LMFDB - Embedded newform 378.2.v.a.79.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("378.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			79.3
Character	$\chi$	$=$	378.79
Dual form			378.2.v.a.67.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 - 0.642788i) q^{2} +(-1.38102 - 1.04536i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.716530 - 4.06364i) q^{5} +(0.385982 + 1.68850i) q^{6} +(2.64332 - 0.113332i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.814451 + 2.88733i) q^{9} +O(q^{10})$	\(q+(-0.766044 - 0.642788i) q^{2} +(-1.38102 - 1.04536i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.716530 - 4.06364i) q^{5} +(0.385982 + 1.68850i) q^{6} +(2.64332 - 0.113332i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.814451 + 2.88733i) q^{9} +(-2.06317 + 3.57351i) q^{10} +(0.842123 - 4.77591i) q^{11} +(0.789665 - 1.54157i) q^{12} +(-0.590412 - 3.34839i) q^{13} +(-2.09775 - 1.61228i) q^{14} +(-3.25842 + 6.36102i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-0.441184 + 0.764153i) q^{17} +(1.23203 - 2.73534i) q^{18} +(1.91125 + 3.31039i) q^{19} +(3.87748 - 1.41129i) q^{20} +(-3.76896 - 2.60671i) q^{21} +(-3.71500 + 3.11726i) q^{22} +(-3.40828 + 2.85988i) q^{23} +(-1.59582 + 0.673322i) q^{24} +(-11.3013 + 4.11334i) q^{25} +(-1.70002 + 2.94453i) q^{26} +(1.89352 - 4.83886i) q^{27} +(0.570618 + 2.58348i) q^{28} +(-1.15181 + 6.53222i) q^{29} +(6.58488 - 2.77835i) q^{30} +(-1.04947 - 5.95187i) q^{31} +(0.939693 + 0.342020i) q^{32} +(-6.15553 + 5.71533i) q^{33} +(0.829154 - 0.301788i) q^{34} +(-2.35456 - 10.6603i) q^{35} +(-2.70204 + 1.30346i) q^{36} -1.85449 q^{37} +(0.663771 - 3.76443i) q^{38} +(-2.68490 + 5.24140i) q^{39} +(-3.87748 - 1.41129i) q^{40} +(0.111244 + 0.630898i) q^{41} +(1.21163 + 4.41950i) q^{42} +(-1.15219 - 0.966799i) q^{43} +4.84959 q^{44} +(11.1495 - 5.37849i) q^{45} +4.44919 q^{46} +(1.04401 - 5.92088i) q^{47} +(1.65527 + 0.509978i) q^{48} +(6.97431 - 0.599146i) q^{49} +(11.3013 + 4.11334i) q^{50} +(1.40810 - 0.594117i) q^{51} +(3.19500 - 1.16288i) q^{52} +(-0.514557 - 0.891239i) q^{53} +(-4.56088 + 2.48965i) q^{54} -20.0110 q^{55} +(1.22351 - 2.34585i) q^{56} +(0.821057 - 6.56966i) q^{57} +(5.08116 - 4.26360i) q^{58} +(4.04471 + 1.47215i) q^{59} +(-6.83020 - 2.10434i) q^{60} +(-2.06698 + 11.7224i) q^{61} +(-3.02184 + 5.23398i) q^{62} +(2.48008 + 7.53984i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-13.1836 + 4.79845i) q^{65} +(8.38916 - 0.421495i) q^{66} +(10.6704 - 8.95354i) q^{67} +(-0.829154 - 0.301788i) q^{68} +(7.69651 - 0.386694i) q^{69} +(-5.04862 + 9.67976i) q^{70} +(6.59709 + 11.4265i) q^{71} +(2.90773 + 0.738330i) q^{72} +4.32518 q^{73} +(1.42062 + 1.19204i) q^{74} +(19.9073 + 6.13331i) q^{75} +(-2.92821 + 2.45706i) q^{76} +(1.68474 - 12.7197i) q^{77} +(5.42586 - 2.28933i) q^{78} +(-0.688892 - 0.578049i) q^{79} +(2.06317 + 3.57351i) q^{80} +(-7.67334 + 4.70317i) q^{81} +(0.320315 - 0.554802i) q^{82} +(2.14100 - 12.1422i) q^{83} +(1.91263 - 4.16435i) q^{84} +(3.42137 + 1.24528i) q^{85} +(0.261179 + 1.48122i) q^{86} +(8.41918 - 7.81709i) q^{87} +(-3.71500 - 3.11726i) q^{88} +(-4.32081 - 7.48386i) q^{89} +(-11.9982 - 3.04659i) q^{90} +(-1.94013 - 8.78397i) q^{91} +(-3.40828 - 2.85988i) q^{92} +(-4.77249 + 9.31674i) q^{93} +(-4.60562 + 3.86458i) q^{94} +(12.0828 - 10.1386i) q^{95} +(-0.940204 - 1.45465i) q^{96} +(8.98017 + 7.53526i) q^{97} +(-5.72776 - 4.02403i) q^{98} +(14.4755 - 1.45826i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8}+O(q^{10}) $ 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8	$ 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8} + 6 q^{10} + 12 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} + 18 q^{19} + 6 q^{22} + 12 q^{23} - 6 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} - 18 q^{35} - 3 q^{36} - 48 q^{39} - 6 q^{41} + 36 q^{42} - 24 q^{43} - 45 q^{45} - 27 q^{47} + 6 q^{48} + 48 q^{49} + 6 q^{50} + 15 q^{51} - 6 q^{52} - 15 q^{53} - 63 q^{54} - 72 q^{55} - 3 q^{56} + 57 q^{57} - 3 q^{58} - 30 q^{59} + 21 q^{60} + 9 q^{61} - 24 q^{62} - 21 q^{63} - 36 q^{64} + 45 q^{65} + 6 q^{67} + 9 q^{68} - 39 q^{69} + 15 q^{70} + 12 q^{71} - 60 q^{73} - 18 q^{74} + 42 q^{75} + 3 q^{77} + 6 q^{78} - 27 q^{79} - 6 q^{80} + 12 q^{81} + 33 q^{82} + 18 q^{83} - 21 q^{84} + 51 q^{85} - 12 q^{86} - 117 q^{87} + 6 q^{88} - 36 q^{89} - 69 q^{90} - 3 q^{91} + 12 q^{92} - 30 q^{93} - 27 q^{94} + 3 q^{95} + 48 q^{97} - 12 q^{98} + 90 q^{99}+O(q^{100}) $ 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8 + 6 * q^10 + 12 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 + 18 * q^19 + 6 * q^22 + 12 * q^23 - 6 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 - 18 * q^35 - 3 * q^36 - 48 * q^39 - 6 * q^41 + 36 * q^42 - 24 * q^43 - 45 * q^45 - 27 * q^47 + 6 * q^48 + 48 * q^49 + 6 * q^50 + 15 * q^51 - 6 * q^52 - 15 * q^53 - 63 * q^54 - 72 * q^55 - 3 * q^56 + 57 * q^57 - 3 * q^58 - 30 * q^59 + 21 * q^60 + 9 * q^61 - 24 * q^62 - 21 * q^63 - 36 * q^64 + 45 * q^65 + 6 * q^67 + 9 * q^68 - 39 * q^69 + 15 * q^70 + 12 * q^71 - 60 * q^73 - 18 * q^74 + 42 * q^75 + 3 * q^77 + 6 * q^78 - 27 * q^79 - 6 * q^80 + 12 * q^81 + 33 * q^82 + 18 * q^83 - 21 * q^84 + 51 * q^85 - 12 * q^86 - 117 * q^87 + 6 * q^88 - 36 * q^89 - 69 * q^90 - 3 * q^91 + 12 * q^92 - 30 * q^93 - 27 * q^94 + 3 * q^95 + 48 * q^97 - 12 * q^98 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$3$	−1.38102	−	1.04536i	−0.797334	−	0.603538i
$3$	−1.38102	−	1.04536i	−0.797334	−	0.603538i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	−0.716530	−	4.06364i	−0.320442	−	1.81732i	−0.539940	−	0.841703i	$-0.681553\pi$
$5$	−0.716530	−	4.06364i	−0.320442	−	1.81732i	0.219498	−	0.975613i	$-0.429558\pi$
$6$	0.385982	+	1.68850i	0.157576	+	0.689326i
$7$	2.64332	−	0.113332i	0.999082	−	0.0428354i
$7$	2.64332	−	0.113332i	0.999082	−	0.0428354i
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	0.814451	+	2.88733i	0.271484	+	0.962443i
$10$	−2.06317	+	3.57351i	−0.652430	+	1.13004i
$11$	0.842123	−	4.77591i	0.253909	−	1.43999i	−0.544947	−	0.838471i	$-0.683450\pi$
$11$	0.842123	−	4.77591i	0.253909	−	1.43999i	0.798856	−	0.601522i	$-0.205439\pi$
$12$	0.789665	−	1.54157i	0.227957	−	0.445012i
$13$	−0.590412	−	3.34839i	−0.163751	−	0.928677i	−0.950343	−	0.311204i	$-0.899268\pi$
$13$	−0.590412	−	3.34839i	−0.163751	−	0.928677i	0.786592	−	0.617473i	$-0.211843\pi$
$14$	−2.09775	−	1.61228i	−0.560648	−	0.430899i
$15$	−3.25842	+	6.36102i	−0.841320	+	1.64241i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−0.441184	+	0.764153i	−0.107003	+	0.185334i	−0.914555	−	0.404462i	$-0.867459\pi$
$17$	−0.441184	+	0.764153i	−0.107003	+	0.185334i	0.807552	+	0.589796i	$0.200792\pi$
$18$	1.23203	−	2.73534i	0.290393	−	0.644726i
$19$	1.91125	+	3.31039i	0.438471	+	0.759455i	0.997572	−	0.0696453i	$-0.0221867\pi$
$19$	1.91125	+	3.31039i	0.438471	+	0.759455i	−0.559100	+	0.829100i	$0.688853\pi$
$20$	3.87748	−	1.41129i	0.867032	−	0.315574i
$21$	−3.76896	−	2.60671i	−0.822455	−	0.568830i
$22$	−3.71500	+	3.11726i	−0.792041	+	0.664601i
$23$	−3.40828	+	2.85988i	−0.710675	+	0.596327i	−0.924788	−	0.380482i	$-0.875758\pi$
$23$	−3.40828	+	2.85988i	−0.710675	+	0.596327i	0.214114	+	0.976809i	$0.431314\pi$
$24$	−1.59582	+	0.673322i	−0.325745	+	0.137441i
$25$	−11.3013	+	4.11334i	−2.26026	+	0.822668i
$26$	−1.70002	+	2.94453i	−0.333402	+	0.577469i
$27$	1.89352	−	4.83886i	0.364408	−	0.931239i
$28$	0.570618	+	2.58348i	0.107837	+	0.488233i
$29$	−1.15181	+	6.53222i	−0.213885	+	1.21300i	0.668946	+	0.743311i	$0.266746\pi$
$29$	−1.15181	+	6.53222i	−0.213885	+	1.21300i	−0.882831	+	0.469691i	$0.844365\pi$
$30$	6.58488	−	2.77835i	1.20223	−	0.507255i
$31$	−1.04947	−	5.95187i	−0.188491	−	1.06899i	−0.921387	−	0.388646i	$-0.872943\pi$
$31$	−1.04947	−	5.95187i	−0.188491	−	1.06899i	0.732896	−	0.680341i	$-0.238168\pi$
$32$	0.939693	+	0.342020i	0.166116	+	0.0604612i
$33$	−6.15553	+	5.71533i	−1.07154	+	0.994911i
$34$	0.829154	−	0.301788i	0.142199	−	0.0517561i
$35$	−2.35456	−	10.6603i	−0.397993	−	1.80192i
$36$	−2.70204	+	1.30346i	−0.450339	+	0.217243i
$37$	−1.85449			−0.304876			−0.152438	−	0.988313i	$-0.548712\pi$
$37$	−1.85449			−0.304876			−0.152438	+	0.988313i	$0.548712\pi$
$38$	0.663771	−	3.76443i	0.107678	−	0.610672i
$39$	−2.68490	+	5.24140i	−0.429928	+	0.839296i
$40$	−3.87748	−	1.41129i	−0.613084	−	0.223144i
$41$	0.111244	+	0.630898i	0.0173734	+	0.0985297i	0.992261	−	0.124166i	$-0.0396255\pi$
$41$	0.111244	+	0.630898i	0.0173734	+	0.0985297i	−0.974888	+	0.222696i	$0.928514\pi$
$42$	1.21163	+	4.41950i	0.186959	+	0.681943i
$43$	−1.15219	−	0.966799i	−0.175707	−	0.147435i	0.550693	−	0.834708i	$-0.314363\pi$
$43$	−1.15219	−	0.966799i	−0.175707	−	0.147435i	−0.726400	+	0.687272i	$0.758808\pi$
$44$	4.84959			0.731103
$45$	11.1495	−	5.37849i	1.66207	−	0.801779i
$46$	4.44919			0.655997
$47$	1.04401	−	5.92088i	0.152285	−	0.863648i	−0.808942	−	0.587888i	$-0.799959\pi$
$47$	1.04401	−	5.92088i	0.152285	−	0.863648i	0.961227	−	0.275760i	$-0.0889295\pi$
$48$	1.65527	+	0.509978i	0.238918	+	0.0736090i
$49$	6.97431	−	0.599146i	0.996330	−	0.0855922i
$50$	11.3013	+	4.11334i	1.59825	+	0.581714i
$51$	1.40810	−	0.594117i	0.197173	−	0.0831931i
$52$	3.19500	−	1.16288i	0.443067	−	0.161263i
$53$	−0.514557	−	0.891239i	−0.0706799	−	0.122421i	0.828520	−	0.559960i	$-0.189184\pi$
$53$	−0.514557	−	0.891239i	−0.0706799	−	0.122421i	−0.899199	+	0.437539i	$0.855850\pi$
