LMFDB - Embedded newform 690.2.q.a.401.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(11,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 0, 9]))

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

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

chi := DirichletCharacter("690.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.q (of order $22$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$16$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			401.3
Character	$\chi$	$=$	690.401
Dual form			690.2.q.a.191.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.755750 + 0.654861i) q^{2} +(-0.906618 - 1.47582i) q^{3} +(0.142315 - 0.989821i) q^{4} +(0.415415 - 0.909632i) q^{5} +(1.65163 + 0.521642i) q^{6} +(-0.302591 + 1.03053i) q^{7} +(0.540641 + 0.841254i) q^{8} +(-1.35609 + 2.67601i) q^{9} +O(q^{10})$	\(q+(-0.755750 + 0.654861i) q^{2} +(-0.906618 - 1.47582i) q^{3} +(0.142315 - 0.989821i) q^{4} +(0.415415 - 0.909632i) q^{5} +(1.65163 + 0.521642i) q^{6} +(-0.302591 + 1.03053i) q^{7} +(0.540641 + 0.841254i) q^{8} +(-1.35609 + 2.67601i) q^{9} +(0.281733 + 0.959493i) q^{10} +(-1.53145 + 1.76739i) q^{11} +(-1.58982 + 0.687359i) q^{12} +(-0.0134436 + 0.00394741i) q^{13} +(-0.446170 - 0.976977i) q^{14} +(-1.71908 + 0.211611i) q^{15} +(-0.959493 - 0.281733i) q^{16} +(0.929456 + 6.46451i) q^{17} +(-0.727550 - 2.91044i) q^{18} +(4.39590 + 0.632035i) q^{19} +(-0.841254 - 0.540641i) q^{20} +(1.79521 - 0.487727i) q^{21} -2.33859i q^{22} +(-4.70867 + 0.910179i) q^{23} +(0.751384 - 1.56058i) q^{24} +(-0.654861 - 0.755750i) q^{25} +(0.00757502 - 0.0117870i) q^{26} +(5.17876 - 0.424774i) q^{27} +(0.976977 + 0.446170i) q^{28} +(-1.21072 + 0.174075i) q^{29} +(1.16062 - 1.28568i) q^{30} +(7.53581 - 4.84297i) q^{31} +(0.909632 - 0.415415i) q^{32} +(3.99679 + 0.657801i) q^{33} +(-4.93579 - 4.27688i) q^{34} +(0.811701 + 0.703343i) q^{35} +(2.45578 + 1.72312i) q^{36} +(-5.17188 + 2.36192i) q^{37} +(-3.73610 + 2.40104i) q^{38} +(0.0180139 + 0.0162616i) q^{39} +(0.989821 - 0.142315i) q^{40} +(10.5420 + 4.81437i) q^{41} +(-1.03734 + 1.54421i) q^{42} +(4.90256 - 7.62854i) q^{43} +(1.53145 + 1.76739i) q^{44} +(1.87084 + 2.34520i) q^{45} +(2.96254 - 3.77139i) q^{46} +8.17538i q^{47} +(0.454107 + 1.67146i) q^{48} +(4.91835 + 3.16083i) q^{49} +(0.989821 + 0.142315i) q^{50} +(8.69779 - 7.23255i) q^{51} +(0.00199400 + 0.0138686i) q^{52} +(-2.01187 - 0.590738i) q^{53} +(-3.63568 + 3.71239i) q^{54} +(0.971487 + 2.12726i) q^{55} +(-1.03053 + 0.302591i) q^{56} +(-3.05263 - 7.06057i) q^{57} +(0.801006 - 0.924411i) q^{58} +(0.995592 + 3.39068i) q^{59} +(-0.0351932 + 1.73169i) q^{60} +(5.07022 + 7.88942i) q^{61} +(-2.52371 + 8.59497i) q^{62} +(-2.34736 - 2.20722i) q^{63} +(-0.415415 + 0.909632i) q^{64} +(-0.00199400 + 0.0138686i) q^{65} +(-3.45134 + 2.12021i) q^{66} +(-0.926160 + 0.802522i) q^{67} +6.53098 q^{68} +(5.61222 + 6.12397i) q^{69} -1.07403 q^{70} +(-5.50372 + 4.76900i) q^{71} +(-2.98436 + 0.305945i) q^{72} +(-2.10508 + 14.6412i) q^{73} +(2.36192 - 5.17188i) q^{74} +(-0.521642 + 1.65163i) q^{75} +(1.25120 - 4.26121i) q^{76} +(-1.35794 - 2.11300i) q^{77} +(-0.0242631 - 0.000493098i) q^{78} +(0.0735815 + 0.250596i) q^{79} +(-0.654861 + 0.755750i) q^{80} +(-5.32205 - 7.25781i) q^{81} +(-11.1199 + 3.26509i) q^{82} +(-4.63306 - 10.1450i) q^{83} +(-0.227277 - 1.84635i) q^{84} +(6.26643 + 1.83999i) q^{85} +(1.29052 + 8.97576i) q^{86} +(1.35456 + 1.62899i) q^{87} +(-2.31479 - 0.332817i) q^{88} +(-1.80462 - 1.15976i) q^{89} +(-2.94967 - 0.547239i) q^{90} -0.0150485i q^{91} +(0.230801 + 4.79027i) q^{92} +(-13.9794 - 6.73077i) q^{93} +(-5.35373 - 6.17854i) q^{94} +(2.40104 - 3.73610i) q^{95} +(-1.43777 - 0.965830i) q^{96} +(-6.66361 - 3.04317i) q^{97} +(-5.78694 + 0.832036i) q^{98} +(-2.65277 - 6.49492i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9}+O(q^{10}) $ 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9	$ 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9} - 12 q^{11} - 12 q^{14} - 16 q^{16} - 8 q^{18} + 16 q^{20} + 62 q^{21} + 4 q^{23} + 2 q^{24} - 16 q^{25} + 42 q^{27} - 2 q^{30} - 4 q^{31} + 16 q^{33} + 2 q^{36} + 72 q^{38} - 124 q^{39} + 44 q^{41} + 44 q^{43} + 12 q^{44} - 2 q^{45} + 4 q^{46} + 70 q^{49} - 2 q^{51} - 52 q^{53} + 92 q^{54} + 10 q^{55} - 54 q^{56} - 38 q^{57} - 36 q^{58} - 44 q^{61} - 220 q^{63} + 16 q^{64} - 34 q^{66} - 44 q^{67} + 22 q^{69} - 12 q^{70} - 36 q^{72} - 28 q^{73} - 24 q^{74} - 88 q^{77} - 54 q^{78} - 44 q^{79} - 16 q^{80} - 66 q^{81} - 28 q^{82} + 4 q^{83} - 18 q^{84} + 158 q^{86} - 64 q^{87} + 80 q^{89} - 8 q^{90} - 4 q^{92} + 4 q^{93} + 24 q^{94} - 2 q^{96} - 88 q^{98} + 190 q^{99}+O(q^{100}) $ 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9 - 12 * q^11 - 12 * q^14 - 16 * q^16 - 8 * q^18 + 16 * q^20 + 62 * q^21 + 4 * q^23 + 2 * q^24 - 16 * q^25 + 42 * q^27 - 2 * q^30 - 4 * q^31 + 16 * q^33 + 2 * q^36 + 72 * q^38 - 124 * q^39 + 44 * q^41 + 44 * q^43 + 12 * q^44 - 2 * q^45 + 4 * q^46 + 70 * q^49 - 2 * q^51 - 52 * q^53 + 92 * q^54 + 10 * q^55 - 54 * q^56 - 38 * q^57 - 36 * q^58 - 44 * q^61 - 220 * q^63 + 16 * q^64 - 34 * q^66 - 44 * q^67 + 22 * q^69 - 12 * q^70 - 36 * q^72 - 28 * q^73 - 24 * q^74 - 88 * q^77 - 54 * q^78 - 44 * q^79 - 16 * q^80 - 66 * q^81 - 28 * q^82 + 4 * q^83 - 18 * q^84 + 158 * q^86 - 64 * q^87 + 80 * q^89 - 8 * q^90 - 4 * q^92 + 4 * q^93 + 24 * q^94 - 2 * q^96 - 88 * q^98 + 190 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{22}\right)$

Coefficient data

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

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

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

$2$	−0.755750	+	0.654861i	−0.534396	+	0.463056i
$2$	−0.755750	+	0.654861i	−0.534396	+	0.463056i
$3$	−0.906618	−	1.47582i	−0.523436	−	0.852065i
$3$	−0.906618	−	1.47582i	−0.523436	−	0.852065i
$4$	0.142315	−	0.989821i	0.0711574	−	0.494911i
$5$	0.415415	−	0.909632i	0.185779	−	0.406800i
$5$	0.415415	−	0.909632i	0.185779	−	0.406800i
$6$	1.65163	+	0.521642i	0.674276	+	0.212959i
$7$	−0.302591	+	1.03053i	−0.114369	+	0.389503i	−0.996705	−	0.0811164i	$-0.974151\pi$
$7$	−0.302591	+	1.03053i	−0.114369	+	0.389503i	0.882336	+	0.470620i	$0.155970\pi$
$8$	0.540641	+	0.841254i	0.191145	+	0.297428i
$9$	−1.35609	+	2.67601i	−0.452030	+	0.892003i
$10$	0.281733	+	0.959493i	0.0890917	+	0.303418i
$11$	−1.53145	+	1.76739i	−0.461751	+	0.532889i	−0.938099	−	0.346368i	$-0.887415\pi$
$11$	−1.53145	+	1.76739i	−0.461751	+	0.532889i	0.476348	+	0.879257i	$0.341960\pi$
$12$	−1.58982	+	0.687359i	−0.458942	+	0.198423i
$13$	−0.0134436	+	0.00394741i	−0.00372859	+	0.00109481i	−0.283596	−	0.958944i	$-0.591528\pi$
$13$	−0.0134436	+	0.00394741i	−0.00372859	+	0.00109481i	0.279868	+	0.960039i	$0.409709\pi$
$14$	−0.446170	−	0.976977i	−0.119244	−	0.261108i
$15$	−1.71908	+	0.211611i	−0.443863	+	0.0546376i
$16$	−0.959493	−	0.281733i	−0.239873	−	0.0704331i
$17$	0.929456	+	6.46451i	0.225426	+	1.56787i	0.717022	+	0.697050i	$0.245504\pi$
$17$	0.929456	+	6.46451i	0.225426	+	1.56787i	−0.491596	+	0.870823i	$0.663586\pi$
$18$	−0.727550	−	2.91044i	−0.171485	−	0.685998i
$19$	4.39590	+	0.632035i	1.00849	+	0.144999i	0.626708	−	0.779254i	$-0.284402\pi$
$19$	4.39590	+	0.632035i	1.00849	+	0.144999i	0.381781	+	0.924253i	$0.375311\pi$
$20$	−0.841254	−	0.540641i	−0.188110	−	0.120891i
$21$	1.79521	−	0.487727i	0.391747	−	0.106431i
$22$		−	2.33859i		−	0.498590i
$23$	−4.70867	+	0.910179i	−0.981826	+	0.189785i
$23$	−4.70867	+	0.910179i	−0.981826	+	0.189785i
$24$	0.751384	−	1.56058i	0.153376	−	0.318553i
$25$	−0.654861	−	0.755750i	−0.130972	−	0.151150i
$26$	0.00757502	−	0.0117870i	0.00148558	−	0.00231161i
$27$	5.17876	−	0.424774i	0.996653	−	0.0817478i
$28$	0.976977	+	0.446170i	0.184631	+	0.0843183i
$29$	−1.21072	+	0.174075i	−0.224825	+	0.0323250i	−0.253807	−	0.967255i	$-0.581683\pi$
$29$	−1.21072	+	0.174075i	−0.224825	+	0.0323250i	0.0289815	+	0.999580i	$0.490774\pi$
$30$	1.16062	−	1.28568i	0.211898	−	0.234732i
$31$	7.53581	−	4.84297i	1.35347	−	0.869823i	0.355574	−	0.934648i	$-0.384285\pi$
$31$	7.53581	−	4.84297i	1.35347	−	0.869823i	0.997897	+	0.0648254i	$0.0206490\pi$
$32$	0.909632	−	0.415415i	0.160802	−	0.0734357i
$33$	3.99679	+	0.657801i	0.695753	+	0.114508i
$34$	−4.93579	−	4.27688i	−0.846481	−	0.733480i
$35$	0.811701	+	0.703343i	0.137203	+	0.118887i
$36$	2.45578	+	1.72312i	0.409297	+	0.287187i
$37$	−5.17188	+	2.36192i	−0.850253	+	0.388297i	−0.792381	−	0.610027i	$-0.791159\pi$
$37$	−5.17188	+	2.36192i	−0.850253	+	0.388297i	−0.0578717	+	0.998324i	$0.518431\pi$
$38$	−3.73610	+	2.40104i	−0.606075	+	0.389501i
$39$	0.0180139	+	0.0162616i	0.00288453	+	0.00260394i
$40$	0.989821	−	0.142315i	0.156505	−	0.0225020i
$41$	10.5420	+	4.81437i	1.64638	+	0.751879i	0.999939	−	0.0110812i	$-0.00352733\pi$
$41$	10.5420	+	4.81437i	1.64638	+	0.751879i	0.646446	+	0.762960i	$0.276255\pi$
$42$	−1.03734	+	1.54421i	−0.160064	+	0.238277i
$43$	4.90256	−	7.62854i	0.747634	−	1.16334i	−0.233939	−	0.972251i	$-0.575161\pi$
$43$	4.90256	−	7.62854i	0.747634	−	1.16334i	0.981573	−	0.191090i	$-0.0612022\pi$
$44$	1.53145	+	1.76739i	0.230875	+	0.266444i
$45$	1.87084	+	2.34520i	0.278889	+	0.349601i
$46$	2.96254	−	3.77139i	0.436802	−	0.556061i
$47$			8.17538i			1.19250i	0.802798	+	0.596251i	$0.203344\pi$
$47$			8.17538i			1.19250i	−0.802798	+	0.596251i	$0.796656\pi$
$48$	0.454107	+	1.67146i	0.0655447	+	0.241255i
$49$	4.91835	+	3.16083i	0.702621	+	0.451547i
$50$	0.989821	+	0.142315i	0.139982	+	0.0201264i
$51$	8.69779	−	7.23255i	1.21793	−	1.01276i
$52$	0.00199400	+	0.0138686i	0.000276518	+	0.00192322i
$53$	−2.01187	−	0.590738i	−0.276351	−	0.0811441i	0.140620	−	0.990064i	$-0.455090\pi$
$53$	−2.01187	−	0.590738i	−0.276351	−	0.0811441i	−0.416972	+	0.908920i	$0.636909\pi$
$54$	−3.63568	+	3.71239i	−0.494753	+	0.505192i
