LMFDB - Embedded newform 324.2.l.a.35.11

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			35.11
Character	$\chi$	$=$	324.35
Dual form			324.2.l.a.287.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.805437 - 1.16244i) q^{2} +(-0.702543 - 1.87255i) q^{4} +(0.710267 - 1.95144i) q^{5} +(3.83975 + 0.677051i) q^{7} +(-2.74258 - 0.691554i) q^{8} +O(q^{10})$	\(q+(0.805437 - 1.16244i) q^{2} +(-0.702543 - 1.87255i) q^{4} +(0.710267 - 1.95144i) q^{5} +(3.83975 + 0.677051i) q^{7} +(-2.74258 - 0.691554i) q^{8} +(-1.69636 - 2.39741i) q^{10} +(-1.46659 + 0.533796i) q^{11} +(-1.23056 + 1.03256i) q^{13} +(3.87971 - 3.91816i) q^{14} +(-3.01287 + 2.63109i) q^{16} +(3.61727 - 2.08843i) q^{17} +(-6.96639 - 4.02205i) q^{19} +(-4.15316 + 0.0409631i) q^{20} +(-0.560741 + 2.13477i) q^{22} +(0.659926 + 3.74263i) q^{23} +(0.526570 + 0.441845i) q^{25} +(0.209156 + 2.26212i) q^{26} +(-1.42978 - 7.66577i) q^{28} +(2.44609 - 2.91513i) q^{29} +(0.621314 - 0.109554i) q^{31} +(0.631814 + 5.62146i) q^{32} +(0.485803 - 5.88697i) q^{34} +(4.04848 - 7.01217i) q^{35} +(0.912171 + 1.57993i) q^{37} +(-10.2864 + 4.85852i) q^{38} +(-3.29749 + 4.86081i) q^{40} +(3.49040 + 4.15970i) q^{41} +(3.14069 + 8.62898i) q^{43} +(2.02990 + 2.37125i) q^{44} +(4.88211 + 2.24732i) q^{46} +(-0.603613 + 3.42326i) q^{47} +(7.70742 + 2.80527i) q^{49} +(0.937738 - 0.256229i) q^{50} +(2.79805 + 1.57887i) q^{52} +6.03391i q^{53} +3.24111i q^{55} +(-10.0626 - 4.51226i) q^{56} +(-1.41850 - 5.19139i) q^{58} +(1.58603 + 0.577267i) q^{59} +(-1.69938 + 9.63768i) q^{61} +(0.373079 - 0.810481i) q^{62} +(7.04351 + 3.79328i) q^{64} +(1.14096 + 3.13477i) q^{65} +(-5.27928 - 6.29160i) q^{67} +(-6.45198 - 5.30630i) q^{68} +(-4.89044 - 10.3540i) q^{70} +(-6.91810 - 11.9825i) q^{71} +(0.999604 - 1.73136i) q^{73} +(2.57127 + 0.212185i) q^{74} +(-2.63729 + 15.8706i) q^{76} +(-5.99276 + 1.05669i) q^{77} +(2.46986 - 2.94347i) q^{79} +(2.99448 + 7.74822i) q^{80} +(7.64671 - 0.707015i) q^{82} +(9.80246 + 8.22524i) q^{83} +(-1.50623 - 8.54225i) q^{85} +(12.5603 + 3.29923i) q^{86} +(4.39140 - 0.449752i) q^{88} +(-8.51207 - 4.91444i) q^{89} +(-5.42415 + 3.13163i) q^{91} +(6.54462 - 3.86510i) q^{92} +(3.49317 + 3.45888i) q^{94} +(-12.7968 + 10.7378i) q^{95} +(13.2890 - 4.83681i) q^{97} +(9.46881 - 6.69996i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.805437	−	1.16244i	0.569530	−	0.821971i
$2$	0.805437	−	1.16244i	0.569530	−	0.821971i
$3$		0			0
$3$		0			0
$4$	−0.702543	−	1.87255i	−0.351271	−	0.936274i
$5$	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	0.843042	−	0.537847i	$-0.180762\pi$
$7$	3.83975	+	0.677051i	1.45129	+	0.255901i	0.608246	+	0.793748i	$0.291873\pi$
$8$	−2.74258	−	0.691554i	−0.969649	−	0.244501i
$9$		0			0
$10$	−1.69636	−	2.39741i	−0.536438	−	0.758127i
$11$	−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	$0.464492\pi$
$12$		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	$0.349286\pi$
$14$	3.87971	−	3.91816i	1.03690	−	1.04717i
$15$		0			0
$16$	−3.01287	+	2.63109i	−0.753217	+	0.657772i
$17$	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	$-0.959293\pi$
$19$	−6.96639	−	4.02205i	−1.59820	−	0.922721i	−0.606366	−	0.795186i	$-0.707373\pi$
$20$	−4.15316	+	0.0409631i	−0.928676	+	0.00915963i
$21$		0			0
$22$	−0.560741	+	2.13477i	−0.119550	+	0.455134i
$23$	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	$0.814768\pi$
$24$		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	−0.117574	−	0.993064i	$-0.537512\pi$
$31$	0.621314	−	0.109554i	0.111591	−	0.0196766i	0.229165	+	0.973388i	$0.426400\pi$
$32$	0.631814	+	5.62146i	0.111690	+	0.993743i
$33$		0			0
$34$	0.485803	−	5.88697i	0.0833144	−	1.00961i
$35$	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	$0.785419\pi$
$38$	−10.2864	+	4.85852i	−1.66867	+	0.788156i
$39$		0			0
$40$	−3.29749	+	4.86081i	−0.521380	+	0.768561i
$41$	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	$0.135786\pi$
$43$	3.14069	+	8.62898i	0.478951	+	1.31591i	−0.431433	+	0.902145i	$0.641992\pi$
$44$	2.02990	+	2.37125i	0.306020	+	0.357480i
$45$		0			0
$46$	4.88211	+	2.24732i	0.719829	+	0.331350i
$47$	−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	$0.973968\pi$
$48$		0			0
$49$	7.70742	+	2.80527i	1.10106	+	0.400753i
$50$	0.937738	−	0.256229i	0.132616	−	0.0362363i
$51$		0			0
$52$	2.79805	+	1.57887i	0.388020	+	0.218949i
$53$			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
$56$	−10.0626	−	4.51226i	−1.34467	−	0.602976i
$57$		0			0
$58$	−1.41850	−	5.19139i	−0.186259	−	0.681663i
$59$	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	$0.576068\pi$
$60$		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	$0.840040\pi$
$62$	0.373079	−	0.810481i	0.0473810	−	0.102931i
$63$		0			0
$64$	7.04351	+	3.79328i	0.880438	+	0.474161i
$65$	1.14096	+	3.13477i	0.141519	+	0.388820i
$66$		0			0
$67$	−5.27928	−	6.29160i	−0.644966	−	0.768641i	0.340179	−	0.940361i	$-0.389512\pi$
$67$	−5.27928	−	6.29160i	−0.644966	−	0.768641i	−0.985146	+	0.171719i	$0.945068\pi$
$68$	−6.45198	−	5.30630i	−0.782418	−	0.643484i
$69$		0			0
$70$	−4.89044	−	10.3540i	−0.584520	−	1.23754i
$71$	−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	$-0.473266\pi$
$72$		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	$0.129341\pi$
$74$	2.57127	+	0.212185i	0.298904	+	0.0246661i
