LMFDB - Embedded newform 378.2.w.a.25.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(25,378)]

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([10, 12]))

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

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

chi := DirichletCharacter("378.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.w (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			25.11
Character	$\chi$	$=$	378.25
Dual form			378.2.w.a.121.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{2} +(1.65621 - 0.506908i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.501605 + 0.182569i) q^{5} +(-1.38296 + 1.04280i) q^{6} +(-1.88202 + 1.85957i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.48609 - 1.67910i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 0.342020i) q^{2} +(1.65621 - 0.506908i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.501605 + 0.182569i) q^{5} +(-1.38296 + 1.04280i) q^{6} +(-1.88202 + 1.85957i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.48609 - 1.67910i) q^{9} -0.533797 q^{10} +(3.49876 - 1.27344i) q^{11} +(0.942899 - 1.45291i) q^{12} +(1.06859 + 6.06025i) q^{13} +(1.13251 - 2.39111i) q^{14} +(0.923311 + 0.0481060i) q^{15} +(0.173648 - 0.984808i) q^{16} +2.18425 q^{17} +(-1.76187 + 2.42813i) q^{18} +2.71876 q^{19} +(0.501605 - 0.182569i) q^{20} +(-2.17440 + 4.03386i) q^{21} +(-2.85221 + 2.39329i) q^{22} +(-0.309811 - 1.75702i) q^{23} +(-0.389111 + 1.68778i) q^{24} +(-3.61195 - 3.03078i) q^{25} +(-3.07687 - 5.32930i) q^{26} +(3.26635 - 4.04116i) q^{27} +(-0.246405 + 2.63425i) q^{28} +(1.83629 - 10.4141i) q^{29} +(-0.884082 + 0.270586i) q^{30} +(1.18040 - 0.990471i) q^{31} +(0.173648 + 0.984808i) q^{32} +(5.14917 - 3.88265i) q^{33} +(-2.05253 + 0.747059i) q^{34} +(-1.28353 + 0.589169i) q^{35} +(0.825151 - 2.88429i) q^{36} +(-5.19917 + 9.00522i) q^{37} +(-2.55480 + 0.929871i) q^{38} +(4.84180 + 9.49540i) q^{39} +(-0.408912 + 0.343118i) q^{40} +(1.45917 + 8.27535i) q^{41} +(0.663608 - 4.53427i) q^{42} +(4.99996 + 4.19547i) q^{43} +(1.86165 - 3.22447i) q^{44} +(1.55359 - 0.388360i) q^{45} +(0.892065 + 1.54510i) q^{46} +(-8.02588 - 6.73451i) q^{47} +(-0.211609 - 1.71908i) q^{48} +(0.0840109 - 6.99950i) q^{49} +(4.43071 + 1.61265i) q^{50} +(3.61759 - 1.10722i) q^{51} +(4.71404 + 3.95555i) q^{52} +(-3.95402 + 6.84856i) q^{53} +(-1.68720 + 4.91461i) q^{54} +1.98749 q^{55} +(-0.669423 - 2.55966i) q^{56} +(4.50285 - 1.37816i) q^{57} +(1.83629 + 10.4141i) q^{58} +(0.492061 + 2.79062i) q^{59} +(0.738219 - 0.556641i) q^{60} +(-4.53366 - 3.80420i) q^{61} +(-0.770450 + 1.33446i) q^{62} +(-1.55648 + 7.78315i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.570408 + 3.23494i) q^{65} +(-3.51070 + 5.40961i) q^{66} +(3.54979 + 1.29202i) q^{67} +(1.67324 - 1.40401i) q^{68} +(-1.40376 - 2.75296i) q^{69} +(1.00462 - 0.992632i) q^{70} +(-4.58179 - 7.93590i) q^{71} +(0.211097 + 2.99256i) q^{72} +(-3.80191 - 6.58510i) q^{73} +(1.80565 - 10.2404i) q^{74} +(-7.51848 - 3.18870i) q^{75} +(2.08269 - 1.74759i) q^{76} +(-4.21668 + 8.90283i) q^{77} +(-7.79742 - 7.26676i) q^{78} +(-13.9134 + 5.06405i) q^{79} +(0.266898 - 0.462282i) q^{80} +(3.36127 - 8.34877i) q^{81} +(-4.20150 - 7.27722i) q^{82} +(0.348371 - 1.97571i) q^{83} +(0.927225 + 4.48779i) q^{84} +(1.09563 + 0.398777i) q^{85} +(-6.13336 - 2.23236i) q^{86} +(-2.23772 - 18.1789i) q^{87} +(-0.646545 + 3.66674i) q^{88} +3.83829 q^{89} +(-1.32707 + 0.896297i) q^{90} +(-13.2806 - 9.41842i) q^{91} +(-1.36672 - 1.14682i) q^{92} +(1.45291 - 2.23879i) q^{93} +(9.84520 + 3.58336i) q^{94} +(1.36374 + 0.496362i) q^{95} +(0.786806 + 1.54303i) q^{96} +(-5.72248 - 4.80173i) q^{97} +(2.31502 + 6.60611i) q^{98} +(6.55999 - 9.04065i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} - 3 q^{7} - 36 q^{8} - 12 q^{9}+O(q^{10}) $ 72 * q + 3 * q^6 - 3 * q^7 - 36 * q^8 - 12 * q^9	$ 72 q + 3 q^{6} - 3 q^{7} - 36 q^{8} - 12 q^{9} + 12 q^{10} - 6 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} + 24 q^{17} + 36 q^{19} - 12 q^{21} - 6 q^{22} + 12 q^{23} - 30 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} + 9 q^{35} + 9 q^{36} + 3 q^{39} - 6 q^{41} + 3 q^{42} + 24 q^{43} - 30 q^{45} - 9 q^{47} - 6 q^{48} + 51 q^{49} + 6 q^{50} + 12 q^{51} + 6 q^{52} - 15 q^{53} - 27 q^{54} + 72 q^{55} + 6 q^{56} - 63 q^{57} + 3 q^{58} + 15 q^{59} - 3 q^{60} - 18 q^{61} - 24 q^{62} - 48 q^{63} - 36 q^{64} - 18 q^{65} - 36 q^{66} + 66 q^{67} - 18 q^{68} - 21 q^{69} - 6 q^{70} + 12 q^{71} - 12 q^{72} - 66 q^{73} + 9 q^{74} + 15 q^{75} - 15 q^{77} + 30 q^{78} + 9 q^{79} - 6 q^{80} - 33 q^{82} - 18 q^{83} - 12 q^{84} + 21 q^{85} - 12 q^{86} - 48 q^{87} + 12 q^{88} + 72 q^{89} + 69 q^{90} + 12 q^{91} + 30 q^{92} + 60 q^{93} - 36 q^{94} + 93 q^{95} - 48 q^{97} + 6 q^{98} - 54 q^{99}+O(q^{100}) $ 72 * q + 3 * q^6 - 3 * q^7 - 36 * q^8 - 12 * q^9 + 12 * q^10 - 6 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^15 + 24 * q^17 + 36 * q^19 - 12 * q^21 - 6 * q^22 + 12 * q^23 - 30 * q^25 - 18 * q^26 - 6 * q^27 + 3 * q^29 + 3 * q^30 + 9 * q^31 - 18 * q^33 + 9 * q^34 + 9 * q^35 + 9 * q^36 + 3 * q^39 - 6 * q^41 + 3 * q^42 + 24 * q^43 - 30 * q^45 - 9 * q^47 - 6 * q^48 + 51 * q^49 + 6 * q^50 + 12 * q^51 + 6 * q^52 - 15 * q^53 - 27 * q^54 + 72 * q^55 + 6 * q^56 - 63 * q^57 + 3 * q^58 + 15 * q^59 - 3 * q^60 - 18 * q^61 - 24 * q^62 - 48 * q^63 - 36 * q^64 - 18 * q^65 - 36 * q^66 + 66 * q^67 - 18 * q^68 - 21 * q^69 - 6 * q^70 + 12 * q^71 - 12 * q^72 - 66 * q^73 + 9 * q^74 + 15 * q^75 - 15 * q^77 + 30 * q^78 + 9 * q^79 - 6 * q^80 - 33 * q^82 - 18 * q^83 - 12 * q^84 + 21 * q^85 - 12 * q^86 - 48 * q^87 + 12 * q^88 + 72 * q^89 + 69 * q^90 + 12 * q^91 + 30 * q^92 + 60 * q^93 - 36 * q^94 + 93 * q^95 - 48 * q^97 + 6 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$3$	1.65621	−	0.506908i	0.956215	−	0.292664i
$3$	1.65621	−	0.506908i	0.956215	−	0.292664i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	0.501605	+	0.182569i	0.224325	+	0.0816475i	0.451737	−	0.892151i	$-0.350804\pi$
$5$	0.501605	+	0.182569i	0.224325	+	0.0816475i	−0.227413	+	0.973798i	$0.573027\pi$
$6$	−1.38296	+	1.04280i	−0.564591	+	0.425720i
$7$	−1.88202	+	1.85957i	−0.711337	+	0.702851i
$7$	−1.88202	+	1.85957i	−0.711337	+	0.702851i
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	2.48609	−	1.67910i	0.828696	−	0.559699i
$10$	−0.533797			−0.168801
$11$	3.49876	−	1.27344i	1.05492	−	0.383958i	0.244400	−	0.969675i	$-0.421409\pi$
$11$	3.49876	−	1.27344i	1.05492	−	0.383958i	0.810516	+	0.585717i	$0.199187\pi$
$12$	0.942899	−	1.45291i	0.272191	−	0.419418i
$13$	1.06859	+	6.06025i	0.296372	+	1.68081i	0.661572	+	0.749882i	$0.269890\pi$
$13$	1.06859	+	6.06025i	0.296372	+	1.68081i	−0.365199	+	0.930929i	$0.618999\pi$
$14$	1.13251	−	2.39111i	0.302677	−	0.639052i
$15$	0.923311	+	0.0481060i	0.238398	+	0.0124209i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	2.18425			0.529759			0.264880	−	0.964281i	$-0.414668\pi$
$17$	2.18425			0.529759			0.264880	+	0.964281i	$0.414668\pi$
$18$	−1.76187	+	2.42813i	−0.415278	+	0.572315i
$19$	2.71876			0.623727			0.311863	−	0.950127i	$-0.399047\pi$
$19$	2.71876			0.623727			0.311863	+	0.950127i	$0.399047\pi$
$20$	0.501605	−	0.182569i	0.112162	−	0.0408237i
$21$	−2.17440	+	4.03386i	−0.474493	+	0.880259i
$22$	−2.85221	+	2.39329i	−0.608094	+	0.510252i
$23$	−0.309811	−	1.75702i	−0.0646000	−	0.366365i	−0.999921	−	0.0125648i	$-0.996000\pi$
$23$	−0.309811	−	1.75702i	−0.0646000	−	0.366365i	0.935321	−	0.353800i	$-0.115111\pi$
$24$	−0.389111	+	1.68778i	−0.0794270	+	0.344516i
$25$	−3.61195	−	3.03078i	−0.722389	−	0.606157i
$26$	−3.07687	−	5.32930i	−0.603424	−	1.04516i
$27$	3.26635	−	4.04116i	0.628608	−	0.777722i
$28$	−0.246405	+	2.63425i	−0.0465661	+	0.497827i
$29$	1.83629	−	10.4141i	0.340991	−	1.93386i	−0.0163112	−	0.999867i	$-0.505192\pi$
$29$	1.83629	−	10.4141i	0.340991	−	1.93386i	0.357302	−	0.933989i	$-0.383697\pi$
$30$	−0.884082	+	0.270586i	−0.161410	+	0.0494020i
$31$	1.18040	−	0.990471i	0.212006	−	0.177894i	−0.530601	−	0.847622i	$-0.678034\pi$
$31$	1.18040	−	0.990471i	0.212006	−	0.177894i	0.742607	+	0.669728i	$0.233589\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	5.14917	−	3.88265i	0.896356	−	0.675882i
$34$	−2.05253	+	0.747059i	−0.352005	+	0.128119i
$35$	−1.28353	+	0.589169i	−0.216956	+	0.0995878i
$36$	0.825151	−	2.88429i	0.137525	−	0.480715i
$37$	−5.19917	+	9.00522i	−0.854738	+	1.48045i	0.0221508	+	0.999755i	$0.492949\pi$
$37$	−5.19917	+	9.00522i	−0.854738	+	1.48045i	−0.876888	+	0.480694i	$0.840385\pi$
$38$	−2.55480	+	0.929871i	−0.414443	+	0.150845i
$39$	4.84180	+	9.49540i	0.775308	+	1.52048i
$40$	−0.408912	+	0.343118i	−0.0646547	+	0.0542517i
$41$	1.45917	+	8.27535i	0.227884	+	1.29239i	0.857095	+	0.515158i	$0.172267\pi$
$41$	1.45917	+	8.27535i	0.227884	+	1.29239i	−0.629212	+	0.777234i	$0.716622\pi$
$42$	0.663608	−	4.53427i	0.102397	−	0.699653i
$43$	4.99996	+	4.19547i	0.762487	+	0.639803i	0.938773	−	0.344536i	$-0.111964\pi$
$43$	4.99996	+	4.19547i	0.762487	+	0.639803i	−0.176286	+	0.984339i	$0.556408\pi$
$44$	1.86165	−	3.22447i	0.280654	−	0.486108i
$45$	1.55359	−	0.388360i	0.231595	−	0.0578933i
$46$	0.892065	+	1.54510i	0.131528	+	0.227813i
$47$	−8.02588	−	6.73451i	−1.17069	−	0.982330i	−0.170699	−	0.985323i	$-0.554603\pi$
$47$	−8.02588	−	6.73451i	−1.17069	−	0.982330i	−0.999996	+	0.00299355i	$0.999047\pi$
$48$	−0.211609	−	1.71908i	−0.0305431	−	0.248127i
$49$	0.0840109	−	6.99950i	0.0120016	−	0.999928i
$50$	4.43071	+	1.61265i	0.626597	+	0.228063i
$51$	3.61759	−	1.10722i	0.506564	−	0.155041i
$52$	4.71404	+	3.95555i	0.653720	+	0.548536i
$53$	−3.95402	+	6.84856i	−0.543126	+	0.940722i	0.455596	+	0.890187i	$0.349426\pi$
$53$	−3.95402	+	6.84856i	−0.543126	+	0.940722i	−0.998722	+	0.0505354i	$0.983907\pi$