$55$	0.971487	+	2.12726i	0.130995	+	0.286840i
$56$	−1.03053	+	0.302591i	−0.137710	+	0.0404354i
$57$	−3.05263	−	7.06057i	−0.404331	−	0.935196i
$58$	0.801006	−	0.924411i	0.105177	−	0.121381i
$59$	0.995592	+	3.39068i	0.129615	+	0.441428i	0.998570	−	0.0534631i	$-0.0170260\pi$
$59$	0.995592	+	3.39068i	0.129615	+	0.441428i	−0.868955	+	0.494892i	$0.835208\pi$
$60$	−0.0351932	+	1.73169i	−0.00454342	+	0.223561i
$61$	5.07022	+	7.88942i	0.649175	+	1.01014i	0.997353	+	0.0727078i	$0.0231640\pi$
$61$	5.07022	+	7.88942i	0.649175	+	1.01014i	−0.348178	+	0.937428i	$0.613200\pi$
$62$	−2.52371	+	8.59497i	−0.320512	+	1.09156i
$63$	−2.34736	−	2.20722i	−0.295740	−	0.278084i
$64$	−0.415415	+	0.909632i	−0.0519269	+	0.113704i
$65$	−0.00199400	+	0.0138686i	−0.000247325	+	0.00172018i
$66$	−3.45134	+	2.12021i	−0.424831	+	0.260980i
$67$	−0.926160	+	0.802522i	−0.113148	+	0.0980437i	−0.709598	−	0.704607i	$-0.751123\pi$
$67$	−0.926160	+	0.802522i	−0.113148	+	0.0980437i	0.596449	+	0.802651i	$0.296578\pi$
$68$	6.53098			0.791998
$69$	5.61222	+	6.12397i	0.675632	+	0.737239i
$70$	−1.07403			−0.128372
$71$	−5.50372	+	4.76900i	−0.653172	+	0.565977i	−0.917145	−	0.398553i	$-0.869512\pi$
$71$	−5.50372	+	4.76900i	−0.653172	+	0.565977i	0.263973	+	0.964530i	$0.414967\pi$
$72$	−2.98436	+	0.305945i	−0.351710	+	0.0360560i
$73$	−2.10508	+	14.6412i	−0.246381	+	1.71362i	0.372415	+	0.928066i	$0.378530\pi$
$73$	−2.10508	+	14.6412i	−0.246381	+	1.71362i	−0.618796	+	0.785552i	$0.712379\pi$
$74$	2.36192	−	5.17188i	0.274568	−	0.601219i
$75$	−0.521642	+	1.65163i	−0.0602340	+	0.190714i
$76$	1.25120	−	4.26121i	0.143523	−	0.488794i
$77$	−1.35794	−	2.11300i	−0.154752	−	0.240799i
$78$	−0.0242631		0.000493098i	−0.00274725		5.58324e-5i
$79$	0.0735815	+	0.250596i	0.00827856	+	0.0281942i	0.963529	−	0.267605i	$-0.0862322\pi$
$79$	0.0735815	+	0.250596i	0.00827856	+	0.0281942i	−0.955250	+	0.295799i	$0.904414\pi$
$80$	−0.654861	+	0.755750i	−0.0732157	+	0.0844954i
$81$	−5.32205	−	7.25781i	−0.591338	−	0.806423i
$82$	−11.1199	+	3.26509i	−1.22798	+	0.360568i
$83$	−4.63306	−	10.1450i	−0.508545	−	1.11356i	−0.973597	−	0.228274i	$-0.926692\pi$
$83$	−4.63306	−	10.1450i	−0.508545	−	1.11356i	0.465052	−	0.885283i	$-0.346036\pi$
$84$	−0.227277	−	1.84635i	−0.0247980	−	0.201453i
$85$	6.26643	+	1.83999i	0.679690	+	0.199575i
$86$	1.29052	+	8.97576i	0.139160	+	0.967881i
$87$	1.35456	+	1.62899i	0.145225	+	0.174646i
$88$	−2.31479	−	0.332817i	−0.246757	−	0.0354784i
$89$	−1.80462	−	1.15976i	−0.191289	−	0.122934i	0.441491	−	0.897266i	$-0.354450\pi$
$89$	−1.80462	−	1.15976i	−0.191289	−	0.122934i	−0.632780	+	0.774332i	$0.718086\pi$
$90$	−2.94967	−	0.547239i	−0.310922	−	0.0576840i
$91$		−	0.0150485i		−	0.00157751i
$92$	0.230801	+	4.79027i	0.0240626	+	0.499421i
$93$	−13.9794	−	6.73077i	−1.44960	−	0.697948i
$94$	−5.35373	−	6.17854i	−0.552196	−	0.637268i
$95$	2.40104	−	3.73610i	0.246342	−	0.383315i
$96$	−1.43777	−	0.965830i	−0.146741	−	0.0985747i
$97$	−6.66361	−	3.04317i	−0.676587	−	0.308987i	0.0473247	−	0.998880i	$-0.484930\pi$
$97$	−6.66361	−	3.04317i	−0.676587	−	0.308987i	−0.723912	+	0.689893i	$0.757658\pi$
$98$	−5.78694	+	0.832036i	−0.584569	+	0.0840484i
$99$	−2.65277	−	6.49492i	−0.266613	−	0.652764i
$100$	−0.841254	+	0.540641i	−0.0841254	+	0.0540641i
$101$	0.905175	−	0.413380i	0.0900683	−	0.0411328i	−0.369871	−	0.929083i	$-0.620598\pi$
$101$	0.905175	−	0.413380i	0.0900683	−	0.0411328i	0.459940	+	0.887950i	$0.347871\pi$
$102$	−1.83704	+	11.1618i	−0.181894	+	1.10519i
$103$	−1.32813	−	1.15084i	−0.130865	−	0.113395i	0.586969	−	0.809609i	$-0.300321\pi$
$103$	−1.32813	−	1.15084i	−0.130865	−	0.113395i	−0.717834	+	0.696214i	$0.754866\pi$
$104$	−0.0105889	−	0.00917538i	−0.00103833	−	0.000899720i
$105$	0.302105	−	1.83559i	0.0294825	−	0.179135i
$106$	1.90732	−	0.871043i	0.185255	−	0.0846032i
$107$	−1.64647	+	1.05812i	−0.159170	+	0.102292i	−0.617801	−	0.786334i	$-0.711976\pi$
$107$	−1.64647	+	1.05812i	−0.159170	+	0.102292i	0.458631	+	0.888627i	$0.348340\pi$
$108$	0.316564	−	5.18650i	0.0304614	−	0.499071i
$109$	14.8069	−	2.12891i	1.41824	−	0.203913i	0.609832	−	0.792531i	$-0.291237\pi$
$109$	14.8069	−	2.12891i	1.41824	−	0.203913i	0.808411	+	0.588618i	$0.200328\pi$
$110$	−2.12726	−	0.971487i	−0.202826	−	0.0926276i
$111$	8.17469	+	5.49141i	0.775907	+	0.521222i
$112$	0.580667	−	0.903536i	0.0548679	−	0.0853761i
$113$	2.73528	+	3.15668i	0.257314	+	0.296956i	0.869678	−	0.493620i	$-0.164327\pi$
$113$	2.73528	+	3.15668i	0.257314	+	0.296956i	−0.612364	+	0.790576i	$0.709781\pi$
$114$	6.93072	+	3.33698i	0.649121	+	0.312536i
$115$	−1.12812	+	4.66126i	−0.105198	+	0.434665i
$116$			1.22317i			0.113569i
$117$	0.00766747	−	0.0413283i	0.000708858	−	0.00382080i
$118$	−2.97284	−	1.91053i	−0.273672	−	0.175878i
$119$	−6.94311	−	0.998268i	−0.636474	−	0.0915111i
$120$	−1.10742	−	1.33177i	−0.101093	−	0.121574i
$121$	0.787140	+	5.47468i	0.0715582	+	0.497698i
$122$	−8.99828	−	2.64213i	−0.814666	−	0.239208i
$123$	−2.45242	−	19.9229i	−0.221127	−	1.79639i
$124$	−3.72122	−	8.14833i	−0.334175	−	0.731741i
$125$	−0.959493	+	0.281733i	−0.0858197	+	0.0251989i
$126$	3.21944	+	0.130912i	0.286811	+	0.0116625i
$127$	2.33453	−	2.69419i	0.207156	−	0.239071i	−0.642658	−	0.766153i	$-0.722168\pi$
$127$	2.33453	−	2.69419i	0.207156	−	0.239071i	0.849814	+	0.527082i	$0.176714\pi$
$128$	−0.281733	−	0.959493i	−0.0249019	−	0.0848080i
$129$	−15.7031	−	0.319134i	−1.38258	−	0.0280982i
$130$	−0.00757502	−	0.0117870i	−0.000664373	−	0.00103378i
$131$	5.46677	−	18.6181i	0.477634	−	1.62667i	−0.270212	−	0.962801i	$-0.587094\pi$
$131$	5.46677	−	18.6181i	0.477634	−	1.62667i	0.747847	−	0.663872i	$-0.231088\pi$
$132$	1.21991	−	3.86250i	0.106179	−	0.336187i
$133$	−1.98149	+	4.33886i	−0.171817	+	0.376226i
$134$	0.174405	−	1.21301i	0.0150663	−	0.104788i
$135$	1.76495	−	4.88722i	0.151902	−	0.420625i
$136$	−4.93579	+	4.27688i	−0.423240	+	0.366740i
$137$	14.3369			1.22488			0.612441	−	0.790516i	$-0.290188\pi$
$137$	14.3369			1.22488			0.612441	+	0.790516i	$0.290188\pi$
$138$	−8.25178	−	0.952959i	−0.702438	−	0.0811213i
$139$	−11.1016			−0.941629			−0.470814	−	0.882232i	$-0.656040\pi$
$139$	−11.1016			−0.941629			−0.470814	+	0.882232i	$0.656040\pi$
$140$	0.811701	−	0.703343i	0.0686013	−	0.0594434i
$141$	12.0654	−	7.41194i	1.01609	−	0.624198i
$142$	1.03640	−	7.20834i	0.0869731	−	0.604911i
$143$	0.0136117	−	0.0298054i	0.00113827	−	0.00249246i
$144$	2.05508	−	2.18556i	0.171256	−	0.182130i
$145$	−0.344607	+	1.17362i	−0.0286181	+	0.0974641i
$146$	−7.99701	−	12.4436i	−0.661837	−	1.02984i
$147$	0.205755	−	10.1243i	0.0169704	−	0.835035i
$148$	1.60184	+	5.45538i	0.131671	+	0.448429i
$149$	−12.1063	+	13.9714i	−0.991785	+	1.14458i	−0.00229234	+	0.999997i	$0.500730\pi$
$149$	−12.1063	+	13.9714i	−0.991785	+	1.14458i	−0.989493	+	0.144583i	$0.953816\pi$
$150$	−0.687359	−	1.58982i	−0.0561226	−	0.129809i
$151$	−4.87363	+	1.43103i	−0.396610	+	0.116455i	−0.473955	−	0.880549i	$-0.657174\pi$
$151$	−4.87363	+	1.43103i	−0.396610	+	0.116455i	0.0773447	+	0.997004i	$0.475356\pi$
$152$	1.84490	+	4.03977i	0.149641	+	0.327669i
$153$	−18.5595	−	6.27921i	−1.50045	−	0.507644i
$154$	2.40999	+	0.707637i	0.194202	+	0.0570230i
$155$	−1.27483	−	8.86665i	−0.102397	−	0.712187i
$156$	0.0186597	−	0.0155163i	0.00149397	−	0.00124230i
$157$	−16.6185	−	2.38938i	−1.32630	−	0.190693i	−0.557496	−	0.830180i	$-0.688238\pi$
$157$	−16.6185	−	2.38938i	−1.32630	−	0.190693i	−0.768802	+	0.639487i	$0.779147\pi$
$158$	−0.219714	−	0.141202i	−0.0174795	−	0.0112334i
$159$	0.952172	+	3.50473i	0.0755122	+	0.277943i
$160$		−	1.00000i		−	0.0790569i
$161$	0.486834	−	5.12783i	0.0383679	−	0.404130i
$162$	8.77499	+	1.99989i	0.689428	+	0.157126i
$163$	13.5246	+	15.6082i	1.05933	+	1.22253i	0.974089	+	0.226166i	$0.0726193\pi$
$163$	13.5246	+	15.6082i	1.05933	+	1.22253i	0.0852372	+	0.996361i	$0.472835\pi$
$164$	6.26565	−	9.74955i	0.489265	−	0.761312i
$165$	2.25869	−	3.36235i	0.175838	−	0.261759i
$166$	10.1450	+	4.63306i	0.787404	+	0.359595i
$167$	4.92851	−	0.708613i	0.381380	−	0.0548341i	0.0510409	−	0.998697i	$-0.483746\pi$
$167$	4.92851	−	0.708613i	0.381380	−	0.0548341i	0.330339	+	0.943862i	$0.392837\pi$
$168$	1.38087	+	1.24654i	0.106536	+	0.0961727i
$169$	−10.9361	+	7.02822i	−0.841241	+	0.540633i
$170$	−5.94079	+	2.71307i	−0.455638	+	0.208083i
$171$	−7.65256	+	10.9064i	−0.585206	+	0.834031i
$172$	−6.85318	−	5.93832i	−0.522550	−	0.452792i
$173$	15.2915	+	13.2502i	1.16259	+	1.00739i	0.999785	+	0.0207324i	$0.00659980\pi$
$173$	15.2915	+	13.2502i	1.16259	+	1.00739i	0.162806	+	0.986658i	$0.447946\pi$
$174$	−2.09047	−	0.344054i	−0.158478	−	0.0260827i
$175$	0.976977	−	0.446170i	0.0738525	−	0.0337273i
$176$	1.96735	−	1.26434i	0.148295	−	0.0953032i
$177$	4.10141	−	4.54336i	0.308281	−	0.341500i
$178$	2.12332	−	0.305287i	0.159150	−	0.0228823i
$179$	−7.48533	−	3.41844i	−0.559480	−	0.255506i	0.115543	−	0.993302i	$-0.463139\pi$
$179$	−7.48533	−	3.41844i	−0.559480	−	0.255506i	−0.675023	+	0.737796i	$0.735866\pi$
$180$	2.58757	−	1.51804i	0.192866	−	0.113148i
$181$	6.70480	−	10.4329i	0.498364	−	0.775469i	−0.497390	−	0.867527i	$-0.665708\pi$
$181$	6.70480	−	10.4329i	0.498364	−	0.775469i	0.995754	+	0.0920579i	$0.0293445\pi$
$182$	0.00985467	+	0.0113729i	0.000730477	+	0.000843015i
$183$	7.04661	−	14.6354i	0.520900	−	1.08188i
$184$	−3.31139	−	3.46911i	−0.244119	−	0.255746i
$185$			5.68569i			0.418020i
$186$	14.9727	−	4.06781i	1.09785	−	0.298266i
$187$	−12.8487	−	8.25738i	−0.939592	−	0.603839i
$188$	8.09216	+	1.16348i	0.590182	+	0.0848553i
$189$	−1.12930	+	5.46540i	−0.0821447	+	0.397549i
$190$	0.632035	+	4.39590i	0.0458526	+	0.318912i
$191$	−4.84068	−	1.42135i	−0.350259	−	0.102845i	0.101870	−	0.994798i	$-0.467517\pi$
$191$	−4.84068	−	1.42135i	−0.350259	−	0.102845i	−0.452130	+	0.891952i	$0.649336\pi$
$192$	1.71908	−	0.211611i	0.124064	−	0.0152717i
