LMFDB - Embedded newform 966.2.r.b.701.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(113,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 0, 13]))

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

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

chi := DirichletCharacter("966.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.r (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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			701.12
Character	$\chi$	$=$	966.701
Dual form			966.2.r.b.113.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.540641 - 0.841254i) q^{2} +(1.71940 + 0.208961i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-4.23656 + 1.24397i) q^{5} +(-0.753788 - 1.55942i) q^{6} +(0.755750 - 0.654861i) q^{7} +(0.989821 - 0.142315i) q^{8} +(2.91267 + 0.718576i) q^{9} +O(q^{10})$	\(q+(-0.540641 - 0.841254i) q^{2} +(1.71940 + 0.208961i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-4.23656 + 1.24397i) q^{5} +(-0.753788 - 1.55942i) q^{6} +(0.755750 - 0.654861i) q^{7} +(0.989821 - 0.142315i) q^{8} +(2.91267 + 0.718576i) q^{9} +(3.33695 + 2.89148i) q^{10} +(-1.70523 - 1.09588i) q^{11} +(-0.904342 + 1.47722i) q^{12} +(0.437268 - 0.504634i) q^{13} +(-0.959493 - 0.281733i) q^{14} +(-7.54427 + 1.25360i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-0.0215412 - 0.0471686i) q^{17} +(-0.970204 - 2.83879i) q^{18} +(-5.67881 - 2.59343i) q^{19} +(0.628379 - 4.37047i) q^{20} +(1.43628 - 0.968045i) q^{21} +2.02701i q^{22} +(-4.72318 - 0.831605i) q^{23} +(1.73164 - 0.0378617i) q^{24} +(12.1947 - 7.83705i) q^{25} +(-0.660930 - 0.0950274i) q^{26} +(4.85789 + 1.84415i) q^{27} +(0.281733 + 0.959493i) q^{28} +(-1.56110 + 0.712931i) q^{29} +(5.13334 + 5.66890i) q^{30} +(-1.25819 - 8.75088i) q^{31} +(-0.281733 + 0.959493i) q^{32} +(-2.70297 - 2.24059i) q^{33} +(-0.0280347 + 0.0436228i) q^{34} +(-2.38715 + 3.71448i) q^{35} +(-1.86361 + 2.35095i) q^{36} +(-1.27423 + 4.33962i) q^{37} +(0.888468 + 6.17943i) q^{38} +(0.857287 - 0.776295i) q^{39} +(-4.01640 + 1.83423i) q^{40} +(-3.00117 - 10.2210i) q^{41} +(-1.59088 - 0.684908i) q^{42} +(-4.72274 - 0.679027i) q^{43} +(1.70523 - 1.09588i) q^{44} +(-13.2336 + 0.578973i) q^{45} +(1.85395 + 4.42299i) q^{46} +4.48195i q^{47} +(-0.968045 - 1.43628i) q^{48} +(0.142315 - 0.989821i) q^{49} +(-13.1859 - 6.02180i) q^{50} +(-0.0271815 - 0.0856029i) q^{51} +(0.277384 + 0.607385i) q^{52} +(-5.92863 - 6.84201i) q^{53} +(-1.07497 - 5.08374i) q^{54} +(8.58754 + 2.52153i) q^{55} +(0.654861 - 0.755750i) q^{56} +(-9.22222 - 5.64579i) q^{57} +(1.44375 + 0.927842i) q^{58} +(-10.5002 - 9.09849i) q^{59} +(1.99369 - 7.38328i) q^{60} +(-8.12561 + 1.16829i) q^{61} +(-6.68148 + 5.78954i) q^{62} +(2.67182 - 1.36433i) q^{63} +(0.959493 - 0.281733i) q^{64} +(-1.22476 + 2.68186i) q^{65} +(-0.423567 + 3.48524i) q^{66} +(2.49026 + 3.87492i) q^{67} +0.0518545 q^{68} +(-7.94726 - 2.41682i) q^{69} +4.41541 q^{70} +(2.99094 + 4.65400i) q^{71} +(2.98529 + 0.296746i) q^{72} +(1.84939 - 4.04960i) q^{73} +(4.33962 - 1.27423i) q^{74} +(22.6052 - 10.9268i) q^{75} +(4.71813 - 4.08828i) q^{76} +(-2.00638 + 0.288474i) q^{77} +(-1.11655 - 0.301499i) q^{78} +(8.52804 + 7.38959i) q^{79} +(3.71448 + 2.38715i) q^{80} +(7.96730 + 4.18595i) q^{81} +(-6.97593 + 8.05065i) q^{82} +(3.07083 + 0.901678i) q^{83} +(0.283914 + 1.70862i) q^{84} +(0.149936 + 0.173036i) q^{85} +(1.98207 + 4.34013i) q^{86} +(-2.83313 + 0.899603i) q^{87} +(-1.84383 - 0.842050i) q^{88} +(-0.599031 + 4.16635i) q^{89} +(7.64167 + 10.8198i) q^{90} -0.667726i q^{91} +(2.71853 - 3.95089i) q^{92} +(-0.334730 - 15.3092i) q^{93} +(3.77046 - 2.42313i) q^{94} +(27.2847 + 3.92295i) q^{95} +(-0.684908 + 1.59088i) q^{96} +(-3.12116 - 10.6297i) q^{97} +(-0.909632 + 0.415415i) q^{98} +(-4.17929 - 4.41729i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{3} + 24 q^{4} + 4 q^{5} + 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^3 + 24 * q^4 + 4 * q^5 + 4 * q^9	$ 240 q - 4 q^{3} + 24 q^{4} + 4 q^{5} + 4 q^{9} + 4 q^{12} - 8 q^{13} - 24 q^{14} + 26 q^{15} - 24 q^{16} - 32 q^{17} + 40 q^{18} - 4 q^{20} + 8 q^{23} + 12 q^{25} + 116 q^{27} + 4 q^{30} + 16 q^{31} + 2 q^{33} - 4 q^{36} + 22 q^{37} + 8 q^{39} - 154 q^{41} - 4 q^{42} + 22 q^{43} - 24 q^{45} + 4 q^{46} - 4 q^{48} + 24 q^{49} - 88 q^{50} - 24 q^{51} + 8 q^{52} + 108 q^{53} + 12 q^{54} - 16 q^{55} + 24 q^{56} - 70 q^{57} - 4 q^{58} - 22 q^{59} - 26 q^{60} + 4 q^{63} + 24 q^{64} - 76 q^{66} - 44 q^{67} + 32 q^{68} - 86 q^{69} + 4 q^{70} + 4 q^{72} - 12 q^{73} + 16 q^{74} - 26 q^{75} - 78 q^{78} + 4 q^{80} - 168 q^{81} + 8 q^{82} - 16 q^{83} - 28 q^{85} - 16 q^{86} + 156 q^{87} - 24 q^{89} - 126 q^{90} - 8 q^{92} - 16 q^{93} - 8 q^{94} + 132 q^{97} - 172 q^{99}+O(q^{100}) $ 240 * q - 4 * q^3 + 24 * q^4 + 4 * q^5 + 4 * q^9 + 4 * q^12 - 8 * q^13 - 24 * q^14 + 26 * q^15 - 24 * q^16 - 32 * q^17 + 40 * q^18 - 4 * q^20 + 8 * q^23 + 12 * q^25 + 116 * q^27 + 4 * q^30 + 16 * q^31 + 2 * q^33 - 4 * q^36 + 22 * q^37 + 8 * q^39 - 154 * q^41 - 4 * q^42 + 22 * q^43 - 24 * q^45 + 4 * q^46 - 4 * q^48 + 24 * q^49 - 88 * q^50 - 24 * q^51 + 8 * q^52 + 108 * q^53 + 12 * q^54 - 16 * q^55 + 24 * q^56 - 70 * q^57 - 4 * q^58 - 22 * q^59 - 26 * q^60 + 4 * q^63 + 24 * q^64 - 76 * q^66 - 44 * q^67 + 32 * q^68 - 86 * q^69 + 4 * q^70 + 4 * q^72 - 12 * q^73 + 16 * q^74 - 26 * q^75 - 78 * q^78 + 4 * q^80 - 168 * q^81 + 8 * q^82 - 16 * q^83 - 28 * q^85 - 16 * q^86 + 156 * q^87 - 24 * q^89 - 126 * q^90 - 8 * q^92 - 16 * q^93 - 8 * q^94 + 132 * q^97 - 172 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$1$	$e\left(\frac{9}{22}\right)$

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 $

$2$	−0.540641	−	0.841254i	−0.382291	−	0.594856i
$2$	−0.540641	−	0.841254i	−0.382291	−	0.594856i
$3$	1.71940	+	0.208961i	0.992696	+	0.120644i
$3$	1.71940	+	0.208961i	0.992696	+	0.120644i
$4$	−0.415415	+	0.909632i	−0.207708	+	0.454816i
$5$	−4.23656	+	1.24397i	−1.89465	+	0.556318i	−0.902593	+	0.430495i	$0.858339\pi$
$5$	−4.23656	+	1.24397i	−1.89465	+	0.556318i	−0.992053	+	0.125823i	$0.959843\pi$
$6$	−0.753788	−	1.55942i	−0.307733	−	0.636632i
$7$	0.755750	−	0.654861i	0.285646	−	0.247514i
$7$	0.755750	−	0.654861i	0.285646	−	0.247514i
$8$	0.989821	−	0.142315i	0.349955	−	0.0503159i
$9$	2.91267	+	0.718576i	0.970890	+	0.239525i
$10$	3.33695	+	2.89148i	1.05523	+	0.914366i
$11$	−1.70523	−	1.09588i	−0.514146	−	0.330421i	0.257707	−	0.966223i	$-0.417033\pi$
$11$	−1.70523	−	1.09588i	−0.514146	−	0.330421i	−0.771852	+	0.635802i	$0.780670\pi$
$12$	−0.904342	+	1.47722i	−0.261061	+	0.426435i
$13$	0.437268	−	0.504634i	0.121276	−	0.139960i	−0.691864	−	0.722027i	$-0.743210\pi$
$13$	0.437268	−	0.504634i	0.121276	−	0.139960i	0.813141	+	0.582067i	$0.197756\pi$
$14$	−0.959493	−	0.281733i	−0.256435	−	0.0752962i
$15$	−7.54427	+	1.25360i	−1.94792	+	0.323677i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	−0.0215412	−	0.0471686i	−0.00522450	−	0.0114401i	0.907002	−	0.421127i	$-0.138365\pi$
$17$	−0.0215412	−	0.0471686i	−0.00522450	−	0.0114401i	−0.912226	+	0.409687i	$0.865638\pi$
$18$	−0.970204	−	2.83879i	−0.228679	−	0.669108i
$19$	−5.67881	−	2.59343i	−1.30281	−	0.594973i	−0.361453	−	0.932390i	$-0.617719\pi$
$19$	−5.67881	−	2.59343i	−1.30281	−	0.594973i	−0.941355	+	0.337417i	$0.890447\pi$
$20$	0.628379	−	4.37047i	0.140510	−	0.977267i
$21$	1.43628	−	0.968045i	0.313421	−	0.211245i
$22$			2.02701i			0.432160i
$23$	−4.72318	−	0.831605i	−0.984851	−	0.173402i
$23$	−4.72318	−	0.831605i	−0.984851	−	0.173402i
$24$	1.73164	−	0.0378617i	0.353469	−	0.00772848i
$25$	12.1947	−	7.83705i	2.43894	−	1.56741i
$26$	−0.660930	−	0.0950274i	−0.129619	−	0.0186364i
$27$	4.85789	+	1.84415i	0.934901	+	0.354908i
$28$	0.281733	+	0.959493i	0.0532424	+	0.181327i
$29$	−1.56110	+	0.712931i	−0.289889	+	0.132388i	−0.555052	−	0.831816i	$-0.687302\pi$
$29$	−1.56110	+	0.712931i	−0.289889	+	0.132388i	0.265163	+	0.964204i	$0.414574\pi$
$30$	5.13334	+	5.66890i	0.937215	+	1.03500i
$31$	−1.25819	−	8.75088i	−0.225977	−	1.57171i	−0.714804	−	0.699325i	$-0.753484\pi$
$31$	−1.25819	−	8.75088i	−0.225977	−	1.57171i	0.488827	−	0.872381i	$-0.337425\pi$
$32$	−0.281733	+	0.959493i	−0.0498038	+	0.169616i
$33$	−2.70297	−	2.24059i	−0.470527	−	0.390037i
$34$	−0.0280347	+	0.0436228i	−0.00480791	+	0.00748125i
$35$	−2.38715	+	3.71448i	−0.403502	+	0.627862i
$36$	−1.86361	+	2.35095i	−0.310601	+	0.391825i
$37$	−1.27423	+	4.33962i	−0.209482	+	0.713430i	0.785979	+	0.618254i	$0.212160\pi$
$37$	−1.27423	+	4.33962i	−0.209482	+	0.713430i	−0.995460	+	0.0951760i	$0.969659\pi$
$38$	0.888468	+	6.17943i	0.144129	+	1.00244i
$39$	0.857287	−	0.776295i	0.137276	−	0.124307i
$40$	−4.01640	+	1.83423i	−0.635049	+	0.290017i
$41$	−3.00117	−	10.2210i	−0.468703	−	1.59626i	−0.766909	−	0.641755i	$-0.778206\pi$
$41$	−3.00117	−	10.2210i	−0.468703	−	1.59626i	0.298206	−	0.954502i	$-0.403612\pi$
$42$	−1.59088	−	0.684908i	−0.245478	−	0.105684i
$43$	−4.72274	−	0.679027i	−0.720210	−	0.103551i	−0.227543	−	0.973768i	$-0.573069\pi$
$43$	−4.72274	−	0.679027i	−0.720210	−	0.103551i	−0.492668	+	0.870217i	$0.663978\pi$
$44$	1.70523	−	1.09588i	0.257073	−	0.165211i
$45$	−13.2336	+	0.578973i	−1.97275	+	0.0863081i
$46$	1.85395	+	4.42299i	0.273351	+	0.652135i
$47$			4.48195i			0.653760i	0.945066	+	0.326880i	$0.105997\pi$
$47$			4.48195i			0.653760i	−0.945066	+	0.326880i	$0.894003\pi$
$48$	−0.968045	−	1.43628i	−0.139725	−	0.207309i
$49$	0.142315	−	0.989821i	0.0203307	−	0.141403i
$50$	−13.1859	−	6.02180i	−1.86477	−	0.851611i
$51$	−0.0271815	−	0.0856029i	−0.00380616	−	0.0119868i
$52$	0.277384	+	0.607385i	0.0384662	+	0.0842292i
$53$	−5.92863	−	6.84201i	−0.814360	−	0.939822i	0.184716	−	0.982792i	$-0.440863\pi$
$53$	−5.92863	−	6.84201i	−0.814360	−	0.939822i	−0.999076	+	0.0429702i	$0.986318\pi$
