LMFDB - Embedded newform 378.2.w.a.25.7

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			25.7
Character	$\chi$	$=$	378.25
Dual form			378.2.w.a.121.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{2} +(-0.135903 + 1.72671i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-1.85969 - 0.676871i) q^{5} +(-0.462863 - 1.66906i) q^{6} +(2.63192 + 0.270209i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.96306 - 0.469329i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 0.342020i) q^{2} +(-0.135903 + 1.72671i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-1.85969 - 0.676871i) q^{5} +(-0.462863 - 1.66906i) q^{6} +(2.63192 + 0.270209i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.96306 - 0.469329i) q^{9} +1.97904 q^{10} +(-3.07817 + 1.12036i) q^{11} +(1.00580 + 1.41009i) q^{12} +(1.17085 + 6.64020i) q^{13} +(-2.56561 + 0.646255i) q^{14} +(1.42150 - 3.11915i) q^{15} +(0.173648 - 0.984808i) q^{16} -0.597167 q^{17} +(2.94489 - 0.572402i) q^{18} -8.31739 q^{19} +(-1.85969 + 0.676871i) q^{20} +(-0.824258 + 4.50784i) q^{21} +(2.50935 - 2.10559i) q^{22} +(0.0861936 + 0.488828i) q^{23} +(-1.42742 - 0.981051i) q^{24} +(-0.829942 - 0.696404i) q^{25} +(-3.37132 - 5.83929i) q^{26} +(1.21308 - 5.05257i) q^{27} +(2.18985 - 1.48477i) q^{28} +(0.221437 - 1.25583i) q^{29} +(-0.268956 + 3.41723i) q^{30} +(-1.15381 + 0.968161i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-1.51621 - 5.46738i) q^{33} +(0.561154 - 0.204243i) q^{34} +(-4.71164 - 2.28397i) q^{35} +(-2.57152 + 1.54509i) q^{36} +(0.271187 - 0.469709i) q^{37} +(7.81579 - 2.84471i) q^{38} +(-11.6248 + 1.11929i) q^{39} +(1.51603 - 1.27210i) q^{40} +(0.421633 + 2.39120i) q^{41} +(-0.767222 - 4.51789i) q^{42} +(-2.94820 - 2.47384i) q^{43} +(-1.63786 + 2.83686i) q^{44} +(5.19269 + 2.87841i) q^{45} +(-0.248185 - 0.429868i) q^{46} +(-0.695651 - 0.583721i) q^{47} +(1.67688 + 0.433678i) q^{48} +(6.85397 + 1.42234i) q^{49} +(1.01807 + 0.370549i) q^{50} +(0.0811566 - 1.03114i) q^{51} +(5.16515 + 4.33408i) q^{52} +(-5.09597 + 8.82648i) q^{53} +(0.588155 + 5.16276i) q^{54} +6.48278 q^{55} +(-1.54997 + 2.14420i) q^{56} +(1.13035 - 14.3617i) q^{57} +(0.221437 + 1.25583i) q^{58} +(2.33822 + 13.2607i) q^{59} +(-0.916024 - 3.30313i) q^{60} +(5.62961 + 4.72380i) q^{61} +(0.753095 - 1.30440i) q^{62} +(-7.67171 - 2.03588i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(2.31715 - 13.1412i) q^{65} +(3.29473 + 4.61908i) q^{66} +(2.56229 + 0.932596i) q^{67} +(-0.457457 + 0.383852i) q^{68} +(-0.855779 + 0.0823984i) q^{69} +(5.20866 + 0.534754i) q^{70} +(-1.32437 - 2.29388i) q^{71} +(1.88798 - 2.33142i) q^{72} +(0.675897 + 1.17069i) q^{73} +(-0.0941822 + 0.534134i) q^{74} +(1.31528 - 1.33843i) q^{75} +(-6.37149 + 5.34631i) q^{76} +(-8.40423 + 2.11695i) q^{77} +(10.5409 - 5.02771i) q^{78} +(-6.67713 + 2.43028i) q^{79} +(-0.989519 + 1.71390i) q^{80} +(8.55946 + 2.78130i) q^{81} +(-1.21404 - 2.10278i) q^{82} +(-1.31290 + 7.44583i) q^{83} +(2.26616 + 3.98303i) q^{84} +(1.11054 + 0.404205i) q^{85} +(3.61651 + 1.31630i) q^{86} +(2.13836 + 0.553028i) q^{87} +(0.568823 - 3.22596i) q^{88} +17.2637 q^{89} +(-5.86401 - 0.928819i) q^{90} +(1.28733 + 17.7928i) q^{91} +(0.380241 + 0.319060i) q^{92} +(-1.51493 - 2.12387i) q^{93} +(0.853342 + 0.310591i) q^{94} +(15.4677 + 5.62979i) q^{95} +(-1.72408 + 0.166002i) q^{96} +(-6.38539 - 5.35798i) q^{97} +(-6.92710 + 1.00764i) q^{98} +(9.64663 - 1.87503i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} - 3 q^{7} - 36 q^{8} - 12 q^{9}+O(q^{10}) $ 72 * q + 3 * q^6 - 3 * q^7 - 36 * q^8 - 12 * q^9	$ 72 q + 3 q^{6} - 3 q^{7} - 36 q^{8} - 12 q^{9} + 12 q^{10} - 6 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} + 24 q^{17} + 36 q^{19} - 12 q^{21} - 6 q^{22} + 12 q^{23} - 30 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} + 9 q^{35} + 9 q^{36} + 3 q^{39} - 6 q^{41} + 3 q^{42} + 24 q^{43} - 30 q^{45} - 9 q^{47} - 6 q^{48} + 51 q^{49} + 6 q^{50} + 12 q^{51} + 6 q^{52} - 15 q^{53} - 27 q^{54} + 72 q^{55} + 6 q^{56} - 63 q^{57} + 3 q^{58} + 15 q^{59} - 3 q^{60} - 18 q^{61} - 24 q^{62} - 48 q^{63} - 36 q^{64} - 18 q^{65} - 36 q^{66} + 66 q^{67} - 18 q^{68} - 21 q^{69} - 6 q^{70} + 12 q^{71} - 12 q^{72} - 66 q^{73} + 9 q^{74} + 15 q^{75} - 15 q^{77} + 30 q^{78} + 9 q^{79} - 6 q^{80} - 33 q^{82} - 18 q^{83} - 12 q^{84} + 21 q^{85} - 12 q^{86} - 48 q^{87} + 12 q^{88} + 72 q^{89} + 69 q^{90} + 12 q^{91} + 30 q^{92} + 60 q^{93} - 36 q^{94} + 93 q^{95} - 48 q^{97} + 6 q^{98} - 54 q^{99}+O(q^{100}) $ 72 * q + 3 * q^6 - 3 * q^7 - 36 * q^8 - 12 * q^9 + 12 * q^10 - 6 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^15 + 24 * q^17 + 36 * q^19 - 12 * q^21 - 6 * q^22 + 12 * q^23 - 30 * q^25 - 18 * q^26 - 6 * q^27 + 3 * q^29 + 3 * q^30 + 9 * q^31 - 18 * q^33 + 9 * q^34 + 9 * q^35 + 9 * q^36 + 3 * q^39 - 6 * q^41 + 3 * q^42 + 24 * q^43 - 30 * q^45 - 9 * q^47 - 6 * q^48 + 51 * q^49 + 6 * q^50 + 12 * q^51 + 6 * q^52 - 15 * q^53 - 27 * q^54 + 72 * q^55 + 6 * q^56 - 63 * q^57 + 3 * q^58 + 15 * q^59 - 3 * q^60 - 18 * q^61 - 24 * q^62 - 48 * q^63 - 36 * q^64 - 18 * q^65 - 36 * q^66 + 66 * q^67 - 18 * q^68 - 21 * q^69 - 6 * q^70 + 12 * q^71 - 12 * q^72 - 66 * q^73 + 9 * q^74 + 15 * q^75 - 15 * q^77 + 30 * q^78 + 9 * q^79 - 6 * q^80 - 33 * q^82 - 18 * q^83 - 12 * q^84 + 21 * q^85 - 12 * q^86 - 48 * q^87 + 12 * q^88 + 72 * q^89 + 69 * q^90 + 12 * q^91 + 30 * q^92 + 60 * q^93 - 36 * q^94 + 93 * q^95 - 48 * q^97 + 6 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$3$	−0.135903	+	1.72671i	−0.0784634	+	0.996917i
$3$	−0.135903	+	1.72671i	−0.0784634	+	0.996917i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−1.85969	−	0.676871i	−0.831677	−	0.302706i	−0.109130	−	0.994027i	$-0.534807\pi$
$5$	−1.85969	−	0.676871i	−0.831677	−	0.302706i	−0.722547	+	0.691322i	$0.757029\pi$
$6$	−0.462863	−	1.66906i	−0.188963	−	0.681390i
$7$	2.63192	+	0.270209i	0.994771	+	0.102130i
$7$	2.63192	+	0.270209i	0.994771	+	0.102130i
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−2.96306	−	0.469329i	−0.987687	−	0.156443i
$10$	1.97904			0.625827
$11$	−3.07817	+	1.12036i	−0.928104	+	0.337802i	−0.761458	−	0.648214i	$-0.775516\pi$
$11$	−3.07817	+	1.12036i	−0.928104	+	0.337802i	−0.166646	+	0.986017i	$0.553294\pi$
$12$	1.00580	+	1.41009i	0.290350	+	0.407059i
$13$	1.17085	+	6.64020i	0.324734	+	1.84166i	0.511537	+	0.859261i	$0.329076\pi$
$13$	1.17085	+	6.64020i	0.324734	+	1.84166i	−0.186803	+	0.982397i	$0.559813\pi$
$14$	−2.56561	+	0.646255i	−0.685688	+	0.172719i
$15$	1.42150	−	3.11915i	0.367029	−	0.805362i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−0.597167			−0.144834			−0.0724172	−	0.997374i	$-0.523071\pi$
$17$	−0.597167			−0.144834			−0.0724172	+	0.997374i	$0.523071\pi$
$18$	2.94489	−	0.572402i	0.694116	−	0.134916i
$19$	−8.31739			−1.90814			−0.954070	−	0.299585i	$-0.903152\pi$
$19$	−8.31739			−1.90814			−0.954070	+	0.299585i	$0.903152\pi$
$20$	−1.85969	+	0.676871i	−0.415839	+	0.151353i
$21$	−0.824258	+	4.50784i	−0.179868	+	0.983691i
$22$	2.50935	−	2.10559i	0.534995	−	0.448914i
$23$	0.0861936	+	0.488828i	0.0179726	+	0.101928i	0.992474	−	0.122452i	$-0.0390756\pi$
$23$	0.0861936	+	0.488828i	0.0179726	+	0.101928i	−0.974502	+	0.224379i	$0.927965\pi$
$24$	−1.42742	−	0.981051i	−0.291372	−	0.200256i
$25$	−0.829942	−	0.696404i	−0.165988	−	0.139281i
$26$	−3.37132	−	5.83929i	−0.661169	−	1.14518i
$27$	1.21308	−	5.05257i	0.233458	−	0.972367i
$28$	2.18985	−	1.48477i	0.413843	−	0.280595i
$29$	0.221437	−	1.25583i	0.0411198	−	0.233202i	−0.957321	−	0.289028i	$-0.906668\pi$
$29$	0.221437	−	1.25583i	0.0411198	−	0.233202i	0.998441	+	0.0558258i	$0.0177792\pi$
$30$	−0.268956	+	3.41723i	−0.0491045	+	0.623897i
$31$	−1.15381	+	0.968161i	−0.207230	+	0.173887i	−0.740496	−	0.672061i	$-0.765409\pi$
$31$	−1.15381	+	0.968161i	−0.207230	+	0.173887i	0.533265	+	0.845948i	$0.320965\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	−1.51621	−	5.46738i	−0.263939	−	0.951748i
$34$	0.561154	−	0.204243i	0.0962371	−	0.0350274i
$35$	−4.71164	−	2.28397i	−0.796413	−	0.386062i
$36$	−2.57152	+	1.54509i	−0.428586	+	0.257515i
$37$	0.271187	−	0.469709i	0.0445828	−	0.0772198i	−0.842873	−	0.538113i	$-0.819137\pi$
$37$	0.271187	−	0.469709i	0.0445828	−	0.0772198i	0.887456	+	0.460893i	$0.152471\pi$
$38$	7.81579	−	2.84471i	1.26789	−	0.461473i
$39$	−11.6248	+	1.11929i	−1.86146	+	0.179230i
$40$	1.51603	−	1.27210i	0.239705	−	0.201137i
$41$	0.421633	+	2.39120i	0.0658480	+	0.373442i	0.999868	+	0.0162228i	$0.00516412\pi$
$41$	0.421633	+	2.39120i	0.0658480	+	0.373442i	−0.934020	+	0.357220i	$0.883725\pi$
$42$	−0.767222	−	4.51789i	−0.118385	−	0.697126i
$43$	−2.94820	−	2.47384i	−0.449597	−	0.377256i	0.389689	−	0.920946i	$-0.372582\pi$
$43$	−2.94820	−	2.47384i	−0.449597	−	0.377256i	−0.839286	+	0.543690i	$0.817027\pi$
$44$	−1.63786	+	2.83686i	−0.246917	+	0.427673i
$45$	5.19269	+	2.87841i	0.774081	+	0.429089i
$46$	−0.248185	−	0.429868i	−0.0365928	−	0.0633806i
$47$	−0.695651	−	0.583721i	−0.101471	−	0.0851444i	0.590641	−	0.806935i	$-0.298875\pi$
$47$	−0.695651	−	0.583721i	−0.101471	−	0.0851444i	−0.692112	+	0.721790i	$0.743320\pi$
$48$	1.67688	+	0.433678i	0.242037	+	0.0625960i
$49$	6.85397	+	1.42234i	0.979139	+	0.203191i
$50$	1.01807	+	0.370549i	0.143977	+	0.0524035i
$51$	0.0811566	−	1.03114i	0.0113642	−	0.144388i
$52$	5.16515	+	4.33408i	0.716278	+	0.601029i
$53$	−5.09597	+	8.82648i	−0.699985	+	1.21241i	0.268486	+	0.963284i	$0.413477\pi$
$53$	−5.09597	+	8.82648i	−0.699985	+	1.21241i	−0.968471	+	0.249127i	$0.919856\pi$
$54$	0.588155	+	5.16276i	0.0800377	+	0.702562i
$55$	6.48278			0.874138
$56$	−1.54997	+	2.14420i	−0.207123	+	0.286531i
$57$	1.13035	−	14.3617i	0.149719	−	1.90226i
$58$	0.221437	+	1.25583i	0.0290761	+	0.164899i
