LMFDB - Embedded newform 405.2.r.a.152.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,2,Mod(8,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 27]))

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

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

chi := DirichletCharacter("405.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			152.7
Character	$\chi$	$=$	405.152
Dual form			405.2.r.a.8.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.263290 - 0.184358i) q^{2} +(-0.648706 - 1.78231i) q^{4} +(-2.21531 + 0.303968i) q^{5} +(2.07991 + 4.46037i) q^{7} +(-0.324162 + 1.20979i) q^{8} +O(q^{10})$	\(q+(-0.263290 - 0.184358i) q^{2} +(-0.648706 - 1.78231i) q^{4} +(-2.21531 + 0.303968i) q^{5} +(2.07991 + 4.46037i) q^{7} +(-0.324162 + 1.20979i) q^{8} +(0.639309 + 0.328378i) q^{10} +(-0.0393995 - 0.0469545i) q^{11} +(0.0455832 + 0.0650996i) q^{13} +(0.274686 - 1.55782i) q^{14} +(-2.59752 + 2.17957i) q^{16} +(1.04290 + 3.89214i) q^{17} +(1.80193 - 1.04035i) q^{19} +(1.97885 + 3.75118i) q^{20} +(0.00171708 + 0.0196263i) q^{22} +(5.88782 + 2.74553i) q^{23} +(4.81521 - 1.34677i) q^{25} -0.0255437i q^{26} +(6.60050 - 6.60050i) q^{28} +(1.24585 + 7.06559i) q^{29} +(0.209263 - 0.0761654i) q^{31} +(3.58112 - 0.313308i) q^{32} +(0.442962 - 1.21703i) q^{34} +(-5.96345 - 9.24888i) q^{35} +(-6.33380 + 1.69714i) q^{37} +(-0.666227 - 0.0582873i) q^{38} +(0.350383 - 2.77860i) q^{40} +(2.22023 + 0.391486i) q^{41} +(-0.325424 + 3.71962i) q^{43} +(-0.0581286 + 0.100682i) q^{44} +(-1.04404 - 1.80834i) q^{46} +(-1.26917 + 0.591824i) q^{47} +(-11.0694 + 13.1920i) q^{49} +(-1.51608 - 0.533130i) q^{50} +(0.0864573 - 0.123474i) q^{52} +(-8.67464 - 8.67464i) q^{53} +(0.101555 + 0.0920427i) q^{55} +(-6.07034 + 1.07036i) q^{56} +(0.974575 - 2.08998i) q^{58} +(0.888968 + 0.745933i) q^{59} +(-6.77967 - 2.46760i) q^{61} +(-0.0691385 - 0.0185256i) q^{62} +(4.87243 + 2.81310i) q^{64} +(-0.120769 - 0.130360i) q^{65} +(6.22807 - 4.36094i) q^{67} +(6.26045 - 4.38361i) q^{68} +(-0.134987 + 3.53455i) q^{70} +(-6.33059 - 3.65497i) q^{71} +(6.42123 + 1.72056i) q^{73} +(1.98051 + 0.720846i) q^{74} +(-3.02314 - 2.53672i) q^{76} +(0.127487 - 0.273398i) q^{77} +(-6.06016 + 1.06857i) q^{79} +(5.09178 - 5.61800i) q^{80} +(-0.512391 - 0.512391i) q^{82} +(2.31193 - 3.30178i) q^{83} +(-3.49342 - 8.30529i) q^{85} +(0.771422 - 0.919344i) q^{86} +(0.0695770 - 0.0324443i) q^{88} +(5.25350 + 9.09933i) q^{89} +(-0.195560 + 0.338719i) q^{91} +(1.07392 - 12.2749i) q^{92} +(0.443268 + 0.0781601i) q^{94} +(-3.67561 + 2.85242i) q^{95} +(9.77698 + 0.855375i) q^{97} +(5.34651 - 1.43259i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.263290	−	0.184358i	−0.186174	−	0.130361i	0.476774	−	0.879026i	$-0.341806\pi$
$2$	−0.263290	−	0.184358i	−0.186174	−	0.130361i	−0.662948	+	0.748665i	$0.730695\pi$
$3$		0			0
$3$		0			0
$4$	−0.648706	−	1.78231i	−0.324353	−	0.891153i
$5$	−2.21531	+	0.303968i	−0.990717	+	0.135939i
$5$	−2.21531	+	0.303968i	−0.990717	+	0.135939i
$6$		0			0
$7$	2.07991	+	4.46037i	0.786130	+	1.68586i	0.726024	+	0.687670i	$0.241366\pi$
$7$	2.07991	+	4.46037i	0.786130	+	1.68586i	0.0601067	+	0.998192i	$0.480856\pi$
$8$	−0.324162	+	1.20979i	−0.114609	+	0.427725i
$9$		0			0
$10$	0.639309	+	0.328378i	0.202167	+	0.103842i
$11$	−0.0393995	−	0.0469545i	−0.0118794	−	0.0141573i	0.760072	−	0.649839i	$-0.225164\pi$
$11$	−0.0393995	−	0.0469545i	−0.0118794	−	0.0141573i	−0.771951	+	0.635682i	$0.780719\pi$
$12$		0			0
$13$	0.0455832	+	0.0650996i	0.0126425	+	0.0180554i	0.825424	−	0.564514i	$-0.190936\pi$
$13$	0.0455832	+	0.0650996i	0.0126425	+	0.0180554i	−0.812781	+	0.582569i	$0.802047\pi$
$14$	0.274686	−	1.55782i	0.0734128	−	0.416345i
$15$		0			0
$16$	−2.59752	+	2.17957i	−0.649379	+	0.544894i
$17$	1.04290	+	3.89214i	0.252939	+	0.943982i	0.969225	+	0.246175i	$0.0791739\pi$
$17$	1.04290	+	3.89214i	0.252939	+	0.943982i	−0.716286	+	0.697807i	$0.754159\pi$
$18$		0			0
$19$	1.80193	−	1.04035i	0.413392	−	0.238672i	−0.278854	−	0.960333i	$-0.589955\pi$
$19$	1.80193	−	1.04035i	0.413392	−	0.238672i	0.692246	+	0.721662i	$0.256621\pi$
$20$	1.97885	+	3.75118i	0.442484	+	0.838789i
$21$		0			0
$22$	0.00171708	+	0.0196263i	0.000366082	+	0.00418434i
$23$	5.88782	+	2.74553i	1.22769	+	0.572483i	0.924768	−	0.380531i	$-0.124259\pi$
$23$	5.88782	+	2.74553i	1.22769	+	0.572483i	0.302926	+	0.953014i	$0.402036\pi$
$24$		0			0
$25$	4.81521	−	1.34677i	0.963041	−	0.269354i
$26$		−	0.0255437i		−	0.00500954i
$27$		0			0
$28$	6.60050	−	6.60050i	1.24738	−	1.24738i
$29$	1.24585	+	7.06559i	0.231349	+	1.31205i	0.850167	+	0.526512i	$0.176501\pi$
$29$	1.24585	+	7.06559i	0.231349	+	1.31205i	−0.618818	+	0.785534i	$0.712388\pi$
$30$		0			0
$31$	0.209263	−	0.0761654i	0.0375847	−	0.0136797i	−0.323159	−	0.946345i	$-0.604745\pi$
$31$	0.209263	−	0.0761654i	0.0375847	−	0.0136797i	0.360744	+	0.932665i	$0.382523\pi$
$32$	3.58112	−	0.313308i	0.633059	−	0.0553855i
$33$		0			0
$34$	0.442962	−	1.21703i	0.0759674	−	0.208719i
$35$	−5.96345	−	9.24888i	−1.00801	−	1.56335i
$36$		0			0
$37$	−6.33380	+	1.69714i	−1.04127	+	0.279007i	−0.738640	−	0.674101i	$-0.764531\pi$
$37$	−6.33380	+	1.69714i	−1.04127	+	0.279007i	−0.302630	+	0.953108i	$0.597865\pi$
$38$	−0.666227	−	0.0582873i	−0.108076	−	0.00945545i
$39$		0			0
$40$	0.350383	−	2.77860i	0.0554004	−	0.439335i
$41$	2.22023	+	0.391486i	0.346742	+	0.0611399i	0.344307	−	0.938857i	$-0.388114\pi$
$41$	2.22023	+	0.391486i	0.346742	+	0.0611399i	0.00243462	+	0.999997i	$0.499225\pi$
$42$		0			0
$43$	−0.325424	+	3.71962i	−0.0496267	+	0.567236i	0.930155	+	0.367167i	$0.119672\pi$
$43$	−0.325424	+	3.71962i	−0.0496267	+	0.567236i	−0.979782	+	0.200069i	$0.935883\pi$
$44$	−0.0581286	+	0.100682i	−0.00876322	+	0.0151783i
$45$		0			0
$46$	−1.04404	−	1.80834i	−0.153936	−	0.266625i
$47$	−1.26917	+	0.591824i	−0.185128	+	0.0863264i	−0.512972	−	0.858405i	$-0.671456\pi$
$47$	−1.26917	+	0.591824i	−0.185128	+	0.0863264i	0.327844	+	0.944732i	$0.393678\pi$
$48$		0			0
$49$	−11.0694	+	13.1920i	−1.58134	+	1.88457i
$50$	−1.51608	−	0.533130i	−0.214407	−	0.0753960i
$51$		0			0
$52$	0.0864573	−	0.123474i	0.0119895	−	0.0171227i
$53$	−8.67464	−	8.67464i	−1.19155	−	1.19155i	−0.976631	−	0.214923i	$-0.931050\pi$
