LMFDB - Embedded newform 378.2.v.a.79.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(67,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8, 12]))

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

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

chi := DirichletCharacter("378.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.v (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			79.6
Character	$\chi$	$=$	378.79
Dual form			378.2.v.a.67.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 - 0.642788i) q^{2} +(-0.402311 - 1.68468i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.256458 + 1.45445i) q^{5} +(-0.774703 + 1.54914i) q^{6} +(2.04878 + 1.67407i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.67629 + 1.35553i) q^{9} +O(q^{10})$	\(q+(-0.766044 - 0.642788i) q^{2} +(-0.402311 - 1.68468i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.256458 + 1.45445i) q^{5} +(-0.774703 + 1.54914i) q^{6} +(2.04878 + 1.67407i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.67629 + 1.35553i) q^{9} +(0.738441 - 1.27902i) q^{10} +(-0.864731 + 4.90413i) q^{11} +(1.58923 - 0.688740i) q^{12} +(0.0222706 + 0.126303i) q^{13} +(-0.493387 - 2.59934i) q^{14} +(2.34710 - 1.01719i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-3.59436 + 6.22561i) q^{17} +(2.92148 + 0.681891i) q^{18} +(1.55105 + 2.68650i) q^{19} +(-1.38782 + 0.505123i) q^{20} +(1.99602 - 4.12503i) q^{21} +(3.81474 - 3.20095i) q^{22} +(1.61573 - 1.35575i) q^{23} +(-1.66013 - 0.493928i) q^{24} +(2.64882 - 0.964093i) q^{25} +(0.0641255 - 0.111069i) q^{26} +(3.36034 + 3.96335i) q^{27} +(-1.29287 + 2.30835i) q^{28} +(0.951657 - 5.39711i) q^{29} +(-2.45182 - 0.729474i) q^{30} +(-0.753430 - 4.27292i) q^{31} +(0.939693 + 0.342020i) q^{32} +(8.60978 - 0.516191i) q^{33} +(6.75518 - 2.45868i) q^{34} +(-1.90941 + 3.40917i) q^{35} +(-1.79967 - 2.40025i) q^{36} +4.12019 q^{37} +(0.538675 - 3.05498i) q^{38} +(0.203820 - 0.0883317i) q^{39} +(1.38782 + 0.505123i) q^{40} +(-1.38763 - 7.86966i) q^{41} +(-4.18056 + 1.87694i) q^{42} +(1.24289 + 1.04291i) q^{43} -4.97979 q^{44} +(-2.65790 - 3.54488i) q^{45} -2.10918 q^{46} +(-1.24940 + 7.08570i) q^{47} +(0.954243 + 1.44548i) q^{48} +(1.39500 + 6.85959i) q^{49} +(-2.64882 - 0.964093i) q^{50} +(11.9342 + 3.55071i) q^{51} +(-0.120517 + 0.0438644i) q^{52} +(0.480436 + 0.832140i) q^{53} +(-0.0265734 - 5.19608i) q^{54} -7.35456 q^{55} +(2.47417 - 0.937262i) q^{56} +(3.90189 - 3.69384i) q^{57} +(-4.19821 + 3.52272i) q^{58} +(-9.31798 - 3.39147i) q^{59} +(1.40930 + 2.13481i) q^{60} +(1.05106 - 5.96088i) q^{61} +(-2.16942 + 3.75754i) q^{62} +(-7.75238 - 1.70311i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.177989 + 0.0647826i) q^{65} +(-6.92728 - 5.13884i) q^{66} +(-9.54040 + 8.00535i) q^{67} +(-6.75518 - 2.45868i) q^{68} +(-2.93404 - 2.17654i) q^{69} +(3.65406 - 1.38423i) q^{70} +(6.07951 + 10.5300i) q^{71} +(-0.164223 + 2.99550i) q^{72} +5.37006 q^{73} +(-3.15625 - 2.64841i) q^{74} +(-2.68984 - 4.07455i) q^{75} +(-2.37635 + 1.99400i) q^{76} +(-9.98149 + 8.59987i) q^{77} +(-0.212914 - 0.0633469i) q^{78} +(10.0443 + 8.42817i) q^{79} +(-0.738441 - 1.27902i) q^{80} +(5.32508 - 7.25559i) q^{81} +(-3.99553 + 6.92046i) q^{82} +(-1.46630 + 8.31582i) q^{83} +(4.40897 + 1.24939i) q^{84} +(-9.97661 - 3.63119i) q^{85} +(-0.281741 - 1.59783i) q^{86} +(-9.47527 + 0.568080i) q^{87} +(3.81474 + 3.20095i) q^{88} +(-3.01940 - 5.22975i) q^{89} +(-0.242538 + 4.42400i) q^{90} +(-0.165812 + 0.296049i) q^{91} +(1.61573 + 1.35575i) q^{92} +(-6.89538 + 2.98833i) q^{93} +(5.51169 - 4.62486i) q^{94} +(-3.50959 + 2.94490i) q^{95} +(0.198146 - 1.72068i) q^{96} +(0.558612 + 0.468731i) q^{97} +(3.34063 - 6.15144i) q^{98} +(-4.33343 - 14.2971i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8}+O(q^{10}) $ 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8	$ 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8} + 6 q^{10} + 12 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} + 18 q^{19} + 6 q^{22} + 12 q^{23} - 6 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} - 18 q^{35} - 3 q^{36} - 48 q^{39} - 6 q^{41} + 36 q^{42} - 24 q^{43} - 45 q^{45} - 27 q^{47} + 6 q^{48} + 48 q^{49} + 6 q^{50} + 15 q^{51} - 6 q^{52} - 15 q^{53} - 63 q^{54} - 72 q^{55} - 3 q^{56} + 57 q^{57} - 3 q^{58} - 30 q^{59} + 21 q^{60} + 9 q^{61} - 24 q^{62} - 21 q^{63} - 36 q^{64} + 45 q^{65} + 6 q^{67} + 9 q^{68} - 39 q^{69} + 15 q^{70} + 12 q^{71} - 60 q^{73} - 18 q^{74} + 42 q^{75} + 3 q^{77} + 6 q^{78} - 27 q^{79} - 6 q^{80} + 12 q^{81} + 33 q^{82} + 18 q^{83} - 21 q^{84} + 51 q^{85} - 12 q^{86} - 117 q^{87} + 6 q^{88} - 36 q^{89} - 69 q^{90} - 3 q^{91} + 12 q^{92} - 30 q^{93} - 27 q^{94} + 3 q^{95} + 48 q^{97} - 12 q^{98} + 90 q^{99}+O(q^{100}) $ 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8 + 6 * q^10 + 12 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 + 18 * q^19 + 6 * q^22 + 12 * q^23 - 6 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 - 18 * q^35 - 3 * q^36 - 48 * q^39 - 6 * q^41 + 36 * q^42 - 24 * q^43 - 45 * q^45 - 27 * q^47 + 6 * q^48 + 48 * q^49 + 6 * q^50 + 15 * q^51 - 6 * q^52 - 15 * q^53 - 63 * q^54 - 72 * q^55 - 3 * q^56 + 57 * q^57 - 3 * q^58 - 30 * q^59 + 21 * q^60 + 9 * q^61 - 24 * q^62 - 21 * q^63 - 36 * q^64 + 45 * q^65 + 6 * q^67 + 9 * q^68 - 39 * q^69 + 15 * q^70 + 12 * q^71 - 60 * q^73 - 18 * q^74 + 42 * q^75 + 3 * q^77 + 6 * q^78 - 27 * q^79 - 6 * q^80 + 12 * q^81 + 33 * q^82 + 18 * q^83 - 21 * q^84 + 51 * q^85 - 12 * q^86 - 117 * q^87 + 6 * q^88 - 36 * q^89 - 69 * q^90 - 3 * q^91 + 12 * q^92 - 30 * q^93 - 27 * q^94 + 3 * q^95 + 48 * q^97 - 12 * q^98 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$3$	−0.402311	−	1.68468i	−0.232274	−	0.972650i
$3$	−0.402311	−	1.68468i	−0.232274	−	0.972650i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	0.256458	+	1.45445i	0.114691	+	0.650448i	0.986902	+	0.161318i	$0.0515744\pi$
$5$	0.256458	+	1.45445i	0.114691	+	0.650448i	−0.872211	+	0.489130i	$0.837314\pi$
$6$	−0.774703	+	1.54914i	−0.316271	+	0.632434i
$7$	2.04878	+	1.67407i	0.774366	+	0.632738i
$7$	2.04878	+	1.67407i	0.774366	+	0.632738i
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−2.67629	+	1.35553i	−0.892097	+	0.451843i
$10$	0.738441	−	1.27902i	0.233516	−	0.404461i
$11$	−0.864731	+	4.90413i	−0.260726	+	1.47865i	0.520209	+	0.854039i	$0.325854\pi$
$11$	−0.864731	+	4.90413i	−0.260726	+	1.47865i	−0.780935	+	0.624612i	$0.785257\pi$
$12$	1.58923	−	0.688740i	0.458770	−	0.198822i
$13$	0.0222706	+	0.126303i	0.00617674	+	0.0350301i	0.987740	−	0.156106i	$-0.0498940\pi$
$13$	0.0222706	+	0.126303i	0.00617674	+	0.0350301i	−0.981564	+	0.191136i	$0.938783\pi$
$14$	−0.493387	−	2.59934i	−0.131863	−	0.694703i
$15$	2.34710	−	1.01719i	0.606018	−	0.262637i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−3.59436	+	6.22561i	−0.871760	+	1.50993i	−0.0115845	+	0.999933i	$0.503688\pi$
$17$	−3.59436	+	6.22561i	−0.871760	+	1.50993i	−0.860175	+	0.509999i	$0.829646\pi$
$18$	2.92148	+	0.681891i	0.688599	+	0.160723i
$19$	1.55105	+	2.68650i	0.355836	+	0.616326i	0.987261	−	0.159111i	$-0.0508629\pi$
$19$	1.55105	+	2.68650i	0.355836	+	0.616326i	−0.631425	+	0.775437i	$0.717530\pi$
$20$	−1.38782	+	0.505123i	−0.310325	+	0.112949i
$21$	1.99602	−	4.12503i	0.435567	−	0.900156i
$22$	3.81474	−	3.20095i	0.813305	−	0.682444i
$23$	1.61573	−	1.35575i	0.336902	−	0.282694i	−0.458603	−	0.888641i	$-0.651650\pi$
$23$	1.61573	−	1.35575i	0.336902	−	0.282694i	0.795505	+	0.605947i	$0.207206\pi$
$24$	−1.66013	−	0.493928i	−0.338873	−	0.100823i
$25$	2.64882	−	0.964093i	0.529765	−	0.192819i
$26$	0.0641255	−	0.111069i	0.0125761	−	0.0217824i
$27$	3.36034	+	3.96335i	0.646697	+	0.762747i
$28$	−1.29287	+	2.30835i	−0.244329	+	0.436238i
$29$	0.951657	−	5.39711i	0.176718	−	1.00222i	−0.759424	−	0.650596i	$-0.774519\pi$
$29$	0.951657	−	5.39711i	0.176718	−	1.00222i	0.936142	−	0.351622i	$-0.114370\pi$
$30$	−2.45182	−	0.729474i	−0.447639	−	0.133183i
$31$	−0.753430	−	4.27292i	−0.135320	−	0.767438i	−0.974636	−	0.223795i	$-0.928155\pi$
$31$	−0.753430	−	4.27292i	−0.135320	−	0.767438i	0.839316	−	0.543644i	$-0.182956\pi$
$32$	0.939693	+	0.342020i	0.166116	+	0.0604612i
$33$	8.60978	−	0.516191i	1.49877	−	0.0898573i
$34$	6.75518	−	2.45868i	1.15850	−	0.421661i
$35$	−1.90941	+	3.40917i	−0.322750	+	0.576254i
$36$	−1.79967	−	2.40025i	−0.299945	−	0.400041i
$37$	4.12019			0.677356			0.338678	−	0.940902i	$-0.390020\pi$
$37$	4.12019			0.677356			0.338678	+	0.940902i	$0.390020\pi$
$38$	0.538675	−	3.05498i	0.0873846	−	0.495583i
$39$	0.203820	−	0.0883317i	0.0326373	−	0.0141444i
$40$	1.38782	+	0.505123i	0.219433	+	0.0798670i
$41$	−1.38763	−	7.86966i	−0.216712	−	1.22903i	−0.877911	−	0.478824i	$-0.841063\pi$
$41$	−1.38763	−	7.86966i	−0.216712	−	1.22903i	0.661199	−	0.750210i	$-0.270048\pi$
$42$	−4.18056	+	1.87694i	−0.645075	+	0.289618i
$43$	1.24289	+	1.04291i	0.189540	+	0.159043i	0.732620	−	0.680638i	$-0.238297\pi$
$43$	1.24289	+	1.04291i	0.189540	+	0.159043i	−0.543080	+	0.839681i	$0.682742\pi$
$44$	−4.97979			−0.750731
$45$	−2.65790	−	3.54488i	−0.396216	−	0.528440i
$46$	−2.10918			−0.310982
$47$	−1.24940	+	7.08570i	−0.182244	+	1.03356i	0.747202	+	0.664597i	$0.231397\pi$
$47$	−1.24940	+	7.08570i	−0.182244	+	1.03356i	−0.929446	+	0.368958i	$0.879714\pi$
$48$	0.954243	+	1.44548i	0.137733	+	0.208637i
$49$	1.39500	+	6.85959i	0.199286	+	0.979941i
$50$	−2.64882	−	0.964093i	−0.374600	−	0.136343i
$51$	11.9342	+	3.55071i	1.67112	+	0.497199i
$52$	−0.120517	+	0.0438644i	−0.0167126	+	0.00608290i
$53$	0.480436	+	0.832140i	0.0659930	+	0.114303i	0.897134	−	0.441758i	$-0.145645\pi$
$53$	0.480436	+	0.832140i	0.0659930	+	0.114303i	−0.831141	+	0.556062i	$0.812312\pi$
$54$	−0.0265734	−	5.19608i	−0.00361618	−	0.707098i
