LMFDB - Embedded newform 324.2.l.a.35.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(35,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, 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("324.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.l (of order $18$, degree $6$, not 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:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			35.12
Character	$\chi$	$=$	324.35
Dual form			324.2.l.a.287.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00492 - 0.995056i) q^{2} +(0.0197253 - 1.99990i) q^{4} +(0.710267 - 1.95144i) q^{5} +(-3.83975 - 0.677051i) q^{7} +(-1.97019 - 2.02937i) q^{8} +O(q^{10})$	\(q+(1.00492 - 0.995056i) q^{2} +(0.0197253 - 1.99990i) q^{4} +(0.710267 - 1.95144i) q^{5} +(-3.83975 - 0.677051i) q^{7} +(-1.97019 - 2.02937i) q^{8} +(-1.22804 - 2.66780i) q^{10} +(1.46659 - 0.533796i) q^{11} +(-1.23056 + 1.03256i) q^{13} +(-4.53234 + 3.14038i) q^{14} +(-3.99922 - 0.0788972i) q^{16} +(3.61727 - 2.08843i) q^{17} +(6.96639 + 4.02205i) q^{19} +(-3.88869 - 1.45896i) q^{20} +(0.942651 - 1.99577i) q^{22} +(-0.659926 - 3.74263i) q^{23} +(0.526570 + 0.441845i) q^{25} +(-0.209156 + 2.26212i) q^{26} +(-1.42978 + 7.66577i) q^{28} +(2.44609 - 2.91513i) q^{29} +(-0.621314 + 0.109554i) q^{31} +(-4.09740 + 3.90017i) q^{32} +(1.55696 - 5.69810i) q^{34} +(-4.04848 + 7.01217i) q^{35} +(0.912171 + 1.57993i) q^{37} +(11.0028 - 2.89012i) q^{38} +(-5.35956 + 2.40333i) q^{40} +(3.49040 + 4.15970i) q^{41} +(-3.14069 - 8.62898i) q^{43} +(-1.03861 - 2.94357i) q^{44} +(-4.38730 - 3.10437i) q^{46} +(0.603613 - 3.42326i) q^{47} +(7.70742 + 2.80527i) q^{49} +(0.968821 - 0.0799486i) q^{50} +(2.04076 + 2.48137i) q^{52} +6.03391i q^{53} -3.24111i q^{55} +(6.19106 + 9.12619i) q^{56} +(-0.442602 - 5.36347i) q^{58} +(-1.58603 - 0.577267i) q^{59} +(-1.69938 + 9.63768i) q^{61} +(-0.515357 + 0.728336i) q^{62} +(-0.236673 + 7.99650i) q^{64} +(1.14096 + 3.13477i) q^{65} +(5.27928 + 6.29160i) q^{67} +(-4.10531 - 7.27539i) q^{68} +(2.90911 + 11.0751i) q^{70} +(6.91810 + 11.9825i) q^{71} +(0.999604 - 1.73136i) q^{73} +(2.48878 + 0.680037i) q^{74} +(8.18112 - 13.8528i) q^{76} +(-5.99276 + 1.05669i) q^{77} +(-2.46986 + 2.94347i) q^{79} +(-2.99448 + 7.74822i) q^{80} +(7.64671 + 0.707015i) q^{82} +(-9.80246 - 8.22524i) q^{83} +(-1.50623 - 8.54225i) q^{85} +(-11.7425 - 5.54626i) q^{86} +(-3.97274 - 1.92458i) q^{88} +(-8.51207 - 4.91444i) q^{89} +(5.42415 - 3.13163i) q^{91} +(-7.49791 + 1.24596i) q^{92} +(-2.79975 - 4.04073i) q^{94} +(12.7968 - 10.7378i) q^{95} +(13.2890 - 4.83681i) q^{97} +(10.5367 - 4.85025i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) $ 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8	$ 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38} - 21 q^{40} + 42 q^{41} - 63 q^{44} - 3 q^{46} - 12 q^{49} - 87 q^{50} - 33 q^{52} - 99 q^{56} - 33 q^{58} - 12 q^{61} - 90 q^{62} - 3 q^{64} - 12 q^{65} - 51 q^{68} - 21 q^{70} - 6 q^{73} - 21 q^{74} - 18 q^{76} - 12 q^{77} - 12 q^{82} - 42 q^{85} + 30 q^{86} + 18 q^{88} + 123 q^{92} + 21 q^{94} - 30 q^{97} + 180 q^{98}+O(q^{100}) $ 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 + 21 * q^14 - 6 * q^16 + 18 * q^17 + 27 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 + 24 * q^29 - 24 * q^32 - 12 * q^34 - 6 * q^37 - 18 * q^38 - 21 * q^40 + 42 * q^41 - 63 * q^44 - 3 * q^46 - 12 * q^49 - 87 * q^50 - 33 * q^52 - 99 * q^56 - 33 * q^58 - 12 * q^61 - 90 * q^62 - 3 * q^64 - 12 * q^65 - 51 * q^68 - 21 * q^70 - 6 * q^73 - 21 * q^74 - 18 * q^76 - 12 * q^77 - 12 * q^82 - 42 * q^85 + 30 * q^86 + 18 * q^88 + 123 * q^92 + 21 * q^94 - 30 * q^97 + 180 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{13}{18}\right)$

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 $

$2$	1.00492	−	0.995056i	0.710585	−	0.703611i
$2$	1.00492	−	0.995056i	0.710585	−	0.703611i
$3$		0			0
$3$		0			0
$4$	0.0197253	−	1.99990i	0.00986263	−	0.999951i
$5$	0.710267	−	1.95144i	0.317641	−	0.872712i	−0.673415	−	0.739265i	$-0.735173\pi$
$5$	0.710267	−	1.95144i	0.317641	−	0.872712i	0.991056	−	0.133447i	$-0.0426046\pi$
$6$		0			0
$7$	−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			0
$10$	−1.22804	−	2.66780i	−0.388339	−	0.843632i
$11$	1.46659	−	0.533796i	0.442195	−	0.160946i	−0.111321	−	0.993785i	$-0.535508\pi$
$11$	1.46659	−	0.533796i	0.442195	−	0.160946i	0.553516	+	0.832839i	$0.313286\pi$
$12$		0			0
$13$	−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
$15$		0			0
$16$	−3.99922	−	0.0788972i	−0.999805	−	0.0197243i
$17$	3.61727	−	2.08843i	0.877318	−	0.506520i	0.00754464	−	0.999972i	$-0.497598\pi$
$17$	3.61727	−	2.08843i	0.877318	−	0.506520i	0.869773	+	0.493452i	$0.164265\pi$
$18$		0			0
$19$	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
$21$		0			0
$22$	0.942651	−	1.99577i	0.200974	−	0.425499i
$23$	−0.659926	−	3.74263i	−0.137604	−	0.780392i	−0.973011	−	0.230759i	$-0.925879\pi$
$23$	−0.659926	−	3.74263i	−0.137604	−	0.780392i	0.835407	−	0.549632i	$-0.185232\pi$
$24$		0			0
$25$	0.526570	+	0.441845i	0.105314	+	0.0883689i
$26$	−0.209156	+	2.26212i	−0.0410188	+	0.443639i
$27$		0			0
$28$	−1.42978	+	7.66577i	−0.270202	+	1.44869i
$29$	2.44609	−	2.91513i	0.454227	−	0.541327i	−0.489521	−	0.871991i	$-0.662828\pi$
$29$	2.44609	−	2.91513i	0.454227	−	0.541327i	0.943748	+	0.330665i	$0.107273\pi$
$30$		0			0
$31$	−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
$33$		0			0
$34$	1.55696	−	5.69810i	0.267016	−	0.977216i
$35$	−4.04848	+	7.01217i	−0.684317	+	1.18527i
$36$		0			0
$37$	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			0
$40$	−5.35956	+	2.40333i	−0.847421	+	0.380000i
$41$	3.49040	+	4.15970i	0.545109	+	0.649636i	0.966325	−	0.257324i	$-0.0828409\pi$
$41$	3.49040	+	4.15970i	0.545109	+	0.649636i	−0.421216	+	0.906960i	$0.638396\pi$
$42$		0			0
$43$	−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
$45$		0			0
$46$	−4.38730	−	3.10437i	−0.646872	−	0.457715i
$47$	0.603613	−	3.42326i	0.0880460	−	0.499334i	−0.908612	−	0.417642i	$-0.862857\pi$
$47$	0.603613	−	3.42326i	0.0880460	−	0.499334i	0.996658	−	0.0816916i	$-0.0260323\pi$
$48$		0			0
$49$	7.70742	+	2.80527i	1.10106	+	0.400753i
$50$	0.968821	−	0.0799486i	0.137012	−	0.0113064i
$51$		0			0
$52$	2.04076	+	2.48137i	0.283002	+	0.344105i
$53$			6.03391i			0.828821i	0.910090	+	0.414411i	$0.136012\pi$
$53$			6.03391i			0.828821i	−0.910090	+	0.414411i	$0.863988\pi$
