LMFDB - Embedded newform 441.2.o.e.146.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(146,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("441.146");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			146.11
Character	$\chi$	$=$	441.146
Dual form			441.2.o.e.293.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.367369 - 0.212101i) q^{2} +(-1.08640 + 1.34897i) q^{3} +(-0.910027 - 1.57621i) q^{4} +(-1.80381 - 3.12430i) q^{5} +(0.685229 - 0.265143i) q^{6} +1.62047i q^{8} +(-0.639450 - 2.93106i) q^{9} +O(q^{10})$	\(q+(-0.367369 - 0.212101i) q^{2} +(-1.08640 + 1.34897i) q^{3} +(-0.910027 - 1.57621i) q^{4} +(-1.80381 - 3.12430i) q^{5} +(0.685229 - 0.265143i) q^{6} +1.62047i q^{8} +(-0.639450 - 2.93106i) q^{9} +1.53036i q^{10} +(3.20952 + 1.85302i) q^{11} +(3.11492 + 0.484804i) q^{12} +(-5.23479 + 3.02231i) q^{13} +(6.17426 + 0.960957i) q^{15} +(-1.47635 + 2.55711i) q^{16} +1.06422 q^{17} +(-0.386765 + 1.21241i) q^{18} +3.65191i q^{19} +(-3.28304 + 5.68639i) q^{20} +(-0.786052 - 1.36148i) q^{22} +(0.314574 - 0.181620i) q^{23} +(-2.18597 - 1.76049i) q^{24} +(-4.00749 + 6.94117i) q^{25} +2.56413 q^{26} +(4.64862 + 2.32172i) q^{27} +(-0.857560 - 0.495112i) q^{29} +(-2.06441 - 1.66259i) q^{30} +(-0.939786 + 0.542586i) q^{31} +(3.89147 - 2.24674i) q^{32} +(-5.98650 + 2.31642i) q^{33} +(-0.390960 - 0.225721i) q^{34} +(-4.03805 + 3.67525i) q^{36} -8.00373 q^{37} +(0.774573 - 1.34160i) q^{38} +(1.61009 - 10.3450i) q^{39} +(5.06283 - 2.92303i) q^{40} +(2.09005 + 3.62007i) q^{41} +(-1.89758 + 3.28670i) q^{43} -6.74518i q^{44} +(-8.00405 + 7.28491i) q^{45} -0.154086 q^{46} +(-2.83849 + 4.91640i) q^{47} +(-1.84556 - 4.76962i) q^{48} +(2.94445 - 1.69998i) q^{50} +(-1.15617 + 1.43560i) q^{51} +(9.52760 + 5.50076i) q^{52} +4.53177i q^{53} +(-1.21532 - 1.83890i) q^{54} -13.3700i q^{55} +(-4.92633 - 3.96745i) q^{57} +(0.210027 + 0.363778i) q^{58} +(-5.62746 - 9.74705i) q^{59} +(-4.10407 - 10.6064i) q^{60} +(-0.0238258 - 0.0137558i) q^{61} +0.460331 q^{62} +3.99926 q^{64} +(18.8852 + 10.9034i) q^{65} +(2.69057 + 0.418758i) q^{66} +(4.86489 + 8.42624i) q^{67} +(-0.968464 - 1.67743i) q^{68} +(-0.0967553 + 0.621664i) q^{69} -5.55775i q^{71} +(4.74970 - 1.03621i) q^{72} -2.25814i q^{73} +(2.94032 + 1.69759i) q^{74} +(-5.00969 - 12.9469i) q^{75} +(5.75619 - 3.32334i) q^{76} +(-2.78569 + 3.45894i) q^{78} +(-3.26604 + 5.65694i) q^{79} +10.6522 q^{80} +(-8.18221 + 3.74853i) q^{81} -1.77320i q^{82} +(-1.52977 + 2.64964i) q^{83} +(-1.91965 - 3.32492i) q^{85} +(1.39422 - 0.804954i) q^{86} +(1.59955 - 0.618932i) q^{87} +(-3.00276 + 5.20093i) q^{88} +14.9590 q^{89} +(4.48557 - 0.978588i) q^{90} +(-0.572542 - 0.330557i) q^{92} +(0.289055 - 1.85721i) q^{93} +(2.08554 - 1.20409i) q^{94} +(11.4097 - 6.58737i) q^{95} +(-1.19692 + 7.69035i) q^{96} +(-1.67018 - 0.964277i) q^{97} +(3.37897 - 10.5922i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4} + 16 q^{9}+O(q^{10}) $ 48 * q + 24 * q^4 + 16 * q^9	$ 48 q + 24 q^{4} + 16 q^{9} - 24 q^{11} - 40 q^{15} - 24 q^{16} - 16 q^{18} - 48 q^{23} - 24 q^{25} - 24 q^{30} + 120 q^{32} - 8 q^{36} + 88 q^{39} + 48 q^{50} + 24 q^{51} + 80 q^{57} - 96 q^{60} - 48 q^{64} + 120 q^{65} + 56 q^{72} - 168 q^{74} - 88 q^{78} - 24 q^{79} - 96 q^{81} - 24 q^{85} + 24 q^{86} - 144 q^{92} - 32 q^{93} + 96 q^{95} - 72 q^{99}+O(q^{100}) $ 48 * q + 24 * q^4 + 16 * q^9 - 24 * q^11 - 40 * q^15 - 24 * q^16 - 16 * q^18 - 48 * q^23 - 24 * q^25 - 24 * q^30 + 120 * q^32 - 8 * q^36 + 88 * q^39 + 48 * q^50 + 24 * q^51 + 80 * q^57 - 96 * q^60 - 48 * q^64 + 120 * q^65 + 56 * q^72 - 168 * q^74 - 88 * q^78 - 24 * q^79 - 96 * q^81 - 24 * q^85 + 24 * q^86 - 144 * q^92 - 32 * q^93 + 96 * q^95 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.367369	−	0.212101i	−0.259769	−	0.149978i	0.364460	−	0.931219i	$-0.381254\pi$
$2$	−0.367369	−	0.212101i	−0.259769	−	0.149978i	−0.624229	+	0.781241i	$0.714587\pi$
$3$	−1.08640	+	1.34897i	−0.627236	+	0.778829i
$3$	−1.08640	+	1.34897i	−0.627236	+	0.778829i
$4$	−0.910027	−	1.57621i	−0.455013	−	0.788106i
$5$	−1.80381	−	3.12430i	−0.806690	−	1.39723i	−0.915144	−	0.403126i	$-0.867923\pi$
$5$	−1.80381	−	3.12430i	−0.806690	−	1.39723i	0.108454	−	0.994101i	$-0.465410\pi$
$6$	0.685229	−	0.265143i	0.279744	−	0.108244i
$7$		0			0
$7$		0			0
$8$			1.62047i			0.572923i
$9$	−0.639450	−	2.93106i	−0.213150	−	0.977020i
$10$			1.53036i			0.483942i
$11$	3.20952	+	1.85302i	0.967706	+	0.558705i	0.898536	−	0.438899i	$-0.144632\pi$
$11$	3.20952	+	1.85302i	0.967706	+	0.558705i	0.0691700	+	0.997605i	$0.477965\pi$
$12$	3.11492	+	0.484804i	0.899201	+	0.139951i
$13$	−5.23479	+	3.02231i	−1.45187	+	0.838238i	−0.998588	−	0.0531292i	$-0.983080\pi$
$13$	−5.23479	+	3.02231i	−1.45187	+	0.838238i	−0.453283	+	0.891367i	$0.649747\pi$
$14$		0			0
$15$	6.17426	+	0.960957i	1.59419	+	0.248118i
$16$	−1.47635	+	2.55711i	−0.369088	+	0.639279i
$17$	1.06422			0.258110			0.129055	−	0.991637i	$-0.458806\pi$
$17$	1.06422			0.258110			0.129055	+	0.991637i	$0.458806\pi$
$18$	−0.386765	+	1.21241i	−0.0911614	+	0.285767i
$19$			3.65191i			0.837806i	0.908031	+	0.418903i	$0.137585\pi$
$19$			3.65191i			0.837806i	−0.908031	+	0.418903i	$0.862415\pi$
$20$	−3.28304	+	5.68639i	−0.734109	+	1.27151i
$21$		0			0
$22$	−0.786052	−	1.36148i	−0.167587	−	0.290269i
$23$	0.314574	−	0.181620i	0.0655933	−	0.0378703i	−0.466845	−	0.884339i	$-0.654609\pi$
$23$	0.314574	−	0.181620i	0.0655933	−	0.0378703i	0.532438	+	0.846469i	$0.321276\pi$
$24$	−2.18597	−	1.76049i	−0.446209	−	0.359358i
$25$	−4.00749	+	6.94117i	−0.801497	+	1.38823i
$26$	2.56413			0.502868
$27$	4.64862	+	2.32172i	0.894627	+	0.446814i
$28$		0			0
$29$	−0.857560	−	0.495112i	−0.159245	−	0.0919401i	0.418260	−	0.908327i	$-0.362640\pi$
$29$	−0.857560	−	0.495112i	−0.159245	−	0.0919401i	−0.577505	+	0.816387i	$0.695973\pi$
$30$	−2.06441	−	1.66259i	−0.376908	−	0.303546i
$31$	−0.939786	+	0.542586i	−0.168791	+	0.0974513i	−0.582015	−	0.813178i	$-0.697736\pi$
$31$	−0.939786	+	0.542586i	−0.168791	+	0.0974513i	0.413225	+	0.910629i	$0.364402\pi$
$32$	3.89147	−	2.24674i	0.687921	−	0.397171i
$33$	−5.98650	+	2.31642i	−1.04212	+	0.403238i
$34$	−0.390960	−	0.225721i	−0.0670490	−	0.0387108i
$35$		0			0
$36$	−4.03805	+	3.67525i	−0.673009	+	0.612542i
$37$	−8.00373			−1.31580			−0.657902	−	0.753103i	$-0.728556\pi$
$37$	−8.00373			−1.31580			−0.657902	+	0.753103i	$0.728556\pi$
$38$	0.774573	−	1.34160i	0.125652	−	0.217636i
$39$	1.61009	−	10.3450i	0.257821	−	1.65653i
$40$	5.06283	−	2.92303i	0.800504	−	0.462171i
$41$	2.09005	+	3.62007i	0.326411	+	0.565360i	0.981797	−	0.189934i	$-0.0608275\pi$
$41$	2.09005	+	3.62007i	0.326411	+	0.565360i	−0.655386	+	0.755294i	$0.727494\pi$
$42$		0			0
$43$	−1.89758	+	3.28670i	−0.289378	+	0.501217i	−0.973661	−	0.227999i	$-0.926782\pi$
$43$	−1.89758	+	3.28670i	−0.289378	+	0.501217i	0.684284	+	0.729216i	$0.260115\pi$
$44$		−	6.74518i		−	1.01687i
$45$	−8.00405	+	7.28491i	−1.19317	+	1.08597i
$46$	−0.154086			−0.0227188
$47$	−2.83849	+	4.91640i	−0.414036	+	0.717131i	−0.995327	−	0.0965648i	$-0.969215\pi$
$47$	−2.83849	+	4.91640i	−0.414036	+	0.717131i	0.581291	+	0.813696i	$0.302548\pi$
$48$	−1.84556	−	4.76962i	−0.266384	−	0.688435i
$49$		0			0
$50$	2.94445	−	1.69998i	0.416408	−	0.240413i
$51$	−1.15617	+	1.43560i	−0.161896	+	0.201024i
$52$	9.52760	+	5.50076i	1.32124	+	0.762819i
$53$			4.53177i			0.622487i	0.950330	+	0.311243i	$0.100745\pi$
$53$			4.53177i			0.622487i	−0.950330	+	0.311243i	$0.899255\pi$
$54$	−1.21532	−	1.83890i	−0.165384	−	0.250243i
$55$		−	13.3700i		−	1.80281i
$56$		0			0
$57$	−4.92633	−	3.96745i	−0.652508	−	0.525502i
$58$	0.210027	+	0.363778i	0.0275779	+	0.0477664i
$59$	−5.62746	−	9.74705i	−0.732633	−	1.26896i	−0.955754	−	0.294167i	$-0.904958\pi$
$59$	−5.62746	−	9.74705i	−0.732633	−	1.26896i	0.223121	−	0.974791i	$-0.428376\pi$
$60$	−4.10407	−	10.6064i	−0.529833	−	1.36929i
$61$	−0.0238258	−	0.0137558i	−0.00305058	−	0.00176126i	0.498474	−	0.866905i	$-0.333894\pi$
$61$	−0.0238258	−	0.0137558i	−0.00305058	−	0.00176126i	−0.501525	+	0.865143i	$0.667227\pi$
$62$	0.460331			0.0584621
$63$		0			0
$64$	3.99926			0.499908
$65$	18.8852	+	10.9034i	2.34242	+	1.35240i
$66$	2.69057	+	0.418758i	0.331186	+	0.0515456i
$67$	4.86489	+	8.42624i	0.594341	+	1.02943i	0.993640	+	0.112608i	$0.0359204\pi$
$67$	4.86489	+	8.42624i	0.594341	+	1.02943i	−0.399298	+	0.916821i	$0.630746\pi$
$68$	−0.968464	−	1.67743i	−0.117444	−	0.203418i
$69$	−0.0967553	+	0.621664i	−0.0116480	+	0.0748396i
