LMFDB - Embedded newform 378.2.w.b.25.12

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			25.12
Character	$\chi$	$=$	378.25
Dual form			378.2.w.b.121.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{2} +(1.73083 + 0.0649612i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-3.37095 - 1.22693i) q^{5} +(1.64867 - 0.530936i) q^{6} +(2.18547 - 1.49122i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.99156 + 0.224874i) q^{9} +O(q^{10})$	\(q+(0.939693 - 0.342020i) q^{2} +(1.73083 + 0.0649612i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-3.37095 - 1.22693i) q^{5} +(1.64867 - 0.530936i) q^{6} +(2.18547 - 1.49122i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.99156 + 0.224874i) q^{9} -3.58729 q^{10} +(2.08059 - 0.757273i) q^{11} +(1.36765 - 1.06279i) q^{12} +(0.493989 + 2.80155i) q^{13} +(1.54364 - 2.14876i) q^{14} +(-5.75485 - 2.34258i) q^{15} +(0.173648 - 0.984808i) q^{16} -3.59671 q^{17} +(2.88806 - 0.811862i) q^{18} +1.62442 q^{19} +(-3.37095 + 1.22693i) q^{20} +(3.87955 - 2.43907i) q^{21} +(1.69611 - 1.42321i) q^{22} +(-1.46976 - 8.33541i) q^{23} +(0.921674 - 1.46646i) q^{24} +(6.02774 + 5.05787i) q^{25} +(1.42239 + 2.46364i) q^{26} +(5.16328 + 0.583554i) q^{27} +(0.715631 - 2.54713i) q^{28} +(-1.16849 + 6.62686i) q^{29} +(-6.20900 - 0.233035i) q^{30} +(-7.36703 + 6.18167i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(3.65034 - 1.17555i) q^{33} +(-3.37980 + 1.23015i) q^{34} +(-9.19672 + 2.34541i) q^{35} +(2.43621 - 1.75067i) q^{36} +(-1.52222 + 2.63656i) q^{37} +(1.52646 - 0.555585i) q^{38} +(0.673020 + 4.88111i) q^{39} +(-2.74802 + 2.30587i) q^{40} +(1.85372 + 10.5129i) q^{41} +(2.81137 - 3.61886i) q^{42} +(1.66936 + 1.40076i) q^{43} +(1.10706 - 1.91748i) q^{44} +(-9.80850 - 4.42846i) q^{45} +(-4.23200 - 7.33004i) q^{46} +(3.84044 + 3.22251i) q^{47} +(0.364530 - 1.69326i) q^{48} +(2.55255 - 6.51801i) q^{49} +(7.39412 + 2.69124i) q^{50} +(-6.22531 - 0.233647i) q^{51} +(2.17922 + 1.82858i) q^{52} +(-5.55919 + 9.62879i) q^{53} +(5.05148 - 1.21758i) q^{54} -7.94268 q^{55} +(-0.198696 - 2.63828i) q^{56} +(2.81160 + 0.105524i) q^{57} +(1.16849 + 6.62686i) q^{58} +(-0.351018 - 1.99072i) q^{59} +(-5.91425 + 1.90462i) q^{60} +(-1.70362 - 1.42951i) q^{61} +(-4.80848 + 8.32854i) q^{62} +(6.87330 - 3.96961i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.77208 - 10.0500i) q^{65} +(3.02814 - 2.35315i) q^{66} +(4.28918 + 1.56113i) q^{67} +(-2.75524 + 2.31192i) q^{68} +(-2.00243 - 14.5227i) q^{69} +(-7.83991 + 5.34942i) q^{70} +(-3.66979 - 6.35627i) q^{71} +(1.69053 - 2.47833i) q^{72} +(-1.94254 - 3.36458i) q^{73} +(-0.528660 + 2.99818i) q^{74} +(10.1044 + 9.14590i) q^{75} +(1.24438 - 1.04416i) q^{76} +(3.41781 - 4.75760i) q^{77} +(2.30187 + 4.35655i) q^{78} +(-0.149228 + 0.0543145i) q^{79} +(-1.79365 + 3.10668i) q^{80} +(8.89886 + 1.34545i) q^{81} +(5.33756 + 9.24492i) q^{82} +(2.54125 - 14.4121i) q^{83} +(1.40410 - 4.36217i) q^{84} +(12.1243 + 4.41290i) q^{85} +(2.04778 + 0.745330i) q^{86} +(-2.45296 + 11.3941i) q^{87} +(0.384477 - 2.18048i) q^{88} -13.8863 q^{89} +(-10.7316 - 0.806688i) q^{90} +(5.25732 + 5.38606i) q^{91} +(-6.48380 - 5.44055i) q^{92} +(-13.1527 + 10.2209i) q^{93} +(4.71100 + 1.71466i) q^{94} +(-5.47585 - 1.99305i) q^{95} +(-0.236582 - 1.71582i) q^{96} +(-0.437555 - 0.367152i) q^{97} +(0.169321 - 6.99795i) q^{98} +(6.39450 - 1.79756i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} + 3 q^{7} + 36 q^{8}+O(q^{10}) $ 72 * q + 3 * q^6 + 3 * q^7 + 36 * q^8	$ 72 q + 3 q^{6} + 3 q^{7} + 36 q^{8} - 12 q^{10} - 6 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} + 24 q^{17} - 36 q^{19} + 18 q^{21} + 6 q^{22} - 6 q^{23} + 30 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} + 9 q^{35} - 3 q^{36} + 51 q^{39} - 6 q^{41} - 27 q^{42} - 24 q^{43} + 18 q^{45} + 27 q^{47} + 6 q^{48} - 69 q^{49} + 6 q^{50} + 6 q^{51} - 6 q^{52} - 15 q^{53} + 45 q^{54} - 72 q^{55} + 6 q^{56} + 57 q^{57} - 3 q^{58} + 15 q^{59} - 33 q^{60} - 18 q^{61} - 24 q^{62} - 12 q^{63} - 36 q^{64} - 90 q^{65} - 36 q^{66} - 66 q^{67} - 18 q^{68} - 39 q^{69} - 12 q^{70} + 12 q^{71} + 30 q^{73} + 9 q^{74} - 21 q^{75} - 87 q^{77} + 6 q^{78} - 45 q^{79} - 6 q^{80} - 24 q^{81} + 33 q^{82} + 18 q^{83} + 6 q^{84} + 51 q^{85} - 12 q^{86} - 18 q^{87} - 12 q^{88} + 72 q^{89} - 69 q^{90} - 30 q^{91} + 12 q^{92} - 48 q^{93} + 21 q^{95} + 48 q^{97} + 6 q^{98} + 90 q^{99}+O(q^{100}) $ 72 * q + 3 * q^6 + 3 * q^7 + 36 * q^8 - 12 * q^10 - 6 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 + 24 * q^17 - 36 * q^19 + 18 * q^21 + 6 * q^22 - 6 * q^23 + 30 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 + 9 * q^35 - 3 * q^36 + 51 * q^39 - 6 * q^41 - 27 * q^42 - 24 * q^43 + 18 * q^45 + 27 * q^47 + 6 * q^48 - 69 * q^49 + 6 * q^50 + 6 * q^51 - 6 * q^52 - 15 * q^53 + 45 * q^54 - 72 * q^55 + 6 * q^56 + 57 * q^57 - 3 * q^58 + 15 * q^59 - 33 * q^60 - 18 * q^61 - 24 * q^62 - 12 * q^63 - 36 * q^64 - 90 * q^65 - 36 * q^66 - 66 * q^67 - 18 * q^68 - 39 * q^69 - 12 * q^70 + 12 * q^71 + 30 * q^73 + 9 * q^74 - 21 * q^75 - 87 * q^77 + 6 * q^78 - 45 * q^79 - 6 * q^80 - 24 * q^81 + 33 * q^82 + 18 * q^83 + 6 * q^84 + 51 * q^85 - 12 * q^86 - 18 * q^87 - 12 * q^88 + 72 * q^89 - 69 * q^90 - 30 * q^91 + 12 * q^92 - 48 * q^93 + 21 * q^95 + 48 * q^97 + 6 * q^98 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	1.73083	+	0.0649612i	0.999296	+	0.0375054i
$3$	1.73083	+	0.0649612i	0.999296	+	0.0375054i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−3.37095	−	1.22693i	−1.50753	−	0.548698i	−0.549536	−	0.835470i	$-0.685196\pi$
$5$	−3.37095	−	1.22693i	−1.50753	−	0.548698i	−0.957999	+	0.286772i	$0.907418\pi$
$6$	1.64867	−	0.530936i	0.673066	−	0.216754i
$7$	2.18547	−	1.49122i	0.826030	−	0.563627i
$7$	2.18547	−	1.49122i	0.826030	−	0.563627i
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	2.99156	+	0.224874i	0.997187	+	0.0749579i
$10$	−3.58729			−1.13440
$11$	2.08059	−	0.757273i	0.627321	−	0.228326i	−0.00874371	−	0.999962i	$-0.502783\pi$
$11$	2.08059	−	0.757273i	0.627321	−	0.228326i	0.636065	+	0.771636i	$0.280561\pi$
$12$	1.36765	−	1.06279i	0.394807	−	0.306802i
$13$	0.493989	+	2.80155i	0.137008	+	0.777011i	0.973440	+	0.228941i	$0.0735262\pi$
$13$	0.493989	+	2.80155i	0.137008	+	0.777011i	−0.836432	+	0.548070i	$0.815363\pi$
$14$	1.54364	−	2.14876i	0.412556	−	0.574280i
$15$	−5.75485	−	2.34258i	−1.48590	−	0.604852i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−3.59671			−0.872331			−0.436165	−	0.899866i	$-0.643664\pi$
$17$	−3.59671			−0.872331			−0.436165	+	0.899866i	$0.643664\pi$
$18$	2.88806	−	0.811862i	0.680722	−	0.191358i
$19$	1.62442			0.372668			0.186334	−	0.982486i	$-0.440339\pi$
$19$	1.62442			0.372668			0.186334	+	0.982486i	$0.440339\pi$
$20$	−3.37095	+	1.22693i	−0.753767	+	0.274349i
$21$	3.87955	−	2.43907i	0.846587	−	0.532250i
$22$	1.69611	−	1.42321i	0.361612	−	0.303429i
$23$	−1.46976	−	8.33541i	−0.306466	−	1.73805i	−0.616525	−	0.787336i	$-0.711460\pi$
$23$	−1.46976	−	8.33541i	−0.306466	−	1.73805i	0.310059	−	0.950717i	$-0.399651\pi$
$24$	0.921674	−	1.46646i	0.188136	−	0.299341i
$25$	6.02774	+	5.05787i	1.20555	+	1.01157i
$26$	1.42239	+	2.46364i	0.278953	+	0.483160i
$27$	5.16328	+	0.583554i	0.993674	+	0.112305i
$28$	0.715631	−	2.54713i	0.135242	−	0.481362i
$29$	−1.16849	+	6.62686i	−0.216984	+	1.23058i	0.660446	+	0.750873i	$0.270367\pi$
$29$	−1.16849	+	6.62686i	−0.216984	+	1.23058i	−0.877430	+	0.479704i	$0.840744\pi$
$30$	−6.20900	−	0.233035i	−1.13360	−	0.0425461i
$31$	−7.36703	+	6.18167i	−1.32316	+	1.11026i	−0.337531	+	0.941314i	$0.609592\pi$
$31$	−7.36703	+	6.18167i	−1.32316	+	1.11026i	−0.985625	+	0.168946i	$0.945964\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$	3.65034	−	1.17555i	0.635443	−	0.204638i
$34$	−3.37980	+	1.23015i	−0.579632	+	0.210969i
$35$	−9.19672	+	2.34541i	−1.55453	+	0.396446i
$36$	2.43621	−	1.75067i	0.406036	−	0.291779i
$37$	−1.52222	+	2.63656i	−0.250251	+	0.433447i	−0.963595	−	0.267367i	$-0.913846\pi$
$37$	−1.52222	+	2.63656i	−0.250251	+	0.433447i	0.713344	+	0.700814i	$0.247180\pi$
$38$	1.52646	−	0.555585i	0.247624	−	0.0901279i
$39$	0.673020	+	4.88111i	0.107770	+	0.781603i
$40$	−2.74802	+	2.30587i	−0.434501	+	0.364589i
$41$	1.85372	+	10.5129i	0.289502	+	1.64185i	0.688747	+	0.725001i	$0.258161\pi$
$41$	1.85372	+	10.5129i	0.289502	+	1.64185i	−0.399246	+	0.916844i	$0.630728\pi$
$42$	2.81137	−	3.61886i	0.433804	−	0.558403i
$43$	1.66936	+	1.40076i	0.254575	+	0.213614i	0.761140	−	0.648588i	$-0.224640\pi$
$43$	1.66936	+	1.40076i	0.254575	+	0.213614i	−0.506564	+	0.862202i	$0.669085\pi$
$44$	1.10706	−	1.91748i	0.166895	−	0.289071i
$45$	−9.80850	−	4.42846i	−1.46216	−	0.660156i
$46$	−4.23200	−	7.33004i	−0.623974	−	1.08075i
$47$	3.84044	+	3.22251i	0.560186	+	0.470052i	0.878373	−	0.477976i	$-0.158629\pi$
$47$	3.84044	+	3.22251i	0.560186	+	0.470052i	−0.318187	+	0.948028i	$0.603074\pi$
$48$	0.364530	−	1.69326i	0.0526154	−	0.244401i
$49$	2.55255	−	6.51801i	0.364650	−	0.931145i
$50$	7.39412	+	2.69124i	1.04569	+	0.380599i
$51$	−6.22531	−	0.233647i	−0.871717	−	0.0327171i
$52$	2.17922	+	1.82858i	0.302204	+	0.253579i
$53$	−5.55919	+	9.62879i	−0.763613	+	1.32262i	0.177364	+	0.984145i	$0.443243\pi$
$53$	−5.55919	+	9.62879i	−0.763613	+	1.32262i	−0.940977	+	0.338471i	$0.890090\pi$
$54$	5.05148	−	1.21758i	0.687420	−	0.165692i
$55$	−7.94268			−1.07099
$56$	−0.198696	−	2.63828i	−0.0265519	−	0.352555i
$57$	2.81160	+	0.105524i	0.372406	+	0.0139771i
$58$	1.16849	+	6.62686i	0.153431	+	0.870150i
$59$	−0.351018	−	1.99072i	−0.0456986	−	0.259170i	0.953396	−	0.301723i	$-0.0975618\pi$
$59$	−0.351018	−	1.99072i	−0.0456986	−	0.259170i	−0.999094	+	0.0425534i	$0.986451\pi$
