LMFDB - Embedded newform 114.2.i.d.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,2,Mod(25,114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(114, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("114.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	114.i (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:	$0.910294583043$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	114.25
Dual form			114.2.i.d.73.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(0.939693 + 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.386659 + 2.19285i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(0.326352 - 0.565258i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(0.939693 + 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.386659 + 2.19285i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(0.326352 - 0.565258i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +(-1.70574 - 1.43128i) q^{10} +(0.766044 + 1.32683i) q^{11} +(0.500000 - 0.866025i) q^{12} +(0.439693 - 0.160035i) q^{13} +(0.113341 + 0.642788i) q^{14} +(-0.386659 + 2.19285i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-1.61334 + 1.35375i) q^{17} -1.00000 q^{18} +(-2.23396 - 3.74292i) q^{19} +2.22668 q^{20} +(0.500000 - 0.419550i) q^{21} +(-1.43969 - 0.524005i) q^{22} +(1.02481 - 5.81201i) q^{23} +(0.173648 + 0.984808i) q^{24} +(0.0393628 - 0.0143269i) q^{25} +(-0.233956 + 0.405223i) q^{26} +(0.500000 + 0.866025i) q^{27} +(-0.500000 - 0.419550i) q^{28} +(-6.38326 - 5.35619i) q^{29} +(-1.11334 - 1.92836i) q^{30} +(4.31908 - 7.48086i) q^{31} +(0.939693 - 0.342020i) q^{32} +(0.266044 + 1.50881i) q^{33} +(0.365715 - 2.07407i) q^{34} +(1.36571 + 0.497079i) q^{35} +(0.766044 - 0.642788i) q^{36} -4.67499 q^{37} +(4.11721 + 1.43128i) q^{38} +0.467911 q^{39} +(-1.70574 + 1.43128i) q^{40} +(-3.26604 - 1.18874i) q^{41} +(-0.113341 + 0.642788i) q^{42} +(1.78699 + 10.1345i) q^{43} +(1.43969 - 0.524005i) q^{44} +(-1.11334 + 1.92836i) q^{45} +(2.95084 + 5.11100i) q^{46} +(-3.55303 - 2.98135i) q^{47} +(-0.766044 - 0.642788i) q^{48} +(3.28699 + 5.69323i) q^{49} +(-0.0209445 + 0.0362770i) q^{50} +(-1.97906 + 0.720317i) q^{51} +(-0.0812519 - 0.460802i) q^{52} +(-2.07532 + 11.7697i) q^{53} +(-0.939693 - 0.342020i) q^{54} +(-2.61334 + 2.19285i) q^{55} +0.652704 q^{56} +(-0.819078 - 4.28125i) q^{57} +8.33275 q^{58} +(10.9042 - 9.14971i) q^{59} +(2.09240 + 0.761570i) q^{60} +(-1.58378 + 8.98205i) q^{61} +(1.50000 + 8.50692i) q^{62} +(0.613341 - 0.223238i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.520945 + 0.902302i) q^{65} +(-1.17365 - 0.984808i) q^{66} +(0.190722 + 0.160035i) q^{67} +(1.05303 + 1.82391i) q^{68} +(2.95084 - 5.11100i) q^{69} +(-1.36571 + 0.497079i) q^{70} +(-0.772441 - 4.38073i) q^{71} +(-0.173648 + 0.984808i) q^{72} +(8.54323 + 3.10948i) q^{73} +(3.58125 - 3.00503i) q^{74} +0.0418891 q^{75} +(-4.07398 + 1.55007i) q^{76} +1.00000 q^{77} +(-0.358441 + 0.300767i) q^{78} +(-11.3302 - 4.12386i) q^{79} +(0.386659 - 2.19285i) q^{80} +(0.173648 + 0.984808i) q^{81} +(3.26604 - 1.18874i) q^{82} +(-1.85457 + 3.21221i) q^{83} +(-0.326352 - 0.565258i) q^{84} +(-3.59240 - 3.01438i) q^{85} +(-7.88326 - 6.61484i) q^{86} +(-4.16637 - 7.21637i) q^{87} +(-0.766044 + 1.32683i) q^{88} +(-15.7554 + 5.73448i) q^{89} +(-0.386659 - 2.19285i) q^{90} +(0.0530334 - 0.300767i) q^{91} +(-5.54576 - 2.01849i) q^{92} +(6.61721 - 5.55250i) q^{93} +4.63816 q^{94} +(7.34389 - 6.34597i) q^{95} +1.00000 q^{96} +(1.89053 - 1.58634i) q^{97} +(-6.17752 - 2.24843i) q^{98} +(-0.266044 + 1.50881i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 9 q^{5} + 3 q^{7} + 3 q^{8}+O(q^{10}) $ 6 * q + 9 * q^5 + 3 * q^7 + 3 * q^8	$ 6 q + 9 q^{5} + 3 q^{7} + 3 q^{8} + 3 q^{12} - 3 q^{13} - 6 q^{14} - 9 q^{15} - 3 q^{17} - 6 q^{18} - 18 q^{19} + 3 q^{21} - 3 q^{22} - 21 q^{23} + 9 q^{25} - 6 q^{26} + 3 q^{27} - 3 q^{28} - 3 q^{29} + 9 q^{31} - 3 q^{33} + 12 q^{34} + 18 q^{35} - 18 q^{37} - 6 q^{38} + 12 q^{39} - 15 q^{41} + 6 q^{42} + 3 q^{43} + 3 q^{44} + 6 q^{46} - 9 q^{47} + 12 q^{49} + 3 q^{50} - 15 q^{51} - 3 q^{52} + 12 q^{53} - 9 q^{55} + 6 q^{56} + 12 q^{57} + 12 q^{58} + 27 q^{59} + 9 q^{60} + 3 q^{61} + 9 q^{62} - 3 q^{63} - 3 q^{64} - 6 q^{66} + 21 q^{67} - 6 q^{68} + 6 q^{69} - 18 q^{70} + 39 q^{71} + 36 q^{73} + 24 q^{74} - 6 q^{75} - 9 q^{76} + 6 q^{77} + 6 q^{78} - 45 q^{79} + 9 q^{80} + 15 q^{82} - 27 q^{83} - 3 q^{84} - 18 q^{85} - 12 q^{86} - 6 q^{87} - 30 q^{89} - 9 q^{90} - 12 q^{91} - 3 q^{92} + 9 q^{93} - 6 q^{94} + 6 q^{96} - 6 q^{97} - 12 q^{98} + 3 q^{99}+O(q^{100}) $ 6 * q + 9 * q^5 + 3 * q^7 + 3 * q^8 + 3 * q^12 - 3 * q^13 - 6 * q^14 - 9 * q^15 - 3 * q^17 - 6 * q^18 - 18 * q^19 + 3 * q^21 - 3 * q^22 - 21 * q^23 + 9 * q^25 - 6 * q^26 + 3 * q^27 - 3 * q^28 - 3 * q^29 + 9 * q^31 - 3 * q^33 + 12 * q^34 + 18 * q^35 - 18 * q^37 - 6 * q^38 + 12 * q^39 - 15 * q^41 + 6 * q^42 + 3 * q^43 + 3 * q^44 + 6 * q^46 - 9 * q^47 + 12 * q^49 + 3 * q^50 - 15 * q^51 - 3 * q^52 + 12 * q^53 - 9 * q^55 + 6 * q^56 + 12 * q^57 + 12 * q^58 + 27 * q^59 + 9 * q^60 + 3 * q^61 + 9 * q^62 - 3 * q^63 - 3 * q^64 - 6 * q^66 + 21 * q^67 - 6 * q^68 + 6 * q^69 - 18 * q^70 + 39 * q^71 + 36 * q^73 + 24 * q^74 - 6 * q^75 - 9 * q^76 + 6 * q^77 + 6 * q^78 - 45 * q^79 + 9 * q^80 + 15 * q^82 - 27 * q^83 - 3 * q^84 - 18 * q^85 - 12 * q^86 - 6 * q^87 - 30 * q^89 - 9 * q^90 - 12 * q^91 - 3 * q^92 + 9 * q^93 - 6 * q^94 + 6 * q^96 - 6 * q^97 - 12 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	0.939693	+	0.342020i	0.542532	+	0.197465i
$3$	0.939693	+	0.342020i	0.542532	+	0.197465i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	0.386659	+	2.19285i	0.172919	+	0.980674i	0.940518	+	0.339743i	$0.110340\pi$
$5$	0.386659	+	2.19285i	0.172919	+	0.980674i	−0.767599	+	0.640930i	$0.778549\pi$
$6$	−0.939693	+	0.342020i	−0.383628	+	0.139629i
$7$	0.326352	−	0.565258i	0.123349	−	0.213647i	−0.797737	−	0.603005i	$-0.793970\pi$
$7$	0.326352	−	0.565258i	0.123349	−	0.213647i	0.921087	+	0.389358i	$0.127303\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	0.766044	+	0.642788i	0.255348	+	0.214263i
$10$	−1.70574	−	1.43128i	−0.539401	−	0.452612i
$11$	0.766044	+	1.32683i	0.230971	+	0.400054i	0.958094	−	0.286453i	$-0.0924764\pi$
$11$	0.766044	+	1.32683i	0.230971	+	0.400054i	−0.727123	+	0.686507i	$0.759143\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	0.439693	−	0.160035i	0.121949	−	0.0443857i	−0.280325	−	0.959905i	$-0.590442\pi$
$13$	0.439693	−	0.160035i	0.121949	−	0.0443857i	0.402274	+	0.915519i	$0.368220\pi$
$14$	0.113341	+	0.642788i	0.0302916	+	0.171792i
$15$	−0.386659	+	2.19285i	−0.0998350	+	0.566192i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−1.61334	+	1.35375i	−0.391293	+	0.328333i	−0.817116	−	0.576473i	$-0.804429\pi$
$17$	−1.61334	+	1.35375i	−0.391293	+	0.328333i	0.425824	+	0.904806i	$0.359984\pi$
$18$	−1.00000			−0.235702
$19$	−2.23396	−	3.74292i	−0.512505	−	0.858685i
$19$	−2.23396	−	3.74292i	−0.512505	−	0.858685i
$20$	2.22668			0.497901
$21$	0.500000	−	0.419550i	0.109109	−	0.0915533i
$22$	−1.43969	−	0.524005i	−0.306943	−	0.111718i
$23$	1.02481	−	5.81201i	0.213689	−	1.21189i	−0.669479	−	0.742831i	$-0.733483\pi$
$23$	1.02481	−	5.81201i	0.213689	−	1.21189i	0.883168	−	0.469058i	$-0.155406\pi$
$24$	0.173648	+	0.984808i	0.0354458	+	0.201023i
$25$	0.0393628	−	0.0143269i	0.00787257	−	0.00286538i
$26$	−0.233956	+	0.405223i	−0.0458825	+	0.0794708i
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$	−0.500000	−	0.419550i	−0.0944911	−	0.0792875i
$29$	−6.38326	−	5.35619i	−1.18534	−	0.994619i	−0.999928	−	0.0119582i	$-0.996193\pi$
$29$	−6.38326	−	5.35619i	−1.18534	−	0.994619i	−0.185412	−	0.982661i	$-0.559362\pi$
$30$	−1.11334	−	1.92836i	−0.203267	−	0.352069i
$31$	4.31908	−	7.48086i	0.775729	−	1.34360i	−0.158654	−	0.987334i	$-0.550716\pi$
$31$	4.31908	−	7.48086i	0.775729	−	1.34360i	0.934384	−	0.356268i	$-0.115951\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	0.266044	+	1.50881i	0.0463124	+	0.262651i
$34$	0.365715	−	2.07407i	0.0627195	−	0.355700i
$35$	1.36571	+	0.497079i	0.230848	+	0.0840218i
$36$	0.766044	−	0.642788i	0.127674	−	0.107131i
$37$	−4.67499			−0.768564			−0.384282	−	0.923216i	$-0.625551\pi$
$37$	−4.67499			−0.768564			−0.384282	+	0.923216i	$0.625551\pi$
$38$	4.11721	+	1.43128i	0.667900	+	0.232185i
$39$	0.467911			0.0749257
$40$	−1.70574	+	1.43128i	−0.269701	+	0.226306i
$41$	−3.26604	−	1.18874i	−0.510070	−	0.185650i	0.0741475	−	0.997247i	$-0.476376\pi$
$41$	−3.26604	−	1.18874i	−0.510070	−	0.185650i	−0.584218	+	0.811597i	$0.698599\pi$
$42$	−0.113341	+	0.642788i	−0.0174889	+	0.0991843i
$43$	1.78699	+	10.1345i	0.272513	+	1.54550i	0.746752	+	0.665103i	$0.231612\pi$
$43$	1.78699	+	10.1345i	0.272513	+	1.54550i	−0.474238	+	0.880396i	$0.657277\pi$
$44$	1.43969	−	0.524005i	0.217042	−	0.0789968i
$45$	−1.11334	+	1.92836i	−0.165967	+	0.287463i
$46$	2.95084	+	5.11100i	0.435077	+	0.753576i
$47$	−3.55303	−	2.98135i	−0.518263	−	0.434874i	0.345763	−	0.938322i	$-0.387620\pi$
$47$	−3.55303	−	2.98135i	−0.518263	−	0.434874i	−0.864026	+	0.503448i	$0.832065\pi$
$48$	−0.766044	−	0.642788i	−0.110569	−	0.0927784i
$49$	3.28699	+	5.69323i	0.469570	+	0.813319i
$50$	−0.0209445	+	0.0362770i	−0.00296200	+	0.00513034i
$51$	−1.97906	+	0.720317i	−0.277123	+	0.100865i
$52$	−0.0812519	−	0.460802i	−0.0112676	−	0.0639018i
$53$	−2.07532	+	11.7697i	−0.285067	+	1.61670i	0.419977	+	0.907535i	$0.362038\pi$
$53$	−2.07532	+	11.7697i	−0.285067	+	1.61670i	−0.705045	+	0.709163i	$0.749073\pi$
$54$	−0.939693	−	0.342020i	−0.127876	−	0.0465430i
$55$	−2.61334	+	2.19285i	−0.352383	+	0.295684i
$56$	0.652704			0.0872212
$57$	−0.819078	−	4.28125i	−0.108490	−	0.567066i
$58$	8.33275			1.09414