$70$		0			0
$71$		−	5.55775i		−	0.659584i	−0.944054	−	0.329792i	$-0.893021\pi$
$71$		−	5.55775i		−	0.659584i	0.944054	−	0.329792i	$-0.106979\pi$
$72$	4.74970	−	1.03621i	0.559757	−	0.122118i
$73$		−	2.25814i		−	0.264296i	−0.991230	−	0.132148i	$-0.957813\pi$
$73$		−	2.25814i		−	0.264296i	0.991230	−	0.132148i	$-0.0421874\pi$
$74$	2.94032	+	1.69759i	0.341805	+	0.197341i
$75$	−5.00969	−	12.9469i	−0.578469	−	1.49498i
$76$	5.75619	−	3.32334i	0.660280	−	0.381213i
$77$		0			0
$78$	−2.78569	+	3.45894i	−0.315417	+	0.391648i
$79$	−3.26604	+	5.65694i	−0.367458	+	0.636456i	−0.989167	−	0.146792i	$-0.953105\pi$
$79$	−3.26604	+	5.65694i	−0.367458	+	0.636456i	0.621710	+	0.783248i	$0.286438\pi$
$80$	10.6522			1.19096
$81$	−8.18221	+	3.74853i	−0.909134	+	0.416503i
$82$		−	1.77320i		−	0.195817i
$83$	−1.52977	+	2.64964i	−0.167914	+	0.290836i	−0.937686	−	0.347483i	$-0.887036\pi$
$83$	−1.52977	+	2.64964i	−0.167914	+	0.290836i	0.769772	+	0.638319i	$0.220370\pi$
$84$		0			0
$85$	−1.91965	−	3.32492i	−0.208215	−	0.360639i
$86$	1.39422	−	0.804954i	0.150343	−	0.0868004i
$87$	1.59955	−	0.618932i	0.171490	−	0.0663564i
$88$	−3.00276	+	5.20093i	−0.320095	+	0.554421i
$89$	14.9590			1.58565			0.792827	−	0.609446i	$-0.208608\pi$
$89$	14.9590			1.58565			0.792827	+	0.609446i	$0.208608\pi$
$90$	4.48557	−	0.978588i	0.472821	−	0.103152i
$91$		0			0
$92$	−0.572542	−	0.330557i	−0.0596916	−	0.0344630i
$93$	0.289055	−	1.85721i	0.0299736	−	0.192584i
$94$	2.08554	−	1.20409i	0.215107	−	0.124192i
$95$	11.4097	−	6.58737i	1.17061	−	0.675850i
$96$	−1.19692	+	7.69035i	−0.122160	+	0.784893i
$97$	−1.67018	−	0.964277i	−0.169581	−	0.0979075i	0.412807	−	0.910818i	$-0.364548\pi$
$97$	−1.67018	−	0.964277i	−0.169581	−	0.0979075i	−0.582388	+	0.812911i	$0.697882\pi$
$98$		0			0
$99$	3.37897	−	10.5922i	0.339600	−	1.06456i
$100$	14.5877			1.45877
$101$	3.21811	−	5.57394i	0.320214	−	0.554627i	−0.660318	−	0.750986i	$-0.729578\pi$
$101$	3.21811	−	5.57394i	0.320214	−	0.554627i	0.980532	+	0.196359i	$0.0629117\pi$
$102$	0.729231	−	0.282170i	0.0722046	−	0.0279389i
$103$	−8.41917	+	4.86081i	−0.829565	+	0.478950i	−0.853704	−	0.520759i	$-0.825649\pi$
$103$	−8.41917	+	4.86081i	−0.829565	+	0.478950i	0.0241385	+	0.999709i	$0.492316\pi$
$104$	−4.89756	−	8.48283i	−0.480246	−	0.831810i
$105$		0			0
$106$	0.961191	−	1.66483i	0.0933591	−	0.161703i
$107$			3.96223i			0.383043i	0.981488	+	0.191522i	$0.0613422\pi$
$107$			3.96223i			0.383043i	−0.981488	+	0.191522i	$0.938658\pi$
$108$	−0.570847	−	9.44003i	−0.0549298	−	0.908367i
$109$	−17.3253			−1.65946			−0.829729	−	0.558166i	$-0.811505\pi$
$109$	−17.3253			−1.65946			−0.829729	+	0.558166i	$0.811505\pi$
$110$	−2.83578	+	4.91172i	−0.270381	+	0.468314i
$111$	8.69529	−	10.7968i	0.825320	−	1.02479i
$112$		0			0
$113$	−8.50273	+	4.90905i	−0.799869	+	0.461805i	−0.843425	−	0.537246i	$-0.819465\pi$
$113$	−8.50273	+	4.90905i	−0.799869	+	0.461805i	0.0435562	+	0.999051i	$0.486131\pi$
$114$	0.968280	+	2.50240i	0.0906877	+	0.234371i
$115$	−1.13487	−	0.655216i	−0.105827	−	0.0610992i
$116$			1.80226i			0.167336i
$117$	12.2060	+	13.4109i	1.12844	+	1.23984i
$118$			4.77435i			0.439515i
$119$		0			0
$120$	−1.55720	+	10.0052i	−0.142153	+	0.913346i
$121$	1.36734	+	2.36830i	0.124303	+	0.215300i
$122$	0.00583524	+	0.0101069i	0.000528298	+	0.000915039i
$123$	−7.15401	−	1.11344i	−0.645055	−	0.100396i
$124$	1.71046	+	0.987535i	0.153604	+	0.0886833i
$125$	10.8769			0.972858
$126$		0			0
$127$	−11.7328			−1.04112			−0.520560	−	0.853825i	$-0.674277\pi$
$127$	−11.7328			−1.04112			−0.520560	+	0.853825i	$0.674277\pi$
$128$	−9.25214	−	5.34173i	−0.817782	−	0.472146i
$129$	−2.37213	−	6.13046i	−0.208854	−	0.539757i
$130$	−4.62522	−	8.01111i	−0.405659	−	0.702621i
$131$	−10.5013	−	18.1888i	−0.917502	−	1.58916i	−0.803197	−	0.595714i	$-0.796869\pi$
$131$	−10.5013	−	18.1888i	−0.917502	−	1.58916i	−0.114305	−	0.993446i	$-0.536464\pi$
$132$	9.09905	+	7.32799i	0.791971	+	0.637820i
$133$		0			0
$134$		−	4.12738i		−	0.356552i
$135$	−1.13151	−	18.7116i	−0.0973846	−	1.61044i
$136$			1.72453i			0.147877i
$137$	−9.76185	−	5.63600i	−0.834011	−	0.481516i	0.0212131	−	0.999775i	$-0.493247\pi$
$137$	−9.76185	−	5.63600i	−0.834011	−	0.481516i	−0.855224	+	0.518259i	$0.826580\pi$
$138$	0.167400	−	0.207858i	0.0142501	−	0.0176941i
$139$	−2.80312	+	1.61838i	−0.237758	+	0.137269i	−0.614146	−	0.789193i	$-0.710499\pi$
$139$	−2.80312	+	1.61838i	−0.237758	+	0.137269i	0.376388	+	0.926462i	$0.377166\pi$
$140$		0			0
$141$	−3.54834	−	9.17024i	−0.298824	−	0.772274i
$142$	−1.17880	+	2.04175i	−0.0989229	+	0.171340i
$143$	−22.4015			−1.87331
$144$	8.43910	+	2.69212i	0.703259	+	0.224344i
$145$			3.57236i			0.296668i
$146$	−0.478954	+	0.829572i	−0.0396385	+	0.0686559i
$147$		0			0
$148$	7.28360	+	12.6156i	0.598709	+	1.03699i
$149$	−15.5066	+	8.95277i	−1.27035	+	0.733439i	−0.975055	−	0.221966i	$-0.928753\pi$
$149$	−15.5066	+	8.95277i	−1.27035	+	0.733439i	−0.295299	+	0.955405i	$0.595419\pi$
$150$	−0.905641	+	5.81885i	−0.0739453	+	0.475107i
$151$	9.29945	−	16.1071i	0.756778	−	1.31078i	−0.187707	−	0.982225i	$-0.560106\pi$
$151$	9.29945	−	16.1071i	0.756778	−	1.31078i	0.944485	−	0.328553i	$-0.106561\pi$
$152$	−5.91782			−0.479998
$153$	−0.680512	−	3.11928i	−0.0550161	−	0.252179i
$154$		0			0
$155$	3.39040	+	1.95745i	0.272323	+	0.157226i
$156$	−17.7712	+	6.87641i	−1.42284	+	0.550553i
$157$	6.64220	−	3.83488i	0.530106	−	0.306057i	−0.210954	−	0.977496i	$-0.567657\pi$
$157$	6.64220	−	3.83488i	0.530106	−	0.306057i	0.741059	+	0.671439i	$0.234324\pi$
$158$	2.39968	−	1.38546i	0.190908	−	0.110221i
$159$	−6.11323	−	4.92334i	−0.484811	−	0.390446i
$160$	−14.0390	−	8.10540i	−1.10988	−	0.640788i
$161$		0			0
$162$	3.80095	+	0.358358i	0.298631	+	0.0281552i
$163$	−3.99313			−0.312766			−0.156383	−	0.987696i	$-0.549983\pi$
$163$	−3.99313			−0.312766			−0.156383	+	0.987696i	$0.549983\pi$
$164$	3.80400	−	6.58872i	0.297042	−	0.514492i
$165$	18.0357	+	14.5252i	1.40408	+	1.13079i
$166$	1.12398	−	0.648930i	0.0872377	−	0.0503667i
$167$	−4.26254	−	7.38293i	−0.329845	−	0.571308i	0.652636	−	0.757672i	$-0.273663\pi$
$167$	−4.26254	−	7.38293i	−0.329845	−	0.571308i	−0.982481	+	0.186363i	$0.940330\pi$
$168$		0			0
$169$	11.7687	−	20.3840i	0.905285	−	1.56800i
$170$			1.62863i			0.124910i
$171$	10.7040	−	2.33521i	0.818553	−	0.178578i
$172$	6.90738			0.526683
$173$	0.217445	−	0.376626i	0.0165320	−	0.0286343i	−0.857641	−	0.514249i	$-0.828071\pi$
$173$	0.217445	−	0.376626i	0.0165320	−	0.0286343i	0.874173	+	0.485615i	$0.161404\pi$
$174$	−0.718901	−	0.111889i	−0.0544997	−	0.00848229i
$175$		0			0
$176$	−9.47675	+	5.47140i	−0.714337	+	0.412423i
$177$	19.2622	+	2.99795i	1.44784	+	0.225340i
$178$	−5.49549	−	3.17282i	−0.411904	−	0.237813i
$179$			17.4172i			1.30183i	0.759153	+	0.650913i	$0.225614\pi$
$179$			17.4172i			1.30183i	−0.759153	+	0.650913i	$0.774386\pi$
$180$	18.7665	+	5.98661i	1.39877	+	0.446216i
$181$			17.7421i			1.31876i	0.751809	+	0.659381i	$0.229182\pi$
$181$			17.7421i			1.31876i	−0.751809	+	0.659381i	$0.770818\pi$
$182$		0			0
$183$	0.0444407	−	0.0171959i	0.00328515	−	0.00127116i
$184$	0.294309	+	0.509759i	0.0216968	+	0.0375799i
$185$	14.4372	+	25.0060i	1.06145	+	1.83848i
$186$	−0.500106	+	0.620974i	−0.0366695	+	0.0455320i
$187$	3.41562	+	1.97201i	0.249775	+	0.144208i
$188$	10.3324			0.753567
$189$		0			0
$190$	−5.58874			−0.405450
$191$	0.215525	+	0.124433i	0.0155948	+	0.00900367i	0.507777	−	0.861488i	$-0.330467\pi$
$191$	0.215525	+	0.124433i	0.0155948	+	0.00900367i	−0.492182	+	0.870492i	$0.663801\pi$
$192$	−4.34482	+	5.39489i	−0.313560	+	0.389343i
$193$	4.14876	+	7.18586i	0.298634	+	0.517250i	0.975824	−	0.218559i	$-0.0701356\pi$
$193$	4.14876	+	7.18586i	0.298634	+	0.517250i	−0.677190	+	0.735809i	$0.736802\pi$
$194$	0.409047	+	0.708491i	0.0293679	+	0.0508667i
$195$	−35.2253	+	13.6301i	−2.52253	+	0.976072i
$196$		0			0
$197$			22.5819i			1.60889i	0.594026	+	0.804446i	$0.297538\pi$
$197$			22.5819i			1.60889i	−0.594026	+	0.804446i	$0.702462\pi$
$198$	−3.48794	+	3.17456i	−0.247877	+	0.225606i
$199$			6.12003i			0.433837i	0.976190	+	0.216919i	$0.0696007\pi$
$199$			6.12003i			0.433837i	−0.976190	+	0.216919i	$0.930399\pi$
$200$	−11.2480	−	6.49401i	−0.795351	−	0.459196i
$201$	−16.6520	−	2.59170i	−1.17454	−	0.182805i
$202$	−2.36447	+	1.36513i	−0.166364	+	0.0960500i
$203$		0			0
$204$	3.31495	+	0.515936i	0.232093	+	0.0361227i
$205$	7.54011	−	13.0599i	0.526624	−	0.912140i
$206$	4.12392			0.287327
