.927499i	−0.463647	−	0.886020i	$-0.653460\pi$
$577$	12.8630	−	22.2793i	0.535492	−	0.927499i	0.999139	−	0.0414795i	$-0.0132071\pi$
$578$	21.8160	+	37.7864i	0.907427	+	1.57171i
$579$	−14.7777	−	40.6015i	−0.614141	−	1.68734i
$580$	1.86265	−	0.677949i	0.0773424	−	0.0281503i
$581$	−5.36105	−	9.28561i	−0.222414	−	0.385232i
$582$	21.5310	−	37.2928i	0.892490	−	1.54584i
$583$	−32.7337	−	17.6145i	−1.35569	−	0.729516i
$584$	4.70532	+	5.60759i	0.194708	+	0.232044i
$585$	−7.48871	−	6.28378i	−0.309620	−	0.259802i
$586$	2.00400	+	11.3652i	0.0827845	+	0.469494i
$587$	19.5686	+	7.12239i	0.807683	+	0.293972i	0.712666	−	0.701503i	$-0.247487\pi$
$587$	19.5686	+	7.12239i	0.807683	+	0.293972i	0.0950163	+	0.995476i	$0.469710\pi$
$588$		−	18.4189i		−	0.759581i
$589$	−38.4026	−	26.5944i	−1.58235	−	1.09580i
$590$			1.61800i			0.0666122i
$591$	−57.5874	−	20.9601i	−2.36883	−	0.862184i
$592$	−5.34724	+	0.942862i	−0.219770	+	0.0387514i
$593$	12.2461	−	14.5943i	0.502886	−	0.599316i	−0.453560	−	0.891226i	$-0.649846\pi$
$593$	12.2461	−	14.5943i	0.502886	−	0.599316i	0.956446	+	0.291910i	$0.0942907\pi$
$594$	8.27589	+	20.7809i	0.339564	+	0.852650i
$595$	−0.532447	+	3.01965i	−0.0218282	+	0.123794i
$596$	−12.4046	−	7.16179i	−0.508111	−	0.293358i
$597$	53.2180	−	30.7254i	2.17807	−	1.25751i
$598$	23.0363	−	8.38453i	0.942024	−	0.342869i
$599$	11.9577	+	32.8534i	0.488577	+	1.34235i	0.901969	+	0.431801i	$0.142122\pi$
$599$	11.9577	+	32.8534i	0.488577	+	1.34235i	−0.413392	+	0.910553i	$0.635656\pi$
$600$	11.8771	−	6.85725i	0.484880	−	0.279946i
$601$	−11.5704	+	20.0405i	−0.471965	+	0.817467i	−0.999485	−	0.0320749i	$-0.989788\pi$
$601$	−11.5704	+	20.0405i	−0.471965	+	0.817467i	0.527520	+	0.849542i	$0.323122\pi$
$602$	−0.818719	+	4.64318i	−0.0333685	+	0.189242i
$603$	−3.04127	−	3.62444i	−0.123850	−	0.147599i
$604$	7.14887	+	5.99862i	0.290884	+	0.244080i
$605$	2.45965	−	4.91811i	0.0999991	−	0.199949i
$606$	24.5153	+	8.92283i	0.995865	+	0.362465i
$607$	24.8612			1.00909			0.504543	−	0.863387i	$-0.331661\pi$
$607$	24.8612			1.00909			0.504543	+	0.863387i	$0.331661\pi$
$608$	1.10634	−	4.21616i	0.0448679	−	0.170988i
$609$	−9.01809			−0.365431
$610$	−0.660204	+	1.81390i	−0.0267309	+	0.0734425i
$611$	−1.90190	−	10.7862i	−0.0769425	−	0.436363i
$612$	26.7072	−	31.8284i	1.07957	−	1.28659i
$613$	−14.9708	−	17.8415i	−0.604665	−	0.720612i	0.373688	−	0.927554i	$-0.378093\pi$
$613$	−14.9708	−	17.8415i	−0.604665	−	0.720612i	−0.978353	+	0.206943i	$0.933649\pi$
$614$	3.53775	−	20.0636i	0.142772	−	0.809701i
$615$	−12.8208	−	7.40209i	−0.516985	−	0.298481i
$616$	−2.55816	+	0.530454i	−0.103071	+	0.0213726i
$617$	5.54368	−	2.01773i	0.223180	−	0.0812309i	−0.228010	−	0.973659i	$-0.573222\pi$
$617$	5.54368	−	2.01773i	0.223180	−	0.0812309i	0.451190	+	0.892428i	$0.351000\pi$
$618$	−8.16456	+	2.97166i	−0.328427	+	0.119538i
$619$	−8.61180	−	14.9161i	−0.346137	−	0.599527i	0.639422	−	0.768856i	$-0.279174\pi$
$619$	−8.61180	−	14.9161i	−0.346137	−	0.599527i	−0.985560	+	0.169328i	$0.945840\pi$
$620$	4.63943	+	2.67858i	0.186324	+	0.107574i
$621$	44.4273	+	7.83374i	1.78281	+	0.314357i
$622$	−10.0064	+	8.39634i	−0.401219	+	0.336663i
$623$	−1.18703	−	0.996035i	−0.0475573	−	0.0399053i
$624$	−10.4206	+	1.83742i	−0.417156	+	0.0735559i
$625$	−20.0286	−	7.28981i	−0.801144	−	0.291592i
$626$	−0.0581356			−0.00232357
$627$	−12.2116	−	39.9135i	−0.487683	−	1.59399i
$628$	−1.21566			−0.0485103
$629$	39.7297	+	14.4604i	1.58412	+	0.576574i
$630$	2.06926	−	0.364867i	0.0824414	−	0.0145366i
$631$	28.1646	+	23.6329i	1.12121	+	0.940810i	0.998665	−	0.0516520i	$-0.0164486\pi$
$631$	28.1646	+	23.6329i	1.12121	+	0.940810i	0.122549	+	0.992462i	$0.460893\pi$
$632$	3.83863	−	3.22099i	0.152692	−	0.128124i
$633$	26.9433	+	4.75083i	1.07090	+	0.188829i
$634$	12.4884	+	7.21017i	0.495977	+	0.286352i
$635$	−4.77022	−	8.26226i	−0.189300	−	0.327878i
$636$	30.4077	−	11.0675i	1.20574	−	0.438854i
$637$	21.9702	−	7.99651i	0.870492	−	0.316833i
$638$	−2.67017	−	12.8771i	−0.105713	−	0.509810i
$639$	−18.5273	−	10.6968i	−0.732930	−	0.423157i
$640$	−0.0868064	+	0.492303i	−0.00343132	+	0.0194600i
