LMFDB - Embedded newform 675.2.ba.b.407.12

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			407.12
Character	$\chi$	$=$	675.407
Dual form			675.2.ba.b.68.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.856769 + 1.22359i) q^{2} +(0.960742 - 1.44117i) q^{3} +(-0.0790861 + 0.217287i) q^{4} +(2.58654 - 0.0591935i) q^{6} +(4.36642 + 2.03610i) q^{7} +(2.55204 - 0.683816i) q^{8} +(-1.15395 - 2.76919i) q^{9} +(-2.25098 + 2.68262i) q^{11} +(0.237167 + 0.322733i) q^{12} +(-3.11626 - 2.18203i) q^{13} +(1.24966 + 7.08719i) q^{14} +(3.37749 + 2.83405i) q^{16} +(1.37108 + 0.367380i) q^{17} +(2.39969 - 3.78452i) q^{18} +(-1.30024 - 0.750693i) q^{19} +(7.12937 - 4.33660i) q^{21} +(-5.21100 - 0.455904i) q^{22} +(0.633988 + 1.35959i) q^{23} +(1.46635 - 4.33489i) q^{24} -5.68253i q^{26} +(-5.09952 - 0.997437i) q^{27} +(-0.787741 + 0.787741i) q^{28} +(0.168770 - 0.957143i) q^{29} +(-2.44873 - 0.891266i) q^{31} +(-0.113453 + 1.29677i) q^{32} +(1.70350 + 5.82135i) q^{33} +(0.725176 + 1.99240i) q^{34} +(0.692970 - 0.0317342i) q^{36} +(1.79413 - 6.69580i) q^{37} +(-0.195461 - 2.23413i) q^{38} +(-6.13860 + 2.39470i) q^{39} +(-0.670363 + 0.118203i) q^{41} +(11.4145 + 5.00798i) q^{42} +(0.200831 - 0.0175704i) q^{43} +(-0.404877 - 0.701267i) q^{44} +(-1.12040 + 1.94060i) q^{46} +(-3.68023 + 7.89228i) q^{47} +(7.32924 - 2.14475i) q^{48} +(10.4204 + 12.4186i) q^{49} +(1.84671 - 1.62300i) q^{51} +(0.720580 - 0.504555i) q^{52} +(2.81838 + 2.81838i) q^{53} +(-3.14865 - 7.09431i) q^{54} +(12.5356 + 2.21036i) q^{56} +(-2.33107 + 1.15264i) q^{57} +(1.31575 - 0.613544i) q^{58} +(-5.69079 + 4.77514i) q^{59} +(-1.08988 + 0.396683i) q^{61} +(-1.00745 - 3.75986i) q^{62} +(0.599704 - 14.4410i) q^{63} +(5.95268 - 3.43678i) q^{64} +(-5.66346 + 7.07194i) q^{66} +(8.79548 - 12.5612i) q^{67} +(-0.188260 + 0.268864i) q^{68} +(2.56850 + 0.392531i) q^{69} +(-11.1295 + 6.42561i) q^{71} +(-4.83854 - 6.27798i) q^{72} +(-0.0920100 - 0.343386i) q^{73} +(9.73009 - 3.54146i) q^{74} +(0.265947 - 0.223156i) q^{76} +(-15.2908 + 7.13022i) q^{77} +(-8.18950 - 5.45945i) q^{78} +(-9.66646 - 1.70446i) q^{79} +(-6.33680 + 6.39100i) q^{81} +(-0.718978 - 0.718978i) q^{82} +(-9.30474 + 6.51525i) q^{83} +(0.378454 + 1.89208i) q^{84} +(0.193565 + 0.230681i) q^{86} +(-1.21726 - 1.16279i) q^{87} +(-3.91017 + 8.38540i) q^{88} +(-2.09630 + 3.63090i) q^{89} +(-9.16409 - 15.8727i) q^{91} +(-0.345561 + 0.0302327i) q^{92} +(-3.63707 + 2.67277i) q^{93} +(-12.8100 + 2.25876i) q^{94} +(1.75987 + 1.40937i) q^{96} +(-0.561155 - 6.41403i) q^{97} +(-6.26740 + 23.3902i) 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 $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.856769	+	1.22359i	0.605827	+	0.865211i	0.998516	−	0.0544607i	$-0.0173439\pi$
$2$	0.856769	+	1.22359i	0.605827	+	0.865211i	−0.392689	+	0.919671i	$0.628455\pi$
$3$	0.960742	−	1.44117i	0.554685	−	0.832061i
$3$	0.960742	−	1.44117i	0.554685	−	0.832061i
$4$	−0.0790861	+	0.217287i	−0.0395430	+	0.108644i
$5$		0			0
$5$		0			0
$6$	2.58654	−	0.0591935i	1.05595	−	0.0241657i
$7$	4.36642	+	2.03610i	1.65035	+	0.769572i	0.999950	+	0.00998196i	$0.00317741\pi$
$7$	4.36642	+	2.03610i	1.65035	+	0.769572i	0.650402	+	0.759590i	$0.274600\pi$
$8$	2.55204	−	0.683816i	0.902281	−	0.241766i
$9$	−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	$0.399255\pi$
$12$	0.237167	+	0.322733i	0.0684641	+	0.0931651i
$13$	−3.11626	−	2.18203i	−0.864295	−	0.605186i	0.0551175	−	0.998480i	$-0.482447\pi$
$13$	−3.11626	−	2.18203i	−0.864295	−	0.605186i	−0.919413	+	0.393294i	$0.871336\pi$
$14$	1.24966	+	7.08719i	0.333986	+	1.89413i
$15$		0			0
$16$	3.37749	+	2.83405i	0.844372	+	0.708512i
$17$	1.37108	+	0.367380i	0.332536	+	0.0891027i	0.421224	−	0.906957i	$-0.361601\pi$
$17$	1.37108	+	0.367380i	0.332536	+	0.0891027i	−0.0886879	+	0.996059i	$0.528267\pi$
$18$	2.39969	−	3.78452i	0.565612	−	0.892019i
$19$	−1.30024	−	0.750693i	−0.298295	−	0.172221i	0.343382	−	0.939196i	$-0.388428\pi$
$19$	−1.30024	−	0.750693i	−0.298295	−	0.172221i	−0.641677	+	0.766975i	$0.721761\pi$
$20$		0			0
$21$	7.12937	−	4.33660i	1.55576	−	0.946323i
$22$	−5.21100	−	0.455904i	−1.11099	−	0.0971990i
$23$	0.633988	+	1.35959i	0.132196	+	0.283494i	0.961252	−	0.275670i	$-0.0888998\pi$
$23$	0.633988	+	1.35959i	0.132196	+	0.283494i	−0.829057	+	0.559165i	$0.811122\pi$
$24$	1.46635	−	4.33489i	0.299318	−	0.884856i
$25$		0			0
$26$		−	5.68253i		−	1.11444i
$27$	−5.09952	−	0.997437i	−0.981403	−	0.191957i
$28$	−0.787741	+	0.787741i	−0.148869	+	0.148869i
$29$	0.168770	−	0.957143i	0.0313398	−	0.177737i	−0.965120	−	0.261808i	$-0.915681\pi$
$29$	0.168770	−	0.957143i	0.0313398	−	0.177737i	0.996460	+	0.0840712i	$0.0267923\pi$
$30$		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	$0.686298\pi$
$32$	−0.113453	+	1.29677i	−0.0200558	+	0.229239i
$33$	1.70350	+	5.82135i	0.296541	+	1.01337i
$34$	0.725176	+	1.99240i	0.124367	+	0.341694i
$35$		0			0
$36$	0.692970	−	0.0317342i	0.115495	−	0.00528903i
$37$	1.79413	−	6.69580i	0.294954	−	1.10078i	−0.646300	−	0.763083i	$-0.723685\pi$
$37$	1.79413	−	6.69580i	0.294954	−	1.10078i	0.941254	−	0.337699i	$-0.109649\pi$
$38$	−0.195461	−	2.23413i	−0.0317080	−	0.362424i
$39$	−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	$0.461372\pi$
$42$	11.4145	+	5.00798i	1.76129	+	0.772748i
$43$	0.200831	−	0.0175704i	0.0306264	−	0.00267946i	−0.0718322	−	0.997417i	$-0.522885\pi$
$43$	0.200831	−	0.0175704i	0.0306264	−	0.00267946i	0.102459	+	0.994737i	$0.467329\pi$
$44$	−0.404877	−	0.701267i	−0.0610375	−	0.105720i
$45$		0			0
$46$	−1.12040	+	1.94060i	−0.165195	+	0.286126i
$47$	−3.68023	+	7.89228i	−0.536817	+	1.15121i	0.431644	+	0.902044i	$0.357934\pi$
$47$	−3.68023	+	7.89228i	−0.536817	+	1.15121i	−0.968461	+	0.249164i	$0.919844\pi$
$48$	7.32924	−	2.14475i	1.05789	−	0.309568i
$49$	10.4204	+	12.4186i	1.48863	+	1.77409i
$50$		0			0
$51$	1.84671	−	1.62300i	0.258591	−	0.227266i
$52$	0.720580	−	0.504555i	0.0999264	−	0.0699692i
$53$	2.81838	+	2.81838i	0.387135	+	0.387135i	0.873664	−	0.486529i	$-0.161737\pi$
$53$	2.81838	+	2.81838i	0.387135	+	0.387135i	−0.486529	+	0.873664i	$0.661737\pi$
$54$	−3.14865	−	7.09431i	−0.428478	−	0.965413i
$55$		0			0
$56$	12.5356	+	2.21036i	1.67514	+	0.295372i
$57$	−2.33107	+	1.15264i	−0.308758	+	0.152671i
$58$	1.31575	−	0.613544i	0.172766	−	0.0805623i
$59$	−5.69079	+	4.77514i	−0.740877	+	0.621670i	−0.933073	−	0.359687i	$-0.882884\pi$
$59$	−5.69079	+	4.77514i	−0.740877	+	0.621670i	0.192196	+	0.981357i	$0.438439\pi$
$60$		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	$0.412545\pi$
$62$	−1.00745	−	3.75986i	−0.127947	−	0.477503i
$63$	0.599704	−	14.4410i	0.0755556	−	1.81939i
$64$	5.95268	−	3.43678i	0.744085	−	0.429598i
$65$		0			0
$66$	−5.66346	+	7.07194i	−0.697124	+	0.870496i
$67$	8.79548	−	12.5612i	1.07454	−	1.53460i	0.250457	−	0.968128i	$-0.419419\pi$
$67$	8.79548	−	12.5612i	1.07454	−	1.53460i	0.824081	−	0.566472i	$-0.191692\pi$
$68$	−0.188260	+	0.268864i	−0.0228299	+	0.0326045i
$69$	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	$0.609401\pi$
$72$	−4.83854	−	6.27798i	−0.570227	−	0.739867i
