LMFDB - Embedded newform 177.9.c.a.58.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,9,Mod(58,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("177.58");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	177.c (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:	$72.1060139808$
Analytic rank:	$0$
Dimension:	$80$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			58.2
Character	$\chi$	$=$	177.58
Dual form			177.9.c.a.58.79

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-31.4468i q^{2} -46.7654 q^{3} -732.900 q^{4} +37.7655 q^{5} +1470.62i q^{6} +1285.94 q^{7} +14997.0i q^{8} +2187.00 q^{9} +O(q^{10})$	\(q-31.4468i q^{2} -46.7654 q^{3} -732.900 q^{4} +37.7655 q^{5} +1470.62i q^{6} +1285.94 q^{7} +14997.0i q^{8} +2187.00 q^{9} -1187.60i q^{10} +6339.18i q^{11} +34274.3 q^{12} +24786.9i q^{13} -40438.6i q^{14} -1766.12 q^{15} +283984. q^{16} +136845. q^{17} -68774.1i q^{18} -233393. q^{19} -27678.3 q^{20} -60137.4 q^{21} +199347. q^{22} -120422. i q^{23} -701338. i q^{24} -389199. q^{25} +779467. q^{26} -102276. q^{27} -942464. q^{28} +111206. q^{29} +55538.7i q^{30} -20065.6i q^{31} -5.09115e6i q^{32} -296454. i q^{33} -4.30332e6i q^{34} +48564.1 q^{35} -1.60285e6 q^{36} -3.36126e6i q^{37} +7.33945e6i q^{38} -1.15917e6i q^{39} +566367. i q^{40} +2.62741e6 q^{41} +1.89113e6i q^{42} +554113. i q^{43} -4.64598e6i q^{44} +82593.1 q^{45} -3.78688e6 q^{46} +3.60410e6i q^{47} -1.32806e7 q^{48} -4.11116e6 q^{49} +1.22390e7i q^{50} -6.39959e6 q^{51} -1.81663e7i q^{52} +4.83376e6 q^{53} +3.21625e6i q^{54} +239402. i q^{55} +1.92852e7i q^{56} +1.09147e7 q^{57} -3.49706e6i q^{58} +(-6.00418e6 - 1.05252e7i) q^{59} +1.29439e6 q^{60} +1.18994e7i q^{61} -630998. q^{62} +2.81235e6 q^{63} -8.74005e7 q^{64} +936087. i q^{65} -9.32252e6 q^{66} +3.03490e7i q^{67} -1.00293e8 q^{68} +5.63158e6i q^{69} -1.52718e6i q^{70} +8.90765e6 q^{71} +3.27984e7i q^{72} -2.96955e7i q^{73} -1.05701e8 q^{74} +1.82010e7 q^{75} +1.71053e8 q^{76} +8.15179e6i q^{77} -3.64521e7 q^{78} +4.37537e7 q^{79} +1.07248e7 q^{80} +4.78297e6 q^{81} -8.26235e7i q^{82} -4.96491e7i q^{83} +4.40747e7 q^{84} +5.16800e6 q^{85} +1.74251e7 q^{86} -5.20058e6 q^{87} -9.50684e7 q^{88} -4.18561e7i q^{89} -2.59729e6i q^{90} +3.18744e7i q^{91} +8.82573e7i q^{92} +938375. i q^{93} +1.13337e8 q^{94} -8.81418e6 q^{95} +2.38090e8i q^{96} -1.47054e8i q^{97} +1.29283e8i q^{98} +1.38638e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9}+O(q^{10}) $ 80 * q - 10240 * q^4 + 160 * q^7 + 174960 * q^9	$ 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9} - 22680 q^{12} - 59616 q^{15} + 1199848 q^{16} - 10608 q^{17} - 27516 q^{19} - 146436 q^{20} - 974696 q^{22} + 5718040 q^{25} - 797484 q^{26} - 3133000 q^{28} + 1725924 q^{29} + 4318800 q^{35} - 22394880 q^{36} - 732180 q^{41} + 22752084 q^{46} + 8703936 q^{48} + 55899176 q^{49} - 10373832 q^{51} - 39265944 q^{53} - 11408040 q^{57} - 33575112 q^{59} - 18034488 q^{60} + 13038600 q^{62} + 349920 q^{63} - 241654260 q^{64} - 35711928 q^{66} + 36772608 q^{68} - 235272660 q^{71} - 63050712 q^{74} + 74363184 q^{75} + 9454680 q^{76} - 10865988 q^{78} + 17252580 q^{79} + 318203976 q^{80} + 382637520 q^{81} - 20743128 q^{84} - 27245820 q^{85} + 105666984 q^{86} + 29437992 q^{87} + 82079788 q^{88} + 121215992 q^{94} - 690837276 q^{95}+O(q^{100}) $ 80 * q - 10240 * q^4 + 160 * q^7 + 174960 * q^9 - 22680 * q^12 - 59616 * q^15 + 1199848 * q^16 - 10608 * q^17 - 27516 * q^19 - 146436 * q^20 - 974696 * q^22 + 5718040 * q^25 - 797484 * q^26 - 3133000 * q^28 + 1725924 * q^29 + 4318800 * q^35 - 22394880 * q^36 - 732180 * q^41 + 22752084 * q^46 + 8703936 * q^48 + 55899176 * q^49 - 10373832 * q^51 - 39265944 * q^53 - 11408040 * q^57 - 33575112 * q^59 - 18034488 * q^60 + 13038600 * q^62 + 349920 * q^63 - 241654260 * q^64 - 35711928 * q^66 + 36772608 * q^68 - 235272660 * q^71 - 63050712 * q^74 + 74363184 * q^75 + 9454680 * q^76 - 10865988 * q^78 + 17252580 * q^79 + 318203976 * q^80 + 382637520 * q^81 - 20743128 * q^84 - 27245820 * q^85 + 105666984 * q^86 + 29437992 * q^87 + 82079788 * q^88 + 121215992 * q^94 - 690837276 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	31.4468i		−	1.96542i	−0.185142	−	0.982712i	$-0.559274\pi$
$2$		−	31.4468i		−	1.96542i	0.185142	−	0.982712i	$-0.440726\pi$
$3$	−46.7654			−0.577350
$3$	−46.7654			−0.577350
$4$	−732.900			−2.86289
$5$	37.7655			0.0604248			0.0302124	−	0.999544i	$-0.490382\pi$
$5$	37.7655			0.0604248			0.0302124	+	0.999544i	$0.490382\pi$
$6$			1470.62i			1.13474i
$7$	1285.94			0.535585			0.267792	−	0.963477i	$-0.413706\pi$
$7$	1285.94			0.535585			0.267792	+	0.963477i	$0.413706\pi$
$8$			14997.0i			3.66137i
$9$	2187.00			0.333333
$10$		−	1187.60i		−	0.118760i
$11$			6339.18i			0.432974i	0.976285	+	0.216487i	$0.0694600\pi$
$11$			6339.18i			0.432974i	−0.976285	+	0.216487i	$0.930540\pi$
$12$	34274.3			1.65289
$13$			24786.9i			0.867857i	0.900947	+	0.433928i	$0.142873\pi$
$13$			24786.9i			0.867857i	−0.900947	+	0.433928i	$0.857127\pi$
$14$		−	40438.6i		−	1.05265i
$15$	−1766.12			−0.0348863
$16$	283984.			4.33325
$17$	136845.			1.63845			0.819223	−	0.573476i	$-0.194405\pi$
$17$	136845.			1.63845			0.819223	+	0.573476i	$0.194405\pi$
$18$		−	68774.1i		−	0.655141i
$19$	−233393.			−1.79091			−0.895453	−	0.445156i	$-0.853148\pi$
$19$	−233393.			−1.79091			−0.895453	+	0.445156i	$0.853148\pi$
$20$	−27678.3			−0.172989
$21$	−60137.4			−0.309220
$22$	199347.			0.850978
$23$		−	120422.i		−	0.430323i	−0.976578	−	0.215161i	$-0.930972\pi$
$23$		−	120422.i		−	0.430323i	0.976578	−	0.215161i	$-0.0690278\pi$
$24$		−	701338.i		−	2.11389i
$25$	−389199.			−0.996349
$26$	779467.			1.70571
$27$	−102276.			−0.192450
$28$	−942464.			−1.53332
$29$	111206.			0.157230			0.0786150	−	0.996905i	$-0.474950\pi$
$29$	111206.			0.157230			0.0786150	+	0.996905i	$0.474950\pi$
$30$			55538.7i			0.0685663i
$31$		−	20065.6i		−	0.0217273i	−0.999941	−	0.0108636i	$-0.996542\pi$
$31$		−	20065.6i		−	0.0217273i	0.999941	−	0.0108636i	$-0.00345807\pi$
$32$		−	5.09115e6i		−	4.85530i
$33$		−	296454.i		−	0.249978i
$34$		−	4.30332e6i		−	3.22024i
$35$	48564.1			0.0323626
$36$	−1.60285e6			−0.954297
$37$		−	3.36126e6i		−	1.79347i	−0.442566	−	0.896736i	$-0.645932\pi$
$37$		−	3.36126e6i		−	1.79347i	0.442566	−	0.896736i	$-0.354068\pi$
$38$			7.33945e6i			3.51989i
$39$		−	1.15917e6i		−	0.501057i
$40$			566367.i			0.221237i
$41$	2.62741e6			0.929806			0.464903	−	0.885362i	$-0.346089\pi$
$41$	2.62741e6			0.929806			0.464903	+	0.885362i	$0.346089\pi$
$42$			1.89113e6i			0.607748i
$43$			554113.i			0.162078i	0.996711	+	0.0810391i	$0.0258239\pi$
$43$			554113.i			0.162078i	−0.996711	+	0.0810391i	$0.974176\pi$
$44$		−	4.64598e6i		−	1.23956i
$45$	82593.1			0.0201416
$46$	−3.78688e6			−0.845767
$47$			3.60410e6i			0.738593i	0.929312	+	0.369297i	$0.120401\pi$
$47$			3.60410e6i			0.738593i	−0.929312	+	0.369297i	$0.879599\pi$
$48$	−1.32806e7			−2.50180
$49$	−4.11116e6			−0.713149
$50$			1.22390e7i			1.95825i
$51$	−6.39959e6			−0.945957
$52$		−	1.81663e7i		−	2.48458i
$53$	4.83376e6			0.612606			0.306303	−	0.951934i	$-0.400908\pi$
