LMFDB - Embedded newform 342.2.x.b.29.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(29,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([3, 17]))

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

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

chi := DirichletCharacter("342.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.x (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			29.7
Character	$\chi$	$=$	342.29
Dual form			342.2.x.b.59.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 + 0.342020i) q^{2} +(0.809890 + 1.53104i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-1.35684 + 0.239247i) q^{5} +(0.237401 + 1.71570i) q^{6} +(-0.687596 - 1.19095i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.68816 + 2.47994i) q^{9} +O(q^{10})$	\(q+(0.939693 + 0.342020i) q^{2} +(0.809890 + 1.53104i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-1.35684 + 0.239247i) q^{5} +(0.237401 + 1.71570i) q^{6} +(-0.687596 - 1.19095i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.68816 + 2.47994i) q^{9} +(-1.35684 - 0.239247i) q^{10} +6.17716i q^{11} +(-0.363721 + 1.69343i) q^{12} +(3.78361 + 0.667152i) q^{13} +(-0.238800 - 1.35430i) q^{14} +(-1.46519 - 1.88361i) q^{15} +(0.173648 + 0.984808i) q^{16} +(4.09510 - 0.722076i) q^{17} +(-2.43454 + 1.75300i) q^{18} +(-1.80509 - 3.96757i) q^{19} +(-1.19318 - 0.688886i) q^{20} +(1.26652 - 2.01728i) q^{21} +(-2.11271 + 5.80463i) q^{22} +(3.37442 - 4.02147i) q^{23} +(-0.920973 + 1.46690i) q^{24} +(-2.91469 + 1.06086i) q^{25} +(3.32725 + 1.92099i) q^{26} +(-5.16411 - 0.576153i) q^{27} +(0.238800 - 1.35430i) q^{28} +(-4.02899 - 3.38072i) q^{29} +(-0.732593 - 2.27114i) q^{30} -8.32873i q^{31} +(-0.173648 + 0.984808i) q^{32} +(-9.45747 + 5.00282i) q^{33} +(4.09510 + 0.722076i) q^{34} +(1.21789 + 1.45143i) q^{35} +(-2.88728 + 0.814621i) q^{36} -0.963873i q^{37} +(-0.339243 - 4.34568i) q^{38} +(2.04287 + 6.33317i) q^{39} +(-0.885614 - 1.05543i) q^{40} +(8.84591 + 3.21965i) q^{41} +(1.88008 - 1.46245i) q^{42} +(5.12876 - 4.30354i) q^{43} +(-3.97060 + 4.73198i) q^{44} +(1.69724 - 3.76877i) q^{45} +(4.54634 - 2.62483i) q^{46} +(2.86610 - 3.41568i) q^{47} +(-1.36714 + 1.06345i) q^{48} +(2.55442 - 4.42439i) q^{49} -3.10175 q^{50} +(4.42210 + 5.68495i) q^{51} +(2.46957 + 2.94312i) q^{52} +(0.893373 - 0.325161i) q^{53} +(-4.65562 - 2.30764i) q^{54} +(-1.47787 - 8.38142i) q^{55} +(0.687596 - 1.19095i) q^{56} +(4.61258 - 5.97696i) q^{57} +(-2.62974 - 4.55484i) q^{58} +(-7.63653 + 6.40781i) q^{59} +(0.0883623 - 2.38473i) q^{60} +(-1.74290 + 9.88446i) q^{61} +(2.84859 - 7.82645i) q^{62} +(4.11427 + 0.305314i) q^{63} +(-0.500000 + 0.866025i) q^{64} -5.29336 q^{65} +(-10.5982 + 1.46647i) q^{66} +(1.22734 + 3.37210i) q^{67} +(3.60117 + 2.07914i) q^{68} +(8.88994 + 1.90941i) q^{69} +(0.648026 + 1.78044i) q^{70} +(2.80475 + 1.02085i) q^{71} +(-2.99177 - 0.222015i) q^{72} +(5.16446 - 4.33350i) q^{73} +(0.329664 - 0.905744i) q^{74} +(-3.98479 - 3.60332i) q^{75} +(1.16753 - 4.19963i) q^{76} +(7.35670 - 4.24739i) q^{77} +(-0.246402 + 6.64993i) q^{78} +(-13.0559 + 2.30211i) q^{79} +(-0.471226 - 1.29468i) q^{80} +(-3.30025 - 8.37307i) q^{81} +(7.21125 + 6.05096i) q^{82} +(-14.8362 + 8.56566i) q^{83} +(2.26689 - 0.731222i) q^{84} +(-5.38364 + 1.95948i) q^{85} +(6.29135 - 2.28986i) q^{86} +(1.91298 - 8.90655i) q^{87} +(-5.34958 + 3.08858i) q^{88} +(3.67347 + 3.08241i) q^{89} +(2.88388 - 2.96100i) q^{90} +(-1.80705 - 4.96483i) q^{91} +(5.16991 - 0.911594i) q^{92} +(12.7516 - 6.74535i) q^{93} +(3.86148 - 2.22943i) q^{94} +(3.39845 + 4.95150i) q^{95} +(-1.64841 + 0.531724i) q^{96} +(4.23377 - 11.6322i) q^{97} +(3.91360 - 3.28390i) q^{98} +(-15.3190 - 10.4280i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{3} - 9 q^{5} - 9 q^{6} + 9 q^{7} + 24 q^{8}+O(q^{10}) $ 48 * q - 6 * q^3 - 9 * q^5 - 9 * q^6 + 9 * q^7 + 24 * q^8	$ 48 q - 6 q^{3} - 9 q^{5} - 9 q^{6} + 9 q^{7} + 24 q^{8} - 9 q^{10} - 6 q^{12} + 15 q^{13} - 6 q^{14} + 12 q^{15} - 27 q^{17} - 9 q^{18} - 12 q^{19} - 9 q^{20} - 15 q^{21} + 18 q^{22} - 3 q^{24} - 9 q^{25} + 18 q^{26} - 12 q^{27} + 6 q^{28} + 45 q^{29} - 27 q^{34} - 18 q^{35} - 3 q^{36} + 24 q^{39} + 27 q^{41} - 3 q^{42} - 15 q^{43} - 9 q^{44} - 63 q^{45} + 27 q^{46} - 27 q^{47} - 9 q^{48} - 33 q^{49} - 6 q^{50} - 42 q^{51} + 21 q^{52} + 9 q^{55} - 9 q^{56} + 36 q^{57} - 9 q^{58} - 9 q^{60} + 69 q^{61} - 3 q^{62} + 3 q^{63} - 24 q^{64} + 18 q^{65} - 6 q^{66} + 21 q^{67} + 36 q^{68} - 12 q^{69} + 27 q^{71} - 9 q^{72} + 66 q^{73} - 15 q^{74} + 24 q^{75} - 27 q^{77} + 63 q^{78} + 33 q^{79} - 9 q^{80} - 9 q^{82} - 81 q^{83} + 6 q^{84} + 18 q^{85} - 30 q^{86} - 72 q^{87} + 9 q^{88} - 18 q^{89} + 60 q^{90} + 51 q^{91} - 18 q^{92} - 84 q^{93} - 54 q^{94} - 27 q^{95} - 3 q^{96} - 108 q^{97} + 42 q^{98} + 15 q^{99}+O(q^{100}) $ 48 * q - 6 * q^3 - 9 * q^5 - 9 * q^6 + 9 * q^7 + 24 * q^8 - 9 * q^10 - 6 * q^12 + 15 * q^13 - 6 * q^14 + 12 * q^15 - 27 * q^17 - 9 * q^18 - 12 * q^19 - 9 * q^20 - 15 * q^21 + 18 * q^22 - 3 * q^24 - 9 * q^25 + 18 * q^26 - 12 * q^27 + 6 * q^28 + 45 * q^29 - 27 * q^34 - 18 * q^35 - 3 * q^36 + 24 * q^39 + 27 * q^41 - 3 * q^42 - 15 * q^43 - 9 * q^44 - 63 * q^45 + 27 * q^46 - 27 * q^47 - 9 * q^48 - 33 * q^49 - 6 * q^50 - 42 * q^51 + 21 * q^52 + 9 * q^55 - 9 * q^56 + 36 * q^57 - 9 * q^58 - 9 * q^60 + 69 * q^61 - 3 * q^62 + 3 * q^63 - 24 * q^64 + 18 * q^65 - 6 * q^66 + 21 * q^67 + 36 * q^68 - 12 * q^69 + 27 * q^71 - 9 * q^72 + 66 * q^73 - 15 * q^74 + 24 * q^75 - 27 * q^77 + 63 * q^78 + 33 * q^79 - 9 * q^80 - 9 * q^82 - 81 * q^83 + 6 * q^84 + 18 * q^85 - 30 * q^86 - 72 * q^87 + 9 * q^88 - 18 * q^89 + 60 * q^90 + 51 * q^91 - 18 * q^92 - 84 * q^93 - 54 * q^94 - 27 * q^95 - 3 * q^96 - 108 * q^97 + 42 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$3$	0.809890	+	1.53104i	0.467590	+	0.883945i
$3$	0.809890	+	1.53104i	0.467590	+	0.883945i
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	−1.35684	+	0.239247i	−0.606797	+	0.106995i	−0.468601	−	0.883410i	$-0.655242\pi$
$5$	−1.35684	+	0.239247i	−0.606797	+	0.106995i	−0.138197	+	0.990405i	$0.544131\pi$
$6$	0.237401	+	1.71570i	0.0969187	+	0.700433i
$7$	−0.687596	−	1.19095i	−0.259887	−	0.450137i	0.706324	−	0.707888i	$-0.250352\pi$
$7$	−0.687596	−	1.19095i	−0.259887	−	0.450137i	−0.966211	+	0.257751i	$0.917019\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−1.68816	+	2.47994i	−0.562719	+	0.826648i
$10$	−1.35684	−	0.239247i	−0.429070	−	0.0756567i
$11$			6.17716i			1.86248i	0.364401	+	0.931242i	$0.381274\pi$
$11$			6.17716i			1.86248i	−0.364401	+	0.931242i	$0.618726\pi$
$12$	−0.363721	+	1.69343i	−0.104997	+	0.488851i
$13$	3.78361	+	0.667152i	1.04938	+	0.185035i	0.671642	−	0.740876i	$-0.265589\pi$
$13$	3.78361	+	0.667152i	1.04938	+	0.185035i	0.377742	+	0.925911i	$0.376701\pi$
$14$	−0.238800	−	1.35430i	−0.0638219	−	0.361952i
$15$	−1.46519	−	1.88361i	−0.378310	−	0.486346i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	4.09510	−	0.722076i	0.993207	−	0.175129i	0.346650	−	0.937995i	$-0.387319\pi$
$17$	4.09510	−	0.722076i	0.993207	−	0.175129i	0.646557	+	0.762865i	$0.276208\pi$
$18$	−2.43454	+	1.75300i	−0.573827	+	0.413186i
$19$	−1.80509	−	3.96757i	−0.414117	−	0.910224i
$19$	−1.80509	−	3.96757i	−0.414117	−	0.910224i
$20$	−1.19318	−	0.688886i	−0.266804	−	0.154040i
$21$	1.26652	−	2.01728i	0.276376	−	0.440206i
$22$	−2.11271	+	5.80463i	−0.450432	+	1.23755i
$23$	3.37442	−	4.02147i	0.703615	−	0.838535i	−0.289316	−	0.957234i	$-0.593428\pi$
$23$	3.37442	−	4.02147i	0.703615	−	0.838535i	0.992930	+	0.118699i	$0.0378722\pi$
$24$	−0.920973	+	1.46690i	−0.187993	+	0.299431i
$25$	−2.91469	+	1.06086i	−0.582938	+	0.212172i
$26$	3.32725	+	1.92099i	0.652527	+	0.376737i
$27$	−5.16411	−	0.576153i	−0.993834	−	0.110881i
$28$	0.238800	−	1.35430i	0.0451289	−	0.255939i
$29$	−4.02899	−	3.38072i	−0.748165	−	0.627785i	0.186852	−	0.982388i	$-0.440171\pi$
$29$	−4.02899	−	3.38072i	−0.748165	−	0.627785i	−0.935017	+	0.354603i	$0.884616\pi$
$30$	−0.732593	−	2.27114i	−0.133753	−	0.414651i
$31$		−	8.32873i		−	1.49588i	−0.663764	−	0.747942i	$-0.731042\pi$
$31$		−	8.32873i		−	1.49588i	0.663764	−	0.747942i	$-0.268958\pi$
$32$	−0.173648	+	0.984808i	−0.0306970	+	0.174091i
$33$	−9.45747	+	5.00282i	−1.64633	+	0.870879i
$34$	4.09510	+	0.722076i	0.702303	+	0.123835i
$35$	1.21789	+	1.45143i	0.205861	+	0.245336i
$36$	−2.88728	+	0.814621i	−0.481214	+	0.135770i
$37$		−	0.963873i		−	0.158460i	−0.996856	−	0.0792299i	$-0.974754\pi$
$37$		−	0.963873i		−	0.158460i	0.996856	−	0.0792299i	$-0.0252461\pi$
$38$	−0.339243	−	4.34568i	−0.0550325	−	0.704962i
$39$	2.04287	+	6.33317i	0.327121	+	1.01412i
$40$	−0.885614	−	1.05543i	−0.140028	−	0.166879i
$41$	8.84591	+	3.21965i	1.38150	+	0.502824i	0.922632	−	0.385681i	$-0.126033\pi$
$41$	8.84591	+	3.21965i	1.38150	+	0.502824i	0.458866	+	0.888505i	$0.348256\pi$
$42$	1.88008	−	1.46245i	0.290103	−	0.225660i
$43$	5.12876	−	4.30354i	0.782128	−	0.656283i	−0.161656	−	0.986847i	$-0.551683\pi$
$43$	5.12876	−	4.30354i	0.782128	−	0.656283i	0.943784	+	0.330564i	$0.107239\pi$
$44$	−3.97060	+	4.73198i	−0.598591	+	0.713373i
$45$	1.69724	−	3.76877i	0.253009	−	0.561816i
$46$	4.54634	−	2.62483i	0.670321	−	0.387010i
$47$	2.86610	−	3.41568i	0.418063	−	0.498228i	−0.515376	−	0.856964i	$-0.672348\pi$
$47$	2.86610	−	3.41568i	0.418063	−	0.498228i	0.933439	+	0.358736i	$0.116792\pi$
$48$	−1.36714	+	1.06345i	−0.197330	+	0.153495i
$49$	2.55442	−	4.42439i	0.364917	−	0.632056i
$50$	−3.10175			−0.438653
$51$	4.42210	+	5.68495i	0.619218	+	0.796052i
$52$	2.46957	+	2.94312i	0.342468	+	0.408138i
$53$	0.893373	−	0.325161i	0.122714	−	0.0446643i	−0.279933	−	0.960019i	$-0.590312\pi$
$53$	0.893373	−	0.325161i	0.122714	−	0.0446643i	0.402647	+	0.915355i	$0.368090\pi$