$55$	−7.35456			−0.991689
$56$	2.47417	−	0.937262i	0.330625	−	0.125247i
$57$	3.90189	−	3.69384i	0.516818	−	0.489261i
$58$	−4.19821	+	3.52272i	−0.551252	+	0.462555i
$59$	−9.31798	−	3.39147i	−1.21310	−	0.441531i	−0.345321	−	0.938485i	$-0.612230\pi$
$59$	−9.31798	−	3.39147i	−1.21310	−	0.441531i	−0.867777	+	0.496953i	$0.834452\pi$
$60$	1.40930	+	2.13481i	0.181940	+	0.275603i
$61$	1.05106	−	5.96088i	0.134575	−	0.763213i	−0.840580	−	0.541688i	$-0.817786\pi$
$61$	1.05106	−	5.96088i	0.134575	−	0.763213i	0.975155	−	0.221525i	$-0.0711034\pi$
$62$	−2.16942	+	3.75754i	−0.275516	+	0.477208i
$63$	−7.75238	−	1.70311i	−0.976708	−	0.214572i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−0.177989	+	0.0647826i	−0.0220768	+	0.00803530i
$66$	−6.92728	−	5.13884i	−0.852689	−	0.632547i
$67$	−9.54040	+	8.00535i	−1.16555	+	0.978009i	−0.999966	−	0.00818779i	$-0.997394\pi$
$67$	−9.54040	+	8.00535i	−1.16555	+	0.978009i	−0.165579	+	0.986197i	$0.552949\pi$
$68$	−6.75518	−	2.45868i	−0.819186	−	0.298159i
$69$	−2.93404	−	2.17654i	−0.353216	−	0.262025i
$70$	3.65406	−	1.38423i	0.436744	−	0.165447i
$71$	6.07951	+	10.5300i	0.721505	+	1.24968i	0.960396	+	0.278637i	$0.0898826\pi$
$71$	6.07951	+	10.5300i	0.721505	+	1.24968i	−0.238891	+	0.971046i	$0.576784\pi$
$72$	−0.164223	+	2.99550i	−0.0193538	+	0.353023i
$73$	5.37006			0.628518			0.314259	−	0.949337i	$-0.398244\pi$
$73$	5.37006			0.628518			0.314259	+	0.949337i	$0.398244\pi$
$74$	−3.15625	−	2.64841i	−0.366907	−	0.307871i
$75$	−2.68984	−	4.07455i	−0.310596	−	0.470489i
$76$	−2.37635	+	1.99400i	−0.272586	+	0.228727i
$77$	−9.98149	+	8.59987i	−1.13750	+	0.980046i
$78$	−0.212914	−	0.0633469i	−0.0241077	−	0.00717262i
$79$	10.0443	+	8.42817i	1.13007	+	0.948243i	0.999069	−	0.0431389i	$-0.0137358\pi$
$79$	10.0443	+	8.42817i	1.13007	+	0.948243i	0.131003	+	0.991382i	$0.458180\pi$
$80$	−0.738441	−	1.27902i	−0.0825602	−	0.142999i
$81$	5.32508	−	7.25559i	0.591675	−	0.806176i
$82$	−3.99553	+	6.92046i	−0.441232	+	0.764237i
$83$	−1.46630	+	8.31582i	−0.160948	+	0.912780i	0.792197	+	0.610265i	$0.208937\pi$
$83$	−1.46630	+	8.31582i	−0.160948	+	0.912780i	−0.953145	+	0.302515i	$0.902174\pi$
$84$	4.40897	+	1.24939i	0.481058	+	0.136320i
$85$	−9.97661	−	3.63119i	−1.08211	−	0.393858i
$86$	−0.281741	−	1.59783i	−0.0303810	−	0.172299i
$87$	−9.47527	+	0.568080i	−1.01586	+	0.0609046i
$88$	3.81474	+	3.20095i	0.406652	+	0.341222i
$89$	−3.01940	−	5.22975i	−0.320056	−	0.554353i	0.660443	−	0.750876i	$-0.270368\pi$
$89$	−3.01940	−	5.22975i	−0.320056	−	0.554353i	−0.980499	+	0.196523i	$0.937035\pi$
$90$	−0.242538	+	4.42400i	−0.0255657	+	0.466331i
$91$	−0.165812	+	0.296049i	−0.0173818	+	0.0310343i
$92$	1.61573	+	1.35575i	0.168451	+	0.141347i
$93$	−6.89538	+	2.98833i	−0.715018	+	0.309875i
$94$	5.51169	−	4.62486i	0.568488	−	0.477018i
$95$	−3.50959	+	2.94490i	−0.360076	+	0.302140i
$96$	0.198146	−	1.72068i	0.0202232	−	0.175616i
$97$	0.558612	+	0.468731i	0.0567185	+	0.0475925i	0.670706	−	0.741723i	$-0.265991\pi$
$97$	0.558612	+	0.468731i	0.0567185	+	0.0475925i	−0.613988	+	0.789316i	$0.710436\pi$
$98$	3.34063	−	6.15144i	0.337454	−	0.621389i
$99$	−4.33343	−	14.2971i	−0.435526	−	1.43691i
$100$	1.40941	+	2.44117i	0.140941	+	0.244117i
$101$	−2.31401	−	1.94169i	−0.230253	−	0.193205i	0.520361	−	0.853947i	$-0.325798\pi$
$101$	−2.31401	−	1.94169i	−0.230253	−	0.193205i	−0.750614	+	0.660741i	$0.770242\pi$
$102$	−6.85978	−	10.3912i	−0.679219	−	1.02888i
$103$	−1.58659	−	8.99802i	−0.156332	−	0.886602i	−0.957558	−	0.288240i	$-0.906930\pi$
$103$	−1.58659	−	8.99802i	−0.156332	−	0.886602i	0.801226	−	0.598361i	$-0.204181\pi$
$104$	0.120517	+	0.0438644i	0.0118176	+	0.00430126i
$105$	6.51153	+	1.84520i	0.635460	+	0.180073i
$106$	0.166854	−	0.946274i	0.0162063	−	0.0919103i
$107$	9.07986	−	15.7268i	0.877783	−	1.52036i	0.0240141	−	0.999712i	$-0.492355\pi$
$107$	9.07986	−	15.7268i	0.877783	−	1.52036i	0.853769	−	0.520653i	$-0.174311\pi$
$108$	−3.31962	+	3.99751i	−0.319431	+	0.384661i
$109$	−7.17154	−	12.4215i	−0.686909	−	1.18976i	−0.972833	−	0.231509i	$-0.925634\pi$
$109$	−7.17154	−	12.4215i	−0.686909	−	1.18976i	0.285923	−	0.958252i	$-0.407700\pi$
$110$	5.63392	+	4.72742i	0.537173	+	0.450742i
$111$	−1.65760	−	6.94121i	−0.157332	−	0.658830i
$112$	−2.49779	−	0.872384i	−0.236019	−	0.0824326i
$113$	11.9541	−	10.0307i	1.12455	−	0.943606i	0.125720	−	0.992066i	$-0.459876\pi$
$113$	11.9541	−	10.0307i	1.12455	−	0.943606i	0.998825	+	0.0484600i	$0.0154313\pi$
$114$	−5.36337	+	0.321556i	−0.502326	+	0.0301165i
$115$	2.38624	+	2.00229i	0.222518	+	0.186714i
$116$	5.48037			0.508840
$117$	−0.230810	−	0.307834i	−0.0213383	−	0.0284593i
$118$	4.95799	+	8.58750i	0.456420	+	0.790543i
$119$	−17.7861	+	6.73771i	−1.63045	+	0.617645i
$120$	0.292638	−	2.54124i	0.0267141	−	0.231983i
$121$	−12.9661	−	4.71929i	−1.17874	−	0.429026i
$122$	−4.63674	+	3.89069i	−0.419791	+	0.352246i
$123$	−12.6996	+	5.50376i	−1.14508	+	0.496258i
$124$	4.07717	−	1.48397i	0.366141	−	0.133264i
$125$	5.77374	+	10.0004i	0.516419	+	0.894464i
$126$	4.84393	+	6.28779i	0.431532	+	0.560161i
$127$	−3.04941	+	5.28174i	−0.270592	+	0.468678i	−0.969013	−	0.247008i	$-0.920553\pi$
$127$	−3.04941	+	5.28174i	−0.270592	+	0.468678i	0.698422	+	0.715686i	$0.253886\pi$
$128$	−0.173648	+	0.984808i	−0.0153485	+	0.0870455i
$129$	1.25694	−	2.51345i	0.110668	−	0.221297i
$130$	0.177989	+	0.0647826i	0.0156107	+	0.00568181i
$131$	5.20770	−	4.36978i	0.454999	−	0.381790i	−0.386288	−	0.922378i	$-0.626243\pi$
$131$	5.20770	−	4.36978i	0.454999	−	0.381790i	0.841287	+	0.540589i	$0.181798\pi$
$132$	2.00342	+	8.38935i	0.174376	+	0.730199i
$133$	−1.31962	+	8.10062i	−0.114425	+	0.702413i
$134$	12.4541			1.07587
$135$	−4.90269	+	5.90386i	−0.421956	+	0.508123i
$136$	3.59436	+	6.22561i	0.308214	+	0.533842i
$137$	2.70480	−	0.984466i	0.231086	−	0.0841086i	−0.223882	−	0.974616i	$-0.571873\pi$
$137$	2.70480	−	0.984466i	0.231086	−	0.0841086i	0.454968	+	0.890508i	$0.349651\pi$
$138$	0.848546	+	3.55329i	0.0722330	+	0.302476i
$139$	−17.0287	−	6.19796i	−1.44436	−	0.525704i	−0.503350	−	0.864083i	$-0.667899\pi$
$139$	−17.0287	−	6.19796i	−1.44436	−	0.525704i	−0.941010	+	0.338379i	$0.890121\pi$
$140$	−3.68894	−	1.28841i	−0.311772	−	0.108890i
$141$	12.4398	−	0.745815i	1.04762	−	0.0628089i
$142$	2.11139	−	11.9743i	0.177184	−	1.00486i
$143$	−0.638663			−0.0534077
$144$	2.05127	−	2.18913i	0.170939	−	0.182427i
$145$	8.09386			0.672159
$146$	−4.11370	−	3.45181i	−0.340452	−	0.285673i
$147$	10.9950	−	5.10982i	0.906851	−	0.421451i
$148$	0.715464	+	4.05760i	0.0588108	+	0.333533i
$149$	12.8392	+	4.67308i	1.05183	+	0.382834i	0.809352	−	0.587324i	$-0.199818\pi$
$149$	12.8392	+	4.67308i	1.05183	+	0.382834i	0.242476	+	0.970158i	$0.422041\pi$
$150$	−0.558537	+	4.85028i	−0.0456044	+	0.396024i
$151$	−2.16722	+	12.2909i	−0.176366	+	1.00022i	0.760189	+	0.649702i	$0.225106\pi$
$151$	−2.16722	+	12.2909i	−0.176366	+	1.00022i	−0.936555	+	0.350520i	$0.886005\pi$
$152$	3.10211			0.251614
$153$	1.18055	−	21.5338i	0.0954418	−	1.74090i
$154$	13.1742	−	0.171907i	1.06160	−	0.0138527i
$155$	6.02150	−	2.19165i	0.483658	−	0.176037i
$156$	0.122383	+	0.185385i	0.00979846	+	0.0148427i
$157$	3.67629	+	1.33806i	0.293400	+	0.106789i	0.484526	−	0.874777i	$-0.338992\pi$
$157$	3.67629	+	1.33806i	0.293400	+	0.106789i	−0.191127	+	0.981565i	$0.561214\pi$
$158$	−2.27686	−	12.9127i	−0.181137	−	1.02728i
$159$	1.20860	−	1.14416i	0.0958486	−	0.0907378i
$160$	−0.256458	+	1.45445i	−0.0202748	+	0.114984i
$161$	5.57989	−	0.0728109i	0.439757	−	0.00573830i
$162$	−8.74305	+	2.13521i	−0.686919	+	0.167758i
$163$	−8.43985	+	14.6183i	−0.661060	+	1.14499i	0.319277	+	0.947661i	$0.396560\pi$
$163$	−8.43985	+	14.6183i	−0.661060	+	1.14499i	−0.980337	+	0.197329i	$0.936773\pi$
$164$	7.50914	−	2.73310i	0.586365	−	0.213419i
$165$	2.95882	+	12.3901i	0.230344	+	0.964566i
$166$	6.46856	−	5.42777i	0.502058	−	0.421276i
$167$	11.7113	−	9.82697i	0.906250	−	0.760434i	−0.0651521	−	0.997875i	$-0.520753\pi$
$167$	11.7113	−	9.82697i	0.906250	−	0.760434i	0.971402	+	0.237442i	$0.0763088\pi$
$168$	−2.57437	−	3.79112i	−0.198617	−	0.292491i
$169$	12.2005	−	4.44064i	0.938504	−	0.341587i
$170$	5.30844	+	9.19449i	0.407139	+	0.705185i
$171$	−7.79271	−	5.08737i	−0.595923	−	0.389041i
$172$	−0.811242	+	1.40511i	−0.0618566	+	0.107139i
$173$	−9.34394	+	3.40092i	−0.710407	+	0.258567i	−0.671848	−	0.740689i	$-0.734499\pi$
$173$	−9.34394	+	3.40092i	−0.710407	+	0.258567i	−0.0385592	+	0.999256i	$0.512277\pi$
$174$	7.62363	+	5.65541i	0.577946	+	0.428736i
$175$	7.04081	+	2.45909i	0.532235	+	0.185890i
$176$	−0.864731	−	4.90413i	−0.0651815	−	0.369663i
$177$	−1.96481	+	17.0622i	−0.147684	+	1.28248i
$178$	−1.04863	+	5.94706i	−0.0785979	+	0.445751i
$179$	7.59958	−	13.1629i	0.568019	−	0.983838i	−0.428742	−	0.903427i	$-0.641043\pi$
$179$	7.59958	−	13.1629i	0.568019	−	0.983838i	0.996762	−	0.0804115i	$-0.0256234\pi$
$180$	3.02949	−	3.23308i	0.225805	−	0.240980i
$181$	−5.62905	+	9.74980i	−0.418404	+	0.724697i	−0.995779	−	0.0917821i	$-0.970744\pi$
$181$	−5.62905	+	9.74980i	−0.418404	+	0.724697i	0.577375	+	0.816479i	$0.304077\pi$
$182$	0.317316	−	0.120205i	0.0235210	−	0.00891018i
$183$	−10.4650	+	0.627421i	−0.773597	+	0.0463803i
$184$	−0.366255	−	2.07714i	−0.0270007	−	0.153129i
$185$	1.05666	+	5.99260i	0.0776869	+	0.440584i
$186$	7.20303	+	2.14307i	0.528152	+	0.157138i
$187$	−27.4231	−	23.0107i	−2.00537	−	1.68271i
$188$	−7.19501			−0.524750
$189$	0.249674	+	13.7455i	0.0181611	+	0.999835i
$190$	4.58145			0.332373
$191$	19.7510	+	16.5731i	1.42913	+	1.19918i	0.946223	+	0.323514i	$0.104864\pi$
$191$	19.7510	+	16.5731i	1.42913	+	1.19918i	0.482909	+	0.875670i	$0.339580\pi$
$192$	−1.25782	+	1.19075i	−0.0907753	+	0.0859351i
$193$	−0.541746	−	3.07239i	−0.0389957	−	0.221156i	0.959082	−	0.283128i	$-0.0913721\pi$
