LMFDB - Embedded newform 177.9.c.a.58.76

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			58.76
Character	$\chi$	$=$	177.58
Dual form			177.9.c.a.58.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+29.1592i q^{2} +46.7654 q^{3} -594.257 q^{4} -890.286 q^{5} +1363.64i q^{6} -1275.54 q^{7} -9863.29i q^{8} +2187.00 q^{9} +O(q^{10})$	\(q+29.1592i q^{2} +46.7654 q^{3} -594.257 q^{4} -890.286 q^{5} +1363.64i q^{6} -1275.54 q^{7} -9863.29i q^{8} +2187.00 q^{9} -25960.0i q^{10} -12776.2i q^{11} -27790.6 q^{12} -22856.4i q^{13} -37193.6i q^{14} -41634.5 q^{15} +135476. q^{16} -85141.2 q^{17} +63771.1i q^{18} -42936.4 q^{19} +529059. q^{20} -59651.0 q^{21} +372544. q^{22} +240016. i q^{23} -461261. i q^{24} +401984. q^{25} +666475. q^{26} +102276. q^{27} +757997. q^{28} +158660. q^{29} -1.21403e6i q^{30} +826585. i q^{31} +1.42535e6i q^{32} -597485. i q^{33} -2.48265e6i q^{34} +1.13559e6 q^{35} -1.29964e6 q^{36} +899334. i q^{37} -1.25199e6i q^{38} -1.06889e6i q^{39} +8.78115e6i q^{40} -2.13093e6 q^{41} -1.73937e6i q^{42} -2.82120e6i q^{43} +7.59236e6i q^{44} -1.94706e6 q^{45} -6.99866e6 q^{46} -5.83048e6i q^{47} +6.33557e6 q^{48} -4.13780e6 q^{49} +1.17215e7i q^{50} -3.98166e6 q^{51} +1.35826e7i q^{52} +1.29905e7 q^{53} +2.98228e6i q^{54} +1.13745e7i q^{55} +1.25810e7i q^{56} -2.00794e6 q^{57} +4.62640e6i q^{58} +(8.68651e6 + 8.44837e6i) q^{59} +2.47416e7 q^{60} +3.72205e6i q^{61} -2.41025e7 q^{62} -2.78960e6 q^{63} -6.88034e6 q^{64} +2.03488e7i q^{65} +1.74222e7 q^{66} +3.14296e6i q^{67} +5.05958e7 q^{68} +1.12244e7i q^{69} +3.31130e7i q^{70} -1.78522e7 q^{71} -2.15710e7i q^{72} -208529. i q^{73} -2.62238e7 q^{74} +1.87989e7 q^{75} +2.55153e7 q^{76} +1.62966e7i q^{77} +3.11679e7 q^{78} -5.74903e7 q^{79} -1.20612e8 q^{80} +4.78297e6 q^{81} -6.21363e7i q^{82} -4.16878e6i q^{83} +3.54480e7 q^{84} +7.58000e7 q^{85} +8.22638e7 q^{86} +7.41980e6 q^{87} -1.26016e8 q^{88} -4.65731e7i q^{89} -5.67745e7i q^{90} +2.91543e7i q^{91} -1.42631e8i q^{92} +3.86556e7i q^{93} +1.70012e8 q^{94} +3.82257e7 q^{95} +6.66571e7i q^{96} +1.21368e8i q^{97} -1.20655e8i q^{98} -2.79416e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			29.1592i			1.82245i	0.411911	+	0.911224i	$0.364861\pi$
$2$			29.1592i			1.82245i	−0.411911	+	0.911224i	$0.635139\pi$
$3$	46.7654			0.577350
$3$	46.7654			0.577350
$4$	−594.257			−2.32132
$5$	−890.286			−1.42446			−0.712229	−	0.701947i	$-0.752314\pi$
$5$	−890.286			−1.42446			−0.712229	+	0.701947i	$0.752314\pi$
$6$			1363.64i			1.05219i
$7$	−1275.54			−0.531253			−0.265626	−	0.964076i	$-0.585579\pi$
$7$	−1275.54			−0.531253			−0.265626	+	0.964076i	$0.585579\pi$
$8$		−	9863.29i		−	2.40803i
$9$	2187.00			0.333333
$10$		−	25960.0i		−	2.59600i
$11$		−	12776.2i		−	0.872633i	−0.899793	−	0.436317i	$-0.856283\pi$
$11$		−	12776.2i		−	0.872633i	0.899793	−	0.436317i	$-0.143717\pi$
$12$	−27790.6			−1.34021
$13$		−	22856.4i		−	0.800268i	−0.916457	−	0.400134i	$-0.868964\pi$
$13$		−	22856.4i		−	0.800268i	0.916457	−	0.400134i	$-0.131036\pi$
$14$		−	37193.6i		−	0.968181i
$15$	−41634.5			−0.822411
$16$	135476.			2.06719
$17$	−85141.2			−1.01940			−0.509700	−	0.860352i	$-0.670243\pi$
$17$	−85141.2			−1.01940			−0.509700	+	0.860352i	$0.670243\pi$
$18$			63771.1i			0.607483i
$19$	−42936.4			−0.329467			−0.164733	−	0.986338i	$-0.552676\pi$
$19$	−42936.4			−0.329467			−0.164733	+	0.986338i	$0.552676\pi$
$20$	529059.			3.30662
$21$	−59651.0			−0.306719
$22$	372544.			1.59033
$23$			240016.i			0.857686i	0.903379	+	0.428843i	$0.141079\pi$
$23$			240016.i			0.857686i	−0.903379	+	0.428843i	$0.858921\pi$
$24$		−	461261.i		−	1.39028i
$25$	401984.			1.02908
$26$	666475.			1.45845
$27$	102276.			0.192450
$28$	757997.			1.23321
$29$	158660.			0.224324			0.112162	−	0.993690i	$-0.464222\pi$
$29$	158660.			0.224324			0.112162	+	0.993690i	$0.464222\pi$
$30$		−	1.21403e6i		−	1.49880i
$31$			826585.i			0.895036i	0.894275	+	0.447518i	$0.147692\pi$
$31$			826585.i			0.895036i	−0.894275	+	0.447518i	$0.852308\pi$
$32$			1.42535e6i			1.35932i
$33$		−	597485.i		−	0.503815i
$34$		−	2.48265e6i		−	1.85780i
$35$	1.13559e6			0.756747
$36$	−1.29964e6			−0.773772
$37$			899334.i			0.479859i	0.970790	+	0.239930i	$0.0771244\pi$
$37$			899334.i			0.479859i	−0.970790	+	0.239930i	$0.922876\pi$
$38$		−	1.25199e6i		−	0.600436i
$39$		−	1.06889e6i		−	0.462035i
$40$			8.78115e6i			3.43014i
$41$	−2.13093e6			−0.754110			−0.377055	−	0.926191i	$-0.623063\pi$
$41$	−2.13093e6			−0.754110			−0.377055	+	0.926191i	$0.623063\pi$
$42$		−	1.73937e6i		−	0.558979i
$43$		−	2.82120e6i		−	0.825201i	−0.910912	−	0.412601i	$-0.864621\pi$
$43$		−	2.82120e6i		−	0.825201i	0.910912	−	0.412601i	$-0.135379\pi$
$44$			7.59236e6i			2.02566i
$45$	−1.94706e6			−0.474819
$46$	−6.99866e6			−1.56309
$47$		−	5.83048e6i		−	1.19485i	−0.801925	−	0.597424i	$-0.796191\pi$
$47$		−	5.83048e6i		−	1.19485i	0.801925	−	0.597424i	$-0.203809\pi$
$48$	6.33557e6			1.19349
$49$	−4.13780e6			−0.717770
$50$			1.17215e7i			1.87544i
$51$	−3.98166e6			−0.588550
$52$			1.35826e7i			1.85767i
$53$	1.29905e7			1.64635			0.823176	−	0.567787i	$-0.192200\pi$
$53$	1.29905e7			1.64635			0.823176	+	0.567787i	$0.192200\pi$
$54$			2.98228e6i			0.350730i
$55$			1.13745e7i			1.24303i
$56$			1.25810e7i			1.27927i
$57$	−2.00794e6			−0.190218
$58$			4.62640e6i			0.408819i
$59$	8.68651e6	+	8.44837e6i	0.716865	+	0.697212i
$59$	8.68651e6	+	8.44837e6i	0.716865	+	0.697212i
$60$	2.47416e7			1.90908
$61$			3.72205e6i			0.268820i	0.990926	+	0.134410i	$0.0429140\pi$
$61$			3.72205e6i			0.268820i	−0.990926	+	0.134410i	$0.957086\pi$
$62$	−2.41025e7			−1.63116
$63$	−2.78960e6			−0.177084
$64$	−6.88034e6			−0.410100
$65$			2.03488e7i			1.13995i
$66$	1.74222e7			0.918177
$67$			3.14296e6i			0.155970i	0.996955	+	0.0779848i	$0.0248486\pi$
$67$			3.14296e6i			0.155970i	−0.996955	+	0.0779848i	$0.975151\pi$
$68$	5.05958e7			2.36635
$69$			1.12244e7i			0.495186i
$70$			3.31130e7i			1.37913i
$71$	−1.78522e7			−0.702520			−0.351260	−	0.936278i	$-0.614247\pi$
$71$	−1.78522e7			−0.702520			−0.351260	+	0.936278i	$0.614247\pi$
$72$		−	2.15710e7i		−	0.802677i
$73$		−	208529.i		−	0.00734303i	−0.999993	−	0.00367152i	$-0.998831\pi$
$73$		−	208529.i		−	0.00734303i	0.999993	−	0.00367152i	$-0.00116868\pi$
$74$	−2.62238e7			−0.874519
$75$	1.87989e7			0.594139
$76$	2.55153e7			0.764796
$77$			1.62966e7i			0.463589i
$78$	3.11679e7			0.842034
$79$	−5.74903e7			−1.47600			−0.738000	−	0.674801i	$-0.764230\pi$
$79$	−5.74903e7			−1.47600			−0.738000	+	0.674801i	$0.764230\pi$
$80$	−1.20612e8			−2.94463
$81$	4.78297e6			0.111111
$82$		−	6.21363e7i		−	1.37433i
