LMFDB - Embedded newform 405.2.r.a.332.7

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			332.7
Character	$\chi$	$=$	405.332
Dual form			405.2.r.a.233.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.184358 - 0.263290i) q^{2} +(0.648706 - 1.78231i) q^{4} +(0.0853346 - 2.23444i) q^{5} +(4.46037 + 2.07991i) q^{7} +(-1.20979 + 0.324162i) q^{8} +(-0.604038 + 0.389469i) q^{10} +(-0.0393995 + 0.0469545i) q^{11} +(-0.0650996 - 0.0455832i) q^{13} +(-0.274686 - 1.55782i) q^{14} +(-2.59752 - 2.17957i) q^{16} +(3.89214 + 1.04290i) q^{17} +(-1.80193 - 1.04035i) q^{19} +(-3.92710 - 1.60159i) q^{20} +(0.0196263 + 0.00171708i) q^{22} +(-2.74553 - 5.88782i) q^{23} +(-4.98544 - 0.381350i) q^{25} +0.0255437i q^{26} +(6.60050 - 6.60050i) q^{28} +(-1.24585 + 7.06559i) q^{29} +(0.209263 + 0.0761654i) q^{31} +(-0.313308 + 3.58112i) q^{32} +(-0.442962 - 1.21703i) q^{34} +(5.02805 - 9.78894i) q^{35} +(1.69714 - 6.33380i) q^{37} +(0.0582873 + 0.666227i) q^{38} +(0.621084 + 2.73086i) q^{40} +(2.22023 - 0.391486i) q^{41} +(-3.71962 + 0.325424i) q^{43} +(0.0581286 + 0.100682i) q^{44} +(-1.04404 + 1.80834i) q^{46} +(0.591824 - 1.26917i) q^{47} +(11.0694 + 13.1920i) q^{49} +(0.818698 + 1.38292i) q^{50} +(-0.123474 + 0.0864573i) q^{52} +(8.67464 + 8.67464i) q^{53} +(0.101555 + 0.0920427i) q^{55} +(-6.07034 - 1.07036i) q^{56} +(2.08998 - 0.974575i) q^{58} +(-0.888968 + 0.745933i) q^{59} +(-6.77967 + 2.46760i) q^{61} +(-0.0185256 - 0.0691385i) q^{62} +(-4.87243 + 2.81310i) q^{64} +(-0.107408 + 0.141571i) q^{65} +(-4.36094 + 6.22807i) q^{67} +(4.38361 - 6.26045i) q^{68} +(-3.50429 + 0.480832i) q^{70} +(-6.33059 + 3.65497i) q^{71} +(-1.72056 - 6.42123i) q^{73} +(-1.98051 + 0.720846i) q^{74} +(-3.02314 + 2.53672i) q^{76} +(-0.273398 + 0.127487i) q^{77} +(6.06016 + 1.06857i) q^{79} +(-5.09178 + 5.61800i) q^{80} +(-0.512391 - 0.512391i) q^{82} +(3.30178 - 2.31193i) q^{83} +(2.66242 - 8.60775i) q^{85} +(0.771422 + 0.919344i) q^{86} +(0.0324443 - 0.0695770i) q^{88} +(-5.25350 + 9.09933i) q^{89} +(-0.195560 - 0.338719i) q^{91} +(-12.2749 + 1.07392i) q^{92} +(-0.443268 + 0.0781601i) q^{94} +(-2.47836 + 3.93753i) q^{95} +(0.855375 + 9.77698i) q^{97} +(1.43259 - 5.34651i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots - 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

Character values

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

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

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 $

$2$	−0.184358	−	0.263290i	−0.130361	−	0.186174i	0.748665	−	0.662948i	$-0.230695\pi$
$2$	−0.184358	−	0.263290i	−0.130361	−	0.186174i	−0.879026	+	0.476774i	$0.841806\pi$
$3$		0			0
$3$		0			0
$4$	0.648706	−	1.78231i	0.324353	−	0.891153i
$5$	0.0853346	−	2.23444i	0.0381628	−	0.999272i
$5$	0.0853346	−	2.23444i	0.0381628	−	0.999272i
$6$		0			0
$7$	4.46037	+	2.07991i	1.68586	+	0.786130i	0.998192	+	0.0601067i	$0.0191441\pi$
$7$	4.46037	+	2.07991i	1.68586	+	0.786130i	0.687670	+	0.726024i	$0.258634\pi$
$8$	−1.20979	+	0.324162i	−0.427725	+	0.114609i
$9$		0			0
$10$	−0.604038	+	0.389469i	−0.191014	+	0.123161i
$11$	−0.0393995	+	0.0469545i	−0.0118794	+	0.0141573i	−0.771951	−	0.635682i	$-0.780719\pi$
$11$	−0.0393995	+	0.0469545i	−0.0118794	+	0.0141573i	0.760072	+	0.649839i	$0.225164\pi$
$12$		0			0
$13$	−0.0650996	−	0.0455832i	−0.0180554	−	0.0126425i	0.564514	−	0.825424i	$-0.309064\pi$
$13$	−0.0650996	−	0.0455832i	−0.0180554	−	0.0126425i	−0.582569	+	0.812781i	$0.697953\pi$
$14$	−0.274686	−	1.55782i	−0.0734128	−	0.416345i
$15$		0			0
$16$	−2.59752	−	2.17957i	−0.649379	−	0.544894i
$17$	3.89214	+	1.04290i	0.943982	+	0.252939i	0.697807	−	0.716286i	$-0.254159\pi$
$17$	3.89214	+	1.04290i	0.943982	+	0.252939i	0.246175	+	0.969225i	$0.420826\pi$
$18$		0			0
$19$	−1.80193	−	1.04035i	−0.413392	−	0.238672i	0.278854	−	0.960333i	$-0.410045\pi$
$19$	−1.80193	−	1.04035i	−0.413392	−	0.238672i	−0.692246	+	0.721662i	$0.743379\pi$
$20$	−3.92710	−	1.60159i	−0.878126	−	0.358126i
$21$		0			0
$22$	0.0196263	+	0.00171708i	0.00418434	+	0.000366082i
$23$	−2.74553	−	5.88782i	−0.572483	−	1.22769i	−0.953014	−	0.302926i	$-0.902036\pi$
$23$	−2.74553	−	5.88782i	−0.572483	−	1.22769i	0.380531	−	0.924768i	$-0.375741\pi$
$24$		0			0
$25$	−4.98544	−	0.381350i	−0.997087	−	0.0762700i
$26$			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	0.618818	+	0.785534i	$0.287612\pi$
$29$	−1.24585	+	7.06559i	−0.231349	+	1.31205i	−0.850167	+	0.526512i	$0.823499\pi$
$30$		0			0
$31$	0.209263	+	0.0761654i	0.0375847	+	0.0136797i	0.360744	−	0.932665i	$-0.382523\pi$
$31$	0.209263	+	0.0761654i	0.0375847	+	0.0136797i	−0.323159	+	0.946345i	$0.604745\pi$
$32$	−0.313308	+	3.58112i	−0.0553855	+	0.633059i
$33$		0			0
$34$	−0.442962	−	1.21703i	−0.0759674	−	0.208719i
$35$	5.02805	−	9.78894i	0.849895	−	1.65463i
$36$		0			0
$37$	1.69714	−	6.33380i	0.279007	−	1.04127i	−0.674101	−	0.738640i	$-0.735469\pi$
$37$	1.69714	−	6.33380i	0.279007	−	1.04127i	0.953108	−	0.302630i	$-0.0978648\pi$
$38$	0.0582873	+	0.666227i	0.00945545	+	0.108076i
$39$		0			0
$40$	0.621084	+	2.73086i	0.0982020	+	0.431787i
$41$	2.22023	−	0.391486i	0.346742	−	0.0611399i	0.00243462	−	0.999997i	$-0.499225\pi$
$41$	2.22023	−	0.391486i	0.346742	−	0.0611399i	0.344307	+	0.938857i	$0.388114\pi$
$42$		0			0
$43$	−3.71962	+	0.325424i	−0.567236	+	0.0496267i	−0.367167	−	0.930155i	$-0.619672\pi$
$43$	−3.71962	+	0.325424i	−0.567236	+	0.0496267i	−0.200069	+	0.979782i	$0.564117\pi$
$44$	0.0581286	+	0.100682i	0.00876322	+	0.0151783i
$45$		0			0
$46$	−1.04404	+	1.80834i	−0.153936	+	0.266625i
$47$	0.591824	−	1.26917i	0.0863264	−	0.185128i	−0.858405	−	0.512972i	$-0.828544\pi$
$47$	0.591824	−	1.26917i	0.0863264	−	0.185128i	0.944732	+	0.327844i	$0.106322\pi$
$48$		0			0
$49$	11.0694	+	13.1920i	1.58134	+	1.88457i
$50$	0.818698	+	1.38292i	0.115781	+	0.195575i
$51$		0			0
$52$	−0.123474	+	0.0864573i	−0.0171227	+	0.0119895i
$53$	8.67464	+	8.67464i	1.19155	+	1.19155i	0.976631	+	0.214923i	$0.0689499\pi$
$53$	8.67464	+	8.67464i	1.19155	+	1.19155i	0.214923	+	0.976631i	$0.431050\pi$
$54$		0			0
$55$	0.101555	+	0.0920427i	0.0136937	+	0.0124110i
$56$	−6.07034	−	1.07036i	−0.811183	−	0.143033i
$57$		0			0
$58$	2.08998	−	0.974575i	0.274428	−	0.127968i
$59$	−0.888968	+	0.745933i	−0.115734	+	0.0971121i	−0.698818	−	0.715300i	$-0.746290\pi$
$59$	−0.888968	+	0.745933i	−0.115734	+	0.0971121i	0.583084	+	0.812412i	$0.301846\pi$
$60$		0			0
$61$	−6.77967	+	2.46760i	−0.868048	+	0.315944i	−0.737377	−	0.675482i	$-0.763936\pi$
$61$	−6.77967	+	2.46760i	−0.868048	+	0.315944i	−0.130672	+	0.991426i	$0.541713\pi$
$62$	−0.0185256	−	0.0691385i	−0.00235275	−	0.00878060i
$63$		0			0
$64$	−4.87243	+	2.81310i	−0.609054	+	0.351637i
$65$	−0.107408	+	0.141571i	−0.0133224	+	0.0175598i
$66$		0			0
$67$	−4.36094	+	6.22807i	−0.532774	+	0.760880i	−0.991835	−	0.127524i	$-0.959297\pi$
$67$	−4.36094	+	6.22807i	−0.532774	+	0.760880i	0.459061	+	0.888405i	$0.348186\pi$
$68$	4.38361	−	6.26045i	0.531591	−	0.759191i
$69$		0			0
$70$	−3.50429	+	0.480832i	−0.418843	+	0.0574704i
$71$	−6.33059	+	3.65497i	−0.751303	+	0.433765i	−0.826165	−	0.563429i	$-0.809482\pi$
$71$	−6.33059	+	3.65497i	−0.751303	+	0.433765i	0.0748614	+	0.997194i	$0.476149\pi$
$72$		0			0
$73$	−1.72056	−	6.42123i	−0.201377	−	0.751549i	−0.990523	−	0.137344i	$-0.956144\pi$
$73$	−1.72056	−	6.42123i	−0.201377	−	0.751549i	0.789147	−	0.614205i	$-0.210523\pi$
$74$	−1.98051	+	0.720846i	−0.230229	+	0.0837966i
