LMFDB - Embedded newform 36.2.h.a.23.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,2,Mod(11,36)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(36, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("36.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	36.h (of order $6$, degree $2$, 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:	$0.287461447277$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.170772624.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 6x^{5} + 6x^{4} - 12x^{3} + 20x^{2} - 24x + 16 $ x^8 - 3x^7 + 5x^6 - 6x^5 + 6x^4 - 12x^3 + 20x^2 - 24*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.2
Root			$1.41203 + 0.0786378i$ of defining polynomial
Character	$\chi$	$=$	36.23
Dual form			36.2.h.a.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.774115 + 1.18353i) q^{2} +(-0.637910 + 1.61030i) q^{3} +(-0.801492 - 1.83238i) q^{4} +(0.686141 + 0.396143i) q^{5} +(-1.41203 - 2.00155i) q^{6} +(2.35143 - 1.35760i) q^{7} +(2.78912 + 0.469882i) q^{8} +(-2.18614 - 2.05446i) q^{9} +O(q^{10})$	\(q+(-0.774115 + 1.18353i) q^{2} +(-0.637910 + 1.61030i) q^{3} +(-0.801492 - 1.83238i) q^{4} +(0.686141 + 0.396143i) q^{5} +(-1.41203 - 2.00155i) q^{6} +(2.35143 - 1.35760i) q^{7} +(2.78912 + 0.469882i) q^{8} +(-2.18614 - 2.05446i) q^{9} +(-1.00000 + 0.505408i) q^{10} +(-1.71352 - 2.96790i) q^{11} +(3.46196 - 0.121749i) q^{12} +(-1.68614 + 2.92048i) q^{13} +(-0.213517 + 3.83392i) q^{14} +(-1.07561 + 0.852189i) q^{15} +(-2.71522 + 2.93727i) q^{16} -2.52434i q^{17} +(4.12384 - 0.996980i) q^{18} +2.20979i q^{19} +(0.175949 - 1.57478i) q^{20} +(0.686141 + 4.65253i) q^{21} +(4.83906 + 0.269495i) q^{22} +(-1.07561 + 1.86301i) q^{23} +(-2.53586 + 4.19159i) q^{24} +(-2.18614 - 3.78651i) q^{25} +(-2.15121 - 4.25639i) q^{26} +(4.70285 - 2.20979i) q^{27} +(-4.37228 - 3.22060i) q^{28} +(-0.686141 + 0.396143i) q^{29} +(-0.175949 - 1.93271i) q^{30} +(-1.47603 - 0.852189i) q^{31} +(-1.37446 - 5.48734i) q^{32} +(5.87228 - 0.866025i) q^{33} +(2.98763 + 1.95413i) q^{34} +2.15121 q^{35} +(-2.01237 + 5.65247i) q^{36} +4.74456 q^{37} +(-2.61535 - 1.71063i) q^{38} +(-3.62725 - 4.57820i) q^{39} +(1.72759 + 1.42730i) q^{40} +(0.127719 + 0.0737384i) q^{41} +(-6.03757 - 2.78953i) q^{42} +(-6.01594 + 3.47331i) q^{43} +(-4.06494 + 5.51856i) q^{44} +(-0.686141 - 2.27567i) q^{45} +(-1.37228 - 2.71519i) q^{46} +(5.77846 + 10.0086i) q^{47} +(-2.99782 - 6.24604i) q^{48} +(0.186141 - 0.322405i) q^{49} +(6.17377 + 0.343827i) q^{50} +(4.06494 + 1.61030i) q^{51} +(6.70285 + 0.748907i) q^{52} +8.51278i q^{53} +(-1.02520 + 7.27660i) q^{54} -2.71519i q^{55} +(7.19633 - 2.68161i) q^{56} +(-3.55842 - 1.40965i) q^{57} +(0.0623037 - 1.11873i) q^{58} +(2.58891 - 4.48412i) q^{59} +(2.42362 + 1.28790i) q^{60} +(-1.68614 - 2.92048i) q^{61} +(2.15121 - 1.08724i) q^{62} +(-7.92967 - 1.86301i) q^{63} +(7.55842 + 2.62112i) q^{64} +(-2.31386 + 1.33591i) q^{65} +(-3.52085 + 7.62043i) q^{66} +(-6.01594 - 3.47331i) q^{67} +(-4.62554 + 2.02324i) q^{68} +(-2.31386 - 2.92048i) q^{69} +(-1.66529 + 2.54603i) q^{70} -1.75079 q^{71} +(-5.13207 - 6.75736i) q^{72} -2.37228 q^{73} +(-3.67284 + 5.61534i) q^{74} +(7.49198 - 1.10489i) q^{75} +(4.04917 - 1.77113i) q^{76} +(-8.05842 - 4.65253i) q^{77} +(8.22635 - 0.748907i) q^{78} +(8.80507 - 5.08361i) q^{79} +(-3.02661 + 0.939764i) q^{80} +(0.558422 + 8.98266i) q^{81} +(-0.186141 + 0.0940770i) q^{82} +(-3.62725 - 6.28258i) q^{83} +(7.97526 - 4.98623i) q^{84} +(1.00000 - 1.73205i) q^{85} +(0.546267 - 9.80880i) q^{86} +(-0.200214 - 1.35760i) q^{87} +(-3.38465 - 9.08299i) q^{88} -5.34363i q^{89} +(3.22448 + 0.949563i) q^{90} +9.15640i q^{91} +(4.27582 + 0.477736i) q^{92} +(2.31386 - 1.83324i) q^{93} +(-16.3187 - 0.908812i) q^{94} +(-0.875393 + 1.51622i) q^{95} +(9.71305 + 1.28714i) q^{96} +(6.24456 + 10.8159i) q^{97} +(0.237482 + 0.469882i) q^{98} +(-2.35143 + 10.0086i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 3 q^{2} - q^{4} - 6 q^{5} - 3 q^{6} - 6 q^{9}+O(q^{10}) $ 8 * q - 3 * q^2 - q^4 - 6 * q^5 - 3 * q^6 - 6 * q^9	$ 8 q - 3 q^{2} - q^{4} - 6 q^{5} - 3 q^{6} - 6 q^{9} - 8 q^{10} + 6 q^{12} - 2 q^{13} + 12 q^{14} - q^{16} + 18 q^{18} + 18 q^{20} - 6 q^{21} + 3 q^{22} + 3 q^{24} - 6 q^{25} - 12 q^{28} + 6 q^{29} - 18 q^{30} - 33 q^{32} + 24 q^{33} + 7 q^{34} - 33 q^{36} - 8 q^{37} - 27 q^{38} + 10 q^{40} + 24 q^{41} - 18 q^{42} + 6 q^{45} + 12 q^{46} + 21 q^{48} - 10 q^{49} + 21 q^{50} + 16 q^{52} + 39 q^{54} + 18 q^{56} + 6 q^{57} + 4 q^{58} + 6 q^{60} - 2 q^{61} + 26 q^{64} - 30 q^{65} - 24 q^{66} - 15 q^{68} - 30 q^{69} - 6 q^{70} - 21 q^{72} + 4 q^{73} - 30 q^{74} - 3 q^{76} - 30 q^{77} - 12 q^{78} - 30 q^{81} + 10 q^{82} + 30 q^{84} + 8 q^{85} + 21 q^{86} - 21 q^{88} + 6 q^{90} + 24 q^{92} + 30 q^{93} - 18 q^{94} + 12 q^{96} + 4 q^{97}+O(q^{100}) $ 8 * q - 3 * q^2 - q^4 - 6 * q^5 - 3 * q^6 - 6 * q^9 - 8 * q^10 + 6 * q^12 - 2 * q^13 + 12 * q^14 - q^16 + 18 * q^18 + 18 * q^20 - 6 * q^21 + 3 * q^22 + 3 * q^24 - 6 * q^25 - 12 * q^28 + 6 * q^29 - 18 * q^30 - 33 * q^32 + 24 * q^33 + 7 * q^34 - 33 * q^36 - 8 * q^37 - 27 * q^38 + 10 * q^40 + 24 * q^41 - 18 * q^42 + 6 * q^45 + 12 * q^46 + 21 * q^48 - 10 * q^49 + 21 * q^50 + 16 * q^52 + 39 * q^54 + 18 * q^56 + 6 * q^57 + 4 * q^58 + 6 * q^60 - 2 * q^61 + 26 * q^64 - 30 * q^65 - 24 * q^66 - 15 * q^68 - 30 * q^69 - 6 * q^70 - 21 * q^72 + 4 * q^73 - 30 * q^74 - 3 * q^76 - 30 * q^77 - 12 * q^78 - 30 * q^81 + 10 * q^82 + 30 * q^84 + 8 * q^85 + 21 * q^86 - 21 * q^88 + 6 * q^90 + 24 * q^92 + 30 * q^93 - 18 * q^94 + 12 * q^96 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.774115	+	1.18353i	−0.547382	+	0.836883i
$2$	−0.774115	+	1.18353i	−0.547382	+	0.836883i
$3$	−0.637910	+	1.61030i	−0.368298	+	0.929708i
$3$	−0.637910	+	1.61030i	−0.368298	+	0.929708i
$4$	−0.801492	−	1.83238i	−0.400746	−	0.916189i
$5$	0.686141	+	0.396143i	0.306851	+	0.177161i	0.645517	−	0.763746i	$-0.276642\pi$
$5$	0.686141	+	0.396143i	0.306851	+	0.177161i	−0.338665	+	0.940907i	$0.609975\pi$
$6$	−1.41203	−	2.00155i	−0.576457	−	0.817127i
$7$	2.35143	−	1.35760i	0.888756	−	0.513124i	0.0152206	−	0.999884i	$-0.495155\pi$
$7$	2.35143	−	1.35760i	0.888756	−	0.513124i	0.873535	+	0.486761i	$0.161822\pi$
$8$	2.78912	+	0.469882i	0.986104	+	0.166128i
$9$	−2.18614	−	2.05446i	−0.728714	−	0.684819i
$10$	−1.00000	+	0.505408i	−0.316228	+	0.159824i
$11$	−1.71352	−	2.96790i	−0.516645	−	0.894855i	−0.999813	−	0.0193276i	$-0.993847\pi$
$11$	−1.71352	−	2.96790i	−0.516645	−	0.894855i	0.483168	−	0.875527i	$-0.339486\pi$
$12$	3.46196	−	0.121749i	0.999382	−	0.0351461i
$13$	−1.68614	+	2.92048i	−0.467651	+	0.809996i	−0.999317	−	0.0369586i	$-0.988233\pi$
$13$	−1.68614	+	2.92048i	−0.467651	+	0.809996i	0.531666	+	0.846954i	$0.321566\pi$
$14$	−0.213517	+	3.83392i	−0.0570648	+	1.02466i
$15$	−1.07561	+	0.852189i	−0.277720	+	0.220034i
$16$	−2.71522	+	2.93727i	−0.678806	+	0.734318i
$17$		−	2.52434i		−	0.612242i	−0.951993	−	0.306121i	$-0.900969\pi$
$17$		−	2.52434i		−	0.612242i	0.951993	−	0.306121i	$-0.0990312\pi$
$18$	4.12384	−	0.996980i	0.971998	−	0.234990i
$19$			2.20979i			0.506960i	0.967341	+	0.253480i	$0.0815752\pi$
$19$			2.20979i			0.506960i	−0.967341	+	0.253480i	$0.918425\pi$
$20$	0.175949	−	1.57478i	0.0393434	−	0.352130i
$21$	0.686141	+	4.65253i	0.149728	+	1.01527i
$22$	4.83906	+	0.269495i	1.03169	+	0.0574564i
$23$	−1.07561	+	1.86301i	−0.224279	+	0.388463i	−0.956103	−	0.293031i	$-0.905336\pi$
$23$	−1.07561	+	1.86301i	−0.224279	+	0.388463i	0.731824	+	0.681494i	$0.238670\pi$
$24$	−2.53586	+	4.19159i	−0.517631	+	0.855604i
$25$	−2.18614	−	3.78651i	−0.437228	−	0.757301i
$26$	−2.15121	−	4.25639i	−0.421888	−	0.834746i
$27$	4.70285	−	2.20979i	0.905065	−	0.425274i
$28$	−4.37228	−	3.22060i	−0.826284	−	0.608637i
$29$	−0.686141	+	0.396143i	−0.127413	+	0.0735620i	−0.562352	−	0.826898i	$-0.690103\pi$
$29$	−0.686141	+	0.396143i	−0.127413	+	0.0735620i	0.434939	+	0.900460i	$0.356770\pi$
$30$	−0.175949	−	1.93271i	−0.0321237	−	0.352862i
$31$	−1.47603	−	0.852189i	−0.265104	−	0.153058i	0.361557	−	0.932350i	$-0.382245\pi$
$31$	−1.47603	−	0.852189i	−0.265104	−	0.153058i	−0.626660	+	0.779292i	$0.715579\pi$
$32$	−1.37446	−	5.48734i	−0.242972	−	0.970033i
$33$	5.87228	−	0.866025i	1.02223	−	0.150756i
$34$	2.98763	+	1.95413i	0.512375	+	0.335130i
$35$	2.15121			0.363621
$36$	−2.01237	+	5.65247i	−0.335395	+	0.942078i
$37$	4.74456			0.780001			0.390001	−	0.920815i	$-0.372475\pi$
$37$	4.74456			0.780001			0.390001	+	0.920815i	$0.372475\pi$
$38$	−2.61535	−	1.71063i	−0.424266	−	0.277501i
$39$	−3.62725	−	4.57820i	−0.580825	−	0.733099i
$40$	1.72759	+	1.42730i	0.273156	+	0.225676i
$41$	0.127719	+	0.0737384i	0.0199463	+	0.0115160i	0.509940	−	0.860210i	$-0.329668\pi$
$41$	0.127719	+	0.0737384i	0.0199463	+	0.0115160i	−0.489994	+	0.871726i	$0.663001\pi$
$42$	−6.03757	−	2.78953i	−0.931617	−	0.430433i
$43$	−6.01594	+	3.47331i	−0.917423	+	0.529674i	−0.882812	−	0.469727i	$-0.844353\pi$
$43$	−6.01594	+	3.47331i	−0.917423	+	0.529674i	−0.0346108	+	0.999401i	$0.511019\pi$
$44$	−4.06494	+	5.51856i	−0.612813	+	0.831954i
$45$	−0.686141	−	2.27567i	−0.102284	−	0.339237i
$46$	−1.37228	−	2.71519i	−0.202332	−	0.400334i
$47$	5.77846	+	10.0086i	0.842875	+	1.45990i	0.887454	+	0.460897i	$0.152472\pi$
$47$	5.77846	+	10.0086i	0.842875	+	1.45990i	−0.0445785	+	0.999006i	$0.514194\pi$
$48$	−2.99782	−	6.24604i	−0.432699	−	0.901539i
$49$	0.186141	−	0.322405i	0.0265915	−	0.0460579i
$50$	6.17377	+	0.343827i	0.873103	+	0.0486244i
$51$	4.06494	+	1.61030i	0.569206	+	0.225487i
$52$	6.70285	+	0.748907i	0.929519	+	0.103855i
$53$			8.51278i			1.16932i	0.811278	+	0.584660i	$0.198772\pi$
$53$			8.51278i			1.16932i	−0.811278	+	0.584660i	$0.801228\pi$
$54$	−1.02520	+	7.27660i	−0.139512	+	0.990220i
$55$		−	2.71519i		−	0.366117i
