LMFDB - Embedded newform 405.2.r.a.368.5

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			368.5
Character	$\chi$	$=$	405.368
Dual form			405.2.r.a.197.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35613 - 0.118646i) q^{2} +(-0.144600 - 0.0254969i) q^{4} +(-1.16254 - 1.91010i) q^{5} +(0.495263 + 0.346787i) q^{7} +(2.82292 + 0.756400i) q^{8} +O(q^{10})$	\(q+(-1.35613 - 0.118646i) q^{2} +(-0.144600 - 0.0254969i) q^{4} +(-1.16254 - 1.91010i) q^{5} +(0.495263 + 0.346787i) q^{7} +(2.82292 + 0.756400i) q^{8} +(1.34993 + 2.72828i) q^{10} +(0.461147 - 1.26699i) q^{11} +(-0.157610 - 1.80149i) q^{13} +(-0.630497 - 0.529050i) q^{14} +(-3.46256 - 1.26027i) q^{16} +(-0.596735 + 0.159895i) q^{17} +(-6.66221 + 3.84643i) q^{19} +(0.119402 + 0.305842i) q^{20} +(-0.775699 + 1.66349i) q^{22} +(-4.35606 - 6.22110i) q^{23} +(-2.29700 + 4.44115i) q^{25} +2.46176i q^{26} +(-0.0627730 - 0.0627730i) q^{28} +(-4.15413 + 3.48573i) q^{29} +(0.651351 - 3.69400i) q^{31} +(-0.751218 - 0.350299i) q^{32} +(0.828222 - 0.146038i) q^{34} +(0.0866357 - 1.34916i) q^{35} +(-1.29170 - 4.82067i) q^{37} +(9.49120 - 4.42582i) q^{38} +(-1.83696 - 6.27142i) q^{40} +(-7.43804 + 8.86431i) q^{41} +(-0.466380 - 1.00015i) q^{43} +(-0.0989861 + 0.171449i) q^{44} +(5.16928 + 8.95346i) q^{46} +(2.99349 - 4.27515i) q^{47} +(-2.26912 - 6.23435i) q^{49} +(3.64196 - 5.75025i) q^{50} +(-0.0231420 + 0.264514i) q^{52} +(-0.231010 + 0.231010i) q^{53} +(-2.95619 + 0.592089i) q^{55} +(1.13578 + 1.35357i) q^{56} +(6.04711 - 4.23423i) q^{58} +(-9.76428 + 3.55391i) q^{59} +(0.173537 + 0.984176i) q^{61} +(-1.32160 + 4.93227i) q^{62} +(7.35941 + 4.24896i) q^{64} +(-3.25781 + 2.39536i) q^{65} +(1.61617 - 0.141397i) q^{67} +(0.0903647 - 0.00790588i) q^{68} +(-0.277562 + 1.81936i) q^{70} +(8.27254 + 4.77616i) q^{71} +(-2.09021 + 7.80078i) q^{73} +(1.17975 + 6.69072i) q^{74} +(1.06143 - 0.386328i) q^{76} +(0.667764 - 0.467574i) q^{77} +(-5.86238 - 6.98651i) q^{79} +(1.61812 + 8.07897i) q^{80} +(11.1387 - 11.1387i) q^{82} +(0.973649 - 11.1289i) q^{83} +(0.999144 + 0.953942i) q^{85} +(0.513808 + 1.41168i) q^{86} +(2.26013 - 3.22780i) q^{88} +(-3.58395 - 6.20758i) q^{89} +(0.546675 - 0.946869i) q^{91} +(0.471268 + 1.01064i) q^{92} +(-4.56680 + 5.44250i) q^{94} +(15.0922 + 8.25389i) q^{95} +(9.46315 - 4.41274i) q^{97} +(2.33754 + 8.72382i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{18}\right)$

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 $

$2$	−1.35613	−	0.118646i	−0.958930	−	0.0838955i	−0.403068	−	0.915170i	$-0.632056\pi$
$2$	−1.35613	−	0.118646i	−0.958930	−	0.0838955i	−0.555862	+	0.831275i	$0.687612\pi$
$3$		0			0
$3$		0			0
$4$	−0.144600	−	0.0254969i	−0.0723000	−	0.0127484i
$5$	−1.16254	−	1.91010i	−0.519904	−	0.854225i
$5$	−1.16254	−	1.91010i	−0.519904	−	0.854225i
$6$		0			0
$7$	0.495263	+	0.346787i	0.187192	+	0.131073i	0.663416	−	0.748251i	$-0.269106\pi$
$7$	0.495263	+	0.346787i	0.187192	+	0.131073i	−0.476224	+	0.879324i	$0.657995\pi$
$8$	2.82292	+	0.756400i	0.998054	+	0.267428i
$9$		0			0
$10$	1.34993	+	2.72828i	0.426886	+	0.862759i
$11$	0.461147	−	1.26699i	0.139041	−	0.382012i	−0.850555	−	0.525886i	$-0.823734\pi$
$11$	0.461147	−	1.26699i	0.139041	−	0.382012i	0.989596	+	0.143874i	$0.0459561\pi$
$12$		0			0
$13$	−0.157610	−	1.80149i	−0.0437132	−	0.499644i	−0.986218	−	0.165451i	$-0.947092\pi$
$13$	−0.157610	−	1.80149i	−0.0437132	−	0.499644i	0.942505	−	0.334193i	$-0.108464\pi$
$14$	−0.630497	−	0.529050i	−0.168507	−	0.141394i
$15$		0			0
$16$	−3.46256	−	1.26027i	−0.865640	−	0.315067i
$17$	−0.596735	+	0.159895i	−0.144729	+	0.0387801i	−0.330456	−	0.943821i	$-0.607203\pi$
$17$	−0.596735	+	0.159895i	−0.144729	+	0.0387801i	0.185727	+	0.982601i	$0.440536\pi$
$18$		0			0
$19$	−6.66221	+	3.84643i	−1.52842	+	0.882432i	−0.528988	+	0.848629i	$0.677428\pi$
$19$	−6.66221	+	3.84643i	−1.52842	+	0.882432i	−0.999429	+	0.0338024i	$0.989238\pi$
$20$	0.119402	+	0.305842i	0.0266990	+	0.0683884i
$21$		0			0
$22$	−0.775699	+	1.66349i	−0.165380	+	0.354658i
$23$	−4.35606	−	6.22110i	−0.908302	−	1.29719i	−0.954486	−	0.298257i	$-0.903595\pi$
$23$	−4.35606	−	6.22110i	−0.908302	−	1.29719i	0.0461838	−	0.998933i	$-0.485294\pi$
$24$		0			0
$25$	−2.29700	+	4.44115i	−0.459399	+	0.888230i
$26$			2.46176i			0.482791i
$27$		0			0
$28$	−0.0627730	−	0.0627730i	−0.0118630	−	0.0118630i
$29$	−4.15413	+	3.48573i	−0.771402	+	0.647283i	−0.941068	−	0.338218i	$-0.890176\pi$
$29$	−4.15413	+	3.48573i	−0.771402	+	0.647283i	0.169665	+	0.985502i	$0.445731\pi$
$30$		0			0
$31$	0.651351	−	3.69400i	0.116986	−	0.663462i	−0.868761	−	0.495231i	$-0.835084\pi$
$31$	0.651351	−	3.69400i	0.116986	−	0.663462i	0.985748	−	0.168231i	$-0.0538054\pi$
$32$	−0.751218	−	0.350299i	−0.132798	−	0.0619247i
$33$		0			0
$34$	0.828222	−	0.146038i	0.142039	−	0.0250453i
$35$	0.0866357	−	1.34916i	0.0146441	−	0.228049i
$36$		0			0
$37$	−1.29170	−	4.82067i	−0.212353	−	0.792514i	−0.987081	−	0.160219i	$-0.948780\pi$
$37$	−1.29170	−	4.82067i	−0.212353	−	0.792514i	0.774728	−	0.632295i	$-0.217887\pi$
$38$	9.49120	−	4.42582i	1.53968	−	0.717963i
$39$		0			0
$40$	−1.83696	−	6.27142i	−0.290449	−	0.991599i
$41$	−7.43804	+	8.86431i	−1.16163	+	1.38437i	−0.252632	+	0.967562i	$0.581296\pi$
$41$	−7.43804	+	8.86431i	−1.16163	+	1.38437i	−0.908994	+	0.416810i	$0.863148\pi$
$42$		0			0
$43$	−0.466380	−	1.00015i	−0.0711223	−	0.152522i	0.867532	−	0.497381i	$-0.165705\pi$
$43$	−0.466380	−	1.00015i	−0.0711223	−	0.152522i	−0.938655	+	0.344858i	$0.887927\pi$
$44$	−0.0989861	+	0.171449i	−0.0149227	+	0.0258469i
$45$		0			0
$46$	5.16928	+	8.95346i	0.762169	+	1.32012i
$47$	2.99349	−	4.27515i	0.436645	−	0.623594i	−0.539168	−	0.842198i	$-0.681261\pi$
$47$	2.99349	−	4.27515i	0.436645	−	0.623594i	0.975814	+	0.218604i	$0.0701502\pi$
$48$		0			0
$49$	−2.26912	−	6.23435i	−0.324160	−	0.890621i
$50$	3.64196	−	5.75025i	0.515050	−	0.813208i
$51$		0			0
$52$	−0.0231420	+	0.264514i	−0.00320922	+	0.0366815i
$53$	−0.231010	+	0.231010i	−0.0317317	+	0.0317317i	−0.722795	−	0.691063i	$-0.757143\pi$
$53$	−0.231010	+	0.231010i	−0.0317317	+	0.0317317i	0.691063	+	0.722795i	$0.257143\pi$
$54$		0			0
$55$	−2.95619	+	0.592089i	−0.398612	+	0.0798373i
$56$	1.13578	+	1.35357i	0.151775	+	0.180878i
$57$		0			0
$58$	6.04711	−	4.23423i	0.794025	−	0.555982i
$59$	−9.76428	+	3.55391i	−1.27120	+	0.462679i	−0.887513	−	0.460784i	$-0.847568\pi$
$59$	−9.76428	+	3.55391i	−1.27120	+	0.462679i	−0.383688	+	0.923463i	$0.625346\pi$
$60$		0			0
$61$	0.173537	+	0.984176i	0.0222191	+	0.126011i	0.993900	−	0.110287i	$-0.0351770\pi$
$61$	0.173537	+	0.984176i	0.0222191	+	0.126011i	−0.971681	+	0.236298i	$0.924066\pi$
$62$	−1.32160	+	4.93227i	−0.167843	+	0.626398i
$63$		0			0
$64$	7.35941	+	4.24896i	0.919927	+	0.531120i
$65$	−3.25781	+	2.39536i	−0.404081	+	0.297108i
$66$		0			0
$67$	1.61617	−	0.141397i	0.197447	−	0.0172743i	0.0119966	−	0.999928i	$-0.496181\pi$
$67$	1.61617	−	0.141397i	0.197447	−	0.0172743i	0.185450	+	0.982654i	$0.440626\pi$
$68$	0.0903647	−	0.00790588i	0.0109583	−	0.000958729i
$69$		0			0
$70$	−0.277562	+	1.81936i	−0.0331750	+	0.217455i
$71$	8.27254	+	4.77616i	0.981770	+	0.566825i	0.902804	−	0.430052i	$-0.141505\pi$
$71$	8.27254	+	4.77616i	0.981770	+	0.566825i	0.0789662	+	0.996877i	$0.474838\pi$
$72$		0			0
$73$	−2.09021	+	7.80078i	−0.244641	+	0.913012i	0.728923	+	0.684596i	$0.240021\pi$
$73$	−2.09021	+	7.80078i	−0.244641	+	0.913012i	−0.973564	+	0.228416i	$0.926645\pi$
$74$	1.17975	+	6.69072i	0.137144	+	0.777781i
$75$		0			0
$76$	1.06143	−	0.386328i	0.121754	−	0.0443149i
$77$	0.667764	−	0.467574i	0.0760988	−	0.0532850i
$78$		0			0
$79$	−5.86238	−	6.98651i	−0.659569	−	0.786044i	0.327754	−	0.944763i	$-0.393708\pi$
$79$	−5.86238	−	6.98651i	−0.659569	−	0.786044i	−0.987324	+	0.158719i	$0.949264\pi$
