LMFDB - Embedded newform 765.2.cc.b.568.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [765,2,Mod(28,765)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(765, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 12, 7]))

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

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

chi := DirichletCharacter("765.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 765 = 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	765.cc (of order $16$, degree $8$, 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:	$6.10855575463$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$18$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 255)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			568.1
Character	$\chi$	$=$	765.568
Dual form			765.2.cc.b.532.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.03325 - 2.49449i) q^{2} +(-3.74064 + 3.74064i) q^{4} +(1.65882 - 1.49944i) q^{5} +(-0.128784 - 0.192738i) q^{7} +(8.20701 + 3.39946i) q^{8} +O(q^{10})$	\(q+(-1.03325 - 2.49449i) q^{2} +(-3.74064 + 3.74064i) q^{4} +(1.65882 - 1.49944i) q^{5} +(-0.128784 - 0.192738i) q^{7} +(8.20701 + 3.39946i) q^{8} +(-5.45431 - 2.58860i) q^{10} +(-1.99662 + 1.33410i) q^{11} +4.63849 q^{13} +(-0.347717 + 0.520396i) q^{14} -13.4046i q^{16} +(-1.87483 - 3.67219i) q^{17} +(-3.42730 - 1.41963i) q^{19} +(-0.596172 + 11.8139i) q^{20} +(5.39089 + 3.60208i) q^{22} +(0.825706 - 4.15110i) q^{23} +(0.503354 - 4.97460i) q^{25} +(-4.79272 - 11.5707i) q^{26} +(1.20270 + 0.239231i) q^{28} +(-1.70788 - 8.58610i) q^{29} +(2.18280 + 1.45850i) q^{31} +(-17.0236 + 7.05142i) q^{32} +(-7.22307 + 8.47103i) q^{34} +(-0.502628 - 0.126614i) q^{35} +(-1.72339 - 8.66406i) q^{37} +10.0162i q^{38} +(18.7112 - 6.66685i) q^{40} +(-0.945732 + 4.75451i) q^{41} +(0.153752 - 0.371191i) q^{43} +(2.47825 - 12.4590i) q^{44} +(-11.2080 + 2.22942i) q^{46} +9.73422i q^{47} +(2.65822 - 6.41751i) q^{49} +(-12.9292 + 3.88439i) q^{50} +(-17.3509 + 17.3509i) q^{52} +(-10.6910 + 4.42835i) q^{53} +(-1.31163 + 5.20683i) q^{55} +(-0.401723 - 2.01960i) q^{56} +(-19.6532 + 13.1319i) q^{58} +(0.594386 + 1.43498i) q^{59} +(-4.69467 - 0.933828i) q^{61} +(1.38283 - 6.95195i) q^{62} +(16.2223 + 16.2223i) q^{64} +(7.69442 - 6.95515i) q^{65} +(1.69680 + 1.69680i) q^{67} +(20.7494 + 6.72330i) q^{68} +(0.203503 + 1.38462i) q^{70} +(8.33019 - 12.4670i) q^{71} +(0.341001 - 0.510345i) q^{73} +(-19.8317 + 13.2511i) q^{74} +(18.1306 - 7.50994i) q^{76} +(0.514263 + 0.213015i) q^{77} +(-1.83806 - 2.75085i) q^{79} +(-20.0995 - 22.2358i) q^{80} +(12.8372 - 2.55349i) q^{82} +(4.21219 + 10.1691i) q^{83} +(-8.61624 - 3.28031i) q^{85} -1.08479 q^{86} +(-20.9215 + 4.16154i) q^{88} +(-1.93036 + 1.93036i) q^{89} +(-0.597362 - 0.894016i) q^{91} +(12.4391 + 18.6165i) q^{92} +(24.2819 - 10.0579i) q^{94} +(-7.81391 + 2.78412i) q^{95} +(-1.26576 + 1.89434i) q^{97} -18.7550 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q+O(q^{10}) $ 144 * q	$ 144 q - 16 q^{10} - 64 q^{14} - 32 q^{19} + 32 q^{20} - 16 q^{25} + 64 q^{26} - 64 q^{28} - 32 q^{31} + 32 q^{34} - 32 q^{37} + 112 q^{40} + 80 q^{41} - 16 q^{46} + 64 q^{50} - 64 q^{52} - 48 q^{53} - 64 q^{55} - 112 q^{58} - 32 q^{59} - 32 q^{64} + 64 q^{67} + 272 q^{68} - 32 q^{70} - 32 q^{71} - 80 q^{73} - 80 q^{74} + 64 q^{76} + 96 q^{77} + 32 q^{79} - 336 q^{80} + 16 q^{83} + 32 q^{85} - 64 q^{86} - 80 q^{88} - 320 q^{92} + 16 q^{94} + 64 q^{95} - 16 q^{97} - 144 q^{98}+O(q^{100}) $ 144 * q - 16 * q^10 - 64 * q^14 - 32 * q^19 + 32 * q^20 - 16 * q^25 + 64 * q^26 - 64 * q^28 - 32 * q^31 + 32 * q^34 - 32 * q^37 + 112 * q^40 + 80 * q^41 - 16 * q^46 + 64 * q^50 - 64 * q^52 - 48 * q^53 - 64 * q^55 - 112 * q^58 - 32 * q^59 - 32 * q^64 + 64 * q^67 + 272 * q^68 - 32 * q^70 - 32 * q^71 - 80 * q^73 - 80 * q^74 + 64 * q^76 + 96 * q^77 + 32 * q^79 - 336 * q^80 + 16 * q^83 + 32 * q^85 - 64 * q^86 - 80 * q^88 - 320 * q^92 + 16 * q^94 + 64 * q^95 - 16 * q^97 - 144 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/765\mathbb{Z}\right)^\times$.

$n$	$307$	$496$	$596$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{11}{16}\right)$	$1$

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 $

$2$	−1.03325	−	2.49449i	−0.730618	−	1.76387i	−0.640529	−	0.767934i	$-0.721285\pi$
$2$	−1.03325	−	2.49449i	−0.730618	−	1.76387i	−0.0900886	−	0.995934i	$-0.528715\pi$
$3$		0			0
$3$		0			0
$4$	−3.74064	+	3.74064i	−1.87032	+	1.87032i
$5$	1.65882	−	1.49944i	0.741846	−	0.670570i
$5$	1.65882	−	1.49944i	0.741846	−	0.670570i
$6$		0			0
$7$	−0.128784	−	0.192738i	−0.0486756	−	0.0728482i	0.806334	−	0.591461i	$-0.201449\pi$
$7$	−0.128784	−	0.192738i	−0.0486756	−	0.0728482i	−0.855009	+	0.518613i	$0.826449\pi$
$8$	8.20701	+	3.39946i	2.90162	+	1.20189i
$9$		0			0
$10$	−5.45431	−	2.58860i	−1.72480	−	0.818587i
$11$	−1.99662	+	1.33410i	−0.602003	+	0.402245i	−0.818889	−	0.573951i	$-0.805410\pi$
$11$	−1.99662	+	1.33410i	−0.602003	+	0.402245i	0.216887	+	0.976197i	$0.430410\pi$
$12$		0			0
$13$	4.63849			1.28649			0.643244	−	0.765662i	$-0.277588\pi$
$13$	4.63849			1.28649			0.643244	+	0.765662i	$0.277588\pi$
$14$	−0.347717	+	0.520396i	−0.0929313	+	0.139082i
$15$		0			0
$16$		−	13.4046i		−	3.35116i
$17$	−1.87483	−	3.67219i	−0.454713	−	0.890638i
$17$	−1.87483	−	3.67219i	−0.454713	−	0.890638i
$18$		0			0
$19$	−3.42730	−	1.41963i	−0.786275	−	0.325686i	−0.0468304	−	0.998903i	$-0.514912\pi$
$19$	−3.42730	−	1.41963i	−0.786275	−	0.325686i	−0.739445	+	0.673217i	$0.764912\pi$
$20$	−0.596172	+	11.8139i	−0.133308	+	2.64167i
$21$		0			0
$22$	5.39089	+	3.60208i	1.14934	+	0.767966i
$23$	0.825706	−	4.15110i	0.172172	−	0.865565i	−0.794050	−	0.607853i	$-0.792031\pi$
$23$	0.825706	−	4.15110i	0.172172	−	0.865565i	0.966222	−	0.257713i	$-0.0829688\pi$
$24$		0			0
$25$	0.503354	−	4.97460i	0.100671	−	0.994920i
$26$	−4.79272	−	11.5707i	−0.939930	−	2.26919i
$27$		0			0
$28$	1.20270	+	0.239231i	0.227288	+	0.0452105i
$29$	−1.70788	−	8.58610i	−0.317146	−	1.59440i	−0.729899	−	0.683555i	$-0.760433\pi$
$29$	−1.70788	−	8.58610i	−0.317146	−	1.59440i	0.412753	−	0.910843i	$-0.364567\pi$
$30$		0			0
$31$	2.18280	+	1.45850i	0.392042	+	0.261954i	0.735931	−	0.677056i	$-0.236745\pi$
$31$	2.18280	+	1.45850i	0.392042	+	0.261954i	−0.343889	+	0.939010i	$0.611745\pi$
$32$	−17.0236	+	7.05142i	−3.00938	+	1.24653i
$33$		0			0
$34$	−7.22307	+	8.47103i	−1.23875	+	1.45277i
$35$	−0.502628	−	0.126614i	−0.0849597	−	0.0214017i
$36$		0			0
$37$	−1.72339	−	8.66406i	−0.283323	−	1.42436i	−0.816004	−	0.578046i	$-0.803815\pi$
$37$	−1.72339	−	8.66406i	−0.283323	−	1.42436i	0.532681	−	0.846316i	$-0.321185\pi$
$38$			10.0162i			1.62484i
$39$		0			0
$40$	18.7112	−	6.66685i	2.95850	−	1.05412i
$41$	−0.945732	+	4.75451i	−0.147698	+	0.742530i	0.833951	+	0.551838i	$0.186073\pi$
$41$	−0.945732	+	4.75451i	−0.147698	+	0.742530i	−0.981650	+	0.190692i	$0.938927\pi$
$42$		0			0
$43$	0.153752	−	0.371191i	0.0234470	−	0.0566061i	−0.911722	−	0.410807i	$-0.865247\pi$
$43$	0.153752	−	0.371191i	0.0234470	−	0.0566061i	0.935169	+	0.354201i	$0.115247\pi$
$44$	2.47825	−	12.4590i	0.373610	−	1.87827i
$45$		0			0
$46$	−11.2080	+	2.22942i	−1.65253	+	0.328709i
$47$			9.73422i			1.41988i	0.704261	+	0.709941i	$0.251278\pi$
$47$			9.73422i			1.41988i	−0.704261	+	0.709941i	$0.748722\pi$
$48$		0			0
$49$	2.65822	−	6.41751i	0.379746	−	0.916788i
$50$	−12.9292	+	3.88439i	−1.82846	+	0.549336i
$51$		0			0
$52$	−17.3509	+	17.3509i	−2.40614	+	2.40614i
$53$	−10.6910	+	4.42835i	−1.46852	+	0.608280i	−0.966521	−	0.256588i	$-0.917402\pi$
$53$	−10.6910	+	4.42835i	−1.46852	+	0.608280i	−0.501998	+	0.864869i	$0.667402\pi$
$54$		0			0
$55$	−1.31163	+	5.20683i	−0.176859	+	0.702089i
$56$	−0.401723	−	2.01960i	−0.0536825	−	0.269880i
$57$		0			0
$58$	−19.6532	+	13.1319i	−2.58059	+	1.72430i
$59$	0.594386	+	1.43498i	0.0773825	+	0.186818i	0.957837	−	0.287314i	$-0.0927622\pi$