$54$	−4.56088	+	2.48965i	−0.620657	+	0.338799i
$55$	−20.0110			−2.69828
$56$	1.22351	−	2.34585i	0.163499	−	0.313477i
$57$	0.821057	−	6.56966i	0.108752	−	0.870173i
$58$	5.08116	−	4.26360i	0.667189	−	0.559838i
$59$	4.04471	+	1.47215i	0.526577	+	0.191658i	0.591609	−	0.806225i	$-0.298493\pi$
$59$	4.04471	+	1.47215i	0.526577	+	0.191658i	−0.0650325	+	0.997883i	$0.520715\pi$
$60$	−6.83020	−	2.10434i	−0.881775	−	0.271669i
$61$	−2.06698	+	11.7224i	−0.264649	+	1.50090i	0.505383	+	0.862895i	$0.331351\pi$
$61$	−2.06698	+	11.7224i	−0.264649	+	1.50090i	−0.770032	+	0.638005i	$0.779760\pi$
$62$	−3.02184	+	5.23398i	−0.383774	+	0.664716i
$63$	2.48008	+	7.53984i	0.312461	+	0.949931i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−13.1836	+	4.79845i	−1.63523	+	0.595174i
$66$	8.38916	−	0.421495i	1.03263	−	0.0518824i
$67$	10.6704	−	8.95354i	1.30360	−	1.09385i	0.314087	−	0.949394i	$-0.398302\pi$
$67$	10.6704	−	8.95354i	1.30360	−	1.09385i	0.989511	−	0.144455i	$-0.0461428\pi$
$68$	−0.829154	−	0.301788i	−0.100550	−	0.0365971i
$69$	7.69651	−	0.386694i	0.926551	−	0.0465525i
$70$	−5.04862	+	9.67976i	−0.603426	+	1.15695i
$71$	6.59709	+	11.4265i	0.782930	+	1.35607i	0.930228	+	0.366982i	$0.119609\pi$
$71$	6.59709	+	11.4265i	0.782930	+	1.35607i	−0.147298	+	0.989092i	$0.547058\pi$
$72$	2.90773	+	0.738330i	0.342679	+	0.0870130i
$73$	4.32518			0.506224			0.253112	−	0.967437i	$-0.418546\pi$
$73$	4.32518			0.506224			0.253112	+	0.967437i	$0.418546\pi$
$74$	1.42062	+	1.19204i	0.165144	+	0.138572i
$75$	19.9073	+	6.13331i	2.29870	+	0.708213i
$76$	−2.92821	+	2.45706i	−0.335889	+	0.281844i
$77$	1.68474	−	12.7197i	0.191994	−	1.44955i
$78$	5.42586	−	2.28933i	0.614357	−	0.259215i
$79$	−0.688892	−	0.578049i	−0.0775064	−	0.0650356i	0.603211	−	0.797581i	$-0.293888\pi$
$79$	−0.688892	−	0.578049i	−0.0775064	−	0.0650356i	−0.680718	+	0.732546i	$0.738332\pi$
$80$	2.06317	+	3.57351i	0.230669	+	0.399530i
$81$	−7.67334	+	4.70317i	−0.852593	+	0.522575i
$82$	0.320315	−	0.554802i	0.0353729	−	0.0612677i
$83$	2.14100	−	12.1422i	0.235005	−	1.33278i	−0.607597	−	0.794245i	$-0.707867\pi$
$83$	2.14100	−	12.1422i	0.235005	−	1.33278i	0.842603	−	0.538536i	$-0.181022\pi$
$84$	1.91263	−	4.16435i	0.208685	−	0.454368i
$85$	3.42137	+	1.24528i	0.371099	+	0.135069i
$86$	0.261179	+	1.48122i	0.0281637	+	0.159724i
$87$	8.41918	−	7.81709i	0.902631	−	0.838080i
$88$	−3.71500	−	3.11726i	−0.396021	−	0.332301i
$89$	−4.32081	−	7.48386i	−0.458005	−	0.793288i	0.540851	−	0.841119i	$-0.318102\pi$
$89$	−4.32081	−	7.48386i	−0.458005	−	0.793288i	−0.998855	+	0.0478310i	$0.984769\pi$
$90$	−11.9982	−	3.04659i	−1.26473	−	0.321139i
$91$	−1.94013	−	8.78397i	−0.203381	−	0.920810i
$92$	−3.40828	−	2.85988i	−0.355337	−	0.298163i
$93$	−4.77249	+	9.31674i	−0.494884	+	0.966101i
$94$	−4.60562	+	3.86458i	−0.475034	+	0.398601i
$95$	12.0828	−	10.1386i	1.23966	−	1.04020i
$96$	−0.940204	−	1.45465i	−0.0959591	−	0.148465i
$97$	8.98017	+	7.53526i	0.911798	+	0.765089i	0.972460	−	0.233069i	$-0.0748768\pi$
$97$	8.98017	+	7.53526i	0.911798	+	0.765089i	−0.0606621	+	0.998158i	$0.519321\pi$
$98$	−5.72776	−	4.02403i	−0.578591	−	0.406488i
$99$	14.4755	−	1.45826i	1.45484	−	0.146561i
$100$	−6.01330	−	10.4153i	−0.601330	−	1.04153i
$101$	−3.49876	−	2.93581i	−0.348140	−	0.292124i	0.451903	−	0.892067i	$-0.350745\pi$
$101$	−3.49876	−	2.93581i	−0.348140	−	0.292124i	−0.800043	+	0.599943i	$0.795190\pi$
$102$	−1.46056	−	0.449988i	−0.144617	−	0.0445555i
$103$	−2.47015	−	14.0089i	−0.243391	−	1.38034i	−0.824200	−	0.566299i	$-0.808375\pi$
$103$	−2.47015	−	14.0089i	−0.243391	−	1.38034i	0.580809	−	0.814040i	$-0.302736\pi$
$104$	−3.19500	−	1.16288i	−0.313295	−	0.114030i
$105$	−7.89215	+	17.1835i	−0.770195	+	1.67694i
$106$	−0.178704	+	1.01348i	−0.0173573	+	0.0984379i
$107$	2.28825	−	3.96337i	0.221214	−	0.383153i	−0.733963	−	0.679189i	$-0.762332\pi$
$107$	2.28825	−	3.96337i	0.221214	−	0.383153i	0.955177	+	0.296036i	$0.0956649\pi$
$108$	5.09415	+	1.02449i	0.490185	+	0.0985819i
$109$	−0.466860	−	0.808625i	−0.0447171	−	0.0774523i	0.842801	−	0.538226i	$-0.180905\pi$
$109$	−0.466860	−	0.808625i	−0.0447171	−	0.0774523i	−0.887518	+	0.460774i	$0.847572\pi$
$110$	15.3293	+	12.8628i	1.46159	+	1.22642i
$111$	2.56109	+	1.93860i	0.243088	+	0.184004i
$112$	−2.44515	+	1.01057i	−0.231045	+	0.0954896i
$113$	7.13187	−	5.98435i	0.670910	−	0.562960i	−0.242425	−	0.970170i	$-0.577943\pi$
$113$	7.13187	−	5.98435i	0.670910	−	0.562960i	0.913334	+	0.407210i	$0.133498\pi$
$114$	−4.85186	+	4.50489i	−0.454419	+	0.421922i
$115$	14.0637	+	11.8008i	1.31144	+	1.10043i
$116$	−6.63299			−0.615857
$117$	9.18705	−	4.43181i	0.849343	−	0.409721i
$118$	−2.15215	−	3.72763i	−0.198121	−	0.343156i
$119$	−1.07959	+	2.06990i	−0.0989657	+	0.189748i
$120$	3.87959	+	6.00238i	0.354157	+	0.547940i
$121$	−11.7636	−	4.28159i	−1.06942	−	0.389235i
$122$	9.11842	−	7.65126i	0.825543	−	0.692712i
$123$	0.505884	−	0.987575i	0.0456140	−	0.0890467i
$124$	5.67920	−	2.06706i	0.510008	−	0.185628i
$125$	14.4971	+	25.1096i	1.29666	+	2.24587i
$126$	2.94666	−	7.37002i	0.262510	−	0.656573i
$127$	−6.11476	+	10.5911i	−0.542598	+	0.939807i	0.456156	+	0.889900i	$0.349226\pi$
$127$	−6.11476	+	10.5911i	−0.542598	+	0.939807i	−0.998754	+	0.0499070i	$0.984108\pi$
$128$	−0.173648	+	0.984808i	−0.0153485	+	0.0870455i
$129$	0.580544	+	2.53962i	0.0511141	+	0.223601i
$130$	13.1836	+	4.79845i	1.15628	+	0.420852i
$131$	−3.36998	+	2.82775i	−0.294437	+	0.247062i	−0.778024	−	0.628234i	$-0.783778\pi$
$131$	−3.36998	+	2.82775i	−0.294437	+	0.247062i	0.483588	+	0.875296i	$0.339333\pi$
$132$	−6.69740	−	5.06956i	−0.582934	−	0.441249i
$133$	5.42723	+	8.53381i	0.470600	+	0.739975i
$134$	−13.9292			−1.20330
$135$	−21.0202	−	4.22740i	−1.80913	−	0.363836i
$136$	0.441184	+	0.764153i	0.0378312	+	0.0655256i
$137$	−14.2249	+	5.17743i	−1.21531	+	0.442338i	−0.868544	−	0.495613i	$-0.834944\pi$
$137$	−14.2249	+	5.17743i	−1.21531	+	0.442338i	−0.346769	+	0.937950i	$0.612721\pi$
$138$	−6.14443	−	4.65100i	−0.523049	−	0.395919i
$139$	−11.1916	−	4.07340i	−0.949256	−	0.345501i	−0.179442	−	0.983769i	$-0.557429\pi$
$139$	−11.1916	−	4.07340i	−0.949256	−	0.345501i	−0.769815	+	0.638268i	$0.779651\pi$
$140$	10.0895	−	4.16993i	0.852718	−	0.352424i
$141$	−7.63124	+	7.08550i	−0.642666	+	0.596707i
$142$	2.29114	−	12.9937i	0.192269	−	1.09041i
$143$	−16.4888			−1.37887
$144$	−1.75286	−	2.43464i	−0.146071	−	0.202887i
$145$	27.3699			2.27295
$146$	−3.31328	−	2.78017i	−0.274209	−	0.230088i
$147$	−10.2580	−	6.46322i	−0.846066	−	0.533078i
$148$	−0.322028	−	1.82631i	−0.0264706	−	0.150122i
$149$	−7.88457	−	2.86975i	−0.645929	−	0.235099i	−0.00177962	−	0.999998i	$-0.500566\pi$
$149$	−7.88457	−	2.86975i	−0.645929	−	0.235099i	−0.644150	+	0.764899i	$0.722789\pi$
$150$	−11.3075	−	17.4945i	−0.923250	−	1.42842i
$151$	1.67108	−	9.47717i	0.135991	−	0.771241i	−0.838174	−	0.545403i	$-0.816377\pi$
$151$	1.67108	−	9.47717i	0.135991	−	0.771241i	0.974165	−	0.225839i	$-0.0725122\pi$
$152$	3.82250			0.310046
$153$	−2.56568	−	0.651478i	−0.207423	−	0.0526689i
$154$	−9.46666	+	8.66094i	−0.762846	+	0.697919i
$155$	−23.4343	+	8.52938i	−1.88229	+	0.685096i
$156$	−5.62800	−	1.73395i	−0.450601	−	0.138827i
$157$	19.0051	+	6.91729i	1.51677	+	0.552060i	0.960339	−	0.278834i	$-0.0899478\pi$
$157$	19.0051	+	6.91729i	1.51677	+	0.552060i	0.556432	+	0.830893i	$0.312170\pi$
$158$	0.156159	+	0.885622i	0.0124233	+	0.0704563i
$159$	−0.221049	+	1.76872i	−0.0175303	+	0.140269i
$160$	0.716530	−	4.06364i	0.0566467	−	0.321259i
$161$	−8.68506	+	7.94586i	−0.684479	+	0.626222i
$162$	8.90126	+	1.32949i	0.699349	+	0.104454i
$163$	7.15218	−	12.3879i	0.560202	−	0.970298i	−0.437277	−	0.899327i	$-0.644057\pi$
$163$	7.15218	−	12.3879i	0.560202	−	0.970298i	0.997478	−	0.0709710i	$-0.0226098\pi$
$164$	−0.601996	+	0.219109i	−0.0470080	+	0.0171095i
$165$	27.6357	+	20.9187i	2.15143	+	1.62852i
$166$	−9.44497	+	7.92527i	−0.733072	+	0.615120i
$167$	2.58223	−	2.16675i	0.199819	−	0.167668i	−0.537388	−	0.843335i	$-0.680589\pi$
$167$	2.58223	−	2.16675i	0.199819	−	0.167668i	0.737207	+	0.675667i	$0.236144\pi$
$168$	−4.14196	+	1.96066i	−0.319559	+	0.151269i
$169$	1.35286	−	0.492401i	0.104066	−	0.0378770i
$170$	−1.82047	−	3.15315i	−0.139624	−	0.241835i
$171$	−8.00155	+	8.21456i	−0.611894	+	0.628183i
$172$	0.752036	−	1.30256i	0.0573422	−	0.0993196i
$173$	−18.7896	+	6.83885i	−1.42855	+	0.519948i	−0.936514	−	0.350629i	$-0.885968\pi$
$173$	−18.7896	+	6.83885i	−1.42855	+	0.519948i	−0.492031	+	0.870577i	$0.663745\pi$
$174$	−11.4742	+	0.576496i	−0.869857	+	0.0437040i
$175$	−29.4069	+	12.1537i	−2.22295	+	0.918733i
$176$	0.842123	+	4.77591i	0.0634774	+	0.359998i
$177$	−4.04691	−	6.26125i	−0.304184	−	0.470625i
$178$	−1.50060	+	8.51033i	−0.112475	+	0.637876i
$179$	5.07505	−	8.79024i	0.379327	−	0.657013i	−0.611638	−	0.791138i	$-0.709489\pi$
$179$	5.07505	−	8.79024i	0.379327	−	0.657013i	0.990964	+	0.134125i	$0.0428223\pi$
$180$	7.23287	+	10.0461i	0.539106	+	0.748795i
$181$	3.93415	−	6.81414i	0.292423	−	0.506491i	−0.681959	−	0.731390i	$-0.738872\pi$
$181$	3.93415	−	6.81414i	0.292423	−	0.506491i	0.974382	+	0.224899i	$0.0722052\pi$
$182$	−4.16000	+	7.97600i	−0.308360	+	0.591221i
$183$	15.1087	−	14.0282i	1.11686	−	1.03699i
$184$	0.772594	+	4.38160i	0.0569564	+	0.323016i
$185$	1.32880	+	7.53597i	0.0976950	+	0.554056i
$186$	9.64462	−	4.06934i	0.707178	−	0.298379i
$187$	3.27800	+	2.75057i	0.239711	+	0.201141i
$188$	6.01221			0.438486
$189$	4.45679	−	13.0053i	0.324183	−	0.945994i