$73$	−0.0920100	−	0.343386i	−0.0107690	−	0.0401903i	0.960332	−	0.278858i	$-0.0899559\pi$
$73$	−0.0920100	−	0.343386i	−0.0107690	−	0.0401903i	−0.971101	+	0.238668i	$0.923289\pi$
$74$	9.73009	−	3.54146i	1.13110	−	0.411687i
$75$		0			0
$76$	0.265947	−	0.223156i	0.0305062	−	0.0255977i
$77$	−15.2908	+	7.13022i	−1.74255	+	0.812564i
$78$	−8.18950	−	5.45945i	−0.927278	−	0.618161i
$79$	−9.66646	−	1.70446i	−1.08756	−	0.191766i	−0.399005	−	0.916949i	$-0.630644\pi$
$79$	−9.66646	−	1.70446i	−1.08756	−	0.191766i	−0.688557	+	0.725182i	$0.741755\pi$
$80$		0			0
$81$	−6.33680	+	6.39100i	−0.704089	+	0.710112i
$82$	−0.718978	−	0.718978i	−0.0793979	−	0.0793979i
$83$	−9.30474	+	6.51525i	−1.02133	+	0.715142i	−0.959143	−	0.282923i	$-0.908696\pi$
$83$	−9.30474	+	6.51525i	−1.02133	+	0.715142i	−0.0621857	+	0.998065i	$0.519807\pi$
$84$	0.378454	+	1.89208i	0.0412927	+	0.206443i
$85$		0			0
$86$	0.193565	+	0.230681i	0.0208726	+	0.0248750i
$87$	−1.21726	−	1.16279i	−0.130504	−	0.124665i
$88$	−3.91017	+	8.38540i	−0.416826	+	0.893886i
$89$	−2.09630	+	3.63090i	−0.222208	+	0.384875i	−0.955478	−	0.295062i	$-0.904660\pi$
$89$	−2.09630	+	3.63090i	−0.222208	+	0.384875i	0.733270	+	0.679937i	$0.237993\pi$
$90$		0			0
$91$	−9.16409	−	15.8727i	−0.960658	−	1.66391i
$92$	−0.345561	+	0.0302327i	−0.0360272	+	0.00315198i
$93$	−3.63707	+	2.67277i	−0.377146	+	0.277153i
$94$	−12.8100	+	2.25876i	−1.32126	+	0.232973i
$95$		0			0
$96$	1.75987	+	1.40937i	0.179616	+	0.143843i
$97$	−0.561155	−	6.41403i	−0.0569767	−	0.651246i	−0.969962	−	0.243255i	$-0.921785\pi$
$97$	−0.561155	−	6.41403i	−0.0569767	−	0.651246i	0.912986	−	0.407991i	$-0.133771\pi$
$98$	−6.26740	+	23.3902i	−0.633103	+	2.36277i
$99$	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	$0.987341\pi$
$102$	3.56810	+	0.869084i	0.353295	+	0.0860521i
$103$	−0.656648	+	7.50553i	−0.0647015	+	0.739541i	0.892675	+	0.450700i	$0.148826\pi$
$103$	−0.656648	+	7.50553i	−0.0647015	+	0.739541i	−0.957377	+	0.288841i	$0.906730\pi$
$104$	−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	$-0.514435\pi$
$107$	9.86451	−	9.86451i	0.953639	−	0.953639i	0.998972	+	0.0453334i	$0.0144350\pi$
$108$	0.620031	−	1.02918i	0.0596625	−	0.0990326i
$109$		−	2.02062i		−	0.193540i	−0.995307	−	0.0967701i	$-0.969149\pi$
$109$		−	2.02062i		−	0.193540i	0.995307	−	0.0967701i	$-0.0308512\pi$
$110$		0			0
$111$	−7.92609	−	9.01859i	−0.752311	−	0.856006i
$112$	8.97714	+	19.2515i	0.848260	+	1.81910i
$113$	−0.774062	−	0.0677216i	−0.0728176	−	0.00637072i	0.0506887	−	0.998715i	$-0.483858\pi$
$113$	−0.774062	−	0.0677216i	−0.0728176	−	0.00637072i	−0.123506	+	0.992344i	$0.539414\pi$
$114$	−3.40756	−	1.86473i	−0.319147	−	0.174648i
$115$		0			0
$116$	0.194627	+	0.112368i	0.0180707	+	0.0104331i
$117$	−2.44644	+	11.1475i	−0.226174	+	1.03058i
$118$	−10.7185	−	2.87202i	−0.986719	−	0.264391i
$119$	5.23869	+	4.39579i	0.480230	+	0.402961i
$120$		0			0
$121$	−0.219379	−	1.24416i	−0.0199435	−	0.113105i
$122$	−1.41915	−	0.993700i	−0.128484	−	0.0899654i
$123$	−0.473695	+	1.07967i	−0.0427116	+	0.0973506i
$124$	0.387321	−	0.461592i	0.0347825	−	0.0414522i
$125$		0			0
$126$	18.1837	−	11.6388i	1.61993	−	1.03687i
$127$	−18.9749	+	5.08430i	−1.68375	+	0.451159i	−0.968765	−	0.247982i	$-0.920232\pi$
$127$	−18.9749	+	5.08430i	−1.68375	+	0.451159i	−0.714983	+	0.699141i	$0.753566\pi$
$128$	11.6648	+	5.43940i	1.03103	+	0.480779i
$129$	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	$0.179569\pi$
$132$	−1.39963	−	0.0902401i	−0.121822	−	0.00785439i
$133$	−4.14891	−	5.92525i	−0.359756	−	0.513784i
$134$	22.9055			1.97874
$135$		0			0
$136$	3.75027			0.321583
$137$	−1.04372	−	1.49059i	−0.0891710	−	0.127349i	0.772088	−	0.635516i	$-0.219212\pi$
$137$	−1.04372	−	1.49059i	−0.0891710	−	0.127349i	−0.861259	+	0.508166i	$0.830324\pi$
$138$	1.72031	+	3.47911i	0.146443	+	0.296161i
$139$	−0.987166	+	2.71222i	−0.0837303	+	0.230047i	−0.974491	−	0.224425i	$-0.927950\pi$
$139$	−0.987166	+	2.71222i	−0.0837303	+	0.230047i	0.890761	+	0.454472i	$0.150172\pi$
$140$		0			0
$141$	7.83838	+	12.8863i	0.660110	+	1.08522i
$142$	−17.3977	−	8.11269i	−1.45998	−	0.680802i
$143$	12.8682	−	3.44802i	1.07609	−	0.288338i
$144$	3.95056	−	12.6232i	0.329214	−	1.05194i
$145$		0			0
$146$	0.341333	−	0.406785i	0.0282489	−	0.0336658i
$147$	27.9087	−	3.08657i	2.30187	−	0.254576i
$148$	1.31302	+	0.919386i	0.107930	+	0.0755731i
$149$	−2.86013	−	16.2206i	−0.234311	−	1.32885i	−0.844059	−	0.536250i	$-0.819840\pi$
$149$	−2.86013	−	16.2206i	−0.234311	−	1.32885i	0.609748	−	0.792596i	$-0.291271\pi$
$150$		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	$0.688517\pi$
$152$	−3.83159	−	1.02667i	−0.310783	−	0.0832741i
$153$	−0.564813	−	4.22072i	−0.0456624	−	0.341225i
$154$	−21.8252	−	12.6008i	−1.75872	−	1.01540i
$155$		0			0
$156$	−0.0348594	−	1.52323i	−0.00279098	−	0.121956i
$157$	14.2497	+	1.24669i	1.13725	+	0.0994965i	0.640188	−	0.768219i	$-0.278857\pi$
$157$	14.2497	+	1.24669i	1.13725	+	0.0994965i	0.497062	+	0.867715i	$0.334412\pi$
$158$	−6.19636	−	13.2881i	−0.492956	−	1.05715i
$159$	6.76951	−	1.35403i	0.536857	−	0.107382i
$160$		0			0
$161$			7.22741i			0.569599i
$162$	−13.2492	−	2.27805i	−1.04095	−	0.178981i
$163$	8.00886	−	8.00886i	0.627302	−	0.627302i	−0.320086	−	0.947388i	$-0.603712\pi$
$163$	8.00886	−	8.00886i	0.627302	−	0.627302i	0.947388	+	0.320086i	$0.103712\pi$
$164$	0.0273323	−	0.155009i	0.00213430	−	0.0121042i
$165$		0			0
$166$	−15.9440	−	5.80315i	−1.23750	−	0.450412i
$167$	−1.21737	+	13.9146i	−0.0942027	+	1.07674i	0.791088	+	0.611703i	$0.209515\pi$
$167$	−1.21737	+	13.9146i	−0.0942027	+	1.07674i	−0.885290	+	0.465039i	$0.846040\pi$
$168$	15.2290	−	15.9423i	1.17494	−	1.22998i
$169$	0.503569	+	1.38354i	0.0387361	+	0.106427i
$170$		0			0
$171$	−0.578401	+	4.46687i	−0.0442314	+	0.341590i
$172$	−0.0120651	+	0.0450275i	−0.000919955	+	0.00343332i
$173$	0.352505	+	4.02915i	0.0268005	+	0.306331i	0.997750	+	0.0670460i	$0.0213574\pi$
$173$	0.352505	+	4.02915i	0.0268005	+	0.306331i	−0.970949	+	0.239285i	$0.923087\pi$
$174$	0.379874	−	2.48568i	0.0287982	−	0.188439i
$175$		0			0
$176$	−15.2053	+	2.68111i	−1.14614	+	0.202096i
$177$	1.41441	+	12.7891i	0.106314	+	0.961285i
$178$	−6.23880	+	0.545824i	−0.467618	+	0.0409112i
$179$	3.24205	+	5.61540i	0.242322	+	0.419714i	0.961375	−	0.275241i	$-0.0887576\pi$
$179$	3.24205	+	5.61540i	0.242322	+	0.419714i	−0.719053	+	0.694955i	$0.755424\pi$
$180$		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	$0.259332\pi$
$182$	11.5702	−	24.8123i	0.857639	−	1.83921i
$183$	−0.475403	+	1.95181i	−0.0351428	+	0.144282i
$184$	2.54767	+	3.03620i	0.187817	+	0.223831i
$185$		0			0
$186$	−6.38651	−	2.16035i	−0.468281	−	0.158404i
$187$	−4.07182	+	2.85112i	−0.297761	+	0.208494i
$188$	−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	$0.446580\pi$
$192$	0.766000	−	11.8807i	0.0552813	−	0.857415i
$193$	−23.1246	+	10.7832i	−1.66455	+	0.776191i	−0.664978	+	0.746863i	$0.731559\pi$
$193$	−23.1246	+	10.7832i	−1.66455	+	0.776191i	−0.999570	+	0.0293284i	$0.990663\pi$
$194$	7.36738	−	6.18197i	0.528947	−	0.443839i
$195$		0			0
$196$	−3.52251	+	1.28209i	−0.251608	+	0.0915779i
$197$	3.24493	+	12.1103i	0.231192	+	0.862820i	0.979829	+	0.199839i	$0.0640421\pi$