$80$	1.61812	+	8.07897i	0.180912	+	0.903256i
$81$		0			0
$82$	11.1387	−	11.1387i	1.23006	−	1.23006i
$83$	0.973649	−	11.1289i	0.106872	−	1.22155i	−0.733557	−	0.679628i	$-0.762141\pi$
$83$	0.973649	−	11.1289i	0.106872	−	1.22155i	0.840429	−	0.541922i	$-0.182303\pi$
$84$		0			0
$85$	0.999144	+	0.953942i	0.108372	+	0.103470i
$86$	0.513808	+	1.41168i	0.0554053	+	0.152225i
$87$		0			0
$88$	2.26013	−	3.22780i	0.240931	−	0.344085i
$89$	−3.58395	−	6.20758i	−0.379898	−	0.658002i	0.611149	−	0.791515i	$-0.290707\pi$
$89$	−3.58395	−	6.20758i	−0.379898	−	0.658002i	−0.991047	+	0.133513i	$0.957374\pi$
$90$		0			0
$91$	0.546675	−	0.946869i	0.0573071	−	0.0992589i
$92$	0.471268	+	1.01064i	0.0491331	+	0.105366i
$93$		0			0
$94$	−4.56680	+	5.44250i	−0.471029	+	0.561351i
$95$	15.0922	+	8.25389i	1.54842	+	0.846831i
$96$		0			0
$97$	9.46315	−	4.41274i	0.960838	−	0.448046i	0.122062	−	0.992523i	$-0.461049\pi$
$97$	9.46315	−	4.41274i	0.960838	−	0.448046i	0.838776	+	0.544477i	$0.183272\pi$
$98$	2.33754	+	8.72382i	0.236127	+	0.881238i
$99$		0			0
$100$	0.445381	−	0.583624i	0.0445381	−	0.0583624i
$101$	7.45128	−	1.31386i	0.741430	−	0.130734i	0.209840	−	0.977736i	$-0.432706\pi$
$101$	7.45128	−	1.31386i	0.741430	−	0.130734i	0.531590	+	0.847002i	$0.321595\pi$
$102$		0			0
$103$	16.2593	+	7.58185i	1.60208	+	0.747062i	0.998728	−	0.0504147i	$-0.0160543\pi$
$103$	16.2593	+	7.58185i	1.60208	+	0.747062i	0.603350	+	0.797476i	$0.293832\pi$
$104$	0.917727	−	5.20469i	0.0899905	−	0.510362i
$105$		0			0
$106$	0.340688	−	0.285871i	0.0330906	−	0.0277663i
$107$	−5.23935	−	5.23935i	−0.506508	−	0.506508i	0.406945	−	0.913453i	$-0.366594\pi$
$107$	−5.23935	−	5.23935i	−0.506508	−	0.506508i	−0.913453	+	0.406945i	$0.866594\pi$
$108$		0			0
$109$		−	2.65288i		−	0.254100i	−0.991896	−	0.127050i	$-0.959449\pi$
$109$		−	2.65288i		−	0.254100i	0.991896	−	0.127050i	$-0.0405508\pi$
$110$	4.07922	−	0.452211i	0.388939	−	0.0431167i
$111$		0			0
$112$	−1.27783	−	1.82494i	−0.120744	−	0.172440i
$113$	3.27041	−	7.01342i	0.307655	−	0.659767i	−0.690312	−	0.723512i	$-0.742527\pi$
$113$	3.27041	−	7.01342i	0.307655	−	0.659767i	0.997966	+	0.0637448i	$0.0203044\pi$
$114$		0			0
$115$	−6.81885	+	15.5528i	−0.635861	+	1.45031i
$116$	0.689562	−	0.398119i	0.0640242	−	0.0369644i
$117$		0			0
$118$	13.6633	−	3.66107i	1.25781	−	0.337029i
$119$	−0.350990	−	0.127750i	−0.0321752	−	0.0117108i
$120$		0			0
$121$	7.03388	+	5.90213i	0.639444	+	0.536557i
$122$	−0.118570	−	1.35526i	−0.0107348	−	0.122700i
$123$		0			0
$124$	−0.188371	+	0.517544i	−0.0169162	+	0.0464769i
$125$	11.1534	−	0.775512i	0.997591	−	0.0693639i
$126$		0			0
$127$	−8.39790	−	2.25021i	−0.745193	−	0.199674i	−0.133808	−	0.991007i	$-0.542721\pi$
$127$	−8.39790	−	2.25021i	−0.745193	−	0.199674i	−0.611385	+	0.791333i	$0.709387\pi$
$128$	−8.11826	−	5.68446i	−0.717559	−	0.502440i
$129$		0			0
$130$	4.70222	−	2.86190i	0.412412	−	0.251005i
$131$	3.98100	+	0.701958i	0.347822	+	0.0613304i	0.344830	−	0.938665i	$-0.387937\pi$
$131$	3.98100	+	0.701958i	0.347822	+	0.0613304i	0.00299187	+	0.999996i	$0.499048\pi$
$132$		0			0
$133$	−4.63344	−	0.405373i	−0.401770	−	0.0351503i
$134$	−2.20852			−0.190787
$135$		0			0
$136$	−1.80548			−0.154819
$137$	13.6356	+	1.19296i	1.16497	+	0.101922i	0.653190	−	0.757194i	$-0.273430\pi$
$137$	13.6356	+	1.19296i	1.16497	+	0.101922i	0.511781	+	0.859116i	$0.328986\pi$
$138$		0			0
$139$	−6.19727	−	1.09275i	−0.525645	−	0.0926854i	−0.0954725	−	0.995432i	$-0.530436\pi$
$139$	−6.19727	−	1.09275i	−0.525645	−	0.0926854i	−0.430173	+	0.902747i	$0.641547\pi$
$140$	−0.0469268	+	0.192879i	−0.00396604	+	0.0163013i
$141$		0			0
$142$	−10.6520	−	7.45860i	−0.893895	−	0.625912i
$143$	−2.35515	−	0.631061i	−0.196948	−	0.0527720i
$144$		0			0
$145$	11.4874	+	3.88252i	0.953980	+	0.322426i
$146$	3.76013	−	10.3309i	0.311191	−	0.854990i
$147$		0			0
$148$	0.0638670	+	0.730003i	0.00524984	+	0.0600059i
$149$	2.60149	+	2.18291i	0.213122	+	0.178831i	0.743099	−	0.669181i	$-0.233355\pi$
$149$	2.60149	+	2.18291i	0.213122	+	0.178831i	−0.529977	+	0.848012i	$0.677799\pi$
$150$		0			0
$151$	−21.3539	−	7.77217i	−1.73775	−	0.632490i	−0.738620	−	0.674122i	$-0.764522\pi$
$151$	−21.3539	−	7.77217i	−1.73775	−	0.632490i	−0.999133	+	0.0416312i	$0.986745\pi$
$152$	−21.7164	+	5.81888i	−1.76143	+	0.471974i
$153$		0			0
$154$	−0.961052	+	0.554864i	−0.0774438	+	0.0447122i
$155$	−7.81314	+	3.05027i	−0.627567	+	0.245004i
$156$		0			0
$157$	−7.80411	+	16.7360i	−0.622836	+	1.33568i	0.301270	+	0.953539i	$0.402589\pi$
$157$	−7.80411	+	16.7360i	−0.622836	+	1.33568i	−0.924106	+	0.382136i	$0.875188\pi$
$158$	7.12124	+	10.1702i	0.566535	+	0.809096i
$159$		0			0
$160$	0.204215	+	1.84214i	0.0161446	+	0.145634i
$161$		−	4.59171i		−	0.361877i
$162$		0			0
$163$	−16.0458	−	16.0458i	−1.25680	−	1.25680i	−0.952611	−	0.304190i	$-0.901614\pi$
$163$	−16.0458	−	16.0458i	−1.25680	−	1.25680i	−0.304190	−	0.952611i	$-0.598386\pi$
$164$	1.30155	−	1.09213i	0.101634	−	0.0852811i
$165$		0			0
$166$	−2.64079	+	14.9767i	−0.204965	+	1.16241i
$167$	−1.23325	−	0.575072i	−0.0954315	−	0.0445004i	0.374316	−	0.927301i	$-0.377877\pi$
$167$	−1.23325	−	0.575072i	−0.0954315	−	0.0445004i	−0.469748	+	0.882801i	$0.655655\pi$
$168$		0			0
$169$	9.58197	−	1.68956i	0.737075	−	0.129966i
$170$	−1.24179	−	1.41222i	−0.0952409	−	0.108312i
$171$		0			0
$172$	0.0419377	+	0.156514i	0.00319772	+	0.0119340i
$173$	−16.6179	+	7.74907i	−1.26344	+	0.589151i	−0.934756	−	0.355289i	$-0.884382\pi$
$173$	−16.6179	+	7.74907i	−1.26344	+	0.589151i	−0.328682	+	0.944441i	$0.606605\pi$
$174$		0			0
$175$	−2.67775	+	1.40297i	−0.202419	+	0.106054i
$176$	−3.19350	+	3.80586i	−0.240719	+	0.286878i
$177$		0			0
$178$	4.12380	+	8.84351i	0.309092	+	0.662849i
$179$	7.37861	−	12.7801i	0.551503	−	0.955231i	−0.446663	−	0.894702i	$-0.647388\pi$
$179$	7.37861	−	12.7801i	0.551503	−	0.955231i	0.998166	−	0.0605291i	$-0.0192788\pi$
$180$		0			0
$181$	−2.27317	−	3.93725i	−0.168964	−	0.292653i	0.769092	−	0.639138i	$-0.220709\pi$
$181$	−2.27317	−	3.93725i	−0.168964	−	0.292653i	−0.938056	+	0.346484i	$0.887375\pi$
$182$	−0.853706	+	1.21922i	−0.0632809	+	0.0903745i
$183$		0			0
$184$	−7.59119	−	20.8566i	−0.559630	−	1.53757i
$185$	−7.70634	+	8.07150i	−0.566581	+	0.593429i
$186$		0			0
$187$	−0.0725974	+	0.829792i	−0.00530885	+	0.0606804i
$188$	−0.541861	+	0.541861i	−0.0395193	+	0.0395193i
$189$		0			0
$190$	−19.4877	−	12.9840i	−1.41379	−	0.941957i
$191$	−11.5901	−	13.8125i	−0.838631	−	0.999441i	−0.999921	−	0.0125340i	$-0.996010\pi$
$191$	−11.5901	−	13.8125i	−0.838631	−	0.999441i	0.161291	−	0.986907i	$-0.448434\pi$
$192$		0			0
$193$	5.09804	−	3.56969i	0.366965	−	0.256952i	−0.375520	−	0.926814i	$-0.622536\pi$
$193$	5.09804	−	3.56969i	0.366965	−	0.256952i	0.742485	+	0.669863i	$0.233647\pi$
$194$	−13.3568	+	4.86149i	−0.958965	+	0.349035i
$195$		0			0
$196$	0.169158	+	0.959342i	0.0120827	+	0.0685244i
$197$	−1.35510	+	5.05729i	−0.0965467	+	0.360317i	−0.997249	−	0.0741188i	$-0.976386\pi$
$197$	−1.35510	+	5.05729i	−0.0965467	+	0.360317i	0.900703	+	0.434436i	$0.143052\pi$
$198$		0			0
$199$	13.9099	+	8.03089i	0.986047	+	0.569294i	0.904090	−	0.427342i	$-0.140550\pi$
$199$	13.9099	+	8.03089i	0.986047	+	0.569294i	0.0819565	+	0.996636i	$0.473883\pi$
$200$	−9.84353	+	10.7996i	−0.696043	+	0.763645i
$201$		0			0
$202$	−10.2608	+	0.897704i	−0.721948	+	0.0631622i
$203$	−3.26619	+	0.285755i	−0.229242	+	0.0200560i
$204$		0			0
$205$	25.5788	+	3.90231i	1.78650	+	0.272549i
$206$	−21.1502	−	12.2111i	−1.47361	−	0.850787i
$207$		0			0
$208$	−1.72463	+	6.43640i	−0.119581	+	0.446284i
$209$	1.80113	+	10.2147i	0.124587	+	0.706567i
$210$		0			0
$211$	−19.6727	+	7.16029i	−1.35433	+	0.492934i	−0.914295	−	0.405048i	$-0.867255\pi$