$190$	−15.7729			−1.14429
$191$	14.0290	+	11.7718i	1.01511	+	0.851774i	0.989005	−	0.147885i	$-0.0472466\pi$
$191$	14.0290	+	11.7718i	1.01511	+	0.851774i	0.0261005	+	0.999659i	$0.491691\pi$
$192$	−0.214796	+	1.71868i	−0.0155015	+	0.124035i
$193$	−3.01938	−	17.1238i	−0.217340	−	1.23260i	−0.876799	−	0.480856i	$-0.840326\pi$
$193$	−3.01938	−	17.1238i	−0.217340	−	1.23260i	0.659459	−	0.751740i	$-0.270785\pi$
$194$	−2.03564	−	11.5447i	−0.146150	−	0.828860i
$195$	23.2230	+	7.15485i	1.66303	+	0.512369i
$196$	1.80112	+	6.76432i	0.128651	+	0.483165i
$197$	−7.77760	+	13.4712i	−0.554131	+	0.959783i	0.443840	+	0.896106i	$0.353616\pi$
$197$	−7.77760	+	13.4712i	−0.554131	+	0.959783i	−0.997971	+	0.0636764i	$0.979717\pi$
$198$	−12.0262	−	8.18758i	−0.854667	−	0.581866i
$199$	−2.37899	+	4.12053i	−0.168642	+	0.292097i	−0.937943	−	0.346790i	$-0.887272\pi$
$199$	−2.37899	+	4.12053i	−0.168642	+	0.292097i	0.769300	+	0.638887i	$0.220605\pi$
$200$	−2.08840	+	11.8439i	−0.147672	+	0.837490i
$201$	−24.0957	+	1.21064i	−1.69958	+	0.0853918i
$202$	0.793106	+	4.49793i	0.0558027	+	0.316473i
$203$	−2.30429	+	17.3973i	−0.161729	+	1.22105i
$204$	0.829605	+	1.28354i	0.0580840	+	0.0898657i
$205$	2.48403	−	0.904115i	0.173493	−	0.0631461i
$206$	−7.11251	+	12.3192i	−0.495552	+	0.858321i
$207$	−11.0333	−	7.51158i	−0.766867	−	0.522091i
$208$	1.70002	+	2.94453i	0.117875	+	0.204166i
$209$	17.4196	−	6.34023i	1.20494	−	0.438563i
$210$	17.0911	−	8.09035i	1.17940	−	0.558287i
$211$	10.4569	−	8.77435i	0.719880	−	0.604051i	−0.207472	−	0.978241i	$-0.566524\pi$
$211$	10.4569	−	8.77435i	0.719880	−	0.604051i	0.927352	+	0.374190i	$0.122079\pi$
$212$	0.788348	−	0.661502i	0.0541439	−	0.0454322i
$213$	2.83405	−	22.6766i	0.194186	−	1.55377i
$214$	−4.30051	+	1.56526i	−0.293976	+	0.106999i
$215$	−3.10315	+	5.37481i	−0.211633	+	0.366559i
$216$	−3.24382	−	4.05927i	−0.220714	−	0.276198i
$217$	−3.44864	−	15.6138i	−0.234109	−	1.05993i
$218$	−0.162139	+	0.919535i	−0.0109814	+	0.0622788i
$219$	−5.97317	−	4.52136i	−0.403629	−	0.305525i
$220$	−3.47488	−	19.7070i	−0.234276	−	1.32865i
$221$	2.81916	+	1.02609i	0.189637	+	0.0690224i
$222$	−0.715798	−	3.13129i	−0.0480412	−	0.210159i
$223$	15.0885	−	5.49178i	1.01040	−	0.367757i	0.216816	−	0.976213i	$-0.430433\pi$
$223$	15.0885	−	5.49178i	1.01040	−	0.367757i	0.793588	+	0.608456i	$0.208211\pi$
$224$	2.52267	+	0.797573i	0.168553	+	0.0532901i
$225$	−21.0809	−	29.2805i	−1.40540	−	1.95203i
$226$	−9.30999			−0.619291
$227$	1.94892	−	11.0529i	0.129354	−	0.733605i	−0.849272	−	0.527956i	$-0.822958\pi$
$227$	1.94892	−	11.0529i	0.129354	−	0.733605i	0.978626	−	0.205649i	$-0.0659304\pi$
$228$	6.61243	−	0.332227i	0.437919	−	0.0220023i
$229$	1.59565	+	0.580771i	0.105444	+	0.0383784i	0.394203	−	0.919023i	$-0.371021\pi$
$229$	1.59565	+	0.580771i	0.105444	+	0.0383784i	−0.288759	+	0.957402i	$0.593243\pi$
$230$	−3.18798	−	18.0799i	−0.210209	−	1.19215i
$231$	−15.6233	+	15.8051i	−1.02794	+	1.03990i
$232$	5.08116	+	4.26360i	0.333595	+	0.279919i
$233$	13.7170			0.898632			0.449316	−	0.893373i	$-0.351668\pi$
$233$	13.7170			0.898632			0.449316	+	0.893373i	$0.351668\pi$
$234$	−9.88640	−	2.51036i	−0.646294	−	0.164107i
$235$	−24.8084			−1.61832
$236$	−0.747433	+	4.23890i	−0.0486537	+	0.275929i
$237$	0.347107	+	1.51844i	0.0225470	+	0.0986331i
$238$	2.15752	−	0.891691i	0.139851	−	0.0577998i
$239$	17.6167	+	6.41194i	1.13953	+	0.414754i	0.841742	−	0.539879i	$-0.181530\pi$
$239$	17.6167	+	6.41194i	1.13953	+	0.414754i	0.297784	+	0.954633i	$0.403752\pi$
$240$	0.886317	−	7.09185i	0.0572115	−	0.457777i
$241$	−12.9707	+	4.72094i	−0.835514	+	0.304102i	−0.724120	−	0.689674i	$-0.757754\pi$
$241$	−12.9707	+	4.72094i	−0.835514	+	0.304102i	−0.111394	+	0.993776i	$0.535532\pi$
$242$	6.25926	+	10.8414i	0.402361	+	0.696909i
$243$	15.5136	+	1.52620i	0.995196	+	0.0979058i
$244$	−11.9032			−0.762027
$245$	−7.43202	−	27.9118i	−0.474814	−	1.78322i
$246$	−1.02233	+	0.431351i	−0.0651814	+	0.0275019i
$247$	9.95604	−	8.35411i	0.633488	−	0.531560i
$248$	−5.67920	−	2.06706i	−0.360630	−	0.131259i
$249$	−15.6497	+	14.5306i	−0.991762	+	0.920837i
$250$	5.03478	−	28.5536i	0.318427	−	1.80589i
$251$	−2.06411	+	3.57515i	−0.130286	+	0.225661i	−0.923787	−	0.382908i	$-0.874923\pi$
$251$	−2.06411	+	3.57515i	−0.130286	+	0.225661i	0.793501	+	0.608569i	$0.208256\pi$
$252$	−6.99463	+	3.75168i	−0.440620	+	0.236334i
$253$	10.7884	+	18.6860i	0.678259	+	1.17478i
$254$	11.4920	−	4.18275i	0.721072	−	0.262449i
$255$	−3.42323	−	5.29631i	−0.214371	−	0.331668i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	12.5419	+	4.56488i	0.782342	+	0.284749i	0.702149	−	0.712030i	$-0.252224\pi$
$257$	12.5419	+	4.56488i	0.782342	+	0.284749i	0.0801930	+	0.996779i	$0.474446\pi$
$258$	1.18771	−	2.31863i	0.0739438	−	0.144351i
$259$	−4.90201	+	0.210172i	−0.304596	+	0.0130595i
$260$	−7.01486	−	12.1501i	−0.435043	−	0.753517i
$261$	−19.7987	+	1.99452i	−1.22551	+	0.123458i
$262$	4.39920			0.271783
$263$	1.83429	+	1.53915i	0.113107	+	0.0949083i	0.697587	−	0.716500i	$-0.254257\pi$
$263$	1.83429	+	1.53915i	0.113107	+	0.0949083i	−0.584480	+	0.811408i	$0.698701\pi$
$264$	1.87185	+	8.18851i	0.115205	+	0.503968i
$265$	−3.25298	+	2.72958i	−0.199829	+	0.167677i
$266$	1.32793	−	10.0258i	0.0814207	−	0.614723i
$267$	−1.85618	+	14.8522i	−0.113596	+	0.908939i
$268$	10.6704	+	8.95354i	0.651799	+	0.546924i
$269$	−10.8626	−	18.8145i	−0.662302	−	1.14714i	−0.980009	−	0.198951i	$-0.936246\pi$
$269$	−10.8626	−	18.8145i	−0.662302	−	1.14714i	0.317708	−	0.948189i	$-0.397087\pi$
$270$	13.3851	+	16.7499i	0.814589	+	1.01937i
$271$	4.02547	−	6.97231i	0.244530	−	0.423538i	−0.717470	−	0.696590i	$-0.754700\pi$
$271$	4.02547	−	6.97231i	0.244530	−	0.423538i	0.961999	+	0.273052i	$0.0880331\pi$
$272$	0.153222	−	0.868962i	0.00929042	−	0.0526886i
$273$	−6.50303	+	14.1590i	−0.393582	+	0.856941i
$274$	14.2249	+	5.17743i	0.859356	+	0.312780i
$275$	10.1279	+	57.4381i	0.610734	+	3.46364i
$276$	1.71731	+	7.51244i	0.103370	+	0.452196i
$277$	−10.1674	−	8.53150i	−0.610903	−	0.512608i	0.284027	−	0.958816i	$-0.408330\pi$
$277$	−10.1674	−	8.53150i	−0.610903	−	0.512608i	−0.894929	+	0.446208i	$0.852774\pi$
$278$	5.95491	+	10.3142i	0.357152	+	0.618605i
$279$	16.3302	−	7.87768i	0.977666	−	0.471624i
$280$	−10.4094	−	3.29105i	−0.622080	−	0.196678i
$281$	7.26027	+	6.09209i	0.433111	+	0.363424i	0.833124	−	0.553086i	$-0.186550\pi$
$281$	7.26027	+	6.09209i	0.433111	+	0.363424i	−0.400013	+	0.916510i	$0.630994\pi$
$282$	10.4003	−	0.522542i	0.619331	−	0.0311169i
$283$	−6.10074	+	5.11913i	−0.362651	+	0.304300i	−0.805846	−	0.592125i	$-0.798289\pi$
$283$	−6.10074	+	5.11913i	−0.362651	+	0.304300i	0.443195	+	0.896425i	$0.353845\pi$
$284$	−10.1073	+	8.48105i	−0.599759	+	0.503258i
$285$	−27.2851	+	1.37088i	−1.61623	+	0.0812039i
$286$	12.6312	+	10.5988i	0.746897	+	0.626721i
$287$	0.365556	+	1.65506i	0.0215781	+	0.0976951i
$288$	−0.222192	+	2.99176i	−0.0130928	+	0.176291i
$289$	8.11071	+	14.0482i	0.477101	+	0.826363i
$290$	−20.9666	−	17.5930i	−1.23120	−	1.03310i
$291$	−4.52478	−	19.7939i	−0.265247	−	1.16034i
$292$	0.751059	+	4.25947i	0.0439524	+	0.249266i
$293$	−16.5881	−	6.03756i	−0.969086	−	0.352718i	−0.191498	−	0.981493i	$-0.561335\pi$
$293$	−16.5881	−	6.03756i	−0.969086	−	0.352718i	−0.777588	+	0.628775i	$0.783557\pi$
$294$	3.70361	+	11.5448i	0.215999	+	0.673309i
$295$	3.08415	−	17.4911i	0.179566	−	1.01837i
$296$	−0.927243	+	1.60603i	−0.0538949	+	0.0933487i
$297$	−21.5154	−	13.1182i	−1.24845	−	0.761195i
$298$	4.19529	+	7.26646i	0.243027	+	0.420935i
$299$	11.5883	+	9.72374i	0.670169	+	0.562338i
$300$	−2.58326	+	20.6699i	−0.149145	+	1.19338i
$301$	−3.15517	−	2.42498i	−0.181861	−	0.139774i
$302$	−7.37193	+	6.18579i	−0.424207	+	0.355952i
$303$	1.76290	+	7.71189i	0.101276	+	0.443036i
$304$	−2.92821	−	2.45706i	−0.167944	−	0.140922i
$305$	49.1167			2.81242
$306$	1.54667	+	2.14825i	0.0884170	+	0.122807i
$307$	7.08446	+	12.2706i	0.404331	+	0.700322i	0.994243	−	0.107145i	$-0.0341710\pi$
$307$	7.08446	+	12.2706i	0.404331	+	0.700322i	−0.589912	+	0.807467i	$0.700838\pi$
$308$	12.8190	−	0.549613i	0.730432	−	0.0313171i
$309$	−11.2330	+	21.9288i	−0.639023	+	1.24749i
$310$	23.4343	+	8.52938i	1.33098	+	0.484436i
$311$	−16.5778	+	13.9104i	−0.940042	+	0.788789i	−0.977593	−	0.210505i	$-0.932489\pi$
$311$	−16.5778	+	13.9104i	−0.940042	+	0.788789i	0.0375503	+	0.999295i	$0.488045\pi$
$312$	3.19674	+	4.94589i	0.180980	+	0.280006i
$313$	8.43934	−	3.07167i	0.477020	−	0.173621i	−0.0923098	−	0.995730i	$-0.529425\pi$
$313$	8.43934	−	3.07167i	0.477020	−	0.173621i	0.569330	+	0.822109i	$0.307203\pi$
$314$	−10.1124	−	17.5152i	−0.570676	−	0.988439i
$315$	28.8622	−	15.4807i	1.62620	−	0.872238i
$316$	0.449642	−	0.778803i	0.0252943	−	0.0438111i
$317$	4.33418	−	24.5804i	0.243432	−	1.38057i	−0.580674	−	0.814136i	$-0.697211\pi$
$317$	4.33418	−	24.5804i	0.243432	−	1.38057i	0.824106	−	0.566435i	$-0.191678\pi$
$318$	1.30624	−	1.21283i	0.0732506	−	0.0680121i
$319$	30.2273	+	11.0019i	1.69241	+	0.615986i
$320$	−3.16095	+	2.65235i	−0.176703	+	0.148271i
$321$	−7.30327	+	3.08146i	−0.407629	+	0.171990i
$322$	11.7606	−	0.504235i	0.655395	−	0.0280999i
$323$	−3.37285			−0.187671
$324$	−5.96418	−	6.74007i	−0.331344	−	0.374448i
$325$	20.4455	+	35.4127i	1.13411	+	1.96434i
$326$	−13.4417	+	4.89238i	−0.744467	+	0.270964i
$327$	−0.200559	+	1.60477i	−0.0110909	+	0.0887438i
$328$	0.601996	+	0.219109i	0.0332397	+	0.0120982i
$329$	2.08863	−	15.7691i	0.115150	−	0.869379i