$197$	3.24493	+	12.1103i	0.231192	+	0.862820i	−0.748637	+	0.662980i	$0.769291\pi$
$198$	4.75075	+	14.9563i	0.337621	+	1.06290i
$199$	−12.0563	+	6.96070i	−0.854648	+	0.493431i	−0.862216	−	0.506540i	$-0.830924\pi$
$199$	−12.0563	+	6.96070i	−0.854648	+	0.493431i	0.00756873	+	0.999971i	$0.497591\pi$
$200$		0			0
$201$	−9.65271	−	24.7439i	−0.680850	−	1.74530i
$202$	5.24183	−	7.48611i	0.368814	−	0.526721i
$203$	2.68576	−	3.83566i	0.188503	−	0.269210i
$204$	0.206609	+	0.529624i	0.0144655	+	0.0370811i
$205$		0			0
$206$	−9.74630	+	5.62703i	−0.679057	+	0.392054i
$207$	3.03337	−	3.32453i	0.210834	−	0.231071i
$208$	−4.34115	−	16.2014i	−0.301005	−	1.12337i
$209$	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	$0.0343339\pi$
$212$	−0.835293	+	0.389504i	−0.0573682	+	0.0267512i
$213$	−1.43216	+	22.2128i	−0.0981299	+	1.52200i
$214$	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
$218$	2.47242	−	1.73120i	0.167453	−	0.117252i
$219$	−0.583276	−	0.197303i	−0.0394141	−	0.0133325i
$220$		0			0
$221$	−3.47101	−	4.13659i	−0.233485	−	0.278257i
$222$	4.24425	−	17.4252i	0.284855	−	1.16950i
$223$	9.25851	−	19.8549i	0.619996	−	1.32959i	−0.305993	−	0.952034i	$-0.598988\pi$
$223$	9.25851	−	19.8549i	0.619996	−	1.32959i	0.925989	−	0.377552i	$-0.123234\pi$
$224$	−3.13574	+	5.43126i	−0.209515	+	0.362891i
$225$		0			0
$226$	−0.580328	−	1.00516i	−0.0386029	−	0.0668621i
$227$	−4.93402	+	0.431671i	−0.327482	+	0.0286510i	−0.249712	−	0.968320i	$-0.580336\pi$
$227$	−4.93402	+	0.431671i	−0.327482	+	0.0286510i	−0.0777708	+	0.996971i	$0.524780\pi$
$228$	−0.0660995	−	0.597670i	−0.00437754	−	0.0395816i
$229$	1.07319	−	0.189232i	0.0709183	−	0.0125048i	−0.138076	−	0.990422i	$-0.544092\pi$
$229$	1.07319	−	0.189232i	0.0709183	−	0.0125048i	0.208995	+	0.977917i	$0.432981\pi$
$230$		0			0
$231$	−4.41465	+	28.8870i	−0.290463	+	1.90062i
$232$	−0.223802	−	2.55807i	−0.0146933	−	0.167946i
$233$	6.86746	−	25.6297i	0.449903	−	1.67906i	−0.252755	−	0.967530i	$-0.581337\pi$
$233$	6.86746	−	25.6297i	0.449903	−	1.67906i	0.702657	−	0.711529i	$-0.251997\pi$
$234$	−15.7360	+	6.55735i	−1.02869	+	0.428667i
$235$		0			0
$236$	−0.587514	−	1.61418i	−0.0382439	−	0.105074i
$237$	−11.7434	+	12.2935i	−0.762815	+	0.798547i
$238$	−0.890302	+	10.1762i	−0.0577097	+	0.659625i
$239$	−1.41158	−	0.513773i	−0.0913075	−	0.0332332i	0.295962	−	0.955200i	$-0.404360\pi$
$239$	−1.41158	−	0.513773i	−0.0913075	−	0.0332332i	−0.387270	+	0.921966i	$0.626582\pi$
$240$		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
$243$	3.12250	+	15.2725i	0.200308	+	0.979733i
$244$		−	0.268188i		−	0.0171690i
$245$		0			0
$246$	−1.72692	+	0.345418i	−0.110105	+	0.0220231i
$247$	2.41385	+	5.17651i	0.153589	+	0.329374i
$248$	−6.85872	−	0.600060i	−0.435529	−	0.0381039i
$249$	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	$0.465130\pi$
$252$	3.09041	+	1.27239i	0.194678	+	0.0801530i
$253$	−5.07436	−	1.35967i	−0.319022	−	0.0854817i
$254$	−22.4782	−	18.8614i	−1.41041	−	1.18347i
$255$		0			0
$256$	0.951288	+	5.39502i	0.0594555	+	0.337189i
$257$	−16.8536	−	11.8010i	−1.05130	−	0.736129i	−0.0857431	−	0.996317i	$-0.527326\pi$
$257$	−16.8536	−	11.8010i	−1.05130	−	0.736129i	−0.965558	+	0.260188i	$0.916215\pi$
$258$	0.518417	−	0.0573345i	0.0322752	−	0.00356949i
$259$	21.4672	−	25.5836i	1.33391	−	1.58969i
$260$		0			0
$261$	−2.84526	+	0.637138i	−0.176117	+	0.0394378i
$262$	−7.04856	+	1.88866i	−0.435461	+	0.116682i
$263$	15.5342	+	7.24374i	0.957882	+	0.446668i	0.837728	−	0.546087i	$-0.183883\pi$
$263$	15.5342	+	7.24374i	0.957882	+	0.446668i	0.120154	+	0.992755i	$0.461661\pi$
$264$	8.32812	+	13.6914i	0.512560	+	0.842649i
$265$		0			0
$266$	3.69544	−	10.1531i	0.226582	−	0.622529i
$267$	3.21875	+	6.50950i	0.196984	+	0.398375i
$268$	2.03380	+	2.90456i	0.124234	+	0.177424i
$269$	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	$0.341968\pi$
$272$	3.58963	+	5.12653i	0.217654	+	0.310841i
$273$	−31.6796	−	2.04252i	−1.91733	−	0.123619i
$274$	0.929644	−	2.55418i	0.0561619	−	0.154303i
$275$		0			0
$276$	−0.288425	+	0.527059i	−0.0173611	+	0.0317252i
$277$	22.2616	+	10.3807i	1.33757	+	0.623718i	0.954003	−	0.299796i	$-0.0969186\pi$
$277$	22.2616	+	10.3807i	1.33757	+	0.623718i	0.383564	+	0.923514i	$0.374696\pi$
$278$	−4.16442	+	1.11585i	−0.249765	+	0.0669244i
$279$	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	$0.215313\pi$
$282$	−9.05190	+	20.6316i	−0.539033	+	1.22859i
$283$	17.6935	+	12.3891i	1.05177	+	0.736457i	0.965655	−	0.259828i	$-0.0836658\pi$
$283$	17.6935	+	12.3891i	1.05177	+	0.736457i	0.0861152	+	0.996285i	$0.472555\pi$
$284$	−0.516015	−	2.92647i	−0.0306199	−	0.173654i
$285$		0			0
$286$	15.2440	+	12.7913i	0.901399	+	0.756364i
$287$	−3.16776	−	0.848799i	−0.186987	−	0.0501030i
$288$	3.72193	−	1.18224i	0.219317	−	0.0696641i
$289$	−12.9775	−	7.49259i	−0.763385	−	0.440740i
$290$		0			0
$291$	−9.78284	−	5.35351i	−0.573480	−	0.313828i
$292$	0.0818900	+	0.00716445i	0.00479225	+	0.000419268i
$293$	3.87450	+	8.30888i	0.226350	+	0.485410i	0.986381	−	0.164477i	$-0.0525938\pi$
$293$	3.87450	+	8.30888i	0.226350	+	0.485410i	−0.760030	+	0.649888i	$0.774816\pi$
$294$	27.6880	+	31.5044i	1.61480	+	1.83737i
$295$		0			0
$296$		−	18.3148i		−	1.06452i
$297$	14.1547	−	11.4348i	0.821338	−	0.663517i
$298$	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
$302$	−0.338164	+	3.86523i	−0.0194591	+	0.222419i
$303$	−10.2959	−	2.50778i	−0.591485	−	0.144068i
$304$	−2.26404	−	6.22039i	−0.129851	−	0.356764i
$305$		0			0
$306$	4.68052	−	4.30728i	0.267568	−	0.246231i
$307$	−1.87870	+	7.01141i	−0.107223	+	0.400162i	−0.998588	−	0.0531246i	$-0.983082\pi$
$307$	−1.87870	+	7.01141i	−0.107223	+	0.400162i	0.891365	+	0.453287i	$0.149749\pi$
$308$	−0.340016	−	3.88640i	−0.0193742	−	0.221448i
$309$	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	$0.222646\pi$
$312$	−14.0284	+	10.3090i	−0.794202	+	0.583634i
$313$	4.11885	−	0.360352i	0.232811	−	0.0203683i	0.0298468	−	0.999554i	$-0.490498\pi$
$313$	4.11885	−	0.360352i	0.232811	−	0.0203683i	0.202964	+	0.979186i	$0.434943\pi$
$314$	10.6833	+	18.5039i	0.602891	+	1.04424i
$315$		0			0
$316$	1.13484	−	1.96560i	0.0638397	−	0.110574i
$317$	13.6040	−	29.1740i	0.764080	−	1.63857i	−0.00546854	−	0.999985i	$-0.501741\pi$
$317$	13.6040	−	29.1740i	0.764080	−	1.63857i	0.769548	−	0.638589i	$-0.220482\pi$
$318$	7.45669	+	7.12303i	0.418151	+	0.399440i
$319$	2.18775	+	2.60726i	0.122490	+	0.145978i
$320$		0			0
$321$	−4.73920	−	23.6937i	−0.264516	−	1.32245i
$322$	−8.84340	+	6.19222i	−0.492824	+	0.345079i
$323$	−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
$327$	−2.91206	−	1.94129i	−0.161037	−	0.107354i
$328$	−1.62996	+	0.760064i	−0.0899996	+	0.0419675i
$329$	−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	$0.371730\pi$
$332$	−0.679805	−	2.53707i	−0.0373091	−	0.139240i
$333$	−20.6123	+	2.75832i	−1.12954	+	0.151155i
$334$	−18.0688	+	10.4320i	−0.988679	+	0.570814i
$335$		0			0
$336$	36.3695	+	5.55817i	1.98412	+	0.303223i
$337$	−9.63175	+	13.7556i	−0.524675	+	0.749313i	−0.990789	−	0.135411i	$-0.956764\pi$
$337$	−9.63175	+	13.7556i	−0.524675	+	0.749313i	0.466115	+	0.884724i	$0.345653\pi$
