LMFDB - Embedded newform 378.2.v.a.67.12

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			67.12
Character	$\chi$	$=$	378.67
Dual form			378.2.v.a.79.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(1.64636 + 0.538065i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.470361 - 2.66755i) q^{5} +(-1.60704 + 0.646075i) q^{6} +(-1.97994 - 1.75495i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.42097 + 1.77169i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(1.64636 + 0.538065i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.470361 - 2.66755i) q^{5} +(-1.60704 + 0.646075i) q^{6} +(-1.97994 - 1.75495i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.42097 + 1.77169i) q^{9} +(1.35435 + 2.34580i) q^{10} +(0.0308115 + 0.174741i) q^{11} +(0.815777 - 1.52791i) q^{12} +(0.667169 - 3.78370i) q^{13} +(2.64478 + 0.0716849i) q^{14} +(2.20970 - 4.13865i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(1.48414 + 2.57060i) q^{17} +(-2.99339 + 0.198975i) q^{18} +(3.31452 - 5.74091i) q^{19} +(-2.54535 - 0.926430i) q^{20} +(-2.31541 - 3.95460i) q^{21} +(-0.135924 - 0.114054i) q^{22} +(-3.65965 - 3.07081i) q^{23} +(0.357200 + 1.69482i) q^{24} +(-2.19612 - 0.799322i) q^{25} +(1.92104 + 3.32733i) q^{26} +(3.03249 + 4.21948i) q^{27} +(-2.07210 + 1.64512i) q^{28} +(1.23286 + 6.99191i) q^{29} +(0.967547 + 4.59076i) q^{30} +(0.356665 - 2.02275i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-0.0432952 + 0.304264i) q^{33} +(-2.78927 - 1.01521i) q^{34} +(-5.61269 + 4.45613i) q^{35} +(2.16517 - 2.07654i) q^{36} +3.75198 q^{37} +(1.15112 + 6.52832i) q^{38} +(3.13428 - 5.87034i) q^{39} +(2.54535 - 0.926430i) q^{40} +(-1.29046 + 7.31858i) q^{41} +(4.31568 + 1.54108i) q^{42} +(-0.763236 + 0.640431i) q^{43} +0.177437 q^{44} +(5.86481 - 5.62473i) q^{45} +4.77733 q^{46} +(-0.391905 - 2.22260i) q^{47} +(-1.36304 - 1.06870i) q^{48} +(0.840332 + 6.94938i) q^{49} +(2.19612 - 0.799322i) q^{50} +(1.06027 + 5.03069i) q^{51} +(-3.61037 - 1.31407i) q^{52} +(-5.79449 + 10.0363i) q^{53} +(-5.03525 - 1.28306i) q^{54} +0.480622 q^{55} +(0.529857 - 2.59215i) q^{56} +(8.54585 - 7.66815i) q^{57} +(-5.43874 - 4.56364i) q^{58} +(7.49897 - 2.72940i) q^{59} +(-3.69206 - 2.89480i) q^{60} +(-0.869688 - 4.93225i) q^{61} +(1.02698 + 1.77877i) q^{62} +(-1.68416 - 7.75652i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-9.77941 - 3.55941i) q^{65} +(-0.162411 - 0.260909i) q^{66} +(8.09348 + 6.79123i) q^{67} +(2.78927 - 1.01521i) q^{68} +(-4.37279 - 7.02477i) q^{69} +(1.43522 - 7.02136i) q^{70} +(4.26162 - 7.38135i) q^{71} +(-0.323845 + 2.98247i) q^{72} -13.6091 q^{73} +(-2.87418 + 2.41172i) q^{74} +(-3.18551 - 2.49762i) q^{75} +(-5.07813 - 4.26106i) q^{76} +(0.245656 - 0.400049i) q^{77} +(1.37239 + 6.51162i) q^{78} +(-9.95510 + 8.35332i) q^{79} +(-1.35435 + 2.34580i) q^{80} +(2.72221 + 8.57844i) q^{81} +(-3.71574 - 6.43585i) q^{82} +(1.84713 + 10.4756i) q^{83} +(-4.29659 + 1.59353i) q^{84} +(7.55529 - 2.74990i) q^{85} +(0.173012 - 0.981197i) q^{86} +(-1.73237 + 12.1745i) q^{87} +(-0.135924 + 0.114054i) q^{88} +(-5.76097 + 9.97830i) q^{89} +(-0.877200 + 8.07862i) q^{90} +(-7.96115 + 6.32067i) q^{91} +(-3.65965 + 3.07081i) q^{92} +(1.67557 - 3.13825i) q^{93} +(1.72888 + 1.45070i) q^{94} +(-13.7551 - 11.5419i) q^{95} +(1.73110 - 0.0574708i) q^{96} +(3.10100 - 2.60205i) q^{97} +(-5.11070 - 4.78338i) q^{98} +(-0.234993 + 0.477631i) 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 $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	1.64636	+	0.538065i	0.950524	+	0.310652i
$3$	1.64636	+	0.538065i	0.950524	+	0.310652i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	0.470361	−	2.66755i	0.210352	−	1.19296i	−0.678441	−	0.734655i	$-0.737344\pi$
$5$	0.470361	−	2.66755i	0.210352	−	1.19296i	0.888793	−	0.458309i	$-0.151545\pi$
$6$	−1.60704	+	0.646075i	−0.656073	+	0.263759i
$7$	−1.97994	−	1.75495i	−0.748347	−	0.663307i
$7$	−1.97994	−	1.75495i	−0.748347	−	0.663307i
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	2.42097	+	1.77169i	0.806991	+	0.590564i
$10$	1.35435	+	2.34580i	0.428283	+	0.741808i
$11$	0.0308115	+	0.174741i	0.00929002	+	0.0526863i	0.989100	−	0.147243i	$-0.0470399\pi$
$11$	0.0308115	+	0.174741i	0.00929002	+	0.0526863i	−0.979810	+	0.199929i	$0.935929\pi$
$12$	0.815777	−	1.52791i	0.235495	−	0.441069i
$13$	0.667169	−	3.78370i	0.185039	−	1.04941i	−0.740865	−	0.671654i	$-0.765584\pi$
$13$	0.667169	−	3.78370i	0.185039	−	1.04941i	0.925905	−	0.377757i	$-0.123305\pi$
$14$	2.64478	+	0.0716849i	0.706847	+	0.0191586i
$15$	2.20970	−	4.13865i	0.570541	−	1.06859i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	1.48414	+	2.57060i	0.359956	+	0.623462i	0.987953	−	0.154753i	$-0.0494583\pi$
$17$	1.48414	+	2.57060i	0.359956	+	0.623462i	−0.627997	+	0.778216i	$0.716125\pi$
$18$	−2.99339	+	0.198975i	−0.705550	+	0.0468989i
$19$	3.31452	−	5.74091i	0.760402	−	1.31705i	−0.182242	−	0.983254i	$-0.558335\pi$
$19$	3.31452	−	5.74091i	0.760402	−	1.31705i	0.942644	−	0.333801i	$-0.108331\pi$
$20$	−2.54535	−	0.926430i	−0.569157	−	0.207156i
$21$	−2.31541	−	3.95460i	−0.505264	−	0.862965i
$22$	−0.135924	−	0.114054i	−0.0289791	−	0.0243164i
$23$	−3.65965	−	3.07081i	−0.763089	−	0.640308i	0.175840	−	0.984419i	$-0.443736\pi$
$23$	−3.65965	−	3.07081i	−0.763089	−	0.640308i	−0.938929	+	0.344111i	$0.888180\pi$
$24$	0.357200	+	1.69482i	0.0729131	+	0.345953i
$25$	−2.19612	−	0.799322i	−0.439224	−	0.159864i
$26$	1.92104	+	3.32733i	0.376746	+	0.652544i
$27$	3.03249	+	4.21948i	0.583604	+	0.812039i
$28$	−2.07210	+	1.64512i	−0.391590	+	0.310898i
$29$	1.23286	+	6.99191i	0.228937	+	1.29836i	0.855015	+	0.518604i	$0.173548\pi$
$29$	1.23286	+	6.99191i	0.228937	+	1.29836i	−0.626078	+	0.779760i	$0.715341\pi$
$30$	0.967547	+	4.59076i	0.176649	+	0.838153i
$31$	0.356665	−	2.02275i	0.0640589	−	0.363296i	−0.935881	−	0.352317i	$-0.885394\pi$
$31$	0.356665	−	2.02275i	0.0640589	−	0.363296i	0.999940	−	0.0109793i	$-0.00349489\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	−0.0432952	+	0.304264i	−0.00753673	+	0.0529656i
$34$	−2.78927	−	1.01521i	−0.478355	−	0.174107i
$35$	−5.61269	+	4.45613i	−0.948718	+	0.753224i
$36$	2.16517	−	2.07654i	0.360862	−	0.346090i
$37$	3.75198			0.616821			0.308411	−	0.951253i	$-0.400203\pi$
$37$	3.75198			0.616821			0.308411	+	0.951253i	$0.400203\pi$
$38$	1.15112	+	6.52832i	0.186736	+	1.05903i
$39$	3.13428	−	5.87034i	0.501886	−	0.940007i
$40$	2.54535	−	0.926430i	0.402455	−	0.146481i
$41$	−1.29046	+	7.31858i	−0.201537	+	1.14297i	0.701261	+	0.712905i	$0.252621\pi$
$41$	−1.29046	+	7.31858i	−0.201537	+	1.14297i	−0.902798	+	0.430066i	$0.858490\pi$
$42$	4.31568	+	1.54108i	0.665923	+	0.237794i
$43$	−0.763236	+	0.640431i	−0.116392	+	0.0976648i	−0.699126	−	0.714998i	$-0.746427\pi$
$43$	−0.763236	+	0.640431i	−0.116392	+	0.0976648i	0.582734	+	0.812663i	$0.301983\pi$
$44$	0.177437			0.0267496
$45$	5.86481	−	5.62473i	0.874274	−	0.838485i
$46$	4.77733			0.704379
$47$	−0.391905	−	2.22260i	−0.0571652	−	0.324200i	0.942793	−	0.333380i	$-0.108189\pi$
$47$	−0.391905	−	2.22260i	−0.0571652	−	0.324200i	−0.999958	+	0.00917968i	$0.997078\pi$
$48$	−1.36304	−	1.06870i	−0.196738	−	0.154254i
$49$	0.840332	+	6.94938i	0.120047	+	0.992768i
$50$	2.19612	−	0.799322i	0.310578	−	0.113041i
$51$	1.06027	+	5.03069i	0.148467	+	0.704437i
$52$	−3.61037	−	1.31407i	−0.500668	−	0.182228i
$53$	−5.79449	+	10.0363i	−0.795934	+	1.37860i	0.126310	+	0.991991i	$0.459686\pi$
$53$	−5.79449	+	10.0363i	−0.795934	+	1.37860i	−0.922244	+	0.386607i	$0.873647\pi$
$54$	−5.03525	−	1.28306i	−0.685211	−	0.174602i
$55$	0.480622			0.0648071
$56$	0.529857	−	2.59215i	0.0708051	−	0.346391i
$57$	8.54585	−	7.66815i	1.13193	−	1.01567i
$58$	−5.43874	−	4.56364i	−0.714141	−	0.599236i
$59$	7.49897	−	2.72940i	0.976283	−	0.355338i	0.195889	−	0.980626i	$-0.437241\pi$
$59$	7.49897	−	2.72940i	0.976283	−	0.355338i	0.780394	+	0.625288i	$0.215019\pi$
$60$	−3.69206	−	2.89480i	−0.476644	−	0.373717i
$61$	−0.869688	−	4.93225i	−0.111352	−	0.631509i	−0.988492	−	0.151274i	$-0.951662\pi$
$61$	−0.869688	−	4.93225i	−0.111352	−	0.631509i	0.877140	−	0.480235i	$-0.159449\pi$
$62$	1.02698	+	1.77877i	0.130426	+	0.225904i
$63$	−1.68416	−	7.75652i	−0.212184	−	0.977230i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−9.77941	−	3.55941i	−1.21299	−	0.441491i
$66$	−0.162411	−	0.260909i	−0.0199914	−	0.0321157i
$67$	8.09348	+	6.79123i	0.988776	+	0.829681i	0.985390	−	0.170313i	$-0.0544779\pi$
$67$	8.09348	+	6.79123i	0.988776	+	0.829681i	0.00338560	+	0.999994i	$0.498922\pi$
$68$	2.78927	−	1.01521i	0.338248	−	0.123112i
$69$	−4.37279	−	7.02477i	−0.526421	−	0.845683i
$70$	1.43522	−	7.02136i	0.171542	−	0.839214i
$71$	4.26162	−	7.38135i	0.505762	−	0.876005i	−0.494216	−	0.869339i	$-0.664545\pi$
$71$	4.26162	−	7.38135i	0.505762	−	0.876005i	0.999978	−	0.00666572i	$-0.00212178\pi$
$72$	−0.323845	+	2.98247i	−0.0381655	+	0.351487i
$73$	−13.6091			−1.59282			−0.796411	−	0.604756i	$-0.793271\pi$
$73$	−13.6091			−1.59282			−0.796411	+	0.604756i	$0.793271\pi$
$74$	−2.87418	+	2.41172i	−0.334117	+	0.280357i
$75$	−3.18551	−	2.49762i	−0.367830	−	0.288401i
$76$	−5.07813	−	4.26106i	−0.582502	−	0.488777i
$77$	0.245656	−	0.400049i	0.0279951	−	0.0455898i
$78$	1.37239	+	6.51162i	0.155392	+	0.737295i