$207$	−0.733492	−	0.805899i	−0.0509812	−	0.0560139i
$208$		−	17.8479i		−	1.23753i
$209$	−6.76705	+	11.7209i	−0.468087	+	0.810750i
$210$		0			0
$211$	1.95472	+	3.38567i	0.134568	+	0.233079i	0.925432	−	0.378913i	$-0.123702\pi$
$211$	1.95472	+	3.38567i	0.134568	+	0.233079i	−0.790864	+	0.611992i	$0.790369\pi$
$212$	7.14303	−	4.12403i	0.490586	−	0.283240i
$213$	7.49725	+	6.03797i	0.513703	+	0.413715i
$214$	0.840392	−	1.45560i	0.0574480	−	0.0995029i
$215$	13.6915			0.933752
$216$	−3.76227	+	7.53295i	−0.255990	+	0.512552i
$217$		0			0
$218$	6.36476	+	3.67470i	0.431076	+	0.248882i
$219$	3.04617	+	2.45326i	0.205841	+	0.165776i
$220$	−21.0739	+	12.1670i	−1.42080	+	0.820302i
$221$	−5.57095	+	3.21639i	−0.374742	+	0.216358i
$222$	−5.48439	+	2.12213i	−0.368088	+	0.142428i
$223$	22.3165	+	12.8845i	1.49443	+	0.862807i	0.999980	−	0.00640186i	$-0.00203779\pi$
$223$	22.3165	+	12.8845i	1.49443	+	0.862807i	0.494446	+	0.869209i	$0.335371\pi$
$224$		0			0
$225$	22.9076	+	7.30765i	1.52717	+	0.487176i
$226$	4.16485			0.277042
$227$	−12.3051	+	21.3130i	−0.816718	+	1.41460i	0.0913703	+	0.995817i	$0.470875\pi$
$227$	−12.3051	+	21.3130i	−0.816718	+	1.41460i	−0.908088	+	0.418779i	$0.862458\pi$
$228$	−1.77046	+	11.3754i	−0.117252	+	0.753356i
$229$	3.94267	−	2.27630i	0.260539	−	0.150422i	−0.364042	−	0.931383i	$-0.618603\pi$
$229$	3.94267	−	2.27630i	0.260539	−	0.150422i	0.624580	+	0.780961i	$0.285270\pi$
$230$	0.277943	+	0.481412i	0.0183270	+	0.0317433i
$231$		0			0
$232$	0.802315	−	1.38965i	0.0526746	−	0.0912351i
$233$		−	26.1353i		−	1.71218i	−0.516826	−	0.856090i	$-0.672887\pi$
$233$		−	26.1353i		−	1.71218i	0.516826	−	0.856090i	$-0.327113\pi$
$234$	−1.63963	−	7.51563i	−0.107186	−	0.491312i
$235$	20.4804			1.33599
$236$	−10.2423	+	17.7402i	−0.666716	+	1.15479i
$237$	−4.08282	−	10.5515i	−0.265207	−	0.685395i
$238$		0			0
$239$	14.8933	−	8.59865i	0.963367	−	0.556200i	0.0661594	−	0.997809i	$-0.478925\pi$
$239$	14.8933	−	8.59865i	0.963367	−	0.556200i	0.897208	+	0.441609i	$0.145592\pi$
$240$	−11.5726	+	14.3696i	−0.747011	+	0.927552i
$241$	−14.4927	−	8.36738i	−0.933559	−	0.538991i	−0.0456237	−	0.998959i	$-0.514528\pi$
$241$	−14.4927	−	8.36738i	−0.933559	−	0.538991i	−0.887935	+	0.459968i	$0.847861\pi$
$242$		−	1.16005i		−	0.0745710i
$243$	3.83253	−	15.1100i	0.245857	−	0.969306i
$244$			0.0500727i			0.00320558i
$245$		0			0
$246$	2.39200	+	1.92641i	0.152508	+	0.122824i
$247$	−11.0372	−	19.1170i	−0.702281	−	1.21639i
$248$	−0.879245	−	1.52290i	−0.0558321	−	0.0967040i
$249$	−1.91234	−	4.94220i	−0.121190	−	0.313199i
$250$	−3.99583	−	2.30699i	−0.252719	−	0.145907i
$251$	−5.33468			−0.336722			−0.168361	−	0.985725i	$-0.553847\pi$
$251$	−5.33468			−0.336722			−0.168361	+	0.985725i	$0.553847\pi$
$252$		0			0
$253$	1.34618			0.0846334
$254$	4.31028	+	2.48854i	0.270451	+	0.156145i
$255$	6.57074	+	1.02266i	0.411476	+	0.0640418i
$256$	−1.73330	−	3.00216i	−0.108331	−	0.187635i
$257$	12.3100	+	21.3216i	0.767878	+	1.33000i	0.938712	+	0.344703i	$0.112021\pi$
$257$	12.3100	+	21.3216i	0.767878	+	1.33000i	−0.170834	+	0.985300i	$0.554646\pi$
$258$	−0.428828	+	2.75527i	−0.0266977	+	0.171536i
$259$		0			0
$260$		−	39.6894i		−	2.46143i
$261$	−0.902837	+	2.83016i	−0.0558842	+	0.175182i
$262$			8.90932i			0.550419i
$263$	−26.6568	−	15.3903i	−1.64373	−	0.949006i	−0.979492	−	0.201482i	$-0.935424\pi$
$263$	−26.6568	−	15.3903i	−1.64373	−	0.949006i	−0.664235	−	0.747524i	$-0.731242\pi$
$264$	−3.75370	−	9.70095i	−0.231024	−	0.597052i
$265$	14.1586	−	8.17447i	0.869756	−	0.502154i
$266$		0			0
$267$	−16.2516	+	20.1793i	−0.994580	+	1.23495i
$268$	8.85436	−	15.3362i	0.540866	−	0.936808i
$269$	−13.9809			−0.852432			−0.426216	−	0.904622i	$-0.640154\pi$
$269$	−13.9809			−0.852432			−0.426216	+	0.904622i	$0.640154\pi$
$270$	−3.55306	+	7.11405i	−0.216232	+	0.432948i
$271$		−	6.46262i		−	0.392576i	−0.980546	−	0.196288i	$-0.937111\pi$
$271$		−	6.46262i		−	0.392576i	0.980546	−	0.196288i	$-0.0628888\pi$
$272$	−1.57115	+	2.72132i	−0.0952652	+	0.165004i
$273$		0			0
$274$	2.39080	+	4.14099i	0.144433	+	0.250166i
$275$	−25.7242	+	14.8519i	−1.55123	+	0.895601i
$276$	1.06792	−	0.413224i	0.0642815	−	0.0248732i
$277$	9.55984	−	16.5581i	0.574395	−	0.994881i	−0.421712	−	0.906730i	$-0.638571\pi$
$277$	9.55984	−	16.5581i	0.574395	−	0.994881i	0.996107	−	0.0881515i	$-0.0280960\pi$
$278$	1.37304			0.0823494
$279$	2.19130	+	2.40761i	0.131190	+	0.144140i
$280$		0			0
$281$	20.0611	+	11.5823i	1.19674	+	0.690940i	0.959828	−	0.280591i	$-0.0905304\pi$
$281$	20.0611	+	11.5823i	1.19674	+	0.690940i	0.236915	+	0.971530i	$0.423864\pi$
$282$	−0.641462	+	4.12147i	−0.0381985	+	0.245430i
$283$	13.8239	−	7.98126i	0.821748	−	0.474436i	−0.0292708	−	0.999572i	$-0.509319\pi$
$283$	13.8239	−	7.98126i	0.821748	−	0.474436i	0.851019	+	0.525135i	$0.175985\pi$
$284$	−8.76020	+	5.05770i	−0.519822	+	0.300120i
$285$	−3.50933	+	22.5478i	−0.207875	+	1.33562i
$286$	8.22963	+	4.75138i	0.486628	+	0.280955i
$287$		0			0
$288$	−9.07373	−	9.96945i	−0.534674	−	0.587455i
$289$	−15.8674			−0.933379
$290$	0.757700	−	1.31237i	0.0444937	−	0.0770653i
$291$	3.11527	−	1.20543i	0.182620	−	0.0706633i
$292$	−3.55931	+	2.05497i	−0.208293	+	0.120258i
$293$	−3.34849	−	5.79975i	−0.195621	−	0.338825i	0.751483	−	0.659752i	$-0.229339\pi$
$293$	−3.34849	−	5.79975i	−0.195621	−	0.338825i	−0.947104	+	0.320927i	$0.896005\pi$
$294$		0			0
$295$	−20.3018	+	35.1637i	−1.18202	+	2.04731i
$296$		−	12.9698i		−	0.753855i
$297$	10.6176	+	16.0656i	0.616098	+	0.932218i
$298$	7.59555			0.439998
$299$	−1.09782	+	1.90148i	−0.0634886	+	0.109966i
$300$	−15.8481	+	19.6784i	−0.914992	+	1.13613i
$301$		0			0
$302$	−6.83266	+	3.94484i	−0.393175	+	0.227000i
$303$	4.02291	+	10.3967i	0.231110	+	0.597275i
$304$	−9.33836	−	5.39150i	−0.535591	−	0.309224i
$305$			0.0992519i			0.00568315i
$306$	−0.411601	+	1.29026i	−0.0235297	+	0.0737594i
$307$			8.59068i			0.490296i	0.969486	+	0.245148i	$0.0788365\pi$
$307$			8.59068i			0.490296i	−0.969486	+	0.245148i	$0.921163\pi$
$308$		0			0
$309$	2.58953	−	16.6380i	0.147313	−	0.946504i
$310$	−0.830352	−	1.43821i	−0.0471608	−	0.0816849i
$311$	2.11723	+	3.66714i	0.120057	+	0.207945i	0.919790	−	0.392411i	$-0.128359\pi$
$311$	2.11723	+	3.66714i	0.120057	+	0.207945i	−0.799733	+	0.600356i	$0.795026\pi$
$312$	16.7638	+	2.60911i	0.949065	+	0.147712i
$313$	3.10288	+	1.79145i	0.175385	+	0.101259i	0.585123	−	0.810945i	$-0.301046\pi$
$313$	3.10288	+	1.79145i	0.175385	+	0.101259i	−0.409737	+	0.912204i	$0.634380\pi$
$314$	−3.25352			−0.183607
$315$		0			0
$316$	11.8887			0.668793
$317$	−7.69566	−	4.44309i	−0.432231	−	0.249549i	0.268065	−	0.963401i	$-0.413616\pi$
$317$	−7.69566	−	4.44309i	−0.432231	−	0.249549i	−0.700297	+	0.713852i	$0.746949\pi$
$318$	1.20157	+	3.10530i	0.0673806	+	0.174137i
$319$	−1.83490	−	3.17814i	−0.102735	−	0.177942i
$320$	−7.21392	−	12.4949i	−0.403271	−	0.698485i
$321$	−5.34494	−	4.30459i	−0.298325	−	0.240259i
$322$		0			0
$323$			3.88642i			0.216246i
$324$	13.3545	+	9.48564i	0.741917	+	0.526980i
$325$		−	48.4474i		−	2.68738i
$326$	1.46695	+	0.846946i	0.0812470	+	0.0469080i
$327$	18.8222	−	23.3713i	1.04087	−	1.29244i
$328$	−5.86622	+	3.38686i	−0.323908	+	0.187008i
$329$		0			0
$330$	−3.54496	−	9.16150i	−0.195144	−	0.504324i
$331$	−7.89126	+	13.6681i	−0.433743	+	0.751265i	−0.997192	−	0.0748861i	$-0.976141\pi$
$331$	−7.89126	+	13.6681i	−0.433743	+	0.751265i	0.563449	+	0.826151i	$0.309474\pi$
$332$	5.56852			0.305612
$333$	5.11798	+	23.4594i	0.280464	+	1.28557i
$334$			3.61635i			0.197878i
$335$	17.5507	−	30.3987i	0.958898	−	1.66086i
$336$		0			0
$337$	−6.79951	−	11.7771i	−0.370393	−	0.641539i	0.619233	−	0.785207i	$-0.287444\pi$
$337$	−6.79951	−	11.7771i	−0.370393	−	0.641539i	−0.989626	+	0.143668i	$0.954110\pi$
$338$	−8.64691	+	4.99230i	−0.470330	+	0.271545i
$339$	2.61523	−	16.8032i	0.142040	−	0.912622i
$340$	−3.49386	+	6.05154i	−0.189481	+	0.328191i
$341$	−4.02168			−0.217786
$342$	−4.42761	−	1.41243i	−0.239417	−	0.0763756i
$343$		0			0
$344$	−5.32600	−	3.07497i	−0.287159	−	0.165791i
$345$	2.11679	−	0.819074i	0.113964	−	0.0440975i
$346$	−0.159765	+	0.0922404i	−0.00858902	+	0.00495887i
$347$	12.0065	−	6.93198i	0.644545	−	0.372128i	−0.141818	−	0.989893i	$-0.545295\pi$
$347$	12.0065	−	6.93198i	0.644545	−	0.372128i	0.786363	+	0.617765i	$0.211962\pi$
$348$	−2.43120	−	1.95799i	−0.130326	−	0.104959i
$349$	1.55204	+	0.896072i	0.0830789	+	0.0479656i	0.540964	−	0.841046i	$-0.318060\pi$