$59$	2.33822	+	13.2607i	0.304410	+	1.72639i	0.626269	+	0.779607i	$0.284581\pi$
$59$	2.33822	+	13.2607i	0.304410	+	1.72639i	−0.321859	+	0.946787i	$0.604308\pi$
$60$	−0.916024	−	3.30313i	−0.118258	−	0.426432i
$61$	5.62961	+	4.72380i	0.720797	+	0.604821i	0.927606	−	0.373561i	$-0.121863\pi$
$61$	5.62961	+	4.72380i	0.720797	+	0.604821i	−0.206808	+	0.978381i	$0.566308\pi$
$62$	0.753095	−	1.30440i	0.0956432	−	0.165659i
$63$	−7.67171	−	2.03588i	−0.966545	−	0.256497i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	2.31715	−	13.1412i	0.287407	−	1.62996i
$66$	3.29473	+	4.61908i	0.405553	+	0.568569i
$67$	2.56229	+	0.932596i	0.313033	+	0.113935i	0.493759	−	0.869599i	$-0.335622\pi$
$67$	2.56229	+	0.932596i	0.313033	+	0.113935i	−0.180726	+	0.983533i	$0.557845\pi$
$68$	−0.457457	+	0.383852i	−0.0554748	+	0.0465489i
$69$	−0.855779	+	0.0823984i	−0.103024	+	0.00991961i
$70$	5.20866	+	0.534754i	0.622554	+	0.0639154i
$71$	−1.32437	−	2.29388i	−0.157174	−	0.272233i	0.776675	−	0.629902i	$-0.216905\pi$
$71$	−1.32437	−	2.29388i	−0.157174	−	0.272233i	−0.933848	+	0.357669i	$0.883572\pi$
$72$	1.88798	−	2.33142i	0.222501	−	0.274761i
$73$	0.675897	+	1.17069i	0.0791078	+	0.137019i	0.902865	−	0.429924i	$-0.141460\pi$
$73$	0.675897	+	1.17069i	0.0791078	+	0.137019i	−0.823757	+	0.566942i	$0.808126\pi$
$74$	−0.0941822	+	0.534134i	−0.0109485	+	0.0620918i
$75$	1.31528	−	1.33843i	0.151875	−	0.154548i
$76$	−6.37149	+	5.34631i	−0.730860	+	0.613264i
$77$	−8.40423	+	2.11695i	−0.957751	+	0.241249i
$78$	10.5409	−	5.02771i	1.19353	−	0.569276i
$79$	−6.67713	+	2.43028i	−0.751236	+	0.273428i	−0.689126	−	0.724642i	$-0.742005\pi$
$79$	−6.67713	+	2.43028i	−0.751236	+	0.273428i	−0.0621102	+	0.998069i	$0.519783\pi$
$80$	−0.989519	+	1.71390i	−0.110632	+	0.191619i
$81$	8.55946	+	2.78130i	0.951051	+	0.309033i
$82$	−1.21404	−	2.10278i	−0.134069	−	0.232214i
$83$	−1.31290	+	7.44583i	−0.144110	+	0.817286i	0.823968	+	0.566636i	$0.191755\pi$
$83$	−1.31290	+	7.44583i	−0.144110	+	0.817286i	−0.968078	+	0.250650i	$0.919356\pi$
$84$	2.26616	+	3.98303i	0.247259	+	0.434584i
$85$	1.11054	+	0.404205i	0.120455	+	0.0438422i
$86$	3.61651	+	1.31630i	0.389978	+	0.141940i
$87$	2.13836	+	0.553028i	0.229256	+	0.0592908i
$88$	0.568823	−	3.22596i	0.0606368	−	0.343888i
$89$	17.2637			1.82995			0.914973	−	0.403516i	$-0.132212\pi$
$89$	17.2637			1.82995			0.914973	+	0.403516i	$0.132212\pi$
$90$	−5.86401	−	0.928819i	−0.618121	−	0.0979061i
$91$	1.28733	+	17.7928i	0.134948	+	1.86519i
$92$	0.380241	+	0.319060i	0.0396428	+	0.0332643i
$93$	−1.51493	−	2.12387i	−0.157091	−	0.220235i
$94$	0.853342	+	0.310591i	0.0880155	+	0.0320350i
$95$	15.4677	+	5.62979i	1.58696	+	0.577605i
$96$	−1.72408	+	0.166002i	−0.175963	+	0.0169425i
$97$	−6.38539	−	5.35798i	−0.648338	−	0.544020i	0.258228	−	0.966084i	$-0.416861\pi$
$97$	−6.38539	−	5.35798i	−0.648338	−	0.544020i	−0.906566	+	0.422064i	$0.861306\pi$
$98$	−6.92710	+	1.00764i	−0.699742	+	0.101787i
$99$	9.64663	−	1.87503i	0.969523	−	0.188448i
$100$	−1.08341			−0.108341
$101$	2.93994	−	16.6733i	0.292535	−	1.65905i	−0.384518	−	0.923117i	$-0.625632\pi$
$101$	2.93994	−	16.6733i	0.292535	−	1.65905i	0.677054	−	0.735934i	$-0.263256\pi$
$102$	0.276407	+	0.996708i	0.0273684	+	0.0986888i
$103$	14.8663	+	5.41089i	1.46482	+	0.533151i	0.946688	−	0.322151i	$-0.104406\pi$
$103$	14.8663	+	5.41089i	1.46482	+	0.533151i	0.518131	+	0.855301i	$0.326628\pi$
$104$	−6.33600	−	2.30612i	−0.621296	−	0.226133i
$105$	4.58408	−	7.82525i	0.447361	−	0.763666i
$106$	1.76981	−	10.0371i	0.171899	−	0.974890i
$107$	1.44677	+	2.50589i	0.139865	+	0.242253i	0.927445	−	0.373959i	$-0.122000\pi$
$107$	1.44677	+	2.50589i	0.139865	+	0.242253i	−0.787580	+	0.616212i	$0.788667\pi$
$108$	−2.31845	−	4.65025i	−0.223093	−	0.447470i
$109$	9.97350	−	17.2746i	0.955288	−	1.65461i	0.221580	−	0.975142i	$-0.428878\pi$
$109$	9.97350	−	17.2746i	0.955288	−	1.65461i	0.733708	−	0.679465i	$-0.237788\pi$
$110$	−6.09182	+	2.21724i	−0.580832	+	0.211406i
$111$	0.774197	+	0.532096i	0.0734836	+	0.0505043i
$112$	0.723132	−	2.54501i	0.0683295	−	0.240481i
$113$	5.52639	−	4.63719i	0.519879	−	0.436230i	−0.344710	−	0.938709i	$-0.612023\pi$
$113$	5.52639	−	4.63719i	0.519879	−	0.436230i	0.864590	+	0.502479i	$0.167578\pi$
$114$	3.84981	+	13.8822i	0.360568	+	1.30019i
$115$	0.170580	−	0.967409i	0.0159067	−	0.0902114i
$116$	−0.637602	−	1.10436i	−0.0591998	−	0.102537i
$117$	−0.352852	−	20.2248i	−0.0326212	−	1.86978i
$118$	−6.73263	−	11.6613i	−0.619789	−	1.07351i
$119$	−1.57170	−	0.161360i	−0.144077	−	0.0147919i
$120$	1.99052	+	2.79063i	0.181709	+	0.254748i
$121$	−0.206552	+	0.173318i	−0.0187774	+	0.0157561i
$122$	−6.90574	−	2.51348i	−0.625216	−	0.227560i
$123$	−4.18621	+	0.403068i	−0.377458	+	0.0363434i
$124$	−0.261547	+	1.48331i	−0.0234876	+	0.133205i
$125$	6.01965	+	10.4263i	0.538414	+	0.932560i
$126$	7.90536	−	0.710778i	0.704266	−	0.0633211i
$127$	4.51749	−	7.82452i	0.400862	−	0.694314i	−0.592968	−	0.805226i	$-0.702044\pi$
$127$	4.51749	−	7.82452i	0.400862	−	0.694314i	0.993830	+	0.110912i	$0.0353772\pi$
$128$	0.766044	+	0.642788i	0.0677094	+	0.0568149i
$129$	4.67227	−	4.75449i	0.411370	−	0.418610i
$130$	2.31715	+	13.1412i	0.203227	+	1.15256i
$131$	2.41480	+	13.6950i	0.210982	+	1.19654i	0.887744	+	0.460338i	$0.152272\pi$
$131$	2.41480	+	13.6950i	0.210982	+	1.19654i	−0.676762	+	0.736202i	$0.736617\pi$
$132$	−4.67585	−	3.21365i	−0.406980	−	0.279712i
$133$	−21.8907	−	2.24744i	−1.89816	−	0.194877i
$134$	−2.72673			−0.235553
$135$	−5.67589	+	8.57509i	−0.488503	+	0.738026i
$136$	0.298584	−	0.517162i	0.0256033	−	0.0443463i
$137$	8.57451	+	7.19487i	0.732570	+	0.614699i	0.930831	−	0.365450i	$-0.119085\pi$
$137$	8.57451	+	7.19487i	0.732570	+	0.614699i	−0.198261	+	0.980149i	$0.563529\pi$
$138$	0.775987	−	0.370123i	0.0660564	−	0.0315069i
$139$	4.89594	+	1.78198i	0.415268	+	0.151145i	0.541200	−	0.840894i	$-0.317970\pi$
$139$	4.89594	+	1.78198i	0.415268	+	0.151145i	−0.125932	+	0.992039i	$0.540192\pi$
$140$	−5.07744	+	1.27896i	−0.429122	+	0.108092i
$141$	1.10246	−	1.12186i	0.0928437	−	0.0944776i
$142$	2.02905	+	1.70258i	0.170274	+	0.142877i
$143$	−11.0435	−	19.1279i	−0.923504	−	1.59956i
$144$	−0.976729	+	2.83655i	−0.0813941	+	0.236379i
$145$	−1.26184	+	2.18557i	−0.104790	+	0.181501i
$146$	−1.03553	−	0.868917i	−0.0857015	−	0.0719121i
$147$	−3.38744	+	11.6415i	−0.279391	+	0.960177i
$148$	−0.0941822	−	0.534134i	−0.00774173	−	0.0439055i
$149$	−8.85276	+	7.42835i	−0.725247	+	0.608554i	−0.928831	−	0.370503i	$-0.879185\pi$
$149$	−8.85276	+	7.42835i	−0.725247	+	0.608554i	0.203585	+	0.979057i	$0.434741\pi$
$150$	−0.778189	+	1.70756i	−0.0635389	+	0.139422i
$151$	−15.4977	+	5.64068i	−1.26118	+	0.459032i	−0.884165	−	0.467175i	$-0.845272\pi$
$151$	−15.4977	+	5.64068i	−1.26118	+	0.459032i	−0.377016	+	0.926207i	$0.623050\pi$
$152$	4.15869	−	7.20307i	0.337315	−	0.584246i
$153$	1.76944	+	0.280268i	0.143051	+	0.0226583i
$154$	7.17335	−	4.86370i	0.578045	−	0.391928i
$155$	2.80104	−	1.01950i	0.224985	−	0.0818879i
$156$	−8.18566	+	8.32972i	−0.655377	+	0.666911i
$157$	2.41219	+	13.6802i	0.192514	+	1.09180i	0.915915	+	0.401371i	$0.131466\pi$
$157$	2.41219	+	13.6802i	0.192514	+	1.09180i	−0.723402	+	0.690427i	$0.757423\pi$
$158$	5.44325	−	4.56743i	0.433041	−	0.363365i
$159$	−14.5482	−	9.99881i	−1.15375	−	0.792957i
$160$	0.343656	−	1.94897i	0.0271684	−	0.154080i
$161$	0.0947684	+	1.30985i	0.00746880	+	0.103230i
$162$	−8.99452	+	0.313941i	−0.706676	+	0.0246655i
$163$	−6.51673	−	11.2873i	−0.510430	−	0.884091i	−0.999927	−	0.0120856i	$-0.996153\pi$
$163$	−6.51673	−	11.2873i	−0.510430	−	0.884091i	0.489497	−	0.872005i	$-0.337180\pi$
$164$	1.86002	+	1.56074i	0.145243	+	0.121874i
$165$	−0.881026	+	11.1939i	−0.0685878	+	0.871443i
$166$	−1.31290	−	7.44583i	−0.101901	−	0.577908i
$167$	−17.4447	+	14.6378i	−1.34991	+	1.13271i	−0.370952	+	0.928652i	$0.620968\pi$
$167$	−17.4447	+	14.6378i	−1.34991	+	1.13271i	−0.978959	+	0.204057i	$0.934587\pi$
$168$	−3.49177	−	2.96775i	−0.269396	−	0.228967i
$169$	−30.5053	+	11.1030i	−2.34656	+	0.854079i
$170$	−1.18182			−0.0906412
$171$	24.6449	+	3.90359i	1.88464	+	0.298515i
$172$	−3.84861			−0.293453
$173$	2.45131	−	13.9021i	0.186369	−	1.05695i	−0.737814	−	0.675004i	$-0.764142\pi$
$173$	2.45131	−	13.9021i	0.186369	−	1.05695i	0.924183	−	0.381949i	$-0.124747\pi$
$174$	−2.19855	+	0.211687i	−0.166672	+	0.0160479i
$175$	−1.99616	−	2.05713i	−0.150896	−	0.155505i
$176$	0.568823	+	3.22596i	0.0428767	+	0.243166i
$177$	−23.2151	+	2.23526i	−1.74496	+	0.168013i
$178$	−16.2225	+	5.90452i	−1.21593	+	0.442563i
$179$	0.0160591			0.00120032			0.000600158	−	1.00000i	$-0.499809\pi$
$179$	0.0160591			0.00120032			0.000600158		1.00000i	$0.499809\pi$
$180$	5.82804	−	1.13280i	0.434396	−	0.0844342i
$181$	−1.97514	+	3.42105i	−0.146811	+	0.254285i	−0.930047	−	0.367440i	$-0.880234\pi$
$181$	−1.97514	+	3.42105i	−0.146811	+	0.254285i	0.783236	+	0.621725i	$0.213568\pi$
$182$	−7.29519	−	16.2795i	−0.540756	−	1.20672i
$183$	−8.92172	+	9.07873i	−0.659512	+	0.671119i
$184$	−0.466434	−	0.169768i	−0.0343860	−	0.0125155i
$185$	−0.822255	+	0.689954i	−0.0604534	+	0.0507264i
$186$	2.14997	+	1.47765i	0.157644	+	0.108346i
$187$	1.83818	−	0.669045i	0.134421	−	0.0489254i
$188$	−0.908108			−0.0662306
$189$	4.55798	−	12.9701i	0.331545	−	0.943440i
$190$	−16.4604			−1.19416
$191$	16.8024	−	6.11556i	1.21578	−	0.442506i	0.347073	−	0.937838i	$-0.387176\pi$
$191$	16.8024	−	6.11556i	1.21578	−	0.442506i	0.868704	+	0.495332i	$0.164954\pi$
$192$	1.56333	−	0.745660i	0.112823	−	0.0538134i
$193$	1.22644	−	1.02911i	0.0882812	−	0.0740767i	−0.597579	−	0.801810i	$-0.703871\pi$
$193$	1.22644	−	1.02911i	0.0882812	−	0.0740767i	0.685860	+	0.727733i	$0.259426\pi$
$194$	7.83284	+	2.85092i	0.562365	+	0.204684i
$195$	22.3761	+	5.78696i	1.60239	+	0.414413i