$56$	7.19633	−	2.68161i	0.961650	−	0.358346i
$57$	−3.55842	−	1.40965i	−0.471325	−	0.186712i
$58$	0.0623037	−	1.11873i	0.00818088	−	0.146896i
$59$	2.58891	−	4.48412i	0.337047	−	0.583783i	−0.646829	−	0.762635i	$-0.723905\pi$
$59$	2.58891	−	4.48412i	0.337047	−	0.583783i	0.983876	+	0.178852i	$0.0572384\pi$
$60$	2.42362	+	1.28790i	0.312888	+	0.166267i
$61$	−1.68614	−	2.92048i	−0.215888	−	0.373929i	0.737659	−	0.675174i	$-0.235931\pi$
$61$	−1.68614	−	2.92048i	−0.215888	−	0.373929i	−0.953547	+	0.301244i	$0.902598\pi$
$62$	2.15121	−	1.08724i	0.273204	−	0.138080i
$63$	−7.92967	−	1.86301i	−0.999045	−	0.234717i
$64$	7.55842	+	2.62112i	0.944803	+	0.327640i
$65$	−2.31386	+	1.33591i	−0.286999	+	0.165699i
$66$	−3.52085	+	7.62043i	−0.433387	+	0.938010i
$67$	−6.01594	−	3.47331i	−0.734964	−	0.424332i	0.0852711	−	0.996358i	$-0.472824\pi$
$67$	−6.01594	−	3.47331i	−0.734964	−	0.424332i	−0.820236	+	0.572026i	$0.806158\pi$
$68$	−4.62554	+	2.02324i	−0.560929	+	0.245353i
$69$	−2.31386	−	2.92048i	−0.278556	−	0.351585i
$70$	−1.66529	+	2.54603i	−0.199040	+	0.304309i
$71$	−1.75079			−0.207780			−0.103890	−	0.994589i	$-0.533129\pi$
$71$	−1.75079			−0.207780			−0.103890	+	0.994589i	$0.533129\pi$
$72$	−5.13207	−	6.75736i	−0.604820	−	0.796362i
$73$	−2.37228			−0.277655			−0.138827	−	0.990317i	$-0.544333\pi$
$73$	−2.37228			−0.277655			−0.138827	+	0.990317i	$0.544333\pi$
$74$	−3.67284	+	5.61534i	−0.426959	+	0.652770i
$75$	7.49198	−	1.10489i	0.865099	−	0.127582i
$76$	4.04917	−	1.77113i	0.464471	−	0.203162i
$77$	−8.05842	−	4.65253i	−0.918342	−	0.530205i
$78$	8.22635	−	0.748907i	0.931451	−	0.0847970i
$79$	8.80507	−	5.08361i	0.990647	−	0.571951i	0.0851797	−	0.996366i	$-0.472854\pi$
$79$	8.80507	−	5.08361i	0.990647	−	0.571951i	0.905468	+	0.424415i	$0.139520\pi$
$80$	−3.02661	+	0.939764i	−0.338385	+	0.105069i
$81$	0.558422	+	8.98266i	0.0620469	+	0.998073i
$82$	−0.186141	+	0.0940770i	−0.0205558	+	0.0103891i
$83$	−3.62725	−	6.28258i	−0.398142	−	0.689603i	0.595355	−	0.803463i	$-0.297012\pi$
$83$	−3.62725	−	6.28258i	−0.398142	−	0.689603i	−0.993497	+	0.113861i	$0.963678\pi$
$84$	7.97526	−	4.98623i	0.870173	−	0.544043i
$85$	1.00000	−	1.73205i	0.108465	−	0.187867i
$86$	0.546267	−	9.80880i	0.0589055	−	1.05771i
$87$	−0.200214	−	1.35760i	−0.0214652	−	0.145550i
$88$	−3.38465	−	9.08299i	−0.360805	−	0.968250i
$89$		−	5.34363i		−	0.566424i	−0.959057	−	0.283212i	$-0.908600\pi$
$89$		−	5.34363i		−	0.566424i	0.959057	−	0.283212i	$-0.0913999\pi$
$90$	3.22448	+	0.949563i	0.339890	+	0.100093i
$91$			9.15640i			0.959852i
$92$	4.27582	+	0.477736i	0.445785	+	0.0498074i
$93$	2.31386	−	1.83324i	0.239936	−	0.190098i
$94$	−16.3187	−	0.908812i	−1.68314	−	0.0937368i
$95$	−0.875393	+	1.51622i	−0.0898134	+	0.155561i
$96$	9.71305	+	1.28714i	0.991334	+	0.131368i
$97$	6.24456	+	10.8159i	0.634039	+	1.09819i	0.986718	+	0.162444i	$0.0519376\pi$
$97$	6.24456	+	10.8159i	0.634039	+	1.09819i	−0.352679	+	0.935745i	$0.614729\pi$
$98$	0.237482	+	0.469882i	0.0239893	+	0.0474652i
$99$	−2.35143	+	10.0086i	−0.236327	+	1.00590i
$100$	−5.18614	+	7.04069i	−0.518614	+	0.704069i
$101$	15.4307	−	8.90892i	1.53541	−	0.886471i	0.536314	−	0.844019i	$-0.319816\pi$
$101$	15.4307	−	8.90892i	1.53541	−	0.886471i	0.999099	−	0.0424521i	$-0.0135170\pi$
$102$	−5.05258	+	3.56443i	−0.500280	+	0.352931i
$103$	12.6325	+	7.29339i	1.24472	+	0.718640i	0.970051	−	0.242899i	$-0.0780985\pi$
$103$	12.6325	+	7.29339i	1.24472	+	0.718640i	0.274669	+	0.961539i	$0.411432\pi$
$104$	−6.07514	+	7.35330i	−0.595716	+	0.721050i
$105$	−1.37228	+	3.46410i	−0.133921	+	0.338062i
$106$	−10.0751	−	6.58987i	−0.978584	−	0.640065i
$107$	−13.2332			−1.27930			−0.639650	−	0.768667i	$-0.720920\pi$
$107$	−13.2332			−1.27930			−0.639650	+	0.768667i	$0.720920\pi$
$108$	−7.81846	−	6.84629i	−0.752332	−	0.658784i
$109$	−9.48913			−0.908893			−0.454447	−	0.890774i	$-0.650163\pi$
$109$	−9.48913			−0.908893			−0.454447	+	0.890774i	$0.650163\pi$
$110$	3.21352	+	2.10187i	0.306397	+	0.200406i
$111$	−3.02661	+	7.64018i	−0.287273	+	0.725173i
$112$	−2.39702	+	10.5930i	−0.226497	+	1.00094i
$113$	13.8030	+	7.96916i	1.29848	+	0.749675i	0.980141	−	0.198303i	$-0.0635430\pi$
$113$	13.8030	+	7.96916i	1.29848	+	0.749675i	0.318335	+	0.947978i	$0.396876\pi$
$114$	4.42299	−	3.12027i	0.414251	−	0.292241i
$115$	−1.47603	+	0.852189i	−0.137641	+	0.0794670i
$116$	1.27582	+	0.939764i	0.118457	+	0.0872549i
$117$	9.68614	−	2.92048i	0.895484	−	0.269999i
$118$	3.30298	+	6.53528i	0.304064	+	0.601621i
$119$	−3.42703	−	5.93580i	−0.314156	−	0.544134i
$120$	−3.40043	+	1.87145i	−0.310415	+	0.170839i
$121$	−0.372281	+	0.644810i	−0.0338438	+	0.0586191i
$122$	4.76175	+	0.265189i	0.431108	+	0.0240091i
$123$	−0.200214	+	0.158627i	−0.0180527	+	0.0143029i
$124$	−0.378504	+	3.38768i	−0.0339906	+	0.304222i
$125$		−	7.42554i		−	0.664160i
$126$	8.34341	−	7.94284i	0.743290	−	0.707604i
$127$		−	16.2912i		−	1.44561i	−0.691053	−	0.722804i	$-0.742853\pi$
$127$		−	16.2912i		−	1.44561i	0.691053	−	0.722804i	$-0.257147\pi$
$128$	−8.95326	+	6.91658i	−0.791364	+	0.611345i
$129$	−1.75544	−	11.9031i	−0.154558	−	1.04801i
$130$	0.210106	−	3.77267i	0.0184275	−	0.330885i
$131$	3.62725	−	6.28258i	0.316914	−	0.548911i	−0.662928	−	0.748683i	$-0.730687\pi$
$131$	3.62725	−	6.28258i	0.316914	−	0.548911i	0.979843	+	0.199771i	$0.0640200\pi$
$132$	−6.29347	−	10.0661i	−0.547776	−	0.876144i
$133$	3.00000	+	5.19615i	0.260133	+	0.450564i
$134$	8.76780	−	4.43132i	0.757423	−	0.382807i
$135$	4.10221	+	0.346781i	0.353062	+	0.0298462i
$136$	1.18614	−	7.04069i	0.101711	−	0.603734i
$137$	−16.2446	+	9.37880i	−1.38787	+	0.801285i	−0.993075	−	0.117485i	$-0.962517\pi$
$137$	−16.2446	+	9.37880i	−1.38787	+	0.801285i	−0.394792	+	0.918771i	$0.629183\pi$
$138$	5.24767	−	0.477736i	0.446712	−	0.0406676i
$139$	8.09262	+	4.67228i	0.686407	+	0.396297i	0.802265	−	0.596968i	$-0.203628\pi$
$139$	8.09262	+	4.67228i	0.686407	+	0.396297i	−0.115858	+	0.993266i	$0.536962\pi$
$140$	−1.72418	−	3.94184i	−0.145720	−	0.333146i
$141$	−19.8030	+	2.92048i	−1.66771	+	0.245949i
$142$	1.35531	−	2.07211i	0.113735	−	0.173887i
$143$	11.5569			0.966438
$144$	11.9704	−	0.842984i	0.997530	−	0.0702487i
$145$	−0.627719			−0.0521292
$146$	1.83642	−	2.80767i	0.151983	−	0.232364i
$147$	0.400428	+	0.505408i	0.0330268	+	0.0416854i
$148$	−3.80273	−	8.69384i	−0.312582	−	0.714629i
$149$	−8.31386	−	4.80001i	−0.681098	−	0.393232i	0.119171	−	0.992874i	$-0.461976\pi$
$149$	−8.31386	−	4.80001i	−0.681098	−	0.393232i	−0.800269	+	0.599642i	$0.795310\pi$
$150$	−4.49198	+	9.72230i	−0.366769	+	0.793823i
$151$	−7.92967	+	4.57820i	−0.645308	+	0.372569i	−0.786656	−	0.617391i	$-0.788190\pi$
$151$	−7.92967	+	4.57820i	−0.645308	+	0.372569i	0.141348	+	0.989960i	$0.454856\pi$
$152$	−1.03834	+	6.16337i	−0.0842204	+	0.499915i
$153$	−5.18614	+	5.51856i	−0.419275	+	0.446149i
$154$	11.7446	−	5.93580i	0.946404	−	0.478320i
$155$	−0.675178	−	1.16944i	−0.0542316	−	0.0939319i
$156$	−5.48179	+	10.3159i	−0.438894	+	0.825931i
$157$	8.43070	−	14.6024i	0.672843	−	1.16540i	−0.304251	−	0.952592i	$-0.598406\pi$
$157$	8.43070	−	14.6024i	0.672843	−	1.16540i	0.977094	−	0.212807i	$-0.0682605\pi$
$158$	−0.799528	+	14.3564i	−0.0636070	+	1.14213i
$159$	−13.7081	−	5.43039i	−1.08713	−	0.430658i
$160$	1.23070	−	4.30957i	0.0972955	−	0.340701i
$161$			5.84096i			0.460332i
$162$	−11.0635	−	6.29270i	−0.869234	−	0.494401i
$163$		−	11.8716i		−	0.929855i	−0.885349	−	0.464928i	$-0.846080\pi$
$163$		−	11.8716i		−	0.929855i	0.885349	−	0.464928i	$-0.153920\pi$
$164$	0.0327513	−	0.293130i	0.00255744	−	0.0228896i
$165$	4.37228	+	1.73205i	0.340382	+	0.134840i
$166$	10.2435	+	0.570478i	0.795052	+	0.0442777i
$167$	−9.60592	+	16.6379i	−0.743329	+	1.28748i	0.207643	+	0.978205i	$0.433421\pi$
$167$	−9.60592	+	16.6379i	−0.743329	+	1.28748i	−0.950972	+	0.309278i	$0.899913\pi$
$168$	−0.272409	+	13.2989i	−0.0210168	+	1.02603i
$169$	0.813859	+	1.40965i	0.0626046	+	0.108434i
$170$	1.27582	+	2.52434i	0.0978510	+	0.193608i
$171$	4.53991	−	4.83090i	0.347175	−	0.369428i
$172$	11.1861	+	8.23966i	0.852935	+	0.628268i
$173$	−4.80298	+	2.77300i	−0.365164	+	0.210828i	−0.671344	−	0.741146i	$-0.734283\pi$
$173$	−4.80298	+	2.77300i	−0.365164	+	0.210828i	0.306180	+	0.951974i	$0.400949\pi$
$174$	1.76175	+	0.813977i	0.133558	+	0.0617074i
$175$	−10.2811	−	5.93580i	−0.777178	−	0.448704i
$176$	13.3701	+	3.02544i	1.00781	+	0.228051i
$177$	5.56930	+	7.02939i	0.418614	+	0.528362i
$178$	6.32435	+	4.13658i	0.474030	+	0.310050i
$179$	18.8114			1.40603			0.703016	−	0.711174i	$-0.251836\pi$
$179$	18.8114			1.40603			0.703016	+	0.711174i	$0.251836\pi$
$180$	−3.61996	+	3.08120i	−0.269816	+	0.229659i
$181$	−4.00000			−0.297318			−0.148659	−	0.988889i	$-0.547496\pi$
$181$	−4.00000			−0.297318			−0.148659	+	0.988889i	$0.547496\pi$
$182$	−10.8369	−	7.08811i	−0.803283	−	0.525405i
$183$	5.77846	−	0.852189i	0.427156	−	0.0629956i
$184$	−3.87539	+	4.69074i	−0.285698	+	0.345806i
$185$	3.25544	+	1.87953i	0.239345	+	0.138186i
$186$	0.378504	+	4.15766i	0.0277532	+	0.304855i
$187$	−7.49198	+	4.32550i	−0.547868	+	0.316312i
$188$	13.7081	−	18.6101i	0.999769	−	1.35728i
$189$	8.05842	−	11.5807i	0.586164	−	0.842375i
$190$	−1.11684	−	2.20979i	−0.0810244	−	0.160315i
$191$	1.95100	+	3.37923i	0.141169	+	0.244512i	0.927937	−	0.372736i	$-0.121580\pi$
$191$	1.95100	+	3.37923i	0.141169	+	0.244512i	−0.786768	+	0.617249i	$0.788247\pi$
$192$	−9.04238	+	10.4993i	−0.652578	+	0.757722i
$193$	1.87228	−	3.24289i	0.134770	−	0.233428i	−0.790740	−	0.612153i	$-0.790304\pi$
$193$	1.87228	−	3.24289i	0.134770	−	0.233428i	0.925509	+	0.378724i	$0.123637\pi$
$194$	−17.6350	−	0.982118i	−1.26612	−	0.0705120i
$195$	−0.675178	−	4.57820i	−0.0483505	−	0.327852i
$196$	−0.739958	−	0.0826752i	−0.0528542	−	0.00590537i
$197$			10.6873i			0.761436i	0.924691	+	0.380718i	$0.124323\pi$