$60$	−5.91425	+	1.90462i	−0.763527	+	0.245886i
$61$	−1.70362	−	1.42951i	−0.218126	−	0.183030i	0.527177	−	0.849756i	$-0.323251\pi$
$61$	−1.70362	−	1.42951i	−0.218126	−	0.183030i	−0.745303	+	0.666726i	$0.767695\pi$
$62$	−4.80848	+	8.32854i	−0.610678	+	1.05773i
$63$	6.87330	−	3.96961i	0.865954	−	0.500124i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	1.77208	−	10.0500i	0.219800	−	1.24655i
$66$	3.02814	−	2.35315i	0.372738	−	0.289653i
$67$	4.28918	+	1.56113i	0.524007	+	0.190723i	0.590460	−	0.807067i	$-0.298946\pi$
$67$	4.28918	+	1.56113i	0.524007	+	0.190723i	−0.0664535	+	0.997790i	$0.521168\pi$
$68$	−2.75524	+	2.31192i	−0.334122	+	0.280362i
$69$	−2.00243	−	14.5227i	−0.241064	−	1.74832i
$70$	−7.83991	+	5.34942i	−0.937049	+	0.639379i
$71$	−3.66979	−	6.35627i	−0.435524	−	0.754351i	0.561814	−	0.827264i	$-0.310104\pi$
$71$	−3.66979	−	6.35627i	−0.435524	−	0.754351i	−0.997338	+	0.0729132i	$0.976770\pi$
$72$	1.69053	−	2.47833i	0.199230	−	0.292074i
$73$	−1.94254	−	3.36458i	−0.227357	−	0.393794i	0.729667	−	0.683803i	$-0.239675\pi$
$73$	−1.94254	−	3.36458i	−0.227357	−	0.393794i	−0.957024	+	0.290009i	$0.906342\pi$
$74$	−0.528660	+	2.99818i	−0.0614555	+	0.348531i
$75$	10.1044	+	9.14590i	1.16676	+	1.05608i
$76$	1.24438	−	1.04416i	0.142740	−	0.119773i
$77$	3.41781	−	4.75760i	0.389495	−	0.542179i
$78$	2.30187	+	4.35655i	0.260635	+	0.493283i
$79$	−0.149228	+	0.0543145i	−0.0167894	+	0.00611086i	−0.350401	−	0.936600i	$-0.613955\pi$
$79$	−0.149228	+	0.0543145i	−0.0167894	+	0.00611086i	0.333612	+	0.942711i	$0.391733\pi$
$80$	−1.79365	+	3.10668i	−0.200536	+	0.347338i
$81$	8.89886	+	1.34545i	0.988763	+	0.149494i
$82$	5.33756	+	9.24492i	0.589435	+	1.02093i
$83$	2.54125	−	14.4121i	0.278938	−	1.58194i	−0.447230	−	0.894419i	$-0.647589\pi$
$83$	2.54125	−	14.4121i	0.278938	−	1.58194i	0.726168	−	0.687517i	$-0.241300\pi$
$84$	1.40410	−	4.36217i	0.153200	−	0.475951i
$85$	12.1243	+	4.41290i	1.31507	+	0.478646i
$86$	2.04778	+	0.745330i	0.220817	+	0.0803710i
$87$	−2.45296	+	11.3941i	−0.262985	+	1.22157i
$88$	0.384477	−	2.18048i	0.0409854	−	0.232440i
$89$	−13.8863			−1.47194			−0.735972	−	0.677012i	$-0.763274\pi$
$89$	−13.8863			−1.47194			−0.735972	+	0.677012i	$0.763274\pi$
$90$	−10.7316	−	0.806688i	−1.13121	−	0.0850323i
$91$	5.25732	+	5.38606i	0.551117	+	0.564613i
$92$	−6.48380	−	5.44055i	−0.675983	−	0.567217i
$93$	−13.1527	+	10.2209i	−1.36387	+	1.05985i
$94$	4.71100	+	1.71466i	0.485903	+	0.176854i
$95$	−5.47585	−	1.99305i	−0.561810	−	0.204482i
$96$	−0.236582	−	1.71582i	−0.0241460	−	0.175120i
$97$	−0.437555	−	0.367152i	−0.0444270	−	0.0372787i	0.620304	−	0.784362i	$-0.287009\pi$
$97$	−0.437555	−	0.367152i	−0.0444270	−	0.0372787i	−0.664731	+	0.747083i	$0.731454\pi$
$98$	0.169321	−	6.99795i	0.0171040	−	0.706900i
$99$	6.39450	−	1.79756i	0.642671	−	0.180661i
$100$	7.86865			0.786865
$101$	2.07613	−	11.7743i	0.206583	−	1.17159i	−0.688347	−	0.725382i	$-0.741663\pi$
$101$	2.07613	−	11.7743i	0.206583	−	1.17159i	0.894930	−	0.446207i	$-0.147226\pi$
$102$	−5.92979	+	1.90962i	−0.587136	+	0.189081i
$103$	−5.87200	−	2.13723i	−0.578585	−	0.210588i	0.0361162	−	0.999348i	$-0.488501\pi$
$103$	−5.87200	−	2.13723i	−0.578585	−	0.210588i	−0.614702	+	0.788760i	$0.710724\pi$
$104$	2.67321	+	0.972969i	0.262130	+	0.0954075i
$105$	−16.0703	+	3.46208i	−1.56830	+	0.337864i
$106$	−1.93069	+	10.9495i	−0.187525	+	1.06351i
$107$	4.96674	+	8.60265i	0.480153	+	0.831649i	0.999741	−	0.0227676i	$-0.00724779\pi$
$107$	4.96674	+	8.60265i	0.480153	+	0.831649i	−0.519588	+	0.854417i	$0.673914\pi$
$108$	4.33040	−	2.87186i	0.416693	−	0.276345i
$109$	4.26967	−	7.39528i	0.408960	−	0.708340i	−0.585813	−	0.810446i	$-0.699225\pi$
$109$	4.26967	−	7.39528i	0.408960	−	0.708340i	0.994773	+	0.102106i	$0.0325582\pi$
$110$	−7.46368	+	2.71656i	−0.711634	+	0.259014i
$111$	−2.80598	+	4.46455i	−0.266331	+	0.423756i
$112$	−1.08906	−	2.41121i	−0.102906	−	0.227838i
$113$	1.86575	−	1.56555i	0.175515	−	0.147274i	−0.550798	−	0.834638i	$-0.685677\pi$
$113$	1.86575	−	1.56555i	0.175515	−	0.147274i	0.726313	+	0.687364i	$0.241232\pi$
$114$	2.67813	−	0.862465i	0.250830	−	0.0807772i
$115$	−5.27245	+	29.9015i	−0.491658	+	2.78833i
$116$	3.36455	+	5.82756i	0.312390	+	0.541076i
$117$	0.847803	+	8.49210i	0.0783794	+	0.785095i
$118$	−1.01072	−	1.75061i	−0.0930439	−	0.161157i
$119$	−7.86050	+	5.36348i	−0.720571	+	0.491669i
$120$	−4.90616	+	3.81255i	−0.447869	+	0.348037i
$121$	−4.67110	+	3.91952i	−0.424645	+	0.356320i
$122$	−2.08980	−	0.760625i	−0.189202	−	0.0688638i
$123$	2.52554	+	18.3166i	0.227720	+	1.65155i
$124$	−1.66997	+	9.47086i	−0.149968	+	0.850509i
$125$	−5.14535	−	8.91200i	−0.460214	−	0.797114i
$126$	5.10110	−	6.08102i	0.454442	−	0.541740i
$127$	5.79857	−	10.0434i	0.514540	−	0.891209i	−0.485318	−	0.874338i	$-0.661296\pi$
$127$	5.79857	−	10.0434i	0.514540	−	0.891209i	0.999858	−	0.0168715i	$-0.00537064\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$	2.79839	+	2.53293i	0.246385	+	0.223012i
$130$	−1.77208	−	10.0500i	−0.155422	−	0.881442i
$131$	2.35770	+	13.3712i	0.205993	+	1.16825i	0.895869	+	0.444319i	$0.146554\pi$
$131$	2.35770	+	13.3712i	0.205993	+	1.16825i	−0.689875	+	0.723928i	$0.742335\pi$
$132$	2.04069	−	3.24692i	0.177620	−	0.282608i
$133$	3.55013	−	2.42237i	0.307835	−	0.210046i
$134$	4.56445			0.394309
$135$	−16.6892	−	8.30209i	−1.43638	−	0.714530i
$136$	−1.79836	+	3.11484i	−0.154208	+	0.267096i
$137$	−10.7235	−	8.99812i	−0.916174	−	0.768761i	0.0571093	−	0.998368i	$-0.481812\pi$
$137$	−10.7235	−	8.99812i	−0.916174	−	0.768761i	−0.973284	+	0.229606i	$0.926256\pi$
$138$	−6.84871	−	12.9620i	−0.583001	−	1.10340i
$139$	17.5833	+	6.39980i	1.49140	+	0.542824i	0.953817	−	0.300389i	$-0.0971164\pi$
$139$	17.5833	+	6.39980i	1.49140	+	0.542824i	0.537580	+	0.843213i	$0.319339\pi$
$140$	−5.53750	+	7.70822i	−0.468004	+	0.651464i
$141$	6.43782	+	5.82711i	0.542163	+	0.490731i
$142$	−5.62245	−	4.71780i	−0.471826	−	0.395909i
$143$	3.14933	+	5.45480i	0.263360	+	0.456153i
$144$	0.740936	−	2.90706i	0.0617447	−	0.242255i
$145$	12.0696	−	20.9052i	1.00233	−	1.73608i
$146$	−2.97614	−	2.49728i	−0.246307	−	0.206676i
$147$	4.84145	−	11.1158i	0.399316	−	0.916813i
$148$	0.528660	+	2.99818i	0.0434556	+	0.246449i
$149$	8.79686	−	7.38145i	0.720667	−	0.604712i	−0.206903	−	0.978362i	$-0.566338\pi$
$149$	8.79686	−	7.38145i	0.720667	−	0.604712i	0.927570	+	0.373650i	$0.121894\pi$
$150$	12.6231	+	5.13841i	1.03068	+	0.419550i
$151$	3.22496	−	1.17379i	0.262444	−	0.0955217i	−0.207447	−	0.978246i	$-0.566515\pi$
$151$	3.22496	−	1.17379i	0.262444	−	0.0955217i	0.469891	+	0.882725i	$0.344293\pi$
$152$	0.812212	−	1.40679i	0.0658791	−	0.114106i
$153$	−10.7598	−	0.808806i	−0.869877	−	0.0653881i
$154$	1.58449	−	5.63964i	0.127682	−	0.454455i
$155$	32.4183	−	11.7993i	2.60390	−	0.947743i
$156$	3.65308	+	3.30654i	0.292480	+	0.264735i
$157$	−3.22135	−	18.2692i	−0.257092	−	1.45804i	−0.790646	−	0.612274i	$-0.790255\pi$
$157$	−3.22135	−	18.2692i	−0.257092	−	1.45804i	0.533554	−	0.845766i	$-0.320856\pi$
$158$	−0.121652	+	0.102078i	−0.00967808	+	0.00812088i
$159$	−10.2475	+	16.3047i	−0.812681	+	1.29305i
$160$	−0.622926	+	3.53279i	−0.0492467	+	0.279292i
$161$	−15.6420	−	16.0251i	−1.23276	−	1.26295i
$162$	8.82237	−	1.77928i	0.693151	−	0.139794i
$163$	−6.60017	−	11.4318i	−0.516965	−	0.895409i	−0.999806	−	0.0197014i	$-0.993728\pi$
$163$	−6.60017	−	11.4318i	−0.516965	−	0.895409i	0.482841	−	0.875708i	$-0.339605\pi$
$164$	8.17762	+	6.86183i	0.638565	+	0.535819i
$165$	−13.7474	−	0.515966i	−1.07024	−	0.0401679i
$166$	−2.54125	−	14.4121i	−0.197239	−	1.11860i
$167$	−1.07295	+	0.900314i	−0.0830276	+	0.0696684i	−0.683357	−	0.730085i	$-0.739481\pi$
$167$	−1.07295	+	0.900314i	−0.0830276	+	0.0696684i	0.600329	+	0.799753i	$0.295036\pi$
$168$	−0.172524	−	4.57933i	−0.0133105	−	0.353303i
$169$	4.61133	−	1.67839i	0.354718	−	0.129107i
$170$	12.9025			0.989573
$171$	4.85956	+	0.365290i	0.371620	+	0.0279344i
$172$	2.17920			0.166162
$173$	−0.862239	+	4.89000i	−0.0655548	+	0.371780i	0.934327	+	0.356417i	$0.116002\pi$
$173$	−0.862239	+	4.89000i	−0.0655548	+	0.371780i	−0.999882	+	0.0153633i	$0.995110\pi$
$174$	1.59198	+	11.5459i	0.120688	+	0.875292i
$175$	20.7158	+	2.06517i	1.56597	+	0.156112i
$176$	−0.384477	−	2.18048i	−0.0289811	−	0.164360i
$177$	−0.478233	−	3.46841i	−0.0359462	−	0.260701i
$178$	−13.0488	+	4.74939i	−0.978052	+	0.355982i
$179$	19.4657			1.45493			0.727467	−	0.686143i	$-0.240698\pi$
$179$	19.4657			1.45493			0.727467	+	0.686143i	$0.240698\pi$
$180$	−10.3603	+	2.91238i	−0.772211	+	0.217076i
$181$	−8.24448	+	14.2799i	−0.612807	+	1.06141i	0.377958	+	0.925823i	$0.376626\pi$
$181$	−8.24448	+	14.2799i	−0.612807	+	1.06141i	−0.990765	+	0.135590i	$0.956707\pi$
$182$	6.78240	+	3.26313i	0.502745	+	0.241880i
$183$	−2.85582	−	2.58491i	−0.211108	−	0.191082i
$184$	−7.95356	−	2.89486i	−0.586344	−	0.213412i
$185$	8.36618	−	7.02005i	0.615093	−	0.516125i
$186$	−8.86371	+	14.1029i	−0.649919	+	1.03408i
$187$	−7.48328	+	2.72369i	−0.547232	+	0.199176i
$188$	5.01334			0.365636
$189$	12.1544	−	6.42423i	0.884102	−	0.467294i
$190$	−5.82728			−0.422755
$191$	−3.31538	+	1.20670i	−0.239893	+	0.0873138i	−0.459169	−	0.888349i	$-0.651853\pi$
$191$	−3.31538	+	1.20670i	−0.239893	+	0.0873138i	0.219276	+	0.975663i	$0.429630\pi$
$192$	−0.809158	−	1.53143i	−0.0583960	−	0.110521i
$193$	−4.96589	+	4.16688i	−0.357453	+	0.299939i	−0.803775	−	0.594934i	$-0.797178\pi$
$193$	−4.96589	+	4.16688i	−0.357453	+	0.299939i	0.446322	+	0.894873i	$0.352734\pi$
$194$	−0.536740	−	0.195358i	−0.0385357	−	0.0140259i
$195$	3.72004	−	17.2797i	0.266397	−	1.23743i
$196$	−2.23433	−	6.63383i	−0.159595	−	0.473845i