$75$		0			0
$76$	−3.02314	+	2.53672i	−0.346778	+	0.290981i
$77$	−0.273398	+	0.127487i	−0.0311565	+	0.0145285i
$78$		0			0
$79$	6.06016	+	1.06857i	0.681821	+	0.120223i	0.503822	−	0.863807i	$-0.331927\pi$
$79$	6.06016	+	1.06857i	0.681821	+	0.120223i	0.177999	+	0.984031i	$0.443038\pi$
$80$	−5.09178	+	5.61800i	−0.569279	+	0.628111i
$81$		0			0
$82$	−0.512391	−	0.512391i	−0.0565841	−	0.0565841i
$83$	3.30178	−	2.31193i	0.362417	−	0.253767i	−0.378158	−	0.925741i	$-0.623442\pi$
$83$	3.30178	−	2.31193i	0.362417	−	0.253767i	0.740575	+	0.671974i	$0.234553\pi$
$84$		0			0
$85$	2.66242	−	8.60775i	0.288780	−	0.933642i
$86$	0.771422	+	0.919344i	0.0831845	+	0.0991355i
$87$		0			0
$88$	0.0324443	−	0.0695770i	0.00345857	−	0.00741693i
$89$	−5.25350	+	9.09933i	−0.556870	+	0.964527i	0.440886	+	0.897563i	$0.354664\pi$
$89$	−5.25350	+	9.09933i	−0.556870	+	0.964527i	−0.997755	+	0.0669633i	$0.978669\pi$
$90$		0			0
$91$	−0.195560	−	0.338719i	−0.0205002	−	0.0355074i
$92$	−12.2749	+	1.07392i	−1.27975	+	0.111964i
$93$		0			0
$94$	−0.443268	+	0.0781601i	−0.0457196	+	0.00806160i
$95$	−2.47836	+	3.93753i	−0.254274	+	0.403982i
$96$		0			0
$97$	0.855375	+	9.77698i	0.0868501	+	0.992702i	0.907161	+	0.420784i	$0.138245\pi$
$97$	0.855375	+	9.77698i	0.0868501	+	0.992702i	−0.820311	+	0.571918i	$0.806200\pi$
$98$	1.43259	−	5.34651i	0.144714	−	0.540079i
$99$		0			0
$100$	−3.91377	+	8.63819i	−0.391377	+	0.863819i
$101$	−1.28534	−	3.53144i	−0.127896	−	0.351391i	0.859173	−	0.511684i	$-0.170978\pi$
$101$	−1.28534	−	3.53144i	−0.127896	−	0.351391i	−0.987069	+	0.160293i	$0.948756\pi$
$102$		0			0
$103$	−0.211590	+	2.41848i	−0.0208485	+	0.238300i	0.978619	+	0.205680i	$0.0659406\pi$
$103$	−0.211590	+	2.41848i	−0.0208485	+	0.238300i	−0.999468	+	0.0326198i	$0.989615\pi$
$104$	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	−0.628284	−	0.777984i	$-0.716242\pi$
$107$	1.54852	−	1.54852i	0.149701	−	0.149701i	0.777984	+	0.628284i	$0.216242\pi$
$108$		0			0
$109$			0.257274i			0.0246424i	0.999924	+	0.0123212i	$0.00392206\pi$
$109$			0.257274i			0.0246424i	−0.999924	+	0.0123212i	$0.996078\pi$
$110$	0.00551151	−	0.0437072i	0.000525502	−	0.00416732i
$111$		0			0
$112$	−7.05257	−	15.1243i	−0.666406	−	1.42911i
$113$	11.2070	+	0.980488i	1.05427	+	0.0922366i	0.601089	−	0.799182i	$-0.294734\pi$
$113$	11.2070	+	0.980488i	1.05427	+	0.0922366i	0.453180	+	0.891419i	$0.350289\pi$
$114$		0			0
$115$	−13.3903	+	5.63229i	−1.24865	+	0.525214i
$116$	11.7848	+	6.80398i	1.09420	+	0.631734i
$117$		0			0
$118$	0.360285	+	0.0965380i	0.0331669	+	0.00888705i
$119$	15.1913	+	12.7470i	1.39258	+	1.16851i
$120$		0			0
$121$	1.90948	+	10.8292i	0.173589	+	0.984471i
$122$	1.89958	+	1.33010i	0.171980	+	0.120422i
$123$		0			0
$124$	0.271500	−	0.323561i	0.0243814	−	0.0290567i
$125$	−1.27753	+	11.1071i	−0.114266	+	0.993450i
$126$		0			0
$127$	7.47317	−	2.00243i	0.663137	−	0.177687i	0.0884755	−	0.996078i	$-0.471801\pi$
$127$	7.47317	−	2.00243i	0.663137	−	0.177687i	0.574661	+	0.818391i	$0.305134\pi$
$128$	8.15493	+	3.80270i	0.720800	+	0.336115i
$129$		0			0
$130$	0.0570759	+	0.00217976i	0.00500589	+	0.000191178i
$131$	−3.14700	+	8.64630i	−0.274954	+	0.755431i	0.722961	+	0.690889i	$0.242781\pi$
$131$	−3.14700	+	8.64630i	−0.274954	+	0.755431i	−0.997915	+	0.0645417i	$0.979441\pi$
$132$		0			0
$133$	−5.87347	−	8.38818i	−0.509294	−	0.727347i
$134$	2.44376			0.211109
$135$		0			0
$136$	−5.04674			−0.432754
$137$	7.88810	+	11.2654i	0.673926	+	0.962466i	0.999854	+	0.0170715i	$0.00543428\pi$
$137$	7.88810	+	11.2654i	0.673926	+	0.962466i	−0.325928	+	0.945394i	$0.605677\pi$
$138$		0			0
$139$	0.364140	−	1.00047i	0.0308860	−	0.0848586i	−0.923291	−	0.384101i	$-0.874512\pi$
$139$	0.364140	−	1.00047i	0.0308860	−	0.0848586i	0.954177	+	0.299242i	$0.0967338\pi$
$140$	−14.1852	−	15.3117i	−1.19886	−	1.29407i
$141$		0			0
$142$	2.12941	+	0.992961i	0.178696	+	0.0833274i
$143$	0.00470524	−	0.00126076i	0.000393472	−	0.000105430i
$144$		0			0
$145$	15.6813	+	3.38672i	1.30226	+	0.281252i
$146$	−1.37345	+	1.63681i	−0.113667	+	0.135464i
$147$		0			0
$148$	−10.1878	−	7.13359i	−0.837434	−	0.586378i
$149$	−3.12678	−	17.7328i	−0.256156	−	1.45273i	−0.793089	−	0.609106i	$-0.791528\pi$
$149$	−3.12678	−	17.7328i	−0.256156	−	1.45273i	0.536933	−	0.843625i	$-0.319583\pi$
$150$		0			0
$151$	7.30896	+	6.13294i	0.594795	+	0.499092i	0.889768	−	0.456414i	$-0.150866\pi$
$151$	7.30896	+	6.13294i	0.594795	+	0.499092i	−0.294973	+	0.955506i	$0.595311\pi$
$152$	2.51720	+	0.674482i	0.204172	+	0.0547077i
$153$		0			0
$154$	0.0839692	+	0.0484796i	0.00676643	+	0.00390660i
$155$	0.188044	−	0.461085i	0.0151041	−	0.0370353i
$156$		0			0
$157$	16.1522	+	1.41313i	1.28908	+	0.112780i	0.710997	−	0.703195i	$-0.248244\pi$
$157$	16.1522	+	1.41313i	1.28908	+	0.112780i	0.578087	+	0.815975i	$0.303799\pi$
$158$	−0.835893	−	1.79258i	−0.0665001	−	0.142610i
$159$		0			0
$160$	7.97507	+	1.00566i	0.630484	+	0.0795045i
$161$		−	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
$167$	−1.13992	+	13.0293i	−0.0882093	+	1.00824i	0.815121	+	0.579291i	$0.196671\pi$
$167$	−1.13992	+	13.0293i	−0.0882093	+	1.00824i	−0.903330	+	0.428946i	$0.858885\pi$
$168$		0			0
$169$	−4.44410	−	12.2101i	−0.341854	−	0.939236i
$170$	−2.75717	+	0.885917i	−0.211466	+	0.0679467i
$171$		0			0
$172$	−1.83293	+	6.84060i	−0.139760	+	0.521591i
$173$	−1.98304	−	22.6663i	−0.150768	−	1.72329i	−0.575360	−	0.817900i	$-0.695138\pi$
$173$	−1.98304	−	22.6663i	−0.150768	−	1.72329i	0.424592	−	0.905385i	$-0.360418\pi$
$174$		0			0
$175$	−21.4437	−	12.0702i	−1.62099	−	0.912421i
$176$	0.204682	−	0.0360909i	0.0154285	−	0.00272046i
$177$		0			0
$178$	3.36429	−	0.294337i	0.252164	−	0.0220615i
$179$	−9.11136	−	15.7813i	−0.681015	−	1.17955i	−0.974671	−	0.223642i	$-0.928205\pi$
$179$	−9.11136	−	15.7813i	−0.681015	−	1.17955i	0.293656	−	0.955911i	$-0.405128\pi$
$180$		0			0
$181$	6.18809	−	10.7181i	0.459957	−	0.796669i	−0.539001	−	0.842305i	$-0.681198\pi$
$181$	6.18809	−	10.7181i	0.459957	−	0.796669i	0.998958	+	0.0456358i	$0.0145314\pi$
$182$	−0.0531285	+	0.113934i	−0.00393815	+	0.00844539i
$183$		0			0
$184$	5.23013	+	6.23302i	0.385570	+	0.459504i
$185$	−14.0077	−	4.33264i	−1.02986	−	0.318542i
$186$		0			0
$187$	−0.202317	+	0.141664i	−0.0147949	+	0.0103595i
$188$	−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	−0.281793	−	0.959475i	$-0.590929\pi$
$191$	−12.0893	−	2.13167i	−0.874752	−	0.154242i	−0.592959	+	0.805233i	$0.702040\pi$
$192$		0			0
$193$	16.0742	−	7.49551i	1.15704	−	0.539538i	0.253205	−	0.967413i	$-0.418515\pi$
$193$	16.0742	−	7.49551i	1.15704	−	0.539538i	0.903838	+	0.427874i	$0.140737\pi$
$194$	2.41649	−	2.02767i	0.173494	−	0.145579i
$195$		0			0
$196$	30.6929	−	11.1713i	2.19235	−	0.797951i
$197$	−2.35826	−	8.80113i	−0.168019	−	0.627055i	−0.997636	−	0.0687218i	$-0.978108\pi$
$197$	−2.35826	−	8.80113i	−0.168019	−	0.627055i	0.829617	−	0.558333i	$-0.188559\pi$
$198$		0			0
$199$	−9.38387	+	5.41778i	−0.665205	+	0.384056i	−0.794257	−	0.607581i	$-0.792140\pi$
$199$	−9.38387	+	5.41778i	−0.665205	+	0.384056i	0.129052	+	0.991638i	$0.458807\pi$
$200$	6.15495	−	1.15474i	0.435221	−	0.0816522i
$201$		0			0
$202$	−0.692831	+	0.989466i	−0.0487474	+	0.0696186i
$203$	−20.2527	+	28.9239i	−1.42146	+	2.03006i
$204$		0			0
$205$	−0.685290	−	4.99437i	−0.0478627	−	0.348822i
$206$	0.675770	−	0.390156i	0.0470831	−	0.0271835i
$207$		0			0
$208$	0.0697452	+	0.260293i	0.00483596	+	0.0180480i