$349$	1.55204	+	0.896072i	0.0830789	+	0.0479656i	−0.457885	+	0.889011i	$0.651393\pi$
$350$		0			0
$351$	−31.3515	+	1.89585i	−1.67342	+	0.101193i
$352$	16.6530			0.887607
$353$	3.88049	−	6.72121i	0.206538	−	0.357734i	−0.744084	−	0.668086i	$-0.767114\pi$
$353$	3.88049	−	6.72121i	0.206538	−	0.357734i	0.950622	+	0.310352i	$0.100447\pi$
$354$	−6.44047	−	5.18688i	−0.342307	−	0.275679i
$355$	−17.3641	+	10.0252i	−0.921589	+	0.532080i
$356$	−13.6131	−	23.5786i	−0.721494	−	1.24966i
$357$		0			0
$358$	3.69421	−	6.39855i	0.195245	−	0.338174i
$359$			22.5810i			1.19178i	0.803066	+	0.595890i	$0.203201\pi$
$359$			22.5810i			1.19178i	−0.803066	+	0.595890i	$0.796799\pi$
$360$	−11.8050	−	12.9703i	−0.622178	−	0.683596i
$361$	5.66354			0.298081
$362$	3.76312	−	6.51791i	0.197785	−	0.342574i
$363$	−4.68025	−	0.728431i	−0.245650	−	0.0382327i
$364$		0			0
$365$	−7.05511	+	4.07327i	−0.369281	+	0.213205i
$366$	−0.0199734	−	0.00310865i	−0.00104403	−	0.000162492i
$367$	13.5263	+	7.80942i	0.706068	+	0.407648i	0.809603	−	0.586977i	$-0.199682\pi$
$367$	13.5263	+	7.80942i	0.706068	+	0.407648i	−0.103536	+	0.994626i	$0.533016\pi$
$368$			1.07254i			0.0559098i
$369$	9.27415	−	8.44090i	0.482793	−	0.439416i
$370$		−	12.2486i		−	0.636773i
$371$		0			0
$372$	−3.19041	+	1.23450i	−0.165415	+	0.0640059i
$373$	12.6229	+	21.8635i	0.653589	+	1.13205i	0.982246	+	0.187600i	$0.0600709\pi$
$373$	12.6229	+	21.8635i	0.653589	+	1.13205i	−0.328656	+	0.944450i	$0.606596\pi$
$374$	−0.836528	−	1.44891i	−0.0432558	−	0.0749213i
$375$	−11.8167	+	14.6726i	−0.610212	+	0.757691i
$376$	−7.96689	−	4.59969i	−0.410861	−	0.237211i
$377$	5.98553			0.308271
$378$		0			0
$379$	14.7721			0.758792			0.379396	−	0.925234i	$-0.376132\pi$
$379$	14.7721			0.758792			0.379396	+	0.925234i	$0.376132\pi$
$380$	−20.7662	−	11.9894i	−1.06528	−	0.615041i
$381$	12.7466	−	15.8273i	0.653028	−	0.810855i
$382$	−0.0527847	−	0.0914258i	−0.00270070	−	0.00467775i
$383$	−5.29503	−	9.17127i	−0.270564	−	0.468630i	0.698443	−	0.715666i	$-0.253877\pi$
$383$	−5.29503	−	9.17127i	−0.270564	−	0.468630i	−0.969006	+	0.247036i	$0.920543\pi$
$384$	17.2574	−	6.67760i	0.880664	−	0.340765i
$385$		0			0
$386$		−	3.51982i		−	0.179154i
$387$	10.8469	+	3.46023i	0.551379	+	0.175893i
$388$			3.51007i			0.178197i
$389$	−11.7642	−	6.79207i	−0.596469	−	0.344371i	0.171182	−	0.985239i	$-0.445241\pi$
$389$	−11.7642	−	6.79207i	−0.596469	−	0.344371i	−0.767651	+	0.640868i	$0.778575\pi$
$390$	15.8316	+	2.46402i	0.801666	+	0.124771i
$391$	0.334775	−	0.193282i	0.0169303	−	0.00977471i
$392$		0			0
$393$	35.9448	+	5.59442i	1.81317	+	0.282201i
$394$	4.78963	−	8.29588i	0.241298	−	0.417940i
$395$	23.5653			1.18570
$396$	−19.7705	+	4.31320i	−0.993505	+	0.216747i
$397$			38.9108i			1.95287i	0.215801	+	0.976437i	$0.430764\pi$
$397$			38.9108i			1.95287i	−0.215801	+	0.976437i	$0.569236\pi$
$398$	1.29806	−	2.24831i	0.0650660	−	0.112698i
$399$		0			0
$400$	−11.8329	−	20.4952i	−0.591645	−	1.02476i
$401$	24.8956	−	14.3735i	1.24323	−	0.717778i	0.273477	−	0.961878i	$-0.411826\pi$
$401$	24.8956	−	14.3735i	1.24323	−	0.717778i	0.969750	+	0.244101i	$0.0784928\pi$
$402$	5.56773	+	4.48401i	0.277693	+	0.223642i
$403$	3.27972	−	5.68065i	0.163375	−	0.282973i
$404$	−11.7143			−0.582807
$405$	26.4707	+	18.8020i	1.31534	+	0.934279i
$406$		0			0
$407$	−25.6881	−	14.8310i	−1.27331	−	0.735147i
$408$	−2.32634	−	1.87354i	−0.115171	−	0.0927539i
$409$	−16.3485	+	9.43879i	−0.808379	+	0.466718i	−0.846393	−	0.532559i	$-0.821230\pi$
$409$	−16.3485	+	9.43879i	−0.808379	+	0.466718i	0.0380133	+	0.999277i	$0.487897\pi$
$410$	−5.54001	+	3.19852i	−0.273601	+	0.157964i
$411$	18.2081	−	7.04547i	0.898141	−	0.347528i
$412$	15.3233	+	8.84693i	0.754927	+	0.435857i
$413$		0			0
$414$	0.0985305	+	0.451636i	0.00484251	+	0.0221967i
$415$	11.0377			0.541818
$416$	−13.5807	+	23.5224i	−0.665848	+	1.15328i
$417$	0.862171	−	5.53955i	0.0422207	−	0.271273i
$418$	4.97201	−	2.87059i	0.243189	−	0.140405i
$419$	−3.31895	−	5.74860i	−0.162142	−	0.280837i	0.773495	−	0.633802i	$-0.218507\pi$
$419$	−3.31895	−	5.74860i	−0.162142	−	0.280837i	−0.935636	+	0.352965i	$0.885173\pi$
$420$		0			0
$421$	−9.70574	+	16.8108i	−0.473029	+	0.819310i	−0.999523	−	0.0308686i	$-0.990173\pi$
$421$	−9.70574	+	16.8108i	−0.473029	+	0.819310i	0.526495	+	0.850178i	$0.323506\pi$
$422$		−	1.65839i		−	0.0807290i
$423$	16.2253	+	5.17598i	0.788903	+	0.251665i
$424$	−7.34360			−0.356637
$425$	−4.26483	+	7.38690i	−0.206874	+	0.358317i
$426$	−1.47360	−	3.80833i	−0.0713962	−	0.184514i
$427$		0			0
$428$	6.24532	−	3.60574i	0.301879	−	0.174290i
$429$	24.3371	−	30.2191i	1.17501	−	1.45899i
$430$	−5.02983	−	2.90397i	−0.242560	−	0.140042i
$431$		−	24.3185i		−	1.17138i	−0.810535	−	0.585690i	$-0.800824\pi$
$431$		−	24.3185i		−	1.17138i	0.810535	−	0.585690i	$-0.199176\pi$
$432$	−12.7999	+	8.45938i	−0.615835	+	0.407002i
$433$			3.32148i			0.159620i	0.996810	+	0.0798101i	$0.0254314\pi$
$433$			3.32148i			0.159620i	−0.996810	+	0.0798101i	$0.974569\pi$
$434$		0			0
$435$	−4.81902	−	3.88103i	−0.231054	−	0.186081i
$436$	15.7664	+	27.3083i	0.755076	+	1.30783i
$437$	0.663259	+	1.14880i	0.0317280	+	0.0549544i
$438$	−0.598732	−	1.54735i	−0.0286085	−	0.0739350i
$439$	−23.3126	−	13.4595i	−1.11265	−	0.642389i	−0.173136	−	0.984898i	$-0.555390\pi$
$439$	−23.3126	−	13.4595i	−1.11265	−	0.642389i	−0.939515	+	0.342509i	$0.888723\pi$
$440$	21.6657			1.03287
$441$		0			0
$442$	2.72879			0.129795
$443$	22.8837	+	13.2119i	1.08724	+	0.627717i	0.932839	−	0.360292i	$-0.117323\pi$
$443$	22.8837	+	13.2119i	1.08724	+	0.627717i	0.154397	+	0.988009i	$0.450656\pi$
$444$	−24.9310	−	3.88024i	−1.18317	−	0.184148i
$445$	−26.9833	−	46.7365i	−1.27913	−	2.21552i
$446$	−5.46560	−	9.46670i	−0.258804	−	0.448261i
$447$	4.76946	−	30.6444i	0.225588	−	1.44943i
$448$		0			0
$449$			19.6314i			0.926464i	0.886237	+	0.463232i	$0.153310\pi$
$449$			19.6314i			0.926464i	−0.886237	+	0.463232i	$0.846690\pi$
$450$	−6.86557	−	7.54331i	−0.323646	−	0.355595i
$451$			15.4916i			0.729470i
$452$	15.4754	+	8.93474i	0.727902	+	0.420255i
$453$	11.6251	+	30.0435i	0.546194	+	1.41157i
$454$	9.04102	−	5.21983i	0.424316	−	0.244979i
$455$		0			0
$456$	6.42914	−	7.98297i	0.301072	−	0.373837i
$457$	12.6244	−	21.8660i	0.590543	−	1.02285i	−0.403617	−	0.914928i	$-0.632247\pi$
$457$	12.6244	−	21.8660i	0.590543	−	1.02285i	0.994159	−	0.107922i	$-0.0344196\pi$
$458$	−1.93122			−0.0902399
$459$	4.94713	+	2.47081i	0.230912	+	0.115327i
$460$			2.38505i			0.111204i
$461$	7.23618	−	12.5334i	0.337023	−	0.583740i	−0.646849	−	0.762618i	$-0.723913\pi$
$461$	7.23618	−	12.5334i	0.337023	−	0.583740i	0.983871	+	0.178878i	$0.0572468\pi$
$462$		0			0
$463$	−10.0168	−	17.3495i	−0.465519	−	0.806302i	0.533706	−	0.845670i	$-0.320799\pi$
$463$	−10.0168	−	17.3495i	−0.465519	−	0.806302i	−0.999225	+	0.0393681i	$0.987466\pi$
$464$	2.53212	−	1.46192i	0.117551	−	0.0678679i
$465$	−6.32389	+	2.44697i	−0.293263	+	0.113476i
$466$	−5.54331	+	9.60130i	−0.256789	+	0.444772i
$467$	23.5630			1.09037			0.545183	−	0.838317i	$-0.316460\pi$
$467$	23.5630			1.09037			0.545183	+	0.838317i	$0.316460\pi$
$468$	10.0306	−	31.4434i	0.463666	−	1.45347i
$469$		0			0
$470$	−7.52386	−	4.34390i	−0.347050	−	0.200369i
$471$	−2.04298	+	13.1264i	−0.0941355	+	0.604831i
$472$	15.7948	−	9.11914i	0.727015	−	0.419742i
$473$	−12.1806	+	7.03248i	−0.560065	+	0.323354i
$474$	−0.738083	+	4.74227i	−0.0339013	+	0.217820i
$475$	−25.3485	−	14.6350i	−1.16307	−	0.671499i
$476$		0			0
$477$	13.2829	−	2.89784i	0.608182	−	0.132683i
$478$	−7.29511			−0.333671
$479$	12.4674	−	21.5941i	0.569648	−	0.986660i	−0.426952	−	0.904274i	$-0.640413\pi$
$479$	12.4674	−	21.5941i	0.569648	−	0.986660i	0.996601	−	0.0823855i	$-0.0262539\pi$
$480$	26.1860	−	10.1324i	1.19522	−	0.462480i
$481$	41.8978	−	24.1897i	1.91038	−	1.10296i
$482$	3.54945	+	6.14783i	0.161673	+	0.280026i
$483$		0			0
$484$	2.48863	−	4.31043i	0.113119	−	0.195929i
$485$			6.95750i			0.315924i
$486$	−4.61279	+	4.73806i	−0.209240	+	0.214923i
$487$	−5.00662			−0.226871			−0.113436	−	0.993545i	$-0.536186\pi$
$487$	−5.00662			−0.226871			−0.113436	+	0.993545i	$0.536186\pi$
$488$	0.0222909	−	0.0386090i	0.00100906	−	0.00174775i
$489$	4.33816	−	5.38662i	0.196178	−	0.243592i
$490$		0			0
$491$	18.6960	−	10.7942i	0.843740	−	0.487134i	−0.0147936	−	0.999891i	$-0.504709\pi$
$491$	18.6960	−	10.7942i	0.843740	−	0.487134i	0.858534	+	0.512757i	$0.171376\pi$
$492$	4.75531	+	12.2895i	0.214386	+	0.554054i
$493$	−0.912628	−	0.526906i	−0.0411027	−	0.0237307i