$53$	−8.67464	−	8.67464i	−1.19155	−	1.19155i	−0.214923	−	0.976631i	$-0.568950\pi$
$54$		0			0
$55$	0.101555	+	0.0920427i	0.0136937	+	0.0124110i
$56$	−6.07034	+	1.07036i	−0.811183	+	0.143033i
$57$		0			0
$58$	0.974575	−	2.08998i	0.127968	−	0.274428i
$59$	0.888968	+	0.745933i	0.115734	+	0.0971121i	0.698818	−	0.715300i	$-0.253710\pi$
$59$	0.888968	+	0.745933i	0.115734	+	0.0971121i	−0.583084	+	0.812412i	$0.698154\pi$
$60$		0			0
$61$	−6.77967	−	2.46760i	−0.868048	−	0.315944i	−0.130672	−	0.991426i	$-0.541713\pi$
$61$	−6.77967	−	2.46760i	−0.868048	−	0.315944i	−0.737377	+	0.675482i	$0.763936\pi$
$62$	−0.0691385	−	0.0185256i	−0.00878060	−	0.00235275i
$63$		0			0
$64$	4.87243	+	2.81310i	0.609054	+	0.351637i
$65$	−0.120769	−	0.130360i	−0.0149796	−	0.0161692i
$66$		0			0
$67$	6.22807	−	4.36094i	0.760880	−	0.532774i	−0.127524	−	0.991835i	$-0.540703\pi$
$67$	6.22807	−	4.36094i	0.760880	−	0.532774i	0.888405	+	0.459061i	$0.151814\pi$
$68$	6.26045	−	4.38361i	0.759191	−	0.531591i
$69$		0			0
$70$	−0.134987	+	3.53455i	−0.0161340	+	0.422459i
$71$	−6.33059	−	3.65497i	−0.751303	−	0.433765i	0.0748614	−	0.997194i	$-0.476149\pi$
$71$	−6.33059	−	3.65497i	−0.751303	−	0.433765i	−0.826165	+	0.563429i	$0.809482\pi$
$72$		0			0
$73$	6.42123	+	1.72056i	0.751549	+	0.201377i	0.614205	−	0.789147i	$-0.289477\pi$
$73$	6.42123	+	1.72056i	0.751549	+	0.201377i	0.137344	+	0.990523i	$0.456144\pi$
$74$	1.98051	+	0.720846i	0.230229	+	0.0837966i
$75$		0			0
$76$	−3.02314	−	2.53672i	−0.346778	−	0.290981i
$77$	0.127487	−	0.273398i	0.0145285	−	0.0311565i
$78$		0			0
$79$	−6.06016	+	1.06857i	−0.681821	+	0.120223i	−0.503822	−	0.863807i	$-0.668073\pi$
$79$	−6.06016	+	1.06857i	−0.681821	+	0.120223i	−0.177999	+	0.984031i	$0.556962\pi$
$80$	5.09178	−	5.61800i	0.569279	−	0.628111i
$81$		0			0
$82$	−0.512391	−	0.512391i	−0.0565841	−	0.0565841i
$83$	2.31193	−	3.30178i	0.253767	−	0.362417i	−0.671974	−	0.740575i	$-0.734553\pi$
$83$	2.31193	−	3.30178i	0.253767	−	0.362417i	0.925741	+	0.378158i	$0.123442\pi$
$84$		0			0
$85$	−3.49342	−	8.30529i	−0.378915	−	0.900835i
$86$	0.771422	−	0.919344i	0.0831845	−	0.0991355i
$87$		0			0
$88$	0.0695770	−	0.0324443i	0.00741693	−	0.00345857i
$89$	5.25350	+	9.09933i	0.556870	+	0.964527i	0.997755	+	0.0669633i	$0.0213311\pi$
$89$	5.25350	+	9.09933i	0.556870	+	0.964527i	−0.440886	+	0.897563i	$0.645336\pi$
$90$		0			0
$91$	−0.195560	+	0.338719i	−0.0205002	+	0.0355074i
$92$	1.07392	−	12.2749i	0.111964	−	1.27975i
$93$		0			0
$94$	0.443268	+	0.0781601i	0.0457196	+	0.00806160i
$95$	−3.67561	+	2.85242i	−0.377109	+	0.292652i
$96$		0			0
$97$	9.77698	+	0.855375i	0.992702	+	0.0868501i	0.571918	−	0.820311i	$-0.306200\pi$
$97$	9.77698	+	0.855375i	0.992702	+	0.0868501i	0.420784	+	0.907161i	$0.361755\pi$
$98$	5.34651	−	1.43259i	0.540079	−	0.144714i
$99$		0			0
$100$	−5.52401	−	7.70852i	−0.552401	−	0.770852i
$101$	−1.28534	+	3.53144i	−0.127896	+	0.351391i	−0.987069	−	0.160293i	$-0.948756\pi$
$101$	−1.28534	+	3.53144i	−0.127896	+	0.351391i	0.859173	+	0.511684i	$0.170978\pi$
$102$		0			0
$103$	−2.41848	+	0.211590i	−0.238300	+	0.0208485i	−0.205680	−	0.978619i	$-0.565941\pi$
$103$	−2.41848	+	0.211590i	−0.238300	+	0.0208485i	−0.0326198	+	0.999468i	$0.510385\pi$
$104$	−0.0935332	+	0.0340433i	−0.00917169	+	0.00333822i
$105$		0			0
$106$	0.684711	+	3.88319i	0.0665050	+	0.377168i
$107$	−1.54852	+	1.54852i	−0.149701	+	0.149701i	−0.777984	−	0.628284i	$-0.783758\pi$
$107$	−1.54852	+	1.54852i	−0.149701	+	0.149701i	0.628284	+	0.777984i	$0.283758\pi$
$108$		0			0
$109$			0.257274i			0.0246424i	0.999924	+	0.0123212i	$0.00392206\pi$
$109$			0.257274i			0.0246424i	−0.999924	+	0.0123212i	$0.996078\pi$
$110$	−0.00976963	−	0.0429564i	−0.000931497	−	0.00409573i
$111$		0			0
$112$	−15.1243	−	7.05257i	−1.42911	−	0.666406i
$113$	−0.980488	−	11.2070i	−0.0922366	−	1.05427i	−0.891419	−	0.453180i	$-0.850289\pi$
$113$	−0.980488	−	11.2070i	−0.0922366	−	1.05427i	0.799182	−	0.601089i	$-0.205266\pi$
$114$		0			0
$115$	−13.8779	−	4.29250i	−1.29412	−	0.400278i
$116$	11.7848	−	6.80398i	1.09420	−	0.631734i
$117$		0			0
$118$	−0.0965380	−	0.360285i	−0.00888705	−	0.0331669i
$119$	−15.1913	+	12.7470i	−1.39258	+	1.16851i
$120$		0			0
$121$	1.90948	−	10.8292i	0.173589	−	0.984471i
$122$	1.33010	+	1.89958i	0.120422	+	0.171980i
$123$		0			0
$124$	−0.271500	−	0.323561i	−0.0243814	−	0.0290567i
$125$	−10.2578	+	4.44718i	−0.917486	+	0.397768i
$126$		0			0
$127$	−2.00243	+	7.47317i	−0.177687	+	0.663137i	0.818391	+	0.574661i	$0.194866\pi$
$127$	−2.00243	+	7.47317i	−0.177687	+	0.663137i	−0.996078	+	0.0884755i	$0.971801\pi$
$128$	−3.80270	−	8.15493i	−0.336115	−	0.720800i
$129$		0			0
$130$	0.00776448	+	0.0565873i	0.000680990	+	0.00496303i
$131$	−3.14700	−	8.64630i	−0.274954	−	0.755431i	−0.997915	−	0.0645417i	$-0.979441\pi$
$131$	−3.14700	−	8.64630i	−0.274954	−	0.755431i	0.722961	−	0.690889i	$-0.242781\pi$
$132$		0			0
$133$	8.38818	+	5.87347i	0.727347	+	0.509294i
$134$	−2.44376			−0.211109
$135$		0			0
$136$	−5.04674			−0.432754
$137$	11.2654	+	7.88810i	0.962466	+	0.673926i	0.945394	−	0.325928i	$-0.105677\pi$
$137$	11.2654	+	7.88810i	0.962466	+	0.673926i	0.0170715	+	0.999854i	$0.494566\pi$
$138$		0			0
$139$	−0.364140	−	1.00047i	−0.0308860	−	0.0848586i	0.923291	−	0.384101i	$-0.125488\pi$
$139$	−0.364140	−	1.00047i	−0.0308860	−	0.0848586i	−0.954177	+	0.299242i	$0.903266\pi$
$140$	−12.6158	+	16.6285i	−1.06623	+	1.40536i
$141$		0			0
$142$	0.992961	+	2.12941i	0.0833274	+	0.178696i
$143$	0.00126076	−	0.00470524i	0.000105430	−	0.000393472i
$144$		0			0
$145$	−4.90767	−	15.2738i	−0.407560	−	1.26842i
$146$	−1.37345	−	1.63681i	−0.113667	−	0.135464i
$147$		0			0
$148$	7.13359	+	10.1878i	0.586378	+	0.837434i
$149$	3.12678	−	17.7328i	0.256156	−	1.45273i	−0.536933	−	0.843625i	$-0.680417\pi$
$149$	3.12678	−	17.7328i	0.256156	−	1.45273i	0.793089	−	0.609106i	$-0.208472\pi$
$150$		0			0
$151$	7.30896	−	6.13294i	0.594795	−	0.499092i	−0.294973	−	0.955506i	$-0.595311\pi$
$151$	7.30896	−	6.13294i	0.594795	−	0.499092i	0.889768	+	0.456414i	$0.150866\pi$
$152$	0.674482	+	2.51720i	0.0547077	+	0.204172i
$153$		0			0
$154$	−0.0839692	+	0.0484796i	−0.00676643	+	0.00390660i
$155$	−0.440430	+	0.232339i	−0.0353762	+	0.0186619i
$156$		0			0