$193$	4.62777	+	10.1334i	0.333114	+	0.729418i	0.999874	−	0.0158541i	$-0.00504672\pi$
$193$	4.62777	+	10.1334i	0.333114	+	0.729418i	−0.666760	+	0.745272i	$0.732319\pi$
$194$	7.02887	−	2.06386i	0.504644	−	0.148177i
$195$	0.0222753	−	0.00963071i	0.00159517	−	0.000689669i
$196$	3.82861	−	4.41845i	0.273472	−	0.315604i
$197$	−4.48824	−	15.2856i	−0.319774	−	1.08905i	−0.949899	−	0.312557i	$-0.898815\pi$
$197$	−4.48824	−	15.2856i	−0.319774	−	1.08905i	0.630125	−	0.776494i	$-0.283004\pi$
$198$	6.25810	+	3.17134i	0.444744	+	0.225377i
$199$	−9.33556	−	14.5264i	−0.661780	−	1.02975i	−0.996180	−	0.0873191i	$-0.972170\pi$
$199$	−9.33556	−	14.5264i	−0.661780	−	1.02975i	0.334400	−	0.942431i	$-0.391466\pi$
$200$	0.281733	−	0.959493i	0.0199215	−	0.0678464i
$201$	2.02405	+	0.639265i	0.142766	+	0.0450902i
$202$	−0.413380	+	0.905175i	−0.0290853	+	0.0636879i
$203$	0.186963	−	1.30036i	0.0131222	−	0.0912671i
$204$	−5.92110	−	9.63856i	−0.414560	−	0.674834i
$205$	8.75861	−	7.58938i	0.611728	−	0.530065i
$206$	1.75737			0.122442
$207$	3.94973	−	13.8347i	0.274525	−	0.961580i
$208$	0.0140112			0.000971501
$209$	−7.84917	+	6.80134i	−0.542938	+	0.470459i
$210$	0.973739	+	1.58508i	0.0671944	+	0.109381i
$211$	−0.342732	+	2.38375i	−0.0235946	+	0.164104i	−0.998212	−	0.0597729i	$-0.980962\pi$
$211$	−0.342732	+	2.38375i	−0.0235946	+	0.164104i	0.974617	+	0.223877i	$0.0718714\pi$
$212$	−0.871043	+	1.90732i	−0.0598235	+	0.130995i
$213$	12.0280	+	3.79884i	0.824142	+	0.260292i
$214$	0.551395	−	1.87788i	0.0376926	−	0.128369i
$215$	−4.90256	−	7.62854i	−0.334352	−	0.520262i
$216$	3.15719	+	4.12700i	0.214820	+	0.280807i
$217$	2.71056	+	9.23130i	0.184004	+	0.626662i
$218$	−9.79616	+	11.3054i	−0.663480	+	0.765697i
$219$	23.5162	−	10.1672i	1.58908	−	0.687037i
$220$	2.24386	−	0.658858i	0.151281	−	0.0444202i
$221$	−0.0380133	−	0.0832375i	−0.00255705	−	0.00559916i
$222$	−9.77413	+	1.20315i	−0.655997	+	0.0807503i
$223$	−17.3525	−	5.09514i	−1.16201	−	0.341196i	−0.356794	−	0.934183i	$-0.616130\pi$
$223$	−17.3525	−	5.09514i	−1.16201	−	0.341196i	−0.805212	+	0.592987i	$0.797949\pi$
$224$	0.152851	+	1.06310i	0.0102128	+	0.0710315i
$225$	2.91044	−	0.727550i	0.194029	−	0.0485033i
$226$	−4.13438	−	0.594434i	−0.275015	−	0.0395411i
$227$	−5.28847	−	3.39869i	−0.351008	−	0.225579i	0.353241	−	0.935532i	$-0.385080\pi$
$227$	−5.28847	−	3.39869i	−0.351008	−	0.225579i	−0.704249	+	0.709953i	$0.748716\pi$
$228$	−7.42314	+	2.01674i	−0.491609	+	0.133562i
$229$			16.6331i			1.09915i	0.835445	+	0.549574i	$0.185210\pi$
$229$			16.6331i			1.09915i	−0.835445	+	0.549574i	$0.814790\pi$
$230$	−2.19990	−	4.26151i	−0.145057	−	0.280996i
$231$	−1.88728	+	3.91977i	−0.124174	+	0.257902i
$232$	−0.801006	−	0.924411i	−0.0525886	−	0.0606905i
$233$	−10.0794	+	15.6839i	−0.660325	+	1.02749i	0.336002	+	0.941861i	$0.390925\pi$
$233$	−10.0794	+	15.6839i	−0.660325	+	1.02749i	−0.996327	+	0.0856252i	$0.972711\pi$
$234$	0.0212696	+	0.0362550i	0.00139044	+	0.00237006i
$235$	7.43659	+	3.39617i	0.485109	+	0.221542i
$236$	3.49785	−	0.502915i	0.227691	−	0.0327370i
$237$	0.303124	−	0.335787i	0.0196900	−	0.0218117i
$238$	5.90098	−	3.79233i	0.382504	−	0.245820i
$239$	−0.879495	+	0.401652i	−0.0568898	+	0.0259807i	−0.443657	−	0.896197i	$-0.646319\pi$
$239$	−0.879495	+	0.401652i	−0.0568898	+	0.0259807i	0.386767	+	0.922177i	$0.373592\pi$
$240$	1.70906	+	0.281281i	0.110319	+	0.0181566i
$241$	−19.2792	−	16.7056i	−1.24188	−	1.07610i	−0.994232	−	0.107250i	$-0.965795\pi$
$241$	−19.2792	−	16.7056i	−1.24188	−	1.07610i	−0.247653	−	0.968849i	$-0.579659\pi$
$242$	−4.18003	−	3.62202i	−0.268703	−	0.232832i
$243$	−5.88616	+	14.4344i	−0.377597	+	0.925970i
$244$	8.53068	−	3.89583i	0.546121	−	0.249405i
$245$	4.91835	−	3.16083i	0.314222	−	0.201938i
$246$	14.9001	+	13.4507i	0.949998	+	0.857587i
$247$	−0.0615918	+	0.00885556i	−0.00391899	+	0.000563466i
$248$	8.14833	+	3.72122i	0.517419	+	0.236298i
$249$	−10.7718	+	16.0352i	−0.682633	+	1.01619i
$250$	0.540641	−	0.841254i	0.0341931	−	0.0532055i
$251$	13.3873	+	15.4497i	0.844998	+	0.975179i	0.999919	−	0.0127475i	$-0.00405778\pi$
$251$	13.3873	+	15.4497i	0.844998	+	0.975179i	−0.154921	+	0.987927i	$0.549512\pi$
$252$	−2.51882	+	2.00935i	−0.158671	+	0.126577i
$253$	5.60247	−	9.71596i	0.352224	−	0.610837i
$254$			3.56493i			0.223684i
$255$	−2.96576	−	10.9163i	−0.185723	−	0.683605i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	−2.68018	−	0.385352i	−0.167185	−	0.0240376i	0.0582139	−	0.998304i	$-0.481459\pi$
$257$	−2.68018	−	0.385352i	−0.167185	−	0.0240376i	−0.225399	+	0.974267i	$0.572369\pi$
$258$	12.0766	−	10.0422i	0.751856	−	0.625197i
$259$	−0.869064	−	6.04447i	−0.0540010	−	0.375585i
$260$	0.0134436	+	0.00394741i	0.000833739	+	0.000244808i
$261$	1.17602	−	3.47596i	0.0727937	−	0.215157i
$262$	8.06076	+	17.6506i	0.497996	+	1.09046i
$263$	−14.4797	+	4.25162i	−0.892856	+	0.262166i	−0.695808	−	0.718228i	$-0.744954\pi$
$263$	−14.4797	+	4.25162i	−0.892856	+	0.262166i	−0.197048	+	0.980394i	$0.563135\pi$
$264$	1.60745	+	3.71795i	0.0989319	+	0.228824i
$265$	−1.37311	+	1.58466i	−0.0843497	+	0.0973448i
$266$	−1.34384	−	4.57669i	−0.0823959	−	0.280615i
$267$	−0.0754949	+	3.71475i	−0.00462021	+	0.227339i
$268$	0.662547	+	1.03094i	0.0404715	+	0.0629749i
$269$	6.59711	−	22.4677i	0.402233	−	1.36988i	−0.470809	−	0.882235i	$-0.656038\pi$
$269$	6.59711	−	22.4677i	0.402233	−	1.36988i	0.873042	−	0.487645i	$-0.162144\pi$
$270$	1.86659	+	4.84931i	0.113597	+	0.295120i
$271$	5.11226	−	11.1943i	0.310548	−	0.680005i	−0.688425	−	0.725307i	$-0.741698\pi$
$271$	5.11226	−	11.1943i	0.310548	−	0.680005i	0.998973	+	0.0453020i	$0.0144250\pi$
$272$	0.929456	−	6.46451i	0.0563565	−	0.391968i
$273$	−0.0222089	+	0.0136432i	−0.00134414	+	0.000825726i
$274$	−10.8351	+	9.38865i	−0.654571	+	0.567189i
$275$	2.33859			0.141023
$276$	6.86033	−	4.68357i	0.412944	−	0.281918i
$277$	−15.1327			−0.909236			−0.454618	−	0.890687i	$-0.650224\pi$
$277$	−15.1327			−0.909236			−0.454618	+	0.890687i	$0.650224\pi$
$278$	8.39006	−	7.27003i	0.503202	−	0.436027i
$279$	2.74060	+	26.7334i	0.164076	+	1.60049i
$280$	−0.152851	+	1.06310i	−0.00913460	+	0.0635325i
$281$	−1.07909	+	2.36287i	−0.0643730	+	0.140957i	−0.939084	−	0.343688i	$-0.888324\pi$
$281$	−1.07909	+	2.36287i	−0.0643730	+	0.140957i	0.874711	+	0.484645i	$0.161051\pi$
$282$	−4.26462	+	13.5027i	−0.253954	+	0.804075i
$283$	−2.94783	+	10.0394i	−0.175230	+	0.596779i	0.824301	+	0.566152i	$0.191569\pi$
$283$	−2.94783	+	10.0394i	−0.175230	+	0.596779i	−0.999531	+	0.0306268i	$0.990250\pi$
$284$	3.93720	+	6.12640i	0.233630	+	0.363535i
$285$	−7.69063	−	0.156297i	−0.455554	−	0.00925821i
$286$	0.00923138	+	0.0314392i	0.000545863	+	0.00185904i
$287$	−8.15126	+	9.40706i	−0.481154	+	0.555281i
$288$	−0.121888	+	2.99752i	−0.00718229	+	0.176631i
$289$	−24.6146	+	7.22749i	−1.44792	+	0.425147i
$290$	−0.508123	−	1.11264i	−0.0298380	−	0.0653362i
$291$	1.55018	+	12.5933i	0.0908730	+	0.738231i
$292$	14.1926	+	4.16731i	0.830556	+	0.243873i
$293$	0.402333	+	2.79829i	0.0235045	+	0.163478i	0.998193	−	0.0600900i	$-0.0191388\pi$
$293$	0.402333	+	2.79829i	0.0235045	+	0.163478i	−0.974688	+	0.223568i	$0.928230\pi$
$294$	6.47448	+	7.78614i	0.377599	+	0.454097i
$295$	3.49785	+	0.502915i	0.203653	+	0.0292809i
$296$	−4.78311	−	3.07392i	−0.278012	−	0.178668i
$297$	−7.18029	+	9.80342i	−0.416643	+	0.568852i
$298$		−	18.4868i		−	1.07091i
$299$	0.0597088	−	0.0308231i	0.00345305	−	0.00178255i
$300$	1.56058	+	0.751384i	0.0901003	+	0.0433812i
$301$	6.37796	+	7.36056i	0.367620	+	0.424256i
$302$	2.74612	−	4.27304i	0.158021	−	0.245886i
$303$	−1.43072	−	0.961098i	−0.0821928	−	0.0552137i
$304$	−4.03977	−	1.84490i	−0.231697	−	0.105812i
$305$	9.28271	−	1.33465i	0.531526	−	0.0764220i
$306$	18.1383	−	7.40838i	1.03690	−	0.423509i
$307$	18.2589	−	11.7343i	1.04209	−	0.669712i	0.0965893	−	0.995324i	$-0.469207\pi$
$307$	18.2589	−	11.7343i	1.04209	−	0.669712i	0.945503	+	0.325612i	$0.105570\pi$
$308$	−2.28475	+	1.04341i	−0.130186	+	0.0594539i
$309$	−0.494315	+	3.00346i	−0.0281206	+	0.170861i
$310$	6.76988	+	5.86613i	0.384503	+	0.333174i
$311$	−2.51844	−	2.18224i	−0.142808	−	0.123744i	0.580527	−	0.814241i	$-0.302846\pi$
$311$	−2.51844	−	2.18224i	−0.142808	−	0.123744i	−0.723335	+	0.690497i	$0.757392\pi$
$312$	−0.00394107	+	0.0239459i	−0.000223119	+	0.00135567i
$313$	7.98020	−	3.64444i	0.451068	−	0.205996i	−0.176910	−	0.984227i	$-0.556610\pi$
$313$	7.98020	−	3.64444i	0.451068	−	0.205996i	0.627978	+	0.778231i	$0.283883\pi$
$314$	14.1241	−	9.07701i	0.797070	−	0.512245i
$315$	−2.98289	+	1.21832i	−0.168067	+	0.0686448i
$316$	0.258517	−	0.0371691i	0.0145427	−	0.00209092i
$317$	−1.53016	−	0.698799i	−0.0859421	−	0.0392485i	0.371980	−	0.928241i	$-0.378679\pi$
$317$	−1.53016	−	0.698799i	−0.0859421	−	0.0392485i	−0.457922	+	0.888992i	$0.651406\pi$
$318$	−3.01471	−	2.02516i	−0.169057	−	0.113565i
$319$	1.54650	−	2.40641i	0.0865875	−	0.134733i
$320$	0.654861	+	0.755750i	0.0366078	+	0.0422477i
$321$	3.05431	+	1.47058i	0.170475	+	0.0820797i
$322$	2.99009	+	4.19417i	0.166631	+	0.233732i
$323$			29.0048i			1.61387i
$324$	−7.94134	+	4.23498i	−0.441186	+	0.235277i
$325$	0.0117870	+	0.00757502i	0.000653823	+	0.000420186i
$326$	−20.4424	−	2.93917i	−1.13220	−	0.162786i
$327$	−16.5661	−	19.9222i	−0.916106	−	1.10170i
$328$	1.64933	+	11.4713i	0.0910690	+	0.633399i
$329$	−8.42496	−	2.47379i	−0.464483	−	0.136385i
$330$	0.494871	+	4.02022i	0.0272418	+	0.221306i
$331$	14.7876	+	32.3803i	0.812799	+	1.77978i	0.594878	+	0.803816i	$0.297200\pi$
$331$	14.7876	+	32.3803i	0.812799	+	1.77978i	0.217921	+	0.975966i	$0.430072\pi$
$332$	−10.7011	+	3.14212i	−0.587298	+	0.172446i
$333$	0.693015	−	17.0430i	0.0379770	−	0.933950i
$334$	−3.26068	+	3.76302i	−0.178416	+	0.205903i
$335$	0.345259	+	1.17584i	0.0188635	+	0.0642433i
$336$	−1.85990	−	0.0377987i	−0.101466	−	0.00206209i
$337$	−9.27288	−	14.4289i	−0.505126	−	0.785991i	0.491253	−	0.871017i	$-0.336539\pi$