$330$	−7.72388	−	33.7885i	−0.425186	−	1.86000i
$331$	−1.02119	+	5.79145i	−0.0561296	+	0.318327i	−0.999926	−	0.0122019i	$-0.996116\pi$
$331$	−1.02119	+	5.79145i	−0.0561296	+	0.318327i	0.943796	+	0.330529i	$0.107227\pi$
$332$	12.3295			0.676671
$333$	−1.51039	−	5.35451i	−0.0827687	−	0.293426i
$334$	−3.37086			−0.184445
$335$	−44.0297	−	36.9453i	−2.40560	−	2.01854i
$336$	4.43321	+	1.16044i	0.241852	+	0.0633073i
$337$	−1.09484	−	6.20913i	−0.0596396	−	0.338233i	0.940359	−	0.340185i	$-0.110490\pi$
$337$	−1.09484	−	6.20913i	−0.0596396	−	0.338233i	−0.999998	+	0.00195217i	$0.999379\pi$
$338$	−1.35286	−	0.492401i	−0.0735859	−	0.0267831i
$339$	−16.1051	+	0.809164i	−0.874707	+	0.0439477i
$340$	−0.632243	+	3.58563i	−0.0342882	+	0.194458i
$341$	−29.3094			−1.58719
$342$	11.4098	−	1.14942i	0.616969	−	0.0621534i
$343$	18.3675	−	2.37415i	0.991749	−	0.128192i
$344$	−1.41337	+	0.514423i	−0.0762035	+	0.0277358i
$345$	−7.08617	−	30.9988i	−0.381507	−	1.66892i
$346$	18.7896	+	6.83885i	1.01013	+	0.367659i
$347$	4.55855	+	25.8528i	0.244716	+	1.38785i	0.821152	+	0.570710i	$0.193332\pi$
$347$	4.55855	+	25.8528i	0.244716	+	1.38785i	−0.576436	+	0.817142i	$0.695557\pi$
$348$	9.16031	+	6.93385i	0.491044	+	0.371693i
$349$	2.81276	−	15.9519i	0.150563	−	0.853887i	−0.812167	−	0.583425i	$-0.801712\pi$
$349$	2.81276	−	15.9519i	0.150563	−	0.853887i	0.962731	−	0.270462i	$-0.0871766\pi$
$350$	30.3392	+	9.59209i	1.62170	+	0.512719i
$351$	−17.3204	−	3.48332i	−0.924493	−	0.185926i
$352$	2.42480	−	4.19987i	0.129242	−	0.223854i
$353$	27.7363	−	10.0952i	1.47625	−	0.537312i	0.526463	−	0.850198i	$-0.323518\pi$
$353$	27.7363	−	10.0952i	1.47625	−	0.537312i	0.949791	+	0.312886i	$0.101296\pi$
$354$	−0.924543	+	7.39770i	−0.0491389	+	0.393184i
$355$	41.7062	−	34.9956i	2.21353	−	1.85737i
$356$	6.61986	−	5.55473i	0.350852	−	0.294400i
$357$	3.65473	−	1.73003i	0.193429	−	0.0915627i
$358$	−9.53797	+	3.47154i	−0.504097	+	0.183476i
$359$	14.6517	+	25.3775i	0.773286	+	1.33937i	0.935753	+	0.352657i	$0.114722\pi$
$359$	14.6517	+	25.3775i	0.773286	+	1.33937i	−0.162466	+	0.986714i	$0.551945\pi$
$360$	0.916836	−	12.3450i	0.0483215	−	0.650638i
$361$	2.19423	−	3.80052i	0.115486	−	0.200027i
$362$	−7.39378	+	2.69111i	−0.388608	+	0.141442i
$363$	11.7700	+	18.2101i	0.617763	+	0.955783i
$364$	8.31362	−	3.43597i	0.435752	−	0.180094i
$365$	−3.09912	−	17.5760i	−0.162215	−	0.919968i
$366$	−20.5911	+	1.03455i	−1.07631	+	0.0540769i
$367$	−3.21927	+	18.2574i	−0.168045	+	0.953028i	0.777825	+	0.628481i	$0.216323\pi$
$367$	−3.21927	+	18.2574i	−0.168045	+	0.953028i	−0.945869	+	0.324547i	$0.894788\pi$
$368$	2.22459	−	3.85311i	0.115965	−	0.200857i
$369$	−1.73101	+	0.835034i	−0.0901127	+	0.0434702i
$370$	3.82611	−	6.62702i	0.198910	−	0.344522i
$371$	−1.46115	−	2.29752i	−0.0758590	−	0.119281i
$372$	−10.0039	−	3.08215i	−0.518680	−	0.159802i
$373$	1.75557	+	9.95634i	0.0909000	+	0.515520i	0.995927	+	0.0901651i	$0.0287395\pi$
$373$	1.75557	+	9.95634i	0.0909000	+	0.515520i	−0.905027	+	0.425355i	$0.860149\pi$
$374$	−0.743062	−	4.21411i	−0.0384228	−	0.217907i
$375$	6.22781	−	49.8316i	0.321602	−	2.57329i
$376$	−4.60562	−	3.86458i	−0.237517	−	0.199300i
$377$	22.5525			1.16151
$378$	−11.7737	+	7.09785i	−0.605575	+	0.365074i
$379$	24.1641			1.24123			0.620614	−	0.784116i	$-0.286883\pi$
$379$	24.1641			1.24123			0.620614	+	0.784116i	$0.286883\pi$
$380$	12.0828	+	10.1386i	0.619832	+	0.520101i
$381$	19.5161	−	8.23441i	0.999841	−	0.421862i
$382$	−3.18012	−	18.0354i	−0.162709	−	0.922770i
$383$	−4.37573	−	24.8160i	−0.223589	−	1.26804i	−0.865364	−	0.501144i	$-0.832913\pi$
$383$	−4.37573	−	24.8160i	−0.223589	−	1.26804i	0.641775	−	0.766893i	$-0.278198\pi$
$384$	1.26929	−	1.17852i	0.0647732	−	0.0601410i
$385$	−52.8956	+	2.26789i	−2.69581	+	0.115582i
$386$	−8.69397	+	15.0584i	−0.442511	+	0.766452i
$387$	1.85307	−	4.11415i	0.0941967	−	0.209134i
$388$	−5.86139	+	10.1522i	−0.297567	+	0.515401i
$389$	4.52411	−	25.6575i	0.229382	−	1.30089i	−0.624747	−	0.780827i	$-0.714798\pi$
$389$	4.52411	−	25.6575i	0.229382	−	1.30089i	0.854129	−	0.520061i	$-0.174091\pi$
$390$	−13.1908	−	20.4084i	−0.667942	−	1.03342i
$391$	−0.681712	−	3.86618i	−0.0344756	−	0.195521i
$392$	2.96828	−	6.33950i	0.149921	−	0.320193i
$393$	7.61003	−	0.382349i	0.383875	−	0.0192870i
$394$	14.6171	−	5.32019i	0.736399	−	0.268027i
$395$	−1.85537	+	3.21360i	−0.0933539	+	0.161694i
$396$	3.94975	+	14.0024i	0.198482	+	0.703645i
$397$	−8.90440	−	15.4229i	−0.446899	−	0.774052i	0.551283	−	0.834318i	$-0.314138\pi$
$397$	−8.90440	−	15.4229i	−0.446899	−	0.774052i	−0.998182	+	0.0602664i	$0.980805\pi$
$398$	4.47104	−	1.62733i	0.224113	−	0.0815705i
$399$	1.42577	−	17.4588i	0.0713776	−	0.874033i
$400$	9.21292	−	7.73056i	0.460646	−	0.386528i
$401$	−6.11327	+	5.12965i	−0.305282	+	0.256162i	−0.782539	−	0.622602i	$-0.786076\pi$
$401$	−6.11327	+	5.12965i	−0.305282	+	0.256162i	0.477257	+	0.878764i	$0.341631\pi$
$402$	19.2366	+	14.5610i	0.959434	+	0.726239i
$403$	−19.3096	+	7.02810i	−0.961878	+	0.350095i
$404$	2.28366	−	3.95541i	0.113616	−	0.196789i
$405$	24.6102	+	27.8118i	1.22289	+	1.38198i
$406$	12.9480	−	11.8459i	0.642596	−	0.587904i
$407$	−1.56170	+	8.85687i	−0.0774108	+	0.439019i
$408$	0.189529	−	1.51651i	0.00938306	−	0.0750783i
$409$	3.45675	+	19.6042i	0.170925	+	0.969366i	0.942742	+	0.333522i	$0.108237\pi$
$409$	3.45675	+	19.6042i	0.170925	+	0.969366i	−0.771817	+	0.635845i	$0.780652\pi$
$410$	−2.48403	−	0.904115i	−0.122678	−	0.0446510i
$411$	25.0571	+	7.71994i	1.23598	+	0.380797i
$412$	13.3671	−	4.86524i	0.658552	−	0.239693i
$413$	10.8583	+	3.43299i	0.534303	+	0.168926i
$414$	3.62364	+	12.8463i	0.178092	+	0.631360i
$415$	−50.8757			−2.49739
$416$	0.590412	−	3.34839i	0.0289473	−	0.164168i
$417$	11.1977	+	17.3247i	0.548351	+	0.848392i
$418$	−17.4196	−	6.34023i	−0.852022	−	0.310111i
$419$	1.47365	+	8.35746i	0.0719923	+	0.408289i	0.999413	+	0.0342680i	$0.0109100\pi$
$419$	1.47365	+	8.35746i	0.0719923	+	0.408289i	−0.927420	+	0.374021i	$0.877979\pi$
$420$	−18.2929	−	4.78837i	−0.892602	−	0.233648i
$421$	−1.00446	−	0.842844i	−0.0489545	−	0.0410777i	0.617982	−	0.786192i	$-0.287950\pi$
$421$	−1.00446	−	0.842844i	−0.0489545	−	0.0410777i	−0.666937	+	0.745114i	$0.732395\pi$
$422$	−13.6505			−0.664494
$423$	17.9458	−	1.80786i	0.872555	−	0.0879011i
$424$	−1.02911			−0.0499782
$425$	1.84274	−	10.4507i	0.0893858	−	0.506932i
$426$	−16.7472	+	15.5496i	−0.811406	+	0.753379i
$427$	−4.13516	+	31.2204i	−0.200115	+	1.51086i
$428$	4.30051	+	1.56526i	0.207873	+	0.0756595i
$429$	22.7715	+	17.2367i	1.09942	+	0.832198i
$430$	5.83201	−	2.12268i	0.281245	−	0.102365i
$431$	3.38092	+	5.85592i	0.162853	+	0.282070i	0.935891	−	0.352290i	$-0.114597\pi$
$431$	3.38092	+	5.85592i	0.162853	+	0.282070i	−0.773038	+	0.634360i	$0.781264\pi$
$432$	−0.124338	+	5.19466i	−0.00598221	+	0.249928i
$433$	−28.9425			−1.39089			−0.695444	−	0.718580i	$-0.744792\pi$
$433$	−28.9425			−1.39089			−0.695444	+	0.718580i	$0.744792\pi$
$434$	−7.39452	+	14.1776i	−0.354949	+	0.680545i
$435$	−37.7985	−	28.6114i	−1.81230	−	1.37181i
$436$	0.715271	−	0.600184i	0.0342553	−	0.0287436i
$437$	−15.9814	−	5.81675i	−0.764494	−	0.278253i
$438$	1.66944	+	7.30304i	0.0797688	+	0.348953i
$439$	−3.35615	+	19.0336i	−0.160180	+	0.908426i	0.793716	+	0.608289i	$0.208144\pi$
$439$	−3.35615	+	19.0336i	−0.160180	+	0.908426i	−0.953896	+	0.300138i	$0.902967\pi$
$440$	−10.0055	+	17.3300i	−0.476994	+	0.826178i
$441$	7.41016	+	19.6492i	0.352865	+	0.935674i
$442$	−1.50005	−	2.59815i	−0.0713499	−	0.123582i
$443$	17.1986	−	6.25977i	0.817129	−	0.297410i	0.100563	−	0.994931i	$-0.467935\pi$
$443$	17.1986	−	6.25977i	0.817129	−	0.297410i	0.716565	+	0.697520i	$0.245713\pi$
$444$	−1.46442	+	2.85882i	−0.0694985	+	0.135673i
$445$	−27.3158	+	22.9206i	−1.29489	+	1.08654i
$446$	−15.0885	−	5.49178i	−0.714463	−	0.260043i
$447$	7.88886	+	12.2054i	0.373130	+	0.577296i
$448$	−1.41981	−	2.23252i	−0.0670797	−	0.105477i
$449$	−7.28274	−	12.6141i	−0.343694	−	0.595295i	0.641422	−	0.767189i	$-0.278345\pi$
$449$	−7.28274	−	12.6141i	−0.343694	−	0.595295i	−0.985116	+	0.171893i	$0.945012\pi$
$450$	−2.67221	+	35.9807i	−0.125969	+	1.69615i
$451$	3.10680			0.146293
$452$	7.13187	+	5.98435i	0.335455	+	0.281480i
$453$	−12.2148	+	11.3413i	−0.573904	+	0.532862i
$454$	−8.59761	+	7.21425i	−0.403506	+	0.338582i
$455$	−34.3048	+	14.1780i	−1.60823	+	0.664673i
$456$	−5.27897	−	3.99589i	−0.247210	−	0.187125i
$457$	30.0051	+	25.1773i	1.40358	+	1.17774i	0.959483	+	0.281765i	$0.0909198\pi$
$457$	30.0051	+	25.1773i	1.40358	+	1.17774i	0.444097	+	0.895979i	$0.353525\pi$
$458$	−0.849030	−	1.47056i	−0.0396726	−	0.0687149i
$459$	2.86224	+	3.58177i	0.133598	+	0.167183i
$460$	−9.17941	+	15.8992i	−0.427992	+	0.741305i
$461$	−1.95543	+	11.0898i	−0.0910736	+	0.516504i	0.904806	+	0.425823i	$0.140015\pi$
$461$	−1.95543	+	11.0898i	−0.0910736	+	0.516504i	−0.995880	+	0.0906809i	$0.971096\pi$
$462$	22.1275	−	2.06491i	1.02946	−	0.0960681i
$463$	−31.1055	−	11.3215i	−1.44559	−	0.526153i	−0.504238	−	0.863565i	$-0.668226\pi$
$463$	−31.1055	−	11.3215i	−1.44559	−	0.526153i	−0.941357	+	0.337412i	$0.890449\pi$
$464$	−1.15181	−	6.53222i	−0.0534713	−	0.303251i
$465$	41.2795	+	12.7180i	1.91429	+	0.589781i
$466$	−10.5078	−	8.81713i	−0.486767	−	0.408446i
$467$	−0.185620	−	0.321503i	−0.00858947	−	0.0148774i	0.861699	−	0.507420i	$-0.169401\pi$
$467$	−0.185620	−	0.321503i	−0.00858947	−	0.0148774i	−0.870288	+	0.492543i	$0.836067\pi$
