LMFDB - Embedded newform 177.9.c.a.58.17

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			58.17
Character	$\chi$	$=$	177.58
Dual form			177.9.c.a.58.64

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-20.4347i q^{2} -46.7654 q^{3} -161.576 q^{4} -84.1426 q^{5} +955.636i q^{6} +4222.23 q^{7} -1929.52i q^{8} +2187.00 q^{9} +O(q^{10})$	\(q-20.4347i q^{2} -46.7654 q^{3} -161.576 q^{4} -84.1426 q^{5} +955.636i q^{6} +4222.23 q^{7} -1929.52i q^{8} +2187.00 q^{9} +1719.43i q^{10} +16999.9i q^{11} +7556.18 q^{12} -10850.2i q^{13} -86279.9i q^{14} +3934.96 q^{15} -80792.6 q^{16} +148049. q^{17} -44690.7i q^{18} -234.411 q^{19} +13595.5 q^{20} -197454. q^{21} +347387. q^{22} +436492. i q^{23} +90234.5i q^{24} -383545. q^{25} -221720. q^{26} -102276. q^{27} -682212. q^{28} -448042. q^{29} -80409.6i q^{30} +1.30895e6i q^{31} +1.15702e6i q^{32} -795005. i q^{33} -3.02533e6i q^{34} -355269. q^{35} -353368. q^{36} +2.71698e6i q^{37} +4790.12i q^{38} +507413. i q^{39} +162354. i q^{40} -4.85649e6 q^{41} +4.03491e6i q^{42} +2.79551e6i q^{43} -2.74678e6i q^{44} -184020. q^{45} +8.91959e6 q^{46} +7.12970e6i q^{47} +3.77830e6 q^{48} +1.20624e7 q^{49} +7.83762e6i q^{50} -6.92355e6 q^{51} +1.75313e6i q^{52} +2.15001e6 q^{53} +2.08998e6i q^{54} -1.43041e6i q^{55} -8.14685e6i q^{56} +10962.3 q^{57} +9.15560e6i q^{58} +(1.16333e7 + 3.39063e6i) q^{59} -635797. q^{60} -1.41049e7i q^{61} +2.67480e7 q^{62} +9.23401e6 q^{63} +2.96035e6 q^{64} +912962. i q^{65} -1.62457e7 q^{66} +3.51125e6i q^{67} -2.39212e7 q^{68} -2.04127e7i q^{69} +7.25981e6i q^{70} -7.59726e6 q^{71} -4.21985e6i q^{72} -3.04904e7i q^{73} +5.55206e7 q^{74} +1.79366e7 q^{75} +37875.3 q^{76} +7.17772e7i q^{77} +1.03688e7 q^{78} -6.38797e7 q^{79} +6.79810e6 q^{80} +4.78297e6 q^{81} +9.92409e7i q^{82} +7.86934e7i q^{83} +3.19039e7 q^{84} -1.24572e7 q^{85} +5.71255e7 q^{86} +2.09528e7 q^{87} +3.28015e7 q^{88} -7.28576e6i q^{89} +3.76039e6i q^{90} -4.58119e7i q^{91} -7.05269e7i q^{92} -6.12136e7i q^{93} +1.45693e8 q^{94} +19723.9 q^{95} -5.41083e7i q^{96} -8.07168e7i q^{97} -2.46491e8i q^{98} +3.71787e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	20.4347i		−	1.27717i	−0.769552	−	0.638584i	$-0.779520\pi$
$2$		−	20.4347i		−	1.27717i	0.769552	−	0.638584i	$-0.220480\pi$
$3$	−46.7654			−0.577350
$3$	−46.7654			−0.577350
$4$	−161.576			−0.631158
$5$	−84.1426			−0.134628			−0.0673140	−	0.997732i	$-0.521443\pi$
$5$	−84.1426			−0.134628			−0.0673140	+	0.997732i	$0.521443\pi$
$6$			955.636i			0.737373i
$7$	4222.23			1.75853			0.879264	−	0.476335i	$-0.158035\pi$
$7$	4222.23			1.75853			0.879264	+	0.476335i	$0.158035\pi$
$8$		−	1929.52i		−	0.471073i
$9$	2187.00			0.333333
$10$			1719.43i			0.171943i
$11$			16999.9i			1.16111i	0.814220	+	0.580557i	$0.197165\pi$
$11$			16999.9i			1.16111i	−0.814220	+	0.580557i	$0.802835\pi$
$12$	7556.18			0.364399
$13$		−	10850.2i		−	0.379895i	−0.981794	−	0.189948i	$-0.939168\pi$
$13$		−	10850.2i		−	0.379895i	0.981794	−	0.189948i	$-0.0608318\pi$
$14$		−	86279.9i		−	2.24594i
$15$	3934.96			0.0777276
$16$	−80792.6			−1.23280
$17$	148049.			1.77259			0.886295	−	0.463121i	$-0.153270\pi$
$17$	148049.			1.77259			0.886295	+	0.463121i	$0.153270\pi$
$18$		−	44690.7i		−	0.425723i
$19$	−234.411			−0.00179872			−0.000899360	−	1.00000i	$-0.500286\pi$
$19$	−234.411			−0.00179872			−0.000899360		1.00000i	$0.500286\pi$
$20$	13595.5			0.0849716
$21$	−197454.			−1.01529
$22$	347387.			1.48294
$23$			436492.i			1.55979i	0.625912	+	0.779894i	$0.284727\pi$
$23$			436492.i			1.55979i	−0.625912	+	0.779894i	$0.715273\pi$
$24$			90234.5i			0.271974i
$25$	−383545.			−0.981875
$26$	−221720.			−0.485190
$27$	−102276.			−0.192450
$28$	−682212.			−1.10991
$29$	−448042.			−0.633471			−0.316735	−	0.948514i	$-0.602587\pi$
$29$	−448042.			−0.633471			−0.316735	+	0.948514i	$0.602587\pi$
$30$		−	80409.6i		−	0.0992712i
$31$			1.30895e6i			1.41735i	0.705536	+	0.708674i	$0.250706\pi$
$31$			1.30895e6i			1.41735i	−0.705536	+	0.708674i	$0.749294\pi$
$32$			1.15702e6i			1.10342i
$33$		−	795005.i		−	0.670369i
$34$		−	3.02533e6i		−	2.26390i
$35$	−355269.			−0.236747
$36$	−353368.			−0.210386
$37$			2.71698e6i			1.44970i	0.688905	+	0.724852i	$0.258092\pi$
$37$			2.71698e6i			1.44970i	−0.688905	+	0.724852i	$0.741908\pi$
$38$			4790.12i			0.00229727i
$39$			507413.i			0.219333i
$40$			162354.i			0.0634197i
$41$	−4.85649e6			−1.71865			−0.859324	−	0.511431i	$-0.829116\pi$
$41$	−4.85649e6			−1.71865			−0.859324	+	0.511431i	$0.829116\pi$
$42$			4.03491e6i			1.29669i
$43$			2.79551e6i			0.817689i	0.912604	+	0.408844i	$0.134068\pi$
$43$			2.79551e6i			0.817689i	−0.912604	+	0.408844i	$0.865932\pi$
$44$		−	2.74678e6i		−	0.732846i
$45$	−184020.			−0.0448760
$46$	8.91959e6			1.99211
$47$			7.12970e6i			1.46110i	0.682860	+	0.730549i	$0.260736\pi$
$47$			7.12970e6i			1.46110i	−0.682860	+	0.730549i	$0.739264\pi$
$48$	3.77830e6			0.711756
$49$	1.20624e7			2.09242
$50$			7.83762e6i			1.25402i
$51$	−6.92355e6			−1.02341
$52$			1.75313e6i			0.239774i
$53$	2.15001e6			0.272482			0.136241	−	0.990676i	$-0.456498\pi$
$53$	2.15001e6			0.272482			0.136241	+	0.990676i	$0.456498\pi$
$54$			2.08998e6i			0.245791i
$55$		−	1.43041e6i		−	0.156318i
$56$		−	8.14685e6i		−	0.828395i
$57$	10962.3			0.00103849
$58$			9.15560e6i			0.809049i
$59$	1.16333e7	+	3.39063e6i	0.960054	+	0.279816i
$59$	1.16333e7	+	3.39063e6i	0.960054	+	0.279816i
$60$	−635797.			−0.0490584
$61$		−	1.41049e7i		−	1.01871i	−0.860557	−	0.509355i	$-0.829884\pi$
$61$		−	1.41049e7i		−	1.01871i	0.860557	−	0.509355i	$-0.170116\pi$
$62$	2.67480e7			1.81019
$63$	9.23401e6			0.586176
$64$	2.96035e6			0.176451
$65$			912962.i			0.0511446i
$66$	−1.62457e7			−0.856174
$67$			3.51125e6i			0.174246i	0.996198	+	0.0871230i	$0.0277673\pi$
$67$			3.51125e6i			0.174246i	−0.996198	+	0.0871230i	$0.972233\pi$
$68$	−2.39212e7			−1.11878
$69$		−	2.04127e7i		−	0.900544i
$70$			7.25981e6i			0.302366i
$71$	−7.59726e6			−0.298967			−0.149484	−	0.988764i	$-0.547761\pi$
$71$	−7.59726e6			−0.298967			−0.149484	+	0.988764i	$0.547761\pi$
$72$		−	4.21985e6i		−	0.157024i
$73$		−	3.04904e7i		−	1.07367i	−0.843687	−	0.536836i	$-0.819619\pi$
$73$		−	3.04904e7i		−	1.07367i	0.843687	−	0.536836i	$-0.180381\pi$
$74$	5.55206e7			1.85151
$75$	1.79366e7			0.566886
$76$	37875.3			0.00113528
$77$			7.17772e7i			2.04185i
$78$	1.03688e7			0.280125
$79$	−6.38797e7			−1.64004			−0.820020	−	0.572335i	$-0.806038\pi$
$79$	−6.38797e7			−1.64004			−0.820020	+	0.572335i	$0.806038\pi$
$80$	6.79810e6			0.165969
$81$	4.78297e6			0.111111
$82$			9.92409e7i			2.19500i
$83$			7.86934e7i			1.65816i	0.559131	+	0.829079i	$0.311135\pi$
