LMFDB - Embedded newform 55.2.j.a.9.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [55,2,Mod(4,55)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(55, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 2]))

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

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

chi := DirichletCharacter("55.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 55 = 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	55.j (of order $10$, degree $4$, 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:	$0.439177211117$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{14} + 25x^{12} - 57x^{10} + 194x^{8} - 303x^{6} + 235x^{4} - 33x^{2} + 121 $ x^16 - 7x^14 + 25x^12 - 57x^10 + 194x^8 - 303x^6 + 235x^4 - 33*x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			9.2
Root			$-0.471815 - 0.649397i$ of defining polynomial
Character	$\chi$	$=$	55.9
Dual form			55.2.j.a.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.763412 - 0.248048i) q^{2} +(-1.03494 - 1.42447i) q^{3} +(-1.09676 - 0.796845i) q^{4} +(1.42953 - 1.71943i) q^{5} +(0.436748 + 1.34417i) q^{6} +(-0.348029 + 0.479022i) q^{7} +(1.58326 + 2.17917i) q^{8} +(-0.0309674 + 0.0953077i) q^{9} +O(q^{10})$	\(q+(-0.763412 - 0.248048i) q^{2} +(-1.03494 - 1.42447i) q^{3} +(-1.09676 - 0.796845i) q^{4} +(1.42953 - 1.71943i) q^{5} +(0.436748 + 1.34417i) q^{6} +(-0.348029 + 0.479022i) q^{7} +(1.58326 + 2.17917i) q^{8} +(-0.0309674 + 0.0953077i) q^{9} +(-1.51782 + 0.958043i) q^{10} +(1.96213 + 2.67395i) q^{11} +2.38699i q^{12} +(-1.70704 - 0.554651i) q^{13} +(0.384510 - 0.279363i) q^{14} +(-3.92875 - 0.256818i) q^{15} +(0.169713 + 0.522322i) q^{16} +(6.73074 - 2.18695i) q^{17} +(0.0472817 - 0.0650777i) q^{18} +(-1.85009 + 1.34417i) q^{19} +(-2.93798 + 0.746695i) q^{20} +1.04254 q^{21} +(-0.834650 - 2.52803i) q^{22} +1.49081i q^{23} +(1.46558 - 4.51060i) q^{24} +(-0.912887 - 4.91596i) q^{25} +(1.16560 + 0.846855i) q^{26} +(-4.85588 + 1.57777i) q^{27} +(0.763412 - 0.248048i) q^{28} +(2.89263 + 2.10162i) q^{29} +(2.93556 + 1.17058i) q^{30} +(1.90578 - 5.86539i) q^{31} -5.82804i q^{32} +(1.77828 - 5.56238i) q^{33} -5.68079 q^{34} +(0.326126 + 1.28319i) q^{35} +(0.109909 - 0.0798539i) q^{36} +(-4.31283 + 5.93610i) q^{37} +(1.74580 - 0.567246i) q^{38} +(0.976598 + 3.00566i) q^{39} +(6.01024 + 0.392882i) q^{40} +(-6.80400 + 4.94339i) q^{41} +(-0.795888 - 0.258600i) q^{42} +9.51936i q^{43} +(-0.0212704 - 4.49621i) q^{44} +(0.119606 + 0.189492i) q^{45} +(0.369792 - 1.13810i) q^{46} +(1.13540 + 1.56274i) q^{47} +(0.568389 - 0.782321i) q^{48} +(2.05478 + 6.32397i) q^{49} +(-0.522483 + 3.97934i) q^{50} +(-10.0811 - 7.32438i) q^{51} +(1.43025 + 1.96857i) q^{52} +(2.26628 + 0.736359i) q^{53} +4.09840 q^{54} +(7.40261 + 0.448742i) q^{55} -1.59489 q^{56} +(3.82947 + 1.24427i) q^{57} +(-1.68697 - 2.32192i) q^{58} +(-0.0309674 - 0.0224991i) q^{59} +(4.10427 + 3.41228i) q^{60} +(-1.06351 - 3.27314i) q^{61} +(-2.90979 + 4.00499i) q^{62} +(-0.0348769 - 0.0480039i) q^{63} +(-1.10621 + 3.40455i) q^{64} +(-3.39395 + 2.14225i) q^{65} +(-2.73729 + 3.80529i) q^{66} -6.79162i q^{67} +(-9.12469 - 2.96479i) q^{68} +(2.12361 - 1.54290i) q^{69} +(0.0693234 - 1.06050i) q^{70} +(-3.64439 - 11.2163i) q^{71} +(-0.256721 + 0.0834136i) q^{72} +(4.01031 - 5.51972i) q^{73} +(4.76490 - 3.46191i) q^{74} +(-6.05785 + 6.38809i) q^{75} +3.10021 q^{76} +(-1.96376 + 0.00929006i) q^{77} -2.53680i q^{78} +(-1.39863 + 4.30453i) q^{79} +(1.14071 + 0.454865i) q^{80} +(7.51625 + 5.46087i) q^{81} +(6.42045 - 2.08613i) q^{82} +(-5.65177 + 1.83637i) q^{83} +(-1.14342 - 0.830744i) q^{84} +(5.86148 - 14.6993i) q^{85} +(2.36125 - 7.26720i) q^{86} -6.29552i q^{87} +(-2.72042 + 8.50937i) q^{88} +6.21375 q^{89} +(-0.0443060 - 0.174328i) q^{90} +(0.859791 - 0.624675i) q^{91} +(1.18795 - 1.63507i) q^{92} +(-10.3274 + 3.35559i) q^{93} +(-0.479142 - 1.47465i) q^{94} +(-0.333554 + 5.10264i) q^{95} +(-8.30186 + 6.03166i) q^{96} +(5.11260 + 1.66119i) q^{97} -5.33748i q^{98} +(-0.315611 + 0.104201i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{9}+O(q^{10}) $ 16 * q - 4 * q^4 - 2 * q^5 - 18 * q^6 + 2 * q^9	$ 16 q - 4 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{9} - 6 q^{11} - 12 q^{14} - 16 q^{15} + 16 q^{16} + 6 q^{19} - 8 q^{20} + 8 q^{21} + 6 q^{24} - 16 q^{25} + 40 q^{26} + 2 q^{29} + 26 q^{30} + 8 q^{31} - 16 q^{34} + 22 q^{35} + 10 q^{36} + 30 q^{39} + 12 q^{40} - 52 q^{41} + 4 q^{44} + 12 q^{45} - 62 q^{46} - 10 q^{49} + 28 q^{50} - 42 q^{51} - 40 q^{54} - 8 q^{55} - 20 q^{56} + 2 q^{59} - 32 q^{60} - 40 q^{61} - 8 q^{64} - 40 q^{65} + 58 q^{66} + 26 q^{69} - 34 q^{70} + 36 q^{71} + 48 q^{74} - 20 q^{75} + 56 q^{76} + 38 q^{79} + 34 q^{80} + 68 q^{81} + 12 q^{84} + 58 q^{85} + 22 q^{86} + 24 q^{89} + 78 q^{90} - 20 q^{91} + 14 q^{94} + 48 q^{95} - 86 q^{96} - 72 q^{99}+O(q^{100}) $ 16 * q - 4 * q^4 - 2 * q^5 - 18 * q^6 + 2 * q^9 - 6 * q^11 - 12 * q^14 - 16 * q^15 + 16 * q^16 + 6 * q^19 - 8 * q^20 + 8 * q^21 + 6 * q^24 - 16 * q^25 + 40 * q^26 + 2 * q^29 + 26 * q^30 + 8 * q^31 - 16 * q^34 + 22 * q^35 + 10 * q^36 + 30 * q^39 + 12 * q^40 - 52 * q^41 + 4 * q^44 + 12 * q^45 - 62 * q^46 - 10 * q^49 + 28 * q^50 - 42 * q^51 - 40 * q^54 - 8 * q^55 - 20 * q^56 + 2 * q^59 - 32 * q^60 - 40 * q^61 - 8 * q^64 - 40 * q^65 + 58 * q^66 + 26 * q^69 - 34 * q^70 + 36 * q^71 + 48 * q^74 - 20 * q^75 + 56 * q^76 + 38 * q^79 + 34 * q^80 + 68 * q^81 + 12 * q^84 + 58 * q^85 + 22 * q^86 + 24 * q^89 + 78 * q^90 - 20 * q^91 + 14 * q^94 + 48 * q^95 - 86 * q^96 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/55\mathbb{Z}\right)^\times$.

$n$	$12$	$46$
$\chi(n)$	$-1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.763412	−	0.248048i	−0.539814	−	0.175396i	0.0264046	−	0.999651i	$-0.491594\pi$
$2$	−0.763412	−	0.248048i	−0.539814	−	0.175396i	−0.566219	+	0.824255i	$0.691594\pi$
$3$	−1.03494	−	1.42447i	−0.597522	−	0.822418i	0.397957	−	0.917404i	$-0.369719\pi$
$3$	−1.03494	−	1.42447i	−0.597522	−	0.822418i	−0.995479	+	0.0949859i	$0.969719\pi$
$4$	−1.09676	−	0.796845i	−0.548382	−	0.398423i
$5$	1.42953	−	1.71943i	0.639305	−	0.768953i
$5$	1.42953	−	1.71943i	0.639305	−	0.768953i
$6$	0.436748	+	1.34417i	0.178302	+	0.548756i
$7$	−0.348029	+	0.479022i	−0.131543	+	0.181053i	−0.869708	−	0.493567i	$-0.835693\pi$
$7$	−0.348029	+	0.479022i	−0.131543	+	0.181053i	0.738165	+	0.674620i	$0.235693\pi$
$8$	1.58326	+	2.17917i	0.559766	+	0.770451i
$9$	−0.0309674	+	0.0953077i	−0.0103225	+	0.0317692i
$10$	−1.51782	+	0.958043i	−0.479977	+	0.302960i
$11$	1.96213	+	2.67395i	0.591606	+	0.806227i
$11$	1.96213	+	2.67395i	0.591606	+	0.806227i
$12$			2.38699i			0.689065i
$13$	−1.70704	−	0.554651i	−0.473448	−	0.153833i	0.0625674	−	0.998041i	$-0.480071\pi$
$13$	−1.70704	−	0.554651i	−0.473448	−	0.153833i	−0.536016	+	0.844208i	$0.680071\pi$
$14$	0.384510	−	0.279363i	0.102765	−	0.0746629i
$15$	−3.92875	−	0.256818i	−1.01440	−	0.0663102i
$16$	0.169713	+	0.522322i	0.0424281	+	0.130580i
$17$	6.73074	−	2.18695i	1.63244	−	0.530413i	0.657612	−	0.753357i	$-0.271567\pi$
$17$	6.73074	−	2.18695i	1.63244	−	0.530413i	0.974831	+	0.222944i	$0.0715666\pi$
$18$	0.0472817	−	0.0650777i	0.0111444	−	0.0153390i
$19$	−1.85009	+	1.34417i	−0.424441	+	0.308374i	−0.779422	−	0.626499i	$-0.784487\pi$
$19$	−1.85009	+	1.34417i	−0.424441	+	0.308374i	0.354981	+	0.934873i	$0.384487\pi$
$20$	−2.93798	+	0.746695i	−0.656952	+	0.166966i
$21$	1.04254			0.227501
$22$	−0.834650	−	2.52803i	−0.177948	−	0.538978i
$23$			1.49081i			0.310855i	0.987847	+	0.155428i	$0.0496756\pi$
$23$			1.49081i			0.310855i	−0.987847	+	0.155428i	$0.950324\pi$
$24$	1.46558	−	4.51060i	0.299161	−	0.920723i
$25$	−0.912887	−	4.91596i	−0.182577	−	0.983191i
$26$	1.16560	+	0.846855i	0.228592	+	0.166082i
$27$	−4.85588	+	1.57777i	−0.934515	+	0.303642i
$28$	0.763412	−	0.248048i	0.144271	−	0.0468766i
$29$	2.89263	+	2.10162i	0.537149	+	0.390261i	0.823025	−	0.568005i	$-0.192285\pi$
$29$	2.89263	+	2.10162i	0.537149	+	0.390261i	−0.285876	+	0.958267i	$0.592285\pi$
$30$	2.93556	+	1.17058i	0.535957	+	0.213717i
$31$	1.90578	−	5.86539i	0.342288	−	1.05346i	−0.620731	−	0.784023i	$-0.713164\pi$
$31$	1.90578	−	5.86539i	0.342288	−	1.05346i	0.963020	−	0.269432i	$-0.0868358\pi$
$32$		−	5.82804i		−	1.03026i
$33$	1.77828	−	5.56238i	0.309559	−	0.968286i
$34$	−5.68079			−0.974248
$35$	0.326126	+	1.28319i	0.0551253	+	0.216898i
$36$	0.109909	−	0.0798539i	0.0183182	−	0.0133090i
$37$	−4.31283	+	5.93610i	−0.709025	+	0.975889i	0.290792	+	0.956786i	$0.406081\pi$
$37$	−4.31283	+	5.93610i	−0.709025	+	0.975889i	−0.999818	+	0.0191031i	$0.993919\pi$
$38$	1.74580	−	0.567246i	0.283207	−	0.0920194i
$39$	0.976598	+	3.00566i	0.156381	+	0.481291i
$40$	6.01024	+	0.392882i	0.950302	+	0.0621202i
$41$	−6.80400	+	4.94339i	−1.06261	+	0.772028i	−0.974569	−	0.224089i	$-0.928059\pi$
$41$	−6.80400	+	4.94339i	−1.06261	+	0.772028i	−0.0880369	+	0.996117i	$0.528059\pi$
$42$	−0.795888	−	0.258600i	−0.122808	−	0.0399028i
$43$			9.51936i			1.45169i	0.687859	+	0.725844i	$0.258551\pi$
$43$			9.51936i			1.45169i	−0.687859	+	0.725844i	$0.741449\pi$
$44$	−0.0212704	−	4.49621i	−0.00320664	−	0.677830i
$45$	0.119606	+	0.189492i	0.0178299	+	0.0282477i
$46$	0.369792	−	1.13810i	0.0545228	−	0.167804i
$47$	1.13540	+	1.56274i	0.165615	+	0.227949i	0.883756	−	0.467948i	$-0.155007\pi$
$47$	1.13540	+	1.56274i	0.165615	+	0.227949i	−0.718141	+	0.695898i	$0.755007\pi$
$48$	0.568389	−	0.782321i	0.0820400	−	0.112918i
$49$	2.05478	+	6.32397i	0.293540	+	0.903424i
$50$	−0.522483	+	3.97934i	−0.0738902	+	0.562764i
$51$	−10.0811	−	7.32438i	−1.41164	−	1.02562i
$52$	1.43025	+	1.96857i	0.198340	+	0.272991i
$53$	2.26628	+	0.736359i	0.311298	+	0.101147i	0.460499	−	0.887660i	$-0.347670\pi$