$157$	1.41313	+	16.1522i	0.112780	+	1.28908i	0.815975	+	0.578087i	$0.196201\pi$
$157$	1.41313	+	16.1522i	0.112780	+	1.28908i	−0.703195	+	0.710997i	$0.748244\pi$
$158$	1.79258	+	0.835893i	0.142610	+	0.0665001i
$159$		0			0
$160$	−7.83807	+	1.78262i	−0.619654	+	0.140929i
$161$			31.9723i			2.51977i
$162$		0			0
$163$	−7.81801	+	7.81801i	−0.612354	+	0.612354i	−0.943559	−	0.331205i	$-0.892545\pi$
$163$	−7.81801	+	7.81801i	−0.612354	+	0.612354i	0.331205	+	0.943559i	$0.392545\pi$
$164$	−0.742528	−	4.21109i	−0.0579817	−	0.328831i
$165$		0			0
$166$	−1.21742	+	0.443103i	−0.0944898	+	0.0343915i
$167$	13.0293	−	1.13992i	1.00824	−	0.0882093i	0.428946	−	0.903330i	$-0.358885\pi$
$167$	13.0293	−	1.13992i	1.00824	−	0.0882093i	0.579291	+	0.815121i	$0.303329\pi$
$168$		0			0
$169$	4.44410	−	12.2101i	0.341854	−	0.939236i
$170$	−0.611361	+	2.83074i	−0.0468892	+	0.217108i
$171$		0			0
$172$	6.84060	−	1.83293i	0.521591	−	0.139760i
$173$	22.6663	+	1.98304i	1.72329	+	0.150768i	0.905385	−	0.424592i	$-0.139582\pi$
$173$	22.6663	+	1.98304i	1.72329	+	0.150768i	0.817900	+	0.575360i	$0.195138\pi$
$174$		0			0
$175$	16.0223	+	18.6765i	1.21117	+	1.41181i
$176$	0.204682	+	0.0360909i	0.0154285	+	0.00272046i
$177$		0			0
$178$	0.294337	−	3.36429i	0.0220615	−	0.252164i
$179$	9.11136	−	15.7813i	0.681015	−	1.17955i	−0.293656	−	0.955911i	$-0.594872\pi$
$179$	9.11136	−	15.7813i	0.681015	−	1.17955i	0.974671	−	0.223642i	$-0.0717945\pi$
$180$		0			0
$181$	6.18809	+	10.7181i	0.459957	+	0.796669i	0.998958	−	0.0456358i	$-0.0145314\pi$
$181$	6.18809	+	10.7181i	0.459957	+	0.796669i	−0.539001	+	0.842305i	$0.681198\pi$
$182$	0.113934	−	0.0531285i	0.00844539	−	0.00393815i
$183$		0			0
$184$	−5.23013	+	6.23302i	−0.385570	+	0.459504i
$185$	13.5155	−	5.68496i	0.993676	−	0.417966i
$186$		0			0
$187$	0.141664	−	0.202317i	0.0103595	−	0.0147949i
$188$	1.87813	+	1.87813i	0.136977	+	0.136977i
$189$		0			0
$190$	1.49362	−	0.0733872i	0.108358	−	0.00532407i
$191$	−12.0893	+	2.13167i	−0.874752	+	0.154242i	−0.592959	−	0.805233i	$-0.702040\pi$
$191$	−12.0893	+	2.13167i	−0.874752	+	0.154242i	−0.281793	+	0.959475i	$0.590929\pi$
$192$		0			0
$193$	7.49551	−	16.0742i	0.539538	−	1.15704i	−0.427874	−	0.903838i	$-0.640737\pi$
$193$	7.49551	−	16.0742i	0.539538	−	1.15704i	0.967413	−	0.253205i	$-0.0814848\pi$
$194$	−2.41649	−	2.02767i	−0.173494	−	0.145579i
$195$		0			0
$196$	30.6929	+	11.1713i	2.19235	+	0.797951i
$197$	−8.80113	−	2.35826i	−0.627055	−	0.168019i	−0.0687218	−	0.997636i	$-0.521892\pi$
$197$	−8.80113	−	2.35826i	−0.627055	−	0.168019i	−0.558333	+	0.829617i	$0.688559\pi$
$198$		0			0
$199$	9.38387	+	5.41778i	0.665205	+	0.384056i	0.794257	−	0.607581i	$-0.207860\pi$
$199$	9.38387	+	5.41778i	0.665205	+	0.384056i	−0.129052	+	0.991638i	$0.541193\pi$
$200$	0.0683980	+	6.26196i	0.00483647	+	0.442787i
$201$		0			0
$202$	0.989466	−	0.692831i	0.0696186	−	0.0487474i
$203$	−28.9239	+	20.2527i	−2.03006	+	1.42146i
$204$		0			0
$205$	−5.03750	−	0.192385i	−0.351834	−	0.0134368i
$206$	0.675770	+	0.390156i	0.0470831	+	0.0271835i
$207$		0			0
$208$	−0.260293	−	0.0697452i	−0.0180480	−	0.00483596i
$209$	−0.119844	−	0.0436198i	−0.00828980	−	0.00301724i
$210$		0			0
$211$	−1.55684	−	1.30634i	−0.107177	−	0.0899325i	0.587624	−	0.809134i	$-0.300063\pi$
$211$	−1.55684	−	1.30634i	−0.107177	−	0.0899325i	−0.694802	+	0.719202i	$0.744508\pi$
$212$	−9.83357	+	21.0882i	−0.675372	+	1.44834i
$213$		0			0
$214$	0.693191	−	0.122228i	0.0473856	−	0.00835535i
$215$	−0.409729	−	8.33903i	−0.0279433	−	0.568717i
$216$		0			0
$217$	0.774973	+	0.774973i	0.0526086	+	0.0526086i
$218$	0.0474305	−	0.0677378i	0.00321240	−	0.00458779i
$219$		0			0
$220$	0.0981690	−	0.240711i	0.00661855	−	0.0162287i
$221$	−0.205838	+	0.245308i	−0.0138462	+	0.0165012i
$222$		0			0
$223$	−2.46881	+	1.15123i	−0.165324	+	0.0770918i	−0.503519	−	0.863984i	$-0.667961\pi$
$223$	−2.46881	+	1.15123i	−0.165324	+	0.0770918i	0.338195	+	0.941076i	$0.390184\pi$
$224$	8.84586	+	15.3215i	0.591039	+	1.02371i
$225$		0			0
$226$	−1.80795	+	3.13146i	−0.120263	+	0.208302i
$227$	1.23497	−	14.1158i	0.0819680	−	0.936899i	−0.838197	−	0.545368i	$-0.816390\pi$
$227$	1.23497	−	14.1158i	0.0819680	−	0.936899i	0.920165	−	0.391531i	$-0.128054\pi$
$228$		0			0
$229$	13.0574	+	2.30237i	0.862857	+	0.152145i	0.587527	−	0.809205i	$-0.300102\pi$
$229$	13.0574	+	2.30237i	0.862857	+	0.152145i	0.275330	+	0.961350i	$0.411213\pi$
$230$	2.86256	+	3.68867i	0.188752	+	0.243224i
$231$		0			0
$232$	−8.95173	−	0.783175i	−0.587710	−	0.0514180i
$233$	6.55427	−	1.75621i	0.429384	−	0.115053i	−0.0376527	−	0.999291i	$-0.511988\pi$
$233$	6.55427	−	1.75621i	0.429384	−	0.115053i	0.467037	+	0.884238i	$0.345321\pi$
$234$		0			0
$235$	2.63171	−	1.69686i	0.171674	−	0.110691i
$236$	0.752801	−	2.06830i	0.0490032	−	0.134635i
$237$		0			0
$238$	6.34972	−	0.555528i	0.411591	−	0.0360095i
$239$	−17.1554	+	6.24407i	−1.10969	+	0.403895i	−0.830881	−	0.556451i	$-0.812163\pi$
$239$	−17.1554	+	6.24407i	−1.10969	+	0.403895i	−0.278812	+	0.960346i	$0.589941\pi$
$240$		0			0
$241$	−2.76886	−	15.7030i	−0.178358	−	1.01152i	−0.934196	−	0.356759i	$-0.883882\pi$
$241$	−2.76886	−	15.7030i	−0.178358	−	1.01152i	0.755839	−	0.654758i	$-0.227229\pi$
$242$	−2.49919	+	2.49919i	−0.160654	+	0.160654i
$243$		0			0
$244$			13.6842i			0.876041i
$245$	20.5122	−	32.5891i	1.31048	−	2.08204i
$246$		0			0
$247$	0.149864	+	0.0698828i	0.00953562	+	0.00444653i
$248$	0.0243091	+	0.277854i	0.00154363	+	0.0176437i
$249$		0			0
$250$	3.52065	+	0.720208i	0.222666	+	0.0455499i
$251$	−14.9016	+	8.60342i	−0.940578	+	0.543043i	−0.890141	−	0.455684i	$-0.849395\pi$
$251$	−14.9016	+	8.60342i	−0.940578	+	0.543043i	−0.0504364	+	0.998727i	$0.516061\pi$
$252$		0			0
$253$	−0.103062	−	0.384632i	−0.00647945	−	0.0241816i
$254$	1.90496	−	1.59845i	0.119528	−	0.100296i
$255$		0			0
$256$	1.45175	−	8.23327i	0.0907343	−	0.514580i
$257$	5.37032	+	7.66961i	0.334991	+	0.478417i	0.950943	−	0.309367i	$-0.100117\pi$
$257$	5.37032	+	7.66961i	0.334991	+	0.478417i	−0.615952	+	0.787784i	$0.711228\pi$
$258$		0			0
$259$	−20.7436	−	24.7212i	−1.28894	−	1.53610i
$260$	−0.153998	+	0.299813i	−0.00955053	+	0.0185936i
$261$		0			0
$262$	−0.765440	+	2.85666i	−0.0472890	+	0.176485i
