LMFDB - Embedded newform 675.2.ba.b.218.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(32,675)] 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("675.32"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([10, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.ba (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [192] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.38990213644$
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			218.12
Character	$\chi$	$=$	675.218
Dual form			675.2.ba.b.257.12

$q$-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} +(1.44117 + 0.960742i) q^{3} +(0.0790861 - 0.217287i) q^{4} +(2.58654 - 0.0591935i) q^{6} +(2.03610 - 4.36642i) q^{7} +(0.683816 + 2.55204i) q^{8} +(1.15395 + 2.76919i) q^{9} +(-2.25098 + 2.68262i) q^{11} +(0.322733 - 0.237167i) q^{12} +(2.18203 - 3.11626i) q^{13} +(-1.24966 - 7.08719i) q^{14} +(3.37749 + 2.83405i) q^{16} +(0.367380 - 1.37108i) q^{17} +(3.78452 + 2.39969i) q^{18} +(1.30024 + 0.750693i) q^{19} +(7.12937 - 4.33660i) q^{21} +(-0.455904 + 5.21100i) q^{22} +(-1.35959 + 0.633988i) q^{23} +(-1.46635 + 4.33489i) q^{24} -5.68253i q^{26} +(-0.997437 + 5.09952i) q^{27} +(-0.787741 - 0.787741i) q^{28} +(-0.168770 + 0.957143i) q^{29} +(-2.44873 - 0.891266i) q^{31} +(1.29677 + 0.113453i) q^{32} +(-5.82135 + 1.70350i) q^{33} +(-0.725176 - 1.99240i) q^{34} +(0.692970 - 0.0317342i) q^{36} +(-6.69580 - 1.79413i) q^{37} +(2.23413 - 0.195461i) q^{38} +(6.13860 - 2.39470i) q^{39} +(-0.670363 + 0.118203i) q^{41} +(5.00798 - 11.4145i) q^{42} +(0.0175704 + 0.200831i) q^{43} +(0.404877 + 0.701267i) q^{44} +(-1.12040 + 1.94060i) q^{46} +(7.89228 + 3.68023i) q^{47} +(2.14475 + 7.32924i) q^{48} +(-10.4204 - 12.4186i) q^{49} +(1.84671 - 1.62300i) q^{51} +(-0.504555 - 0.720580i) q^{52} +(-2.81838 + 2.81838i) q^{53} +(3.14865 + 7.09431i) q^{54} +(12.5356 + 2.21036i) q^{56} +(1.15264 + 2.33107i) q^{57} +(0.613544 + 1.31575i) q^{58} +(5.69079 - 4.77514i) q^{59} +(-1.08988 + 0.396683i) q^{61} +(-3.75986 + 1.00745i) q^{62} +(14.4410 + 0.599704i) q^{63} +(-5.95268 + 3.43678i) q^{64} +(-5.66346 + 7.07194i) q^{66} +(-12.5612 - 8.79548i) q^{67} +(-0.268864 - 0.188260i) q^{68} +(-2.56850 - 0.392531i) q^{69} +(-11.1295 + 6.42561i) q^{71} +(-6.27798 + 4.83854i) q^{72} +(0.343386 - 0.0920100i) q^{73} +(-9.73009 + 3.54146i) q^{74} +(0.265947 - 0.223156i) q^{76} +(7.13022 + 15.2908i) q^{77} +(5.45945 - 8.18950i) q^{78} +(9.66646 + 1.70446i) q^{79} +(-6.33680 + 6.39100i) q^{81} +(-0.718978 + 0.718978i) q^{82} +(-6.51525 - 9.30474i) q^{83} +(-0.378454 - 1.89208i) q^{84} +(0.193565 + 0.230681i) q^{86} +(-1.16279 + 1.21726i) q^{87} +(-8.38540 - 3.91017i) q^{88} +(2.09630 - 3.63090i) q^{89} +(-9.16409 - 15.8727i) q^{91} +(0.0302327 + 0.345561i) q^{92} +(-2.67277 - 3.63707i) q^{93} +(12.8100 - 2.25876i) q^{94} +(1.75987 + 1.40937i) q^{96} +(-6.41403 + 0.561155i) q^{97} +(-23.3902 - 6.26740i) q^{98} +(-10.0262 - 3.13779i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8} - 36 q^{11} + 12 q^{12} + 12 q^{13} - 24 q^{16} + 18 q^{17} + 54 q^{18} - 24 q^{21} + 12 q^{22} + 36 q^{23} + 36 q^{27} + 24 q^{28} - 24 q^{31}+ \cdots - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8 - 36 * q^11 + 12 * q^12 + 12 * q^13 - 24 * q^16 + 18 * q^17 + 54 * q^18 - 24 * q^21 + 12 * q^22 + 36 * q^23 + 36 * q^27 + 24 * q^28 - 24 * q^31 + 48 * q^32 + 6 * q^33 + 12 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^41 + 24 * q^42 + 12 * q^43 - 12 * q^46 + 6 * q^47 - 12 * q^48 + 144 * q^51 - 12 * q^52 + 180 * q^56 + 12 * q^57 + 12 * q^58 - 60 * q^61 + 18 * q^62 + 54 * q^63 + 72 * q^66 - 24 * q^67 + 60 * q^68 - 36 * q^71 - 180 * q^72 + 6 * q^73 - 72 * q^76 - 132 * q^77 - 78 * q^78 + 12 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^86 - 144 * q^87 + 48 * q^88 - 12 * q^91 - 258 * q^92 - 180 * q^93 - 12 * q^96 - 24 * q^97 - 324 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{3}{4}\right)$

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	−0.0544607	−	0.998516i	$-0.517344\pi$
$2$	1.22359	−	0.856769i	0.865211	−	0.605827i	0.919671	+	0.392689i	$0.128455\pi$
$3$	1.44117	+	0.960742i	0.832061	+	0.554685i
$3$	1.44117	+	0.960742i	0.832061	+	0.554685i
$4$	0.0790861	−	0.217287i	0.0395430	−	0.108644i
$5$		0			0
$5$		0			0
$6$	2.58654	−	0.0591935i	1.05595	−	0.0241657i
$7$	2.03610	−	4.36642i	0.769572	−	1.65035i	0.00998196	−	0.999950i	$-0.496823\pi$
$7$	2.03610	−	4.36642i	0.769572	−	1.65035i	0.759590	−	0.650402i	$-0.225400\pi$
$8$	0.683816	+	2.55204i	0.241766	+	0.902281i
$9$	1.15395	+	2.76919i	0.384650	+	0.923063i
$10$		0			0
$11$	−2.25098	+	2.68262i	−0.678697	+	0.808839i	−0.989940	−	0.141491i	$-0.954810\pi$
$11$	−2.25098	+	2.68262i	−0.678697	+	0.808839i	0.311243	+	0.950330i	$0.399255\pi$
$12$	0.322733	−	0.237167i	0.0931651	−	0.0684641i
$13$	2.18203	−	3.11626i	0.605186	−	0.864295i	−0.393294	−	0.919413i	$-0.628664\pi$
$13$	2.18203	−	3.11626i	0.605186	−	0.864295i	0.998480	+	0.0551175i	$0.0175533\pi$
$14$	−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	−0.906957	−	0.421224i	$-0.861601\pi$
$17$	0.367380	−	1.37108i	0.0891027	−	0.332536i	0.996059	+	0.0886879i	$0.0282674\pi$
$18$	3.78452	+	2.39969i	0.892019	+	0.565612i
$19$	1.30024	+	0.750693i	0.298295	+	0.172221i	0.641677	−	0.766975i	$-0.278239\pi$
$19$	1.30024	+	0.750693i	0.298295	+	0.172221i	−0.343382	+	0.939196i	$0.611572\pi$
$20$		0			0
$21$	7.12937	−	4.33660i	1.55576	−	0.946323i
$22$	−0.455904	+	5.21100i	−0.0971990	+	1.11099i
$23$	−1.35959	+	0.633988i	−0.283494	+	0.132196i	−0.559165	−	0.829057i	$-0.688878\pi$
$23$	−1.35959	+	0.633988i	−0.283494	+	0.132196i	0.275670	+	0.961252i	$0.411100\pi$
$24$	−1.46635	+	4.33489i	−0.299318	+	0.884856i
$25$		0			0
$26$		−	5.68253i		−	1.11444i
$27$	−0.997437	+	5.09952i	−0.191957	+	0.981403i
$28$	−0.787741	−	0.787741i	−0.148869	−	0.148869i
$29$	−0.168770	+	0.957143i	−0.0313398	+	0.177737i	−0.996460	−	0.0840712i	$-0.973208\pi$
$29$	−0.168770	+	0.957143i	−0.0313398	+	0.177737i	0.965120	+	0.261808i	$0.0843188\pi$
$30$		0			0
$31$	−2.44873	−	0.891266i	−0.439806	−	0.160076i	0.112620	−	0.993638i	$-0.464076\pi$
$31$	−2.44873	−	0.891266i	−0.439806	−	0.160076i	−0.552426	+	0.833562i	$0.686298\pi$
$32$	1.29677	+	0.113453i	0.229239	+	0.0200558i
$33$	−5.82135	+	1.70350i	−1.01337	+	0.296541i
$34$	−0.725176	−	1.99240i	−0.124367	−	0.341694i
$35$		0			0
$36$	0.692970	−	0.0317342i	0.115495	−	0.00528903i
$37$	−6.69580	−	1.79413i	−1.10078	−	0.294954i	−0.337699	−	0.941254i	$-0.609649\pi$
$37$	−6.69580	−	1.79413i	−1.10078	−	0.294954i	−0.763083	+	0.646300i	$0.776315\pi$
$38$	2.23413	−	0.195461i	0.362424	−	0.0317080i
$39$	6.13860	−	2.39470i	0.982963	−	0.383459i
$40$		0			0
$41$	−0.670363	+	0.118203i	−0.104693	+	0.0184602i	−0.225749	−	0.974185i	$-0.572483\pi$
$41$	−0.670363	+	0.118203i	−0.104693	+	0.0184602i	0.121056	+	0.992646i	$0.461372\pi$
$42$	5.00798	−	11.4145i	0.772748	−	1.76129i
$43$	0.0175704	+	0.200831i	0.00267946	+	0.0306264i	0.997417	−	0.0718322i	$-0.0228846\pi$
$43$	0.0175704	+	0.200831i	0.00267946	+	0.0306264i	−0.994737	+	0.102459i	$0.967329\pi$
$44$	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	0.902044	−	0.431644i	$-0.142066\pi$
$47$	7.89228	+	3.68023i	1.15121	+	0.536817i	0.249164	+	0.968461i	$0.419844\pi$
$48$	2.14475	+	7.32924i	0.309568	+	1.05789i
$49$	−10.4204	−	12.4186i	−1.48863	−	1.77409i
$50$		0			0
$51$	1.84671	−	1.62300i	0.258591	−	0.227266i
$52$	−0.504555	−	0.720580i	−0.0699692	−	0.0999264i
$53$	−2.81838	+	2.81838i	−0.387135	+	0.387135i	−0.873664	−	0.486529i	$-0.838263\pi$
$53$	−2.81838	+	2.81838i	−0.387135	+	0.387135i	0.486529	+	0.873664i	$0.338263\pi$
$54$	3.14865	+	7.09431i	0.428478	+	0.965413i
$55$		0			0
$56$	12.5356	+	2.21036i	1.67514	+	0.295372i
$57$	1.15264	+	2.33107i	0.152671	+	0.308758i
$58$	0.613544	+	1.31575i	0.0805623	+	0.172766i
$59$	5.69079	−	4.77514i	0.740877	−	0.621670i	−0.192196	−	0.981357i	$-0.561561\pi$