$83$			7.86934e7i			1.65816i	−0.559131	+	0.829079i	$0.688865\pi$
$84$	3.19039e7			0.640806
$85$	−1.24572e7			−0.238640
$86$	5.71255e7			1.04433
$87$	2.09528e7			0.365735
$88$	3.28015e7			0.546969
$89$		−	7.28576e6i		−	0.116122i	−0.998313	−	0.0580611i	$-0.981508\pi$
$89$		−	7.28576e6i		−	0.116122i	0.998313	−	0.0580611i	$-0.0184918\pi$
$90$			3.76039e6i			0.0573142i
$91$		−	4.58119e7i		−	0.668056i
$92$		−	7.05269e7i		−	0.984472i
$93$		−	6.12136e7i		−	0.818307i
$94$	1.45693e8			1.86607
$95$	19723.9			0.000242158
$96$		−	5.41083e7i		−	0.637058i
$97$		−	8.07168e7i		−	0.911752i	−0.890043	−	0.455876i	$-0.849326\pi$
$97$		−	8.07168e7i		−	0.911752i	0.890043	−	0.455876i	$-0.150674\pi$
$98$		−	2.46491e8i		−	2.67237i
$99$			3.71787e7i			0.387038i
$100$	6.19718e7			0.619718
$101$		−	8.63367e7i		−	0.829679i	−0.909895	−	0.414839i	$-0.863838\pi$
$101$		−	8.63367e7i		−	0.829679i	0.909895	−	0.414839i	$-0.136162\pi$
$102$			1.41480e8i			1.30706i
$103$		−	375851.i		−	0.00333939i	−0.999999	−	0.00166970i	$-0.999469\pi$
$103$		−	375851.i		−	0.00333939i	0.999999	−	0.00166970i	$-0.000531481\pi$
$104$	−2.09356e7			−0.178958
$105$	1.66143e7			0.136686
$106$		−	4.39348e7i		−	0.348005i
$107$	6.61773e7			0.504863			0.252432	−	0.967615i	$-0.418770\pi$
$107$	6.61773e7			0.504863			0.252432	+	0.967615i	$0.418770\pi$
$108$	1.65254e7			0.121466
$109$			2.66505e7i			0.188799i	0.995534	+	0.0943995i	$0.0300931\pi$
$109$			2.66505e7i			0.188799i	−0.995534	+	0.0943995i	$0.969907\pi$
$110$	−2.92300e7			−0.199645
$111$		−	1.27060e8i		−	0.836987i
$112$	−3.41125e8			−2.16791
$113$			5.90478e7i			0.362151i	0.983469	+	0.181076i	$0.0579579\pi$
$113$			5.90478e7i			0.362151i	−0.983469	+	0.181076i	$0.942042\pi$
$114$		−	224012.i		−	0.00132633i
$115$		−	3.67276e7i		−	0.209991i
$116$	7.23930e7			0.399820
$117$		−	2.37294e7i		−	0.126632i
$118$	6.92865e7	−	2.37723e8i	0.357372	−	1.22615i
$119$	6.25094e8			3.11715
$120$		−	7.59256e6i		−	0.0366154i
$121$	−7.46364e7			−0.348184
$122$	−2.88229e8			−1.30106
$123$	2.27116e8			0.992262
$124$		−	2.11496e8i		−	0.894571i
$125$	6.51406e7			0.266816
$126$		−	1.88694e8i		−	0.748645i
$127$	−2.53094e8			−0.972898			−0.486449	−	0.873709i	$-0.661708\pi$
$127$	−2.53094e8			−0.972898			−0.486449	+	0.873709i	$0.661708\pi$
$128$			2.35702e8i			0.878059i
$129$		−	1.30733e8i		−	0.472093i
$130$	1.86561e7			0.0653202
$131$			6.07442e7i			0.206262i	0.994668	+	0.103131i	$0.0328861\pi$
$131$			6.07442e7i			0.206262i	−0.994668	+	0.103131i	$0.967114\pi$
$132$			1.28454e8i			0.423109i
$133$	−989736.			−0.00316310
$134$	7.17513e7			0.222541
$135$	8.60575e6			0.0259092
$136$		−	2.85662e8i		−	0.835020i
$137$	2.93273e8			0.832512			0.416256	−	0.909248i	$-0.363342\pi$
$137$	2.93273e8			0.832512			0.416256	+	0.909248i	$0.363342\pi$
$138$	−4.17128e8			−1.15015
$139$	6.58855e8			1.76494			0.882472	−	0.470365i	$-0.155878\pi$
$139$	6.58855e8			1.76494			0.882472	+	0.470365i	$0.155878\pi$
$140$	5.74031e7			0.149425
$141$		−	3.33423e8i		−	0.843566i
$142$			1.55248e8i			0.381831i
$143$	1.84452e8			0.441101
$144$	−1.76693e8			−0.410933
$145$	3.76994e7			0.0852830
$146$	−6.23062e8			−1.37126
$147$	−5.64102e8			−1.20806
$148$		−	4.39000e8i		−	0.914992i
$149$			5.48129e8i			1.11208i	0.831154	+	0.556042i	$0.187681\pi$
$149$			5.48129e8i			1.11208i	−0.831154	+	0.556042i	$0.812319\pi$
$150$		−	3.66529e8i		−	0.724009i
$151$			1.29386e8i			0.248874i	0.992228	+	0.124437i	$0.0397125\pi$
$151$			1.29386e8i			0.248874i	−0.992228	+	0.124437i	$0.960288\pi$
$152$			452300.i			0.000847329i
$153$	3.23782e8			0.590864
$154$	1.46675e9			2.60779
$155$		−	1.10139e8i		−	0.190815i
$156$		−	8.19860e7i		−	0.138434i
$157$		−	9.49411e8i		−	1.56263i	−0.624138	−	0.781314i	$-0.714550\pi$
$157$		−	9.49411e8i		−	1.56263i	0.624138	−	0.781314i	$-0.285450\pi$
$158$			1.30536e9i			2.09461i
$159$	−1.00546e8			−0.157317
$160$		−	9.73543e7i		−	0.148551i
$161$			1.84297e9i			2.74293i
$162$		−	9.77385e7i		−	0.141908i
$163$	5.58380e8			0.791006			0.395503	−	0.918465i	$-0.370570\pi$
$163$	5.58380e8			0.791006			0.395503	+	0.918465i	$0.370570\pi$
$164$	7.84695e8			1.08474
$165$			6.68937e7i			0.0902505i
$166$	1.60808e9			2.11775
$167$	−4.71534e8			−0.606244			−0.303122	−	0.952952i	$-0.598029\pi$
$167$	−4.71534e8			−0.606244			−0.303122	+	0.952952i	$0.598029\pi$
$168$			3.80990e8i			0.478274i
$169$	6.98004e8			0.855680
$170$			2.54559e8i			0.304784i
$171$	−512657.			−0.000599573
$172$		−	4.51689e8i		−	0.516091i
$173$		−	1.77517e8i		−	0.198178i	−0.995079	−	0.0990889i	$-0.968407\pi$
$173$		−	1.77517e8i		−	0.198178i	0.995079	−	0.0990889i	$-0.0315928\pi$
$174$		−	4.28165e8i		−	0.467104i
$175$	−1.61941e9			−1.72666
$176$		−	1.37346e9i		−	1.43142i
$177$	−5.44036e8	−	1.58564e8i	−0.554287	−	0.161552i
$178$	−1.48882e8			−0.148307
$179$			9.28138e8i			0.904067i	0.892001	+	0.452033i	$0.149301\pi$
$179$			9.28138e8i			0.904067i	−0.892001	+	0.452033i	$0.850699\pi$
$180$	2.97333e7			0.0283239
$181$	2.70900e7			0.0252403			0.0126202	−	0.999920i	$-0.495983\pi$
$181$	2.70900e7			0.0252403			0.0126202	+	0.999920i	$0.495983\pi$
$182$	−9.36152e8			−0.853220
$183$			6.59621e8i			0.588152i
$184$	8.42219e8			0.734774
$185$		−	2.28613e8i		−	0.195171i
$186$	−1.25088e9			−1.04512
$187$			2.51680e9i			2.05818i
$188$		−	1.15199e9i		−	0.922184i
$189$	−4.31832e8			−0.338429
$190$		−	403053.i		−	0.000309277i
$191$			1.66805e9i			1.25336i	0.779277	+	0.626680i	$0.215587\pi$
$191$			1.66805e9i			1.25336i	−0.779277	+	0.626680i	$0.784413\pi$
$192$	−1.38442e8			−0.101874
$193$	−1.59245e9			−1.14772			−0.573860	−	0.818953i	$-0.694555\pi$
$193$	−1.59245e9			−1.14772			−0.573860	+	0.818953i	$0.694555\pi$
$194$	−1.64942e9			−1.16446
$195$		−	4.26950e7i		−	0.0295283i
$196$	−1.94900e9			−1.32065
$197$	2.77911e9			1.84519			0.922593	−	0.385774i	$-0.126066\pi$
$197$	2.77911e9			1.84519			0.922593	+	0.385774i	$0.126066\pi$
$198$	7.59735e8			0.494312
$199$	2.17073e9			1.38418			0.692092	−	0.721809i	$-0.256689\pi$
$199$	2.17073e9			1.38418			0.692092	+	0.721809i	$0.256689\pi$
$200$			7.40056e8i			0.462535i
$201$		−	1.64205e8i		−	0.100601i
$202$	−1.76426e9			−1.05964
$203$	−1.89173e9			−1.11398
$204$	1.11868e9			0.645931
$205$	4.08638e8			0.231378
$206$	−7.68040e6			−0.00426496
$207$			9.54609e8i			0.519929i
$208$			8.76615e8i			0.468334i
$209$		−	3.98495e6i		−	0.00208852i
$210$		−	3.39508e8i		−	0.174571i
$211$		−	2.21937e9i		−	1.11970i	−0.828595	−	0.559849i	$-0.810859\pi$
$211$		−	2.21937e9i		−	1.11970i	0.828595	−	0.559849i	$-0.189141\pi$
$212$	−3.47391e8			−0.171979
$213$	3.55288e8			0.172609
$214$		−	1.35231e9i		−	0.644795i
$215$		−	2.35222e8i		−	0.110084i
$216$			1.97343e8i			0.0906581i