$75$		0			0
$76$	−2.63729	+	15.8706i	−0.302518	+	1.82048i
$77$	−5.99276	+	1.05669i	−0.682938	+	0.120420i
$78$		0			0
$79$	2.46986	−	2.94347i	0.277881	−	0.331166i	−0.608994	−	0.793175i	$-0.708427\pi$
$79$	2.46986	−	2.94347i	0.277881	−	0.331166i	0.886875	+	0.462009i	$0.152871\pi$
$80$	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	0.995579	−	0.0939267i	$-0.0299419\pi$
$83$	9.80246	+	8.22524i	1.07596	+	0.902838i	0.0803808	+	0.996764i	$0.474386\pi$
$84$		0			0
$85$	−1.50623	−	8.54225i	−0.163374	−	0.926537i
$86$	12.5603	+	3.29923i	1.35441	+	0.355765i
$87$		0			0
$88$	4.39140	−	0.449752i	0.468125	−	0.0479437i
$89$	−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
$92$	6.54462	−	3.86510i	0.682324	−	0.402964i
$93$		0			0
$94$	3.49317	+	3.45888i	0.360293	+	0.356757i
$95$	−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	$0.133971\pi$
$98$	9.46881	−	6.69996i	0.956494	−	0.676798i
$99$		0			0
$100$	0.457437	−	1.29644i	0.0457437	−	0.129644i
$101$	−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	$-0.776632\pi$
$103$	2.39786	−	6.58805i	0.236268	−	0.649140i	0.999994	−	0.00359939i	$-0.00114572\pi$
$104$	4.08899	−	1.98089i	0.400959	−	0.194242i
$105$		0			0
$106$	7.01407	+	4.85993i	0.681267	+	0.472039i
$107$	−8.93007			−0.863303			−0.431651	−	0.902041i	$-0.642069\pi$
$107$	−8.93007			−0.863303			−0.431651	+	0.902041i	$0.642069\pi$
$108$		0			0
$109$	−3.86311			−0.370019			−0.185010	−	0.982737i	$-0.559232\pi$
$109$	−3.86311			−0.370019			−0.185010	+	0.982737i	$0.559232\pi$
$110$	3.76761	+	2.61051i	0.359227	+	0.248903i
$111$		0			0
$112$	−13.3500	+	8.06285i	−1.26146	+	0.761868i
$113$	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
$116$	−7.17721	−	2.53241i	−0.666387	−	0.235128i
$117$		0			0
$118$	1.94848	−	1.37871i	0.179373	−	0.126921i
$119$	15.3034	−	5.56998i	1.40286	−	0.510599i
$120$		0			0
$121$	−6.56053	+	5.50494i	−0.596412	+	0.500449i
$122$	9.83449	+	9.73797i	0.890373	+	0.881635i
$123$		0			0
$124$	−0.641645	−	1.08647i	−0.0576215	−	0.0975682i
$125$	10.2285	−	5.90545i	0.914869	−	0.528200i
$126$		0			0
$127$	6.30337	+	3.63925i	0.559333	+	0.322931i	0.752878	−	0.658160i	$-0.228665\pi$
$127$	6.30337	+	3.63925i	0.559333	+	0.322931i	−0.193545	+	0.981091i	$0.561998\pi$
$128$	10.0826	−	5.13242i	0.891182	−	0.453646i
$129$		0			0
$130$	4.56296	+	1.19856i	0.400198	+	0.105120i
$131$	−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	$0.960451\pi$
$132$		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	−0.0245942	−	0.999698i	$-0.507829\pi$
$139$	3.46870	−	0.611626i	0.294211	−	0.0518774i	0.318806	+	0.947820i	$0.396718\pi$
$140$	−15.9748	−	2.65462i	−1.35012	−	0.224356i
$141$		0			0
$142$	−19.5011	−	1.60926i	−1.63649	−	0.135046i
$143$	1.25356	−	2.17122i	0.104828	−	0.181567i
$144$		0			0
$145$	−3.95134	−	6.84393i	−0.328141	−	0.568357i
$146$	−1.20749	−	2.55649i	−0.0999329	−	0.211576i
$147$		0			0
$148$	2.31765	−	2.81805i	0.190510	−	0.231642i
$149$	−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	0.857755	−	0.514058i	$-0.171858\pi$
$151$	−1.59444	−	4.38068i	−0.129754	−	0.356495i	−0.987509	+	0.157563i	$0.949636\pi$
$152$	16.3244	+	15.8484i	1.32409	+	1.28548i
$153$		0			0
$154$	−3.59845	+	7.81733i	−0.289972	+	0.629938i
$155$	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	$0.809290\pi$
$158$	−1.43229	−	5.24185i	−0.113947	−	0.417019i
$159$		0			0
$160$	11.4187	+	2.75979i	0.902729	+	0.218181i
$161$			14.8175i			1.16779i
$162$		0			0
$163$		−	5.19011i		−	0.406521i	−0.979125	−	0.203260i	$-0.934846\pi$
$163$		−	5.19011i		−	0.406521i	0.979125	−	0.203260i	$-0.0651538\pi$
$164$	5.33708	−	9.45831i	0.416756	−	0.738570i
$165$		0			0
$166$	17.4566	−	4.76988i	1.35490	−	0.370214i
$167$	−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	$0.817236\pi$
$168$		0			0
$169$	−1.80933	+	10.2612i	−0.139179	+	0.789325i
$170$	−11.1430	−	5.12934i	−0.854633	−	0.393402i
$171$		0			0
$172$	13.9517	−	11.9433i	1.06381	−	0.910670i
$173$	−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
$176$	3.01419	−	5.46700i	0.227203	−	0.412090i
$177$		0			0
$178$	−12.5687	+	5.93651i	−0.942063	+	0.444960i
$179$	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	$0.651327\pi$
$180$		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	$0.213995\pi$
$182$	−0.728467	+	8.82759i	−0.0539976	+	0.654345i
$183$		0			0
$184$	0.778326	−	10.7208i	0.0573790	−	0.790350i
$185$	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	0.351490	−	0.936192i	$-0.385675\pi$
$191$	−7.04065	−	5.90780i	−0.509443	−	0.427474i	−0.860933	+	0.508718i	$0.830120\pi$
$192$		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	$0.908569\pi$
$194$	5.08097	−	19.3435i	0.364792	−	1.38878i
$195$		0			0
$196$	−0.161788	−	16.4033i	−0.0115563	−	1.17167i
$197$	−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	−0.969622	−	0.244606i	$-0.921341\pi$
$199$	−17.5290	+	10.1204i	−1.24260	+	0.717414i	−0.272976	+	0.962021i	$0.588008\pi$
$200$	−1.13860	−	1.57595i	−0.0805113	−	0.111436i
$201$		0			0
$202$	−3.49957	+	3.53426i	−0.246229	+	0.248670i
$203$	11.3661	−	9.53725i	0.797741	−	0.669384i
$204$		0			0
$205$	10.5965	−	3.85682i	0.740094	−	0.269372i
$206$	−5.72691	−	8.09363i	−0.399013	−	0.563910i
$207$		0			0
$208$	0.990753	−	6.34870i	0.0686963	−	0.440203i
$209$	12.3638	+	2.18007i	0.855223	+	0.150799i
$210$		0			0