$468$	5.95980	+	8.27790i	0.275492	+	0.382646i
$469$	27.1906	−	24.8764i	1.25555	−	1.14869i
$470$	19.0043	+	15.9465i	0.876604	+	0.735558i
$471$	−19.0154	−	29.4201i	−0.876185	−	1.35561i
$472$	3.29728	−	2.76675i	0.151770	−	0.127350i
$473$	−5.58763	+	4.68858i	−0.256919	+	0.215581i
$474$	0.710133	−	1.38631i	0.0326175	−	0.0636752i
$475$	−35.2164	−	29.5501i	−1.61584	−	1.35585i
$476$	−2.22592	−	0.703752i	−0.102025	−	0.0322564i
$477$	2.15422	−	2.21157i	0.0986350	−	0.101261i
$478$	−9.37363	−	16.2356i	−0.428740	−	0.742599i
$479$	9.71015	+	8.14778i	0.443668	+	0.372282i	0.837080	−	0.547081i	$-0.184261\pi$
$479$	9.71015	+	8.14778i	0.443668	+	0.372282i	−0.393412	+	0.919362i	$0.628705\pi$
$480$	−5.23751	+	4.86295i	−0.239058	+	0.221963i
$481$	1.09491	+	6.20955i	0.0499236	+	0.283131i
$482$	12.9707	+	4.72094i	0.590798	+	0.215033i
$483$	20.3005	−	1.89442i	0.923707	−	0.0861990i
$484$	2.17382	−	12.3283i	0.0988100	−	0.560379i
$485$	24.1860	−	41.8914i	1.09823	−	1.90219i
$486$	−10.9031	−	11.1411i	−0.494573	−	0.505369i
$487$	−1.14260	−	1.97904i	−0.0517762	−	0.0896790i	0.838976	−	0.544169i	$-0.183155\pi$
$487$	−1.14260	−	1.97904i	−0.0517762	−	0.0896790i	−0.890752	+	0.454490i	$0.849822\pi$
$488$	9.11842	+	7.65126i	0.412771	+	0.346356i
$489$	−22.8272	+	9.63144i	−1.03228	+	0.435549i
$490$	−12.2481	+	26.1589i	−0.553313	+	1.18174i
$491$	−10.0281	+	8.41455i	−0.452560	+	0.379743i	−0.840385	−	0.541990i	$-0.817671\pi$
$491$	−10.0281	+	8.41455i	−0.452560	+	0.379743i	0.387825	+	0.921733i	$0.373227\pi$
$492$	1.06042	+	0.326708i	0.0478073	+	0.0147291i
$493$	−4.48345	−	3.76206i	−0.201925	−	0.169435i
$494$	−12.9967			−0.584749
$495$	−16.2980	−	57.7784i	−0.732540	−	2.59695i
$496$	3.02184	+	5.23398i	0.135685	+	0.235013i
$497$	18.7332	+	29.4562i	0.840300	+	1.32129i
$498$	21.3285	−	1.07160i	0.955751	−	0.0480196i
$499$	−16.9440	−	6.16711i	−0.758517	−	0.276078i	−0.0663321	−	0.997798i	$-0.521130\pi$
$499$	−16.9440	−	6.16711i	−0.758517	−	0.276078i	−0.692185	+	0.721720i	$0.743352\pi$
$500$	−22.2108	+	18.6371i	−0.993296	+	0.833475i
$501$	−5.83114	+	0.292973i	−0.260516	+	0.0130891i
$502$	3.87926	−	1.41194i	0.173140	−	0.0630178i
$503$	−1.29790	−	2.24802i	−0.0578703	−	0.100234i	0.835639	−	0.549279i	$-0.185098\pi$
$503$	−1.29790	−	2.24802i	−0.0578703	−	0.100234i	−0.893509	+	0.449045i	$0.851764\pi$
$504$	7.76973	+	1.62211i	0.346091	+	0.0722543i
$505$	−9.42312	+	16.3213i	−0.419323	+	0.726290i
$506$	3.74676	−	21.2489i	0.166564	−	0.944631i
$507$	−2.38307	−	0.734207i	−0.105836	−	0.0326073i
$508$	−11.4920	−	4.18275i	−0.509875	−	0.185579i
$509$	23.4069	−	19.6407i	1.03749	−	0.870559i	0.0457680	−	0.998952i	$-0.485427\pi$
$509$	23.4069	−	19.6407i	1.03749	−	0.870559i	0.991723	+	0.128394i	$0.0409821\pi$
$510$	−0.782058	+	6.25761i	−0.0346301	+	0.277092i
$511$	11.4328	−	0.490180i	0.505759	−	0.0216843i
$512$	−1.00000			−0.0441942
$513$	19.6375	−	2.98001i	0.867017	−	0.131570i
$514$	−6.67340	−	11.5587i	−0.294351	−	0.509831i
$515$	−55.1573	+	20.0756i	−2.43052	+	0.884637i
$516$	−2.40023	+	1.01272i	−0.105664	+	0.0445827i
$517$	−27.3984	−	9.97220i	−1.20498	−	0.438577i
$518$	3.89025	+	2.98995i	0.170928	+	0.131371i
$519$	33.0979	+	10.1972i	1.45284	+	0.447609i
$520$	−2.43623	+	13.8166i	−0.106836	+	0.605897i
$521$	−18.0784			−0.792029			−0.396015	−	0.918244i	$-0.629607\pi$
$521$	−18.0784			−0.792029			−0.396015	+	0.918244i	$0.629607\pi$
$522$	16.4488	+	11.1985i	0.719943	+	0.490145i
$523$	−35.9468			−1.57185			−0.785923	−	0.618325i	$-0.787812\pi$
$523$	−35.9468			−1.57185			−0.785923	+	0.618325i	$0.787812\pi$
$524$	−3.36998	−	2.82775i	−0.147218	−	0.123531i
$525$	53.3165	+	13.9562i	2.32692	+	0.609097i
$526$	−0.415800	−	2.35812i	−0.0181298	−	0.102819i
$527$	5.01115	+	1.82391i	0.218289	+	0.0794507i
$528$	3.82955	−	7.47597i	0.166660	−	0.325350i
$529$	−0.556493	+	3.15603i	−0.0241954	+	0.137219i
$530$	4.24647			0.184455
$531$	−0.956377	+	12.8774i	−0.0415032	+	0.558832i
$532$	−7.46174	+	6.82666i	−0.323507	+	0.295973i
$533$	2.04681	−	0.744979i	0.0886574	−	0.0322686i
$534$	10.9687	−	10.1843i	0.474663	−	0.440718i
$535$	−17.7453	−	6.45876i	−0.767197	−	0.279237i
$536$	−2.41879	−	13.7176i	−0.104476	−	0.592511i
$537$	−16.1977	+	6.83428i	−0.698983	+	0.294921i
$538$	−3.77253	+	21.3951i	−0.162645	+	0.922406i
$539$	3.01176	−	33.8133i	0.129726	−	1.45644i
$540$	0.513060	−	21.4349i	0.0220786	−	0.922411i
$541$	−5.82799	+	10.0944i	−0.250565	+	0.433991i	−0.963682	−	0.267054i	$-0.913950\pi$
$541$	−5.82799	+	10.0944i	−0.250565	+	0.433991i	0.713116	+	0.701046i	$0.247283\pi$
$542$	−7.56540	+	2.75358i	−0.324962	+	0.118276i
$543$	−12.5564	+	5.29789i	−0.538845	+	0.227354i
$544$	−0.675933	+	0.567175i	−0.0289804	+	0.0243174i
$545$	−2.95145	+	2.47656i	−0.126426	+	0.106084i
$546$	14.0828	−	6.66635i	0.602690	−	0.285293i
$547$	29.5482	−	10.7547i	1.26339	−	0.459836i	0.378485	−	0.925607i	$-0.376445\pi$
$547$	29.5482	−	10.7547i	1.26339	−	0.459836i	0.884905	+	0.465771i	$0.154223\pi$
$548$	−7.56890	−	13.1097i	−0.323327	−	0.560019i
$549$	−35.5299	+	3.57928i	−1.51638	+	0.152760i
$550$	29.1621	−	50.5102i	1.24347	−	2.15376i
$551$	−23.8256	+	8.67179i	−1.01500	+	0.369431i
$552$	3.51337	−	6.85872i	0.149539	−	0.291927i
$553$	−1.88647	−	1.44990i	−0.0802211	−	0.0616559i
$554$	2.30477	+	13.0710i	0.0979204	+	0.555334i
$555$	6.04270	−	11.7964i	0.256498	−	0.500730i
$556$	2.06812	−	11.7289i	0.0877077	−	0.497415i
$557$	−10.0141	+	17.3450i	−0.424312	+	0.734930i	−0.996356	−	0.0852933i	$-0.972817\pi$
$557$	−10.0141	+	17.3450i	−0.424312	+	0.734930i	0.572044	+	0.820223i	$0.306151\pi$
$558$	−17.5734	−	4.46223i	−0.743940	−	0.188901i
$559$	−2.55696	+	4.42878i	−0.108148	+	0.187317i
$560$	5.85861	+	9.21211i	0.247571	+	0.389283i
$561$	−1.65166	−	7.22528i	−0.0697332	−	0.305052i
$562$	−1.64577	−	9.33362i	−0.0694226	−	0.393715i
$563$	−2.61180	−	14.8123i	−0.110074	−	0.624262i	−0.989072	−	0.147436i	$-0.952898\pi$
$563$	−2.61180	−	14.8123i	−0.110074	−	0.624262i	0.878997	−	0.476827i	$-0.158213\pi$
$564$	−8.30301	−	6.28492i	−0.349620	−	0.264643i
$565$	−29.4284	−	24.6934i	−1.23806	−	1.03886i
$566$	7.96395			0.334750
$567$	−19.7501	+	13.3016i	−0.829426	+	0.558616i
$568$	13.1942			0.553615
$569$	8.15332	+	6.84145i	0.341805	+	0.286808i	0.797489	−	0.603333i	$-0.206161\pi$
$569$	8.15332	+	6.84145i	0.341805	+	0.286808i	−0.455684	+	0.890141i	$0.650605\pi$
$570$	21.7828	+	16.4884i	0.912380	+	0.690621i
$571$	7.84461	+	44.4890i	0.328287	+	1.86181i	0.485493	+	0.874241i	$0.338640\pi$
$571$	7.84461	+	44.4890i	0.328287	+	1.86181i	−0.157206	+	0.987566i	$0.550249\pi$
$572$	−2.86326	−	16.2383i	−0.119719	−	0.678959i
$573$	−7.06871	−	30.9224i	−0.295300	−	1.29180i
$574$	0.783820	−	1.50282i	0.0327160	−	0.0627267i
$575$	26.7543	−	46.3399i	1.11573	−	1.93251i
$576$	2.09328	−	2.14900i	0.0872198	−	0.0895416i
$577$	−6.53116	+	11.3123i	−0.271896	+	0.470937i	−0.969347	−	0.245695i	$-0.920984\pi$
$577$	−6.53116	+	11.3123i	−0.271896	+	0.470937i	0.697452	+	0.716632i	$0.254317\pi$
$578$	2.81682	−	15.9750i	0.117164	−	0.664472i
$579$	−13.7307	+	26.8047i	−0.570626	+	1.11396i
$580$	4.75273	+	26.9541i	0.197347	+	1.11921i
$581$	4.28325	−	32.3384i	0.177699	−	1.34162i
$582$	−9.25707	+	18.0714i	−0.383718	+	0.749086i
$583$	−4.68980	+	1.70695i	−0.194232	+	0.0706946i
$584$	2.16259	−	3.74571i	0.0894885	−	0.154999i
$585$	−24.5921	−	34.1574i	−1.01676	−	1.41223i
$586$	8.82633	+	15.2877i	0.364612	+	0.631527i
$587$	18.9086	−	6.88215i	0.780439	−	0.284057i	0.0790835	−	0.996868i	$-0.474801\pi$
$587$	18.9086	−	6.88215i	0.780439	−	0.284057i	0.701356	+	0.712811i	$0.252578\pi$
$588$	4.58375	−	11.2245i	0.189031	−	0.462890i
$589$	17.6972	−	14.8497i	0.729199	−	0.611870i
$590$	−13.6057	+	11.4165i	−0.560136	+	0.470010i
$591$	24.8233	−	10.4737i	1.02109	−	0.430828i
$592$	1.74265	−	0.634272i	0.0716224	−	0.0260684i
$593$	−7.21974	+	12.5050i	−0.296479	+	0.513517i	−0.975328	−	0.220761i	$-0.929146\pi$
$593$	−7.21974	+	12.5050i	−0.296479	+	0.513517i	0.678849	+	0.734278i	$0.262479\pi$
$594$	8.04955	+	23.8790i	0.330277	+	0.979766i
$595$	9.18490	+	2.90391i	0.376544	+	0.119049i
$596$	1.45701	−	8.26312i	0.0596815	−	0.338470i
$597$	7.59288	−	3.20365i	0.310756	−	0.131117i
$598$	−2.62685	−	14.8976i	−0.107420	−	0.609209i
$599$	−12.1359	−	4.41711i	−0.495860	−	0.180478i	0.0819710	−	0.996635i	$-0.473879\pi$
$599$	−12.1359	−	4.41711i	−0.495860	−	0.180478i	−0.577831	+	0.816156i	$0.696101\pi$
$600$	15.2652	−	14.1736i	0.623201	−	0.578634i
$601$	4.96025	−	1.80538i	0.202333	−	0.0736432i	−0.238866	−	0.971053i	$-0.576776\pi$
$601$	4.96025	−	1.80538i	0.202333	−	0.0736432i	0.441199	+	0.897409i	$0.354553\pi$
$602$	0.858251	+	3.88575i	0.0349797	+	0.158371i
$603$	34.5423	+	23.5168i	1.40667	+	0.957677i
$604$	9.62337			0.391570
$605$	−8.96990	+	50.8708i	−0.364678	+	2.06819i
$606$	3.60665	−	7.04082i	0.146510	−	0.286014i
$607$	−38.4370	−	13.9899i	−1.56011	−	0.567834i	−0.589349	−	0.807879i	$-0.700616\pi$
$607$	−38.4370	−	13.9899i	−1.56011	−	0.567834i	−0.970762	+	0.240045i	$0.922838\pi$
$608$	0.663771	+	3.76443i	0.0269195	+	0.152668i
$609$	21.3687	−	21.6173i	0.865903	−	0.875976i
$610$	−37.6256	−	31.5716i	−1.52342	−	1.27830i
$611$	−20.4418			−0.826987
$612$	0.196055	−	2.63983i	0.00792504	−	0.106709i
$613$	0.453328			0.0183097			0.00915486	−	0.999958i	$-0.497086\pi$
$613$	0.453328			0.0183097			0.00915486	+	0.999958i	$0.497086\pi$
$614$	2.46041	−	13.9537i	0.0992939	−	0.563124i
$615$	−4.37563	−	1.34810i	−0.176443	−	0.0543608i
$616$	−10.1732	−	7.81889i	−0.409891	−	0.315032i