$54$	−4.65562	−	2.30764i	−0.633550	−	0.314030i
$55$	−1.47787	−	8.38142i	−0.199276	−	1.13015i
$56$	0.687596	−	1.19095i	0.0918839	−	0.159148i
$57$	4.61258	−	5.97696i	0.610951	−	0.791668i
$58$	−2.62974	−	4.55484i	−0.345301	−	0.598079i
$59$	−7.63653	+	6.40781i	−0.994192	+	0.834226i	−0.986169	−	0.165742i	$-0.946998\pi$
$59$	−7.63653	+	6.40781i	−0.994192	+	0.834226i	−0.00802258	+	0.999968i	$0.502554\pi$
$60$	0.0883623	−	2.38473i	0.0114075	−	0.307868i
$61$	−1.74290	+	9.88446i	−0.223155	+	1.26558i	0.643025	+	0.765845i	$0.277679\pi$
$61$	−1.74290	+	9.88446i	−0.223155	+	1.26558i	−0.866181	+	0.499731i	$0.833432\pi$
$62$	2.84859	−	7.82645i	0.361772	−	0.993960i
$63$	4.11427	+	0.305314i	0.518349	+	0.0384659i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−5.29336			−0.656561
$66$	−10.5982	+	1.46647i	−1.30455	+	0.180510i
$67$	1.22734	+	3.37210i	0.149944	+	0.411967i	0.991810	−	0.127718i	$-0.0407654\pi$
$67$	1.22734	+	3.37210i	0.149944	+	0.411967i	−0.841867	+	0.539686i	$0.818543\pi$
$68$	3.60117	+	2.07914i	0.436706	+	0.252132i
$69$	8.88994	+	1.90941i	1.07022	+	0.229866i
$70$	0.648026	+	1.78044i	0.0774539	+	0.212803i
$71$	2.80475	+	1.02085i	0.332863	+	0.121152i	0.503044	−	0.864261i	$-0.332213\pi$
$71$	2.80475	+	1.02085i	0.332863	+	0.121152i	−0.170182	+	0.985413i	$0.554435\pi$
$72$	−2.99177	−	0.222015i	−0.352584	−	0.0261647i
$73$	5.16446	−	4.33350i	0.604455	−	0.507198i	−0.288419	−	0.957504i	$-0.593130\pi$
$73$	5.16446	−	4.33350i	0.604455	−	0.507198i	0.892874	+	0.450306i	$0.148685\pi$
$74$	0.329664	−	0.905744i	0.0383227	−	0.105291i
$75$	−3.98479	−	3.60332i	−0.460124	−	0.416076i
$76$	1.16753	−	4.19963i	0.133924	−	0.481731i
$77$	7.35670	−	4.24739i	0.838374	−	0.484035i
$78$	−0.246402	+	6.64993i	−0.0278996	+	0.752957i
$79$	−13.0559	+	2.30211i	−1.46891	+	0.259008i	−0.850136	−	0.526563i	$-0.823480\pi$
$79$	−13.0559	+	2.30211i	−1.46891	+	0.259008i	−0.618771	+	0.785571i	$0.712369\pi$
$80$	−0.471226	−	1.29468i	−0.0526846	−	0.144750i
$81$	−3.30025	−	8.37307i	−0.366694	−	0.930342i
$82$	7.21125	+	6.05096i	0.796349	+	0.668216i
$83$	−14.8362	+	8.56566i	−1.62848	+	0.940203i	−0.643933	+	0.765082i	$0.722699\pi$
$83$	−14.8362	+	8.56566i	−1.62848	+	0.940203i	−0.984547	+	0.175122i	$0.943968\pi$
$84$	2.26689	−	0.731222i	0.247338	−	0.0797829i
$85$	−5.38364	+	1.95948i	−0.583937	+	0.212536i
$86$	6.29135	−	2.28986i	0.678414	−	0.246922i
$87$	1.91298	−	8.90655i	0.205093	−	0.954883i
$88$	−5.34958	+	3.08858i	−0.570267	+	0.329244i
$89$	3.67347	+	3.08241i	0.389387	+	0.326735i	0.816374	−	0.577523i	$-0.195981\pi$
$89$	3.67347	+	3.08241i	0.389387	+	0.326735i	−0.426987	+	0.904258i	$0.640425\pi$
$90$	2.88388	−	2.96100i	0.303988	−	0.312117i
$91$	−1.80705	−	4.96483i	−0.189430	−	0.520455i
$92$	5.16991	−	0.911594i	0.539000	−	0.0950402i
$93$	12.7516	−	6.74535i	1.32228	−	0.699461i
$94$	3.86148	−	2.22943i	0.398281	−	0.229948i
$95$	3.39845	+	4.95150i	0.348674	+	0.508013i
$96$	−1.64841	+	0.531724i	−0.168241	+	0.0542688i
$97$	4.23377	−	11.6322i	0.429874	−	1.18107i	−0.516015	−	0.856580i	$-0.672585\pi$
$97$	4.23377	−	11.6322i	0.429874	−	1.18107i	0.945889	−	0.324490i	$-0.105193\pi$
$98$	3.91360	−	3.28390i	0.395334	−	0.331724i
$99$	−15.3190	−	10.4280i	−1.53962	−	1.04806i
$100$	−2.91469	−	1.06086i	−0.291469	−	0.106086i
$101$	4.57423	+	12.5676i	0.455152	+	1.25052i	0.929054	+	0.369943i	$0.120623\pi$
$101$	4.57423	+	12.5676i	0.455152	+	1.25052i	−0.473902	+	0.880578i	$0.657155\pi$
$102$	2.21105	+	6.85455i	0.218927	+	0.678702i
$103$	−4.29410	−	2.47920i	−0.423110	−	0.244283i	0.273297	−	0.961930i	$-0.411886\pi$
$103$	−4.29410	−	2.47920i	−0.423110	−	0.244283i	−0.696407	+	0.717647i	$0.745219\pi$
$104$	1.31403	+	3.61028i	0.128852	+	0.354017i
$105$	−1.23583	+	3.04013i	−0.120605	+	0.296686i
$106$	0.950708			0.0923409
$107$	−3.76080	+	6.51390i	−0.363571	+	0.629723i	−0.988546	−	0.150922i	$-0.951776\pi$
$107$	−3.76080	+	6.51390i	−0.363571	+	0.629723i	0.624975	+	0.780645i	$0.285109\pi$
$108$	−3.58560	−	3.76079i	−0.345024	−	0.361882i
$109$	4.06967	−	11.1813i	0.389804	−	1.07098i	−0.577286	−	0.816542i	$-0.695888\pi$
$109$	4.06967	−	11.1813i	0.389804	−	1.07098i	0.967090	−	0.254435i	$-0.0818896\pi$
$110$	1.47787	−	8.38142i	0.140909	−	0.799137i
$111$	1.47573	−	0.780631i	0.140070	−	0.0740942i
$112$	1.05346	−	0.883957i	0.0995425	−	0.0835261i
$113$	1.26328	+	2.18807i	0.118840	+	0.205837i	0.919308	−	0.393538i	$-0.128749\pi$
$113$	1.26328	+	2.18807i	0.118840	+	0.205837i	−0.800468	+	0.599375i	$0.795416\pi$
$114$	6.37865	−	4.03891i	0.597415	−	0.378279i
$115$	−3.61642	+	6.26382i	−0.337233	+	0.584104i
$116$	−0.913298	−	5.17957i	−0.0847976	−	0.480911i
$117$	−8.04183	+	8.25688i	−0.743467	+	0.763349i
$118$	−9.36759	+	3.40952i	−0.862357	+	0.313872i
$119$	−3.67573	−	4.38057i	−0.336954	−	0.401566i
$120$	0.898660	−	2.21069i	0.0820361	−	0.201808i
$121$	−27.1573			−2.46885
$122$	−5.01847	+	8.69225i	−0.454351	+	0.786960i
$123$	2.23481	+	16.1510i	0.201506	+	1.45629i
$124$	5.35361	−	6.38018i	0.480768	−	0.572957i
$125$	9.66688	−	5.58118i	0.864632	−	0.499196i
$126$	3.76172	+	1.69406i	0.335121	+	0.150919i
$127$	1.21166	−	1.44400i	0.107518	−	0.128135i	−0.709602	−	0.704603i	$-0.751125\pi$
$127$	1.21166	−	1.44400i	0.107518	−	0.128135i	0.817120	+	0.576468i	$0.195570\pi$
$128$	−0.766044	+	0.642788i	−0.0677094	+	0.0568149i
$129$	10.7426	+	4.36693i	0.945834	+	0.384487i
$130$	−4.97414	−	1.81044i	−0.436261	−	0.158786i
$131$	−10.7710	−	12.8364i	−0.941068	−	1.12152i	−0.992426	−	0.122840i	$-0.960800\pi$
$131$	−10.7710	−	12.8364i	−0.941068	−	1.12152i	0.0513589	−	0.998680i	$-0.483645\pi$
$132$	−10.4606	−	2.24676i	−0.910478	−	0.195556i
$133$	−3.48401	+	4.87787i	−0.302102	+	0.422965i
$134$			3.58851i			0.310000i
$135$	7.14472	−	0.453754i	0.614919	−	0.0390529i
$136$	2.67289	+	3.18542i	0.229198	+	0.273148i
$137$	−4.41070	−	0.777726i	−0.376832	−	0.0664456i	−0.0179755	−	0.999838i	$-0.505722\pi$
$137$	−4.41070	−	0.777726i	−0.376832	−	0.0664456i	−0.358856	+	0.933393i	$0.616833\pi$
$138$	7.70075	+	4.83480i	0.655531	+	0.411565i
$139$	−0.753862	+	4.27536i	−0.0639418	+	0.362632i	0.936002	+	0.351996i	$0.114497\pi$
$139$	−0.753862	+	4.27536i	−0.0639418	+	0.362632i	−0.999943	+	0.0106362i	$0.996614\pi$
$140$			1.89470i			0.160131i
$141$	7.55076	+	1.62178i	0.635888	+	0.136578i
$142$	2.28646	+	1.91856i	0.191875	+	0.161002i
$143$	−4.12111	+	23.3720i	−0.344624	+	1.95446i
$144$	−2.73541	−	1.23187i	−0.227951	−	0.102656i
$145$	6.27552	+	3.62318i	0.521154	+	0.300888i
$146$	6.33515	−	2.30581i	0.524301	−	0.190830i
$147$	8.84271	+	0.327652i	0.729334	+	0.0270243i
$148$	0.619566	−	0.738370i	0.0509280	−	0.0606936i
$149$	4.51276	−	12.3987i	0.369699	−	1.01574i	−0.605777	−	0.795635i	$-0.707137\pi$
$149$	4.51276	−	12.3987i	0.369699	−	1.01574i	0.975476	−	0.220106i	$-0.0706403\pi$
$150$	−2.51207	−	4.74889i	−0.205110	−	0.387745i
$151$	6.84124	+	3.94979i	0.556732	+	0.321430i	0.751833	−	0.659354i	$-0.229170\pi$
$151$	6.84124	+	3.94979i	0.556732	+	0.321430i	−0.195101	+	0.980783i	$0.562503\pi$
$152$	2.53347	−	3.54704i	0.205492	−	0.287703i
$153$	−5.12246	+	11.3746i	−0.414126	+	0.919581i
$154$	8.36573	−	1.47510i	0.674130	−	0.118867i
$155$	1.99263	+	11.3008i	0.160052	+	0.907698i
$156$	−2.50595	+	6.16462i	−0.200637	+	0.493565i
$157$	2.05545	+	11.6570i	0.164043	+	0.930333i	0.950046	+	0.312111i	$0.101036\pi$
$157$	2.05545	+	11.6570i	0.164043	+	0.930333i	−0.786003	+	0.618223i	$0.787853\pi$
$158$	−13.0559	−	2.30211i	−1.03867	−	0.183146i
$159$	1.22137	+	1.10444i	0.0968608	+	0.0875881i
$160$		−	1.37777i		−	0.108922i
$161$	−7.10962	−	1.25362i	−0.560316	−	0.0987989i
$162$	−0.237459	−	8.99687i	−0.0186566	−	0.706861i
$163$	−3.79491	−	6.57298i	−0.297240	−	0.514835i	0.678263	−	0.734819i	$-0.262733\pi$
$163$	−3.79491	−	6.57298i	−0.297240	−	0.514835i	−0.975504	+	0.219984i	$0.929400\pi$
$164$	4.70681	+	8.15243i	0.367540	+	0.636598i
$165$	11.6354	−	9.05070i	0.905812	−	0.704596i
$166$	−16.8711	+	2.97482i	−1.30945	+	0.230891i
$167$	−4.34925	−	3.64946i	−0.336555	−	0.282403i	0.458809	−	0.888535i	$-0.348276\pi$
$167$	−4.34925	−	3.64946i	−0.336555	−	0.282403i	−0.795365	+	0.606131i	$0.792721\pi$
$168$	2.38027	+	0.0881969i	0.183642	+	0.00680454i
$169$	1.65459	+	0.602223i	0.127277	+	0.0463249i
$170$	−5.72915			−0.439405
$171$	12.8866	+	2.22136i	0.985466	+	0.169871i
$172$	6.69511			0.510498
$173$	0.647152	+	0.235544i	0.0492021	+	0.0179081i	0.366504	−	0.930416i	$-0.380555\pi$
$173$	0.647152	+	0.235544i	0.0492021	+	0.0179081i	−0.317302	+	0.948325i	$0.602777\pi$
$174$	4.84383	−	7.71514i	0.367210	−	0.584883i
$175$	3.26756	+	2.74181i	0.247004	+	0.207261i
$176$	−6.08332	+	1.07265i	−0.458547	+	0.0808542i
$177$	−15.9954	−	6.50220i	−1.20228	−	0.488736i
$178$	2.39769	+	4.15292i	0.179714	+	0.311274i
$179$	−5.62387	−	9.74082i	−0.420347	−	0.728063i	0.575626	−	0.817713i	$-0.304758\pi$
$179$	−5.62387	−	9.74082i	−0.420347	−	0.728063i	−0.995973	+	0.0896501i	$0.971425\pi$
$180$	3.72268	−	1.79608i	0.277472	−	0.133872i
$181$	14.4736	+	2.55208i	1.07581	+	0.189694i	0.683362	−	0.730080i	$-0.260517\pi$
$181$	14.4736	+	2.55208i	1.07581	+	0.189694i	0.392448	+	0.919774i	$0.371628\pi$
$182$		−	5.28346i		−	0.391636i
$183$	−16.5450	+	5.33688i	−1.22305	+	0.394514i
$184$	5.16991	+	0.911594i	0.381131	+	0.0672036i
$185$	0.230604	+	1.30782i	0.0169544	+	0.0961529i
$186$	14.2896	−	1.97725i	1.04777	−	0.144979i
$187$	4.46038	+	25.2961i	0.326175	+	1.84983i
$188$	4.39111	−	0.774272i	0.320255	−	0.0564696i
$189$	2.86465	+	6.54637i	0.208373	+	0.476178i
$190$	1.49999	+	5.81523i	0.108821	+	0.421881i
$191$	−0.127187	−	0.0734315i	−0.00920294	−	0.00531332i	0.495391	−	0.868670i	$-0.335025\pi$
$191$	−0.127187	−	0.0734315i	−0.00920294	−	0.00531332i	−0.504594	+	0.863357i	$0.668358\pi$
$192$	−1.73086	−	0.0641342i	−0.124914	−	0.00462849i