$494$			9.36399i			0.421306i
$495$	−39.1882	+	8.54943i	−1.76138	+	0.384268i
$496$		−	3.20419i		−	0.143872i
$497$		0			0
$498$	−0.345709	+	2.22122i	−0.0154916	+	0.0995351i
$499$	−17.9065	−	31.0149i	−0.801604	−	1.38842i	−0.918560	−	0.395282i	$-0.870647\pi$
$499$	−17.9065	−	31.0149i	−0.801604	−	1.38842i	0.116956	−	0.993137i	$-0.462686\pi$
$500$	−9.89826	−	17.1443i	−0.442664	−	0.766716i
$501$	14.5902	+	2.27081i	0.651842	+	0.101452i
$502$	1.95979	+	1.13149i	0.0874699	+	0.0505008i
$503$	−23.9969			−1.06997			−0.534984	−	0.844862i	$-0.679682\pi$
$503$	−23.9969			−1.06997			−0.534984	+	0.844862i	$0.679682\pi$
$504$		0			0
$505$	−23.2195			−1.03325
$506$	−0.494543	−	0.285525i	−0.0219851	−	0.0126931i
$507$	14.7119	+	38.0209i	0.653376	+	1.68857i
$508$	10.6772	+	18.4934i	0.473724	+	0.820514i
$509$	−9.07094	−	15.7113i	−0.402062	−	0.696392i	0.591912	−	0.806002i	$-0.298373\pi$
$509$	−9.07094	−	15.7113i	−0.402062	−	0.696392i	−0.993975	+	0.109610i	$0.965040\pi$
$510$	−2.19698	−	1.76935i	−0.0972838	−	0.0783483i
$511$		0			0
$512$			22.8374i			1.00928i
$513$	−8.47870	+	16.9763i	−0.374344	+	0.749524i
$514$		−	10.4438i		−	0.460658i
$515$	30.3732	+	17.5360i	1.33840	+	0.772728i
$516$	−7.50421	+	9.31786i	−0.330354	+	0.410196i
$517$	−18.2203	+	10.5195i	−0.801330	+	0.462648i
$518$		0			0
$519$	0.271824	+	0.702495i	0.0119318	+	0.0308361i
$520$	−17.6686	+	30.6029i	−0.774819	+	1.34203i
$521$	−0.839387			−0.0367742			−0.0183871	−	0.999831i	$-0.505853\pi$
$521$	−0.839387			−0.0367742			−0.0183871	+	0.999831i	$0.505853\pi$
$522$	0.931952	−	0.848220i	0.0407904	−	0.0371256i
$523$		−	16.2832i		−	0.712015i	−0.934483	−	0.356008i	$-0.884138\pi$
$523$		−	16.2832i		−	0.712015i	0.934483	−	0.356008i	$-0.115862\pi$
$524$	−19.1129	+	33.1045i	−0.834951	+	1.44618i
$525$		0			0
$526$	6.52858	+	11.3078i	0.284660	+	0.493045i
$527$	−1.00014	+	0.577428i	−0.0435666	+	0.0251532i
$528$	2.91482	−	18.7280i	0.126851	−	0.815033i
$529$	−11.4340	+	19.8043i	−0.497132	+	0.861057i
$530$	−6.93524			−0.301247
$531$	−24.9707	+	22.7272i	−1.08364	+	0.986275i
$532$		0			0
$533$	−21.8819	−	12.6335i	−0.947812	−	0.547219i
$534$	10.2504	−	3.96629i	0.443577	−	0.171638i
$535$	12.3792	−	7.14713i	0.535199	−	0.308997i
$536$	−13.6545	+	7.88342i	−0.589784	+	0.340512i
$537$	−23.4954	−	18.9222i	−1.01390	−	0.816552i
$538$	5.13615	+	2.96536i	0.221435	+	0.127846i
$539$		0			0
$540$	−28.4638	+	18.8115i	−1.22488	+	0.809520i
$541$	−1.86693			−0.0802657			−0.0401328	−	0.999194i	$-0.512778\pi$
$541$	−1.86693			−0.0802657			−0.0401328	+	0.999194i	$0.512778\pi$
$542$	−1.37072	+	2.37417i	−0.0588777	+	0.101979i
$543$	−23.9336	−	19.2751i	−1.02709	−	0.827175i
$544$	4.14136	−	2.39102i	0.177559	−	0.102514i
$545$	31.2515	+	54.1292i	1.33867	+	2.31864i
$546$		0			0
$547$	7.55792	−	13.0907i	0.323153	−	0.559718i	−0.657984	−	0.753032i	$-0.728590\pi$
$547$	7.55792	−	13.0907i	0.323153	−	0.559718i	0.981137	+	0.193315i	$0.0619238\pi$
$548$			20.5157i			0.876386i
$549$	−0.0250838	+	0.0786310i	−0.00107055	+	0.00335589i
$550$	12.6004			0.537281
$551$	1.80811	−	3.13173i	0.0770279	−	0.133416i
$552$	−1.00739	−	0.156789i	−0.0428773	−	0.00667339i
$553$		0			0
$554$	−7.02398	+	4.05529i	−0.298420	+	0.172293i
$555$	−49.4171	−	7.69124i	−2.09764	−	0.326475i
$556$	5.10183	+	2.94554i	0.216366	+	0.124919i
$557$			6.32176i			0.267862i	0.990991	+	0.133931i	$0.0427600\pi$
$557$			6.32176i			0.267862i	−0.990991	+	0.133931i	$0.957240\pi$
$558$	−0.294359	−	1.34926i	−0.0124612	−	0.0571186i
$559$		−	22.9402i		−	0.970269i
$560$		0			0
$561$	−6.37093	+	2.46517i	−0.268981	+	0.104080i
$562$	−4.91321	−	8.50992i	−0.207251	−	0.358970i
$563$	−4.82545	−	8.35793i	−0.203369	−	0.352245i	0.746243	−	0.665673i	$-0.231856\pi$
$563$	−4.82545	−	8.35793i	−0.203369	−	0.352245i	−0.949612	+	0.313429i	$0.898522\pi$
$564$	−11.2252	+	13.9381i	−0.472665	+	0.586900i
$565$	30.6747	+	17.7100i	1.29049	+	0.745066i
$566$	−6.77132			−0.284620
$567$		0			0
$568$	9.00618			0.377891
$569$	13.4785	+	7.78184i	0.565050	+	0.326232i	0.755170	−	0.655529i	$-0.227554\pi$
$569$	13.4785	+	7.78184i	0.565050	+	0.326232i	−0.190120	+	0.981761i	$0.560888\pi$
$570$	6.07163	−	7.53905i	0.254313	−	0.315776i
$571$	20.9434	+	36.2750i	0.876454	+	1.51806i	0.855206	+	0.518288i	$0.173431\pi$
$571$	20.9434	+	36.2750i	0.876454	+	1.51806i	0.0212481	+	0.999774i	$0.493236\pi$
$572$	20.3860	+	35.3096i	0.852382	+	1.47637i
$573$	−0.402004	+	0.155552i	−0.0167939	+	0.00649827i
$574$		0			0
$575$			2.91135i			0.121412i
$576$	−2.55733	−	11.7221i	−0.106555	−	0.488420i
$577$			40.3472i			1.67968i	0.542837	+	0.839838i	$0.317350\pi$
$577$			40.3472i			1.67968i	−0.542837	+	0.839838i	$0.682650\pi$
$578$	5.82921	+	3.36549i	0.242463	+	0.139986i
$579$	−14.2008	−	2.21019i	−0.590163	−	0.0918525i
$580$	5.63080	−	3.25094i	0.233806	−	0.134988i
$581$		0			0
$582$	−1.40013	−	0.217914i	−0.0580371	−	0.00903284i
$583$	−8.39744	+	14.5448i	−0.347787	+	0.602384i
$584$	3.65926			0.151421
$585$	19.8823	−	62.3257i	0.822031	−	2.57685i
$586$			2.84086i			0.117355i
$587$	1.91520	−	3.31723i	0.0790490	−	0.136917i	−0.823791	−	0.566894i	$-0.808145\pi$
$587$	1.91520	−	3.31723i	0.0790490	−	0.136917i	0.902840	+	0.429977i	$0.141478\pi$
$588$		0			0
$589$	−1.98148	−	3.43202i	−0.0816453	−	0.141414i
$590$	14.9165	−	8.61204i	0.614102	−	0.354552i
$591$	−30.4623	−	24.5330i	−1.25305	−	1.00915i
$592$	11.8163	−	20.4664i	0.485647	−	0.841166i
$593$	−12.5143			−0.513902			−0.256951	−	0.966424i	$-0.582718\pi$
$593$	−12.5143			−0.513902			−0.256951	+	0.966424i	$0.582718\pi$
$594$	−0.493079	−	8.15399i	−0.0202313	−	0.334562i
$595$		0			0
$596$	28.2229	+	16.2945i	1.15606	+	0.667449i
$597$	−8.25575	−	6.64883i	−0.337885	−	0.272119i
$598$	0.806611	−	0.465697i	0.0329848	−	0.0190438i
$599$	6.62258	−	3.82355i	0.270591	−	0.156226i	−0.358565	−	0.933505i	$-0.616734\pi$
$599$	6.62258	−	3.82355i	0.270591	−	0.156226i	0.629156	+	0.777279i	$0.283401\pi$
$600$	20.9801	−	8.11806i	0.856508	−	0.331418i
$601$	−29.8513	−	17.2346i	−1.21766	−	0.703015i	−0.253242	−	0.967403i	$-0.581497\pi$
$601$	−29.8513	−	17.2346i	−1.21766	−	0.703015i	−0.964416	+	0.264388i	$0.914830\pi$
$602$		0			0
$603$	21.5869	−	19.6474i	0.879088	−	0.800105i
$604$	−33.8510			−1.37738
$605$	4.93285	−	8.54394i	0.200549	−	0.347361i
$606$	0.727253	−	4.67268i	0.0295426	−	0.189815i
$607$	−10.7472	+	6.20488i	−0.436214	+	0.251848i	−0.701990	−	0.712186i	$-0.747705\pi$
$607$	−10.7472	+	6.20488i	−0.436214	+	0.251848i	0.265776	+	0.964035i	$0.414372\pi$
$608$	8.20490	+	14.2113i	0.332753	+	0.576344i
$609$		0			0
$610$	0.0210514	−	0.0364621i	0.000852346	−	0.00147631i
$611$		−	34.3151i		−	1.38824i
$612$	−4.29736	+	3.91126i	−0.173710	+	0.158103i
$613$	−1.66896			−0.0674088			−0.0337044	−	0.999432i	$-0.510730\pi$
$613$	−1.66896			−0.0674088			−0.0337044	+	0.999432i	$0.510730\pi$
$614$	1.82209	−	3.15595i	0.0735335	−	0.127364i
$615$	9.42577	+	24.3597i	0.380084	+	0.982277i
$616$		0			0
$617$	−13.5698	+	7.83453i	−0.546300	+	0.315406i	−0.747628	−	0.664118i	$-0.768807\pi$
$617$	−13.5698	+	7.83453i	−0.546300	+	0.315406i	0.201329	+	0.979524i	$0.435474\pi$
$618$	−4.48025	+	5.56305i	−0.180222	+	0.223779i
$619$	3.10436	+	1.79230i	0.124775	+	0.0720387i	0.561088	−	0.827756i	$-0.310383\pi$
$619$	3.10436	+	1.79230i	0.124775	+	0.0720387i	−0.436314	+	0.899795i	$0.643716\pi$
$620$		−	7.12532i		−	0.286160i
$621$	1.88400	−	0.113927i	0.0756025	−	0.00457175i
$622$		−	1.79626i		−	0.0720234i
$623$		0			0
$624$	24.0764	+	19.3901i	0.963827	+	0.776225i
$625$	0.417550	+	0.723218i	0.0167020	+	0.0289287i
$626$	−0.759935	−	1.31625i	−0.0303731	−	0.0526078i
$627$	−8.45938	−	21.8622i	−0.337835	−	0.873091i
$628$	−12.0892	−	6.97968i	−0.482410	−	0.278520i
$629$	−8.51769			−0.339622
$630$		0			0
$631$	23.1493			0.921557			0.460779	−	0.887515i	$-0.347570\pi$
$631$	23.1493			0.921557			0.460779	+	0.887515i	$0.347570\pi$
$632$	−9.16691	−	5.29252i	−0.364640	−	0.210525i
$633$	−6.69079	−	1.04135i	−0.265935	−	0.0413899i
$634$	1.88476	+	3.26451i	0.0748536	+	0.129650i
$635$	21.1638	+	36.6568i	0.839861	+	1.45468i
$636$	−2.19702	+	14.1161i	−0.0871176	+	0.559741i
$637$		0			0
$638$			1.55674i			0.0616318i
$639$	−16.2901	+	3.55390i	−0.644426	+	0.140590i
$640$			38.5419i			1.52350i
$641$	20.3567	+	11.7529i	0.804041	+	0.464213i	0.844882	−	0.534953i	$-0.179671\pi$
$641$	20.3567	+	11.7529i	0.804041	+	0.464213i	−0.0408415	+	0.999166i	$0.513004\pi$
$642$	1.05056	+	2.71504i	0.0414623	+	0.107154i