$211$	−19.6727	+	7.16029i	−1.35433	+	0.492934i	−0.440031	+	0.897983i	$0.645033\pi$
$212$	0.0392941	−	0.0275140i	0.00269873	−	0.00188967i
$213$		0			0
$214$	6.48362	+	7.72688i	0.443211	+	0.528199i
$215$	−1.36821	+	2.05355i	−0.0933114	+	0.140051i
$216$		0			0
$217$	1.60362	−	1.60362i	0.108861	−	0.108861i
$218$	−0.314754	+	3.59765i	−0.0213178	+	0.243664i
$219$		0			0
$220$	0.442561	−	0.0102426i	0.0298374	−	0.000690558i
$221$	0.382100	+	1.04981i	0.0257028	+	0.0706180i
$222$		0			0
$223$	9.26122	−	13.2264i	0.620177	−	0.885705i	−0.379035	−	0.925382i	$-0.623744\pi$
$223$	9.26122	−	13.2264i	0.620177	−	0.885705i	0.999213	+	0.0396772i	$0.0126330\pi$
$224$	−0.250572	−	0.434003i	−0.0167420	−	0.0289980i
$225$		0			0
$226$	−5.26723	+	9.12310i	−0.350371	+	0.606860i
$227$	−4.42259	−	9.48428i	−0.293538	−	0.629494i	0.703130	−	0.711061i	$-0.251785\pi$
$227$	−4.42259	−	9.48428i	−0.293538	−	0.629494i	−0.996668	+	0.0815674i	$0.974007\pi$
$228$		0			0
$229$	5.43987	−	6.48298i	0.359476	−	0.428407i	−0.555749	−	0.831350i	$-0.687568\pi$
$229$	5.43987	−	6.48298i	0.359476	−	0.428407i	0.915225	+	0.402943i	$0.132013\pi$
$230$	11.0925	−	20.2826i	0.731421	−	1.33740i
$231$		0			0
$232$	−14.3634	+	6.69776i	−0.943003	+	0.439729i
$233$	−3.39926	−	12.6862i	−0.222693	−	0.831100i	−0.983316	−	0.181907i	$-0.941773\pi$
$233$	−3.39926	−	12.6862i	−0.222693	−	0.831100i	0.760623	−	0.649194i	$-0.224894\pi$
$234$		0			0
$235$	−11.6460	−	0.747845i	−0.759703	−	0.0487841i
$236$	1.50253	−	0.264936i	0.0978062	−	0.0172459i
$237$		0			0
$238$	0.460832	+	0.214889i	0.0298713	+	0.0139292i
$239$	0.262840	−	1.49064i	0.0170017	−	0.0964214i	−0.975126	−	0.221651i	$-0.928856\pi$
$239$	0.262840	−	1.49064i	0.0170017	−	0.0964214i	0.992128	+	0.125229i	$0.0399666\pi$
$240$		0			0
$241$	18.7538	−	15.7363i	1.20804	−	1.01367i	0.208677	−	0.977985i	$-0.433084\pi$
$241$	18.7538	−	15.7363i	1.20804	−	1.01367i	0.999363	−	0.0356816i	$-0.0113602\pi$
$242$	−8.83860	−	8.83860i	−0.568167	−	0.568167i
$243$		0			0
$244$		−	0.146736i		−	0.00939383i
$245$	−9.27031	+	11.5819i	−0.592259	+	0.739943i
$246$		0			0
$247$	7.97934	+	11.3957i	0.507713	+	0.725090i
$248$	4.63286	−	9.93519i	0.294187	−	0.630885i
$249$		0			0
$250$	−15.2175	−	0.271612i	−0.962439	−	0.0171783i
$251$	6.15607	−	3.55421i	0.388568	−	0.224340i	−0.292972	−	0.956121i	$-0.594644\pi$
$251$	6.15607	−	3.55421i	0.388568	−	0.224340i	0.681539	+	0.731781i	$0.261311\pi$
$252$		0			0
$253$	−9.89086	+	2.65025i	−0.621833	+	0.166620i
$254$	11.1217	+	4.04796i	0.697836	+	0.253992i
$255$		0			0
$256$	−2.68459	−	2.25263i	−0.167787	−	0.140790i
$257$	−1.19053	−	13.6078i	−0.0742633	−	0.848834i	−0.938394	−	0.345567i	$-0.887687\pi$
$257$	−1.19053	−	13.6078i	−0.0742633	−	0.848834i	0.864131	−	0.503267i	$-0.167869\pi$
$258$		0			0
$259$	1.03202	−	2.83544i	0.0641264	−	0.176186i
$260$	0.532153	−	0.263305i	0.0330027	−	0.0163295i
$261$		0			0
$262$	−5.31548	−	1.42428i	−0.328391	−	0.0879922i
$263$	6.43173	+	4.50355i	0.396598	+	0.277701i	0.754815	−	0.655937i	$-0.227727\pi$
$263$	6.43173	+	4.50355i	0.396598	+	0.277701i	−0.358218	+	0.933638i	$0.616615\pi$
$264$		0			0
$265$	0.709812	+	0.172695i	0.0436034	+	0.0106085i
$266$	6.23546	+	1.09948i	0.382320	+	0.0674134i
$267$		0			0
$268$	−0.237303	−	0.0207614i	−0.0144956	−	0.00126820i
$269$	28.0785			1.71198			0.855988	−	0.516995i	$-0.172949\pi$
$269$	28.0785			1.71198			0.855988	+	0.516995i	$0.172949\pi$
$270$		0			0
$271$	−2.80897			−0.170633			−0.0853163	−	0.996354i	$-0.527190\pi$
$271$	−2.80897			−0.170633			−0.0853163	+	0.996354i	$0.527190\pi$
$272$	2.26774	+	0.198402i	0.137502	+	0.0120299i
$273$		0			0
$274$	−18.3502	−	3.23563i	−1.10857	−	0.195472i
$275$	4.56764	+	4.95829i	0.275439	+	0.298996i
$276$		0			0
$277$	2.39206	+	1.67494i	0.143725	+	0.100637i	0.643227	−	0.765675i	$-0.277595\pi$
$277$	2.39206	+	1.67494i	0.143725	+	0.100637i	−0.499503	+	0.866312i	$0.666484\pi$
$278$	8.27466	+	2.21719i	0.496281	+	0.132978i
$279$		0			0
$280$	1.26507	−	3.74304i	0.0756023	−	0.223689i
$281$	−5.14517	+	14.1362i	−0.306935	+	0.843297i	0.686315	+	0.727304i	$0.259227\pi$
$281$	−5.14517	+	14.1362i	−0.306935	+	0.843297i	−0.993250	+	0.115992i	$0.962995\pi$
$282$		0			0
$283$	1.20465	+	13.7692i	0.0716091	+	0.818496i	0.944056	+	0.329786i	$0.106977\pi$
$283$	1.20465	+	13.7692i	0.0716091	+	0.818496i	−0.872446	+	0.488710i	$0.837468\pi$
$284$	−1.07443	−	0.901556i	−0.0637558	−	0.0534975i
$285$		0			0
$286$	3.11902	+	1.13523i	0.184432	+	0.0671277i
$287$	−6.75781	+	1.81075i	−0.398901	+	0.106885i
$288$		0			0
$289$	−14.3919	+	8.30917i	−0.846583	+	0.488775i
$290$	−15.1178	−	6.62815i	−0.887750	−	0.389218i
$291$		0			0
$292$	0.501140	−	1.07470i	0.0293270	−	0.0628920i
$293$	11.1301	+	15.8954i	0.650227	+	0.928621i	0.999966	−	0.00822650i	$-0.00261861\pi$
$293$	11.1301	+	15.8954i	0.650227	+	0.928621i	−0.349739	+	0.936847i	$0.613730\pi$
$294$		0			0
$295$	18.1397	+	14.5192i	1.05613	+	0.845342i
$296$		−	14.5854i		−	0.847761i
$297$		0			0
$298$	−3.26896	−	3.26896i	−0.189366	−	0.189366i
$299$	−10.5207	+	8.82792i	−0.608428	+	0.510532i
$300$		0			0
$301$	0.115860	−	0.657074i	0.00667805	−	0.0378731i
$302$	28.0365	+	13.0736i	1.61332	+	0.752304i
$303$		0			0
$304$	27.9159	−	4.92232i	1.60108	−	0.282314i
$305$	1.67813	−	1.47562i	0.0960897	−	0.0844936i
$306$		0			0
$307$	−1.06560	−	3.97686i	−0.0608167	−	0.226971i	0.928828	−	0.370512i	$-0.120818\pi$
$307$	−1.06560	−	3.97686i	−0.0608167	−	0.226971i	−0.989644	+	0.143541i	$0.954151\pi$
$308$	−0.108480	+	0.0505852i	−0.00618124	+	0.00288236i
$309$		0			0
$310$	10.9576	−	3.20957i	0.622347	−	0.182291i
$311$	−2.34841	+	2.79872i	−0.133166	+	0.158701i	−0.828507	−	0.559979i	$-0.810809\pi$
$311$	−2.34841	+	2.79872i	−0.133166	+	0.158701i	0.695341	+	0.718680i	$0.255254\pi$
$312$		0			0
$313$	8.22932	+	17.6478i	0.465148	+	0.997514i	0.989301	+	0.145890i	$0.0466044\pi$
$313$	8.22932	+	17.6478i	0.465148	+	0.997514i	−0.524152	+	0.851624i	$0.675618\pi$
$314$	12.5691	−	21.7702i	0.709313	−	1.22857i
$315$		0			0
$316$	0.669566	+	1.15972i	0.0376660	+	0.0652395i
$317$	6.73196	−	9.61423i	0.378104	−	0.539989i	−0.584325	−	0.811519i	$-0.698641\pi$
$317$	6.73196	−	9.61423i	0.378104	−	0.539989i	0.962430	+	0.271530i	$0.0875297\pi$
$318$		0			0
$319$	2.50072	+	6.87067i	0.140013	+	0.384684i
$320$	−0.439663	−	18.9968i	−0.0245779	−	1.06196i
$321$		0			0
$322$	−0.544788	+	6.22696i	−0.0303599	+	0.347015i
$323$	3.36055	−	3.36055i	0.186986	−	0.186986i
$324$		0			0
$325$	8.36272	+	3.43805i	0.463880	+	0.190709i
$326$	19.8564	+	23.6639i	1.09974	+	1.31062i
$327$		0			0
$328$	−27.7020	+	19.3971i	−1.52959	+	1.07103i
$329$	2.96513	−	1.07922i	0.163473	−	0.0594993i
$330$		0			0
$331$	−2.17274	−	12.3222i	−0.119424	−	0.677290i	−0.984464	−	0.175586i	$-0.943818\pi$
$331$	−2.17274	−	12.3222i	−0.119424	−	0.677290i	0.865040	−	0.501704i	$-0.167293\pi$
$332$	−0.424541	+	1.58441i	−0.0232997	+	0.0869556i
$333$		0			0
$334$	1.60421	+	0.926193i	0.0877787	+	0.0506790i
$335$	−2.14895	−	2.92267i	−0.117409	−	0.159683i
$336$		0			0
$337$	21.7105	−	1.89942i	1.18265	−	0.103468i	0.521183	−	0.853445i	$-0.325491\pi$
$337$	21.7105	−	1.89942i	1.18265	−	0.103468i	0.661464	+	0.749977i	$0.269935\pi$
$338$	−13.1949	+	1.15440i	−0.717706	+	0.0627912i
$339$		0			0
$340$	−0.120154	−	0.163415i	−0.00651625	−	0.00886242i
$341$	−4.37989	−	2.52873i	−0.237184	−	0.136938i
$342$		0			0
$343$	2.13356	−	7.96256i	0.115202	−	0.429938i
$344$	−0.560037	−	3.17613i	−0.0301952	−	0.171245i
$345$		0			0
$346$	23.4555	−	8.53711i	1.26098	−	0.458958i
$347$	−21.9674	+	15.3818i	−1.17927	+	0.825736i	−0.987795	−	0.155761i	$-0.950217\pi$
$347$	−21.9674	+	15.3818i	−1.17927	+	0.825736i	−0.191478	+	0.981497i	$0.561328\pi$
$348$		0			0
$349$	−6.78403	−	8.08489i	−0.363141	−	0.432774i	0.553277	−	0.832997i	$-0.313377\pi$