$83$		−	4.16878e6i		−	0.0878408i	−0.999035	−	0.0439204i	$-0.986015\pi$
$83$		−	4.16878e6i		−	0.0878408i	0.999035	−	0.0439204i	$-0.0139848\pi$
$84$	3.54480e7			0.711992
$85$	7.58000e7			1.45209
$86$	8.22638e7			1.50389
$87$	7.41980e6			0.129514
$88$	−1.26016e8			−2.10133
$89$		−	4.65731e7i		−	0.742292i	−0.928574	−	0.371146i	$-0.878965\pi$
$89$		−	4.65731e7i		−	0.742292i	0.928574	−	0.371146i	$-0.121035\pi$
$90$		−	5.67745e7i		−	0.865333i
$91$			2.91543e7i			0.425144i
$92$		−	1.42631e8i		−	1.99096i
$93$			3.86556e7i			0.516750i
$94$	1.70012e8			2.17755
$95$	3.82257e7			0.469311
$96$			6.66571e7i			0.784805i
$97$			1.21368e8i			1.37094i	0.728101	+	0.685470i	$0.240403\pi$
$97$			1.21368e8i			1.37094i	−0.728101	+	0.685470i	$0.759597\pi$
$98$		−	1.20655e8i		−	1.30810i
$99$		−	2.79416e7i		−	0.290878i
$100$	−2.38882e8			−2.38882
$101$		−	1.87669e8i		−	1.80346i	−0.432297	−	0.901731i	$-0.642297\pi$
$101$		−	1.87669e8i		−	1.80346i	0.432297	−	0.901731i	$-0.357703\pi$
$102$		−	1.16102e8i		−	1.07260i
$103$			1.37271e8i			1.21964i	0.792540	+	0.609819i	$0.208758\pi$
$103$			1.37271e8i			1.21964i	−0.792540	+	0.609819i	$0.791242\pi$
$104$	−2.25440e8			−1.92707
$105$	5.31065e7			0.436908
$106$			3.78792e8i			3.00039i
$107$	−3.65182e7			−0.278596			−0.139298	−	0.990251i	$-0.544485\pi$
$107$	−3.65182e7			−0.278596			−0.139298	+	0.990251i	$0.544485\pi$
$108$	−6.07782e7			−0.446738
$109$			1.21819e8i			0.862998i	0.902114	+	0.431499i	$0.142015\pi$
$109$			1.21819e8i			0.862998i	−0.902114	+	0.431499i	$0.857985\pi$
$110$	−3.31671e8			−2.26536
$111$			4.20577e7i			0.277047i
$112$	−1.72804e8			−1.09820
$113$			1.15797e8i			0.710204i	0.934827	+	0.355102i	$0.115554\pi$
$113$			1.15797e8i			0.710204i	−0.934827	+	0.355102i	$0.884446\pi$
$114$		−	5.85498e7i		−	0.346662i
$115$		−	2.13683e8i		−	1.22174i
$116$	−9.42849e7			−0.520727
$117$		−	4.99870e7i		−	0.266756i
$118$	−2.46347e8	+	2.53291e8i	−1.27063	+	1.30645i
$119$	1.08601e8			0.541559
$120$			4.10654e8i			1.98039i
$121$	5.11270e7			0.238511
$122$	−1.08532e8			−0.489911
$123$	−9.96539e7			−0.435385
$124$		−	4.91204e8i		−	2.07766i
$125$	−1.01127e7			−0.0414216
$126$		−	8.13425e7i		−	0.322727i
$127$	−3.04346e7			−0.116991			−0.0584954	−	0.998288i	$-0.518630\pi$
$127$	−3.04346e7			−0.116991			−0.0584954	+	0.998288i	$0.518630\pi$
$128$			1.64265e8i			0.611936i
$129$		−	1.31934e8i		−	0.476430i
$130$	−5.93353e8			−2.07749
$131$			1.54953e8i			0.526155i	0.964775	+	0.263077i	$0.0847375\pi$
$131$			1.54953e8i			0.526155i	−0.964775	+	0.263077i	$0.915263\pi$
$132$			3.55060e8i			1.16951i
$133$	5.47671e7			0.175030
$134$	−9.16461e7			−0.284246
$135$	−9.10548e7			−0.274137
$136$			8.39773e8i			2.45474i
$137$	−3.52274e8			−0.999997			−0.499999	−	0.866026i	$-0.666666\pi$
$137$	−3.52274e8			−0.999997			−0.499999	+	0.866026i	$0.666666\pi$
$138$	−3.27295e8			−0.902450
$139$	7.36864e8			1.97391			0.986957	−	0.160986i	$-0.0514674\pi$
$139$	7.36864e8			1.97391			0.986957	+	0.160986i	$0.0514674\pi$
$140$	−6.74834e8			−1.75665
$141$		−	2.72665e8i		−	0.689846i
$142$		−	5.20556e8i		−	1.28031i
$143$	−2.92019e8			−0.698340
$144$	2.96285e8			0.689064
$145$	−1.41253e8			−0.319540
$146$	6.08054e6			0.0133823
$147$	−1.93506e8			−0.414405
$148$		−	5.34435e8i		−	1.11391i
$149$		−	3.98415e8i		−	0.808333i	−0.914686	−	0.404166i	$-0.867562\pi$
$149$		−	3.98415e8i		−	0.808333i	0.914686	−	0.404166i	$-0.132438\pi$
$150$			5.48161e8i			1.08279i
$151$			6.37835e8i			1.22688i	0.789743	+	0.613438i	$0.210214\pi$
$151$			6.37835e8i			1.22688i	−0.789743	+	0.613438i	$0.789786\pi$
$152$			4.23495e8i			0.793366i
$153$	−1.86204e8			−0.339800
$154$	−4.75194e8			−0.844867
$155$		−	7.35897e8i		−	1.27494i
$156$			6.35195e8i			1.07253i
$157$		−	6.02298e8i		−	0.991318i	−0.868517	−	0.495659i	$-0.834927\pi$
$157$		−	6.02298e8i		−	0.991318i	0.868517	−	0.495659i	$-0.165073\pi$
$158$		−	1.67637e9i		−	2.68993i
$159$	6.07506e8			0.950521
$160$		−	1.26897e9i		−	1.93630i
$161$		−	3.06149e8i		−	0.455648i
$162$			1.39467e8i			0.202494i
$163$	8.36185e8			1.18455			0.592273	−	0.805737i	$-0.298231\pi$
$163$	8.36185e8			1.18455			0.592273	+	0.805737i	$0.298231\pi$
$164$	1.26632e9			1.75053
$165$			5.31932e8i			0.717663i
$166$	1.21558e8			0.160085
$167$	9.61416e8			1.23608			0.618038	−	0.786148i	$-0.287928\pi$
$167$	9.61416e8			1.23608			0.618038	+	0.786148i	$0.287928\pi$
$168$			5.88355e8i			0.738589i
$169$	2.93314e8			0.359572
$170$			2.21027e9i			2.64636i
$171$	−9.39020e7			−0.109822
$172$			1.67652e9i			1.91555i
$173$			1.32604e9i			1.48038i	0.672400	+	0.740188i	$0.265263\pi$
$173$			1.32604e9i			1.48038i	−0.672400	+	0.740188i	$0.734737\pi$
$174$			2.16355e8i			0.236032i
$175$	−5.12746e8			−0.546701
$176$		−	1.73087e9i		−	1.80390i
$177$	4.06228e8	+	3.95091e8i	0.413882	+	0.402536i
$178$	1.35803e9			1.35279
$179$		−	1.02503e9i		−	0.998447i	−0.866473	−	0.499223i	$-0.833619\pi$
$179$		−	1.02503e9i		−	0.998447i	0.866473	−	0.499223i	$-0.166381\pi$
$180$	1.15705e9			1.10221
$181$	1.51215e9			1.40890			0.704451	−	0.709753i	$-0.251193\pi$
$181$	1.51215e9			1.40890			0.704451	+	0.709753i	$0.251193\pi$
$182$	−8.50114e8			−0.774804
$183$			1.74063e8i			0.155204i
$184$	2.36735e9			2.06533
$185$		−	8.00664e8i		−	0.683539i
$186$	−1.12716e9			−0.941749
$187$			1.08778e9i			0.889562i
$188$			3.46480e9i			2.77362i
$189$	−1.30457e8			−0.102240
$190$			1.11463e9i			0.855295i
$191$		−	1.66824e9i		−	1.25350i	−0.779220	−	0.626750i	$-0.784385\pi$
$191$		−	1.66824e9i		−	1.25350i	0.779220	−	0.626750i	$-0.215615\pi$
$192$	−3.21762e8			−0.236771
$193$	1.12322e9			0.809538			0.404769	−	0.914419i	$-0.367352\pi$
$193$	1.12322e9			0.809538			0.404769	+	0.914419i	$0.367352\pi$
$194$	−3.53900e9			−2.49847
$195$			9.51618e8i			0.658149i
$196$	2.45892e9			1.66617
$197$	7.15552e8			0.475090			0.237545	−	0.971376i	$-0.423657\pi$
$197$	7.15552e8			0.475090			0.237545	+	0.971376i	$0.423657\pi$
$198$	8.14754e8			0.530110
$199$	1.62982e8			0.103927			0.0519634	−	0.998649i	$-0.483452\pi$
$199$	1.62982e8			0.103927			0.0519634	+	0.998649i	$0.483452\pi$
$200$		−	3.96489e9i		−	2.47805i
$201$			1.46982e8i			0.0900491i
$202$	5.47227e9			3.28672
$203$	−2.02377e8			−0.119173
$204$	2.36613e9			1.36621
$205$	1.89714e9			1.07420
$206$	−4.00272e9			−2.22273
$207$			5.24915e8i			0.285895i
$208$		−	3.09649e9i		−	1.65431i
$209$			5.48565e8i			0.287504i
$210$			1.54854e9i			0.796242i
$211$			3.40476e7i			0.0171774i	0.999963	+	0.00858868i	$0.00273390\pi$
$211$			3.40476e7i			0.0171774i	−0.999963	+	0.00858868i	$0.997266\pi$
$212$	−7.71970e9			−3.82170
$213$	−8.34865e8			−0.405600
$214$		−	1.06484e9i		−	0.507726i
$215$			2.51167e9i			1.17546i
$216$		−	1.00878e9i		−	0.463426i