$211$	3.30764	−	9.08767i	0.227707	−	0.625621i	−0.772245	−	0.635324i	$-0.780866\pi$
$211$	3.30764	−	9.08767i	0.227707	−	0.625621i	0.999953	+	0.00970319i	$0.00308867\pi$
$212$	11.2988	−	4.23908i	0.776004	−	0.291141i
$213$		0			0
$214$	−7.19261	+	10.3807i	−0.491677	+	0.709609i
$215$	19.0697			1.30054
$216$		0			0
$217$	2.45986			0.166986
$218$	−3.11150	+	4.49065i	−0.210737	+	0.304145i
$219$		0			0
$220$	6.06914	−	2.27702i	0.409181	−	0.153517i
$221$	−2.29484	+	6.30502i	−0.154368	+	0.424121i
$222$		0			0
$223$	−21.5385	−	3.79782i	−1.44232	−	0.254321i	−0.602908	−	0.797811i	$-0.705991\pi$
$223$	−21.5385	−	3.79782i	−1.44232	−	0.254321i	−0.839416	+	0.543490i	$0.817103\pi$
$224$	−1.38001	+	22.0128i	−0.0922059	+	1.47079i
$225$		0			0
$226$	−0.444190	−	0.627758i	−0.0295471	−	0.0417578i
$227$	−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	$0.440868\pi$
$228$		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	$0.0312739\pi$
$230$	7.85313	−	7.93097i	0.517820	−	0.522953i
$231$		0			0
$232$	−8.72457	+	6.30339i	−0.572796	+	0.413838i
$233$	−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
$236$	−0.0332926	−	3.37547i	−0.00216716	−	0.219724i
$237$		0			0
$238$	5.85114	−	22.2756i	0.379273	−	1.44391i
$239$	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	$0.886243\pi$
$240$		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
$248$	−1.77977	−	0.129210i	−0.113015	−	0.00820485i
$249$		0			0
$250$	1.37370	−	16.6466i	0.0868805	−	1.05282i
$251$	−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	$0.272944\pi$
$252$		0			0
$253$	−2.96564	−	5.13665i	−0.186448	−	0.322938i
$254$	9.30738	−	4.39611i	0.583997	−	0.275837i
$255$		0			0
$256$	2.15474	−	15.8542i	0.134671	−	0.990890i
$257$	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
$260$	5.06843	−	4.33882i	0.314331	−	0.269082i
$261$		0			0
$262$	−1.47814	−	0.680412i	−0.0913196	−	0.0420360i
$263$	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	$-0.0956444\pi$
$264$		0			0
$265$	11.7748	+	4.28569i	0.723322	+	0.263268i
$266$	−42.7866	+	11.6911i	−2.62341	+	0.716826i
$267$		0			0
$268$	−8.07240	+	14.3058i	−0.493100	+	0.873867i
$269$		−	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	$0.0659179\pi$
$271$			6.76954i			0.411220i	−0.978634	+	0.205610i	$0.934082\pi$
$272$	−5.40351	+	15.8095i	−0.327636	+	0.958594i
$273$		0			0
$274$	6.71925	+	24.5909i	0.405925	+	1.48559i
$275$	−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	$0.875116\pi$
$278$	2.08284	−	4.52479i	0.124921	−	0.271379i
$279$		0			0
$280$	−15.9526	+	16.4317i	−0.953348	+	0.981982i
$281$	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	0.863507	−	0.504336i	$-0.168263\pi$
$283$	3.64860	+	4.34824i	0.216887	+	0.258476i	−0.646621	+	0.762812i	$0.723818\pi$
$284$	−17.5776	+	21.3727i	−1.04304	+	1.26824i
$285$		0			0
$286$	−1.51426	−	3.20597i	−0.0895401	−	0.189573i
$287$	10.5859	+	18.3354i	0.624868	+	1.08230i
$288$		0			0
$289$	0.223112	−	0.386442i	0.0131243	−	0.0227319i
$290$	−11.1382	−	0.919144i	−0.654059	−	0.0539740i
$291$		0			0
$292$	−3.94433	−	0.655448i	−0.230824	−	0.0383572i
$293$	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
$302$	−6.37651	−	1.67492i	−0.366927	−	0.0963810i
$303$		0			0
$304$	31.5712	−	6.21130i	1.81073	−	0.356242i
$305$	17.6004	+	10.1616i	1.00779	+	0.581850i
$306$		0			0
$307$	25.2053	−	14.5523i	1.43854	−	0.830541i	0.440792	−	0.897609i	$-0.354698\pi$
$307$	25.2053	−	14.5523i	1.43854	−	0.830541i	0.997748	+	0.0670680i	$0.0213645\pi$
$308$	6.18886	+	10.4794i	0.352643	+	0.597117i
$309$		0			0
$310$	−1.31662	−	1.30370i	−0.0747791	−	0.0740452i
$311$	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	$0.224749\pi$
$312$		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	$0.247189\pi$
$314$	−16.8706	+	11.9373i	−0.952063	+	0.673663i
$315$		0			0
$316$	−7.24696	−	2.55702i	−0.407673	−	0.143844i
$317$	−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
$320$	12.4052	−	11.0508i	0.693469	−	0.617756i
$321$		0			0
$322$	17.2245	+	11.9346i	0.959886	+	0.665089i
$323$	−33.5991			−1.86951
$324$		0			0
$325$	−1.10421			−0.0612506
$326$	−6.03320	−	4.18031i	−0.334148	−	0.231526i
$327$		0			0
$328$	−6.69606	−	13.8221i	−0.369728	−	0.763199i
$329$	−4.63544	+	12.7358i	−0.255560	+	0.702146i
$330$		0			0
$331$	−2.67374	−	0.471452i	−0.146962	−	0.0259133i	0.0996832	−	0.995019i	$-0.468217\pi$
$331$	−2.67374	−	0.471452i	−0.146962	−	0.0259133i	−0.246645	+	0.969106i	$0.579328\pi$
$332$	8.51551	−	24.1342i	0.467349	−	1.32453i
$333$		0			0
$334$	−17.9991	+	12.7359i	−0.984869	+	0.696876i
$335$	−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	$0.224781\pi$
$338$	10.4708	+	10.3680i	0.569535	+	0.563946i
$339$		0			0
$340$	−14.9376	+	8.82178i	−0.810104	+	0.478428i
$341$	−0.852735	+	0.492327i	−0.0461782	+	0.0266610i
$342$		0			0
$343$	4.05892	+	2.34342i	0.219161	+	0.126533i
$344$	−2.64620	−	25.8376i	−0.142674	−	1.39307i
$345$		0			0
$346$	−17.6087	−	4.62529i	−0.946650	−	0.248657i
$347$	−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	$-0.419492\pi$
$348$		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
$356$	−3.22244	+	19.3919i	−0.170789	+	1.02777i
$357$		0			0
$358$	20.4083	+	1.68412i	1.07861	+	0.0890087i
$359$	−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	$0.953005\pi$
$360$		0			0
$361$	22.8537	+	39.5838i	1.20283	+	2.08336i