$54$	−1.68720	+	4.91461i	−0.229599	+	0.668793i
$55$	1.98749			0.267993
$56$	−0.669423	−	2.55966i	−0.0894554	−	0.342049i
$57$	4.50285	−	1.37816i	0.596417	−	0.182542i
$58$	1.83629	+	10.4141i	0.241117	+	1.36744i
$59$	0.492061	+	2.79062i	0.0640609	+	0.363307i	0.999940	+	0.0109852i	$0.00349677\pi$
$59$	0.492061	+	2.79062i	0.0640609	+	0.363307i	−0.935879	+	0.352322i	$0.885392\pi$
$60$	0.738219	−	0.556641i	0.0953037	−	0.0718621i
$61$	−4.53366	−	3.80420i	−0.580476	−	0.487077i	0.304627	−	0.952472i	$-0.401468\pi$
$61$	−4.53366	−	3.80420i	−0.580476	−	0.487077i	−0.885103	+	0.465394i	$0.845913\pi$
$62$	−0.770450	+	1.33446i	−0.0978472	+	0.169476i
$63$	−1.55648	+	7.78315i	−0.196098	+	0.980584i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−0.570408	+	3.23494i	−0.0707504	+	0.401245i
$66$	−3.51070	+	5.40961i	−0.432137	+	0.665878i
$67$	3.54979	+	1.29202i	0.433676	+	0.157845i	0.549628	−	0.835410i	$-0.314770\pi$
$67$	3.54979	+	1.29202i	0.433676	+	0.157845i	−0.115952	+	0.993255i	$0.536992\pi$
$68$	1.67324	−	1.40401i	0.202910	−	0.170261i
$69$	−1.40376	−	2.75296i	−0.168993	−	0.331418i
$70$	1.00462	−	0.992632i	0.120075	−	0.118642i
$71$	−4.58179	−	7.93590i	−0.543759	−	0.941818i	−0.998684	−	0.0512884i	$-0.983667\pi$
$71$	−4.58179	−	7.93590i	−0.543759	−	0.941818i	0.454925	−	0.890530i	$-0.349666\pi$
$72$	0.211097	+	2.99256i	0.0248780	+	0.352677i
$73$	−3.80191	−	6.58510i	−0.444980	−	0.770727i	0.553071	−	0.833134i	$-0.313456\pi$
$73$	−3.80191	−	6.58510i	−0.444980	−	0.770727i	−0.998051	+	0.0624067i	$0.980122\pi$
$74$	1.80565	−	10.2404i	0.209903	−	1.19042i
$75$	−7.51848	−	3.18870i	−0.868160	−	0.368199i
$76$	2.08269	−	1.74759i	0.238901	−	0.200462i
$77$	−4.21668	+	8.90283i	−0.480536	+	1.01457i
$78$	−7.79742	−	7.26676i	−0.882884	−	0.822799i
$79$	−13.9134	+	5.06405i	−1.56538	+	0.569750i	−0.971960	−	0.235147i	$-0.924443\pi$
$79$	−13.9134	+	5.06405i	−1.56538	+	0.569750i	−0.593415	+	0.804897i	$0.702221\pi$
$80$	0.266898	−	0.462282i	0.0298401	−	0.0516847i
$81$	3.36127	−	8.34877i	0.373474	−	0.927641i
$82$	−4.20150	−	7.27722i	−0.463978	−	0.803634i
$83$	0.348371	−	1.97571i	0.0382386	−	0.216862i	−0.959701	−	0.281023i	$-0.909326\pi$
$83$	0.348371	−	1.97571i	0.0382386	−	0.216862i	0.997940	+	0.0641614i	$0.0204372\pi$
$84$	0.927225	+	4.48779i	0.101169	+	0.489658i
$85$	1.09563	+	0.398777i	0.118838	+	0.0432535i
$86$	−6.13336	−	2.23236i	−0.661377	−	0.240722i
$87$	−2.23772	−	18.1789i	−0.239908	−	1.94898i
$88$	−0.646545	+	3.66674i	−0.0689219	+	0.390875i
$89$	3.83829			0.406858			0.203429	−	0.979090i	$-0.434791\pi$
$89$	3.83829			0.406858			0.203429	+	0.979090i	$0.434791\pi$
$90$	−1.32707	+	0.896297i	−0.139885	+	0.0944779i
$91$	−13.2806	−	9.41842i	−1.39218	−	0.987318i
$92$	−1.36672	−	1.14682i	−0.142491	−	0.119564i
$93$	1.45291	−	2.23879i	0.150660	−	0.232151i
$94$	9.84520	+	3.58336i	1.01545	+	0.369595i
$95$	1.36374	+	0.496362i	0.139917	+	0.0509257i
$96$	0.786806	+	1.54303i	0.0803030	+	0.157485i
$97$	−5.72248	−	4.80173i	−0.581030	−	0.487542i	0.304255	−	0.952591i	$-0.401592\pi$
$97$	−5.72248	−	4.80173i	−0.581030	−	0.487542i	−0.885285	+	0.465049i	$0.846037\pi$
$98$	2.31502	+	6.60611i	0.233853	+	0.667318i
$99$	6.55999	−	9.04065i	0.659303	−	0.908619i
$100$	−4.71506			−0.471506
$101$	−0.302535	+	1.71576i	−0.0301033	+	0.170725i	−0.996153	−	0.0876323i	$-0.972070\pi$
$101$	−0.302535	+	1.71576i	−0.0301033	+	0.170725i	0.966050	+	0.258357i	$0.0831810\pi$
$102$	−3.02073	+	2.27773i	−0.299097	+	0.225529i
$103$	2.95448	+	1.07534i	0.291114	+	0.105957i	0.483449	−	0.875373i	$-0.339384\pi$
$103$	2.95448	+	1.07534i	0.291114	+	0.105957i	−0.192335	+	0.981329i	$0.561606\pi$
$104$	−5.78263	−	2.10470i	−0.567033	−	0.206383i
$105$	−1.82715	+	1.62642i	−0.178311	+	0.158723i
$106$	1.37322	−	7.78789i	0.133379	−	0.756427i
$107$	−6.59506	−	11.4230i	−0.637569	−	1.10430i	−0.985965	−	0.166954i	$-0.946607\pi$
$107$	−6.59506	−	11.4230i	−0.637569	−	1.10430i	0.348396	−	0.937347i	$-0.386726\pi$
$108$	−0.0954433	−	5.19528i	−0.00918403	−	0.499916i
$109$	−7.15909	+	12.3999i	−0.685716	+	1.18769i	0.287495	+	0.957782i	$0.407177\pi$
$109$	−7.15909	+	12.3999i	−0.685716	+	1.18769i	−0.973211	+	0.229913i	$0.926156\pi$
$110$	−1.86763	+	0.679760i	−0.178071	+	0.0648126i
$111$	−4.04611	+	17.5501i	−0.384040	+	1.66578i
$112$	1.50451	+	2.17634i	0.142163	+	0.205645i
$113$	−10.5821	+	8.87944i	−0.995481	+	0.835308i	−0.986352	−	0.164651i	$-0.947350\pi$
$113$	−10.5821	+	8.87944i	−0.995481	+	0.835308i	−0.00912887	+	0.999958i	$0.502906\pi$
$114$	−3.75994	+	2.83511i	−0.352150	+	0.265533i
$115$	0.165376	−	0.937894i	0.0154214	−	0.0874591i
$116$	−5.28739	−	9.15803i	−0.490922	−	0.850302i
$117$	12.8323	+	13.2721i	1.18635	+	1.22700i
$118$	−1.41683	−	2.45403i	−0.130430	−	0.225912i
$119$	−4.11081	+	4.06177i	−0.376838	+	0.372342i
$120$	−0.503316	+	0.775558i	−0.0459463	+	0.0707984i
$121$	2.19317	−	1.84028i	0.199379	−	0.167299i
$122$	5.56136	+	2.02417i	0.503502	+	0.183260i
$123$	6.61153	+	12.9661i	0.596142	+	1.16911i
$124$	0.267574	−	1.51749i	0.0240289	−	0.136275i
$125$	−2.59293	−	4.49109i	−0.231919	−	0.401696i
$126$	−1.19938	−	7.84611i	−0.106850	−	0.698987i
$127$	10.2055	−	17.6765i	0.905592	−	1.56853i	0.0854719	−	0.996341i	$-0.472760\pi$
$127$	10.2055	−	17.6765i	0.905592	−	1.56853i	0.820120	−	0.572191i	$-0.193906\pi$
$128$	0.766044	+	0.642788i	0.0677094	+	0.0568149i
$129$	10.4077	+	4.41407i	0.916349	+	0.388637i
$130$	−0.570408	−	3.23494i	−0.0500281	−	0.283723i
$131$	−0.652134	−	3.69844i	−0.0569773	−	0.323134i	0.942975	−	0.332862i	$-0.108014\pi$
$131$	−0.652134	−	3.69844i	−0.0569773	−	0.323134i	−0.999953	+	0.00972830i	$0.996903\pi$
$132$	1.44878	−	6.28410i	0.126100	−	0.546961i
$133$	−5.11677	+	5.05572i	−0.443680	+	0.438387i
$134$	−3.77761			−0.326336
$135$	2.37621	−	1.43073i	0.204511	−	0.123138i
$136$	−1.09213	+	1.89162i	−0.0936491	+	0.162205i
$137$	−3.25751	−	2.73338i	−0.278308	−	0.233528i	0.492939	−	0.870064i	$-0.335922\pi$
$137$	−3.25751	−	2.73338i	−0.278308	−	0.233528i	−0.771247	+	0.636535i	$0.780367\pi$
$138$	2.26067	+	2.10682i	0.192441	+	0.179345i
$139$	2.40909	+	0.876837i	0.204336	+	0.0743723i	0.442161	−	0.896936i	$-0.354212\pi$
$139$	2.40909	+	0.876837i	0.204336	+	0.0743723i	−0.237824	+	0.971308i	$0.576434\pi$
$140$	−0.604531	+	1.27637i	−0.0510922	+	0.107873i
$141$	−16.7064	−	7.08541i	−1.40693	−	0.596699i
$142$	7.01972	+	5.89024i	0.589082	+	0.494298i
$143$	11.4561	+	19.8426i	0.958009	+	1.65932i
$144$	−1.22188	−	2.73989i	−0.101824	−	0.228324i
$145$	2.82239	−	4.88853i	0.234387	−	0.405970i
$146$	5.82486	+	4.88764i	0.482069	+	0.404504i
$147$	−3.40896	−	11.6352i	−0.281166	−	0.959659i
$148$	1.80565	+	10.2404i	0.148424	+	0.841752i
$149$	−8.48248	+	7.11765i	−0.694912	+	0.583100i	−0.920321	−	0.391164i	$-0.872073\pi$
$149$	−8.48248	+	7.11765i	−0.694912	+	0.583100i	0.225409	+	0.974264i	$0.427628\pi$
$150$	8.15566	+	0.424924i	0.665907	+	0.0346949i
$151$	1.36470	−	0.496710i	0.111058	−	0.0404217i	−0.285894	−	0.958261i	$-0.592290\pi$
$151$	1.36470	−	0.496710i	0.111058	−	0.0404217i	0.396951	+	0.917840i	$0.370068\pi$
$152$	−1.35938	+	2.35452i	−0.110260	+	0.190977i
$153$	5.43025	−	3.66757i	0.439009	−	0.296506i
$154$	0.917439	−	9.80812i	0.0739293	−	0.790360i
$155$	0.772923	−	0.281321i	0.0620826	−	0.0225962i
$156$	9.81256	+	4.16165i	0.785633	+	0.333199i
$157$	−2.17087	−	12.3116i	−0.173255	−	0.982576i	−0.940139	−	0.340791i	$-0.889305\pi$
$157$	−2.17087	−	12.3116i	−0.173255	−	0.982576i	0.766884	−	0.641785i	$-0.221806\pi$
$158$	11.3423	−	9.51730i	0.902343	−	0.757156i
$159$	−3.07711	+	13.3470i	−0.244030	+	1.05849i
$160$	−0.0926928	+	0.525687i	−0.00732801	+	0.0415592i
$161$	3.85038	+	2.73064i	0.303452	+	0.215205i
$162$	−0.303112	+	8.99489i	−0.0238147	+	0.706706i
$163$	−0.994136	−	1.72189i	−0.0778668	−	0.134869i	0.824463	−	0.565916i	$-0.191478\pi$
$163$	−0.994136	−	1.72189i	−0.0778668	−	0.134869i	−0.902329	+	0.431047i	$0.858144\pi$
$164$	6.43708	+	5.40135i	0.502651	+	0.421774i
$165$	3.29170	−	1.00747i	0.256259	−	0.0784317i
$166$	0.348371	+	1.97571i	0.0270388	+	0.153345i
$167$	12.6179	−	10.5876i	0.976400	−	0.819297i	−0.00714251	−	0.999974i	$-0.502274\pi$
$167$	12.6179	−	10.5876i	0.976400	−	0.819297i	0.983542	+	0.180678i	$0.0578291\pi$
$168$	−2.40622	−	3.90001i	−0.185644	−	0.300893i
$169$	−23.3688	+	8.50554i	−1.79760	+	0.654272i
$170$	−1.16595			−0.0894241
$171$	6.75908	−	4.56506i	0.516880	−	0.349099i
$172$	6.52699			0.497678
$173$	−1.40691	+	7.97900i	−0.106966	+	0.606632i	0.883451	+	0.468523i	$0.155214\pi$
$173$	−1.40691	+	7.97900i	−0.106966	+	0.606632i	−0.990417	+	0.138109i	$0.955897\pi$
$174$	8.32030	+	16.3172i	0.630761	+	1.23700i
$175$	12.4337	−	1.01266i	0.939900	−	0.0765501i
$176$	−0.646545	−	3.66674i	−0.0487351	−	0.276391i
$177$	2.22955	+	4.37243i	0.167583	+	0.328652i
$178$	−3.60681	+	1.31277i	−0.270342	+	0.0983964i
$179$	−4.53898			−0.339259			−0.169630	−	0.985508i	$-0.554257\pi$
$179$	−4.53898			−0.339259			−0.169630	+	0.985508i	$0.554257\pi$
$180$	0.940482	−	1.29613i	0.0700994	−	0.0966076i
$181$	2.05546	−	3.56016i	0.152781	−	0.264625i	−0.779468	−	0.626442i	$-0.784510\pi$
$181$	2.05546	−	3.56016i	0.152781	−	0.264625i	0.932249	+	0.361818i	$0.117844\pi$
$182$	15.7009	+	4.30820i	1.16383	+	0.319345i
$183$	−9.43710	−	4.00241i	−0.697610	−	0.295867i
$184$	1.67653	+	0.610208i	0.123596	+	0.0449851i
$185$	−4.25200	+	3.56785i	−0.312613	+	0.262314i
$186$	−0.599582	+	2.60070i	−0.0439635	+	0.190692i
$187$	7.64218	−	2.78152i	0.558851	−	0.203405i
$188$	−10.4770			−0.764117
$189$	1.36748	+	13.6795i	0.0994699	+	0.995041i
$190$	−1.45127			−0.105286
$191$	13.8897	−	5.05545i	1.00503	−	0.365800i	0.213505	−	0.976942i	$-0.431512\pi$
$191$	13.8897	−	5.05545i	1.00503	−	0.365800i	0.791521	+	0.611142i	$0.209290\pi$
$192$	−1.26710	−	1.18087i	−0.0914452	−	0.0852219i