$217$		−	1.05434e9i		−	0.475491i
$218$	−3.55214e9			−1.57277
$219$		−	9.75194e6i		−	0.00423950i
$220$		−	6.75937e9i		−	2.88546i
$221$			1.94603e9i			0.815792i
$222$	−1.22637e9			−0.504904
$223$	−8.46796e8			−0.342420			−0.171210	−	0.985235i	$-0.554768\pi$
$223$	−8.46796e8			−0.342420			−0.171210	+	0.985235i	$0.554768\pi$
$224$		−	1.81809e9i		−	0.722144i
$225$	8.79139e8			0.343026
$226$	−3.37654e9			−1.29431
$227$			9.21542e8i			0.347066i	0.984828	+	0.173533i	$0.0555183\pi$
$227$			9.21542e8i			0.347066i	−0.984828	+	0.173533i	$0.944482\pi$
$228$	1.19323e9			0.441555
$229$			2.37081e9i			0.862095i	0.902329	+	0.431048i	$0.141856\pi$
$229$			2.37081e9i			0.862095i	−0.902329	+	0.431048i	$0.858144\pi$
$230$	6.23081e9			2.22655
$231$			7.62115e8i			0.267653i
$232$		−	1.56491e9i		−	0.540179i
$233$		−	1.46452e8i		−	0.0496903i	−0.999691	−	0.0248452i	$-0.992091\pi$
$233$		−	1.46452e8i		−	0.0496903i	0.999691	−	0.0248452i	$-0.00790928\pi$
$234$	1.45758e9			0.486149
$235$			5.19079e9i			1.70201i
$236$	−5.16202e9	−	5.02050e9i	−1.66407	−	1.61845i
$237$	−2.68856e9			−0.852169
$238$			3.16671e9i			0.986963i
$239$	4.57915e9			1.40344			0.701720	−	0.712453i	$-0.252416\pi$
$239$	4.57915e9			1.40344			0.701720	+	0.712453i	$0.252416\pi$
$240$	−5.64047e9			−1.70008
$241$	5.33390e9			1.58116			0.790582	−	0.612357i	$-0.209778\pi$
$241$	5.33390e9			1.58116			0.790582	+	0.612357i	$0.209778\pi$
$242$			1.49082e9i			0.434675i
$243$	2.23677e8			0.0641500
$244$		−	2.21185e9i		−	0.624017i
$245$	3.68383e9			1.02243
$246$		−	2.90583e9i		−	0.793467i
$247$			9.81374e8i			0.263662i
$248$	8.15285e9			2.15528
$249$		−	1.94954e8i		−	0.0507149i
$250$		−	2.94878e8i		−	0.0754887i
$251$	2.14584e9			0.540632			0.270316	−	0.962772i	$-0.412872\pi$
$251$	2.14584e9			0.540632			0.270316	+	0.962772i	$0.412872\pi$
$252$	1.65774e9			0.411069
$253$	3.06650e9			0.748446
$254$		−	8.87446e8i		−	0.213210i
$255$	3.54482e9			0.838365
$256$	−6.55121e9			−1.52532
$257$	−1.33536e9			−0.306102			−0.153051	−	0.988218i	$-0.548910\pi$
$257$	−1.33536e9			−0.306102			−0.153051	+	0.988218i	$0.548910\pi$
$258$	3.84710e9			0.868269
$259$		−	1.14713e9i		−	0.254927i
$260$		−	1.20924e10i		−	2.64618i
$261$	3.46990e8			0.0747747
$262$	−4.51829e9			−0.958890
$263$	3.46742e9			0.724742			0.362371	−	0.932034i	$-0.381967\pi$
$263$	3.46742e9			0.724742			0.362371	+	0.932034i	$0.381967\pi$
$264$	−5.89317e9			−1.21320
$265$	−1.15653e10			−2.34516
$266$			1.59696e9i			0.318983i
$267$		−	2.17801e9i		−	0.428563i
$268$		−	1.86773e9i		−	0.362055i
$269$			3.17574e8i			0.0606508i	0.999540	+	0.0303254i	$0.00965435\pi$
$269$			3.17574e8i			0.0606508i	−0.999540	+	0.0303254i	$0.990346\pi$
$270$		−	2.65508e9i		−	0.499600i
$271$	6.39999e8			0.118659			0.0593297	−	0.998238i	$-0.481104\pi$
$271$	6.39999e8			0.118659			0.0593297	+	0.998238i	$0.481104\pi$
$272$	−1.15346e10			−2.10730
$273$			1.36341e9i			0.245457i
$274$		−	1.02720e10i		−	1.82244i
$275$		−	5.13584e9i		−	0.898008i
$276$		−	6.67020e9i		−	1.14948i
$277$	−8.41688e9			−1.42966			−0.714829	−	0.699299i	$-0.753496\pi$
$277$	−8.41688e9			−1.42966			−0.714829	+	0.699299i	$0.753496\pi$
$278$			2.14863e10i			3.59735i
$279$			1.80774e9i			0.298345i
$280$		−	1.12007e10i		−	1.82227i
$281$	−8.79263e9			−1.41024			−0.705121	−	0.709087i	$-0.749107\pi$
$281$	−8.79263e9			−1.41024			−0.705121	+	0.709087i	$0.749107\pi$
$282$	7.95067e9			1.25721
$283$		−	1.03836e9i		−	0.161884i	−0.996719	−	0.0809418i	$-0.974207\pi$
$283$		−	1.03836e9i		−	0.161884i	0.996719	−	0.0809418i	$-0.0257928\pi$
$284$	1.06088e10			1.63077
$285$	1.78764e9			0.270957
$286$		−	8.51503e9i		−	1.27269i
$287$	2.71809e9			0.400623
$288$			3.11725e9i			0.453107i
$289$	2.73273e8			0.0391747
$290$		−	4.11882e9i		−	0.582345i
$291$			5.67584e9i			0.791513i
$292$			1.23920e8i			0.0170455i
$293$	8.39608e9			1.13922			0.569608	−	0.821916i	$-0.307095\pi$
$293$	8.39608e9			1.13922			0.569608	+	0.821916i	$0.307095\pi$
$294$		−	5.64247e9i		−	0.755231i
$295$	−7.73348e9	−	7.52146e9i	−1.02114	−	0.993149i
$296$	8.87039e9			1.15552
$297$		−	1.30670e9i		−	0.167938i
$298$	1.16174e10			1.47314
$299$	5.48591e9			0.686379
$300$	−1.11714e10			−1.37918
$301$			3.59855e9i			0.438390i
$302$	−1.85987e10			−2.23592
$303$		−	8.77641e9i		−	1.04123i
$304$	−5.81684e9			−0.681071
$305$		−	3.31368e9i		−	0.382923i
$306$		−	5.42955e9i		−	0.619267i
$307$	−3.44203e9			−0.387491			−0.193745	−	0.981052i	$-0.562064\pi$
$307$	−3.44203e9			−0.387491			−0.193745	+	0.981052i	$0.562064\pi$
$308$		−	9.68434e9i		−	1.07614i
$309$			6.41955e9i			0.704159i
$310$	2.14581e10			2.32351
$311$	5.52302e9			0.590384			0.295192	−	0.955438i	$-0.404616\pi$
$311$	5.52302e9			0.590384			0.295192	+	0.955438i	$0.404616\pi$
$312$	−1.05428e10			−1.11259
$313$			7.74206e9i			0.806639i	0.915059	+	0.403319i	$0.132144\pi$
$313$			7.74206e9i			0.806639i	−0.915059	+	0.403319i	$0.867856\pi$
$314$	1.75625e10			1.80662
$315$	2.48354e9			0.252249
$316$	3.41640e10			3.42626
$317$	5.51270e8			0.0545918			0.0272959	−	0.999627i	$-0.491310\pi$
$317$	5.51270e8			0.0545918			0.0272959	+	0.999627i	$0.491310\pi$
$318$			1.77144e10i			1.73228i
$319$		−	2.02708e9i		−	0.195753i
$320$	6.12547e9			0.584170
$321$	−1.70779e9			−0.160847
$322$	8.92706e9			0.830395
$323$	3.65566e9			0.335858
$324$	−2.84231e9			−0.257924
$325$		−	9.18792e9i		−	0.823539i
$326$			2.43825e10i			2.15877i
$327$			5.69692e9i			0.498252i
$328$			2.10180e10i			1.81592i
$329$			7.43700e9i			0.634767i
$330$	−1.55107e10			−1.30790
$331$	−1.83436e10			−1.52818			−0.764088	−	0.645112i	$-0.776811\pi$
$331$	−1.83436e10			−1.52818			−0.764088	+	0.645112i	$0.776811\pi$
$332$			2.47732e9i			0.203906i
$333$			1.96684e9i			0.159953i
$334$			2.80341e10i			2.25268i
$335$		−	2.79813e9i		−	0.222172i
$336$	−8.08126e9			−0.634047
$337$			2.40138e10i			1.86184i	0.365229	+	0.930918i	$0.380991\pi$
$337$			2.40138e10i			1.86184i	−0.365229	+	0.930918i	$0.619009\pi$
$338$			8.55278e9i			0.655301i
$339$			5.41529e9i			0.410037i
$340$	−4.50447e10			−3.37076
$341$	1.05606e10			0.781039
$342$		−	2.73810e9i		−	0.200145i
$343$	1.26311e10			0.912570
$344$	−2.78263e10			−1.98711
$345$		−	9.99295e9i		−	0.705371i
$346$	−3.86662e10			−2.69791
$347$		−	1.66067e10i		−	1.14542i	−0.819758	−	0.572711i	$-0.805892\pi$
$347$		−	1.66067e10i		−	1.14542i	0.819758	−	0.572711i	$-0.194108\pi$
$348$	−4.40927e9			−0.300642
$349$		−	1.61798e9i		−	0.109061i	−0.998512	−	0.0545306i	$-0.982634\pi$
$349$		−	1.61798e9i		−	0.109061i	0.998512	−	0.0545306i	$-0.0173662\pi$
$350$		−	1.49512e10i		−	0.996334i
$351$		−	2.33766e9i		−	0.154012i
$352$	1.82106e10			1.18619