$337$	−9.27288	−	14.4289i	−0.505126	−	0.785991i	−0.996379	+	0.0850257i	$0.972903\pi$
$338$	3.66247	−	12.4732i	0.199212	−	0.678454i
$339$	2.17884	−	6.89869i	0.118338	−	0.374685i
$340$	2.71307	−	5.94079i	0.147137	−	0.322185i
$341$	−2.98131	+	20.7355i	−0.161447	+	1.12289i
$342$	−1.35873	−	13.2539i	−0.0734719	−	0.716686i
$343$	−10.4275	+	9.03546i	−0.563031	+	0.487869i
$344$	9.06806			0.488917
$345$	7.90196	−	2.56107i	0.425427	−	0.137883i
$346$	−20.2335			−1.08776
$347$	18.3018	−	15.8586i	0.982495	−	0.851336i	−0.00639629	−	0.999980i	$-0.502036\pi$
$347$	18.3018	−	15.8586i	0.982495	−	0.851336i	0.988891	+	0.148643i	$0.0474906\pi$
$348$	1.80518	−	1.10895i	0.0967678	−	0.0594459i
$349$	−3.65367	+	25.4118i	−0.195576	+	1.36026i	0.621355	+	0.783529i	$0.286583\pi$
$349$	−3.65367	+	25.4118i	−0.195576	+	1.36026i	−0.816931	+	0.576735i	$0.804327\pi$
$350$	−0.446170	+	0.976977i	−0.0238488	+	0.0522216i
$351$	−0.0679446	+	0.0261532i	−0.00362662	+	0.00139595i
$352$	−0.658858	+	2.24386i	−0.0351173	+	0.119598i
$353$	−1.35976	−	2.11583i	−0.0723727	−	0.112614i	0.803181	−	0.595735i	$-0.203139\pi$
$353$	−1.35976	−	2.11583i	−0.0723727	−	0.112614i	−0.875553	+	0.483121i	$0.839503\pi$
$354$	−0.124366	+	6.11949i	−0.00661000	+	0.325247i
$355$	2.05171	+	6.98748i	0.108893	+	0.370857i
$356$	−1.40478	+	1.62120i	−0.0744531	+	0.0859235i
$357$	4.82148	+	11.1518i	0.255180	+	0.590217i
$358$	7.89564	−	2.31837i	0.417297	−	0.122530i
$359$	10.4139	+	22.8033i	0.549625	+	1.20351i	0.956957	+	0.290231i	$0.0937322\pi$
$359$	10.4139	+	22.8033i	0.549625	+	1.20351i	−0.407331	+	0.913280i	$0.633541\pi$
$360$	−0.961450	+	2.84176i	−0.0506729	+	0.149774i
$361$	0.694110	+	0.203809i	0.0365321	+	0.0107268i
$362$	1.76493	+	12.2753i	0.0927626	+	0.645178i
$363$	7.36601	−	6.12512i	0.386615	−	0.321485i
$364$	−0.0148953	−	0.00214163i	−0.000780728	−	0.000112252i
$365$	12.4436	+	7.99701i	0.651327	+	0.418582i
$366$	4.25869	+	15.6753i	0.222605	+	0.819359i
$367$			2.71584i			0.141766i	0.997485	+	0.0708829i	$0.0225817\pi$
$367$			2.71584i			0.141766i	−0.997485	+	0.0708829i	$0.977418\pi$
$368$	4.77436	+	0.453276i	0.248881	+	0.0236286i
$369$	−27.1792	+	21.6818i	−1.41489	+	1.12871i
$370$	−3.72333	−	4.29696i	−0.193567	−	0.223388i
$371$	1.21754	−	1.89454i	0.0632118	−	0.0983594i
$372$	−8.65174	+	12.8793i	−0.448572	+	0.667759i
$373$	25.4924	+	11.6420i	1.31995	+	0.602800i	0.945855	−	0.324591i	$-0.105227\pi$
$373$	25.4924	+	11.6420i	1.31995	+	0.602800i	0.374094	+	0.927391i	$0.377954\pi$
$374$	15.1179	−	2.17362i	0.781726	−	0.112395i
$375$	1.28568	+	1.16062i	0.0663922	+	0.0599339i
$376$	−6.87757	+	4.41994i	−0.354683	+	0.227941i
$377$	0.0155893	−	0.00711941i	0.000802892	−	0.000366668i
$378$	−2.72560	−	4.87001i	−0.140190	−	0.250486i
$379$	0.592293	+	0.513225i	0.0304240	+	0.0263626i	0.669940	−	0.742415i	$-0.266320\pi$
$379$	0.592293	+	0.513225i	0.0304240	+	0.0263626i	−0.639516	+	0.768778i	$0.720865\pi$
$380$	−3.35636	−	2.90831i	−0.172178	−	0.149193i
$381$	−6.09267	−	1.00275i	−0.312137	−	0.0513722i
$382$	4.58913	−	2.09579i	0.234800	−	0.107230i
$383$	11.5620	−	7.43046i	0.590792	−	0.379679i	−0.210819	−	0.977525i	$-0.567613\pi$
$383$	11.5620	−	7.43046i	0.590792	−	0.379679i	0.801611	+	0.597846i	$0.203977\pi$
$384$	−1.16062	+	1.28568i	−0.0592274	+	0.0656096i
$385$	−2.48617	+	0.357457i	−0.126707	+	0.0182177i
$386$	−10.1334	−	4.62777i	−0.515777	−	0.235547i
$387$	13.7657	+	23.4643i	0.699751	+	1.19276i
$388$	−3.96052	+	6.16270i	−0.201065	+	0.312863i
$389$	−5.01019	−	5.78207i	−0.254027	−	0.293163i	0.614385	−	0.789007i	$-0.289404\pi$
$389$	−5.01019	−	5.78207i	−0.254027	−	0.293163i	−0.868412	+	0.495844i	$0.834859\pi$
$390$	−0.0105278	+	0.0218656i	−0.000533095	+	0.00110721i
$391$	−10.2604	−	29.5933i	−0.518889	−	1.49660i
$392$			5.84645i			0.295290i
$393$	−32.4333	+	8.81154i	−1.63604	+	0.444483i
$394$	13.4019	+	8.61288i	0.675178	+	0.433910i
$395$	0.258517	+	0.0371691i	0.0130074	+	0.00187018i
$396$	−6.80634	+	1.70144i	−0.342032	+	0.0855007i
$397$	1.40912	+	9.80067i	0.0707219	+	0.491882i	0.994141	+	0.108089i	$0.0344732\pi$
$397$	1.40912	+	9.80067i	0.0707219	+	0.491882i	−0.923419	+	0.383793i	$0.874618\pi$
$398$	16.5681	+	4.86484i	0.830485	+	0.243852i
$399$	8.19982	−	1.00936i	0.410505	−	0.0505313i
$400$	0.415415	+	0.909632i	0.0207708	+	0.0454816i
$401$	16.1734	−	4.74895i	0.807663	−	0.237151i	0.148267	−	0.988947i	$-0.452630\pi$
$401$	16.1734	−	4.74895i	0.807663	−	0.237151i	0.659396	+	0.751796i	$0.270812\pi$
$402$	−1.94831	+	0.842348i	−0.0971726	+	0.0420125i
$403$	−0.0821914	+	0.0948540i	−0.00409425	+	0.00472501i
$404$	−0.280352	−	0.954792i	−0.0139480	−	0.0475027i
$405$	−8.81280	+	1.82610i	−0.437911	+	0.0907396i
$406$	0.710255	+	1.10518i	0.0352494	+	0.0548491i
$407$	3.74606	−	12.7579i	0.185685	−	0.632386i
$408$	10.7868	+	3.40683i	0.534025	+	0.168663i
$409$	12.0567	−	26.4004i	0.596164	−	1.30542i	−0.335481	−	0.942047i	$-0.608899\pi$
$409$	12.0567	−	26.4004i	0.596164	−	1.30542i	0.931645	−	0.363370i	$-0.118374\pi$
$410$	−1.64933	+	11.4713i	−0.0814546	+	0.566529i
$411$	−12.9981	−	21.1586i	−0.641147	−	1.04368i
$412$	−1.32813	+	1.15084i	−0.0654325	+	0.0566976i
$413$	−3.79545			−0.186762
$414$	6.07481	+	13.0421i	0.298561	+	0.640985i
$415$	−11.1529			−0.547472
$416$	−0.0105889	+	0.00917538i	−0.000519166	+	0.000449860i
$417$	10.0649	+	16.3840i	0.492882	+	0.802329i
$418$	1.47807	−	10.2802i	0.0722949	−	0.502822i
$419$	9.92680	−	21.7367i	0.484956	−	1.06191i	−0.496115	−	0.868257i	$-0.665241\pi$
$419$	9.92680	−	21.7367i	0.484956	−	1.06191i	0.981071	−	0.193649i	$-0.0620321\pi$
$420$	−1.77391	−	0.560262i	−0.0865580	−	0.0273380i
$421$	6.58980	−	22.4428i	0.321167	−	1.09379i	−0.627788	−	0.778384i	$-0.716040\pi$
$421$	6.58980	−	22.4428i	0.321167	−	1.09379i	0.948955	−	0.315411i	$-0.102142\pi$
$422$	−1.30201	−	2.02596i	−0.0633807	−	0.0986223i
$423$	−21.8774	−	11.0865i	−1.06371	−	0.539046i
$424$	−0.590738	−	2.01187i	−0.0286888	−	0.0977049i
$425$	4.27688	−	4.93579i	0.207459	−	0.239421i
$426$	−11.5778	+	5.00567i	−0.560948	+	0.242525i
$427$	−9.66447	+	2.83775i	−0.467697	+	0.137328i
$428$	0.813033	+	1.78029i	0.0392994	+	0.0860538i
$429$	−0.0563280	+	0.00693374i	−0.00271954	+	0.000334764i
$430$	8.70074	+	2.55477i	0.419587	+	0.123202i
$431$	−2.81370	−	19.5697i	−0.135531	−	0.942639i	−0.938170	−	0.346174i	$-0.887481\pi$
$431$	−2.81370	−	19.5697i	−0.135531	−	0.942639i	0.802639	−	0.596465i	$-0.203429\pi$
$432$	−5.08866	−	1.05146i	−0.244828	−	0.0505883i
$433$	24.5291	+	3.52675i	1.17879	+	0.169485i	0.703730	−	0.710468i	$-0.251516\pi$
$433$	24.5291	+	3.52675i	1.17879	+	0.169485i	0.475062	+	0.879952i	$0.342426\pi$
$434$	−8.09372	−	5.20152i	−0.388511	−	0.249681i
$435$	2.04448	−	0.555450i	0.0980255	−	0.0266318i
$436$		−	14.9592i		−	0.716414i
$437$	−21.2741	+	1.02501i	−1.01768	+	0.0490329i
$438$	−11.1143	+	23.0837i	−0.531060	+	1.10298i
$439$	6.16044	+	7.10953i	0.294022	+	0.339319i	0.883471	−	0.468486i	$-0.155200\pi$
$439$	6.16044	+	7.10953i	0.294022	+	0.339319i	−0.589449	+	0.807806i	$0.700655\pi$
$440$	−1.26434	+	1.96735i	−0.0602750	+	0.0937897i
$441$	−15.1281	+	8.87517i	−0.720387	+	0.422627i
$442$	0.0832375	+	0.0380133i	0.00395921	+	0.00180811i
$443$	12.7030	−	1.82642i	0.603540	−	0.0867759i	0.166230	−	0.986087i	$-0.446841\pi$
$443$	12.7030	−	1.82642i	0.603540	−	0.0867759i	0.437309	+	0.899311i	$0.355931\pi$
$444$	6.59890	−	7.30998i	0.313170	−	0.346916i
$445$	−1.80462	+	1.15976i	−0.0855472	+	0.0549778i
$446$	16.4507	−	7.51279i	0.778964	−	0.355741i
$447$	31.5950	+	5.19998i	1.49439	+	0.245951i
$448$	−0.811701	−	0.703343i	−0.0383493	−	0.0332298i
$449$	2.28971	+	1.98404i	0.108058	+	0.0936328i	0.707214	−	0.706999i	$-0.249952\pi$
$449$	2.28971	+	1.98404i	0.108058	+	0.0936328i	−0.599156	+	0.800632i	$0.704497\pi$
$450$	−1.72312	+	2.45578i	−0.0812287	+	0.115767i
$451$	−24.6535	+	11.2589i	−1.16089	+	0.530159i
$452$	3.51382	−	2.25820i	0.165276	−	0.106217i
$453$	6.53045	+	5.89520i	0.306827	+	0.276981i
$454$	6.22243	−	0.894650i	0.292033	−	0.0419880i
$455$	−0.0136886	−	0.00625137i	−0.000641731	−	0.000293069i
$456$	4.28935	−	6.38527i	0.200867	−	0.299018i
$457$	13.8636	−	21.5722i	0.648512	−	1.00911i	−0.348896	−	0.937161i	$-0.613443\pi$
$457$	13.8636	−	21.5722i	0.648512	−	1.00911i	0.997409	−	0.0719438i	$-0.0229202\pi$
$458$	−10.8924	−	12.5705i	−0.508968	−	0.587380i
$459$	7.55938	+	33.0833i	0.352842	+	1.54420i
$460$	4.45327	+	1.78001i	0.207635	+	0.0829933i
$461$		−	27.3066i		−	1.27180i	−0.771773	−	0.635899i	$-0.780630\pi$
$461$		−	27.3066i		−	1.27180i	0.771773	−	0.635899i	$-0.219370\pi$
$462$	−1.14059	−	4.19827i	−0.0530652	−	0.195321i
$463$	27.1386	+	17.4409i	1.26124	+	0.810549i	0.988453	−	0.151526i	$-0.0484186\pi$
$463$	27.1386	+	17.4409i	1.26124	+	0.810549i	0.272786	+	0.962075i	$0.412055\pi$
$464$	1.21072	+	0.174075i	0.0562063	+	0.00808124i
$465$	−11.9298	+	9.92009i	−0.553231	+	0.460033i
$466$	−2.65325	−	18.4537i	−0.122909	−	0.854852i
$467$	−22.7759	−	6.68762i	−1.05394	−	0.309466i	−0.291534	−	0.956560i	$-0.594166\pi$
$467$	−22.7759	−	6.68762i	−1.05394	−	0.309466i	−0.762410	+	0.647094i	$0.775984\pi$
$468$	−0.0398165	−	0.0134711i	−0.00184052	−	0.000622700i
$469$	−0.546775	−	1.19727i	−0.0252477	−	0.0552848i
$470$	−7.84422	+	2.30327i	−0.361827	+	0.106242i
$471$	11.5403	+	26.6921i	0.531749	+	1.22991i
$472$	−2.31416	+	2.67068i	−0.106518	+	0.122928i
$473$	5.97457	+	20.3475i	0.274711	+	0.935579i
$474$	−0.00919158	+	0.452275i	−0.000422183	+	0.0207737i
$475$	−2.40104	−	3.73610i	−0.110167	−	0.171424i
$476$	−1.97621	+	6.73037i	−0.0905796	+	0.308486i
$477$	4.30909	−	4.58268i	0.197300	−	0.209827i
$478$	0.401652	−	0.879495i	0.0183711	−	0.0402272i
$479$	−1.32769	+	9.23430i	−0.0606638	+	0.421926i	0.936747	+	0.350008i	$0.113821\pi$
$479$	−1.32769	+	9.23430i	−0.0606638	+	0.421926i	−0.997411	+	0.0719180i	$0.977088\pi$
$480$	−1.47582	+	0.906618i	−0.0673617	+	0.0413812i