$209$	0.119844	−	0.0436198i	0.00828980	−	0.00301724i
$210$		0			0
$211$	−1.55684	+	1.30634i	−0.107177	+	0.0899325i	−0.694802	−	0.719202i	$-0.744508\pi$
$211$	−1.55684	+	1.30634i	−0.107177	+	0.0899325i	0.587624	+	0.809134i	$0.300063\pi$
$212$	21.0882	−	9.83357i	1.44834	−	0.675372i
$213$		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
$218$	0.0677378	−	0.0474305i	0.00458779	−	0.00321240i
$219$		0			0
$220$	0.229928	−	0.121293i	0.0155017	−	0.00817759i
$221$	−0.205838	−	0.245308i	−0.0138462	−	0.0165012i
$222$		0			0
$223$	−1.15123	+	2.46881i	−0.0770918	+	0.165324i	−0.941076	−	0.338195i	$-0.890184\pi$
$223$	−1.15123	+	2.46881i	−0.0770918	+	0.165324i	0.863984	+	0.503519i	$0.167961\pi$
$224$	−8.84586	+	15.3215i	−0.591039	+	1.02371i
$225$		0			0
$226$	−1.80795	−	3.13146i	−0.120263	−	0.208302i
$227$	−14.1158	+	1.23497i	−0.936899	+	0.0819680i	−0.545368	−	0.838197i	$-0.683610\pi$
$227$	−14.1158	+	1.23497i	−0.936899	+	0.0819680i	−0.391531	+	0.920165i	$0.628054\pi$
$228$		0			0
$229$	−13.0574	+	2.30237i	−0.862857	+	0.152145i	−0.587527	−	0.809205i	$-0.699898\pi$
$229$	−13.0574	+	2.30237i	−0.862857	+	0.152145i	−0.275330	+	0.961350i	$0.588787\pi$
$230$	3.95153	+	2.48717i	0.260556	+	0.163999i
$231$		0			0
$232$	−0.783175	−	8.95173i	−0.0514180	−	0.587710i
$233$	1.75621	−	6.55427i	0.115053	−	0.429384i	−0.884238	−	0.467037i	$-0.845321\pi$
$233$	1.75621	−	6.55427i	0.115053	−	0.429384i	0.999291	+	0.0376527i	$0.0119881\pi$
$234$		0			0
$235$	−2.78538	−	1.43070i	−0.181698	−	0.0933285i
$236$	0.752801	+	2.06830i	0.0490032	+	0.134635i
$237$		0			0
$238$	0.555528	−	6.34972i	0.0360095	−	0.411591i
$239$	17.1554	+	6.24407i	1.10969	+	0.403895i	0.830881	−	0.556451i	$-0.187837\pi$
$239$	17.1554	+	6.24407i	1.10969	+	0.403895i	0.278812	+	0.960346i	$0.410059\pi$
$240$		0			0
$241$	−2.76886	+	15.7030i	−0.178358	+	1.01152i	0.755839	+	0.654758i	$0.227229\pi$
$241$	−2.76886	+	15.7030i	−0.178358	+	1.01152i	−0.934196	+	0.356759i	$0.883882\pi$
$242$	2.49919	−	2.49919i	0.160654	−	0.160654i
$243$		0			0
$244$			13.6842i			0.876041i
$245$	30.4213	−	23.6081i	1.94355	−	1.50827i
$246$		0			0
$247$	0.0698828	+	0.149864i	0.00444653	+	0.00953562i
$248$	−0.277854	−	0.0243091i	−0.0176437	−	0.00154363i
$249$		0			0
$250$	3.15992	−	1.71132i	0.199851	−	0.108233i
$251$	−14.9016	−	8.60342i	−0.940578	−	0.543043i	−0.0504364	−	0.998727i	$-0.516061\pi$
$251$	−14.9016	−	8.60342i	−0.940578	−	0.543043i	−0.890141	+	0.455684i	$0.849395\pi$
$252$		0			0
$253$	0.384632	+	0.103062i	0.0241816	+	0.00647945i
$254$	−1.90496	−	1.59845i	−0.119528	−	0.100296i
$255$		0			0
$256$	1.45175	+	8.23327i	0.0907343	+	0.514580i
$257$	7.66961	+	5.37032i	0.478417	+	0.334991i	0.787784	−	0.615952i	$-0.211228\pi$
$257$	7.66961	+	5.37032i	0.478417	+	0.334991i	−0.309367	+	0.950943i	$0.600117\pi$
$258$		0			0
$259$	20.7436	−	24.7212i	1.28894	−	1.53610i
$260$	0.182647	+	0.283273i	0.0113273	+	0.0175678i
$261$		0			0
$262$	2.85666	−	0.765440i	0.176485	−	0.0472890i
$263$	−0.828096	−	0.386147i	−0.0510626	−	0.0238109i	0.396919	−	0.917854i	$-0.370079\pi$
$263$	−0.828096	−	0.386147i	−0.0510626	−	0.0238109i	−0.447982	+	0.894043i	$0.647857\pi$
$264$		0			0
$265$	20.1232	−	18.6427i	1.23616	−	1.14521i
$266$	−1.12571	+	3.09285i	−0.0690215	+	0.189635i
$267$		0			0
$268$	8.27136	+	11.8127i	0.505254	+	0.721577i
$269$	−27.6508			−1.68590			−0.842951	−	0.537990i	$-0.819184\pi$
$269$	−27.6508			−1.68590			−0.842951	+	0.537990i	$0.819184\pi$
$270$		0			0
$271$	−18.0879			−1.09876			−0.549380	−	0.835572i	$-0.685136\pi$
$271$	−18.0879			−1.09876			−0.549380	+	0.835572i	$0.685136\pi$
$272$	−7.83682	−	11.1921i	−0.475177	−	0.678623i
$273$		0			0
$274$	1.51183	−	4.15372i	0.0913330	−	0.250935i
$275$	0.214330	−	0.219064i	0.0129246	−	0.0132100i
$276$		0			0
$277$	4.69280	+	2.18829i	0.281963	+	0.131481i	0.558455	−	0.829535i	$-0.311394\pi$
$277$	4.69280	+	2.18829i	0.281963	+	0.131481i	−0.276492	+	0.961016i	$0.589172\pi$
$278$	−0.330545	+	0.0885694i	−0.0198248	+	0.00531204i
$279$		0			0
$280$	−2.90967	+	13.4725i	−0.173886	+	0.805134i
$281$	4.92653	−	5.87122i	0.293892	−	0.350247i	−0.598812	−	0.800889i	$-0.704360\pi$
$281$	4.92653	−	5.87122i	0.293892	−	0.350247i	0.892705	+	0.450642i	$0.148805\pi$
$282$		0			0
$283$	−7.76215	−	5.43511i	−0.461412	−	0.323084i	0.319652	−	0.947535i	$-0.396434\pi$
$283$	−7.76215	−	5.43511i	−0.461412	−	0.323084i	−0.781064	+	0.624451i	$0.785323\pi$
$284$	2.40758	+	13.6541i	0.142863	+	0.810219i
$285$		0			0
$286$	−0.00119939	−	0.00100641i	−7.09216e−5	−	5.95103e-5i
$287$	10.7173	+	2.87169i	0.632622	+	0.169511i
$288$		0			0
$289$	−0.661319	−	0.381813i	−0.0389011	−	0.0224596i
$290$	−1.99928	−	4.75310i	−0.117402	−	0.279112i
$291$		0			0
$292$	−12.5607	−	1.09892i	−0.735062	−	0.0643096i
$293$	3.61107	+	7.74397i	0.210961	+	0.452408i	0.983106	−	0.183039i	$-0.0585936\pi$
$293$	3.61107	+	7.74397i	0.210961	+	0.452408i	−0.772144	+	0.635447i	$0.780816\pi$
$294$		0			0
$295$	1.59088	+	2.05000i	0.0926247	+	0.119356i
$296$			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
$302$	0.267281	−	3.05503i	0.0153803	−	0.175797i
$303$		0			0
$304$	2.41304	+	6.62976i	0.138397	+	0.380243i
$305$	4.93516	+	15.3593i	0.282586	+	0.879473i
$306$		0			0
$307$	5.49053	−	20.4909i	0.313361	−	1.16948i	−0.612145	−	0.790746i	$-0.709693\pi$
$307$	5.49053	−	20.4909i	0.313361	−	1.16948i	0.925506	−	0.378734i	$-0.123640\pi$
$308$	0.0498668	+	0.569980i	0.00284142	+	0.0324776i
$309$		0			0
$310$	−0.156067	+	0.0354944i	−0.00886399	+	0.00201595i
$311$	19.3816	−	3.41750i	1.09903	−	0.193788i	0.405413	−	0.914134i	$-0.367128\pi$
$311$	19.3816	−	3.41750i	1.09903	−	0.193788i	0.693616	+	0.720345i	$0.256017\pi$
$312$		0			0
$313$	4.18556	−	0.366189i	0.236582	−	0.0206983i	0.0317519	−	0.999496i	$-0.489891\pi$
$313$	4.18556	−	0.366189i	0.236582	−	0.0206983i	0.204830	+	0.978798i	$0.434336\pi$
$314$	−2.60572	−	4.51323i	−0.147049	−	0.254696i
$315$		0			0
$316$	5.83578	−	10.1079i	0.328288	−	0.568612i
$317$	7.05644	−	15.1326i	0.396329	−	0.849930i	−0.602334	−	0.798244i	$-0.705763\pi$
$317$	7.05644	−	15.1326i	0.396329	−	0.849930i	0.998663	−	0.0516863i	$-0.0164596\pi$
$318$		0			0
$319$	−0.282675	−	0.336879i	−0.0158268	−	0.0188616i
$320$	5.86991	+	11.1272i	0.328138	+	0.622029i
$321$		0			0
$322$	−8.41799	+	5.89434i	−0.469116	+	0.328479i
$323$	−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
$328$	−2.55911	+	1.19333i	−0.141303	+	0.0658907i
$329$	5.27951	−	4.43004i	0.291069	−	0.244236i
$330$		0			0
$331$	−12.4570	+	4.53397i	−0.684698	+	0.249210i	−0.660863	−	0.750506i	$-0.729810\pi$
$331$	−12.4570	+	4.53397i	−0.684698	+	0.249210i	−0.0238345	+	0.999716i	$0.507587\pi$
$332$	−1.97868	−	7.38454i	−0.108594	−	0.405279i
$333$		0			0
$334$	3.64064	−	2.10192i	0.199207	−	0.115012i
$335$	13.5441	+	10.2757i	0.739994	+	0.561423i
$336$		0			0
$337$	−12.1886	+	17.4071i	−0.663953	+	0.948223i	0.336027	+	0.941852i	$0.390917\pi$
$337$	−12.1886	+	17.4071i	−0.663953	+	0.948223i	−0.999980	+	0.00637058i	$0.997972\pi$
$338$	−2.39549	+	3.42111i	−0.130297	+	0.186084i
$339$		0			0
$340$	−13.6145	−	10.3292i	−0.738351	−	0.560177i
$341$	−0.0118212	+	0.00682495i	−0.000640152	+	0.000369592i
$342$		0			0
$343$	13.0191	+	48.5880i	0.702966	+	2.62350i
$344$	4.39446	−	1.59945i	0.236934	−	0.0862368i
$345$		0			0
$346$	−5.60222	+	4.70082i	−0.301177	+	0.252718i
$347$	−28.5852	+	13.3295i	−1.53453	+	0.715565i	−0.992207	−	0.124603i	$-0.960234\pi$
$347$	−28.5852	+	13.3295i	−1.53453	+	0.715565i	−0.542327	+	0.840168i	$0.682456\pi$