$196$	6.16471	−	3.31608i	0.440336	−	0.236863i
$197$	9.50079	−	16.4558i	0.676903	−	1.17243i	−0.299006	−	0.954251i	$-0.596655\pi$
$197$	9.50079	−	16.4558i	0.676903	−	1.17243i	0.975909	−	0.218179i	$-0.0700118\pi$
$198$	−8.42357	+	5.06130i	−0.598637	+	0.359691i
$199$	−8.32437			−0.590099			−0.295050	−	0.955482i	$-0.595336\pi$
$199$	−8.32437			−0.590099			−0.295050	+	0.955482i	$0.595336\pi$
$200$	1.01807	−	0.370549i	0.0719887	−	0.0262017i
$201$	−1.95854	+	4.29758i	−0.138145	+	0.303128i
$202$	2.93994	+	16.6733i	0.206854	+	1.17313i
$203$	0.922140	−	3.24541i	0.0647216	−	0.227783i
$204$	−0.600632	−	0.842062i	−0.0420526	−	0.0589561i
$205$	0.834427	−	4.73227i	0.0582789	−	0.330516i
$206$	−15.8204			−1.10226
$207$	−0.0259757	−	1.48888i	−0.00180544	−	0.103484i
$208$	6.74263			0.467517
$209$	25.6024	−	9.31849i	1.77095	−	0.644574i
$210$	−1.63124	+	8.92118i	−0.112566	+	0.615620i
$211$	3.59633	−	3.01768i	0.247581	−	0.207745i	−0.510549	−	0.859849i	$-0.670558\pi$
$211$	3.59633	−	3.01768i	0.247581	−	0.207745i	0.758130	+	0.652103i	$0.226113\pi$
$212$	1.76981	+	10.0371i	0.121551	+	0.689351i
$213$	4.14085	−	1.97506i	0.283726	−	0.135329i
$214$	−2.21659	−	1.85994i	−0.151523	−	0.127143i
$215$	3.80827	+	6.59611i	0.259722	+	0.449851i
$216$	3.76911	+	3.57684i	0.256455	+	0.243373i
$217$	−3.29834	+	2.23635i	−0.223906	+	0.151813i
$218$	−3.46376	+	19.6440i	−0.234595	+	1.33046i
$219$	−2.11330	+	1.00798i	−0.142803	+	0.0681130i
$220$	4.96610	−	4.16705i	0.334814	−	0.280942i
$221$	−0.699191	−	3.96531i	−0.0470327	−	0.266736i
$222$	−0.909495	−	0.235216i	−0.0610413	−	0.0157866i
$223$	1.46317	−	0.532550i	0.0979810	−	0.0356622i	−0.292565	−	0.956246i	$-0.594509\pi$
$223$	1.46317	−	0.532550i	0.0979810	−	0.0356622i	0.390546	+	0.920584i	$0.372286\pi$
$224$	0.190923	+	2.63885i	0.0127566	+	0.176316i
$225$	2.13233	+	2.45300i	0.142155	+	0.163533i
$226$	−3.60710	+	6.24767i	−0.239940	+	0.415589i
$227$	−4.21133	+	1.53280i	−0.279516	+	0.101735i	−0.477974	−	0.878374i	$-0.658629\pi$
$227$	−4.21133	+	1.53280i	−0.279516	+	0.101735i	0.198458	+	0.980109i	$0.436407\pi$
$228$	−8.36563	−	11.7283i	−0.554028	−	0.776725i
$229$	−14.1068	+	11.8370i	−0.932203	+	0.782212i	−0.976212	−	0.216820i	$-0.930432\pi$
$229$	−14.1068	+	11.8370i	−0.932203	+	0.782212i	0.0440083	+	0.999031i	$0.485987\pi$
$230$	0.170580	+	0.967409i	0.0112477	+	0.0637891i
$231$	−2.51321	−	14.7994i	−0.165357	−	0.973727i
$232$	0.976863	+	0.819685i	0.0641342	+	0.0538150i
$233$	−5.20659	+	9.01807i	−0.341095	+	0.590794i	−0.984636	−	0.174618i	$-0.944131\pi$
$233$	−5.20659	+	9.01807i	−0.341095	+	0.590794i	0.643541	+	0.765411i	$0.277464\pi$
$234$	7.24887	+	18.8844i	0.473873	+	1.23451i
$235$	0.898590	+	1.55640i	0.0586175	+	0.101529i
$236$	10.3150	+	8.65530i	0.671448	+	0.563412i
$237$	−3.28895	−	11.8598i	−0.213640	−	0.770374i
$238$	1.53210	−	0.385922i	0.0993112	−	0.0250156i
$239$	−9.03426	−	3.28820i	−0.584378	−	0.212696i	0.0328769	−	0.999459i	$-0.489533\pi$
$239$	−9.03426	−	3.28820i	−0.584378	−	0.212696i	−0.617255	+	0.786763i	$0.711755\pi$
$240$	−2.82493	−	1.94154i	−0.182348	−	0.125326i
$241$	21.8749	+	18.3552i	1.40909	+	1.18236i	0.956891	+	0.290446i	$0.0938037\pi$
$241$	21.8749	+	18.3552i	1.40909	+	1.18236i	0.452196	+	0.891919i	$0.350641\pi$
$242$	0.134817	−	0.233510i	0.00866637	−	0.0150106i
$243$	−5.96575	+	14.4017i	−0.382703	+	0.923871i
$244$	7.34893			0.470467
$245$	−11.7835	−	7.28435i	−0.752821	−	0.465380i
$246$	3.79589	−	1.81053i	0.242017	−	0.115435i
$247$	−9.73837	−	55.2291i	−0.619638	−	3.51414i
$248$	−0.261547	−	1.48331i	−0.0166083	−	0.0941902i
$249$	−12.6784	−	3.27891i	−0.803459	−	0.207792i
$250$	−9.22264	−	7.73871i	−0.583291	−	0.489439i
$251$	−3.73667	+	6.47211i	−0.235857	+	0.408516i	−0.959521	−	0.281636i	$-0.909123\pi$
$251$	−3.73667	+	6.47211i	−0.235857	+	0.408516i	0.723665	+	0.690152i	$0.242456\pi$
$252$	−7.18551	+	3.37171i	−0.452645	+	0.212398i
$253$	−0.812984	−	1.40813i	−0.0511119	−	0.0885284i
$254$	−1.56891	+	8.89772i	−0.0984420	+	0.558293i
$255$	−0.848871	+	1.86266i	−0.0531584	+	0.116644i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	21.3551	−	17.9191i	1.33209	−	1.11776i	0.348512	−	0.937304i	$-0.386687\pi$
$257$	21.3551	−	17.9191i	1.33209	−	1.11776i	0.983583	−	0.180456i	$-0.0577573\pi$
$258$	−2.76436	+	6.06577i	−0.172102	+	0.377638i
$259$	0.840661	−	1.16296i	0.0522361	−	0.0722628i
$260$	−6.67196	−	11.5562i	−0.413777	−	0.716683i
$261$	−1.24553	+	3.61718i	−0.0770963	+	0.223898i
$262$	−6.95315	−	12.0432i	−0.429567	−	0.744032i
$263$	2.12582	−	12.0561i	0.131084	−	0.743414i	−0.846423	−	0.532511i	$-0.821249\pi$
$263$	2.12582	−	12.0561i	0.131084	−	0.743414i	0.977507	−	0.210903i	$-0.0676404\pi$
$264$	5.49299	+	1.42061i	0.338070	+	0.0874325i
$265$	15.4513	−	12.9652i	0.949165	−	0.796444i
$266$	21.3392	−	5.37515i	1.30839	−	0.329572i
$267$	−2.34618	+	29.8094i	−0.143584	+	1.82430i
$268$	2.56229	−	0.932596i	0.156516	−	0.0569673i
$269$	11.6402	−	20.1614i	0.709713	−	1.22926i	−0.255250	−	0.966875i	$-0.582158\pi$
$269$	11.6402	−	20.1614i	0.709713	−	1.22926i	0.964963	−	0.262384i	$-0.0845088\pi$
$270$	2.40074	−	9.99922i	0.146104	−	0.608533i
$271$	10.0745	+	17.4496i	0.611985	+	1.05999i	0.990905	+	0.134560i	$0.0429621\pi$
$271$	10.0745	+	17.4496i	0.611985	+	1.05999i	−0.378920	+	0.925429i	$0.623705\pi$
$272$	−0.103697	+	0.588095i	−0.00628756	+	0.0356585i
$273$	−30.8980	−	0.195250i	−1.87003	−	0.0118171i
$274$	−10.5182	−	3.82831i	−0.635428	−	0.231277i
$275$	3.33493	+	1.21382i	0.201104	+	0.0731958i
$276$	−0.602600	+	0.613205i	−0.0362723	+	0.0369106i
$277$	−1.77777	+	10.0822i	−0.106816	+	0.605783i	0.883664	+	0.468123i	$0.155069\pi$
$277$	−1.77777	+	10.0822i	−0.106816	+	0.605783i	−0.990479	+	0.137661i	$0.956042\pi$
$278$	−5.21015			−0.312484
$279$	3.87319	−	2.32720i	0.231882	−	0.139326i
$280$	4.33380	−	2.93842i	0.258994	−	0.175604i
$281$	13.9814	+	11.7318i	0.834061	+	0.699860i	0.956220	−	0.292650i	$-0.0945372\pi$
$281$	13.9814	+	11.7318i	0.834061	+	0.699860i	−0.122158	+	0.992511i	$0.538982\pi$
$282$	−0.652273	+	1.43127i	−0.0388423	+	0.0852306i
$283$	−7.30633	−	2.65929i	−0.434316	−	0.158078i	0.115604	−	0.993295i	$-0.463120\pi$
$283$	−7.30633	−	2.65929i	−0.434316	−	0.158078i	−0.549920	+	0.835217i	$0.685342\pi$
$284$	−2.48900	−	0.905923i	−0.147695	−	0.0537566i
$285$	−11.8231	+	25.9432i	−0.700342	+	1.53674i
$286$	16.9196	+	14.1972i	1.00048	+	0.839501i
$287$	0.463578	+	6.40736i	0.0273642	+	0.378215i
$288$	−0.0523315	−	2.99954i	−0.00308366	−	0.176750i
$289$	−16.6434			−0.979023
$290$	0.438232	−	2.48534i	0.0257338	−	0.145944i
$291$	10.1195	−	10.2976i	0.593214	−	0.603653i
$292$	1.27027	+	0.462341i	0.0743370	+	0.0270565i
$293$	−15.8822	−	5.78065i	−0.927849	−	0.337709i	−0.166492	−	0.986043i	$-0.553244\pi$
$293$	−15.8822	−	5.78065i	−0.927849	−	0.337709i	−0.761357	+	0.648333i	$0.775466\pi$
$294$	−0.798488	−	12.0980i	−0.0465688	−	0.705572i
$295$	4.62742	−	26.2434i	0.269419	−	1.52795i
$296$	0.271187	+	0.469709i	0.0157624	+	0.0273013i
$297$	1.92663	+	16.9118i	0.111795	+	0.981320i
$298$	5.77823	−	10.0082i	0.334724	−	0.579759i
$299$	−3.14500	+	1.14468i	−0.181880	+	0.0661988i
$300$	0.147238	−	1.87074i	0.00850081	−	0.108007i
$301$	−7.09097	−	7.30756i	−0.408717	−	0.421201i
$302$	12.6338	−	10.6010i	0.726994	−	0.610020i
$303$	28.3903	+	7.34237i	1.63098	+	0.421808i
$304$	−1.44430	+	8.19103i	−0.0828362	+	0.469788i
$305$	−7.27190	−	12.5953i	−0.416388	−	0.721205i
$306$	−1.75859	+	0.341820i	−0.100532	+	0.0195405i
$307$	−9.92235	−	17.1860i	−0.566298	−	0.980858i	−0.996928	−	0.0783287i	$-0.975042\pi$
$307$	−9.92235	−	17.1860i	−0.566298	−	0.980858i	0.430629	−	0.902529i	$-0.358292\pi$
$308$	−5.07726	+	7.02381i	−0.289304	+	0.400219i
$309$	−11.3634	+	24.9344i	−0.646442	+	1.41847i
$310$	−2.28343	+	1.91603i	−0.129690	+	0.108823i
$311$	−21.6746	−	7.88892i	−1.22906	−	0.447340i	−0.355782	−	0.934569i	$-0.615785\pi$
$311$	−21.6746	−	7.88892i	−1.22906	−	0.447340i	−0.873274	+	0.487229i	$0.838008\pi$
$312$	4.84307	−	10.6270i	0.274185	−	0.601637i
$313$	1.34541	−	7.63022i	0.0760473	−	0.431286i	−0.922884	−	0.385077i	$-0.874175\pi$
$313$	1.34541	−	7.63022i	0.0760473	−	0.431286i	0.998932	−	0.0462089i	$-0.0147140\pi$
$314$	−6.94562	−	12.0302i	−0.391964	−	0.678901i
$315$	12.8890	+	8.97886i	0.726210	+	0.505901i
$316$	−3.55283	+	6.15368i	−0.199862	+	0.346171i
$317$	21.4591	+	18.0064i	1.20527	+	1.01134i	0.999464	+	0.0327444i	$0.0104247\pi$
$317$	21.4591	+	18.0064i	1.20527	+	1.01134i	0.205802	+	0.978594i	$0.434020\pi$
$318$	17.0907	+	4.42002i	0.958396	+	0.247862i
$319$	0.725366	+	4.11375i	0.0406127	+	0.230326i
$320$	0.343656	+	1.94897i	0.0192110	+	0.108951i
$321$	−4.52356	+	2.15760i	−0.252481	+	0.120426i
$322$	−0.537047	−	1.19844i	−0.0299284	−	0.0667864i
$323$	4.96687			0.276364
$324$	8.34471	−	3.37132i	0.463595	−	0.187295i
$325$	3.65252	−	6.32636i	0.202606	−	0.350923i
$326$	9.98421	+	8.37775i	0.552975	+	0.464001i
$327$	28.4728	+	19.5690i	1.57455	+	1.08217i
$328$	−2.28166	−	0.830455i	−0.125983	−	0.0458542i
$329$	−1.67317	−	1.72428i	−0.0922448	−	0.0950624i
$330$	−3.00064	−	10.8201i	−0.165180	−	0.595629i
$331$	7.81248	+	6.55545i	0.429413	+	0.360320i	0.831730	−	0.555180i	$-0.187351\pi$
$331$	7.81248	+	6.55545i	0.429413	+	0.360320i	−0.402317	+	0.915500i	$0.631795\pi$
$332$	3.78035	+	6.54775i	0.207473	+	0.359355i
$333$	−1.02399	+	1.26450i	−0.0561144	+	0.0692943i
$334$	11.3862	−	19.7215i	0.623026	−	1.07911i
$335$	−4.13380	−	3.46867i	−0.225854	−	0.189514i
$336$	4.29622	+	1.59451i	0.234378	+	0.0869878i
$337$	0.475096	+	2.69440i	0.0258801	+	0.146774i	0.995010	−	0.0997786i	$-0.0318135\pi$
$337$	0.475096	+	2.69440i	0.0258801	+	0.146774i	−0.969130	+	0.246552i	$0.920702\pi$
$338$	24.8682	−	20.8669i	1.35265	−	1.13501i
$339$	7.25604	+	10.1727i	0.394094	+	0.552504i