$643$	4.83255	−	2.79007i	0.190577	−	0.110030i	−0.401676	−	0.915782i	$-0.631572\pi$
$643$	4.83255	−	2.79007i	0.190577	−	0.110030i	0.592253	+	0.805752i	$0.298239\pi$
$644$		0			0
$645$	−14.8745	+	18.4694i	−0.585683	+	0.727233i
$646$	0.824312	−	1.42775i	0.0324321	−	0.0561741i
$647$	−3.90178			−0.153395			−0.0766974	−	0.997054i	$-0.524438\pi$
$647$	−3.90178			−0.153395			−0.0766974	+	0.997054i	$0.524438\pi$
$648$	−6.07438	−	13.2590i	−0.238624	−	0.520864i
$649$		−	41.7111i		−	1.63730i
$650$	−10.2757	+	17.7981i	−0.403047	+	0.698098i
$651$		0			0
$652$	3.63386	+	6.29402i	0.142313	+	0.246493i
$653$	−5.29484	+	3.05698i	−0.207203	+	0.119629i	−0.600011	−	0.799992i	$-0.704837\pi$
$653$	−5.29484	+	3.05698i	−0.207203	+	0.119629i	0.392808	+	0.919621i	$0.371504\pi$
$654$	−11.8718	+	4.59368i	−0.464223	+	0.179627i
$655$	−37.8847	+	65.6183i	−1.48028	+	2.56392i
$656$	−12.3426			−0.481896
$657$	−6.61875	+	1.44397i	−0.258222	+	0.0563346i
$658$		0			0
$659$	24.7031	+	14.2623i	0.962296	+	0.555582i	0.896879	−	0.442276i	$-0.145829\pi$
$659$	24.7031	+	14.2623i	0.962296	+	0.555582i	0.0654174	+	0.997858i	$0.479162\pi$
$660$	6.48182	−	41.6465i	0.252305	−	1.62109i
$661$	−21.7672	+	12.5673i	−0.846648	+	0.488812i	−0.859518	−	0.511105i	$-0.829236\pi$
$661$	−21.7672	+	12.5673i	−0.846648	+	0.488812i	0.0128707	+	0.999917i	$0.495903\pi$
$662$	5.79801	−	3.34748i	0.225346	−	0.130104i
$663$	1.71349	−	11.0093i	0.0665463	−	0.427568i
$664$	−4.29366	−	2.47895i	−0.166626	−	0.0962018i
$665$		0			0
$666$	3.09556	−	9.70378i	0.119951	−	0.376014i
$667$	−0.359688			−0.0139272
$668$	−7.75804	+	13.4373i	−0.300168	+	0.519906i
$669$	−41.6255	+	16.1066i	−1.60934	+	0.622718i
$670$	−12.8952	+	7.44503i	−0.498184	+	0.287627i
$671$	−0.0509796	−	0.0882993i	−0.00196805	−	0.00340875i
$672$		0			0
$673$	12.5278	−	21.6988i	0.482912	−	0.836428i	−0.516895	−	0.856049i	$-0.672912\pi$
$673$	12.5278	−	21.6988i	0.482912	−	0.836428i	0.999808	+	0.0196203i	$0.00624575\pi$
$674$			5.76872i			0.222203i
$675$	−34.7447	+	22.9626i	−1.33732	+	0.883830i
$676$	−42.8393			−1.64767
$677$	16.8081	−	29.1126i	0.645989	−	1.11889i	−0.338083	−	0.941116i	$-0.609778\pi$
$677$	16.8081	−	29.1126i	0.645989	−	1.11889i	0.984072	−	0.177770i	$-0.0568883\pi$
$678$	−4.52471	+	5.61827i	−0.173771	+	0.215768i
$679$		0			0
$680$	5.38794	−	3.11073i	0.206618	−	0.119291i
$681$	−15.3824	−	39.7538i	−0.589454	−	1.52337i
$682$	1.47744	+	0.853001i	0.0565742	+	0.0326631i
$683$		−	38.5467i		−	1.47495i	−0.675375	−	0.737475i	$-0.736018\pi$
$683$		−	38.5467i		−	1.47495i	0.675375	−	0.737475i	$-0.263982\pi$
$684$	−13.4217	−	14.7466i	−0.513191	−	0.563851i
$685$			40.6652i			1.55374i
$686$		0			0
$687$	−1.21267	+	7.79153i	−0.0462661	+	0.297265i
$688$	−5.60297	−	9.70464i	−0.213611	−	0.369986i
$689$	−13.6964	−	23.7229i	−0.521792	−	0.903770i
$690$	−0.951370	−	0.148070i	−0.0362180	−	0.00563694i
$691$	26.1768	+	15.1132i	0.995812	+	0.574932i	0.907006	−	0.421117i	$-0.138362\pi$
$691$	26.1768	+	15.1132i	0.995812	+	0.574932i	0.0888052	+	0.996049i	$0.471695\pi$
$692$	−0.791523			−0.0300892
$693$		0			0
$694$	−5.88111			−0.223244
$695$	10.1126	+	5.83852i	0.383593	+	0.221468i
$696$	1.00296	+	2.59202i	0.0380171	+	0.0982504i
$697$	2.22426	+	3.85253i	0.0842499	+	0.145925i
$698$	−0.380115	−	0.658378i	−0.0143876	−	0.0249200i
$699$	35.2558	+	28.3935i	1.33350	+	1.07394i
$700$		0			0
$701$		−	29.6057i		−	1.11819i	−0.829103	−	0.559096i	$-0.811148\pi$
$701$		−	29.6057i		−	1.11819i	0.829103	−	0.559096i	$-0.188852\pi$
$702$	11.9197	+	5.95319i	0.449879	+	0.224689i
$703$		−	29.2289i		−	1.10239i
$704$	12.8357	+	7.41070i	0.483764	+	0.279301i
$705$	−22.2500	+	27.6275i	−0.837984	+	1.04051i
$706$	−2.85114	+	1.64611i	−0.107304	+	0.0619521i
$707$		0			0
$708$	−12.8037	−	33.0895i	−0.481193	−	1.24358i
$709$	−1.78201	+	3.08652i	−0.0669246	+	0.115917i	−0.897546	−	0.440921i	$-0.854652\pi$
$709$	−1.78201	+	3.08652i	−0.0669246	+	0.115917i	0.830622	+	0.556837i	$0.187985\pi$
$710$	8.50536			0.319200
$711$	18.6693	+	5.95561i	0.700153	+	0.223353i
$712$			24.2407i			0.908458i
$713$	−0.197088	+	0.341367i	−0.00738102	+	0.0127843i
$714$		0			0
$715$	40.4082	+	69.9891i	1.51118	+	2.61744i
$716$	27.4533	−	15.8501i	1.02598	−	0.592348i
$717$	−4.58081	+	29.4322i	−0.171074	+	1.09917i
$718$	4.78944	−	8.29556i	0.178740	−	0.309588i
$719$	1.61282			0.0601480			0.0300740	−	0.999548i	$-0.490426\pi$
$719$	1.61282			0.0601480			0.0300740	+	0.999548i	$0.490426\pi$
$720$	−6.81157	−	31.2223i	−0.253852	−	1.16359i
$721$		0			0
$722$	−2.08061	−	1.20124i	−0.0774322	−	0.0447055i
$723$	27.0323	−	10.4599i	1.00534	−	0.389009i
$724$	27.9654	−	16.1458i	1.03933	−	0.600055i
$725$	6.87332	−	3.96831i	0.255269	−	0.147379i
$726$	1.56488	+	1.26029i	0.0580781	+	0.0467736i
$727$	−10.4930	−	6.05816i	−0.389166	−	0.224685i	0.292633	−	0.956225i	$-0.405469\pi$
$727$	−10.4930	−	6.05816i	−0.389166	−	0.224685i	−0.681799	+	0.731540i	$0.738802\pi$
$728$		0			0
$729$	16.2193	+	21.5855i	0.600714	+	0.799464i
$730$	3.45577			0.127904
$731$	−2.01943	+	3.49775i	−0.0746913	+	0.129369i
$732$	−0.0675467	−	0.0543993i	−0.00249660	−	0.00201065i
$733$	−34.9931	+	20.2033i	−1.29250	+	0.746225i	−0.979097	−	0.203396i	$-0.934802\pi$
$733$	−34.9931	+	20.2033i	−1.29250	+	0.746225i	−0.313403	+	0.949620i	$0.601469\pi$
$734$	−3.31277	−	5.73788i	−0.122276	−	0.211789i
$735$		0			0
$736$	0.816104	−	1.41353i	0.0300820	−	0.0521035i
$737$			36.0589i			1.32825i
$738$	−5.19736	+	1.13387i	−0.191317	+	0.0417384i
$739$	−20.4634			−0.752760			−0.376380	−	0.926465i	$-0.622831\pi$
$739$	−20.4634			−0.752760			−0.376380	+	0.926465i	$0.622831\pi$
$740$	26.2765	−	45.5123i	0.965944	−	1.67306i
$741$	37.7792	+	5.87992i	1.38785	+	0.216004i
$742$		0			0
$743$	37.1209	−	21.4318i	1.36184	−	0.786256i	0.371967	−	0.928246i	$-0.378683\pi$
$743$	37.1209	−	21.4318i	1.36184	−	0.786256i	0.989868	+	0.141990i	$0.0453501\pi$
$744$	3.00956	+	0.468406i	0.110336	+	0.0171726i
$745$	55.9422	+	32.2982i	2.04956	+	1.18332i
$746$		−	10.7093i		−	0.392095i
$747$	8.74446	+	2.78953i	0.319943	+	0.102064i
$748$		−	7.17832i		−	0.262465i
$749$		0			0
$750$	7.45316	−	2.88393i	0.272151	−	0.105306i
$751$	21.5028	+	37.2440i	0.784649	+	1.35905i	0.929209	+	0.369556i	$0.120490\pi$
$751$	21.5028	+	37.2440i	0.784649	+	1.35905i	−0.144559	+	0.989496i	$0.546177\pi$
$752$	−8.38120	−	14.5167i	−0.305631	−	0.529368i
$753$	5.79562	−	7.19633i	0.211204	−	0.262249i
$754$	−2.19890	−	1.26953i	−0.0800792	−	0.0462337i
$755$	−67.0979			−2.44194
$756$		0			0
$757$	−13.0766			−0.475276			−0.237638	−	0.971354i	$-0.576373\pi$
$757$	−13.0766			−0.475276			−0.237638	+	0.971354i	$0.576373\pi$
$758$	−5.42682	−	3.13317i	−0.197111	−	0.113802i
$759$	−1.46249	+	1.81595i	−0.0530851	+	0.0659149i
$760$	10.6746	+	18.4890i	0.387210	+	0.670667i
$761$	−11.5916	−	20.0773i	−0.420196	−	0.727801i	0.575762	−	0.817617i	$-0.304705\pi$
$761$	−11.5916	−	20.0773i	−0.420196	−	0.727801i	−0.995958	+	0.0898160i	$0.971372\pi$
$762$	−8.03968	+	3.11088i	−0.291247	+	0.112695i
$763$		0			0
$764$		−	0.452950i		−	0.0163872i
$765$	−8.51803	+	7.75271i	−0.307970	+	0.280300i
$766$			4.49232i			0.162314i
$767$	58.9172	+	34.0159i	2.12738	+	1.22824i
$768$	5.93288	+	0.923390i	0.214085	+	0.0333200i
$769$	−11.4527	+	6.61219i	−0.412993	+	0.238442i	−0.692075	−	0.721826i	$-0.743303\pi$
$769$	−11.4527	+	6.61219i	−0.412993	+	0.238442i	0.279082	+	0.960267i	$0.409970\pi$
$770$		0			0
$771$	−42.1359	−	6.55799i	−1.51749	−	0.236180i
$772$	7.55096	−	13.0787i	0.271765	−	0.470711i
$773$	−19.6319			−0.706110			−0.353055	−	0.935603i	$-0.614857\pi$
$773$	−19.6319			−0.706110			−0.353055	+	0.935603i	$0.614857\pi$
$774$	−3.25090	−	3.57182i	−0.116851	−	0.128386i
$775$		−	8.69762i		−	0.312428i
$776$	1.56258	−	2.70647i	0.0560935	−	0.0971567i
$777$		0			0
$778$	2.88120	+	4.99039i	0.103296	+	0.178914i
$779$	−13.2202	+	7.63267i	−0.473662	+	0.273469i
$780$	53.5399	+	43.1188i	1.91704	+	1.54390i
$781$	10.2986	−	17.8377i	0.368513	−	0.638284i
$782$	−0.163981			−0.00586395
$783$	−2.83696	−	4.29260i	−0.101385	−	0.153405i
$784$		0			0
$785$	−23.9626	−	13.8348i	−0.855262	−	0.493786i
$786$	−12.0184	−	9.67912i	−0.428683	−	0.345243i
$787$	−14.8621	+	8.58063i	−0.529776	+	0.305866i	−0.740925	−	0.671588i	$-0.765613\pi$
$787$	−14.8621	+	8.58063i	−0.529776	+	0.305866i	0.211149	+	0.977454i	$0.432279\pi$
$788$	35.5938	−	20.5501i	1.26798	−	0.732067i
$789$	49.7211	−	19.2391i	1.77012	−	0.684932i
$790$	−8.65715	−	4.99821i	−0.308008	−	0.177828i
$791$		0			0
$792$	17.1643	+	5.47553i	0.609909	+	0.194564i