$193$	−0.655025	+	1.79967i	−0.0471497	+	0.129543i	−0.961033	−	0.276435i	$-0.910847\pi$
$193$	−0.655025	+	1.79967i	−0.0471497	+	0.129543i	0.913883	+	0.405978i	$0.133069\pi$
$194$	7.95689	−	9.48265i	0.571271	−	0.680815i
$195$	−4.28704	−	8.10435i	−0.307001	−	0.580364i
$196$	4.80074	−	1.74733i	0.342910	−	0.124809i
$197$	−18.7456	−	10.8228i	−1.33557	−	0.771093i	−0.349424	−	0.936965i	$-0.613623\pi$
$197$	−18.7456	−	10.8228i	−1.33557	−	0.771093i	−0.986147	+	0.165872i	$0.946956\pi$
$198$	−10.8286	−	15.0385i	−0.769553	−	1.06874i
$199$	−2.15239	+	12.2068i	−0.152579	+	0.865317i	0.808388	+	0.588651i	$0.200341\pi$
$199$	−2.15239	+	12.2068i	−0.152579	+	0.865317i	−0.960966	+	0.276666i	$0.910770\pi$
$200$	−2.37608	−	1.99376i	−0.168014	−	0.140980i
$201$	−4.16880	+	4.61014i	−0.294044	+	0.325174i
$202$			13.3741i			0.941001i
$203$	−1.25596	+	7.12291i	−0.0881511	+	0.499930i
$204$	−0.266687	+	7.19740i	−0.0186719	+	0.503919i
$205$	−12.7728	−	2.25218i	−0.892089	−	0.157299i
$206$	−3.18720	−	3.79835i	−0.222063	−	0.264644i
$207$	4.27648	+	15.1572i	0.297236	+	1.05350i
$208$			3.84198i			0.266393i
$209$	24.5083	−	11.1504i	1.69528	−	0.771286i
$210$	−2.20109	+	2.43411i	−0.151889	+	0.167970i
$211$	−0.253960	−	0.302658i	−0.0174833	−	0.0208358i	0.757232	−	0.653146i	$-0.226551\pi$
$211$	−0.253960	−	0.302658i	−0.0174833	−	0.0208358i	−0.774715	+	0.632310i	$0.782107\pi$
$212$	0.893373	+	0.325161i	0.0613571	+	0.0223322i
$213$	0.708585	+	5.12096i	0.0485514	+	0.350882i
$214$	−5.76189	+	4.83480i	−0.393874	+	0.330500i
$215$	−5.92929	+	7.06625i	−0.404374	+	0.481914i
$216$	−2.08309	−	4.76033i	−0.141737	−	0.323899i
$217$	−9.91912	+	5.72681i	−0.673354	+	0.388761i
$218$	7.64848	−	9.11511i	0.518021	−	0.617353i
$219$	10.8174	+	4.39734i	0.730972	+	0.297144i
$220$	4.25536	−	7.37050i	0.286896	−	0.496919i
$221$	15.9760			1.07466
$222$	1.65372	−	0.228825i	0.110990	−	0.0153577i
$223$	9.27539	+	11.0540i	0.621126	+	0.740229i	0.981264	−	0.192670i	$-0.0617146\pi$
$223$	9.27539	+	11.0540i	0.621126	+	0.740229i	−0.360137	+	0.932899i	$0.617270\pi$
$224$	1.29226	−	0.470344i	0.0863427	−	0.0314262i
$225$	2.28958	−	9.01916i	0.152639	−	0.601278i
$226$	0.438734	+	2.48818i	0.0291842	+	0.165512i
$227$	−1.55430	+	2.69212i	−0.103162	+	0.178683i	−0.912986	−	0.407991i	$-0.866229\pi$
$227$	−1.55430	+	2.69212i	−0.103162	+	0.178683i	0.809824	+	0.586674i	$0.199563\pi$
$228$	7.37536	−	1.61371i	0.488445	−	0.106871i
$229$	−1.35406	−	2.34529i	−0.0894785	−	0.154981i	0.817812	−	0.575485i	$-0.195187\pi$
$229$	−1.35406	−	2.34529i	−0.0894785	−	0.154981i	−0.907291	+	0.420504i	$0.861853\pi$
$230$	−5.54067	+	4.64917i	−0.365341	+	0.306557i
$231$	12.4610	+	7.82347i	0.819876	+	0.514747i
$232$	0.913298	−	5.17957i	0.0599609	−	0.340055i
$233$	−1.45101	+	3.98661i	−0.0950587	+	0.261172i	−0.978104	−	0.208116i	$-0.933267\pi$
$233$	−1.45101	+	3.98661i	−0.0950587	+	0.261172i	0.883045	+	0.469287i	$0.155489\pi$
$234$	−10.3809	+	5.00846i	−0.678618	+	0.327413i
$235$	−3.07164	+	5.32024i	−0.200372	+	0.347054i
$236$	−9.96878			−0.648913
$237$	−14.0985	−	18.1247i	−0.915795	−	1.17732i
$238$	−1.95582	−	5.37356i	−0.126777	−	0.348316i
$239$	−18.4023	−	10.6246i	−1.19035	−	0.687248i	−0.231963	−	0.972725i	$-0.574515\pi$
$239$	−18.4023	−	10.6246i	−1.19035	−	0.687248i	−0.958386	+	0.285476i	$0.907848\pi$
$240$	1.60057	−	1.77001i	0.103316	−	0.114254i
$241$	−2.46429	−	6.77059i	−0.158739	−	0.436132i	0.834671	−	0.550749i	$-0.185658\pi$
$241$	−2.46429	−	6.77059i	−0.158739	−	0.436132i	−0.993410	+	0.114617i	$0.963436\pi$
$242$	−25.5195	−	9.28835i	−1.64046	−	0.597078i
$243$	10.1467	−	11.8341i	0.650909	−	0.759156i
$244$	−7.68875	+	6.45163i	−0.492222	+	0.413023i
$245$	−2.40742	+	6.61433i	−0.153804	+	0.422574i
$246$	−3.42393	+	15.9413i	−0.218302	+	1.01638i
$247$	−4.18279	−	16.2160i	−0.266145	−	1.03180i
$248$	7.21289	−	4.16437i	0.458019	−	0.264437i
$249$	−25.1300	−	15.7775i	−1.59255	−	0.999858i
$250$	10.9928	−	1.93832i	0.695244	−	0.122590i
$251$	7.58363	+	20.8359i	0.478675	+	1.31515i	0.910619	+	0.413248i	$0.135606\pi$
$251$	7.58363	+	20.8359i	0.478675	+	1.31515i	−0.431944	+	0.901900i	$0.642172\pi$
$252$	2.95546	+	2.87848i	0.186176	+	0.181327i
$253$	24.8413	+	20.8443i	1.56176	+	1.31047i
$254$	1.63247	−	0.942507i	0.102430	−	0.0591382i
$255$	−7.36020	−	6.65559i	−0.460913	−	0.416789i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−13.2302	+	4.81541i	−0.825279	+	0.300377i	−0.719920	−	0.694057i	$-0.755821\pi$
$257$	−13.2302	+	4.81541i	−0.825279	+	0.300377i	−0.105359	+	0.994434i	$0.533599\pi$
$258$	8.60117	+	7.77776i	0.535485	+	0.484222i
$259$	−1.14793	+	0.662756i	−0.0713287	+	0.0411816i
$260$	−4.05495	−	3.40251i	−0.251477	−	0.211015i
$261$	15.1856	−	4.28448i	0.939964	−	0.265202i
$262$	−5.73113	−	15.7462i	−0.354071	−	0.972801i
$263$	−24.3756	+	4.29808i	−1.50307	+	0.265031i	−0.863753	−	0.503915i	$-0.831892\pi$
$263$	−24.3756	+	4.29808i	−1.50307	+	0.265031i	−0.639313	+	0.768946i	$0.720781\pi$
$264$	−9.06130	−	5.68900i	−0.557685	−	0.350134i
$265$	−1.13437	+	0.654929i	−0.0696838	+	0.0402320i
$266$	−4.94223	+	3.39209i	−0.303028	+	0.207983i
$267$	−1.74418	+	8.12064i	−0.106742	+	0.496975i
$268$	−1.22734	+	3.37210i	−0.0749719	+	0.205984i
$269$	−0.834822	+	0.700499i	−0.0509000	+	0.0427102i	−0.667883	−	0.744266i	$-0.732799\pi$
$269$	−0.834822	+	0.700499i	−0.0509000	+	0.0427102i	0.616983	+	0.786977i	$0.288355\pi$
$270$	6.86903	+	2.01725i	0.418036	+	0.122766i
$271$	11.6354	+	4.23493i	0.706799	+	0.257254i	0.670311	−	0.742080i	$-0.266161\pi$
$271$	11.6354	+	4.23493i	0.706799	+	0.257254i	0.0364879	+	0.999334i	$0.488383\pi$
$272$	1.42221	+	3.90750i	0.0862343	+	0.236927i
$273$	6.13783	−	6.78762i	0.371478	−	0.410806i
$274$	−3.87871	−	2.23937i	−0.234321	−	0.135285i
$275$	−6.55310	−	18.0045i	−0.395167	−	1.08571i
$276$	5.58274	+	7.17704i	0.336041	+	0.432007i
$277$	29.7528			1.78767			0.893835	−	0.448396i	$-0.148005\pi$
$277$	29.7528			1.78767			0.893835	+	0.448396i	$0.148005\pi$
$278$	−2.17066	+	3.75969i	−0.130188	+	0.225491i
$279$	20.6548	+	14.0602i	1.23657	+	0.841763i
$280$	−0.648026	+	1.78044i	−0.0387270	+	0.106401i
$281$	2.73752	−	15.5253i	0.163307	−	0.926160i	−0.787486	−	0.616333i	$-0.788618\pi$
$281$	2.73752	−	15.5253i	0.163307	−	0.926160i	0.950793	−	0.309827i	$-0.100271\pi$
$282$	6.54071	+	4.10648i	0.389494	+	0.244538i
$283$	−11.6653	+	9.78834i	−0.693430	+	0.581857i	−0.919896	−	0.392162i	$-0.871727\pi$
$283$	−11.6653	+	9.78834i	−0.693430	+	0.581857i	0.226466	+	0.974019i	$0.427283\pi$
$284$	1.49238	+	2.58487i	0.0885563	+	0.153384i
$285$	−4.82856	+	9.21333i	−0.286019	+	0.545751i
$286$	−11.8663	+	20.5530i	−0.701666	+	1.21532i
$287$	−2.24797	−	12.7489i	−0.132693	−	0.752542i
$288$	−2.14912	−	2.09315i	−0.126638	−	0.123340i
$289$	0.273654	−	0.0996020i	0.0160973	−	0.00585894i
$290$	4.65786	+	5.55103i	0.273519	+	0.325967i
$291$	21.2382	−	2.93872i	1.24501	−	0.172271i
$292$	6.74173			0.394530
$293$	−3.32832	+	5.76482i	−0.194443	+	0.336785i	−0.946718	−	0.322065i	$-0.895623\pi$
$293$	−3.32832	+	5.76482i	−0.194443	+	0.336785i	0.752275	+	0.658849i	$0.228956\pi$
$294$	8.19737	+	3.33228i	0.478080	+	0.194342i
$295$	8.82850	−	10.5214i	0.514015	−	0.612579i
$296$	0.834739	−	0.481937i	0.0485182	−	0.0280120i
$297$	3.55899	−	31.8995i	0.206513	−	1.85100i
$298$	8.48121	−	10.1075i	0.491303	−	0.585512i
$299$	15.4504	−	12.9644i	0.893520	−	0.749752i
$300$	−0.736359	−	5.32168i	−0.0425137	−	0.307247i
$301$	−8.65182	−	3.14900i	−0.498683	−	0.181506i
$302$	5.07775	+	6.05143i	0.292192	+	0.348221i
$303$	−15.5368	+	17.1817i	−0.892568	+	0.987061i
$304$	3.59385	−	2.46663i	0.206121	−	0.141471i
$305$		−	13.8286i		−	0.791824i
$306$	−8.70388	+	8.93664i	−0.497568	+	0.510873i
$307$	−9.28943	−	11.0707i	−0.530176	−	0.631839i	0.432780	−	0.901500i	$-0.357533\pi$
$307$	−9.28943	−	11.0707i	−0.530176	−	0.631839i	−0.962955	+	0.269661i	$0.913088\pi$
$308$	8.36573	+	1.47510i	0.476682	+	0.0840519i
$309$	0.318003	−	8.58231i	0.0180906	−	0.488230i
$310$	−1.99263	+	11.3008i	−0.113174	+	0.641840i
$311$		−	31.4299i		−	1.78223i	−0.453779	−	0.891114i	$-0.649925\pi$
$311$		−	31.4299i		−	1.78223i	0.453779	−	0.891114i	$-0.350075\pi$
$312$	−4.46325	+	4.93576i	−0.252682	+	0.279432i
$313$	21.3600	+	17.9231i	1.20734	+	1.01308i	0.999390	+	0.0349352i	$0.0111225\pi$
$313$	21.3600	+	17.9231i	1.20734	+	1.01308i	0.207947	+	0.978140i	$0.433322\pi$
$314$	−2.05545	+	11.6570i	−0.115996	+	0.657845i
$315$	−5.65544	+	0.570066i	−0.318648	+	0.0321196i
$316$	−11.4812	−	6.62867i	−0.645868	−	0.372892i
$317$	−10.8922	+	3.96444i	−0.611767	+	0.222665i	−0.629276	−	0.777182i	$-0.716649\pi$
$317$	−10.8922	+	3.96444i	−0.611767	+	0.222665i	0.0175090	+	0.999847i	$0.494426\pi$
$318$	0.769968	+	1.45557i	0.0431777	+	0.0816243i
$319$	20.8833	−	24.8877i	1.16924	−	1.39344i
$320$	0.471226	−	1.29468i	0.0263423	−	0.0723749i
$321$	−13.0189	−	0.482392i	−0.726643	−	0.0269245i
$322$	−6.25209	−	3.60965i	−0.348416	−	0.201158i
$323$	−10.2569	−	14.9442i	−0.570711	−	0.831517i
$324$	2.85397	−	8.53551i	0.158554	−	0.474195i
$325$	−11.7358	+	2.06934i	−0.650985	+	0.114786i
$326$	−1.31796	−	7.47452i	−0.0729950	−	0.413975i
$327$	20.4150	−	2.82482i	1.12895	−	0.156213i
$328$	1.63466	+	9.27060i	0.0902589	+	0.511883i
$329$	−6.03863	−	1.06477i	−0.332920	−	0.0587028i
$330$	14.0292	−	4.52535i	0.772281	−	0.249112i
$331$		−	20.0472i		−	1.10190i	−0.834540	−	0.550948i	$-0.814266\pi$
$331$		−	20.0472i		−	1.10190i	0.834540	−	0.550948i	$-0.185734\pi$
$332$	−16.8711	−	2.97482i	−0.925920	−	0.163265i
$333$	2.39035	+	1.62717i	0.130990	+	0.0891683i
$334$	−2.83877	−	4.91690i	−0.155331	−	0.269041i
$335$	−2.47207	−	4.28176i	−0.135064	−	0.233937i
$336$	2.20656	+	0.896978i	0.120378	+	0.0489342i
$337$	−0.739272	+	0.130354i	−0.0402707	+	0.00710081i	−0.193747	−	0.981051i	$-0.562064\pi$
$337$	−0.739272	+	0.130354i	−0.0402707	+	0.00710081i	0.153477	+	0.988152i	$0.450953\pi$
