LMFDB - Embedded newform 108.2.l.a.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,2,Mod(11,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("108.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	108.l (of order $18$, 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:	$0.862384341830$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.5
Character	$\chi$	$=$	108.11
Dual form			108.2.l.a.59.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00492 + 0.995056i) q^{2} +(-1.23220 + 1.21724i) q^{3} +(0.0197253 - 1.99990i) q^{4} +(-0.710267 + 1.95144i) q^{5} +(0.0270364 - 2.44934i) q^{6} +(-3.83975 - 0.677051i) q^{7} +(1.97019 + 2.02937i) q^{8} +(0.0366374 - 2.99978i) q^{9} +O(q^{10})$	\(q+(-1.00492 + 0.995056i) q^{2} +(-1.23220 + 1.21724i) q^{3} +(0.0197253 - 1.99990i) q^{4} +(-0.710267 + 1.95144i) q^{5} +(0.0270364 - 2.44934i) q^{6} +(-3.83975 - 0.677051i) q^{7} +(1.97019 + 2.02937i) q^{8} +(0.0366374 - 2.99978i) q^{9} +(-1.22804 - 2.66780i) q^{10} +(-1.46659 + 0.533796i) q^{11} +(2.41006 + 2.48829i) q^{12} +(-1.23056 + 1.03256i) q^{13} +(4.53234 - 3.14038i) q^{14} +(-1.50019 - 3.26914i) q^{15} +(-3.99922 - 0.0788972i) q^{16} +(-3.61727 + 2.08843i) q^{17} +(2.94813 + 3.05099i) q^{18} +(6.96639 + 4.02205i) q^{19} +(3.88869 + 1.45896i) q^{20} +(5.55548 - 3.83965i) q^{21} +(0.942651 - 1.99577i) q^{22} +(0.659926 + 3.74263i) q^{23} +(-4.89791 - 0.102384i) q^{24} +(0.526570 + 0.441845i) q^{25} +(0.209156 - 2.26212i) q^{26} +(3.60631 + 3.74092i) q^{27} +(-1.42978 + 7.66577i) q^{28} +(-2.44609 + 2.91513i) q^{29} +(4.76055 + 1.79245i) q^{30} +(-0.621314 + 0.109554i) q^{31} +(4.09740 - 3.90017i) q^{32} +(1.15738 - 2.44295i) q^{33} +(1.55696 - 5.69810i) q^{34} +(4.04848 - 7.01217i) q^{35} +(-5.99854 - 0.132443i) q^{36} +(0.912171 + 1.57993i) q^{37} +(-11.0028 + 2.89012i) q^{38} +(0.259418 - 2.77022i) q^{39} +(-5.35956 + 2.40333i) q^{40} +(-3.49040 - 4.15970i) q^{41} +(-1.76214 + 9.38655i) q^{42} +(-3.14069 - 8.62898i) q^{43} +(1.03861 + 2.94357i) q^{44} +(5.82787 + 2.20214i) q^{45} +(-4.38730 - 3.10437i) q^{46} +(-0.603613 + 3.42326i) q^{47} +(5.02388 - 4.77081i) q^{48} +(7.70742 + 2.80527i) q^{49} +(-0.968821 + 0.0799486i) q^{50} +(1.91508 - 6.97647i) q^{51} +(2.04076 + 2.48137i) q^{52} -6.03391i q^{53} +(-7.34648 - 0.170840i) q^{54} -3.24111i q^{55} +(-6.19106 - 9.12619i) q^{56} +(-13.4798 + 3.52382i) q^{57} +(-0.442602 - 5.36347i) q^{58} +(1.58603 + 0.577267i) q^{59} +(-6.56755 + 2.93575i) q^{60} +(-1.69938 + 9.63768i) q^{61} +(0.515357 - 0.728336i) q^{62} +(-2.17168 + 11.4936i) q^{63} +(-0.236673 + 7.99650i) q^{64} +(-1.14096 - 3.13477i) q^{65} +(1.26780 + 3.60662i) q^{66} +(5.27928 + 6.29160i) q^{67} +(4.10531 + 7.27539i) q^{68} +(-5.36885 - 3.80838i) q^{69} +(2.90911 + 11.0751i) q^{70} +(-6.91810 - 11.9825i) q^{71} +(6.15983 - 5.83579i) q^{72} +(0.999604 - 1.73136i) q^{73} +(-2.48878 - 0.680037i) q^{74} +(-1.18667 + 0.0965224i) q^{75} +(8.18112 - 13.8528i) q^{76} +(5.99276 - 1.05669i) q^{77} +(2.49583 + 3.04198i) q^{78} +(-2.46986 + 2.94347i) q^{79} +(2.99448 - 7.74822i) q^{80} +(-8.99732 - 0.219808i) q^{81} +(7.64671 + 0.707015i) q^{82} +(9.80246 + 8.22524i) q^{83} +(-7.56933 - 11.1862i) q^{84} +(-1.50623 - 8.54225i) q^{85} +(11.7425 + 5.54626i) q^{86} +(-0.534356 - 6.56951i) q^{87} +(-3.97274 - 1.92458i) q^{88} +(8.51207 + 4.91444i) q^{89} +(-8.04779 + 3.58609i) q^{90} +(5.42415 - 3.13163i) q^{91} +(7.49791 - 1.24596i) q^{92} +(0.632229 - 0.891283i) q^{93} +(-2.79975 - 4.04073i) q^{94} +(-12.7968 + 10.7378i) q^{95} +(-0.301371 + 9.79332i) q^{96} +(13.2890 - 4.83681i) q^{97} +(-10.5367 + 4.85025i) q^{98} +(1.54754 + 4.41901i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) $ 96 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 9 * q^8 - 12 * q^9	$ 96 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 15 q^{12} - 12 q^{13} - 21 q^{14} - 6 q^{16} - 18 q^{17} - 27 q^{18} - 27 q^{20} - 12 q^{21} - 6 q^{22} - 12 q^{24} - 12 q^{25} - 12 q^{28} - 24 q^{29} + 9 q^{30} + 24 q^{32} - 42 q^{33} - 12 q^{34} + 24 q^{36} - 6 q^{37} + 18 q^{38} - 21 q^{40} - 42 q^{41} + 54 q^{42} + 63 q^{44} - 24 q^{45} - 3 q^{46} + 69 q^{48} - 12 q^{49} + 87 q^{50} - 33 q^{52} + 78 q^{54} + 99 q^{56} - 24 q^{57} - 33 q^{58} + 102 q^{60} - 12 q^{61} + 90 q^{62} - 3 q^{64} + 12 q^{65} + 87 q^{66} + 51 q^{68} + 12 q^{69} - 21 q^{70} + 12 q^{72} - 6 q^{73} + 21 q^{74} - 18 q^{76} + 12 q^{77} - 24 q^{78} + 12 q^{81} - 12 q^{82} - 12 q^{84} - 42 q^{85} - 30 q^{86} + 18 q^{88} - 78 q^{90} - 123 q^{92} + 60 q^{93} + 21 q^{94} - 138 q^{96} - 30 q^{97} - 180 q^{98}+O(q^{100}) $ 96 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 15 * q^12 - 12 * q^13 - 21 * q^14 - 6 * q^16 - 18 * q^17 - 27 * q^18 - 27 * q^20 - 12 * q^21 - 6 * q^22 - 12 * q^24 - 12 * q^25 - 12 * q^28 - 24 * q^29 + 9 * q^30 + 24 * q^32 - 42 * q^33 - 12 * q^34 + 24 * q^36 - 6 * q^37 + 18 * q^38 - 21 * q^40 - 42 * q^41 + 54 * q^42 + 63 * q^44 - 24 * q^45 - 3 * q^46 + 69 * q^48 - 12 * q^49 + 87 * q^50 - 33 * q^52 + 78 * q^54 + 99 * q^56 - 24 * q^57 - 33 * q^58 + 102 * q^60 - 12 * q^61 + 90 * q^62 - 3 * q^64 + 12 * q^65 + 87 * q^66 + 51 * q^68 + 12 * q^69 - 21 * q^70 + 12 * q^72 - 6 * q^73 + 21 * q^74 - 18 * q^76 + 12 * q^77 - 24 * q^78 + 12 * q^81 - 12 * q^82 - 12 * q^84 - 42 * q^85 - 30 * q^86 + 18 * q^88 - 78 * q^90 - 123 * q^92 + 60 * q^93 + 21 * q^94 - 138 * q^96 - 30 * q^97 - 180 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$-1$

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 $

$2$	−1.00492	+	0.995056i	−0.710585	+	0.703611i
$2$	−1.00492	+	0.995056i	−0.710585	+	0.703611i
$3$	−1.23220	+	1.21724i	−0.711411	+	0.702776i
$3$	−1.23220	+	1.21724i	−0.711411	+	0.702776i
$4$	0.0197253	−	1.99990i	0.00986263	−	0.999951i
$5$	−0.710267	+	1.95144i	−0.317641	+	0.872712i	0.673415	+	0.739265i	$0.264827\pi$
$5$	−0.710267	+	1.95144i	−0.317641	+	0.872712i	−0.991056	+	0.133447i	$0.957395\pi$
$6$	0.0270364	−	2.44934i	0.0110376	−	0.999939i
$7$	−3.83975	−	0.677051i	−1.45129	−	0.255901i	−0.608246	−	0.793748i	$-0.708127\pi$
$7$	−3.83975	−	0.677051i	−1.45129	−	0.255901i	−0.843042	+	0.537847i	$0.819238\pi$
$8$	1.97019	+	2.02937i	0.696569	+	0.717490i
$9$	0.0366374	−	2.99978i	0.0122125	−	0.999925i
$10$	−1.22804	−	2.66780i	−0.388339	−	0.843632i
$11$	−1.46659	+	0.533796i	−0.442195	+	0.160946i	−0.553516	−	0.832839i	$-0.686714\pi$
$11$	−1.46659	+	0.533796i	−0.442195	+	0.160946i	0.111321	+	0.993785i	$0.464492\pi$
$12$	2.41006	+	2.48829i	0.695725	+	0.718308i
$13$	−1.23056	+	1.03256i	−0.341297	+	0.286382i	−0.797284	−	0.603604i	$-0.793731\pi$
$13$	−1.23056	+	1.03256i	−0.341297	+	0.286382i	0.455987	+	0.889986i	$0.349286\pi$
$14$	4.53234	−	3.14038i	1.21132	−	0.839303i
$15$	−1.50019	−	3.26914i	−0.387347	−	0.844088i
$16$	−3.99922	−	0.0788972i	−0.999805	−	0.0197243i
$17$	−3.61727	+	2.08843i	−0.877318	+	0.506520i	−0.869773	−	0.493452i	$-0.835735\pi$
$17$	−3.61727	+	2.08843i	−0.877318	+	0.506520i	−0.00754464	+	0.999972i	$0.502402\pi$
$18$	2.94813	+	3.05099i	0.694881	+	0.719125i
$19$	6.96639	+	4.02205i	1.59820	+	0.922721i	0.991834	+	0.127535i	$0.0407065\pi$
$19$	6.96639	+	4.02205i	1.59820	+	0.922721i	0.606366	+	0.795186i	$0.292627\pi$
$20$	3.88869	+	1.45896i	0.869537	+	0.326233i
$21$	5.55548	−	3.83965i	1.21230	−	0.837879i
$22$	0.942651	−	1.99577i	0.200974	−	0.425499i
$23$	0.659926	+	3.74263i	0.137604	+	0.780392i	0.973011	+	0.230759i	$0.0741210\pi$
$23$	0.659926	+	3.74263i	0.137604	+	0.780392i	−0.835407	+	0.549632i	$0.814768\pi$
$24$	−4.89791	−	0.102384i	−0.999782	−	0.0208991i
$25$	0.526570	+	0.441845i	0.105314	+	0.0883689i
$26$	0.209156	−	2.26212i	0.0410188	−	0.443639i
$27$	3.60631	+	3.74092i	0.694035	+	0.719941i
$28$	−1.42978	+	7.66577i	−0.270202	+	1.44869i
$29$	−2.44609	+	2.91513i	−0.454227	+	0.541327i	−0.943748	−	0.330665i	$-0.892727\pi$
$29$	−2.44609	+	2.91513i	−0.454227	+	0.541327i	0.489521	+	0.871991i	$0.337172\pi$
$30$	4.76055	+	1.79245i	0.869153	+	0.327254i
$31$	−0.621314	+	0.109554i	−0.111591	+	0.0196766i	−0.229165	−	0.973388i	$-0.573600\pi$
$31$	−0.621314	+	0.109554i	−0.111591	+	0.0196766i	0.117574	+	0.993064i	$0.462488\pi$
$32$	4.09740	−	3.90017i	0.724325	−	0.689458i
$33$	1.15738	−	2.44295i	0.201474	−	0.425262i
$34$	1.55696	−	5.69810i	0.267016	−	0.977216i
$35$	4.04848	−	7.01217i	0.684317	−	1.18527i
$36$	−5.99854	−	0.132443i	−0.999756	−	0.0220738i
$37$	0.912171	+	1.57993i	0.149960	+	0.259738i	0.931212	−	0.364477i	$-0.118752\pi$
$37$	0.912171	+	1.57993i	0.149960	+	0.259738i	−0.781252	+	0.624215i	$0.785419\pi$
$38$	−11.0028	+	2.89012i	−1.78489	+	0.468839i
$39$	0.259418	−	2.77022i	0.0415401	−	0.443590i
$40$	−5.35956	+	2.40333i	−0.847421	+	0.380000i
$41$	−3.49040	−	4.15970i	−0.545109	−	0.649636i	0.421216	−	0.906960i	$-0.361604\pi$
$41$	−3.49040	−	4.15970i	−0.545109	−	0.649636i	−0.966325	+	0.257324i	$0.917159\pi$
$42$	−1.76214	+	9.38655i	−0.271904	+	1.44838i
$43$	−3.14069	−	8.62898i	−0.478951	−	1.31591i	−0.910385	−	0.413763i	$-0.864214\pi$
$43$	−3.14069	−	8.62898i	−0.478951	−	1.31591i	0.431433	−	0.902145i	$-0.358008\pi$
$44$	1.03861	+	2.94357i	0.156577	+	0.443760i
$45$	5.82787	+	2.20214i	0.868768	+	0.328275i
$46$	−4.38730	−	3.10437i	−0.646872	−	0.457715i
$47$	−0.603613	+	3.42326i	−0.0880460	+	0.499334i	0.908612	+	0.417642i	$0.137143\pi$
$47$	−0.603613	+	3.42326i	−0.0880460	+	0.499334i	−0.996658	+	0.0816916i	$0.973968\pi$
$48$	5.02388	−	4.77081i	0.725135	−	0.688607i
$49$	7.70742	+	2.80527i	1.10106	+	0.400753i
$50$	−0.968821	+	0.0799486i	−0.137012	+	0.0113064i
$51$	1.91508	−	6.97647i	0.268164	−	0.976901i
$52$	2.04076	+	2.48137i	0.283002	+	0.344105i
$53$		−	6.03391i		−	0.828821i	−0.910090	−	0.414411i	$-0.863988\pi$
$53$		−	6.03391i		−	0.828821i	0.910090	−	0.414411i	$-0.136012\pi$
$54$	−7.34648	−	0.170840i	−0.999730	−	0.0232484i
$55$		−	3.24111i		−	0.437032i
$56$	−6.19106	−	9.12619i	−0.827316	−	1.21954i
$57$	−13.4798	+	3.52382i	−1.78544	+	0.466742i