$353$			1.39661e10i			0.899449i	0.893167	+	0.449724i	$0.148478\pi$
$353$			1.39661e10i			0.899449i	−0.893167	+	0.449724i	$0.851522\pi$
$354$	−1.15205e10	+	1.18453e10i	−0.733600	+	0.754279i
$355$	1.58936e10			1.00071
$356$			2.76764e10i			1.72310i
$357$	5.07876e9			0.312669
$358$	2.98890e10			1.81962
$359$	1.39663e10			0.840819			0.420409	−	0.907335i	$-0.361886\pi$
$359$	1.39663e10			0.840819			0.420409	+	0.907335i	$0.361886\pi$
$360$			1.92044e10i			1.14338i
$361$	−1.51400e10			−0.891452
$362$			4.40930e10i			2.56765i
$363$	2.39097e9			0.137705
$364$		−	1.73251e10i		−	0.986895i
$365$			1.85651e8i			0.0104598i
$366$	−5.07553e9			−0.282850
$367$		−	2.00449e10i		−	1.10494i	−0.833533	−	0.552470i	$-0.813685\pi$
$367$		−	2.00449e10i		−	1.10494i	0.833533	−	0.552470i	$-0.186315\pi$
$368$			3.25163e10i			1.77300i
$369$	−4.66035e9			−0.251370
$370$	2.33467e10			1.24571
$371$	−1.65699e10			−0.874629
$372$		−	2.29713e10i		−	1.19954i
$373$	2.88197e10			1.48886			0.744430	−	0.667700i	$-0.232721\pi$
$373$	2.88197e10			1.48886			0.744430	+	0.667700i	$0.232721\pi$
$374$	−3.17189e10			−1.62118
$375$	−4.72924e8			−0.0239148
$376$	−5.75077e10			−2.87723
$377$		−	3.62641e9i		−	0.179519i
$378$		−	3.80401e9i		−	0.186326i
$379$	2.19596e10			1.06431			0.532155	−	0.846647i	$-0.321382\pi$
$379$	2.19596e10			1.06431			0.532155	+	0.846647i	$0.321382\pi$
$380$	−2.27159e10			−1.08942
$381$	−1.42328e9			−0.0675447
$382$	4.86444e10			2.28444
$383$	−1.78028e10			−0.827355			−0.413678	−	0.910423i	$-0.635756\pi$
$383$	−1.78028e10			−0.827355			−0.413678	+	0.910423i	$0.635756\pi$
$384$			7.68193e9i			0.353301i
$385$		−	1.45086e10i		−	0.660363i
$386$			3.27523e10i			1.47534i
$387$		−	6.16996e9i		−	0.275067i
$388$		−	7.21240e10i		−	3.18239i
$389$	−3.83303e10			−1.67396			−0.836979	−	0.547236i	$-0.815680\pi$
$389$	−3.83303e10			−1.67396			−0.836979	+	0.547236i	$0.815680\pi$
$390$	−2.77484e10			−1.19944
$391$		−	2.04352e10i		−	0.874325i
$392$			4.08124e10i			1.72841i
$393$			7.24641e9i			0.303776i
$394$			2.08649e10i			0.865828i
$395$	5.11828e10			2.10250
$396$			1.66045e10i			0.675219i
$397$			3.53449e10i			1.42287i	0.702753	+	0.711434i	$0.251954\pi$
$397$			3.53449e10i			1.42287i	−0.702753	+	0.711434i	$0.748046\pi$
$398$			4.75243e9i			0.189401i
$399$	2.56120e9			0.101054
$400$	5.44590e10			2.12731
$401$		−	2.59132e10i		−	1.00217i	−0.865397	−	0.501087i	$-0.832934\pi$
$401$		−	2.59132e10i		−	1.00217i	0.865397	−	0.501087i	$-0.167066\pi$
$402$	−4.28587e9			−0.164110
$403$	1.88928e10			0.716269
$404$			1.11524e11i			4.18641i
$405$	−4.25821e9			−0.158273
$406$		−	5.90115e9i		−	0.217186i
$407$	1.14901e10			0.418741
$408$			3.92723e10i			1.41725i
$409$		−	4.37463e10i		−	1.56332i	−0.623704	−	0.781660i	$-0.714373\pi$
$409$		−	4.37463e10i		−	1.56332i	0.623704	−	0.781660i	$-0.285627\pi$
$410$			5.53190e10i			1.95767i
$411$	−1.64742e10			−0.577349
$412$		−	8.15745e10i		−	2.83117i
$413$	−1.10800e10	−	1.07762e10i	−0.380837	−	0.370396i
$414$	−1.53061e10			−0.521030
$415$			3.71140e9i			0.125125i
$416$	3.25785e10			1.08782
$417$	3.44597e10			1.13964
$418$	−1.59957e10			−0.523960
$419$		−	1.01547e10i		−	0.329467i	−0.986338	−	0.164734i	$-0.947324\pi$
$419$		−	1.01547e10i		−	0.329467i	0.986338	−	0.164734i	$-0.0526765\pi$
$420$	−3.15589e10			−1.01420
$421$		−	7.44469e9i		−	0.236983i	−0.992955	−	0.118492i	$-0.962194\pi$
$421$		−	7.44469e9i		−	0.236983i	0.992955	−	0.118492i	$-0.0378059\pi$
$422$	−9.92799e8			−0.0313049
$423$		−	1.27513e10i		−	0.398283i
$424$		−	1.28129e11i		−	3.96446i
$425$	−3.42254e10			−1.04904
$426$		−	2.43440e10i		−	0.739185i
$427$		−	4.74761e9i		−	0.142812i
$428$	2.17012e10			0.646708
$429$	−1.36564e10			−0.403187
$430$	−7.32383e10			−2.14222
$431$		−	4.50007e10i		−	1.30410i	−0.758177	−	0.652049i	$-0.773910\pi$
$431$		−	4.50007e10i		−	1.30410i	0.758177	−	0.652049i	$-0.226090\pi$
$432$	1.38559e10			0.397832
$433$	4.18729e10			1.19119			0.595596	−	0.803284i	$-0.296916\pi$
$433$	4.18729e10			1.19119			0.595596	+	0.803284i	$0.296916\pi$
$434$	3.07437e10			0.866557
$435$	−6.60574e9			−0.184487
$436$		−	7.23919e10i		−	2.00329i
$437$		−	1.03054e10i		−	0.282579i
$438$	2.84359e8			0.00772627
$439$	−2.03288e10			−0.547335			−0.273668	−	0.961824i	$-0.588237\pi$
$439$	−2.03288e10			−0.547335			−0.273668	+	0.961824i	$0.588237\pi$
$440$	1.12190e11			2.99325
$441$	−9.04938e9			−0.239257
$442$	−5.67445e10			−1.48674
$443$		−	3.55878e10i		−	0.924032i	−0.886872	−	0.462016i	$-0.847126\pi$
$443$		−	3.55878e10i		−	0.924032i	0.886872	−	0.462016i	$-0.152874\pi$
$444$		−	2.49931e10i		−	0.643114i
$445$			4.14634e10i			1.05736i
$446$		−	2.46919e10i		−	0.624043i
$447$		−	1.86320e10i		−	0.466691i
$448$	8.77614e9			0.217867
$449$	−6.58262e10			−1.61962			−0.809811	−	0.586691i	$-0.800430\pi$
$449$	−6.58262e10			−1.61962			−0.809811	+	0.586691i	$0.800430\pi$
$450$			2.56350e10i			0.625148i
$451$			2.72253e10i			0.658061i
$452$		−	6.88132e10i		−	1.64861i
$453$			2.98286e10i			0.708337i
$454$	−2.68714e10			−0.632509
$455$		−	2.59556e10i		−	0.605600i
$456$			1.98049e10i			0.458050i
$457$		−	4.19545e10i		−	0.961864i	−0.876758	−	0.480932i	$-0.840298\pi$
$457$		−	4.19545e10i		−	0.961864i	0.876758	−	0.480932i	$-0.159702\pi$
$458$	−6.91309e10			−1.57112
$459$	−8.70789e9			−0.196183
$460$			1.26982e11i			2.83604i
$461$	1.04144e10			0.230586			0.115293	−	0.993332i	$-0.463219\pi$
$461$	1.04144e10			0.230586			0.115293	+	0.993332i	$0.463219\pi$
$462$	−2.22226e10			−0.487784
$463$		−	5.76532e10i		−	1.25458i	−0.778785	−	0.627291i	$-0.784164\pi$
$463$		−	5.76532e10i		−	1.25458i	0.778785	−	0.627291i	$-0.215836\pi$
$464$	2.14946e10			0.463721
$465$		−	3.44145e10i		−	0.736088i
$466$	4.27042e9			0.0905580
$467$		−	5.62245e10i		−	1.18211i	−0.806631	−	0.591055i	$-0.798711\pi$
$467$		−	5.62245e10i		−	1.18211i	0.806631	−	0.591055i	$-0.201289\pi$
$468$			2.97052e10i			0.619225i
$469$		−	4.00897e9i		−	0.0828593i
$470$	−1.51359e11			−3.10183
$471$		−	2.81667e10i		−	0.572338i
$472$	8.33287e10	−	8.56776e10i	1.67891	−	1.72623i
$473$	−3.60443e10			−0.720098
$474$		−	7.83961e10i		−	1.55303i
$475$	−1.72598e10			−0.339047
$476$	−6.45368e10			−1.25713
$477$	2.84102e10			0.548784
$478$			1.33524e11i			2.55769i
$479$	−2.26275e10			−0.429828			−0.214914	−	0.976633i	$-0.568947\pi$
$479$	−2.26275e10			−0.429828			−0.214914	+	0.976633i	$0.568947\pi$
$480$		−	5.93439e10i		−	1.11792i
$481$	2.05556e10			0.384016
$482$			1.55532e11i			2.88159i
$483$		−	1.43172e10i		−	0.263069i
$484$	−3.03826e10			−0.553660
$485$		−	1.08053e11i		−	1.95285i
$486$			6.52224e9i			0.116910i
$487$	−7.63144e10			−1.35672			−0.678360	−	0.734729i	$-0.737309\pi$