$59$	0.594386	+	1.43498i	0.0773825	+	0.186818i	−0.880454	+	0.474131i	$0.842762\pi$
$60$		0			0
$61$	−4.69467	−	0.933828i	−0.601091	−	0.119564i	−0.114841	−	0.993384i	$-0.536636\pi$
$61$	−4.69467	−	0.933828i	−0.601091	−	0.119564i	−0.486250	+	0.873820i	$0.661636\pi$
$62$	1.38283	−	6.95195i	0.175619	−	0.882899i
$63$		0			0
$64$	16.2223	+	16.2223i	2.02779	+	2.02779i
$65$	7.69442	−	6.95515i	0.954375	−	0.862680i
$66$		0			0
$67$	1.69680	+	1.69680i	0.207297	+	0.207297i	0.803118	−	0.595820i	$-0.203173\pi$
$67$	1.69680	+	1.69680i	0.207297	+	0.207297i	−0.595820	+	0.803118i	$0.703173\pi$
$68$	20.7494	+	6.72330i	2.51624	+	0.815319i
$69$		0			0
$70$	0.203503	+	1.38462i	0.0243232	+	0.165494i
$71$	8.33019	−	12.4670i	0.988612	−	1.47956i	0.114746	−	0.993395i	$-0.463395\pi$
$71$	8.33019	−	12.4670i	0.988612	−	1.47956i	0.873866	−	0.486167i	$-0.161605\pi$
$72$		0			0
$73$	0.341001	−	0.510345i	0.0399112	−	0.0597313i	−0.810977	−	0.585077i	$-0.801064\pi$
$73$	0.341001	−	0.510345i	0.0399112	−	0.0597313i	0.850889	+	0.525346i	$0.176064\pi$
$74$	−19.8317	+	13.2511i	−2.30539	+	1.54041i
$75$		0			0
$76$	18.1306	−	7.50994i	2.07972	−	0.861449i
$77$	0.514263	+	0.213015i	0.0586057	+	0.0242753i
$78$		0			0
$79$	−1.83806	−	2.75085i	−0.206798	−	0.309495i	0.713543	−	0.700611i	$-0.247089\pi$
$79$	−1.83806	−	2.75085i	−0.206798	−	0.309495i	−0.920341	+	0.391116i	$0.872089\pi$
$80$	−20.0995	−	22.2358i	−2.24719	−	2.48604i
$81$		0			0
$82$	12.8372	−	2.55349i	1.41764	−	0.281985i
$83$	4.21219	+	10.1691i	0.462348	+	1.11621i	0.967431	+	0.253136i	$0.0814622\pi$
$83$	4.21219	+	10.1691i	0.462348	+	1.11621i	−0.505082	+	0.863071i	$0.668538\pi$
$84$		0			0
$85$	−8.61624	−	3.28031i	−0.934562	−	0.355799i
$86$	−1.08479			−0.116976
$87$		0			0
$88$	−20.9215	+	4.16154i	−2.23024	+	0.443622i
$89$	−1.93036	+	1.93036i	−0.204618	+	0.204618i	−0.801975	−	0.597357i	$-0.796217\pi$
$89$	−1.93036	+	1.93036i	−0.204618	+	0.204618i	0.597357	+	0.801975i	$0.296217\pi$
$90$		0			0
$91$	−0.597362	−	0.894016i	−0.0626206	−	0.0937183i
$92$	12.4391	+	18.6165i	1.29687	+	1.94090i
$93$		0			0
$94$	24.2819	−	10.0579i	2.50448	−	1.03739i
$95$	−7.81391	+	2.78412i	−0.801691	+	0.285644i
$96$		0			0
$97$	−1.26576	+	1.89434i	−0.128518	+	0.192341i	−0.890148	−	0.455671i	$-0.849399\pi$
$97$	−1.26576	+	1.89434i	−0.128518	+	0.192341i	0.761630	+	0.648012i	$0.224399\pi$
$98$	−18.7550			−1.89454
$99$		0			0
$100$	16.7253	+	20.4910i	1.67253	+	2.04910i
$101$		−	13.3521i		−	1.32858i	−0.747474	−	0.664291i	$-0.768733\pi$
$101$		−	13.3521i		−	1.32858i	0.747474	−	0.664291i	$-0.231267\pi$
$102$		0			0
$103$	−2.55818	−	2.55818i	−0.252065	−	0.252065i	0.569752	−	0.821817i	$-0.307039\pi$
$103$	−2.55818	−	2.55818i	−0.252065	−	0.252065i	−0.821817	+	0.569752i	$0.807039\pi$
$104$	38.0682	+	15.7684i	3.73289	+	1.54621i
$105$		0			0
$106$	22.0929	+	22.0929i	2.14585	+	2.14585i
$107$	10.6901	+	7.14290i	1.03345	+	0.690531i	0.951985	−	0.306145i	$-0.0990394\pi$
$107$	10.6901	+	7.14290i	1.03345	+	0.690531i	0.0814674	+	0.996676i	$0.474039\pi$
$108$		0			0
$109$	4.78880	+	0.952552i	0.458684	+	0.0912379i	0.419024	−	0.907975i	$-0.362372\pi$
$109$	4.78880	+	0.952552i	0.458684	+	0.0912379i	0.0396603	+	0.999213i	$0.487372\pi$
$110$	14.3436	−	2.10813i	1.36761	−	0.201002i
$111$		0			0
$112$	−2.58359	+	1.72630i	−0.244126	+	0.163120i
$113$	7.23760	+	1.43965i	0.680856	+	0.135431i	0.523389	−	0.852094i	$-0.324667\pi$
$113$	7.23760	+	1.43965i	0.680856	+	0.135431i	0.157467	+	0.987524i	$0.449667\pi$
$114$		0			0
$115$	−4.85464	−	8.12402i	−0.452698	−	0.757569i
$116$	38.5061	+	25.7289i	3.57520	+	2.38887i
$117$		0			0
$118$	2.96538	−	2.96538i	0.272985	−	0.272985i
$119$	−0.466325	+	0.834270i	−0.0427480	+	0.0764774i
$120$		0			0
$121$	−2.00285	+	4.83531i	−0.182077	+	0.439574i
$122$	2.52135	+	12.6757i	0.228272	+	1.14760i
$123$		0			0
$124$	−13.6208	+	2.70934i	−1.22318	+	0.243306i
$125$	−6.62414	−	9.00670i	−0.592481	−	0.805584i
$126$		0			0
$127$	3.42848	−	8.27709i	0.304229	−	0.734473i	−0.695642	−	0.718389i	$-0.744880\pi$
$127$	3.42848	−	8.27709i	0.304229	−	0.734473i	0.999871	−	0.0160846i	$-0.00512010\pi$
$128$	9.60179	−	23.1808i	0.848687	−	2.04891i
$129$		0			0
$130$	−25.2998	−	12.0072i	−2.21894	−	1.05310i
$131$	−0.825089	+	0.164120i	−0.0720884	+	0.0143393i	−0.231003	−	0.972953i	$-0.574201\pi$
$131$	−0.825089	+	0.164120i	−0.0720884	+	0.0143393i	0.158914	+	0.987292i	$0.449201\pi$
$132$		0			0
$133$	0.167762	+	0.843396i	0.0145468	+	0.0731317i
$134$	2.47943	−	5.98586i	0.214190	−	0.517100i
$135$		0			0
$136$	−2.90328	−	36.5111i	−0.248954	−	3.13080i
$137$	7.82486	−	7.82486i	0.668523	−	0.668523i	−0.288851	−	0.957374i	$-0.593273\pi$
$137$	7.82486	−	7.82486i	0.668523	−	0.668523i	0.957374	+	0.288851i	$0.0932732\pi$
$138$		0			0
$139$	5.08042	+	3.39463i	0.430916	+	0.287929i	0.752051	−	0.659105i	$-0.229065\pi$
$139$	5.08042	+	3.39463i	0.430916	+	0.287929i	−0.321136	+	0.947033i	$0.604065\pi$
$140$	2.35377	−	1.40653i	0.198930	−	0.118874i
$141$		0			0
$142$	−39.7059	−	7.89800i	−3.33205	−	0.662786i
$143$	−9.26130	+	6.18820i	−0.774469	+	0.517484i
$144$		0			0
$145$	−15.7074	−	11.6819i	−1.30443	−	0.970129i
$146$	−1.62539	−	0.323309i	−0.134518	−	0.0267573i
$147$		0			0
$148$	38.8557	+	25.9625i	3.19392	+	2.13411i
$149$	−7.15371	−	7.15371i	−0.586055	−	0.586055i	0.350506	−	0.936560i	$-0.386010\pi$
$149$	−7.15371	−	7.15371i	−0.586055	−	0.586055i	−0.936560	+	0.350506i	$0.886010\pi$
$150$		0			0
$151$	−16.7122	−	6.92240i	−1.36002	−	0.563337i	−0.420953	−	0.907083i	$-0.638304\pi$
$151$	−16.7122	−	6.92240i	−1.36002	−	0.563337i	−0.939063	+	0.343746i	$0.888304\pi$
$152$	−23.3019	−	23.3019i	−1.89003	−	1.89003i
$153$		0			0
$154$		−	1.50292i		−	0.121109i
$155$	5.80780	−	0.853592i	0.466494	−	0.0685622i
$156$		0			0
$157$	10.2083			0.814707			0.407354	−	0.913270i	$-0.366452\pi$
$157$	10.2083			0.814707			0.407354	+	0.913270i	$0.366452\pi$
$158$	−4.96279	+	7.42734i	−0.394818	+	0.590887i
$159$		0			0
$160$	−17.6659	+	37.2230i	−1.39661	+	2.94273i
$161$	−0.906414	+	0.375449i	−0.0714355	+	0.0295895i
$162$		0			0
$163$	−8.51972	−	12.7507i	−0.667316	−	0.998709i	−0.998479	−	0.0551356i	$-0.982441\pi$
$163$	−8.51972	−	12.7507i	−0.667316	−	0.998709i	0.331163	−	0.943574i	$-0.392559\pi$
$164$	−14.2473	−	21.3226i	−1.11253	−	1.66501i
$165$		0			0
$166$	21.0145	−	21.0145i	1.63104	−	1.63104i
$167$	−21.4623	+	4.26911i	−1.66080	+	0.330354i	−0.934212	−	0.356719i	$-0.883896\pi$
$167$	−21.4623	+	4.26911i	−1.66080	+	0.330354i	−0.726589	+	0.687072i	$0.758896\pi$
$168$		0			0
$169$	8.51564			0.655049
$170$	0.720047	+	24.8825i	0.0552251	+	1.90840i
$171$		0			0
$172$	0.813359	+	1.96362i	0.0620181	+	0.149725i
$173$	10.0169	−	1.99249i	0.761574	−	0.151486i	0.201000	−	0.979591i	$-0.435581\pi$
$173$	10.0169	−	1.99249i	0.761574	−	0.151486i	0.560573	+	0.828105i	$0.310581\pi$
$174$		0			0
$175$	−1.02362	+	0.543631i	−0.0773784	+	0.0410947i
$176$	17.8831	+	26.7639i	1.34799	+	2.01741i
$177$		0			0
$178$	6.80980	+	2.82071i	0.510416	+	0.211421i
$179$	13.0625	−	5.41068i	0.976340	−	0.404413i	0.163271	−	0.986581i	$-0.447795\pi$
$179$	13.0625	−	5.41068i	0.976340	−	0.404413i	0.813069	+	0.582168i	$0.197795\pi$
$180$		0			0
$181$	−10.2379	+	6.84076i	−0.760979	+	0.508470i	−0.874476	−	0.485068i	$-0.838795\pi$
$181$	−10.2379	+	6.84076i	−0.760979	+	0.508470i	0.113497	+	0.993538i	$0.463795\pi$
$182$	−1.61288	+	2.41385i	−0.119555	+	0.178927i
$183$		0			0
$184$	20.8881	−	31.2612i	1.53989	−	2.30461i
$185$	−15.8500	−	11.7880i	−1.16532	−	0.866669i
$186$		0			0
$187$	8.64238	+	4.83076i	0.631994	+	0.353261i
$188$	−36.4122	−	36.4122i	−2.65563	−	2.65563i
$189$		0			0
$190$	15.0187	+	16.6150i	1.08957	+	1.20538i
$191$	−3.47438	−	3.47438i	−0.251397	−	0.251397i	0.570146	−	0.821543i	$-0.306887\pi$
$191$	−3.47438	−	3.47438i	−0.251397	−	0.251397i	−0.821543	+	0.570146i	$0.806887\pi$
$192$		0			0