$53$	2.26628	+	0.736359i	0.311298	+	0.101147i	−0.149202	+	0.988807i	$0.547670\pi$
$54$	4.09840			0.557722
$55$	7.40261	+	0.448742i	0.998168	+	0.0605083i
$56$	−1.59489			−0.213126
$57$	3.82947	+	1.24427i	0.507225	+	0.164807i
$58$	−1.68697	−	2.32192i	−0.221510	−	0.304882i
$59$	−0.0309674	−	0.0224991i	−0.00403161	−	0.00292913i	0.585768	−	0.810479i	$-0.300793\pi$
$59$	−0.0309674	−	0.0224991i	−0.00403161	−	0.00292913i	−0.589799	+	0.807550i	$0.700793\pi$
$60$	4.10427	+	3.41228i	0.529859	+	0.440523i
$61$	−1.06351	−	3.27314i	−0.136168	−	0.419082i	0.859602	−	0.510965i	$-0.170712\pi$
$61$	−1.06351	−	3.27314i	−0.136168	−	0.419082i	−0.995770	+	0.0918822i	$0.970712\pi$
$62$	−2.90979	+	4.00499i	−0.369544	+	0.508634i
$63$	−0.0348769	−	0.0480039i	−0.00439408	−	0.00604793i
$64$	−1.10621	+	3.40455i	−0.138276	+	0.425569i
$65$	−3.39395	+	2.14225i	−0.420968	+	0.265713i
$66$	−2.73729	+	3.80529i	−0.336938	+	0.468399i
$67$		−	6.79162i		−	0.829728i	−0.909883	−	0.414864i	$-0.863829\pi$
$67$		−	6.79162i		−	0.829728i	0.909883	−	0.414864i	$-0.136171\pi$
$68$	−9.12469	−	2.96479i	−1.10653	−	0.359534i
$69$	2.12361	−	1.54290i	0.255653	−	0.185743i
$70$	0.0693234	−	1.06050i	0.00828574	−	0.126754i
$71$	−3.64439	−	11.2163i	−0.432510	−	1.33113i	−0.895617	−	0.444826i	$-0.853265\pi$
$71$	−3.64439	−	11.2163i	−0.432510	−	1.33113i	0.463107	−	0.886302i	$-0.346735\pi$
$72$	−0.256721	+	0.0834136i	−0.0302548	+	0.00983038i
$73$	4.01031	−	5.51972i	0.469372	−	0.646035i	−0.507048	−	0.861918i	$-0.669263\pi$
$73$	4.01031	−	5.51972i	0.469372	−	0.646035i	0.976419	+	0.215884i	$0.0692632\pi$
$74$	4.76490	−	3.46191i	0.553909	−	0.402438i
$75$	−6.05785	+	6.38809i	−0.699501	+	0.737633i
$76$	3.10021			0.355619
$77$	−1.96376	+	0.00929006i	−0.223791	+	0.00105870i
$78$		−	2.53680i		−	0.287236i
$79$	−1.39863	+	4.30453i	−0.157358	+	0.484298i	−0.998392	−	0.0566840i	$-0.981947\pi$
$79$	−1.39863	+	4.30453i	−0.157358	+	0.484298i	0.841034	+	0.540982i	$0.181947\pi$
$80$	1.14071	+	0.454865i	0.127535	+	0.0508555i
$81$	7.51625	+	5.46087i	0.835139	+	0.606764i
$82$	6.42045	−	2.08613i	0.709020	−	0.230375i
$83$	−5.65177	+	1.83637i	−0.620363	+	0.201568i	−0.602301	−	0.798269i	$-0.705749\pi$
$83$	−5.65177	+	1.83637i	−0.620363	+	0.201568i	−0.0180613	+	0.999837i	$0.505749\pi$
$84$	−1.14342	−	0.830744i	−0.124757	−	0.0906416i
$85$	5.86148	−	14.6993i	0.635767	−	1.59437i
$86$	2.36125	−	7.26720i	0.254621	−	0.783642i
$87$		−	6.29552i		−	0.674951i
$88$	−2.72042	+	8.50937i	−0.289998	+	0.907102i
$89$	6.21375			0.658656			0.329328	−	0.944216i	$-0.393178\pi$
$89$	6.21375			0.658656			0.329328	+	0.944216i	$0.393178\pi$
$90$	−0.0443060	−	0.174328i	−0.00467026	−	0.0183758i
$91$	0.859791	−	0.624675i	0.0901306	−	0.0654837i
$92$	1.18795	−	1.63507i	0.123852	−	0.170467i
$93$	−10.3274	+	3.35559i	−1.07091	+	0.347958i
$94$	−0.479142	−	1.47465i	−0.0494197	−	0.152098i
$95$	−0.333554	+	5.10264i	−0.0342219	+	0.523520i
$96$	−8.30186	+	6.03166i	−0.847305	+	0.615603i
$97$	5.11260	+	1.66119i	0.519106	+	0.168668i	0.556840	−	0.830620i	$-0.312014\pi$
$97$	5.11260	+	1.66119i	0.519106	+	0.168668i	−0.0377334	+	0.999288i	$0.512014\pi$
$98$		−	5.33748i		−	0.539167i
$99$	−0.315611	+	0.104201i	−0.0317201	+	0.0104726i
$100$	−2.91604	+	6.11907i	−0.291604	+	0.611907i
$101$	−3.06894	+	9.44523i	−0.305371	+	0.939835i	0.674167	+	0.738579i	$0.264503\pi$
$101$	−3.06894	+	9.44523i	−0.305371	+	0.939835i	−0.979538	+	0.201257i	$0.935497\pi$
$102$	5.87927	+	8.09212i	0.582135	+	0.801239i
$103$	7.94766	−	10.9390i	0.783107	−	1.07785i	−0.211826	−	0.977307i	$-0.567941\pi$
$103$	7.94766	−	10.9390i	0.783107	−	1.07785i	0.994932	−	0.100546i	$-0.0320590\pi$
$104$	−1.49401	−	4.59808i	−0.146499	−	0.450879i
$105$	1.49034	−	1.79258i	0.145443	−	0.174938i
$106$	−1.54745	−	1.12429i	−0.150302	−	0.109201i
$107$	−3.29418	−	4.53405i	−0.318461	−	0.438323i	0.619536	−	0.784968i	$-0.287321\pi$
$107$	−3.29418	−	4.53405i	−0.318461	−	0.438323i	−0.937996	+	0.346645i	$0.887321\pi$
$108$	6.58300	+	2.13895i	0.633449	+	0.205820i
$109$	−18.6001			−1.78157			−0.890784	−	0.454428i	$-0.849844\pi$
$109$	−18.6001			−1.78157			−0.890784	+	0.454428i	$0.849844\pi$
$110$	−5.53993	−	2.17877i	−0.528212	−	0.207738i
$111$	12.9193			1.22625
$112$	−0.309268	−	0.100487i	−0.0292231	−	0.00949516i
$113$	6.93668	+	9.54752i	0.652548	+	0.898155i	0.999206	−	0.0398362i	$-0.0126836\pi$
$113$	6.93668	+	9.54752i	0.652548	+	0.898155i	−0.346658	+	0.937992i	$0.612684\pi$
$114$	−2.61482	−	1.89978i	−0.244901	−	0.177931i
$115$	2.56335	+	2.13116i	0.239033	+	0.198732i
$116$	−1.49787	−	4.60997i	−0.139074	−	0.428025i
$117$	0.105725	−	0.145518i	0.00977429	−	0.0134532i
$118$	0.0180600	+	0.0248575i	0.00166256	+	0.00228832i
$119$	−1.29490	+	3.98529i	−0.118703	+	0.365331i
$120$	−5.66057	−	8.96801i	−0.516737	−	0.818664i
$121$	−3.30005	+	10.4933i	−0.300005	+	0.953938i
$122$			2.76255i			0.250110i
$123$	14.0834	+	4.57598i	1.26986	+	0.412603i
$124$	−6.76400	+	4.91433i	−0.607425	+	0.441320i
$125$	−9.75765	−	5.45786i	−0.872751	−	0.488166i
$126$	0.0147182	+	0.0452979i	0.00131120	+	0.00403546i
$127$	−15.2707	+	4.96177i	−1.35506	+	0.440286i	−0.894391	−	0.447287i	$-0.852390\pi$
$127$	−15.2707	+	4.96177i	−1.35506	+	0.440286i	−0.460669	+	0.887572i	$0.652390\pi$
$128$	−5.16229	+	7.10528i	−0.456286	+	0.628024i
$129$	13.5600	−	9.85195i	1.19390	−	0.867416i
$130$	3.12236	−	0.793557i	0.273849	−	0.0695996i
$131$	18.0296			1.57525			0.787625	−	0.616154i	$-0.211310\pi$
$131$	18.0296			1.57525			0.787625	+	0.616154i	$0.211310\pi$
$132$	−6.38271	+	4.68360i	−0.555543	+	0.407655i
$133$		−	1.35405i		−	0.117411i
$134$	−1.68464	+	5.18480i	−0.145531	+	0.447899i
$135$	−4.22876	+	10.6048i	−0.363954	+	0.912718i
$136$	15.4222	+	11.2049i	1.32244	+	0.960811i
$137$	−3.83473	+	1.24598i	−0.327623	+	0.106451i	−0.468210	−	0.883617i	$-0.655101\pi$
$137$	−3.83473	+	1.24598i	−0.327623	+	0.106451i	0.140587	+	0.990068i	$0.455101\pi$
$138$	−2.00390	+	0.651108i	−0.170584	+	0.0554260i
$139$	6.41949	+	4.66403i	0.544494	+	0.395598i	0.825751	−	0.564035i	$-0.190752\pi$
$139$	6.41949	+	4.66403i	0.544494	+	0.395598i	−0.281258	+	0.959632i	$0.590752\pi$
$140$	0.664820	−	1.66723i	0.0561875	−	0.140906i
$141$	1.05101	−	3.23468i	0.0885111	−	0.272409i
$142$			9.46663i			0.794422i
$143$	−1.86633	−	5.65285i	−0.156071	−	0.472715i
$144$	−0.0550368			−0.00458640
$145$	7.74870	−	1.96935i	0.643495	−	0.163546i
$146$	−4.43068	+	3.21907i	−0.366685	+	0.266412i
$147$	6.88173	−	9.47189i	0.567596	−	0.781228i
$148$	9.46031	−	3.07384i	0.777633	−	0.252668i
$149$	−3.86298	−	11.8890i	−0.316468	−	0.973988i	−0.975146	−	0.221563i	$-0.928884\pi$
$149$	−3.86298	−	11.8890i	−0.316468	−	0.973988i	0.658678	−	0.752425i	$-0.271116\pi$
$150$	6.20919	−	3.37411i	0.506978	−	0.275495i
$151$	−6.79775	+	4.93885i	−0.553193	+	0.401918i	−0.828961	−	0.559306i	$-0.811068\pi$
$151$	−6.79775	+	4.93885i	−0.553193	+	0.401918i	0.275768	+	0.961224i	$0.411068\pi$
$152$	−5.85835	−	1.90349i	−0.475175	−	0.154394i
$153$			0.709215i			0.0573367i
$154$	1.50146	+	0.480014i	0.120991	+	0.0386807i
$155$	−7.36076	−	11.6616i	−0.591231	−	0.936683i
$156$	1.32395	−	4.07470i	0.106001	−	0.326237i
$157$	−8.22657	−	11.3229i	−0.656552	−	0.903666i	0.342809	−	0.939405i	$-0.388621\pi$
$157$	−8.22657	−	11.3229i	−0.656552	−	0.903666i	−0.999361	+	0.0357391i	$0.988621\pi$
$158$	2.13546	−	2.93921i	0.169888	−	0.233831i
$159$	−1.29654	−	3.99034i	−0.102822	−	0.316454i
$160$	−10.0209	−	8.33135i	−0.792222	−	0.658651i
$161$	−0.714130	−	0.518846i	−0.0562813	−	0.0408908i
$162$	−4.38344	−	6.03329i	−0.344395	−	0.474020i
$163$	−11.2619	−	3.65922i	−0.882101	−	0.286612i	−0.167272	−	0.985911i	$-0.553496\pi$
$163$	−11.2619	−	3.65922i	−0.882101	−	0.286612i	−0.714830	+	0.699299i	$0.753496\pi$
$164$	11.4015			0.890307
$165$	−7.02202	−	11.0092i	−0.546664	−	0.857066i
$166$	4.77014			0.370235
$167$	8.29919	+	2.69657i	0.642210	+	0.208667i	0.611976	−	0.790876i	$-0.290375\pi$
$167$	8.29919	+	2.69657i	0.642210	+	0.208667i	0.0302340	+	0.999543i	$0.490375\pi$
$168$	1.65061	+	2.27187i	0.127347	+	0.175278i
$169$	−7.91087	−	5.74758i	−0.608528	−	0.442122i
$170$	−8.12087	+	9.76773i	−0.622842	+	0.749151i
$171$	−0.0708175	−	0.217954i	−0.00541555	−	0.0166673i
$172$	7.58546	−	10.4405i	0.578386	−	0.796080i
$173$	−5.39505	−	7.42565i	−0.410178	−	0.564562i	0.553084	−	0.833126i	$-0.313451\pi$
$173$	−5.39505	−	7.42565i	−0.410178	−	0.564562i	−0.963262	+	0.268564i	$0.913451\pi$
$174$	−1.56159	+	4.80608i	−0.118384	+	0.364348i
$175$	2.67256	+	1.27361i	0.202027	+	0.0962755i
$176$	−1.06366	+	1.47867i	−0.0801767	+	0.111459i
$177$			0.0673973i			0.00506589i
$178$	−4.74365	−	1.54130i	−0.355552	−	0.115526i
$179$	1.17159	−	0.851209i	0.0875687	−	0.0636224i	−0.543139	−	0.839642i	$-0.682765\pi$
$179$	1.17159	−	0.851209i	0.0875687	−	0.0636224i	0.630708	+	0.776020i	$0.282765\pi$
$180$	0.0198156	−	0.303135i	0.00147697	−	0.0225944i
$181$	0.245206	+	0.754665i	0.0182260	+	0.0560938i	0.959756	−	0.280836i	$-0.0906116\pi$
$181$	0.245206	+	0.754665i	0.0182260	+	0.0560938i	−0.941530	+	0.336930i	$0.890612\pi$
$182$	−0.811324	+	0.263615i	−0.0601393	+	0.0195404i
$183$	−3.56182	+	4.90243i	−0.263298	+	0.362398i
$184$	−3.24872	+	2.36033i	−0.239499	+	0.174006i
$185$	4.04140	+	15.9015i	0.297129	+	1.16910i
$186$	8.71644			0.639120
$187$	19.0544	+	13.7066i	1.39340	+	1.00233i
$188$		−	2.61869i		−	0.190988i
$189$	0.934204	−	2.87518i	0.0679533	−	0.209139i
$190$	1.52034	−	3.81268i	0.110297	−	0.276601i
$191$	6.59373	+	4.79062i	0.477105	+	0.346637i	0.800204	−	0.599728i	$-0.204725\pi$
$191$	6.59373	+	4.79062i	0.477105	+	0.346637i	−0.323099	+	0.946365i	$0.604725\pi$
$192$	5.99454	−	1.94774i	0.432618	−	0.140566i
$193$	−4.15456	+	1.34990i	−0.299052	+	0.0971678i	−0.454700	−	0.890645i	$-0.650253\pi$
$193$	−4.15456	+	1.34990i	−0.299052	+	0.0971678i	0.155648	+	0.987813i	$0.450253\pi$
$194$	−3.49097	−	2.53634i	−0.250637	−	0.182098i