$59$	5.69079	−	4.77514i	0.740877	−	0.621670i	0.933073	+	0.359687i	$0.117116\pi$
$60$		0			0
$61$	−1.08988	+	0.396683i	−0.139544	+	0.0507900i	−0.410848	−	0.911704i	$-0.634767\pi$
$61$	−1.08988	+	0.396683i	−0.139544	+	0.0507900i	0.271304	+	0.962494i	$0.412545\pi$
$62$	−3.75986	+	1.00745i	−0.477503	+	0.127947i
$63$	14.4410	+	0.599704i	1.81939	+	0.0755556i
$64$	−5.95268	+	3.43678i	−0.744085	+	0.429598i
$65$		0			0
$66$	−5.66346	+	7.07194i	−0.697124	+	0.870496i
$67$	−12.5612	−	8.79548i	−1.53460	−	1.07454i	−0.968128	−	0.250457i	$-0.919419\pi$
$67$	−12.5612	−	8.79548i	−1.53460	−	1.07454i	−0.566472	−	0.824081i	$-0.691692\pi$
$68$	−0.268864	−	0.188260i	−0.0326045	−	0.0228299i
$69$	−2.56850	−	0.392531i	−0.309211	−	0.0472552i
$70$		0			0
$71$	−11.1295	+	6.42561i	−1.32083	+	0.762579i	−0.983860	−	0.178938i	$-0.942734\pi$
$71$	−11.1295	+	6.42561i	−1.32083	+	0.762579i	−0.336966	+	0.941517i	$0.609401\pi$
$72$	−6.27798	+	4.83854i	−0.739867	+	0.570227i
$73$	0.343386	−	0.0920100i	0.0401903	−	0.0107690i	−0.238668	−	0.971101i	$-0.576711\pi$
$73$	0.343386	−	0.0920100i	0.0401903	−	0.0107690i	0.278858	+	0.960332i	$0.410044\pi$
$74$	−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
$78$	5.45945	−	8.18950i	0.618161	−	0.927278i
$79$	9.66646	+	1.70446i	1.08756	+	0.191766i	0.688557	−	0.725182i	$-0.258245\pi$
$79$	9.66646	+	1.70446i	1.08756	+	0.191766i	0.399005	+	0.916949i	$0.369356\pi$
$80$		0			0
$81$	−6.33680	+	6.39100i	−0.704089	+	0.710112i
$82$	−0.718978	+	0.718978i	−0.0793979	+	0.0793979i
$83$	−6.51525	−	9.30474i	−0.715142	−	1.02133i	−0.998065	−	0.0621857i	$-0.980193\pi$
$83$	−6.51525	−	9.30474i	−0.715142	−	1.02133i	0.282923	−	0.959143i	$-0.408696\pi$
$84$	−0.378454	−	1.89208i	−0.0412927	−	0.206443i
$85$		0			0
$86$	0.193565	+	0.230681i	0.0208726	+	0.0248750i
$87$	−1.16279	+	1.21726i	−0.124665	+	0.130504i
$88$	−8.38540	−	3.91017i	−0.893886	−	0.416826i
$89$	2.09630	−	3.63090i	0.222208	−	0.384875i	−0.733270	−	0.679937i	$-0.762007\pi$
$89$	2.09630	−	3.63090i	0.222208	−	0.384875i	0.955478	+	0.295062i	$0.0953403\pi$
$90$		0			0
$91$	−9.16409	−	15.8727i	−0.960658	−	1.66391i
$92$	0.0302327	+	0.345561i	0.00315198	+	0.0360272i
$93$	−2.67277	−	3.63707i	−0.277153	−	0.377146i
$94$	12.8100	−	2.25876i	1.32126	−	0.232973i
$95$		0			0
$96$	1.75987	+	1.40937i	0.179616	+	0.143843i
$97$	−6.41403	+	0.561155i	−0.651246	+	0.0569767i	−0.407991	−	0.912986i	$-0.633771\pi$
$97$	−6.41403	+	0.561155i	−0.651246	+	0.0569767i	−0.243255	+	0.969962i	$0.578215\pi$
$98$	−23.3902	−	6.26740i	−2.36277	−	0.633103i
$99$	−10.0262	−	3.13779i	−1.00767	−	0.315360i
$100$		0			0
$101$	−2.09253	−	5.74917i	−0.208214	−	0.572064i	0.790995	−	0.611823i	$-0.209563\pi$
$101$	−2.09253	−	5.74917i	−0.208214	−	0.572064i	−0.999209	+	0.0397585i	$0.987341\pi$
$102$	0.869084	−	3.56810i	0.0860521	−	0.353295i
$103$	−7.50553	−	0.656648i	−0.739541	−	0.0647015i	−0.288841	−	0.957377i	$-0.593270\pi$
$103$	−7.50553	−	0.656648i	−0.739541	−	0.0647015i	−0.450700	+	0.892675i	$0.648826\pi$
$104$	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	0.0453334	−	0.998972i	$-0.485565\pi$
$107$	−9.86451	−	9.86451i	−0.953639	−	0.953639i	−0.998972	+	0.0453334i	$0.985565\pi$
$108$	1.02918	+	0.620031i	0.0990326	+	0.0596625i
$109$			2.02062i			0.193540i	0.995307	+	0.0967701i	$0.0308512\pi$
$109$			2.02062i			0.193540i	−0.995307	+	0.0967701i	$0.969149\pi$
$110$		0			0
$111$	−7.92609	−	9.01859i	−0.752311	−	0.856006i
$112$	19.2515	−	8.97714i	1.81910	−	0.848260i
$113$	0.0677216	−	0.774062i	0.00637072	−	0.0728176i	−0.992344	−	0.123506i	$-0.960586\pi$
$113$	0.0677216	−	0.774062i	0.00637072	−	0.0728176i	0.998715	+	0.0506887i	$0.0161416\pi$
$114$	3.40756	+	1.86473i	0.319147	+	0.174648i
$115$		0			0
$116$	0.194627	+	0.112368i	0.0180707	+	0.0104331i
$117$	11.1475	+	2.44644i	1.03058	+	0.226174i
$118$	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
$123$	−1.07967	−	0.473695i	−0.0973506	−	0.0427116i
$124$	−0.387321	+	0.461592i	−0.0347825	+	0.0414522i
$125$		0			0
$126$	18.1837	−	11.6388i	1.61993	−	1.03687i
$127$	5.08430	+	18.9749i	0.451159	+	1.68375i	0.699141	+	0.714983i	$0.253566\pi$
$127$	5.08430	+	18.9749i	0.451159	+	1.68375i	−0.247982	+	0.968765i	$0.579768\pi$
$128$	−5.43940	+	11.6648i	−0.480779	+	1.03103i
$129$	−0.167625	+	0.306312i	−0.0147585	+	0.0269693i
$130$		0			0
$131$	−1.67084	+	4.59061i	−0.145982	+	0.401083i	−0.991035	−	0.133599i	$-0.957347\pi$
$131$	−1.67084	+	4.59061i	−0.145982	+	0.401083i	0.845053	+	0.534682i	$0.179569\pi$
$132$	−0.0902401	+	1.39963i	−0.00785439	+	0.121822i
$133$	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	−0.635516	−	0.772088i	$-0.719212\pi$
$137$	−1.49059	+	1.04372i	−0.127349	+	0.0891710i	0.508166	+	0.861259i	$0.330324\pi$
$138$	−3.47911	+	1.72031i	−0.296161	+	0.146443i
$139$	0.987166	−	2.71222i	0.0837303	−	0.230047i	−0.890761	−	0.454472i	$-0.849828\pi$
$139$	0.987166	−	2.71222i	0.0837303	−	0.230047i	0.974491	+	0.224425i	$0.0720503\pi$
$140$		0			0
$141$	7.83838	+	12.8863i	0.660110	+	1.08522i
$142$	−8.11269	+	17.3977i	−0.680802	+	1.45998i
$143$	3.44802	+	12.8682i	0.288338	+	1.07609i
$144$	−3.95056	+	12.6232i	−0.329214	+	1.05194i
$145$		0			0
$146$	0.341333	−	0.406785i	0.0282489	−	0.0336658i
$147$	−3.08657	−	27.9087i	−0.254576	−	2.30187i
$148$	−0.919386	+	1.31302i	−0.0755731	+	0.107930i
$149$	2.86013	+	16.2206i	0.234311	+	1.32885i	0.844059	+	0.536250i	$0.180160\pi$
$149$	2.86013	+	16.2206i	0.234311	+	1.32885i	−0.609748	+	0.792596i	$0.708729\pi$
$150$		0			0
$151$	1.98981	+	1.66965i	0.161929	+	0.135874i	0.720152	−	0.693817i	$-0.244072\pi$
$151$	1.98981	+	1.66965i	0.161929	+	0.135874i	−0.558223	+	0.829691i	$0.688517\pi$
$152$	−1.02667	+	3.83159i	−0.0832741	+	0.310783i
$153$	4.22072	−	0.564813i	0.341225	−	0.0456624i
$154$	21.8252	+	12.6008i	1.75872	+	1.01540i
$155$		0			0
$156$	−0.0348594	−	1.52323i	−0.00279098	−	0.121956i
$157$	1.24669	−	14.2497i	0.0994965	−	1.13725i	−0.768219	−	0.640188i	$-0.778857\pi$
$157$	1.24669	−	14.2497i	0.0994965	−	1.13725i	0.867715	−	0.497062i	$-0.165588\pi$
$158$	13.2881	−	6.19636i	1.05715	−	0.492956i
$159$	−6.76951	+	1.35403i	−0.536857	+	0.107382i
$160$		0			0
$161$			7.22741i			0.569599i
$162$	−2.27805	+	13.2492i	−0.178981	+	1.04095i
$163$	8.00886	+	8.00886i	0.627302	+	0.627302i	0.947388	−	0.320086i	$-0.103712\pi$
$163$	8.00886	+	8.00886i	0.627302	+	0.627302i	−0.320086	+	0.947388i	$0.603712\pi$
$164$	−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	0.611703	−	0.791088i	$-0.290485\pi$
$167$	13.9146	+	1.21737i	1.07674	+	0.0942027i	0.465039	+	0.885290i	$0.346040\pi$
$168$	15.9423	+	15.2290i	1.22998	+	1.17494i
$169$	−0.503569	−	1.38354i	−0.0387361	−	0.106427i
$170$		0			0
$171$	−0.578401	+	4.46687i	−0.0442314	+	0.341590i
$172$	0.0450275	+	0.0120651i	0.00343332	+	0.000919955i
$173$	−4.02915	+	0.352505i	−0.306331	+	0.0268005i	−0.239285	−	0.970949i	$-0.576913\pi$
$173$	−4.02915	+	0.352505i	−0.306331	+	0.0268005i	−0.0670460	+	0.997750i	$0.521357\pi$
$174$	−0.379874	+	2.48568i	−0.0287982	+	0.188439i
$175$		0			0
$176$	−15.2053	+	2.68111i	−1.14614	+	0.202096i
$177$	12.7891	−	1.41441i	0.961285	−	0.106314i
$178$	−0.545824	−	6.23880i	−0.0409112	−	0.467618i
$179$	−3.24205	−	5.61540i	−0.242322	−	0.419714i	0.719053	−	0.694955i	$-0.244576\pi$
$179$	−3.24205	−	5.61540i	−0.242322	−	0.419714i	−0.961375	+	0.275241i	$0.911242\pi$
$180$		0			0
$181$	−3.86147	+	6.68826i	−0.287021	+	0.497135i	−0.973097	−	0.230395i	$-0.925998\pi$
$181$	−3.86147	+	6.68826i	−0.287021	+	0.497135i	0.686076	+	0.727530i	$0.259332\pi$
$182$	−24.8123	−	11.5702i	−1.83921	−	0.857639i
$183$	−1.95181	−	0.475403i	−0.144282	−	0.0351428i
$184$	−2.54767	−	3.03620i	−0.187817	−	0.223831i
$185$		0			0
$186$	−6.38651	−	2.16035i	−0.468281	−	0.158404i
$187$	2.85112	+	4.07182i	0.208494	+	0.297761i
$188$	1.42384	−	1.42384i	0.103844	−	0.103844i
$189$	20.2358	+	14.7383i	1.47194	+	1.07206i
$190$		0			0
$191$	9.13822	+	1.61131i	0.661218	+	0.116591i	0.494180	−	0.869360i	$-0.335468\pi$
$191$	9.13822	+	1.61131i	0.661218	+	0.116591i	0.167039	+	0.985950i	$0.446580\pi$