$193$	−3.89310	+	3.26670i	−0.280232	+	0.235142i	−0.772060	−	0.635550i	$-0.780773\pi$
$193$	−3.89310	+	3.26670i	−0.280232	+	0.235142i	0.491828	+	0.870692i	$0.336329\pi$
$194$	7.01966	+	2.55495i	0.503982	+	0.183435i
$195$	0.695102	+	5.64690i	0.0497773	+	0.404383i
$196$	−4.43483	−	5.41593i	−0.316774	−	0.386852i
$197$	1.89075	−	3.27487i	0.134710	−	0.233325i	−0.790776	−	0.612105i	$-0.790323\pi$
$197$	1.89075	−	3.27487i	0.134710	−	0.233325i	0.925487	+	0.378780i	$0.123656\pi$
$198$	−3.07229	+	10.7391i	−0.218338	+	0.763193i
$199$	21.0474			1.49201			0.746005	−	0.665940i	$-0.231969\pi$
$199$	21.0474			1.49201			0.746005	+	0.665940i	$0.231969\pi$
$200$	4.43071	−	1.61265i	0.313298	−	0.114031i
$201$	6.53415	+	0.340440i	0.460883	+	0.0240128i
$202$	−0.302535	−	1.71576i	−0.0212863	−	0.120720i
$203$	15.9098	+	23.0143i	1.11665	+	1.61529i
$204$	2.05953	−	3.17352i	0.144196	−	0.222191i
$205$	−0.778899	+	4.41735i	−0.0544006	+	0.308521i
$206$	−3.14410			−0.219060
$207$	−3.72043	−	3.84792i	−0.258588	−	0.267449i
$208$	6.15374			0.426685
$209$	9.51229	−	3.46219i	0.657979	−	0.239485i
$210$	1.16069	−	2.15326i	0.0800950	−	0.148589i
$211$	−0.403942	+	0.338947i	−0.0278085	+	0.0233341i	−0.656586	−	0.754251i	$-0.728000\pi$
$211$	−0.403942	+	0.338947i	−0.0278085	+	0.0233341i	0.628777	+	0.777585i	$0.283556\pi$
$212$	1.37322	+	7.78789i	0.0943128	+	0.534875i
$213$	−11.6112	−	10.8210i	−0.795587	−	0.741443i
$214$	10.1042	+	8.47845i	0.690710	+	0.579575i
$215$	1.74204	+	3.01731i	0.118806	+	0.205779i
$216$	1.86658	+	4.84932i	0.127004	+	0.329954i
$217$	−0.379685	+	4.05912i	−0.0257747	+	0.275551i
$218$	2.48632	−	14.1006i	0.168395	−	0.955016i
$219$	−9.63481	−	8.97911i	−0.651060	−	0.606752i
$220$	1.52250	−	1.27753i	0.102647	−	0.0861312i
$221$	2.33406	+	13.2371i	0.157006	+	0.890425i
$222$	−2.20038	−	17.8755i	−0.147680	−	1.19973i
$223$	5.24765	−	1.90999i	0.351408	−	0.127902i	−0.160284	−	0.987071i	$-0.551241\pi$
$223$	5.24765	−	1.90999i	0.351408	−	0.127902i	0.511692	+	0.859169i	$0.329019\pi$
$224$	−2.15813	−	1.53052i	−0.144196	−	0.102262i
$225$	−14.0686	−	1.46999i	−0.937906	−	0.0979990i
$226$	6.90698	−	11.9632i	0.459445	−	0.795783i
$227$	0.0901182	−	0.0328003i	0.00598135	−	0.00217703i	−0.339028	−	0.940776i	$-0.610098\pi$
$227$	0.0901182	−	0.0328003i	0.00598135	−	0.00217703i	0.345009	+	0.938599i	$0.387876\pi$
$228$	2.56352	−	3.95011i	0.169773	−	0.261602i
$229$	13.6734	−	11.4733i	0.903563	−	0.758179i	−0.0673209	−	0.997731i	$-0.521445\pi$
$229$	13.6734	−	11.4733i	0.903563	−	0.758179i	0.970883	+	0.239552i	$0.0770007\pi$
$230$	0.165376	+	0.937894i	0.0109046	+	0.0618429i
$231$	−2.47081	+	16.8825i	−0.162567	+	1.11078i
$232$	8.10076	+	6.79734i	0.531841	+	0.446267i
$233$	1.13445	−	1.96492i	0.0743200	−	0.128726i	−0.826470	−	0.562980i	$-0.809655\pi$
$233$	1.13445	−	1.96492i	0.0743200	−	0.128726i	0.900790	+	0.434254i	$0.142988\pi$
$234$	−16.5978	−	8.08274i	−1.08503	−	0.528385i
$235$	−2.79631	−	4.84334i	−0.182411	−	0.315945i
$236$	2.17071	+	1.82145i	0.141302	+	0.118566i
$237$	−20.4765	+	15.4399i	−1.33009	+	1.00293i
$238$	2.47369	−	5.22279i	0.160346	−	0.338543i
$239$	15.4607	+	5.62725i	1.00007	+	0.363997i	0.789612	−	0.613606i	$-0.210282\pi$
$239$	15.4607	+	5.62725i	1.00007	+	0.363997i	0.210460	+	0.977602i	$0.432504\pi$
$240$	0.207706	−	0.900930i	0.0134074	−	0.0581548i
$241$	13.7441	+	11.5327i	0.885337	+	0.742886i	0.967269	−	0.253752i	$-0.0816648\pi$
$241$	13.7441	+	11.5327i	0.885337	+	0.742886i	−0.0819326	+	0.996638i	$0.526109\pi$
$242$	−1.43149	+	2.47941i	−0.0920195	+	0.159382i
$243$	1.33492	−	15.5312i	0.0856351	−	0.996327i
$244$	−5.91828			−0.378879
$245$	1.32003	−	3.49564i	0.0843338	−	0.223328i
$246$	−10.6475	−	9.92285i	−0.678858	−	0.632658i
$247$	2.90523	+	16.4764i	0.184855	+	1.04837i
$248$	0.267574	+	1.51749i	0.0169910	+	0.0963607i
$249$	−0.424526	−	3.44879i	−0.0269033	−	0.218558i
$250$	3.97261	+	3.33341i	0.251250	+	0.210823i
$251$	0.0690199	−	0.119546i	0.00435650	−	0.00754568i	−0.863839	−	0.503768i	$-0.831947\pi$
$251$	0.0690199	−	0.119546i	0.00435650	−	0.00754568i	0.868195	+	0.496222i	$0.165280\pi$
$252$	3.81058	+	6.96272i	0.240044	+	0.438610i
$253$	−3.32143	−	5.75288i	−0.208816	−	0.361680i
$254$	−3.54433	+	20.1009i	−0.222391	+	1.26124i
$255$	2.01674	+	0.105076i	0.126293	+	0.00658010i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−15.6146	+	13.1022i	−0.974014	+	0.817295i	−0.983176	−	0.182663i	$-0.941528\pi$
$257$	−15.6146	+	13.1022i	−0.974014	+	0.817295i	0.00916174	+	0.999958i	$0.497084\pi$
$258$	−11.2898	−	0.588215i	−0.702870	−	0.0366207i
$259$	−6.96088	−	26.6162i	−0.432528	−	1.65385i
$260$	1.64242	+	2.84476i	0.101859	+	0.176425i
$261$	−12.9212	−	28.9738i	−0.799799	−	1.79343i
$262$	1.87775	+	3.25235i	0.116008	+	0.200931i
$263$	2.68773	−	15.2429i	0.165733	−	0.939916i	−0.782573	−	0.622559i	$-0.786093\pi$
$263$	2.68773	−	15.2429i	0.165733	−	0.939916i	0.948306	−	0.317358i	$-0.102796\pi$
$264$	0.787883	+	6.40064i	0.0484908	+	0.393932i
$265$	−3.23369	+	2.71339i	−0.198644	+	0.166682i
$266$	3.07903	−	6.50086i	0.188787	−	0.398593i
$267$	6.35702	−	1.94566i	0.389044	−	0.119072i
$268$	3.54979	−	1.29202i	0.216838	−	0.0789226i
$269$	−13.6222	+	23.5944i	−0.830562	+	1.43858i	0.0670304	+	0.997751i	$0.478648\pi$
$269$	−13.6222	+	23.5944i	−0.830562	+	1.43858i	−0.897593	+	0.440825i	$0.854686\pi$
$270$	−1.74356	+	2.15716i	−0.106110	+	0.131281i
$271$	3.21867	+	5.57491i	0.195521	+	0.338651i	0.947071	−	0.321024i	$-0.104027\pi$
$271$	3.21867	+	5.57491i	0.195521	+	0.338651i	−0.751551	+	0.659676i	$0.770694\pi$
$272$	0.379292	−	2.15107i	0.0229979	−	0.130428i
$273$	−26.7697	−	8.86689i	−1.62018	−	0.536649i
$274$	3.99593	+	1.45440i	0.241403	+	0.0878635i
$275$	−16.4969	−	6.00437i	−0.994798	−	0.362077i
$276$	−2.84492	−	1.20657i	−0.171244	−	0.0726270i
$277$	0.0868347	−	0.492464i	0.00521739	−	0.0295893i	−0.982088	−	0.188423i	$-0.939662\pi$
$277$	0.0868347	−	0.492464i	0.00521739	−	0.0295893i	0.987305	+	0.158834i	$0.0507734\pi$
$278$	−2.56370			−0.153760
$279$	1.27148	−	4.44440i	0.0761212	−	0.266079i
$280$	0.131530	−	1.40616i	0.00786042	−	0.0840339i
$281$	−15.8449	−	13.2954i	−0.945226	−	0.793138i	0.0332615	−	0.999447i	$-0.489411\pi$
$281$	−15.8449	−	13.2954i	−0.945226	−	0.793138i	−0.978487	+	0.206308i	$0.933855\pi$
$282$	18.1222	+	0.944196i	1.07916	+	0.0562261i
$283$	21.5873	+	7.85713i	1.28323	+	0.467058i	0.891500	−	0.453022i	$-0.149654\pi$
$283$	21.5873	+	7.85713i	1.28323	+	0.467058i	0.391732	+	0.920080i	$0.371876\pi$
$284$	−8.61096	−	3.13413i	−0.510966	−	0.185977i
$285$	2.51026	+	0.130789i	0.148695	+	0.00774726i
$286$	−17.5518	−	14.7277i	−1.03786	−	0.870867i
$287$	−18.1348	−	12.8610i	−1.07046	−	0.759159i
$288$	2.08529	+	2.15675i	0.122877	+	0.127088i
$289$	−12.2290			−0.719355
$290$	−0.980207	+	5.55903i	−0.0575597	+	0.326437i
$291$	−11.9117	−	5.05192i	−0.698275	−	0.296149i
$292$	−7.14525	−	2.60066i	−0.418144	−	0.152192i
$293$	30.3169	+	11.0344i	1.77113	+	0.644639i	0.999968	+	0.00799968i	$0.00254641\pi$
$293$	30.3169	+	11.0344i	1.77113	+	0.644639i	0.771162	+	0.636639i	$0.219676\pi$
$294$	7.18287	+	9.76762i	0.418913	+	0.569659i
$295$	−0.262661	+	1.48962i	−0.0152927	+	0.0867292i
$296$	−5.19917	−	9.00522i	−0.302195	−	0.523418i
$297$	6.28196	−	18.2986i	0.364516	−	1.06179i
$298$	5.53655	−	9.58958i	0.320724	−	0.555509i
$299$	10.3170	−	3.75506i	0.596645	−	0.217161i
$300$	−7.80915	+	2.39010i	−0.450861	+	0.137993i
$301$	−17.2118	+	1.40181i	−0.992071	+	0.0807991i
$302$	−1.11251	+	0.933510i	−0.0640180	+	0.0537175i
$303$	0.368671	+	2.99502i	0.0211796	+	0.172060i
$304$	0.472108	−	2.67746i	0.0270772	−	0.153563i
$305$	−1.57958	−	2.73591i	−0.0904464	−	0.156658i
$306$	−3.84838	+	5.30364i	−0.219997	+	0.303189i
$307$	−0.224919	−	0.389571i	−0.0128368	−	0.0222340i	0.859536	−	0.511076i	$-0.170753\pi$
$307$	−0.224919	−	0.389571i	−0.0128368	−	0.0222340i	−0.872372	+	0.488842i	$0.837420\pi$
$308$	2.49246	+	9.53040i	0.142021	+	0.543045i
$309$	5.43836	+	0.283348i	0.309377	+	0.0161191i
$310$	−0.630092	+	0.528710i	−0.0357868	+	0.0300287i
$311$	−15.3904	−	5.60164i	−0.872708	−	0.317640i	−0.133445	−	0.991056i	$-0.542604\pi$
$311$	−15.3904	−	5.60164i	−0.872708	−	0.317640i	−0.739263	+	0.673417i	$0.764826\pi$
$312$	−10.6442	−	0.554578i	−0.602607	−	0.0313968i
$313$	−1.67045	+	9.47360i	−0.0944194	+	0.535479i	0.900504	+	0.434847i	$0.143198\pi$
$313$	−1.67045	+	9.47360i	−0.0944194	+	0.535479i	−0.994924	+	0.100632i	$0.967914\pi$
$314$	6.25078	+	10.8267i	0.352752	+	0.610985i
$315$	−2.20170	+	3.61990i	−0.124052	+	0.203958i
$316$	−7.40314	+	12.8226i	−0.416459	+	0.721329i
$317$	−0.0638640	−	0.0535883i	−0.00358696	−	0.00300982i	0.640992	−	0.767547i	$-0.278523\pi$
$317$	−0.0638640	−	0.0535883i	−0.00358696	−	0.00300982i	−0.644579	+	0.764537i	$0.722967\pi$
$318$	−1.67341	−	13.5945i	−0.0938401	−	0.762342i
$319$	−6.83707	−	38.7750i	−0.382802	−	2.17098i
$320$	−0.0926928	−	0.525687i	−0.00518169	−	0.0293868i
$321$	−16.7132	−	15.5758i	−0.932842	−	0.869357i
$322$	−4.55211	−	1.24906i	−0.253679	−	0.0696073i
$323$	5.93846			0.330425
$324$	−2.79160	−	8.55611i	−0.155089	−	0.475339i
$325$	14.5076	−	25.1280i	0.804739	−	1.39385i
$326$	1.52311	+	1.27804i	0.0843570	+	0.0707839i
$327$	−5.57136	+	24.1659i	−0.308097	+	1.33638i
$328$	−7.89624	−	2.87400i	−0.435997	−	0.158690i
$329$	27.6282	−	2.25017i	1.52319	−	0.124056i
$330$	−2.74861	+	2.07254i	−0.151306	+	0.114090i
$331$	−8.52042	−	7.14948i	−0.468324	−	0.392971i	0.377859	−	0.925863i	$-0.376661\pi$
$331$	−8.52042	−	7.14948i	−0.468324	−	0.392971i	−0.846183	+	0.532893i	$0.821105\pi$
$332$	−1.00309	−	1.73741i	−0.0550519	−	0.0953527i
$333$	2.19505	+	31.1177i	0.120288	+	1.70524i
$334$	−8.23573	+	14.2647i	−0.450639	+	0.780530i
$335$	1.54471	+	1.29617i	0.0843965	+	0.0708171i
$336$	3.59499	+	2.84184i	0.196123	+	0.155035i
$337$	3.16376	+	17.9426i	0.172341	+	0.977393i	0.941169	+	0.337937i	$0.109729\pi$