$362$	2.40752	+	5.09716i	0.126536	+	0.267901i
$363$		0			0
$364$	9.67483	+	7.95687i	0.507099	+	0.417053i
$365$	−2.66867	−	3.18040i	−0.139685	−	0.166470i
$366$		0			0
$367$	−8.45358	−	23.2260i	−0.441273	−	1.21239i	−0.938655	−	0.344856i	$-0.887928\pi$
$367$	−8.45358	−	23.2260i	−0.441273	−	1.21239i	0.497382	−	0.867531i	$-0.334295\pi$
$368$	−11.8355	−	9.53971i	−0.616966	−	0.497292i
$369$		0			0
$370$	2.24036	−	4.86698i	0.116471	−	0.253022i
$371$	−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	$0.774374\pi$
$374$	2.42997	+	8.89312i	0.125651	+	0.459852i
$375$		0			0
$376$	4.02282	−	8.97114i	0.207461	−	0.462651i
$377$			6.11300i			0.314835i
$378$		0			0
$379$		−	8.62366i		−	0.442968i	−0.975164	−	0.221484i	$-0.928910\pi$
$379$		−	8.62366i		−	0.442968i	0.975164	−	0.221484i	$-0.0710900\pi$
$380$	29.0973	+	16.4189i	1.49266	+	0.842270i
$381$		0			0
$382$	−12.5383	+	3.42598i	−0.641514	+	0.175288i
$383$	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	$0.330298\pi$
$384$		0			0
$385$	−2.19440	+	12.4451i	−0.111837	+	0.634259i
$386$	4.01439	+	1.84789i	0.204327	+	0.0940553i
$387$		0			0
$388$	−18.3933	−	21.4863i	−0.933777	−	1.09080i
$389$	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
$392$	−19.1982	−	13.0238i	−0.969657	−	0.657800i
$393$		0			0
$394$	−21.3857	+	10.1010i	−1.07740	+	0.508882i
$395$	−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	$0.130083\pi$
$398$	−2.35416	+	28.5278i	−0.118003	+	1.42997i
$399$		0			0
$400$	−2.74902	+	0.0542330i	−0.137451	+	0.00271165i
$401$	−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	$-0.225322\pi$
$410$	4.05151	−	15.4243i	0.200090	−	0.761751i
$411$		0			0
$412$	−14.0210	+	0.138291i	−0.690767	+	0.00681311i
$413$	5.69911	+	3.29038i	0.280435	+	0.161909i
$414$		0			0
$415$	23.0135	−	13.2868i	1.12969	−	0.652225i
$416$	−6.58201	−	6.26517i	−0.322709	−	0.307175i
$417$		0			0
$418$	12.4925	−	12.6163i	0.611028	−	0.617084i
$419$	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	$0.165650\pi$
$420$		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	$0.296003\pi$
$422$	−7.89979	−	11.1645i	−0.384556	−	0.543479i
$423$		0			0
$424$	4.17277	−	16.5485i	0.202648	−	0.803666i
$425$	2.82751	+	0.498566i	0.137154	+	0.0241840i
$426$		0			0
$427$	−13.0504	+	35.8557i	−0.631553	+	1.73518i
$428$	6.27376	+	16.7220i	0.303254	+	0.808288i
$429$		0			0
$430$	15.3594	−	22.1674i	0.740698	−	1.06901i
$431$	39.3589			1.89585			0.947926	−	0.318492i	$-0.103176\pi$
$431$	39.3589			1.89585			0.947926	+	0.318492i	$0.103176\pi$
$432$		0			0
$433$	17.6193			0.846728			0.423364	−	0.905960i	$-0.360849\pi$
$433$	17.6193			0.846728			0.423364	+	0.905960i	$0.360849\pi$
$434$	1.98126	−	2.85945i	0.0951037	−	0.137258i
$435$		0			0
$436$	2.71400	+	7.23387i	0.129977	+	0.346439i
$437$	10.4557	−	28.7269i	0.500165	−	1.37419i
$438$		0			0
$439$	−15.3376	−	2.70443i	−0.732022	−	0.129075i	−0.204801	−	0.978804i	$-0.565655\pi$
$439$	−15.3376	−	2.70443i	−0.732022	−	0.129075i	−0.527221	+	0.849728i	$0.676766\pi$
$440$	2.24140	−	8.88902i	0.106855	−	0.423767i
$441$		0			0
$442$	5.48087	+	7.74591i	0.260698	+	0.368435i
$443$	−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	$0.440456\pi$
$444$		0			0
$445$	−15.6361	+	13.1202i	−0.741222	+	0.621959i
$446$	−21.7626	+	21.9783i	−1.03049	+	1.04070i
$447$		0			0
$448$	24.4770	+	19.3341i	1.15643	+	0.913449i
$449$	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
$452$	−1.08750	+	0.0107261i	−0.0511517	+	0.000504515i
$453$		0			0
$454$	−1.76006	+	6.70065i	−0.0826039	+	0.314477i
$455$	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	−0.379321	−	0.925265i	$-0.623842\pi$
$463$	−9.02239	+	1.59089i	−0.419306	+	0.0739350i	−0.0399855	+	0.999200i	$0.512731\pi$
$464$	0.300238	+	15.2188i	0.0139382	+	0.706514i
$465$		0			0
$466$	−0.572018	+	6.93174i	−0.0264982	+	0.321106i
$467$	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	$-0.00262063\pi$
$468$		0			0
$469$	−16.0114	−	27.7325i	−0.739336	−	1.28057i
$470$	9.23090	−	4.35999i	0.425790	−	0.201111i
$471$		0			0
$472$	−3.95060	−	2.68002i	−0.181841	−	0.123358i
$473$	−9.21224	−	10.9787i	−0.423579	−	0.504802i
$474$		0			0
$475$	−1.89117	−	5.19595i	−0.0867729	−	0.238407i
$476$	−21.1813	−	24.7432i	−0.970845	−	1.13410i
$477$		0			0
$478$	7.22228	+	3.32455i	0.330340	+	0.152061i
$479$	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	$-0.176087\pi$
$480$		0			0
$481$	−2.75386	−	1.00232i	−0.125565	−	0.0457020i
$482$	0.730519	−	0.199608i	0.0332742	−	0.00909191i
$483$		0			0
$484$	14.9173	+	8.41745i	0.678060	+	0.382611i
$485$		−	29.3682i		−	1.33354i
$486$		0			0
$487$			18.3923i			0.833436i	0.909036	+	0.416718i	$0.136820\pi$
$487$			18.3923i			0.833436i	−0.909036	+	0.416718i	$0.863180\pi$
$488$	11.3257	−	25.2569i	0.512689	−	1.14333i
$489$		0			0
$490$	−6.34921	−	23.2366i	−0.286828	−	1.04972i
$491$	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	$0.446367\pi$
$492$		0			0
$493$	2.76010	−	15.6533i	0.124309	−	0.704990i
$494$	7.64131	−	16.6001i	0.343799	−	0.746872i
$495$		0			0
$496$	−1.58369	+	1.96481i	−0.0711097	+	0.0882224i
$497$	−18.4510	−	50.6937i	−0.827641	−	2.27392i
$498$		0			0
$499$	2.64022	+	3.14650i	0.118193	+	0.140857i	0.821896	−	0.569637i	$-0.192916\pi$
$499$	2.64022	+	3.14650i	0.118193	+	0.140857i	−0.703704	+	0.710494i	$0.748472\pi$