$348$		0			0
$349$	−16.6978	−	2.94427i	−0.893813	−	0.157603i	−0.292168	−	0.956367i	$-0.594377\pi$
$349$	−16.6978	−	2.94427i	−0.893813	−	0.157603i	−0.601645	+	0.798764i	$0.705488\pi$
$350$	0.775353	+	7.87116i	0.0414444	+	0.420731i
$351$		0			0
$352$	−0.155806	−	0.155806i	−0.00830448	−	0.00830448i
$353$	−15.5802	+	10.9094i	−0.829252	+	0.580648i	−0.909299	−	0.416143i	$-0.863382\pi$
$353$	−15.5802	+	10.9094i	−0.829252	+	0.580648i	0.0800474	+	0.996791i	$0.474493\pi$
$354$		0			0
$355$	7.62659	+	14.4572i	0.404777	+	0.767310i
$356$	12.8098	+	15.2661i	0.678918	+	0.809103i
$357$		0			0
$358$	−2.47532	+	5.30835i	−0.130825	+	0.280555i
$359$	15.6916	−	27.1786i	0.828170	−	1.43443i	−0.0713028	−	0.997455i	$-0.522716\pi$
$359$	15.6916	−	27.1786i	0.828170	−	1.43443i	0.899473	−	0.436977i	$-0.143951\pi$
$360$		0			0
$361$	−7.33536	−	12.7052i	−0.386072	−	0.668696i
$362$	−3.96279	+	0.346699i	−0.208280	+	0.0182221i
$363$		0			0
$364$	−0.730562	+	0.128818i	−0.0382919	+	0.00675189i
$365$	−14.4947	+	3.29654i	−0.758686	+	0.172549i
$366$		0			0
$367$	1.56237	+	17.8579i	0.0815549	+	0.932177i	0.921212	+	0.389060i	$0.127200\pi$
$367$	1.56237	+	17.8579i	0.0815549	+	0.932177i	−0.839657	+	0.543117i	$0.817244\pi$
$368$	−5.70137	+	21.2778i	−0.297204	+	1.10918i
$369$		0			0
$370$	1.44168	+	4.48684i	0.0749494	+	0.233260i
$371$	20.6497	+	56.7346i	1.07208	+	2.94551i
$372$		0			0
$373$	−0.441145	+	5.04230i	−0.0228416	+	0.261081i	0.976184	+	0.216945i	$0.0696091\pi$
$373$	−0.441145	+	5.04230i	−0.0228416	+	0.261081i	−0.999026	+	0.0441361i	$0.985946\pi$
$374$	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	$-0.0817653\pi$
$380$	5.41016	+	6.97149i	0.277535	+	0.357630i
$381$		0			0
$382$	1.66751	+	3.57599i	0.0853173	+	0.182963i
$383$	−19.1117	−	1.67206i	−0.976561	−	0.0854380i	−0.412312	−	0.911043i	$-0.635279\pi$
$383$	−19.1117	−	1.67206i	−0.976561	−	0.0854380i	−0.564249	+	0.825605i	$0.690834\pi$
$384$		0			0
$385$	0.261533	+	0.621769i	0.0133289	+	0.0316883i
$386$	−4.93689	−	2.85032i	−0.251281	−	0.145077i
$387$		0			0
$388$	17.9805	+	4.81785i	0.912819	+	0.244589i
$389$	5.65836	+	4.74792i	0.286890	+	0.240729i	0.774863	−	0.632130i	$-0.217819\pi$
$389$	5.65836	+	4.74792i	0.286890	+	0.240729i	−0.487973	+	0.872859i	$0.662263\pi$
$390$		0			0
$391$	−4.54562	−	25.7795i	−0.229882	−	1.30373i
$392$	−17.6680	−	12.3713i	−0.892368	−	0.624843i
$393$		0			0
$394$	−1.88249	+	2.24346i	−0.0948384	+	0.113024i
$395$	2.90479	−	13.4499i	0.146156	−	0.676736i
$396$		0			0
$397$	−12.4735	+	3.34227i	−0.626028	+	0.167744i	−0.557866	−	0.829931i	$-0.688380\pi$
$397$	−12.4735	+	3.34227i	−0.626028	+	0.167744i	−0.0681611	+	0.997674i	$0.521713\pi$
$398$	3.15644	+	1.47187i	0.158218	+	0.0737783i
$399$		0			0
$400$	12.1186	+	11.8567i	0.605928	+	0.592834i
$401$	2.92360	−	8.03253i	0.145998	−	0.401125i	−0.845041	−	0.534702i	$-0.820424\pi$
$401$	2.92360	−	8.03253i	0.145998	−	0.401125i	0.991039	+	0.133576i	$0.0426461\pi$
$402$		0			0
$403$	−0.0101511	−	0.0144972i	−0.000505660	−	0.000722158i
$404$	−7.12791			−0.354627
$405$		0			0
$406$	11.3491			0.563248
$407$	0.230534	+	0.329237i	0.0114272	+	0.0163197i
$408$		0			0
$409$	4.56883	−	12.5528i	0.225914	−	0.620694i	−0.774008	−	0.633176i	$-0.781751\pi$
$409$	4.56883	−	12.5528i	0.225914	−	0.620694i	0.999922	+	0.0124819i	$0.00397323\pi$
$410$	−1.18863	+	1.10118i	−0.0587023	+	0.0543835i
$411$		0			0
$412$	4.17321	+	1.94600i	0.205599	+	0.0958725i
$413$	−5.51659	+	1.47817i	−0.271454	+	0.0727359i
$414$		0			0
$415$	−4.88411	−	7.57490i	−0.239751	−	0.371837i
$416$	0.183635	−	0.218848i	0.00900347	−	0.0107299i
$417$		0			0
$418$	−0.0335789	−	0.0235122i	−0.00164240	−	0.00115002i
$419$	−4.65475	−	26.3984i	−0.227399	−	1.28964i	−0.858045	−	0.513574i	$-0.828321\pi$
$419$	−4.65475	−	26.3984i	−0.227399	−	1.28964i	0.630646	−	0.776071i	$-0.282790\pi$
$420$		0			0
$421$	19.3371	+	16.2257i	0.942432	+	0.790794i	0.978007	−	0.208573i	$-0.0668818\pi$
$421$	19.3371	+	16.2257i	0.942432	+	0.790794i	−0.0355751	+	0.999367i	$0.511326\pi$
$422$	0.630963	+	0.169066i	0.0307148	+	0.00823001i
$423$		0			0
$424$	−13.3065	−	7.68250i	−0.646220	−	0.373095i
$425$	−19.0063	−	6.68355i	−0.921941	−	0.324200i
$426$		0			0
$427$	−35.3722	−	3.09467i	−1.71178	−	0.149762i
$428$	−1.75540	−	3.76447i	−0.0848504	−	0.181962i
$429$		0			0
$430$	2.12005	−	1.64524i	0.102238	−	0.0793406i
$431$			23.0274i			1.10919i	0.832121	+	0.554595i	$0.187127\pi$
$431$			23.0274i			1.10919i	−0.832121	+	0.554595i	$0.812873\pi$
$432$		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
$437$	−1.17810	+	13.4658i	−0.0563562	+	0.644154i
$438$		0			0
$439$	−10.8870	−	29.9118i	−0.519609	−	1.42761i	−0.870952	−	0.491367i	$-0.836497\pi$
$439$	−10.8870	−	29.9118i	−0.519609	−	1.42761i	0.351343	−	0.936247i	$-0.385725\pi$
$440$	−0.152697	−	0.0784321i	−0.00727954	−	0.00373910i
$441$		0			0
$442$	−0.0266394	+	0.0994197i	−0.00126711	+	0.00472891i
$443$	−0.783237	−	8.95244i	−0.0372127	−	0.425343i	−0.991835	−	0.127525i	$-0.959297\pi$
$443$	−0.783237	−	8.95244i	−0.0372127	−	0.425343i	0.954623	−	0.297818i	$-0.0962589\pi$
$444$		0			0
$445$	19.8836	+	12.5151i	0.942572	+	0.593273i
$446$	0.862251	−	0.152038i	0.0408288	−	0.00719922i
$447$		0			0
$448$	−27.5838	+	2.41327i	−1.30321	+	0.114016i
$449$	5.30209	+	9.18349i	0.250221	+	0.433396i	0.963587	−	0.267396i	$-0.0861633\pi$
$449$	5.30209	+	9.18349i	0.250221	+	0.433396i	−0.713365	+	0.700792i	$0.752830\pi$
$450$		0			0
$451$	−0.0690940	+	0.119674i	−0.00325351	+	0.00563524i
$452$	9.01760	−	19.3383i	0.424152	−	0.909598i
$453$		0			0
$454$	2.92752	+	3.48888i	0.137395	+	0.163741i
$455$	−0.773535	+	0.408062i	−0.0362639	+	0.0191302i
$456$		0			0
$457$	27.2519	−	19.0820i	1.27479	−	0.892617i	0.277119	−	0.960836i	$-0.410620\pi$
$457$	27.2519	−	19.0820i	1.27479	−	0.892617i	0.997670	+	0.0682185i	$0.0217315\pi$
$458$	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	−0.00908790	−	0.999959i	$-0.502893\pi$
$461$	−7.72166	−	1.36154i	−0.359634	−	0.0634131i	−0.350546	+	0.936546i	$0.614004\pi$
$462$		0			0
$463$	−16.0360	+	7.47769i	−0.745254	+	0.347518i	−0.757873	−	0.652403i	$-0.773761\pi$
$463$	−16.0360	+	7.47769i	−0.745254	+	0.347518i	0.0126183	+	0.999920i	$0.495983\pi$
$464$	18.6361	−	15.6375i	0.865159	−	0.725955i
$465$		0			0
$466$	−2.04945	+	0.745938i	−0.0949388	+	0.0345549i
$467$	4.09572	+	15.2854i	0.189527	+	0.707325i	0.993616	+	0.112816i	$0.0359870\pi$
$467$	4.09572	+	15.2854i	0.189527	+	0.707325i	−0.804089	+	0.594509i	$0.797346\pi$
$468$		0			0
$469$	−32.4052	+	18.7092i	−1.49633	+	0.863909i
$470$	0.136818	+	0.997125i	0.00631094	+	0.0459939i
$471$		0			0
$472$	0.833661	−	1.19059i	0.0383724	−	0.0548014i
$473$	0.131271	−	0.187475i	0.00603585	−	0.00862009i
$474$		0			0
$475$	8.58668	+	5.87375i	0.393984	+	0.269506i
$476$	32.5737	−	18.8064i	1.49301	−	0.861991i
$477$		0			0
$478$	−1.51874	−	5.66800i	−0.0694654	−	0.259248i
$479$	−25.2585	+	9.19333i	−1.15409	+	0.420054i	−0.846982	−	0.531621i	$-0.821583\pi$
$479$	−25.2585	+	9.19333i	−1.15409	+	0.420054i	−0.307106	+	0.951675i	$0.599361\pi$
$480$		0			0
$481$	−0.399198	+	0.334967i	−0.0182019	+	0.0152732i
$482$	4.64490	−	2.16595i	0.211569	−	0.0986564i
$483$		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	$0.878476\pi$
$488$	7.40208	−	5.18299i	0.335076	−	0.234623i
$489$		0			0
$490$	−11.8242	−	3.65728i	−0.534163	−	0.165219i
$491$	−8.64628	−	10.3042i	−0.390201	−	0.465024i	0.534805	−	0.844976i	$-0.320385\pi$