$53$	4.83376e6			0.612606			0.306303	+	0.951934i	$0.400908\pi$
$54$			3.21625e6i			0.378246i
$55$			239402.i			0.0261624i
$56$			1.92852e7i			1.96097i
$57$	1.09147e7			1.03398
$58$		−	3.49706e6i		−	0.309024i
$59$	−6.00418e6	−	1.05252e7i	−0.495502	−	0.868607i
$59$	−6.00418e6	−	1.05252e7i	−0.495502	−	0.868607i
$60$	1.29439e6			0.0998755
$61$			1.18994e7i			0.859418i	0.902967	+	0.429709i	$0.141384\pi$
$61$			1.18994e7i			0.859418i	−0.902967	+	0.429709i	$0.858616\pi$
$62$	−630998.			−0.0427033
$63$	2.81235e6			0.178528
$64$	−8.74005e7			−5.20947
$65$			936087.i			0.0524400i
$66$	−9.32252e6			−0.491312
$67$			3.03490e7i			1.50607i	0.657981	+	0.753034i	$0.271411\pi$
$67$			3.03490e7i			1.50607i	−0.657981	+	0.753034i	$0.728589\pi$
$68$	−1.00293e8			−4.69069
$69$			5.63158e6i			0.248447i
$70$		−	1.52718e6i		−	0.0636062i
$71$	8.90765e6			0.350534			0.175267	−	0.984521i	$-0.443921\pi$
$71$	8.90765e6			0.350534			0.175267	+	0.984521i	$0.443921\pi$
$72$			3.27984e7i			1.22046i
$73$		−	2.96955e7i		−	1.04568i	−0.852430	−	0.522841i	$-0.824872\pi$
$73$		−	2.96955e7i		−	1.04568i	0.852430	−	0.522841i	$-0.175128\pi$
$74$	−1.05701e8			−3.52493
$75$	1.82010e7			0.575242
$76$	1.71053e8			5.12717
$77$			8.15179e6i			0.231894i
$78$	−3.64521e7			−0.984790
$79$	4.37537e7			1.12333			0.561663	−	0.827366i	$-0.310162\pi$
$79$	4.37537e7			1.12333			0.561663	+	0.827366i	$0.310162\pi$
$80$	1.07248e7			0.261835
$81$	4.78297e6			0.111111
$82$		−	8.26235e7i		−	1.82746i
$83$		−	4.96491e7i		−	1.04616i	−0.852283	−	0.523081i	$-0.824782\pi$
$83$		−	4.96491e7i		−	1.04616i	0.852283	−	0.523081i	$-0.175218\pi$
$84$	4.40747e7			0.885263
$85$	5.16800e6			0.0990027
$86$	1.74251e7			0.318552
$87$	−5.20058e6			−0.0907768
$88$	−9.50684e7			−1.58528
$89$		−	4.18561e7i		−	0.667112i	−0.942730	−	0.333556i	$-0.891751\pi$
$89$		−	4.18561e7i		−	0.667112i	0.942730	−	0.333556i	$-0.108249\pi$
$90$		−	2.59729e6i		−	0.0395867i
$91$			3.18744e7i			0.464811i
$92$			8.82573e7i			1.23197i
$93$			938375.i			0.0125442i
$94$	1.13337e8			1.45165
$95$	−8.81418e6			−0.108215
$96$			2.38090e8i			2.80321i
$97$		−	1.47054e8i		−	1.66107i	−0.556965	−	0.830536i	$-0.688034\pi$
$97$		−	1.47054e8i		−	1.66107i	0.556965	−	0.830536i	$-0.311966\pi$
$98$			1.29283e8i			1.40164i
$99$			1.38638e7i			0.144325i
$100$	2.85244e8			2.85244
$101$		−	3.69158e7i		−	0.354753i	−0.984143	−	0.177377i	$-0.943239\pi$
$101$		−	3.69158e7i		−	0.354753i	0.984143	−	0.177377i	$-0.0567610\pi$
$102$			2.01246e8i			1.85921i
$103$			1.29093e8i			1.14697i	0.819214	+	0.573487i	$0.194410\pi$
$103$			1.29093e8i			1.14697i	−0.819214	+	0.573487i	$0.805590\pi$
$104$	−3.71728e8			−3.17754
$105$	−2.27112e6			−0.0186845
$106$		−	1.52006e8i		−	1.20403i
$107$	−1.28854e8			−0.983018			−0.491509	−	0.870872i	$-0.663555\pi$
$107$	−1.28854e8			−0.983018			−0.491509	+	0.870872i	$0.663555\pi$
$108$	7.49580e7			0.550963
$109$		−	1.07097e8i		−	0.758700i	−0.925253	−	0.379350i	$-0.876148\pi$
$109$		−	1.07097e8i		−	0.758700i	0.925253	−	0.379350i	$-0.123852\pi$
$110$	7.52842e6			0.0514201
$111$			1.57190e8i			1.03546i
$112$	3.65186e8			2.32082
$113$		−	5.80716e7i		−	0.356164i	−0.984016	−	0.178082i	$-0.943011\pi$
$113$		−	5.80716e7i		−	0.356164i	0.984016	−	0.178082i	$-0.0569892\pi$
$114$		−	3.43232e8i		−	2.03221i
$115$		−	4.54779e6i		−	0.0260022i
$116$	−8.15027e7			−0.450132
$117$			5.42089e7i			0.289286i
$118$	−3.30984e8	+	1.88812e8i	−1.70718	+	0.973872i
$119$	1.75974e8			0.877526
$120$		−	2.64864e7i		−	0.127731i
$121$	1.74174e8			0.812533
$122$	3.74197e8			1.68912
$123$	−1.22872e8			−0.536824
$124$			1.47061e7i			0.0622028i
$125$	−2.94504e7			−0.120629
$126$		−	8.84393e7i		−	0.350884i
$127$	−2.65214e8			−1.01949			−0.509743	−	0.860327i	$-0.670260\pi$
$127$	−2.65214e8			−1.01949			−0.509743	+	0.860327i	$0.670260\pi$
$128$			1.44513e9i			5.38352i
$129$		−	2.59133e7i		−	0.0935759i
$130$	2.94369e7			0.103067
$131$			2.83603e8i			0.962999i	0.876446	+	0.481500i	$0.159908\pi$
$131$			2.83603e8i			0.962999i	−0.876446	+	0.481500i	$0.840092\pi$
$132$			2.17271e8i			0.715659i
$133$	−3.00129e8			−0.959182
$134$	9.54377e8			2.96006
$135$	−3.86250e6			−0.0116288
$136$			2.05225e9i			5.99895i
$137$	−3.73666e8			−1.06072			−0.530361	−	0.847772i	$-0.677944\pi$
$137$	−3.73666e8			−1.06072			−0.530361	+	0.847772i	$0.677944\pi$
$138$	1.77095e8			0.488304
$139$	−3.45656e8			−0.925945			−0.462972	−	0.886373i	$-0.653217\pi$
$139$	−3.45656e8			−0.925945			−0.462972	+	0.886373i	$0.653217\pi$
$140$	−3.55926e7			−0.0926505
$141$		−	1.68547e8i		−	0.426427i
$142$		−	2.80117e8i		−	0.688947i
$143$	−1.57128e8			−0.375760
$144$	6.21072e8			1.44442
$145$	4.19974e6			0.00950058
$146$	−9.33828e8			−2.05521
$147$	1.92260e8			0.411737
$148$			2.46346e9i			5.13451i
$149$			2.68970e8i			0.545706i	0.962056	+	0.272853i	$0.0879672\pi$
$149$			2.68970e8i			0.545706i	−0.962056	+	0.272853i	$0.912033\pi$
$150$		−	5.72364e8i		−	1.13059i
$151$		−	7.64144e8i		−	1.46983i	−0.678159	−	0.734915i	$-0.737222\pi$
$151$		−	7.64144e8i		−	1.46983i	0.678159	−	0.734915i	$-0.262778\pi$
$152$		−	3.50018e9i		−	6.55716i
$153$	2.99279e8			0.546148
$154$	2.56348e8			0.455771
$155$		−	757786.i		−	0.00131286i
$156$			8.49553e8i			1.43447i
$157$		−	6.96606e8i		−	1.14654i	−0.819367	−	0.573269i	$-0.805675\pi$
$157$		−	6.96606e8i		−	1.14654i	0.819367	−	0.573269i	$-0.194325\pi$
$158$		−	1.37591e9i		−	2.20781i
$159$	−2.26053e8			−0.353689
$160$		−	1.92270e8i		−	0.293380i
$161$		−	1.54855e8i		−	0.230474i
$162$		−	1.50409e8i		−	0.218380i
$163$	1.03636e9			1.46811			0.734055	−	0.679090i	$-0.237625\pi$
$163$	1.03636e9			1.46811			0.734055	+	0.679090i	$0.237625\pi$
$164$	−1.92563e9			−2.66193
$165$		−	1.11957e7i		−	0.0151049i
$166$	−1.56130e9			−2.05615
$167$	−1.15681e9			−1.48729			−0.743645	−	0.668575i	$-0.766905\pi$
$167$	−1.15681e9			−1.48729			−0.743645	+	0.668575i	$0.766905\pi$
$168$		−	9.01878e8i		−	1.13217i
$169$	2.01342e8			0.246825
$170$		−	1.62517e8i		−	0.194582i
$171$	−5.10430e8			−0.596969
$172$		−	4.06109e8i		−	0.464012i
$173$			5.23234e8i			0.584133i	0.956398	+	0.292066i	$0.0943429\pi$
$173$			5.23234e8i			0.584133i	−0.956398	+	0.292066i	$0.905657\pi$
$174$			1.63541e8i			0.178415i
$175$	−5.00486e8			−0.533629
$176$			1.80022e9i			1.87619i
$177$	2.80788e8	+	4.92216e8i	0.286078	+	0.501490i
$178$	−1.31624e9			−1.31116
$179$		−	1.17775e9i		−	1.14720i	−0.819135	−	0.573601i	$-0.805546\pi$
$179$		−	1.17775e9i		−	1.14720i	0.819135	−	0.573601i	$-0.194454\pi$
$180$	−6.05325e7			−0.0576631
$181$	−2.07305e8			−0.193150			−0.0965752	−	0.995326i	$-0.530789\pi$
$181$	−2.07305e8			−0.193150			−0.0965752	+	0.995326i	$0.530789\pi$
$182$	1.00235e9			0.913550
$183$		−	5.56478e8i		−	0.496185i
$184$	1.80596e9			1.57557
$185$		−	1.26939e8i		−	0.108370i
$186$	2.95089e7			0.0246548
$187$			8.67482e8i			0.709405i
$188$		−	2.64144e9i		−	2.11451i
$189$	−1.31521e8			−0.103073
$190$			2.77178e8i			0.212688i
$191$		−	9.75780e8i		−	0.733193i	−0.930380	−	0.366597i	$-0.880523\pi$
$191$		−	9.75780e8i		−	0.733193i	0.930380	−	0.366597i	$-0.119477\pi$
$192$	4.08732e9			3.00769