$197$			10.6873i			0.761436i	−0.924691	+	0.380718i	$0.875677\pi$
$198$	−10.0252	−	10.5308i	−0.712460	−	0.748390i
$199$			19.3236i			1.36981i	0.728630	+	0.684907i	$0.240157\pi$
$199$			19.3236i			1.36981i	−0.728630	+	0.684907i	$0.759843\pi$
$200$	−4.31821	−	11.5883i	−0.305343	−	0.819414i
$201$	9.43070	−	7.47182i	0.665191	−	0.527022i
$202$	−1.40116	+	25.1592i	−0.0985850	+	1.77020i
$203$	−1.07561	+	1.86301i	−0.0754928	+	0.130757i
$204$	−0.307337	−	8.73916i	−0.0215179	−	0.611864i
$205$	0.0584220	+	0.101190i	0.00408037	+	0.00706741i
$206$	−18.4110	+	9.30506i	−1.28275	+	0.648315i
$207$	6.17889	−	1.86301i	0.429463	−	0.129488i
$208$	−4.00000	−	12.8824i	−0.277350	−	0.893234i
$209$	6.55842	−	3.78651i	0.453656	−	0.261918i
$210$	−3.03757	−	4.30575i	−0.209612	−	0.297125i
$211$	−5.30350	−	3.06198i	−0.365108	−	0.210795i	0.306211	−	0.951964i	$-0.400939\pi$
$211$	−5.30350	−	3.06198i	−0.365108	−	0.210795i	−0.671319	+	0.741169i	$0.734272\pi$
$212$	15.5986	−	6.82292i	1.07132	−	0.468600i
$213$	1.11684	−	2.81929i	0.0765249	−	0.193175i
$214$	10.2440	−	15.6619i	0.700265	−	1.07062i
$215$	−5.50371			−0.375350
$216$	14.1552	−	3.95358i	0.963138	−	0.269007i
$217$	−4.62772			−0.314150
$218$	7.34568	−	11.2307i	0.497512	−	0.760637i
$219$	1.51330	−	3.82009i	0.102260	−	0.258138i
$220$	−4.97526	+	2.17621i	−0.335432	+	0.146720i
$221$	7.37228	+	4.25639i	0.495913	+	0.286316i
$222$	−6.69944	−	9.49646i	−0.449637	−	0.637360i
$223$	−1.47603	+	0.852189i	−0.0988426	+	0.0570668i	−0.548606	−	0.836081i	$-0.684841\pi$
$223$	−1.47603	+	0.852189i	−0.0988426	+	0.0570668i	0.449764	+	0.893147i	$0.351508\pi$
$224$	−10.6815	−	11.0371i	−0.713690	−	0.737448i
$225$	−3.00000	+	12.7692i	−0.200000	+	0.851278i
$226$	−20.1168	+	10.1672i	−1.33815	+	0.676313i
$227$	9.44298	+	16.3557i	0.626752	+	1.08557i	0.988199	+	0.153174i	$0.0489496\pi$
$227$	9.44298	+	16.3557i	0.626752	+	1.08557i	−0.361447	+	0.932393i	$0.617717\pi$
$228$	0.269040	+	7.65020i	0.0178176	+	0.506647i
$229$	−4.68614	+	8.11663i	−0.309669	+	0.536362i	−0.978290	−	0.207241i	$-0.933552\pi$
$229$	−4.68614	+	8.11663i	−0.309669	+	0.536362i	0.668621	+	0.743603i	$0.266885\pi$
$230$	0.134029	−	2.40663i	0.00883759	−	0.158688i
$231$	12.6325	−	10.0086i	0.831159	−	0.658517i
$232$	−2.09987	+	0.782488i	−0.137863	+	0.0513729i
$233$		−	28.0627i		−	1.83845i	−0.393737	−	0.919223i	$-0.628818\pi$
$233$		−	28.0627i		−	1.83845i	0.393737	−	0.919223i	$-0.371182\pi$
$234$	−4.04171	+	13.7246i	−0.264215	+	0.897208i
$235$			9.15640i			0.597298i
$236$	−10.2916	−	1.14988i	−0.669926	−	0.0748506i
$237$	2.56930	+	17.4217i	0.166894	+	1.13166i
$238$	9.67812	+	0.538989i	0.627339	+	0.0349375i
$239$	8.33010	−	14.4282i	0.538830	−	0.933280i	−0.460138	−	0.887847i	$-0.652200\pi$
$239$	8.33010	−	14.4282i	0.538830	−	0.933280i	0.998967	−	0.0454327i	$-0.0144667\pi$
$240$	0.417400	−	5.47323i	0.0269431	−	0.353296i
$241$	−8.24456	−	14.2800i	−0.531079	−	0.919856i	−0.999342	−	0.0362667i	$-0.988453\pi$
$241$	−8.24456	−	14.2800i	−0.531079	−	0.919856i	0.468263	−	0.883589i	$-0.344880\pi$
$242$	−0.474964	−	0.939764i	−0.0305319	−	0.0604103i
$243$	−14.8210	−	4.83090i	−0.950768	−	0.309903i
$244$	−4.00000	+	5.43039i	−0.256074	+	0.347645i
$245$	0.255437	−	0.147477i	0.0163193	−	0.00942195i
$246$	−0.0327513	−	0.359755i	−0.00208814	−	0.0229372i
$247$	−6.45364	−	3.72601i	−0.410635	−	0.237080i
$248$	−3.71642	−	3.07042i	−0.235993	−	0.194972i
$249$	12.4307	−	1.83324i	0.787764	−	0.116177i
$250$	8.78835	+	5.74822i	0.555824	+	0.363549i
$251$	−16.7347			−1.05629			−0.528144	−	0.849155i	$-0.677112\pi$
$251$	−16.7347			−1.05629			−0.528144	+	0.849155i	$0.677112\pi$
$252$	2.94184	+	16.0233i	0.185318	+	1.00938i
$253$	7.37228			0.463491
$254$	19.2811	+	12.6112i	1.20980	+	0.791300i
$255$	2.15121	+	2.71519i	0.134714	+	0.170032i
$256$	−1.25513	−	15.9507i	−0.0784457	−	0.996918i
$257$	−9.98913	−	5.76722i	−0.623105	−	0.359750i	0.154972	−	0.987919i	$-0.450471\pi$
$257$	−9.98913	−	5.76722i	−0.623105	−	0.359750i	−0.778077	+	0.628169i	$0.783805\pi$
$258$	15.4466	+	7.13679i	0.961666	+	0.444317i
$259$	11.1565	−	6.44121i	0.693231	−	0.400237i
$260$	4.30243	+	3.16915i	0.266825	+	0.196542i
$261$	2.31386	+	0.543620i	0.143224	+	0.0336493i
$262$	4.62772	+	9.15640i	0.285901	+	0.565684i
$263$	−6.25343	−	10.8313i	−0.385603	−	0.667884i	0.606250	−	0.795274i	$-0.292673\pi$
$263$	−6.25343	−	10.8313i	−0.385603	−	0.667884i	−0.991853	+	0.127391i	$0.959340\pi$
$264$	16.7854	+	0.343827i	1.03307	+	0.0211611i
$265$	−3.37228	+	5.84096i	−0.207158	+	0.358807i
$266$	−8.47215	−	0.471827i	−0.519461	−	0.0289296i
$267$	8.60485	+	3.40876i	0.526608	+	0.208613i
$268$	−1.54269	+	13.8073i	−0.0942345	+	0.843416i
$269$			24.9484i			1.52113i	0.649260	+	0.760566i	$0.275079\pi$
$269$			24.9484i			1.52113i	−0.649260	+	0.760566i	$0.724921\pi$
$270$	−3.58601	+	4.58665i	−0.218238	+	0.279134i
$271$			1.38712i			0.0842618i	0.999112	+	0.0421309i	$0.0134147\pi$
$271$			1.38712i			0.0842618i	−0.999112	+	0.0421309i	$0.986585\pi$
$272$	7.41467	+	6.85414i	0.449580	+	0.415593i
$273$	−14.7446	−	5.84096i	−0.892382	−	0.353511i
$274$	1.47506	−	26.4862i	0.0891115	−	1.60009i
$275$	−7.49198	+	12.9765i	−0.451783	+	0.782512i
$276$	−3.49689	+	6.58061i	−0.210488	+	0.396106i
$277$	−0.313859	−	0.543620i	−0.0188580	−	0.0326630i	0.856442	−	0.516243i	$-0.172670\pi$
$277$	−0.313859	−	0.543620i	−0.0188580	−	0.0326630i	−0.875300	+	0.483580i	$0.839336\pi$
$278$	−11.7944	+	5.96099i	−0.707381	+	0.357516i
$279$	1.47603	+	4.89545i	0.0883679	+	0.293083i
$280$	6.00000	+	1.01082i	0.358569	+	0.0604078i
$281$	−5.56930	+	3.21543i	−0.332236	+	0.191817i	−0.656834	−	0.754036i	$-0.728105\pi$
$281$	−5.56930	+	3.21543i	−0.332236	+	0.191817i	0.324597	+	0.945852i	$0.394771\pi$
$282$	11.8733	−	25.6982i	0.707045	−	1.53031i
$283$	8.80507	+	5.08361i	0.523407	+	0.302189i	0.738327	−	0.674442i	$-0.235616\pi$
$283$	8.80507	+	5.08361i	0.523407	+	0.302189i	−0.214921	+	0.976632i	$0.568949\pi$
$284$	1.40324	+	3.20810i	0.0832669	+	0.190366i
$285$	−1.88316	−	2.37686i	−0.111549	−	0.140793i
$286$	−8.94639	+	13.6780i	−0.529011	+	0.808796i
$287$	0.400428			0.0236365
$288$	−8.26873	+	14.8199i	−0.487240	+	0.873268i
$289$	10.6277			0.625160
$290$	0.485927	−	0.742925i	0.0285346	−	0.0436260i
$291$	−21.4003	+	3.15605i	−1.25451	+	0.185011i
$292$	1.90136	+	4.34692i	0.111269	+	0.254384i
$293$	−17.3139	−	9.99616i	−1.01149	−	0.583982i	−0.0998599	−	0.995002i	$-0.531839\pi$
$293$	−17.3139	−	9.99616i	−1.01149	−	0.583982i	−0.911627	+	0.411020i	$0.865173\pi$
$294$	−0.908144	+	0.0826752i	−0.0529640	+	0.00482172i
$295$	3.55271	−	2.05116i	0.206847	−	0.119423i
$296$	13.2332	+	2.22938i	0.769163	+	0.129580i
$297$	−14.6168	−	10.1711i	−0.848155	−	0.590186i
$298$	12.1168	−	6.12395i	0.701910	−	0.354751i
$299$	−3.62725	−	6.28258i	−0.209769	−	0.363331i
$300$	−8.02934	−	12.8426i	−0.463574	−	0.741467i
$301$	−9.43070	+	16.3345i	−0.543577	+	0.941502i
$302$	0.720040	−	12.9291i	0.0414336	−	0.743984i
$303$	4.50264	+	30.5312i	0.258670	+	1.75397i
$304$	−6.49074	−	6.00006i	−0.372270	−	0.344127i
$305$		−	2.67181i		−	0.152988i
$306$	−2.51671	−	10.4100i	−0.143871	−	0.595098i
$307$		−	25.9530i		−	1.48121i	−0.671938	−	0.740607i	$-0.734538\pi$
$307$		−	25.9530i		−	1.48121i	0.671938	−	0.740607i	$-0.265462\pi$
$308$	−2.06644	+	18.4950i	−0.117747	+	1.05385i
$309$	−19.8030	+	15.6896i	−1.12655	+	0.892553i
$310$	1.90674	+	0.106189i	0.108295	+	0.00603114i
$311$	15.6591	−	27.1224i	0.887948	−	1.53797i	0.0456512	−	0.998957i	$-0.485464\pi$
$311$	15.6591	−	27.1224i	0.887948	−	1.53797i	0.842297	−	0.539014i	$-0.181203\pi$
$312$	−7.96563	−	14.4735i	−0.450965	−	0.819403i
$313$	−2.24456	−	3.88770i	−0.126870	−	0.219746i	0.795592	−	0.605832i	$-0.207160\pi$
$313$	−2.24456	−	3.88770i	−0.126870	−	0.219746i	−0.922462	+	0.386087i	$0.873826\pi$
$314$	10.7561	+	21.2819i	0.607000	+	1.20101i
$315$	−4.70285	−	4.41957i	−0.264976	−	0.249015i
$316$	−16.3723	−	12.0597i	−0.921013	−	0.678414i
$317$	20.6644	−	11.9306i	1.16063	−	0.670089i	0.209173	−	0.977879i	$-0.432923\pi$
$317$	20.6644	−	11.9306i	1.16063	−	0.670089i	0.951454	+	0.307790i	$0.0995893\pi$
$318$	17.0387	−	12.0203i	0.955483	−	0.674063i
$319$	2.35143	+	1.35760i	0.131655	+	0.0760109i
$320$	4.14780	+	4.79268i	0.231869	+	0.267919i
$321$	8.44158	−	21.3094i	0.471163	−	1.18937i
$322$	−6.91296	−	4.52158i	−0.385244	−	0.251978i
$323$	5.57825			0.310382
$324$	16.0121	−	8.22277i	0.889559	−	0.456820i
$325$	14.7446			0.817881
$326$	14.0504	+	9.18998i	0.778180	+	0.508986i
$327$	6.05321	−	15.2804i	0.334743	−	0.845005i
$328$	0.321575	+	0.265678i	0.0177560	+	0.0146696i
$329$	27.1753	+	15.6896i	1.49822	+	0.864998i
$330$	−5.43459	+	3.83392i	−0.299164	+	0.211051i
$331$	24.1149	−	13.9228i	1.32548	−	0.765264i	0.340879	−	0.940107i	$-0.389275\pi$
$331$	24.1149	−	13.9228i	1.32548	−	0.765264i	0.984596	+	0.174843i	$0.0559419\pi$
$332$	−8.60485	+	11.6819i	−0.472253	+	0.641129i
$333$	−10.3723	−	9.74749i	−0.568398	−	0.534159i
$334$	−12.2554	−	24.2486i	−0.670588	−	1.32682i
$335$	−2.75186	−	4.76635i	−0.150350	−	0.260414i
$336$	−15.5288	−	10.6173i	−0.847164	−	0.579220i
$337$	2.12772	−	3.68532i	0.115904	−	0.200752i	−0.802237	−	0.597006i	$-0.796357\pi$
$337$	2.12772	−	3.68532i	0.115904	−	0.200752i	0.918141	+	0.396254i	$0.129690\pi$
$338$	−2.29838	−	0.128000i	−0.125015	−	0.00696230i
$339$	−21.6378	+	17.1434i	−1.17520	+	0.931099i
$340$	−3.97526	−	0.444155i	−0.215589	−	0.0240877i
$341$			5.84096i			0.316306i
$342$	2.20311	+	9.11280i	0.119131	+	0.492764i
$343$			17.9955i			0.971668i
$344$	−18.4113	+	6.86070i	−0.992668	+	0.369904i
$345$	−0.430703	−	2.92048i	−0.0231883	−	0.157233i
$346$	0.436126	−	7.83111i	0.0234463	−	0.421003i
$347$	−3.86473	+	6.69391i	−0.207470	+	0.359348i	−0.950917	−	0.309447i	$-0.899856\pi$
$347$	−3.86473	+	6.69391i	−0.207470	+	0.359348i	0.743447	+	0.668795i	$0.233189\pi$