$338$	−1.26145	+	1.80154i	−0.0686140	+	0.0979909i
$339$	−0.841272	+	1.05049i	−0.0456916	+	0.0570549i
$340$		0			0
$341$	7.90298	−	4.56279i	0.427970	−	0.247089i
$342$	−5.96118	+	3.11934i	−0.322344	+	0.168675i
$343$	11.4860	+	42.8663i	0.620185	+	2.31456i
$344$	0.500513	−	0.182172i	0.0269858	−	0.00982205i
$345$		0			0
$346$	−4.62803	+	3.88338i	−0.248804	+	0.208772i
$347$	2.84711	−	1.32763i	0.152841	−	0.0712708i	−0.344693	−	0.938716i	$-0.612017\pi$
$347$	2.84711	−	1.32763i	0.152841	−	0.0712708i	0.497534	+	0.867445i	$0.334239\pi$
$348$	0.348929	−	0.172535i	0.0187045	−	0.00924883i
$349$	12.2555	+	2.16098i	0.656022	+	0.115674i	0.491744	−	0.870740i	$-0.336360\pi$
$349$	12.2555	+	2.16098i	0.656022	+	0.115674i	0.164278	+	0.986414i	$0.447471\pi$
$350$		0			0
$351$	13.7150	+	14.2356i	0.732053	+	0.759839i
$352$	−3.22337	−	3.22337i	−0.171806	−	0.171806i
$353$	14.8642	−	10.4080i	0.791143	−	0.553964i	−0.106694	−	0.994292i	$-0.534027\pi$
$353$	14.8642	−	10.4080i	0.791143	−	0.553964i	0.897837	+	0.440327i	$0.145138\pi$
$354$	−14.4368	+	12.6879i	−0.767307	+	0.674356i
$355$		0			0
$356$	−0.623160	−	0.742654i	−0.0330274	−	0.0393606i
$357$	11.3681	−	3.32664i	0.601665	−	0.176064i
$358$	−4.09327	+	8.77805i	−0.216336	+	0.463934i
$359$	5.27373	−	9.13437i	0.278337	−	0.482094i	−0.692635	−	0.721289i	$-0.743550\pi$
$359$	5.27373	−	9.13437i	0.278337	−	0.482094i	0.970972	+	0.239195i	$0.0768835\pi$
$360$		0			0
$361$	−8.37292	−	14.5023i	−0.440680	−	0.763280i
$362$	−11.4921	+	1.00543i	−0.604011	+	0.0528441i
$363$	−2.00381	−	0.879154i	−0.105173	−	0.0461436i
$364$	4.17368	−	0.735932i	0.218760	−	0.0385733i
$365$		0			0
$366$	−2.79553	+	1.09055i	−0.146125	+	0.0570040i
$367$	0.310757	+	3.55196i	0.0162214	+	0.185411i	0.999982	+	0.00592799i	$0.00188695\pi$
$367$	0.310757	+	3.55196i	0.0162214	+	0.185411i	−0.983761	+	0.179483i	$0.942557\pi$
$368$	−1.71186	+	6.38875i	−0.0892369	+	0.333037i
$369$	1.10089	+	1.71996i	0.0573101	+	0.0895376i
$370$		0			0
$371$	6.56775	+	18.0448i	0.340981	+	0.936837i
$372$	−0.293117	−	1.00167i	−0.0151974	−	0.0519340i
$373$	2.19980	−	25.1438i	0.113901	−	1.30190i	−0.697151	−	0.716925i	$-0.745549\pi$
$373$	2.19980	−	25.1438i	0.113901	−	1.30190i	0.811052	−	0.584974i	$-0.198895\pi$
$374$	−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
$378$	0.696344	−	37.3877i	0.0358161	−	1.92302i
$379$			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			0
$381$	−10.9026	+	32.2307i	−0.558558	+	1.65123i
$382$	5.85775	+	12.5620i	0.299709	+	0.642727i
$383$	−37.7169	−	3.29980i	−1.92724	−	0.168612i	−0.941517	−	0.336965i	$-0.890599\pi$
$383$	−37.7169	−	3.29980i	−1.92724	−	0.168612i	−0.985727	+	0.168353i	$0.946155\pi$
$384$	19.0460	−	11.5851i	0.971936	−	0.591202i
$385$		0			0
$386$	−33.0067	−	19.0564i	−1.68000	−	0.969947i
$387$	−0.280404	−	0.535863i	−0.0142538	−	0.0272395i
$388$	1.43807	+	0.385329i	0.0730067	+	0.0195621i
$389$	−2.93798	−	2.46526i	−0.148962	−	0.124994i	0.565261	−	0.824912i	$-0.308775\pi$
$389$	−2.93798	−	2.46526i	−0.148962	−	0.124994i	−0.714223	+	0.699918i	$0.753220\pi$
$390$		0			0
$391$	0.369762	+	2.09702i	0.0186997	+	0.106051i
$392$	35.0854	+	24.5671i	1.77208	+	1.24082i
$393$	5.01060	+	6.81836i	0.252751	+	0.343941i
$394$	−12.0379	+	14.3462i	−0.606459	+	0.722749i
$395$		0			0
$396$	−1.47473	+	1.93041i	−0.0741081	+	0.0970066i
$397$	4.33915	−	1.16267i	0.217776	−	0.0583528i	−0.148281	−	0.988945i	$-0.547374\pi$
$397$	4.33915	−	1.16267i	0.217776	−	0.0583528i	0.366057	+	0.930592i	$0.380707\pi$
$398$	−18.8465	−	8.78827i	−0.944690	−	0.440516i
$399$	−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	$0.193023\pi$
$402$	22.0063	−	33.0108i	1.09757	−	1.64643i
$403$	5.68612	+	8.12063i	0.283246	+	0.404517i
$404$	1.41471			0.0703845
$405$		0			0
$406$	6.99435			0.347124
$407$	13.9237	+	19.8851i	0.690172	+	0.985667i
$408$	3.60304	−	5.40478i	0.178377	−	0.267576i
$409$	−8.00244	+	21.9865i	−0.395695	+	1.08716i	0.568665	+	0.822569i	$0.307460\pi$
$409$	−8.00244	+	21.9865i	−0.395695	+	1.08716i	−0.964360	+	0.264594i	$0.914762\pi$
$410$		0			0
$411$	−3.15094	+	0.0721099i	−0.155424	+	0.00355692i
$412$	−1.57892	−	0.736264i	−0.0777879	−	0.0362731i
$413$	−34.5710	+	9.26327i	−1.70113	+	0.455816i
$414$	6.66677	+	0.863260i	0.327654	+	0.0424269i
$415$		0			0
$416$	3.18315	−	3.79353i	0.156067	−	0.185993i
$417$	2.96036	+	4.02842i	0.144969	+	0.197272i
$418$	6.43330	+	4.50465i	0.314663	+	0.220329i
$419$	−0.258905	−	1.46832i	−0.0126483	−	0.0717323i	0.977830	−	0.209399i	$-0.0671508\pi$
$419$	−0.258905	−	1.46832i	−0.0126483	−	0.0717323i	−0.990479	+	0.137667i	$0.956040\pi$
$420$		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	$0.871115\pi$
$422$	29.0229	+	7.77666i	1.41281	+	0.378562i
$423$	26.1020	+	1.08396i	1.26912	+	0.0527040i
$424$	9.11988	+	5.26536i	0.442900	+	0.255709i
$425$		0			0
$426$	−28.4065	+	17.2789i	−1.37630	+	0.837165i
$427$	−5.56655	−	0.487010i	−0.269384	−	0.0235681i
$428$	1.36329	+	2.92358i	0.0658969	+	0.141316i
$429$	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	$0.846137\pi$
$432$	−14.3968	−	17.8211i	−0.692665	−	0.857419i
$433$	15.0405	−	15.0405i	0.722800	−	0.722800i	−0.246375	−	0.969175i	$-0.579239\pi$
$433$	15.0405	−	15.0405i	0.722800	−	0.722800i	0.969175	+	0.246375i	$0.0792395\pi$
$434$	3.25648	−	18.4684i	0.156316	−	0.886512i
$435$		0			0
$436$	0.439055	+	0.159803i	0.0210269	+	0.00765317i
$437$	0.196300	−	2.24372i	0.00939031	−	0.107332i
$438$	−0.258314	−	0.882735i	−0.0123427	−	0.0421787i
$439$	−3.41885	−	9.39321i	−0.163173	−	0.448314i	0.830979	−	0.556303i	$-0.187781\pi$
$439$	−3.41885	−	9.39321i	−0.163173	−	0.448314i	−0.994152	+	0.107990i	$0.965559\pi$
$440$		0			0
$441$	22.3648	−	43.1866i	1.06499	−	2.05650i
$442$	2.08765	−	7.79120i	0.0992992	−	0.370590i
$443$	−2.69183	−	30.7678i	−0.127893	−	1.46182i	−0.740832	−	0.671690i	$-0.765569\pi$
$443$	−2.69183	−	30.7678i	−0.127893	−	1.46182i	0.612939	−	0.790130i	$-0.289987\pi$
$444$	2.58647	−	1.00899i	0.122748	−	0.0478847i
$445$		0			0
$446$	32.2268	−	5.68245i	1.52598	−	0.269072i
$447$	−26.1246	−	11.4619i	−1.23565	−	0.542129i
$448$	32.9895	−	2.88621i	1.55861	−	0.136361i
$449$	0.854949	+	1.48081i	0.0403475	+	0.0698840i	0.885494	−	0.464651i	$-0.153820\pi$
$449$	0.854949	+	1.48081i	0.0403475	+	0.0698840i	−0.845146	+	0.534535i	$0.820487\pi$
$450$		0			0
$451$	1.19188	−	2.06440i	0.0561235	−	0.0972088i
$452$	0.0759325	−	0.162838i	0.00357157	−	0.00765925i
$453$	4.31795	−	1.26356i	0.202875	−	0.0593671i
$454$	−4.75550	−	5.66739i	−0.223187	−	0.265984i
$455$		0			0
$456$	−5.16078	+	4.53561i	−0.241676	+	0.212400i
$457$	29.8380	−	20.8928i	1.39576	−	0.977323i	0.397548	−	0.917582i	$-0.369861\pi$
$457$	29.8380	−	20.8928i	1.39576	−	0.977323i	0.998214	−	0.0597413i	$-0.0190276\pi$
$458$	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	$0.687407\pi$
$462$	−39.1282	+	19.3477i	−1.82041	+	0.900137i
$463$	26.0036	−	12.1257i	1.20849	−	0.563527i	0.289259	−	0.957251i	$-0.406591\pi$
$463$	26.0036	−	12.1257i	1.20849	−	0.563527i	0.919229	+	0.393724i	$0.128813\pi$
$464$	3.28261	−	2.75443i	0.152391	−	0.127871i
$465$		0			0
$466$	37.2442	−	13.5558i	1.72530	−	0.627959i