$197$	2.61375	−	4.52715i	0.186222	−	0.322546i	−0.757766	−	0.652527i	$-0.773709\pi$
$197$	2.61375	−	4.52715i	0.186222	−	0.322546i	0.943988	+	0.329981i	$0.107042\pi$
$198$	5.39406	−	3.87620i	0.383339	−	0.275469i
$199$	−13.5829			−0.962865			−0.481433	−	0.876483i	$-0.659883\pi$
$199$	−13.5829			−0.962865			−0.481433	+	0.876483i	$0.659883\pi$
$200$	7.39412	−	2.69124i	0.522843	−	0.190299i
$201$	7.32244	+	2.98069i	0.516485	+	0.210242i
$202$	−2.07613	−	11.7743i	−0.146076	−	0.828438i
$203$	7.32837	+	16.2253i	0.514351	+	1.13879i
$204$	−4.91905	+	3.82257i	−0.344402	+	0.267633i
$205$	6.64981	−	37.7130i	0.464443	−	2.63399i
$206$	−6.24885			−0.435378
$207$	−2.52245	−	25.2664i	−0.175323	−	1.75614i
$208$	2.84477			0.197249
$209$	3.37976	−	1.23013i	0.233783	−	0.0850899i
$210$	−13.9171	+	8.74967i	−0.960370	+	0.603784i
$211$	−11.5932	+	9.72788i	−0.798112	+	0.669695i	−0.947739	−	0.319047i	$-0.896637\pi$
$211$	−11.5932	+	9.72788i	−0.798112	+	0.669695i	0.149627	+	0.988742i	$0.452193\pi$
$212$	1.93069	+	10.9495i	0.132600	+	0.752012i
$213$	−5.93889	−	11.2400i	−0.406926	−	0.770154i
$214$	7.60949	+	6.38512i	0.520174	+	0.436478i
$215$	−3.90871	−	6.77008i	−0.266572	−	0.461716i
$216$	3.08701	−	4.17975i	0.210045	−	0.284396i
$217$	−6.88220	+	24.4957i	−0.467194	+	1.66287i
$218$	1.48284	−	8.40961i	0.100431	−	0.569570i
$219$	−3.14364	−	5.94971i	−0.212428	−	0.402044i
$220$	−6.08445	+	5.10546i	−0.410213	+	0.344210i
$221$	−1.77674	−	10.0764i	−0.119516	−	0.677811i
$222$	−1.10979	+	5.15501i	−0.0744841	+	0.345981i
$223$	3.65517	−	1.33037i	0.244768	−	0.0890883i	−0.216723	−	0.976233i	$-0.569537\pi$
$223$	3.65517	−	1.33037i	0.244768	−	0.0890883i	0.461491	+	0.887145i	$0.347315\pi$
$224$	−1.84806	−	1.89332i	−0.123479	−	0.126503i
$225$	16.8950	+	16.4864i	1.12633	+	1.09909i
$226$	1.21778	−	2.10926i	0.0810055	−	0.140306i
$227$	−3.42521	+	1.24667i	−0.227339	+	0.0827446i	−0.453178	−	0.891420i	$-0.649710\pi$
$227$	−3.42521	+	1.24667i	−0.227339	+	0.0827446i	0.225839	+	0.974165i	$0.427488\pi$
$228$	2.22164	−	1.72643i	0.147132	−	0.114335i
$229$	13.2812	−	11.1443i	0.877648	−	0.736434i	−0.0880460	−	0.996116i	$-0.528062\pi$
$229$	13.2812	−	11.1443i	0.877648	−	0.736434i	0.965694	+	0.259682i	$0.0836178\pi$
$230$	5.27245	+	29.9015i	0.347655	+	1.97165i
$231$	6.22471	−	8.01259i	0.409556	−	0.527190i
$232$	5.15478	+	4.32538i	0.338428	+	0.283975i
$233$	−7.29135	+	12.6290i	−0.477672	+	0.827353i	−0.999672	−	0.0255928i	$-0.991853\pi$
$233$	−7.29135	+	12.6290i	−0.477672	+	0.827353i	0.522000	+	0.852945i	$0.325186\pi$
$234$	3.70114	+	7.69000i	0.241951	+	0.502711i
$235$	−8.99216	−	15.5749i	−0.586584	−	1.01599i
$236$	−1.54851	−	1.29935i	−0.100799	−	0.0845805i
$237$	−0.261817	+	0.0843152i	−0.0170068	+	0.00547686i
$238$	−5.55204	+	7.72847i	−0.359885	+	0.500962i
$239$	−0.222801	−	0.0810929i	−0.0144118	−	0.00524546i	0.334804	−	0.942288i	$-0.391330\pi$
$239$	−0.222801	−	0.0810929i	−0.0144118	−	0.00524546i	−0.349216	+	0.937042i	$0.613552\pi$
$240$	−3.30631	+	5.26063i	−0.213422	+	0.339572i
$241$	−4.87146	−	4.08764i	−0.313798	−	0.263308i	0.472262	−	0.881458i	$-0.343438\pi$
$241$	−4.87146	−	4.08764i	−0.313798	−	0.263308i	−0.786060	+	0.618151i	$0.787882\pi$
$242$	−3.04884	+	5.28075i	−0.195987	+	0.339460i
$243$	15.3150	+	2.90682i	0.982460	+	0.186473i
$244$	−2.22392			−0.142372
$245$	−16.6016	+	18.8401i	−1.06064	+	1.20365i
$246$	8.63786	+	16.3481i	0.550730	+	1.04232i
$247$	0.802448	+	4.55091i	0.0510585	+	0.289567i
$248$	1.66997	+	9.47086i	0.106043	+	0.601401i
$249$	5.33470	−	24.7799i	0.338073	−	1.57036i
$250$	−7.88313	−	6.61473i	−0.498573	−	0.418352i
$251$	3.41197	−	5.90971i	0.215362	−	0.373018i	−0.738023	−	0.674776i	$-0.764240\pi$
$251$	3.41197	−	5.90971i	0.215362	−	0.373018i	0.953384	+	0.301758i	$0.0975735\pi$
$252$	2.71364	−	7.45897i	0.170943	−	0.469871i
$253$	−9.37014	−	16.2296i	−0.589096	−	1.02034i
$254$	2.01382	−	11.4210i	0.126358	−	0.716615i
$255$	20.6985	+	8.42560i	1.29619	+	0.527631i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	18.2804	−	15.3391i	1.14030	−	0.956826i	0.140853	−	0.990031i	$-0.455016\pi$
$257$	18.2804	−	15.3391i	1.14030	−	0.956826i	0.999449	+	0.0332044i	$0.0105712\pi$
$258$	3.49594	+	1.42307i	0.217648	+	0.0885963i
$259$	0.604918	+	8.03207i	0.0375878	+	0.499088i
$260$	−5.10251	−	8.83781i	−0.316444	−	0.548097i
$261$	−4.98583	+	19.5619i	−0.308615	+	1.21085i
$262$	6.78873	+	11.7584i	0.419409	+	0.726438i
$263$	−5.05056	+	28.6431i	−0.311431	+	1.76621i	0.280140	+	0.959959i	$0.409619\pi$
$263$	−5.05056	+	28.6431i	−0.311431	+	1.76621i	−0.591571	+	0.806253i	$0.701492\pi$
$264$	0.807112	−	3.74907i	0.0496743	−	0.230739i
$265$	30.5536	−	25.6375i	1.87689	−	1.57490i
$266$	2.50753	−	3.49049i	0.153747	−	0.214016i
$267$	−24.0348	−	0.902070i	−1.47091	−	0.0552058i
$268$	4.28918	−	1.56113i	0.262003	−	0.0953615i
$269$	−6.95270	+	12.0424i	−0.423913	+	0.734239i	−0.996318	−	0.0857317i	$-0.972677\pi$
$269$	−6.95270	+	12.0424i	−0.423913	+	0.734239i	0.572405	+	0.819971i	$0.306011\pi$
$270$	−18.5222	−	2.09338i	−1.12722	−	0.127399i
$271$	−13.9492	−	24.1607i	−0.847352	−	1.46766i	−0.883563	−	0.468312i	$-0.844862\pi$
$271$	−13.9492	−	24.1607i	−0.847352	−	1.46766i	0.0362113	−	0.999344i	$-0.488471\pi$
$272$	−0.624563	+	3.54207i	−0.0378697	+	0.214770i
$273$	8.74965	+	9.66389i	0.529553	+	0.584885i
$274$	−13.1544	−	4.78780i	−0.794685	−	0.289242i
$275$	16.3714	+	5.95872i	0.987235	+	0.359324i
$276$	−10.8689	−	9.83788i	−0.654233	−	0.592171i
$277$	−3.26436	+	18.5131i	−0.196136	+	1.11234i	0.714655	+	0.699477i	$0.246584\pi$
$277$	−3.26436	+	18.5131i	−0.196136	+	1.11234i	−0.910791	+	0.412867i	$0.864527\pi$
$278$	18.7118			1.12226
$279$	−23.4290	+	16.8362i	−1.40266	+	1.00796i
$280$	−2.56718	+	9.13730i	−0.153418	+	0.546058i
$281$	−3.57699	−	3.00145i	−0.213385	−	0.179052i	0.529830	−	0.848104i	$-0.322256\pi$
$281$	−3.57699	−	3.00145i	−0.213385	−	0.179052i	−0.743215	+	0.669052i	$0.766700\pi$
$282$	8.04257	+	3.27383i	0.478928	+	0.194954i
$283$	−1.46224	−	0.532211i	−0.0869210	−	0.0316367i	0.298194	−	0.954505i	$-0.403616\pi$
$283$	−1.46224	−	0.532211i	−0.0869210	−	0.0316367i	−0.385115	+	0.922869i	$0.625838\pi$
$284$	−6.89696	−	2.51029i	−0.409259	−	0.148958i
$285$	−9.34831	−	3.80535i	−0.553746	−	0.225409i
$286$	4.82505	+	4.04870i	0.285311	+	0.239404i
$287$	19.7283	+	20.2114i	1.16452	+	1.19304i
$288$	−0.298022	−	2.98516i	−0.0175611	−	0.175902i
$289$	−4.06366			−0.239039
$290$	4.19173	−	23.7725i	0.246147	−	1.39597i
$291$	−0.733483	−	0.663903i	−0.0429976	−	0.0389187i
$292$	−3.65078	−	1.32878i	−0.213646	−	0.0777607i
$293$	−4.88736	−	1.77885i	−0.285523	−	0.103922i	0.195289	−	0.980746i	$-0.437436\pi$
$293$	−4.88736	−	1.77885i	−0.285523	−	0.103922i	−0.480811	+	0.876824i	$0.659658\pi$
$294$	0.747661	−	12.1013i	0.0436045	−	0.705761i
$295$	−1.25920	+	7.14129i	−0.0733136	+	0.415782i
$296$	1.52222	+	2.63656i	0.0884770	+	0.153247i
$297$	11.1846	−	2.69587i	0.648995	−	0.156430i
$298$	5.74175	−	9.94500i	0.332610	−	0.576098i
$299$	22.6260	−	8.23521i	1.30850	−	0.476254i
$300$	13.6193	+	0.511157i	0.786312	+	0.0295117i
$301$	5.73718	+	0.571941i	0.330686	+	0.0329661i
$302$	2.62901	−	2.20600i	0.151283	−	0.126941i
$303$	4.35831	−	20.2445i	0.250378	−	1.16302i
$304$	0.282078	−	1.59974i	0.0161783	−	0.0917516i
$305$	3.98892	+	6.90902i	0.228405	+	0.395609i
$306$	−10.3875	+	2.92003i	−0.593815	+	0.166927i
$307$	−3.18238	−	5.51205i	−0.181628	−	0.314589i	0.760807	−	0.648978i	$-0.224803\pi$
$307$	−3.18238	−	5.51205i	−0.181628	−	0.314589i	−0.942435	+	0.334389i	$0.891470\pi$
$308$	−0.439937	−	5.84146i	−0.0250677	−	0.332848i
$309$	−10.0246	−	4.08064i	−0.570280	−	0.232140i
$310$	26.4277	−	22.1754i	1.50099	−	1.25948i
$311$	−13.8696	−	5.04811i	−0.786472	−	0.286252i	−0.0826032	−	0.996583i	$-0.526323\pi$
$311$	−13.8696	−	5.04811i	−0.786472	−	0.286252i	−0.703869	+	0.710330i	$0.748546\pi$
$312$	4.56367	+	1.85770i	0.258367	+	0.105172i
$313$	0.192909	−	1.09404i	0.0109038	−	0.0618388i	−0.978870	−	0.204482i	$-0.934449\pi$
$313$	0.192909	−	1.09404i	0.0109038	−	0.0618388i	0.989774	+	0.142643i	$0.0455601\pi$
$314$	−9.27551	−	16.0657i	−0.523447	−	0.906638i
$315$	−28.0400	+	4.94833i	−1.57987	+	0.278807i
$316$	−0.0794025	+	0.137529i	−0.00446674	+	0.00773662i
$317$	20.9110	+	17.5464i	1.17448	+	0.985504i	1.00000		0.000842418i	$0.000268150\pi$
$317$	20.9110	+	17.5464i	1.17448	+	0.985504i	0.174478	+	0.984661i	$0.444176\pi$
$318$	−4.05298	+	18.8263i	−0.227280	+	1.05572i
$319$	2.58718	+	14.6726i	0.144854	+	0.821510i
$320$	0.622926	+	3.53279i	0.0348226	+	0.197489i
$321$	8.03776	+	15.2124i	0.448624	+	0.849073i
$322$	−20.1796	−	9.70874i	−1.12456	−	0.541047i
$323$	−5.84258			−0.325090
$324$	7.68176	−	4.68941i	0.426765	−	0.260523i
$325$	−11.1923	+	19.3856i	−0.620835	+	1.07532i
$326$	−10.1120	−	8.48501i	−0.560054	−	0.469941i
$327$	7.87049	−	12.5226i	0.435239	−	0.692503i
$328$	10.0313	+	3.65111i	0.553888	+	0.201599i
$329$	13.1986	+	1.31578i	0.727664	+	0.0725410i
$330$	−13.0948	+	4.21705i	−0.720847	+	0.232141i
$331$	−20.2457	−	16.9881i	−1.11280	−	0.933752i	−0.114584	−	0.993414i	$-0.536554\pi$
$331$	−20.2457	−	16.9881i	−1.11280	−	0.933752i	−0.998219	+	0.0596612i	$0.980998\pi$
$332$	−7.31723	−	12.6738i	−0.401585	−	0.695566i
$333$	−5.14669	+	7.54511i	−0.282037	+	0.413469i
$334$	−0.700320	+	1.21299i	−0.0383198	+	0.0663719i
$335$	−12.5432	−	10.5250i	−0.685310	−	0.575043i
$336$	−1.72834	−	4.24415i	−0.0942888	−	0.231538i
$337$	−0.424932	−	2.40991i	−0.0231475	−	0.131276i	0.971044	−	0.238900i	$-0.0767869\pi$
$337$	−0.424932	−	2.40991i	−0.0231475	−	0.131276i	−0.994192	+	0.107624i	$0.965676\pi$
$338$	3.75919	−	3.15434i	0.204473	−	0.171573i
$339$	3.33100	−	2.58850i	0.180915	−	0.140588i
$340$	12.1243	−	4.41290i	0.657535	−	0.239323i