$58$	−0.442602	−	5.36347i	−0.0581165	−	0.704258i
$59$	1.58603	+	0.577267i	0.206483	+	0.0751537i	0.443191	−	0.896427i	$-0.353846\pi$
$59$	1.58603	+	0.577267i	0.206483	+	0.0751537i	−0.236708	+	0.971581i	$0.576068\pi$
$60$	−6.56755	+	2.93575i	−0.847867	+	0.379004i
$61$	−1.69938	+	9.63768i	−0.217584	+	1.23398i	0.658783	+	0.752333i	$0.271072\pi$
$61$	−1.69938	+	9.63768i	−0.217584	+	1.23398i	−0.876366	+	0.481645i	$0.840040\pi$
$62$	0.515357	−	0.728336i	0.0654505	−	0.0924987i
$63$	−2.17168	+	11.4936i	−0.273606	+	1.44806i
$64$	−0.236673	+	7.99650i	−0.0295841	+	0.999562i
$65$	−1.14096	−	3.13477i	−0.141519	−	0.388820i
$66$	1.26780	+	3.60662i	0.156055	+	0.443944i
$67$	5.27928	+	6.29160i	0.644966	+	0.768641i	0.985146	−	0.171719i	$-0.0549323\pi$
$67$	5.27928	+	6.29160i	0.644966	+	0.768641i	−0.340179	+	0.940361i	$0.610488\pi$
$68$	4.10531	+	7.27539i	0.497842	+	0.882271i
$69$	−5.36885	−	3.80838i	−0.646333	−	0.458475i
$70$	2.90911	+	11.0751i	0.347705	+	1.32373i
$71$	−6.91810	−	11.9825i	−0.821028	−	1.42206i	−0.904917	−	0.425587i	$-0.860068\pi$
$71$	−6.91810	−	11.9825i	−0.821028	−	1.42206i	0.0838895	−	0.996475i	$-0.473266\pi$
$72$	6.15983	−	5.83579i	0.725943	−	0.687754i
$73$	0.999604	−	1.73136i	0.116995	−	0.202641i	−0.801581	−	0.597887i	$-0.796007\pi$
$73$	0.999604	−	1.73136i	0.116995	−	0.202641i	0.918575	+	0.395246i	$0.129341\pi$
$74$	−2.48878	−	0.680037i	−0.289314	−	0.0790527i
$75$	−1.18667	+	0.0965224i	−0.137025	+	0.0111455i
$76$	8.18112	−	13.8528i	0.938439	−	1.58902i
$77$	5.99276	−	1.05669i	0.682938	−	0.120420i
$78$	2.49583	+	3.04198i	0.282597	+	0.344437i
$79$	−2.46986	+	2.94347i	−0.277881	+	0.331166i	−0.886875	−	0.462009i	$-0.847129\pi$
$79$	−2.46986	+	2.94347i	−0.277881	+	0.331166i	0.608994	+	0.793175i	$0.291573\pi$
$80$	2.99448	−	7.74822i	0.334793	−	0.866277i
$81$	−8.99732	−	0.219808i	−0.999702	−	0.0244231i
$82$	7.64671	+	0.707015i	0.844438	+	0.0780767i
$83$	9.80246	+	8.22524i	1.07596	+	0.902838i	0.995579	−	0.0939267i	$-0.0299419\pi$
$83$	9.80246	+	8.22524i	1.07596	+	0.902838i	0.0803808	+	0.996764i	$0.474386\pi$
$84$	−7.56933	−	11.1862i	−0.825882	−	1.22051i
$85$	−1.50623	−	8.54225i	−0.163374	−	0.926537i
$86$	11.7425	+	5.54626i	1.26622	+	0.598069i
$87$	−0.534356	−	6.56951i	−0.0572890	−	0.704326i
$88$	−3.97274	−	1.92458i	−0.423496	−	0.205161i
$89$	8.51207	+	4.91444i	0.902277	+	0.520930i	0.877938	−	0.478774i	$-0.158919\pi$
$89$	8.51207	+	4.91444i	0.902277	+	0.520930i	0.0243390	+	0.999704i	$0.492252\pi$
$90$	−8.04779	+	3.58609i	−0.848312	+	0.378007i
$91$	5.42415	−	3.13163i	0.568605	−	0.328284i
$92$	7.49791	−	1.24596i	0.781711	−	0.129901i
$93$	0.632229	−	0.891283i	0.0655591	−	0.0924218i
$94$	−2.79975	−	4.04073i	−0.288773	−	0.416769i
$95$	−12.7968	+	10.7378i	−1.31292	+	1.10167i
$96$	−0.301371	+	9.79332i	−0.0307585	+	0.999527i
$97$	13.2890	−	4.83681i	1.34930	−	0.491104i	0.436569	−	0.899671i	$-0.356194\pi$
$97$	13.2890	−	4.83681i	1.34930	−	0.491104i	0.912728	+	0.408567i	$0.133971\pi$
$98$	−10.5367	+	4.85025i	−1.06437	+	0.489949i
$99$	1.54754	+	4.41901i	0.155533	+	0.444127i
$100$	0.894033	−	1.04437i	0.0894033	−	0.104437i
$101$	3.46353	+	0.610714i	0.344634	+	0.0607683i	0.343286	−	0.939231i	$-0.388460\pi$
$101$	3.46353	+	0.610714i	0.344634	+	0.0607683i	0.00134779	+	0.999999i	$0.499571\pi$
$102$	5.01749	+	8.91640i	0.496805	+	0.882855i
$103$	−2.39786	+	6.58805i	−0.236268	+	0.649140i	0.763726	+	0.645541i	$0.223368\pi$
$103$	−2.39786	+	6.58805i	−0.236268	+	0.649140i	−0.999994	+	0.00359939i	$0.998854\pi$
$104$	−4.51990	−	0.462912i	−0.443213	−	0.0453923i
$105$	3.54698	+	13.5684i	0.346149	+	1.32414i
$106$	6.00408	+	6.06359i	0.583168	+	0.588948i
$107$	−8.93007			−0.863303			−0.431651	−	0.902041i	$-0.642069\pi$
$107$	−8.93007			−0.863303			−0.431651	+	0.902041i	$0.642069\pi$
$108$	7.55262	−	7.13848i	0.726751	−	0.686901i
$109$	−3.86311			−0.370019			−0.185010	−	0.982737i	$-0.559232\pi$
$109$	−3.86311			−0.370019			−0.185010	+	0.982737i	$0.559232\pi$
$110$	3.22509	+	3.25706i	0.307500	+	0.310548i
$111$	−3.04713	−	0.836453i	−0.289221	−	0.0793926i
$112$	15.3026	+	3.01062i	1.44596	+	0.284477i
$113$	−0.185982	+	0.510982i	−0.0174958	+	0.0480692i	−0.948133	−	0.317874i	$-0.897031\pi$
$113$	−0.185982	+	0.510982i	−0.0174958	+	0.0480692i	0.930637	+	0.365943i	$0.119253\pi$
$114$	10.0397	−	16.9543i	0.940305	−	1.58792i
$115$	−7.77225	−	1.37046i	−0.724766	−	0.127796i
$116$	5.78173	+	4.94944i	0.536821	+	0.459544i
$117$	3.05238	+	3.72924i	0.282192	+	0.344769i
$118$	−2.16824	+	0.998080i	−0.199603	+	0.0918808i
$119$	15.3034	−	5.56998i	1.40286	−	0.510599i
$120$	3.67862	−	9.48527i	0.335811	−	0.865883i
$121$	−6.56053	+	5.50494i	−0.596412	+	0.500449i
$122$	−7.88229	−	11.3761i	−0.713629	−	1.02994i
$123$	9.36424	+	0.876916i	0.844345	+	0.0790689i
$124$	0.206843	+	1.24473i	0.0185750	+	0.111780i
$125$	−10.2285	+	5.90545i	−0.914869	+	0.528200i
$126$	−9.25440	−	13.7111i	−0.824447	−	1.22148i
$127$	−6.30337	−	3.63925i	−0.559333	−	0.322931i	0.193545	−	0.981091i	$-0.438002\pi$
$127$	−6.30337	−	3.63925i	−0.559333	−	0.322931i	−0.752878	+	0.658160i	$0.771335\pi$
$128$	−7.71913	−	8.27134i	−0.682281	−	0.731090i
$129$	14.3735	+	6.80965i	1.26552	+	0.599556i
$130$	4.26585	+	2.01487i	0.374140	+	0.176716i
$131$	−0.199803	−	1.13314i	−0.0174569	−	0.0990028i	0.974834	−	0.222930i	$-0.0715622\pi$
$131$	−0.199803	−	1.13314i	−0.0174569	−	0.0990028i	−0.992291	+	0.123927i	$0.960451\pi$
$132$	−4.86282	−	2.36283i	−0.423255	−	0.205658i
$133$	−24.0261	−	20.1603i	−2.08332	−	1.74812i
$134$	−11.5657	−	1.06937i	−0.999128	−	0.0923794i
$135$	−9.86165	+	4.38046i	−0.848755	+	0.377010i
$136$	−11.3649	−	3.22616i	−0.974535	−	0.276641i
$137$	11.5868	−	13.8086i	0.989923	−	1.17974i	0.00621375	−	0.999981i	$-0.498022\pi$
$137$	11.5868	−	13.8086i	0.989923	−	1.17974i	0.983710	−	0.179764i	$-0.0575335\pi$
$138$	9.18481	−	1.51520i	0.781863	−	0.128982i
$139$	−3.46870	+	0.611626i	−0.294211	+	0.0518774i	−0.318806	−	0.947820i	$-0.603282\pi$
$139$	−3.46870	+	0.611626i	−0.294211	+	0.0518774i	0.0245942	+	0.999698i	$0.492171\pi$
$140$	−13.9438	−	8.23487i	−1.17847	−	0.695974i
$141$	−3.42317	−	4.95289i	−0.288283	−	0.417108i
$142$	18.8754	+	5.15755i	1.58399	+	0.432812i
$143$	1.25356	−	2.17122i	0.104828	−	0.181567i
$144$	−0.383195	+	11.9939i	−0.0319329	+	0.999490i
$145$	−3.95134	−	6.84393i	−0.328141	−	0.568357i
$146$	0.718285	+	2.73454i	0.0594457	+	0.226312i
$147$	−12.9118	+	5.92515i	−1.06495	+	0.488698i
$148$	3.17769	−	1.79309i	0.261205	−	0.147391i
$149$	9.84611	+	11.7341i	0.806624	+	0.961298i	0.999803	−	0.0198661i	$-0.00632398\pi$
$149$	9.84611	+	11.7341i	0.806624	+	0.961298i	−0.193178	+	0.981164i	$0.561880\pi$
$150$	1.09646	−	1.27780i	0.0895260	−	0.104332i
$151$	1.59444	+	4.38068i	0.129754	+	0.356495i	0.987509	−	0.157563i	$-0.0503638\pi$
$151$	1.59444	+	4.38068i	0.129754	+	0.356495i	−0.857755	+	0.514058i	$0.828142\pi$
$152$	5.56292	+	22.0616i	0.451213	+	1.78943i
$153$	6.13231	+	10.9275i	0.495768	+	0.883438i
$154$	−4.97078	+	7.02502i	−0.400557	+	0.566092i
$155$	0.227510	−	1.29027i	0.0182740	−	0.103637i
$156$	−5.53506	−	0.573454i	−0.443159	−	0.0459130i
$157$	−13.7323	−	4.99816i	−1.09596	−	0.398897i	−0.270134	−	0.962823i	$-0.587068\pi$
$157$	−13.7323	−	4.99816i	−1.09596	−	0.398897i	−0.825825	+	0.563926i	$0.809290\pi$
$158$	−0.446904	−	5.41560i	−0.0355538	−	0.430842i
$159$	7.34474	+	7.43499i	0.582476	+	0.589633i
$160$	4.70070	+	10.7660i	0.371623	+	0.851128i
$161$		−	14.8175i		−	1.16779i
$162$	9.26030	−	8.73195i	0.727558	−	0.686047i
$163$			5.19011i			0.406521i	0.979125	+	0.203260i	$0.0651538\pi$
$163$			5.19011i			0.406521i	−0.979125	+	0.203260i	$0.934846\pi$
$164$	−8.38784	+	6.89842i	−0.654981	+	0.538676i
$165$	3.94522	+	3.99370i	0.307135	+	0.310909i
$166$	−18.0353	+	1.48830i	−1.39981	+	0.115514i
$167$	−14.6509	−	5.33250i	−1.13372	−	0.412642i	−0.294081	−	0.955781i	$-0.595013\pi$
$167$	−14.6509	−	5.33250i	−1.13372	−	0.412642i	−0.839643	+	0.543139i	$0.817236\pi$
$168$	18.7374	+	3.70926i	1.44562	+	0.286176i
$169$	−1.80933	+	10.2612i	−0.139179	+	0.789325i
$170$	10.0137	+	7.08549i	0.768013	+	0.543432i
$171$	12.3205	−	20.7503i	0.942170	−	1.58681i
$172$	−17.3191	+	6.11087i	−1.32057	+	0.465950i
$173$	4.40303	+	12.0972i	0.334757	+	0.919736i	0.986856	+	0.161603i	$0.0516663\pi$
$173$	4.40303	+	12.0972i	0.334757	+	0.919736i	−0.652099	+	0.758134i	$0.726112\pi$
$174$	7.07402	+	6.07012i	0.536280	+	0.460174i
$175$	−1.72274	−	2.05309i	−0.130227	−	0.155199i
$176$	5.90735	−	2.01906i	0.445283	−	0.152192i
$177$	−2.65698	+	1.21927i	−0.199711	+	0.0916462i
$178$	−13.4441	+	3.53137i	−1.00768	+	0.264687i
$179$	7.23994	+	12.5399i	0.541139	+	0.937280i	0.998839	+	0.0481733i	$0.0153400\pi$
$179$	7.23994	+	12.5399i	0.541139	+	0.937280i	−0.457700	+	0.889107i	$0.651327\pi$
$180$	4.51902	−	11.6117i	0.336828	−	0.865488i
$181$	−1.99303	+	3.45202i	−0.148140	+	0.256587i	−0.930540	−	0.366190i	$-0.880662\pi$
$181$	−1.99303	+	3.45202i	−0.148140	+	0.256587i	0.782400	+	0.622777i	$0.213995\pi$
$182$	−2.33468	+	8.54437i	−0.173058	+	0.633351i
$183$	−9.63742	−	13.9441i	−0.712418	−	1.03078i
$184$	−6.29499	+	8.71293i	−0.464072	+	0.642326i
$185$	−3.73102	+	0.657880i	−0.274310	+	0.0483683i
$186$	0.251538	+	1.52477i	0.0184437	+	0.111802i
$187$	4.19027	−	4.99377i	0.306423	−	0.365181i
$188$	6.83428	+	1.27469i	0.498441	+	0.0929665i
$189$	−11.3145	−	16.8059i	−0.823012	−	1.22245i
$190$	2.17504	−	23.5241i	0.157794	−	1.70662i
$191$	−7.04065	−	5.90780i	−0.509443	−	0.427474i	0.351490	−	0.936192i	$-0.385675\pi$
$191$	−7.04065	−	5.90780i	−0.509443	−	0.427474i	−0.860933	+	0.508718i	$0.830120\pi$
$192$	−9.44206	−	10.1414i	−0.681422	−	0.731891i
$193$	0.542633	+	3.07743i	0.0390596	+	0.221518i	0.998089	−	0.0617875i	$-0.0196801\pi$
$193$	0.542633	+	3.07743i	0.0390596	+	0.221518i	−0.959030	+	0.283305i	$0.908569\pi$
$194$	−8.54151	+	18.0839i	−0.613244	+	1.29835i
$195$	5.22167	+	2.47384i	0.373932	+	0.177155i
$196$	5.76230	−	15.3588i	0.411593	−	1.09705i
$197$	14.4834	+	8.36197i	1.03190	+	0.595766i	0.917527	−	0.397673i	$-0.130182\pi$