$79$	−9.95510	+	8.35332i	−1.12004	+	0.939822i	−0.998606	−	0.0527775i	$-0.983193\pi$
$79$	−9.95510	+	8.35332i	−1.12004	+	0.939822i	−0.121430	+	0.992600i	$0.538748\pi$
$80$	−1.35435	+	2.34580i	−0.151421	+	0.262269i
$81$	2.72221	+	8.57844i	0.302468	+	0.953160i
$82$	−3.71574	−	6.43585i	−0.410335	−	0.710721i
$83$	1.84713	+	10.4756i	0.202749	+	1.14985i	0.900943	+	0.433937i	$0.142876\pi$
$83$	1.84713	+	10.4756i	0.202749	+	1.14985i	−0.698194	+	0.715908i	$0.746013\pi$
$84$	−4.29659	+	1.59353i	−0.468796	+	0.173868i
$85$	7.55529	−	2.74990i	0.819486	−	0.298269i
$86$	0.173012	−	0.981197i	0.0186563	−	0.105805i
$87$	−1.73237	+	12.1745i	−0.185730	+	1.30525i
$88$	−0.135924	+	0.114054i	−0.0144896	+	0.0121582i
$89$	−5.76097	+	9.97830i	−0.610662	+	1.05770i	0.380467	+	0.924794i	$0.375763\pi$
$89$	−5.76097	+	9.97830i	−0.610662	+	1.05770i	−0.991129	+	0.132903i	$0.957570\pi$
$90$	−0.877200	+	8.07862i	−0.0924649	+	0.851561i
$91$	−7.96115	+	6.32067i	−0.834555	+	0.662586i
$92$	−3.65965	+	3.07081i	−0.381545	+	0.320154i
$93$	1.67557	−	3.13825i	0.173748	−	0.325421i
$94$	1.72888	+	1.45070i	0.178320	+	0.149628i
$95$	−13.7551	−	11.5419i	−1.41125	−	1.18418i
$96$	1.73110	−	0.0574708i	0.176679	−	0.00586559i
$97$	3.10100	−	2.60205i	0.314859	−	0.264198i	−0.471638	−	0.881792i	$-0.656337\pi$
$97$	3.10100	−	2.60205i	0.314859	−	0.264198i	0.786497	+	0.617594i	$0.211893\pi$
$98$	−5.11070	−	4.78338i	−0.516259	−	0.483194i
$99$	−0.234993	+	0.477631i	−0.0236177	+	0.0480037i
$100$	−1.16853	+	2.02395i	−0.116853	+	0.202395i
$101$	2.66907	−	2.23962i	0.265583	−	0.222850i	−0.500265	−	0.865872i	$-0.666764\pi$
$101$	2.66907	−	2.23962i	0.265583	−	0.222850i	0.765848	+	0.643022i	$0.222320\pi$
$102$	−4.04587	−	3.17220i	−0.400601	−	0.314095i
$103$	−0.509432	+	2.88913i	−0.0501959	+	0.284675i	−0.999565	−	0.0294874i	$-0.990613\pi$
$103$	−0.509432	+	2.88913i	−0.0501959	+	0.284675i	0.949369	+	0.314162i	$0.101724\pi$
$104$	3.61037	−	1.31407i	0.354026	−	0.128855i
$105$	−11.6382	+	4.31638i	−1.13577	+	0.421236i
$106$	−2.01240	−	11.4129i	−0.195462	−	1.10852i
$107$	−9.51267	−	16.4764i	−0.919624	−	1.59284i	−0.799986	−	0.600018i	$-0.795160\pi$
$107$	−9.51267	−	16.4764i	−0.919624	−	1.59284i	−0.119638	−	0.992818i	$-0.538173\pi$
$108$	4.68196	−	2.25372i	0.450522	−	0.216864i
$109$	−6.38227	+	11.0544i	−0.611311	+	1.05882i	0.379709	+	0.925106i	$0.376024\pi$
$109$	−6.38227	+	11.0544i	−0.611311	+	1.05882i	−0.991020	+	0.133715i	$0.957309\pi$
$110$	−0.368178	+	0.308938i	−0.0351044	+	0.0294561i
$111$	6.17709	+	2.01881i	0.586303	+	0.191617i
$112$	1.26031	+	2.32629i	0.119088	+	0.219814i
$113$	−1.31534	−	1.10370i	−0.123736	−	0.103827i	0.578820	−	0.815456i	$-0.303514\pi$
$113$	−1.31534	−	1.10370i	−0.123736	−	0.103827i	−0.702556	+	0.711628i	$0.747958\pi$
$114$	−1.61751	+	11.3673i	−0.151494	+	1.06465i
$115$	−9.91289	+	8.31790i	−0.924382	+	0.775649i
$116$	7.09977			0.659197
$117$	8.31876	−	7.97822i	0.769070	−	0.737587i
$118$	−3.99012	+	6.91109i	−0.367320	+	0.636218i
$119$	1.57276	−	7.69422i	0.144175	−	0.705328i
$120$	4.68902	−	0.155671i	0.428047	−	0.0142108i
$121$	10.3070	−	3.75145i	0.937003	−	0.341041i
$122$	3.83661	+	3.21930i	0.347350	+	0.291461i
$123$	−6.06243	+	11.3546i	−0.546631	+	1.02381i
$124$	−1.93008	−	0.702493i	−0.173327	−	0.0630857i
$125$	3.60655	−	6.24673i	0.322580	−	0.558725i
$126$	6.27593	+	4.85928i	0.559105	+	0.432900i
$127$	−6.79445	−	11.7683i	−0.602910	−	1.04427i	−0.992378	−	0.123230i	$-0.960675\pi$
$127$	−6.79445	−	11.7683i	−0.602910	−	1.04427i	0.389468	−	0.921040i	$-0.372659\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	−1.60115	+	0.643706i	−0.140974	+	0.0566752i
$130$	9.77941	−	3.55941i	0.857711	−	0.312181i
$131$	0.466191	+	0.391181i	0.0407313	+	0.0341776i	0.662926	−	0.748685i	$-0.269314\pi$
$131$	0.466191	+	0.391181i	0.0407313	+	0.0341776i	−0.622195	+	0.782862i	$0.713759\pi$
$132$	0.292124	+	0.0954724i	0.0254261	+	0.00830981i
$133$	−16.6375	+	5.54987i	−1.44266	+	0.481234i
$134$	−10.5653			−0.912702
$135$	12.6820	−	6.10465i	1.09150	−	0.525405i
$136$	−1.48414	+	2.57060i	−0.127264	+	0.220427i
$137$	14.2399	+	5.18289i	1.21659	+	0.442804i	0.868987	−	0.494836i	$-0.164772\pi$
$137$	14.2399	+	5.18289i	1.21659	+	0.442804i	0.347608	+	0.937640i	$0.386994\pi$
$138$	7.86518	+	2.57052i	0.669529	+	0.218817i
$139$	0.350742	−	0.127660i	0.0297496	−	0.0108280i	−0.327103	−	0.944989i	$-0.606072\pi$
$139$	0.350742	−	0.127660i	0.0297496	−	0.0108280i	0.356852	+	0.934161i	$0.383850\pi$
$140$	3.41380	+	6.30122i	0.288519	+	0.532550i
$141$	0.550691	−	3.87006i	0.0463765	−	0.325918i
$142$	1.48005	+	8.39376i	0.124203	+	0.704389i
$143$	0.681724			0.0570086
$144$	−1.66901	−	2.49287i	−0.139085	−	0.207739i
$145$	19.2311			1.59706
$146$	10.4252	−	8.74774i	0.862792	−	0.723968i
$147$	−2.35573	+	11.8933i	−0.194298	+	0.980943i
$148$	0.651524	−	3.69498i	0.0535549	−	0.303725i
$149$	−5.68573	+	2.06944i	−0.465793	+	0.169535i	−0.564246	−	0.825607i	$-0.690833\pi$
$149$	−5.68573	+	2.06944i	−0.465793	+	0.169535i	0.0984526	+	0.995142i	$0.468611\pi$
$150$	4.04568	−	0.134313i	0.330328	−	0.0109666i
$151$	0.580939	+	3.29467i	0.0472762	+	0.268116i	0.999279	−	0.0379735i	$-0.0120903\pi$
$151$	0.580939	+	3.29467i	0.0472762	+	0.268116i	−0.952003	+	0.306090i	$0.900979\pi$
$152$	6.62903			0.537685
$153$	−0.961261	+	8.85279i	−0.0777134	+	0.715706i
$154$	0.0689634	+	0.464360i	0.00555723	+	0.0374192i
$155$	−5.22802	−	1.90284i	−0.419924	−	0.152840i
$156$	−5.23690	−	4.10603i	−0.419287	−	0.328746i
$157$	2.03431	−	0.740427i	0.162355	−	0.0590925i	−0.259564	−	0.965726i	$-0.583579\pi$
$157$	2.03431	−	0.740427i	0.162355	−	0.0590925i	0.421919	+	0.906633i	$0.361357\pi$
$158$	2.25664	−	12.7980i	0.179529	−	1.01816i
$159$	−14.9400	+	13.4056i	−1.18482	+	1.06313i
$160$	−0.470361	−	2.66755i	−0.0371853	−	0.210888i
$161$	1.85678	+	12.5025i	0.146335	+	0.985335i
$162$	−7.59945	−	4.82166i	−0.597069	−	0.378826i
$163$	−10.6508	−	18.4477i	−0.834234	−	1.44493i	−0.894653	−	0.446762i	$-0.852577\pi$
$163$	−10.6508	−	18.4477i	−0.834234	−	1.44493i	0.0604194	−	0.998173i	$-0.480756\pi$
$164$	6.98331	+	2.54172i	0.545305	+	0.198475i
$165$	0.791275	+	0.258606i	0.0616007	+	0.0201325i
$166$	−8.14857	−	6.83746i	−0.632451	−	0.530690i
$167$	−4.51240	−	3.78636i	−0.349180	−	0.292997i	0.451281	−	0.892382i	$-0.350967\pi$
$167$	−4.51240	−	3.78636i	−0.349180	−	0.292997i	−0.800461	+	0.599385i	$0.795412\pi$
$168$	2.26708	−	3.98251i	0.174909	−	0.307257i
$169$	−1.65530	−	0.602480i	−0.127331	−	0.0463446i
$170$	−4.02008	+	6.96299i	−0.308326	+	0.534037i
$171$	18.1955	−	8.02628i	1.39144	−	0.613785i
$172$	0.498167	+	0.862850i	0.0379849	+	0.0657917i
$173$	23.0121	+	8.37570i	1.74957	+	0.636793i	0.999693	−	0.0247800i	$-0.00788851\pi$
$173$	23.0121	+	8.37570i	1.74957	+	0.636793i	0.749881	+	0.661573i	$0.230111\pi$
$174$	−6.49856	−	10.4398i	−0.492654	−	0.791437i
$175$	2.94542	+	5.43668i	0.222653	+	0.410974i
$176$	0.0308115	−	0.174741i	0.00232251	−	0.0131716i
$177$	13.8146	−	0.458631i	1.03837	−	0.0344728i
$178$	−2.00076	−	11.3469i	−0.149964	−	0.850486i
$179$	−0.928729	−	1.60861i	−0.0694165	−	0.120233i	0.829228	−	0.558910i	$-0.188780\pi$
$179$	−0.928729	−	1.60861i	−0.0694165	−	0.120233i	−0.898645	+	0.438677i	$0.855447\pi$
$180$	−4.52086	−	6.75243i	−0.336965	−	0.503297i
$181$	13.3692	+	23.1562i	0.993727	+	1.72119i	0.593716	+	0.804675i	$0.297660\pi$
$181$	13.3692	+	23.1562i	0.993727	+	1.72119i	0.400011	+	0.916510i	$0.369006\pi$
$182$	2.03575	−	9.95924i	0.150900	−	0.738228i
$183$	1.22205	−	8.58818i	0.0903368	−	0.634856i
$184$	0.829575	−	4.70475i	0.0611571	−	0.346839i
$185$	1.76478	−	10.0086i	0.129749	−	0.735846i
$186$	0.733670	+	3.48107i	0.0537953	+	0.255245i
$187$	−0.403461	+	0.338544i	−0.0295040	+	0.0247568i
$188$	−2.25689			−0.164601
$189$	1.40079	−	13.6762i	0.101893	−	0.994795i
$190$	17.9561			1.30267
$191$	−8.38574	+	7.03647i	−0.606771	+	0.509141i	−0.893614	−	0.448836i	$-0.851839\pi$
$191$	−8.38574	+	7.03647i	−0.606771	+	0.509141i	0.286843	+	0.957978i	$0.407394\pi$
$192$	−1.28916	+	1.15675i	−0.0930368	+	0.0834815i
$193$	2.20826	−	12.5237i	0.158954	−	0.901473i	−0.796127	−	0.605129i	$-0.793122\pi$
$193$	2.20826	−	12.5237i	0.158954	−	0.901473i	0.955081	−	0.296344i	$-0.0957674\pi$
$194$	−0.702941	+	3.98657i	−0.0504682	+	0.286219i
$195$	−14.1852	−	11.1220i	−1.01582	−	0.796464i
$196$	6.98972	+	0.379182i	0.499266	+	0.0270844i
$197$	−9.46164	−	16.3880i	−0.674114	−	1.16760i	−0.976727	−	0.214486i	$-0.931192\pi$
$197$	−9.46164	−	16.3880i	−0.674114	−	1.16760i	0.302613	−	0.953113i	$-0.402141\pi$
$198$	−0.127000	−	0.516938i	−0.00902551	−	0.0367371i
$199$	7.81431	+	13.5348i	0.553942	+	0.959456i	0.997985	+	0.0634503i	$0.0202104\pi$
$199$	7.81431	+	13.5348i	0.553942	+	0.959456i	−0.444043	+	0.896006i	$0.646456\pi$
$200$	−0.405826	−	2.30156i	−0.0286963	−	0.162745i
$201$	9.67061	+	15.5356i	0.682112	+	1.09580i
$202$	−0.605030	+	3.43129i	−0.0425697	+	0.241425i
$203$	9.82942	−	16.0072i	0.689890	−	1.12348i
$204$	5.13837	−	0.170589i	0.359758	−	0.0119436i
$205$	18.9157	+	6.88475i	1.32113	+	0.480852i
$206$	−1.46685	−	2.54066i	−0.102200	−	0.177016i
$207$	−3.41937	−	13.9181i	−0.237663	−	0.967376i
$208$	−1.92104	+	3.32733i	−0.133200	+	0.230709i
$209$	1.10530	+	0.402295i	0.0764550	+	0.0278273i
$210$	6.14084	−	10.7874i	0.423758	−	0.744402i