$263$	0.386147	+	0.828096i	0.0238109	+	0.0510626i	0.917854	−	0.396919i	$-0.129921\pi$
$263$	0.386147	+	0.828096i	0.0238109	+	0.0510626i	−0.894043	+	0.447982i	$0.852143\pi$
$264$		0			0
$265$	21.8538	+	16.5802i	1.34247	+	1.01851i
$266$	−1.12571	−	3.09285i	−0.0690215	−	0.189635i
$267$		0			0
$268$	−11.8127	−	8.27136i	−0.721577	−	0.505254i
$269$	27.6508			1.68590			0.842951	−	0.537990i	$-0.180816\pi$
$269$	27.6508			1.68590			0.842951	+	0.537990i	$0.180816\pi$
$270$		0			0
$271$	−18.0879			−1.09876			−0.549380	−	0.835572i	$-0.685136\pi$
$271$	−18.0879			−1.09876			−0.549380	+	0.835572i	$0.685136\pi$
$272$	−11.1921	−	7.83682i	−0.678623	−	0.475177i
$273$		0			0
$274$	−1.51183	−	4.15372i	−0.0913330	−	0.250935i
$275$	−0.252954	−	0.173034i	−0.0152537	−	0.0104343i
$276$		0			0
$277$	2.18829	+	4.69280i	0.131481	+	0.281963i	0.961016	−	0.276492i	$-0.0891721\pi$
$277$	2.18829	+	4.69280i	0.131481	+	0.281963i	−0.829535	+	0.558455i	$0.811394\pi$
$278$	−0.0885694	+	0.330545i	−0.00531204	+	0.0198248i
$279$		0			0
$280$	13.1223	−	4.21638i	0.784209	−	0.251977i
$281$	4.92653	+	5.87122i	0.293892	+	0.350247i	0.892705	−	0.450642i	$-0.148805\pi$
$281$	4.92653	+	5.87122i	0.293892	+	0.350247i	−0.598812	+	0.800889i	$0.704360\pi$
$282$		0			0
$283$	5.43511	+	7.76215i	0.323084	+	0.461412i	0.947535	−	0.319652i	$-0.103566\pi$
$283$	5.43511	+	7.76215i	0.323084	+	0.461412i	−0.624451	+	0.781064i	$0.714677\pi$
$284$	−2.40758	+	13.6541i	−0.142863	+	0.810219i
$285$		0			0
$286$	−0.00119939	+	0.00100641i	−7.09216e−5	+	5.95103e-5i
$287$	2.87169	+	10.7173i	0.169511	+	0.632622i
$288$		0			0
$289$	0.661319	−	0.381813i	0.0389011	−	0.0224596i
$290$	−1.52370	+	4.92620i	−0.0894747	+	0.289277i
$291$		0			0
$292$	−1.09892	−	12.5607i	−0.0643096	−	0.735062i
$293$	−7.74397	−	3.61107i	−0.452408	−	0.210961i	0.183039	−	0.983106i	$-0.441406\pi$
$293$	−7.74397	−	3.61107i	−0.452408	−	0.210961i	−0.635447	+	0.772144i	$0.719184\pi$
$294$		0			0
$295$	−2.19608	−	1.38225i	−0.127861	−	0.0804780i
$296$		−	8.21271i		−	0.477354i
$297$		0			0
$298$	−4.09244	+	4.09244i	−0.237069	+	0.237069i
$299$	0.0896526	+	0.508445i	0.00518474	+	0.0294041i
$300$		0			0
$301$	−17.2677	+	6.28494i	−0.995295	+	0.362258i
$302$	−3.05503	+	0.267281i	−0.175797	+	0.0153803i
$303$		0			0
$304$	−2.41304	+	6.62976i	−0.138397	+	0.380243i
$305$	15.7692	+	3.40570i	0.902939	+	0.195010i
$306$		0			0
$307$	−20.4909	+	5.49053i	−1.16948	+	0.313361i	−0.790746	−	0.612145i	$-0.790307\pi$
$307$	−20.4909	+	5.49053i	−1.16948	+	0.313361i	−0.378734	+	0.925506i	$0.623640\pi$
$308$	−0.569980	−	0.0498668i	−0.0324776	−	0.00284142i
$309$		0			0
$310$	0.158795	+	0.0200241i	0.00901892	+	0.00113729i
$311$	19.3816	+	3.41750i	1.09903	+	0.193788i	0.693616	−	0.720345i	$-0.256017\pi$
$311$	19.3816	+	3.41750i	1.09903	+	0.193788i	0.405413	+	0.914134i	$0.367128\pi$
$312$		0			0
$313$	0.366189	−	4.18556i	0.0206983	−	0.236582i	−0.978798	−	0.204830i	$-0.934336\pi$
$313$	0.366189	−	4.18556i	0.0206983	−	0.236582i	0.999496	−	0.0317519i	$-0.0101087\pi$
$314$	2.60572	−	4.51323i	0.147049	−	0.254696i
$315$		0			0
$316$	5.83578	+	10.1079i	0.328288	+	0.568612i
$317$	−15.1326	+	7.05644i	−0.849930	+	0.396329i	−0.798244	−	0.602334i	$-0.794237\pi$
$317$	−15.1326	+	7.05644i	−0.849930	+	0.396329i	−0.0516863	+	0.998663i	$0.516460\pi$
$318$		0			0
$319$	0.282675	−	0.336879i	0.0158268	−	0.0188616i
$320$	−11.6490	−	4.75082i	−0.651201	−	0.265579i
$321$		0			0
$322$	5.89434	−	8.41799i	0.328479	−	0.469116i
$323$	5.92840	+	5.92840i	0.329865	+	0.329865i
$324$		0			0
$325$	0.307167	+	0.252078i	0.0170386	+	0.0139828i
$326$	3.49972	−	0.617095i	0.193831	−	0.0341777i
$327$		0			0
$328$	−1.19333	+	2.55911i	−0.0658907	+	0.141303i
$329$	−5.27951	−	4.43004i	−0.291069	−	0.244236i
$330$		0			0
$331$	−12.4570	−	4.53397i	−0.684698	−	0.249210i	−0.0238345	−	0.999716i	$-0.507587\pi$
$331$	−12.4570	−	4.53397i	−0.684698	−	0.249210i	−0.660863	+	0.750506i	$0.729810\pi$
$332$	−7.38454	−	1.97868i	−0.405279	−	0.108594i
$333$		0			0
$334$	−3.64064	−	2.10192i	−0.199207	−	0.115012i
$335$	−12.4715	+	11.5540i	−0.681393	+	0.631261i
$336$		0			0
$337$	17.4071	−	12.1886i	0.948223	−	0.663953i	0.00637058	−	0.999980i	$-0.497972\pi$
$337$	17.4071	−	12.1886i	0.948223	−	0.663953i	0.941852	+	0.336027i	$0.109083\pi$
$338$	−3.42111	+	2.39549i	−0.186084	+	0.130297i
$339$		0			0
$340$	−12.5364	+	11.6140i	−0.679880	+	0.629860i
$341$	−0.0118212	−	0.00682495i	−0.000640152	−	0.000369592i
$342$		0			0
$343$	−48.5880	−	13.0191i	−2.62350	−	0.702966i
$344$	−4.39446	−	1.59945i	−0.236934	−	0.0862368i
$345$		0			0
$346$	−5.60222	−	4.70082i	−0.301177	−	0.252718i
$347$	13.3295	−	28.5852i	0.715565	−	1.53453i	−0.124603	−	0.992207i	$-0.539766\pi$
$347$	13.3295	−	28.5852i	0.715565	−	1.53453i	0.840168	−	0.542327i	$-0.182456\pi$
$348$		0			0
$349$	16.6978	−	2.94427i	0.893813	−	0.157603i	0.292168	−	0.956367i	$-0.405623\pi$
$349$	16.6978	−	2.94427i	0.893813	−	0.157603i	0.601645	+	0.798764i	$0.294512\pi$
$350$	−0.775353	−	7.87116i	−0.0414444	−	0.420731i
$351$		0			0
$352$	−0.155806	−	0.155806i	−0.00830448	−	0.00830448i
$353$	−10.9094	+	15.5802i	−0.580648	+	0.829252i	−0.996791	−	0.0800474i	$-0.974493\pi$
$353$	−10.9094	+	15.5802i	−0.580648	+	0.829252i	0.416143	+	0.909299i	$0.363382\pi$
$354$		0			0
$355$	15.1352	+	6.17260i	0.803294	+	0.327607i
$356$	12.8098	−	15.2661i	0.678918	−	0.809103i
$357$		0			0
$358$	−5.30835	+	2.47532i	−0.280555	+	0.130825i
$359$	−15.6916	−	27.1786i	−0.828170	−	1.43443i	−0.899473	−	0.436977i	$-0.856049\pi$
$359$	−15.6916	−	27.1786i	−0.828170	−	1.43443i	0.0713028	−	0.997455i	$-0.477284\pi$
$360$		0			0
$361$	−7.33536	+	12.7052i	−0.386072	+	0.668696i
$362$	0.346699	−	3.96279i	0.0182221	−	0.208280i
$363$		0			0
$364$	0.730562	+	0.128818i	0.0382919	+	0.00675189i
$365$	−14.7480	−	1.85974i	−0.771947	−	0.0973430i
$366$		0			0
$367$	17.8579	+	1.56237i	0.932177	+	0.0815549i	0.543117	−	0.839657i	$-0.317244\pi$
$367$	17.8579	+	1.56237i	0.932177	+	0.0815549i	0.389060	+	0.921212i	$0.372800\pi$
$368$	−21.2778	+	5.70137i	−1.10918	+	0.297204i
$369$		0			0
$370$	−4.60655	−	0.994887i	−0.239483	−	0.0517217i
$371$	20.6497	−	56.7346i	1.07208	−	2.94551i
$372$		0			0
$373$	−5.04230	+	0.441145i	−0.261081	+	0.0228416i	−0.216945	−	0.976184i	$-0.569609\pi$