$197$	14.4834	+	8.36197i	1.03190	+	0.595766i	0.114369	+	0.993438i	$0.463515\pi$
$198$	−5.95231	−	2.90086i	−0.423013	−	0.206155i
$199$	17.5290	−	10.1204i	1.24260	−	0.717414i	0.272976	−	0.962021i	$-0.411992\pi$
$199$	17.5290	−	10.1204i	1.24260	−	0.717414i	0.969622	+	0.244606i	$0.0786587\pi$
$200$	0.140779	+	1.93912i	0.00995460	+	0.137117i
$201$	−14.1635	−	1.32635i	−0.999019	−	0.0935533i
$202$	−4.08826	+	2.83269i	−0.287649	+	0.199307i
$203$	11.3661	−	9.53725i	0.797741	−	0.669384i
$204$	−13.9145	−	3.96758i	−0.974209	−	0.277786i
$205$	10.5965	−	3.85682i	0.740094	−	0.269372i
$206$	−4.14583	−	9.00646i	−0.288854	−	0.627510i
$207$	11.2512	−	1.84251i	0.782014	−	0.128063i
$208$	5.00276	−	4.03237i	0.346879	−	0.279594i
$209$	−12.3638	−	2.18007i	−0.855223	−	0.150799i
$210$	−17.0657	−	10.1057i	−1.17765	−	0.697358i
$211$	−3.30764	+	9.08767i	−0.227707	+	0.625621i	−0.999953	−	0.00970319i	$-0.996911\pi$
$211$	−3.30764	+	9.08767i	−0.227707	+	0.625621i	0.772245	+	0.635324i	$0.219134\pi$
$212$	−12.0672	−	0.119020i	−0.828781	−	0.00817436i
$213$	23.1101	+	6.34384i	1.58348	+	0.434673i
$214$	8.97400	−	8.88593i	0.613450	−	0.607429i
$215$	19.0697			1.30054
$216$	−0.486576	+	14.6889i	−0.0331073	+	0.999452i
$217$	2.45986			0.166986
$218$	3.88212	−	3.84402i	0.262930	−	0.260350i
$219$	0.875780	+	3.35015i	0.0591797	+	0.226382i
$220$	−6.48191	−	0.0639318i	−0.437010	−	0.00431028i
$221$	2.29484	−	6.30502i	0.154368	−	0.424121i
$222$	3.89444	−	2.19150i	0.261378	−	0.147084i
$223$	21.5385	+	3.79782i	1.44232	+	0.254321i	0.839416	−	0.543490i	$-0.182897\pi$
$223$	21.5385	+	3.79782i	1.44232	+	0.254321i	0.602908	+	0.797811i	$0.294009\pi$
$224$	−18.3736	+	12.2015i	−1.22764	+	0.815247i
$225$	1.34473	−	1.56340i	0.0896485	−	0.104227i
$226$	−0.321559	−	0.698559i	−0.0213898	−	0.0464675i
$227$	−4.60337	+	1.67549i	−0.305536	+	0.111206i	−0.490238	−	0.871588i	$-0.663090\pi$
$227$	−4.60337	+	1.67549i	−0.305536	+	0.111206i	0.184702	+	0.982795i	$0.440868\pi$
$228$	6.78141	+	27.0278i	0.449110	+	1.78996i
$229$	16.2130	−	13.6043i	1.07139	−	0.899000i	0.0762090	−	0.997092i	$-0.475718\pi$
$229$	16.2130	−	13.6043i	1.07139	−	0.899000i	0.995177	+	0.0980919i	$0.0312739\pi$
$230$	9.17416	−	6.35663i	0.604926	−	0.419144i
$231$	−6.09804	+	8.59669i	−0.401221	+	0.565621i
$232$	−10.7351	+	0.779365i	−0.704797	+	0.0511678i
$233$	4.25923	−	2.45907i	0.279032	−	0.161099i	−0.353953	−	0.935263i	$-0.615163\pi$
$233$	4.25923	−	2.45907i	0.279032	−	0.161099i	0.632985	+	0.774164i	$0.281830\pi$
$234$	−6.77820	−	0.710299i	−0.443105	−	0.0464337i
$235$	−6.25157	−	3.60935i	−0.407807	−	0.235448i
$236$	1.18576	−	3.16051i	0.0771866	−	0.205732i
$237$	−0.539549	−	6.63336i	−0.0350475	−	0.430883i
$238$	−9.83623	+	20.8251i	−0.637588	+	1.34989i
$239$	0.976252	+	5.53660i	0.0631485	+	0.358133i	0.999965	+	0.00831291i	$0.00264611\pi$
$239$	0.976252	+	5.53660i	0.0631485	+	0.358133i	−0.936817	+	0.349820i	$0.886243\pi$
$240$	5.74167	+	13.1924i	0.370623	+	0.851564i
$241$	0.410210	+	0.344207i	0.0264239	+	0.0221723i	0.655904	−	0.754844i	$-0.272288\pi$
$241$	0.410210	+	0.344207i	0.0264239	+	0.0221723i	−0.629480	+	0.777017i	$0.716732\pi$
$242$	1.11508	−	12.0601i	0.0716799	−	0.775254i
$243$	11.3541	−	10.6811i	0.728363	−	0.685191i
$244$	19.2409	+	3.58871i	1.23177	+	0.229743i
$245$	−10.9487	+	13.0481i	−0.699484	+	0.833613i
$246$	−10.2829	+	8.43672i	−0.655613	+	0.537906i
$247$	−12.7256	+	2.24387i	−0.809711	+	0.142774i
$248$	−1.44644	−	1.04503i	−0.0918487	−	0.0663596i
$249$	−22.0907	+	1.79683i	−1.39994	+	0.113870i
$250$	4.40260	−	16.1125i	0.278445	−	1.01904i
$251$	−5.19194	+	8.99271i	−0.327713	+	0.567615i	−0.982058	−	0.188581i	$-0.939611\pi$
$251$	−5.19194	+	8.99271i	−0.327713	+	0.567615i	0.654345	+	0.756196i	$0.272944\pi$
$252$	22.9432	+	4.56986i	1.44529	+	0.287874i
$253$	−2.96564	−	5.13665i	−0.186448	−	0.322938i
$254$	9.95563	−	2.61505i	0.624672	−	0.164083i
$255$	12.2540	+	8.69232i	0.767374	+	0.544334i
$256$	15.9876	+	0.631055i	0.999222	+	0.0394409i
$257$	−6.62146	−	7.89114i	−0.413035	−	0.492236i	0.518913	−	0.854827i	$-0.326337\pi$
$257$	−6.62146	−	7.89114i	−0.413035	−	0.492236i	−0.931948	+	0.362591i	$0.881892\pi$
$258$	−21.2202	+	7.45933i	−1.32111	+	0.464398i
$259$	−2.43282	−	6.68411i	−0.151168	−	0.415330i
$260$	−6.29174	+	2.21998i	−0.390197	+	0.137677i
$261$	8.65513	+	7.44452i	0.535739	+	0.460804i
$262$	1.32832	+	0.939898i	0.0820641	+	0.0580671i
$263$	2.57586	−	14.6085i	0.158835	−	0.900796i	−0.796361	−	0.604821i	$-0.793245\pi$
$263$	2.57586	−	14.6085i	0.158835	−	0.900796i	0.955196	−	0.295975i	$-0.0956444\pi$
$264$	7.23790	−	2.46433i	0.445462	−	0.151669i
$265$	11.7748	+	4.28569i	0.723322	+	0.263268i
$266$	44.2048	−	3.64785i	2.71037	−	0.223664i
$267$	−16.4707	+	4.30568i	−1.00799	+	0.263503i
$268$	12.6867	−	10.4339i	0.774965	−	0.637354i
$269$			10.7768i			0.657070i	0.944492	+	0.328535i	$0.106555\pi$
$269$			10.7768i			0.657070i	−0.944492	+	0.328535i	$0.893445\pi$
$270$	5.55135	−	14.2149i	0.337845	−	0.865092i
$271$		−	6.76954i		−	0.411220i	−0.978634	−	0.205610i	$-0.934082\pi$
$271$		−	6.76954i		−	0.411220i	0.978634	−	0.205610i	$-0.0659179\pi$
$272$	14.6311	−	8.06672i	0.887138	−	0.489117i
$273$	−2.87168	+	10.4613i	−0.173802	+	0.633147i
$274$	2.09654	+	25.4060i	0.126657	+	1.53483i
$275$	−1.00812	−	0.366925i	−0.0607919	−	0.0221264i
$276$	−7.72228	+	10.6621i	−0.464827	+	0.641780i
$277$	−3.10391	+	17.6031i	−0.186496	+	1.05767i	0.737523	+	0.675322i	$0.235995\pi$
$277$	−3.10391	+	17.6031i	−0.186496	+	1.05767i	−0.924019	+	0.382348i	$0.875116\pi$
$278$	2.87716	−	4.06619i	0.172561	−	0.243874i
$279$	0.305875	+	1.86782i	0.0183123	+	0.111823i
$280$	22.2065	−	5.59948i	1.32710	−	0.334633i
$281$	−3.61833	−	9.94129i	−0.215852	−	0.593048i	0.783756	−	0.621069i	$-0.213301\pi$
$281$	−3.61833	−	9.94129i	−0.215852	−	0.593048i	−0.999607	+	0.0280216i	$0.991079\pi$
$282$	8.36841	+	1.57101i	0.498331	+	0.0935520i
$283$	−3.64860	−	4.34824i	−0.216887	−	0.258476i	0.646621	−	0.762812i	$-0.276182\pi$
$283$	−3.64860	−	4.34824i	−0.216887	−	0.258476i	−0.863507	+	0.504336i	$0.831737\pi$
$284$	−24.1003	+	13.5992i	−1.43009	+	0.806963i
$285$	2.69772	−	28.8079i	0.159799	−	1.70643i
$286$	0.900767	+	3.42926i	0.0532634	+	0.202777i
$287$	10.5859	+	18.3354i	0.624868	+	1.08230i
$288$	−11.5495	−	12.4342i	−0.680561	−	0.732691i
$289$	0.223112	−	0.386442i	0.0131243	−	0.0227319i
$290$	10.7809	+	2.94578i	0.633075	+	0.172982i
$291$	−10.4872	+	22.1359i	−0.614769	+	1.29763i
$292$	−3.44284	−	2.03326i	−0.201477	−	0.118988i
$293$	−21.8702	+	3.85630i	−1.27767	+	0.225288i	−0.770990	−	0.636847i	$-0.780238\pi$
$293$	−21.8702	+	3.85630i	−1.27767	+	0.225288i	−0.506679	+	0.862135i	$0.669127\pi$
$294$	7.07945	−	18.8023i	0.412882	−	1.09657i
$295$	−2.25301	+	2.68503i	−0.131175	+	0.156328i
$296$	−1.40910	+	4.96389i	−0.0819023	+	0.288521i
$297$	−7.28589	−	3.56138i	−0.422770	−	0.206652i
$298$	−21.5707	−	1.99442i	−1.24956	−	0.115534i
$299$	−4.67658	−	3.92412i	−0.270454	−	0.226938i
$300$	0.169628	+	2.37513i	0.00979348	+	0.137128i
$301$	6.21721	+	35.2595i	0.358354	+	2.03233i
$302$	−5.96131	−	2.81568i	−0.343035	−	0.162024i
$303$	−5.01115	+	3.46344i	−0.287883	+	0.198969i
$304$	−27.5428	−	16.6347i	−1.57969	−	0.954065i
$305$	−17.6004	−	10.1616i	−1.00779	−	0.581850i
$306$	−17.0360	−	4.87929i	−0.973882	−	0.278930i
$307$	−25.2053	+	14.5523i	−1.43854	+	0.830541i	−0.997748	−	0.0670680i	$-0.978636\pi$
$307$	−25.2053	+	14.5523i	−1.43854	+	0.830541i	−0.440792	+	0.897609i	$0.645302\pi$
$308$	−1.99506	−	12.0058i	−0.113679	−	0.684093i
$309$	−5.06462	−	11.0366i	−0.288116	−	0.627849i
$310$	1.05526	+	1.52300i	0.0599350	+	0.0865008i
$311$	4.48037	−	3.75948i	0.254059	−	0.213180i	−0.506859	−	0.862029i	$-0.669194\pi$
$311$	4.48037	−	3.75948i	0.254059	−	0.213180i	0.760918	+	0.648848i	$0.224749\pi$
$312$	6.13290	−	4.93142i	0.347207	−	0.279187i
$313$	14.3175	−	5.21116i	0.809276	−	0.294552i	0.0959511	−	0.995386i	$-0.469411\pi$
$313$	14.3175	−	5.21116i	0.809276	−	0.294552i	0.713325	+	0.700834i	$0.247189\pi$
$314$	18.7733	−	8.64170i	1.05944	−	0.487679i
$315$	−20.8866	−	12.4014i	−1.17683	−	0.698741i
$316$	5.83793	+	4.99754i	0.328409	+	0.281134i
$317$	12.5020	+	2.20444i	0.702181	+	0.123813i	0.513329	−	0.858192i	$-0.328412\pi$
$317$	12.5020	+	2.20444i	0.702181	+	0.123813i	0.188852	+	0.982006i	$0.439523\pi$
$318$	−14.7791	−	0.163135i	−0.828771	−	0.00914816i
$319$	2.03133	−	5.58103i	0.113733	−	0.312478i
$320$	−15.4366	−	6.14150i	−0.862933	−	0.343321i
$321$	11.0036	−	10.8701i	0.614163	−	0.606708i
$322$	14.7443	+	14.8904i	0.821668	+	0.829812i
$323$	−33.5991			−1.86951
$324$	−0.617069	+	17.9894i	−0.0342816	+	0.999412i
$325$	−1.10421			−0.0612506
$326$	−5.16445	−	5.21564i	−0.286033	−	0.288868i
$327$	4.76013	−	4.70235i	0.263236	−	0.260041i
$328$	1.56479	−	15.2787i	0.0864013	−	0.843627i
$329$	4.63544	−	12.7358i	0.255560	−	0.702146i
$330$	−7.93859	−	0.0876279i	−0.437005	−	0.00482376i
$331$	2.67374	+	0.471452i	0.146962	+	0.0259133i	0.246645	−	0.969106i	$-0.420672\pi$
$331$	2.67374	+	0.471452i	0.146962	+	0.0259133i	−0.0996832	+	0.995019i	$0.531783\pi$
$332$	16.6430	−	19.4417i	0.913405	−	1.06700i
$333$	4.77285	−	2.67843i	0.261550	−	0.146777i
$334$	20.0291	−	9.21977i	1.09595	−	0.504483i
$335$	−16.0274	+	5.83350i	−0.875670	+	0.318718i
$336$	−22.5205	+	14.9173i	−1.22860	+	0.813804i
$337$	4.66114	−	3.91116i	0.253908	−	0.213054i	−0.506945	−	0.861979i	$-0.669225\pi$
$337$	4.66114	−	3.91116i	0.253908	−	0.213054i	0.760853	+	0.648924i	$0.224781\pi$
$338$	−8.39227	−	12.1121i	−0.456479	−	0.658811i
$339$	−0.392822	−	0.856019i	−0.0213352	−	0.0464926i
$340$	−17.1134	+	2.84381i	−0.928104	+	0.154227i
$341$	0.852735	−	0.492327i	0.0461782	−	0.0266610i
$342$	8.26660	+	33.1119i	0.447006	+	1.79049i
$343$	−4.05892	−	2.34342i	−0.219161	−	0.126533i
$344$	11.3236	−	23.3744i	0.610528	−	1.26026i
$345$	11.2451	−	7.77204i	0.605418	−	0.418433i
$346$	−16.4621	−	7.77548i	−0.885010	−	0.418012i