$338$	1.34884	+	1.13181i	0.0733671	+	0.0615623i
$339$	−2.32690	+	3.70624i	−0.126380	+	0.201295i
$340$	−5.38364	−	1.95948i	−0.291969	−	0.106268i
$341$	51.4479			2.78606
$342$	11.3497	+	6.49488i	0.613723	+	0.351203i
$343$	−16.6520			−0.899123
$344$	6.29135	+	2.28986i	0.339207	+	0.123461i
$345$	−12.5190	−	0.463872i	−0.674003	−	0.0249740i
$346$	0.527563	+	0.442678i	0.0283620	+	0.0237985i
$347$	13.0793	−	2.30623i	0.702133	−	0.123805i	0.188826	−	0.982010i	$-0.439532\pi$
$347$	13.0793	−	2.30623i	0.702133	−	0.123805i	0.513306	+	0.858206i	$0.328421\pi$
$348$	7.19045	−	5.59317i	0.385449	−	0.299826i
$349$	−1.34868	−	2.33598i	−0.0721931	−	0.125042i	0.827669	−	0.561216i	$-0.189666\pi$
$349$	−1.34868	−	2.33598i	−0.0721931	−	0.125042i	−0.899862	+	0.436174i	$0.856333\pi$
$350$	2.13275	+	3.69403i	0.114000	+	0.197454i
$351$	−19.1546	−	5.62518i	−1.02240	−	0.300250i
$352$	−6.08332	−	1.07265i	−0.324242	−	0.0571726i
$353$		−	10.8725i		−	0.578685i	−0.957226	−	0.289343i	$-0.906563\pi$
$353$		−	10.8725i		−	0.578685i	0.957226	−	0.289343i	$-0.0934367\pi$
$354$	−12.8068	−	11.5808i	−0.680675	−	0.615513i
$355$	−4.04984	−	0.714095i	−0.214943	−	0.0379002i
$356$	0.832709	+	4.72252i	0.0441335	+	0.250293i
$357$	3.72988	−	9.17546i	0.197406	−	0.485617i
$358$	−1.95315	−	11.0769i	−0.103227	−	0.585430i
$359$	4.70326	−	0.829312i	0.248229	−	0.0437694i	−0.0481492	−	0.998840i	$-0.515332\pi$
$359$	4.70326	−	0.829312i	0.248229	−	0.0437694i	0.296378	+	0.955071i	$0.404221\pi$
$360$	4.11247	−	0.414535i	0.216746	−	0.0218479i
$361$	−12.4833	+	14.3237i	−0.657014	+	0.753878i
$362$	12.7278	+	7.34841i	0.668960	+	0.386224i
$363$	−21.9944	−	41.5789i	−1.15441	−	2.18233i
$364$	1.80705	−	4.96483i	0.0947151	−	0.260228i
$365$	−5.97057	+	7.11545i	−0.312514	+	0.372440i
$366$	−17.3726	−	0.643712i	−0.908079	−	0.0336474i
$367$	−26.5415	+	9.66032i	−1.38546	+	0.504264i	−0.923827	−	0.382809i	$-0.874957\pi$
$367$	−26.5415	+	9.66032i	−1.38546	+	0.504264i	−0.461628	+	0.887074i	$0.652734\pi$
$368$	4.54634	+	2.62483i	0.236994	+	0.136829i
$369$	−22.9178	+	16.5021i	−1.19305	+	0.859064i
$370$	−0.230604	+	1.30782i	−0.0119885	+	0.0679904i
$371$	−1.00153	−	0.840385i	−0.0519969	−	0.0436306i
$372$	14.1041	+	3.02934i	0.731265	+	0.157064i
$373$			20.3739i			1.05492i	0.849579	+	0.527461i	$0.176856\pi$
$373$			20.3739i			1.05492i	−0.849579	+	0.527461i	$0.823144\pi$
$374$	−4.46038	+	25.2961i	−0.230641	+	1.30803i
$375$	16.3741	+	10.2802i	0.845555	+	0.530869i
$376$	4.39111	+	0.774272i	0.226454	+	0.0399300i
$377$	−12.9887	−	15.4793i	−0.668950	−	0.797224i
$378$	0.452904	+	7.13134i	0.0232949	+	0.366797i
$379$		−	30.0101i		−	1.54151i	−0.637129	−	0.770757i	$-0.719878\pi$
$379$		−	30.0101i		−	1.54151i	0.637129	−	0.770757i	$-0.280122\pi$
$380$	−0.579394	+	5.97755i	−0.0297223	+	0.306642i
$381$	3.19214	+	0.685619i	0.163538	+	0.0351254i
$382$	−0.0944017	−	0.112504i	−0.00483001	−	0.00575618i
$383$	15.5379	+	5.65533i	0.793949	+	0.288974i	0.706976	−	0.707237i	$-0.250059\pi$
$383$	15.5379	+	5.65533i	0.793949	+	0.288974i	0.0869721	+	0.996211i	$0.472281\pi$
$384$	−1.60454	−	0.652256i	−0.0818815	−	0.0332853i
$385$	−8.96569	+	7.52311i	−0.456934	+	0.383413i
$386$	−1.23104	+	1.46710i	−0.0626585	+	0.0746735i
$387$	2.01438	+	19.9841i	0.102397	+	1.01585i
$388$	10.7203	−	6.18936i	0.544240	−	0.314217i
$389$	6.87883	−	8.19787i	0.348771	−	0.415649i	−0.562930	−	0.826505i	$-0.690326\pi$
$389$	6.87883	−	8.19787i	0.348771	−	0.415649i	0.911700	+	0.410856i	$0.134770\pi$
$390$	−1.25665	−	9.08185i	−0.0636330	−	0.459877i
$391$	10.9148	−	18.9049i	0.551983	−	0.956062i
$392$	5.10884			0.258036
$393$	10.9297	−	26.8869i	0.551329	−	1.35626i
$394$	−13.9135	−	16.5815i	−0.700953	−	0.835364i
$395$	17.1640	−	6.24720i	0.863616	−	0.314331i
$396$	−5.03204	−	17.8352i	−0.252870	−	0.896253i
$397$	−1.62939	−	9.24072i	−0.0817767	−	0.463779i	−0.998006	−	0.0631237i	$-0.979894\pi$
$397$	−1.62939	−	9.24072i	−0.0817767	−	0.463779i	0.916229	−	0.400655i	$-0.131217\pi$
$398$	−6.19755	+	10.7345i	−0.310655	+	0.538071i
$399$	−10.2899	−	1.38362i	−0.515138	−	0.0692678i
$400$	−1.55087	−	2.68619i	−0.0775437	−	0.134310i
$401$	−9.03232	+	7.57901i	−0.451052	+	0.378478i	−0.839826	−	0.542855i	$-0.817343\pi$
$401$	−9.03232	+	7.57901i	−0.451052	+	0.378478i	0.388774	+	0.921333i	$0.372899\pi$
$402$	−5.49415	+	2.90630i	−0.274023	+	0.144953i
$403$	5.55653	−	31.5127i	0.276791	−	1.56976i
$404$	−4.57423	+	12.5676i	−0.227576	+	0.625261i
$405$	6.48115	+	10.5713i	0.322051	+	0.525294i
$406$	−3.61639	+	6.26378i	−0.179479	+	0.310866i
$407$	5.95400			0.295129
$408$	−2.71226	+	6.67213i	−0.134277	+	0.330320i
$409$	7.42665	+	20.4046i	0.367224	+	1.00894i	0.976412	+	0.215914i	$0.0692732\pi$
$409$	7.42665	+	20.4046i	0.367224	+	1.00894i	−0.609188	+	0.793026i	$0.708505\pi$
$410$	−11.2322	−	6.48491i	−0.554718	−	0.320267i
$411$	−2.38145	−	7.38283i	−0.117468	−	0.364168i
$412$	−1.69587	−	4.65937i	−0.0835496	−	0.229551i
$413$	12.8822	+	4.68875i	0.633894	+	0.230719i
$414$	−1.16550	+	15.7058i	−0.0572814	+	0.771898i
$415$	18.0810	−	15.1717i	0.887560	−	0.744752i
$416$	−1.31403	+	3.61028i	−0.0644258	+	0.177008i
$417$	−7.15629	+	2.30838i	−0.350445	+	0.113042i
$418$	26.8440	−	2.09556i	1.31298	−	0.102497i
$419$	13.9740	−	8.06788i	0.682674	−	0.394142i	−0.118188	−	0.992991i	$-0.537708\pi$
$419$	13.9740	−	8.06788i	0.682674	−	0.394142i	0.800862	+	0.598849i	$0.204375\pi$
$420$	−2.90086	+	1.53450i	−0.141547	+	0.0748759i
$421$	−1.25437	+	0.221180i	−0.0611344	+	0.0107796i	−0.204132	−	0.978943i	$-0.565437\pi$
$421$	−1.25437	+	0.221180i	−0.0611344	+	0.0107796i	0.142997	+	0.989723i	$0.454326\pi$
$422$	−0.135129	−	0.371265i	−0.00657800	−	0.0180729i
$423$	3.63227	+	12.8740i	0.176607	+	0.625953i
$424$	0.728284	+	0.611103i	0.0353686	+	0.0296778i
$425$	−11.1699	+	6.44895i	−0.541820	+	0.312820i
$426$	−1.08562	+	5.05448i	−0.0525984	+	0.244890i
$427$	12.9703	−	4.72081i	0.627678	−	0.228456i
$428$	−7.06800	+	2.57254i	−0.341645	+	0.124348i
$429$	−39.1210	+	12.6191i	−1.88878	+	0.609258i
$430$	−7.98851	+	4.61217i	−0.385240	+	0.222419i
$431$	17.9703	+	15.0789i	0.865601	+	0.726325i	0.963167	−	0.268904i	$-0.0866613\pi$
$431$	17.9703	+	15.0789i	0.865601	+	0.726325i	−0.0975662	+	0.995229i	$0.531106\pi$
$432$	−0.329339	−	5.18570i	−0.0158453	−	0.249497i
$433$	9.28703	+	25.5159i	0.446306	+	1.22622i	0.935277	+	0.353916i	$0.115150\pi$
$433$	9.28703	+	25.5159i	0.446306	+	1.22622i	−0.488971	+	0.872300i	$0.662628\pi$
$434$	−11.2796	+	1.98890i	−0.541438	+	0.0954702i
$435$	−0.464739	+	12.5424i	−0.0222825	+	0.601364i
$436$	10.3048	−	5.94946i	0.493509	−	0.284928i
$437$	−22.0466	−	6.12911i	−1.05463	−	0.293195i
$438$	8.66105	+	7.83191i	0.413841	+	0.374223i
$439$	9.00419	−	24.7388i	0.429746	−	1.18072i	−0.516221	−	0.856456i	$-0.672662\pi$
$439$	9.00419	−	24.7388i	0.429746	−	1.18072i	0.945967	−	0.324263i	$-0.105116\pi$
$440$	6.51959	−	5.47058i	0.310809	−	0.260800i
$441$	6.65997	+	13.8039i	0.317142	+	0.657328i
$442$	15.0125	+	5.46411i	0.714072	+	0.259901i
$443$	3.94805	+	10.8472i	0.187578	+	0.515365i	0.997460	−	0.0712268i	$-0.0226914\pi$
$443$	3.94805	+	10.8472i	0.187578	+	0.515365i	−0.809882	+	0.586592i	$0.800469\pi$
$444$	1.63225	+	0.350581i	0.0774633	+	0.0166378i
$445$	−5.72177	−	3.30347i	−0.271238	−	0.156599i
$446$	4.93533	+	13.5597i	0.233695	+	0.642071i
$447$	22.6377	−	3.13237i	1.07073	−	0.148156i
$448$	1.37519			0.0649718
$449$	11.8654	−	20.5514i	0.559962	−	0.969883i	−0.437537	−	0.899201i	$-0.644149\pi$
$449$	11.8654	−	20.5514i	0.559962	−	0.969883i	0.997499	−	0.0706823i	$-0.0225177\pi$
$450$	5.23624	−	7.69216i	0.246839	−	0.362612i
$451$	−19.8883	+	54.6426i	−0.936502	+	2.57302i
$452$	−0.438734	+	2.48818i	−0.0206363	+	0.117034i
$453$	−0.506634	+	13.6731i	−0.0238037	+	0.642418i
$454$	−2.38132	+	1.99817i	−0.111761	+	0.0937787i
$455$	3.63970	+	6.30414i	0.170632	+	0.295543i
$456$	7.48249	+	1.00613i	0.350400	+	0.0471164i
$457$	−3.80360	+	6.58803i	−0.177925	+	0.308175i	−0.941170	−	0.337935i	$-0.890272\pi$
$457$	−3.80360	+	6.58803i	−0.177925	+	0.308175i	0.763245	+	0.646110i	$0.223605\pi$
$458$	−0.470259	−	2.66697i	−0.0219737	−	0.124619i
$459$	−21.5636	+	1.36948i	−1.00650	+	0.0639219i
$460$	−6.79664	+	2.47377i	−0.316895	+	0.115340i
$461$	−11.7463	−	13.9987i	−0.547078	−	0.651982i	0.419681	−	0.907672i	$-0.362142\pi$
$461$	−11.7463	−	13.9987i	−0.547078	−	0.651982i	−0.966759	+	0.255690i	$0.917698\pi$
$462$	9.03376	+	11.6136i	0.420289	+	0.540313i
$463$	−7.47850			−0.347556			−0.173778	−	0.984785i	$-0.555597\pi$
$463$	−7.47850			−0.347556			−0.173778	+	0.984785i	$0.555597\pi$
$464$	2.62974	−	4.55484i	0.122082	−	0.211453i
$465$	−15.6881	+	12.2032i	−0.727517	+	0.565908i
$466$	−2.72700	+	3.24992i	−0.126326	+	0.150549i
$467$	−11.0195	+	6.36212i	−0.509922	+	0.294404i	−0.732802	−	0.680442i	$-0.761788\pi$
$467$	−11.0195	+	6.36212i	−0.509922	+	0.294404i	0.222879	+	0.974846i	$0.428454\pi$
$468$	−11.4678	+	1.15595i	−0.530100	+	0.0534338i
$469$	3.17209	−	3.78035i	0.146473	−	0.174560i
$470$	−4.70602	+	3.94882i	−0.217073	+	0.182146i
$471$	−16.1827	+	12.5879i	−0.745659	+	0.580020i
$472$	−9.36759	−	3.40952i	−0.431178	−	0.156936i
$473$	26.5836	+	31.6811i	1.22232	+	1.45670i
$474$	−7.04924	−	21.8536i	−0.323782	−	1.00377i
$475$	9.47032	+	9.64929i	0.434528	+	0.442740i
$476$		−	5.71842i		−	0.262104i
$477$	−0.701773	+	2.76444i	−0.0321320	+	0.126575i
$478$	−13.6587	−	16.2778i	−0.624736	−	0.744531i
$479$	−14.1188	−	2.48953i	−0.645105	−	0.113749i	−0.158483	−	0.987362i	$-0.550660\pi$
$479$	−14.1188	−	2.48953i	−0.645105	−	0.113749i	−0.486623	+	0.873612i	$0.661771\pi$
$480$	2.10942	−	1.11584i	0.0962814	−	0.0509310i
$481$	0.643050	−	3.64692i	0.0293206	−	0.166285i
$482$		−	7.20511i		−	0.328184i
$483$	−3.83867	−	11.9004i	−0.174666	−	0.541487i
$484$	−20.8037	−	17.4564i	−0.945623	−	0.793472i
