LMFDB - Embedded newform 180.8.e.a.71.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,8,Mod(71,180)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(180, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("180.71");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	180.e (of order $2$, degree $1$, 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:	$56.2293045871$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.5
Character	$\chi$	$=$	180.71
Dual form			180.8.e.a.71.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-10.3734 - 4.51586i) q^{2} +(87.2140 + 93.6895i) q^{4} -125.000i q^{5} +1388.07i q^{7} +(-481.616 - 1365.72i) q^{8} +O(q^{10})$	\(q+(-10.3734 - 4.51586i) q^{2} +(87.2140 + 93.6895i) q^{4} -125.000i q^{5} +1388.07i q^{7} +(-481.616 - 1365.72i) q^{8} +(-564.482 + 1296.67i) q^{10} +1274.75 q^{11} +5059.27 q^{13} +(6268.35 - 14399.0i) q^{14} +(-1171.43 + 16342.1i) q^{16} +2128.10i q^{17} +23853.7i q^{19} +(11711.2 - 10901.8i) q^{20} +(-13223.5 - 5756.60i) q^{22} +42721.8 q^{23} -15625.0 q^{25} +(-52481.7 - 22846.9i) q^{26} +(-130048. + 121060. i) q^{28} +180459. i q^{29} -211817. i q^{31} +(85950.2 - 164232. i) q^{32} +(9610.18 - 22075.6i) q^{34} +173509. q^{35} -36469.8 q^{37} +(107720. - 247443. i) q^{38} +(-170715. + 60202.0i) q^{40} -686323. i q^{41} +200617. i q^{43} +(111176. + 119431. i) q^{44} +(-443170. - 192926. i) q^{46} -481676. q^{47} -1.10321e6 q^{49} +(162084. + 70560.3i) q^{50} +(441239. + 474000. i) q^{52} -296100. i q^{53} -159344. i q^{55} +(1.89572e6 - 668519. i) q^{56} +(814928. - 1.87197e6i) q^{58} +414433. q^{59} -1.97109e6 q^{61} +(-956536. + 2.19726e6i) q^{62} +(-1.63324e6 + 1.31551e6i) q^{64} -632409. i q^{65} +1.99804e6i q^{67} +(-199380. + 185600. i) q^{68} +(-1.79988e6 - 783544. i) q^{70} -73437.9 q^{71} -1.14008e6 q^{73} +(378315. + 164693. i) q^{74} +(-2.23484e6 + 2.08038e6i) q^{76} +1.76945e6i q^{77} +6.89870e6i q^{79} +(2.04276e6 + 146429. i) q^{80} +(-3.09934e6 + 7.11949e6i) q^{82} +5.76938e6 q^{83} +266012. q^{85} +(905960. - 2.08108e6i) q^{86} +(-613940. - 1.74096e6i) q^{88} +1.18002e7i q^{89} +7.02264e6i q^{91} +(3.72594e6 + 4.00258e6i) q^{92} +(4.99661e6 + 2.17518e6i) q^{94} +2.98171e6 q^{95} +1.53911e7 q^{97} +(1.14440e7 + 4.98193e6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 52 q^{4}+O(q^{10}) $ 56 * q + 52 * q^4	$ 56 q + 52 q^{4} - 6500 q^{10} + 14128 q^{13} - 8060 q^{16} + 259088 q^{22} - 875000 q^{25} - 490976 q^{28} + 40912 q^{34} + 1268048 q^{37} - 266500 q^{40} + 3108200 q^{46} - 3522056 q^{49} - 8882216 q^{52} + 8807592 q^{58} - 3944912 q^{61} - 16633580 q^{64} + 4533000 q^{70} + 7602384 q^{73} - 38876976 q^{76} + 33213064 q^{82} - 15068000 q^{85} - 56145472 q^{88} + 29409456 q^{94} - 45595824 q^{97}+O(q^{100}) $ 56 * q + 52 * q^4 - 6500 * q^10 + 14128 * q^13 - 8060 * q^16 + 259088 * q^22 - 875000 * q^25 - 490976 * q^28 + 40912 * q^34 + 1268048 * q^37 - 266500 * q^40 + 3108200 * q^46 - 3522056 * q^49 - 8882216 * q^52 + 8807592 * q^58 - 3944912 * q^61 - 16633580 * q^64 + 4533000 * q^70 + 7602384 * q^73 - 38876976 * q^76 + 33213064 * q^82 - 15068000 * q^85 - 56145472 * q^88 + 29409456 * q^94 - 45595824 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−10.3734	−	4.51586i	−0.916886	−	0.399149i
$2$	−10.3734	−	4.51586i	−0.916886	−	0.399149i
$3$		0			0
$3$		0			0
$4$	87.2140	+	93.6895i	0.681360	+	0.731949i
$5$		−	125.000i		−	0.447214i
$5$		−	125.000i		−	0.447214i
$6$		0			0
$7$			1388.07i			1.52957i	0.644285	+	0.764786i	$0.277155\pi$
$7$			1388.07i			1.52957i	−0.644285	+	0.764786i	$0.722845\pi$
$8$	−481.616	−	1365.72i	−0.332572	−	0.943078i
$9$		0			0
$10$	−564.482	+	1296.67i	−0.178505	+	0.410044i
$11$	1274.75			0.288769			0.144385	−	0.989522i	$-0.453880\pi$
$11$	1274.75			0.288769			0.144385	+	0.989522i	$0.453880\pi$
$12$		0			0
$13$	5059.27			0.638684			0.319342	−	0.947640i	$-0.396538\pi$
$13$	5059.27			0.638684			0.319342	+	0.947640i	$0.396538\pi$
$14$	6268.35	−	14399.0i	0.610527	−	1.40244i
$15$		0			0
$16$	−1171.43	+	16342.1i	−0.0714983	+	0.997441i
$17$			2128.10i			0.105056i	0.998619	+	0.0525279i	$0.0167278\pi$
$17$			2128.10i			0.105056i	−0.998619	+	0.0525279i	$0.983272\pi$
$18$		0			0
$19$			23853.7i			0.797844i	0.916985	+	0.398922i	$0.130616\pi$
$19$			23853.7i			0.797844i	−0.916985	+	0.398922i	$0.869384\pi$
$20$	11711.2	−	10901.8i	0.327337	−	0.304713i
$21$		0			0
$22$	−13223.5	−	5756.60i	−0.264768	−	0.115262i
$23$	42721.8			0.732154			0.366077	−	0.930585i	$-0.380701\pi$
$23$	42721.8			0.732154			0.366077	+	0.930585i	$0.380701\pi$
$24$		0			0
$25$	−15625.0			−0.200000
$26$	−52481.7	−	22846.9i	−0.585600	−	0.254930i
$27$		0			0
$28$	−130048.	+	121060.i	−1.11957	+	1.04219i
$29$			180459.i			1.37400i	0.726659	+	0.686999i	$0.241072\pi$
$29$			180459.i			1.37400i	−0.726659	+	0.686999i	$0.758928\pi$
$30$		0			0
$31$		−	211817.i		−	1.27701i	−0.769617	−	0.638506i	$-0.779553\pi$
$31$		−	211817.i		−	1.27701i	0.769617	−	0.638506i	$-0.220447\pi$
$32$	85950.2	−	164232.i	0.463684	−	0.886001i
$33$		0			0
$34$	9610.18	−	22075.6i	0.0419330	−	0.0963242i
$35$	173509.			0.684045
$36$		0			0
$37$	−36469.8			−0.118366			−0.0591831	−	0.998247i	$-0.518850\pi$
$37$	−36469.8			−0.118366			−0.0591831	+	0.998247i	$0.518850\pi$
$38$	107720.	−	247443.i	0.318459	−	0.731532i
$39$		0			0
$40$	−170715.	+	60202.0i	−0.421757	+	0.148731i
$41$		−	686323.i		−	1.55520i	−0.628762	−	0.777598i	$-0.716438\pi$
$41$		−	686323.i		−	1.55520i	0.628762	−	0.777598i	$-0.283562\pi$
$42$		0			0
$43$			200617.i			0.384794i	0.981317	+	0.192397i	$0.0616262\pi$
$43$			200617.i			0.384794i	−0.981317	+	0.192397i	$0.938374\pi$
$44$	111176.	+	119431.i	0.196756	+	0.211364i
$45$		0			0
$46$	−443170.	−	192926.i	−0.671302	−	0.292239i
$47$	−481676.			−0.676726			−0.338363	−	0.941016i	$-0.609873\pi$
$47$	−481676.			−0.676726			−0.338363	+	0.941016i	$0.609873\pi$
$48$		0			0
$49$	−1.10321e6			−1.33959
$50$	162084.	+	70560.3i	0.183377	+	0.0798299i
$51$		0			0
$52$	441239.	+	474000.i	0.435173	+	0.467484i
$53$		−	296100.i		−	0.273195i	−0.990627	−	0.136598i	$-0.956383\pi$
$53$		−	296100.i		−	0.273195i	0.990627	−	0.136598i	$-0.0436168\pi$
$54$		0			0
$55$		−	159344.i		−	0.129142i
$56$	1.89572e6	−	668519.i	1.44250	−	0.508693i
$57$		0			0
$58$	814928.	−	1.87197e6i	0.548430	−	1.25980i
$59$	414433.			0.262708			0.131354	−	0.991336i	$-0.458068\pi$
$59$	414433.			0.262708			0.131354	+	0.991336i	$0.458068\pi$
$60$		0			0
$61$	−1.97109e6			−1.11187			−0.555933	−	0.831227i	$-0.687639\pi$
$61$	−1.97109e6			−1.11187			−0.555933	+	0.831227i	$0.687639\pi$
$62$	−956536.	+	2.19726e6i	−0.509718	+	1.17087i
$63$		0			0
$64$	−1.63324e6	+	1.31551e6i	−0.778792	+	0.627283i
$65$		−	632409.i		−	0.285628i
$66$		0			0
$67$			1.99804e6i			0.811599i	0.913962	+	0.405799i	$0.133007\pi$
$67$			1.99804e6i			0.811599i	−0.913962	+	0.405799i	$0.866993\pi$
$68$	−199380.	+	185600.i	−0.0768955	+	0.0715808i
$69$		0			0