$347$	−5.88732	−	33.3886i	−0.316048	−	1.79240i	−0.566283	−	0.824211i	$-0.691619\pi$
$347$	−5.88732	−	33.3886i	−0.316048	−	1.79240i	0.250235	−	0.968185i	$-0.419492\pi$
$348$	−13.1489	+	0.939075i	−0.704857	+	0.0503397i
$349$	6.08210	+	5.10349i	0.325568	+	0.273184i	0.790891	−	0.611957i	$-0.209618\pi$
$349$	6.08210	+	5.10349i	0.325568	+	0.273184i	−0.465323	+	0.885141i	$0.654062\pi$
$350$	3.77416	+	0.348959i	0.201737	+	0.0186526i
$351$	−8.30054	−	0.879689i	−0.443050	−	0.0469543i
$352$	−3.92733	+	7.90714i	−0.209327	+	0.421452i
$353$	−7.52927	+	8.97303i	−0.400742	+	0.477586i	−0.928246	−	0.371967i	$-0.878684\pi$
$353$	−7.52927	+	8.97303i	−0.400742	+	0.477586i	0.527504	+	0.849553i	$0.323128\pi$
$354$	1.45680	−	3.86911i	0.0774282	−	0.205641i
$355$	28.2969	−	4.98951i	1.50184	−	0.264815i
$356$	9.99631	−	16.9264i	0.529804	−	0.897096i
$357$	−12.0768	+	25.4913i	−0.639174	+	1.34914i
$358$	−19.7535	−	5.39748i	−1.04401	−	0.285266i
$359$	−11.7844	+	20.4112i	−0.621957	+	1.07726i	0.367164	+	0.930156i	$0.380329\pi$
$359$	−11.7844	+	20.4112i	−0.621957	+	1.07726i	−0.989121	+	0.147105i	$0.953005\pi$
$360$	7.01309	+	16.1655i	0.369622	+	0.851999i
$361$	22.8537	+	39.5838i	1.20283	+	2.08336i
$362$	−1.43213	−	5.45218i	−0.0752709	−	0.286560i
$363$	1.38304	−	14.7690i	0.0725908	−	0.775169i
$364$	−6.15597	−	10.9095i	−0.322661	−	0.571815i
$365$	2.66867	+	3.18040i	0.139685	+	0.166470i
$366$	23.5600	+	4.42293i	1.23150	+	0.231190i
$367$	8.45358	+	23.2260i	0.441273	+	1.21239i	0.938655	+	0.344856i	$0.112072\pi$
$367$	8.45358	+	23.2260i	0.441273	+	1.21239i	−0.497382	+	0.867531i	$0.665705\pi$
$368$	−2.34391	−	15.0197i	−0.122185	−	0.782954i
$369$	−12.6060	+	10.3180i	−0.656245	+	0.537135i
$370$	3.09475	−	4.37370i	0.160888	−	0.227378i
$371$	−4.08527	+	23.1687i	−0.212096	+	1.20286i
$372$	−1.77001	−	1.28198i	−0.0917707	−	0.0664674i
$373$	−17.8113	−	6.48278i	−0.922234	−	0.335666i	−0.163107	−	0.986608i	$-0.552152\pi$
$373$	−17.8113	−	6.48278i	−0.922234	−	0.335666i	−0.759127	+	0.650943i	$0.774374\pi$
$374$	0.758200	+	9.18789i	0.0392056	+	0.475095i
$375$	5.41525	−	19.7273i	0.279642	−	1.01871i
$376$	−8.13629	+	5.51953i	−0.419597	+	0.284648i
$377$		−	6.11300i		−	0.314835i
$378$	28.0930	+	5.62993i	1.44495	+	0.289572i
$379$			8.62366i			0.442968i	0.975164	+	0.221484i	$0.0710900\pi$
$379$			8.62366i			0.442968i	−0.975164	+	0.221484i	$0.928910\pi$
$380$	21.2221	+	25.8042i	1.08867	+	1.32373i
$381$	12.1969	−	3.18844i	0.624864	−	0.163349i
$382$	12.9539	−	1.06898i	0.662778	−	0.0546935i
$383$	28.3995	+	10.3366i	1.45115	+	0.528174i	0.942911	−	0.333044i	$-0.108076\pi$
$383$	28.3995	+	10.3366i	1.45115	+	0.528174i	0.508236	+	0.861218i	$0.330298\pi$
$384$	19.5797	+	0.795888i	0.999175	+	0.0406150i
$385$	−2.19440	+	12.4451i	−0.111837	+	0.634259i
$386$	−3.60752	−	2.55261i	−0.183618	−	0.129925i
$387$	−26.0001	+	9.10523i	−1.32166	+	0.462845i
$388$	−9.41103	−	26.6722i	−0.477773	−	1.35408i
$389$	−9.65520	−	26.5275i	−0.489538	−	1.34500i	−0.901099	−	0.433613i	$-0.857238\pi$
$389$	−9.65520	−	26.5275i	−0.489538	−	1.34500i	0.411561	−	0.911382i	$-0.364984\pi$
$390$	−7.70897	+	2.70985i	−0.390359	+	0.137219i
$391$	−10.2034	−	12.1599i	−0.516006	−	0.614952i
$392$	9.49218	+	21.1681i	0.479428	+	1.06915i
$393$	1.62550	+	1.15305i	0.0819958	+	0.0581635i
$394$	−22.8752	+	6.00865i	−1.15244	+	0.302712i
$395$	−3.98975	−	6.91044i	−0.200746	−	0.347702i
$396$	8.86812	−	3.00776i	0.445640	−	0.151146i
$397$	2.28495	−	3.95765i	0.114678	−	0.198629i	−0.802973	−	0.596016i	$-0.796750\pi$
$397$	2.28495	−	3.95765i	0.114678	−	0.198629i	0.917651	+	0.397387i	$0.130083\pi$
$398$	−7.54489	+	27.6125i	−0.378191	+	1.38409i
$399$	54.1449	−	4.40408i	2.71063	−	0.220480i
$400$	−2.07101	−	1.80858i	−0.103550	−	0.0904290i
$401$	2.44801	−	0.431651i	0.122248	−	0.0215556i	−0.112189	−	0.993687i	$-0.535786\pi$
$401$	2.44801	−	0.431651i	0.122248	−	0.0215556i	0.234437	+	0.972131i	$0.424675\pi$
$402$	15.5530	−	12.7606i	0.775713	−	0.636443i
$403$	0.651444	−	0.776360i	0.0324507	−	0.0386733i
$404$	1.28969	−	6.91468i	0.0641643	−	0.344018i
$405$	6.81944	−	17.4016i	0.338861	−	0.864694i
$406$	−1.93186	+	20.8940i	−0.0958767	+	1.03695i
$407$	−2.18114	−	1.83020i	−0.108115	−	0.0907195i
$408$	17.9309	−	9.85861i	0.887712	−	0.488074i
$409$	−3.57089	−	20.2515i	−0.176569	−	1.00137i	−0.936317	−	0.351155i	$-0.885789\pi$
$409$	−3.57089	−	20.2515i	−0.176569	−	1.00137i	0.759748	−	0.650217i	$-0.225322\pi$
$410$	−6.81091	+	14.4200i	−0.336367	+	0.712151i
$411$	2.53117	+	31.1188i	0.124853	+	1.53498i
$412$	13.1282	+	4.92543i	0.646778	+	0.242658i
$413$	−5.69911	−	3.29038i	−0.280435	−	0.161909i
$414$	−9.47316	+	13.0472i	−0.465581	+	0.641234i
$415$	−23.0135	+	13.2868i	−1.12969	+	0.652225i
$416$	−1.01494	+	9.03023i	−0.0497613	+	0.442743i
$417$	3.52964	−	4.97590i	0.172847	−	0.243671i
$418$	14.5939	−	10.1119i	0.713813	−	0.494589i
$419$	10.8202	−	9.07925i	0.528603	−	0.443550i	−0.339016	−	0.940781i	$-0.610094\pi$
$419$	10.8202	−	9.07925i	0.528603	−	0.443550i	0.867619	+	0.497230i	$0.165650\pi$
$420$	27.2054	−	6.82597i	1.32749	−	0.333073i
$421$	11.0936	−	4.03776i	0.540671	−	0.196788i	−0.0572256	−	0.998361i	$-0.518225\pi$
$421$	11.0936	−	4.03776i	0.540671	−	0.196788i	0.597897	+	0.801573i	$0.296003\pi$
$422$	−5.71883	−	12.4237i	−0.278388	−	0.604775i
$423$	10.2469	+	1.93612i	0.498221	+	0.0941375i
$424$	12.2450	−	11.8880i	0.594671	−	0.577331i
$425$	−2.82751	−	0.498566i	−0.137154	−	0.0241840i
$426$	−29.5363	+	16.6208i	−1.43104	+	0.805282i
$427$	13.0504	−	35.8557i	0.631553	−	1.73518i
$428$	−0.176148	+	17.8593i	−0.00851444	+	0.863261i
$429$	1.09827	+	4.20126i	0.0530252	+	0.202839i
$430$	−19.1635	+	18.9754i	−0.924147	+	0.915077i
$431$	39.3589			1.89585			0.947926	−	0.318492i	$-0.103176\pi$
$431$	39.3589			1.89585			0.947926	+	0.318492i	$0.103176\pi$
$432$	−14.1273	−	15.2453i	−0.679700	−	0.733490i
$433$	17.6193			0.846728			0.423364	−	0.905960i	$-0.360849\pi$
$433$	17.6193			0.846728			0.423364	+	0.905960i	$0.360849\pi$
$434$	−2.47196	+	2.44770i	−0.118658	+	0.117493i
$435$	13.1996	+	3.62335i	0.632871	+	0.173726i
$436$	−0.0762010	+	7.72585i	−0.00364937	+	0.370001i
$437$	−10.4557	+	28.7269i	−0.500165	+	1.37419i
$438$	−4.21368	−	2.49518i	−0.201337	−	0.119224i
$439$	15.3376	+	2.70443i	0.732022	+	0.129075i	0.527221	−	0.849728i	$-0.323234\pi$
$439$	15.3376	+	2.70443i	0.732022	+	0.129075i	0.204801	+	0.978804i	$0.434345\pi$
$440$	6.57741	−	6.38562i	0.313566	−	0.304423i
$441$	8.69757	−	23.0178i	0.414170	−	1.09608i
$442$	3.96772	+	8.61953i	0.188725	+	0.409989i
$443$	−6.38031	+	2.32224i	−0.303138	+	0.110333i	−0.489111	−	0.872222i	$-0.662679\pi$
$443$	−6.38031	+	2.32224i	−0.303138	+	0.110333i	0.185973	+	0.982555i	$0.440456\pi$
$444$	−1.73293	+	6.07747i	−0.0822412	+	0.288424i
$445$	−15.6361	+	13.1202i	−0.741222	+	0.621959i
$446$	−25.4235	+	17.6155i	−1.20384	+	0.834119i
$447$	−26.4157	−	2.47370i	−1.24942	−	0.117002i
$448$	6.32280	−	30.5443i	0.298724	−	1.44308i
$449$	−11.8597	+	6.84721i	−0.559694	+	0.323140i	−0.753023	−	0.657994i	$-0.771405\pi$
$449$	−11.8597	+	6.84721i	−0.559694	+	0.323140i	0.193328	+	0.981134i	$0.438072\pi$
$450$	0.204333	+	2.90917i	0.00963235	+	0.137140i
$451$	7.33944	+	4.23743i	0.345601	+	0.199533i
$452$	1.01825	+	0.382026i	0.0478943	+	0.0179690i
$453$	−7.29703	−	3.45706i	−0.342844	−	0.162427i
$454$	2.95881	−	6.26434i	0.138864	−	0.294000i
$455$	2.25861	+	12.8092i	0.105885	+	0.600505i
$456$	−33.7090	−	20.4129i	−1.57857	−	0.955920i
$457$	−29.1778	−	24.4831i	−1.36488	−	1.14527i	−0.974442	−	0.224640i	$-0.927879\pi$
$457$	−29.1778	−	24.4831i	−1.36488	−	1.14527i	−0.390437	−	0.920629i	$-0.627676\pi$
$458$	−2.75569	+	29.8041i	−0.128765	+	1.39266i
$459$	−20.8577	−	6.00040i	−0.973554	−	0.280075i
$460$	−2.89409	+	15.5167i	−0.134938	+	0.723470i
$461$	3.18317	−	3.79355i	0.148255	−	0.176683i	−0.686806	−	0.726841i	$-0.740988\pi$
$461$	3.18317	−	3.79355i	0.148255	−	0.176683i	0.835061	+	0.550157i	$0.185432\pi$
$462$	−2.42616	−	14.7069i	−0.112875	−	0.684226i
$463$	9.02239	−	1.59089i	0.419306	−	0.0739350i	0.0399855	−	0.999200i	$-0.487269\pi$
$463$	9.02239	−	1.59089i	0.419306	−	0.0739350i	0.379321	+	0.925265i	$0.376158\pi$
$464$	10.0124	−	11.4653i	0.464816	−	0.532262i
$465$	1.29024	+	1.86681i	0.0598333	+	0.0865712i
$466$	−1.83327	+	6.70934i	−0.0849247	+	0.310804i
$467$	10.9588	−	18.9812i	0.507113	−	0.878345i	−0.492853	−	0.870112i	$-0.664046\pi$
$467$	10.9588	−	18.9812i	0.507113	−	0.878345i	0.999966	−	0.00823285i	$-0.00262063\pi$
$468$	7.51833	−	6.03090i	0.347535	−	0.278778i
$469$	−16.0114	−	27.7325i	−0.739336	−	1.28057i
$470$	9.87383	−	2.59356i	0.455446	−	0.119632i
$471$	23.0050	−	10.5569i	1.06001	−	0.486434i
$472$	1.95329	+	4.35596i	0.0899077	+	0.200499i
$473$	9.21224	+	10.9787i	0.423579	+	0.504802i
$474$	7.14277	+	6.12911i	0.328078	+	0.281519i
$475$	1.89117	+	5.19595i	0.0867729	+	0.238407i
$476$	−10.8376	−	30.7152i	−0.496739	−	1.40783i
$477$	−18.1004	−	0.221067i	−0.828759	−	0.0101219i
$478$	−6.49028	−	4.59241i	−0.296859	−	0.210052i
$479$	5.05595	−	28.6737i	0.231012	−	1.31014i	−0.619839	−	0.784729i	$-0.712802\pi$
$479$	5.05595	−	28.6737i	0.231012	−	1.31014i	0.850851	−	0.525406i	$-0.176087\pi$
$480$	−18.8971	−	7.54399i	−0.862529	−	0.344334i
$481$	−2.75386	−	1.00232i	−0.125565	−	0.0457020i
$482$	−0.754733	+	0.0622818i	−0.0343772	+	0.00283686i
$483$	18.0366	+	18.2582i	0.820692	+	0.830777i
$484$	10.8799	+	13.2290i	0.494542	+	0.601319i
$485$			29.3682i			1.33354i
$486$	−0.781639	+	22.0315i	−0.0354559	+	0.999371i
$487$		−	18.3923i		−	0.833436i	−0.909036	−	0.416718i	$-0.863180\pi$
$487$		−	18.3923i		−	0.833436i	0.909036	−	0.416718i	$-0.136820\pi$
$488$	−22.9065	+	15.5394i	−1.03693	+	0.703436i
$489$	−6.31763	−	6.39526i	−0.285693	−	0.289204i
$490$	−1.98108	−	24.0068i	−0.0894962	−	1.08452i
$491$	20.6040	+	7.49924i	0.929845	+	0.338436i	0.762148	−	0.647403i	$-0.224145\pi$
$491$	20.6040	+	7.49924i	0.929845	+	0.338436i	0.167697	+	0.985839i	$0.446367\pi$
$492$	1.93846	−	18.7103i	0.0873925	−	0.843525i