$341$	−10.6465	+	18.4404i	−0.576543	+	0.998601i
$342$	4.69143	−	1.31881i	0.253683	−	0.0713129i
$343$	−4.14125	−	18.0513i	−0.223606	−	0.974680i
$344$	2.04778	−	0.745330i	0.110409	−	0.0401855i
$345$	−11.0682	+	51.4120i	−0.595890	+	2.76793i
$346$	0.862239	+	4.89000i	0.0463543	+	0.262888i
$347$	−10.1795	+	8.54158i	−0.546462	+	0.458536i	−0.873741	−	0.486392i	$-0.838313\pi$
$347$	−10.1795	+	8.54158i	−0.546462	+	0.458536i	0.327279	+	0.944928i	$0.393868\pi$
$348$	5.44490	+	10.3051i	0.291877	+	0.552411i
$349$	1.90954	−	10.8295i	0.102215	−	0.579691i	−0.890081	−	0.455802i	$-0.849352\pi$
$349$	1.90954	−	10.8295i	0.102215	−	0.579691i	0.992296	−	0.123889i	$-0.0395365\pi$
$350$	20.1728	−	5.14461i	1.07828	−	0.274991i
$351$	0.915748	+	14.7535i	0.0488790	+	0.787482i
$352$	−1.10706	−	1.91748i	−0.0590064	−	0.102202i
$353$	−12.0769	−	10.1337i	−0.642788	−	0.539363i	0.262085	−	0.965045i	$-0.415590\pi$
$353$	−12.0769	−	10.1337i	−0.642788	−	0.539363i	−0.904873	+	0.425682i	$0.860034\pi$
$354$	−1.63566	−	3.09567i	−0.0869342	−	0.164533i
$355$	4.57202	+	25.9292i	0.242658	+	1.37618i
$356$	−10.6375	+	8.92593i	−0.563787	+	0.473074i
$357$	−13.9536	+	8.77265i	−0.738504	+	0.464298i
$358$	18.2918	−	6.65766i	0.966749	−	0.351868i
$359$	−1.90969			−0.100789			−0.0503947	−	0.998729i	$-0.516048\pi$
$359$	−1.90969			−0.100789			−0.0503947	+	0.998729i	$0.516048\pi$
$360$	−8.73941	+	6.28018i	−0.460607	+	0.330994i
$361$	−16.3612			−0.861118
$362$	−2.86328	+	16.2385i	−0.150490	+	0.853474i
$363$	−8.33951	+	6.48059i	−0.437711	+	0.340143i
$364$	7.48943	+	0.746623i	0.392553	+	0.0391337i
$365$	2.42012	+	13.7252i	0.126675	+	0.718409i
$366$	−3.56768	−	1.45227i	−0.186486	−	0.0759114i
$367$	21.4632	−	7.81197i	1.12037	−	0.407782i	0.285583	−	0.958354i	$-0.407813\pi$
$367$	21.4632	−	7.81197i	1.12037	−	0.407782i	0.834788	+	0.550572i	$0.185590\pi$
$368$	−8.46400			−0.441216
$369$	3.18142	+	31.8669i	0.165618	+	1.65893i
$370$	5.46063	−	9.45809i	0.283885	−	0.491703i
$371$	2.20918	+	29.3334i	0.114695	+	1.52291i
$372$	−3.50567	+	16.2840i	−0.181761	+	0.844286i
$373$	−24.1775	−	8.79990i	−1.25187	−	0.455642i	−0.370834	−	0.928699i	$-0.620928\pi$
$373$	−24.1775	−	8.79990i	−1.25187	−	0.455642i	−0.881031	+	0.473058i	$0.843150\pi$
$374$	−6.10043	+	5.11887i	−0.315446	+	0.264690i
$375$	−8.32680	−	15.7594i	−0.429994	−	0.813813i
$376$	4.71100	−	1.71466i	0.242951	−	0.0884270i
$377$	−19.1427			−0.985900
$378$	9.22418	−	10.1938i	0.474441	−	0.524315i
$379$	3.07838			0.158126			0.0790629	−	0.996870i	$-0.474807\pi$
$379$	3.07838			0.158126			0.0790629	+	0.996870i	$0.474807\pi$
$380$	−5.47585	+	1.99305i	−0.280905	+	0.102241i
$381$	10.6888	−	17.0068i	0.547603	−	0.871284i
$382$	−2.70272	+	2.26785i	−0.138283	+	0.116034i
$383$	5.45760	+	1.98640i	0.278870	+	0.101500i	0.477669	−	0.878540i	$-0.341482\pi$
$383$	5.45760	+	1.98640i	0.278870	+	0.101500i	−0.198799	+	0.980040i	$0.563704\pi$
$384$	−1.28414	−	1.16232i	−0.0655309	−	0.0593144i
$385$	−17.3585	+	11.8443i	−0.884670	+	0.603639i
$386$	−3.24126	+	5.61402i	−0.164976	+	0.285746i
$387$	4.67900	+	4.56586i	0.237847	+	0.232096i
$388$	−0.571187			−0.0289976
$389$	31.1397	−	11.3339i	1.57885	−	0.574653i	0.603893	−	0.797065i	$-0.293615\pi$
$389$	31.1397	−	11.3339i	1.57885	−	0.574653i	0.974953	+	0.222413i	$0.0713932\pi$
$390$	−2.41432	−	17.5099i	−0.122254	−	0.886651i
$391$	5.28630	+	29.9801i	0.267339	+	1.51616i
$392$	−4.36849	−	5.46958i	−0.220642	−	0.276255i
$393$	3.21218	+	23.2965i	0.162033	+	1.17515i
$394$	0.907746	−	5.14808i	0.0457316	−	0.259357i
$395$	0.569679			0.0286637
$396$	3.74302	−	5.48731i	0.188094	−	0.275748i
$397$	0.939696			0.0471620			0.0235810	−	0.999722i	$-0.492493\pi$
$397$	0.939696			0.0471620			0.0235810	+	0.999722i	$0.492493\pi$
$398$	−12.7637	+	4.64562i	−0.639788	+	0.232864i
$399$	6.30203	−	3.96209i	0.315496	−	0.198353i
$400$	6.02774	−	5.05787i	0.301387	−	0.252894i
$401$	0.233721	+	1.32550i	0.0116714	+	0.0661921i	0.990087	−	0.140454i	$-0.0448562\pi$
$401$	0.233721	+	1.32550i	0.0116714	+	0.0661921i	−0.978416	+	0.206646i	$0.933745\pi$
$402$	7.90030	+	0.296512i	0.394031	+	0.0147887i
$403$	−20.9575	−	17.5854i	−1.04397	−	0.875993i
$404$	−5.97798	−	10.3542i	−0.297416	−	0.515139i
$405$	−28.3469	−	15.4537i	−1.40857	−	0.767899i
$406$	12.4358	+	12.7403i	0.617178	+	0.632292i
$407$	−1.17052	+	6.63832i	−0.0580203	+	0.329049i
$408$	−3.31500	+	5.27445i	−0.164117	+	0.261124i
$409$	−27.8603	+	23.3776i	−1.37760	+	1.15595i	−0.407513	+	0.913199i	$0.633604\pi$
$409$	−27.8603	+	23.3776i	−1.37760	+	1.15595i	−0.970090	+	0.242747i	$0.921952\pi$
$410$	−6.64981	−	37.7130i	−0.328411	−	1.86251i
$411$	−17.9761	−	16.2709i	−0.886697	−	0.802582i
$412$	−5.87200	+	2.13723i	−0.289293	+	0.105294i
$413$	−3.73573	−	3.82721i	−0.183823	−	0.188325i
$414$	−11.0119	−	22.8799i	−0.541208	−	1.12449i
$415$	−26.2490	+	45.4646i	−1.28851	+	2.23177i
$416$	2.67321	−	0.972969i	0.131065	−	0.0477037i
$417$	30.0180	+	12.2192i	1.46999	+	0.598377i
$418$	2.75520	−	2.31189i	0.134761	−	0.113078i
$419$	−2.57976	−	14.6305i	−0.126029	−	0.714748i	−0.980691	−	0.195563i	$-0.937347\pi$
$419$	−2.57976	−	14.6305i	−0.126029	−	0.714748i	0.854662	−	0.519185i	$-0.173765\pi$
$420$	−10.0852	+	12.9819i	−0.492108	+	0.633453i
$421$	−13.0356	−	10.9382i	−0.635317	−	0.533094i	0.267259	−	0.963625i	$-0.413882\pi$
$421$	−13.0356	−	10.9382i	−0.635317	−	0.533094i	−0.902576	+	0.430531i	$0.858326\pi$
$422$	−7.56695	+	13.1063i	−0.368353	+	0.638007i
$423$	10.7643	+	10.5040i	0.523376	+	0.510720i
$424$	5.55919	+	9.62879i	0.269978	+	0.467616i
$425$	−21.6800	−	18.1917i	−1.05164	−	0.882428i
$426$	−9.42505	−	8.53096i	−0.456645	−	0.413326i
$427$	−5.85492	−	0.583678i	−0.283339	−	0.0282462i
$428$	9.33442	+	3.39745i	0.451196	+	0.164222i
$429$	5.09661	+	9.64592i	0.246067	+	0.465709i
$430$	−5.98849	−	5.02494i	−0.288791	−	0.242324i
$431$	0.143736	−	0.248959i	0.00692354	−	0.0119919i	−0.862543	−	0.505984i	$-0.831129\pi$
$431$	0.143736	−	0.248959i	0.00692354	−	0.0119919i	0.869466	+	0.493992i	$0.164463\pi$
$432$	1.47128	−	4.98351i	0.0707871	−	0.239769i
$433$	20.9438			1.00649			0.503246	−	0.864143i	$-0.332139\pi$
$433$	20.9438			1.00649			0.503246	+	0.864143i	$0.332139\pi$
$434$	1.91086	+	25.3723i	0.0917241	+	1.21791i
$435$	22.2485	−	35.3993i	1.06673	−	1.69727i
$436$	−1.48284	−	8.40961i	−0.0710152	−	0.402747i
$437$	−2.38751	−	13.5402i	−0.114210	−	0.647717i
$438$	−4.98898	−	4.51571i	−0.238383	−	0.215769i
$439$	10.4066	+	8.73214i	0.496678	+	0.416762i	0.856412	−	0.516292i	$-0.172688\pi$
$439$	10.4066	+	8.73214i	0.496678	+	0.416762i	−0.359734	+	0.933055i	$0.617133\pi$
$440$	−3.97134	+	6.87856i	−0.189326	+	0.327923i
$441$	9.10184	−	18.9250i	0.433421	−	0.901192i
$442$	−5.11591	−	8.86102i	−0.243339	−	0.421476i
$443$	−4.90278	+	27.8050i	−0.232938	+	1.32106i	0.613975	+	0.789325i	$0.289569\pi$
$443$	−4.90278	+	27.8050i	−0.232938	+	1.32106i	−0.846913	+	0.531731i	$0.821542\pi$
$444$	0.720257	+	5.22369i	0.0341819	+	0.247905i
$445$	46.8100	+	17.0374i	2.21901	+	0.807652i
$446$	2.97972	−	2.50028i	0.141094	−	0.118392i
$447$	15.7054	−	12.2046i	0.742840	−	0.577257i
$448$	−2.38417	−	1.14706i	−0.112641	−	0.0541937i
$449$	1.63600	+	2.83364i	0.0772078	+	0.133728i	0.902044	−	0.431644i	$-0.142066\pi$
$449$	1.63600	+	2.83364i	0.0772078	+	0.133728i	−0.824836	+	0.565371i	$0.808733\pi$
$450$	21.5148	+	9.71374i	1.01422	+	0.457910i
$451$	11.8180	+	20.4693i	0.556487	+	0.963864i
$452$	0.422931	−	2.39856i	0.0198930	−	0.112819i
$453$	5.65812	−	1.82214i	0.265842	−	0.0856115i
$454$	−2.79225	+	2.34298i	−0.131047	+	0.109961i
$455$	−11.1139	−	24.6065i	−0.521026	−	1.15357i
$456$	1.49719	−	2.38216i	0.0701123	−	0.111555i
$457$	29.4950	−	10.7353i	1.37972	−	0.502177i	0.457627	−	0.889144i	$-0.348700\pi$
$457$	29.4950	−	10.7353i	1.37972	−	0.502177i	0.922093	+	0.386967i	$0.126477\pi$
$458$	8.66870	−	15.0146i	0.405062	−	0.701588i
$459$	−18.5708	−	2.09888i	−0.866812	−	0.0979671i
$460$	15.1814	+	26.2950i	0.707837	+	1.22601i
$461$	1.11842	−	6.34290i	0.0520902	−	0.295418i	−0.947622	−	0.319393i	$-0.896521\pi$
$461$	1.11842	−	6.34290i	0.0520902	−	0.295418i	0.999713	+	0.0239747i	$0.00763212\pi$
$462$	3.10885	−	9.65835i	0.144637	−	0.449347i
$463$	−36.0530	−	13.1222i	−1.67553	−	0.609841i	−0.682839	−	0.730568i	$-0.739255\pi$
$463$	−36.0530	−	13.1222i	−1.67553	−	0.609841i	−0.992686	+	0.120727i	$0.961477\pi$
$464$	6.32328	+	2.30148i	0.293551	+	0.106844i
$465$	56.8772	−	18.3167i	2.63762	−	0.849416i
$466$	−2.53226	+	14.3612i	−0.117305	+	0.665268i
$467$	6.19492			0.286667			0.143333	−	0.989674i	$-0.454218\pi$
$467$	6.19492			0.286667			0.143333	+	0.989674i	$0.454218\pi$
$468$	6.10807	+	5.96037i	0.282346	+	0.275518i
$469$	11.7019	−	2.98429i	0.540342	−	0.137801i
$470$	−13.7768	−	11.5601i	−0.635476	−	0.533227i
$471$	−4.38883	−	31.8302i	−0.202227	−	1.46666i
$472$	−1.89952	−	0.691370i	−0.0874327	−	0.0318229i
$473$	4.53402	+	1.65025i	0.208474	+	0.0758784i
$474$	−0.217190	+	0.168777i	−0.00997585	+	0.00775218i
$475$	9.79160	+	8.21613i	0.449269	+	0.376982i
$476$	−2.57392	+	9.16129i	−0.117975	+	0.419907i
$477$	−18.7959	+	27.5550i	−0.860605	+	1.26166i
$478$	−0.237100			−0.0108447
$479$	5.82320	−	33.0250i	0.266069	−	1.50895i	−0.499905	−	0.866080i	$-0.666632\pi$
$479$	5.82320	−	33.0250i	0.266069	−	1.50895i	0.765974	−	0.642871i	$-0.222257\pi$
$480$	−1.30768	+	6.07420i	−0.0596869	+	0.277248i
$481$	−8.13841	−	2.96214i	−0.371080	−	0.135062i
$482$	−5.97573	−	2.17499i	−0.272187	−	0.0990679i
$483$	−26.0327	−	28.7528i	−1.18453	−	1.30830i
$484$	−1.05885	+	6.00505i	−0.0481296	+	0.272957i
$485$	1.02451	+	1.77450i	0.0465205	+	0.0805758i
$486$	15.3856	−	2.50653i	0.697906	−	0.113699i