$195$	6.56410	+	2.61749i	0.470065	+	0.187442i
$196$	2.78561	−	8.57324i	0.198972	−	0.612374i
$197$			15.6525i			1.11520i	0.830111	+	0.557599i	$0.188277\pi$
$197$			15.6525i			1.11520i	−0.830111	+	0.557599i	$0.811723\pi$
$198$	0.266788	−	0.00126211i	0.0189598	−	8.96940e-5i
$199$	−1.43830			−0.101959			−0.0509793	−	0.998700i	$-0.516234\pi$
$199$	−1.43830			−0.101959			−0.0509793	+	0.998700i	$0.516234\pi$
$200$	9.26735	−	9.77255i	0.655301	−	0.691024i
$201$	−9.67446	+	7.02890i	−0.682383	+	0.495781i
$202$	4.68573	−	6.44936i	0.329687	−	0.453775i
$203$	−2.01344	+	0.654208i	−0.141316	+	0.0459164i
$204$	5.22023	+	16.0662i	0.365489	+	1.12486i
$205$	−1.22669	+	18.7657i	−0.0856761	+	1.31066i
$206$	−8.78074	+	6.37958i	−0.611783	+	0.444486i
$207$	−0.142086	−	0.0461665i	−0.00987564	−	0.00320879i
$208$		−	0.985756i		−	0.0683499i
$209$	−7.22439	−	2.30962i	−0.499721	−	0.159760i
$210$	−1.58239	+	0.998799i	−0.109195	+	0.0689237i
$211$	2.68267	−	8.25641i	0.184683	−	0.568395i	−0.815260	−	0.579095i	$-0.803406\pi$
$211$	2.68267	−	8.25641i	0.184683	−	0.568395i	0.999943	+	0.0107002i	$0.00340605\pi$
$212$	−1.89881	−	2.61349i	−0.130411	−	0.179495i
$213$	−12.2055	+	16.7995i	−0.836310	+	1.15108i
$214$	1.39016	+	4.27846i	0.0950292	+	0.292470i
$215$	16.3679	+	13.6082i	1.11628	+	0.928072i
$216$	−11.1263	−	8.08375i	−0.757051	−	0.550030i
$217$	2.14638	+	2.95424i	0.145706	+	0.200547i
$218$	14.1995	+	4.61371i	0.961715	+	0.312480i
$219$	−12.0131			−0.811770
$220$	−7.76133	−	6.39090i	−0.523269	−	0.430874i
$221$	−12.7026			−0.854472
$222$	−9.86276	−	3.20461i	−0.661945	−	0.215079i
$223$	−3.70660	−	5.10169i	−0.248212	−	0.341635i	0.666672	−	0.745351i	$-0.267718\pi$
$223$	−3.70660	−	5.10169i	−0.248212	−	0.341635i	−0.914884	+	0.403717i	$0.867718\pi$
$224$	2.79175	+	2.02833i	0.186532	+	0.135523i
$225$	0.496798	+	0.0652290i	0.0331199	+	0.00434860i
$226$	−2.92731	−	9.00932i	−0.194721	−	0.599291i
$227$	−0.656444	+	0.903517i	−0.0435697	+	0.0599686i	−0.830246	−	0.557397i	$-0.811800\pi$
$227$	−0.656444	+	0.903517i	−0.0435697	+	0.0599686i	0.786676	+	0.617366i	$0.211800\pi$
$228$	−3.20853	−	4.41616i	−0.212490	−	0.292467i
$229$	1.29669	−	3.99079i	0.0856874	−	0.263719i	−0.899028	−	0.437892i	$-0.855725\pi$
$229$	1.29669	−	3.99079i	0.0856874	−	0.263719i	0.984715	+	0.174173i	$0.0557253\pi$
$230$	−1.42826	−	2.26278i	−0.0941767	−	0.149204i
$231$	2.04561	+	2.78771i	0.134591	+	0.183418i
$232$			9.63094i			0.632302i
$233$	6.44766	+	2.09497i	0.422400	+	0.137246i	0.512501	−	0.858686i	$-0.328719\pi$
$233$	6.44766	+	2.09497i	0.422400	+	0.137246i	−0.0901010	+	0.995933i	$0.528719\pi$
$234$	−0.116807	+	0.0848655i	−0.00763593	+	0.00554783i
$235$	4.31011	+	0.281747i	0.281161	+	0.0183791i
$236$	0.0160356	+	0.0493524i	0.00104383	+	0.00321257i
$237$	7.57917	−	2.46262i	0.492320	−	0.159965i
$238$	1.97708	−	2.72122i	0.128155	−	0.176391i
$239$	3.55812	−	2.58513i	0.230156	−	0.167218i	−0.466731	−	0.884400i	$-0.654568\pi$
$239$	3.55812	−	2.58513i	0.230156	−	0.167218i	0.696886	+	0.717182i	$0.254568\pi$
$240$	−0.532617	−	2.09566i	−0.0343803	−	0.135274i
$241$	−9.61218			−0.619175			−0.309587	−	0.950871i	$-0.600191\pi$
$241$	−9.61218			−0.619175			−0.309587	+	0.950871i	$0.600191\pi$
$242$	5.12214	−	7.19215i	0.329264	−	0.462329i
$243$		−	1.04101i		−	0.0667807i
$244$	−1.44177	+	4.43731i	−0.0922998	+	0.284070i
$245$	13.8110	+	5.50725i	0.882352	+	0.351845i
$246$	−9.61640	−	6.98672i	−0.613119	−	0.445457i
$247$	3.90373	−	1.26840i	0.248389	−	0.0807064i
$248$	15.7990	−	5.13340i	1.00324	−	0.325971i
$249$	8.46509	+	6.15025i	0.536453	+	0.389756i
$250$	6.09530	+	6.58696i	0.385501	+	0.416596i
$251$	4.14719	−	12.7637i	0.261768	−	0.805640i	−0.730652	−	0.682750i	$-0.760784\pi$
$251$	4.14719	−	12.7637i	0.261768	−	0.805640i	0.992420	−	0.122890i	$-0.0392163\pi$
$252$			0.0804405i			0.00506727i
$253$	−3.98636	+	2.92517i	−0.250620	+	0.183904i
$254$	12.8886			0.808704
$255$	−27.0051	+	6.86341i	−1.69112	+	0.429803i
$256$	11.4956	−	8.35202i	0.718473	−	0.522001i
$257$	−6.35829	+	8.75143i	−0.396619	+	0.545899i	−0.959891	−	0.280372i	$-0.909542\pi$
$257$	−6.35829	+	8.75143i	−0.396619	+	0.545899i	0.563272	+	0.826271i	$0.309542\pi$
$258$	−12.7957	+	4.15756i	−0.796623	+	0.258838i
$259$	−1.34253	−	4.13188i	−0.0834207	−	0.256742i
$260$	5.42940	+	0.354914i	0.336717	+	0.0220108i
$261$	−0.289878	+	0.210609i	−0.0179430	+	0.0130364i
$262$	−13.7640	−	4.47219i	−0.850342	−	0.276293i
$263$		−	24.6351i		−	1.51906i	−0.650471	−	0.759531i	$-0.725428\pi$
$263$		−	24.6351i		−	1.51906i	0.650471	−	0.759531i	$-0.274572\pi$
$264$	14.9368	−	4.93151i	0.919297	−	0.303513i
$265$	4.50584	−	2.84407i	0.276791	−	0.174710i
$266$	−0.335868	+	1.03370i	−0.0205934	+	0.0633799i
$267$	−6.43084	−	8.85130i	−0.393561	−	0.541691i
$268$	−5.41187	+	7.44880i	−0.330582	+	0.455008i
$269$	1.48359	+	4.56603i	0.0904563	+	0.278396i	0.986043	−	0.166491i	$-0.0532438\pi$
$269$	1.48359	+	4.56603i	0.0904563	+	0.278396i	−0.895587	+	0.444887i	$0.853244\pi$
$270$	5.85879	−	7.04692i	0.356555	−	0.428862i
$271$	−18.8746	−	13.7132i	−1.14655	−	0.833019i	−0.158534	−	0.987353i	$-0.550677\pi$
$271$	−18.8746	−	13.7132i	−1.14655	−	0.833019i	−0.988019	+	0.154334i	$0.950677\pi$
$272$	2.28458	+	3.14446i	0.138523	+	0.190661i
$273$	−1.77966	−	0.578247i	−0.107710	−	0.0349971i
$274$	3.23654			0.195527
$275$	11.3538	−	12.0868i	0.684662	−	0.728861i
$276$	−3.55855			−0.214200
$277$	−20.8256	−	6.76663i	−1.25129	−	0.406568i	−0.392905	−	0.919579i	$-0.628530\pi$
$277$	−20.8256	−	6.76663i	−1.25129	−	0.406568i	−0.858382	+	0.513012i	$0.828530\pi$
$278$	−3.74381	−	5.15291i	−0.224539	−	0.309051i
$279$	0.500000	+	0.363271i	0.0299342	+	0.0217485i
$280$	−2.27994	+	2.74230i	−0.136252	+	0.163884i
$281$	4.87488	+	15.0033i	0.290811	+	0.895024i	0.984596	+	0.174842i	$0.0559416\pi$
$281$	4.87488	+	15.0033i	0.290811	+	0.895024i	−0.693785	+	0.720182i	$0.744058\pi$
$282$	−1.60471	+	2.20869i	−0.0955590	+	0.131526i
$283$	13.2893	+	18.2912i	0.789968	+	1.08730i	0.994112	+	0.108356i	$0.0345588\pi$
$283$	13.2893	+	18.2912i	0.789968	+	1.08730i	−0.204144	+	0.978941i	$0.565441\pi$
$284$	−4.94061	+	15.2056i	−0.293171	+	0.902288i
$285$	7.61377	−	4.80578i	0.451001	−	0.284670i
$286$	0.0226054	+	4.77839i	0.00133668	+	0.282552i
$287$		−	4.97971i		−	0.293943i
$288$	0.555457	+	0.180479i	0.0327306	+	0.0106348i
$289$	26.7668	−	19.4472i	1.57452	−	1.14395i
$290$	−6.40395	−	0.418619i	−0.376053	−	0.0245821i
$291$	−2.92492	−	9.00198i	−0.171462	−	0.527705i
$292$	−8.79673	+	2.85823i	−0.514790	+	0.167265i
$293$	7.79380	−	10.7272i	0.455319	−	0.626693i	−0.518211	−	0.855253i	$-0.673402\pi$
$293$	7.79380	−	10.7272i	0.455319	−	0.626693i	0.973530	+	0.228560i	$0.0734018\pi$
$294$	−7.60308	+	5.52396i	−0.443421	+	0.322164i
$295$	−0.0829544	+	0.0210831i	−0.00482979	+	0.00122751i
$296$	−19.7641			−1.14876
$297$	−13.7468	−	9.88860i	−0.797669	−	0.573795i
$298$			10.0344i			0.581280i
$299$	0.826880	−	2.54487i	0.0478197	−	0.147174i
$300$	11.7344	−	2.17905i	0.677483	−	0.125808i
$301$	−4.55998	−	3.31302i	−0.262833	−	0.190959i
$302$	6.41455	−	2.08421i	0.369116	−	0.119933i
$303$	16.6306	−	5.40361i	0.955404	−	0.310429i
$304$	−1.01607	−	0.738221i	−0.0582758	−	0.0423399i
$305$	−7.14825	−	2.85042i	−0.409308	−	0.163215i
$306$	0.175919	−	0.541424i	0.0100566	−	0.0309511i
$307$			10.0161i			0.571650i	0.958282	+	0.285825i	$0.0922676\pi$
$307$			10.0161i			0.571650i	−0.958282	+	0.285825i	$0.907732\pi$
$308$	2.16119	+	1.55463i	0.123145	+	0.0885830i
$309$	−23.8076			−1.35437
$310$	2.72666	+	10.7284i	0.154864	+	0.609334i
$311$	2.75734	−	2.00332i	0.156354	−	0.113598i	−0.506857	−	0.862030i	$-0.669193\pi$
$311$	2.75734	−	2.00332i	0.156354	−	0.113598i	0.663212	+	0.748432i	$0.269193\pi$
$312$	−5.00362	+	6.88690i	−0.283274	+	0.389894i
$313$	23.3017	−	7.57117i	1.31709	−	0.427948i	0.435594	−	0.900143i	$-0.356538\pi$
$313$	23.3017	−	7.57117i	1.31709	−	0.427948i	0.881494	+	0.472196i	$0.156538\pi$
$314$	3.47164	+	10.6846i	0.195916	+	0.602968i
$315$	−0.132397	−	0.00865464i	−0.00745973	−	0.000487634i
$316$	4.96401	−	3.60657i	0.279247	−	0.202885i
$317$	6.64646	+	2.15957i	0.373303	+	0.121293i	0.489659	−	0.871914i	$-0.337121\pi$
$317$	6.64646	+	2.15957i	0.373303	+	0.121293i	−0.116356	+	0.993208i	$0.537121\pi$
$318$			3.36787i			0.188861i
$319$	0.0560993	+	11.8584i	0.00314096	+	0.663945i
$320$	4.27254	+	6.76895i	0.238842	+	0.378396i
$321$	−3.04935	+	9.38493i	−0.170198	+	0.523816i
$322$	0.416477	+	0.573232i	0.0232094	+	0.0319449i
$323$	−9.51286	+	13.0933i	−0.529310	+	0.728532i
$324$	−3.89208	−	11.9786i	−0.216226	−	0.665476i
$325$	−1.16831	+	8.89808i	−0.0648060	+	0.493577i
$326$	7.68982	+	5.58698i	0.425900	+	0.309434i
$327$	19.2500	+	26.4953i	1.06453	+	1.46519i
$328$	−21.5449	−	7.00037i	−1.18962	−	0.386531i
$329$	−1.14374			−0.0630563
$330$	2.62989	+	10.1464i	0.144771	+	0.558539i
$331$	5.64321			0.310179			0.155089	−	0.987900i	$-0.450433\pi$
$331$	5.64321			0.310179			0.155089	+	0.987900i	$0.450433\pi$
$332$	7.66196	+	2.48952i	0.420505	+	0.136630i
$333$	−0.432200	−	0.594872i	−0.0236844	−	0.0325988i
$334$	−5.66682	−	4.11719i	−0.310075	−	0.225282i
$335$	−11.6777	−	9.70882i	−0.638022	−	0.530450i
$336$	0.176932	+	0.544542i	0.00965245	+	0.0297072i
$337$	13.2936	−	18.2970i	0.724146	−	0.996702i	−0.275230	−	0.961379i	$-0.588754\pi$
$337$	13.2936	−	18.2970i	0.724146	−	0.996702i	0.999376	−	0.0353234i	$-0.0112461\pi$
$338$	4.61358	+	6.35005i	0.250946	+	0.345397i
$339$	6.42112	−	19.7622i	0.348748	−	1.07333i
$340$	−18.1418	+	11.4510i	−0.983876	+	0.621018i
$341$	19.4232	−	6.41272i	1.05182	−	0.347268i
$342$			0.183955i			0.00994713i
$343$	−7.68631	−	2.49743i	−0.415022	−	0.134849i
$344$	−20.7443	+	15.0716i	−1.11846	+	0.812605i
$345$	0.382867	−	5.85703i	0.0206129	−	0.315332i
$346$	2.27673	+	7.00706i	0.122398	+	0.376702i