$349$	−6.78403	−	8.08489i	−0.363141	−	0.432774i	−0.916418	+	0.400223i	$0.868933\pi$
$350$	3.79784	−	1.58490i	0.203003	−	0.0847167i
$351$		0			0
$352$	−0.790247	+	0.790247i	−0.0421203	+	0.0421203i
$353$	−1.15719	+	13.2268i	−0.0615911	+	0.703989i	0.901140	+	0.433528i	$0.142732\pi$
$353$	−1.15719	+	13.2268i	−0.0615911	+	0.703989i	−0.962731	+	0.270461i	$0.912824\pi$
$354$		0			0
$355$	−0.494215	−	21.3539i	−0.0262302	−	1.13335i
$356$	0.359965	+	0.988995i	0.0190781	+	0.0524166i
$357$		0			0
$358$	−11.5227	+	16.4561i	−0.608992	+	0.869731i
$359$	6.52848	+	11.3077i	0.344560	+	0.596796i	0.985274	−	0.170984i	$-0.0546947\pi$
$359$	6.52848	+	11.3077i	0.344560	+	0.596796i	−0.640714	+	0.767780i	$0.721361\pi$
$360$		0			0
$361$	20.0901	−	34.7970i	1.05737	−	1.83142i
$362$	2.61558	+	5.60913i	0.137472	+	0.294809i
$363$		0			0
$364$	−0.103191	+	0.122979i	−0.00540870	+	0.00644584i
$365$	17.3303	−	5.07620i	0.907107	−	0.265700i
$366$		0			0
$367$	11.4204	−	5.32542i	0.596140	−	0.277985i	−0.101038	−	0.994883i	$-0.532216\pi$
$367$	11.4204	−	5.32542i	0.596140	−	0.277985i	0.697178	+	0.716898i	$0.254439\pi$
$368$	7.24287	+	27.0308i	0.377561	+	1.40908i
$369$		0			0
$370$	11.4085	−	10.0317i	0.593098	−	0.521523i
$371$	−0.194522	+	0.0342995i	−0.0100991	+	0.00178074i
$372$		0			0
$373$	−30.1641	−	14.0658i	−1.56184	−	0.728297i	−0.566439	−	0.824104i	$-0.691679\pi$
$373$	−30.1641	−	14.0658i	−1.56184	−	0.728297i	−0.995400	+	0.0958064i	$0.969457\pi$
$374$	0.196903	−	1.11669i	0.0101816	−	0.0577429i
$375$		0			0
$376$	11.6841	−	9.80414i	0.602562	−	0.505610i
$377$	6.93424	+	6.93424i	0.357131	+	0.357131i
$378$		0			0
$379$			13.6970i			0.703566i	0.936082	+	0.351783i	$0.114424\pi$
$379$			13.6970i			0.703566i	−0.936082	+	0.351783i	$0.885576\pi$
$380$	−1.97188	−	1.57832i	−0.101155	−	0.0809659i
$381$		0			0
$382$	14.0789	+	20.1068i	0.720339	+	1.02875i
$383$	1.77906	−	3.81521i	0.0909059	−	0.194948i	−0.855598	−	0.517641i	$-0.826810\pi$
$383$	1.77906	−	3.81521i	0.0909059	−	0.194948i	0.946504	+	0.322693i	$0.104588\pi$
$384$		0			0
$385$	−1.66942	−	0.731926i	−0.0850814	−	0.0373024i
$386$	−7.33715	+	4.23610i	−0.373451	+	0.215612i
$387$		0			0
$388$	−1.48088	+	0.396801i	−0.0751804	+	0.0201445i
$389$	7.63677	+	2.77956i	0.387200	+	0.140929i	0.528283	−	0.849069i	$-0.322836\pi$
$389$	7.63677	+	2.77956i	0.387200	+	0.140929i	−0.141083	+	0.989998i	$0.545058\pi$
$390$		0			0
$391$	3.59414	+	3.01584i	0.181763	+	0.152517i
$392$	−1.68988	−	19.3154i	−0.0853520	−	0.975577i
$393$		0			0
$394$	2.43772	−	6.69758i	0.122810	−	0.337419i
$395$	−6.52971	+	19.3199i	−0.328546	+	0.972088i
$396$		0			0
$397$	23.0217	+	6.16864i	1.15543	+	0.309595i	0.785137	−	0.619322i	$-0.212592\pi$
$397$	23.0217	+	6.16864i	1.15543	+	0.309595i	0.370288	+	0.928917i	$0.379259\pi$
$398$	−17.9108	−	12.5413i	−0.897788	−	0.628638i
$399$		0			0
$400$	13.5505	−	12.4829i	0.677527	−	0.624146i
$401$	12.0856	+	2.13102i	0.603527	+	0.106418i	0.467059	−	0.884226i	$-0.345314\pi$
$401$	12.0856	+	2.13102i	0.603527	+	0.106418i	0.136468	+	0.990644i	$0.456425\pi$
$402$		0			0
$403$	−6.75736	−	0.591193i	−0.336608	−	0.0294494i
$404$	−1.11095			−0.0552721
$405$		0			0
$406$	4.46329			0.221509
$407$	−6.70341	−	0.586472i	−0.332276	−	0.0290703i
$408$		0			0
$409$	−0.997728	−	0.175926i	−0.0493345	−	0.00869900i	0.148926	−	0.988848i	$-0.452418\pi$
$409$	−0.997728	−	0.175926i	−0.0493345	−	0.00869900i	−0.198261	+	0.980149i	$0.563529\pi$
$410$	−34.2252	−	8.32686i	−1.69026	−	0.411234i
$411$		0			0
$412$	−2.15778	−	1.51090i	−0.106306	−	0.0744365i
$413$	−6.06833	−	1.62601i	−0.298603	−	0.0800105i
$414$		0			0
$415$	−22.3892	+	11.0780i	−1.09904	+	0.543797i
$416$	−0.512661	+	1.40852i	−0.0251353	+	0.0690586i
$417$		0			0
$418$	−1.23063	−	14.0662i	−0.0601923	−	0.688001i
$419$	−16.2085	−	13.6005i	−0.791837	−	0.664430i	0.154362	−	0.988014i	$-0.450668\pi$
$419$	−16.2085	−	13.6005i	−0.791837	−	0.664430i	−0.946199	+	0.323584i	$0.895112\pi$
$420$		0			0
$421$	−13.4378	−	4.89097i	−0.654920	−	0.238371i	−0.00687840	−	0.999976i	$-0.502189\pi$
$421$	−13.4378	−	4.89097i	−0.654920	−	0.238371i	−0.648042	+	0.761605i	$0.724412\pi$
$422$	27.5283	−	7.37620i	1.34006	−	0.359068i
$423$		0			0
$424$	−0.826860	+	0.477388i	−0.0401558	+	0.0231840i
$425$	0.660583	−	3.01747i	0.0320430	−	0.146369i
$426$		0			0
$427$	−0.255353	+	0.547606i	−0.0123574	+	0.0265005i
$428$	0.624023	+	0.891198i	0.0301633	+	0.0430777i
$429$		0			0
$430$	2.09912	−	2.62256i	0.101229	−	0.126471i
$431$			9.05726i			0.436273i	0.975918	+	0.218136i	$0.0699978\pi$
$431$			9.05726i			0.436273i	−0.975918	+	0.218136i	$0.930002\pi$
$432$		0			0
$433$	−9.70288	−	9.70288i	−0.466290	−	0.466290i	0.434420	−	0.900710i	$-0.356953\pi$
$433$	−9.70288	−	9.70288i	−0.466290	−	0.466290i	−0.900710	+	0.434420i	$0.856953\pi$
$434$	−2.36498	+	1.98446i	−0.113523	+	0.0952570i
$435$		0			0
$436$	−0.0676401	+	0.383606i	−0.00323937	+	0.0183714i
$437$	52.9501	+	24.6910i	2.53294	+	1.18113i
$438$		0			0
$439$	7.70527	−	1.35865i	0.367752	−	0.0648447i	0.0132817	−	0.999912i	$-0.495772\pi$
$439$	7.70527	−	1.35865i	0.367752	−	0.0648447i	0.354471	+	0.935067i	$0.384661\pi$
$440$	−8.79294	−	0.564635i	−0.419187	−	0.0269179i
$441$		0			0
$442$	−0.393622	−	1.46902i	−0.0187227	−	0.0698740i
$443$	−8.90936	+	4.15450i	−0.423297	+	0.197386i	−0.622581	−	0.782555i	$-0.713916\pi$
$443$	−8.90936	+	4.15450i	−0.423297	+	0.197386i	0.199285	+	0.979942i	$0.436138\pi$
$444$		0			0
$445$	−7.69064	+	14.0623i	−0.364571	+	0.666616i
$446$	−14.1287	+	16.8379i	−0.669013	+	0.797299i
$447$		0			0
$448$	2.17136	+	4.65650i	0.102587	+	0.219999i
$449$	0.516059	−	0.893841i	0.0243543	−	0.0421830i	−0.853591	−	0.520943i	$-0.825580\pi$
$449$	0.516059	−	0.893841i	0.0243543	−	0.0421830i	0.877946	+	0.478760i	$0.158914\pi$
$450$		0			0
$451$	7.80096	+	13.5117i	0.367333	+	0.636239i
$452$	−0.651722	+	0.930755i	−0.0306544	+	0.0437790i
$453$		0			0
$454$	4.87234	+	13.3867i	0.228670	+	0.628267i
$455$	−2.44415	+	0.0565675i	−0.114584	+	0.00265192i
$456$		0			0
$457$	0.333737	−	3.81463i	0.0156115	−	0.178441i	−0.984386	−	0.176026i	$-0.943676\pi$
$457$	0.333737	−	3.81463i	0.0156115	−	0.178441i	0.999997	−	0.00241489i	$-0.000768684\pi$
$458$	−8.14635	+	8.14635i	−0.380654	+	0.380654i
$459$		0			0
$460$	1.38255	−	2.07508i	0.0644619	−	0.0967510i
$461$	−5.22971	−	6.23252i	−0.243572	−	0.290278i	0.630384	−	0.776284i	$-0.282898\pi$
$461$	−5.22971	−	6.23252i	−0.243572	−	0.290278i	−0.873955	+	0.486006i	$0.838453\pi$
$462$		0			0
$463$	24.1647	−	16.9203i	1.12303	−	0.786354i	0.143901	−	0.989592i	$-0.454035\pi$
$463$	24.1647	−	16.9203i	1.12303	−	0.786354i	0.979129	+	0.203238i	$0.0651465\pi$
$464$	18.7769	−	6.83422i	0.871694	−	0.317271i
$465$		0			0
$466$	3.10467	+	17.6075i	0.143821	+	0.815650i
$467$	3.40841	−	12.7204i	0.157723	−	0.588629i	−0.841134	−	0.540826i	$-0.818112\pi$
$467$	3.40841	−	12.7204i	0.157723	−	0.588629i	0.998857	−	0.0478022i	$-0.0152217\pi$
$468$		0			0
$469$	0.849464	+	0.490438i	0.0392246	+	0.0226463i
$470$	15.7048	+	2.39593i	0.724409	+	0.110516i
$471$		0			0
$472$	−30.2520	+	2.64671i	−1.39246	+	0.121824i
$473$	−1.48226	+	0.129681i	−0.0681542	+	0.00596272i
$474$		0			0
$475$	−1.77948	−	38.4231i	−0.0816484	−	1.76297i
$476$	0.0474959	+	0.0274218i	0.00217697	+	0.00125688i
$477$		0			0
$478$	−0.533304	+	1.99032i	−0.0243928	+	0.0910350i
$479$	1.80216	+	10.2206i	0.0823429	+	0.466990i	0.997898	+	0.0647982i	$0.0206404\pi$
$479$	1.80216	+	10.2206i	0.0823429	+	0.466990i	−0.915555	+	0.402192i	$0.868249\pi$
$480$		0			0
$481$	−8.48082	+	3.08676i	−0.386692	+	0.140744i
$482$	−27.2997	+	19.1155i	−1.24347	+	0.870686i
$483$		0			0
$484$	−0.866613	−	1.03279i	−0.0393915	−	0.0469450i
$485$	−19.4301	−	12.9456i	−0.882275	−	0.587830i
$486$		0			0
$487$	−0.394954	+	0.394954i	−0.0178971	+	0.0178971i	−0.715999	−	0.698102i	$-0.754028\pi$