$491$	−8.64628	−	10.3042i	−0.390201	−	0.465024i	−0.925006	+	0.379952i	$0.875941\pi$
$492$		0			0
$493$	−12.2177	+	26.2010i	−0.550258	+	1.18003i
$494$	0.0265743	−	0.0460281i	0.00119563	−	0.00207090i
$495$		0			0
$496$	−0.377555	−	0.653944i	−0.0169527	−	0.0293630i
$497$	−35.8388	+	3.13549i	−1.60759	+	0.140646i
$498$		0			0
$499$	37.5256	−	6.61678i	1.67988	−	0.296208i	0.749281	−	0.662252i	$-0.230399\pi$
$499$	37.5256	−	6.61678i	1.67988	−	0.296208i	0.930597	+	0.366044i	$0.119288\pi$
$500$	18.9675	+	9.48221i	0.848254	+	0.424057i
$501$		0			0
$502$	0.482022	+	5.50954i	0.0215137	+	0.245903i
$503$	−4.95246	+	18.4828i	−0.220819	+	0.824109i	0.763217	+	0.646142i	$0.223619\pi$
$503$	−4.95246	+	18.4828i	−0.220819	+	0.824109i	−0.984036	+	0.177967i	$0.943048\pi$
$504$		0			0
$505$	−8.00047	+	2.57066i	−0.356016	+	0.114393i
$506$	−0.0437748	−	0.120270i	−0.00194603	−	0.00534666i
$507$		0			0
$508$	1.27895	−	14.6185i	0.0567442	−	0.648590i
$509$	22.8762	+	8.32625i	1.01397	+	0.369054i	0.794956	−	0.606667i	$-0.207494\pi$
$509$	22.8762	+	8.32625i	1.01397	+	0.369054i	0.219013	+	0.975722i	$0.429716\pi$
$510$		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
$515$	5.38589	+	0.679164i	0.237331	+	0.0299275i
$516$		0			0
$517$	0.0362758	+	0.0777936i	0.00159541	+	0.00342136i
$518$	−10.3331	−	0.904028i	−0.454010	−	0.0397207i
$519$		0			0
$520$	0.0840493	−	0.206089i	0.00368581	−	0.00903761i
$521$	−23.8927	−	13.7944i	−1.04676	−	0.604345i	−0.125017	−	0.992155i	$-0.539898\pi$
$521$	−23.8927	−	13.7944i	−1.04676	−	0.604345i	−0.921739	+	0.387810i	$0.873232\pi$
$522$		0			0
$523$	−12.5250	−	3.35607i	−0.547681	−	0.146751i	−0.0256401	−	0.999671i	$-0.508162\pi$
$523$	−12.5250	−	3.35607i	−0.547681	−	0.146751i	−0.522041	+	0.852921i	$0.674829\pi$
$524$	13.3689	+	11.2178i	0.584022	+	0.490053i
$525$		0			0
$526$	0.0509971	+	0.289219i	0.00222358	+	0.0126105i
$527$	0.735047	+	0.514685i	0.0320191	+	0.0224200i
$528$		0			0
$529$	−12.3443	+	14.7114i	−0.536709	+	0.639625i
$530$	−8.61831	−	1.86131i	−0.374356	−	0.0808503i
$531$		0			0
$532$	−18.7605	+	5.02685i	−0.813369	+	0.217942i
$533$	−0.162381	−	0.0757196i	−0.00703351	−	0.00327978i
$534$		0			0
$535$	−3.32793	−	3.59221i	−0.143879	−	0.155305i
$536$	3.25692	−	8.94831i	0.140677	−	0.386508i
$537$		0			0
$538$	5.09765	+	7.28020i	0.219775	+	0.313872i
$539$	−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	$0.197505\pi$
$542$	3.33464	+	4.76236i	0.143235	+	0.204561i
$543$		0			0
$544$	−4.95417	+	13.6115i	−0.212408	+	0.583587i
$545$	0.574864	+	0.0219544i	0.0246245	+	0.000940423i
$546$		0			0
$547$	−13.4509	−	6.27224i	−0.575117	−	0.268182i	0.113223	−	0.993570i	$-0.463883\pi$
$547$	−13.4509	−	6.27224i	−0.575117	−	0.268182i	−0.688340	+	0.725388i	$0.741660\pi$
$548$	25.1954	−	6.75109i	1.07629	−	0.288392i
$549$		0			0
$550$	−0.0971908	−	0.0160449i	−0.00414423	−	0.000684155i
$551$	9.59560	−	11.4356i	0.408786	−	0.487173i
$552$		0			0
$553$	24.8080	+	17.3708i	1.05494	+	0.738680i
$554$	−0.288999	−	1.63900i	−0.0122784	−	0.0696342i
$555$		0			0
$556$	−1.54692	−	1.29802i	−0.0656040	−	0.0550483i
$557$	−13.9965	−	3.75036i	−0.593052	−	0.158908i	−0.0502041	−	0.998739i	$-0.515987\pi$
$557$	−13.9965	−	3.75036i	−0.593052	−	0.158908i	−0.542847	+	0.839831i	$0.682654\pi$
$558$		0			0
$559$	0.256980	+	0.148367i	0.0108691	+	0.00627527i
$560$	−34.3961	+	14.4679i	−1.45350	+	0.611381i
$561$		0			0
$562$	−2.45408	−	0.214704i	−0.103519	−	0.00905674i
$563$	−14.4812	−	31.0550i	−0.610309	−	1.30881i	−0.932169	−	0.362025i	$-0.882086\pi$
$563$	−14.4812	−	31.0550i	−0.610309	−	1.30881i	0.321859	−	0.946787i	$-0.395692\pi$
$564$		0			0
$565$	3.14719	−	24.9578i	0.132403	−	1.04998i
$566$			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	$-0.896018\pi$
$569$	1.25548	−	7.12016i	0.0526323	−	0.298493i	0.999749	+	0.0223961i	$0.00712951\pi$
$570$		0			0
$571$	25.3539	+	9.22807i	1.06103	+	0.386183i	0.812815	−	0.582522i	$-0.197934\pi$
$571$	25.3539	+	9.22807i	1.06103	+	0.386183i	0.248214	+	0.968705i	$0.420156\pi$
$572$	0.000805249	−	0.00920404i	3.36691e−5	−	0.000384840i
$573$		0			0
$574$	−1.21973	−	3.35118i	−0.0509105	−	0.139876i
$575$	11.4424	+	30.4003i	0.477180	+	1.26778i
$576$		0			0
$577$	1.64754	−	6.14870i	0.0685880	−	0.255974i	−0.923115	−	0.384524i	$-0.874366\pi$
$577$	1.64754	−	6.14870i	0.0685880	−	0.255974i	0.991703	+	0.128550i	$0.0410323\pi$
$578$	0.0213918	+	0.244509i	0.000889781	+	0.0101702i
$579$		0			0
$580$	16.2087	−	25.7519i	0.673031	−	1.06929i
$581$	19.5357	−	3.44468i	0.810479	−	0.142909i
$582$		0			0
$583$	−0.749091	+	0.0655370i	−0.0310242	+	0.00271426i
$584$	4.16304	+	7.21060i	0.172268	+	0.298377i
$585$		0			0
$586$	1.37318	−	2.37842i	0.0567256	−	0.0982517i
$587$	16.0039	−	34.3204i	0.660550	−	1.41656i	−0.235177	−	0.971952i	$-0.575567\pi$
$587$	16.0039	−	34.3204i	0.660550	−	1.41656i	0.895728	−	0.444603i	$-0.146655\pi$
$588$		0			0
$589$	−0.297839	−	0.354951i	−0.0122722	−	0.0146255i
$590$	0.246453	−	0.796797i	0.0101463	−	0.0328036i
$591$		0			0
$592$	−18.2133	+	12.7531i	−0.748563	+	0.524149i
$593$	−3.48236	−	3.48236i	−0.143004	−	0.143004i	0.631981	−	0.774984i	$-0.282242\pi$
$593$	−3.48236	−	3.48236i	−0.143004	−	0.143004i	−0.774984	+	0.631981i	$0.782242\pi$
$594$		0			0
$595$	29.7787	−	32.8562i	1.22081	−	1.34697i
$596$	−33.6337	−	5.93053i	−1.37769	−	0.242924i
$597$		0			0
$598$	0.150397	−	0.0701311i	0.00615018	−	0.00286788i
$599$	−7.62357	+	6.39694i	−0.311491	+	0.261372i	−0.785108	−	0.619359i	$-0.787392\pi$
$599$	−7.62357	+	6.39694i	−0.311491	+	0.261372i	0.473617	+	0.880731i	$0.342948\pi$
$600$		0			0
$601$	−16.6225	+	6.05010i	−0.678046	+	0.246789i	−0.658008	−	0.753011i	$-0.728601\pi$
$601$	−16.6225	+	6.05010i	−0.678046	+	0.246789i	−0.0200379	+	0.999799i	$0.506379\pi$
$602$	1.52868	+	5.70510i	0.0623042	+	0.232523i
$603$		0			0
$604$	15.6721	−	9.04832i	0.637691	−	0.368171i
$605$	24.3601	−	3.34251i	0.990379	−	0.135892i
$606$		0			0
$607$	8.36932	−	11.9526i	0.339700	−	0.485142i	−0.612563	−	0.790422i	$-0.709861\pi$
$607$	8.36932	−	11.9526i	0.339700	−	0.485142i	0.952263	+	0.305280i	$0.0987501\pi$
$608$	4.29017	−	6.12699i	0.173989	−	0.248482i
$609$		0			0
$610$	3.13413	−	4.13099i	0.126897	−	0.167259i
$611$	−0.0963805	+	0.0556453i	−0.00389914	+	0.00225117i
$612$		0			0
$613$	−9.82295	−	36.6597i	−0.396745	−	1.48067i	−0.818787	−	0.574097i	$-0.805353\pi$
$613$	−9.82295	−	36.6597i	−0.396745	−	1.48067i	0.422042	−	0.906576i	$-0.361313\pi$
$614$	−6.40729	+	2.33206i	−0.258577	+	0.0941143i
$615$		0			0
$616$	0.289427	−	0.242858i	0.0116613	−	0.00978503i
$617$	−4.95529	+	2.31069i	−0.199493	+	0.0930249i	−0.519797	−	0.854290i	$-0.673993\pi$
$617$	−4.95529	+	2.31069i	−0.199493	+	0.0930249i	0.320305	+	0.947315i	$0.396215\pi$
$618$		0			0
$619$	−35.6556	−	6.28705i	−1.43312	−	0.252698i	−0.597440	−	0.801913i	$-0.703816\pi$
$619$	−35.6556	−	6.28705i	−1.43312	−	0.252698i	−0.835681	+	0.549215i	$0.814927\pi$
$620$	−0.699809	−	0.634261i	−0.0281050	−	0.0254726i
$621$		0			0
$622$	−4.47294	−	4.47294i	−0.179349	−	0.179349i
$623$	−42.3583	+	29.6596i	−1.69705	+	1.18829i
$624$		0			0
$625$	24.7091	+	3.80239i	0.988366	+	0.152096i
$626$	−0.868056	−	1.03451i	−0.0346945	−	0.0413473i
$627$		0			0
$628$	12.9967	−	27.8714i	0.518623	−	1.11219i
$629$	13.2110	−	22.8821i	0.526756	−	0.912368i
$630$		0			0
$631$	8.04151	+	13.9283i	0.320128	+	0.554477i	0.980514	−	0.196449i	$-0.0629409\pi$
$631$	8.04151	+	13.9283i	0.320128	+	0.554477i	−0.660387	+	0.750926i	$0.729608\pi$