$347$	0.173468	−	0.0563630i	0.00931223	−	0.00302573i	−0.304357	−	0.952558i	$-0.598442\pi$
$347$	0.173468	−	0.0563630i	0.00931223	−	0.00302573i	0.313669	+	0.949532i	$0.398442\pi$
$348$	−5.01656	+	6.90470i	−0.268916	+	0.370131i
$349$	−12.4809	+	9.06792i	−0.668089	+	0.485395i	−0.869385	−	0.494136i	$-0.835485\pi$
$349$	−12.4809	+	9.06792i	−0.668089	+	0.485395i	0.201296	+	0.979530i	$0.435485\pi$
$350$	−1.72435	−	1.63521i	−0.0921704	−	0.0874056i
$351$	9.16431			0.489155
$352$	15.5839	−	11.4354i	0.830625	−	0.609508i
$353$			23.9103i			1.27262i	0.771435	+	0.636308i	$0.219539\pi$
$353$			23.9103i			1.27262i	−0.771435	+	0.636308i	$0.780461\pi$
$354$	0.0167177	−	0.0514519i	0.000888537	−	0.00273464i
$355$	−24.4954	−	9.76774i	−1.30008	−	0.518418i
$356$	−6.81501	−	4.95139i	−0.361195	−	0.262423i
$357$	7.01707	−	2.27998i	0.371383	−	0.120670i
$358$	−1.10555	+	0.359214i	−0.0584299	+	0.0189850i
$359$	−7.09293	−	5.15332i	−0.374351	−	0.271982i	0.384662	−	0.923057i	$-0.374318\pi$
$359$	−7.09293	−	5.15332i	−0.374351	−	0.271982i	−0.759013	+	0.651076i	$0.774318\pi$
$360$	−0.223566	+	0.560656i	−0.0117830	+	0.0295491i
$361$	−4.25527	+	13.0964i	−0.223962	+	0.689283i
$362$		−	0.636943i		−	0.0334770i
$363$	18.3628	−	6.15910i	0.963795	−	0.323269i
$364$	−1.44076			−0.0755161
$365$	−3.75792	−	14.7861i	−0.196698	−	0.773938i
$366$	3.93518	−	2.85907i	0.205695	−	0.149446i
$367$	3.16365	−	4.35439i	0.165141	−	0.227297i	−0.718424	−	0.695605i	$-0.755136\pi$
$367$	3.16365	−	4.35439i	0.165141	−	0.227297i	0.883565	+	0.468308i	$0.155136\pi$
$368$	−0.778682	+	0.253009i	−0.0405916	+	0.0131890i
$369$	−0.260442	−	0.801557i	−0.0135581	−	0.0417274i
$370$	0.859066	−	13.1418i	0.0446607	−	0.683211i
$371$	−1.14146	+	0.829322i	−0.0592619	+	0.0430563i
$372$	14.0006	+	4.54908i	0.725899	+	0.235859i
$373$			3.22450i			0.166958i	0.996510	+	0.0834792i	$0.0266032\pi$
$373$			3.22450i			0.166958i	−0.996510	+	0.0834792i	$0.973397\pi$
$374$	−11.1465	−	15.1902i	−0.576371	−	0.785465i
$375$	2.32400	+	19.5480i	0.120011	+	1.00946i
$376$	−1.60784	+	4.94844i	−0.0829183	+	0.255196i
$377$	−3.77218	−	5.19196i	−0.194277	−	0.267400i
$378$	−1.42637	+	1.96322i	−0.0733643	+	0.100977i
$379$	6.07632	+	18.7010i	0.312119	+	0.960605i	0.976924	+	0.213588i	$0.0685149\pi$
$379$	6.07632	+	18.7010i	0.312119	+	0.960605i	−0.664804	+	0.747017i	$0.731485\pi$
$380$	4.43185	−	5.33060i	0.227349	−	0.273454i
$381$	22.8722	+	16.6176i	1.17178	+	0.851345i
$382$	−3.84543	−	5.29278i	−0.196749	−	0.270802i
$383$	−26.6059	−	8.64478i	−1.35950	−	0.441728i	−0.463623	−	0.886033i	$-0.653451\pi$
$383$	−26.6059	−	8.64478i	−1.35950	−	0.441728i	−0.895876	+	0.444305i	$0.853451\pi$
$384$	15.4639			0.789139
$385$	−2.79128	+	3.38983i	−0.142257	+	0.172762i
$386$	3.50648			0.178475
$387$	−0.907269	−	0.294789i	−0.0461191	−	0.0149850i
$388$	−4.28361	−	5.89588i	−0.217467	−	0.299318i
$389$	10.5496	+	7.66472i	0.534885	+	0.388617i	0.822182	−	0.569225i	$-0.192757\pi$
$389$	10.5496	+	7.66472i	0.534885	+	0.388617i	−0.287297	+	0.957842i	$0.592757\pi$
$390$	−4.36185	−	3.62643i	−0.220871	−	0.183632i
$391$	3.26033	+	10.0343i	0.164882	+	0.507454i
$392$	−10.5277	+	14.4902i	−0.531730	+	0.731864i
$393$	−18.6595	−	25.6826i	−0.941247	−	1.29552i
$394$	3.88258	−	11.9493i	0.195601	−	0.601999i
$395$	5.40197	+	8.55830i	0.271803	+	0.430615i
$396$	0.429183	+	0.137209i	0.0215672	+	0.00689499i
$397$		−	1.82243i		−	0.0914651i	−0.998954	−	0.0457325i	$-0.985438\pi$
$397$		−	1.82243i		−	0.0914651i	0.998954	−	0.0457325i	$-0.0145622\pi$
$398$	1.09802	+	0.356768i	0.0550387	+	0.0178831i
$399$	−1.92880	+	1.40135i	−0.0965607	+	0.0701555i
$400$	2.41278	−	1.31112i	0.120639	−	0.0655560i
$401$	1.66277	+	5.11749i	0.0830349	+	0.255555i	0.983951	−	0.178438i	$-0.0571043\pi$
$401$	1.66277	+	5.11749i	0.0830349	+	0.255555i	−0.900916	+	0.433993i	$0.857104\pi$
$402$	9.12910	−	2.96622i	0.455318	−	0.147942i
$403$	−6.50649	+	8.95542i	−0.324111	+	0.446101i
$404$	10.8923	−	7.91371i	0.541912	−	0.393722i
$405$	20.1343	−	5.11719i	1.00048	−	0.254275i
$406$	1.69936			0.0843379
$407$	−24.3352	+	0.115124i	−1.20625	+	0.00570647i
$408$		−	33.5648i		−	1.66171i
$409$	11.3354	−	34.8867i	0.560499	−	1.72504i	−0.120462	−	0.992718i	$-0.538438\pi$
$409$	11.3354	−	34.8867i	0.560499	−	1.72504i	0.680961	−	0.732320i	$-0.261562\pi$
$410$	5.59127	−	14.0217i	0.276133	−	0.692483i
$411$	5.74357	+	4.17295i	0.283309	+	0.205836i
$412$	−17.4334	+	5.66446i	−0.858883	+	0.279068i
$413$	0.0215551	−	0.00700368i	0.00106066	−	0.000344629i
$414$	0.0970185	+	0.0704881i	0.00476820	+	0.00346430i
$415$	−4.92186	+	12.3430i	−0.241605	+	0.605893i
$416$	−3.23253	+	9.94870i	−0.158488	+	0.487775i
$417$		−	13.9713i		−	0.684180i
$418$	4.94229	+	3.55518i	0.241735	+	0.173890i
$419$	−2.86630			−0.140028			−0.0700141	−	0.997546i	$-0.522304\pi$
$419$	−2.86630			−0.140028			−0.0700141	+	0.997546i	$0.522304\pi$
$420$	−3.06296	+	0.778460i	−0.149457	+	0.0379850i
$421$	−3.76982	+	2.73893i	−0.183730	+	0.133487i	−0.675848	−	0.737041i	$-0.736223\pi$
$421$	−3.76982	+	2.73893i	−0.183730	+	0.133487i	0.492119	+	0.870528i	$0.336223\pi$
$422$	−4.09597	+	5.63761i	−0.199389	+	0.274435i
$423$	−0.184102	+	0.0598182i	−0.00895132	+	0.00290846i
$424$	1.98345	+	6.10445i	0.0963251	+	0.296458i
$425$	−16.8954	−	31.0916i	−0.819545	−	1.50816i
$426$	13.4849	−	9.79738i	0.653347	−	0.474685i
$427$	1.93804	+	0.629706i	0.0937881	+	0.0304736i
$428$			7.59774i			0.367250i
$429$	−6.12078	+	8.50889i	−0.295514	+	0.410813i
$430$	−9.11996	−	14.4487i	−0.439803	−	0.696778i
$431$	6.41801	−	19.7526i	0.309145	−	0.951450i	−0.668953	−	0.743304i	$-0.733257\pi$
$431$	6.41801	−	19.7526i	0.309145	−	0.951450i	0.978098	−	0.208145i	$-0.0667426\pi$
$432$	−1.64821	−	2.26856i	−0.0792995	−	0.109146i
$433$	7.52199	−	10.3531i	0.361484	−	0.497540i	−0.589078	−	0.808076i	$-0.700509\pi$
$433$	7.52199	−	10.3531i	0.361484	−	0.497540i	0.950561	+	0.310537i	$0.100509\pi$
$434$	−0.905781	−	2.78771i	−0.0434789	−	0.133814i
$435$	−10.8247	−	8.99964i	−0.519005	−	0.431500i
$436$	20.3999	+	14.8214i	0.976979	+	0.709817i
$437$	−2.00390	−	2.75814i	−0.0958598	−	0.131940i
$438$	9.17095	+	2.97982i	0.438205	+	0.142381i
$439$	10.6208			0.506905			0.253452	−	0.967348i	$-0.418434\pi$
$439$	10.6208			0.506905			0.253452	+	0.967348i	$0.418434\pi$
$440$	10.7423	+	16.8420i	0.512121	+	0.802910i
$441$	−0.666354			−0.0317312
$442$	9.69735	+	3.15086i	0.461256	+	0.149871i
$443$	3.87876	+	5.33865i	0.184285	+	0.253647i	0.891157	−	0.453695i	$-0.149894\pi$
$443$	3.87876	+	5.33865i	0.184285	+	0.253647i	−0.706872	+	0.707342i	$0.749894\pi$
$444$	−14.1694	−	10.2947i	−0.672452	−	0.488565i
$445$	8.88274	−	10.6841i	0.421082	−	0.506475i
$446$	1.56420	+	4.81411i	0.0740669	+	0.227955i
$447$	−12.9376	+	17.8071i	−0.611929	+	0.842248i
$448$	−1.24586	−	1.71478i	−0.0588614	−	0.0810158i
$449$	−4.21130	+	12.9610i	−0.198743	+	0.611670i	0.801169	+	0.598438i	$0.204212\pi$
$449$	−4.21130	+	12.9610i	−0.198743	+	0.611670i	−0.999912	+	0.0132314i	$0.995788\pi$
$450$	−0.363082	−	0.173026i	−0.0171159	−	0.00815654i
$451$	−26.5688	−	8.49397i	−1.25107	−	0.399965i
$452$		−	15.9988i		−	0.752522i
$453$	14.0705	+	4.57178i	0.661090	+	0.214801i
$454$	0.725253	−	0.526927i	0.0340378	−	0.0247299i
$455$	0.155012	−	2.37134i	0.00726707	−	0.111170i
$456$	3.35156	+	10.3150i	0.156951	+	0.483046i
$457$	12.8392	−	4.17169i	0.600590	−	0.195144i	0.00708664	−	0.999975i	$-0.497744\pi$
$457$	12.8392	−	4.17169i	0.600590	−	0.195144i	0.593504	+	0.804831i	$0.297744\pi$
$458$	−1.97981	+	2.72498i	−0.0925105	+	0.127330i
$459$	−29.2332	+	21.2391i	−1.36449	+	0.991358i
$460$	−1.11318	−	4.37997i	−0.0519023	−	0.204217i
$461$	11.3217			0.527303			0.263652	−	0.964618i	$-0.415073\pi$
$461$	11.3217			0.527303			0.263652	+	0.964618i	$0.415073\pi$
$462$	−0.870156	−	2.63558i	−0.0404833	−	0.122618i
$463$			4.82990i			0.224464i	0.993682	+	0.112232i	$0.0358001\pi$
$463$			4.82990i			0.224464i	−0.993682	+	0.112232i	$0.964200\pi$
$464$	−0.606806	+	1.86756i	−0.0281703	+	0.0866992i
$465$	−8.99368	+	22.5542i	−0.417072	+	1.04593i
$466$	−4.40257	−	3.19865i	−0.203945	−	0.148175i
$467$	−22.8418	+	7.42175i	−1.05699	+	0.343437i	−0.785409	−	0.618978i	$-0.787547\pi$
$467$	−22.8418	+	7.42175i	−1.05699	+	0.343437i	−0.271583	+	0.962415i	$0.587547\pi$
$468$	−0.231911	+	0.0753524i	−0.0107201	+	0.00348317i
$469$	3.25333	+	2.36368i	0.150225	+	0.109145i
$470$	−3.22050	−	1.28420i	−0.148551	−	0.0592358i
$471$	−7.61514	+	23.4370i	−0.350887	+	1.07992i
$472$		−	0.103105i		−	0.00474579i
$473$	−25.4543	+	18.6783i	−1.17039	+	0.858828i
$474$	−6.39688			−0.293818
$475$	8.29682	+	7.86791i	0.380684	+	0.361004i
$476$	4.59586	−	3.33909i	0.210651	−	0.153047i
$477$	−0.140361	+	0.193191i	−0.00642671	+	0.00884561i
$478$	−3.35755	+	1.09093i	−0.153571	+	0.0498981i
$479$	−13.3573	−	41.1095i	−0.610309	−	1.87834i	−0.455052	−	0.890465i	$-0.650379\pi$
$479$	−13.3573	−	41.1095i	−0.610309	−	1.87834i	−0.155258	−	0.987874i	$-0.549621\pi$
$480$	−1.49675	+	22.8969i	−0.0683168	+	1.04510i
$481$	10.6546	−	7.74106i	0.485810	−	0.352962i
$482$	7.33805	+	2.38428i	0.334239	+	0.108601i
$483$			1.55423i			0.0707199i
$484$	11.9809	−	8.87905i	0.544588	−	0.403593i
$485$	10.1649	−	6.41606i	0.461565	−	0.291338i
$486$	−0.258219	+	0.794718i	−0.0117131	+	0.0360491i
$487$	24.6640	+	33.9471i	1.11763	+	1.53829i	0.809666	+	0.586891i	$0.199648\pi$
$487$	24.6640	+	33.9471i	1.11763	+	1.53829i	0.307966	+	0.951397i	$0.400352\pi$
$488$	5.44890	−	7.49977i	0.246660	−	0.339499i
$489$	6.44294	+	19.8293i	0.291360	+	0.896713i
$490$	−9.17743	−	7.63009i	−0.414594	−	0.344692i
$491$	7.32956	+	5.32524i	0.330778	+	0.240325i	0.740761	−	0.671769i	$-0.234465\pi$
$491$	7.32956	+	5.32524i	0.330778	+	0.240325i	−0.409982	+	0.912093i	$0.634465\pi$
$492$	−11.7998	−	16.2411i	−0.531978	−	0.732205i
$493$	24.0657	+	7.81942i	1.08386	+	0.352169i
$494$	−3.29478			−0.148239