$487$	−0.394954	+	0.394954i	−0.0178971	+	0.0178971i	0.698102	+	0.715999i	$0.254028\pi$
$488$	−0.254550	+	2.90952i	−0.0115229	+	0.131708i
$489$		0			0
$490$	13.9459	−	14.6067i	0.630012	−	0.659865i
$491$	−4.58477	−	12.5966i	−0.206908	−	0.568475i	0.792220	−	0.610236i	$-0.208925\pi$
$491$	−4.58477	−	12.5966i	−0.206908	−	0.568475i	−0.999128	+	0.0417610i	$0.986703\pi$
$492$		0			0
$493$	1.92156	−	2.74428i	0.0865429	−	0.123596i
$494$	−9.46898	−	16.4008i	−0.426030	−	0.737905i
$495$		0			0
$496$	−6.91077	+	11.9698i	−0.310303	+	0.537460i
$497$	2.44078	+	5.23426i	0.109484	+	0.234789i
$498$		0			0
$499$	1.07489	−	1.28100i	0.0481187	−	0.0573456i	−0.741448	−	0.671010i	$-0.765861\pi$
$499$	1.07489	−	1.28100i	0.0481187	−	0.0573456i	0.789567	+	0.613664i	$0.210305\pi$
$500$	−1.63256	−	0.172238i	−0.0730101	−	0.00770272i
$501$		0			0
$502$	−8.77014	+	4.08958i	−0.391430	+	0.182527i
$503$	1.14574	+	4.27597i	0.0510861	+	0.190656i	0.986753	−	0.162227i	$-0.0518678\pi$
$503$	1.14574	+	4.27597i	0.0510861	+	0.190656i	−0.935667	+	0.352884i	$0.885201\pi$
$504$		0			0
$505$	−11.1720	−	12.7053i	−0.497149	−	0.565379i
$506$	13.7277	−	2.42057i	0.610273	−	0.107608i
$507$		0			0
$508$	1.15696	+	0.539501i	0.0513319	+	0.0239365i
$509$	−2.24592	+	12.7373i	−0.0995488	+	0.564569i	0.893709	+	0.448646i	$0.148094\pi$
$509$	−2.24592	+	12.7373i	−0.0995488	+	0.564569i	−0.993258	+	0.115923i	$0.963017\pi$
$510$		0			0
$511$	−3.74041	+	3.13858i	−0.165466	+	0.138843i
$512$	17.3890	+	17.3890i	0.768494	+	0.768494i
$513$		0			0
$514$			18.5953i			0.820202i
$515$	−4.42001	−	39.8712i	−0.194769	−	1.75694i
$516$		0			0
$517$	−4.03613	−	5.76419i	−0.177509	−	0.253509i
$518$	−1.73597	+	3.72279i	−0.0762739	+	0.163570i
$519$		0			0
$520$	−11.0084	+	4.29771i	−0.482750	+	0.188467i
$521$	−30.4199	+	17.5629i	−1.33272	+	0.769446i	−0.985716	−	0.168417i	$-0.946134\pi$
$521$	−30.4199	+	17.5629i	−1.33272	+	0.769446i	−0.347004	+	0.937864i	$0.612801\pi$
$522$		0			0
$523$	−17.4537	+	4.67671i	−0.763198	+	0.204498i	−0.619364	−	0.785104i	$-0.712610\pi$
$523$	−17.4537	+	4.67671i	−0.763198	+	0.204498i	−0.143834	+	0.989602i	$0.545943\pi$
$524$	−0.557755	−	0.203006i	−0.0243656	−	0.00886837i
$525$		0			0
$526$	−8.18795	−	6.87050i	−0.357011	−	0.299568i
$527$	0.201966	+	2.30848i	0.00879779	+	0.100559i
$528$		0			0
$529$	−11.8604	+	32.5861i	−0.515668	+	1.41679i
$530$	−0.942108	−	0.318413i	−0.0409226	−	0.0138310i
$531$		0			0
$532$	0.659659	+	0.176755i	0.0285999	+	0.00766331i
$533$	17.1413	+	12.0025i	0.742471	+	0.519884i
$534$		0			0
$535$	−3.91675	+	16.0987i	−0.169336	+	0.696007i
$536$	4.66928	+	0.823320i	0.201682	+	0.0355620i
$537$		0			0
$538$	−38.0781	−	3.33141i	−1.64167	−	0.143627i
$539$	−8.94525			−0.385299
$540$		0			0
$541$	34.9191			1.50129			0.750645	−	0.660705i	$-0.229743\pi$
$541$	34.9191			1.50129			0.750645	+	0.660705i	$0.229743\pi$
$542$	3.80933	+	0.333273i	0.163625	+	0.0143153i
$543$		0			0
$544$	0.504289	+	0.0889198i	0.0216212	+	0.00381240i
$545$	−5.06727	+	3.08408i	−0.217058	+	0.132107i
$546$		0			0
$547$	−30.4652	−	21.3320i	−1.30260	−	0.912089i	−0.303430	−	0.952854i	$-0.598132\pi$
$547$	−30.4652	−	21.3320i	−1.30260	−	0.912089i	−0.999169	+	0.0407643i	$0.987021\pi$
$548$	−1.94130	−	0.520169i	−0.0829281	−	0.0222205i
$549$		0			0
$550$	−5.60604	−	7.26603i	−0.239042	−	0.309825i
$551$	14.2681	−	39.2012i	0.607841	−	1.67003i
$552$		0			0
$553$	−0.480589	−	5.49316i	−0.0204367	−	0.233593i
$554$	−3.04522	−	2.55524i	−0.129379	−	0.108562i
$555$		0			0
$556$	0.868263	+	0.316022i	0.0368225	+	0.0134023i
$557$	−2.98290	+	0.799267i	−0.126390	+	0.0338660i	−0.321459	−	0.946923i	$-0.604173\pi$
$557$	−2.98290	+	0.799267i	−0.126390	+	0.0338660i	0.195070	+	0.980789i	$0.437507\pi$
$558$		0			0
$559$	−1.72826	+	0.997814i	−0.0730978	+	0.0422030i
$560$	−2.00028	+	4.56236i	−0.0845274	+	0.192795i
$561$		0			0
$562$	8.65473	−	18.5601i	0.365078	−	0.782912i
$563$	−0.209362	−	0.299000i	−0.00882355	−	0.0126013i	0.814716	−	0.579860i	$-0.196893\pi$
$563$	−0.209362	−	0.299000i	−0.00882355	−	0.0126013i	−0.823540	+	0.567259i	$0.808004\pi$
$564$		0			0
$565$	−17.1984	+	1.90656i	−0.723540	+	0.0802096i
$566$		−	18.8158i		−	0.790888i
$567$		0			0
$568$	19.7401	+	19.7401i	0.828275	+	0.828275i
$569$	27.7295	−	23.2678i	1.16248	−	0.975439i	0.162546	−	0.986701i	$-0.448029\pi$
$569$	27.7295	−	23.2678i	1.16248	−	0.975439i	0.999937	+	0.0112621i	$0.00358491\pi$
$570$		0			0
$571$	−2.67641	+	15.1787i	−0.112004	+	0.635207i	0.876186	+	0.481974i	$0.160080\pi$
$571$	−2.67641	+	15.1787i	−0.112004	+	0.635207i	−0.988190	+	0.153234i	$0.951031\pi$
$572$	0.324465	+	0.151300i	0.0135666	+	0.00632619i
$573$		0			0
$574$	9.37932	−	1.65383i	0.391485	−	0.0690294i
$575$	37.6347	−	5.05607i	1.56948	−	0.210853i
$576$		0			0
$577$	8.03655	+	29.9928i	0.334566	+	1.24862i	0.904339	+	0.426815i	$0.140365\pi$
$577$	8.03655	+	29.9928i	0.334566	+	1.24862i	−0.569773	+	0.821802i	$0.692969\pi$
$578$	20.5032	−	9.56078i	0.852819	−	0.397676i
$579$		0			0
$580$	−1.56209	−	0.854306i	−0.0648623	−	0.0354731i
$581$	4.34155	−	5.17406i	0.180118	−	0.214656i
$582$		0			0
$583$	0.186158	+	0.399217i	0.00770987	+	0.0165339i
$584$	−11.8010	+	20.4400i	−0.488330	+	0.845812i
$585$		0			0
$586$	−13.2079	−	22.8768i	−0.545615	−	0.945033i
$587$	19.3893	−	27.6907i	0.800280	−	1.14292i	−0.186754	−	0.982407i	$-0.559797\pi$
$587$	19.3893	−	27.6907i	0.800280	−	1.14292i	0.987034	−	0.160512i	$-0.0513145\pi$
$588$		0			0
$589$	9.86926	+	27.1156i	0.406656	+	1.11728i
$590$	−22.8772	−	21.8422i	−0.941838	−	0.899229i
$591$		0			0
$592$	−1.60277	+	18.3198i	−0.0658735	+	0.752937i
$593$	−21.3177	+	21.3177i	−0.875411	+	0.875411i	−0.993056	−	0.117644i	$-0.962466\pi$
$593$	−21.3177	+	21.3177i	−0.875411	+	0.875411i	0.117644	+	0.993056i	$0.462466\pi$
$594$		0			0
$595$	0.164025	+	0.818942i	0.00672435	+	0.0335734i
$596$	−0.320517	−	0.381978i	−0.0131289	−	0.0156464i
$597$		0			0
$598$	15.3149	−	10.7236i	0.626271	−	0.438520i
$599$	−30.7669	+	11.1982i	−1.25710	+	0.457548i	−0.882796	−	0.469757i	$-0.844341\pi$
$599$	−30.7669	+	11.1982i	−1.25710	+	0.457548i	−0.374307	+	0.927305i	$0.622119\pi$
$600$		0			0
$601$	7.03545	+	39.9000i	0.286982	+	1.62756i	0.698119	+	0.715982i	$0.254021\pi$
$601$	7.03545	+	39.9000i	0.286982	+	1.62756i	−0.411137	+	0.911574i	$0.634868\pi$
$602$	−0.235081	+	0.877332i	−0.00958117	+	0.0357574i
$603$		0			0
$604$	2.88960	+	1.66831i	0.117576	+	0.0678827i
$605$	3.09650	−	20.2969i	0.125891	−	0.825187i
$606$		0			0
$607$	27.2286	−	2.38219i	1.10517	−	0.0966903i	0.480069	−	0.877231i	$-0.340612\pi$
$607$	27.2286	−	2.38219i	1.10517	−	0.0966903i	0.625105	+	0.780540i	$0.285056\pi$
$608$	6.35218	−	0.555744i	0.257615	−	0.0225384i
$609$		0			0
$610$	−2.45085	+	1.80203i	−0.0992319	+	0.0729619i
$611$	−8.17344	−	4.71894i	−0.330662	−	0.190908i
$612$		0			0
$613$	9.10986	−	33.9985i	0.367944	−	1.37318i	−0.495442	−	0.868641i	$-0.664994\pi$
$613$	9.10986	−	33.9985i	0.367944	−	1.37318i	0.863386	−	0.504544i	$-0.168339\pi$
$614$	0.973249	+	5.51957i	0.0392771	+	0.222752i
$615$		0			0
$616$	2.23872	−	0.814828i	0.0902006	−	0.0328303i
$617$	−8.99369	+	6.29745i	−0.362072	+	0.253526i	−0.740430	−	0.672134i	$-0.765378\pi$
$617$	−8.99369	+	6.29745i	−0.362072	+	0.253526i	0.378357	+	0.925660i	$0.376489\pi$
$618$		0			0
$619$	4.17573	+	4.97644i	0.167837	+	0.200020i	0.843406	−	0.537276i	$-0.180547\pi$
$619$	4.17573	+	4.97644i	0.167837	+	0.200020i	−0.675570	+	0.737296i	$0.736102\pi$
$620$	1.20755	−	0.241859i	0.0484965	−	0.00971328i
$621$		0			0
$622$	3.51681	−	3.51681i	0.141011	−	0.141011i
$623$	0.377710	−	4.31725i	0.0151327	−	0.172967i
$624$		0			0
$625$	−14.4476	−	20.4026i	−0.577904	−	0.816105i
$626$	−9.06619	−	24.9091i	−0.362358	−	0.995570i
$627$		0			0
$628$	1.55519	−	2.22104i	0.0620588	−	0.0886291i