$54$	−1.07497	−	5.08374i	−0.146285	−	0.691810i
$55$	8.58754	+	2.52153i	1.15794	+	0.340003i
$56$	0.654861	−	0.755750i	0.0875094	−	0.100991i
$57$	−9.22222	−	5.64579i	−1.22151	−	0.747803i
$58$	1.44375	+	0.927842i	0.189574	+	0.121832i
$59$	−10.5002	−	9.09849i	−1.36701	−	1.18452i	−0.962915	−	0.269806i	$-0.913040\pi$
$59$	−10.5002	−	9.09849i	−1.36701	−	1.18452i	−0.404097	−	0.914716i	$-0.632414\pi$
$60$	1.99369	−	7.38328i	0.257385	−	0.953177i
$61$	−8.12561	+	1.16829i	−1.04038	+	0.149584i	−0.641266	−	0.767319i	$-0.721590\pi$
$61$	−8.12561	+	1.16829i	−1.04038	+	0.149584i	−0.399112	+	0.916902i	$0.630681\pi$
$62$	−6.68148	+	5.78954i	−0.848549	+	0.735272i
$63$	2.67182	−	1.36433i	0.336617	−	0.171889i
$64$	0.959493	−	0.281733i	0.119937	−	0.0352166i
$65$	−1.22476	+	2.68186i	−0.151913	+	0.332643i
$66$	−0.423567	+	3.48524i	−0.0521374	+	0.429003i
$67$	2.49026	+	3.87492i	0.304233	+	0.473396i	0.959385	−	0.282101i	$-0.0910315\pi$
$67$	2.49026	+	3.87492i	0.304233	+	0.473396i	−0.655151	+	0.755498i	$0.727395\pi$
$68$	0.0518545			0.00628829
$69$	−7.94726	−	2.41682i	−0.956738	−	0.290951i
$70$	4.41541			0.527743
$71$	2.99094	+	4.65400i	0.354959	+	0.552328i	0.972112	−	0.234516i	$-0.0753504\pi$
$71$	2.99094	+	4.65400i	0.354959	+	0.552328i	−0.617153	+	0.786843i	$0.711714\pi$
$72$	2.98529	+	0.296746i	0.351820	+	0.0349718i
$73$	1.84939	−	4.04960i	0.216455	−	0.473970i	−0.769992	−	0.638054i	$-0.779740\pi$
$73$	1.84939	−	4.04960i	0.216455	−	0.473970i	0.986446	+	0.164084i	$0.0524669\pi$
$74$	4.33962	−	1.27423i	0.504471	−	0.148126i
$75$	22.6052	−	10.9268i	2.61022	−	1.26172i
$76$	4.71813	−	4.08828i	0.541206	−	0.468958i
$77$	−2.00638	+	0.288474i	−0.228648	+	0.0328746i
$78$	−1.11655	−	0.301499i	−0.126424	−	0.0341380i
$79$	8.52804	+	7.38959i	0.959480	+	0.831394i	0.985742	−	0.168261i	$-0.0538153\pi$
$79$	8.52804	+	7.38959i	0.959480	+	0.831394i	−0.0262629	+	0.999655i	$0.508361\pi$
$80$	3.71448	+	2.38715i	0.415292	+	0.266892i
$81$	7.96730	+	4.18595i	0.885255	+	0.465106i
$82$	−6.97593	+	8.05065i	−0.770362	+	0.889045i
$83$	3.07083	+	0.901678i	0.337068	+	0.0989721i	0.445886	−	0.895090i	$-0.352889\pi$
$83$	3.07083	+	0.901678i	0.337068	+	0.0989721i	−0.108818	+	0.994062i	$0.534707\pi$
$84$	0.283914	+	1.70862i	0.0309776	+	0.186426i
$85$	0.149936	+	0.173036i	0.0162629	+	0.0187684i
$86$	1.98207	+	4.34013i	0.213732	+	0.468008i
$87$	−2.83313	+	0.899603i	−0.303744	+	0.0964476i
$88$	−1.84383	−	0.842050i	−0.196553	−	0.0897628i
$89$	−0.599031	+	4.16635i	−0.0634972	+	0.441633i	0.933128	+	0.359545i	$0.117068\pi$
$89$	−0.599031	+	4.16635i	−0.0634972	+	0.441633i	−0.996625	+	0.0820880i	$0.973841\pi$
$90$	7.64167	+	10.8198i	0.805503	+	1.14050i
$91$		−	0.667726i		−	0.0699967i
$92$	2.71853	−	3.95089i	0.283427	−	0.411909i
$93$	−0.334730	−	15.3092i	−0.0347099	−	1.58749i
$94$	3.77046	−	2.42313i	0.388893	−	0.249926i
$95$	27.2847	+	3.92295i	2.79935	+	0.402486i
$96$	−0.684908	+	1.59088i	−0.0699031	+	0.162369i
$97$	−3.12116	−	10.6297i	−0.316905	−	1.07928i	−0.951810	−	0.306690i	$-0.900779\pi$
$97$	−3.12116	−	10.6297i	−0.316905	−	1.07928i	0.634904	−	0.772591i	$-0.281040\pi$
$98$	−0.909632	+	0.415415i	−0.0918867	+	0.0419633i
$99$	−4.17929	−	4.41729i	−0.420035	−	0.443954i
$100$	2.06298	+	14.3483i	0.206298	+	1.43483i
$101$	−2.01384	+	6.85851i	−0.200384	+	0.682447i	0.796576	+	0.604538i	$0.206642\pi$
$101$	−2.01384	+	6.85851i	−0.200384	+	0.682447i	−0.996961	+	0.0779085i	$0.975176\pi$
$102$	−0.0573183	+	0.0691469i	−0.00567536	+	0.00684656i
$103$	−7.09067	+	11.0333i	−0.698664	+	1.08714i	0.292725	+	0.956197i	$0.405438\pi$
$103$	−7.09067	+	11.0333i	−0.698664	+	1.08714i	−0.991389	+	0.130946i	$0.958198\pi$
$104$	0.361000	−	0.561727i	0.0353990	−	0.0550819i
$105$	−4.88065	+	5.88785i	−0.476303	+	0.574596i
$106$	−2.55060	+	8.68655i	−0.247736	+	0.843712i
$107$	0.126948	+	0.882943i	0.0122725	+	0.0853573i	0.995037	−	0.0995038i	$-0.0317256\pi$
$107$	0.126948	+	0.882943i	0.0122725	+	0.0853573i	−0.982765	+	0.184861i	$0.940816\pi$
$108$	−3.69554	+	3.65280i	−0.355604	+	0.351491i
$109$	9.33001	−	4.26087i	0.893653	−	0.408118i	0.0849846	−	0.996382i	$-0.472916\pi$
$109$	9.33001	−	4.26087i	0.893653	−	0.408118i	0.808669	+	0.588265i	$0.200189\pi$
$110$	−2.52153	−	8.58754i	−0.240418	−	0.818790i
$111$	−3.09772	+	7.19528i	−0.294023	+	0.682946i
$112$	−0.989821	−	0.142315i	−0.0935293	−	0.0134475i
$113$	7.42439	−	4.77136i	0.698428	−	0.448852i	−0.142645	−	0.989774i	$-0.545561\pi$
$113$	7.42439	−	4.77136i	0.698428	−	0.448852i	0.841073	+	0.540922i	$0.181924\pi$
$114$	0.236370	+	10.8106i	0.0221380	+	1.01250i
$115$	21.0445	−	2.35233i	1.96241	−	0.219356i
$116$		−	1.71619i		−	0.159344i
$117$	1.63623	−	1.15562i	0.151270	−	0.106837i
$118$	−1.97729	+	13.7524i	−0.182024	+	1.26601i
$119$	−0.0471686	−	0.0215412i	−0.00432393	−	0.00197467i
$120$	−7.28908	+	2.31450i	−0.665399	+	0.211284i
$121$	−2.86272	−	6.26849i	−0.260247	−	0.569862i
$122$	5.37586	+	6.20407i	0.486708	+	0.561690i
$123$	−3.02440	−	18.2012i	−0.272701	−	1.64114i
$124$	8.48275	+	2.49076i	0.761774	+	0.223677i
$125$	−27.4571	+	31.6872i	−2.45584	+	2.83419i
$126$	−2.59224	−	1.51006i	−0.230935	−	0.134527i
$127$	−5.83082	−	3.74724i	−0.517401	−	0.332514i	0.255742	−	0.966745i	$-0.417680\pi$
$127$	−5.83082	−	3.74724i	−0.517401	−	0.332514i	−0.773143	+	0.634231i	$0.781317\pi$
$128$	−0.755750	−	0.654861i	−0.0667995	−	0.0578821i
$129$	−7.97838	−	2.15439i	−0.702457	−	0.189683i
$130$	2.91828	−	0.419585i	0.255950	−	0.0368000i
$131$	5.54451	−	4.80434i	0.484426	−	0.419757i	−0.378104	−	0.925763i	$-0.623424\pi$
$131$	5.54451	−	4.80434i	0.484426	−	0.419757i	0.862530	+	0.506006i	$0.168879\pi$
$132$	3.16097	−	1.52794i	0.275127	−	0.132990i
$133$	−5.99009	+	1.75885i	−0.519407	+	0.152512i
$134$	1.91345	−	4.18987i	0.165297	−	0.361950i
$135$	−22.8748	−	1.76982i	−1.96875	−	0.152322i
$136$	−0.0280347	−	0.0436228i	−0.00240395	−	0.00374063i
$137$	16.3715			1.39871			0.699357	−	0.714773i	$-0.253470\pi$
$137$	16.3715			1.39871			0.699357	+	0.714773i	$0.253470\pi$
$138$	2.26345	+	7.99230i	0.192678	+	0.680349i
$139$	8.18423			0.694177			0.347089	−	0.937832i	$-0.387170\pi$
$139$	8.18423			0.694177			0.347089	+	0.937832i	$0.387170\pi$
$140$	−2.38715	−	3.71448i	−0.201751	−	0.313931i
$141$	−0.936555	+	7.70627i	−0.0788721	+	0.648985i
$142$	2.29817	−	5.03228i	0.192858	−	0.422300i
$143$	−1.29866	+	0.381322i	−0.108600	+	0.0318877i
$144$	−1.36433	−	2.67182i	−0.113694	−	0.222651i
$145$	5.72683	−	4.96233i	0.475587	−	0.412099i
$146$	−4.40660	+	0.633573i	−0.364692	+	0.0524349i
$147$	0.451530	−	1.67216i	0.0372416	−	0.137917i
$148$	−3.41813	−	2.96182i	−0.280968	−	0.243460i
$149$	−3.00149	−	1.92894i	−0.245892	−	0.158025i	0.411890	−	0.911234i	$-0.364869\pi$
$149$	−3.00149	−	1.92894i	−0.245892	−	0.158025i	−0.657782	+	0.753209i	$0.728505\pi$
$150$	−21.4135	−	13.1092i	−1.74841	−	1.07036i
$151$	−13.0579	+	15.0697i	−1.06264	+	1.22635i	−0.0895365	+	0.995984i	$0.528539\pi$
$151$	−13.0579	+	15.0697i	−1.06264	+	1.22635i	−0.973103	+	0.230368i	$0.926007\pi$
$152$	−5.99009	−	1.75885i	−0.485861	−	0.142662i
$153$	−0.0288481	−	0.152865i	−0.00233223	−	0.0123584i
$154$	1.32741	+	1.53191i	0.106966	+	0.123445i
$155$	16.2162	+	35.5085i	1.30251	+	2.85211i
$156$	0.350013	+	1.10230i	0.0280235	+	0.0882547i
$157$	8.23501	+	3.76080i	0.657225	+	0.300145i	0.715973	−	0.698128i	$-0.245983\pi$
$157$	8.23501	+	3.76080i	0.657225	+	0.300145i	−0.0587476	+	0.998273i	$0.518711\pi$
$158$	1.60591	−	11.1694i	0.127759	−	0.888586i
$159$	−8.76397	−	13.0030i	−0.695028	−	1.03120i
$160$		−	4.41541i		−	0.349069i
$161$	−4.11413	+	2.46454i	−0.324239	+	0.194233i
$162$	−0.786000	−	8.96561i	−0.0617540	−	0.704405i
$163$	−15.2723	+	9.81490i	−1.19622	+	0.768762i	−0.978298	−	0.207205i	$-0.933563\pi$
$163$	−15.2723	+	9.81490i	−1.19622	+	0.768762i	−0.217920	+	0.975967i	$0.569927\pi$
$164$	10.5441	+	1.51601i	0.823356	+	0.118381i
$165$	14.2385	+	6.12998i	1.10847	+	0.477218i
$166$	−0.901678	−	3.07083i	−0.0699838	−	0.238343i
$167$	−1.51760	+	0.693066i	−0.117436	+	0.0536311i	−0.473266	−	0.880919i	$-0.656925\pi$
$167$	−1.51760	+	0.693066i	−0.117436	+	0.0536311i	0.355831	+	0.934550i	$0.384198\pi$
$168$	1.28389	−	1.16259i	0.0990542	−	0.0896962i
$169$	1.78664	+	12.4264i	0.137434	+	0.955874i
$170$	0.0645052	−	0.219685i	0.00494733	−	0.0168490i
$171$	−14.6769	−	11.6345i	−1.12237	−	0.889709i
$172$	2.57956	−	4.01387i	0.196690	−	0.306055i
$173$	2.44573	−	3.80563i	0.185946	−	0.289337i	−0.735748	−	0.677255i	$-0.763169\pi$
$173$	2.44573	−	3.80563i	0.185946	−	0.289337i	0.921694	+	0.387918i	$0.126806\pi$
$174$	2.28850	+	1.89702i	0.173491	+	0.143813i
$175$	4.08396	−	13.9087i	0.308718	−	1.05140i
$176$	0.288474	+	2.00638i	0.0217445	+	0.151236i
$177$	−16.1528	−	17.8381i	−1.21412	−	1.34079i
$178$	3.82882	−	1.74856i	0.286982	−	0.131060i
$179$	0.970294	+	3.30452i	0.0725232	+	0.246991i	0.987774	−	0.155894i	$-0.0498257\pi$
$179$	0.970294	+	3.30452i	0.0725232	+	0.246991i	−0.915251	+	0.402885i	$0.868008\pi$
$180$	4.97077	−	12.2782i	0.370500	−	0.915163i
$181$	−11.4251	−	1.64268i	−0.849219	−	0.122099i	−0.296054	−	0.955171i	$-0.595671\pi$
$181$	−11.4251	−	1.64268i	−0.849219	−	0.122099i	−0.553165	+	0.833072i	$0.686580\pi$
$182$	−0.561727	+	0.361000i	−0.0416380	+	0.0267591i
$183$	−14.2153	+	0.310813i	−1.05082	+	0.0229759i
$184$	−4.79345	−	0.150962i	−0.353378	−	0.0111290i
$185$		−	19.9702i		−	1.46823i
$186$	−12.6979	+	8.55836i	−0.931058	+	0.627529i
$187$	−0.0149587	+	0.104040i	−0.00109389	+	0.00760814i
$188$	−4.07693	−	1.86187i	−0.297340	−	0.135791i
$189$	4.87901	−	1.78752i	0.354896	−	0.130023i
$190$	−11.4510	−	25.0743i	−0.830746	−	1.81908i
$191$	1.82043	+	2.10089i	0.131722	+	0.152015i	0.817779	−	0.575533i	$-0.195205\pi$
$191$	1.82043	+	2.10089i	0.131722	+	0.152015i	−0.686057	+	0.727548i	$0.740660\pi$
$192$	1.70862	−	0.283914i	0.123309	−	0.0204897i