$54$		0			0
$55$		−	3.24111i		−	0.437032i
$56$	6.19106	+	9.12619i	0.827316	+	1.21954i
$57$		0			0
$58$	−0.442602	−	5.36347i	−0.0581165	−	0.704258i
$59$	−1.58603	−	0.577267i	−0.206483	−	0.0751537i	0.236708	−	0.971581i	$-0.423932\pi$
$59$	−1.58603	−	0.577267i	−0.206483	−	0.0751537i	−0.443191	+	0.896427i	$0.646154\pi$
$60$		0			0
$61$	−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
$63$		0			0
$64$	−0.236673	+	7.99650i	−0.0295841	+	0.999562i
$65$	1.14096	+	3.13477i	0.141519	+	0.388820i
$66$		0			0
$67$	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
$69$		0			0
$70$	2.90911	+	11.0751i	0.347705	+	1.32373i
$71$	6.91810	+	11.9825i	0.821028	+	1.42206i	0.904917	+	0.425587i	$0.139932\pi$
$71$	6.91810	+	11.9825i	0.821028	+	1.42206i	−0.0838895	+	0.996475i	$0.526734\pi$
$72$		0			0
$73$	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
$75$		0			0
$76$	8.18112	−	13.8528i	0.938439	−	1.58902i
$77$	−5.99276	+	1.05669i	−0.682938	+	0.120420i
$78$		0			0
$79$	−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
$81$		0			0
$82$	7.64671	+	0.707015i	0.844438	+	0.0780767i
$83$	−9.80246	−	8.22524i	−1.07596	−	0.902838i	−0.0803808	−	0.996764i	$-0.525614\pi$
$83$	−9.80246	−	8.22524i	−1.07596	−	0.902838i	−0.995579	+	0.0939267i	$0.970058\pi$
$84$		0			0
$85$	−1.50623	−	8.54225i	−0.163374	−	0.926537i
$86$	−11.7425	−	5.54626i	−1.26622	−	0.598069i
$87$		0			0
$88$	−3.97274	−	1.92458i	−0.423496	−	0.205161i
$89$	−8.51207	−	4.91444i	−0.902277	−	0.520930i	−0.0243390	−	0.999704i	$-0.507748\pi$
$89$	−8.51207	−	4.91444i	−0.902277	−	0.520930i	−0.877938	+	0.478774i	$0.841081\pi$
$90$		0			0
$91$	5.42415	−	3.13163i	0.568605	−	0.328284i
$92$	−7.49791	+	1.24596i	−0.781711	+	0.129901i
$93$		0			0
$94$	−2.79975	−	4.04073i	−0.288773	−	0.416769i
$95$	12.7968	−	10.7378i	1.31292	−	1.10167i
$96$		0			0
$97$	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
$99$		0			0
$100$	0.894033	−	1.04437i	0.0894033	−	0.104437i
$101$	−3.46353	−	0.610714i	−0.344634	−	0.0607683i	−0.00134779	−	0.999999i	$-0.500429\pi$
$101$	−3.46353	−	0.610714i	−0.344634	−	0.0607683i	−0.343286	+	0.939231i	$0.611540\pi$
$102$		0			0
$103$	−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
$105$		0			0
$106$	6.00408	+	6.06359i	0.583168	+	0.588948i
$107$	8.93007			0.863303			0.431651	−	0.902041i	$-0.357931\pi$
$107$	8.93007			0.863303			0.431651	+	0.902041i	$0.357931\pi$
$108$		0			0
$109$	−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
$111$		0			0
$112$	15.3026	+	3.01062i	1.44596	+	0.284477i
$113$	0.185982	−	0.510982i	0.0174958	−	0.0480692i	−0.930637	−	0.365943i	$-0.880747\pi$
$113$	0.185982	−	0.510982i	0.0174958	−	0.0480692i	0.948133	+	0.317874i	$0.102969\pi$
$114$		0			0
$115$	−7.77225	−	1.37046i	−0.724766	−	0.127796i
$116$	−5.78173	−	4.94944i	−0.536821	−	0.459544i
$117$		0			0
$118$	−2.16824	+	0.998080i	−0.199603	+	0.0918808i
$119$	−15.3034	+	5.56998i	−1.40286	+	0.510599i
$120$		0			0
$121$	−6.56053	+	5.50494i	−0.596412	+	0.500449i
$122$	7.88229	+	11.3761i	0.713629	+	1.02994i
$123$		0			0
$124$	0.206843	+	1.24473i	0.0185750	+	0.111780i
$125$	10.2285	−	5.90545i	0.914869	−	0.528200i
$126$		0			0
$127$	−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
$129$		0			0
$130$	4.26585	+	2.01487i	0.374140	+	0.176716i
$131$	0.199803	+	1.13314i	0.0174569	+	0.0990028i	0.992291	−	0.123927i	$-0.0395490\pi$
$131$	0.199803	+	1.13314i	0.0174569	+	0.0990028i	−0.974834	+	0.222930i	$0.928438\pi$
$132$		0			0
$133$	−24.0261	−	20.1603i	−2.08332	−	1.74812i
$134$	11.5657	+	1.06937i	0.999128	+	0.0923794i
$135$		0			0
$136$	−11.3649	−	3.22616i	−0.974535	−	0.276641i
$137$	−11.5868	+	13.8086i	−0.989923	+	1.17974i	−0.00621375	+	0.999981i	$0.501978\pi$
$137$	−11.5868	+	13.8086i	−0.989923	+	1.17974i	−0.983710	+	0.179764i	$0.942467\pi$
$138$		0			0
$139$	−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
$141$		0			0
$142$	18.8754	+	5.15755i	1.58399	+	0.432812i
$143$	−1.25356	+	2.17122i	−0.104828	+	0.181567i
$144$		0			0
$145$	−3.95134	−	6.84393i	−0.328141	−	0.568357i
$146$	−0.718285	−	2.73454i	−0.0594457	−	0.226312i
$147$		0			0
$148$	3.17769	−	1.79309i	0.261205	−	0.147391i
$149$	−9.84611	−	11.7341i	−0.806624	−	0.961298i	0.193178	−	0.981164i	$-0.438120\pi$
$149$	−9.84611	−	11.7341i	−0.806624	−	0.961298i	−0.999803	+	0.0198661i	$0.993676\pi$
$150$		0			0
$151$	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
$153$		0			0
$154$	−4.97078	+	7.02502i	−0.400557	+	0.566092i
$155$	−0.227510	+	1.29027i	−0.0182740	+	0.103637i
$156$		0			0
$157$	−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
$159$		0			0
$160$	4.70070	+	10.7660i	0.371623	+	0.851128i
$161$			14.8175i			1.16779i
$162$		0			0
$163$			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
$165$		0			0
$166$	−18.0353	+	1.48830i	−1.39981	+	0.115514i
$167$	14.6509	+	5.33250i	1.13372	+	0.412642i	0.839643	−	0.543139i	$-0.182764\pi$
$167$	14.6509	+	5.33250i	1.13372	+	0.412642i	0.294081	+	0.955781i	$0.404987\pi$
$168$		0			0
$169$	−1.80933	+	10.2612i	−0.139179	+	0.789325i
$170$	−10.0137	−	7.08549i	−0.768013	−	0.543432i
$171$		0			0
$172$	−17.3191	+	6.11087i	−1.32057	+	0.465950i
$173$	−4.40303	−	12.0972i	−0.334757	−	0.919736i	−0.986856	−	0.161603i	$-0.948334\pi$
$173$	−4.40303	−	12.0972i	−0.334757	−	0.919736i	0.652099	−	0.758134i	$-0.273888\pi$
$174$		0			0
$175$	−1.72274	−	2.05309i	−0.130227	−	0.155199i
$176$	−5.90735	+	2.01906i	−0.445283	+	0.152192i
$177$		0			0
$178$	−13.4441	+	3.53137i	−1.00768	+	0.264687i
$179$	−7.23994	−	12.5399i	−0.541139	−	0.937280i	−0.998839	−	0.0481733i	$-0.984660\pi$
$179$	−7.23994	−	12.5399i	−0.541139	−	0.937280i	0.457700	−	0.889107i	$-0.348673\pi$
$180$		0			0
$181$	−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
$183$		0			0
$184$	−6.29499	+	8.71293i	−0.464072	+	0.642326i
$185$	3.73102	−	0.657880i	0.274310	−	0.0483683i
$186$		0			0
$187$	4.19027	−	4.99377i	0.306423	−	0.365181i
$188$	−6.83428	−	1.27469i	−0.498441	−	0.0929665i
$189$		0			0
$190$	2.17504	−	23.5241i	0.157794	−	1.70662i
$191$	7.04065	+	5.90780i	0.509443	+	0.427474i	0.860933	−	0.508718i	$-0.169880\pi$
$191$	7.04065	+	5.90780i	0.509443	+	0.427474i	−0.351490	+	0.936192i	$0.614325\pi$
$192$		0			0
$193$	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
$195$		0			0
$196$	5.76230	−	15.3588i	0.411593	−	1.09705i
$197$	−14.4834	−	8.36197i	−1.03190	−	0.595766i	−0.114369	−	0.993438i	$-0.536485\pi$