$211$	15.6591	+	13.1396i	1.07802	+	0.904566i	0.995755	−	0.0920443i	$-0.0293401\pi$
$211$	15.6591	+	13.1396i	1.07802	+	0.904566i	0.0822651	+	0.996610i	$0.473785\pi$
$212$	8.87767	+	7.44925i	0.609721	+	0.511616i
$213$	10.9878	−	9.85929i	0.752871	−	0.675547i
$214$	17.8780	+	6.50705i	1.22211	+	0.444813i
$215$	1.34939	+	2.33720i	0.0920273	+	0.159396i
$216$	−2.13793	+	4.73595i	−0.145468	+	0.322241i
$217$	−4.25599	+	3.37899i	−0.288915	+	0.229381i
$218$	−2.21654	−	12.5706i	−0.150123	−	0.851390i
$219$	−22.4054	−	7.32257i	−1.51401	−	0.494813i
$220$	0.0834592	−	0.473321i	0.00562682	−	0.0319113i
$221$	10.7166	−	3.90051i	0.720874	−	0.262377i
$222$	−6.02959	+	2.42406i	−0.404680	+	0.162692i
$223$	10.7369	+	3.90792i	0.718997	+	0.261693i	0.675500	−	0.737360i	$-0.263928\pi$
$223$	10.7369	+	3.90792i	0.718997	+	0.261693i	0.0434969	+	0.999054i	$0.486150\pi$
$224$	−2.46076	−	0.971930i	−0.164417	−	0.0649398i
$225$	−3.90059	−	5.82598i	−0.260039	−	0.388399i
$226$	1.71705			0.114216
$227$	4.46238	+	25.3074i	0.296179	+	1.67971i	0.662372	+	0.749175i	$0.269550\pi$
$227$	4.46238	+	25.3074i	0.296179	+	1.67971i	−0.366194	+	0.930539i	$0.619339\pi$
$228$	−6.06768	−	9.74758i	−0.401842	−	0.645549i
$229$	18.3905	−	6.69359i	1.21528	−	0.442325i	0.346746	−	0.937959i	$-0.387286\pi$
$229$	18.3905	−	6.69359i	1.21528	−	0.442325i	0.868531	+	0.495634i	$0.165064\pi$
$230$	2.24707	−	12.7438i	0.148167	−	0.840299i
$231$	0.619689	−	0.526444i	0.0407725	−	0.0346375i
$232$	−5.43874	+	4.56364i	−0.357071	+	0.299618i
$233$	−16.0128			−1.04903			−0.524516	−	0.851401i	$-0.675754\pi$
$233$	−16.0128			−1.04903			−0.524516	+	0.851401i	$0.675754\pi$
$234$	−1.24424	+	11.4589i	−0.0813383	+	0.749090i
$235$	−6.11324			−0.398784
$236$	−1.38575	−	7.85900i	−0.0902049	−	0.511578i
$237$	−20.8843	+	8.39605i	−1.35658	+	0.545382i
$238$	3.74094	+	6.90507i	0.242489	+	0.447589i
$239$	−0.473446	+	0.172320i	−0.0306246	+	0.0111465i	−0.357287	−	0.933995i	$-0.616298\pi$
$239$	−0.473446	+	0.172320i	−0.0306246	+	0.0111465i	0.326662	+	0.945141i	$0.394076\pi$
$240$	−3.49194	+	3.13330i	−0.225404	+	0.202254i
$241$	5.27310	+	1.91925i	0.339670	+	0.123630i	0.506223	−	0.862403i	$-0.331041\pi$
$241$	5.27310	+	1.91925i	0.339670	+	0.123630i	−0.166553	+	0.986033i	$0.553264\pi$
$242$	−5.48426	+	9.49901i	−0.352541	+	0.610620i
$243$	−0.134034	+	15.5879i	−0.00859831	+	0.999963i
$244$	−5.00833			−0.320626
$245$	18.9331	+	1.02709i	1.20959	+	0.0656184i
$246$	−2.65452	−	12.5950i	−0.169246	−	0.803029i
$247$	−19.5106	−	16.3713i	−1.24143	−	1.04168i
$248$	1.93008	−	0.702493i	0.122560	−	0.0446083i
$249$	−2.59552	+	18.2404i	−0.164484	+	1.15594i
$250$	1.25254	+	7.10352i	0.0792177	+	0.449266i
$251$	−12.1635	−	21.0678i	−0.767753	−	1.32979i	−0.938779	−	0.344520i	$-0.888042\pi$
$251$	−12.1635	−	21.0678i	−0.767753	−	1.32979i	0.171026	−	0.985267i	$-0.445292\pi$
$252$	−7.93113	+	0.311665i	−0.499614	+	0.0196330i
$253$	0.423836	−	0.734106i	0.0266464	−	0.0461529i
$254$	12.7694	+	4.64768i	0.801222	+	0.291621i
$255$	13.9183	−	0.462075i	0.871599	−	0.0289363i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	4.21629	−	1.53461i	0.263005	−	0.0957260i	−0.207152	−	0.978309i	$-0.566419\pi$
$257$	4.21629	−	1.53461i	0.263005	−	0.0957260i	0.470157	+	0.882583i	$0.344197\pi$
$258$	0.812787	−	1.52231i	0.0506019	−	0.0947748i
$259$	−7.42869	−	6.58452i	−0.461597	−	0.409142i
$260$	−5.20352	+	9.01275i	−0.322708	+	0.558947i
$261$	−9.40279	+	19.1115i	−0.582018	+	1.18297i
$262$	−0.608569			−0.0375975
$263$	−14.7307	+	12.3605i	−0.908334	+	0.762183i	−0.971801	−	0.235801i	$-0.924229\pi$
$263$	−14.7307	+	12.3605i	−0.908334	+	0.762183i	0.0634673	+	0.997984i	$0.479784\pi$
$264$	−0.285148	+	0.114637i	−0.0175497	+	0.00705544i
$265$	24.0470	+	20.1778i	1.47719	+	1.23951i
$266$	9.17770	−	14.9458i	0.562721	−	0.916388i
$267$	−14.8536	+	13.3280i	−0.909024	+	0.815663i
$268$	8.09348	−	6.79123i	0.494388	−	0.414841i
$269$	4.90760	−	8.50022i	0.299222	−	0.518267i	−0.676736	−	0.736226i	$-0.736606\pi$
$269$	4.90760	−	8.50022i	0.299222	−	0.518267i	0.975958	+	0.217958i	$0.0699396\pi$
$270$	−5.79100	+	12.8283i	−0.352429	+	0.780705i
$271$	13.4194	+	23.2431i	0.815172	+	1.41192i	0.909204	+	0.416350i	$0.136691\pi$
$271$	13.4194	+	23.2431i	0.815172	+	1.41192i	−0.0940323	+	0.995569i	$0.529976\pi$
$272$	−0.515436	−	2.92318i	−0.0312529	−	0.177244i
$273$	−16.5078	+	6.12244i	−0.999098	+	0.370547i
$274$	−14.2399	+	5.18289i	−0.860262	+	0.313110i
$275$	0.0720084	−	0.408380i	0.00434227	−	0.0246262i
$276$	−7.67738	+	3.08651i	−0.462124	+	0.185786i
$277$	8.38048	−	7.03206i	0.503534	−	0.422516i	−0.355313	−	0.934747i	$-0.615626\pi$
$277$	8.38048	−	7.03206i	0.503534	−	0.422516i	0.858847	+	0.512232i	$0.171181\pi$
$278$	−0.186626	+	0.323246i	−0.0111931	+	0.0193870i
$279$	4.44716	−	4.26511i	0.266245	−	0.255346i
$280$	−6.66547	−	2.63267i	−0.398338	−	0.157332i
$281$	−7.38124	+	6.19360i	−0.440328	+	0.369479i	−0.835832	−	0.548985i	$-0.815014\pi$
$281$	−7.38124	+	6.19360i	−0.440328	+	0.369479i	0.395504	+	0.918464i	$0.370570\pi$
$282$	2.06578	+	3.31862i	0.123015	+	0.197621i
$283$	−21.4945	−	18.0360i	−1.27771	−	1.07213i	−0.993555	−	0.113352i	$-0.963841\pi$
$283$	−21.4945	−	18.0360i	−1.27771	−	1.07213i	−0.284159	−	0.958777i	$-0.591714\pi$
$284$	−6.52918	−	5.47864i	−0.387436	−	0.325097i
$285$	−16.4355	−	26.4033i	−0.973557	−	1.56400i
$286$	−0.522231	+	0.438204i	−0.0308802	+	0.0259115i
$287$	15.3988	−	12.2257i	0.908960	−	0.721658i
$288$	2.88092	+	0.836826i	0.169760	+	0.0493104i
$289$	4.09467	−	7.09218i	0.240863	−	0.417187i
$290$	−14.7319	+	12.3615i	−0.865088	+	0.725895i
$291$	6.50543	−	2.61536i	0.381355	−	0.153315i
$292$	−2.36319	+	13.4023i	−0.138295	+	0.784311i
$293$	−20.3854	+	7.41968i	−1.19093	+	0.433462i	−0.860049	−	0.510211i	$-0.829567\pi$
$293$	−20.3854	+	7.41968i	−1.19093	+	0.433462i	−0.330879	+	0.943673i	$0.607345\pi$
$294$	−5.84027	−	10.6250i	−0.340611	−	0.619664i
$295$	−3.75359	−	21.2877i	−0.218543	−	1.23942i
$296$	1.87599	+	3.24931i	0.109040	+	0.188862i
$297$	−0.643879	+	0.659909i	−0.0373617	+	0.0382918i
$298$	3.02531	−	5.24000i	0.175252	−	0.303545i
$299$	−14.0606	+	11.7983i	−0.813148	+	0.682312i
$300$	−3.01284	+	2.70340i	−0.173946	+	0.156081i
$301$	2.63508	+	0.0714221i	0.151884	+	0.00411670i
$302$	−2.56280	−	2.15044i	−0.147472	−	0.123744i
$303$	5.59930	−	2.25107i	0.321672	−	0.129321i
$304$	−5.07813	+	4.26106i	−0.291251	+	0.244388i
$305$	−13.5661			−0.776792
$306$	−4.95409	−	7.39952i	−0.283207	−	0.423002i
$307$	−8.29924	+	14.3747i	−0.473663	+	0.820408i	−0.999545	−	0.0301493i	$-0.990402\pi$
$307$	−8.29924	+	14.3747i	−0.473663	+	0.820408i	0.525883	+	0.850557i	$0.323735\pi$
$308$	−0.351314	−	0.311391i	−0.0200180	−	0.0177432i
$309$	−2.39325	+	4.48243i	−0.136147	+	0.254997i
$310$	5.22802	−	1.90284i	0.296931	−	0.108074i
$311$	6.96116	+	5.84111i	0.394731	+	0.331219i	0.818453	−	0.574574i	$-0.194832\pi$
$311$	6.96116	+	5.84111i	0.394731	+	0.331219i	−0.423722	+	0.905792i	$0.639277\pi$
$312$	6.65100	−	0.220807i	0.376539	−	0.0125007i
$313$	−26.0542	−	9.48296i	−1.47267	−	0.536008i	−0.523847	−	0.851813i	$-0.675504\pi$
$313$	−26.0542	−	9.48296i	−1.47267	−	0.536008i	−0.948824	+	0.315804i	$0.897726\pi$
$314$	−1.08243	+	1.87483i	−0.0610851	+	0.105803i
$315$	−21.4831	+	0.844206i	−1.21043	+	0.0475656i
$316$	6.49773	+	11.2544i	0.365526	+	0.633110i
$317$	0.0269795	+	0.153009i	0.00151532	+	0.00859382i	0.985556	−	0.169350i	$-0.0541667\pi$
$317$	0.0269795	+	0.153009i	0.00151532	+	0.00859382i	−0.984041	+	0.177943i	$0.943056\pi$
$318$	2.82776	−	19.8725i	0.158573	−	1.11440i
$319$	−1.18379	+	0.430863i	−0.0662792	+	0.0241237i
$320$	2.07499	+	1.74112i	0.115995	+	0.0973315i
$321$	−6.79584	−	32.2445i	−0.379307	−	1.79971i
$322$	−9.45883	−	8.38396i	−0.527120	−	0.467220i
$323$	19.6768			1.09485
$324$	8.92082	−	1.19122i	0.495601	−	0.0661790i
$325$	−4.48958	+	7.77618i	−0.249037	+	0.431345i
$326$	20.0169	+	7.28556i	1.10863	+	0.403510i
$327$	−16.4555	+	14.7654i	−0.909990	+	0.816529i
$328$	−6.98331	+	2.54172i	−0.385589	+	0.140343i
$329$	−3.12460	+	5.08839i	−0.172265	+	0.280532i
$330$	−0.772381	+	0.310518i	−0.0425182	+	0.0170935i
$331$	1.42818	+	8.09961i	0.0784998	+	0.445195i	0.998571	+	0.0534432i	$0.0170196\pi$
$331$	1.42818	+	8.09961i	0.0784998	+	0.445195i	−0.920071	+	0.391752i	$0.871869\pi$
$332$	10.6372			0.583792
$333$	9.08343	+	6.64735i	0.497769	+	0.364273i
$334$	5.89052			0.322315
$335$	21.9228	−	18.3954i	1.19777	−	1.00505i
$336$	0.823221	+	4.50803i	0.0449104	+	0.245933i
$337$	−2.10040	+	11.9120i	−0.114416	+	0.648886i	0.872622	+	0.488397i	$0.162418\pi$
$337$	−2.10040	+	11.9120i	−0.114416	+	0.648886i	−0.987038	+	0.160489i	$0.948693\pi$
$338$	1.65530	−	0.602480i	0.0900365	−	0.0327706i
$339$	−1.57165	−	2.52482i	−0.0853603	−	0.137129i
$340$	−1.39616	−	7.91802i	−0.0757174	−	0.429415i
$341$	0.364446			0.0197358
$342$	−8.77935	+	17.8443i	−0.474733	+	0.964910i
$343$	10.5320	−	15.2341i	0.568673	−	0.822564i
$344$	−0.936248	−	0.340766i	−0.0504791	−	0.0183729i
$345$	−20.7957	+	8.36044i	−1.11960	+	0.450111i
$346$	−23.0121	+	8.37570i	−1.23714	+	0.450281i
$347$	3.00453	−	17.0396i	0.161292	−	0.914731i	−0.791514	−	0.611151i	$-0.790707\pi$
$347$	3.00453	−	17.0396i	0.161292	−	0.914731i	0.952806	−	0.303580i	$-0.0981820\pi$
$348$	11.6887	+	3.82014i	0.626582	+	0.204781i