$193$	−1.21425	+	6.10445i	−0.0874037	+	0.439408i	0.912159	+	0.409836i	$0.134414\pi$
$193$	−1.21425	+	6.10445i	−0.0874037	+	0.439408i	−0.999563	+	0.0295714i	$0.990586\pi$
$194$	6.03324	+	1.20009i	0.433162	+	0.0861612i
$195$		0			0
$196$	14.0622	+	33.9490i	1.00444	+	2.42493i
$197$	3.62031	−	2.41901i	0.257936	−	0.172348i	−0.419878	−	0.907580i	$-0.637927\pi$
$197$	3.62031	−	2.41901i	0.257936	−	0.172348i	0.677815	+	0.735233i	$0.262927\pi$
$198$		0			0
$199$	−1.40541	−	7.06547i	−0.0996268	−	0.500858i	−0.998088	−	0.0618053i	$-0.980314\pi$
$199$	−1.40541	−	7.06547i	−0.0996268	−	0.500858i	0.898461	−	0.439053i	$-0.144686\pi$
$200$	21.0420	−	39.1155i	1.48789	−	2.76588i
$201$		0			0
$202$	−33.3066	+	13.7960i	−2.34344	+	0.970686i
$203$	−1.43492	+	1.43492i	−0.100712	+	0.100712i
$204$		0			0
$205$	5.56032	+	9.30494i	0.388349	+	0.649885i
$206$	−3.73810	+	9.02458i	−0.260446	+	0.628772i
$207$		0			0
$208$		−	62.1773i		−	4.31122i
$209$	8.73692	−	1.73788i	0.604346	−	0.120212i
$210$		0			0
$211$	−3.61185	+	18.1580i	−0.248650	+	1.25005i	0.631509	+	0.775369i	$0.282436\pi$
$211$	−3.61185	+	18.1580i	−0.248650	+	1.25005i	−0.880159	+	0.474680i	$0.842564\pi$
$212$	23.4262	−	56.5559i	1.60892	−	3.88428i
$213$		0			0
$214$	6.77232	−	34.0467i	0.462946	−	2.32739i
$215$	−0.301532	−	0.846281i	−0.0205643	−	0.0577159i
$216$		0			0
$217$		−	0.608540i		−	0.0413104i
$218$	−2.57190	−	12.9298i	−0.174191	−	0.875718i
$219$		0			0
$220$	−14.5706	−	24.3832i	−0.982348	−	1.64392i
$221$	−8.69639	−	17.0335i	−0.584982	−	1.14579i
$222$		0			0
$223$	24.5599	−	10.1730i	1.64465	−	0.681236i	0.647895	−	0.761730i	$-0.275650\pi$
$223$	24.5599	−	10.1730i	1.64465	−	0.681236i	0.996755	+	0.0804938i	$0.0256497\pi$
$224$	3.55144	+	2.37300i	0.237291	+	0.158553i
$225$		0			0
$226$	−3.88707	−	19.5416i	−0.258564	−	1.29989i
$227$	7.09032	+	1.41035i	0.470601	+	0.0936084i	0.424693	−	0.905337i	$-0.360382\pi$
$227$	7.09032	+	1.41035i	0.470601	+	0.0936084i	0.0459080	+	0.998946i	$0.485382\pi$
$228$		0			0
$229$	6.34424	+	15.3163i	0.419239	+	1.01213i	0.982569	+	0.185900i	$0.0595202\pi$
$229$	6.34424	+	15.3163i	0.419239	+	1.01213i	−0.563330	+	0.826232i	$0.690480\pi$
$230$	−15.2492	+	20.5040i	−1.00550	+	1.35199i
$231$		0			0
$232$	15.1715	−	76.2721i	0.996055	−	5.00751i
$233$	18.1414	+	12.1217i	1.18848	+	0.794119i	0.982831	−	0.184506i	$-0.0590687\pi$
$233$	18.1414	+	12.1217i	1.18848	+	0.794119i	0.205651	+	0.978625i	$0.434069\pi$
$234$		0			0
$235$	14.5959	+	16.1473i	0.952131	+	1.05333i
$236$	−7.59111	−	3.14434i	−0.494139	−	0.204679i
$237$		0			0
$238$	2.56290	+	0.301233i	0.166128	+	0.0195260i
$239$		−	2.31380i		−	0.149667i	−0.997196	−	0.0748336i	$-0.976157\pi$
$239$		−	2.31380i		−	0.149667i	0.997196	−	0.0748336i	$-0.0238426\pi$
$240$		0			0
$241$	3.85243	−	5.76557i	0.248157	−	0.371393i	−0.686390	−	0.727234i	$-0.740805\pi$
$241$	3.85243	−	5.76557i	0.248157	−	0.371393i	0.934547	+	0.355841i	$0.115805\pi$
$242$	14.1311			0.908379
$243$		0			0
$244$	21.0542	−	14.0680i	1.34786	−	0.900608i
$245$	−5.21318	−	14.6313i	−0.333058	−	0.934762i
$246$		0			0
$247$	−15.8975	−	6.58496i	−1.01153	−	0.418991i
$248$	12.9561	+	19.3902i	0.822716	+	1.23128i
$249$		0			0
$250$	−15.6227	+	25.8300i	−0.988066	+	1.63363i
$251$	−13.3925	+	13.3925i	−0.845329	+	0.845329i	−0.989546	−	0.144217i	$-0.953934\pi$
$251$	−13.3925	+	13.3925i	−0.845329	+	0.845329i	0.144217	+	0.989546i	$0.453934\pi$
$252$		0			0
$253$	3.88936	+	9.38974i	0.244522	+	0.590328i
$254$	−24.1896			−1.51779
$255$		0			0
$256$	−21.8615			−1.36634
$257$	0.233227	+	0.563059i	0.0145483	+	0.0351227i	0.930987	−	0.365053i	$-0.118949\pi$
$257$	0.233227	+	0.563059i	0.0145483	+	0.0351227i	−0.916438	+	0.400176i	$0.868949\pi$
$258$		0			0
$259$	−1.44795	+	1.44795i	−0.0899713	+	0.0899713i
$260$	−2.76534	+	54.7987i	−0.171499	+	3.39847i
$261$		0			0
$262$	1.26192	+	1.88860i	0.0779616	+	0.116678i
$263$	24.9396	+	10.3303i	1.53784	+	0.636994i	0.981067	−	0.193670i	$-0.0620391\pi$
$263$	24.9396	+	10.3303i	1.53784	+	0.636994i	0.556774	+	0.830664i	$0.312039\pi$
$264$		0			0
$265$	−11.0943	+	23.3763i	−0.681520	+	1.43600i
$266$	1.93050	−	1.28992i	0.118367	−	0.0790900i
$267$		0			0
$268$	−12.6942			−0.775424
$269$	3.70109	−	5.53907i	0.225659	−	0.337723i	−0.701312	−	0.712854i	$-0.747402\pi$
$269$	3.70109	−	5.53907i	0.225659	−	0.337723i	0.926972	+	0.375131i	$0.122402\pi$
$270$		0			0
$271$			14.8170i			0.900067i	0.893012	+	0.450033i	$0.148588\pi$
$271$			14.8170i			0.900067i	−0.893012	+	0.450033i	$0.851412\pi$
$272$	−49.2244	+	25.1314i	−2.98467	+	1.52381i
$273$		0			0
$274$	−27.6040	−	11.4340i	−1.66762	−	0.690751i
$275$	5.63159	+	10.6039i	0.339598	+	0.639439i
$276$		0			0
$277$	20.8247	+	13.9146i	1.25124	+	0.836050i	0.991560	−	0.129646i	$-0.0413841\pi$
$277$	20.8247	+	13.9146i	1.25124	+	0.836050i	0.259676	+	0.965696i	$0.416384\pi$
$278$	3.21851	−	16.1805i	0.193033	−	0.970444i
$279$		0			0
$280$	−3.69466	−	2.74779i	−0.220798	−	0.164212i
$281$	9.79616	+	23.6500i	0.584390	+	1.41084i	0.888797	+	0.458300i	$0.151542\pi$
$281$	9.79616	+	23.6500i	0.584390	+	1.41084i	−0.304407	+	0.952542i	$0.598458\pi$
$282$		0			0
$283$	14.7852	+	2.94095i	0.878886	+	0.174821i	0.613855	−	0.789419i	$-0.289618\pi$
$283$	14.7852	+	2.94095i	0.878886	+	0.174821i	0.265031	+	0.964240i	$0.414618\pi$
$284$	15.4744	+	77.7948i	0.918234	+	4.61627i
$285$		0			0
$286$	25.0056	+	16.7082i	1.47861	+	0.987978i
$287$	1.03817	−	0.430025i	0.0612813	−	0.0253836i
$288$		0			0
$289$	−9.97003	+	13.7695i	−0.586472	+	0.809969i
$290$	−12.9107	+	51.2522i	−0.758140	+	3.00963i
$291$		0			0
$292$	0.633452	+	3.18458i	0.0370700	+	0.186363i
$293$		−	20.3722i		−	1.19015i	−0.803669	−	0.595077i	$-0.797121\pi$
$293$		−	20.3722i		−	1.19015i	0.803669	−	0.595077i	$-0.202879\pi$
$294$		0			0
$295$	3.13764	+	1.48912i	0.182680	+	0.0866997i
$296$	15.3092	−	76.9646i	0.889830	−	4.47348i
$297$		0			0
$298$	−10.4533	+	25.2364i	−0.605541	+	1.46190i
$299$	3.83003	−	19.2549i	0.221497	−	1.11354i
$300$		0			0
$301$	−0.0913435	+	0.0181694i	−0.00526495	+	0.00104726i
$302$			48.8408i			2.81047i
$303$		0			0
$304$	−19.0296	+	45.9416i	−1.09143	+	2.63493i
$305$	−9.18782	+	5.49033i	−0.526093	+	0.314375i
$306$		0			0
$307$	12.1383	−	12.1383i	0.692769	−	0.692769i	−0.270071	−	0.962840i	$-0.587047\pi$
$307$	12.1383	−	12.1383i	0.692769	−	0.692769i	0.962840	+	0.270071i	$0.0870473\pi$
$308$	−2.72048	+	1.12686i	−0.155014	+	0.0642089i
$309$		0			0
$310$	−8.13018	−	13.6055i	−0.461763	−	0.772740i
$311$	−1.88449	−	9.47397i	−0.106860	−	0.537220i	−0.996716	−	0.0809787i	$-0.974195\pi$
$311$	−1.88449	−	9.47397i	−0.106860	−	0.537220i	0.889856	−	0.456241i	$-0.150805\pi$
$312$		0			0
$313$	7.25785	−	4.84954i	0.410238	−	0.274112i	−0.333280	−	0.942828i	$-0.608156\pi$
$313$	7.25785	−	4.84954i	0.410238	−	0.274112i	0.743518	+	0.668715i	$0.233156\pi$
$314$	−10.5477	−	25.4643i	−0.595240	−	1.43704i
$315$		0			0
$316$	17.1655	+	3.41443i	0.965634	+	0.192076i
$317$	2.89628	−	14.5606i	0.162671	−	0.817804i	−0.810145	−	0.586229i	$-0.800612\pi$
$317$	2.89628	−	14.5606i	0.162671	−	0.817804i	0.972817	−	0.231576i	$-0.0743881\pi$
$318$		0			0
$319$	14.8647	+	14.8647i	0.832262	+	0.832262i
$320$	51.2343	+	2.58547i	2.86408	+	0.144532i
$321$		0			0
$322$	1.87310	+	1.87310i	0.104384	+	0.104384i
$323$	1.21243	+	15.2473i	0.0674612	+	0.848380i
$324$		0			0
$325$	2.33480	−	23.0747i	0.129512	−	1.27995i
$326$	−23.0033	+	34.4269i	−1.27404	+	1.90673i
$327$		0			0
$328$	−23.9244	+	35.8054i	−1.32100	+	1.97702i
$329$	1.87616	−	1.25361i	0.103436	−	0.0691136i
$330$		0			0
$331$	−9.13247	+	3.78279i	−0.501966	+	0.207921i	−0.619275	−	0.785174i	$-0.712573\pi$
$331$	−9.13247	+	3.78279i	−0.501966	+	0.207921i	0.117309	+	0.993095i	$0.462573\pi$
$332$	−53.7954	−	22.2828i	−2.95240	−	1.22293i
$333$		0			0
$334$	32.8251	+	49.1263i	1.79611	+	2.68807i
$335$	5.35894	+	0.270431i	0.292790	+	0.0147752i
$336$		0			0