$193$	−11.7375	−	3.44644i	−0.844883	−	0.248080i	−0.169484	−	0.985533i	$-0.554210\pi$
$193$	−11.7375	−	3.44644i	−0.844883	−	0.248080i	−0.675399	+	0.737453i	$0.736028\pi$
$194$	−7.25483	+	8.37252i	−0.520867	+	0.601112i
$195$	−2.66626	+	4.35525i	−0.190935	+	0.311886i
$196$	0.841254	+	0.540641i	0.0600895	+	0.0386172i
$197$	12.7001	+	11.0047i	0.904844	+	0.784052i	0.976977	−	0.213343i	$-0.0684352\pi$
$197$	12.7001	+	11.0047i	0.904844	+	0.784052i	−0.0721330	+	0.997395i	$0.522981\pi$
$198$	−1.45656	+	5.90401i	−0.103513	+	0.419580i
$199$	17.0938	−	2.45772i	1.21175	−	0.174223i	0.493335	−	0.869839i	$-0.335778\pi$
$199$	17.0938	−	2.45772i	1.21175	−	0.174223i	0.718414	+	0.695616i	$0.244869\pi$
$200$	10.9552	−	9.49277i	0.774653	−	0.671240i
$201$	3.47204	+	7.18290i	0.244899	+	0.506642i
$202$	6.85851	−	2.01384i	0.482563	−	0.141693i
$203$	−0.712931	+	1.56110i	−0.0500379	+	0.109568i
$204$	0.0891587	+	0.0108356i	0.00624236	+	0.000758643i
$205$	25.4292	+	39.5686i	1.77605	+	2.76359i
$206$	13.1153			0.913786
$207$	−13.1595	−	5.81616i	−0.914648	−	0.404251i
$208$	−0.667726			−0.0462985
$209$	6.84158	+	10.6457i	0.473242	+	0.736379i
$210$	7.59186	+	0.922650i	0.523888	+	0.0636689i
$211$	−4.96101	+	10.8631i	−0.341530	+	0.747846i	−0.999989	−	0.00477065i	$-0.998481\pi$
$211$	−4.96101	+	10.8631i	−0.341530	+	0.747846i	0.658459	+	0.752617i	$0.271209\pi$
$212$	8.68655	−	2.55060i	0.596595	−	0.175176i
$213$	4.17012	+	8.62707i	0.285732	+	0.591117i
$214$	0.674145	−	0.584150i	0.0460836	−	0.0399317i
$215$	20.8528	−	2.99818i	1.42215	−	0.204474i
$216$	5.07089	+	1.13403i	0.345031	+	0.0771613i
$217$	−6.68148	−	5.78954i	−0.453569	−	0.393020i
$218$	−8.62866	−	5.54530i	−0.584407	−	0.375575i
$219$	4.02605	−	6.57643i	0.272055	−	0.444394i
$220$	−5.86106	+	6.76402i	−0.395152	+	0.456030i
$221$	−0.0332221	−	0.00975489i	−0.00223476	−	0.000656185i
$222$	7.72781	−	1.28409i	0.518657	−	0.0861828i
$223$	−14.1353	−	16.3130i	−0.946568	−	1.09240i	−0.995610	−	0.0936005i	$-0.970162\pi$
$223$	−14.1353	−	16.3130i	−0.946568	−	1.09240i	0.0490422	−	0.998797i	$-0.484383\pi$
$224$	0.415415	+	0.909632i	0.0277561	+	0.0607773i
$225$	41.1506	−	14.0639i	2.74338	−	0.937596i
$226$	−8.02785	−	3.66620i	−0.534005	−	0.243872i
$227$	1.18873	−	8.26779i	0.0788987	−	0.548752i	−0.911584	−	0.411114i	$-0.865140\pi$
$227$	1.18873	−	8.26779i	0.0788987	−	0.548752i	0.990483	−	0.137638i	$-0.0439512\pi$
$228$	8.96664	−	6.04348i	0.593830	−	0.400239i
$229$		−	25.1715i		−	1.66338i	−0.555241	−	0.831689i	$-0.687374\pi$
$229$		−	25.1715i		−	1.66338i	0.555241	−	0.831689i	$-0.312626\pi$
$230$	−13.3564	−	16.4320i	−0.880697	−	1.08349i
$231$	−3.51004	+	0.0767460i	−0.230944	+	0.00504952i
$232$	−1.44375	+	0.927842i	−0.0947869	+	0.0609158i
$233$	28.1495	+	4.04729i	1.84414	+	0.265147i	0.973815	−	0.227340i	$-0.0730030\pi$
$233$	28.1495	+	4.04729i	1.84414	+	0.265147i	0.870320	+	0.492487i	$0.163912\pi$
$234$	−1.85679	−	0.751712i	−0.121382	−	0.0491409i
$235$	−5.57539	−	18.9880i	−0.363698	−	1.23864i
$236$	12.6382	−	5.77168i	0.822678	−	0.375705i
$237$	13.1190	+	14.4877i	0.852169	+	0.941076i
$238$	0.00737967	+	0.0513267i	0.000478353	+	0.00332702i
$239$	4.25691	−	14.4977i	0.275357	−	0.937779i	−0.699441	−	0.714690i	$-0.746568\pi$
$239$	4.25691	−	14.4977i	0.275357	−	0.937779i	0.974798	−	0.223089i	$-0.0716141\pi$
$240$	5.88785	+	4.88065i	0.380059	+	0.315045i
$241$	−6.46788	+	10.0642i	−0.416633	+	0.648293i	−0.984613	−	0.174749i	$-0.944089\pi$
$241$	−6.46788	+	10.0642i	−0.416633	+	0.648293i	0.567980	+	0.823042i	$0.307725\pi$
$242$	−3.72568	+	5.79727i	−0.239496	+	0.372663i
$243$	12.8243	+	8.86218i	0.822677	+	0.568509i
$244$	2.31279	−	7.87664i	0.148061	−	0.504250i
$245$	0.628379	+	4.37047i	0.0401456	+	0.279219i
$246$	−13.6767	+	12.3846i	−0.871993	+	0.789612i
$247$	−3.79189	+	1.73170i	−0.241272	+	0.110185i
$248$	−2.49076	−	8.48275i	−0.158163	−	0.538655i
$249$	5.09158	+	2.19203i	0.322666	+	0.138914i
$250$	41.5014	+	5.96700i	2.62478	+	0.377386i
$251$	22.2850	−	14.3217i	1.40662	−	0.903978i	0.406663	−	0.913578i	$-0.366692\pi$
$251$	22.2850	−	14.3217i	1.40662	−	0.903978i	0.999954	+	0.00960055i	$0.00305600\pi$
$252$	0.131125	+	2.99713i	0.00826012	+	0.188802i
$253$	7.14276	+	6.59413i	0.449062	+	0.414570i
$254$			6.93111i			0.434896i
$255$	0.221643	+	0.328849i	0.0138798	+	0.0205933i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	−8.05447	−	3.67835i	−0.502424	−	0.229449i	0.148047	−	0.988980i	$-0.452701\pi$
$257$	−8.05447	−	3.67835i	−0.502424	−	0.229449i	−0.650471	+	0.759531i	$0.725429\pi$
$258$	2.50105	+	7.87659i	0.155709	+	0.490375i
$259$	1.87885	+	4.11411i	0.116746	+	0.255638i
$260$	−1.93072	−	2.22817i	−0.119738	−	0.138185i
$261$	−5.05927	+	0.954763i	−0.313161	+	0.0590983i
$262$	−7.03925	−	2.06691i	−0.434887	−	0.127694i
$263$	−6.68517	+	7.71509i	−0.412225	+	0.475733i	−0.923453	−	0.383712i	$-0.874645\pi$
$263$	−6.68517	+	7.71509i	−0.412225	+	0.475733i	0.511228	+	0.859445i	$0.329191\pi$
$264$	−2.99433	−	1.83311i	−0.184288	−	0.112820i
$265$	33.6282	+	21.6115i	2.06576	+	1.32759i
$266$	4.71813	+	4.08828i	0.289287	+	0.250669i
$267$	−1.90058	+	7.03845i	−0.116314	+	0.430746i
$268$	−4.55924	+	0.655519i	−0.278500	+	0.0400422i
$269$	−5.66262	+	4.90669i	−0.345256	+	0.299166i	−0.810176	−	0.586187i	$-0.800629\pi$
$269$	−5.66262	+	4.90669i	−0.345256	+	0.299166i	0.464920	+	0.885353i	$0.346083\pi$
$270$	10.8782	+	20.2003i	0.662025	+	1.22935i
$271$	−2.41973	+	0.710496i	−0.146988	+	0.0431596i	−0.354399	−	0.935094i	$-0.615314\pi$
$271$	−2.41973	+	0.710496i	−0.146988	+	0.0431596i	0.207411	+	0.978254i	$0.433496\pi$
$272$	−0.0215412	+	0.0471686i	−0.00130612	+	0.00286001i
$273$	0.139529	−	1.14809i	0.00844468	−	0.0694855i
$274$	−8.85111	−	13.7726i	−0.534715	−	0.832033i
$275$	−29.3832			−1.77188
$276$	5.49983	−	6.22510i	0.331051	−	0.374707i
$277$	2.57135			0.154498			0.0772488	−	0.997012i	$-0.475386\pi$
$277$	2.57135			0.154498			0.0772488	+	0.997012i	$0.475386\pi$
$278$	−4.42473	−	6.88501i	−0.265378	−	0.412936i
$279$	2.62349	−	26.3925i	0.157064	−	1.58008i
$280$	−1.83423	+	4.01640i	−0.109616	+	0.240026i
$281$	−8.98635	+	2.63863i	−0.536081	+	0.157408i	−0.538557	−	0.842589i	$-0.681030\pi$
$281$	−8.98635	+	2.63863i	−0.536081	+	0.157408i	0.00247562	+	0.999997i	$0.499212\pi$
$282$	6.98926	−	3.37844i	0.416205	−	0.201183i
$283$	−19.6835	+	17.0558i	−1.17006	+	1.01386i	−0.170468	+	0.985363i	$0.554528\pi$
$283$	−19.6835	+	17.0558i	−1.17006	+	1.01386i	−0.999594	+	0.0285008i	$0.990927\pi$
$284$	−5.47591	+	0.787316i	−0.324935	+	0.0467186i
$285$	46.0936	+	12.4466i	2.73035	+	0.737272i
$286$	1.02290	+	0.886346i	0.0604852	+	0.0524107i
$287$	−8.96148	−	5.75919i	−0.528980	−	0.339955i
$288$	−1.51006	+	2.59224i	−0.0889813	+	0.152749i
$289$	11.1309	−	12.8457i	0.654757	−	0.755630i
$290$	−7.27073	−	2.13488i	−0.426952	−	0.125364i
$291$	−3.14532	−	18.9289i	−0.184382	−	1.10963i
$292$	2.91538	+	3.36453i	0.170610	+	0.196894i
$293$	−5.40088	−	11.8263i	−0.315523	−	0.690898i	0.683723	−	0.729742i	$-0.260360\pi$
$293$	−5.40088	−	11.8263i	−0.315523	−	0.690898i	−0.999245	+	0.0388438i	$0.987633\pi$
$294$	−1.65083	+	0.524187i	−0.0962782	+	0.0305712i
$295$	55.8030	+	25.4844i	3.24897	+	1.48376i
$296$	−0.643666	+	4.47679i	−0.0374123	+	0.260208i
$297$	−6.26283	−	8.46839i	−0.363406	−	0.491386i
$298$			3.56788i			0.206682i
$299$	−2.48495	+	2.01984i	−0.143708	+	0.116811i
$300$	0.548838	+	25.1016i	0.0316872	+	1.44924i
$301$	−4.01387	+	2.57956i	−0.231356	+	0.148683i
$302$	19.7371	+	2.83776i	1.13574	+	0.163295i
$303$	−4.89576	+	11.3717i	−0.281254	+	0.653287i
$304$	1.75885	+	5.99009i	0.100877	+	0.343555i
$305$	32.9713	−	15.0575i	1.88793	−	0.862189i
$306$	−0.113002	+	0.106914i	−0.00645990	+	0.00611186i
$307$	3.77862	+	26.2809i	0.215657	+	1.49993i	0.753816	+	0.657086i	$0.228211\pi$
$307$	3.77862	+	26.2809i	0.215657	+	1.49993i	−0.538158	+	0.842844i	$0.680880\pi$
$308$	0.571075	−	1.94490i	0.0325400	−	0.110821i
$309$	−14.4972	+	17.4890i	−0.824718	+	0.994913i
$310$	21.1045	−	32.8392i	1.19866	−	1.86514i
$311$	−18.5922	+	28.9300i	−1.05427	+	1.64047i	−0.340264	+	0.940330i	$0.610516\pi$
$311$	−18.5922	+	28.9300i	−1.05427	+	1.64047i	−0.714003	+	0.700142i	$0.753120\pi$
$312$	0.738083	−	0.890398i	0.0417857	−	0.0504089i
$313$	1.59868	−	5.44461i	0.0903628	−	0.307748i	−0.901893	−	0.431960i	$-0.857822\pi$
$313$	1.59868	−	5.44461i	0.0903628	−	0.307748i	0.992256	+	0.124212i	$0.0396404\pi$
$314$	−1.28839	−	8.96097i	−0.0727083	−	0.505697i
$315$	−9.62212	+	9.10371i	−0.542145	+	0.512936i
$316$	−10.2645	+	4.68763i	−0.577422	+	0.263700i
$317$	−4.42026	−	15.0540i	−0.248267	−	0.845519i	−0.985470	−	0.169848i	$-0.945672\pi$
$317$	−4.42026	−	15.0540i	−0.248267	−	0.845519i	0.737203	−	0.675671i	$-0.236146\pi$
$318$	−6.20066	+	14.4027i	−0.347715	+	0.807662i
$319$	3.44332	+	0.495075i	0.192789	+	0.0277189i
$320$	−3.71448	+	2.38715i	−0.207646	+	0.133446i
$321$	0.0337735	+	1.54466i	0.00188505	+	0.0862144i
$322$	4.29757	+	2.12859i	0.239494	+	0.118622i
$323$			0.323727i			0.0180126i
$324$	−7.11741	+	5.50840i	−0.395412	+	0.306022i
$325$	1.37750	−	9.58075i	0.0764101	−	0.531444i
$326$	16.5136	+	7.54153i	0.914606	+	0.417686i
$327$	16.9324	−	5.37653i	0.936363	−	0.297323i
$328$	−4.42522	−	9.68989i	−0.244342	−	0.535034i
$329$	2.93505	+	3.38723i	0.161815	+	0.186744i
$330$	−2.54105	−	15.2923i	−0.139880	−	0.841814i
$331$	−5.20703	−	1.52892i	−0.286204	−	0.0840371i	0.135480	−	0.990780i	$-0.456743\pi$
$331$	−5.20703	−	1.52892i	−0.286204	−	0.0840371i	−0.421684	+	0.906743i	$0.638561\pi$
$332$	−2.09587	+	2.41876i	−0.115026	+	0.132747i
$333$	−6.82976	+	11.7243i	−0.374268	+	0.642486i
$334$	1.40352	+	0.901990i	0.0767974	+	0.0493547i
$335$	−15.3704	−	13.3185i	−0.839773	−	0.727668i
$336$	−1.67216	−	0.451530i	−0.0912238	−	0.0246330i
$337$	−22.3867	+	3.21872i	−1.21948	+	0.175335i	−0.721846	−	0.692053i	$-0.756706\pi$