$481$	0.0602055	−	0.0521683i	0.00274513	−	0.00237867i
$482$	25.5101			1.16195
$483$	−8.00913	+	3.93050i	−0.364428	+	0.178844i
$484$	5.53098			0.251408
$485$	−5.53633	+	4.79725i	−0.251392	+	0.217832i
$486$	−5.00408	−	14.7634i	−0.226990	−	0.669683i
$487$	5.29052	−	36.7964i	0.239736	−	1.66740i	−0.413694	−	0.910416i	$-0.635762\pi$
$487$	5.29052	−	36.7964i	0.239736	−	1.66740i	0.653430	−	0.756987i	$-0.273329\pi$
$488$	−3.89583	+	8.53068i	−0.176356	+	0.386166i
$489$	10.7733	−	34.1105i	0.487183	−	1.54253i
$490$	−1.64713	+	5.60963i	−0.0744100	+	0.253417i
$491$	9.52224	+	14.8169i	0.429733	+	0.668677i	0.986828	−	0.161771i	$-0.0517207\pi$
$491$	9.52224	+	14.8169i	0.429733	+	0.668677i	−0.557096	+	0.830448i	$0.688084\pi$
$492$	−20.0691	−	0.407865i	−0.904786	−	0.0183880i
$493$	−2.25062	−	7.66492i	−0.101363	−	0.345210i
$494$	0.0407488	−	0.0470266i	0.00183338	−	0.00211583i
$495$	−7.00999	−	0.285046i	−0.315076	−	0.0128118i
$496$	−8.59497	+	2.52371i	−0.385926	+	0.113318i
$497$	−3.24922	−	7.11480i	−0.145748	−	0.319143i
$498$	−2.36006	−	19.1726i	−0.105757	−	0.859145i
$499$	7.27234	+	2.13535i	0.325555	+	0.0955915i	0.440426	−	0.897789i	$-0.354827\pi$
$499$	7.27234	+	2.13535i	0.325555	+	0.0955915i	−0.114871	+	0.993380i	$0.536646\pi$
$500$	0.142315	+	0.989821i	0.00636451	+	0.0442662i
$501$	−5.51406	−	6.63115i	−0.246350	−	0.296258i
$502$	−20.2349	−	2.90933i	−0.903126	−	0.129850i
$503$	−24.9898	−	16.0600i	−1.11424	−	0.716080i	−0.152028	−	0.988376i	$-0.548580\pi$
$503$	−24.9898	−	16.0600i	−1.11424	−	0.716080i	−0.962213	+	0.272297i	$0.912217\pi$
$504$	0.587754	−	3.16804i	0.0261806	−	0.141116i
$505$		−	0.995100i		−	0.0442814i
$506$	2.12854	+	11.0117i	0.0946251	+	0.489528i
$507$	20.2873	+	9.76785i	0.900990	+	0.433805i
$508$	−2.33453	−	2.69419i	−0.103578	−	0.119536i
$509$	4.48649	−	6.98112i	0.198860	−	0.309433i	−0.727474	−	0.686135i	$-0.759306\pi$
$509$	4.48649	−	6.98112i	0.198860	−	0.309433i	0.926334	+	0.376703i	$0.122942\pi$
$510$	9.39003	+	6.30782i	0.415797	+	0.279315i
$511$	−14.4512	−	6.59962i	−0.639282	−	0.291950i
$512$	−0.989821	+	0.142315i	−0.0437443	+	0.00628949i
$513$	23.0338	+	1.40590i	1.01697	+	0.0620718i
$514$	2.27790	−	1.46392i	0.100474	−	0.0645705i
$515$	−1.59856	+	0.730040i	−0.0704411	+	0.0321694i
$516$	−2.55067	+	15.4978i	−0.112287	+	0.682255i
$517$	−14.4491	−	12.5202i	−0.635470	−	0.550638i
$518$	4.61508	+	3.99899i	0.202775	+	0.175706i
$519$	5.69130	−	34.5803i	0.249821	−	1.51791i
$520$	−0.0127450	+	0.00582046i	−0.000558906	+	0.000255244i
$521$	−19.2324	+	12.3599i	−0.842587	+	0.541498i	−0.889254	−	0.457413i	$-0.848776\pi$
$521$	−19.2324	+	12.3599i	−0.842587	+	0.541498i	0.0466676	+	0.998910i	$0.485140\pi$
$522$	1.38750	+	3.39708i	0.0607290	+	0.148686i
$523$	25.0226	−	3.59770i	1.09416	−	0.157316i	0.428478	−	0.903552i	$-0.359050\pi$
$523$	25.0226	−	3.59770i	1.09416	−	0.157316i	0.665682	+	0.746236i	$0.268141\pi$
$524$	−17.6506	−	8.06076i	−0.771070	−	0.352136i
$525$	−1.54421	−	1.03734i	−0.0673949	−	0.0452730i
$526$	8.15880	−	12.6953i	0.355741	−	0.553543i
$527$	38.3116	+	44.2139i	1.66888	+	1.92599i
$528$	−3.64957	−	1.75718i	−0.158827	−	0.0764716i
$529$	21.3431	−	8.57146i	0.927963	−	0.372672i
$530$		−	2.09680i		−	0.0910793i
$531$	−10.4236	−	1.93384i	−0.452345	−	0.0839217i
$532$	4.01270	+	2.57880i	0.173972	+	0.111805i
$533$	−0.160727	−	0.0231091i	−0.00696187	−	0.00100097i
$534$	−2.37559	−	2.85686i	−0.102802	−	0.123628i
$535$	0.278533	+	1.93724i	0.0120420	+	0.0837541i
$536$	−1.17584	−	0.345259i	−0.0507888	−	0.0149129i
$537$	1.74134	+	14.1462i	0.0751443	+	0.610454i
$538$	9.72745	+	21.3001i	0.419380	+	0.918315i
$539$	−13.1186	+	3.85198i	−0.565060	+	0.165917i
$540$	−4.58630	−	2.44251i	−0.197363	−	0.105109i
$541$	−3.86331	+	4.45850i	−0.166097	+	0.191686i	−0.832696	−	0.553730i	$-0.813204\pi$
$541$	−3.86331	+	4.45850i	−0.166097	+	0.191686i	0.666599	+	0.745416i	$0.267749\pi$
$542$	3.46711	+	11.8079i	0.148925	+	0.507193i
$543$	−21.4757	−	0.436451i	−0.921612	−	0.0187299i
$544$	3.53092	+	5.49421i	0.151387	+	0.235562i
$545$	4.21448	−	14.3532i	0.180529	−	0.614824i
$546$	0.00784993	−	0.0248546i	0.000335946	−	0.00106368i
$547$	8.68918	−	19.0266i	0.371522	−	0.813521i	−0.627858	−	0.778328i	$-0.716068\pi$
$547$	8.68918	−	19.0266i	0.371522	−	0.813521i	0.999381	−	0.0351928i	$-0.0112045\pi$
$548$	2.04035	−	14.1909i	0.0871594	−	0.606207i
$549$	−27.9878	+	2.86920i	−1.19449	+	0.122455i
$550$	−1.76739	+	1.53145i	−0.0753618	+	0.0653014i
$551$	−5.43223			−0.231421
$552$	−2.11761	+	8.03217i	−0.0901315	+	0.341872i
$553$	−0.280511			−0.0119285
$554$	11.4365	−	9.90981i	0.485892	−	0.421028i
$555$	8.39105	−	5.15475i	0.356180	−	0.218807i
$556$	−1.57993	+	10.9886i	−0.0670039	+	0.466022i
$557$	15.5462	−	34.0414i	0.658714	−	1.44238i	−0.225002	−	0.974358i	$-0.572239\pi$
$557$	15.5462	−	34.0414i	0.658714	−	1.44238i	0.883716	−	0.468024i	$-0.155034\pi$
$558$	−19.5778	−	18.4090i	−0.828796	−	0.779316i
$559$	−0.0357953	+	0.121908i	−0.00151398	+	0.00515615i
$560$	−0.580667	−	0.903536i	−0.0245377	−	0.0381814i
$561$	−0.537517	+	26.4487i	−0.0226940	+	1.11666i
$562$	−0.731832	−	2.49239i	−0.0308705	−	0.105135i
$563$	25.9743	−	29.9760i	1.09469	−	1.26334i	0.132430	−	0.991192i	$-0.457722\pi$
$563$	25.9743	−	29.9760i	1.09469	−	1.26334i	0.962257	−	0.272144i	$-0.0877326\pi$
$564$	−5.61942	−	12.9974i	−0.236620	−	0.547290i
$565$	4.00770	−	1.17677i	0.168605	−	0.0495069i
$566$	−4.34657	−	9.51767i	−0.182700	−	0.400057i
$567$	9.08979	−	3.28838i	0.381735	−	0.138099i
$568$	−6.98748	−	2.05171i	−0.293188	−	0.0860878i
$569$	−3.57508	−	24.8652i	−0.149875	−	1.04240i	−0.916421	−	0.400215i	$-0.868936\pi$
$569$	−3.57508	−	24.8652i	−0.149875	−	1.04240i	0.766546	−	0.642189i	$-0.221974\pi$
$570$	5.91454	−	4.91817i	0.247733	−	0.206000i
$571$	−23.5635	−	3.38792i	−0.986103	−	0.141780i	−0.369649	−	0.929171i	$-0.620522\pi$
$571$	−23.5635	−	3.38792i	−0.986103	−	0.141780i	−0.616454	+	0.787391i	$0.711431\pi$
$572$	−0.0275649	−	0.0177149i	−0.00115255	−	0.000740697i
$573$	2.29099	+	8.43260i	0.0957074	+	0.352277i
$574$		−	12.4473i		−	0.519541i
$575$	3.77139	+	2.96254i	0.157278	+	0.123546i
$576$	−1.87084	−	2.34520i	−0.0779518	−	0.0977165i
$577$	17.3468	+	20.0193i	0.722156	+	0.833412i	0.991565	−	0.129613i	$-0.0413737\pi$
$577$	17.3468	+	20.0193i	0.722156	+	0.833412i	−0.269409	+	0.963026i	$0.586828\pi$
$578$	13.8695	−	21.5813i	0.576893	−	0.897664i
$579$	10.7595	−	16.0169i	0.447148	−	0.665639i
$580$	1.11264	+	0.508123i	0.0461997	+	0.0210987i
$581$	11.8566	−	1.70473i	0.491896	−	0.0707240i
$582$	−9.41839	−	8.50221i	−0.390405	−	0.352428i
$583$	4.12515	−	2.65107i	0.170846	−	0.109796i
$584$	−13.4550	+	6.14470i	−0.556773	+	0.254270i
$585$	−0.0344084	−	0.0241430i	−0.00142261	−	0.000998189i
$586$	−2.13655	−	1.85133i	−0.0882601	−	0.0764778i
$587$	7.32572	+	6.34777i	0.302365	+	0.262001i	0.792807	−	0.609473i	$-0.208619\pi$
$587$	7.32572	+	6.34777i	0.302365	+	0.262001i	−0.490442	+	0.871474i	$0.663165\pi$
$588$	−9.99192	−	1.64449i	−0.412060	−	0.0678177i
$589$	36.1876	−	16.5263i	1.49108	−	0.680955i
$590$	−2.97284	+	1.91053i	−0.122390	+	0.0786552i
$591$	−18.4896	+	20.4820i	−0.760561	+	0.842517i
$592$	5.62782	−	0.809158i	0.231302	−	0.0332562i
$593$	−13.5069	−	6.16837i	−0.554660	−	0.253305i	0.118307	−	0.992977i	$-0.462253\pi$
$593$	−13.5069	−	6.16837i	−0.554660	−	0.253305i	−0.672967	+	0.739672i	$0.734981\pi$
$594$	−0.993374	−	12.1110i	−0.0407586	−	0.496921i
$595$	−3.79233	+	5.90098i	−0.155470	+	0.241916i
$596$	12.1063	+	13.9714i	0.495892	+	0.572290i
$597$	−12.9746	+	26.9475i	−0.531015	+	1.10289i
$598$	−0.0249400	+	0.0623955i	−0.00101987	+	0.00255154i
$599$		−	32.0753i		−	1.31056i	−0.755386	−	0.655280i	$-0.772551\pi$
$599$		−	32.0753i		−	1.31056i	0.755386	−	0.655280i	$-0.227449\pi$
$600$	−1.67146	+	0.454107i	−0.0682372	+	0.0185388i
$601$	0.511530	+	0.328740i	0.0208657	+	0.0134096i	0.551032	−	0.834484i	$-0.314234\pi$
$601$	0.511530	+	0.328740i	0.0208657	+	0.0134096i	−0.530166	+	0.847894i	$0.677871\pi$
$602$	−9.64028	−	1.38606i	−0.392909	−	0.0564917i
$603$	−0.891601	−	3.56670i	−0.0363088	−	0.145247i
$604$	0.722871	+	5.02767i	0.0294132	+	0.204573i
$605$	5.30694	+	1.55826i	0.215758	+	0.0633521i
$606$	1.71065	−	0.210574i	0.0694905	−	0.00855398i
$607$	10.6675	+	23.3586i	0.432982	+	0.948098i	0.992834	+	0.119505i	$0.0381308\pi$
$607$	10.6675	+	23.3586i	0.432982	+	0.948098i	−0.559852	+	0.828593i	$0.689142\pi$
$608$	4.26121	−	1.25120i	0.172815	−	0.0507430i
$609$	−2.08860	+	0.903002i	−0.0846342	+	0.0365915i
$610$	−6.14139	+	7.08755i	−0.248658	+	0.286966i
$611$	−0.0322715	−	0.109907i	−0.00130557	−	0.00444635i
$612$	−8.85659	+	17.4770i	−0.358007	+	0.706465i
$613$	−14.1689	−	22.0472i	−0.572275	−	0.890477i	0.427634	−	0.903952i	$-0.359347\pi$
$613$	−14.1689	−	22.0472i	−0.572275	−	0.890477i	−0.999909	+	0.0134748i	$0.995711\pi$
$614$	−6.11485	+	20.8253i	−0.246775	+	0.840439i
$615$	−19.1413	−	6.04547i	−0.771851	−	0.243777i
$616$	1.04341	−	2.28475i	0.0420402	−	0.0920553i
$617$	2.40830	−	16.7501i	0.0969544	−	0.674333i	−0.882149	−	0.470970i	$-0.843904\pi$
$617$	2.40830	−	16.7501i	0.0969544	−	0.674333i	0.979103	−	0.203363i	$-0.0651870\pi$
$618$	−1.59327	−	2.59357i	−0.0640906	−	0.104329i
$619$	−32.5856	+	28.2356i	−1.30973	+	1.13488i	−0.327980	+	0.944685i	$0.606368\pi$
$619$	−32.5856	+	28.2356i	−1.30973	+	1.13488i	−0.981746	+	0.190199i	$0.939087\pi$
$620$	−8.95783			−0.359755
$621$	−23.9985	+	6.71372i	−0.963025	+	0.269412i
$622$	3.33238			0.133616
$623$	1.74123	−	1.50878i	0.0697608	−	0.0604480i
$624$	−0.0127028	−	0.0206780i	−0.000508519	−	0.000827782i
$625$	−0.142315	+	0.989821i	−0.00569259	+	0.0395929i
$626$	−3.64444	+	7.98020i	−0.145661	+	0.318953i
$627$	17.1538	+	5.41774i	0.685055	+	0.216364i
$628$	−4.73011	+	16.1093i	−0.188752	+	0.642830i
$629$	−20.0757	−	31.2384i	−0.800470	−	1.24556i
$630$	1.45649	−	2.87413i	0.0580278	−	0.114508i