$793$	0.166298			0.00590540
$794$	8.25299	−	14.2946i	0.292888	−	0.507297i
$795$	−4.35484	+	27.9803i	−0.154450	+	0.992360i
$796$	9.64647	−	5.56939i	0.341910	−	0.197402i
$797$	11.2772	+	19.5326i	0.399458	+	0.691882i	0.993659	−	0.112435i	$-0.0358650\pi$
$797$	11.2772	+	19.5326i	0.399458	+	0.691882i	−0.594201	+	0.804317i	$0.702532\pi$
$798$		0			0
$799$	−3.02076	+	5.23211i	−0.106867	+	0.185099i
$800$			36.0151i			1.27333i
$801$	−9.56555	−	43.8458i	−0.337982	−	1.54922i
$802$	−12.1945			−0.430603
$803$	4.18438	−	7.24755i	0.147663	−	0.255761i
$804$	11.0687	+	28.6056i	0.390362	+	1.00884i
$805$		0			0
$806$	−2.40974	+	1.39126i	−0.0848794	+	0.0490051i
$807$	15.1889	−	18.8599i	0.534676	−	0.663899i
$808$	9.03240	+	5.21486i	0.317759	+	0.183458i
$809$			48.2178i			1.69525i	0.530598	+	0.847624i	$0.321967\pi$
$809$			48.2178i			1.69525i	−0.530598	+	0.847624i	$0.678033\pi$
$810$	−5.73660	−	12.5217i	−0.201563	−	0.439968i
$811$		−	11.2304i		−	0.394354i	−0.980368	−	0.197177i	$-0.936823\pi$
$811$		−	11.2304i		−	0.394354i	0.980368	−	0.197177i	$-0.0631774\pi$
$812$		0			0
$813$	8.71789	+	7.02102i	0.305750	+	0.246238i
$814$	6.29134	+	10.8969i	0.220511	+	0.381937i
$815$	7.20287	+	12.4757i	0.252305	+	0.437006i
$816$	−1.96407	−	5.07590i	−0.0687563	−	0.177692i
$817$	−12.0027	−	6.92978i	−0.419922	−	0.242442i
$818$	8.00789			0.279989
$819$		0			0
$820$	−27.4468			−0.958484
$821$	−34.6778	−	20.0212i	−1.21026	−	0.698746i	−0.247447	−	0.968902i	$-0.579591\pi$
$821$	−34.6778	−	20.0212i	−1.21026	−	0.698746i	−0.962817	+	0.270156i	$0.912925\pi$
$822$	−8.18345	−	1.27367i	−0.285431	−	0.0444242i
$823$	−4.98922	−	8.64158i	−0.173913	−	0.301227i	0.765871	−	0.642994i	$-0.222308\pi$
$823$	−4.98922	−	8.64158i	−0.173913	−	0.301227i	−0.939785	+	0.341767i	$0.888975\pi$
$824$	−7.87680	−	13.6430i	−0.274401	−	0.475277i
$825$	7.91213	−	50.8364i	0.275465	−	1.76989i
$826$		0			0
$827$			20.8802i			0.726077i	0.931774	+	0.363038i	$0.118261\pi$
$827$			20.8802i			0.726077i	−0.931774	+	0.363038i	$0.881739\pi$
$828$	−0.602771	+	1.88953i	−0.0209477	+	0.0656657i
$829$			16.0646i			0.557945i	0.960299	+	0.278973i	$0.0899939\pi$
$829$			16.0646i			0.557945i	−0.960299	+	0.278973i	$0.910006\pi$
$830$	−4.05490	−	2.34110i	−0.140748	−	0.0812607i
$831$	11.9506	+	30.8848i	0.414561	+	1.07138i
$832$	−20.9353	+	12.0870i	−0.725801	+	0.419042i
$833$		0			0
$834$	−1.49168	+	1.85219i	−0.0516525	+	0.0641361i
$835$	−15.3776	+	26.6349i	−0.532165	+	0.921737i
$836$	24.6328			0.851943
$837$	−5.62844	+	0.340357i	−0.194547	+	0.0117645i
$838$			2.81581i			0.0972705i
$839$	10.1943	−	17.6570i	0.351946	−	0.609589i	−0.634644	−	0.772805i	$-0.718853\pi$
$839$	10.1943	−	17.6570i	0.351946	−	0.609589i	0.986590	+	0.163216i	$0.0521866\pi$
$840$		0			0
$841$	−14.0097	−	24.2656i	−0.483094	−	0.836743i
$842$	7.13117	−	4.11719i	0.245756	−	0.141888i
$843$	−37.4186	+	14.4788i	−1.28876	+	0.498676i
$844$	3.55769	−	6.16210i	0.122461	−	0.212108i
$845$	−84.9142			−2.92114
$846$	−4.86286	−	5.34290i	−0.167188	−	0.183693i
$847$		0			0
$848$	−11.5883	−	6.69048i	−0.397942	−	0.229752i
$849$	−4.25191	+	27.3190i	−0.145925	+	0.937585i
$850$	3.13353	−	1.80914i	0.107479	−	0.0620531i
$851$	−2.51777	+	1.45363i	−0.0863079	+	0.0498299i
$852$	2.69442	−	17.3120i	0.0923094	−	0.593099i
$853$	−7.80792	−	4.50790i	−0.267338	−	0.154348i	0.360339	−	0.932821i	$-0.382661\pi$
$853$	−7.80792	−	4.50790i	−0.267338	−	0.154348i	−0.627677	+	0.778474i	$0.715994\pi$
$854$		0			0
$855$	−26.6039	−	29.2301i	−0.909833	−	0.999648i
$856$	−6.42068			−0.219454
$857$	16.1658	−	28.0000i	0.552213	−	0.956461i	−0.445902	−	0.895082i	$-0.647117\pi$
$857$	16.1658	−	28.0000i	0.552213	−	0.956461i	0.998115	−	0.0613789i	$-0.0195498\pi$
$858$	−15.3502	+	5.93962i	−0.524047	+	0.202775i
$859$	−38.1416	+	22.0211i	−1.30138	+	0.751349i	−0.980640	−	0.195819i	$-0.937263\pi$
$859$	−38.1416	+	22.0211i	−1.30138	+	0.751349i	−0.320735	+	0.947169i	$0.603930\pi$
$860$	−12.4596	−	21.5807i	−0.424870	−	0.735896i
$861$		0			0
$862$	−5.15796	+	8.93385i	−0.175681	+	0.304288i
$863$		−	6.12763i		−	0.208587i	−0.994547	−	0.104293i	$-0.966742\pi$
$863$		−	6.12763i		−	0.208587i	0.994547	−	0.104293i	$-0.0332581\pi$
$864$	23.3062	−	1.40935i	0.792894	−	0.0479470i
$865$	−1.56892			−0.0533449
$866$	0.704488	−	1.22021i	0.0239395	−	0.0414644i
$867$	17.2385	−	21.4047i	0.585449	−	0.726943i
$868$		0			0
$869$	−20.9648	+	12.1040i	−0.711182	+	0.410601i
$870$	0.947188	+	2.44789i	0.0321127	+	0.0829911i
$871$	−50.9334	−	29.4064i	−1.72581	−	0.996398i
$872$		−	28.0751i		−	0.950742i
$873$	−1.75836	+	5.51199i	−0.0595114	+	0.186553i
$874$		−	0.562710i		−	0.0190340i
$875$		0			0
$876$	1.09476	−	7.03394i	0.0369884	−	0.237655i
$877$	1.13204	+	1.96075i	0.0382263	+	0.0662099i	0.884506	−	0.466530i	$-0.154496\pi$
$877$	1.13204	+	1.96075i	0.0382263	+	0.0662099i	−0.846279	+	0.532740i	$0.821163\pi$
$878$	5.70956	+	9.88924i	0.192688	+	0.333746i
$879$	11.4615	+	1.78386i	0.386587	+	0.0601681i
$880$	34.1886	+	19.7388i	1.15250	+	0.665394i
$881$	19.2955			0.650083			0.325041	−	0.945700i	$-0.394622\pi$
$881$	19.2955			0.650083			0.325041	+	0.945700i	$0.394622\pi$
$882$		0			0
$883$	−0.833572			−0.0280519			−0.0140260	−	0.999902i	$-0.504465\pi$
$883$	−0.833572			−0.0280519			−0.0140260	+	0.999902i	$0.504465\pi$
$884$	10.1394	+	5.85400i	0.341026	+	0.196891i
$885$	−25.3789	−	65.5886i	−0.853103	−	2.20474i
$886$	−5.60451	−	9.70729i	−0.188287	−	0.326123i
$887$	28.7740	+	49.8380i	0.966136	+	1.67340i	0.706532	+	0.707681i	$0.250259\pi$
$887$	28.7740	+	49.8380i	0.966136	+	1.67340i	0.259604	+	0.965715i	$0.416408\pi$
$888$	17.4959	+	14.0905i	0.587124	+	0.472845i
$889$		0			0
$890$			22.8927i			0.767365i
$891$	−33.2070	−	3.13079i	−1.11248	−	0.104885i
$892$		−	46.9008i		−	1.57035i
$893$	−17.9543	−	10.3659i	−0.600817	−	0.346882i
$894$	−8.25184	+	10.2462i	−0.275983	+	0.342683i
$895$	54.4166	−	31.4174i	1.81895	−	1.05017i
$896$		0			0
$897$	−1.37237	−	3.54671i	−0.0458220	−	0.118421i
$898$	4.16384	−	7.21198i	0.138949	−	0.240667i
$899$	1.07456			0.0358387
$900$	−9.32808	−	42.7573i	−0.310936	−	1.42524i
$901$			4.82278i			0.160670i
$902$	3.28577	−	5.69112i	0.109404	−	0.189494i
$903$		0			0
$904$	−7.95498	−	13.7784i	−0.264579	−	0.458263i
$905$	55.4317	−	32.0035i	1.84261	−	1.06383i
$906$	2.10156	−	13.5027i	0.0698196	−	0.448599i
$907$	5.05621	−	8.75761i	0.167889	−	0.290792i	−0.769789	−	0.638299i	$-0.779638\pi$
$907$	5.05621	−	8.75761i	0.167889	−	0.290792i	0.937677	+	0.347507i	$0.112972\pi$
$908$	44.7918			1.48647
$909$	−18.3954	−	5.86823i	−0.610135	−	0.194637i
$910$		0			0
$911$	−16.9986	−	9.81416i	−0.563190	−	0.325158i	0.191235	−	0.981544i	$-0.438751\pi$
$911$	−16.9986	−	9.81416i	−0.563190	−	0.325158i	−0.754425	+	0.656387i	$0.772084\pi$
$912$	17.4182	−	6.73983i	0.576775	−	0.223178i
$913$	−9.81965	+	5.66937i	−0.324983	+	0.187629i
$914$	−9.27560	+	5.35527i	−0.306810	+	0.177137i
$915$	−0.133888	−	0.107828i	−0.00442620	−	0.00356467i
$916$	−7.17586	−	4.14299i	−0.237097	−	0.136888i
$917$		0			0
$918$	−1.29336	−	1.95699i	−0.0426873	−	0.0645902i
$919$	17.0487			0.562384			0.281192	−	0.959652i	$-0.409270\pi$
$919$	17.0487			0.562384			0.281192	+	0.959652i	$0.409270\pi$
$920$	1.06176	−	1.83902i	0.0350051	−	0.0606306i
$921$	−11.5886	−	9.33295i	−0.381857	−	0.307531i
$922$	−5.31670	+	3.06960i	−0.175096	+	0.101092i
$923$	16.7972	+	29.0937i	0.552888	+	0.957630i
$924$		0			0
$925$	32.0748	−	55.5552i	1.05461	−	1.82664i
$926$			8.49825i			0.279270i
$927$	19.6310	+	21.5688i	0.644765	+	0.708413i
$928$	−4.44956			−0.146064
$929$	−4.32511	+	7.49131i	−0.141902	+	0.245782i	−0.928213	−	0.372049i	$-0.878655\pi$
$929$	−4.32511	+	7.49131i	−0.141902	+	0.245782i	0.786311	+	0.617831i	$0.211989\pi$
$930$	2.84220	+	0.442358i	0.0931995	+	0.0145055i
$931$		0			0
$932$	−41.1948	+	23.7838i	−1.34938	+	0.779065i
$933$	−7.24703	−	1.12792i	−0.237257	−	0.0369265i
$934$	−8.65632	−	4.99773i	−0.283244	−	0.163531i
$935$		−	14.2285i		−	0.465323i
$936$	−21.7319	+	19.7794i	−0.710330	+	0.646510i
$937$		−	34.9586i		−	1.14205i	−0.820933	−	0.571025i	$-0.806546\pi$
$937$		−	34.9586i		−	1.14205i	0.820933	−	0.571025i	$-0.193454\pi$
$938$		0			0
$939$	−5.78760	+	2.23946i	−0.188871	+	0.0730821i
$940$	−18.6377	−	32.2815i	−0.607895	−	1.05291i
$941$	20.5472	+	35.5887i	0.669818	+	1.16016i	0.977955	+	0.208817i	$0.0669614\pi$
$941$	20.5472	+	35.5887i	0.669818	+	1.16016i	−0.308136	+	0.951342i	$0.599705\pi$
$942$	3.53464	−	4.38891i	0.115165	−	0.142998i
