LMFDB - Embedded newform 441.2.o.e.146.12

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			146.12
Character	$\chi$	$=$	441.146
Dual form			441.2.o.e.293.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.367369 - 0.212101i) q^{2} +(1.08640 - 1.34897i) q^{3} +(-0.910027 - 1.57621i) q^{4} +(1.80381 + 3.12430i) q^{5} +(-0.685229 + 0.265143i) q^{6} +1.62047i q^{8} +(-0.639450 - 2.93106i) q^{9} +O(q^{10})$	\(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	$0.132077\pi$
$5$	1.80381	+	3.12430i	0.806690	+	1.39723i	−0.108454	+	0.994101i	$0.534590\pi$
$6$	−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	0.453283	−	0.891367i	$-0.350253\pi$
$13$	5.23479	−	3.02231i	1.45187	−	0.838238i	0.998588	+	0.0531292i	$0.0169195\pi$
$14$		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	$-0.541194\pi$
$17$	−1.06422			−0.258110			−0.129055	+	0.991637i	$0.541194\pi$
$18$	−0.386765	+	1.21241i	−0.0911614	+	0.285767i
$19$		−	3.65191i		−	0.837806i	−0.908031	−	0.418903i	$-0.862415\pi$
$19$		−	3.65191i		−	0.837806i	0.908031	−	0.418903i	$-0.137585\pi$
$20$	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	−0.413225	−	0.910629i	$-0.635598\pi$
$31$	0.939786	−	0.542586i	0.168791	−	0.0974513i	0.582015	+	0.813178i	$0.302264\pi$
$32$	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	0.655386	−	0.755294i	$-0.272506\pi$
$41$	−2.09005	−	3.62007i	−0.326411	−	0.565360i	−0.981797	+	0.189934i	$0.939173\pi$
$42$		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	−0.581291	−	0.813696i	$-0.697452\pi$
$47$	2.83849	−	4.91640i	0.414036	−	0.717131i	0.995327	+	0.0965648i	$0.0307855\pi$
$48$	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	$0.0950422\pi$
$59$	5.62746	+	9.74705i	0.732633	+	1.26896i	−0.223121	+	0.974791i	$0.571624\pi$
$60$	−4.10407	−	10.6064i	−0.529833	−	1.36929i
$61$	0.0238258	+	0.0137558i	0.00305058	+	0.00176126i	0.501525	−	0.865143i	$-0.332773\pi$
$61$	0.0238258	+	0.0137558i	0.00305058	+	0.00176126i	−0.498474	+	0.866905i	$0.666106\pi$
$62$	−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	$0.0421874\pi$
$73$			2.25814i			0.264296i	−0.991230	+	0.132148i	$0.957813\pi$
$74$	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	−0.769772	−	0.638319i	$-0.779630\pi$
$83$	1.52977	−	2.64964i	0.167914	−	0.290836i	0.937686	+	0.347483i	$0.112964\pi$
$84$		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	$-0.791392\pi$
$89$	−14.9590			−1.58565			−0.792827	+	0.609446i	$0.791392\pi$
$90$	−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	0.582388	−	0.812911i	$-0.302118\pi$
$97$	1.67018	+	0.964277i	0.169581	+	0.0979075i	−0.412807	+	0.910818i	$0.635452\pi$
$98$		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	−0.980532	−	0.196359i	$-0.937088\pi$
$101$	−3.21811	+	5.57394i	−0.320214	+	0.554627i	0.660318	+	0.750986i	$0.270422\pi$
$102$	0.729231	−	0.282170i	0.0722046	−	0.0279389i
$103$	8.41917	−	4.86081i	0.829565	−	0.478950i	−0.0241385	−	0.999709i	$-0.507684\pi$
$103$	8.41917	−	4.86081i	0.829565	−	0.478950i	0.853704	+	0.520759i	$0.174351\pi$
$104$	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	$0.203131\pi$
$131$	10.5013	+	18.1888i	0.917502	+	1.58916i	0.114305	+	0.993446i	$0.463536\pi$
$132$	−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	−0.376388	−	0.926462i	$-0.622834\pi$
$139$	2.80312	−	1.61838i	0.237758	−	0.137269i	0.614146	+	0.789193i	$0.289501\pi$
$140$		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	−0.741059	−	0.671439i	$-0.765676\pi$
$157$	−6.64220	+	3.83488i	−0.530106	+	0.306057i	0.210954	+	0.977496i	$0.432343\pi$
$158$	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	0.982481	−	0.186363i	$-0.0596702\pi$
$167$	4.26254	+	7.38293i	0.329845	+	0.571308i	−0.652636	+	0.757672i	$0.726337\pi$
$168$		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	−0.874173	−	0.485615i	$-0.838596\pi$
$173$	−0.217445	+	0.376626i	−0.0165320	+	0.0286343i	0.857641	+	0.514249i	$0.171929\pi$
$174$	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	$-0.770818\pi$