$337$	−22.3867	+	3.21872i	−1.21948	+	0.175335i	−0.497633	+	0.867388i	$0.665797\pi$
$338$	9.48779	−	8.22121i	0.516068	−	0.447175i
$339$	13.7625	−	6.65247i	0.747478	−	0.361313i
$340$	−0.219685	+	0.0645052i	−0.0119141	+	0.00349829i
$341$	−7.44446	+	16.3011i	−0.403140	+	0.882753i
$342$	−1.85258	+	18.6371i	−0.100176	+	1.00778i
$343$	−0.540641	−	0.841254i	−0.0291919	−	0.0454234i
$344$	−4.77130			−0.257251
$345$	36.6755	+	0.352892i	1.97454	+	0.0189990i
$346$	−4.52376			−0.243199
$347$	−2.88985	−	4.49669i	−0.155135	−	0.241395i	0.754982	−	0.655745i	$-0.227645\pi$
$347$	−2.88985	−	4.49669i	−0.155135	−	0.241395i	−0.910118	+	0.414350i	$0.864009\pi$
$348$	0.358617	−	2.95082i	0.0192239	−	0.158180i
$349$	−5.82811	+	12.7618i	−0.311972	+	0.683123i	−0.999055	−	0.0434554i	$-0.986163\pi$
$349$	−5.82811	+	12.7618i	−0.311972	+	0.683123i	0.687084	+	0.726578i	$0.258891\pi$
$350$	−13.9087	+	4.08396i	−0.743450	+	0.218297i
$351$	3.05482	−	1.64507i	0.163054	−	0.0878072i
$352$	1.53191	−	1.32741i	0.0816512	−	0.0707511i
$353$	27.7358	−	3.98781i	1.47623	−	0.212250i	0.643293	−	0.765620i	$-0.277568\pi$
$353$	27.7358	−	3.98781i	1.47623	−	0.212250i	0.832935	+	0.553370i	$0.186659\pi$
$354$	−6.27346	+	23.2326i	−0.333431	+	1.23480i
$355$	−18.4607	−	15.9963i	−0.979792	−	0.848995i
$356$	−3.54100	−	2.27566i	−0.187673	−	0.120610i
$357$	−0.0766003	−	0.0468943i	−0.00405412	−	0.00248191i
$358$	2.25536	−	2.60282i	0.119199	−	0.137563i
$359$	−25.6623	−	7.53514i	−1.35441	−	0.397690i	−0.477619	−	0.878567i	$-0.658500\pi$
$359$	−25.6623	−	7.53514i	−1.35441	−	0.397690i	−0.876788	+	0.480878i	$0.840318\pi$
$360$	−13.0165	+	2.45641i	−0.686029	+	0.129464i
$361$	13.0807	+	15.0959i	0.688457	+	0.794521i
$362$	4.79495	+	10.4995i	0.252017	+	0.551840i
$363$	−3.61229	−	11.3762i	−0.189596	−	0.597097i
$364$	0.607385	+	0.277384i	0.0318356	+	0.0145388i
$365$	−2.79748	+	19.4569i	−0.146427	+	1.01842i
$366$	7.94684	+	11.7906i	0.415388	+	0.616306i
$367$		−	21.6181i		−	1.12845i	−0.825620	−	0.564227i	$-0.809174\pi$
$367$		−	21.6181i		−	1.12845i	0.825620	−	0.564227i	$-0.190826\pi$
$368$	2.46454	+	4.11413i	0.128473	+	0.214464i
$369$	−1.39682	−	31.9271i	−0.0727154	−	1.66206i
$370$	−16.8000	+	10.7967i	−0.873388	+	0.561293i
$371$	−8.96112	−	1.28841i	−0.465238	−	0.0668912i
$372$	14.0648	+	6.05518i	0.729224	+	0.313947i
$373$	−4.40797	−	15.0122i	−0.228236	−	0.777301i	−0.991374	−	0.131065i	$-0.958160\pi$
$373$	−4.40797	−	15.0122i	−0.228236	−	0.777301i	0.763138	−	0.646236i	$-0.223658\pi$
$374$	0.0956111	−	0.0436641i	0.00494393	−	0.00225782i
$375$	−53.8311	+	48.7454i	−2.77983	+	2.51720i
$376$	0.637848	+	4.43633i	0.0328945	+	0.228786i
$377$	−0.322850	+	1.09953i	−0.0166276	+	0.0566285i
$378$	−4.14155	−	3.13808i	−0.213018	−	0.161405i
$379$	14.1110	−	21.9571i	0.724833	−	1.12786i	−0.261835	−	0.965113i	$-0.584328\pi$
$379$	14.1110	−	21.9571i	0.724833	−	1.12786i	0.986667	−	0.162749i	$-0.0520361\pi$
$380$	−14.9029	+	23.1894i	−0.764504	+	1.18959i
$381$	−9.24248	−	7.66142i	−0.473507	−	0.392506i
$382$	0.783181	−	2.66727i	0.0400710	−	0.136469i
$383$	−2.68821	−	18.6969i	−0.137361	−	0.955369i	−0.935609	−	0.353039i	$-0.885148\pi$
$383$	−2.68821	−	18.6969i	−0.137361	−	0.955369i	0.798247	−	0.602330i	$-0.205761\pi$
$384$	−1.16259	−	1.28389i	−0.0593284	−	0.0655182i
$385$	8.14128	−	3.71800i	0.414918	−	0.189487i
$386$	3.44644	+	11.7375i	0.175419	+	0.597423i
$387$	−13.2678	−	5.37143i	−0.674442	−	0.273045i
$388$	10.9657	+	1.57663i	0.556698	+	0.0800410i
$389$	19.3648	−	12.4450i	0.981833	−	0.630986i	0.0518761	−	0.998654i	$-0.483480\pi$
$389$	19.3648	−	12.4450i	0.981833	−	0.630986i	0.929957	+	0.367667i	$0.119844\pi$
$390$	5.10536	−	0.111627i	0.258520	−	0.00565246i
$391$	0.0625172	+	0.240699i	0.00316163	+	0.0121727i
$392$		−	1.00000i		−	0.0505076i
$393$	10.5371	−	7.10200i	0.531528	−	0.358248i
$394$	2.39155	−	16.6336i	0.120484	−	0.837988i
$395$	−45.3219	−	20.6978i	−2.28039	−	1.04142i
$396$	5.75425	−	1.96661i	0.289162	−	0.0988260i
$397$	−1.47398	−	3.22757i	−0.0739771	−	0.161987i	0.869030	−	0.494759i	$-0.164744\pi$
$397$	−1.47398	−	3.22757i	−0.0739771	−	0.161987i	−0.943008	+	0.332771i	$0.892016\pi$
$398$	−11.3092	−	13.0515i	−0.566878	−	0.654212i
$399$	−10.6669	+	1.77247i	−0.534013	+	0.0887344i
$400$	−13.9087	−	4.08396i	−0.695434	−	0.204198i
$401$	9.44943	−	10.9052i	0.471882	−	0.544581i	−0.469052	−	0.883170i	$-0.655404\pi$
$401$	9.44943	−	10.9052i	0.471882	−	0.544581i	0.940934	+	0.338590i	$0.109950\pi$
$402$	4.16551	−	6.80423i	0.207757	−	0.339364i
$403$	−4.96616	−	3.19156i	−0.247382	−	0.158983i
$404$	−5.40214	−	4.68098i	−0.268766	−	0.232887i
$405$	−38.9611	−	7.82297i	−1.93599	−	0.388727i
$406$	1.69872	−	0.244239i	0.0843061	−	0.0121214i
$407$	6.92857	−	6.00364i	0.343437	−	0.297590i
$408$	−0.0390873	−	0.0808632i	−0.00193511	−	0.00400333i
$409$	−30.0599	+	8.82638i	−1.48637	+	0.436436i	−0.921379	−	0.388664i	$-0.872937\pi$
$409$	−30.0599	+	8.82638i	−1.48637	+	0.436436i	−0.564986	+	0.825100i	$0.691118\pi$
$410$	19.5392	−	42.7848i	0.964971	−	2.11299i
$411$	28.1492	+	3.42102i	1.38850	+	0.168746i
$412$	−7.09067	−	11.0333i	−0.349332	−	0.543571i
$413$	−13.8938			−0.683668
$414$	2.22170	+	14.2149i	0.109191	+	0.698625i
$415$	−14.1314			−0.693684
$416$	0.361000	+	0.561727i	0.0176995	+	0.0275409i
$417$	14.0720	+	1.71019i	0.689107	+	0.0837482i
$418$	5.25690	−	11.5110i	0.257123	−	0.563022i
$419$	−6.84853	+	2.01091i	−0.334572	+	0.0982393i	−0.444704	−	0.895678i	$-0.646691\pi$
$419$	−6.84853	+	2.01091i	−0.334572	+	0.0982393i	0.110131	+	0.993917i	$0.464873\pi$
$420$	−3.32829	−	6.88550i	−0.162404	−	0.335978i
$421$	−16.5030	+	14.2999i	−0.804307	+	0.696936i	−0.956602	−	0.291399i	$-0.905879\pi$
$421$	−16.5030	+	14.2999i	−0.804307	+	0.696936i	0.152294	+	0.988335i	$0.451334\pi$
$422$	11.8207	−	1.69957i	0.575425	−	0.0827336i
$423$	−3.22062	+	13.0544i	−0.156592	+	0.634729i
$424$	−6.84201	−	5.92863i	−0.332277	−	0.287920i
$425$	−0.632350	−	0.406387i	−0.0306735	−	0.0197127i
$426$	5.00302	−	8.17227i	0.242397	−	0.395948i
$427$	−5.37586	+	6.20407i	−0.260156	+	0.300236i
$428$	−0.855889	−	0.251312i	−0.0413710	−	0.0121476i
$429$	−2.31260	+	0.384274i	−0.111653	+	0.0185529i
$430$	−13.7961	−	15.9216i	−0.665308	−	0.767806i
$431$	−4.68412	−	10.2568i	−0.225626	−	0.494052i	0.762635	−	0.646830i	$-0.223905\pi$
$431$	−4.68412	−	10.2568i	−0.225626	−	0.494052i	−0.988261	+	0.152778i	$0.951178\pi$
$432$	−1.78752	−	4.87901i	−0.0860022	−	0.234742i
$433$	−0.679557	−	0.310343i	−0.0326574	−	0.0149142i	0.399019	−	0.916943i	$-0.369351\pi$
$433$	−0.679557	−	0.310343i	−0.0326574	−	0.0149142i	−0.431677	+	0.902028i	$0.642078\pi$
$434$	−1.25819	+	8.75088i	−0.0603949	+	0.420056i
$435$	10.8836	−	7.33554i	0.521831	−	0.351712i
$436$			10.2569i			0.491217i
$437$	24.6653	+	16.9717i	1.17990	+	0.811869i
$438$	−7.70909	+	0.168557i	−0.368355	+	0.00805395i
$439$	2.97992	−	1.91508i	0.142224	−	0.0914018i	−0.467594	−	0.883943i	$-0.654879\pi$
$439$	2.97992	−	1.91508i	0.142224	−	0.0914018i	0.609818	+	0.792542i	$0.291243\pi$
$440$	8.85898	+	1.27373i	0.422335	+	0.0607227i
$441$	1.12578	−	2.78076i	0.0536085	−	0.132417i
$442$	0.00975489	+	0.0332221i	0.000463993	+	0.00158021i
$443$	−2.87841	+	1.31453i	−0.136758	+	0.0624551i	−0.482618	−	0.875831i	$-0.660314\pi$
$443$	−2.87841	+	1.31453i	−0.136758	+	0.0624551i	0.345861	+	0.938286i	$0.387587\pi$
$444$	−5.25822	−	5.80681i	−0.249544	−	0.275579i
$445$	−2.64497	−	18.3962i	−0.125384	−	0.872062i
$446$	−6.08124	+	20.7108i	−0.287955	+	0.980685i
$447$	−4.75769	−	3.94382i	−0.225031	−	0.186536i
$448$	0.540641	−	0.841254i	0.0255429	−	0.0397455i
$449$	5.46498	−	8.50367i	0.257908	−	0.401313i	−0.688019	−	0.725693i	$-0.741519\pi$
$449$	5.46498	−	8.50367i	0.257908	−	0.401313i	0.945927	+	0.324380i	$0.105156\pi$
$450$	−34.0791	−	27.0146i	−1.60650	−	1.27348i
$451$	−6.08339	+	20.7181i	−0.286456	+	0.975579i
$452$	1.25598	+	8.73556i	0.0590765	+	0.410886i
$453$	−25.6008	+	23.1822i	−1.20283	+	1.08919i
$454$	−7.59798	+	3.46988i	−0.356591	+	0.162850i
$455$	0.830628	+	2.82886i	0.0389405	+	0.132619i
$456$	−9.93183	−	4.27586i	−0.465101	−	0.200236i
$457$	14.2769	+	2.05270i	0.667843	+	0.0960214i	0.467894	−	0.883785i	$-0.345013\pi$
$457$	14.2769	+	2.05270i	0.667843	+	0.0960214i	0.199950	+	0.979806i	$0.435922\pi$
$458$	−21.1756	+	13.6087i	−0.989471	+	0.635894i
$459$	−0.0176584	−	0.268865i	−0.000824226	−	0.0125495i
$460$	−6.60245	+	20.1200i	−0.307841	+	0.938098i
$461$		−	21.0570i		−	0.980722i	−0.871519	−	0.490361i	$-0.836865\pi$
$461$		−	21.0570i		−	0.980722i	0.871519	−	0.490361i	$-0.163135\pi$
$462$	1.96224	+	2.91135i	0.0912915	+	0.135448i
$463$	0.338015	−	2.35094i	0.0157089	−	0.109258i	−0.980458	−	0.196727i	$-0.936969\pi$
$463$	0.338015	−	2.35094i	0.0157089	−	0.109258i	0.996167	+	0.0874691i	$0.0278779\pi$
$464$	1.56110	+	0.712931i	0.0724723	+	0.0330970i
$465$	20.4622	+	64.4418i	0.948911	+	2.98842i
$466$	−11.8140	−	25.8690i	−0.547272	−	1.19836i
$467$	2.51957	+	2.90774i	0.116592	+	0.134554i	0.811045	−	0.584984i	$-0.198899\pi$
$467$	2.51957	+	2.90774i	0.116592	+	0.134554i	−0.694453	+	0.719538i	$0.744354\pi$
$468$	0.371474	+	1.96843i	0.0171714	+	0.0909909i
$469$	4.41954	+	1.29769i	0.204075	+	0.0599220i
$470$	−12.9595	+	14.9560i	−0.597776	+	0.689870i
$471$	13.3734	+	8.18712i	0.616214	+	0.377243i
$472$	−11.6882	−	7.51154i	−0.537993	−	0.345747i
$473$	7.30921	+	6.33347i	0.336078	+	0.291213i
$474$	5.09517	−	18.8690i	0.234029	−	0.866683i
$475$	−89.5762	+	12.8791i	−4.11004	+	0.590934i
$476$	0.0391890	−	0.0339575i	0.00179623	−	0.00155644i
$477$	−12.3516	−	24.1887i	−0.565543	−	1.10752i
$478$	−14.4977	+	4.25691i	−0.663110	+	0.194707i
$479$	−15.6881	+	34.3522i	−0.716809	+	1.56959i	0.101514	+	0.994834i	$0.467631\pi$
$479$	−15.6881	+	34.3522i	−0.716809	+	1.56959i	−0.818323	+	0.574758i	$0.805096\pi$
$480$	0.922650	−	7.59186i	0.0421130	−	0.346519i
$481$	1.63274	+	2.54060i	0.0744466	+	0.115841i