$193$	−1.78978e9			−1.28994			−0.644971	−	0.764207i	$-0.723131\pi$
$193$	−1.78978e9			−1.28994			−0.644971	+	0.764207i	$0.723131\pi$
$194$	−4.62436e9			−3.26471
$195$		−	4.37765e7i		−	0.0302763i
$196$	3.01307e9			2.04167
$197$	−2.59972e9			−1.72608			−0.863041	−	0.505134i	$-0.831443\pi$
$197$	−2.59972e9			−1.72608			−0.863041	+	0.505134i	$0.831443\pi$
$198$	4.35971e8			0.283659
$199$	5.03763e8			0.321229			0.160614	−	0.987017i	$-0.448652\pi$
$199$	5.03763e8			0.321229			0.160614	+	0.987017i	$0.448652\pi$
$200$		−	5.83680e9i		−	3.64800i
$201$		−	1.41928e9i		−	0.869529i
$202$	−1.16088e9			−0.697240
$203$	1.43004e8			0.0842100
$204$	4.69026e9			2.70817
$205$	9.92253e7			0.0561833
$206$	4.05956e9			2.25429
$207$		−	2.63363e8i		−	0.143441i
$208$			7.03907e9i			3.76064i
$209$		−	1.47952e9i		−	0.775416i
$210$			7.14193e7i			0.0367230i
$211$		−	5.13610e8i		−	0.259122i	−0.991571	−	0.129561i	$-0.958643\pi$
$211$		−	5.13610e8i		−	0.259122i	0.991571	−	0.129561i	$-0.0413568\pi$
$212$	−3.54266e9			−1.75382
$213$	−4.16569e8			−0.202381
$214$			4.05203e9i			1.93205i
$215$			2.09263e7i			0.00979354i
$216$		−	1.53383e9i		−	0.704631i
$217$		−	2.58031e7i		−	0.0116368i
$218$	−3.36784e9			−1.49117
$219$			1.38872e9i			0.603724i
$220$		−	1.75458e8i		−	0.0749000i
$221$			3.39195e9i			1.42194i
$222$	4.94313e9			2.03512
$223$	−1.39299e9			−0.563286			−0.281643	−	0.959519i	$-0.590879\pi$
$223$	−1.39299e9			−0.563286			−0.281643	+	0.959519i	$0.590879\pi$
$224$		−	6.54691e9i		−	2.60042i
$225$	−8.51178e8			−0.332116
$226$	−1.82616e9			−0.700013
$227$		−	2.01523e9i		−	0.758966i	−0.925199	−	0.379483i	$-0.876102\pi$
$227$		−	2.01523e9i		−	0.758966i	0.925199	−	0.379483i	$-0.123898\pi$
$228$	−7.99938e9			−2.96017
$229$			2.76680e9i			1.00609i	0.864260	+	0.503045i	$0.167787\pi$
$229$			2.76680e9i			1.00609i	−0.864260	+	0.503045i	$0.832213\pi$
$230$	−1.43013e8			−0.0511053
$231$		−	3.81222e8i		−	0.133884i
$232$			1.66775e9i			0.575677i
$233$			2.29527e9i			0.778771i	0.921075	+	0.389385i	$0.127313\pi$
$233$			2.29527e9i			0.778771i	−0.921075	+	0.389385i	$0.872687\pi$
$234$	1.70469e9			0.568569
$235$			1.36111e8i			0.0446293i
$236$	4.40046e9	+	7.71393e9i	1.41857	+	2.48672i
$237$	−2.04616e9			−0.648553
$238$		−	5.53381e9i		−	1.72471i
$239$	2.38655e9			0.731442			0.365721	−	0.930725i	$-0.380823\pi$
$239$	2.38655e9			0.731442			0.365721	+	0.930725i	$0.380823\pi$
$240$	−5.01548e8			−0.151171
$241$	−4.37727e9			−1.29758			−0.648791	−	0.760967i	$-0.724725\pi$
$241$	−4.37727e9			−1.29758			−0.648791	+	0.760967i	$0.724725\pi$
$242$		−	5.47720e9i		−	1.59697i
$243$	−2.23677e8			−0.0641500
$244$		−	8.72105e9i		−	2.46042i
$245$	−1.55260e8			−0.0430919
$246$			3.86392e9i			1.05509i
$247$		−	5.78507e9i		−	1.55425i
$248$	3.00923e8			0.0795515
$249$			2.32186e9i			0.604002i
$250$			9.26121e8i			0.237087i
$251$	−3.87770e8			−0.0976967			−0.0488483	−	0.998806i	$-0.515555\pi$
$251$	−3.87770e8			−0.0976967			−0.0488483	+	0.998806i	$0.515555\pi$
$252$	−2.06117e9			−0.511107
$253$	7.63376e8			0.186319
$254$			8.34012e9i			2.00372i
$255$	−2.41683e8			−0.0571592
$256$	2.30701e10			5.37143
$257$	3.53688e9			0.810751			0.405375	−	0.914150i	$-0.367141\pi$
$257$	3.53688e9			0.810751			0.405375	+	0.914150i	$0.367141\pi$
$258$	−8.14890e8			−0.183916
$259$		−	4.32237e9i		−	0.960556i
$260$		−	6.86058e8i		−	0.150130i
$261$	2.43207e8			0.0524100
$262$	8.91841e9			1.89270
$263$	−7.41461e9			−1.54976			−0.774881	−	0.632107i	$-0.782190\pi$
$263$	−7.41461e9			−1.54976			−0.774881	+	0.632107i	$0.782190\pi$
$264$	4.44591e9			0.915261
$265$	1.82549e8			0.0370166
$266$			9.43808e9i			1.88520i
$267$			1.95742e9i			0.385157i
$268$		−	2.22428e10i		−	4.31171i
$269$		−	9.97114e9i		−	1.90430i	−0.305628	−	0.952151i	$-0.598866\pi$
$269$		−	9.97114e9i		−	1.90430i	0.305628	−	0.952151i	$-0.401134\pi$
$270$			1.21463e8i			0.0228554i
$271$	−1.49482e9			−0.277147			−0.138574	−	0.990352i	$-0.544252\pi$
$271$	−1.49482e9			−0.277147			−0.138574	+	0.990352i	$0.544252\pi$
$272$	3.88616e10			7.09979
$273$		−	1.49062e9i		−	0.268359i
$274$			1.17506e10i			2.08477i
$275$		−	2.46720e9i		−	0.431393i
$276$		−	4.12738e9i		−	0.711277i
$277$	2.03151e9			0.345063			0.172532	−	0.985004i	$-0.444805\pi$
$277$	2.03151e9			0.345063			0.172532	+	0.985004i	$0.444805\pi$
$278$			1.08698e10i			1.81987i
$279$		−	4.38834e7i		−	0.00724242i
$280$			7.28314e8i			0.118491i
$281$	−3.16483e9			−0.507604			−0.253802	−	0.967256i	$-0.581681\pi$
$281$	−3.16483e9			−0.507604			−0.253802	+	0.967256i	$0.581681\pi$
$282$	−5.30026e9			−0.838110
$283$		−	3.37837e9i		−	0.526698i	−0.964701	−	0.263349i	$-0.915173\pi$
$283$		−	3.37837e9i		−	0.526698i	0.964701	−	0.263349i	$-0.0848270\pi$
$284$	−6.52841e9			−1.00354
$285$	4.12199e8			0.0624780
$286$			4.94118e9i			0.738527i
$287$	3.37869e9			0.497990
$288$		−	1.11343e10i		−	1.61843i
$289$	1.17507e10			1.68450
$290$		−	1.32068e8i		−	0.0186727i
$291$			6.87701e9i			0.959020i
$292$			2.17638e10i			2.99367i
$293$	−7.85832e8			−0.106625			−0.0533125	−	0.998578i	$-0.516978\pi$
$293$	−7.85832e8			−0.106625			−0.0533125	+	0.998578i	$0.516978\pi$
$294$		−	6.04596e9i		−	0.809237i
$295$	−2.26751e8	−	3.97490e8i	−0.0299406	−	0.0524853i
$296$	5.04086e10			6.56656
$297$		−	6.48345e8i		−	0.0833260i
$298$	8.45823e9			1.07254
$299$	2.98488e9			0.373459
$300$	−1.33395e10			−1.64686
$301$			7.12555e8i			0.0868066i
$302$	−2.40299e10			−2.88884
$303$			1.72638e9i			0.204817i
$304$	−6.62797e10			−7.76044
$305$			4.49385e8i			0.0519301i
$306$		−	9.41136e9i		−	1.07341i
$307$	5.01321e9			0.564368			0.282184	−	0.959360i	$-0.408941\pi$
$307$	5.01321e9			0.564368			0.282184	+	0.959360i	$0.408941\pi$
$308$		−	5.97445e9i		−	0.663888i
$309$		−	6.03708e9i		−	0.662206i
$310$	−2.38299e7			−0.00258034
$311$	1.21298e10			1.29661			0.648306	−	0.761380i	$-0.275478\pi$
$311$	1.21298e10			1.29661			0.648306	+	0.761380i	$0.275478\pi$
$312$	1.73840e10			1.83456
$313$		−	1.81441e10i		−	1.89042i	−0.326457	−	0.945212i	$-0.605855\pi$
$313$		−	1.81441e10i		−	1.89042i	0.326457	−	0.945212i	$-0.394145\pi$
$314$	−2.19060e10			−2.25343
$315$	1.06210e8			0.0107875
$316$	−3.20671e10			−3.21596
$317$	−1.64494e10			−1.62897			−0.814485	−	0.580184i	$-0.802981\pi$
$317$	−1.64494e10			−1.62897			−0.814485	+	0.580184i	$0.802981\pi$
$318$			7.10862e9i			0.695148i
$319$			7.04953e8i			0.0680766i
$320$	−3.30072e9			−0.314781
$321$	6.02589e9			0.567546
$322$	−4.86970e9			−0.452980
$323$	−3.19385e10			−2.93430
$324$	−3.50544e9			−0.318099
$325$		−	9.64701e9i		−	0.864688i
$326$		−	3.25901e10i		−	2.88546i
$327$			5.00841e9i			0.438035i
$328$			3.94031e10i			3.40436i
$329$			4.63465e9i			0.395579i
$330$	−3.52069e8			−0.0296874
$331$	−8.69871e9			−0.724674			−0.362337	−	0.932047i	$-0.618021\pi$
$331$	−8.69871e9			−0.724674			−0.362337	+	0.932047i	$0.618021\pi$
$332$			3.63878e10i			2.99505i
$333$		−	7.35106e9i		−	0.597824i
$334$			3.63779e10i			2.92315i
$335$			1.14614e9i			0.0910038i
$336$	−1.70780e10			−1.33993
$337$		−	1.15654e10i		−	0.896688i	−0.893861	−	0.448344i	$-0.852014\pi$
$337$		−	1.15654e10i		−	0.896688i	0.893861	−	0.448344i	$-0.147986\pi$
$338$		−	6.33157e9i		−	0.485115i