$217$			5.52669e9i			2.49245i
$218$	5.44595e8			0.241128
$219$			1.42589e9i			0.619885i
$220$			2.31121e8i			0.0986617i
$221$		−	1.60635e9i		−	0.673399i
$222$	−2.59644e9			−1.06897
$223$	−2.31335e9			−0.935454			−0.467727	−	0.883873i	$-0.654927\pi$
$223$	−2.31335e9			−0.935454			−0.467727	+	0.883873i	$0.654927\pi$
$224$			4.88518e9i			1.94039i
$225$	−8.38813e8			−0.327292
$226$	1.20662e9			0.462528
$227$			4.23736e9i			1.59585i	0.602757	+	0.797925i	$0.294069\pi$
$227$			4.23736e9i			1.59585i	−0.602757	+	0.797925i	$0.705931\pi$
$228$	−1.77125e6			−0.000655452
$229$		−	3.99400e9i		−	1.45233i	−0.687518	−	0.726167i	$-0.741300\pi$
$229$		−	3.99400e9i		−	1.45233i	0.687518	−	0.726167i	$-0.258700\pi$
$230$	−7.50517e8			−0.268194
$231$		−	3.35669e9i		−	1.17886i
$232$			8.64504e8i			0.298411i
$233$			2.46144e8i			0.0835151i	0.999128	+	0.0417575i	$0.0132957\pi$
$233$			2.46144e8i			0.0835151i	−0.999128	+	0.0417575i	$0.986704\pi$
$234$	−4.84902e8			−0.161730
$235$		−	5.99911e8i		−	0.196705i
$236$	−1.87967e9	−	5.47846e8i	−0.605946	−	0.176608i
$237$	2.98736e9			0.946877
$238$		−	1.27736e10i		−	3.98112i
$239$	−1.94711e9			−0.596760			−0.298380	−	0.954447i	$-0.596446\pi$
$239$	−1.94711e9			−0.596760			−0.298380	+	0.954447i	$0.596446\pi$
$240$	−3.17916e8			−0.0958223
$241$	−7.52200e8			−0.222980			−0.111490	−	0.993766i	$-0.535562\pi$
$241$	−7.52200e8			−0.222980			−0.111490	+	0.993766i	$0.535562\pi$
$242$			1.52517e9i			0.444690i
$243$	−2.23677e8			−0.0641500
$244$			2.27902e9i			0.642967i
$245$	−1.01496e9			−0.281699
$246$		−	4.64104e9i		−	1.26729i
$247$			2.54340e6i			0.000683325i
$248$	2.52564e9			0.667675
$249$		−	3.68013e9i		−	0.957338i
$250$		−	1.33113e9i		−	0.340769i
$251$	−6.59545e9			−1.66169			−0.830845	−	0.556505i	$-0.812142\pi$
$251$	−6.59545e9			−1.66169			−0.830845	+	0.556505i	$0.812142\pi$
$252$	−1.49200e9			−0.369970
$253$	−7.42031e9			−1.81109
$254$			5.17190e9i			1.24255i
$255$	5.82565e8			0.137779
$256$	5.57435e9			1.29788
$257$	7.30477e9			1.67446			0.837228	−	0.546854i	$-0.184175\pi$
$257$	7.30477e9			1.67446			0.837228	+	0.546854i	$0.184175\pi$
$258$	−2.67149e9			−0.602942
$259$			1.14717e10i			2.54934i
$260$		−	1.47513e8i		−	0.0322803i
$261$	−9.79868e8			−0.211157
$262$	1.24129e9			0.263432
$263$	−3.41679e9			−0.714160			−0.357080	−	0.934074i	$-0.616228\pi$
$263$	−3.41679e9			−0.714160			−0.357080	+	0.934074i	$0.616228\pi$
$264$	−1.53397e9			−0.315793
$265$	−1.80907e8			−0.0366837
$266$			2.02249e7i			0.00403981i
$267$			3.40721e8i			0.0670431i
$268$		−	5.67335e8i		−	0.109977i
$269$		−	4.46436e9i		−	0.852610i	−0.904580	−	0.426305i	$-0.859815\pi$
$269$		−	4.46436e9i		−	0.852610i	0.904580	−	0.426305i	$-0.140185\pi$
$270$		−	1.75856e8i		−	0.0330904i
$271$	−7.44341e9			−1.38005			−0.690025	−	0.723785i	$-0.742401\pi$
$271$	−7.44341e9			−1.38005			−0.690025	+	0.723785i	$0.742401\pi$
$272$	−1.19612e10			−2.18525
$273$			2.14241e9i			0.385702i
$274$		−	5.99295e9i		−	1.06326i
$275$		−	6.52021e9i		−	1.14007i
$276$			3.29822e9i			0.568385i
$277$	−3.80187e8			−0.0645770			−0.0322885	−	0.999479i	$-0.510280\pi$
$277$	−3.80187e8			−0.0645770			−0.0322885	+	0.999479i	$0.510280\pi$
$278$		−	1.34635e10i		−	2.25413i
$279$			2.86268e9i			0.472450i
$280$			6.85497e8i			0.111525i
$281$	−1.92388e9			−0.308570			−0.154285	−	0.988026i	$-0.549307\pi$
$281$	−1.92388e9			−0.308570			−0.154285	+	0.988026i	$0.549307\pi$
$282$	−6.81339e9			−1.07738
$283$		−	9.46539e9i		−	1.47568i	−0.674975	−	0.737841i	$-0.735846\pi$
$283$		−	9.46539e9i		−	1.47568i	0.674975	−	0.737841i	$-0.264154\pi$
$284$	1.22754e9			0.188695
$285$	−922397.			−0.000139810
$286$		−	3.76921e9i		−	0.563360i
$287$	−2.05052e10			−3.02229
$288$			2.53039e9i			0.367805i
$289$	1.49426e10			2.14208
$290$		−	7.70375e8i		−	0.108921i
$291$			3.77475e9i			0.526400i
$292$			4.92653e9i			0.677657i
$293$	8.12893e9			1.10297			0.551484	−	0.834186i	$-0.314062\pi$
$293$	8.12893e9			1.10297			0.551484	+	0.834186i	$0.314062\pi$
$294$			1.15273e10i			1.54290i
$295$	−9.78857e8	−	2.85296e8i	−0.129250	−	0.0376711i
$296$	5.24245e9			0.682916
$297$		−	1.73868e9i		−	0.223456i
$298$	1.12008e10			1.42032
$299$	4.73602e9			0.592556
$300$	−2.89814e9			−0.357795
$301$			1.18033e10i			1.43793i
$302$	2.64396e9			0.317854
$303$			4.03757e9i			0.479015i
$304$	1.89387e7			0.00221746
$305$			1.18682e9i			0.137147i
$306$		−	6.61639e9i		−	0.754632i
$307$	4.09629e9			0.461144			0.230572	−	0.973055i	$-0.425940\pi$
$307$	4.09629e9			0.461144			0.230572	+	0.973055i	$0.425940\pi$
$308$		−	1.15975e10i		−	1.28873i
$309$			1.75768e7i			0.00192800i
$310$	−2.25065e9			−0.243703
$311$	1.03626e10			1.10771			0.553854	−	0.832614i	$-0.313157\pi$
$311$	1.03626e10			1.10771			0.553854	+	0.832614i	$0.313157\pi$
$312$	9.79061e8			0.103322
$313$			2.85666e9i			0.297633i	0.988865	+	0.148816i	$0.0475464\pi$
$313$			2.85666e9i			0.297633i	−0.988865	+	0.148816i	$0.952454\pi$
$314$	−1.94009e10			−1.99574
$315$	−7.76973e8			−0.0789158
$316$	1.03215e10			1.03512
$317$	1.46869e10			1.45443			0.727216	−	0.686408i	$-0.240814\pi$
$317$	1.46869e10			1.45443			0.727216	+	0.686408i	$0.240814\pi$
$318$			2.05463e9i			0.200921i
$319$		−	7.61665e9i		−	0.735531i
$320$	−2.49091e8			−0.0237552
$321$	−3.09480e9			−0.291483
$322$	3.76605e10			3.50318
$323$	−3.47042e7			−0.00318839
$324$	−7.72815e8			−0.0701287
$325$			4.16153e9i			0.373010i
$326$		−	1.14103e10i		−	1.01025i
$327$		−	1.24632e9i		−	0.109003i
$328$			9.37067e9i			0.809609i
$329$			3.01032e10i			2.56938i
$330$	1.36695e9			0.115265
$331$	6.01117e9			0.500780			0.250390	−	0.968145i	$-0.419441\pi$
$331$	6.01117e9			0.500780			0.250390	+	0.968145i	$0.419441\pi$
$332$		−	1.27150e10i		−	1.04656i
$333$			5.94203e9i			0.483235i
$334$			9.63566e9i			0.774275i
$335$		−	2.95446e8i		−	0.0234584i
$336$	1.59528e10			1.25164
$337$		−	9.23729e9i		−	0.716185i	−0.933686	−	0.358092i	$-0.883427\pi$
$337$		−	9.23729e9i		−	0.716185i	0.933686	−	0.358092i	$-0.116573\pi$
$338$		−	1.42635e10i		−	1.09285i
$339$		−	2.76139e9i		−	0.209088i
$340$	2.01279e9			0.150620
$341$	−2.22520e10			−1.64570
$342$			1.04760e7i			0.000765756i
$343$	2.65898e10			1.92105
$344$	5.39399e9			0.385191
$345$			1.71758e9i			0.121238i
$346$	−3.62750e9			−0.253106
$347$		−	4.51897e9i		−	0.311689i	−0.987782	−	0.155844i	$-0.950190\pi$
$347$		−	4.51897e9i		−	0.311689i	0.987782	−	0.155844i	$-0.0498098\pi$
$348$	−3.38549e9			−0.230836
$349$		−	9.56963e9i		−	0.645050i	−0.946561	−	0.322525i	$-0.895468\pi$
$349$		−	9.56963e9i		−	0.645050i	0.946561	−	0.322525i	$-0.104532\pi$
$350$			3.30922e10i			2.20523i
$351$			1.10971e9i			0.0731109i
$352$	−1.96691e10			−1.28119