$193$	−0.541746	−	3.07239i	−0.0389957	−	0.221156i	−0.998078	+	0.0619722i	$0.980261\pi$
$194$	−0.126627	−	0.718138i	−0.00909130	−	0.0515593i
$195$	0.180745	+	0.273791i	0.0129434	+	0.0196066i
$196$	−6.51314	+	2.56496i	−0.465224	+	0.183212i
$197$	−3.60060	+	6.23641i	−0.256532	+	0.444326i	−0.965310	−	0.261105i	$-0.915913\pi$
$197$	−3.60060	+	6.23641i	−0.256532	+	0.444326i	0.708779	+	0.705431i	$0.249247\pi$
$198$	−5.87038	+	13.7377i	−0.417189	+	0.976293i
$199$	7.92868	−	13.7329i	0.562049	−	0.973498i	−0.435268	−	0.900301i	$-0.643346\pi$
$199$	7.92868	−	13.7329i	0.562049	−	0.973498i	0.997317	−	0.0731970i	$-0.0233202\pi$
$200$	0.489483	−	2.77599i	0.0346117	−	0.196292i
$201$	17.3247	+	12.8519i	1.22199	+	0.906502i
$202$	0.524545	+	2.97484i	0.0369068	+	0.209309i
$203$	10.9849	−	9.46436i	0.770986	−	0.664268i
$204$	−1.42441	+	12.3695i	−0.0997289	+	0.866036i
$205$	11.0901	−	4.03647i	0.774567	−	0.281919i
$206$	−4.56842	+	7.91273i	−0.318297	+	0.551306i
$207$	−2.48639	+	5.81856i	−0.172816	+	0.404418i
$208$	−0.0641255	−	0.111069i	−0.00444631	−	0.00770123i
$209$	−14.5162	+	5.28347i	−1.00411	+	0.365465i
$210$	−3.80205	−	5.59904i	−0.262366	−	0.386370i
$211$	13.5243	−	11.3483i	0.931054	−	0.781247i	−0.0449521	−	0.998989i	$-0.514314\pi$
$211$	13.5243	−	11.3483i	0.931054	−	0.781247i	0.976006	+	0.217742i	$0.0698691\pi$
$212$	−0.736071	+	0.617637i	−0.0505535	+	0.0424195i
$213$	15.2939	−	14.4784i	1.04792	−	0.992041i
$214$	−17.0645	+	6.21099i	−1.16651	+	0.424574i
$215$	−1.19811	+	2.07519i	−0.0817103	+	0.141526i
$216$	5.11253	−	0.928460i	0.347864	−	0.0631737i
$217$	5.60953	−	10.0156i	0.380800	−	0.679900i
$218$	−2.49065	+	14.1252i	−0.168688	+	0.956678i
$219$	−2.16043	−	9.04682i	−0.145988	−	0.611328i
$220$	−1.27711	−	7.24283i	−0.0861025	−	0.488311i
$221$	−0.866359	−	0.315329i	−0.0582776	−	0.0212113i
$222$	−3.19193	+	6.38276i	−0.214228	+	0.428383i
$223$	−7.32614	+	2.66650i	−0.490594	+	0.178562i	−0.575459	−	0.817831i	$-0.695177\pi$
$223$	−7.32614	+	2.66650i	−0.490594	+	0.178562i	0.0848644	+	0.996393i	$0.472954\pi$
$224$	1.35266	+	2.27383i	0.0903783	+	0.151927i
$225$	−5.78217	+	6.17075i	−0.385478	+	0.411384i
$226$	−15.6049			−1.03803
$227$	−1.57829	+	8.95093i	−0.104755	+	0.594094i	0.886563	+	0.462607i	$0.153086\pi$
$227$	−1.57829	+	8.95093i	−0.104755	+	0.594094i	−0.991318	+	0.131486i	$0.958025\pi$
$228$	4.31528	+	3.20118i	0.285786	+	0.212004i
$229$	−26.7996	−	9.75426i	−1.77097	−	0.644580i	−0.999970	−	0.00774177i	$-0.997536\pi$
$229$	−26.7996	−	9.75426i	−1.77097	−	0.644580i	−0.770998	−	0.636838i	$-0.780242\pi$
$230$	−0.540916	−	3.06769i	−0.0356669	−	0.202277i
$231$	18.5037	+	13.3558i	1.21745	+	0.878747i
$232$	−4.19821	−	3.52272i	−0.275626	−	0.231278i
$233$	4.74962			0.311158			0.155579	−	0.987823i	$-0.450276\pi$
$233$	4.74962			0.311158			0.155579	+	0.987823i	$0.450276\pi$
$234$	−0.0210617	+	0.384176i	−0.00137685	+	0.0251144i
$235$	−10.6262			−0.693175
$236$	1.72189	−	9.76534i	0.112086	−	0.635670i
$237$	10.1578	−	20.3122i	0.659822	−	1.31942i
$238$	17.9559	+	6.27132i	1.16391	+	0.406509i
$239$	8.82413	+	3.21172i	0.570786	+	0.207749i	0.611258	−	0.791432i	$-0.290664\pi$
$239$	8.82413	+	3.21172i	0.570786	+	0.207749i	−0.0404719	+	0.999181i	$0.512886\pi$
$240$	−1.85765	+	1.75860i	−0.119911	+	0.113517i
$241$	27.1521	−	9.88255i	1.74902	−	0.636591i	0.749348	−	0.662177i	$-0.230367\pi$
$241$	27.1521	−	9.88255i	1.74902	−	0.636591i	0.999673	+	0.0255856i	$0.00814505\pi$
$242$	6.89914	+	11.9497i	0.443493	+	0.768153i
$243$	−14.3657	−	6.05205i	−0.921559	−	0.388239i
$244$	6.05284			0.387493
$245$	−9.61914	+	3.78815i	−0.614544	+	0.242016i
$246$	13.2662	+	3.94701i	0.845822	+	0.251652i
$247$	−0.304770	+	0.255732i	−0.0193920	+	0.0162718i
$248$	−4.07717	−	1.48397i	−0.258900	−	0.0942321i
$249$	14.5994	−	0.875293i	0.925200	−	0.0554694i
$250$	2.00520	−	11.3720i	0.126820	−	0.719231i
$251$	8.57593	−	14.8539i	0.541308	−	0.937573i	−0.457521	−	0.889199i	$-0.651263\pi$
$251$	8.57593	−	14.8539i	0.541308	−	0.937573i	0.998829	−	0.0483742i	$-0.0154040\pi$
$252$	0.331048	−	7.93035i	0.0208540	−	0.499565i
$253$	5.25163	+	9.09609i	0.330167	+	0.571866i
$254$	5.73102	−	2.08592i	0.359596	−	0.130882i
$255$	−2.10369	+	18.2683i	−0.131738	+	1.14400i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−20.2235	−	7.36074i	−1.26150	−	0.459150i	−0.377231	−	0.926119i	$-0.623124\pi$
$257$	−20.2235	−	7.36074i	−1.26150	−	0.459150i	−0.884274	+	0.466969i	$0.845346\pi$
$258$	−2.57849	+	1.11747i	−0.160530	+	0.0695707i
$259$	8.44137	+	6.89748i	0.524521	+	0.428588i
$260$	−0.0947059	−	0.164035i	−0.00587341	−	0.0101730i
$261$	4.76904	+	15.7342i	0.295196	+	0.973926i
$262$	−6.79817			−0.419993
$263$	−8.02072	−	6.73018i	−0.494579	−	0.415001i	0.361085	−	0.932533i	$-0.382406\pi$
$263$	−8.02072	−	6.73018i	−0.494579	−	0.415001i	−0.855664	+	0.517532i	$0.826851\pi$
$264$	3.85786	−	7.71439i	0.237435	−	0.474788i
$265$	−1.08709	+	0.912177i	−0.0667794	+	0.0560346i
$266$	6.21786	−	5.35720i	0.381242	−	0.328471i
$267$	−7.59572	+	7.19071i	−0.464851	+	0.440064i
$268$	−9.54040	−	8.00535i	−0.582773	−	0.489004i
$269$	−1.08274	−	1.87535i	−0.0660156	−	0.114342i	0.831128	−	0.556080i	$-0.187695\pi$
$269$	−1.08274	−	1.87535i	−0.0660156	−	0.114342i	−0.897144	+	0.441738i	$0.854362\pi$
$270$	7.55060	−	1.37123i	0.459515	−	0.0834502i
$271$	5.46952	−	9.47348i	0.332249	−	0.575473i	−0.650703	−	0.759332i	$-0.725526\pi$
$271$	5.46952	−	9.47348i	0.332249	−	0.575473i	0.982953	+	0.183859i	$0.0588591\pi$
$272$	1.24831	−	7.07950i	0.0756897	−	0.429258i
$273$	0.565455	+	0.160236i	0.0342229	+	0.00969791i
$274$	−2.70480	−	0.984466i	−0.163403	−	0.0594738i
$275$	2.43752	+	13.8239i	0.146988	+	0.833610i
$276$	1.63399	−	3.26741i	0.0983545	−	0.196675i
$277$	−8.09585	−	6.79322i	−0.486432	−	0.408165i	0.366313	−	0.930492i	$-0.380620\pi$
$277$	−8.09585	−	6.79322i	−0.486432	−	0.408165i	−0.852746	+	0.522326i	$0.825064\pi$
$278$	9.06081	+	15.6938i	0.543431	+	0.941250i
$279$	7.80847	+	10.4143i	0.467481	+	0.623486i
$280$	1.99772	+	3.35818i	0.119386	+	0.200690i
$281$	−0.458484	−	0.384713i	−0.0273508	−	0.0229501i	0.629010	−	0.777397i	$-0.283461\pi$
$281$	−0.458484	−	0.384713i	−0.0273508	−	0.0229501i	−0.656361	+	0.754447i	$0.727905\pi$
$282$	−10.0088	−	7.42481i	−0.596017	−	0.442141i
$283$	−18.3624	+	15.4078i	−1.09153	+	0.915901i	−0.996827	−	0.0796042i	$-0.974634\pi$
$283$	−18.3624	+	15.4078i	−1.09153	+	0.915901i	−0.0947023	+	0.995506i	$0.530190\pi$
$284$	−9.31435	+	7.81567i	−0.552705	+	0.463774i
$285$	6.37315	+	4.72777i	0.377513	+	0.280049i
$286$	0.489244	+	0.410525i	0.0289296	+	0.0242748i
$287$	10.3314	−	18.4462i	0.609842	−	1.08884i
$288$	−2.97851	+	0.358436i	−0.175510	+	0.0211210i
$289$	−17.3388	−	30.0317i	−1.01993	−	1.76657i
$290$	−6.20026	−	5.20264i	−0.364092	−	0.305509i
$291$	0.564927	−	1.12966i	0.0331166	−	0.0662218i
$292$	0.932500	+	5.28847i	0.0545705	+	0.309484i
$293$	−8.68671	−	3.16170i	−0.507483	−	0.184709i	0.0755737	−	0.997140i	$-0.475921\pi$
$293$	−8.68671	−	3.16170i	−0.507483	−	0.184709i	−0.583057	+	0.812432i	$0.698143\pi$
$294$	−11.7072	−	3.15310i	−0.682776	−	0.183892i
$295$	2.54303	−	14.4223i	0.148061	−	0.839696i
$296$	2.06010	−	3.56819i	0.119741	−	0.207397i
$297$	−22.3426	+	13.0523i	−1.29645	+	0.757371i
$298$	−6.83159	−	11.8327i	−0.395744	−	0.685448i
$299$	0.207218	+	0.173877i	0.0119838	+	0.0100556i
$300$	3.54557	−	3.35651i	0.204703	−	0.193788i
$301$	0.800513	+	4.21739i	0.0461408	+	0.243086i
$302$	9.56065	−	8.02234i	0.550153	−	0.461634i
$303$	−2.34017	+	4.67954i	−0.134439	+	0.268832i
$304$	−2.37635	−	1.99400i	−0.136293	−	0.114363i
$305$	8.93933			0.511864
$306$	−14.7460	+	15.7370i	−0.842974	+	0.899625i
$307$	11.7241	+	20.3067i	0.669127	+	1.15896i	0.978149	+	0.207907i	$0.0666652\pi$
$307$	11.7241	+	20.3067i	0.669127	+	1.15896i	−0.309022	+	0.951055i	$0.600002\pi$
$308$	−10.2025	−	8.33650i	−0.581341	−	0.475016i
$309$	−14.5205	+	6.29291i	−0.826041	+	0.357991i
$310$	−6.02150	−	2.19165i	−0.341998	−	0.124477i
$311$	15.8906	−	13.3338i	0.901075	−	0.756092i	−0.0693249	−	0.997594i	$-0.522085\pi$
$311$	15.8906	−	13.3338i	0.901075	−	0.756092i	0.970400	+	0.241502i	$0.0776401\pi$
$312$	0.0254124	−	0.220679i	0.00143870	−	0.0124935i
$313$	12.9956	−	4.73001i	0.734554	−	0.267356i	0.0524629	−	0.998623i	$-0.483293\pi$
$313$	12.9956	−	4.73001i	0.734554	−	0.267356i	0.682091	+	0.731267i	$0.261071\pi$
$314$	−1.95611	−	3.38808i	−0.110390	−	0.191201i
$315$	0.488918	−	11.7122i	0.0275474	−	0.659907i
$316$	−6.55595	+	11.3552i	−0.368801	+	0.638782i
$317$	2.93314	−	16.6347i	0.164742	−	0.934297i	−0.784588	−	0.620017i	$-0.787126\pi$
$317$	2.93314	−	16.6347i	0.164742	−	0.934297i	0.949330	−	0.314280i	$-0.101763\pi$
$318$	−1.66130	+	0.0996014i	−0.0931609	+	0.00558537i
$319$	25.6452	+	9.33410i	1.43586	+	0.522609i
$320$	1.13136	−	0.949322i	0.0632448	−	0.0530687i
$321$	−30.1475	−	8.96960i	−1.68267	−	0.500634i
$322$	−4.32124	−	3.53091i	−0.240814	−	0.196770i
$323$	−22.3001			−1.24081
$324$	8.07005	+	3.98426i	0.448336	+	0.221348i
$325$	0.180758	+	0.313082i	0.0100267	+	0.0173667i
$326$	15.8617	−	5.77320i	0.878500	−	0.319748i
$327$	−18.0410	+	17.0790i	−0.997671	+	0.944474i
$328$	−7.50914	−	2.73310i	−0.414623	−	0.150910i
$329$	−14.4217	+	12.4255i	−0.795093	+	0.685038i
$330$	5.69760	−	11.3932i	0.313643	−	0.627177i
$331$	−1.66530	+	9.44437i	−0.0915330	+	0.519109i	0.904222	+	0.427063i	$0.140452\pi$
$331$	−1.66530	+	9.44437i	−0.0915330	+	0.519109i	−0.995755	+	0.0920461i	$0.970659\pi$
$332$	−8.44411			−0.463431
$333$	−11.0268	+	5.58505i	−0.604267	+	0.306059i
$334$	−15.2881			−0.836525
$335$	−14.0900	−	11.8230i	−0.769822	−	0.645957i
$336$	−0.464801	+	4.55894i	−0.0253570	+	0.248711i
$337$	1.60895	+	9.12481i	0.0876451	+	0.497060i	0.996754	+	0.0805024i	$0.0256525\pi$