$340$	1.11054	−	0.404205i	0.0602277	−	0.0219211i
$341$	2.46693	−	4.27285i	0.133592	−	0.231388i
$342$	−24.4938	+	4.76089i	−1.32447	+	0.257439i
$343$	17.6548	+	5.59548i	0.953267	+	0.302128i
$344$	3.61651	−	1.31630i	0.194989	−	0.0709702i
$345$	1.64725	+	0.426016i	0.0886852	+	0.0229359i
$346$	2.45131	+	13.9021i	0.131783	+	0.747379i
$347$	1.86371	−	1.56384i	0.100049	−	0.0839514i	−0.591391	−	0.806385i	$-0.701421\pi$
$347$	1.86371	−	1.56384i	0.100049	−	0.0839514i	0.691440	+	0.722434i	$0.256977\pi$
$348$	1.99356	−	0.950869i	0.106866	−	0.0509719i
$349$	−0.745200	+	4.22624i	−0.0398896	+	0.226225i	−0.998235	−	0.0593863i	$-0.981086\pi$
$349$	−0.745200	+	4.22624i	−0.0398896	+	0.226225i	0.958345	+	0.285612i	$0.0921968\pi$
$350$	2.57936	+	1.25035i	0.137873	+	0.0668338i
$351$	34.9704	+	2.13933i	1.86658	+	0.114189i
$352$	−1.63786	−	2.83686i	−0.0872983	−	0.151205i
$353$	−16.6699	−	13.9877i	−0.887247	−	0.744489i	0.0804088	−	0.996762i	$-0.474377\pi$
$353$	−16.6699	−	13.9877i	−0.887247	−	0.744489i	−0.967656	+	0.252273i	$0.918822\pi$
$354$	21.0506	−	10.0405i	1.11883	−	0.533647i
$355$	0.910256	+	5.16232i	0.0483114	+	0.273987i
$356$	13.2247	−	11.0969i	0.700910	−	0.588133i
$357$	0.492220	−	2.69193i	0.0260510	−	0.142472i
$358$	−0.0150906	+	0.00549254i	−0.000797565	+	0.000290290i
$359$	−29.0412			−1.53274			−0.766369	−	0.642401i	$-0.777939\pi$
$359$	−29.0412			−1.53274			−0.766369	+	0.642401i	$0.777939\pi$
$360$	−5.08912	+	3.05779i	−0.268220	+	0.161160i
$361$	50.1789			2.64099
$362$	0.685960	−	3.89027i	0.0360533	−	0.204468i
$363$	−0.271198	−	0.380210i	−0.0142342	−	0.0199558i
$364$	12.4231	+	12.8026i	0.651150	+	0.671039i
$365$	−0.464553	−	2.63461i	−0.0243158	−	0.137902i
$366$	5.27857	−	11.5826i	0.275915	−	0.605433i
$367$	−20.2574	+	7.37309i	−1.05743	+	0.384872i	−0.811461	−	0.584406i	$-0.801327\pi$
$367$	−20.2574	+	7.37309i	−1.05743	+	0.384872i	−0.245966	+	0.969278i	$0.579105\pi$
$368$	0.496369			0.0258750
$369$	−0.127065	−	7.28315i	−0.00661476	−	0.379146i
$370$	0.536689	−	0.929572i	0.0279011	−	0.0483262i
$371$	−15.7972	+	21.8536i	−0.820148	+	1.13458i
$372$	−2.52570	−	0.653202i	−0.130951	−	0.0338669i
$373$	−0.843931	−	0.307166i	−0.0436971	−	0.0159044i	0.320079	−	0.947391i	$-0.396290\pi$
$373$	−0.843931	−	0.307166i	−0.0436971	−	0.0159044i	−0.363776	+	0.931486i	$0.618513\pi$
$374$	−1.49850	+	1.25739i	−0.0774857	+	0.0650182i
$375$	−18.8214	+	8.97723i	−0.971931	+	0.463582i
$376$	0.853342	−	0.310591i	0.0440078	−	0.0160175i
$377$	8.59823			0.442831
$378$	0.152949	+	13.7469i	0.00786683	+	0.707063i
$379$	−24.5625			−1.26169			−0.630845	−	0.775909i	$-0.717291\pi$
$379$	−24.5625			−1.26169			−0.630845	+	0.775909i	$0.717291\pi$
$380$	15.4677	−	5.62979i	0.793478	−	0.288802i
$381$	12.8968	+	8.86377i	0.660721	+	0.454105i
$382$	−13.6974	+	11.4935i	−0.700821	+	0.588058i
$383$	8.52532	+	3.10296i	0.435624	+	0.158554i	0.550517	−	0.834824i	$-0.314431\pi$
$383$	8.52532	+	3.10296i	0.435624	+	0.158554i	−0.114894	+	0.993378i	$0.536653\pi$
$384$	−1.21402	+	1.23538i	−0.0619525	+	0.0630428i
$385$	17.0621	+	1.75171i	0.869567	+	0.0892753i
$386$	−0.800503	+	1.38651i	−0.0407445	+	0.0705716i
$387$	7.57466	+	8.71380i	0.385042	+	0.442948i
$388$	−8.33553			−0.423172
$389$	−29.4368	+	10.7141i	−1.49251	+	0.543227i	−0.954108	−	0.299464i	$-0.903192\pi$
$389$	−29.4368	+	10.7141i	−1.49251	+	0.543227i	−0.538398	+	0.842691i	$0.680970\pi$
$390$	−23.0059	+	2.21512i	−1.16495	+	0.112167i
$391$	−0.0514720	−	0.291912i	−0.00260305	−	0.0147626i
$392$	−4.65877	+	5.22455i	−0.235303	+	0.263879i
$393$	−23.9755	+	2.30848i	−1.20941	+	0.116447i
$394$	−3.29959	+	18.7129i	−0.166231	+	0.942742i
$395$	14.0624			0.707554
$396$	6.18450	−	7.63709i	0.310783	−	0.383778i
$397$	3.84476			0.192963			0.0964814	−	0.995335i	$-0.469241\pi$
$397$	3.84476			0.192963			0.0964814	+	0.995335i	$0.469241\pi$
$398$	7.82235	−	2.84710i	0.392099	−	0.142712i
$399$	6.85567	−	37.4934i	0.343213	−	1.87702i
$400$	−0.829942	+	0.696404i	−0.0414971	+	0.0348202i
$401$	1.67002	+	9.47115i	0.0833968	+	0.472967i	0.997691	+	0.0679161i	$0.0216350\pi$
$401$	1.67002	+	9.47115i	0.0833968	+	0.472967i	−0.914294	+	0.405051i	$0.867254\pi$
$402$	0.370569	−	4.70827i	0.0184823	−	0.234827i
$403$	−7.77971	−	6.52795i	−0.387535	−	0.325180i
$404$	−8.46523	−	14.6622i	−0.421161	−	0.729472i
$405$	−14.0353	−	10.9660i	−0.697421	−	0.544905i
$406$	0.243466	+	3.36508i	0.0120830	+	0.167006i
$407$	−0.308515	+	1.74968i	−0.0152925	+	0.0867282i
$408$	0.852411	+	0.585851i	0.0422006	+	0.0290040i
$409$	−3.78477	+	3.17580i	−0.187145	+	0.157033i	−0.731547	−	0.681791i	$-0.761201\pi$
$409$	−3.78477	+	3.17580i	−0.187145	+	0.157033i	0.544402	+	0.838825i	$0.316757\pi$
$410$	0.834427	+	4.73227i	0.0412094	+	0.233710i
$411$	−13.5888	+	13.8279i	−0.670284	+	0.682080i
$412$	14.8663	−	5.41089i	0.732410	−	0.266575i
$413$	2.57083	+	35.5328i	0.126502	+	1.74846i
$414$	0.533636	+	1.39021i	0.0262268	+	0.0683249i
$415$	7.48145	−	12.9582i	0.367250	−	0.636095i
$416$	−6.33600	+	2.30612i	−0.310648	+	0.113067i
$417$	−3.74233	+	8.21170i	−0.183263	+	0.402128i
$418$	−20.8712	+	17.5130i	−1.02085	+	0.856591i
$419$	4.41265	+	25.0254i	0.215572	+	1.22257i	0.879911	+	0.475138i	$0.157602\pi$
$419$	4.41265	+	25.0254i	0.215572	+	1.22257i	−0.664339	+	0.747431i	$0.731287\pi$
$420$	−1.51836	−	8.94108i	−0.0740885	−	0.436280i
$421$	11.3843	+	9.55254i	0.554836	+	0.465562i	0.876575	−	0.481266i	$-0.159823\pi$
$421$	11.3843	+	9.55254i	0.554836	+	0.465562i	−0.321739	+	0.946828i	$0.604267\pi$
$422$	−2.34734	+	4.06571i	−0.114267	+	0.197915i
$423$	1.78730	+	2.05609i	0.0869015	+	0.0999705i
$424$	−5.09597	−	8.82648i	−0.247482	−	0.428652i
$425$	0.495614	+	0.415870i	0.0240408	+	0.0201726i
$426$	−3.21561	+	3.27220i	−0.155797	+	0.158539i
$427$	13.5402	+	13.9538i	0.655258	+	0.675273i
$428$	2.71905	+	0.989652i	0.131430	+	0.0478366i
$429$	34.5292	−	16.4694i	1.66709	−	0.795150i
$430$	−5.83460	−	4.89581i	−0.281370	−	0.236097i
$431$	−4.89865	+	8.48471i	−0.235960	+	0.408694i	−0.959551	−	0.281534i	$-0.909157\pi$
$431$	−4.89865	+	8.48471i	−0.235960	+	0.408694i	0.723591	+	0.690228i	$0.242490\pi$
$432$	−4.76516	−	2.07202i	−0.229264	−	0.0996902i
$433$	27.3619			1.31493			0.657464	−	0.753486i	$-0.271629\pi$
$433$	27.3619			1.31493			0.657464	+	0.753486i	$0.271629\pi$
$434$	2.33455	−	3.22958i	0.112062	−	0.155025i
$435$	−3.60236	−	2.47585i	−0.172720	−	0.118708i
$436$	−3.46376	−	19.6440i	−0.165884	−	0.940775i
$437$	−0.716905	−	4.06577i	−0.0342942	−	0.194492i
$438$	1.64110	−	1.66998i	0.0784148	−	0.0797948i
$439$	−24.7810	−	20.7937i	−1.18273	−	0.992431i	−0.999957	−	0.00927658i	$-0.997047\pi$
$439$	−24.7810	−	20.7937i	−1.18273	−	0.992431i	−0.182776	−	0.983155i	$-0.558508\pi$
$440$	−3.24139	+	5.61425i	−0.154527	+	0.267649i
$441$	−19.6412	−	7.43124i	−0.935295	−	0.353869i
$442$	2.01324	+	3.48703i	0.0957601	+	0.165861i
$443$	5.30279	−	30.0736i	0.251943	−	1.42884i	−0.551856	−	0.833939i	$-0.686080\pi$
$443$	5.30279	−	30.0736i	0.251943	−	1.42884i	0.803799	−	0.594901i	$-0.202809\pi$
$444$	0.935094	−	0.0900353i	0.0443776	−	0.00427289i
$445$	−32.1050	−	11.6853i	−1.52192	−	0.553935i
$446$	−1.19279	+	1.00087i	−0.0564800	+	0.0473924i
$447$	−11.6235	−	16.2957i	−0.549773	−	0.770760i
$448$	−1.08195	−	2.41441i	−0.0511173	−	0.114070i
$449$	−5.77134	−	9.99626i	−0.272366	−	0.471753i	0.697101	−	0.716973i	$-0.254473\pi$
$449$	−5.77134	−	9.99626i	−0.272366	−	0.471753i	−0.969467	+	0.245221i	$0.921140\pi$
$450$	−2.84271	−	1.57577i	−0.134006	−	0.0742825i
$451$	−3.97687	−	6.88814i	−0.187264	−	0.324350i
$452$	1.25273	−	7.10459i	0.0589235	−	0.334172i
$453$	−7.63366	−	27.5265i	−0.358661	−	1.29331i
$454$	3.43311	−	2.88072i	0.161124	−	0.135199i
$455$	9.64941	−	33.9604i	0.452371	−	1.59209i
$456$	11.8724	+	8.15977i	0.555978	+	0.382116i
$457$	11.8760	−	4.32252i	0.555537	−	0.202199i	−0.0489679	−	0.998800i	$-0.515593\pi$
$457$	11.8760	−	4.32252i	0.555537	−	0.202199i	0.604505	+	0.796601i	$0.293371\pi$
$458$	9.20756	−	15.9480i	0.430241	−	0.745199i
$459$	−0.724413	+	3.01723i	−0.0338127	+	0.140832i
$460$	−0.491166	−	0.850725i	−0.0229008	−	0.0396653i
$461$	−3.47332	+	19.6982i	−0.161768	+	0.917434i	0.790566	+	0.612377i	$0.209787\pi$
$461$	−3.47332	+	19.6982i	−0.161768	+	0.917434i	−0.952334	+	0.305057i	$0.901324\pi$
$462$	7.42333	+	13.0473i	0.345364	+	0.607015i
$463$	12.0406	+	4.38242i	0.559574	+	0.203668i	0.606295	−	0.795240i	$-0.292655\pi$
$463$	12.0406	+	4.38242i	0.559574	+	0.203668i	−0.0467212	+	0.998908i	$0.514877\pi$
$464$	−1.19830	−	0.436145i	−0.0556297	−	0.0202475i
$465$	1.37971	+	4.97514i	0.0639823	+	0.230717i
$466$	1.80823	−	10.2550i	0.0837646	−	0.475053i
$467$	−27.7523			−1.28422			−0.642112	−	0.766611i	$-0.721941\pi$
$467$	−27.7523			−1.28422			−0.642112	+	0.766611i	$0.721941\pi$
$468$	−13.2706	−	15.2663i	−0.613432	−	0.705685i
$469$	6.49173	+	3.14687i	0.299760	+	0.145309i
$470$	−1.37672	−	1.15520i	−0.0635033	−	0.0532856i
$471$	−23.9496	+	2.30598i	−1.10354	+	0.106254i
$472$	−12.6532	−	4.60539i	−0.582411	−	0.211980i
$473$	11.8467	+	4.31184i	0.544711	+	0.198258i
$474$	7.14687	+	10.0196i	0.328267	+	0.460217i
$475$	6.90294	+	5.79226i	0.316729	+	0.265767i
$476$	−1.30771	+	0.886657i	−0.0599387	+	0.0406399i
$477$	19.2422	−	23.7617i	0.881039	−	1.08797i
$478$	9.61406			0.439737
$479$	−2.47993	+	14.0644i	−0.113311	+	0.642617i	0.874262	+	0.485454i	$0.161346\pi$
$479$	−2.47993	+	14.0644i	−0.113311	+	0.642617i	−0.987573	+	0.157163i	$0.949765\pi$
$480$	3.31861	+	0.858265i	0.151473	+	0.0391743i
$481$	3.43648	+	1.25078i	0.156690	+	0.0570305i
$482$	−26.8336	−	9.76662i	−1.22224	−	0.444857i
$483$	−2.27460	−	0.0143736i	−0.103498	−	0.000654023i
$484$	−0.0468215	+	0.265538i	−0.00212825	+	0.0120699i
$485$	8.24816	+	14.2862i	0.374530	+	0.648705i
$486$	0.680293	−	15.5736i	0.0308587	−	0.706433i