$482$	11.9634			0.544916
$483$	−7.58882	+	3.37784i	−0.345303	+	0.153697i
$484$	6.89123			0.313238
$485$	26.4459	+	41.1506i	1.20085	+	1.86855i
$486$	0.522017	−	15.5797i	0.0236792	−	0.706710i
$487$	11.9106	−	26.0806i	0.539722	−	1.18183i	−0.421696	−	0.906737i	$-0.638565\pi$
$487$	11.9106	−	26.0806i	0.539722	−	1.18183i	0.961419	−	0.275090i	$-0.0887076\pi$
$488$	−7.87664	+	2.31279i	−0.356559	+	0.104695i
$489$	−28.3101	+	13.6844i	−1.28023	+	0.618831i
$490$	3.33695	−	2.89148i	0.150748	−	0.130624i
$491$	−20.1840	+	2.90201i	−0.910889	+	0.130966i	−0.581799	−	0.813332i	$-0.697651\pi$
$491$	−20.1840	+	2.90201i	−0.910889	+	0.130966i	−0.329090	+	0.944299i	$0.606742\pi$
$492$	17.8127	+	4.80994i	0.803061	+	0.216849i
$493$	0.0672558	+	0.0582775i	0.00302905	+	0.00262469i
$494$	3.50685	+	2.25372i	0.157781	+	0.101399i
$495$	23.2008	+	13.5152i	1.04280	+	0.607462i
$496$	−5.78954	+	6.68148i	−0.259958	+	0.300008i
$497$	5.30812	+	1.55861i	0.238102	+	0.0699130i
$498$	−0.908660	−	5.46841i	−0.0407180	−	0.245045i
$499$	0.163169	+	0.188307i	0.00730445	+	0.00842979i	0.759390	−	0.650636i	$-0.225497\pi$
$499$	0.163169	+	0.188307i	0.00730445	+	0.00842979i	−0.752086	+	0.659065i	$0.770952\pi$
$500$	−17.4176	−	38.1392i	−0.778938	−	1.70564i
$501$	−2.75419	+	0.874538i	−0.123048	+	0.0390715i
$502$	−24.0964	−	11.0044i	−1.07547	−	0.491152i
$503$	−0.435009	+	3.02556i	−0.0193961	+	0.134903i	−0.997219	−	0.0745326i	$-0.976254\pi$
$503$	−0.435009	+	3.02556i	−0.0193961	+	0.134903i	0.977822	+	0.209435i	$0.0671626\pi$
$504$	2.45046	−	1.73068i	0.109152	−	0.0770907i
$505$		−	31.5616i		−	1.40447i
$506$	1.68567	−	9.57393i	0.0749372	−	0.425613i
$507$	0.475321	+	21.7392i	0.0211097	+	0.965472i
$508$	5.83082	−	3.74724i	0.258701	−	0.166257i
$509$	11.2273	+	1.61424i	0.497641	+	0.0715500i	0.386566	−	0.922262i	$-0.373661\pi$
$509$	11.2273	+	1.61424i	0.497641	+	0.0715500i	0.111076	+	0.993812i	$0.464570\pi$
$510$	0.156816	−	0.364247i	0.00694393	−	0.0161291i
$511$	−1.25425	−	4.27158i	−0.0554847	−	0.188963i
$512$	0.909632	−	0.415415i	0.0402004	−	0.0183589i
$513$	−22.8044	−	23.0712i	−1.00684	−	1.01862i
$514$	1.26015	+	8.76452i	0.0555827	+	0.386586i
$515$	16.3150	−	55.5637i	0.718924	−	2.44843i
$516$	5.27404	−	6.36242i	0.232177	−	0.280090i
$517$	4.91170	−	7.64275i	0.216016	−	0.336128i
$518$	2.44523	−	3.80485i	0.107437	−	0.167175i
$519$	5.00042	−	6.03234i	0.219494	−	0.264790i
$520$	−0.830628	+	2.82886i	−0.0364255	+	0.124054i
$521$	0.633522	+	4.40624i	0.0277551	+	0.193041i	0.998982	−	0.0451161i	$-0.0143658\pi$
$521$	0.633522	+	4.40624i	0.0277551	+	0.193041i	−0.971227	+	0.238157i	$0.923457\pi$
$522$	3.53844	+	3.73994i	0.154874	+	0.163693i
$523$	−34.6346	+	15.8171i	−1.51446	+	0.691632i	−0.987407	−	0.158198i	$-0.949432\pi$
$523$	−34.6346	+	15.8171i	−1.51446	+	0.691632i	−0.527056	+	0.849830i	$0.676704\pi$
$524$	2.06691	+	7.03925i	0.0902935	+	0.307511i
$525$	9.92833	−	23.0612i	0.433308	−	1.00647i
$526$	10.1046	+	1.45283i	0.440583	+	0.0633462i
$527$	−0.385664	+	0.247851i	−0.0167998	+	0.0107966i
$528$	0.0767460	+	3.51004i	0.00333994	+	0.152755i
$529$	21.6169	+	7.85564i	0.939864	+	0.341550i
$530$		−	39.9739i		−	1.73636i
$531$	−24.0457	−	34.0461i	−1.04350	−	1.47748i
$532$	0.888468	−	6.17943i	0.0385200	−	0.267912i
$533$	−6.47019	−	2.95484i	−0.280255	−	0.127988i
$534$	6.94866	−	2.20640i	0.300698	−	0.0954805i
$535$	−1.63617	−	3.58272i	−0.0707379	−	0.154894i
$536$	3.01637	+	3.48107i	0.130287	+	0.150359i
$537$	0.977807	+	5.88454i	0.0421955	+	0.253937i
$538$	7.18921	+	2.11094i	0.309949	+	0.0910093i
$539$	−1.32741	+	1.53191i	−0.0571755	+	0.0659841i
$540$	11.1124	−	20.0724i	0.478202	−	0.863780i
$541$	18.5041	+	11.8918i	0.795552	+	0.511270i	0.874161	−	0.485635i	$-0.161412\pi$
$541$	18.5041	+	11.8918i	0.795552	+	0.511270i	−0.0786097	+	0.996905i	$0.525048\pi$
$542$	1.90591	+	1.65148i	0.0818659	+	0.0709372i
$543$	−19.3010	−	5.21182i	−0.828286	−	0.223660i
$544$	0.0513267	−	0.00737967i	0.00220062	−	0.000316401i
$545$	−34.2268	+	29.6576i	−1.46611	+	1.27039i
$546$	−1.04127	+	0.503324i	−0.0445622	+	0.0215403i
$547$	17.6330	−	5.17753i	0.753934	−	0.221375i	0.117889	−	0.993027i	$-0.462387\pi$
$547$	17.6330	−	5.17753i	0.753934	−	0.221375i	0.636045	+	0.771652i	$0.280569\pi$
$548$	−6.80098	+	14.8921i	−0.290523	+	0.636157i
$549$	−24.5067	−	2.43604i	−1.04592	−	0.103967i
$550$	15.8858	+	24.7188i	0.677372	+	1.05401i
$551$	10.7141			0.456437
$552$	−8.21032	−	1.26121i	−0.349454	−	0.0536807i
$553$	11.2842			0.479854
$554$	−1.39018	−	2.16316i	−0.0590630	−	0.0919038i
$555$	4.17299	−	34.3367i	0.177134	−	1.45751i
$556$	−3.39985	+	7.44464i	−0.144186	+	0.315723i
$557$	−6.39101	+	1.87657i	−0.270796	+	0.0795128i	−0.414311	−	0.910135i	$-0.635977\pi$
$557$	−6.39101	+	1.87657i	−0.270796	+	0.0795128i	0.143516	+	0.989648i	$0.454159\pi$
$558$	−23.6212	+	12.0619i	−0.999965	+	0.510619i
$559$	−2.40776	+	2.08634i	−0.101837	+	0.0882426i
$560$	4.37047	−	0.628379i	0.184686	−	0.0265538i
$561$	−0.0474602	+	0.175760i	−0.00200377	+	0.00742060i
$562$	7.07815	+	6.13325i	0.298574	+	0.258716i
$563$	6.23553	+	4.00733i	0.262796	+	0.168889i	0.665403	−	0.746484i	$-0.268260\pi$
$563$	6.23553	+	4.00733i	0.262796	+	0.168889i	−0.402607	+	0.915373i	$0.631896\pi$
$564$	−6.62081	−	4.05322i	−0.278786	−	0.170671i
$565$	−25.5184	+	29.4498i	−1.07357	+	1.23896i
$566$	24.9900	+	7.33772i	1.05041	+	0.308427i
$567$	8.76250	−	2.05394i	0.367990	−	0.0862574i
$568$	3.62283	+	4.18097i	0.152011	+	0.175430i
$569$	−6.51287	−	14.2612i	−0.273034	−	0.597861i	0.722594	−	0.691273i	$-0.242950\pi$
$569$	−6.51287	−	14.2612i	−0.273034	−	0.597861i	−0.995628	+	0.0934123i	$0.970223\pi$
$570$	−14.4494	−	45.5055i	−0.605217	−	1.90602i
$571$	25.1837	+	11.5010i	1.05390	+	0.481302i	0.865562	−	0.500802i	$-0.166961\pi$
$571$	25.1837	+	11.5010i	1.05390	+	0.481302i	0.188342	+	0.982103i	$0.439689\pi$
$572$	0.192621	−	1.33971i	0.00805390	−	0.0560161i
$573$	2.69104	+	3.99267i	0.112420	+	0.166796i
$574$			10.6525i			0.444628i
$575$	−64.1151	+	26.8747i	−2.67378	+	1.12075i
$576$	2.99713	−	0.131125i	0.124881	−	0.00546356i
$577$	21.2370	−	13.6482i	0.884106	−	0.568181i	−0.0179306	−	0.999839i	$-0.505708\pi$
$577$	21.2370	−	13.6482i	0.884106	−	0.568181i	0.902037	+	0.431659i	$0.142071\pi$
$578$	−16.8243	−	2.41897i	−0.699799	−	0.100616i
$579$	−19.4613	−	8.37849i	−0.808783	−	0.348198i
$580$	2.13488	+	7.27073i	0.0886461	+	0.301901i
$581$	2.91126	−	1.32953i	0.120779	−	0.0551580i
$582$	−14.2235	+	12.8797i	−0.589583	+	0.533882i
$583$	2.61163	+	18.1643i	0.108163	+	0.752287i
$584$	1.25425	−	4.27158i	0.0519011	−	0.176759i
$585$	−5.49445	+	6.93128i	−0.227167	+	0.286573i
$586$	−7.02896	+	10.9373i	−0.290364	+	0.451814i
$587$	8.75666	−	13.6256i	0.361426	−	0.562390i	−0.612153	−	0.790739i	$-0.709696\pi$
$587$	8.75666	−	13.6256i	0.361426	−	0.562390i	0.973579	+	0.228349i	$0.0733328\pi$
$588$	1.33348	+	1.10537i	0.0549917	+	0.0455846i
$589$	−15.5498	+	52.9576i	−0.640717	+	2.18208i
$590$	−8.73055	−	60.7223i	−0.359431	−	2.49990i
$591$	19.5370	+	21.5753i	0.803644	+	0.887489i
$592$	4.11411	−	1.87885i	0.169089	−	0.0772203i
$593$	12.2193	+	41.6152i	0.501788	+	1.70893i	0.687373	+	0.726304i	$0.258764\pi$
$593$	12.2193	+	41.6152i	0.501788	+	1.70893i	−0.185585	+	0.982628i	$0.559418\pi$
$594$	−3.73812	+	9.84699i	−0.153377	+	0.404027i
$595$	0.226629	+	0.0325843i	0.00929087	+	0.00133583i
$596$	3.00149	−	1.92894i	0.122946	−	0.0790125i
$597$	29.9047	−	0.653856i	1.22392	−	0.0267605i
$598$	3.04267	+	0.998464i	0.124424	+	0.0408302i
$599$			42.5512i			1.73859i	0.494291	+	0.869297i	$0.335428\pi$
$599$			42.5512i			1.73859i	−0.494291	+	0.869297i	$0.664572\pi$
$600$	20.8201	−	14.0326i	0.849975	−	0.572880i
$601$	0.934758	−	6.50138i	0.0381296	−	0.265197i	−0.961835	−	0.273631i	$-0.911775\pi$
$601$	0.934758	−	6.50138i	0.0381296	−	0.265197i	0.999964	+	0.00843361i	$0.00268453\pi$
$602$	4.34013	+	1.98207i	0.176890	+	0.0807831i
$603$	4.46888	+	13.0758i	0.181987	+	0.532487i
$604$	−8.28339	−	18.1381i	−0.337046	−	0.738028i
$605$	19.9259	+	22.9957i	0.810101	+	0.934907i
$606$	12.2133	−	2.02943i	0.496133	−	0.0824400i
$607$	−19.4231	−	5.70313i	−0.788359	−	0.231483i	−0.137319	−	0.990527i	$-0.543849\pi$
$607$	−19.4231	−	5.70313i	−0.788359	−	0.231483i	−0.651040	+	0.759044i	$0.725667\pi$
$608$	4.08828	−	4.71813i	0.165802	−	0.191345i
$609$	−1.55202	+	2.53518i	−0.0628911	+	0.102731i
$610$	−30.4928	−	19.5965i	−1.23462	−	0.793440i
$611$	2.26174	+	1.95981i	0.0915004	+	0.0792856i
$612$	0.151035	+	0.0372614i	0.00610524	+	0.00150620i
$613$	7.49726	−	1.07794i	0.302812	−	0.0435377i	0.0107657	−	0.999942i	$-0.496573\pi$
$613$	7.49726	−	1.07794i	0.302812	−	0.0435377i	0.292046	+	0.956404i	$0.405664\pi$
$614$	20.0660	−	17.3873i	0.809798	−	0.701694i
$615$	35.4547	+	73.3480i	1.42967	+	2.95768i
$616$	−1.94490	+	0.571075i	−0.0783623	+	0.0230092i
$617$	10.3828	−	22.7353i	0.417998	−	0.915287i	−0.577126	−	0.816655i	$-0.695826\pi$
$617$	10.3828	−	22.7353i	0.417998	−	0.915287i	0.995124	−	0.0986324i	$-0.0314468\pi$
$618$	22.5504	+	2.74059i	0.907112	+	0.110243i
$619$	16.7628	+	26.0835i	0.673756	+	1.04838i	0.994852	+	0.101338i	$0.0323123\pi$
$619$	16.7628	+	26.0835i	0.673756	+	1.04838i	−0.321096	+	0.947047i	$0.604051\pi$
$620$	−39.0361			−1.56773
$621$	−21.4111	−	12.7501i	−0.859197	−	0.511645i
$622$	34.3892			1.37888
$623$	2.27566	+	3.54100i	0.0911726	+	0.141867i
$624$	−1.14809	−	0.139529i	−0.0459603	−	0.00558563i
$625$	46.7968	−	102.471i	1.87187	−	4.09883i
$626$	−5.44461	+	1.59868i	−0.217610	+	0.0638962i
$627$	9.53887	+	19.7338i	0.380946	+	0.788094i
$628$	−6.84189	+	5.92853i	−0.273021	+	0.236574i
$629$	0.232142	−	0.0333770i	0.00925611	−	0.00133083i
$630$	12.8606	+	3.17281i	0.512380	+	0.126408i
$631$	2.67179	+	2.31512i	0.106362	+	0.0921633i	0.706418	−	0.707794i	$-0.250310\pi$
$631$	2.67179	+	2.31512i	0.106362	+	0.0921633i	−0.600056	+	0.799958i	$0.704855\pi$