$337$	1.60895	+	9.12481i	0.0876451	+	0.497060i	−0.909109	+	0.416558i	$0.863236\pi$
$338$	−12.2005	−	4.44064i	−0.663622	−	0.241539i
$339$	−21.7077	−	16.1034i	−1.17900	−	0.874614i
$340$	1.84360	−	10.4556i	0.0999834	−	0.567034i
$341$	21.6065			1.17006
$342$	2.69946	+	8.90620i	0.145970	+	0.481592i
$343$	−8.62536	+	16.3891i	−0.465726	+	0.884929i
$344$	1.52464	−	0.554922i	0.0822029	−	0.0299194i
$345$	2.41321	−	4.82559i	0.129923	−	0.259801i
$346$	9.34394	+	3.40092i	0.502333	+	0.182834i
$347$	−4.07756	−	23.1250i	−0.218895	−	1.24141i	−0.874018	−	0.485893i	$-0.838495\pi$
$347$	−4.07756	−	23.1250i	−0.218895	−	1.24141i	0.655124	−	0.755522i	$-0.272617\pi$
$348$	−2.20481	−	9.23267i	−0.118190	−	0.494923i
$349$	−3.13495	+	17.7792i	−0.167810	+	0.951697i	0.778310	+	0.627880i	$0.216077\pi$
$349$	−3.13495	+	17.7792i	−0.167810	+	0.951697i	−0.946120	+	0.323817i	$0.895034\pi$
$350$	−3.81290	−	6.40952i	−0.203808	−	0.342603i
$351$	−0.425745	+	0.512685i	−0.0227246	+	0.0273651i
$352$	−2.48989	+	4.31262i	−0.132712	+	0.229864i
$353$	1.53937	−	0.560283i	0.0819322	−	0.0298209i	−0.300729	−	0.953710i	$-0.597230\pi$
$353$	1.53937	−	0.560283i	0.0819322	−	0.0298209i	0.382661	+	0.923889i	$0.375008\pi$
$354$	12.4725	−	11.8075i	0.662907	−	0.627560i
$355$	−13.7562	+	11.5428i	−0.730103	+	0.612629i
$356$	4.62599	−	3.88167i	0.245177	−	0.205728i
$357$	18.5064	+	27.2533i	0.979465	+	1.44240i
$358$	−14.2825	+	5.19842i	−0.754856	+	0.274745i
$359$	−7.71210	−	13.3577i	−0.407029	−	0.704995i	0.587526	−	0.809205i	$-0.300102\pi$
$359$	−7.71210	−	13.3577i	−0.407029	−	0.704995i	−0.994555	+	0.104210i	$0.966769\pi$
$360$	−4.39891	+	0.529367i	−0.231843	+	0.0279001i
$361$	4.68847	−	8.12067i	0.246762	−	0.427404i
$362$	10.5792	−	3.85050i	0.556028	−	0.202378i
$363$	−2.73407	+	23.7424i	−0.143502	+	1.24615i
$364$	−0.320344	−	0.111884i	−0.0167906	−	0.00586433i
$365$	1.37719	+	7.81045i	0.0720856	+	0.408818i
$366$	8.41998	+	6.24616i	0.440119	+	0.326492i
$367$	0.558254	−	3.16602i	0.0291406	−	0.165265i	−0.966765	−	0.255668i	$-0.917705\pi$
$367$	0.558254	−	3.16602i	0.0291406	−	0.165265i	0.995905	+	0.0904034i	$0.0288157\pi$
$368$	−1.05459	+	1.82660i	−0.0549743	+	0.0952183i
$369$	14.3813	+	19.1805i	0.748659	+	0.998498i
$370$	3.04252	−	5.26980i	0.158173	−	0.273964i
$371$	−0.408750	+	2.50915i	−0.0212212	+	0.130269i
$372$	−4.14030	−	6.27171i	−0.214665	−	0.325173i
$373$	−5.12951	−	29.0909i	−0.265596	−	1.50627i	−0.767333	−	0.641249i	$-0.778417\pi$
$373$	−5.12951	−	29.0909i	−0.265596	−	1.50627i	0.501737	−	0.865020i	$-0.332694\pi$
$374$	6.21630	+	35.2544i	0.321437	+	1.82296i
$375$	14.5246	−	13.7502i	0.750049	−	0.710056i
$376$	5.51169	+	4.62486i	0.284244	+	0.238509i
$377$	0.702864			0.0361993
$378$	8.64415	−	10.6901i	0.444607	−	0.549840i
$379$	−12.2076			−0.627063			−0.313532	−	0.949578i	$-0.601512\pi$
$379$	−12.2076			−0.627063			−0.313532	+	0.949578i	$0.601512\pi$
$380$	−3.50959	−	2.94490i	−0.180038	−	0.151070i
$381$	10.1248	+	3.01238i	0.518712	+	0.154329i
$382$	−4.47719	−	25.3914i	−0.229073	−	1.29914i
$383$	4.07145	+	23.0904i	0.208042	+	1.17986i	0.892581	+	0.450887i	$0.148892\pi$
$383$	4.07145	+	23.0904i	0.208042	+	1.17986i	−0.684540	+	0.728976i	$0.739997\pi$
$384$	1.72895	−	0.103657i	0.0882299	−	0.00528974i
$385$	−15.0679	−	12.3120i	−0.767930	−	0.627479i
$386$	−1.55990	+	2.70182i	−0.0793966	+	0.137519i
$387$	−4.74005	−	1.10636i	−0.240950	−	0.0562393i
$388$	−0.364608	+	0.631520i	−0.0185102	+	0.0320606i
$389$	−2.82565	+	16.0251i	−0.143266	+	0.812503i	0.825477	+	0.564436i	$0.190906\pi$
$389$	−2.82565	+	16.0251i	−0.143266	+	0.812503i	−0.968743	+	0.248067i	$0.920205\pi$
$390$	0.0375312	−	0.325917i	0.00190046	−	0.0165034i
$391$	2.63290	+	14.9319i	0.133152	+	0.755140i
$392$	6.63808	+	2.22169i	0.335274	+	0.112212i
$393$	−9.45680	−	7.01530i	−0.477032	−	0.353875i
$394$	6.76691	−	2.46295i	0.340912	−	0.124082i
$395$	−9.68237	+	16.7704i	−0.487173	+	0.843808i
$396$	13.3274	−	6.75025i	0.669725	−	0.339213i
$397$	8.72174	+	15.1065i	0.437732	+	0.758173i	0.997514	−	0.0704661i	$-0.0224487\pi$
$397$	8.72174	+	15.1065i	0.437732	+	0.758173i	−0.559783	+	0.828640i	$0.689115\pi$
$398$	−14.9010	+	5.42354i	−0.746922	+	0.271857i
$399$	14.1778	−	1.03583i	0.709780	−	0.0518565i
$400$	−2.15934	+	1.81190i	−0.107967	+	0.0905951i
$401$	2.94550	−	2.47157i	0.147091	−	0.123424i	−0.566273	−	0.824218i	$-0.691615\pi$
$401$	2.94550	−	2.47157i	0.147091	−	0.123424i	0.713364	+	0.700794i	$0.247171\pi$
$402$	−5.01042	−	20.9812i	−0.249897	−	1.04645i
$403$	0.522901	−	0.190321i	0.0260476	−	0.00948054i
$404$	1.51037	−	2.61603i	0.0751435	−	0.130152i
$405$	11.9185	+	5.88428i	0.592236	+	0.292392i
$406$	−14.4985	+	0.189188i	−0.719547	+	0.00938923i
$407$	−3.56286	+	20.2060i	−0.176604	+	1.00157i
$408$	9.04211	−	8.55997i	0.447651	−	0.423782i
$409$	−5.76134	−	32.6742i	−0.284880	−	1.61563i	−0.705715	−	0.708496i	$-0.749374\pi$
$409$	−5.76134	−	32.6742i	−0.284880	−	1.61563i	0.420835	−	0.907137i	$-0.361737\pi$
$410$	−11.0901	−	4.03647i	−0.547702	−	0.199347i
$411$	−2.74668	−	4.16066i	−0.135484	−	0.205230i
$412$	8.58581	−	3.12498i	0.422993	−	0.153957i
$413$	−13.4130	−	22.5473i	−0.660008	−	1.10948i
$414$	5.64478	−	2.85906i	0.277426	−	0.140515i
$415$	−12.4710			−0.612175
$416$	−0.0222706	+	0.126303i	−0.00109190	+	0.00619250i
$417$	−3.59072	+	31.1815i	−0.175838	+	1.52696i
$418$	14.5162	+	5.28347i	0.710011	+	0.258423i
$419$	2.08673	+	11.8344i	0.101943	+	0.578150i	0.992397	+	0.123076i	$0.0392760\pi$
$419$	2.08673	+	11.8344i	0.101943	+	0.578150i	−0.890454	+	0.455074i	$0.849613\pi$
$420$	−0.686456	+	6.73302i	−0.0334956	+	0.328538i
$421$	−25.1466	−	21.1005i	−1.22557	−	1.02838i	−0.998514	−	0.0544942i	$-0.982645\pi$
$421$	−25.1466	−	21.1005i	−1.22557	−	1.02838i	−0.227056	−	0.973882i	$-0.572910\pi$
$422$	−17.6548			−0.859421
$423$	−6.26112	−	20.6570i	−0.304426	−	1.00438i
$424$	0.960872			0.0466641
$425$	−3.51875	+	19.9558i	−0.170684	+	0.968000i
$426$	−21.0223	+	1.26037i	−1.01853	+	0.0610652i
$427$	12.1323	−	10.4530i	0.587124	−	0.505855i
$428$	17.0645	+	6.21099i	0.824846	+	0.300219i
$429$	0.256941	+	1.07594i	0.0124052	+	0.0519470i
$430$	2.25171	−	0.819555i	0.108587	−	0.0395224i
$431$	−5.20063	−	9.00776i	−0.250506	−	0.433889i	0.713159	−	0.701002i	$-0.247264\pi$
$431$	−5.20063	−	9.00776i	−0.250506	−	0.433889i	−0.963665	+	0.267113i	$0.913930\pi$
$432$	−4.51323	−	2.57503i	−0.217143	−	0.123891i
$433$	28.9506			1.39128			0.695639	−	0.718392i	$-0.255121\pi$
$433$	28.9506			1.39128			0.695639	+	0.718392i	$0.255121\pi$
$434$	−10.7350	+	4.06662i	−0.515298	+	0.195204i
$435$	−3.25625	−	13.6356i	−0.156125	−	0.653776i
$436$	10.9874	−	9.21956i	0.526203	−	0.441537i
$437$	6.14831	+	2.23780i	0.294114	+	0.107049i
$438$	−4.16020	+	8.31897i	−0.198782	+	0.397496i
$439$	−5.14234	+	29.1637i	−0.245431	+	1.39191i	0.574060	+	0.818813i	$0.305368\pi$
$439$	−5.14234	+	29.1637i	−0.245431	+	1.39191i	−0.819491	+	0.573093i	$0.805743\pi$
$440$	−3.67728	+	6.36923i	−0.175307	+	0.303641i
$441$	−13.0318	−	16.4673i	−0.620562	−	0.784157i
$442$	0.460980	+	0.798441i	0.0219266	+	0.0379780i
$443$	28.6600	−	10.4314i	1.36168	−	0.495609i	0.445104	−	0.895479i	$-0.353167\pi$
$443$	28.6600	−	10.4314i	1.36168	−	0.495609i	0.916572	+	0.399870i	$0.130945\pi$
$444$	6.54792	−	2.83774i	0.310750	−	0.134673i
$445$	6.83204	−	5.73276i	0.323870	−	0.271759i
$446$	7.32614	+	2.66650i	0.346903	+	0.126262i
$447$	2.70730	−	23.5100i	0.128051	−	1.11198i
$448$	0.425394	−	2.61133i	0.0200980	−	0.123374i
$449$	3.63600	+	6.29774i	0.171594	+	0.297209i	0.938977	−	0.343980i	$-0.111775\pi$
$449$	3.63600	+	6.29774i	0.171594	+	0.297209i	−0.767384	+	0.641188i	$0.778442\pi$
$450$	8.39588	−	1.01037i	0.395786	−	0.0476291i
$451$	39.7938			1.87382
$452$	11.9541	+	10.0307i	0.562273	+	0.471803i
$453$	21.5782	−	1.29370i	1.01383	−	0.0607833i
$454$	6.96258	−	5.84230i	0.326770	−	0.274193i
$455$	−0.473110	−	0.165240i	−0.0221798	−	0.00774656i
$456$	−1.24801	−	5.22606i	−0.0584435	−	0.244732i
$457$	6.25047	+	5.24477i	0.292385	+	0.245340i	0.777166	−	0.629295i	$-0.216656\pi$
$457$	6.25047	+	5.24477i	0.292385	+	0.245340i	−0.484782	+	0.874635i	$0.661101\pi$
$458$	14.2598	+	24.6987i	0.666315	+	1.15409i
$459$	−36.7525	+	6.67443i	−1.71546	+	0.311536i
$460$	−1.55750	+	2.69768i	−0.0726190	+	0.125780i
$461$	5.71301	−	32.4001i	0.266082	−	1.50902i	−0.499856	−	0.866109i	$-0.666614\pi$
$461$	5.71301	−	32.4001i	0.266082	−	1.50902i	0.765938	−	0.642915i	$-0.222275\pi$
$462$	−5.58971	−	22.1251i	−0.260057	−	1.02935i
$463$	22.4995	+	8.18914i	1.04564	+	0.380581i	0.807015	−	0.590531i	$-0.201082\pi$
$463$	22.4995	+	8.18914i	1.04564	+	0.380581i	0.238624	+	0.971112i	$0.423304\pi$
$464$	0.951657	+	5.39711i	0.0441796	+	0.250555i
$465$	−6.11474	−	9.26257i	−0.283564	−	0.429542i
$466$	−3.63842	−	3.05300i	−0.168547	−	0.141427i
$467$	−12.4373	−	21.5421i	−0.575530	−	0.996847i	−0.995984	−	0.0895333i	$-0.971462\pi$
$467$	−12.4373	−	21.5421i	−0.575530	−	0.996847i	0.420454	−	0.907314i	$-0.361871\pi$
$468$	0.263078	−	0.280758i	0.0121608	−	0.0129780i
$469$	−32.9477	+	0.429928i	−1.52138	+	0.0198522i
$470$	8.14012	+	6.83037i	0.375476	+	0.315062i
$471$	0.775191	−	6.73168i	0.0357189	−	0.310179i
$472$	−7.59609	+	6.37387i	−0.349638	+	0.293381i
$473$	−6.18935	+	5.19348i	−0.284587	+	0.238797i
$474$	−20.8378	+	9.03070i	−0.957110	+	0.414794i
$475$	6.69850	+	5.62071i	0.307348	+	0.257896i
$476$	−9.72388	−	16.3459i	−0.445693	−	0.749214i
$477$	−2.41378	−	1.57580i	−0.110519	−	0.0721511i
$478$	−4.69522	−	8.13237i	−0.214755	−	0.371966i
$479$	−3.32322	−	2.78851i	−0.151842	−	0.127410i	0.563702	−	0.825978i	$-0.309377\pi$
$479$	−3.32322	−	2.78851i	−0.151842	−	0.127410i	−0.715544	+	0.698568i	$0.753821\pi$
$480$	2.55345	−	0.153090i	0.116549	−	0.00698755i
$481$	0.0917590	+	0.520391i	0.00418385	+	0.0237278i
$482$	−27.1521	−	9.88255i	−1.23674	−	0.450138i
