LMFDB - Embedded newform 405.2.r.a.152.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,2,Mod(8,405)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("405.8"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([2, 27])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.r (of order $36$, degree $12$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			152.12
Character	$\chi$	$=$	405.152
Dual form			405.2.r.a.8.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.22359 + 0.856769i) q^{2} +(0.0790861 + 0.217287i) q^{4} +(-2.10603 - 0.751431i) q^{5} +(-2.03610 - 4.36642i) q^{7} +(0.683816 - 2.55204i) q^{8} +(-1.93312 - 2.72382i) q^{10} +(2.25098 + 2.68262i) q^{11} +(-2.18203 - 3.11626i) q^{13} +(1.24966 - 7.08719i) q^{14} +(3.37749 - 2.83405i) q^{16} +(0.367380 + 1.37108i) q^{17} +(1.30024 - 0.750693i) q^{19} +(-0.00328108 - 0.517040i) q^{20} +(0.455904 + 5.21100i) q^{22} +(-1.35959 - 0.633988i) q^{23} +(3.87070 + 3.16507i) q^{25} -5.68253i q^{26} +(0.787741 - 0.787741i) q^{28} +(0.168770 + 0.957143i) q^{29} +(-2.44873 + 0.891266i) q^{31} +(1.29677 - 0.113453i) q^{32} +(-0.725176 + 1.99240i) q^{34} +(1.00701 + 10.7258i) q^{35} +(6.69580 - 1.79413i) q^{37} +(2.23413 + 0.195461i) q^{38} +(-3.35782 + 4.86082i) q^{40} +(0.670363 + 0.118203i) q^{41} +(-0.0175704 + 0.200831i) q^{43} +(-0.404877 + 0.701267i) q^{44} +(-1.12040 - 1.94060i) q^{46} +(7.89228 - 3.68023i) q^{47} +(-10.4204 + 12.4186i) q^{49} +(2.02443 + 7.18905i) q^{50} +(0.504555 - 0.720580i) q^{52} +(-2.81838 - 2.81838i) q^{53} +(-2.72483 - 7.34112i) q^{55} +(-12.5356 + 2.21036i) q^{56} +(-0.613544 + 1.31575i) q^{58} +(-5.69079 - 4.77514i) q^{59} +(-1.08988 - 0.396683i) q^{61} +(-3.75986 - 1.00745i) q^{62} +(-5.95268 - 3.43678i) q^{64} +(2.25376 + 8.20258i) q^{65} +(12.5612 - 8.79548i) q^{67} +(-0.268864 + 0.188260i) q^{68} +(-7.95735 + 13.9868i) q^{70} +(11.1295 + 6.42561i) q^{71} +(-0.343386 - 0.0920100i) q^{73} +(9.73009 + 3.54146i) q^{74} +(0.265947 + 0.223156i) q^{76} +(7.13022 - 15.2908i) q^{77} +(9.66646 - 1.70446i) q^{79} +(-9.24267 + 3.43063i) q^{80} +(0.718978 + 0.718978i) q^{82} +(-6.51525 + 9.30474i) q^{83} +(0.256560 - 3.16359i) q^{85} +(-0.193565 + 0.230681i) q^{86} +(8.38540 - 3.91017i) q^{88} +(-2.09630 - 3.63090i) q^{89} +(-9.16409 + 15.8727i) q^{91} +(0.0302327 - 0.345561i) q^{92} +(12.8100 + 2.25876i) q^{94} +(-3.30243 + 0.603940i) q^{95} +(6.41403 + 0.561155i) q^{97} +(-23.3902 + 6.26740i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	1.22359	+	0.856769i	0.865211	+	0.605827i	0.919671	−	0.392689i	$-0.128455\pi$
$2$	1.22359	+	0.856769i	0.865211	+	0.605827i	−0.0544607	+	0.998516i	$0.517344\pi$
$3$		0			0
$3$		0			0
$4$	0.0790861	+	0.217287i	0.0395430	+	0.108644i
$5$	−2.10603	−	0.751431i	−0.941844	−	0.336050i
$5$	−2.10603	−	0.751431i	−0.941844	−	0.336050i
$6$		0			0
$7$	−2.03610	−	4.36642i	−0.769572	−	1.65035i	−0.759590	−	0.650402i	$-0.774600\pi$
$7$	−2.03610	−	4.36642i	−0.769572	−	1.65035i	−0.00998196	−	0.999950i	$-0.503177\pi$
$8$	0.683816	−	2.55204i	0.241766	−	0.902281i
$9$		0			0
$10$	−1.93312	−	2.72382i	−0.611305	−	0.861349i
$11$	2.25098	+	2.68262i	0.678697	+	0.808839i	0.989940	−	0.141491i	$-0.0451897\pi$
$11$	2.25098	+	2.68262i	0.678697	+	0.808839i	−0.311243	+	0.950330i	$0.600745\pi$
$12$		0			0
$13$	−2.18203	−	3.11626i	−0.605186	−	0.864295i	0.393294	−	0.919413i	$-0.371336\pi$
$13$	−2.18203	−	3.11626i	−0.605186	−	0.864295i	−0.998480	+	0.0551175i	$0.982447\pi$
$14$	1.24966	−	7.08719i	0.333986	−	1.89413i
$15$		0			0
$16$	3.37749	−	2.83405i	0.844372	−	0.708512i
$17$	0.367380	+	1.37108i	0.0891027	+	0.332536i	0.996059	−	0.0886879i	$-0.0282674\pi$
$17$	0.367380	+	1.37108i	0.0891027	+	0.332536i	−0.906957	+	0.421224i	$0.861601\pi$
$18$		0			0
$19$	1.30024	−	0.750693i	0.298295	−	0.172221i	−0.343382	−	0.939196i	$-0.611572\pi$
$19$	1.30024	−	0.750693i	0.298295	−	0.172221i	0.641677	+	0.766975i	$0.278239\pi$
$20$	−0.00328108	−	0.517040i	−0.000733673	−	0.115614i
$21$		0			0
$22$	0.455904	+	5.21100i	0.0971990	+	1.11099i
$23$	−1.35959	−	0.633988i	−0.283494	−	0.132196i	0.275670	−	0.961252i	$-0.411100\pi$
$23$	−1.35959	−	0.633988i	−0.283494	−	0.132196i	−0.559165	+	0.829057i	$0.688878\pi$
$24$		0			0
$25$	3.87070	+	3.16507i	0.774141	+	0.633014i
$26$		−	5.68253i		−	1.11444i
$27$		0			0
$28$	0.787741	−	0.787741i	0.148869	−	0.148869i
$29$	0.168770	+	0.957143i	0.0313398	+	0.177737i	0.996460	−	0.0840712i	$-0.0267923\pi$
$29$	0.168770	+	0.957143i	0.0313398	+	0.177737i	−0.965120	+	0.261808i	$0.915681\pi$
$30$		0			0
$31$	−2.44873	+	0.891266i	−0.439806	+	0.160076i	−0.552426	−	0.833562i	$-0.686298\pi$
$31$	−2.44873	+	0.891266i	−0.439806	+	0.160076i	0.112620	+	0.993638i	$0.464076\pi$
$32$	1.29677	−	0.113453i	0.229239	−	0.0200558i
$33$		0			0
$34$	−0.725176	+	1.99240i	−0.124367	+	0.341694i
$35$	1.00701	+	10.7258i	0.170216	+	1.81299i
$36$		0			0
$37$	6.69580	−	1.79413i	1.10078	−	0.294954i	0.337699	−	0.941254i	$-0.390351\pi$
$37$	6.69580	−	1.79413i	1.10078	−	0.294954i	0.763083	+	0.646300i	$0.223685\pi$
$38$	2.23413	+	0.195461i	0.362424	+	0.0317080i
$39$		0			0
$40$	−3.35782	+	4.86082i	−0.530917	+	0.768563i
$41$	0.670363	+	0.118203i	0.104693	+	0.0184602i	0.225749	−	0.974185i	$-0.427517\pi$
$41$	0.670363	+	0.118203i	0.104693	+	0.0184602i	−0.121056	+	0.992646i	$0.538628\pi$
$42$		0			0
$43$	−0.0175704	+	0.200831i	−0.00267946	+	0.0306264i	−0.997417	−	0.0718322i	$-0.977115\pi$
$43$	−0.0175704	+	0.200831i	−0.00267946	+	0.0306264i	0.994737	+	0.102459i	$0.0326709\pi$
$44$	−0.404877	+	0.701267i	−0.0610375	+	0.105720i
$45$		0			0
$46$	−1.12040	−	1.94060i	−0.165195	−	0.286126i
$47$	7.89228	−	3.68023i	1.15121	−	0.536817i	0.249164	−	0.968461i	$-0.419844\pi$
$47$	7.89228	−	3.68023i	1.15121	−	0.536817i	0.902044	+	0.431644i	$0.142066\pi$
$48$		0			0
$49$	−10.4204	+	12.4186i	−1.48863	+	1.77409i
$50$	2.02443	+	7.18905i	0.286298	+	1.01669i
$51$		0			0
$52$	0.504555	−	0.720580i	0.0699692	−	0.0999264i
$53$	−2.81838	−	2.81838i	−0.387135	−	0.387135i	0.486529	−	0.873664i	$-0.338263\pi$
$53$	−2.81838	−	2.81838i	−0.387135	−	0.387135i	−0.873664	+	0.486529i	$0.838263\pi$
$54$		0			0
$55$	−2.72483	−	7.34112i	−0.367416	−	0.989877i
$56$	−12.5356	+	2.21036i	−1.67514	+	0.295372i
$57$		0			0
$58$	−0.613544	+	1.31575i	−0.0805623	+	0.172766i
$59$	−5.69079	−	4.77514i	−0.740877	−	0.621670i	0.192196	−	0.981357i	$-0.438439\pi$
$59$	−5.69079	−	4.77514i	−0.740877	−	0.621670i	−0.933073	+	0.359687i	$0.882884\pi$
$60$		0			0
$61$	−1.08988	−	0.396683i	−0.139544	−	0.0507900i	0.271304	−	0.962494i	$-0.412545\pi$
$61$	−1.08988	−	0.396683i	−0.139544	−	0.0507900i	−0.410848	+	0.911704i	$0.634767\pi$
$62$	−3.75986	−	1.00745i	−0.477503	−	0.127947i
$63$		0			0
$64$	−5.95268	−	3.43678i	−0.744085	−	0.429598i
$65$	2.25376	+	8.20258i	0.279544	+	1.01740i
$66$		0			0
$67$	12.5612	−	8.79548i	1.53460	−	1.07454i	0.566472	−	0.824081i	$-0.308308\pi$
$67$	12.5612	−	8.79548i	1.53460	−	1.07454i	0.968128	−	0.250457i	$-0.0805810\pi$
$68$	−0.268864	+	0.188260i	−0.0326045	+	0.0228299i
$69$		0			0
$70$	−7.95735	+	13.9868i	−0.951086	+	1.67174i
$71$	11.1295	+	6.42561i	1.32083	+	0.762579i	0.983860	−	0.178938i	$-0.0572661\pi$
$71$	11.1295	+	6.42561i	1.32083	+	0.762579i	0.336966	+	0.941517i	$0.390599\pi$
$72$		0			0
$73$	−0.343386	−	0.0920100i	−0.0401903	−	0.0107690i	0.238668	−	0.971101i	$-0.423289\pi$
$73$	−0.343386	−	0.0920100i	−0.0401903	−	0.0107690i	−0.278858	+	0.960332i	$0.589956\pi$
$74$	9.73009	+	3.54146i	1.13110	+	0.411687i
$75$		0			0
$76$	0.265947	+	0.223156i	0.0305062	+	0.0255977i
$77$	7.13022	−	15.2908i	0.812564	−	1.74255i
$78$		0			0
$79$	9.66646	−	1.70446i	1.08756	−	0.191766i	0.399005	−	0.916949i	$-0.369356\pi$