$629$	1.54160	+	2.67013i	0.0614676	+	0.106465i
$630$		0			0
$631$	−3.56646	+	6.17729i	−0.141979	+	0.245914i	−0.928242	−	0.371978i	$-0.878680\pi$
$631$	−3.56646	+	6.17729i	−0.141979	+	0.245914i	0.786263	+	0.617892i	$0.212013\pi$
$632$	−11.2645	−	24.1567i	−0.448076	−	0.960902i
$633$		0			0
$634$	−10.2701	+	12.2394i	−0.407878	+	0.486090i
$635$	5.46477	+	18.6568i	0.216863	+	0.740374i
$636$		0			0
$637$	−10.8735	+	5.07039i	−0.430823	+	0.200896i
$638$	−2.57613	−	9.61423i	−0.101990	−	0.380631i
$639$		0			0
$640$	−1.42012	+	22.1151i	−0.0561350	+	0.874178i
$641$	−22.7641	+	4.01393i	−0.899128	+	0.158541i	−0.604063	−	0.796937i	$-0.706452\pi$
$641$	−22.7641	+	4.01393i	−0.899128	+	0.158541i	−0.295065	+	0.955477i	$0.595341\pi$
$642$		0			0
$643$	19.3507	+	9.02340i	0.763119	+	0.355848i	0.764899	−	0.644150i	$-0.222789\pi$
$643$	19.3507	+	9.02340i	0.763119	+	0.355848i	−0.00178012	+	0.999998i	$0.500567\pi$
$644$	−0.117074	+	0.663961i	−0.00461337	+	0.0261637i
$645$		0			0
$646$	−4.95607	+	4.15863i	−0.194994	+	0.163619i
$647$	−10.9929	−	10.9929i	−0.432177	−	0.432177i	0.457192	−	0.889368i	$-0.348855\pi$
$647$	−10.9929	−	10.9929i	−0.432177	−	0.432177i	−0.889368	+	0.457192i	$0.848855\pi$
$648$		0			0
$649$			14.0101i			0.549945i
$650$	−10.9330	−	5.65465i	−0.428829	−	0.221794i
$651$		0			0
$652$	1.91110	+	2.72933i	0.0748445	+	0.106889i
$653$	11.2306	−	24.0841i	0.439488	−	0.942484i	−0.554417	−	0.832239i	$-0.687059\pi$
$653$	11.2306	−	24.0841i	0.439488	−	0.942484i	0.993904	−	0.110245i	$-0.0351636\pi$
$654$		0			0
$655$	−3.28727	−	8.42019i	−0.128444	−	0.329004i
$656$	36.9261	−	21.3193i	1.44172	−	0.832378i
$657$		0			0
$658$	−4.14915	+	1.11176i	−0.161751	+	0.0433410i
$659$	8.34013	+	3.03556i	0.324885	+	0.118249i	0.499314	−	0.866421i	$-0.333586\pi$
$659$	8.34013	+	3.03556i	0.324885	+	0.118249i	−0.174428	+	0.984670i	$0.555808\pi$
$660$		0			0
$661$	−25.3280	−	21.2527i	−0.985145	−	0.826635i	−0.000287075	−	1.00000i	$-0.500091\pi$
$661$	−25.3280	−	21.2527i	−0.985145	−	0.826635i	−0.984858	+	0.173365i	$0.944536\pi$
$662$	1.48454	+	16.9683i	0.0576981	+	0.659492i
$663$		0			0
$664$	11.1664	−	30.6794i	0.433340	−	1.19059i
$665$	4.61226	+	9.32162i	0.178856	+	0.361477i
$666$		0			0
$667$	39.7807	+	10.6592i	1.54032	+	0.412726i
$668$	0.163665	+	0.114599i	0.00633238	+	0.00443398i
$669$		0			0
$670$	2.56749	+	4.21850i	0.0991908	+	0.162975i
$671$	1.32697	+	0.233980i	0.0512270	+	0.00903270i
$672$		0			0
$673$	−33.5092	−	2.93167i	−1.29168	−	0.113008i	−0.579484	−	0.814984i	$-0.696746\pi$
$673$	−33.5092	−	2.93167i	−1.29168	−	0.113008i	−0.712201	+	0.701976i	$0.752301\pi$
$674$	−29.6677			−1.14276
$675$		0			0
$676$	−1.42863			−0.0549473
$677$	−26.5016	−	2.31859i	−1.01854	−	0.0891106i	−0.434363	−	0.900738i	$-0.643027\pi$
$677$	−26.5016	−	2.31859i	−1.01854	−	0.0891106i	−0.584176	+	0.811627i	$0.698582\pi$
$678$		0			0
$679$	6.21703	+	1.09623i	0.238588	+	0.0420695i
$680$	2.09895	+	3.44866i	0.0804909	+	0.132250i
$681$		0			0
$682$	5.63968	+	3.94895i	0.215955	+	0.151213i
$683$	−12.7453	−	3.41509i	−0.487684	−	0.130675i	0.00659412	−	0.999978i	$-0.497901\pi$
$683$	−12.7453	−	3.41509i	−0.487684	−	0.130675i	−0.494278	+	0.869304i	$0.664568\pi$
$684$		0			0
$685$	−13.5733	−	27.4324i	−0.518609	−	1.04814i
$686$	−3.83812	+	10.5451i	−0.146540	+	0.402615i
$687$		0			0
$688$	0.354404	+	4.05086i	0.0135115	+	0.154438i
$689$	0.452572	+	0.379753i	0.0172416	+	0.0144674i
$690$		0			0
$691$	−17.4857	−	6.36426i	−0.665186	−	0.242108i	−0.0127124	−	0.999919i	$-0.504047\pi$
$691$	−17.4857	−	6.36426i	−0.665186	−	0.242108i	−0.652474	+	0.757811i	$0.726269\pi$
$692$	2.60053	−	0.696810i	0.0988573	−	0.0264887i
$693$		0			0
$694$	31.6157	−	18.2533i	1.20012	−	0.692887i
$695$	5.11732	+	13.1078i	0.194111	+	0.497207i
$696$		0			0
$697$	3.02118	−	6.47894i	0.114435	−	0.245407i
$698$	8.24080	+	11.7691i	0.311919	+	0.445466i
$699$		0			0
$700$	0.422974	−	0.134595i	0.0159869	−	0.00508721i
$701$			35.6956i			1.34820i	0.738639	+	0.674102i	$0.235469\pi$
$701$			35.6956i			1.34820i	−0.738639	+	0.674102i	$0.764531\pi$
$702$		0			0
$703$	27.1479	+	27.1479i	1.02390	+	1.02390i
$704$	8.77716	−	7.36491i	0.330802	−	0.277576i
$705$		0			0
$706$	3.13861	−	17.7999i	0.118123	−	0.669909i
$707$	4.14598	+	1.93330i	0.155925	+	0.0727092i
$708$		0			0
$709$	−17.3058	+	3.05148i	−0.649933	+	0.114601i	−0.488888	−	0.872346i	$-0.662597\pi$
$709$	−17.3058	+	3.05148i	−0.649933	+	0.114601i	−0.161045	+	0.986947i	$0.551486\pi$
$710$	−1.86334	+	29.0173i	−0.0699298	+	1.08900i
$711$		0			0
$712$	−5.42180	−	20.2344i	−0.203190	−	0.758317i
$713$	−25.8181	+	12.0392i	−0.966894	+	0.450870i
$714$		0			0
$715$	1.53257	+	5.23222i	0.0573148	+	0.195674i
$716$	−1.39280	+	1.65987i	−0.0520514	+	0.0620324i
$717$		0			0
$718$	−7.51187	−	16.1093i	−0.280341	−	0.601192i
$719$	−13.2107	+	22.8817i	−0.492677	+	0.853342i	−0.999964	−	0.00843523i	$-0.997315\pi$
$719$	−13.2107	+	22.8817i	−0.492677	+	0.853342i	0.507287	+	0.861777i	$0.330648\pi$
$720$		0			0
$721$	5.42336	+	9.39353i	0.201976	+	0.349833i
$722$	−31.3733	+	44.8057i	−1.16759	+	1.66750i
$723$		0			0
$724$	0.228313	+	0.627285i	0.00848519	+	0.0233129i
$725$	−5.93861	−	26.4558i	−0.220555	−	0.982544i
$726$		0			0
$727$	−0.914614	+	10.4541i	−0.0339212	+	0.387721i	0.960189	+	0.279350i	$0.0901189\pi$
$727$	−0.914614	+	10.4541i	−0.0339212	+	0.387721i	−0.994111	+	0.108371i	$0.965437\pi$
$728$	2.25943	−	2.25943i	0.0837402	−	0.0837402i
$729$		0			0
$730$	−24.1044	+	4.82783i	−0.892143	+	0.178686i
$731$	0.438224	+	0.522256i	0.0162083	+	0.0193163i
$732$		0			0
$733$	−13.8177	+	9.67529i	−0.510370	+	0.357365i	−0.800219	−	0.599707i	$-0.795284\pi$
$733$	−13.8177	+	9.67529i	−0.510370	+	0.357365i	0.289849	+	0.957072i	$0.406395\pi$
$734$	−16.1194	+	5.86698i	−0.594978	+	0.216554i
$735$		0			0
$736$	1.09311	+	6.19933i	0.0402925	+	0.228510i
$737$	0.566144	−	2.11288i	0.0208542	−	0.0778288i
$738$		0			0
$739$	−31.2734	−	18.0557i	−1.15041	−	0.664190i	−0.201424	−	0.979504i	$-0.564557\pi$
$739$	−31.2734	−	18.0557i	−1.15041	−	0.664190i	−0.948988	+	0.315314i	$0.897890\pi$
$740$	1.32013	−	0.970651i	0.0485291	−	0.0356819i
$741$		0			0
$742$	0.267867	−	0.0234353i	0.00983370	−	0.000860337i
$743$	−21.5696	+	1.88710i	−0.791313	+	0.0692309i	−0.475643	−	0.879638i	$-0.657785\pi$
$743$	−21.5696	+	1.88710i	−0.791313	+	0.0692309i	−0.315670	+	0.948869i	$0.602229\pi$
$744$		0			0
$745$	1.14524	−	7.50683i	0.0419585	−	0.275029i
$746$	39.2377	+	22.6539i	1.43659	+	0.829417i
$747$		0			0
$748$	0.0316547	−	0.118137i	0.00115741	−	0.00431951i
$749$	−0.777919	−	4.41180i	−0.0284245	−	0.161204i
$750$		0			0
$751$	−14.1719	+	5.15816i	−0.517141	+	0.188224i	−0.587388	−	0.809306i	$-0.699844\pi$
$751$	−14.1719	+	5.15816i	−0.517141	+	0.188224i	0.0702468	+	0.997530i	$0.477621\pi$
$752$	−15.7530	+	11.0304i	−0.574452	+	0.402236i
$753$		0			0
$754$	−8.58102	−	10.2265i	−0.312502	−	0.372426i
$755$	9.97909	+	49.8236i	0.363176	+	1.81327i
$756$		0			0
$757$	−20.5414	+	20.5414i	−0.746590	+	0.746590i	−0.973837	−	0.227247i	$-0.927027\pi$
$757$	−20.5414	+	20.5414i	−0.746590	+	0.746590i	0.227247	+	0.973837i	$0.427027\pi$
$758$	1.62509	−	18.5749i	0.0590260	−	0.674670i
$759$		0			0
$760$	36.3608	+	34.7158i	1.31895	+	1.25928i
$761$	−9.96854	−	27.3884i	−0.361359	−	0.992827i	−0.978549	−	0.206013i	$-0.933951\pi$
$761$	−9.96854	−	27.3884i	−0.361359	−	0.992827i	0.617190	−	0.786814i	$-0.288271\pi$
$762$		0			0
$763$	0.919983	−	1.31387i	0.0333056	−	0.0475654i
$764$	1.32375	+	2.29281i	0.0478917	+	0.0829508i
$765$		0			0
$766$	−2.86530	+	4.96285i	−0.103528	+	0.179315i
$767$	7.94128	+	17.0301i	0.286743	+	0.614922i
$768$		0			0
$769$	10.6700	−	12.7160i	0.384770	−	0.458552i	−0.538543	−	0.842598i	$-0.681025\pi$
$769$	10.6700	−	12.7160i	0.384770	−	0.458552i	0.923314	+	0.384046i	$0.125470\pi$