$349$	3.32385	+	18.8505i	0.177922	+	1.00904i	0.934717	+	0.355392i	$0.115653\pi$
$349$	3.32385	+	18.8505i	0.177922	+	1.00904i	−0.756796	+	0.653651i	$0.773236\pi$
$350$	−5.75095	−	2.27146i	−0.307401	−	0.121415i
$351$	17.9884	−	8.65896i	0.960152	−	0.462181i
$352$	0.0887183	+	0.153665i	0.00472870	+	0.00819035i
$353$	−7.71249	−	2.80712i	−0.410495	−	0.149408i	0.128515	−	0.991708i	$-0.458979\pi$
$353$	−7.71249	−	2.80712i	−0.410495	−	0.149408i	−0.539009	+	0.842300i	$0.681201\pi$
$354$	−10.2878	+	9.23117i	−0.546789	+	0.490631i
$355$	−17.6856	−	14.8400i	−0.938655	−	0.787625i
$356$	8.82632	+	7.40616i	0.467794	+	0.392526i
$357$	6.72932	−	11.8212i	0.356153	−	0.625643i
$358$	1.74544	+	0.635288i	0.0922493	+	0.0335760i
$359$	3.61796	−	6.26650i	0.190949	−	0.330733i	−0.754616	−	0.656167i	$-0.772177\pi$
$359$	3.61796	−	6.26650i	0.190949	−	0.330733i	0.945565	+	0.325433i	$0.105510\pi$
$360$	7.80356	+	2.26671i	0.411284	+	0.119466i
$361$	−12.4720	−	21.6022i	−0.656422	−	1.13696i
$362$	−25.1259	−	9.14509i	−1.32059	−	0.480655i
$363$	18.9876	−	0.630370i	0.996589	−	0.0330858i
$364$	4.84220	+	8.93778i	0.253800	+	0.468467i
$365$	−6.40118	+	36.3029i	−0.335053	+	1.90018i
$366$	4.58423	+	7.36445i	0.239621	+	0.384946i
$367$	0.0873127	+	0.495175i	0.00455769	+	0.0258479i	0.987002	−	0.160709i	$-0.0513781\pi$
$367$	0.0873127	+	0.495175i	0.00455769	+	0.0258479i	−0.982444	+	0.186557i	$0.940267\pi$
$368$	2.38867	+	4.13729i	0.124518	+	0.215671i
$369$	−16.0905	+	15.4318i	−0.837636	+	0.803346i
$370$	5.08149	+	8.80140i	0.264174	+	0.457563i
$371$	29.0860	−	9.70236i	1.51007	−	0.503721i
$372$	−2.79961	−	2.19506i	−0.145153	−	0.113809i
$373$	−3.29585	+	18.6917i	−0.170653	+	0.967819i	0.772390	+	0.635148i	$0.219061\pi$
$373$	−3.29585	+	18.6917i	−0.170653	+	0.967819i	−0.943043	+	0.332671i	$0.892050\pi$
$374$	0.0914571	−	0.518679i	0.00472913	−	0.0268202i
$375$	9.29882	−	8.34378i	0.480189	−	0.430871i
$376$	1.72888	−	1.45070i	0.0891601	−	0.0748142i
$377$	27.2778			1.40488
$378$	7.71781	+	11.3770i	0.396961	+	0.585168i
$379$	−4.15899			−0.213633			−0.106817	−	0.994279i	$-0.534066\pi$
$379$	−4.15899			−0.213633			−0.106817	+	0.994279i	$0.534066\pi$
$380$	−13.7551	+	11.5419i	−0.705624	+	0.592089i
$381$	−4.85395	−	23.0307i	−0.248675	−	1.17990i
$382$	1.90089	−	10.7805i	0.0972582	−	0.551578i
$383$	1.11348	−	6.31483i	0.0568959	−	0.322673i	−0.943054	−	0.332639i	$-0.892061\pi$
$383$	1.11348	−	6.31483i	0.0568959	−	0.322673i	0.999950	+	0.00996561i	$0.00317220\pi$
$384$	0.244004	−	1.71478i	0.0124518	−	0.0875069i
$385$	−0.951604	−	0.843466i	−0.0484982	−	0.0429870i
$386$	6.35843	+	11.0131i	0.323635	+	0.560553i
$387$	−2.98242	+	0.198246i	−0.151605	+	0.0100774i
$388$	−2.02404	−	3.50573i	−0.102755	−	0.177977i
$389$	−4.23532	−	24.0197i	−0.214739	−	1.21785i	−0.881358	−	0.472449i	$-0.843370\pi$
$389$	−4.23532	−	24.0197i	−0.214739	−	1.21785i	0.666619	−	0.745399i	$-0.267741\pi$
$390$	18.0156	−	0.598101i	0.912254	−	0.0302860i
$391$	2.46241	−	13.9650i	0.124529	−	0.706240i
$392$	−5.59817	+	4.20244i	−0.282750	+	0.212255i
$393$	0.557035	+	0.894863i	0.0280987	+	0.0451399i
$394$	17.7821	+	6.47214i	0.895848	+	0.326062i
$395$	17.6004	+	30.4848i	0.885573	+	1.53386i
$396$	0.429569	+	0.314363i	0.0215866	+	0.0157973i
$397$	−0.410570	+	0.711128i	−0.0206059	+	0.0356905i	−0.876144	−	0.482049i	$-0.839893\pi$
$397$	−0.410570	+	0.711128i	−0.0206059	+	0.0356905i	0.855539	+	0.517739i	$0.173226\pi$
$398$	−14.6861	−	5.34531i	−0.736148	−	0.267936i
$399$	−30.3775	+	0.184978i	−1.52078	+	0.00926048i
$400$	1.79029	+	1.50223i	0.0895146	+	0.0751117i
$401$	2.47609	+	2.07769i	0.123650	+	0.103755i	0.702516	−	0.711668i	$-0.252060\pi$
$401$	2.47609	+	2.07769i	0.123650	+	0.103755i	−0.578866	+	0.815423i	$0.696504\pi$
$402$	−17.3942	−	5.68481i	−0.867544	−	0.283533i
$403$	−7.41552	−	2.69903i	−0.369393	−	0.134448i
$404$	−1.74211	−	3.01743i	−0.0866734	−	0.150123i
$405$	24.1638	−	3.22667i	1.20071	−	0.160334i
$406$	2.75943	+	18.5804i	0.136948	+	0.922131i
$407$	0.115604	+	0.655624i	0.00573028	+	0.0324981i
$408$	−3.82657	+	3.43356i	−0.189443	+	0.169987i
$409$	6.33598	−	35.9332i	0.313294	−	1.77678i	−0.268335	−	0.963326i	$-0.586473\pi$
$409$	6.33598	−	35.9332i	0.313294	−	1.77678i	0.581629	−	0.813454i	$-0.302416\pi$
$410$	−18.9157	+	6.88475i	−0.934180	+	0.340014i
$411$	20.6552	+	16.1949i	1.01884	+	0.798834i
$412$	2.75678	+	1.00339i	0.135817	+	0.0494333i
$413$	−19.6375	−	7.75623i	−0.966297	−	0.381659i
$414$	11.5658	+	8.46396i	0.568427	+	0.415981i
$415$	28.8130			1.41437
$416$	−0.667169	−	3.78370i	−0.0327107	−	0.185511i
$417$	0.646135	−	0.0214511i	0.0316414	−	0.00105046i
$418$	−1.10530	+	0.402295i	−0.0540618	+	0.0196769i
$419$	0.0695245	−	0.394293i	0.00339649	−	0.0192625i	−0.983062	−	0.183271i	$-0.941331\pi$
$419$	0.0695245	−	0.394293i	0.00339649	−	0.0192625i	0.986459	+	0.164009i	$0.0524425\pi$
$420$	2.22986	+	12.2109i	0.108806	+	0.595831i
$421$	−21.2259	+	17.8107i	−1.03449	+	0.868039i	−0.991378	−	0.131031i	$-0.958171\pi$
$421$	−21.2259	+	17.8107i	−1.03449	+	0.868039i	−0.0431104	+	0.999070i	$0.513727\pi$
$422$	−20.4416			−0.995080
$423$	2.98898	−	6.07519i	0.145329	−	0.295386i
$424$	−11.5890			−0.562810
$425$	−1.20460	−	6.83165i	−0.0584319	−	0.331384i
$426$	−2.07971	+	14.6155i	−0.100762	+	0.708122i
$427$	−6.93389	+	11.2918i	−0.335555	+	0.546449i
$428$	−17.8780	+	6.50705i	−0.864164	+	0.314530i
$429$	1.12236	+	0.366812i	0.0541881	+	0.0177099i
$430$	−2.53601	−	0.923034i	−0.122297	−	0.0445126i
$431$	12.8050	−	22.1789i	0.616795	−	1.06832i	−0.373272	−	0.927722i	$-0.621764\pi$
$431$	12.8050	−	22.1789i	0.616795	−	1.06832i	0.990067	−	0.140598i	$-0.0449024\pi$
$432$	−1.40647	−	5.00218i	−0.0676686	−	0.240668i
$433$	23.6635			1.13719			0.568597	−	0.822616i	$-0.307486\pi$
$433$	23.6635			1.13719			0.568597	+	0.822616i	$0.307486\pi$
$434$	1.08830	−	5.32415i	0.0522401	−	0.255567i
$435$	31.6613	+	10.3476i	1.51804	+	0.496130i
$436$	9.77820	+	8.20489i	0.468291	+	0.392943i
$437$	−29.7592	+	10.8315i	−1.42358	+	0.518139i
$438$	21.8704	−	8.79248i	1.04501	−	0.420121i
$439$	−7.17946	−	40.7167i	−0.342657	−	1.94330i	−0.331761	−	0.943363i	$-0.607643\pi$
$439$	−7.17946	−	40.7167i	−0.342657	−	1.94330i	−0.0108955	−	0.999941i	$-0.503468\pi$
$440$	0.240311	+	0.416231i	0.0114564	+	0.0198430i
$441$	−10.2777	+	18.3131i	−0.489416	+	0.872050i
$442$	−5.70217	+	9.87644i	−0.271224	+	0.469774i
$443$	3.10579	+	1.13042i	0.147561	+	0.0537077i	0.414745	−	0.909938i	$-0.363871\pi$
$443$	3.10579	+	1.13042i	0.147561	+	0.0537077i	−0.267184	+	0.963646i	$0.586093\pi$
$444$	3.06078	−	5.73268i	0.145258	−	0.272061i
$445$	23.9079	+	20.0611i	1.13334	+	0.950986i
$446$	−10.7369	+	3.90792i	−0.508408	+	0.185045i
$447$	−10.4742	+	0.347735i	−0.495414	+	0.0164473i
$448$	2.50980	−	0.837206i	0.118577	−	0.0395543i
$449$	−1.00518	+	1.74103i	−0.0474375	+	0.0821641i	−0.888769	−	0.458355i	$-0.848439\pi$
$449$	−1.00518	+	1.74103i	−0.0474375	+	0.0821641i	0.841332	+	0.540519i	$0.181772\pi$
$450$	6.73290	+	1.95571i	0.317392	+	0.0921932i
$451$	−1.31862			−0.0620912
$452$	−1.31534	+	1.10370i	−0.0618682	+	0.0519136i
$453$	−0.816315	+	5.73678i	−0.0383538	+	0.269537i
$454$	−19.6857	−	16.5183i	−0.923895	−	0.775240i
$455$	13.1161	+	24.2098i	0.614891	+	1.13497i
$456$	10.9137	+	3.56685i	0.511083	+	0.167033i
$457$	31.0153	−	26.0249i	1.45083	−	1.21739i	0.518865	−	0.854856i	$-0.326355\pi$
$457$	31.0153	−	26.0249i	1.45083	−	1.21739i	0.931969	−	0.362538i	$-0.118090\pi$
$458$	−9.78538	+	16.9488i	−0.457241	+	0.791964i
$459$	−6.34596	+	14.0576i	−0.296204	+	0.656153i
$460$	6.47018	+	11.2067i	0.301674	+	0.522514i
$461$	−3.63234	−	20.6000i	−0.169175	−	0.959439i	−0.944655	−	0.328066i	$-0.893603\pi$
$461$	−3.63234	−	20.6000i	−0.169175	−	0.959439i	0.775480	−	0.631373i	$-0.217508\pi$
$462$	−0.136318	+	0.801608i	−0.00634207	+	0.0372942i
$463$	−0.370865	+	0.134984i	−0.0172356	+	0.00627323i	−0.350624	−	0.936516i	$-0.614030\pi$
$463$	−0.370865	+	0.134984i	−0.0172356	+	0.00627323i	0.333388	+	0.942790i	$0.391808\pi$
$464$	1.23286	−	6.99191i	0.0572342	−	0.324591i
$465$	−7.58332	−	5.94577i	−0.351668	−	0.275728i
$466$	12.2665	−	10.2928i	0.568235	−	0.476805i
$467$	6.47747	−	11.2193i	0.299742	−	0.519168i	−0.676335	−	0.736594i	$-0.736433\pi$
$467$	6.47747	−	11.2193i	0.299742	−	0.519168i	0.976077	+	0.217426i	$0.0697662\pi$
$468$	−6.41248	−	9.57778i	−0.296417	−	0.442733i
$469$	−4.10636	−	27.6499i	−0.189614	−	1.27675i
$470$	4.68301	−	3.92952i	0.216011	−	0.181255i
$471$	3.74759	−	0.124416i	0.172680	−	0.00573281i
$472$	6.11322	+	5.12960i	0.281384	+	0.236109i
$473$	−0.135426	−	0.113636i	−0.00622689	−	0.00522498i
$474$	10.6014	−	19.8559i	0.486939	−	0.912012i
$475$	−11.8679	+	9.95836i	−0.544537	+	0.456921i
$476$	−7.30422	−	2.88495i	−0.334788	−	0.132232i
$477$	−31.8096	+	14.0317i	−1.45646	+	0.642466i
$478$	0.251915	−	0.436330i	0.0115223	−	0.0199573i
$479$	−16.2565	+	13.6408i	−0.742777	+	0.623264i	−0.933582	−	0.358364i	$-0.883335\pi$
$479$	−16.2565	+	13.6408i	−0.742777	+	0.623264i	0.190805	+	0.981628i	$0.438890\pi$
$480$	0.660934	−	4.64482i	0.0301674	−	0.212006i
$481$	2.50320	−	14.1964i	0.114136	−	0.647299i
$482$	−5.27310	+	1.91925i	−0.240183	+	0.0874195i
$483$	−3.67024	+	21.5826i	−0.167002	+	0.982044i
$484$	−1.90466	−	10.8019i	−0.0865756	−	0.490995i
$485$	−5.48251	−	9.49599i	−0.248948	−	0.431191i