$373$	−5.04230	+	0.441145i	−0.261081	+	0.0228416i	−0.0441361	+	0.999026i	$0.514054\pi$
$374$	−0.0745975	+	0.0271513i	−0.00385734	+	0.00140396i
$375$		0			0
$376$	−0.304566	−	1.72728i	−0.0157068	−	0.0890775i
$377$	−0.403177	+	0.403177i	−0.0207647	+	0.0207647i
$378$		0			0
$379$		−	9.89195i		−	0.508115i	−0.967189	−	0.254058i	$-0.918235\pi$
$379$		−	9.89195i		−	0.508115i	0.967189	−	0.254058i	$-0.0817653\pi$
$380$	7.46828	+	4.70068i	0.383114	+	0.241140i
$381$		0			0
$382$	3.57599	+	1.66751i	0.182963	+	0.0853173i
$383$	1.67206	+	19.1117i	0.0854380	+	0.976561i	0.911043	+	0.412312i	$0.135279\pi$
$383$	1.67206	+	19.1117i	0.0854380	+	0.976561i	−0.825605	+	0.564249i	$0.809166\pi$
$384$		0			0
$385$	−0.199320	+	0.644413i	−0.0101583	+	0.0328423i
$386$	−4.93689	+	2.85032i	−0.251281	+	0.145077i
$387$		0			0
$388$	−4.81785	−	17.9805i	−0.244589	−	0.912819i
$389$	−5.65836	+	4.74792i	−0.286890	+	0.240729i	−0.774863	−	0.632130i	$-0.782181\pi$
$389$	−5.65836	+	4.74792i	−0.286890	+	0.240729i	0.487973	+	0.872859i	$0.337737\pi$
$390$		0			0
$391$	−4.54562	+	25.7795i	−0.229882	+	1.30373i
$392$	−12.3713	−	17.6680i	−0.624843	−	0.892368i
$393$		0			0
$394$	1.88249	+	2.24346i	0.0948384	+	0.113024i
$395$	13.1003	−	4.20931i	0.659149	−	0.211793i
$396$		0			0
$397$	3.34227	−	12.4735i	0.167744	−	0.626028i	−0.829931	−	0.557866i	$-0.811620\pi$
$397$	3.34227	−	12.4735i	0.167744	−	0.626028i	0.997674	−	0.0681611i	$-0.0217132\pi$
$398$	−1.47187	−	3.15644i	−0.0737783	−	0.158218i
$399$		0			0
$400$	−9.57219	+	13.9934i	−0.478610	+	0.699668i
$401$	2.92360	+	8.03253i	0.145998	+	0.401125i	0.991039	−	0.133576i	$-0.0426461\pi$
$401$	2.92360	+	8.03253i	0.145998	+	0.401125i	−0.845041	+	0.534702i	$0.820424\pi$
$402$		0			0
$403$	0.0144972	+	0.0101511i	0.000722158	+	0.000505660i
$404$	7.12791			0.354627
$405$		0			0
$406$	11.3491			0.563248
$407$	0.329237	+	0.230534i	0.0163197	+	0.0114272i
$408$		0			0
$409$	−4.56883	−	12.5528i	−0.225914	−	0.620694i	0.774008	−	0.633176i	$-0.218249\pi$
$409$	−4.56883	−	12.5528i	−0.225914	−	0.620694i	−0.999922	+	0.0124819i	$0.996027\pi$
$410$	1.29086	+	0.979355i	0.0637508	+	0.0483669i
$411$		0			0
$412$	1.94600	+	4.17321i	0.0958725	+	0.205599i
$413$	−1.47817	+	5.51659i	−0.0727359	+	0.271454i
$414$		0			0
$415$	−4.11801	+	8.01721i	−0.202145	+	0.393550i
$416$	0.183635	+	0.218848i	0.00900347	+	0.0107299i
$417$		0			0
$418$	0.0235122	+	0.0335789i	0.00115002	+	0.00164240i
$419$	4.65475	−	26.3984i	0.227399	−	1.28964i	−0.630646	−	0.776071i	$-0.717210\pi$
$419$	4.65475	−	26.3984i	0.227399	−	1.28964i	0.858045	−	0.513574i	$-0.171679\pi$
$420$		0			0
$421$	19.3371	−	16.2257i	0.942432	−	0.790794i	−0.0355751	−	0.999367i	$-0.511326\pi$
$421$	19.3371	−	16.2257i	0.942432	−	0.790794i	0.978007	+	0.208573i	$0.0668818\pi$
$422$	0.169066	+	0.630963i	0.00823001	+	0.0307148i
$423$		0			0
$424$	13.3065	−	7.68250i	0.646220	−	0.373095i
$425$	10.2636	+	17.3369i	0.497856	+	0.840964i
$426$		0			0
$427$	−3.09467	−	35.3722i	−0.149762	−	1.71178i
$428$	3.76447	+	1.75540i	0.181962	+	0.0848504i
$429$		0			0
$430$	−1.42949	+	2.27112i	−0.0689360	+	0.109523i
$431$		−	23.0274i		−	1.10919i	−0.832121	−	0.554595i	$-0.812873\pi$
$431$		−	23.0274i		−	1.10919i	0.832121	−	0.554595i	$-0.187127\pi$
$432$		0			0
$433$	12.8672	−	12.8672i	0.618357	−	0.618357i	−0.326752	−	0.945110i	$-0.605954\pi$
$433$	12.8672	−	12.8672i	0.618357	−	0.618357i	0.945110	+	0.326752i	$0.105954\pi$
$434$	−0.0611705	−	0.346915i	−0.00293628	−	0.0166525i
$435$		0			0
$436$	0.458542	−	0.166896i	0.0219602	−	0.00799285i
$437$	13.4658	−	1.17810i	0.644154	−	0.0563562i
$438$		0			0
$439$	10.8870	−	29.9118i	0.519609	−	1.42761i	−0.351343	−	0.936247i	$-0.614275\pi$
$439$	10.8870	−	29.9118i	0.519609	−	1.42761i	0.870952	−	0.491367i	$-0.163503\pi$
$440$	−0.144273	+	0.0930233i	−0.00687793	+	0.00443471i
$441$		0			0
$442$	0.0994197	−	0.0266394i	0.00472891	−	0.00126711i
$443$	8.95244	+	0.783237i	0.425343	+	0.0372127i	0.297818	−	0.954623i	$-0.403741\pi$
$443$	8.95244	+	0.783237i	0.425343	+	0.0372127i	0.127525	+	0.991835i	$0.459297\pi$
$444$		0			0
$445$	−14.4040	−	18.5609i	−0.682817	−	0.879873i
$446$	0.862251	+	0.152038i	0.0408288	+	0.00719922i
$447$		0			0
$448$	−2.41327	+	27.5838i	−0.114016	+	1.30321i
$449$	−5.30209	+	9.18349i	−0.250221	+	0.433396i	−0.963587	−	0.267396i	$-0.913837\pi$
$449$	−5.30209	+	9.18349i	−0.250221	+	0.433396i	0.713365	+	0.700792i	$0.247170\pi$
$450$		0			0
$451$	−0.0690940	−	0.119674i	−0.00325351	−	0.00563524i
$452$	−19.3383	+	9.01760i	−0.909598	+	0.424152i
$453$		0			0
$454$	−2.92752	+	3.48888i	−0.137395	+	0.163741i
$455$	0.330266	−	0.809812i	0.0154831	−	0.0379646i
$456$		0			0
$457$	−19.0820	+	27.2519i	−0.892617	+	1.27479i	0.0682185	+	0.997670i	$0.478268\pi$
$457$	−19.0820	+	27.2519i	−0.892617	+	1.27479i	−0.960836	+	0.277119i	$0.910620\pi$
$458$	−3.01343	−	3.01343i	−0.140808	−	0.140808i
$459$		0			0
$460$	1.35213	+	27.5192i	0.0630432	+	1.28309i
$461$	−7.72166	+	1.36154i	−0.359634	+	0.0634131i	−0.350546	−	0.936546i	$-0.614004\pi$
$461$	−7.72166	+	1.36154i	−0.359634	+	0.0634131i	−0.00908790	+	0.999959i	$0.502893\pi$
$462$		0			0
$463$	−7.47769	+	16.0360i	−0.347518	+	0.745254i	−0.999920	−	0.0126183i	$-0.995983\pi$
$463$	−7.47769	+	16.0360i	−0.347518	+	0.745254i	0.652403	+	0.757873i	$0.273761\pi$
$464$	−18.6361	−	15.6375i	−0.865159	−	0.725955i
$465$		0			0
$466$	−2.04945	−	0.745938i	−0.0949388	−	0.0345549i
$467$	15.2854	+	4.09572i	0.707325	+	0.189527i	0.594509	−	0.804089i	$-0.297346\pi$
$467$	15.2854	+	4.09572i	0.707325	+	0.189527i	0.112816	+	0.993616i	$0.464013\pi$
$468$		0			0
$469$	32.4052	+	18.7092i	1.49633	+	0.863909i
$470$	−1.00573	−	0.0384096i	−0.0463911	−	0.00177170i
$471$		0			0
$472$	−1.19059	+	0.833661i	−0.0548014	+	0.0383724i
$473$	0.187475	−	0.131271i	0.00862009	−	0.00603585i
$474$		0			0
$475$	7.27557	−	7.43627i	0.333826	−	0.341199i
$476$	32.5737	+	18.8064i	1.49301	+	0.861991i
$477$		0			0
$478$	5.66800	+	1.51874i	0.259248	+	0.0694654i
$479$	25.2585	+	9.19333i	1.15409	+	0.420054i	0.846982	−	0.531621i	$-0.178417\pi$
$479$	25.2585	+	9.19333i	1.15409	+	0.420054i	0.307106	+	0.951675i	$0.400639\pi$
$480$		0			0
$481$	−0.399198	−	0.334967i	−0.0182019	−	0.0152732i
$482$	−2.16595	+	4.64490i	−0.0986564	+	0.211569i
$483$		0			0