$197$	−14.4834	−	8.36197i	−1.03190	−	0.595766i	−0.917527	+	0.397673i	$0.869818\pi$
$198$		0			0
$199$	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
$201$		0			0
$202$	−4.08826	+	2.83269i	−0.287649	+	0.199307i
$203$	−11.3661	+	9.53725i	−0.797741	+	0.669384i
$204$		0			0
$205$	10.5965	−	3.85682i	0.740094	−	0.269372i
$206$	4.14583	+	9.00646i	0.288854	+	0.627510i
$207$		0			0
$208$	5.00276	−	4.03237i	0.346879	−	0.279594i
$209$	12.3638	+	2.18007i	0.855223	+	0.150799i
$210$		0			0
$211$	−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
$213$		0			0
$214$	8.97400	−	8.88593i	0.613450	−	0.607429i
$215$	−19.0697			−1.30054
$216$		0			0
$217$	2.45986			0.166986
$218$	−3.88212	+	3.84402i	−0.262930	+	0.260350i
$219$		0			0
$220$	−6.48191	−	0.0639318i	−0.437010	−	0.00431028i
$221$	−2.29484	+	6.30502i	−0.154368	+	0.424121i
$222$		0			0
$223$	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
$225$		0			0
$226$	−0.321559	−	0.698559i	−0.0213898	−	0.0464675i
$227$	4.60337	−	1.67549i	0.305536	−	0.111206i	−0.184702	−	0.982795i	$-0.559132\pi$
$227$	4.60337	−	1.67549i	0.305536	−	0.111206i	0.490238	+	0.871588i	$0.336910\pi$
$228$		0			0
$229$	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
$231$		0			0
$232$	−10.7351	+	0.779365i	−0.704797	+	0.0511678i
$233$	−4.25923	+	2.45907i	−0.279032	+	0.161099i	−0.632985	−	0.774164i	$-0.718170\pi$
$233$	−4.25923	+	2.45907i	−0.279032	+	0.161099i	0.353953	+	0.935263i	$0.384837\pi$
$234$		0			0
$235$	−6.25157	−	3.60935i	−0.407807	−	0.235448i
$236$	−1.18576	+	3.16051i	−0.0771866	+	0.205732i
$237$		0			0
$238$	−9.83623	+	20.8251i	−0.637588	+	1.34989i
$239$	−0.976252	−	5.53660i	−0.0631485	−	0.358133i	−0.999965	−	0.00831291i	$-0.997354\pi$
$239$	−0.976252	−	5.53660i	−0.0631485	−	0.358133i	0.936817	−	0.349820i	$-0.113757\pi$
$240$		0			0
$241$	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
$243$		0			0
$244$	19.2409	+	3.58871i	1.23177	+	0.229743i
$245$	10.9487	−	13.0481i	0.699484	−	0.833613i
$246$		0			0
$247$	−12.7256	+	2.24387i	−0.809711	+	0.142774i
$248$	1.44644	+	1.04503i	0.0918487	+	0.0663596i
$249$		0			0
$250$	4.40260	−	16.1125i	0.278445	−	1.01904i
$251$	5.19194	−	8.99271i	0.327713	−	0.567615i	−0.654345	−	0.756196i	$-0.727056\pi$
$251$	5.19194	−	8.99271i	0.327713	−	0.567615i	0.982058	+	0.188581i	$0.0603889\pi$
$252$		0			0
$253$	−2.96564	−	5.13665i	−0.186448	−	0.322938i
$254$	−9.95563	+	2.61505i	−0.624672	+	0.164083i
$255$		0			0
$256$	15.9876	+	0.631055i	0.999222	+	0.0394409i
$257$	6.62146	+	7.89114i	0.413035	+	0.492236i	0.931948	−	0.362591i	$-0.118108\pi$
$257$	6.62146	+	7.89114i	0.413035	+	0.492236i	−0.518913	+	0.854827i	$0.673663\pi$
$258$		0			0
$259$	−2.43282	−	6.68411i	−0.151168	−	0.415330i
$260$	6.29174	−	2.21998i	0.390197	−	0.137677i
$261$		0			0
$262$	1.32832	+	0.939898i	0.0820641	+	0.0580671i
$263$	−2.57586	+	14.6085i	−0.158835	+	0.900796i	0.796361	+	0.604821i	$0.206755\pi$
$263$	−2.57586	+	14.6085i	−0.158835	+	0.900796i	−0.955196	+	0.295975i	$0.904356\pi$
$264$		0			0
$265$	11.7748	+	4.28569i	0.723322	+	0.263268i
$266$	−44.2048	+	3.64785i	−2.71037	+	0.223664i
$267$		0			0
$268$	12.6867	−	10.4339i	0.774965	−	0.637354i
$269$		−	10.7768i		−	0.657070i	−0.944492	−	0.328535i	$-0.893445\pi$
$269$		−	10.7768i		−	0.657070i	0.944492	−	0.328535i	$-0.106555\pi$
$270$		0			0
$271$		−	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
$273$		0			0
$274$	2.09654	+	25.4060i	0.126657	+	1.53483i
$275$	1.00812	+	0.366925i	0.0607919	+	0.0221264i
$276$		0			0
$277$	−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			0
$280$	22.2065	−	5.59948i	1.32710	−	0.334633i
$281$	3.61833	+	9.94129i	0.215852	+	0.593048i	0.999607	−	0.0280216i	$-0.00892073\pi$
$281$	3.61833	+	9.94129i	0.215852	+	0.593048i	−0.783756	+	0.621069i	$0.786699\pi$
$282$		0			0
$283$	−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
$285$		0			0
$286$	0.900767	+	3.42926i	0.0532634	+	0.202777i
$287$	−10.5859	−	18.3354i	−0.624868	−	1.08230i
$288$		0			0
$289$	0.223112	−	0.386442i	0.0131243	−	0.0227319i
$290$	−10.7809	−	2.94578i	−0.633075	−	0.172982i
$291$		0			0
$292$	−3.44284	−	2.03326i	−0.201477	−	0.118988i
$293$	21.8702	−	3.85630i	1.27767	−	0.225288i	0.506679	−	0.862135i	$-0.330873\pi$
$293$	21.8702	−	3.85630i	1.27767	−	0.225288i	0.770990	+	0.636847i	$0.219762\pi$
$294$		0			0
$295$	−2.25301	+	2.68503i	−0.131175	+	0.156328i
$296$	1.40910	−	4.96389i	0.0819023	−	0.288521i
$297$		0			0
$298$	−21.5707	−	1.99442i	−1.24956	−	0.115534i
$299$	4.67658	+	3.92412i	0.270454	+	0.226938i
$300$		0			0
$301$	6.21721	+	35.2595i	0.358354	+	2.03233i
$302$	5.96131	+	2.81568i	0.343035	+	0.162024i
$303$		0			0
$304$	−27.5428	−	16.6347i	−1.57969	−	0.954065i
$305$	17.6004	+	10.1616i	1.00779	+	0.581850i
$306$		0			0
$307$	−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
$309$		0			0
$310$	1.05526	+	1.52300i	0.0599350	+	0.0865008i
$311$	−4.48037	+	3.75948i	−0.254059	+	0.213180i	−0.760918	−	0.648848i	$-0.775251\pi$
$311$	−4.48037	+	3.75948i	−0.254059	+	0.213180i	0.506859	+	0.862029i	$0.330806\pi$
$312$		0			0
$313$	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
$315$		0			0
$316$	5.83793	+	4.99754i	0.328409	+	0.281134i
$317$	−12.5020	−	2.20444i	−0.702181	−	0.123813i	−0.188852	−	0.982006i	$-0.560477\pi$
$317$	−12.5020	−	2.20444i	−0.702181	−	0.123813i	−0.513329	+	0.858192i	$0.671588\pi$
$318$		0			0
$319$	2.03133	−	5.58103i	0.113733	−	0.312478i
$320$	15.4366	+	6.14150i	0.862933	+	0.343321i
$321$		0			0
$322$	14.7443	+	14.8904i	0.821668	+	0.829812i
$323$	33.5991			1.86951
$324$		0			0
$325$	−1.10421			−0.0612506
$326$	5.16445	+	5.21564i	0.286033	+	0.288868i
$327$		0			0
$328$	1.56479	−	15.2787i	0.0864013	−	0.843627i
$329$	−4.63544	+	12.7358i	−0.255560	+	0.702146i
$330$		0			0
$331$	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
$333$		0			0
$334$	20.0291	−	9.21977i	1.09595	−	0.504483i
$335$	16.0274	−	5.83350i	0.875670	−	0.318718i
$336$		0			0
$337$	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			0
$340$	−17.1134	+	2.84381i	−0.928104	+	0.154227i
$341$	−0.852735	+	0.492327i	−0.0461782	+	0.0266610i
$342$		0			0
$343$	−4.05892	−	2.34342i	−0.219161	−	0.126533i
$344$	−11.3236	+	23.3744i	−0.610528	+	1.26026i
$345$		0			0
$346$	−16.4621	−	7.77548i	−0.885010	−	0.418012i
$347$	5.88732	+	33.3886i	0.316048	+	1.79240i	0.566283	+	0.824211i	$0.308381\pi$
