LMFDB - Embedded newform 177.11.c.a.58.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,11,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, 11, names="a")

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

chi := DirichletCharacter("177.58");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 11 $
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:	$112.458233723$
Analytic rank:	$0$
Dimension:	$100$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			58.2
Character	$\chi$	$=$	177.58
Dual form			177.11.c.a.58.99

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-63.4607i q^{2} -140.296 q^{3} -3003.25 q^{4} +3537.19 q^{5} +8903.28i q^{6} -15274.6 q^{7} +125605. i q^{8} +19683.0 q^{9} +O(q^{10})$	\(q-63.4607i q^{2} -140.296 q^{3} -3003.25 q^{4} +3537.19 q^{5} +8903.28i q^{6} -15274.6 q^{7} +125605. i q^{8} +19683.0 q^{9} -224473. i q^{10} -271175. i q^{11} +421345. q^{12} -568274. i q^{13} +969335. i q^{14} -496254. q^{15} +4.89563e6 q^{16} -787841. q^{17} -1.24910e6i q^{18} -2.77833e6 q^{19} -1.06231e7 q^{20} +2.14297e6 q^{21} -1.72089e7 q^{22} +8.00619e6i q^{23} -1.76219e7i q^{24} +2.74610e6 q^{25} -3.60631e7 q^{26} -2.76145e6 q^{27} +4.58735e7 q^{28} -3.11900e7 q^{29} +3.14926e7i q^{30} -4.29591e7i q^{31} -1.82061e8i q^{32} +3.80447e7i q^{33} +4.99969e7i q^{34} -5.40291e7 q^{35} -5.91131e7 q^{36} +6.24534e7i q^{37} +1.76315e8i q^{38} +7.97267e7i q^{39} +4.44288e8i q^{40} +6.93263e7 q^{41} -1.35994e8i q^{42} -9.52345e7i q^{43} +8.14406e8i q^{44} +6.96226e7 q^{45} +5.08078e8 q^{46} -3.13127e8i q^{47} -6.86838e8 q^{48} -4.91622e7 q^{49} -1.74269e8i q^{50} +1.10531e8 q^{51} +1.70667e9i q^{52} -1.32764e8 q^{53} +1.75243e8i q^{54} -9.59197e8i q^{55} -1.91856e9i q^{56} +3.89789e8 q^{57} +1.97934e9i q^{58} +(-5.75728e8 - 4.23855e8i) q^{59} +1.49038e9 q^{60} +8.26364e8i q^{61} -2.72621e9 q^{62} -3.00650e8 q^{63} -6.54056e9 q^{64} -2.01010e9i q^{65} +2.41434e9 q^{66} -1.28334e8i q^{67} +2.36609e9 q^{68} -1.12324e9i q^{69} +3.42873e9i q^{70} +1.24650e9 q^{71} +2.47228e9i q^{72} +2.30278e9i q^{73} +3.96333e9 q^{74} -3.85268e8 q^{75} +8.34403e9 q^{76} +4.14208e9i q^{77} +5.05951e9 q^{78} -1.18761e9 q^{79} +1.73168e10 q^{80} +3.87420e8 q^{81} -4.39949e9i q^{82} +2.67136e9i q^{83} -6.43587e9 q^{84} -2.78674e9 q^{85} -6.04364e9 q^{86} +4.37583e9 q^{87} +3.40608e10 q^{88} +4.15156e9i q^{89} -4.41829e9i q^{90} +8.68016e9i q^{91} -2.40446e10i q^{92} +6.02700e9i q^{93} -1.98712e10 q^{94} -9.82749e9 q^{95} +2.55424e10i q^{96} -6.37540e9i q^{97} +3.11987e9i q^{98} -5.33753e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 51200 q^{4} + 18392 q^{7} + 1968300 q^{9}+O(q^{10}) $ 100 * q - 51200 * q^4 + 18392 * q^7 + 1968300 * q^9	$ 100 q - 51200 q^{4} + 18392 q^{7} + 1968300 q^{9} + 620136 q^{12} + 662904 q^{15} + 27925160 q^{16} - 2053136 q^{17} - 5169828 q^{19} - 1076324 q^{20} - 1829224 q^{22} + 215378180 q^{25} - 22082700 