$641$	26.4693	+	31.5449i	1.04548	+	1.24595i	0.968526	+	0.248914i	$0.0800737\pi$
$641$	26.4693	+	31.5449i	1.04548	+	1.24595i	0.0769499	+	0.997035i	$0.475482\pi$
$642$	2.99880	−	3.57383i	0.118353	−	0.141048i
$643$	−2.91259	−	16.5181i	−0.114861	−	0.651411i	−0.986819	−	0.161830i	$-0.948261\pi$
$643$	−2.91259	−	16.5181i	−0.114861	−	0.651411i	0.871957	−	0.489582i	$-0.162851\pi$
$644$	−1.80214	+	4.95135i	−0.0710144	+	0.195110i
$645$	8.63872			0.340149
$646$	−23.8754	+	24.1241i	−0.939366	+	0.949151i
$647$	−14.5065			−0.570311			−0.285156	−	0.958481i	$-0.592045\pi$
$647$	−14.5065			−0.570311			−0.285156	+	0.958481i	$0.592045\pi$
$648$	−3.25535	−	1.18485i	−0.127882	−	0.0465454i
$649$	10.6228	+	1.54691i	0.416980	+	0.0607217i
$650$	13.3358	+	11.1901i	0.523074	+	0.438911i
$651$	−15.6664	−	18.6705i	−0.614016	−	0.731756i
$652$	−1.31573	+	7.46188i	−0.0515280	+	0.292230i
$653$	−6.68284	+	11.5750i	−0.261520	+	0.452965i	−0.966646	−	0.256116i	$-0.917557\pi$
$653$	−6.68284	+	11.5750i	−0.261520	+	0.452965i	0.705126	+	0.709082i	$0.250890\pi$
$654$	−14.7810	+	8.53382i	−0.577983	+	0.333699i
$655$	0.553137	+	1.51973i	0.0216128	+	0.0593808i
$656$	−9.63856	+	3.50815i	−0.376323	+	0.136970i
$657$	−33.8269	+	19.5300i	−1.31971	+	0.761936i
$658$	2.03872	+	1.17706i	0.0794777	+	0.0458865i
$659$	−0.999779	+	5.67003i	−0.0389459	+	0.220873i	−0.998069	−	0.0621164i	$-0.980215\pi$
$659$	−0.999779	+	5.67003i	−0.0389459	+	0.220873i	0.959123	+	0.282989i	$0.0913261\pi$
$660$	1.77108	+	4.44721i	0.0689392	+	0.173107i
$661$	3.10063	−	3.69519i	0.120600	−	0.143726i	−0.702366	−	0.711816i	$-0.747873\pi$
$661$	3.10063	−	3.69519i	0.120600	−	0.143726i	0.822966	+	0.568090i	$0.192317\pi$
$662$	−7.02792	+	1.23921i	−0.273148	+	0.0481634i
$663$	77.4241	+	28.1801i	3.00690	+	1.09442i
$664$			13.6115i			0.528229i
$665$	−1.70912	+	0.158456i	−0.0662769	+	0.00614466i
$666$		−	28.9726i		−	1.12266i
$667$	−24.9238	−	9.07152i	−0.965054	−	0.351251i
$668$	0.647307	+	3.67106i	0.0250451	+	0.142038i
$669$	−21.7098	−	18.2167i	−0.839348	−	0.704297i
$670$	−0.284922	−	0.339557i	−0.0110075	−	0.0131182i
$671$	11.2777	+	6.06868i	0.435370	+	0.234279i
$672$	1.13716	−	1.96961i	0.0438667	−	0.0759794i
$673$	14.8054	+	25.6438i	0.570707	+	0.988494i	0.996493	+	0.0836704i	$0.0266643\pi$
$673$	14.8054	+	25.6438i	0.570707	+	0.988494i	−0.425786	+	0.904824i	$0.640002\pi$
$674$	7.54552	−	2.74634i	0.290642	−	0.105785i
$675$	10.9569	+	30.1039i	0.421733	+	1.15870i
$676$	−0.215762	−	0.373710i	−0.00829852	−	0.0143735i
$677$	−20.8524	+	36.1174i	−0.801423	+	1.38811i	0.117256	+	0.993102i	$0.462590\pi$
$677$	−20.8524	+	36.1174i	−0.801423	+	1.38811i	−0.918679	+	0.395004i	$0.870743\pi$
$678$	−2.06717	+	11.7235i	−0.0793894	+	0.450239i
$679$	−9.00006	+	7.55195i	−0.345391	+	0.289817i
$680$	2.50207	−	2.98185i	0.0959501	−	0.114349i
$681$	53.4941	−	9.43246i	2.04990	−	0.361453i
$682$	22.0214	−	27.8986i	0.843243	−	1.06829i
$683$		−	4.77644i		−	0.182765i	−0.995816	−	0.0913827i	$-0.970871\pi$
$683$		−	4.77644i		−	0.182765i	0.995816	−	0.0913827i	$-0.0291286\pi$
$684$	21.1302	+	9.72022i	0.807934	+	0.371662i
$685$	−1.98205			−0.0757304
$686$	−3.60466	+	9.90373i	−0.137627	+	0.378126i
$687$	28.9900	−	5.11172i	1.10604	−	0.195024i
$688$	3.84732	−	4.58506i	0.146678	−	0.174804i
$689$	26.4028	+	31.4657i	1.00587	+	1.19875i
$690$	9.50766	+	1.67646i	0.361951	+	0.0638217i
$691$	13.2420	−	22.9358i	0.503750	−	0.872520i	−0.496241	−	0.868185i	$-0.665287\pi$
$691$	13.2420	−	22.9358i	0.503750	−	0.872520i	0.999991	−	0.00433510i	$-0.00137991\pi$
$692$	−2.15635	−	3.73491i	−0.0819721	−	0.141980i
$693$	−0.417134	−	13.9343i	−0.0158456	−	0.529319i
$694$	6.50002	+	17.8587i	0.246738	+	0.677906i
$695$	−8.29454	+	4.78885i	−0.314630	+	0.181652i
$696$	9.91452	+	5.72415i	0.375809	+	0.216973i
$697$	78.6555	+	13.8691i	2.97929	+	0.525329i
$698$	−9.43053	−	11.2389i	−0.356951	−	0.425398i
$699$	−28.3971	−	23.8280i	−1.07408	−	0.901257i
$700$	−3.68492	+	0.649750i	−0.139277	+	0.0245583i
$701$	13.7893	−	37.8857i	0.520814	−	1.43092i	−0.348803	−	0.937196i	$-0.613412\pi$
$701$	13.7893	−	37.8857i	0.520814	−	1.43092i	0.869617	−	0.493728i	$-0.164366\pi$