$353$			1.43592e10i			0.924765i	0.886680	+	0.462383i	$0.153005\pi$
$353$			1.43592e10i			0.924765i	−0.886680	+	0.462383i	$0.846995\pi$
$354$	−3.24021e9	+	1.11172e10i	−0.206329	+	0.707918i
$355$	6.39253e8			0.0402494
$356$			1.17721e9i			0.0732914i
$357$	−2.92328e10			−1.79969
$358$	1.89662e10			1.15464
$359$	−1.48076e10			−0.891468			−0.445734	−	0.895165i	$-0.647057\pi$
$359$	−1.48076e10			−0.891468			−0.445734	+	0.895165i	$0.647057\pi$
$360$			3.55069e8i			0.0211399i
$361$	−1.69835e10			−0.999997
$362$		−	5.53576e8i		−	0.0322361i
$363$	3.49040e9			0.201024
$364$			7.40213e9i			0.421649i
$365$			2.56554e9i			0.144546i
$366$	1.34791e10			0.751169
$367$		−	8.19127e9i		−	0.451530i	−0.974182	−	0.225765i	$-0.927512\pi$
$367$		−	8.19127e9i		−	0.451530i	0.974182	−	0.225765i	$-0.0724882\pi$
$368$		−	3.52654e10i		−	1.92290i
$369$	−1.06211e10			−0.572883
$370$	−4.67164e9			−0.249266
$371$	9.07783e9			0.479167
$372$			9.89068e9i			0.516481i
$373$	−2.78651e9			−0.143955			−0.0719773	−	0.997406i	$-0.522931\pi$
$373$	−2.78651e9			−0.143955			−0.0719773	+	0.997406i	$0.522931\pi$
$374$	5.14301e10			2.62864
$375$	−3.04633e9			−0.154046
$376$	1.37569e10			0.688284
$377$			4.86134e9i			0.240652i
$378$			8.82435e9i			0.432231i
$379$	6.27714e9			0.304232			0.152116	−	0.988363i	$-0.451391\pi$
$379$	6.27714e9			0.304232			0.152116	+	0.988363i	$0.451391\pi$
$380$	−3.18692e6			−0.000152840
$381$	1.18360e10			0.561703
$382$	3.40861e10			1.60075
$383$	−2.98388e10			−1.38671			−0.693356	−	0.720596i	$-0.743868\pi$
$383$	−2.98388e10			−1.38671			−0.693356	+	0.720596i	$0.743868\pi$
$384$		−	1.10227e10i		−	0.506948i
$385$		−	6.03952e9i		−	0.274890i
$386$			3.25412e10i			1.46583i
$387$			6.11379e9i			0.272563i
$388$			1.30419e10i			0.575460i
$389$	−7.12005e9			−0.310946			−0.155473	−	0.987840i	$-0.549690\pi$
$389$	−7.12005e9			−0.310946			−0.155473	+	0.987840i	$0.549690\pi$
$390$	−8.72459e8			−0.0377126
$391$			6.46221e10i			2.76486i
$392$		−	2.32746e10i		−	0.985683i
$393$		−	2.84073e9i		−	0.119086i
$394$		−	5.67902e10i		−	2.35661i
$395$	5.37500e9			0.220795
$396$		−	6.00720e9i		−	0.244282i
$397$			8.70816e9i			0.350562i	0.984518	+	0.175281i	$0.0560833\pi$
$397$			8.70816e9i			0.350562i	−0.984518	+	0.175281i	$0.943917\pi$
$398$		−	4.43582e10i		−	1.76784i
$399$	4.62854e7			0.00182622
$400$	3.09876e10			1.21045
$401$		−	4.74740e10i		−	1.83602i	−0.396555	−	0.918011i	$-0.629794\pi$
$401$		−	4.74740e10i		−	1.83602i	0.396555	−	0.918011i	$-0.370206\pi$
$402$	−3.35548e9			−0.128484
$403$	1.42024e10			0.538444
$404$			1.39500e10i			0.523658i
$405$	−4.02451e8			−0.0149587
$406$			3.86570e10i			1.42273i
$407$	−4.61882e10			−1.68327
$408$			1.33591e10i			0.482099i
$409$			2.06671e10i			0.738563i	0.929318	+	0.369281i	$0.120396\pi$
$409$			2.06671e10i			0.738563i	−0.929318	+	0.369281i	$0.879604\pi$
$410$		−	8.35038e9i		−	0.295509i
$411$	−1.37150e10			−0.480651
$412$			6.07287e7i			0.00210768i
$413$	4.91185e10	+	1.43160e10i	1.68828	+	0.492064i
$414$	1.95071e10			0.664037
$415$		−	6.62147e9i		−	0.223235i
$416$	1.25538e10			0.419183
$417$	−3.08116e10			−1.01899
$418$	−8.14313e7			−0.00266739
$419$		−	5.71901e10i		−	1.85551i	−0.373184	−	0.927757i	$-0.621734\pi$
$419$		−	5.71901e10i		−	1.85551i	0.373184	−	0.927757i	$-0.378266\pi$
$420$	−2.68448e9			−0.0862705
$421$		−	4.00029e10i		−	1.27339i	−0.771114	−	0.636697i	$-0.780300\pi$
$421$		−	4.00029e10i		−	1.27339i	0.771114	−	0.636697i	$-0.219700\pi$
$422$	−4.53522e10			−1.43004
$423$			1.55926e10i			0.487033i
$424$		−	4.14848e9i		−	0.128359i
$425$	−5.67833e10			−1.74046
$426$		−	7.26021e9i		−	0.220450i
$427$		−	5.95540e10i		−	1.79143i
$428$	−1.06927e10			−0.318649
$429$	−8.62595e9			−0.254670
$430$	−4.80668e9			−0.140596
$431$			1.70819e10i			0.495024i	0.968885	+	0.247512i	$0.0796130\pi$
$431$			1.70819e10i			0.495024i	−0.968885	+	0.247512i	$0.920387\pi$
$432$	8.26314e9			0.237252
$433$	4.49387e10			1.27841			0.639203	−	0.769038i	$-0.279264\pi$
$433$	4.49387e10			1.27841			0.639203	+	0.769038i	$0.279264\pi$
$434$	1.12936e11			3.18327
$435$	−1.76303e9			−0.0492381
$436$		−	4.30610e9i		−	0.119162i
$437$		−	1.02319e8i		−	0.00280562i
$438$	2.91377e10			0.791697
$439$	−3.55016e10			−0.955850			−0.477925	−	0.878401i	$-0.658611\pi$
$439$	−3.55016e10			−0.955850			−0.477925	+	0.878401i	$0.658611\pi$
$440$	−2.76000e9			−0.0736374
$441$	2.63804e10			0.697474
$442$	−3.28253e10			−0.860043
$443$		−	3.35104e9i		−	0.0870092i	−0.999053	−	0.0435046i	$-0.986148\pi$
$443$		−	3.35104e9i		−	0.0870092i	0.999053	−	0.0435046i	$-0.0138523\pi$
$444$			2.05300e10i			0.528271i
$445$			6.13043e8i			0.0156333i
$446$			4.72726e10i			1.19473i
$447$		−	2.56335e10i		−	0.642062i
$448$	1.24993e10			0.310293
$449$	−2.40863e10			−0.592632			−0.296316	−	0.955090i	$-0.595758\pi$
$449$	−2.40863e10			−0.592632			−0.296316	+	0.955090i	$0.595758\pi$
$450$			1.71409e10i			0.418007i
$451$		−	8.25597e10i		−	1.99555i
$452$		−	9.54074e9i		−	0.228575i
$453$		−	6.05079e9i		−	0.143688i
$454$	8.65892e10			2.03817
$455$			3.85473e9i			0.0899391i
$456$		−	2.11520e7i		−	0.000489205i
$457$		−	6.83044e10i		−	1.56597i	−0.622040	−	0.782985i	$-0.713696\pi$
$457$		−	6.83044e10i		−	1.56597i	0.622040	−	0.782985i	$-0.286304\pi$
$458$	−8.16162e10			−1.85487
$459$	−1.51418e10			−0.341135
$460$			5.93431e9i			0.132538i
$461$	4.28118e9			0.0947894			0.0473947	−	0.998876i	$-0.484908\pi$
$461$	4.28118e9			0.0947894			0.0473947	+	0.998876i	$0.484908\pi$
$462$	−6.85929e10			−1.50561
$463$			6.77595e10i			1.47450i	0.675618	+	0.737252i	$0.263877\pi$
$463$			6.77595e10i			1.47450i	−0.675618	+	0.737252i	$0.736123\pi$
$464$	3.61985e10			0.780941
$465$			5.15067e9i			0.110167i
$466$	5.02987e9			0.106663
$467$			4.88768e10i			1.02763i	0.857902	+	0.513814i	$0.171768\pi$
$467$			4.88768e10i			1.02763i	−0.857902	+	0.513814i	$0.828232\pi$
$468$			3.83411e9i			0.0799246i
$469$			1.48253e10i			0.306416i
$470$	−1.22590e10			−0.251225
$471$			4.43996e10i			0.902184i
$472$	6.54227e9	−	2.24467e10i	0.131814	−	0.452255i
$473$	−4.75234e10			−0.949429
$474$		−	6.10457e10i		−	1.20932i
$475$	8.99072e7			0.00176612
$476$	−1.01001e11			−1.96741
$477$	4.70208e9			0.0908272
$478$			3.97887e10i			0.762163i
$479$	−2.15148e10			−0.408692			−0.204346	−	0.978899i	$-0.565507\pi$
$479$	−2.15148e10			−0.408692			−0.204346	+	0.978899i	$0.565507\pi$
$480$			4.55281e9i			0.0857659i
$481$	2.94797e10			0.550735
$482$			1.53710e10i			0.284782i
$483$		−	8.61872e10i		−	1.58363i
$484$	1.20595e10			0.219759
$485$			6.79172e9i			0.122747i
$486$			4.57078e9i			0.0819304i
$487$	−2.81619e10			−0.500663			−0.250332	−	0.968160i	$-0.580540\pi$