$192$	−11.8807	−	0.766000i	−0.857415	−	0.0552813i
$193$	−10.7832	−	23.1246i	−0.776191	−	1.66455i	−0.746863	−	0.664978i	$-0.768441\pi$
$193$	−10.7832	−	23.1246i	−0.776191	−	1.66455i	−0.0293284	−	0.999570i	$-0.509337\pi$
$194$	−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	0.199839	−	0.979829i	$-0.435958\pi$
$197$	12.1103	−	3.24493i	0.862820	−	0.231192i	0.662980	+	0.748637i	$0.269291\pi$
$198$	−14.9563	+	4.75075i	−1.06290	+	0.337621i
$199$	12.0563	−	6.96070i	0.854648	−	0.493431i	−0.00756873	−	0.999971i	$-0.502409\pi$
$199$	12.0563	−	6.96070i	0.854648	−	0.493431i	0.862216	+	0.506540i	$0.169076\pi$
$200$		0			0
$201$	−9.65271	−	24.7439i	−0.680850	−	1.74530i
$202$	−7.48611	−	5.24183i	−0.526721	−	0.368814i
$203$	3.83566	+	2.68576i	0.269210	+	0.188503i
$204$	−0.206609	−	0.529624i	−0.0144655	−	0.0370811i
$205$		0			0
$206$	−9.74630	+	5.62703i	−0.679057	+	0.392054i
$207$	−3.32453	−	3.03337i	−0.231071	−	0.210834i
$208$	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	0.0666204	−	0.997778i	$-0.478778\pi$
$211$	15.4091	−	12.9298i	1.06081	−	0.890124i	0.994188	+	0.107654i	$0.0343339\pi$
$212$	0.389504	+	0.835293i	0.0267512	+	0.0573682i
$213$	−22.2128	−	1.43216i	−1.52200	−	0.0981299i
$214$	−20.5218	−	3.61854i	−1.40284	−	0.247358i
$215$		0			0
$216$	−13.6962	+	0.941639i	−0.931911	+	0.0640704i
$217$	−8.87750	+	8.87750i	−0.602644	+	0.602644i
$218$	1.73120	+	2.47242i	0.117252	+	0.167453i
$219$	0.583276	+	0.197303i	0.0394141	+	0.0133325i
$220$		0			0
$221$	−3.47101	−	4.13659i	−0.233485	−	0.278257i
$222$	−17.4252	−	4.24425i	−1.16950	−	0.284855i
$223$	19.8549	+	9.25851i	1.32959	+	0.619996i	0.952034	−	0.305993i	$-0.0989883\pi$
$223$	19.8549	+	9.25851i	1.32959	+	0.619996i	0.377552	+	0.925989i	$0.376766\pi$
$224$	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	0.996971	+	0.0777708i	$0.0247802\pi$
$227$	0.431671	+	4.93402i	0.0286510	+	0.327482i	−0.968320	+	0.249712i	$0.919664\pi$
$228$	0.597670	−	0.0660995i	0.0395816	−	0.00437754i
$229$	−1.07319	+	0.189232i	−0.0709183	+	0.0125048i	−0.208995	−	0.977917i	$-0.567019\pi$
$229$	−1.07319	+	0.189232i	−0.0709183	+	0.0125048i	0.138076	+	0.990422i	$0.455908\pi$
$230$		0			0
$231$	−4.41465	+	28.8870i	−0.290463	+	1.90062i
$232$	−2.55807	+	0.223802i	−0.167946	+	0.0146933i
$233$	25.6297	+	6.86746i	1.67906	+	0.449903i	0.967530	−	0.252755i	$-0.0813365\pi$
$233$	25.6297	+	6.86746i	1.67906	+	0.449903i	0.711529	+	0.702657i	$0.248003\pi$
$234$	15.7360	−	6.55735i	1.02869	−	0.428667i
$235$		0			0
$236$	−0.587514	−	1.61418i	−0.0382439	−	0.105074i
$237$	12.2935	+	11.7434i	0.798547	+	0.762815i
$238$	−10.1762	−	0.890302i	−0.659625	−	0.0577097i
$239$	1.41158	+	0.513773i	0.0913075	+	0.0332332i	0.387270	−	0.921966i	$-0.373418\pi$
$239$	1.41158	+	0.513773i	0.0913075	+	0.0332332i	−0.295962	+	0.955200i	$0.595640\pi$
$240$		0			0
$241$	0.572431	−	3.24642i	0.0368735	−	0.209120i	−0.960805	−	0.277227i	$-0.910585\pi$
$241$	0.572431	−	3.24642i	0.0368735	−	0.209120i	0.997678	+	0.0681065i	$0.0216958\pi$
$242$	−1.33439	−	1.33439i	−0.0857777	−	0.0857777i
$243$	−15.2725	+	3.12250i	−0.979733	+	0.200308i
$244$			0.268188i			0.0171690i
$245$		0			0
$246$	−1.72692	+	0.345418i	−0.110105	+	0.0220231i
$247$	5.17651	−	2.41385i	0.329374	−	0.153589i
$248$	0.600060	−	6.85872i	0.0381039	−	0.435529i
$249$	−0.450134	−	19.6692i	−0.0285261	−	1.24649i
$250$		0			0
$251$	16.2363	+	9.37404i	1.02483	+	0.591684i	0.915498	−	0.402322i	$-0.131797\pi$
$251$	16.2363	+	9.37404i	1.02483	+	0.591684i	0.109328	+	0.994006i	$0.465130\pi$
$252$	1.27239	−	3.09041i	0.0801530	−	0.194678i
$253$	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	0.260188	+	0.965558i	$0.416215\pi$
$257$	−11.8010	+	16.8536i	−0.736129	+	1.05130i	−0.996317	+	0.0857431i	$0.972674\pi$
$258$	0.0573345	+	0.518417i	0.00356949	+	0.0322752i
$259$	−21.4672	+	25.5836i	−1.33391	+	1.58969i
$260$		0			0
$261$	−2.84526	+	0.637138i	−0.176117	+	0.0394378i
$262$	1.88866	+	7.04856i	0.116682	+	0.435461i
$263$	−7.24374	+	15.5342i	−0.446668	+	0.957882i	0.546087	+	0.837728i	$0.316117\pi$
$263$	−7.24374	+	15.5342i	−0.446668	+	0.957882i	−0.992755	+	0.120154i	$0.961661\pi$
$264$	−8.32812	−	13.6914i	−0.512560	−	0.842649i
$265$		0			0
$266$	3.69544	−	10.1531i	0.226582	−	0.622529i
$267$	6.50950	−	3.21875i	0.398375	−	0.196984i
$268$	−2.90456	+	2.03380i	−0.177424	+	0.124234i
$269$	−5.61280			−0.342218			−0.171109	−	0.985252i	$-0.554735\pi$
$269$	−5.61280			−0.342218			−0.171109	+	0.985252i	$0.554735\pi$
$270$		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
$273$	2.04252	−	31.6796i	0.123619	−	1.91733i
$274$	−0.929644	+	2.55418i	−0.0561619	+	0.154303i
$275$		0			0
$276$	−0.288425	+	0.527059i	−0.0173611	+	0.0317252i
$277$	10.3807	−	22.2616i	0.623718	−	1.33757i	−0.299796	−	0.954003i	$-0.596919\pi$
$277$	10.3807	−	22.2616i	0.623718	−	1.33757i	0.923514	−	0.383564i	$-0.125304\pi$
$278$	−1.11585	−	4.16442i	−0.0669244	−	0.249765i
$279$	−0.357631	−	7.80948i	−0.0214108	−	0.467541i
$280$		0			0
$281$	0.467705	−	0.557389i	0.0279010	−	0.0332511i	−0.751914	−	0.659262i	$-0.770869\pi$
$281$	0.467705	−	0.557389i	0.0279010	−	0.0332511i	0.779814	+	0.626011i	$0.215313\pi$
$282$	20.6316	+	9.05190i	1.22859	+	0.539033i
$283$	−12.3891	+	17.6935i	−0.736457	+	1.05177i	0.259828	+	0.965655i	$0.416334\pi$
$283$	−12.3891	+	17.6935i	−0.736457	+	1.05177i	−0.996285	+	0.0861152i	$0.972555\pi$
$284$	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
$288$	1.18224	+	3.72193i	0.0696641	+	0.219317i
$289$	12.9775	+	7.49259i	0.763385	+	0.440740i
$290$		0			0
$291$	−9.78284	−	5.35351i	−0.573480	−	0.313828i
$292$	0.00716445	−	0.0818900i	0.000419268	−	0.00479225i
$293$	−8.30888	+	3.87450i	−0.485410	+	0.226350i	−0.649888	−	0.760030i	$-0.725184\pi$
$293$	−8.30888	+	3.87450i	−0.485410	+	0.226350i	0.164477	+	0.986381i	$0.447406\pi$
$294$	−27.6880	−	31.5044i	−1.61480	−	1.83737i
$295$		0			0
$296$		−	18.3148i		−	1.06452i
$297$	−11.4348	−	14.1547i	−0.663517	−	0.821338i
$298$	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
$303$	2.50778	−	10.2959i	0.144068	−	0.591485i
$304$	2.26404	+	6.22039i	0.129851	+	0.356764i
$305$		0			0
$306$	4.68052	−	4.30728i	0.267568	−	0.246231i
$307$	7.01141	+	1.87870i	0.400162	+	0.107223i	0.453287	−	0.891365i	$-0.350251\pi$
$307$	7.01141	+	1.87870i	0.400162	+	0.107223i	−0.0531246	+	0.998588i	$0.516918\pi$
$308$	3.88640	−	0.340016i	0.221448	−	0.0193742i
$309$	−10.1859	−	8.15722i	−0.579454	−	0.464048i
$310$		0			0
$311$	22.2915	−	3.93059i	1.26404	−	0.222884i	0.498847	−	0.866690i	$-0.333757\pi$
$311$	22.2915	−	3.93059i	1.26404	−	0.222884i	0.765188	+	0.643807i	$0.222646\pi$
$312$	10.3090	+	14.0284i	0.583634	+	0.794202i
$313$	0.360352	+	4.11885i	0.0203683	+	0.232811i	0.999554	+	0.0298468i	$0.00950194\pi$
$313$	0.360352	+	4.11885i	0.0203683	+	0.232811i	−0.979186	+	0.202964i	$0.934943\pi$
$314$	−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	−0.638589	−	0.769548i	$-0.720482\pi$
$317$	−29.1740	−	13.6040i	−1.63857	−	0.764080i	−0.999985	+	0.00546854i	$0.998259\pi$
$318$	−7.12303	+	7.45669i	−0.399440	+	0.418151i
$319$	−2.18775	−	2.60726i	−0.122490	−	0.145978i
$320$		0			0
$321$	−4.73920	−	23.6937i	−0.264516	−	1.32245i
$322$	6.19222	+	8.84340i	0.345079	+	0.492824i
$323$	1.50694	−	1.50694i	0.0838485	−	0.0838485i
$324$	0.887530	+	1.88235i	0.0493072	+	0.104575i
$325$		0			0
$326$	16.6613	+	2.93784i	0.922785	+	0.162712i
$327$	−1.94129	+	2.91206i	−0.107354	+	0.161037i
$328$	−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	−0.290891	−	0.956756i	$-0.593952\pi$
$331$	1.84234	−	0.670556i	0.101264	−	0.0368571i	0.392155	+	0.919899i	$0.371730\pi$
$332$	−2.53707	+	0.679805i	−0.139240	+	0.0373091i
$333$	−2.75832	−	20.6123i	−0.151155	−	1.12954i
$334$	18.0688	−	10.4320i	0.988679	−	0.570814i
$335$		0			0
$336$	36.3695	+	5.55817i	1.98412	+	0.303223i
$337$	13.7556	+	9.63175i	0.749313	+	0.524675i	0.884724	−	0.466115i	$-0.154347\pi$