$79$	9.66646	−	1.70446i	1.08756	−	0.191766i	0.688557	+	0.725182i	$0.258245\pi$
$80$	−9.24267	+	3.43063i	−1.03336	+	0.383557i
$81$		0			0
$82$	0.718978	+	0.718978i	0.0793979	+	0.0793979i
$83$	−6.51525	+	9.30474i	−0.715142	+	1.02133i	0.282923	+	0.959143i	$0.408696\pi$
$83$	−6.51525	+	9.30474i	−0.715142	+	1.02133i	−0.998065	+	0.0621857i	$0.980193\pi$
$84$		0			0
$85$	0.256560	−	3.16359i	0.0278279	−	0.343140i
$86$	−0.193565	+	0.230681i	−0.0208726	+	0.0248750i
$87$		0			0
$88$	8.38540	−	3.91017i	0.893886	−	0.416826i
$89$	−2.09630	−	3.63090i	−0.222208	−	0.384875i	0.733270	−	0.679937i	$-0.237993\pi$
$89$	−2.09630	−	3.63090i	−0.222208	−	0.384875i	−0.955478	+	0.295062i	$0.904660\pi$
$90$		0			0
$91$	−9.16409	+	15.8727i	−0.960658	+	1.66391i
$92$	0.0302327	−	0.345561i	0.00315198	−	0.0360272i
$93$		0			0
$94$	12.8100	+	2.25876i	1.32126	+	0.232973i
$95$	−3.30243	+	0.603940i	−0.338822	+	0.0619630i
$96$		0			0
$97$	6.41403	+	0.561155i	0.651246	+	0.0569767i	0.407991	−	0.912986i	$-0.366229\pi$
$97$	6.41403	+	0.561155i	0.651246	+	0.0569767i	0.243255	+	0.969962i	$0.421785\pi$
$98$	−23.3902	+	6.26740i	−2.36277	+	0.633103i
$99$		0			0
$100$	−0.381610	+	1.09137i	−0.0381610	+	0.109137i
$101$	2.09253	−	5.74917i	0.208214	−	0.572064i	−0.790995	−	0.611823i	$-0.790437\pi$
$101$	2.09253	−	5.74917i	0.208214	−	0.572064i	0.999209	+	0.0397585i	$0.0126589\pi$
$102$		0			0
$103$	7.50553	−	0.656648i	0.739541	−	0.0647015i	0.288841	−	0.957377i	$-0.406730\pi$
$103$	7.50553	−	0.656648i	0.739541	−	0.0647015i	0.450700	+	0.892675i	$0.351174\pi$
$104$	−9.44492	+	3.43767i	−0.926151	+	0.337091i
$105$		0			0
$106$	−1.03385	−	5.86326i	−0.100416	−	0.569490i
$107$	−9.86451	+	9.86451i	−0.953639	+	0.953639i	−0.998972	−	0.0453334i	$-0.985565\pi$
$107$	−9.86451	+	9.86451i	−0.953639	+	0.953639i	0.0453334	+	0.998972i	$0.485565\pi$
$108$		0			0
$109$		−	2.02062i		−	0.193540i	−0.995307	−	0.0967701i	$-0.969149\pi$
$109$		−	2.02062i		−	0.193540i	0.995307	−	0.0967701i	$-0.0308512\pi$
$110$	2.95556	−	11.3171i	0.281802	−	1.07904i
$111$		0			0
$112$	−19.2515	−	8.97714i	−1.81910	−	0.848260i
$113$	0.0677216	+	0.774062i	0.00637072	+	0.0728176i	0.998715	−	0.0506887i	$-0.0161416\pi$
$113$	0.0677216	+	0.774062i	0.00637072	+	0.0728176i	−0.992344	+	0.123506i	$0.960586\pi$
$114$		0			0
$115$	2.38694	+	2.35683i	0.222583	+	0.219776i
$116$	−0.194627	+	0.112368i	−0.0180707	+	0.0104331i
$117$		0			0
$118$	−2.87202	−	10.7185i	−0.264391	−	0.986719i
$119$	5.23869	−	4.39579i	0.480230	−	0.402961i
$120$		0			0
$121$	−0.219379	+	1.24416i	−0.0199435	+	0.113105i
$122$	−0.993700	−	1.41915i	−0.0899654	−	0.128484i
$123$		0			0
$124$	−0.387321	−	0.461592i	−0.0347825	−	0.0414522i
$125$	−5.77347	−	9.57429i	−0.516395	−	0.856350i
$126$		0			0
$127$	−5.08430	+	18.9749i	−0.451159	+	1.68375i	0.247982	+	0.968765i	$0.420232\pi$
$127$	−5.08430	+	18.9749i	−0.451159	+	1.68375i	−0.699141	+	0.714983i	$0.746434\pi$
$128$	−5.43940	−	11.6648i	−0.480779	−	1.03103i
$129$		0			0
$130$	−4.27003	+	11.9676i	−0.374506	+	1.04962i
$131$	1.67084	+	4.59061i	0.145982	+	0.401083i	0.991035	−	0.133599i	$-0.0426535\pi$
$131$	1.67084	+	4.59061i	0.145982	+	0.401083i	−0.845053	+	0.534682i	$0.820431\pi$
$132$		0			0
$133$	−5.92525	−	4.14891i	−0.513784	−	0.359756i
$134$	22.9055			1.97874
$135$		0			0
$136$	3.75027			0.321583
$137$	−1.49059	−	1.04372i	−0.127349	−	0.0891710i	0.508166	−	0.861259i	$-0.330324\pi$
$137$	−1.49059	−	1.04372i	−0.127349	−	0.0891710i	−0.635516	+	0.772088i	$0.719212\pi$
$138$		0			0
$139$	0.987166	+	2.71222i	0.0837303	+	0.230047i	0.974491	−	0.224425i	$-0.0720503\pi$
$139$	0.987166	+	2.71222i	0.0837303	+	0.230047i	−0.890761	+	0.454472i	$0.849828\pi$
$140$	−2.25094	+	1.06707i	−0.190239	+	0.0901839i
$141$		0			0
$142$	8.11269	+	17.3977i	0.680802	+	1.45998i
$143$	3.44802	−	12.8682i	0.288338	−	1.07609i
$144$		0			0
$145$	0.363792	−	2.14259i	0.0302113	−	0.177932i
$146$	−0.341333	−	0.406785i	−0.0282489	−	0.0336658i
$147$		0			0
$148$	0.919386	+	1.31302i	0.0755731	+	0.107930i
$149$	−2.86013	+	16.2206i	−0.234311	+	1.32885i	0.609748	+	0.792596i	$0.291271\pi$
$149$	−2.86013	+	16.2206i	−0.234311	+	1.32885i	−0.844059	+	0.536250i	$0.819840\pi$
$150$		0			0
$151$	1.98981	−	1.66965i	0.161929	−	0.135874i	−0.558223	−	0.829691i	$-0.688517\pi$
$151$	1.98981	−	1.66965i	0.161929	−	0.135874i	0.720152	+	0.693817i	$0.244072\pi$
$152$	−1.02667	−	3.83159i	−0.0832741	−	0.310783i
$153$		0			0
$154$	21.8252	−	12.6008i	1.75872	−	1.01540i
$155$	5.82683	−	0.0369764i	0.468022	−	0.00297002i
$156$		0			0
$157$	−1.24669	−	14.2497i	−0.0994965	−	1.13725i	−0.867715	−	0.497062i	$-0.834412\pi$
$157$	−1.24669	−	14.2497i	−0.0994965	−	1.13725i	0.768219	−	0.640188i	$-0.221143\pi$
$158$	13.2881	+	6.19636i	1.05715	+	0.492956i
$159$		0			0
$160$	−2.81629	−	0.735501i	−0.222648	−	0.0581465i
$161$			7.22741i			0.569599i
$162$		0			0
$163$	−8.00886	+	8.00886i	−0.627302	+	0.627302i	−0.947388	−	0.320086i	$-0.896288\pi$
$163$	−8.00886	+	8.00886i	−0.627302	+	0.627302i	0.320086	+	0.947388i	$0.396288\pi$
$164$	0.0273323	+	0.155009i	0.00213430	+	0.0121042i
$165$		0			0
$166$	−15.9440	+	5.80315i	−1.23750	+	0.450412i
$167$	13.9146	−	1.21737i	1.07674	−	0.0942027i	0.465039	−	0.885290i	$-0.346040\pi$
$167$	13.9146	−	1.21737i	1.07674	−	0.0942027i	0.611703	+	0.791088i	$0.290485\pi$
$168$		0			0
$169$	−0.503569	+	1.38354i	−0.0387361	+	0.106427i
$170$	3.02439	−	3.65114i	0.231960	−	0.280029i
$171$		0			0
$172$	−0.0450275	+	0.0120651i	−0.00343332	+	0.000919955i
$173$	−4.02915	−	0.352505i	−0.306331	−	0.0268005i	−0.0670460	−	0.997750i	$-0.521357\pi$
$173$	−4.02915	−	0.352505i	−0.306331	−	0.0268005i	−0.239285	+	0.970949i	$0.576913\pi$
$174$		0			0
$175$	5.93890	−	23.3455i	0.448939	−	1.76475i
$176$	15.2053	+	2.68111i	1.14614	+	0.202096i
$177$		0			0
$178$	0.545824	−	6.23880i	0.0409112	−	0.467618i
$179$	3.24205	−	5.61540i	0.242322	−	0.419714i	−0.719053	−	0.694955i	$-0.755424\pi$
$179$	3.24205	−	5.61540i	0.242322	−	0.419714i	0.961375	+	0.275241i	$0.0887576\pi$
$180$		0			0
$181$	−3.86147	−	6.68826i	−0.287021	−	0.497135i	0.686076	−	0.727530i	$-0.259332\pi$
$181$	−3.86147	−	6.68826i	−0.287021	−	0.497135i	−0.973097	+	0.230395i	$0.925998\pi$
$182$	−24.8123	+	11.5702i	−1.83921	+	0.857639i
$183$		0			0
$184$	−2.54767	+	3.03620i	−0.187817	+	0.223831i
$185$	−15.4497	−	1.25294i	−1.13588	−	0.0921177i
$186$		0			0
$187$	−2.85112	+	4.07182i	−0.208494	+	0.297761i
$188$	1.42384	+	1.42384i	0.103844	+	0.103844i
$189$		0			0
$190$	−4.55827	−	2.09044i	−0.330692	−	0.151657i
$191$	−9.13822	+	1.61131i	−0.661218	+	0.116591i	−0.494180	−	0.869360i	$-0.664532\pi$
$191$	−9.13822	+	1.61131i	−0.661218	+	0.116591i	−0.167039	+	0.985950i	$0.553420\pi$
$192$		0			0
$193$	10.7832	−	23.1246i	0.776191	−	1.66455i	0.0293284	−	0.999570i	$-0.490663\pi$
$193$	10.7832	−	23.1246i	0.776191	−	1.66455i	0.746863	−	0.664978i	$-0.231559\pi$
$194$	7.36738	+	6.18197i	0.528947	+	0.443839i
$195$		0			0
$196$	−3.52251	−	1.28209i	−0.251608	−	0.0915779i
$197$	12.1103	+	3.24493i	0.862820	+	0.231192i	0.662980	−	0.748637i	$-0.269291\pi$
$197$	12.1103	+	3.24493i	0.862820	+	0.231192i	0.199839	+	0.979829i	$0.435958\pi$
$198$		0			0
$199$	12.0563	+	6.96070i	0.854648	+	0.493431i	0.862216	−	0.506540i	$-0.169076\pi$
$199$	12.0563	+	6.96070i	0.854648	+	0.493431i	−0.00756873	+	0.999971i	$0.502409\pi$
$200$	10.7242	−	7.71385i	0.758317	−	0.545452i
$201$		0			0
$202$	7.48611	−	5.24183i	0.526721	−	0.368814i
$203$	3.83566	−	2.68576i	0.269210	−	0.188503i
$204$		0			0
$205$	−1.32298	−	0.752670i	−0.0924010	−	0.0525688i
$206$	9.74630	+	5.62703i	0.679057	+	0.392054i
$207$		0			0
$208$	−16.2014	−	4.34115i	−1.12337	−	0.301005i
$209$	4.94063	+	1.79824i	0.341751	+	0.124387i
$210$		0			0
$211$	15.4091	+	12.9298i	1.06081	+	0.890124i	0.994188	−	0.107654i	$-0.0343339\pi$