$337$	3.16376	+	17.9426i	0.172341	+	0.977393i	−0.768828	+	0.639456i	$0.779160\pi$
$338$	19.0504	−	15.9852i	1.03621	−	0.869479i
$339$	−13.0252	+	20.0704i	−0.707430	+	1.09008i
$340$	1.09563	−	0.398777i	0.0594190	−	0.0216267i
$341$	2.86862	−	4.96859i	0.155344	−	0.269064i
$342$	−4.79011	+	6.60150i	−0.259020	+	0.356968i
$343$	12.8579	+	13.3294i	0.694263	+	0.719721i
$344$	−6.13336	+	2.23236i	−0.330689	+	0.120361i
$345$	−0.201528	−	1.63718i	−0.0108499	−	0.0881430i
$346$	−1.40691	−	7.97900i	−0.0756361	−	0.428954i
$347$	−9.48956	+	7.96269i	−0.509426	+	0.427459i	−0.860927	−	0.508728i	$-0.830116\pi$
$347$	−9.48956	+	7.96269i	−0.509426	+	0.427459i	0.351501	+	0.936188i	$0.385671\pi$
$348$	−13.3993	−	12.4874i	−0.718280	−	0.669397i
$349$	−0.465111	+	2.63777i	−0.0248968	+	0.141197i	−0.994722	−	0.102603i	$-0.967283\pi$
$349$	−0.465111	+	2.63777i	−0.0248968	+	0.141197i	0.969826	+	0.243800i	$0.0783940\pi$
$350$	−11.3375	+	5.20417i	−0.606016	+	0.278175i
$351$	27.9808	+	15.4765i	1.49351	+	0.826077i
$352$	1.86165	+	3.22447i	0.0992263	+	0.171865i
$353$	5.84821	+	4.90723i	0.311269	+	0.261185i	0.785016	−	0.619475i	$-0.212655\pi$
$353$	5.84821	+	4.90723i	0.311269	+	0.261185i	−0.473747	+	0.880661i	$0.657099\pi$
$354$	−3.59055	−	3.34619i	−0.190835	−	0.177848i
$355$	−0.849399	−	4.81718i	−0.0450814	−	0.255669i
$356$	2.94030	−	2.46720i	0.155836	−	0.130762i
$357$	−4.74944	+	8.81096i	−0.251367	+	0.466326i
$358$	4.26525	−	1.55242i	0.225425	−	0.0820481i
$359$	−5.86980			−0.309796			−0.154898	−	0.987930i	$-0.549505\pi$
$359$	−5.86980			−0.309796			−0.154898	+	0.987930i	$0.549505\pi$
$360$	−0.440463	+	1.53962i	−0.0232144	+	0.0811453i
$361$	−11.6083			−0.610965
$362$	−0.713855	+	4.04847i	−0.0375194	+	0.212783i
$363$	2.69950	−	4.15964i	0.141687	−	0.218324i
$364$	−16.2275	+	1.32165i	−0.850554	+	0.0692733i
$365$	−0.704819	−	3.99723i	−0.0368919	−	0.209224i
$366$	10.2369	+	0.533358i	0.535090	+	0.0278791i
$367$	−30.2990	+	11.0279i	−1.58160	+	0.575654i	−0.975550	−	0.219775i	$-0.929468\pi$
$367$	−30.2990	+	11.0279i	−1.58160	+	0.575654i	−0.606046	+	0.795430i	$0.707245\pi$
$368$	−1.78413			−0.0930042
$369$	17.5227	+	18.1232i	0.912197	+	0.943454i
$370$	2.77530	−	4.80696i	0.144281	−	0.249902i
$371$	−5.29382	−	20.2419i	−0.274841	−	1.05091i
$372$	−0.326068	−	2.64892i	−0.0169058	−	0.137340i
$373$	7.41889	+	2.70025i	0.384135	+	0.139814i	0.526867	−	0.849948i	$-0.323366\pi$
$373$	7.41889	+	2.70025i	0.384135	+	0.139814i	−0.142732	+	0.989761i	$0.545589\pi$
$374$	−6.22996	+	5.22756i	−0.322144	+	0.270311i
$375$	−6.57103	−	6.12383i	−0.339326	−	0.316233i
$376$	9.84520	−	3.58336i	0.507727	−	0.184798i
$377$	65.0745			3.35151
$378$	−5.96370	−	12.3869i	−0.306739	−	0.637111i
$379$	7.39451			0.379830			0.189915	−	0.981801i	$-0.439179\pi$
$379$	7.39451			0.379830			0.189915	+	0.981801i	$0.439179\pi$
$380$	1.36374	−	0.496362i	0.0699586	−	0.0254628i
$381$	7.94216	−	34.4492i	0.406889	−	1.76489i
$382$	−11.3230	+	9.50114i	−0.579336	+	0.486121i
$383$	−30.3777	−	11.0566i	−1.55223	−	0.564964i	−0.583288	−	0.812266i	$-0.698234\pi$
$383$	−30.3777	−	11.0566i	−1.55223	−	0.564964i	−0.968939	+	0.247302i	$0.920456\pi$
$384$	1.59457	+	0.676279i	0.0813724	+	0.0345112i
$385$	−3.74049	+	3.69587i	−0.190633	+	0.188359i
$386$	2.54104	−	4.40121i	0.129336	−	0.224016i
$387$	19.4749	+	2.03488i	0.989967	+	0.103439i
$388$	−7.47017			−0.379240
$389$	16.0096	−	5.82703i	0.811720	−	0.295442i	0.0973860	−	0.995247i	$-0.468952\pi$
$389$	16.0096	−	5.82703i	0.811720	−	0.295442i	0.714334	+	0.699805i	$0.246730\pi$
$390$	−2.58454	−	5.06861i	−0.130873	−	0.256659i
$391$	−0.676705	−	3.83779i	−0.0342225	−	0.194085i
$392$	6.01974	+	3.57250i	0.304043	+	0.180439i
$393$	−2.95484	−	5.79483i	−0.149052	−	0.292311i
$394$	−0.656650	+	3.72405i	−0.0330816	+	0.187615i
$395$	−7.90355			−0.397671
$396$	−0.785976	−	11.1422i	−0.0394968	−	0.559918i
$397$	24.1808			1.21360			0.606799	−	0.794855i	$-0.292453\pi$
$397$	24.1808			1.21360			0.606799	+	0.794855i	$0.292453\pi$
$398$	−19.7781	+	7.19864i	−0.991386	+	0.360835i
$399$	−5.91167	+	10.9671i	−0.295954	+	0.549041i
$400$	−3.61195	+	3.03078i	−0.180597	+	0.151539i
$401$	−2.86034	−	16.2218i	−0.142839	−	0.810078i	−0.969077	−	0.246758i	$-0.920635\pi$
$401$	−2.86034	−	16.2218i	−0.142839	−	0.810078i	0.826238	−	0.563320i	$-0.190476\pi$
$402$	−6.25653	+	1.91490i	−0.312047	+	0.0955066i
$403$	7.26386	+	6.09510i	0.361839	+	0.303619i
$404$	0.871114	+	1.50881i	0.0433396	+	0.0750663i
$405$	3.21026	−	3.57412i	0.159519	−	0.177599i
$406$	−22.8217	−	16.1849i	−1.13262	−	0.803244i
$407$	−6.72298	+	38.1279i	−0.333246	+	1.88993i
$408$	−0.849918	+	3.68653i	−0.0420772	+	0.182511i
$409$	−7.81279	+	6.55571i	−0.386318	+	0.324159i	−0.815177	−	0.579212i	$-0.803360\pi$
$409$	−7.81279	+	6.55571i	−0.386318	+	0.324159i	0.428859	+	0.903371i	$0.358916\pi$
$410$	−0.778899	−	4.41735i	−0.0384671	−	0.218158i
$411$	−6.78071	−	2.87580i	−0.334468	−	0.141853i
$412$	2.95448	−	1.07534i	0.145557	−	0.0529784i
$413$	−6.11541	−	4.33698i	−0.300920	−	0.213409i
$414$	4.81213	+	2.34340i	0.236503	+	0.115172i
$415$	0.535448	−	0.927423i	0.0262841	−	0.0455254i
$416$	−5.78263	+	2.10470i	−0.283517	+	0.103192i
$417$	4.43444	+	0.231042i	0.217156	+	0.0113142i
$418$	−7.75449	+	6.50679i	−0.379285	+	0.318258i
$419$	−6.20977	−	35.2174i	−0.303367	−	1.72048i	−0.631092	−	0.775708i	$-0.717393\pi$
$419$	−6.20977	−	35.2174i	−0.303367	−	1.72048i	0.327725	−	0.944773i	$-0.393718\pi$
$420$	−0.354232	+	2.42038i	−0.0172847	+	0.118102i
$421$	25.2202	+	21.1622i	1.22916	+	1.03138i	0.998293	+	0.0583970i	$0.0185989\pi$
$421$	25.2202	+	21.1622i	1.22916	+	1.03138i	0.230862	+	0.972987i	$0.425846\pi$
$422$	0.263654	−	0.456662i	0.0128345	−	0.0222300i
$423$	−31.2609	−	3.26636i	−1.51996	−	0.158816i
$424$	−3.95402	−	6.84856i	−0.192024	−	0.332595i
$425$	−7.88941	−	6.62000i	−0.382692	−	0.321117i
$426$	14.6120	+	6.19715i	0.707952	+	0.300253i
$427$	15.6066	−	1.27108i	0.755257	−	0.0615118i
$428$	−12.3947	−	4.51129i	−0.599119	−	0.218061i
$429$	29.0321	+	27.0563i	1.40169	+	1.30629i
$430$	−2.66896	−	2.23953i	−0.128709	−	0.108000i
$431$	−1.03187	+	1.78725i	−0.0497034	+	0.0860888i	−0.889807	−	0.456338i	$-0.849161\pi$
$431$	−1.03187	+	1.78725i	−0.0497034	+	0.0860888i	0.840103	+	0.542426i	$0.182494\pi$
$432$	−3.41257	−	3.91846i	−0.164187	−	0.188527i
$433$	29.0541			1.39625			0.698124	−	0.715977i	$-0.254018\pi$
$433$	29.0541			1.39625			0.698124	+	0.715977i	$0.254018\pi$
$434$	−1.03151	−	3.94418i	−0.0495142	−	0.189327i
$435$	2.19645	−	9.52714i	0.105312	−	0.456792i
$436$	2.48632	+	14.1006i	0.119073	+	0.675298i
$437$	−0.842302	−	4.77693i	−0.0402928	−	0.228512i
$438$	12.1248	+	5.14230i	0.579345	+	0.245709i
$439$	26.9910	+	22.6481i	1.28821	+	1.08094i	0.992056	+	0.125797i	$0.0401487\pi$
$439$	26.9910	+	22.6481i	1.28821	+	1.08094i	0.296154	+	0.955140i	$0.404296\pi$
$440$	−0.993743	+	1.72121i	−0.0473748	+	0.0820556i
$441$	−11.5440	−	17.5424i	−0.549713	−	0.835354i
$442$	−6.72066	−	11.6405i	−0.319669	−	0.553684i
$443$	−1.05504	+	5.98344i	−0.0501266	+	0.284282i	−0.999559	−	0.0296890i	$-0.990548\pi$
$443$	−1.05504	+	5.98344i	−0.0501266	+	0.284282i	0.949433	+	0.313971i	$0.101659\pi$
$444$	8.18147	+	16.0449i	0.388275	+	0.761458i
$445$	1.92530	+	0.700753i	0.0912681	+	0.0332189i
$446$	−4.27792	+	3.58960i	−0.202565	+	0.169973i
$447$	−10.4408	+	16.0882i	−0.493833	+	0.760945i
$448$	2.55144	+	0.700094i	0.120544	+	0.0330763i
$449$	8.11231	+	14.0509i	0.382843	+	0.663104i	0.991467	−	0.130355i	$-0.0416116\pi$
$449$	8.11231	+	14.0509i	0.382843	+	0.663104i	−0.608624	+	0.793459i	$0.708278\pi$
$450$	13.7229	−	3.43041i	0.646905	−	0.161711i
$451$	15.6435	+	27.0953i	0.736622	+	1.27587i
$452$	−2.39877	+	13.6041i	−0.112829	+	0.639883i
$453$	2.00845	−	1.51444i	0.0943652	−	0.0711544i
$454$	−0.0734650	+	0.0616445i	−0.00344788	+	0.00289312i
$455$	−4.94208	−	7.14894i	−0.231688	−	0.335148i
$456$	−1.05790	+	4.58866i	−0.0495408	+	0.214884i
$457$	−30.2877	+	11.0238i	−1.41680	+	0.515672i	−0.933117	−	0.359573i	$-0.882922\pi$
$457$	−30.2877	+	11.0238i	−1.41680	+	0.515672i	−0.483680	+	0.875245i	$0.660700\pi$
$458$	−8.92467	+	15.4580i	−0.417022	+	0.722304i
$459$	7.13453	−	8.82692i	0.333011	−	0.412005i
$460$	−0.476181	−	0.824770i	−0.0222021	−	0.0384551i
$461$	4.89315	−	27.7504i	0.227896	−	1.29247i	−0.629173	−	0.777265i	$-0.716606\pi$
$461$	4.89315	−	27.7504i	0.227896	−	1.29247i	0.857070	−	0.515200i	$-0.172282\pi$
$462$	−3.45234	−	16.7094i	−0.160617	−	0.777391i
$463$	5.73184	+	2.08622i	0.266381	+	0.0969548i	0.471758	−	0.881728i	$-0.343620\pi$
$463$	5.73184	+	2.08622i	0.266381	+	0.0969548i	−0.205377	+	0.978683i	$0.565842\pi$
$464$	−9.93705	−	3.61679i	−0.461316	−	0.167905i
$465$	1.13752	−	0.857728i	0.0527513	−	0.0397762i
$466$	−0.393989	+	2.23442i	−0.0182512	+	0.103508i
$467$	−5.53985			−0.256354			−0.128177	−	0.991751i	$-0.540913\pi$
$467$	−5.53985			−0.256354			−0.128177	+	0.991751i	$0.540913\pi$
$468$	18.3613	+	1.91851i	0.848750	+	0.0886833i
$469$	−9.08338	+	4.16947i	−0.419432	+	0.192528i
$470$	4.28419	+	3.59486i	0.197615	+	0.165819i
$471$	−9.83631	−	19.2903i	−0.453233	−	0.888849i
$472$	−2.66278	−	0.969171i	−0.122564	−	0.0446097i
$473$	22.8364	+	8.31175i	1.05002	+	0.382175i
$474$	13.9608	−	21.5122i	0.641242	−	0.988087i
$475$	−9.82002	−	8.23998i	−0.450573	−	0.378076i
$476$	−0.538210	+	5.75387i	−0.0246688	+	0.263728i
$477$	1.66936	+	23.6653i	0.0764347	+	1.08356i
$478$	−16.4530			−0.752542
$479$	−4.49413	+	25.4875i	−0.205342	+	1.16455i	0.691559	+	0.722320i	$0.256924\pi$
$479$	−4.49413	+	25.4875i	−0.205342	+	1.16455i	−0.896901	+	0.442232i	$0.854187\pi$
$480$	0.112956	+	0.917637i	0.00515571	+	0.0418842i
$481$	−60.1296	−	21.8854i	−2.74168	−	0.997888i
$482$	−16.8597	−	6.13641i	−0.767937	−	0.279506i
$483$	7.76123	+	2.57074i	0.353148	+	0.116973i
$484$	0.497150	−	2.81948i	0.0225977	−	0.128158i
