LMFDB - Embedded newform 378.2.w.a.121.7

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			121.7
Character	$\chi$	$=$	378.121
Dual form			378.2.w.a.25.7

$q$-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 $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.939693	−	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	−0.722547	−	0.691322i	$-0.757029\pi$
$5$	−1.85969	+	0.676871i	−0.831677	+	0.302706i	−0.109130	+	0.994027i	$0.534807\pi$
$6$	−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	−0.166646	−	0.986017i	$-0.553294\pi$
$11$	−3.07817	−	1.12036i	−0.928104	−	0.337802i	−0.761458	+	0.648214i	$0.775516\pi$
$12$	1.00580	−	1.41009i	0.290350	−	0.407059i
$13$	1.17085	−	6.64020i	0.324734	−	1.84166i	−0.186803	−	0.982397i	$-0.559813\pi$
$13$	1.17085	−	6.64020i	0.324734	−	1.84166i	0.511537	−	0.859261i	$-0.329076\pi$
$14$	−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	−0.974502	−	0.224379i	$-0.927965\pi$
$23$	0.0861936	−	0.488828i	0.0179726	−	0.101928i	0.992474	+	0.122452i	$0.0390756\pi$
$24$	−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	0.998441	−	0.0558258i	$-0.0177792\pi$
$29$	0.221437	+	1.25583i	0.0411198	+	0.233202i	−0.957321	+	0.289028i	$0.906668\pi$
$30$	−0.268956	−	3.41723i	−0.0491045	−	0.623897i
$31$	−1.15381	−	0.968161i	−0.207230	−	0.173887i	0.533265	−	0.845948i	$-0.320965\pi$
$31$	−1.15381	−	0.968161i	−0.207230	−	0.173887i	−0.740496	+	0.672061i	$0.765409\pi$
$32$	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	0.887456	−	0.460893i	$-0.152471\pi$
$37$	0.271187	+	0.469709i	0.0445828	+	0.0772198i	−0.842873	+	0.538113i	$0.819137\pi$
$38$	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	−0.934020	−	0.357220i	$-0.883725\pi$
$41$	0.421633	−	2.39120i	0.0658480	−	0.373442i	0.999868	−	0.0162228i	$-0.00516412\pi$
$42$	−0.767222	+	4.51789i	−0.118385	+	0.697126i
$43$	−2.94820	+	2.47384i	−0.449597	+	0.377256i	−0.839286	−	0.543690i	$-0.817027\pi$
$43$	−2.94820	+	2.47384i	−0.449597	+	0.377256i	0.389689	+	0.920946i	$0.372582\pi$
$44$	−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	−0.692112	−	0.721790i	$-0.743320\pi$
$47$	−0.695651	+	0.583721i	−0.101471	+	0.0851444i	0.590641	+	0.806935i	$0.298875\pi$
$48$	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	−0.968471	−	0.249127i	$-0.919856\pi$
$53$	−5.09597	−	8.82648i	−0.699985	−	1.21241i	0.268486	−	0.963284i	$-0.413477\pi$
$54$	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	−0.321859	−	0.946787i	$-0.604308\pi$
$59$	2.33822	−	13.2607i	0.304410	−	1.72639i	0.626269	−	0.779607i	$-0.284581\pi$
$60$	−0.916024	+	3.30313i	−0.118258	+	0.426432i
$61$	5.62961	−	4.72380i	0.720797	−	0.604821i	−0.206808	−	0.978381i	$-0.566308\pi$
$61$	5.62961	−	4.72380i	0.720797	−	0.604821i	0.927606	+	0.373561i	$0.121863\pi$
$62$	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	−0.180726	−	0.983533i	$-0.557845\pi$
$67$	2.56229	−	0.932596i	0.313033	−	0.113935i	0.493759	+	0.869599i	$0.335622\pi$
$68$	−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	−0.933848	−	0.357669i	$-0.883572\pi$
$71$	−1.32437	+	2.29388i	−0.157174	+	0.272233i	0.776675	+	0.629902i	$0.216905\pi$
$72$	1.88798	+	2.33142i	0.222501	+	0.274761i
$73$	0.675897	−	1.17069i	0.0791078	−	0.137019i	−0.823757	−	0.566942i	$-0.808126\pi$
$73$	0.675897	−	1.17069i	0.0791078	−	0.137019i	0.902865	+	0.429924i	$0.141460\pi$
$74$	−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	−0.0621102	−	0.998069i	$-0.519783\pi$
$79$	−6.67713	−	2.43028i	−0.751236	−	0.273428i	−0.689126	+	0.724642i	$0.742005\pi$