$181$		−	17.7421i		−	1.31876i	0.751809	−	0.659381i	$-0.229182\pi$
$182$		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	$-0.930399\pi$
$199$		−	6.12003i		−	0.433837i	0.976190	−	0.216919i	$-0.0696007\pi$
$200$	−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	−0.494446	−	0.869209i	$-0.664629\pi$
$223$	−22.3165	−	12.8845i	−1.49443	−	0.862807i	−0.999980	+	0.00640186i	$0.997962\pi$
$224$		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	$-0.529125\pi$
$227$	12.3051	−	21.3130i	0.816718	−	1.41460i	0.908088	−	0.418779i	$-0.137542\pi$
$228$	−1.77046	+	11.3754i	−0.117252	+	0.753356i
$229$	−3.94267	+	2.27630i	−0.260539	+	0.150422i	−0.624580	−	0.780961i	$-0.714730\pi$
$229$	−3.94267	+	2.27630i	−0.260539	+	0.150422i	0.364042	+	0.931383i	$0.381397\pi$
$230$	−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	0.887935	−	0.459968i	$-0.152139\pi$
$241$	14.4927	+	8.36738i	0.933559	+	0.538991i	0.0456237	+	0.998959i	$0.485472\pi$
$242$		−	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	$-0.446153\pi$
$251$	5.33468			0.336722			0.168361	+	0.985725i	$0.446153\pi$
$252$		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	$-0.887979\pi$
$257$	−12.3100	−	21.3216i	−0.767878	−	1.33000i	0.170834	−	0.985300i	$-0.445354\pi$
$258$	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	$-0.359846\pi$
$269$	13.9809			0.852432			0.426216	+	0.904622i	$0.359846\pi$
$270$	−3.55306	+	7.11405i	−0.216232	+	0.432948i
$271$			6.46262i			0.392576i	0.980546	+	0.196288i	$0.0628888\pi$
$271$			6.46262i			0.392576i	−0.980546	+	0.196288i	$0.937111\pi$
$272$	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	−0.851019	−	0.525135i	$-0.824015\pi$
$283$	−13.8239	+	7.98126i	−0.821748	+	0.474436i	0.0292708	+	0.999572i	$0.490681\pi$
$284$	−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	0.947104	−	0.320927i	$-0.103995\pi$
$293$	3.34849	+	5.79975i	0.195621	+	0.338825i	−0.751483	+	0.659752i	$0.770661\pi$
$294$		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	$-0.921163\pi$
$307$		−	8.59068i		−	0.490296i	0.969486	−	0.245148i	$-0.0788365\pi$
$308$		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	0.799733	−	0.600356i	$-0.204974\pi$
$311$	−2.11723	−	3.66714i	−0.120057	−	0.207945i	−0.919790	+	0.392411i	$0.871641\pi$
$312$	16.7638	+	2.60911i	0.949065	+	0.147712i
$313$	−3.10288	−	1.79145i	−0.175385	−	0.101259i	0.409737	−	0.912204i	$-0.365620\pi$
$313$	−3.10288	−	1.79145i	−0.175385	−	0.101259i	−0.585123	+	0.810945i	$0.698954\pi$
$314$	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	0.457885	−	0.889011i	$-0.348607\pi$
$349$	−1.55204	−	0.896072i	−0.0830789	−	0.0479656i	−0.540964	+	0.841046i	$0.681940\pi$
$350$		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	−0.950622	−	0.310352i	$-0.899553\pi$
$353$	−3.88049	+	6.72121i	−0.206538	+	0.357734i	0.744084	+	0.668086i	$0.232886\pi$
$354$	−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	0.103536	−	0.994626i	$-0.466984\pi$
$367$	−13.5263	−	7.80942i	−0.706068	−	0.407648i	−0.809603	+	0.586977i	$0.800318\pi$
$368$			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	0.969006	−	0.247036i	$-0.0794566\pi$
$383$	5.29503	+	9.17127i	0.270564	+	0.468630i	−0.698443	+	0.715666i	$0.746123\pi$
$384$	−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	$-0.569236\pi$
$397$		−	38.9108i		−	1.95287i	0.215801	−	0.976437i	$-0.430764\pi$
$398$	−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	−0.0380133	−	0.999277i	$-0.512103\pi$
$409$	16.3485	−	9.43879i	0.808379	−	0.466718i	0.846393	+	0.532559i	$0.178770\pi$
$410$	−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	0.935636	−	0.352965i	$-0.114827\pi$
$419$	3.31895	+	5.74860i	0.162142	+	0.280837i	−0.773495	+	0.633802i	$0.781493\pi$
$420$		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	$-0.974569\pi$
$433$		−	3.32148i		−	0.159620i	0.996810	−	0.0798101i	$-0.0254314\pi$
$434$		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	0.939515	−	0.342509i	$-0.111277\pi$