$487$	7.75756	−	13.4365i	0.351528	−	0.608865i	−0.634989	−	0.772521i	$-0.718995\pi$
$487$	7.75756	−	13.4365i	0.351528	−	0.608865i	0.986517	+	0.163656i	$0.0523287\pi$
$488$	−2.08980	+	0.760625i	−0.0946008	+	0.0344319i
$489$	−10.6812	−	20.2153i	−0.483018	−	0.914168i
$490$	−9.15674	+	23.3820i	−0.413659	+	1.05629i
$491$	−17.5894	+	14.7593i	−0.793801	+	0.666078i	−0.946683	−	0.322167i	$-0.895589\pi$
$491$	−17.5894	+	14.7593i	−0.793801	+	0.666078i	0.152882	+	0.988244i	$0.451144\pi$
$492$	13.7083	+	12.4079i	0.618019	+	0.559392i
$493$	4.20274	−	23.8349i	0.189282	−	1.07347i
$494$	2.31056	+	4.00200i	0.103957	+	0.180058i
$495$	−23.7610	−	1.78610i	−1.06798	−	0.0802792i
$496$	4.80848	+	8.32854i	0.215907	+	0.373962i
$497$	−17.4988	−	8.41898i	−0.784928	−	0.377643i
$498$	−3.46224	−	25.1101i	−0.155147	−	1.12521i
$499$	−23.6514	+	19.8459i	−1.05878	+	0.888424i	−0.993990	−	0.109474i	$-0.965083\pi$
$499$	−23.6514	+	19.8459i	−1.05878	+	0.888424i	−0.0647931	+	0.997899i	$0.520639\pi$
$500$	−9.67009	−	3.51962i	−0.432459	−	0.157402i
$501$	−1.91559	+	1.48859i	−0.0855821	+	0.0665054i
$502$	1.18497	−	6.72028i	0.0528876	−	0.299941i
$503$	15.5416	+	26.9189i	0.692966	+	1.20025i	0.970861	+	0.239642i	$0.0770299\pi$
$503$	15.5416	+	26.9189i	0.692966	+	1.20025i	−0.277895	+	0.960611i	$0.589637\pi$
$504$	−0.00113232	−	7.93725i	−5.04376e−5	−	0.353553i
$505$	−21.4448	+	37.1434i	−0.954279	+	1.65286i
$506$	−14.3559	−	12.0460i	−0.638197	−	0.535511i
$507$	8.09047	−	2.60545i	0.359311	−	0.115712i
$508$	−2.01382	−	11.4210i	−0.0893489	−	0.506723i
$509$	1.22611	+	6.95362i	0.0543464	+	0.308214i	0.999849	−	0.0174020i	$-0.00553950\pi$
$509$	1.22611	+	6.95362i	0.0543464	+	0.308214i	−0.945502	+	0.325616i	$0.894428\pi$
$510$	22.3320	+	0.838158i	0.988877	+	0.0371143i
$511$	−9.26267	−	4.45643i	−0.409757	−	0.197141i
$512$	−1.00000			−0.0441942
$513$	8.38735	+	0.947939i	0.370311	+	0.0418525i
$514$	11.9317	−	20.6663i	0.526285	−	0.911552i
$515$	17.1720	+	14.4090i	0.756689	+	0.634937i
$516$	3.77183	+	0.141563i	0.166045	+	0.00623198i
$517$	10.4307	+	3.79647i	0.458742	+	0.166968i
$518$	3.31557	+	7.34078i	0.145678	+	0.322535i
$519$	−1.81005	+	8.40776i	−0.0794525	+	0.369060i
$520$	−7.81750	−	6.55966i	−0.342820	−	0.287660i
$521$	3.61772	+	6.26607i	0.158495	+	0.274521i	0.934326	−	0.356419i	$-0.116002\pi$
$521$	3.61772	+	6.26607i	0.158495	+	0.274521i	−0.775831	+	0.630941i	$0.782669\pi$
$522$	2.00541	+	20.0874i	0.0877746	+	0.879202i
$523$	8.63323	−	14.9532i	0.377505	−	0.653858i	−0.613194	−	0.789933i	$-0.710115\pi$
$523$	8.63323	−	14.9532i	0.377505	−	0.653858i	0.990699	+	0.136075i	$0.0434488\pi$
$524$	10.4009	+	8.72743i	0.454367	+	0.381259i
$525$	35.7214	+	4.92018i	1.55901	+	0.214734i
$526$	5.05056	+	28.6431i	0.220215	+	1.24890i
$527$	26.4971	−	22.2337i	1.15423	−	0.968514i
$528$	−0.523819	−	3.79902i	−0.0227963	−	0.165331i
$529$	−45.7059	+	16.6356i	−1.98721	+	0.723287i
$530$	19.9424	−	34.5413i	0.866243	−	1.50038i
$531$	−0.602430	−	6.03429i	−0.0261432	−	0.261866i
$532$	1.16249	−	4.13762i	0.0504002	−	0.179388i
$533$	−28.5368	+	10.3866i	−1.23607	+	0.449892i
$534$	−22.8939	+	7.37273i	−0.990715	+	0.319049i
$535$	−6.18783	−	35.0929i	−0.267523	−	1.51720i
$536$	3.49657	−	2.93397i	0.151029	−	0.126728i
$537$	33.6918	+	1.26451i	1.45391	+	0.0545678i
$538$	−2.41465	+	13.6941i	−0.104103	+	0.590396i
$539$	0.374895	−	15.4943i	0.0161479	−	0.667386i
$540$	−18.1211	+	4.36783i	−0.779810	+	0.187961i
$541$	5.96279	+	10.3279i	0.256360	+	0.444029i	0.965264	−	0.261276i	$-0.0841433\pi$
$541$	5.96279	+	10.3279i	0.256360	+	0.444029i	−0.708904	+	0.705305i	$0.750810\pi$
$542$	−21.3714	−	17.9327i	−0.917979	−	0.770276i
$543$	−15.1974	+	24.1805i	−0.652185	+	1.03768i
$544$	0.624563	+	3.54207i	0.0267779	+	0.151865i
$545$	−23.4663	+	19.6906i	−1.00519	+	0.843451i
$546$	11.5272	+	6.08853i	0.493320	+	0.260565i
$547$	24.4309	−	8.89212i	1.04459	−	0.380199i	0.237971	−	0.971272i	$-0.423518\pi$
$547$	24.4309	−	8.89212i	1.04459	−	0.380199i	0.806618	+	0.591073i	$0.201295\pi$
$548$	−13.9986			−0.597990
$549$	−4.77503	−	4.65956i	−0.203793	−	0.198865i
$550$	17.4221			0.742882
$551$	−1.89813	+	10.7648i	−0.0808630	+	0.458597i
$552$	−13.5782	−	5.52718i	−0.577927	−	0.235253i
$553$	−0.245138	+	0.341233i	−0.0104243	+	0.0145107i
$554$	3.26436	+	18.5131i	0.138689	+	0.786546i
$555$	14.9365	−	11.6071i	0.634018	−	0.492692i
$556$	17.5833	−	6.39980i	0.745698	−	0.271412i
$557$	29.5309			1.25126			0.625632	−	0.780119i	$-0.284841\pi$
$557$	29.5309			1.25126			0.625632	+	0.780119i	$0.284841\pi$
$558$	−16.2577	+	23.8340i	−0.688245	+	1.00897i
$559$	−3.09966	+	5.36877i	−0.131102	+	0.227075i
$560$	0.712782	+	9.46428i	0.0301205	+	0.399939i
$561$	−13.1292	+	4.22813i	−0.554317	+	0.178512i
$562$	−4.38783	−	1.59704i	−0.185089	−	0.0673670i
$563$	18.2419	−	15.3067i	0.768803	−	0.645102i	−0.171599	−	0.985167i	$-0.554893\pi$
$563$	18.2419	−	15.3067i	0.768803	−	0.645102i	0.940402	+	0.340064i	$0.110449\pi$
$564$	8.67725	+	0.325673i	0.365378	+	0.0137133i
$565$	−8.21015	+	2.98825i	−0.345404	+	0.125717i
$566$	−1.55608			−0.0654070
$567$	21.4545	−	10.3297i	0.901006	−	0.433806i
$568$	−7.33959			−0.307962
$569$	5.52481	−	2.01087i	0.231612	−	0.0842999i	−0.223607	−	0.974679i	$-0.571783\pi$
$569$	5.52481	−	2.01087i	0.231612	−	0.0842999i	0.455219	+	0.890380i	$0.349561\pi$
$570$	−10.0860	−	0.378547i	−0.422458	−	0.0158556i
$571$	−18.8800	+	15.8422i	−0.790103	+	0.662975i	−0.945771	−	0.324834i	$-0.894691\pi$
$571$	−18.8800	+	15.8422i	−0.790103	+	0.662975i	0.155668	+	0.987809i	$0.450247\pi$
$572$	5.91880	+	2.15427i	0.247477	+	0.0900744i
$573$	−5.81676	+	1.87322i	−0.242999	+	0.0782551i
$574$	25.4513	+	12.2450i	1.06231	+	0.511098i
$575$	33.3001	−	57.6775i	1.38871	−	2.40532i
$576$	−1.30103	−	2.70320i	−0.0542097	−	0.112633i
$577$	14.6795			0.611115			0.305558	−	0.952174i	$-0.401157\pi$
$577$	14.6795			0.611115			0.305558	+	0.952174i	$0.401157\pi$
$578$	−3.81859	+	1.38985i	−0.158832	+	0.0578103i
$579$	−8.86581	+	6.88958i	−0.368451	+	0.286321i
$580$	−4.19173	−	23.7725i	−0.174052	−	0.987098i
$581$	−15.9378	−	35.2868i	−0.661210	−	1.46394i
$582$	−0.916317	−	0.372998i	−0.0379826	−	0.0154613i
$583$	−4.27476	+	24.2434i	−0.177043	+	1.00406i
$584$	−3.88508			−0.160766
$585$	7.56127	−	29.6666i	0.312620	−	1.22656i
$586$	−5.20102			−0.214852
$587$	18.3049	−	6.66246i	0.755526	−	0.274989i	0.0645969	−	0.997911i	$-0.479424\pi$
$587$	18.3049	−	6.66246i	0.755526	−	0.274989i	0.690929	+	0.722922i	$0.257202\pi$
$588$	−3.43631	−	11.6272i	−0.141711	−	0.479498i
$589$	−11.9672	+	10.0416i	−0.493098	+	0.413759i
$590$	1.25920	+	7.14129i	0.0518406	+	0.294002i
$591$	4.81805	−	7.66594i	0.198188	−	0.315335i
$592$	2.33217	+	1.95692i	0.0958516	+	0.0804291i
$593$	−10.1112	−	17.5131i	−0.415217	−	0.719178i	0.580234	−	0.814450i	$-0.302961\pi$
$593$	−10.1112	−	17.5131i	−0.415217	−	0.719178i	−0.995451	+	0.0952724i	$0.969628\pi$
$594$	9.58802	−	6.35864i	0.393401	−	0.260898i
$595$	33.0780	−	8.43576i	1.35606	−	0.345832i
$596$	1.99409	−	11.3090i	0.0816810	−	0.463236i
$597$	−23.5097	−	0.882360i	−0.962188	−	0.0361126i
$598$	18.4449	−	15.4771i	0.754269	−	0.632907i
$599$	6.21362	+	35.2392i	0.253882	+	1.43983i	0.798927	+	0.601428i	$0.205401\pi$
$599$	6.21362	+	35.2392i	0.253882	+	1.43983i	−0.545046	+	0.838406i	$0.683488\pi$
$600$	12.9728	−	4.17775i	0.529612	−	0.170556i
$601$	41.2382	−	15.0095i	1.68214	−	0.612250i	0.688541	−	0.725197i	$-0.258251\pi$
$601$	41.2382	−	15.0095i	1.68214	−	0.612250i	0.993601	+	0.112947i	$0.0360292\pi$
$602$	5.58680	−	1.42478i	0.227701	−	0.0580698i
$603$	12.4803	+	5.63475i	0.508237	+	0.229465i
$604$	1.71597	−	2.97214i	0.0698217	−	0.120935i
$605$	20.5550	−	7.48141i	0.835680	−	0.304162i
$606$	−2.82856	−	20.5142i	−0.114902	−	0.833334i
$607$	26.1108	−	21.9096i	1.05981	−	0.889282i	0.0657150	−	0.997838i	$-0.479067\pi$
$607$	26.1108	−	21.9096i	1.05981	−	0.889282i	0.994090	+	0.108556i	$0.0346227\pi$
$608$	−0.282078	−	1.59974i	−0.0114398	−	0.0648782i
$609$	11.6302	+	28.5593i	0.471278	+	1.15728i
$610$	6.11138	+	5.12806i	0.247443	+	0.207629i
$611$	−7.13090	+	12.3511i	−0.288486	+	0.499672i
$612$	−8.76236	+	6.29667i	−0.354197	+	0.254528i
$613$	5.64101	+	9.77051i	0.227838	+	0.394627i	0.957167	−	0.289536i	$-0.0935009\pi$
$613$	5.64101	+	9.77051i	0.227838	+	0.394627i	−0.729329	+	0.684163i	$0.760168\pi$
$614$	−4.87570	−	4.09120i	−0.196767	−	0.165107i
$615$	13.9596	−	64.8428i	0.562905	−	2.61472i
$616$	−2.41130	−	5.33871i	−0.0971541	−	0.215103i
$617$	−12.4010	−	4.51360i	−0.499246	−	0.181711i	0.0801090	−	0.996786i	$-0.474473\pi$
$617$	−12.4010	−	4.51360i	−0.499246	−	0.181711i	−0.579355	+	0.815076i	$0.696695\pi$
$618$	−10.8157	−	0.405933i	−0.435072	−	0.0163290i
$619$	17.9630	+	15.0728i	0.721995	+	0.605826i	0.927936	−	0.372738i	$-0.121581\pi$
$619$	17.9630	+	15.0728i	0.721995	+	0.605826i	−0.205941	+	0.978564i	$0.566026\pi$
$620$	17.2494	−	29.8769i	0.692754	−	1.19988i
$621$	−2.72461	−	43.8957i	−0.109335	−	1.76148i
$622$	−14.7597			−0.591810
$623$	−30.3481	+	20.7075i	−1.21587	+	0.829627i
$624$	4.92382	+	0.184800i	0.197111	+	0.00739791i
$625$	−0.421542	−	2.39068i	−0.0168617	−	0.0956273i
$626$	−0.192909	−	1.09404i	−0.00771018	−	0.0437266i
$627$	5.92970	−	1.90960i	0.236810	−	0.0762620i
$628$	−14.2109	−	11.9244i	−0.567077	−	0.475834i
$629$	5.47498	−	9.48294i	0.218302	−	0.378109i
$630$	−24.6565	+	14.2401i	−0.982339	+	0.567341i
$631$	4.36566	+	7.56154i	0.173794	+	0.301020i	0.939743	−	0.341881i	$-0.111064\pi$
$631$	4.36566	+	7.56154i	0.173794	+	0.301020i	−0.765949	+	0.642901i	$0.777731\pi$
$632$	−0.0275762	+	0.156392i	−0.00109692	+	0.00622095i
$633$	−20.6979	+	16.0842i	−0.822667	+	0.639291i
$634$	25.6511	+	9.33624i	1.01874	+	0.370789i
$635$	−31.8692	+	26.7415i	−1.26469	+	1.06120i