$211$	15.4091	+	12.9298i	1.06081	+	0.890124i	0.0666204	+	0.997778i	$0.478778\pi$
$212$	0.389504	−	0.835293i	0.0267512	−	0.0573682i
$213$		0			0
$214$	−20.5218	+	3.61854i	−1.40284	+	0.247358i
$215$	0.187914	−	0.409752i	0.0128157	−	0.0279449i
$216$		0			0
$217$	8.87750	+	8.87750i	0.602644	+	0.602644i
$218$	1.73120	−	2.47242i	0.117252	−	0.167453i
$219$		0			0
$220$	1.37964	−	1.17265i	0.0930150	−	0.0790601i
$221$	3.47101	−	4.13659i	0.233485	−	0.278257i
$222$		0			0
$223$	−19.8549	+	9.25851i	−1.32959	+	0.619996i	−0.952034	−	0.305993i	$-0.901012\pi$
$223$	−19.8549	+	9.25851i	−1.32959	+	0.619996i	−0.377552	+	0.925989i	$0.623234\pi$
$224$	−3.13574	−	5.43126i	−0.209515	−	0.362891i
$225$		0			0
$226$	−0.580328	+	1.00516i	−0.0386029	+	0.0668621i
$227$	0.431671	−	4.93402i	0.0286510	−	0.327482i	−0.968320	−	0.249712i	$-0.919664\pi$
$227$	0.431671	−	4.93402i	0.0286510	−	0.327482i	0.996971	−	0.0777708i	$-0.0247802\pi$
$228$		0			0
$229$	−1.07319	−	0.189232i	−0.0709183	−	0.0125048i	0.138076	−	0.990422i	$-0.455908\pi$
$229$	−1.07319	−	0.189232i	−0.0709183	−	0.0125048i	−0.208995	+	0.977917i	$0.567019\pi$
$230$	0.901377	+	4.92886i	0.0594351	+	0.324999i
$231$		0			0
$232$	2.55807	+	0.223802i	0.167946	+	0.0146933i
$233$	25.6297	−	6.86746i	1.67906	−	0.449903i	0.711529	−	0.702657i	$-0.248003\pi$
$233$	25.6297	−	6.86746i	1.67906	−	0.449903i	0.967530	+	0.252755i	$0.0813365\pi$
$234$		0			0
$235$	−19.3868	+	1.82016i	−1.26466	+	0.118734i
$236$	0.587514	−	1.61418i	0.0382439	−	0.105074i
$237$		0			0
$238$	10.1762	−	0.890302i	0.659625	−	0.0577097i
$239$	−1.41158	+	0.513773i	−0.0913075	+	0.0332332i	−0.387270	−	0.921966i	$-0.626582\pi$
$239$	−1.41158	+	0.513773i	−0.0913075	+	0.0332332i	0.295962	+	0.955200i	$0.404360\pi$
$240$		0			0
$241$	0.572431	+	3.24642i	0.0368735	+	0.209120i	0.997678	−	0.0681065i	$-0.0216958\pi$
$241$	0.572431	+	3.24642i	0.0368735	+	0.209120i	−0.960805	+	0.277227i	$0.910585\pi$
$242$	−1.33439	+	1.33439i	−0.0857777	+	0.0857777i
$243$		0			0
$244$		−	0.268188i		−	0.0171690i
$245$	31.2775	−	18.3237i	1.99824	−	1.17066i
$246$		0			0
$247$	−5.17651	−	2.41385i	−0.329374	−	0.153589i
$248$	0.600060	+	6.85872i	0.0381039	+	0.435529i
$249$		0			0
$250$	1.13857	−	16.6616i	0.0720095	−	1.05377i
$251$	−16.2363	+	9.37404i	−1.02483	+	0.591684i	−0.915498	−	0.402322i	$-0.868203\pi$
$251$	−16.2363	+	9.37404i	−1.02483	+	0.591684i	−0.109328	+	0.994006i	$0.534870\pi$
$252$		0			0
$253$	−1.35967	−	5.07436i	−0.0854817	−	0.319022i
$254$	−22.4782	+	18.8614i	−1.41041	+	1.18347i
$255$		0			0
$256$	0.951288	−	5.39502i	0.0594555	−	0.337189i
$257$	−11.8010	−	16.8536i	−0.736129	−	1.05130i	−0.996317	−	0.0857431i	$-0.972674\pi$
$257$	−11.8010	−	16.8536i	−0.736129	−	1.05130i	0.260188	−	0.965558i	$-0.416215\pi$
$258$		0			0
$259$	−21.4672	−	25.5836i	−1.33391	−	1.58969i
$260$	−1.60407	+	1.13842i	−0.0994804	+	0.0706019i
$261$		0			0
$262$	−1.88866	+	7.04856i	−0.116682	+	0.435461i
$263$	−7.24374	−	15.5342i	−0.446668	−	0.957882i	−0.992755	−	0.120154i	$-0.961661\pi$
$263$	−7.24374	−	15.5342i	−0.446668	−	0.957882i	0.546087	−	0.837728i	$-0.316117\pi$
$264$		0			0
$265$	3.81777	+	8.05341i	0.234524	+	0.494717i
$266$	−3.69544	−	10.1531i	−0.226582	−	0.622529i
$267$		0			0
$268$	2.90456	+	2.03380i	0.177424	+	0.124234i
$269$	5.61280			0.342218			0.171109	−	0.985252i	$-0.445265\pi$
$269$	5.61280			0.342218			0.171109	+	0.985252i	$0.445265\pi$
$270$		0			0
$271$	15.6827			0.952656			0.476328	−	0.879268i	$-0.341968\pi$
$271$	15.6827			0.952656			0.476328	+	0.879268i	$0.341968\pi$
$272$	5.12653	+	3.58963i	0.310841	+	0.217654i
$273$		0			0
$274$	−0.929644	−	2.55418i	−0.0561619	−	0.154303i
$275$	0.222218	+	17.5081i	0.0134003	+	1.05578i
$276$		0			0
$277$	−10.3807	−	22.2616i	−0.623718	−	1.33757i	−0.923514	−	0.383564i	$-0.874696\pi$
$277$	−10.3807	−	22.2616i	−0.623718	−	1.33757i	0.299796	−	0.954003i	$-0.403081\pi$
$278$	−1.11585	+	4.16442i	−0.0669244	+	0.249765i
$279$		0			0
$280$	28.0612	+	4.76455i	1.67698	+	0.284736i
$281$	−0.467705	−	0.557389i	−0.0279010	−	0.0332511i	0.751914	−	0.659262i	$-0.229131\pi$
$281$	−0.467705	−	0.557389i	−0.0279010	−	0.0332511i	−0.779814	+	0.626011i	$0.784687\pi$
$282$		0			0
$283$	12.3891	+	17.6935i	0.736457	+	1.05177i	0.996285	+	0.0861152i	$0.0274453\pi$
$283$	12.3891	+	17.6935i	0.736457	+	1.05177i	−0.259828	+	0.965655i	$0.583666\pi$
$284$	−0.516015	+	2.92647i	−0.0306199	+	0.173654i
$285$		0			0
$286$	15.2440	−	12.7913i	0.901399	−	0.756364i
$287$	−0.848799	−	3.16776i	−0.0501030	−	0.186987i
$288$		0			0
$289$	12.9775	−	7.49259i	0.763385	−	0.440740i
$290$	2.28084	−	2.30997i	0.133935	−	0.135646i
$291$		0			0
$292$	−0.00716445	−	0.0818900i	−0.000419268	−	0.00479225i
$293$	−8.30888	−	3.87450i	−0.485410	−	0.226350i	0.164477	−	0.986381i	$-0.447406\pi$
$293$	−8.30888	−	3.87450i	−0.485410	−	0.226350i	−0.649888	+	0.760030i	$0.725184\pi$
$294$		0			0
$295$	8.39676	+	14.3328i	0.488879	+	0.834488i
$296$		−	18.3148i		−	1.06452i
$297$		0			0
$298$	−17.3970	+	17.3970i	−1.00778	+	1.00778i
$299$	0.990996	+	5.62022i	0.0573108	+	0.325026i
$300$		0			0
$301$	0.912687	−	0.332191i	0.0526064	−	0.0191472i
$302$	3.86523	−	0.338164i	0.222419	−	0.0194591i
$303$		0			0
$304$	2.26404	−	6.22039i	0.129851	−	0.356764i
$305$	1.99723	+	1.65439i	0.114361	+	0.0947303i
$306$		0			0
$307$	−7.01141	+	1.87870i	−0.400162	+	0.107223i	−0.453287	−	0.891365i	$-0.649749\pi$
$307$	−7.01141	+	1.87870i	−0.400162	+	0.107223i	0.0531246	+	0.998588i	$0.483082\pi$
$308$	3.88640	+	0.340016i	0.221448	+	0.0193742i
$309$		0			0
$310$	7.16134	+	4.94700i	0.406737	+	0.280971i
$311$	−22.2915	−	3.93059i	−1.26404	−	0.222884i	−0.498847	−	0.866690i	$-0.666243\pi$
$311$	−22.2915	−	3.93059i	−1.26404	−	0.222884i	−0.765188	+	0.643807i	$0.777354\pi$
$312$		0			0
$313$	−0.360352	+	4.11885i	−0.0203683	+	0.232811i	0.979186	+	0.202964i	$0.0650575\pi$
$313$	−0.360352	+	4.11885i	−0.0203683	+	0.232811i	−0.999554	+	0.0298468i	$0.990498\pi$
$314$	10.6833	−	18.5039i	0.602891	−	1.04424i
$315$		0			0
$316$	1.13484	+	1.96560i	0.0638397	+	0.110574i
$317$	−29.1740	+	13.6040i	−1.63857	+	0.764080i	−0.999985	−	0.00546854i	$-0.998259\pi$
$317$	−29.1740	+	13.6040i	−1.63857	+	0.764080i	−0.638589	+	0.769548i	$0.720482\pi$
$318$		0			0
$319$	−2.18775	+	2.60726i	−0.122490	+	0.145978i
$320$	9.95400	+	11.7110i	0.556446	+	0.654664i
$321$		0			0
$322$	−6.19222	+	8.84340i	−0.345079	+	0.492824i
$323$	1.50694	+	1.50694i	0.0838485	+	0.0838485i
$324$		0			0
$325$	1.41719	−	18.9684i	0.0786117	−	1.05218i
$326$	−16.6613	+	2.93784i	−0.922785	+	0.162712i
$327$		0			0
$328$	0.760064	−	1.62996i	0.0419675	−	0.0899996i
$329$	−32.1389	−	26.9677i	−1.77187	−	1.48678i
$330$		0			0
$331$	1.84234	+	0.670556i	0.101264	+	0.0368571i	0.392155	−	0.919899i	$-0.371730\pi$
$331$	1.84234	+	0.670556i	0.101264	+	0.0368571i	−0.290891	+	0.956756i	$0.593952\pi$
$332$	−2.53707	−	0.679805i	−0.139240	−	0.0373091i
$333$		0			0
$334$	18.0688	+	10.4320i	0.988679	+	0.570814i
$335$	−33.0635	+	9.08461i	−1.80645	+	0.496345i
$336$		0			0
$337$	−13.7556	+	9.63175i	−0.749313	+	0.524675i	−0.884724	−	0.466115i	$-0.845653\pi$
$337$	−13.7556	+	9.63175i	−0.749313	+	0.524675i	0.135411	+	0.990789i	$0.456764\pi$
$338$	−1.80154	+	1.26145i	−0.0979909	+	0.0686140i
$339$		0			0
$340$	0.707699	−	0.194449i	0.0383803	−	0.0105455i
$341$	−7.90298	−	4.56279i	−0.427970	−	0.247089i
$342$		0			0
$343$	42.8663	+	11.4860i	2.31456	+	0.620185i
$344$	0.500513	+	0.182172i	0.0269858	+	0.00982205i
$345$		0			0
$346$	−4.62803	−	3.88338i	−0.248804	−	0.208772i
$347$	−1.32763	+	2.84711i	−0.0712708	+	0.152841i	−0.938716	−	0.344693i	$-0.887983\pi$
$347$	−1.32763	+	2.84711i	−0.0712708	+	0.152841i	0.867445	+	0.497534i	$0.165761\pi$
$348$		0			0