$483$	−2.36751	−	9.37103i	−0.107726	−	0.426397i
$484$	2.39605	−	13.5886i	0.108911	−	0.617666i
$485$	−0.538484	+	0.932681i	−0.0244513	+	0.0423509i
$486$	7.11457	+	13.8702i	0.322723	+	0.629166i
$487$	18.1088	+	31.3654i	0.820589	+	1.42130i	0.905244	+	0.424891i	$0.139688\pi$
$487$	18.1088	+	31.3654i	0.820589	+	1.42130i	−0.0846555	+	0.996410i	$0.526979\pi$
$488$	−4.63674	−	3.89069i	−0.209895	−	0.176123i
$489$	28.0225	+	8.33737i	1.26722	+	0.377029i
$490$	9.80366	+	3.28117i	0.442884	+	0.148228i
$491$	12.6889	−	10.6473i	0.572644	−	0.480505i	−0.309878	−	0.950776i	$-0.600288\pi$
$491$	12.6889	−	10.6473i	0.572644	−	0.480505i	0.882522	+	0.470271i	$0.155844\pi$
$492$	−7.62541	−	11.5509i	−0.343780	−	0.520756i
$493$	30.1797	+	25.3238i	1.35923	+	1.14053i
$494$	0.397848			0.0179000
$495$	19.6829	−	9.96932i	0.884683	−	0.448088i
$496$	2.16942	+	3.75754i	0.0974097	+	0.168718i
$497$	−5.17238	+	31.7512i	−0.232013	+	1.42424i
$498$	−11.7464	−	8.71380i	−0.526370	−	0.390475i
$499$	15.0563	+	5.48003i	0.674011	+	0.245320i	0.656274	−	0.754523i	$-0.272132\pi$
$499$	15.0563	+	5.48003i	0.674011	+	0.245320i	0.0177371	+	0.999843i	$0.494354\pi$
$500$	−8.84588	+	7.42257i	−0.395600	+	0.331948i
$501$	−21.2669	−	15.7763i	−0.950135	−	0.704835i
$502$	−16.1175	+	5.86628i	−0.719358	+	0.261825i
$503$	−5.13150	−	8.88802i	−0.228802	−	0.396297i	0.728651	−	0.684885i	$-0.240148\pi$
$503$	−5.13150	−	8.88802i	−0.228802	−	0.396297i	−0.957453	+	0.288588i	$0.906814\pi$
$504$	−5.35113	+	5.86221i	−0.238358	+	0.261123i
$505$	2.23063	−	3.86357i	0.0992618	−	0.171927i
$506$	1.82387	−	10.3437i	0.0810810	−	0.459833i
$507$	−12.3895	−	18.7675i	−0.550235	−	0.833494i
$508$	−5.73102	−	2.08592i	−0.254273	−	0.0925478i
$509$	3.43191	−	2.87971i	0.152117	−	0.127641i	−0.563553	−	0.826080i	$-0.690566\pi$
$509$	3.43191	−	2.87971i	0.152117	−	0.127641i	0.715670	+	0.698439i	$0.246122\pi$
$510$	13.3541	−	12.6421i	0.591331	−	0.559800i
$511$	11.0021	+	8.98983i	0.486703	+	0.397687i
$512$	−1.00000			−0.0441942
$513$	−5.43549	+	15.1749i	−0.239983	+	0.669989i
$514$	10.7607	+	18.6380i	0.474633	+	0.822089i
$515$	12.6802	−	4.61523i	0.558758	−	0.203371i
$516$	2.69354	+	0.801391i	0.118576	+	0.0352793i
$517$	−33.6688	−	12.2544i	−1.48075	−	0.538950i
$518$	−2.03285	−	10.7098i	−0.0893184	−	0.470561i
$519$	9.48863	+	14.3733i	0.416504	+	0.630919i
$520$	−0.0328910	+	0.186534i	−0.00144237	+	0.00818006i
$521$	3.68073			0.161256			0.0806279	−	0.996744i	$-0.474307\pi$
$521$	3.68073			0.161256			0.0806279	+	0.996744i	$0.474307\pi$
$522$	6.46049	−	15.1186i	0.282768	−	0.661724i
$523$	6.43819			0.281522			0.140761	−	0.990044i	$-0.455045\pi$
$523$	6.43819			0.281522			0.140761	+	0.990044i	$0.455045\pi$
$524$	5.20770	+	4.36978i	0.227500	+	0.190895i
$525$	1.31019	−	12.8508i	0.0571813	−	0.560856i
$526$	1.81815	+	10.3112i	0.0792751	+	0.449591i
$527$	29.3096	+	10.6678i	1.27675	+	0.464698i
$528$	−7.91400	+	3.42978i	−0.344413	+	0.149262i
$529$	−3.22141	+	18.2695i	−0.140061	+	0.794327i
$530$	1.41910			0.0616416
$531$	29.5349	−	3.55424i	1.28170	−	0.154241i
$532$	−8.20670	+	0.107088i	−0.355806	+	0.00464284i
$533$	0.963055	−	0.350523i	0.0417145	−	0.0151829i
$534$	10.4408	−	0.625966i	0.451816	−	0.0270882i
$535$	25.2023	+	9.17290i	1.08959	+	0.396579i
$536$	2.16263	+	12.2649i	0.0934115	+	0.529763i
$537$	−25.2326	−	7.50730i	−1.08887	−	0.323964i
$538$	−0.376030	+	2.13257i	−0.0162118	+	0.0919418i
$539$	−34.8466	+	0.909569i	−1.50095	+	0.0391779i
$540$	−6.66551	−	3.80301i	−0.286838	−	0.163656i
$541$	0.412078	−	0.713739i	0.0177166	−	0.0306861i	−0.857031	−	0.515265i	$-0.827694\pi$
$541$	0.412078	−	0.713739i	0.0177166	−	0.0306861i	0.874748	+	0.484578i	$0.161027\pi$
$542$	−10.2793	+	3.74137i	−0.441535	+	0.160706i
$543$	18.6899	+	5.56070i	0.802061	+	0.238632i
$544$	−5.50687	+	4.62082i	−0.236105	+	0.198116i
$545$	16.2272	−	13.6162i	0.695095	−	0.583254i
$546$	−0.330166	−	0.486215i	−0.0141298	−	0.0208081i
$547$	−1.44375	+	0.525482i	−0.0617303	+	0.0224680i	−0.372701	−	0.927952i	$-0.621568\pi$
$547$	−1.44375	+	0.525482i	−0.0617303	+	0.0224680i	0.310970	+	0.950420i	$0.399346\pi$
$548$	1.43919	+	2.49276i	0.0614793	+	0.106485i
$549$	5.26720	+	17.3778i	0.224799	+	0.741667i
$550$	7.01856	−	12.1565i	0.299272	−	0.518355i
$551$	15.9754	−	5.81458i	0.680576	−	0.247709i
$552$	−3.35196	+	1.45268i	−0.142669	+	0.0618300i
$553$	6.46925	+	34.0823i	0.275100	+	1.44933i
$554$	1.83518	+	10.4078i	0.0779693	+	0.442186i
$555$	9.67050	−	4.19101i	0.410490	−	0.177899i
$556$	3.14679	−	17.8463i	0.133453	−	0.756852i
$557$	2.81772	−	4.88044i	0.119391	−	0.206791i	−0.800136	−	0.599819i	$-0.795239\pi$
$557$	2.81772	−	4.88044i	0.119391	−	0.206791i	0.919526	+	0.393028i	$0.128573\pi$
$558$	0.712535	−	12.9970i	0.0301640	−	0.550206i
$559$	−0.104043	+	0.180207i	−0.00440053	+	0.00762195i
$560$	0.628257	−	3.85663i	0.0265487	−	0.162972i
$561$	−27.7330	+	55.4565i	−1.17089	+	2.34138i
$562$	0.103930	+	0.589415i	0.00438401	+	0.0248630i
$563$	6.36411	+	36.0927i	0.268215	+	1.52112i	0.759720	+	0.650250i	$0.225336\pi$
$563$	6.36411	+	36.0927i	0.268215	+	1.52112i	−0.491505	+	0.870875i	$0.663553\pi$
$564$	2.89463	+	12.1213i	0.121886	+	0.510398i
$565$	17.6548	+	14.8141i	0.742742	+	0.623234i
$566$	23.9704			1.00755
$567$	23.0563	−	5.95057i	0.968272	−	0.249900i
$568$	12.1590			0.510181
$569$	−35.3036	−	29.6232i	−1.48000	−	1.24187i	−0.906182	−	0.422888i	$-0.861016\pi$
$569$	−35.3036	−	29.6232i	−1.48000	−	1.24187i	−0.573820	−	0.818981i	$-0.694539\pi$
$570$	−1.84317	−	7.71827i	−0.0772017	−	0.323283i
$571$	2.07847	+	11.7876i	0.0869813	+	0.493295i	0.996911	+	0.0785338i	$0.0250238\pi$
$571$	2.07847	+	11.7876i	0.0869813	+	0.493295i	−0.909930	+	0.414761i	$0.863865\pi$
$572$	−0.110903	−	0.628960i	−0.00463707	−	0.0262981i
$573$	19.9743	−	39.9416i	0.834437	−	1.66859i
$574$	−19.7713	+	7.48972i	−0.825237	+	0.312615i
$575$	2.97270	−	5.14886i	0.123970	−	0.214722i
$576$	2.51207	+	1.63997i	0.104670	+	0.0683322i
$577$	−3.46871	+	6.00798i	−0.144404	+	0.250115i	−0.929150	−	0.369702i	$-0.879460\pi$
$577$	−3.46871	+	6.00798i	−0.144404	+	0.250115i	0.784746	+	0.619817i	$0.212793\pi$
$578$	−6.02170	+	34.1508i	−0.250470	+	1.42048i
$579$	−4.95805	+	2.14873i	−0.206050	+	0.0892980i
$580$	1.40548	+	7.97090i	0.0583596	+	0.330974i
$581$	−16.9254	+	14.5826i	−0.702183	+	0.604988i
$582$	−1.15889	+	0.502241i	−0.0480375	+	0.0208186i
$583$	−4.49637	+	1.63655i	−0.186221	+	0.0677788i
$584$	2.68503	−	4.65060i	0.111107	−	0.192443i
$585$	0.388535	−	0.414646i	0.0160640	−	0.0171435i
$586$	4.62210	+	8.00571i	0.190937	+	0.330713i
$587$	6.05588	−	2.20416i	0.249953	−	0.0909754i	−0.214005	−	0.976832i	$-0.568651\pi$
$587$	6.05588	−	2.20416i	0.249953	−	0.0909754i	0.463958	+	0.885857i	$0.346429\pi$
$588$	6.94145	+	9.94064i	0.286260	+	0.409945i
$589$	10.3106	−	8.65161i	0.424840	−	0.356483i
$590$	−11.2185	+	9.41346i	−0.461859	+	0.387546i
$591$	11.9549	+	3.55687i	0.491760	+	0.146310i
$592$	−3.87172	+	1.40919i	−0.159127	+	0.0579173i
$593$	−10.6110	+	18.3789i	−0.435743	+	0.754730i	−0.997356	−	0.0726705i	$-0.976848\pi$
$593$	−10.6110	+	18.3789i	−0.435743	+	0.754730i	0.561613	+	0.827400i	$0.310181\pi$
$594$	25.5053	+	4.36290i	1.04649	+	0.179012i
$595$	−14.3610	−	24.1410i	−0.588745	−	0.989685i
$596$	−2.37259	+	13.4556i	−0.0971850	+	0.551163i
$597$	−26.3253	−	7.83240i	−1.07742	−	0.320559i
$598$	−0.0469726	−	0.266395i	−0.00192085	−	0.0108937i
$599$	−24.2420	−	8.82335i	−0.990499	−	0.360512i	−0.204586	−	0.978849i	$-0.565585\pi$
$599$	−24.2420	−	8.82335i	−0.990499	−	0.360512i	−0.785914	+	0.618336i	$0.787807\pi$
$600$	−4.87359	+	0.292191i	−0.198963	+	0.0119286i
$601$	−13.2906	+	4.83740i	−0.542137	+	0.197322i	−0.598549	−	0.801086i	$-0.704256\pi$
$601$	−13.2906	+	4.83740i	−0.542137	+	0.197322i	0.0564126	+	0.998408i	$0.482034\pi$
$602$	2.09766	−	3.74527i	0.0854941	−	0.152646i
$603$	14.6814	−	34.3569i	0.597873	−	1.39912i
$604$	−12.4805			−0.507826
$605$	3.53868	−	20.0688i	0.143868	−	0.815914i
$606$	4.80062	−	2.08050i	0.195012	−	0.0845145i
$607$	15.0238	+	5.46822i	0.609797	+	0.221948i	0.628415	−	0.777879i	$-0.283704\pi$
$607$	15.0238	+	5.46822i	0.609797	+	0.221948i	−0.0186172	+	0.999827i	$0.505926\pi$
$608$	0.538675	+	3.05498i	0.0218462	+	0.123896i
$609$	−20.3637	−	14.6984i	−0.825181	−	0.595608i
$610$	−6.84792	−	5.74609i	−0.277264	−	0.232652i
$611$	−0.922767			−0.0373312
$612$	21.4117	−	2.57669i	0.865515	−	0.104157i
$613$	7.13183			0.288052			0.144026	−	0.989574i	$-0.453995\pi$
$613$	7.13183			0.288052			0.144026	+	0.989574i	$0.453995\pi$
$614$	4.07172	−	23.0919i	0.164321	−	0.931912i
$615$	−11.2618	−	17.0594i	−0.454121	−	0.687900i
$616$	2.45696	+	12.9442i	0.0989939	+	0.521535i
$617$	−19.5666	−	7.12168i	−0.787724	−	0.286708i	−0.0833342	−	0.996522i	$-0.526557\pi$
$617$	−19.5666	−	7.12168i	−0.787724	−	0.286708i	−0.704389	+	0.709814i	$0.748779\pi$
$618$	15.1683	+	4.51294i	0.610160	+	0.181537i
$619$	2.44990	−	0.891691i	0.0984699	−	0.0358401i	−0.292315	−	0.956322i	$-0.594426\pi$
$619$	2.44990	−	0.891691i	0.0984699	−	0.0358401i	0.390785	+	0.920482i	$0.372203\pi$
$620$	3.20397	+	5.54944i	0.128675	+	0.222871i
$621$	10.8027	+	1.84790i	0.433498	+	0.0741535i
$622$	−20.7438			−0.831749
$623$	2.56887	−	15.7693i	0.102920	−	0.631783i
$624$	−0.161317	+	0.152715i	−0.00645784	+	0.00611350i
$625$	−2.26762	+	1.90276i	−0.0907048	+	0.0761104i
$626$	−12.9956	−	4.73001i	−0.519408	−	0.189049i
$627$	14.7410	+	22.3296i	0.588698	+	0.891757i
$628$	−0.679350	+	3.85279i	−0.0271090	+	0.153743i
$629$	−14.8094	+	25.6507i	−0.590491	+	1.02276i
$630$	−7.90298	+	8.65779i	−0.314862	+	0.344934i
$631$	−12.2131	−	21.1537i	−0.486196	−	0.842116i	0.513678	−	0.857983i	$-0.328283\pi$
$631$	−12.2131	−	21.1537i	−0.486196	−	0.842116i	−0.999874	+	0.0158668i	$0.994949\pi$
$632$	12.3212	−	4.48453i	0.490109	−	0.178385i