$495$	−0.272008	+	0.691630i	−0.0122258	+	0.0310864i
$496$	3.38705			0.152083
$497$	6.64120	+	2.15786i	0.297898	+	0.0967931i
$498$	−4.93680	−	6.79492i	−0.221223	−	0.304488i
$499$	24.4965	+	17.7977i	1.09661	+	0.796736i	0.980504	−	0.196501i	$-0.0629578\pi$
$499$	24.4965	+	17.7977i	1.09661	+	0.796736i	0.116109	+	0.993236i	$0.462958\pi$
$500$	6.35276	+	13.7613i	0.284104	+	0.615425i
$501$	−4.74796	−	14.6127i	−0.212123	−	0.652849i
$502$	−6.33203	+	8.71530i	−0.282612	+	0.388983i
$503$	10.6177	+	14.6139i	0.473418	+	0.651604i	0.977223	−	0.212213i	$-0.0680672\pi$
$503$	10.6177	+	14.6139i	0.473418	+	0.651604i	−0.503806	+	0.863817i	$0.668067\pi$
$504$	0.0493894	−	0.152005i	0.00219998	−	0.00677084i
$505$	11.8533	+	18.7791i	0.527464	+	0.835658i
$506$	3.76881	−	1.24430i	0.167544	−	0.0553161i
$507$			17.2172i			0.764642i
$508$	20.7022	+	6.72654i	0.918510	+	0.298442i
$509$	−20.1572	+	14.6451i	−0.893453	+	0.649132i	−0.936776	−	0.349929i	$-0.886206\pi$
$509$	−20.1572	+	14.6451i	−0.893453	+	0.649132i	0.0433229	+	0.999061i	$0.486206\pi$
$510$	22.3184	+	1.45893i	0.988277	+	0.0646026i
$511$	1.24836	+	3.84205i	0.0552241	+	0.169962i
$512$	5.85796	−	1.90337i	0.258888	−	0.0841177i
$513$	6.86304	−	9.44617i	0.303011	−	0.417058i
$514$	7.02477	−	5.10379i	0.309849	−	0.225119i
$515$	−7.44747	−	29.3031i	−0.328175	−	1.29125i
$516$	−22.7226			−1.00031
$517$	−1.95089	+	6.10231i	−0.0858002	+	0.268379i
$518$			3.48734i			0.153225i
$519$	−4.99407	+	15.3702i	−0.219216	+	0.674676i
$520$	−10.0418	−	4.00425i	−0.440363	−	0.175598i
$521$	−29.3537	−	21.3267i	−1.28601	−	0.934339i	−0.286291	−	0.958143i	$-0.592422\pi$
$521$	−29.3537	−	21.3267i	−1.28601	−	0.934339i	−0.999717	+	0.0238032i	$0.992422\pi$
$522$	0.273537	−	0.0888777i	0.0119724	−	0.00389007i
$523$	−23.4978	+	7.63489i	−1.02749	+	0.333850i	−0.773796	−	0.633435i	$-0.781644\pi$
$523$	−23.4978	+	7.63489i	−1.02749	+	0.333850i	−0.253690	+	0.967286i	$0.581644\pi$
$524$	−19.7742	−	14.3668i	−0.863839	−	0.627616i
$525$	−0.951722	−	5.12509i	−0.0415366	−	0.223677i
$526$	−6.11067	+	18.8067i	−0.266438	+	0.820011i
$527$		−	43.6462i		−	1.90126i
$528$	3.20715	−	0.0151722i	0.139573	−	0.000660285i
$529$	20.7775			0.903369
$530$	−4.14527	+	1.05353i	−0.180059	+	0.0457625i
$531$	0.00310332	−	0.00225469i	0.000134672	−	9.78453e-5i
$532$	−1.07897	+	1.48507i	−0.0467791	+	0.0643859i
$533$	14.3566	−	4.66473i	0.621852	−	0.202052i
$534$	2.71384	+	8.35234i	0.117439	+	0.361441i
$535$	−12.5051	−	0.817446i	−0.540644	−	0.0353413i
$536$	14.8001	−	10.7529i	0.639265	−	0.464453i
$537$	−2.42504	−	0.787945i	−0.104648	−	0.0340023i
$538$		−	3.85376i		−	0.166148i
$539$	−12.8782	+	17.9029i	−0.554705	+	0.771131i
$540$	13.0884	−	8.26132i	0.563233	−	0.355511i
$541$	−3.87568	+	11.9281i	−0.166628	+	0.512829i	−0.999153	−	0.0411593i	$-0.986895\pi$
$541$	−3.87568	+	11.9281i	−0.166628	+	0.512829i	0.832524	+	0.553989i	$0.186895\pi$
$542$	11.0076	+	15.1507i	0.472817	+	0.650776i
$543$	0.821226	−	1.13032i	0.0352422	−	0.0485067i
$544$	−12.7456	−	39.2270i	−0.546464	−	1.68184i
$545$	−26.5894	+	31.9816i	−1.13897	+	1.36994i
$546$	1.21518	+	0.882881i	0.0520050	+	0.0377838i
$547$	−18.0689	−	24.8698i	−0.772572	−	1.06335i	−0.996063	−	0.0886479i	$-0.971745\pi$
$547$	−18.0689	−	24.8698i	−0.772572	−	1.06335i	0.223491	−	0.974706i	$-0.428255\pi$
$548$	5.19865	+	1.68914i	0.222075	+	0.0721566i
$549$	0.344889			0.0147195
$550$	−11.6658	+	6.41091i	−0.497429	+	0.273362i
$551$	−8.17659			−0.348334
$552$	6.72445	+	2.18491i	0.286212	+	0.0929958i
$553$	−1.57520	−	2.16808i	−0.0669843	−	0.0921960i
$554$	14.2200	+	10.3315i	0.604151	+	0.438942i
$555$	18.4686	−	22.2139i	0.783946	−	0.942926i
$556$	−3.32415	−	10.2307i	−0.140975	−	0.433877i
$557$	7.89359	−	10.8646i	0.334462	−	0.460347i	−0.608352	−	0.793668i	$-0.708169\pi$
$557$	7.89359	−	10.8646i	0.334462	−	0.460347i	0.942814	+	0.333320i	$0.108169\pi$
$558$	−0.291597	−	0.401350i	−0.0123443	−	0.0169905i
$559$	5.27993	−	16.2499i	0.223317	−	0.687299i
$560$	−0.614889	+	0.388116i	−0.0259838	+	0.0164009i
$561$	−0.195512	−	41.3279i	−0.00825452	−	1.74487i
$562$		−	12.6629i		−	0.534154i
$563$	−29.0454	−	9.43741i	−1.22412	−	0.397740i	−0.375537	−	0.926807i	$-0.622542\pi$
$563$	−29.0454	−	9.43741i	−1.22412	−	0.397740i	−0.848580	+	0.529068i	$0.822542\pi$
$564$	−3.73025	+	2.71019i	−0.157072	+	0.114119i
$565$	26.3325	+	1.72133i	1.10782	+	0.0724167i
$566$	−5.60814	−	17.2601i	−0.235728	−	0.725495i
$567$	−5.23175	+	1.69990i	−0.219713	+	0.0713891i
$568$	18.6721	−	25.7000i	0.783465	−	1.07835i
$569$	20.8082	−	15.1181i	0.872327	−	0.633783i	−0.0588833	−	0.998265i	$-0.518754\pi$
$569$	20.8082	−	15.1181i	0.872327	−	0.633783i	0.931210	+	0.364482i	$0.118754\pi$
$570$	−7.00451	+	1.78021i	−0.293387	+	0.0745650i
$571$	−27.1115			−1.13458			−0.567291	−	0.823518i	$-0.692008\pi$
$571$	−27.1115			−1.13458			−0.567291	+	0.823518i	$0.692008\pi$
$572$	−2.45752	+	7.68702i	−0.102754	+	0.321410i
$573$		−	14.3506i		−	0.599504i
$574$	−1.23520	+	3.80157i	−0.0515564	+	0.158674i
$575$	7.32876	−	1.36094i	0.305630	−	0.0567552i
$576$	−0.290224	−	0.210860i	−0.0120927	−	0.00878583i
$577$	−2.72968	+	0.886926i	−0.113638	+	0.0369232i	−0.365284	−	0.930896i	$-0.619028\pi$
$577$	−2.72968	+	0.886926i	−0.113638	+	0.0369232i	0.251646	+	0.967819i	$0.419028\pi$
$578$	−25.2579	+	8.20680i	−1.05059	+	0.341358i
$579$	6.22260	+	4.52098i	0.258602	+	0.187886i
$580$	−10.0678	−	4.01460i	−0.418041	−	0.166697i
$581$	1.08732	−	3.34643i	0.0451097	−	0.138833i
$582$			7.59774i			0.314936i
$583$	2.47776	+	7.50476i	0.102618	+	0.310816i
$584$	18.3777			0.760476
$585$	−0.0990712	−	0.389810i	−0.00409609	−	0.0161166i
$586$	−8.61075	+	6.25608i	−0.355707	+	0.258436i
$587$	26.3539	−	36.2731i	1.08774	−	1.49715i	0.237042	−	0.971499i	$-0.423822\pi$
$587$	26.3539	−	36.2731i	1.08774	−	1.49715i	0.850701	−	0.525651i	$-0.176178\pi$
$588$	−15.0953	+	4.90475i	−0.622518	+	0.202268i
$589$	4.35822	+	13.4132i	0.179577	+	0.552682i
$590$	0.0685580	+	0.00448156i	0.00282249	+	0.000184503i
$591$	22.2966	−	16.1994i	0.917159	−	0.666355i
$592$	−3.83250	−	1.24525i	−0.157515	−	0.0511796i
$593$			6.09322i			0.250219i	0.992143	+	0.125109i	$0.0399282\pi$
$593$			6.09322i			0.250219i	−0.992143	+	0.125109i	$0.960072\pi$
$594$	8.04162	+	10.9589i	0.329952	+	0.449651i
$595$	5.00133	+	7.92358i	0.205035	+	0.324835i
$596$	−5.23695	+	16.1177i	−0.214514	+	0.660206i
$597$	1.48855	+	2.04882i	0.0609225	+	0.0838526i
$598$	−1.26250	+	1.73768i	−0.0516275	+	0.0710591i
$599$	3.99674	+	12.3007i	0.163302	+	0.502593i	0.998907	−	0.0467381i	$-0.0148826\pi$
$599$	3.99674	+	12.3007i	0.163302	+	0.502593i	−0.835605	+	0.549331i	$0.814883\pi$
$600$	−23.5118	−	3.08708i	−0.959867	−	0.126029i
$601$	8.93729	+	6.49332i	0.364560	+	0.264868i	0.754951	−	0.655781i	$-0.227660\pi$
$601$	8.93729	+	6.49332i	0.364560	+	0.264868i	−0.390392	+	0.920649i	$0.627660\pi$
$602$	2.65936	+	3.66029i	0.108387	+	0.149182i
$603$	0.647294	+	0.210318i	0.0263598	+	0.00856483i
$604$	11.3910			0.463494
$605$	13.3250	+	20.6747i	0.541738	+	0.840547i
$606$	−14.0364			−0.570188
$607$	0.110239	+	0.0358189i	0.00447448	+	0.00145385i	0.311253	−	0.950327i	$-0.399251\pi$
$607$	0.110239	+	0.0358189i	0.00447448	+	0.00145385i	−0.306779	+	0.951781i	$0.599251\pi$
$608$	7.83388	+	10.7824i	0.317706	+	0.437285i
$609$	3.01569	+	2.19103i	0.122202	+	0.0887849i
$610$	4.75002	+	3.94915i	0.192323	+	0.159897i
$611$	−1.07139	−	3.29741i	−0.0433440	−	0.133399i
$612$	0.565135	−	0.777842i	0.0228442	−	0.0314424i
$613$	−11.1941	−	15.4074i	−0.452125	−	0.622297i	0.520727	−	0.853723i	$-0.325661\pi$
$613$	−11.1941	−	15.4074i	−0.452125	−	0.622297i	−0.972853	+	0.231426i	$0.925661\pi$
$614$	2.48447	−	7.64643i	0.100265	−	0.308585i
$615$	28.0008	−	17.6740i	1.12910	−	0.712684i
$616$	−3.12938	−	4.26465i	−0.126086	−	0.171828i
$617$			30.8894i			1.24356i	0.783192	+	0.621780i	$0.213590\pi$
$617$			30.8894i			1.24356i	−0.783192	+	0.621780i	$0.786410\pi$
$618$	18.1750	+	5.90543i	0.731108	+	0.237551i
$619$	27.1584	−	19.7317i	1.09159	−	0.793086i	0.111922	−	0.993717i	$-0.464299\pi$
$619$	27.1584	−	19.7317i	1.09159	−	0.793086i	0.979667	+	0.200631i	$0.0642993\pi$
$620$	−1.21948	+	18.6554i	−0.0489756	+	0.749220i
$621$	−2.35216	−	7.23920i	−0.0943889	−	0.290499i
$622$	−2.60191	+	0.845410i	−0.104327	+	0.0338979i
$623$	−2.16257	+	2.97652i	−0.0866414	+	0.119252i
$624$	−1.40418	+	1.02020i	−0.0562122	+	0.0408405i
$625$	−23.3333	+	8.97543i	−0.933331	+	0.359017i
$626$	−19.6668			−0.786043
$627$	4.18681	+	12.6812i	0.167205	+	0.506440i
$628$			18.9738i			0.757139i
$629$	−16.0466	+	49.3863i	−0.639819	+	1.96916i
$630$	0.0989267	+	0.0394478i	0.00394134	+	0.00157164i
$631$	−19.9482	−	14.4932i	−0.794123	−	0.576964i	0.115061	−	0.993358i	$-0.463294\pi$
$631$	−19.9482	−	14.4932i	−0.794123	−	0.576964i	−0.909184	+	0.416394i	$0.863294\pi$
$632$	−11.5947	+	3.76734i	−0.461211	+	0.149857i
$633$	−14.5374	+	4.72349i	−0.577810	+	0.187742i
$634$	−4.53832	−	3.29728i	−0.180240	−	0.130952i
$635$	−13.2986	+	33.3500i	−0.527738	+	1.32345i
$636$	−1.75768	+	5.40960i	−0.0696967	+	0.214504i
$637$		−	11.9350i		−	0.472880i
$638$	2.89863	−	9.06679i	0.114758	−	0.358958i
$639$	1.18186			0.0467535
$640$	4.83739	+	19.0334i	0.191215	+	0.752361i
$641$	−5.67644	+	4.12418i	−0.224206	+	0.162895i	−0.694218	−	0.719765i	$-0.744250\pi$
$641$	−5.67644	+	4.12418i	−0.224206	+	0.162895i	0.470012	+	0.882660i	$0.344250\pi$
$642$	4.65582	−	6.40818i	0.183751	−	0.252911i
$643$	11.6528	−	3.78623i	0.459543	−	0.149315i	−0.0700915	−	0.997541i	$-0.522329\pi$
$643$	11.6528	−	3.78623i	0.459543	−	0.149315i	0.529634	+	0.848226i	$0.322329\pi$
$644$	0.369792	+	1.13810i	0.0145718	+	0.0448475i
$645$	2.44474	−	37.3992i	0.0962617	−	1.47259i
$646$	10.5100	−	7.63596i	0.413510	−	0.300433i
$647$	5.82060	+	1.89123i	0.228832	+	0.0743519i	0.421188	−	0.906973i	$-0.361613\pi$