$70$	−1.79988e6	−	783544.i	−0.627191	−	0.273036i
$71$	−73437.9			−0.0243510			−0.0121755	−	0.999926i	$-0.503876\pi$
$71$	−73437.9			−0.0243510			−0.0121755	+	0.999926i	$0.503876\pi$
$72$		0			0
$73$	−1.14008e6			−0.343008			−0.171504	−	0.985183i	$-0.554863\pi$
$73$	−1.14008e6			−0.343008			−0.171504	+	0.985183i	$0.554863\pi$
$74$	378315.	+	164693.i	0.108528	+	0.0472458i
$75$		0			0
$76$	−2.23484e6	+	2.08038e6i	−0.583981	+	0.543618i
$77$			1.76945e6i			0.441693i
$78$		0			0
$79$			6.89870e6i			1.57424i	0.616797	+	0.787122i	$0.288430\pi$
$79$			6.89870e6i			1.57424i	−0.616797	+	0.787122i	$0.711570\pi$
$80$	2.04276e6	+	146429.i	0.446069	+	0.0319750i
$81$		0			0
$82$	−3.09934e6	+	7.11949e6i	−0.620756	+	1.42594i
$83$	5.76938e6			1.10753			0.553765	−	0.832673i	$-0.313191\pi$
$83$	5.76938e6			1.10753			0.553765	+	0.832673i	$0.313191\pi$
$84$		0			0
$85$	266012.			0.0469824
$86$	905960.	−	2.08108e6i	0.153590	−	0.352813i
$87$		0			0
$88$	−613940.	−	1.74096e6i	−0.0960366	−	0.272332i
$89$			1.18002e7i			1.77429i	0.461492	+	0.887144i	$0.347314\pi$
$89$			1.18002e7i			1.77429i	−0.461492	+	0.887144i	$0.652686\pi$
$90$		0			0
$91$			7.02264e6i			0.976912i
$92$	3.72594e6	+	4.00258e6i	0.498860	+	0.535899i
$93$		0			0
$94$	4.99661e6	+	2.17518e6i	0.620480	+	0.270115i
$95$	2.98171e6			0.356806
$96$		0			0
$97$	1.53911e7			1.71225			0.856125	−	0.516769i	$-0.172865\pi$
$97$	1.53911e7			1.71225			0.856125	+	0.516769i	$0.172865\pi$
$98$	1.14440e7	+	4.98193e6i	1.22825	+	0.534696i
$99$		0			0
$100$	−1.36272e6	−	1.46390e6i	−0.136272	−	0.146390i
$101$			1.43217e7i			1.38315i	0.722304	+	0.691576i	$0.243083\pi$
$101$			1.43217e7i			1.38315i	−0.722304	+	0.691576i	$0.756917\pi$
$102$		0			0
$103$			1.02455e7i			0.923852i	0.886919	+	0.461926i	$0.152841\pi$
$103$			1.02455e7i			0.923852i	−0.886919	+	0.461926i	$0.847159\pi$
$104$	−2.43662e6	−	6.90956e6i	−0.212408	−	0.602329i
$105$		0			0
$106$	−1.33715e6	+	3.07156e6i	−0.109046	+	0.250489i
$107$	−1.51837e7			−1.19822			−0.599108	−	0.800668i	$-0.704478\pi$
$107$	−1.51837e7			−1.19822			−0.599108	+	0.800668i	$0.704478\pi$
$108$		0			0
$109$	−8.62207e6			−0.637704			−0.318852	−	0.947805i	$-0.603297\pi$
$109$	−8.62207e6			−0.637704			−0.318852	+	0.947805i	$0.603297\pi$
$110$	−719574.	+	1.65293e6i	−0.0515468	+	0.118408i
$111$		0			0
$112$	−2.26840e7	−	1.62603e6i	−1.52566	−	0.109362i
$113$			1.66840e7i			1.08774i	0.839168	+	0.543872i	$0.183042\pi$
$113$			1.66840e7i			1.08774i	−0.839168	+	0.543872i	$0.816958\pi$
$114$		0			0
$115$		−	5.34023e6i		−	0.327429i
$116$	−1.69071e7	+	1.57386e7i	−1.00570	+	0.936186i
$117$		0			0
$118$	−4.29907e6	−	1.87152e6i	−0.240873	−	0.104860i
$119$	−2.95396e6			−0.160690
$120$		0			0
$121$	−1.78622e7			−0.916612
$122$	2.04469e7	+	8.90117e6i	1.01945	+	0.443800i
$123$		0			0
$124$	1.98450e7	−	1.84734e7i	0.934707	−	0.870104i
$125$			1.95312e6i			0.0894427i
$126$		0			0
$127$			5.94760e6i			0.257649i	0.991667	+	0.128825i	$0.0411204\pi$
$127$			5.94760e6i			0.257649i	−0.991667	+	0.128825i	$0.958880\pi$
$128$	2.28829e7	−	6.27075e6i	0.964443	−	0.264292i
$129$		0			0
$130$	−2.85587e6	+	6.56021e6i	−0.114008	+	0.261888i
$131$	−5.06835e7			−1.96978			−0.984888	−	0.173194i	$-0.944591\pi$
$131$	−5.06835e7			−1.96978			−0.984888	+	0.173194i	$0.944591\pi$
$132$		0			0
$133$	−3.31107e7			−1.22036
$134$	9.02285e6	−	2.07264e7i	0.323949	−	0.744144i
$135$		0			0
$136$	2.90639e6	−	1.02492e6i	0.0990758	−	0.0349386i
$137$		−	5.05137e7i		−	1.67837i	−0.543847	−	0.839184i	$-0.683033\pi$
$137$		−	5.05137e7i		−	1.67837i	0.543847	−	0.839184i	$-0.316967\pi$
$138$		0			0
$139$			2.58217e7i			0.815517i	0.913090	+	0.407759i	$0.133690\pi$
$139$			2.58217e7i			0.815517i	−0.913090	+	0.407759i	$0.866310\pi$
$140$	1.51324e7	+	1.62560e7i	0.466081	+	0.500686i
$141$		0			0
$142$	761799.	+	331635.i	0.0223271	+	0.00971967i
$143$	6.44931e6			0.184432
$144$		0			0
$145$	2.25574e7			0.614470
$146$	1.18265e7	+	5.14843e6i	0.314499	+	0.136911i
$147$		0			0
$148$	−3.18068e6	−	3.41684e6i	−0.0806499	−	0.0866380i
$149$		−	9.26731e6i		−	0.229510i	−0.993394	−	0.114755i	$-0.963392\pi$
$149$		−	9.26731e6i		−	0.229510i	0.993394	−	0.114755i	$-0.0366083\pi$
$150$		0			0
$151$			6.86837e7i			1.62343i	0.584052	+	0.811716i	$0.301466\pi$
$151$			6.86837e7i			1.62343i	−0.584052	+	0.811716i	$0.698534\pi$
$152$	3.25775e7	−	1.14883e7i	0.752429	−	0.265340i
$153$		0			0
$154$	7.99058e6	−	1.83552e7i	0.176301	−	0.404982i
$155$	−2.64771e7			−0.571097
$156$		0			0
$157$	8.31581e7			1.71497			0.857484	−	0.514511i	$-0.172027\pi$
$157$	8.31581e7			1.71497			0.857484	+	0.514511i	$0.172027\pi$
$158$	3.11536e7	−	7.15628e7i	0.628359	−	1.44340i
$159$		0			0
$160$	−2.05291e7	−	1.07438e7i	−0.396232	−	0.207366i
$161$			5.93011e7i			1.11988i
$162$		0			0
$163$		−	3.24488e7i		−	0.586870i	−0.955979	−	0.293435i	$-0.905202\pi$
$163$		−	3.24488e7i		−	0.586870i	0.955979	−	0.293435i	$-0.0947984\pi$
$164$	6.43012e7	−	5.98570e7i	1.13832	−	1.05965i
$165$		0			0
$166$	−5.98479e7	−	2.60537e7i	−1.01548	−	0.442070i
$167$	−3.77804e6			−0.0627710			−0.0313855	−	0.999507i	$-0.509992\pi$
$167$	−3.77804e6			−0.0627710			−0.0313855	+	0.999507i	$0.509992\pi$
$168$		0			0
$169$	−3.71523e7			−0.592083
$170$	−2.75944e6	−	1.20127e6i	−0.0430775	−	0.0187530i
$171$		0			0
$172$	−1.87957e7	+	1.74966e7i	−0.281650	+	0.262183i
$173$			6.30647e6i			0.0926029i	0.998928	+	0.0463015i	$0.0147435\pi$
$173$			6.30647e6i			0.0926029i	−0.998928	+	0.0463015i	$0.985257\pi$
$174$		0			0
$175$		−	2.16887e7i		−	0.305914i
$176$	−1.49328e6	+	2.08321e7i	−0.0206465	+	0.288030i
$177$		0			0
$178$	5.32880e7	−	1.22408e8i	0.708206	−	1.62682i
$179$	−6.09712e7			−0.794583			−0.397292	−	0.917692i	$-0.630050\pi$
$179$	−6.09712e7			−0.794583			−0.397292	+	0.917692i	$0.630050\pi$
$180$		0			0
$181$	2.80856e7			0.352054			0.176027	−	0.984385i	$-0.443675\pi$
$181$	2.80856e7			0.352054			0.176027	+	0.984385i	$0.443675\pi$
$182$	3.17133e7	−	7.28485e7i	0.389934	−	0.895717i
$183$		0			0
$184$	−2.05755e7	−	5.83462e7i	−0.243494	−	0.690478i
$185$			4.55873e6i			0.0529350i
$186$		0			0
$187$			2.71279e6i			0.0303369i
$188$	−4.20089e7	−	4.51280e7i	−0.461094	−	0.495329i
$189$		0			0
$190$	−3.09304e7	−	1.34650e7i	−0.327151	−	0.142419i
$191$	−8.12894e7			−0.844145			−0.422073	−	0.906562i	$-0.638697\pi$
$191$	−8.12894e7			−0.844145			−0.422073	+	0.906562i	$0.638697\pi$
$192$		0			0
$193$	1.39405e8			1.39581			0.697905	−	0.716190i	$-0.254116\pi$
$193$	1.39405e8			1.39581			0.697905	+	0.716190i	$0.254116\pi$
$194$	−1.59657e8	−	6.95038e7i	−1.56994	−	0.683444i
$195$		0			0
$196$	−9.62152e7	−	1.03359e8i	−0.912741	−	0.980510i
$197$		−	3.91502e6i		−	0.0364840i	−0.999834	−	0.0182420i	$-0.994193\pi$
$197$		−	3.91502e6i		−	0.0364840i	0.999834	−	0.0182420i	$-0.00580693\pi$
$198$		0			0
$199$			1.30105e8i			1.17033i	0.810915	+	0.585164i	$0.198970\pi$
$199$			1.30105e8i			1.17033i	−0.810915	+	0.585164i	$0.801030\pi$
$200$	7.52525e6	+	2.13394e7i	0.0665144	+	0.188616i