$487$	−18.8491	+	32.6476i	−0.854134	+	1.47940i	0.0233124	+	0.999728i	$0.492579\pi$
$487$	−18.8491	+	32.6476i	−0.854134	+	1.47940i	−0.877446	+	0.479675i	$0.840755\pi$
$488$	−6.90574	+	2.51348i	−0.312608	+	0.113780i
$489$	20.3756	−	9.71854i	0.921415	−	0.439488i
$490$	13.5643	+	2.81486i	0.612771	+	0.127162i
$491$	−9.35212	+	7.84736i	−0.422055	+	0.354146i	−0.828944	−	0.559331i	$-0.811058\pi$
$491$	−9.35212	+	7.84736i	−0.422055	+	0.354146i	0.406889	+	0.913478i	$0.366614\pi$
$492$	−2.94774	+	2.99961i	−0.132894	+	0.135233i
$493$	−0.132235	+	0.749941i	−0.00595556	+	0.0337756i
$494$	28.0405	+	48.5676i	1.26160	+	2.18516i
$495$	−19.2089	−	3.04255i	−0.863374	−	0.136753i
$496$	0.753095	+	1.30440i	0.0338150	+	0.0585693i
$497$	−2.86581	−	6.39515i	−0.128549	−	0.286862i
$498$	13.0352	−	1.25509i	0.584122	−	0.0562421i
$499$	3.49982	−	2.93670i	0.156673	−	0.131465i	−0.561081	−	0.827761i	$-0.689614\pi$
$499$	3.49982	−	2.93670i	0.156673	−	0.131465i	0.717755	+	0.696296i	$0.245170\pi$
$500$	11.3132	+	4.11768i	0.505943	+	0.184148i
$501$	−22.9045	−	32.1113i	−1.02330	−	1.43463i
$502$	1.29773	−	7.35981i	0.0579207	−	0.328484i
$503$	−2.44425	−	4.23357i	−0.108984	−	0.188766i	0.806375	−	0.591405i	$-0.201426\pi$
$503$	−2.44425	−	4.23357i	−0.108984	−	0.188766i	−0.915359	+	0.402639i	$0.868093\pi$
$504$	5.59898	−	5.62596i	0.249398	−	0.250600i
$505$	−16.7530	+	29.0171i	−0.745499	+	1.29124i
$506$	1.24556	+	1.04515i	0.0553721	+	0.0464627i
$507$	−15.0260	−	54.1828i	−0.667326	−	2.40634i
$508$	−1.56891	−	8.89772i	−0.0696090	−	0.394772i
$509$	1.06298	+	6.02848i	0.0471159	+	0.267208i	0.999261	−	0.0384389i	$-0.0122385\pi$
$509$	1.06298	+	6.02848i	0.0471159	+	0.267208i	−0.952145	+	0.305647i	$0.901127\pi$
$510$	0.160612	−	2.04066i	0.00711201	−	0.0903617i
$511$	1.46257	+	3.26379i	0.0647005	+	0.144382i
$512$	1.00000			0.0441942
$513$	−10.0897	+	42.0241i	−0.445470	+	1.85541i
$514$	−13.9386	+	24.1423i	−0.614803	+	1.06487i
$515$	−23.9842	−	20.1251i	−1.05687	−	0.886818i
$516$	0.523035	−	6.64543i	0.0230253	−	0.292549i
$517$	2.79531	+	1.01741i	0.122938	+	0.0447457i
$518$	−0.392208	+	1.38035i	−0.0172326	+	0.0606490i
$519$	23.6717	+	6.12202i	1.03907	+	0.268727i
$520$	10.2220	+	8.57730i	0.448266	+	0.376140i
$521$	−8.64813	−	14.9790i	−0.378881	−	0.656242i	0.612018	−	0.790844i	$-0.290358\pi$
$521$	−8.64813	−	14.9790i	−0.378881	−	0.656242i	−0.990900	+	0.134602i	$0.957025\pi$
$522$	−0.0667333	−	3.82503i	−0.00292084	−	0.167417i
$523$	−17.0831	+	29.5888i	−0.746991	+	1.29383i	0.202267	+	0.979330i	$0.435169\pi$
$523$	−17.0831	+	29.5888i	−0.746991	+	1.29383i	−0.949259	+	0.314497i	$0.898164\pi$
$524$	10.6528	+	8.93879i	0.465371	+	0.390493i
$525$	3.82336	−	3.16723i	0.166865	−	0.138229i
$526$	2.12582	+	12.0561i	0.0926903	+	0.525673i
$527$	0.689017	−	0.578154i	0.0300141	−	0.0251848i
$528$	−5.64760	+	0.543778i	−0.245780	+	0.0236649i
$529$	21.3814	−	7.78220i	0.929626	−	0.338356i
$530$	−10.0851	+	17.4679i	−0.438069	+	0.758758i
$531$	−0.704657	−	40.3896i	−0.0305795	−	1.75276i
$532$	−18.2138	+	12.3494i	−0.789670	+	0.535415i
$533$	−15.3844	+	5.59945i	−0.666370	+	0.242539i
$534$	−7.99072	−	28.8141i	−0.345792	−	1.24691i
$535$	−0.994386	−	5.63944i	−0.0429910	−	0.243814i
$536$	−2.08879	+	1.75271i	−0.0902222	+	0.0757054i
$537$	−0.00218248	+	0.0277295i	−9.41808e−5	+	0.00119661i
$538$	−4.04259	+	22.9266i	−0.174288	+	0.988438i
$539$	−22.6913	+	3.30074i	−0.977382	+	0.142173i
$540$	1.16398	+	10.2173i	0.0500897	+	0.439682i
$541$	14.2140	+	24.6193i	0.611107	+	1.05847i	0.991054	+	0.133460i	$0.0426087\pi$
$541$	14.2140	+	24.6193i	0.611107	+	1.05847i	−0.379948	+	0.925008i	$0.624058\pi$
$542$	−15.4351	−	12.9516i	−0.662994	−	0.556318i
$543$	−5.63874	−	3.87543i	−0.241981	−	0.166311i
$544$	−0.103697	−	0.588095i	−0.00444597	−	0.0252144i
$545$	−30.2403	+	25.3746i	−1.29535	+	1.08693i
$546$	29.1014	−	10.3843i	1.24542	−	0.444405i
$547$	12.8925	−	4.69250i	0.551245	−	0.200637i	−0.0513547	−	0.998680i	$-0.516354\pi$
$547$	12.8925	−	4.69250i	0.551245	−	0.200637i	0.602599	+	0.798044i	$0.294132\pi$
$548$	11.1932			0.478151
$549$	−14.4639	−	16.6391i	−0.617302	−	0.710137i
$550$	−3.54896			−0.151328
$551$	−1.84177	+	10.4452i	−0.0784623	+	0.444982i
$552$	0.356530	−	0.782325i	0.0151749	−	0.0332980i
$553$	−18.2303	+	4.59206i	−0.775233	+	0.195274i
$554$	−1.77777	−	10.0822i	−0.0755303	−	0.428353i
$555$	−1.07960	−	1.51356i	−0.0458267	−	0.0642472i
$556$	4.89594	−	1.78198i	0.207634	−	0.0755726i
$557$	17.5746			0.744658			0.372329	−	0.928101i	$-0.378559\pi$
$557$	17.5746			0.744658			0.372329	+	0.928101i	$0.378559\pi$
$558$	−2.84366	+	3.51157i	−0.120382	+	0.148656i
$559$	12.9749	−	22.4731i	0.548778	−	0.950512i
$560$	−3.06744	+	4.24346i	−0.129623	+	0.179319i
$561$	0.905433	+	3.26494i	0.0382274	+	0.137846i
$562$	−17.1507	−	6.24236i	−0.723460	−	0.263318i
$563$	20.5293	−	17.2261i	0.865206	−	0.725994i	−0.0978771	−	0.995199i	$-0.531205\pi$
$563$	20.5293	−	17.2261i	0.865206	−	0.725994i	0.963083	+	0.269205i	$0.0867608\pi$
$564$	0.123414	−	1.56804i	0.00519667	−	0.0660264i
$565$	−13.4161	+	4.88307i	−0.564421	+	0.205432i
$566$	7.77524			0.326818
$567$	21.7763	+	9.63300i	0.914517	+	0.404548i
$568$	2.64874			0.111139
$569$	−2.39038	+	0.870026i	−0.100210	+	0.0364734i	−0.391638	−	0.920119i	$-0.628092\pi$
$569$	−2.39038	+	0.870026i	−0.100210	+	0.0364734i	0.291429	+	0.956593i	$0.405869\pi$
$570$	2.23701	−	28.4224i	0.0936981	−	1.19048i
$571$	16.4205	−	13.7784i	0.687174	−	0.576608i	−0.230918	−	0.972973i	$-0.574173\pi$
$571$	16.4205	−	13.7784i	0.687174	−	0.576608i	0.918093	+	0.396365i	$0.129729\pi$
$572$	−20.7550	−	7.55420i	−0.867810	−	0.315857i
$573$	8.27632	+	29.8439i	0.345748	+	1.24675i
$574$	−2.62707	−	5.86240i	−0.109652	−	0.244692i
$575$	0.268886	−	0.465724i	0.0112133	−	0.0194220i
$576$	1.07508	+	2.80075i	0.0447950	+	0.116698i
$577$	−7.87337			−0.327773			−0.163886	−	0.986479i	$-0.552403\pi$
$577$	−7.87337			−0.327773			−0.163886	+	0.986479i	$0.552403\pi$
$578$	15.6397	−	5.69237i	0.650525	−	0.236772i
$579$	1.61029	+	2.25757i	0.0669215	+	0.0938213i
$580$	0.438232	+	2.48534i	0.0181966	+	0.103198i
$581$	−5.46738	+	19.2420i	−0.226825	+	0.798295i
$582$	−5.98722	+	13.1376i	−0.248178	+	0.544571i
$583$	5.79741	−	32.8788i	0.240104	−	1.36170i
$584$	−1.35179			−0.0559377
$585$	−13.0334	+	37.8507i	−0.538864	+	1.56493i
$586$	16.9015			0.698195
$587$	−38.9778	+	14.1868i	−1.60879	+	0.585550i	−0.981199	−	0.192997i	$-0.938179\pi$
$587$	−38.9778	+	14.1868i	−1.60879	+	0.585550i	−0.627586	+	0.778547i	$0.715957\pi$
$588$	4.88810	+	11.0953i	0.201582	+	0.457564i
$589$	9.59667	−	8.05256i	0.395424	−	0.331800i
$590$	4.62742	+	26.2434i	0.190508	+	1.08042i
$591$	27.1233	+	18.6415i	1.11570	+	0.766809i
$592$	−0.415482	−	0.348631i	−0.0170762	−	0.0143287i
$593$	4.52774	+	7.84227i	0.185932	+	0.322043i	0.943890	−	0.330260i	$-0.107136\pi$
$593$	4.52774	+	7.84227i	0.185932	+	0.322043i	−0.757958	+	0.652303i	$0.773803\pi$
$594$	−7.59461	−	15.2329i	−0.311611	−	0.625014i
$595$	2.81364	+	1.36391i	0.115348	+	0.0559150i
$596$	−2.00676	+	11.3809i	−0.0822000	+	0.466180i
$597$	1.13130	−	14.3738i	0.0463012	−	0.588280i
$598$	2.56382	−	2.15130i	0.104843	−	0.0879733i
$599$	−4.79039	−	27.1676i	−0.195730	−	1.11004i	−0.911375	−	0.411576i	$-0.864978\pi$
$599$	−4.79039	−	27.1676i	−0.195730	−	1.11004i	0.715645	−	0.698464i	$-0.246133\pi$
$600$	0.501472	+	1.80828i	0.0204725	+	0.0738226i
$601$	−24.5814	+	8.94690i	−1.00270	+	0.364952i	−0.790624	−	0.612302i	$-0.790244\pi$
$601$	−24.5814	+	8.94690i	−1.00270	+	0.364952i	−0.212073	+	0.977254i	$0.568021\pi$
$602$	9.16267	+	4.44161i	0.373442	+	0.181026i
$603$	−7.15451	−	3.96589i	−0.291354	−	0.161504i
$604$	−8.24613	+	14.2827i	−0.335530	+	0.581155i
$605$	0.501435	−	0.182507i	0.0203862	−	0.00741998i
$606$	−29.1894	+	2.81050i	−1.18574	+	0.114169i
$607$	8.36130	−	7.01597i	0.339375	−	0.284769i	−0.457132	−	0.889399i	$-0.651123\pi$
$607$	8.36130	−	7.01597i	0.339375	−	0.284769i	0.796507	+	0.604630i	$0.206679\pi$
$608$	−1.44430	−	8.19103i	−0.0585740	−	0.332190i
$609$	5.47856	+	2.03333i	0.222002	+	0.0823946i
$610$	11.1412	+	9.34858i	0.451094	+	0.378513i
$611$	3.06152	−	5.30271i	0.123856	−	0.214525i
$612$	1.53563	−	0.922679i	0.0620740	−	0.0372971i
$613$	0.191047	+	0.330903i	0.00771630	+	0.0133650i	0.869858	−	0.493303i	$-0.164210\pi$
$613$	0.191047	+	0.330903i	0.00771630	+	0.0133650i	−0.862141	+	0.506668i	$0.830877\pi$
$614$	15.2019	+	12.7559i	0.613500	+	0.514787i
$615$	8.05786	+	2.08394i	0.324924	+	0.0840326i
$616$	2.36878	−	8.33675i	0.0954409	−	0.335897i
$617$	25.9351	+	9.43961i	1.04411	+	0.380024i	0.806436	−	0.591321i	$-0.201393\pi$
$617$	25.9351	+	9.43961i	1.04411	+	0.380024i	0.237672	+	0.971345i	$0.423616\pi$
$618$	2.15003	−	27.3172i	0.0864869	−	1.09886i
$619$	5.47984	+	4.59813i	0.220253	+	0.184814i	0.746237	−	0.665680i	$-0.231858\pi$
$619$	5.47984	+	4.59813i	0.220253	+	0.184814i	−0.525984	+	0.850494i	$0.676303\pi$
$620$	1.49040	−	2.58145i	0.0598560	−	0.103674i
$621$	2.57440	+	0.157490i	0.103307	+	0.00631986i
$622$	23.0657			0.924849
$623$	45.4365	+	4.66480i	1.82038	+	0.186891i
$624$	−0.916341	+	11.6426i	−0.0366830	+	0.466076i
$625$	−3.19672	−	18.1295i	−0.127869	−	0.725179i
$626$	1.34541	+	7.63022i	0.0537736	+	0.304965i
$627$	12.6109	+	45.4743i	0.503632	+	1.81607i
$628$	10.6413	+	8.92911i	0.424634	+	0.356310i
$629$	−0.161944	+	0.280495i	−0.00645713	+	0.0111841i
$630$	−15.1826	−	4.02908i	−0.604890	−	0.160523i
$631$	4.02933	+	6.97900i	0.160405	+	0.277830i	0.935014	−	0.354611i	$-0.115387\pi$
$631$	4.02933	+	6.97900i	0.160405	+	0.277830i	−0.774609	+	0.632440i	$0.782053\pi$
$632$	1.23388	−	6.99770i	0.0490813	−	0.278354i
$633$	4.72191	+	6.61993i	0.187679	+	0.263119i
$634$	−26.3235	−	9.58099i	−1.04544	−	0.380510i
$635$	−13.6973	+	11.4934i	−0.543561	+	0.456102i
$636$	−17.5717	+	1.69189i	−0.696763	+	0.0670876i