$647$	5.82060	+	1.89123i	0.228832	+	0.0743519i	−0.192357	+	0.981325i	$0.561613\pi$
$648$			25.0251i			0.983079i
$649$	−0.000600576	−	0.126952i	−2.35747e−5	−	0.00498328i
$650$	3.09905	−	6.50310i	0.121555	−	0.255073i
$651$	1.98685	−	6.11491i	0.0778710	−	0.239662i
$652$	9.43583	+	12.9873i	0.369536	+	0.508622i
$653$	22.3544	−	30.7682i	0.874795	−	1.20405i	−0.103041	−	0.994677i	$-0.532857\pi$
$653$	22.3544	−	30.7682i	0.874795	−	1.20405i	0.977835	−	0.209375i	$-0.0671428\pi$
$654$	−8.12356	−	25.0017i	−0.317656	−	0.977645i
$655$	25.7738	−	31.0006i	1.00707	−	1.21129i
$656$	−3.73676	−	2.71492i	−0.145896	−	0.106000i
$657$	0.401883	+	0.553145i	0.0156790	+	0.0215802i
$658$	0.873144	+	0.283702i	0.0340387	+	0.0110598i
$659$	−15.7879			−0.615011			−0.307505	−	0.951546i	$-0.599494\pi$
$659$	−15.7879			−0.615011			−0.307505	+	0.951546i	$0.599494\pi$
$660$	−1.07114	+	17.6700i	−0.0416942	+	0.687803i
$661$	−24.5794			−0.956027			−0.478014	−	0.878352i	$-0.658643\pi$
$661$	−24.5794			−0.956027			−0.478014	+	0.878352i	$0.658643\pi$
$662$	−4.30809	−	1.39978i	−0.167439	−	0.0544042i
$663$	13.1464	+	18.0945i	0.510566	+	0.702733i
$664$	−12.9500	−	9.40870i	−0.502556	−	0.365128i
$665$	−2.32819	−	1.93565i	−0.0902833	−	0.0750613i
$666$	0.182390	+	0.561338i	0.00706746	+	0.0217514i
$667$	−3.13312	+	4.31237i	−0.121315	+	0.166976i
$668$	−6.95350	−	9.57067i	−0.269039	−	0.370300i
$669$	−3.43111	+	10.5599i	−0.132654	+	0.408268i
$670$	6.50666	+	10.3085i	0.251374	+	0.398251i
$671$	6.66547	−	9.26611i	0.257318	−	0.357714i
$672$		−	6.07597i		−	0.234385i
$673$	−28.5063	−	9.26226i	−1.09884	−	0.357034i	−0.297182	−	0.954821i	$-0.596047\pi$
$673$	−28.5063	−	9.26226i	−1.09884	−	0.357034i	−0.801655	+	0.597787i	$0.796047\pi$
$674$	−14.6870	+	10.6707i	−0.565722	+	0.411021i
$675$	12.1891	+	22.4310i	0.469160	+	0.863369i
$676$	4.09642	+	12.6075i	0.157555	+	0.484903i
$677$	−3.57321	+	1.16101i	−0.137330	+	0.0446211i	−0.376875	−	0.926264i	$-0.623001\pi$
$677$	−3.57321	+	1.16101i	−0.137330	+	0.0446211i	0.239546	+	0.970885i	$0.423001\pi$
$678$	−9.80393	+	13.4940i	−0.376518	+	0.518232i
$679$	−2.57508	+	1.87091i	−0.0988225	+	0.0717988i
$680$	41.3125	−	10.4997i	1.58426	−	0.402645i
$681$	1.96641			0.0753531
$682$	−16.4185	+	0.0776720i	−0.628699	+	0.00297421i
$683$		−	21.0157i		−	0.804144i	−0.915608	−	0.402072i	$-0.868290\pi$
$683$		−	21.0157i		−	0.804144i	0.915608	−	0.402072i	$-0.131710\pi$
$684$	−0.0960054	+	0.295474i	−0.00367086	+	0.0112977i
$685$	−3.33949	+	8.37472i	−0.127595	+	0.319982i
$686$	5.24834	+	3.81314i	0.200382	+	0.145586i
$687$	−7.02675	+	2.28313i	−0.268087	+	0.0871068i
$688$	−4.97217	+	1.61555i	−0.189562	+	0.0615925i
$689$	−3.46021	−	2.51399i	−0.131824	−	0.0957754i
$690$	−1.74511	+	4.37636i	−0.0664351	+	0.166605i
$691$	−11.8299	+	36.4088i	−0.450032	+	1.38506i	0.426837	+	0.904328i	$0.359628\pi$
$691$	−11.8299	+	36.4088i	−0.450032	+	1.38506i	−0.876870	+	0.480728i	$0.840372\pi$
$692$			12.4432i			0.473020i
$693$	0.0599271	−	0.187449i	0.00227644	−	0.00712061i
$694$	−0.146408			−0.00555757
$695$	17.1963	−	4.37049i	0.652294	−	0.165782i
$696$	13.7190	−	9.96742i	0.520017	−	0.377814i
$697$	−34.9850	+	48.1527i	−1.32515	+	1.82391i
$698$	11.7774	−	3.82670i	0.445780	−	0.144843i
$699$	−3.68870	−	11.3527i	−0.139520	−	0.429397i
$700$	−1.91630	−	3.52646i	−0.0724294	−	0.133288i
$701$	27.6963	−	20.1225i	1.04607	−	0.760016i	0.0746112	−	0.997213i	$-0.476228\pi$
$701$	27.6963	−	20.1225i	1.04607	−	0.760016i	0.971462	+	0.237196i	$0.0762284\pi$
$702$	−6.99614	−	2.27318i	−0.264052	−	0.0857958i
$703$		−	16.7795i		−	0.632852i
$704$	−11.2741	+	3.72224i	−0.424910	+	0.140287i
$705$	−4.05936	−	6.43121i	−0.152884	−	0.242214i
$706$	5.93089	−	18.2534i	0.223212	−	0.686976i
$707$	−3.45639	−	4.75731i	−0.129991	−	0.178917i
$708$	0.0537052	−	0.0739189i	0.00201836	−	0.00277804i
$709$	1.27462	+	3.92289i	0.0478695	+	0.147327i	0.972134	−	0.234425i	$-0.0753207\pi$
$709$	1.27462	+	3.92289i	0.0478695	+	0.147327i	−0.924265	+	0.381752i	$0.875321\pi$
$710$	16.2772	+	13.5328i	0.610873	+	0.507878i
$711$	−0.366944	−	0.266600i	−0.0137615	−	0.00999828i
$712$	9.83795	+	13.5408i	0.368693	+	0.507462i
$713$	8.74418	+	2.84116i	0.327472	+	0.106402i
$714$	−5.92246			−0.221642
$715$	−12.3877	−	4.87189i	−0.463272	−	0.182198i
$716$	−1.96324			−0.0733697
$717$	−7.36487	−	2.39299i	−0.275046	−	0.0893679i
$718$	4.13656	+	5.69349i	0.154375	+	0.212479i
$719$	23.7524	+	17.2571i	0.885814	+	0.643582i	0.934783	−	0.355218i	$-0.115594\pi$
$719$	23.7524	+	17.2571i	0.885814	+	0.643582i	−0.0489689	+	0.998800i	$0.515594\pi$
$720$	−0.0786768	+	0.0946320i	−0.00293211	+	0.00352673i
$721$	2.47400	+	7.61420i	0.0921367	+	0.283568i
$722$	6.49706	−	8.94243i	0.241795	−	0.332803i
$723$	9.94801	+	13.6923i	0.369970	+	0.509221i
$724$	0.332419	−	1.02308i	0.0123543	−	0.0380225i
$725$	7.69084	−	16.1386i	0.285630	−	0.599373i
$726$	−15.5461	+	0.147093i	−0.576970	+	0.00545912i
$727$		−	44.0893i		−	1.63518i	−0.575799	−	0.817591i	$-0.695309\pi$
$727$		−	44.0893i		−	1.63518i	0.575799	−	0.817591i	$-0.304691\pi$
$728$	2.72254	+	0.884606i	0.100904	+	0.0327857i
$729$	21.0659	−	15.3052i	0.780217	−	0.566861i
$730$	−0.798808	+	12.2200i	−0.0295652	+	0.452283i
$731$	20.8184	+	64.0723i	0.769995	+	2.36980i
$732$	7.81296	−	2.53858i	0.288775	−	0.0938287i
$733$	−28.7715	+	39.6006i	−1.06270	+	1.46268i	−0.185446	+	0.982654i	$0.559373\pi$
$733$	−28.7715	+	39.6006i	−1.06270	+	1.46268i	−0.877254	+	0.480026i	$0.840627\pi$
$734$	−3.49526	+	2.53946i	−0.129012	+	0.0937331i
$735$	−6.44862	−	25.3730i	−0.237861	−	0.935898i
$736$	8.68849			0.320262
$737$	18.1605	−	13.3261i	0.668949	−	0.490872i
$738$			0.676520i			0.0249031i
$739$	6.38498	−	19.6509i	0.234875	−	0.722872i	−0.762263	−	0.647268i	$-0.775912\pi$
$739$	6.38498	−	19.6509i	0.234875	−	0.722872i	0.997138	−	0.0756039i	$-0.0240884\pi$
$740$	8.23854	−	20.6605i	0.302855	−	0.759495i
$741$	−5.84692	−	4.24804i	−0.214792	−	0.156056i
$742$	1.07712	−	0.349977i	0.0395423	−	0.0128481i
$743$	28.6868	−	9.32091i	1.05242	−	0.341951i	0.268801	−	0.963196i	$-0.413373\pi$
$743$	28.6868	−	9.32091i	1.05242	−	0.341951i	0.783617	+	0.621245i	$0.213373\pi$
$744$	−23.6634	−	17.1924i	−0.867541	−	0.630305i
$745$	−25.9646	−	10.3536i	−0.951271	−	0.379327i
$746$	0.799830	−	2.46162i	0.0292839	−	0.0901264i
$747$		−	0.595525i		−	0.0217891i
$748$	−9.97615	−	30.2163i	−0.364764	−	1.10482i
$749$	3.31838			0.121251
$750$	3.07467	−	15.4997i	0.112271	−	0.565968i
$751$	−9.78637	+	7.11021i	−0.357110	+	0.259455i	−0.751846	−	0.659339i	$-0.770836\pi$
$751$	−9.78637	+	7.11021i	−0.357110	+	0.259455i	0.394736	+	0.918795i	$0.370836\pi$
$752$	−0.623562	+	0.858259i	−0.0227390	+	0.0312975i
$753$	−22.4737	+	7.30213i	−0.818986	+	0.266105i
$754$	1.59187	+	4.89929i	0.0579726	+	0.178421i
$755$	−1.22557	+	18.7485i	−0.0446030	+	0.682328i
$756$	−3.31568	+	2.40898i	−0.120590	+	0.0876138i
$757$	19.6013	+	6.36886i	0.712423	+	0.231480i	0.642735	−	0.766089i	$-0.277800\pi$
$757$	19.6013	+	6.36886i	0.712423	+	0.231480i	0.0696881	+	0.997569i	$0.477800\pi$
$758$		−	15.7838i		−	0.573293i
$759$	8.29245	+	2.65108i	0.300997	+	0.0962280i
$760$	−11.6476	+	7.35192i	−0.422503	+	0.266682i
$761$	6.44146	−	19.8248i	0.233503	−	0.718648i	−0.763814	−	0.645437i	$-0.776675\pi$
$761$	6.44146	−	19.8248i	0.233503	−	0.718648i	0.997316	−	0.0732111i	$-0.0233247\pi$
$762$	−13.3389	−	18.3595i	−0.483219	−	0.665093i
$763$	6.47339	−	8.90985i	0.234352	−	0.322558i
$764$	−3.41437	−	10.5084i	−0.123528	−	0.380179i
$765$	1.21945	+	1.01384i	0.0440892	+	0.0366556i
$766$	18.1670	+	13.1991i	0.656399	+	0.476902i
$767$	0.0403834	+	0.0555830i	0.00145816	+	0.00200699i
$768$	−23.7944	−	7.73127i	−0.858607	−	0.278978i
$769$	−10.7167			−0.386455			−0.193228	−	0.981154i	$-0.561896\pi$
$769$	−10.7167			−0.386455			−0.193228	+	0.981154i	$0.561896\pi$
$770$	2.97174	−	1.89547i	0.107094	−	0.0683080i
$771$	19.0466			0.685946
$772$	5.63223	+	1.83002i	0.202708	+	0.0658639i
$773$	−11.9651	−	16.4686i	−0.430355	−	0.592333i	0.537679	−	0.843149i	$-0.319301\pi$
$773$	−11.9651	−	16.4686i	−0.430355	−	0.592333i	−0.968035	+	0.250816i	$0.919301\pi$
$774$	0.619498	+	0.450092i	0.0222674	+	0.0161782i
$775$	−30.5738	−	4.01430i	−1.09824	−	0.144198i
$776$	4.47456	+	13.7713i	0.160627	+	0.494361i
$777$	−4.49630	+	6.18863i	−0.161304	+	0.222016i
$778$	−6.15247	−	8.46814i	−0.220577	−	0.303598i
$779$	5.94326	−	18.2915i	0.212939	−	0.655360i
$780$	−5.11353	−	8.10134i	−0.183094	−	0.290074i
$781$	22.8410	−	31.7528i	0.817317	−	1.13620i
$782$		−	8.46898i		−	0.302850i
$783$	−17.3622	−	5.64131i	−0.620474	−	0.201604i
$784$	−2.95442	+	2.14651i	−0.105515	+	0.0766612i
$785$	−31.2291	−	2.04141i	−1.11461	−	0.0728610i
$786$	7.87438	+	24.2348i	0.280870	+	0.864428i
$787$	−13.5261	+	4.39491i	−0.482154	+	0.156661i	−0.540002	−	0.841664i	$-0.681576\pi$
$787$	−13.5261	+	4.39491i	−0.482154	+	0.156661i	0.0578472	+	0.998325i	$0.481576\pi$
$788$	12.4727	−	17.1671i	0.444320	−	0.611554i
$789$	−35.0919	+	25.4958i	−1.24930	+	0.907673i
$790$	−2.00106	−	7.87346i	−0.0711946	−	0.280125i
$791$	−6.98764			−0.248452
$792$	−0.726764	−	0.522790i	−0.0258244	−	0.0185765i
$793$			6.17726i			0.219361i
$794$	−0.452049	+	1.39126i	−0.0160426	+	0.0493741i
$795$	−8.71455	−	3.47500i	−0.309073	−	0.123245i
$796$	1.57748	+	1.14610i	0.0559122	+	0.0406226i
$797$	42.8341	−	13.9176i	1.51726	−	0.492988i	0.572264	−	0.820069i	$-0.306065\pi$
$797$	42.8341	−	13.9176i	1.51726	−	0.492988i	0.944996	+	0.327081i	$0.106065\pi$
$798$	1.82007	−	0.591377i	0.0644298	−	0.0209345i
$799$	11.0597	+	8.03534i	0.391264	+	0.284270i
$800$	−28.6504	+	5.32034i	−1.01294	+	0.188102i
$801$	−0.192423	+	0.592218i	−0.00679894	+	0.0209250i
$802$		−	4.31920i		−	0.152516i
$803$	22.6283	−	0.107049i	0.798534	−	0.00377766i
$804$	16.2115			0.571737
$805$	−1.91299	+	0.486192i	−0.0674240	+	0.0171360i
$806$	7.18851	−	5.22276i	0.253204	−	0.183964i