$617$	−13.9621	−	5.08178i	−0.562092	−	0.204585i	0.0453190	−	0.998973i	$-0.485570\pi$
$617$	−13.9621	−	5.08178i	−0.562092	−	0.204585i	−0.607411	+	0.794388i	$0.707792\pi$
$618$	22.7006	−	9.57802i	0.913150	−	0.385284i
$619$	4.89484	−	1.78158i	0.196740	−	0.0716076i	−0.241771	−	0.970333i	$-0.577728\pi$
$619$	4.89484	−	1.78158i	0.196740	−	0.0716076i	0.438511	+	0.898726i	$0.355506\pi$
$620$	−12.4691	−	21.5971i	−0.500772	−	0.867362i
$621$	7.38494	+	21.9074i	0.296348	+	0.879115i
$622$	21.6408			0.867718
$623$	−12.2695	−	19.2926i	−0.491565	−	0.772941i
$624$	0.730315	−	5.84359i	0.0292360	−	0.233931i
$625$	45.5845	−	38.2499i	1.82338	−	1.53000i
$626$	−8.43934	−	3.07167i	−0.337304	−	0.122769i
$627$	−30.6847	−	9.45376i	−1.22543	−	0.377547i
$628$	−3.51200	+	19.9175i	−0.140144	+	0.794796i
$629$	0.818169	−	1.41711i	0.0326226	−	0.0565039i
$630$	−32.0605	−	6.69335i	−1.27732	−	0.266669i
$631$	−12.8407	−	22.2408i	−0.511182	−	0.885393i	−0.999916	−	0.0129600i	$-0.995875\pi$
$631$	−12.8407	−	22.2408i	−0.511182	−	0.885393i	0.488734	−	0.872433i	$-0.337459\pi$
$632$	−0.845051	+	0.307573i	−0.0336143	+	0.0122346i
$633$	−23.6135	+	1.18641i	−0.938553	+	0.0471555i
$634$	−19.1201	+	16.0437i	−0.759358	+	0.637177i
$635$	47.4198	+	17.2594i	1.88180	+	0.684918i
$636$	−1.78023	+	0.0894439i	−0.0705908	+	0.00354668i
$637$	−6.12389	−	22.9990i	−0.242637	−	0.911253i
$638$	−16.0836	−	27.8577i	−0.636757	−	1.10290i
$639$	−27.6190	+	28.3543i	−1.09259	+	1.12168i
$640$	4.12633			0.163108
$641$	27.7342	+	23.2718i	1.09544	+	0.919179i	0.997110	−	0.0759751i	$-0.0242069\pi$
$641$	27.7342	+	23.2718i	1.09544	+	0.919179i	0.0983254	+	0.995154i	$0.468651\pi$
$642$	7.57535	+	2.33392i	0.298975	+	0.0921123i
$643$	−24.6267	+	20.6643i	−0.971184	+	0.814920i	−0.982736	−	0.185013i	$-0.940767\pi$
$643$	−24.6267	+	20.6643i	−0.971184	+	0.814920i	0.0115524	+	0.999933i	$0.496323\pi$
$644$	−9.33329	−	7.17333i	−0.367783	−	0.282669i
$645$	9.90413	−	4.17884i	0.389975	−	0.164542i
$646$	2.58376	+	2.16803i	0.101657	+	0.0853000i
$647$	4.24619	+	7.35461i	0.166935	+	0.289140i	0.937341	−	0.348414i	$-0.113280\pi$
$647$	4.24619	+	7.35461i	0.166935	+	0.289140i	−0.770406	+	0.637554i	$0.779946\pi$
$648$	0.236398	+	8.99689i	0.00928659	+	0.353431i
$649$	10.4370	−	18.0775i	0.409689	−	0.709602i
$650$	7.10065	−	40.2698i	0.278511	−	1.57951i
$651$	−11.5593	+	25.1680i	−0.453046	+	0.986413i
$652$	13.4417	+	4.89238i	0.526418	+	0.191600i
$653$	8.29801	+	47.0604i	0.324726	+	1.84161i	0.511591	+	0.859229i	$0.329056\pi$
$653$	8.29801	+	47.0604i	0.324726	+	1.84161i	−0.186865	+	0.982386i	$0.559833\pi$
$654$	1.18516	−	1.10041i	0.0463435	−	0.0430293i
$655$	13.9057	+	11.6682i	0.543339	+	0.455915i
$656$	−0.320315	−	0.554802i	−0.0125062	−	0.0216614i
$657$	3.52264	+	12.4882i	0.137431	+	0.487211i
$658$	−11.7362	+	10.7373i	−0.457524	+	0.418583i
$659$	20.1511	+	16.9088i	0.784977	+	0.658674i	0.944497	−	0.328521i	$-0.106550\pi$
$659$	20.1511	+	16.9088i	0.784977	+	0.658674i	−0.159520	+	0.987195i	$0.550995\pi$
$660$	−15.8020	+	30.8483i	−0.615092	+	1.20077i
$661$	−4.33944	+	3.64122i	−0.168785	+	0.141627i	−0.723267	−	0.690568i	$-0.757361\pi$
$661$	−4.33944	+	3.64122i	−0.168785	+	0.141627i	0.554483	+	0.832195i	$0.312916\pi$
$662$	4.50495	−	3.78010i	0.175090	−	0.146918i
$663$	−2.82070	−	4.36409i	−0.109547	−	0.169487i
$664$	−9.44497	−	7.92527i	−0.366536	−	0.307560i
$665$	30.7896	−	28.1691i	1.19397	−	1.09235i
$666$	−2.28479	+	5.07265i	−0.0885338	+	0.196561i
$667$	−14.7557	−	25.5576i	−0.571343	−	0.989595i
$668$	2.58223	+	2.16675i	0.0999094	+	0.0838339i
$669$	−26.5785	−	8.18866i	−1.02758	−	0.316592i
$670$	9.98071	+	56.6034i	0.385589	+	2.18678i
$671$	54.2446	+	19.7434i	2.09409	+	0.762186i
$672$	−2.65012	−	3.73856i	−0.102231	−	0.144218i
$673$	−2.60899	+	14.7963i	−0.100569	+	0.570356i	0.892329	+	0.451386i	$0.149070\pi$
$673$	−2.60899	+	14.7963i	−0.100569	+	0.570356i	−0.992898	+	0.118970i	$0.962041\pi$
$674$	−3.15246	+	5.46022i	−0.121428	+	0.210320i
$675$	−1.49536	+	62.4742i	−0.0575566	+	2.40463i
$676$	0.719842	+	1.24680i	0.0276862	+	0.0479540i
$677$	6.55478	+	5.50011i	0.251921	+	0.211387i	0.759999	−	0.649924i	$-0.225199\pi$
$677$	6.55478	+	5.50011i	0.251921	+	0.211387i	−0.508078	+	0.861311i	$0.669644\pi$
$678$	12.8573	+	9.73228i	0.493782	+	0.373766i
$679$	24.5915	+	18.9004i	0.943734	+	0.725330i
$680$	2.78912	−	2.34035i	0.106958	−	0.0897484i
$681$	−14.2457	+	13.2270i	−0.545897	+	0.506858i
$682$	22.4523	+	18.8397i	0.859743	+	0.721410i
$683$	34.5767			1.32304			0.661519	−	0.749928i	$-0.269912\pi$
$683$	34.5767			1.32304			0.661519	+	0.749928i	$0.269912\pi$
$684$	−9.47922	−	6.45355i	−0.362447	−	0.246758i
$685$	31.2318	+	54.0950i	1.19330	+	2.06686i
$686$	−15.5964	−	9.98767i	−0.595472	−	0.381331i
$687$	−1.59652	−	2.47009i	−0.0609111	−	0.0942398i
$688$	1.41337	+	0.514423i	0.0538840	+	0.0196122i
$689$	−2.68042	+	2.24914i	−0.102116	+	0.0856853i
$690$	−14.4973	+	28.3014i	−0.551904	+	1.07741i
$691$	−16.3345	+	5.94526i	−0.621393	+	0.226168i	−0.633481	−	0.773759i	$-0.718374\pi$
$691$	−16.3345	+	5.94526i	−0.621393	+	0.226168i	0.0120880	+	0.999927i	$0.496152\pi$
$692$	−9.99773	−	17.3166i	−0.380057	−	0.658277i
$693$	38.0982	−	5.49519i	1.44723	−	0.208745i
$694$	13.1258	−	22.7346i	0.498249	−	0.862993i
$695$	−8.53374	+	48.3972i	−0.323703	+	1.83581i
$696$	−2.56021	−	11.1998i	−0.0970445	−	0.424526i
$697$	−0.531182	−	0.193334i	−0.0201199	−	0.00732306i
$698$	−12.4084	+	10.4119i	−0.469665	+	0.394096i
$699$	−18.9435	−	14.3392i	−0.716510	−	0.542359i
$700$	−17.0755	−	26.8496i	−0.645393	−	1.01482i
$701$	−22.5868			−0.853091			−0.426545	−	0.904466i	$-0.640270\pi$
$701$	−22.5868			−0.853091			−0.426545	+	0.904466i	$0.640270\pi$
$702$	11.0291	+	13.8017i	0.416268	+	0.520911i
$703$	−3.54439	−	6.13907i	−0.133679	−	0.231539i
$704$	−4.55712	+	1.65866i	−0.171753	+	0.0625130i
$705$	34.2610	+	25.9337i	1.29034	+	0.976718i
$706$	−27.7363	−	10.0952i	−1.04387	−	0.379937i
$707$	−9.58109	−	7.36378i	−0.360334	−	0.276943i
$708$	5.46339	−	5.07269i	0.205327	−	0.190643i
$709$	−2.82740	+	16.0350i	−0.106185	+	0.602206i	0.884555	+	0.466436i	$0.154462\pi$
$709$	−2.82740	+	16.0350i	−0.106185	+	0.602206i	−0.990740	+	0.135770i	$0.956649\pi$
$710$	−54.4435			−2.04323
$711$	1.10795	−	2.45985i	0.0415513	−	0.0922515i
$712$	−8.64162			−0.323858
$713$	20.5985	+	17.2842i	0.771421	+	0.647299i
$714$	−3.91172	−	1.02394i	−0.146393	−	0.0383198i
$715$	11.8147	+	67.0047i	0.441846	+	2.50583i
$716$	9.53797	+	3.47154i	0.356451	+	0.129737i
$717$	−17.6262	−	27.2708i	−0.658264	−	1.01845i
$718$	5.08848	−	28.8582i	0.189900	−	1.07698i
$719$	24.9736			0.931359			0.465679	−	0.884954i	$-0.345810\pi$
$719$	24.9736			0.931359			0.465679	+	0.884954i	$0.345810\pi$
$720$	−8.63755	+	8.86748i	−0.321902	+	0.330472i
$721$	−8.11706	−	36.7501i	−0.302295	−	1.36865i
$722$	−4.12380	+	1.50094i	−0.153472	+	0.0558592i
$723$	22.8479	+	7.03927i	0.849721	+	0.261793i
$724$	7.39378	+	2.69111i	0.274788	+	0.100014i
$725$	−13.8523	−	78.5604i	−0.514462	−	2.91766i
$726$	2.68892	−	21.5153i	0.0997953	−	0.798509i
$727$	−0.128082	+	0.726392i	−0.00475032	+	0.0269404i	−0.987091	−	0.160162i	$-0.948798\pi$
$727$	−0.128082	+	0.726392i	−0.00475032	+	0.0269404i	0.982340	+	0.187102i	$0.0599095\pi$
$728$	−8.57720	−	2.71178i	−0.317892	−	0.100505i
$729$	−19.8292	−	18.3250i	−0.734414	−	0.678702i
$730$	−8.92355	+	15.4560i	−0.330276	+	0.572054i
$731$	1.24711	−	0.453910i	0.0461259	−	0.0167885i
$732$	16.4387	+	12.4432i	0.607590	+	0.459912i
$733$	−13.3370	+	11.1910i	−0.492612	+	0.413350i	−0.854961	−	0.518692i	$-0.826419\pi$
$733$	−13.3370	+	11.1910i	−0.492612	+	0.413350i	0.362350	+	0.932042i	$0.381975\pi$
$734$	14.2017	−	11.9167i	0.524196	−	0.439852i
$735$	−18.9141	+	46.3160i	−0.697656	+	1.70839i
$736$	−4.18087	+	1.52171i	−0.154109	+	0.0560911i
$737$	−33.7755	−	58.5010i	−1.24414	−	2.15491i
$738$	1.86278	+	0.472997i	0.0685698	+	0.0174112i
$739$	17.2716	−	29.9153i	0.635346	−	1.10045i	−0.351095	−	0.936340i	$-0.614191\pi$
$739$	17.2716	−	29.9153i	0.635346	−	1.10045i	0.986442	−	0.164112i	$-0.0524760\pi$
$740$	−7.19074	+	2.61722i	−0.264337	+	0.0962108i
$741$	−22.4826	+	1.12959i	−0.825918	+	0.0414964i
$742$	−0.357512	+	2.69921i	−0.0131247	+	0.0990910i
$743$	−8.31833	−	47.1756i	−0.305170	−	1.73070i	−0.622704	−	0.782457i	$-0.713966\pi$
$743$	−8.31833	−	47.1756i	−0.305170	−	1.73070i	0.317534	−	0.948247i	$-0.397145\pi$
$744$	5.68229	+	8.79146i	0.208323	+	0.322311i
$745$	−6.01211	+	34.0964i	−0.220267	+	1.24919i
$746$	5.05497	−	8.75546i	0.185075	−	0.320560i
$747$	36.8023	−	3.70746i	1.34653	−	0.135649i
$748$	−2.13956	+	3.70583i	−0.0782301	+	0.135498i
$749$	5.59941	−	10.7358i	0.204598	−	0.392277i
$750$	−36.8019	+	34.1701i	−1.34382	+	1.24771i
$751$	−3.78293	−	21.4541i	−0.138041	−	0.782871i	−0.972694	−	0.232093i	$-0.925443\pi$
$751$	−3.78293	−	21.4541i	−0.138041	−	0.782871i	0.834652	−	0.550777i	$-0.185669\pi$
$752$	1.04401	+	5.92088i	0.0380711	+	0.215912i
$753$	6.58790	−	2.77962i	0.240076	−	0.101295i
$754$	−17.2762	−	14.4964i	−0.629162	−	0.527929i
$755$	−39.7092			−1.44517
$756$	13.5816	+	2.13074i	0.493958	+	0.0774941i
$757$	−1.80404			−0.0655689			−0.0327845	−	0.999462i	$-0.510437\pi$
$757$	−1.80404			−0.0655689			−0.0327845	+	0.999462i	$0.510437\pi$
$758$	−18.5108	−	15.5324i	−0.672343	−	0.564163i
$759$	4.63459	−	37.0835i	0.168225	−	1.34605i
$760$	−2.73894	−	15.5333i	−0.0993518	−	0.563452i
$761$	6.58960	+	37.3715i	0.238873	+	1.35471i	0.834302	+	0.551307i	$0.185871\pi$