$487$	−2.81619e10			−0.500663			−0.250332	+	0.968160i	$0.580540\pi$
$488$	−2.72156e10			−0.479887
$489$	−2.61129e10			−0.456688
$490$			2.07404e10i			0.359776i
$491$	7.94224e10			1.36652			0.683261	−	0.730174i	$-0.260561\pi$
$491$	7.94224e10			1.36652			0.683261	+	0.730174i	$0.260561\pi$
$492$	−3.66965e10			−0.626274
$493$	−6.63319e10			−1.12288
$494$	5.19736e7			0.000872721
$495$		−	3.12831e9i		−	0.0521062i
$496$		−	1.05754e11i		−	1.74730i
$497$	−3.20773e10			−0.525742
$498$	−7.52022e10			−1.22268
$499$	3.92428e10			0.632934			0.316467	−	0.948604i	$-0.397503\pi$
$499$	3.92428e10			0.632934			0.316467	+	0.948604i	$0.397503\pi$
$500$	−1.05252e10			−0.168403
$501$	2.20515e10			0.350015
$502$			1.34776e11i			2.12226i
$503$		−	1.08109e11i		−	1.68884i	−0.535682	−	0.844420i	$-0.679945\pi$
$503$		−	1.08109e11i		−	1.68884i	0.535682	−	0.844420i	$-0.320055\pi$
$504$		−	1.78172e10i		−	0.276132i
$505$			7.26459e9i			0.111698i
$506$			1.51632e11i			2.31307i
$507$	−3.26424e10			−0.494027
$508$	4.08941e10			0.614052
$509$		−	8.80269e10i		−	1.31143i	−0.755010	−	0.655714i	$-0.772368\pi$
$509$		−	8.80269e10i		−	1.31143i	0.755010	−	0.655714i	$-0.227632\pi$
$510$		−	1.19045e10i		−	0.175967i
$511$		−	1.28737e11i		−	1.88808i
$512$		−	5.35704e10i		−	0.779551i
$513$	2.39746e7			0.000346164
$514$		−	1.49271e11i		−	2.13856i
$515$			3.16251e7i			0.000449576i
$516$			2.11234e10i			0.297965i
$517$	−1.21204e11			−1.69650
$518$	2.34420e11			3.25594
$519$			8.30164e9i			0.114418i
$520$	1.76157e9			0.0240928
$521$	1.43493e10			0.194751			0.0973753	−	0.995248i	$-0.468955\pi$
$521$	1.43493e10			0.194751			0.0973753	+	0.995248i	$0.468955\pi$
$522$			2.00233e10i			0.269683i
$523$	6.50338e10			0.869226			0.434613	−	0.900617i	$-0.356885\pi$
$523$	6.50338e10			0.869226			0.434613	+	0.900617i	$0.356885\pi$
$524$		−	9.81484e9i		−	0.130184i
$525$	7.57325e10			0.996885
$526$			6.98210e10i			0.912102i
$527$			1.93788e11i			2.51238i
$528$			6.42305e10i			0.826429i
$529$	−1.12215e11			−1.43294
$530$			3.69679e9i			0.0468512i
$531$	2.54421e10	+	7.41531e9i	0.320018	+	0.0932720i
$532$	1.59918e8			0.00199642
$533$			5.26938e10i			0.652906i
$534$	6.96254e9			0.0856254
$535$	−5.56832e9			−0.0679688
$536$	6.77501e9			0.0820826
$537$		−	4.34047e10i		−	0.521963i
$538$	−9.12278e10			−1.08893
$539$			2.05059e11i			2.42954i
$540$	−1.39049e9			−0.0163528
$541$			9.79103e10i			1.14298i	0.820608	+	0.571491i	$0.193635\pi$
$541$			9.79103e10i			1.14298i	−0.820608	+	0.571491i	$0.806365\pi$
$542$			1.52104e11i			1.76256i
$543$	−1.26687e9			−0.0145725
$544$			1.71295e11i			1.95591i
$545$		−	2.24244e9i		−	0.0254176i
$546$	4.37795e10			0.492607
$547$	8.18786e10			0.914579			0.457290	−	0.889318i	$-0.348820\pi$
$547$	8.18786e10			0.914579			0.457290	+	0.889318i	$0.348820\pi$
$548$	−4.73861e10			−0.525447
$549$		−	3.08474e10i		−	0.339570i
$550$	−1.33238e11			−1.45606
$551$	1.05026e8			0.00113944
$552$	−3.93867e10			−0.424222
$553$	−2.69714e11			−2.88406
$554$			7.76900e9i			0.0824757i
$555$			1.06912e10i			0.112682i
$556$	−1.06456e11			−1.11396
$557$	−5.69753e10			−0.591924			−0.295962	−	0.955200i	$-0.595640\pi$
$557$	−5.69753e10			−0.591924			−0.295962	+	0.955200i	$0.595640\pi$
$558$	5.84979e10			0.603398
$559$	3.03319e10			0.310636
$560$	2.87031e10			0.291861
$561$		−	1.17699e11i		−	1.18829i
$562$			3.93140e10i			0.394096i
$563$		−	4.36537e10i		−	0.434498i	−0.976116	−	0.217249i	$-0.930292\pi$
$563$		−	4.36537e10i		−	0.434498i	0.976116	−	0.217249i	$-0.0697083\pi$
$564$			5.38733e10i			0.532423i
$565$		−	4.96843e9i		−	0.0487557i
$566$	−1.93422e11			−1.88469
$567$	2.01948e10			0.195392
$568$			1.46590e10i			0.140835i
$569$		−	2.52046e10i		−	0.240453i	−0.992746	−	0.120226i	$-0.961638\pi$
$569$		−	2.52046e10i		−	0.240453i	0.992746	−	0.120226i	$-0.0383621\pi$
$570$			1.88489e7i			0.000178561i
$571$			1.02282e11i			0.962173i	0.876673	+	0.481087i	$0.159758\pi$
$571$			1.02282e11i			0.962173i	−0.876673	+	0.481087i	$0.840242\pi$
$572$	−2.98030e10			−0.278405
$573$		−	7.80070e10i		−	0.723628i
$574$			4.19017e11i			3.85997i
$575$		−	1.67414e11i		−	1.53152i
$576$	6.47429e9			0.0588169
$577$	−1.11183e11			−1.00308			−0.501539	−	0.865135i	$-0.667233\pi$
$577$	−1.11183e11			−1.00308			−0.501539	+	0.865135i	$0.667233\pi$
$578$		−	3.05348e11i		−	2.73579i
$579$	7.44715e10			0.662637
$580$	−6.09133e9			−0.0538270
$581$			3.32261e11i			2.91592i
$582$	7.71358e10			0.672302
$583$			3.65499e10i			0.316382i
$584$	−5.88317e10			−0.505778
$585$			1.99665e9i			0.0170482i
$586$		−	1.66112e11i		−	1.40868i
$587$			2.19724e11i			1.85066i	0.379166	+	0.925329i	$0.376211\pi$
$587$			2.19724e11i			1.85066i	−0.379166	+	0.925329i	$0.623789\pi$
$588$	9.11456e10			0.762477
$589$		−	3.06833e8i		−	0.00254941i
$590$	−5.82994e9	+	2.00026e10i	−0.0481123	+	0.165074i
$591$	−1.29966e11			−1.06532
$592$		−	2.19512e11i		−	1.78719i
$593$	8.88296e10			0.718354			0.359177	−	0.933269i	$-0.383057\pi$
$593$	8.88296e10			0.718354			0.359177	+	0.933269i	$0.383057\pi$
$594$	−3.55293e10			−0.285391
$595$	−5.25970e10			−0.419656
$596$		−	8.85648e10i		−	0.701901i
$597$	−1.01515e11			−0.799159
$598$		−	9.67792e10i		−	0.756793i
$599$	1.55066e11			1.20451			0.602253	−	0.798305i	$-0.294270\pi$
$599$	1.55066e11			1.20451			0.602253	+	0.798305i	$0.294270\pi$
$600$		−	3.46090e10i		−	0.267045i
$601$		−	2.03126e11i		−	1.55693i	−0.627691	−	0.778463i	$-0.716000\pi$
$601$		−	2.03126e11i		−	1.55693i	0.627691	−	0.778463i	$-0.284000\pi$
$602$	2.41197e11			1.83648
$603$			7.67910e9i			0.0580820i
$604$		−	2.09057e10i		−	0.157079i
$605$	6.28009e9			0.0468754
$606$	8.25064e10			0.611783
$607$	6.46251e10			0.476043			0.238022	−	0.971260i	$-0.423501\pi$
$607$	6.46251e10			0.476043			0.238022	+	0.971260i	$0.423501\pi$
$608$		−	2.71217e8i		−	0.00198474i
$609$	8.84676e10			0.643154
$610$	2.42523e10			0.175160
$611$	7.73585e10			0.555064
$612$	−5.23156e10			−0.372928
$613$			9.94284e10i			0.704156i	0.935971	+	0.352078i	$0.114525\pi$
$613$			9.94284e10i			0.704156i	−0.935971	+	0.352078i	$0.885475\pi$
$614$		−	8.37063e10i		−	0.588959i
$615$	−1.91101e10			−0.133586
$616$	1.38495e11			0.961861
$617$	−8.35450e10			−0.576474			−0.288237	−	0.957559i	$-0.593069\pi$
$617$	−8.35450e10			−0.576474			−0.288237	+	0.957559i	$0.593069\pi$
$618$	3.59177e8			0.00246238
$619$	−2.26233e11			−1.54096			−0.770482	−	0.637462i	$-0.779984\pi$
$619$	−2.26233e11			−1.54096			−0.770482	+	0.637462i	$0.779984\pi$
$620$			1.77958e10i			0.120434i
$621$		−	4.46426e10i		−	0.300181i
$622$		−	2.11755e11i		−	1.41473i
$623$		−	3.07621e10i		−	0.204204i
$624$		−	4.09952e10i		−	0.270393i
$625$	1.44341e11			0.945954
$626$	5.83749e10			0.380127