$59$	10.9042	−	9.14971i	1.41961	−	1.19119i	0.468055	−	0.883699i	$-0.344955\pi$
$59$	10.9042	−	9.14971i	1.41961	−	1.19119i	0.951551	−	0.307492i	$-0.0994896\pi$
$60$	2.09240	+	0.761570i	0.270127	+	0.0983183i
$61$	−1.58378	+	8.98205i	−0.202782	+	1.15003i	0.698110	+	0.715991i	$0.254025\pi$
$61$	−1.58378	+	8.98205i	−0.202782	+	1.15003i	−0.900892	+	0.434043i	$0.857086\pi$
$62$	1.50000	+	8.50692i	0.190500	+	1.08038i
$63$	0.613341	−	0.223238i	0.0772737	−	0.0281253i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	0.520945	+	0.902302i	0.0646152	+	0.111917i
$66$	−1.17365	−	0.984808i	−0.144466	−	0.121221i
$67$	0.190722	+	0.160035i	0.0233004	+	0.0195514i	0.654363	−	0.756180i	$-0.272937\pi$
$67$	0.190722	+	0.160035i	0.0233004	+	0.0195514i	−0.631063	+	0.775732i	$0.717381\pi$
$68$	1.05303	+	1.82391i	0.127699	+	0.221181i
$69$	2.95084	−	5.11100i	0.355239	−	0.615292i
$70$	−1.36571	+	0.497079i	−0.163234	+	0.0594124i
$71$	−0.772441	−	4.38073i	−0.0916719	−	0.519897i	−0.995716	−	0.0924590i	$-0.970527\pi$
$71$	−0.772441	−	4.38073i	−0.0916719	−	0.519897i	0.904045	−	0.427438i	$-0.140584\pi$
$72$	−0.173648	+	0.984808i	−0.0204646	+	0.116061i
$73$	8.54323	+	3.10948i	0.999910	+	0.363937i	0.789550	−	0.613687i	$-0.210314\pi$
$73$	8.54323	+	3.10948i	0.999910	+	0.363937i	0.210360	+	0.977624i	$0.432536\pi$
$74$	3.58125	−	3.00503i	0.416312	−	0.349327i
$75$	0.0418891			0.00483693
$76$	−4.07398	+	1.55007i	−0.467317	+	0.177805i
$77$	1.00000			0.113961
$78$	−0.358441	+	0.300767i	−0.0405854	+	0.0340552i
$79$	−11.3302	−	4.12386i	−1.27475	−	0.463971i	−0.386057	−	0.922475i	$-0.626163\pi$
$79$	−11.3302	−	4.12386i	−1.27475	−	0.463971i	−0.888692	+	0.458504i	$0.848385\pi$
$80$	0.386659	−	2.19285i	0.0432298	−	0.245168i
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$	3.26604	−	1.18874i	0.360674	−	0.131275i
$83$	−1.85457	+	3.21221i	−0.203566	+	0.352586i	−0.949675	−	0.313238i	$-0.898586\pi$
$83$	−1.85457	+	3.21221i	−0.203566	+	0.352586i	0.746109	+	0.665824i	$0.231920\pi$
$84$	−0.326352	−	0.565258i	−0.0356079	−	0.0616747i
$85$	−3.59240	−	3.01438i	−0.389650	−	0.326955i
$86$	−7.88326	−	6.61484i	−0.850073	−	0.713296i
$87$	−4.16637	−	7.21637i	−0.446682	−	0.773676i
$88$	−0.766044	+	1.32683i	−0.0816606	+	0.141440i
$89$	−15.7554	+	5.73448i	−1.67007	+	0.607854i	−0.991896	−	0.127051i	$-0.959449\pi$
$89$	−15.7554	+	5.73448i	−1.67007	+	0.607854i	−0.678169	+	0.734906i	$0.737226\pi$
$90$	−0.386659	−	2.19285i	−0.0407575	−	0.231147i
$91$	0.0530334	−	0.300767i	0.00555941	−	0.0315290i
$92$	−5.54576	−	2.01849i	−0.578185	−	0.210442i
$93$	6.61721	−	5.55250i	0.686173	−	0.575767i
$94$	4.63816			0.478389
$95$	7.34389	−	6.34597i	0.753468	−	0.651083i
$96$	1.00000			0.102062
$97$	1.89053	−	1.58634i	0.191954	−	0.161069i	−0.541746	−	0.840543i	$-0.682236\pi$
$97$	1.89053	−	1.58634i	0.191954	−	0.161069i	0.733700	+	0.679474i	$0.237792\pi$
$98$	−6.17752	−	2.24843i	−0.624024	−	0.227126i
$99$	−0.266044	+	1.50881i	−0.0267385	+	0.151641i
$100$	−0.00727396	−	0.0412527i	−0.000727396	−	0.00412527i
$101$	5.39306	−	1.96291i	0.536629	−	0.195317i	−0.0594668	−	0.998230i	$-0.518940\pi$
$101$	5.39306	−	1.96291i	0.536629	−	0.195317i	0.596096	+	0.802913i	$0.296718\pi$
$102$	1.05303	−	1.82391i	0.104266	−	0.180594i
$103$	6.90420	+	11.9584i	0.680291	+	1.17830i	0.974892	+	0.222678i	$0.0714800\pi$
$103$	6.90420	+	11.9584i	0.680291	+	1.17830i	−0.294601	+	0.955620i	$0.595187\pi$
$104$	0.358441	+	0.300767i	0.0351480	+	0.0294927i
$105$	1.11334	+	0.934204i	0.108651	+	0.0911690i
$106$	−5.97565	−	10.3501i	−0.580407	−	1.00529i
$107$	−0.956767	+	1.65717i	−0.0924941	+	0.160205i	−0.908560	−	0.417754i	$-0.862817\pi$
$107$	−0.956767	+	1.65717i	−0.0924941	+	0.160205i	0.816066	+	0.577959i	$0.196151\pi$
$108$	0.939693	−	0.342020i	0.0904220	−	0.0329109i
$109$	−2.05169	−	11.6357i	−0.196516	−	1.11450i	−0.910243	−	0.414074i	$-0.864105\pi$
$109$	−2.05169	−	11.6357i	−0.196516	−	1.11450i	0.713727	−	0.700424i	$-0.247006\pi$
$110$	0.592396	−	3.35965i	0.0564828	−	0.320330i
$111$	−4.39306	−	1.59894i	−0.416970	−	0.151765i
$112$	−0.500000	+	0.419550i	−0.0472456	+	0.0396437i
$113$	5.39693			0.507700			0.253850	−	0.967244i	$-0.418303\pi$
$113$	5.39693			0.507700			0.253850	+	0.967244i	$0.418303\pi$
$114$	3.37939	+	2.75314i	0.316508	+	0.257855i
$115$	13.1411			1.22542
$116$	−6.38326	+	5.35619i	−0.592670	+	0.497310i
$117$	0.439693	+	0.160035i	0.0406496	+	0.0147952i
$118$	−2.47178	+	14.0182i	−0.227546	+	1.29048i
$119$	0.238703	+	1.35375i	0.0218819	+	0.124098i
$120$	−2.09240	+	0.761570i	−0.191009	+	0.0695215i
$121$	4.32635	−	7.49346i	0.393305	−	0.681224i
$122$	−4.56031	−	7.89868i	−0.412871	−	0.715113i
$123$	−2.66250	−	2.23411i	−0.240070	−	0.201443i
$124$	−6.61721	−	5.55250i	−0.594243	−	0.498629i
$125$	5.61334	+	9.72259i	0.502072	+	0.869615i
$126$	−0.326352	+	0.565258i	−0.0290737	+	0.0503572i
$127$	−9.09152	+	3.30904i	−0.806742	+	0.293630i	−0.712277	−	0.701898i	$-0.752336\pi$
$127$	−9.09152	+	3.30904i	−0.806742	+	0.293630i	−0.0944646	+	0.995528i	$0.530114\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	−1.78699	+	10.1345i	−0.157336	+	0.892295i
$130$	−0.979055	−	0.356347i	−0.0858688	−	0.0312537i
$131$	−1.45677	+	1.22237i	−0.127278	+	0.106799i	−0.704205	−	0.709997i	$-0.748696\pi$
$131$	−1.45677	+	1.22237i	−0.127278	+	0.106799i	0.576927	+	0.816796i	$0.304252\pi$
$132$	1.53209			0.133351
$133$	−2.84477	+	0.0412527i	−0.246673	+	0.00357706i
$134$	−0.248970			−0.0215078
$135$	−1.70574	+	1.43128i	−0.146806	+	0.123185i
$136$	−1.97906	−	0.720317i	−0.169703	−	0.0617667i
$137$	−0.308811	+	1.75135i	−0.0263835	+	0.149628i	−0.995154	−	0.0983323i	$-0.968649\pi$
$137$	−0.308811	+	1.75135i	−0.0263835	+	0.149628i	0.968770	+	0.247960i	$0.0797603\pi$
$138$	1.02481	+	5.81201i	0.0872380	+	0.494752i
$139$	0.705737	−	0.256867i	0.0598598	−	0.0217872i	−0.311917	−	0.950109i	$-0.600971\pi$
$139$	0.705737	−	0.256867i	0.0598598	−	0.0217872i	0.371777	+	0.928322i	$0.378749\pi$
$140$	0.726682	−	1.25865i	0.0614158	−	0.106375i
$141$	−2.31908	−	4.01676i	−0.195302	−	0.338272i
$142$	3.40760	+	2.85932i	0.285960	+	0.239949i
$143$	0.549163	+	0.460802i	0.0459233	+	0.0385342i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	9.27719	−	16.0686i	0.770429	−	1.33442i
$146$	−8.54323	+	3.10948i	−0.707043	+	0.257343i
$147$	1.14156	+	6.47410i	0.0941542	+	0.533975i
$148$	−0.811804	+	4.60397i	−0.0667299	+	0.378444i
$149$	5.61721	+	2.04450i	0.460180	+	0.167492i	0.561699	−	0.827342i	$-0.310148\pi$
$149$	5.61721	+	2.04450i	0.460180	+	0.167492i	−0.101519	+	0.994834i	$0.532370\pi$
$150$	−0.0320889	+	0.0269258i	−0.00262005	+	0.00219848i
$151$	−16.5749			−1.34885			−0.674424	−	0.738345i	$-0.735608\pi$
$151$	−16.5749			−1.34885			−0.674424	+	0.738345i	$0.735608\pi$
$152$	2.12449	−	3.80612i	0.172319	−	0.308717i
$153$	−2.10607			−0.170265
$154$	−0.766044	+	0.642788i	−0.0617296	+	0.0517973i
$155$	18.0744	+	6.57856i	1.45177	+	0.528403i
$156$	0.0812519	−	0.460802i	0.00650536	−	0.0368937i
$157$	−2.90033	−	16.4486i	−0.231472	−	1.31274i	−0.849919	−	0.526914i	$-0.823349\pi$
$157$	−2.90033	−	16.4486i	−0.231472	−	1.31274i	0.618447	−	0.785826i	$-0.287762\pi$
$158$	11.3302	−	4.12386i	0.901384	−	0.328077i
$159$	−5.97565	+	10.3501i	−0.473900	+	0.820819i
$160$	1.11334	+	1.92836i	0.0880173	+	0.152450i
$161$	−2.95084	−	2.47605i	−0.232559	−	0.195140i
$162$	−0.766044	−	0.642788i	−0.0601861	−	0.0505022i
$163$	7.92855	+	13.7326i	0.621012	+	1.07562i	0.989298	+	0.145911i	$0.0466115\pi$
$163$	7.92855	+	13.7326i	0.621012	+	1.07562i	−0.368286	+	0.929713i	$0.620055\pi$
$164$	−1.73783	+	3.01000i	−0.135701	+	0.235042i
$165$	−3.20574	+	1.16679i	−0.249566	+	0.0908347i
$166$	−0.644086	−	3.65279i	−0.0499907	−	0.283512i
$167$	−0.393056	+	2.22913i	−0.0304156	+	0.172495i	−0.996232	−	0.0867333i	$-0.972357\pi$
$167$	−0.393056	+	2.22913i	−0.0304156	+	0.172495i	0.965816	+	0.259229i	$0.0834683\pi$
$168$	0.613341	+	0.223238i	0.0473203	+	0.0172232i
$169$	−9.79086	+	8.21551i	−0.753143	+	0.631962i
$170$	4.68954			0.359671
$171$	0.694593	−	4.30320i	0.0531168	−	0.329074i
$172$	10.2909			0.784671
$173$	7.16637	−	6.01330i	0.544849	−	0.457183i	−0.328343	−	0.944559i	$-0.606490\pi$
$173$	7.16637	−	6.01330i	0.544849	−	0.457183i	0.873192	+	0.487376i	$0.162046\pi$
$174$	7.83022	+	2.84997i	0.593608	+	0.216056i
$175$	0.00474774	−	0.0269258i	0.000358895	−	0.00203540i
$176$	−0.266044	−	1.50881i	−0.0200539	−	0.113731i
$177$	13.3760	−	4.86846i	1.00540	−	0.365936i
$178$	8.38326	−	14.5202i	0.628352	−	1.08834i
$179$	7.88919	+	13.6645i	0.589665	+	1.02133i	0.994276	+	0.106841i	$0.0340737\pi$
$179$	7.88919	+	13.6645i	0.589665	+	1.02133i	−0.404611	+	0.914489i	$0.632593\pi$
$180$	1.70574	+	1.43128i	0.127138	+	0.106682i
$181$	5.36437	+	4.50124i	0.398731	+	0.334575i	0.820003	−	0.572360i	$-0.193972\pi$
$181$	5.36437	+	4.50124i	0.398731	+	0.334575i	−0.421272	+	0.906934i	$0.638416\pi$
$182$	0.152704	+	0.264490i	0.0113191	+	0.0196053i
$183$	−4.56031	+	7.89868i	−0.337108	+	0.583888i
$184$	5.54576	−	2.01849i	0.408839	−	0.148805i
$185$	−1.80763	−	10.2516i	−0.132900	−	0.753711i
$186$	−1.50000	+	8.50692i	−0.109985	+	0.623758i
$187$	−3.03209	−	1.10359i	−0.221728	−	0.0807025i
$188$	−3.55303	+	2.98135i	−0.259132	+	0.217437i
$189$	0.652704			0.0474772
$190$	−1.54664	+	9.58186i	−0.112205	+	0.695141i
$191$	4.39187			0.317785			0.158892	−	0.987296i	$-0.449208\pi$
$191$	4.39187			0.317785			0.158892	+	0.987296i	$0.449208\pi$
$192$	−0.766044	+	0.642788i	−0.0552845	+	0.0463892i
$193$	−4.56418	−	1.66122i	−0.328537	−	0.119578i	0.172485	−	0.985012i	$-0.444820\pi$
$193$	−4.56418	−	1.66122i	−0.328537	−	0.119578i	−0.501022	+	0.865434i	$0.667042\pi$
$194$	−0.428548	+	2.43042i	−0.0307680	+	0.174494i
$195$	0.180922	+	1.02606i	0.0129561	+	0.0734777i