$348$	−2.32716	+	1.45497i	−0.124749	+	0.0779946i
$349$	5.68614	+	9.84868i	0.304372	+	0.527188i	0.977121	−	0.212683i	$-0.0682200\pi$
$349$	5.68614	+	9.84868i	0.304372	+	0.527188i	−0.672749	+	0.739871i	$0.734887\pi$
$350$	14.9840	−	7.57301i	0.800926	−	0.404795i
$351$	−1.47603	+	17.4606i	−0.0787849	+	0.931978i
$352$	−13.9307	+	13.4819i	−0.742509	+	0.718587i
$353$	−4.24456	+	2.45060i	−0.225915	+	0.130432i	−0.608686	−	0.793411i	$-0.708303\pi$
$353$	−4.24456	+	2.45060i	−0.225915	+	0.130432i	0.382771	+	0.923843i	$0.374970\pi$
$354$	−12.6308	+	1.14988i	−0.671318	+	0.0611152i
$355$	−1.20128	−	0.693562i	−0.0637576	−	0.0368105i
$356$	−9.79155	+	4.28287i	−0.518951	+	0.226992i
$357$	11.7446	−	1.73205i	0.621588	−	0.0916698i
$358$	−14.5622	+	22.2639i	−0.769636	+	1.17668i
$359$	−29.9679			−1.58165			−0.790823	−	0.612045i	$-0.790347\pi$
$359$	−29.9679			−1.58165			−0.790823	+	0.612045i	$0.790347\pi$
$360$	−0.844434	−	6.66953i	−0.0445056	−	0.351515i
$361$	14.1168			0.742992
$362$	3.09646	−	4.73412i	0.162746	−	0.248820i
$363$	−0.800857	−	1.01082i	−0.0420341	−	0.0530541i
$364$	16.7780	−	7.33878i	0.879406	−	0.384656i
$365$	−1.62772	−	0.939764i	−0.0851987	−	0.0491895i
$366$	−3.46460	+	7.49868i	−0.181098	+	0.391962i
$367$	−11.7571	+	6.78799i	−0.613718	+	0.354330i	−0.774419	−	0.632673i	$-0.781958\pi$
$367$	−11.7571	+	6.78799i	−0.613718	+	0.354330i	0.160701	+	0.987003i	$0.448624\pi$
$368$	−2.55164	−	8.21782i	−0.133014	−	0.428384i
$369$	−0.127719	−	0.423595i	−0.00664877	−	0.0220515i
$370$	−4.74456	+	2.39794i	−0.246658	+	0.124663i
$371$	11.5569	+	20.0172i	0.600006	+	1.03924i
$372$	−5.21373	−	2.77054i	−0.270319	−	0.143646i
$373$	−4.43070	+	7.67420i	−0.229413	+	0.397355i	−0.957634	−	0.287987i	$-0.907014\pi$
$373$	−4.43070	+	7.67420i	−0.229413	+	0.397355i	0.728221	+	0.685342i	$0.240347\pi$
$374$	0.680295	−	12.2154i	0.0351772	−	0.631644i
$375$	11.9574	+	4.73683i	0.617475	+	0.244609i
$376$	11.4140	+	30.6304i	0.588632	+	1.57964i
$377$		−	2.67181i		−	0.137605i
$378$	7.46801	+	18.5022i	0.384113	+	0.951651i
$379$			9.66181i			0.496294i	0.968722	+	0.248147i	$0.0798216\pi$
$379$			9.66181i			0.496294i	−0.968722	+	0.248147i	$0.920178\pi$
$380$	3.47992	+	0.388810i	0.178516	+	0.0199455i
$381$	26.2337	+	10.3923i	1.34399	+	0.532414i
$382$	−5.50972	−	0.306845i	−0.281902	−	0.0156995i
$383$	−0.200214	+	0.346781i	−0.0102305	+	0.0177197i	−0.871095	−	0.491114i	$-0.836590\pi$
$383$	−0.200214	+	0.346781i	−0.0102305	+	0.0177197i	0.860865	+	0.508834i	$0.169923\pi$
$384$	−5.42640	−	18.8296i	−0.276915	−	0.960894i
$385$	−3.68614	−	6.38458i	−0.187863	−	0.325388i
$386$	2.38870	+	4.72627i	0.121581	+	0.240561i
$387$	20.2875	+	4.76635i	1.03127	+	0.242287i
$388$	14.8139	−	20.1113i	0.752060	−	1.02099i
$389$	7.19702	−	4.15520i	0.364903	−	0.210677i	−0.306326	−	0.951927i	$-0.599100\pi$
$389$	7.19702	−	4.15520i	0.364903	−	0.210677i	0.671229	+	0.741250i	$0.265767\pi$
$390$	5.94111	+	2.74496i	0.300840	+	0.138996i
$391$	4.70285	+	2.71519i	0.237834	+	0.137313i
$392$	0.670662	−	0.811764i	0.0338735	−	0.0410002i
$393$	7.80298	+	9.84868i	0.393609	+	0.496800i
$394$	−12.6487	−	8.27317i	−0.637232	−	0.416796i
$395$	8.05535			0.405309
$396$	20.2242	−	3.71309i	1.01630	−	0.186590i
$397$	−7.25544			−0.364140			−0.182070	−	0.983286i	$-0.558280\pi$
$397$	−7.25544			−0.364140			−0.182070	+	0.983286i	$0.558280\pi$
$398$	−22.8701	−	14.9587i	−1.14637	−	0.749812i
$399$	−10.2811	+	1.51622i	−0.514699	+	0.0759062i
$400$	17.0579	+	3.85992i	0.852893	+	0.192996i
$401$	−18.9891	−	10.9634i	−0.948272	−	0.547485i	−0.0557281	−	0.998446i	$-0.517748\pi$
$401$	−18.9891	−	10.9634i	−0.948272	−	0.547485i	−0.892544	+	0.450961i	$0.851081\pi$
$402$	1.54269	+	16.9456i	0.0769421	+	0.845169i
$403$	4.97760	−	2.87382i	0.247952	−	0.143155i
$404$	−28.6921	−	21.1345i	−1.42749	−	1.05148i
$405$	−3.17527	+	6.38458i	−0.157780	+	0.317252i
$406$	−1.37228	−	2.71519i	−0.0681052	−	0.134753i
$407$	−8.12989	−	14.0814i	−0.402984	−	0.697988i
$408$	10.5810	+	6.40137i	0.523837	+	0.316915i
$409$	−1.12772	+	1.95327i	−0.0557621	+	0.0965828i	−0.892559	−	0.450931i	$-0.851092\pi$
$409$	−1.12772	+	1.95327i	−0.0557621	+	0.0965828i	0.836797	+	0.547513i	$0.184426\pi$
$410$	−0.164987	−	0.00918836i	−0.00814811	−	0.000453781i
$411$	−4.74012	−	32.1415i	−0.233813	−	1.58542i
$412$	3.23939	−	28.9932i	0.159594	−	1.42839i
$413$		−	14.0588i		−	0.691788i
$414$	−2.57825	+	8.75509i	−0.126714	+	0.430289i
$415$		−	5.74764i		−	0.282141i
$416$	18.3432	+	5.23834i	0.899349	+	0.256831i
$417$	−12.6861	+	10.0511i	−0.621243	+	0.492203i
$418$	−0.595525	+	10.6933i	−0.0291281	+	0.523026i
$419$	−2.82639	+	4.89545i	−0.138078	+	0.239159i	−0.926769	−	0.375631i	$-0.877426\pi$
$419$	−2.82639	+	4.89545i	−0.138078	+	0.239159i	0.788691	+	0.614790i	$0.210759\pi$
$420$	7.44742	−	0.261909i	0.363397	−	0.0127799i
$421$	−14.8030	−	25.6395i	−0.721453	−	1.24959i	−0.960417	−	0.278565i	$-0.910141\pi$
$421$	−14.8030	−	25.6395i	−0.721453	−	1.24959i	0.238964	−	0.971028i	$-0.423192\pi$
$422$	7.72946	−	3.90653i	0.376264	−	0.190167i
$423$	7.92967	−	33.7518i	0.385554	−	1.64107i
$424$	−4.00000	+	23.7432i	−0.194257	+	1.15307i
$425$	−9.55842	+	5.51856i	−0.463652	+	0.267689i
$426$	2.47215	+	3.50428i	0.119776	+	0.169783i
$427$	−7.92967	−	4.57820i	−0.383744	−	0.221555i
$428$	10.6063	+	24.2482i	0.512674	+	1.17208i
$429$	−7.37228	+	18.6101i	−0.355937	+	0.898505i
$430$	4.26051	−	6.51381i	0.205460	−	0.314124i
$431$	14.6581			0.706054			0.353027	−	0.935613i	$-0.385152\pi$
$431$	14.6581			0.706054			0.353027	+	0.935613i	$0.385152\pi$
$432$	−6.27855	+	19.8136i	−0.302077	+	0.953283i
$433$	−14.3723			−0.690688			−0.345344	−	0.938476i	$-0.612238\pi$
$433$	−14.3723			−0.690688			−0.345344	+	0.938476i	$0.612238\pi$
$434$	3.58239	−	5.47705i	0.171960	−	0.262907i
$435$	0.400428	−	1.01082i	0.0191991	−	0.0484649i
$436$	7.60545	+	17.3877i	0.364235	+	0.832718i
$437$	−4.11684	−	2.37686i	−0.196935	−	0.113701i
$438$	3.34972	+	4.74823i	0.160056	+	0.226879i
$439$	−28.4919	+	16.4498i	−1.35984	+	0.785106i	−0.989602	−	0.143830i	$-0.954058\pi$
$439$	−28.4919	+	16.4498i	−1.35984	+	0.785106i	−0.370241	+	0.928936i	$0.620725\pi$
$440$	1.27582	−	7.57301i	0.0608224	−	0.361029i
$441$	−1.06930	+	0.322405i	−0.0509189	+	0.0153526i
$442$	−10.7446	+	5.43039i	−0.511067	+	0.258297i
$443$	−2.58891	−	4.48412i	−0.123003	−	0.213047i	0.797948	−	0.602727i	$-0.205919\pi$
$443$	−2.58891	−	4.48412i	−0.123003	−	0.213047i	−0.920950	+	0.389680i	$0.872586\pi$
$444$	16.4255	−	0.577648i	0.779519	−	0.0274140i
$445$	2.11684	−	3.66648i	0.100348	−	0.173808i
$446$	0.134029	−	2.40663i	0.00634644	−	0.113957i
$447$	13.0330	−	10.3258i	0.616438	−	0.488396i
$448$	21.3315	−	4.09793i	1.00782	−	0.193609i
$449$		−	3.81396i		−	0.179992i	−0.995942	−	0.0899959i	$-0.971315\pi$
$449$		−	3.81396i		−	0.179992i	0.995942	−	0.0899959i	$-0.0286854\pi$
$450$	−12.7904	−	13.4354i	−0.602943	−	0.633351i
$451$		−	0.505408i		−	0.0237987i
$452$	3.53954	−	31.6795i	0.166486	−	1.49008i
$453$	−2.31386	−	15.6896i	−0.108715	−	0.737164i
$454$	−26.6675	−	1.48515i	−1.25157	−	0.0697016i
$455$	−3.62725	+	6.28258i	−0.170048	+	0.294532i
$456$	−9.26251	−	5.60371i	−0.433757	−	0.262418i
$457$	2.98913	+	5.17732i	0.139825	+	0.242185i	0.927430	−	0.373996i	$-0.122013\pi$
$457$	2.98913	+	5.17732i	0.139825	+	0.242185i	−0.787605	+	0.616180i	$0.788679\pi$
$458$	−5.97868	−	11.8294i	−0.279365	−	0.552752i
$459$	−5.57825	−	11.8716i	−0.260370	−	0.554119i
$460$	2.74456	+	2.02163i	0.127966	+	0.0942591i
$461$	−19.8030	+	11.4333i	−0.922317	+	0.532500i	−0.884373	−	0.466780i	$-0.845414\pi$
$461$	−19.8030	+	11.4333i	−0.922317	+	0.532500i	−0.0379435	+	0.999280i	$0.512081\pi$
$462$	2.06644	+	22.6988i	0.0961396	+	1.05604i
$463$	−18.2108	−	10.5140i	−0.846327	−	0.488627i	0.0130831	−	0.999914i	$-0.495835\pi$
$463$	−18.2108	−	10.5140i	−0.846327	−	0.488627i	−0.859410	+	0.511288i	$0.829169\pi$
$464$	0.699444	−	3.09100i	0.0324709	−	0.143496i
$465$	2.31386	−	0.341241i	0.107303	−	0.0158247i
$466$	33.2130	+	21.7237i	1.53856	+	1.00633i
$467$	24.3897			1.12862			0.564310	−	0.825563i	$-0.309142\pi$
$467$	24.3897			1.12862			0.564310	+	0.825563i	$0.309142\pi$
$468$	−13.1148	−	15.4079i	−0.606231	−	0.712232i
$469$	−18.8614			−0.870939
$470$	−10.8369	−	7.08811i	−0.499868	−	0.326950i
$471$	18.1362	+	22.8910i	0.835674	+	1.05476i
$472$	9.32780	−	11.2903i	0.429347	−	0.519678i
$473$	20.6168	+	11.9031i	0.947963	+	0.547307i
$474$	−22.6081	−	10.4456i	−1.03842	−	0.479780i
$475$	8.36737	−	4.83090i	0.383921	−	0.221657i
$476$	−8.12989	+	11.0371i	−0.372633	+	0.505885i
$477$	17.4891	−	18.6101i	0.800772	−	0.852099i
$478$	10.6277	+	21.0280i	0.486101	+	0.961798i
$479$	4.90307	+	8.49236i	0.224027	+	0.388026i	0.956027	−	0.293278i	$-0.0947463\pi$
$479$	4.90307	+	8.49236i	0.224027	+	0.388026i	−0.732000	+	0.681304i	$0.761413\pi$
$480$	6.15462	+	4.73092i	0.280919	+	0.215936i
$481$	−8.00000	+	13.8564i	−0.364769	+	0.631798i
$482$	23.2831	+	1.29667i	1.06051	+	0.0590617i
$483$	−9.40571	−	3.72601i	−0.427975	−	0.169539i
$484$	1.47992	+	0.165350i	0.0672689	+	0.00751593i
$485$			9.89497i			0.449308i
$486$	17.1907	−	13.8015i	0.779786	−	0.626047i
$487$			17.9365i			0.812780i	0.913700	+	0.406390i	$0.133213\pi$
$487$			17.9365i			0.812780i	−0.913700	+	0.406390i	$0.866787\pi$
$488$	−3.33057	−	8.93787i	−0.150768	−	0.404598i
$489$	19.1168	+	7.57301i	0.864494	+	0.342464i
$490$	−0.0231945	+	0.416482i	−0.00104782	+	0.0188147i
$491$	−12.3950	+	21.4689i	−0.559381	+	0.968876i	0.438168	+	0.898893i	$0.355628\pi$
$491$	−12.3950	+	21.4689i	−0.559381	+	0.968876i	−0.997548	+	0.0699824i	$0.977706\pi$
$492$	0.451135	+	0.239730i	0.0203387	+	0.0108079i
$493$	1.00000	+	1.73205i	0.0450377	+	0.0780076i
$494$	9.40571	−	4.75372i	0.423183	−	0.213880i
$495$	−5.57825	+	5.93580i	−0.250724	+	0.266794i
$496$	6.51087	−	2.02163i	0.292347	−	0.0907740i