$485$	−2.96158	+	16.7959i	−0.134478	+	0.762664i
$486$	13.5822	−	7.65003i	0.616103	−	0.347012i
$487$	−8.34212	−	4.81632i	−0.378017	−	0.218248i	0.298938	−	0.954273i	$-0.403368\pi$
$487$	−8.34212	−	4.81632i	−0.378017	−	0.218248i	−0.676955	+	0.736024i	$0.736701\pi$
$488$	−9.43165	+	3.43284i	−0.426951	+	0.155397i
$489$	6.99002	−	11.1335i	0.316100	−	0.503476i
$490$	−4.52447	+	5.39205i	−0.204395	+	0.243588i
$491$	−12.4633	+	34.2426i	−0.562461	+	1.54535i	0.253556	+	0.967321i	$0.418400\pi$
$491$	−12.4633	+	34.2426i	−0.562461	+	1.54535i	−0.816017	+	0.578028i	$0.803822\pi$
$492$	−8.66969	+	13.8089i	−0.390860	+	0.622552i
$493$	−18.9402	−	10.9352i	−0.853026	−	0.492495i
$494$	1.61567	−	16.6687i	0.0726922	−	0.749959i
$495$	23.2803	+	10.4841i	1.04637	+	0.471226i
$496$	8.20220	−	1.44627i	0.368290	−	0.0649394i
$497$	−0.712759	−	4.04226i	−0.0319716	−	0.181320i
$498$	−18.2183	−	23.4210i	−0.816380	−	1.04952i
$499$	0.727997	+	4.12868i	0.0325896	+	0.184825i	0.996757	−	0.0804695i	$-0.0256419\pi$
$499$	0.727997	+	4.12868i	0.0325896	+	0.184825i	−0.964167	+	0.265294i	$0.914531\pi$
$500$	10.9928	+	1.93832i	0.491612	+	0.0866844i
$501$	2.06504	−	9.61453i	0.0922594	−	0.429546i
$502$			22.1731i			0.989632i
$503$	−9.32742	−	1.64468i	−0.415889	−	0.0733325i	−0.0382115	−	0.999270i	$-0.512166\pi$
$503$	−9.32742	−	1.64468i	−0.415889	−	0.0733325i	−0.377677	+	0.925937i	$0.623277\pi$
$504$	1.79272	+	3.71572i	0.0798542	+	0.165511i
$505$	−9.21325	−	15.9578i	−0.409984	−	0.710114i
$506$	16.2140	+	28.0835i	0.720800	+	1.24846i
$507$	0.418012	+	3.02098i	0.0185646	+	0.134167i
$508$	1.85638	−	0.327329i	0.0823634	−	0.0145229i
$509$	7.63418	+	6.40584i	0.338379	+	0.283934i	0.796104	−	0.605160i	$-0.206891\pi$
$509$	7.63418	+	6.40584i	0.338379	+	0.283934i	−0.457725	+	0.889094i	$0.651335\pi$
$510$	−4.63998	−	8.77154i	−0.205462	−	0.388410i
$511$	−8.71206	−	3.17093i	−0.385399	−	0.140274i
$512$	−1.00000			−0.0441942
$513$	7.03578	+	21.5290i	0.310637	+	0.950529i
$514$	−14.0793			−0.621012
$515$	6.41955	+	2.33652i	0.282879	+	0.102960i
$516$	5.42230	+	10.2505i	0.238704	+	0.451252i
$517$	21.0992	+	17.7043i	0.927942	+	0.778636i
$518$	−1.30537	+	0.230173i	−0.0573548	+	0.0101132i
$519$	0.163495	+	1.18158i	0.00717662	+	0.0518656i
$520$	−2.64668	−	4.58419i	−0.116065	−	0.201030i
$521$	4.11178	+	7.12181i	0.180140	+	0.312012i	0.941928	−	0.335814i	$-0.109011\pi$
$521$	4.11178	+	7.12181i	0.180140	+	0.312012i	−0.761788	+	0.647827i	$0.775678\pi$
$522$	15.7352	+	1.16768i	0.688709	+	0.0511081i
$523$	31.4512	+	5.54569i	1.37526	+	0.242496i	0.811940	−	0.583741i	$-0.198412\pi$
$523$	31.4512	+	5.54569i	1.37526	+	0.242496i	0.563323	+	0.826237i	$0.309523\pi$
$524$		−	16.7567i		−	0.732021i
$525$	−1.55145	+	7.22333i	−0.0677109	+	0.315252i
$526$	−24.3756	−	4.29808i	−1.06283	−	0.187405i
$527$	−6.01398	−	34.1070i	−0.261973	−	1.48572i
$528$	−6.56909	−	8.44506i	−0.285883	−	0.367524i
$529$	−0.791651	−	4.48968i	−0.0344196	−	0.195203i
$530$	−1.28996	+	0.227454i	−0.0560322	+	0.00987999i
$531$	−2.99935	−	29.7556i	−0.130161	−	1.29128i
$532$	−5.80434	+	1.49718i	−0.251650	+	0.0649111i
$533$	31.3215	+	18.0834i	1.35668	+	0.783281i
$534$	−4.41642	+	7.03436i	−0.191117	+	0.304407i
$535$	3.54437	−	9.73809i	0.153237	−	0.421014i
$536$	−2.30665	+	2.74896i	−0.0996321	+	0.118737i
$537$	10.3589	−	16.4993i	0.447018	−	0.711999i
$538$	−1.02406	+	0.372728i	−0.0441504	+	0.0160694i
$539$	27.3302	+	15.7791i	1.17719	+	0.679653i
$540$	5.76484	+	4.24494i	0.248079	+	0.182673i
$541$	4.10495	−	23.2804i	0.176486	−	1.00090i	−0.759929	−	0.650006i	$-0.774766\pi$
$541$	4.10495	−	23.2804i	0.176486	−	1.00090i	0.936415	−	0.350895i	$-0.114122\pi$
$542$	9.48525	+	7.95907i	0.407426	+	0.341871i
$543$	7.81465	+	24.2265i	0.335359	+	1.03966i
$544$			4.15827i			0.178284i
$545$	−2.84679	+	16.1449i	−0.121943	+	0.691573i
$546$	8.08918	−	4.27902i	0.346185	−	0.183125i
$547$	−5.88589	−	1.03784i	−0.251663	−	0.0443749i	0.0463935	−	0.998923i	$-0.485227\pi$
$547$	−5.88589	−	1.03784i	−0.251663	−	0.0443749i	−0.298056	+	0.954548i	$0.596338\pi$
$548$	−2.87888	−	3.43092i	−0.122980	−	0.146562i
$549$	−21.5706	−	21.0088i	−0.920612	−	0.896635i
$550$		−	19.1600i		−	0.816985i
$551$	−6.14057	+	22.0878i	−0.261597	+	0.940973i
$552$	2.79137	+	8.65362i	0.118809	+	0.368322i
$553$	11.7189	+	13.9661i	0.498339	+	0.593897i
$554$	27.9584	+	10.1760i	1.18784	+	0.432339i
$555$	−1.81556	+	1.41225i	−0.0770663	+	0.0599469i
$556$	−3.32564	+	2.79055i	−0.141039	+	0.118346i
$557$	−20.9125	+	24.9226i	−0.886092	+	1.05600i	0.111966	+	0.993712i	$0.464285\pi$
$557$	−20.9125	+	24.9226i	−0.886092	+	1.05600i	−0.998058	+	0.0622912i	$0.980159\pi$
$558$	14.6003	+	20.2766i	0.618079	+	0.858378i
$559$	22.2763	−	12.8612i	0.942188	−	0.543972i
$560$	−1.21789	+	1.45143i	−0.0514653	+	0.0613339i
$561$	−35.1169	+	27.3160i	−1.48263	+	1.15328i
$562$	7.88238	−	13.6527i	0.332498	−	0.575904i
$563$	32.2244			1.35810			0.679048	−	0.734094i	$-0.262393\pi$
$563$	32.2244			1.35810			0.679048	+	0.734094i	$0.262393\pi$
$564$	4.74176	+	6.09589i	0.199664	+	0.256683i
$565$	−2.23757	−	2.66663i	−0.0941351	−	0.112186i
$566$	−14.3096	+	5.20827i	−0.601477	+	0.218920i
$567$	−7.70269	+	9.68773i	−0.323483	+	0.406847i
$568$	0.518297	+	2.93941i	0.0217473	+	0.123335i
$569$	8.53175	−	14.7774i	0.357670	−	0.619502i	−0.629901	−	0.776675i	$-0.716905\pi$
$569$	8.53175	−	14.7774i	0.357670	−	0.619502i	0.987571	+	0.157173i	$0.0502381\pi$
$570$	−7.68851	+	7.00623i	−0.322036	+	0.293459i
$571$	23.6382	+	40.9425i	0.989227	+	1.71339i	0.621388	+	0.783503i	$0.286569\pi$
$571$	23.6382	+	40.9425i	0.989227	+	1.71339i	0.367839	+	0.929890i	$0.380098\pi$
$572$	−18.1802	+	15.2550i	−0.760150	+	0.637842i
$573$	0.00941894	−	0.254200i	0.000393482	−	0.0106193i
$574$	2.24797	−	12.7489i	0.0938284	−	0.532127i
$575$	−5.56915	+	15.3011i	−0.232250	+	0.638101i
$576$	−1.30362	−	2.70196i	−0.0543173	−	0.112582i
$577$	−19.1918	+	33.2412i	−0.798965	+	1.38385i	0.121326	+	0.992613i	$0.461285\pi$
$577$	−19.1918	+	33.2412i	−0.798965	+	1.38385i	−0.920291	+	0.391235i	$0.872048\pi$
$578$	0.291217			0.0121130
$579$	−3.28586	+	0.454663i	−0.136556	+	0.0188951i
$580$	2.47840	+	6.80934i	0.102910	+	0.282743i
$581$	20.4026	+	11.7794i	0.846442	+	0.488693i
$582$	20.9625	+	4.50240i	0.868924	+	0.186631i
$583$	2.00857	+	5.51851i	0.0831866	+	0.228553i
$584$	6.33515	+	2.30581i	0.262150	+	0.0954150i
$585$	8.93603	−	13.1273i	0.369460	−	0.542745i
$586$	−5.09929	+	4.27881i	−0.210650	+	0.176756i
$587$	−9.58364	+	26.3308i	−0.395559	+	1.08679i	0.568865	+	0.822431i	$0.307383\pi$
$587$	−9.58364	+	26.3308i	−0.395559	+	1.08679i	−0.964424	+	0.264359i	$0.914840\pi$
$588$	6.56330	+	5.93498i	0.270666	+	0.244754i
$589$	−33.0449	+	15.0341i	−1.36159	+	0.619471i
$590$	11.8946	−	6.86735i	0.489693	−	0.282724i
$591$	1.38822	−	37.4656i	0.0571039	−	1.54113i
$592$	0.949230	−	0.167375i	0.0390131	−	0.00687906i
$593$	−6.16446	−	16.9367i	−0.253144	−	0.695508i	−0.999549	−	0.0300163i	$-0.990444\pi$
$593$	−6.16446	−	16.9367i	−0.253144	−	0.695508i	0.746405	−	0.665492i	$-0.231778\pi$
$594$	14.2546	−	28.7585i	0.584875	−	1.17998i
$595$	6.03542	+	5.06432i	0.247428	+	0.207617i
$596$	11.4267	−	6.59721i	0.468056	−	0.270232i
$597$	−20.4323	+	6.59077i	−0.836237	+	0.269742i
$598$	18.9527	−	6.89823i	0.775035	−	0.282090i
$599$	−11.3120	+	4.11722i	−0.462195	+	0.168225i	−0.562613	−	0.826720i	$-0.690204\pi$
$599$	−11.3120	+	4.11722i	−0.462195	+	0.168225i	0.100419	+	0.994945i	$0.467982\pi$
$600$	1.12817	−	5.25259i	0.0460574	−	0.214436i
$601$	−1.66766	+	0.962824i	−0.0680252	+	0.0392744i	−0.533627	−	0.845720i	$-0.679171\pi$
$601$	−1.66766	+	0.962824i	−0.0680252	+	0.0392744i	0.465602	+	0.884994i	$0.345838\pi$
$602$	−7.05303	−	5.91819i	−0.287460	−	0.241208i
$603$	−10.4346	−	2.64889i	−0.424928	−	0.107871i
$604$	2.70182	+	7.42318i	0.109935	+	0.302045i
$605$	36.8481	−	6.49732i	1.49809	−	0.264154i
$606$	−20.4763	+	10.8316i	−0.831794	+	0.440003i
$607$	35.6672	−	20.5925i	1.44769	−	0.835823i	0.449344	−	0.893359i	$-0.351658\pi$
$607$	35.6672	−	20.5925i	1.44769	−	0.835823i	0.998343	+	0.0575356i	$0.0183243\pi$
$608$	4.22075	−	1.08871i	0.171174	−	0.0441529i
$609$	−11.9226	+	3.84584i	−0.483129	+	0.155841i
$610$	4.72967	−	12.9947i	0.191499	−	0.526138i
$611$	13.1230	−	11.0115i	0.530898	−	0.445476i
$612$	−11.2355	+	5.42079i	−0.454167	+	0.219122i
$613$	−10.2122	−	3.71692i	−0.412465	−	0.150125i	0.127449	−	0.991845i	$-0.459321\pi$
$613$	−10.2122	−	3.71692i	−0.412465	−	0.150125i	−0.539914	+	0.841720i	$0.681543\pi$
$614$	−4.94280	−	13.5802i	−0.199475	−	0.548054i
$615$	−6.89635	−	21.3796i	−0.278088	−	0.862110i
$616$	7.35670	+	4.24739i	0.296410	+	0.171132i
$617$	5.38331	+	14.7905i	0.216724	+	0.595444i	0.999644	−	0.0266782i	$-0.00849294\pi$
$617$	5.38331	+	14.7905i	0.216724	+	0.595444i	−0.782920	+	0.622122i	$0.786271\pi$
$618$	3.23415	−	7.95597i	0.130096	−	0.320036i
$619$	−27.6011			−1.10938			−0.554692	−	0.832056i	$-0.687164\pi$
$619$	−27.6011			−1.10938			−0.554692	+	0.832056i	$0.687164\pi$
$620$	−5.73754	+	9.93772i	−0.230425	+	0.399108i
$621$	−19.7428	+	18.8232i	−0.792253	+	0.755347i
$622$	10.7497	−	29.5345i	0.431023	−	1.18422i
$623$	1.14513	−	6.49438i	0.0458789	−	0.260192i
$624$	−5.88221	+	3.11158i	−0.235477	+	0.124563i
$625$	0.0992503	−	0.0832809i	0.00397001	−	0.00333124i
$626$	13.9417	+	24.1478i	0.557223	+	0.965139i
$627$	36.9207	+	28.4927i	1.47447	+	1.13789i
$628$	−5.91844	+	10.2510i	−0.236171	+	0.409061i
$629$	−0.695990	−	3.94715i	−0.0277509	−	0.157383i
$630$	−5.50935	−	1.39859i	−0.219498	−	0.0557211i
$631$	−21.5975	+	7.86085i	−0.859783	+	0.312935i	−0.734022	−	0.679125i	$-0.762359\pi$
$631$	−21.5975	+	7.86085i	−0.859783	+	0.312935i	−0.125760	+	0.992061i	$0.540137\pi$
$632$	−8.52165	−	10.1557i	−0.338973	−	0.403973i
$633$	0.257701	−	0.633943i	0.0102427	−	0.0251970i