$631$	−1.26895	−	4.32165i	−0.0505161	−	0.172042i	0.930371	−	0.366619i	$-0.119485\pi$
$631$	−1.26895	−	4.32165i	−0.0505161	−	0.172042i	−0.980887	+	0.194577i	$0.937667\pi$
$632$	−0.171033	+	0.197383i	−0.00680334	+	0.00785147i
$633$	3.82872	−	1.65534i	0.152178	−	0.0657939i
$634$	1.61403	−	0.473922i	0.0641013	−	0.0188219i
$635$	−1.48093	−	3.24277i	−0.0587687	−	0.128686i
$636$	3.60456	−	0.443706i	0.142930	−	0.0175941i
$637$	−0.0785975	−	0.0230783i	−0.00311415	−	0.000914396i
$638$	0.407091	+	2.83138i	0.0161169	+	0.112096i
$639$	−5.29836	−	21.1952i	−0.209600	−	0.838469i
$640$	−0.989821	−	0.142315i	−0.0391261	−	0.00562549i
$641$	−7.93814	−	5.10153i	−0.313537	−	0.201498i	0.374402	−	0.927267i	$-0.377848\pi$
$641$	−7.93814	−	5.10153i	−0.313537	−	0.201498i	−0.687939	+	0.725768i	$0.741484\pi$
$642$	−3.27132	+	0.888759i	−0.129109	+	0.0350765i
$643$			17.0506i			0.672410i	0.941789	+	0.336205i	$0.109144\pi$
$643$			17.0506i			0.672410i	−0.941789	+	0.336205i	$0.890856\pi$
$644$	−5.00636	−	1.21165i	−0.197278	−	0.0477455i
$645$	−6.81360	+	14.1515i	−0.268285	+	0.557214i
$646$	−18.9941	−	21.9204i	−0.747313	−	0.862445i
$647$	5.79317	−	9.01434i	0.227753	−	0.354390i	−0.708504	−	0.705707i	$-0.750630\pi$
$647$	5.79317	−	9.01434i	0.227753	−	0.354390i	0.936257	+	0.351317i	$0.114266\pi$
$648$	3.22834	−	8.40106i	0.126821	−	0.330025i
$649$	−7.51735	−	3.43306i	−0.295082	−	0.134759i
$650$	−0.0138686	+	0.00199400i	−0.000543970	+	7.82111e-5i
$651$	11.1663	−	12.3696i	0.437642	−	0.484801i
$652$	17.3741	−	11.1656i	0.680421	−	0.437280i
$653$	9.97368	−	4.55483i	0.390300	−	0.178244i	−0.210592	−	0.977574i	$-0.567539\pi$
$653$	9.97368	−	4.55483i	0.390300	−	0.178244i	0.600893	+	0.799330i	$0.294812\pi$
$654$	25.5661	+	4.20772i	0.999712	+	0.164535i
$655$	−14.6647	−	12.7070i	−0.572995	−	0.496503i
$656$	−8.75861	−	7.58938i	−0.341966	−	0.296316i
$657$	−36.3252	−	25.4879i	−1.41718	−	0.994379i
$658$	7.98715	−	3.64761i	0.311372	−	0.142199i
$659$	−17.6946	+	11.3716i	−0.689282	+	0.442975i	−0.837830	−	0.545931i	$-0.816176\pi$
$659$	−17.6946	+	11.3716i	−0.689282	+	0.442975i	0.148549	+	0.988905i	$0.452540\pi$
$660$	−3.00668	−	2.71421i	−0.117035	−	0.105650i
$661$	−46.2410	+	6.64846i	−1.79857	+	0.258595i	−0.958745	−	0.284267i	$-0.908250\pi$
$661$	−46.2410	+	6.64846i	−1.79857	+	0.258595i	−0.839822	+	0.542862i	$0.817341\pi$
$662$	−32.3803	−	14.7876i	−1.25850	−	0.574736i
$663$	−0.0883801	+	0.131565i	−0.00343240	+	0.00510958i
$664$	6.02969	−	9.38238i	0.233997	−	0.364107i
$665$	3.12362	+	3.60485i	0.121129	+	0.139790i
$666$	10.6370	+	13.3341i	0.412177	+	0.516684i
$667$	5.54244	−	1.92164i	0.214604	−	0.0744060i
$668$		−	4.97919i		−	0.192651i
$669$	8.21253	+	30.2284i	0.317515	+	1.16870i
$670$	−1.03094	−	0.662547i	−0.0398288	−	0.0255964i
$671$	−21.7085	−	3.12121i	−0.838047	−	0.120493i
$672$	1.43037	−	1.18941i	0.0551778	−	0.0458824i
$673$	6.09781	+	42.4112i	0.235053	+	1.63483i	0.675718	+	0.737160i	$0.263834\pi$
$673$	6.09781	+	42.4112i	0.235053	+	1.63483i	−0.440665	+	0.897672i	$0.645257\pi$
$674$	16.4569	+	4.83218i	0.633896	+	0.186129i
$675$	−3.71239	−	3.63568i	−0.142890	−	0.139937i
$676$	5.40031	+	11.8250i	0.207704	+	0.454809i
$677$	−9.09841	+	2.67153i	−0.349680	+	0.102675i	−0.451856	−	0.892091i	$-0.649238\pi$
$677$	−9.09841	+	2.67153i	−0.349680	+	0.102675i	0.102176	+	0.994766i	$0.467420\pi$
$678$	2.87102	+	6.64052i	0.110261	+	0.255028i
$679$	5.15242	−	5.94621i	0.197732	−	0.228195i
$680$	1.83999	+	6.26643i	0.0705604	+	0.240307i
$681$	−0.221239	+	10.8861i	−0.00847790	+	0.417158i
$682$	−11.3257	−	17.6232i	−0.433685	−	0.674827i
$683$	13.2518	−	45.1315i	0.507067	−	1.72691i	−0.164883	−	0.986313i	$-0.552725\pi$
$683$	13.2518	−	45.1315i	0.507067	−	1.72691i	0.671950	−	0.740597i	$-0.265457\pi$
$684$	9.70629	+	9.12681i	0.371129	+	0.348972i
$685$	5.95575	−	13.0413i	0.227558	−	0.498282i
$686$	1.96359	−	13.6571i	0.0749704	−	0.521430i
$687$	24.5475	−	15.0799i	0.936546	−	0.575334i
$688$	−6.85318	+	5.93832i	−0.261275	+	0.226396i
$689$	0.0293787			0.00111924
$690$	−4.29476	+	7.11021i	−0.163499	+	0.270681i
$691$	−20.2800			−0.771488			−0.385744	−	0.922606i	$-0.626055\pi$
$691$	−20.2800			−0.771488			−0.385744	+	0.922606i	$0.626055\pi$
$692$	15.2915	−	13.2502i	0.581295	−	0.503695i
$693$	7.49591	−	0.768452i	0.284746	−	0.0291911i
$694$	−3.44641	+	23.9703i	−0.130824	+	0.909901i
$695$	−4.61179	+	10.0984i	−0.174935	+	0.383054i
$696$	−0.638057	+	2.02023i	−0.0241855	+	0.0765766i
$697$	−21.3242	+	72.6236i	−0.807712	+	2.75082i
$698$	−13.8800	−	21.5976i	−0.525364	−	0.817482i
$699$	32.2848	+	0.656124i	1.22112	+	0.0248169i
$700$	−0.302591	−	1.03053i	−0.0114369	−	0.0389503i
$701$	−6.41032	+	7.39790i	−0.242114	+	0.279415i	−0.863781	−	0.503867i	$-0.831910\pi$
$701$	−6.41032	+	7.39790i	−0.242114	+	0.279415i	0.621667	+	0.783282i	$0.286456\pi$
$702$	0.0342224	−	0.0642595i	0.00129164	−	0.00242532i
$703$	−24.2279	+	7.11396i	−0.913773	+	0.268308i
$704$	−0.971487	−	2.12726i	−0.0366143	−	0.0801741i
$705$	−1.73000	−	14.0541i	−0.0651555	−	0.529308i
$706$	2.41321	+	0.708582i	0.0908223	+	0.0266678i
$707$	0.152102	+	1.05789i	0.00572039	+	0.0397862i
$708$	−3.91343	−	4.70625i	−0.147076	−	0.176872i
$709$	−38.3480	−	5.51361i	−1.44019	−	0.207068i	−0.622451	−	0.782659i	$-0.713863\pi$
$709$	−38.3480	−	5.51361i	−1.44019	−	0.207068i	−0.817738	+	0.575591i	$0.804772\pi$
$710$	−6.12640	−	3.93720i	−0.229920	−	0.147760i
$711$	−0.770379	−	0.142925i	−0.0288915	−	0.00536011i
$712$		−	2.14516i		−	0.0803931i
$713$	−31.0757	+	29.6629i	−1.16379	+	1.11088i
$714$	−10.9467	−	5.27059i	−0.409671	−	0.197247i
$715$	−0.0214575	−	0.0247632i	−0.000802464	−	0.000926093i
$716$	−4.44892	+	6.92265i	−0.166264	+	0.258712i
$717$	1.39013	+	0.933831i	0.0519154	+	0.0348746i
$718$	−22.8033	−	10.4139i	−0.851011	−	0.388644i
$719$	−8.87795	+	1.27646i	−0.331092	+	0.0476038i	−0.305856	−	0.952078i	$-0.598943\pi$
$719$	−8.87795	+	1.27646i	−0.331092	+	0.0476038i	−0.0252355	+	0.999682i	$0.508034\pi$
$720$	−1.13434	−	2.77728i	−0.0422745	−	0.103503i
$721$	1.58785	−	1.02045i	0.0591346	−	0.0380035i
$722$	−0.658040	+	0.300517i	−0.0244897	+	0.0111841i
$723$	−7.17549	+	43.5982i	−0.266859	+	1.62144i
$724$	−9.37249	−	8.12131i	−0.348326	−	0.301826i
$725$	0.924411	+	0.801006i	0.0343318	+	0.0297486i
$726$	−1.55576	+	9.45277i	−0.0577396	+	0.350825i
$727$	3.55788	−	1.62483i	0.131955	−	0.0602617i	−0.348344	−	0.937367i	$-0.613256\pi$
$727$	3.55788	−	1.62483i	0.131955	−	0.0602617i	0.480298	+	0.877105i	$0.340528\pi$
$728$	0.0126596	−	0.00813584i	0.000469196	−	0.000301534i
$729$	26.6391	−	4.39960i	0.986635	−	0.162948i
$730$	−14.6412	+	2.10508i	−0.541894	+	0.0779125i
$731$	53.8715	+	24.6023i	1.99251	+	0.909948i
$732$	−13.4836	−	9.05772i	−0.498369	−	0.334783i
$733$	25.5466	−	39.7513i	0.943585	−	1.46825i	0.0609767	−	0.998139i	$-0.480578\pi$
$733$	25.5466	−	39.7513i	0.943585	−	1.46825i	0.882609	−	0.470108i	$-0.155785\pi$
$734$	−1.77850	−	2.05250i	−0.0656456	−	0.0757590i
$735$	−9.12387	−	4.39293i	−0.336539	−	0.162036i
$736$	−3.90506	+	2.78398i	−0.143942	+	0.102619i
$737$		−	2.86591i		−	0.105567i
$738$	6.34212	−	34.1846i	0.233457	−	1.25835i
$739$	28.7228	+	18.4590i	1.05659	+	0.679026i	0.949034	−	0.315174i	$-0.102063\pi$
$739$	28.7228	+	18.4590i	1.05659	+	0.679026i	0.107551	+	0.994200i	$0.465699\pi$
$740$	5.62782	+	0.809158i	0.206883	+	0.0297452i
$741$	0.0689094	+	0.0828698i	0.00253145	+	0.00304430i
$742$	0.320499	+	2.22912i	0.0117659	+	0.0818335i
$743$	−9.62516	−	2.82620i	−0.353113	−	0.103683i	0.100365	−	0.994951i	$-0.467999\pi$
$743$	−9.62516	−	2.82620i	−0.353113	−	0.103683i	−0.453478	+	0.891267i	$0.649817\pi$
$744$	−1.89557	−	15.3992i	−0.0694951	−	0.564562i
$745$	7.67969	+	16.8162i	0.281362	+	0.616097i
$746$	−26.8898	+	7.89556i	−0.984505	+	0.289077i
$747$	33.4309	+	1.35939i	1.22317	+	0.0497376i
$748$	−10.0019	+	11.5428i	−0.365706	+	0.422047i
$749$	−0.592218	−	2.01691i	−0.0216392	−	0.0736963i
$750$	−1.73169	−	0.0351932i	−0.0632325	−	0.00128507i
$751$	3.06750	+	4.77312i	0.111935	+	0.174174i	0.892701	−	0.450649i	$-0.148808\pi$
$751$	3.06750	+	4.77312i	0.111935	+	0.174174i	−0.780767	+	0.624823i	$0.785171\pi$
$752$	2.30327	−	7.84422i	0.0839916	−	0.286049i
$753$	10.6639	−	33.7642i	0.388614	−	1.23044i
$754$	−0.00711941	+	0.0155893i	−0.000259274	+	0.000567730i
$755$	−0.722871	+	5.02767i	−0.0263080	+	0.182976i
$756$	5.24905	+	1.89562i	0.190906	+	0.0689429i
$757$	15.5221	−	13.4500i	0.564160	−	0.488847i	−0.325456	−	0.945557i	$-0.605518\pi$
$757$	15.5221	−	13.4500i	0.564160	−	0.488847i	0.889616	+	0.456710i	$0.150972\pi$
$758$	−0.783716			−0.0284658
$759$	−19.4183	+	0.540428i	−0.704840	+	0.0196163i
$760$	4.44110			0.161096
$761$	28.6955	−	24.8648i	1.04021	−	0.901349i	0.0449905	−	0.998987i	$-0.485674\pi$
$761$	28.6955	−	24.8648i	1.04021	−	0.901349i	0.995222	+	0.0976381i	$0.0311288\pi$
$762$	5.26119	−	3.23203i	0.190593	−	0.117084i
$763$	−2.28652	+	15.9031i	−0.0827777	+	0.575732i
$764$	−2.09579	+	4.58913i	−0.0758229	+	0.166029i
$765$	−13.4217	+	14.2738i	−0.485262	+	0.516072i
$766$	−3.87208	+	13.1871i	−0.139904	+	0.476469i
$767$	−0.0267688	−	0.0416530i	−0.000966564	−	0.00150400i
$768$	0.0351932	−	1.73169i	0.00126992	−	0.0624871i
$769$	−4.89053	−	16.6556i	−0.176357	−	0.600616i	−0.999464	−	0.0327305i	$-0.989580\pi$
$769$	−4.89053	−	16.6556i	−0.176357	−	0.600616i	0.823107	−	0.567886i	$-0.192238\pi$
$770$	1.64483	−	1.89824i	0.0592757	−	0.0684078i
$771$	1.86119	+	4.30483i	0.0670291	+	0.155035i
$772$	10.6889	−	3.13853i	0.384700	−	0.112958i
$773$	2.54020	+	5.56227i	0.0913647	+	0.200061i	0.949798	−	0.312865i	$-0.101289\pi$
$773$	2.54020	+	5.56227i	0.0913647	+	0.200061i	−0.858433	+	0.512926i	$0.828562\pi$
$774$	−25.7693	−	8.71849i	−0.926258	−	0.313380i
$775$	−8.59497	−	2.52371i	−0.308741	−	0.0906544i
$776$	−1.04254	−	7.25105i	−0.0374251	−	0.260297i
$777$	−8.13264	+	6.76261i	−0.291757	+	0.242607i
$778$	7.57290	+	1.08882i	0.271502	+	0.0390360i