$337$	7.03011	−	1.39838i	0.382954	−	0.0761744i	0.000140879	−	1.00000i	$-0.499955\pi$
$337$	7.03011	−	1.39838i	0.382954	−	0.0761744i	0.382814	+	0.923826i	$0.374955\pi$
$338$	−8.79878	−	21.2421i	−0.478590	−	1.15542i
$339$		0			0
$340$	44.5007	−	19.9598i	2.41339	−	1.08247i
$341$	−6.30399			−0.341380
$342$		0			0
$343$	−3.17069	+	0.630689i	−0.171201	+	0.0340540i
$344$	2.52369	−	2.52369i	0.136068	−	0.136068i
$345$		0			0
$346$	−15.3202	−	22.9284i	−0.823622	−	1.23264i
$347$	6.06926	+	9.08329i	0.325815	+	0.487617i	0.957828	−	0.287341i	$-0.0927712\pi$
$347$	6.06926	+	9.08329i	0.325815	+	0.487617i	−0.632013	+	0.774958i	$0.717771\pi$
$348$		0			0
$349$	−10.0229	+	4.15161i	−0.536512	+	0.222231i	−0.634453	−	0.772962i	$-0.718775\pi$
$349$	−10.0229	+	4.15161i	−0.536512	+	0.222231i	0.0979405	+	0.995192i	$0.468775\pi$
$350$	2.41373	+	1.99170i	0.129020	+	0.106461i
$351$		0			0
$352$	24.5824	−	36.7902i	1.31025	−	1.96092i
$353$	−8.66257			−0.461062			−0.230531	−	0.973065i	$-0.574046\pi$
$353$	−8.66257			−0.461062			−0.230531	+	0.973065i	$0.574046\pi$
$354$		0			0
$355$	−4.87528	−	33.1711i	−0.258753	−	1.76054i
$356$		−	14.4416i		−	0.765401i
$357$		0			0
$358$	−26.9937	−	26.9937i	−1.42666	−	1.42666i
$359$	26.0893	+	10.8065i	1.37694	+	0.570347i	0.943661	−	0.330913i	$-0.107357\pi$
$359$	26.0893	+	10.8065i	1.37694	+	0.570347i	0.433278	+	0.901260i	$0.357357\pi$
$360$		0			0
$361$	−3.70403	−	3.70403i	−0.194949	−	0.194949i
$362$	27.6425	+	18.4701i	1.45286	+	0.970769i
$363$		0			0
$364$	5.57871	+	1.10967i	0.292404	+	0.0581627i
$365$	−0.199572	−	1.35788i	−0.0104461	−	0.0710747i
$366$		0			0
$367$	−12.9000	+	8.61949i	−0.673373	+	0.449934i	−0.844671	−	0.535286i	$-0.820204\pi$
$367$	−12.9000	+	8.61949i	−0.673373	+	0.449934i	0.171298	+	0.985219i	$0.445204\pi$
$368$	−55.6440	−	11.0683i	−2.90065	−	0.576974i
$369$		0			0
$370$	−13.0279	+	51.7176i	−0.677288	+	2.68867i
$371$	2.23034	+	1.49026i	0.115793	+	0.0773706i
$372$		0			0
$373$	−12.1420	+	12.1420i	−0.628686	+	0.628686i	−0.947738	−	0.319051i	$-0.896636\pi$
$373$	−12.1420	+	12.1420i	−0.628686	+	0.628686i	0.319051	+	0.947738i	$0.396636\pi$
$374$	3.12053	−	26.5497i	0.161359	−	1.37285i
$375$		0			0
$376$	−33.0911	+	79.8889i	−1.70654	+	4.11995i
$377$	−7.92200	−	39.8266i	−0.408004	−	2.05117i
$378$		0			0
$379$	4.77160	−	0.949130i	0.245100	−	0.0487535i	−0.0710111	−	0.997476i	$-0.522623\pi$
$379$	4.77160	−	0.949130i	0.245100	−	0.0487535i	0.316112	+	0.948722i	$0.397623\pi$
$380$	18.8147	−	39.6434i	0.965172	−	2.03366i
$381$		0			0
$382$	−5.07688	+	12.2567i	−0.259756	+	0.627106i
$383$	−9.90180	+	23.9051i	−0.505959	+	1.22149i	0.440233	+	0.897884i	$0.354896\pi$
$383$	−9.90180	+	23.9051i	−0.505959	+	1.22149i	−0.946191	+	0.323608i	$0.895104\pi$
$384$		0			0
$385$	1.17247	−	0.417755i	0.0597547	−	0.0212907i
$386$	16.4821	−	3.27849i	0.838916	−	0.166871i
$387$		0			0
$388$	−2.35130	−	11.8208i	−0.119369	−	0.600109i
$389$	−1.50465	+	3.63255i	−0.0762889	+	0.184178i	−0.957423	−	0.288689i	$-0.906781\pi$
$389$	−1.50465	+	3.63255i	−0.0762889	+	0.184178i	0.881134	+	0.472866i	$0.156781\pi$
$390$		0			0
$391$	−16.7917	+	4.75046i	−0.849194	+	0.240241i
$392$	43.6321	−	43.6321i	2.20375	−	2.20375i
$393$		0			0
$394$	−9.77487	−	6.53136i	−0.492451	−	0.329045i
$395$	−7.17375	−	1.80710i	−0.360951	−	0.0909251i
$396$		0			0
$397$	32.0455	+	6.37424i	1.60832	+	0.319914i	0.915845	−	0.401532i	$-0.131522\pi$
$397$	32.0455	+	6.37424i	1.60832	+	0.319914i	0.692470	+	0.721446i	$0.256522\pi$
$398$	−16.1726	+	10.8062i	−0.810658	+	0.541664i
$399$		0			0
$400$	−66.6827	−	6.74728i	−3.33413	−	0.337364i
$401$	12.5954	+	2.50539i	0.628986	+	0.125113i	0.499282	−	0.866440i	$-0.333597\pi$
$401$	12.5954	+	2.50539i	0.628986	+	0.125113i	0.129704	+	0.991553i	$0.458597\pi$
$402$		0			0
$403$	10.1249	+	6.76524i	0.504357	+	0.337001i
$404$	49.9454	+	49.9454i	2.48487	+	2.48487i
$405$		0			0
$406$	5.06203	+	2.09676i	0.251224	+	0.104060i
$407$	14.9996	+	14.9996i	0.743505	+	0.743505i
$408$		0			0
$409$		−	5.19675i		−	0.256963i	−0.991712	−	0.128481i	$-0.958990\pi$
$409$		−	5.19675i		−	0.256963i	0.991712	−	0.128481i	$-0.0410102\pi$
$410$	17.4658	−	23.4845i	0.862577	−	1.15981i
$411$		0			0
$412$	19.1384			0.942883
$413$	0.200028	−	0.299362i	0.00984271	−	0.0147307i
$414$		0			0
$415$	22.2353	+	10.5528i	1.09149	+	0.518017i
$416$	−78.9641	+	32.7080i	−3.87153	+	1.60364i
$417$		0			0
$418$	−13.3625	−	19.9985i	−0.653584	−	0.978157i
$419$	6.48950	+	9.71223i	0.317033	+	0.474473i	0.955423	−	0.295239i	$-0.0953994\pi$
$419$	6.48950	+	9.71223i	0.317033	+	0.474473i	−0.638390	+	0.769713i	$0.720399\pi$
$420$		0			0
$421$	20.9588	−	20.9588i	1.02147	−	1.02147i	0.0217040	−	0.999764i	$-0.493091\pi$
$421$	20.9588	−	20.9588i	1.02147	−	1.02147i	0.999764	−	0.0217040i	$-0.00690915\pi$
$422$	49.0268	−	9.75204i	2.38659	−	0.474722i
$423$		0			0
$424$	−102.795			−4.99217
$425$	−19.2114	+	7.47811i	−0.931890	+	0.362742i
$426$		0			0
$427$	0.424612	+	1.02510i	0.0205484	+	0.0496083i
$428$	−66.7069	+	13.2688i	−3.22440	+	0.641373i
$429$		0			0
$430$	−1.79948	+	1.62659i	−0.0867785	+	0.0784409i
$431$	−5.39807	−	8.07878i	−0.260016	−	0.389141i	0.678376	−	0.734715i	$-0.262684\pi$
$431$	−5.39807	−	8.07878i	−0.260016	−	0.389141i	−0.938391	+	0.345574i	$0.887684\pi$
$432$		0			0
$433$	7.43813	+	3.08097i	0.357454	+	0.148062i	0.554181	−	0.832396i	$-0.313031\pi$
$433$	7.43813	+	3.08097i	0.357454	+	0.148062i	−0.196728	+	0.980458i	$0.563031\pi$
$434$	−1.51799	+	0.628773i	−0.0728660	+	0.0301821i
$435$		0			0
$436$	−21.4763	+	14.3500i	−1.02853	+	0.687242i
$437$	−8.72298	+	13.0549i	−0.417277	+	0.624499i
$438$		0			0
$439$	3.26022	−	4.87926i	0.155602	−	0.232875i	−0.745476	−	0.666533i	$-0.767778\pi$
$439$	3.26022	−	4.87926i	0.155602	−	0.232875i	0.901077	+	0.433658i	$0.142778\pi$
$440$	−28.4649	+	38.2737i	−1.35701	+	1.82463i
$441$		0			0
$442$	−33.5042	+	39.2928i	−1.59363	+	1.86897i
$443$	4.70713	+	4.70713i	0.223642	+	0.223642i	0.810030	−	0.586388i	$-0.199451\pi$
$443$	4.70713	+	4.70713i	0.223642	+	0.223642i	−0.586388	+	0.810030i	$0.699451\pi$
$444$		0			0
$445$	−0.307655	+	6.09658i	−0.0145843	+	0.289005i
$446$	−50.7529	−	50.7529i	−2.40322	−	2.40322i
$447$		0			0
$448$	1.03749	−	5.21583i	0.0490170	−	0.246425i
$449$	−2.61208	−	0.519574i	−0.123271	−	0.0245202i	0.133069	−	0.991107i	$-0.457517\pi$
$449$	−2.61208	−	0.519574i	−0.123271	−	0.0245202i	−0.256340	+	0.966587i	$0.582517\pi$
$450$		0			0
$451$	−4.45472	−	10.7546i	−0.209765	−	0.506416i
$452$	−32.4584	+	21.6880i	−1.52672	+	1.02012i
$453$		0			0
$454$	−3.80797	−	19.1440i	−0.178717	−	0.898471i
$455$	−2.33144	−	0.587300i	−0.109300	−	0.0275330i
$456$		0			0
$457$	−10.2716	+	4.25465i	−0.480486	+	0.199024i	−0.609762	−	0.792585i	$-0.708735\pi$
$457$	−10.2716	+	4.25465i	−0.480486	+	0.199024i	0.129275	+	0.991609i	$0.458735\pi$
$458$	31.6512	−	31.6512i	1.47896	−	1.47896i
$459$		0			0
$460$	48.5485	+	12.2296i	2.26359	+	0.570207i
$461$	−14.4449	+	34.8732i	−0.672768	+	1.62421i	0.104118	+	0.994565i	$0.466798\pi$
$461$	−14.4449	+	34.8732i	−0.672768	+	1.62421i	−0.776886	+	0.629641i	$0.783202\pi$
$462$		0			0
$463$			6.44300i			0.299432i	0.988729	+	0.149716i	$0.0478359\pi$
$463$			6.44300i			0.299432i	−0.988729	+	0.149716i	$0.952164\pi$
$464$	−115.093	+	22.8935i	−5.34308	+	1.06280i
$465$		0			0
$466$	11.4928	−	57.7782i	0.532394	−	2.67652i
$467$	−1.85150	+	4.46992i	−0.0856774	+	0.206843i	−0.960911	−	0.276856i	$-0.910707\pi$
$467$	−1.85150	+	4.46992i	−0.0856774	+	0.206843i	0.875234	+	0.483700i	$0.160707\pi$
$468$		0			0
$469$	0.108518	−	0.545559i	0.00501091	−	0.0251916i
$470$	25.1980	−	53.0934i	1.16230	−	2.44902i
$471$		0			0
$472$			13.7975i			0.635079i
$473$	0.188220	+	0.946247i	0.00865437	+	0.0435085i
$474$		0			0
$475$	−8.78724	+	16.3348i	−0.403186	+	0.749494i
$476$	−1.37635	−	4.86506i	−0.0630848	−	0.222990i
$477$		0			0
$478$	−5.77174	+	2.39073i	−0.263993	+	0.109350i