$702$		−	24.7171i		−	0.932886i
$703$	−1.94058	+	23.5879i	−0.0731904	+	0.889636i
$704$	3.14915	+	1.04059i	0.118688	+	0.0392186i
$705$	1.47524	−	4.05320i	0.0555609	−	0.152652i
$706$	−3.95397	−	22.4241i	−0.148810	−	0.843941i
$707$	−5.45257	−	4.57525i	−0.205065	−	0.172070i
$708$	−7.15861	+	6.00679i	−0.269037	+	0.225749i
$709$	0.169225	−	0.959725i	0.00635539	−	0.0360432i	−0.981465	−	0.191641i	$-0.938619\pi$
$709$	0.169225	−	0.959725i	0.00635539	−	0.0360432i	0.987821	+	0.155597i	$0.0497303\pi$
$710$	−1.73574	−	1.00213i	−0.0651412	−	0.0376093i
$711$	13.3691	+	23.1559i	0.501379	+	0.868414i
$712$	0.672799	+	1.84850i	0.0252142	+	0.0692755i
$713$	−24.5171	−	67.3601i	−0.918172	−	2.52266i
$714$	−15.3367	+	8.85465i	−0.573961	+	0.331377i
$715$	−4.53577	+	4.04331i	−0.169628	+	0.151211i
$716$	1.44863	+	0.255432i	0.0541377	+	0.00954594i
$717$	−28.4880	+	23.9043i	−1.06391	+	0.892723i
$718$	−4.71934	+	5.62429i	−0.176124	+	0.209897i
$719$	4.31581	+	24.4762i	0.160953	+	0.912808i	0.953140	+	0.302530i	$0.0978312\pi$
$719$	4.31581	+	24.4762i	0.160953	+	0.912808i	−0.792187	+	0.610278i	$0.791058\pi$
$720$	−2.50655	−	0.912310i	−0.0934136	−	0.0339998i
$721$	2.37052			0.0882828
$722$	−16.5520	−	9.32899i	−0.616003	−	0.347189i
$723$		−	73.5954i		−	2.73704i
$724$	−0.848847	+	2.33219i	−0.0315472	+	0.0866751i
$725$	−3.27068	−	18.5489i	−0.121470	−	0.688890i
$726$	30.8908	−	7.37596i	1.14647	−	0.273747i
$727$	−31.3409	+	26.2981i	−1.16237	+	0.975344i	−0.999935	−	0.0113751i	$-0.996379\pi$
$727$	−31.3409	+	26.2981i	−1.16237	+	0.975344i	−0.162435	+	0.986719i	$0.551935\pi$
$728$	2.84307	+	0.501310i	0.105371	+	0.0185798i
$729$	−19.9655	+	34.5813i	−0.739463	+	1.28079i
$730$	−3.16909	+	1.82967i	−0.117293	+	0.0677192i
$731$	−43.7953	+	15.9402i	−1.61983	+	0.589570i
$732$	−10.4763	+	3.81306i	−0.387215	+	0.140935i
$733$	−14.4049	+	8.31667i	−0.532057	+	0.307183i	−0.741854	−	0.670562i	$-0.766053\pi$
$733$	−14.4049	+	8.31667i	−0.532057	+	0.307183i	0.209797	+	0.977745i	$0.432720\pi$
$734$	0.750500	−	1.29990i	0.0277015	−	0.0479804i
$735$	9.06767	+	1.59887i	0.334466	+	0.0589754i
$736$	5.12411	−	4.29964i	0.188877	−	0.158487i
$737$	−2.50172	+	1.54598i	−0.0921520	+	0.0569468i
$738$	−9.50399	−	53.8998i	−0.349847	−	1.98408i
$739$	2.48978	−	6.84061i	0.0915880	−	0.251636i	−0.885437	−	0.464759i	$-0.846141\pi$
$739$	2.48978	−	6.84061i	0.0915880	−	0.251636i	0.977025	+	0.213122i	$0.0683633\pi$
$740$		−	2.71431i		−	0.0997800i
$741$	−3.78176	+	45.9676i	−0.138926	+	1.68866i
$742$	−8.82864			−0.324110
$743$	−22.4314	−	8.16437i	−0.822929	−	0.299522i	−0.103975	−	0.994580i	$-0.533156\pi$
$743$	−22.4314	−	8.16437i	−0.822929	−	0.299522i	−0.718953	+	0.695058i	$0.755379\pi$
$744$	5.37279	+	30.4706i	0.196976	+	1.11711i
$745$	4.60257	−	5.48513i	0.168625	−	0.200960i
$746$	−7.81582	+	6.55825i	−0.286158	+	0.240115i
$747$	−71.5265	−	12.6121i	−2.61702	−	0.461451i
$748$	−17.1848	−	19.2778i	−0.628338	−	0.704868i
$749$	−1.10232	+	0.636424i	−0.0402779	+	0.0232544i
$750$	4.81303	+	13.2237i	0.175747	+	0.482861i
$751$	−7.57596	−	20.8148i	−0.276451	−	0.759542i	−0.997758	−	0.0669265i	$-0.978681\pi$
$751$	−7.57596	−	20.8148i	−0.276451	−	0.759542i	0.721307	−	0.692615i	$-0.243542\pi$
$752$	−1.49425	−	2.58812i	−0.0544898	−	0.0943791i
$753$	22.0702	+	12.7422i	0.804283	+	0.464353i
$754$	−2.52346	+	14.3113i	−0.0918991	+	0.521186i
$755$	−3.57371	+	2.99870i	−0.130061	+	0.109134i
$756$	4.06969	+	3.41488i	0.148013	+	0.124198i
$757$	−2.84816	−	16.1527i	−0.103518	−	0.587080i	−0.991802	−	0.127785i	$-0.959213\pi$
$757$	−2.84816	−	16.1527i	−0.103518	−	0.587080i	0.888284	−	0.459295i	$-0.151898\pi$
$758$	−2.93459	+	8.06272i	−0.106589	+	0.292851i
$759$	20.0965	−	60.8184i	0.729456	−	2.20757i
$760$	1.97959	+	0.910643i	0.0718074	+	0.0330325i
$761$			1.78365i			0.0646573i	0.999477	+	0.0323287i	$0.0102923\pi$
$761$			1.78365i			0.0646573i	−0.999477	+	0.0323287i	$0.989708\pi$
$762$	18.8458	−	51.7785i	0.682712	−	1.87574i
$763$	4.58587	−	0.808612i	0.166020	−	0.0292737i
$764$	10.0569	+	8.43871i	0.363845	+	0.305302i
$765$	13.3509	+	15.9109i	0.482701	+	0.575261i