$439$	23.3126	+	13.4595i	1.11265	+	0.642389i	0.173136	+	0.984898i	$0.444610\pi$
$440$	−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	−0.983871	−	0.178878i	$-0.942753\pi$
$461$	−7.23618	+	12.5334i	−0.337023	+	0.583740i	0.646849	+	0.762618i	$0.276087\pi$
$462$		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	$-0.683540\pi$
$467$	−23.5630			−1.09037			−0.545183	+	0.838317i	$0.683540\pi$
$468$	−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	$0.359587\pi$
$479$	−12.4674	+	21.5941i	−0.569648	+	0.986660i	−0.996601	+	0.0823855i	$0.973746\pi$
$480$	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	$-0.320318\pi$
$503$	23.9969			1.06997			0.534984	+	0.844862i	$0.320318\pi$
$504$		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	0.993975	−	0.109610i	$-0.0349602\pi$
$509$	9.07094	+	15.7113i	0.402062	+	0.696392i	−0.591912	+	0.806002i	$0.701627\pi$
$510$	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	$-0.494147\pi$
$521$	0.839387			0.0367742			0.0183871	+	0.999831i	$0.494147\pi$
$522$	0.931952	−	0.848220i	0.0407904	−	0.0371256i
$523$			16.2832i			0.712015i	0.934483	+	0.356008i	$0.115862\pi$
$523$			16.2832i			0.712015i	−0.934483	+	0.356008i	$0.884138\pi$
$524$	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	0.949612	−	0.313429i	$-0.101478\pi$
$563$	4.82545	+	8.35793i	0.203369	+	0.352245i	−0.746243	+	0.665673i	$0.768144\pi$
$564$	−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	$-0.682650\pi$
$577$		−	40.3472i		−	1.67968i	0.542837	−	0.839838i	$-0.317350\pi$
$578$	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	−0.902840	−	0.429977i	$-0.858522\pi$
$587$	−1.91520	+	3.31723i	−0.0790490	+	0.136917i	0.823791	+	0.566894i	$0.191855\pi$
$588$		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	$-0.417282\pi$
$593$	12.5143			0.513902			0.256951	+	0.966424i	$0.417282\pi$
$594$	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	0.964416	−	0.264388i	$-0.0851698\pi$
$601$	29.8513	+	17.2346i	1.21766	+	0.703015i	0.253242	+	0.967403i	$0.418503\pi$
$602$		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	−0.265776	−	0.964035i	$-0.585628\pi$
$607$	10.7472	−	6.20488i	0.436214	−	0.251848i	0.701990	+	0.712186i	$0.252295\pi$
$608$	−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	0.436314	−	0.899795i	$-0.356284\pi$
$619$	−3.10436	−	1.79230i	−0.124775	−	0.0720387i	−0.561088	+	0.827756i	$0.689617\pi$
$620$		−	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	−0.592253	−	0.805752i	$-0.701761\pi$
$643$	−4.83255	+	2.79007i	−0.190577	+	0.110030i	0.401676	+	0.915782i	$0.368428\pi$
$644$		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	$-0.475562\pi$
$647$	3.90178			0.153395			0.0766974	+	0.997054i	$0.475562\pi$
$648$	−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	−0.0128707	−	0.999917i	$-0.504097\pi$
$661$	21.7672	−	12.5673i	0.846648	−	0.488812i	0.859518	+	0.511105i	$0.170764\pi$
$662$	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	$0.390222\pi$
$677$	−16.8081	+	29.1126i	−0.645989	+	1.11889i	−0.984072	+	0.177770i	$0.943112\pi$
$678$	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	−0.0888052	−	0.996049i	$-0.528305\pi$
$691$	−26.1768	−	15.1132i	−0.995812	−	0.574932i	−0.907006	+	0.421117i	$0.861638\pi$
$692$	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	$-0.509574\pi$
$719$	−1.61282			−0.0601480			−0.0300740	+	0.999548i	$0.509574\pi$
$720$	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	0.681799	−	0.731540i	$-0.261198\pi$
$727$	10.4930	+	6.05816i	0.389166	+	0.224685i	−0.292633	+	0.956225i	$0.594531\pi$
$728$		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	0.313403	−	0.949620i	$-0.398531\pi$
$733$	34.9931	−	20.2033i	1.29250	−	0.746225i	0.979097	+	0.203396i	$0.0651977\pi$
$734$	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	0.995958	−	0.0898160i	$-0.0286279\pi$
$761$	11.5916	+	20.0773i	0.420196	+	0.727801i	−0.575762	+	0.817617i	$0.695295\pi$