$479$	19.4825	+	13.0178i	0.890177	+	0.594797i	0.914356	−	0.404910i	$-0.132697\pi$
$479$	19.4825	+	13.0178i	0.890177	+	0.594797i	−0.0241791	+	0.999708i	$0.507697\pi$
$480$		0			0
$481$	−7.99393	−	40.1882i	−0.364492	−	1.83242i
$482$	−18.3627	−	3.65256i	−0.836396	−	0.166370i
$483$		0			0
$484$	−10.5952	−	25.5791i	−0.481600	−	1.16269i
$485$	0.740789	+	5.04029i	0.0336375	+	0.228868i
$486$		0			0
$487$	2.55488	−	12.8443i	0.115773	−	0.582029i	−0.878730	−	0.477319i	$-0.841609\pi$
$487$	2.55488	−	12.8443i	0.115773	−	0.582029i	0.994503	−	0.104710i	$-0.0333914\pi$
$488$	−35.3547	−	23.6233i	−1.60043	−	1.06937i
$489$		0			0
$490$	−31.1111	+	28.1220i	−1.40546	+	1.27042i
$491$	−36.2266	−	15.0056i	−1.63488	−	0.677191i	−0.639118	−	0.769109i	$-0.720700\pi$
$491$	−36.2266	−	15.0056i	−1.63488	−	0.677191i	−0.995767	+	0.0919174i	$0.970700\pi$
$492$		0			0
$493$	−28.3278	+	22.3691i	−1.27582	+	1.00746i
$494$			46.4600i			2.09033i
$495$		0			0
$496$	19.5506	−	29.2596i	0.877850	−	1.31380i
$497$	−3.47566			−0.155905
$498$		0			0
$499$	0.628901	−	0.420218i	0.0281535	−	0.0188115i	−0.541414	−	0.840756i	$-0.682111\pi$
$499$	0.628901	−	0.420218i	0.0281535	−	0.0188115i	0.569567	+	0.821945i	$0.307111\pi$
$500$	58.4694	+	8.91229i	2.61483	+	0.398570i
$501$		0			0
$502$	47.2453	+	19.5697i	2.10866	+	0.873436i
$503$	6.06211	+	9.07259i	0.270296	+	0.404527i	0.941641	−	0.336618i	$-0.109283\pi$
$503$	6.06211	+	9.07259i	0.270296	+	0.404527i	−0.671345	+	0.741145i	$0.734283\pi$
$504$		0			0
$505$	−20.0207	−	22.1487i	−0.890908	−	0.985604i
$506$	19.4039	−	19.4039i	0.862608	−	0.862608i
$507$		0			0
$508$	18.1369	+	43.7863i	0.804695	+	1.94270i
$509$	−4.10691			−0.182036			−0.0910178	−	0.995849i	$-0.529012\pi$
$509$	−4.10691			−0.182036			−0.0910178	+	0.995849i	$0.529012\pi$
$510$		0			0
$511$	−0.142278			−0.00629402
$512$	3.38481	+	8.17165i	0.149589	+	0.361140i
$513$		0			0
$514$	1.16356	−	1.16356i	0.0513225	−	0.0513225i
$515$	−8.07939	−	0.407715i	−0.356020	−	0.0179661i
$516$		0			0
$517$	−12.9864	−	19.4355i	−0.571141	−	0.854773i
$518$	5.10799	+	2.11580i	0.224432	+	0.0929629i
$519$		0			0
$520$	86.7919	−	30.9242i	3.80608	−	1.35611i
$521$	11.2256	−	7.50073i	0.491804	−	0.328613i	−0.284816	−	0.958582i	$-0.591933\pi$
$521$	11.2256	−	7.50073i	0.491804	−	0.328613i	0.776620	+	0.629969i	$0.216933\pi$
$522$		0			0
$523$	−2.98052			−0.130329			−0.0651645	−	0.997875i	$-0.520757\pi$
$523$	−2.98052			−0.130329			−0.0651645	+	0.997875i	$0.520757\pi$
$524$	2.47244	−	3.70028i	0.108009	−	0.161647i
$525$		0			0
$526$		−	72.8852i		−	3.17795i
$527$	1.26352	−	10.7501i	0.0550398	−	0.468282i
$528$		0			0
$529$	4.69935	+	1.94653i	0.204319	+	0.0846319i
$530$	69.7751	+	3.52110i	3.03084	+	0.152947i
$531$		0			0
$532$	−3.78238	−	2.52730i	−0.163987	−	0.109573i
$533$	−4.38677	+	22.0538i	−0.190012	+	0.955256i
$534$		0			0
$535$	28.4433	−	4.18041i	1.22971	−	0.180735i
$536$	8.15747	+	19.6939i	0.352349	+	0.850645i
$537$		0			0
$538$	−17.6413	−	3.50907i	−0.760570	−	0.151287i
$539$	3.25414	+	16.3596i	0.140166	+	0.704660i
$540$		0			0
$541$	−12.5466	−	8.38339i	−0.539422	−	0.360430i	0.255818	−	0.966725i	$-0.417655\pi$
$541$	−12.5466	−	8.38339i	−0.539422	−	0.360430i	−0.795240	+	0.606295i	$0.792655\pi$
$542$	36.9607	−	15.3096i	1.58760	−	0.657605i
$543$		0			0
$544$	57.8106	+	49.2939i	2.47861	+	2.11346i
$545$	9.37205	−	5.60042i	0.401454	−	0.239895i
$546$		0			0
$547$	8.11597	+	40.8017i	0.347014	+	1.74456i	0.621916	+	0.783084i	$0.286355\pi$
$547$	8.11597	+	40.8017i	0.347014	+	1.74456i	−0.274902	+	0.961472i	$0.588645\pi$
$548$			58.5400i			2.50070i
$549$		0			0
$550$	20.6324	−	25.0044i	0.879769	−	1.06619i
$551$	−6.33569	+	31.8517i	−0.269909	+	1.35693i
$552$		0			0
$553$	−0.293483	+	0.708530i	−0.0124802	+	0.0301298i
$554$	13.1927	−	66.3243i	0.560505	−	2.81785i
$555$		0			0
$556$	−31.7021	+	6.30594i	−1.34447	+	0.267431i
$557$		−	5.57074i		−	0.236040i	−0.993011	−	0.118020i	$-0.962345\pi$
$557$		−	5.57074i		−	0.236040i	0.993011	−	0.118020i	$-0.0376546\pi$
$558$		0			0
$559$	0.713179	−	1.72177i	0.0301643	−	0.0728230i
$560$	−1.69722	+	6.73755i	−0.0717206	+	0.284713i
$561$		0			0
$562$	48.8728	−	48.8728i	2.06157	−	2.06157i
$563$	−10.5768	+	4.38107i	−0.445761	+	0.184640i	−0.594261	−	0.804272i	$-0.702555\pi$
$563$	−10.5768	+	4.38107i	−0.445761	+	0.184640i	0.148500	+	0.988912i	$0.452555\pi$
$564$		0			0
$565$	14.1645	−	8.46424i	0.595906	−	0.356093i
$566$	−7.94060	−	39.9201i	−0.333768	−	1.67797i
$567$		0			0
$568$	110.747	−	73.9988i	4.64684	−	3.10492i
$569$	2.89254	+	6.98321i	0.121262	+	0.292751i	0.972841	−	0.231474i	$-0.0743549\pi$
$569$	2.89254	+	6.98321i	0.121262	+	0.292751i	−0.851579	+	0.524226i	$0.824355\pi$
$570$		0			0
$571$	−14.8956	−	2.96293i	−0.623363	−	0.123995i	−0.126704	−	0.991941i	$-0.540440\pi$
$571$	−14.8956	−	2.96293i	−0.623363	−	0.123995i	−0.496659	+	0.867946i	$0.665440\pi$
$572$	11.4953	−	57.7910i	0.480645	−	2.41636i
$573$		0			0
$574$	−2.14538	−	2.14538i	−0.0895465	−	0.0895465i
$575$	−20.2345	−	6.19703i	−0.843835	−	0.258434i
$576$		0			0
$577$	−1.61896	−	1.61896i	−0.0673983	−	0.0673983i	0.672604	−	0.740002i	$-0.265176\pi$
$577$	−1.61896	−	1.61896i	−0.0673983	−	0.0673983i	−0.740002	+	0.672604i	$0.765176\pi$
$578$	44.6493	+	10.6428i	1.85717	+	0.442682i
$579$		0			0
$580$	102.454	−	15.0580i	4.25415	−	0.625247i
$581$	1.41752	−	2.12147i	0.0588087	−	0.0880134i
$582$		0			0
$583$	15.4379	−	23.1045i	0.639375	−	0.956892i
$584$	4.53350	−	3.02918i	0.187597	−	0.125349i
$585$		0			0
$586$	−50.8181	+	21.0495i	−2.09927	+	0.869548i
$587$	21.2630	+	8.80743i	0.877618	+	0.363521i	0.775573	−	0.631258i	$-0.217461\pi$
$587$	21.2630	+	8.80743i	0.877618	+	0.363521i	0.102046	+	0.994780i	$0.467461\pi$
$588$		0			0
$589$	−5.41056	−	8.09748i	−0.222938	−	0.333651i
$590$	0.472613	−	9.36543i	0.0194572	−	0.385568i
$591$		0			0
$592$	−116.139	+	23.1014i	−4.77326	+	0.949461i
$593$	−3.03115	−	7.31785i	−0.124474	−	0.300508i	0.849342	−	0.527843i	$-0.176999\pi$
$593$	−3.03115	−	7.31785i	−0.124474	−	0.300508i	−0.973817	+	0.227335i	$0.926999\pi$
$594$		0			0
$595$	0.477390	+	2.08313i	0.0195711	+	0.0854000i
$596$	53.5189			2.19222
$597$		0			0
$598$	−51.9884	+	10.3411i	−2.12596	+	0.422880i
$599$	20.5921	−	20.5921i	0.841371	−	0.841371i	−0.147666	−	0.989037i	$-0.547176\pi$
$599$	20.5921	−	20.5921i	0.841371	−	0.841371i	0.989037	+	0.147666i	$0.0471762\pi$
$600$		0			0
$601$	−8.73137	−	13.0674i	−0.356160	−	0.533031i	0.609518	−	0.792772i	$-0.291363\pi$
$601$	−8.73137	−	13.0674i	−0.356160	−	0.533031i	−0.965678	+	0.259741i	$0.916363\pi$
$602$	0.139704	+	0.209082i	0.00569390	+	0.00852153i
$603$		0			0
$604$	88.4083	−	36.6199i	3.59728	−	1.49004i
$605$	3.92790	+	11.0241i	0.159692	+	0.448192i
$606$		0			0
$607$	−3.73293	+	5.58672i	−0.151515	+	0.226758i	−0.899461	−	0.437002i	$-0.856040\pi$
$607$	−3.73293	+	5.58672i	−0.151515	+	0.226758i	0.747946	+	0.663760i	$0.231040\pi$
$608$	68.3555			2.77218
$609$		0			0
$610$	23.1889	+	17.2460i	0.938890	+	0.698270i
$611$			45.1521i			1.82666i
$612$		0			0
$613$	12.5690	+	12.5690i	0.507656	+	0.507656i	0.913806	−	0.406150i	$-0.133129\pi$
$613$	12.5690	+	12.5690i	0.507656	+	0.507656i	−0.406150	+	0.913806i	$0.633129\pi$
$614$	−42.8207	−	17.7369i	−1.72810	−	0.715803i
$615$		0			0
$616$	3.49643	+	3.49643i	0.140875	+	0.140875i
$617$	4.08683	+	2.73074i	0.164530	+	0.109935i	0.635109	−	0.772422i	$-0.280955\pi$
$617$	4.08683	+	2.73074i	0.164530	+	0.109935i	−0.470579	+	0.882358i	$0.655955\pi$
$618$		0			0
$619$	−39.6838	−	7.89360i	−1.59503	−	0.317271i	−0.683957	−	0.729522i	$-0.739742\pi$
$619$	−39.6838	−	7.89360i	−1.59503	−	0.317271i	−0.911070	+	0.412252i	$0.864742\pi$
$620$	−18.5319	+	24.9179i	−0.744259	+	1.00073i
$621$		0			0
$622$	−21.6855	+	14.4898i	−0.869511	+	0.580989i
$623$	0.620653	+	0.123456i	0.0248659	+	0.00494614i
$624$		0			0
$625$	−24.4933	−	5.00797i	−0.979731	−	0.200319i