$339$			2.71574e9i			0.205631i
$340$	−3.78763e9			−0.283434
$341$	1.27199e8			0.00940735
$342$			1.60514e10i			1.17330i
$343$	−1.26999e10			−0.917536
$344$	−8.31001e9			−0.593428
$345$			2.12679e8i			0.0150124i
$346$	1.64540e10			1.14807
$347$		−	8.66659e9i		−	0.597765i	−0.954290	−	0.298882i	$-0.903386\pi$
$347$		−	8.66659e9i		−	0.597765i	0.954290	−	0.298882i	$-0.0966138\pi$
$348$	3.81150e9			0.259884
$349$			2.55465e10i			1.72199i	0.508617	+	0.860993i	$0.330157\pi$
$349$			2.55465e10i			1.72199i	−0.508617	+	0.860993i	$0.669843\pi$
$350$			1.57387e10i			1.04881i
$351$		−	2.53510e9i		−	0.167019i
$352$	3.22737e10			2.10222
$353$		−	1.53693e10i		−	0.989819i	−0.868945	−	0.494909i	$-0.835201\pi$
$353$		−	1.53693e10i		−	0.989819i	0.868945	−	0.494909i	$-0.164799\pi$
$354$	1.54786e10	−	8.82987e9i	0.985641	−	0.562265i
$355$	3.36401e8			0.0211809
$356$			3.06763e10i			1.90987i
$357$	−8.22948e9			−0.506640
$358$	−3.70364e10			−2.25474
$359$	9.62493e8			0.0579455			0.0289728	−	0.999580i	$-0.490776\pi$
$359$	9.62493e8			0.0579455			0.0289728	+	0.999580i	$0.490776\pi$
$360$			1.23865e9i			0.0737458i
$361$	3.74886e10			2.20734
$362$			6.51908e9i			0.379622i
$363$	−8.14530e9			−0.469116
$364$		−	2.33607e10i		−	1.33070i
$365$		−	1.12147e9i		−	0.0631850i
$366$	−1.74995e10			−0.975215
$367$		−	1.39474e10i		−	0.768825i	−0.923161	−	0.384413i	$-0.874404\pi$
$367$		−	1.39474e10i		−	0.768825i	0.923161	−	0.384413i	$-0.125596\pi$
$368$		−	3.41979e10i		−	1.86470i
$369$	5.74614e9			0.309935
$370$	−3.99183e9			−0.212993
$371$	6.21592e9			0.328103
$372$		−	6.87735e8i		−	0.0359128i
$373$	−3.78415e9			−0.195494			−0.0977469	−	0.995211i	$-0.531164\pi$
$373$	−3.78415e9			−0.195494			−0.0977469	+	0.995211i	$0.531164\pi$
$374$	2.72795e10			1.39428
$375$	1.37726e9			0.0696451
$376$	−5.40505e10			−2.70426
$377$			2.75644e9i			0.136453i
$378$			4.13590e9i			0.202583i
$379$	5.94715e9			0.288238			0.144119	−	0.989560i	$-0.453965\pi$
$379$	5.94715e9			0.288238			0.144119	+	0.989560i	$0.453965\pi$
$380$	6.45991e9			0.309808
$381$	1.24028e10			0.588601
$382$	−3.06851e10			−1.44104
$383$	4.08122e10			1.89668			0.948341	−	0.317254i	$-0.102761\pi$
$383$	4.08122e10			1.89668			0.948341	+	0.317254i	$0.102761\pi$
$384$		−	6.75820e10i		−	3.10818i
$385$			3.07856e8i			0.0140122i
$386$			5.62828e10i			2.53528i
$387$			1.21185e9i			0.0540261i
$388$			1.07775e11i			4.75547i
$389$	2.01704e10			0.880878			0.440439	−	0.897782i	$-0.354823\pi$
$389$	2.01704e10			0.880878			0.440439	+	0.897782i	$0.354823\pi$
$390$	−1.37663e9			−0.0595057
$391$		−	1.64791e10i		−	0.705061i
$392$		−	6.16549e10i		−	2.61110i
$393$		−	1.32628e10i		−	0.555988i
$394$			8.17528e10i			3.39248i
$395$	1.65238e9			0.0678767
$396$		−	1.01608e10i		−	0.413186i
$397$		−	1.20249e10i		−	0.484082i	−0.970266	−	0.242041i	$-0.922183\pi$
$397$		−	1.20249e10i		−	0.484082i	0.970266	−	0.242041i	$-0.0778169\pi$
$398$		−	1.58417e10i		−	0.631350i
$399$	1.40356e10			0.553784
$400$	−1.10526e11			−4.31743
$401$		−	2.78698e10i		−	1.07785i	−0.842355	−	0.538923i	$-0.818831\pi$
$401$		−	2.78698e10i		−	1.07785i	0.842355	−	0.538923i	$-0.181169\pi$
$402$	−4.46318e10			−1.70899
$403$	4.97363e8			0.0188562
$404$			2.70555e10i			1.01562i
$405$	1.80631e8			0.00671386
$406$		−	4.49701e9i		−	0.165508i
$407$	2.13076e10			0.776527
$408$		−	9.59744e10i		−	3.46350i
$409$		−	1.72521e10i		−	0.616521i	−0.951302	−	0.308261i	$-0.900253\pi$
$409$		−	1.72521e10i		−	0.616521i	0.951302	−	0.308261i	$-0.0997469\pi$
$410$		−	3.12032e9i		−	0.110424i
$411$	1.74746e10			0.612408
$412$		−	9.46122e10i		−	3.28366i
$413$	−7.72101e9	−	1.35348e10i	−0.265384	−	0.465212i
$414$	−8.28191e9			−0.281922
$415$		−	1.87502e9i		−	0.0632141i
$416$	1.26194e11			4.21371
$417$	1.61647e10			0.534594
$418$	−4.65260e10			−1.52402
$419$			1.82949e10i			0.593573i	0.954944	+	0.296786i	$0.0959149\pi$
$419$			1.82949e10i			0.593573i	−0.954944	+	0.296786i	$0.904085\pi$
$420$	1.66450e9			0.0534918
$421$			2.14261e10i			0.682046i	0.940055	+	0.341023i	$0.110773\pi$
$421$			2.14261e10i			0.682046i	−0.940055	+	0.341023i	$0.889227\pi$
$422$	−1.61514e10			−0.509284
$423$			7.88217e9i			0.246198i
$424$			7.24917e10i			2.24298i
$425$	−5.32597e10			−1.63246
$426$			1.30998e10i			0.397764i
$427$			1.53019e10i			0.460291i
$428$	9.44368e10			2.81427
$429$	7.34816e9			0.216945
$430$	6.58066e8			0.0192484
$431$		−	4.23508e9i		−	0.122730i	−0.998115	−	0.0613652i	$-0.980455\pi$
$431$		−	4.23508e9i		−	0.122730i	0.998115	−	0.0613652i	$-0.0195454\pi$
$432$	−2.90447e10			−0.833934
$433$	−2.36362e9			−0.0672397			−0.0336199	−	0.999435i	$-0.510704\pi$
$433$	−2.36362e9			−0.0672397			−0.0336199	+	0.999435i	$0.510704\pi$
$434$	−8.11425e8			−0.0228712
$435$	−1.96402e8			−0.00548516
$436$			7.84911e10i			2.17207i
$437$			2.81056e10i			0.770668i
$438$	4.36708e10			1.18657
$439$	4.85762e10			1.30787			0.653937	−	0.756549i	$-0.273116\pi$
$439$	4.85762e10			1.30787			0.653937	+	0.756549i	$0.273116\pi$
$440$	−3.59030e9			−0.0957901
$441$	−8.99111e9			−0.237716
$442$	1.06666e11			2.79471
$443$		−	5.86159e10i		−	1.52195i	−0.648781	−	0.760975i	$-0.724721\pi$
$443$		−	5.86159e10i		−	1.52195i	0.648781	−	0.760975i	$-0.275279\pi$
$444$		−	1.15205e11i		−	2.96441i
$445$		−	1.58072e9i		−	0.0403101i
$446$			4.38051e10i			1.10710i
$447$		−	1.25785e10i		−	0.315063i
$448$	−1.12392e11			−2.79011
$449$	5.15270e10			1.26780			0.633898	−	0.773417i	$-0.281454\pi$
$449$	5.15270e10			1.26780			0.633898	+	0.773417i	$0.281454\pi$
$450$			2.67668e10i			0.652749i
$451$			1.66556e10i			0.402582i
$452$			4.25606e10i			1.01966i
$453$			3.57355e10i			0.848607i
$454$	−6.33726e10			−1.49169
$455$			1.20375e9i			0.0280861i
$456$			1.63687e11i			3.78578i
$457$			9.53474e9i			0.218597i	0.994009	+	0.109299i	$0.0348604\pi$
$457$			9.53474e9i			0.218597i	−0.994009	+	0.109299i	$0.965140\pi$
$458$	8.70071e10			1.97739
$459$	−1.39959e10			−0.315319
$460$			3.33308e9i			0.0744413i
$461$	−2.27246e10			−0.503144			−0.251572	−	0.967839i	$-0.580948\pi$
$461$	−2.27246e10			−0.503144			−0.251572	+	0.967839i	$0.580948\pi$
$462$	−1.19882e10			−0.263139
$463$			3.40934e10i			0.741902i	0.928652	+	0.370951i	$0.120968\pi$
$463$			3.40934e10i			0.741902i	−0.928652	+	0.370951i	$0.879032\pi$
$464$	3.15806e10			0.681317
$465$			3.54382e7i			0.000757983i
$466$	7.21788e10			1.53061
$467$			5.25875e10i			1.10564i	0.833299	+	0.552822i	$0.186449\pi$
$467$			5.25875e10i			1.10564i	−0.833299	+	0.552822i	$0.813551\pi$
$468$		−	3.97297e10i		−	0.828193i
$469$			3.90269e10i			0.806627i
$470$	4.28024e9			0.0877155
$471$			3.25770e10i			0.661954i
$472$	1.57846e11	−	9.00445e10i	3.18029	−	1.81422i
$473$	−3.51262e9			−0.0701757
$474$			6.43450e10i			1.27468i
$475$	9.08361e10			1.78437
$476$	−1.28971e11			−2.51226
$477$	1.05714e10			0.204202
$478$		−	7.50494e10i		−	1.43759i
$479$	5.04232e10			0.957830			0.478915	−	0.877861i	$-0.341030\pi$
$479$	5.04232e10			0.957830			0.478915	+	0.877861i	$0.341030\pi$
$480$			8.99157e9i			0.169383i
$481$	8.33150e10			1.55648
$482$			1.37651e11i			2.55030i
$483$			7.24187e9i			0.133064i
$484$	−1.27652e11			−2.32619