$632$	−7.67791	+	0.671730i	−0.305411	+	0.0267200i
$633$		0			0
$634$	−5.28517	+	0.931918i	−0.209901	+	0.0370112i
$635$	−3.83659	−	16.8692i	−0.152250	−	0.669435i
$636$		0			0
$637$	−0.119280	−	1.36337i	−0.00472603	−	0.0540188i
$638$	−0.0365836	+	0.136532i	−0.00144836	+	0.00540535i
$639$		0			0
$640$	9.19281	−	17.8972i	0.363378	−	0.707448i
$641$	−12.7590	−	35.0551i	−0.503951	−	1.38459i	−0.887387	−	0.461026i	$-0.847482\pi$
$641$	−12.7590	−	35.0551i	−0.503951	−	1.38459i	0.383436	−	0.923567i	$-0.374741\pi$
$642$		0			0
$643$	−1.25970	+	14.3985i	−0.0496779	+	0.567821i	0.930043	+	0.367452i	$0.119770\pi$
$643$	−1.25970	+	14.3985i	−0.0496779	+	0.567821i	−0.979720	+	0.200369i	$0.935786\pi$
$644$	−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	−0.238408	−	0.971165i	$-0.576626\pi$
$647$	18.6385	−	18.6385i	0.732757	−	0.732757i	0.971165	+	0.238408i	$0.0766256\pi$
$648$		0			0
$649$		−	0.0711305i		−	0.00279212i
$650$	0.00974110	−	0.127347i	0.000382077	−	0.00499494i
$651$		0			0
$652$	8.86250	+	19.0057i	0.347082	+	0.744320i
$653$	15.1018	+	1.32123i	0.590977	+	0.0517038i	0.378722	−	0.925510i	$-0.376364\pi$
$653$	15.1018	+	1.32123i	0.590977	+	0.0517038i	0.212255	+	0.977214i	$0.431919\pi$
$654$		0			0
$655$	19.0511	+	7.76960i	0.744388	+	0.303583i
$656$	−6.62035	−	3.82226i	−0.258481	−	0.149234i
$657$		0			0
$658$	−2.13970	−	0.573332i	−0.0834144	−	0.0223508i
$659$	14.6857	+	12.3228i	0.572075	+	0.480028i	0.882334	−	0.470624i	$-0.155971\pi$
$659$	14.6857	+	12.3228i	0.572075	+	0.480028i	−0.310258	+	0.950652i	$0.600416\pi$
$660$		0			0
$661$	3.24511	+	18.4039i	0.126220	+	0.715829i	0.980576	+	0.196141i	$0.0628409\pi$
$661$	3.24511	+	18.4039i	0.126220	+	0.715829i	−0.854356	+	0.519689i	$0.826048\pi$
$662$	3.49029	+	2.44393i	0.135654	+	0.0949860i
$663$		0			0
$664$	−3.24502	+	3.86726i	−0.125931	+	0.150079i
$665$	−19.2441	+	12.4081i	−0.746253	+	0.481165i
$666$		0			0
$667$	45.0214	−	12.0634i	1.74324	−	0.467099i
$668$	22.4827	+	10.4839i	0.869883	+	0.405633i
$669$		0			0
$670$	0.208538	−	5.46044i	0.00805651	−	0.210955i
$671$	0.151251	−	0.415559i	0.00583898	−	0.0160425i
$672$		0			0
$673$	−4.69863	−	6.71034i	−0.181119	−	0.258665i	0.718318	−	0.695715i	$-0.244912\pi$
$673$	−4.69863	−	6.71034i	−0.181119	−	0.258665i	−0.899437	+	0.437050i	$0.856023\pi$
$674$	6.83016			0.263088
$675$		0			0
$676$	−24.6450			−0.947884
$677$	22.9922	+	32.8363i	0.883663	+	1.26200i	0.964180	+	0.265249i	$0.0854541\pi$
$677$	22.9922	+	32.8363i	0.883663	+	1.26200i	−0.0805166	+	0.996753i	$0.525657\pi$
$678$		0			0
$679$	−16.5199	+	45.3880i	−0.633976	+	1.74183i
$680$	−0.430661	+	11.2766i	−0.0165151	+	0.432439i
$681$		0			0
$682$	0.00397627	+	0.00185416i	0.000152259	+	7.09996e-5i
$683$	0.912231	−	0.244432i	0.0349056	−	0.00935292i	−0.241324	−	0.970445i	$-0.577582\pi$
$683$	0.912231	−	0.244432i	0.0349056	−	0.00935292i	0.276230	+	0.961092i	$0.410915\pi$
$684$		0			0
$685$	25.8449	−	16.6642i	0.987484	−	0.636705i
$686$	10.3926	−	12.3854i	0.396790	−	0.472876i
$687$		0			0
$688$	10.3710	+	7.26189i	0.395393	+	0.276857i
$689$	−0.169298	−	0.960134i	−0.00644972	−	0.0365782i
$690$		0			0
$691$	−19.0181	−	15.9581i	−0.723481	−	0.607073i	0.204865	−	0.978790i	$-0.434325\pi$
$691$	−19.0181	−	15.9581i	−0.723481	−	0.607073i	−0.928346	+	0.371717i	$0.878769\pi$
$692$	−41.6847	−	11.1694i	−1.58461	−	0.424596i
$693$		0			0
$694$	8.77943	+	5.06881i	0.333263	+	0.192409i
$695$	−2.20441	−	0.899024i	−0.0836180	−	0.0341019i
$696$		0			0
$697$	9.04972	+	0.791748i	0.342783	+	0.0299896i
$698$	2.30317	+	4.93917i	0.0871763	+	0.186950i
$699$		0			0
$700$	−35.4235	+	30.3893i	−1.33888	+	1.14861i
$701$			30.1877i			1.14018i	0.821584	+	0.570088i	$0.193091\pi$
$701$			30.1877i			1.14018i	−0.821584	+	0.570088i	$0.806909\pi$
$702$		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
$707$	1.61197	−	18.4249i	0.0606244	−	0.692940i
$708$		0			0
$709$	17.1846	+	47.2142i	0.645379	+	1.77317i	0.634127	+	0.773229i	$0.281360\pi$
$709$	17.1846	+	47.2142i	0.645379	+	1.77317i	0.0112523	+	0.999937i	$0.496418\pi$
$710$	2.40042	−	4.67331i	0.0900863	−	0.175386i
$711$		0			0
$712$	3.40597	−	12.7113i	0.127644	−	0.476374i
$713$	−0.126090	−	1.44121i	−0.00472211	−	0.0539739i
$714$		0			0
$715$	−0.00241558	−	0.0106211i	−9.03376e−5	−	0.000397208i
$716$	−34.0378	+	6.00178i	−1.27205	+	0.224297i
$717$		0			0
$718$	−10.0487	+	0.879150i	−0.375015	+	0.0328096i
$719$	6.68387	+	11.5768i	0.249266	+	0.431742i	0.963322	−	0.268346i	$-0.0864772\pi$
$719$	6.68387	+	11.5768i	0.249266	+	0.431742i	−0.714056	+	0.700089i	$0.753144\pi$
$720$		0			0
$721$	−5.97397	+	10.3472i	−0.222482	+	0.385351i
$722$	−1.99283	+	4.27363i	−0.0741654	+	0.159048i
$723$		0			0
$724$	−15.0887	−	17.9820i	−0.560766	−	0.668295i
$725$	8.90558	−	34.7499i	0.330745	−	1.29058i
$726$		0			0
$727$	−19.5460	+	13.6862i	−0.724920	+	0.507595i	−0.876830	−	0.480800i	$-0.840346\pi$
$727$	−19.5460	+	13.6862i	−0.724920	+	0.507595i	0.151910	+	0.988394i	$0.451458\pi$
$728$	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
$733$	−21.1646	+	9.86921i	−0.781732	+	0.364527i	−0.772161	−	0.635427i	$-0.780824\pi$
$733$	−21.1646	+	9.86921i	−0.781732	+	0.364527i	−0.00957046	+	0.999954i	$0.503046\pi$
$734$	4.41379	−	3.70361i	0.162916	−	0.136703i
$735$		0			0
$736$	21.9452	−	7.98740i	0.808910	−	0.294419i
$737$	−0.120617	−	0.450149i	−0.00444299	−	0.0165815i
$738$		0			0
$739$	3.52276	−	2.03387i	0.129587	−	0.0748169i	−0.433805	−	0.901007i	$-0.642829\pi$
$739$	3.52276	−	2.03387i	0.129587	−	0.0748169i	0.563392	+	0.826190i	$0.309496\pi$
$740$	−16.8089	+	22.1553i	−0.617909	+	0.814446i
$741$		0			0
$742$	11.1307	−	15.8963i	0.408622	−	0.583572i
$743$	28.8659	−	41.2248i	1.05899	−	1.51239i	0.214569	−	0.976709i	$-0.431165\pi$
$743$	28.8659	−	41.2248i	1.05899	−	1.51239i	0.844419	−	0.535683i	$-0.179946\pi$
$744$		0			0
$745$	−39.8898	+	5.47337i	−1.46145	+	0.200529i
$746$	1.40892	−	0.813439i	0.0515842	−	0.0297821i
$747$		0			0
$748$	0.121244	+	0.452489i	0.00443313	+	0.0165447i
$749$	10.1277	−	3.68619i	0.370059	−	0.134691i
$750$		0			0
$751$	2.00167	−	1.67960i	0.0730419	−	0.0612895i	−0.605536	−	0.795818i	$-0.707041\pi$
$751$	2.00167	−	1.67960i	0.0730419	−	0.0612895i	0.678578	+	0.734529i	$0.262597\pi$
$752$	−4.30353	+	2.00677i	−0.156933	+	0.0731793i
$753$		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	$0.485692\pi$
$758$	−2.60445	+	1.82366i	−0.0945980	+	0.0662383i
$759$		0			0
$760$	1.72189	−	5.56697i	0.0624596	−	0.201935i
$761$	−3.22815	−	3.84716i	−0.117020	−	0.139459i	0.704354	−	0.709849i	$-0.251237\pi$
$761$	−3.22815	−	3.84716i	−0.117020	−	0.139459i	−0.821374	+	0.570389i	$0.806792\pi$
$762$		0			0
$763$	−0.535106	+	1.14754i	−0.0193722	+	0.0415437i
$764$	−11.6417	+	20.1640i	−0.421182	+	0.729509i
$765$		0			0
$766$	3.08315	+	5.34017i	0.111399	+	0.192948i
$767$	0.0918735	−	0.00803789i	0.00331736	−	0.000290231i
$768$		0			0
$769$	41.2856	−	7.27976i	1.48880	−	0.262515i	0.630709	−	0.776019i	$-0.282764\pi$
$769$	41.2856	−	7.27976i	1.48880	−	0.262515i	0.858087	+	0.513504i	$0.171653\pi$
$770$	0.115490	−	0.183487i	0.00416198	−	0.00661241i
$771$		0			0
$772$	−2.93187	−	33.5115i	−0.105520	−	1.20610i
$773$	1.57609	−	5.88204i	0.0566879	−	0.211562i	−0.931772	−	0.363043i	$-0.881738\pi$
$773$	1.57609	−	5.88204i	0.0566879	−	0.211562i	0.988460	+	0.151481i	$0.0484043\pi$
$774$		0			0
$775$	−1.01422	−	0.459520i	−0.0364319	−	0.0165064i
$776$	−4.20415	−	11.5508i	−0.150920	−	0.414650i
$777$		0			0
$778$	0.206920	−	2.36511i	0.00741844	−	0.0847932i