$626$	−19.5963	−	13.0938i	−0.783225	−	0.523334i
$627$		0			0
$628$	−38.1854	+	38.1854i	−1.52376	+	1.52376i
$629$	−28.5851	+	22.5722i	−1.13976	+	0.900014i
$630$		0			0
$631$	−7.13656	+	17.2292i	−0.284102	+	0.685883i	−0.999923	−	0.0124010i	$-0.996053\pi$
$631$	−7.13656	+	17.2292i	−0.284102	+	0.685883i	0.715821	+	0.698284i	$0.246053\pi$
$632$	−5.73359	−	28.8247i	−0.228070	−	1.14659i
$633$		0			0
$634$	−39.3138	+	7.82000i	−1.56135	+	0.310572i
$635$	−6.72378	−	18.8710i	−0.266825	−	0.748873i
$636$		0			0
$637$	12.3301	−	29.7676i	0.488538	−	1.17944i
$638$	21.7208	−	52.4386i	0.859934	−	2.07607i
$639$		0			0
$640$	−18.8306	−	52.8500i	−0.744344	−	2.08908i
$641$	34.2513	−	6.81301i	1.35285	−	0.269098i	0.535154	−	0.844754i	$-0.320253\pi$
$641$	34.2513	−	6.81301i	1.35285	−	0.269098i	0.817692	+	0.575656i	$0.195253\pi$
$642$		0			0
$643$	4.49010	+	22.5732i	0.177072	+	0.890202i	0.962507	+	0.271257i	$0.0874395\pi$
$643$	4.49010	+	22.5732i	0.177072	+	0.890202i	−0.785435	+	0.618945i	$0.787561\pi$
$644$	1.98615	−	4.79499i	0.0782652	−	0.188949i
$645$		0			0
$646$	36.7813	−	18.7786i	1.44714	−	0.738835i
$647$	13.6212	−	13.6212i	0.535506	−	0.535506i	−0.386700	−	0.922206i	$-0.626385\pi$
$647$	13.6212	−	13.6212i	0.535506	−	0.535506i	0.922206	+	0.386700i	$0.126385\pi$
$648$		0			0
$649$	−3.10116	−	2.07213i	−0.121731	−	0.0813381i
$650$	−59.9718	+	18.0177i	−2.35229	+	0.706714i
$651$		0			0
$652$	79.5648	+	15.8264i	3.11600	+	0.619811i
$653$	15.7505	−	10.5242i	0.616365	−	0.411842i	−0.207816	−	0.978168i	$-0.566636\pi$
$653$	15.7505	−	10.5242i	0.616365	−	0.411842i	0.824181	+	0.566326i	$0.191636\pi$
$654$		0			0
$655$	−1.12258	+	1.50942i	−0.0438630	+	0.0589778i
$656$	63.7325	+	12.6772i	2.48834	+	0.494961i
$657$		0			0
$658$	−5.06565	−	3.38476i	−0.197479	−	0.131952i
$659$	−35.9699	−	35.9699i	−1.40119	−	1.40119i	−0.796343	−	0.604845i	$-0.793235\pi$
$659$	−35.9699	−	35.9699i	−1.40119	−	1.40119i	−0.604845	−	0.796343i	$-0.706765\pi$
$660$		0			0
$661$	36.3654	+	15.0630i	1.41445	+	0.585884i	0.953459	−	0.301522i	$-0.0974945\pi$
$661$	36.3654	+	15.0630i	1.41445	+	0.585884i	0.460990	+	0.887406i	$0.347495\pi$
$662$	18.8722	+	18.8722i	0.733490	+	0.733490i
$663$		0			0
$664$			97.7774i			3.79450i
$665$	1.54291	+	1.14749i	0.0598315	+	0.0444978i
$666$		0			0
$667$	−37.0520			−1.43466
$668$	64.3134	−	96.2518i	2.48836	−	3.72410i
$669$		0			0
$670$	−4.86253	−	13.6472i	−0.187856	−	0.527238i
$671$	10.6193	−	4.39865i	0.409953	−	0.169808i
$672$		0			0
$673$	7.63240	+	11.4227i	0.294207	+	0.440312i	0.948897	−	0.315585i	$-0.102201\pi$
$673$	7.63240	+	11.4227i	0.294207	+	0.440312i	−0.654690	+	0.755898i	$0.727201\pi$
$674$	−10.7521	−	16.0916i	−0.414155	−	0.619827i
$675$		0			0
$676$	−31.8539	+	31.8539i	−1.22515	+	1.22515i
$677$	−14.5438	+	2.89294i	−0.558963	+	0.111185i	−0.466483	−	0.884530i	$-0.654479\pi$
$677$	−14.5438	+	2.89294i	−0.558963	+	0.111185i	−0.0924795	+	0.995715i	$0.529479\pi$
$678$		0			0
$679$	0.528120			0.0202674
$680$	−59.5623	−	56.2120i	−2.28411	−	2.15563i
$681$		0			0
$682$	6.51360	+	15.7252i	0.249419	+	0.602150i
$683$	−31.0373	+	6.17370i	−1.18761	+	0.236230i	−0.749075	−	0.662485i	$-0.769502\pi$
$683$	−31.0373	+	6.17370i	−1.18761	+	0.236230i	−0.438533	+	0.898715i	$0.644502\pi$
$684$		0			0
$685$	1.24710	−	24.7129i	0.0476494	−	0.944233i
$686$	4.84936	+	7.25758i	0.185149	+	0.277096i
$687$		0			0
$688$	−4.97568	−	2.06099i	−0.189696	−	0.0785746i
$689$	−49.5901	+	20.5409i	−1.88923	+	0.782545i
$690$		0			0
$691$	−5.63634	+	3.76608i	−0.214417	+	0.143269i	−0.658141	−	0.752895i	$-0.728657\pi$
$691$	−5.63634	+	3.76608i	−0.214417	+	0.143269i	0.443724	+	0.896163i	$0.353657\pi$
$692$	−30.0166	+	44.9230i	−1.14106	+	1.70771i
$693$		0			0
$694$	16.3871	−	24.5250i	0.622045	−	0.930956i
$695$	13.5175	−	1.98672i	0.512749	−	0.0753606i
$696$		0			0
$697$	19.2326	−	5.44099i	0.728486	−	0.206092i
$698$	20.7123	+	20.7123i	0.783971	+	0.783971i
$699$		0			0
$700$	1.79546	−	5.86252i	0.0678621	−	0.221582i
$701$	−11.9002	−	11.9002i	−0.449464	−	0.449464i	0.445712	−	0.895176i	$-0.352951\pi$
$701$	−11.9002	−	11.9002i	−0.449464	−	0.449464i	−0.895176	+	0.445712i	$0.852951\pi$
$702$		0			0
$703$	−6.39321	+	32.1409i	−0.241125	+	1.21222i
$704$	−54.0319	−	10.7476i	−2.03640	−	0.405066i
$705$		0			0
$706$	8.95060	+	21.6087i	0.336860	+	0.813253i
$707$	−2.57346	+	1.71953i	−0.0967849	+	0.0646696i
$708$		0			0
$709$	4.09610	+	20.5925i	0.153832	+	0.773368i	0.978257	+	0.207396i	$0.0664989\pi$
$709$	4.09610	+	20.5925i	0.153832	+	0.773368i	−0.824425	+	0.565972i	$0.808501\pi$
$710$	−77.7075	+	46.4354i	−2.91631	+	1.74269i
$711$		0			0
$712$	−22.4047	+	9.28032i	−0.839650	+	0.347795i
$713$	7.85673	−	7.85673i	0.294237	−	0.294237i
$714$		0			0
$715$	−6.08397	+	24.1519i	−0.227527	+	0.903229i
$716$	−28.6228	+	69.1016i	−1.06969	+	2.58245i
$717$		0			0
$718$		−	76.2452i		−	2.84544i
$719$	20.5699	−	4.09161i	0.767128	−	0.152591i	0.204011	−	0.978969i	$-0.434602\pi$
$719$	20.5699	−	4.09161i	0.767128	−	0.152591i	0.563117	+	0.826377i	$0.309602\pi$
$720$		0			0
$721$	−0.163608	+	0.822510i	−0.00609306	+	0.0306319i
$722$	−5.41246	+	13.0668i	−0.201431	+	0.486298i
$723$		0			0
$724$	12.7076	−	63.8852i	0.472273	−	2.37428i
$725$	−43.5721	+	4.17418i	−1.61823	+	0.155025i
$726$		0			0
$727$		−	45.5044i		−	1.68767i	−0.536606	−	0.843833i	$-0.680294\pi$
$727$		−	45.5044i		−	1.68767i	0.536606	−	0.843833i	$-0.319706\pi$
$728$	−1.86339	−	9.36790i	−0.0690619	−	0.347198i
$729$		0			0
$730$	−3.18100	+	1.90086i	−0.117734	+	0.0703540i
$731$	−1.65134	+	0.131311i	−0.0610772	+	0.00485672i
$732$		0			0
$733$	−33.0977	+	13.7095i	−1.22249	+	0.506372i	−0.898200	−	0.439586i	$-0.855125\pi$
$733$	−33.0977	+	13.7095i	−1.22249	+	0.506372i	−0.324289	+	0.945958i	$0.605125\pi$
$734$	34.8301	+	23.2727i	1.28560	+	0.859011i
$735$		0			0
$736$	15.2147	+	76.4893i	0.560820	+	2.81943i
$737$	−5.65156	−	1.12417i	−0.208178	−	0.0414092i
$738$		0			0
$739$	0.607382	+	1.46635i	0.0223429	+	0.0539405i	0.934657	−	0.355550i	$-0.115706\pi$
$739$	0.607382	+	1.46635i	0.0223429	+	0.0539405i	−0.912314	+	0.409491i	$0.865706\pi$
$740$	103.384	−	15.1947i	3.80046	−	0.558567i
$741$		0			0
$742$	1.41294	−	7.10335i	0.0518708	−	0.260772i
$743$	−13.4664	−	8.99795i	−0.494034	−	0.330103i	0.283470	−	0.958981i	$-0.408514\pi$
$743$	−13.4664	−	8.99795i	−0.494034	−	0.330103i	−0.777504	+	0.628878i	$0.783514\pi$
$744$		0			0
$745$	−22.5933	−	1.14014i	−0.827753	−	0.0417714i
$746$	42.8336	+	17.7423i	1.56825	+	0.649590i
$747$		0			0
$748$	−50.3982	+	14.2579i	−1.84274	+	0.521320i
$749$		−	2.98028i		−	0.108897i
$750$		0			0
$751$	3.97323	−	5.94636i	0.144985	−	0.216986i	−0.751868	−	0.659313i	$-0.770847\pi$
$751$	3.97323	−	5.94636i	0.144985	−	0.216986i	0.896854	+	0.442328i	$0.145847\pi$
$752$	130.484			4.75825
$753$		0			0
$754$	−91.1614	+	60.9121i	−3.31990	+	2.21829i
$755$	−38.1021	+	13.5759i	−1.38668	+	0.494077i
$756$		0			0
$757$	−38.1876	−	15.8178i	−1.38795	−	0.574908i	−0.441356	−	0.897332i	$-0.645502\pi$
$757$	−38.1876	−	15.8178i	−1.38795	−	0.574908i	−0.946595	+	0.322424i	$0.895502\pi$
$758$	−7.29784	−	10.9220i	−0.265070	−	0.396705i
$759$		0			0
$760$	−73.5934	−	3.71378i	−2.66951	−	0.134713i
$761$	−19.6987	+	19.6987i	−0.714077	+	0.714077i	−0.967385	−	0.253309i	$-0.918481\pi$
$761$	−19.6987	+	19.6987i	−0.714077	+	0.714077i	0.253309	+	0.967385i	$0.418481\pi$
$762$		0			0
$763$	−0.433126	−	1.04566i	−0.0156802	−	0.0378554i
$764$	25.9928			0.940386
$765$		0			0
$766$	69.8619			2.52421
$767$	2.75706	+	6.65613i	0.0995516	+	0.240339i
$768$		0			0
$769$	−1.46441	+	1.46441i	−0.0528080	+	0.0528080i	−0.733018	−	0.680210i	$-0.761889\pi$
$769$	−1.46441	+	1.46441i	−0.0528080	+	0.0528080i	0.680210	+	0.733018i	$0.261889\pi$
$770$	−2.25354	−	2.49307i	−0.0812119	−	0.0898440i
$771$		0			0
$772$	−18.2925	−	27.3766i	−0.658360	−	0.985306i
$773$	40.9343	+	16.9555i	1.47231	+	0.609849i	0.967383	−	0.253316i	$-0.0815214\pi$