$80$	−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	−0.968078	−	0.250650i	$-0.919356\pi$
$83$	−1.31290	−	7.44583i	−0.144110	−	0.817286i	0.823968	−	0.566636i	$-0.191755\pi$
$84$	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	−0.906566	−	0.422064i	$-0.861306\pi$
$97$	−6.38539	+	5.35798i	−0.648338	+	0.544020i	0.258228	+	0.966084i	$0.416861\pi$
$98$	−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	0.677054	+	0.735934i	$0.263256\pi$
$101$	2.93994	+	16.6733i	0.292535	+	1.65905i	−0.384518	+	0.923117i	$0.625632\pi$
$102$	0.276407	−	0.996708i	0.0273684	−	0.0986888i
$103$	14.8663	−	5.41089i	1.46482	−	0.533151i	0.518131	−	0.855301i	$-0.326628\pi$
$103$	14.8663	−	5.41089i	1.46482	−	0.533151i	0.946688	+	0.322151i	$0.104406\pi$
$104$	−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	−0.787580	−	0.616212i	$-0.788667\pi$
$107$	1.44677	−	2.50589i	0.139865	−	0.242253i	0.927445	+	0.373959i	$0.122000\pi$
$108$	−2.31845	+	4.65025i	−0.223093	+	0.447470i
$109$	9.97350	+	17.2746i	0.955288	+	1.65461i	0.733708	+	0.679465i	$0.237788\pi$
$109$	9.97350	+	17.2746i	0.955288	+	1.65461i	0.221580	+	0.975142i	$0.428878\pi$
$110$	−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	0.864590	−	0.502479i	$-0.167578\pi$
$113$	5.52639	+	4.63719i	0.519879	+	0.436230i	−0.344710	+	0.938709i	$0.612023\pi$
$114$	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	0.993830	−	0.110912i	$-0.0353772\pi$
$127$	4.51749	+	7.82452i	0.400862	+	0.694314i	−0.592968	+	0.805226i	$0.702044\pi$
$128$	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	−0.676762	−	0.736202i	$-0.736617\pi$
$131$	2.41480	−	13.6950i	0.210982	−	1.19654i	0.887744	−	0.460338i	$-0.152272\pi$
$132$	−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	−0.198261	−	0.980149i	$-0.563529\pi$
$137$	8.57451	−	7.19487i	0.732570	−	0.614699i	0.930831	+	0.365450i	$0.119085\pi$
$138$	0.775987	+	0.370123i	0.0660564	+	0.0315069i
$139$	4.89594	−	1.78198i	0.415268	−	0.151145i	−0.125932	−	0.992039i	$-0.540192\pi$
$139$	4.89594	−	1.78198i	0.415268	−	0.151145i	0.541200	+	0.840894i	$0.317970\pi$
$140$	−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	0.203585	−	0.979057i	$-0.434741\pi$
$149$	−8.85276	−	7.42835i	−0.725247	−	0.608554i	−0.928831	+	0.370503i	$0.879185\pi$
$150$	−0.778189	−	1.70756i	−0.0635389	−	0.139422i
$151$	−15.4977	−	5.64068i	−1.26118	−	0.459032i	−0.377016	−	0.926207i	$-0.623050\pi$
$151$	−15.4977	−	5.64068i	−1.26118	−	0.459032i	−0.884165	+	0.467175i	$0.845272\pi$
$152$	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	−0.723402	−	0.690427i	$-0.757423\pi$
$157$	2.41219	−	13.6802i	0.192514	−	1.09180i	0.915915	−	0.401371i	$-0.131466\pi$
$158$	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	0.489497	+	0.872005i	$0.337180\pi$
$163$	−6.51673	+	11.2873i	−0.510430	+	0.884091i	−0.999927	+	0.0120856i	$0.996153\pi$
$164$	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	−0.978959	−	0.204057i	$-0.934587\pi$
$167$	−17.4447	−	14.6378i	−1.34991	−	1.13271i	−0.370952	−	0.928652i	$-0.620968\pi$
$168$	−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	0.924183	+	0.381949i	$0.124747\pi$
$173$	2.45131	+	13.9021i	0.186369	+	1.05695i	−0.737814	+	0.675004i	$0.764142\pi$
$174$	−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	0.783236	−	0.621725i	$-0.213568\pi$
$181$	−1.97514	−	3.42105i	−0.146811	−	0.254285i	−0.930047	+	0.367440i	$0.880234\pi$
$182$	−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	0.868704	−	0.495332i	$-0.164954\pi$
$191$	16.8024	+	6.11556i	1.21578	+	0.442506i	0.347073	+	0.937838i	$0.387176\pi$
$192$	1.56333	+	0.745660i	0.112823	+	0.0538134i