$337$	13.7556	+	9.63175i	0.749313	+	0.524675i	−0.135411	+	0.990789i	$0.543236\pi$
$338$	−1.80154	−	1.26145i	−0.0979909	−	0.0686140i
$339$	0.841272	−	1.05049i	0.0456916	−	0.0570549i
$340$		0			0
$341$	7.90298	−	4.56279i	0.427970	−	0.247089i
$342$	3.11934	+	5.96118i	0.168675	+	0.322344i
$343$	−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	0.867445	−	0.497534i	$-0.165761\pi$
$347$	−1.32763	−	2.84711i	−0.0712708	−	0.152841i	−0.938716	+	0.344693i	$0.887983\pi$
$348$	0.172535	+	0.348929i	0.00924883	+	0.0187045i
$349$	−12.2555	−	2.16098i	−0.656022	−	0.115674i	−0.164278	−	0.986414i	$-0.552529\pi$
$349$	−12.2555	−	2.16098i	−0.656022	−	0.115674i	−0.491744	+	0.870740i	$0.663640\pi$
$350$		0			0
$351$	13.7150	+	14.2356i	0.732053	+	0.759839i
$352$	−3.22337	+	3.22337i	−0.171806	+	0.171806i
$353$	10.4080	+	14.8642i	0.553964	+	0.791143i	0.994292	−	0.106694i	$-0.0340265\pi$
$353$	10.4080	+	14.8642i	0.553964	+	0.791143i	−0.440327	+	0.897837i	$0.645138\pi$
$354$	14.4368	−	12.6879i	0.767307	−	0.674356i
$355$		0			0
$356$	−0.623160	−	0.742654i	−0.0330274	−	0.0393606i
$357$	−3.32664	−	11.3681i	−0.176064	−	0.601665i
$358$	−8.77805	−	4.09327i	−0.463934	−	0.216336i
$359$	−5.27373	+	9.13437i	−0.278337	+	0.482094i	−0.970972	−	0.239195i	$-0.923117\pi$
$359$	−5.27373	+	9.13437i	−0.278337	+	0.482094i	0.692635	+	0.721289i	$0.256450\pi$
$360$		0			0
$361$	−8.37292	−	14.5023i	−0.440680	−	0.763280i
$362$	1.00543	+	11.4921i	0.0528441	+	0.604011i
$363$	0.879154	−	2.00381i	0.0461436	−	0.105173i
$364$	−4.17368	+	0.735932i	−0.218760	+	0.0385733i
$365$		0			0
$366$	−2.79553	+	1.09055i	−0.146125	+	0.0570040i
$367$	3.55196	−	0.310757i	0.185411	−	0.0162214i	0.00592799	−	0.999982i	$-0.498113\pi$
$367$	3.55196	−	0.310757i	0.185411	−	0.0162214i	0.179483	+	0.983761i	$0.442557\pi$
$368$	−6.38875	−	1.71186i	−0.333037	−	0.0892369i
$369$	−1.10089	−	1.71996i	−0.0573101	−	0.0895376i
$370$		0			0
$371$	6.56775	+	18.0448i	0.340981	+	0.936837i
$372$	−1.00167	+	0.293117i	−0.0519340	+	0.0151974i
$373$	25.1438	+	2.19980i	1.30190	+	0.113901i	0.716925	−	0.697151i	$-0.245549\pi$
$373$	25.1438	+	2.19980i	1.30190	+	0.113901i	0.584974	+	0.811052i	$0.301105\pi$
$374$	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
$378$	37.3877	+	0.696344i	1.92302	+	0.0358161i
$379$		−	27.8698i		−	1.43158i	−0.698317	−	0.715788i	$-0.746068\pi$
$379$		−	27.8698i		−	1.43158i	0.698317	−	0.715788i	$-0.253932\pi$
$380$		0			0
$381$	−10.9026	+	32.2307i	−0.558558	+	1.65123i
$382$	12.5620	−	5.85775i	0.642727	−	0.299709i
$383$	3.29980	−	37.7169i	0.168612	−	1.92724i	−0.168353	−	0.985727i	$-0.553845\pi$
$383$	3.29980	−	37.7169i	0.168612	−	1.92724i	0.336965	−	0.941517i	$-0.390599\pi$
$384$	−19.0460	+	11.5851i	−0.971936	+	0.591202i
$385$		0			0
$386$	−33.0067	−	19.0564i	−1.68000	−	0.969947i
$387$	−0.535863	+	0.280404i	−0.0272395	+	0.0142538i
$388$	−0.385329	+	1.43807i	−0.0195621	+	0.0730067i
$389$	2.93798	+	2.46526i	0.148962	+	0.124994i	0.714223	−	0.699918i	$-0.246780\pi$
$389$	2.93798	+	2.46526i	0.148962	+	0.124994i	−0.565261	+	0.824912i	$0.691225\pi$
$390$		0			0
$391$	0.369762	+	2.09702i	0.0186997	+	0.106051i
$392$	24.5671	−	35.0854i	1.24082	−	1.77208i
$393$	−6.81836	+	5.01060i	−0.343941	+	0.252751i
$394$	12.0379	−	14.3462i	0.606459	−	0.722749i
$395$		0			0
$396$	−1.47473	+	1.93041i	−0.0741081	+	0.0970066i
$397$	−1.16267	−	4.33915i	−0.0583528	−	0.217776i	0.930592	−	0.366057i	$-0.119293\pi$
$397$	−1.16267	−	4.33915i	−0.0583528	−	0.217776i	−0.988945	+	0.148281i	$0.952626\pi$
$398$	8.78827	−	18.8465i	0.440516	−	0.944690i
$399$	12.5253	−	0.286645i	0.627051	−	0.0143502i
$400$		0			0
$401$	−3.48616	+	9.57816i	−0.174091	+	0.478310i	−0.995796	−	0.0916029i	$-0.970801\pi$
$401$	−3.48616	+	9.57816i	−0.174091	+	0.478310i	0.821705	+	0.569913i	$0.193023\pi$
$402$	−33.0108	−	22.0063i	−1.64643	−	1.09757i
$403$	−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
$408$	5.40478	+	3.60304i	0.267576	+	0.178377i
$409$	8.00244	−	21.9865i	0.395695	−	1.08716i	−0.568665	−	0.822569i	$-0.692540\pi$
$409$	8.00244	−	21.9865i	0.395695	−	1.08716i	0.964360	−	0.264594i	$-0.0852380\pi$
$410$		0			0
$411$	−3.15094	+	0.0721099i	−0.155424	+	0.00355692i
$412$	−0.736264	+	1.57892i	−0.0362731	+	0.0777879i
$413$	−9.26327	−	34.5710i	−0.455816	−	1.70113i
$414$	−6.66677	−	0.863260i	−0.327654	−	0.0424269i
$415$		0			0
$416$	3.18315	−	3.79353i	0.156067	−	0.185993i
$417$	4.02842	−	2.96036i	0.197272	−	0.144969i
$418$	−4.50465	+	6.43330i	−0.220329	+	0.314663i
$419$	0.258905	+	1.46832i	0.0126483	+	0.0717323i	0.990479	−	0.137667i	$-0.0439603\pi$
$419$	0.258905	+	1.46832i	0.0126483	+	0.0717323i	−0.977830	+	0.209399i	$0.932849\pi$
$420$		0			0
$421$	−14.1741	−	11.8935i	−0.690802	−	0.579652i	0.228338	−	0.973582i	$-0.426671\pi$
$421$	−14.1741	−	11.8935i	−0.690802	−	0.579652i	−0.919140	+	0.393930i	$0.871115\pi$
$422$	7.77666	−	29.0229i	0.378562	−	1.41281i
$423$	−1.08396	+	26.1020i	−0.0527040	+	1.26912i
$424$	−9.11988	−	5.26536i	−0.442900	−	0.255709i
$425$		0			0
$426$	−28.4065	+	17.2789i	−1.37630	+	0.837165i
$427$	−0.487010	+	5.56655i	−0.0235681	+	0.269384i
$428$	−2.92358	+	1.36329i	−0.141316	+	0.0658969i
$429$	−7.39383	+	21.8579i	−0.356977	+	1.05531i
$430$		0			0
$431$			19.2978i			0.929541i	0.885431	+	0.464771i	$0.153863\pi$
$431$			19.2978i			0.929541i	−0.885431	+	0.464771i	$0.846137\pi$
$432$	−17.8211	+	14.3968i	−0.857419	+	0.692665i
$433$	15.0405	+	15.0405i	0.722800	+	0.722800i	0.969175	−	0.246375i	$-0.0792395\pi$
$433$	15.0405	+	15.0405i	0.722800	+	0.722800i	−0.246375	+	0.969175i	$0.579239\pi$
$434$	−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
$438$	0.882735	−	0.258314i	0.0421787	−	0.0123427i
$439$	3.41885	+	9.39321i	0.163173	+	0.448314i	0.994152	−	0.107990i	$-0.0344414\pi$
$439$	3.41885	+	9.39321i	0.163173	+	0.448314i	−0.830979	+	0.556303i	$0.812219\pi$
$440$		0			0
$441$	22.3648	−	43.1866i	1.06499	−	2.05650i
$442$	−7.79120	−	2.08765i	−0.370590	−	0.0992992i
$443$	30.7678	−	2.69183i	1.46182	−	0.127893i	0.671690	−	0.740832i	$-0.265569\pi$
$443$	30.7678	−	2.69183i	1.46182	−	0.127893i	0.790130	+	0.612939i	$0.210013\pi$
$444$	−2.58647	+	1.00899i	−0.122748	+	0.0478847i
$445$		0			0
$446$	32.2268	−	5.68245i	1.52598	−	0.269072i
$447$	−11.4619	+	26.1246i	−0.542129	+	1.23565i
$448$	2.88621	+	32.9895i	0.136361	+	1.55861i
$449$	−0.854949	−	1.48081i	−0.0403475	−	0.0698840i	0.845146	−	0.534535i	$-0.179513\pi$
$449$	−0.854949	−	1.48081i	−0.0403475	−	0.0698840i	−0.885494	+	0.464651i	$0.846180\pi$
$450$		0			0
$451$	1.19188	−	2.06440i	0.0561235	−	0.0972088i
$452$	−0.162838	−	0.0759325i	−0.00765925	−	0.00357157i
$453$	1.26356	+	4.31795i	0.0593671	+	0.202875i
$454$	4.75550	+	5.66739i	0.223187	+	0.265984i
$455$		0			0
$456$	−5.16078	+	4.53561i	−0.241676	+	0.212400i
$457$	−20.8928	−	29.8380i	−0.977323	−	1.39576i	−0.917582	−	0.397548i	$-0.869861\pi$
$457$	−20.8928	−	29.8380i	−0.977323	−	1.39576i	−0.0597413	−	0.998214i	$-0.519028\pi$
$458$	−1.15102	+	1.15102i	−0.0537835	+	0.0537835i
$459$	6.62542	+	3.24103i	0.309248	+	0.151278i
$460$		0			0
$461$	−17.0206	−	3.00119i	−0.792728	−	0.139779i	−0.237401	−	0.971412i	$-0.576296\pi$
$461$	−17.0206	−	3.00119i	−0.792728	−	0.139779i	−0.555327	+	0.831632i	$0.687407\pi$
$462$	19.3477	+	39.1282i	0.900137	+	1.82041i
$463$	12.1257	+	26.0036i	0.563527	+	1.20849i	0.957251	+	0.289259i	$0.0934089\pi$
$463$	12.1257	+	26.0036i	0.563527	+	1.20849i	−0.393724	+	0.919229i	$0.628813\pi$
$464$	−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	−0.748280	−	0.663382i	$-0.769120\pi$
$467$	−23.0066	+	6.16460i	−1.06462	+	0.285264i	−0.316339	+	0.948646i	$0.602454\pi$
$468$	1.41319	−	2.22872i	0.0653247	−	0.103023i
$469$	−63.9806	+	36.9392i	−2.95435	+	1.70570i
$470$		0			0
$471$	15.4870	−	19.3385i	0.713602	−	0.891071i
$472$	16.0778	+	11.2578i	0.740040	+	0.518181i
$473$	−0.578303	−	0.404932i	−0.0265904	−	0.0186188i
$474$	25.1036	+	3.83646i	1.15305	+	0.176214i
$475$		0			0
$476$	−1.36946	+	0.790656i	−0.0627689	+	0.0362396i