$634$	−11.5912			−0.460347
$635$	−1.29856	+	2.24917i	−0.0515318	+	0.0892556i
$636$	0.225699	+	1.63113i	0.00894956	+	0.0646786i
$637$	12.6167	−	15.0360i	0.499891	−	0.595747i
$638$	28.1360	−	16.2443i	1.11391	−	0.643118i
$639$	−7.26651	+	5.23228i	−0.287459	+	0.206986i
$640$	0.885614	−	1.05543i	0.0350070	−	0.0417197i
$641$	−17.3411	+	14.5509i	−0.684934	+	0.574728i	−0.917443	−	0.397866i	$-0.869751\pi$
$641$	−17.3411	+	14.5509i	−0.684934	+	0.574728i	0.232509	+	0.972594i	$0.425306\pi$
$642$	−12.0688	−	4.90602i	−0.476316	−	0.193625i
$643$	−16.4586	−	5.99044i	−0.649064	−	0.236240i	−0.00355618	−	0.999994i	$-0.501132\pi$
$643$	−16.4586	−	5.99044i	−0.649064	−	0.236240i	−0.645508	+	0.763754i	$0.723354\pi$
$644$	−4.64047	−	5.53030i	−0.182860	−	0.217924i
$645$	−15.6208	−	3.35509i	−0.615067	−	0.132106i
$646$	−4.52714	−	17.5510i	−0.178118	−	0.690535i
$647$		−	34.8571i		−	1.37038i	−0.728366	−	0.685188i	$-0.759720\pi$
$647$		−	34.8571i		−	1.37038i	0.728366	−	0.685188i	$-0.240280\pi$
$648$	5.60117	−	7.04464i	0.220035	−	0.276739i
$649$	−39.5821	−	47.1721i	−1.55373	−	1.85167i
$650$	−11.7358	−	2.06934i	−0.460316	−	0.0811661i
$651$	−16.8014	−	10.5485i	−0.658497	−	0.413427i
$652$	1.31796	−	7.47452i	0.0516152	−	0.292725i
$653$		−	13.3995i		−	0.524362i	−0.965019	−	0.262181i	$-0.915558\pi$
$653$		−	13.3995i		−	0.524362i	0.965019	−	0.262181i	$-0.0844417\pi$
$654$	20.1500	+	4.32789i	0.787928	+	0.169234i
$655$	17.6856	+	14.8400i	0.691034	+	0.579846i
$656$	−1.63466	+	9.27060i	−0.0638227	+	0.361956i
$657$	2.02841	+	20.1232i	0.0791358	+	0.785081i
$658$	−5.31028	−	3.06589i	−0.207016	−	0.119521i
$659$	2.12483	−	0.773373i	0.0827715	−	0.0301264i	−0.300303	−	0.953844i	$-0.597088\pi$
$659$	2.12483	−	0.773373i	0.0827715	−	0.0301264i	0.383074	+	0.923718i	$0.374865\pi$
$660$	14.7309	+	0.545828i	0.573399	+	0.0212463i
$661$	30.1277	−	35.9048i	1.17183	−	1.39653i	0.270882	−	0.962613i	$-0.412685\pi$
$661$	30.1277	−	35.9048i	1.17183	−	1.39653i	0.900950	−	0.433922i	$-0.142871\pi$
$662$	6.85656	−	18.8382i	0.266488	−	0.732169i
$663$	12.9388	+	24.4598i	0.502501	+	0.949941i
$664$	−14.8362	−	8.56566i	−0.575755	−	0.332412i
$665$	3.56023	−	7.45203i	0.138060	−	0.288977i
$666$	1.68967	+	2.34659i	0.0654734	+	0.0909284i
$667$	−27.1910	+	4.79450i	−1.05284	+	0.185644i
$668$	−0.985896	−	5.59129i	−0.0381455	−	0.216334i
$669$	−9.41203	+	23.1535i	−0.363890	+	0.895166i
$670$	−0.858542	−	4.86903i	−0.0331684	−	0.188107i
$671$	−61.0579	−	10.7662i	−2.35712	−	0.415623i
$672$	1.76670	+	1.59757i	0.0681520	+	0.0616276i
$673$		−	5.43397i		−	0.209464i	−0.994500	−	0.104732i	$-0.966602\pi$
$673$		−	5.43397i		−	0.209464i	0.994500	−	0.104732i	$-0.0333985\pi$
$674$	−0.739272	−	0.130354i	−0.0284757	−	0.00502103i
$675$	15.6630	−	3.79909i	0.602869	−	0.146227i
$676$	0.880392	+	1.52488i	0.0338612	+	0.0586493i
$677$	−20.0321	−	34.6967i	−0.769898	−	1.33350i	−0.937618	−	0.347667i	$-0.886974\pi$
$677$	−20.0321	−	34.6967i	−0.769898	−	1.33350i	0.167720	−	0.985835i	$-0.446359\pi$
$678$	−3.45418	+	2.68687i	−0.132657	+	0.103189i
$679$	−16.7645	+	2.95603i	−0.643363	+	0.113442i
$680$	−4.38878	−	3.68262i	−0.168302	−	0.141222i
$681$	−5.38056	−	0.199367i	−0.206183	−	0.00763978i
$682$	48.3452	+	17.5962i	1.85123	+	0.673794i
$683$	0.574740			0.0219918			0.0109959	−	0.999940i	$-0.496500\pi$
$683$	0.574740			0.0219918			0.0109959	+	0.999940i	$0.496500\pi$
$684$	8.44388	+	9.98503i	0.322860	+	0.381787i
$685$	6.17069			0.235770
$686$	−15.6478	−	5.69532i	−0.597434	−	0.217448i
$687$	2.49410	−	3.97254i	0.0951558	−	0.151562i
$688$	5.12876	+	4.30354i	0.195532	+	0.164071i
$689$	3.59711	−	0.634267i	0.137039	−	0.0241636i
$690$	−11.6054	−	4.71766i	−0.441810	−	0.179598i
$691$	−16.7794	−	29.0628i	−0.638319	−	1.10560i	−0.985801	−	0.167915i	$-0.946297\pi$
$691$	−16.7794	−	29.0628i	−0.638319	−	1.10560i	0.347482	−	0.937687i	$-0.387037\pi$
$692$	0.344342	+	0.596418i	0.0130899	+	0.0226724i
$693$	−1.88597	+	25.4145i	−0.0716421	+	0.965416i
$694$	13.0793	+	2.30623i	0.496483	+	0.0875433i
$695$		−	5.98134i		−	0.226885i
$696$	8.66979	−	2.79659i	0.328628	−	0.106004i
$697$	38.5497	+	6.79735i	1.46017	+	0.257468i
$698$	−0.468391	−	2.65638i	−0.0177289	−	0.100545i
$699$	−7.27881	+	1.00717i	−0.275310	+	0.0380945i
$700$	0.740696	+	4.20070i	0.0279957	+	0.158771i
$701$	−21.2431	+	3.74574i	−0.802342	+	0.141474i	−0.559758	−	0.828656i	$-0.689106\pi$
$701$	−21.2431	+	3.74574i	−0.802342	+	0.141474i	−0.242584	+	0.970131i	$0.577995\pi$
$702$	−16.0755	−	11.8372i	−0.606731	−	0.446766i
$703$	−3.82424	+	1.73988i	−0.144234	+	0.0656209i
$704$	−5.34958	−	3.08858i	−0.201620	−	0.116405i
$705$	−10.6332	−	0.393994i	−0.400469	−	0.0148387i
$706$	3.71862	−	10.2168i	0.139952	−	0.384515i
$707$	11.8222	−	14.0891i	0.444618	−	0.529875i
$708$	−8.07362	−	15.2626i	−0.303425	−	0.573603i
$709$	42.1690	−	15.3483i	1.58369	−	0.576416i	0.607687	−	0.794176i	$-0.292097\pi$
$709$	42.1690	−	15.3483i	1.58369	−	0.576416i	0.976002	+	0.217760i	$0.0698752\pi$
$710$	−3.56137	−	2.05616i	−0.133656	−	0.0771661i
$711$	16.3314	−	36.2643i	0.612474	−	1.36002i
$712$	−0.832709	+	4.72252i	−0.0312071	+	0.176984i
$713$	−33.4938	−	28.1046i	−1.25435	−	1.05253i
$714$	6.64313	−	7.34642i	0.248613	−	0.274933i
$715$		−	32.6980i		−	1.22283i
$716$	1.95315	−	11.0769i	0.0729926	−	0.413961i
$717$	1.36280	−	36.7795i	0.0508947	−	1.37355i
$718$	4.70326	+	0.829312i	0.175524	+	0.0309497i
$719$	17.0800	+	20.3552i	0.636977	+	0.759120i	0.983889	−	0.178778i	$-0.0572143\pi$
$719$	17.0800	+	20.3552i	0.636977	+	0.759120i	−0.346912	+	0.937898i	$0.612770\pi$
$720$	4.00624	+	1.01701i	0.149304	+	0.0379018i
$721$			6.81875i			0.253944i
$722$	−16.6294	+	9.19033i	−0.618883	+	0.342029i
$723$	8.37023	−	9.25636i	0.311292	−	0.344248i
$724$	9.44694	+	11.2584i	0.351093	+	0.418416i
$725$	15.3297	+	5.57956i	0.569332	+	0.207220i
$726$	−6.44718	−	46.5939i	−0.239277	−	1.72926i
$727$	10.1190	−	8.49082i	0.375291	−	0.314907i	−0.435559	−	0.900160i	$-0.643449\pi$
$727$	10.1190	−	8.49082i	0.375291	−	0.314907i	0.810851	+	0.585253i	$0.199005\pi$
$728$	3.39614	−	4.04736i	0.125869	−	0.150005i
$729$	26.3361	+	5.95063i	0.975411	+	0.220394i
$730$	−8.04413	+	4.64428i	−0.297727	+	0.171893i
$731$	17.8953	−	21.3268i	0.661881	−	0.788798i
$732$	−16.1047	−	6.54666i	−0.595248	−	0.241972i
$733$	−9.88584	+	17.1228i	−0.365142	+	0.632444i	−0.988799	−	0.149254i	$-0.952313\pi$
$733$	−9.88584	+	17.1228i	−0.365142	+	0.632444i	0.623657	+	0.781698i	$0.285646\pi$
$734$	−28.2449			−1.04254
$735$	−12.0765	+	1.67103i	−0.445450	+	0.0616367i
$736$	3.37442	+	4.02147i	0.124383	+	0.148233i
$737$	−20.8300	+	7.58149i	−0.767282	+	0.279268i
$738$	−27.1798	+	7.66853i	−1.00050	+	0.282282i
$739$	−1.52558	−	8.65199i	−0.0561194	−	0.318269i	0.943806	−	0.330500i	$-0.107218\pi$
$739$	−1.52558	−	8.65199i	−0.0561194	−	0.318269i	−0.999925	+	0.0122318i	$0.996106\pi$
$740$	−0.663998	+	1.15008i	−0.0244091	+	0.0422777i
$741$	21.4397	−	19.5372i	0.787609	−	0.717717i
$742$	−0.653703	−	1.13225i	−0.0239982	−	0.0415661i
$743$	−17.4167	+	14.6143i	−0.638956	+	0.536147i	−0.903697	−	0.428172i	$-0.859158\pi$
$743$	−17.4167	+	14.6143i	−0.638956	+	0.536147i	0.264742	+	0.964319i	$0.414713\pi$
$744$	12.2175	+	7.67054i	0.447914	+	0.281216i
$745$	−3.15673	+	17.9027i	−0.115654	+	0.655905i
$746$	−6.96830	+	19.1452i	−0.255127	+	0.700957i
$747$	3.80341	−	51.2530i	0.139160	−	1.87525i
$748$	−12.8432	+	22.2450i	−0.469592	+	0.813358i
$749$	10.3437			0.377949
$750$	11.8706	+	15.2605i	0.433452	+	0.557236i
$751$	−16.9103	−	46.4608i	−0.617067	−	1.69538i	−0.714053	−	0.700092i	$-0.753143\pi$
$751$	−16.9103	−	46.4608i	−0.617067	−	1.69538i	0.0969862	−	0.995286i	$-0.469080\pi$
$752$	3.86148	+	2.22943i	0.140814	+	0.0812988i
$753$	−25.7586	+	28.4856i	−0.938696	+	1.03807i
$754$	−6.91112	−	18.9882i	−0.251688	−	0.691508i
$755$	−10.2274	−	3.72249i	−0.372215	−	0.135475i
$756$	−2.01347	+	6.85617i	−0.0732293	+	0.249357i
$757$	−15.6606	+	13.1408i	−0.569193	+	0.477610i	−0.881378	−	0.472412i	$-0.843384\pi$
$757$	−15.6606	+	13.1408i	−0.569193	+	0.477610i	0.312185	+	0.950021i	$0.398939\pi$
$758$	10.2640	−	28.2002i	0.372807	−	1.02428i
$759$	−11.7947	+	54.9146i	−0.428122	+	1.99327i
$760$	−2.58890	+	5.41890i	−0.0939091	+	0.196564i
$761$	12.7869	−	7.38251i	0.463524	−	0.267616i	−0.250001	−	0.968246i	$-0.580431\pi$
$761$	12.7869	−	7.38251i	0.463524	−	0.267616i	0.713525	+	0.700630i	$0.247098\pi$
$762$	2.76514	+	1.73605i	0.100170	+	0.0628904i
$763$	−16.1147	+	2.84146i	−0.583392	+	0.102868i
$764$	−0.0502301	−	0.138006i	−0.00181726	−	0.00499288i
$765$	4.22902	−	16.6590i	0.152900	−	0.602309i
$766$	12.6666	+	10.6285i	0.457663	+	0.384025i
$767$	−33.1686	+	19.1499i	−1.19765	+	0.691463i
$768$	−1.28469	−	1.16171i	−0.0463574	−	0.0419195i
$769$	−9.23348	+	3.36071i	−0.332968	+	0.121190i	−0.503093	−	0.864232i	$-0.667805\pi$
$769$	−9.23348	+	3.36071i	−0.332968	+	0.121190i	0.170126	+	0.985422i	$0.445583\pi$
$770$	−10.9980	+	4.00296i	−0.396342	+	0.144257i
$771$	−18.0876	−	16.3560i	−0.651409	−	0.589048i
$772$	−1.65858	+	0.957582i	−0.0596937	+	0.0344641i
$773$	34.4729	+	28.9262i	1.23990	+	1.04040i	0.997531	+	0.0702205i	$0.0223703\pi$
$773$	34.4729	+	28.9262i	1.23990	+	1.04040i	0.242373	+	0.970183i	$0.422074\pi$
$774$	−4.94205	+	19.4678i	−0.177638	+	0.699757i
$775$	8.83562	+	24.2757i	0.317385	+	0.872007i
$776$	12.1907	−	2.14954i	0.437619	−	0.0771641i
$777$	−1.94440	−	1.22076i	−0.0697549	−	0.0437945i
$778$	9.26782	−	5.35078i	0.332268	−	0.191835i
$779$	−3.19350	−	40.9085i	−0.114419	−	1.46570i
$780$	1.92531	−	8.96395i	0.0689371	−	0.320961i
$781$	−6.30593	+	17.3254i	−0.225644	+	0.619952i
$782$	16.7224	−	14.0317i	0.597991	−	0.501774i
$783$	18.8583	+	19.7797i	0.673942	+	0.706871i
$784$	4.80074	+	1.74733i	0.171455	+	0.0624046i
$785$	−5.57784	−	15.3250i	−0.199082	−	0.546972i