$500$	−18.2442	−	15.0046i	−0.815906	−	0.671026i
$501$		0			0
$502$	6.27172	+	13.2784i	0.279921	+	0.592644i
$503$	−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	$0.930705\pi$
$504$		0			0
$505$	−3.65181	+	6.32511i	−0.162503	+	0.281464i
$506$	−8.35969	−	0.689855i	−0.371634	−	0.0306678i
$507$		0			0
$508$	2.38628	−	14.3601i	0.105874	−	0.637126i
$509$	−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
$518$	9.72937	+	2.55562i	0.427484	+	0.112288i
$519$		0			0
$520$	−0.961322	−	9.38640i	−0.0421568	−	0.411621i
$521$	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	0.415189	−	0.909735i	$-0.363716\pi$
$523$	32.2601	−	18.6254i	1.41064	−	0.814432i	0.995448	+	0.0953038i	$0.0303822\pi$
$524$	−1.98149	+	1.17022i	−0.0865616	+	0.0511212i
$525$		0			0
$526$	−14.9068	−	14.7605i	−0.649967	−	0.643588i
$527$	2.01867	−	1.69386i	0.0879344	−	0.0737858i
$528$		0			0
$529$	8.04118	−	2.92675i	0.349617	−	0.127250i
$530$	14.4658	−	10.2357i	0.628352	−	0.444611i
$531$		0			0
$532$	−20.8717	+	59.1534i	−0.904903	+	2.56462i
$533$	−8.59032	−	1.51470i	−0.372088	−	0.0656091i
$534$		0			0
$535$	−6.34274	+	17.4265i	−0.274221	+	0.753415i
$536$	10.1279	+	20.9061i	0.437457	+	0.903007i
$537$		0			0
$538$	−12.5273	−	8.67999i	−0.540092	−	0.374221i
$539$	−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	$0.692956\pi$
$542$	7.86920	+	5.45244i	0.338011	+	0.234202i
$543$		0			0
$544$	14.0255	+	19.0149i	0.601338	+	0.815255i
$545$	−2.74384	+	7.53865i	−0.117533	+	0.322920i
$546$		0			0
$547$	25.2688	+	4.45558i	1.08042	+	0.190507i	0.685400	−	0.728167i	$-0.259627\pi$
$547$	25.2688	+	4.45558i	1.08042	+	0.190507i	0.395017	+	0.918674i	$0.370739\pi$
$548$	33.9974	+	11.9956i	1.45230	+	0.512429i
$549$		0			0
$550$	−1.23851	+	0.876345i	−0.0528101	+	0.0373675i
$551$	−28.7652	+	10.4697i	−1.22544	+	0.446023i
$552$		0			0
$553$	11.4765	−	9.62995i	0.488031	−	0.409507i
$554$	17.9626	+	17.7863i	0.763159	+	0.755669i
$555$		0			0
$556$	−3.58221	−	6.06562i	−0.151920	−	0.257239i
$557$	−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
$560$	6.25211	+	31.7786i	0.264200	+	1.34289i
$561$		0			0
$562$	14.4705	+	3.80098i	0.610402	+	0.160335i
$563$	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	$0.646724\pi$
$564$		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	−0.608886	−	0.793257i	$-0.708383\pi$
$571$	−21.7388	+	3.83314i	−0.909742	+	0.160412i	−0.300856	+	0.953670i	$0.597272\pi$
$572$	−4.94639	−	0.821966i	−0.206819	−	0.0343681i
$573$		0			0
$574$	29.8401	+	2.46246i	1.24550	+	0.102781i
$575$	−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	$-0.389502\pi$
$578$	−0.269513	−	0.570610i	−0.0112103	−	0.0237342i
$579$		0			0
$580$	−10.0396	+	12.2072i	−0.416871	+	0.506878i
$581$	32.0701	+	38.2196i	1.33049	+	1.58562i
$582$		0			0
$583$	−3.22088	−	8.84929i	−0.133395	−	0.366500i
$584$	−3.93883	+	4.05713i	−0.162990	+	0.167885i
$585$		0			0
$586$	13.1323	−	28.5288i	0.542491	−	1.17851i
$587$	−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	$0.846876\pi$
$588$		0			0
$589$	−4.76895	−	1.73576i	−0.196501	−	0.0715206i
$590$	−1.30654	−	4.78161i	−0.0537892	−	0.196856i
$591$		0			0
$592$	−6.90518	−	2.36011i	−0.283801	−	0.0969998i
$593$		−	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
$596$	−15.0554	+	26.6810i	−0.616694	+	1.09290i
$597$		0			0
$598$	−8.32825	+	2.27563i	−0.340568	+	0.0930573i
$599$	−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	$0.734743\pi$
$600$		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	$0.790165\pi$
$602$	45.9947	+	21.1722i	1.87461	+	0.862914i
$603$		0			0
$604$	−7.08288	+	6.06328i	−0.288198	+	0.246711i
$605$	6.08285	+	16.7125i	0.247303	+	0.679459i
$606$		0			0
$607$	−0.359975	−	0.429002i	−0.0146109	−	0.0174126i	0.758689	−	0.651452i	$-0.225840\pi$
$607$	−0.359975	−	0.429002i	−0.0146109	−	0.0174126i	−0.773300	+	0.634040i	$0.781396\pi$
$608$	18.2083	−	41.7025i	0.738445	−	1.69126i
$609$		0			0
$610$	25.9882	−	12.2749i	1.05223	−	0.496996i
$611$	−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	$0.196270\pi$
$614$	3.38508	−	41.0206i	0.136611	−	1.65546i
$615$		0			0
$616$	17.1664	+	1.24627i	0.691653	+	0.0502136i
$617$	−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	−0.241463	−	0.970410i	$-0.577627\pi$
$619$	18.8124	−	22.4198i	0.756134	−	0.901126i	0.997597	+	0.0692842i	$0.0220715\pi$
$620$	−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
$626$	5.47421	−	20.8406i	0.218793	−	0.832957i
$627$		0			0
$628$	0.288258	+	29.2259i	0.0115028	+	1.16624i
$629$	6.59915	+	3.81002i	0.263125	+	0.151915i
$630$		0			0
$631$	−35.5567	+	20.5286i	−1.41549	+	0.817232i	−0.995898	−	0.0904814i	$-0.971159\pi$
$631$	−35.5567	+	20.5286i	−1.41549	+	0.817232i	−0.419590	+	0.907714i	$0.637826\pi$
$632$	−8.80936	+	6.36465i	−0.350418	+	0.253172i
$633$		0			0
$634$	−12.6321	+	12.7573i	−0.501684	+	0.506657i
$635$	11.5789	−	9.71582i	0.459493	−	0.385561i
$636$		0			0
$637$	−12.3811	+	4.50635i	−0.490557	+	0.178548i
$638$	4.85152	+	6.85647i	0.192073	+	0.271450i
$639$		0			0
$640$	−2.85430	−	23.3210i	−0.112826	−	0.921842i
$641$	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	−0.975067	−	0.221911i	$-0.928771\pi$
$643$	−2.16758	+	5.95537i	−0.0854809	+	0.234857i	0.889586	+	0.456768i	$0.150993\pi$
$644$	27.7466	−	10.4100i	1.09337	−	0.410210i
$645$		0			0
$646$	−27.0620	+	39.0570i	−1.06474	+	1.53668i