$487$	−7.63144e10			−1.35672			−0.678360	+	0.734729i	$0.737309\pi$
$488$	3.67116e10			0.647328
$489$	3.91045e10			0.683898
$490$			1.07417e11i			1.86333i
$491$	5.10608e10			0.878540			0.439270	−	0.898355i	$-0.355237\pi$
$491$	5.10608e10			0.878540			0.439270	+	0.898355i	$0.355237\pi$
$492$	5.92200e10			1.01067
$493$	−1.35085e10			−0.228676
$494$	−2.86161e10			−0.480509
$495$			2.48760e10i			0.414343i
$496$			1.11982e11i			1.85021i
$497$	2.27712e10			0.373216
$498$	5.68471e9			0.0924253
$499$	1.13655e11			1.83309			0.916547	−	0.399927i	$-0.130965\pi$
$499$	1.13655e11			1.83309			0.916547	+	0.399927i	$0.130965\pi$
$500$	6.00954e9			0.0961527
$501$	4.49610e10			0.713649
$502$			6.25708e10i			0.985274i
$503$			8.60576e10i			1.34437i	0.740385	+	0.672183i	$0.234643\pi$
$503$			8.60576e10i			1.34437i	−0.740385	+	0.672183i	$0.765357\pi$
$504$			2.75147e10i			0.426424i
$505$			1.67079e11i			2.56896i
$506$			8.94165e10i			1.36400i
$507$	1.37169e10			0.207599
$508$	1.80859e10			0.271573
$509$		−	4.60652e10i		−	0.686281i	−0.939284	−	0.343140i	$-0.888509\pi$
$509$		−	4.60652e10i		−	0.686281i	0.939284	−	0.343140i	$-0.111491\pi$
$510$			1.03364e11i			1.52788i
$511$			2.65987e8i			0.00390101i
$512$		−	1.48976e11i		−	2.16788i
$513$	−4.39136e9			−0.0634059
$514$		−	3.89380e10i		−	0.557854i
$515$		−	1.22211e11i		−	1.73732i
$516$			7.84029e10i			1.10594i
$517$	−7.44915e10			−1.04266
$518$	3.34495e10			0.464591
$519$			6.20127e10i			0.854695i
$520$	2.00706e11			2.74503
$521$	−1.14549e11			−1.55468			−0.777341	−	0.629079i	$-0.783432\pi$
$521$	−1.14549e11			−1.55468			−0.777341	+	0.629079i	$0.783432\pi$
$522$			1.01179e10i			0.136273i
$523$	1.09614e11			1.46508			0.732538	−	0.680726i	$-0.238335\pi$
$523$	1.09614e11			1.46508			0.732538	+	0.680726i	$0.238335\pi$
$524$		−	9.20816e10i		−	1.22137i
$525$	−2.39788e10			−0.315638
$526$			1.01107e11i			1.32080i
$527$		−	7.03765e10i		−	0.912399i
$528$		−	8.09446e10i		−	1.04148i
$529$	2.07034e10			0.264374
$530$		−	3.37233e11i		−	4.27393i
$531$	1.89974e10	+	1.84766e10i	0.238955	+	0.232404i
$532$	−3.25457e10			−0.406300
$533$			4.87056e10i			0.603490i
$534$	6.35089e10			0.781033
$535$	3.25116e10			0.396847
$536$	3.09999e10			0.375579
$537$		−	4.79359e10i		−	0.576453i
$538$	−9.26020e9			−0.110533
$539$			5.28655e10i			0.626350i
$540$	5.41099e10			0.636359
$541$			8.07139e10i			0.942235i	0.882071	+	0.471117i	$0.156149\pi$
$541$			8.07139e10i			0.942235i	−0.882071	+	0.471117i	$0.843851\pi$
$542$			1.86618e10i			0.216250i
$543$	7.07163e10			0.813429
$544$		−	1.21356e11i		−	1.38569i
$545$		−	1.08454e11i		−	1.22930i
$546$	−3.97559e10			−0.447333
$547$	−5.62430e10			−0.628231			−0.314116	−	0.949385i	$-0.601708\pi$
$547$	−5.62430e10			−0.628231			−0.314116	+	0.949385i	$0.601708\pi$
$548$	2.09342e11			2.32131
$549$			8.14011e9i			0.0896068i
$550$	1.49757e11			1.63657
$551$	−6.81230e9			−0.0739073
$552$	1.10710e11			1.19242
$553$	7.33311e10			0.784129
$554$		−	2.45429e11i		−	2.60548i
$555$		−	3.74434e10i		−	0.394642i
$556$	−4.37887e11			−4.58208
$557$	5.95234e9			0.0618396			0.0309198	−	0.999522i	$-0.490156\pi$
$557$	5.95234e9			0.0618396			0.0309198	+	0.999522i	$0.490156\pi$
$558$	−5.27122e10			−0.543719
$559$	−6.44826e10			−0.660382
$560$	1.53845e11			1.56434
$561$			5.08706e10i			0.513589i
$562$		−	2.56386e11i		−	2.57009i
$563$		−	9.63638e10i		−	0.959137i	−0.877505	−	0.479568i	$-0.840793\pi$
$563$		−	9.63638e10i		−	0.959137i	0.877505	−	0.479568i	$-0.159207\pi$
$564$			1.62033e11i			1.60135i
$565$		−	1.03092e11i		−	1.01166i
$566$	3.02778e10			0.295025
$567$	−6.10086e9			−0.0590281
$568$			1.76082e11i			1.69169i
$569$			1.91921e11i			1.83094i	0.402388	+	0.915469i	$0.368180\pi$
$569$			1.91921e11i			1.83094i	−0.402388	+	0.915469i	$0.631820\pi$
$570$			5.21261e10i			0.493805i
$571$		−	1.35989e9i		−	0.0127926i	−0.999980	−	0.00639632i	$-0.997964\pi$
$571$		−	1.35989e9i		−	0.0127926i	0.999980	−	0.00639632i	$-0.00203603\pi$
$572$	1.73534e11			1.62107
$573$		−	7.80157e10i		−	0.723708i
$574$			7.92572e10i			0.730114i
$575$			9.64825e10i			0.882627i
$576$	−1.50473e10			−0.136700
$577$	2.20647e10			0.199065			0.0995327	−	0.995034i	$-0.468265\pi$
$577$	2.20647e10			0.199065			0.0995327	+	0.995034i	$0.468265\pi$
$578$			7.96841e9i			0.0713938i
$579$	5.25280e10			0.467387
$580$	8.39405e10			0.741754
$581$			5.31743e9i			0.0466657i
$582$	−1.65503e11			−1.44249
$583$		−	1.65970e11i		−	1.43666i
$584$	−2.05678e9			−0.0176822
$585$			4.45028e10i			0.379982i
$586$			2.44823e11i			2.07616i
$587$			7.62512e10i			0.642236i	0.947039	+	0.321118i	$0.104059\pi$
$587$			7.62512e10i			0.642236i	−0.947039	+	0.321118i	$0.895941\pi$
$588$	1.14992e11			0.961965
$589$		−	3.54906e10i		−	0.294885i
$590$	2.19320e11	−	2.25502e11i	1.80996	−	1.86098i
$591$	3.34631e10			0.274294
$592$			1.21838e11i			0.991962i
$593$	−1.64770e11			−1.33248			−0.666239	−	0.745739i	$-0.732097\pi$
$593$	−1.64770e11			−1.33248			−0.666239	+	0.745739i	$0.732097\pi$
$594$	3.81023e10			0.306059
$595$	−9.66858e10			−0.771427
$596$			2.36761e11i			1.87640i
$597$	7.62192e9			0.0600022
$598$			1.59965e11i			1.25089i
$599$	1.81857e11			1.41261			0.706304	−	0.707909i	$-0.250361\pi$
$599$	1.81857e11			1.41261			0.706304	+	0.707909i	$0.250361\pi$
$600$		−	1.85419e11i		−	1.43070i
$601$			2.62909e10i			0.201515i	0.994911	+	0.100758i	$0.0321266\pi$
$601$			2.62909e10i			0.201515i	−0.994911	+	0.100758i	$0.967873\pi$
$602$	−1.04931e11			−0.798944
$603$			6.87366e9i			0.0519899i
$604$		−	3.79038e11i		−	2.84797i
$605$	−4.55177e10			−0.339749
$606$	2.55913e11			1.89759
$607$	1.28964e11			0.949977			0.474989	−	0.879992i	$-0.342452\pi$
$607$	1.28964e11			0.949977			0.474989	+	0.879992i	$0.342452\pi$
$608$		−	6.11995e10i		−	0.447851i
$609$	−9.46424e9			−0.0688044
$610$	9.66243e10			0.697858
$611$	−1.33264e11			−0.956199
$612$	1.10653e11			0.788783
$613$		−	8.23122e10i		−	0.582938i	−0.956580	−	0.291469i	$-0.905856\pi$
$613$		−	8.23122e10i		−	0.582938i	0.956580	−	0.291469i	$-0.0941440\pi$
$614$		−	1.00367e11i		−	0.706181i
$615$	8.87205e10			0.620188
$616$	1.60738e11			1.11634
$617$	−1.13854e10			−0.0785614			−0.0392807	−	0.999228i	$-0.512507\pi$
$617$	−1.13854e10			−0.0785614			−0.0392807	+	0.999228i	$0.512507\pi$
$618$	−1.87189e11			−1.28329
$619$	8.04699e10			0.548114			0.274057	−	0.961713i	$-0.411634\pi$
$619$	8.04699e10			0.548114			0.274057	+	0.961713i	$0.411634\pi$
$620$			4.37312e11i			2.95954i
$621$			2.45478e10i			0.165062i
$622$			1.61047e11i			1.07594i
$623$			5.94057e10i			0.394345i
$624$		−	1.44809e11i		−	0.955115i
$625$	−1.48022e11			−0.970076
$626$	−2.25752e11			−1.47006
$627$			2.56539e10i			0.165990i