q^{26} - 102921320 q^{28} - 112503588 q^{29} - 76491392 q^{35} - 1007769600 q^{36} + 473464516 q^{41} + 1215405588 q^{46} - 1676272320 q^{48} + 1975297276 q^{49} + 733970808 q^{51} + 3267506728 q^{53} + 591502824 q^{57} + 508142200 q^{59} + 1264196808 q^{60} - 6538206968 q^{62} + 362009736 q^{63} - 10324137972 q^{64} - 2764346616 q^{66} + 9997685952 q^{68} + 14908523204 q^{71} + 4863508712 q^{74} + 1890481680 q^{75} + 2044437240 q^{76} - 758396196 q^{78} - 3599839500 q^{79} - 23217941144 q^{80} + 38742048900 q^{81} - 13094894808 q^{84} + 23360564412 q^{85} + 12186923752 q^{86} + 7965322272 q^{87} + 32415437996 q^{88} - 22098322280 q^{94} + 7834510028 q^{95}+O(q^{100}) $ 100 * q - 51200 * q^4 + 18392 * q^7 + 1968300 * q^9 + 620136 * q^12 + 662904 * q^15 + 27925160 * q^16 - 2053136 * q^17 - 5169828 * q^19 - 1076324 * q^20 - 1829224 * q^22 + 215378180 * q^25 - 22082700 * q^26 - 102921320 * q^28 - 112503588 * q^29 - 76491392 * q^35 - 1007769600 * q^36 + 473464516 * q^41 + 1215405588 * q^46 - 1676272320 * q^48 + 1975297276 * q^49 + 733970808 * q^51 + 3267506728 * q^53 + 591502824 * q^57 + 508142200 * q^59 + 1264196808 * q^60 - 6538206968 * q^62 + 362009736 * q^63 - 10324137972 * q^64 - 2764346616 * q^66 + 9997685952 * q^68 + 14908523204 * q^71 + 4863508712 * q^74 + 1890481680 * q^75 + 2044437240 * q^76 - 758396196 * q^78 - 3599839500 * q^79 - 23217941144 * q^80 + 38742048900 * q^81 - 13094894808 * q^84 + 23360564412 * q^85 + 12186923752 * q^86 + 7965322272 * q^87 + 32415437996 * q^88 - 22098322280 * q^94 + 7834510028 * 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 $

$2$		−	63.4607i		−	1.98315i	−0.129551	−	0.991573i	$-0.541354\pi$
$2$		−	63.4607i		−	1.98315i	0.129551	−	0.991573i	$-0.458646\pi$
$3$	−140.296			−0.577350
$3$	−140.296			−0.577350
$4$	−3003.25			−2.93287
$5$	3537.19			1.13190			0.565951	−	0.824439i	$-0.308509\pi$
$5$	3537.19			1.13190			0.565951	+	0.824439i	$0.308509\pi$
$6$			8903.28i			1.14497i
$7$	−15274.6			−0.908823			−0.454411	−	0.890792i	$-0.650150\pi$
$7$	−15274.6			−0.908823			−0.454411	+	0.890792i	$0.650150\pi$
$8$			125605.i			3.83315i
$9$	19683.0			0.333333
$10$		−	224473.i		−	2.24473i
$11$		−	271175.i		−	1.68378i	−0.539648	−	0.841891i	$-0.681443\pi$
$11$		−	271175.i		−	1.68378i	0.539648	−	0.841891i	$-0.318557\pi$
$12$	421345.			1.69329
$13$		−	568274.i		−	1.53053i	−0.643717	−	0.765264i	$-0.722608\pi$
$13$		−	568274.i		−	1.53053i	0.643717	−	0.765264i	$-0.277392\pi$
$14$			969335.i			1.80233i
$15$	−496254.			−0.653504
$16$	4.89563e6			4.66884
$17$	−787841.			−0.554873			−0.277437	−	0.960744i	$-0.589485\pi$
$17$	−787841.			−0.554873			−0.277437	+	0.960744i	$0.589485\pi$
$18$		−	1.24910e6i		−	0.661048i
$19$	−2.77833e6			−1.12206			−0.561030	−	0.827796i	$-0.689595\pi$
$19$	−2.77833e6			−1.12206			−0.561030	+	0.827796i	$0.689595\pi$
$20$	−1.06231e7			−3.31972
$21$	2.14297e6			0.524709
$22$	−1.72089e7			−3.33918