$637$	−1.41965	+	47.1771i	−0.0562487	+	1.86922i
$638$	−2.08861	−	3.61757i	−0.0826888	−	0.143221i
$639$	2.84761	+	7.41846i	0.112650	+	0.293470i
$640$	−0.989519	−	1.71390i	−0.0391142	−	0.0677477i
$641$	3.35327	−	19.0173i	0.132446	−	0.751140i	−0.844158	−	0.536095i	$-0.819899\pi$
$641$	3.35327	−	19.0173i	0.132446	−	0.751140i	0.976604	−	0.215045i	$-0.0689899\pi$
$642$	3.51281	−	3.57463i	0.138640	−	0.141080i
$643$	25.5593	−	21.4468i	1.00796	−	0.845780i	0.0198936	−	0.999802i	$-0.493667\pi$
$643$	25.5593	−	21.4468i	1.00796	−	0.845780i	0.988067	+	0.154022i	$0.0492228\pi$
$644$	0.914549	+	0.942484i	0.0360383	+	0.0371391i
$645$	−11.9071	+	5.67935i	−0.468843	+	0.223624i
$646$	−4.66733	+	1.69877i	−0.183634	+	0.0668372i
$647$	−13.1461	+	22.7697i	−0.516827	+	0.895170i	0.482982	+	0.875630i	$0.339554\pi$
$647$	−13.1461	+	22.7697i	−0.516827	+	0.895170i	−0.999809	+	0.0195402i	$0.993780\pi$
$648$	−6.68841	+	6.02206i	−0.262745	+	0.236569i
$649$	−22.0542	−	38.1990i	−0.865704	−	1.49944i
$650$	−1.26851	+	7.19407i	−0.0497550	+	0.282174i
$651$	−3.41327	−	5.99920i	−0.133777	−	0.235127i
$652$	−12.2475	−	4.45771i	−0.479647	−	0.174577i
$653$	12.6772	+	4.61411i	0.496096	+	0.180564i	0.577937	−	0.816081i	$-0.303858\pi$
$653$	12.6772	+	4.61411i	0.496096	+	0.180564i	−0.0818414	+	0.996645i	$0.526080\pi$
$654$	−33.4487	−	8.65058i	−1.30795	−	0.338264i
$655$	4.77898	−	27.1030i	0.186730	−	1.05900i
$656$	2.42809			0.0948009
$657$	−1.45329	−	3.78604i	−0.0566981	−	0.147707i
$658$	2.16200	+	1.04803i	0.0842836	+	0.0408565i
$659$	9.39594	+	7.88413i	0.366014	+	0.307122i	0.807182	−	0.590302i	$-0.200991\pi$
$659$	9.39594	+	7.88413i	0.366014	+	0.307122i	−0.441168	+	0.897424i	$0.645436\pi$
$660$	6.52039	+	9.14133i	0.253806	+	0.355826i
$661$	−15.5327	−	5.65345i	−0.604153	−	0.219894i	0.0217899	−	0.999763i	$-0.493064\pi$
$661$	−15.5327	−	5.65345i	−0.604153	−	0.219894i	−0.625943	+	0.779869i	$0.715286\pi$
$662$	−9.58343	−	3.48808i	−0.372471	−	0.135568i
$663$	6.94196	−	0.668405i	0.269603	−	0.0259587i
$664$	−5.79183	−	4.85992i	−0.224767	−	0.188601i
$665$	39.1886	+	18.9967i	1.51967	+	0.736659i
$666$	0.529752	−	1.53847i	0.0205275	−	0.0596145i
$667$	0.632972			0.0245088
$668$	−3.95439	+	22.4265i	−0.153000	+	0.867706i
$669$	0.720711	+	2.59884i	0.0278643	+	0.100477i
$670$	5.07086	+	1.84564i	0.195904	+	0.0713034i
$671$	−22.6213	−	8.23347i	−0.873285	−	0.317850i
$672$	−4.58248	−	0.0289576i	−0.176773	−	0.00111706i
$673$	−3.81185	+	21.6181i	−0.146936	+	0.833315i	0.818856	+	0.573998i	$0.194608\pi$
$673$	−3.81185	+	21.6181i	−0.146936	+	0.833315i	−0.965792	+	0.259317i	$0.916503\pi$
$674$	−1.36798	−	2.36942i	−0.0526928	−	0.0912666i
$675$	−4.52541	+	3.34854i	−0.174183	+	0.128885i
$676$	−16.2315	+	28.1138i	−0.624290	+	1.08130i
$677$	−16.7791	+	6.10710i	−0.644874	+	0.234715i	−0.643692	−	0.765284i	$-0.722598\pi$
$677$	−16.7791	+	6.10710i	−0.644874	+	0.234715i	−0.00118145	+	0.999999i	$0.500376\pi$
$678$	−10.2977	−	7.07749i	−0.395481	−	0.271809i
$679$	−15.3580	−	15.8271i	−0.589387	−	0.607390i
$680$	−0.905324	+	0.759657i	−0.0347176	+	0.0291315i
$681$	−2.07437	−	7.48006i	−0.0794900	−	0.286636i
$682$	−0.856757	+	4.85891i	−0.0328069	+	0.186057i
$683$	11.1265	+	19.2717i	0.425744	+	0.737411i	0.996490	−	0.0837165i	$-0.0266790\pi$
$683$	11.1265	+	19.2717i	0.425744	+	0.737411i	−0.570745	+	0.821127i	$0.693346\pi$
$684$	21.3883	−	12.8511i	0.817801	−	0.491375i
$685$	−11.0759	−	19.1840i	−0.423189	−	0.732985i
$686$	−18.5038	+	0.780251i	−0.706479	+	0.0297901i
$687$	−18.5219	−	25.9670i	−0.706656	−	0.990704i
$688$	−2.94820	+	2.47384i	−0.112399	+	0.0943141i
$689$	−64.5761	−	23.5038i	−2.46016	−	0.895423i
$690$	−1.69362	+	0.163070i	−0.0644749	+	0.00620795i
$691$	5.54248	−	31.4330i	0.210846	−	1.19577i	−0.677125	−	0.735868i	$-0.736774\pi$
$691$	5.54248	−	31.4330i	0.210846	−	1.19577i	0.887971	−	0.459899i	$-0.152114\pi$
$692$	−7.05826	−	12.2253i	−0.268315	−	0.464735i
$693$	25.8958	−	2.32831i	0.983700	−	0.0884453i
$694$	−1.21645	+	2.10696i	−0.0461759	+	0.0799790i
$695$	−7.89875	−	6.62783i	−0.299616	−	0.251408i
$696$	−1.54812	+	1.57536i	−0.0586812	+	0.0597139i
$697$	−0.251785	−	1.42795i	−0.00953705	−	0.0540873i
$698$	−0.745200	−	4.22624i	−0.0282062	−	0.159966i
$699$	−14.8640	−	10.2159i	−0.562209	−	0.386399i
$700$	−2.85145	−	0.292748i	−0.107775	−	0.0110648i
$701$	−26.6856			−1.00790			−0.503950	−	0.863733i	$-0.668121\pi$
$701$	−26.6856			−1.00790			−0.503950	+	0.863733i	$0.668121\pi$
$702$	−33.5931	+	9.95025i	−1.26789	+	0.375548i
$703$	−2.25557	+	3.90675i	−0.0850703	+	0.147346i
$704$	2.50935	+	2.10559i	0.0945747	+	0.0793576i
$705$	−2.80958	+	1.34009i	−0.105815	+	0.0504705i
$706$	20.4486	+	7.44269i	0.769594	+	0.280109i
$707$	12.2430	−	43.0882i	0.460444	−	1.62050i
$708$	−16.3470	+	16.6347i	−0.614359	+	0.625171i
$709$	1.09945	+	0.922550i	0.0412908	+	0.0346471i	0.663200	−	0.748443i	$-0.269198\pi$
$709$	1.09945	+	0.922550i	0.0412908	+	0.0346471i	−0.621909	+	0.783090i	$0.713643\pi$
$710$	−2.62098	−	4.53967i	−0.0983635	−	0.170371i
$711$	20.9253	−	4.06729i	0.784762	−	0.152535i
$712$	−8.63183	+	14.9508i	−0.323492	+	0.560304i
$713$	−0.572715	−	0.480565i	−0.0214484	−	0.0179973i
$714$	0.458160	+	2.69794i	0.0171462	+	0.100968i
$715$	7.59033	+	43.0469i	0.283862	+	1.60986i
$716$	0.0123020	−	0.0103226i	0.000459747	−	0.000385774i
$717$	6.90556	−	15.1527i	0.257893	−	0.565888i
$718$	27.2898	−	9.93269i	1.01845	−	0.370685i
$719$	20.5818	−	35.6488i	0.767573	−	1.32947i	−0.171303	−	0.985218i	$-0.554798\pi$
$719$	20.5818	−	35.6488i	0.767573	−	1.32947i	0.938876	−	0.344257i	$-0.111869\pi$
$720$	3.73638	−	4.61397i	0.139247	−	0.171953i
$721$	37.6648	+	18.2580i	1.40271	+	0.679964i
$722$	−47.1527	+	17.1622i	−1.75484	+	0.638711i
$723$	−34.6670	+	35.2771i	−1.28928	+	1.31197i
$724$	0.685960	+	3.89027i	0.0254935	+	0.144581i
$725$	−1.05834	+	0.888057i	−0.0393059	+	0.0329816i
$726$	0.384882	+	0.264525i	0.0142843	+	0.00981743i
$727$	−3.36954	+	19.1096i	−0.124969	+	0.708737i	0.856357	+	0.516385i	$0.172723\pi$
$727$	−3.36954	+	19.1096i	−0.124969	+	0.708737i	−0.981326	+	0.192352i	$0.938389\pi$
$728$	−16.0527	−	7.78155i	−0.594952	−	0.288403i
$729$	−24.0569	−	12.2584i	−0.890995	−	0.454013i
$730$	1.33763	+	2.31684i	0.0495078	+	0.0857500i
$731$	1.76057	+	1.47729i	0.0651171	+	0.0546397i
$732$	−0.998739	+	12.6895i	−0.0369144	+	0.469017i
$733$	−4.18968	−	23.7608i	−0.154749	−	0.877626i	−0.959015	−	0.283356i	$-0.908552\pi$
$733$	−4.18968	−	23.7608i	−0.154749	−	0.877626i	0.804266	−	0.594270i	$-0.202559\pi$
$734$	16.5140	−	13.8569i	0.609542	−	0.511467i
$735$	14.1794	−	19.3567i	0.523014	−	0.713984i
$736$	−0.466434	+	0.169768i	−0.0171930	+	0.00625774i
$737$	−8.93201			−0.329015
$738$	2.61039	+	6.80046i	0.0960897	+	0.250329i
$739$	39.7604			1.46261			0.731304	−	0.682051i	$-0.238912\pi$
$739$	39.7604			1.46261			0.731304	+	0.682051i	$0.238912\pi$
$740$	−0.186390	+	1.05707i	−0.00685184	+	0.0388587i
$741$	96.6881	−	9.30959i	3.55193	−	0.341996i
$742$	7.37012	−	25.9386i	0.270566	−	0.952236i
$743$	0.703175	+	3.98791i	0.0257970	+	0.146302i	0.994986	−	0.100017i	$-0.0318899\pi$
$743$	0.703175	+	3.98791i	0.0257970	+	0.146302i	−0.969189	+	0.246320i	$0.920779\pi$
$744$	2.59679	−	0.250031i	0.0952029	−	0.00916659i
$745$	21.4914	−	7.82223i	0.787384	−	0.286584i
$746$	0.898092			0.0328815
$747$	7.38475	−	21.4463i	0.270194	−	0.784678i
$748$	0.978078	−	1.69408i	0.0357621	−	0.0619417i
$749$	3.13067	+	6.98622i	0.114392	+	0.255271i
$750$	14.6159	−	14.8731i	0.533697	−	0.543089i
$751$	15.3769	+	5.59673i	0.561111	+	0.204228i	0.606976	−	0.794720i	$-0.292382\pi$
$751$	15.3769	+	5.59673i	0.561111	+	0.204228i	−0.0458655	+	0.998948i	$0.514605\pi$
$752$	−0.695651	+	0.583721i	−0.0253678	+	0.0212861i
$753$	−10.6676	−	7.33173i	−0.388750	−	0.267183i
$754$	−8.07969	+	2.94077i	−0.294245	+	0.107096i
$755$	32.6388			1.18785
$756$	−4.84543	−	12.8655i	−0.176227	−	0.467915i
$757$	14.9344			0.542799			0.271400	−	0.962467i	$-0.412514\pi$
$757$	14.9344			0.542799			0.271400	+	0.962467i	$0.412514\pi$
$758$	23.0812	−	8.40086i	0.838346	−	0.305133i
$759$	2.54192	−	1.21242i	0.0922658	−	0.0440081i
$760$	−12.6094	+	10.5806i	−0.457391	+	0.383797i
$761$	−30.4167	−	11.0708i	−1.10260	−	0.401315i	−0.274329	−	0.961636i	$-0.588456\pi$
$761$	−30.4167	−	11.0708i	−1.10260	−	0.401315i	−0.828276	+	0.560321i	$0.810678\pi$
$762$	−15.1506	−	3.91827i	−0.548847	−	0.141944i
$763$	30.9172	−	42.7704i	1.11928	−	1.54839i
$764$	8.94035	−	15.4851i	0.323451	−	0.560233i
$765$	−3.10091	−	1.71889i	−0.112113	−	0.0621468i
$766$	−9.07246			−0.327801
$767$	−85.3158	+	31.0524i	−3.08058	+	1.12124i
$768$	0.718277	−	1.57610i	0.0259186	−	0.0568725i
$769$	1.34579	+	7.63237i	0.0485305	+	0.275230i	0.999411	−	0.0343292i	$-0.0109295\pi$
$769$	1.34579	+	7.63237i	0.0485305	+	0.275230i	−0.950880	+	0.309560i	$0.899818\pi$
$770$	−16.6323	+	4.18953i	−0.599386	+	0.150980i
$771$	28.0388	+	39.3093i	1.00979	+	1.41569i
$772$	0.278012	−	1.57668i	0.0100059	−	0.0567461i
$773$	44.1719			1.58875			0.794377	−	0.607425i	$-0.207798\pi$
$773$	44.1719			1.58875			0.794377	+	0.607425i	$0.207798\pi$
$774$	−10.0982	−	5.59761i	−0.362971	−	0.201202i
$775$	1.63182			0.0586169
$776$	7.83284	−	2.85092i	0.281182	−	0.102342i
$777$	1.89385	+	1.60963i	0.0679414	+	0.0577451i
$778$	23.9971	−	20.1360i	0.860338	−	0.721909i
$779$	−3.50688	−	19.8885i	−0.125647	−	0.712580i
$780$	20.8609	−	9.95003i	0.746940	−	0.356268i
$781$	6.64662	+	5.57717i	0.237835	+	0.199567i
$782$	0.148208	+	0.256703i	0.00529990	+	0.00917969i
$783$	−6.07655	−	2.64225i	−0.217158	−	0.0944263i
$784$	2.59091	−	6.50286i	0.0925325	−	0.232245i
$785$	4.77381	−	27.0736i	0.170385	−	0.966299i
$786$	21.7401	−	10.3694i	0.775443	−	0.369863i
$787$	−22.5876	+	18.9533i	−0.805161	+	0.675611i	−0.949448	−	0.313925i	$-0.898356\pi$