$628$			3.57920e11i			2.30116i
$629$		−	7.65704e10i		−	0.489168i
$630$			7.24181e10i			0.459711i
$631$	−5.81751e10			−0.366961			−0.183480	−	0.983023i	$-0.558736\pi$
$631$	−5.81751e10			−0.366961			−0.183480	+	0.983023i	$0.558736\pi$
$632$			5.67044e11i			3.55425i
$633$			1.59225e9i			0.00991736i
$634$			1.60746e10i			0.0994908i
$635$	2.70955e10			0.166649
$636$	−3.61015e11			−2.20646
$637$			9.45755e10i			0.574408i
$638$	5.91079e10			0.356749
$639$	−3.90428e10			−0.234173
$640$		−	1.46243e11i		−	0.871676i
$641$	−2.09645e11			−1.24180			−0.620901	−	0.783889i	$-0.713233\pi$
$641$	−2.09645e11			−1.24180			−0.620901	+	0.783889i	$0.713233\pi$
$642$		−	4.97976e10i		−	0.293136i
$643$	−1.94489e11			−1.13776			−0.568880	−	0.822420i	$-0.692623\pi$
$643$	−1.94489e11			−1.13776			−0.568880	+	0.822420i	$0.692623\pi$
$644$			1.81931e11i			1.05770i
$645$			1.17459e11i			0.678654i
$646$			1.06596e11i			0.612084i
$647$	−5.57482e10			−0.318137			−0.159068	−	0.987268i	$-0.550849\pi$
$647$	−5.57482e10			−0.318137			−0.159068	+	0.987268i	$0.550849\pi$
$648$		−	4.71758e10i		−	0.267559i
$649$	1.07938e11	−	1.10981e11i	0.608410	−	0.625560i
$650$	2.67912e11			1.50086
$651$		−	4.93066e10i		−	0.274525i
$652$	−4.96909e11			−2.74971
$653$	3.92742e9			0.0216000			0.0108000	−	0.999942i	$-0.496562\pi$
$653$	3.92742e9			0.0216000			0.0108000	+	0.999942i	$0.496562\pi$
$654$	−1.66117e11			−0.908038
$655$		−	1.37952e11i		−	0.749485i
$656$	−2.88690e11			−1.55889
$657$		−	4.56053e8i		−	0.00244768i
$658$	−2.16857e11			−1.15683
$659$			2.60169e10i			0.137947i	0.997618	+	0.0689737i	$0.0219724\pi$
$659$			2.60169e10i			0.137947i	−0.997618	+	0.0689737i	$0.978028\pi$
$660$		−	3.16104e11i		−	1.66592i
$661$	1.77345e10			0.0928994			0.0464497	−	0.998921i	$-0.485209\pi$
$661$	1.77345e10			0.0928994			0.0464497	+	0.998921i	$0.485209\pi$
$662$		−	5.34885e11i		−	2.78502i
$663$			9.10066e10i			0.470998i
$664$	−4.11179e10			−0.211523
$665$	−4.87583e10			−0.249323
$666$	−5.73515e10			−0.291506
$667$			3.80809e10i			0.192400i
$668$	−5.71328e11			−2.86932
$669$	−3.96007e10			−0.197696
$670$	8.15913e10			0.404897
$671$	4.75537e10			0.234582
$672$		−	8.50237e10i		−	0.416930i
$673$		−	2.86465e11i		−	1.39640i	−0.715901	−	0.698201i	$-0.753984\pi$
$673$		−	2.86465e11i		−	1.39640i	0.715901	−	0.698201i	$-0.246016\pi$
$674$	−7.00222e11			−3.39310
$675$	4.11133e10			0.198046
$676$	−1.74304e11			−0.834680
$677$	2.56441e11			1.22077			0.610384	−	0.792105i	$-0.291015\pi$
$677$	2.56441e11			1.22077			0.610384	+	0.792105i	$0.291015\pi$
$678$	−1.57905e11			−0.747271
$679$		−	1.54810e11i		−	0.728316i
$680$		−	7.47638e11i		−	3.49668i
$681$			4.30962e10i			0.200378i
$682$			3.07939e11i			1.42340i
$683$			1.79075e11i			0.822909i	0.911430	+	0.411454i	$0.134979\pi$
$683$			1.79075e11i			0.822909i	−0.911430	+	0.411454i	$0.865021\pi$
$684$	5.58019e10			0.254932
$685$	3.13625e11			1.42445
$686$			3.68314e11i			1.66311i
$687$			1.10872e11i			0.497731i
$688$		−	3.82203e11i		−	1.70585i
$689$		−	2.96917e11i		−	1.31752i
$690$	2.91386e11			1.28550
$691$			4.39431e11i			1.92743i	0.266933	+	0.963715i	$0.413990\pi$
$691$			4.39431e11i			1.92743i	−0.266933	+	0.963715i	$0.586010\pi$
$692$		−	7.88008e11i		−	3.43642i
$693$			3.56406e10i			0.154530i
$694$	4.84237e11			2.08747
$695$	−6.56020e11			−2.81176
$696$		−	7.31837e10i		−	0.311873i
$697$	1.81430e11			0.768739
$698$	4.71788e10			0.198758
$699$		−	6.84889e9i		−	0.0286887i
$700$	3.04703e11			1.26907
$701$		−	2.08687e11i		−	0.864216i	−0.901822	−	0.432108i	$-0.857770\pi$
$701$		−	2.08687e11i		−	0.864216i	0.901822	−	0.432108i	$-0.142230\pi$
$702$	6.81643e10			0.280678
$703$		−	3.86142e10i		−	0.158098i
$704$			8.79047e10i			0.357867i
$705$			2.42749e11i			0.982656i
$706$	−4.07240e11			−1.63920
$707$			2.39379e11i			0.958095i
$708$	−2.41404e11	−	2.34786e11i	−0.960752	−	0.934412i
$709$	3.22930e11			1.27798			0.638989	−	0.769216i	$-0.279353\pi$
$709$	3.22930e11			1.27798			0.638989	+	0.769216i	$0.279353\pi$
$710$			4.63443e11i			1.82374i
$711$	−1.25731e11			−0.492000
$712$	−4.59364e11			−1.78746
$713$	−1.98393e11			−0.767661
$714$			1.48092e11i			0.569823i
$715$	2.59980e11			0.994756
$716$			6.09132e11i			2.31771i
$717$	2.14146e11			0.810276
$718$			4.07245e11i			1.53235i
$719$		−	3.22948e11i		−	1.20842i	−0.796826	−	0.604209i	$-0.793489\pi$
$719$		−	3.22948e11i		−	1.20842i	0.796826	−	0.604209i	$-0.206511\pi$
$720$	−2.63778e11			−0.981543
$721$		−	1.75095e11i		−	0.647937i
$722$		−	4.41471e11i		−	1.62462i
$723$	2.49442e11			0.912885
$724$	−8.98606e11			−3.27051
$725$	6.37788e10			0.230847
$726$			6.97188e10i			0.250959i
$727$	1.06099e11			0.379818			0.189909	−	0.981802i	$-0.439181\pi$
$727$	1.06099e11			0.379818			0.189909	+	0.981802i	$0.439181\pi$
$728$	2.87557e11			1.02376
$729$	1.04604e10			0.0370370
$730$	−5.41342e9			−0.0190625
$731$			2.40200e11i			0.841209i
$732$		−	1.03438e11i		−	0.360277i
$733$	2.17378e10			0.0753009			0.0376504	−	0.999291i	$-0.488013\pi$
$733$	2.17378e10			0.0753009			0.0376504	+	0.999291i	$0.488013\pi$
$734$	5.84491e11			2.01370
$735$	1.72276e11			0.590302
$736$	−3.42107e11			−1.16587
$737$	4.01552e10			0.136104
$738$		−	1.35892e11i		−	0.458109i
$739$			3.55658e11i			1.19249i	0.802802	+	0.596246i	$0.203342\pi$
$739$			3.55658e11i			1.19249i	−0.802802	+	0.596246i	$0.796658\pi$
$740$			4.75800e11i			1.58671i
$741$			4.58943e10i			0.152225i
$742$		−	4.83164e11i		−	1.59397i
$743$	5.31380e11			1.74361			0.871806	−	0.489851i	$-0.162949\pi$
$743$	5.31380e11			1.74361			0.871806	+	0.489851i	$0.162949\pi$
$744$	3.81271e11			1.24435
$745$			3.54703e11i			1.15144i
$746$			8.40358e11i			2.71337i
$747$		−	9.11712e9i		−	0.0292803i
$748$		−	6.46423e11i		−	2.06495i
$749$	4.65803e10			0.148005
$750$		−	1.37901e10i		−	0.0435834i
$751$			4.24872e11i			1.33567i	0.744311	+	0.667834i	$0.232778\pi$
$751$			4.24872e11i			1.33567i	−0.744311	+	0.667834i	$0.767222\pi$
$752$		−	7.89888e11i		−	2.46998i
$753$	1.00351e11			0.312134
$754$	1.05743e11			0.327165
$755$		−	5.67856e11i		−	1.74763i
$756$	7.75249e10			0.237331
$757$	−2.31078e11			−0.703680			−0.351840	−	0.936060i	$-0.614444\pi$
$757$	−2.31078e11			−0.703680			−0.351840	+	0.936060i	$0.614444\pi$
$758$			6.40325e11i			1.93965i
$759$	1.43406e11			0.432115
$760$		−	3.77031e11i		−	1.13012i
$761$	6.45763e11			1.92546			0.962730	−	0.270465i	$-0.0871775\pi$
$761$	6.45763e11			1.92546			0.962730	+	0.270465i	$0.0871775\pi$
$762$		−	4.15017e10i		−	0.123097i
$763$		−	1.55385e11i		−	0.458470i
$764$			9.91362e11i			2.90977i
$765$	1.65775e11			0.484030
$766$		−	5.19113e11i		−	1.50781i
$767$	1.93100e11	−	1.98543e11i	0.557956	−	0.573684i