$349$	−12.2555	+	2.16098i	−0.656022	+	0.115674i	−0.491744	−	0.870740i	$-0.663640\pi$
$349$	−12.2555	+	2.16098i	−0.656022	+	0.115674i	−0.164278	+	0.986414i	$0.552529\pi$
$350$	27.2685	−	23.4771i	1.45756	−	1.25491i
$351$		0			0
$352$	3.22337	+	3.22337i	0.171806	+	0.171806i
$353$	10.4080	−	14.8642i	0.553964	−	0.791143i	−0.440327	−	0.897837i	$-0.645138\pi$
$353$	10.4080	−	14.8642i	0.553964	−	0.791143i	0.994292	+	0.106694i	$0.0340265\pi$
$354$		0			0
$355$	−18.6106	−	21.8955i	−0.987747	−	1.16209i
$356$	0.623160	−	0.742654i	0.0330274	−	0.0393606i
$357$		0			0
$358$	8.77805	−	4.09327i	0.463934	−	0.216336i
$359$	5.27373	+	9.13437i	0.278337	+	0.482094i	0.970972	−	0.239195i	$-0.0768835\pi$
$359$	5.27373	+	9.13437i	0.278337	+	0.482094i	−0.692635	+	0.721289i	$0.743550\pi$
$360$		0			0
$361$	−8.37292	+	14.5023i	−0.440680	+	0.763280i
$362$	1.00543	−	11.4921i	0.0528441	−	0.604011i
$363$		0			0
$364$	−4.17368	−	0.735932i	−0.218760	−	0.0385733i
$365$	0.654041	+	0.451806i	0.0342341	+	0.0236486i
$366$		0			0
$367$	−3.55196	−	0.310757i	−0.185411	−	0.0162214i	−0.00592799	−	0.999982i	$-0.501887\pi$
$367$	−3.55196	−	0.310757i	−0.185411	−	0.0162214i	−0.179483	+	0.983761i	$0.557443\pi$
$368$	−6.38875	+	1.71186i	−0.333037	+	0.0892369i
$369$		0			0
$370$	−17.8307	−	14.7699i	−0.926972	−	0.767851i
$371$	−6.56775	+	18.0448i	−0.340981	+	0.936837i
$372$		0			0
$373$	−25.1438	+	2.19980i	−1.30190	+	0.113901i	−0.716925	−	0.697151i	$-0.754451\pi$
$373$	−25.1438	+	2.19980i	−1.30190	+	0.113901i	−0.584974	+	0.811052i	$0.698895\pi$
$374$	−6.97721	+	2.53950i	−0.360783	+	0.131314i
$375$		0			0
$376$	−3.99522	−	22.6580i	−0.206038	−	1.16850i
$377$	2.61445	−	2.61445i	0.134651	−	0.134651i
$378$		0			0
$379$			27.8698i			1.43158i	0.698317	+	0.715788i	$0.253932\pi$
$379$			27.8698i			1.43158i	−0.698317	+	0.715788i	$0.746068\pi$
$380$	−0.392405	−	0.669813i	−0.0201299	−	0.0343607i
$381$		0			0
$382$	−12.5620	−	5.85775i	−0.642727	−	0.299709i
$383$	3.29980	+	37.7169i	0.168612	+	1.92724i	0.336965	+	0.941517i	$0.390599\pi$
$383$	3.29980	+	37.7169i	0.168612	+	1.92724i	−0.168353	+	0.985727i	$0.553845\pi$
$384$		0			0
$385$	−26.5064	+	26.8450i	−1.35089	+	1.36815i
$386$	33.0067	−	19.0564i	1.68000	−	0.969947i
$387$		0			0
$388$	0.385329	+	1.43807i	0.0195621	+	0.0730067i
$389$	−2.93798	+	2.46526i	−0.148962	+	0.124994i	−0.714223	−	0.699918i	$-0.753220\pi$
$389$	−2.93798	+	2.46526i	−0.148962	+	0.124994i	0.565261	+	0.824912i	$0.308775\pi$
$390$		0			0
$391$	0.369762	−	2.09702i	0.0186997	−	0.106051i
$392$	24.5671	+	35.0854i	1.24082	+	1.77208i
$393$		0			0
$394$	12.0379	+	14.3462i	0.606459	+	0.722749i
$395$	−21.6386	−	3.67404i	−1.08876	−	0.184861i
$396$		0			0
$397$	1.16267	−	4.33915i	0.0583528	−	0.217776i	−0.930592	−	0.366057i	$-0.880707\pi$
$397$	1.16267	−	4.33915i	0.0583528	−	0.217776i	0.988945	+	0.148281i	$0.0473742\pi$
$398$	8.78827	+	18.8465i	0.440516	+	0.944690i
$399$		0			0
$400$	22.0432	−	0.279779i	1.10216	−	0.0139889i
$401$	3.48616	+	9.57816i	0.174091	+	0.478310i	0.995796	−	0.0916029i	$-0.0291990\pi$
$401$	3.48616	+	9.57816i	0.174091	+	0.478310i	−0.821705	+	0.569913i	$0.806977\pi$
$402$		0			0
$403$	8.12063	+	5.68612i	0.404517	+	0.283246i
$404$	1.41471			0.0703845
$405$		0			0
$406$	6.99435			0.347124
$407$	19.8851	+	13.9237i	0.985667	+	0.690172i
$408$		0			0
$409$	8.00244	+	21.9865i	0.395695	+	1.08716i	0.964360	+	0.264594i	$0.0852380\pi$
$409$	8.00244	+	21.9865i	0.395695	+	1.08716i	−0.568665	+	0.822569i	$0.692540\pi$
$410$	−0.973926	−	2.05445i	−0.0480988	−	0.101462i
$411$		0			0
$412$	0.736264	+	1.57892i	0.0362731	+	0.0777879i
$413$	−9.26327	+	34.5710i	−0.455816	+	1.70113i
$414$		0			0
$415$	20.7132	−	14.7003i	1.01677	−	0.721609i
$416$	−3.18315	−	3.79353i	−0.156067	−	0.185993i
$417$		0			0
$418$	4.50465	+	6.43330i	0.220329	+	0.314663i
$419$	−0.258905	+	1.46832i	−0.0126483	+	0.0717323i	−0.990479	−	0.137667i	$-0.956040\pi$
$419$	−0.258905	+	1.46832i	−0.0126483	+	0.0717323i	0.977830	+	0.209399i	$0.0671508\pi$
$420$		0			0
$421$	−14.1741	+	11.8935i	−0.690802	+	0.579652i	−0.919140	−	0.393930i	$-0.871115\pi$
$421$	−14.1741	+	11.8935i	−0.690802	+	0.579652i	0.228338	+	0.973582i	$0.426671\pi$
$422$	7.77666	+	29.0229i	0.378562	+	1.41281i
$423$		0			0
$424$	−9.11988	+	5.26536i	−0.442900	+	0.255709i
$425$	−2.91755	+	6.46983i	−0.141522	+	0.313833i
$426$		0			0
$427$	0.487010	+	5.56655i	0.0235681	+	0.269384i
$428$	−2.92358	−	1.36329i	−0.141316	−	0.0658969i
$429$		0			0
$430$	0.580994	−	0.340371i	0.0280180	−	0.0164141i
$431$			19.2978i			0.929541i	0.885431	+	0.464771i	$0.153863\pi$
$431$			19.2978i			0.929541i	−0.885431	+	0.464771i	$0.846137\pi$
$432$		0			0
$433$	−15.0405	+	15.0405i	−0.722800	+	0.722800i	−0.969175	−	0.246375i	$-0.920761\pi$
$433$	−15.0405	+	15.0405i	−0.722800	+	0.722800i	0.246375	+	0.969175i	$0.420761\pi$
$434$	3.25648	+	18.4684i	0.156316	+	0.886512i
$435$		0			0
$436$	0.439055	−	0.159803i	0.0210269	−	0.00765317i
$437$	−2.24372	+	0.196300i	−0.107332	+	0.00939031i
$438$		0			0
$439$	3.41885	−	9.39321i	0.163173	−	0.448314i	−0.830979	−	0.556303i	$-0.812219\pi$
$439$	3.41885	−	9.39321i	0.163173	−	0.448314i	0.994152	+	0.107990i	$0.0344414\pi$
$440$	−20.5981	+	1.93389i	−0.981976	+	0.0921944i
$441$		0			0
$442$	7.79120	−	2.08765i	0.370590	−	0.0992992i
$443$	30.7678	+	2.69183i	1.46182	+	0.127893i	0.790130	−	0.612939i	$-0.210013\pi$
$443$	30.7678	+	2.69183i	1.46182	+	0.127893i	0.671690	+	0.740832i	$0.265569\pi$
$444$		0			0
$445$	1.68650	+	9.22201i	0.0799477	+	0.437165i
$446$	−32.2268	−	5.68245i	−1.52598	−	0.269072i
$447$		0			0
$448$	−2.88621	+	32.9895i	−0.136361	+	1.55861i
$449$	0.854949	−	1.48081i	0.0403475	−	0.0698840i	−0.845146	−	0.534535i	$-0.820487\pi$
$449$	0.854949	−	1.48081i	0.0403475	−	0.0698840i	0.885494	+	0.464651i	$0.153820\pi$
$450$		0			0
$451$	1.19188	+	2.06440i	0.0561235	+	0.0972088i
$452$	−0.162838	+	0.0759325i	−0.00765925	+	0.00357157i
$453$		0			0
$454$	4.75550	−	5.66739i	0.223187	−	0.265984i
$455$	31.2270	−	26.5421i	1.46395	−	1.24431i
$456$		0			0
$457$	20.8928	−	29.8380i	0.977323	−	1.39576i	0.0597413	−	0.998214i	$-0.480972\pi$
$457$	20.8928	−	29.8380i	0.977323	−	1.39576i	0.917582	−	0.397548i	$-0.130139\pi$
$458$	−1.15102	−	1.15102i	−0.0537835	−	0.0537835i
$459$		0			0
$460$	−0.323336	+	0.705044i	−0.0150756	+	0.0328728i
$461$	17.0206	−	3.00119i	0.792728	−	0.139779i	0.237401	−	0.971412i	$-0.423704\pi$
$461$	17.0206	−	3.00119i	0.792728	−	0.139779i	0.555327	+	0.831632i	$0.312593\pi$
$462$		0			0
$463$	−12.1257	+	26.0036i	−0.563527	+	1.20849i	0.393724	+	0.919229i	$0.371187\pi$
$463$	−12.1257	+	26.0036i	−0.563527	+	1.20849i	−0.957251	+	0.289259i	$0.906591\pi$
$464$	3.28261	+	2.75443i	0.152391	+	0.127871i
$465$		0			0
$466$	37.2442	+	13.5558i	1.72530	+	0.627959i
$467$	−23.0066	−	6.16460i	−1.06462	−	0.285264i	−0.316339	−	0.948646i	$-0.602454\pi$
$467$	−23.0066	−	6.16460i	−1.06462	−	0.285264i	−0.748280	+	0.663382i	$0.769120\pi$
$468$		0			0
$469$	−63.9806	−	36.9392i	−2.95435	−	1.70570i
$470$	−25.2810	−	14.3829i	−1.16613	−	0.663432i
$471$		0			0
$472$	−16.0778	+	11.2578i	−0.740040	+	0.518181i
$473$	−0.578303	+	0.404932i	−0.0265904	+	0.0186188i
$474$		0			0
$475$	7.40883	+	1.20963i	0.339940	+	0.0555018i
$476$	1.36946	+	0.790656i	0.0627689	+	0.0362396i
$477$		0			0
$478$	−2.16738	−	0.580749i	−0.0991338	−	0.0265628i
$479$	3.81746	+	1.38944i	0.174424	+	0.0634853i	0.427756	−	0.903894i	$-0.359304\pi$
$479$	3.81746	+	1.38944i	0.174424	+	0.0634853i	−0.253332	+	0.967379i	$0.581526\pi$
$480$		0			0
$481$	−20.2014	−	16.9510i	−0.921105	−	0.772899i
$482$	−2.08101	+	4.46274i	−0.0947873	+	0.203272i
$483$		0			0
$484$	−0.287690	+	0.0507274i	−0.0130768	+	0.00230579i
$485$	−13.0865	−	6.00151i	−0.594225	−	0.272515i