$647$	18.0068			0.707921			0.353961	−	0.935260i	$-0.384835\pi$
$647$	18.0068			0.707921			0.353961	+	0.935260i	$0.384835\pi$
$648$		0			0
$649$	−2.63420			−0.103401
$650$	−0.889372	+	1.28358i	−0.0348840	+	0.0503462i
$651$		0			0
$652$	−9.71873	+	3.64628i	−0.380615	+	0.142799i
$653$	−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
$656$	−21.4607	−	3.34906i	−0.837898	−	0.130759i
$657$		0			0
$658$	11.0710	+	15.6463i	0.431594	+	0.609956i
$659$	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	$0.248353\pi$
$660$		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	$0.307585\pi$
$662$	−2.70156	+	2.72834i	−0.104999	+	0.106040i
$663$		0			0
$664$	−21.1959	−	29.3373i	−0.822559	−	1.13851i
$665$	−56.4065	+	32.5663i	−2.18735	+	1.26287i
$666$		0			0
$667$	12.5245	+	7.23102i	0.484950	+	0.279986i
$668$	0.307541	+	31.1809i	0.0118991	+	1.20642i
$669$		0			0
$670$	−6.12796	+	23.3294i	−0.236744	+	0.901295i
$671$	−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
$680$	−1.77647	+	24.4695i	−0.0681245	+	0.938361i
$681$		0			0
$682$	−0.114523	+	1.38779i	−0.00438531	+	0.0531414i
$683$	−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	$0.276419\pi$
$684$		0			0
$685$	18.7169	+	32.4187i	0.715137	+	1.23865i
$686$	5.99330	−	2.83078i	0.228825	−	0.108080i
$687$		0			0
$688$	−32.1661	−	17.7345i	−1.22632	−	0.676123i
$689$	−6.23040	−	7.42510i	−0.237359	−	0.282874i
$690$		0			0
$691$	13.8889	+	38.1594i	0.528358	+	1.45165i	0.861003	+	0.508600i	$0.169837\pi$
$691$	13.8889	+	38.1594i	0.528358	+	1.45165i	−0.332644	+	0.943052i	$0.607941\pi$
$692$	−19.5593	+	16.7437i	−0.743534	+	0.636501i
$693$		0			0
$694$	−43.5542	−	20.0488i	−1.65330	−	0.761041i
$695$	1.27015	−	7.20339i	0.0481796	−	0.273240i
$696$		0			0
$697$	21.3130	+	7.75730i	0.807287	+	0.293829i
$698$	10.8313	−	2.95955i	0.409969	−	0.112021i
$699$		0			0
$700$	2.63420	−	4.66830i	0.0995634	−	0.176445i
$701$			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
$704$	−12.3548	−	1.80341i	−0.465639	−	0.0679685i
$705$		0			0
$706$	−4.36628	−	15.9795i	−0.164327	−	0.601398i
$707$	−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	$-0.0560111\pi$
$710$	−16.9914	+	36.9122i	−0.637674	+	1.38529i
$711$		0			0
$712$	19.9464	+	19.3648i	0.747524	+	0.725727i
$713$	0.820042	+	2.25305i	0.0307108	+	0.0843773i
$714$		0			0
$715$	−3.34666	−	3.98839i	−0.125158	−	0.149157i
$716$	18.3953	−	22.3670i	0.687464	−	0.835894i
$717$		0			0
$718$	14.2352	+	30.1386i	0.531254	+	1.12476i
$719$	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	$0.655590\pi$
$720$		0			0
$721$	13.6676	−	23.6730i	0.509008	−	0.881628i
$722$	64.4211	+	5.31614i	2.39751	+	0.197846i
$723$		0			0
$724$	7.86426	+	1.30684i	0.292273	+	0.0485684i
$725$	2.57607	−	0.454231i	0.0956729	−	0.0168697i
$726$		0			0
$727$	−15.5596	+	18.5432i	−0.577074	+	0.687730i	−0.973067	−	0.230524i	$-0.925956\pi$
$727$	−15.5596	+	18.5432i	−0.577074	+	0.687730i	0.395993	+	0.918254i	$0.370401\pi$
$728$	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	$0.994945\pi$
$734$	−33.8077	−	8.88030i	−1.24787	−	0.327778i
$735$		0			0
$736$	−20.6221	+	6.07439i	−0.760140	+	0.223905i
$737$	11.1010	+	6.40916i	0.408910	+	0.236084i
$738$		0			0
$739$	−26.7466	+	15.4422i	−0.983891	+	0.568050i	−0.903443	−	0.428709i	$-0.858969\pi$
$739$	−26.7466	+	15.4422i	−0.983891	+	0.568050i	−0.0804485	+	0.996759i	$0.525635\pi$
$740$	−3.85312	−	6.52433i	−0.141643	−	0.239839i
$741$		0			0
$742$	23.6418	+	23.4098i	0.867919	+	0.859401i
$743$	−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	$0.348975\pi$
$744$		0			0
$745$	−29.8919	+	10.8797i	−1.09515	+	0.398603i
$746$	−21.8817	+	15.4831i	−0.801147	+	0.566878i
$747$		0			0
$748$	12.2949	+	4.33815i	0.449547	+	0.158618i
$749$	−34.2892	−	6.04612i	−1.25290	−	0.220920i
$750$		0			0
$751$	17.8334	−	48.9969i	0.650750	−	1.78792i	0.0357937	−	0.999359i	$-0.488604\pi$
$751$	17.8334	−	48.9969i	0.650750	−	1.78792i	0.614956	−	0.788561i	$-0.289174\pi$
$752$	−7.18829	−	11.9020i	−0.262130	−	0.434021i
$753$		0			0
$754$	7.10600	+	4.92363i	0.258785	+	0.179308i
$755$	−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	$0.309507\pi$
$758$	−10.0245	−	6.94582i	−0.364107	−	0.252283i
$759$		0			0
$760$	42.5220	−	20.5996i	1.54244	−	0.747226i
$761$	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
$764$	−6.11629	+	17.3344i	−0.221280	+	0.627138i
$765$		0			0
$766$	34.8897	−	24.6873i	1.26062	−	0.891989i
$767$	−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	$0.939284\pi$
$770$	12.6992	+	12.5746i	0.457648	+	0.453156i
$771$		0			0
$772$	5.38140	−	3.17813i	0.193681	−	0.114383i
$773$	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
$776$	−39.7912	+	4.07527i	−1.42842	+	0.146294i
$777$		0			0
$778$	38.6133	+	10.1426i	1.38435	+	0.363629i
$779$	−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	−0.402121	−	0.915586i	$-0.631727\pi$
$787$	−13.0966	+	2.30928i	−0.466843	+	0.0823170i	−0.0647215	+	0.997903i	$0.520616\pi$
$788$	−5.48301	+	32.9954i	−0.195324	+	1.17541i
$789$		0			0
$790$	−11.2465	−	0.928078i	−0.400132	−	0.0330195i
$791$	1.06009	−	1.83612i	0.0376924	−	0.0652851i
$792$		0			0
$793$	−7.86033	−	13.6145i	−0.279128	−	0.483465i
$794$	−2.76015	−	5.84376i	−0.0979542	−	0.207387i
$795$		0			0
$796$	31.2658	+	25.7139i	1.10819	+	0.911405i