$196$	6.17752	−	2.24843i	0.441251	−	0.160602i
$197$	−10.1420	+	17.5665i	−0.722589	+	1.25156i	0.237369	+	0.971420i	$0.423715\pi$
$197$	−10.1420	+	17.5665i	−0.722589	+	1.25156i	−0.959959	+	0.280142i	$0.909618\pi$
$198$	−0.766044	−	1.32683i	−0.0544404	−	0.0942936i
$199$	−17.2062	−	14.4377i	−1.21972	−	1.02346i	−0.998840	−	0.0481609i	$-0.984664\pi$
$199$	−17.2062	−	14.4377i	−1.21972	−	1.02346i	−0.220876	−	0.975302i	$-0.570892\pi$
$200$	0.0320889	+	0.0269258i	0.00226903	+	0.00190394i
$201$	0.124485	+	0.215615i	0.00878051	+	0.0152083i
$202$	−2.86959	+	4.97027i	−0.201903	+	0.349707i
$203$	−5.11081	+	1.86018i	−0.358709	+	0.130559i
$204$	0.365715	+	2.07407i	0.0256051	+	0.145214i
$205$	1.34389	−	7.62159i	0.0938615	−	0.532315i
$206$	−12.9757	−	4.72275i	−0.904057	−	0.329050i
$207$	4.52094	−	3.79352i	0.314227	−	0.263668i
$208$	−0.467911			−0.0324438
$209$	3.25490	−	5.83132i	0.225146	−	0.403361i
$210$	−1.45336			−0.100292
$211$	−7.62836	+	6.40095i	−0.525158	+	0.440660i	−0.866425	−	0.499307i	$-0.833588\pi$
$211$	−7.62836	+	6.40095i	−0.525158	+	0.440660i	0.341268	+	0.939966i	$0.389144\pi$
$212$	11.2306	+	4.08759i	0.771317	+	0.280737i
$213$	0.772441	−	4.38073i	0.0529268	−	0.300163i
$214$	−0.332282	−	1.88446i	−0.0227143	−	0.128819i
$215$	−21.5326	+	7.83721i	−1.46851	+	0.534493i
$216$	−0.500000	+	0.866025i	−0.0340207	+	0.0589256i
$217$	−2.81908	−	4.88279i	−0.191371	−	0.331465i
$218$	9.05097	+	7.59467i	0.613009	+	0.514376i
$219$	6.96451	+	5.84392i	0.470618	+	0.394895i
$220$	1.70574	+	2.95442i	0.115001	+	0.199187i
$221$	−0.492726	+	0.853427i	−0.0331443	+	0.0574077i
$222$	4.39306	−	1.59894i	0.294843	−	0.107314i
$223$	0.333626	+	1.89209i	0.0223412	+	0.126703i	0.993939	−	0.109937i	$-0.0350648\pi$
$223$	0.333626	+	1.89209i	0.0223412	+	0.126703i	−0.971597	+	0.236640i	$0.923954\pi$
$224$	0.113341	−	0.642788i	0.00757290	−	0.0429481i
$225$	0.0393628	+	0.0143269i	0.00262419	+	0.000955127i
$226$	−4.13429	+	3.46908i	−0.275009	+	0.230760i
$227$	0.901674			0.0598462			0.0299231	−	0.999552i	$-0.490474\pi$
$227$	0.901674			0.0598462			0.0299231	+	0.999552i	$0.490474\pi$
$228$	−4.35844	+	0.0632028i	−0.288645	+	0.00418571i
$229$	−0.354103			−0.0233998			−0.0116999	−	0.999932i	$-0.503724\pi$
$229$	−0.354103			−0.0233998			−0.0116999	+	0.999932i	$0.503724\pi$
$230$	−10.0667	+	8.44697i	−0.663779	+	0.556977i
$231$	0.939693	+	0.342020i	0.0618272	+	0.0225033i
$232$	1.44697	−	8.20616i	0.0949980	−	0.538760i
$233$	−2.90033	−	16.4486i	−0.190007	−	1.07758i	−0.919352	−	0.393437i	$-0.871286\pi$
$233$	−2.90033	−	16.4486i	−0.190007	−	1.07758i	0.729345	−	0.684146i	$-0.239825\pi$
$234$	−0.439693	+	0.160035i	−0.0287436	+	0.0104618i
$235$	5.16385	−	8.94405i	0.336852	−	0.583445i
$236$	−7.11721	−	12.3274i	−0.463291	−	0.802444i
$237$	−9.23648	−	7.75033i	−0.599974	−	0.503438i
$238$	−1.05303	−	0.883600i	−0.0682580	−	0.0572753i
$239$	−5.02734	−	8.70761i	−0.325192	−	0.563248i	0.656359	−	0.754448i	$-0.272095\pi$
$239$	−5.02734	−	8.70761i	−0.325192	−	0.563248i	−0.981551	+	0.191200i	$0.938762\pi$
$240$	1.11334	−	1.92836i	0.0718658	−	0.124475i
$241$	21.7062	−	7.90041i	1.39822	−	0.508910i	0.470570	−	0.882363i	$-0.344048\pi$
$241$	21.7062	−	7.90041i	1.39822	−	0.508910i	0.927649	+	0.373452i	$0.121826\pi$
$242$	1.50253	+	8.52125i	0.0965860	+	0.547767i
$243$	−0.173648	+	0.984808i	−0.0111395	+	0.0631754i
$244$	8.57057	+	3.11943i	0.548675	+	0.199701i
$245$	−11.2135	+	9.40923i	−0.716403	+	0.601133i
$246$	3.47565			0.221599
$247$	−1.58125	−	1.28822i	−0.100613	−	0.0819676i
$248$	8.63816			0.548523
$249$	−2.84137	+	2.38419i	−0.180064	+	0.151092i
$250$	−10.5496	−	3.83975i	−0.667217	−	0.242847i
$251$	2.11200	−	11.9777i	0.133308	−	0.756027i	−0.842715	−	0.538360i	$-0.819044\pi$
$251$	2.11200	−	11.9777i	0.133308	−	0.756027i	0.976023	−	0.217667i	$-0.0698448\pi$
$252$	−0.113341	−	0.642788i	−0.00713980	−	0.0404918i
$253$	8.49660	−	3.09251i	0.534176	−	0.194424i
$254$	4.83750	−	8.37879i	0.303532	−	0.525732i
$255$	−2.34477	−	4.06126i	−0.146835	−	0.254326i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−3.02300	−	2.53660i	−0.188570	−	0.158229i	0.543615	−	0.839334i	$-0.317055\pi$
$257$	−3.02300	−	2.53660i	−0.188570	−	0.158229i	−0.732185	+	0.681106i	$0.761499\pi$
$258$	−5.14543	−	8.91215i	−0.320340	−	0.554846i
$259$	−1.52569	+	2.64258i	−0.0948019	+	0.164202i
$260$	0.979055	−	0.356347i	0.0607184	−	0.0220997i
$261$	−1.44697	−	8.20616i	−0.0895650	−	0.507948i
$262$	0.330222	−	1.87278i	0.0204012	−	0.115701i
$263$	−8.52229	−	3.10186i	−0.525507	−	0.191269i	0.0656242	−	0.997844i	$-0.479096\pi$
$263$	−8.52229	−	3.10186i	−0.525507	−	0.191269i	−0.591131	+	0.806576i	$0.701318\pi$
$264$	−1.17365	+	0.984808i	−0.0722331	+	0.0606107i
$265$	−26.6117			−1.63475
$266$	2.15270	−	1.86018i	0.131991	−	0.114055i
$267$	−16.7665			−1.02609
$268$	0.190722	−	0.160035i	0.0116502	−	0.00977570i
$269$	26.3234	+	9.58094i	1.60497	+	0.584160i	0.980436	−	0.196840i	$-0.0630678\pi$
$269$	26.3234	+	9.58094i	1.60497	+	0.584160i	0.624531	+	0.781000i	$0.285290\pi$
$270$	0.386659	−	2.19285i	0.0235313	−	0.133453i
$271$	−2.92350	−	16.5800i	−0.177590	−	1.00716i	−0.935112	−	0.354352i	$-0.884701\pi$
$271$	−2.92350	−	16.5800i	−0.177590	−	1.00716i	0.757522	−	0.652809i	$-0.226410\pi$
$272$	1.97906	−	0.720317i	0.119998	−	0.0436757i
$273$	0.152704	−	0.264490i	0.00924205	−	0.0160077i
$274$	−0.889185	−	1.54011i	−0.0537177	−	0.0930417i
$275$	0.0491630	+	0.0412527i	0.00296464	+	0.00248763i
$276$	−4.52094	−	3.79352i	−0.272129	−	0.228343i
$277$	9.57532	+	16.5849i	0.575325	+	0.996493i	0.996006	+	0.0892840i	$0.0284579\pi$
$277$	9.57532	+	16.5849i	0.575325	+	0.996493i	−0.420681	+	0.907209i	$0.638209\pi$
$278$	−0.375515	+	0.650411i	−0.0225219	+	0.0390090i
$279$	8.11721	−	2.95442i	0.485965	−	0.176877i
$280$	0.252374	+	1.43128i	0.0150822	+	0.0855355i
$281$	−0.687319	+	3.89798i	−0.0410020	+	0.232534i	−0.998421	−	0.0561668i	$-0.982112\pi$
$281$	−0.687319	+	3.89798i	−0.0410020	+	0.232534i	0.957419	+	0.288701i	$0.0932232\pi$
$282$	4.35844	+	1.58634i	0.259541	+	0.0944653i
$283$	−5.03802	+	4.22740i	−0.299479	+	0.251293i	−0.780127	−	0.625621i	$-0.784846\pi$
$283$	−5.03802	+	4.22740i	−0.299479	+	0.251293i	0.480648	+	0.876913i	$0.340401\pi$
$284$	−4.44831			−0.263959
$285$	9.07145	−	3.45150i	0.537346	−	0.204449i
$286$	−0.716881			−0.0423901
$287$	−1.73783	+	1.45821i	−0.102581	+	0.0860754i
$288$	0.939693	+	0.342020i	0.0553719	+	0.0201537i
$289$	−2.18180	+	12.3736i	−0.128341	+	0.727859i
$290$	3.22193	+	18.2725i	0.189198	+	1.07300i
$291$	2.31908	−	0.844075i	0.135947	−	0.0494806i
$292$	4.54576	−	7.87349i	0.266020	−	0.460761i
$293$	−10.8478	−	18.7889i	−0.633733	−	1.09766i	−0.986782	−	0.162053i	$-0.948188\pi$
$293$	−10.8478	−	18.7889i	−0.633733	−	1.09766i	0.353049	−	0.935605i	$-0.385145\pi$
$294$	−5.03596	−	4.22567i	−0.293703	−	0.246446i
$295$	24.2802	+	20.3735i	1.41365	+	1.18619i
$296$	−2.33750	−	4.04866i	−0.135864	−	0.235324i
$297$	−0.766044	+	1.32683i	−0.0444504	+	0.0769904i
$298$	−5.61721	+	2.04450i	−0.325396	+	0.118435i
$299$	−0.479522	−	2.71951i	−0.0277315	−	0.157273i
$300$	0.00727396	−	0.0412527i	0.000419962	−	0.00238172i
$301$	6.31180	+	2.29731i	0.363806	+	0.132415i
$302$	12.6971	−	10.6541i	0.730637	−	0.613077i
$303$	5.73917			0.329707
$304$	0.819078	+	4.28125i	0.0469773	+	0.245547i
$305$	−20.3087			−1.16287
$306$	1.61334	−	1.35375i	0.0922286	−	0.0773889i
$307$	−16.7271	−	6.08818i	−0.954669	−	0.347471i	−0.182727	−	0.983164i	$-0.558492\pi$
$307$	−16.7271	−	6.08818i	−0.954669	−	0.347471i	−0.771942	+	0.635693i	$0.780715\pi$
$308$	0.173648	−	0.984808i	0.00989452	−	0.0561146i
$309$	2.39780	+	13.5986i	0.136406	+	0.773598i
$310$	−18.0744	+	6.57856i	−1.02656	+	0.373637i
$311$	0.812681	−	1.40761i	0.0460829	−	0.0798180i	−0.842064	−	0.539378i	$-0.818659\pi$
$311$	0.812681	−	1.40761i	0.0460829	−	0.0798180i	0.888147	+	0.459560i	$0.151993\pi$
$312$	0.233956	+	0.405223i	0.0132451	+	0.0229412i
$313$	23.0371	+	19.3305i	1.30214	+	1.09262i	0.989772	+	0.142660i	$0.0455654\pi$
$313$	23.0371	+	19.3305i	1.30214	+	1.09262i	0.312364	+	0.949962i	$0.398879\pi$
$314$	12.7947	+	10.7361i	0.722048	+	0.605871i
$315$	0.726682	+	1.25865i	0.0409439	+	0.0709169i
$316$	−6.02869	+	10.4420i	−0.339140	+	0.587408i
$317$	10.6493	−	3.87603i	0.598124	−	0.217699i	−0.0251747	−	0.999683i	$-0.508014\pi$
$317$	10.6493	−	3.87603i	0.598124	−	0.217699i	0.623299	+	0.781984i	$0.285792\pi$
$318$	−2.07532	−	11.7697i	−0.116378	−	0.660014i
$319$	2.21688	−	12.5726i	0.124122	−	0.703928i
$320$	−2.09240	−	0.761570i	−0.116969	−	0.0425731i
$321$	−1.46585	+	1.23000i	−0.0818159	+	0.0686517i
$322$	3.85204			0.214666
$323$	8.67112	+	3.01438i	0.482474	+	0.167724i
$324$	1.00000			0.0555556
$325$	0.0150147	−	0.0125989i	0.000832868	−	0.000698859i
$326$	−14.9008	−	5.42345i	−0.825279	−	0.300377i
$327$	2.05169	−	11.6357i	0.113459	−	0.643456i
$328$	−0.603541	−	3.42285i	−0.0333250	−	0.188995i
$329$	−2.84477	+	1.03541i	−0.156837	+	0.0570841i
$330$	1.70574	−	2.95442i	0.0938977	−	0.162636i
$331$	16.0621	+	27.8204i	0.882854	+	1.52915i	0.848154	+	0.529750i	$0.177714\pi$
$331$	16.0621	+	27.8204i	0.882854	+	1.52915i	0.0347000	+	0.999398i	$0.488952\pi$
$332$	2.84137	+	2.38419i	0.155940	+	0.130849i
$333$	−3.58125	−	3.00503i	−0.196251	−	0.164674i
$334$	−1.13176	−	1.96026i	−0.0619271	−	0.107261i
$335$	−0.277189	+	0.480105i	−0.0151444	+	0.0262309i
$336$	−0.613341	+	0.223238i	−0.0334605	+	0.0121786i
$337$	5.26739	+	29.8728i	0.286933	+	1.62728i	0.698298	+	0.715807i	$0.253941\pi$
$337$	5.26739	+	29.8728i	0.286933	+	1.62728i	−0.411365	+	0.911471i	$0.634948\pi$
$338$	2.21941	−	12.5869i	0.120720	−	0.684636i
$339$	5.07145	+	1.84586i	0.275443	+	0.100253i
$340$	−3.59240	+	3.01438i	−0.194825	+	0.163478i
$341$	13.2344			0.716684
$342$	2.23396	+	3.74292i	0.120798	+	0.202394i