$347$	5.88732	+	33.3886i	0.316048	+	1.79240i	−0.250235	+	0.968185i	$0.580508\pi$
$348$		0			0
$349$	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
$351$		0			0
$352$	−3.92733	+	7.90714i	−0.209327	+	0.421452i
$353$	7.52927	−	8.97303i	0.400742	−	0.477586i	−0.527504	−	0.849553i	$-0.676872\pi$
$353$	7.52927	−	8.97303i	0.400742	−	0.477586i	0.928246	+	0.371967i	$0.121316\pi$
$354$		0			0
$355$	28.2969	−	4.98951i	1.50184	−	0.264815i
$356$	−9.99631	+	16.9264i	−0.529804	+	0.897096i
$357$		0			0
$358$	−19.7535	−	5.39748i	−1.04401	−	0.285266i
$359$	11.7844	−	20.4112i	0.621957	−	1.07726i	−0.367164	−	0.930156i	$-0.619671\pi$
$359$	11.7844	−	20.4112i	0.621957	−	1.07726i	0.989121	−	0.147105i	$-0.0469955\pi$
$360$		0			0
$361$	22.8537	+	39.5838i	1.20283	+	2.08336i
$362$	1.43213	+	5.45218i	0.0752709	+	0.286560i
$363$		0			0
$364$	−6.15597	−	10.9095i	−0.322661	−	0.571815i
$365$	−2.66867	−	3.18040i	−0.139685	−	0.166470i
$366$		0			0
$367$	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
$369$		0			0
$370$	3.09475	−	4.37370i	0.160888	−	0.227378i
$371$	4.08527	−	23.1687i	0.212096	−	1.20286i
$372$		0			0
$373$	−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
$375$		0			0
$376$	−8.13629	+	5.51953i	−0.419597	+	0.284648i
$377$			6.11300i			0.314835i
$378$		0			0
$379$			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
$381$		0			0
$382$	12.9539	−	1.06898i	0.662778	−	0.0546935i
$383$	−28.3995	−	10.3366i	−1.45115	−	0.528174i	−0.508236	−	0.861218i	$-0.669702\pi$
$383$	−28.3995	−	10.3366i	−1.45115	−	0.528174i	−0.942911	+	0.333044i	$0.891924\pi$
$384$		0			0
$385$	−2.19440	+	12.4451i	−0.111837	+	0.634259i
$386$	3.60752	+	2.55261i	0.183618	+	0.129925i
$387$		0			0
$388$	−9.41103	−	26.6722i	−0.477773	−	1.35408i
$389$	9.65520	+	26.5275i	0.489538	+	1.34500i	0.901099	+	0.433613i	$0.142762\pi$
$389$	9.65520	+	26.5275i	0.489538	+	1.34500i	−0.411561	+	0.911382i	$0.635016\pi$
$390$		0			0
$391$	−10.2034	−	12.1599i	−0.516006	−	0.614952i
$392$	−9.49218	−	21.1681i	−0.479428	−	1.06915i
$393$		0			0
$394$	−22.8752	+	6.00865i	−1.15244	+	0.302712i
$395$	3.98975	+	6.91044i	0.200746	+	0.347702i
$396$		0			0
$397$	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
$399$		0			0
$400$	−2.07101	−	1.80858i	−0.103550	−	0.0904290i
$401$	−2.44801	+	0.431651i	−0.122248	+	0.0215556i	−0.234437	−	0.972131i	$-0.575325\pi$
$401$	−2.44801	+	0.431651i	−0.122248	+	0.0215556i	0.112189	+	0.993687i	$0.464214\pi$
$402$		0			0
$403$	0.651444	−	0.776360i	0.0324507	−	0.0386733i
$404$	−1.28969	+	6.91468i	−0.0641643	+	0.344018i
$405$		0			0
$406$	−1.93186	+	20.8940i	−0.0958767	+	1.03695i
$407$	2.18114	+	1.83020i	0.108115	+	0.0907195i
$408$		0			0
$409$	−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
$411$		0			0
$412$	13.1282	+	4.92543i	0.646778	+	0.242658i
$413$	5.69911	+	3.29038i	0.280435	+	0.161909i
$414$		0			0
$415$	−23.0135	+	13.2868i	−1.12969	+	0.652225i
$416$	1.01494	−	9.03023i	0.0497613	−	0.442743i
$417$		0			0
$418$	14.5939	−	10.1119i	0.713813	−	0.494589i
$419$	−10.8202	+	9.07925i	−0.528603	+	0.443550i	−0.867619	−	0.497230i	$-0.834350\pi$
$419$	−10.8202	+	9.07925i	−0.528603	+	0.443550i	0.339016	+	0.940781i	$0.389906\pi$
$420$		0			0
$421$	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
$423$		0			0
$424$	12.2450	−	11.8880i	0.594671	−	0.577331i
$425$	2.82751	+	0.498566i	0.137154	+	0.0241840i
$426$		0			0
$427$	13.0504	−	35.8557i	0.631553	−	1.73518i
$428$	0.176148	−	17.8593i	0.00851444	−	0.863261i
$429$		0			0
$430$	−19.1635	+	18.9754i	−0.924147	+	0.915077i
$431$	−39.3589			−1.89585			−0.947926	−	0.318492i	$-0.896824\pi$
$431$	−39.3589			−1.89585			−0.947926	+	0.318492i	$0.896824\pi$
$432$		0			0
$433$	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
$435$		0			0
$436$	−0.0762010	+	7.72585i	−0.00364937	+	0.370001i
$437$	10.4557	−	28.7269i	0.500165	−	1.37419i
$438$		0			0
$439$	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
$441$		0			0
$442$	3.96772	+	8.61953i	0.188725	+	0.409989i
$443$	6.38031	−	2.32224i	0.303138	−	0.110333i	−0.185973	−	0.982555i	$-0.559544\pi$
$443$	6.38031	−	2.32224i	0.303138	−	0.110333i	0.489111	+	0.872222i	$0.337321\pi$
$444$		0			0
$445$	−15.6361	+	13.1202i	−0.741222	+	0.621959i
$446$	25.4235	−	17.6155i	1.20384	−	0.834119i
$447$		0			0
$448$	6.32280	−	30.5443i	0.298724	−	1.44308i
$449$	11.8597	−	6.84721i	0.559694	−	0.323140i	−0.193328	−	0.981134i	$-0.561928\pi$
$449$	11.8597	−	6.84721i	0.559694	−	0.323140i	0.753023	+	0.657994i	$0.228595\pi$
$450$		0			0
$451$	7.33944	+	4.23743i	0.345601	+	0.199533i
$452$	−1.01825	−	0.382026i	−0.0478943	−	0.0179690i
$453$		0			0
$454$	2.95881	−	6.26434i	0.138864	−	0.294000i
$455$	−2.25861	−	12.8092i	−0.105885	−	0.600505i
$456$		0			0
$457$	−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
$459$		0			0
$460$	−2.89409	+	15.5167i	−0.134938	+	0.723470i
$461$	−3.18317	+	3.79355i	−0.148255	+	0.176683i	−0.835061	−	0.550157i	$-0.814568\pi$
$461$	−3.18317	+	3.79355i	−0.148255	+	0.176683i	0.686806	+	0.726841i	$0.259012\pi$
$462$		0			0
$463$	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
$465$		0			0
$466$	−1.83327	+	6.70934i	−0.0849247	+	0.310804i
$467$	−10.9588	+	18.9812i	−0.507113	+	0.878345i	0.492853	+	0.870112i	$0.335954\pi$
$467$	−10.9588	+	18.9812i	−0.507113	+	0.878345i	−0.999966	+	0.00823285i	$0.997379\pi$
$468$		0			0
$469$	−16.0114	−	27.7325i	−0.739336	−	1.28057i
$470$	−9.87383	+	2.59356i	−0.455446	+	0.119632i
$471$		0			0
$472$	1.95329	+	4.35596i	0.0899077	+	0.200499i
$473$	−9.21224	−	10.9787i	−0.423579	−	0.504802i
$474$		0			0
$475$	1.89117	+	5.19595i	0.0867729	+	0.238407i
$476$	10.8376	+	30.7152i	0.496739	+	1.40783i
$477$		0			0
$478$	−6.49028	−	4.59241i	−0.296859	−	0.210052i
$479$	−5.05595	+	28.6737i	−0.231012	+	1.31014i	0.619839	+	0.784729i	$0.287198\pi$
$479$	−5.05595	+	28.6737i	−0.231012	+	1.31014i	−0.850851	+	0.525406i	$0.823913\pi$
$480$		0			0
$481$	−2.75386	−	1.00232i	−0.125565	−	0.0457020i
$482$	0.754733	−	0.0622818i	0.0343772	−	0.00283686i
$483$		0			0
$484$	10.8799	+	13.2290i	0.494542	+	0.601319i
$485$		−	29.3682i		−	1.33354i
$486$		0			0
$487$		−	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
$489$		0			0
$490$	−1.98108	−	24.0068i	−0.0894962	−	1.08452i
$491$	−20.6040	−	7.49924i	−0.929845	−	0.338436i	−0.167697	−	0.985839i	$-0.553633\pi$
$491$	−20.6040	−	7.49924i	−0.929845	−	0.338436i	−0.762148	+	0.647403i	$0.775855\pi$
$492$		0			0