$773$	40.9343	+	16.9555i	1.47231	+	0.609849i	0.504922	+	0.863165i	$0.331521\pi$
$774$		0			0
$775$	8.35417	−	10.1244i	0.300091	−	0.363679i
$776$	−16.8278	+	11.2440i	−0.604083	+	0.403635i
$777$		0			0
$778$	10.6160			0.380603
$779$	9.99096	−	14.9525i	0.357963	−	0.535730i
$780$		0			0
$781$			36.0051i			1.28837i
$782$	29.2000	+	36.9783i	1.04419	+	1.32234i
$783$		0			0
$784$	−86.0244	−	35.6325i	−3.07230	−	1.27259i
$785$	16.9336	−	15.3067i	0.604387	−	0.546319i
$786$		0			0
$787$	42.7335	+	28.5536i	1.52328	+	1.01783i	0.984501	+	0.175380i	$0.0561155\pi$
$787$	42.7335	+	28.5536i	1.52328	+	1.01783i	0.538782	+	0.842445i	$0.318885\pi$
$788$	−4.49361	+	22.5909i	−0.160078	+	0.804768i
$789$		0			0
$790$	2.90449	+	19.7620i	0.103337	+	0.703101i
$791$	−0.654609	−	1.58037i	−0.0232752	−	0.0561913i
$792$		0			0
$793$	−21.7762	−	4.33156i	−0.773296	−	0.153818i
$794$	−17.2105	−	86.5231i	−0.610778	−	3.07059i
$795$		0			0
$796$	31.6865	+	21.1722i	1.12310	+	0.750430i
$797$	−2.64102	+	1.09395i	−0.0935497	+	0.0387496i	−0.428968	−	0.903320i	$-0.641123\pi$
$797$	−2.64102	+	1.09395i	−0.0935497	+	0.0387496i	0.335418	+	0.942069i	$0.391123\pi$
$798$		0			0
$799$	35.7460	−	18.2500i	1.26460	−	0.645639i
$800$	26.5091	+	88.2351i	0.937237	+	3.11958i
$801$		0			0
$802$	−6.76458	−	34.0078i	−0.238866	−	1.20086i
$803$			1.47389i			0.0520125i
$804$		0			0
$805$	−0.940613	+	1.98192i	−0.0331522	+	0.0698534i
$806$	6.41425	−	32.2466i	0.225932	−	1.13584i
$807$		0			0
$808$	45.3898	−	109.581i	1.59681	−	3.85504i
$809$	4.67677	−	23.5117i	0.164427	−	0.826628i	−0.807231	−	0.590236i	$-0.799035\pi$
$809$	4.67677	−	23.5117i	0.164427	−	0.826628i	0.971658	−	0.236393i	$-0.0759652\pi$
$810$		0			0
$811$	37.3936	−	7.43805i	1.31307	−	0.261185i	0.511599	−	0.859224i	$-0.329053\pi$
$811$	37.3936	−	7.43805i	1.31307	−	0.261185i	0.801467	+	0.598039i	$0.204053\pi$
$812$		−	10.7351i		−	0.376727i
$813$		0			0
$814$	21.9180	−	52.9148i	0.768226	−	1.85466i
$815$	−33.2515	−	8.37621i	−1.16475	−	0.293406i
$816$		0			0
$817$	−1.05391	+	1.05391i	−0.0368716	+	0.0368716i
$818$	−12.9632	+	5.36954i	−0.453248	+	0.187741i
$819$		0			0
$820$	−55.6056	−	14.0073i	−1.94183	−	0.489156i
$821$	−4.19072	−	21.0682i	−0.146257	−	0.735285i	−0.982402	−	0.186777i	$-0.940196\pi$
$821$	−4.19072	−	21.0682i	−0.146257	−	0.735285i	0.836145	−	0.548508i	$-0.184804\pi$
$822$		0			0
$823$	−4.97024	+	3.32101i	−0.173252	+	0.115763i	−0.639173	−	0.769063i	$-0.720723\pi$
$823$	−4.97024	+	3.32101i	−0.173252	+	0.115763i	0.465921	+	0.884826i	$0.345723\pi$
$824$	−12.2986	−	29.6914i	−0.428442	−	1.03435i
$825$		0			0
$826$	−0.953433	−	0.189650i	−0.0331742	−	0.00659876i
$827$	−8.76311	+	44.0551i	−0.304723	+	1.53195i	0.460194	+	0.887818i	$0.347780\pi$
$827$	−8.76311	+	44.0551i	−0.304723	+	1.53195i	−0.764917	+	0.644128i	$0.777220\pi$
$828$		0			0
$829$	−27.0517	−	27.0517i	−0.939546	−	0.939546i	0.0587284	−	0.998274i	$-0.481295\pi$
$829$	−27.0517	−	27.0517i	−0.939546	−	0.939546i	−0.998274	+	0.0587284i	$0.981295\pi$
$830$	3.34923	−	66.3693i	0.116254	−	2.30371i
$831$		0			0
$832$	75.2472	+	75.2472i	2.60873	+	2.60873i
$833$	−28.5501	+	2.27023i	−0.989201	+	0.0786590i
$834$		0			0
$835$	−29.2007	+	39.2631i	−1.01053	+	1.35876i
$836$	−26.1809	+	39.1825i	−0.905485	+	1.35515i
$837$		0			0
$838$	17.5217	−	26.2231i	0.605278	−	0.905863i
$839$	17.0696	−	11.4056i	0.589309	−	0.393764i	−0.224860	−	0.974391i	$-0.572193\pi$
$839$	17.0696	−	11.4056i	0.589309	−	0.393764i	0.814170	+	0.580627i	$0.197193\pi$
$840$		0			0
$841$	−44.0117	+	18.2302i	−1.51764	+	0.628629i
$842$	−73.9370	−	30.6257i	−2.54804	−	1.05543i
$843$		0			0
$844$	−54.4119	−	81.4332i	−1.87293	−	2.80305i
$845$	14.1259	−	12.7687i	0.485945	−	0.439256i
$846$		0			0
$847$	1.18988	−	0.236683i	0.0408849	−	0.00813251i
$848$	59.3604	+	143.309i	2.03844	+	4.92124i
$849$		0			0
$850$	38.5042	+	40.1958i	1.32068	+	1.37870i
$851$	−37.3884			−1.28166
$852$		0			0
$853$	20.5757	−	4.09276i	0.704499	−	0.140134i	0.170176	−	0.985414i	$-0.445566\pi$
$853$	20.5757	−	4.09276i	0.704499	−	0.140134i	0.534323	+	0.845280i	$0.320566\pi$
$854$	2.11838	−	2.11838i	0.0724894	−	0.0724894i
$855$		0			0
$856$	63.4519	+	94.9625i	2.16874	+	3.24575i
$857$	−25.3643	−	37.9604i	−0.866428	−	1.29670i	−0.953774	−	0.300524i	$-0.902839\pi$
$857$	−25.3643	−	37.9604i	−0.866428	−	1.29670i	0.0873459	−	0.996178i	$-0.472161\pi$
$858$		0			0
$859$	14.4972	−	6.00493i	0.494637	−	0.204885i	−0.121398	−	0.992604i	$-0.538738\pi$
$859$	14.4972	−	6.00493i	0.494637	−	0.204885i	0.616035	+	0.787718i	$0.288738\pi$
$860$	4.29355	+	2.03771i	0.146409	+	0.0694853i
$861$		0			0
$862$	−14.5748	+	21.8128i	−0.496421	+	0.742947i
$863$	−14.5702			−0.495975			−0.247988	−	0.968763i	$-0.579769\pi$
$863$	−14.5702			−0.495975			−0.247988	+	0.968763i	$0.579769\pi$
$864$		0			0
$865$	13.6287	−	18.3250i	0.463388	−	0.623068i
$866$		−	21.7377i		−	0.738678i
$867$		0			0
$868$	2.27633	+	2.27633i	0.0772636	+	0.0772636i
$869$	7.33981	+	3.04025i	0.248986	+	0.103133i
$870$		0			0
$871$	7.87060	+	7.87060i	0.266685	+	0.266685i
$872$	36.0636	+	24.0969i	1.22127	+	0.816025i
$873$		0			0
$874$	41.5782	+	8.27041i	1.40640	+	0.279751i
$875$	−0.882855	+	2.43664i	−0.0298460	+	0.0823735i
$876$		0			0
$877$	18.2754	−	12.2112i	0.617117	−	0.412345i	−0.207340	−	0.978269i	$-0.566481\pi$
$877$	18.2754	−	12.2112i	0.617117	−	0.412345i	0.824457	+	0.565924i	$0.191481\pi$
$878$	−15.5399	−	3.09107i	−0.524445	−	0.104319i
$879$		0			0
$880$	69.7957	+	17.5819i	2.35281	+	0.592684i
$881$	12.7703	+	8.53282i	0.430241	+	0.287478i	0.751774	−	0.659420i	$-0.229198\pi$
$881$	12.7703	+	8.53282i	0.430241	+	0.287478i	−0.321533	+	0.946898i	$0.604198\pi$
$882$		0			0
$883$	13.3887	−	13.3887i	0.450567	−	0.450567i	−0.444976	−	0.895543i	$-0.646788\pi$
$883$	13.3887	−	13.3887i	0.450567	−	0.450567i	0.895543	+	0.444976i	$0.146788\pi$
$884$	96.2460	+	31.1860i	3.23710	+	1.04890i
$885$		0			0
$886$	6.87822	−	16.6055i	0.231078	−	0.557872i
$887$	−7.62909	−	38.3540i	−0.256160	−	1.28780i	−0.867898	−	0.496742i	$-0.834529\pi$
$887$	−7.62909	−	38.3540i	−0.256160	−	1.28780i	0.611738	−	0.791060i	$-0.290471\pi$
$888$		0			0
$889$	−2.03685	+	0.405154i	−0.0683136	+	0.0135884i
$890$	15.5257	−	5.53185i	0.520423	−	0.185428i
$891$		0			0
$892$	−53.8159	+	129.923i	−1.80189	+	4.35015i
$893$	13.8190	−	33.3620i	0.462436	−	1.11642i
$894$		0			0
$895$	13.5554	−	28.5618i	0.453106	−	0.954717i
$896$	−5.70438	+	1.13467i	−0.190570	+	0.0379067i
$897$		0			0
$898$	1.40286	+	7.05263i	0.0468139	+	0.235349i
$899$	8.79485	−	21.2327i	0.293325	−	0.708149i
$900$		0			0
$901$	36.3055	+	30.9570i	1.20951	+	1.03133i
$902$	−22.2245	+	22.2245i	−0.739994	+	0.739994i
$903$		0			0
$904$	54.5050	+	36.4191i	1.81281	+	1.21128i
$905$	−6.72554	+	26.6987i	−0.223564	+	0.887496i
$906$		0			0
$907$	−29.3742	−	5.84288i	−0.975353	−	0.194010i	−0.318412	−	0.947952i	$-0.603150\pi$
$907$	−29.3742	−	5.84288i	−0.975353	−	0.194010i	−0.656940	+	0.753943i	$0.728150\pi$
$908$	−31.7980	+	21.2467i	−1.05525	+	0.705097i
$909$		0			0
$910$	0.943947	+	6.42257i	0.0312915	+	0.212906i
$911$	34.1209	+	6.78706i	1.13047	+	0.224865i	0.724671	−	0.689095i	$-0.241992\pi$
$911$	34.1209	+	6.78706i	1.13047	+	0.224865i	0.405803	+	0.913960i	$0.366992\pi$
$912$		0			0
$913$	−21.9768	−	14.6844i	−0.727324	−	0.485983i
$914$	21.2263	+	21.2263i	0.702104	+	0.702104i
$915$		0			0
$916$	−81.0244	−	33.5614i	−2.67712	−	1.10890i
$917$	0.137890	+	0.137890i	0.00455354	+	0.00455354i
$918$		0			0
$919$			29.8893i			0.985957i	0.870041	+	0.492979i	$0.164092\pi$
$919$			29.8893i			0.985957i	−0.870041	+	0.492979i	$0.835908\pi$
$920$	−12.2248	−	83.1771i	−0.403041	−	2.74227i
$921$		0			0
$922$	101.916			3.35642
$923$	38.6395	−	57.8282i	1.27184	−	1.90344i
$924$		0			0
$925$	−43.9677	+	4.21208i	−1.44565	+	0.138492i
$926$	16.0720	−	6.65723i	0.528158	−	0.218770i
$927$		0			0
$928$	89.6185	+	134.124i	2.94187	+	4.40282i