$632$	9.49289	+	6.10071i	0.377607	+	0.242673i
$633$	−10.7999	+	17.6413i	−0.429258	+	0.701180i
$634$	−10.2745	+	11.8574i	−0.408052	+	0.470917i
$635$	29.3640	+	8.62206i	1.16528	+	0.342156i
$636$	15.4686	−	2.57035i	0.613371	−	0.101921i
$637$	−0.437268	−	0.504634i	−0.0173252	−	0.0199943i
$638$	−1.44512	−	3.16437i	−0.0572128	−	0.125278i
$639$	5.36738	+	15.7048i	0.212330	+	0.621271i
$640$	4.01640	+	1.83423i	0.158762	+	0.0725042i
$641$	−0.866219	+	6.02469i	−0.0342136	+	0.237961i	−0.999751	−	0.0223025i	$-0.992900\pi$
$641$	−0.866219	+	6.02469i	−0.0342136	+	0.237961i	0.965538	+	0.260263i	$0.0838094\pi$
$642$	1.28119	−	0.863518i	0.0505645	−	0.0340803i
$643$		−	31.2785i		−	1.23350i	−0.787158	−	0.616752i	$-0.788448\pi$
$643$		−	31.2785i		−	1.23350i	0.787158	−	0.616752i	$-0.211552\pi$
$644$	−0.532755	−	4.76615i	−0.0209935	−	0.187813i
$645$	36.4808	−	0.797642i	1.43643	−	0.0314071i
$646$	0.272336	−	0.175020i	0.0107149	−	0.00688606i
$647$	−20.9630	−	3.01402i	−0.824139	−	0.118493i	−0.282674	−	0.959216i	$-0.591221\pi$
$647$	−20.9630	−	3.01402i	−0.824139	−	0.118493i	−0.541466	+	0.840723i	$0.682130\pi$
$648$	8.48192	+	3.00948i	0.333201	+	0.118223i
$649$	7.93438	+	27.0220i	0.311452	+	1.06071i
$650$	−8.80457	+	4.02091i	−0.345344	+	0.157713i
$651$	−10.2784	−	11.3507i	−0.402840	−	0.444869i
$652$	−2.58361	−	17.9694i	−0.101182	−	0.703736i
$653$	−6.25652	+	21.3078i	−0.244837	+	0.833837i	0.741761	+	0.670664i	$0.233991\pi$
$653$	−6.25652	+	21.3078i	−0.244837	+	0.833837i	−0.986598	+	0.163172i	$0.947827\pi$
$654$	−13.6774	−	11.3377i	−0.534827	−	0.443337i
$655$	−17.5132	+	27.2510i	−0.684296	+	1.06479i
$656$	−5.75919	+	8.96148i	−0.224859	+	0.349887i
$657$	8.29661	−	10.4662i	0.323682	−	0.408326i
$658$	1.26271	−	4.30040i	0.0492256	−	0.167647i
$659$	−4.61985	−	32.1318i	−0.179964	−	1.25168i	−0.856841	−	0.515581i	$-0.827576\pi$
$659$	−4.61985	−	32.1318i	−0.179964	−	1.25168i	0.676877	−	0.736096i	$-0.263333\pi$
$660$	−11.4909	+	10.4053i	−0.447283	+	0.405027i
$661$	1.82895	−	0.835254i	0.0711380	−	0.0324876i	−0.379528	−	0.925180i	$-0.623914\pi$
$661$	1.82895	−	0.835254i	0.0711380	−	0.0324876i	0.450666	+	0.892692i	$0.351186\pi$
$662$	1.52892	+	5.20703i	0.0594232	+	0.202377i
$663$	−0.0550837	−	0.0237147i	−0.00213927	−	0.000921002i
$664$	3.16790	+	0.455475i	0.122938	+	0.0176759i
$665$	23.1894	−	14.9029i	0.899247	−	0.577911i
$666$	13.5555	−	0.593058i	0.525266	−	0.0229805i
$667$	7.96624	−	2.06908i	0.308454	−	0.0801152i
$668$		−	1.66837i		−	0.0645512i
$669$	−20.8954	−	31.0022i	−0.807863	−	1.19862i
$670$	−2.89439	+	20.1309i	−0.111820	+	0.777725i
$671$	15.1363	+	6.91253i	0.584331	+	0.266855i
$672$	0.524187	+	1.65083i	0.0202209	+	0.0636820i
$673$	−17.2423	−	37.7553i	−0.664641	−	1.45536i	−0.878134	−	0.478415i	$-0.841211\pi$
$673$	−17.2423	−	37.7553i	−0.664641	−	1.45536i	0.213493	−	0.976945i	$-0.431516\pi$
$674$	14.8109	+	17.0927i	0.570494	+	0.658386i
$675$	73.6932	−	15.5826i	2.83645	−	0.599776i
$676$	−12.0456	−	3.53691i	−0.463293	−	0.136035i
$677$	12.7613	−	14.7273i	0.490455	−	0.566016i	−0.455532	−	0.890219i	$-0.650551\pi$
$677$	12.7613	−	14.7273i	0.490455	−	0.566016i	0.945987	+	0.324204i	$0.105096\pi$
$678$	−13.0370	−	7.98117i	−0.500683	−	0.306515i
$679$	−9.31977	−	5.98945i	−0.357660	−	0.229854i
$680$	0.173036	+	0.149936i	0.00663562	+	0.00574980i
$681$	3.77155	−	13.9672i	0.144526	−	0.535226i
$682$	17.7381	−	2.55036i	0.679228	−	0.0976582i
$683$	−15.1524	+	13.1296i	−0.579789	+	0.502390i	−0.894662	−	0.446744i	$-0.852584\pi$
$683$	−15.1524	+	13.1296i	−0.579789	+	0.502390i	0.314873	+	0.949134i	$0.398038\pi$
$684$	16.6801	−	8.51748i	0.637779	−	0.325674i
$685$	−69.3589	+	20.3656i	−2.65007	+	0.778130i
$686$	−0.415415	+	0.909632i	−0.0158606	+	0.0347299i
$687$	5.25987	−	43.2798i	0.200676	−	1.65123i
$688$	2.57956	+	4.01387i	0.0983448	+	0.153028i
$689$	−6.04511			−0.230300
$690$	−19.5314	−	31.0442i	−0.743547	−	1.18183i
$691$	−31.8766			−1.21264			−0.606322	−	0.795219i	$-0.707356\pi$
$691$	−31.8766			−1.21264			−0.606322	+	0.795219i	$0.707356\pi$
$692$	2.44573	+	3.80563i	0.0929728	+	0.144668i
$693$	−6.05121	−	0.601506i	−0.229866	−	0.0228493i
$694$	−2.22049	+	4.86219i	−0.0842886	+	0.184566i
$695$	−34.6729	+	10.1809i	−1.31522	+	0.386183i
$696$	−2.67627	+	1.29364i	−0.101444	+	0.0490354i
$697$	−0.417463	+	0.361733i	−0.0158125	+	0.0137016i
$698$	13.8868	−	1.99662i	0.525624	−	0.0755733i
$699$	47.5545	+	12.8411i	1.79868	+	0.485694i
$700$	10.9552	+	9.49277i	0.414069	+	0.358793i
$701$	0.804545	+	0.517050i	0.0303873	+	0.0195287i	0.555746	−	0.831352i	$-0.312433\pi$
$701$	0.804545	+	0.517050i	0.0303873	+	0.0195287i	−0.525359	+	0.850881i	$0.676069\pi$
$702$	−3.03548	−	1.68049i	−0.114567	−	0.0634260i
$703$	18.4906	−	21.3393i	0.697386	−	0.804826i
$704$	−1.94490	−	0.571075i	−0.0733012	−	0.0215232i
$705$	−5.61856	−	33.8131i	−0.211607	−	1.27347i
$706$	−18.3499	−	21.1769i	−0.690606	−	0.797002i
$707$	2.96941	+	6.50210i	0.111676	+	0.244537i
$708$	22.9362	−	7.28293i	0.861996	−	0.273709i
$709$	4.00797	+	1.83038i	0.150522	+	0.0687412i	0.489252	−	0.872143i	$-0.337270\pi$
$709$	4.00797	+	1.83038i	0.150522	+	0.0687412i	−0.338730	+	0.940884i	$0.609997\pi$
$710$	−3.47633	+	24.1784i	−0.130464	+	0.907398i
$711$	19.5294	+	27.6515i	0.732409	+	1.03701i
$712$			4.20920i			0.157746i
$713$	−1.33463	+	42.3783i	−0.0499824	+	1.58708i
$714$	0.00196330	+	0.0897932i	7.34747e−5	+	0.00336043i
$715$	5.02750	−	3.23098i	0.188018	−	0.120832i
$716$	−3.40897	−	0.490136i	−0.127399	−	0.0183172i
$717$	10.3488	−	24.0378i	0.386483	−	0.897710i
$718$	7.53514	+	25.6623i	0.281209	+	0.957710i
$719$	−22.3259	+	10.1959i	−0.832616	+	0.380243i	−0.785663	−	0.618654i	$-0.787678\pi$
$719$	−22.3259	+	10.1959i	−0.832616	+	0.380243i	−0.0469522	+	0.998897i	$0.514951\pi$
$720$	9.10371	+	9.62212i	0.339275	+	0.358595i
$721$	1.86650	+	12.9818i	0.0695122	+	0.483468i
$722$	5.62754	−	19.1656i	0.209435	−	0.713271i
$723$	−13.2239	+	15.9529i	−0.491802	+	0.593294i
$724$	6.24038	−	9.71022i	0.231922	−	0.360877i
$725$	−13.4499	+	20.9284i	−0.499516	+	0.777262i
$726$	−7.61734	+	9.18931i	−0.282706	+	0.341047i
$727$	2.65748	−	9.05053i	0.0985603	−	0.335666i	−0.895420	−	0.445222i	$-0.853125\pi$
$727$	2.65748	−	9.05053i	0.0985603	−	0.335666i	0.993981	+	0.109556i	$0.0349430\pi$
$728$	−0.0950274	−	0.660930i	−0.00352195	−	0.0244957i
$729$	20.1982	+	17.9174i	0.748081	+	0.663607i
$730$	17.8806	−	8.16582i	0.661792	−	0.302230i
$731$	0.0697045	+	0.237392i	0.00257811	+	0.00878025i
$732$	5.62252	−	13.0598i	0.207814	−	0.482704i
$733$	−30.0538	−	4.32109i	−1.11006	−	0.159603i	−0.437196	−	0.899366i	$-0.644028\pi$
$733$	−30.0538	−	4.32109i	−1.11006	−	0.159603i	−0.672867	+	0.739763i	$0.734937\pi$
$734$	−18.1863	+	11.6876i	−0.671268	+	0.431398i
$735$	0.167175	+	7.64589i	0.00616634	+	0.282023i
$736$	2.12859	−	4.29757i	0.0784610	−	0.158410i
$737$		−	9.33665i		−	0.343920i
$738$	−26.1036	+	18.4362i	−0.960886	+	0.678644i
$739$	3.70803	−	25.7899i	0.136402	−	0.948697i	−0.800557	−	0.599257i	$-0.795463\pi$
$739$	3.70803	−	25.7899i	0.136402	−	0.948697i	0.936959	−	0.349440i	$-0.113628\pi$
$740$	18.1655	+	8.29590i	0.667777	+	0.304963i
$741$	−6.88164	+	2.18512i	−0.252803	+	0.0802725i
$742$	3.76086	+	8.23514i	0.138066	+	0.302322i
$743$	13.7253	+	15.8399i	0.503534	+	0.581110i	0.949431	−	0.313975i	$-0.101661\pi$
$743$	13.7253	+	15.8399i	0.503534	+	0.581110i	−0.445897	+	0.895084i	$0.647115\pi$
$744$	−2.51005	−	15.1057i	−0.0920228	−	0.553802i
$745$	15.1155	+	4.43832i	0.553790	+	0.162607i
$746$	−10.2459	+	11.8244i	−0.375130	+	0.432923i
$747$	8.29640	+	4.83292i	0.303550	+	0.176827i
$748$	−0.0884239	−	0.0568266i	−0.00323310	−	0.00207779i
$749$	0.674145	+	0.584150i	0.0246327	+	0.0213444i
$750$	70.1106	+	18.9318i	2.56008	+	0.691293i
$751$	33.0957	−	4.75844i	1.20768	−	0.173638i	0.491074	−	0.871118i	$-0.336604\pi$
$751$	33.0957	−	4.75844i	1.20768	−	0.173638i	0.716604	+	0.697480i	$0.245695\pi$
$752$	3.38723	−	2.93505i	0.123520	−	0.107030i
$753$	41.3095	−	19.9680i	1.50540	−	0.727675i
$754$	1.09953	−	0.322850i	0.0400424	−	0.0117575i
$755$	36.5746	−	80.0871i	1.33108	−	2.91467i
$756$	−0.400828	+	5.18067i	−0.0145780	+	0.188419i
$757$	−5.60399	−	8.71997i	−0.203680	−	0.316933i	0.724353	−	0.689429i	$-0.242138\pi$
$757$	−5.60399	−	8.71997i	−0.203680	−	0.316933i	−0.928034	+	0.372496i	$0.878502\pi$
$758$	−26.1005			−0.948012
$759$	10.9033	+	12.8305i	0.395766	+	0.465718i
$760$	27.5653			0.999899
$761$	−11.9137	−	18.5380i	−0.431870	−	0.672003i	0.555304	−	0.831647i	$-0.312602\pi$
$761$	−11.9137	−	18.5380i	−0.431870	−	0.672003i	−0.987175	+	0.159644i	$0.948965\pi$
$762$	−1.44833	+	11.9173i	−0.0524676	+	0.431720i
$763$	4.26087	−	9.33001i	0.154254	−	0.337769i
$764$	−2.66727	+	0.783181i	−0.0964984	+	0.0283345i
$765$	0.312376	+	0.611737i	0.0112940	+	0.0221174i
$766$	−14.2755	+	12.3698i	−0.515795	+	0.446939i
$767$	−9.18281	+	1.32029i	−0.331572	+	0.0476729i
$768$	−0.451530	+	1.67216i	−0.0162932	+	0.0603389i
$769$	−20.2122	−	17.5139i	−0.728869	−	0.631569i	0.209258	−	0.977861i	$-0.432895\pi$
$769$	−20.2122	−	17.5139i	−0.728869	−	0.631569i	−0.938127	+	0.346292i	$0.887441\pi$
$770$	−7.52929	−	4.83878i	−0.271337	−	0.174378i
$771$	−13.0802	−	8.00763i	−0.471072	−	0.288388i
$772$	8.01092	−	9.24509i	0.288319	−	0.332738i
$773$	−24.4972	−	7.19302i	−0.881102	−	0.258715i	−0.190272	−	0.981731i	$-0.560937\pi$
$773$	−24.4972	−	7.19302i	−0.881102	−	0.258715i	−0.690831	+	0.723016i	$0.742755\pi$
$774$	2.65440	+	14.0656i	0.0954106	+	0.505579i
$775$	−83.9244	−	96.8539i	−3.01465	−	3.47909i
$776$	−4.60215	−	10.0773i	−0.165208	−	0.361754i
$777$	2.37081	+	7.46641i	0.0850522	+	0.267856i
$778$	−20.9388	−	9.56242i	−0.750692	−	0.342829i
$779$	−9.46444	+	65.8266i	−0.339099	+	2.35848i
$780$	−2.85407	−	4.23455i	−0.102192	−	0.151621i
$781$		−	11.2139i		−	0.401263i