$779$	−4.40798	−	1.60437i	−0.157932	−	0.0574827i
$780$		0			0
$781$	0.0778050	−	0.441254i	0.00278408	−	0.0157893i
$782$	−5.94947	+	5.94947i	−0.212753	+	0.212753i
$783$		0			0
$784$		−	58.3929i		−	2.08546i
$785$	4.53590	−	35.9705i	0.161893	−	1.28384i
$786$		0			0
$787$	−1.76535	−	3.78582i	−0.0629281	−	0.134950i	0.872328	−	0.488920i	$-0.162609\pi$
$787$	−1.76535	−	3.78582i	−0.0629281	−	0.134950i	−0.935257	+	0.353971i	$0.884831\pi$
$788$	−17.2161	−	1.50622i	−0.613299	−	0.0536567i
$789$		0			0
$790$	−4.07674	+	1.71478i	−0.145044	+	0.0610093i
$791$	47.9482	+	27.6829i	1.70484	+	0.984291i
$792$		0			0
$793$	0.553835	+	0.148400i	0.0196673	+	0.00526983i
$794$	3.17958	+	2.66798i	0.112839	+	0.0946831i
$795$		0			0
$796$	3.56877	+	20.2395i	0.126492	+	0.717369i
$797$	35.6551	+	24.9660i	1.26297	+	0.884339i	0.996827	−	0.0795948i	$-0.0253626\pi$
$797$	35.6551	+	24.9660i	1.26297	+	0.884339i	0.266140	+	0.963934i	$0.414252\pi$
$798$		0			0
$799$	3.62708	−	4.32258i	0.128317	−	0.152922i
$800$	2.92764	−	17.7340i	0.103508	−	0.626991i
$801$		0			0
$802$	−2.65388	+	0.711104i	−0.0937116	+	0.0251100i
$803$	0.369296	+	0.172205i	0.0130322	+	0.00607699i
$804$		0			0
$805$	−71.4401	−	2.72834i	−2.51793	−	0.0961614i
$806$	−0.00194555	+	0.00534535i	−6.85290e−5	+	0.000188282i
$807$		0			0
$808$	2.69975	+	3.85564i	0.0949768	+	0.135641i
$809$	16.9733			0.596751			0.298375	−	0.954449i	$-0.403555\pi$
$809$	16.9733			0.596751			0.298375	+	0.954449i	$0.403555\pi$
$810$		0			0
$811$	−40.1642			−1.41036			−0.705178	−	0.709030i	$-0.749133\pi$
$811$	−40.1642			−1.41036			−0.705178	+	0.709030i	$0.749133\pi$
$812$	38.4131	+	54.8597i	1.34804	+	1.92520i
$813$		0			0
$814$	0.0441841	−	0.121395i	0.00154865	−	0.00425489i
$815$	16.8017	+	18.1360i	0.588539	+	0.635277i
$816$		0			0
$817$	7.04105	+	3.28330i	0.246335	+	0.114868i
$818$	−4.14732	+	1.11127i	−0.145008	+	0.0388547i
$819$		0			0
$820$	−9.34606	−	2.01849i	−0.326378	−	0.0704886i
$821$	−10.6701	+	12.7162i	−0.372390	+	0.443797i	−0.919397	−	0.393331i	$-0.871323\pi$
$821$	−10.6701	+	12.7162i	−0.372390	+	0.443797i	0.547007	+	0.837128i	$0.315767\pi$
$822$		0			0
$823$	7.03825	+	4.92823i	0.245338	+	0.171787i	0.689778	−	0.724021i	$-0.257708\pi$
$823$	7.03825	+	4.92823i	0.245338	+	0.171787i	−0.444440	+	0.895809i	$0.646597\pi$
$824$	−0.528001	−	2.99444i	−0.0183938	−	0.104316i
$825$		0			0
$826$	1.40621	+	1.17995i	0.0489285	+	0.0410558i
$827$	8.98430	+	2.40734i	0.312415	+	0.0837113i	0.411620	−	0.911356i	$-0.364963\pi$
$827$	8.98430	+	2.40734i	0.312415	+	0.0837113i	−0.0992048	+	0.995067i	$0.531630\pi$
$828$		0			0
$829$	−36.4376	−	21.0373i	−1.26553	−	0.730655i	−0.291392	−	0.956604i	$-0.594118\pi$
$829$	−36.4376	−	21.0373i	−1.26553	−	0.730655i	−0.974139	+	0.225949i	$0.927452\pi$
$830$	−1.09398	+	2.68243i	−0.0379724	+	0.0931085i
$831$		0			0
$832$	0.445423	+	0.0389695i	0.0154423	+	0.00135102i
$833$	29.3257	+	62.8893i	1.01608	+	2.17898i
$834$		0			0
$835$	29.0159	+	3.65892i	1.00414	+	0.126622i
$836$		−	0.241896i		−	0.00836613i
$837$		0			0
$838$	−6.09230	+	6.09230i	−0.210455	+	0.210455i
$839$	6.54601	−	37.1243i	0.225993	−	1.28167i	−0.634783	−	0.772690i	$-0.718911\pi$
$839$	6.54601	−	37.1243i	0.225993	−	1.28167i	0.860777	−	0.508983i	$-0.169978\pi$
$840$		0			0
$841$	−21.1193	−	7.68679i	−0.728251	−	0.265062i
$842$	0.707136	−	8.08261i	0.0243695	−	0.278545i
$843$		0			0
$844$	1.31837	+	3.62220i	0.0453803	+	0.124681i
$845$	−27.6619	+	8.88813i	−0.951598	+	0.305761i
$846$		0			0
$847$	−14.0067	+	52.2737i	−0.481276	+	1.79615i
$848$	−3.62549	−	41.4395i	−0.124500	−	1.42304i
$849$		0			0
$850$	1.74425	+	6.23634i	0.0598271	+	0.213905i
$851$	−41.9518	+	7.39723i	−1.43809	+	0.253574i
$852$		0			0
$853$	40.4116	−	3.53555i	1.38367	−	0.121055i	0.629123	−	0.777306i	$-0.283414\pi$
$853$	40.4116	−	3.53555i	1.38367	−	0.121055i	0.754543	+	0.656251i	$0.227859\pi$
$854$	5.70635	+	9.88369i	0.195267	+	0.338213i
$855$		0			0
$856$	−1.37141	+	2.37535i	−0.0468738	+	0.0811879i
$857$	−15.2865	+	32.7821i	−0.522178	+	1.11982i	0.451580	+	0.892231i	$0.350861\pi$
$857$	−15.2865	+	32.7821i	−0.522178	+	1.11982i	−0.973758	+	0.227585i	$0.926917\pi$
$858$		0			0
$859$	−26.6915	−	31.8097i	−0.910701	−	1.08533i	−0.996034	−	0.0889788i	$-0.971640\pi$
$859$	−26.6915	−	31.8097i	−0.910701	−	1.08533i	0.0853324	−	0.996353i	$-0.472805\pi$
$860$	15.1285	+	4.67932i	0.515877	+	0.159563i
$861$		0			0
$862$	6.06288	−	4.24528i	0.206503	−	0.144595i
$863$	−1.97436	−	1.97436i	−0.0672079	−	0.0672079i	0.672704	−	0.739912i	$-0.265133\pi$
$863$	−1.97436	−	1.97436i	−0.0672079	−	0.0672079i	−0.739912	+	0.672704i	$0.765133\pi$
$864$		0			0
$865$	−50.8156	+	2.49677i	−1.72778	+	0.0848927i
$866$	−5.75997	−	1.01564i	−0.195732	−	0.0345128i
$867$		0			0
$868$	1.88397	−	0.878509i	0.0639460	−	0.0298185i
$869$	−0.288942	+	0.242451i	−0.00980167	+	0.00822458i
$870$		0			0
$871$	0.567792	−	0.206659i	0.0192389	−	0.00700238i
$872$	−0.0833986	−	0.311248i	−0.00282423	−	0.0105402i
$873$		0			0
$874$	3.76259	−	2.17233i	0.127272	−	0.0734803i
$875$	−28.8000	+	46.8847i	−0.973618	+	1.58499i
$876$		0			0
$877$	21.7084	−	31.0028i	0.733042	−	1.04689i	−0.263570	−	0.964640i	$-0.584900\pi$
$877$	21.7084	−	31.0028i	0.733042	−	1.04689i	0.996612	−	0.0822516i	$-0.0262111\pi$
$878$	−5.86839	+	8.38093i	−0.198049	+	0.282843i
$879$		0			0
$880$	−0.0631765	−	0.460429i	−0.00212968	−	0.0155211i
$881$	14.1727	−	8.18263i	0.477491	−	0.275680i	−0.241879	−	0.970306i	$-0.577764\pi$
$881$	14.1727	−	8.18263i	0.477491	−	0.275680i	0.719370	+	0.694627i	$0.244430\pi$
$882$		0			0
$883$	0.217699	+	0.812463i	0.00732615	+	0.0273416i	0.969492	−	0.245122i	$-0.0788281\pi$
$883$	0.217699	+	0.812463i	0.00732615	+	0.0273416i	−0.962166	+	0.272464i	$0.912161\pi$
$884$	−0.570743	+	0.207734i	−0.0191962	+	0.00698683i
$885$		0			0
$886$	−2.21269	+	1.85667i	−0.0743369	+	0.0623761i
$887$	22.8678	−	10.6634i	0.767825	−	0.358043i	0.00108401	−	0.999999i	$-0.499655\pi$
$887$	22.8678	−	10.6634i	0.767825	−	0.358043i	0.766741	+	0.641957i	$0.221877\pi$
$888$		0			0
$889$	37.4980	+	6.61191i	1.25764	+	0.221756i
$890$	−0.370588	−	7.54241i	−0.0124221	−	0.252822i
$891$		0			0
$892$	3.65337	+	3.65337i	0.122324	+	0.122324i
$893$	−2.38680	+	1.67126i	−0.0798714	+	0.0559265i
$894$		0			0
$895$	−36.0400	+	19.0121i	−1.20468	+	0.635504i
$896$	28.4647	+	33.9229i	0.950940	+	1.13329i
$897$		0			0
$898$	1.44044	−	3.08904i	0.0480682	−	0.103083i
$899$	−0.798864	+	1.38367i	−0.0266436	+	0.0461481i
$900$		0			0
$901$	24.7162	+	42.8097i	0.823415	+	1.42620i
$902$	0.0442471	−	0.00387112i	0.00147327	−	0.000128894i
$903$		0			0
$904$	−13.8760	+	2.44671i	−0.461509	+	0.0813764i
$905$	−23.4209	−	14.7415i	−0.778536	−	0.490025i
$906$		0			0
$907$	0.265160	+	3.03079i	0.00880450	+	0.100636i	0.999325	−	0.0367266i	$-0.0116931\pi$
$907$	0.265160	+	3.03079i	0.00880450	+	0.100636i	−0.990521	+	0.137362i	$0.956138\pi$
$908$	−6.95591	+	25.9598i	−0.230840	+	0.861507i
$909$		0			0
$910$	0.250046	+	0.128435i	0.00828894	+	0.00425758i
$911$	16.0677	+	44.1456i	0.532346	+	1.46261i	0.856272	+	0.516526i	$0.172775\pi$
$911$	16.0677	+	44.1456i	0.532346	+	1.46261i	−0.323926	+	0.946082i	$0.605003\pi$
$912$		0			0
$913$	−0.0215329	+	0.246122i	−0.000712635	+	0.00814546i
$914$	−10.0482	−	3.65724i	−0.332365	−	0.120971i
$915$		0			0
$916$	−4.36689	+	24.7658i	−0.144286	+	0.818287i
$917$	−32.0203	+	32.0203i	−1.05740	+	1.05740i
$918$		0			0
$919$			57.4802i			1.89610i	0.318128	+	0.948048i	$0.396946\pi$