$497$	−4.11684	+	2.37686i	−0.184666	+	0.106617i
$498$	−7.45310	+	16.1313i	−0.333981	+	0.722859i
$499$	0.437696	+	0.252704i	0.0195940	+	0.0113126i	0.509765	−	0.860314i	$-0.329732\pi$
$499$	0.437696	+	0.252704i	0.0195940	+	0.0113126i	−0.490171	+	0.871626i	$0.663066\pi$
$500$	−13.6064	+	5.95150i	−0.608496	+	0.266159i
$501$	−20.6644	−	26.0820i	−0.923217	−	1.16526i
$502$	12.9546	−	19.8061i	0.578193	−	0.883989i
$503$	12.9073			0.575507			0.287754	−	0.957704i	$-0.407092\pi$
$503$	12.9073			0.575507			0.287754	+	0.957704i	$0.407092\pi$
$504$	−21.2415	−	8.92216i	−0.946169	−	0.397425i
$505$	14.1168			0.628191
$506$	−5.70699	+	8.72532i	−0.253707	+	0.387888i
$507$	−2.78912	+	0.411331i	−0.123869	+	0.0182679i
$508$	−29.8516	+	13.0572i	−1.32445	+	0.579321i
$509$	15.6861	+	9.05640i	0.695276	+	0.401418i	0.805586	−	0.592480i	$-0.201851\pi$
$509$	15.6861	+	9.05640i	0.695276	+	0.401418i	−0.110310	+	0.993897i	$0.535184\pi$
$510$	−4.87880	+	0.444155i	−0.216037	+	0.0196675i
$511$	−5.57825	+	3.22060i	−0.246767	+	0.142471i
$512$	19.8498	+	10.8622i	0.877244	+	0.480045i
$513$	4.88316	+	10.3923i	0.215597	+	0.458831i
$514$	14.5584	−	7.35794i	0.642144	−	0.324545i
$515$	5.77846	+	10.0086i	0.254629	+	0.441031i
$516$	−20.4041	+	12.7569i	−0.898240	+	0.561591i
$517$	19.8030	−	34.2998i	0.870934	−	1.50850i
$518$	−1.01304	+	18.1903i	−0.0445106	+	0.799236i
$519$	−1.40150	−	9.50318i	−0.0615190	−	0.417143i
$520$	−7.08136	+	2.63877i	−0.310538	+	0.115718i
$521$			10.4472i			0.457700i	0.973462	+	0.228850i	$0.0734966\pi$
$521$			10.4472i			0.457700i	−0.973462	+	0.228850i	$0.926503\pi$
$522$	−2.43459	+	2.31770i	−0.106559	+	0.101443i
$523$		−	4.41957i		−	0.193254i	−0.995321	−	0.0966272i	$-0.969195\pi$
$523$		−	4.41957i		−	0.193254i	0.995321	−	0.0966272i	$-0.0308055\pi$
$524$	−14.4193	−	1.61106i	−0.629909	−	0.0703794i
$525$	16.1168	−	12.7692i	0.703397	−	0.557292i
$526$	17.6600	+	0.983512i	0.770012	+	0.0428832i
$527$	−2.15121	+	3.72601i	−0.0937083	+	0.162308i
$528$	−13.4008	+	19.5999i	−0.583195	+	0.852978i
$529$	9.18614	+	15.9109i	0.399397	+	0.691777i
$530$	−4.30243	−	8.51278i	−0.186885	−	0.369771i
$531$	−14.8722	+	4.48412i	−0.645396	+	0.194594i
$532$	7.11684	−	9.66181i	0.308554	−	0.418892i
$533$	−0.430703	+	0.248667i	−0.0186558	+	0.0107709i
$534$	−10.6955	+	7.54534i	−0.462840	+	0.326519i
$535$	−9.07982	−	5.24224i	−0.392555	−	0.226642i
$536$	−15.1472	−	12.5143i	−0.654258	−	0.540534i
$537$	−12.0000	+	30.2921i	−0.517838	+	1.30720i
$538$	−29.5272	−	19.3130i	−1.27301	−	0.832641i
$539$	−1.27582			−0.0549535
$540$	−2.65245	−	7.79475i	−0.114143	−	0.335433i
$541$	36.9783			1.58982			0.794910	−	0.606728i	$-0.207518\pi$
$541$	36.9783			1.58982			0.794910	+	0.606728i	$0.207518\pi$
$542$	−1.64170	−	1.07379i	−0.0705172	−	0.0461234i
$543$	2.55164	−	6.44121i	0.109501	−	0.276419i
$544$	−13.8519	+	3.46959i	−0.593895	+	0.148758i
$545$	−6.51087	−	3.75906i	−0.278895	−	0.161020i
$546$	18.3269	−	12.9291i	0.784321	−	0.553313i
$547$	−7.21723	+	4.16687i	−0.308586	+	0.178162i	−0.646294	−	0.763089i	$-0.723682\pi$
$547$	−7.21723	+	4.16687i	−0.308586	+	0.178162i	0.337707	+	0.941251i	$0.390349\pi$
$548$	30.2054	+	22.2492i	1.29031	+	0.950437i
$549$	−2.31386	+	9.84868i	−0.0987531	+	0.420332i
$550$	−9.55842	−	18.9123i	−0.407572	−	0.806423i
$551$	−0.875393	−	1.51622i	−0.0372930	−	0.0645933i
$552$	−5.08136	−	9.23282i	−0.216277	−	0.392975i
$553$	13.8030	−	23.9075i	0.586963	−	1.01665i
$554$	0.886355	+	0.0493624i	0.0376576	+	0.00209721i
$555$	−5.10328	+	4.04326i	−0.216622	+	0.171627i
$556$	2.07521	−	18.5735i	0.0880086	−	0.787693i
$557$		−	20.4897i		−	0.868175i	−0.900871	−	0.434087i	$-0.857071\pi$
$557$		−	20.4897i		−	0.868175i	0.900871	−	0.434087i	$-0.142929\pi$
$558$	−6.93654	−	2.04271i	−0.293647	−	0.0864749i
$559$		−	23.4259i		−	0.990811i
$560$	−5.84102	+	6.31870i	−0.246828	+	0.267014i
$561$	−2.18614	−	14.8236i	−0.0922989	−	0.625854i
$562$	0.505710	−	9.08055i	0.0213321	−	0.383040i
$563$	5.54098	−	9.59726i	0.233524	−	0.404476i	−0.725318	−	0.688414i	$-0.758307\pi$
$563$	5.54098	−	9.59726i	0.233524	−	0.404476i	0.958843	+	0.283937i	$0.0916408\pi$
$564$	21.2234	+	33.9458i	0.893664	+	1.42938i
$565$	6.31386	+	10.9359i	0.265626	+	0.460078i
$566$	−12.8327	+	6.48577i	−0.539400	+	0.272617i
$567$	13.5079	+	20.3640i	0.567279	+	0.855206i
$568$	−4.88316	−	0.822662i	−0.204893	−	0.0345181i
$569$	0.989125	−	0.571072i	0.0414663	−	0.0239406i	−0.479124	−	0.877747i	$-0.659045\pi$
$569$	0.989125	−	0.571072i	0.0414663	−	0.0239406i	0.520590	+	0.853807i	$0.325712\pi$
$570$	4.27087	−	0.388810i	0.178887	−	0.0162854i
$571$	14.5463	+	8.39829i	0.608742	+	0.351457i	0.772473	−	0.635048i	$-0.219020\pi$
$571$	14.5463	+	8.39829i	0.608742	+	0.351457i	−0.163731	+	0.986505i	$0.552353\pi$
$572$	−9.26278	−	21.1767i	−0.387296	−	0.885441i
$573$	−6.68614	+	0.986051i	−0.279318	+	0.0411929i
$574$	−0.309978	+	0.473919i	−0.0129382	+	0.0197810i
$575$	9.40571			0.392245
$576$	−11.1388	−	21.2586i	−0.464117	−	0.885774i
$577$	−42.8397			−1.78344			−0.891719	−	0.452589i	$-0.850500\pi$
$577$	−42.8397			−1.78344			−0.891719	+	0.452589i	$0.850500\pi$
$578$	−8.22708	+	12.5782i	−0.342201	+	0.523186i
$579$	4.02768	+	5.08361i	0.167385	+	0.211268i
$580$	0.503111	+	1.15022i	0.0208906	+	0.0477602i
$581$	−17.0584	−	9.84868i	−0.707703	−	0.408592i
$582$	12.8310	−	27.7711i	0.531863	−	1.15115i
$583$	25.2651	−	14.5868i	1.04637	−	0.604123i
$584$	−6.61659	−	1.11469i	−0.273796	−	0.0461263i
$585$	7.80298	+	1.83324i	0.322614	+	0.0757952i
$586$	25.2337	−	12.7533i	1.04239	−	0.526834i
$587$	−6.41637	−	11.1135i	−0.264832	−	0.458702i	0.702688	−	0.711499i	$-0.251983\pi$
$587$	−6.41637	−	11.1135i	−0.264832	−	0.458702i	−0.967520	+	0.252796i	$0.918650\pi$
$588$	0.605159	−	1.13882i	0.0249563	−	0.0469640i
$589$	1.88316	−	3.26172i	0.0775941	−	0.134397i
$590$	−0.322598	+	5.79258i	−0.0132811	+	0.238477i
$591$	−17.2097	−	6.81751i	−0.707913	−	0.280435i
$592$	−12.8825	+	13.9361i	−0.529469	+	0.572769i
$593$			15.4410i			0.634085i	0.948411	+	0.317043i	$0.102690\pi$
$593$			15.4410i			0.634085i	−0.948411	+	0.317043i	$0.897310\pi$
$594$	23.3529	−	9.42589i	0.958182	−	0.386749i
$595$		−	5.43039i		−	0.222624i
$596$	−2.13195	+	19.0813i	−0.0873279	+	0.781601i
$597$	−31.1168	−	12.3267i	−1.27353	−	0.504500i
$598$	10.2435	+	0.570478i	0.418889	+	0.0233286i
$599$	9.20550	−	15.9444i	0.376126	−	0.651470i	−0.614369	−	0.789019i	$-0.710589\pi$
$599$	9.20550	−	15.9444i	0.376126	−	0.651470i	0.990495	+	0.137549i	$0.0439225\pi$
$600$	21.4152	+	0.438661i	0.874273	+	0.0179083i
$601$	14.9891	+	25.9619i	0.611419	+	1.05901i	0.991001	+	0.133851i	$0.0427344\pi$
$601$	14.9891	+	25.9619i	0.611419	+	1.05901i	−0.379582	+	0.925158i	$0.623932\pi$
$602$	−12.0319	−	23.8063i	−0.490383	−	0.970272i
$603$	6.01594	+	19.9526i	0.244988	+	0.812534i
$604$	14.7446	+	10.8608i	0.599948	+	0.441919i
$605$	−0.510875	+	0.294954i	−0.0207700	+	0.0119916i
$606$	−39.6202	−	18.3056i	−1.60946	−	0.743615i
$607$	33.1947	+	19.1650i	1.34733	+	0.777883i	0.987871	−	0.155277i	$-0.0496270\pi$
$607$	33.1947	+	19.1650i	1.34733	+	0.777883i	0.359462	+	0.933160i	$0.382960\pi$
$608$	12.1258	−	3.03726i	0.491768	−	0.123177i
$609$	−2.31386	−	2.92048i	−0.0937623	−	0.118344i
$610$	3.16218	+	2.06829i	0.128033	+	0.0837427i
$611$	−38.9732			−1.57669
$612$	14.2687	+	5.07990i	0.576779	+	0.205343i
$613$	−30.2337			−1.22113			−0.610564	−	0.791967i	$-0.709057\pi$
$613$	−30.2337			−1.22113			−0.610564	+	0.791967i	$0.709057\pi$
$614$	30.7162	+	20.0906i	1.23960	+	0.810790i
$615$	−0.200214	+	0.0295269i	−0.00807341	+	0.00119064i
$616$	−20.2898	−	16.7630i	−0.817499	−	0.675400i
$617$	7.24456	+	4.18265i	0.291655	+	0.168387i	0.638688	−	0.769466i	$-0.279477\pi$
$617$	7.24456	+	4.18265i	0.291655	+	0.168387i	−0.347033	+	0.937853i	$0.612811\pi$
$618$	−3.23939	−	35.5830i	−0.130308	−	1.43136i
$619$	−23.9520	+	13.8287i	−0.962711	+	0.555821i	−0.897006	−	0.442018i	$-0.854263\pi$
$619$	−23.9520	+	13.8287i	−0.962711	+	0.555821i	−0.0657046	+	0.997839i	$0.520930\pi$
$620$	−1.60171	+	2.17448i	−0.0643263	+	0.0873293i
$621$	−0.941578	+	11.1383i	−0.0377842	+	0.446965i
$622$	19.9783	+	39.5289i	0.801055	+	1.58497i
$623$	−7.25450	−	12.5652i	−0.290645	−	0.503412i
$624$	23.2962	+	1.77662i	0.932595	+	0.0711217i
$625$	−7.98913	+	13.8376i	−0.319565	+	0.553503i
$626$	6.33876	+	0.353015i	0.253348	+	0.0141093i
$627$	1.91373	+	12.9765i	0.0764271	+	0.518231i
$628$	−33.5143	−	3.74454i	−1.33737	−	0.149423i
$629$		−	11.9769i		−	0.477549i
$630$	8.87125	−	2.14472i	0.353439	−	0.0854476i
$631$		−	17.9365i		−	0.714040i	−0.934097	−	0.357020i	$-0.883793\pi$
$631$		−	17.9365i		−	0.714040i	0.934097	−	0.357020i	$-0.116207\pi$
$632$	26.9471	−	10.0415i	1.07190	−	0.399428i
$633$	8.31386	−	6.58696i	0.330446	−	0.261808i
$634$	−1.87639	+	33.6926i	−0.0745210	+	1.33810i
$635$	6.45364	−	11.1780i	0.256105	−	0.443587i
$636$	1.03643	+	29.4709i	0.0410970	+	1.16860i
$637$	0.627719	+	1.08724i	0.0248711	+	0.0430780i
$638$	−3.42703	+	1.73205i	−0.135678	+	0.0685725i
$639$	3.82746	+	3.59691i	0.151412	+	0.142292i
$640$	−8.88316	+	1.19897i	−0.351138	+	0.0473935i
$641$	23.8723	−	13.7827i	0.942898	−	0.544383i	0.0520307	−	0.998645i	$-0.483431\pi$
$641$	23.8723	−	13.7827i	0.942898	−	0.544383i	0.890868	+	0.454263i	$0.150097\pi$
$642$	18.6856	+	26.4868i	0.737461	+	1.04535i
$643$	5.46644	+	3.15605i	0.215575	+	0.124463i	0.603900	−	0.797060i	$-0.293613\pi$
$643$	5.46644	+	3.15605i	0.215575	+	0.124463i	−0.388324	+	0.921523i	$0.626946\pi$
$644$	10.7029	−	4.68148i	0.421752	−	0.184476i
$645$	3.51087	−	8.86263i	0.138241	−	0.348966i
$646$	−4.31821	+	6.60203i	−0.169898	+	0.259753i
$647$	−36.9711			−1.45348			−0.726741	−	0.686912i	$-0.758966\pi$
$647$	−36.9711			−1.45348			−0.726741	+	0.686912i	$0.758966\pi$
$648$	−2.66328	+	25.3161i	−0.104624	+	0.994512i
$649$	−17.7446			−0.696535