$486$		0			0
$487$	−18.4638	−	18.4638i	−0.836676	−	0.836676i	0.151744	−	0.988420i	$-0.451511\pi$
$487$	−18.4638	−	18.4638i	−0.836676	−	0.836676i	−0.988420	+	0.151744i	$0.951511\pi$
$488$	−1.75763	+	2.51015i	−0.0795640	+	0.113629i
$489$		0			0
$490$	53.9700	+	4.37685i	2.43812	+	0.197726i
$491$	16.4502	−	19.6046i	0.742387	−	0.884743i	−0.254211	−	0.967149i	$-0.581816\pi$
$491$	16.4502	−	19.6046i	0.742387	−	0.884743i	0.996599	+	0.0824057i	$0.0262603\pi$
$492$		0			0
$493$	−1.25032	+	0.583032i	−0.0563114	+	0.0262585i
$494$	−4.26583	−	7.38864i	−0.191929	−	0.332431i
$495$		0			0
$496$	−5.74468	+	9.95007i	−0.257944	+	0.446771i
$497$	5.39623	−	61.6791i	0.242054	−	2.76669i
$498$		0			0
$499$	5.75147	+	1.01414i	0.257471	+	0.0453991i	0.300894	−	0.953658i	$-0.402715\pi$
$499$	5.75147	+	1.01414i	0.257471	+	0.0453991i	−0.0434226	+	0.999057i	$0.513826\pi$
$500$	1.62377	−	2.01169i	0.0726171	−	0.0899657i
$501$		0			0
$502$	−27.8980	−	2.44076i	−1.24515	−	0.108936i
$503$	20.0094	−	5.36150i	0.892174	−	0.239057i	0.216522	−	0.976278i	$-0.430529\pi$
$503$	20.0094	−	5.36150i	0.892174	−	0.239057i	0.675652	+	0.737221i	$0.263862\pi$
$504$		0			0
$505$	−8.72703	+	10.5355i	−0.388348	+	0.468825i
$506$	2.68387	−	7.37387i	0.119312	−	0.327808i
$507$		0			0
$508$	−4.52509	+	0.395894i	−0.200769	+	0.0175650i
$509$	−7.40545	+	2.69536i	−0.328241	+	0.119470i	−0.500884	−	0.865515i	$-0.666992\pi$
$509$	−7.40545	+	2.69536i	−0.328241	+	0.119470i	0.172643	+	0.984984i	$0.444769\pi$
$510$		0			0
$511$	0.297412	+	1.68671i	0.0131567	+	0.0746156i
$512$	−12.4157	+	12.4157i	−0.548699	+	0.548699i
$513$		0			0
$514$		−	30.7328i		−	1.35556i
$515$	−16.3003	−	4.25697i	−0.718276	−	0.187584i
$516$		0			0
$517$	27.6380	+	12.8878i	1.21552	+	0.566806i
$518$	−4.34787	−	49.6964i	−0.191035	−	2.18354i
$519$		0			0
$520$	22.4744	−	0.142620i	0.985569	−	0.00625432i
$521$	7.49714	−	4.32848i	0.328456	−	0.189634i	−0.326700	−	0.945128i	$-0.605937\pi$
$521$	7.49714	−	4.32848i	0.328456	−	0.189634i	0.655155	+	0.755494i	$0.272603\pi$
$522$		0			0
$523$	3.40449	+	12.7057i	0.148868	+	0.555583i	0.999553	+	0.0299067i	$0.00952102\pi$
$523$	3.40449	+	12.7057i	0.148868	+	0.555583i	−0.850685	+	0.525676i	$0.823812\pi$
$524$	−0.865339	+	0.726106i	−0.0378025	+	0.0317201i
$525$		0			0
$526$	4.44587	−	25.2138i	0.193849	−	1.09937i
$527$	−2.12161	−	3.02998i	−0.0924189	−	0.131988i
$528$		0			0
$529$	−13.3376	−	15.8951i	−0.579894	−	0.691091i
$530$	−2.22852	+	13.1250i	−0.0968006	+	0.570116i
$531$		0			0
$532$	0.432899	−	1.61560i	0.0187686	−	0.0700452i
$533$	−1.09440	−	2.34695i	−0.0474037	−	0.101658i
$534$		0			0
$535$	28.1874	−	13.3624i	1.21865	−	0.577708i
$536$	−13.8568	−	38.0712i	−0.598523	−	1.64443i
$537$		0			0
$538$	6.86778	+	4.80887i	0.296091	+	0.207325i
$539$	−56.7706			−2.44528
$540$		0			0
$541$	27.5170			1.18305			0.591523	−	0.806288i	$-0.298527\pi$
$541$	27.5170			1.18305			0.591523	+	0.806288i	$0.298527\pi$
$542$	19.1892	+	13.4364i	0.824248	+	0.577145i
$543$		0			0
$544$	0.631962	+	1.73630i	0.0270951	+	0.0744433i
$545$	−1.51836	+	4.25548i	−0.0650392	+	0.182285i
$546$		0			0
$547$	13.8936	+	29.7950i	0.594049	+	1.27394i	0.941743	+	0.336334i	$0.109187\pi$
$547$	13.8936	+	29.7950i	0.594049	+	1.27394i	−0.347694	+	0.937608i	$0.613035\pi$
$548$	0.108902	−	0.406429i	0.00465208	−	0.0173618i
$549$		0			0
$550$	−14.7285	+	21.6132i	−0.628026	+	0.921590i
$551$	0.937961	+	1.11782i	0.0399585	+	0.0476207i
$552$		0			0
$553$	−27.1242	−	38.7374i	−1.15344	−	1.64728i
$554$	6.37122	−	36.1330i	0.270687	−	1.53514i
$555$		0			0
$556$	−0.511259	+	0.428997i	−0.0216822	+	0.0181935i
$557$	6.74775	+	25.1830i	0.285911	+	1.06704i	0.948171	+	0.317761i	$0.102931\pi$
$557$	6.74775	+	25.1830i	0.285911	+	1.06704i	−0.662259	+	0.749275i	$0.730402\pi$
$558$		0			0
$559$	0.664181	−	0.383465i	0.0280919	−	0.0162188i
$560$	33.7986	+	33.3723i	1.42825	+	1.41024i
$561$		0			0
$562$	−0.0947268	−	1.08273i	−0.00399581	−	0.0456723i
$563$	27.4015	+	12.7775i	1.15484	+	0.538510i	0.903161	−	0.429302i	$-0.141240\pi$
$563$	27.4015	+	12.7775i	1.15484	+	0.538510i	0.251676	+	0.967811i	$0.419018\pi$
$564$		0			0
$565$	0.439031	−	1.68108i	0.0184702	−	0.0707237i
$566$			32.2643i			1.35617i
$567$		0			0
$568$	24.0089	−	24.0089i	1.00739	−	1.00739i
$569$	−3.82709	−	21.7045i	−0.160440	−	0.909901i	−0.953642	−	0.300943i	$-0.902699\pi$
$569$	−3.82709	−	21.7045i	−0.160440	−	0.909901i	0.793202	−	0.608959i	$-0.208412\pi$
$570$		0			0
$571$	−5.69726	+	2.07363i	−0.238423	+	0.0867789i	−0.458468	−	0.888711i	$-0.651602\pi$
$571$	−5.69726	+	2.07363i	−0.238423	+	0.0867789i	0.220045	+	0.975490i	$0.429380\pi$
$572$	3.06878	−	0.268484i	0.128312	−	0.0112259i
$573$		0			0
$574$	1.67545	−	4.60327i	0.0699321	−	0.192137i
$575$	−3.25596	−	6.75718i	−0.135783	−	0.281794i
$576$		0			0
$577$	−15.9120	+	4.26360i	−0.662424	+	0.177496i	−0.574340	−	0.818617i	$-0.694741\pi$
$577$	−15.9120	+	4.26360i	−0.662424	+	0.177496i	−0.0880841	+	0.996113i	$0.528074\pi$
$578$	22.2986	+	1.95088i	0.927501	+	0.0811458i
$579$		0			0
$580$	0.494328	−	0.0904014i	0.0205258	−	0.00375371i
$581$	53.8941	+	9.50299i	2.23590	+	0.394250i
$582$		0			0
$583$	1.21651	−	13.9048i	0.0503827	−	0.575877i
$584$	−0.469626	+	0.813416i	−0.0194332	+	0.0336594i
$585$		0			0
$586$	−6.84714	−	11.8596i	−0.282853	−	0.489916i
$587$	−2.17389	+	1.01370i	−0.0897262	+	0.0418400i	−0.466963	−	0.884277i	$-0.654652\pi$
$587$	−2.17389	+	1.01370i	−0.0897262	+	0.0418400i	0.377237	+	0.926117i	$0.376874\pi$
$588$		0			0
$589$	−2.51487	+	2.99711i	−0.103623	+	0.123494i
$590$	−2.00568	+	24.7316i	−0.0825724	+	1.01818i
$591$		0			0
$592$	17.5303	−	25.0359i	0.720491	−	1.02897i
$593$	−19.8531	−	19.8531i	−0.815268	−	0.815268i	0.170150	−	0.985418i	$-0.445575\pi$
$593$	−19.8531	−	19.8531i	−0.815268	−	0.815268i	−0.985418	+	0.170150i	$0.945575\pi$
$594$		0			0
$595$	−14.3360	+	5.32113i	−0.587717	+	0.218145i
$596$	−3.75073	+	0.661355i	−0.153636	+	0.0270902i
$597$		0			0
$598$	−3.60265	+	7.72592i	−0.147323	+	0.315936i
$599$	12.9672	+	10.8807i	0.529824	+	0.444575i	0.868041	−	0.496493i	$-0.165379\pi$
$599$	12.9672	+	10.8807i	0.529824	+	0.444575i	−0.338217	+	0.941068i	$0.609824\pi$
$600$		0			0
$601$	−24.9557	−	9.08314i	−1.01796	−	0.370509i	−0.221478	−	0.975165i	$-0.571088\pi$
$601$	−24.9557	−	9.08314i	−1.01796	−	0.370509i	−0.796486	+	0.604656i	$0.793310\pi$
$602$	1.40137	+	0.375496i	0.0571155	+	0.0153041i
$603$		0			0
$604$	0.520160	+	0.300315i	0.0211650	+	0.0122196i
$605$	1.39692	−	2.45539i	0.0567928	−	0.0998256i
$606$		0			0
$607$	5.34086	−	3.73971i	0.216779	−	0.151790i	−0.460144	−	0.887844i	$-0.652202\pi$
$607$	5.34086	−	3.73971i	0.216779	−	0.151790i	0.676922	+	0.736054i	$0.263313\pi$
$608$	1.60095	−	1.12099i	0.0649270	−	0.0454623i
$609$		0			0
$610$	1.02637	+	3.73547i	0.0415563	+	0.151245i
$611$	−28.6898	−	16.5640i	−1.16066	−	0.670109i
$612$		0			0
$613$	10.5860	+	2.83651i	0.427565	+	0.114566i	0.466183	−	0.884688i	$-0.345629\pi$
$613$	10.5860	+	2.83651i	0.427565	+	0.114566i	−0.0386179	+	0.999254i	$0.512296\pi$
$614$	−10.1887	−	3.70839i	−0.411183	−	0.149658i
$615$		0			0
$616$	−34.1469	−	28.6527i	−1.37582	−	1.15445i
$617$	−14.6963	+	31.5164i	−0.591652	+	1.26880i	0.351421	+	0.936217i	$0.385698\pi$
$617$	−14.6963	+	31.5164i	−0.591652	+	1.26880i	−0.943073	+	0.332585i	$0.892079\pi$
$618$		0			0
$619$	−31.5714	+	5.56690i	−1.26896	+	0.223753i	−0.767288	−	0.641303i	$-0.778394\pi$
$619$	−31.5714	+	5.56690i	−1.26896	+	0.223753i	−0.501676	+	0.865056i	$0.667283\pi$
$620$	0.468855	+	1.26317i	0.0188297	+	0.0507301i
$621$		0			0
$622$	−23.9081	−	23.9081i	−0.958628	−	0.958628i
$623$	−11.5858	+	16.5462i	−0.464175	+	0.662910i
$624$		0			0
$625$	4.96468	+	24.5021i	0.198587	+	0.980083i