$484$	−20.5396	+	3.62169i	−0.933619	+	0.164622i
$485$	−21.9191	+	1.07697i	−0.995293	+	0.0489026i
$486$		0			0
$487$	−12.2573	−	12.2573i	−0.555433	−	0.555433i	0.372571	−	0.928004i	$-0.378476\pi$
$487$	−12.2573	−	12.2573i	−0.555433	−	0.555433i	−0.928004	+	0.372571i	$0.878476\pi$
$488$	5.18299	−	7.40208i	0.234623	−	0.335076i
$489$		0			0
$490$	−11.4087	+	4.79881i	−0.515393	+	0.216788i
$491$	−8.64628	+	10.3042i	−0.390201	+	0.465024i	−0.925006	−	0.379952i	$-0.875941\pi$
$491$	−8.64628	+	10.3042i	−0.390201	+	0.465024i	0.534805	+	0.844976i	$0.320385\pi$
$492$		0			0
$493$	−26.2010	+	12.2177i	−1.18003	+	0.550258i
$494$	−0.0265743	−	0.0460281i	−0.00119563	−	0.00207090i
$495$		0			0
$496$	−0.377555	+	0.653944i	−0.0169527	+	0.0293630i
$497$	3.13549	−	35.8388i	0.140646	−	1.60759i
$498$		0			0
$499$	−37.5256	−	6.61678i	−1.67988	−	0.296208i	−0.749281	−	0.662252i	$-0.769601\pi$
$499$	−37.5256	−	6.61678i	−1.67988	−	0.296208i	−0.930597	+	0.366044i	$0.880712\pi$
$500$	14.5805	+	15.3976i	0.652061	+	0.688603i
$501$		0			0
$502$	5.50954	+	0.482022i	0.245903	+	0.0215137i
$503$	−18.4828	+	4.95246i	−0.824109	+	0.220819i	−0.646142	−	0.763217i	$-0.723619\pi$
$503$	−18.4828	+	4.95246i	−0.824109	+	0.220819i	−0.177967	+	0.984036i	$0.556952\pi$
$504$		0			0
$505$	1.77398	−	8.21394i	0.0789411	−	0.365515i
$506$	−0.0437748	+	0.120270i	−0.00194603	+	0.00534666i
$507$		0			0
$508$	14.6185	−	1.27895i	0.648590	−	0.0567442i
$509$	−22.8762	+	8.32625i	−1.01397	+	0.369054i	−0.794956	−	0.606667i	$-0.792506\pi$
$509$	−22.8762	+	8.32625i	−1.01397	+	0.369054i	−0.219013	+	0.975722i	$0.570284\pi$
$510$		0			0
$511$	5.68120	+	32.2197i	0.251322	+	1.42532i
$512$	−14.6251	+	14.6251i	−0.646346	+	0.646346i
$513$		0			0
$514$		−	3.00939i		−	0.132739i
$515$	5.29337	−	1.20388i	0.233254	−	0.0530492i
$516$		0			0
$517$	0.0777936	+	0.0362758i	0.00342136	+	0.00159541i
$518$	0.904028	+	10.3331i	0.0397207	+	0.454010i
$519$		0			0
$520$	0.196857	−	0.103848i	0.00863276	−	0.00455402i
$521$	−23.8927	+	13.7944i	−1.04676	+	0.604345i	−0.921739	−	0.387810i	$-0.873232\pi$
$521$	−23.8927	+	13.7944i	−1.04676	+	0.604345i	−0.125017	+	0.992155i	$0.539898\pi$
$522$		0			0
$523$	3.35607	+	12.5250i	0.146751	+	0.547681i	0.999671	+	0.0256401i	$0.00816240\pi$
$523$	3.35607	+	12.5250i	0.146751	+	0.547681i	−0.852921	+	0.522041i	$0.825171\pi$
$524$	−13.3689	+	11.2178i	−0.584022	+	0.490053i
$525$		0			0
$526$	0.0509971	−	0.289219i	0.00222358	−	0.0126105i
$527$	0.514685	+	0.735047i	0.0224200	+	0.0320191i
$528$		0			0
$529$	12.3443	+	14.7114i	0.536709	+	0.639625i
$530$	−2.69721	−	8.39434i	−0.117159	−	0.364627i
$531$		0			0
$532$	5.02685	−	18.7605i	0.217942	−	0.813369i
$533$	0.0757196	+	0.162381i	0.00327978	+	0.00703351i
$534$		0			0
$535$	2.95975	−	3.90115i	0.127961	−	0.168661i
$536$	3.25692	+	8.94831i	0.140677	+	0.386508i
$537$		0			0
$538$	−7.28020	−	5.09765i	−0.313872	−	0.219775i
$539$	1.05555			0.0454659
$540$		0			0
$541$	37.8477			1.62720			0.813600	−	0.581425i	$-0.197505\pi$
$541$	37.8477			1.62720			0.813600	+	0.581425i	$0.197505\pi$
$542$	4.76236	+	3.33464i	0.204561	+	0.143235i
$543$		0			0
$544$	4.95417	+	13.6115i	0.212408	+	0.583587i
$545$	−0.0782032	−	0.569943i	−0.00334986	−	0.0244137i
$546$		0			0
$547$	−6.27224	−	13.4509i	−0.268182	−	0.575117i	0.725388	−	0.688340i	$-0.241660\pi$
$547$	−6.27224	−	13.4509i	−0.268182	−	0.575117i	−0.993570	+	0.113223i	$0.963883\pi$
$548$	6.75109	−	25.1954i	0.288392	−	1.07629i
$549$		0			0
$550$	0.0347001	+	0.0921921i	0.00147962	+	0.00393109i
$551$	9.59560	+	11.4356i	0.408786	+	0.487173i
$552$		0			0
$553$	−17.3708	−	24.8080i	−0.738680	−	1.05494i
$554$	0.288999	−	1.63900i	0.0122784	−	0.0696342i
$555$		0			0
$556$	−1.54692	+	1.29802i	−0.0656040	+	0.0550483i
$557$	−3.75036	−	13.9965i	−0.158908	−	0.593052i	−0.998739	−	0.0502041i	$-0.984013\pi$
$557$	−3.75036	−	13.9965i	−0.158908	−	0.593052i	0.839831	−	0.542847i	$-0.182654\pi$
$558$		0			0
$559$	−0.256980	+	0.148367i	−0.0108691	+	0.00627527i
$560$	35.6488	+	11.0263i	1.50644	+	0.465948i
$561$		0			0
$562$	−0.214704	−	2.45408i	−0.00905674	−	0.103519i
$563$	31.0550	+	14.4812i	1.30881	+	0.610309i	0.946787	−	0.321859i	$-0.104308\pi$
$563$	31.0550	+	14.4812i	1.30881	+	0.610309i	0.362025	+	0.932169i	$0.382086\pi$
$564$		0			0
$565$	5.57867	+	24.5290i	0.234696	+	1.03194i
$566$		−	3.04570i		−	0.128020i
$567$		0			0
$568$	6.47388	−	6.47388i	0.271638	−	0.271638i
$569$	−1.25548	−	7.12016i	−0.0526323	−	0.298493i	0.947117	−	0.320889i	$-0.103982\pi$
$569$	−1.25548	−	7.12016i	−0.0526323	−	0.298493i	−0.999749	+	0.0223961i	$0.992870\pi$
$570$		0			0
$571$	25.3539	−	9.22807i	1.06103	−	0.386183i	0.248214	−	0.968705i	$-0.420156\pi$
$571$	25.3539	−	9.22807i	1.06103	−	0.386183i	0.812815	+	0.582522i	$0.197934\pi$
$572$	−0.00920404		0.000805249i	−0.000384840		3.36691e-5i
$573$		0			0
$574$	1.21973	−	3.35118i	0.0509105	−	0.139876i
$575$	32.0486	+	5.29079i	1.33652	+	0.220641i
$576$		0			0
$577$	−6.14870	+	1.64754i	−0.255974	+	0.0685880i	−0.384524	−	0.923115i	$-0.625634\pi$
$577$	−6.14870	+	1.64754i	−0.255974	+	0.0685880i	0.128550	+	0.991703i	$0.458968\pi$
$578$	−0.244509	−	0.0213918i	−0.0101702	−	0.000889781i
$579$		0			0
$580$	−24.0389	+	18.6552i	−0.998161	+	0.774613i
$581$	19.5357	+	3.44468i	0.810479	+	0.142909i
$582$		0			0
$583$	−0.0655370	+	0.749091i	−0.00271426	+	0.0310242i
$584$	−4.16304	+	7.21060i	−0.172268	+	0.298377i
$585$		0			0
$586$	1.37318	+	2.37842i	0.0567256	+	0.0982517i
$587$	−34.3204	+	16.0039i	−1.41656	+	0.660550i	−0.971952	−	0.235177i	$-0.924433\pi$
$587$	−34.3204	+	16.0039i	−1.41656	+	0.660550i	−0.444603	+	0.895728i	$0.646655\pi$
$588$		0			0
$589$	0.297839	−	0.354951i	0.0122722	−	0.0146255i
$590$	0.323377	+	0.768799i	0.0133132	+	0.0316509i
$591$		0			0
$592$	12.7531	−	18.2133i	0.524149	−	0.748563i
$593$	3.48236	+	3.48236i	0.143004	+	0.143004i	0.774984	−	0.631981i	$-0.217758\pi$
$593$	3.48236	+	3.48236i	0.143004	+	0.143004i	−0.631981	+	0.774984i	$0.717758\pi$
$594$		0			0
$595$	29.7787	−	32.8562i	1.22081	−	1.34697i
$596$	−33.6337	+	5.93053i	−1.37769	+	0.242924i
$597$		0			0
$598$	0.0701311	−	0.150397i	0.00286788	−	0.00615018i
$599$	7.62357	+	6.39694i	0.311491	+	0.261372i	0.785108	−	0.619359i	$-0.212608\pi$