$766$	20.4717	+	3.60971i	0.739672	+	0.130424i
$767$	−10.2729	−	5.93104i	−0.370931	−	0.214157i
$768$	−2.50039	+	1.44360i	−0.0902250	+	0.0520914i
$769$	13.2854	+	36.5012i	0.479082	+	1.31627i	0.910274	+	0.414007i	$0.135871\pi$
$769$	13.2854	+	36.5012i	0.479082	+	1.31627i	−0.431191	+	0.902261i	$0.641907\pi$
$770$	−0.0390793	−	1.30544i	−0.00140832	−	0.0470448i
$771$	−19.4035	−	33.6079i	−0.698801	−	1.21036i
$772$	7.48254	−	12.9601i	0.269303	−	0.466446i
$773$	−32.6300	−	5.75355i	−1.17362	−	0.206941i	−0.447355	−	0.894357i	$-0.647634\pi$
$773$	−32.6300	−	5.75355i	−1.17362	−	0.206941i	−0.726264	+	0.687416i	$0.758745\pi$
$774$	20.5290	+	24.4655i	0.737900	+	0.879395i
$775$	32.7207	−	38.9951i	1.17536	−	1.40074i
$776$	14.6882	−	2.58993i	0.527277	−	0.0929731i
$777$	−4.22357	+	11.6042i	−0.151520	+	0.416297i
$778$	29.4659			1.05640
$779$	4.12744	+	44.5189i	0.147881	+	1.59506i
$780$		−	5.28957i		−	0.189397i
$781$	−8.23883	+	10.4377i	−0.294808	+	0.373489i
$782$	−51.2940	+	9.04452i	−1.83427	+	0.323431i
$783$	−17.1896	+	20.4858i	−0.614307	+	0.732102i
$784$	4.88698	−	4.10066i	0.174535	−	0.146452i
$785$	0.105527	−	0.598476i	0.00376644	−	0.0213605i
$786$	−4.67032	+	8.08923i	−0.166585	+	0.288533i
$787$	−14.2687	−	24.7141i	−0.508625	−	0.880964i	−0.999950	−	0.00998763i	$-0.996821\pi$
$787$	−14.2687	−	24.7141i	−0.508625	−	0.880964i	0.491326	−	0.870976i	$-0.336513\pi$
$788$	−7.25967	−	19.9458i	−0.258615	−	0.710539i
$789$	35.7328	−	13.0057i	1.27212	−	0.463014i
$790$	1.25249	+	2.16937i	0.0445615	+	0.0771827i
$791$	1.62395	−	2.81277i	0.0577411	−	0.100011i
$792$	−8.38606	+	15.5842i	−0.297986	+	0.553759i
$793$	−9.09652	−	10.8408i	−0.323027	−	0.384969i
$794$	12.9215	+	10.8424i	0.458567	+	0.384783i
$795$	2.80898	+	15.9305i	0.0996243	+	0.564997i
$796$	20.0003	+	7.27952i	0.708892	+	0.258016i
$797$			3.27299i			0.115935i	0.998318	+	0.0579676i	$0.0184620\pi$
$797$			3.27299i			0.115935i	−0.998318	+	0.0579676i	$0.981538\pi$
$798$	−7.04613	−	6.97349i	−0.249430	−	0.246859i
$799$			23.2705i			0.823250i
$800$	4.46364	+	1.62463i	0.157813	+	0.0574394i
$801$	−10.3370	+	1.82269i	−0.365240	+	0.0644016i
$802$	−10.5538	+	12.5775i	−0.372666	+	0.444126i
$803$	8.98261	+	22.5555i	0.316989	+	0.795965i
$804$	0.444554	−	2.52119i	0.0156782	−	0.0889156i
$805$	−2.28113	−	1.31701i	−0.0803992	−	0.0464185i
$806$	−34.0131	+	19.6375i	−1.19806	+	0.691700i
$807$	36.9476	−	13.4478i	1.30062	−	0.473385i
$808$	3.09048	+	8.49102i	0.108723	+	0.298713i
$809$	7.33202	−	4.23314i	0.257780	−	0.148829i	−0.365541	−	0.930795i	$-0.619116\pi$
$809$	7.33202	−	4.23314i	0.257780	−	0.148829i	0.623321	+	0.781966i	$0.285783\pi$
$810$	0.865892	−	1.49977i	0.0304243	−	0.0526965i
$811$	4.34357	−	24.6336i	0.152523	−	0.865003i	−0.808492	−	0.588507i	$-0.799716\pi$
$811$	4.34357	−	24.6336i	0.152523	−	0.865003i	0.961015	−	0.276496i	$-0.0891731\pi$
$812$	−2.00773	−	2.39272i	−0.0704575	−	0.0839680i
$813$	36.2872	+	30.4486i	1.27265	+	1.06788i
$814$	−17.8204	−	2.59505i	−0.624605	−	0.0909565i
$815$	−3.55929	−	1.29548i	−0.124677	−	0.0453786i
$816$	22.4816			0.787014
$817$	−15.0749	−	21.2936i	−0.527405	−	0.744967i
$818$	26.7147			0.934058
$819$	−5.26862	+	14.4754i	−0.184100	+	0.505812i
$820$	−0.890386	−	5.04963i	−0.0310936	−	0.176341i
$821$	28.9790	−	34.5358i	1.01137	−	1.20531i	0.0327891	−	0.999462i	$-0.489561\pi$
$821$	28.9790	−	34.5358i	1.01137	−	1.20531i	0.978584	−	0.205846i	$-0.0659945\pi$
$822$	−7.35831	−	8.76929i	−0.256651	−	0.305864i
$823$	−0.364500	+	2.06718i	−0.0127057	+	0.0720575i	−0.990501	−	0.137503i	$-0.956092\pi$
$823$	−0.364500	+	2.06718i	−0.0127057	+	0.0720575i	0.977796	+	0.209561i	$0.0672034\pi$
$824$	−2.60616	−	1.50467i	−0.0907899	−	0.0524175i
$825$	44.5384	−	9.23536i	1.55063	−	0.321534i
$826$	2.39584	−	0.872013i	0.0833618	−	0.0303412i
$827$	15.6696	−	5.70329i	0.544887	−	0.198323i	−0.0548863	−	0.998493i	$-0.517480\pi$
$827$	15.6696	−	5.70329i	0.544887	−	0.198323i	0.599773	+	0.800170i	$0.295257\pi$
$828$	17.8461	+	30.9104i	0.620195	+	1.07421i
$829$	−7.45885	−	4.30637i	−0.259056	−	0.149566i	0.364848	−	0.931067i	$-0.381121\pi$