$787$	−22.5876	+	18.9533i	−0.805161	+	0.675611i	0.144286	+	0.989536i	$0.453911\pi$
$788$	−3.29959	−	18.7129i	−0.117543	−	0.666619i
$789$	20.5286	+	5.30914i	0.730837	+	0.189011i
$790$	−13.2143	+	4.80961i	−0.470143	+	0.171118i
$791$	15.7980	−	10.7114i	0.561713	−	0.380854i
$792$	−3.19949	+	9.29175i	−0.113689	+	0.330168i
$793$	−24.7756	+	42.9125i	−0.879806	+	1.52387i
$794$	−3.61289	+	1.31498i	−0.128217	+	0.0466670i
$795$	20.2872	+	28.4419i	0.719514	+	1.00873i
$796$	−6.37684	+	5.35080i	−0.226021	+	0.189654i
$797$	−1.33276	−	7.55843i	−0.0472086	−	0.267733i	0.952063	−	0.305903i	$-0.0989584\pi$
$797$	−1.33276	−	7.55843i	−0.0472086	−	0.267733i	−0.999271	+	0.0381697i	$0.987847\pi$
$798$	6.38128	+	37.5771i	0.225895	+	1.33021i
$799$	0.415420	+	0.348579i	0.0146965	+	0.0123318i
$800$	0.541706	−	0.938262i	0.0191522	−	0.0331726i
$801$	−51.1533	−	8.10234i	−1.80741	−	0.286282i
$802$	−4.80863	−	8.32879i	−0.169799	−	0.294100i
$803$	−3.39213	−	2.84633i	−0.119706	−	0.100445i
$804$	1.26210	+	4.55107i	0.0445109	+	0.160504i
$805$	0.710356	−	2.50005i	0.0250368	−	0.0881151i
$806$	9.54322	+	3.47345i	0.336146	+	0.122347i
$807$	33.2309	+	22.8392i	1.16978	+	0.803977i
$808$	12.9695	+	10.8827i	0.456265	+	0.382852i
$809$	−1.28247	+	2.22131i	−0.0450893	+	0.0780970i	−0.887689	−	0.460443i	$-0.847691\pi$
$809$	−1.28247	+	2.22131i	−0.0450893	+	0.0780970i	0.842600	+	0.538540i	$0.181024\pi$
$810$	16.9395	+	5.50430i	0.595193	+	0.193401i
$811$	−30.9165			−1.08563			−0.542813	−	0.839853i	$-0.682641\pi$
$811$	−30.9165			−1.08563			−0.542813	+	0.839853i	$0.682641\pi$
$812$	−1.37971	−	3.07887i	−0.0484182	−	0.108047i
$813$	−31.4996	+	15.0244i	−1.10474	+	0.526928i
$814$	−0.308515	−	1.74968i	−0.0108134	−	0.0613261i
$815$	4.47903	+	25.4019i	0.156894	+	0.889788i
$816$	−1.00138	−	0.258978i	−0.0350552	−	0.00906606i
$817$	24.5213	+	20.5758i	0.857893	+	0.719858i
$818$	2.47033	−	4.27874i	0.0863732	−	0.149603i
$819$	4.53626	−	53.3254i	0.158510	−	1.86334i
$820$	−2.40264	−	4.16149i	−0.0839037	−	0.145325i
$821$	4.72531	−	26.7986i	0.164915	−	0.935277i	−0.784238	−	0.620460i	$-0.786946\pi$
$821$	4.72531	−	26.7986i	0.164915	−	0.935277i	0.949152	−	0.314817i	$-0.101943\pi$
$822$	8.03984	−	17.6416i	0.280422	−	0.615322i
$823$	26.4584	+	9.63006i	0.922281	+	0.335683i	0.759146	−	0.650921i	$-0.225617\pi$
$823$	26.4584	+	9.63006i	0.922281	+	0.335683i	0.163136	+	0.986604i	$0.447839\pi$
$824$	−12.1191	+	10.1691i	−0.422189	+	0.354259i
$825$	−2.54913	+	5.59350i	−0.0887494	+	0.194741i
$826$	−14.5687	−	32.5107i	−0.506911	−	1.13119i
$827$	20.5074	+	35.5199i	0.713112	+	1.23515i	0.963683	+	0.267048i	$0.0860483\pi$
$827$	20.5074	+	35.5199i	0.713112	+	1.23515i	−0.250571	+	0.968098i	$0.580618\pi$
$828$	−0.976933	−	1.12385i	−0.0339508	−	0.0390566i
$829$	−0.820089	−	1.42044i	−0.0284829	−	0.0493338i	0.851433	−	0.524464i	$-0.175734\pi$
$829$	−0.820089	−	1.42044i	−0.0284829	−	0.0493338i	−0.879915	+	0.475130i	$0.842401\pi$
$830$	−2.59828	+	14.7356i	−0.0901876	+	0.511479i
$831$	−17.1675	−	4.43990i	−0.595534	−	0.154018i
$832$	5.16515	−	4.33408i	0.179070	−	0.150257i
$833$	−4.09297	−	0.849373i	−0.141813	−	0.0294290i
$834$	0.708073	−	8.99642i	0.0245185	−	0.311521i
$835$	42.3496	−	15.4140i	1.46557	−	0.533423i
$836$	13.6227	−	23.5953i	0.471152	−	0.816059i
$837$	3.49203	+	7.00416i	0.120702	+	0.242099i
$838$	−12.7057	−	22.0069i	−0.438912	−	0.760217i
$839$	−4.26667	+	24.1975i	−0.147302	+	0.835389i	0.818188	+	0.574950i	$0.194979\pi$
$839$	−4.26667	+	24.1975i	−0.147302	+	0.835389i	−0.965490	+	0.260439i	$0.916133\pi$
$840$	4.48482	+	7.88256i	0.154741	+	0.271974i
$841$	25.7230	+	9.36241i	0.887000	+	0.322842i
$842$	−13.9649	−	5.08280i	−0.481261	−	0.175165i
$843$	−22.1575	+	22.5475i	−0.763146	+	0.776576i
$844$	0.815221	−	4.62335i	0.0280611	−	0.159142i
$845$	64.2456			2.21012
$846$	−2.38274	−	1.32080i	−0.0819202	−	0.0454100i
$847$	−0.590459	+	0.400345i	−0.0202884	+	0.0137560i
$848$	7.80748	+	6.55125i	0.268110	+	0.224971i
$849$	5.58477	−	12.2545i	0.191669	−	0.420574i
$850$	−0.607961	−	0.221280i	−0.0208529	−	0.00758983i
$851$	0.252982	+	0.0920778i	0.00867210	+	0.00315639i
$852$	1.90253	−	4.17467i	0.0651795	−	0.143022i
$853$	−34.2916	−	28.7741i	−1.17412	−	0.985205i	−1.00000		0.000481297i	$-0.999847\pi$
$853$	−34.2916	−	28.7741i	−1.17412	−	0.985205i	−0.174122	−	0.984724i	$-0.555709\pi$
$854$	−17.4962	−	8.48127i	−0.598706	−	0.290223i
$855$	−43.1896	−	23.9409i	−1.47705	−	0.818761i
$856$	−2.89355			−0.0988994
$857$	7.36323	−	41.7590i	0.251523	−	1.42646i	−0.553318	−	0.832970i	$-0.686639\pi$
$857$	7.36323	−	41.7590i	0.251523	−	1.42646i	0.804842	−	0.593490i	$-0.202250\pi$
$858$	−26.8140	+	27.2859i	−0.915414	+	0.931524i
$859$	25.0936	+	9.13332i	0.856182	+	0.311625i	0.732558	−	0.680704i	$-0.238326\pi$
$859$	25.0936	+	9.13332i	0.856182	+	0.311625i	0.123624	+	0.992329i	$0.460548\pi$
$860$	7.15720	+	2.60501i	0.244059	+	0.0888300i
$861$	−11.1267	−	0.0703115i	−0.379196	−	0.00239621i
$862$	1.70128	−	9.64846i	0.0579459	−	0.328628i
$863$	−19.2799	−	33.3937i	−0.656294	−	1.13673i	−0.981568	−	0.191115i	$-0.938790\pi$
$863$	−19.2799	−	33.3937i	−0.656294	−	1.13673i	0.325274	−	0.945620i	$-0.394544\pi$
$864$	5.18646	+	0.317284i	0.176447	+	0.0107942i
$865$	−13.9686	+	24.1942i	−0.474945	+	0.822629i
$866$	−25.7118	+	9.35831i	−0.873721	+	0.318008i
$867$	2.26188	−	28.7383i	0.0768174	−	0.976005i
$868$	−1.08917	+	3.83327i	−0.0369690	+	0.130110i
$869$	17.8306	−	14.9616i	0.604861	−	0.507538i
$870$	4.23190	+	1.09446i	0.143475	+	0.0371058i
$871$	−3.19258	+	18.1060i	−0.108176	+	0.613498i
$872$	9.97350	+	17.2746i	0.337745	+	0.584992i
$873$	16.4056	+	18.8729i	0.555247	+	0.638749i
$874$	2.06425	+	3.57538i	0.0698242	+	0.120939i
$875$	13.0259	+	29.0678i	0.440357	+	0.982672i
$876$	−0.970963	+	2.13056i	−0.0328058	+	0.0719849i
$877$	−11.1457	+	9.35234i	−0.376363	+	0.315806i	−0.811273	−	0.584668i	$-0.801225\pi$
$877$	−11.1457	+	9.35234i	−0.376363	+	0.315806i	0.434910	+	0.900474i	$0.356780\pi$
$878$	30.3984	+	11.0641i	1.02590	+	0.373396i
$879$	12.1400	−	26.6384i	0.409470	−	0.898491i
$880$	1.12572	−	6.38429i	0.0379481	−	0.215214i
$881$	0.548666	+	0.950317i	0.0184850	+	0.0320170i	0.875120	−	0.483906i	$-0.160782\pi$
$881$	0.548666	+	0.950317i	0.0184850	+	0.0320170i	−0.856635	+	0.515923i	$0.827449\pi$
$882$	20.9983	+	0.265395i	0.707050	+	0.00893632i
$883$	5.25393	−	9.10007i	0.176809	−	0.306242i	−0.763977	−	0.645244i	$-0.776756\pi$
$883$	5.25393	−	9.10007i	0.176809	−	0.306242i	0.940786	+	0.339002i	$0.110089\pi$
$884$	−3.08446	−	2.58817i	−0.103742	−	0.0870496i
$885$	44.6859	+	11.5568i	1.50210	+	0.388476i
$886$	5.30279	+	30.0736i	0.178151	+	1.01034i
$887$	−3.68967	−	20.9252i	−0.123887	−	0.702598i	−0.981963	−	0.189075i	$-0.939451\pi$
$887$	−3.68967	−	20.9252i	−0.123887	−	0.702598i	0.858076	−	0.513523i	$-0.171660\pi$
$888$	−0.847907	+	0.404427i	−0.0284539	+	0.0135717i
$889$	14.0039	−	19.3728i	0.469676	−	0.649744i
$890$	34.1654			1.14523
$891$	−29.4636	+	1.02838i	−0.987067	+	0.0344522i
$892$	0.778536	−	1.34846i	0.0260673	−	0.0451499i
$893$	5.78600	+	4.85503i	0.193621	+	0.162467i
$894$	16.4960	+	11.3375i	0.551708	+	0.379182i
$895$	−0.0298649	−	0.0108699i	−0.000998275	−	0.000363342i
$896$	1.84248	+	1.89876i	0.0615529	+	0.0634330i
$897$	−1.54913	−	5.58606i	−0.0517238	−	0.186513i
$898$	8.84221	+	7.41949i	0.295068	+	0.247592i
$899$	0.960350	+	1.66337i	0.0320295	+	0.0554767i
$900$	3.21022	+	0.508476i	0.107007	+	0.0169492i
$901$	3.04315	−	5.27089i	0.101382	−	0.175599i
$902$	6.09292	+	5.11257i	0.202872	+	0.170230i
$903$	13.5817	−	11.2509i	0.451972	−	0.374408i
$904$	1.25273	+	7.10459i	0.0416652	+	0.236295i
$905$	5.98876	−	5.02516i	0.199073	−	0.167042i
$906$	16.5879	+	23.2556i	0.551097	+	0.772616i
$907$	48.9447	−	17.8144i	1.62518	−	0.591518i	0.640822	−	0.767689i	$-0.278594\pi$
$907$	48.9447	−	17.8144i	1.62518	−	0.591518i	0.984360	+	0.176171i	$0.0563713\pi$
$908$	−2.24080	+	3.88118i	−0.0743636	+	0.128802i
$909$	−16.5365	+	48.0241i	−0.548480	+	1.59286i
$910$	2.54766	+	35.2126i	0.0844543	+	1.16729i
$911$	16.4653	−	5.99289i	0.545521	−	0.198553i	−0.0545343	−	0.998512i	$-0.517367\pi$
$911$	16.4653	−	5.99289i	0.545521	−	0.198553i	0.600055	+	0.799958i	$0.295145\pi$
$912$	−13.9472	−	3.60707i	−0.461840	−	0.119442i
$913$	−4.30070	−	24.3905i	−0.142332	−	0.807207i
$914$	−9.68142	+	8.12368i	−0.320233	+	0.268707i
$915$	22.7367	−	10.8447i	0.751653	−	0.358516i
$916$	−3.19775	+	18.1353i	−0.105657	+	0.599209i
$917$	2.65504	+	36.6967i	0.0876770	+	1.21183i
$918$	−0.351227	−	3.08303i	−0.0115922	−	0.101755i
$919$	6.90514	+	11.9601i	0.227780	+	0.394526i	0.957150	−	0.289593i	$-0.0935201\pi$
$919$	6.90514	+	11.9601i	0.227780	+	0.394526i	−0.729370	+	0.684119i	$0.760187\pi$
$920$	0.752511	+	0.631431i	0.0248095	+	0.0208177i
$921$	31.0238	−	14.7974i	1.02227	−	0.487591i
$922$	−3.47332	−	19.6982i	−0.114388	−	0.648724i
$923$	13.6812	−	11.4799i	0.450321	−	0.377864i
$924$	−11.4381	−	9.72152i	−0.376285	−	0.319814i
$925$	−0.552177	+	0.200976i	−0.0181555	+	0.00660805i
$926$	−12.8133			−0.421072
$927$	−41.5102	−	23.0100i	−1.36338	−	0.755747i
$928$	1.27520			0.0418606
$929$	−6.66894	+	37.8215i	−0.218801	+	1.24088i	0.655387	+	0.755293i	$0.272506\pi$
$929$	−6.66894	+	37.8215i	−0.218801	+	1.24088i	−0.874188	+	0.485588i	$0.838605\pi$
$930$	−2.99810	−	4.20322i	−0.0983115	−	0.137829i
$931$	−57.0071	−	11.8301i	−1.86833	−	0.387717i
$932$	1.80823	+	10.2550i	0.0592305	+	0.335913i
$933$	16.5675	−	36.3537i	0.542397	−	1.19017i
$934$	26.0786	−	9.49185i	0.853319	−	0.310583i
$935$	−3.87130			−0.126605
$936$	17.6916	+	9.80683i	0.578269	+	0.320546i
$937$	−11.1865	+	19.3756i	−0.365447	+	0.632973i	−0.988848	−	0.148930i	$-0.952417\pi$
$937$	−11.1865	+	19.3756i	−0.365447	+	0.632973i	0.623401	+	0.781902i	$0.285750\pi$
$938$	−7.17652	−	0.736787i	−0.234322	−	0.0240570i