$493$	2.76010	−	15.6533i	0.124309	−	0.704990i
$494$	−10.5554	+	14.9176i	−0.474911	+	0.671175i
$495$		0			0
$496$	2.49342	−	0.389112i	0.111958	−	0.0174717i
$497$	−18.4510	−	50.6937i	−0.827641	−	2.27392i
$498$		0			0
$499$	−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
$501$		0			0
$502$	−3.73077	−	14.2032i	−0.166512	−	0.633921i
$503$	6.75419	+	11.6986i	0.301155	+	0.521615i	0.976398	−	0.215980i	$-0.0692947\pi$
$503$	6.75419	+	11.6986i	0.301155	+	0.521615i	−0.675243	+	0.737595i	$0.735961\pi$
$504$		0			0
$505$	−3.65181	+	6.32511i	−0.162503	+	0.281464i
$506$	−8.09149	−	2.21093i	−0.359710	−	0.0982879i
$507$		0			0
$508$	−7.40248	+	12.5343i	−0.328432	+	0.556121i
$509$	−21.5105	+	3.79288i	−0.953436	+	0.168116i	−0.628665	−	0.777676i	$-0.716398\pi$
$509$	−21.5105	+	3.79288i	−0.953436	+	0.168116i	−0.324771	+	0.945793i	$0.605287\pi$
$510$		0			0
$511$	−5.01045	+	5.97122i	−0.221649	+	0.264151i
$512$	16.6941	−	15.2744i	0.737783	−	0.675038i
$513$		0			0
$514$	14.5062	+	1.34124i	0.639839	+	0.0591595i
$515$	11.1531	+	9.35856i	0.491464	+	0.412387i
$516$		0			0
$517$	−0.942069	−	5.34274i	−0.0414321	−	0.234973i
$518$	−9.09585	−	4.29620i	−0.399649	−	0.188764i
$519$		0			0
$520$	4.11369	−	8.49154i	0.180397	−	0.372379i
$521$	9.60080	+	5.54303i	0.420619	+	0.242844i	0.695342	−	0.718679i	$-0.255253\pi$
$521$	9.60080	+	5.54303i	0.420619	+	0.242844i	−0.274723	+	0.961523i	$0.588586\pi$
$522$		0			0
$523$	−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
$525$		0			0
$526$	11.9477	+	17.2434i	0.520945	+	0.751850i
$527$	−2.01867	+	1.69386i	−0.0879344	+	0.0737858i
$528$		0			0
$529$	8.04118	−	2.92675i	0.349617	−	0.127250i
$530$	16.0973	−	7.40985i	0.699220	−	0.321863i
$531$		0			0
$532$	−40.7925	+	47.6521i	−1.76858	+	2.06598i
$533$	−8.59032	−	1.51470i	−0.372088	−	0.0656091i
$534$		0			0
$535$	6.34274	−	17.4265i	0.274221	−	0.753415i
$536$	2.36677	−	23.1093i	0.102229	−	0.998168i
$537$		0			0
$538$	−10.7235	−	10.8298i	−0.462322	−	0.466904i
$539$	12.8011			0.551382
$540$		0			0
$541$	−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
$543$		0			0
$544$	−6.67619	+	22.6651i	−0.286239	+	0.971759i
$545$	−2.74384	+	7.53865i	−0.117533	+	0.322920i
$546$		0			0
$547$	−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
$549$		0			0
$550$	1.37819	−	0.634405i	0.0587662	−	0.0270511i
$551$	28.7652	−	10.4697i	1.22544	−	0.446023i
$552$		0			0
$553$	11.4765	−	9.62995i	0.488031	−	0.409507i
$554$	14.3969	+	20.7783i	0.611667	+	0.882785i
$555$		0			0
$556$	1.15477	+	6.94913i	0.0489732	+	0.294709i
$557$	−37.6968	+	21.7643i	−1.59727	+	0.922182i	−0.605255	+	0.796032i	$0.706929\pi$
$557$	−37.6968	+	21.7643i	−1.59727	+	0.922182i	−0.992011	+	0.126150i	$0.959738\pi$
$558$		0			0
$559$	12.7748	+	7.37554i	0.540317	+	0.311952i
$560$	16.7440	−	27.7238i	0.707563	−	1.17154i
$561$		0			0
$562$	13.5283	+	6.38975i	0.570656	+	0.269535i
$563$	−6.63186	−	37.6111i	−0.279500	−	1.58512i	−0.724296	−	0.689489i	$-0.757835\pi$
$563$	−6.63186	−	37.6111i	−0.279500	−	1.58512i	0.444796	−	0.895632i	$-0.353276\pi$
$564$		0			0
$565$	−0.865056	−	0.725868i	−0.0363932	−	0.0305375i
$566$	−7.99329	−	0.739060i	−0.335983	−	0.0310650i
$567$		0			0
$568$	10.6869	−	37.6472i	0.448413	−	1.57964i
$569$	−9.07986	+	10.8210i	−0.380648	+	0.453638i	−0.922019	−	0.387146i	$-0.873461\pi$
$569$	−9.07986	+	10.8210i	−0.380648	+	0.453638i	0.541371	+	0.840784i	$0.317905\pi$
$570$		0			0
$571$	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
$573$		0			0
$574$	−28.8828	−	7.89197i	−1.20554	−	0.329405i
$575$	1.30616	−	2.26234i	0.0544707	−	0.0943461i
$576$		0			0
$577$	−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
$579$		0			0
$580$	−13.7651	+	7.76730i	−0.571566	+	0.322520i
$581$	32.0701	+	38.2196i	1.33049	+	1.58562i
$582$		0			0
$583$	3.22088	+	8.84929i	0.133395	+	0.366500i
$584$	−5.48299	+	1.38256i	−0.226888	+	0.0572107i
$585$		0			0
$586$	18.1405	−	25.6373i	0.749378	−	1.05907i
$587$	5.12957	−	29.0912i	0.211720	−	1.20072i	−0.674788	−	0.738011i	$-0.735765\pi$
$587$	5.12957	−	29.0912i	0.211720	−	1.20072i	0.886508	−	0.462712i	$-0.153124\pi$
$588$		0			0
$589$	−4.76895	−	1.73576i	−0.196501	−	0.0715206i
$590$	0.407666	+	4.94011i	0.0167833	+	0.203381i
$591$		0			0
$592$	−3.52332	−	6.39045i	−0.144808	−	0.262646i
$593$		−	21.9478i		−	0.901289i	−0.892704	−	0.450644i	$-0.851194\pi$
$593$		−	21.9478i		−	0.901289i	0.892704	−	0.450644i	$-0.148806\pi$
$594$		0			0
$595$			33.8199i			1.38648i
$596$	−23.6613	+	19.4598i	−0.969206	+	0.797104i
$597$		0			0
$598$	8.60431	−	0.710042i	0.351856	−	0.0290358i
$599$	17.4194	+	6.34015i	0.711739	+	0.259052i	0.672414	−	0.740175i	$-0.265257\pi$
$599$	17.4194	+	6.34015i	0.711739	+	0.259052i	0.0393241	+	0.999227i	$0.487480\pi$
$600$		0			0
$601$	−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
$603$		0			0
$604$	8.79239	−	3.10231i	0.357757	−	0.126231i
$605$	6.08285	+	16.7125i	0.247303	+	0.679459i
$606$		0			0
$607$	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
$609$		0			0
$610$	27.7983	−	7.30180i	1.12552	−	0.295641i
$611$	2.79195	+	4.83580i	0.112950	+	0.195636i
$612$		0			0
$613$	−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
$615$		0			0
$616$	13.9513	+	10.0796i	0.562114	+	0.406120i
$617$	−31.2585	+	5.51173i	−1.25842	+	0.221894i	−0.762794	−	0.646641i	$-0.776173\pi$
$617$	−31.2585	+	5.51173i	−1.25842	+	0.221894i	−0.495628	+	0.868535i	$0.665062\pi$
$618$		0			0
$619$	−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
$621$		0			0
$622$	−0.761519	+	8.23620i	−0.0305341	+	0.330241i
$623$	29.3569	+	24.6333i	1.17616	+	0.986914i
$624$		0			0
$625$	−3.66234	−	20.7701i	−0.146493	−	0.830806i
$626$	9.20258	−	19.4836i	0.367809	−	0.778720i
$627$		0			0
$628$	−10.2667	+	27.3647i	−0.409686	+	1.09197i
$629$	6.59915	+	3.81002i	0.263125	+	0.151915i
$630$		0			0
$631$	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
$633$		0			0
$634$	−14.7570	+	10.2249i	−0.586076	+	0.406082i
$635$	−11.5789	+	9.71582i	−0.459493	+	0.385561i
$636$		0			0
$637$	−12.3811	+	4.50635i	−0.490557	+	0.178548i
$638$	−3.51212	−	7.62977i	−0.139046	−	0.302066i
$639$		0			0
$640$	21.6237	−	9.18859i	0.854752	−	0.363211i
$641$	22.4050	+	3.95061i	0.884944	+	0.156040i	0.597606	−	0.801790i	$-0.296119\pi$
$641$	22.4050	+	3.95061i	0.884944	+	0.156040i	0.287338	+	0.957829i	$0.407230\pi$
$642$		0			0
$643$	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
$645$		0			0