$770$	2.17711	+	1.19066i	0.0784576	+	0.0429083i
$771$		0			0
$772$	−0.828193	+	0.386193i	−0.0298073	+	0.0138994i
$773$	−7.98684	−	29.8073i	−0.287267	−	1.07209i	−0.947167	−	0.320741i	$-0.896068\pi$
$773$	−7.98684	−	29.8073i	−0.287267	−	1.07209i	0.659900	−	0.751353i	$-0.270598\pi$
$774$		0			0
$775$	14.9094	+	11.3779i	0.535563	+	0.408704i
$776$	30.0516	−	5.29890i	1.07879	−	0.190219i
$777$		0			0
$778$	−10.0267	−	4.67552i	−0.359474	−	0.167625i
$779$	15.4578	−	87.6658i	0.553835	−	3.14095i
$780$		0			0
$781$	9.86620	−	8.27872i	0.353040	−	0.296236i
$782$	−4.51630	−	4.51630i	−0.161503	−	0.161503i
$783$		0			0
$784$			24.4465i			0.873089i
$785$	41.0400	−	4.54958i	1.46478	−	0.162381i
$786$		0			0
$787$	−31.1666	−	44.5105i	−1.11097	−	1.58663i	−0.759601	−	0.650389i	$-0.774606\pi$
$787$	−31.1666	−	44.5105i	−1.11097	−	1.58663i	−0.351367	−	0.936238i	$-0.614283\pi$
$788$	0.324892	−	0.696734i	0.0115738	−	0.0248201i
$789$		0			0
$790$	11.1474	−	25.4256i	0.396606	−	0.904601i
$791$	4.05188	−	2.33935i	0.144068	−	0.0831778i
$792$		0			0
$793$	1.74563	−	0.467741i	0.0619892	−	0.0166100i
$794$	−30.4885	−	11.0969i	−1.08200	−	0.393815i
$795$		0			0
$796$	−1.80661	−	1.51592i	−0.0640335	−	0.0537305i
$797$	−2.76406	−	31.5934i	−0.0979081	−	1.11909i	−0.873157	−	0.487439i	$-0.837931\pi$
$797$	−2.76406	−	31.5934i	−0.0979081	−	1.11909i	0.775249	−	0.631656i	$-0.217624\pi$
$798$		0			0
$799$	−1.10275	+	3.02977i	−0.0390124	+	0.107186i
$800$	3.28128	−	2.53164i	0.116011	−	0.0895069i
$801$		0			0
$802$	−16.1368	−	4.32385i	−0.569812	−	0.152681i
$803$	8.91961	+	6.24558i	0.314766	+	0.220402i
$804$		0			0
$805$	−8.77064	+	5.33805i	−0.309124	+	0.188141i
$806$	9.09373	+	1.60347i	0.320313	+	0.0564798i
$807$		0			0
$808$	22.0282	+	1.92722i	0.774950	+	0.0677993i
$809$	16.9032			0.594286			0.297143	−	0.954833i	$-0.403966\pi$
$809$	16.9032			0.594286			0.297143	+	0.954833i	$0.403966\pi$
$810$		0			0
$811$	3.82992			0.134487			0.0672434	−	0.997737i	$-0.478580\pi$
$811$	3.82992			0.134487			0.0672434	+	0.997737i	$0.478580\pi$
$812$	0.479577	+	0.0419575i	0.0168298	+	0.00147242i
$813$		0			0
$814$	9.02112	+	1.59067i	0.316190	+	0.0557528i
$815$	−11.9952	+	49.3030i	−0.420175	+	1.72701i
$816$		0			0
$817$	6.95415	+	4.86935i	0.243295	+	0.170357i
$818$	1.33218	+	0.356956i	0.0465785	+	0.0124807i
$819$		0			0
$820$	−3.59919	−	1.21645i	−0.125689	−	0.0424803i
$821$	−8.11493	+	22.2956i	−0.283213	+	0.778122i	0.713761	+	0.700389i	$0.246990\pi$
$821$	−8.11493	+	22.2956i	−0.283213	+	0.778122i	−0.996974	+	0.0777325i	$0.975232\pi$
$822$		0			0
$823$	−0.888066	−	10.1506i	−0.0309561	−	0.353829i	−0.995838	−	0.0911443i	$-0.970948\pi$
$823$	−0.888066	−	10.1506i	−0.0309561	−	0.353829i	0.964882	−	0.262685i	$-0.0846080\pi$
$824$	40.1639	+	33.7015i	1.39918	+	1.17405i
$825$		0			0
$826$	8.03654	+	2.92506i	0.279627	+	0.101776i
$827$	27.0882	−	7.25827i	0.941950	−	0.252395i	0.245007	−	0.969521i	$-0.421210\pi$
$827$	27.0882	−	7.25827i	0.941950	−	0.252395i	0.696943	+	0.717127i	$0.254543\pi$
$828$		0			0
$829$	27.7547	−	16.0242i	0.963962	−	0.556544i	0.0665716	−	0.997782i	$-0.478794\pi$
$829$	27.7547	−	16.0242i	0.963962	−	0.556544i	0.897390	+	0.441238i	$0.145461\pi$
$830$	31.6770	−	12.3668i	1.09953	−	0.429258i
$831$		0			0
$832$	6.49455	−	13.9276i	0.225158	−	0.482853i
$833$	2.35090	+	3.35743i	0.0814539	+	0.116328i
$834$		0			0
$835$	0.335251	+	3.02417i	0.0116019	+	0.104656i
$836$		−	1.52297i		−	0.0526731i
$837$		0			0
$838$	20.3672	+	20.3672i	0.703573	+	0.703573i
$839$	−11.5345	+	9.67859i	−0.398215	+	0.334142i	−0.819803	−	0.572645i	$-0.805917\pi$
$839$	−11.5345	+	9.67859i	−0.398215	+	0.334142i	0.421588	+	0.906787i	$0.361473\pi$
$840$		0			0
$841$	0.0706876	−	0.400889i	0.00243750	−	0.0138238i
$842$	17.6432	+	8.22715i	0.608024	+	0.283526i
$843$		0			0
$844$	3.02724	−	0.533784i	0.104202	−	0.0183736i
$845$	−14.3667	−	16.3384i	−0.494228	−	0.562057i
$846$		0			0
$847$	1.43684	+	5.36236i	0.0493704	+	0.184253i
$848$	1.09102	−	0.508751i	0.0374658	−	0.0174706i
$849$		0			0
$850$	−1.25385	+	4.01371i	−0.0430066	+	0.137669i
$851$	−24.3632	+	29.0349i	−0.835160	+	0.995304i
$852$		0			0
$853$	10.9551	+	23.4934i	0.375097	+	0.804398i	0.999724	+	0.0234754i	$0.00747313\pi$
$853$	10.9551	+	23.4934i	0.375097	+	0.804398i	−0.624627	+	0.780923i	$0.714749\pi$
$854$	0.411263	−	0.712329i	0.0140731	−	0.0243754i
$855$		0			0
$856$	−10.8272	−	18.7533i	−0.370068	−	0.640976i
$857$	9.96651	−	14.2337i	0.340450	−	0.486212i	−0.612022	−	0.790841i	$-0.709643\pi$
$857$	9.96651	−	14.2337i	0.340450	−	0.486212i	0.952471	+	0.304629i	$0.0985324\pi$
$858$		0			0
$859$	−8.27669	−	22.7400i	−0.282397	−	0.775879i	−0.997075	−	0.0764258i	$-0.975649\pi$
$859$	−8.27669	−	22.7400i	−0.282397	−	0.775879i	0.714678	−	0.699453i	$-0.246573\pi$
$860$	0.250203	−	0.262059i	0.00853185	−	0.00893613i
$861$		0			0
$862$	1.07461	−	12.2828i	0.0366013	−	0.418355i
$863$	34.9760	−	34.9760i	1.19060	−	1.19060i	0.213699	−	0.976900i	$-0.431449\pi$
$863$	34.9760	−	34.9760i	1.19060	−	1.19060i	0.976900	−	0.213699i	$-0.0685511\pi$
$864$		0			0
$865$	34.1206	+	22.7334i	1.16013	+	0.772958i
$866$	12.0072	+	14.3096i	0.408020	+	0.486259i
$867$		0			0
$868$	−0.272771	+	0.190996i	−0.00925844	+	0.00648283i
$869$	−11.5553	+	4.20577i	−0.391985	+	0.142671i
$870$		0			0
$871$	−0.509449	−	2.88923i	−0.0172620	−	0.0978979i
$872$	2.00664	−	7.48887i	0.0679533	−	0.253605i
$873$		0			0
$874$	−68.8777	−	39.7666i	−2.32982	−	1.34512i
$875$	5.79281	+	3.48377i	0.195833	+	0.117773i
$876$		0			0
$877$	−0.729539	+	0.0638264i	−0.0246348	+	0.00215526i	−0.0994665	−	0.995041i	$-0.531714\pi$
$877$	−0.729539	+	0.0638264i	−0.0246348	+	0.00215526i	0.0748317	+	0.997196i	$0.476158\pi$
$878$	−10.6106	+	0.928303i	−0.358089	+	0.0313287i
$879$		0			0
$880$	10.9822	+	1.67544i	0.370209	+	0.0564792i
$881$	−23.4491	−	13.5383i	−0.790020	−	0.456118i	0.0499497	−	0.998752i	$-0.484094\pi$
$881$	−23.4491	−	13.5383i	−0.790020	−	0.456118i	−0.839970	+	0.542634i	$0.817427\pi$
$882$		0			0
$883$	−4.83571	+	18.0471i	−0.162735	+	0.607334i	0.835584	+	0.549363i	$0.185130\pi$
$883$	−4.83571	+	18.0471i	−0.162735	+	0.607334i	−0.998318	+	0.0579709i	$0.981537\pi$
$884$	−0.0284848	−	0.161545i	−0.000958046	−	0.00543335i
$885$		0			0
$886$	12.5752	−	4.57699i	0.422471	−	0.153767i
$887$	10.1719	−	7.12245i	0.341539	−	0.239148i	−0.390204	−	0.920728i	$-0.627596\pi$
$887$	10.1719	−	7.12245i	0.341539	−	0.239148i	0.731744	+	0.681580i	$0.238707\pi$
$888$		0			0
$889$	−3.37883	−	4.02673i	−0.113322	−	0.135052i
$890$	12.0980	−	18.1578i	0.405524	−	0.608652i
$891$		0			0
$892$	−1.67640	+	1.67640i	−0.0561302	+	0.0561302i
$893$	−3.49921	+	39.9962i	−0.117097	+	1.33842i
$894$		0			0
$895$	−32.9893	+	0.763505i	−1.10271	+	0.0255212i
$896$	−2.04937	−	5.63061i	−0.0684648	−	0.188105i
$897$		0			0
$898$	−0.805895	+	1.15094i	−0.0268931	+	0.0384073i
$899$	10.1705	+	17.6158i	0.339204	+	0.587519i
$900$		0			0
$901$	0.100914	−	0.174789i	0.00336195	−	0.00582307i
$902$	−8.97602	−	19.2491i	−0.298869	−	0.640926i
$903$		0			0
$904$	14.5371	−	17.3246i	0.483496	−	0.576208i
$905$	−4.87790	+	8.91921i	−0.162147	+	0.296485i
$906$		0			0
$907$	−0.322094	+	0.150195i	−0.0106950	+	0.00498714i	−0.427958	−	0.903798i	$-0.640767\pi$
$907$	−0.322094	+	0.150195i	−0.0106950	+	0.00498714i	0.417263	+	0.908786i	$0.362989\pi$
$908$	0.397687	+	1.48419i	0.0131977	+	0.0492545i
$909$		0			0
$910$	3.32130	+	0.213276i	0.110100	+	0.00707003i
$911$	−39.6436	+	6.99023i	−1.31345	+	0.231597i	−0.786125	−	0.618067i	$-0.787916\pi$
$911$	−39.6436	+	6.99023i	−1.31345	+	0.231597i	−0.527324	+	0.849664i	$0.676805\pi$
$912$		0			0
$913$	−13.6512	−	6.36564i	−0.451787	−	0.210672i
$914$	−0.905182	+	5.13354i	−0.0299407	+	0.169802i
$915$		0			0
$916$	−0.951900	+	0.798739i	−0.0314517	+	0.0263911i