$782$	0.168690	−	0.182725i	0.00603234	−	0.00653422i
$783$	−8.89841	+	0.584428i	−0.318003	+	0.0208857i
$784$	−0.841254	+	0.540641i	−0.0300448	+	0.0193086i
$785$	−39.5664	−	5.68879i	−1.41219	−	0.203042i
$786$	−11.6714	−	5.02478i	−0.416305	−	0.179228i
$787$	−0.297578	−	1.01346i	−0.0106075	−	0.0361259i	0.954019	−	0.299746i	$-0.0969018\pi$
$787$	−0.297578	−	1.01346i	−0.0106075	−	0.0361259i	−0.964627	+	0.263620i	$0.915084\pi$
$788$	−15.2860	+	6.98090i	−0.544542	+	0.248684i
$789$	−13.1066	+	11.8684i	−0.466608	+	0.422526i
$790$	7.09076	+	49.3173i	0.252278	+	1.75463i
$791$	2.48640	−	8.46790i	0.0884062	−	0.301084i
$792$	−4.76540	−	3.77755i	−0.169331	−	0.134229i
$793$	−2.96351	+	4.61131i	−0.105237	+	0.163752i
$794$	−1.91831	+	2.98495i	−0.0680783	+	0.105932i
$795$	53.3043	+	44.1859i	1.89051	+	1.56711i
$796$	−4.86541	+	16.5701i	−0.172450	+	0.587310i
$797$	−2.20825	−	15.3587i	−0.0782202	−	0.544033i	−0.990821	−	0.135181i	$-0.956838\pi$
$797$	−2.20825	−	15.3587i	−0.0782202	−	0.544033i	0.912601	−	0.408852i	$-0.134071\pi$
$798$	7.25805	+	8.01529i	0.256932	+	0.283738i
$799$	0.211407	−	0.0965464i	0.00747905	−	0.00341557i
$800$	4.08396	+	13.9087i	0.144390	+	0.491746i
$801$	−4.73862	+	11.7048i	−0.167431	+	0.413568i
$802$	−14.2828	−	2.05356i	−0.504343	−	0.0725136i
$803$	−7.59152	+	4.87878i	−0.267899	+	0.172168i
$804$	−7.97613	+	0.174395i	−0.281296	+	0.00615045i
$805$	14.3639	−	15.5590i	0.506262	−	0.548383i
$806$			5.90328i			0.207934i
$807$	−10.7616	+	7.25329i	−0.378827	+	0.255328i
$808$	−1.01727	+	7.07530i	−0.0357876	+	0.248908i
$809$	−21.8590	−	9.98267i	−0.768521	−	0.350972i	−0.00773127	−	0.999970i	$-0.502461\pi$
$809$	−21.8590	−	9.98267i	−0.768521	−	0.350972i	−0.760790	+	0.648998i	$0.775188\pi$
$810$	14.4828	+	37.0056i	0.508875	+	1.30024i
$811$	0.225698	+	0.494209i	0.00792532	+	0.0173540i	0.913553	−	0.406719i	$-0.133327\pi$
$811$	0.225698	+	0.494209i	0.00792532	+	0.0173540i	−0.905628	+	0.424073i	$0.860600\pi$
$812$	−1.12387	−	1.29701i	−0.0394399	−	0.0455161i
$813$	−4.30894	+	0.715997i	−0.151121	+	0.0251111i
$814$	−8.79646	−	2.58287i	−0.308316	−	0.0905296i
$815$	52.4925	−	60.5796i	1.83873	−	2.12201i
$816$	−0.0468943	+	0.0766003i	−0.00164163	+	0.00268155i
$817$	25.0585	+	16.1041i	0.876687	+	0.563412i
$818$	23.6768	+	20.5161i	0.827841	+	0.717328i
$819$	0.479812	−	1.94487i	0.0167660	−	0.0679591i
$820$	−46.5566	+	6.69382i	−1.62583	+	0.233758i
$821$	25.7429	−	22.3063i	0.898433	−	0.778497i	−0.0774033	−	0.997000i	$-0.524663\pi$
$821$	25.7429	−	22.3063i	0.898433	−	0.778497i	0.975836	+	0.218503i	$0.0701175\pi$
$822$	−12.3407	−	25.5301i	−0.430430	−	0.890466i
$823$	26.2486	−	7.70727i	0.914967	−	0.268659i	0.209837	−	0.977736i	$-0.432707\pi$
$823$	26.2486	−	7.70727i	0.914967	−	0.268659i	0.705130	+	0.709078i	$0.250889\pi$
$824$	−5.44829	+	11.9301i	−0.189800	+	0.415605i
$825$	−50.5215	−	6.13996i	−1.75893	−	0.213766i
$826$	7.51154	+	11.6882i	0.261360	+	0.406684i
$827$	32.0618			1.11490			0.557448	−	0.830212i	$-0.311781\pi$
$827$	32.0618			1.11490			0.557448	+	0.830212i	$0.311781\pi$
$828$	10.7572	−	9.55418i	0.373839	−	0.332031i
$829$	36.1678			1.25616			0.628080	−	0.778149i	$-0.283841\pi$
$829$	36.1678			1.25616			0.628080	+	0.778149i	$0.283841\pi$
$830$	7.64002	+	11.8881i	0.265189	+	0.412642i
$831$	4.42118	+	0.537313i	0.153369	+	0.0186392i
$832$	0.277384	−	0.607385i	0.00961654	−	0.0210573i
$833$	−0.0497541	+	0.0146091i	−0.00172388	+	0.000506176i
$834$	−6.16917	−	12.7627i	−0.213621	−	0.441936i
$835$	5.56726	−	4.82406i	0.192663	−	0.166944i
$836$	−12.5258	+	1.80093i	−0.433213	+	0.0622866i
$837$	10.0259	−	44.8311i	0.346544	−	1.54959i
$838$	5.39428	+	4.67417i	0.186342	+	0.161466i
$839$	−11.3082	−	7.26735i	−0.390403	−	0.250897i	0.330684	−	0.943742i	$-0.392721\pi$
$839$	−11.3082	−	7.26735i	−0.390403	−	0.250897i	−0.721087	+	0.692845i	$0.756357\pi$
$840$	−3.99304	+	6.52251i	−0.137773	+	0.225048i
$841$	−17.0622	+	19.6908i	−0.588352	+	0.678994i
$842$	20.9521	+	6.15208i	0.722056	+	0.212015i
$843$	−16.0025	+	2.65906i	−0.551156	+	0.0915830i
$844$	−7.82054	−	9.02538i	−0.269194	−	0.310667i
$845$	−23.0272	−	50.4225i	−0.792158	−	1.73459i
$846$	12.7233	−	4.34841i	0.437436	−	0.149501i
$847$	−6.26849	−	2.86272i	−0.215388	−	0.0983643i
$848$	−1.28841	+	8.96112i	−0.0442443	+	0.307726i
$849$	−37.4078	+	25.2127i	−1.28383	+	0.865298i
$850$			0.751676i			0.0257823i
$851$	9.62726	−	19.4372i	0.330018	−	0.666298i
$852$	−9.57979	+	0.209459i	−0.328198	+	0.00717595i
$853$	41.7390	−	26.8240i	1.42912	−	0.918438i	0.429234	−	0.903194i	$-0.358784\pi$
$853$	41.7390	−	26.8240i	1.42912	−	0.918438i	0.999884	−	0.0152444i	$-0.00485263\pi$
$854$	8.12561	+	1.16829i	0.278053	+	0.0399779i
$855$	76.6525	+	31.0324i	2.62146	+	1.06129i
$856$	0.251312	+	0.855889i	0.00858966	+	0.0292537i
$857$	31.5450	−	14.4061i	1.07756	−	0.492103i	0.204072	−	0.978956i	$-0.434582\pi$
$857$	31.5450	−	14.4061i	1.07756	−	0.492103i	0.873484	+	0.486853i	$0.161855\pi$
$858$	1.57356	+	1.73773i	0.0537204	+	0.0593251i
$859$	4.59392	+	31.9514i	0.156742	+	1.09017i	0.904586	+	0.426292i	$0.140180\pi$
$859$	4.59392	+	31.9514i	0.156742	+	1.09017i	−0.747843	+	0.663875i	$0.768910\pi$
$860$	−5.93533	+	20.2139i	−0.202393	+	0.689288i
$861$	−14.2049	−	11.7750i	−0.484102	−	0.401290i
$862$	−6.09613	+	9.48577i	−0.207635	+	0.323086i
$863$	24.1235	−	37.5369i	0.821173	−	1.27777i	−0.136710	−	0.990611i	$-0.543653\pi$
$863$	24.1235	−	37.5369i	0.821173	−	1.27777i	0.957883	−	0.287159i	$-0.0927109\pi$
$864$	−3.13808	+	4.14155i	−0.106760	+	0.140898i
$865$	−5.62741	+	19.1652i	−0.191338	+	0.651636i
$866$	0.106319	+	0.739464i	0.00361286	+	0.0251280i
$867$	21.8227	−	19.7610i	0.741137	−	0.671118i
$868$	8.04194	−	3.67263i	0.272961	−	0.124657i
$869$	−6.44413	−	21.9467i	−0.218602	−	0.744490i
$870$	−12.0552	−	5.19001i	−0.408709	−	0.175958i
$871$	3.04432	+	0.437708i	0.103153	+	0.0148312i
$872$	8.62866	−	5.54530i	0.292203	−	0.187788i
$873$	−1.45266	−	33.2035i	−0.0491652	−	1.12377i
$874$	0.942451	−	29.9254i	0.0318789	−	1.01224i
$875$			41.9281i			1.41743i
$876$	4.30965	+	6.39417i	0.145610	+	0.216039i
$877$	−7.32748	+	50.9638i	−0.247431	+	1.72092i	0.365520	+	0.930803i	$0.380891\pi$
$877$	−7.32748	+	50.9638i	−0.247431	+	1.72092i	−0.612952	+	0.790120i	$0.710018\pi$
$878$	−3.22213	−	1.47150i	−0.108742	−	0.0496607i
$879$	−6.81503	−	21.4627i	−0.229865	−	0.723918i
$880$	−3.71800	−	8.14128i	−0.125334	−	0.274443i
$881$	−29.2386	−	33.7432i	−0.985074	−	1.13684i	−0.990592	−	0.136851i	$-0.956302\pi$
$881$	−29.2386	−	33.7432i	−0.985074	−	1.13684i	0.00551774	−	0.999985i	$-0.498244\pi$
$882$	−2.94797	+	0.556327i	−0.0992632	+	0.0187325i
$883$	−17.5932	−	5.16584i	−0.592060	−	0.173844i	−0.0280415	−	0.999607i	$-0.508927\pi$
$883$	−17.5932	−	5.16584i	−0.592060	−	0.173844i	−0.564018	+	0.825762i	$0.690745\pi$
$884$	0.0226743	−	0.0261676i	0.000762620	−	0.000880110i
$885$	90.6224	+	55.4785i	3.04624	+	1.86489i
$886$	2.66204	+	1.71079i	0.0894329	+	0.0574751i
$887$	15.9737	+	13.8413i	0.536343	+	0.464744i	0.880418	−	0.474198i	$-0.157262\pi$
$887$	15.9737	+	13.8413i	0.536343	+	0.464744i	−0.344075	+	0.938942i	$0.611807\pi$
$888$	−2.04220	+	7.56290i	−0.0685316	+	0.253794i
$889$	−6.86056	+	0.986399i	−0.230096	+	0.0330828i
$890$	−14.0459	+	12.1708i	−0.470818	+	0.407966i
$891$	−8.99875	−	15.8692i	−0.301469	−	0.531639i
$892$	20.7108	−	6.08124i	0.693449	−	0.203615i
$893$	11.6236	−	25.4522i	0.388969	−	0.851724i
$894$	−0.745549	+	6.13461i	−0.0249349	+	0.205172i
$895$	−8.22141	−	12.7928i	−0.274811	−	0.427615i
$896$	−1.00000			−0.0334077
$897$	−4.69469	+	2.95366i	−0.156751	+	0.0986198i
$898$	−10.1083			−0.337320
$899$	8.20293	+	12.7640i	0.273583	+	0.425704i
$900$	−4.30159	+	43.2743i	−0.143386	+	1.44248i
$901$	−0.195018	+	0.427030i	−0.00649699	+	0.0142264i
$902$	20.7181	−	6.08339i	0.689838	−	0.202555i
$903$	−7.44048	+	3.59655i	−0.247604	+	0.119686i
$904$	6.66978	−	5.77940i	0.221834	−	0.192220i
$905$	50.4464	−	7.25310i	1.67690	−	0.241101i
$906$	33.3429	+	9.00353i	1.10774	+	0.299122i
$907$	15.1274	+	13.1079i	0.502295	+	0.435241i	0.868791	−	0.495178i	$-0.164897\pi$
$907$	15.1274	+	13.1079i	0.502295	+	0.435241i	−0.366496	+	0.930420i	$0.619443\pi$
$908$	7.02683	+	4.51587i	0.233194	+	0.149864i
$909$	−10.7940	+	18.5295i	−0.358015	+	0.614584i
$910$	1.93072	−	2.22817i	0.0640027	−	0.0738630i
$911$	−23.9835	−	7.04218i	−0.794608	−	0.233318i	−0.140859	−	0.990030i	$-0.544987\pi$
$911$	−23.9835	−	7.04218i	−0.794608	−	0.233318i	−0.653749	+	0.756712i	$0.726805\pi$
$912$	1.77247	+	10.6669i	0.0586923	+	0.353216i
$913$	−4.24834	−	4.90285i	−0.140600	−	0.162261i
$914$	−5.99181	−	13.1202i	−0.198191	−	0.433979i
$915$	59.8373	−	19.0001i	1.97816	−	0.628124i
$916$	22.8968	+	10.4566i	0.756531	+	0.345496i
$917$	1.04408	−	7.26176i	0.0344787	−	0.239804i
$918$	−0.216637	+	0.160215i	−0.00715007	+	0.00528787i
$919$		−	49.7345i		−	1.64059i	−0.571941	−	0.820294i	$-0.693810\pi$
$919$		−	49.7345i		−	1.64059i	0.571941	−	0.820294i	$-0.306190\pi$
$920$	20.4955	−	5.32333i	0.675718	−	0.175505i
$921$	1.00527	+	45.9769i	0.0331248	+	1.51499i
$922$	−17.7143	+	11.3843i	−0.583388	+	0.374921i
$923$	3.65641	+	0.525712i	0.120352	+	0.0173040i
$924$	1.38831	−	3.22473i	0.0456722	−	0.106086i
$925$	18.4710	+	62.9066i	0.607324	+	2.06836i
$926$	−2.16049	+	0.986661i	−0.0709980	+	0.0324237i
$927$	−28.5810	+	27.0412i	−0.938724	+	0.888148i
$928$	−0.244239	−	1.69872i	−0.00801755	−	0.0557633i
$929$	−8.47678	+	28.8693i	−0.278114	+	0.947170i	0.695415	+	0.718608i	$0.255220\pi$
$929$	−8.47678	+	28.8693i	−0.278114	+	0.947170i	−0.973529	+	0.228562i	$0.926598\pi$
$930$	43.1492	−	52.0538i	1.41492	−	1.70691i
$931$	−3.37521	+	5.25193i	−0.110618	+	0.172125i
$932$	−15.3753	+	23.9244i	−0.503634	+	0.783669i
$933$	−38.0127	+	45.8573i	−1.24448	+	1.50130i
$934$	1.08396	−	3.69164i	0.0354683	−	0.120794i
$935$	−0.0660487	−	0.459378i	−0.00216002	−	0.0150233i