$646$	33.7644	−	33.4330i	1.32844	−	1.31540i
$647$	−18.0068			−0.707921			−0.353961	−	0.935260i	$-0.615165\pi$
$647$	−18.0068			−0.707921			−0.353961	+	0.935260i	$0.615165\pi$
$648$		0			0
$649$	−2.63420			−0.103401
$650$	−1.10964	+	1.09875i	−0.0435237	+	0.0430966i
$651$		0			0
$652$	10.3797	+	0.102376i	0.406501	+	0.00400937i
$653$	−7.29835	+	20.0521i	−0.285607	+	0.784698i	0.711061	+	0.703130i	$0.248215\pi$
$653$	−7.29835	+	20.0521i	−0.285607	+	0.784698i	−0.996668	+	0.0815677i	$0.974007\pi$
$654$		0			0
$655$	2.35317	+	0.414927i	0.0919459	+	0.0162126i
$656$	−13.6307	−	16.9109i	−0.532190	−	0.660262i
$657$		0			0
$658$	8.01457	+	17.4110i	0.312440	+	0.678750i
$659$	−20.6155	+	7.50342i	−0.803065	+	0.292292i	−0.710756	−	0.703439i	$-0.751647\pi$
$659$	−20.6155	+	7.50342i	−0.803065	+	0.292292i	−0.0923092	+	0.995730i	$0.529425\pi$
$660$		0			0
$661$	−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
$663$		0			0
$664$	2.62070	+	36.0981i	0.101703	+	1.40088i
$665$	−56.4065	+	32.5663i	−2.18735	+	1.26287i
$666$		0			0
$667$	−12.5245	−	7.23102i	−0.484950	−	0.279986i
$668$	10.9535	−	29.1953i	0.423803	−	1.12960i
$669$		0			0
$670$	10.3016	−	21.8104i	0.397985	−	0.842608i
$671$	2.65225	+	15.0417i	0.102389	+	0.580678i
$672$		0			0
$673$	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			0
$676$	20.4858	+	3.82089i	0.787914	+	0.146957i
$677$	1.36103	−	1.62201i	0.0523085	−	0.0623388i	−0.739256	−	0.673425i	$-0.764823\pi$
$677$	1.36103	−	1.62201i	0.0523085	−	0.0623388i	0.791564	+	0.611086i	$0.209267\pi$
$678$		0			0
$679$	−54.3013	+	9.57479i	−2.08389	+	0.367447i
$680$	−14.3678	+	19.8866i	−0.550980	+	0.762616i
$681$		0			0
$682$	−0.367037	+	1.34327i	−0.0140546	+	0.0514364i
$683$	8.83350	−	15.3001i	0.338004	−	0.585441i	−0.646053	−	0.763293i	$-0.723581\pi$
$683$	8.83350	−	15.3001i	0.338004	−	0.585441i	0.984057	+	0.177852i	$0.0569148\pi$
$684$		0			0
$685$	18.7169	+	32.4187i	0.715137	+	1.23865i
$686$	−6.41072	+	1.68391i	−0.244763	+	0.0642919i
$687$		0			0
$688$	11.8795	+	34.7570i	0.452903	+	1.32510i
$689$	−6.23040	−	7.42510i	−0.237359	−	0.282874i
$690$		0			0
$691$	−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
$693$		0			0
$694$	39.1399	+	27.6947i	1.48573	+	1.05128i
$695$	−1.27015	+	7.20339i	−0.0481796	+	0.273240i
$696$		0			0
$697$	21.3130	+	7.75730i	0.807287	+	0.293829i
$698$	11.1903	−	0.923440i	0.423559	−	0.0349527i
$699$		0			0
$700$	−4.13996	+	3.40482i	−0.156476	+	0.128690i
$701$			20.3598i			0.768979i	0.923129	+	0.384490i	$0.125623\pi$
$701$			20.3598i			0.768979i	−0.923129	+	0.384490i	$0.874377\pi$
$702$		0			0
$703$			14.6752i			0.553485i
$704$	3.92140	+	11.8539i	0.147793	+	0.446763i
$705$		0			0
$706$	−1.36237	−	16.5092i	−0.0512734	−	0.621332i
$707$	12.8856	+	4.68997i	0.484613	+	0.176385i
$708$		0			0
$709$	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
$711$		0			0
$712$	6.79720	+	26.9565i	0.254736	+	1.01024i
$713$	0.820042	+	2.25305i	0.0307108	+	0.0843773i
$714$		0			0
$715$	3.34666	+	3.98839i	0.125158	+	0.149157i
$716$	−25.2215	+	14.2318i	−0.942571	+	0.531868i
$717$		0			0
$718$	−8.46791	−	32.2377i	−0.316020	−	1.20310i
$719$	−14.2069	−	24.6070i	−0.529827	−	0.917687i	−0.999395	−	0.0347903i	$-0.988924\pi$
$719$	−14.2069	−	24.6070i	−0.529827	−	0.917687i	0.469568	−	0.882896i	$-0.344410\pi$
$720$		0			0
$721$	13.6676	−	23.6730i	0.509008	−	0.881628i
$722$	62.3543	+	17.0378i	2.32059	+	0.634081i
$723$		0			0
$724$	6.86439	+	4.05395i	0.255113	+	0.150664i
$725$	2.57607	−	0.454231i	0.0956729	−	0.0168697i
$726$		0			0
$727$	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			0
$730$	−5.84648	−	0.540566i	−0.216388	−	0.0200072i
$731$	−29.3818	−	24.6543i	−1.08673	−	0.911871i
$732$		0			0
$733$	−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
$735$		0			0
$736$	17.3008	+	12.7612i	0.637718	+	0.470385i
$737$	11.1010	+	6.40916i	0.408910	+	0.236084i
$738$		0			0
$739$	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
$741$		0			0
$742$	−18.9488	−	27.3477i	−0.695632	−	1.00397i
$743$	9.26330	−	7.77283i	0.339837	−	0.285157i	−0.456857	−	0.889540i	$-0.651025\pi$
$743$	9.26330	−	7.77283i	0.339837	−	0.285157i	0.796694	+	0.604383i	$0.206580\pi$
$744$		0			0
$745$	−29.8919	+	10.8797i	−1.09515	+	0.398603i
$746$	−24.3497	+	11.2086i	−0.891504	+	0.410375i
$747$		0			0
$748$	−9.90440	−	8.47864i	−0.362141	−	0.310010i
$749$	−34.2892	−	6.04612i	−1.25290	−	0.220920i
$750$		0			0
$751$	−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
$753$		0			0
$754$	6.08278	+	6.14307i	0.221522	+	0.223717i
$755$	9.68114			0.352333
$756$		0			0
$757$	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
$759$		0			0
$760$	−47.0031	−	4.81389i	−1.70498	−	0.174618i
$761$	13.5388	−	37.1974i	0.490779	−	1.34841i	−0.409189	−	0.912450i	$-0.634188\pi$
$761$	13.5388	−	37.1974i	0.490779	−	1.34841i	0.899968	−	0.435956i	$-0.143590\pi$
$762$		0			0
$763$	14.8334	+	2.61553i	0.537005	+	0.0946884i
$764$	11.9539	−	13.9641i	0.432477	−	0.505202i
$765$		0			0
$766$	−38.8247	+	17.8717i	−1.40279	+	0.645730i
$767$	2.54777	−	0.927313i	0.0919947	−	0.0334833i
$768$		0			0
$769$	−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
$771$		0			0
$772$	6.16526	−	1.02451i	0.221892	−	0.0368729i
$773$	35.9391	−	20.7494i	1.29264	−	0.746306i	0.313518	−	0.949582i	$-0.398492\pi$
$773$	35.9391	−	20.7494i	1.29264	−	0.746306i	0.979121	+	0.203277i	$0.0651591\pi$
$774$		0			0
$775$	−0.375571	−	0.216836i	−0.0134909	−	0.00778899i
$776$	−35.9977	−	17.4389i	−1.29224	−	0.626020i
$777$		0			0
$778$	36.0990	+	17.0505i	1.29421	+	0.611289i
$779$	7.58500	+	43.0167i	0.271761	+	1.54123i
$780$		0			0
$781$	16.5423	+	13.8806i	0.591929	+	0.496687i
$782$	−22.3533	−	2.06679i	−0.799354	−	0.0739082i
$783$		0			0
$784$	−30.6024	−	11.8270i	−1.09294	−	0.422393i
$785$	−19.5073	+	23.2478i	−0.696244	+	0.829751i
$786$		0			0
$787$	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
$789$		0			0
$790$	10.8857	+	2.97441i	0.387294	+	0.105825i
$791$	−1.06009	+	1.83612i	−0.0376924	+	0.0652851i
$792$		0			0
$793$	−7.86033	−	13.6145i	−0.279128	−	0.483465i
$794$	−1.64189	−	6.25077i	−0.0582686	−	0.221832i
$795$		0			0
$796$	−19.8940	−	35.2559i	−0.705124	−	1.24961i
$797$	−11.9713	−	14.2669i	−0.424047	−	0.505359i	0.511148	−	0.859493i	$-0.329220\pi$
$797$	−11.9713	−	14.2669i	−0.424047	−	0.505359i	−0.935195	+	0.354133i	$0.884776\pi$
$798$		0			0
$799$	−4.96582	−	13.6435i	−0.175678	−	0.482671i