$626$	−3.96982	+	4.73105i	−0.158666	+	0.189091i
$627$		0			0
$628$	2.99768	−	1.39784i	0.119620	−	0.0557799i
$629$	4.91980	+	8.52135i	0.196165	+	0.339768i
$630$		0			0
$631$	22.4076	−	38.8111i	0.892033	−	1.54505i	0.0545987	−	0.998508i	$-0.482612\pi$
$631$	22.4076	−	38.8111i	0.892033	−	1.54505i	0.837434	−	0.546538i	$-0.184055\pi$
$632$	2.26024	−	25.8347i	0.0899076	−	1.02765i
$633$		0			0
$634$	−47.3526	−	8.34954i	−1.88061	−	0.331603i
$635$	24.9660	−	36.1411i	0.990745	−	1.43422i
$636$		0			0
$637$	61.4373	+	5.37507i	2.43423	+	0.212968i
$638$	−4.91073	+	1.31583i	−0.194418	+	0.0520940i
$639$		0			0
$640$	2.69021	+	28.6538i	0.106340	+	1.13264i
$641$	15.6160	−	42.9045i	0.616794	−	1.69463i	−0.0979055	−	0.995196i	$-0.531214\pi$
$641$	15.6160	−	42.9045i	0.616794	−	1.69463i	0.714699	−	0.699432i	$-0.246563\pi$
$642$		0			0
$643$	36.2904	−	3.17500i	1.43115	−	0.125210i	0.654940	−	0.755681i	$-0.272694\pi$
$643$	36.2904	−	3.17500i	1.43115	−	0.125210i	0.776212	+	0.630472i	$0.217138\pi$
$644$	−1.57042	+	0.571587i	−0.0618833	+	0.0225237i
$645$		0			0
$646$	0.552782	+	3.13498i	0.0217489	+	0.123344i
$647$	32.3432	−	32.3432i	1.27154	−	1.27154i	0.326266	−	0.945278i	$-0.394209\pi$
$647$	32.3432	−	32.3432i	1.27154	−	1.27154i	0.945278	−	0.326266i	$-0.105791\pi$
$648$		0			0
$649$		−	26.0149i		−	1.02118i
$650$	17.9856	−	21.9954i	0.705453	−	0.862730i
$651$		0			0
$652$	−2.37361	−	1.10683i	−0.0929578	−	0.0433469i
$653$	1.03997	+	11.8869i	0.0406971	+	0.465170i	0.989012	+	0.147838i	$0.0472314\pi$
$653$	1.03997	+	11.8869i	0.0406971	+	0.465170i	−0.948314	+	0.317332i	$0.897213\pi$
$654$		0			0
$655$	−0.0693192	−	10.9235i	−0.00270852	−	0.426815i
$656$	2.59913	−	1.50061i	0.101479	−	0.0585890i
$657$		0			0
$658$	−16.2198	−	60.5331i	−0.632314	−	2.35983i
$659$	−17.0150	+	14.2773i	−0.662811	+	0.556165i	−0.910928	−	0.412565i	$-0.864633\pi$
$659$	−17.0150	+	14.2773i	−0.662811	+	0.556165i	0.248117	+	0.968730i	$0.420188\pi$
$660$		0			0
$661$	−7.45553	+	42.2824i	−0.289986	+	1.64460i	0.396923	+	0.917852i	$0.370078\pi$
$661$	−7.45553	+	42.2824i	−0.289986	+	1.64460i	−0.686909	+	0.726743i	$0.741033\pi$
$662$	1.67976	+	2.39894i	0.0652857	+	0.0932376i
$663$		0			0
$664$	19.2908	+	22.9899i	0.748629	+	0.892181i
$665$	9.36113	+	13.1901i	0.363009	+	0.511491i
$666$		0			0
$667$	0.377358	−	1.40832i	0.0146114	−	0.0545304i
$668$	1.36497	+	2.92718i	0.0528122	+	0.113256i
$669$		0			0
$670$	−48.2397	−	17.2119i	−1.86366	−	0.664955i
$671$	−1.38915	−	3.81665i	−0.0536274	−	0.147340i
$672$		0			0
$673$	35.1820	+	24.6347i	1.35617	+	0.949599i	0.999884	+	0.0152212i	$0.00484525\pi$
$673$	35.1820	+	24.6347i	1.35617	+	0.949599i	0.356284	+	0.934378i	$0.384044\pi$
$674$	−25.0834			−0.966176
$675$		0			0
$676$	−0.340452			−0.0130943
$677$	−22.0638	−	15.4492i	−0.847979	−	0.593761i	0.0667769	−	0.997768i	$-0.478728\pi$
$677$	−22.0638	−	15.4492i	−0.847979	−	0.593761i	−0.914756	+	0.404007i	$0.867617\pi$
$678$		0			0
$679$	−10.6093	−	29.1489i	−0.407149	−	1.11863i
$680$	−7.89817	−	2.81807i	−0.302881	−	0.108068i
$681$		0			0
$682$	−5.76078	−	12.3540i	−0.220592	−	0.473060i
$683$	4.90923	−	18.3215i	0.187846	−	0.701053i	−0.806157	−	0.591702i	$-0.798456\pi$
$683$	4.90923	−	18.3215i	0.187846	−	0.701053i	0.994003	−	0.109351i	$-0.0348771\pi$
$684$		0			0
$685$	2.35493	+	3.31818i	0.0899774	+	0.126781i
$686$	42.6101	+	50.7807i	1.62686	+	1.93882i
$687$		0			0
$688$	0.509820	+	0.728099i	0.0194367	+	0.0277585i
$689$	−2.63302	+	14.9326i	−0.100310	+	0.568887i
$690$		0			0
$691$	17.4026	−	14.6025i	0.662025	−	0.555505i	−0.248668	−	0.968589i	$-0.579993\pi$
$691$	17.4026	−	14.6025i	0.662025	−	0.555505i	0.910693	+	0.413084i	$0.135548\pi$
$692$	−0.242055	−	0.903362i	−0.00920155	−	0.0343407i
$693$		0			0
$694$	−4.06379	+	2.34623i	−0.154259	+	0.0890616i
$695$	−0.0409551	−	6.45379i	−0.00155351	−	0.244806i
$696$		0			0
$697$	0.0842119	+	0.962547i	0.00318975	+	0.0364591i
$698$	−16.8472	−	7.85598i	−0.637676	−	0.297353i
$699$		0			0
$700$	5.54236	−	0.555856i	0.209482	−	0.0210094i
$701$			28.7752i			1.08682i	0.839466	+	0.543412i	$0.182868\pi$
$701$			28.7752i			1.08682i	−0.839466	+	0.543412i	$0.817132\pi$
$702$		0			0
$703$	7.35929	−	7.35929i	0.277561	−	0.277561i
$704$	−4.17981	−	23.7049i	−0.157533	−	0.893412i
$705$		0			0
$706$	25.4704	−	9.27048i	0.958592	−	0.348899i
$707$	−29.3639	+	2.56901i	−1.10434	+	0.0966175i
$708$		0			0
$709$	−0.183502	+	0.504167i	−0.00689155	+	0.0189344i	−0.943091	−	0.332536i	$-0.892096\pi$
$709$	−0.183502	+	0.504167i	−0.00689155	+	0.0189344i	0.936199	+	0.351470i	$0.114318\pi$
$710$	−4.01236	−	42.7362i	−0.150581	−	1.60386i
$711$		0			0
$712$	−10.6997	+	2.86697i	−0.400988	+	0.107444i
$713$	3.89433	+	0.340710i	0.145844	+	0.0127597i
$714$		0			0
$715$	−16.9312	+	24.5098i	−0.633191	+	0.916615i
$716$	1.47655	+	0.260356i	0.0551814	+	0.00972997i
$717$		0			0
$718$	−1.37315	+	15.6951i	−0.0512453	+	0.585737i
$719$	−2.44660	+	4.23763i	−0.0912427	+	0.158037i	−0.908034	−	0.418896i	$-0.862417\pi$
$719$	−2.44660	+	4.23763i	−0.0912427	+	0.158037i	0.816792	+	0.576933i	$0.195751\pi$
$720$		0			0
$721$	−18.1492	−	31.4353i	−0.675911	−	1.17071i
$722$	−22.6702	+	10.5713i	−0.843697	+	0.393422i
$723$		0			0
$724$	1.14789	−	1.36800i	0.0426608	−	0.0508412i
$725$	−2.37616	+	4.23898i	−0.0882485	+	0.157432i
$726$		0			0
$727$	−2.82025	+	4.02773i	−0.104597	+	0.149380i	−0.868038	−	0.496497i	$-0.834619\pi$
$727$	−2.82025	+	4.02773i	−0.104597	+	0.149380i	0.763441	+	0.645877i	$0.223508\pi$
$728$	34.2411	+	34.2411i	1.26906	+	1.26906i
$729$		0			0
$730$	0.413186	+	1.11319i	0.0152927	+	0.0412010i
$731$	−0.281810	+	0.0496908i	−0.0104231	+	0.00183788i
$732$		0			0
$733$	−6.00742	+	12.8830i	−0.221889	+	0.475843i	−0.985466	−	0.169874i	$-0.945664\pi$
$733$	−6.00742	+	12.8830i	−0.221889	+	0.475843i	0.763576	+	0.645717i	$0.223442\pi$
$734$	−4.07991	−	3.42345i	−0.150592	−	0.126362i
$735$		0			0
$736$	−1.83501	−	0.667889i	−0.0676394	−	0.0246187i
$737$	51.8700	+	13.8985i	1.91066	+	0.511959i
$738$		0			0
$739$	28.3320	+	16.3575i	1.04221	+	0.601721i	0.920459	−	0.390840i	$-0.127815\pi$
$739$	28.3320	+	16.3575i	1.04221	+	0.601721i	0.121752	+	0.992561i	$0.461149\pi$
$740$	−0.949609	−	3.45611i	−0.0349083	−	0.127049i
$741$		0			0
$742$	−23.4964	+	16.4524i	−0.862581	+	0.603986i
$743$	−0.889212	+	0.622633i	−0.0326220	+	0.0228422i	−0.589774	−	0.807569i	$-0.700783\pi$
$743$	−0.889212	+	0.622633i	−0.0326220	+	0.0228422i	0.557152	+	0.830411i	$0.311894\pi$
$744$		0			0
$745$	18.2122	−	32.0119i	0.667244	−	1.17283i
$746$	−32.6505	−	18.8508i	−1.19542	−	0.690177i
$747$		0			0
$748$	−1.11024	−	0.297487i	−0.0405943	−	0.0108772i
$749$	63.1577	+	22.9875i	2.30773	+	0.839946i
$750$		0			0
$751$	−9.61953	−	8.07175i	−0.351022	−	0.294542i	0.450178	−	0.892939i	$-0.351360\pi$
$751$	−9.61953	−	8.07175i	−0.351022	−	0.294542i	−0.801200	+	0.598396i	$0.795805\pi$
$752$	16.2261	−	34.7970i	0.591706	−	1.26892i
$753$		0			0
$754$	5.43899	−	0.959041i	0.198076	−	0.0349262i
$755$	−5.44523	+	2.02112i	−0.198172	+	0.0735563i
$756$		0			0
$757$	−3.04376	−	3.04376i	−0.110627	−	0.110627i	0.649626	−	0.760254i	$-0.274925\pi$
$757$	−3.04376	−	3.04376i	−0.110627	−	0.110627i	−0.760254	+	0.649626i	$0.774925\pi$
$758$	−23.8780	+	34.1013i	−0.867288	+	1.23862i
$759$		0			0
$760$	−0.716978	+	8.84091i	−0.0260075	+	0.320694i
$761$	11.3467	−	13.5225i	0.411319	−	0.490191i	−0.520117	−	0.854095i	$-0.674112\pi$
$761$	11.3467	−	13.5225i	0.411319	−	0.490191i	0.931437	+	0.363904i	$0.118556\pi$
$762$		0			0
$763$	−8.82288	+	4.11418i	−0.319410	+	0.148943i
$764$	−1.07282	−	1.85819i	−0.0388134	−	0.0672268i
$765$		0			0
$766$	−28.2771	+	48.9773i	−1.02169	+	1.76962i
$767$	−2.46311	+	28.1535i	−0.0889377	+	1.01656i
$768$		0			0