$761$	6.58960	+	37.3715i	0.238873	+	1.35471i	−0.595430	+	0.803407i	$0.703018\pi$
$762$	−20.2432	−	6.23679i	−0.733333	−	0.225935i
$763$	−1.32570	−	2.08455i	−0.0479937	−	0.0754657i
$764$	−9.15680	+	15.8600i	−0.331281	+	0.573796i
$765$	−0.808986	+	10.8928i	−0.0292490	+	0.393831i
$766$	−12.5994	+	21.8228i	−0.455235	+	0.788490i
$767$	2.54131	−	14.4125i	0.0917612	−	0.520404i
$768$	−1.72987	+	0.0869135i	−0.0624213	+	0.00313622i
$769$	−6.85804	−	38.8939i	−0.247307	−	1.40255i	−0.815073	−	0.579359i	$-0.803303\pi$
$769$	−6.85804	−	38.8939i	−0.247307	−	1.40255i	0.567765	−	0.823190i	$-0.307808\pi$
$770$	41.9781	+	32.2633i	1.51279	+	1.16269i
$771$	−12.5487	−	19.4150i	−0.451931	−	0.699213i
$772$	16.3393	−	5.94703i	0.588065	−	0.214038i
$773$	−16.9784	+	29.4074i	−0.610670	+	1.05771i	0.380458	+	0.924798i	$0.375766\pi$
$773$	−16.9784	+	29.4074i	−0.610670	+	1.05771i	−0.991128	+	0.132913i	$0.957567\pi$
$774$	−4.06406	+	1.96049i	−0.146080	+	0.0704685i
$775$	36.3425	+	62.9471i	1.30546	+	2.26113i
$776$	11.0158	−	4.00943i	0.395444	−	0.143930i
$777$	6.98949	+	4.83410i	0.250747	+	0.173422i
$778$	−19.9580	+	16.7468i	−0.715529	+	0.600400i
$779$	−1.87590	+	1.57407i	−0.0672111	+	0.0563968i
$780$	−3.01352	+	24.1126i	−0.107901	+	0.863370i
$781$	60.1275	−	21.8846i	2.15153	−	0.783093i
$782$	−1.96291	+	3.39986i	−0.0701935	+	0.121579i
$783$	29.4275	+	17.9423i	1.05165	+	0.641206i
$784$	−6.34879	+	2.94837i	−0.226742	+	0.105299i
$785$	14.4917	−	82.1863i	0.517230	−	2.93336i
$786$	−6.07539	−	4.59874i	−0.216702	−	0.164032i
$787$	−4.61331	−	26.1634i	−0.164447	−	0.932624i	−0.949633	−	0.313364i	$-0.898544\pi$
$787$	−4.61331	−	26.1634i	−0.164447	−	0.932624i	0.785186	−	0.619260i	$-0.212567\pi$
$788$	−14.6171	−	5.32019i	−0.520713	−	0.189524i
$789$	−0.924233	−	4.04310i	−0.0329036	−	0.143938i
$790$	3.48696	−	1.26915i	0.124060	−	0.0451543i
$791$	18.1736	−	16.6268i	0.646179	−	0.591182i
$792$	5.97486	−	13.2653i	0.212307	−	0.471361i
$793$	40.4716			1.43719
$794$	−3.09247	+	17.5382i	−0.109747	+	0.622409i
$795$	7.34583	−	0.369075i	0.260530	−	0.0130898i
$796$	−4.47104	−	1.62733i	−0.158472	−	0.0576790i
$797$	6.43037	+	36.4684i	0.227775	+	1.29178i	0.857308	+	0.514804i	$0.172135\pi$
$797$	6.43037	+	36.4684i	0.227775	+	1.29178i	−0.629533	+	0.776974i	$0.716754\pi$
$798$	−12.3145	+	12.4577i	−0.435928	+	0.441000i
$799$	4.06385	+	3.40998i	0.143769	+	0.120636i
$800$	−12.0266			−0.425205
$801$	18.0893	−	18.5708i	0.639153	−	0.656168i
$802$	7.98031			0.281795
$803$	3.64233	−	20.6567i	0.128535	−	0.728958i
$804$	−5.37643	−	23.5195i	−0.189612	−	0.829467i
$805$	38.5123	+	29.5995i	1.35738	+	1.04325i
$806$	19.3096	+	7.02810i	0.680150	+	0.247554i
$807$	−4.66646	+	37.3385i	−0.164267	+	1.31438i
$808$	−4.29187	+	1.56211i	−0.150987	+	0.0549549i
$809$	4.25444	+	7.36891i	0.149578	+	0.259077i	0.931072	−	0.364836i	$-0.118875\pi$
$809$	4.25444	+	7.36891i	0.149578	+	0.259077i	−0.781493	+	0.623913i	$0.785542\pi$
$810$	−0.975456	−	37.1242i	−0.0342740	−	1.30441i
$811$	25.0396			0.879259			0.439629	−	0.898179i	$-0.355110\pi$
$811$	25.0396			0.879259			0.439629	+	0.898179i	$0.355110\pi$
$812$	−17.5331	+	0.751729i	−0.615292	+	0.0263805i
$813$	−12.8478	+	5.42087i	−0.450593	+	0.190118i
$814$	6.88942	−	5.78091i	0.241474	−	0.202621i
$815$	−55.4649	−	20.1876i	−1.94285	−	0.707140i
$816$	−1.11998	+	1.03989i	−0.0392071	+	0.0364033i
$817$	0.998359	−	5.66198i	0.0349282	−	0.198087i
$818$	9.95332	−	17.2397i	0.348010	−	0.602771i
$819$	23.7821	−	12.7559i	0.831013	−	0.445727i
$820$	1.32173	+	2.28930i	0.0461567	+	0.0799458i
$821$	28.5615	−	10.3955i	0.996804	−	0.362807i	0.208453	−	0.978032i	$-0.433157\pi$
$821$	28.5615	−	10.3955i	0.996804	−	0.362807i	0.788351	+	0.615225i	$0.210935\pi$
$822$	−14.2326	−	22.0202i	−0.496419	−	0.768044i
$823$	−36.2735	+	30.4371i	−1.26441	+	1.06097i	−0.269217	+	0.963079i	$0.586765\pi$
$823$	−36.2735	+	30.4371i	−1.26441	+	1.06097i	−0.995197	+	0.0978904i	$0.968791\pi$
$824$	−13.3671	−	4.86524i	−0.465667	−	0.169489i
$825$	46.0565	−	89.9106i	1.60348	−	3.13028i
$826$	−6.11128	−	9.60941i	−0.212638	−	0.334354i
$827$	1.08487	+	1.87905i	0.0377247	+	0.0653411i	0.884271	−	0.466974i	$-0.154656\pi$
$827$	1.08487	+	1.87905i	0.0377247	+	0.0653411i	−0.846547	+	0.532315i	$0.821322\pi$
$828$	5.48155	−	12.1701i	0.190497	−	0.422938i
$829$	12.2132			0.424183			0.212091	−	0.977250i	$-0.431973\pi$
$829$	12.2132			0.424183			0.212091	+	0.977250i	$0.431973\pi$
$830$	38.9731	+	32.7023i	1.35277	+	1.13511i
$831$	5.12300	+	22.4108i	0.177715	+	0.777423i
$832$	−2.60459	+	2.18551i	−0.0902978	+	0.0757688i
$833$	−2.61911	+	5.59377i	−0.0907469	+	0.193813i
$834$	2.55818	−	20.4692i	0.0885824	−	0.708789i
$835$	−10.6551	−	8.94071i	−0.368736	−	0.309406i
$836$	9.26879	+	16.0540i	0.320568	+	0.555240i
$837$	−30.7875	−	6.19171i	−1.06417	−	0.214017i
$838$	4.24319	−	7.34943i	0.146579	−	0.253882i
$839$	−6.32072	+	35.8466i	−0.218216	+	1.23756i	0.657023	+	0.753870i	$0.271815\pi$
$839$	−6.32072	+	35.8466i	−0.218216	+	1.23756i	−0.875239	+	0.483691i	$0.839296\pi$
$840$	10.9353	+	15.4266i	0.377303	+	0.532267i
$841$	−14.0921	−	5.12911i	−0.485935	−	0.176866i
$842$	0.227693	+	1.29131i	0.00784682	+	0.0445015i
$843$	−3.65818	−	16.0029i	−0.125994	−	0.551169i
$844$	10.4569	+	8.77435i	0.359940	+	0.302025i
$845$	−2.97031	−	5.14472i	−0.102182	−	0.176984i
$846$	−14.9094	−	10.1504i	−0.512594	−	0.348979i
$847$	−31.5801	−	9.98443i	−1.08511	−	0.343069i
$848$	0.788348	+	0.661502i	0.0270720	+	0.0227161i
$849$	13.7766	−	0.692174i	0.472811	−	0.0237554i
$850$	−8.12918	+	6.82119i	−0.278829	+	0.233965i
$851$	6.32060	−	5.30362i	0.216667	−	0.181806i
$852$	22.8242	−	1.14675i	0.781944	−	0.0392871i
$853$	−5.63338	−	4.72697i	−0.192883	−	0.161848i	0.541232	−	0.840874i	$-0.317958\pi$
$853$	−5.63338	−	4.72697i	−0.192883	−	0.161848i	−0.734115	+	0.679025i	$0.762403\pi$
$854$	23.2358	−	21.2582i	0.795112	−	0.727439i
$855$	39.1144	+	26.6295i	1.33768	+	0.910709i
$856$	−2.28825	−	3.96337i	−0.0782108	−	0.135465i
$857$	−12.8936	−	10.8190i	−0.440438	−	0.369571i	0.395435	−	0.918494i	$-0.370594\pi$
$857$	−12.8936	−	10.8190i	−0.440438	−	0.369571i	−0.835873	+	0.548923i	$0.815038\pi$
$858$	−6.36439	−	27.8413i	−0.217277	−	0.950487i
$859$	3.47241	+	19.6930i	0.118477	+	0.671916i	0.984970	+	0.172727i	$0.0552577\pi$
$859$	3.47241	+	19.6930i	0.118477	+	0.671916i	−0.866493	+	0.499190i	$0.833631\pi$
$860$	−5.83201	−	2.12268i	−0.198870	−	0.0723828i
$861$	1.22529	−	2.66781i	0.0417578	−	0.0909188i
$862$	1.17418	−	6.65911i	0.0399928	−	0.226810i
$863$	−24.1843	+	41.8885i	−0.823245	+	1.42590i	0.0800091	+	0.996794i	$0.474505\pi$
$863$	−24.1843	+	41.8885i	−0.823245	+	1.42590i	−0.903254	+	0.429107i	$0.858828\pi$
$864$	3.43431	−	3.89942i	0.116838	−	0.132661i
$865$	41.2539	+	71.4539i	1.40268	+	2.42951i
$866$	22.1712	+	18.6039i	0.753410	+	0.632186i
$867$	3.48429	−	27.8795i	0.118333	−	0.946836i
$868$	14.7777	−	6.10754i	0.501588	−	0.207304i
$869$	−3.34084	+	2.80330i	−0.113330	+	0.0950954i
$870$	10.5643	+	46.2140i	0.358163	+	1.56680i
$871$	−36.2799	−	30.4424i	−1.22930	−	1.03150i
$872$	−0.933720			−0.0316198
$873$	−14.4429	+	32.0658i	−0.488817	+	1.08526i
$874$	8.50352	+	14.7285i	0.287636	+	0.498200i
$875$	41.1661	+	64.7299i	1.39167	+	2.18827i
$876$	3.41544	−	6.66755i	0.115397	−	0.225276i
$877$	6.66263	+	2.42500i	0.224981	+	0.0818864i	0.452051	−	0.891992i	$-0.350692\pi$
$877$	6.66263	+	2.42500i	0.224981	+	0.0818864i	−0.227070	+	0.973878i	$0.572915\pi$
$878$	14.8055	−	12.4233i	0.499663	−	0.419267i
$879$	16.5971	+	25.6785i	0.559806	+	0.866114i
$880$	18.8042	−	6.84417i	0.633890	−	0.230717i
$881$	13.0583	+	22.6176i	0.439944	+	0.762005i	0.997685	−	0.0680101i	$-0.0216650\pi$
$881$	13.0583	+	22.6176i	0.439944	+	0.762005i	−0.557741	+	0.830015i	$0.688332\pi$
$882$	6.95372	−	19.8153i	0.234144	−	0.667216i
$883$	−8.43955	+	14.6177i	−0.284013	+	0.491926i	−0.972369	−	0.233447i	$-0.924999\pi$
$883$	−8.43955	+	14.6177i	−0.284013	+	0.491926i	0.688356	+	0.725373i	$0.258333\pi$
$884$	−0.520960	+	2.95451i	−0.0175218	+	0.0993710i
$885$	−22.5438	+	20.9316i	−0.757800	+	0.703607i
$886$	−17.1986	−	6.25977i	−0.577797	−	0.210301i
$887$	−13.7337	+	11.5240i	−0.461133	+	0.386937i	−0.843548	−	0.537054i	$-0.819537\pi$
$887$	−13.7337	+	11.5240i	−0.461133	+	0.386937i	0.382415	+	0.923991i	$0.375093\pi$
$888$	2.95942	−	1.24867i	0.0993118	−	0.0419025i
$889$	−14.9630	+	28.6887i	−0.501843	+	0.962186i
$890$	35.6582			1.19526
$891$	16.0001	+	40.6079i	0.536022	+	1.36041i
$892$	8.02844	+	13.9057i	0.268812	+	0.465596i
$893$	21.5957	−	7.86021i	0.722674	−	0.263032i
$894$	1.80226	−	14.4207i	0.0602766	−	0.482302i
$895$	−39.3568	−	14.3247i	−1.31555	−	0.478822i
$896$	−0.347398	+	2.62284i	−0.0116058	+	0.0876231i
$897$	−5.83892	−	25.5426i	−0.194956	−	0.852844i
$898$	−2.52927	+	14.3442i	−0.0844028	+	0.478672i
$899$	40.0877			1.33700
$900$	25.1750	−	25.8452i	0.839167	−	0.861506i
$901$	0.908057			0.0302518
$902$	−2.37994	−	1.99701i	−0.0792435	−	0.0664932i
$903$	1.82239	+	6.64724i	0.0606452	+	0.221206i
$904$	−1.61666	−	9.16855i	−0.0537694	−	0.304942i
$905$	−30.5092	−	11.1044i	−1.01416	−	0.369124i
$906$	16.6472	−	0.836401i	0.553065	−	0.0277876i
$907$	−5.59340	+	31.7217i	−0.185726	+	1.05330i	0.739294	+	0.673383i	$0.235160\pi$
$907$	−5.59340	+	31.7217i	−0.185726	+	1.05330i	−0.925019	+	0.379920i	$0.875952\pi$
$908$	11.2234			0.372461
$909$	5.62709	−	12.4932i	0.186639	−	0.414372i
$910$	35.3924	+	11.1897i	1.17325	+	0.370936i
$911$	−14.7843	+	5.38106i	−0.489827	+	0.178283i	−0.575113	−	0.818074i	$-0.695042\pi$