$486$	−9.91702	−	12.0272i	−0.449845	−	0.545563i
$487$	−3.24479	+	5.62015i	−0.147036	+	0.254673i	−0.930131	−	0.367229i	$-0.880307\pi$
$487$	−3.24479	+	5.62015i	−0.147036	+	0.254673i	0.783095	+	0.621902i	$0.213640\pi$
$488$	3.83661	−	3.21930i	0.173675	−	0.145731i
$489$	−7.60891	−	36.1023i	−0.344087	−	1.63260i
$490$	−15.1638	+	11.3831i	−0.685029	+	0.514238i
$491$	−9.79013	−	8.21489i	−0.441822	−	0.370733i	0.394568	−	0.918867i	$-0.370894\pi$
$491$	−9.79013	−	8.21489i	−0.441822	−	0.370733i	−0.836391	+	0.548134i	$0.815339\pi$
$492$	10.1294	+	7.94204i	0.456669	+	0.358055i
$493$	−16.1437	+	13.5461i	−0.727074	+	0.610088i
$494$	25.4692			1.14591
$495$	1.16357	+	0.851515i	0.0522987	+	0.0382728i
$496$	−1.02698	+	1.77877i	−0.0461126	+	0.0798693i
$497$	−21.3916	+	7.13571i	−0.959545	+	0.320081i
$498$	−9.73644	−	15.6413i	−0.436300	−	0.700905i
$499$	9.66766	−	3.51874i	0.432784	−	0.157520i	−0.116436	−	0.993198i	$-0.537147\pi$
$499$	9.66766	−	3.51874i	0.432784	−	0.157520i	0.549220	+	0.835678i	$0.314925\pi$
$500$	−5.52556	−	4.63649i	−0.247111	−	0.207350i
$501$	−5.39171	−	8.66165i	−0.240884	−	0.386974i
$502$	22.8599	+	8.32032i	1.02029	+	0.371354i
$503$	−5.54574	+	9.60550i	−0.247272	+	0.428288i	−0.962768	−	0.270329i	$-0.912868\pi$
$503$	−5.54574	+	9.60550i	−0.247272	+	0.428288i	0.715496	+	0.698617i	$0.246201\pi$
$504$	5.87527	−	5.33678i	0.261705	−	0.237719i
$505$	−4.71887	−	8.17332i	−0.209987	−	0.363708i
$506$	0.147197	+	0.834795i	0.00654370	+	0.0371112i
$507$	−2.40104	−	1.88256i	−0.106634	−	0.0836073i
$508$	−12.7694	+	4.64768i	−0.566550	+	0.206207i
$509$	−5.41656	−	4.54503i	−0.240085	−	0.201455i	0.514804	−	0.857308i	$-0.327865\pi$
$509$	−5.41656	−	4.54503i	−0.240085	−	0.201455i	−0.754889	+	0.655853i	$0.772309\pi$
$510$	−10.3650	+	9.30049i	−0.458971	+	0.411833i
$511$	26.9452	+	23.8832i	1.19198	+	1.05653i
$512$	−1.00000			−0.0441942
$513$	34.2749	−	3.42375i	1.51327	−	0.151162i
$514$	−2.24344	+	3.88576i	−0.0989540	+	0.171393i
$515$	7.46729	+	2.71787i	0.329048	+	0.119764i
$516$	0.355890	+	1.68860i	0.0156672	+	0.0743367i
$517$	0.376304	−	0.136964i	0.0165498	−	0.00602365i
$518$	9.92315	+	0.268960i	0.435998	+	0.0118174i
$519$	33.3793	+	26.1714i	1.46519	+	1.14880i
$520$	−1.80716	−	10.2489i	−0.0792493	−	0.449445i
$521$	17.5985			0.771003			0.385501	−	0.922707i	$-0.374028\pi$
$521$	17.5985			0.771003			0.385501	+	0.922707i	$0.374028\pi$
$522$	−5.08166	−	20.6842i	−0.222418	−	0.905324i
$523$	−40.7062			−1.77996			−0.889979	−	0.456002i	$-0.849281\pi$
$523$	−40.7062			−1.77996			−0.889979	+	0.456002i	$0.849281\pi$
$524$	0.466191	−	0.391181i	0.0203656	−	0.0170888i
$525$	1.92392	+	10.5355i	0.0839667	+	0.459808i
$526$	3.33918	−	18.9374i	0.145595	−	0.825711i
$527$	5.72902	−	2.08519i	0.249560	−	0.0908323i
$528$	0.144749	−	0.271107i	0.00629938	−	0.0117984i
$529$	−0.0307548	−	0.174419i	−0.00133716	−	0.00758343i
$530$	−31.3911			−1.36354
$531$	22.9905	+	6.67807i	0.997701	+	0.289804i
$532$	2.57647	+	17.3485i	0.111704	+	0.752152i
$533$	26.8304	+	9.76546i	1.16215	+	0.422989i
$534$	2.81140	−	19.7576i	0.121661	−	0.854994i
$535$	−48.4261	+	17.6256i	−2.09364	+	0.762023i
$536$	−1.83464	+	10.4048i	−0.0792445	+	0.449418i
$537$	−0.663483	−	3.14805i	−0.0286314	−	0.135849i
$538$	1.70439	+	9.66609i	0.0734816	+	0.416735i
$539$	−1.18845	+	0.360961i	−0.0511901	+	0.0155477i
$540$	−3.80970	−	13.5494i	−0.163943	−	0.583074i
$541$	−19.0647	−	33.0211i	−0.819657	−	1.41969i	−0.905935	−	0.423416i	$-0.860831\pi$
$541$	−19.0647	−	33.0211i	−0.819657	−	1.41969i	0.0862785	−	0.996271i	$-0.472502\pi$
$542$	−25.2203	−	9.17943i	−1.08330	−	0.394290i
$543$	9.55096	+	45.3168i	0.409871	+	1.94473i
$544$	2.27383	+	1.90797i	0.0974897	+	0.0818036i
$545$	26.4862	+	22.2246i	1.13455	+	0.951997i
$546$	8.71029	−	15.3011i	0.372766	−	0.654826i
$547$	−13.0678	−	4.75627i	−0.558737	−	0.203364i	0.0471873	−	0.998886i	$-0.484974\pi$
$547$	−13.0678	−	4.75627i	−0.558737	−	0.203364i	−0.605924	+	0.795523i	$0.707196\pi$
$548$	7.57688	−	13.1235i	0.323668	−	0.560610i
$549$	6.63294	−	13.4816i	0.283087	−	0.575383i
$550$	0.207340	+	0.359123i	0.00884101	+	0.0153131i
$551$	44.2262	+	16.0970i	1.88410	+	0.685757i
$552$	3.89724	−	7.29933i	0.165877	−	0.310680i
$553$	34.3701	+	0.931579i	1.46157	+	0.0396148i
$554$	−1.89970	+	10.7737i	−0.0807106	+	0.457732i
$555$	8.29073	−	15.5281i	0.351922	−	0.659132i
$556$	−0.0648145	−	0.367581i	−0.00274875	−	0.0155889i
$557$	11.2190	+	19.4318i	0.475363	+	0.823353i	0.999602	−	0.0282186i	$-0.00898346\pi$
$557$	11.2190	+	19.4318i	0.475363	+	0.823353i	−0.524239	+	0.851571i	$0.675650\pi$
$558$	−0.665162	+	6.12585i	−0.0281585	+	0.259328i
$559$	1.91399	+	3.31514i	0.0809533	+	0.140215i
$560$	6.79829	−	2.26774i	0.287280	−	0.0958296i
$561$	−0.846398	+	0.340275i	−0.0357349	+	0.0143664i
$562$	1.67319	−	9.48914i	0.0705794	−	0.400275i
$563$	−3.58845	+	20.3511i	−0.151235	+	0.857696i	0.810913	+	0.585167i	$0.198971\pi$
$563$	−3.58845	+	20.3511i	−0.151235	+	0.857696i	−0.962148	+	0.272529i	$0.912140\pi$
$564$	−3.71564	−	1.21435i	−0.156457	−	0.0511335i
$565$	−3.56285	+	2.98959i	−0.149890	+	0.125773i
$566$	28.0590			1.17941
$567$	9.66488	−	21.7621i	0.405887	−	0.913923i
$568$	8.52325			0.357627
$569$	−10.4665	+	8.78245i	−0.438779	+	0.368180i	−0.835252	−	0.549867i	$-0.814678\pi$
$569$	−10.4665	+	8.78245i	−0.438779	+	0.368180i	0.396473	+	0.918046i	$0.370234\pi$
$570$	29.5621	+	9.66153i	1.23822	+	0.404677i
$571$	−6.47937	+	36.7463i	−0.271153	+	1.53779i	0.479768	+	0.877395i	$0.340721\pi$
$571$	−6.47937	+	36.7463i	−0.271153	+	1.53779i	−0.750922	+	0.660391i	$0.770390\pi$
$572$	0.118380	−	0.671367i	0.00494972	−	0.0280713i
$573$	−17.5920	+	7.07246i	−0.734916	+	0.295456i
$574$	−3.93762	+	19.2635i	−0.164353	+	0.804044i
$575$	5.58246	+	9.66910i	0.232805	+	0.403229i
$576$	−2.74482	+	1.21078i	−0.114367	+	0.0504490i
$577$	−13.9415	−	24.1473i	−0.580391	−	1.00527i	−0.995433	−	0.0954644i	$-0.969566\pi$
$577$	−13.9415	−	24.1473i	−0.580391	−	1.00527i	0.415042	−	0.909802i	$-0.363767\pi$
$578$	1.42206	+	8.06493i	0.0591501	+	0.335457i
$579$	10.3741	−	19.4302i	0.431134	−	0.807492i
$580$	3.33945	−	18.9390i	0.138663	−	0.786398i
$581$	14.7269	−	23.9827i	0.610974	−	0.994969i
$582$	−3.30233	+	6.18509i	−0.136886	+	0.256380i
$583$	−1.93230	−	0.703298i	−0.0800275	−	0.0291276i
$584$	−6.80453	−	11.7858i	−0.281574	−	0.487700i
$585$	−17.3695	−	25.9434i	−0.718140	−	1.07263i
$586$	10.8468	−	18.7873i	0.448079	−	0.776096i
$587$	−25.3917	−	9.24182i	−1.04803	−	0.381451i	−0.240109	−	0.970746i	$-0.577183\pi$
$587$	−25.3917	−	9.24182i	−1.04803	−	0.381451i	−0.807918	+	0.589295i	$0.799406\pi$
$588$	11.3035	+	4.38519i	0.466150	+	0.180842i
$589$	−10.4302	−	8.75201i	−0.429770	−	0.360620i
$590$	16.5589	+	13.8946i	0.681718	+	0.572030i
$591$	−6.75939	−	32.0715i	−0.278044	−	1.31925i
$592$	−3.52571	−	1.28325i	−0.144906	−	0.0527413i
$593$	−8.84000	−	15.3113i	−0.363015	−	0.628761i	0.625440	−	0.780272i	$-0.284919\pi$
$593$	−8.84000	−	15.3113i	−0.363015	−	0.628761i	−0.988456	+	0.151511i	$0.951586\pi$
$594$	0.0690587	−	0.919397i	0.00283351	−	0.0377233i
$595$	−19.7849	−	7.81448i	−0.811104	−	0.320362i
$596$	1.05068	+	5.95871i	0.0430375	+	0.244078i
$597$	5.58254	+	26.4877i	0.228478	+	1.08407i
$598$	3.18729	−	18.0760i	0.130338	−	0.739183i
$599$	−5.28196	+	1.92248i	−0.215815	+	0.0785502i	−0.447665	−	0.894201i	$-0.647744\pi$
$599$	−5.28196	+	1.92248i	−0.215815	+	0.0785502i	0.231850	+	0.972752i	$0.425522\pi$
$600$	0.570253	−	4.00754i	0.0232805	−	0.163607i
$601$	−4.77864	−	1.73928i	−0.194925	−	0.0709468i	0.242713	−	0.970098i	$-0.421963\pi$
$601$	−4.77864	−	1.73928i	−0.194925	−	0.0709468i	−0.437638	+	0.899151i	$0.644185\pi$
$602$	−2.06450	+	1.63909i	−0.0841428	+	0.0668042i
$603$	7.56210	+	30.7805i	0.307953	+	1.25348i
$604$	3.34550			0.136126
$605$	−5.15916	−	29.2591i	−0.209750	−	1.18955i
$606$	−2.84235	+	5.32358i	−0.115463	+	0.216256i
$607$	15.8993	−	5.78687i	0.645332	−	0.234882i	0.00144124	−	0.999999i	$-0.499541\pi$
$607$	15.8993	−	5.78687i	0.645332	−	0.234882i	0.643891	+	0.765117i	$0.277319\pi$
$608$	1.15112	−	6.52832i	0.0466840	−	0.264758i
$609$	24.7956	−	21.0646i	1.00477	−	0.853581i
$610$	10.3922	−	8.72011i	0.420769	−	0.353067i
$611$	−8.67114			−0.350797
$612$	8.55137	+	2.48393i	0.345669	+	0.100407i
$613$	−40.0502			−1.61761			−0.808805	−	0.588077i	$-0.799885\pi$
$613$	−40.0502			−1.61761			−0.808805	+	0.588077i	$0.799885\pi$
$614$	−2.88230	−	16.3463i	−0.116320	−	0.659683i
$615$	27.4375	+	21.5126i	1.10639	+	0.867473i
$616$	0.469281	+	0.0127195i	0.0189079	+	0.000512484i
$617$	−39.3959	+	14.3389i	−1.58602	+	0.577263i	−0.976502	−	0.215510i	$-0.930859\pi$
$617$	−39.3959	+	14.3389i	−1.58602	+	0.577263i	−0.609516	+	0.792773i	$0.708636\pi$
$618$	−1.04792	−	4.97210i	−0.0421534	−	0.200007i
$619$	10.3367	+	3.76225i	0.415467	+	0.151218i	0.541292	−	0.840835i	$-0.317935\pi$
$619$	10.3367	+	3.76225i	0.415467	+	0.151218i	−0.125825	+	0.992052i	$0.540158\pi$
$620$	−2.78177	+	4.81817i	−0.111719	+	0.193502i
$621$	1.85935	−	24.7540i	0.0746131	−	0.993344i
$622$	−9.08715			−0.364361
$623$	28.9177	−	9.64624i	1.15857	−	0.386469i
$624$	−4.95303	+	4.44433i	−0.198280	+	0.177916i
$625$	−23.9186	−	20.0700i	−0.956742	−	0.802802i
$626$	26.0542	−	9.48296i	1.04134	−	0.379015i
$627$	1.60325	+	1.25704i	0.0640276	+	0.0502014i
$628$	−0.375924	−	2.13197i	−0.0150010	−	0.0850750i