$650$	−11.4140	+	17.4506i	−0.447693	+	0.684471i
$651$	2.95207	−	7.45202i	0.115701	−	0.292068i
$652$	−21.7533	+	9.51498i	−0.851923	+	0.372635i
$653$	6.68614	+	3.86025i	0.261649	+	0.151063i	0.625087	−	0.780555i	$-0.285064\pi$
$653$	6.68614	+	3.86025i	0.261649	+	0.151063i	−0.363438	+	0.931619i	$0.618397\pi$
$654$	13.3989	+	18.9929i	0.523938	+	0.742682i
$655$	4.97760	−	2.87382i	0.194491	−	0.112290i
$656$	−0.563374	+	0.174928i	−0.0219961	+	0.00682980i
$657$	5.18614	+	4.87375i	0.202331	+	0.190143i
$658$	−39.6060	+	20.0172i	−1.54400	+	0.780351i
$659$	−8.33010	−	14.4282i	−0.324495	−	0.562041i	0.656915	−	0.753964i	$-0.271861\pi$
$659$	−8.33010	−	14.4282i	−0.324495	−	0.562041i	−0.981410	+	0.191923i	$0.938528\pi$
$660$	−0.330574	−	9.39990i	−0.0128676	−	0.365891i
$661$	−10.6861	+	18.5089i	−0.415643	+	0.719914i	−0.995496	−	0.0948069i	$-0.969777\pi$
$661$	−10.6861	+	18.5089i	−0.415643	+	0.719914i	0.579853	+	0.814721i	$0.303110\pi$
$662$	−2.18971	+	39.3186i	−0.0851055	+	1.52816i
$663$	−11.5569	+	9.15640i	−0.448834	+	0.355605i
$664$	−7.16477	−	19.2273i	−0.278047	−	0.746163i
$665$			4.75372i			0.184341i
$666$	19.5658	−	4.73023i	0.758159	−	0.183293i
$667$		−	1.70438i		−	0.0659938i
$668$	38.1861	+	4.26652i	1.47746	+	0.165076i
$669$	−0.430703	−	2.92048i	−0.0166520	−	0.112912i
$670$	7.77138	+	0.432800i	0.300235	+	0.0167205i
$671$	−5.77846	+	10.0086i	−0.223075	+	0.386377i
$672$	24.5869	−	10.1598i	0.948462	−	0.391922i
$673$	−0.569297	−	0.986051i	−0.0219448	−	0.0380095i	0.854844	−	0.518884i	$-0.173652\pi$
$673$	−0.569297	−	0.986051i	−0.0219448	−	0.0380095i	−0.876789	+	0.480875i	$0.840319\pi$
$674$	2.71459	+	5.37108i	0.104562	+	0.206886i
$675$	−18.6485	−	12.9765i	−0.717780	−	0.499465i
$676$	1.93070	−	2.62112i	0.0742578	−	0.100812i
$677$	28.5475	−	16.4819i	1.09717	−	0.633452i	0.161695	−	0.986841i	$-0.448304\pi$
$677$	28.5475	−	16.4819i	1.09717	−	0.633452i	0.935477	+	0.353389i	$0.114971\pi$
$678$	−3.53954	−	38.8800i	−0.135935	−	1.49318i
$679$	29.3673	+	16.9552i	1.12701	+	0.650681i
$680$	3.60298	−	4.36102i	0.138168	−	0.167238i
$681$	−32.3614	+	4.77256i	−1.24009	+	0.182885i
$682$	−6.91296	−	4.52158i	−0.264711	−	0.173140i
$683$	−2.07668			−0.0794618			−0.0397309	−	0.999210i	$-0.512650\pi$
$683$	−2.07668			−0.0794618			−0.0397309	+	0.999210i	$0.512650\pi$
$684$	−12.4907	−	4.44690i	−0.477596	−	0.170032i
$685$	−14.8614			−0.567825
$686$	−21.2983	−	13.9306i	−0.813172	−	0.531874i
$687$	−10.0809	−	12.7238i	−0.384610	−	0.485443i
$688$	6.13258	−	27.1013i	0.233802	−	1.03323i
$689$	−24.8614	−	14.3537i	−0.947144	−	0.546834i
$690$	3.78989	+	1.75104i	0.144279	+	0.0666609i
$691$	10.0064	−	5.77717i	0.380660	−	0.219774i	−0.297446	−	0.954739i	$-0.596135\pi$
$691$	10.0064	−	5.77717i	0.380660	−	0.219774i	0.678105	+	0.734965i	$0.262801\pi$
$692$	8.93075	+	6.57835i	0.339496	+	0.250071i
$693$	8.05842	+	26.7268i	0.306114	+	1.01527i
$694$	−4.93070	−	9.75588i	−0.187167	−	0.370328i
$695$	3.70178	+	6.41168i	0.140417	+	0.243209i
$696$	0.0794884	−	3.88058i	0.00301300	−	0.147093i
$697$	0.186141	−	0.322405i	0.00705058	−	0.0122120i
$698$	−16.0580	−	0.894292i	−0.607802	−	0.0338494i
$699$	45.1894	+	17.9015i	1.70922	+	0.677096i
$700$	−2.63641	+	23.5964i	−0.0996470	+	0.891859i
$701$		−	26.1282i		−	0.986850i	−0.869788	−	0.493425i	$-0.835745\pi$
$701$		−	26.1282i		−	0.986850i	0.869788	−	0.493425i	$-0.164255\pi$
$702$	−19.5226	−	15.2635i	−0.736831	−	0.576082i
$703$			10.4845i			0.395429i
$704$	−5.17227	−	26.9240i	−0.194937	−	1.01473i
$705$	−14.7446	−	5.84096i	−0.555312	−	0.219983i
$706$	0.385420	−	6.92062i	0.0145055	−	0.260461i
$707$	24.1895	−	41.8974i	0.909738	−	1.57571i
$708$	8.41677	−	15.8391i	0.316321	−	0.595268i
$709$	2.43070	+	4.21010i	0.0912870	+	0.158114i	0.908053	−	0.418855i	$-0.137569\pi$
$709$	2.43070	+	4.21010i	0.0912870	+	0.158114i	−0.816766	+	0.576969i	$0.804235\pi$
$710$	1.75079	−	0.884861i	0.0657058	−	0.0332082i
$711$	−29.6932	−	6.97614i	−1.11358	−	0.261626i
$712$	2.51087	−	14.9040i	0.0940990	−	0.558553i
$713$	3.17527	−	1.83324i	0.118915	−	0.0686554i
$714$	−7.04171	+	15.2409i	−0.263529	+	0.570375i
$715$	7.92967	+	4.57820i	0.296553	+	0.171215i
$716$	−15.0772	−	34.4696i	−0.563461	−	1.28819i
$717$	17.9198	+	22.6179i	0.669228	+	0.844679i
$718$	23.1986	−	35.4680i	0.865765	−	1.32365i
$719$	7.65492			0.285481			0.142740	−	0.989760i	$-0.454409\pi$
$719$	7.65492			0.285481			0.142740	+	0.989760i	$0.454409\pi$
$720$	8.54729	+	4.16357i	0.318539	+	0.155167i
$721$	39.6060			1.47500
$722$	−10.9281	+	16.7077i	−0.406700	+	0.621797i
$723$	28.2544	−	4.16687i	1.05079	−	0.154968i
$724$	3.20597	+	7.32951i	0.119149	+	0.272399i
$725$	3.00000	+	1.73205i	0.111417	+	0.0643268i
$726$	1.81629	−	0.165350i	0.0674088	−	0.00613673i
$727$	−2.67732	+	1.54575i	−0.0992963	+	0.0573287i	−0.548826	−	0.835937i	$-0.684925\pi$
$727$	−2.67732	+	1.54575i	−0.0992963	+	0.0573287i	0.449530	+	0.893265i	$0.351592\pi$
$728$	−4.30243	+	25.5383i	−0.159459	+	0.946514i
$729$	17.2337	−	20.7846i	0.638285	−	0.769800i
$730$	2.37228	−	1.19897i	0.0878021	−	0.0443759i
$731$	8.76780	+	15.1863i	0.324289	+	0.561685i
$732$	−6.19292	−	9.90531i	−0.228897	−	0.366111i
$733$	2.68614	−	4.65253i	0.0992149	−	0.171845i	−0.812145	−	0.583456i	$-0.801700\pi$
$733$	2.68614	−	4.65253i	0.0992149	−	0.171845i	0.911360	+	0.411610i	$0.135034\pi$
$734$	1.06759	−	19.1696i	0.0394053	−	0.707564i
$735$	0.0745360	+	0.505408i	0.00274930	+	0.0186423i
$736$	11.7013	+	3.34159i	0.431316	+	0.123173i
$737$			23.8063i			0.876916i
$738$	0.600207	+	0.176752i	0.0220939	+	0.00650634i
$739$		−	9.66181i		−	0.355415i	−0.984083	−	0.177708i	$-0.943132\pi$
$739$		−	9.66181i		−	0.355415i	0.984083	−	0.177708i	$-0.0568681\pi$
$740$	0.834801	−	7.47162i	0.0306879	−	0.274662i
$741$	10.1168	−	8.01544i	0.371652	−	0.294455i
$742$	−32.6373	−	1.81762i	−1.19815	−	0.0667270i
$743$	−22.5132	+	38.9940i	−0.825929	+	1.43055i	0.0752776	+	0.997163i	$0.476016\pi$
$743$	−22.5132	+	38.9940i	−0.825929	+	1.43055i	−0.901207	+	0.433389i	$0.857318\pi$
$744$	7.31505	−	4.02589i	0.268183	−	0.147596i
$745$	−3.80298	−	6.58696i	−0.139331	−	0.241328i
$746$	−5.65278	−	11.1846i	−0.206963	−	0.409497i
$747$	−4.97760	+	21.1866i	−0.182121	+	0.775178i
$748$	13.9307	+	10.2613i	0.509357	+	0.375190i
$749$	−31.1168	+	17.9653i	−1.13698	+	0.656438i
$750$	−14.8625	+	10.4850i	−0.542704	+	0.382860i
$751$	−39.9743	−	23.0792i	−1.45868	−	0.842170i	−0.459735	−	0.888056i	$-0.652056\pi$
$751$	−39.9743	−	23.0792i	−1.45868	−	0.842170i	−0.998947	+	0.0458859i	$0.985389\pi$
$752$	−45.0878	−	10.2026i	−1.64418	−	0.372052i
$753$	10.6753	−	26.9480i	0.389028	−	0.982039i
$754$	3.16218	+	2.06829i	0.115160	+	0.0753228i
$755$	−7.25450			−0.264018
$756$	−27.6790	−	5.48422i	−1.00668	−	0.199459i
$757$	14.0000			0.508839			0.254419	−	0.967094i	$-0.418116\pi$
$757$	14.0000			0.508839			0.254419	+	0.967094i	$0.418116\pi$
$758$	−11.4350	−	7.47935i	−0.415340	−	0.271662i
$759$	−4.70285	+	11.8716i	−0.170703	+	0.430912i
$760$	−3.15402	+	3.81761i	−0.114408	+	0.138479i
$761$	−16.5475	−	9.55373i	−0.599848	−	0.346322i	0.169134	−	0.985593i	$-0.445903\pi$
$761$	−16.5475	−	9.55373i	−0.599848	−	0.346322i	−0.768982	+	0.639271i	$0.779236\pi$
$762$	−32.6075	+	23.0035i	−1.18125	+	0.833330i
$763$	−22.3130	+	12.8824i	−0.807784	+	0.466375i
$764$	4.62832	−	6.28339i	0.167447	−	0.227325i
$765$	−5.74456	+	1.73205i	−0.207695	+	0.0626224i
$766$	−0.255437	−	0.505408i	−0.00922933	−	0.0182611i
$767$	8.73053	+	15.1217i	0.315241	+	0.546014i
$768$	26.4861	+	8.15397i	0.955734	+	0.294231i
$769$	27.5475	−	47.7138i	0.993390	−	1.72060i	0.397285	−	0.917695i	$-0.369952\pi$
$769$	27.5475	−	47.7138i	0.993390	−	1.72060i	0.596105	−	0.802907i	$-0.296714\pi$
$770$	10.4098	+	0.579740i	0.375145	+	0.0208924i
$771$	15.6591	−	12.4065i	0.563950	−	0.446810i
$772$	−7.44281	−	0.831582i	−0.267873	−	0.0299293i
$773$			45.7330i			1.64490i	0.568835	+	0.822451i	$0.307394\pi$
$773$			45.7330i			1.64490i	−0.568835	+	0.822451i	$0.692606\pi$
$774$	−21.3460	+	20.3211i	−0.767264	+	0.730428i
$775$			7.45202i			0.267685i
$776$	12.3347	+	33.1011i	0.442789	+	1.18826i
$777$	3.25544	+	22.0742i	0.116788	+	0.791909i
$778$	−0.653512	+	11.7345i	−0.0234295	+	0.420702i
$779$	−0.162946	+	0.282231i	−0.00583815	+	0.0101120i
$780$	−7.84785	+	4.90657i	−0.280998	+	0.175683i
$781$	3.00000	+	5.19615i	0.107348	+	0.185933i
$782$	−6.85407	+	3.46410i	−0.245101	+	0.123876i
$783$	−2.35143	+	3.37923i	−0.0840332	+	0.120764i
$784$	0.441578	+	1.42215i	0.0157706	+	0.0507910i
$785$	11.5693	−	6.67954i	0.412926	−	0.238403i
$786$	−17.6966	+	1.61106i	−0.631218	+	0.0574646i
$787$	−17.0095	−	9.82043i	−0.606323	−	0.350061i	0.165202	−	0.986260i	$-0.447172\pi$
$787$	−17.0095	−	9.82043i	−0.606323	−	0.350061i	−0.771525	+	0.636199i	$0.780506\pi$
$788$	19.5831	−	8.56575i	0.697619	−	0.305142i
$789$	21.4307	−	3.16053i	0.762953	−	0.112518i
$790$	−6.23577	+	9.53376i	−0.221859	+	0.339196i
$791$	43.2756			1.53870
$792$	−11.2613	+	26.8103i	−0.400152	+	0.952663i
$793$	11.3723			0.403842
$794$	5.61654	−	8.58704i	0.199324	−	0.304742i
$795$	−7.25450	−	9.15640i	−0.257290	−	0.324744i
$796$	35.4082	−	15.4877i	1.25501	−	0.548947i
$797$	40.8030	+	23.5576i	1.44532	+	0.834454i	0.998197	−	0.0600211i	$-0.0191168\pi$
$797$	40.8030	+	23.5576i	1.44532	+	0.834454i	0.447119	+	0.894475i	$0.352450\pi$
$798$	6.16426	−	13.3417i	0.218212	−	0.472292i
$799$	25.2651	−	14.5868i	0.893814	−	0.516043i
$800$	−17.7731	+	17.2005i	−0.628373	+	0.608129i
$801$	−10.9783	+	11.6819i	−0.387897	+	0.412761i
$802$	27.6753	−	13.9873i	0.977248	−	0.493909i
$803$	4.06494	+	7.04069i	0.143449	+	0.248461i
$804$	−21.2498	−	11.2920i	−0.749424	−	0.398239i
$805$	−2.31386	+	4.00772i	−0.0815528	+	0.141254i
$806$	−0.451982	+	8.11582i	−0.0159204	+	0.285868i
$807$	−40.1745	−	15.9149i	−1.41421	−	0.560230i
$808$	47.2243	−	17.5975i	1.66134	−	0.619077i