$343$	8.85978			0.478383
$344$	−7.88326	+	6.61484i	−0.425037	+	0.356648i
$345$	12.3486	+	4.49454i	0.664828	+	0.241978i
$346$	−1.62449	+	9.21291i	−0.0873329	+	0.495289i
$347$	0.747626	+	4.24000i	0.0401347	+	0.227615i	0.998277	−	0.0586772i	$-0.0186883\pi$
$347$	0.747626	+	4.24000i	0.0401347	+	0.227615i	−0.958142	+	0.286292i	$0.907577\pi$
$348$	−7.83022	+	2.84997i	−0.419744	+	0.152774i
$349$	1.33022	−	2.30401i	0.0712052	−	0.123331i	−0.828225	−	0.560396i	$-0.810649\pi$
$349$	1.33022	−	2.30401i	0.0712052	−	0.123331i	0.899430	+	0.437065i	$0.143982\pi$
$350$	0.0136706	+	0.0236781i	0.000730723	+	0.00126565i
$351$	0.358441	+	0.300767i	0.0191321	+	0.0160538i
$352$	1.17365	+	0.984808i	0.0625557	+	0.0524904i
$353$	−18.0963	−	31.3437i	−0.963167	−	1.66825i	−0.714461	−	0.699675i	$-0.753328\pi$
$353$	−18.0963	−	31.3437i	−0.963167	−	1.66825i	−0.248706	−	0.968579i	$-0.580005\pi$
$354$	−7.11721	+	12.3274i	−0.378276	+	0.655192i
$355$	9.30763	−	3.38770i	0.493998	−	0.179800i
$356$	2.91147	+	16.5118i	0.154308	+	0.875123i
$357$	−0.238703	+	1.35375i	−0.0126335	+	0.0716482i
$358$	−14.8268	−	5.39652i	−0.783622	−	0.285215i
$359$	1.43376	−	1.20307i	0.0756711	−	0.0634956i	−0.604168	−	0.796857i	$-0.706494\pi$
$359$	1.43376	−	1.20307i	0.0756711	−	0.0634956i	0.679839	+	0.733362i	$0.262050\pi$
$360$	−2.22668			−0.117356
$361$	−9.01889	+	16.7230i	−0.474678	+	0.880159i
$362$	−7.00269			−0.368053
$363$	6.62836	−	5.56185i	0.347898	−	0.291921i
$364$	−0.286989	−	0.104455i	−0.0150423	−	0.00547495i
$365$	−3.51532	+	19.9364i	−0.184000	+	1.04352i
$366$	−1.58378	−	8.98205i	−0.0827854	−	0.469499i
$367$	−3.32635	+	1.21069i	−0.173634	+	0.0631977i	−0.427374	−	0.904075i	$-0.640561\pi$
$367$	−3.32635	+	1.21069i	−0.173634	+	0.0631977i	0.253740	+	0.967272i	$0.418339\pi$
$368$	−2.95084	+	5.11100i	−0.153823	+	0.266429i
$369$	−1.73783	−	3.01000i	−0.0904676	−	0.156694i
$370$	7.97431	+	6.69124i	0.414565	+	0.347861i
$371$	5.97565	+	5.01417i	0.310240	+	0.260323i
$372$	−4.31908	−	7.48086i	−0.223934	−	0.387865i
$373$	−8.25924	+	14.3054i	−0.427647	+	0.740707i	−0.996664	−	0.0816196i	$-0.973991\pi$
$373$	−8.25924	+	14.3054i	−0.427647	+	0.740707i	0.569016	+	0.822326i	$0.307324\pi$
$374$	3.03209	−	1.10359i	0.156786	−	0.0570653i
$375$	1.94949	+	11.0561i	0.100671	+	0.570936i
$376$	0.805407	−	4.56769i	0.0415357	−	0.235561i
$377$	−3.66385	−	1.33353i	−0.188698	−	0.0686804i
$378$	−0.500000	+	0.419550i	−0.0257172	+	0.0215793i
$379$	−3.56893			−0.183323			−0.0916617	−	0.995790i	$-0.529218\pi$
$379$	−3.56893			−0.183323			−0.0916617	+	0.995790i	$0.529218\pi$
$380$	−4.97431	−	8.33429i	−0.255177	−	0.427540i
$381$	−9.67499			−0.495665
$382$	−3.36437	+	2.82304i	−0.172136	+	0.144439i
$383$	11.3366	+	4.12619i	0.579274	+	0.210839i	0.615005	−	0.788523i	$-0.289154\pi$
$383$	11.3366	+	4.12619i	0.579274	+	0.210839i	−0.0357313	+	0.999361i	$0.511376\pi$
$384$	0.173648	−	0.984808i	0.00886145	−	0.0502558i
$385$	0.386659	+	2.19285i	0.0197060	+	0.111758i
$386$	4.56418	−	1.66122i	0.232311	−	0.0845541i
$387$	−5.14543	+	8.91215i	−0.261557	+	0.453030i
$388$	−1.23396	−	2.13727i	−0.0626446	−	0.108504i
$389$	14.4743	+	12.1454i	0.733877	+	0.615796i	0.931185	−	0.364546i	$-0.118776\pi$
$389$	14.4743	+	12.1454i	0.733877	+	0.615796i	−0.197309	+	0.980341i	$0.563220\pi$
$390$	−0.798133	−	0.669713i	−0.0404151	−	0.0339123i
$391$	6.21466	+	10.7641i	0.314289	+	0.544364i
$392$	−3.28699	+	5.69323i	−0.166018	+	0.287552i
$393$	−1.78699	+	0.650411i	−0.0901417	+	0.0328089i
$394$	−3.52229	−	19.9759i	−0.177450	−	1.00637i
$395$	4.66209	−	26.4400i	0.234575	−	1.33034i
$396$	1.43969	+	0.524005i	0.0723473	+	0.0263323i
$397$	13.9743	−	11.7258i	0.701350	−	0.588503i	−0.220807	−	0.975318i	$-0.570869\pi$
$397$	13.9743	−	11.7258i	0.701350	−	0.588503i	0.922157	+	0.386815i	$0.126425\pi$
$398$	22.4611			1.12587
$399$	−2.68732	−	0.934204i	−0.134534	−	0.0467687i
$400$	−0.0418891			−0.00209445
$401$	25.9577	−	21.7811i	1.29627	−	1.08770i	0.305488	−	0.952196i	$-0.401180\pi$
$401$	25.9577	−	21.7811i	1.29627	−	1.08770i	0.990777	−	0.135500i	$-0.0432642\pi$
$402$	−0.233956	−	0.0851529i	−0.0116686	−	0.00424704i
$403$	0.701867	−	3.98048i	0.0349625	−	0.198282i
$404$	−0.996596	−	5.65198i	−0.0495825	−	0.281196i
$405$	−2.09240	+	0.761570i	−0.103972	+	0.0378427i
$406$	2.71941	−	4.71015i	0.134962	−	0.233761i
$407$	−3.58125	−	6.20291i	−0.177516	−	0.307467i
$408$	−1.61334	−	1.35375i	−0.0798723	−	0.0670208i
$409$	−0.132474	−	0.111159i	−0.00655043	−	0.00549647i	0.639507	−	0.768786i	$-0.279139\pi$
$409$	−0.132474	−	0.111159i	−0.00655043	−	0.00549647i	−0.646057	+	0.763289i	$0.723583\pi$
$410$	3.86959	+	6.70232i	0.191105	+	0.331004i
$411$	−0.889185	+	1.54011i	−0.0438603	+	0.0759682i
$412$	12.9757	−	4.72275i	0.639264	−	0.232673i
$413$	−1.61334	−	9.14971i	−0.0793873	−	0.450228i
$414$	−1.02481	+	5.81201i	−0.0503669	+	0.285645i
$415$	−7.76099	−	2.82477i	−0.380972	−	0.138663i
$416$	0.358441	−	0.300767i	0.0175740	−	0.0147463i
$417$	0.751030			0.0367781
$418$	1.25490	+	6.55926i	0.0613792	+	0.320824i
$419$	−36.5800			−1.78705			−0.893524	−	0.449015i	$-0.851775\pi$
$419$	−36.5800			−1.78705			−0.893524	+	0.449015i	$0.851775\pi$
$420$	1.11334	−	0.934204i	0.0543255	−	0.0455845i
$421$	−34.6400	−	12.6079i	−1.68825	−	0.614472i	−0.693845	−	0.720124i	$-0.744085\pi$
$421$	−34.6400	−	12.6079i	−1.68825	−	0.614472i	−0.994403	+	0.105652i	$0.966307\pi$
$422$	1.72921	−	9.80682i	0.0841765	−	0.477389i
$423$	−0.805407	−	4.56769i	−0.0391602	−	0.222089i
$424$	−11.2306	+	4.08759i	−0.545404	+	0.198511i
$425$	−0.0441106	+	0.0764018i	−0.00213968	+	0.00370603i
$426$	2.22416	+	3.85235i	0.107761	+	0.186647i
$427$	4.56031	+	3.82655i	0.220689	+	0.185180i
$428$	1.46585	+	1.23000i	0.0708546	+	0.0594541i
$429$	0.358441	+	0.620838i	0.0173057	+	0.0299743i
$430$	11.4572	−	19.8445i	0.552517	−	0.956987i
$431$	17.7763	−	6.47005i	0.856255	−	0.311651i	0.123667	−	0.992324i	$-0.460535\pi$
$431$	17.7763	−	6.47005i	0.856255	−	0.311651i	0.732588	+	0.680673i	$0.238312\pi$
$432$	−0.173648	−	0.984808i	−0.00835465	−	0.0473816i
$433$	3.86659	−	21.9285i	0.185817	−	1.05382i	−0.739085	−	0.673612i	$-0.764742\pi$
$433$	3.86659	−	21.9285i	0.185817	−	1.05382i	0.924902	−	0.380206i	$-0.124147\pi$
$434$	5.29813	+	1.92836i	0.254319	+	0.0925644i
$435$	14.2135	−	11.9265i	0.681484	−	0.571833i
$436$	−11.8152			−0.565846
$437$	−24.0433	+	9.14798i	−1.15015	+	0.437607i
$438$	−9.09152			−0.434410
$439$	25.6156	−	21.4941i	1.22257	−	1.02586i	0.223880	−	0.974617i	$-0.428128\pi$
$439$	25.6156	−	21.4941i	1.22257	−	1.02586i	0.998686	−	0.0512387i	$-0.0163169\pi$
$440$	−3.20574	−	1.16679i	−0.152828	−	0.0556247i
$441$	−1.14156	+	6.47410i	−0.0543600	+	0.308291i
$442$	−0.171122	−	0.970481i	−0.00813944	−	0.0461611i
$443$	−32.7904	+	11.9347i	−1.55792	+	0.567037i	−0.970259	−	0.242069i	$-0.922174\pi$
$443$	−32.7904	+	11.9347i	−1.55792	+	0.567037i	−0.587662	+	0.809106i	$0.699952\pi$
$444$	−2.33750	+	4.04866i	−0.110933	+	0.192141i
$445$	−18.6668	−	32.3319i	−0.884893	−	1.53268i
$446$	−1.47178	−	1.23497i	−0.0696909	−	0.0584776i
$447$	4.57919	+	3.84240i	0.216588	+	0.181739i
$448$	0.326352	+	0.565258i	0.0154187	+	0.0267059i
$449$	4.09152	−	7.08672i	0.193091	−	0.334443i	−0.753182	−	0.657812i	$-0.771482\pi$
$449$	4.09152	−	7.08672i	0.193091	−	0.334443i	0.946273	+	0.323369i	$0.104815\pi$
$450$	−0.0393628	+	0.0143269i	−0.00185558	+	0.000675377i
$451$	−0.924678	−	5.24411i	−0.0435414	−	0.246935i
$452$	0.937166	−	5.31493i	0.0440806	−	0.249994i
$453$	−15.5753	−	5.66895i	−0.731792	−	0.266351i
$454$	−0.690722	+	0.579585i	−0.0324172	+	0.0272013i
$455$	0.680045			0.0318810
$456$	3.29813	−	2.84997i	0.154449	−	0.133462i
$457$	−41.0259			−1.91911			−0.959556	−	0.281519i	$-0.909162\pi$
$457$	−41.0259			−1.91911			−0.959556	+	0.281519i	$0.909162\pi$
$458$	0.271259	−	0.227613i	0.0126751	−	0.0106357i
$459$	−1.97906	−	0.720317i	−0.0923744	−	0.0336215i
$460$	2.28194	−	12.9415i	0.106396	−	0.603401i
$461$	−0.802719	−	4.55245i	−0.0373863	−	0.212029i	0.960392	−	0.278653i	$-0.0898880\pi$
$461$	−0.802719	−	4.55245i	−0.0373863	−	0.212029i	−0.997778	+	0.0666248i	$0.978777\pi$
$462$	−0.939693	+	0.342020i	−0.0437185	+	0.0159122i
$463$	−2.75624	+	4.77396i	−0.128094	+	0.221865i	−0.922938	−	0.384949i	$-0.874219\pi$
$463$	−2.75624	+	4.77396i	−0.128094	+	0.221865i	0.794844	+	0.606813i	$0.207552\pi$
$464$	4.16637	+	7.21637i	0.193419	+	0.335012i
$465$	14.7344	+	12.3636i	0.683292	+	0.573350i
$466$	12.7947	+	10.7361i	0.592704	+	0.497338i
$467$	−5.58466	−	9.67291i	−0.258427	−	0.447609i	0.707394	−	0.706820i	$-0.249871\pi$
$467$	−5.58466	−	9.67291i	−0.258427	−	0.447609i	−0.965821	+	0.259211i	$0.916537\pi$
$468$	0.233956	−	0.405223i	0.0108146	−	0.0187314i
$469$	0.152704	−	0.0555796i	0.00705120	−	0.00256643i
$470$	1.79339	+	10.1708i	0.0827227	+	0.469144i
$471$	2.90033	−	16.4486i	0.133640	−	0.757911i
$472$	13.3760	+	4.86846i	0.615679	+	0.224089i
$473$	−12.0778	+	10.1345i	−0.555340	+	0.465986i
$474$	12.0574			0.553813
$475$	−0.141559	−	0.115326i	−0.00649519	−	0.00529153i
$476$	1.37464			0.0630064
$477$	−9.15523	+	7.68215i	−0.419189	+	0.351741i
$478$	9.44831	+	3.43890i	0.432156	+	0.157292i
$479$	1.50459	−	8.53293i	0.0687463	−	0.389879i	−0.930948	−	0.365152i	$-0.881017\pi$
$479$	1.50459	−	8.53293i	0.0687463	−	0.389879i	0.999694	−	0.0247276i	$-0.00787184\pi$
$480$	0.386659	+	2.19285i	0.0176485	+	0.100090i
$481$	−2.05556	+	0.748163i	−0.0937255	+	0.0341133i
$482$	−11.5496	+	20.0045i	−0.526071	+	0.911182i
$483$	−1.92602	−	3.33597i	−0.0876370	−	0.151792i
$484$	−6.62836	−	5.56185i	−0.301289	−	0.252811i
$485$	4.20961	+	3.53228i	0.191148	+	0.160393i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	0.0471036	−	0.0815859i	0.00213447	−	0.00369701i	−0.864956	−	0.501847i	$-0.832654\pi$