$629$	5.56845	+	9.64484i	0.222029	+	0.384565i
$630$	15.9143	−	14.4557i	0.634042	−	0.575931i
$631$	5.94267	−	10.2930i	0.236574	−	0.409758i	−0.723155	−	0.690686i	$-0.757309\pi$
$631$	5.94267	−	10.2930i	0.236574	−	0.409758i	0.959729	+	0.280928i	$0.0906421\pi$
$632$	−12.2117	−	4.44471i	−0.485757	−	0.176801i
$633$	18.7106	+	30.0581i	0.743678	+	1.19470i
$634$	−0.119020	−	0.0998692i	−0.00472687	−	0.00396631i
$635$	−34.5884	+	12.5892i	−1.37260	+	0.499586i
$636$	10.6076	+	17.0409i	0.420619	+	0.675715i
$637$	26.8550	+	1.45684i	1.06404	+	0.0577223i
$638$	0.629879	−	1.09098i	0.0249371	−	0.0431924i
$639$	23.3947	−	10.3197i	0.925482	−	0.408243i
$640$	−2.70870			−0.107071
$641$	19.6892	−	16.5212i	0.777677	−	0.652549i	−0.164985	−	0.986296i	$-0.552758\pi$
$641$	19.6892	−	16.5212i	0.777677	−	0.652549i	0.942663	+	0.333747i	$0.108313\pi$
$642$	25.9323	+	20.3324i	1.02347	+	0.802457i
$643$	−24.6695	−	20.7001i	−0.972869	−	0.816334i	0.0101297	−	0.999949i	$-0.496776\pi$
$643$	−24.6695	−	20.7001i	−0.972869	−	0.816334i	−0.982998	+	0.183615i	$0.941220\pi$
$644$	12.6350	+	0.342463i	0.497888	+	0.0134949i
$645$	0.964000	+	4.57393i	0.0379575	+	0.180098i
$646$	−15.0733	+	12.6480i	−0.593051	+	0.497629i
$647$	16.8971	−	29.2666i	0.664292	−	1.15059i	−0.315185	−	0.949030i	$-0.602067\pi$
$647$	16.8971	−	29.2666i	0.664292	−	1.15059i	0.979477	−	0.201557i	$-0.0646001\pi$
$648$	−6.06804	+	6.64672i	−0.238375	+	0.261108i
$649$	0.707993	+	1.22628i	0.0277912	+	0.0481357i
$650$	−1.55922	−	8.84275i	−0.0611575	−	0.346841i
$651$	−8.82498	+	3.27302i	−0.345878	+	0.128280i
$652$	−20.0169	+	7.28556i	−0.783923	+	0.285325i
$653$	0.0985233	−	0.558753i	0.00385551	−	0.0218657i	−0.982819	−	0.184570i	$-0.940911\pi$
$653$	0.0985233	−	0.558753i	0.00385551	−	0.0218657i	0.986675	+	0.162705i	$0.0520218\pi$
$654$	3.11460	−	21.8883i	0.121790	−	0.855902i
$655$	1.26277	−	1.05959i	0.0493406	−	0.0414017i
$656$	3.71574	−	6.43585i	0.145075	−	0.251278i
$657$	−32.9472	−	24.1111i	−1.28539	−	0.940663i
$658$	−0.877175	−	5.90639i	−0.0341958	−	0.230255i
$659$	−15.5335	+	13.0341i	−0.605098	+	0.507738i	−0.893080	−	0.449898i	$-0.851460\pi$
$659$	−15.5335	+	13.0341i	−0.605098	+	0.507738i	0.287982	+	0.957636i	$0.407016\pi$
$660$	0.392081	−	0.734348i	0.0152617	−	0.0285844i
$661$	−20.8604	−	17.5039i	−0.811375	−	0.680824i	0.139561	−	0.990214i	$-0.455431\pi$
$661$	−20.8604	−	17.5039i	−0.811375	−	0.680824i	−0.950935	+	0.309389i	$0.899875\pi$
$662$	−6.30038	−	5.28664i	−0.244871	−	0.205471i
$663$	19.7420	−	0.655417i	0.766716	−	0.0254543i
$664$	−8.14857	+	6.83746i	−0.316226	+	0.265345i
$665$	6.97890	+	46.9919i	0.270630	+	1.82227i
$666$	−11.2311	+	0.746551i	−0.435198	+	0.0289282i
$667$	16.9590	−	29.3738i	0.656654	−	1.13736i
$668$	−4.51240	+	3.78636i	−0.174590	+	0.146498i
$669$	15.5741	+	12.2110i	0.602128	+	0.472104i
$670$	−4.96950	+	28.1834i	−0.191988	+	1.08882i
$671$	0.835069	−	0.303940i	0.0322375	−	0.0117335i
$672$	−3.52833	−	2.92419i	−0.136108	−	0.112803i
$673$	−2.12626	−	12.0586i	−0.0819614	−	0.464826i	−0.997971	−	0.0636700i	$-0.979720\pi$
$673$	−2.12626	−	12.0586i	−0.0819614	−	0.464826i	0.916010	−	0.401156i	$-0.131392\pi$
$674$	−6.04786	−	10.4752i	−0.232955	−	0.403490i
$675$	−3.28700	−	11.6904i	−0.126517	−	0.449964i
$676$	−0.880767	+	1.52553i	−0.0338757	+	0.0586744i
$677$	−22.9513	+	19.2584i	−0.882089	+	0.740160i	−0.966607	−	0.256262i	$-0.917509\pi$
$677$	−22.9513	+	19.2584i	−0.882089	+	0.740160i	0.0845188	+	0.996422i	$0.473065\pi$
$678$	2.82687	+	0.923885i	0.108565	+	0.0354816i
$679$	−10.7063	−	0.290186i	−0.410869	−	0.0111363i
$680$	6.15913	+	5.16812i	0.236192	+	0.198188i
$681$	−6.27038	+	44.0661i	−0.240281	+	1.68862i
$682$	−0.279182	+	0.234261i	−0.0106904	+	0.00897033i
$683$	−23.1631			−0.886312			−0.443156	−	0.896445i	$-0.646141\pi$
$683$	−23.1631			−0.886312			−0.443156	+	0.896445i	$0.646141\pi$
$684$	−4.74473	−	19.3128i	−0.181419	−	0.738443i
$685$	20.5235	−	35.5477i	0.784163	−	1.35821i
$686$	1.72433	+	18.4398i	0.0658351	+	0.704035i
$687$	33.8789	−	1.12475i	1.29256	−	0.0429118i
$688$	0.936248	−	0.340766i	0.0356941	−	0.0129916i
$689$	34.1087	+	28.6206i	1.29944	+	1.09036i
$690$	10.5565	−	19.7717i	0.401877	−	0.752696i
$691$	21.9628	+	7.99379i	0.835503	+	0.304098i	0.724115	−	0.689679i	$-0.242248\pi$
$691$	21.9628	+	7.99379i	0.835503	+	0.304098i	0.111387	+	0.993777i	$0.464471\pi$
$692$	12.2445	−	21.2080i	0.465464	−	0.806208i
$693$	1.30349	−	0.533281i	0.0495155	−	0.0202577i
$694$	8.65121	+	14.9843i	0.328395	+	0.568797i
$695$	−0.175563	−	0.995668i	−0.00665949	−	0.0377678i
$696$	−11.4096	+	4.58698i	−0.432481	+	0.173869i
$697$	−20.7284	+	7.54451i	−0.785143	+	0.285769i
$698$	−14.6631	−	12.3038i	−0.555005	−	0.465705i
$699$	−26.3627	−	8.61592i	−0.997130	−	0.325884i
$700$	5.86555	−	1.95660i	0.221697	−	0.0739526i
$701$	−0.320064			−0.0120886			−0.00604432	−	0.999982i	$-0.501924\pi$
$701$	−0.320064			−0.0120886			−0.00604432	+	0.999982i	$0.501924\pi$
$702$	−8.21407	+	18.1959i	−0.310020	+	0.686760i
$703$	12.4360	−	21.5398i	0.469032	−	0.812388i
$704$	−0.166736	−	0.0606869i	−0.00628409	−	0.00228722i
$705$	−10.0646	−	3.28932i	−0.379054	−	0.123883i
$706$	7.71249	−	2.80712i	0.290264	−	0.105647i
$707$	−9.21502	−	0.249767i	−0.346566	−	0.00939344i
$708$	1.94721	−	13.6843i	0.0731807	−	0.514289i
$709$	6.08606	+	34.5158i	0.228567	+	1.29627i	0.855748	+	0.517393i	$0.173098\pi$
$709$	6.08606	+	34.5158i	0.228567	+	1.29627i	−0.627181	+	0.778874i	$0.715791\pi$
$710$	23.0869			0.866437
$711$	−38.9006	+	2.58578i	−1.45888	+	0.0969742i
$712$	−11.5219			−0.431803
$713$	−7.51674	+	6.30729i	−0.281504	+	0.236210i
$714$	2.44355	+	13.3811i	0.0914475	+	0.500774i
$715$	0.320656	−	1.81853i	0.0119919	−	0.0680093i
$716$	−1.74544	+	0.635288i	−0.0652301	+	0.0237418i
$717$	−0.872179	+	0.0289556i	−0.0325721	+	0.00108136i
$718$	1.25651	+	7.12600i	0.0468924	+	0.265940i
$719$	9.37869			0.349766			0.174883	−	0.984589i	$-0.444045\pi$
$719$	9.37869			0.349766			0.174883	+	0.984589i	$0.444045\pi$
$720$	−7.43489	+	3.27963i	−0.277082	+	0.122225i
$721$	6.07892	−	4.82629i	0.226391	−	0.179740i
$722$	23.4397	+	8.53137i	0.872337	+	0.317505i
$723$	7.64871	+	5.99704i	0.284459	+	0.223032i
$724$	25.1259	−	9.14509i	0.933798	−	0.339875i
$725$	2.88127	−	16.3405i	0.107008	−	0.606871i
$726$	−14.1401	+	12.6879i	−0.524789	+	0.470891i
$727$	3.06199	+	17.3654i	0.113563	+	0.644047i	0.987452	+	0.157921i	$0.0504792\pi$
$727$	3.06199	+	17.3654i	0.113563	+	0.644047i	−0.873889	+	0.486126i	$0.838410\pi$
$728$	−9.45443	−	3.73423i	−0.350405	−	0.138400i
$729$	−8.60796	+	25.5911i	−0.318813	+	0.947817i
$730$	−18.4315	−	31.9242i	−0.682179	−	1.18157i
$731$	−2.77904	−	1.01149i	−0.102787	−	0.0374112i
$732$	−8.24550	−	2.69481i	−0.304762	−	0.0996030i
$733$	3.49856	+	2.93564i	0.129222	+	0.108430i	0.705108	−	0.709100i	$-0.250898\pi$
$733$	3.49856	+	2.93564i	0.129222	+	0.108430i	−0.575886	+	0.817530i	$0.695343\pi$
$734$	−0.385178	−	0.323203i	−0.0142172	−	0.0119296i
$735$	30.6179	+	11.8782i	1.12936	+	0.438133i
$736$	−4.48922	−	1.63394i	−0.165475	−	0.0602280i
$737$	−0.937334	+	1.62351i	−0.0345271	+	0.0598027i
$738$	2.40665	−	22.1642i	0.0885900	−	0.815874i
$739$	22.3693	+	38.7448i	0.822868	+	1.42525i	0.903538	+	0.428508i	$0.140961\pi$
$739$	22.3693	+	38.7448i	0.822868	+	1.42525i	−0.0806701	+	0.996741i	$0.525706\pi$
$740$	−9.55008	−	3.47595i	−0.351068	−	0.127778i
$741$	−23.3125	−	37.4509i	−0.856406	−	1.37579i
$742$	−16.0446	+	26.1285i	−0.589016	+	0.959209i
$743$	−1.12966	+	6.40660i	−0.0414431	+	0.235035i	−0.998492	−	0.0548897i	$-0.982519\pi$
$743$	−1.12966	+	6.40660i	−0.0414431	+	0.235035i	0.957049	+	0.289925i	$0.0936304\pi$
$744$	3.55559	−	0.118042i	0.130354	−	0.00432764i
$745$	2.84598	+	16.1404i	0.104269	+	0.591337i
$746$	−9.49002	−	16.4372i	−0.347454	−	0.601808i
$747$	−14.0877	+	28.6337i	−0.515441	+	1.04765i
$748$	0.263340	+	0.456119i	0.00962867	+	0.0166773i
$749$	−10.0807	+	49.3166i	−0.368341	+	1.80199i
$750$	−1.76003	+	12.3689i	−0.0642671	+	0.451647i
$751$	−9.24817	+	52.4490i	−0.337471	+	1.91389i	0.0638624	+	0.997959i	$0.479658\pi$
$751$	−9.24817	+	52.4490i	−0.337471	+	1.91389i	−0.401333	+	0.915932i	$0.631453\pi$
$752$	−0.391905	+	2.22260i	−0.0142913	+	0.0810500i
$753$	−8.68959	−	41.2298i	−0.316666	−	1.50250i
$754$	−20.8960	+	17.5339i	−0.760989	+	0.638545i
$755$	9.06195			0.329798
$756$	−13.2252	−	3.75436i	−0.480994	−	0.136545i
$757$	−8.69526			−0.316035			−0.158017	−	0.987436i	$-0.550510\pi$
$757$	−8.69526			−0.316035			−0.158017	+	0.987436i	$0.550510\pi$
$758$	3.18597	−	2.67335i	0.115720	−	0.0971004i
$759$	1.09278	−	0.980548i	0.0396655	−	0.0355916i
$760$	3.11804	−	17.6833i	0.113103	−	0.641440i
$761$	1.02044	−	5.78723i	0.0369911	−	0.209787i	−0.960710	−	0.277554i	$-0.910476\pi$
$761$	1.02044	−	5.78723i	0.0369911	−	0.209787i	0.997701	+	0.0677669i	$0.0215874\pi$
$762$	18.5222	+	14.5225i	0.670988	+	0.526094i
$763$	32.0364	−	10.6866i	1.15980	−	0.386879i
$764$	5.47340	+	9.48021i	0.198021	+	0.342982i
$765$	23.1631	+	6.72822i	0.837464	+	0.243259i
$766$	3.20613	+	5.55317i	0.115842	+	0.200644i
$767$	−5.32417	−	30.1949i	−0.192245	−	1.09027i
$768$	0.915320	+	1.47044i	0.0330288	+	0.0530599i
$769$	4.78310	−	27.1263i	0.172483	−	0.978200i	−0.768526	−	0.639819i	$-0.779009\pi$
$769$	4.78310	−	27.1263i	0.172483	−	0.978200i	0.941009	−	0.338382i	$-0.109879\pi$