$201$		0			0
$202$	6.46748e7	−	1.48564e8i	0.552084	−	1.26819i
$203$	−2.50491e8			−2.10163
$204$		0			0
$205$	−8.57904e7			−0.695505
$206$	4.62672e7	−	1.06280e8i	0.368755	−	0.847067i
$207$		0			0
$208$	−5.92657e6	+	8.26789e7i	−0.0456648	+	0.637049i
$209$			3.04075e7i			0.230393i
$210$		0			0
$211$		−	2.60892e8i		−	1.91193i	−0.293478	−	0.955966i	$-0.594813\pi$
$211$		−	2.60892e8i		−	1.91193i	0.293478	−	0.955966i	$-0.405187\pi$
$212$	2.77415e7	−	2.58241e7i	0.199965	−	0.186144i
$213$		0			0
$214$	1.57507e8	+	6.85676e7i	1.09863	+	0.478267i
$215$	2.50772e7			0.172085
$216$		0			0
$217$	2.94018e8			1.95328
$218$	8.94400e7	+	3.89361e7i	0.584701	+	0.254539i
$219$		0			0
$220$	1.49288e7	−	1.38970e7i	0.0945250	−	0.0879918i
$221$			1.07666e7i			0.0670974i
$222$		0			0
$223$			2.42169e8i			1.46235i	0.682188	+	0.731177i	$0.261029\pi$
$223$			2.42169e8i			1.46235i	−0.682188	+	0.731177i	$0.738971\pi$
$224$	2.27967e8	+	1.19305e8i	1.35520	+	0.709237i
$225$		0			0
$226$	7.53428e7	−	1.73070e8i	0.434172	−	0.997337i
$227$	−1.94751e8			−1.10507			−0.552533	−	0.833491i	$-0.686339\pi$
$227$	−1.94751e8			−1.10507			−0.552533	+	0.833491i	$0.686339\pi$
$228$		0			0
$229$	2.75124e8			1.51392			0.756962	−	0.653459i	$-0.226683\pi$
$229$	2.75124e8			1.51392			0.756962	+	0.653459i	$0.226683\pi$
$230$	−2.41157e7	+	5.53962e7i	−0.130693	+	0.300215i
$231$		0			0
$232$	2.46457e8	−	8.69119e7i	1.29579	−	0.456953i
$233$		−	7.45064e7i		−	0.385876i	−0.981211	−	0.192938i	$-0.938198\pi$
$233$		−	7.45064e7i		−	0.385876i	0.981211	−	0.192938i	$-0.0618017\pi$
$234$		0			0
$235$			6.02095e7i			0.302641i
$236$	3.61444e7	+	3.88280e7i	0.178998	+	0.192289i
$237$		0			0
$238$	3.06425e7	+	1.33397e7i	0.147335	+	0.0641394i
$239$	−2.97345e8			−1.40886			−0.704430	−	0.709774i	$-0.748797\pi$
$239$	−2.97345e8			−1.40886			−0.704430	+	0.709774i	$0.748797\pi$
$240$		0			0
$241$	−3.88935e8			−1.78985			−0.894927	−	0.446213i	$-0.852773\pi$
$241$	−3.88935e8			−1.78985			−0.894927	+	0.446213i	$0.852773\pi$
$242$	1.85291e8	+	8.06631e7i	0.840429	+	0.365865i
$243$		0			0
$244$	−1.71907e8	−	1.84670e8i	−0.757580	−	0.813829i
$245$			1.37901e8i			0.599082i
$246$		0			0
$247$			1.20682e8i			0.509570i
$248$	−2.89283e8	+	1.02014e8i	−1.20432	+	0.424698i
$249$		0			0
$250$	8.82004e6	−	2.02605e7i	0.0357010	−	0.0820088i
$251$	2.53923e7			0.101355			0.0506773	−	0.998715i	$-0.483862\pi$
$251$	2.53923e7			0.101355			0.0506773	+	0.998715i	$0.483862\pi$
$252$		0			0
$253$	5.44597e7			0.211424
$254$	2.68585e7	−	6.16967e7i	0.102841	−	0.236235i
$255$		0			0
$256$	−2.65691e8	−	3.82871e7i	−0.989776	−	0.142631i
$257$			3.79437e8i			1.39436i	0.716898	+	0.697178i	$0.245561\pi$
$257$			3.79437e8i			1.39436i	−0.716898	+	0.697178i	$0.754439\pi$
$258$		0			0
$259$		−	5.06228e7i		−	0.181049i
$260$	5.92500e7	−	5.51549e7i	0.209065	−	0.194615i
$261$		0			0
$262$	5.25759e8	+	2.28879e8i	1.80606	+	0.786235i
$263$	−1.74589e8			−0.591796			−0.295898	−	0.955220i	$-0.595619\pi$
$263$	−1.74589e8			−0.591796			−0.295898	+	0.955220i	$0.595619\pi$
$264$		0			0
$265$	−3.70126e7			−0.122177
$266$	3.43470e8	+	1.49523e8i	1.11893	+	0.487105i
$267$		0			0
$268$	−1.87195e8	+	1.74257e8i	−0.594049	+	0.552991i
$269$		−	4.94410e8i		−	1.54865i	−0.632787	−	0.774326i	$-0.718089\pi$
$269$		−	4.94410e8i		−	1.54865i	0.632787	−	0.774326i	$-0.281911\pi$
$270$		0			0
$271$			6.86161e7i			0.209427i	0.994502	+	0.104714i	$0.0333926\pi$
$271$			6.86161e7i			0.209427i	−0.994502	+	0.104714i	$0.966607\pi$
$272$	−3.47775e7	−	2.49291e6i	−0.104787	−	0.00751131i
$273$		0			0
$274$	−2.28113e8	+	5.23998e8i	−0.669920	+	1.53887i
$275$	−1.99180e7			−0.0577538
$276$		0			0
$277$	−1.73658e8			−0.490926			−0.245463	−	0.969406i	$-0.578940\pi$
$277$	−1.73658e8			−0.490926			−0.245463	+	0.969406i	$0.578940\pi$
$278$	1.16607e8	−	2.67858e8i	0.325513	−	0.747736i
$279$		0			0
$280$	−8.35648e7	−	2.36966e8i	−0.227494	−	0.645108i
$281$			4.13387e8i			1.11144i	0.831371	+	0.555718i	$0.187556\pi$
$281$			4.13387e8i			1.11144i	−0.831371	+	0.555718i	$0.812444\pi$
$282$		0			0
$283$			7.34823e7i			0.192722i	0.995346	+	0.0963608i	$0.0307203\pi$
$283$			7.34823e7i			0.192722i	−0.995346	+	0.0963608i	$0.969280\pi$
$284$	−6.40482e6	−	6.88036e6i	−0.0165918	−	0.0178237i
$285$		0			0
$286$	−6.69011e7	−	2.91242e7i	−0.169103	−	0.0736160i
$287$	9.52668e8			2.37878
$288$		0			0
$289$	4.05810e8			0.988963
$290$	−2.33996e8	−	1.01866e8i	−0.563399	−	0.245265i
$291$		0			0
$292$	−9.94307e7	−	1.06813e8i	−0.233712	−	0.251064i
$293$			5.46995e7i			0.127042i	0.997981	+	0.0635209i	$0.0202329\pi$
$293$			5.46995e7i			0.127042i	−0.997981	+	0.0635209i	$0.979767\pi$
$294$		0			0
$295$		−	5.18042e7i		−	0.117486i
$296$	1.75644e7	+	4.98077e7i	0.0393653	+	0.111628i
$297$		0			0
$298$	−4.18499e7	+	9.61334e7i	−0.0916088	+	0.210435i
$299$	2.16141e8			0.467615
$300$		0			0
$301$	−2.78472e8			−0.588571
$302$	3.10166e8	−	7.12482e8i	0.647992	−	1.48850i
$303$		0			0
$304$	−3.89818e8	−	2.79429e7i	−0.795802	−	0.0570445i
$305$			2.46386e8i			0.497241i
$306$		0			0
$307$			965988.i			0.00190541i	1.00000		0.000952703i	$0.000303255\pi$
$307$			965988.i			0.00190541i	−1.00000		0.000952703i	$0.999697\pi$
$308$	−1.65779e8	+	1.54321e8i	−0.323297	+	0.300952i
$309$		0			0
$310$	2.74657e8	+	1.19567e8i	0.523631	+	0.227953i
$311$	−8.59641e7			−0.162052			−0.0810262	−	0.996712i	$-0.525820\pi$
$311$	−8.59641e7			−0.162052			−0.0810262	+	0.996712i	$0.525820\pi$
$312$		0			0
$313$	−2.98238e8			−0.549741			−0.274871	−	0.961481i	$-0.588635\pi$
$313$	−2.98238e8			−0.549741			−0.274871	+	0.961481i	$0.588635\pi$
$314$	−8.62631e8	−	3.75530e8i	−1.57243	−	0.684528i
$315$		0			0
$316$	−6.46335e8	+	6.01663e8i	−1.15227	+	1.07263i
$317$		−	26528.4i		−	4.67740e-5i	−1.00000		2.33870e-5i	$-0.999993\pi$
$317$		−	26528.4i		−	4.67740e-5i	1.00000		2.33870e-5i	$-7.44431e-6\pi$
$318$		0			0
$319$			2.30040e8i			0.396768i
$320$	1.64438e8	+	2.04156e8i	0.280529	+	0.348286i
$321$		0			0
$322$	2.67795e8	−	6.15153e8i	0.447000	−	1.02680i
$323$	−5.07629e7			−0.0838181
$324$		0			0
$325$	−7.90511e7			−0.127737
$326$	−1.46534e8	+	3.36603e8i	−0.234249	+	0.538093i
$327$		0			0
$328$	−9.37327e8	+	3.30544e8i	−1.46667	+	0.517215i
$329$		−	6.68603e8i		−	1.03510i
$330$		0			0
$331$			6.71463e7i			0.101771i	0.998704	+	0.0508855i	$0.0162044\pi$
$331$			6.71463e7i			0.101771i	−0.998704	+	0.0508855i	$0.983796\pi$
$332$	5.03171e8	+	5.40530e8i	0.754626	+	0.810655i
$333$		0			0
$334$	3.91911e7	+	1.70611e7i	0.0575539	+	0.0250550i
$335$	2.49754e8			0.362958
$336$		0			0
$337$	−8.24251e8			−1.17315			−0.586577	−	0.809894i	$-0.699525\pi$
$337$	−8.24251e8			−1.17315			−0.586577	+	0.809894i	$0.699525\pi$
$338$	3.85395e8	+	1.67775e8i	0.542872	+	0.236330i
$339$		0			0
$340$	2.32000e7	+	2.49225e7i	0.0320119	+	0.0343887i
$341$		−	2.70014e8i		−	0.368762i
$342$		0			0
$343$		−	3.88196e8i		−	0.519423i
$344$	2.73988e8	−	9.66205e7i	0.362891	−	0.127972i
$345$		0			0