$779$	43.2988	+	27.8264i	1.55134	+	0.996985i
$780$	−0.00636257	−	0.0234192i	−0.000227817	−	0.000838541i
$781$		−	17.0307i		−	0.609408i
$782$	27.1337	+	15.6460i	0.970300	+	0.559499i
$783$	−6.19609	+	1.41578i	−0.221430	+	0.0505957i
$784$	−3.82861	−	4.41845i	−0.136736	−	0.157802i
$785$	−9.07701	+	14.1241i	−0.323972	+	0.504111i
$786$	18.7411	−	27.8986i	0.668472	−	0.995110i
$787$	−26.8960	−	12.2830i	−0.958738	−	0.437841i	−0.126320	−	0.991990i	$-0.540317\pi$
$787$	−26.8960	−	12.2830i	−0.958738	−	0.437841i	−0.832418	+	0.554148i	$0.813044\pi$
$788$	−15.7687	+	2.26720i	−0.561737	+	0.0807656i
$789$	19.4022	+	17.5148i	0.690735	+	0.623544i
$790$	−0.219714	+	0.141202i	−0.00781709	+	0.00502374i
$791$	−4.08073	+	1.86360i	−0.145094	+	0.0662622i
$792$	4.02968	−	5.74307i	0.143188	−	0.204071i
$793$	−0.0993049	−	0.0860482i	−0.00352642	−	0.00305566i
$794$	−7.48302	−	6.48408i	−0.265563	−	0.230111i
$795$	3.58356	+	0.589790i	0.127096	+	0.0209177i
$796$	−15.7071	+	7.17321i	−0.556725	+	0.254248i
$797$	11.8537	−	7.61791i	0.419880	−	0.269840i	−0.313595	−	0.949557i	$-0.601533\pi$
$797$	11.8537	−	7.61791i	0.419880	−	0.269840i	0.733475	+	0.679716i	$0.237897\pi$
$798$	−5.53602	+	6.13257i	−0.195973	+	0.217091i
$799$	−52.8498	+	7.59865i	−1.86969	+	0.268821i
$800$	−0.909632	−	0.415415i	−0.0321603	−	0.0146871i
$801$	5.55075	−	3.25644i	0.196126	−	0.115061i
$802$	−9.11317	+	14.1804i	−0.321797	+	0.500726i
$803$	−22.6528	−	26.1428i	−0.799401	−	0.922558i
$804$	0.920810	−	1.91247i	0.0324745	−	0.0674477i
$805$	−4.46220	−	2.57302i	−0.157272	−	0.0906870i
$806$		−	0.125510i		−	0.00442089i
$807$	−39.1393	+	10.6335i	−1.37777	+	0.374316i
$808$	0.837132	+	0.537992i	0.0294502	+	0.0189265i
$809$	18.6774	+	2.68541i	0.656663	+	0.0944138i	0.462589	−	0.886573i	$-0.346921\pi$
$809$	18.6774	+	2.68541i	0.656663	+	0.0944138i	0.194074	+	0.980987i	$0.437830\pi$
$810$	5.46443	−	7.15123i	0.192000	−	0.251269i
$811$	−1.68119	−	11.6929i	−0.0590346	−	0.410595i	−0.997815	−	0.0660772i	$-0.978952\pi$
$811$	−1.68119	−	11.6929i	−0.0590346	−	0.410595i	0.938780	−	0.344517i	$-0.111957\pi$
$812$	−1.26051	−	0.370120i	−0.0442353	−	0.0129887i
$813$	−21.1556	+	2.60417i	−0.741961	+	0.0913321i
$814$	5.52357	+	12.0949i	0.193601	+	0.423927i
$815$	19.8160	−	5.81851i	0.694125	−	0.203813i
$816$	−10.3831	+	4.48913i	−0.363482	+	0.157151i
$817$	26.3727	−	30.4357i	0.922664	−	1.06481i
$818$	8.17678	+	27.8475i	0.285894	+	0.973667i
$819$	0.0402699	+	0.0204071i	0.00140715	+	0.000713082i
$820$	−6.26565	−	9.74955i	−0.218806	−	0.340469i
$821$	2.77933	−	9.46553i	0.0969993	−	0.330349i	−0.896669	−	0.442701i	$-0.854020\pi$
$821$	2.77933	−	9.46553i	0.0969993	−	0.330349i	0.993668	+	0.112352i	$0.0358384\pi$
$822$	23.6792	+	7.47871i	0.825908	+	0.260850i
$823$	4.06195	−	8.89443i	0.141591	−	0.310040i	−0.825530	−	0.564358i	$-0.809124\pi$
$823$	4.06195	−	8.89443i	0.141591	−	0.310040i	0.967121	+	0.254318i	$0.0818509\pi$
$824$	0.250100	−	1.73949i	0.00871266	−	0.0605979i
$825$	−2.12021	−	3.45134i	−0.0738163	−	0.120160i
$826$	2.86841	−	2.48549i	0.0998047	−	0.0864812i
$827$	−43.9502			−1.52830			−0.764149	−	0.645040i	$-0.776841\pi$
$827$	−43.9502			−1.52830			−0.764149	+	0.645040i	$0.776841\pi$
$828$	−13.1318	−	5.87841i	−0.456362	−	0.204289i
$829$	48.6613			1.69008			0.845038	−	0.534706i	$-0.179578\pi$
$829$	48.6613			1.69008			0.845038	+	0.534706i	$0.179578\pi$
$830$	8.42877	−	7.30357i	0.292567	−	0.253511i
$831$	13.7196	+	22.3331i	0.475927	+	0.774728i
$832$	0.00199400	−	0.0138686i	6.91295e−5	−	0.000480806i
$833$	−15.8618	+	34.7325i	−0.549579	+	1.20341i
$834$	−18.3358	−	5.79108i	−0.634918	−	0.200529i
$835$	1.40280	−	4.77750i	0.0485459	−	0.165332i
$836$	5.61506	+	8.73721i	0.194201	+	0.302183i
$837$	36.9690	−	28.2816i	1.27783	−	0.977555i
$838$	6.73231	+	22.9281i	0.232564	+	0.792040i
$839$	−27.3867	+	31.6060i	−0.945495	+	1.09116i	0.0502254	+	0.998738i	$0.484006\pi$
$839$	−27.3867	+	31.6060i	−0.945495	+	1.09116i	−0.995720	+	0.0924210i	$0.970539\pi$
$840$	1.70753	−	0.738247i	0.0589152	−	0.0254719i
$841$	−26.3898	+	7.74873i	−0.909992	+	0.267198i
$842$	9.71667	+	21.2765i	0.334858	+	0.733238i
$843$	4.46549	−	0.549683i	0.153800	−	0.0189321i
$844$	2.31071	+	0.678487i	0.0795380	+	0.0233545i
$845$	1.85006	+	12.8675i	0.0636442	+	0.442655i
$846$	23.7940	−	5.94799i	0.818053	−	0.204496i
$847$	−5.88000	−	0.845416i	−0.202039	−	0.0290488i
$848$	1.76394	+	1.13362i	0.0605740	+	0.0389286i
$849$	17.4889	−	4.75141i	0.600216	−	0.163068i
$850$			6.53098i			0.224011i
$851$	22.2029	−	15.8288i	0.761107	−	0.542606i
$852$	5.47193	−	11.3649i	0.187465	−	0.389355i
$853$	26.4489	+	30.5236i	0.905593	+	1.04511i	0.998776	+	0.0494608i	$0.0157503\pi$
$853$	26.4489	+	30.5236i	0.905593	+	1.04511i	−0.0931833	+	0.995649i	$0.529704\pi$
$854$	5.44559	−	8.47351i	0.186344	−	0.289957i
$855$	6.74180	+	11.4917i	0.230565	+	0.393007i
$856$	−1.78029	−	0.813033i	−0.0608492	−	0.0277889i
$857$	−41.6107	+	5.98272i	−1.42140	+	0.204366i	−0.809754	−	0.586769i	$-0.800400\pi$
$857$	−41.6107	+	5.98272i	−1.42140	+	0.204366i	−0.611641	+	0.791135i	$0.709490\pi$
$858$	0.0380293	−	0.0421272i	0.00129830	−	0.00143820i
$859$	27.8308	−	17.8858i	0.949574	−	0.610254i	0.0284802	−	0.999594i	$-0.490933\pi$
$859$	27.8308	−	17.8858i	0.949574	−	0.610254i	0.921094	+	0.389340i	$0.127297\pi$
$860$	−8.24860	+	3.76701i	−0.281275	+	0.128454i
$861$	21.2732	+	3.50119i	0.724989	+	0.119320i
$862$	14.9419	+	12.9472i	0.508922	+	0.440984i
$863$	−14.8429	−	12.8614i	−0.505258	−	0.437809i	0.364561	−	0.931180i	$-0.381219\pi$
$863$	−14.8429	−	12.8614i	−0.505258	−	0.437809i	−0.869819	+	0.493371i	$0.835765\pi$
$864$	4.53431	−	2.53772i	0.154260	−	0.0863351i
$865$	18.4051	−	8.40532i	0.625791	−	0.285789i
$866$	−20.8474	+	13.3978i	−0.708422	+	0.455275i
$867$	32.9825	+	29.7741i	1.12014	+	1.01118i
$868$	9.52309	−	1.36921i	0.323235	−	0.0464742i
$869$	−0.555587	−	0.253728i	−0.0188470	−	0.00860714i
$870$	−1.18138	+	1.75863i	−0.0400524	+	0.0596233i
$871$	0.00928308	−	0.0144447i	0.000314545	−	0.000489442i
$872$	9.79616	+	11.3054i	0.331740	+	0.382848i
$873$	17.1800	−	13.7051i	0.581455	−	0.463846i
$874$	15.4067	−	14.7062i	0.521138	−	0.497446i
$875$		−	1.07403i		−	0.0363090i
$876$	−6.71702	−	24.7238i	−0.226947	−	0.835340i
$877$	29.0705	+	18.6825i	0.981640	+	0.630862i	0.929905	−	0.367799i	$-0.119888\pi$
$877$	29.0705	+	18.6825i	0.981640	+	0.630862i	0.0517351	+	0.998661i	$0.483525\pi$
$878$	−9.31151	−	1.33879i	−0.314248	−	0.0451821i
$879$	3.76500	−	3.13075i	0.126990	−	0.105597i
$880$	−0.332817	−	2.31479i	−0.0112192	−	0.0780316i
$881$	−5.44008	−	1.59735i	−0.183281	−	0.0538162i	0.188804	−	0.982015i	$-0.439539\pi$
$881$	−5.44008	−	1.59735i	−0.183281	−	0.0538162i	−0.372085	+	0.928199i	$0.621357\pi$
$882$	5.62107	−	16.6142i	0.189271	−	0.559430i
$883$	0.169022	+	0.370107i	0.00568805	+	0.0124551i	0.912455	−	0.409178i	$-0.134184\pi$
$883$	0.169022	+	0.370107i	0.00568805	+	0.0124551i	−0.906767	+	0.421633i	$0.861457\pi$
$884$	−0.0878002	+	0.0257805i	−0.00295304	+	0.000867090i
$885$	−2.42900	−	5.61815i	−0.0816500	−	0.188852i
$886$	−8.40426	+	9.69904i	−0.282347	+	0.325846i
$887$	−2.65477	−	9.04130i	−0.0891383	−	0.303577i	0.902842	−	0.429973i	$-0.141477\pi$
$887$	−2.65477	−	9.04130i	−0.0891383	−	0.303577i	−0.991980	+	0.126396i	$0.959659\pi$
$888$	−0.200097	+	9.84587i	−0.00671483	+	0.330406i
$889$	2.07004	+	3.22104i	0.0694268	+	0.108030i
$890$	0.604360	−	2.05826i	0.0202582	−	0.0689931i
$891$	20.9779	+	1.70886i	0.702785	+	0.0572490i
$892$	−7.51279	+	16.4507i	−0.251547	+	0.550811i
$893$	−5.16713	+	35.9382i	−0.172911	+	1.20262i
$894$	−27.2832	+	16.7605i	−0.912486	+	0.560554i
$895$	−6.21904	+	5.38883i	−0.207880	+	0.180129i
$896$	1.07403			0.0358810
$897$	−0.0996225	−	0.0601746i	−0.00332630	−	0.00200917i
$898$	−3.02972			−0.101103
$899$	−8.28071	+	7.17528i	−0.276177	+	0.239309i
$900$	−0.305945	−	2.98436i	−0.0101982	−	0.0994786i
$901$	1.94889	−	13.5548i	0.0649268	−	0.451576i
$902$	11.2589	−	24.6535i	0.374879	−	0.820871i
$903$	5.08049	−	16.0859i	0.169068	−	0.535306i
$904$	−1.17677	+	4.00770i	−0.0391387	+	0.133294i
$905$	−6.70480	−	10.4329i	−0.222875	−	0.346800i
$906$	−8.79592	−	0.178759i	−0.292225	−	0.00593888i
$907$	7.23935	+	24.6549i	0.240379	+	0.818654i	0.987990	+	0.154518i	$0.0493824\pi$
$907$	7.23935	+	24.6549i	0.240379	+	0.818654i	−0.747611	+	0.664136i	$0.768799\pi$
$908$	−4.11673	+	4.75096i	−0.136618	+	0.157666i
$909$	−0.121290	+	2.98284i	−0.00402295	+	0.0989344i
$910$	0.0144389	−	0.00423965i	0.000478646	−	0.000140543i
$911$	18.7738	+	41.1088i	0.622003	+	1.36200i	0.914054	+	0.405593i	$0.132935\pi$
$911$	18.7738	+	41.1088i	0.622003	+	1.36200i	−0.292051	+	0.956403i	$0.594338\pi$
$912$	0.939785	+	7.63460i	0.0311194	+	0.252807i
$913$	25.0255	+	7.34815i	0.828223	+	0.243188i
$914$	3.64937	+	25.3819i	0.120710	+	0.839559i
$915$	−10.3856	−	12.4896i	−0.343337	−	0.412893i
$916$	16.4638	+	2.36714i	0.543981	+	0.0782126i
$917$	17.5323	+	11.2673i	0.578968	+	0.372080i
$918$	−27.3780	−	20.0524i	−0.903608	−	0.661827i
$919$		−	30.4059i		−	1.00300i	−0.865159	−	0.501498i	$-0.832782\pi$
$919$		−	30.4059i		−	1.00300i	0.865159	−	0.501498i	$-0.167218\pi$
$920$	−4.53121	+	1.57103i	−0.149390	+	0.0517953i
$921$	−33.8716	−	16.3084i	−1.11611	−	0.537379i
$922$	17.8821	+	20.6370i	0.588914	+	0.679643i
$923$	0.0551648	−	0.0858382i	0.00181577	−	0.00282540i
$924$	3.61128	+	2.42591i	0.118802	+	0.0798065i
$925$	5.17188	+	2.36192i	0.170051	+	0.0776595i
$926$	−31.9314	+	4.59104i	−1.04933	+	0.150871i
$927$	4.88071	−	1.99347i	0.160304	−	0.0654740i
$928$	−1.02900	+	0.661296i	−0.0337785	+	0.0217081i
$929$	45.6198	−	20.8339i	1.49674	−	0.683536i	0.512224	−	0.858852i	$-0.328822\pi$
$929$	45.6198	−	20.8339i	1.49674	−	0.683536i	0.984512	+	0.175315i	$0.0560945\pi$
$930$	2.51966	−	15.3095i	0.0826230	−	0.502017i
$931$	19.6228	+	17.0033i	0.643111	+	0.557259i