$477$	−11.0569	−	4.55236i	−0.506261	−	0.208438i
$478$	2.16738	−	0.580749i	0.0991338	−	0.0265628i
$479$	−3.81746	+	1.38944i	−0.174424	+	0.0634853i	−0.427756	−	0.903894i	$-0.640696\pi$
$479$	−3.81746	+	1.38944i	−0.174424	+	0.0634853i	0.253332	+	0.967379i	$0.418474\pi$
$480$		0			0
$481$	−20.2014	+	16.9510i	−0.921105	+	0.772899i
$482$	−2.08101	−	4.46274i	−0.0947873	−	0.203272i
$483$	−6.94367	+	10.4159i	−0.315948	+	0.473941i
$484$	−0.287690	−	0.0507274i	−0.0130768	−	0.00230579i
$485$		0			0
$486$	−16.0121	+	16.9057i	−0.726323	+	0.766858i
$487$	18.4638	−	18.4638i	0.836676	−	0.836676i	−0.151744	−	0.988420i	$-0.548489\pi$
$487$	18.4638	−	18.4638i	0.836676	−	0.836676i	0.988420	+	0.151744i	$0.0484889\pi$
$488$	−1.75763	−	2.51015i	−0.0795640	−	0.113629i
$489$	3.84769	+	19.2366i	0.173998	+	0.869908i
$490$		0			0
$491$	−16.4502	−	19.6046i	−0.742387	−	0.884743i	0.254211	−	0.967149i	$-0.418184\pi$
$491$	−16.4502	−	19.6046i	−0.742387	−	0.884743i	−0.996599	+	0.0824057i	$0.973740\pi$
$492$	−0.188315	+	0.197136i	−0.00848988	+	0.00888757i
$493$	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
$498$	−17.4027	−	23.6814i	−0.779836	−	1.06119i
$499$	5.75147	−	1.01414i	0.257471	−	0.0453991i	−0.0434226	−	0.999057i	$-0.513826\pi$
$499$	5.75147	−	1.01414i	0.257471	−	0.0453991i	0.300894	+	0.953658i	$0.402715\pi$
$500$		0			0
$501$	18.8837	+	15.1228i	0.843662	+	0.675635i
$502$	27.8980	−	2.44076i	1.24515	−	0.108936i
$503$	20.0094	+	5.36150i	0.892174	+	0.239057i	0.675652	−	0.737221i	$-0.263862\pi$
$503$	20.0094	+	5.36150i	0.892174	+	0.239057i	0.216522	+	0.976278i	$0.430529\pi$
$504$	8.34452	+	37.2640i	0.371695	+	1.65987i
$505$		0			0
$506$	−2.68387	−	7.37387i	−0.119312	−	0.327808i
$507$	0.603500	−	2.47772i	0.0268024	−	0.110040i
$508$	4.52509	+	0.395894i	0.200769	+	0.0175650i
$509$	7.40545	+	2.69536i	0.328241	+	0.119470i	0.500884	−	0.865515i	$-0.333008\pi$
$509$	7.40545	+	2.69536i	0.328241	+	0.119470i	−0.172643	+	0.984984i	$0.555231\pi$
$510$		0			0
$511$	0.297412	−	1.68671i	0.0131567	−	0.0746156i
$512$	−12.4157	−	12.4157i	−0.548699	−	0.548699i
$513$	−5.12508	+	5.88182i	−0.226278	+	0.259689i
$514$			30.7328i			1.35556i
$515$		0			0
$516$	0.0533010	+	0.0606477i	0.00234644	+	0.00266987i
$517$	−27.6380	+	12.8878i	−1.21552	+	0.566806i
$518$	−4.34787	+	49.6964i	−0.191035	+	2.18354i
$519$	−6.14537	−	3.36296i	−0.269752	−	0.147617i
$520$		0			0
$521$	−7.49714	−	4.32848i	−0.328456	−	0.189634i	0.326700	−	0.945128i	$-0.394063\pi$
$521$	−7.49714	−	4.32848i	−0.328456	−	0.189634i	−0.655155	+	0.755494i	$0.727397\pi$
$522$	−2.93556	+	3.21733i	−0.128486	+	0.140819i
$523$	−3.40449	+	12.7057i	−0.148868	+	0.555583i	0.850685	+	0.525676i	$0.176188\pi$
$523$	−3.40449	+	12.7057i	−0.148868	+	0.555583i	−0.999553	+	0.0299067i	$0.990479\pi$
$524$	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
$528$	−24.4893	−	10.7445i	−1.06576	−	0.467593i
$529$	−13.3376	+	15.8951i	−0.579894	+	0.691091i
$530$		0			0
$531$	19.7901	+	10.2486i	0.858818	+	0.444751i
$532$	−0.432899	−	1.61560i	−0.0187686	−	0.0700452i
$533$	−1.09440	+	2.34695i	−0.0474037	+	0.101658i
$534$	5.20725	−	9.51557i	0.225340	−	0.411779i
$535$		0			0
$536$	13.8568	−	38.0712i	0.598523	−	1.64443i
$537$	0.722598	−	11.2075i	0.0311824	−	0.483640i
$538$	−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
$543$	−11.9907	+	5.92906i	−0.514572	+	0.254440i
$544$	0.631962	−	1.73630i	0.0270951	−	0.0744433i
$545$		0			0
$546$	−24.6429	−	40.5128i	−1.05462	−	1.73379i
$547$	−13.8936	+	29.7950i	−0.594049	+	1.27394i	0.347694	+	0.937608i	$0.386965\pi$
$547$	−13.8936	+	29.7950i	−0.594049	+	1.27394i	−0.941743	+	0.336334i	$0.890813\pi$
$548$	0.108902	+	0.406429i	0.00465208	+	0.0173618i
$549$	−2.35615	−	2.56032i	−0.100558	−	0.109272i
$550$		0			0
$551$	−0.937961	+	1.11782i	−0.0399585	+	0.0476207i
$552$	−0.754628	−	6.82333i	−0.0321191	−	0.290420i
$553$	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	−0.662259	−	0.749275i	$-0.730402\pi$
$557$	6.74775	−	25.1830i	0.285911	−	1.06704i	0.948171	−	0.317761i	$-0.102931\pi$
$558$	−7.12851	−	9.24922i	−0.301774	−	0.391551i
$559$	0.664181	+	0.383465i	0.0280919	+	0.0162188i
$560$		0			0
$561$	0.196982	+	8.60737i	0.00831657	+	0.363404i
$562$	0.0947268	−	1.08273i	0.00399581	−	0.0456723i
$563$	27.4015	−	12.7775i	1.15484	−	0.538510i	0.251676	−	0.967811i	$-0.419018\pi$
$563$	27.4015	−	12.7775i	1.15484	−	0.538510i	0.903161	+	0.429302i	$0.141240\pi$
$564$	3.41993	−	0.684052i	0.144005	−	0.0288038i
$565$		0			0
$566$			32.2643i			1.35617i
$567$	15.0035	+	40.6819i	0.630087	+	1.70848i
$568$	−24.0089	−	24.0089i	−1.00739	−	1.00739i
$569$	3.82709	−	21.7045i	0.160440	−	0.909901i	−0.793202	−	0.608959i	$-0.791588\pi$
$569$	3.82709	−	21.7045i	0.160440	−	0.909901i	0.953642	−	0.300943i	$-0.0973013\pi$
$570$		0			0
$571$	−5.69726	−	2.07363i	−0.238423	−	0.0867789i	0.220045	−	0.975490i	$-0.429380\pi$
$571$	−5.69726	−	2.07363i	−0.238423	−	0.0867789i	−0.458468	+	0.888711i	$0.651602\pi$
$572$	3.06878	+	0.268484i	0.128312	+	0.0112259i
$573$	11.6217	+	11.1017i	0.485503	+	0.463778i
$574$	1.67545	+	4.60327i	0.0699321	+	0.192137i
$575$		0			0
$576$	−16.3862	−	12.5182i	−0.682758	−	0.521592i
$577$	15.9120	+	4.26360i	0.662424	+	0.177496i	0.574340	−	0.818617i	$-0.305259\pi$
$577$	15.9120	+	4.26360i	0.662424	+	0.177496i	0.0880841	+	0.996113i	$0.471926\pi$
$578$	22.2986	−	1.95088i	0.927501	−	0.0811458i
$579$	6.67638	−	43.6864i	0.277461	−	1.81555i
$580$		0			0
$581$	−53.8941	+	9.50299i	−2.23590	+	0.394250i
$582$	−16.5569	+	1.83112i	−0.686307	+	0.0759023i
$583$	−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	0.377237	−	0.926117i	$-0.376874\pi$
$587$	−2.17389	−	1.01370i	−0.0897262	−	0.0418400i	−0.466963	+	0.884277i	$0.654652\pi$
$588$	−6.30830	−	1.53652i	−0.260150	−	0.0633648i
$589$	−2.51487	−	2.99711i	−0.103623	−	0.123494i
$590$		0			0
$591$	20.5705	+	6.95833i	0.846157	+	0.286227i
$592$	−17.5303	−	25.0359i	−0.720491	−	1.02897i
$593$	−19.8531	+	19.8531i	−0.815268	+	0.815268i	−0.985418	−	0.170150i	$-0.945575\pi$
$593$	−19.8531	+	19.8531i	−0.815268	+	0.815268i	0.170150	+	0.985418i	$0.445575\pi$
$594$	−26.1189	−	7.52254i	−1.07167	−	0.308653i
$595$		0			0
$596$	3.75073	+	0.661355i	0.153636	+	0.0270902i
$597$	24.0626	+	1.55142i	0.984817	+	0.0634955i
$598$	3.60265	+	7.72592i	0.147323	+	0.315936i
$599$	−12.9672	+	10.8807i	−0.529824	+	0.444575i	−0.868041	−	0.496493i	$-0.834621\pi$
$599$	−12.9672	+	10.8807i	−0.529824	+	0.444575i	0.338217	+	0.941068i	$0.390176\pi$
$600$		0			0
$601$	−24.9557	+	9.08314i	−1.01796	+	0.370509i	−0.796486	−	0.604656i	$-0.793310\pi$
$601$	−24.9557	+	9.08314i	−1.01796	+	0.370509i	−0.221478	+	0.975165i	$0.571088\pi$
$602$	1.40137	−	0.375496i	0.0571155	−	0.0153041i
$603$	9.86129	−	44.9340i	0.401583	−	1.82985i
$604$	0.520160	−	0.300315i	0.0211650	−	0.0122196i
$605$		0			0
$606$	−5.75272	−	14.7466i	−0.233688	−	0.599040i
$607$	−5.34086	−	3.73971i	−0.216779	−	0.151790i	0.460144	−	0.887844i	$-0.347798\pi$
$607$	−5.34086	−	3.73971i	−0.216779	−	0.151790i	−0.676922	+	0.736054i	$0.736687\pi$
$608$	1.60095	+	1.12099i	0.0649270	+	0.0454623i
$609$	2.94752	+	7.55571i	0.119440	+	0.306173i
$610$		0			0
$611$	28.6898	−	16.5640i	1.16066	−	0.670109i
$612$	0.211073	−	0.961776i	0.00853213	−	0.0388775i
$613$	−10.5860	+	2.83651i	−0.427565	+	0.114566i	−0.466183	−	0.884688i	$-0.654371\pi$
$613$	−10.5860	+	2.83651i	−0.427565	+	0.114566i	0.0386179	+	0.999254i	$0.487704\pi$
$614$	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	−0.943073	−	0.332585i	$-0.892079\pi$
$617$	−14.6963	−	31.5164i	−0.591652	−	1.26880i	0.351421	−	0.936217i	$-0.385698\pi$
$618$	−19.4522	−	1.25417i	−0.782483	−	0.0504501i
$619$	−31.5714	−	5.56690i	−1.26896	−	0.223753i	−0.501676	−	0.865056i	$-0.667283\pi$
$619$	−31.5714	−	5.56690i	−1.26896	−	0.223753i	−0.767288	+	0.641303i	$0.778394\pi$
$620$		0			0
$621$	−1.87693	−	7.56563i	−0.0753185	−	0.303598i
$622$	23.9081	−	23.9081i	0.958628	−	0.958628i
$623$	−11.5858	−	16.5462i	−0.464175	−	0.662910i