$493$	2.76010	−	15.6533i	0.124309	−	0.704990i
$494$	10.5554	−	14.9176i	0.474911	−	0.671175i
$495$	−9.72261	−	0.118746i	−0.436999	−	0.00533723i
$496$	2.49342	−	0.389112i	0.111958	−	0.0174717i
$497$	18.4510	+	50.6937i	0.827641	+	2.27392i
$498$	20.4114	−	23.7872i	0.914659	−	1.06593i
$499$	−2.64022	−	3.14650i	−0.118193	−	0.140857i	0.703704	−	0.710494i	$-0.251528\pi$
$499$	−2.64022	−	3.14650i	−0.118193	−	0.140857i	−0.821896	+	0.569637i	$0.807084\pi$
$500$	11.6086	+	20.5726i	0.519151	+	0.920033i
$501$	24.5438	−	11.2630i	1.09654	−	0.503195i
$502$	−3.73077	−	14.2032i	−0.166512	−	0.633921i
$503$	−6.75419	−	11.6986i	−0.301155	−	0.521615i	0.675243	−	0.737595i	$-0.264039\pi$
$503$	−6.75419	−	11.6986i	−0.301155	−	0.521615i	−0.976398	+	0.215980i	$0.930705\pi$
$504$	−27.6033	+	18.2374i	−1.22955	+	0.812360i
$505$	−3.65181	+	6.32511i	−0.162503	+	0.281464i
$506$	8.09149	+	2.21093i	0.359710	+	0.0982879i
$507$	−10.2610	−	14.8463i	−0.455705	−	0.659347i
$508$	−7.40248	+	12.5343i	−0.328432	+	0.556121i
$509$	21.5105	−	3.79288i	0.953436	−	0.168116i	0.324771	−	0.945793i	$-0.394713\pi$
$509$	21.5105	−	3.79288i	0.953436	−	0.168116i	0.628665	+	0.777676i	$0.283602\pi$
$510$	−20.9636	+	3.45832i	−0.928284	+	0.153137i
$511$	−5.01045	+	5.97122i	−0.221649	+	0.264151i
$512$	−16.6941	+	15.2744i	−0.737783	+	0.675038i
$513$	10.0768	+	40.5655i	0.444902	+	1.79101i
$514$	14.5062	+	1.34124i	0.639839	+	0.0591595i
$515$	−11.1531	−	9.35856i	−0.491464	−	0.412387i
$516$	13.9022	−	28.6114i	0.612009	−	1.25954i
$517$	−0.942069	−	5.34274i	−0.0414321	−	0.234973i
$518$	9.09585	+	4.29620i	0.399649	+	0.188764i
$519$	−20.1507	−	9.54666i	−0.884518	−	0.419052i
$520$	4.11369	−	8.49154i	0.180397	−	0.372379i
$521$	−9.60080	−	5.54303i	−0.420619	−	0.242844i	0.274723	−	0.961523i	$-0.411414\pi$
$521$	−9.60080	−	5.54303i	−0.420619	−	0.242844i	−0.695342	+	0.718679i	$0.744747\pi$
$522$	−16.1054	+	1.13120i	−0.704915	+	0.0495115i
$523$	−32.2601	+	18.6254i	−1.41064	+	0.814432i	−0.995448	−	0.0953038i	$-0.969618\pi$
$523$	−32.2601	+	18.6254i	−1.41064	+	0.814432i	−0.415189	+	0.909735i	$0.636284\pi$
$524$	−2.27011	+	0.377235i	−0.0991701	+	0.0164796i
$525$	4.62187	+	0.432816i	0.201715	+	0.0188896i
$526$	11.9477	+	17.2434i	0.520945	+	0.751850i
$527$	2.01867	−	1.69386i	0.0879344	−	0.0737858i
$528$	−4.82135	+	9.67857i	−0.209822	+	0.421206i
$529$	8.04118	−	2.92675i	0.349617	−	0.127250i
$530$	−16.0973	+	7.40985i	−0.699220	+	0.321863i
$531$	1.78978	−	4.73658i	0.0776698	−	0.205550i
$532$	−40.7925	+	47.6521i	−1.76858	+	2.06598i
$533$	8.59032	+	1.51470i	0.372088	+	0.0656091i
$534$	12.2673	−	20.7161i	0.530857	−	0.896473i
$535$	6.34274	−	17.4265i	0.274221	−	0.753415i
$536$	−2.36677	+	23.1093i	−0.102229	+	0.998168i
$537$	−24.1852	−	6.63896i	−1.04367	−	0.286492i
$538$	−10.7235	−	10.8298i	−0.462322	−	0.466904i
$539$	−12.8011			−0.551382
$540$	8.56597	+	19.8087i	0.368621	+	0.852432i
$541$	−26.5037			−1.13948			−0.569741	−	0.821825i	$-0.692956\pi$
$541$	−26.5037			−1.13948			−0.569741	+	0.821825i	$0.692956\pi$
$542$	6.73607	+	6.80284i	0.289339	+	0.292207i
$543$	−1.74614	−	6.67958i	−0.0749342	−	0.286648i
$544$	−6.67619	+	22.6651i	−0.286239	+	0.971759i
$545$	2.74384	−	7.53865i	0.117533	−	0.322920i
$546$	−7.52379	−	13.3703i	−0.321988	−	0.572194i
$547$	−25.2688	−	4.45558i	−1.08042	−	0.190507i	−0.395017	−	0.918674i	$-0.629261\pi$
$547$	−25.2688	−	4.45558i	−1.08042	−	0.190507i	−0.685400	+	0.728167i	$0.740373\pi$
$548$	−27.3872	−	23.4448i	−1.16992	−	1.00151i
$549$	28.8486	+	5.45087i	1.23123	+	0.232637i
$550$	1.37819	−	0.634405i	0.0587662	−	0.0270511i
$551$	−28.7652	+	10.4697i	−1.22544	+	0.446023i
$552$	−2.84907	−	18.3986i	−0.121265	−	0.783097i
$553$	11.4765	−	9.62995i	0.488031	−	0.409507i
$554$	−14.3969	−	20.7783i	−0.611667	−	0.882785i
$555$	3.79657	−	5.35221i	0.161155	−	0.227188i
$556$	1.15477	+	6.94913i	0.0489732	+	0.294709i
$557$	37.6968	−	21.7643i	1.59727	−	0.922182i	0.605255	−	0.796032i	$-0.293071\pi$
$557$	37.6968	−	21.7643i	1.59727	−	0.922182i	0.992011	−	0.126150i	$-0.0402620\pi$
$558$	−2.16596	−	1.57264i	−0.0916925	−	0.0665752i
$559$	12.7748	+	7.37554i	0.540317	+	0.311952i
$560$	−16.7440	+	27.7238i	−0.707563	+	1.17154i
$561$	0.915379	+	11.2539i	0.0386473	+	0.475140i
$562$	13.5283	+	6.38975i	0.570656	+	0.269535i
$563$	6.63186	+	37.6111i	0.279500	+	1.58512i	0.724296	+	0.689489i	$0.242165\pi$
$563$	6.63186	+	37.6111i	0.279500	+	1.58512i	−0.444796	+	0.895632i	$0.646724\pi$
$564$	−9.97281	+	6.74830i	−0.419931	+	0.284155i
$565$	−0.865056	−	0.725868i	−0.0363932	−	0.0305375i
$566$	7.99329	+	0.739060i	0.335983	+	0.0310650i
$567$	34.3986	+	6.93565i	1.44461	+	0.291270i
$568$	10.6869	−	37.6472i	0.448413	−	1.57964i
$569$	9.07986	−	10.8210i	0.380648	−	0.453638i	−0.541371	−	0.840784i	$-0.682095\pi$
$569$	9.07986	−	10.8210i	0.380648	−	0.453638i	0.922019	+	0.387146i	$0.126539\pi$
$570$	25.9545	+	31.6340i	1.08712	+	1.32500i
$571$	21.7388	−	3.83314i	0.909742	−	0.160412i	0.300856	−	0.953670i	$-0.402728\pi$
$571$	21.7388	−	3.83314i	0.909742	−	0.160412i	0.608886	+	0.793257i	$0.291617\pi$
$572$	−4.31751	−	2.54982i	−0.180524	−	0.106613i
$573$	15.8667	−	1.29058i	0.662842	−	0.0539147i
$574$	−28.8828	−	7.89197i	−1.20554	−	0.329405i
$575$	−1.30616	+	2.26234i	−0.0544707	+	0.0943461i
$576$	23.9790	+	1.00294i	0.999126	+	0.0417890i
$577$	−15.4757	−	26.8047i	−0.644262	−	1.11589i	−0.984471	−	0.175544i	$-0.943831\pi$
$577$	−15.4757	−	26.8047i	−0.644262	−	1.11589i	0.340210	−	0.940350i	$-0.389502\pi$
$578$	0.160322	+	0.610352i	0.00666850	+	0.0253873i
$579$	−4.41461	−	3.13149i	−0.183465	−	0.130140i
$580$	−13.7651	+	7.76730i	−0.571566	+	0.322520i
$581$	−32.0701	−	38.2196i	−1.33049	−	1.58562i
$582$	−11.4877	−	32.6801i	−0.476181	−	1.35464i
$583$	3.22088	+	8.84929i	0.133395	+	0.366500i
$584$	5.48299	−	1.38256i	0.226888	−	0.0572107i
$585$	−9.44541	+	3.30778i	−0.390520	+	0.136760i
$586$	18.1405	−	25.6373i	0.749378	−	1.05907i
$587$	−5.12957	+	29.0912i	−0.211720	+	1.20072i	0.674788	+	0.738011i	$0.264235\pi$
$587$	−5.12957	+	29.0912i	−0.211720	+	1.20072i	−0.886508	+	0.462712i	$0.846876\pi$
$588$	11.5950	+	25.9392i	0.478171	+	1.06971i
$589$	−4.76895	−	1.73576i	−0.196501	−	0.0715206i
$590$	−0.407666	−	4.94011i	−0.0167833	−	0.203381i
$591$	−28.0250	+	7.32614i	−1.15279	+	0.301357i
$592$	−3.52332	−	6.39045i	−0.144808	−	0.262646i
$593$			21.9478i			0.901289i	0.892704	+	0.450644i	$0.148806\pi$
$593$			21.9478i			0.901289i	−0.892704	+	0.450644i	$0.851194\pi$
$594$	10.8655	−	3.67097i	0.445817	−	0.150622i
$595$			33.8199i			1.38648i
$596$	23.6613	−	19.4598i	0.969206	−	0.797104i
$597$	−9.28029	+	33.8074i	−0.379817	+	1.38364i
$598$	8.60431	−	0.710042i	0.351856	−	0.0290358i
$599$	−17.4194	−	6.34015i	−0.711739	−	0.259052i	−0.0393241	−	0.999227i	$-0.512520\pi$
$599$	−17.4194	−	6.34015i	−0.711739	−	0.259052i	−0.672414	+	0.740175i	$0.734743\pi$
$600$	−2.53385	−	2.21803i	−0.103444	−	0.0905506i
$601$	−6.30431	+	35.7535i	−0.257158	+	1.45842i	0.533314	+	0.845917i	$0.320947\pi$
$601$	−6.30431	+	35.7535i	−0.257158	+	1.45842i	−0.790472	+	0.612498i	$0.790165\pi$
$602$	−41.3330	−	29.2465i	−1.68461	−	1.19200i
$603$	19.0668	−	15.6061i	0.776460	−	0.635531i
$604$	8.79239	−	3.10231i	0.357757	−	0.126231i
$605$	−6.08285	−	16.7125i	−0.247303	−	0.679459i
$606$	1.58949	−	8.46685i	0.0645685	−	0.343942i
$607$	0.359975	+	0.429002i	0.0146109	+	0.0174126i	0.773300	−	0.634040i	$-0.218604\pi$
$607$	0.359975	+	0.429002i	0.0146109	+	0.0174126i	−0.758689	+	0.651452i	$0.774160\pi$
$608$	44.2308	−	10.6901i	1.79379	−	0.433542i
$609$	−2.39610	+	25.5871i	−0.0970951	+	1.03684i
$610$	27.7983	−	7.30180i	1.12552	−	0.295641i
$611$	−2.79195	−	4.83580i	−0.112950	−	0.195636i
$612$	21.9750	−	12.0485i	0.888285	−	0.487031i
$613$	−2.29929	+	3.98248i	−0.0928673	+	0.160851i	−0.908717	−	0.417414i	$-0.862937\pi$
$613$	−2.29929	+	3.98248i	−0.0928673	+	0.160851i	0.815849	+	0.578265i	$0.196270\pi$
$614$	10.8489	−	39.7045i	0.437827	−	1.60234i
$615$	−8.36237	+	17.6509i	−0.337203	+	0.711755i
$616$	13.9513	+	10.0796i	0.562114	+	0.406120i
$617$	31.2585	−	5.51173i	1.25842	−	0.221894i	0.495628	−	0.868535i	$-0.334938\pi$
$617$	31.2585	−	5.51173i	1.25842	−	0.221894i	0.762794	+	0.646641i	$0.223827\pi$
$618$	16.0716	+	6.05128i	0.646493	+	0.243418i
$619$	−18.8124	+	22.4198i	−0.756134	+	0.901126i	−0.997597	−	0.0692842i	$-0.977928\pi$
$619$	−18.8124	+	22.4198i	−0.756134	+	0.901126i	0.241463	+	0.970410i	$0.422373\pi$
$620$	−2.57593	−	0.480448i	−0.103452	−	0.0192953i
$621$	−11.6210	+	15.9658i	−0.466334	+	0.640686i
$622$	−0.761519	+	8.23620i	−0.0305341	+	0.330241i
$623$	−29.3569	−	24.6333i	−1.17616	−	0.986914i
$624$	−1.25603	+	11.0583i	−0.0502815	+	0.442685i
$625$	−3.66234	−	20.7701i	−0.146493	−	0.830806i
$626$	−9.20258	+	19.4836i	−0.367809	+	0.778720i
$627$	17.8884	−	12.3635i	0.714393	−	0.493750i
$628$	−10.2667	+	27.3647i	−0.409686	+	1.09197i
$629$	−6.59915	−	3.81002i	−0.263125	−	0.151915i
$630$	33.3295	−	8.32091i	1.32788	−	0.331513i
$631$	35.5567	−	20.5286i	1.41549	−	0.817232i	0.419590	−	0.907714i	$-0.362174\pi$
$631$	35.5567	−	20.5286i	1.41549	−	0.817232i	0.995898	+	0.0904814i	$0.0288406\pi$
$632$	−10.8395	+	0.786940i	−0.431171	+	0.0313028i
$633$	−6.98623	−	15.2240i	−0.277678	−	0.605101i
$634$	−14.7570	+	10.2249i	−0.586076	+	0.406082i
$635$	11.5789	−	9.71582i	0.459493	−	0.385561i
$636$	15.0141	−	14.5421i	0.595349	−	0.576632i
$637$	−12.3811	+	4.50635i	−0.490557	+	0.178548i
$638$	3.51212	+	7.62977i	0.139046	+	0.302066i
$639$	−36.1983	+	20.3138i	−1.43198	+	0.803600i
$640$	21.6237	−	9.18859i	0.854752	−	0.363211i
$641$	−22.4050	−	3.95061i	−0.884944	−	0.156040i	−0.287338	−	0.957829i	$-0.592770\pi$
$641$	−22.4050	−	3.95061i	−0.884944	−	0.156040i	−0.597606	+	0.801790i	$0.703881\pi$
$642$	−0.241437	+	21.8728i	−0.00952875	+	0.863250i
$643$	2.16758	−	5.95537i	0.0854809	−	0.234857i	−0.889586	−	0.456768i	$-0.849007\pi$
$643$	2.16758	−	5.95537i	0.0854809	−	0.234857i	0.975067	+	0.221911i	$0.0712293\pi$
$644$	−29.6337	−	0.292280i	−1.16773	−	0.0115174i