$23$			8.00619e6i			1.24390i	0.783055	+	0.621952i	$0.213660\pi$
$23$			8.00619e6i			1.24390i	−0.783055	+	0.621952i	$0.786340\pi$
$24$		−	1.76219e7i		−	2.21307i
$25$	2.74610e6			0.281201
$26$	−3.60631e7			−3.03526
$27$	−2.76145e6			−0.192450
$28$	4.58735e7			2.66546
$29$	−3.11900e7			−1.52063			−0.760317	−	0.649552i	$-0.774957\pi$
$29$	−3.11900e7			−1.52063			−0.760317	+	0.649552i	$0.774957\pi$
$30$			3.14926e7i			1.29599i
$31$		−	4.29591e7i		−	1.50054i	−0.661133	−	0.750269i	$-0.729924\pi$
$31$		−	4.29591e7i		−	1.50054i	0.661133	−	0.750269i	$-0.270076\pi$
$32$		−	1.82061e8i		−	5.42583i
$33$			3.80447e7i			0.972131i
$34$			4.99969e7i			1.10039i
$35$	−5.40291e7			−1.02870
$36$	−5.91131e7			−0.977622
$37$			6.24534e7i			0.900632i	0.892869	+	0.450316i	$0.148689\pi$
$37$			6.24534e7i			0.900632i	−0.892869	+	0.450316i	$0.851311\pi$
$38$			1.76315e8i			2.22521i
$39$			7.97267e7i			0.883651i
$40$			4.44288e8i			4.33875i
$41$	6.93263e7			0.598382			0.299191	−	0.954193i	$-0.403283\pi$
$41$	6.93263e7			0.598382			0.299191	+	0.954193i	$0.403283\pi$
$42$		−	1.35994e8i		−	1.04057i
$43$		−	9.52345e7i		−	0.647816i	−0.946089	−	0.323908i	$-0.895003\pi$
$43$		−	9.52345e7i		−	0.647816i	0.946089	−	0.323908i	$-0.104997\pi$
$44$			8.14406e8i			4.93830i
$45$	6.96226e7			0.377300
$46$	5.08078e8			2.46684
$47$		−	3.13127e8i		−	1.36531i	−0.730741	−	0.682654i	$-0.760825\pi$
$47$		−	3.13127e8i		−	1.36531i	0.730741	−	0.682654i	$-0.239175\pi$
$48$	−6.86838e8			−2.69555
$49$	−4.91622e7			−0.174041
$50$		−	1.74269e8i		−	0.557662i
$51$	1.10531e8			0.320356
$52$			1.70667e9i			4.48883i
$53$	−1.32764e8			−0.317469			−0.158734	−	0.987321i	$-0.550741\pi$
$53$	−1.32764e8			−0.317469			−0.158734	+	0.987321i	$0.550741\pi$
$54$			1.75243e8i			0.381657i
$55$		−	9.59197e8i		−	1.90587i
$56$		−	1.91856e9i		−	3.48366i
$57$	3.89789e8			0.647821
$58$			1.97934e9i			3.01564i
$59$	−5.75728e8	−	4.23855e8i	−0.805300	−	0.592868i
$59$	−5.75728e8	−	4.23855e8i	−0.805300	−	0.592868i
$60$	1.49038e9			1.91664
$61$			8.26364e8i			0.978413i	0.872168	+	0.489206i	$0.162713\pi$
$61$			8.26364e8i			0.978413i	−0.872168	+	0.489206i	$0.837287\pi$
$62$	−2.72621e9			−2.97578
$63$	−3.00650e8			−0.302941
$64$	−6.54056e9			−6.09137
$65$		−	2.01010e9i		−	1.73241i
$66$	2.41434e9			1.92788
$67$		−	1.28334e8i		−	0.0950533i	−0.998870	−	0.0475266i	$-0.984866\pi$
$67$		−	1.28334e8i		−	0.0950533i	0.998870	−	0.0475266i	$-0.0151339\pi$
$68$	2.36609e9			1.62737
$69$		−	1.12324e9i		−	0.718168i
$70$			3.42873e9i			2.04006i
$71$	1.24650e9			0.690878			0.345439	−	0.938441i	$-0.387730\pi$
$71$	1.24650e9			0.690878			0.345439	+	0.938441i	$0.387730\pi$
$72$			2.47228e9i			1.27772i
$73$			2.30278e9i			1.11081i	0.831581	+	0.555404i	$0.187436\pi$
$73$			2.30278e9i			1.11081i	−0.831581	+	0.555404i	$0.812564\pi$
$74$	3.96333e9			1.78608
$75$	−3.85268e8			−0.162351
$76$	8.34403e9			3.29085
$77$			4.14208e9i			1.53026i
$78$	5.05951e9			1.75241