$193$	1.22644	+	1.02911i	0.0882812	+	0.0740767i	0.685860	−	0.727733i	$-0.259426\pi$
$193$	1.22644	+	1.02911i	0.0882812	+	0.0740767i	−0.597579	+	0.801810i	$0.703871\pi$
$194$	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	0.975909	+	0.218179i	$0.0700118\pi$
$197$	9.50079	+	16.4558i	0.676903	+	1.17243i	−0.299006	+	0.954251i	$0.596655\pi$
$198$	−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	0.758130	−	0.652103i	$-0.226113\pi$
$211$	3.59633	+	3.01768i	0.247581	+	0.207745i	−0.510549	+	0.859849i	$0.670558\pi$
$212$	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	0.390546	−	0.920584i	$-0.372286\pi$
$223$	1.46317	+	0.532550i	0.0979810	+	0.0356622i	−0.292565	+	0.956246i	$0.594509\pi$
$224$	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	0.198458	−	0.980109i	$-0.436407\pi$
$227$	−4.21133	−	1.53280i	−0.279516	−	0.101735i	−0.477974	+	0.878374i	$0.658629\pi$
$228$	−8.36563	+	11.7283i	−0.554028	+	0.776725i
$229$	−14.1068	−	11.8370i	−0.932203	−	0.782212i	0.0440083	−	0.999031i	$-0.485987\pi$
$229$	−14.1068	−	11.8370i	−0.932203	−	0.782212i	−0.976212	+	0.216820i	$0.930432\pi$
$230$	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	0.643541	−	0.765411i	$-0.277464\pi$
$233$	−5.20659	−	9.01807i	−0.341095	−	0.590794i	−0.984636	+	0.174618i	$0.944131\pi$
$234$	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	−0.617255	−	0.786763i	$-0.711755\pi$
$239$	−9.03426	+	3.28820i	−0.584378	+	0.212696i	0.0328769	+	0.999459i	$0.489533\pi$
$240$	−2.82493	+	1.94154i	−0.182348	+	0.125326i
$241$	21.8749	−	18.3552i	1.40909	−	1.18236i	0.452196	−	0.891919i	$-0.350641\pi$
$241$	21.8749	−	18.3552i	1.40909	−	1.18236i	0.956891	−	0.290446i	$-0.0938037\pi$
$242$	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	0.723665	−	0.690152i	$-0.242456\pi$
$251$	−3.73667	−	6.47211i	−0.235857	−	0.408516i	−0.959521	+	0.281636i	$0.909123\pi$
$252$	−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	0.983583	+	0.180456i	$0.0577573\pi$
$257$	21.3551	+	17.9191i	1.33209	+	1.11776i	0.348512	+	0.937304i	$0.386687\pi$
$258$	−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	0.977507	+	0.210903i	$0.0676404\pi$
$263$	2.12582	+	12.0561i	0.131084	+	0.743414i	−0.846423	+	0.532511i	$0.821249\pi$
$264$	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	0.964963	+	0.262384i	$0.0845088\pi$
$269$	11.6402	+	20.1614i	0.709713	+	1.22926i	−0.255250	+	0.966875i	$0.582158\pi$
$270$	2.40074	+	9.99922i	0.146104	+	0.608533i
$271$	10.0745	−	17.4496i	0.611985	−	1.05999i	−0.378920	−	0.925429i	$-0.623705\pi$
$271$	10.0745	−	17.4496i	0.611985	−	1.05999i	0.990905	−	0.134560i	$-0.0429621\pi$
$272$	−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	−0.990479	−	0.137661i	$-0.956042\pi$
$277$	−1.77777	−	10.0822i	−0.106816	−	0.605783i	0.883664	−	0.468123i	$-0.155069\pi$
$278$	−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	−0.122158	−	0.992511i	$-0.538982\pi$
$281$	13.9814	−	11.7318i	0.834061	−	0.699860i	0.956220	+	0.292650i	$0.0945372\pi$
$282$	−0.652273	−	1.43127i	−0.0388423	−	0.0852306i
$283$	−7.30633	+	2.65929i	−0.434316	+	0.158078i	−0.549920	−	0.835217i	$-0.685342\pi$
$283$	−7.30633	+	2.65929i	−0.434316	+	0.158078i	0.115604	+	0.993295i	$0.463120\pi$
$284$	−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	−0.761357	−	0.648333i	$-0.775466\pi$
$293$	−15.8822	+	5.78065i	−0.927849	+	0.337709i	−0.166492	+	0.986043i	$0.553244\pi$
$294$	−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	0.430629	+	0.902529i	$0.358292\pi$
$307$	−9.92235	+	17.1860i	−0.566298	+	0.980858i	−0.996928	+	0.0783287i	$0.975042\pi$