$809$		−	27.1778i		−	0.955521i	−0.878490	−	0.477760i	$-0.841449\pi$
$809$		−	27.1778i		−	0.955521i	0.878490	−	0.477760i	$-0.158551\pi$
$810$	−5.09833	−	8.70043i	−0.179137	−	0.305702i
$811$			25.9530i			0.911332i	0.890151	+	0.455666i	$0.150599\pi$
$811$			25.9530i			0.911332i	−0.890151	+	0.455666i	$0.849401\pi$
$812$	4.27582	+	0.477736i	0.150052	+	0.0167652i
$813$	−2.23369	−	0.884861i	−0.0783389	−	0.0310334i
$814$	22.9592	+	1.27863i	0.804720	+	0.0448161i
$815$	4.70285	−	8.14558i	0.164734	−	0.285327i
$816$	−15.7671	+	7.56752i	−0.551960	+	0.264916i
$817$	−7.67527	−	13.2940i	−0.268524	−	0.465096i
$818$	−1.43877	−	2.84674i	−0.0503053	−	0.0995340i
$819$	18.8114	−	20.0172i	0.657324	−	0.699457i
$820$	0.138593	−	0.188154i	0.00483989	−	0.00657062i
$821$	−18.6861	+	10.7884i	−0.652151	+	0.376519i	−0.789280	−	0.614034i	$-0.789546\pi$
$821$	−18.6861	+	10.7884i	−0.652151	+	0.376519i	0.137129	+	0.990553i	$0.456213\pi$
$822$	41.7098	+	19.2711i	1.45480	+	0.672158i
$823$	−25.8657	−	14.9336i	−0.901622	−	0.520552i	−0.0238957	−	0.999714i	$-0.507607\pi$
$823$	−25.8657	−	14.9336i	−0.901622	−	0.520552i	−0.877726	+	0.479163i	$0.840940\pi$
$824$	31.8067	+	26.2780i	1.10804	+	0.915437i
$825$	−16.1168	−	20.3422i	−0.561116	−	0.708224i
$826$	16.6390	+	10.8831i	0.578945	+	0.378672i
$827$	7.00314			0.243523			0.121762	−	0.992559i	$-0.461146\pi$
$827$	7.00314			0.243523			0.121762	+	0.992559i	$0.461146\pi$
$828$	−8.36606	−	9.82888i	−0.290741	−	0.341577i
$829$	−13.7663			−0.478124			−0.239062	−	0.971004i	$-0.576840\pi$
$829$	−13.7663			−0.478124			−0.239062	+	0.971004i	$0.576840\pi$
$830$	6.80251	+	4.44934i	0.236119	+	0.154439i
$831$	1.07561	−	0.158627i	0.0373124	−	0.00550271i
$832$	−20.3995	+	17.6547i	−0.707225	+	0.612065i
$833$	−0.813859	−	0.469882i	−0.0281986	−	0.0162804i
$834$	−2.07521	−	22.7951i	−0.0718588	−	0.789331i
$835$	−13.1820	+	7.61065i	−0.456183	+	0.263377i
$836$	−12.1948	−	8.98266i	−0.421767	−	0.310672i
$837$	−8.82473	−	0.746000i	−0.305027	−	0.0257855i
$838$	−3.60597	−	7.13477i	−0.124566	−	0.246466i
$839$	22.8391	+	39.5585i	0.788493	+	1.36571i	0.926890	+	0.375333i	$0.122472\pi$
$839$	22.8391	+	39.5585i	0.788493	+	1.36571i	−0.138397	+	0.990377i	$0.544195\pi$
$840$	−5.45518	+	9.01700i	−0.188222	+	0.311116i
$841$	−14.1861	+	24.5711i	−0.489177	+	0.847280i
$842$	41.8044	+	2.32815i	1.44067	+	0.0802333i
$843$	−1.62511	−	11.0194i	−0.0559717	−	0.379528i
$844$	−1.35999	+	12.1722i	−0.0468128	+	0.418983i
$845$			1.28962i			0.0443643i
$846$	33.8078	+	35.5128i	1.16234	+	1.22095i
$847$			2.02163i			0.0694641i
$848$	−25.0043	−	23.1141i	−0.858653	−	0.793741i
$849$	−13.8030	+	10.9359i	−0.473717	+	0.375320i
$850$	0.867935	−	15.5847i	0.0297699	−	0.534550i
$851$	−5.10328	+	8.83915i	−0.174938	+	0.303002i
$852$	−6.06115	+	0.213157i	−0.207652	+	0.00730264i
$853$	−2.19702	−	3.80534i	−0.0752244	−	0.130292i	0.825959	−	0.563730i	$-0.190634\pi$
$853$	−2.19702	−	3.80534i	−0.0752244	−	0.130292i	−0.901184	+	0.433437i	$0.857301\pi$
$854$	11.5569	−	5.84096i	0.395470	−	0.199874i
$855$	5.02875	−	1.51622i	0.171980	−	0.0518538i
$856$	−36.9090	−	6.21803i	−1.26152	−	0.212528i
$857$	−22.0367	+	12.7229i	−0.752758	+	0.434605i	−0.826690	−	0.562658i	$-0.809779\pi$
$857$	−22.0367	+	12.7229i	−0.752758	+	0.434605i	0.0739313	+	0.997263i	$0.476445\pi$
$858$	−16.3187	−	23.1317i	−0.557110	−	0.789703i
$859$	−30.4056	−	17.5547i	−1.03743	−	0.598958i	−0.118323	−	0.992975i	$-0.537752\pi$
$859$	−30.4056	−	17.5547i	−1.03743	−	0.598958i	−0.919103	+	0.394017i	$0.871085\pi$
$860$	4.41118	+	10.0849i	0.150420	+	0.343892i
$861$	−0.255437	+	0.644810i	−0.00870528	+	0.0219751i
$862$	−11.3470	+	17.3483i	−0.386481	+	0.590885i
$863$	4.15335			0.141382			0.0706909	−	0.997498i	$-0.477480\pi$
$863$	4.15335			0.141382			0.0706909	+	0.997498i	$0.477480\pi$
$864$	−18.5897	−	22.7689i	−0.632435	−	0.774613i
$865$	−4.39403			−0.149402
$866$	11.1258	−	17.0100i	0.378070	−	0.578025i
$867$	−6.77953	+	17.1138i	−0.230245	+	0.581216i
$868$	3.70908	+	8.47973i	0.125894	+	0.287821i
$869$	−30.1753	−	17.4217i	−1.02363	−	0.590991i
$870$	0.886355	+	1.25641i	0.0300502	+	0.0425962i
$871$	20.2875	−	11.7130i	0.687414	−	0.396879i
$872$	−26.4663	−	4.45877i	−0.896264	−	0.150993i
$873$	8.56930	−	36.4743i	0.290027	−	1.23447i
$874$	6.00000	−	3.03245i	0.202953	−	0.102574i
$875$	−10.0809	−	17.4606i	−0.340796	−	0.590276i
$876$	−8.21275	+	0.288824i	−0.277483	+	0.00975846i
$877$	−13.6861	+	23.7051i	−0.462148	+	0.800464i	−0.999068	−	0.0431693i	$-0.986254\pi$
$877$	−13.6861	+	23.7051i	−0.462148	+	0.800464i	0.536920	+	0.843633i	$0.319588\pi$
$878$	2.58715	−	46.4551i	0.0873122	−	1.56778i
$879$	27.1415	−	21.5039i	0.915461	−	0.725308i
$880$	7.97526	+	7.37236i	0.268846	+	0.248522i
$881$			19.7899i			0.666740i	0.942796	+	0.333370i	$0.108186\pi$
$881$			19.7899i			0.666740i	−0.942796	+	0.333370i	$0.891814\pi$
$882$	0.446182	−	1.51512i	0.0150237	−	0.0510169i
$883$			34.7921i			1.17085i	0.810727	+	0.585424i	$0.199072\pi$
$883$			34.7921i			1.17085i	−0.810727	+	0.585424i	$0.800928\pi$
$884$	1.89049	−	16.9203i	0.0635842	−	0.569090i
$885$	1.03667	+	7.02939i	0.0348474	+	0.236290i
$886$	7.31121	+	0.407173i	0.245625	+	0.0136792i
$887$	2.75186	−	4.76635i	0.0923983	−	0.160039i	−0.816122	−	0.577880i	$-0.803880\pi$
$887$	2.75186	−	4.76635i	0.0923983	−	0.160039i	0.908520	+	0.417842i	$0.137213\pi$
$888$	−12.0316	+	19.8872i	−0.403753	+	0.667372i
$889$	−22.1168	−	38.3075i	−0.741775	−	1.28479i
$890$	2.70071	+	5.34363i	0.0905281	+	0.179119i
$891$	25.7028	−	17.0493i	0.861075	−	0.571172i
$892$	2.74456	+	2.02163i	0.0918948	+	0.0676893i
$893$	−22.1168	+	12.7692i	−0.740112	+	0.427304i
$894$	2.13195	+	23.4183i	0.0713029	+	0.783225i
$895$	12.9073	+	7.45202i	0.431443	+	0.249094i
$896$	−11.6630	+	28.4188i	−0.389634	+	0.949404i
$897$	12.4307	−	1.83324i	0.415049	−	0.0612101i
$898$	4.51394	+	2.95244i	0.150632	+	0.0985243i
$899$	1.35036			0.0450369
$900$	25.8024	−	4.73724i	0.860081	−	0.157908i
$901$	21.4891			0.715907
$902$	0.598166	+	0.391244i	0.0199168	+	0.0130270i
$903$	−20.2875	−	25.6062i	−0.675124	−	0.852121i
$904$	34.7537	+	28.7127i	1.15589	+	0.954971i
$905$	−2.74456	−	1.58457i	−0.0912323	−	0.0526730i
$906$	20.3604	+	9.40707i	0.676428	+	0.312529i
$907$	−21.3258	+	12.3125i	−0.708111	+	0.408828i	−0.810361	−	0.585930i	$-0.800729\pi$
$907$	−21.3258	+	12.3125i	−0.708111	+	0.408828i	0.102250	+	0.994759i	$0.467396\pi$
$908$	22.4014	−	30.4121i	0.743417	−	1.00926i
$909$	−52.0367	−	12.2255i	−1.72595	−	0.405496i
$910$	−4.62772	−	9.15640i	−0.153407	−	0.303532i
$911$	−6.57932	−	11.3957i	−0.217983	−	0.377557i	0.736209	−	0.676755i	$-0.236614\pi$
$911$	−6.57932	−	11.3957i	−0.217983	−	0.377557i	−0.954191	+	0.299198i	$0.903281\pi$
$912$	13.8024	−	6.62455i	0.457044	−	0.219361i
$913$	−12.4307	+	21.5306i	−0.411396	+	0.712559i
$914$	−8.44144	−	0.470117i	−0.279218	−	0.0155501i
$915$	4.30243	+	1.70438i	0.142234	+	0.0563450i
$916$	18.6286	+	2.08137i	0.615508	+	0.0687704i
$917$		−	19.6974i		−	0.650464i
$918$	18.3686	+	2.58795i	0.606254	+	0.0854151i
$919$		−	46.0993i		−	1.52067i	−0.649529	−	0.760337i	$-0.725034\pi$
$919$		−	46.0993i		−	1.52067i	0.649529	−	0.760337i	$-0.274966\pi$
$920$	−4.51727	+	1.68330i	−0.148930	+	0.0554967i
$921$	41.7921	+	16.5557i	1.37710	+	0.545528i
$922$	1.79817	−	32.2881i	0.0592197	−	1.06335i
$923$	2.95207	−	5.11313i	0.0971686	−	0.168301i
$924$	−28.4644	−	15.1258i	−0.936410	−	0.497602i
$925$	−10.3723	−	17.9653i	−0.341039	−	0.590696i
$926$	26.5409	−	13.4140i	0.872187	−	0.440811i
$927$	−12.6325	−	41.8974i	−0.414907	−	1.37609i
$928$	3.11684	+	3.22060i	0.102315	+	0.105721i
$929$	30.4307	−	17.5692i	0.998399	−	0.576426i	0.0906248	−	0.995885i	$-0.471114\pi$
$929$	30.4307	−	17.5692i	0.998399	−	0.576426i	0.907774	+	0.419459i	$0.137780\pi$
$930$	−1.38732	+	3.00268i	−0.0454922	+	0.0984619i
$931$	0.712446	+	0.411331i	0.0233495	+	0.0134808i
$932$	−51.4214	+	22.4920i	−1.68437	+	0.736750i
$933$	33.6861	+	42.5176i	1.10283	+	1.39196i
$934$	−18.8804	+	28.8659i	−0.617786	+	0.944522i
$935$	−6.85407			−0.224152
$936$	28.3881	−	3.59424i	0.927895	−	0.117481i
$937$	−11.7228			−0.382968			−0.191484	−	0.981496i	$-0.561330\pi$
$937$	−11.7228			−0.382968			−0.191484	+	0.981496i	$0.561330\pi$
$938$	14.6009	−	22.3231i	0.476736	−	0.728874i
$939$	7.69219	−	1.13442i	0.251025	−	0.0370204i
$940$	16.7780	−	7.33878i	0.547238	−	0.239365i
$941$	31.8030	+	18.3615i	1.03675	+	0.598567i	0.918910	−	0.394466i	$-0.129071\pi$
$941$	31.8030	+	18.3615i	1.03675	+	0.598567i	0.117837	+	0.993033i	$0.462404\pi$
$942$	−41.1317	+	3.74454i	−1.34014	+	0.122004i
$943$	−0.274750	+	0.158627i	−0.00894709	+	0.00516561i
$944$	6.14162	+	19.7797i	0.199893	+	0.643775i
$945$	10.1168	−	4.75372i	0.329101	−	0.154639i
$946$	−30.0475	+	15.1863i	−0.976930	+	0.493748i
$947$	−22.2757	−	38.5827i	−0.723864	−	1.25377i	−0.959440	−	0.281913i	$-0.909031\pi$
$947$	−22.2757	−	38.5827i	−0.723864	−	1.25377i	0.235576	−	0.971856i	$-0.424302\pi$
$948$	29.8639	−	18.6713i	0.969934	−	0.606415i
$949$	4.00000	−	6.92820i	0.129845	−	0.224899i
$950$	−0.759784	+	13.6427i	−0.0246506	+	0.442628i
$951$	6.02982	+	40.8865i	0.195530	+	1.32584i
$952$	−6.76930	−	18.1660i	−0.219394	−	0.588763i
$953$		−	32.8164i		−	1.06303i	−0.847050	−	0.531514i	$-0.821623\pi$
$953$		−	32.8164i		−	1.06303i	0.847050	−	0.531514i	$-0.178377\pi$
$954$	8.48707	+	35.1053i	0.274779	+	1.13658i
$955$			3.09150i			0.100039i
$956$	−33.1144	−	3.69985i	−1.07100	−	0.119662i
$957$	−3.68614	+	2.92048i	−0.119156	+	0.0944058i
$958$	−13.8465	−	0.771134i	−0.447361	−	0.0249142i
$959$	−25.4653	+	44.1071i	−0.822317	+	1.42429i
$960$	−10.3636	+	3.62191i	−0.334483	+	0.116897i
$961$	−14.0475	−	24.3311i	−0.453147	−	0.784873i
$962$	−10.2066	−	20.1947i	−0.329073	−	0.651103i
$963$	28.9296	+	27.1870i	0.932243	+	0.876088i
$964$	−19.5584	+	26.5525i	−0.629934	+	0.855197i