$485$	−1.99378	−	3.45332i	−0.0905327	−	0.156807i
$486$	4.05757	+	15.0511i	0.184055	+	0.682733i
$487$	−13.3297	+	23.0877i	−0.604026	+	1.04620i	0.388178	+	0.921584i	$0.373105\pi$
$487$	−13.3297	+	23.0877i	−0.604026	+	1.04620i	−0.992205	+	0.124620i	$0.960229\pi$
$488$	5.56136	−	2.02417i	0.251751	−	0.0916299i
$489$	−2.51935	−	2.34789i	−0.113929	−	0.106175i
$490$	−0.0448448	+	3.73631i	−0.00202588	+	0.168789i
$491$	6.83700	−	5.73692i	0.308549	−	0.258904i	−0.475343	−	0.879801i	$-0.657676\pi$
$491$	6.83700	−	5.73692i	0.308549	−	0.258904i	0.783892	+	0.620897i	$0.213232\pi$
$492$	13.3992	+	5.68278i	0.604081	+	0.256200i
$493$	4.01093	−	22.7471i	0.180643	−	1.02448i
$494$	−8.36528	−	14.4891i	−0.376372	−	0.651895i
$495$	4.94107	−	3.33718i	0.222084	−	0.149995i
$496$	−0.770450	−	1.33446i	−0.0345942	−	0.0599189i
$497$	23.3804	+	6.41538i	1.04875	+	0.287769i
$498$	1.57848	+	3.09560i	0.0707333	+	0.138717i
$499$	28.7294	−	24.1068i	1.28611	−	1.07917i	0.293734	−	0.955887i	$-0.405102\pi$
$499$	28.7294	−	24.1068i	1.28611	−	1.07917i	0.992371	−	0.123283i	$-0.0393424\pi$
$500$	−4.87312	−	1.77367i	−0.217933	−	0.0793210i
$501$	15.5309	−	23.9315i	0.693870	−	1.06918i
$502$	−0.0239704	+	0.135943i	−0.00106985	+	0.00606742i
$503$	0.558023	+	0.966525i	0.0248810	+	0.0430952i	0.878198	−	0.478298i	$-0.158746\pi$
$503$	0.558023	+	0.966525i	0.0248810	+	0.0430952i	−0.853317	+	0.521393i	$0.825413\pi$
$504$	−5.96217	−	5.23952i	−0.265576	−	0.233387i
$505$	−0.464998	+	0.805400i	−0.0206921	+	0.0358398i
$506$	5.08872	+	4.26994i	0.226221	+	0.189822i
$507$	−34.3922	+	25.9328i	−1.52741	+	1.15172i
$508$	−3.54433	−	20.1009i	−0.157254	−	0.891834i
$509$	−5.44189	−	30.8625i	−0.241208	−	1.36796i	−0.829138	−	0.559044i	$-0.811168\pi$
$509$	−5.44189	−	30.8625i	−0.241208	−	1.36796i	0.587930	−	0.808912i	$-0.299943\pi$
$510$	−1.93106	+	0.591028i	−0.0855087	+	0.0261712i
$511$	19.4007	+	5.32339i	0.858237	+	0.235493i
$512$	1.00000			0.0441942
$513$	8.88041	−	10.9870i	0.392080	−	0.485086i
$514$	10.1917	−	17.6526i	0.449538	−	0.778622i
$515$	1.28566	+	1.07880i	0.0566529	+	0.0475374i
$516$	10.8101	−	3.30858i	0.475887	−	0.145652i
$517$	−36.6566	−	13.3419i	−1.61216	−	0.586777i
$518$	15.6444	+	22.6303i	0.687374	+	0.994319i
$519$	1.71447	+	13.9281i	0.0752570	+	0.611376i
$520$	−2.51634	−	2.11146i	−0.110349	−	0.0925936i
$521$	0.657554	+	1.13892i	0.0288080	+	0.0498969i	0.880070	−	0.474844i	$-0.157496\pi$
$521$	0.657554	+	1.13892i	0.0288080	+	0.0498969i	−0.851262	+	0.524741i	$0.824162\pi$
$522$	22.0515	+	22.8071i	0.965169	+	0.998241i
$523$	−8.17597	+	14.1612i	−0.357510	+	0.619226i	−0.987544	−	0.157342i	$-0.949708\pi$
$523$	−8.17597	+	14.1612i	−0.357510	+	0.619226i	0.630034	+	0.776568i	$0.283041\pi$
$524$	−2.87687	−	2.41398i	−0.125677	−	0.105455i
$525$	20.0796	−	7.97993i	0.876344	−	0.348273i
$526$	2.68773	+	15.2429i	0.117191	+	0.664621i
$527$	2.57829	−	2.16344i	0.112312	−	0.0942409i
$528$	−2.92951	−	5.74516i	−0.127491	−	0.250026i
$529$	18.6218	−	6.77777i	0.809643	−	0.294686i
$530$	2.11064	−	3.65574i	0.0916804	−	0.158795i
$531$	5.90902	+	6.11150i	0.256430	+	0.265217i
$532$	−0.669916	+	7.16190i	−0.0290445	+	0.310508i
$533$	−48.5914	+	17.6858i	−2.10473	+	0.766059i
$534$	−5.30819	+	4.00255i	−0.229708	+	0.173207i
$535$	−1.22263	−	6.93388i	−0.0528589	−	0.299778i
$536$	−2.89382	+	2.42820i	−0.124994	+	0.104882i
$537$	−7.51752	+	2.30085i	−0.324405	+	0.0992889i
$538$	4.73095	−	26.8306i	0.203966	−	1.15675i
$539$	−8.61953	−	24.5965i	−0.371270	−	1.05945i
$540$	0.900623	−	2.62340i	0.0387566	−	0.112893i
$541$	−3.48995	−	6.04477i	−0.150045	−	0.259885i	0.781199	−	0.624282i	$-0.214608\pi$
$541$	−3.48995	−	6.04477i	−0.150045	−	0.259885i	−0.931244	+	0.364397i	$0.881275\pi$
$542$	−4.93129	−	4.13785i	−0.211817	−	0.177736i
$543$	1.59961	−	6.93832i	0.0686457	−	0.297752i
$544$	0.379292	+	2.15107i	0.0162620	+	0.0922263i
$545$	−5.85487	+	4.91282i	−0.250795	+	0.210442i
$546$	28.1880	−	0.823631i	1.20633	−	0.0352481i
$547$	18.8244	−	6.85153i	0.804875	−	0.292950i	0.0933697	−	0.995632i	$-0.470236\pi$
$547$	18.8244	−	6.85153i	0.804875	−	0.292950i	0.711505	+	0.702681i	$0.248014\pi$
$548$	−4.25238			−0.181653
$549$	−17.6587	−	1.84510i	−0.753655	−	0.0787472i
$550$	17.5556			0.748573
$551$	4.99244	−	28.3135i	0.212685	−	1.20620i
$552$	3.08602	+	0.160787i	0.131350	+	0.00684353i
$553$	16.7683	−	35.4035i	0.713061	−	1.50551i
$554$	0.0868347	+	0.492464i	0.00368925	+	0.0209228i
$555$	−5.23365	+	8.06450i	−0.222156	+	0.342319i
$556$	2.40909	−	0.876837i	0.102168	−	0.0371862i
$557$	−13.0785			−0.554153			−0.277076	−	0.960848i	$-0.589366\pi$
$557$	−13.0785			−0.554153			−0.277076	+	0.960848i	$0.589366\pi$
$558$	0.325279	+	4.61124i	0.0137701	+	0.195209i
$559$	−20.0827	+	34.7842i	−0.849407	+	1.47122i
$560$	0.357336	+	1.36634i	0.0151002	+	0.0577384i
$561$	11.2471	−	8.48068i	0.474853	−	0.358055i
$562$	19.4366	+	7.07435i	0.819884	+	0.298413i
$563$	4.71551	−	3.95678i	0.198735	−	0.166759i	−0.537989	−	0.842952i	$-0.680816\pi$
$563$	4.71551	−	3.95678i	0.198735	−	0.166759i	0.736724	+	0.676193i	$0.236371\pi$
$564$	−17.3522	+	5.31090i	−0.730660	+	0.223629i
$565$	−6.92915	+	2.52200i	−0.291511	+	0.106102i
$566$	−22.9727			−0.965615
$567$	9.19912	+	21.9631i	0.386327	+	0.922362i
$568$	9.16359			0.384496
$569$	−10.2618	+	3.73498i	−0.430196	+	0.156578i	−0.548037	−	0.836454i	$-0.684625\pi$
$569$	−10.2618	+	3.73498i	−0.430196	+	0.156578i	0.117842	+	0.993032i	$0.462403\pi$
$570$	−2.40361	+	0.735659i	−0.100676	+	0.0308134i
$571$	−33.5163	+	28.1235i	−1.40261	+	1.17693i	−0.442690	+	0.896675i	$0.645976\pi$
$571$	−33.5163	+	28.1235i	−1.40261	+	1.17693i	−0.959924	+	0.280259i	$0.909580\pi$
$572$	21.5305	+	7.83645i	0.900234	+	0.327658i
$573$	20.4417	−	15.4137i	0.853965	−	0.643918i
$574$	21.4398	+	5.88290i	0.894880	+	0.245547i
$575$	−4.20614	+	7.28525i	−0.175408	+	0.303816i
$576$	−2.69718	−	1.31347i	−0.112383	−	0.0547278i
$577$	30.9749			1.28950			0.644752	−	0.764392i	$-0.276961\pi$
$577$	30.9749			1.28950			0.644752	+	0.764392i	$0.276961\pi$
$578$	11.4915	−	4.18258i	0.477985	−	0.173972i
$579$	−4.79189	+	7.38380i	−0.199144	+	0.306860i
$580$	−0.980207	−	5.55903i	−0.0407009	−	0.230826i
$581$	3.01832	+	4.36614i	0.125221	+	0.181138i
$582$	12.9212	+	0.673215i	0.535600	+	0.0279057i
$583$	−5.11290	+	28.9967i	−0.211755	+	1.20092i
$584$	7.60381			0.314648
$585$	4.01370	+	9.00012i	0.165946	+	0.372109i
$586$	−32.2625			−1.33275
$587$	−17.2058	+	6.26239i	−0.710158	+	0.258476i	−0.671742	−	0.740785i	$-0.734454\pi$
$587$	−17.2058	+	6.26239i	−0.710158	+	0.258476i	−0.0384165	+	0.999262i	$0.512231\pi$
$588$	−10.0904	−	6.72188i	−0.416121	−	0.277206i
$589$	3.20922	−	2.69285i	0.132234	−	0.110957i
$590$	−0.262661	−	1.48962i	−0.0108136	−	0.0613268i
$591$	1.47142	−	6.38232i	0.0605263	−	0.262534i
$592$	7.96558	+	6.68392i	0.327383	+	0.274707i
$593$	4.86034	+	8.41836i	0.199590	+	0.345701i	0.948396	−	0.317089i	$-0.102706\pi$
$593$	4.86034	+	8.41836i	0.199590	+	0.345701i	−0.748805	+	0.662790i	$0.769372\pi$
$594$	0.355364	+	19.3436i	0.0145808	+	0.793677i
$595$	−2.80356	+	1.28690i	−0.114935	+	0.0527576i
$596$	−1.92282	+	10.9049i	−0.0787619	+	0.446681i
$597$	34.8590	−	10.6691i	1.42668	−	0.436657i
$598$	−8.41046	+	7.05721i	−0.343929	+	0.288591i
$599$	−2.08939	−	11.8495i	−0.0853700	−	0.484157i	−0.997276	−	0.0737585i	$-0.976501\pi$
$599$	−2.08939	−	11.8495i	−0.0853700	−	0.484157i	0.911906	−	0.410399i	$-0.134611\pi$
$600$	6.52074	−	4.91685i	0.266208	−	0.200730i
$601$	−24.9525	+	9.08198i	−1.01784	+	0.370462i	−0.796437	−	0.604722i	$-0.793284\pi$
$601$	−24.9525	+	9.08198i	−1.01784	+	0.370462i	−0.221398	+	0.975183i	$0.571062\pi$
$602$	15.6943	−	7.20405i	0.639654	−	0.293615i
$603$	10.9945	−	2.74837i	0.447731	−	0.111922i
$604$	0.726142	−	1.25771i	0.0295463	−	0.0511757i
$605$	1.43608	−	0.522691i	0.0583851	−	0.0212504i
$606$	−1.37080	−	2.68831i	−0.0556848	−	0.109205i
$607$	−11.6181	+	9.74877i	−0.471565	+	0.395690i	−0.847365	−	0.531011i	$-0.821812\pi$
$607$	−11.6181	+	9.74877i	−0.471565	+	0.395690i	0.375800	+	0.926701i	$0.377368\pi$
$608$	0.472108	+	2.67746i	0.0191465	+	0.108585i
$609$	38.0163	+	30.0518i	1.54050	+	1.21776i
$610$	2.42006	+	2.03067i	0.0979852	+	0.0822193i
$611$	32.2365	−	55.8353i	1.30415	−	2.25885i
$612$	1.80234	−	6.30002i	0.0728552	−	0.254663i
$613$	−1.38229	−	2.39420i	−0.0558304	−	0.0967010i	0.836759	−	0.547571i	$-0.184447\pi$
$613$	−1.38229	−	2.39420i	−0.0558304	−	0.0967010i	−0.892590	+	0.450870i	$0.851114\pi$
$614$	0.344596	+	0.289150i	0.0139068	+	0.0116691i
$615$	0.949170	+	7.71091i	0.0382742	+	0.310934i
$616$	−5.60174	−	8.10317i	−0.225700	−	0.326486i
$617$	11.9987	+	4.36716i	0.483048	+	0.175815i	0.572054	−	0.820216i	$-0.306147\pi$
$617$	11.9987	+	4.36716i	0.483048	+	0.175815i	−0.0890059	+	0.996031i	$0.528369\pi$
$618$	−5.20729	+	1.59377i	−0.209468	+	0.0641108i
$619$	−16.3049	−	13.6814i	−0.655348	−	0.549902i	0.253341	−	0.967377i	$-0.418471\pi$
$619$	−16.3049	−	13.6814i	−0.655348	−	0.549902i	−0.908688	+	0.417475i	$0.862915\pi$
$620$	0.411264	−	0.712329i	0.0165167	−	0.0286078i
$621$	−8.11237	−	4.48705i	−0.325538	−	0.180059i
$622$	16.3781			0.656702
$623$	−7.22374	+	7.13756i	−0.289413	+	0.285960i
$624$	10.1919	−	3.11938i	0.408003	−	0.124875i
$625$	3.61312	+	20.4910i	0.144525	+	0.819640i
$626$	−1.67045	−	9.47360i	−0.0667646	−	0.378641i
$627$	13.9994	−	10.5560i	0.559081	−	0.421566i
$628$	−9.57676	−	8.03585i	−0.382154	−	0.320665i
$629$	−11.3563	+	19.6697i	−0.452805	+	0.784281i
$630$	0.830842	−	4.15462i	0.0331015	−	0.165524i
$631$	22.3795	+	38.7625i	0.890916	+	1.54311i	0.838780	+	0.544471i	$0.183270\pi$
$631$	22.3795	+	38.7625i	0.890916	+	1.54311i	0.0521360	+	0.998640i	$0.483397\pi$
$632$	2.57108	−	14.5813i	0.102272	−	0.580015i
$633$	−0.497199	+	0.766131i	−0.0197619	+	0.0304510i
$634$	0.0783408	+	0.0285137i	0.00311131	+	0.00113242i