$943$	1.31495	+	0.759187i	0.0428207	+	0.0247225i
$944$	33.2324			1.08162
$945$		0			0
$946$	5.96637			0.193983
$947$	−29.2164	−	16.8681i	−0.949405	−	0.548139i	−0.0565088	−	0.998402i	$-0.517997\pi$
$947$	−29.2164	−	16.8681i	−0.949405	−	0.548139i	−0.892896	+	0.450263i	$0.851330\pi$
$948$	−12.9160	+	16.0375i	−0.419491	+	0.520875i
$949$	6.82481	+	11.8209i	0.221543	+	0.383723i
$950$	6.20818	+	10.7529i	0.201420	+	0.348869i
$951$	14.3542	−	5.55423i	0.465467	−	0.180108i
$952$		0			0
$953$		−	18.7823i		−	0.608420i	−0.952605	−	0.304210i	$-0.901608\pi$
$953$		−	18.7823i		−	0.608420i	0.952605	−	0.304210i	$-0.0983925\pi$
$954$	−5.49435	−	1.75273i	−0.177886	−	0.0567468i
$955$		−	0.897817i		−	0.0290527i
$956$	−27.1066	−	15.6500i	−0.876690	−	0.506157i
$957$	6.28067	+	0.977519i	0.203025	+	0.0315987i
$958$	−9.16024	+	5.28867i	−0.295954	+	0.170869i
$959$		0			0
$960$	24.6925	+	3.84312i	0.796946	+	0.124036i
$961$	−14.9112	+	25.8270i	−0.481006	+	0.833128i
$962$	−20.5226			−0.661676
$963$	11.6135	−	2.53365i	0.374241	−	0.0816457i
$964$			30.4582i			0.980992i
$965$	14.9672	−	25.9239i	0.481810	−	0.834520i
$966$		0			0
$967$	−17.5860	−	30.4599i	−0.565529	−	0.979525i	−0.997000	−	0.0773981i	$-0.975339\pi$
$967$	−17.5860	−	30.4599i	−0.565529	−	0.979525i	0.431471	−	0.902127i	$-0.357995\pi$
$968$	−3.83776	+	2.21573i	−0.123350	+	0.0712163i
$969$	−5.24267	−	4.22222i	−0.168419	−	0.135637i
$970$	1.47569	−	2.55597i	0.0473816	−	0.0820673i
$971$	−39.5962			−1.27070			−0.635351	−	0.772223i	$-0.719145\pi$
$971$	−39.5962			−1.27070			−0.635351	+	0.772223i	$0.719145\pi$
$972$	−27.3043	+	7.70961i	−0.875784	+	0.247286i
$973$		0			0
$974$	1.83928	+	1.06191i	0.0589342	+	0.0340257i
$975$	65.3542	+	52.6335i	2.09301	+	1.68562i
$976$	0.0703505	−	0.0406169i	0.00225187	−	0.00130012i
$977$	−30.3364	+	17.5147i	−0.970546	+	0.560345i	−0.899403	−	0.437121i	$-0.855998\pi$
$977$	−30.3364	+	17.5147i	−0.970546	+	0.560345i	−0.0711433	+	0.997466i	$0.522665\pi$
$978$	−2.73621	+	1.05875i	−0.0874944	+	0.0338552i
$979$	48.0113	+	27.7193i	1.53445	+	0.885914i
$980$		0			0
$981$	11.0786	+	50.7813i	0.353714	+	1.62132i
$982$	−9.15779			−0.292237
$983$	22.0865	−	38.2550i	0.704451	−	1.22015i	−0.262438	−	0.964949i	$-0.584526\pi$
$983$	22.0865	−	38.2550i	0.704451	−	1.22015i	0.966889	−	0.255197i	$-0.0821403\pi$
$984$	1.80430	−	11.5929i	0.0575191	−	0.369567i
$985$	70.5524	−	40.7335i	2.24799	−	1.29788i
$986$	0.223514	+	0.387138i	0.00711814	+	0.0123290i
$987$		0			0
$988$	−20.0883	+	34.7940i	−0.639094	+	1.10694i
$989$			1.37855i			0.0438353i
$990$	16.2099	+	5.17104i	0.515183	+	0.164347i
$991$	26.8886			0.854146			0.427073	−	0.904217i	$-0.359545\pi$
$991$	26.8886			0.854146			0.427073	+	0.904217i	$0.359545\pi$
$992$	−2.43810	+	4.22291i	−0.0774097	+	0.134078i
$993$	−9.86473	−	25.4941i	−0.313048	−	0.809032i
$994$		0			0
$995$	19.1208	−	11.0394i	0.606170	−	0.349972i
$996$	−6.04967	+	7.51178i	−0.191691	+	0.238020i
$997$	26.9780	+	15.5757i	0.854401	+	0.493289i	0.862133	−	0.506681i	$-0.169128\pi$
$997$	26.9780	+	15.5757i	0.854401	+	0.493289i	−0.00773220	+	0.999970i	$0.502461\pi$
$998$			15.1919i			0.480891i
$999$	−37.2063	−	18.5824i	−1.17715	−	0.587920i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.o.e.146.11	✓	48
3.2	odd	2		1323.2.o.e.440.13		48
7.2	even	3		441.2.i.d.227.13		48
7.3	odd	6		441.2.s.d.362.13		48
7.4	even	3		441.2.s.d.362.14		48
7.5	odd	6		441.2.i.d.227.14		48
7.6	odd	2	inner	441.2.o.e.146.12	yes	48
9.4	even	3		1323.2.o.e.881.14		48
9.5	odd	6	inner	441.2.o.e.293.12	yes	48
21.2	odd	6		1323.2.i.d.521.3		48
21.5	even	6		1323.2.i.d.521.19		48
21.11	odd	6		1323.2.s.d.656.12		48
21.17	even	6		1323.2.s.d.656.11		48
21.20	even	2		1323.2.o.e.440.14		48
63.4	even	3		1323.2.i.d.1097.19		48
63.5	even	6		441.2.s.d.374.14		48
63.13	odd	6		1323.2.o.e.881.13		48
63.23	odd	6		441.2.s.d.374.13		48
63.31	odd	6		1323.2.i.d.1097.3		48
63.32	odd	6		441.2.i.d.68.12		48
63.40	odd	6		1323.2.s.d.962.12		48
63.41	even	6	inner	441.2.o.e.293.11	yes	48
63.58	even	3		1323.2.s.d.962.11		48
63.59	even	6		441.2.i.d.68.11		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.11		48	63.59	even	6
441.2.i.d.68.12		48	63.32	odd	6
441.2.i.d.227.13		48	7.2	even	3
441.2.i.d.227.14		48	7.5	odd	6
441.2.o.e.146.11	✓	48	1.1	even	1	trivial
441.2.o.e.146.12	yes	48	7.6	odd	2	inner
441.2.o.e.293.11	yes	48	63.41	even	6	inner
441.2.o.e.293.12	yes	48	9.5	odd	6	inner
441.2.s.d.362.13		48	7.3	odd	6
441.2.s.d.362.14		48	7.4	even	3
441.2.s.d.374.13		48	63.23	odd	6
441.2.s.d.374.14		48	63.5	even	6
1323.2.i.d.521.3		48	21.2	odd	6
1323.2.i.d.521.19		48	21.5	even	6
1323.2.i.d.1097.3		48	63.31	odd	6
1323.2.i.d.1097.19		48	63.4	even	3
1323.2.o.e.440.13		48	3.2	odd	2
1323.2.o.e.440.14		48	21.20	even	2
1323.2.o.e.881.13		48	63.13	odd	6
1323.2.o.e.881.14		48	9.4	even	3
1323.2.s.d.656.11		48	21.17	even	6
1323.2.s.d.656.12		48	21.11	odd	6
1323.2.s.d.962.11		48	63.58	even	3
1323.2.s.d.962.12		48	63.40	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.367369 - 0.212101i) q^{2} +(-1.08640 + 1.34897i) q^{3} +(-0.910027 - 1.57621i) q^{4} +(-1.80381 - 3.12430i) q^{5} +(0.685229 - 0.265143i) q^{6} +1.62047i q^{8} +(-0.639450 - 2.93106i) q^{9} +O(q^{10})\)	\(q+(-0.367369 - 0.212101i) q^{2} +(-1.08640 + 1.34897i) q^{3} +(-0.910027 - 1.57621i) q^{4} +(-1.80381 - 3.12430i) q^{5} +(0.685229 - 0.265143i) q^{6} +1.62047i q^{8} +(-0.639450 - 2.93106i) q^{9} +1.53036i q^{10} +(3.20952 + 1.85302i) q^{11} +(3.11492 + 0.484804i) q^{12} +(-5.23479 + 3.02231i) q^{13} +(6.17426 + 0.960957i) q^{15} +(-1.47635 + 2.55711i) q^{16} +1.06422 q^{17} +(-0.386765 + 1.21241i) q^{18} +3.65191i q^{19} +(-3.28304 + 5.68639i) q^{20} +(-0.786052 - 1.36148i) q^{22} +(0.314574 - 0.181620i) q^{23} +(-2.18597 - 1.76049i) q^{24} +(-4.00749 + 6.94117i) q^{25} +2.56413 q^{26} +(4.64862 + 2.32172i) q^{27} +(-0.857560 - 0.495112i) q^{29} +(-2.06441 - 1.66259i) q^{30} +(-0.939786 + 0.542586i) q^{31} +(3.89147 - 2.24674i) q^{32} +(-5.98650 + 2.31642i) q^{33} +(-0.390960 - 0.225721i) q^{34} +(-4.03805 + 3.67525i) q^{36} -8.00373 q^{37} +(0.774573 - 1.34160i) q^{38} +(1.61009 - 10.3450i) q^{39} +(5.06283 - 2.92303i) q^{40} +(2.09005 + 3.62007i) q^{41} +(-1.89758 + 3.28670i) q^{43} -6.74518i q^{44} +(-8.00405 + 7.28491i) q^{45} -0.154086 q^{46} +(-2.83849 + 4.91640i) q^{47} +(-1.84556 - 4.76962i) q^{48} +(2.94445 - 1.69998i) q^{50} +(-1.15617 + 1.43560i) q^{51} +(9.52760 + 5.50076i) q^{52} +4.53177i q^{53} +(-1.21532 - 1.83890i) q^{54} -13.3700i q^{55} +(-4.92633 - 3.96745i) q^{57} +(0.210027 + 0.363778i) q^{58} +(-5.62746 - 9.74705i) q^{59} +(-4.10407 - 10.6064i) q^{60} +(-0.0238258 - 0.0137558i) q^{61} +0.460331 q^{62} +3.99926 q^{64} +(18.8852 + 10.9034i) q^{65} +(2.69057 + 0.418758i) q^{66} +(4.86489 + 8.42624i) q^{67} +(-0.968464 - 1.67743i) q^{68} +(-0.0967553 + 0.621664i) q^{69} -5.55775i q^{71} +(4.74970 - 1.03621i) q^{72} -2.25814i q^{73} +(2.94032 + 1.69759i) q^{74} +(-5.00969 - 12.9469i) q^{75} +(5.75619 - 3.32334i) q^{76} +(-2.78569 + 3.45894i) q^{78} +(-3.26604 + 5.65694i) q^{79} +10.6522 q^{80} +(-8.18221 + 3.74853i) q^{81} -1.77320i q^{82} +(-1.52977 + 2.64964i) q^{83} +(-1.91965 - 3.32492i) q^{85} +(1.39422 - 0.804954i) q^{86} +(1.59955 - 0.618932i) q^{87} +(-3.00276 + 5.20093i) q^{88} +14.9590 q^{89} +(4.48557 - 0.978588i) q^{90} +(-0.572542 - 0.330557i) q^{92} +(0.289055 - 1.85721i) q^{93} +(2.08554 - 1.20409i) q^{94} +(11.4097 - 6.58737i) q^{95} +(-1.19692 + 7.69035i) q^{96} +(-1.67018 - 0.964277i) q^{97} +(3.37897 - 10.5922i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4} + 16 q^{9}+O(q^{10}) \) 48 * q + 24 * q^4 + 16 * q^9	\( 48 q + 24 q^{4} + 16 q^{9} - 24 q^{11} - 40 q^{15} - 24 q^{16} - 16 q^{18} - 48 q^{23} - 24 q^{25} - 24 q^{30} + 120 q^{32} - 8 q^{36} + 88 q^{39} + 48 q^{50} + 24 q^{51} + 80 q^{57} - 96 q^{60} - 48 q^{64} + 120 q^{65} + 56 q^{72} - 168 q^{74} - 88 q^{78} - 24 q^{79} - 96 q^{81} - 24 q^{85} + 24 q^{86} - 144 q^{92} - 32 q^{93} + 96 q^{95} - 72 q^{99}+O(q^{100}) \) 48 * q + 24 * q^4 + 16 * q^9 - 24 * q^11 - 40 * q^15 - 24 * q^16 - 16 * q^18 - 48 * q^23 - 24 * q^25 - 24 * q^30 + 120 * q^32 - 8 * q^36 + 88 * q^39 + 48 * q^50 + 24 * q^51 + 80 * q^57 - 96 * q^60 - 48 * q^64 + 120 * q^65 + 56 * q^72 - 168 * q^74 - 88 * q^78 - 24 * q^79 - 96 * q^81 - 24 * q^85 + 24 * q^86 - 144 * q^92 - 32 * q^93 + 96 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

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