$636$	2.63040	+	19.0771i	0.104302	+	0.756456i
$637$	19.5215	+	3.93127i	0.773469	+	0.155763i
$638$	7.44950	+	12.9029i	0.294928	+	0.510831i
$639$	−9.54905	−	19.8404i	−0.377755	−	0.784874i
$640$	1.79365	+	3.10668i	0.0709001	+	0.122802i
$641$	−5.70400	+	32.3490i	−0.225295	+	1.27771i	0.636827	+	0.771007i	$0.280247\pi$
$641$	−5.70400	+	32.3490i	−0.225295	+	1.27771i	−0.862121	+	0.506702i	$0.830864\pi$
$642$	12.7560	+	11.5459i	0.503438	+	0.455680i
$643$	12.6672	−	10.6290i	0.499545	−	0.419168i	−0.357887	−	0.933765i	$-0.616503\pi$
$643$	12.6672	−	10.6290i	0.499545	−	0.419168i	0.857432	+	0.514597i	$0.172058\pi$
$644$	−22.2832	−	2.22142i	−0.878080	−	0.0875360i
$645$	−6.32553	−	11.9718i	−0.249067	−	0.471389i
$646$	−5.49023	+	1.99828i	−0.216010	+	0.0786213i
$647$	4.75023	−	8.22764i	0.186751	−	0.323462i	−0.757414	−	0.652935i	$-0.773538\pi$
$647$	4.75023	−	8.22764i	0.186751	−	0.323462i	0.944165	+	0.329473i	$0.106871\pi$
$648$	5.61462	−	7.03392i	0.220563	−	0.276318i
$649$	−2.23784	−	3.87606i	−0.0878430	−	0.152148i
$650$	−3.88703	+	22.0444i	−0.152462	+	0.864654i
$651$	−13.5032	+	41.9508i	−0.529232	+	1.64418i
$652$	−12.4043	−	4.51478i	−0.485788	−	0.176812i
$653$	15.0865	+	5.49104i	0.590381	+	0.214881i	0.619897	−	0.784683i	$-0.287174\pi$
$653$	15.0865	+	5.49104i	0.590381	+	0.214881i	−0.0295159	+	0.999564i	$0.509397\pi$
$654$	3.11285	−	14.4593i	0.121722	−	0.565403i
$655$	8.45776	−	47.9664i	0.330472	−	1.87420i
$656$	10.6751			0.416793
$657$	−5.05462	−	10.5022i	−0.197200	−	0.409728i
$658$	12.8527	−	3.27777i	0.501050	−	0.127781i
$659$	−26.5624	−	22.2885i	−1.03472	−	0.868237i	−0.0433188	−	0.999061i	$-0.513793\pi$
$659$	−26.5624	−	22.2885i	−1.03472	−	0.868237i	−0.991406	+	0.130825i	$0.958238\pi$
$660$	−10.8628	+	8.44144i	−0.422834	+	0.328582i
$661$	−29.1235	−	10.6001i	−1.13277	−	0.412296i	−0.293474	−	0.955967i	$-0.594812\pi$
$661$	−29.1235	−	10.6001i	−1.13277	−	0.412296i	−0.839298	+	0.543671i	$0.817034\pi$
$662$	−24.8350	−	9.03920i	−0.965239	−	0.351318i
$663$	−2.42066	−	17.5559i	−0.0940107	−	0.681816i
$664$	−11.2106	−	9.40685i	−0.435057	−	0.365057i
$665$	−14.9394	+	3.80993i	−0.579324	+	0.147743i
$666$	−2.25573	+	8.85036i	−0.0874078	+	0.342944i
$667$	56.9550			2.20531
$668$	−0.243219	+	1.37936i	−0.00941041	+	0.0533691i
$669$	6.41290	−	2.06521i	0.247937	−	0.0798455i
$670$	−15.3865	−	5.60024i	−0.594434	−	0.216356i
$671$	−4.62706	−	1.68411i	−0.178626	−	0.0650145i
$672$	−3.07570	−	3.39707i	−0.118648	−	0.131045i
$673$	5.06620	−	28.7318i	0.195288	−	1.10753i	−0.716721	−	0.697360i	$-0.754358\pi$
$673$	5.06620	−	28.7318i	0.195288	−	1.10753i	0.912009	−	0.410171i	$-0.134531\pi$
$674$	−1.22354	−	2.11924i	−0.0471292	−	0.0816301i
$675$	28.1714	+	29.6327i	1.08432	+	1.14056i
$676$	2.45364	−	4.24983i	0.0943707	−	0.163455i
$677$	32.7903	−	11.9347i	1.26023	−	0.458688i	0.376387	−	0.926463i	$-0.377166\pi$
$677$	32.7903	−	11.9347i	1.26023	−	0.458688i	0.883848	+	0.467775i	$0.154944\pi$
$678$	2.24479	−	3.57166i	0.0862108	−	0.137169i
$679$	−1.50377	−	0.149911i	−0.0577092	−	0.00575305i
$680$	9.88385	−	8.29354i	0.379028	−	0.318043i
$681$	−6.00944	+	1.93528i	−0.230282	+	0.0741599i
$682$	−3.69751	+	20.9696i	−0.141585	+	0.802968i
$683$	−3.62981	−	6.28702i	−0.138891	−	0.240566i	0.788186	−	0.615437i	$-0.211020\pi$
$683$	−3.62981	−	6.28702i	−0.138891	−	0.240566i	−0.927077	+	0.374871i	$0.877687\pi$
$684$	3.95744	−	2.84384i	0.151317	−	0.108737i
$685$	25.1085	+	43.4892i	0.959347	+	1.66164i
$686$	−10.0654	−	15.5463i	−0.384299	−	0.593561i
$687$	23.7115	−	18.4261i	0.904651	−	0.703000i
$688$	1.66936	−	1.40076i	0.0636439	−	0.0534035i
$689$	−29.7218	−	10.8178i	−1.13231	−	0.412127i
$690$	7.18328	+	52.0970i	0.273463	+	1.98330i
$691$	−6.49426	+	36.8308i	−0.247053	+	1.40111i	0.568622	+	0.822599i	$0.307477\pi$
$691$	−6.49426	+	36.8308i	−0.247053	+	1.40111i	−0.815675	+	0.578510i	$0.803634\pi$
$692$	2.48272	+	4.30020i	0.0943788	+	0.163469i
$693$	11.2944	−	13.4641i	0.429040	−	0.511458i
$694$	−6.64417	+	11.5080i	−0.252209	+	0.436839i
$695$	−51.4204	−	43.1468i	−1.95049	−	1.63665i
$696$	8.64108	+	7.82136i	0.327539	+	0.296468i
$697$	−6.66728	−	37.8120i	−0.252541	−	1.43223i
$698$	−1.90954	−	10.8295i	−0.0722770	−	0.409903i
$699$	−13.4405	+	21.3850i	−0.508366	+	0.808855i
$700$	17.1967	−	11.7339i	0.649974	−	0.443498i
$701$	−25.3690			−0.958175			−0.479088	−	0.877767i	$-0.659032\pi$
$701$	−25.3690			−0.958175			−0.479088	+	0.877767i	$0.659032\pi$
$702$	5.90651	+	13.5505i	0.222927	+	0.511432i
$703$	−2.47272	+	4.28288i	−0.0932605	+	0.161532i
$704$	−1.69611	−	1.42321i	−0.0639246	−	0.0536391i
$705$	−14.5522	−	27.5416i	−0.548066	−	1.03728i
$706$	−14.8145	−	5.39203i	−0.557551	−	0.202932i
$707$	−13.0207	−	28.8284i	−0.489695	−	1.08420i
$708$	−2.59580	−	2.34955i	−0.0975560	−	0.0883015i
$709$	22.4329	+	18.8234i	0.842484	+	0.706928i	0.958121	−	0.286363i	$-0.0924465\pi$
$709$	22.4329	+	18.8234i	0.842484	+	0.706928i	−0.115637	+	0.993292i	$0.536891\pi$
$710$	13.1646	+	22.8018i	0.494059	+	0.855736i
$711$	−0.458638	+	0.128928i	−0.0172003	+	0.00483516i
$712$	−6.94314	+	12.0259i	−0.260205	+	0.450689i
$713$	62.3545	+	52.3216i	2.33519	+	1.95946i
$714$	−10.1117	+	13.0160i	−0.378421	+	0.487112i
$715$	−3.92360	−	22.2518i	−0.146734	−	0.832171i
$716$	14.9116	−	12.5123i	0.557272	−	0.467607i
$717$	−0.380363	−	0.154832i	−0.0142049	−	0.00578229i
$718$	−1.79452	+	0.653151i	−0.0669708	+	0.0243754i
$719$	−3.41415	+	5.91348i	−0.127326	+	0.220536i	−0.922640	−	0.385663i	$-0.873973\pi$
$719$	−3.41415	+	5.91348i	−0.127326	+	0.220536i	0.795314	+	0.606198i	$0.207306\pi$
$720$	−6.06441	+	8.89049i	−0.226007	+	0.331329i
$721$	−16.0202	+	4.08556i	−0.596622	+	0.152154i
$722$	−15.3745	+	5.59588i	−0.572181	+	0.208257i
$723$	−8.16614	−	7.39147i	−0.303702	−	0.274892i
$724$	2.86328	+	16.2385i	0.106413	+	0.603497i
$725$	−40.5612	+	34.0349i	−1.50641	+	1.26402i
$726$	−5.62008	+	8.94204i	−0.208581	+	0.331870i
$727$	−6.67878	+	37.8773i	−0.247702	+	1.40479i	0.566429	+	0.824110i	$0.308324\pi$
$727$	−6.67878	+	37.8773i	−0.247702	+	1.40479i	−0.814132	+	0.580680i	$0.802787\pi$
$728$	7.29312	−	1.85994i	0.270301	−	0.0689340i
$729$	26.3189	+	6.02611i	0.974775	+	0.223189i
$730$	6.96846	+	12.0697i	0.257914	+	0.446720i
$731$	−6.00422	−	5.03814i	−0.222074	−	0.186342i
$732$	−3.84923	−	0.144468i	−0.142272	−	0.00533971i
$733$	7.00285	+	39.7151i	0.258656	+	1.46691i	0.786510	+	0.617577i	$0.211886\pi$
$733$	7.00285	+	39.7151i	0.258656	+	1.46691i	−0.527854	+	0.849335i	$0.677003\pi$
$734$	17.4970	−	14.6817i	0.645825	−	0.541912i
$735$	−29.9585	+	31.5306i	−1.10504	+	1.16302i
$736$	−7.95356	+	2.89486i	−0.293172	+	0.106706i
$737$	10.1062			0.372268
$738$	13.8887	+	28.8570i	0.511250	+	1.06224i
$739$	16.3349			0.600889			0.300445	−	0.953799i	$-0.402865\pi$
$739$	16.3349			0.600889			0.300445	+	0.953799i	$0.402865\pi$
$740$	1.89646	−	10.7553i	0.0697152	−	0.395374i
$741$	1.09327	+	7.92898i	0.0401623	+	0.291278i
$742$	12.1086	+	26.8088i	0.444519	+	0.984181i
$743$	−2.57617	−	14.6102i	−0.0945104	−	0.535995i	−0.994896	−	0.100903i	$-0.967827\pi$
$743$	−2.57617	−	14.6102i	−0.0945104	−	0.535995i	0.900386	−	0.435092i	$-0.143284\pi$
$744$	2.27520	+	16.5010i	0.0834128	+	0.604955i
$745$	−38.7103	+	14.0894i	−1.41823	+	0.516195i
$746$	−25.7292			−0.942013
$747$	10.8432	−	42.5433i	0.396732	−	1.55658i
$748$	−3.98177	+	6.89663i	−0.145588	+	0.252166i
$749$	23.6831	+	11.3943i	0.865360	+	0.416340i
$750$	−13.2147	−	11.9611i	−0.482532	−	0.436757i
$751$	−17.6308	−	6.41707i	−0.643356	−	0.234162i	−0.000321659	−	1.00000i	$-0.500102\pi$
$751$	−17.6308	−	6.41707i	−0.643356	−	0.234162i	−0.643034	+	0.765838i	$0.722325\pi$
$752$	3.84044	−	3.22251i	0.140047	−	0.117513i
$753$	6.28946	−	10.0071i	0.229201	−	0.364678i
$754$	−17.9883	+	6.54720i	−0.655094	+	0.238435i
$755$	−12.3113			−0.448056
$756$	5.18139	−	12.7339i	0.188445	−	0.463129i
$757$	−21.7187			−0.789379			−0.394690	−	0.918815i	$-0.629148\pi$
$757$	−21.7187			−0.789379			−0.394690	+	0.918815i	$0.629148\pi$
$758$	2.89273	−	1.05287i	0.105069	−	0.0382419i
$759$	−15.1638	−	28.6993i	−0.550413	−	1.04172i
$760$	−4.46395	+	3.74570i	−0.161925	+	0.135871i
$761$	−39.0444	−	14.2110i	−1.41536	−	0.515148i	−0.482660	−	0.875808i	$-0.660329\pi$
$761$	−39.0444	−	14.2110i	−1.41536	−	0.515148i	−0.932697	+	0.360660i	$0.882552\pi$
$762$	4.22751	−	19.6369i	0.153146	−	0.711371i
$763$	−1.69674	−	22.5292i	−0.0614260	−	0.815610i
$764$	−1.76408	+	3.05547i	−0.0638221	+	0.110543i
$765$	35.2783	+	15.9279i	1.27549	+	0.575874i
$766$	5.80785			0.209846
$767$	5.40371	−	1.96679i	0.195117	−	0.0710166i
$768$	−1.60423	−	0.653023i	−0.0578877	−	0.0235639i
$769$	−4.20100	−	23.8250i	−0.151492	−	0.859153i	−0.961923	−	0.273319i	$-0.911878\pi$
$769$	−4.20100	−	23.8250i	−0.151492	−	0.859153i	0.810431	−	0.585833i	$-0.199233\pi$
$770$	−12.2607	+	17.0669i	−0.441844	+	0.615049i
$771$	32.6368	−	25.3619i	1.17538	−	0.913386i
$772$	−1.12568	+	6.38403i	−0.0405140	+	0.229766i
$773$	13.1177			0.471810			0.235905	−	0.971776i	$-0.424195\pi$
$773$	13.1177			0.471810			0.235905	+	0.971776i	$0.424195\pi$
$774$	5.95844	+	2.69019i	0.214172	+	0.0966969i
$775$	−75.6726			−2.71824
$776$	−0.536740	+	0.195358i	−0.0192679	+	0.00701293i
$777$	0.525239	+	13.9415i	0.0188428	+	0.500147i
$778$	25.3853	−	21.3008i	0.910108	−	0.763671i
$779$	3.01122	+	17.0775i	0.107888	+	0.611864i
$780$	−8.25747	−	15.6282i	−0.295665	−	0.559580i
$781$	−12.4488	−	10.4458i	−0.445452	−	0.373778i
$782$	15.2213	+	26.3640i	0.544312	+	0.942776i
$783$	−9.90040	+	33.5345i	−0.353811	+	1.19842i
$784$	−5.97574	−	3.64561i	−0.213419	−	0.130200i
$785$	−11.5559	+	65.5369i	−0.412449	+	2.33911i
$786$	10.9863	+	20.7929i	0.391869	+	0.741657i
$787$	−21.9744	+	18.4387i	−0.783304	+	0.657270i	−0.944078	−	0.329721i	$-0.893045\pi$