$624$	27.5197	+	9.30903i	1.10167	+	0.372659i
$625$		0			0
$626$	3.96982	+	4.73105i	0.158666	+	0.189091i
$627$	−8.84795	−	2.15510i	−0.353353	−	0.0860663i
$628$	−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	0.837434	+	0.546538i	$0.184055\pi$
$631$	22.4076	+	38.8111i	0.892033	+	1.54505i	0.0545987	+	0.998508i	$0.482612\pi$
$632$	2.26024	+	25.8347i	0.0899076	+	1.02765i
$633$	34.6294	−	3.82985i	1.37640	−	0.152223i
$634$	−47.3526	+	8.34954i	−1.88061	+	0.331603i
$635$		0			0
$636$	−0.241160	+	1.57801i	−0.00956262	+	0.0625723i
$637$	−61.4373	+	5.37507i	−2.43423	+	0.212968i
$638$	−4.91073	−	1.31583i	−0.194418	−	0.0520940i
$639$	−30.6366	−	23.4048i	−1.21196	−	0.925879i
$640$		0			0
$641$	−15.6160	−	42.9045i	−0.616794	−	1.69463i	−0.714699	−	0.699432i	$-0.753437\pi$
$641$	−15.6160	−	42.9045i	−0.616794	−	1.69463i	0.0979055	−	0.995196i	$-0.468786\pi$
$642$	−26.0989	−	24.9311i	−1.03004	−	0.983950i
$643$	−36.2904	−	3.17500i	−1.43115	−	0.125210i	−0.654940	−	0.755681i	$-0.727306\pi$
$643$	−36.2904	−	3.17500i	−1.43115	−	0.125210i	−0.776212	+	0.630472i	$0.782862\pi$
$644$	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	0.945278	+	0.326266i	$0.105791\pi$
$647$	32.3432	+	32.3432i	1.27154	+	1.27154i	0.326266	+	0.945278i	$0.394209\pi$
$648$	−20.6433	−	11.8015i	−0.810945	−	0.463606i
$649$			26.0149i			1.02118i
$650$		0			0
$651$	−21.3230	+	4.26501i	−0.835714	+	0.167159i
$652$	2.37361	−	1.10683i	0.0929578	−	0.0433469i
$653$	1.03997	−	11.8869i	0.0406971	−	0.465170i	−0.948314	−	0.317332i	$-0.897213\pi$
$653$	1.03997	−	11.8869i	0.0406971	−	0.465170i	0.989012	−	0.147838i	$-0.0472314\pi$
$654$	0.119608	+	5.22642i	0.00467703	+	0.204369i
$655$		0			0
$656$	−2.59913	−	1.50061i	−0.101479	−	0.0585890i
$657$	0.651043	+	0.844725i	0.0253996	+	0.0329559i
$658$	16.2198	−	60.5331i	0.632314	−	2.35983i
$659$	17.0150	+	14.2773i	0.662811	+	0.556165i	0.910928	−	0.412565i	$-0.135367\pi$
$659$	17.0150	+	14.2773i	0.662811	+	0.556165i	−0.248117	+	0.968730i	$0.579812\pi$
$660$		0			0
$661$	−7.45553	−	42.2824i	−0.289986	−	1.64460i	−0.686909	−	0.726743i	$-0.741033\pi$
$661$	−7.45553	−	42.2824i	−0.289986	−	1.64460i	0.396923	−	0.917852i	$-0.370078\pi$
$662$	1.67976	−	2.39894i	0.0652857	−	0.0932376i
$663$	−1.02813	−	9.29628i	−0.0399291	−	0.361038i
$664$	19.2908	−	22.9899i	0.748629	−	0.892181i
$665$		0			0
$666$	−21.0350	−	22.8578i	−0.815090	−	0.885721i
$667$	−0.377358	−	1.40832i	−0.0146114	−	0.0545304i
$668$	1.36497	−	2.92718i	0.0528122	−	0.113256i
$669$	19.7193	+	32.4186i	0.762393	+	1.25337i
$670$		0			0
$671$	1.38915	−	3.81665i	0.0536274	−	0.147340i
$672$	9.73718	−	4.81474i	0.375620	−	0.185733i
$673$	−35.1820	+	24.6347i	−1.35617	+	0.949599i	−0.356284	+	0.934378i	$0.615956\pi$
$673$	−35.1820	+	24.6347i	−1.35617	+	0.949599i	−0.999884	+	0.0152212i	$0.995155\pi$
$674$	25.0834			0.966176
$675$		0			0
$676$	−0.340452			−0.0130943
$677$	−22.0638	+	15.4492i	−0.847979	+	0.593761i	−0.914756	−	0.404007i	$-0.867617\pi$
$677$	−22.0638	+	15.4492i	−0.847979	+	0.593761i	0.0667769	+	0.997768i	$0.478728\pi$
$678$	0.129345	−	2.00615i	0.00496748	−	0.0770458i
$679$	−10.6093	+	29.1489i	−0.407149	+	1.11863i
$680$		0			0
$681$	−4.11821	+	7.52549i	−0.157810	+	0.288377i
$682$	5.76078	−	12.3540i	0.220592	−	0.473060i
$683$	4.90923	+	18.3215i	0.187846	+	0.701053i	0.994003	+	0.109351i	$0.0348771\pi$
$683$	4.90923	+	18.3215i	0.187846	+	0.701053i	−0.806157	+	0.591702i	$0.798456\pi$
$684$	0.924849	+	0.478946i	0.0353625	+	0.0183130i
$685$		0			0
$686$	−42.6101	+	50.7807i	−1.62686	+	1.93882i
$687$	−1.72845	−	0.758341i	−0.0659445	−	0.0289325i
$688$	−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	0.910693	−	0.413084i	$-0.135548\pi$
$691$	17.4026	+	14.6025i	0.662025	+	0.555505i	−0.248668	+	0.968589i	$0.579993\pi$
$692$	−0.242055	+	0.903362i	−0.00920155	+	0.0343407i
$693$	−34.1152	+	37.3897i	−1.29593	+	1.42032i
$694$	−4.06379	−	2.34623i	−0.154259	−	0.0890616i
$695$		0			0
$696$	−3.90164	−	2.13511i	−0.147891	−	0.0809311i
$697$	−0.0842119	+	0.962547i	−0.00318975	+	0.0364591i
$698$	−16.8472	+	7.85598i	−0.637676	+	0.297353i
$699$	30.3390	+	34.5207i	1.14752	+	1.30569i
$700$		0			0
$701$			28.7752i			1.08682i	0.839466	+	0.543412i	$0.182868\pi$
$701$			28.7752i			1.08682i	−0.839466	+	0.543412i	$0.817132\pi$
$702$	28.9782	+	5.66797i	1.09371	+	0.213924i
$703$	−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
$708$	0.704104	−	2.89076i	0.0264618	−	0.108641i
$709$	−0.183502	−	0.504167i	−0.00689155	−	0.0189344i	0.936199	−	0.351470i	$-0.114318\pi$
$709$	−0.183502	−	0.504167i	−0.00689155	−	0.0189344i	−0.943091	+	0.332536i	$0.892096\pi$
$710$		0			0
$711$	6.43464	+	28.7351i	0.241318	+	1.07765i
$712$	10.6997	+	2.86697i	0.400988	+	0.107444i
$713$	3.89433	−	0.340710i	0.145844	−	0.0127597i
$714$	−13.8103	−	11.0598i	−0.516837	−	0.413902i
$715$		0			0
$716$	−1.47655	+	0.260356i	−0.0551814	+	0.00972997i
$717$	1.54073	+	2.09660i	0.0575394	+	0.0782989i
$718$	1.37315	+	15.6951i	0.0512453	+	0.585737i
$719$	2.44660	+	4.23763i	0.0912427	+	0.158037i	0.908034	−	0.418896i	$-0.137583\pi$
$719$	2.44660	+	4.23763i	0.0912427	+	0.158037i	−0.816792	+	0.576933i	$0.804249\pi$
$720$		0			0
$721$	−18.1492	+	31.4353i	−0.675911	+	1.17071i
$722$	−22.6702	−	10.5713i	−0.843697	−	0.393422i
$723$	3.94394	−	4.12869i	0.146677	−	0.153548i
$724$	1.14789	+	1.36800i	0.0426608	+	0.0508412i
$725$		0			0
$726$	−0.641079	−	3.20508i	−0.0237927	−	0.118952i
$727$	2.82025	+	4.02773i	0.104597	+	0.149380i	0.868038	−	0.496497i	$-0.165381\pi$
$727$	2.82025	+	4.02773i	0.104597	+	0.149380i	−0.763441	+	0.645877i	$0.776492\pi$
$728$	34.2411	−	34.2411i	1.26906	−	1.26906i
$729$	−25.0102	−	10.1729i	−0.926305	−	0.376774i
$730$		0			0
$731$	0.281810	+	0.0496908i	0.0104231	+	0.00183788i
$732$	−0.257660	+	0.386505i	−0.00952339	+	0.0142857i
$733$	6.00742	+	12.8830i	0.221889	+	0.475843i	0.985466	−	0.169874i	$-0.0543362\pi$
$733$	6.00742	+	12.8830i	0.221889	+	0.475843i	−0.763576	+	0.645717i	$0.776558\pi$
$734$	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
$738$	−2.82065	−	1.16132i	−0.103830	−	0.0427488i
$739$	28.3320	−	16.3575i	1.04221	−	0.601721i	0.121752	−	0.992561i	$-0.461149\pi$
$739$	28.3320	−	16.3575i	1.04221	−	0.601721i	0.920459	+	0.390840i	$0.127815\pi$
$740$		0			0
$741$	9.77933	+	1.49453i	0.359253	+	0.0549028i
$742$	23.4964	+	16.4524i	0.862581	+	0.603986i
$743$	−0.889212	−	0.622633i	−0.0326220	−	0.0228422i	0.557152	−	0.830411i	$-0.311894\pi$
$743$	−0.889212	−	0.622633i	−0.0326220	−	0.0228422i	−0.589774	+	0.807569i	$0.700783\pi$
$744$	7.45425	−	9.30809i	0.273286	−	0.341251i
$745$		0			0
$746$	32.6505	−	18.8508i	1.19542	−	0.690177i
$747$	18.2483	−	28.7792i	0.667671	−	1.05297i
$748$	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	−0.801200	−	0.598396i	$-0.795805\pi$
$751$	−9.61953	+	8.07175i	−0.351022	+	0.294542i	0.450178	+	0.892939i	$0.351360\pi$
$752$	16.2261	+	34.7970i	0.591706	+	1.26892i
$753$	14.3933	+	29.1085i	0.524520	+	1.06077i
$754$	5.43899	+	0.959041i	0.198076	+	0.0349262i
$755$		0			0
$756$	4.80282	−	3.23138i	0.174677	−	0.117524i
$757$	3.04376	−	3.04376i	0.110627	−	0.110627i	−0.649626	−	0.760254i	$-0.725075\pi$
$757$	3.04376	−	3.04376i	0.110627	−	0.110627i	0.760254	+	0.649626i	$0.225075\pi$
$758$	−23.8780	−	34.1013i	−0.867288	−	1.23862i
$759$	6.83466	−	6.00672i	0.248083	−	0.218030i
$760$		0			0
$761$	−11.3467	−	13.5225i	−0.411319	−	0.490191i	0.520117	−	0.854095i	$-0.325888\pi$
$761$	−11.3467	−	13.5225i	−0.411319	−	0.490191i	−0.931437	+	0.363904i	$0.881444\pi$
$762$	14.2739	+	48.7783i	0.517090	+	1.76705i
$763$	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
$768$	−3.81226	+	8.68909i	−0.137563	+	0.313541i
$769$	29.6816	−	5.23367i	1.07035	−	0.188731i	0.389404	−	0.921067i	$-0.372681\pi$
$769$	29.6816	−	5.23367i	1.07035	−	0.188731i	0.680943	+	0.732336i	$0.261570\pi$
$770$		0			0
$771$	−33.1993	+	12.9512i	−1.19564	+	0.466427i
$772$	−5.87749	+	0.514213i	−0.211535	+	0.0185069i