$487$	0.0471036	−	0.0815859i	0.00213447	−	0.00369701i	0.867091	+	0.498150i	$0.165987\pi$
$488$	−8.57057	+	3.11943i	−0.387972	+	0.141210i
$489$	2.75356	+	15.6162i	0.124520	+	0.706189i
$490$	2.54189	−	14.4158i	0.114831	−	0.651238i
$491$	26.3075	+	9.57516i	1.18724	+	0.432121i	0.858754	−	0.512388i	$-0.171239\pi$
$491$	26.3075	+	9.57516i	1.18724	+	0.432121i	0.328488	+	0.944508i	$0.393461\pi$
$492$	−2.66250	+	2.23411i	−0.120035	+	0.100721i
$493$	17.5493			0.790382
$494$	2.03936	−	0.0295733i	0.0917553	−	0.00133056i
$495$	−3.41147			−0.153334
$496$	−6.61721	+	5.55250i	−0.297122	+	0.249315i
$497$	−2.72833	−	0.993031i	−0.122382	−	0.0445435i
$498$	0.644086	−	3.65279i	0.0288622	−	0.163685i
$499$	−6.42144	−	36.4178i	−0.287463	−	1.63028i	−0.696353	−	0.717700i	$-0.745195\pi$
$499$	−6.42144	−	36.4178i	−0.287463	−	1.63028i	0.408890	−	0.912584i	$-0.365916\pi$
$500$	10.5496	−	3.83975i	0.471794	−	0.171719i
$501$	−1.13176	+	1.96026i	−0.0505633	+	0.0875781i
$502$	6.08125	+	10.5330i	0.271420	+	0.470112i
$503$	−17.3084	−	14.5235i	−0.771743	−	0.647570i	0.169411	−	0.985545i	$-0.445813\pi$
$503$	−17.3084	−	14.5235i	−0.771743	−	0.647570i	−0.941155	+	0.337976i	$0.890258\pi$
$504$	0.500000	+	0.419550i	0.0222718	+	0.0186882i
$505$	6.38965	+	11.0672i	0.284336	+	0.492484i
$506$	−4.52094	+	7.83051i	−0.200980	+	0.348108i
$507$	−12.0103	+	4.37138i	−0.533395	+	0.194140i
$508$	1.68004	+	9.52801i	0.0745399	+	0.422737i
$509$	−7.71869	+	43.7749i	−0.342125	+	1.94029i	−0.00174780	+	0.999998i	$0.500556\pi$
$509$	−7.71869	+	43.7749i	−0.342125	+	1.94029i	−0.340377	+	0.940289i	$0.610555\pi$
$510$	4.40673	+	1.60392i	0.195133	+	0.0710226i
$511$	4.54576	−	3.81435i	0.201093	−	0.168737i
$512$	−1.00000			−0.0441942
$513$	2.12449	−	3.80612i	0.0937983	−	0.168044i
$514$	3.94625			0.174062
$515$	−23.5535	+	19.7637i	−1.03789	+	0.870894i
$516$	9.67024	+	3.51968i	0.425709	+	0.154945i
$517$	1.23396	−	6.99811i	0.0542693	−	0.307777i
$518$	−0.529867	−	3.00503i	−0.0232810	−	0.132033i
$519$	8.79086	−	3.19961i	0.385876	−	0.140447i
$520$	−0.520945	+	0.902302i	−0.0228449	+	0.0395686i
$521$	12.1322	+	21.0136i	0.531522	+	0.920624i	0.999323	+	0.0367899i	$0.0117132\pi$
$521$	12.1322	+	21.0136i	0.531522	+	0.920624i	−0.467801	+	0.883834i	$0.654953\pi$
$522$	6.38326	+	5.35619i	0.279388	+	0.234434i
$523$	−18.5462	−	15.5621i	−0.810970	−	0.680485i	0.139869	−	0.990170i	$-0.455332\pi$
$523$	−18.5462	−	15.5621i	−0.810970	−	0.680485i	−0.950839	+	0.309685i	$0.899776\pi$
$524$	0.950837	+	1.64690i	0.0415375	+	0.0719451i
$525$	0.0136706	−	0.0236781i	0.000596633	−	0.00103340i
$526$	8.52229	−	3.10186i	0.371589	−	0.135247i
$527$	3.15910	+	17.9161i	0.137613	+	0.780440i
$528$	0.266044	−	1.50881i	0.0115781	−	0.0656627i
$529$	−11.1163	−	4.04601i	−0.483319	−	0.175914i
$530$	20.3858	−	17.1057i	0.885502	−	0.743024i
$531$	14.2344			0.617721
$532$	−0.453363	+	2.80872i	−0.0196558	+	0.121773i
$533$	−1.62630			−0.0704427
$534$	12.8439	−	10.7773i	0.555810	−	0.466380i
$535$	−4.00387	−	1.45729i	−0.173102	−	0.0630041i
$536$	−0.0432332	+	0.245188i	−0.00186739	+	0.0105905i
$537$	2.73989	+	15.5387i	0.118235	+	0.670543i
$538$	−26.3234	+	9.58094i	−1.13488	+	0.413064i
$539$	−5.03596	+	8.72254i	−0.216914	+	0.375706i
$540$	1.11334	+	1.92836i	0.0479106	+	0.0829835i
$541$	26.2219	+	22.0028i	1.12737	+	0.945975i	0.998953	−	0.0457455i	$-0.0145663\pi$
$541$	26.2219	+	22.0028i	1.12737	+	0.945975i	0.128416	+	0.991720i	$0.459011\pi$
$542$	12.8969	+	10.8218i	0.553970	+	0.464836i
$543$	3.50134	+	6.06451i	0.150257	+	0.260253i
$544$	−1.05303	+	1.82391i	−0.0451484	+	0.0781994i
$545$	24.7221	−	8.99811i	1.05898	−	0.385437i
$546$	0.0530334	+	0.300767i	0.00226962	+	0.0128717i
$547$	4.39218	−	24.9093i	0.187796	−	1.06504i	−0.734514	−	0.678593i	$-0.762590\pi$
$547$	4.39218	−	24.9093i	0.187796	−	1.06504i	0.922310	−	0.386451i	$-0.126299\pi$
$548$	1.67112	+	0.608239i	0.0713868	+	0.0259827i
$549$	−6.98680	+	5.86262i	−0.298189	+	0.250210i
$550$	−0.0641778			−0.00273655
$551$	−5.78787	+	35.8575i	−0.246571	+	1.52758i
$552$	5.90167			0.251192
$553$	−6.02869	+	5.05867i	−0.256366	+	0.215116i
$554$	−17.9957	−	6.54991i	−0.764565	−	0.278279i
$555$	1.80763	−	10.2516i	0.0767296	−	0.435155i
$556$	−0.130415	−	0.739620i	−0.00553083	−	0.0313669i
$557$	10.2369	−	3.72594i	0.433753	−	0.157873i	−0.115910	−	0.993260i	$-0.536978\pi$
$557$	10.2369	−	3.72594i	0.433753	−	0.157873i	0.549663	+	0.835386i	$0.314756\pi$
$558$	−4.31908	+	7.48086i	−0.182841	+	0.316690i
$559$	2.40760	+	4.17009i	0.101831	+	0.176376i
$560$	−1.11334	−	0.934204i	−0.0470472	−	0.0394773i
$561$	−2.47178	−	2.07407i	−0.104359	−	0.0875673i
$562$	−1.97906	−	3.42782i	−0.0834814	−	0.144594i
$563$	−8.64337	+	14.9708i	−0.364275	+	0.630942i	−0.988659	−	0.150175i	$-0.952016\pi$
$563$	−8.64337	+	14.9708i	−0.364275	+	0.630942i	0.624385	+	0.781117i	$0.285350\pi$
$564$	−4.35844	+	1.58634i	−0.183523	+	0.0667971i
$565$	2.08677	+	11.8347i	0.0877911	+	0.497888i
$566$	1.14203	−	6.47675i	0.0480029	−	0.272238i
$567$	0.613341	+	0.223238i	0.0257579	+	0.00937511i
$568$	3.40760	−	2.85932i	0.142980	−	0.119974i
$569$	6.47834			0.271586			0.135793	−	0.990737i	$-0.456642\pi$
$569$	6.47834			0.271586			0.135793	+	0.990737i	$0.456642\pi$
$570$	−4.73055	+	8.47502i	−0.198141	+	0.354980i
$571$	38.5476			1.61317			0.806583	−	0.591121i	$-0.201314\pi$
$571$	38.5476			1.61317			0.806583	+	0.591121i	$0.201314\pi$
$572$	0.549163	−	0.460802i	0.0229617	−	0.0192671i
$573$	4.12701	+	1.50211i	0.172408	+	0.0627515i
$574$	0.393933	−	2.23411i	0.0164425	−	0.0932498i
$575$	−0.0429285	−	0.243460i	−0.00179024	−	0.0101530i
$576$	−0.939693	+	0.342020i	−0.0391539	+	0.0142508i
$577$	5.72756	−	9.92042i	0.238441	−	0.412993i	−0.721826	−	0.692075i	$-0.756697\pi$
$577$	5.72756	−	9.92042i	0.238441	−	0.412993i	0.960267	+	0.279082i	$0.0900302\pi$
$578$	−6.28224	−	10.8812i	−0.261307	−	0.452597i
$579$	−3.72075	−	3.12208i	−0.154629	−	0.129749i
$580$	−14.2135	−	11.9265i	−0.590183	−	0.495222i
$581$	1.21048	+	2.09662i	0.0502194	+	0.0869825i
$582$	−1.23396	+	2.13727i	−0.0511491	+	0.0885928i
$583$	−17.2062	+	6.26255i	−0.712608	+	0.259368i
$584$	1.57873	+	8.95340i	0.0653281	+	0.370494i
$585$	−0.180922	+	1.02606i	−0.00748021	+	0.0424224i
$586$	20.3871	+	7.42031i	0.842184	+	0.306530i
$587$	32.7467	−	27.4778i	1.35160	−	1.13413i	0.373124	−	0.927781i	$-0.378286\pi$
$587$	32.7467	−	27.4778i	1.35160	−	1.13413i	0.978479	−	0.206348i	$-0.0661580\pi$
$588$	6.57398			0.271106
$589$	−37.6489	+	0.545955i	−1.55130	+	0.0224957i
$590$	−31.6955			−1.30488
$591$	−15.5385	+	13.0383i	−0.639168	+	0.536326i
$592$	4.39306	+	1.59894i	0.180553	+	0.0657161i
$593$	5.68092	−	32.2181i	0.233288	−	1.32304i	−0.612903	−	0.790158i	$-0.709998\pi$
$593$	5.68092	−	32.2181i	0.233288	−	1.32304i	0.846190	−	0.532881i	$-0.178891\pi$
$594$	−0.266044	−	1.50881i	−0.0109159	−	0.0619073i
$595$	−2.87629	+	1.04688i	−0.117916	+	0.0429180i
$596$	2.98886	−	5.17685i	0.122428	−	0.212052i
$597$	−11.2306	−	19.4519i	−0.459636	−	0.796113i
$598$	2.11540	+	1.77503i	0.0865051	+	0.0725864i
$599$	7.05896	+	5.92317i	0.288421	+	0.242014i	0.775506	−	0.631341i	$-0.217495\pi$
$599$	7.05896	+	5.92317i	0.288421	+	0.242014i	−0.487084	+	0.873355i	$0.661939\pi$
$600$	0.0209445	+	0.0362770i	0.000855057	+	0.00148100i
$601$	−4.83884	+	8.38112i	−0.197380	+	0.341873i	−0.947678	−	0.319227i	$-0.896577\pi$
$601$	−4.83884	+	8.38112i	−0.197380	+	0.341873i	0.750298	+	0.661100i	$0.229910\pi$
$602$	−6.31180	+	2.29731i	−0.257250	+	0.0936313i
$603$	0.0432332	+	0.245188i	0.00176059	+	0.00998482i
$604$	−2.87820	+	16.3231i	−0.117112	+	0.664178i
$605$	18.1049	+	6.58964i	0.736068	+	0.267907i
$606$	−4.39646	+	3.68907i	−0.178594	+	0.149858i
$607$	36.4766			1.48054			0.740269	−	0.672310i	$-0.234698\pi$
$607$	36.4766			1.48054			0.740269	+	0.672310i	$0.234698\pi$
$608$	−3.37939	−	2.75314i	−0.137052	−	0.111654i
$609$	−5.43882			−0.220392
$610$	15.5574	−	13.0542i	0.629900	−	0.528548i
$611$	−2.03936	−	0.742267i	−0.0825038	−	0.0300289i
$612$	−0.365715	+	2.07407i	−0.0147831	+	0.0838393i
$613$	−2.02987	−	11.5119i	−0.0819856	−	0.464963i	−0.997966	−	0.0637414i	$-0.979697\pi$
$613$	−2.02987	−	11.5119i	−0.0819856	−	0.464963i	0.915981	−	0.401222i	$-0.131414\pi$
$614$	16.7271	−	6.08818i	0.675053	−	0.245699i
$615$	3.86959	−	6.70232i	0.156037	−	0.270264i
$616$	0.500000	+	0.866025i	0.0201456	+	0.0348932i
$617$	13.6459	+	11.4503i	0.549363	+	0.460970i	0.874725	−	0.484619i	$-0.161042\pi$
$617$	13.6459	+	11.4503i	0.549363	+	0.460970i	−0.325362	+	0.945589i	$0.605486\pi$
$618$	−10.5778	−	8.87587i	−0.425503	−	0.357040i
$619$	−13.9932	−	24.2369i	−0.562434	−	0.974164i	−0.997283	−	0.0736609i	$-0.976532\pi$
$619$	−13.9932	−	24.2369i	−0.562434	−	0.974164i	0.434849	−	0.900503i	$-0.356802\pi$
$620$	9.61721	−	16.6575i	0.386236	−	0.668981i
$621$	5.54576	−	2.01849i	0.222544	−	0.0809993i
$622$	0.282241	+	1.60067i	0.0113168	+	0.0641810i
$623$	−1.90033	+	10.7773i	−0.0761351	+	0.431784i
$624$	−0.439693	−	0.160035i	−0.0176018	−	0.00640653i
$625$	−18.9893	+	15.9339i	−0.759573	+	0.637357i
$626$	−30.0729			−1.20195
$627$	5.05303	−	4.36640i	0.201799	−	0.174377i
$628$	−16.7023			−0.666496
$629$	7.54236	−	6.32879i	0.300733	−	0.252345i
$630$	−1.36571	−	0.497079i	−0.0544114	−	0.0198041i
$631$	−0.653170	+	3.70431i	−0.0260023	+	0.147466i	−0.995045	−	0.0994276i	$-0.968299\pi$
$631$	−0.653170	+	3.70431i	−0.0260023	+	0.147466i	0.969042	+	0.246894i	$0.0794099\pi$
$632$	−2.09374	−	11.8742i	−0.0832845	−	0.472330i
$633$	−9.35756	+	3.40587i	−0.371930	+	0.135371i
$634$	−5.66637	+	9.81445i	−0.225040	+	0.389782i
$635$	−10.7716	−	18.6569i	−0.427456	−	0.740376i
$636$	9.15523	+	7.68215i	0.363028	+	0.304617i
$637$	2.35638	+	1.97724i	0.0933632	+	0.0783410i
$638$	6.38326	+	11.0561i	0.252716	+	0.437716i