$346$	2.84791e7	−	6.54194e7i	0.0369624	−	0.0849063i
$347$	1.28368e9			1.64932			0.824658	−	0.565632i	$-0.191368\pi$
$347$	1.28368e9			1.64932			0.824658	+	0.565632i	$0.191368\pi$
$348$		0			0
$349$	−1.18584e9			−1.49327			−0.746633	−	0.665236i	$-0.768331\pi$
$349$	−1.18584e9			−1.49327			−0.746633	+	0.665236i	$0.768331\pi$
$350$	−9.79430e7	+	2.24985e8i	−0.122105	+	0.280488i
$351$		0			0
$352$	1.09565e8	−	2.09355e8i	0.133898	−	0.255850i
$353$		−	1.00167e9i		−	1.21203i	−0.795455	−	0.606013i	$-0.792768\pi$
$353$		−	1.00167e9i		−	1.21203i	0.795455	−	0.606013i	$-0.207232\pi$
$354$		0			0
$355$			9.17974e6i			0.0108901i
$356$	−1.10555e9	+	1.02914e9i	−1.29869	+	1.20893i
$357$		0			0
$358$	6.32478e8	+	2.75338e8i	0.728542	+	0.317157i
$359$	1.77057e7			0.0201968			0.0100984	−	0.999949i	$-0.496786\pi$
$359$	1.77057e7			0.0201968			0.0100984	+	0.999949i	$0.496786\pi$
$360$		0			0
$361$	3.24874e8			0.363446
$362$	−2.91343e8	−	1.26831e8i	−0.322793	−	0.140522i
$363$		0			0
$364$	−6.57947e8	+	6.12473e8i	−0.715050	+	0.665629i
$365$			1.42510e8i			0.153398i
$366$		0			0
$367$		−	7.44392e8i		−	0.786086i	−0.919520	−	0.393043i	$-0.871422\pi$
$367$		−	7.44392e8i		−	0.786086i	0.919520	−	0.393043i	$-0.128578\pi$
$368$	−5.00456e7	+	6.98163e8i	−0.0523478	+	0.730280i
$369$		0			0
$370$	2.05866e7	−	4.72894e7i	0.0211290	−	0.0485353i
$371$	4.11009e8			0.417872
$372$		0			0
$373$	−9.77494e8			−0.975288			−0.487644	−	0.873042i	$-0.662144\pi$
$373$	−9.77494e8			−0.975288			−0.487644	+	0.873042i	$0.662144\pi$
$374$	1.22506e7	−	2.81408e7i	0.0121089	−	0.0278155i
$375$		0			0
$376$	2.31983e8	+	6.57836e8i	0.225060	+	0.638205i
$377$			9.12991e8i			0.877550i
$378$		0			0
$379$			1.31410e9i			1.23991i	0.784637	+	0.619956i	$0.212849\pi$
$379$			1.31410e9i			1.23991i	−0.784637	+	0.619956i	$0.787151\pi$
$380$	2.60047e8	+	2.79355e8i	0.243114	+	0.261164i
$381$		0			0
$382$	8.43246e8	+	3.67092e8i	0.773985	+	0.336940i
$383$	1.23095e9			1.11955			0.559777	−	0.828643i	$-0.310887\pi$
$383$	1.23095e9			1.11955			0.559777	+	0.828643i	$0.310887\pi$
$384$		0			0
$385$	2.21181e8			0.197531
$386$	−1.44610e9	−	6.29532e8i	−1.27980	−	0.557137i
$387$		0			0
$388$	1.34232e9	+	1.44198e9i	1.16666	+	1.25328i
$389$		−	5.87639e8i		−	0.506159i	−0.967445	−	0.253080i	$-0.918557\pi$
$389$		−	5.87639e8i		−	0.506159i	0.967445	−	0.253080i	$-0.0814435\pi$
$390$		0			0
$391$			9.09162e7i			0.0769170i
$392$	5.31322e8	+	1.50668e9i	0.445509	+	1.26334i
$393$		0			0
$394$	−1.76797e7	+	4.06120e7i	−0.0145626	+	0.0334517i
$395$	8.62337e8			0.704024
$396$		0			0
$397$	2.06080e9			1.65298			0.826491	−	0.562950i	$-0.190334\pi$
$397$	2.06080e9			1.65298			0.826491	+	0.562950i	$0.190334\pi$
$398$	5.87535e8	−	1.34963e9i	0.467136	−	1.07306i
$399$		0			0
$400$	1.83036e7	−	2.55345e8i	0.0142997	−	0.199488i
$401$		−	3.11261e8i		−	0.241057i	−0.992710	−	0.120528i	$-0.961541\pi$
$401$		−	3.11261e8i		−	0.241057i	0.992710	−	0.120528i	$-0.0384589\pi$
$402$		0			0
$403$		−	1.07164e9i		−	0.815607i
$404$	−1.34179e9	+	1.24905e9i	−1.01240	+	0.942423i
$405$		0			0
$406$	2.59843e9	+	1.13118e9i	1.92695	+	0.838863i
$407$	−4.64899e7			−0.0341805
$408$		0			0
$409$	−5.20601e8			−0.376247			−0.188124	−	0.982145i	$-0.560241\pi$
$409$	−5.20601e8			−0.376247			−0.188124	+	0.982145i	$0.560241\pi$
$410$	8.89936e8	+	3.87417e8i	0.637699	+	0.277610i
$411$		0			0
$412$	−9.59894e8	+	8.93550e8i	−0.676212	+	0.629475i
$413$			5.75264e8i			0.401830i
$414$		0			0
$415$		−	7.21172e8i		−	0.495303i
$416$	4.34845e8	−	8.30896e8i	0.296147	−	0.565874i
$417$		0			0
$418$	1.37316e8	−	3.15429e8i	0.0919611	−	0.211244i
$419$	4.15734e8			0.276100			0.138050	−	0.990425i	$-0.455917\pi$
$419$	4.15734e8			0.276100			0.138050	+	0.990425i	$0.455917\pi$
$420$		0			0
$421$	1.68760e8			0.110225			0.0551126	−	0.998480i	$-0.482448\pi$
$421$	1.68760e8			0.110225			0.0551126	+	0.998480i	$0.482448\pi$
$422$	−1.17815e9	+	2.70633e9i	−0.763146	+	1.75302i
$423$		0			0
$424$	−4.04391e8	+	1.42607e8i	−0.257645	+	0.0908572i
$425$		−	3.32515e7i		−	0.0210112i
$426$		0			0
$427$		−	2.73602e9i		−	1.70068i
$428$	−1.32423e9	−	1.42256e9i	−0.816416	−	0.877033i
$429$		0			0
$430$	−2.60135e8	−	1.13245e8i	−0.157783	−	0.0686878i
$431$	−1.13854e9			−0.684980			−0.342490	−	0.939521i	$-0.611270\pi$
$431$	−1.13854e9			−0.684980			−0.342490	+	0.939521i	$0.611270\pi$
$432$		0			0
$433$	1.11009e8			0.0657128			0.0328564	−	0.999460i	$-0.489540\pi$
$433$	1.11009e8			0.0657128			0.0328564	+	0.999460i	$0.489540\pi$
$434$	−3.04996e9	−	1.32774e9i	−1.79094	−	0.779651i
$435$		0			0
$436$	−7.51965e8	−	8.07797e8i	−0.434505	−	0.466766i
$437$			1.01907e9i			0.584144i
$438$		0			0
$439$		−	5.48170e8i		−	0.309236i	−0.987974	−	0.154618i	$-0.950585\pi$
$439$		−	5.48170e8i		−	0.309236i	0.987974	−	0.154618i	$-0.0494146\pi$
$440$	−2.17620e8	+	7.67425e7i	−0.121791	+	0.0429489i
$441$		0			0
$442$	4.86205e7	−	1.11686e8i	0.0267819	−	0.0615207i
$443$	−1.18940e9			−0.650000			−0.325000	−	0.945714i	$-0.605364\pi$
$443$	−1.18940e9			−0.650000			−0.325000	+	0.945714i	$0.605364\pi$
$444$		0			0
$445$	1.47502e9			0.793486
$446$	1.09360e9	−	2.51212e9i	0.583697	−	1.34081i
$447$		0			0
$448$	−1.82602e9	−	2.26707e9i	−0.959473	−	1.19122i
$449$			3.00630e8i			0.156737i	0.996924	+	0.0783683i	$0.0249710\pi$
$449$			3.00630e8i			0.156737i	−0.996924	+	0.0783683i	$0.975029\pi$
$450$		0			0
$451$		−	8.74891e8i		−	0.449093i
$452$	−1.56312e9	+	1.45508e9i	−0.796173	+	0.741144i
$453$		0			0
$454$	2.02022e9	+	8.79467e8i	1.01322	+	0.441087i
$455$	8.77830e8			0.436888
$456$		0			0
$457$	2.61862e9			1.28341			0.641706	−	0.766951i	$-0.278227\pi$
$457$	2.61862e9			1.28341			0.641706	+	0.766951i	$0.278227\pi$
$458$	−2.85397e9	−	1.24242e9i	−1.38810	−	0.604282i
$459$		0			0
$460$	5.00323e8	−	4.65743e8i	0.239661	−	0.223097i
$461$		−	1.88686e9i		−	0.896986i	−0.893786	−	0.448493i	$-0.851961\pi$
$461$		−	1.88686e9i		−	0.896986i	0.893786	−	0.448493i	$-0.148039\pi$
$462$		0			0
$463$		−	3.44113e9i		−	1.61127i	−0.592415	−	0.805633i	$-0.701825\pi$
$463$		−	3.44113e9i		−	1.61127i	0.592415	−	0.805633i	$-0.298175\pi$
$464$	−2.94907e9	−	2.11395e8i	−1.37048	−	0.0982385i
$465$		0			0
$466$	−3.36461e8	+	7.72883e8i	−0.154022	+	0.353804i
$467$	1.02699e9			0.466613			0.233307	−	0.972403i	$-0.425045\pi$
$467$	1.02699e9			0.466613			0.233307	+	0.972403i	$0.425045\pi$
$468$		0			0
$469$	−2.77342e9			−1.24140
$470$	2.71898e8	−	6.24576e8i	0.120799	−	0.277487i
$471$		0			0
$472$	−1.99598e8	−	5.66001e8i	−0.0873692	−	0.247754i
$473$			2.55737e8i			0.111117i
$474$		0			0
$475$		−	3.72714e8i		−	0.159569i
$476$	−2.57626e8	−	2.76755e8i	−0.109488	−	0.117617i
$477$		0			0
$478$	3.08447e9	+	1.34277e9i	1.29176	+	0.562345i
$479$	−1.64738e9			−0.684887			−0.342444	−	0.939538i	$-0.611255\pi$
$479$	−1.64738e9			−0.684887			−0.342444	+	0.939538i	$0.611255\pi$
$480$		0			0
$481$	−1.84511e8			−0.0755986
$482$	4.03457e9	+	1.75638e9i	1.64109	+	0.714419i
$483$		0			0