$627$			1.86358e8i			0.00120581i
$628$			1.53402e11i			0.986265i
$629$			4.02245e11i			2.56973i
$630$			1.58772e10i			0.100789i
$631$	−3.47458e10			−0.219172			−0.109586	−	0.993977i	$-0.534952\pi$
$631$	−3.47458e10			−0.219172			−0.109586	+	0.993977i	$0.534952\pi$
$632$			1.23257e11i			0.772579i
$633$			1.03790e11i			0.646457i
$634$		−	3.00123e11i		−	1.85755i
$635$	2.12960e10			0.130979
$636$	1.62459e10			0.0992921
$637$		−	1.30879e11i		−	0.794900i
$638$	−1.55644e11			−0.939397
$639$	−1.66152e10			−0.0996557
$640$		−	1.98326e10i		−	0.118211i
$641$	−1.29053e11			−0.764424			−0.382212	−	0.924075i	$-0.624838\pi$
$641$	−1.29053e11			−0.764424			−0.382212	+	0.924075i	$0.624838\pi$
$642$			6.32414e10i			0.372273i
$643$	1.09423e11			0.640123			0.320062	−	0.947397i	$-0.396296\pi$
$643$	1.09423e11			0.640123			0.320062	+	0.947397i	$0.396296\pi$
$644$		−	2.97781e11i		−	1.73122i
$645$			1.10002e10i			0.0635569i
$646$			7.09170e8i			0.00407211i
$647$	2.14235e11			1.22257			0.611283	−	0.791412i	$-0.290654\pi$
$647$	2.14235e11			1.22257			0.611283	+	0.791412i	$0.290654\pi$
$648$		−	9.22881e9i		−	0.0523415i
$649$	−5.76402e10	+	1.97765e11i	−0.324898	+	1.11473i
$650$	8.50397e10			0.476396
$651$		−	2.58458e11i		−	1.43902i
$652$	−9.02211e10			−0.499250
$653$	2.65634e11			1.46093			0.730467	−	0.682947i	$-0.239302\pi$
$653$	2.65634e11			1.46093			0.730467	+	0.682947i	$0.239302\pi$
$654$	−2.54682e10			−0.139215
$655$		−	5.11118e9i		−	0.0277687i
$656$	3.92369e11			2.11875
$657$		−	6.66825e10i		−	0.357891i
$658$	6.15149e11			3.28153
$659$		−	1.38564e11i		−	0.734698i	−0.930083	−	0.367349i	$-0.880266\pi$
$659$		−	1.38564e11i		−	0.734698i	0.930083	−	0.367349i	$-0.119734\pi$
$660$		−	1.08085e10i		−	0.0569623i
$661$	−1.59272e11			−0.834319			−0.417160	−	0.908833i	$-0.636974\pi$
$661$	−1.59272e11			−0.834319			−0.417160	+	0.908833i	$0.636974\pi$
$662$		−	1.22836e11i		−	0.639580i
$663$			7.51217e10i			0.388787i
$664$	1.51840e11			0.781114
$665$	8.32789e7			0.000425842
$666$	1.21424e11			0.617172
$667$		−	1.95567e11i		−	0.988080i
$668$	7.61888e10			0.382636
$669$	1.08185e11			0.540084
$670$	−6.03734e9			−0.0299603
$671$	2.39781e11			1.18284
$672$		−	2.28457e11i		−	1.12028i
$673$			3.26959e11i			1.59380i	0.604114	+	0.796898i	$0.293527\pi$
$673$			3.26959e11i			1.59380i	−0.604114	+	0.796898i	$0.706473\pi$
$674$	−1.88761e11			−0.914688
$675$	3.92274e10			0.188962
$676$	−1.12781e11			−0.540069
$677$	−1.41939e11			−0.675690			−0.337845	−	0.941202i	$-0.609698\pi$
$677$	−1.41939e11			−0.675690			−0.337845	+	0.941202i	$0.609698\pi$
$678$	−5.64282e10			−0.267041
$679$		−	3.40804e11i		−	1.60334i
$680$			2.40363e10i			0.112417i
$681$		−	1.98162e11i		−	0.921365i
$682$			4.54712e11i			2.10184i
$683$		−	9.39417e10i		−	0.431693i	−0.976427	−	0.215847i	$-0.930749\pi$
$683$		−	9.39417e10i		−	0.431693i	0.976427	−	0.215847i	$-0.0692512\pi$
$684$	8.28333e7			0.000378426
$685$	−2.46768e10			−0.112079
$686$		−	5.43355e11i		−	2.45351i
$687$			1.86781e11i			0.838505i
$688$		−	2.25857e11i		−	1.00804i
$689$		−	2.33280e10i		−	0.103514i
$690$	3.50982e10			0.154842
$691$		−	1.24138e10i		−	0.0544494i	−0.999629	−	0.0272247i	$-0.991333\pi$
$691$		−	1.24138e10i		−	0.0544494i	0.999629	−	0.0272247i	$-0.00866696\pi$
$692$			2.86825e10i			0.125081i
$693$			1.56977e11i			0.680617i
$694$	−9.23436e10			−0.398079
$695$	−5.54378e10			−0.237611
$696$		−	4.04288e10i		−	0.172288i
$697$	−7.18996e11			−3.04646
$698$	−1.95552e11			−0.823837
$699$		−	1.15110e10i		−	0.0482175i
$700$	2.61659e11			1.08979
$701$		−	7.13533e10i		−	0.295489i	−0.989026	−	0.147745i	$-0.952799\pi$
$701$		−	7.13533e10i		−	0.295489i	0.989026	−	0.147745i	$-0.0472014\pi$
$702$	2.26766e10			0.0933748
$703$		−	6.36889e8i		−	0.00260761i
$704$			5.03255e10i			0.204879i
$705$			2.80551e10i			0.113568i
$706$	2.93426e11			1.18108
$707$		−	3.64533e11i		−	1.45901i
$708$	8.79035e10	+	2.56202e10i	0.349843	+	0.101965i
$709$	−2.84497e11			−1.12588			−0.562942	−	0.826497i	$-0.690330\pi$
$709$	−2.84497e11			−1.12588			−0.562942	+	0.826497i	$0.690330\pi$
$710$		−	1.30629e10i		−	0.0514052i
$711$	−1.39705e11			−0.546680
$712$	−1.40580e10			−0.0547020
$713$	−5.71347e11			−2.21076
$714$			5.97363e11i			2.29850i
$715$	−1.55202e10			−0.0593846
$716$		−	1.49965e11i		−	0.570609i
$717$	9.10575e10			0.344540
$718$			3.02588e11i			1.13855i
$719$		−	3.11106e11i		−	1.16411i	−0.813151	−	0.582053i	$-0.802249\pi$
$719$		−	3.11106e11i		−	1.16411i	0.813151	−	0.582053i	$-0.197751\pi$
$720$	1.48674e10			0.0553231
$721$		−	1.58693e9i		−	0.00587241i
$722$			3.47053e11i			1.27716i
$723$	3.51769e10			0.128737
$724$	−4.37711e9			−0.0159306
$725$	1.71844e11			0.621989
$726$		−	7.13252e10i		−	0.256742i
$727$	4.55240e11			1.62968			0.814840	−	0.579686i	$-0.196825\pi$
$727$	4.55240e11			1.62968			0.814840	+	0.579686i	$0.196825\pi$
$728$	−8.83948e10			−0.314703
$729$	1.04604e10			0.0370370
$730$	5.24260e10			0.184610
$731$			4.13872e11i			1.44943i
$732$		−	1.06579e11i		−	0.371217i
$733$	2.37585e11			0.823005			0.411502	−	0.911409i	$-0.365004\pi$
$733$	2.37585e11			0.823005			0.411502	+	0.911409i	$0.365004\pi$
$734$	−1.67386e11			−0.576680
$735$	4.74650e10			0.162639
$736$	−5.05029e11			−1.72109
$737$	−5.96908e10			−0.202319
$738$			2.17040e11i			0.731668i
$739$			1.01236e11i			0.339435i	0.985493	+	0.169718i	$0.0542856\pi$
$739$			1.01236e11i			0.339435i	−0.985493	+	0.169718i	$0.945714\pi$
$740$			3.69386e10i			0.123184i
$741$		−	1.18943e8i		−	0.000394518i
$742$		−	1.85503e11i		−	0.611976i
$743$	−2.77292e11			−0.909877			−0.454938	−	0.890523i	$-0.650339\pi$
$743$	−2.77292e11			−0.909877			−0.454938	+	0.890523i	$0.650339\pi$
$744$	−1.18113e11			−0.385482
$745$		−	4.61210e10i		−	0.149718i
$746$			5.69415e10i			0.183854i
$747$			1.72103e11i			0.552720i
$748$		−	4.06656e11i		−	1.29904i
$749$	2.79415e11			0.887816
$750$			6.22507e10i			0.196743i
$751$			2.20002e10i			0.0691619i	0.999402	+	0.0345810i	$0.0110097\pi$
$751$			2.20002e10i			0.0691619i	−0.999402	+	0.0345810i	$0.988990\pi$
$752$		−	5.76027e11i		−	1.80124i
$753$	3.08439e11			0.959377
$754$	9.93399e10			0.307354
$755$		−	1.08869e10i		−	0.0335054i
$756$	6.97739e10			0.213602
$757$	3.91803e11			1.19312			0.596560	−	0.802569i	$-0.296534\pi$
$757$	3.91803e11			1.19312			0.596560	+	0.802569i	$0.296534\pi$
$758$		−	1.28271e11i		−	0.388556i
$759$	3.47014e11			1.04563
$760$		−	3.80576e7i		−	0.000114074i
$761$	3.95967e11			1.18065			0.590324	−	0.807167i	$-0.299000\pi$
$761$	3.95967e11			1.18065			0.590324	+	0.807167i	$0.299000\pi$
$762$		−	2.41866e11i		−	0.717389i
$763$			1.12525e11i			0.332008i
$764$		−	2.69518e11i		−	0.791068i
$765$	−2.72439e10			−0.0795468