$770$	1.27114	+	0.0344534i	0.0458087	+	0.00124161i
$771$	7.76723	−	0.257865i	0.279730	−	0.00928678i
$772$	−11.9499	−	4.34942i	−0.430088	−	0.156539i
$773$	0.136031	+	0.235612i	0.00489268	+	0.00847437i	0.868461	−	0.495757i	$-0.165109\pi$
$773$	0.136031	+	0.235612i	0.00489268	+	0.00847437i	−0.863569	+	0.504231i	$0.831776\pi$
$774$	2.15724	−	2.06893i	0.0775403	−	0.0743661i
$775$	−2.40010	+	4.15710i	−0.0862143	+	0.149328i
$776$	3.80394	+	1.38452i	0.136554	+	0.0497015i
$777$	−8.68737	−	14.8376i	−0.311658	−	0.532295i
$778$	18.6840	+	15.6778i	0.669855	+	0.562075i
$779$	37.7381	+	31.6660i	1.35211	+	1.13455i
$780$	−13.4163	+	12.0384i	−0.480380	+	0.431043i
$781$	1.42113	+	0.517249i	0.0508520	+	0.0185086i
$782$	7.09022	+	12.2806i	0.253546	+	0.439154i
$783$	−25.7635	+	26.4049i	−0.920714	+	0.943636i
$784$	1.58717	−	6.81769i	0.0566848	−	0.243489i
$785$	−1.01827	−	5.77488i	−0.0363435	−	0.206114i
$786$	−1.00192	−	0.327450i	−0.0357373	−	0.0116797i
$787$	−1.84354	+	10.4552i	−0.0657150	+	0.372688i	0.934160	+	0.356855i	$0.116151\pi$
$787$	−1.84354	+	10.4552i	−0.0657150	+	0.372688i	−0.999875	+	0.0158330i	$0.994960\pi$
$788$	−17.7821	+	6.47214i	−0.633460	+	0.230561i
$789$	−30.9027	+	12.4237i	−1.10017	+	0.442297i
$790$	−33.0780	−	12.0394i	−1.17686	−	0.428342i
$791$	0.667358	+	4.49360i	0.0237285	+	0.159774i
$792$	−0.531137	+	0.0353055i	−0.0188731	+	0.00125453i
$793$	−19.2424			−0.683317
$794$	−0.142589	−	0.808665i	−0.00506031	−	0.0286984i
$795$	28.7329	+	46.1586i	1.01905	+	1.63708i
$796$	14.6861	−	5.34531i	0.520535	−	0.189459i
$797$	−4.14074	+	23.4833i	−0.146672	+	0.831820i	0.819337	+	0.573313i	$0.194342\pi$
$797$	−4.14074	+	23.4833i	−0.146672	+	0.831820i	−0.966009	+	0.258508i	$0.916769\pi$
$798$	23.1516	−	19.6680i	0.819557	−	0.696238i
$799$	5.13179	−	4.30608i	0.181550	−	0.152338i
$800$	−2.33706			−0.0826276
$801$	−31.6256	+	13.9505i	−1.11744	+	0.492917i
$802$	−3.23231			−0.114137
$803$	−0.419316	−	2.37806i	−0.0147973	−	0.0839199i
$804$	16.9789	−	6.82597i	0.598798	−	0.240733i
$805$	34.2244	+	0.927629i	1.20625	+	0.0326946i
$806$	7.41552	−	2.69903i	0.261201	−	0.0950692i
$807$	12.6533	−	11.3538i	0.445418	−	0.399672i
$808$	3.27410	+	1.19168i	0.115183	+	0.0419230i
$809$	−22.6759	+	39.2758i	−0.797242	+	1.38086i	0.124164	+	0.992262i	$0.460375\pi$
$809$	−22.6759	+	39.2758i	−0.797242	+	1.38086i	−0.921406	+	0.388602i	$0.872958\pi$
$810$	−16.4365	+	18.0040i	−0.577520	+	0.632595i
$811$	−6.37444			−0.223837			−0.111918	−	0.993717i	$-0.535700\pi$
$811$	−6.37444			−0.223837			−0.111918	+	0.993717i	$0.535700\pi$
$812$	−14.0571	−	12.4597i	−0.493308	−	0.437250i
$813$	9.58683	+	45.4870i	0.336225	+	1.59530i
$814$	−0.509985	−	0.427928i	−0.0178750	−	0.0149989i
$815$	−54.2199	+	19.7344i	−1.89924	+	0.691266i
$816$	0.724271	−	5.08993i	0.0253546	−	0.178183i
$817$	1.14690	+	6.50439i	0.0401249	+	0.227560i
$818$	18.2437	+	31.5991i	0.637877	+	1.10484i
$819$	−30.4720	+	1.19744i	−1.06478	+	0.0418419i
$820$	10.0648	−	17.4328i	0.351479	−	0.608780i
$821$	−41.1405	−	14.9739i	−1.43581	−	0.522593i	−0.497222	−	0.867623i	$-0.665647\pi$
$821$	−41.1405	−	14.9739i	−1.43581	−	0.522593i	−0.938592	+	0.345030i	$0.887869\pi$
$822$	−26.2326	+	0.870899i	−0.914968	+	0.0303761i
$823$	1.88895	+	1.58502i	0.0658448	+	0.0552504i	0.675116	−	0.737711i	$-0.264094\pi$
$823$	1.88895	+	1.58502i	0.0658448	+	0.0552504i	−0.609271	+	0.792962i	$0.708538\pi$
$824$	−2.75678	+	1.00339i	−0.0960370	+	0.0349546i
$825$	0.338287	−	0.633593i	0.0117776	−	0.0220589i
$826$	20.0288	−	6.68111i	0.696891	−	0.232465i
$827$	15.7313	−	27.2475i	0.547033	−	0.947488i	−0.451443	−	0.892300i	$-0.649091\pi$
$827$	15.7313	−	27.2475i	0.547033	−	0.947488i	0.998476	−	0.0551884i	$-0.0175759\pi$
$828$	−14.3004	+	0.950571i	−0.496974	+	0.0330346i
$829$	14.2115			0.493587			0.246793	−	0.969068i	$-0.420623\pi$
$829$	14.2115			0.493587			0.246793	+	0.969068i	$0.420623\pi$
$830$	−22.0720	+	18.5206i	−0.766131	+	0.642860i
$831$	17.5810	−	7.06802i	0.609877	−	0.245187i
$832$	2.94320	+	2.46964i	0.102037	+	0.0856193i
$833$	−16.6169	+	12.4740i	−0.575742	+	0.432198i
$834$	−0.481180	+	0.431760i	−0.0166619	+	0.0149506i
$835$	−12.2228	+	10.2561i	−0.422986	+	0.354927i
$836$	0.588116	−	1.01865i	0.0203404	−	0.0352306i
$837$	9.61652	−	4.62903i	0.332395	−	0.160003i
$838$	0.200188	+	0.346736i	0.00691537	+	0.0119778i
$839$	−5.90110	−	33.4668i	−0.203729	−	1.15540i	−0.899428	−	0.437070i	$-0.856016\pi$
$839$	−5.90110	−	33.4668i	−0.203729	−	1.15540i	0.695699	−	0.718333i	$-0.255095\pi$
$840$	−9.55719	−	7.92076i	−0.329754	−	0.273292i
$841$	−20.1157	+	7.32152i	−0.693645	+	0.252466i
$842$	4.81153	−	27.2875i	0.165816	−	0.940390i
$843$	−15.4847	+	6.22527i	−0.533322	+	0.214410i
$844$	15.6591	−	13.1396i	0.539010	−	0.452283i
$845$	−2.38574	+	4.13221i	−0.0820718	+	0.142153i
$846$	1.61537	+	6.57515i	0.0555375	+	0.226058i
$847$	−26.9909	−	10.6606i	−0.927419	−	0.366304i
$848$	8.87767	−	7.44925i	0.304860	−	0.255808i
$849$	−25.6830	−	41.2591i	−0.881438	−	1.41601i
$850$	5.31408	+	4.45904i	0.182271	+	0.152944i
$851$	−13.7309	−	11.5216i	−0.470690	−	0.394956i
$852$	−7.80150	−	12.5329i	−0.267275	−	0.429370i
$853$	−21.9409	+	18.4106i	−0.751242	+	0.630367i	−0.935831	−	0.352449i	$-0.885349\pi$
$853$	−21.9409	+	18.4106i	−0.751242	+	0.630367i	0.184589	+	0.982816i	$0.440905\pi$
$854$	−1.94657	−	13.1071i	−0.0666101	−	0.448514i
$855$	−12.8520	−	52.3126i	−0.439531	−	1.78905i
$856$	9.51267	−	16.4764i	0.325136	−	0.563153i
$857$	17.3552	−	14.5627i	0.592842	−	0.497454i	−0.296294	−	0.955097i	$-0.595751\pi$
$857$	17.3552	−	14.5627i	0.592842	−	0.497454i	0.889136	+	0.457643i	$0.151306\pi$
$858$	−1.09556	+	0.440445i	−0.0374018	+	0.0150365i
$859$	−3.57537	+	20.2770i	−0.121990	+	0.691841i	0.861060	+	0.508503i	$0.169801\pi$
$859$	−3.57537	+	20.2770i	−0.121990	+	0.691841i	−0.983050	+	0.183337i	$0.941310\pi$
$860$	2.53601	−	0.923034i	0.0864774	−	0.0314752i
$861$	31.9300	−	11.8423i	1.08817	−	0.403583i
$862$	4.44713	+	25.2209i	0.151470	+	0.859027i
$863$	−8.15261	−	14.1207i	−0.277518	−	0.480676i	0.693249	−	0.720698i	$-0.256179\pi$
$863$	−8.15261	−	14.1207i	−0.277518	−	0.480676i	−0.970767	+	0.240022i	$0.922845\pi$
$864$	4.29276	+	2.92784i	0.146043	+	0.0996070i
$865$	33.1666	−	57.4462i	1.12770	−	1.95323i
$866$	−18.1273	+	15.2106i	−0.615990	+	0.516877i
$867$	10.5573	−	9.47305i	0.358546	−	0.321722i
$868$	2.58861	+	4.77808i	0.0878632	+	0.162179i
$869$	−1.76640	−	1.48218i	−0.0599210	−	0.0502797i
$870$	−30.9053	+	12.4248i	−1.04779	+	0.421239i
$871$	31.0957	−	26.0924i	1.05364	−	0.884108i
$872$	−12.7645			−0.432262
$873$	12.1175	−	0.805466i	0.410115	−	0.0272609i
$874$	15.8345	−	27.4262i	0.535611	−	0.927706i
$875$	−18.1034	+	6.03886i	−0.612008	+	0.204151i
$876$	−11.1020	+	20.7934i	−0.375101	+	0.702545i
$877$	−0.193806	+	0.0705395i	−0.00654436	+	0.00238195i	−0.345290	−	0.938496i	$-0.612220\pi$
$877$	−0.193806	+	0.0705395i	−0.00654436	+	0.00238195i	0.338746	+	0.940878i	$0.389997\pi$
$878$	31.6720	+	26.5760i	1.06888	+	0.896895i
$879$	−37.5539	+	1.24675i	−1.26666	+	0.0420520i
$880$	−0.451637	−	0.164383i	−0.0152247	−	0.00554133i
$881$	−8.11471	+	14.0551i	−0.273392	+	0.473528i	−0.969728	−	0.244187i	$-0.921479\pi$
$881$	−8.11471	+	14.0551i	−0.273392	+	0.473528i	0.696336	+	0.717715i	$0.254812\pi$
$882$	−3.89820	−	20.6350i	−0.131259	−	0.694817i
$883$	3.36832	+	5.83410i	0.113353	+	0.196333i	0.917120	−	0.398611i	$-0.130508\pi$
$883$	3.36832	+	5.83410i	0.113353	+	0.196333i	−0.803767	+	0.594944i	$0.797174\pi$
$884$	−1.98034	−	11.2311i	−0.0666061	−	0.377742i
$885$	5.27441	−	37.0668i	0.177297	−	1.24599i
$886$	−3.10579	+	1.13042i	−0.104341	+	0.0379771i
$887$	−7.72075	−	6.47848i	−0.259237	−	0.217526i	0.503900	−	0.863762i	$-0.331898\pi$
$887$	−7.72075	−	6.47848i	−0.259237	−	0.217526i	−0.763138	+	0.646236i	$0.776342\pi$
$888$	1.34020	+	6.35892i	0.0449743	+	0.213391i
$889$	−7.20017	+	35.2245i	−0.241486	+	1.18139i
$890$	−31.2095			−1.04614
$891$	−1.41513	+	0.739996i	−0.0474086	+	0.0247908i
$892$	5.71299	−	9.89519i	0.191285	−	0.331316i
$893$	−14.0587	−	5.11696i	−0.470458	−	0.171233i
$894$	7.80020	−	6.99908i	0.260878	−	0.234084i
$895$	−4.72787	+	1.72081i	−0.158035	+	0.0575202i
$896$	−1.38447	+	2.25460i	−0.0462519	+	0.0753210i
$897$	−29.4970	+	11.8586i	−0.984878	+	0.395948i
$898$	−0.349096	−	1.97982i	−0.0116495	−	0.0660675i
$899$	14.5826			0.486356
$900$	−6.41481	+	2.82966i	−0.213827	+	0.0943220i
$901$	−34.3993			−1.14601
$902$	1.01012	−	0.847590i	0.0336333	−	0.0282217i
$903$	4.29985	+	1.53543i	0.143090	+	0.0510960i
$904$	0.298163	−	1.69096i	0.00991674	−	0.0562406i
$905$	68.0586	−	24.7713i	2.26235	−	0.823426i
$906$	−3.06220	−	4.91935i	−0.101735	−	0.163434i
$907$	−6.33594	−	35.9329i	−0.210382	−	1.19313i	−0.888743	−	0.458405i	$-0.848421\pi$
$907$	−6.33594	−	35.9329i	−0.210382	−	1.19313i	0.678362	−	0.734728i	$-0.262690\pi$
$908$	25.6978			0.852813
$909$	10.4297	−	0.693275i	0.345930	−	0.0229945i
$910$	−25.6092	−	10.1149i	−0.848938	−	0.335306i
$911$	10.4193	+	3.79232i	0.345207	+	0.125645i	0.508804	−	0.860882i	$-0.330088\pi$
$911$	10.4193	+	3.79232i	0.345207	+	0.125645i	−0.163598	+	0.986527i	$0.552310\pi$
$912$	−10.6531	+	4.28285i	−0.352761	+	0.141819i
$913$	−1.77360	+	0.645538i	−0.0586976	+	0.0213642i
$914$	−7.03060	+	39.8725i	−0.232551	+	1.31886i