$829$	−7.45885	−	4.30637i	−0.259056	−	0.149566i	−0.623904	+	0.781501i	$0.714454\pi$
$830$	−6.70099	−	1.18157i	−0.232595	−	0.0410127i
$831$	54.1568	−	45.4430i	1.87868	−	1.57640i
$832$	−2.80748	−	2.35576i	−0.0973318	−	0.0816711i
$833$	−48.9203	+	8.62596i	−1.69499	+	0.298872i
$834$	−51.9808	−	18.9195i	−1.79995	−	0.655127i
$835$	−1.86347			−0.0644879
$836$	7.87131	−	12.1261i	0.272235	−	0.419390i
$837$	−72.2749			−2.49818
$838$	1.37779	+	0.501473i	0.0475948	+	0.0173231i
$839$	−32.4599	+	5.72355i	−1.12064	+	0.197599i	−0.703121	−	0.711070i	$-0.748211\pi$
$839$	−32.4599	+	5.72355i	−1.12064	+	0.197599i	−0.417518	+	0.908669i	$0.637100\pi$
$840$	0.870934	+	0.730801i	0.0300501	+	0.0252150i
$841$	−10.1710	+	8.53445i	−0.350723	+	0.294291i
$842$	33.7064	+	5.94335i	1.16160	+	0.204821i
$843$	56.7672	+	32.7746i	1.95517	+	1.12882i
$844$	4.73797	+	8.20641i	0.163088	+	0.282476i
$845$	0.202708	−	0.0737797i	0.00697337	−	0.00253810i
$846$	14.9847	−	5.45400i	0.515186	−	0.187512i
$847$	−8.60803	−	0.991513i	−0.295776	−	0.0340688i
$848$	9.70624	+	5.60390i	0.333314	+	0.192439i
$849$	4.60823	−	26.1346i	0.158154	−	0.896937i
$850$	−23.7751	−	28.3340i	−0.815478	−	0.971848i
$851$	−23.3458	+	27.8225i	−0.800285	+	0.953743i
$852$	−2.01011	−	11.3999i	−0.0688653	−	0.390554i
$853$	−14.6382	+	40.2180i	−0.501201	+	1.37704i	0.388902	+	0.921279i	$0.372855\pi$
$853$	−14.6382	+	40.2180i	−0.501201	+	1.37704i	−0.890103	+	0.455760i	$0.849368\pi$
$854$	3.04172			0.104085
$855$	−6.61953	+	9.55870i	−0.226383	+	0.326901i
$856$	1.61586			0.0552289
$857$	15.1134	+	5.50082i	0.516263	+	0.187904i	0.586994	−	0.809591i	$-0.300311\pi$
$857$	15.1134	+	5.50082i	0.516263	+	0.187904i	−0.0707314	+	0.997495i	$0.522533\pi$
$858$	−34.7279	−	5.05717i	−1.18559	−	0.172649i
$859$	28.5637	+	23.9678i	0.974580	+	0.817770i	0.983263	−	0.182192i	$-0.0583194\pi$
$859$	28.5637	+	23.9678i	0.974580	+	0.817770i	−0.00868267	+	0.999962i	$0.502764\pi$
$860$	1.92327	+	2.29206i	0.0655829	+	0.0781587i
$861$	−4.05086	+	22.9735i	−0.138053	+	0.782936i
$862$	13.9311	−	24.1294i	0.474495	−	0.821850i
$863$	−11.7449	+	6.78092i	−0.399801	+	0.230825i	−0.686398	−	0.727226i	$-0.740809\pi$
$863$	−11.7449	+	6.78092i	−0.399801	+	0.230825i	0.286597	+	0.958051i	$0.407476\pi$
$864$	−2.30667	−	6.33753i	−0.0784746	−	0.215607i
$865$	2.02589	−	0.737364i	0.0688824	−	0.0250711i
$866$	−16.0332	+	9.25675i	−0.544829	+	0.314557i
$867$	−109.097	−	62.9872i	−3.70513	−	2.13916i
$868$	1.46587	−	8.31338i	0.0497550	−	0.282174i
$869$	15.4401	−	6.14897i	0.523771	−	0.208589i
$870$	−3.67866	+	4.38406i	−0.124718	+	0.148634i
$871$	3.20031	−	0.564300i	0.108438	−	0.0191206i
$872$	−5.55498	−	2.02185i	−0.188115	−	0.0684684i
$873$			79.5843i			2.69352i
$874$	−12.4590	−	26.3609i	−0.421431	−	0.891671i
$875$		−	3.83940i		−	0.129796i
$876$	−19.8602	−	7.22854i	−0.671016	−	0.244230i
$877$	−8.89263	−	50.4326i	−0.300283	−	1.70299i	−0.644918	−	0.764252i	$-0.723108\pi$
$877$	−8.89263	−	50.4326i	−0.300283	−	1.70299i	0.344635	−	0.938737i	$-0.388003\pi$
$878$	−22.2787	−	18.6940i	−0.751869	−	0.630893i
$879$	−21.4176	−	25.5245i	−0.722399	−	0.860922i
$880$	−0.785652	+	1.46001i	−0.0264843	+	0.0492169i
$881$	−7.53399	+	13.0493i	−0.253827	+	0.439641i	−0.964576	−	0.263804i	$-0.915023\pi$
$881$	−7.53399	+	13.0493i	−0.253827	+	0.439641i	0.710749	+	0.703445i	$0.248356\pi$
$882$	17.0202	+	29.4799i	0.573101	+	0.992640i
$883$	−24.2866	+	8.83960i	−0.817309	+	0.297476i	−0.716639	−	0.697444i	$-0.754321\pi$
$883$	−24.2866	+	8.83960i	−0.817309	+	0.297476i	−0.100669	+	0.994920i	$0.532098\pi$
$884$	9.76035	+	26.8163i	0.328276	+	0.901931i
$885$	−2.33575	−	4.04564i	−0.0785154	−	0.135993i
$886$	−11.1555	+	19.3219i	−0.374776	+	0.649132i
$887$	−5.20281	+	29.5066i	−0.174693	+	0.990735i	0.763804	+	0.645448i	$0.223329\pi$
$887$	−5.20281	+	29.5066i	−0.174693	+	0.990735i	−0.938497	+	0.345287i	$0.887782\pi$
$888$	12.0090	−	10.0768i	0.402997	−	0.338155i
$889$	−9.66335	+	11.5163i	−0.324098	+	0.386245i
$890$	−0.968426	+	0.170760i	−0.0324617	+	0.00572388i
$891$	−9.01867	−	7.11876i	−0.302137	−	0.238488i
$892$		−	9.81577i		−	0.328656i
$893$	−12.5651	+	3.43668i	−0.420475	+	0.115004i