$635$	8.34631	−	7.00338i	0.331213	−	0.277921i
$636$	6.22209	+	12.2023i	0.246722	+	0.483854i
$637$	42.5085	−	6.97044i	1.68425	−	0.276179i
$638$	19.6866	+	34.0981i	0.779398	+	1.34996i
$639$	−24.7159	−	12.0361i	−0.977746	−	0.476140i
$640$	0.266898	+	0.462282i	0.0105501	+	0.0182733i
$641$	2.56788	−	14.5632i	0.101425	−	0.575210i	−0.891163	−	0.453683i	$-0.850110\pi$
$641$	2.56788	−	14.5632i	0.101425	−	0.575210i	0.992588	−	0.121527i	$-0.0387791\pi$
$642$	21.0325	+	8.92021i	0.830088	+	0.352053i
$643$	−5.58511	+	4.68647i	−0.220255	+	0.184816i	−0.746238	−	0.665679i	$-0.768142\pi$
$643$	−5.58511	+	4.68647i	−0.220255	+	0.184816i	0.525983	+	0.850495i	$0.323698\pi$
$644$	4.70478	−	0.383181i	0.185394	−	0.0150994i
$645$	4.41469	+	4.11425i	0.173828	+	0.161998i
$646$	−5.58033	+	2.03107i	−0.219555	+	0.0799115i
$647$	9.57823	−	16.5900i	0.376559	−	0.652219i	−0.614000	−	0.789306i	$-0.710441\pi$
$647$	9.57823	−	16.5900i	0.376559	−	0.652219i	0.990559	+	0.137087i	$0.0437738\pi$
$648$	5.54961	+	7.08533i	0.218009	+	0.278338i
$649$	5.27530	+	9.13709i	0.207074	+	0.358662i
$650$	−5.03845	+	28.5745i	−0.197624	+	1.12078i
$651$	1.42876	+	6.91523i	0.0559976	+	0.271029i
$652$	−1.86837	−	0.680029i	−0.0731708	−	0.0266320i
$653$	−30.8528	−	11.2295i	−1.20736	−	0.439445i	−0.341576	−	0.939854i	$-0.610961\pi$
$653$	−30.8528	−	11.2295i	−1.20736	−	0.439445i	−0.865789	+	0.500409i	$0.833183\pi$
$654$	−3.02985	−	24.6140i	−0.118476	−	0.962484i
$655$	0.348107	−	1.97421i	0.0136017	−	0.0771389i
$656$	8.40301			0.328082
$657$	−20.5089	−	9.98736i	−0.800128	−	0.389644i
$658$	−25.1924	+	11.5639i	−0.982101	+	0.450806i
$659$	−19.8827	−	16.6836i	−0.774522	−	0.649901i	0.167341	−	0.985899i	$-0.446482\pi$
$659$	−19.8827	−	16.6836i	−0.774522	−	0.649901i	−0.941863	+	0.335998i	$0.890926\pi$
$660$	1.87400	−	2.88763i	0.0729453	−	0.112401i
$661$	0.213470	+	0.0776966i	0.00830301	+	0.00302205i	0.346168	−	0.938172i	$-0.387483\pi$
$661$	0.213470	+	0.0776966i	0.00830301	+	0.00302205i	−0.337865	+	0.941194i	$0.609705\pi$
$662$	10.4518	+	3.80416i	0.406222	+	0.147853i
$663$	10.5757	+	20.7404i	0.410727	+	0.805489i
$664$	1.53683	+	1.28955i	0.0596405	+	0.0500443i
$665$	−3.48962	+	1.60181i	−0.135321	+	0.0621156i
$666$	−12.7055	−	28.4903i	−0.492330	−	1.10398i
$667$	−18.8668			−0.730525
$668$	2.86024	−	16.2212i	0.110666	−	0.627618i
$669$	7.72303	−	5.82342i	0.298590	−	0.225146i
$670$	−1.89487	−	0.689675i	−0.0732051	−	0.0266445i
$671$	−20.7066	−	7.53660i	−0.799371	−	0.290947i
$672$	−4.35015	−	1.44089i	−0.167811	−	0.0555837i
$673$	2.17438	−	12.3315i	0.0838161	−	0.475345i	−0.913790	−	0.406188i	$-0.866858\pi$
$673$	2.17438	−	12.3315i	0.0838161	−	0.475345i	0.997606	−	0.0691572i	$-0.0220310\pi$
$674$	−9.10967	−	15.7784i	−0.350892	−	0.607762i
$675$	−24.0457	+	4.69688i	−0.925521	+	0.180783i
$676$	−12.4343	+	21.5368i	−0.478241	+	0.828338i
$677$	2.83704	−	1.03260i	0.109036	−	0.0396860i	−0.286926	−	0.957953i	$-0.592633\pi$
$677$	2.83704	−	1.03260i	0.109036	−	0.0396860i	0.395962	+	0.918267i	$0.370411\pi$
$678$	5.37517	−	23.3149i	0.206432	−	0.895403i
$679$	19.6990	−	1.60438i	0.755977	−	0.0615705i
$680$	−0.893168	+	0.749457i	−0.0342514	+	0.0287403i
$681$	0.132628	−	0.100006i	0.00508232	−	0.00383224i
$682$	−0.996260	+	5.65007i	−0.0381488	+	0.216352i
$683$	16.8637	+	29.2087i	0.645270	+	1.11764i	0.984239	+	0.176843i	$0.0565883\pi$
$683$	16.8637	+	29.2087i	0.645270	+	1.11764i	−0.338969	+	0.940797i	$0.610078\pi$
$684$	2.24339	−	7.84169i	0.0857781	−	0.299835i
$685$	−1.13495	−	1.96580i	−0.0433643	−	0.0751092i
$686$	−16.6414	−	8.12789i	−0.635373	−	0.310324i
$687$	16.8301	−	25.9334i	0.642109	−	0.989422i
$688$	4.99996	−	4.19547i	0.190622	−	0.159951i
$689$	−45.7292	−	16.6441i	−1.74214	−	0.634088i
$690$	0.749324	+	1.46952i	0.0285263	+	0.0559438i
$691$	2.36432	−	13.4087i	0.0899428	−	0.510091i	−0.906237	−	0.422769i	$-0.861058\pi$
$691$	2.36432	−	13.4087i	0.0899428	−	0.510091i	0.996180	−	0.0873218i	$-0.0278308\pi$
$692$	4.05104	+	7.01662i	0.153998	+	0.266732i
$693$	4.46567	+	29.2134i	0.169637	+	1.10973i
$694$	6.19387	−	10.7281i	0.235116	−	0.407233i
$695$	1.04833	+	0.879651i	0.0397653	+	0.0333671i
$696$	16.8622	+	7.15151i	0.639161	+	0.271077i
$697$	3.18719	+	18.0755i	0.120723	+	0.684657i
$698$	−0.465111	−	2.63777i	−0.0176047	−	0.0998412i
$699$	0.882851	−	3.82938i	0.0333925	−	0.144841i
$700$	8.87385	−	8.76798i	0.335400	−	0.331398i
$701$	24.7530			0.934907			0.467454	−	0.884018i	$-0.345171\pi$
$701$	24.7530			0.934907			0.467454	+	0.884018i	$0.345171\pi$
$702$	−31.5867	−	4.97319i	−1.19216	−	0.187701i
$703$	−14.1353	+	24.4830i	−0.533123	+	0.923395i
$704$	−2.85221	−	2.39329i	−0.107497	−	0.0902006i
$705$	−7.08641	−	6.60414i	−0.266890	−	0.248726i
$706$	−7.17389	−	2.61108i	−0.269993	−	0.0982694i
$707$	−2.62120	−	3.79168i	−0.0985802	−	0.142601i
$708$	4.51847	+	1.91635i	0.169815	+	0.0720209i
$709$	6.95426	+	5.83531i	0.261173	+	0.219150i	0.763966	−	0.645257i	$-0.223250\pi$
$709$	6.95426	+	5.83531i	0.261173	+	0.219150i	−0.502793	+	0.864407i	$0.667694\pi$
$710$	2.44575	+	4.23616i	0.0917873	+	0.158980i
$711$	−26.0868	+	35.9515i	−0.978332	+	1.34829i
$712$	−1.91914	+	3.32405i	−0.0719229	+	0.124574i
$713$	−2.10598	−	1.76713i	−0.0788696	−	0.0661795i
$714$	1.44949	−	9.90400i	0.0542457	−	0.370648i
$715$	2.12380	+	12.0447i	0.0794256	+	0.450445i
$716$	−3.47706	+	2.91760i	−0.129944	+	0.109036i
$717$	28.4588	+	1.48275i	1.06281	+	0.0553744i
$718$	5.51580	−	2.00759i	0.205848	−	0.0749225i
$719$	−21.5592	+	37.3417i	−0.804024	+	1.39261i	0.112924	+	0.993604i	$0.463978\pi$
$719$	−21.5592	+	37.3417i	−0.804024	+	1.39261i	−0.916948	+	0.399007i	$0.869355\pi$
$720$	−0.112683	−	1.59742i	−0.00419943	−	0.0595324i
$721$	−7.56008	+	3.47024i	−0.281552	+	0.129239i
$722$	10.9083	−	3.97028i	0.405964	−	0.147759i
$723$	28.6092	+	12.1336i	1.06399	+	0.451253i
$724$	−0.713855	−	4.04847i	−0.0265302	−	0.150460i
$725$	−38.1956	+	32.0499i	−1.41855	+	1.19030i
$726$	−1.11402	+	4.83206i	−0.0413450	+	0.179335i
$727$	8.91327	−	50.5497i	0.330575	−	1.87478i	−0.136611	−	0.990625i	$-0.543621\pi$
$727$	8.91327	−	50.5497i	0.330575	−	1.87478i	0.467186	−	0.884159i	$-0.345268\pi$
$728$	14.7969	−	6.79209i	0.548408	−	0.251732i
$729$	−5.66198	−	26.3997i	−0.209703	−	0.977765i
$730$	2.02945	+	3.51510i	0.0751132	+	0.130100i
$731$	10.9212	+	9.16396i	0.403935	+	0.338941i
$732$	−9.80193	+	3.00002i	−0.362290	+	0.110884i
$733$	2.55769	+	14.5054i	0.0944706	+	0.535769i	0.994908	+	0.100784i	$0.0321352\pi$
$733$	2.55769	+	14.5054i	0.0944706	+	0.535769i	−0.900438	+	0.434985i	$0.856754\pi$
$734$	24.7000	−	20.7258i	0.911694	−	0.765002i
$735$	0.414286	−	6.45867i	0.0152812	−	0.238232i
$736$	1.67653	−	0.610208i	0.0617978	−	0.0224926i
$737$	14.0652			0.518098
$738$	−22.6645	−	11.0371i	−0.834290	−	0.406280i
$739$	−22.7035			−0.835163			−0.417582	−	0.908639i	$-0.637122\pi$
$739$	−22.7035			−0.835163			−0.417582	+	0.908639i	$0.637122\pi$
$740$	−0.963851	+	5.46627i	−0.0354319	+	0.200944i
$741$	13.1637	+	25.8157i	0.483580	+	0.948364i
$742$	11.8977	+	17.2106i	0.436778	+	0.631820i
$743$	0.754568	+	4.27937i	0.0276824	+	0.156995i	0.995516	−	0.0945983i	$-0.0301567\pi$
$743$	0.754568	+	4.27937i	0.0276824	+	0.156995i	−0.967833	+	0.251593i	$0.919046\pi$
$744$	1.21239	+	2.37765i	0.0444483	+	0.0871689i
$745$	−5.55432	+	2.02161i	−0.203494	+	0.0740659i
$746$	−7.89501			−0.289057
$747$	−2.45132	−	5.49673i	−0.0896893	−	0.201115i
$748$	4.06632	−	7.04307i	0.148679	−	0.257520i
$749$	33.6539	+	9.23433i	1.22969	+	0.337415i
$750$	8.26922	+	3.50710i	0.301949	+	0.128061i
$751$	4.32897	+	1.57562i	0.157966	+	0.0574950i	0.419793	−	0.907620i	$-0.362103\pi$
$751$	4.32897	+	1.57562i	0.157966	+	0.0574950i	−0.261827	+	0.965115i	$0.584325\pi$
$752$	−8.02588	+	6.73451i	−0.292674	+	0.245582i
$753$	0.0537129	−	0.232981i	0.00195741	−	0.00849028i
$754$	−61.1500	+	22.2568i	−2.22695	+	0.810544i
$755$	0.775225			0.0282133
$756$	9.84060	+	9.60014i	0.357899	+	0.349154i
$757$	−19.5732			−0.711398			−0.355699	−	0.934600i	$-0.615757\pi$
$757$	−19.5732			−0.711398			−0.355699	+	0.934600i	$0.615757\pi$
$758$	−6.94856	+	2.52907i	−0.252383	+	0.0918600i
$759$	−8.41717	−	7.84434i	−0.305524	−	0.284731i
$760$	−1.11173	+	0.932856i	−0.0403268	+	0.0338382i
$761$	25.9189	+	9.43372i	0.939561	+	0.341972i	0.765992	−	0.642850i	$-0.222248\pi$
$761$	25.9189	+	9.43372i	0.939561	+	0.341972i	0.173568	+	0.984822i	$0.444470\pi$
$762$	4.31915	+	35.0881i	0.156466	+	1.27111i
$763$	−9.58491	−	36.6497i	−0.346997	−	1.32681i
$764$	7.39057	−	12.8008i	0.267382	−	0.463118i
$765$	3.39342	−	0.848277i	0.122690	−	0.0306695i
$766$	32.3272			1.16803
$767$	−16.3860	+	5.96403i	−0.591665	+	0.215349i
$768$	−1.72970	−	0.0901205i	−0.0624153	−	0.00325194i
$769$	6.13303	+	34.7821i	0.221163	+	1.25428i	0.869886	+	0.493252i	$0.164192\pi$
$769$	6.13303	+	34.7821i	0.221163	+	1.25428i	−0.648724	+	0.761024i	$0.724697\pi$
$770$	2.25085	−	4.75230i	0.0811151	−	0.171261i
$771$	−19.2195	+	29.6153i	−0.692175	+	1.06657i
$772$	−0.882494	+	5.00487i	−0.0317617	+	0.180129i
$773$	16.7767			0.603416			0.301708	−	0.953400i	$-0.402443\pi$
$773$	16.7767			0.603416			0.301708	+	0.953400i	$0.402443\pi$
$774$	−18.9964	+	4.74866i	−0.682812	+	0.170687i
$775$	−7.26543			−0.260982
$776$	7.01966	−	2.55495i	0.251991	−	0.0917173i
$777$	−25.0207	−	40.5536i	−0.897612	−	1.45485i
$778$	−13.0512	+	10.9512i	−0.467907	+	0.392621i
$779$	3.96713	+	22.4987i	0.142137	+	0.806099i
$780$	4.16224	+	3.87897i	0.149032	+	0.138890i
$781$	−26.1365	−	21.9311i	−0.935238	−	0.784758i
$782$	1.94850	+	3.37489i	0.0696781	+	0.120686i
$783$	−36.0872	−	41.4369i	−1.28965	−	1.48083i
$784$	−6.87857	−	1.29818i	−0.245663	−	0.0463637i
$785$	1.15881	−	6.57192i	0.0413596	−	0.234562i
$786$	4.75859	+	4.43474i	0.169733	+	0.158182i
$787$	−4.67532	+	3.92306i	−0.166657	+	0.139842i	−0.722302	−	0.691578i	$-0.756916\pi$