$769$	29.6816	+	5.23367i	1.07035	+	0.188731i	0.680943	−	0.732336i	$-0.261570\pi$
$769$	29.6816	+	5.23367i	1.07035	+	0.188731i	0.389404	+	0.921067i	$0.372681\pi$
$770$	−55.4330	+	10.1375i	−1.99767	+	0.365328i
$771$		0			0
$772$	5.87749	+	0.514213i	0.211535	+	0.0185069i
$773$	−43.5713	+	11.6749i	−1.56715	+	0.419917i	−0.934919	−	0.354862i	$-0.884528\pi$
$773$	−43.5713	+	11.6749i	−1.56715	+	0.419917i	−0.632232	+	0.774779i	$0.717861\pi$
$774$		0			0
$775$	−12.2992	−	4.30058i	−0.441802	−	0.154482i
$776$	5.81811	−	15.9851i	0.208858	−	0.573832i
$777$		0			0
$778$	−5.70705	+	0.499302i	−0.204608	+	0.0179008i
$779$	0.960366	−	0.349545i	0.0344087	−	0.0125237i
$780$		0			0
$781$	7.81482	+	44.3200i	0.279636	+	1.58590i
$782$	2.24910	−	2.24910i	0.0804277	−	0.0804277i
$783$		0			0
$784$			71.4757i			2.55270i
$785$	−8.08211	+	30.9471i	−0.288463	+	1.10455i
$786$		0			0
$787$	31.9138	+	14.8817i	1.13761	+	0.530474i	0.897825	−	0.440353i	$-0.145147\pi$
$787$	31.9138	+	14.8817i	1.13761	+	0.530474i	0.239780	+	0.970827i	$0.422925\pi$
$788$	0.252670	+	2.88803i	0.00900100	+	0.102882i
$789$		0			0
$790$	−23.3290	−	23.0348i	−0.830010	−	0.819542i
$791$	3.24199	−	1.87177i	0.115272	−	0.0665523i
$792$		0			0
$793$	1.14198	+	4.26192i	0.0405528	+	0.151345i
$794$	5.14028	−	4.31321i	0.182422	−	0.153070i
$795$		0			0
$796$	−0.558987	+	3.17017i	−0.0198128	+	0.112364i
$797$	−19.7333	−	28.1820i	−0.698989	−	0.998259i	−0.999017	−	0.0443290i	$-0.985885\pi$
$797$	−19.7333	−	28.1820i	−0.698989	−	0.998259i	0.300028	−	0.953930i	$-0.403004\pi$
$798$		0			0
$799$	7.94536	+	9.46891i	0.281087	+	0.334986i
$800$	5.37851	+	3.66524i	0.190159	+	0.129586i
$801$		0			0
$802$	−3.94062	+	14.7066i	−0.139148	+	0.519308i
$803$	−0.526128	−	1.12829i	−0.0185667	−	0.0398163i
$804$		0			0
$805$	5.43090	−	15.2211i	0.191414	−	0.536474i
$806$	5.06465	+	13.9150i	0.178395	+	0.490135i
$807$		0			0
$808$	−13.2412	−	9.27159i	−0.465824	−	0.326173i
$809$	54.0630			1.90075			0.950377	−	0.311100i	$-0.100698\pi$
$809$	54.0630			1.90075			0.950377	+	0.311100i	$0.100698\pi$
$810$		0			0
$811$	24.1241			0.847112			0.423556	−	0.905870i	$-0.360782\pi$
$811$	24.1241			0.847112			0.423556	+	0.905870i	$0.360782\pi$
$812$	0.886927	+	0.621033i	0.0311250	+	0.0217940i
$813$		0			0
$814$	12.4019	+	34.0739i	0.434685	+	1.19429i
$815$	22.8850	−	10.8488i	0.801626	−	0.380016i
$816$		0			0
$817$	0.127917	+	0.274318i	0.00447523	+	0.00959717i
$818$	−9.04564	+	33.7588i	−0.316273	+	1.18035i
$819$		0			0
$820$	0.0589162	−	0.346993i	0.00205744	−	0.0121175i
$821$	5.28957	+	6.30386i	0.184607	+	0.220006i	0.850409	−	0.526123i	$-0.176355\pi$
$821$	5.28957	+	6.30386i	0.184607	+	0.220006i	−0.665802	+	0.746129i	$0.731910\pi$
$822$		0			0
$823$	−1.52906	−	2.18373i	−0.0532998	−	0.0761200i	0.791617	−	0.611017i	$-0.209239\pi$
$823$	−1.52906	−	2.18373i	−0.0532998	−	0.0761200i	−0.844917	+	0.534897i	$0.820350\pi$
$824$	3.45661	−	19.6034i	0.120417	−	0.682917i
$825$		0			0
$826$	−40.9538	+	34.3643i	−1.42497	+	1.19569i
$827$	−2.00765	−	7.49264i	−0.0698128	−	0.260545i	0.922194	−	0.386727i	$-0.126394\pi$
$827$	−2.00765	−	7.49264i	−0.0698128	−	0.260545i	−0.992007	+	0.126182i	$0.959728\pi$
$828$		0			0
$829$	36.4123	−	21.0226i	1.26465	−	0.730147i	0.290680	−	0.956820i	$-0.406118\pi$
$829$	36.4123	−	21.0226i	1.26465	−	0.730147i	0.973971	+	0.226674i	$0.0727851\pi$
$830$	37.9392	−	0.240758i	1.31689	−	0.00835684i
$831$		0			0
$832$	2.27902	+	26.0493i	0.0790106	+	0.903096i
$833$	−20.8552	−	9.72492i	−0.722588	−	0.336948i
$834$		0			0
$835$	−30.2192	−	7.89203i	−1.04578	−	0.273115i
$836$			1.21575i			0.0420477i
$837$		0			0
$838$	−1.57481	+	1.57481i	−0.0544008	+	0.0544008i
$839$	7.44120	+	42.2011i	0.256899	+	1.45694i	0.791152	+	0.611620i	$0.209482\pi$
$839$	7.44120	+	42.2011i	0.256899	+	1.45694i	−0.534253	+	0.845325i	$0.679407\pi$
$840$		0			0
$841$	26.3634	−	9.59551i	0.909084	−	0.330880i
$842$	−27.5332	+	2.40885i	−0.948858	+	0.0830143i
$843$		0			0
$844$	−1.59083	+	4.37077i	−0.0547587	+	0.150448i
$845$	2.10017	−	2.53539i	0.0722480	−	0.0872199i
$846$		0			0
$847$	5.87920	−	1.57533i	0.202012	−	0.0541289i
$848$	−17.5065	−	1.53162i	−0.601175	−	0.0525960i
$849$		0			0
$850$	−9.11303	+	5.41677i	−0.312574	+	0.185794i
$851$	−10.2410	−	1.80577i	−0.351057	−	0.0619008i
$852$		0			0
$853$	1.49745	−	17.1159i	0.0512717	−	0.586038i	−0.926490	−	0.376319i	$-0.877190\pi$
$853$	1.49745	−	17.1159i	0.0512717	−	0.586038i	0.977762	−	0.209719i	$-0.0672549\pi$
$854$	−4.17334	+	7.22844i	−0.142809	+	0.247352i
$855$		0			0
$856$	18.4291	+	31.9201i	0.629893	+	1.09101i
$857$	−19.2921	+	8.99607i	−0.659007	+	0.307300i	−0.723201	−	0.690637i	$-0.757330\pi$
$857$	−19.2921	+	8.99607i	−0.659007	+	0.307300i	0.0641943	+	0.997937i	$0.479552\pi$
$858$		0			0
$859$	−5.67148	+	6.75901i	−0.193509	+	0.230615i	−0.854071	−	0.520157i	$-0.825874\pi$
$859$	−5.67148	+	6.75901i	−0.193509	+	0.230615i	0.660562	+	0.750771i	$0.270318\pi$
$860$	0.103895	+	0.00842568i	0.00354280	+	0.000287313i
$861$		0			0
$862$	−16.5337	+	23.6126i	−0.563141	+	0.804249i
$863$	−31.7542	−	31.7542i	−1.08093	−	1.08093i	−0.996423	−	0.0845039i	$-0.973069\pi$
$863$	−31.7542	−	31.7542i	−1.08093	−	1.08093i	−0.0845039	−	0.996423i	$-0.526931\pi$
$864$		0			0
$865$	8.22063	+	3.77002i	0.279510	+	0.128184i
$866$	−31.2896	+	5.51721i	−1.06327	+	0.187482i
$867$		0			0
$868$	−1.22688	+	2.63105i	−0.0416430	+	0.0893038i
$869$	26.3314	+	22.0947i	0.893233	+	0.749511i
$870$		0			0
$871$	−54.8180	−	19.9521i	−1.85744	−	0.676052i
$872$	−5.15670	−	1.38173i	−0.174628	−	0.0467914i
$873$		0			0
$874$	−2.91359	−	1.68216i	−0.0985535	−	0.0568999i
$875$	−30.0500	+	44.7036i	−1.01588	+	1.51126i
$876$		0			0
$877$	−15.8993	+	11.1328i	−0.536880	+	0.375928i	−0.810344	−	0.585955i	$-0.800720\pi$
$877$	−15.8993	+	11.1328i	−0.536880	+	0.375928i	0.273464	+	0.961882i	$0.411831\pi$
$878$	12.2311	−	8.56430i	0.412779	−	0.289031i
$879$		0			0
$880$	−30.0082	−	17.0722i	−1.01158	−	0.575505i
$881$	11.7101	+	6.76081i	0.394522	+	0.227778i	0.684118	−	0.729372i	$-0.260187\pi$
$881$	11.7101	+	6.76081i	0.394522	+	0.227778i	−0.289595	+	0.957149i	$0.593521\pi$
$882$		0			0
$883$	−30.0253	−	8.04527i	−1.01043	−	0.270745i	−0.284623	−	0.958640i	$-0.591868\pi$
$883$	−30.0253	−	8.04527i	−1.01043	−	0.270745i	−0.725810	+	0.687895i	$0.758535\pi$
$884$	1.17334	+	0.427060i	0.0394636	+	0.0143636i
$885$		0			0
$886$	35.3409	+	29.6546i	1.18730	+	0.996264i
$887$	−10.0974	+	21.6538i	−0.339036	+	0.727065i	−0.999722	−	0.0235979i	$-0.992488\pi$
$887$	−10.0974	+	21.6538i	−0.339036	+	0.727065i	0.660686	+	0.750663i	$0.270266\pi$
$888$		0			0
$889$	93.2044	−	16.4345i	3.12598	−	0.551194i
$890$	−5.83755	+	12.7289i	−0.195675	+	0.426675i
$891$		0			0
$892$	−3.58201	−	3.58201i	−0.119934	−	0.119934i
$893$	7.49912	−	10.7099i	0.250949	−	0.358392i
$894$		0			0
$895$	−11.0474	+	9.39000i	−0.369275	+	0.313873i
$896$	−39.8584	+	47.5014i	−1.33158	+	1.58691i
$897$		0			0
$898$	2.31483	−	1.07942i	0.0772467	−	0.0360207i
$899$	−1.26634	−	2.19337i	−0.0422349	−	0.0731529i
$900$		0			0
$901$	2.82881	−	4.89965i	0.0942414	−	0.163231i
$902$	−0.310336	+	3.54715i	−0.0103330	+	0.118107i
$903$		0			0
$904$	2.02174	+	0.356488i	0.0672422	+	0.0118566i
$905$	3.10659	+	16.9873i	0.103267	+	0.564677i
$906$		0			0
$907$	−20.9061	−	1.82905i	−0.694175	−	0.0607325i	−0.265393	−	0.964140i	$-0.585502\pi$
$907$	−20.9061	−	1.82905i	−0.694175	−	0.0607325i	−0.428782	+	0.903408i	$0.641057\pi$
$908$	1.10624	−	0.296416i	0.0367118	−	0.00983690i
$909$		0			0
$910$	60.9496	−	5.72236i	2.02046	−	0.189694i
$911$	9.46462	−	26.0038i	0.313577	−	0.861545i	−0.678351	−	0.734738i	$-0.737305\pi$
$911$	9.46462	−	26.0038i	0.313577	−	0.861545i	0.991927	−	0.126807i	$-0.0404728\pi$
$912$		0			0
$913$	−39.6268	+	3.46689i	−1.31145	+	0.114737i