$768$	−3.06370e11			−0.880645
$769$			2.79860e11i			0.800268i	0.916457	+	0.400134i	$0.131036\pi$
$769$			2.79860e11i			0.800268i	−0.916457	+	0.400134i	$0.868964\pi$
$770$	4.23059e11			1.20348
$771$	−6.24486e10			−0.176728
$772$	−6.67484e11			−1.87919
$773$		−	4.82350e11i		−	1.35096i	−0.737376	−	0.675482i	$-0.763935\pi$
$773$		−	4.82350e11i		−	1.35096i	0.737376	−	0.675482i	$-0.236065\pi$
$774$	1.79911e11			0.501295
$775$			3.32274e11i			0.921063i
$776$	1.19709e12			3.30127
$777$		−	5.36462e10i		−	0.147182i
$778$		−	1.11768e12i		−	3.05070i
$779$	9.14947e10			0.248454
$780$		−	5.65506e11i		−	1.52777i
$781$			2.28084e11i			0.613042i
$782$	5.95875e11			1.59341
$783$	1.62271e10			0.0431712
$784$	−5.60571e11			−1.48377
$785$			5.36217e11i			1.41209i
$786$	−2.11299e11			−0.553615
$787$	−1.43532e11			−0.374154			−0.187077	−	0.982345i	$-0.559901\pi$
$787$	−1.43532e11			−0.374154			−0.187077	+	0.982345i	$0.559901\pi$
$788$	−4.25222e11			−1.10284
$789$	1.62155e11			0.418430
$790$			1.49245e12i			3.83170i
$791$		−	1.47703e11i		−	0.377298i
$792$	−2.75596e11			−0.700442
$793$	8.50727e10			0.215128
$794$	−1.03063e12			−2.59310
$795$	−5.40854e11			−1.35398
$796$	−9.68533e10			−0.241247
$797$		−	1.80387e11i		−	0.447066i	−0.974696	−	0.223533i	$-0.928241\pi$
$797$		−	1.80387e11i		−	0.447066i	0.974696	−	0.223533i	$-0.0717590\pi$
$798$			7.46825e10i			0.184165i
$799$			4.96414e11i			1.21803i
$800$			5.72969e11i			1.39885i
$801$		−	1.01855e11i		−	0.247431i
$802$	7.55607e11			1.82641
$803$	−2.66422e9			−0.00640777
$804$		−	8.73449e10i		−	0.209032i
$805$			2.72560e11i			0.649052i
$806$			5.50898e11i			1.30536i
$807$			1.48515e10i			0.0350167i
$808$	−1.85103e12			−4.34279
$809$			4.87184e11i			1.13736i	0.822558	+	0.568682i	$0.192546\pi$
$809$			4.87184e11i			1.13736i	−0.822558	+	0.568682i	$0.807454\pi$
$810$		−	1.24166e11i		−	0.288444i
$811$			5.86687e11i			1.35620i	0.734970	+	0.678099i	$0.237196\pi$
$811$			5.86687e11i			1.35620i	−0.734970	+	0.678099i	$0.762804\pi$
$812$	1.20264e11			0.276638
$813$	2.99298e10			0.0685080
$814$			3.35041e11i			0.763134i
$815$	−7.44444e11			−1.68734
$816$	−5.39418e11			−1.21665
$817$			1.21132e11i			0.271876i
$818$	1.27561e12			2.84907
$819$			6.37604e10i			0.141715i
$820$	−1.12739e12			−2.49355
$821$			8.80893e11i			1.93888i	0.245330	+	0.969440i	$0.421104\pi$
$821$			8.80893e11i			1.93888i	−0.245330	+	0.969440i	$0.578896\pi$
$822$		−	4.80375e11i		−	1.05219i
$823$			5.45871e11i			1.18985i	0.803782	+	0.594923i	$0.202818\pi$
$823$			5.45871e11i			1.18985i	−0.803782	+	0.594923i	$0.797182\pi$
$824$	1.35395e12			2.93693
$825$		−	2.40179e11i		−	0.518465i
$826$	3.14226e11	−	3.23083e11i	0.675027	−	0.694055i
$827$	−2.86702e11			−0.612926			−0.306463	−	0.951883i	$-0.599146\pi$
$827$	−2.86702e11			−0.612926			−0.306463	+	0.951883i	$0.599146\pi$
$828$		−	3.11934e11i		−	0.663654i
$829$	2.89742e11			0.613470			0.306735	−	0.951795i	$-0.400764\pi$
$829$	2.89742e11			0.613470			0.306735	+	0.951795i	$0.400764\pi$
$830$	−1.08221e11			−0.228035
$831$	−3.93619e11			−0.825414
$832$			1.57260e11i			0.328190i
$833$	3.52298e11			0.731695
$834$			1.00482e12i			2.07693i
$835$	−8.55935e11			−1.76074
$836$		−	3.25989e11i		−	0.667387i
$837$			8.45397e10i			0.172250i
$838$	2.96104e11			0.600437
$839$		−	6.08996e11i		−	1.22904i	−0.788901	−	0.614521i	$-0.789349\pi$
$839$		−	6.08996e11i		−	1.22904i	0.788901	−	0.614521i	$-0.210651\pi$
$840$		−	5.23805e11i		−	1.05209i
$841$	−4.75073e11			−0.949679
$842$	2.17081e11			0.431890
$843$	−4.11191e11			−0.814203
$844$		−	2.02330e10i		−	0.0398741i
$845$	−2.61133e11			−0.512195
$846$	3.71816e11			0.725850
$847$	−6.52145e10			−0.126710
$848$	1.75990e12			3.40333
$849$		−	4.85594e10i		−	0.0934636i
$850$		−	9.97984e11i		−	1.91182i
$851$	−2.15854e11			−0.411569
$852$	4.96124e11			0.941526
$853$	9.48214e11			1.79106			0.895530	−	0.445001i	$-0.146797\pi$
$853$	9.48214e11			1.79106			0.895530	+	0.445001i	$0.146797\pi$
$854$	1.38436e11			0.260267
$855$	8.35996e10			0.156437
$856$			3.60190e11i			0.670866i
$857$		−	4.54875e11i		−	0.843275i	−0.906765	−	0.421637i	$-0.861456\pi$
$857$		−	4.54875e11i		−	0.843275i	0.906765	−	0.421637i	$-0.138544\pi$
$858$		−	3.98209e11i		−	0.734787i
$859$			1.16812e11i			0.214543i	0.994230	+	0.107272i	$0.0342115\pi$
$859$			1.16812e11i			0.214543i	−0.994230	+	0.107272i	$0.965789\pi$
$860$		−	1.49258e12i		−	2.72862i
$861$	1.27112e11			0.231300
$862$	1.31218e12			2.37665
$863$		−	5.00910e11i		−	0.903060i	−0.892256	−	0.451530i	$-0.850878\pi$
$863$		−	5.00910e11i		−	0.903060i	0.892256	−	0.451530i	$-0.149122\pi$
$864$			1.45779e11i			0.261602i
$865$		−	1.18055e12i		−	2.10873i
$866$			1.22098e12i			2.17089i
$867$	1.27797e10			0.0226175
$868$			6.26549e11i			1.10376i
$869$			7.34509e11i			1.28801i
$870$		−	1.92618e11i		−	0.336217i
$871$	7.18369e10			0.124817
$872$	1.20154e12			2.07812
$873$			2.65433e11i			0.456980i
$874$	3.00498e11			0.514986
$875$	1.28991e10			0.0220054
$876$			5.79516e9i			0.00984122i
$877$	4.10501e11			0.693931			0.346965	−	0.937878i	$-0.387212\pi$
$877$	4.10501e11			0.693931			0.346965	+	0.937878i	$0.387212\pi$
$878$		−	5.92771e11i		−	0.997490i
$879$	3.92646e11			0.657727
$880$			1.54097e12i			2.56958i
$881$		−	1.94073e11i		−	0.322152i	−0.986942	−	0.161076i	$-0.948503\pi$
$881$		−	1.94073e11i		−	0.322152i	0.986942	−	0.161076i	$-0.0514965\pi$
$882$		−	2.63872e11i		−	0.436033i
$883$	−2.35883e11			−0.388019			−0.194010	−	0.981000i	$-0.562149\pi$
$883$	−2.35883e11			−0.388019			−0.194010	+	0.981000i	$0.562149\pi$
$884$		−	1.15644e12i		−	1.89371i
$885$	−3.61659e11	−	3.51744e11i	−0.589558	−	0.573395i
$886$	1.03771e12			1.68400
$887$		−	5.90694e11i		−	0.954263i	−0.878832	−	0.477132i	$-0.841677\pi$
$887$		−	5.90694e11i		−	0.954263i	0.878832	−	0.477132i	$-0.158323\pi$
$888$	4.14827e11			0.667138
$889$	3.88204e10			0.0621517
$890$	−1.20904e12			−1.92699
$891$		−	6.11083e10i		−	0.0969592i
$892$	5.03215e11			0.794866
$893$			2.50340e11i			0.393663i
$894$	5.43294e11			0.850520
$895$			9.12570e11i			1.42224i
$896$		−	2.09527e11i		−	0.325093i
$897$	2.56551e11			0.396281
$898$		−	1.91944e12i		−	2.95168i
$899$			1.31146e11i			0.200778i
$900$	−5.22434e11			−0.796273
$901$	−1.10603e12			−1.67829
$902$	−7.93867e11			−1.19928
$903$			1.68287e11i			0.253105i
$904$	1.14214e12			1.71019
$905$	−1.34625e12			−2.00692
$906$	−8.69777e11			−1.29091
$907$	−1.01120e12			−1.49419			−0.747095	−	0.664717i	$-0.768552\pi$
$907$	−1.01120e12			−1.49419			−0.747095	+	0.664717i	$0.768552\pi$
$908$		−	5.47633e11i		−	0.805649i
$909$		−	4.10432e11i		−	0.601154i
$910$	7.56845e11			1.10367
$911$	−8.37637e10			−0.121614			−0.0608068	−	0.998150i	$-0.519367\pi$