$599$	7.62357	+	6.39694i	0.311491	+	0.261372i	−0.473617	+	0.880731i	$0.657052\pi$
$600$		0			0
$601$	−16.6225	−	6.05010i	−0.678046	−	0.246789i	−0.0200379	−	0.999799i	$-0.506379\pi$
$601$	−16.6225	−	6.05010i	−0.678046	−	0.246789i	−0.658008	+	0.753011i	$0.728601\pi$
$602$	5.70510	+	1.52868i	0.232523	+	0.0623042i
$603$		0			0
$604$	−15.6721	−	9.04832i	−0.637691	−	0.368171i
$605$	−0.938360	+	24.5704i	−0.0381498	+	0.998930i
$606$		0			0
$607$	−11.9526	+	8.36932i	−0.485142	+	0.339700i	−0.790422	−	0.612563i	$-0.790139\pi$
$607$	−11.9526	+	8.36932i	−0.485142	+	0.339700i	0.305280	+	0.952263i	$0.401250\pi$
$608$	6.12699	−	4.29017i	0.248482	−	0.173989i
$609$		0			0
$610$	−3.52400	−	3.80385i	−0.142683	−	0.154014i
$611$	−0.0963805	−	0.0556453i	−0.00389914	−	0.00225117i
$612$		0			0
$613$	36.6597	+	9.82295i	1.48067	+	0.396745i	0.906576	−	0.422042i	$-0.138687\pi$
$613$	36.6597	+	9.82295i	1.48067	+	0.396745i	0.574097	+	0.818787i	$0.305353\pi$
$614$	6.40729	+	2.33206i	0.258577	+	0.0941143i
$615$		0			0
$616$	0.289427	+	0.242858i	0.0116613	+	0.00978503i
$617$	2.31069	−	4.95529i	0.0930249	−	0.199493i	−0.854290	−	0.519797i	$-0.826007\pi$
$617$	2.31069	−	4.95529i	0.0930249	−	0.199493i	0.947315	+	0.320305i	$0.103785\pi$
$618$		0			0
$619$	35.6556	−	6.28705i	1.43312	−	0.252698i	0.597440	−	0.801913i	$-0.296184\pi$
$619$	35.6556	−	6.28705i	1.43312	−	0.252698i	0.835681	+	0.549215i	$0.185073\pi$
$620$	0.699809	+	0.634261i	0.0281050	+	0.0254726i
$621$		0			0
$622$	−4.47294	−	4.47294i	−0.179349	−	0.179349i
$623$	−29.6596	+	42.3583i	−1.18829	+	1.69705i
$624$		0			0
$625$	21.3724	−	12.9699i	0.854897	−	0.518797i
$626$	−0.868056	+	1.03451i	−0.0346945	+	0.0413473i
$627$		0			0
$628$	27.8714	−	12.9967i	1.11219	−	0.518623i
$629$	−13.2110	−	22.8821i	−0.526756	−	0.912368i
$630$		0			0
$631$	8.04151	−	13.9283i	0.320128	−	0.554477i	−0.660387	−	0.750926i	$-0.729608\pi$
$631$	8.04151	−	13.9283i	0.320128	−	0.554477i	0.980514	+	0.196449i	$0.0629409\pi$
$632$	0.671730	−	7.67791i	0.0267200	−	0.305411i
$633$		0			0
$634$	5.28517	+	0.931918i	0.209901	+	0.0370112i
$635$	2.16440	−	17.1641i	0.0858916	−	0.681135i
$636$		0			0
$637$	−1.36337	−	0.119280i	−0.0540188	−	0.00472603i
$638$	−0.136532	+	0.0365836i	−0.00540535	+	0.00144836i
$639$		0			0
$640$	10.9030	+	16.9098i	0.430979	+	0.668418i
$641$	−12.7590	+	35.0551i	−0.503951	+	1.38459i	0.383436	+	0.923567i	$0.374741\pi$
$641$	−12.7590	+	35.0551i	−0.503951	+	1.38459i	−0.887387	+	0.461026i	$0.847482\pi$
$642$		0			0
$643$	−14.3985	+	1.25970i	−0.567821	+	0.0496779i	−0.367452	−	0.930043i	$-0.619770\pi$
$643$	−14.3985	+	1.25970i	−0.567821	+	0.0496779i	−0.200369	+	0.979720i	$0.564214\pi$
$644$	56.9844	−	20.7406i	2.24550	−	0.817295i
$645$		0			0
$646$	−0.467943	−	2.65384i	−0.0184110	−	0.104414i
$647$	−18.6385	+	18.6385i	−0.732757	+	0.732757i	−0.971165	−	0.238408i	$-0.923374\pi$
$647$	−18.6385	+	18.6385i	−0.732757	+	0.732757i	0.238408	+	0.971165i	$0.423374\pi$
$648$		0			0
$649$		−	0.0711305i		−	0.00279212i
$650$	−0.0344015	−	0.122998i	−0.00134934	−	0.00482439i
$651$		0			0
$652$	19.0057	+	8.86250i	0.744320	+	0.347082i
$653$	−1.32123	−	15.1018i	−0.0517038	−	0.590977i	−0.977214	−	0.212255i	$-0.931919\pi$
$653$	−1.32123	−	15.1018i	−0.0517038	−	0.590977i	0.925510	−	0.378722i	$-0.123636\pi$
$654$		0			0
$655$	9.59978	+	18.1977i	0.375094	+	0.711042i
$656$	−6.62035	+	3.82226i	−0.258481	+	0.149234i
$657$		0			0
$658$	0.573332	+	2.13970i	0.0223508	+	0.0834144i
$659$	−14.6857	+	12.3228i	−0.572075	+	0.480028i	−0.882334	−	0.470624i	$-0.844029\pi$
$659$	−14.6857	+	12.3228i	−0.572075	+	0.480028i	0.310258	+	0.950652i	$0.399584\pi$
$660$		0			0
$661$	3.24511	−	18.4039i	0.126220	−	0.715829i	−0.854356	−	0.519689i	$-0.826048\pi$
$661$	3.24511	−	18.4039i	0.126220	−	0.715829i	0.980576	−	0.196141i	$-0.0628409\pi$
$662$	2.44393	+	3.49029i	0.0949860	+	0.135654i
$663$		0			0
$664$	3.24502	+	3.86726i	0.125931	+	0.150079i
$665$	−20.3678	−	10.4618i	−0.789828	−	0.405692i
$666$		0			0
$667$	−12.0634	+	45.0214i	−0.467099	+	1.74324i
$668$	−10.4839	−	22.4827i	−0.405633	−	0.869883i
$669$		0			0
$670$	5.41370	−	0.742827i	0.209149	−	0.0286979i
$671$	0.151251	+	0.415559i	0.00583898	+	0.0160425i
$672$		0			0
$673$	6.71034	+	4.69863i	0.258665	+	0.181119i	0.695715	−	0.718318i	$-0.255088\pi$
$673$	6.71034	+	4.69863i	0.258665	+	0.181119i	−0.437050	+	0.899437i	$0.643977\pi$
$674$	−6.83016			−0.263088
$675$		0			0
$676$	−24.6450			−0.947884
$677$	32.8363	+	22.9922i	1.26200	+	0.883663i	0.996753	−	0.0805166i	$-0.0256570\pi$
$677$	32.8363	+	22.9922i	1.26200	+	0.883663i	0.265249	+	0.964180i	$0.414546\pi$
$678$		0			0
$679$	16.5199	+	45.3880i	0.633976	+	1.74183i
$680$	11.1801	−	1.53405i	0.428737	−	0.0588280i
$681$		0			0
$682$	0.00185416	+	0.00397627i	7.09996e−5	+	0.000152259i
$683$	0.244432	−	0.912231i	0.00935292	−	0.0349056i	−0.961092	−	0.276230i	$-0.910915\pi$
$683$	0.244432	−	0.912231i	0.00935292	−	0.0349056i	0.970445	+	0.241324i	$0.0775817\pi$
$684$		0			0
$685$	−27.3540	−	14.0503i	−1.04514	−	0.536834i
$686$	10.3926	+	12.3854i	0.396790	+	0.472876i
$687$		0			0
$688$	−7.26189	−	10.3710i	−0.276857	−	0.395393i
$689$	0.169298	−	0.960134i	0.00644972	−	0.0365782i
$690$		0			0
$691$	−19.0181	+	15.9581i	−0.723481	+	0.607073i	−0.928346	−	0.371717i	$-0.878769\pi$
$691$	−19.0181	+	15.9581i	−0.723481	+	0.607073i	0.204865	+	0.978790i	$0.434325\pi$
$692$	−11.1694	−	41.6847i	−0.424596	−	1.58461i
$693$		0			0
$694$	−8.77943	+	5.06881i	−0.333263	+	0.192409i
$695$	1.11079	+	2.10566i	0.0421348	+	0.0798722i
$696$		0			0
$697$	0.791748	+	9.04972i	0.0299896	+	0.342783i
$698$	−4.93917	−	2.30317i	−0.186950	−	0.0871763i
$699$		0			0
$700$	22.8934	−	40.6721i	0.865290	−	1.53726i
$701$		−	30.1877i		−	1.14018i	−0.821584	−	0.570088i	$-0.806909\pi$
$701$		−	30.1877i		−	1.14018i	0.821584	−	0.570088i	$-0.193091\pi$
$702$		0			0
$703$	−9.64747	+	9.64747i	−0.363861	+	0.363861i
$704$	−0.0598837	−	0.339617i	−0.00225695	−	0.0127998i
$705$		0			0
$706$	5.74467	−	2.09089i	0.216204	−	0.0786917i
$707$	−18.4249	+	1.61197i	−0.692940	+	0.0606244i
$708$		0			0
$709$	−17.1846	+	47.2142i	−0.645379	+	1.77317i	−0.0112523	+	0.999937i	$0.503582\pi$
$709$	−17.1846	+	47.2142i	−0.645379	+	1.77317i	−0.634127	+	0.773229i	$0.718640\pi$