$485$		−	5.55355e9i		−	0.100370i
$486$			7.03393e9i			0.126082i
$487$	5.41279e10			0.962289			0.481145	−	0.876641i	$-0.340221\pi$
$487$	5.41279e10			0.962289			0.481145	+	0.876641i	$0.340221\pi$
$488$	−1.78454e11			−3.14665
$489$	−4.84656e10			−0.847614
$490$			4.88243e9i			0.0846938i
$491$	−7.11541e10			−1.22426			−0.612131	−	0.790757i	$-0.709687\pi$
$491$	−7.11541e10			−1.22426			−0.612131	+	0.790757i	$0.709687\pi$
$492$	9.00527e10			1.53687
$493$	1.52179e10			0.257613
$494$	−1.81922e11			−3.05476
$495$			5.23572e8i			0.00872079i
$496$		−	5.69830e9i		−	0.0941496i
$497$	1.14547e10			0.187740
$498$	7.30150e10			1.18712
$499$	−6.70056e10			−1.08071			−0.540355	−	0.841437i	$-0.681710\pi$
$499$	−6.70056e10			−1.08071			−0.540355	+	0.841437i	$0.681710\pi$
$500$	2.15842e10			0.345347
$501$	5.40986e10			0.858687
$502$			1.21941e10i			0.192015i
$503$		−	7.59711e10i		−	1.18680i	−0.804909	−	0.593398i	$-0.797786\pi$
$503$		−	7.59711e10i		−	1.18680i	0.804909	−	0.593398i	$-0.202214\pi$
$504$			4.21767e10i			0.653657i
$505$		−	1.39414e9i		−	0.0214359i
$506$		−	2.40057e10i		−	0.366195i
$507$	−9.41585e9			−0.142504
$508$	1.94375e11			2.91868
$509$		−	1.73280e10i		−	0.258152i	−0.991635	−	0.129076i	$-0.958799\pi$
$509$		−	1.73280e10i		−	0.258152i	0.991635	−	0.129076i	$-0.0412012\pi$
$510$			7.60017e9i			0.112342i
$511$		−	3.81866e10i		−	0.560051i
$512$		−	3.55528e11i		−	5.17361i
$513$	2.38704e10			0.344660
$514$		−	1.11223e11i		−	1.59347i
$515$			4.87526e9i			0.0693057i
$516$			1.89919e10i			0.267897i
$517$	−2.28470e10			−0.319792
$518$	−1.35925e11			−1.88790
$519$		−	2.44692e10i		−	0.337249i
$520$	−1.40385e10			−0.192002
$521$	−2.24043e10			−0.304075			−0.152037	−	0.988375i	$-0.548583\pi$
$521$	−2.24043e10			−0.304075			−0.152037	+	0.988375i	$0.548583\pi$
$522$		−	7.64808e9i		−	0.103008i
$523$	1.85587e10			0.248050			0.124025	−	0.992279i	$-0.460420\pi$
$523$	1.85587e10			0.248050			0.124025	+	0.992279i	$0.460420\pi$
$524$		−	2.07853e11i		−	2.75696i
$525$	2.34054e10			0.308091
$526$			2.33166e11i			3.04594i
$527$		−	2.74587e9i		−	0.0355989i
$528$		−	8.41881e10i		−	1.08322i
$529$	6.38095e10			0.814822
$530$		−	5.74058e9i		−	0.0727533i
$531$	−1.31311e10	−	2.30187e10i	−0.165167	−	0.289536i
$532$	2.19964e11			2.74603
$533$			6.51252e10i			0.806938i
$534$	6.15545e10			0.756998
$535$	−4.86622e9			−0.0593986
$536$	−4.55142e11			−5.51427
$537$			5.50778e10i			0.662337i
$538$	−3.13560e11			−3.74276
$539$		−	2.60614e10i		−	0.308775i
$540$	2.83082e9			0.0332918
$541$		−	1.21915e11i		−	1.42320i	−0.702583	−	0.711602i	$-0.747970\pi$
$541$		−	1.21915e11i		−	1.42320i	0.702583	−	0.711602i	$-0.252030\pi$
$542$			4.70071e10i			0.544711i
$543$	9.69470e9			0.111515
$544$		−	6.96697e11i		−	7.95515i
$545$		−	4.04456e9i		−	0.0458442i
$546$	−4.68751e10			−0.527438
$547$	−2.86927e10			−0.320496			−0.160248	−	0.987077i	$-0.551229\pi$
$547$	−2.86927e10			−0.320496			−0.160248	+	0.987077i	$0.551229\pi$
$548$	2.73860e11			3.03673
$549$			2.60239e10i			0.286473i
$550$	−7.75855e10			−0.847871
$551$	−2.59546e10			−0.281584
$552$	−8.44566e10			−0.909656
$553$	5.62645e10			0.601636
$554$		−	6.38843e10i		−	0.678196i
$555$			5.93637e9i			0.0625675i
$556$	2.53331e11			2.65088
$557$	−6.01837e9			−0.0625256			−0.0312628	−	0.999511i	$-0.509953\pi$
$557$	−6.01837e9			−0.0625256			−0.0312628	+	0.999511i	$0.509953\pi$
$558$	−1.37999e9			−0.0142344
$559$	−1.37347e10			−0.140661
$560$	1.37914e10			0.140235
$561$		−	4.05681e10i		−	0.409575i
$562$			9.95236e10i			0.997656i
$563$			1.35572e11i			1.34939i	0.738097	+	0.674695i	$0.235725\pi$
$563$			1.35572e11i			1.34939i	−0.738097	+	0.674695i	$0.764275\pi$
$564$			1.23528e11i			1.22081i
$565$		−	2.19310e9i		−	0.0215211i
$566$	−1.06239e11			−1.03518
$567$	6.15061e9			0.0595094
$568$			1.33588e11i			1.28343i
$569$		−	1.49267e11i		−	1.42402i	−0.702171	−	0.712008i	$-0.747786\pi$
$569$		−	1.49267e11i		−	1.42402i	0.702171	−	0.712008i	$-0.252214\pi$
$570$		−	1.29623e10i		−	0.122796i
$571$			1.48625e11i			1.39813i	0.715058	+	0.699065i	$0.246400\pi$
$571$			1.48625e11i			1.39813i	−0.715058	+	0.699065i	$0.753600\pi$
$572$	1.15159e11			1.07576
$573$			4.56327e10i			0.423309i
$574$		−	1.06249e11i		−	0.978761i
$575$			4.68681e10i			0.428752i
$576$	−1.91145e11			−1.73649
$577$	9.53737e10			0.860449			0.430225	−	0.902722i	$-0.358434\pi$
$577$	9.53737e10			0.860449			0.430225	+	0.902722i	$0.358434\pi$
$578$		−	3.69521e11i		−	3.31076i
$579$	8.36997e10			0.744749
$580$	−3.07799e9			−0.0271991
$581$		−	6.38457e10i		−	0.560309i
$582$	2.16260e11			1.88488
$583$			3.06421e10i			0.265243i
$584$	4.45342e11			3.82862
$585$			2.04722e9i			0.0174800i
$586$			2.47119e10i			0.209563i
$587$			5.24214e10i			0.441526i	0.975327	+	0.220763i	$0.0708548\pi$
$587$			5.24214e10i			0.441526i	−0.975327	+	0.220763i	$0.929145\pi$
$588$	−1.40907e11			−1.17876
$589$			4.68316e9i			0.0389115i
$590$	−1.24998e10	+	7.13058e9i	−0.103156	+	0.0588460i
$591$	1.21577e11			0.996554
$592$		−	9.54542e11i		−	7.77156i
$593$	9.14118e8			0.00739237			0.00369618	−	0.999993i	$-0.498823\pi$
$593$	9.14118e8			0.00739237			0.00369618	+	0.999993i	$0.498823\pi$
$594$	−2.03884e10			−0.163771
$595$	6.64573e9			0.0530243
$596$		−	1.97128e11i		−	1.56229i
$597$	−2.35587e10			−0.185461
$598$		−	9.38649e10i		−	0.734004i
$599$	−2.33750e11			−1.81570			−0.907851	−	0.419292i	$-0.862278\pi$
$599$	−2.33750e11			−1.81570			−0.907851	+	0.419292i	$0.862278\pi$
$600$			2.72960e11i			2.10617i
$601$		−	1.03825e11i		−	0.795799i	−0.917429	−	0.397900i	$-0.869739\pi$
$601$		−	1.03825e11i		−	0.795799i	0.917429	−	0.397900i	$-0.130261\pi$
$602$	2.24076e10			0.170612
$603$			6.63732e10i			0.502023i
$604$			5.60041e11i			4.20796i
$605$	6.57775e9			0.0490971
$606$	5.42891e10			0.402552
$607$	1.68867e11			1.24391			0.621956	−	0.783052i	$-0.286338\pi$
$607$	1.68867e11			1.24391			0.621956	+	0.783052i	$0.286338\pi$
$608$			1.18824e12i			8.69539i
$609$	−6.68763e9			−0.0486186
$610$	1.41317e10			0.102065
$611$	−8.93343e10			−0.640993
$612$	−2.19342e11			−1.56356
$613$		−	6.54092e10i		−	0.463230i	−0.972807	−	0.231615i	$-0.925599\pi$
$613$		−	6.54092e10i		−	0.463230i	0.972807	−	0.231615i	$-0.0744010\pi$
$614$		−	1.57649e11i		−	1.10922i
$615$	−4.64031e9			−0.0324374
$616$	−1.22252e11			−0.849051
$617$	−1.26499e11			−0.872861			−0.436431	−	0.899738i	$-0.643758\pi$
$617$	−1.26499e11			−0.872861			−0.436431	+	0.899738i	$0.643758\pi$
$618$	−1.89847e11			−1.30152
$619$	−2.43799e11			−1.66062			−0.830308	−	0.557305i	$-0.811835\pi$
$619$	−2.43799e11			−1.66062			−0.830308	+	0.557305i	$0.811835\pi$
$620$			5.55381e8i			0.00375859i
$621$			1.23163e10i			0.0828157i
$622$		−	3.81442e11i		−	2.54839i
$623$		−	5.38244e10i		−	0.357295i
$624$		−	3.29184e11i		−	2.17121i
$625$	1.50919e11			0.989060
$626$	−5.70575e11			−3.71548
$627$			6.91902e10i			0.447687i
$628$			5.10542e11i			3.28241i
$629$		−	4.59970e11i		−	2.93851i
$630$		−	3.33995e9i		−	0.0212021i
$631$	−2.22925e11			−1.40618			−0.703089	−	0.711102i	$-0.748197\pi$
$631$	−2.22925e11			−1.40618			−0.703089	+	0.711102i	$0.748197\pi$
$632$			6.56172e11i			4.11291i