$797$	−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
$800$	−2.15112	+	3.23926i	−0.0760535	+	0.114525i
$801$		0			0
$802$	−1.46995	+	3.19334i	−0.0519058	+	0.112761i
$803$	−0.541816	+	3.07279i	−0.0191203	+	0.108437i
$804$		0			0
$805$	28.9156	+	10.5244i	1.01914	+	0.370937i
$806$	0.377777	+	1.38257i	0.0133066	+	0.0486991i
$807$		0			0
$808$	9.07667	+	4.07015i	0.319316	+	0.143187i
$809$		−	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	$-0.999611\pi$
$811$		−	0.0696662i		−	0.00244631i	0.999999	−	0.00122316i	$-0.000389343\pi$
$812$	−25.8441	−	14.5832i	−0.906950	−	0.511768i
$813$		0			0
$814$	−3.88427	+	1.06135i	−0.136144	+	0.0372001i
$815$	−10.1282	−	3.68637i	−0.354776	−	0.129128i
$816$		0			0
$817$	12.8269	−	72.7449i	0.448756	−	2.54502i
$818$	−26.4173	−	12.1604i	−0.923660	−	0.425177i
$819$		0			0
$820$	−14.6666	−	17.1329i	−0.512180	−	0.598308i
$821$	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	0.660782	−	0.750578i	$-0.270225\pi$
$823$	−5.54068	−	6.60312i	−0.193136	−	0.230170i	−0.853918	+	0.520407i	$0.825780\pi$
$824$	−11.1323	+	16.4100i	−0.387812	+	0.571670i
$825$		0			0
$826$	8.41515	−	3.97469i	0.292800	−	0.138297i
$827$	−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	$0.971507\pi$
$828$		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	$0.178475\pi$
$830$	3.09073	−	37.4535i	0.107281	−	1.30003i
$831$		0			0
$832$	−12.5843	+	2.60500i	−0.436282	+	0.0903122i
$833$	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	0.882322	−	0.470646i	$-0.155979\pi$
$839$	16.5694	+	13.9034i	0.572040	+	0.479999i	−0.310282	+	0.950645i	$0.600424\pi$
$840$		0			0
$841$	2.52114	+	14.2981i	0.0869358	+	0.493037i
$842$	4.24157	−	16.1479i	0.146174	−	0.556493i
$843$		0			0
$844$	−19.3409	+	0.190761i	−0.665740	+	0.00656627i
$845$	18.7391	+	10.8190i	0.644645	+	0.372186i
$846$		0			0
$847$	−28.9179	+	16.6958i	−0.993631	+	0.573673i
$848$	−15.8758	−	18.1794i	−0.545176	−	0.624282i
$849$		0			0
$850$	2.85694	−	2.88525i	0.0979921	−	0.0989634i
$851$	−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	$0.362288\pi$
$854$	31.1689	+	44.0498i	1.06658	+	1.50735i
$855$		0			0
$856$	24.4915	+	6.17563i	0.837101	+	0.211079i
$857$	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	−0.870062	−	0.492943i	$-0.835921\pi$
$859$	3.32072	−	9.12361i	0.113302	−	0.311293i	0.983363	+	0.181649i	$0.0581435\pi$
$860$	−13.3973	−	35.7089i	−0.456844	−	1.21766i
$861$		0			0
$862$	31.7011	−	45.7524i	1.07974	−	1.55833i
$863$	−18.1528			−0.617929			−0.308964	−	0.951074i	$-0.599982\pi$
$863$	−18.1528			−0.617929			−0.308964	+	0.951074i	$0.599982\pi$
$864$		0			0
$865$	−26.7344			−0.908997
$866$	14.1912	−	20.4814i	0.482237	−	0.695985i
$867$		0			0
$868$	−1.72816	−	4.60621i	−0.0586575	−	0.156345i
$869$	−2.05107	+	5.63527i	−0.0695778	+	0.191164i
$870$		0			0
$871$	12.9930	+	2.29101i	0.440250	+	0.0776279i
$872$	10.5949	+	2.67155i	0.358789	+	0.0904701i
$873$		0			0
$874$	−24.9719	−	35.2918i	−0.844686	−	1.19376i
$875$	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	$0.104189\pi$
$878$	−15.4972	+	15.6508i	−0.523004	+	0.528188i
$879$		0			0
$880$	−8.52766	−	9.76504i	−0.287467	−	0.329180i
$881$	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	0.896658	−	0.442725i	$-0.145988\pi$
$883$	28.5735	+	16.4969i	0.961575	+	0.555166i	0.0649179	+	0.997891i	$0.479321\pi$
$884$	13.4187	−	0.132350i	0.451319	−	0.00445141i
$885$		0			0
$886$	−2.43946	+	9.28716i	−0.0819554	+	0.312008i
$887$	−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	$0.964226\pi$
$888$		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
$896$	42.1895	−	12.8808i	1.40945	−	0.430316i
$897$		0			0
$898$	1.59277	−	19.3012i	0.0531514	−	0.644090i
$899$	1.20042	−	2.07919i	0.0400363	−	0.0693450i
$900$		0			0
$901$	12.6014	+	21.8263i	0.419814	+	0.727140i
$902$	−10.8372	+	5.11869i	−0.360840	+	0.170434i
$903$		0			0
$904$	−0.863444	+	1.27279i	−0.0287177	+	0.0423325i
$905$	5.32084	+	6.34114i	0.176871	+	0.210786i
$906$		0			0
$907$	−9.85576	−	27.0785i	−0.327255	−	0.899126i	−0.988803	−	0.149224i	$-0.952323\pi$
$907$	−9.85576	−	27.0785i	−0.327255	−	0.899126i	0.661548	−	0.749903i	$-0.269900\pi$
$908$	6.37150	+	7.44292i	0.211446	+	0.247002i
$909$		0			0
$910$	16.7091	+	7.69151i	0.553903	+	0.254971i
$911$	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	$0.00502189\pi$
$912$		0			0
$913$	−18.7668	−	6.83057i	−0.621092	−	0.226059i
$914$	−51.9610	+	14.1979i	−1.71872	+	0.469625i
$915$		0			0
$916$	−36.8651	−	20.8020i	−1.21806	−	0.687318i
$917$		−	4.48624i		−	0.148149i
$918$		0			0
$919$			56.1944i			1.85368i	0.375453	+	0.926842i	$0.377487\pi$
$919$			56.1944i			1.85368i	−0.375453	+	0.926842i	$0.622513\pi$
$920$	−20.3683	−	9.13352i	−0.671522	−	0.301123i
$921$		0			0
$922$	1.84594	+	6.75572i	0.0607929	+	0.222488i
$923$	20.8859	+	7.60184i	0.687467	+	0.250217i
$924$		0			0
$925$	−0.217760	+	1.23498i	−0.00715992	+	0.0406059i
$926$	−5.41765	+	11.7694i	−0.178035	+	0.386765i
$927$		0			0
$928$	17.9328	+	11.9088i	0.588672	+	0.390924i
$929$	−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
$932$	7.59702	+	6.24801i	0.248849	+	0.204660i
$933$		0			0
$934$	−13.2379	−	28.0271i	−0.433158	−	0.917076i
$935$	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	$0.884116\pi$
$938$	−45.1336	−	3.72449i	−1.47366	−	0.121609i
$939$		0			0
$940$	2.36668	−	14.2421i	0.0771925	−	0.464525i