$787$	−21.9744	+	18.4387i	−0.783304	+	0.657270i	0.160774	+	0.986991i	$0.448601\pi$
$788$	−0.907746	−	5.14808i	−0.0323371	−	0.183393i
$789$	−10.6024	+	49.2484i	−0.377454	+	1.75329i
$790$	0.535323	−	0.194842i	0.0190460	−	0.00693216i
$791$	1.74296	−	6.20369i	0.0619726	−	0.220578i
$792$	1.64052	−	6.43658i	0.0582933	−	0.228714i
$793$	3.16327	−	5.47895i	0.112331	−	0.194563i
$794$	0.883025	−	0.321395i	0.0313374	−	0.0114059i
$795$	54.5485	−	42.3894i	1.93464	−	1.50340i
$796$	−10.4051	+	8.73091i	−0.368799	+	0.309459i
$797$	2.10926	+	11.9622i	0.0747139	+	0.423723i	0.999106	+	0.0422795i	$0.0134620\pi$
$797$	2.10926	+	11.9622i	0.0747139	+	0.423723i	−0.924392	+	0.381444i	$0.875427\pi$
$798$	4.56686	−	5.87857i	0.161665	−	0.208099i
$799$	−13.8130	−	11.5905i	−0.488668	−	0.410041i
$800$	3.93433	−	6.81445i	0.139099	−	0.240927i
$801$	−41.5417	−	3.12266i	−1.46780	−	0.110334i
$802$	0.672972	+	1.16562i	0.0237635	+	0.0411595i
$803$	−6.58953	−	5.52927i	−0.232539	−	0.195124i
$804$	7.52527	−	2.42343i	0.265396	−	0.0854678i
$805$	33.0669	+	73.2112i	1.16545	+	2.58036i
$806$	−25.7082	−	9.35701i	−0.905532	−	0.329587i
$807$	−12.8162	+	20.3918i	−0.451153	+	0.717824i
$808$	−9.15880	−	7.68514i	−0.322205	−	0.270362i
$809$	19.9107	−	34.4863i	0.700021	−	1.21247i	−0.268437	−	0.963297i	$-0.586507\pi$
$809$	19.9107	−	34.4863i	0.700021	−	1.21247i	0.968458	−	0.249175i	$-0.0801596\pi$
$810$	−31.9228	−	4.82651i	−1.12165	−	0.169586i
$811$	−47.8526			−1.68033			−0.840166	−	0.542329i	$-0.817543\pi$
$811$	−47.8526			−1.68033			−0.840166	+	0.542329i	$0.817543\pi$
$812$	16.0433	+	7.71870i	0.563008	+	0.270873i
$813$	−22.5742	−	42.7242i	−0.791711	−	1.49840i
$814$	1.17052	+	6.63832i	0.0410265	+	0.232673i
$815$	8.22284	+	46.6340i	0.288033	+	1.63352i
$816$	−1.31111	+	6.09016i	−0.0458980	+	0.213198i
$817$	2.71175	+	2.27543i	0.0948722	+	0.0796072i
$818$	−18.1845	+	31.4965i	−0.635807	+	1.10125i
$819$	14.5164	+	17.2950i	0.507244	+	0.604335i
$820$	−19.1474	−	33.1642i	−0.668655	−	1.15815i
$821$	−0.522087	+	2.96090i	−0.0182210	+	0.103336i	−0.992562	−	0.121741i	$-0.961152\pi$
$821$	−0.522087	+	2.96090i	−0.0182210	+	0.103336i	0.974341	+	0.225077i	$0.0722634\pi$
$822$	−22.4570	−	9.14140i	−0.783278	−	0.318843i
$823$	−33.0655	−	12.0349i	−1.15259	−	0.419509i	−0.306146	−	0.951985i	$-0.599040\pi$
$823$	−33.0655	−	12.0349i	−1.15259	−	0.419509i	−0.846445	+	0.532476i	$0.821262\pi$
$824$	−4.78690	+	4.01668i	−0.166760	+	0.139928i
$825$	27.9491	+	11.3770i	0.973064	+	0.396098i
$826$	−4.81943	−	2.31871i	−0.167689	−	0.0806782i
$827$	−0.410700	−	0.711353i	−0.0142814	−	0.0247362i	0.858796	−	0.512317i	$-0.171213\pi$
$827$	−0.410700	−	0.711353i	−0.0142814	−	0.0247362i	−0.873078	+	0.487581i	$0.837879\pi$
$828$	−18.1732	−	17.7338i	−0.631563	−	0.616291i
$829$	7.23767	+	12.5360i	0.251375	+	0.435394i	0.963905	−	0.266248i	$-0.0857840\pi$
$829$	7.23767	+	12.5360i	0.251375	+	0.435394i	−0.712530	+	0.701642i	$0.752451\pi$
$830$	−9.11619	+	51.7005i	−0.316428	+	1.79455i
$831$	−6.85269	+	31.8310i	−0.237717	+	1.10421i
$832$	2.17922	−	1.82858i	0.0755509	−	0.0633947i
$833$	−9.18079	+	23.4434i	−0.318095	+	0.812266i
$834$	32.3869	+	1.21554i	1.12147	+	0.0420906i
$835$	4.72149	−	1.71848i	0.163394	−	0.0594705i
$836$	1.79833	−	3.11480i	0.0621966	−	0.107728i
$837$	−41.6454	+	27.6186i	−1.43947	+	0.954639i
$838$	−7.42812	−	12.8659i	−0.256600	−	0.444444i
$839$	0.519920	−	2.94861i	0.0179496	−	0.101797i	−0.974517	−	0.224315i	$-0.927986\pi$
$839$	0.519920	−	2.94861i	0.0179496	−	0.101797i	0.992466	+	0.122517i	$0.0390967\pi$
$840$	−5.03692	+	15.6484i	−0.173790	+	0.539920i
$841$	−15.2988	−	5.56832i	−0.527546	−	0.192011i
$842$	−15.9905	−	5.82008i	−0.551070	−	0.200573i
$843$	−5.99619	−	5.42737i	−0.206520	−	0.186929i
$844$	−2.62797	+	14.9040i	−0.0904586	+	0.513016i
$845$	−17.6038			−0.605590
$846$	13.7077	+	6.18890i	0.471279	+	0.212779i
$847$	−4.36370	+	15.5316i	−0.149938	+	0.533672i
$848$	8.51717	+	7.14675i	0.292481	+	0.245421i
$849$	−2.49631	−	1.01616i	−0.0856733	−	0.0348744i
$850$	−26.5945	−	9.67961i	−0.912184	−	0.332008i
$851$	24.2141	+	8.81320i	0.830048	+	0.302113i
$852$	−11.7744	−	4.79292i	−0.403384	−	0.164203i
$853$	32.2146	+	27.0312i	1.10301	+	0.925532i	0.997624	−	0.0688994i	$-0.0219487\pi$
$853$	32.2146	+	27.0312i	1.10301	+	0.925532i	0.105383	+	0.994432i	$0.466393\pi$
$854$	−5.70145	+	1.45402i	−0.195100	+	0.0497556i
$855$	−15.9331	−	7.19369i	−0.544902	−	0.246019i
$856$	9.93348			0.339519
$857$	−6.85053	+	38.8513i	−0.234010	+	1.32714i	0.610679	+	0.791878i	$0.290896\pi$
$857$	−6.85053	+	38.8513i	−0.234010	+	1.32714i	−0.844689	+	0.535257i	$0.820215\pi$
$858$	8.08834	+	7.32106i	0.276131	+	0.249937i
$859$	−10.1290	−	3.68664i	−0.345596	−	0.125787i	0.163390	−	0.986562i	$-0.447757\pi$
$859$	−10.1290	−	3.68664i	−0.345596	−	0.125787i	−0.508986	+	0.860775i	$0.669979\pi$
$860$	−7.34597	−	2.67371i	−0.250495	−	0.0911729i
$861$	32.8334	+	36.2641i	1.11896	+	1.23588i
$862$	0.0499191	−	0.283105i	0.00170025	−	0.00964261i
$863$	21.2282	+	36.7683i	0.722617	+	1.25161i	0.959947	+	0.280180i	$0.0903942\pi$
$863$	21.2282	+	36.7683i	0.722617	+	1.25161i	−0.237331	+	0.971429i	$0.576272\pi$
$864$	−0.321906	−	5.18617i	−0.0109515	−	0.176437i
$865$	8.90623	−	15.4261i	0.302821	−	0.524501i
$866$	19.6807	−	7.16319i	0.668777	−	0.243415i
$867$	−7.03351	−	0.263980i	−0.238871	−	0.00896523i
$868$	10.4734	+	23.1886i	0.355492	+	0.787071i
$869$	−0.269351	+	0.226012i	−0.00913710	+	0.00766694i
$870$	8.79947	−	40.8739i	0.298330	−	1.38575i
$871$	−2.25479	+	12.7876i	−0.0764007	+	0.433290i
$872$	−4.26967	−	7.39528i	−0.144589	−	0.250436i
$873$	−1.22641	−	1.19675i	−0.0415076	−	0.0405039i
$874$	−6.87456	−	11.9071i	−0.232535	−	0.402763i
$875$	−24.5347	−	11.8041i	−0.829425	−	0.399051i
$876$	−6.23257	−	2.53705i	−0.210579	−	0.0857189i
$877$	20.1971	−	16.9474i	0.682007	−	0.572272i	−0.234585	−	0.972096i	$-0.575373\pi$
$877$	20.1971	−	16.9474i	0.682007	−	0.572272i	0.916592	+	0.399823i	$0.130929\pi$
$878$	12.7655	+	4.64628i	0.430816	+	0.156804i
$879$	−8.34365	−	3.39639i	−0.281424	−	0.114557i
$880$	−1.37923	+	7.82201i	−0.0464939	+	0.263680i
$881$	−17.4217	−	30.1753i	−0.586953	−	1.01663i	−0.994629	−	0.103506i	$-0.966994\pi$
$881$	−17.4217	−	30.1753i	−0.586953	−	1.01663i	0.407676	−	0.913127i	$-0.366339\pi$
$882$	2.08019	−	20.8967i	0.0700436	−	0.703629i
$883$	11.9222	−	20.6499i	0.401214	−	0.694923i	−0.592658	−	0.805454i	$-0.701922\pi$
$883$	11.9222	−	20.6499i	0.401214	−	0.694923i	0.993873	+	0.110530i	$0.0352549\pi$
$884$	−7.83803	−	6.57689i	−0.263622	−	0.221205i
$885$	−2.64338	+	12.2786i	−0.0888561	+	0.412740i
$886$	4.90278	+	27.8050i	0.164712	+	0.934128i
$887$	−6.35957	−	36.0669i	−0.213533	−	1.21101i	−0.883433	−	0.468557i	$-0.844774\pi$
$887$	−6.35957	−	36.0669i	−0.213533	−	1.21101i	0.669900	−	0.742451i	$-0.266337\pi$
$888$	2.46343	+	4.66232i	0.0826672	+	0.156457i
$889$	−2.30431	−	30.5965i	−0.0772841	−	1.02617i
$890$	49.8141			1.66977
$891$	19.5337	−	3.93954i	0.654405	−	0.131980i
$892$	1.94487	−	3.36862i	0.0651192	−	0.112790i
$893$	6.23850	+	5.23473i	0.208764	+	0.175173i
$894$	10.5840	−	16.8401i	0.353983	−	0.563218i
$895$	−65.6179	−	23.8829i	−2.19336	−	0.798319i
$896$	−2.63270	−	0.262455i	−0.0879524	−	0.00876800i
$897$	39.6969	−	12.7839i	1.32544	−	0.426844i
$898$	2.50650	+	2.10321i	0.0836431	+	0.0701849i
$899$	−32.3567	−	56.0435i	−1.07916	−	1.86916i
$900$	23.5395	+	1.76945i	0.784652	+	0.0589818i
$901$	19.9948	−	34.6320i	0.666123	−	1.15376i
$902$	18.1062	+	15.1929i	0.602870	+	0.505868i
$903$	9.89294	+	1.36263i	0.329216	+	0.0453454i
$904$	−0.422931	−	2.39856i	−0.0140665	−	0.0797749i
$905$	45.3120	−	38.0213i	1.50622	−	1.26387i
$906$	4.69369	−	3.64744i	0.155937	−	0.121178i
$907$	−5.67769	+	2.06651i	−0.188525	+	0.0686173i	−0.434557	−	0.900644i	$-0.643095\pi$
$907$	−5.67769	+	2.06651i	−0.188525	+	0.0686173i	0.246033	+	0.969262i	$0.420873\pi$
$908$	−1.82251	+	3.15669i	−0.0604822	+	0.104758i
$909$	8.85861	−	34.7567i	0.293821	−	1.15281i
$910$	−18.8595	−	19.3214i	−0.625187	−	0.640497i
$911$	36.8589	−	13.4155i	1.22119	−	0.444477i	0.350618	−	0.936519i	$-0.385972\pi$
$911$	36.8589	−	13.4155i	1.22119	−	0.444477i	0.870571	+	0.492042i	$0.163749\pi$
$912$	0.592151	−	2.75057i	0.0196081	−	0.0910803i
$913$	−5.62662	−	31.9101i	−0.186214	−	1.05607i
$914$	24.0446	−	20.1758i	0.795324	−	0.667356i
$915$	6.45534	+	12.2175i	0.213407	+	0.403897i
$916$	3.01061	−	17.0740i	0.0994733	−	0.564141i
$917$	25.0920	+	25.7065i	0.828612	+	0.848903i
$918$	−18.1687	+	4.37930i	−0.599658	+	0.144538i
$919$	11.7174	+	20.2951i	0.386521	+	0.669473i	0.991979	−	0.126404i	$-0.0403434\pi$
$919$	11.7174	+	20.2951i	0.386521	+	0.669473i	−0.605458	+	0.795877i	$0.707010\pi$
$920$	23.2593	+	19.5168i	0.766835	+	0.643451i
$921$	−5.15010	−	9.74717i	−0.169702	−	0.321180i
$922$	−1.11842	−	6.34290i	−0.0368333	−	0.208892i
$923$	15.9946	−	13.4211i	0.526468	−	0.441759i
$924$	−0.381989	−	10.1392i	−0.0125665	−	0.333554i
$925$	−22.5109	+	8.19329i	−0.740153	+	0.269394i
$926$	−38.3668			−1.26081
$927$	−17.0858	−	7.71412i	−0.561172	−	0.253365i
$928$	6.72909			0.220893
$929$	−2.18771	+	12.4071i	−0.0717764	+	0.407064i	0.927658	+	0.373431i	$0.121819\pi$
$929$	−2.18771	+	12.4071i	−0.0717764	+	0.407064i	−0.999434	+	0.0336331i	$0.989292\pi$
$930$	47.1824	−	36.6652i	1.54717	−	1.20230i
$931$	4.14642	−	10.5880i	0.135893	−	0.347008i
$932$	2.53226	+	14.3612i	0.0829469	+	0.470415i
$933$	−23.6780	−	9.63842i	−0.775182	−	0.315548i
$934$	5.82132	−	2.11879i	0.190480	−	0.0693289i
$935$	28.5675			0.934258
$936$	7.77827	+	3.51183i	0.254241	+	0.114788i
$937$	7.17883	−	12.4341i	0.234522	−	0.406205i	−0.724611	−	0.689158i	$-0.757981\pi$