$308$	−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	−0.873274	−	0.487229i	$-0.838008\pi$
$311$	−21.6746	+	7.88892i	−1.22906	+	0.447340i	−0.355782	+	0.934569i	$0.615785\pi$
$312$	4.84307	+	10.6270i	0.274185	+	0.601637i
$313$	1.34541	+	7.63022i	0.0760473	+	0.431286i	0.998932	+	0.0462089i	$0.0147140\pi$
$313$	1.34541	+	7.63022i	0.0760473	+	0.431286i	−0.922884	+	0.385077i	$0.874175\pi$
$314$	−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	0.205802	−	0.978594i	$-0.434020\pi$
$317$	21.4591	−	18.0064i	1.20527	−	1.01134i	0.999464	−	0.0327444i	$-0.0104247\pi$
$318$	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	−0.402317	−	0.915500i	$-0.631795\pi$
$331$	7.81248	−	6.55545i	0.429413	−	0.360320i	0.831730	+	0.555180i	$0.187351\pi$
$332$	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	−0.969130	−	0.246552i	$-0.920702\pi$
$337$	0.475096	−	2.69440i	0.0258801	−	0.146774i	0.995010	+	0.0997786i	$0.0318135\pi$
$338$	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	0.691440	−	0.722434i	$-0.256977\pi$
$347$	1.86371	+	1.56384i	0.100049	+	0.0839514i	−0.591391	+	0.806385i	$0.701421\pi$
$348$	1.99356	+	0.950869i	0.106866	+	0.0509719i
$349$	−0.745200	−	4.22624i	−0.0398896	−	0.226225i	0.958345	−	0.285612i	$-0.0921968\pi$
$349$	−0.745200	−	4.22624i	−0.0398896	−	0.226225i	−0.998235	+	0.0593863i	$0.981086\pi$
$350$	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	−0.967656	−	0.252273i	$-0.918822\pi$
$353$	−16.6699	+	13.9877i	−0.887247	+	0.744489i	0.0804088	+	0.996762i	$0.474377\pi$
$354$	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	−0.245966	−	0.969278i	$-0.579105\pi$
$367$	−20.2574	−	7.37309i	−1.05743	−	0.384872i	−0.811461	+	0.584406i	$0.801327\pi$
$368$	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	−0.363776	−	0.931486i	$-0.618513\pi$
$373$	−0.843931	+	0.307166i	−0.0436971	+	0.0159044i	0.320079	+	0.947391i	$0.396290\pi$
$374$	−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	−0.114894	−	0.993378i	$-0.536653\pi$
$383$	8.52532	−	3.10296i	0.435624	−	0.158554i	0.550517	+	0.834824i	$0.314431\pi$
$384$	−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	−0.538398	−	0.842691i	$-0.680970\pi$
$389$	−29.4368	−	10.7141i	−1.49251	−	0.543227i	−0.954108	+	0.299464i	$0.903192\pi$
$390$	−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	−0.914294	−	0.405051i	$-0.867254\pi$
$401$	1.67002	−	9.47115i	0.0833968	−	0.472967i	0.997691	−	0.0679161i	$-0.0216350\pi$
$402$	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	0.544402	−	0.838825i	$-0.316757\pi$
$409$	−3.78477	−	3.17580i	−0.187145	−	0.157033i	−0.731547	+	0.681791i	$0.761201\pi$
$410$	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	−0.664339	−	0.747431i	$-0.731287\pi$
$419$	4.41265	−	25.0254i	0.215572	−	1.22257i	0.879911	−	0.475138i	$-0.157602\pi$
$420$	−1.51836	+	8.94108i	−0.0740885	+	0.436280i
$421$	11.3843	−	9.55254i	0.554836	−	0.465562i	−0.321739	−	0.946828i	$-0.604267\pi$
$421$	11.3843	−	9.55254i	0.554836	−	0.465562i	0.876575	+	0.481266i	$0.159823\pi$
$422$	−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	0.723591	−	0.690228i	$-0.242490\pi$
$431$	−4.89865	−	8.48471i	−0.235960	−	0.408694i	−0.959551	+	0.281534i	$0.909157\pi$
$432$	−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	−0.182776	+	0.983155i	$0.558508\pi$
$439$	−24.7810	+	20.7937i	−1.18273	+	0.992431i	−0.999957	+	0.00927658i	$0.997047\pi$
$440$	−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	0.803799	+	0.594901i	$0.202809\pi$
$443$	5.30279	+	30.0736i	0.251943	+	1.42884i	−0.551856	+	0.833939i	$0.686080\pi$