$467$	−6.16460	−	23.0066i	−0.285264	−	1.06462i	−0.948646	−	0.316339i	$-0.897546\pi$
$467$	−6.16460	−	23.0066i	−0.285264	−	1.06462i	0.663382	−	0.748280i	$-0.269120\pi$
$468$	−2.22872	−	1.41319i	−0.103023	−	0.0653247i
$469$	63.9806	−	36.9392i	2.95435	−	1.70570i
$470$		0			0
$471$	15.4870	−	19.3385i	0.713602	−	0.891071i
$472$	−11.2578	+	16.0778i	−0.518181	+	0.740040i
$473$	−0.404932	+	0.578303i	−0.0186188	+	0.0265904i
$474$	−25.1036	−	3.83646i	−1.15305	−	0.176214i
$475$		0			0
$476$	−1.36946	+	0.790656i	−0.0627689	+	0.0362396i
$477$	4.55236	−	11.0569i	0.208438	−	0.506261i
$478$	−0.580749	−	2.16738i	−0.0265628	−	0.0991338i
$479$	3.81746	−	1.38944i	0.174424	−	0.0634853i	−0.253332	−	0.967379i	$-0.581526\pi$
$479$	3.81746	−	1.38944i	0.174424	−	0.0634853i	0.427756	+	0.903894i	$0.359304\pi$
$480$		0			0
$481$	−20.2014	+	16.9510i	−0.921105	+	0.772899i
$482$	4.46274	−	2.08101i	0.203272	−	0.0947873i
$483$	10.4159	+	6.94367i	0.473941	+	0.315948i
$484$	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	0.988420	−	0.151744i	$-0.0484889\pi$
$487$	18.4638	+	18.4638i	0.836676	+	0.836676i	−0.151744	+	0.988420i	$0.548489\pi$
$488$	−2.51015	+	1.75763i	−0.113629	+	0.0795640i
$489$	−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	$0.973740\pi$
$492$	−0.197136	−	0.188315i	−0.00888757	−	0.00848988i
$493$	0.583032	−	1.25032i	0.0262585	−	0.0563114i
$494$	−4.26583	+	7.38864i	−0.191929	+	0.332431i
$495$		0			0
$496$	−5.74468	−	9.95007i	−0.257944	−	0.446771i
$497$	−61.6791	+	5.39623i	−2.76669	+	0.242054i
$498$	−23.6814	+	17.4027i	−1.06119	+	0.779836i
$499$	−5.75147	+	1.01414i	−0.257471	+	0.0453991i	−0.300894	−	0.953658i	$-0.597285\pi$
$499$	−5.75147	+	1.01414i	−0.257471	+	0.0453991i	0.0434226	+	0.999057i	$0.486174\pi$
$500$		0			0
$501$	18.8837	+	15.1228i	0.843662	+	0.675635i
$502$	2.44076	+	27.8980i	0.108936	+	1.24515i
$503$	5.36150	−	20.0094i	0.239057	−	0.892174i	−0.737221	−	0.675652i	$-0.763862\pi$
$503$	5.36150	−	20.0094i	0.239057	−	0.892174i	0.976278	−	0.216522i	$-0.0694712\pi$
$504$	−8.34452	−	37.2640i	−0.371695	−	1.65987i
$505$		0			0
$506$	−2.68387	−	7.37387i	−0.119312	−	0.327808i
$507$	2.47772	+	0.603500i	0.110040	+	0.0268024i
$508$	0.395894	−	4.52509i	0.0175650	−	0.200769i
$509$	−7.40545	−	2.69536i	−0.328241	−	0.119470i	0.172643	−	0.984984i	$-0.444769\pi$
$509$	−7.40545	−	2.69536i	−0.328241	−	0.119470i	−0.500884	+	0.865515i	$0.666992\pi$
$510$		0			0
$511$	0.297412	−	1.68671i	0.0131567	−	0.0746156i
$512$	12.4157	−	12.4157i	0.548699	−	0.548699i
$513$	5.88182	+	5.12508i	0.259689	+	0.226278i
$514$		−	30.7328i		−	1.35556i
$515$		0			0
$516$	0.0533010	+	0.0606477i	0.00234644	+	0.00266987i
$517$	−12.8878	−	27.6380i	−0.566806	−	1.21552i
$518$	49.6964	+	4.34787i	2.18354	+	0.191035i
$519$	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	$0.727397\pi$
$522$	−3.21733	−	2.93556i	−0.140819	−	0.128486i
$523$	12.7057	+	3.40449i	0.555583	+	0.148868i	0.525676	−	0.850685i	$-0.323812\pi$
$523$	12.7057	+	3.40449i	0.555583	+	0.148868i	0.0299067	+	0.999553i	$0.490479\pi$
$524$	−0.865339	−	0.726106i	−0.0378025	−	0.0317201i
$525$		0			0
$526$	4.44587	+	25.2138i	0.193849	+	1.09937i
$527$	−3.02998	−	2.12161i	−0.131988	−	0.0924189i
$528$	−10.7445	+	24.4893i	−0.467593	+	1.06576i
$529$	13.3376	−	15.8951i	0.579894	−	0.691091i
$530$		0			0
$531$	19.7901	+	10.2486i	0.858818	+	0.444751i
$532$	1.61560	−	0.432899i	0.0700452	−	0.0187686i
$533$	2.34695	+	1.09440i	0.101658	+	0.0474037i
$534$	−5.20725	+	9.51557i	−0.225340	+	0.411779i
$535$		0			0
$536$	13.8568	−	38.0712i	0.598523	−	1.64443i
$537$	11.2075	+	0.722598i	0.483640	+	0.0311824i
$538$	4.80887	+	6.86778i	0.207325	+	0.296091i
$539$	−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	$0.298527\pi$
$542$	13.4364	+	19.1892i	0.577145	+	0.824248i
$543$	5.92906	+	11.9907i	0.254440	+	0.514572i
$544$	−0.631962	+	1.73630i	−0.0270951	+	0.0744433i
$545$		0			0
$546$	−24.6429	−	40.5128i	−1.05462	−	1.73379i
$547$	−29.7950	−	13.8936i	−1.27394	−	0.594049i	−0.336334	−	0.941743i	$-0.609187\pi$
$547$	−29.7950	−	13.8936i	−1.27394	−	0.594049i	−0.937608	+	0.347694i	$0.886965\pi$
$548$	0.406429	−	0.108902i	0.0173618	−	0.00465208i
$549$	2.35615	+	2.56032i	0.100558	+	0.109272i
$550$		0			0
$551$	−0.937961	+	1.11782i	−0.0399585	+	0.0476207i
$552$	6.82333	−	0.754628i	0.290420	−	0.0321191i
$553$	−38.7374	−	27.1242i	−1.64728	−	1.15344i
$554$	6.37122	+	36.1330i	0.270687	+	1.53514i
$555$		0			0
$556$	−0.511259	−	0.428997i	−0.0216822	−	0.0181935i
$557$	25.1830	+	6.74775i	1.06704	+	0.285911i	0.749275	−	0.662259i	$-0.230402\pi$
$557$	25.1830	+	6.74775i	1.06704	+	0.285911i	0.317761	+	0.948171i	$0.397069\pi$
$558$	−9.24922	+	7.12851i	−0.391551	+	0.301774i
$559$	−0.664181	−	0.383465i	−0.0280919	−	0.0162188i
$560$		0			0
$561$	0.196982	+	8.60737i	0.00831657	+	0.363404i
$562$	1.08273	+	0.0947268i	0.0456723	+	0.00399581i
$563$	−12.7775	−	27.4015i	−0.538510	−	1.15484i	−0.967811	−	0.251676i	$-0.919018\pi$
$563$	−12.7775	−	27.4015i	−0.538510	−	1.15484i	0.429302	−	0.903161i	$-0.358760\pi$
$564$	−3.41993	+	0.684052i	−0.144005	+	0.0288038i
$565$		0			0
$566$			32.2643i			1.35617i
$567$	−40.6819	+	15.0035i	−1.70848	+	0.630087i
$568$	−24.0089	+	24.0089i	−1.00739	+	1.00739i
$569$	−3.82709	+	21.7045i	−0.160440	+	0.909901i	0.793202	+	0.608959i	$0.208412\pi$
$569$	−3.82709	+	21.7045i	−0.160440	+	0.909901i	−0.953642	+	0.300943i	$0.902699\pi$
$570$		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	$0.651602\pi$
$572$	−0.268484	+	3.06878i	−0.0112259	+	0.128312i
$573$	11.1017	−	11.6217i	0.463778	−	0.485503i
$574$	−1.67545	−	4.60327i	−0.0699321	−	0.192137i
$575$		0			0
$576$	−16.3862	−	12.5182i	−0.682758	−	0.521592i
$577$	−4.26360	+	15.9120i	−0.177496	+	0.662424i	0.818617	+	0.574340i	$0.194741\pi$
$577$	−4.26360	+	15.9120i	−0.177496	+	0.662424i	−0.996113	+	0.0880841i	$0.971926\pi$
$578$	−1.95088	−	22.2986i	−0.0811458	−	0.927501i
$579$	−6.67638	+	43.6864i	−0.277461	+	1.81555i
$580$		0			0
$581$	−53.8941	+	9.50299i	−2.23590	+	0.394250i
$582$	−1.83112	−	16.5569i	−0.0759023	−	0.686307i
$583$	−13.9048	+	1.21651i	−0.575877	+	0.0503827i
$584$	−0.469626	−	0.813416i	−0.0194332	−	0.0336594i
$585$		0			0
$586$	−6.84714	+	11.8596i	−0.282853	+	0.489916i
$587$	1.01370	−	2.17389i	0.0418400	−	0.0897262i	−0.884277	−	0.466963i	$-0.845348\pi$
$587$	1.01370	−	2.17389i	0.0418400	−	0.0897262i	0.926117	+	0.377237i	$0.123126\pi$
$588$	−1.53652	+	6.30830i	−0.0633648	+	0.260150i
$589$	2.51487	+	2.99711i	0.103623	+	0.123494i
$590$		0			0
$591$	20.5705	+	6.95833i	0.846157	+	0.286227i
$592$	25.0359	−	17.5303i	1.02897	−	0.720491i
$593$	19.8531	+	19.8531i	0.815268	+	0.815268i	0.985418	−	0.170150i	$-0.0544254\pi$
$593$	19.8531	+	19.8531i	0.815268	+	0.815268i	−0.170150	+	0.985418i	$0.554425\pi$
$594$	26.1189	+	7.52254i	1.07167	+	0.308653i
$595$		0			0
$596$	3.75073	+	0.661355i	0.153636	+	0.0270902i
$597$	−1.55142	+	24.0626i	−0.0634955	+	0.984817i
$598$	7.72592	−	3.60265i	0.315936	−	0.147323i
$599$	12.9672	−	10.8807i	0.529824	−	0.444575i	−0.338217	−	0.941068i	$-0.609824\pi$
$599$	12.9672	−	10.8807i	0.529824	−	0.444575i	0.868041	+	0.496493i	$0.165379\pi$