$773$	−43.5713	−	11.6749i	−1.56715	−	0.419917i	−0.632232	−	0.774779i	$-0.717861\pi$
$773$	−43.5713	−	11.6749i	−1.56715	−	0.419917i	−0.934919	+	0.354862i	$0.884528\pi$
$774$	−0.415436	+	0.802212i	−0.0149326	+	0.0288349i
$775$		0			0
$776$	−5.81811	−	15.9851i	−0.208858	−	0.573832i
$777$	−55.5172	+	16.2459i	−1.99167	+	0.582820i
$778$	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
$783$	−4.71263	−	1.81534i	−0.168416	−	0.0648748i
$784$		−	71.4757i		−	2.55270i
$785$		0			0
$786$	−4.04997	+	11.9727i	−0.144458	+	0.427052i
$787$	−31.9138	+	14.8817i	−1.13761	+	0.530474i	−0.897825	−	0.440353i	$-0.854853\pi$
$787$	−31.9138	+	14.8817i	−1.13761	+	0.530474i	−0.239780	+	0.970827i	$0.577075\pi$
$788$	0.252670	−	2.88803i	0.00900100	−	0.102882i
$789$	−25.3639	+	15.4281i	−0.902978	+	0.549256i
$790$		0			0
$791$	−3.24199	−	1.87177i	−0.115272	−	0.0665523i
$792$	1.15169	−	27.7329i	0.0409234	−	0.985445i
$793$	−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	0.300028	+	0.953930i	$0.403004\pi$
$797$	−19.7333	+	28.1820i	−0.698989	+	0.998259i	−0.999017	+	0.0443290i	$0.985885\pi$
$798$	15.0803	−	11.0821i	0.533837	−	0.392300i
$799$	7.94536	−	9.46891i	0.281087	−	0.334986i
$800$		0			0
$801$	12.4737	+	1.61518i	0.440736	+	0.0570696i
$802$	3.94062	+	14.7066i	0.139148	+	0.519308i
$803$	−0.526128	+	1.12829i	−0.0185667	+	0.0398163i
$804$	−6.13993	+	0.140514i	−0.216539	+	0.00495553i
$805$		0			0
$806$	−5.06465	+	13.9150i	−0.178395	+	0.490135i
$807$	−8.08901	−	5.39245i	−0.284746	−	0.189823i
$808$	13.2412	−	9.27159i	0.465824	−	0.326173i
$809$	−54.0630			−1.90075			−0.950377	−	0.311100i	$-0.899302\pi$
$809$	−54.0630			−1.90075			−0.950377	+	0.311100i	$0.899302\pi$
$810$		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
$813$	22.6014	+	15.0670i	0.792667	+	0.528424i
$814$	12.4019	−	34.0739i	0.434685	−	1.19429i
$815$		0			0
$816$	10.8369	−	0.248005i	0.379368	−	0.00868192i
$817$	−0.127917	+	0.274318i	−0.00447523	+	0.00959717i
$818$	−9.04564	−	33.7588i	−0.316273	−	1.18035i
$819$	33.3795	−	43.6933i	1.16637	−	1.52677i
$820$		0			0
$821$	−5.28957	+	6.30386i	−0.184607	+	0.220006i	−0.850409	−	0.526123i	$-0.823645\pi$
$821$	−5.28957	+	6.30386i	−0.184607	+	0.220006i	0.665802	+	0.746129i	$0.268090\pi$
$822$	−3.79368	+	2.78786i	−0.132320	+	0.0972377i
$823$	1.52906	−	2.18373i	0.0532998	−	0.0761200i	−0.791617	−	0.611017i	$-0.790761\pi$
$823$	1.52906	−	2.18373i	0.0532998	−	0.0761200i	0.844917	+	0.534897i	$0.179650\pi$
$824$	−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	−0.992007	−	0.126182i	$-0.959728\pi$
$827$	−2.00765	+	7.49264i	−0.0698128	+	0.260545i	0.922194	+	0.386727i	$0.126394\pi$
$828$	−0.922037	+	0.482480i	−0.0320430	+	0.0167673i
$829$	36.4123	+	21.0226i	1.26465	+	0.730147i	0.973971	−	0.226674i	$-0.0727851\pi$
$829$	36.4123	+	21.0226i	1.26465	+	0.730147i	0.290680	+	0.956820i	$0.406118\pi$
$830$		0			0
$831$	36.3480	−	22.1095i	1.26090	−	0.766971i
$832$	−2.27902	+	26.0493i	−0.0790106	+	0.903096i
$833$	−20.8552	+	9.72492i	−0.722588	+	0.336948i
$834$	2.39280	−	7.07369i	0.0828559	−	0.244942i
$835$		0			0
$836$			1.21575i			0.0420477i
$837$	6.98749	−	11.5984i	0.241523	−	0.400899i
$838$	1.57481	+	1.57481i	0.0544008	+	0.0544008i
$839$	−7.44120	+	42.2011i	−0.256899	+	1.45694i	0.534253	+	0.845325i	$0.320593\pi$
$839$	−7.44120	+	42.2011i	−0.256899	+	1.45694i	−0.791152	+	0.611620i	$0.790518\pi$
$840$		0			0
$841$	26.3634	+	9.59551i	0.909084	+	0.330880i
$842$	−27.5332	−	2.40885i	−0.948858	−	0.0830143i
$843$	1.20955	−	0.353949i	0.0416591	−	0.0121907i
$844$	−1.59083	−	4.37077i	−0.0547587	−	0.150448i
$845$		0			0
$846$	21.0371	+	32.8669i	0.723269	+	1.12999i
$847$	−5.87920	−	1.57533i	−0.202012	−	0.0541289i
$848$	−17.5065	+	1.53162i	−0.601175	+	0.0525960i
$849$	−34.8538	+	13.5966i	−1.19618	+	0.466635i
$850$		0			0
$851$	10.2410	−	1.80577i	0.351057	−	0.0619008i
$852$	−2.06791	+	4.71330i	−0.0708456	+	0.161475i
$853$	−1.49745	−	17.1159i	−0.0512717	−	0.586038i	−0.977762	−	0.209719i	$-0.932745\pi$
$853$	−1.49745	−	17.1159i	−0.0512717	−	0.586038i	0.926490	−	0.376319i	$-0.122810\pi$
$854$	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	0.0641943	−	0.997937i	$-0.479552\pi$
$857$	−19.2921	−	8.99607i	−0.659007	−	0.307300i	−0.723201	+	0.690637i	$0.757330\pi$
$858$	9.68017	+	33.0800i	0.330475	+	1.12933i
$859$	−5.67148	−	6.75901i	−0.193509	−	0.230615i	0.660562	−	0.750771i	$-0.270318\pi$
$859$	−5.67148	−	6.75901i	−0.193509	−	0.230615i	−0.854071	+	0.520157i	$0.825874\pi$
$860$		0			0
$861$	−4.26666	+	3.74981i	−0.145408	+	0.127793i
$862$	16.5337	+	23.6126i	0.563141	+	0.804249i
$863$	−31.7542	+	31.7542i	−1.08093	+	1.08093i	−0.0845039	+	0.996423i	$0.526931\pi$
$863$	−31.7542	+	31.7542i	−1.08093	+	1.08093i	−0.996423	+	0.0845039i	$0.973069\pi$
$864$	−1.87201	+	6.49976i	−0.0636870	+	0.221126i
$865$		0			0
$866$	31.2896	+	5.51721i	1.06327	+	0.187482i
$867$	11.5044	+	23.2662i	0.390710	+	0.790160i
$868$	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
$873$	−8.95541	−	17.1141i	−0.303095	−	0.579225i
$874$	−2.91359	+	1.68216i	−0.0985535	+	0.0568999i
$875$		0			0
$876$	0.0890004	−	0.111134i	0.00300705	−	0.00375488i
$877$	15.8993	+	11.1328i	0.536880	+	0.375928i	0.810344	−	0.585955i	$-0.199280\pi$
$877$	15.8993	+	11.1328i	0.536880	+	0.375928i	−0.273464	+	0.961882i	$0.588169\pi$
$878$	12.2311	+	8.56430i	0.412779	+	0.289031i
$879$	−15.6969	−	2.39888i	−0.529444	−	0.0809123i
$880$		0			0
$881$	−11.7101	+	6.76081i	−0.394522	+	0.227778i	−0.684118	−	0.729372i	$-0.739813\pi$
$881$	−11.7101	+	6.76081i	−0.394522	+	0.227778i	0.289595	+	0.957149i	$0.406479\pi$
$882$	−9.63555	−	72.0042i	−0.324446	−	2.42451i
$883$	30.0253	−	8.04527i	1.01043	−	0.270745i	0.284623	−	0.958640i	$-0.408132\pi$
$883$	30.0253	−	8.04527i	1.01043	−	0.270745i	0.725810	+	0.687895i	$0.241465\pi$
$884$	−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	0.660686	−	0.750663i	$-0.270266\pi$
$887$	−10.0974	−	21.6538i	−0.339036	−	0.727065i	−0.999722	+	0.0235979i	$0.992488\pi$
$888$	17.5958	−	26.3947i	0.590476	−	0.885749i
$889$	93.2044	+	16.4345i	3.12598	+	0.551194i
$890$		0			0
$891$	−2.88058	−	31.3852i	−0.0965030	−	1.05145i
$892$	3.58201	−	3.58201i	0.119934	−	0.119934i
$893$	7.49912	+	10.7099i	0.250949	+	0.358392i
$894$	8.35801	+	41.7860i	0.279534	+	1.39753i
$895$		0			0
$896$	39.8584	+	47.5014i	1.33158	+	1.58691i
$897$	−6.82778	+	7.14761i	−0.227973	+	0.238652i
$898$	−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
$903$	0.996189	+	1.35560i	0.0331511	+	0.0451116i
$904$	2.02174	−	0.356488i	0.0672422	−	0.0118566i
$905$		0			0
$906$	5.24557	+	4.20084i	0.174272	+	0.139563i
$907$	20.9061	−	1.82905i	0.694175	−	0.0607325i	0.265393	−	0.964140i	$-0.414498\pi$
$907$	20.9061	−	1.82905i	0.694175	−	0.0607325i	0.428782	+	0.903408i	$0.358943\pi$
$908$	1.10624	+	0.296416i	0.0367118	+	0.00983690i
$909$	13.5059	−	12.4289i	0.447961	−	0.412239i
$910$		0			0
$911$	−9.46462	−	26.0038i	−0.313577	−	0.861545i	−0.991927	−	0.126807i	$-0.959527\pi$
$911$	−9.46462	−	26.0038i	−0.313577	−	0.861545i	0.678351	−	0.734738i	$-0.262695\pi$
$912$	−2.71333	+	11.1398i	−0.0898472	+	0.368876i
$913$	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
$918$	10.8836	−	1.71075i	0.359213	−	0.0564632i
$919$		−	21.5936i		−	0.712307i	−0.934427	−	0.356154i	$-0.884088\pi$
$919$		−	21.5936i		−	0.712307i	0.934427	−	0.356154i	$-0.115912\pi$
$920$		0			0
$921$	8.29969	+	9.44368i	0.273484	+	0.311180i
$922$	−23.3976	+	10.9105i	−0.770559	+	0.359318i
$923$	−4.26098	+	48.7032i	−0.140252	+	1.60309i
$924$	5.92763	+	3.24380i	0.195005	+	0.106713i
$925$		0			0
$926$	37.1159	+	21.4289i	1.21970	+	0.704197i
$927$	−6.84261	−	21.5419i	−0.224741	−	0.707530i
$928$	−0.327447	+	1.22205i	−0.0107490	+	0.0401158i
$929$	−12.2976	−	10.3189i	−0.403472	−	0.338553i	0.418362	−	0.908280i	$-0.362604\pi$
$929$	−12.2976	−	10.3189i	−0.403472	−	0.338553i	−0.821834	+	0.569727i	$0.807049\pi$
$930$		0			0
$931$	−4.22650	−	23.9697i	−0.138518	−	0.785575i
$932$	3.51917	−	5.02589i	0.115274	−	0.164628i