$633$			2.40192e10i			0.149604i
$634$			5.17281e11i			3.20162i
$635$	−1.00159e10			−0.0616022
$636$	1.65674e11			1.01257
$637$		−	1.01903e11i		−	0.618911i
$638$	2.21685e10			0.133799
$639$	1.94810e10			0.116845
$640$			5.45760e10i			0.325298i
$641$	−1.03535e11			−0.613273			−0.306637	−	0.951827i	$-0.599204\pi$
$641$	−1.03535e11			−0.613273			−0.306637	+	0.951827i	$0.599204\pi$
$642$		−	1.89495e11i		−	1.11547i
$643$	−2.49767e11			−1.46114			−0.730569	−	0.682839i	$-0.760745\pi$
$643$	−2.49767e11			−1.46114			−0.730569	+	0.682839i	$0.760745\pi$
$644$			1.13493e11i			0.659823i
$645$		−	9.78628e8i		−	0.00565430i
$646$			1.00436e12i			5.76714i
$647$	−1.61624e10			−0.0922333			−0.0461167	−	0.998936i	$-0.514685\pi$
$647$	−1.61624e10			−0.0922333			−0.0461167	+	0.998936i	$0.514685\pi$
$648$			7.17300e10i			0.406819i
$649$	6.67212e10	−	3.80616e10i	0.376084	−	0.214540i
$650$	−3.03368e11			−1.69948
$651$			1.20669e9i			0.00671850i
$652$	−7.59546e11			−4.20304
$653$	4.42350e10			0.243284			0.121642	−	0.992574i	$-0.461184\pi$
$653$	4.42350e10			0.243284			0.121642	+	0.992574i	$0.461184\pi$
$654$	1.57498e11			0.860925
$655$			1.07104e10i			0.0581890i
$656$	7.46141e11			4.02908
$657$		−	6.49441e10i		−	0.348560i
$658$	1.45745e11			0.777481
$659$		−	5.50304e10i		−	0.291784i	−0.989301	−	0.145892i	$-0.953395\pi$
$659$		−	5.50304e10i		−	0.291784i	0.989301	−	0.145892i	$-0.0466052\pi$
$660$			8.20535e9i			0.0432435i
$661$	1.96165e11			1.02758			0.513790	−	0.857916i	$-0.328241\pi$
$661$	1.96165e11			1.02758			0.513790	+	0.857916i	$0.328241\pi$
$662$			2.73546e11i			1.42429i
$663$		−	1.58626e11i		−	0.820955i
$664$	7.44586e11			3.83039
$665$	−1.13345e10			−0.0579583
$666$	−2.31167e11			−1.17498
$667$		−	1.33916e10i		−	0.0676597i
$668$	8.47825e11			4.25795
$669$	6.51438e10			0.325214
$670$	3.60425e10			0.178861
$671$	−7.54322e10			−0.372106
$672$			3.06169e11i			1.50136i
$673$		−	2.22802e11i		−	1.08607i	−0.839710	−	0.543036i	$-0.817275\pi$
$673$		−	2.22802e11i		−	1.08607i	0.839710	−	0.543036i	$-0.182725\pi$
$674$	−3.63695e11			−1.76237
$675$	3.98056e10			0.191747
$676$	−1.47564e11			−0.706632
$677$	4.92757e10			0.234573			0.117287	−	0.993098i	$-0.462580\pi$
$677$	4.92757e10			0.234573			0.117287	+	0.993098i	$0.462580\pi$
$678$	8.54012e10			0.404153
$679$		−	1.89102e11i		−	0.889645i
$680$			7.75043e10i			0.362485i
$681$			9.42432e10i			0.438189i
$682$		−	4.00001e9i		−	0.0184894i
$683$		−	4.89565e10i		−	0.224971i	−0.993653	−	0.112486i	$-0.964119\pi$
$683$		−	4.89565e10i		−	0.224971i	0.993653	−	0.112486i	$-0.0358812\pi$
$684$	3.74094e11			1.70906
$685$	−1.41117e10			−0.0640939
$686$			3.99370e11i			1.80335i
$687$		−	1.29391e11i		−	0.580866i
$688$			1.57359e11i			0.702325i
$689$			1.19814e11i			0.531655i
$690$	6.68808e9			0.0295056
$691$			2.12401e11i			0.931633i	0.884881	+	0.465817i	$0.154239\pi$
$691$			2.12401e11i			0.931633i	−0.884881	+	0.465817i	$0.845761\pi$
$692$		−	3.83478e11i		−	1.67231i
$693$			1.78280e10i			0.0772981i
$694$	−2.72536e11			−1.17486
$695$	−1.30539e10			−0.0559500
$696$		−	7.79929e10i		−	0.332367i
$697$	3.59547e11			1.52344
$698$	8.03355e11			3.38443
$699$		−	1.07339e11i		−	0.449623i
$700$	3.66806e11			1.52772
$701$		−	3.64391e11i		−	1.50902i	−0.656287	−	0.754512i	$-0.727874\pi$
$701$		−	3.64391e11i		−	1.50902i	0.656287	−	0.754512i	$-0.272126\pi$
$702$	−7.97206e10			−0.328263
$703$			7.84492e11i			3.21194i
$704$		−	5.54047e11i		−	2.25557i
$705$		−	6.36526e9i		−	0.0257668i
$706$	−4.83315e11			−1.94541
$707$		−	4.74714e10i		−	0.190000i
$708$	−2.05789e11	−	3.60745e11i	−0.819011	−	1.43571i
$709$	2.29697e10			0.0909015			0.0454508	−	0.998967i	$-0.485528\pi$
$709$	2.29697e10			0.0909015			0.0454508	+	0.998967i	$0.485528\pi$
$710$		−	1.05787e10i		−	0.0416294i
$711$	9.56893e10			0.374442
$712$	6.27715e11			2.44254
$713$	−2.41634e9			−0.00934974
$714$			2.58791e11i			0.995762i
$715$	−5.93402e9			−0.0227052
$716$			8.63171e11i			3.28431i
$717$	−1.11608e11			−0.422298
$718$		−	3.02673e10i		−	0.113888i
$719$		−	2.79967e11i		−	1.04759i	−0.851844	−	0.523796i	$-0.824515\pi$
$719$		−	2.79967e11i		−	1.04759i	0.851844	−	0.523796i	$-0.175485\pi$
$720$	2.34551e10			0.0872785
$721$			1.66006e11i			0.614302i
$722$		−	1.17889e12i		−	4.33836i
$723$	2.04705e11			0.749159
$724$	1.51934e11			0.552968
$725$	−4.32812e10			−0.156656
$726$			2.56143e11i			0.922012i
$727$	2.27790e11			0.815450			0.407725	−	0.913105i	$-0.366322\pi$
$727$	2.27790e11			0.815450			0.407725	+	0.913105i	$0.366322\pi$
$728$	−4.78019e11			−1.70184
$729$	1.04604e10			0.0370370
$730$	−3.52665e10			−0.124185
$731$			7.58274e10i			0.265556i
$732$			4.07843e11i			1.42052i
$733$	−2.02311e11			−0.700815			−0.350408	−	0.936597i	$-0.613957\pi$
$733$	−2.02311e11			−0.700815			−0.350408	+	0.936597i	$0.613957\pi$
$734$	−4.38599e11			−1.51107
$735$	7.26079e9			0.0248791
$736$	−6.13087e11			−2.08935
$737$	−1.92388e11			−0.652089
$738$		−	1.80698e11i		−	0.609154i
$739$		−	5.04605e11i		−	1.69190i	−0.533264	−	0.845949i	$-0.679035\pi$
$739$		−	5.04605e11i		−	1.69190i	0.533264	−	0.845949i	$-0.320965\pi$
$740$			9.30339e10i			0.310252i
$741$			2.70541e11i			0.897346i
$742$		−	1.95471e11i		−	0.644861i
$743$	−3.95146e11			−1.29659			−0.648294	−	0.761390i	$-0.724517\pi$
$743$	−3.95146e11			−1.29659			−0.648294	+	0.761390i	$0.724517\pi$
$744$	−1.40728e10			−0.0459291
$745$			1.01578e10i			0.0329741i
$746$			1.18999e11i			0.384228i
$747$		−	1.08583e11i		−	0.348721i
$748$		−	6.35778e11i		−	2.03095i
$749$	−1.65698e11			−0.526490
$750$		−	4.33104e10i		−	0.136882i
$751$		−	3.95840e11i		−	1.24440i	−0.782859	−	0.622200i	$-0.786239\pi$
$751$		−	3.95840e11i		−	1.24440i	0.782859	−	0.622200i	$-0.213761\pi$
$752$			1.02351e12i			3.20051i
$753$	1.81342e10			0.0564052
$754$	8.66812e10			0.268188
$755$		−	2.88583e10i		−	0.0888142i
$756$	9.63913e10			0.295088
$757$	−5.41866e11			−1.65009			−0.825047	−	0.565064i	$-0.808851\pi$
$757$	−5.41866e11			−1.65009			−0.825047	+	0.565064i	$0.808851\pi$
$758$		−	1.87019e11i		−	0.566511i
$759$	−3.56996e10			−0.107571
$760$		−	1.32186e11i		−	0.396215i
$761$	−2.60900e11			−0.777921			−0.388960	−	0.921255i	$-0.627166\pi$
$761$	−2.60900e11			−0.777921			−0.388960	+	0.921255i	$0.627166\pi$
$762$		−	3.90029e11i		−	1.15685i
$763$		−	1.37720e11i		−	0.406348i
$764$			7.15149e11i			2.09905i
$765$	1.13024e10			0.0330009
$766$		−	1.28341e12i		−	3.72778i
$767$	2.60887e11	−	1.48825e11i	0.753826	−	0.430025i
$768$	−1.07888e12			−3.10120
$769$		−	6.34131e10i		−	0.181332i	−0.995881	−	0.0906658i	$-0.971101\pi$
$769$		−	6.34131e10i		−	0.181332i	0.995881	−	0.0906658i	$-0.0288995\pi$
$770$	9.68109e9			0.0275398
$771$	−1.65403e11			−0.468087
$772$	1.31173e12			3.69296
$773$			5.07360e11i			1.42101i	0.703691	+	0.710506i	$0.251534\pi$
$773$			5.07360e11i			1.42101i	−0.703691	+	0.710506i	$0.748466\pi$
$774$	3.81086e10			0.106184
$775$			7.80950e9i			0.0216479i
$776$	2.20536e12			6.08180
$777$			2.02137e11i			0.554577i
$778$		−	6.34294e11i		−	1.73130i
$779$	−6.13218e11			−1.66519
$780$			3.20838e10i			0.0866776i
$781$			5.64671e10i			0.151772i
$782$	−5.18215e11			−1.38574