$911$	−8.37637e10			−0.121614			−0.0608068	+	0.998150i	$0.519367\pi$
$912$	−2.72027e11			−0.393217
$913$	−5.32612e10			−0.0766528
$914$	1.22336e12			1.75295
$915$		−	1.54966e11i		−	0.221081i
$916$		−	1.40887e12i		−	2.00120i
$917$		−	1.97648e11i		−	0.279521i
$918$		−	2.53915e11i		−	0.357534i
$919$			1.25971e12i			1.76608i	0.469299	+	0.883040i	$0.344507\pi$
$919$			1.25971e12i			1.76608i	−0.469299	+	0.883040i	$0.655493\pi$
$920$	−2.10761e12			−2.94198
$921$	−1.60968e11			−0.223718
$922$			3.03676e11i			0.420230i
$923$			4.08038e11i			0.562204i
$924$		−	4.52892e11i		−	0.621308i
$925$			3.61518e11i			0.493813i
$926$	1.68112e12			2.28641
$927$			3.00213e11i			0.406546i
$928$			2.26147e11i			0.304929i
$929$		−	4.44456e11i		−	0.596714i	−0.954454	−	0.298357i	$-0.903561\pi$
$929$		−	4.44456e11i		−	0.596714i	0.954454	−	0.298357i	$-0.0964386\pi$
$930$	1.00350e12			1.34148
$931$	1.77663e11			0.236481
$932$			8.70302e10i			0.115347i
$933$	2.58286e11			0.340859
$934$	1.63946e12			2.15434
$935$		−	9.68438e11i		−	1.26714i
$936$	−4.93037e11			−0.642356
$937$		−	1.29134e12i		−	1.67526i	−0.546240	−	0.837629i	$-0.683941\pi$
$937$		−	1.29134e12i		−	1.67526i	0.546240	−	0.837629i	$-0.316059\pi$
$938$	1.16898e11			0.151007
$939$			3.62060e11i			0.465713i
$940$		−	3.08467e12i		−	3.95091i
$941$		−	1.48233e12i		−	1.89055i	−0.326281	−	0.945273i	$-0.605796\pi$
$941$		−	1.48233e12i		−	1.89055i	0.326281	−	0.945273i	$-0.394204\pi$
$942$	8.21317e11			1.04306
$943$		−	5.11458e11i		−	0.646790i
$944$	1.17681e12	+	1.14455e12i	1.48190	+	1.44127i
$945$	1.16144e11			0.145636
$946$		−	1.05102e12i		−	1.31234i
$947$	1.33380e12			1.65840			0.829202	−	0.558950i	$-0.188796\pi$
$947$	1.33380e12			1.65840			0.829202	+	0.558950i	$0.188796\pi$
$948$	1.59769e12			1.97815
$949$	−4.76624e9			−0.00587639
$950$		−	5.03280e11i		−	0.617896i
$951$	2.57804e10			0.0315186
$952$		−	1.07116e12i		−	1.30409i
$953$	−7.31368e11			−0.886675			−0.443337	−	0.896355i	$-0.646206\pi$
$953$	−7.31368e11			−0.886675			−0.443337	+	0.896355i	$0.646206\pi$
$954$			8.28419e11i			1.00013i
$955$			1.48521e12i			1.78556i
$956$	−2.72119e12			−3.25783
$957$		−	9.47970e10i		−	0.113018i
$958$		−	6.59800e11i		−	0.783340i
$959$	4.49339e11			0.531251
$960$	2.86460e11			0.337271
$961$	1.69648e11			0.198910
$962$			5.99383e11i			0.699849i
$963$	−7.98653e10			−0.0928652
$964$	−3.16971e12			−3.67038
$965$	−9.99991e11			−1.15315
$966$	4.17477e11			0.479429
$967$		−	1.50872e12i		−	1.72545i	−0.505676	−	0.862723i	$-0.668757\pi$
$967$		−	1.50872e12i		−	1.72545i	0.505676	−	0.862723i	$-0.331243\pi$
$968$		−	5.04281e11i		−	0.574343i
$969$	1.70958e11			0.193908
$970$	3.15072e12			3.55896
$971$	−1.00628e12			−1.13198			−0.565992	−	0.824411i	$-0.691507\pi$
$971$	−1.00628e12			−1.13198			−0.565992	+	0.824411i	$0.691507\pi$
$972$	−1.32922e11			−0.148913
$973$	−9.39898e11			−1.04865
$974$		−	2.22526e12i		−	2.47255i
$975$		−	4.29677e11i		−	0.475470i
$976$			5.04246e11i			0.555704i
$977$			1.68814e12i			1.85281i	0.376531	+	0.926404i	$0.377117\pi$
$977$			1.68814e12i			1.85281i	−0.376531	+	0.926404i	$0.622883\pi$
$978$			1.14025e12i			1.24637i
$979$	−5.95028e11			−0.647749
$980$	−2.18914e12			−2.37339
$981$			2.66418e11i			0.287666i
$982$			1.48889e12i			1.60109i
$983$		−	7.83043e11i		−	0.838632i	−0.907840	−	0.419316i	$-0.862270\pi$
$983$		−	7.83043e11i		−	0.838632i	0.907840	−	0.419316i	$-0.137730\pi$
$984$			9.82916e11i			1.04842i
$985$	−6.37046e11			−0.676746
$986$		−	3.93897e11i		−	0.416750i
$987$			3.47794e11i			0.366483i
$988$		−	5.83188e11i		−	0.612042i
$989$	6.77132e11			0.707764
$990$	−7.25364e11			−0.755118
$991$		−	5.44855e11i		−	0.564919i	−0.959279	−	0.282459i	$-0.908850\pi$
$991$		−	5.44855e11i		−	0.564919i	0.959279	−	0.282459i	$-0.0911502\pi$
$992$	−1.17817e12			−1.21664
$993$	−8.57847e11			−0.882293
$994$			6.63988e11i			0.680166i
$995$	−1.45101e11			−0.148039
$996$			1.15853e11i			0.117725i
$997$	−3.40258e11			−0.344372			−0.172186	−	0.985064i	$-0.555083\pi$
$997$	−3.40258e11			−0.344372			−0.172186	+	0.985064i	$0.555083\pi$
$998$			3.31407e12i			3.34072i
$999$			9.19801e10i			0.0923490i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.9.c.a.58.76	yes	80
59.58	odd	2	inner	177.9.c.a.58.5	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.9.c.a.58.5	✓	80	59.58	odd	2	inner
177.9.c.a.58.76	yes	80	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	177.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+29.1592i q^{2} +46.7654 q^{3} -594.257 q^{4} -890.286 q^{5} +1363.64i q^{6} -1275.54 q^{7} -9863.29i q^{8} +2187.00 q^{9} +O(q^{10})\)	\(q+29.1592i q^{2} +46.7654 q^{3} -594.257 q^{4} -890.286 q^{5} +1363.64i q^{6} -1275.54 q^{7} -9863.29i q^{8} +2187.00 q^{9} -25960.0i q^{10} -12776.2i q^{11} -27790.6 q^{12} -22856.4i q^{13} -37193.6i q^{14} -41634.5 q^{15} +135476. q^{16} -85141.2 q^{17} +63771.1i q^{18} -42936.4 q^{19} +529059. q^{20} -59651.0 q^{21} +372544. q^{22} +240016. i q^{23} -461261. i q^{24} +401984. q^{25} +666475. q^{26} +102276. q^{27} +757997. q^{28} +158660. q^{29} -1.21403e6i q^{30} +826585. i q^{31} +1.42535e6i q^{32} -597485. i q^{33} -2.48265e6i q^{34} +1.13559e6 q^{35} -1.29964e6 q^{36} +899334. i q^{37} -1.25199e6i q^{38} -1.06889e6i q^{39} +8.78115e6i q^{40} -2.13093e6 q^{41} -1.73937e6i q^{42} -2.82120e6i q^{43} +7.59236e6i q^{44} -1.94706e6 q^{45} -6.99866e6 q^{46} -5.83048e6i q^{47} +6.33557e6 q^{48} -4.13780e6 q^{49} +1.17215e7i q^{50} -3.98166e6 q^{51} +1.35826e7i q^{52} +1.29905e7 q^{53} +2.98228e6i q^{54} +1.13745e7i q^{55} +1.25810e7i q^{56} -2.00794e6 q^{57} +4.62640e6i q^{58} +(8.68651e6 + 8.44837e6i) q^{59} +2.47416e7 q^{60} +3.72205e6i q^{61} -2.41025e7 q^{62} -2.78960e6 q^{63} -6.88034e6 q^{64} +2.03488e7i q^{65} +1.74222e7 q^{66} +3.14296e6i q^{67} +5.05958e7 q^{68} +1.12244e7i q^{69} +3.31130e7i q^{70} -1.78522e7 q^{71} -2.15710e7i q^{72} -208529. i q^{73} -2.62238e7 q^{74} +1.87989e7 q^{75} +2.55153e7 q^{76} +1.62966e7i q^{77} +3.11679e7 q^{78} -5.74903e7 q^{79} -1.20612e8 q^{80} +4.78297e6 q^{81} -6.21363e7i q^{82} -4.16878e6i q^{83} +3.54480e7 q^{84} +7.58000e7 q^{85} +8.22638e7 q^{86} +7.41980e6 q^{87} -1.26016e8 q^{88} -4.65731e7i q^{89} -5.67745e7i q^{90} +2.91543e7i q^{91} -1.42631e8i q^{92} +3.86556e7i q^{93} +1.70012e8 q^{94} +3.82257e7 q^{95} +6.66571e7i q^{96} +1.21368e8i q^{97} -1.20655e8i q^{98} -2.79416e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9}+O(q^{10}) \) 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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Database

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