$766$			6.09746e11i			1.77106i
$767$	3.67890e10	−	1.26224e11i	0.106301	−	0.364720i
$768$	−2.60687e11			−0.749331
$769$			3.19883e11i			0.914714i	0.889283	+	0.457357i	$0.151204\pi$
$769$			3.19883e11i			0.914714i	−0.889283	+	0.457357i	$0.848796\pi$
$770$	−1.23416e11			−0.351081
$771$	−3.41610e11			−0.966748
$772$	2.57302e11			0.724393
$773$			1.40067e11i			0.392299i	0.980574	+	0.196150i	$0.0628438\pi$
$773$			1.40067e11i			0.392299i	−0.980574	+	0.196150i	$0.937156\pi$
$774$	1.24933e11			0.348109
$775$		−	5.02042e11i		−	1.39166i
$776$	−1.55744e11			−0.429502
$777$		−	5.36478e11i		−	1.47186i
$778$			1.45496e11i			0.397130i
$779$	1.13841e9			0.00309137
$780$			6.89851e9i			0.0186370i
$781$		−	1.29152e11i		−	0.347135i
$782$	1.32053e12			3.53120
$783$	4.58239e10			0.121912
$784$	−9.74552e11			−2.57953
$785$			7.98859e10i			0.210374i
$786$	−5.80494e10			−0.152092
$787$	2.32885e11			0.607076			0.303538	−	0.952819i	$-0.401832\pi$
$787$	2.32885e11			0.607076			0.303538	+	0.952819i	$0.401832\pi$
$788$	−4.49038e11			−1.16460
$789$	1.59787e11			0.412320
$790$		−	1.09836e11i		−	0.281993i
$791$			2.49313e11i			0.636853i
$792$	7.17369e10			0.182323
$793$	−1.53041e11			−0.387003
$794$	1.77949e11			0.447726
$795$	8.46020e9			0.0211793
$796$	−3.50739e11			−0.873639
$797$			6.69338e11i			1.65887i	0.558604	+	0.829435i	$0.311337\pi$
$797$			6.69338e11i			1.65887i	−0.558604	+	0.829435i	$0.688663\pi$
$798$		−	9.45827e8i		−	0.00233239i
$799$			1.05554e12i			2.58993i
$800$		−	4.43768e11i		−	1.08342i
$801$		−	1.59340e10i		−	0.0387074i
$802$	−9.70115e11			−2.34491
$803$	5.18332e11			1.24665
$804$			2.65317e10i			0.0634951i
$805$		−	1.55072e11i		−	0.369275i
$806$		−	2.90221e11i		−	0.687683i
$807$			2.08778e11i			0.492254i
$808$	−1.66588e11			−0.390839
$809$		−	2.91420e11i		−	0.680339i	−0.940364	−	0.340169i	$-0.889516\pi$
$809$		−	2.91420e11i		−	0.680339i	0.940364	−	0.340169i	$-0.110484\pi$
$810$			8.22397e9i			0.0191047i
$811$			6.88447e11i			1.59143i	0.605673	+	0.795714i	$0.292904\pi$
$811$			6.88447e11i			1.59143i	−0.605673	+	0.795714i	$0.707096\pi$
$812$	3.05660e11			0.703095
$813$	3.48094e11			0.796773
$814$			9.43842e11i			2.14982i
$815$	−4.69836e10			−0.106492
$816$	5.59371e11			1.26165
$817$		−	6.55299e8i		−	0.00147079i
$818$	4.22327e11			0.943268
$819$		−	1.00191e11i		−	0.222685i
$820$	−6.60262e10			−0.146036
$821$		−	2.77935e10i		−	0.0611744i	−0.999532	−	0.0305872i	$-0.990262\pi$
$821$		−	2.77935e10i		−	0.0611744i	0.999532	−	0.0305872i	$-0.00973773\pi$
$822$			2.80263e11i			0.613872i
$823$			5.04528e11i			1.09973i	0.835254	+	0.549865i	$0.185321\pi$
$823$			5.04528e11i			1.09973i	−0.835254	+	0.549865i	$0.814679\pi$
$824$	−7.25211e8			−0.00157310
$825$			3.04920e11i			0.658219i
$826$	2.92543e11	−	1.00372e12i	0.628449	−	2.15622i
$827$	7.60680e10			0.162622			0.0813111	−	0.996689i	$-0.474089\pi$
$827$	7.60680e10			0.162622			0.0813111	+	0.996689i	$0.474089\pi$
$828$		−	1.54242e11i		−	0.328157i
$829$	1.46583e11			0.310360			0.155180	−	0.987886i	$-0.450404\pi$
$829$	1.46583e11			0.310360			0.155180	+	0.987886i	$0.450404\pi$
$830$	−1.35308e11			−0.285108
$831$	1.77796e10			0.0372835
$832$		−	3.21203e10i		−	0.0670327i
$833$	1.78582e12			3.70901
$834$			6.29626e11i			1.30142i
$835$	3.96761e10			0.0816175
$836$			6.43875e8i			0.00131818i
$837$		−	1.33874e11i		−	0.272769i
$838$	−1.16866e12			−2.36980
$839$			5.48092e11i			1.10613i	0.833139	+	0.553064i	$0.186542\pi$
$839$			5.48092e11i			1.10613i	−0.833139	+	0.553064i	$0.813458\pi$
$840$		−	3.20575e10i		−	0.0643891i
$841$	−2.99505e11			−0.598715
$842$	−8.17447e11			−1.62634
$843$	8.99712e10			0.178153
$844$			3.58599e11i			0.706706i
$845$	−5.87319e10			−0.115199
$846$	3.18631e11			0.622023
$847$	−3.15132e11			−0.612292
$848$	−1.73705e11			−0.335915
$849$			4.42652e11i			0.851985i
$850$			1.16035e12i			2.22286i
$851$	−1.18594e12			−2.26123
$852$	−5.74063e10			−0.108943
$853$	6.75878e10			0.127665			0.0638325	−	0.997961i	$-0.479668\pi$
$853$	6.75878e10			0.127665			0.0638325	+	0.997961i	$0.479668\pi$
$854$	−1.21697e12			−2.28796
$855$	4.31363e7			8.07194e−5
$856$		−	1.27690e11i		−	0.237828i
$857$		−	2.08190e11i		−	0.385956i	−0.981203	−	0.192978i	$-0.938185\pi$
$857$		−	2.08190e11i		−	0.385956i	0.981203	−	0.192978i	$-0.0618145\pi$
$858$			1.76269e11i			0.325256i
$859$		−	2.96754e11i		−	0.545035i	−0.962151	−	0.272518i	$-0.912144\pi$
$859$		−	2.96754e11i		−	0.545035i	0.962151	−	0.272518i	$-0.0878563\pi$
$860$			3.80063e10i			0.0694803i
$861$	9.58933e11			1.74492
$862$	3.49063e11			0.632229
$863$			3.36820e11i			0.607233i	0.952794	+	0.303616i	$0.0981941\pi$
$863$			3.36820e11i			0.607233i	−0.952794	+	0.303616i	$0.901806\pi$
$864$		−	1.18335e11i		−	0.212353i
$865$			1.49367e10i			0.0266803i
$866$		−	9.18308e11i		−	1.63274i
$867$	−6.98797e11			−1.23673
$868$		−	8.92983e11i		−	1.57313i
$869$		−	1.08595e12i		−	1.90427i
$870$			3.60269e10i			0.0628854i
$871$	3.80977e10			0.0661952
$872$	5.14226e10			0.0889381
$873$		−	1.76528e11i		−	0.303917i
$874$	−2.09085e9			−0.00358325
$875$	2.75039e11			0.469204
$876$		−	2.30391e11i		−	0.391245i
$877$	5.78985e11			0.978743			0.489372	−	0.872075i	$-0.337226\pi$
$877$	5.78985e11			0.978743			0.489372	+	0.872075i	$0.337226\pi$
$878$			7.25464e11i			1.22078i
$879$	−3.80152e11			−0.636799
$880$			1.15567e11i			0.192709i
$881$		−	7.42279e10i		−	0.123215i	−0.998100	−	0.0616075i	$-0.980377\pi$
$881$		−	7.42279e10i		−	0.123215i	0.998100	−	0.0616075i	$-0.0196227\pi$
$882$		−	5.39076e11i		−	0.890791i
$883$	2.28952e11			0.376618			0.188309	−	0.982110i	$-0.439699\pi$
$883$	2.28952e11			0.376618			0.188309	+	0.982110i	$0.439699\pi$
$884$			2.59549e11i			0.425021i
$885$	4.57766e10	+	1.33420e10i	0.0746226	+	0.0217494i
$886$	−6.84775e10			−0.111125
$887$			2.03616e10i			0.0328941i	0.999865	+	0.0164471i	$0.00523550\pi$
$887$			2.03616e10i			0.0328941i	−0.999865	+	0.0164471i	$0.994765\pi$
$888$	−2.45165e11			−0.394282
$889$	−1.06862e12			−1.71087
$890$	1.25273e10			0.0199664
$891$			8.13098e10i			0.129013i
$892$	3.73783e11			0.590419
$893$		−	1.67128e9i		−	0.00262811i
$894$	−5.23812e11			−0.820021
$895$		−	7.80959e10i		−	0.121713i
$896$			9.95188e11i			1.54409i
$897$	−2.21482e11			−0.342112
$898$			4.92197e11i			0.756891i
$899$		−	5.86465e11i		−	0.897849i
$900$	1.35532e11			0.206573
$901$	3.18306e11			0.482998
$902$	−1.68708e12			−2.54865
$903$		−	5.51985e11i		−	0.830188i
$904$	1.13934e11			0.170600
$905$	−2.27942e9			−0.00339806
$906$	−1.23646e11			−0.183513
$907$	2.49305e11			0.368386			0.184193	−	0.982890i	$-0.441033\pi$
$907$	2.49305e11			0.368386			0.184193	+	0.982890i	$0.441033\pi$