$807$	4.96875	−	6.83889i	0.174908	−	0.240740i
$808$	−25.4416	+	8.26649i	−0.895034	+	0.290814i
$809$	−7.34698	−	22.6117i	−0.258306	−	0.794984i	−0.993160	−	0.116759i	$-0.962749\pi$
$809$	−7.34698	−	22.6117i	−0.258306	−	0.794984i	0.734854	−	0.678225i	$-0.237251\pi$
$810$	−16.6401	−	1.08774i	−0.584673	−	0.0382194i
$811$	6.63288	−	4.81907i	0.232912	−	0.169220i	−0.465208	−	0.885202i	$-0.654020\pi$
$811$	6.63288	−	4.81907i	0.232912	−	0.169220i	0.698120	+	0.715981i	$0.254020\pi$
$812$	2.72957	+	0.886893i	0.0957893	+	0.0311238i
$813$			41.0787i			1.44069i
$814$	18.6064	+	5.94841i	0.652152	+	0.208492i
$815$	−22.3910	+	14.1331i	−0.784323	+	0.495062i
$816$	2.11478	−	6.50864i	0.0740322	−	0.227848i
$817$	−12.7957	−	17.6117i	−0.447663	−	0.616156i
$818$	−17.3071	+	23.8212i	−0.605130	+	0.832890i
$819$	0.0329109	+	0.101289i	0.00115000	+	0.00353933i
$820$	16.2988	−	19.6041i	0.569178	−	0.684604i
$821$	35.1415	+	25.5318i	1.22645	+	0.891066i	0.996619	−	0.0821658i	$-0.0261837\pi$
$821$	35.1415	+	25.5318i	1.22645	+	0.891066i	0.229828	+	0.973231i	$0.426184\pi$
$822$	−3.34962	−	4.61036i	−0.116831	−	0.160805i
$823$	49.1507	+	15.9700i	1.71328	+	0.556680i	0.990875	−	0.134785i	$-0.0430345\pi$
$823$	49.1507	+	15.9700i	1.71328	+	0.556680i	0.722410	+	0.691465i	$0.243034\pi$
$824$	36.4211			1.26879
$825$	−28.9678	−	3.66412i	−1.00853	−	0.127568i
$826$	−0.0181927			−0.000633004
$827$	24.0692	+	7.82057i	0.836970	+	0.271948i	0.695978	−	0.718063i	$-0.254971\pi$
$827$	24.0692	+	7.82057i	0.836970	+	0.271948i	0.140991	+	0.990011i	$0.454971\pi$
$828$	0.119047	+	0.163854i	0.00413717	+	0.00569432i
$829$	−33.8784	−	24.6141i	−1.17665	−	0.854883i	−0.184856	−	0.982766i	$-0.559182\pi$
$829$	−33.8784	−	24.6141i	−1.17665	−	0.854883i	−0.991789	+	0.127883i	$0.959182\pi$
$830$	6.81906	−	8.20193i	0.236693	−	0.284693i
$831$	11.9143	+	36.6684i	0.413302	+	1.27201i
$832$	3.77668	−	5.19815i	0.130933	−	0.180213i
$833$	27.6604	+	38.0713i	0.958376	+	1.31909i
$834$	−3.46556	+	10.6659i	−0.120003	+	0.369330i
$835$	16.5005	−	10.4151i	0.571024	−	0.360428i
$836$	6.08303	+	8.28982i	0.210386	+	0.286710i
$837$			31.4885i			1.08840i
$838$	2.18817	+	0.710980i	0.0755891	+	0.0245604i
$839$	−11.6376	+	8.45518i	−0.401773	+	0.291905i	−0.770263	−	0.637727i	$-0.779875\pi$
$839$	−11.6376	+	8.45518i	−0.401773	+	0.291905i	0.368490	+	0.929632i	$0.379875\pi$
$840$	6.26592	+	0.409596i	0.216195	+	0.0141324i
$841$	−5.01097	−	15.4222i	−0.172792	−	0.531800i
$842$	3.55731	−	1.15584i	0.122593	−	0.0398329i
$843$	16.3266	−	22.4716i	0.562318	−	0.773965i
$844$	−9.52134	+	6.91766i	−0.327738	+	0.238116i
$845$	−21.1914	+	5.38585i	−0.729006	+	0.185279i
$846$	0.155383			0.00534218
$847$	−3.87801	−	5.23278i	−0.133250	−	0.179800i
$848$			1.30870i			0.0449408i
$849$	12.3016	−	37.8605i	0.422190	−	1.29937i
$850$	5.18592	+	27.9265i	0.177876	+	0.957872i
$851$	−8.84960	−	6.42961i	−0.303360	−	0.220404i
$852$	26.7732	−	8.69914i	0.917235	−	0.298028i
$853$	40.8968	−	13.2882i	1.40028	−	0.454978i	0.490998	−	0.871161i	$-0.336632\pi$
$853$	40.8968	−	13.2882i	1.40028	−	0.454978i	0.909281	+	0.416183i	$0.136632\pi$
$854$	−1.32332	−	0.961450i	−0.0452832	−	0.0329001i
$855$	−0.475992	−	0.189806i	−0.0162786	−	0.00649122i
$856$	4.66492	−	14.3571i	0.159444	−	0.490717i
$857$			54.3052i			1.85503i	0.373784	+	0.927516i	$0.378060\pi$
$857$			54.3052i			1.85503i	−0.373784	+	0.927516i	$0.621940\pi$
$858$	6.78328	−	4.97754i	0.231578	−	0.169931i
$859$	−24.3361			−0.830336			−0.415168	−	0.909745i	$-0.636277\pi$
$859$	−24.3361			−0.830336			−0.415168	+	0.909745i	$0.636277\pi$
$860$	−7.10806	−	27.9677i	−0.242383	−	0.953689i
$861$	−7.09344	+	5.15369i	−0.241744	+	0.175637i
$862$	−9.79917	+	13.4874i	−0.333761	+	0.459383i
$863$	−37.2339	+	12.0980i	−1.26746	+	0.411822i	−0.864146	−	0.503241i	$-0.832141\pi$
$863$	−37.2339	+	12.0980i	−1.26746	+	0.411822i	−0.403312	+	0.915063i	$0.632141\pi$
$864$	9.19531	+	28.3003i	0.312831	+	0.962795i
$865$	−20.4803	−	1.33877i	−0.696351	−	0.0455196i
$866$	−8.31045	+	6.03789i	−0.282400	+	0.205176i
$867$	−55.4039	−	18.0018i	−1.88162	−	0.611374i
$868$		−	4.95043i		−	0.168029i
$869$	−14.2544	+	4.70621i	−0.483548	+	0.159647i
$870$	6.03138	+	9.55548i	0.204483	+	0.323961i
$871$	−3.76698	+	11.5936i	−0.127639	+	0.392833i
$872$	−29.4487	−	40.5327i	−0.997260	−	1.37261i
$873$	−0.316648	+	0.435828i	−0.0107169	+	0.0147505i
$874$	0.845656	+	2.60266i	0.0286047	+	0.0880363i
$875$	6.01038	−	2.77463i	0.203188	−	0.0937995i
$876$	13.1755	+	9.57259i	0.445160	+	0.323428i
$877$	25.3266	+	34.8591i	0.855219	+	1.17711i	0.982689	+	0.185265i	$0.0593145\pi$
$877$	25.3266	+	34.8591i	0.855219	+	1.17711i	−0.127470	+	0.991842i	$0.540686\pi$
$878$	−8.10808	−	2.63447i	−0.273634	−	0.0889092i
$879$	−23.3468			−0.787466
$880$	1.02193	+	3.94270i	0.0344492	+	0.132908i
$881$	−38.1083			−1.28390			−0.641950	−	0.766746i	$-0.721874\pi$
$881$	−38.1083			−1.28390			−0.641950	+	0.766746i	$0.721874\pi$
$882$	0.508703	+	0.165288i	0.0171289	+	0.00556552i
$883$	−17.0611	−	23.4826i	−0.574152	−	0.790252i	0.418887	−	0.908038i	$-0.362420\pi$
$883$	−17.0611	−	23.4826i	−0.574152	−	0.790252i	−0.993039	+	0.117786i	$0.962420\pi$
$884$	13.9318	+	10.1220i	0.468577	+	0.340441i
$885$	0.115885	+	0.0963464i	0.00389543	+	0.00323865i
$886$	−1.63685	−	5.03771i	−0.0549911	−	0.169245i
$887$	−1.30003	+	1.78934i	−0.0436508	+	0.0600801i	−0.830284	−	0.557340i	$-0.811822\pi$
$887$	−1.30003	+	1.78934i	−0.0436508	+	0.0600801i	0.786634	+	0.617420i	$0.211822\pi$
$888$	20.4546	+	28.1533i	0.686411	+	0.944764i
$889$	2.93788	−	9.04186i	0.0985332	−	0.303254i
$890$	−9.43136	+	5.95304i	−0.316140	+	0.199546i
$891$	0.145769	+	30.8131i	0.00488344	+	1.03228i
$892$			8.54894i			0.286240i
$893$	−4.20118	−	1.36505i	−0.140587	−	0.0456796i
$894$	14.2938	−	10.3850i	0.478055	−	0.347327i
$895$	0.211226	−	3.23130i	0.00706051	−	0.108010i
$896$	−1.60695	−	4.94569i	−0.0536845	−	0.165224i
$897$	−4.48087	+	1.45592i	−0.149612	+	0.0486118i
$898$	6.42991	−	8.85002i	0.214569	−	0.295329i
$899$	17.8396	−	12.9612i	0.594983	−	0.432280i
$900$	−0.492893	−	0.467412i	−0.0164298	−	0.0155804i
$901$	16.8641			0.561825
$902$	18.1760	+	13.0747i	0.605195	+	0.435340i
$903$			9.92432i			0.330261i
$904$	−9.82309	+	30.2323i	−0.326711	+	1.00551i
$905$	1.64812	+	0.657203i	0.0547855	+	0.0218462i
$906$	−9.60757	−	6.98031i	−0.319190	−	0.231905i
$907$	25.3802	−	8.24653i	0.842736	−	0.273822i	0.144336	−	0.989529i	$-0.453895\pi$
$907$	25.3802	−	8.24653i	0.842736	−	0.273822i	0.698401	+	0.715707i	$0.253895\pi$
$908$	1.43993	−	0.467861i	0.0477857	−	0.0155265i
$909$	−0.805166	−	0.584988i	−0.0267057	−	0.0194028i
$910$	−0.706544	+	1.77186i	−0.0234217	+	0.0587366i
$911$	−11.2092	+	34.4983i	−0.371376	+	1.14298i	0.574515	+	0.818494i	$0.305191\pi$
$911$	−11.2092	+	34.4983i	−0.371376	+	1.14298i	−0.945891	+	0.324484i	$0.894809\pi$
$912$			2.21138i			0.0732261i
$913$	−15.9999	−	11.5094i	−0.529520	−	0.380904i
$914$	−10.8363			−0.358434
$915$	3.33766	+	13.1325i	0.110340	+	0.434146i
$916$	−4.60220	+	3.34369i	−0.152061	+	0.110479i
$917$	−6.27482	+	8.63655i	−0.207213	+	0.285204i
$918$	27.5853	−	8.96300i	0.910450	−	0.295823i
$919$	9.16908	+	28.2195i	0.302460	+	0.930876i	0.980613	+	0.195955i	$0.0627808\pi$
$919$	9.16908	+	28.2195i	0.302460	+	0.930876i	−0.678153	+	0.734921i	$0.737219\pi$
$920$	−0.585713	+	8.96012i	−0.0193104	+	0.295406i
$921$	14.2677	−	10.3661i	0.470135	−	0.341573i
$922$	−8.64311	−	2.80832i	−0.284646	−	0.0924870i
$923$			21.1680i			0.696754i
$924$	−0.0221753	−	4.68749i	−0.000729514	−	0.154207i
$925$	33.1188	+	15.7827i	1.08894	+	0.518932i
$926$	1.19805	−	3.68720i	0.0393702	−	0.121169i
$927$	0.796455	+	1.09623i	0.0261590	+	0.0360048i
$928$	12.2483	−	16.8584i	0.402071	−	0.553403i
$929$	−8.58220	−	26.4133i	−0.281573	−	0.866592i	−0.987405	−	0.158213i	$-0.949427\pi$
$929$	−8.58220	−	26.4133i	−0.281573	−	0.866592i	0.705832	−	0.708379i	$-0.250573\pi$
$930$	12.4604	−	14.9873i	0.408593	−	0.491453i
$931$	−12.3020	−	8.93795i	−0.403183	−	0.292930i
$932$	−5.40219	−	7.43548i	−0.176955	−	0.243557i
$933$	−5.70735	−	1.85443i	−0.186850	−	0.0607113i
$934$	19.2786			0.630817
$935$	50.8064	−	13.1688i	1.66155	−	0.430665i
$936$	0.484498			0.0158363
$937$	−28.7620	−	9.34532i	−0.939612	−	0.305298i	−0.201125	−	0.979566i	$-0.564460\pi$
$937$	−28.7620	−	9.34532i	−0.939612	−	0.305298i	−0.738487	+	0.674267i	$0.764460\pi$
$938$	−1.89733	−	2.61144i	−0.0619499	−	0.0852667i
$939$	−34.9007	−	25.3568i	−1.13894	−	0.827489i
$940$	−4.50266	−	3.74350i	−0.146861	−	0.122100i
$941$	−1.85618	−	5.71273i	−0.0605097	−	0.186230i	0.916232	−	0.400647i	$-0.131215\pi$
$941$	−1.85618	−	5.71273i	−0.0605097	−	0.186230i	−0.976742	+	0.214418i	$0.931215\pi$
$942$	11.6270	−	16.0032i	0.378828	−	0.521412i
$943$	−7.36966	−	10.1435i	−0.239989	−	0.330317i
$944$	0.00649622	−	0.0199933i	0.000211434	−	0.000650727i
$945$	−3.60821	−	5.71646i	−0.117375	−	0.185956i
$946$	24.0652	−	7.94533i	0.782428	−	0.258325i
$947$			10.0218i			0.325665i	0.986654	+	0.162833i	$0.0520630\pi$
$947$			10.0218i			0.325665i	−0.986654	+	0.162833i	$0.947937\pi$
$948$	−10.2749	−	3.33851i	−0.333713	−	0.108430i
$949$	−9.90729	+	7.19807i	−0.321604	+	0.233659i
$950$	−4.38228	−	8.06446i	−0.142180	−	0.261646i
$951$	−3.80244	−	11.7027i	−0.123303	−	0.379486i
$952$	−10.7348	+	3.48794i	−0.347916	+	0.113045i
$953$	5.74934	−	7.91329i	0.186239	−	0.256336i	−0.705680	−	0.708530i	$-0.749359\pi$
$953$	5.74934	−	7.91329i	0.186239	−	0.256336i	0.891920	+	0.452194i	$0.149359\pi$
$954$	0.155074	−	0.112668i	0.00502071	−	0.00364776i
$955$	17.6631	−	4.48912i	0.571564	−	0.145264i
$956$	−5.96237			−0.192837
$957$	16.8339	−	12.3527i	0.544164	−	0.399305i
$958$			34.6967i			1.12100i
$959$	0.737749	−	2.27056i	0.0238231	−	0.0733201i
$960$	5.22036	−	13.0915i	0.168486	−	0.422528i
$961$	−5.69127	−	4.13495i	−0.183589	−	0.133385i