$633$	−24.5592	−	18.2187i	−0.976140	−	0.724127i
$634$	−12.9395	+	10.8575i	−0.513893	+	0.431207i
$635$	−8.46404	−	3.08066i	−0.335885	−	0.122252i
$636$	1.33665	+	0.991562i	0.0530016	+	0.0393180i
$637$	−0.835317	+	0.328959i	−0.0330965	+	0.0130338i
$638$	−13.6455	−	23.6348i	−0.540232	−	0.935710i
$639$	−30.5443	−	19.9404i	−1.20831	−	0.788832i
$640$	−1.47688			−0.0583789
$641$	−3.36632	−	2.82468i	−0.132962	−	0.111568i	0.573882	−	0.818938i	$-0.305437\pi$
$641$	−3.36632	−	2.82468i	−0.132962	−	0.111568i	−0.706843	+	0.707370i	$0.749881\pi$
$642$	17.3288	+	26.2495i	0.683912	+	1.03599i
$643$	−19.6269	+	16.4689i	−0.774008	+	0.649470i	−0.941732	−	0.336364i	$-0.890803\pi$
$643$	−19.6269	+	16.4689i	−0.774008	+	0.649470i	0.167724	+	0.985834i	$0.446358\pi$
$644$	1.04064	+	5.48247i	0.0410070	+	0.216040i
$645$	3.97803	+	1.18356i	0.156635	+	0.0466026i
$646$	17.0829	+	14.3343i	0.672118	+	0.563974i
$647$	23.6990	+	41.0479i	0.931704	+	1.61376i	0.780409	+	0.625269i	$0.215011\pi$
$647$	23.6990	+	41.0479i	0.931704	+	1.61376i	0.151295	+	0.988489i	$0.451656\pi$
$648$	−3.62098	−	8.23945i	−0.142246	−	0.323676i
$649$	24.6898	−	42.7639i	0.969158	−	1.67863i
$650$	0.0627767	−	0.356024i	0.00246230	−	0.0139644i
$651$	−19.1298	−	5.42090i	−0.749755	−	0.212462i
$652$	−15.8617	−	5.77320i	−0.621194	−	0.226096i
$653$	8.52789	+	48.3641i	0.333722	+	1.89263i	0.439501	+	0.898242i	$0.355155\pi$
$653$	8.52789	+	48.3641i	0.333722	+	1.89263i	−0.105779	+	0.994390i	$0.533734\pi$
$654$	24.7984	−	1.48677i	0.969695	−	0.0581371i
$655$	7.69117	+	6.45365i	0.300519	+	0.252165i
$656$	3.99553	+	6.92046i	0.155999	+	0.270199i
$657$	−14.3718	+	7.27927i	−0.560699	+	0.283991i
$658$	19.0346	−	0.248379i	0.742045	−	0.00968280i
$659$	−16.9942	−	14.2598i	−0.662000	−	0.555484i	0.248685	−	0.968584i	$-0.420001\pi$
$659$	−16.9942	−	14.2598i	−0.662000	−	0.555484i	−0.910686	+	0.413100i	$0.864446\pi$
$660$	−11.6880	+	5.06538i	−0.454957	+	0.197170i
$661$	2.51453	−	2.10995i	0.0978041	−	0.0820674i	−0.592574	−	0.805516i	$-0.701888\pi$
$661$	2.51453	−	2.10995i	0.0978041	−	0.0820674i	0.690379	+	0.723448i	$0.257444\pi$
$662$	7.34641	−	6.16437i	0.285526	−	0.239585i
$663$	−0.182683	+	1.58640i	−0.00709480	+	0.0616106i
$664$	6.46856	+	5.42777i	0.251029	+	0.210638i
$665$	−12.1203	+	0.158156i	−0.470006	+	0.00613302i
$666$	12.0370	+	2.80952i	0.466426	+	0.108867i
$667$	−5.77954	−	10.0105i	−0.223785	−	0.387607i
$668$	11.7113	+	9.82697i	0.453125	+	0.380217i
$669$	7.43958	+	11.2694i	0.287631	+	0.435702i
$670$	3.19395	+	18.1138i	0.123393	+	0.699798i
$671$	28.3241	+	10.3091i	1.09344	+	0.397979i
$672$	3.28649	−	3.19358i	0.126779	−	0.123195i
$673$	−5.14845	+	29.1983i	−0.198458	+	1.12551i	0.708949	+	0.705260i	$0.249170\pi$
$673$	−5.14845	+	29.1983i	−0.198458	+	1.12551i	−0.907407	+	0.420253i	$0.861941\pi$
$674$	4.63279	−	8.02422i	0.178448	−	0.309081i
$675$	12.7220	+	7.25854i	0.489669	+	0.279381i
$676$	6.49178	+	11.2441i	0.249684	+	0.432465i
$677$	−8.88765	−	7.45762i	−0.341580	−	0.286620i	0.455819	−	0.890073i	$-0.349347\pi$
$677$	−8.88765	−	7.45762i	−0.341580	−	0.286620i	−0.797398	+	0.603453i	$0.793791\pi$
$678$	6.27804	+	26.2893i	0.241107	+	1.00964i
$679$	0.359786	+	1.89548i	0.0138073	+	0.0727419i
$680$	−8.13300	+	6.82440i	−0.311886	+	0.261704i
$681$	15.7144	−	0.942142i	0.602177	−	0.0361030i
$682$	−16.5515	−	13.8884i	−0.633790	−	0.531813i
$683$	21.3244			0.815956			0.407978	−	0.912992i	$-0.366234\pi$
$683$	21.3244			0.815956			0.407978	+	0.912992i	$0.366234\pi$
$684$	3.65689	−	8.55773i	0.139825	−	0.327213i
$685$	2.12552	+	3.68151i	0.0812119	+	0.140663i
$686$	17.1421	−	7.01052i	0.654490	−	0.267663i
$687$	−5.65103	+	49.0730i	−0.215600	+	1.87225i
$688$	−1.52464	−	0.554922i	−0.0581262	−	0.0211562i
$689$	−0.0944019	+	0.0792126i	−0.00359642	+	0.00301776i
$690$	−4.95045	+	2.14543i	−0.188460	+	0.0816752i
$691$	−27.2041	+	9.90149i	−1.03489	+	0.376670i	−0.802942	−	0.596057i	$-0.796733\pi$
$691$	−27.2041	+	9.90149i	−1.03489	+	0.376670i	−0.231951	+	0.972727i	$0.574511\pi$
$692$	−4.97181	−	8.61142i	−0.189000	−	0.327357i
$693$	15.0560	−	36.5460i	0.571930	−	1.38827i
$694$	−11.7409	+	20.3358i	−0.445677	+	0.771935i
$695$	4.64743	−	26.3569i	0.176287	−	0.999774i
$696$	−4.24566	+	8.48986i	−0.160931	+	0.321807i
$697$	53.9810	+	19.6475i	2.04468	+	0.744202i
$698$	13.8297	−	11.6045i	0.523463	−	0.439238i
$699$	−1.91082	−	8.00159i	−0.0722740	−	0.302648i
$700$	−1.19911	+	7.36086i	−0.0453221	+	0.278214i
$701$	−29.1013			−1.09914			−0.549571	−	0.835447i	$-0.685209\pi$
$701$	−29.1013			−1.09914			−0.549571	+	0.835447i	$0.685209\pi$
$702$	0.655687	−	0.119076i	0.0247473	−	0.00449423i
$703$	6.39064	+	11.0689i	0.241027	+	0.417472i
$704$	4.67947	−	1.70319i	0.176364	−	0.0641913i
$705$	4.27503	+	17.9017i	0.161007	+	0.674217i
$706$	−1.53937	−	0.560283i	−0.0579348	−	0.0210865i
$707$	−1.49039	−	7.85191i	−0.0560519	−	0.295301i
$708$	−17.1442	+	1.02786i	−0.644319	+	0.0386295i
$709$	−3.87812	+	21.9939i	−0.145646	+	0.825998i	0.821201	+	0.570640i	$0.193305\pi$
$709$	−3.87812	+	21.9939i	−0.145646	+	0.825998i	−0.966846	+	0.255359i	$0.917806\pi$
$710$	17.9574			0.673931
$711$	−38.3061	−	8.94089i	−1.43659	−	0.335310i
$712$	−6.03880			−0.226314
$713$	−7.01036	−	5.88239i	−0.262540	−	0.220297i
$714$	3.34132	−	32.7729i	0.125046	−	1.22650i
$715$	−0.163790	−	0.928900i	−0.00612541	−	0.0347389i
$716$	14.2825	+	5.19842i	0.533764	+	0.194274i
$717$	1.86068	−	16.1580i	0.0694883	−	0.603430i
$718$	−2.67838	+	15.1899i	−0.0999564	+	0.566881i
$719$	−18.5189			−0.690640			−0.345320	−	0.938485i	$-0.612230\pi$
$719$	−18.5189			−0.690640			−0.345320	+	0.938485i	$0.612230\pi$
$720$	3.71003	+	2.42205i	0.138265	+	0.0902643i
$721$	11.8127	−	21.0910i	0.439928	−	0.785471i
$722$	−8.81144	+	3.20710i	−0.327928	+	0.119356i
$723$	−27.5725	−	41.7667i	−1.02543	−	1.55332i
$724$	−10.5792	−	3.85050i	−0.393171	−	0.143103i
$725$	−2.68255	−	15.2135i	−0.0996273	−	0.565015i
$726$	17.3557	−	16.4303i	0.644132	−	0.609786i
$727$	8.54634	−	48.4687i	0.316966	−	1.79760i	−0.244011	−	0.969773i	$-0.578463\pi$
$727$	8.54634	−	48.4687i	0.316966	−	1.79760i	0.560977	−	0.827831i	$-0.310426\pi$
$728$	0.173480	+	0.291621i	0.00642960	+	0.0108082i
$729$	−4.41630	+	26.6364i	−0.163567	+	0.986532i
$730$	3.96547	−	6.86840i	0.146769	−	0.254211i
$731$	−10.9602	+	3.98918i	−0.405377	+	0.147545i
$732$	−2.43512	−	10.1971i	−0.0900047	−	0.376895i
$733$	25.8492	−	21.6901i	0.954763	−	0.801141i	−0.0253300	−	0.999679i	$-0.508064\pi$
$733$	25.8492	−	21.6901i	0.954763	−	0.801141i	0.980093	+	0.198538i	$0.0636192\pi$
$734$	−2.46272	+	2.06647i	−0.0909008	+	0.0762748i
$735$	10.2517	+	14.6812i	0.378140	+	0.541523i
$736$	1.98198	−	0.721382i	0.0730568	−	0.0265905i
$737$	−31.0094	−	53.7099i	−1.14225	−	1.97843i
$738$	1.31231	−	23.9372i	0.0483069	−	0.881142i
$739$	20.2771	−	35.1209i	0.745904	−	1.29194i	−0.203867	−	0.978999i	$-0.565351\pi$
$739$	20.2771	−	35.1209i	0.745904	−	1.29194i	0.949771	−	0.312945i	$-0.101316\pi$
$740$	−5.71807	+	2.08121i	−0.210200	+	0.0765067i
$741$	0.553439	+	0.410555i	0.0203311	+	0.0150821i
$742$	1.92597	−	1.65938i	0.0707047	−	0.0609179i
$743$	−4.55051	−	25.8072i	−0.166942	−	0.946776i	−0.947039	−	0.321117i	$-0.895942\pi$
$743$	−4.55051	−	25.8072i	−0.166942	−	0.946776i	0.780097	−	0.625658i	$-0.215170\pi$
$744$	−0.859722	+	7.46574i	−0.0315189	+	0.273707i
$745$	−3.50403	+	19.8724i	−0.128378	+	0.728067i
$746$	−14.7698	+	25.5821i	−0.540762	+	0.936627i
$747$	−7.34809	−	24.2432i	−0.268852	−	0.887012i
$748$	17.8991	−	31.0022i	0.654457	−	1.13355i
$749$	44.9303	−	17.0204i	1.64172	−	0.621912i
$750$	−19.9650	+	1.19698i	−0.729017	+	0.0437075i
$751$	1.03253	+	5.85580i	0.0376777	+	0.213681i	0.997834	−	0.0657827i	$-0.0209544\pi$
$751$	1.03253	+	5.85580i	0.0376777	+	0.213681i	−0.960156	+	0.279464i	$0.909843\pi$
$752$	−1.24940	−	7.08570i	−0.0455609	−	0.258389i
$753$	−28.4743	−	8.47179i	−1.03766	−	0.308729i
$754$	−0.538425	−	0.451792i	−0.0196083	−	0.0164533i
$755$	−18.4323			−0.670820
$756$	−13.4933	+	2.63276i	−0.490746	+	0.0957524i
$757$	30.3047			1.10144			0.550722	−	0.834689i	$-0.314352\pi$
$757$	30.3047			1.10144			0.550722	+	0.834689i	$0.314352\pi$
$758$	9.35158	+	7.84690i	0.339665	+	0.285012i
$759$	13.2112	−	12.5068i	0.479537	−	0.453967i
$760$	0.795560	+	4.51184i	0.0288580	+	0.163662i
$761$	−2.15823	−	12.2399i	−0.0782359	−	0.443698i	−0.998612	−	0.0526642i	$-0.983229\pi$
$761$	−2.15823	−	12.2399i	−0.0782359	−	0.443698i	0.920376	−	0.391034i	$-0.127882\pi$
$762$	−5.81976	−	8.81575i	−0.210828	−	0.319361i
$763$	6.10147	−	37.4545i	0.220888	−	1.35594i
$764$	−12.8916	+	22.3288i	−0.466400	+	0.807829i
$765$	31.6225	−	3.80547i	1.14331	−	0.137587i
$766$	11.7233	−	20.3053i	0.423580	−	0.733661i
$767$	0.220835	−	1.25242i	0.00797388	−	0.0452221i
$768$	−1.39108	−	1.03194i	−0.0501962	−	0.0372369i
$769$	8.29013	+	47.0156i	0.298950	+	1.69543i	0.650701	+	0.759334i	$0.274475\pi$
$769$	8.29013	+	47.0156i	0.298950	+	1.69543i	−0.351752	+	0.936093i	$0.614414\pi$
$770$	3.62865	+	19.1170i	0.130767	+	0.688929i
$771$	−4.26437	+	37.0313i	−0.153577	+	1.33365i
$772$	2.93164	−	1.06703i	0.105512	−	0.0384033i
$773$	−7.39943	+	12.8162i	−0.266139	+	0.460966i	−0.967861	−	0.251484i	$-0.919081\pi$
$773$	−7.39943	+	12.8162i	−0.266139	+	0.460966i	0.701722	+	0.712450i	$0.252415\pi$
$774$	2.91993	+	3.89436i	0.104955	+	0.139980i
$775$	−6.11519	−	10.5918i	−0.219664	−	0.380469i
$776$	0.685240	−	0.249407i	0.0245987	−	0.00895318i
$777$	8.22399	−	16.9959i	0.295034	−	0.609726i
$778$	12.4653	−	10.4596i	0.446902	−	0.374996i
$779$	18.9896	−	15.9341i	0.680372	−	0.570900i
$780$	−0.238246	+	0.225542i	−0.00853057	+	0.00807571i
$781$	−56.8977	+	20.7091i	−2.03596	+	0.741029i
$782$	7.58114	−	13.1309i	0.271101	−	0.469561i
$783$	24.5885	−	14.3644i	0.878723	−	0.513340i
$784$	−3.65699	−	5.96879i	−0.130607	−	0.213171i