$600$		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	$0.571088\pi$
$602$	0.375496	+	1.40137i	0.0153041	+	0.0571155i
$603$	−44.9340	−	9.86129i	−1.82985	−	0.401583i
$604$	−0.520160	+	0.300315i	−0.0211650	+	0.0122196i
$605$		0			0
$606$	−5.75272	−	14.7466i	−0.233688	−	0.599040i
$607$	3.73971	−	5.34086i	0.151790	−	0.216779i	−0.736054	−	0.676922i	$-0.763313\pi$
$607$	3.73971	−	5.34086i	0.151790	−	0.216779i	0.887844	+	0.460144i	$0.152202\pi$
$608$	1.12099	−	1.60095i	0.0454623	−	0.0649270i
$609$	−2.94752	−	7.55571i	−0.119440	−	0.306173i
$610$		0			0
$611$	28.6898	−	16.5640i	1.16066	−	0.670109i
$612$	0.961776	+	0.211073i	0.0388775	+	0.00853213i
$613$	2.83651	+	10.5860i	0.114566	+	0.427565i	0.999254	−	0.0386179i	$-0.0122955\pi$
$613$	2.83651	+	10.5860i	0.114566	+	0.427565i	−0.884688	+	0.466183i	$0.845629\pi$
$614$	−10.1887	+	3.70839i	−0.411183	+	0.149658i
$615$		0			0
$616$	−34.1469	+	28.6527i	−1.37582	+	1.15445i
$617$	31.5164	−	14.6963i	1.26880	−	0.591652i	0.332585	−	0.943073i	$-0.392079\pi$
$617$	31.5164	−	14.6963i	1.26880	−	0.591652i	0.936217	+	0.351421i	$0.114302\pi$
$618$	−1.25417	+	19.4522i	−0.0504501	+	0.782483i
$619$	31.5714	+	5.56690i	1.26896	+	0.223753i	0.767288	−	0.641303i	$-0.221606\pi$
$619$	31.5714	+	5.56690i	1.26896	+	0.223753i	0.501676	+	0.865056i	$0.332717\pi$
$620$		0			0
$621$	−1.87693	−	7.56563i	−0.0753185	−	0.303598i
$622$	23.9081	+	23.9081i	0.958628	+	0.958628i
$623$	−16.5462	+	11.5858i	−0.662910	+	0.464175i
$624$	−27.5197	−	9.30903i	−1.10167	−	0.372659i
$625$		0			0
$626$	3.96982	+	4.73105i	0.158666	+	0.189091i
$627$	2.15510	−	8.84795i	0.0860663	−	0.353353i
$628$	−1.39784	+	2.99768i	−0.0557799	+	0.119620i
$629$	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	$0.482612\pi$
$632$	−25.8347	+	2.26024i	−1.02765	+	0.0899076i
$633$	−3.82985	−	34.6294i	−0.152223	−	1.37640i
$634$	47.3526	−	8.34954i	1.88061	−	0.331603i
$635$		0			0
$636$	−0.241160	+	1.57801i	−0.00956262	+	0.0625723i
$637$	−5.37507	−	61.4373i	−0.212968	−	2.43423i
$638$	−1.31583	+	4.91073i	−0.0520940	+	0.194418i
$639$	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	$-0.468786\pi$
$642$	24.9311	−	26.0989i	0.983950	−	1.03004i
$643$	−3.17500	+	36.2904i	−0.125210	+	1.43115i	0.630472	+	0.776212i	$0.282862\pi$
$643$	−3.17500	+	36.2904i	−0.125210	+	1.43115i	−0.755681	+	0.654940i	$0.772694\pi$
$644$	−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	$0.605791\pi$
$647$	−32.3432	+	32.3432i	−1.27154	+	1.27154i	−0.945278	+	0.326266i	$0.894209\pi$
$648$	−11.8015	+	20.6433i	−0.463606	+	0.810945i
$649$		−	26.0149i		−	1.02118i
$650$		0			0
$651$	−21.3230	+	4.26501i	−0.835714	+	0.167159i
$652$	1.10683	+	2.37361i	0.0433469	+	0.0929578i
$653$	−11.8869	−	1.03997i	−0.465170	−	0.0406971i	−0.147838	−	0.989012i	$-0.547231\pi$
$653$	−11.8869	−	1.03997i	−0.465170	−	0.0406971i	−0.317332	+	0.948314i	$0.602787\pi$
$654$	−0.119608	−	5.22642i	−0.00467703	−	0.204369i
$655$		0			0
$656$	−2.59913	−	1.50061i	−0.101479	−	0.0585890i
$657$	−0.844725	+	0.651043i	−0.0329559	+	0.0253996i
$658$	−60.5331	−	16.2198i	−2.35983	−	0.632314i
$659$	−17.0150	−	14.2773i	−0.662811	−	0.556165i	0.248117	−	0.968730i	$-0.420188\pi$
$659$	−17.0150	−	14.2773i	−0.662811	−	0.556165i	−0.910928	+	0.412565i	$0.864633\pi$
$660$		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	$-0.370078\pi$
$662$	2.39894	+	1.67976i	0.0932376	+	0.0652857i
$663$	−9.29628	+	1.02813i	−0.361038	+	0.0399291i
$664$	−19.2908	+	22.9899i	−0.748629	+	0.892181i
$665$		0			0
$666$	−21.0350	−	22.8578i	−0.815090	−	0.885721i
$667$	1.40832	−	0.377358i	0.0545304	−	0.0146114i
$668$	−2.92718	−	1.36497i	−0.113256	−	0.0528122i
$669$	−19.7193	−	32.4186i	−0.762393	−	1.25337i
$670$		0			0
$671$	1.38915	−	3.81665i	0.0536274	−	0.147340i
$672$	4.81474	+	9.73718i	0.185733	+	0.375620i
$673$	24.6347	+	35.1820i	0.949599	+	1.35617i	0.934378	+	0.356284i	$0.115956\pi$
$673$	24.6347	+	35.1820i	0.949599	+	1.35617i	0.0152212	+	0.999884i	$0.495155\pi$
$674$	−25.0834			−0.966176
$675$		0			0
$676$	−0.340452			−0.0130943
$677$	−15.4492	−	22.0638i	−0.593761	−	0.847979i	0.404007	−	0.914756i	$-0.367617\pi$
$677$	−15.4492	−	22.0638i	−0.593761	−	0.847979i	−0.997768	+	0.0667769i	$0.978728\pi$
$678$	−2.00615	−	0.129345i	−0.0770458	−	0.00496748i
$679$	10.6093	−	29.1489i	0.407149	−	1.11863i
$680$		0			0
$681$	−4.11821	+	7.52549i	−0.157810	+	0.288377i
$682$	12.3540	+	5.76078i	0.473060	+	0.220592i
$683$	18.3215	−	4.90923i	0.701053	−	0.187846i	0.109351	−	0.994003i	$-0.465123\pi$
$683$	18.3215	−	4.90923i	0.701053	−	0.187846i	0.591702	+	0.806157i	$0.298456\pi$
$684$	−0.924849	−	0.478946i	−0.0353625	−	0.0183130i
$685$		0			0
$686$	−42.6101	+	50.7807i	−1.62686	+	1.93882i
$687$	0.758341	−	1.72845i	0.0289325	−	0.0659445i
$688$	0.728099	+	0.509820i	0.0277585	+	0.0194367i
$689$	−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	$0.579993\pi$
$692$	−0.903362	−	0.242055i	−0.0343407	−	0.00920155i
$693$	37.3897	+	34.1152i	1.42032	+	1.29593i
$694$	4.06379	+	2.34623i	0.154259	+	0.0890616i
$695$		0			0
$696$	−3.90164	−	2.13511i	−0.147891	−	0.0809311i
$697$	−0.962547	−	0.0842119i	−0.0364591	−	0.00318975i
$698$	7.85598	+	16.8472i	0.297353	+	0.637676i
$699$	−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	$0.817132\pi$
$702$	−5.66797	+	28.9782i	−0.213924	+	1.09371i
$703$	−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
$707$	2.56901	−	29.3639i	0.0966175	−	1.10434i
$708$	−2.89076	−	0.704104i	−0.108641	−	0.0264618i
$709$	0.183502	+	0.504167i	0.00689155	+	0.0189344i	0.943091	−	0.332536i	$-0.107904\pi$
$709$	0.183502	+	0.504167i	0.00689155	+	0.0189344i	−0.936199	+	0.351470i	$0.885682\pi$
$710$		0			0
$711$	6.43464	+	28.7351i	0.241318	+	1.07765i
$712$	−2.86697	+	10.6997i	−0.107444	+	0.400988i
$713$	−0.340710	−	3.89433i	−0.0127597	−	0.145844i
$714$	13.8103	+	11.0598i	0.516837	+	0.413902i
$715$		0			0
$716$	−1.47655	+	0.260356i	−0.0551814	+	0.00972997i
$717$	−2.09660	+	1.54073i	−0.0782989	+	0.0575394i
$718$	15.6951	−	1.37315i	0.585737	−	0.0512453i
$719$	−2.44660	−	4.23763i	−0.0912427	−	0.158037i	0.816792	−	0.576933i	$-0.195751\pi$
$719$	−2.44660	−	4.23763i	−0.0912427	−	0.158037i	−0.908034	+	0.418896i	$0.862417\pi$
$720$		0			0
$721$	−18.1492	+	31.4353i	−0.675911	+	1.17071i
$722$	10.5713	−	22.6702i	0.393422	−	0.843697i
$723$	−4.12869	−	3.94394i	−0.153548	−	0.146677i
$724$	−1.14789	−	1.36800i	−0.0426608	−	0.0508412i
$725$		0			0
$726$	−0.641079	−	3.20508i	−0.0237927	−	0.118952i
$727$	−4.02773	+	2.82025i	−0.149380	+	0.104597i	−0.645877	−	0.763441i	$-0.723508\pi$
$727$	−4.02773	+	2.82025i	−0.149380	+	0.104597i	0.496497	+	0.868038i	$0.334619\pi$
$728$	−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
$732$	−0.386505	−	0.257660i	−0.0142857	−	0.00952339i
$733$	12.8830	−	6.00742i	0.475843	−	0.221889i	−0.169874	−	0.985466i	$-0.554336\pi$
$733$	12.8830	−	6.00742i	0.475843	−	0.221889i	0.645717	+	0.763576i	$0.276558\pi$
$734$	−4.07991	+	3.42345i	−0.150592	+	0.126362i
$735$		0			0
$736$	−1.83501	+	0.667889i	−0.0676394	+	0.0246187i
$737$	13.8985	+	51.8700i	0.511959	+	1.91066i
$738$	−1.16132	+	2.82065i	−0.0427488	+	0.103830i