$444$	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	−0.969467	−	0.245221i	$-0.921140\pi$
$449$	−5.77134	+	9.99626i	−0.272366	+	0.471753i	0.697101	+	0.716973i	$0.254473\pi$
$450$	−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	0.604505	−	0.796601i	$-0.293371\pi$
$457$	11.8760	+	4.32252i	0.555537	+	0.202199i	−0.0489679	+	0.998800i	$0.515593\pi$
$458$	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	−0.952334	−	0.305057i	$-0.901324\pi$
$461$	−3.47332	−	19.6982i	−0.161768	−	0.917434i	0.790566	−	0.612377i	$-0.209787\pi$
$462$	7.42333	−	13.0473i	0.345364	−	0.607015i
$463$	12.0406	−	4.38242i	0.559574	−	0.203668i	−0.0467212	−	0.998908i	$-0.514877\pi$
$463$	12.0406	−	4.38242i	0.559574	−	0.203668i	0.606295	+	0.795240i	$0.292655\pi$
$464$	−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	−0.987573	−	0.157163i	$-0.949765\pi$
$479$	−2.47993	−	14.0644i	−0.113311	−	0.642617i	0.874262	−	0.485454i	$-0.161346\pi$
$480$	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	−0.877446	−	0.479675i	$-0.840755\pi$
$487$	−18.8491	−	32.6476i	−0.854134	−	1.47940i	0.0233124	−	0.999728i	$-0.492579\pi$
$488$	−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	0.406889	−	0.913478i	$-0.366614\pi$
$491$	−9.35212	−	7.84736i	−0.422055	−	0.354146i	−0.828944	+	0.559331i	$0.811058\pi$
$492$	−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	0.717755	−	0.696296i	$-0.245170\pi$
$499$	3.49982	+	2.93670i	0.156673	+	0.131465i	−0.561081	+	0.827761i	$0.689614\pi$
$500$	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	−0.915359	−	0.402639i	$-0.868093\pi$
$503$	−2.44425	+	4.23357i	−0.108984	+	0.188766i	0.806375	+	0.591405i	$0.201426\pi$
$504$	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	−0.952145	−	0.305647i	$-0.901127\pi$
$509$	1.06298	−	6.02848i	0.0471159	−	0.267208i	0.999261	+	0.0384389i	$0.0122385\pi$
$510$	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	−0.990900	−	0.134602i	$-0.957025\pi$
$521$	−8.64813	+	14.9790i	−0.378881	+	0.656242i	0.612018	+	0.790844i	$0.290358\pi$
$522$	−0.0667333	+	3.82503i	−0.00292084	+	0.167417i
$523$	−17.0831	−	29.5888i	−0.746991	−	1.29383i	−0.949259	−	0.314497i	$-0.898164\pi$
$523$	−17.0831	−	29.5888i	−0.746991	−	1.29383i	0.202267	−	0.979330i	$-0.435169\pi$
$524$	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	−0.379948	−	0.925008i	$-0.624058\pi$
$541$	14.2140	−	24.6193i	0.611107	−	1.05847i	0.991054	−	0.133460i	$-0.0426087\pi$
$542$	−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	0.602599	−	0.798044i	$-0.294132\pi$
$547$	12.8925	+	4.69250i	0.551245	+	0.200637i	−0.0513547	+	0.998680i	$0.516354\pi$
$548$	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	0.963083	−	0.269205i	$-0.0867608\pi$
$563$	20.5293	+	17.2261i	0.865206	+	0.725994i	−0.0978771	+	0.995199i	$0.531205\pi$
$564$	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	0.291429	−	0.956593i	$-0.405869\pi$
$569$	−2.39038	−	0.870026i	−0.100210	−	0.0364734i	−0.391638	+	0.920119i	$0.628092\pi$
$570$	2.23701	+	28.4224i	0.0936981	+	1.19048i
$571$	16.4205	+	13.7784i	0.687174	+	0.576608i	0.918093	−	0.396365i	$-0.129729\pi$
$571$	16.4205	+	13.7784i	0.687174	+	0.576608i	−0.230918	+	0.972973i	$0.574173\pi$
$572$	−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	−0.627586	−	0.778547i	$-0.715957\pi$
$587$	−38.9778	−	14.1868i	−1.60879	−	0.585550i	−0.981199	+	0.192997i	$0.938179\pi$
$588$	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	−0.757958	−	0.652303i	$-0.773803\pi$
$593$	4.52774	−	7.84227i	0.185932	−	0.322043i	0.943890	+	0.330260i	$0.107136\pi$