$917$	1.72821	+	1.72821i	0.0570707	+	0.0570707i
$918$		0			0
$919$		−	40.7569i		−	1.34445i	−0.740349	−	0.672223i	$-0.765340\pi$
$919$		−	40.7569i		−	1.34445i	0.740349	−	0.672223i	$-0.234660\pi$
$920$	−31.0133	+	38.7466i	−1.02248	+	1.27744i
$921$		0			0
$922$	6.35271	+	9.07260i	0.209215	+	0.298790i
$923$	7.30037	−	15.6557i	0.240294	−	0.515313i
$924$		0			0
$925$	24.3763	+	5.33646i	0.801489	+	0.175462i
$926$	−34.7781	+	20.0791i	−1.14288	+	0.659841i
$927$		0			0
$928$	4.34170	−	1.16336i	0.142523	−	0.0381890i
$929$	23.3744	+	8.50760i	0.766891	+	0.279125i	0.695695	−	0.718337i	$-0.255096\pi$
$929$	23.3744	+	8.50760i	0.766891	+	0.279125i	0.0711955	+	0.997462i	$0.477319\pi$
$930$		0			0
$931$	39.0973	+	32.8065i	1.28136	+	1.07519i
$932$	0.168074	+	1.92109i	0.00550545	+	0.0629275i
$933$		0			0
$934$	−6.13148	+	16.8461i	−0.200628	+	0.551221i
$935$	1.66939	−	0.825999i	0.0545948	−	0.0270130i
$936$		0			0
$937$	−23.0665	−	6.18064i	−0.753549	−	0.201913i	−0.138457	−	0.990368i	$-0.544214\pi$
$937$	−23.0665	−	6.18064i	−0.753549	−	0.201913i	−0.615092	+	0.788456i	$0.710881\pi$
$938$	−1.09380	−	0.765884i	−0.0357137	−	0.0250070i
$939$		0			0
$940$	1.66495	+	0.405076i	0.0543046	+	0.0132121i
$941$	53.8645	+	9.49777i	1.75593	+	0.309618i	0.956629	−	0.291308i	$-0.0940904\pi$
$941$	53.8645	+	9.49777i	1.75593	+	0.309618i	0.799304	+	0.600926i	$0.205202\pi$
$942$		0			0
$943$	87.5463	+	7.65931i	2.85090	+	0.249421i
$944$	38.2883			1.24618
$945$		0			0
$946$	2.02552			0.0658553
$947$	4.89270	+	0.428056i	0.158992	+	0.0139100i	0.166374	−	0.986063i	$-0.446794\pi$
$947$	4.89270	+	0.428056i	0.158992	+	0.0139100i	−0.00738203	+	0.999973i	$0.502350\pi$
$948$		0			0
$949$	14.3825	+	2.53602i	0.466875	+	0.0823226i
$950$	−2.14554	+	52.3179i	−0.0696105	+	1.69742i
$951$		0			0
$952$	−0.894188	−	0.626117i	−0.0289808	−	0.0202926i
$953$	12.3494	+	3.30900i	0.400035	+	0.107189i	0.453227	−	0.891395i	$-0.350273\pi$
$953$	12.3494	+	3.30900i	0.400035	+	0.107189i	−0.0531917	+	0.998584i	$0.516939\pi$
$954$		0			0
$955$	−12.9094	+	38.1960i	−0.417740	+	1.23599i
$956$	−0.0760133	+	0.208845i	−0.00245844	+	0.00675452i
$957$		0			0
$958$	−1.23134	−	14.0743i	−0.0397827	−	0.454719i
$959$	6.33952	+	5.31949i	0.204714	+	0.171775i
$960$		0			0
$961$	15.9091	+	5.79044i	0.513197	+	0.186789i
$962$	11.8673	−	3.17984i	0.382618	−	0.102522i
$963$		0			0
$964$	−3.11303	+	1.79731i	−0.100264	+	0.0578874i
$965$	−12.7452	−	5.58789i	−0.410281	−	0.179880i
$966$		0			0
$967$	15.9653	−	34.2378i	0.513411	−	1.10101i	−0.463250	−	0.886227i	$-0.653317\pi$
$967$	15.9653	−	34.2378i	0.513411	−	1.10101i	0.976661	−	0.214786i	$-0.0689053\pi$
$968$	15.3917	+	21.9817i	0.494709	+	0.706518i
$969$		0			0
$970$	24.8138	+	19.8613i	0.796724	+	0.637707i
$971$		−	17.4880i		−	0.561217i	−0.959822	−	0.280608i	$-0.909464\pi$
$971$		−	17.4880i		−	0.561217i	0.959822	−	0.280608i	$-0.0905362\pi$
$972$		0			0
$973$	−2.69033	−	2.69033i	−0.0862479	−	0.0862479i
$974$	0.582470	−	0.488750i	0.0186635	−	0.0156606i
$975$		0			0
$976$	0.639444	−	3.62647i	0.0204681	−	0.116080i
$977$	−55.0455	−	25.6682i	−1.76106	−	0.821197i	−0.980607	−	0.195986i	$-0.937209\pi$
$977$	−55.0455	−	25.6682i	−1.76106	−	0.821197i	−0.780456	−	0.625211i	$-0.785013\pi$
$978$		0			0
$979$	−9.51767	+	1.67822i	−0.304186	+	0.0536362i
$980$	1.63579	−	1.43838i	0.0522534	−	0.0459475i
$981$		0			0
$982$	4.72302	+	17.6266i	0.150718	+	0.562486i
$983$	22.0353	−	10.2752i	0.702816	−	0.327729i	−0.0381489	−	0.999272i	$-0.512146\pi$
$983$	22.0353	−	10.2752i	0.702816	−	0.327729i	0.740965	+	0.671543i	$0.234368\pi$
$984$		0			0
$985$	11.2353	−	3.29093i	0.357987	−	0.104858i
$986$	−2.93149	+	3.49362i	−0.0933577	+	0.111259i
$987$		0			0
$988$	−0.863258	−	1.85126i	−0.0274639	−	0.0588965i
$989$	−4.19049	+	7.25813i	−0.133250	+	0.230795i
$990$		0			0
$991$	−7.89179	−	13.6690i	−0.250691	−	0.434209i	0.713025	−	0.701138i	$-0.247324\pi$
$991$	−7.89179	−	13.6690i	−0.250691	−	0.434209i	−0.963716	+	0.266929i	$0.913991\pi$
$992$	−1.78331	+	2.54683i	−0.0566202	+	0.0808620i
$993$		0			0
$994$	−2.68899	−	7.38794i	−0.0852896	−	0.234331i
$995$	−0.831000	−	35.9056i	−0.0263445	−	1.13828i
$996$		0			0
$997$	0.356003	−	4.06914i	0.0112747	−	0.128871i	−0.988471	−	0.151409i	$-0.951619\pi$
$997$	0.356003	−	4.06914i	0.0112747	−	0.128871i	0.999746	+	0.0225378i	$0.00717461\pi$
$998$	−1.60968	+	1.60968i	−0.0509535	+	0.0509535i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.r.a.368.5		192
3.2	odd	2		135.2.q.a.113.12	yes	192
5.2	odd	4	inner	405.2.r.a.287.12		192
15.2	even	4		135.2.q.a.32.5	✓	192
15.8	even	4		675.2.ba.b.32.12		192
15.14	odd	2		675.2.ba.b.518.5		192
27.11	odd	18	inner	405.2.r.a.278.12		192
27.16	even	9		135.2.q.a.38.5	yes	192
135.43	odd	36		675.2.ba.b.632.5		192
135.92	even	36	inner	405.2.r.a.197.5		192
135.97	odd	36		135.2.q.a.92.12	yes	192
135.124	even	18		675.2.ba.b.443.12		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.5	✓	192	15.2	even	4
135.2.q.a.38.5	yes	192	27.16	even	9
135.2.q.a.92.12	yes	192	135.97	odd	36
135.2.q.a.113.12	yes	192	3.2	odd	2
405.2.r.a.197.5		192	135.92	even	36	inner
405.2.r.a.278.12		192	27.11	odd	18	inner
405.2.r.a.287.12		192	5.2	odd	4	inner
405.2.r.a.368.5		192	1.1	even	1	trivial
675.2.ba.b.32.12		192	15.8	even	4
675.2.ba.b.443.12		192	135.124	even	18
675.2.ba.b.518.5		192	15.14	odd	2
675.2.ba.b.632.5		192	135.43	odd	36

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)

\(f(q)\)	\(=\)	\(q+(-1.35613 - 0.118646i) q^{2} +(-0.144600 - 0.0254969i) q^{4} +(-1.16254 - 1.91010i) q^{5} +(0.495263 + 0.346787i) q^{7} +(2.82292 + 0.756400i) q^{8} +O(q^{10})\)	\(q+(-1.35613 - 0.118646i) q^{2} +(-0.144600 - 0.0254969i) q^{4} +(-1.16254 - 1.91010i) q^{5} +(0.495263 + 0.346787i) q^{7} +(2.82292 + 0.756400i) q^{8} +(1.34993 + 2.72828i) q^{10} +(0.461147 - 1.26699i) q^{11} +(-0.157610 - 1.80149i) q^{13} +(-0.630497 - 0.529050i) q^{14} +(-3.46256 - 1.26027i) q^{16} +(-0.596735 + 0.159895i) q^{17} +(-6.66221 + 3.84643i) q^{19} +(0.119402 + 0.305842i) q^{20} +(-0.775699 + 1.66349i) q^{22} +(-4.35606 - 6.22110i) q^{23} +(-2.29700 + 4.44115i) q^{25} +2.46176i q^{26} +(-0.0627730 - 0.0627730i) q^{28} +(-4.15413 + 3.48573i) q^{29} +(0.651351 - 3.69400i) q^{31} +(-0.751218 - 0.350299i) q^{32} +(0.828222 - 0.146038i) q^{34} +(0.0866357 - 1.34916i) q^{35} +(-1.29170 - 4.82067i) q^{37} +(9.49120 - 4.42582i) q^{38} +(-1.83696 - 6.27142i) q^{40} +(-7.43804 + 8.86431i) q^{41} +(-0.466380 - 1.00015i) q^{43} +(-0.0989861 + 0.171449i) q^{44} +(5.16928 + 8.95346i) q^{46} +(2.99349 - 4.27515i) q^{47} +(-2.26912 - 6.23435i) q^{49} +(3.64196 - 5.75025i) q^{50} +(-0.0231420 + 0.264514i) q^{52} +(-0.231010 + 0.231010i) q^{53} +(-2.95619 + 0.592089i) q^{55} +(1.13578 + 1.35357i) q^{56} +(6.04711 - 4.23423i) q^{58} +(-9.76428 + 3.55391i) q^{59} +(0.173537 + 0.984176i) q^{61} +(-1.32160 + 4.93227i) q^{62} +(7.35941 + 4.24896i) q^{64} +(-3.25781 + 2.39536i) q^{65} +(1.61617 - 0.141397i) q^{67} +(0.0903647 - 0.00790588i) q^{68} +(-0.277562 + 1.81936i) q^{70} +(8.27254 + 4.77616i) q^{71} +(-2.09021 + 7.80078i) q^{73} +(1.17975 + 6.69072i) q^{74} +(1.06143 - 0.386328i) q^{76} +(0.667764 - 0.467574i) q^{77} +(-5.86238 - 6.98651i) q^{79} +(1.61812 + 8.07897i) q^{80} +(11.1387 - 11.1387i) q^{82} +(0.973649 - 11.1289i) q^{83} +(0.999144 + 0.953942i) q^{85} +(0.513808 + 1.41168i) q^{86} +(2.26013 - 3.22780i) q^{88} +(-3.58395 - 6.20758i) q^{89} +(0.546675 - 0.946869i) q^{91} +(0.471268 + 1.01064i) q^{92} +(-4.56680 + 5.44250i) q^{94} +(15.0922 + 8.25389i) q^{95} +(9.46315 - 4.41274i) q^{97} +(2.33754 + 8.72382i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) 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

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