$894$	41.3550			1.38312
$895$	−0.251500	+	0.690990i	−0.00840672	+	0.0230973i
$896$	0.775755	−	0.136787i	0.0259162	−	0.00456972i
$897$	−45.4958	+	54.2198i	−1.51906	+	1.81035i
$898$	−20.3851	−	24.2940i	−0.680258	−	0.810700i
$899$	41.8474	+	7.37882i	1.39569	+	0.246098i
$900$	−12.6731	+	21.9504i	−0.422436	+	0.731681i
$901$	−43.6357	−	75.5792i	−1.45371	−	2.51791i
$902$	−34.0039	+	1.01793i	−1.13221	+	0.0338934i
$903$	−4.65578	−	12.7917i	−0.154935	−	0.425680i
$904$	−3.57076	+	2.06158i	−0.118762	+	0.0685671i
$905$	−1.07446	−	0.620339i	−0.0357162	−	0.0206208i
$906$	−26.5346	−	4.67876i	−0.881552	−	0.155441i
$907$	−15.5355	−	18.5144i	−0.515846	−	0.614762i	0.443747	−	0.896152i	$-0.353649\pi$
$907$	−15.5355	−	18.5144i	−0.515846	−	0.614762i	−0.959593	+	0.281390i	$0.909204\pi$
$908$	14.4123	+	12.0933i	0.478288	+	0.401331i
$909$	−47.4826	+	8.37247i	−1.57490	+	0.277697i
$910$	−0.493593	+	1.35614i	−0.0163624	+	0.0449555i
$911$		−	26.2708i		−	0.870390i	−0.900336	−	0.435195i	$-0.856679\pi$
$911$		−	26.2708i		−	0.870390i	0.900336	−	0.435195i	$-0.143321\pi$
$912$	3.32018	+	12.1391i	0.109942	+	0.401967i
$913$	−14.1640	+	42.8647i	−0.468759	+	1.41862i
$914$	−3.28290	+	9.01971i	−0.108589	+	0.298345i
$915$	−0.967773	−	5.48852i	−0.0319936	−	0.181445i
$916$	7.81042	+	6.55372i	0.258063	+	0.216541i
$917$	1.95221	−	1.63810i	0.0644677	−	0.0540948i
$918$	−9.11918	+	51.7174i	−0.300978	+	1.70693i
$919$	29.9493	+	17.2912i	0.987935	+	0.570385i	0.904656	−	0.426142i	$-0.140128\pi$
$919$	29.9493	+	17.2912i	0.987935	+	0.570385i	0.0832786	+	0.996526i	$0.473461\pi$
$920$	1.67192	+	2.89585i	0.0551216	+	0.0954734i
$921$	20.1180	+	55.2739i	0.662912	+	1.82134i
$922$	8.49804	+	23.3482i	0.279868	+	0.768931i
$923$	12.7253	−	7.34693i	0.418857	−	0.241827i
$924$	5.63064	−	5.01930i	0.185234	−	0.165123i
$925$	−25.3999	−	4.47869i	−0.835144	−	0.147258i
$926$	−11.5163	+	9.66336i	−0.378451	+	0.317558i
$927$	10.3216	−	12.3008i	0.339006	−	0.404011i
$928$	0.688548	+	3.90495i	0.0226027	+	0.128186i
$929$	−10.6555	−	3.87827i	−0.349595	−	0.127242i	0.161253	−	0.986913i	$-0.448446\pi$
$929$	−10.6555	−	3.87827i	−0.349595	−	0.127242i	−0.510848	+	0.859671i	$0.670669\pi$
$930$	−15.4672			−0.507188
$931$	−11.8824	−	25.1410i	−0.389430	−	0.823963i
$932$		−	12.8393i		−	0.420567i
$933$	12.8989	−	35.4393i	0.422290	−	1.16023i
$934$	5.41502	+	30.7101i	0.177185	+	1.00486i
$935$	10.9823	−	6.78669i	0.359159	−	0.221949i
$936$	14.9805	−	12.5701i	0.489652	−	0.410867i
$937$	25.7464	+	4.53978i	0.841098	+	0.148308i	0.577568	−	0.816343i	$-0.304002\pi$
$937$	25.7464	+	4.53978i	0.841098	+	0.148308i	0.263530	+	0.964651i	$0.415113\pi$
$938$	−0.349238	+	0.604897i	−0.0114030	+	0.0197506i
$939$	0.145362	−	0.0839245i	0.00474370	−	0.00273877i
$940$	1.40385	−	0.510960i	0.0457886	−	0.0166657i
$941$	−22.5350	+	8.20206i	−0.734619	+	0.267380i	−0.682119	−	0.731241i	$-0.738941\pi$
$941$	−22.5350	+	8.20206i	−0.734619	+	0.267380i	−0.0525004	+	0.998621i	$0.516719\pi$
$942$	3.03963	−	1.75493i	0.0990366	−	0.0571788i
$943$	−34.3053	+	59.4185i	−1.11713	+	1.93493i
$944$	−3.18750	−	0.562041i	−0.103744	−	0.0182929i
$945$	−2.03443	+	1.70709i	−0.0661801	+	0.0555317i
$946$	16.8870	−	10.4356i	0.549043	−	0.339290i
$947$	5.64264	+	32.0010i	0.183361	+	1.03989i	0.928043	+	0.372474i	$0.121490\pi$
$947$	5.64264	+	32.0010i	0.183361	+	1.03989i	−0.744681	+	0.667420i	$0.767399\pi$
$948$	−4.94823	+	13.5952i	−0.160711	+	0.441550i
$949$		−	26.8278i		−	0.870867i
$950$	11.7880	−	17.0220i	0.382453	−	0.552267i
$951$	−41.6344			−1.35009
$952$	−5.76382	−	2.09786i	−0.186806	−	0.0679920i
$953$	3.69961	+	20.9815i	0.119842	+	0.679659i	0.984238	+	0.176847i	$0.0565899\pi$
$953$	3.69961	+	20.9815i	0.119842	+	0.679659i	−0.864396	+	0.502811i	$0.832299\pi$
$954$	−38.4412	+	45.8125i	−1.24458	+	1.48323i
$955$	−5.02741	+	4.21850i	−0.162683	+	0.136507i
$956$	−12.6848	−	2.23667i	−0.410256	−	0.0723391i
$957$	25.2659	+	28.3432i	0.816730	+	0.916204i
$958$	−14.2020	+	8.19955i	−0.458847	+	0.264916i
$959$	1.06822	+	2.93490i	0.0344945	+	0.0947728i
$960$	−0.493639	−	1.35626i	−0.0159321	−	0.0437732i