$645$	−23.4977	+	23.2125i	−0.925221	+	0.913990i
$646$	33.7644	−	33.4330i	1.32844	−	1.31540i
$647$	18.0068			0.707921			0.353961	−	0.935260i	$-0.384835\pi$
$647$	18.0068			0.707921			0.353961	+	0.935260i	$0.384835\pi$
$648$	−17.2804	−	18.6919i	−0.678838	−	0.734288i
$649$	−2.63420			−0.103401
$650$	1.10964	−	1.09875i	0.0435237	−	0.0430966i
$651$	−3.03105	+	2.99425i	−0.118796	+	0.117354i
$652$	10.3797	+	0.102376i	0.406501	+	0.00400937i
$653$	7.29835	−	20.0521i	0.285607	−	0.784698i	−0.711061	−	0.703130i	$-0.751785\pi$
$653$	7.29835	−	20.0521i	0.285607	−	0.784698i	0.996668	−	0.0815677i	$-0.0259927\pi$
$654$	−0.104445	+	9.46208i	−0.00408411	+	0.369997i
$655$	2.35317	+	0.414927i	0.0919459	+	0.0162126i
$656$	13.6307	+	16.9109i	0.532190	+	0.660262i
$657$	−5.15708	−	3.06202i	−0.201197	−	0.119461i
$658$	8.01457	+	17.4110i	0.312440	+	0.678750i
$659$	20.6155	−	7.50342i	0.803065	−	0.292292i	0.0923092	−	0.995730i	$-0.470575\pi$
$659$	20.6155	−	7.50342i	0.803065	−	0.292292i	0.710756	+	0.703439i	$0.248353\pi$
$660$	8.06484	−	7.81129i	0.313923	−	0.304054i
$661$	−3.68314	+	3.09052i	−0.143258	+	0.120207i	−0.711600	−	0.702585i	$-0.752029\pi$
$661$	−3.68314	+	3.09052i	−0.143258	+	0.120207i	0.568343	+	0.822792i	$0.307585\pi$
$662$	−3.15601	+	2.18675i	−0.122662	+	0.0849903i
$663$	4.84704	+	10.5624i	0.188243	+	0.410211i
$664$	2.62070	+	36.0981i	0.101703	+	1.40088i
$665$	56.4065	−	32.5663i	2.18735	−	1.26287i
$666$	−2.13114	+	7.44085i	−0.0825801	+	0.288327i
$667$	−12.5245	−	7.23102i	−0.484950	−	0.279986i
$668$	−10.9535	+	29.1953i	−0.423803	+	1.12960i
$669$	−31.1626	+	21.5379i	−1.20482	+	0.832704i
$670$	10.3016	−	21.8104i	0.397985	−	0.842608i
$671$	−2.65225	−	15.0417i	−0.102389	−	0.580678i
$672$	7.78777	−	37.3999i	0.300420	−	1.44273i
$673$	7.58757	+	6.36672i	0.292479	+	0.245419i	0.777206	−	0.629247i	$-0.216636\pi$
$673$	7.58757	+	6.36672i	0.292479	+	0.245419i	−0.484727	+	0.874666i	$0.661081\pi$
$674$	−0.792243	+	8.56849i	−0.0305160	+	0.330046i
$675$	0.246069	+	3.56329i	0.00947121	+	0.137151i
$676$	20.4858	+	3.82089i	0.787914	+	0.146957i
$677$	−1.36103	+	1.62201i	−0.0523085	+	0.0623388i	−0.791564	−	0.611086i	$-0.790733\pi$
$677$	−1.36103	+	1.62201i	−0.0523085	+	0.0623388i	0.739256	+	0.673425i	$0.235177\pi$
$678$	1.24654	+	0.469349i	0.0478732	+	0.0180253i
$679$	−54.3013	+	9.57479i	−2.08389	+	0.367447i
$680$	14.3678	−	19.8866i	0.550980	−	0.762616i
$681$	3.63280	−	7.66796i	0.139209	−	0.293837i
$682$	−0.367037	+	1.34327i	−0.0140546	+	0.0514364i
$683$	−8.83350	+	15.3001i	−0.338004	+	0.585441i	−0.984057	−	0.177852i	$-0.943085\pi$
$683$	−8.83350	+	15.3001i	−0.338004	+	0.585441i	0.646053	+	0.763293i	$0.276419\pi$
$684$	−41.2555	−	25.0491i	−1.57744	−	0.957774i
$685$	18.7169	+	32.4187i	0.715137	+	1.23865i
$686$	6.41072	−	1.68391i	0.244763	−	0.0642919i
$687$	−3.41790	+	36.4985i	−0.130401	+	1.39250i
$688$	11.8795	+	34.7570i	0.452903	+	1.32510i
$689$	6.23040	+	7.42510i	0.237359	+	0.282874i
$690$	−3.56685	+	18.9998i	−0.135788	+	0.723311i
$691$	−13.8889	−	38.1594i	−0.528358	−	1.45165i	−0.861003	−	0.508600i	$-0.830163\pi$
$691$	−13.8889	−	38.1594i	−0.528358	−	1.45165i	0.332644	−	0.943052i	$-0.392059\pi$
$692$	24.2802	−	8.56702i	0.922993	−	0.325669i
$693$	−2.95026	−	18.0156i	−0.112071	−	0.684358i
$694$	39.1399	+	27.6947i	1.48573	+	1.05128i
$695$	1.27015	−	7.20339i	0.0481796	−	0.273240i
$696$	12.2792	−	14.0276i	0.465441	−	0.531716i
$697$	21.3130	+	7.75730i	0.807287	+	0.293829i
$698$	−11.1903	+	0.923440i	−0.423559	+	0.0349527i
$699$	−2.25494	+	8.21459i	−0.0852898	+	0.310704i
$700$	−4.13996	+	3.40482i	−0.156476	+	0.128690i
$701$		−	20.3598i		−	0.768979i	−0.923129	−	0.384490i	$-0.874377\pi$
$701$		−	20.3598i		−	0.768979i	0.923129	−	0.384490i	$-0.125623\pi$
$702$	9.21671	−	7.37549i	0.347862	−	0.278370i
$703$			14.6752i			0.553485i
$704$	−3.92140	−	11.8539i	−0.147793	−	0.446763i
$705$	12.0966	−	3.16224i	0.455586	−	0.119097i
$706$	−1.36237	−	16.5092i	−0.0512734	−	0.621332i
$707$	−12.8856	−	4.68997i	−0.484613	−	0.176385i
$708$	2.38602	+	5.33775i	0.0896720	+	0.200605i
$709$	3.17526	−	18.0078i	0.119249	−	0.676296i	−0.865309	−	0.501239i	$-0.832878\pi$
$709$	3.17526	−	18.0078i	0.119249	−	0.676296i	0.984558	−	0.175057i	$-0.0560111\pi$
$710$	−23.4713	+	33.1711i	−0.880860	+	1.24489i
$711$	8.73925	+	7.51687i	0.327747	+	0.281905i
$712$	6.79720	+	26.9565i	0.254736	+	1.01024i
$713$	−0.820042	−	2.25305i	−0.0307108	−	0.0843773i
$714$	−13.2290	−	37.6338i	−0.495084	−	1.40841i
$715$	3.34666	+	3.98839i	0.125158	+	0.149157i
$716$	25.2215	−	14.2318i	0.942571	−	0.531868i
$717$	−7.94233	−	5.63387i	−0.296612	−	0.210401i
$718$	−8.46791	−	32.2377i	−0.316020	−	1.20310i
$719$	14.2069	+	24.6070i	0.529827	+	0.917687i	0.999395	+	0.0347903i	$0.0110763\pi$
$719$	14.2069	+	24.6070i	0.529827	+	0.917687i	−0.469568	+	0.882896i	$0.655590\pi$
$720$	−23.1332	−	9.26665i	−0.862124	−	0.345347i
$721$	13.6676	−	23.6730i	0.509008	−	0.881628i
$722$	−62.3543	−	17.0378i	−2.32059	−	0.634081i
$723$	−0.924445	+	0.0751932i	−0.0343805	+	0.00279646i
$724$	6.86439	+	4.05395i	0.255113	+	0.150664i
$725$	−2.57607	+	0.454231i	−0.0956729	+	0.0168697i
$726$	13.3061	+	16.2178i	0.493836	+	0.601899i
$727$	15.5596	−	18.5432i	0.577074	−	0.687730i	−0.395993	−	0.918254i	$-0.629599\pi$
$727$	15.5596	−	18.5432i	0.577074	−	0.687730i	0.973067	+	0.230524i	$0.0740439\pi$
$728$	17.0419	+	4.83767i	0.631614	+	0.179296i
$729$	−0.989012	+	26.9819i	−0.0366301	+	0.999329i
$730$	−5.84648	−	0.540566i	−0.216388	−	0.0200072i
$731$	29.3818	+	24.6543i	1.08673	+	0.911871i
$732$	−28.0770	+	18.9988i	−1.03775	+	0.702218i
$733$	−1.48552	−	8.42479i	−0.0548689	−	0.311177i	0.945005	−	0.327056i	$-0.106056\pi$
$733$	−1.48552	−	8.42479i	−0.0548689	−	0.311177i	−0.999874	+	0.0158789i	$0.994945\pi$
$734$	−31.6064	−	14.9285i	−1.16661	−	0.551020i
$735$	−2.39177	−	29.4051i	−0.0882218	−	1.08462i
$736$	17.3008	+	12.7612i	0.637718	+	0.470385i
$737$	−11.1010	−	6.40916i	−0.408910	−	0.236084i
$738$	2.40104	−	22.9125i	0.0883836	−	0.843421i
$739$	26.7466	−	15.4422i	0.983891	−	0.568050i	0.0804485	−	0.996759i	$-0.474365\pi$
$739$	26.7466	−	15.4422i	0.983891	−	0.568050i	0.903443	+	0.428709i	$0.141031\pi$
$740$	1.24210	+	7.47466i	0.0456605	+	0.274774i
$741$	12.9492	−	18.2551i	0.475699	−	0.670616i
$742$	−18.9488	−	27.3477i	−0.695632	−	1.00397i
$743$	−9.26330	+	7.77283i	−0.339837	+	0.285157i	−0.796694	−	0.604383i	$-0.793420\pi$
$743$	−9.26330	+	7.77283i	−0.339837	+	0.285157i	0.456857	+	0.889540i	$0.348975\pi$
$744$	3.05436	−	0.472975i	0.111978	−	0.0173401i
$745$	−29.8919	+	10.8797i	−1.09515	+	0.398603i
$746$	24.3497	−	11.2086i	0.891504	−	0.410375i
$747$	25.0330	−	29.1038i	0.915910	−	1.06485i
$748$	−9.90440	−	8.47864i	−0.362141	−	0.310010i
$749$	34.2892	+	6.04612i	1.25290	+	0.220920i
$750$	14.1879	+	25.2128i	0.518069	+	0.920643i
$751$	−17.8334	+	48.9969i	−0.650750	+	1.78792i	−0.0357937	+	0.999359i	$0.511396\pi$
$751$	−17.8334	+	48.9969i	−0.650750	+	1.78792i	−0.614956	+	0.788561i	$0.710826\pi$
$752$	2.68407	−	13.6427i	0.0978779	−	0.497500i
$753$	−4.54880	−	17.4007i	−0.165768	−	0.634116i
$754$	6.08278	+	6.14307i	0.221522	+	0.223717i
$755$	−9.68114			−0.352333
$756$	−33.8333	+	22.2965i	−1.23050	+	0.810915i
$757$	31.0004			1.12673			0.563365	−	0.826208i	$-0.309507\pi$
$757$	31.0004			1.12673			0.563365	+	0.826208i	$0.309507\pi$
$758$	−8.58103	−	8.66609i	−0.311677	−	0.314766i
$759$	9.90682	+	2.71947i	0.359595	+	0.0987105i
$760$	−47.0031	−	4.81389i	−1.70498	−	0.174618i
$761$	−13.5388	+	37.1974i	−0.490779	+	1.34841i	0.409189	+	0.912450i	$0.365812\pi$
$761$	−13.5388	+	37.1974i	−0.490779	+	1.34841i	−0.899968	+	0.435956i	$0.856410\pi$
$762$	−9.08418	+	15.3407i	−0.329085	+	0.555735i
$763$	14.8334	+	2.61553i	0.537005	+	0.0946884i
$764$	−11.9539	+	13.9641i	−0.432477	+	0.505202i
$765$	−25.6800	+	4.20539i	−0.928463	+	0.152046i
$766$	−38.8247	+	17.8717i	−1.40279	+	0.645730i
$767$	−2.54777	+	0.927313i	−0.0919947	+	0.0334833i
$768$	−20.4680	+	18.6832i	−0.738576	+	0.674170i
$769$	−37.1336	+	31.1588i	−1.33907	+	1.12361i	−0.357208	+	0.934025i	$0.616271\pi$
$769$	−37.1336	+	31.1588i	−1.33907	+	1.12361i	−0.981863	+	0.189590i	$0.939284\pi$
$770$	−10.1783	−	14.6898i	−0.366802	−	0.529385i
$771$	17.7644	+	1.66355i	0.639769	+	0.0599113i
$772$	6.16526	−	1.02451i	0.221892	−	0.0368729i
$773$	−35.9391	+	20.7494i	−1.29264	+	0.746306i	−0.979121	−	0.203277i	$-0.934841\pi$
$773$	−35.9391	+	20.7494i	−1.29264	+	0.746306i	−0.313518	+	0.949582i	$0.601508\pi$
$774$	17.0678	−	35.0216i	0.613488	−	1.25882i
$775$	−0.375571	−	0.216836i	−0.0134909	−	0.00778899i
$776$	35.9977	+	17.4389i	1.29224	+	0.626020i
$777$	11.1339	+	5.27483i	0.399427	+	0.189234i
$778$	36.0990	+	17.0505i	1.29421	+	0.611289i
$779$	−7.58500	−	43.0167i	−0.271761	−	1.54123i
$780$	5.05043	−	10.3940i	0.180834	−	0.372166i
$781$	16.5423	+	13.8806i	0.591929	+	0.496687i
$782$	22.3533	+	2.06679i	0.799354	+	0.0739082i
$783$	−19.7266	+	1.36226i	−0.704973	+	0.0486832i
$784$	−30.6024	−	11.8270i	−1.09294	−	0.422393i
$785$	19.5073	−	23.2478i	0.696244	−	0.829751i
$786$	−2.78084	+	0.458749i	−0.0991894	+	0.0163630i
$787$	13.0966	−	2.30928i	0.466843	−	0.0823170i	0.0647215	−	0.997903i	$-0.479384\pi$
$787$	13.0966	−	2.30928i	0.466843	−	0.0823170i	0.402121	+	0.915586i	$0.368273\pi$
$788$	17.0088	−	28.8004i	0.605914	−	1.02597i
$789$	14.6081	+	21.1360i	0.520061	+	0.752462i
$790$	10.8857	+	2.97441i	0.387294	+	0.105825i
$791$	1.06009	−	1.83612i	0.0376924	−	0.0652851i
$792$	−5.91885	+	11.8468i	−0.210317	+	0.420959i
$793$	−7.86033	−	13.6145i	−0.279128	−	0.483465i
$794$	1.64189	+	6.25077i	0.0582686	+	0.221832i
$795$	−19.7257	+	9.05201i	−0.699598	+	0.321042i
$796$	−19.8940	−	35.2559i	−0.705124	−	1.24961i
$797$	11.9713	+	14.2669i	0.424047	+	0.505359i	0.935195	−	0.354133i	$-0.115224\pi$
$797$	11.9713	+	14.2669i	0.424047	+	0.505359i	−0.511148	+	0.859493i	$0.670780\pi$
$798$	−50.0289	+	58.3029i	−1.77100	+	2.06390i
$799$	−4.96582	−	13.6435i	−0.175678	−	0.482671i