$783$	−1.13737e10			−0.0302589
$784$	−1.16750e12			−3.09025
$785$		−	2.63077e10i		−	0.0692793i
$786$	−4.17073e11			−1.09275
$787$	6.40280e11			1.66906			0.834529	−	0.550964i	$-0.185740\pi$
$787$	6.40280e11			1.66906			0.834529	+	0.550964i	$0.185740\pi$
$788$	1.90533e12			4.94158
$789$	3.46747e11			0.894756
$790$		−	5.19620e10i		−	0.133407i
$791$		−	7.46765e10i		−	0.190756i
$792$	−2.07915e11			−0.528426
$793$	−2.94948e11			−0.745852
$794$	−3.78144e11			−0.951427
$795$	−8.53698e9			−0.0213715
$796$	−3.69208e11			−0.919642
$797$		−	6.06231e11i		−	1.50247i	−0.660037	−	0.751233i	$-0.729459\pi$
$797$		−	6.06231e11i		−	1.50247i	0.660037	−	0.751233i	$-0.270541\pi$
$798$		−	4.41375e11i		−	1.08842i
$799$			4.93202e11i			1.21014i
$800$			1.98147e12i			4.83757i
$801$		−	9.15393e10i		−	0.222371i
$802$	−8.76416e11			−2.11842
$803$	1.88245e11			0.452753
$804$			1.04019e12i			2.48937i
$805$		−	5.84818e9i		−	0.0139264i
$806$		−	1.56405e10i		−	0.0370603i
$807$			4.66304e11i			1.09945i
$808$	5.53624e11			1.29888
$809$			6.46751e11i			1.50988i	0.655793	+	0.754941i	$0.272334\pi$
$809$			6.46751e11i			1.50988i	−0.655793	+	0.754941i	$0.727666\pi$
$810$		−	5.68027e9i		−	0.0131956i
$811$			1.83649e11i			0.424527i	0.977212	+	0.212264i	$0.0680836\pi$
$811$			1.83649e11i			0.424527i	−0.977212	+	0.212264i	$0.931916\pi$
$812$	−1.04807e11			−0.241084
$813$	6.99056e10			0.160011
$814$		−	6.70055e11i		−	1.52621i
$815$	3.91385e10			0.0887102
$816$	−1.81738e12			−4.09907
$817$		−	1.29326e11i		−	0.290267i
$818$	−5.42522e11			−1.21173
$819$			6.97093e10i			0.154937i
$820$	−7.27222e10			−0.160847
$821$			3.97488e10i			0.0874886i	0.999043	+	0.0437443i	$0.0139287\pi$
$821$			3.97488e10i			0.0874886i	−0.999043	+	0.0437443i	$0.986071\pi$
$822$		−	5.49521e11i		−	1.20364i
$823$			6.97400e11i			1.52014i	0.649843	+	0.760069i	$0.274835\pi$
$823$			6.97400e11i			1.52014i	−0.649843	+	0.760069i	$0.725165\pi$
$824$	−1.93600e12			−4.19950
$825$			1.15380e11i			0.249065i
$826$	−4.25625e11	+	2.42801e11i	−0.914339	+	0.521591i
$827$	−3.51532e10			−0.0751523			−0.0375762	−	0.999294i	$-0.511964\pi$
$827$	−3.51532e10			−0.0751523			−0.0375762	+	0.999294i	$0.511964\pi$
$828$			1.93019e11i			0.410656i
$829$	−5.39651e11			−1.14260			−0.571301	−	0.820741i	$-0.693561\pi$
$829$	−5.39651e11			−1.14260			−0.571301	+	0.820741i	$0.693561\pi$
$830$	−5.89634e10			−0.124243
$831$	−9.50041e10			−0.199222
$832$		−	2.16638e12i		−	4.52108i
$833$	−5.62590e11			−1.16846
$834$		−	5.08329e11i		−	1.05070i
$835$	−4.36874e10			−0.0898691
$836$			1.08434e12i			2.21993i
$837$			2.05223e9i			0.00418141i
$838$	5.75316e11			1.16662
$839$			3.62761e11i			0.732105i	0.930594	+	0.366052i	$0.119291\pi$
$839$			3.62761e11i			0.732105i	−0.930594	+	0.366052i	$0.880709\pi$
$840$		−	3.40599e10i		−	0.0684110i
$841$	−4.87880e11			−0.975279
$842$	6.73780e11			1.34051
$843$	1.48004e11			0.293065
$844$			3.76425e11i			0.741837i
$845$	7.60379e9			0.0149143
$846$	2.47869e11			0.483883
$847$	2.23977e11			0.435180
$848$	1.37271e12			2.65458
$849$			1.57991e11i			0.304089i
$850$			1.67485e12i			3.20848i
$851$	−4.04769e11			−0.771772
$852$	3.05304e11			0.579393
$853$	7.41672e11			1.40093			0.700464	−	0.713688i	$-0.252977\pi$
$853$	7.41672e11			1.40093			0.700464	+	0.713688i	$0.252977\pi$
$854$	4.81194e11			0.904667
$855$	−1.92766e10			−0.0360717
$856$		−	1.93241e12i		−	3.59919i
$857$		−	9.54747e11i		−	1.76997i	−0.465622	−	0.884984i	$-0.654169\pi$
$857$		−	9.54747e11i		−	1.76997i	0.465622	−	0.884984i	$-0.345831\pi$
$858$		−	2.31076e11i		−	0.426389i
$859$		−	8.77659e11i		−	1.61196i	−0.591945	−	0.805978i	$-0.701640\pi$
$859$		−	8.77659e11i		−	1.61196i	0.591945	−	0.805978i	$-0.298360\pi$
$860$		−	1.53369e10i		−	0.0280378i
$861$	−1.58006e11			−0.287514
$862$	−1.33180e11			−0.241217
$863$		−	3.12773e11i		−	0.563879i	−0.959432	−	0.281940i	$-0.909022\pi$
$863$		−	3.12773e11i		−	0.563879i	0.959432	−	0.281940i	$-0.0909777\pi$
$864$			5.20702e11i			0.934403i
$865$			1.97602e10i			0.0352961i
$866$			7.43282e10i			0.132155i
$867$	−5.49525e11			−0.972548
$868$			1.89111e10i			0.0333148i
$869$			2.77362e11i			0.486372i
$870$			6.17622e9i			0.0107807i
$871$	−7.52256e11			−1.30705
$872$	1.60612e12			2.77788
$873$		−	3.21606e11i		−	0.553691i
$874$	8.83831e11			1.51469
$875$	−3.78714e10			−0.0646070
$876$		−	1.01779e12i		−	1.72840i
$877$	−6.05923e11			−1.02428			−0.512141	−	0.858902i	$-0.671147\pi$
$877$	−6.05923e11			−1.02428			−0.512141	+	0.858902i	$0.671147\pi$
$878$		−	1.52757e12i		−	2.57053i
$879$	3.67497e10			0.0615600
$880$			6.79863e10i			0.113368i
$881$			2.12994e11i			0.353561i	0.984250	+	0.176781i	$0.0565683\pi$
$881$			2.12994e11i			0.353561i	−0.984250	+	0.176781i	$0.943432\pi$
$882$			2.82742e11i			0.467213i
$883$	−6.53778e10			−0.107544			−0.0537722	−	0.998553i	$-0.517124\pi$
$883$	−6.53778e10			−0.107544			−0.0537722	+	0.998553i	$0.517124\pi$
$884$		−	2.48596e12i		−	4.07085i
$885$	1.06041e10	+	1.85888e10i	0.0172862	+	0.0303024i
$886$	−1.84328e12			−2.99128
$887$			3.58256e11i			0.578760i	0.957214	+	0.289380i	$0.0934491\pi$
$887$			3.58256e11i			0.578760i	−0.957214	+	0.289380i	$0.906551\pi$
$888$	−2.35738e12			−3.79121
$889$	−3.41049e11			−0.546021
$890$	−4.97084e10			−0.0792264
$891$			3.03201e10i			0.0481083i
$892$	1.02092e12			1.61263
$893$		−	8.41170e11i		−	1.32275i
$894$	−3.95552e11			−0.619233
$895$		−	4.44782e10i		−	0.0693194i
$896$			1.85835e12i			2.88333i
$897$	−1.39589e11			−0.215616
$898$		−	1.62036e12i		−	2.49175i
$899$		−	2.23141e9i		−	0.00341618i
$900$	6.23828e11			0.950812
$901$	6.61474e11			1.00372
$902$	5.23765e11			0.791244
$903$		−	3.33229e10i		−	0.0501178i
$904$	8.70897e11			1.30405
$905$	−7.82897e9			−0.0116711
$906$	1.12377e12			1.66787
$907$	1.02572e12			1.51566			0.757828	−	0.652455i	$-0.226261\pi$
$907$	1.02572e12			1.51566			0.757828	+	0.652455i	$0.226261\pi$
$908$			1.47696e12i			2.17284i
$909$		−	8.07347e10i		−	0.118251i
$910$	3.78541e10			0.0552010
$911$	−8.88767e11			−1.29037			−0.645185	−	0.764026i	$-0.723220\pi$
$911$	−8.88767e11			−1.29037			−0.645185	+	0.764026i	$0.723220\pi$
$912$	3.09960e12			4.48049
$913$	3.14735e11			0.452962
$914$	2.99837e11			0.429636
$915$		−	2.10157e10i		−	0.0299819i
$916$		−	2.02779e12i		−	2.88032i
$917$			3.64696e11i			0.515768i
$918$			4.40126e11i			0.619735i
$919$			6.31141e11i			0.884839i	0.896808	+	0.442420i	$0.145880\pi$
$919$			6.31141e11i			0.884839i	−0.896808	+	0.442420i	$0.854120\pi$
$920$	6.82031e10			0.0952035
$921$	−2.34445e11			−0.325838
$922$			7.14615e11i			0.988891i
$923$			2.20793e11i			0.304213i
$924$			2.79397e11i			0.383296i
$925$			1.30820e12i			1.78692i
$926$	1.07213e12			1.45815
$927$			2.82326e11i			0.382325i
$928$		−	5.66166e11i		−	0.763399i
$929$			9.20295e11i			1.23556i	0.786350	+	0.617781i	$0.211968\pi$
$929$			9.20295e11i			1.23556i	−0.786350	+	0.617781i	$0.788032\pi$
$930$	1.11442e9			0.00148976
$931$	9.59515e11			1.27718
$932$		−	1.68220e12i		−	2.22953i
$933$	−5.67252e11			−0.748600
$934$	1.65371e12			2.17306
$935$			3.27609e10i			0.0428656i
$936$	−8.12968e11			−1.05918