$911$	−14.7843	+	5.38106i	−0.489827	+	0.178283i	0.0852857	+	0.996357i	$0.472820\pi$
$912$	1.47542	+	6.45428i	0.0488559	+	0.213723i
$913$	−56.1872	−	20.4505i	−1.85952	−	0.676812i
$914$	−6.80161	−	38.5738i	−0.224977	−	1.27591i
$915$	−67.8314	−	51.3446i	−2.24244	−	1.69740i
$916$	−0.294865	+	1.67226i	−0.00974262	+	0.0552531i
$917$	−8.58747	+	7.85658i	−0.283583	+	0.259447i
$918$	0.109712	−	4.58360i	0.00362103	−	0.151281i
$919$	22.7788	−	39.4541i	0.751404	−	1.30147i	−0.195738	−	0.980656i	$-0.562710\pi$
$919$	22.7788	−	39.4541i	0.751404	−	1.30147i	0.947142	−	0.320814i	$-0.103957\pi$
$920$	17.2517	−	6.27909i	0.568770	−	0.207015i
$921$	3.04342	−	24.3518i	0.100284	−	0.802420i
$922$	8.62634	−	7.23836i	0.284093	−	0.238383i
$923$	34.3654	−	28.8360i	1.13115	−	0.949147i
$924$	−18.2779	−	12.6415i	−0.601300	−	0.415873i
$925$	20.9581	−	7.62814i	0.689099	−	0.250812i
$926$	16.5509	+	28.6670i	0.543896	+	0.942055i
$927$	38.4365	−	18.5417i	1.26242	−	0.608989i
$928$	−3.31649	+	5.74433i	−0.108869	+	0.188567i
$929$	14.1217	−	5.13989i	0.463319	−	0.168634i	−0.0998044	−	0.995007i	$-0.531822\pi$
$929$	14.1217	−	5.13989i	0.463319	−	0.168634i	0.563124	+	0.826373i	$0.309599\pi$
$930$	−23.4470	−	36.2765i	−0.768858	−	1.18955i
$931$	15.3131	+	21.9425i	0.501866	+	0.719138i
$932$	2.38194	+	13.5086i	0.0780229	+	0.442490i
$933$	37.4358	−	1.88088i	1.22559	−	0.0615772i
$934$	−0.0644652	+	0.365600i	−0.00210936	+	0.0119628i
$935$	8.82854	−	15.2915i	0.288724	−	0.500085i
$936$	0.755462	−	10.1721i	0.0246930	−	0.332486i
$937$	17.4175	−	30.1681i	0.569006	−	0.985548i	−0.427658	−	0.903940i	$-0.640661\pi$
$937$	17.4175	−	30.1681i	0.569006	−	0.985548i	0.996665	−	0.0816073i	$-0.0260053\pi$
$938$	−36.8195	+	1.57863i	−1.20220	+	0.0515440i
$939$	−14.8659	−	4.58009i	−0.485131	−	0.149466i
$940$	−4.30793	−	24.4315i	−0.140509	−	0.796867i
$941$	7.60921	+	43.1540i	0.248053	+	1.40678i	0.813294	+	0.581853i	$0.197672\pi$
$941$	7.60921	+	43.1540i	0.248053	+	1.40678i	−0.565241	+	0.824926i	$0.691217\pi$
$942$	−4.34420	+	34.7600i	−0.141542	+	1.13254i
$943$	−2.18345	−	1.83213i	−0.0711028	−	0.0596623i
$944$	−4.30429			−0.140093
$945$	−56.0422	−	8.79212i	−1.82305	−	0.286008i
$946$	7.29413			0.237153
$947$	27.1618	+	22.7914i	0.882639	+	0.740622i	0.966720	−	0.255837i	$-0.0823511\pi$
$947$	27.1618	+	22.7914i	0.882639	+	0.740622i	−0.0840813	+	0.996459i	$0.526796\pi$
$948$	−1.43509	+	0.605508i	−0.0466097	+	0.0196660i
$949$	−2.55363	−	14.4824i	−0.0828945	−	0.470118i
$950$	7.98291	+	45.2734i	0.259000	+	1.46886i
$951$	−31.6809	+	29.4153i	−1.02732	+	0.953856i
$952$	1.25279	+	1.96990i	0.0406033	+	0.0638449i
$953$	−13.2814	+	23.0041i	−0.430227	+	0.745176i	−0.996893	−	0.0787723i	$-0.974900\pi$
$953$	−13.2814	+	23.0041i	−0.430227	+	0.745176i	0.566665	+	0.823948i	$0.308233\pi$
$954$	−3.07180	+	0.309453i	−0.0994531	+	0.0100189i
$955$	37.7840	−	65.4438i	1.22266	−	2.11771i
$956$	−3.25543	+	18.4624i	−0.105288	+	0.597118i
$957$	−30.2438	−	46.7922i	−0.977643	−	1.51258i
$958$	−2.20111	−	12.4831i	−0.0711147	−	0.403311i
$959$	−37.0142	+	15.2978i	−1.19525	+	0.493990i
$960$	7.13801	−	0.358634i	0.230378	−	0.0115749i
$961$	−5.19283	+	1.89004i	−0.167511	+	0.0609689i
$962$	3.15267	−	5.46059i	0.101646	−	0.176056i
$963$	13.3072	+	3.37897i	0.428819	+	0.108886i
$964$	−6.90155	−	11.9538i	−0.222284	−	0.385007i
$965$	−67.4215	+	24.5394i	−2.17037	+	0.789951i
$966$	−16.7688	−	11.5977i	−0.539528	−	0.373151i
$967$	17.8608	−	14.9870i	0.574365	−	0.481949i	−0.308726	−	0.951151i	$-0.599903\pi$
$967$	17.8608	−	14.9870i	0.574365	−	0.481949i	0.883091	+	0.469202i	$0.155458\pi$
$968$	−9.58975	+	8.04675i	−0.308226	+	0.258632i
$969$	4.65799	+	3.52584i	0.149636	+	0.113266i
$970$	−45.4549	+	16.5442i	−1.45947	+	0.531203i
$971$	2.09917	−	3.63586i	0.0673655	−	0.116680i	−0.830375	−	0.557204i	$-0.811874\pi$
$971$	2.09917	−	3.63586i	0.0673655	−	0.116680i	0.897741	+	0.440524i	$0.145207\pi$
$972$	1.19089	+	15.5429i	0.0381978	+	0.498539i
$973$	−30.0446	−	9.49894i	−0.963185	−	0.304522i
$974$	−0.396821	+	2.25048i	−0.0127150	+	0.0721102i
$975$	8.78321	−	70.2786i	0.281288	−	2.25072i
$976$	−2.06698	−	11.7224i	−0.0661623	−	0.375225i
$977$	−0.847711	−	0.308542i	−0.0271207	−	0.00987112i	0.328424	−	0.944530i	$-0.393482\pi$
$977$	−0.847711	−	0.308542i	−0.0271207	−	0.00987112i	−0.355545	+	0.934659i	$0.615705\pi$
$978$	23.6776	+	7.29491i	0.757126	+	0.233265i
$979$	−39.3809	+	14.3335i	−1.25862	+	0.458100i
$980$	26.1972	−	12.1659i	0.836839	−	0.388627i
$981$	1.95453	−	2.00656i	0.0624034	−	0.0640647i
$982$	13.0907			0.417742
$983$	5.47726	−	31.0631i	0.174697	−	0.990758i	−0.763795	−	0.645459i	$-0.776666\pi$
$983$	5.47726	−	31.0631i	0.174697	−	0.990758i	0.938493	−	0.345299i	$-0.112223\pi$
$984$	−0.602323	−	0.931896i	−0.0192014	−	0.0297078i
$985$	60.3150	+	21.9529i	1.92180	+	0.699476i
$986$	1.01632	+	5.76382i	0.0323661	+	0.183557i
$987$	−19.3688	+	19.5941i	−0.616516	+	0.623688i
$988$	9.95604	+	8.35411i	0.316744	+	0.265780i
$989$	6.69190			0.212790
$990$	−24.6543	+	54.7370i	−0.783564	+	1.73965i
$991$	20.1596			0.640389			0.320195	−	0.947352i	$-0.396252\pi$
$991$	20.1596			0.640389			0.320195	+	0.947352i	$0.396252\pi$
$992$	1.04947	−	5.95187i	0.0333208	−	0.188972i
$993$	7.46442	−	6.93061i	0.236876	−	0.219936i
$994$	4.58363	−	34.6063i	0.145384	−	1.09764i
$995$	18.4490	+	6.71489i	0.584873	+	0.212876i
$996$	−17.0274	−	12.8888i	−0.539533	−	0.408397i
$997$	0.820235	−	0.298541i	0.0259771	−	0.00945489i	−0.328999	−	0.944330i	$-0.606711\pi$
$997$	0.820235	−	0.298541i	0.0259771	−	0.00945489i	0.354976	+	0.934875i	$0.384489\pi$
$998$	9.01571	+	15.6157i	0.285387	+	0.494305i
$999$	−3.51151	+	8.97360i	−0.111099	+	0.283912i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.v.a.79.3	yes	72
7.4	even	3		378.2.w.b.25.6	yes	72
27.13	even	9		378.2.w.b.121.6	yes	72
189.67	even	9	inner	378.2.v.a.67.3	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.v.a.67.3	✓	72	189.67	even	9	inner
378.2.v.a.79.3	yes	72	1.1	even	1	trivial
378.2.w.b.25.6	yes	72	7.4	even	3
378.2.w.b.121.6	yes	72	27.13	even	9

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.766044 - 0.642788i) q^{2} +(-1.38102 - 1.04536i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.716530 - 4.06364i) q^{5} +(0.385982 + 1.68850i) q^{6} +(2.64332 - 0.113332i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.814451 + 2.88733i) q^{9} +O(q^{10})\)	\(q+(-0.766044 - 0.642788i) q^{2} +(-1.38102 - 1.04536i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.716530 - 4.06364i) q^{5} +(0.385982 + 1.68850i) q^{6} +(2.64332 - 0.113332i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.814451 + 2.88733i) q^{9} +(-2.06317 + 3.57351i) q^{10} +(0.842123 - 4.77591i) q^{11} +(0.789665 - 1.54157i) q^{12} +(-0.590412 - 3.34839i) q^{13} +(-2.09775 - 1.61228i) q^{14} +(-3.25842 + 6.36102i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-0.441184 + 0.764153i) q^{17} +(1.23203 - 2.73534i) q^{18} +(1.91125 + 3.31039i) q^{19} +(3.87748 - 1.41129i) q^{20} +(-3.76896 - 2.60671i) q^{21} +(-3.71500 + 3.11726i) q^{22} +(-3.40828 + 2.85988i) q^{23} +(-1.59582 + 0.673322i) q^{24} +(-11.3013 + 4.11334i) q^{25} +(-1.70002 + 2.94453i) q^{26} +(1.89352 - 4.83886i) q^{27} +(0.570618 + 2.58348i) q^{28} +(-1.15181 + 6.53222i) q^{29} +(6.58488 - 2.77835i) q^{30} +(-1.04947 - 5.95187i) q^{31} +(0.939693 + 0.342020i) q^{32} +(-6.15553 + 5.71533i) q^{33} +(0.829154 - 0.301788i) q^{34} +(-2.35456 - 10.6603i) q^{35} +(-2.70204 + 1.30346i) q^{36} -1.85449 q^{37} +(0.663771 - 3.76443i) q^{38} +(-2.68490 + 5.24140i) q^{39} +(-3.87748 - 1.41129i) q^{40} +(0.111244 + 0.630898i) q^{41} +(1.21163 + 4.41950i) q^{42} +(-1.15219 - 0.966799i) q^{43} +4.84959 q^{44} +(11.1495 - 5.37849i) q^{45} +4.44919 q^{46} +(1.04401 - 5.92088i) q^{47} +(1.65527 + 0.509978i) q^{48} +(6.97431 - 0.599146i) q^{49} +(11.3013 + 4.11334i) q^{50} +(1.40810 - 0.594117i) q^{51} +(3.19500 - 1.16288i) q^{52} +(-0.514557 - 0.891239i) q^{53} +(-4.56088 + 2.48965i) q^{54} -20.0110 q^{55} +(1.22351 - 2.34585i) q^{56} +(0.821057 - 6.56966i) q^{57} +(5.08116 - 4.26360i) q^{58} +(4.04471 + 1.47215i) q^{59} +(-6.83020 - 2.10434i) q^{60} +(-2.06698 + 11.7224i) q^{61} +(-3.02184 + 5.23398i) q^{62} +(2.48008 + 7.53984i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-13.1836 + 4.79845i) q^{65} +(8.38916 - 0.421495i) q^{66} +(10.6704 - 8.95354i) q^{67} +(-0.829154 - 0.301788i) q^{68} +(7.69651 - 0.386694i) q^{69} +(-5.04862 + 9.67976i) q^{70} +(6.59709 + 11.4265i) q^{71} +(2.90773 + 0.738330i) q^{72} +4.32518 q^{73} +(1.42062 + 1.19204i) q^{74} +(19.9073 + 6.13331i) q^{75} +(-2.92821 + 2.45706i) q^{76} +(1.68474 - 12.7197i) q^{77} +(5.42586 - 2.28933i) q^{78} +(-0.688892 - 0.578049i) q^{79} +(2.06317 + 3.57351i) q^{80} +(-7.67334 + 4.70317i) q^{81} +(0.320315 - 0.554802i) q^{82} +(2.14100 - 12.1422i) q^{83} +(1.91263 - 4.16435i) q^{84} +(3.42137 + 1.24528i) q^{85} +(0.261179 + 1.48122i) q^{86} +(8.41918 - 7.81709i) q^{87} +(-3.71500 - 3.11726i) q^{88} +(-4.32081 - 7.48386i) q^{89} +(-11.9982 - 3.04659i) q^{90} +(-1.94013 - 8.78397i) q^{91} +(-3.40828 - 2.85988i) q^{92} +(-4.77249 + 9.31674i) q^{93} +(-4.60562 + 3.86458i) q^{94} +(12.0828 - 10.1386i) q^{95} +(-0.940204 - 1.45465i) q^{96} +(8.98017 + 7.53526i) q^{97} +(-5.72776 - 4.02403i) q^{98} +(14.4755 - 1.45826i) 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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