$800$	3.88084	−	0.243295i	0.137208	−	0.00860178i
$801$	15.0541	−	25.3542i	0.531910	−	0.895848i
$802$	−2.03054	+	2.86968i	−0.0717008	+	0.101332i
$803$	−0.541816	+	3.07279i	−0.0191203	+	0.108437i
$804$	−2.93194	+	28.2995i	−0.103402	+	0.998048i
$805$	28.9156	+	10.5244i	1.01914	+	0.370937i
$806$	0.117874	+	1.42840i	0.00415194	+	0.0503133i
$807$	−13.1179	−	13.2791i	−0.461773	−	0.467447i
$808$	5.58446	+	8.23200i	0.196461	+	0.289601i
$809$			28.0309i			0.985513i	0.870167	+	0.492756i	$0.164011\pi$
$809$			28.0309i			0.985513i	−0.870167	+	0.492756i	$0.835989\pi$
$810$	10.4626	+	24.2730i	0.367619	+	0.852865i
$811$			0.0696662i			0.00244631i	0.999999	+	0.00122316i	$0.000389343\pi$
$811$			0.0696662i			0.00244631i	−0.999999	+	0.00122316i	$0.999611\pi$
$812$	−18.8494	−	22.9191i	−0.661484	−	0.804304i
$813$	8.24018	+	8.34143i	0.288996	+	0.292547i
$814$	4.01302	−	0.331161i	0.140656	−	0.0116072i
$815$	−10.1282	−	3.68637i	−0.354776	−	0.129128i
$816$	−8.20923	+	27.7494i	−0.287381	+	0.971422i
$817$	12.8269	−	72.7449i	0.448756	−	2.54502i
$818$	23.7398	+	16.7979i	0.830044	+	0.587325i
$819$	−9.19548	−	16.3860i	−0.321316	−	0.572572i
$820$	−7.50426	−	21.2681i	−0.262060	−	0.742715i
$821$	−0.0220034	−	0.0604539i	−0.000767925	−	0.00210986i	0.939308	−	0.343075i	$-0.111468\pi$
$821$	−0.0220034	−	0.0604539i	−0.000767925	−	0.00210986i	−0.940076	+	0.340965i	$0.889246\pi$
$822$	−33.5086	−	28.7532i	−1.16875	−	1.00288i
$823$	5.54068	+	6.60312i	0.193136	+	0.230170i	0.853918	−	0.520407i	$-0.174220\pi$
$823$	5.54068	+	6.60312i	0.193136	+	0.230170i	−0.660782	+	0.750578i	$0.729775\pi$
$824$	−18.0938	+	8.11361i	−0.630328	+	0.282651i
$825$	1.68884	−	0.775001i	0.0587980	−	0.0269821i
$826$	9.00126	−	2.36437i	0.313194	−	0.0822668i
$827$	−12.0949	−	20.9489i	−0.420580	−	0.728466i	0.575416	−	0.817861i	$-0.304840\pi$
$827$	−12.0949	−	20.9489i	−0.420580	−	0.728466i	−0.995996	+	0.0893948i	$0.971507\pi$
$828$	−3.46291	−	22.5377i	−0.120344	−	0.783239i
$829$	−1.06786	+	1.84960i	−0.0370885	+	0.0642391i	−0.883974	−	0.467536i	$-0.845142\pi$
$829$	−1.06786	+	1.84960i	−0.0370885	+	0.0642391i	0.846885	+	0.531776i	$0.178475\pi$
$830$	9.90553	−	36.2519i	0.343826	−	1.25832i
$831$	−17.6027	−	25.4688i	−0.610630	−	0.883503i
$832$	−7.96566	−	10.0846i	−0.276160	−	0.349620i
$833$	−33.7385	+	5.94900i	−1.16897	+	0.206121i
$834$	1.40430	+	8.51257i	0.0486269	+	0.294766i
$835$	20.8122	−	24.8030i	0.720235	−	0.858342i
$836$	−4.60382	+	24.6834i	−0.159226	+	0.853694i
$837$	−2.65049	−	1.92920i	−0.0916142	−	0.0666829i
$838$	−1.83909	+	19.8906i	−0.0635303	+	0.687111i
$839$	16.5694	+	13.9034i	0.572040	+	0.479999i	0.882322	−	0.470646i	$-0.155979\pi$
$839$	16.5694	+	13.9034i	0.572040	+	0.479999i	−0.310282	+	0.950645i	$0.600424\pi$
$840$	−20.5470	+	33.9305i	−0.708939	+	1.17071i
$841$	2.52114	+	14.2981i	0.0869358	+	0.493037i
$842$	−7.13042	+	15.0964i	−0.245731	+	0.520257i
$843$	16.5595	+	7.84527i	0.570339	+	0.270206i
$844$	18.1092	+	6.79422i	0.623345	+	0.233867i
$845$	−18.7391	−	10.8190i	−0.644645	−	0.372186i
$846$	−12.2239	+	8.25059i	−0.420265	+	0.283661i
$847$	28.9179	−	16.6958i	0.993631	−	0.573673i
$848$	−0.476059	+	24.1309i	−0.0163479	+	0.828660i
$849$	9.78867	+	0.916662i	0.335946	+	0.0314598i
$850$	3.33752	−	2.31251i	0.114476	−	0.0793186i
$851$	−5.31111	+	4.45655i	−0.182063	+	0.152769i
$852$	13.1429	−	46.0929i	0.450269	−	1.57912i
$853$	4.58175	−	1.66762i	0.156876	−	0.0570982i	−0.262388	−	0.964962i	$-0.584510\pi$
$853$	4.58175	−	1.66762i	0.156876	−	0.0570982i	0.419265	+	0.907864i	$0.362288\pi$
$854$	22.5638	+	49.0180i	0.772118	+	1.67736i
$855$	31.7421	+	38.7809i	1.08556	+	1.32628i
$856$	−17.5940	−	18.1224i	−0.601350	−	0.619411i
$857$	−30.6940	−	5.41218i	−1.04849	−	0.184877i	−0.377244	−	0.926114i	$-0.623128\pi$
$857$	−30.6940	−	5.41218i	−1.04849	−	0.184877i	−0.671243	+	0.741237i	$0.734239\pi$
$858$	−5.28417	−	3.12909i	−0.180399	−	0.106825i
$859$	−3.32072	+	9.12361i	−0.113302	+	0.311293i	−0.983363	−	0.181649i	$-0.941857\pi$
$859$	−3.32072	+	9.12361i	−0.113302	+	0.311293i	0.870062	+	0.492943i	$0.164079\pi$
$860$	0.376155	−	38.1376i	0.0128268	−	1.30048i
$861$	−35.3626	−	9.70721i	−1.20516	−	0.330821i
$862$	−39.5525	+	39.1643i	−1.34716	+	1.33394i
$863$	−18.1528			−0.617929			−0.308964	−	0.951074i	$-0.599982\pi$
$863$	−18.1528			−0.617929			−0.308964	+	0.951074i	$0.599982\pi$
$864$	29.3667	+	1.26285i	0.999077	+	0.0429629i
$865$	−26.7344			−0.908997
$866$	−17.7059	+	17.5322i	−0.601672	+	0.595767i
$867$	0.195475	+	0.747756i	0.00663867	+	0.0253951i
$868$	0.0485215	−	4.91949i	0.00164693	−	0.166978i
$869$	2.05107	−	5.63527i	0.0695778	−	0.191164i
$870$	−16.8699	+	9.49315i	−0.571944	+	0.321848i
$871$	−12.9930	−	2.29101i	−0.440250	−	0.0776279i
$872$	−7.61109	−	7.83968i	−0.257744	−	0.265485i
$873$	−14.0225	−	40.0413i	−0.474589	−	1.35519i
$874$	−18.0777	−	39.2722i	−0.611487	−	1.32840i
$875$	43.2733	−	15.7502i	1.46291	−	0.532454i
$876$	6.71725	−	1.68539i	0.226955	−	0.0569441i
$877$	23.5348	−	19.7481i	0.794715	−	0.666845i	−0.152192	−	0.988351i	$-0.548633\pi$
$877$	23.5348	−	19.7481i	0.794715	−	0.666845i	0.946908	+	0.321506i	$0.104189\pi$
$878$	−18.1041	+	12.5440i	−0.610983	+	0.423340i
$879$	22.2544	−	31.3731i	0.750622	−	1.05819i
$880$	−0.255715	+	12.9619i	−0.00862015	+	0.436947i
$881$	−29.9676	+	17.3018i	−1.00963	+	0.582912i	−0.911084	−	0.412220i	$-0.864753\pi$
$881$	−29.9676	+	17.3018i	−1.00963	+	0.582912i	−0.0985488	+	0.995132i	$0.531420\pi$
$882$	14.1636	+	31.7856i	0.476914	+	1.07028i
$883$	−28.5735	−	16.4969i	−0.961575	−	0.555166i	−0.0649179	−	0.997891i	$-0.520679\pi$
$883$	−28.5735	−	16.4969i	−0.961575	−	0.555166i	−0.896658	+	0.442725i	$0.854012\pi$
$884$	−12.5642	−	4.71382i	−0.422578	−	0.158543i
$885$	−0.492177	−	6.05095i	−0.0165443	−	0.203401i
$886$	4.10093	−	8.68243i	0.137773	−	0.291692i
$887$	−0.642373	−	3.64308i	−0.0215688	−	0.122323i	0.972122	−	0.234474i	$-0.0753369\pi$
$887$	−0.642373	−	3.64308i	−0.0215688	−	0.122323i	−0.993691	+	0.112152i	$0.964226\pi$
$888$	−4.30597	−	7.83173i	−0.144499	−	0.262816i
$889$	21.7394	+	18.2415i	0.729116	+	0.611801i
$890$	2.65763	−	28.7436i	0.0890841	−	0.963488i
$891$	13.3127	−	4.48037i	0.445994	−	0.150098i
$892$	8.02012	−	43.0000i	0.268533	−	1.43975i
$893$	−17.9735	+	21.4200i	−0.601461	+	0.716793i
$894$	29.0071	−	23.7992i	0.970142	−	0.795965i
$895$	−29.6133	+	5.22162i	−0.989863	+	0.174540i
$896$	24.0394	+	36.9861i	0.803100	+	1.23562i
$897$	10.5391	−	0.857237i	0.351890	−	0.0286223i
$898$	5.10469	−	18.6820i	0.170346	−	0.623425i
$899$	1.20042	−	2.07919i	0.0400363	−	0.0693450i
$900$	−3.10013	−	2.72016i	−0.103338	−	0.0906721i
$901$	12.6014	+	21.8263i	0.419814	+	0.727140i
$902$	−11.5920	+	3.04488i	−0.385972	+	0.101384i
$903$	−50.5803	−	35.8790i	−1.68321	−	1.19398i
$904$	−1.40339	+	0.629308i	−0.0466762	+	0.0209305i
$905$	−5.32084	−	6.34114i	−0.176871	−	0.210786i
$906$	10.7729	−	3.78689i	0.357905	−	0.125811i
$907$	9.85576	+	27.0785i	0.327255	+	0.899126i	0.988803	+	0.149224i	$0.0476774\pi$
$907$	9.85576	+	27.0785i	0.327255	+	0.899126i	−0.661548	+	0.749903i	$0.730100\pi$
$908$	3.26001	+	9.23934i	0.108187	+	0.306618i
$909$	1.95890	−	10.3674i	0.0649726	−	0.343866i
$910$	−15.0156	−	10.6248i	−0.497763	−	0.352208i
$911$	1.65716	−	9.39822i	0.0549041	−	0.311377i	−0.944971	−	0.327153i	$-0.893911\pi$
$911$	1.65716	−	9.39822i	0.0549041	−	0.311377i	0.999876	+	0.0157761i	$0.00502189\pi$
$912$	54.1867	−	13.0290i	1.79430	−	0.431434i
$913$	−18.7668	−	6.83057i	−0.621092	−	0.226059i
$914$	53.6834	−	4.43004i	1.77569	−	0.146533i
$915$	34.0563	−	8.90283i	1.12587	−	0.294318i
$916$	−26.8875	−	32.6928i	−0.888390	−	1.08020i
$917$			4.48624i			0.148149i
$918$	26.9310	−	14.7247i	0.888856	−	0.485986i
$919$		−	56.1944i		−	1.85368i	−0.375453	−	0.926842i	$-0.622513\pi$
$919$		−	56.1944i		−	1.85368i	0.375453	−	0.926842i	$-0.377487\pi$
$920$	−12.5317	−	18.4728i	−0.413157	−	0.609031i
$921$	13.3443	−	48.6122i	0.439709	−	1.60183i
$922$	0.575972	+	6.97965i	0.0189686	+	0.229862i
$923$	20.8859	+	7.60184i	0.687467	+	0.250217i
$924$	17.0723	+	12.3651i	0.561636	+	0.406780i
$925$	−0.217760	+	1.23498i	−0.00715992	+	0.0406059i
$926$	−7.48375	+	10.5765i	−0.245931	+	0.347566i
$927$	19.6748	+	7.43440i	0.646206	+	0.244178i
$928$	1.34690	+	21.4846i	0.0442142	+	0.705267i
$929$	2.40637	+	6.61143i	0.0789503	+	0.216914i	0.972888	−	0.231277i	$-0.0742905\pi$
$929$	2.40637	+	6.61143i	0.0789503	+	0.216914i	−0.893938	+	0.448192i	$0.852068\pi$
$930$	−3.15416	−	0.592133i	−0.103429	−	0.0194168i
$931$	42.4100	+	50.5422i	1.38993	+	1.65646i
$932$	−4.83388	−	8.56656i	−0.158339	−	0.280607i
$933$	−0.944518	+	10.0861i	−0.0309221	+	0.330205i
$934$	7.87466	+	29.9792i	0.257667	+	0.980950i
$935$	6.76885	+	11.7240i	0.221365	+	0.383416i
$936$	−1.55423	+	13.5417i	−0.0508016	+	0.442625i
$937$	−23.7414	+	41.1212i	−0.775596	+	1.34337i	0.158862	+	0.987301i	$0.449217\pi$
$937$	−23.7414	+	41.1212i	−0.775596	+	1.34337i	−0.934459	+	0.356072i	$0.884116\pi$
$938$	43.6855	+	11.9367i	1.42638	+	0.389747i
$939$	−11.2988	+	23.8491i	−0.368724	+	0.778287i
$940$	−7.34165	+	12.4313i	−0.239458	+	0.405465i
$941$	−5.15723	+	0.909359i	−0.168121	+	0.0296442i	−0.257075	−	0.966391i	$-0.582759\pi$
$941$	−5.15723	+	0.909359i	−0.168121	+	0.0296442i	0.0889540	+	0.996036i	$0.471648\pi$
$942$	−12.6135	+	33.5000i	−0.410969	+	1.09149i
$943$	13.2648	−	15.8084i	0.431961	−	0.514791i
$944$	−6.29733	−	2.43375i	−0.204961	−	0.0792119i
$945$	40.8320	−	10.1430i	1.32827	−	0.329953i
$946$	−20.1820	−	1.86603i	−0.656174	−	0.0606698i
$947$	37.3876	+	31.3719i	1.21493	+	1.01945i	0.999074	+	0.0430267i	$0.0137001\pi$
$947$	37.3876	+	31.3719i	1.21493	+	1.01945i	0.215860	+	0.976424i	$0.430744\pi$
$948$	−13.2767	+	0.948202i	−0.431208	+	0.0307962i
$949$	0.557671	+	3.16271i	0.0181028	+	0.102666i
$950$	−7.07074	−	3.33969i	−0.229405	−	0.108354i
$951$	−18.0883	+	12.5016i	−0.586553	+	0.405393i
$952$	41.4542	+	20.0823i	1.34354	+	0.650871i
$953$	21.3286	+	12.3141i	0.690901	+	0.398892i	0.803950	−	0.594697i	$-0.202728\pi$