$936$	1.45512	−	1.37672i	0.0475620	−	0.0449995i
$937$	37.5599	−	17.1530i	1.22703	−	0.560365i	0.306810	−	0.951771i	$-0.400738\pi$
$937$	37.5599	−	17.1530i	1.22703	−	0.560365i	0.920218	+	0.391405i	$0.128011\pi$
$938$	−1.29769	−	4.41954i	−0.0423712	−	0.144303i
$939$	3.88649	−	9.02740i	0.126831	−	0.294598i
$940$	19.5882	+	2.81636i	0.638898	+	0.0918596i
$941$	−34.8514	+	22.3976i	−1.13612	+	0.730142i	−0.966829	−	0.255423i	$-0.917785\pi$
$941$	−34.8514	+	22.3976i	−1.13612	+	0.730142i	−0.169294	+	0.985566i	$0.554149\pi$
$942$	−0.342766	−	15.6767i	−0.0111679	−	0.510775i
$943$	5.67519	+	50.7716i	0.184809	+	1.65335i
$944$			13.8938i			0.452204i
$945$	−18.4466	+	13.6423i	−0.600068	+	0.443783i
$946$	1.37639	−	9.57303i	0.0447504	−	0.311246i
$947$	−7.50935	−	3.42940i	−0.244021	−	0.111441i	0.289651	−	0.957132i	$-0.406461\pi$
$947$	−7.50935	−	3.42940i	−0.244021	−	0.111441i	−0.533672	+	0.845692i	$0.679188\pi$
$948$	−18.6283	+	5.91503i	−0.605018	+	0.192111i
$949$	−1.23489	−	2.70402i	−0.0400861	−	0.0877763i
$950$	59.2631	+	68.3933i	1.92275	+	2.21897i
$951$	−4.45449	−	26.8076i	−0.144447	−	0.869295i
$952$	−0.0497541	−	0.0146091i	−0.00161254	−	0.000473484i
$953$	−2.37992	+	2.74657i	−0.0770931	+	0.0889702i	−0.792986	−	0.609240i	$-0.791475\pi$
$953$	−2.37992	+	2.74657i	−0.0770931	+	0.0889702i	0.715893	+	0.698210i	$0.246020\pi$
$954$	−13.6710	+	23.4683i	−0.442615	+	0.759813i
$955$	−10.3258	−	6.63598i	−0.334135	−	0.214735i
$956$	11.4192	+	9.89479i	0.369323	+	0.320021i
$957$	5.81700	+	1.57075i	0.188037	+	0.0507753i
$958$	37.3806	−	5.37451i	1.20771	−	0.173643i
$959$	12.3728	−	10.7211i	0.399538	−	0.346201i
$960$	−6.88550	+	3.32829i	−0.222229	+	0.107420i
$961$	−45.2507	+	13.2868i	−1.45970	+	0.428606i
$962$	1.25456	−	2.74710i	0.0404486	−	0.0885701i
$963$	−0.264704	+	2.66294i	−0.00852996	+	0.0858121i
$964$	−6.46788	−	10.0642i	−0.208316	−	0.324146i
$965$	54.0138			1.73877
$966$	6.94444	+	4.55793i	0.223434	+	0.146649i
$967$	7.22320			0.232282			0.116141	−	0.993233i	$-0.462947\pi$
$967$	7.22320			0.232282			0.116141	+	0.993233i	$0.462947\pi$
$968$	−3.72568	−	5.79727i	−0.119748	−	0.186331i
$969$	−0.0676464	+	0.556615i	−0.00217311	+	0.0178811i
$970$	20.3204	−	44.4954i	0.652448	−	1.42866i
$971$	−2.81447	+	0.826404i	−0.0903208	+	0.0265206i	−0.326581	−	0.945169i	$-0.605897\pi$
$971$	−2.81447	+	0.826404i	−0.0903208	+	0.0265206i	0.236260	+	0.971690i	$0.424078\pi$
$972$	−13.3887	+	7.98388i	−0.429443	+	0.256083i
$973$	6.18523	−	5.35953i	0.198289	−	0.171819i
$974$	−28.3798	+	4.08040i	−0.909348	+	0.130744i
$975$	4.37048	−	16.1853i	0.139968	−	0.518344i
$976$	6.20407	+	5.37586i	0.198588	+	0.172077i
$977$	9.81866	+	6.31007i	0.314127	+	0.201877i	0.688198	−	0.725523i	$-0.258402\pi$
$977$	9.81866	+	6.31007i	0.314127	+	0.201877i	−0.374071	+	0.927400i	$0.622038\pi$
$978$	26.8177	+	16.4176i	0.857534	+	0.524977i
$979$	5.58733	−	6.44812i	0.178572	−	0.206083i
$980$	−4.23656	−	1.24397i	−0.135332	−	0.0397370i
$981$	30.2370	−	5.70620i	0.965394	−	0.182185i
$982$	13.3536	+	15.4109i	0.426131	+	0.491781i
$983$	−22.1586	−	48.5205i	−0.706749	−	1.54756i	−0.831591	−	0.555388i	$-0.812570\pi$
$983$	−22.1586	−	48.5205i	−0.706749	−	1.54756i	0.124843	−	0.992177i	$-0.460157\pi$
$984$	−5.58391	−	17.5855i	−0.178009	−	0.560605i
$985$	−67.4941	−	30.8235i	−2.15054	−	0.982120i
$986$	0.0126649	−	0.0880864i	0.000403333	−	0.00280524i
$987$	4.33873	+	6.43732i	0.138103	+	0.204902i
$988$		−	4.16860i		−	0.132621i
$989$	21.7417	+	7.13462i	0.691344	+	0.226868i
$990$	−1.17358	−	26.8246i	−0.0372989	−	0.852541i
$991$	−21.2735	+	13.6716i	−0.675774	+	0.434294i	−0.833003	−	0.553268i	$-0.813380\pi$
$991$	−21.2735	+	13.6716i	−0.675774	+	0.434294i	0.157229	+	0.987562i	$0.449744\pi$
$992$	8.75088	+	1.25819i	0.277841	+	0.0399475i
$993$	−8.63347	−	3.71689i	−0.273975	−	0.117952i
$994$	−1.55861	−	5.30812i	−0.0494360	−	0.168363i
$995$	−69.3616	+	31.6764i	−2.19891	+	1.00421i
$996$	−4.10906	+	3.72086i	−0.130201	+	0.117900i
$997$	2.93065	+	20.3831i	0.0928148	+	0.645541i	0.982124	+	0.188235i	$0.0602765\pi$
$997$	2.93065	+	20.3831i	0.0928148	+	0.645541i	−0.889309	+	0.457306i	$0.848814\pi$
$998$	0.0701982	−	0.239073i	0.00222209	−	0.00756773i
$999$	−14.1930	+	18.7315i	−0.449047	+	0.592640i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.r.b.701.12	yes	240
3.2	odd	2		966.2.r.a.701.14	yes	240
23.21	odd	22		966.2.r.a.113.14	✓	240
69.44	even	22	inner	966.2.r.b.113.12	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.r.a.113.14	✓	240	23.21	odd	22
966.2.r.a.701.14	yes	240	3.2	odd	2
966.2.r.b.113.12	yes	240	69.44	even	22	inner
966.2.r.b.701.12	yes	240	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.r (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.540641 - 0.841254i) q^{2} +(1.71940 + 0.208961i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-4.23656 + 1.24397i) q^{5} +(-0.753788 - 1.55942i) q^{6} +(0.755750 - 0.654861i) q^{7} +(0.989821 - 0.142315i) q^{8} +(2.91267 + 0.718576i) q^{9} +O(q^{10})\)	\(q+(-0.540641 - 0.841254i) q^{2} +(1.71940 + 0.208961i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-4.23656 + 1.24397i) q^{5} +(-0.753788 - 1.55942i) q^{6} +(0.755750 - 0.654861i) q^{7} +(0.989821 - 0.142315i) q^{8} +(2.91267 + 0.718576i) q^{9} +(3.33695 + 2.89148i) q^{10} +(-1.70523 - 1.09588i) q^{11} +(-0.904342 + 1.47722i) q^{12} +(0.437268 - 0.504634i) q^{13} +(-0.959493 - 0.281733i) q^{14} +(-7.54427 + 1.25360i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-0.0215412 - 0.0471686i) q^{17} +(-0.970204 - 2.83879i) q^{18} +(-5.67881 - 2.59343i) q^{19} +(0.628379 - 4.37047i) q^{20} +(1.43628 - 0.968045i) q^{21} +2.02701i q^{22} +(-4.72318 - 0.831605i) q^{23} +(1.73164 - 0.0378617i) q^{24} +(12.1947 - 7.83705i) q^{25} +(-0.660930 - 0.0950274i) q^{26} +(4.85789 + 1.84415i) q^{27} +(0.281733 + 0.959493i) q^{28} +(-1.56110 + 0.712931i) q^{29} +(5.13334 + 5.66890i) q^{30} +(-1.25819 - 8.75088i) q^{31} +(-0.281733 + 0.959493i) q^{32} +(-2.70297 - 2.24059i) q^{33} +(-0.0280347 + 0.0436228i) q^{34} +(-2.38715 + 3.71448i) q^{35} +(-1.86361 + 2.35095i) q^{36} +(-1.27423 + 4.33962i) q^{37} +(0.888468 + 6.17943i) q^{38} +(0.857287 - 0.776295i) q^{39} +(-4.01640 + 1.83423i) q^{40} +(-3.00117 - 10.2210i) q^{41} +(-1.59088 - 0.684908i) q^{42} +(-4.72274 - 0.679027i) q^{43} +(1.70523 - 1.09588i) q^{44} +(-13.2336 + 0.578973i) q^{45} +(1.85395 + 4.42299i) q^{46} +4.48195i q^{47} +(-0.968045 - 1.43628i) q^{48} +(0.142315 - 0.989821i) q^{49} +(-13.1859 - 6.02180i) q^{50} +(-0.0271815 - 0.0856029i) q^{51} +(0.277384 + 0.607385i) q^{52} +(-5.92863 - 6.84201i) q^{53} +(-1.07497 - 5.08374i) q^{54} +(8.58754 + 2.52153i) q^{55} +(0.654861 - 0.755750i) q^{56} +(-9.22222 - 5.64579i) q^{57} +(1.44375 + 0.927842i) q^{58} +(-10.5002 - 9.09849i) q^{59} +(1.99369 - 7.38328i) q^{60} +(-8.12561 + 1.16829i) q^{61} +(-6.68148 + 5.78954i) q^{62} +(2.67182 - 1.36433i) q^{63} +(0.959493 - 0.281733i) q^{64} +(-1.22476 + 2.68186i) q^{65} +(-0.423567 + 3.48524i) q^{66} +(2.49026 + 3.87492i) q^{67} +0.0518545 q^{68} +(-7.94726 - 2.41682i) q^{69} +4.41541 q^{70} +(2.99094 + 4.65400i) q^{71} +(2.98529 + 0.296746i) q^{72} +(1.84939 - 4.04960i) q^{73} +(4.33962 - 1.27423i) q^{74} +(22.6052 - 10.9268i) q^{75} +(4.71813 - 4.08828i) q^{76} +(-2.00638 + 0.288474i) q^{77} +(-1.11655 - 0.301499i) q^{78} +(8.52804 + 7.38959i) q^{79} +(3.71448 + 2.38715i) q^{80} +(7.96730 + 4.18595i) q^{81} +(-6.97593 + 8.05065i) q^{82} +(3.07083 + 0.901678i) q^{83} +(0.283914 + 1.70862i) q^{84} +(0.149936 + 0.173036i) q^{85} +(1.98207 + 4.34013i) q^{86} +(-2.83313 + 0.899603i) q^{87} +(-1.84383 - 0.842050i) q^{88} +(-0.599031 + 4.16635i) q^{89} +(7.64167 + 10.8198i) q^{90} -0.667726i q^{91} +(2.71853 - 3.95089i) q^{92} +(-0.334730 - 15.3092i) q^{93} +(3.77046 - 2.42313i) q^{94} +(27.2847 + 3.92295i) q^{95} +(-0.684908 + 1.59088i) q^{96} +(-3.12116 - 10.6297i) q^{97} +(-0.909632 + 0.415415i) q^{98} +(-4.17929 - 4.41729i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{3} + 24 q^{4} + 4 q^{5} + 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^3 + 24 * q^4 + 4 * q^5 + 4 * q^9	\( 240 q - 4 q^{3} + 24 q^{4} + 4 q^{5} + 4 q^{9} + 4 q^{12} - 8 q^{13} - 24 q^{14} + 26 q^{15} - 24 q^{16} - 32 q^{17} + 40 q^{18} - 4 q^{20} + 8 q^{23} + 12 q^{25} + 116 q^{27} + 4 q^{30} + 16 q^{31} + 2 q^{33} - 4 q^{36} + 22 q^{37} + 8 q^{39} - 154 q^{41} - 4 q^{42} + 22 q^{43} - 24 q^{45} + 4 q^{46} - 4 q^{48} + 24 q^{49} - 88 q^{50} - 24 q^{51} + 8 q^{52} + 108 q^{53} + 12 q^{54} - 16 q^{55} + 24 q^{56} - 70 q^{57} - 4 q^{58} - 22 q^{59} - 26 q^{60} + 4 q^{63} + 24 q^{64} - 76 q^{66} - 44 q^{67} + 32 q^{68} - 86 q^{69} + 4 q^{70} + 4 q^{72} - 12 q^{73} + 16 q^{74} - 26 q^{75} - 78 q^{78} + 4 q^{80} - 168 q^{81} + 8 q^{82} - 16 q^{83} - 28 q^{85} - 16 q^{86} + 156 q^{87} - 24 q^{89} - 126 q^{90} - 8 q^{92} - 16 q^{93} - 8 q^{94} + 132 q^{97} - 172 q^{99}+O(q^{100}) \) 240 * q - 4 * q^3 + 24 * q^4 + 4 * q^5 + 4 * q^9 + 4 * q^12 - 8 * q^13 - 24 * q^14 + 26 * q^15 - 24 * q^16 - 32 * q^17 + 40 * q^18 - 4 * q^20 + 8 * q^23 + 12 * q^25 + 116 * q^27 + 4 * q^30 + 16 * q^31 + 2 * q^33 - 4 * q^36 + 22 * q^37 + 8 * q^39 - 154 * q^41 - 4 * q^42 + 22 * q^43 - 24 * q^45 + 4 * q^46 - 4 * q^48 + 24 * q^49 - 88 * q^50 - 24 * q^51 + 8 * q^52 + 108 * q^53 + 12 * q^54 - 16 * q^55 + 24 * q^56 - 70 * q^57 - 4 * q^58 - 22 * q^59 - 26 * q^60 + 4 * q^63 + 24 * q^64 - 76 * q^66 - 44 * q^67 + 32 * q^68 - 86 * q^69 + 4 * q^70 + 4 * q^72 - 12 * q^73 + 16 * q^74 - 26 * q^75 - 78 * q^78 + 4 * q^80 - 168 * q^81 + 8 * q^82 - 16 * q^83 - 28 * q^85 - 16 * q^86 + 156 * q^87 - 24 * q^89 - 126 * q^90 - 8 * q^92 - 16 * q^93 - 8 * q^94 + 132 * q^97 - 172 * q^99

Introduction

L-functions

Modular forms

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