$939$	12.9923	+	3.36011i	0.423989	+	0.109653i
$940$	1.68880	+	0.614672i	0.0550825	+	0.0200484i
$941$	−28.5392	+	23.9473i	−0.930352	+	0.780658i	−0.975881	−	0.218305i	$-0.929947\pi$
$941$	−28.5392	+	23.9473i	−0.930352	+	0.780658i	0.0455284	+	0.998963i	$0.485503\pi$
$942$	21.7165	−	10.3581i	0.707563	−	0.337487i
$943$	−1.13254	+	0.412212i	−0.0368807	+	0.0134235i
$944$	13.4653			0.438257
$945$	−17.2555	+	21.0352i	−0.561323	+	0.684277i
$946$	−12.6070			−0.409888
$947$	30.1269	−	10.9653i	0.978992	−	0.356324i	0.197544	−	0.980294i	$-0.436704\pi$
$947$	30.1269	−	10.9653i	0.978992	−	0.356324i	0.781448	+	0.623970i	$0.214481\pi$
$948$	−10.1428	−	6.97101i	−0.329422	−	0.226408i
$949$	−6.98223	+	5.85879i	−0.226653	+	0.190184i
$950$	−8.46771	−	3.08200i	−0.274729	−	0.0999932i
$951$	−34.0081	+	34.6066i	−1.10279	+	1.12220i
$952$	0.925590	−	1.28045i	0.0299985	−	0.0414996i
$953$	−9.41490	+	16.3071i	−0.304979	+	0.528238i	−0.977257	−	0.212060i	$-0.931983\pi$
$953$	−9.41490	+	16.3071i	−0.304979	+	0.528238i	0.672278	+	0.740299i	$0.265316\pi$
$954$	−9.95476	+	28.9099i	−0.322297	+	0.935993i
$955$	−35.3866			−1.14508
$956$	−9.03426	+	3.28820i	−0.292189	+	0.106348i
$957$	−7.20184	+	0.693427i	−0.232802	+	0.0224153i
$958$	−2.47993	−	14.0644i	−0.0801228	−	0.454399i
$959$	20.6233	+	21.2532i	0.665961	+	0.686302i
$960$	−3.41201	+	0.328525i	−0.110122	+	0.0106031i
$961$	−4.98915	+	28.2949i	−0.160940	+	0.912739i
$962$	−3.65703			−0.117907
$963$	−3.11079	−	8.10411i	−0.100244	−	0.261151i
$964$	28.5557			0.919717
$965$	−2.97737	+	1.08367i	−0.0958449	+	0.0348847i
$966$	2.14234	−	0.764453i	0.0689288	−	0.0245959i
$967$	−3.87252	+	3.24943i	−0.124532	+	0.104495i	−0.702927	−	0.711262i	$-0.748124\pi$
$967$	−3.87252	+	3.24943i	−0.124532	+	0.104495i	0.578395	+	0.815757i	$0.303679\pi$
$968$	−0.0468215	−	0.265538i	−0.00150490	−	0.00853471i
$969$	−0.675010	+	8.57635i	−0.0216845	+	0.275512i
$970$	−12.6369	−	10.6036i	−0.405747	−	0.340462i
$971$	14.7914	+	25.6194i	0.474677	+	0.822165i	0.999579	−	0.0289974i	$-0.00923145\pi$
$971$	14.7914	+	25.6194i	0.474677	+	0.822165i	−0.524902	+	0.851163i	$0.675898\pi$
$972$	4.68722	+	14.8671i	0.150343	+	0.476862i
$973$	12.4042	+	6.01294i	0.397660	+	0.192766i
$974$	6.54622	−	37.1255i	0.209754	−	1.18958i
$975$	10.4274	+	7.16662i	0.333944	+	0.229515i
$976$	5.62961	−	4.72380i	0.180199	−	0.151205i
$977$	−4.27891	−	24.2669i	−0.136894	−	0.776367i	−0.973522	−	0.228594i	$-0.926587\pi$
$977$	−4.27891	−	24.2669i	−0.136894	−	0.776367i	0.836627	−	0.547772i	$-0.184524\pi$
$978$	−15.8228	+	16.1013i	−0.505958	+	0.514863i
$979$	−53.1406	+	19.3416i	−1.69838	+	0.618160i
$980$	−13.7090	+	1.99415i	−0.437917	+	0.0637008i
$981$	−37.6596	+	46.5049i	−1.20238	+	1.48479i
$982$	6.10416	−	10.5727i	0.194792	−	0.337389i
$983$	44.7193	−	16.2765i	1.42633	−	0.519140i	0.490449	−	0.871470i	$-0.336833\pi$
$983$	44.7193	−	16.2765i	1.42633	−	0.519140i	0.935876	+	0.352330i	$0.114610\pi$
$984$	1.74404	−	3.82690i	0.0555979	−	0.121997i
$985$	−28.8070	+	24.1719i	−0.917866	+	0.770181i
$986$	−0.132235	−	0.749941i	−0.00421122	−	0.0238830i
$987$	3.20471	−	2.65475i	0.102007	−	0.0845015i
$988$	−42.9606	−	36.0482i	−1.36676	−	1.14685i
$989$	0.955165	−	1.65439i	0.0303725	−	0.0526067i
$990$	19.0910	−	3.71075i	0.606753	−	0.117936i
$991$	−13.6708	−	23.6786i	−0.434268	−	0.752174i	0.562968	−	0.826479i	$-0.309660\pi$
$991$	−13.6708	−	23.6786i	−0.434268	−	0.752174i	−0.997236	+	0.0743049i	$0.976326\pi$
$992$	−1.15381	−	0.968161i	−0.0366335	−	0.0307391i
$993$	−12.3811	+	12.5990i	−0.392903	+	0.399817i
$994$	4.88025	+	5.02931i	0.154792	+	0.159520i
$995$	15.4807	+	5.63452i	0.490772	+	0.178626i
$996$	−11.8198	+	5.63771i	−0.374526	+	0.178638i
$997$	10.5639	+	8.86412i	0.334561	+	0.280730i	0.794555	−	0.607192i	$-0.207704\pi$
$997$	10.5639	+	8.86412i	0.334561	+	0.280730i	−0.459995	+	0.887922i	$0.652149\pi$
$998$	−2.28434	+	3.95660i	−0.0723097	+	0.125244i
$999$	−2.04427	−	1.93999i	−0.0646777	−	0.0613784i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.w.a.25.7	yes	72
7.2	even	3		378.2.v.b.79.3	yes	72
27.13	even	9		378.2.v.b.67.3	✓	72
189.121	even	9	inner	378.2.w.a.121.7	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.v.b.67.3	✓	72	27.13	even	9
378.2.v.b.79.3	yes	72	7.2	even	3
378.2.w.a.25.7	yes	72	1.1	even	1	trivial
378.2.w.a.121.7	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)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{2} +(-0.135903 + 1.72671i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-1.85969 - 0.676871i) q^{5} +(-0.462863 - 1.66906i) q^{6} +(2.63192 + 0.270209i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.96306 - 0.469329i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 0.342020i) q^{2} +(-0.135903 + 1.72671i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-1.85969 - 0.676871i) q^{5} +(-0.462863 - 1.66906i) q^{6} +(2.63192 + 0.270209i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.96306 - 0.469329i) q^{9} +1.97904 q^{10} +(-3.07817 + 1.12036i) q^{11} +(1.00580 + 1.41009i) q^{12} +(1.17085 + 6.64020i) q^{13} +(-2.56561 + 0.646255i) q^{14} +(1.42150 - 3.11915i) q^{15} +(0.173648 - 0.984808i) q^{16} -0.597167 q^{17} +(2.94489 - 0.572402i) q^{18} -8.31739 q^{19} +(-1.85969 + 0.676871i) q^{20} +(-0.824258 + 4.50784i) q^{21} +(2.50935 - 2.10559i) q^{22} +(0.0861936 + 0.488828i) q^{23} +(-1.42742 - 0.981051i) q^{24} +(-0.829942 - 0.696404i) q^{25} +(-3.37132 - 5.83929i) q^{26} +(1.21308 - 5.05257i) q^{27} +(2.18985 - 1.48477i) q^{28} +(0.221437 - 1.25583i) q^{29} +(-0.268956 + 3.41723i) q^{30} +(-1.15381 + 0.968161i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-1.51621 - 5.46738i) q^{33} +(0.561154 - 0.204243i) q^{34} +(-4.71164 - 2.28397i) q^{35} +(-2.57152 + 1.54509i) q^{36} +(0.271187 - 0.469709i) q^{37} +(7.81579 - 2.84471i) q^{38} +(-11.6248 + 1.11929i) q^{39} +(1.51603 - 1.27210i) q^{40} +(0.421633 + 2.39120i) q^{41} +(-0.767222 - 4.51789i) q^{42} +(-2.94820 - 2.47384i) q^{43} +(-1.63786 + 2.83686i) q^{44} +(5.19269 + 2.87841i) q^{45} +(-0.248185 - 0.429868i) q^{46} +(-0.695651 - 0.583721i) q^{47} +(1.67688 + 0.433678i) q^{48} +(6.85397 + 1.42234i) q^{49} +(1.01807 + 0.370549i) q^{50} +(0.0811566 - 1.03114i) q^{51} +(5.16515 + 4.33408i) q^{52} +(-5.09597 + 8.82648i) q^{53} +(0.588155 + 5.16276i) q^{54} +6.48278 q^{55} +(-1.54997 + 2.14420i) q^{56} +(1.13035 - 14.3617i) q^{57} +(0.221437 + 1.25583i) q^{58} +(2.33822 + 13.2607i) q^{59} +(-0.916024 - 3.30313i) q^{60} +(5.62961 + 4.72380i) q^{61} +(0.753095 - 1.30440i) q^{62} +(-7.67171 - 2.03588i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(2.31715 - 13.1412i) q^{65} +(3.29473 + 4.61908i) q^{66} +(2.56229 + 0.932596i) q^{67} +(-0.457457 + 0.383852i) q^{68} +(-0.855779 + 0.0823984i) q^{69} +(5.20866 + 0.534754i) q^{70} +(-1.32437 - 2.29388i) q^{71} +(1.88798 - 2.33142i) q^{72} +(0.675897 + 1.17069i) q^{73} +(-0.0941822 + 0.534134i) q^{74} +(1.31528 - 1.33843i) q^{75} +(-6.37149 + 5.34631i) q^{76} +(-8.40423 + 2.11695i) q^{77} +(10.5409 - 5.02771i) q^{78} +(-6.67713 + 2.43028i) q^{79} +(-0.989519 + 1.71390i) q^{80} +(8.55946 + 2.78130i) q^{81} +(-1.21404 - 2.10278i) q^{82} +(-1.31290 + 7.44583i) q^{83} +(2.26616 + 3.98303i) q^{84} +(1.11054 + 0.404205i) q^{85} +(3.61651 + 1.31630i) q^{86} +(2.13836 + 0.553028i) q^{87} +(0.568823 - 3.22596i) q^{88} +17.2637 q^{89} +(-5.86401 - 0.928819i) q^{90} +(1.28733 + 17.7928i) q^{91} +(0.380241 + 0.319060i) q^{92} +(-1.51493 - 2.12387i) q^{93} +(0.853342 + 0.310591i) q^{94} +(15.4677 + 5.62979i) q^{95} +(-1.72408 + 0.166002i) q^{96} +(-6.38539 - 5.35798i) q^{97} +(-6.92710 + 1.00764i) q^{98} +(9.64663 - 1.87503i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} - 3 q^{7} - 36 q^{8} - 12 q^{9}+O(q^{10}) \) 72 * q + 3 * q^6 - 3 * q^7 - 36 * q^8 - 12 * q^9	\( 72 q + 3 q^{6} - 3 q^{7} - 36 q^{8} - 12 q^{9} + 12 q^{10} - 6 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} + 24 q^{17} + 36 q^{19} - 12 q^{21} - 6 q^{22} + 12 q^{23} - 30 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} + 9 q^{35} + 9 q^{36} + 3 q^{39} - 6 q^{41} + 3 q^{42} + 24 q^{43} - 30 q^{45} - 9 q^{47} - 6 q^{48} + 51 q^{49} + 6 q^{50} + 12 q^{51} + 6 q^{52} - 15 q^{53} - 27 q^{54} + 72 q^{55} + 6 q^{56} - 63 q^{57} + 3 q^{58} + 15 q^{59} - 3 q^{60} - 18 q^{61} - 24 q^{62} - 48 q^{63} - 36 q^{64} - 18 q^{65} - 36 q^{66} + 66 q^{67} - 18 q^{68} - 21 q^{69} - 6 q^{70} + 12 q^{71} - 12 q^{72} - 66 q^{73} + 9 q^{74} + 15 q^{75} - 15 q^{77} + 30 q^{78} + 9 q^{79} - 6 q^{80} - 33 q^{82} - 18 q^{83} - 12 q^{84} + 21 q^{85} - 12 q^{86} - 48 q^{87} + 12 q^{88} + 72 q^{89} + 69 q^{90} + 12 q^{91} + 30 q^{92} + 60 q^{93} - 36 q^{94} + 93 q^{95} - 48 q^{97} + 6 q^{98} - 54 q^{99}+O(q^{100}) \) 72 * q + 3 * q^6 - 3 * q^7 - 36 * q^8 - 12 * q^9 + 12 * q^10 - 6 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^15 + 24 * q^17 + 36 * q^19 - 12 * q^21 - 6 * q^22 + 12 * q^23 - 30 * q^25 - 18 * q^26 - 6 * q^27 + 3 * q^29 + 3 * q^30 + 9 * q^31 - 18 * q^33 + 9 * q^34 + 9 * q^35 + 9 * q^36 + 3 * q^39 - 6 * q^41 + 3 * q^42 + 24 * q^43 - 30 * q^45 - 9 * q^47 - 6 * q^48 + 51 * q^49 + 6 * q^50 + 12 * q^51 + 6 * q^52 - 15 * q^53 - 27 * q^54 + 72 * q^55 + 6 * q^56 - 63 * q^57 + 3 * q^58 + 15 * q^59 - 3 * q^60 - 18 * q^61 - 24 * q^62 - 48 * q^63 - 36 * q^64 - 18 * q^65 - 36 * q^66 + 66 * q^67 - 18 * q^68 - 21 * q^69 - 6 * q^70 + 12 * q^71 - 12 * q^72 - 66 * q^73 + 9 * q^74 + 15 * q^75 - 15 * q^77 + 30 * q^78 + 9 * q^79 - 6 * q^80 - 33 * q^82 - 18 * q^83 - 12 * q^84 + 21 * q^85 - 12 * q^86 - 48 * q^87 + 12 * q^88 + 72 * q^89 + 69 * q^90 + 12 * q^91 + 30 * q^92 + 60 * q^93 - 36 * q^94 + 93 * q^95 - 48 * q^97 + 6 * q^98 - 54 * q^99

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