$787$	−4.67532	+	3.92306i	−0.166657	+	0.139842i	0.555645	+	0.831420i	$0.312471\pi$
$788$	−0.656650	−	3.72405i	−0.0233922	−	0.132664i
$789$	−3.27529	−	26.6079i	−0.116603	−	0.947266i
$790$	7.42691	−	2.70317i	0.264237	−	0.0961746i
$791$	3.40382	−	36.3895i	0.121026	−	1.29386i
$792$	4.54944	+	10.2014i	0.161657	+	0.362492i
$793$	18.2098	−	31.5403i	0.646648	−	1.12003i
$794$	−22.7225	+	8.27032i	−0.806392	+	0.293503i
$795$	−3.98024	+	6.13314i	−0.141165	+	0.217520i
$796$	16.1232	−	13.5290i	0.571473	−	0.479523i
$797$	−9.28900	−	52.6805i	−0.329033	−	1.86604i	−0.479667	−	0.877451i	$-0.659243\pi$
$797$	−9.28900	−	52.6805i	−0.329033	−	1.86604i	0.150634	−	0.988590i	$-0.451869\pi$
$798$	1.80419	−	12.3276i	0.0638677	−	0.436392i
$799$	−17.5306	−	14.7099i	−0.620186	−	0.520398i
$800$	2.35753	−	4.08336i	0.0833513	−	0.144369i
$801$	9.54232	−	6.44486i	0.337161	−	0.227718i
$802$	8.23603	+	14.2652i	0.290824	+	0.503722i
$803$	−21.6877	−	18.1981i	−0.765343	−	0.642199i
$804$	5.22428	−	3.93928i	0.184246	−	0.138928i
$805$	1.43284	+	2.07266i	0.0505009	+	0.0730518i
$806$	−8.91044	−	3.24314i	−0.313857	−	0.114235i
$807$	−10.6011	+	45.9826i	−0.373178	+	1.61866i
$808$	−1.33462	−	1.11988i	−0.0469519	−	0.0393973i
$809$	22.7376	−	39.3827i	0.799411	−	1.38462i	−0.120589	−	0.992703i	$-0.538478\pi$
$809$	22.7376	−	39.3827i	0.799411	−	1.38462i	0.920000	−	0.391918i	$-0.128188\pi$
$810$	−1.79423	+	4.45654i	−0.0630429	+	0.156587i
$811$	22.6718			0.796114			0.398057	−	0.917361i	$-0.369685\pi$
$811$	22.6718			0.796114			0.398057	+	0.917361i	$0.369685\pi$
$812$	26.9810	+	7.40335i	0.946847	+	0.259807i
$813$	8.15678	+	7.60166i	0.286071	+	0.266602i
$814$	−6.72298	−	38.1279i	−0.235640	−	1.33638i
$815$	−0.184299	−	1.04521i	−0.00645570	−	0.0366121i
$816$	−0.462207	−	3.75490i	−0.0161805	−	0.131448i
$817$	13.5937	+	11.4065i	0.475583	+	0.399062i
$818$	5.09944	−	8.83249i	0.178298	−	0.308821i
$819$	−48.8311	−	1.11568i	−1.70630	−	0.0389848i
$820$	2.24275	+	3.88456i	0.0783202	+	0.135655i
$821$	−1.62714	+	9.22797i	−0.0567876	+	0.322058i	−0.999947	−	0.0102819i	$-0.996727\pi$
$821$	−1.62714	+	9.22797i	−0.0567876	+	0.322058i	0.943160	+	0.332340i	$0.107838\pi$
$822$	7.35536	+	0.383227i	0.256548	+	0.0133666i
$823$	−10.9845	−	3.99804i	−0.382897	−	0.139363i	0.143398	−	0.989665i	$-0.454197\pi$
$823$	−10.9845	−	3.99804i	−0.382897	−	0.139363i	−0.526295	+	0.850302i	$0.676419\pi$
$824$	−2.40852	+	2.02099i	−0.0839047	+	0.0704044i
$825$	−30.3660	−	1.58212i	−1.05721	−	0.0550823i
$826$	7.22994	+	1.98383i	0.251562	+	0.0690264i
$827$	−20.2574	−	35.0868i	−0.704417	−	1.22009i	−0.966901	−	0.255150i	$-0.917875\pi$
$827$	−20.2574	−	35.0868i	−0.704417	−	1.22009i	0.262484	−	0.964936i	$-0.415458\pi$
$828$	−5.32341	−	0.556227i	−0.185001	−	0.0193302i
$829$	−24.5799	−	42.5737i	−0.853697	−	1.47865i	−0.877849	−	0.478938i	$-0.841022\pi$
$829$	−24.5799	−	42.5737i	−0.853697	−	1.47865i	0.0241522	−	0.999708i	$-0.492311\pi$
$830$	−0.185959	+	1.05463i	−0.00645473	+	0.0366066i
$831$	−0.105817	−	0.859643i	−0.00367076	−	0.0298207i
$832$	4.71404	−	3.95555i	0.163430	−	0.137134i
$833$	0.183501	−	15.2887i	0.00635794	−	0.529721i
$834$	−4.24603	+	1.29956i	−0.147028	+	0.0450001i
$835$	8.26216	−	3.00718i	0.285924	−	0.104068i
$836$	5.06138	−	8.76658i	0.175052	−	0.303198i
$837$	−0.147068	−	8.00540i	−0.00508343	−	0.276707i
$838$	17.8803	+	30.9696i	0.617666	+	1.06983i
$839$	−7.70527	+	43.6987i	−0.266015	+	1.50865i	0.500113	+	0.865960i	$0.333292\pi$
$839$	−7.70527	+	43.6987i	−0.266015	+	1.50865i	−0.766128	+	0.642688i	$0.777819\pi$
$840$	−0.494950	−	2.39557i	−0.0170774	−	0.0826549i
$841$	−77.8311	−	28.3282i	−2.68383	−	0.976835i
$842$	−30.9371	−	11.2602i	−1.06616	−	0.388052i
$843$	−32.9820	−	13.9882i	−1.13596	−	0.481778i
$844$	−0.0915661	+	0.519297i	−0.00315184	+	0.0178750i
$845$	−13.2747			−0.456665
$846$	30.4928	−	7.62250i	1.04837	−	0.262067i
$847$	−0.705451	+	7.54180i	−0.0242396	+	0.259139i
$848$	6.05791	+	5.08319i	0.208029	+	0.174557i
$849$	39.7360	+	2.07031i	1.36374	+	0.0710529i
$850$	9.67779	+	3.52243i	0.331945	+	0.120818i
$851$	17.4331	+	6.34515i	0.597601	+	0.217509i
$852$	−15.8503	−	0.825827i	−0.543022	−	0.0282924i
$853$	16.8048	+	14.1009i	0.575385	+	0.482806i	0.883428	−	0.468567i	$-0.155230\pi$
$853$	16.8048	+	14.1009i	0.575385	+	0.482806i	−0.308043	+	0.951373i	$0.599674\pi$
$854$	−14.2307	+	6.53220i	−0.486964	+	0.223527i
$855$	4.22383	−	1.05586i	0.144452	−	0.0361096i
$856$	13.1901			0.450829
$857$	−1.97234	+	11.1857i	−0.0673740	+	0.382097i	0.932412	+	0.361398i	$0.117700\pi$
$857$	−1.97234	+	11.1857i	−0.0673740	+	0.382097i	−0.999786	+	0.0206992i	$0.993411\pi$
$858$	−36.5351	−	15.4951i	−1.24729	−	0.528993i
$859$	33.1701	+	12.0729i	1.13175	+	0.411922i	0.838926	−	0.544245i	$-0.183184\pi$
$859$	33.1701	+	12.0729i	1.13175	+	0.411922i	0.292821	+	0.956167i	$0.405406\pi$
$860$	3.27397	+	1.19163i	0.111641	+	0.0406341i
$861$	−36.5544	−	12.1078i	−1.24577	−	0.412634i
$862$	0.358364	−	2.03238i	0.0122059	−	0.0692233i
$863$	2.87507	+	4.97977i	0.0978685	+	0.169513i	0.910802	−	0.412843i	$-0.135464\pi$
$863$	2.87507	+	4.97977i	0.0978685	+	0.169513i	−0.812934	+	0.582356i	$0.802131\pi$
$864$	4.54696	+	2.51498i	0.154691	+	0.0855614i
$865$	−2.16243	+	3.74545i	−0.0735250	+	0.127349i
$866$	−27.3019	+	9.93707i	−0.927756	+	0.337675i
$867$	−20.2539	+	6.19900i	−0.687859	+	0.210529i
$868$	2.31830	+	3.35352i	0.0786881	+	0.113826i
$869$	−42.2307	+	35.4358i	−1.43258	+	1.20208i
$870$	1.19449	+	9.70382i	0.0404969	+	0.328990i
$871$	−4.03670	+	22.8933i	−0.136778	+	0.775709i
$872$	−7.15909	−	12.3999i	−0.242437	−	0.419914i
$873$	−22.2892	−	2.32893i	−0.754374	−	0.0788222i
$874$	2.42531	+	4.20076i	0.0820374	+	0.142093i
$875$	13.2315	+	3.63060i	0.447305	+	0.122737i
$876$	−13.1524	−	0.685260i	−0.444377	−	0.0231528i
$877$	−6.29198	+	5.27960i	−0.212465	+	0.178279i	−0.742809	−	0.669503i	$-0.766507\pi$
$877$	−6.29198	+	5.27960i	−0.212465	+	0.178279i	0.530344	+	0.847782i	$0.322063\pi$
$878$	−33.1094	−	12.0508i	−1.11739	−	0.406696i
$879$	55.8047	+	2.90752i	1.88224	+	0.0980681i
$880$	0.345123	−	1.95729i	0.0116341	−	0.0659803i
$881$	25.0282	+	43.3501i	0.843221	+	1.46050i	0.887157	+	0.461468i	$0.152677\pi$
$881$	25.0282	+	43.3501i	0.843221	+	1.46050i	−0.0439356	+	0.999034i	$0.513990\pi$
$882$	16.8476	+	12.5362i	0.567290	+	0.422116i
$883$	−1.24292	+	2.15280i	−0.0418276	+	0.0724474i	−0.886181	−	0.463339i	$-0.846651\pi$
$883$	−1.24292	+	2.15280i	−0.0418276	+	0.0724474i	0.844354	+	0.535786i	$0.179985\pi$
$884$	10.2967	+	8.63992i	0.346314	+	0.290592i
$885$	0.320080	+	2.60028i	0.0107594	+	0.0874074i
$886$	−1.05504	−	5.98344i	−0.0354448	−	0.201018i
$887$	8.20600	+	46.5386i	0.275531	+	1.56261i	0.737271	+	0.675597i	$0.236114\pi$
$887$	8.20600	+	46.5386i	0.275531	+	1.56261i	−0.461741	+	0.887015i	$0.652775\pi$
$888$	−13.1757	−	12.2791i	−0.442149	−	0.412059i
$889$	13.6636	+	52.2453i	0.458262	+	1.75225i
$890$	−2.04887			−0.0686781
$891$	1.12858	−	33.4907i	0.0378088	−	1.12198i
$892$	2.79221	−	4.83626i	0.0934902	−	0.161930i
$893$	−21.8205	−	18.3095i	−0.730194	−	0.612705i
$894$	4.30867	−	18.6889i	0.144103	−	0.625051i
$895$	−2.27678	−	0.828678i	−0.0761042	−	0.0276997i
$896$	−2.63702	+	0.214772i	−0.0880966	+	0.00717502i
$897$	15.1836	−	11.4489i	0.506966	−	0.382269i
$898$	−12.4288	−	10.4290i	−0.414754	−	0.348020i
$899$	−8.14734	−	14.1116i	−0.271729	−	0.470649i
$900$	−11.7221	+	7.91704i	−0.390735	+	0.263901i
$901$	−8.63658	+	14.9590i	−0.287726	+	0.498356i
$902$	−23.9672	−	20.1109i	−0.798020	−	0.669618i
$903$	−27.7958	+	11.0465i	−0.924987	+	0.367605i
$904$	−2.39877	−	13.6041i	−0.0797819	−	0.452465i
$905$	1.68101	−	1.41053i	0.0558785	−	0.0468877i
$906$	−1.36936	+	2.11004i	−0.0454938	+	0.0701012i
$907$	2.30769	−	0.839931i	0.0766257	−	0.0278895i	−0.303423	−	0.952856i	$-0.598129\pi$
$907$	2.30769	−	0.839931i	0.0766257	−	0.0278895i	0.380049	+	0.924967i	$0.375907\pi$
$908$	0.0479509	−	0.0830533i	0.00159131	−	0.00275622i
$909$	2.12880	+	4.77352i	0.0706078	+	0.158328i
$910$	7.08912	+	5.02752i	0.235002	+	0.166661i
$911$	29.9239	−	10.8914i	0.991422	−	0.360848i	0.205151	−	0.978730i	$-0.434231\pi$
$911$	29.9239	−	10.8914i	0.991422	−	0.360848i	0.786271	+	0.617882i	$0.212009\pi$
$912$	−0.575314	−	4.67376i	−0.0190505	−	0.154764i
$913$	−1.29709	−	7.35616i	−0.0429274	−	0.243453i
$914$	24.6907	−	20.7180i	0.816697	−	0.685290i
$915$	−4.00298	−	3.73055i	−0.132334	−	0.123328i
$916$	3.09950	−	17.5782i	0.102410	−	0.580799i
$917$	8.10483	+	5.74785i	0.267645	+	0.189811i
$918$	−3.68528	+	10.7347i	−0.121632	+	0.354299i
$919$	−9.85716	−	17.0731i	−0.325158	−	0.563190i	0.656387	−	0.754425i	$-0.272084\pi$
$919$	−9.85716	−	17.0731i	−0.325158	−	0.563190i	−0.981544	+	0.191235i	$0.938751\pi$
$920$	0.729552	+	0.612167i	0.0240526	+	0.0201825i
$921$	−0.569990	−	0.531199i	−0.0187818	−	0.0175036i
$922$	4.89315	+	27.7504i	0.161147	+	0.913911i
$923$	43.1975	−	36.2470i	1.42186	−	1.19309i
$924$	8.95909	+	14.5209i	0.294732	+	0.477703i
$925$	46.0720	−	16.7688i	1.51484	−	0.551356i
$926$	−6.09969			−0.200448
$927$	9.15071	−	2.28746i	0.300549	−	0.0751302i
$928$	10.5748			0.347134
$929$	−0.529069	+	3.00050i	−0.0173582	+	0.0984431i	−0.992256	−	0.124210i	$-0.960360\pi$
$929$	−0.529069	+	3.00050i	−0.0173582	+	0.0984431i	0.974898	+	0.222653i	$0.0714716\pi$
$930$	−0.775560	+	1.19506i	−0.0254316	+	0.0391874i
$931$	0.228406	−	19.0300i	0.00748569	−	0.623682i
$932$	−0.393989	−	2.23442i	−0.0129055	−	0.0731909i
$933$	−28.3293	−	1.47600i	−0.927458	−	0.0483221i
$934$	5.20576	−	1.89474i	0.170338	−	0.0619978i
$935$	4.34117			0.141972
$936$	−17.9101	+	4.47711i	−0.585410	+	0.146339i
$937$	−25.2760	+	43.7794i	−0.825732	+	1.43021i	0.0756261	+	0.997136i	$0.475904\pi$
$937$	−25.2760	+	43.7794i	−0.825732	+	1.43021i	−0.901358	+	0.433074i	$0.857429\pi$