$800$	−3.88084	+	0.243295i	−0.137208	+	0.00860178i
$801$		0			0
$802$	−2.03054	+	2.86968i	−0.0717008	+	0.101332i
$803$	0.541816	−	3.07279i	0.0191203	−	0.108437i
$804$		0			0
$805$	28.9156	+	10.5244i	1.01914	+	0.370937i
$806$	−0.117874	−	1.42840i	−0.00415194	−	0.0503133i
$807$		0			0
$808$	5.58446	+	8.23200i	0.196461	+	0.289601i
$809$		−	28.0309i		−	0.985513i	−0.870167	−	0.492756i	$-0.835989\pi$
$809$		−	28.0309i		−	0.985513i	0.870167	−	0.492756i	$-0.164011\pi$
$810$		0			0
$811$			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
$813$		0			0
$814$	4.01302	−	0.331161i	0.140656	−	0.0116072i
$815$	10.1282	+	3.68637i	0.354776	+	0.129128i
$816$		0			0
$817$	12.8269	−	72.7449i	0.448756	−	2.54502i
$818$	−23.7398	−	16.7979i	−0.830044	−	0.587325i
$819$		0			0
$820$	−7.50426	−	21.2681i	−0.262060	−	0.742715i
$821$	0.0220034	+	0.0604539i	0.000767925	+	0.00210986i	0.940076	−	0.340965i	$-0.110754\pi$
$821$	0.0220034	+	0.0604539i	0.000767925	+	0.00210986i	−0.939308	+	0.343075i	$0.888532\pi$
$822$		0			0
$823$	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
$825$		0			0
$826$	9.00126	−	2.36437i	0.313194	−	0.0822668i
$827$	12.0949	+	20.9489i	0.420580	+	0.728466i	0.995996	−	0.0893948i	$-0.0284933\pi$
$827$	12.0949	+	20.9489i	0.420580	+	0.728466i	−0.575416	+	0.817861i	$0.695160\pi$
$828$		0			0
$829$	−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
$831$		0			0
$832$	−7.96566	−	10.0846i	−0.276160	−	0.349620i
$833$	33.7385	−	5.94900i	1.16897	−	0.206121i
$834$		0			0
$835$	20.8122	−	24.8030i	0.720235	−	0.858342i
$836$	4.60382	−	24.6834i	0.159226	−	0.853694i
$837$		0			0
$838$	−1.83909	+	19.8906i	−0.0635303	+	0.687111i
$839$	−16.5694	−	13.9034i	−0.572040	−	0.479999i	0.310282	−	0.950645i	$-0.399576\pi$
$839$	−16.5694	−	13.9034i	−0.572040	−	0.479999i	−0.882322	+	0.470646i	$0.844021\pi$
$840$		0			0
$841$	2.52114	+	14.2981i	0.0869358	+	0.493037i
$842$	7.13042	−	15.0964i	0.245731	−	0.520257i
$843$		0			0
$844$	18.1092	+	6.79422i	0.623345	+	0.233867i
$845$	18.7391	+	10.8190i	0.644645	+	0.372186i
$846$		0			0
$847$	28.9179	−	16.6958i	0.993631	−	0.573673i
$848$	0.476059	−	24.1309i	0.0163479	−	0.828660i
$849$		0			0
$850$	3.33752	−	2.31251i	0.114476	−	0.0793186i
$851$	5.31111	−	4.45655i	0.182063	−	0.152769i
$852$		0			0
$853$	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
$855$		0			0
$856$	−17.5940	−	18.1224i	−0.601350	−	0.619411i
$857$	30.6940	+	5.41218i	1.04849	+	0.184877i	0.671243	−	0.741237i	$-0.265761\pi$
$857$	30.6940	+	5.41218i	1.04849	+	0.184877i	0.377244	+	0.926114i	$0.376872\pi$
$858$		0			0
$859$	−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
$861$		0			0
$862$	−39.5525	+	39.1643i	−1.34716	+	1.33394i
$863$	18.1528			0.617929			0.308964	−	0.951074i	$-0.400018\pi$
$863$	18.1528			0.617929			0.308964	+	0.951074i	$0.400018\pi$
$864$		0			0
$865$	−26.7344			−0.908997
$866$	17.7059	−	17.5322i	0.601672	−	0.595767i
$867$		0			0
$868$	0.0485215	−	4.91949i	0.00164693	−	0.166978i
$869$	−2.05107	+	5.63527i	−0.0695778	+	0.191164i
$870$		0			0
$871$	−12.9930	−	2.29101i	−0.440250	−	0.0776279i
$872$	7.61109	+	7.83968i	0.257744	+	0.265485i
$873$		0			0
$874$	−18.0777	−	39.2722i	−0.611487	−	1.32840i
$875$	−43.2733	+	15.7502i	−1.46291	+	0.532454i
$876$		0			0
$877$	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
$879$		0			0
$880$	−0.255715	+	12.9619i	−0.00862015	+	0.436947i
$881$	29.9676	−	17.3018i	1.00963	−	0.582912i	0.0985488	−	0.995132i	$-0.468580\pi$
$881$	29.9676	−	17.3018i	1.00963	−	0.582912i	0.911084	+	0.412220i	$0.135247\pi$
$882$		0			0
$883$	−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			0
$886$	4.10093	−	8.68243i	0.137773	−	0.291692i
$887$	0.642373	+	3.64308i	0.0215688	+	0.122323i	0.993691	−	0.112152i	$-0.0357742\pi$
$887$	0.642373	+	3.64308i	0.0215688	+	0.122323i	−0.972122	+	0.234474i	$0.924663\pi$
$888$		0			0
$889$	21.7394	+	18.2415i	0.729116	+	0.611801i
$890$	−2.65763	+	28.7436i	−0.0890841	+	0.963488i
$891$		0			0
$892$	8.02012	−	43.0000i	0.268533	−	1.43975i
$893$	17.9735	−	21.4200i	0.601461	−	0.716793i
$894$		0			0
$895$	−29.6133	+	5.22162i	−0.989863	+	0.174540i
$896$	−24.0394	−	36.9861i	−0.803100	−	1.23562i
$897$		0			0
$898$	5.10469	−	18.6820i	0.170346	−	0.623425i
$899$	−1.20042	+	2.07919i	−0.0400363	+	0.0693450i
$900$		0			0
$901$	12.6014	+	21.8263i	0.419814	+	0.727140i
$902$	11.5920	−	3.04488i	0.385972	−	0.101384i
$903$		0			0
$904$	−1.40339	+	0.629308i	−0.0466762	+	0.0209305i
$905$	5.32084	+	6.34114i	0.176871	+	0.210786i
$906$		0			0
$907$	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
$909$		0			0
$910$	−15.0156	−	10.6248i	−0.497763	−	0.352208i
$911$	−1.65716	+	9.39822i	−0.0549041	+	0.311377i	−0.999876	−	0.0157761i	$-0.994978\pi$
$911$	−1.65716	+	9.39822i	−0.0549041	+	0.311377i	0.944971	+	0.327153i	$0.106089\pi$
$912$		0			0
$913$	−18.7668	−	6.83057i	−0.621092	−	0.226059i
$914$	−53.6834	+	4.43004i	−1.77569	+	0.146533i
$915$		0			0
$916$	−26.8875	−	32.6928i	−0.888390	−	1.08020i
$917$		−	4.48624i		−	0.148149i
$918$		0			0
$919$		−	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
$921$		0			0
$922$	0.575972	+	6.97965i	0.0189686	+	0.229862i
$923$	−20.8859	−	7.60184i	−0.687467	−	0.250217i
$924$		0			0
$925$	−0.217760	+	1.23498i	−0.00715992	+	0.0406059i
$926$	7.48375	−	10.5765i	0.245931	−	0.347566i
$927$		0			0
$928$	1.34690	+	21.4846i	0.0442142	+	0.705267i
$929$	−2.40637	−	6.61143i	−0.0789503	−	0.216914i	0.893938	−	0.448192i	$-0.147932\pi$
$929$	−2.40637	−	6.61143i	−0.0789503	−	0.216914i	−0.972888	+	0.231277i	$0.925710\pi$
$930$		0			0
$931$	42.4100	+	50.5422i	1.38993	+	1.65646i
$932$	4.83388	+	8.56656i	0.158339	+	0.280607i
$933$		0			0
$934$	7.87466	+	29.9792i	0.257667	+	0.980950i
$935$	−6.76885	−	11.7240i	−0.221365	−	0.383416i
$936$		0			0
$937$	−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
$939$		0			0
$940$	−7.34165	+	12.4313i	−0.239458	+	0.405465i
$941$	5.15723	−	0.909359i	0.168121	−	0.0296442i	−0.0889540	−	0.996036i	$-0.528352\pi$
$941$	5.15723	−	0.909359i	0.168121	−	0.0296442i	0.257075	+	0.966391i	$0.417241\pi$
$942$		0			0
$943$	13.2648	−	15.8084i	0.431961	−	0.514791i
$944$	6.29733	+	2.43375i	0.204961	+	0.0792119i
$945$		0			0
$946$	−20.1820	−	1.86603i	−0.656174	−	0.0606698i
$947$	−37.3876	−	31.3719i	−1.21493	−	1.01945i	−0.999074	−	0.0430267i	$-0.986300\pi$
$947$	−37.3876	−	31.3719i	−1.21493	−	1.01945i	−0.215860	−	0.976424i	$-0.569256\pi$