$739$	−28.3320	+	16.3575i	−1.04221	+	0.601721i	−0.920459	−	0.390840i	$-0.872185\pi$
$739$	−28.3320	+	16.3575i	−1.04221	+	0.601721i	−0.121752	+	0.992561i	$0.538851\pi$
$740$		0			0
$741$	9.77933	+	1.49453i	0.359253	+	0.0549028i
$742$	−16.4524	+	23.4964i	−0.603986	+	0.862581i
$743$	−0.622633	+	0.889212i	−0.0228422	+	0.0326220i	−0.830411	−	0.557152i	$-0.811894\pi$
$743$	−0.622633	+	0.889212i	−0.0228422	+	0.0326220i	0.807569	+	0.589774i	$0.200783\pi$
$744$	−7.45425	+	9.30809i	−0.273286	+	0.341251i
$745$		0			0
$746$	32.6505	−	18.8508i	1.19542	−	0.690177i
$747$	28.7792	+	18.2483i	1.05297	+	0.667671i
$748$	−0.297487	−	1.11024i	−0.0108772	−	0.0405943i
$749$	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	$0.351360\pi$
$752$	−34.7970	+	16.2261i	−1.26892	+	0.591706i
$753$	29.1085	−	14.3933i	1.06077	−	0.524520i
$754$	−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	0.760254	−	0.649626i	$-0.225075\pi$
$757$	3.04376	+	3.04376i	0.110627	+	0.110627i	−0.649626	+	0.760254i	$0.725075\pi$
$758$	−34.1013	+	23.8780i	−1.23862	+	0.867288i
$759$	−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	$0.881444\pi$
$762$	−48.7783	+	14.2739i	−1.76705	+	0.517090i
$763$	4.11418	−	8.82288i	0.148943	−	0.319410i
$764$	−1.07282	+	1.85819i	−0.0388134	+	0.0672268i
$765$		0			0
$766$	−28.2771	−	48.9773i	−1.02169	−	1.76962i
$767$	28.1535	−	2.46311i	1.01656	−	0.0889377i
$768$	8.68909	+	3.81226i	0.313541	+	0.137563i
$769$	−29.6816	+	5.23367i	−1.07035	+	0.188731i	−0.680943	−	0.732336i	$-0.738430\pi$
$769$	−29.6816	+	5.23367i	−1.07035	+	0.188731i	−0.389404	+	0.921067i	$0.627319\pi$
$770$		0			0
$771$	−33.1993	+	12.9512i	−1.19564	+	0.466427i
$772$	−0.514213	−	5.87749i	−0.0185069	−	0.211535i
$773$	−11.6749	+	43.5713i	−0.419917	+	1.56715i	0.354862	+	0.934919i	$0.384528\pi$
$773$	−11.6749	+	43.5713i	−0.419917	+	1.56715i	−0.774779	+	0.632232i	$0.782139\pi$
$774$	0.415436	−	0.802212i	0.0149326	−	0.0288349i
$775$		0			0
$776$	−5.81811	−	15.9851i	−0.208858	−	0.573832i
$777$	−16.2459	−	55.5172i	−0.582820	−	1.99167i
$778$	0.499302	−	5.70705i	0.0179008	−	0.204608i
$779$	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
$783$	−1.81534	+	4.71263i	−0.0648748	+	0.168416i
$784$			71.4757i			2.55270i
$785$		0			0
$786$	−4.04997	+	11.9727i	−0.144458	+	0.427052i
$787$	−14.8817	−	31.9138i	−0.530474	−	1.13761i	−0.970827	−	0.239780i	$-0.922925\pi$
$787$	−14.8817	−	31.9138i	−0.530474	−	1.13761i	0.440353	−	0.897825i	$-0.354853\pi$
$788$	−2.88803	−	0.252670i	−0.102882	−	0.00900100i
$789$	25.3639	−	15.4281i	0.902978	−	0.549256i
$790$		0			0
$791$	−3.24199	−	1.87177i	−0.115272	−	0.0665523i
$792$	27.7329	+	1.15169i	0.985445	+	0.0409234i
$793$	4.26192	+	1.14198i	0.151345	+	0.0405528i
$794$	5.14028	+	4.31321i	0.182422	+	0.153070i
$795$		0			0
$796$	−0.558987	−	3.17017i	−0.0198128	−	0.112364i
$797$	−28.1820	−	19.7333i	−0.998259	−	0.698989i	−0.0443290	−	0.999017i	$-0.514115\pi$
$797$	−28.1820	−	19.7333i	−0.998259	−	0.698989i	−0.953930	+	0.300028i	$0.903004\pi$
$798$	−11.0821	−	15.0803i	−0.392300	−	0.533837i
$799$	−7.94536	+	9.46891i	−0.281087	+	0.334986i
$800$		0			0
$801$	12.4737	+	1.61518i	0.440736	+	0.0570696i
$802$	−14.7066	+	3.94062i	−0.519308	+	0.139148i
$803$	1.12829	+	0.526128i	0.0398163	+	0.0185667i
$804$	6.13993	−	0.140514i	0.216539	−	0.00495553i
$805$		0			0
$806$	−5.06465	+	13.9150i	−0.178395	+	0.490135i
$807$	5.39245	−	8.08901i	0.189823	−	0.284746i
$808$	−9.27159	−	13.2412i	−0.326173	−	0.465824i
$809$	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	$0.360782\pi$
$812$	0.621033	+	0.886927i	0.0217940	+	0.0311250i
$813$	15.0670	−	22.6014i	0.528424	−	0.792667i
$814$	−12.4019	+	34.0739i	−0.434685	+	1.19429i
$815$		0			0
$816$	10.8369	−	0.248005i	0.379368	−	0.00868192i
$817$	−0.274318	−	0.127917i	−0.00959717	−	0.00447523i
$818$	−33.7588	+	9.04564i	−1.18035	+	0.316273i
$819$	−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	$0.268090\pi$
$822$	−2.78786	−	3.79368i	−0.0972377	−	0.132320i
$823$	−2.18373	−	1.52906i	−0.0761200	−	0.0532998i	0.534897	−	0.844917i	$-0.320350\pi$
$823$	−2.18373	−	1.52906i	−0.0761200	−	0.0532998i	−0.611017	+	0.791617i	$0.709239\pi$
$824$	3.45661	+	19.6034i	0.120417	+	0.682917i
$825$		0			0
$826$	−40.9538	−	34.3643i	−1.42497	−	1.19569i
$827$	−7.49264	−	2.00765i	−0.260545	−	0.0698128i	0.126182	−	0.992007i	$-0.459728\pi$
$827$	−7.49264	−	2.00765i	−0.260545	−	0.0698128i	−0.386727	+	0.922194i	$0.626394\pi$
$828$	0.482480	+	0.922037i	0.0167673	+	0.0320430i
$829$	−36.4123	−	21.0226i	−1.26465	−	0.730147i	−0.290680	−	0.956820i	$-0.593882\pi$
$829$	−36.4123	−	21.0226i	−1.26465	−	0.730147i	−0.973971	+	0.226674i	$0.927215\pi$
$830$		0			0
$831$	36.3480	−	22.1095i	1.26090	−	0.766971i
$832$	−26.0493	−	2.27902i	−0.903096	−	0.0790106i
$833$	9.72492	+	20.8552i	0.336948	+	0.722588i
$834$	−2.39280	+	7.07369i	−0.0828559	+	0.244942i
$835$		0			0
$836$			1.21575i			0.0420477i
$837$	11.5984	+	6.98749i	0.400899	+	0.241523i
$838$	1.57481	−	1.57481i	0.0544008	−	0.0544008i
$839$	7.44120	−	42.2011i	0.256899	−	1.45694i	−0.534253	−	0.845325i	$-0.679407\pi$
$839$	7.44120	−	42.2011i	0.256899	−	1.45694i	0.791152	−	0.611620i	$-0.209482\pi$
$840$		0			0
$841$	26.3634	+	9.59551i	0.909084	+	0.330880i
$842$	2.40885	−	27.5332i	0.0830143	−	0.948858i
$843$	−0.353949	−	1.20955i	−0.0121907	−	0.0416591i
$844$	1.59083	+	4.37077i	0.0547587	+	0.150448i
$845$		0			0
$846$	21.0371	+	32.8669i	0.723269	+	1.12999i
$847$	1.57533	−	5.87920i	0.0541289	−	0.202012i
$848$	1.53162	+	17.5065i	0.0525960	+	0.601175i
$849$	34.8538	−	13.5966i	1.19618	−	0.466635i
$850$		0			0
$851$	10.2410	−	1.80577i	0.351057	−	0.0619008i
$852$	−4.71330	−	2.06791i	−0.161475	−	0.0708456i
$853$	−17.1159	+	1.49745i	−0.586038	+	0.0512717i	−0.376319	−	0.926490i	$-0.622810\pi$
$853$	−17.1159	+	1.49745i	−0.586038	+	0.0512717i	−0.209719	+	0.977762i	$0.567255\pi$
$854$	−4.17334	−	7.22844i	−0.142809	−	0.247352i
$855$		0			0
$856$	18.4291	−	31.9201i	0.629893	−	1.09101i
$857$	8.99607	−	19.2921i	0.307300	−	0.659007i	−0.690637	−	0.723201i	$-0.742670\pi$
$857$	8.99607	−	19.2921i	0.307300	−	0.659007i	0.997937	+	0.0641943i	$0.0204477\pi$
$858$	33.0800	−	9.68017i	1.12933	−	0.330475i
$859$	5.67148	+	6.75901i	0.193509	+	0.230615i	0.854071	−	0.520157i	$-0.174126\pi$
$859$	5.67148	+	6.75901i	0.193509	+	0.230615i	−0.660562	+	0.750771i	$0.729682\pi$
$860$		0			0
$861$	−4.26666	+	3.74981i	−0.145408	+	0.127793i
$862$	−23.6126	+	16.5337i	−0.804249	+	0.563141i
$863$	31.7542	+	31.7542i	1.08093	+	1.08093i	0.996423	+	0.0845039i	$0.0269306\pi$
$863$	31.7542	+	31.7542i	1.08093	+	1.08093i	0.0845039	+	0.996423i	$0.473069\pi$
$864$	1.87201	−	6.49976i	0.0636870	−	0.221126i
$865$		0			0
$866$	31.2896	+	5.51721i	1.06327	+	0.187482i
$867$	−23.2662	+	11.5044i	−0.790160	+	0.390710i
$868$	2.63105	−	1.22688i	0.0893038	−	0.0416430i
$869$	26.3314	−	22.0947i	0.893233	−	0.749511i
$870$		0			0
$871$	−54.8180	+	19.9521i	−1.85744	+	0.676052i
$872$	−1.38173	−	5.15670i	−0.0467914	−	0.174628i
$873$	−17.1141	+	8.95541i	−0.579225	+	0.303095i
$874$	2.91359	−	1.68216i	0.0985535	−	0.0568999i
$875$		0			0
$876$	0.0890004	−	0.111134i	0.00300705	−	0.00375488i