$908$		−	6.84658e11i		−	1.00723i
$909$		−	1.88818e11i		−	0.276560i
$910$	7.87703e10			0.114867
$911$	−4.03680e11			−0.586089			−0.293044	−	0.956099i	$-0.594668\pi$
$911$	−4.03680e11			−0.586089			−0.293044	+	0.956099i	$0.594668\pi$
$912$	−8.85674e8			−0.00128025
$913$	−1.33778e12			−1.92531
$914$	−1.39578e12			−2.00001
$915$		−	5.55022e10i		−	0.0791818i
$916$			6.45337e11i			0.916652i
$917$			2.56476e11i			0.362718i
$918$			3.09418e11i			0.435687i
$919$		−	8.46490e11i		−	1.18675i	−0.804926	−	0.593376i	$-0.797795\pi$
$919$		−	8.46490e11i		−	1.18675i	0.804926	−	0.593376i	$-0.202205\pi$
$920$	−7.08664e10			−0.0989212
$921$	−1.91564e11			−0.266242
$922$		−	8.74845e10i		−	0.121062i
$923$			8.24316e10i			0.113576i
$924$			5.42362e11i			0.744049i
$925$		−	1.04208e12i		−	1.42343i
$926$	1.38464e12			1.88319
$927$		−	8.21987e8i		−	0.00111313i
$928$		−	5.18392e11i		−	0.698982i
$929$			1.13911e12i			1.52933i	0.644425	+	0.764667i	$0.277097\pi$
$929$			1.13911e12i			1.52933i	−0.644425	+	0.764667i	$0.722903\pi$
$930$	1.05252e11			0.140702
$931$	−2.82756e9			−0.00376368
$932$		−	3.97710e10i		−	0.0527112i
$933$	−4.84609e11			−0.639535
$934$	9.98783e11			1.31245
$935$		−	2.11770e11i		−	0.277089i
$936$	−4.57862e10			−0.0596528
$937$			1.89986e11i			0.246470i	0.992378	+	0.123235i	$0.0393269\pi$
$937$			1.89986e11i			0.246470i	−0.992378	+	0.123235i	$0.960673\pi$
$938$	3.02950e11			0.391345
$939$		−	1.33593e11i		−	0.171838i
$940$			9.69315e10i			0.124152i
$941$			2.18970e11i			0.279271i	0.990203	+	0.139635i	$0.0445930\pi$
$941$			2.18970e11i			0.279271i	−0.990203	+	0.139635i	$0.955407\pi$
$942$	9.07291e11			1.15224
$943$		−	2.11982e12i		−	2.68073i
$944$	−9.39886e11	−	2.73938e11i	−1.18355	−	0.344956i
$945$	3.63354e10			0.0455620
$946$			9.71125e11i			1.21258i
$947$	−8.41999e11			−1.04692			−0.523458	−	0.852051i	$-0.675358\pi$
$947$	−8.41999e11			−1.04692			−0.523458	+	0.852051i	$0.675358\pi$
$948$	−4.82687e11			−0.597629
$949$	−3.30826e11			−0.407883
$950$		−	1.83722e9i		−	0.00225563i
$951$	−6.86839e11			−0.839717
$952$		−	1.20613e12i		−	1.46841i
$953$	−5.16512e11			−0.626194			−0.313097	−	0.949721i	$-0.601367\pi$
$953$	−5.16512e11			−0.626194			−0.313097	+	0.949721i	$0.601367\pi$
$954$		−	9.60854e10i		−	0.116002i
$955$		−	1.40354e11i		−	0.168738i
$956$	3.14608e11			0.376650
$957$			3.56195e11i			0.424659i
$958$			4.39649e11i			0.521968i
$959$	1.23827e12			1.46400
$960$	1.16489e10			0.0137151
$961$	−8.60463e11			−1.00888
$962$		−	6.02409e11i		−	0.703382i
$963$	1.44730e11			0.168288
$964$	1.21538e11			0.140735
$965$	1.33993e11			0.154515
$966$	−1.76121e12			−2.02256
$967$		−	1.23460e12i		−	1.41196i	−0.708233	−	0.705979i	$-0.750507\pi$
$967$		−	1.23460e12i		−	1.41196i	0.708233	−	0.705979i	$-0.249493\pi$
$968$			1.44012e11i			0.164020i
$969$	1.62296e9			0.00184082
$970$	1.38787e11			0.156769
$971$	9.51392e11			1.07024			0.535122	−	0.844775i	$-0.320266\pi$
$971$	9.51392e11			1.07024			0.535122	+	0.844775i	$0.320266\pi$
$972$	3.61410e10			0.0404888
$973$	2.78184e12			3.10370
$974$			5.75479e11i			0.639431i
$975$		−	1.94616e11i		−	0.215357i
$976$			1.13957e12i			1.25586i
$977$		−	2.98478e10i		−	0.0327592i	−0.999866	−	0.0163796i	$-0.994786\pi$
$977$		−	2.98478e10i		−	0.0327592i	0.999866	−	0.0163796i	$-0.00521403\pi$
$978$			5.33608e11i			0.583267i
$979$	1.23857e11			0.134831
$980$	1.63994e11			0.177796
$981$			5.82847e10i			0.0629330i
$982$		−	1.62297e12i		−	1.74528i
$983$			4.95858e11i			0.531059i	0.964103	+	0.265530i	$0.0855468\pi$
$983$			4.95858e11i			0.531059i	−0.964103	+	0.265530i	$0.914453\pi$
$984$		−	4.38223e11i		−	0.467428i
$985$	−2.33841e11			−0.248414
$986$			1.35547e12i			1.43411i
$987$		−	1.40779e12i		−	1.48343i
$988$		−	4.10954e8i		−	0.000431286i
$989$	−1.22022e12			−1.27542
$990$	−6.39260e10			−0.0665483
$991$			1.63001e12i			1.69004i	0.534738	+	0.845018i	$0.320410\pi$
$991$			1.63001e12i			1.69004i	−0.534738	+	0.845018i	$0.679590\pi$
$992$	−1.51448e12			−1.56393
$993$	−2.81115e11			−0.289125
$994$			6.55490e11i			0.671461i
$995$	−1.82651e11			−0.186350
$996$			5.94622e11i			0.604232i
$997$	2.40129e11			0.243033			0.121516	−	0.992589i	$-0.461224\pi$
$997$	2.40129e11			0.243033			0.121516	+	0.992589i	$0.461224\pi$
$998$		−	8.01915e11i		−	0.808363i
$999$		−	2.77881e11i		−	0.278996i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.9.c.a.58.17	✓	80
59.58	odd	2	inner	177.9.c.a.58.64	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.9.c.a.58.17	✓	80	1.1	even	1	trivial
177.9.c.a.58.64	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)

\(f(q)\)	\(=\)	\(q-20.4347i q^{2} -46.7654 q^{3} -161.576 q^{4} -84.1426 q^{5} +955.636i q^{6} +4222.23 q^{7} -1929.52i q^{8} +2187.00 q^{9} +O(q^{10})\)	\(q-20.4347i q^{2} -46.7654 q^{3} -161.576 q^{4} -84.1426 q^{5} +955.636i q^{6} +4222.23 q^{7} -1929.52i q^{8} +2187.00 q^{9} +1719.43i q^{10} +16999.9i q^{11} +7556.18 q^{12} -10850.2i q^{13} -86279.9i q^{14} +3934.96 q^{15} -80792.6 q^{16} +148049. q^{17} -44690.7i q^{18} -234.411 q^{19} +13595.5 q^{20} -197454. q^{21} +347387. q^{22} +436492. i q^{23} +90234.5i q^{24} -383545. q^{25} -221720. q^{26} -102276. q^{27} -682212. q^{28} -448042. q^{29} -80409.6i q^{30} +1.30895e6i q^{31} +1.15702e6i q^{32} -795005. i q^{33} -3.02533e6i q^{34} -355269. q^{35} -353368. q^{36} +2.71698e6i q^{37} +4790.12i q^{38} +507413. i q^{39} +162354. i q^{40} -4.85649e6 q^{41} +4.03491e6i q^{42} +2.79551e6i q^{43} -2.74678e6i q^{44} -184020. q^{45} +8.91959e6 q^{46} +7.12970e6i q^{47} +3.77830e6 q^{48} +1.20624e7 q^{49} +7.83762e6i q^{50} -6.92355e6 q^{51} +1.75313e6i q^{52} +2.15001e6 q^{53} +2.08998e6i q^{54} -1.43041e6i q^{55} -8.14685e6i q^{56} +10962.3 q^{57} +9.15560e6i q^{58} +(1.16333e7 + 3.39063e6i) q^{59} -635797. q^{60} -1.41049e7i q^{61} +2.67480e7 q^{62} +9.23401e6 q^{63} +2.96035e6 q^{64} +912962. i q^{65} -1.62457e7 q^{66} +3.51125e6i q^{67} -2.39212e7 q^{68} -2.04127e7i q^{69} +7.25981e6i q^{70} -7.59726e6 q^{71} -4.21985e6i q^{72} -3.04904e7i q^{73} +5.55206e7 q^{74} +1.79366e7 q^{75} +37875.3 q^{76} +7.17772e7i q^{77} +1.03688e7 q^{78} -6.38797e7 q^{79} +6.79810e6 q^{80} +4.78297e6 q^{81} +9.92409e7i q^{82} +7.86934e7i q^{83} +3.19039e7 q^{84} -1.24572e7 q^{85} +5.71255e7 q^{86} +2.09528e7 q^{87} +3.28015e7 q^{88} -7.28576e6i q^{89} +3.76039e6i q^{90} -4.58119e7i q^{91} -7.05269e7i q^{92} -6.12136e7i q^{93} +1.45693e8 q^{94} +19723.9 q^{95} -5.41083e7i q^{96} -8.07168e7i q^{97} -2.46491e8i q^{98} +3.71787e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9}+O(q^{10}) \) 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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