$594$	−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	0.715645	+	0.698464i	$0.246133\pi$
$599$	−4.79039	+	27.1676i	−0.195730	+	1.11004i	−0.911375	+	0.411576i	$0.864978\pi$
$600$	0.501472	−	1.80828i	0.0204725	−	0.0738226i
$601$	−24.5814	−	8.94690i	−1.00270	−	0.364952i	−0.212073	−	0.977254i	$-0.568021\pi$
$601$	−24.5814	−	8.94690i	−1.00270	−	0.364952i	−0.790624	+	0.612302i	$0.790244\pi$
$602$	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	0.796507	−	0.604630i	$-0.206679\pi$
$607$	8.36130	+	7.01597i	0.339375	+	0.284769i	−0.457132	+	0.889399i	$0.651123\pi$
$608$	−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	−0.862141	−	0.506668i	$-0.830877\pi$
$613$	0.191047	−	0.330903i	0.00771630	−	0.0133650i	0.869858	+	0.493303i	$0.164210\pi$
$614$	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	0.237672	−	0.971345i	$-0.423616\pi$
$617$	25.9351	−	9.43961i	1.04411	−	0.380024i	0.806436	+	0.591321i	$0.201393\pi$
$618$	2.15003	+	27.3172i	0.0864869	+	1.09886i
$619$	5.47984	−	4.59813i	0.220253	−	0.184814i	−0.525984	−	0.850494i	$-0.676303\pi$
$619$	5.47984	−	4.59813i	0.220253	−	0.184814i	0.746237	+	0.665680i	$0.231858\pi$
$620$	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	−0.774609	−	0.632440i	$-0.782053\pi$
$631$	4.02933	−	6.97900i	0.160405	−	0.277830i	0.935014	+	0.354611i	$0.115387\pi$
$632$	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	0.976604	+	0.215045i	$0.0689899\pi$
$641$	3.35327	+	19.0173i	0.132446	+	0.751140i	−0.844158	+	0.536095i	$0.819899\pi$
$642$	3.51281	+	3.57463i	0.138640	+	0.141080i
$643$	25.5593	+	21.4468i	1.00796	+	0.845780i	0.988067	−	0.154022i	$-0.0492228\pi$
$643$	25.5593	+	21.4468i	1.00796	+	0.845780i	0.0198936	+	0.999802i	$0.493667\pi$
$644$	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	−0.999809	−	0.0195402i	$-0.993780\pi$
$647$	−13.1461	−	22.7697i	−0.516827	−	0.895170i	0.482982	−	0.875630i	$-0.339554\pi$
$648$	−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	−0.0818414	−	0.996645i	$-0.526080\pi$
$653$	12.6772	−	4.61411i	0.496096	−	0.180564i	0.577937	+	0.816081i	$0.303858\pi$
$654$	−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	−0.441168	−	0.897424i	$-0.645436\pi$
$659$	9.39594	−	7.88413i	0.366014	−	0.307122i	0.807182	+	0.590302i	$0.200991\pi$
$660$	6.52039	−	9.14133i	0.253806	−	0.355826i
$661$	−15.5327	+	5.65345i	−0.604153	+	0.219894i	−0.625943	−	0.779869i	$-0.715286\pi$
$661$	−15.5327	+	5.65345i	−0.604153	+	0.219894i	0.0217899	+	0.999763i	$0.493064\pi$
$662$	−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	−0.965792	−	0.259317i	$-0.916503\pi$
$673$	−3.81185	−	21.6181i	−0.146936	−	0.833315i	0.818856	−	0.573998i	$-0.194608\pi$
$674$	−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	−0.00118145	−	0.999999i	$-0.500376\pi$
$677$	−16.7791	−	6.10710i	−0.644874	−	0.234715i	−0.643692	+	0.765284i	$0.722598\pi$
$678$	−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	−0.570745	−	0.821127i	$-0.693346\pi$
$683$	11.1265	−	19.2717i	0.425744	−	0.737411i	0.996490	+	0.0837165i	$0.0266790\pi$
$684$	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	0.887971	+	0.459899i	$0.152114\pi$
$691$	5.54248	+	31.4330i	0.210846	+	1.19577i	−0.677125	+	0.735868i	$0.736774\pi$
$692$	−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	−0.621909	−	0.783090i	$-0.713643\pi$
$709$	1.09945	−	0.922550i	0.0412908	−	0.0346471i	0.663200	+	0.748443i	$0.269198\pi$
$710$	−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	0.938876	+	0.344257i	$0.111869\pi$
$719$	20.5818	+	35.6488i	0.767573	+	1.32947i	−0.171303	+	0.985218i	$0.554798\pi$