$786$	19.4664	−	21.5272i	0.694343	−	0.767851i
$787$	33.3488	+	19.2540i	1.18876	+	0.686329i	0.958024	−	0.286688i	$-0.0925541\pi$
$787$	33.3488	+	19.2540i	1.18876	+	0.686329i	0.230733	+	0.973017i	$0.425887\pi$
$788$	−7.40323	−	20.3402i	−0.263729	−	0.724590i
$789$	−26.3221	−	33.8391i	−0.937092	−	1.20470i
$790$	18.2656			0.649860
$791$	1.73726	−	3.00902i	0.0617699	−	0.106989i
$792$	1.37142	−	18.4807i	0.0487314	−	0.656682i
$793$	−13.1889	+	36.2362i	−0.468351	+	1.28678i
$794$	1.62939	−	9.24072i	0.0578248	−	0.327941i
$795$	−1.92144	−	1.20634i	−0.0681463	−	0.0427846i
$796$	−9.49520	+	7.96742i	−0.336548	+	0.282398i
$797$	7.57940	+	13.1279i	0.268476	+	0.465014i	0.968468	−	0.249136i	$-0.0801467\pi$
$797$	7.57940	+	13.1279i	0.268476	+	0.465014i	−0.699992	+	0.714150i	$0.746813\pi$
$798$	−9.19609	−	4.81952i	−0.325538	−	0.170609i
$799$	9.27056	−	16.0571i	0.327969	−	0.568059i
$800$	−0.538613	−	3.05462i	−0.0190428	−	0.107997i
$801$	−13.8456	+	3.90641i	−0.489210	+	0.138026i
$802$	−11.0798	+	4.03271i	−0.391241	+	0.142400i
$803$	26.7687	+	31.9017i	0.944648	+	1.12579i
$804$	−6.15682	+	0.851917i	−0.217134	+	0.0300448i
$805$	9.94654			0.350569
$806$	15.9994	−	27.7118i	0.563555	−	0.976105i
$807$	−1.74860	−	0.710818i	−0.0615538	−	0.0250220i
$808$	−8.59673	+	10.2452i	−0.302432	+	0.360424i
$809$	4.27607	−	2.46879i	0.150339	−	0.0867980i	−0.422944	−	0.906156i	$-0.639003\pi$
$809$	4.27607	−	2.46879i	0.150339	−	0.0867980i	0.573282	+	0.819358i	$0.305670\pi$
$810$	2.47467	+	12.1505i	0.0869511	+	0.426925i
$811$	21.8811	−	26.0769i	0.768349	−	0.915683i	−0.229996	−	0.973192i	$-0.573871\pi$
$811$	21.8811	−	26.0769i	0.768349	−	0.915683i	0.998345	+	0.0575088i	$0.0183157\pi$
$812$	−5.54064	+	4.64915i	−0.194438	+	0.163153i
$813$	2.93953	+	21.2440i	0.103094	+	0.745061i
$814$	5.59493	+	2.03639i	0.196102	+	0.0713753i
$815$	6.72165	+	8.01056i	0.235449	+	0.280598i
$816$	−4.83069	+	5.34210i	−0.169108	+	0.187011i
$817$	−26.3325	−	12.5804i	−0.921257	−	0.440133i
$818$			21.7141i			0.759215i
$819$	15.3631	+	3.90003i	0.536829	+	0.136278i
$820$	−8.33683	−	9.93545i	−0.291135	−	0.346961i
$821$	31.8660	+	5.61884i	1.11213	+	0.196099i	0.699384	−	0.714746i	$-0.253458\pi$
$821$	31.8660	+	5.61884i	1.11213	+	0.196099i	0.412748	+	0.910845i	$0.364569\pi$
$822$	0.287241	−	7.75209i	0.0100187	−	0.270385i
$823$	−4.62666	+	26.2391i	−0.161275	+	0.914637i	0.791547	+	0.611108i	$0.209276\pi$
$823$	−4.62666	+	26.2391i	−0.161275	+	0.914637i	−0.952822	+	0.303529i	$0.901835\pi$
$824$		−	4.95840i		−	0.172734i
$825$	22.2583	−	24.6147i	0.774934	−	0.856974i
$826$	10.5017	+	8.81198i	0.365401	+	0.306608i
$827$	9.66729	−	54.8259i	0.336165	−	1.90648i	−0.0792552	−	0.996854i	$-0.525254\pi$
$827$	9.66729	−	54.8259i	0.336165	−	1.90648i	0.415420	−	0.909630i	$-0.363635\pi$
$828$	−6.46691	+	14.3600i	−0.224741	+	0.499044i
$829$	29.6636	+	17.1263i	1.03026	+	0.594820i	0.917059	−	0.398752i	$-0.130557\pi$
$829$	29.6636	+	17.1263i	1.03026	+	0.594820i	0.113200	+	0.993572i	$0.463890\pi$
$830$	22.1796	−	8.07272i	0.769865	−	0.280208i
$831$	24.0965	+	45.5526i	0.835897	+	1.58020i
$832$	−2.46957	+	2.94312i	−0.0856171	+	0.102034i
$833$	7.26586	−	19.9628i	0.251747	−	0.691670i
$834$	−7.51423	−	0.278427i	−0.260196	−	0.00964114i
$835$	6.77436	+	3.91118i	0.234437	+	0.135352i
$836$	25.9418	+	7.21199i	0.897215	+	0.249432i
$837$	−4.79862	+	43.0105i	−0.165865	+	1.48666i
$838$	15.8906	−	2.80195i	0.548933	−	0.0967916i
$839$	2.19645	+	12.4567i	0.0758299	+	0.430053i	0.998961	+	0.0455679i	$0.0145097\pi$
$839$	2.19645	+	12.4567i	0.0758299	+	0.430053i	−0.923131	+	0.384485i	$0.874379\pi$
$840$	−3.25075	+	0.449805i	−0.112161	+	0.0155197i
$841$	−0.232332	−	1.31762i	−0.00801146	−	0.0454353i
$842$	−1.25437	−	0.221180i	−0.0432285	−	0.00762236i
$843$	25.9869	−	8.38250i	0.895035	−	0.288709i
$844$		−	0.395092i		−	0.0135996i
$845$	−2.38910	−	0.421263i	−0.0821876	−	0.0144919i
$846$	−0.989933	+	13.3399i	−0.0340346	+	0.458634i
$847$	18.6733	+	32.3431i	0.641621	+	1.11132i
$848$	0.475354	+	0.823337i	0.0163237	+	0.0282735i
$849$	−24.4339	−	9.93254i	−0.838570	−	0.340884i
$850$	−12.7020	+	2.23970i	−0.435673	+	0.0768210i
$851$	−3.87619	−	3.25251i	−0.132874	−	0.111495i
$852$	−2.74888	+	4.37835i	−0.0941751	+	0.150000i
$853$	−44.2956	−	16.1223i	−1.51665	−	0.552016i	−0.556343	−	0.830953i	$-0.687796\pi$
$853$	−44.2956	−	16.1223i	−1.51665	−	0.552016i	−0.960310	+	0.278937i	$0.910018\pi$
$854$	13.8027			0.472320
$855$	−18.0166	+	0.0690710i	−0.616154	+	0.00236218i
$856$	−7.52161			−0.257083
$857$	−13.6608	−	4.97211i	−0.466643	−	0.169844i	0.0979882	−	0.995188i	$-0.468759\pi$
$857$	−13.6608	−	4.97211i	−0.466643	−	0.169844i	−0.564631	+	0.825344i	$0.690981\pi$
$858$	−41.0777	−	1.52207i	−1.40237	−	0.0519625i
$859$	34.8189	+	29.2165i	1.18800	+	0.996854i	0.999892	+	0.0147071i	$0.00468157\pi$
$859$	34.8189	+	29.2165i	1.18800	+	0.996854i	0.188113	+	0.982147i	$0.439763\pi$
$860$	−9.08420	+	1.60179i	−0.309769	+	0.0546206i
$861$	17.6984	−	13.7669i	0.603160	−	0.469175i
$862$	11.7293	+	20.3158i	0.399502	+	0.691957i
$863$	23.7381	+	41.1156i	0.808055	+	1.39959i	0.914209	+	0.405243i	$0.132813\pi$
$863$	23.7381	+	41.1156i	0.808055	+	1.39959i	−0.106154	+	0.994350i	$0.533854\pi$
$864$	1.46414	−	4.98561i	0.0498110	−	0.169614i
$865$	−0.934435	−	0.164766i	−0.0317717	−	0.00560221i
$866$			27.1535i			0.922712i
$867$	0.374124	+	0.338309i	0.0127059	+	0.0114896i
$868$	−11.2796	−	1.98890i	−0.382855	−	0.0675076i
$869$	−14.2205	−	80.6486i	−0.482398	−	2.73582i
$870$	−4.72648	+	11.6271i	−0.160243	+	0.394195i
$871$	2.39408	+	13.5775i	0.0811204	+	0.460057i
$872$	11.7182	−	2.06623i	0.396827	−	0.0699713i
$873$	21.6999	+	30.1365i	0.734431	+	1.01997i
$874$	−18.6208	−	13.2999i	−0.629857	−	0.449875i
$875$	−13.2938	−	7.67519i	−0.449413	−	0.259469i
$876$	5.46006	+	10.3218i	0.184478	+	0.348743i
$877$	−17.5718	+	48.2782i	−0.593359	+	1.63024i	0.170868	+	0.985294i	$0.445343\pi$
$877$	−17.5718	+	48.2782i	−0.593359	+	1.63024i	−0.764228	+	0.644947i	$0.776880\pi$
$878$	16.9223	−	20.1673i	0.571101	−	0.680612i
$879$	−11.5217	−	0.426919i	−0.388619	−	0.0143996i
$880$	7.99746	−	2.91084i	0.269594	−	0.0981243i
$881$	−25.8080	−	14.9003i	−0.869494	−	0.502003i	−0.00231390	−	0.999997i	$-0.500737\pi$
$881$	−25.8080	−	14.9003i	−0.869494	−	0.502003i	−0.867180	+	0.497995i	$0.834070\pi$
$882$	1.53712	+	15.2493i	0.0517574	+	0.513469i
$883$	5.21093	−	29.5526i	0.175362	−	0.994525i	−0.762364	−	0.647148i	$-0.775961\pi$
$883$	5.21093	−	29.5526i	0.175362	−	0.994525i	0.937726	−	0.347377i	$-0.112927\pi$
$884$	12.2383	+	10.2692i	0.411619	+	0.345389i
$885$	23.2588	+	4.99560i	0.781835	+	0.167925i
$886$			11.5433i			0.387806i
$887$	4.40717	−	24.9943i	0.147978	−	0.839227i	−0.816949	−	0.576710i	$-0.804336\pi$
$887$	4.40717	−	24.9943i	0.147978	−	0.839227i	0.964927	−	0.262517i	$-0.0845527\pi$
$888$	1.41391	+	0.887701i	0.0474477	+	0.0297893i
$889$	−2.55288	−	0.450141i	−0.0856207	−	0.0150972i
$890$	−4.24685	−	5.06120i	−0.142355	−	0.169652i
$891$	51.7218	−	20.3862i	1.73275	−	0.682962i
$892$			14.4299i			0.483150i
$893$	−18.7255	−	5.20582i	−0.626626	−	0.174206i
$894$	22.3438	+	4.79909i	0.747289	+	0.160506i
$895$	9.96115	+	11.8712i	0.332965	+	0.396812i
$896$	1.29226	+	0.470344i	0.0431713	+	0.0157131i
$897$	32.3622	+	13.1554i	1.08054	+	0.439246i
$898$	18.1788	−	15.2538i	0.606635	−	0.509027i
$899$	−28.1571	+	33.5564i	−0.939093	+	1.11917i
$900$	7.55133	−	5.43737i	0.251711	−	0.181246i
$901$	3.42366	−	1.97665i	0.114059	−	0.0658518i
$902$	−37.3777	+	44.5451i	−1.24454	+	1.48319i
$903$	−2.18577	−	15.7966i	−0.0727379	−	0.525678i
$904$	−1.26328	+	2.18807i	−0.0420162	+	0.0727742i
$905$	−20.2489			−0.673095
$906$	−5.15255	+	12.6752i	−0.171182	+	0.421106i
$907$	24.6662	+	29.3961i	0.819029	+	0.976081i	0.999973	−	0.00741281i	$-0.00235959\pi$
$907$	24.6662	+	29.3961i	0.819029	+	0.976081i	−0.180944	+	0.983493i	$0.557915\pi$
$908$	−2.92113	+	1.06320i	−0.0969410	+	0.0352836i
$909$	−38.8889	−	9.87223i	−1.28986	−	0.327441i
$910$	1.26405	+	7.16881i	0.0419030	+	0.237644i
$911$	−19.7201	+	34.1562i	−0.653356	+	1.13165i	0.328947	+	0.944348i	$0.393306\pi$
$911$	−19.7201	+	34.1562i	−0.653356	+	1.13165i	−0.982303	+	0.187298i	$0.940027\pi$
$912$	6.68713	+	3.50462i	0.221433	+	0.116049i
$913$	−52.9115	−	91.6454i	−1.75111	−	3.03302i
$914$	−5.82745	+	4.88981i	−0.192755	+	0.161741i
$915$	21.1721	−	11.1997i	0.699930	−	0.370249i
$916$	0.470259	−	2.66697i	0.0155378	−	0.0881191i
$917$	−7.88142	+	21.6540i	−0.260267	+	0.715078i
$918$	−20.7315	−	6.08828i	−0.684242	−	0.200943i
$919$	−19.6297	+	33.9997i	−0.647525	+	1.12155i	0.336187	+	0.941795i	$0.390862\pi$
$919$	−19.6297	+	33.9997i	−0.647525	+	1.12155i	−0.983712	+	0.179751i	$0.942471\pi$
$920$	−7.23283			−0.238459
$921$	9.42627	−	23.1885i	0.310606	−	0.764088i
$922$	−6.25006	−	17.1719i	−0.205835	−	0.565526i
$923$	9.93103	+	5.73368i	0.326884	+	0.188726i
$924$	4.51688	+	14.0029i	0.148594	+	0.460663i
$925$	1.02253	+	2.80939i	0.0336207	+	0.0923721i
$926$	−7.02750	−	2.55780i	−0.230938	−	0.0840545i
$927$	13.3974	−	6.46385i	0.440028	−	0.212301i
$928$	4.02899	−	3.38072i	0.132258	−	0.110978i
$929$	−6.39819	+	17.5789i	−0.209918	+	0.576745i	−0.999310	−	0.0371448i	$-0.988174\pi$
$929$	−6.39819	+	17.5789i	−0.209918	+	0.576745i	0.789392	+	0.613889i	$0.210396\pi$
$930$	−18.9157	+	6.10157i	−0.620270	+	0.200078i
$931$	−22.1651	−	2.14842i	−0.726431	−	0.0704117i
$932$	−3.67408	+	2.12123i	−0.120349	+	0.0694833i
$933$	48.1204	−	25.4548i	1.57539	−	0.833352i
$934$	−12.5309	+	2.20954i	−0.410025	+	0.0722984i
$935$	−12.1040	−	33.2556i	−0.395845	−	1.08757i
$936$	−11.1716	−	2.83599i	−0.365155	−	0.0926971i
$937$	22.6680	+	19.0208i	0.740533	+	0.621381i	0.932981	−	0.359926i	$-0.117198\pi$
$937$	22.6680	+	19.0208i	0.740533	+	0.621381i	−0.192448	+	0.981307i	$0.561643\pi$