$484$	−1.55783e9	−	1.67350e9i	−0.624543	−	0.670913i
$485$		−	1.92388e9i		−	0.765742i
$486$		0			0
$487$		−	3.64629e9i		−	1.43054i	−0.698848	−	0.715270i	$-0.746304\pi$
$487$		−	3.64629e9i		−	1.43054i	0.698848	−	0.715270i	$-0.253696\pi$
$488$	9.49308e8	+	2.69196e9i	0.369775	+	1.04858i
$489$		0			0
$490$	6.22742e8	−	1.43050e9i	0.239123	−	0.549290i
$491$	3.38039e9			1.28879			0.644394	−	0.764694i	$-0.277110\pi$
$491$	3.38039e9			1.28879			0.644394	+	0.764694i	$0.277110\pi$
$492$		0			0
$493$	−3.84034e8			−0.144346
$494$	5.44984e8	−	1.25188e9i	0.203394	−	0.467217i
$495$		0			0
$496$	3.46153e9	+	2.48129e8i	1.27374	+	0.0913042i
$497$		−	1.01937e8i		−	0.0372465i
$498$		0			0
$499$			5.37118e9i			1.93516i	0.252557	+	0.967582i	$0.418729\pi$
$499$			5.37118e9i			1.93516i	−0.252557	+	0.967582i	$0.581271\pi$
$500$	−1.82987e8	+	1.70340e8i	−0.0654675	+	0.0609427i
$501$		0			0
$502$	−2.63404e8	−	1.14668e8i	−0.0929306	−	0.0404556i
$503$	−2.47520e8			−0.0867205			−0.0433603	−	0.999060i	$-0.513806\pi$
$503$	−2.47520e8			−0.0867205			−0.0433603	+	0.999060i	$0.513806\pi$
$504$		0			0
$505$	1.79021e9			0.618564
$506$	−5.64931e8	−	2.45932e8i	−0.193851	−	0.0843896i
$507$		0			0
$508$	−5.57227e8	+	5.18714e8i	−0.188586	+	0.175552i
$509$		−	3.85325e9i		−	1.29513i	−0.762008	−	0.647567i	$-0.775787\pi$
$509$		−	3.85325e9i		−	1.29513i	0.762008	−	0.647567i	$-0.224213\pi$
$510$		0			0
$511$		−	1.58251e9i		−	0.524655i
$512$	2.58321e9	+	1.59699e9i	0.850581	+	0.525845i
$513$		0			0
$514$	1.71348e9	−	3.93605e9i	0.556557	−	1.27847i
$515$	1.28069e9			0.413159
$516$		0			0
$517$	−6.14017e8			−0.195418
$518$	−2.28606e8	+	5.25130e8i	−0.0722658	+	0.166002i
$519$		0			0
$520$	−8.63695e8	+	3.04578e8i	−0.269370	+	0.0949919i
$521$		−	5.29537e9i		−	1.64046i	−0.572037	−	0.820228i	$-0.693847\pi$
$521$		−	5.29537e9i		−	1.64046i	0.572037	−	0.820228i	$-0.306153\pi$
$522$		0			0
$523$			5.38577e9i			1.64624i	0.567870	+	0.823118i	$0.307767\pi$
$523$			5.38577e9i			1.64624i	−0.567870	+	0.823118i	$0.692233\pi$
$524$	−4.42031e9	−	4.74851e9i	−1.34213	−	1.44178i
$525$		0			0
$526$	1.81108e9	+	7.88420e8i	0.542609	+	0.236215i
$527$	4.50767e8			0.134157
$528$		0			0
$529$	−1.57967e9			−0.463951
$530$	3.83945e8	+	1.67143e8i	0.112022	+	0.0487668i
$531$		0			0
$532$	−2.88772e9	−	3.10212e9i	−0.831503	−	0.893240i
$533$		−	3.47229e9i		−	0.993279i
$534$		0			0
$535$			1.89797e9i			0.535859i
$536$	2.72876e9	−	9.62285e8i	0.765401	−	0.269915i
$537$		0			0
$538$	−2.23268e9	+	5.12870e9i	−0.618144	+	1.41994i
$539$	−1.40632e9			−0.386832
$540$		0			0
$541$	3.71676e9			1.00919			0.504596	−	0.863356i	$-0.331641\pi$
$541$	3.71676e9			1.00919			0.504596	+	0.863356i	$0.331641\pi$
$542$	3.09861e8	−	7.11781e8i	0.0835929	−	0.192021i
$543$		0			0
$544$	3.49503e8	+	1.82910e8i	0.0930795	+	0.0487127i
$545$			1.07776e9i			0.285190i
$546$		0			0
$547$		−	1.11566e9i		−	0.291459i	−0.989324	−	0.145729i	$-0.953447\pi$
$547$		−	1.11566e9i		−	0.291459i	0.989324	−	0.145729i	$-0.0465529\pi$
$548$	4.73260e9	−	4.40551e9i	1.22848	−	1.14357i
$549$		0			0
$550$	2.06617e8	+	8.99468e7i	0.0529537	+	0.0230524i
$551$	−4.30461e9			−1.09623
$552$		0			0
$553$	−9.57591e9			−2.40792
$554$	1.80142e9	+	7.84216e8i	0.450123	+	0.195953i
$555$		0			0
$556$	−2.41922e9	+	2.25202e9i	−0.596917	+	0.555661i
$557$			6.11433e9i			1.49919i	0.661899	+	0.749593i	$0.269751\pi$
$557$			6.11433e9i			1.49919i	−0.661899	+	0.749593i	$0.730249\pi$
$558$		0			0
$559$			1.01498e9i			0.245762i
$560$	−2.03254e8	+	2.83550e9i	−0.0489081	+	0.682294i
$561$		0			0
$562$	1.86680e9	−	4.28822e9i	0.443629	−	1.01906i
$563$	−5.60380e9			−1.32344			−0.661719	−	0.749752i	$-0.730173\pi$
$563$	−5.60380e9			−1.32344			−0.661719	+	0.749752i	$0.730173\pi$
$564$		0			0
$565$	2.08550e9			0.486454
$566$	3.31836e8	−	7.62260e8i	0.0769247	−	0.176704i
$567$		0			0
$568$	3.53689e7	+	1.00296e8i	0.00809845	+	0.0229649i
$569$		−	8.85912e8i		−	0.201603i	−0.994907	−	0.100802i	$-0.967859\pi$
$569$		−	8.85912e8i		−	0.201603i	0.994907	−	0.100802i	$-0.0321408\pi$
$570$		0			0
$571$		−	9.80940e8i		−	0.220504i	−0.993904	−	0.110252i	$-0.964834\pi$
$571$		−	9.80940e8i		−	0.220504i	0.993904	−	0.110252i	$-0.0351657\pi$
$572$	5.62470e8	+	6.04232e8i	0.125665	+	0.134995i
$573$		0			0
$574$	−9.88238e9	−	4.30211e9i	−2.18107	−	0.949490i
$575$	−6.67529e8			−0.146431
$576$		0			0
$577$	−2.56135e9			−0.555078			−0.277539	−	0.960714i	$-0.589519\pi$
$577$	−2.56135e9			−0.555078			−0.277539	+	0.960714i	$0.589519\pi$
$578$	−4.20962e9	−	1.83258e9i	−0.906766	−	0.394744i
$579$		0			0
$580$	1.96732e9	+	2.11339e9i	0.418675	+	0.449761i
$581$			8.00832e9i			1.69405i
$582$		0			0
$583$		−	3.77454e8i		−	0.0788904i
$584$	5.49079e8	+	1.55703e9i	0.114075	+	0.323483i
$585$		0			0
$586$	2.47015e8	−	5.67418e8i	0.0507086	−	0.116483i
$587$	3.32117e9			0.677731			0.338866	−	0.940835i	$-0.389957\pi$
$587$	3.32117e9			0.677731			0.338866	+	0.940835i	$0.389957\pi$
$588$		0			0
$589$	5.05262e9			1.01886
$590$	−2.33940e8	+	5.37384e8i	−0.0468946	+	0.107722i
$591$		0			0
$592$	4.27218e7	−	5.95992e8i	0.00846298	−	0.118063i
$593$			5.53216e9i			1.08944i	0.838618	+	0.544720i	$0.183364\pi$
$593$			5.53216e9i			1.08944i	−0.838618	+	0.544720i	$0.816636\pi$
$594$		0			0
$595$			3.69245e8i			0.0718629i
$596$	8.68249e8	−	8.08240e8i	0.167990	−	0.156379i
$597$		0			0
$598$	−2.24211e9	−	9.76063e8i	−0.428750	−	0.186648i
$599$	6.28128e9			1.19414			0.597069	−	0.802190i	$-0.296332\pi$
$599$	6.28128e9			1.19414			0.597069	+	0.802190i	$0.296332\pi$
$600$		0			0
$601$	2.99628e9			0.563017			0.281508	−	0.959559i	$-0.409165\pi$
$601$	2.99628e9			0.563017			0.281508	+	0.959559i	$0.409165\pi$
$602$	2.88869e9	+	1.25754e9i	0.539652	+	0.234928i
$603$		0			0
$604$	−6.43494e9	+	5.99018e9i	−1.18827	+	1.10614i
$605$			2.23277e9i			0.409921i
$606$		0			0
$607$		−	1.95237e9i		−	0.354324i	−0.984182	−	0.177162i	$-0.943308\pi$
$607$		−	1.95237e9i		−	0.354324i	0.984182	−	0.177162i	$-0.0566917\pi$
$608$	3.91755e9	+	2.05023e9i	0.706890	+	0.369947i
$609$		0			0
$610$	1.11265e9	−	2.55586e9i	0.198474	−	0.455914i
$611$	−2.43693e9			−0.432214
$612$		0			0
$613$	8.14854e9			1.42879			0.714395	−	0.699743i	$-0.246702\pi$
$613$	8.14854e9			1.42879			0.714395	+	0.699743i	$0.246702\pi$
$614$	4.36227e6	−	1.00206e7i	0.000760541	−	0.00174704i
$615$		0			0
$616$	2.41658e9	−	8.52195e8i	0.416551	−	0.146895i
$617$			6.31911e9i			1.08307i	0.840677	+	0.541537i	$0.182157\pi$
$617$			6.31911e9i			1.08307i	−0.840677	+	0.541537i	$0.817843\pi$
$618$		0			0
$619$			7.12960e9i			1.20823i	0.796899	+	0.604113i	$0.206472\pi$
$619$			7.12960e9i			1.20823i	−0.796899	+	0.604113i	$0.793528\pi$
$620$	−2.30918e9	−	2.48063e9i	−0.389122	−	0.418014i
$621$		0			0
$622$	8.91738e8	+	3.88202e8i	0.148584	+	0.0646832i
$623$	−1.63796e10			−2.71390
$624$		0			0
$625$	2.44141e8			0.0400000
$626$	3.09374e9	+	1.34680e9i	0.504050	+	0.219429i
$627$		0			0
$628$	7.25255e9	+	7.79104e9i	1.16851	+	1.25527i
$629$		−	7.76113e7i		−	0.0124351i