$937$	7.17883	−	12.4341i	0.234522	−	0.406205i	0.959134	+	0.282953i	$0.0913141\pi$
$938$	9.97547	−	6.80658i	0.325711	−	0.222243i
$939$	0.404963	−	1.88107i	0.0132155	−	0.0613863i
$940$	−16.8997	−	6.15100i	−0.551208	−	0.200623i
$941$	34.0266	−	28.5517i	1.10924	−	0.930759i	0.111224	−	0.993795i	$-0.464523\pi$
$941$	34.0266	−	28.5517i	1.10924	−	0.930759i	0.998011	+	0.0630362i	$0.0200784\pi$
$942$	−15.0107	−	28.4095i	−0.489075	−	0.925632i
$943$	84.9052	−	30.9029i	2.76489	−	1.00634i
$944$	−2.02143			−0.0657920
$945$	−48.8539	+	6.74321i	−1.58922	+	0.219357i
$946$	4.82500			0.156874
$947$	31.1772	−	11.3476i	1.01312	−	0.368746i	0.218491	−	0.975839i	$-0.429887\pi$
$947$	31.1772	−	11.3476i	1.01312	−	0.368746i	0.794631	+	0.607093i	$0.207664\pi$
$948$	−0.146366	+	0.232882i	−0.00475376	+	0.00756365i
$949$	8.46645	−	7.10419i	0.274833	−	0.230612i
$950$	12.0112	+	4.37171i	0.389694	+	0.141837i
$951$	35.0536	+	31.7283i	1.13669	+	1.02886i
$952$	0.714654	+	9.48913i	0.0231621	+	0.307545i
$953$	−10.8009	+	18.7078i	−0.349877	+	0.606005i	−0.986227	−	0.165395i	$-0.947110\pi$
$953$	−10.8009	+	18.7078i	−0.349877	+	0.606005i	0.636350	+	0.771400i	$0.280443\pi$
$954$	−8.23801	+	32.3218i	−0.266715	+	1.04646i
$955$	12.6565			0.409555
$956$	−0.222801	+	0.0810929i	−0.00720589	+	0.00262273i
$957$	3.52483	+	25.5640i	0.113942	+	0.826365i
$958$	−5.82320	−	33.0250i	−0.188139	−	1.06699i
$959$	−36.8541	−	3.67400i	−1.19008	−	0.118640i
$960$	0.848687	+	6.15514i	0.0273913	+	0.198656i
$961$	10.6769	−	60.5520i	0.344418	−	1.95329i
$962$	−8.66071			−0.279233
$963$	12.9238	+	26.8522i	0.416464	+	0.865301i
$964$	−6.35923			−0.204817
$965$	21.8522	−	7.95356i	0.703448	−	0.256034i
$966$	−34.2968	−	18.1151i	−1.10348	−	0.582844i
$967$	−36.0689	+	30.2654i	−1.15990	+	0.973269i	−0.999904	−	0.0138489i	$-0.995592\pi$
$967$	−36.0689	+	30.2654i	−1.15990	+	0.973269i	−0.159993	+	0.987118i	$0.551147\pi$
$968$	1.05885	+	6.00505i	0.0340328	+	0.193010i
$969$	−10.1125	−	0.379541i	−0.324861	−	0.0121926i
$970$	1.56964	+	1.31708i	0.0503980	+	0.0422889i
$971$	27.4481	+	47.5416i	0.880853	+	1.52568i	0.850395	+	0.526146i	$0.176363\pi$
$971$	27.4481	+	47.5416i	0.880853	+	1.52568i	0.0304582	+	0.999536i	$0.490303\pi$
$972$	13.6005	−	7.61756i	0.436235	−	0.244333i
$973$	47.9713	−	12.2339i	1.53789	−	0.392202i
$974$	2.69417	−	15.2794i	0.0863268	−	0.489584i
$975$	−20.6312	+	32.8261i	−0.660728	+	1.05128i
$976$	−1.70362	+	1.42951i	−0.0545316	+	0.0457574i
$977$	−9.94392	−	56.3948i	−0.318134	−	1.80423i	−0.554080	−	0.832463i	$-0.686930\pi$
$977$	−9.94392	−	56.3948i	−0.318134	−	1.80423i	0.235946	−	0.971766i	$-0.424181\pi$
$978$	−16.9510	−	15.3430i	−0.542035	−	0.490616i
$979$	−28.8917	+	10.5157i	−0.923381	+	0.336083i
$980$	−0.607402	+	25.1037i	−0.0194027	+	0.801908i
$981$	14.4360	−	21.1633i	0.460905	−	0.675692i
$982$	−11.4807	+	19.8852i	−0.366364	+	0.634561i
$983$	10.1431	−	3.69179i	0.323515	−	0.117750i	−0.175157	−	0.984540i	$-0.556043\pi$
$983$	10.1431	−	3.69179i	0.323515	−	0.117750i	0.498672	+	0.866791i	$0.333821\pi$
$984$	17.1254	+	6.97110i	0.545937	+	0.222231i
$985$	−14.3653	+	12.0539i	−0.457716	+	0.384070i
$986$	−4.20274	−	23.8349i	−0.133842	−	0.759058i
$987$	22.7591	+	3.13478i	0.724432	+	0.0997813i
$988$	3.53998	+	2.97039i	0.112622	+	0.0945008i
$989$	9.22236	−	15.9736i	0.293254	−	0.507931i
$990$	−22.9389	+	6.44836i	−0.729047	+	0.204942i
$991$	19.8530	+	34.3864i	0.630652	+	1.09232i	0.987419	+	0.158128i	$0.0505458\pi$
$991$	19.8530	+	34.3864i	0.630652	+	1.09232i	−0.356767	+	0.934193i	$0.616121\pi$
$992$	7.36703	+	6.18167i	0.233903	+	0.196268i
$993$	−33.9383	−	30.7188i	−1.07700	−	0.974831i
$994$	−19.3229	−	1.92631i	−0.612887	−	0.0610988i
$995$	45.7872	+	16.6652i	1.45155	+	0.528322i
$996$	−11.8416	−	22.4116i	−0.375215	−	0.710138i
$997$	18.8219	+	15.7935i	0.596097	+	0.500185i	0.890188	−	0.455593i	$-0.150573\pi$
$997$	18.8219	+	15.7935i	0.596097	+	0.500185i	−0.294091	+	0.955777i	$0.595017\pi$
$998$	−15.4374	+	26.7383i	−0.488661	+	0.846386i
$999$	−9.39820	+	12.7250i	−0.297346	+	0.402601i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.w.b.25.12	yes	72
7.2	even	3		378.2.v.a.79.4	yes	72
27.13	even	9		378.2.v.a.67.4	✓	72
189.121	even	9	inner	378.2.w.b.121.12	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.v.a.67.4	✓	72	27.13	even	9
378.2.v.a.79.4	yes	72	7.2	even	3
378.2.w.b.25.12	yes	72	1.1	even	1	trivial
378.2.w.b.121.12	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)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(1.73083 + 0.0649612i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-3.37095 - 1.22693i) q^{5} +(1.64867 - 0.530936i) q^{6} +(2.18547 - 1.49122i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.99156 + 0.224874i) q^{9} +O(q^{10})\)	\(q+(0.939693 - 0.342020i) q^{2} +(1.73083 + 0.0649612i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-3.37095 - 1.22693i) q^{5} +(1.64867 - 0.530936i) q^{6} +(2.18547 - 1.49122i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.99156 + 0.224874i) q^{9} -3.58729 q^{10} +(2.08059 - 0.757273i) q^{11} +(1.36765 - 1.06279i) q^{12} +(0.493989 + 2.80155i) q^{13} +(1.54364 - 2.14876i) q^{14} +(-5.75485 - 2.34258i) q^{15} +(0.173648 - 0.984808i) q^{16} -3.59671 q^{17} +(2.88806 - 0.811862i) q^{18} +1.62442 q^{19} +(-3.37095 + 1.22693i) q^{20} +(3.87955 - 2.43907i) q^{21} +(1.69611 - 1.42321i) q^{22} +(-1.46976 - 8.33541i) q^{23} +(0.921674 - 1.46646i) q^{24} +(6.02774 + 5.05787i) q^{25} +(1.42239 + 2.46364i) q^{26} +(5.16328 + 0.583554i) q^{27} +(0.715631 - 2.54713i) q^{28} +(-1.16849 + 6.62686i) q^{29} +(-6.20900 - 0.233035i) q^{30} +(-7.36703 + 6.18167i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(3.65034 - 1.17555i) q^{33} +(-3.37980 + 1.23015i) q^{34} +(-9.19672 + 2.34541i) q^{35} +(2.43621 - 1.75067i) q^{36} +(-1.52222 + 2.63656i) q^{37} +(1.52646 - 0.555585i) q^{38} +(0.673020 + 4.88111i) q^{39} +(-2.74802 + 2.30587i) q^{40} +(1.85372 + 10.5129i) q^{41} +(2.81137 - 3.61886i) q^{42} +(1.66936 + 1.40076i) q^{43} +(1.10706 - 1.91748i) q^{44} +(-9.80850 - 4.42846i) q^{45} +(-4.23200 - 7.33004i) q^{46} +(3.84044 + 3.22251i) q^{47} +(0.364530 - 1.69326i) q^{48} +(2.55255 - 6.51801i) q^{49} +(7.39412 + 2.69124i) q^{50} +(-6.22531 - 0.233647i) q^{51} +(2.17922 + 1.82858i) q^{52} +(-5.55919 + 9.62879i) q^{53} +(5.05148 - 1.21758i) q^{54} -7.94268 q^{55} +(-0.198696 - 2.63828i) q^{56} +(2.81160 + 0.105524i) q^{57} +(1.16849 + 6.62686i) q^{58} +(-0.351018 - 1.99072i) q^{59} +(-5.91425 + 1.90462i) q^{60} +(-1.70362 - 1.42951i) q^{61} +(-4.80848 + 8.32854i) q^{62} +(6.87330 - 3.96961i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.77208 - 10.0500i) q^{65} +(3.02814 - 2.35315i) q^{66} +(4.28918 + 1.56113i) q^{67} +(-2.75524 + 2.31192i) q^{68} +(-2.00243 - 14.5227i) q^{69} +(-7.83991 + 5.34942i) q^{70} +(-3.66979 - 6.35627i) q^{71} +(1.69053 - 2.47833i) q^{72} +(-1.94254 - 3.36458i) q^{73} +(-0.528660 + 2.99818i) q^{74} +(10.1044 + 9.14590i) q^{75} +(1.24438 - 1.04416i) q^{76} +(3.41781 - 4.75760i) q^{77} +(2.30187 + 4.35655i) q^{78} +(-0.149228 + 0.0543145i) q^{79} +(-1.79365 + 3.10668i) q^{80} +(8.89886 + 1.34545i) q^{81} +(5.33756 + 9.24492i) q^{82} +(2.54125 - 14.4121i) q^{83} +(1.40410 - 4.36217i) q^{84} +(12.1243 + 4.41290i) q^{85} +(2.04778 + 0.745330i) q^{86} +(-2.45296 + 11.3941i) q^{87} +(0.384477 - 2.18048i) q^{88} -13.8863 q^{89} +(-10.7316 - 0.806688i) q^{90} +(5.25732 + 5.38606i) q^{91} +(-6.48380 - 5.44055i) q^{92} +(-13.1527 + 10.2209i) q^{93} +(4.71100 + 1.71466i) q^{94} +(-5.47585 - 1.99305i) q^{95} +(-0.236582 - 1.71582i) q^{96} +(-0.437555 - 0.367152i) q^{97} +(0.169321 - 6.99795i) q^{98} +(6.39450 - 1.79756i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} + 3 q^{7} + 36 q^{8}+O(q^{10}) \) 72 * q + 3 * q^6 + 3 * q^7 + 36 * q^8	\( 72 q + 3 q^{6} + 3 q^{7} + 36 q^{8} - 12 q^{10} - 6 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} + 24 q^{17} - 36 q^{19} + 18 q^{21} + 6 q^{22} - 6 q^{23} + 30 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} + 9 q^{35} - 3 q^{36} + 51 q^{39} - 6 q^{41} - 27 q^{42} - 24 q^{43} + 18 q^{45} + 27 q^{47} + 6 q^{48} - 69 q^{49} + 6 q^{50} + 6 q^{51} - 6 q^{52} - 15 q^{53} + 45 q^{54} - 72 q^{55} + 6 q^{56} + 57 q^{57} - 3 q^{58} + 15 q^{59} - 33 q^{60} - 18 q^{61} - 24 q^{62} - 12 q^{63} - 36 q^{64} - 90 q^{65} - 36 q^{66} - 66 q^{67} - 18 q^{68} - 39 q^{69} - 12 q^{70} + 12 q^{71} + 30 q^{73} + 9 q^{74} - 21 q^{75} - 87 q^{77} + 6 q^{78} - 45 q^{79} - 6 q^{80} - 24 q^{81} + 33 q^{82} + 18 q^{83} + 6 q^{84} + 51 q^{85} - 12 q^{86} - 18 q^{87} - 12 q^{88} + 72 q^{89} - 69 q^{90} - 30 q^{91} + 12 q^{92} - 48 q^{93} + 21 q^{95} + 48 q^{97} + 6 q^{98} + 90 q^{99}+O(q^{100}) \) 72 * q + 3 * q^6 + 3 * q^7 + 36 * q^8 - 12 * q^10 - 6 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 + 24 * q^17 - 36 * q^19 + 18 * q^21 + 6 * q^22 - 6 * q^23 + 30 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 + 9 * q^35 - 3 * q^36 + 51 * q^39 - 6 * q^41 - 27 * q^42 - 24 * q^43 + 18 * q^45 + 27 * q^47 + 6 * q^48 - 69 * q^49 + 6 * q^50 + 6 * q^51 - 6 * q^52 - 15 * q^53 + 45 * q^54 - 72 * q^55 + 6 * q^56 + 57 * q^57 - 3 * q^58 + 15 * q^59 - 33 * q^60 - 18 * q^61 - 24 * q^62 - 12 * q^63 - 36 * q^64 - 90 * q^65 - 36 * q^66 - 66 * q^67 - 18 * q^68 - 39 * q^69 - 12 * q^70 + 12 * q^71 + 30 * q^73 + 9 * q^74 - 21 * q^75 - 87 * q^77 + 6 * q^78 - 45 * q^79 - 6 * q^80 - 24 * q^81 + 33 * q^82 + 18 * q^83 + 6 * q^84 + 51 * q^85 - 12 * q^86 - 18 * q^87 - 12 * q^88 + 72 * q^89 - 69 * q^90 - 30 * q^91 + 12 * q^92 - 48 * q^93 + 21 * q^95 + 48 * q^97 + 6 * q^98 + 90 * q^99

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