$938$	7.10954	−	7.02472i	0.232135	−	0.229365i
$939$	2.03562	+	16.5371i	0.0664300	+	0.539667i
$940$	−5.25534	−	1.91279i	−0.171410	−	0.0623882i
$941$	16.5551	−	13.8914i	0.539681	−	0.452846i	−0.331748	−	0.943368i	$-0.607638\pi$
$941$	16.5551	−	13.8914i	0.539681	−	0.452846i	0.871429	+	0.490522i	$0.163194\pi$
$942$	15.8408	+	14.7627i	0.516120	+	0.480995i
$943$	14.0879	−	5.12758i	0.458766	−	0.166977i
$944$	2.83367			0.0922280
$945$	−1.81153	+	7.11139i	−0.0589290	+	0.231333i
$946$	−24.3019			−0.790124
$947$	−23.2399	+	8.45862i	−0.755194	+	0.274868i	−0.690790	−	0.723056i	$-0.742737\pi$
$947$	−23.2399	+	8.45862i	−0.755194	+	0.274868i	−0.0644043	+	0.997924i	$0.520515\pi$
$948$	−5.76130	+	24.9897i	−0.187118	+	0.811628i
$949$	35.8447	−	30.0773i	1.16357	−	0.976349i
$950$	12.0460	+	4.38440i	0.390825	+	0.142249i
$951$	−0.132937	−	0.0563804i	−0.00431077	−	0.00182826i
$952$	−1.46219	−	5.59095i	−0.0473898	−	0.181204i
$953$	−6.49025	+	11.2414i	−0.210240	+	0.364146i	−0.951790	−	0.306752i	$-0.900758\pi$
$953$	−6.49025	+	11.2414i	−0.210240	+	0.364146i	0.741550	+	0.670898i	$0.234091\pi$
$954$	−9.66269	−	21.6672i	−0.312841	−	0.701500i
$955$	7.89013			0.255319
$956$	15.4607	−	5.62725i	0.500036	−	0.181998i
$957$	−30.9790	−	60.7538i	−1.00141	−	1.96389i
$958$	−4.49413	−	25.4875i	−0.145199	−	0.823462i
$959$	11.2136	−	0.913291i	0.362106	−	0.0294917i
$960$	−0.419994	−	0.823664i	−0.0135553	−	0.0265836i
$961$	−4.97079	+	28.1907i	−0.160348	+	0.909379i
$962$	63.9886			2.06308
$963$	−35.5762	−	17.3248i	−1.14643	−	0.558284i
$964$	17.9417			0.577862
$965$	−2.54920	+	0.927832i	−0.0820616	+	0.0298680i
$966$	−8.17242	+	0.238792i	−0.262943	+	0.00768300i
$967$	−2.16173	+	1.81391i	−0.0695166	+	0.0583314i	−0.676884	−	0.736090i	$-0.736670\pi$
$967$	−2.16173	+	1.81391i	−0.0695166	+	0.0583314i	0.607367	+	0.794421i	$0.292226\pi$
$968$	0.497150	+	2.81948i	0.0159790	+	0.0906215i
$969$	9.83537	−	3.01026i	0.315957	−	0.0967034i
$970$	3.05464	+	2.56315i	0.0980786	+	0.0822977i
$971$	23.0863	+	39.9867i	0.740875	+	1.28323i	0.952097	+	0.305795i	$0.0989224\pi$
$971$	23.0863	+	39.9867i	0.740875	+	1.28323i	−0.211222	+	0.977438i	$0.567744\pi$
$972$	−8.96065	−	12.7557i	−0.287413	−	0.409138i
$973$	−6.16450	+	2.82964i	−0.197625	+	0.0907141i
$974$	4.62936	−	26.2544i	0.148334	−	0.841245i
$975$	11.2902	−	48.9713i	0.361575	−	1.56834i
$976$	−4.53366	+	3.80420i	−0.145119	+	0.121769i
$977$	7.68492	+	43.5833i	0.245862	+	1.39435i	0.818482	+	0.574533i	$0.194816\pi$
$977$	7.68492	+	43.5833i	0.245862	+	1.39435i	−0.572619	+	0.819821i	$0.694073\pi$
$978$	3.17044	+	1.34463i	0.101379	+	0.0429965i
$979$	13.4292	−	4.88784i	0.429200	−	0.156216i
$980$	−1.23575	−	3.52632i	−0.0394747	−	0.112644i
$981$	3.02252	+	42.8480i	0.0965015	+	1.36803i
$982$	−4.46253	+	7.72933i	−0.142405	+	0.246653i
$983$	2.34910	−	0.855002i	0.0749246	−	0.0272703i	−0.304286	−	0.952581i	$-0.598418\pi$
$983$	2.34910	−	0.855002i	0.0749246	−	0.0272703i	0.379211	+	0.925310i	$0.376196\pi$
$984$	−14.5347	−	0.757283i	−0.463350	−	0.0241413i
$985$	1.54630	−	1.29750i	0.0492692	−	0.0413418i
$986$	4.01093	+	22.7471i	0.127734	+	0.724415i
$987$	44.6175	−	17.7317i	1.42019	−	0.564407i
$988$	12.8163	+	10.7542i	0.407742	+	0.342136i
$989$	5.82249	−	10.0849i	0.185145	−	0.320680i
$990$	−3.50170	+	4.82587i	−0.111291	+	0.153376i
$991$	3.77332	+	6.53558i	0.119863	+	0.207610i	0.919713	−	0.392590i	$-0.128421\pi$
$991$	3.77332	+	6.53558i	0.119863	+	0.207610i	−0.799850	+	0.600200i	$0.795088\pi$
$992$	1.18040	+	0.990471i	0.0374777	+	0.0314475i
$993$	−17.7358	−	7.52199i	−0.562827	−	0.238703i
$994$	−24.1646	+	1.96808i	−0.766453	+	0.0624237i
$995$	10.5575	+	3.84261i	0.334695	+	0.121819i
$996$	−2.54204	−	2.36904i	−0.0805477	−	0.0750660i
$997$	−7.80923	−	6.55272i	−0.247321	−	0.207527i	0.510697	−	0.859761i	$-0.329387\pi$
$997$	−7.80923	−	6.55272i	−0.247321	−	0.207527i	−0.758018	+	0.652234i	$0.773832\pi$
$998$	−18.7518	+	32.4791i	−0.593578	+	1.02811i
$999$	19.4093	+	50.4248i	0.614082	+	1.59537i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.w.a.25.11	yes	72
7.2	even	3		378.2.v.b.79.6	yes	72
27.13	even	9		378.2.v.b.67.6	✓	72
189.121	even	9	inner	378.2.w.a.121.11	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.v.b.67.6	✓	72	27.13	even	9
378.2.v.b.79.6	yes	72	7.2	even	3
378.2.w.a.25.11	yes	72	1.1	even	1	trivial
378.2.w.a.121.11	yes	72	189.121	even	9	inner

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.w (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{2} +(1.65621 - 0.506908i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.501605 + 0.182569i) q^{5} +(-1.38296 + 1.04280i) q^{6} +(-1.88202 + 1.85957i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.48609 - 1.67910i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 0.342020i) q^{2} +(1.65621 - 0.506908i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.501605 + 0.182569i) q^{5} +(-1.38296 + 1.04280i) q^{6} +(-1.88202 + 1.85957i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.48609 - 1.67910i) q^{9} -0.533797 q^{10} +(3.49876 - 1.27344i) q^{11} +(0.942899 - 1.45291i) q^{12} +(1.06859 + 6.06025i) q^{13} +(1.13251 - 2.39111i) q^{14} +(0.923311 + 0.0481060i) q^{15} +(0.173648 - 0.984808i) q^{16} +2.18425 q^{17} +(-1.76187 + 2.42813i) q^{18} +2.71876 q^{19} +(0.501605 - 0.182569i) q^{20} +(-2.17440 + 4.03386i) q^{21} +(-2.85221 + 2.39329i) q^{22} +(-0.309811 - 1.75702i) q^{23} +(-0.389111 + 1.68778i) q^{24} +(-3.61195 - 3.03078i) q^{25} +(-3.07687 - 5.32930i) q^{26} +(3.26635 - 4.04116i) q^{27} +(-0.246405 + 2.63425i) q^{28} +(1.83629 - 10.4141i) q^{29} +(-0.884082 + 0.270586i) q^{30} +(1.18040 - 0.990471i) q^{31} +(0.173648 + 0.984808i) q^{32} +(5.14917 - 3.88265i) q^{33} +(-2.05253 + 0.747059i) q^{34} +(-1.28353 + 0.589169i) q^{35} +(0.825151 - 2.88429i) q^{36} +(-5.19917 + 9.00522i) q^{37} +(-2.55480 + 0.929871i) q^{38} +(4.84180 + 9.49540i) q^{39} +(-0.408912 + 0.343118i) q^{40} +(1.45917 + 8.27535i) q^{41} +(0.663608 - 4.53427i) q^{42} +(4.99996 + 4.19547i) q^{43} +(1.86165 - 3.22447i) q^{44} +(1.55359 - 0.388360i) q^{45} +(0.892065 + 1.54510i) q^{46} +(-8.02588 - 6.73451i) q^{47} +(-0.211609 - 1.71908i) q^{48} +(0.0840109 - 6.99950i) q^{49} +(4.43071 + 1.61265i) q^{50} +(3.61759 - 1.10722i) q^{51} +(4.71404 + 3.95555i) q^{52} +(-3.95402 + 6.84856i) q^{53} +(-1.68720 + 4.91461i) q^{54} +1.98749 q^{55} +(-0.669423 - 2.55966i) q^{56} +(4.50285 - 1.37816i) q^{57} +(1.83629 + 10.4141i) q^{58} +(0.492061 + 2.79062i) q^{59} +(0.738219 - 0.556641i) q^{60} +(-4.53366 - 3.80420i) q^{61} +(-0.770450 + 1.33446i) q^{62} +(-1.55648 + 7.78315i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.570408 + 3.23494i) q^{65} +(-3.51070 + 5.40961i) q^{66} +(3.54979 + 1.29202i) q^{67} +(1.67324 - 1.40401i) q^{68} +(-1.40376 - 2.75296i) q^{69} +(1.00462 - 0.992632i) q^{70} +(-4.58179 - 7.93590i) q^{71} +(0.211097 + 2.99256i) q^{72} +(-3.80191 - 6.58510i) q^{73} +(1.80565 - 10.2404i) q^{74} +(-7.51848 - 3.18870i) q^{75} +(2.08269 - 1.74759i) q^{76} +(-4.21668 + 8.90283i) q^{77} +(-7.79742 - 7.26676i) q^{78} +(-13.9134 + 5.06405i) q^{79} +(0.266898 - 0.462282i) q^{80} +(3.36127 - 8.34877i) q^{81} +(-4.20150 - 7.27722i) q^{82} +(0.348371 - 1.97571i) q^{83} +(0.927225 + 4.48779i) q^{84} +(1.09563 + 0.398777i) q^{85} +(-6.13336 - 2.23236i) q^{86} +(-2.23772 - 18.1789i) q^{87} +(-0.646545 + 3.66674i) q^{88} +3.83829 q^{89} +(-1.32707 + 0.896297i) q^{90} +(-13.2806 - 9.41842i) q^{91} +(-1.36672 - 1.14682i) q^{92} +(1.45291 - 2.23879i) q^{93} +(9.84520 + 3.58336i) q^{94} +(1.36374 + 0.496362i) q^{95} +(0.786806 + 1.54303i) q^{96} +(-5.72248 - 4.80173i) q^{97} +(2.31502 + 6.60611i) q^{98} +(6.55999 - 9.04065i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} - 3 q^{7} - 36 q^{8} - 12 q^{9}+O(q^{10}) \) 72 * q + 3 * q^6 - 3 * q^7 - 36 * q^8 - 12 * q^9	\( 72 q + 3 q^{6} - 3 q^{7} - 36 q^{8} - 12 q^{9} + 12 q^{10} - 6 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} + 24 q^{17} + 36 q^{19} - 12 q^{21} - 6 q^{22} + 12 q^{23} - 30 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} + 9 q^{35} + 9 q^{36} + 3 q^{39} - 6 q^{41} + 3 q^{42} + 24 q^{43} - 30 q^{45} - 9 q^{47} - 6 q^{48} + 51 q^{49} + 6 q^{50} + 12 q^{51} + 6 q^{52} - 15 q^{53} - 27 q^{54} + 72 q^{55} + 6 q^{56} - 63 q^{57} + 3 q^{58} + 15 q^{59} - 3 q^{60} - 18 q^{61} - 24 q^{62} - 48 q^{63} - 36 q^{64} - 18 q^{65} - 36 q^{66} + 66 q^{67} - 18 q^{68} - 21 q^{69} - 6 q^{70} + 12 q^{71} - 12 q^{72} - 66 q^{73} + 9 q^{74} + 15 q^{75} - 15 q^{77} + 30 q^{78} + 9 q^{79} - 6 q^{80} - 33 q^{82} - 18 q^{83} - 12 q^{84} + 21 q^{85} - 12 q^{86} - 48 q^{87} + 12 q^{88} + 72 q^{89} + 69 q^{90} + 12 q^{91} + 30 q^{92} + 60 q^{93} - 36 q^{94} + 93 q^{95} - 48 q^{97} + 6 q^{98} - 54 q^{99}+O(q^{100}) \) 72 * q + 3 * q^6 - 3 * q^7 - 36 * q^8 - 12 * q^9 + 12 * q^10 - 6 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^15 + 24 * q^17 + 36 * q^19 - 12 * q^21 - 6 * q^22 + 12 * q^23 - 30 * q^25 - 18 * q^26 - 6 * q^27 + 3 * q^29 + 3 * q^30 + 9 * q^31 - 18 * q^33 + 9 * q^34 + 9 * q^35 + 9 * q^36 + 3 * q^39 - 6 * q^41 + 3 * q^42 + 24 * q^43 - 30 * q^45 - 9 * q^47 - 6 * q^48 + 51 * q^49 + 6 * q^50 + 12 * q^51 + 6 * q^52 - 15 * q^53 - 27 * q^54 + 72 * q^55 + 6 * q^56 - 63 * q^57 + 3 * q^58 + 15 * q^59 - 3 * q^60 - 18 * q^61 - 24 * q^62 - 48 * q^63 - 36 * q^64 - 18 * q^65 - 36 * q^66 + 66 * q^67 - 18 * q^68 - 21 * q^69 - 6 * q^70 + 12 * q^71 - 12 * q^72 - 66 * q^73 + 9 * q^74 + 15 * q^75 - 15 * q^77 + 30 * q^78 + 9 * q^79 - 6 * q^80 - 33 * q^82 - 18 * q^83 - 12 * q^84 + 21 * q^85 - 12 * q^86 - 48 * q^87 + 12 * q^88 + 72 * q^89 + 69 * q^90 + 12 * q^91 + 30 * q^92 + 60 * q^93 - 36 * q^94 + 93 * q^95 - 48 * q^97 + 6 * q^98 - 54 * q^99

Introduction

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