$877$	−11.1328	+	15.8993i	−0.375928	+	0.536880i	−0.961882	−	0.273464i	$-0.911831\pi$
$877$	−11.1328	+	15.8993i	−0.375928	+	0.536880i	0.585955	+	0.810344i	$0.300720\pi$
$878$	8.56430	−	12.2311i	0.289031	−	0.412779i
$879$	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	$0.406479\pi$
$882$	72.0042	−	9.63555i	2.42451	−	0.324446i
$883$	−8.04527	−	30.0253i	−0.270745	−	1.01043i	−0.958640	−	0.284623i	$-0.908132\pi$
$883$	−8.04527	−	30.0253i	−0.270745	−	1.01043i	0.687895	−	0.725810i	$-0.258535\pi$
$884$	1.17334	−	0.427060i	0.0394636	−	0.0143636i
$885$		0			0
$886$	35.3409	−	29.6546i	1.18730	−	0.996264i
$887$	21.6538	−	10.0974i	0.727065	−	0.339036i	−0.0235979	−	0.999722i	$-0.507512\pi$
$887$	21.6538	−	10.0974i	0.727065	−	0.339036i	0.750663	+	0.660686i	$0.229734\pi$
$888$	−26.3947	−	17.5958i	−0.885749	−	0.590476i
$889$	−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
$893$	10.7099	−	7.49912i	0.358392	−	0.250949i
$894$	−8.35801	−	41.7860i	−0.279534	−	1.39753i
$895$		0			0
$896$	39.8584	+	47.5014i	1.33158	+	1.58691i
$897$	−7.14761	−	6.82778i	−0.238652	−	0.227973i
$898$	−1.07942	+	2.31483i	−0.0360207	+	0.0772467i
$899$	−1.26634	+	2.19337i	−0.0422349	+	0.0731529i
$900$		0			0
$901$	2.82881	+	4.89965i	0.0942414	+	0.163231i
$902$	3.54715	−	0.310336i	0.118107	−	0.0103330i
$903$	1.35560	−	0.996189i	0.0451116	−	0.0331511i
$904$	−2.02174	+	0.356488i	−0.0672422	+	0.0118566i
$905$		0			0
$906$	5.24557	+	4.20084i	0.174272	+	0.139563i
$907$	1.82905	+	20.9061i	0.0607325	+	0.694175i	0.964140	+	0.265393i	$0.0855017\pi$
$907$	1.82905	+	20.9061i	0.0607325	+	0.694175i	−0.903408	+	0.428782i	$0.858943\pi$
$908$	0.296416	−	1.10624i	0.00983690	−	0.0367118i
$909$	−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	$-0.262695\pi$
$912$	−11.1398	−	2.71333i	−0.368876	−	0.0898472i
$913$	3.46689	−	39.6268i	0.114737	−	1.31145i
$914$	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
$918$	−1.71075	−	10.8836i	−0.0564632	−	0.359213i
$919$			21.5936i			0.712307i	0.934427	+	0.356154i	$0.115912\pi$
$919$			21.5936i			0.712307i	−0.934427	+	0.356154i	$0.884088\pi$
$920$		0			0
$921$	8.29969	+	9.44368i	0.273484	+	0.311180i
$922$	−10.9105	−	23.3976i	−0.359318	−	0.770559i
$923$	48.7032	+	4.26098i	1.60309	+	0.140252i
$924$	−5.92763	−	3.24380i	−0.195005	−	0.106713i
$925$		0			0
$926$	37.1159	+	21.4289i	1.21970	+	0.704197i
$927$	21.5419	−	6.84261i	0.707530	−	0.224741i
$928$	1.22205	+	0.327447i	0.0401158	+	0.0107490i
$929$	12.2976	+	10.3189i	0.403472	+	0.338553i	0.821834	−	0.569727i	$-0.192951\pi$
$929$	12.2976	+	10.3189i	0.403472	+	0.338553i	−0.418362	+	0.908280i	$0.637396\pi$
$930$		0			0
$931$	−4.22650	−	23.9697i	−0.138518	−	0.785575i
$932$	5.02589	+	3.51917i	0.164628	+	0.115274i
$933$	15.7517	−	35.9022i	0.515688	−	1.17538i
$934$	22.8691	−	27.2543i	0.748299	−	0.891788i
$935$		0			0
$936$	1.37940	+	30.1217i	0.0450872	+	0.984557i
$937$	−21.0951	+	5.65242i	−0.689148	+	0.184657i	−0.586365	−	0.810047i	$-0.699441\pi$
$937$	−21.0951	+	5.65242i	−0.689148	+	0.184657i	−0.102783	+	0.994704i	$0.532775\pi$
$938$	100.015	+	46.6379i	3.26561	+	1.52278i
$939$	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	$0.180469\pi$
$942$	36.9312	+	2.38112i	1.20328	+	0.0775810i
$943$	−0.585710	−	0.836480i	−0.0190733	−	0.0272395i
$944$	−32.7535			−1.06604
$945$		0			0
$946$	−1.05454			−0.0342861
$947$	9.47761	+	13.5354i	0.307981	+	0.439843i	0.943069	−	0.332597i	$-0.107925\pi$
$947$	9.47761	+	13.5354i	0.307981	+	0.439843i	−0.635088	+	0.772440i	$0.719036\pi$
$948$	−1.74248	−	3.52393i	−0.0565930	−	0.114452i
$949$	−0.462551	+	1.27085i	−0.0150150	+	0.0412535i
$950$		0			0
$951$	−28.9747	−	47.6344i	−0.939570	−	1.54465i
$952$	16.3753	+	7.63591i	0.530725	+	0.247481i
$953$	−5.23599	+	1.40298i	−0.169610	+	0.0454469i	−0.342625	−	0.939472i	$-0.611316\pi$
$953$	−5.23599	+	1.40298i	−0.169610	+	0.0454469i	0.173014	+	0.984919i	$0.444649\pi$
$954$	17.4295	−	3.90297i	0.564300	−	0.126363i
$955$		0			0
$956$	0.223273	−	0.266086i	0.00722115	−	0.00860583i
$957$	5.85937	−	0.648018i	0.189406	−	0.0209475i
$958$	4.97080	+	3.48059i	0.160599	+	0.112453i
$959$	−1.52234	−	8.63365i	−0.0491591	−	0.278795i
$960$		0			0
$961$	−18.5454	−	15.5615i	−0.598240	−	0.501983i
$962$	−38.0491	−	10.1952i	−1.22675	−	0.328707i
$963$	−38.6998	−	15.9335i	−1.24708	−	0.513451i
$964$	0.660134	+	0.381128i	0.0212615	+	0.0122753i
$965$		0			0
$966$	0.427816	+	18.6940i	0.0137647	+	0.601469i
$967$	58.9559	+	5.15797i	1.89589	+	0.165869i	0.974742	−	0.223335i	$-0.0716944\pi$
$967$	58.9559	+	5.15797i	1.89589	+	0.165869i	0.921152	+	0.389204i	$0.127250\pi$
$968$	−1.41064	−	3.02513i	−0.0453397	−	0.0972312i
$969$	−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	$-0.142976\pi$
$972$	−3.56547	−	0.529365i	−0.114362	−	0.0169794i
$973$	−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
$977$	−1.40489	+	16.0579i	−0.0449463	+	0.513738i	0.940035	+	0.341078i	$0.110792\pi$
$977$	−1.40489	+	16.0579i	−0.0449463	+	0.513738i	−0.984981	+	0.172661i	$0.944764\pi$
$978$	20.2412	−	21.1893i	0.647241	−	0.677559i
$979$	−5.02158	−	13.7967i	−0.160490	−	0.440944i
$980$		0			0
$981$	−5.59548	+	2.33169i	−0.178650	+	0.0744452i
$982$	9.89401	−	36.9250i	0.315731	−	1.17832i
$983$	−3.77419	−	43.1392i	−0.120378	−	1.37593i	−0.780682	−	0.624929i	$-0.785128\pi$
$983$	−3.77419	−	43.1392i	−0.120378	−	1.37593i	0.660304	−	0.750999i	$-0.270427\pi$
$984$	−0.470591	+	3.07928i	−0.0150019	+	0.0981638i
$985$		0			0
$986$	2.02940	−	0.357838i	0.0646293	−	0.0113959i
$987$	7.98793	+	72.2267i	0.254259	+	2.29900i
$988$	−1.31569	+	0.115108i	−0.0418577	+	0.00366208i
$989$	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	$0.901910\pi$
$992$	1.43359	−	3.07434i	0.0455164	−	0.0976103i
$993$	0.803625	−	3.29935i	0.0255023	−	0.104702i
$994$	−59.4476	−	70.8468i	−1.88556	−	2.24713i
$995$		0			0
$996$	−4.30947	−	1.45775i	−0.136551	−	0.0461906i
$997$	−8.29837	+	5.81058i	−0.262812	+	0.184023i	−0.697554	−	0.716532i	$-0.745728\pi$
$997$	−8.29837	+	5.81058i	−0.262812	+	0.184023i	0.434742	+	0.900555i	$0.356839\pi$
$998$	−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.407.12		192
5.2	odd	4		135.2.q.a.83.5	yes	192
5.3	odd	4	inner	675.2.ba.b.218.12		192
5.4	even	2		135.2.q.a.2.5	✓	192
15.2	even	4		405.2.r.a.8.12		192
15.14	odd	2		405.2.r.a.332.12		192
27.14	odd	18	inner	675.2.ba.b.257.12		192
135.14	odd	18		135.2.q.a.122.5	yes	192
135.67	odd	36		405.2.r.a.233.12		192
135.68	even	36	inner	675.2.ba.b.68.12		192
135.94	even	18		405.2.r.a.152.12		192
135.122	even	36		135.2.q.a.68.5	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.5	✓	192	5.4	even	2
135.2.q.a.68.5	yes	192	135.122	even	36
135.2.q.a.83.5	yes	192	5.2	odd	4
135.2.q.a.122.5	yes	192	135.14	odd	18
405.2.r.a.8.12		192	15.2	even	4
405.2.r.a.152.12		192	135.94	even	18
405.2.r.a.233.12		192	135.67	odd	36
405.2.r.a.332.12		192	15.14	odd	2
675.2.ba.b.68.12		192	135.68	even	36	inner
675.2.ba.b.218.12		192	5.3	odd	4	inner
675.2.ba.b.257.12		192	27.14	odd	18	inner
675.2.ba.b.407.12		192	1.1	even	1	trivial

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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more