$639$	2.22416	−	3.85235i	0.0879862	−	0.152397i
$640$	2.09240	−	0.761570i	0.0827092	−	0.0301037i
$641$	2.91329	+	16.5221i	0.115068	+	0.652582i	0.986717	+	0.162451i	$0.0519400\pi$
$641$	2.91329	+	16.5221i	0.115068	+	0.652582i	−0.871649	+	0.490131i	$0.836949\pi$
$642$	0.332282	−	1.88446i	0.0131141	−	0.0743738i
$643$	20.8396	+	7.58500i	0.821834	+	0.299123i	0.718503	−	0.695524i	$-0.244828\pi$
$643$	20.8396	+	7.58500i	0.821834	+	0.299123i	0.103331	+	0.994647i	$0.467050\pi$
$644$	−2.95084	+	2.47605i	−0.116279	+	0.0975699i
$645$	−22.9145			−0.902256
$646$	−8.58007	+	3.26454i	−0.337578	+	0.128442i
$647$	16.6759			0.655598			0.327799	−	0.944747i	$-0.393693\pi$
$647$	16.6759			0.655598			0.327799	+	0.944747i	$0.393693\pi$
$648$	−0.766044	+	0.642788i	−0.0300931	+	0.0252511i
$649$	20.4932	+	7.45891i	0.804428	+	0.292788i
$650$	−0.00340357	+	0.0193026i	−0.000133499	+	0.000757110i
$651$	−0.979055	−	5.55250i	−0.0383722	−	0.217620i
$652$	14.9008	−	5.42345i	0.583560	−	0.212399i
$653$	13.4033	−	23.2152i	0.524513	−	0.908482i	−0.475080	−	0.879943i	$-0.657581\pi$
$653$	13.4033	−	23.2152i	0.524513	−	0.908482i	0.999593	−	0.0285398i	$-0.00908575\pi$
$654$	5.90760	+	10.2323i	0.231006	+	0.400113i
$655$	−3.24376	−	2.72183i	−0.126744	−	0.106351i
$656$	2.66250	+	2.23411i	0.103953	+	0.0872272i
$657$	4.54576	+	7.87349i	0.177347	+	0.307174i
$658$	1.51367	−	2.62175i	0.0590090	−	0.102207i
$659$	16.6116	−	6.04612i	0.647096	−	0.235524i	0.00244038	−	0.999997i	$-0.499223\pi$
$659$	16.6116	−	6.04612i	0.647096	−	0.235524i	0.644655	+	0.764474i	$0.277001\pi$
$660$	0.592396	+	3.35965i	0.0230590	+	0.130774i
$661$	1.50593	−	8.54055i	0.0585739	−	0.332189i	−0.941413	−	0.337255i	$-0.890502\pi$
$661$	1.50593	−	8.54055i	0.0585739	−	0.332189i	0.999987	+	0.00506615i	$0.00161261\pi$
$662$	−30.1869	−	10.9871i	−1.17325	−	0.427027i
$663$	−0.754900	+	0.633436i	−0.0293179	+	0.0246006i
$664$	−3.70914			−0.143943
$665$	−1.19042	−	6.22221i	−0.0461624	−	0.241287i
$666$	4.67499			0.181152
$667$	−37.6719	+	31.6105i	−1.45866	+	1.22396i
$668$	2.12701	+	0.774169i	0.0822965	+	0.0299535i
$669$	−0.333626	+	1.89209i	−0.0128987	+	0.0731523i
$670$	−0.0962667	−	0.545955i	−0.00371911	−	0.0210921i
$671$	−13.1309	+	4.77925i	−0.506912	+	0.184501i
$672$	0.326352	−	0.565258i	0.0125893	−	0.0218053i
$673$	−1.08243	−	1.87483i	−0.0417248	−	0.0722694i	0.844409	−	0.535699i	$-0.179952\pi$
$673$	−1.08243	−	1.87483i	−0.0417248	−	0.0722694i	−0.886134	+	0.463430i	$0.846619\pi$
$674$	−23.2369	−	19.4981i	−0.895054	−	0.751039i
$675$	0.0320889	+	0.0269258i	0.00123510	+	0.00103637i
$676$	6.39053	+	11.0687i	0.245790	+	0.425720i
$677$	−6.37686	+	11.0450i	−0.245083	+	0.424496i	−0.962155	−	0.272503i	$-0.912148\pi$
$677$	−6.37686	+	11.0450i	−0.245083	+	0.424496i	0.717072	+	0.696999i	$0.245482\pi$
$678$	−5.07145	+	1.84586i	−0.194768	+	0.0708897i
$679$	−0.279715	−	1.58634i	−0.0107345	−	0.0608782i
$680$	0.814330	−	4.61830i	0.0312281	−	0.177104i
$681$	0.847296	+	0.308391i	0.0324685	+	0.0118176i
$682$	−10.1382	+	8.50692i	−0.388210	+	0.325747i
$683$	−25.2608			−0.966579			−0.483289	−	0.875461i	$-0.660558\pi$
$683$	−25.2608			−0.966579			−0.483289	+	0.875461i	$0.660558\pi$
$684$	−4.11721	−	1.43128i	−0.157426	−	0.0547265i
$685$	−3.95987			−0.151299
$686$	−6.78699	+	5.69496i	−0.259128	+	0.217435i
$687$	−0.332748	−	0.121111i	−0.0126951	−	0.00462065i
$688$	1.78699	−	10.1345i	0.0681283	−	0.386375i
$689$	0.971066	+	5.50719i	0.0369947	+	0.209807i
$690$	−12.3486	+	4.49454i	−0.470105	+	0.171104i
$691$	−7.64796	+	13.2466i	−0.290942	+	0.503926i	−0.974033	−	0.226407i	$-0.927302\pi$
$691$	−7.64796	+	13.2466i	−0.290942	+	0.503926i	0.683091	+	0.730333i	$0.260635\pi$
$692$	−4.67752	−	8.10170i	−0.177813	−	0.307980i
$693$	0.766044	+	0.642788i	0.0290996	+	0.0244175i
$694$	−3.29813	−	2.76746i	−0.125195	−	0.105051i
$695$	0.836152	+	1.44826i	0.0317171	+	0.0549355i
$696$	4.16637	−	7.21637i	0.157926	−	0.273536i
$697$	6.87851	−	2.50357i	0.260542	−	0.0948296i
$698$	0.461981	+	2.62003i	0.0174863	+	0.0991695i
$699$	2.90033	−	16.4486i	0.109701	−	0.622143i
$700$	−0.0256923	−	0.00935122i	−0.000971077	−	0.000353443i
$701$	30.5369	−	25.6235i	1.15336	−	0.967786i	0.153570	−	0.988138i	$-0.450923\pi$
$701$	30.5369	−	25.6235i	1.15336	−	0.967786i	0.999793	+	0.0203518i	$0.00647861\pi$
$702$	−0.467911			−0.0176602
$703$	10.4437	+	17.4981i	0.393893	+	0.659954i
$704$	−1.53209			−0.0577428
$705$	7.91147	−	6.63852i	0.297963	−	0.250021i
$706$	34.0099	+	12.3786i	1.27998	+	0.465874i
$707$	0.650482	−	3.68907i	0.0244639	−	0.138742i
$708$	−2.47178	−	14.0182i	−0.0928952	−	0.526835i
$709$	−22.4351	+	8.16571i	−0.842568	+	0.306670i	−0.727006	−	0.686631i	$-0.759089\pi$
$709$	−22.4351	+	8.16571i	−0.842568	+	0.306670i	−0.115562	+	0.993300i	$0.536867\pi$
$710$	−4.95249	+	8.57796i	−0.185863	+	0.321925i
$711$	−6.02869	−	10.4420i	−0.226093	−	0.391605i
$712$	−12.8439	−	10.7773i	−0.481345	−	0.403897i
$713$	−39.0526	−	32.7690i	−1.46253	−	1.22721i
$714$	−0.687319	−	1.19047i	−0.0257223	−	0.0445523i
$715$	−0.798133	+	1.38241i	−0.0298485	+	0.0516991i
$716$	14.8268	−	5.39652i	0.554104	−	0.201677i
$717$	−1.74598	−	9.90193i	−0.0652047	−	0.369794i
$718$	−0.325008	+	1.84321i	−0.0121292	+	0.0687880i
$719$	34.3050	+	12.4860i	1.27936	+	0.465649i	0.890221	−	0.455530i	$-0.150550\pi$
$719$	34.3050	+	12.4860i	1.27936	+	0.465649i	0.389140	+	0.921179i	$0.372772\pi$
$720$	1.70574	−	1.43128i	0.0635691	−	0.0533408i
$721$	9.01279			0.335654
$722$	−3.84049	−	18.6078i	−0.142928	−	0.692511i
$723$	23.0993			0.859071
$724$	5.36437	−	4.50124i	0.199365	−	0.167287i
$725$	−0.328001	−	0.119382i	−0.0121816	−	0.00443375i
$726$	−1.50253	+	8.52125i	−0.0557640	+	0.316253i
$727$	5.59580	+	31.7354i	0.207537	+	1.17700i	0.893398	+	0.449267i	$0.148315\pi$
$727$	5.59580	+	31.7354i	0.207537	+	1.17700i	−0.685861	+	0.727733i	$0.740574\pi$
$728$	0.286989	−	0.104455i	0.0106365	−	0.00387138i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	−10.1220	−	17.5317i	−0.374631	−	0.648879i
$731$	−16.6027	−	13.9313i	−0.614072	−	0.515267i
$732$	6.98680	+	5.86262i	0.258239	+	0.216689i
$733$	3.48767	+	6.04083i	0.128820	+	0.223123i	0.923220	−	0.384272i	$-0.125548\pi$
$733$	3.48767	+	6.04083i	0.128820	+	0.223123i	−0.794400	+	0.607396i	$0.792214\pi$
$734$	1.76991	−	3.06558i	0.0653287	−	0.113153i
$735$	−13.7554	+	5.00654i	−0.507374	+	0.184669i
$736$	−1.02481	−	5.81201i	−0.0377752	−	0.214234i
$737$	−0.0662372	+	0.375650i	−0.00243988	+	0.0138372i
$738$	3.26604	+	1.18874i	0.120225	+	0.0437582i
$739$	18.6682	−	15.6645i	0.686720	−	0.576227i	−0.231241	−	0.972896i	$-0.574279\pi$
$739$	18.6682	−	15.6645i	0.686720	−	0.576227i	0.917961	+	0.396670i	$0.129834\pi$
$740$	−10.4097			−0.382669
$741$	−1.04529	−	1.75135i	−0.0383998	−	0.0643376i
$742$	−7.80066			−0.286371
$743$	−29.1536	+	24.4628i	−1.06954	+	0.897453i	−0.995011	−	0.0997653i	$-0.968191\pi$
$743$	−29.1536	+	24.4628i	−1.06954	+	0.897453i	−0.0745322	+	0.997219i	$0.523746\pi$
$744$	8.11721	+	2.95442i	0.297591	+	0.108314i
$745$	−2.31134	+	13.1082i	−0.0846808	+	0.480249i
$746$	−2.86840	−	16.2675i	−0.105020	−	0.595596i
$747$	−3.48545	+	1.26860i	−0.127526	+	0.0464157i
$748$	−1.61334	+	2.79439i	−0.0589896	+	0.102173i
$749$	0.624485	+	1.08164i	0.0228182	+	0.0395223i
$750$	−8.60014	−	7.21637i	−0.314033	−	0.263505i
$751$	−2.24897	−	1.88711i	−0.0820661	−	0.0688616i	0.600832	−	0.799376i	$-0.294836\pi$
$751$	−2.24897	−	1.88711i	−0.0820661	−	0.0688616i	−0.682898	+	0.730514i	$0.739281\pi$
$752$	2.31908	+	4.01676i	0.0845681	+	0.146476i
$753$	6.08125	−	10.5330i	0.221613	−	0.383845i
$754$	3.66385	−	1.33353i	0.133429	−	0.0485644i
$755$	−6.40884	−	36.3463i	−0.233242	−	1.32278i
$756$	0.113341	−	0.642788i	0.00412216	−	0.0233780i
$757$	−10.6800	−	3.88722i	−0.388173	−	0.141283i	0.140559	−	0.990072i	$-0.455110\pi$
$757$	−10.6800	−	3.88722i	−0.388173	−	0.141283i	−0.528732	+	0.848789i	$0.677332\pi$
$758$	2.73396	−	2.29406i	0.0993017	−	0.0833241i
$759$	9.04189			0.328200
$760$	9.16772	+	3.18701i	0.332548	+	0.115605i
$761$	10.4976			0.380538			0.190269	−	0.981732i	$-0.439064\pi$
$761$	10.4976			0.380538			0.190269	+	0.981732i	$0.439064\pi$
$762$	7.41147	−	6.21897i	0.268489	−	0.225289i
$763$	−7.24675	−	2.63760i	−0.262350	−	0.0954876i
$764$	0.762641	−	4.32515i	0.0275914	−	0.156478i
$765$	−0.814330	−	4.61830i	−0.0294422	−	0.166975i
$766$	−11.3366	+	4.12619i	−0.409609	+	0.149085i
$767$	3.33022	−	5.76811i	0.120247	−	0.208275i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	5.93036	+	4.97616i	0.213854	+	0.179445i	0.743422	−	0.668823i	$-0.233201\pi$
$769$	5.93036	+	4.97616i	0.213854	+	0.179445i	−0.529568	+	0.848268i	$0.677646\pi$
$770$	−1.70574	−	1.43128i	−0.0614705	−	0.0515799i
$771$	−1.97313	−	3.41755i	−0.0710604	−	0.123080i
$772$	−2.42855	+	4.20637i	−0.0874054	+	0.151391i
$773$	5.78224	−	2.10456i	0.207973	−	0.0756959i	−0.235933	−	0.971769i	$-0.575815\pi$
$773$	5.78224	−	2.10456i	0.207973	−	0.0756959i	0.443906	+	0.896073i	$0.353592\pi$
$774$	−1.78699	−	10.1345i	−0.0642320	−	0.364278i
$775$	0.0628336	−	0.356347i	0.00225705	−	0.0128004i
$776$	2.31908	+	0.844075i	0.0832500	+	0.0303005i
$777$	−2.33750	+	1.96139i	−0.0838572	+	0.0703646i
$778$	−18.8949			−0.677414
$779$	2.84683	+	14.8801i	0.101998	+	0.533136i
$780$	1.04189			0.0373056
$781$	5.22075	−	4.38073i	0.186813	−	0.156755i
$782$	−11.6797	−	4.25108i	−0.417667	−	0.152018i
$783$	1.44697	−	8.20616i	0.0517104	−	0.293264i
$784$	−1.14156	−	6.47410i	−0.0407700	−	0.231218i
$785$	34.9479	−	12.7200i	1.24734	−	0.453996i
$786$	0.950837	−	1.64690i	0.0339152	−	0.0587429i
$787$	4.02600	+	6.97323i	0.143511	+	0.248569i	0.928817	−	0.370540i	$-0.120827\pi$
$787$	4.02600	+	6.97323i	0.143511	+	0.248569i	−0.785305	+	0.619109i	$0.787494\pi$