$720$	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	−0.981326	−	0.192352i	$-0.938389\pi$
$727$	−3.36954	−	19.1096i	−0.124969	−	0.708737i	0.856357	−	0.516385i	$-0.172723\pi$
$728$	−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	0.804266	+	0.594270i	$0.202559\pi$
$733$	−4.18968	+	23.7608i	−0.154749	+	0.877626i	−0.959015	+	0.283356i	$0.908552\pi$
$734$	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	−0.969189	−	0.246320i	$-0.920779\pi$
$743$	0.703175	−	3.98791i	0.0257970	−	0.146302i	0.994986	+	0.100017i	$0.0318899\pi$
$744$	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	−0.0458655	−	0.998948i	$-0.514605\pi$
$751$	15.3769	−	5.59673i	0.561111	−	0.204228i	0.606976	+	0.794720i	$0.292382\pi$
$752$	−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	−0.828276	−	0.560321i	$-0.810678\pi$
$761$	−30.4167	+	11.0708i	−1.10260	+	0.401315i	−0.274329	+	0.961636i	$0.588456\pi$
$762$	−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	−0.950880	−	0.309560i	$-0.899818\pi$
$769$	1.34579	−	7.63237i	0.0485305	−	0.275230i	0.999411	+	0.0343292i	$0.0109295\pi$
$770$	−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	0.144286	−	0.989536i	$-0.453911\pi$
$787$	−22.5876	−	18.9533i	−0.805161	−	0.675611i	−0.949448	+	0.313925i	$0.898356\pi$
$788$	−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	−0.999271	−	0.0381697i	$-0.987847\pi$
$797$	−1.33276	+	7.55843i	−0.0472086	+	0.267733i	0.952063	+	0.305903i	$0.0989584\pi$
$798$	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	0.842600	−	0.538540i	$-0.181024\pi$
$809$	−1.28247	−	2.22131i	−0.0450893	−	0.0780970i	−0.887689	+	0.460443i	$0.847691\pi$
$810$	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	0.949152	+	0.314817i	$0.101943\pi$
$821$	4.72531	+	26.7986i	0.164915	+	0.935277i	−0.784238	+	0.620460i	$0.786946\pi$
$822$	8.03984	+	17.6416i	0.280422	+	0.615322i
$823$	26.4584	−	9.63006i	0.922281	−	0.335683i	0.163136	−	0.986604i	$-0.447839\pi$
$823$	26.4584	−	9.63006i	0.922281	−	0.335683i	0.759146	+	0.650921i	$0.225617\pi$
$824$	−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	−0.250571	−	0.968098i	$-0.580618\pi$
$827$	20.5074	−	35.5199i	0.713112	−	1.23515i	0.963683	−	0.267048i	$-0.0860483\pi$
$828$	−0.976933	+	1.12385i	−0.0339508	+	0.0390566i
$829$	−0.820089	+	1.42044i	−0.0284829	+	0.0493338i	−0.879915	−	0.475130i	$-0.842401\pi$
$829$	−0.820089	+	1.42044i	−0.0284829	+	0.0493338i	0.851433	+	0.524464i	$0.175734\pi$
$830$	−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	−0.965490	−	0.260439i	$-0.916133\pi$
$839$	−4.26667	−	24.1975i	−0.147302	−	0.835389i	0.818188	−	0.574950i	$-0.194979\pi$
$840$	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	−0.174122	+	0.984724i	$0.555709\pi$
$853$	−34.2916	+	28.7741i	−1.17412	+	0.985205i	−1.00000		0.000481297i	$0.999847\pi$
$854$	−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	0.804842	+	0.593490i	$0.202250\pi$
$857$	7.36323	+	41.7590i	0.251523	+	1.42646i	−0.553318	+	0.832970i	$0.686639\pi$
$858$	−26.8140	−	27.2859i	−0.915414	−	0.931524i
$859$	25.0936	−	9.13332i	0.856182	−	0.311625i	0.123624	−	0.992329i	$-0.460548\pi$
$859$	25.0936	−	9.13332i	0.856182	−	0.311625i	0.732558	+	0.680704i	$0.238326\pi$
$860$	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	0.325274	+	0.945620i	$0.394544\pi$
$863$	−19.2799	+	33.3937i	−0.656294	+	1.13673i	−0.981568	+	0.191115i	$0.938790\pi$
$864$	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	0.434910	−	0.900474i	$-0.356780\pi$
$877$	−11.1457	−	9.35234i	−0.376363	−	0.315806i	−0.811273	+	0.584668i	$0.801225\pi$