$961$	41.9216	+	72.6104i	1.35231	+	2.34227i
$962$	17.2334	+	9.94971i	0.555627	+	0.320792i
$963$	−1.49721	+	8.49110i	−0.0482469	+	0.273622i
$964$	19.5266	−	16.3848i	0.628911	−	0.527719i
$965$	5.73079	+	4.80870i	0.184481	+	0.154798i
$966$	−2.64171	−	14.9819i	−0.0849955	−	0.482034i
$967$	−6.74565	+	18.5335i	−0.216926	+	0.595998i	−0.999652	−	0.0263674i	$-0.991606\pi$
$967$	−6.74565	+	18.5335i	−0.216926	+	0.595998i	0.782727	+	0.622366i	$0.213828\pi$
$968$	8.83435	+	6.55395i	0.283947	+	0.210652i
$969$	24.8722	−	94.7862i	0.799012	−	3.04497i
$970$			7.45589i			0.239394i
$971$	−4.49698	+	12.3554i	−0.144315	+	0.396502i	−0.990699	−	0.136071i	$-0.956553\pi$
$971$	−4.49698	+	12.3554i	−0.144315	+	0.396502i	0.846384	+	0.532573i	$0.178775\pi$
$972$	−10.0753	+	1.77655i	−0.323166	+	0.0569828i
$973$	11.5613	+	9.70110i	0.370639	+	0.311003i
$974$	−1.03581	−	1.23442i	−0.0331893	−	0.0395535i
$975$	−49.4987	−	8.72796i	−1.58523	−	0.279518i
$976$	−3.34407	−	1.93070i	−0.107041	−	0.0618003i
$977$	17.3067	−	9.99203i	0.553690	−	0.319673i	−0.196919	−	0.980420i	$-0.563094\pi$
$977$	17.3067	−	9.99203i	0.553690	−	0.319673i	0.750609	+	0.660747i	$0.229760\pi$
$978$	−7.48212	−	20.5570i	−0.239252	−	0.657339i
$979$	0.195221	+	6.52132i	0.00623929	+	0.208422i
$980$	1.59455	+	2.76184i	0.0509360	+	0.0882237i
$981$	15.7716	−	27.3172i	0.503549	−	0.872172i
$982$	−6.34089	−	1.11807i	−0.202346	−	0.0356790i
$983$	6.24814	+	7.44624i	0.199285	+	0.237498i	0.856427	−	0.516268i	$-0.172679\pi$
$983$	6.24814	+	7.44624i	0.199285	+	0.237498i	−0.657142	+	0.753767i	$0.728235\pi$
$984$	19.0358	−	22.6860i	0.606839	−	0.723202i
$985$	10.4496	−	1.84254i	0.332951	−	0.0587082i
$986$	10.5601	−	29.0136i	0.336301	−	0.923980i
$987$	−6.79680			−0.216344
$988$	−13.0383	+	9.23053i	−0.414802	+	0.293662i
$989$		−	40.0364i		−	1.27308i
$990$	−6.94418	−	5.48129i	−0.220700	−	0.174207i
$991$	36.0836	−	6.36251i	1.14623	−	0.202112i	0.431902	−	0.901921i	$-0.357843\pi$
$991$	36.0836	−	6.36251i	1.14623	−	0.202112i	0.714330	+	0.699809i	$0.246732\pi$
$992$	−6.88843	+	8.20931i	−0.218708	+	0.260646i
$993$	15.7836	−	13.2440i	0.500878	−	0.420286i
$994$	−0.548424	+	3.11027i	−0.0173950	+	0.0986518i
$995$	−5.31989	+	9.21431i	−0.168652	+	0.292113i
$996$	−19.6496	−	34.0340i	−0.622620	−	1.07841i
$997$	−13.3167	−	36.5872i	−0.421743	−	1.15873i	−0.950708	−	0.310086i	$-0.899642\pi$
$997$	−13.3167	−	36.5872i	−0.421743	−	1.15873i	0.528965	−	0.848643i	$-0.322580\pi$
$998$	17.2771	−	6.28835i	0.546897	−	0.199054i
$999$	18.3097	+	31.7134i	0.579295	+	1.00337i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.q.b.395.10	yes	60
11.10	odd	2		418.2.q.a.395.10	yes	60
19.14	odd	18		418.2.q.a.109.10	✓	60
209.109	even	18	inner	418.2.q.b.109.10	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.q.a.109.10	✓	60	19.14	odd	18
418.2.q.a.395.10	yes	60	11.10	odd	2
418.2.q.b.109.10	yes	60	209.109	even	18	inner
418.2.q.b.395.10	yes	60	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.q (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{2} +(2.84334 - 0.501357i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.382944 + 0.321328i) q^{5} +(-2.84334 - 0.501357i) q^{6} +(0.682188 + 0.393861i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(5.01412 - 1.82499i) q^{9} +O(q^{10})\)	\(q+(-0.939693 - 0.342020i) q^{2} +(2.84334 - 0.501357i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.382944 + 0.321328i) q^{5} +(-2.84334 - 0.501357i) q^{6} +(0.682188 + 0.393861i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(5.01412 - 1.82499i) q^{9} +(0.469750 - 0.170975i) q^{10} +(-0.673402 - 3.24754i) q^{11} +(2.50039 + 1.44360i) q^{12} +(-0.636404 + 3.60923i) q^{13} +(-0.506338 - 0.603431i) q^{14} +(-0.927739 + 1.10564i) q^{15} +(0.173648 + 0.984808i) q^{16} +(2.66319 - 7.31706i) q^{17} -5.33592 q^{18} +(4.34422 + 0.357400i) q^{19} -0.499898 q^{20} +(2.13715 + 0.777861i) q^{21} +(-0.477934 + 3.28201i) q^{22} +(5.12411 + 4.29964i) q^{23} +(-1.85586 - 2.21172i) q^{24} +(-0.824847 + 4.67794i) q^{25} +(1.83245 - 3.17390i) q^{26} +(5.84070 - 3.37213i) q^{27} +(0.269417 + 0.740217i) q^{28} +(-3.72606 + 1.35618i) q^{29} +(1.24994 - 0.721652i) q^{30} +(-9.28076 - 5.35825i) q^{31} +(0.173648 - 0.984808i) q^{32} +(-3.54288 - 8.89624i) q^{33} +(-5.00517 + 5.96493i) q^{34} +(-0.387799 + 0.0683793i) q^{35} +(5.01412 + 1.82499i) q^{36} +5.42973i q^{37} +(-3.96000 - 1.82166i) q^{38} +10.5813i q^{39} +(0.469750 + 0.170975i) q^{40} +(1.78113 + 10.1013i) q^{41} +(-1.74222 - 1.46190i) q^{42} +(-3.84732 - 4.58506i) q^{43} +(1.57162 - 2.92062i) q^{44} +(-1.33371 + 2.31005i) q^{45} +(-3.34452 - 5.79289i) q^{46} +(-2.80828 + 1.02213i) q^{47} +(0.987480 + 2.71308i) q^{48} +(-3.18975 - 5.52480i) q^{49} +(2.37505 - 4.11371i) q^{50} +(3.90389 - 22.1401i) q^{51} +(-2.80748 + 2.35576i) q^{52} +(7.20424 - 8.58567i) q^{53} +(-6.64180 + 1.17113i) q^{54} +(1.30140 + 1.02724i) q^{55} -0.787723i q^{56} +(12.5313 - 1.16180i) q^{57} +3.96519 q^{58} +(-1.10701 + 3.04147i) q^{59} +(-1.42138 + 0.250627i) q^{60} +(-2.48206 + 2.95801i) q^{61} +(6.88843 + 8.20931i) q^{62} +(4.13937 + 0.729882i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.916039 - 1.58663i) q^{65} +(0.286529 + 9.57147i) q^{66} +(-0.303270 - 0.833227i) q^{67} +(6.74344 - 3.89333i) q^{68} +(16.7252 + 9.65631i) q^{69} +(0.387799 + 0.0683793i) q^{70} +(-2.57716 - 3.07134i) q^{71} +(-4.08755 - 3.42986i) q^{72} +(-7.20898 + 1.27114i) q^{73} +(1.85708 - 5.10227i) q^{74} +13.7145i q^{75} +(3.09814 + 3.06620i) q^{76} +(0.819695 - 2.48066i) q^{77} +(3.61902 - 9.94318i) q^{78} +(0.870146 + 4.93484i) q^{79} +(-0.382944 - 0.321328i) q^{80} +(2.65379 - 2.22679i) q^{81} +(1.78113 - 10.1013i) q^{82} +(-11.7879 - 6.80575i) q^{83} +(1.13716 + 1.96961i) q^{84} +(1.33133 + 3.65779i) q^{85} +(2.04712 + 5.62441i) q^{86} +(-9.91452 + 5.72415i) q^{87} +(-2.47575 + 2.20695i) q^{88} +(-1.93725 - 0.341589i) q^{89} +(2.04336 - 1.71458i) q^{90} +(-1.85568 + 2.21152i) q^{91} +(1.16154 + 6.58743i) q^{92} +(-29.0747 - 10.5823i) q^{93} +2.98851 q^{94} +(-1.77844 + 1.25906i) q^{95} -2.88720i q^{96} +(-5.10117 + 14.0153i) q^{97} +(1.10779 + 6.28257i) q^{98} +(-9.30326 - 15.0546i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 3 q^{3} + 3 q^{6} + 18 q^{7} - 30 q^{8} - 3 q^{9}+O(q^{10}) \) 60 * q - 3 * q^3 + 3 * q^6 + 18 * q^7 - 30 * q^8 - 3 * q^9	\( 60 q - 3 q^{3} + 3 q^{6} + 18 q^{7} - 30 q^{8} - 3 q^{9} + 3 q^{11} - 6 q^{13} - 12 q^{14} + 24 q^{15} + 6 q^{17} - 60 q^{18} + 30 q^{19} - 12 q^{20} - 12 q^{21} + 12 q^{22} - 3 q^{24} - 12 q^{25} + 6 q^{26} + 9 q^{27} - 6 q^{28} + 3 q^{29} - 9 q^{31} + 9 q^{33} - 6 q^{34} + 24 q^{35} - 3 q^{36} + 6 q^{38} - 15 q^{41} + 6 q^{42} + 3 q^{43} - 12 q^{44} - 48 q^{45} - 3 q^{46} + 54 q^{47} - 6 q^{48} + 6 q^{49} - 36 q^{50} + 45 q^{51} + 3 q^{52} + 24 q^{53} + 27 q^{54} - 48 q^{55} - 30 q^{57} + 24 q^{58} - 39 q^{59} + 12 q^{60} - 54 q^{61} + 66 q^{63} - 30 q^{64} - 30 q^{66} + 9 q^{67} + 27 q^{68} + 54 q^{69} - 24 q^{70} - 33 q^{71} + 6 q^{72} - 12 q^{74} + 18 q^{77} - 36 q^{79} - 93 q^{81} - 15 q^{82} + 36 q^{83} - 24 q^{84} + 60 q^{85} - 3 q^{86} - 54 q^{87} + 3 q^{88} - 3 q^{89} + 24 q^{90} - 12 q^{91} - 102 q^{93} + 12 q^{94} - 24 q^{95} - 6 q^{97} + 18 q^{98} + 75 q^{99}+O(q^{100}) \) 60 * q - 3 * q^3 + 3 * q^6 + 18 * q^7 - 30 * q^8 - 3 * q^9 + 3 * q^11 - 6 * q^13 - 12 * q^14 + 24 * q^15 + 6 * q^17 - 60 * q^18 + 30 * q^19 - 12 * q^20 - 12 * q^21 + 12 * q^22 - 3 * q^24 - 12 * q^25 + 6 * q^26 + 9 * q^27 - 6 * q^28 + 3 * q^29 - 9 * q^31 + 9 * q^33 - 6 * q^34 + 24 * q^35 - 3 * q^36 + 6 * q^38 - 15 * q^41 + 6 * q^42 + 3 * q^43 - 12 * q^44 - 48 * q^45 - 3 * q^46 + 54 * q^47 - 6 * q^48 + 6 * q^49 - 36 * q^50 + 45 * q^51 + 3 * q^52 + 24 * q^53 + 27 * q^54 - 48 * q^55 - 30 * q^57 + 24 * q^58 - 39 * q^59 + 12 * q^60 - 54 * q^61 + 66 * q^63 - 30 * q^64 - 30 * q^66 + 9 * q^67 + 27 * q^68 + 54 * q^69 - 24 * q^70 - 33 * q^71 + 6 * q^72 - 12 * q^74 + 18 * q^77 - 36 * q^79 - 93 * q^81 - 15 * q^82 + 36 * q^83 - 24 * q^84 + 60 * q^85 - 3 * q^86 - 54 * q^87 + 3 * q^88 - 3 * q^89 + 24 * q^90 - 12 * q^91 - 102 * q^93 + 12 * q^94 - 24 * q^95 - 6 * q^97 + 18 * q^98 + 75 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more