$762$	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	−0.279082	−	0.960267i	$-0.590030\pi$
$769$	11.4527	−	6.61219i	0.412993	−	0.238442i	0.692075	+	0.721826i	$0.256697\pi$
$770$		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	$-0.385143\pi$
$773$	19.6319			0.706110			0.353055	+	0.935603i	$0.385143\pi$
$774$	−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	−0.211149	−	0.977454i	$-0.567721\pi$
$787$	14.8621	−	8.58063i	0.529776	−	0.305866i	0.740925	+	0.671588i	$0.234387\pi$
$788$	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	0.594201	−	0.804317i	$-0.297468\pi$
$797$	−11.2772	−	19.5326i	−0.399458	−	0.691882i	−0.993659	+	0.112435i	$0.964135\pi$
$798$		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	$0.0631774\pi$
$811$			11.2304i			0.394354i	−0.980368	+	0.197177i	$0.936823\pi$
$812$		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	$-0.910006\pi$
$829$		−	16.0646i		−	0.557945i	0.960299	−	0.278973i	$-0.0899939\pi$
$830$	−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	−0.986590	−	0.163216i	$-0.947813\pi$
$839$	−10.1943	+	17.6570i	−0.351946	+	0.609589i	0.634644	+	0.772805i	$0.281147\pi$
$840$		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	0.627677	−	0.778474i	$-0.284006\pi$
$853$	7.80792	+	4.50790i	0.267338	+	0.154348i	−0.360339	+	0.932821i	$0.617339\pi$
$854$		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	$0.352883\pi$
$857$	−16.1658	+	28.0000i	−0.552213	+	0.956461i	−0.998115	+	0.0613789i	$0.980450\pi$
$858$	−15.3502	+	5.93962i	−0.524047	+	0.202775i
$859$	38.1416	−	22.0211i	1.30138	−	0.751349i	0.320735	−	0.947169i	$-0.396070\pi$
$859$	38.1416	−	22.0211i	1.30138	−	0.751349i	0.980640	+	0.195819i	$0.0627366\pi$
$860$	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	$-0.605378\pi$
$881$	−19.2955			−0.650083			−0.325041	+	0.945700i	$0.605378\pi$
$882$		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	$-0.749741\pi$
$887$	−28.7740	−	49.8380i	−0.966136	−	1.67340i	−0.259604	−	0.965715i	$-0.583592\pi$
$888$	−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	−0.786311	−	0.617831i	$-0.788011\pi$
$929$	4.32511	−	7.49131i	0.141902	−	0.245782i	0.928213	+	0.372049i	$0.121345\pi$
$930$	−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	$0.193454\pi$
$937$			34.9586i			1.14205i	−0.820933	+	0.571025i	$0.806546\pi$
$938$		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	$-0.933039\pi$
$941$	−20.5472	−	35.5887i	−0.669818	−	1.16016i	0.308136	−	0.951342i	$-0.400295\pi$
$942$	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	$-0.280855\pi$
$971$	39.5962			1.27070			0.635351	+	0.772223i	$0.280855\pi$
$972$	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	$0.415474\pi$
$983$	−22.0865	+	38.2550i	−0.704451	+	1.22015i	−0.966889	+	0.255197i	$0.917860\pi$
$984$	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	0.00773220	−	0.999970i	$-0.497539\pi$
$997$	−26.9780	−	15.5757i	−0.854401	−	0.493289i	−0.862133	+	0.506681i	$0.830872\pi$
$998$			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.146.12	yes	48
3.2	odd	2		1323.2.o.e.440.14		48
7.2	even	3		441.2.i.d.227.14		48
7.3	odd	6		441.2.s.d.362.14		48
7.4	even	3		441.2.s.d.362.13		48
7.5	odd	6		441.2.i.d.227.13		48
7.6	odd	2	inner	441.2.o.e.146.11	✓	48
9.4	even	3		1323.2.o.e.881.13		48
9.5	odd	6	inner	441.2.o.e.293.11	yes	48
21.2	odd	6		1323.2.i.d.521.19		48
21.5	even	6		1323.2.i.d.521.3		48
21.11	odd	6		1323.2.s.d.656.11		48
21.17	even	6		1323.2.s.d.656.12		48
21.20	even	2		1323.2.o.e.440.13		48
63.4	even	3		1323.2.i.d.1097.3		48
63.5	even	6		441.2.s.d.374.13		48
63.13	odd	6		1323.2.o.e.881.14		48
63.23	odd	6		441.2.s.d.374.14		48
63.31	odd	6		1323.2.i.d.1097.19		48
63.32	odd	6		441.2.i.d.68.11		48
63.40	odd	6		1323.2.s.d.962.11		48
63.41	even	6	inner	441.2.o.e.293.12	yes	48
63.58	even	3		1323.2.s.d.962.12		48
63.59	even	6		441.2.i.d.68.12		48

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

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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