$965$	2.56930	−	1.48338i	0.0827086	−	0.0477518i
$966$	11.6910	−	8.24759i	0.376150	−	0.265362i
$967$	48.7282	+	28.1332i	1.56699	+	0.904704i	0.996517	+	0.0833895i	$0.0265746\pi$
$967$	48.7282	+	28.1332i	1.56699	+	0.904704i	0.570476	+	0.821314i	$0.306759\pi$
$968$	−1.34132	+	1.62353i	−0.0431118	+	0.0521821i
$969$	−3.55842	+	8.98266i	−0.114313	+	0.288565i
$970$	−11.7110	−	7.65985i	−0.376018	−	0.245943i
$971$	24.7156			0.793160			0.396580	−	0.918000i	$-0.370197\pi$
$971$	24.7156			0.793160			0.396580	+	0.918000i	$0.370197\pi$
$972$	3.02687	+	31.0296i	0.0970869	+	0.995276i
$973$	25.3723			0.813398
$974$	−21.2284	−	13.8849i	−0.680202	−	0.444901i
$975$	−9.40571	+	23.7432i	−0.301224	+	0.760391i
$976$	13.1565	+	2.97710i	0.421129	+	0.0952948i
$977$	−18.6386	−	10.7610i	−0.596301	−	0.344275i	0.171284	−	0.985222i	$-0.445209\pi$
$977$	−18.6386	−	10.7610i	−0.596301	−	0.344275i	−0.767585	+	0.640947i	$0.778542\pi$
$978$	−23.7615	+	16.7630i	−0.759810	+	0.536021i
$979$	−15.8593	+	9.15640i	−0.506867	+	0.292640i
$980$	−0.474964	−	0.349857i	−0.0151722	−	0.0111758i
$981$	20.7446	+	19.4950i	0.662323	+	0.622427i
$982$	−15.8139	−	31.2893i	−0.504641	−	0.998481i
$983$	8.40464	+	14.5573i	0.268066	+	0.464305i	0.968362	−	0.249548i	$-0.0802820\pi$
$983$	8.40464	+	14.5573i	0.268066	+	0.464305i	−0.700296	+	0.713852i	$0.746949\pi$
$984$	−0.632958	+	0.348353i	−0.0201780	+	0.0111051i
$985$	−4.23369	+	7.33296i	−0.134897	+	0.233648i
$986$	−2.82405	−	0.157276i	−0.0899361	−	0.00500868i
$987$	−42.6004	+	33.7518i	−1.35599	+	1.07433i
$988$	−1.65492	+	14.8119i	−0.0526502	+	0.471229i
$989$		−	14.9436i		−	0.475180i
$990$	−2.70699	−	11.1970i	−0.0860339	−	0.355865i
$991$			16.2912i			0.517506i	0.965944	+	0.258753i	$0.0833116\pi$
$991$			16.2912i			0.517506i	−0.965944	+	0.258753i	$0.916688\pi$
$992$	−2.64750	+	9.27080i	−0.0840583	+	0.294348i
$993$	7.03667	+	47.7138i	0.223302	+	1.51415i
$994$	0.373822	−	6.71238i	0.0118569	−	0.212904i
$995$	−7.65492	+	13.2587i	−0.242677	+	0.420330i
$996$	−13.3223	−	21.3084i	−0.422133	−	0.675183i
$997$	26.4307	+	45.7793i	0.837069	+	1.44985i	0.892335	+	0.451374i	$0.149066\pi$
$997$	26.4307	+	45.7793i	0.837069	+	1.44985i	−0.0552661	+	0.998472i	$0.517601\pi$
$998$	−0.637910	+	0.322405i	−0.0201927	+	0.0102056i
$999$	22.3130	−	10.4845i	0.705952	−	0.331714i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.2.h.a.23.2	yes	8
3.2	odd	2		108.2.h.a.71.3		8
4.3	odd	2	inner	36.2.h.a.23.1	yes	8
5.2	odd	4		900.2.o.a.599.2		16
5.3	odd	4		900.2.o.a.599.7		16
5.4	even	2		900.2.r.c.851.3		8
8.3	odd	2		576.2.s.f.383.2		8
8.5	even	2		576.2.s.f.383.3		8
9.2	odd	6	inner	36.2.h.a.11.1	✓	8
9.4	even	3		324.2.b.b.323.3		8
9.5	odd	6		324.2.b.b.323.6		8
9.7	even	3		108.2.h.a.35.4		8
12.11	even	2		108.2.h.a.71.4		8
20.3	even	4		900.2.o.a.599.5		16
20.7	even	4		900.2.o.a.599.4		16
20.19	odd	2		900.2.r.c.851.4		8
24.5	odd	2		1728.2.s.f.1151.4		8
24.11	even	2		1728.2.s.f.1151.3		8
36.7	odd	6		108.2.h.a.35.3		8
36.11	even	6	inner	36.2.h.a.11.2	yes	8
36.23	even	6		324.2.b.b.323.4		8
36.31	odd	6		324.2.b.b.323.5		8
45.2	even	12		900.2.o.a.299.5		16
45.29	odd	6		900.2.r.c.551.4		8
45.38	even	12		900.2.o.a.299.4		16
72.5	odd	6		5184.2.c.j.5183.4		8
72.11	even	6		576.2.s.f.191.3		8
72.13	even	6		5184.2.c.j.5183.6		8
72.29	odd	6		576.2.s.f.191.2		8
72.43	odd	6		1728.2.s.f.575.4		8
72.59	even	6		5184.2.c.j.5183.3		8
72.61	even	6		1728.2.s.f.575.3		8
72.67	odd	6		5184.2.c.j.5183.5		8
180.47	odd	12		900.2.o.a.299.7		16
180.83	odd	12		900.2.o.a.299.2		16
180.119	even	6		900.2.r.c.551.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.2.h.a.11.1	✓	8	9.2	odd	6	inner
36.2.h.a.11.2	yes	8	36.11	even	6	inner
36.2.h.a.23.1	yes	8	4.3	odd	2	inner
36.2.h.a.23.2	yes	8	1.1	even	1	trivial
108.2.h.a.35.3		8	36.7	odd	6
108.2.h.a.35.4		8	9.7	even	3
108.2.h.a.71.3		8	3.2	odd	2
108.2.h.a.71.4		8	12.11	even	2
324.2.b.b.323.3		8	9.4	even	3
324.2.b.b.323.4		8	36.23	even	6
324.2.b.b.323.5		8	36.31	odd	6
324.2.b.b.323.6		8	9.5	odd	6
576.2.s.f.191.2		8	72.29	odd	6
576.2.s.f.191.3		8	72.11	even	6
576.2.s.f.383.2		8	8.3	odd	2
576.2.s.f.383.3		8	8.5	even	2
900.2.o.a.299.2		16	180.83	odd	12
900.2.o.a.299.4		16	45.38	even	12
900.2.o.a.299.5		16	45.2	even	12
900.2.o.a.299.7		16	180.47	odd	12
900.2.o.a.599.2		16	5.2	odd	4
900.2.o.a.599.4		16	20.7	even	4
900.2.o.a.599.5		16	20.3	even	4
900.2.o.a.599.7		16	5.3	odd	4
900.2.r.c.551.3		8	180.119	even	6
900.2.r.c.551.4		8	45.29	odd	6
900.2.r.c.851.3		8	5.4	even	2
900.2.r.c.851.4		8	20.19	odd	2
1728.2.s.f.575.3		8	72.61	even	6
1728.2.s.f.575.4		8	72.43	odd	6
1728.2.s.f.1151.3		8	24.11	even	2
1728.2.s.f.1151.4		8	24.5	odd	2
5184.2.c.j.5183.3		8	72.59	even	6
5184.2.c.j.5183.4		8	72.5	odd	6
5184.2.c.j.5183.5		8	72.67	odd	6
5184.2.c.j.5183.6		8	72.13	even	6

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:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	36.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.774115 + 1.18353i) q^{2} +(-0.637910 + 1.61030i) q^{3} +(-0.801492 - 1.83238i) q^{4} +(0.686141 + 0.396143i) q^{5} +(-1.41203 - 2.00155i) q^{6} +(2.35143 - 1.35760i) q^{7} +(2.78912 + 0.469882i) q^{8} +(-2.18614 - 2.05446i) q^{9} +O(q^{10})\)	\(q+(-0.774115 + 1.18353i) q^{2} +(-0.637910 + 1.61030i) q^{3} +(-0.801492 - 1.83238i) q^{4} +(0.686141 + 0.396143i) q^{5} +(-1.41203 - 2.00155i) q^{6} +(2.35143 - 1.35760i) q^{7} +(2.78912 + 0.469882i) q^{8} +(-2.18614 - 2.05446i) q^{9} +(-1.00000 + 0.505408i) q^{10} +(-1.71352 - 2.96790i) q^{11} +(3.46196 - 0.121749i) q^{12} +(-1.68614 + 2.92048i) q^{13} +(-0.213517 + 3.83392i) q^{14} +(-1.07561 + 0.852189i) q^{15} +(-2.71522 + 2.93727i) q^{16} -2.52434i q^{17} +(4.12384 - 0.996980i) q^{18} +2.20979i q^{19} +(0.175949 - 1.57478i) q^{20} +(0.686141 + 4.65253i) q^{21} +(4.83906 + 0.269495i) q^{22} +(-1.07561 + 1.86301i) q^{23} +(-2.53586 + 4.19159i) q^{24} +(-2.18614 - 3.78651i) q^{25} +(-2.15121 - 4.25639i) q^{26} +(4.70285 - 2.20979i) q^{27} +(-4.37228 - 3.22060i) q^{28} +(-0.686141 + 0.396143i) q^{29} +(-0.175949 - 1.93271i) q^{30} +(-1.47603 - 0.852189i) q^{31} +(-1.37446 - 5.48734i) q^{32} +(5.87228 - 0.866025i) q^{33} +(2.98763 + 1.95413i) q^{34} +2.15121 q^{35} +(-2.01237 + 5.65247i) q^{36} +4.74456 q^{37} +(-2.61535 - 1.71063i) q^{38} +(-3.62725 - 4.57820i) q^{39} +(1.72759 + 1.42730i) q^{40} +(0.127719 + 0.0737384i) q^{41} +(-6.03757 - 2.78953i) q^{42} +(-6.01594 + 3.47331i) q^{43} +(-4.06494 + 5.51856i) q^{44} +(-0.686141 - 2.27567i) q^{45} +(-1.37228 - 2.71519i) q^{46} +(5.77846 + 10.0086i) q^{47} +(-2.99782 - 6.24604i) q^{48} +(0.186141 - 0.322405i) q^{49} +(6.17377 + 0.343827i) q^{50} +(4.06494 + 1.61030i) q^{51} +(6.70285 + 0.748907i) q^{52} +8.51278i q^{53} +(-1.02520 + 7.27660i) q^{54} -2.71519i q^{55} +(7.19633 - 2.68161i) q^{56} +(-3.55842 - 1.40965i) q^{57} +(0.0623037 - 1.11873i) q^{58} +(2.58891 - 4.48412i) q^{59} +(2.42362 + 1.28790i) q^{60} +(-1.68614 - 2.92048i) q^{61} +(2.15121 - 1.08724i) q^{62} +(-7.92967 - 1.86301i) q^{63} +(7.55842 + 2.62112i) q^{64} +(-2.31386 + 1.33591i) q^{65} +(-3.52085 + 7.62043i) q^{66} +(-6.01594 - 3.47331i) q^{67} +(-4.62554 + 2.02324i) q^{68} +(-2.31386 - 2.92048i) q^{69} +(-1.66529 + 2.54603i) q^{70} -1.75079 q^{71} +(-5.13207 - 6.75736i) q^{72} -2.37228 q^{73} +(-3.67284 + 5.61534i) q^{74} +(7.49198 - 1.10489i) q^{75} +(4.04917 - 1.77113i) q^{76} +(-8.05842 - 4.65253i) q^{77} +(8.22635 - 0.748907i) q^{78} +(8.80507 - 5.08361i) q^{79} +(-3.02661 + 0.939764i) q^{80} +(0.558422 + 8.98266i) q^{81} +(-0.186141 + 0.0940770i) q^{82} +(-3.62725 - 6.28258i) q^{83} +(7.97526 - 4.98623i) q^{84} +(1.00000 - 1.73205i) q^{85} +(0.546267 - 9.80880i) q^{86} +(-0.200214 - 1.35760i) q^{87} +(-3.38465 - 9.08299i) q^{88} -5.34363i q^{89} +(3.22448 + 0.949563i) q^{90} +9.15640i q^{91} +(4.27582 + 0.477736i) q^{92} +(2.31386 - 1.83324i) q^{93} +(-16.3187 - 0.908812i) q^{94} +(-0.875393 + 1.51622i) q^{95} +(9.71305 + 1.28714i) q^{96} +(6.24456 + 10.8159i) q^{97} +(0.237482 + 0.469882i) q^{98} +(-2.35143 + 10.0086i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{2} - q^{4} - 6 q^{5} - 3 q^{6} - 6 q^{9}+O(q^{10}) \) 8 * q - 3 * q^2 - q^4 - 6 * q^5 - 3 * q^6 - 6 * q^9	\( 8 q - 3 q^{2} - q^{4} - 6 q^{5} - 3 q^{6} - 6 q^{9} - 8 q^{10} + 6 q^{12} - 2 q^{13} + 12 q^{14} - q^{16} + 18 q^{18} + 18 q^{20} - 6 q^{21} + 3 q^{22} + 3 q^{24} - 6 q^{25} - 12 q^{28} + 6 q^{29} - 18 q^{30} - 33 q^{32} + 24 q^{33} + 7 q^{34} - 33 q^{36} - 8 q^{37} - 27 q^{38} + 10 q^{40} + 24 q^{41} - 18 q^{42} + 6 q^{45} + 12 q^{46} + 21 q^{48} - 10 q^{49} + 21 q^{50} + 16 q^{52} + 39 q^{54} + 18 q^{56} + 6 q^{57} + 4 q^{58} + 6 q^{60} - 2 q^{61} + 26 q^{64} - 30 q^{65} - 24 q^{66} - 15 q^{68} - 30 q^{69} - 6 q^{70} - 21 q^{72} + 4 q^{73} - 30 q^{74} - 3 q^{76} - 30 q^{77} - 12 q^{78} - 30 q^{81} + 10 q^{82} + 30 q^{84} + 8 q^{85} + 21 q^{86} - 21 q^{88} + 6 q^{90} + 24 q^{92} + 30 q^{93} - 18 q^{94} + 12 q^{96} + 4 q^{97}+O(q^{100}) \) 8 * q - 3 * q^2 - q^4 - 6 * q^5 - 3 * q^6 - 6 * q^9 - 8 * q^10 + 6 * q^12 - 2 * q^13 + 12 * q^14 - q^16 + 18 * q^18 + 18 * q^20 - 6 * q^21 + 3 * q^22 + 3 * q^24 - 6 * q^25 - 12 * q^28 + 6 * q^29 - 18 * q^30 - 33 * q^32 + 24 * q^33 + 7 * q^34 - 33 * q^36 - 8 * q^37 - 27 * q^38 + 10 * q^40 + 24 * q^41 - 18 * q^42 + 6 * q^45 + 12 * q^46 + 21 * q^48 - 10 * q^49 + 21 * q^50 + 16 * q^52 + 39 * q^54 + 18 * q^56 + 6 * q^57 + 4 * q^58 + 6 * q^60 - 2 * q^61 + 26 * q^64 - 30 * q^65 - 24 * q^66 - 15 * q^68 - 30 * q^69 - 6 * q^70 - 21 * q^72 + 4 * q^73 - 30 * q^74 - 3 * q^76 - 30 * q^77 - 12 * q^78 - 30 * q^81 + 10 * q^82 + 30 * q^84 + 8 * q^85 + 21 * q^86 - 21 * q^88 + 6 * q^90 + 24 * q^92 + 30 * q^93 - 18 * q^94 + 12 * q^96 + 4 * q^97

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