$953$	21.3286	+	12.3141i	0.690901	+	0.398892i	−0.113048	+	0.993589i	$0.536061\pi$
$954$	18.4094	−	17.7887i	0.596026	−	0.575932i
$955$	16.5295	−	9.54330i	0.534882	−	0.308814i
$956$	11.0919	−	1.84320i	0.358738	−	0.0596133i
$957$	4.29047	+	9.34957i	0.138691	+	0.302229i
$958$	23.4511	+	33.8457i	0.757672	+	1.09351i
$959$	−53.8393	+	45.1766i	−1.73856	+	1.45883i
$960$	26.4967	−	11.2225i	0.855178	−	0.362206i
$961$	−28.7564	+	10.4665i	−0.927627	+	0.337629i
$962$	3.76478	−	1.73299i	0.121381	−	0.0558739i
$963$	−0.327174	+	26.7882i	−0.0105430	+	0.863238i
$964$	0.696472	−	0.813590i	0.0224319	−	0.0262040i
$965$	−6.39084	−	1.12688i	−0.205728	−	0.0362755i
$966$	−36.2932	−	0.400613i	−1.16772	−	0.0128895i
$967$	−18.4093	+	50.5793i	−0.592005	+	1.62652i	0.174775	+	0.984608i	$0.444080\pi$
$967$	−18.4093	+	50.5793i	−0.592005	+	1.62652i	−0.766779	+	0.641911i	$0.778142\pi$
$968$	−24.0971	−	2.46794i	−0.774509	−	0.0793225i
$969$	41.4009	−	40.8983i	1.32999	−	1.31384i
$970$	−29.2231	−	29.5127i	−0.938296	−	0.947596i
$971$	6.81102			0.218576			0.109288	−	0.994010i	$-0.465143\pi$
$971$	6.81102			0.218576			0.109288	+	0.994010i	$0.465143\pi$
$972$	−21.1371	−	22.9177i	−0.677974	−	0.735086i
$973$	13.7330			0.440261
$974$	18.3014	+	18.4828i	0.586415	+	0.592227i
$975$	1.36061	−	1.34409i	0.0435744	−	0.0430454i
$976$	7.55659	−	38.4091i	0.241881	−	1.22945i
$977$	3.48869	−	9.58509i	0.111613	−	0.306654i	−0.871293	−	0.490764i	$-0.836718\pi$
$977$	3.48869	−	9.58509i	0.111613	−	0.306654i	0.982906	+	0.184109i	$0.0589401\pi$
$978$	12.7124	+	0.140322i	0.406496	+	0.00448700i
$979$	−15.1071	−	2.66378i	−0.482824	−	0.0851348i
$980$	25.8790	+	22.1536i	0.826674	+	0.707672i
$981$	−0.141534	+	11.5885i	−0.00451884	+	0.369992i
$982$	−28.1675	+	12.9660i	−0.898861	+	0.413762i
$983$	47.7474	−	17.3786i	1.52290	−	0.554292i	0.561033	−	0.827793i	$-0.310404\pi$
$983$	47.7474	−	17.3786i	1.52290	−	0.554292i	0.961872	+	0.273501i	$0.0881817\pi$
$984$	16.6698	+	20.7312i	0.531414	+	0.660886i
$985$	−26.6050	+	22.3242i	−0.847705	+	0.711309i
$986$	12.8023	+	18.4768i	0.407707	+	0.588421i
$987$	9.79074	+	21.3355i	0.311643	+	0.679116i
$988$	4.23650	+	25.4942i	0.134781	+	0.811079i
$989$	30.2224	−	17.4489i	0.961018	−	0.554844i
$990$	9.88860	−	9.55522i	0.314280	−	0.303685i
$991$	−13.8256	−	7.98220i	−0.439184	−	0.253563i	0.264067	−	0.964504i	$-0.414936\pi$
$991$	−13.8256	−	7.98220i	−0.439184	−	0.253563i	−0.703251	+	0.710941i	$0.748269\pi$
$992$	−2.11849	+	2.87212i	−0.0672622	+	0.0911898i
$993$	−3.86845	+	2.67366i	−0.122762	+	0.0848461i
$994$	−68.9849	−	32.5833i	−2.18807	−	1.03348i
$995$	7.29906	+	41.3950i	0.231396	+	1.31231i
$996$	3.15774	+	44.2147i	0.100057	+	1.40100i
$997$	29.5349	+	24.7827i	0.935379	+	0.784876i	0.976775	−	0.214267i	$-0.0687361\pi$
$997$	29.5349	+	24.7827i	0.935379	+	0.784876i	−0.0413962	+	0.999143i	$0.513181\pi$
$998$	5.78415	+	0.534803i	0.183094	+	0.0169289i
$999$	−2.62081	+	9.11008i	−0.0829188	+	0.288230i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.2.l.a.11.5	✓	96
3.2	odd	2		324.2.l.a.35.12		96
4.3	odd	2	inner	108.2.l.a.11.6	yes	96
9.2	odd	6		972.2.l.a.755.3		96
9.4	even	3		972.2.l.c.431.8		96
9.5	odd	6		972.2.l.b.431.9		96
9.7	even	3		972.2.l.d.755.14		96
12.11	even	2		324.2.l.a.35.11		96
27.4	even	9		972.2.l.a.215.1		96
27.5	odd	18	inner	108.2.l.a.59.6	yes	96
27.13	even	9		972.2.l.b.539.11		96
27.14	odd	18		972.2.l.c.539.6		96
27.22	even	9		324.2.l.a.287.11		96
27.23	odd	18		972.2.l.d.215.16		96
36.7	odd	6		972.2.l.d.755.16		96
36.11	even	6		972.2.l.a.755.1		96
36.23	even	6		972.2.l.b.431.11		96
36.31	odd	6		972.2.l.c.431.6		96
108.23	even	18		972.2.l.d.215.14		96
108.31	odd	18		972.2.l.a.215.3		96
108.59	even	18	inner	108.2.l.a.59.5	yes	96
108.67	odd	18		972.2.l.b.539.9		96
108.95	even	18		972.2.l.c.539.8		96
108.103	odd	18		324.2.l.a.287.12		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.11.5	✓	96	1.1	even	1	trivial
108.2.l.a.11.6	yes	96	4.3	odd	2	inner
108.2.l.a.59.5	yes	96	108.59	even	18	inner
108.2.l.a.59.6	yes	96	27.5	odd	18	inner
324.2.l.a.35.11		96	12.11	even	2
324.2.l.a.35.12		96	3.2	odd	2
324.2.l.a.287.11		96	27.22	even	9
324.2.l.a.287.12		96	108.103	odd	18
972.2.l.a.215.1		96	27.4	even	9
972.2.l.a.215.3		96	108.31	odd	18
972.2.l.a.755.1		96	36.11	even	6
972.2.l.a.755.3		96	9.2	odd	6
972.2.l.b.431.9		96	9.5	odd	6
972.2.l.b.431.11		96	36.23	even	6
972.2.l.b.539.9		96	108.67	odd	18
972.2.l.b.539.11		96	27.13	even	9
972.2.l.c.431.6		96	36.31	odd	6
972.2.l.c.431.8		96	9.4	even	3
972.2.l.c.539.6		96	27.14	odd	18
972.2.l.c.539.8		96	108.95	even	18
972.2.l.d.215.14		96	108.23	even	18
972.2.l.d.215.16		96	27.23	odd	18
972.2.l.d.755.14		96	9.7	even	3
972.2.l.d.755.16		96	36.7	odd	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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	108.l (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00492 + 0.995056i) q^{2} +(-1.23220 + 1.21724i) q^{3} +(0.0197253 - 1.99990i) q^{4} +(-0.710267 + 1.95144i) q^{5} +(0.0270364 - 2.44934i) q^{6} +(-3.83975 - 0.677051i) q^{7} +(1.97019 + 2.02937i) q^{8} +(0.0366374 - 2.99978i) q^{9} +O(q^{10})\)	\(q+(-1.00492 + 0.995056i) q^{2} +(-1.23220 + 1.21724i) q^{3} +(0.0197253 - 1.99990i) q^{4} +(-0.710267 + 1.95144i) q^{5} +(0.0270364 - 2.44934i) q^{6} +(-3.83975 - 0.677051i) q^{7} +(1.97019 + 2.02937i) q^{8} +(0.0366374 - 2.99978i) q^{9} +(-1.22804 - 2.66780i) q^{10} +(-1.46659 + 0.533796i) q^{11} +(2.41006 + 2.48829i) q^{12} +(-1.23056 + 1.03256i) q^{13} +(4.53234 - 3.14038i) q^{14} +(-1.50019 - 3.26914i) q^{15} +(-3.99922 - 0.0788972i) q^{16} +(-3.61727 + 2.08843i) q^{17} +(2.94813 + 3.05099i) q^{18} +(6.96639 + 4.02205i) q^{19} +(3.88869 + 1.45896i) q^{20} +(5.55548 - 3.83965i) q^{21} +(0.942651 - 1.99577i) q^{22} +(0.659926 + 3.74263i) q^{23} +(-4.89791 - 0.102384i) q^{24} +(0.526570 + 0.441845i) q^{25} +(0.209156 - 2.26212i) q^{26} +(3.60631 + 3.74092i) q^{27} +(-1.42978 + 7.66577i) q^{28} +(-2.44609 + 2.91513i) q^{29} +(4.76055 + 1.79245i) q^{30} +(-0.621314 + 0.109554i) q^{31} +(4.09740 - 3.90017i) q^{32} +(1.15738 - 2.44295i) q^{33} +(1.55696 - 5.69810i) q^{34} +(4.04848 - 7.01217i) q^{35} +(-5.99854 - 0.132443i) q^{36} +(0.912171 + 1.57993i) q^{37} +(-11.0028 + 2.89012i) q^{38} +(0.259418 - 2.77022i) q^{39} +(-5.35956 + 2.40333i) q^{40} +(-3.49040 - 4.15970i) q^{41} +(-1.76214 + 9.38655i) q^{42} +(-3.14069 - 8.62898i) q^{43} +(1.03861 + 2.94357i) q^{44} +(5.82787 + 2.20214i) q^{45} +(-4.38730 - 3.10437i) q^{46} +(-0.603613 + 3.42326i) q^{47} +(5.02388 - 4.77081i) q^{48} +(7.70742 + 2.80527i) q^{49} +(-0.968821 + 0.0799486i) q^{50} +(1.91508 - 6.97647i) q^{51} +(2.04076 + 2.48137i) q^{52} -6.03391i q^{53} +(-7.34648 - 0.170840i) q^{54} -3.24111i q^{55} +(-6.19106 - 9.12619i) q^{56} +(-13.4798 + 3.52382i) q^{57} +(-0.442602 - 5.36347i) q^{58} +(1.58603 + 0.577267i) q^{59} +(-6.56755 + 2.93575i) q^{60} +(-1.69938 + 9.63768i) q^{61} +(0.515357 - 0.728336i) q^{62} +(-2.17168 + 11.4936i) q^{63} +(-0.236673 + 7.99650i) q^{64} +(-1.14096 - 3.13477i) q^{65} +(1.26780 + 3.60662i) q^{66} +(5.27928 + 6.29160i) q^{67} +(4.10531 + 7.27539i) q^{68} +(-5.36885 - 3.80838i) q^{69} +(2.90911 + 11.0751i) q^{70} +(-6.91810 - 11.9825i) q^{71} +(6.15983 - 5.83579i) q^{72} +(0.999604 - 1.73136i) q^{73} +(-2.48878 - 0.680037i) q^{74} +(-1.18667 + 0.0965224i) q^{75} +(8.18112 - 13.8528i) q^{76} +(5.99276 - 1.05669i) q^{77} +(2.49583 + 3.04198i) q^{78} +(-2.46986 + 2.94347i) q^{79} +(2.99448 - 7.74822i) q^{80} +(-8.99732 - 0.219808i) q^{81} +(7.64671 + 0.707015i) q^{82} +(9.80246 + 8.22524i) q^{83} +(-7.56933 - 11.1862i) q^{84} +(-1.50623 - 8.54225i) q^{85} +(11.7425 + 5.54626i) q^{86} +(-0.534356 - 6.56951i) q^{87} +(-3.97274 - 1.92458i) q^{88} +(8.51207 + 4.91444i) q^{89} +(-8.04779 + 3.58609i) q^{90} +(5.42415 - 3.13163i) q^{91} +(7.49791 - 1.24596i) q^{92} +(0.632229 - 0.891283i) q^{93} +(-2.79975 - 4.04073i) q^{94} +(-12.7968 + 10.7378i) q^{95} +(-0.301371 + 9.79332i) q^{96} +(13.2890 - 4.83681i) q^{97} +(-10.5367 + 4.85025i) q^{98} +(1.54754 + 4.41901i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) \) 96 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 9 * q^8 - 12 * q^9	\( 96 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 15 q^{12} - 12 q^{13} - 21 q^{14} - 6 q^{16} - 18 q^{17} - 27 q^{18} - 27 q^{20} - 12 q^{21} - 6 q^{22} - 12 q^{24} - 12 q^{25} - 12 q^{28} - 24 q^{29} + 9 q^{30} + 24 q^{32} - 42 q^{33} - 12 q^{34} + 24 q^{36} - 6 q^{37} + 18 q^{38} - 21 q^{40} - 42 q^{41} + 54 q^{42} + 63 q^{44} - 24 q^{45} - 3 q^{46} + 69 q^{48} - 12 q^{49} + 87 q^{50} - 33 q^{52} + 78 q^{54} + 99 q^{56} - 24 q^{57} - 33 q^{58} + 102 q^{60} - 12 q^{61} + 90 q^{62} - 3 q^{64} + 12 q^{65} + 87 q^{66} + 51 q^{68} + 12 q^{69} - 21 q^{70} + 12 q^{72} - 6 q^{73} + 21 q^{74} - 18 q^{76} + 12 q^{77} - 24 q^{78} + 12 q^{81} - 12 q^{82} - 12 q^{84} - 42 q^{85} - 30 q^{86} + 18 q^{88} - 78 q^{90} - 123 q^{92} + 60 q^{93} + 21 q^{94} - 138 q^{96} - 30 q^{97} - 180 q^{98}+O(q^{100}) \) 96 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 15 * q^12 - 12 * q^13 - 21 * q^14 - 6 * q^16 - 18 * q^17 - 27 * q^18 - 27 * q^20 - 12 * q^21 - 6 * q^22 - 12 * q^24 - 12 * q^25 - 12 * q^28 - 24 * q^29 + 9 * q^30 + 24 * q^32 - 42 * q^33 - 12 * q^34 + 24 * q^36 - 6 * q^37 + 18 * q^38 - 21 * q^40 - 42 * q^41 + 54 * q^42 + 63 * q^44 - 24 * q^45 - 3 * q^46 + 69 * q^48 - 12 * q^49 + 87 * q^50 - 33 * q^52 + 78 * q^54 + 99 * q^56 - 24 * q^57 - 33 * q^58 + 102 * q^60 - 12 * q^61 + 90 * q^62 - 3 * q^64 + 12 * q^65 + 87 * q^66 + 51 * q^68 + 12 * q^69 - 21 * q^70 + 12 * q^72 - 6 * q^73 + 21 * q^74 - 18 * q^76 + 12 * q^77 - 24 * q^78 + 12 * q^81 - 12 * q^82 - 12 * q^84 - 42 * q^85 - 30 * q^86 + 18 * q^88 - 78 * q^90 - 123 * q^92 + 60 * q^93 + 21 * q^94 - 138 * q^96 - 30 * q^97 - 180 * q^98

Introduction

L-functions

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