$948$		0			0
$949$	0.557671	+	3.16271i	0.0181028	+	0.102666i
$950$	7.07074	+	3.33969i	0.229405	+	0.108354i
$951$		0			0
$952$	41.4542	+	20.0823i	1.34354	+	0.650871i
$953$	−21.3286	−	12.3141i	−0.690901	−	0.398892i	0.113048	−	0.993589i	$-0.463939\pi$
$953$	−21.3286	−	12.3141i	−0.690901	−	0.398892i	−0.803950	+	0.594697i	$0.797272\pi$
$954$		0			0
$955$	16.5295	−	9.54330i	0.534882	−	0.308814i
$956$	−11.0919	+	1.84320i	−0.358738	+	0.0596133i
$957$		0			0
$958$	23.4511	+	33.8457i	0.757672	+	1.09351i
$959$	53.8393	−	45.1766i	1.73856	−	1.45883i
$960$		0			0
$961$	−28.7564	+	10.4665i	−0.927627	+	0.337629i
$962$	−3.76478	+	1.73299i	−0.121381	+	0.0558739i
$963$		0			0
$964$	0.696472	−	0.813590i	0.0224319	−	0.0262040i
$965$	6.39084	+	1.12688i	0.205728	+	0.0362755i
$966$		0			0
$967$	−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
$969$		0			0
$970$	−29.2231	−	29.5127i	−0.938296	−	0.947596i
$971$	−6.81102			−0.218576			−0.109288	−	0.994010i	$-0.534857\pi$
$971$	−6.81102			−0.218576			−0.109288	+	0.994010i	$0.534857\pi$
$972$		0			0
$973$	13.7330			0.440261
$974$	−18.3014	−	18.4828i	−0.586415	−	0.592227i
$975$		0			0
$976$	7.55659	−	38.4091i	0.241881	−	1.22945i
$977$	−3.48869	+	9.58509i	−0.111613	+	0.306654i	−0.982906	−	0.184109i	$-0.941060\pi$
$977$	−3.48869	+	9.58509i	−0.111613	+	0.306654i	0.871293	+	0.490764i	$0.163282\pi$
$978$		0			0
$979$	−15.1071	−	2.66378i	−0.482824	−	0.0851348i
$980$	−25.8790	−	22.1536i	−0.826674	−	0.707672i
$981$		0			0
$982$	−28.1675	+	12.9660i	−0.898861	+	0.413762i
$983$	−47.7474	+	17.3786i	−1.52290	+	0.554292i	−0.961872	−	0.273501i	$-0.911818\pi$
$983$	−47.7474	+	17.3786i	−1.52290	+	0.554292i	−0.561033	+	0.827793i	$0.689596\pi$
$984$		0			0
$985$	−26.6050	+	22.3242i	−0.847705	+	0.711309i
$986$	−12.8023	−	18.4768i	−0.407707	−	0.588421i
$987$		0			0
$988$	4.23650	+	25.4942i	0.134781	+	0.811079i
$989$	−30.2224	+	17.4489i	−0.961018	+	0.554844i
$990$		0			0
$991$	−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
$993$		0			0
$994$	−68.9849	−	32.5833i	−2.18807	−	1.03348i
$995$	−7.29906	−	41.3950i	−0.231396	−	1.31231i
$996$		0			0
$997$	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
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.11.5	✓	96	3.2	odd	2
108.2.l.a.11.6	yes	96	12.11	even	2
108.2.l.a.59.5	yes	96	108.103	odd	18
108.2.l.a.59.6	yes	96	27.22	even	9
324.2.l.a.35.11		96	4.3	odd	2	inner
324.2.l.a.35.12		96	1.1	even	1	trivial
324.2.l.a.287.11		96	27.5	odd	18	inner
324.2.l.a.287.12		96	108.59	even	18	inner
972.2.l.a.215.1		96	27.23	odd	18
972.2.l.a.215.3		96	108.23	even	18
972.2.l.a.755.1		96	36.7	odd	6
972.2.l.a.755.3		96	9.7	even	3
972.2.l.b.431.9		96	9.4	even	3
972.2.l.b.431.11		96	36.31	odd	6
972.2.l.b.539.9		96	108.95	even	18
972.2.l.b.539.11		96	27.14	odd	18
972.2.l.c.431.6		96	36.23	even	6
972.2.l.c.431.8		96	9.5	odd	6
972.2.l.c.539.6		96	27.13	even	9
972.2.l.c.539.8		96	108.67	odd	18
972.2.l.d.215.14		96	108.31	odd	18
972.2.l.d.215.16		96	27.4	even	9
972.2.l.d.755.14		96	9.2	odd	6
972.2.l.d.755.16		96	36.11	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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.l (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00492 - 0.995056i) q^{2} +(0.0197253 - 1.99990i) q^{4} +(0.710267 - 1.95144i) q^{5} +(-3.83975 - 0.677051i) q^{7} +(-1.97019 - 2.02937i) q^{8} +O(q^{10})\)	\(q+(1.00492 - 0.995056i) q^{2} +(0.0197253 - 1.99990i) q^{4} +(0.710267 - 1.95144i) q^{5} +(-3.83975 - 0.677051i) q^{7} +(-1.97019 - 2.02937i) q^{8} +(-1.22804 - 2.66780i) q^{10} +(1.46659 - 0.533796i) q^{11} +(-1.23056 + 1.03256i) q^{13} +(-4.53234 + 3.14038i) q^{14} +(-3.99922 - 0.0788972i) q^{16} +(3.61727 - 2.08843i) q^{17} +(6.96639 + 4.02205i) q^{19} +(-3.88869 - 1.45896i) q^{20} +(0.942651 - 1.99577i) q^{22} +(-0.659926 - 3.74263i) q^{23} +(0.526570 + 0.441845i) q^{25} +(-0.209156 + 2.26212i) q^{26} +(-1.42978 + 7.66577i) q^{28} +(2.44609 - 2.91513i) q^{29} +(-0.621314 + 0.109554i) q^{31} +(-4.09740 + 3.90017i) q^{32} +(1.55696 - 5.69810i) q^{34} +(-4.04848 + 7.01217i) q^{35} +(0.912171 + 1.57993i) q^{37} +(11.0028 - 2.89012i) q^{38} +(-5.35956 + 2.40333i) q^{40} +(3.49040 + 4.15970i) q^{41} +(-3.14069 - 8.62898i) q^{43} +(-1.03861 - 2.94357i) q^{44} +(-4.38730 - 3.10437i) q^{46} +(0.603613 - 3.42326i) q^{47} +(7.70742 + 2.80527i) q^{49} +(0.968821 - 0.0799486i) q^{50} +(2.04076 + 2.48137i) q^{52} +6.03391i q^{53} -3.24111i q^{55} +(6.19106 + 9.12619i) q^{56} +(-0.442602 - 5.36347i) q^{58} +(-1.58603 - 0.577267i) q^{59} +(-1.69938 + 9.63768i) q^{61} +(-0.515357 + 0.728336i) q^{62} +(-0.236673 + 7.99650i) q^{64} +(1.14096 + 3.13477i) q^{65} +(5.27928 + 6.29160i) q^{67} +(-4.10531 - 7.27539i) q^{68} +(2.90911 + 11.0751i) q^{70} +(6.91810 + 11.9825i) q^{71} +(0.999604 - 1.73136i) q^{73} +(2.48878 + 0.680037i) q^{74} +(8.18112 - 13.8528i) q^{76} +(-5.99276 + 1.05669i) q^{77} +(-2.46986 + 2.94347i) q^{79} +(-2.99448 + 7.74822i) q^{80} +(7.64671 + 0.707015i) q^{82} +(-9.80246 - 8.22524i) q^{83} +(-1.50623 - 8.54225i) q^{85} +(-11.7425 - 5.54626i) q^{86} +(-3.97274 - 1.92458i) q^{88} +(-8.51207 - 4.91444i) q^{89} +(5.42415 - 3.13163i) q^{91} +(-7.49791 + 1.24596i) q^{92} +(-2.79975 - 4.04073i) q^{94} +(12.7968 - 10.7378i) q^{95} +(13.2890 - 4.83681i) q^{97} +(10.5367 - 4.85025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) \) 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38} - 21 q^{40} + 42 q^{41} - 63 q^{44} - 3 q^{46} - 12 q^{49} - 87 q^{50} - 33 q^{52} - 99 q^{56} - 33 q^{58} - 12 q^{61} - 90 q^{62} - 3 q^{64} - 12 q^{65} - 51 q^{68} - 21 q^{70} - 6 q^{73} - 21 q^{74} - 18 q^{76} - 12 q^{77} - 12 q^{82} - 42 q^{85} + 30 q^{86} + 18 q^{88} + 123 q^{92} + 21 q^{94} - 30 q^{97} + 180 q^{98}+O(q^{100}) \) 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 + 21 * q^14 - 6 * q^16 + 18 * q^17 + 27 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 + 24 * q^29 - 24 * q^32 - 12 * q^34 - 6 * q^37 - 18 * q^38 - 21 * q^40 + 42 * q^41 - 63 * q^44 - 3 * q^46 - 12 * q^49 - 87 * q^50 - 33 * q^52 - 99 * q^56 - 33 * q^58 - 12 * q^61 - 90 * q^62 - 3 * q^64 - 12 * q^65 - 51 * q^68 - 21 * q^70 - 6 * q^73 - 21 * q^74 - 18 * q^76 - 12 * q^77 - 12 * q^82 - 42 * q^85 + 30 * q^86 + 18 * q^88 + 123 * q^92 + 21 * q^94 - 30 * q^97 + 180 * q^98

Introduction

L-functions

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