$929$	15.4822	+	23.1707i	0.507953	+	0.760206i	0.993479	−	0.114016i	$-0.0363717\pi$
$929$	15.4822	+	23.1707i	0.507953	+	0.760206i	−0.485525	+	0.874223i	$0.661372\pi$
$930$		0			0
$931$	−18.2210	+	18.2210i	−0.597170	+	0.597170i
$932$	−113.203	+	22.5175i	−3.70810	+	0.737587i
$933$		0			0
$934$	13.0632			0.427442
$935$	21.5796	−	4.94538i	0.705728	−	0.161731i
$936$		0			0
$937$	−0.339978	−	0.820779i	−0.0111066	−	0.0268137i	0.918229	−	0.396050i	$-0.129619\pi$
$937$	−0.339978	−	0.820779i	−0.0111066	−	0.0268137i	−0.929336	+	0.369236i	$0.879619\pi$
$938$	−1.47301	+	0.293001i	−0.0480956	+	0.00956682i
$939$		0			0
$940$	−114.999	−	5.80327i	−3.75086	−	0.189282i
$941$	2.61006	+	3.90624i	0.0850856	+	0.127340i	0.871571	−	0.490269i	$-0.163102\pi$
$941$	2.61006	+	3.90624i	0.0850856	+	0.127340i	−0.786485	+	0.617609i	$0.788102\pi$
$942$		0			0
$943$	18.9556	+	7.85166i	0.617279	+	0.255685i
$944$	19.2353	−	7.96753i	0.626056	−	0.259321i
$945$		0			0
$946$	2.16592	−	1.44722i	0.0704202	−	0.0470532i
$947$	20.3956	−	30.5241i	0.662767	−	0.991900i	−0.335981	−	0.941869i	$-0.609068\pi$
$947$	20.3956	−	30.5241i	0.662767	−	0.991900i	0.998748	−	0.0500317i	$-0.0159322\pi$
$948$		0			0
$949$	1.58173	−	2.36723i	0.0513452	−	0.0768436i
$950$	49.8264	+	5.04168i	1.61658	+	0.163574i
$951$		0			0
$952$	−6.66320	+	5.26161i	−0.215956	+	0.170530i
$953$	20.8325	+	20.8325i	0.674831	+	0.674831i	0.958826	−	0.283995i	$-0.0916598\pi$
$953$	20.8325	+	20.8325i	0.674831	+	0.674831i	−0.283995	+	0.958826i	$0.591660\pi$
$954$		0			0
$955$	−10.9730	−	0.553736i	−0.355077	−	0.0179185i
$956$	8.65509	+	8.65509i	0.279926	+	0.279926i
$957$		0			0
$958$	12.3424	−	62.0494i	0.398765	−	2.00472i
$959$	−2.51586	−	0.500437i	−0.0812415	−	0.0161599i
$960$		0			0
$961$	−9.22580	−	22.2730i	−0.297606	−	0.718485i
$962$	−91.9891	+	61.4652i	−2.96585	+	1.98172i
$963$		0			0
$964$	7.15637	+	35.9775i	0.230491	+	1.15876i
$965$	7.13904	+	11.9469i	0.229814	+	0.384583i
$966$		0			0
$967$	−47.9926	+	19.8792i	−1.54334	+	0.639272i	−0.982096	−	0.188379i	$-0.939677\pi$
$967$	−47.9926	+	19.8792i	−1.54334	+	0.639272i	−0.561243	+	0.827651i	$0.689677\pi$
$968$	−32.8749	+	32.8749i	−1.05664	+	1.05664i
$969$		0			0
$970$	11.8075	−	7.05577i	0.379116	−	0.226547i
$971$	−6.87896	+	16.6073i	−0.220756	+	0.532953i	−0.994993	−	0.0999431i	$-0.968134\pi$
$971$	−6.87896	+	16.6073i	−0.220756	+	0.532953i	0.774237	+	0.632896i	$0.218134\pi$
$972$		0			0
$973$		−	1.41636i		−	0.0454066i
$974$	−34.6797	+	6.89821i	−1.11121	+	0.221033i
$975$		0			0
$976$	−12.5176	+	62.9303i	−0.400679	+	2.01435i
$977$	−0.429605	+	1.03716i	−0.0137443	+	0.0331816i	−0.930603	−	0.366031i	$-0.880716\pi$
$977$	−0.429605	+	1.03716i	−0.0137443	+	0.0331816i	0.916858	+	0.399213i	$0.130716\pi$
$978$		0			0
$979$	1.27890	−	6.42948i	0.0408739	−	0.205487i
$980$	74.2311	+	35.2299i	2.37123	+	1.12538i
$981$		0			0
$982$			105.871i			3.37849i
$983$	10.6986	+	53.7855i	0.341232	+	1.71549i	0.646234	+	0.763140i	$0.276343\pi$
$983$	10.6986	+	53.7855i	0.341232	+	1.71549i	−0.305001	+	0.952352i	$0.598657\pi$
$984$		0			0
$985$	2.37827	−	9.44114i	0.0757778	−	0.300820i
$986$	85.0692	+	47.5505i	2.70916	+	1.51432i
$987$		0			0
$988$	84.0987	−	34.8348i	2.67554	−	1.10824i
$989$	−1.41390	−	0.944737i	−0.0449594	−	0.0300409i
$990$		0			0
$991$	−1.54751	−	7.77984i	−0.0491581	−	0.247135i	0.948391	−	0.317103i	$-0.102710\pi$
$991$	−1.54751	−	7.77984i	−0.0491581	−	0.247135i	−0.997549	+	0.0699684i	$0.977710\pi$
$992$	−47.4437	−	9.43713i	−1.50634	−	0.299629i
$993$		0			0
$994$	3.59123	+	8.66999i	0.113907	+	0.274995i
$995$	−12.9256	−	9.61300i	−0.409768	−	0.304753i
$996$		0			0
$997$	0.809494	−	4.06960i	0.0256369	−	0.128886i	−0.965847	−	0.259112i	$-0.916570\pi$
$997$	0.809494	−	4.06960i	0.0256369	−	0.128886i	0.991484	+	0.130226i	$0.0415703\pi$
$998$	−1.69804	−	1.13459i	−0.0537505	−	0.0359149i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	765.2.cc.b.568.1		144
3.2	odd	2		255.2.bi.a.58.18	yes	144
5.2	odd	4		765.2.bx.b.262.18		144
15.2	even	4		255.2.bd.a.7.1	✓	144
17.5	odd	16		765.2.bx.b.73.18		144
51.5	even	16		255.2.bd.a.73.1	yes	144
85.22	even	16	inner	765.2.cc.b.532.1		144
255.107	odd	16		255.2.bi.a.22.18	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
255.2.bd.a.7.1	✓	144	15.2	even	4
255.2.bd.a.73.1	yes	144	51.5	even	16
255.2.bi.a.22.18	yes	144	255.107	odd	16
255.2.bi.a.58.18	yes	144	3.2	odd	2
765.2.bx.b.73.18		144	17.5	odd	16
765.2.bx.b.262.18		144	5.2	odd	4
765.2.cc.b.532.1		144	85.22	even	16	inner
765.2.cc.b.568.1		144	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 765 = 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	765.cc (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.03325 - 2.49449i) q^{2} +(-3.74064 + 3.74064i) q^{4} +(1.65882 - 1.49944i) q^{5} +(-0.128784 - 0.192738i) q^{7} +(8.20701 + 3.39946i) q^{8} +O(q^{10})\)	\(q+(-1.03325 - 2.49449i) q^{2} +(-3.74064 + 3.74064i) q^{4} +(1.65882 - 1.49944i) q^{5} +(-0.128784 - 0.192738i) q^{7} +(8.20701 + 3.39946i) q^{8} +(-5.45431 - 2.58860i) q^{10} +(-1.99662 + 1.33410i) q^{11} +4.63849 q^{13} +(-0.347717 + 0.520396i) q^{14} -13.4046i q^{16} +(-1.87483 - 3.67219i) q^{17} +(-3.42730 - 1.41963i) q^{19} +(-0.596172 + 11.8139i) q^{20} +(5.39089 + 3.60208i) q^{22} +(0.825706 - 4.15110i) q^{23} +(0.503354 - 4.97460i) q^{25} +(-4.79272 - 11.5707i) q^{26} +(1.20270 + 0.239231i) q^{28} +(-1.70788 - 8.58610i) q^{29} +(2.18280 + 1.45850i) q^{31} +(-17.0236 + 7.05142i) q^{32} +(-7.22307 + 8.47103i) q^{34} +(-0.502628 - 0.126614i) q^{35} +(-1.72339 - 8.66406i) q^{37} +10.0162i q^{38} +(18.7112 - 6.66685i) q^{40} +(-0.945732 + 4.75451i) q^{41} +(0.153752 - 0.371191i) q^{43} +(2.47825 - 12.4590i) q^{44} +(-11.2080 + 2.22942i) q^{46} +9.73422i q^{47} +(2.65822 - 6.41751i) q^{49} +(-12.9292 + 3.88439i) q^{50} +(-17.3509 + 17.3509i) q^{52} +(-10.6910 + 4.42835i) q^{53} +(-1.31163 + 5.20683i) q^{55} +(-0.401723 - 2.01960i) q^{56} +(-19.6532 + 13.1319i) q^{58} +(0.594386 + 1.43498i) q^{59} +(-4.69467 - 0.933828i) q^{61} +(1.38283 - 6.95195i) q^{62} +(16.2223 + 16.2223i) q^{64} +(7.69442 - 6.95515i) q^{65} +(1.69680 + 1.69680i) q^{67} +(20.7494 + 6.72330i) q^{68} +(0.203503 + 1.38462i) q^{70} +(8.33019 - 12.4670i) q^{71} +(0.341001 - 0.510345i) q^{73} +(-19.8317 + 13.2511i) q^{74} +(18.1306 - 7.50994i) q^{76} +(0.514263 + 0.213015i) q^{77} +(-1.83806 - 2.75085i) q^{79} +(-20.0995 - 22.2358i) q^{80} +(12.8372 - 2.55349i) q^{82} +(4.21219 + 10.1691i) q^{83} +(-8.61624 - 3.28031i) q^{85} -1.08479 q^{86} +(-20.9215 + 4.16154i) q^{88} +(-1.93036 + 1.93036i) q^{89} +(-0.597362 - 0.894016i) q^{91} +(12.4391 + 18.6165i) q^{92} +(24.2819 - 10.0579i) q^{94} +(-7.81391 + 2.78412i) q^{95} +(-1.26576 + 1.89434i) q^{97} -18.7550 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q+O(q^{10}) \) 144 * q	\( 144 q - 16 q^{10} - 64 q^{14} - 32 q^{19} + 32 q^{20} - 16 q^{25} + 64 q^{26} - 64 q^{28} - 32 q^{31} + 32 q^{34} - 32 q^{37} + 112 q^{40} + 80 q^{41} - 16 q^{46} + 64 q^{50} - 64 q^{52} - 48 q^{53} - 64 q^{55} - 112 q^{58} - 32 q^{59} - 32 q^{64} + 64 q^{67} + 272 q^{68} - 32 q^{70} - 32 q^{71} - 80 q^{73} - 80 q^{74} + 64 q^{76} + 96 q^{77} + 32 q^{79} - 336 q^{80} + 16 q^{83} + 32 q^{85} - 64 q^{86} - 80 q^{88} - 320 q^{92} + 16 q^{94} + 64 q^{95} - 16 q^{97} - 144 q^{98}+O(q^{100}) \) 144 * q - 16 * q^10 - 64 * q^14 - 32 * q^19 + 32 * q^20 - 16 * q^25 + 64 * q^26 - 64 * q^28 - 32 * q^31 + 32 * q^34 - 32 * q^37 + 112 * q^40 + 80 * q^41 - 16 * q^46 + 64 * q^50 - 64 * q^52 - 48 * q^53 - 64 * q^55 - 112 * q^58 - 32 * q^59 - 32 * q^64 + 64 * q^67 + 272 * q^68 - 32 * q^70 - 32 * q^71 - 80 * q^73 - 80 * q^74 + 64 * q^76 + 96 * q^77 + 32 * q^79 - 336 * q^80 + 16 * q^83 + 32 * q^85 - 64 * q^86 - 80 * q^88 - 320 * q^92 + 16 * q^94 + 64 * q^95 - 16 * q^97 - 144 * q^98

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