$941$	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	$0.0137001\pi$
$947$	37.3876	+	31.3719i	1.21493	+	1.01945i	0.215860	+	0.976424i	$0.430744\pi$
$948$		0			0
$949$	0.557671	+	3.16271i	0.0181028	+	0.102666i
$950$	−7.56321	−	1.98663i	−0.245383	−	0.0644549i
$951$		0			0
$952$	−45.8228	+	4.69301i	−1.48512	+	0.152101i
$953$	−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
$956$	9.68169	−	5.71778i	0.313128	−	0.184926i
$957$		0			0
$958$	−29.2593	−	28.9721i	−0.945324	−	0.936047i
$959$	−53.8393	+	45.1766i	−1.73856	+	1.45883i
$960$		0			0
$961$	−28.7564	+	10.4665i	−0.927627	+	0.337629i
$962$	−3.38320	+	2.39390i	−0.109079	+	0.0771823i
$963$		0			0
$964$	0.356354	−	1.00996i	0.0114774	−	0.0325285i
$965$	6.39084	+	1.12688i	0.205728	+	0.0362755i
$966$		0			0
$967$	18.4093	−	50.5793i	0.592005	−	1.62652i	−0.174775	−	0.984608i	$-0.555920\pi$
$967$	18.4093	−	50.5793i	0.592005	−	1.62652i	0.766779	−	0.641911i	$-0.221858\pi$
$968$	21.7998	−	10.5608i	0.700671	−	0.339436i
$969$		0			0
$970$	−34.1389	−	23.6543i	−1.09613	−	0.759493i
$971$	6.81102			0.218576			0.109288	−	0.994010i	$-0.465143\pi$
$971$	6.81102			0.218576			0.109288	+	0.994010i	$0.465143\pi$
$972$		0			0
$973$	13.7330			0.440261
$974$	21.3800	+	14.8139i	0.685060	+	0.474667i
$975$		0			0
$976$	−20.2376	−	33.5083i	−0.647789	−	1.07257i
$977$	−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
$980$	−32.1251	−	11.3350i	−1.02620	−	0.362084i
$981$		0			0
$982$	25.3126	−	17.9108i	0.807759	−	0.571556i
$983$	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	$0.0881817\pi$
$984$		0			0
$985$	−26.6050	+	22.3242i	−0.847705	+	0.711309i
$986$	−15.9730	−	15.8162i	−0.508684	−	0.503691i
$987$		0			0
$988$	−13.1420	−	22.2529i	−0.418104	−	0.707959i
$989$	−30.2224	+	17.4489i	−0.961018	+	0.554844i
$990$		0			0
$991$	13.8256	+	7.98220i	0.439184	+	0.253563i	0.703251	−	0.710941i	$-0.251731\pi$
$991$	13.8256	+	7.98220i	0.439184	+	0.253563i	−0.264067	+	0.964504i	$0.585064\pi$
$992$	1.00841	+	3.42347i	0.0320171	+	0.108695i
$993$		0			0
$994$	−73.7896	−	19.3824i	−2.34047	−	0.614772i
$995$	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.35.11		96
3.2	odd	2		108.2.l.a.11.6	yes	96
4.3	odd	2	inner	324.2.l.a.35.12		96
9.2	odd	6		972.2.l.d.755.16		96
9.4	even	3		972.2.l.b.431.11		96
9.5	odd	6		972.2.l.c.431.6		96
9.7	even	3		972.2.l.a.755.1		96
12.11	even	2		108.2.l.a.11.5	✓	96
27.4	even	9		972.2.l.d.215.14		96
27.5	odd	18	inner	324.2.l.a.287.12		96
27.13	even	9		972.2.l.c.539.8		96
27.14	odd	18		972.2.l.b.539.9		96
27.22	even	9		108.2.l.a.59.5	yes	96
27.23	odd	18		972.2.l.a.215.3		96
36.7	odd	6		972.2.l.a.755.3		96
36.11	even	6		972.2.l.d.755.14		96
36.23	even	6		972.2.l.c.431.8		96
36.31	odd	6		972.2.l.b.431.9		96
108.23	even	18		972.2.l.a.215.1		96
108.31	odd	18		972.2.l.d.215.16		96
108.59	even	18	inner	324.2.l.a.287.11		96
108.67	odd	18		972.2.l.c.539.6		96
108.95	even	18		972.2.l.b.539.11		96
108.103	odd	18		108.2.l.a.59.6	yes	96

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

\(f(q)\)	\(=\)	\(q+(0.805437 - 1.16244i) q^{2} +(-0.702543 - 1.87255i) q^{4} +(0.710267 - 1.95144i) q^{5} +(3.83975 + 0.677051i) q^{7} +(-2.74258 - 0.691554i) q^{8} +O(q^{10})\)	\(q+(0.805437 - 1.16244i) q^{2} +(-0.702543 - 1.87255i) q^{4} +(0.710267 - 1.95144i) q^{5} +(3.83975 + 0.677051i) q^{7} +(-2.74258 - 0.691554i) q^{8} +(-1.69636 - 2.39741i) q^{10} +(-1.46659 + 0.533796i) q^{11} +(-1.23056 + 1.03256i) q^{13} +(3.87971 - 3.91816i) q^{14} +(-3.01287 + 2.63109i) q^{16} +(3.61727 - 2.08843i) q^{17} +(-6.96639 - 4.02205i) q^{19} +(-4.15316 + 0.0409631i) q^{20} +(-0.560741 + 2.13477i) q^{22} +(0.659926 + 3.74263i) q^{23} +(0.526570 + 0.441845i) q^{25} +(0.209156 + 2.26212i) q^{26} +(-1.42978 - 7.66577i) q^{28} +(2.44609 - 2.91513i) q^{29} +(0.621314 - 0.109554i) q^{31} +(0.631814 + 5.62146i) q^{32} +(0.485803 - 5.88697i) q^{34} +(4.04848 - 7.01217i) q^{35} +(0.912171 + 1.57993i) q^{37} +(-10.2864 + 4.85852i) q^{38} +(-3.29749 + 4.86081i) q^{40} +(3.49040 + 4.15970i) q^{41} +(3.14069 + 8.62898i) q^{43} +(2.02990 + 2.37125i) q^{44} +(4.88211 + 2.24732i) q^{46} +(-0.603613 + 3.42326i) q^{47} +(7.70742 + 2.80527i) q^{49} +(0.937738 - 0.256229i) q^{50} +(2.79805 + 1.57887i) q^{52} +6.03391i q^{53} +3.24111i q^{55} +(-10.0626 - 4.51226i) q^{56} +(-1.41850 - 5.19139i) q^{58} +(1.58603 + 0.577267i) q^{59} +(-1.69938 + 9.63768i) q^{61} +(0.373079 - 0.810481i) q^{62} +(7.04351 + 3.79328i) q^{64} +(1.14096 + 3.13477i) q^{65} +(-5.27928 - 6.29160i) q^{67} +(-6.45198 - 5.30630i) q^{68} +(-4.89044 - 10.3540i) q^{70} +(-6.91810 - 11.9825i) q^{71} +(0.999604 - 1.73136i) q^{73} +(2.57127 + 0.212185i) q^{74} +(-2.63729 + 15.8706i) q^{76} +(-5.99276 + 1.05669i) q^{77} +(2.46986 - 2.94347i) q^{79} +(2.99448 + 7.74822i) q^{80} +(7.64671 - 0.707015i) q^{82} +(9.80246 + 8.22524i) q^{83} +(-1.50623 - 8.54225i) q^{85} +(12.5603 + 3.29923i) q^{86} +(4.39140 - 0.449752i) q^{88} +(-8.51207 - 4.91444i) q^{89} +(-5.42415 + 3.13163i) q^{91} +(6.54462 - 3.86510i) q^{92} +(3.49317 + 3.45888i) q^{94} +(-12.7968 + 10.7378i) q^{95} +(13.2890 - 4.83681i) q^{97} +(9.46881 - 6.69996i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) \) 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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