$630$		0			0
$631$			1.13764e10i			1.80262i	0.433179	+	0.901308i	$0.357392\pi$
$631$			1.13764e10i			1.80262i	−0.433179	+	0.901308i	$0.642608\pi$
$632$	9.42171e9	−	3.32252e9i	1.48464	−	0.523550i
$633$		0			0
$634$	−119799.	+	275190.i	−1.86698e−5	+	4.28864e-5i
$635$	7.43450e8			0.115224
$636$		0			0
$637$	−5.58142e9			−0.855573
$638$	1.03883e9	−	2.38630e9i	0.158370	−	0.363791i
$639$		0			0
$640$	−7.83844e8	−	2.86036e9i	−0.118195	−	0.431312i
$641$			4.41682e9i			0.662378i	0.943564	+	0.331189i	$0.107450\pi$
$641$			4.41682e9i			0.662378i	−0.943564	+	0.331189i	$0.892550\pi$
$642$		0			0
$643$		−	8.15377e9i		−	1.20954i	−0.796400	−	0.604770i	$-0.793265\pi$
$643$		−	8.15377e9i		−	1.20954i	0.796400	−	0.604770i	$-0.206735\pi$
$644$	−5.55589e9	+	5.17189e9i	−0.819696	+	0.763042i
$645$		0			0
$646$	5.26583e8	+	2.29238e8i	0.0768516	+	0.0334559i
$647$	9.42404e9			1.36796			0.683978	−	0.729503i	$-0.260248\pi$
$647$	9.42404e9			1.36796			0.683978	+	0.729503i	$0.260248\pi$
$648$		0			0
$649$	5.28299e8			0.0758619
$650$	8.20027e8	+	3.56984e8i	0.117120	+	0.0509861i
$651$		0			0
$652$	3.04011e9	−	2.82999e9i	0.429559	−	0.399869i
$653$			4.35680e9i			0.612310i	0.951982	+	0.306155i	$0.0990426\pi$
$653$			4.35680e9i			0.612310i	−0.951982	+	0.306155i	$0.900957\pi$
$654$		0			0
$655$			6.33543e9i			0.880910i
$656$	1.12159e10	+	8.03979e8i	1.55122	+	0.111194i
$657$		0			0
$658$	−3.01932e9	+	6.93567e9i	−0.413160	+	0.949069i
$659$	−8.87427e9			−1.20791			−0.603954	−	0.797019i	$-0.706409\pi$
$659$	−8.87427e9			−1.20791			−0.603954	+	0.797019i	$0.706409\pi$
$660$		0			0
$661$	−4.29408e9			−0.578315			−0.289158	−	0.957282i	$-0.593375\pi$
$661$	−4.29408e9			−0.578315			−0.289158	+	0.957282i	$0.593375\pi$
$662$	3.03223e8	−	6.96535e8i	0.0406219	−	0.0933125i
$663$		0			0
$664$	−2.77862e9	−	7.87937e9i	−0.368334	−	1.04449i
$665$			4.13884e9i			0.545761i
$666$		0			0
$667$			7.70954e9i			1.00598i
$668$	−3.29498e8	−	3.53963e8i	−0.0427696	−	0.0459452i
$669$		0			0
$670$	−2.59080e9	−	1.12786e9i	−0.332791	−	0.144874i
$671$	−2.51265e9			−0.321073
$672$		0			0
$673$	3.56482e8			0.0450801			0.0225401	−	0.999746i	$-0.492825\pi$
$673$	3.56482e8			0.0450801			0.0225401	+	0.999746i	$0.492825\pi$
$674$	8.55027e9	+	3.72220e9i	1.07565	+	0.468263i
$675$		0			0
$676$	−3.24020e9	−	3.48078e9i	−0.403421	−	0.433374i
$677$			3.63293e9i			0.449984i	0.974361	+	0.224992i	$0.0722356\pi$
$677$			3.63293e9i			0.449984i	−0.974361	+	0.224992i	$0.927764\pi$
$678$		0			0
$679$			2.13639e10i			2.61901i
$680$	−1.28116e8	−	3.63299e8i	−0.0156250	−	0.0443080i
$681$		0			0
$682$	−1.21934e9	+	2.80096e9i	−0.147191	+	0.338112i
$683$	−2.58826e9			−0.310839			−0.155419	−	0.987849i	$-0.549673\pi$
$683$	−2.58826e9			−0.310839			−0.155419	+	0.987849i	$0.549673\pi$
$684$		0			0
$685$	−6.31422e9			−0.750589
$686$	−1.75304e9	+	4.02690e9i	−0.207327	+	0.476252i
$687$		0			0
$688$	−3.27850e9	−	2.35009e8i	−0.383810	−	0.0275122i
$689$		−	1.49805e9i		−	0.174486i
$690$		0			0
$691$		−	6.90304e9i		−	0.795916i	−0.917404	−	0.397958i	$-0.869719\pi$
$691$		−	6.90304e9i		−	0.795916i	0.917404	−	0.397958i	$-0.130281\pi$
$692$	−5.90849e8	+	5.50012e8i	−0.0677806	+	0.0630959i
$693$		0			0
$694$	−1.33161e10	−	5.79692e9i	−1.51223	−	0.658323i
$695$	3.22771e9			0.364710
$696$		0			0
$697$	1.46056e9			0.163382
$698$	1.23012e10	+	5.35509e9i	1.36915	+	0.596036i
$699$		0			0
$700$	2.03200e9	−	1.89156e9i	0.223914	−	0.208438i
$701$		−	7.33386e9i		−	0.804118i	−0.915614	−	0.402059i	$-0.868295\pi$
$701$		−	7.33386e9i		−	0.804118i	0.915614	−	0.402059i	$-0.131705\pi$
$702$		0			0
$703$		−	8.69939e8i		−	0.0944377i
$704$	−2.08198e9	+	1.67694e9i	−0.224891	+	0.181140i
$705$		0			0
$706$	−4.52339e9	+	1.03907e10i	−0.483780	+	1.11129i
$707$	−1.98796e10			−2.11563
$708$		0			0
$709$	9.51734e9			1.00289			0.501446	−	0.865189i	$-0.332802\pi$
$709$	9.51734e9			1.00289			0.501446	+	0.865189i	$0.332802\pi$
$710$	4.14544e7	−	9.52249e7i	0.00434677	−	0.00998496i
$711$		0			0
$712$	1.61158e10	−	5.68316e9i	1.67329	−	0.590079i
$713$		−	9.04921e9i		−	0.934969i
$714$		0			0
$715$		−	8.06163e8i		−	0.0824806i
$716$	−5.31755e9	−	5.71236e9i	−0.541397	−	0.581594i
$717$		0			0
$718$	−1.83668e8	−	7.99564e7i	−0.0185181	−	0.00806153i
$719$	4.62867e9			0.464414			0.232207	−	0.972666i	$-0.425405\pi$
$719$	4.62867e9			0.464414			0.232207	+	0.972666i	$0.425405\pi$
$720$		0			0
$721$	−1.42215e10			−1.41310
$722$	−3.37004e9	−	1.46708e9i	−0.333238	−	0.145069i
$723$		0			0
$724$	2.44946e9	+	2.63133e9i	0.239875	+	0.257685i
$725$		−	2.81967e9i		−	0.274799i
$726$		0			0
$727$			1.60152e10i			1.54583i	0.634508	+	0.772916i	$0.281203\pi$
$727$			1.60152e10i			1.54583i	−0.634508	+	0.772916i	$0.718797\pi$
$728$	9.59098e9	−	3.38221e9i	0.921304	−	0.324894i
$729$		0			0
$730$	6.43554e8	−	1.47831e9i	0.0612287	−	0.140648i
$731$	−4.26933e8			−0.0404249
$732$		0			0
$733$	−3.80187e9			−0.356561			−0.178280	−	0.983980i	$-0.557053\pi$
$733$	−3.80187e9			−0.356561			−0.178280	+	0.983980i	$0.557053\pi$
$734$	−3.36157e9	+	7.72186e9i	−0.313766	+	0.720752i
$735$		0			0
$736$	3.67195e9	−	7.01631e9i	0.339488	−	0.648689i
$737$			2.54700e9i			0.234365i
$738$		0			0
$739$			1.89875e9i			0.173066i	0.996249	+	0.0865329i	$0.0275788\pi$
$739$			1.89875e9i			0.173066i	−0.996249	+	0.0865329i	$0.972421\pi$
$740$	−4.27105e8	+	3.97585e8i	−0.0387457	+	0.0360677i
$741$		0			0
$742$	−4.26356e9	−	1.85606e9i	−0.383141	−	0.166793i
$743$	4.94150e9			0.441976			0.220988	−	0.975277i	$-0.429072\pi$
$743$	4.94150e9			0.441976			0.220988	+	0.975277i	$0.429072\pi$
$744$		0			0
$745$	−1.15841e9			−0.102640
$746$	1.01399e10	+	4.41422e9i	0.894228	+	0.389286i
$747$		0			0
$748$	−2.54160e8	+	2.36594e8i	−0.0222050	+	0.0206703i
$749$		−	2.10761e10i		−	1.83276i
$750$		0			0
$751$		−	1.62845e10i		−	1.40292i	−0.712706	−	0.701462i	$-0.752531\pi$
$751$		−	1.62845e10i		−	1.40292i	0.712706	−	0.701462i	$-0.247469\pi$
$752$	5.64249e8	−	7.87159e9i	0.0483848	−	0.674994i
$753$		0			0
$754$	4.12294e9	−	9.47080e9i	0.350273	−	0.804613i
$755$	8.58546e9			0.726021
$756$		0			0
$757$	1.17549e10			0.984878			0.492439	−	0.870347i	$-0.336105\pi$
$757$	1.17549e10			0.984878			0.492439	+	0.870347i	$0.336105\pi$
$758$	5.93428e9	−	1.36316e10i	0.494910	−	1.13686i
$759$		0			0
$760$	−1.43604e9	−	4.07219e9i	−0.118664	−	0.336496i
$761$			9.44142e9i			0.776588i	0.921535	+	0.388294i	$0.126936\pi$
$761$			9.44142e9i			0.776588i	−0.921535	+	0.388294i	$0.873064\pi$
$762$		0			0
$763$		−	1.19681e10i		−	0.975413i
$764$	−7.08958e9	−	7.61596e9i	−0.575166	−	0.617871i
$765$		0			0
$766$	−1.27691e10	−	5.55880e9i	−1.02650	−	0.446869i
$767$	2.09673e9			0.167787
$768$		0			0
$769$	2.11490e10			1.67706			0.838528	−	0.544858i	$-0.183416\pi$
$769$	2.11490e10			1.67706			0.838528	+	0.544858i	$0.183416\pi$
$770$	−2.29440e9	−	9.98823e8i	−0.181114	−	0.0788444i
$771$		0			0
$772$	1.21580e10	+	1.30607e10i	0.951049	+	1.02166i
$773$			1.65319e10i			1.28735i	0.765301	+	0.643673i	$0.222590\pi$