$788$	15.5385	+	13.0383i	0.553536	+	0.464472i
$789$	−6.94743	−	5.82959i	−0.247335	−	0.207539i
$790$	13.4240	+	23.2510i	0.477603	+	0.827233i
$791$	1.76130	−	3.05066i	0.0626245	−	0.108469i
$792$	−1.43969	+	0.524005i	−0.0511572	+	0.0186197i
$793$	0.741067	+	4.20280i	0.0263161	+	0.149246i
$794$	−3.16772	+	17.9650i	−0.112418	+	0.637555i
$795$	−25.0069	−	9.10175i	−0.886902	−	0.322806i
$796$	−17.2062	+	14.4377i	−0.609858	+	0.511731i
$797$	10.2139			0.361794			0.180897	−	0.983502i	$-0.442100\pi$
$797$	10.2139			0.361794			0.180897	+	0.983502i	$0.442100\pi$
$798$	2.65910	−	1.01173i	0.0941311	−	0.0358150i
$799$	9.76827			0.345576
$800$	0.0320889	−	0.0269258i	0.00113451	−	0.000951970i
$801$	−15.7554	−	5.73448i	−0.556689	−	0.202618i
$802$	−5.88413	+	33.3706i	−0.207776	+	1.17836i
$803$	2.41875	+	13.7174i	0.0853558	+	0.484077i
$804$	0.233956	−	0.0851529i	0.00825098	−	0.00300311i
$805$	4.28864	−	7.42814i	0.151155	−	0.261807i
$806$	2.02094	+	3.50038i	0.0711847	+	0.123296i
$807$	21.4590	+	18.0063i	0.755394	+	0.633851i
$808$	4.39646	+	3.68907i	0.154667	+	0.129781i
$809$	−23.6498	−	40.9626i	−0.831482	−	1.44017i	−0.896863	−	0.442308i	$-0.854160\pi$
$809$	−23.6498	−	40.9626i	−0.831482	−	1.44017i	0.0653817	−	0.997860i	$-0.479173\pi$
$810$	1.11334	−	1.92836i	0.0391188	−	0.0677558i
$811$	−49.5023	+	18.0174i	−1.73826	+	0.632675i	−0.999162	−	0.0409232i	$-0.986970\pi$
$811$	−49.5023	+	18.0174i	−1.73826	+	0.632675i	−0.739098	+	0.673598i	$0.764748\pi$
$812$	0.944440	+	5.35619i	0.0331434	+	0.187965i
$813$	2.92350	−	16.5800i	0.102531	−	0.581485i
$814$	6.73055	+	2.44972i	0.235906	+	0.0858627i
$815$	−27.0480	+	22.6960i	−0.947451	+	0.795006i
$816$	2.10607			0.0737271
$817$	33.9406	−	29.3286i	1.18743	−	1.02608i
$818$	0.172933			0.00604646
$819$	0.233956	−	0.196312i	0.00817507	−	0.00685970i
$820$	−7.27244	−	2.64695i	−0.253965	−	0.0924356i
$821$	−9.57697	+	54.3137i	−0.334239	+	1.89556i	0.100384	+	0.994949i	$0.467993\pi$
$821$	−9.57697	+	54.3137i	−0.334239	+	1.89556i	−0.434623	+	0.900613i	$0.643118\pi$
$822$	−0.308811	−	1.75135i	−0.0107710	−	0.0610855i
$823$	23.1573	−	8.42858i	0.807214	−	0.293802i	0.0947417	−	0.995502i	$-0.469797\pi$
$823$	23.1573	−	8.42858i	0.807214	−	0.293802i	0.712473	+	0.701700i	$0.247575\pi$
$824$	−6.90420	+	11.9584i	−0.240519	+	0.416591i
$825$	0.0320889	+	0.0555796i	0.00111719	+	0.00193503i
$826$	7.11721	+	5.97205i	0.247639	+	0.207794i
$827$	28.7698	+	24.1407i	1.00042	+	0.839454i	0.987043	−	0.160456i	$-0.0512966\pi$
$827$	28.7698	+	24.1407i	1.00042	+	0.839454i	0.0133794	+	0.999910i	$0.495741\pi$
$828$	−2.95084	−	5.11100i	−0.102549	−	0.177620i
$829$	6.50000	−	11.2583i	0.225754	−	0.391018i	−0.730791	−	0.682601i	$-0.760849\pi$
$829$	6.50000	−	11.2583i	0.225754	−	0.391018i	0.956545	+	0.291583i	$0.0941820\pi$
$830$	7.76099	−	2.82477i	0.269388	−	0.0980492i
$831$	3.32547	+	18.8597i	0.115359	+	0.654236i
$832$	−0.0812519	+	0.460802i	−0.00281690	+	0.0159755i
$833$	−13.0103	−	4.73535i	−0.450779	−	0.164070i
$834$	−0.575322	+	0.482753i	−0.0199218	+	0.0167164i
$835$	−5.04013			−0.174421
$836$	−5.17752	−	4.21805i	−0.179068	−	0.145884i
$837$	8.63816			0.298578
$838$	28.0219	−	23.5131i	0.968000	−	0.812248i
$839$	17.7062	+	6.44453i	0.611286	+	0.222490i	0.629066	−	0.777352i	$-0.283438\pi$
$839$	17.7062	+	6.44453i	0.611286	+	0.222490i	−0.0177798	+	0.999842i	$0.505660\pi$
$840$	−0.252374	+	1.43128i	−0.00870773	+	0.0493840i
$841$	7.02141	+	39.8204i	0.242118	+	1.37312i
$842$	34.6400	−	12.6079i	1.19377	−	0.434498i
$843$	−1.97906	+	3.42782i	−0.0681623	+	0.118061i
$844$	4.97906	+	8.62398i	0.171386	+	0.296850i
$845$	−21.8011	−	18.2933i	−0.749982	−	0.629309i
$846$	3.55303	+	2.98135i	0.122156	+	0.102501i
$847$	−2.82383	−	4.89101i	−0.0970278	−	0.168057i
$848$	5.97565	−	10.3501i	0.205205	−	0.355425i
$849$	−6.18004	+	2.24935i	−0.212099	+	0.0771976i
$850$	−0.0153194	−	0.0868809i	−0.000525453	−	0.00297999i
$851$	−4.79100	+	27.1711i	−0.164233	+	0.931414i
$852$	−4.18004	−	1.52141i	−0.143206	−	0.0521227i
$853$	−9.06006	+	7.60229i	−0.310211	+	0.260298i	−0.784579	−	0.620029i	$-0.787121\pi$
$853$	−9.06006	+	7.60229i	−0.310211	+	0.260298i	0.474369	+	0.880326i	$0.342676\pi$
$854$	−5.95306			−0.203709
$855$	9.70486	−	0.140732i	0.331899	−	0.00481295i
$856$	−1.91353			−0.0654032
$857$	15.1573	−	12.7185i	0.517763	−	0.434455i	−0.346088	−	0.938202i	$-0.612490\pi$
$857$	15.1573	−	12.7185i	0.517763	−	0.434455i	0.863851	+	0.503747i	$0.168046\pi$
$858$	−0.673648	−	0.245188i	−0.0229980	−	0.00837058i
$859$	5.59105	−	31.7084i	0.190764	−	1.08188i	−0.727559	−	0.686046i	$-0.759345\pi$
$859$	5.59105	−	31.7084i	0.190764	−	1.08188i	0.918323	−	0.395832i	$-0.129544\pi$
$860$	3.97906	+	22.5663i	0.135685	+	0.769506i
$861$	−2.13176	+	0.775897i	−0.0726502	+	0.0264425i
$862$	−9.45858	+	16.3827i	−0.322160	+	0.557998i
$863$	19.1150	+	33.1081i	0.650682	+	1.12701i	0.982958	+	0.183832i	$0.0588502\pi$
$863$	19.1150	+	33.1081i	0.650682	+	1.12701i	−0.332276	+	0.943182i	$0.607817\pi$
$864$	0.766044	+	0.642788i	0.0260614	+	0.0218681i
$865$	15.9572	+	13.3897i	0.542562	+	0.455264i
$866$	11.1334	+	19.2836i	0.378329	+	0.655284i
$867$	−6.28224	+	10.8812i	−0.213356	+	0.369544i
$868$	−5.29813	+	1.92836i	−0.179830	+	0.0654529i
$869$	−3.20780	−	18.1923i	−0.108817	−	0.617132i
$870$	−3.22193	+	18.2725i	−0.109234	+	0.619496i
$871$	0.109470	+	0.0398440i	0.00370926	+	0.00135006i
$872$	9.05097	−	7.59467i	0.306505	−	0.257188i
$873$	2.46791			0.0835261
$874$	12.5380	−	22.4625i	0.424105	−	0.759805i
$875$	7.32770			0.247721
$876$	6.96451	−	5.84392i	0.235309	−	0.197448i
$877$	28.1202	+	10.2349i	0.949552	+	0.345609i	0.769931	−	0.638127i	$-0.220291\pi$
$877$	28.1202	+	10.2349i	0.949552	+	0.345609i	0.179621	+	0.983736i	$0.442513\pi$
$878$	−5.80659	+	32.9308i	−0.195963	+	1.11136i
$879$	−3.76739	−	21.3659i	−0.127071	−	0.720655i
$880$	3.20574	−	1.16679i	0.108065	−	0.0393326i
$881$	20.4158	−	35.3612i	0.687826	−	1.19135i	−0.284714	−	0.958613i	$-0.591898\pi$
$881$	20.4158	−	35.3612i	0.687826	−	1.19135i	0.972540	−	0.232737i	$-0.0747682\pi$
$882$	−3.28699	−	5.69323i	−0.110679	−	0.191701i
$883$	−18.8275	−	15.7982i	−0.633597	−	0.531651i	0.268447	−	0.963294i	$-0.413489\pi$
$883$	−18.8275	−	15.7982i	−0.633597	−	0.531651i	−0.902044	+	0.431643i	$0.857934\pi$
$884$	0.754900	+	0.633436i	0.0253900	+	0.0213048i
$885$	15.8478	+	27.4491i	0.532717	+	0.922692i
$886$	17.4474	−	30.2198i	0.586158	−	1.01526i
$887$	−22.6113	+	8.22983i	−0.759213	+	0.276331i	−0.692477	−	0.721440i	$-0.743481\pi$
$887$	−22.6113	+	8.22983i	−0.759213	+	0.276331i	−0.0667355	+	0.997771i	$0.521258\pi$
$888$	−0.811804	−	4.60397i	−0.0272424	−	0.154499i
$889$	−1.09657	+	6.21897i	−0.0367778	+	0.208577i
$890$	35.0822	+	12.7689i	1.17596	+	0.428014i
$891$	−1.17365	+	0.984808i	−0.0393187	+	0.0329923i
$892$	1.92127			0.0643290
$893$	−3.22163	+	19.9589i	−0.107808	+	0.667900i
$894$	−5.97771			−0.199925
$895$	−26.9138	+	22.5833i	−0.899628	+	0.754877i
$896$	−0.613341	−	0.223238i	−0.0204903	−	0.00745785i
$897$	0.479522	−	2.71951i	0.0160108	−	0.0908017i
$898$	1.42097	+	8.05872i	0.0474184	+	0.268923i
$899$	−67.6387	+	24.6185i	−2.25588	+	0.821072i
$900$	0.0209445	−	0.0362770i	0.000698151	−	0.00120923i
$901$	−12.5851	−	21.7981i	−0.419271	−	0.726199i
$902$	4.07919	+	3.42285i	0.135822	+	0.113968i
$903$	5.14543	+	4.31753i	0.171229	+	0.143678i
$904$	2.69846	+	4.67388i	0.0897495	+	0.155451i
$905$	−7.79638	+	13.5037i	−0.259160	+	0.448879i
$906$	15.5753	−	5.66895i	0.517455	−	0.188338i
$907$	0.0871817	+	0.494432i	0.00289482	+	0.0164173i	0.986221	−	0.165433i	$-0.0529023\pi$
$907$	0.0871817	+	0.494432i	0.00289482	+	0.0164173i	−0.983326	+	0.181851i	$0.941791\pi$
$908$	0.156574	−	0.887975i	0.00519609	−	0.0294685i
$909$	5.39306	+	1.96291i	0.178876	+	0.0651057i
$910$	−0.520945	+	0.437124i	−0.0172691	+	0.0144905i
$911$	−11.2243			−0.371878			−0.185939	−	0.982561i	$-0.559533\pi$
$911$	−11.2243			−0.371878			−0.185939	+	0.982561i	$0.559533\pi$
$912$	−0.694593	+	4.30320i	−0.0230003	+	0.142493i
$913$	−5.68273			−0.188071
$914$	31.4277	−	26.3709i	1.03953	−	0.872273i
$915$	−19.0839	−	6.94599i	−0.630896	−	0.229627i
$916$	−0.0614894	+	0.348724i	−0.00203167	+	0.0115222i
$917$	0.215537	+	1.22237i	0.00711767	+	0.0403663i
$918$	1.97906	−	0.720317i	0.0653186	−	0.0237740i
$919$	−11.7699	+	20.3861i	−0.388254	+	0.672475i	−0.992215	−	0.124539i	$-0.960255\pi$
$919$	−11.7699	+	20.3861i	−0.388254	+	0.672475i	0.603961	+	0.797014i	$0.293588\pi$
$920$	6.57057	+	11.3806i	0.216625	+	0.375206i
$921$	−13.6361	−	11.4420i	−0.449325	−	0.377028i
$922$	3.54117	+	2.97140i	0.116622	+	0.0978578i
$923$	−1.04071	−	1.80256i	−0.0342553	−	0.0593319i
$924$	0.500000	−	0.866025i	0.0164488	−	0.0284901i
$925$	−0.184021	+	0.0669782i	−0.00605057	+	0.00220223i
$926$	−0.957234	−	5.42874i	−0.0314566	−	0.178400i
$927$	−2.39780	+	13.5986i	−0.0787542	+	0.446637i
$928$	−7.83022	−	2.84997i	−0.257040	−	0.0935548i
$929$	−26.8865	+	22.5604i	−0.882117	+	0.740184i	−0.966613	−	0.256239i	$-0.917516\pi$
$929$	−26.8865	+	22.5604i	−0.882117	+	0.740184i	0.0844960	+	0.996424i	$0.473072\pi$
$930$	−19.2344			−0.630722
$931$	13.9663	−	25.0214i	0.457728	−	0.820042i
$932$	−16.7023			−0.547103
$933$	1.24510	−	1.04476i	0.0407627	−	0.0342040i
$934$	10.4957	+	3.82013i	0.343430	+	0.124998i
$935$	1.24763	−	7.07564i	0.0408017	−	0.231398i
$936$	0.0812519	+	0.460802i	0.00265580	+	0.0150618i
$937$	42.1095	−	15.3266i	1.37566	−	0.500699i	0.454799	−	0.890594i	$-0.349711\pi$
$937$	42.1095	−	15.3266i	1.37566	−	0.500699i	0.920859	+	0.389895i	$0.127489\pi$
$938$	−0.0812519	+	0.140732i	−0.00265297	+	0.00459508i
$939$	15.0364	+	26.0439i	0.490695	+	0.849909i
$940$	−7.91147	−	6.63852i	−0.258044	−	0.216524i
$941$	−9.56805	−	8.02855i	−0.311909	−	0.261723i	0.473371	−	0.880863i	$-0.343037\pi$