$932$	14.0898	+	12.2089i	0.461527	+	0.399915i
$933$	−0.937334	+	5.69523i	−0.0306869	+	0.186454i
$934$	21.5924	−	9.86090i	0.706523	−	0.322658i
$935$	−12.8487	+	8.25738i	−0.420198	+	0.270045i
$936$	0.0389129	−	0.0158935i	0.00127191	−	0.000519495i
$937$	35.3553	−	5.08333i	1.15501	−	0.166065i	0.461922	−	0.886920i	$-0.347160\pi$
$937$	35.3553	−	5.08333i	1.15501	−	0.166065i	0.693086	+	0.720855i	$0.256251\pi$
$938$	1.19727	+	0.546775i	0.0390923	+	0.0178528i
$939$	−12.6135	−	8.47323i	−0.411627	−	0.276513i
$940$	4.41994	−	6.87757i	0.144163	−	0.224321i
$941$	33.3978	+	38.5432i	1.08874	+	1.25647i	0.964461	+	0.264224i	$0.0851157\pi$
$941$	33.3978	+	38.5432i	1.08874	+	1.25647i	0.124277	+	0.992248i	$0.460339\pi$
$942$	−26.2012	−	12.6153i	−0.853681	−	0.411027i
$943$	−54.0208	−	13.0742i	−1.75916	−	0.425754i
$944$		−	3.53382i		−	0.115016i
$945$	4.50237	+	3.29766i	0.146462	+	0.107273i
$946$	−17.8401	−	11.4651i	−0.580030	−	0.372763i
$947$	−16.8861	−	2.42786i	−0.548726	−	0.0788948i	−0.137624	−	0.990485i	$-0.543947\pi$
$947$	−16.8861	−	2.42786i	−0.548726	−	0.0788948i	−0.411101	+	0.911590i	$0.634856\pi$
$948$	−0.289231	−	0.347826i	−0.00939377	−	0.0112969i
$949$	−0.0294947	−	0.205140i	−0.000957438	−	0.00665913i
$950$	4.26121	+	1.25120i	0.138252	+	0.0405944i
$951$	0.355965	+	2.89178i	0.0115430	+	0.0937723i
$952$	−2.91393	−	6.38062i	−0.0944410	−	0.206797i
$953$	41.7166	−	12.2491i	1.35133	−	0.396788i	0.475634	−	0.879643i	$-0.342219\pi$
$953$	41.7166	−	12.2491i	1.35133	−	0.396788i	0.875700	+	0.482856i	$0.160400\pi$
$954$	−0.255574	+	6.28521i	−0.00827452	+	0.203491i
$955$	−3.30380	+	3.81279i	−0.106908	+	0.123379i
$956$	0.272398	+	0.927704i	0.00881000	+	0.0300041i
$957$	−4.95351	−	0.100670i	−0.160124	−	0.00325420i
$958$	−5.04378	−	7.84827i	−0.162957	−	0.253566i
$959$	−4.33820	+	14.7746i	−0.140088	+	0.477096i
$960$	0.521642	−	1.65163i	0.0168359	−	0.0533062i
$961$	20.4562	−	44.7927i	0.659876	−	1.44493i
$962$	−0.0113373	+	0.0788524i	−0.000365528	+	0.00254230i
$963$	−0.598783	−	5.84086i	−0.0192955	−	0.188219i
$964$	−19.2792	+	16.7056i	−0.620942	+	0.538050i
$965$	11.1401			0.358613
$966$	3.47896	−	8.21534i	0.111934	−	0.264324i
$967$	20.5107			0.659578			0.329789	−	0.944055i	$-0.393022\pi$
$967$	20.5107			0.659578			0.329789	+	0.944055i	$0.393022\pi$
$968$	−4.18003	+	3.62202i	−0.134351	+	0.116416i
$969$	42.8058	−	26.2962i	1.37512	−	0.844757i
$970$	1.04254	−	7.25105i	0.0334740	−	0.232817i
$971$	−23.6512	+	51.7889i	−0.759003	+	1.66199i	−0.00952669	+	0.999955i	$0.503032\pi$
$971$	−23.6512	+	51.7889i	−0.759003	+	1.66199i	−0.749477	+	0.662031i	$0.769695\pi$
$972$	13.4498	+	7.88048i	0.431404	+	0.252767i
$973$	3.35925	−	11.4406i	0.107693	−	0.366768i
$974$	20.0982	+	31.2734i	0.643988	+	1.00206i
$975$	0.000493098	−	0.0242631i	1.57918e−5	−	0.000777040i
$976$	−2.64213	−	8.99828i	−0.0845727	−	0.288028i
$977$	6.45333	−	7.44754i	0.206460	−	0.238268i	−0.643070	−	0.765807i	$-0.722340\pi$
$977$	6.45333	−	7.44754i	0.206460	−	0.238268i	0.849531	+	0.527539i	$0.176885\pi$
$978$	14.1957	+	32.8340i	0.453929	+	1.04991i
$979$	4.81344	−	1.41335i	0.153838	−	0.0451710i
$980$	−2.42870	−	5.31812i	−0.0775821	−	0.169881i
$981$	−14.3825	+	42.5104i	−0.459197	+	1.35725i
$982$	−16.8994	−	4.96212i	−0.539283	−	0.158348i
$983$	−7.01461	−	48.7877i	−0.223731	−	1.55609i	−0.723745	−	0.690068i	$-0.757581\pi$
$983$	−7.01461	−	48.7877i	−0.223731	−	1.55609i	0.500013	−	0.866018i	$-0.333328\pi$
$984$	15.4343	−	12.8342i	0.492028	−	0.409141i
$985$	−15.7687	−	2.26720i	−0.502433	−	0.0722390i
$986$	6.72036	+	4.31891i	0.214020	+	0.137542i
$987$	3.98735	+	14.6765i	0.126919	+	0.467159i
$988$			0.0622251i			0.00197965i
$989$	−16.1412	+	40.3825i	−0.513261	+	1.28409i
$990$	5.48446	−	4.37514i	0.174308	−	0.139051i
$991$	−12.8970	−	14.8839i	−0.409687	−	0.472804i	0.512981	−	0.858400i	$-0.328541\pi$
$991$	−12.8970	−	14.8839i	−0.409687	−	0.472804i	−0.922668	+	0.385596i	$0.873996\pi$
$992$	4.84297	−	7.53581i	0.153764	−	0.239262i
$993$	34.3808	−	51.1804i	1.09104	−	1.62416i
$994$	7.11480	+	3.24922i	0.225668	+	0.103059i
$995$	−17.0918	+	2.45743i	−0.541847	+	0.0779059i
$996$	14.3390	+	12.9442i	0.454349	+	0.410152i
$997$	21.7934	−	14.0058i	0.690205	−	0.443568i	−0.147954	−	0.988994i	$-0.547269\pi$
$997$	21.7934	−	14.0058i	0.690205	−	0.443568i	0.838159	+	0.545427i	$0.183632\pi$
$998$	−6.89442	+	3.14858i	−0.218239	+	0.0996665i
$999$	−25.7807	+	14.4287i	−0.815664	+	0.456504i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.q.a.401.3	yes	160
3.2	odd	2		690.2.q.b.401.9	yes	160
23.7	odd	22		690.2.q.b.191.9	yes	160
69.53	even	22	inner	690.2.q.a.191.3	✓	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.q.a.191.3	✓	160	69.53	even	22	inner
690.2.q.a.401.3	yes	160	1.1	even	1	trivial
690.2.q.b.191.9	yes	160	23.7	odd	22
690.2.q.b.401.9	yes	160	3.2	odd	2

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.q (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.755750 + 0.654861i) q^{2} +(-0.906618 - 1.47582i) q^{3} +(0.142315 - 0.989821i) q^{4} +(0.415415 - 0.909632i) q^{5} +(1.65163 + 0.521642i) q^{6} +(-0.302591 + 1.03053i) q^{7} +(0.540641 + 0.841254i) q^{8} +(-1.35609 + 2.67601i) q^{9} +O(q^{10})\)	\(q+(-0.755750 + 0.654861i) q^{2} +(-0.906618 - 1.47582i) q^{3} +(0.142315 - 0.989821i) q^{4} +(0.415415 - 0.909632i) q^{5} +(1.65163 + 0.521642i) q^{6} +(-0.302591 + 1.03053i) q^{7} +(0.540641 + 0.841254i) q^{8} +(-1.35609 + 2.67601i) q^{9} +(0.281733 + 0.959493i) q^{10} +(-1.53145 + 1.76739i) q^{11} +(-1.58982 + 0.687359i) q^{12} +(-0.0134436 + 0.00394741i) q^{13} +(-0.446170 - 0.976977i) q^{14} +(-1.71908 + 0.211611i) q^{15} +(-0.959493 - 0.281733i) q^{16} +(0.929456 + 6.46451i) q^{17} +(-0.727550 - 2.91044i) q^{18} +(4.39590 + 0.632035i) q^{19} +(-0.841254 - 0.540641i) q^{20} +(1.79521 - 0.487727i) q^{21} -2.33859i q^{22} +(-4.70867 + 0.910179i) q^{23} +(0.751384 - 1.56058i) q^{24} +(-0.654861 - 0.755750i) q^{25} +(0.00757502 - 0.0117870i) q^{26} +(5.17876 - 0.424774i) q^{27} +(0.976977 + 0.446170i) q^{28} +(-1.21072 + 0.174075i) q^{29} +(1.16062 - 1.28568i) q^{30} +(7.53581 - 4.84297i) q^{31} +(0.909632 - 0.415415i) q^{32} +(3.99679 + 0.657801i) q^{33} +(-4.93579 - 4.27688i) q^{34} +(0.811701 + 0.703343i) q^{35} +(2.45578 + 1.72312i) q^{36} +(-5.17188 + 2.36192i) q^{37} +(-3.73610 + 2.40104i) q^{38} +(0.0180139 + 0.0162616i) q^{39} +(0.989821 - 0.142315i) q^{40} +(10.5420 + 4.81437i) q^{41} +(-1.03734 + 1.54421i) q^{42} +(4.90256 - 7.62854i) q^{43} +(1.53145 + 1.76739i) q^{44} +(1.87084 + 2.34520i) q^{45} +(2.96254 - 3.77139i) q^{46} +8.17538i q^{47} +(0.454107 + 1.67146i) q^{48} +(4.91835 + 3.16083i) q^{49} +(0.989821 + 0.142315i) q^{50} +(8.69779 - 7.23255i) q^{51} +(0.00199400 + 0.0138686i) q^{52} +(-2.01187 - 0.590738i) q^{53} +(-3.63568 + 3.71239i) q^{54} +(0.971487 + 2.12726i) q^{55} +(-1.03053 + 0.302591i) q^{56} +(-3.05263 - 7.06057i) q^{57} +(0.801006 - 0.924411i) q^{58} +(0.995592 + 3.39068i) q^{59} +(-0.0351932 + 1.73169i) q^{60} +(5.07022 + 7.88942i) q^{61} +(-2.52371 + 8.59497i) q^{62} +(-2.34736 - 2.20722i) q^{63} +(-0.415415 + 0.909632i) q^{64} +(-0.00199400 + 0.0138686i) q^{65} +(-3.45134 + 2.12021i) q^{66} +(-0.926160 + 0.802522i) q^{67} +6.53098 q^{68} +(5.61222 + 6.12397i) q^{69} -1.07403 q^{70} +(-5.50372 + 4.76900i) q^{71} +(-2.98436 + 0.305945i) q^{72} +(-2.10508 + 14.6412i) q^{73} +(2.36192 - 5.17188i) q^{74} +(-0.521642 + 1.65163i) q^{75} +(1.25120 - 4.26121i) q^{76} +(-1.35794 - 2.11300i) q^{77} +(-0.0242631 - 0.000493098i) q^{78} +(0.0735815 + 0.250596i) q^{79} +(-0.654861 + 0.755750i) q^{80} +(-5.32205 - 7.25781i) q^{81} +(-11.1199 + 3.26509i) q^{82} +(-4.63306 - 10.1450i) q^{83} +(-0.227277 - 1.84635i) q^{84} +(6.26643 + 1.83999i) q^{85} +(1.29052 + 8.97576i) q^{86} +(1.35456 + 1.62899i) q^{87} +(-2.31479 - 0.332817i) q^{88} +(-1.80462 - 1.15976i) q^{89} +(-2.94967 - 0.547239i) q^{90} -0.0150485i q^{91} +(0.230801 + 4.79027i) q^{92} +(-13.9794 - 6.73077i) q^{93} +(-5.35373 - 6.17854i) q^{94} +(2.40104 - 3.73610i) q^{95} +(-1.43777 - 0.965830i) q^{96} +(-6.66361 - 3.04317i) q^{97} +(-5.78694 + 0.832036i) q^{98} +(-2.65277 - 6.49492i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9}+O(q^{10}) \) 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9	\( 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9} - 12 q^{11} - 12 q^{14} - 16 q^{16} - 8 q^{18} + 16 q^{20} + 62 q^{21} + 4 q^{23} + 2 q^{24} - 16 q^{25} + 42 q^{27} - 2 q^{30} - 4 q^{31} + 16 q^{33} + 2 q^{36} + 72 q^{38} - 124 q^{39} + 44 q^{41} + 44 q^{43} + 12 q^{44} - 2 q^{45} + 4 q^{46} + 70 q^{49} - 2 q^{51} - 52 q^{53} + 92 q^{54} + 10 q^{55} - 54 q^{56} - 38 q^{57} - 36 q^{58} - 44 q^{61} - 220 q^{63} + 16 q^{64} - 34 q^{66} - 44 q^{67} + 22 q^{69} - 12 q^{70} - 36 q^{72} - 28 q^{73} - 24 q^{74} - 88 q^{77} - 54 q^{78} - 44 q^{79} - 16 q^{80} - 66 q^{81} - 28 q^{82} + 4 q^{83} - 18 q^{84} + 158 q^{86} - 64 q^{87} + 80 q^{89} - 8 q^{90} - 4 q^{92} + 4 q^{93} + 24 q^{94} - 2 q^{96} - 88 q^{98} + 190 q^{99}+O(q^{100}) \) 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9 - 12 * q^11 - 12 * q^14 - 16 * q^16 - 8 * q^18 + 16 * q^20 + 62 * q^21 + 4 * q^23 + 2 * q^24 - 16 * q^25 + 42 * q^27 - 2 * q^30 - 4 * q^31 + 16 * q^33 + 2 * q^36 + 72 * q^38 - 124 * q^39 + 44 * q^41 + 44 * q^43 + 12 * q^44 - 2 * q^45 + 4 * q^46 + 70 * q^49 - 2 * q^51 - 52 * q^53 + 92 * q^54 + 10 * q^55 - 54 * q^56 - 38 * q^57 - 36 * q^58 - 44 * q^61 - 220 * q^63 + 16 * q^64 - 34 * q^66 - 44 * q^67 + 22 * q^69 - 12 * q^70 - 36 * q^72 - 28 * q^73 - 24 * q^74 - 88 * q^77 - 54 * q^78 - 44 * q^79 - 16 * q^80 - 66 * q^81 - 28 * q^82 + 4 * q^83 - 18 * q^84 + 158 * q^86 - 64 * q^87 + 80 * q^89 - 8 * q^90 - 4 * q^92 + 4 * q^93 + 24 * q^94 - 2 * q^96 - 88 * q^98 + 190 * q^99

Introduction

L-functions

Modular forms

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