$914$	51.1285	−	18.6093i	1.69118	−	0.615539i
$915$		0			0
$916$	−0.0437565	−	0.248156i	−0.00144576	−	0.00819929i
$917$	16.6425	−	16.6425i	0.549585	−	0.549585i
$918$		0			0
$919$			21.5936i			0.712307i	0.934427	+	0.356154i	$0.115912\pi$
$919$			21.5936i			0.712307i	−0.934427	+	0.356154i	$0.884088\pi$
$920$	7.64695	−	4.47991i	0.252113	−	0.147698i
$921$		0			0
$922$	23.3976	+	10.9105i	0.770559	+	0.359318i
$923$	−4.26098	−	48.7032i	−0.140252	−	1.60309i
$924$		0			0
$925$	31.5960	+	14.2481i	1.03887	+	0.468475i
$926$	−37.1159	+	21.4289i	−1.21970	+	0.704197i
$927$		0			0
$928$	0.327447	+	1.22205i	0.0107490	+	0.0401158i
$929$	12.2976	−	10.3189i	0.403472	−	0.338553i	−0.418362	−	0.908280i	$-0.637396\pi$
$929$	12.2976	−	10.3189i	0.403472	−	0.338553i	0.821834	+	0.569727i	$0.192951\pi$
$930$		0			0
$931$	−4.22650	+	23.9697i	−0.138518	+	0.785575i
$932$	3.51917	+	5.02589i	0.115274	+	0.164628i
$933$		0			0
$934$	−22.8691	−	27.2543i	−0.748299	−	0.891788i
$935$	9.06422	−	6.43294i	0.296432	−	0.210380i
$936$		0			0
$937$	−5.65242	+	21.0951i	−0.184657	+	0.689148i	0.810047	+	0.586365i	$0.199441\pi$
$937$	−5.65242	+	21.0951i	−0.184657	+	0.689148i	−0.994704	+	0.102783i	$0.967225\pi$
$938$	−46.6379	−	100.015i	−1.52278	−	3.26561i
$939$		0			0
$940$	−1.92872	−	4.06855i	−0.0629080	−	0.132702i
$941$	4.53610	+	12.4628i	0.147872	+	0.406276i	0.991409	−	0.130795i	$-0.0417529\pi$
$941$	4.53610	+	12.4628i	0.147872	+	0.406276i	−0.843537	+	0.537071i	$0.819531\pi$
$942$		0			0
$943$	−0.836480	−	0.585710i	−0.0272395	−	0.0190733i
$944$	−32.7535			−1.06604
$945$		0			0
$946$	−1.05454			−0.0342861
$947$	13.5354	+	9.47761i	0.439843	+	0.307981i	0.772440	−	0.635088i	$-0.219036\pi$
$947$	13.5354	+	9.47761i	0.439843	+	0.307981i	−0.332597	+	0.943069i	$0.607925\pi$
$948$		0			0
$949$	0.462551	+	1.27085i	0.0150150	+	0.0412535i
$950$	8.02901	+	7.82776i	0.260496	+	0.253966i
$951$		0			0
$952$	−7.63591	−	16.3753i	−0.247481	−	0.530725i
$953$	−1.40298	+	5.23599i	−0.0454469	+	0.169610i	−0.984919	−	0.173014i	$-0.944649\pi$
$953$	−1.40298	+	5.23599i	−0.0454469	+	0.169610i	0.939472	+	0.342625i	$0.111316\pi$
$954$		0			0
$955$	20.4561	+	3.47327i	0.661945	+	0.112392i
$956$	−0.223273	−	0.266086i	−0.00722115	−	0.00860583i
$957$		0			0
$958$	3.48059	+	4.97080i	0.112453	+	0.160599i
$959$	−1.52234	+	8.63365i	−0.0491591	+	0.278795i
$960$		0			0
$961$	−18.5454	+	15.5615i	−0.598240	+	0.501983i
$962$	−10.1952	−	38.0491i	−0.328707	−	1.22675i
$963$		0			0
$964$	−0.660134	+	0.381128i	−0.0212615	+	0.0122753i
$965$	−40.0863	+	40.5983i	−1.29042	+	1.30691i
$966$		0			0
$967$	−5.15797	−	58.9559i	−0.165869	−	1.89589i	−0.389204	−	0.921152i	$-0.627250\pi$
$967$	−5.15797	−	58.9559i	−0.165869	−	1.89589i	0.223335	−	0.974742i	$-0.428306\pi$
$968$	3.02513	+	1.41064i	0.0972312	+	0.0453397i
$969$		0			0
$970$	−10.8706	−	18.5555i	−0.349033	−	0.595780i
$971$		−	27.0614i		−	0.868442i	−0.900806	−	0.434221i	$-0.857024\pi$
$971$		−	27.0614i		−	0.868442i	0.900806	−	0.434221i	$-0.142976\pi$
$972$		0			0
$973$	9.83272	−	9.83272i	0.315222	−	0.315222i
$974$	−6.77297	−	38.4114i	−0.217020	−	1.23078i
$975$		0			0
$976$	−4.80526	+	1.74897i	−0.153813	+	0.0559833i
$977$	16.0579	−	1.40489i	0.513738	−	0.0449463i	0.172661	−	0.984981i	$-0.444764\pi$
$977$	16.0579	−	1.40489i	0.513738	−	0.0449463i	0.341078	+	0.940035i	$0.389208\pi$
$978$		0			0
$979$	5.02158	−	13.7967i	0.160490	−	0.440944i
$980$	6.45511	+	5.34704i	0.206201	+	0.170805i
$981$		0			0
$982$	36.9250	−	9.89401i	1.17832	−	0.315731i
$983$	43.1392	+	3.77419i	1.37593	+	0.120378i	0.750999	−	0.660304i	$-0.229573\pi$
$983$	43.1392	+	3.77419i	1.37593	+	0.120378i	0.624929	+	0.780682i	$0.285128\pi$
$984$		0			0
$985$	−23.0662	−	15.9339i	−0.734950	−	0.507697i
$986$	−2.02940	−	0.357838i	−0.0646293	−	0.0113959i
$987$		0			0
$988$	0.115108	−	1.31569i	0.00366208	−	0.0418577i
$989$	0.151213	−	0.261908i	0.00480829	−	0.00832820i
$990$		0			0
$991$	−23.2675	−	40.3005i	−0.739117	−	1.28019i	−0.952893	−	0.303306i	$-0.901910\pi$
$991$	−23.2675	−	40.3005i	−0.739117	−	1.28019i	0.213776	−	0.976883i	$-0.431424\pi$
$992$	−3.07434	+	1.43359i	−0.0976103	+	0.0455164i
$993$		0			0
$994$	59.4476	−	70.8468i	1.88556	−	2.24713i
$995$	−20.1604	−	23.7189i	−0.639127	−	0.751939i
$996$		0			0
$997$	−5.81058	+	8.29837i	−0.184023	+	0.262812i	−0.900555	−	0.434742i	$-0.856839\pi$
$997$	−5.81058	+	8.29837i	−0.184023	+	0.262812i	0.716532	+	0.697554i	$0.245728\pi$
$998$	6.16857	+	6.16857i	0.195263	+	0.195263i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.r.a.152.12		192
3.2	odd	2		135.2.q.a.122.5	yes	192
5.3	odd	4	inner	405.2.r.a.233.12		192
15.2	even	4		675.2.ba.b.68.12		192
15.8	even	4		135.2.q.a.68.5	yes	192
15.14	odd	2		675.2.ba.b.257.12		192
27.2	odd	18	inner	405.2.r.a.332.12		192
27.25	even	9		135.2.q.a.2.5	✓	192
135.52	odd	36		675.2.ba.b.218.12		192
135.79	even	18		675.2.ba.b.407.12		192
135.83	even	36	inner	405.2.r.a.8.12		192
135.133	odd	36		135.2.q.a.83.5	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.5	✓	192	27.25	even	9
135.2.q.a.68.5	yes	192	15.8	even	4
135.2.q.a.83.5	yes	192	135.133	odd	36
135.2.q.a.122.5	yes	192	3.2	odd	2
405.2.r.a.8.12		192	135.83	even	36	inner
405.2.r.a.152.12		192	1.1	even	1	trivial
405.2.r.a.233.12		192	5.3	odd	4	inner
405.2.r.a.332.12		192	27.2	odd	18	inner
675.2.ba.b.68.12		192	15.2	even	4
675.2.ba.b.218.12		192	135.52	odd	36
675.2.ba.b.257.12		192	15.14	odd	2
675.2.ba.b.407.12		192	135.79	even	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.r (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22359 + 0.856769i) q^{2} +(0.0790861 + 0.217287i) q^{4} +(-2.10603 - 0.751431i) q^{5} +(-2.03610 - 4.36642i) q^{7} +(0.683816 - 2.55204i) q^{8} +(-1.93312 - 2.72382i) q^{10} +(2.25098 + 2.68262i) q^{11} +(-2.18203 - 3.11626i) q^{13} +(1.24966 - 7.08719i) q^{14} +(3.37749 - 2.83405i) q^{16} +(0.367380 + 1.37108i) q^{17} +(1.30024 - 0.750693i) q^{19} +(-0.00328108 - 0.517040i) q^{20} +(0.455904 + 5.21100i) q^{22} +(-1.35959 - 0.633988i) q^{23} +(3.87070 + 3.16507i) q^{25} -5.68253i q^{26} +(0.787741 - 0.787741i) q^{28} +(0.168770 + 0.957143i) q^{29} +(-2.44873 + 0.891266i) q^{31} +(1.29677 - 0.113453i) q^{32} +(-0.725176 + 1.99240i) q^{34} +(1.00701 + 10.7258i) q^{35} +(6.69580 - 1.79413i) q^{37} +(2.23413 + 0.195461i) q^{38} +(-3.35782 + 4.86082i) q^{40} +(0.670363 + 0.118203i) q^{41} +(-0.0175704 + 0.200831i) q^{43} +(-0.404877 + 0.701267i) q^{44} +(-1.12040 - 1.94060i) q^{46} +(7.89228 - 3.68023i) q^{47} +(-10.4204 + 12.4186i) q^{49} +(2.02443 + 7.18905i) q^{50} +(0.504555 - 0.720580i) q^{52} +(-2.81838 - 2.81838i) q^{53} +(-2.72483 - 7.34112i) q^{55} +(-12.5356 + 2.21036i) q^{56} +(-0.613544 + 1.31575i) q^{58} +(-5.69079 - 4.77514i) q^{59} +(-1.08988 - 0.396683i) q^{61} +(-3.75986 - 1.00745i) q^{62} +(-5.95268 - 3.43678i) q^{64} +(2.25376 + 8.20258i) q^{65} +(12.5612 - 8.79548i) q^{67} +(-0.268864 + 0.188260i) q^{68} +(-7.95735 + 13.9868i) q^{70} +(11.1295 + 6.42561i) q^{71} +(-0.343386 - 0.0920100i) q^{73} +(9.73009 + 3.54146i) q^{74} +(0.265947 + 0.223156i) q^{76} +(7.13022 - 15.2908i) q^{77} +(9.66646 - 1.70446i) q^{79} +(-9.24267 + 3.43063i) q^{80} +(0.718978 + 0.718978i) q^{82} +(-6.51525 + 9.30474i) q^{83} +(0.256560 - 3.16359i) q^{85} +(-0.193565 + 0.230681i) q^{86} +(8.38540 - 3.91017i) q^{88} +(-2.09630 - 3.63090i) q^{89} +(-9.16409 + 15.8727i) q^{91} +(0.0302327 - 0.345561i) q^{92} +(12.8100 + 2.25876i) q^{94} +(-3.30243 + 0.603940i) q^{95} +(6.41403 + 0.561155i) q^{97} +(-23.3902 + 6.26740i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Introduction

L-functions

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Database

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