$773$			1.65319e10i			1.28735i	−0.765301	+	0.643673i	$0.777410\pi$
$774$		0			0
$775$			3.30964e9i			0.255402i
$776$	−7.41257e9	−	2.10199e10i	−0.569447	−	1.61479i
$777$		0			0
$778$	−2.65370e9	+	6.09581e9i	−0.202033	+	0.464090i
$779$	1.63713e10			1.24080
$780$		0			0
$781$	−9.36150e7			−0.00703181
$782$	4.10565e8	−	9.43108e8i	0.0307014	−	0.0705241i
$783$		0			0
$784$	1.29233e9	−	1.80287e10i	0.0957783	−	1.33616i
$785$		−	1.03948e10i		−	0.766957i
$786$		0			0
$787$		−	1.09180e10i		−	0.798424i	−0.916859	−	0.399212i	$-0.869284\pi$
$787$		−	1.09180e10i		−	0.798424i	0.916859	−	0.399212i	$-0.130716\pi$
$788$	3.66796e8	−	3.41445e8i	0.0267044	−	0.0248587i
$789$		0			0
$790$	−8.94535e9	−	3.89419e9i	−0.645509	−	0.281011i
$791$	−2.31587e10			−1.66378
$792$		0			0
$793$	−9.97228e9			−0.710131
$794$	−2.13774e10	−	9.30626e9i	−1.51560	−	0.659787i
$795$		0			0
$796$	−1.21895e10	+	1.13470e10i	−0.856621	+	0.797415i
$797$		−	7.66964e9i		−	0.536625i	−0.963332	−	0.268313i	$-0.913534\pi$
$797$		−	7.66964e9i		−	0.536625i	0.963332	−	0.268313i	$-0.0864660\pi$
$798$		0			0
$799$		−	1.02505e9i		−	0.0710940i
$800$	−1.34297e9	+	2.56613e9i	−0.0927367	+	0.177200i
$801$		0			0
$802$	−1.40561e9	+	3.22883e9i	−0.0962177	+	0.221022i
$803$	−1.45331e9			−0.0990502
$804$		0			0
$805$	7.41263e9			0.500826
$806$	−4.83937e9	+	1.11165e10i	−0.325549	+	0.747818i
$807$		0			0
$808$	1.95595e10	−	6.89756e9i	1.30442	−	0.459998i
$809$			2.72033e9i			0.180635i	0.995913	+	0.0903176i	$0.0287882\pi$
$809$			2.72033e9i			0.180635i	−0.995913	+	0.0903176i	$0.971212\pi$
$810$		0			0
$811$		−	1.71763e10i		−	1.13072i	−0.824843	−	0.565362i	$-0.808736\pi$
$811$		−	1.71763e10i		−	1.13072i	0.824843	−	0.565362i	$-0.191264\pi$
$812$	−2.18463e10	−	2.34683e10i	−1.43196	−	1.53828i
$813$		0			0
$814$	4.82258e8	+	2.09942e8i	0.0313396	+	0.0136431i
$815$	−4.05610e9			−0.262456
$816$		0			0
$817$	−4.78546e9			−0.307006
$818$	5.40039e9	+	2.35096e9i	0.344976	+	0.150179i
$819$		0			0
$820$	−7.48212e9	−	8.03765e9i	−0.473889	−	0.509074i
$821$			6.39259e9i			0.403158i	0.979472	+	0.201579i	$0.0646073\pi$
$821$			6.39259e9i			0.403158i	−0.979472	+	0.201579i	$0.935393\pi$
$822$		0			0
$823$		−	2.32623e10i		−	1.45463i	−0.686302	−	0.727317i	$-0.740767\pi$
$823$		−	2.32623e10i		−	1.45463i	0.686302	−	0.727317i	$-0.259233\pi$
$824$	1.39925e10	−	4.93439e9i	0.871264	−	0.307247i
$825$		0			0
$826$	2.59781e9	−	5.96744e9i	0.160390	−	0.368432i
$827$	−2.12297e10			−1.30519			−0.652596	−	0.757706i	$-0.726320\pi$
$827$	−2.12297e10			−1.30519			−0.652596	+	0.757706i	$0.726320\pi$
$828$		0			0
$829$	1.29024e10			0.786558			0.393279	−	0.919419i	$-0.371341\pi$
$829$	1.29024e10			0.786558			0.393279	+	0.919419i	$0.371341\pi$
$830$	−3.25671e9	+	7.48099e9i	−0.197700	+	0.454136i
$831$		0			0
$832$	−8.26302e9	+	6.65550e9i	−0.497402	+	0.400635i
$833$		−	2.34773e9i		−	0.140731i
$834$		0			0
$835$			4.72255e8i			0.0280721i
$836$	−2.84886e9	+	2.65196e9i	−0.168636	+	0.156980i
$837$		0			0
$838$	−4.31257e9	−	1.87740e9i	−0.253152	−	0.110205i
$839$	1.84935e10			1.08107			0.540533	−	0.841323i	$-0.318223\pi$
$839$	1.84935e10			1.08107			0.540533	+	0.841323i	$0.318223\pi$
$840$		0			0
$841$	−1.53156e10			−0.887868
$842$	−1.75061e9	−	7.62094e8i	−0.101064	−	0.0439963i
$843$		0			0
$844$	2.44428e10	−	2.27535e10i	1.39944	−	1.30271i
$845$			4.64404e9i			0.264788i
$846$		0			0
$847$		−	2.47940e10i		−	1.40202i
$848$	4.83889e9	+	3.46861e8i	0.272496	+	0.0195330i
$849$		0			0
$850$	−1.50159e8	+	3.44930e8i	−0.00838659	+	0.0192648i
$851$	−1.55806e9			−0.0866622
$852$		0			0
$853$	−1.72439e9			−0.0951289			−0.0475645	−	0.998868i	$-0.515146\pi$
$853$	−1.72439e9			−0.0951289			−0.0475645	+	0.998868i	$0.515146\pi$
$854$	−1.23555e10	+	2.83818e10i	−0.678824	+	1.55933i
$855$		0			0
$856$	7.31272e9	+	2.07368e10i	0.398493	+	1.13001i
$857$		−	3.20959e10i		−	1.74188i	−0.491394	−	0.870938i	$-0.663512\pi$
$857$		−	3.20959e10i		−	1.74188i	0.491394	−	0.870938i	$-0.336488\pi$
$858$		0			0
$859$			1.91824e10i			1.03259i	0.856412	+	0.516294i	$0.172689\pi$
$859$			1.91824e10i			1.03259i	−0.856412	+	0.516294i	$0.827311\pi$
$860$	2.18708e9	+	2.34947e9i	0.117252	+	0.125958i
$861$		0			0
$862$	1.18105e10	+	5.14149e9i	0.628049	+	0.273409i
$863$	4.00789e8			0.0212265			0.0106132	−	0.999944i	$-0.496622\pi$
$863$	4.00789e8			0.0212265			0.0106132	+	0.999944i	$0.496622\pi$
$864$		0			0
$865$	7.88308e8			0.0414133
$866$	−1.15154e9	−	5.01301e8i	−0.0602512	−	0.0262292i
$867$		0			0
$868$	2.56425e10	+	2.75464e10i	1.33089	+	1.42970i
$869$			8.79412e9i			0.454593i
$870$		0			0
$871$			1.01086e10i			0.518355i
$872$	4.15252e9	+	1.17754e10i	0.212082	+	0.601404i
$873$		0			0
$874$	4.60199e9	−	1.05712e10i	0.233161	−	0.535594i
$875$	−2.71108e9			−0.136809
$876$		0			0
$877$	2.12489e10			1.06375			0.531874	−	0.846824i	$-0.321488\pi$
$877$	2.12489e10			1.06375			0.531874	+	0.846824i	$0.321488\pi$
$878$	−2.47546e9	+	5.68638e9i	−0.123431	+	0.283534i
$879$		0			0
$880$	2.60401e9	+	1.86660e8i	0.128811	+	0.00923340i
$881$			1.54138e10i			0.759443i	0.925101	+	0.379722i	$0.123980\pi$
$881$			1.54138e10i			0.759443i	−0.925101	+	0.379722i	$0.876020\pi$
$882$		0			0
$883$		−	3.71941e10i		−	1.81807i	−0.416715	−	0.909037i	$-0.636819\pi$
$883$		−	3.71941e10i		−	1.81807i	0.416715	−	0.909037i	$-0.363181\pi$
$884$	−1.00872e9	+	9.38999e8i	−0.0491119	+	0.0457175i
$885$		0			0
$886$	1.23381e10	+	5.37115e9i	0.595976	+	0.259447i
$887$	3.14440e10			1.51288			0.756441	−	0.654062i	$-0.226937\pi$
$887$	3.14440e10			1.51288			0.756441	+	0.654062i	$0.226937\pi$
$888$		0			0
$889$	−8.25571e9			−0.394093
$890$	−1.53010e10	−	6.66100e9i	−0.727536	−	0.316719i
$891$		0			0
$892$	−2.26887e10	+	2.11206e10i	−1.07037	+	0.996388i
$893$		−	1.14898e10i		−	0.539921i
$894$		0			0
$895$			7.62140e9i			0.355348i
$896$	8.70427e9	+	3.17632e10i	0.404254	+	1.47518i
$897$		0			0
$898$	1.35760e9	−	3.11855e9i	0.0625613	−	0.143710i
$899$	3.82243e10			1.75461
$900$		0			0
$901$	6.30130e8			0.0287008
$902$	−3.95088e9	+	9.07558e9i	−0.179255	+	0.411767i
$903$		0			0
$904$	2.27858e10	−	8.03529e9i	1.02583	−	0.361753i
$905$		−	3.51070e9i		−	0.157443i
$906$		0			0
$907$			3.48462e10i			1.55071i	0.631528	+	0.775353i	$0.282428\pi$
$907$			3.48462e10i			1.55071i	−0.631528	+	0.775353i	$0.717572\pi$
$908$	−1.69850e10	−	1.82461e10i	−0.752948	−	0.808852i
$909$		0			0
$910$	−9.10607e9	−	3.96416e9i	−0.400577	−	0.174384i
$911$	−1.90773e10			−0.835991			−0.417995	−	0.908449i	$-0.637267\pi$
$911$	−1.90773e10			−0.835991			−0.417995	+	0.908449i	$0.637267\pi$
$912$		0			0
$913$	7.35452e9			0.319821
$914$	−2.71640e10	−	1.18253e10i	−1.17674	−	0.512273i
$915$		0			0
$916$	2.39947e10	+	2.57762e10i	1.03153	+	1.10812i
$917$		−	7.03524e10i		−	3.01291i
$918$		0			0
$919$			2.88024e10i			1.22412i	0.790811	+	0.612060i	$0.209659\pi$
$919$			2.88024e10i			1.22412i	−0.790811	+	0.612060i	$0.790341\pi$
$920$	−7.29327e9	+	2.57194e9i	−0.308791	+	0.108894i