$710$	−2.84699	−	4.41548i	−0.106846	−	0.165710i
$711$		0			0
$712$	−12.7113	+	3.40597i	−0.476374	+	0.127644i
$713$	1.44121	+	0.126090i	0.0539739	+	0.00472211i
$714$		0			0
$715$	−0.00136274	+	0.0108068i	−5.09637e−5	+	0.000404151i
$716$	−34.0378	−	6.00178i	−1.27205	−	0.224297i
$717$		0			0
$718$	−0.879150	+	10.0487i	−0.0328096	+	0.375015i
$719$	−6.68387	+	11.5768i	−0.249266	+	0.431742i	−0.963322	−	0.268346i	$-0.913523\pi$
$719$	−6.68387	+	11.5768i	−0.249266	+	0.431742i	0.714056	+	0.700089i	$0.246856\pi$
$720$		0			0
$721$	−5.97397	−	10.3472i	−0.222482	−	0.385351i
$722$	4.27363	−	1.99283i	0.159048	−	0.0741654i
$723$		0			0
$724$	15.0887	−	17.9820i	0.560766	−	0.668295i
$725$	15.5147	+	32.3444i	0.576203	+	1.20124i
$726$		0			0
$727$	13.6862	−	19.5460i	0.507595	−	0.724920i	−0.480800	−	0.876830i	$-0.659654\pi$
$727$	13.6862	−	19.5460i	0.507595	−	0.724920i	0.988394	+	0.151910i	$0.0485425\pi$
$728$	−0.346386	−	0.346386i	−0.0128379	−	0.0128379i
$729$		0			0
$730$	3.54015	+	3.20856i	0.131027	+	0.118754i
$731$	−14.8167	+	2.61258i	−0.548014	+	0.0966296i
$732$		0			0
$733$	−9.86921	+	21.1646i	−0.364527	+	0.781732i	0.635427	+	0.772161i	$0.280824\pi$
$733$	−9.86921	+	21.1646i	−0.364527	+	0.781732i	−0.999954	+	0.00957046i	$0.996954\pi$
$734$	−4.41379	−	3.70361i	−0.162916	−	0.136703i
$735$		0			0
$736$	21.9452	+	7.98740i	0.808910	+	0.294419i
$737$	−0.450149	−	0.120617i	−0.0165815	−	0.00444299i
$738$		0			0
$739$	−3.52276	−	2.03387i	−0.129587	−	0.0748169i	0.433805	−	0.901007i	$-0.357171\pi$
$739$	−3.52276	−	2.03387i	−0.129587	−	0.0748169i	−0.563392	+	0.826190i	$0.690504\pi$
$740$	−18.8999	−	20.4008i	−0.694774	−	0.749949i
$741$		0			0
$742$	−15.8963	+	11.1307i	−0.583572	+	0.408622i
$743$	41.2248	−	28.8659i	1.51239	−	1.05899i	0.535683	−	0.844419i	$-0.320054\pi$
$743$	41.2248	−	28.8659i	1.51239	−	1.05899i	0.976709	−	0.214569i	$-0.0688345\pi$
$744$		0			0
$745$	−1.53657	+	40.2342i	−0.0562955	+	1.47407i
$746$	1.40892	+	0.813439i	0.0515842	+	0.0297821i
$747$		0			0
$748$	−0.452489	−	0.121244i	−0.0165447	−	0.00443313i
$749$	−10.1277	−	3.68619i	−0.370059	−	0.134691i
$750$		0			0
$751$	2.00167	+	1.67960i	0.0730419	+	0.0612895i	0.678578	−	0.734529i	$-0.262597\pi$
$751$	2.00167	+	1.67960i	0.0730419	+	0.0612895i	−0.605536	+	0.795818i	$0.707041\pi$
$752$	2.00677	−	4.30353i	0.0731793	−	0.156933i
$753$		0			0
$754$	0.180481	−	0.0318237i	0.00657274	−	0.00115895i
$755$	−14.3274	+	15.8081i	−0.521427	+	0.575315i
$756$		0			0
$757$	28.7222	+	28.7222i	1.04393	+	1.04393i	0.998990	+	0.0449357i	$0.0143083\pi$
$757$	28.7222	+	28.7222i	1.04393	+	1.04393i	0.0449357	+	0.998990i	$0.485692\pi$
$758$	−1.82366	+	2.60445i	−0.0662383	+	0.0945980i
$759$		0			0
$760$	−2.25934	−	5.37136i	−0.0819547	−	0.194840i
$761$	−3.22815	+	3.84716i	−0.117020	+	0.139459i	−0.821374	−	0.570389i	$-0.806792\pi$
$761$	−3.22815	+	3.84716i	−0.117020	+	0.139459i	0.704354	+	0.709849i	$0.251237\pi$
$762$		0			0
$763$	−1.14754	+	0.535106i	−0.0415437	+	0.0193722i
$764$	11.6417	+	20.1640i	0.421182	+	0.729509i
$765$		0			0
$766$	3.08315	−	5.34017i	0.111399	−	0.192948i
$767$	−0.00803789	+	0.0918735i	−0.000290231	+	0.00331736i
$768$		0			0
$769$	−41.2856	−	7.27976i	−1.48880	−	0.262515i	−0.630709	−	0.776019i	$-0.717236\pi$
$769$	−41.2856	−	7.27976i	−1.48880	−	0.262515i	−0.858087	+	0.513504i	$0.828347\pi$
$770$	0.171282	−	0.132921i	0.00617256	−	0.00479015i
$771$		0			0
$772$	−33.5115	−	2.93187i	−1.20610	−	0.105520i
$773$	5.88204	−	1.57609i	0.211562	−	0.0566879i	−0.151481	−	0.988460i	$-0.548404\pi$
$773$	5.88204	−	1.57609i	0.211562	−	0.0566879i	0.363043	+	0.931772i	$0.381738\pi$
$774$		0			0
$775$	0.905066	−	0.648580i	0.0325109	−	0.0232977i
$776$	−4.20415	+	11.5508i	−0.150920	+	0.414650i
$777$		0			0
$778$	2.36511	−	0.206920i	0.0847932	−	0.00741844i
$779$	4.40798	−	1.60437i	0.157932	−	0.0574827i
$780$		0			0
$781$	0.0778050	+	0.441254i	0.00278408	+	0.0157893i

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

\(f(q)\)	\(=\)	\(q+(-0.263290 - 0.184358i) q^{2} +(-0.648706 - 1.78231i) q^{4} +(-2.21531 + 0.303968i) q^{5} +(2.07991 + 4.46037i) q^{7} +(-0.324162 + 1.20979i) q^{8} +O(q^{10})\)	\(q+(-0.263290 - 0.184358i) q^{2} +(-0.648706 - 1.78231i) q^{4} +(-2.21531 + 0.303968i) q^{5} +(2.07991 + 4.46037i) q^{7} +(-0.324162 + 1.20979i) q^{8} +(0.639309 + 0.328378i) q^{10} +(-0.0393995 - 0.0469545i) q^{11} +(0.0455832 + 0.0650996i) q^{13} +(0.274686 - 1.55782i) q^{14} +(-2.59752 + 2.17957i) q^{16} +(1.04290 + 3.89214i) q^{17} +(1.80193 - 1.04035i) q^{19} +(1.97885 + 3.75118i) q^{20} +(0.00171708 + 0.0196263i) q^{22} +(5.88782 + 2.74553i) q^{23} +(4.81521 - 1.34677i) q^{25} -0.0255437i q^{26} +(6.60050 - 6.60050i) q^{28} +(1.24585 + 7.06559i) q^{29} +(0.209263 - 0.0761654i) q^{31} +(3.58112 - 0.313308i) q^{32} +(0.442962 - 1.21703i) q^{34} +(-5.96345 - 9.24888i) q^{35} +(-6.33380 + 1.69714i) q^{37} +(-0.666227 - 0.0582873i) q^{38} +(0.350383 - 2.77860i) q^{40} +(2.22023 + 0.391486i) q^{41} +(-0.325424 + 3.71962i) q^{43} +(-0.0581286 + 0.100682i) q^{44} +(-1.04404 - 1.80834i) q^{46} +(-1.26917 + 0.591824i) q^{47} +(-11.0694 + 13.1920i) q^{49} +(-1.51608 - 0.533130i) q^{50} +(0.0864573 - 0.123474i) q^{52} +(-8.67464 - 8.67464i) q^{53} +(0.101555 + 0.0920427i) q^{55} +(-6.07034 + 1.07036i) q^{56} +(0.974575 - 2.08998i) q^{58} +(0.888968 + 0.745933i) q^{59} +(-6.77967 - 2.46760i) q^{61} +(-0.0691385 - 0.0185256i) q^{62} +(4.87243 + 2.81310i) q^{64} +(-0.120769 - 0.130360i) q^{65} +(6.22807 - 4.36094i) q^{67} +(6.26045 - 4.38361i) q^{68} +(-0.134987 + 3.53455i) q^{70} +(-6.33059 - 3.65497i) q^{71} +(6.42123 + 1.72056i) q^{73} +(1.98051 + 0.720846i) q^{74} +(-3.02314 - 2.53672i) q^{76} +(0.127487 - 0.273398i) q^{77} +(-6.06016 + 1.06857i) q^{79} +(5.09178 - 5.61800i) q^{80} +(-0.512391 - 0.512391i) q^{82} +(2.31193 - 3.30178i) q^{83} +(-3.49342 - 8.30529i) q^{85} +(0.771422 - 0.919344i) q^{86} +(0.0695770 - 0.0324443i) q^{88} +(5.25350 + 9.09933i) q^{89} +(-0.195560 + 0.338719i) q^{91} +(1.07392 - 12.2749i) q^{92} +(0.443268 + 0.0781601i) q^{94} +(-3.67561 + 2.85242i) q^{95} +(9.77698 + 0.855375i) q^{97} +(5.34651 - 1.43259i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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