$962$	−10.0540	+	3.26676i	−0.324155	+	0.105324i
$963$	0.534142	−	0.173553i	0.0172125	−	0.00559268i
$964$	10.5423	+	7.65942i	0.339544	+	0.246693i
$965$	−3.61801	+	9.07320i	−0.116468	+	0.292077i
$966$	0.385523	−	1.18652i	0.0124040	−	0.0381756i
$967$		−	1.22635i		−	0.0394367i	−0.999806	−	0.0197184i	$-0.993723\pi$
$967$		−	1.22635i		−	0.0394367i	0.999806	−	0.0197184i	$-0.00627695\pi$
$968$	−28.0915	+	9.42224i	−0.902895	+	0.302842i
$969$	28.4963			0.915432
$970$	−9.35151	+	2.37671i	−0.300259	+	0.0763116i
$971$	36.1199	−	26.2426i	1.15914	−	0.842167i	0.169473	−	0.985535i	$-0.445793\pi$
$971$	36.1199	−	26.2426i	1.15914	−	0.842167i	0.989669	+	0.143368i	$0.0457933\pi$
$972$	−0.829522	+	1.14174i	−0.0266069	+	0.0366213i
$973$	−4.46834	+	1.45185i	−0.143248	+	0.0465442i
$974$	−10.4083	−	32.0335i	−0.333503	−	1.02642i
$975$	13.8842	−	7.54474i	0.444649	−	0.241625i
$976$	1.52914	−	1.11099i	0.0489466	−	0.0355618i
$977$	−44.9328	−	14.5996i	−1.43753	−	0.467081i	−0.516402	−	0.856346i	$-0.672729\pi$
$977$	−44.9328	−	14.5996i	−1.43753	−	0.467081i	−0.921126	+	0.389265i	$0.872729\pi$
$978$		−	16.7361i		−	0.535162i
$979$	12.1922	+	16.6153i	0.389665	+	0.531026i
$980$	−10.7590	−	17.0454i	−0.343683	−	0.544495i
$981$	0.575996	−	1.77273i	0.0183901	−	0.0565991i
$982$	−4.27456	−	5.88343i	−0.136407	−	0.187748i
$983$	−8.19082	+	11.2737i	−0.261247	+	0.359575i	−0.919410	−	0.393300i	$-0.871333\pi$
$983$	−8.19082	+	11.2737i	−0.261247	+	0.359575i	0.658164	+	0.752875i	$0.271333\pi$
$984$	12.3259	+	37.9351i	0.392934	+	1.20933i
$985$	26.9135	+	22.3758i	0.857535	+	0.712952i
$986$	−16.4325	−	11.9389i	−0.523316	−	0.380211i
$987$	1.18370	+	1.62922i	0.0376775	+	0.0518587i
$988$	−5.29219	−	1.71954i	−0.168367	−	0.0547058i
$989$	−14.1916			−0.451265
$990$	0.379211	−	0.460528i	0.0120521	−	0.0146365i
$991$	36.5755			1.16186			0.580930	−	0.813953i	$-0.302689\pi$
$991$	36.5755			1.16186			0.580930	+	0.813953i	$0.302689\pi$
$992$	−34.1837	−	11.1070i	−1.08533	−	0.352646i
$993$	−5.84037	−	8.03858i	−0.185339	−	0.255097i
$994$	−4.53472	−	3.29467i	−0.143833	−	0.104501i
$995$	−2.05610	+	2.47306i	−0.0651827	+	0.0784013i
$996$	−4.38341	−	13.4907i	−0.138894	−	0.427470i
$997$	11.3687	−	15.6476i	0.360049	−	0.495565i	−0.590113	−	0.807320i	$-0.700917\pi$
$997$	11.3687	−	15.6476i	0.360049	−	0.495565i	0.950162	+	0.311755i	$0.100917\pi$
$998$	−14.2862	−	19.6633i	−0.452222	−	0.622431i
$999$	11.5768	−	35.6297i	0.366273	−	1.12727i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	55.2.j.a.9.2	✓	16
3.2	odd	2		495.2.ba.a.64.3		16
4.3	odd	2		880.2.cd.c.449.3		16
5.2	odd	4		275.2.h.d.251.3		16
5.3	odd	4		275.2.h.d.251.2		16
5.4	even	2	inner	55.2.j.a.9.3	yes	16
11.2	odd	10		605.2.j.g.124.2		16
11.3	even	5		605.2.j.h.444.2		16
11.4	even	5		605.2.b.g.364.4		8
11.5	even	5	inner	55.2.j.a.49.3	yes	16
11.6	odd	10		605.2.j.d.269.2		16
11.7	odd	10		605.2.b.f.364.5		8
11.8	odd	10		605.2.j.g.444.3		16
11.9	even	5		605.2.j.h.124.3		16
11.10	odd	2		605.2.j.d.9.3		16
15.14	odd	2		495.2.ba.a.64.2		16
20.19	odd	2		880.2.cd.c.449.2		16
33.5	odd	10		495.2.ba.a.379.2		16
44.27	odd	10		880.2.cd.c.49.2		16
55.4	even	10		605.2.b.g.364.5		8
55.7	even	20		3025.2.a.bk.1.4		8
55.9	even	10		605.2.j.h.124.2		16
55.14	even	10		605.2.j.h.444.3		16
55.18	even	20		3025.2.a.bk.1.5		8
55.19	odd	10		605.2.j.g.444.2		16
55.24	odd	10		605.2.j.g.124.3		16
55.27	odd	20		275.2.h.d.126.3		16
55.29	odd	10		605.2.b.f.364.4		8
55.37	odd	20		3025.2.a.bl.1.5		8
55.38	odd	20		275.2.h.d.126.2		16
55.39	odd	10		605.2.j.d.269.3		16
55.48	odd	20		3025.2.a.bl.1.4		8
55.49	even	10	inner	55.2.j.a.49.2	yes	16
55.54	odd	2		605.2.j.d.9.2		16
165.104	odd	10		495.2.ba.a.379.3		16
220.159	odd	10		880.2.cd.c.49.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.j.a.9.2	✓	16	1.1	even	1	trivial
55.2.j.a.9.3	yes	16	5.4	even	2	inner
55.2.j.a.49.2	yes	16	55.49	even	10	inner
55.2.j.a.49.3	yes	16	11.5	even	5	inner
275.2.h.d.126.2		16	55.38	odd	20
275.2.h.d.126.3		16	55.27	odd	20
275.2.h.d.251.2		16	5.3	odd	4
275.2.h.d.251.3		16	5.2	odd	4
495.2.ba.a.64.2		16	15.14	odd	2
495.2.ba.a.64.3		16	3.2	odd	2
495.2.ba.a.379.2		16	33.5	odd	10
495.2.ba.a.379.3		16	165.104	odd	10
605.2.b.f.364.4		8	55.29	odd	10
605.2.b.f.364.5		8	11.7	odd	10
605.2.b.g.364.4		8	11.4	even	5
605.2.b.g.364.5		8	55.4	even	10
605.2.j.d.9.2		16	55.54	odd	2
605.2.j.d.9.3		16	11.10	odd	2
605.2.j.d.269.2		16	11.6	odd	10
605.2.j.d.269.3		16	55.39	odd	10
605.2.j.g.124.2		16	11.2	odd	10
605.2.j.g.124.3		16	55.24	odd	10
605.2.j.g.444.2		16	55.19	odd	10
605.2.j.g.444.3		16	11.8	odd	10
605.2.j.h.124.2		16	55.9	even	10
605.2.j.h.124.3		16	11.9	even	5
605.2.j.h.444.2		16	11.3	even	5
605.2.j.h.444.3		16	55.14	even	10
880.2.cd.c.49.2		16	44.27	odd	10
880.2.cd.c.49.3		16	220.159	odd	10
880.2.cd.c.449.2		16	20.19	odd	2
880.2.cd.c.449.3		16	4.3	odd	2
3025.2.a.bk.1.4		8	55.7	even	20
3025.2.a.bk.1.5		8	55.18	even	20
3025.2.a.bl.1.4		8	55.48	odd	20
3025.2.a.bl.1.5		8	55.37	odd	20

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:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	55.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.763412 - 0.248048i) q^{2} +(-1.03494 - 1.42447i) q^{3} +(-1.09676 - 0.796845i) q^{4} +(1.42953 - 1.71943i) q^{5} +(0.436748 + 1.34417i) q^{6} +(-0.348029 + 0.479022i) q^{7} +(1.58326 + 2.17917i) q^{8} +(-0.0309674 + 0.0953077i) q^{9} +O(q^{10})\)	\(q+(-0.763412 - 0.248048i) q^{2} +(-1.03494 - 1.42447i) q^{3} +(-1.09676 - 0.796845i) q^{4} +(1.42953 - 1.71943i) q^{5} +(0.436748 + 1.34417i) q^{6} +(-0.348029 + 0.479022i) q^{7} +(1.58326 + 2.17917i) q^{8} +(-0.0309674 + 0.0953077i) q^{9} +(-1.51782 + 0.958043i) q^{10} +(1.96213 + 2.67395i) q^{11} +2.38699i q^{12} +(-1.70704 - 0.554651i) q^{13} +(0.384510 - 0.279363i) q^{14} +(-3.92875 - 0.256818i) q^{15} +(0.169713 + 0.522322i) q^{16} +(6.73074 - 2.18695i) q^{17} +(0.0472817 - 0.0650777i) q^{18} +(-1.85009 + 1.34417i) q^{19} +(-2.93798 + 0.746695i) q^{20} +1.04254 q^{21} +(-0.834650 - 2.52803i) q^{22} +1.49081i q^{23} +(1.46558 - 4.51060i) q^{24} +(-0.912887 - 4.91596i) q^{25} +(1.16560 + 0.846855i) q^{26} +(-4.85588 + 1.57777i) q^{27} +(0.763412 - 0.248048i) q^{28} +(2.89263 + 2.10162i) q^{29} +(2.93556 + 1.17058i) q^{30} +(1.90578 - 5.86539i) q^{31} -5.82804i q^{32} +(1.77828 - 5.56238i) q^{33} -5.68079 q^{34} +(0.326126 + 1.28319i) q^{35} +(0.109909 - 0.0798539i) q^{36} +(-4.31283 + 5.93610i) q^{37} +(1.74580 - 0.567246i) q^{38} +(0.976598 + 3.00566i) q^{39} +(6.01024 + 0.392882i) q^{40} +(-6.80400 + 4.94339i) q^{41} +(-0.795888 - 0.258600i) q^{42} +9.51936i q^{43} +(-0.0212704 - 4.49621i) q^{44} +(0.119606 + 0.189492i) q^{45} +(0.369792 - 1.13810i) q^{46} +(1.13540 + 1.56274i) q^{47} +(0.568389 - 0.782321i) q^{48} +(2.05478 + 6.32397i) q^{49} +(-0.522483 + 3.97934i) q^{50} +(-10.0811 - 7.32438i) q^{51} +(1.43025 + 1.96857i) q^{52} +(2.26628 + 0.736359i) q^{53} +4.09840 q^{54} +(7.40261 + 0.448742i) q^{55} -1.59489 q^{56} +(3.82947 + 1.24427i) q^{57} +(-1.68697 - 2.32192i) q^{58} +(-0.0309674 - 0.0224991i) q^{59} +(4.10427 + 3.41228i) q^{60} +(-1.06351 - 3.27314i) q^{61} +(-2.90979 + 4.00499i) q^{62} +(-0.0348769 - 0.0480039i) q^{63} +(-1.10621 + 3.40455i) q^{64} +(-3.39395 + 2.14225i) q^{65} +(-2.73729 + 3.80529i) q^{66} -6.79162i q^{67} +(-9.12469 - 2.96479i) q^{68} +(2.12361 - 1.54290i) q^{69} +(0.0693234 - 1.06050i) q^{70} +(-3.64439 - 11.2163i) q^{71} +(-0.256721 + 0.0834136i) q^{72} +(4.01031 - 5.51972i) q^{73} +(4.76490 - 3.46191i) q^{74} +(-6.05785 + 6.38809i) q^{75} +3.10021 q^{76} +(-1.96376 + 0.00929006i) q^{77} -2.53680i q^{78} +(-1.39863 + 4.30453i) q^{79} +(1.14071 + 0.454865i) q^{80} +(7.51625 + 5.46087i) q^{81} +(6.42045 - 2.08613i) q^{82} +(-5.65177 + 1.83637i) q^{83} +(-1.14342 - 0.830744i) q^{84} +(5.86148 - 14.6993i) q^{85} +(2.36125 - 7.26720i) q^{86} -6.29552i q^{87} +(-2.72042 + 8.50937i) q^{88} +6.21375 q^{89} +(-0.0443060 - 0.174328i) q^{90} +(0.859791 - 0.624675i) q^{91} +(1.18795 - 1.63507i) q^{92} +(-10.3274 + 3.35559i) q^{93} +(-0.479142 - 1.47465i) q^{94} +(-0.333554 + 5.10264i) q^{95} +(-8.30186 + 6.03166i) q^{96} +(5.11260 + 1.66119i) q^{97} -5.33748i q^{98} +(-0.315611 + 0.104201i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{9}+O(q^{10}) \) 16 * q - 4 * q^4 - 2 * q^5 - 18 * q^6 + 2 * q^9	\( 16 q - 4 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{9} - 6 q^{11} - 12 q^{14} - 16 q^{15} + 16 q^{16} + 6 q^{19} - 8 q^{20} + 8 q^{21} + 6 q^{24} - 16 q^{25} + 40 q^{26} + 2 q^{29} + 26 q^{30} + 8 q^{31} - 16 q^{34} + 22 q^{35} + 10 q^{36} + 30 q^{39} + 12 q^{40} - 52 q^{41} + 4 q^{44} + 12 q^{45} - 62 q^{46} - 10 q^{49} + 28 q^{50} - 42 q^{51} - 40 q^{54} - 8 q^{55} - 20 q^{56} + 2 q^{59} - 32 q^{60} - 40 q^{61} - 8 q^{64} - 40 q^{65} + 58 q^{66} + 26 q^{69} - 34 q^{70} + 36 q^{71} + 48 q^{74} - 20 q^{75} + 56 q^{76} + 38 q^{79} + 34 q^{80} + 68 q^{81} + 12 q^{84} + 58 q^{85} + 22 q^{86} + 24 q^{89} + 78 q^{90} - 20 q^{91} + 14 q^{94} + 48 q^{95} - 86 q^{96} - 72 q^{99}+O(q^{100}) \) 16 * q - 4 * q^4 - 2 * q^5 - 18 * q^6 + 2 * q^9 - 6 * q^11 - 12 * q^14 - 16 * q^15 + 16 * q^16 + 6 * q^19 - 8 * q^20 + 8 * q^21 + 6 * q^24 - 16 * q^25 + 40 * q^26 + 2 * q^29 + 26 * q^30 + 8 * q^31 - 16 * q^34 + 22 * q^35 + 10 * q^36 + 30 * q^39 + 12 * q^40 - 52 * q^41 + 4 * q^44 + 12 * q^45 - 62 * q^46 - 10 * q^49 + 28 * q^50 - 42 * q^51 - 40 * q^54 - 8 * q^55 - 20 * q^56 + 2 * q^59 - 32 * q^60 - 40 * q^61 - 8 * q^64 - 40 * q^65 + 58 * q^66 + 26 * q^69 - 34 * q^70 + 36 * q^71 + 48 * q^74 - 20 * q^75 + 56 * q^76 + 38 * q^79 + 34 * q^80 + 68 * q^81 + 12 * q^84 + 58 * q^85 + 22 * q^86 + 24 * q^89 + 78 * q^90 - 20 * q^91 + 14 * q^94 + 48 * q^95 - 86 * q^96 - 72 * q^99

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