$938$	4.27374	−	2.46745i	0.139543	−	0.0805650i
$939$	−10.1418	+	47.2187i	−0.330965	+	1.54092i
$940$	−5.77279	+	2.10113i	−0.188288	+	0.0685311i
$941$	−48.2254	+	17.5526i	−1.57210	+	0.572199i	−0.973468	−	0.228823i	$-0.926512\pi$
$941$	−48.2254	+	17.5526i	−1.57210	+	0.572199i	−0.598635	+	0.801022i	$0.704290\pi$
$942$	−19.5121	+	6.29394i	−0.635738	+	0.205068i
$943$	42.7975	−	24.7092i	1.39368	−	0.804641i
$944$	−7.63653	−	6.40781i	−0.248548	−	0.208556i
$945$	−5.45308	−	8.19701i	−0.177389	−	0.266649i
$946$	14.1449	+	38.8627i	0.459889	+	1.26353i
$947$	−18.9221	+	3.33647i	−0.614885	+	0.108421i	−0.472412	−	0.881378i	$-0.656617\pi$
$947$	−18.9221	+	3.33647i	−0.614885	+	0.108421i	−0.142473	+	0.989799i	$0.545505\pi$
$948$	0.850249	−	22.9466i	0.0276148	−	0.745272i
$949$	22.4314	−	12.9508i	0.728154	−	0.420400i
$950$	5.59894	+	12.3064i	0.181654	+	0.399273i
$951$	−14.8912	−	13.4656i	−0.482880	−	0.436653i
$952$	1.95582	−	5.37356i	0.0633884	−	0.174158i
$953$	−33.9021	+	28.4472i	−1.09820	+	0.921496i	−0.997302	−	0.0734014i	$-0.976615\pi$
$953$	−33.9021	+	28.4472i	−1.09820	+	0.921496i	−0.100894	+	0.994897i	$0.532170\pi$
$954$	−1.60494	+	2.35770i	−0.0519620	+	0.0763334i
$955$	0.190141	+	0.0692056i	0.00615281	+	0.00223944i
$956$	−7.26766	−	19.9677i	−0.235053	−	0.645802i
$957$	55.0172	+	11.8168i	1.77845	+	0.381983i
$958$	−12.4159	−	7.16831i	−0.401139	−	0.231598i
$959$	2.10655	+	5.78770i	0.0680240	+	0.186894i
$960$	2.36385	−	0.327085i	0.0762929	−	0.0105566i
$961$	−38.3678			−1.23767
$962$	1.85159	−	3.20705i	0.0596976	−	0.103399i
$963$	−9.80529	−	20.3231i	−0.315971	−	0.654902i
$964$	2.46429	−	6.77059i	0.0793696	−	0.218066i
$965$	0.458198	−	2.59857i	0.0147499	−	0.0836510i
$966$	0.463004	−	12.4956i	0.0148969	−	0.402040i
$967$	10.9449	−	9.18390i	0.351966	−	0.295334i	−0.449613	−	0.893223i	$-0.648438\pi$
$967$	10.9449	−	9.18390i	0.351966	−	0.295334i	0.801579	+	0.597889i	$0.203994\pi$
$968$	−13.5787	−	23.5189i	−0.436435	−	0.755927i
$969$	14.5731	−	27.8069i	0.468157	−	0.893286i
$970$	−8.52752	+	14.7701i	−0.273802	+	0.474239i
$971$	6.91734	+	39.2302i	0.221988	+	1.25896i	0.868360	+	0.495935i	$0.165174\pi$
$971$	6.91734	+	39.2302i	0.221988	+	1.25896i	−0.646372	+	0.763023i	$0.723714\pi$
$972$	15.3796	−	2.54328i	0.493301	−	0.0815757i
$973$	5.61011	−	2.04191i	0.179852	−	0.0654607i
$974$	−6.19175	−	7.37904i	−0.198396	−	0.236440i
$975$	−12.6729	−	16.2920i	−0.405859	−	0.521762i
$976$	−10.0369			−0.321275
$977$	−3.80997	+	6.59906i	−0.121892	+	0.211122i	−0.920514	−	0.390710i	$-0.872229\pi$
$977$	−3.80997	+	6.59906i	−0.121892	+	0.211122i	0.798622	+	0.601833i	$0.205563\pi$
$978$	10.3764	−	8.07138i	0.331800	−	0.258094i
$979$	−19.0405	+	22.6916i	−0.608538	+	0.725228i
$980$	−6.09580	+	3.51941i	−0.194723	+	0.112423i
$981$	20.8588	+	28.9684i	0.665971	+	0.924890i
$982$	−23.4233	+	27.9149i	−0.747469	+	0.890799i
$983$	17.7867	−	14.9248i	0.567308	−	0.476028i	−0.313443	−	0.949607i	$-0.601483\pi$
$983$	17.7867	−	14.9248i	0.567308	−	0.476028i	0.880751	+	0.473579i	$0.157038\pi$
$984$	−12.8698	+	10.0109i	−0.410273	+	0.319136i
$985$	28.0242	+	10.2000i	0.892924	+	0.324998i
$986$	−14.0580	−	16.7536i	−0.447697	−	0.533544i
$987$	−3.26041	−	10.1077i	−0.103780	−	0.321732i
$988$	7.21925	−	15.1108i	0.229675	−	0.480740i
$989$		−	35.1471i		−	1.11761i
$990$	18.2906	+	17.8142i	0.581313	+	0.566172i
$991$	11.9256	+	14.2124i	0.378829	+	0.451471i	0.921444	−	0.388510i	$-0.127010\pi$
$991$	11.9256	+	14.2124i	0.378829	+	0.451471i	−0.542615	+	0.839981i	$0.682566\pi$
$992$	8.20220	+	1.44627i	0.260420	+	0.0459191i
$993$	30.6931	−	16.2361i	0.974016	−	0.515236i
$994$	0.712759	−	4.04226i	0.0226073	−	0.128213i
$995$		−	17.0776i		−	0.541397i
$996$	−9.10913	−	28.2395i	−0.288634	−	0.894803i
$997$	24.1836	+	20.2924i	0.765901	+	0.642667i	0.939656	−	0.342122i	$-0.111145\pi$
$997$	24.1836	+	20.2924i	0.765901	+	0.642667i	−0.173754	+	0.984789i	$0.555590\pi$
$998$	−0.727997	+	4.12868i	−0.0230444	+	0.130691i
$999$	−0.555338	+	4.97755i	−0.0175701	+	0.157483i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.x.b.29.7	✓	48
9.5	odd	6		342.2.bf.b.257.6	yes	48
19.2	odd	18		342.2.bf.b.173.6	yes	48
171.59	even	18	inner	342.2.x.b.59.7	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.x.b.29.7	✓	48	1.1	even	1	trivial
342.2.x.b.59.7	yes	48	171.59	even	18	inner
342.2.bf.b.173.6	yes	48	19.2	odd	18
342.2.bf.b.257.6	yes	48	9.5	odd	6

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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{2} +(0.809890 + 1.53104i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-1.35684 + 0.239247i) q^{5} +(0.237401 + 1.71570i) q^{6} +(-0.687596 - 1.19095i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.68816 + 2.47994i) q^{9} +O(q^{10})\)	\(q+(0.939693 + 0.342020i) q^{2} +(0.809890 + 1.53104i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-1.35684 + 0.239247i) q^{5} +(0.237401 + 1.71570i) q^{6} +(-0.687596 - 1.19095i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.68816 + 2.47994i) q^{9} +(-1.35684 - 0.239247i) q^{10} +6.17716i q^{11} +(-0.363721 + 1.69343i) q^{12} +(3.78361 + 0.667152i) q^{13} +(-0.238800 - 1.35430i) q^{14} +(-1.46519 - 1.88361i) q^{15} +(0.173648 + 0.984808i) q^{16} +(4.09510 - 0.722076i) q^{17} +(-2.43454 + 1.75300i) q^{18} +(-1.80509 - 3.96757i) q^{19} +(-1.19318 - 0.688886i) q^{20} +(1.26652 - 2.01728i) q^{21} +(-2.11271 + 5.80463i) q^{22} +(3.37442 - 4.02147i) q^{23} +(-0.920973 + 1.46690i) q^{24} +(-2.91469 + 1.06086i) q^{25} +(3.32725 + 1.92099i) q^{26} +(-5.16411 - 0.576153i) q^{27} +(0.238800 - 1.35430i) q^{28} +(-4.02899 - 3.38072i) q^{29} +(-0.732593 - 2.27114i) q^{30} -8.32873i q^{31} +(-0.173648 + 0.984808i) q^{32} +(-9.45747 + 5.00282i) q^{33} +(4.09510 + 0.722076i) q^{34} +(1.21789 + 1.45143i) q^{35} +(-2.88728 + 0.814621i) q^{36} -0.963873i q^{37} +(-0.339243 - 4.34568i) q^{38} +(2.04287 + 6.33317i) q^{39} +(-0.885614 - 1.05543i) q^{40} +(8.84591 + 3.21965i) q^{41} +(1.88008 - 1.46245i) q^{42} +(5.12876 - 4.30354i) q^{43} +(-3.97060 + 4.73198i) q^{44} +(1.69724 - 3.76877i) q^{45} +(4.54634 - 2.62483i) q^{46} +(2.86610 - 3.41568i) q^{47} +(-1.36714 + 1.06345i) q^{48} +(2.55442 - 4.42439i) q^{49} -3.10175 q^{50} +(4.42210 + 5.68495i) q^{51} +(2.46957 + 2.94312i) q^{52} +(0.893373 - 0.325161i) q^{53} +(-4.65562 - 2.30764i) q^{54} +(-1.47787 - 8.38142i) q^{55} +(0.687596 - 1.19095i) q^{56} +(4.61258 - 5.97696i) q^{57} +(-2.62974 - 4.55484i) q^{58} +(-7.63653 + 6.40781i) q^{59} +(0.0883623 - 2.38473i) q^{60} +(-1.74290 + 9.88446i) q^{61} +(2.84859 - 7.82645i) q^{62} +(4.11427 + 0.305314i) q^{63} +(-0.500000 + 0.866025i) q^{64} -5.29336 q^{65} +(-10.5982 + 1.46647i) q^{66} +(1.22734 + 3.37210i) q^{67} +(3.60117 + 2.07914i) q^{68} +(8.88994 + 1.90941i) q^{69} +(0.648026 + 1.78044i) q^{70} +(2.80475 + 1.02085i) q^{71} +(-2.99177 - 0.222015i) q^{72} +(5.16446 - 4.33350i) q^{73} +(0.329664 - 0.905744i) q^{74} +(-3.98479 - 3.60332i) q^{75} +(1.16753 - 4.19963i) q^{76} +(7.35670 - 4.24739i) q^{77} +(-0.246402 + 6.64993i) q^{78} +(-13.0559 + 2.30211i) q^{79} +(-0.471226 - 1.29468i) q^{80} +(-3.30025 - 8.37307i) q^{81} +(7.21125 + 6.05096i) q^{82} +(-14.8362 + 8.56566i) q^{83} +(2.26689 - 0.731222i) q^{84} +(-5.38364 + 1.95948i) q^{85} +(6.29135 - 2.28986i) q^{86} +(1.91298 - 8.90655i) q^{87} +(-5.34958 + 3.08858i) q^{88} +(3.67347 + 3.08241i) q^{89} +(2.88388 - 2.96100i) q^{90} +(-1.80705 - 4.96483i) q^{91} +(5.16991 - 0.911594i) q^{92} +(12.7516 - 6.74535i) q^{93} +(3.86148 - 2.22943i) q^{94} +(3.39845 + 4.95150i) q^{95} +(-1.64841 + 0.531724i) q^{96} +(4.23377 - 11.6322i) q^{97} +(3.91360 - 3.28390i) q^{98} +(-15.3190 - 10.4280i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{3} - 9 q^{5} - 9 q^{6} + 9 q^{7} + 24 q^{8}+O(q^{10}) \) 48 * q - 6 * q^3 - 9 * q^5 - 9 * q^6 + 9 * q^7 + 24 * q^8	\( 48 q - 6 q^{3} - 9 q^{5} - 9 q^{6} + 9 q^{7} + 24 q^{8} - 9 q^{10} - 6 q^{12} + 15 q^{13} - 6 q^{14} + 12 q^{15} - 27 q^{17} - 9 q^{18} - 12 q^{19} - 9 q^{20} - 15 q^{21} + 18 q^{22} - 3 q^{24} - 9 q^{25} + 18 q^{26} - 12 q^{27} + 6 q^{28} + 45 q^{29} - 27 q^{34} - 18 q^{35} - 3 q^{36} + 24 q^{39} + 27 q^{41} - 3 q^{42} - 15 q^{43} - 9 q^{44} - 63 q^{45} + 27 q^{46} - 27 q^{47} - 9 q^{48} - 33 q^{49} - 6 q^{50} - 42 q^{51} + 21 q^{52} + 9 q^{55} - 9 q^{56} + 36 q^{57} - 9 q^{58} - 9 q^{60} + 69 q^{61} - 3 q^{62} + 3 q^{63} - 24 q^{64} + 18 q^{65} - 6 q^{66} + 21 q^{67} + 36 q^{68} - 12 q^{69} + 27 q^{71} - 9 q^{72} + 66 q^{73} - 15 q^{74} + 24 q^{75} - 27 q^{77} + 63 q^{78} + 33 q^{79} - 9 q^{80} - 9 q^{82} - 81 q^{83} + 6 q^{84} + 18 q^{85} - 30 q^{86} - 72 q^{87} + 9 q^{88} - 18 q^{89} + 60 q^{90} + 51 q^{91} - 18 q^{92} - 84 q^{93} - 54 q^{94} - 27 q^{95} - 3 q^{96} - 108 q^{97} + 42 q^{98} + 15 q^{99}+O(q^{100}) \) 48 * q - 6 * q^3 - 9 * q^5 - 9 * q^6 + 9 * q^7 + 24 * q^8 - 9 * q^10 - 6 * q^12 + 15 * q^13 - 6 * q^14 + 12 * q^15 - 27 * q^17 - 9 * q^18 - 12 * q^19 - 9 * q^20 - 15 * q^21 + 18 * q^22 - 3 * q^24 - 9 * q^25 + 18 * q^26 - 12 * q^27 + 6 * q^28 + 45 * q^29 - 27 * q^34 - 18 * q^35 - 3 * q^36 + 24 * q^39 + 27 * q^41 - 3 * q^42 - 15 * q^43 - 9 * q^44 - 63 * q^45 + 27 * q^46 - 27 * q^47 - 9 * q^48 - 33 * q^49 - 6 * q^50 - 42 * q^51 + 21 * q^52 + 9 * q^55 - 9 * q^56 + 36 * q^57 - 9 * q^58 - 9 * q^60 + 69 * q^61 - 3 * q^62 + 3 * q^63 - 24 * q^64 + 18 * q^65 - 6 * q^66 + 21 * q^67 + 36 * q^68 - 12 * q^69 + 27 * q^71 - 9 * q^72 + 66 * q^73 - 15 * q^74 + 24 * q^75 - 27 * q^77 + 63 * q^78 + 33 * q^79 - 9 * q^80 - 9 * q^82 - 81 * q^83 + 6 * q^84 + 18 * q^85 - 30 * q^86 - 72 * q^87 + 9 * q^88 - 18 * q^89 + 60 * q^90 + 51 * q^91 - 18 * q^92 - 84 * q^93 - 54 * q^94 - 27 * q^95 - 3 * q^96 - 108 * q^97 + 42 * q^98 + 15 * q^99

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