$785$	−1.00332	+	5.69011i	−0.0358100	+	0.203089i
$786$	2.73498	+	11.4527i	0.0975535	+	0.408506i
$787$	−5.44047	−	30.8544i	−0.193932	−	1.09984i	−0.913932	−	0.405868i	$-0.866969\pi$
$787$	−5.44047	−	30.8544i	−0.193932	−	1.09984i	0.720000	−	0.693974i	$-0.244142\pi$
$788$	−6.76691	−	2.46295i	−0.241061	−	0.0877391i
$789$	−8.11138	+	16.2200i	−0.288773	+	0.577446i
$790$	18.1969	−	6.62313i	0.647417	−	0.235640i
$791$	41.2833	−	0.538698i	1.46786	−	0.0191539i
$792$	−14.5483	−	3.39567i	−0.516952	−	0.120660i
$793$	0.776283			0.0275666
$794$	3.02903	−	17.1785i	0.107496	−	0.609641i
$795$	1.97407	+	1.46442i	0.0700132	+	0.0519376i
$796$	14.9010	+	5.42354i	0.528154	+	0.192232i
$797$	4.90675	+	27.8275i	0.173806	+	0.985702i	0.939513	+	0.342513i	$0.111278\pi$
$797$	4.90675	+	27.8275i	0.173806	+	0.985702i	−0.765707	+	0.643189i	$0.777611\pi$
$798$	−11.5267	−	8.31985i	−0.408040	−	0.294519i
$799$	−39.6220	−	33.2468i	−1.40173	−	1.17619i
$800$	2.81882			0.0996603
$801$	15.1699	+	9.90346i	0.536002	+	0.349922i
$802$	−3.84508			−0.135775
$803$	−4.64365	+	26.3355i	−0.163871	+	0.929358i
$804$	−9.64824	+	19.2932i	−0.340267	+	0.680417i
$805$	1.53691	+	8.09697i	0.0541688	+	0.285381i
$806$	−0.522901	−	0.190321i	−0.0184184	−	0.00670375i
$807$	−2.72377	+	2.57854i	−0.0958814	+	0.0907689i
$808$	−2.83856	+	1.03315i	−0.0998602	+	0.0363461i
$809$	−16.1538	−	27.9791i	−0.567936	−	0.983693i	−0.996770	−	0.0803102i	$-0.974409\pi$
$809$	−16.1538	−	27.9791i	−0.567936	−	0.983693i	0.428834	−	0.903383i	$-0.358924\pi$
$810$	−5.34777	−	12.1687i	−0.187901	−	0.427564i
$811$	−10.0881			−0.354241			−0.177121	−	0.984189i	$-0.556678\pi$
$811$	−10.0881			−0.354241			−0.177121	+	0.984189i	$0.556678\pi$
$812$	11.2281	+	9.17451i	0.394028	+	0.321962i
$813$	−18.1602	−	5.40310i	−0.636907	−	0.189495i
$814$	15.7175	−	13.1885i	0.550897	−	0.462257i
$815$	−23.4259	−	8.52634i	−0.820574	−	0.298665i
$816$	−12.4289	+	0.745162i	−0.435098	+	0.0260859i
$817$	−0.873991	+	4.95665i	−0.0305771	+	0.173411i
$818$	−16.5891	+	28.7332i	−0.580025	+	1.00463i
$819$	0.0424572	−	1.01708i	0.00148358	−	0.0355395i
$820$	5.90093	+	10.2207i	0.206069	+	0.356922i
$821$	−16.9071	+	6.15368i	−0.590062	+	0.214765i	−0.619757	−	0.784794i	$-0.712769\pi$
$821$	−16.9071	+	6.15368i	−0.590062	+	0.214765i	0.0296946	+	0.999559i	$0.490547\pi$
$822$	−0.570340	+	4.95278i	−0.0198929	+	0.172748i
$823$	−22.4657	+	18.8510i	−0.783105	+	0.657103i	−0.944029	−	0.329864i	$-0.892997\pi$
$823$	−22.4657	+	18.8510i	−0.783105	+	0.657103i	0.160923	+	0.986967i	$0.448553\pi$
$824$	−8.58581	−	3.12498i	−0.299101	−	0.108864i
$825$	22.3081	−	9.66793i	0.776670	−	0.336594i
$826$	−4.21820	+	25.8939i	−0.146770	+	0.900964i
$827$	−9.08092	−	15.7286i	−0.315775	−	0.546938i	0.663827	−	0.747886i	$-0.268931\pi$
$827$	−9.08092	−	15.7286i	−0.315775	−	0.546938i	−0.979602	+	0.200948i	$0.935598\pi$
$828$	−6.16192	−	1.43823i	−0.214141	−	0.0499820i
$829$	7.37269			0.256064			0.128032	−	0.991770i	$-0.459134\pi$
$829$	7.37269			0.256064			0.128032	+	0.991770i	$0.459134\pi$
$830$	9.55330	+	8.01617i	0.331600	+	0.278245i
$831$	−8.18736	+	16.3719i	−0.284016	+	0.567935i
$832$	0.0982460	−	0.0824382i	0.00340607	−	0.00285803i
$833$	−47.7193	−	15.9711i	−1.65337	−	0.553365i
$834$	22.7937	−	21.5783i	0.789282	−	0.747197i
$835$	17.2963	+	14.5133i	0.598562	+	0.502253i
$836$	−7.72391	−	13.3782i	−0.267137	−	0.462695i
$837$	14.4033	−	17.3445i	0.497850	−	0.599515i
$838$	6.00850	−	10.4070i	0.207560	−	0.359505i
$839$	−1.52037	+	8.62246i	−0.0524891	+	0.297681i	−0.999740	−	0.0228132i	$-0.992738\pi$
$839$	−1.52037	+	8.62246i	−0.0524891	+	0.297681i	0.947251	+	0.320494i	$0.103849\pi$
$840$	4.85376	−	4.71655i	0.167471	−	0.162736i
$841$	−0.972095	−	0.353814i	−0.0335205	−	0.0122005i
$842$	5.70027	+	32.3279i	0.196444	+	1.11409i
$843$	−0.463666	+	0.927172i	−0.0159695	+	0.0319335i
$844$	13.5243	+	11.3483i	0.465527	+	0.390624i
$845$	9.58759	+	16.6062i	0.329823	+	0.571270i
$846$	−8.48177	+	19.8487i	−0.291609	+	0.682414i
$847$	−18.6644	−	31.3750i	−0.641315	−	1.07806i
$848$	−0.736071	−	0.617637i	−0.0252768	−	0.0212097i
$849$	33.3447	+	24.7359i	1.14439	+	0.848936i
$850$	15.5229	−	13.0252i	0.532430	−	0.446762i
$851$	6.65710	−	5.58597i	0.228202	−	0.191485i
$852$	16.9142	+	12.5474i	0.579470	+	0.429866i
$853$	−32.1911	−	27.0116i	−1.10220	−	0.924858i	−0.104632	−	0.994511i	$-0.533366\pi$
$853$	−32.1911	−	27.0116i	−1.10220	−	0.924858i	−0.997571	+	0.0696531i	$0.977811\pi$
$854$	−16.0129	+	0.208950i	−0.547951	+	0.00715011i
$855$	5.40079	−	12.6388i	0.184703	−	0.432236i
$856$	−9.07986	−	15.7268i	−0.310343	−	0.537530i
$857$	17.8947	+	15.0155i	0.611272	+	0.512918i	0.895047	−	0.445973i	$-0.147142\pi$
$857$	17.8947	+	15.0155i	0.611272	+	0.512918i	−0.283774	+	0.958891i	$0.591587\pi$
$858$	0.494774	−	0.989378i	0.0168913	−	0.0337768i
$859$	−0.389069	−	2.20652i	−0.0132749	−	0.0752856i	0.977451	−	0.211164i	$-0.0677254\pi$
$859$	−0.389069	−	2.20652i	−0.0132749	−	0.0752856i	−0.990726	+	0.135878i	$0.956614\pi$
$860$	−2.25171	−	0.819555i	−0.0767826	−	0.0279466i
$861$	−35.2323	−	9.98396i	−1.20071	−	0.340252i
$862$	−1.80616	+	10.2432i	−0.0615181	+	0.348886i
$863$	−21.1156	+	36.5733i	−0.718784	+	1.24497i	0.242698	+	0.970102i	$0.421967\pi$
$863$	−21.1156	+	36.5733i	−0.718784	+	1.24497i	−0.961482	+	0.274868i	$0.911366\pi$
$864$	1.80214	+	4.87363i	0.0613099	+	0.165804i
$865$	−7.34278	−	12.7181i	−0.249662	−	0.432427i
$866$	−22.1775	−	18.6091i	−0.753620	−	0.632363i
$867$	−43.6182	+	41.2924i	−1.48135	+	1.40236i
$868$	10.8375	+	3.78513i	0.367848	+	0.128476i
$869$	−50.0185	+	41.9705i	−1.69676	+	1.42375i
$870$	−6.27034	+	12.5385i	−0.212585	+	0.425096i
$871$	−1.22357	−	1.02669i	−0.0414590	−	0.0347882i
$872$	−14.3431			−0.485718
$873$	−2.13039	−	0.497246i	−0.0721028	−	0.0168292i
$874$	−3.27145	−	5.66632i	−0.110658	−	0.191666i
$875$	−4.91223	+	30.1543i	−0.166064	+	1.01940i
$876$	8.53423	−	3.69857i	0.288345	−	0.124963i
$877$	−20.2389	−	7.36637i	−0.683420	−	0.248745i	−0.0231050	−	0.999733i	$-0.507355\pi$
$877$	−20.2389	−	7.36637i	−0.683420	−	0.248745i	−0.660315	+	0.750988i	$0.729577\pi$
$878$	22.6853	−	19.0352i	0.765592	−	0.642408i
$879$	−1.83170	+	15.9063i	−0.0617817	+	0.536506i
$880$	6.91102	−	2.51541i	0.232971	−	0.0847944i
$881$	18.0694	+	31.2972i	0.608775	+	1.05443i	0.991443	+	0.130543i	$0.0416719\pi$
$881$	18.0694	+	31.2972i	0.608775	+	1.05443i	−0.382668	+	0.923886i	$0.624995\pi$
$882$	−0.602032	+	20.9914i	−0.0202715	+	0.706816i
$883$	13.4012	−	23.2116i	0.450987	−	0.781132i	−0.547461	−	0.836831i	$-0.684406\pi$
$883$	13.4012	−	23.2116i	0.450987	−	0.781132i	0.998448	+	0.0556995i	$0.0177389\pi$
$884$	0.160097	−	0.907954i	0.00538463	−	0.0305378i
$885$	−25.3200	+	1.51803i	−0.851122	+	0.0510282i
$886$	−28.6600	−	10.4314i	−0.962850	−	0.350449i
$887$	19.3732	−	16.2561i	0.650489	−	0.545825i	−0.256730	−	0.966483i	$-0.582645\pi$
$887$	19.3732	−	16.2561i	0.650489	−	0.545825i	0.907219	+	0.420658i	$0.138201\pi$
$888$	−6.84006	−	2.03508i	−0.229537	−	0.0682928i
$889$	−15.0896	+	5.71620i	−0.506088	+	0.191715i
$890$	−8.91860			−0.298952
$891$	30.9776	+	32.3890i	1.03779	+	1.08507i
$892$	−3.89816	−	6.75181i	−0.130520	−	0.226067i
$893$	−20.9736	+	7.63378i	−0.701856	+	0.255455i
$894$	−17.1858	+	16.2695i	−0.574780	+	0.544132i
$895$	21.0936	+	7.67745i	0.705082	+	0.256629i
$896$	−2.00440	+	1.72696i	−0.0669623	+	0.0576936i
$897$	0.209561	−	0.419049i	0.00699703	−	0.0139916i
$898$	1.26277	−	7.16152i	0.0421392	−	0.238983i
$899$	−23.7784			−0.793055
$900$	−7.08107	−	4.62278i	−0.236036	−	0.154093i
$901$	−6.90743			−0.230120
$902$	−30.4838	−	25.5789i	−1.01500	−	0.851686i
$903$	6.78289	−	3.04531i	0.225721	−	0.101342i
$904$	−2.70977	−	15.3679i	−0.0901256	−	0.511128i
$905$	−15.6242	−	5.68673i	−0.519365	−	0.189033i
$906$	−17.3614	−	12.8792i	−0.576794	−	0.427881i
$907$	6.03988	−	34.2539i	0.200551	−	1.13738i	−0.703738	−	0.710460i	$-0.748487\pi$
$907$	6.03988	−	34.2539i	0.200551	−	1.13738i	0.904289	−	0.426922i	$-0.140402\pi$
$908$	−9.08901			−0.301629
$909$	8.82500	+	2.05981i	0.292707	+	0.0683196i
$910$	0.256209	+	0.430691i	0.00849326	+	0.0142773i
$911$	25.8389	−	9.40459i	0.856081	−	0.311588i	0.123564	−	0.992337i	$-0.460568\pi$
$911$	25.8389	−	9.40459i	0.856081	−	0.311588i	0.732517	+	0.680749i	$0.238345\pi$
$912$	−2.40321	+	4.80560i	−0.0795783	+	0.159129i
$913$	−39.5139	−	14.3819i	−1.30772	−	0.475971i
$914$	−1.41687	−	8.03545i	−0.0468658	−	0.265789i
$915$	−3.59639	−	15.0599i	−0.118893	−	0.497865i
$916$	4.95237	−	28.0863i	0.163631	−	0.927996i
$917$	17.9847	−	0.234680i	0.593909	−	0.00774980i
$918$	32.4443	+	18.5111i	1.07082	+	0.610959i
$919$	−23.0212	+	39.8739i	−0.759400	+	1.31532i	0.183758	+	0.982972i	$0.441174\pi$
$919$	−23.0212	+	39.8739i	−0.759400	+	1.31532i	−0.943157	+	0.332347i	$0.892160\pi$
$920$	2.92715	−	1.06540i	0.0965053	−	0.0351251i
$921$	29.4935	−	27.9209i	0.971844	−	0.920024i
$922$	−25.2028	+	21.1477i	−0.830010	+	0.696461i
$923$	−1.19458	+	1.00237i	−0.0393199	+	0.0329933i
$924$	−9.93975	+	20.5418i	−0.326994	+	0.675775i
$925$	10.9137	−	3.97225i	0.358839	−	0.130607i
$926$	−11.9717	−	20.7356i	−0.393415	−	0.681415i
$927$	16.4433	+	21.9307i	0.540068	+	0.720297i
$928$	2.74019	−	4.74614i	0.0899510	−	0.155800i
$929$	31.6966	−	11.5366i	1.03993	−	0.378504i	0.235078	−	0.971977i	$-0.424466\pi$
$929$	31.6966	−	11.5366i	1.03993	−	0.378504i	0.804854	+	0.593472i	$0.202243\pi$
$930$	−1.26971	+	11.0260i	−0.0416354	+	0.361557i
$931$	−16.2646	+	14.3873i	−0.533050	+	0.471523i
$932$	0.824763	+	4.67746i	0.0270160	+	0.153215i
$933$	−28.8562	−	21.4063i	−0.944710	−	0.700811i
$934$	−4.31943	+	24.4967i	−0.141336	+	0.801557i
$935$	26.4349	−	45.7866i	0.864514	−	1.49738i
$936$	−0.381997	+	0.0459698i	−0.0124860	+	0.00150257i
$937$	7.72979	−	13.3884i	0.252521	−	0.437380i	−0.711698	−	0.702486i	$-0.752074\pi$