$919$			57.4802i			1.89610i	−0.318128	+	0.948048i	$0.603054\pi$
$920$	14.3736	−	11.1545i	0.473884	−	0.367753i
$921$		0			0
$922$	1.06507	+	2.28405i	0.0350762	+	0.0752211i
$923$	0.578725	+	0.0506318i	0.0190490	+	0.00166657i
$924$		0			0
$925$	−10.8764	+	30.9295i	−0.357612	+	1.01696i
$926$	4.92516	+	2.84354i	0.161851	+	0.0934446i
$927$		0			0
$928$	−24.9124	−	6.67526i	−0.817790	−	0.219126i
$929$	−40.6798	−	34.1344i	−1.33466	−	1.11991i	−0.982963	−	0.183802i	$-0.941160\pi$
$929$	−40.6798	−	34.1344i	−1.33466	−	1.11991i	−0.351699	−	0.936113i	$-0.614396\pi$
$930$		0			0
$931$	−6.22206	−	35.2871i	−0.203920	−	1.15649i
$932$	−10.5424	−	7.38190i	−0.345329	−	0.241802i
$933$		0			0
$934$	3.26943	−	3.89635i	0.106979	−	0.127492i
$935$	0.299275	+	0.464154i	0.00978734	+	0.0151795i
$936$		0			0
$937$	−27.8763	+	7.46943i	−0.910679	+	0.244016i	−0.683597	−	0.729860i	$-0.739585\pi$
$937$	−27.8763	+	7.46943i	−0.910679	+	0.244016i	−0.227082	+	0.973876i	$0.572919\pi$
$938$	10.9001	+	5.08280i	0.355901	+	0.165959i
$939$		0			0
$940$	−4.35684	+	4.03630i	−0.142104	+	0.131650i
$941$	−4.85822	+	13.3478i	−0.158373	+	0.435127i	−0.993347	−	0.115163i	$-0.963261\pi$
$941$	−4.85822	+	13.3478i	−0.158373	+	0.435127i	0.834973	+	0.550291i	$0.185483\pi$
$942$		0			0
$943$	−8.40071	−	11.9975i	−0.273565	−	0.390691i
$944$	3.93492			0.128071
$945$		0			0
$946$	−0.0735611			−0.00239168
$947$	−1.16551	−	1.66453i	−0.0378741	−	0.0540898i	0.799768	−	0.600309i	$-0.204956\pi$
$947$	−1.16551	−	1.66453i	−0.0378741	−	0.0540898i	−0.837643	+	0.546219i	$0.816067\pi$
$948$		0			0
$949$	−0.180693	+	0.496449i	−0.00586553	+	0.0161154i
$950$	−0.0365221	−	3.34366i	−0.00118493	−	0.108483i
$951$		0			0
$952$	−22.5103	−	10.4967i	−0.729564	−	0.340201i
$953$	23.1836	−	6.21202i	0.750990	−	0.201227i	0.137033	−	0.990567i	$-0.456243\pi$
$953$	23.1836	−	6.21202i	0.750990	−	0.201227i	0.613957	+	0.789339i	$0.289577\pi$
$954$		0			0
$955$	−5.79473	+	26.8309i	−0.187513	+	0.868228i
$956$	22.2577	−	26.5257i	0.719865	−	0.857901i
$957$		0			0
$958$	7.07711	+	4.95544i	0.228651	+	0.160103i
$959$	11.7529	+	66.6543i	0.379522	+	2.15238i
$960$		0			0
$961$	−23.7094	−	19.8945i	−0.764819	−	0.641759i
$962$	0.161789	+	0.0433512i	0.00521628	+	0.00139770i
$963$		0			0
$964$	26.1913	+	15.1216i	0.843566	+	0.487033i
$965$	−15.3766	−	36.5564i	−0.494989	−	1.17679i
$966$		0			0
$967$	9.40347	+	0.822697i	0.302395	+	0.0264561i	0.237344	−	0.971426i	$-0.423723\pi$
$967$	9.40347	+	0.822697i	0.302395	+	0.0264561i	0.0650515	+	0.997882i	$0.479279\pi$
$968$	−5.82048	−	12.4821i	−0.187077	−	0.401189i
$969$		0			0
$970$	−4.32450	−	5.57253i	−0.138851	−	0.178923i
$971$		−	16.0188i		−	0.514066i	−0.966403	−	0.257033i	$-0.917255\pi$
$971$		−	16.0188i		−	0.514066i	0.966403	−	0.257033i	$-0.0827450\pi$
$972$		0			0
$973$	3.70508	−	3.70508i	0.118779	−	0.118779i
$974$	−0.967501	+	5.48697i	−0.0310007	+	0.175814i
$975$		0			0
$976$	22.9886	+	8.36718i	0.735848	+	0.267827i
$977$	1.38013	−	15.7750i	0.0441544	−	0.504687i	−0.941627	−	0.336657i	$-0.890704\pi$
$977$	1.38013	−	15.7750i	0.0441544	−	0.504687i	0.985782	−	0.168030i	$-0.0537406\pi$
$978$		0			0
$979$	−0.220269	−	0.605185i	−0.00703984	−	0.0193418i
$980$	−22.3425	−	69.5348i	−0.713704	−	2.22121i
$981$		0			0
$982$	−1.11900	+	4.17615i	−0.0357086	+	0.133266i
$983$	3.78597	+	43.2738i	0.120754	+	1.38022i	0.778814	+	0.627255i	$0.215822\pi$
$983$	3.78597	+	43.2738i	0.120754	+	1.38022i	−0.658060	+	0.752965i	$0.728623\pi$
$984$		0			0
$985$	−19.8668	+	4.51834i	−0.633010	+	0.143966i
$986$	9.15088	−	1.61355i	0.291424	−	0.0513858i
$987$		0			0
$988$	0.312437	−	0.0273347i	0.00993995	−	0.000869633i
$989$	12.1284	+	21.0070i	0.385660	+	0.667982i
$990$		0			0
$991$	−5.77036	+	9.99455i	−0.183301	+	0.317487i	−0.943003	−	0.332785i	$-0.892012\pi$
$991$	−5.77036	+	9.99455i	−0.183301	+	0.317487i	0.759701	+	0.650272i	$0.225345\pi$
$992$	−0.338321	+	0.725532i	−0.0107417	+	0.0230357i
$993$		0			0
$994$	7.43270	+	8.85795i	0.235751	+	0.280957i
$995$	11.3049	+	21.4300i	0.358391	+	0.679377i
$996$		0			0
$997$	19.9126	−	13.9430i	0.630639	−	0.441579i	−0.214059	−	0.976821i	$-0.568669\pi$
$997$	19.9126	−	13.9430i	0.630639	−	0.441579i	0.844699	+	0.535242i	$0.179780\pi$
$998$	−8.66028	−	8.66028i	−0.274136	−	0.274136i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.r.a.332.7		192
3.2	odd	2		135.2.q.a.2.10	✓	192
5.3	odd	4	inner	405.2.r.a.8.7		192
15.2	even	4		675.2.ba.b.218.7		192
15.8	even	4		135.2.q.a.83.10	yes	192
15.14	odd	2		675.2.ba.b.407.7		192
27.13	even	9		135.2.q.a.122.10	yes	192
27.14	odd	18	inner	405.2.r.a.152.7		192
135.13	odd	36		135.2.q.a.68.10	yes	192
135.67	odd	36		675.2.ba.b.68.7		192
135.68	even	36	inner	405.2.r.a.233.7		192
135.94	even	18		675.2.ba.b.257.7		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.10	✓	192	3.2	odd	2
135.2.q.a.68.10	yes	192	135.13	odd	36
135.2.q.a.83.10	yes	192	15.8	even	4
135.2.q.a.122.10	yes	192	27.13	even	9
405.2.r.a.8.7		192	5.3	odd	4	inner
405.2.r.a.152.7		192	27.14	odd	18	inner
405.2.r.a.233.7		192	135.68	even	36	inner
405.2.r.a.332.7		192	1.1	even	1	trivial
675.2.ba.b.68.7		192	135.67	odd	36
675.2.ba.b.218.7		192	15.2	even	4
675.2.ba.b.257.7		192	135.94	even	18
675.2.ba.b.407.7		192	15.14	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-0.184358 - 0.263290i) q^{2} +(0.648706 - 1.78231i) q^{4} +(0.0853346 - 2.23444i) q^{5} +(4.46037 + 2.07991i) q^{7} +(-1.20979 + 0.324162i) q^{8} +(-0.604038 + 0.389469i) q^{10} +(-0.0393995 + 0.0469545i) q^{11} +(-0.0650996 - 0.0455832i) q^{13} +(-0.274686 - 1.55782i) q^{14} +(-2.59752 - 2.17957i) q^{16} +(3.89214 + 1.04290i) q^{17} +(-1.80193 - 1.04035i) q^{19} +(-3.92710 - 1.60159i) q^{20} +(0.0196263 + 0.00171708i) q^{22} +(-2.74553 - 5.88782i) q^{23} +(-4.98544 - 0.381350i) q^{25} +0.0255437i q^{26} +(6.60050 - 6.60050i) q^{28} +(-1.24585 + 7.06559i) q^{29} +(0.209263 + 0.0761654i) q^{31} +(-0.313308 + 3.58112i) q^{32} +(-0.442962 - 1.21703i) q^{34} +(5.02805 - 9.78894i) q^{35} +(1.69714 - 6.33380i) q^{37} +(0.0582873 + 0.666227i) q^{38} +(0.621084 + 2.73086i) q^{40} +(2.22023 - 0.391486i) q^{41} +(-3.71962 + 0.325424i) q^{43} +(0.0581286 + 0.100682i) q^{44} +(-1.04404 + 1.80834i) q^{46} +(0.591824 - 1.26917i) q^{47} +(11.0694 + 13.1920i) q^{49} +(0.818698 + 1.38292i) q^{50} +(-0.123474 + 0.0864573i) q^{52} +(8.67464 + 8.67464i) q^{53} +(0.101555 + 0.0920427i) q^{55} +(-6.07034 - 1.07036i) q^{56} +(2.08998 - 0.974575i) q^{58} +(-0.888968 + 0.745933i) q^{59} +(-6.77967 + 2.46760i) q^{61} +(-0.0185256 - 0.0691385i) q^{62} +(-4.87243 + 2.81310i) q^{64} +(-0.107408 + 0.141571i) q^{65} +(-4.36094 + 6.22807i) q^{67} +(4.38361 - 6.26045i) q^{68} +(-3.50429 + 0.480832i) q^{70} +(-6.33059 + 3.65497i) q^{71} +(-1.72056 - 6.42123i) q^{73} +(-1.98051 + 0.720846i) q^{74} +(-3.02314 + 2.53672i) q^{76} +(-0.273398 + 0.127487i) q^{77} +(6.06016 + 1.06857i) q^{79} +(-5.09178 + 5.61800i) q^{80} +(-0.512391 - 0.512391i) q^{82} +(3.30178 - 2.31193i) q^{83} +(2.66242 - 8.60775i) q^{85} +(0.771422 + 0.919344i) q^{86} +(0.0324443 - 0.0695770i) q^{88} +(-5.25350 + 9.09933i) q^{89} +(-0.195560 - 0.338719i) q^{91} +(-12.2749 + 1.07392i) q^{92} +(-0.443268 + 0.0781601i) q^{94} +(-2.47836 + 3.93753i) q^{95} +(0.855375 + 9.77698i) q^{97} +(1.43259 - 5.34651i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) \) 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

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