$941$	−9.56805	−	8.02855i	−0.311909	−	0.261723i	−0.785281	+	0.619140i	$0.787481\pi$
$942$	8.35117	+	14.4646i	0.272096	+	0.471284i
$943$	−10.2561	+	17.7641i	−0.333984	+	0.578477i
$944$	−13.3760	+	4.86846i	−0.435351	+	0.158455i
$945$	0.252374	+	1.43128i	0.00820972	+	0.0465597i
$946$	2.73783	−	15.5270i	0.0890144	−	0.504826i
$947$	−48.5925	−	17.6862i	−1.57904	−	0.574724i	−0.604047	−	0.796949i	$-0.706446\pi$
$947$	−48.5925	−	17.6862i	−1.57904	−	0.574724i	−0.974996	+	0.222224i	$0.928668\pi$
$948$	−9.23648	+	7.75033i	−0.299987	+	0.251719i
$949$	4.25402			0.138091
$950$	0.182571	−	0.00264750i	0.00592339	−	8.58964e-5i
$951$	11.3327			0.367490
$952$	−1.05303	+	0.883600i	−0.0341290	+	0.0286376i
$953$	−37.2841	−	13.5703i	−1.20775	−	0.439585i	−0.341827	−	0.939763i	$-0.611046\pi$
$953$	−37.2841	−	13.5703i	−1.20775	−	0.439585i	−0.865922	+	0.500178i	$0.833268\pi$
$954$	2.07532	−	11.7697i	0.0671910	−	0.381059i
$955$	1.69816	+	9.63073i	0.0549511	+	0.311643i
$956$	−9.44831	+	3.43890i	−0.305580	+	0.111222i
$957$	6.38326	−	11.0561i	0.206341	−	0.357394i
$958$	4.33228	+	7.50373i	0.139970	+	0.242435i
$959$	0.889185	+	0.746115i	0.0287133	+	0.0240933i
$960$	−1.70574	−	1.43128i	−0.0550524	−	0.0461945i
$961$	−21.8089	−	37.7741i	−0.703512	−	1.21852i
$962$	1.09374	−	1.89441i	0.0352636	−	0.0610784i
$963$	−1.79813	+	0.654467i	−0.0579440	+	0.0210899i
$964$	−4.01114	−	22.7483i	−0.129190	−	0.732674i
$965$	1.87804	−	10.6509i	0.0604563	−	0.342865i
$966$	3.61974	+	1.31748i	0.116463	+	0.0423891i
$967$	21.0346	−	17.6501i	0.676428	−	0.567590i	−0.238532	−	0.971135i	$-0.576666\pi$
$967$	21.0346	−	17.6501i	0.676428	−	0.567590i	0.914960	+	0.403544i	$0.132222\pi$
$968$	8.65270			0.278108
$969$	7.11721	+	5.79829i	0.228638	+	0.186268i
$970$	−5.49525			−0.176442
$971$	−17.8503	+	14.9782i	−0.572843	+	0.480672i	−0.882588	−	0.470147i	$-0.844201\pi$
$971$	−17.8503	+	14.9782i	−0.572843	+	0.480672i	0.309745	+	0.950820i	$0.399756\pi$
$972$	0.939693	+	0.342020i	0.0301407	+	0.0109703i
$973$	0.0851223	−	0.482753i	0.00272890	−	0.0154763i
$974$	0.0163589	+	0.0927760i	0.000524174	+	0.00297274i
$975$	0.0184183	−	0.00670372i	0.000589858	−	0.000214691i
$976$	4.56031	−	7.89868i	0.145972	−	0.252831i
$977$	−6.73009	−	11.6568i	−0.215315	−	0.372936i	0.738055	−	0.674740i	$-0.235744\pi$
$977$	−6.73009	−	11.6568i	−0.215315	−	0.372936i	−0.953370	+	0.301805i	$0.902411\pi$
$978$	−12.1472	−	10.1927i	−0.388426	−	0.325928i
$979$	−19.6780	−	16.5118i	−0.628911	−	0.527719i
$980$	7.31908	+	12.6770i	0.233799	+	0.404952i
$981$	5.90760	−	10.2323i	0.188615	−	0.326691i
$982$	−26.3075	+	9.57516i	−0.839507	+	0.305555i
$983$	−7.94727	−	45.0712i	−0.253479	−	1.43755i	−0.799948	−	0.600069i	$-0.795140\pi$
$983$	−7.94727	−	45.0712i	−0.253479	−	1.43755i	0.546469	−	0.837479i	$-0.315971\pi$
$984$	0.603541	−	3.42285i	0.0192402	−	0.109116i
$985$	−42.4423	−	15.4477i	−1.35232	−	0.492205i
$986$	−13.4436	+	11.2805i	−0.428130	+	0.359244i
$987$	−3.02734			−0.0963613
$988$	−1.54323	+	1.33353i	−0.0490968	+	0.0424253i
$989$	60.7333			1.93121
$990$	2.61334	−	2.19285i	0.0830574	−	0.0696935i
$991$	−23.5164	−	8.55925i	−0.747022	−	0.271894i	−0.0596698	−	0.998218i	$-0.519005\pi$
$991$	−23.5164	−	8.55925i	−0.747022	−	0.271894i	−0.687352	+	0.726324i	$0.741227\pi$
$992$	1.50000	−	8.50692i	0.0476250	−	0.270095i
$993$	5.57832	+	31.6362i	0.177022	+	1.00394i
$994$	2.72833	−	0.993031i	0.0865374	−	0.0314970i
$995$	25.0069	−	43.3132i	0.792771	−	1.37312i
$996$	1.85457	+	3.21221i	0.0587643	+	0.101783i
$997$	−20.4677	−	17.1745i	−0.648220	−	0.543921i	0.258310	−	0.966062i	$-0.416834\pi$
$997$	−20.4677	−	17.1745i	−0.648220	−	0.543921i	−0.906530	+	0.422141i	$0.861279\pi$
$998$	28.3280	+	23.7700i	0.896707	+	0.752427i
$999$	−2.33750	−	4.04866i	−0.0739551	−	0.128094i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.2.i.d.25.1	✓	6
3.2	odd	2		342.2.u.a.253.1		6
4.3	odd	2		912.2.bo.f.481.1		6
19.4	even	9		2166.2.a.o.1.3		3
19.15	odd	18		2166.2.a.u.1.3		3
19.16	even	9	inner	114.2.i.d.73.1	yes	6
57.23	odd	18		6498.2.a.bs.1.1		3
57.35	odd	18		342.2.u.a.73.1		6
57.53	even	18		6498.2.a.bn.1.1		3
76.35	odd	18		912.2.bo.f.529.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.i.d.25.1	✓	6	1.1	even	1	trivial
114.2.i.d.73.1	yes	6	19.16	even	9	inner
342.2.u.a.73.1		6	57.35	odd	18
342.2.u.a.253.1		6	3.2	odd	2
912.2.bo.f.481.1		6	4.3	odd	2
912.2.bo.f.529.1		6	76.35	odd	18
2166.2.a.o.1.3		3	19.4	even	9
2166.2.a.u.1.3		3	19.15	odd	18
6498.2.a.bn.1.1		3	57.53	even	18
6498.2.a.bs.1.1		3	57.23	odd	18

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:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	114.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(0.939693 + 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.386659 + 2.19285i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(0.326352 - 0.565258i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(0.939693 + 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.386659 + 2.19285i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(0.326352 - 0.565258i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +(-1.70574 - 1.43128i) q^{10} +(0.766044 + 1.32683i) q^{11} +(0.500000 - 0.866025i) q^{12} +(0.439693 - 0.160035i) q^{13} +(0.113341 + 0.642788i) q^{14} +(-0.386659 + 2.19285i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-1.61334 + 1.35375i) q^{17} -1.00000 q^{18} +(-2.23396 - 3.74292i) q^{19} +2.22668 q^{20} +(0.500000 - 0.419550i) q^{21} +(-1.43969 - 0.524005i) q^{22} +(1.02481 - 5.81201i) q^{23} +(0.173648 + 0.984808i) q^{24} +(0.0393628 - 0.0143269i) q^{25} +(-0.233956 + 0.405223i) q^{26} +(0.500000 + 0.866025i) q^{27} +(-0.500000 - 0.419550i) q^{28} +(-6.38326 - 5.35619i) q^{29} +(-1.11334 - 1.92836i) q^{30} +(4.31908 - 7.48086i) q^{31} +(0.939693 - 0.342020i) q^{32} +(0.266044 + 1.50881i) q^{33} +(0.365715 - 2.07407i) q^{34} +(1.36571 + 0.497079i) q^{35} +(0.766044 - 0.642788i) q^{36} -4.67499 q^{37} +(4.11721 + 1.43128i) q^{38} +0.467911 q^{39} +(-1.70574 + 1.43128i) q^{40} +(-3.26604 - 1.18874i) q^{41} +(-0.113341 + 0.642788i) q^{42} +(1.78699 + 10.1345i) q^{43} +(1.43969 - 0.524005i) q^{44} +(-1.11334 + 1.92836i) q^{45} +(2.95084 + 5.11100i) q^{46} +(-3.55303 - 2.98135i) q^{47} +(-0.766044 - 0.642788i) q^{48} +(3.28699 + 5.69323i) q^{49} +(-0.0209445 + 0.0362770i) q^{50} +(-1.97906 + 0.720317i) q^{51} +(-0.0812519 - 0.460802i) q^{52} +(-2.07532 + 11.7697i) q^{53} +(-0.939693 - 0.342020i) q^{54} +(-2.61334 + 2.19285i) q^{55} +0.652704 q^{56} +(-0.819078 - 4.28125i) q^{57} +8.33275 q^{58} +(10.9042 - 9.14971i) q^{59} +(2.09240 + 0.761570i) q^{60} +(-1.58378 + 8.98205i) q^{61} +(1.50000 + 8.50692i) q^{62} +(0.613341 - 0.223238i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.520945 + 0.902302i) q^{65} +(-1.17365 - 0.984808i) q^{66} +(0.190722 + 0.160035i) q^{67} +(1.05303 + 1.82391i) q^{68} +(2.95084 - 5.11100i) q^{69} +(-1.36571 + 0.497079i) q^{70} +(-0.772441 - 4.38073i) q^{71} +(-0.173648 + 0.984808i) q^{72} +(8.54323 + 3.10948i) q^{73} +(3.58125 - 3.00503i) q^{74} +0.0418891 q^{75} +(-4.07398 + 1.55007i) q^{76} +1.00000 q^{77} +(-0.358441 + 0.300767i) q^{78} +(-11.3302 - 4.12386i) q^{79} +(0.386659 - 2.19285i) q^{80} +(0.173648 + 0.984808i) q^{81} +(3.26604 - 1.18874i) q^{82} +(-1.85457 + 3.21221i) q^{83} +(-0.326352 - 0.565258i) q^{84} +(-3.59240 - 3.01438i) q^{85} +(-7.88326 - 6.61484i) q^{86} +(-4.16637 - 7.21637i) q^{87} +(-0.766044 + 1.32683i) q^{88} +(-15.7554 + 5.73448i) q^{89} +(-0.386659 - 2.19285i) q^{90} +(0.0530334 - 0.300767i) q^{91} +(-5.54576 - 2.01849i) q^{92} +(6.61721 - 5.55250i) q^{93} +4.63816 q^{94} +(7.34389 - 6.34597i) q^{95} +1.00000 q^{96} +(1.89053 - 1.58634i) q^{97} +(-6.17752 - 2.24843i) q^{98} +(-0.266044 + 1.50881i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 9 q^{5} + 3 q^{7} + 3 q^{8}+O(q^{10}) \) 6 * q + 9 * q^5 + 3 * q^7 + 3 * q^8	\( 6 q + 9 q^{5} + 3 q^{7} + 3 q^{8} + 3 q^{12} - 3 q^{13} - 6 q^{14} - 9 q^{15} - 3 q^{17} - 6 q^{18} - 18 q^{19} + 3 q^{21} - 3 q^{22} - 21 q^{23} + 9 q^{25} - 6 q^{26} + 3 q^{27} - 3 q^{28} - 3 q^{29} + 9 q^{31} - 3 q^{33} + 12 q^{34} + 18 q^{35} - 18 q^{37} - 6 q^{38} + 12 q^{39} - 15 q^{41} + 6 q^{42} + 3 q^{43} + 3 q^{44} + 6 q^{46} - 9 q^{47} + 12 q^{49} + 3 q^{50} - 15 q^{51} - 3 q^{52} + 12 q^{53} - 9 q^{55} + 6 q^{56} + 12 q^{57} + 12 q^{58} + 27 q^{59} + 9 q^{60} + 3 q^{61} + 9 q^{62} - 3 q^{63} - 3 q^{64} - 6 q^{66} + 21 q^{67} - 6 q^{68} + 6 q^{69} - 18 q^{70} + 39 q^{71} + 36 q^{73} + 24 q^{74} - 6 q^{75} - 9 q^{76} + 6 q^{77} + 6 q^{78} - 45 q^{79} + 9 q^{80} + 15 q^{82} - 27 q^{83} - 3 q^{84} - 18 q^{85} - 12 q^{86} - 6 q^{87} - 30 q^{89} - 9 q^{90} - 12 q^{91} - 3 q^{92} + 9 q^{93} - 6 q^{94} + 6 q^{96} - 6 q^{97} - 12 q^{98} + 3 q^{99}+O(q^{100}) \) 6 * q + 9 * q^5 + 3 * q^7 + 3 * q^8 + 3 * q^12 - 3 * q^13 - 6 * q^14 - 9 * q^15 - 3 * q^17 - 6 * q^18 - 18 * q^19 + 3 * q^21 - 3 * q^22 - 21 * q^23 + 9 * q^25 - 6 * q^26 + 3 * q^27 - 3 * q^28 - 3 * q^29 + 9 * q^31 - 3 * q^33 + 12 * q^34 + 18 * q^35 - 18 * q^37 - 6 * q^38 + 12 * q^39 - 15 * q^41 + 6 * q^42 + 3 * q^43 + 3 * q^44 + 6 * q^46 - 9 * q^47 + 12 * q^49 + 3 * q^50 - 15 * q^51 - 3 * q^52 + 12 * q^53 - 9 * q^55 + 6 * q^56 + 12 * q^57 + 12 * q^58 + 27 * q^59 + 9 * q^60 + 3 * q^61 + 9 * q^62 - 3 * q^63 - 3 * q^64 - 6 * q^66 + 21 * q^67 - 6 * q^68 + 6 * q^69 - 18 * q^70 + 39 * q^71 + 36 * q^73 + 24 * q^74 - 6 * q^75 - 9 * q^76 + 6 * q^77 + 6 * q^78 - 45 * q^79 + 9 * q^80 + 15 * q^82 - 27 * q^83 - 3 * q^84 - 18 * q^85 - 12 * q^86 - 6 * q^87 - 30 * q^89 - 9 * q^90 - 12 * q^91 - 3 * q^92 + 9 * q^93 - 6 * q^94 + 6 * q^96 - 6 * q^97 - 12 * q^98 + 3 * q^99

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