$921$		0			0
$922$	−8.52078e9	+	1.95731e10i	−0.358032	+	0.822434i
$923$	−3.71542e8			−0.0155526
$924$		0			0
$925$	5.69841e8			0.0236732
$926$	−1.55396e10	+	3.56961e10i	−0.643136	+	1.47735i
$927$		0			0
$928$	2.96372e10	+	1.55105e10i	1.21736	+	0.637100i
$929$			8.38741e9i			0.343220i	0.985165	+	0.171610i	$0.0548969\pi$
$929$			8.38741e9i			0.343220i	−0.985165	+	0.171610i	$0.945103\pi$
$930$		0			0
$931$		−	2.63156e10i		−	1.06878i
$932$	6.98047e9	−	6.49800e9i	0.282442	−	0.262920i
$933$		0			0
$934$	−1.06534e10	−	4.63774e9i	−0.427831	−	0.186248i
$935$	3.39099e8			0.0135671
$936$		0			0
$937$	−8.65060e9			−0.343524			−0.171762	−	0.985138i	$-0.554946\pi$
$937$	−8.65060e9			−0.343524			−0.171762	+	0.985138i	$0.554946\pi$
$938$	2.87698e10	+	1.25244e10i	1.13822	+	0.495503i
$939$		0			0
$940$	−5.64100e9	+	5.25112e9i	−0.221518	+	0.206207i
$941$			6.88394e9i			0.269323i	0.990892	+	0.134661i	$0.0429947\pi$
$941$			6.88394e9i			0.269323i	−0.990892	+	0.134661i	$0.957005\pi$
$942$		0			0
$943$		−	2.93210e10i		−	1.13864i
$944$	−4.85479e8	+	6.77270e9i	−0.0187832	+	0.262035i
$945$		0			0
$946$	1.15487e9	−	2.65286e9i	0.0443522	−	0.101881i
$947$	−4.68933e10			−1.79426			−0.897131	−	0.441765i	$-0.854352\pi$
$947$	−4.68933e10			−1.79426			−0.897131	+	0.441765i	$0.854352\pi$
$948$		0			0
$949$	−5.76796e9			−0.219074
$950$	−1.68312e9	+	3.86630e9i	−0.0636918	+	0.146306i
$951$		0			0
$952$	1.42267e9	+	4.03428e9i	0.0534411	+	0.151543i
$953$			5.25172e10i			1.96551i	0.184900	+	0.982757i	$0.440804\pi$
$953$			5.25172e10i			1.96551i	−0.184900	+	0.982757i	$0.559196\pi$
$954$		0			0
$955$			1.01612e10i			0.377513i
$956$	−2.59326e10	−	2.78581e10i	−0.959940	−	1.03121i
$957$		0			0
$958$	1.70889e10	+	7.43933e9i	0.627964	+	0.273372i
$959$	7.01168e10			2.56718
$960$		0			0
$961$	−1.73538e10			−0.630759
$962$	1.91400e9	+	8.33224e8i	0.0693152	+	0.0301751i
$963$		0			0
$964$	−3.39206e10	−	3.64391e10i	−1.21953	−	1.31008i
$965$		−	1.74256e10i		−	0.624226i
$966$		0			0
$967$		−	5.02244e10i		−	1.78617i	−0.449891	−	0.893084i	$-0.648537\pi$
$967$		−	5.02244e10i		−	1.78617i	0.449891	−	0.893084i	$-0.351463\pi$
$968$	8.60271e9	+	2.43948e10i	0.304840	+	0.864437i
$969$		0			0
$970$	−8.68798e9	+	1.99572e10i	−0.305645	+	0.702098i
$971$	5.32761e10			1.86752			0.933760	−	0.357901i	$-0.116507\pi$
$971$	5.32761e10			1.86752			0.933760	+	0.357901i	$0.116507\pi$
$972$		0			0
$973$	−3.58425e10			−1.24739
$974$	−1.64661e10	+	3.78244e10i	−0.570999	+	1.31164i
$975$		0			0
$976$	2.30899e9	−	3.22117e10i	0.0794965	−	1.10902i
$977$			2.46419e10i			0.845364i	0.906278	+	0.422682i	$0.138911\pi$
$977$			2.46419e10i			0.845364i	−0.906278	+	0.422682i	$0.861089\pi$
$978$		0			0
$979$			1.50423e10i			0.512360i
$980$	−1.29199e10	+	1.20269e10i	−0.438497	+	0.408190i
$981$		0			0
$982$	−3.50661e10	−	1.52654e10i	−1.18167	−	0.514419i
$983$	−2.33510e10			−0.784094			−0.392047	−	0.919945i	$-0.628233\pi$
$983$	−2.33510e10			−0.784094			−0.392047	+	0.919945i	$0.628233\pi$
$984$		0			0
$985$	−4.89378e8			−0.0163161
$986$	3.98373e9	+	1.73425e9i	0.132349	+	0.0576158i
$987$		0			0
$988$	−1.13066e10	+	1.05252e10i	−0.372979	+	0.347200i
$989$			8.57074e9i			0.281729i
$990$		0			0
$991$		−	1.63390e10i		−	0.533295i	−0.963794	−	0.266648i	$-0.914084\pi$
$991$		−	1.63390e10i		−	0.533295i	0.963794	−	0.266648i	$-0.0859160\pi$
$992$	−3.47872e10	−	1.82057e10i	−1.13143	−	0.592130i
$993$		0			0
$994$	−4.60335e8	+	1.05743e9i	−0.0148669	+	0.0341508i
$995$	1.62631e10			0.523387
$996$		0			0
$997$	1.98464e10			0.634233			0.317117	−	0.948387i	$-0.397285\pi$
$997$	1.98464e10			0.634233			0.317117	+	0.948387i	$0.397285\pi$
$998$	2.42555e10	−	5.57173e10i	0.772420	−	1.77432i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.8.e.a.71.5	✓	56
3.2	odd	2	inner	180.8.e.a.71.52	yes	56
4.3	odd	2	inner	180.8.e.a.71.51	yes	56
12.11	even	2	inner	180.8.e.a.71.6	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.8.e.a.71.5	✓	56	1.1	even	1	trivial
180.8.e.a.71.6	yes	56	12.11	even	2	inner
180.8.e.a.71.51	yes	56	4.3	odd	2	inner
180.8.e.a.71.52	yes	56	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	180.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-10.3734 - 4.51586i) q^{2} +(87.2140 + 93.6895i) q^{4} -125.000i q^{5} +1388.07i q^{7} +(-481.616 - 1365.72i) q^{8} +O(q^{10})\)	\(q+(-10.3734 - 4.51586i) q^{2} +(87.2140 + 93.6895i) q^{4} -125.000i q^{5} +1388.07i q^{7} +(-481.616 - 1365.72i) q^{8} +(-564.482 + 1296.67i) q^{10} +1274.75 q^{11} +5059.27 q^{13} +(6268.35 - 14399.0i) q^{14} +(-1171.43 + 16342.1i) q^{16} +2128.10i q^{17} +23853.7i q^{19} +(11711.2 - 10901.8i) q^{20} +(-13223.5 - 5756.60i) q^{22} +42721.8 q^{23} -15625.0 q^{25} +(-52481.7 - 22846.9i) q^{26} +(-130048. + 121060. i) q^{28} +180459. i q^{29} -211817. i q^{31} +(85950.2 - 164232. i) q^{32} +(9610.18 - 22075.6i) q^{34} +173509. q^{35} -36469.8 q^{37} +(107720. - 247443. i) q^{38} +(-170715. + 60202.0i) q^{40} -686323. i q^{41} +200617. i q^{43} +(111176. + 119431. i) q^{44} +(-443170. - 192926. i) q^{46} -481676. q^{47} -1.10321e6 q^{49} +(162084. + 70560.3i) q^{50} +(441239. + 474000. i) q^{52} -296100. i q^{53} -159344. i q^{55} +(1.89572e6 - 668519. i) q^{56} +(814928. - 1.87197e6i) q^{58} +414433. q^{59} -1.97109e6 q^{61} +(-956536. + 2.19726e6i) q^{62} +(-1.63324e6 + 1.31551e6i) q^{64} -632409. i q^{65} +1.99804e6i q^{67} +(-199380. + 185600. i) q^{68} +(-1.79988e6 - 783544. i) q^{70} -73437.9 q^{71} -1.14008e6 q^{73} +(378315. + 164693. i) q^{74} +(-2.23484e6 + 2.08038e6i) q^{76} +1.76945e6i q^{77} +6.89870e6i q^{79} +(2.04276e6 + 146429. i) q^{80} +(-3.09934e6 + 7.11949e6i) q^{82} +5.76938e6 q^{83} +266012. q^{85} +(905960. - 2.08108e6i) q^{86} +(-613940. - 1.74096e6i) q^{88} +1.18002e7i q^{89} +7.02264e6i q^{91} +(3.72594e6 + 4.00258e6i) q^{92} +(4.99661e6 + 2.17518e6i) q^{94} +2.98171e6 q^{95} +1.53911e7 q^{97} +(1.14440e7 + 4.98193e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 52 q^{4}+O(q^{10}) \) 56 * q + 52 * q^4	\( 56 q + 52 q^{4} - 6500 q^{10} + 14128 q^{13} - 8060 q^{16} + 259088 q^{22} - 875000 q^{25} - 490976 q^{28} + 40912 q^{34} + 1268048 q^{37} - 266500 q^{40} + 3108200 q^{46} - 3522056 q^{49} - 8882216 q^{52} + 8807592 q^{58} - 3944912 q^{61} - 16633580 q^{64} + 4533000 q^{70} + 7602384 q^{73} - 38876976 q^{76} + 33213064 q^{82} - 15068000 q^{85} - 56145472 q^{88} + 29409456 q^{94} - 45595824 q^{97}+O(q^{100}) \) 56 * q + 52 * q^4 - 6500 * q^10 + 14128 * q^13 - 8060 * q^16 + 259088 * q^22 - 875000 * q^25 - 490976 * q^28 + 40912 * q^34 + 1268048 * q^37 - 266500 * q^40 + 3108200 * q^46 - 3522056 * q^49 - 8882216 * q^52 + 8807592 * q^58 - 3944912 * q^61 - 16633580 * q^64 + 4533000 * q^70 + 7602384 * q^73 - 38876976 * q^76 + 33213064 * q^82 - 15068000 * q^85 - 56145472 * q^88 + 29409456 * q^94 - 45595824 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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