$878$	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	−0.856635	−	0.515923i	$-0.827449\pi$
$881$	0.548666	−	0.950317i	0.0184850	−	0.0320170i	0.875120	+	0.483906i	$0.160782\pi$
$882$	20.9983	−	0.265395i	0.707050	−	0.00893632i
$883$	5.25393	+	9.10007i	0.176809	+	0.306242i	0.940786	−	0.339002i	$-0.110089\pi$
$883$	5.25393	+	9.10007i	0.176809	+	0.306242i	−0.763977	+	0.645244i	$0.776756\pi$
$884$	−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	0.858076	+	0.513523i	$0.171660\pi$
$887$	−3.68967	+	20.9252i	−0.123887	+	0.702598i	−0.981963	+	0.189075i	$0.939451\pi$
$888$	−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	0.984360	−	0.176171i	$-0.0563713\pi$
$907$	48.9447	+	17.8144i	1.62518	+	0.591518i	0.640822	+	0.767689i	$0.278594\pi$
$908$	−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	0.600055	−	0.799958i	$-0.295145\pi$
$911$	16.4653	+	5.99289i	0.545521	+	0.198553i	−0.0545343	+	0.998512i	$0.517367\pi$
$912$	−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	−0.729370	−	0.684119i	$-0.760187\pi$
$919$	6.90514	−	11.9601i	0.227780	−	0.394526i	0.957150	+	0.289593i	$0.0935201\pi$
$920$	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	−0.874188	−	0.485588i	$-0.838605\pi$
$929$	−6.66894	−	37.8215i	−0.218801	−	1.24088i	0.655387	−	0.755293i	$-0.272506\pi$
$930$	−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	0.623401	−	0.781902i	$-0.285750\pi$
$937$	−11.1865	−	19.3756i	−0.365447	−	0.632973i	−0.988848	+	0.148930i	$0.952417\pi$
$938$	−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	0.0455284	−	0.998963i	$-0.485503\pi$
$941$	−28.5392	−	23.9473i	−0.930352	−	0.780658i	−0.975881	+	0.218305i	$0.929947\pi$
$942$	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	0.781448	−	0.623970i	$-0.214481\pi$
$947$	30.1269	+	10.9653i	0.978992	+	0.356324i	0.197544	+	0.980294i	$0.436704\pi$
$948$	−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	0.672278	−	0.740299i	$-0.265316\pi$
$953$	−9.41490	−	16.3071i	−0.304979	−	0.528238i	−0.977257	+	0.212060i	$0.931983\pi$
$954$	−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	0.578395	−	0.815757i	$-0.303679\pi$
$967$	−3.87252	−	3.24943i	−0.124532	−	0.104495i	−0.702927	+	0.711262i	$0.748124\pi$
$968$	−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	−0.524902	−	0.851163i	$-0.675898\pi$
$971$	14.7914	−	25.6194i	0.474677	−	0.822165i	0.999579	+	0.0289974i	$0.00923145\pi$
$972$	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	0.836627	+	0.547772i	$0.184524\pi$
$977$	−4.27891	+	24.2669i	−0.136894	+	0.776367i	−0.973522	+	0.228594i	$0.926587\pi$
$978$	−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	0.935876	−	0.352330i	$-0.114610\pi$
$983$	44.7193	+	16.2765i	1.42633	+	0.519140i	0.490449	+	0.871470i	$0.336833\pi$
$984$	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	−0.997236	−	0.0743049i	$-0.976326\pi$
$991$	−13.6708	+	23.6786i	−0.434268	+	0.752174i	0.562968	+	0.826479i	$0.309660\pi$
$992$	−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	−0.459995	−	0.887922i	$-0.652149\pi$
$997$	10.5639	−	8.86412i	0.334561	−	0.280730i	0.794555	+	0.607192i	$0.207704\pi$
$998$	−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.121.7	yes	72
7.4	even	3		378.2.v.b.67.3	✓	72
27.25	even	9		378.2.v.b.79.3	yes	72
189.25	even	9	inner	378.2.w.a.25.7	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.v.b.67.3	✓	72	7.4	even	3
378.2.v.b.79.3	yes	72	27.25	even	9
378.2.w.a.25.7	yes	72	189.25	even	9	inner
378.2.w.a.121.7	yes	72	1.1	even	1	trivial

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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