$933$	35.9022	+	15.7517i	1.17538	+	0.515688i
$934$	−22.8691	+	27.2543i	−0.748299	+	0.891788i
$935$		0			0
$936$	1.37940	+	30.1217i	0.0450872	+	0.984557i
$937$	5.65242	+	21.0951i	0.184657	+	0.689148i	0.994704	+	0.102783i	$0.0327748\pi$
$937$	5.65242	+	21.0951i	0.184657	+	0.689148i	−0.810047	+	0.586365i	$0.800559\pi$
$938$	−46.6379	+	100.015i	−1.52278	+	3.26561i
$939$	−3.43782	+	6.28217i	−0.112189	+	0.205011i
$940$		0			0
$941$	−4.53610	+	12.4628i	−0.147872	+	0.406276i	−0.991409	−	0.130795i	$-0.958247\pi$
$941$	−4.53610	+	12.4628i	−0.147872	+	0.406276i	0.843537	+	0.537071i	$0.180469\pi$
$942$	2.38112	−	36.9312i	0.0775810	−	1.20328i
$943$	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	−0.332597	−	0.943069i	$-0.607925\pi$
$947$	13.5354	−	9.47761i	0.439843	−	0.307981i	0.772440	+	0.635088i	$0.219036\pi$
$948$	3.52393	−	1.74248i	0.114452	−	0.0565930i
$949$	0.462551	−	1.27085i	0.0150150	−	0.0412535i
$950$		0			0
$951$	−28.9747	−	47.6344i	−0.939570	−	1.54465i
$952$	7.63591	−	16.3753i	0.247481	−	0.530725i
$953$	−1.40298	−	5.23599i	−0.0454469	−	0.169610i	0.939472	−	0.342625i	$-0.111316\pi$
$953$	−1.40298	−	5.23599i	−0.0454469	−	0.169610i	−0.984919	+	0.173014i	$0.944649\pi$
$954$	−17.4295	+	3.90297i	−0.564300	+	0.126363i
$955$		0			0
$956$	0.223273	−	0.266086i	0.00722115	−	0.00860583i
$957$	−0.648018	−	5.85937i	−0.0209475	−	0.189406i
$958$	−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
$963$	15.9335	−	38.6998i	0.513451	−	1.24708i
$964$	−0.660134	−	0.381128i	−0.0212615	−	0.0122753i
$965$		0			0
$966$	0.427816	+	18.6940i	0.0137647	+	0.601469i
$967$	5.15797	−	58.9559i	0.165869	−	1.89589i	−0.223335	−	0.974742i	$-0.571694\pi$
$967$	5.15797	−	58.9559i	0.165869	−	1.89589i	0.389204	−	0.921152i	$-0.372750\pi$
$968$	3.02513	−	1.41064i	0.0972312	−	0.0453397i
$969$	3.61954	−	0.723979i	0.116276	−	0.0232575i
$970$		0			0
$971$		−	27.0614i		−	0.868442i	−0.900806	−	0.434221i	$-0.857024\pi$
$971$		−	27.0614i		−	0.868442i	0.900806	−	0.434221i	$-0.142976\pi$
$972$	−0.529365	+	3.56547i	−0.0169794	+	0.114362i
$973$	−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	0.341078	−	0.940035i	$-0.389208\pi$
$977$	16.0579	+	1.40489i	0.513738	+	0.0449463i	0.172661	+	0.984981i	$0.444764\pi$
$978$	21.1893	+	20.2412i	0.677559	+	0.647241i
$979$	5.02158	+	13.7967i	0.160490	+	0.440944i
$980$		0			0
$981$	−5.59548	+	2.33169i	−0.178650	+	0.0744452i
$982$	−36.9250	−	9.89401i	−1.17832	−	0.315731i
$983$	43.1392	−	3.77419i	1.37593	−	0.120378i	0.624929	−	0.780682i	$-0.285128\pi$
$983$	43.1392	−	3.77419i	1.37593	−	0.120378i	0.750999	+	0.660304i	$0.229573\pi$
$984$	0.470591	−	3.07928i	0.0150019	−	0.0981638i
$985$		0			0
$986$	2.02940	−	0.357838i	0.0646293	−	0.0113959i
$987$	72.2267	−	7.98793i	2.29900	−	0.254259i
$988$	−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	0.213776	+	0.976883i	$0.431424\pi$
$991$	−23.2675	+	40.3005i	−0.739117	+	1.28019i	−0.952893	+	0.303306i	$0.901910\pi$
$992$	−3.07434	−	1.43359i	−0.0976103	−	0.0455164i
$993$	3.29935	+	0.803625i	0.104702	+	0.0255023i
$994$	59.4476	+	70.8468i	1.88556	+	2.24713i
$995$		0			0
$996$	−4.30947	−	1.45775i	−0.136551	−	0.0461906i
$997$	5.81058	+	8.29837i	0.184023	+	0.262812i	0.900555	−	0.434742i	$-0.143161\pi$
$997$	5.81058	+	8.29837i	0.184023	+	0.262812i	−0.716532	+	0.697554i	$0.754272\pi$
$998$	6.16857	−	6.16857i	0.195263	−	0.195263i
$999$	15.8279	−	32.3558i	0.500771	−	1.02369i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.ba.b.218.12		192
5.2	odd	4	inner	675.2.ba.b.407.12		192
5.3	odd	4		135.2.q.a.2.5	✓	192
5.4	even	2		135.2.q.a.83.5	yes	192
15.8	even	4		405.2.r.a.332.12		192
15.14	odd	2		405.2.r.a.8.12		192
27.14	odd	18	inner	675.2.ba.b.68.12		192
135.13	odd	36		405.2.r.a.152.12		192
135.14	odd	18		135.2.q.a.68.5	yes	192
135.68	even	36		135.2.q.a.122.5	yes	192
135.94	even	18		405.2.r.a.233.12		192
135.122	even	36	inner	675.2.ba.b.257.12		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.5	✓	192	5.3	odd	4
135.2.q.a.68.5	yes	192	135.14	odd	18
135.2.q.a.83.5	yes	192	5.4	even	2
135.2.q.a.122.5	yes	192	135.68	even	36
405.2.r.a.8.12		192	15.14	odd	2
405.2.r.a.152.12		192	135.13	odd	36
405.2.r.a.233.12		192	135.94	even	18
405.2.r.a.332.12		192	15.8	even	4
675.2.ba.b.68.12		192	27.14	odd	18	inner
675.2.ba.b.218.12		192	1.1	even	1	trivial
675.2.ba.b.257.12		192	135.122	even	36	inner
675.2.ba.b.407.12		192	5.2	odd	4	inner

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.ba (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22359 - 0.856769i) q^{2} +(1.44117 + 0.960742i) q^{3} +(0.0790861 - 0.217287i) q^{4} +(2.58654 - 0.0591935i) q^{6} +(2.03610 - 4.36642i) q^{7} +(0.683816 + 2.55204i) q^{8} +(1.15395 + 2.76919i) q^{9} +(-2.25098 + 2.68262i) q^{11} +(0.322733 - 0.237167i) q^{12} +(2.18203 - 3.11626i) q^{13} +(-1.24966 - 7.08719i) q^{14} +(3.37749 + 2.83405i) q^{16} +(0.367380 - 1.37108i) q^{17} +(3.78452 + 2.39969i) q^{18} +(1.30024 + 0.750693i) q^{19} +(7.12937 - 4.33660i) q^{21} +(-0.455904 + 5.21100i) q^{22} +(-1.35959 + 0.633988i) q^{23} +(-1.46635 + 4.33489i) q^{24} -5.68253i q^{26} +(-0.997437 + 5.09952i) q^{27} +(-0.787741 - 0.787741i) q^{28} +(-0.168770 + 0.957143i) q^{29} +(-2.44873 - 0.891266i) q^{31} +(1.29677 + 0.113453i) q^{32} +(-5.82135 + 1.70350i) q^{33} +(-0.725176 - 1.99240i) q^{34} +(0.692970 - 0.0317342i) q^{36} +(-6.69580 - 1.79413i) q^{37} +(2.23413 - 0.195461i) q^{38} +(6.13860 - 2.39470i) q^{39} +(-0.670363 + 0.118203i) q^{41} +(5.00798 - 11.4145i) q^{42} +(0.0175704 + 0.200831i) q^{43} +(0.404877 + 0.701267i) q^{44} +(-1.12040 + 1.94060i) q^{46} +(7.89228 + 3.68023i) q^{47} +(2.14475 + 7.32924i) q^{48} +(-10.4204 - 12.4186i) q^{49} +(1.84671 - 1.62300i) q^{51} +(-0.504555 - 0.720580i) q^{52} +(-2.81838 + 2.81838i) q^{53} +(3.14865 + 7.09431i) q^{54} +(12.5356 + 2.21036i) q^{56} +(1.15264 + 2.33107i) q^{57} +(0.613544 + 1.31575i) q^{58} +(5.69079 - 4.77514i) q^{59} +(-1.08988 + 0.396683i) q^{61} +(-3.75986 + 1.00745i) q^{62} +(14.4410 + 0.599704i) q^{63} +(-5.95268 + 3.43678i) q^{64} +(-5.66346 + 7.07194i) q^{66} +(-12.5612 - 8.79548i) q^{67} +(-0.268864 - 0.188260i) q^{68} +(-2.56850 - 0.392531i) q^{69} +(-11.1295 + 6.42561i) q^{71} +(-6.27798 + 4.83854i) q^{72} +(0.343386 - 0.0920100i) q^{73} +(-9.73009 + 3.54146i) q^{74} +(0.265947 - 0.223156i) q^{76} +(7.13022 + 15.2908i) q^{77} +(5.45945 - 8.18950i) q^{78} +(9.66646 + 1.70446i) q^{79} +(-6.33680 + 6.39100i) q^{81} +(-0.718978 + 0.718978i) q^{82} +(-6.51525 - 9.30474i) q^{83} +(-0.378454 - 1.89208i) q^{84} +(0.193565 + 0.230681i) q^{86} +(-1.16279 + 1.21726i) q^{87} +(-8.38540 - 3.91017i) q^{88} +(2.09630 - 3.63090i) q^{89} +(-9.16409 - 15.8727i) q^{91} +(0.0302327 + 0.345561i) q^{92} +(-2.67277 - 3.63707i) q^{93} +(12.8100 - 2.25876i) q^{94} +(1.75987 + 1.40937i) q^{96} +(-6.41403 + 0.561155i) q^{97} +(-23.3902 - 6.26740i) q^{98} +(-10.0262 - 3.13779i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8} - 36 q^{11} + 12 q^{12} + 12 q^{13} - 24 q^{16} + 18 q^{17} + 54 q^{18} - 24 q^{21} + 12 q^{22} + 36 q^{23} + 36 q^{27} + 24 q^{28} - 24 q^{31}+ \cdots - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8 - 36 * q^11 + 12 * q^12 + 12 * q^13 - 24 * q^16 + 18 * q^17 + 54 * q^18 - 24 * q^21 + 12 * q^22 + 36 * q^23 + 36 * q^27 + 24 * q^28 - 24 * q^31 + 48 * q^32 + 6 * q^33 + 12 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^41 + 24 * q^42 + 12 * q^43 - 12 * q^46 + 6 * q^47 - 12 * q^48 + 144 * q^51 - 12 * q^52 + 180 * q^56 + 12 * q^57 + 12 * q^58 - 60 * q^61 + 18 * q^62 + 54 * q^63 + 72 * q^66 - 24 * q^67 + 60 * q^68 - 36 * q^71 - 180 * q^72 + 6 * q^73 - 72 * q^76 - 132 * q^77 - 78 * q^78 + 12 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^86 - 144 * q^87 + 48 * q^88 - 12 * q^91 - 258 * q^92 - 180 * q^93 - 12 * q^96 - 24 * q^97 - 324 * q^98

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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