$937$	7.72979	−	13.3884i	0.252521	−	0.437380i	0.964219	+	0.265106i	$0.0854069\pi$
$938$	25.5157	+	20.8490i	0.833118	+	0.680744i
$939$	−13.1968	−	19.9905i	−0.430662	−	0.652365i
$940$	−1.84522	−	10.4647i	−0.0601843	−	0.341322i
$941$	−3.08456	−	17.4934i	−0.100554	−	0.570269i	−0.992903	−	0.118924i	$-0.962055\pi$
$941$	−3.08456	−	17.4934i	−0.100554	−	0.570269i	0.892350	−	0.451345i	$-0.149056\pi$
$942$	−4.92087	+	4.65848i	−0.160331	+	0.151782i
$943$	−12.9114	−	10.8339i	−0.420452	−	0.352801i
$944$	9.91599			0.322738
$945$	−19.9280	+	3.88827i	−0.648257	+	0.126485i
$946$	8.07962			0.262691
$947$	11.7217	+	9.83565i	0.380903	+	0.319616i	0.813057	−	0.582184i	$-0.197802\pi$
$947$	11.7217	+	9.83565i	0.380903	+	0.319616i	−0.432154	+	0.901800i	$0.642246\pi$
$948$	21.7675	+	6.47634i	0.706975	+	0.210342i
$949$	0.119594	+	0.678252i	0.00388219	+	0.0220170i
$950$	−1.51843	−	8.61143i	−0.0492643	−	0.279392i
$951$	−29.2042	+	1.75091i	−0.947010	+	0.0567770i
$952$	−3.05804	+	18.7721i	−0.0991116	+	0.608407i
$953$	−9.73375	+	16.8594i	−0.315307	+	0.546128i	−0.979503	−	0.201431i	$-0.935441\pi$
$953$	−9.73375	+	16.8594i	−0.315307	+	0.546128i	0.664196	+	0.747559i	$0.268774\pi$
$954$	0.836154	+	2.75868i	0.0270715	+	0.0893156i
$955$	−19.0393	+	32.9770i	−0.616097	+	1.06711i
$956$	−1.63063	+	9.24779i	−0.0527385	+	0.299095i
$957$	5.40762	−	46.9592i	0.174803	−	1.51798i
$958$	0.753313	+	4.27225i	0.0243384	+	0.138030i
$959$	7.18960	+	2.51106i	0.232164	+	0.0810863i
$960$	−2.05446	−	1.52405i	−0.0663074	−	0.0491886i
$961$	11.4403	−	4.16393i	0.369042	−	0.134320i
$962$	0.264210	−	0.457624i	0.00851846	−	0.0147544i
$963$	−2.98224	+	54.3974i	−0.0961012	+	1.75293i
$964$	14.4473	+	25.0235i	0.465317	+	0.805953i
$965$	4.32969	−	1.57588i	0.139378	−	0.0507294i
$966$	−4.20996	+	8.70044i	−0.135453	+	0.279932i
$967$	−24.2875	+	20.3797i	−0.781034	+	0.655366i	−0.943509	−	0.331347i	$-0.892497\pi$
$967$	−24.2875	+	20.3797i	−0.781034	+	0.655366i	0.162475	+	0.986713i	$0.448052\pi$
$968$	−10.5701	+	8.86936i	−0.339736	+	0.285072i
$969$	8.97159	+	37.5686i	0.288209	+	1.20688i
$970$	1.01202	−	0.368344i	0.0324939	−	0.0118268i
$971$	0.112027	−	0.194036i	0.00359511	−	0.00622692i	−0.864222	−	0.503110i	$-0.832189\pi$
$971$	0.112027	−	0.194036i	0.00359511	−	0.00622692i	0.867817	+	0.496883i	$0.165522\pi$
$972$	3.46553	−	15.1984i	0.111157	−	0.487488i
$973$	−24.5124	−	41.2055i	−0.785830	−	1.32099i
$974$	6.28913	−	35.6674i	0.201517	−	1.14286i
$975$	0.454723	−	0.430476i	0.0145628	−	0.0137863i
$976$	1.05106	+	5.96088i	0.0336437	+	0.190803i
$977$	24.7231	+	8.99846i	0.790961	+	0.287886i	0.705735	−	0.708476i	$-0.250617\pi$
$977$	24.7231	+	8.99846i	0.790961	+	0.287886i	0.0852254	+	0.996362i	$0.472839\pi$
$978$	−16.1073	−	24.3993i	−0.515056	−	0.780204i
$979$	28.2584	−	10.2852i	0.903142	−	0.328717i
$980$	−5.40094	−	8.81520i	−0.172527	−	0.281591i
$981$	36.0308	+	23.5223i	1.15038	+	0.751008i
$982$	−16.5642			−0.528586
$983$	5.67121	−	32.1630i	0.180884	−	1.02584i	−0.750247	−	0.661157i	$-0.770066\pi$
$983$	5.67121	−	32.1630i	0.180884	−	1.02584i	0.931131	−	0.364685i	$-0.118823\pi$
$984$	−1.58340	+	13.7501i	−0.0504768	+	0.438336i
$985$	−9.99392	−	3.63749i	−0.318433	−	0.115900i
$986$	−6.84119	−	38.7983i	−0.217868	−	1.23559i
$987$	26.7349	+	19.2970i	0.850982	+	0.614231i
$988$	−0.304770	−	0.255732i	−0.00969601	−	0.00813592i
$989$	3.42211			0.108817
$990$	−21.4862	−	5.01501i	−0.682875	−	0.159387i
$991$	−45.8056			−1.45506			−0.727531	−	0.686075i	$-0.759332\pi$
$991$	−45.8056			−1.45506			−0.727531	+	0.686075i	$0.759332\pi$
$992$	0.753430	−	4.27292i	0.0239214	−	0.135665i
$993$	16.5807	−	0.994080i	0.526173	−	0.0315462i
$994$	24.3715	−	20.9981i	0.773019	−	0.666019i
$995$	22.0071	+	8.00993i	0.697672	+	0.253932i
$996$	3.39716	+	14.2256i	0.107643	+	0.450756i
$997$	7.81209	−	2.84337i	0.247412	−	0.0900504i	−0.215338	−	0.976540i	$-0.569085\pi$
$997$	7.81209	−	2.84337i	0.247412	−	0.0900504i	0.462749	+	0.886489i	$0.346863\pi$
$998$	−8.01127	−	13.8759i	−0.253592	−	0.439235i
$999$	13.8452	+	16.3298i	0.438044	+	0.516651i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.v.a.79.6	yes	72
7.4	even	3		378.2.w.b.25.4	yes	72
27.13	even	9		378.2.w.b.121.4	yes	72
189.67	even	9	inner	378.2.v.a.67.6	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.v.a.67.6	✓	72	189.67	even	9	inner
378.2.v.a.79.6	yes	72	1.1	even	1	trivial
378.2.w.b.25.4	yes	72	7.4	even	3
378.2.w.b.121.4	yes	72	27.13	even	9

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.v (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 - 0.642788i) q^{2} +(-0.402311 - 1.68468i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.256458 + 1.45445i) q^{5} +(-0.774703 + 1.54914i) q^{6} +(2.04878 + 1.67407i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.67629 + 1.35553i) q^{9} +O(q^{10})\)	\(q+(-0.766044 - 0.642788i) q^{2} +(-0.402311 - 1.68468i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.256458 + 1.45445i) q^{5} +(-0.774703 + 1.54914i) q^{6} +(2.04878 + 1.67407i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.67629 + 1.35553i) q^{9} +(0.738441 - 1.27902i) q^{10} +(-0.864731 + 4.90413i) q^{11} +(1.58923 - 0.688740i) q^{12} +(0.0222706 + 0.126303i) q^{13} +(-0.493387 - 2.59934i) q^{14} +(2.34710 - 1.01719i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-3.59436 + 6.22561i) q^{17} +(2.92148 + 0.681891i) q^{18} +(1.55105 + 2.68650i) q^{19} +(-1.38782 + 0.505123i) q^{20} +(1.99602 - 4.12503i) q^{21} +(3.81474 - 3.20095i) q^{22} +(1.61573 - 1.35575i) q^{23} +(-1.66013 - 0.493928i) q^{24} +(2.64882 - 0.964093i) q^{25} +(0.0641255 - 0.111069i) q^{26} +(3.36034 + 3.96335i) q^{27} +(-1.29287 + 2.30835i) q^{28} +(0.951657 - 5.39711i) q^{29} +(-2.45182 - 0.729474i) q^{30} +(-0.753430 - 4.27292i) q^{31} +(0.939693 + 0.342020i) q^{32} +(8.60978 - 0.516191i) q^{33} +(6.75518 - 2.45868i) q^{34} +(-1.90941 + 3.40917i) q^{35} +(-1.79967 - 2.40025i) q^{36} +4.12019 q^{37} +(0.538675 - 3.05498i) q^{38} +(0.203820 - 0.0883317i) q^{39} +(1.38782 + 0.505123i) q^{40} +(-1.38763 - 7.86966i) q^{41} +(-4.18056 + 1.87694i) q^{42} +(1.24289 + 1.04291i) q^{43} -4.97979 q^{44} +(-2.65790 - 3.54488i) q^{45} -2.10918 q^{46} +(-1.24940 + 7.08570i) q^{47} +(0.954243 + 1.44548i) q^{48} +(1.39500 + 6.85959i) q^{49} +(-2.64882 - 0.964093i) q^{50} +(11.9342 + 3.55071i) q^{51} +(-0.120517 + 0.0438644i) q^{52} +(0.480436 + 0.832140i) q^{53} +(-0.0265734 - 5.19608i) q^{54} -7.35456 q^{55} +(2.47417 - 0.937262i) q^{56} +(3.90189 - 3.69384i) q^{57} +(-4.19821 + 3.52272i) q^{58} +(-9.31798 - 3.39147i) q^{59} +(1.40930 + 2.13481i) q^{60} +(1.05106 - 5.96088i) q^{61} +(-2.16942 + 3.75754i) q^{62} +(-7.75238 - 1.70311i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.177989 + 0.0647826i) q^{65} +(-6.92728 - 5.13884i) q^{66} +(-9.54040 + 8.00535i) q^{67} +(-6.75518 - 2.45868i) q^{68} +(-2.93404 - 2.17654i) q^{69} +(3.65406 - 1.38423i) q^{70} +(6.07951 + 10.5300i) q^{71} +(-0.164223 + 2.99550i) q^{72} +5.37006 q^{73} +(-3.15625 - 2.64841i) q^{74} +(-2.68984 - 4.07455i) q^{75} +(-2.37635 + 1.99400i) q^{76} +(-9.98149 + 8.59987i) q^{77} +(-0.212914 - 0.0633469i) q^{78} +(10.0443 + 8.42817i) q^{79} +(-0.738441 - 1.27902i) q^{80} +(5.32508 - 7.25559i) q^{81} +(-3.99553 + 6.92046i) q^{82} +(-1.46630 + 8.31582i) q^{83} +(4.40897 + 1.24939i) q^{84} +(-9.97661 - 3.63119i) q^{85} +(-0.281741 - 1.59783i) q^{86} +(-9.47527 + 0.568080i) q^{87} +(3.81474 + 3.20095i) q^{88} +(-3.01940 - 5.22975i) q^{89} +(-0.242538 + 4.42400i) q^{90} +(-0.165812 + 0.296049i) q^{91} +(1.61573 + 1.35575i) q^{92} +(-6.89538 + 2.98833i) q^{93} +(5.51169 - 4.62486i) q^{94} +(-3.50959 + 2.94490i) q^{95} +(0.198146 - 1.72068i) q^{96} +(0.558612 + 0.468731i) q^{97} +(3.34063 - 6.15144i) q^{98} +(-4.33343 - 14.2971i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8}+O(q^{10}) \) 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8	\( 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8} + 6 q^{10} + 12 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} + 18 q^{19} + 6 q^{22} + 12 q^{23} - 6 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} - 18 q^{35} - 3 q^{36} - 48 q^{39} - 6 q^{41} + 36 q^{42} - 24 q^{43} - 45 q^{45} - 27 q^{47} + 6 q^{48} + 48 q^{49} + 6 q^{50} + 15 q^{51} - 6 q^{52} - 15 q^{53} - 63 q^{54} - 72 q^{55} - 3 q^{56} + 57 q^{57} - 3 q^{58} - 30 q^{59} + 21 q^{60} + 9 q^{61} - 24 q^{62} - 21 q^{63} - 36 q^{64} + 45 q^{65} + 6 q^{67} + 9 q^{68} - 39 q^{69} + 15 q^{70} + 12 q^{71} - 60 q^{73} - 18 q^{74} + 42 q^{75} + 3 q^{77} + 6 q^{78} - 27 q^{79} - 6 q^{80} + 12 q^{81} + 33 q^{82} + 18 q^{83} - 21 q^{84} + 51 q^{85} - 12 q^{86} - 117 q^{87} + 6 q^{88} - 36 q^{89} - 69 q^{90} - 3 q^{91} + 12 q^{92} - 30 q^{93} - 27 q^{94} + 3 q^{95} + 48 q^{97} - 12 q^{98} + 90 q^{99}+O(q^{100}) \) 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8 + 6 * q^10 + 12 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 + 18 * q^19 + 6 * q^22 + 12 * q^23 - 6 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 - 18 * q^35 - 3 * q^36 - 48 * q^39 - 6 * q^41 + 36 * q^42 - 24 * q^43 - 45 * q^45 - 27 * q^47 + 6 * q^48 + 48 * q^49 + 6 * q^50 + 15 * q^51 - 6 * q^52 - 15 * q^53 - 63 * q^54 - 72 * q^55 - 3 * q^56 + 57 * q^57 - 3 * q^58 - 30 * q^59 + 21 * q^60 + 9 * q^61 - 24 * q^62 - 21 * q^63 - 36 * q^64 + 45 * q^65 + 6 * q^67 + 9 * q^68 - 39 * q^69 + 15 * q^70 + 12 * q^71 - 60 * q^73 - 18 * q^74 + 42 * q^75 + 3 * q^77 + 6 * q^78 - 27 * q^79 - 6 * q^80 + 12 * q^81 + 33 * q^82 + 18 * q^83 - 21 * q^84 + 51 * q^85 - 12 * q^86 - 117 * q^87 + 6 * q^88 - 36 * q^89 - 69 * q^90 - 3 * q^91 + 12 * q^92 - 30 * q^93 - 27 * q^94 + 3 * q^95 + 48 * q^97 - 12 * q^98 + 90 * q^99

Introduction

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