$915$	−22.3346	−	7.29943i	−0.738359	−	0.241312i
$916$	−3.39843	−	19.2734i	−0.112287	−	0.636812i
$917$	−0.236530	−	1.59265i	−0.00781090	−	0.0525941i
$918$	−4.17478	−	14.8479i	−0.137788	−	0.490052i
$919$	7.68593	+	13.3124i	0.253535	+	0.439136i	0.964497	−	0.264095i	$-0.0850732\pi$
$919$	7.68593	+	13.3124i	0.253535	+	0.439136i	−0.710961	+	0.703231i	$0.751740\pi$
$920$	−12.1600	−	4.42586i	−0.400902	−	0.145916i
$921$	−21.3980	+	19.2003i	−0.705089	+	0.632673i
$922$	16.0240	+	13.4457i	0.527722	+	0.442811i
$923$	−25.0856	−	21.0493i	−0.825703	−	0.692847i
$924$	−0.410838	−	0.701691i	−0.0135156	−	0.0230839i
$925$	−8.23979	−	2.99904i	−0.270923	−	0.0986078i
$926$	0.197333	−	0.341791i	0.00648477	−	0.0112320i
$927$	−6.35198	+	6.09196i	−0.208626	+	0.200086i
$928$	3.54988	+	6.14858i	0.116531	+	0.201837i
$929$	−4.71640	−	1.71663i	−0.154740	−	0.0563208i	0.263489	−	0.964662i	$-0.415127\pi$
$929$	−4.71640	−	1.71663i	−0.154740	−	0.0563208i	−0.418229	+	0.908342i	$0.637349\pi$
$930$	9.63103	−	0.319741i	0.315814	−	0.0104847i
$931$	42.6810	+	18.2096i	1.39881	+	0.596794i
$932$	−2.78059	+	15.7695i	−0.0910813	+	0.516547i
$933$	8.31765	+	13.3621i	0.272308	+	0.437455i
$934$	2.24960	+	12.7581i	0.0736092	+	0.417459i
$935$	0.713310	+	1.23549i	0.0233277	+	0.0404048i
$936$	11.0687	+	3.21515i	0.361793	+	0.105090i
$937$	25.1330	+	43.5316i	0.821059	+	1.42212i	0.904895	+	0.425636i	$0.139950\pi$
$937$	25.1330	+	43.5316i	0.821059	+	1.42212i	−0.0838358	+	0.996480i	$0.526717\pi$
$938$	20.9186	+	18.5415i	0.683018	+	0.605401i
$939$	−37.7920	−	29.6312i	−1.23330	−	0.966977i
$940$	−1.06155	+	6.02037i	−0.0346240	+	0.196363i
$941$	5.32699	−	30.2108i	0.173655	−	0.984845i	−0.766030	−	0.642805i	$-0.777771\pi$
$941$	5.32699	−	30.2108i	0.173655	−	0.984845i	0.939685	−	0.342041i	$-0.111118\pi$
$942$	−2.79084	+	2.50421i	−0.0909306	+	0.0815916i
$943$	27.1966	−	22.8207i	0.885643	−	0.743143i
$944$	−7.98024			−0.259735
$945$	−35.8230	−	10.1694i	−1.16532	−	0.330811i
$946$	0.176786			0.00574781
$947$	−37.3438	+	31.3352i	−1.21351	+	1.01826i	−0.214373	+	0.976752i	$0.568771\pi$
$947$	−37.3438	+	31.3352i	−1.21351	+	1.01826i	−0.999138	+	0.0415046i	$0.986785\pi$
$948$	4.64198	+	22.0250i	0.150764	+	0.715337i
$949$	−9.07955	+	51.4927i	−0.294735	+	1.67152i
$950$	2.69024	−	15.2571i	0.0872828	−	0.495005i
$951$	−0.0379107	+	0.266423i	−0.00122934	+	0.00863936i
$952$	7.44977	−	2.48506i	0.241448	−	0.0805412i
$953$	−2.37877	−	4.12014i	−0.0770558	−	0.133465i	0.824923	−	0.565246i	$-0.191219\pi$
$953$	−2.37877	−	4.12014i	−0.0770558	−	0.133465i	−0.901978	+	0.431781i	$0.857885\pi$
$954$	15.3482	−	31.1957i	0.496916	−	1.01000i
$955$	14.8258	+	25.6791i	0.479752	+	0.830955i
$956$	0.0874892	+	0.496176i	0.00282960	+	0.0160475i
$957$	−2.18076	+	0.0723994i	−0.0704941	+	0.00234034i
$958$	3.68504	−	20.8989i	0.119058	−	0.675213i
$959$	−19.0984	−	35.2520i	−0.616720	−	1.13835i
$960$	2.47933	+	3.98298i	0.0800200	+	0.128550i
$961$	25.1662	+	9.15974i	0.811812	+	0.295475i
$962$	7.20769	+	12.4841i	0.232385	+	0.402503i
$963$	6.16126	−	56.7425i	0.198544	−	1.82850i
$964$	2.80576	−	4.85971i	0.0903674	−	0.156521i
$965$	−32.3688	−	11.7813i	−1.04199	−	0.379253i
$966$	−11.0615	−	18.8924i	−0.355897	−	0.607854i
$967$	−39.1724	−	32.8696i	−1.25970	−	1.05701i	−0.995714	−	0.0924884i	$-0.970518\pi$
$967$	−39.1724	−	32.8696i	−1.25970	−	1.05701i	−0.263987	−	0.964526i	$-0.585038\pi$
$968$	8.40237	+	7.05043i	0.270062	+	0.226609i
$969$	32.3950	+	10.5874i	1.04068	+	0.340116i
$970$	10.3037	+	3.75026i	0.330833	+	0.120414i
$971$	9.71365	+	16.8245i	0.311726	+	0.539925i	0.978736	−	0.205124i	$-0.0657597\pi$
$971$	9.71365	+	16.8245i	0.311726	+	0.539925i	−0.667010	+	0.745048i	$0.732426\pi$
$972$	15.3278	+	2.83881i	0.491639	+	0.0910547i
$973$	−0.918484	−	0.362775i	−0.0294453	−	0.0116300i
$974$	−1.12691	−	6.39100i	−0.0361084	−	0.204781i
$975$	−11.5755	+	10.3867i	−0.370714	+	0.332640i
$976$	−0.869688	+	4.93225i	−0.0278380	+	0.157877i
$977$	39.2510	−	14.2862i	1.25575	−	0.457055i	0.373409	−	0.927667i	$-0.378189\pi$
$977$	39.2510	−	14.2862i	1.25575	−	0.457055i	0.882341	+	0.470611i	$0.155967\pi$
$978$	29.0349	+	22.7650i	0.928432	+	0.727946i
$979$	−1.92112	−	0.699231i	−0.0613993	−	0.0223475i
$980$	4.29918	−	18.4671i	0.137332	−	0.589909i
$981$	−35.0363	+	15.4550i	−1.11862	+	0.493440i
$982$	12.7801			0.407830
$983$	1.37556	+	7.80121i	0.0438737	+	0.248820i	0.998855	−	0.0478470i	$-0.0152360\pi$
$983$	1.37556	+	7.80121i	0.0438737	+	0.248820i	−0.954981	+	0.296667i	$0.904125\pi$
$984$	−12.8646	+	0.427094i	−0.410109	+	0.0136152i
$985$	−48.1663	+	17.5311i	−1.53471	+	0.558587i
$986$	3.65947	−	20.7539i	0.116541	−	0.660939i
$987$	−7.88209	+	6.69607i	−0.250890	+	0.213138i
$988$	−19.5106	+	16.3713i	−0.620714	+	0.520841i
$989$	4.75982			0.151353
$990$	−1.43869	+	0.0956320i	−0.0457246	+	0.00303938i
$991$	−6.46702			−0.205432			−0.102716	−	0.994711i	$-0.532753\pi$
$991$	−6.46702			−0.205432			−0.102716	+	0.994711i	$0.532753\pi$
$992$	−0.356665	−	2.02275i	−0.0113241	−	0.0642223i
$993$	−2.00683	+	14.1033i	−0.0636847	+	0.447554i
$994$	11.8002	−	19.2165i	0.374279	−	0.609512i
$995$	39.7803	−	14.4788i	1.26112	−	0.459010i
$996$	17.5126	+	5.72351i	0.554908	+	0.181356i
$997$	19.7595	+	7.19188i	0.625791	+	0.227769i	0.635398	−	0.772185i	$-0.280836\pi$
$997$	19.7595	+	7.19188i	0.625791	+	0.227769i	−0.00960744	+	0.999954i	$0.503058\pi$
$998$	−5.14405	+	8.90976i	−0.162832	+	0.282034i
$999$	11.3778	+	15.8314i	0.359979	+	0.500883i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.v.a.67.12	✓	72
7.2	even	3		378.2.w.b.121.3	yes	72
27.25	even	9		378.2.w.b.25.3	yes	72
189.79	even	9	inner	378.2.v.a.79.12	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.v.a.67.12	✓	72	1.1	even	1	trivial
378.2.v.a.79.12	yes	72	189.79	even	9	inner
378.2.w.b.25.3	yes	72	27.25	even	9
378.2.w.b.121.3	yes	72	7.2	even	3

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)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(1.64636 + 0.538065i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.470361 - 2.66755i) q^{5} +(-1.60704 + 0.646075i) q^{6} +(-1.97994 - 1.75495i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.42097 + 1.77169i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(1.64636 + 0.538065i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.470361 - 2.66755i) q^{5} +(-1.60704 + 0.646075i) q^{6} +(-1.97994 - 1.75495i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.42097 + 1.77169i) q^{9} +(1.35435 + 2.34580i) q^{10} +(0.0308115 + 0.174741i) q^{11} +(0.815777 - 1.52791i) q^{12} +(0.667169 - 3.78370i) q^{13} +(2.64478 + 0.0716849i) q^{14} +(2.20970 - 4.13865i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(1.48414 + 2.57060i) q^{17} +(-2.99339 + 0.198975i) q^{18} +(3.31452 - 5.74091i) q^{19} +(-2.54535 - 0.926430i) q^{20} +(-2.31541 - 3.95460i) q^{21} +(-0.135924 - 0.114054i) q^{22} +(-3.65965 - 3.07081i) q^{23} +(0.357200 + 1.69482i) q^{24} +(-2.19612 - 0.799322i) q^{25} +(1.92104 + 3.32733i) q^{26} +(3.03249 + 4.21948i) q^{27} +(-2.07210 + 1.64512i) q^{28} +(1.23286 + 6.99191i) q^{29} +(0.967547 + 4.59076i) q^{30} +(0.356665 - 2.02275i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-0.0432952 + 0.304264i) q^{33} +(-2.78927 - 1.01521i) q^{34} +(-5.61269 + 4.45613i) q^{35} +(2.16517 - 2.07654i) q^{36} +3.75198 q^{37} +(1.15112 + 6.52832i) q^{38} +(3.13428 - 5.87034i) q^{39} +(2.54535 - 0.926430i) q^{40} +(-1.29046 + 7.31858i) q^{41} +(4.31568 + 1.54108i) q^{42} +(-0.763236 + 0.640431i) q^{43} +0.177437 q^{44} +(5.86481 - 5.62473i) q^{45} +4.77733 q^{46} +(-0.391905 - 2.22260i) q^{47} +(-1.36304 - 1.06870i) q^{48} +(0.840332 + 6.94938i) q^{49} +(2.19612 - 0.799322i) q^{50} +(1.06027 + 5.03069i) q^{51} +(-3.61037 - 1.31407i) q^{52} +(-5.79449 + 10.0363i) q^{53} +(-5.03525 - 1.28306i) q^{54} +0.480622 q^{55} +(0.529857 - 2.59215i) q^{56} +(8.54585 - 7.66815i) q^{57} +(-5.43874 - 4.56364i) q^{58} +(7.49897 - 2.72940i) q^{59} +(-3.69206 - 2.89480i) q^{60} +(-0.869688 - 4.93225i) q^{61} +(1.02698 + 1.77877i) q^{62} +(-1.68416 - 7.75652i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-9.77941 - 3.55941i) q^{65} +(-0.162411 - 0.260909i) q^{66} +(8.09348 + 6.79123i) q^{67} +(2.78927 - 1.01521i) q^{68} +(-4.37279 - 7.02477i) q^{69} +(1.43522 - 7.02136i) q^{70} +(4.26162 - 7.38135i) q^{71} +(-0.323845 + 2.98247i) q^{72} -13.6091 q^{73} +(-2.87418 + 2.41172i) q^{74} +(-3.18551 - 2.49762i) q^{75} +(-5.07813 - 4.26106i) q^{76} +(0.245656 - 0.400049i) q^{77} +(1.37239 + 6.51162i) q^{78} +(-9.95510 + 8.35332i) q^{79} +(-1.35435 + 2.34580i) q^{80} +(2.72221 + 8.57844i) q^{81} +(-3.71574 - 6.43585i) q^{82} +(1.84713 + 10.4756i) q^{83} +(-4.29659 + 1.59353i) q^{84} +(7.55529 - 2.74990i) q^{85} +(0.173012 - 0.981197i) q^{86} +(-1.73237 + 12.1745i) q^{87} +(-0.135924 + 0.114054i) q^{88} +(-5.76097 + 9.97830i) q^{89} +(-0.877200 + 8.07862i) q^{90} +(-7.96115 + 6.32067i) q^{91} +(-3.65965 + 3.07081i) q^{92} +(1.67557 - 3.13825i) q^{93} +(1.72888 + 1.45070i) q^{94} +(-13.7551 - 11.5419i) q^{95} +(1.73110 - 0.0574708i) q^{96} +(3.10100 - 2.60205i) q^{97} +(-5.11070 - 4.78338i) q^{98} +(-0.234993 + 0.477631i) 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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