$937$		−	1.09382e12i		−	1.41901i	−0.704700	−	0.709505i	$-0.748918\pi$
$937$		−	1.09382e12i		−	1.41901i	0.704700	−	0.709505i	$-0.251082\pi$
$938$	1.22727e12			1.58536
$939$			8.48518e11i			1.09144i
$940$		−	9.97554e10i		−	0.127769i
$941$			1.08436e12i			1.38298i	0.722385	+	0.691491i	$0.243046\pi$
$941$			1.08436e12i			1.38298i	−0.722385	+	0.691491i	$0.756954\pi$
$942$	1.02444e12			1.30102
$943$		−	3.16398e11i		−	0.400117i
$944$	−1.70509e12	−	2.98899e12i	−2.14714	−	3.76389i
$945$	−4.96693e9			−0.00622818
$946$			1.10461e11i			0.137925i
$947$	5.05965e11			0.629102			0.314551	−	0.949241i	$-0.398146\pi$
$947$	5.05965e11			0.629102			0.314551	+	0.949241i	$0.398146\pi$
$948$	1.49963e12			1.85674
$949$	7.36058e11			0.907502
$950$		−	2.85650e12i		−	3.50704i
$951$	7.69263e11			0.940487
$952$			2.63907e12i			3.21295i
$953$	6.22650e11			0.754870			0.377435	−	0.926036i	$-0.376806\pi$
$953$	6.22650e11			0.754870			0.377435	+	0.926036i	$0.376806\pi$
$954$		−	3.32437e11i		−	0.401344i
$955$		−	3.68508e10i		−	0.0443030i
$956$	−1.74910e12			−2.09404
$957$		−	3.29674e10i		−	0.0393040i
$958$		−	1.58565e12i		−	1.88254i
$959$	−4.80512e11			−0.568107
$960$	1.54359e11			0.181739
$961$	8.52488e11			0.999528
$962$		−	2.61999e12i		−	3.05914i
$963$	−2.81803e11			−0.327673
$964$	3.20810e12			3.71483
$965$	−6.75919e10			−0.0779445
$966$	2.27733e11			0.261528
$967$			9.61074e11i			1.09914i	0.835449	+	0.549568i	$0.185207\pi$
$967$			9.61074e11i			1.09914i	−0.835449	+	0.549568i	$0.814793\pi$
$968$			2.61208e12i			2.97498i
$969$	1.49362e12			1.69412
$970$	−1.74641e11			−0.197269
$971$	−1.69794e12			−1.91005			−0.955027	−	0.296517i	$-0.904175\pi$
$971$	−1.69794e12			−1.91005			−0.955027	+	0.296517i	$0.904175\pi$
$972$	1.63933e11			0.183654
$973$	−4.44493e11			−0.495922
$974$		−	1.70215e12i		−	1.89131i
$975$			4.51146e11i			0.499228i
$976$			3.37923e12i			3.72407i
$977$			7.00675e11i			0.769022i	0.923121	+	0.384511i	$0.125630\pi$
$977$			7.00675e11i			0.769022i	−0.923121	+	0.384511i	$0.874370\pi$
$978$			1.52409e12i			1.66592i
$979$	2.65333e11			0.288843
$980$	1.13790e11			0.123367
$981$		−	2.34220e11i		−	0.252900i
$982$			2.23757e12i			2.40619i
$983$			5.84966e11i			0.626494i	0.949672	+	0.313247i	$0.101417\pi$
$983$			5.84966e11i			0.626494i	−0.949672	+	0.313247i	$0.898583\pi$
$984$		−	1.84270e12i		−	1.96551i
$985$	−9.81796e10			−0.104298
$986$		−	4.78554e11i		−	0.506318i
$987$		−	2.16741e11i		−	0.228388i
$988$			4.23988e12i			4.44965i
$989$	6.67274e10			0.0697460
$990$	1.64647e10			0.0171400
$991$			1.01041e12i			1.04762i	0.851835	+	0.523810i	$0.175490\pi$
$991$			1.01041e12i			1.04762i	−0.851835	+	0.523810i	$0.824510\pi$
$992$	−1.02157e11			−0.105492
$993$	4.06798e11			0.418391
$994$		−	3.60213e11i		−	0.368989i
$995$	1.90249e10			0.0194102
$996$		−	1.70169e12i		−	1.72919i
$997$	−6.93851e11			−0.702241			−0.351120	−	0.936330i	$-0.614199\pi$
$997$	−6.93851e11			−0.702241			−0.351120	+	0.936330i	$0.614199\pi$
$998$			2.10711e12i			2.12405i
$999$			3.43775e11i			0.345154i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.9.c.a.58.2	✓	80
59.58	odd	2	inner	177.9.c.a.58.79	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.9.c.a.58.2	✓	80	1.1	even	1	trivial
177.9.c.a.58.79	yes	80	59.58	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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	177.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-31.4468i q^{2} -46.7654 q^{3} -732.900 q^{4} +37.7655 q^{5} +1470.62i q^{6} +1285.94 q^{7} +14997.0i q^{8} +2187.00 q^{9} +O(q^{10})\)	\(q-31.4468i q^{2} -46.7654 q^{3} -732.900 q^{4} +37.7655 q^{5} +1470.62i q^{6} +1285.94 q^{7} +14997.0i q^{8} +2187.00 q^{9} -1187.60i q^{10} +6339.18i q^{11} +34274.3 q^{12} +24786.9i q^{13} -40438.6i q^{14} -1766.12 q^{15} +283984. q^{16} +136845. q^{17} -68774.1i q^{18} -233393. q^{19} -27678.3 q^{20} -60137.4 q^{21} +199347. q^{22} -120422. i q^{23} -701338. i q^{24} -389199. q^{25} +779467. q^{26} -102276. q^{27} -942464. q^{28} +111206. q^{29} +55538.7i q^{30} -20065.6i q^{31} -5.09115e6i q^{32} -296454. i q^{33} -4.30332e6i q^{34} +48564.1 q^{35} -1.60285e6 q^{36} -3.36126e6i q^{37} +7.33945e6i q^{38} -1.15917e6i q^{39} +566367. i q^{40} +2.62741e6 q^{41} +1.89113e6i q^{42} +554113. i q^{43} -4.64598e6i q^{44} +82593.1 q^{45} -3.78688e6 q^{46} +3.60410e6i q^{47} -1.32806e7 q^{48} -4.11116e6 q^{49} +1.22390e7i q^{50} -6.39959e6 q^{51} -1.81663e7i q^{52} +4.83376e6 q^{53} +3.21625e6i q^{54} +239402. i q^{55} +1.92852e7i q^{56} +1.09147e7 q^{57} -3.49706e6i q^{58} +(-6.00418e6 - 1.05252e7i) q^{59} +1.29439e6 q^{60} +1.18994e7i q^{61} -630998. q^{62} +2.81235e6 q^{63} -8.74005e7 q^{64} +936087. i q^{65} -9.32252e6 q^{66} +3.03490e7i q^{67} -1.00293e8 q^{68} +5.63158e6i q^{69} -1.52718e6i q^{70} +8.90765e6 q^{71} +3.27984e7i q^{72} -2.96955e7i q^{73} -1.05701e8 q^{74} +1.82010e7 q^{75} +1.71053e8 q^{76} +8.15179e6i q^{77} -3.64521e7 q^{78} +4.37537e7 q^{79} +1.07248e7 q^{80} +4.78297e6 q^{81} -8.26235e7i q^{82} -4.96491e7i q^{83} +4.40747e7 q^{84} +5.16800e6 q^{85} +1.74251e7 q^{86} -5.20058e6 q^{87} -9.50684e7 q^{88} -4.18561e7i q^{89} -2.59729e6i q^{90} +3.18744e7i q^{91} +8.82573e7i q^{92} +938375. i q^{93} +1.13337e8 q^{94} -8.81418e6 q^{95} +2.38090e8i q^{96} -1.47054e8i q^{97} +1.29283e8i q^{98} +1.38638e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9}+O(q^{10}) \) 80 * q - 10240 * q^4 + 160 * q^7 + 174960 * q^9	\( 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9} - 22680 q^{12} - 59616 q^{15} + 1199848 q^{16} - 10608 q^{17} - 27516 q^{19} - 146436 q^{20} - 974696 q^{22} + 5718040 q^{25} - 797484 q^{26} - 3133000 q^{28} + 1725924 q^{29} + 4318800 q^{35} - 22394880 q^{36} - 732180 q^{41} + 22752084 q^{46} + 8703936 q^{48} + 55899176 q^{49} - 10373832 q^{51} - 39265944 q^{53} - 11408040 q^{57} - 33575112 q^{59} - 18034488 q^{60} + 13038600 q^{62} + 349920 q^{63} - 241654260 q^{64} - 35711928 q^{66} + 36772608 q^{68} - 235272660 q^{71} - 63050712 q^{74} + 74363184 q^{75} + 9454680 q^{76} - 10865988 q^{78} + 17252580 q^{79} + 318203976 q^{80} + 382637520 q^{81} - 20743128 q^{84} - 27245820 q^{85} + 105666984 q^{86} + 29437992 q^{87} + 82079788 q^{88} + 121215992 q^{94} - 690837276 q^{95}+O(q^{100}) \) 80 * q - 10240 * q^4 + 160 * q^7 + 174960 * q^9 - 22680 * q^12 - 59616 * q^15 + 1199848 * q^16 - 10608 * q^17 - 27516 * q^19 - 146436 * q^20 - 974696 * q^22 + 5718040 * q^25 - 797484 * q^26 - 3133000 * q^28 + 1725924 * q^29 + 4318800 * q^35 - 22394880 * q^36 - 732180 * q^41 + 22752084 * q^46 + 8703936 * q^48 + 55899176 * q^49 - 10373832 * q^51 - 39265944 * q^53 - 11408040 * q^57 - 33575112 * q^59 - 18034488 * q^60 + 13038600 * q^62 + 349920 * q^63 - 241654260 * q^64 - 35711928 * q^66 + 36772608 * q^68 - 235272660 * q^71 - 63050712 * q^74 + 74363184 * q^75 + 9454680 * q^76 - 10865988 * q^78 + 17252580 * q^79 + 318203976 * q^80 + 382637520 * q^81 - 20743128 * q^84 - 27245820 * q^85 + 105666984 * q^86 + 29437992 * q^87 + 82079788 * q^88 + 121215992 * q^94 - 690837276 * q^95

Introduction

L-functions

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