$79$	−1.18761e9			−0.385957			−0.192979	−	0.981203i	$-0.561815\pi$
$79$	−1.18761e9			−0.385957			−0.192979	+	0.981203i	$0.561815\pi$
$80$	1.73168e10			5.28466
$81$	3.87420e8			0.111111
$82$		−	4.39949e9i		−	1.18668i
$83$			2.67136e9i			0.678177i	0.940755	+	0.339088i	$0.110119\pi$
$83$			2.67136e9i			0.678177i	−0.940755	+	0.339088i	$0.889881\pi$
$84$	−6.43587e9			−1.53890
$85$	−2.78674e9			−0.628062
$86$	−6.04364e9			−1.28471
$87$	4.37583e9			0.877939
$88$	3.40608e10			6.45419
$89$			4.15156e9i			0.743466i	0.928340	+	0.371733i	$0.121236\pi$
$89$			4.15156e9i			0.743466i	−0.928340	+	0.371733i	$0.878764\pi$
$90$		−	4.41829e9i		−	0.748242i
$91$			8.68016e9i			1.39098i
$92$		−	2.40446e10i		−	3.64820i
$93$			6.02700e9i			0.866336i
$94$	−1.98712e10			−2.70761
$95$	−9.82749e9			−1.27006
$96$			2.55424e10i			3.13260i
$97$		−	6.37540e9i		−	0.742418i	−0.928549	−	0.371209i	$-0.878943\pi$
$97$		−	6.37540e9i		−	0.742418i	0.928549	−	0.371209i	$-0.121057\pi$
$98$			3.11987e9i			0.345148i
$99$		−	5.33753e9i		−	0.561260i
$100$	−8.24725e9			−0.824725
$101$			5.60220e9i			0.533030i	0.963831	+	0.266515i	$0.0858722\pi$
$101$			5.60220e9i			0.533030i	−0.963831	+	0.266515i	$0.914128\pi$
$102$		−	7.01437e9i		−	0.635313i
$103$		−	8.39383e9i		−	0.724060i	−0.932167	−	0.362030i	$-0.882084\pi$
$103$		−	8.39383e9i		−	0.724060i	0.932167	−	0.362030i	$-0.117916\pi$
$104$	7.13780e10			5.86675
$105$	7.58008e9			0.593919
$106$			8.42529e9i			0.629587i
$107$	1.66010e10			1.18363			0.591814	−	0.806075i	$-0.298412\pi$
$107$	1.66010e10			1.18363			0.591814	+	0.806075i	$0.298412\pi$
$108$	8.29333e9			0.564430
$109$		−	1.14611e10i		−	0.744892i	−0.928054	−	0.372446i	$-0.878519\pi$
$109$		−	1.14611e10i		−	0.744892i	0.928054	−	0.372446i	$-0.121481\pi$
$110$	−6.08713e10			−3.77963
$111$		−	8.76196e9i		−	0.519980i
$112$	−7.47787e10			−4.24314
$113$		−	2.70084e10i		−	1.46591i	−0.680279	−	0.732953i	$-0.738141\pi$
$113$		−	2.70084e10i		−	1.46591i	0.680279	−	0.732953i	$-0.261859\pi$
$114$		−	2.47363e10i		−	1.28472i
$115$			2.83194e10i			1.40798i
$116$	9.36714e10			4.45982
$117$		−	1.11853e10i		−	0.510176i
$118$	−2.68981e10	+	3.65361e10i	−1.17574	+	1.59703i
$119$	1.20339e10			0.504282
$120$		−	6.23319e10i		−	2.50498i
$121$	−4.75983e10			−1.83512
$122$	5.24416e10			1.94033
$123$	−9.72621e9			−0.345476
$124$			1.29017e11i			4.40088i
$125$	−2.48294e10			−0.813610
$126$			1.90794e10i			0.600776i
$127$	5.99776e9			0.181539			0.0907696	−	0.995872i	$-0.471067\pi$
$127$	5.99776e9			0.181539			0.0907696	+	0.995872i	$0.471067\pi$
$128$			2.28638e11i			6.65424i
$129$			1.33610e10i			0.374017i
$130$	−1.27562e11			−3.43561
$131$		−	3.52715e10i		−	0.914256i	−0.889401	−	0.457128i	$-0.848878\pi$
$131$		−	3.52715e10i		−	0.914256i	0.889401	−	0.457128i	$-0.151122\pi$
$132$		−	1.14258e11i		−	2.85113i
$133$	4.24378e10			1.01975
$134$	−8.14415e9			−0.188504
$135$	−9.76777e9			−0.217835
$136$		−	9.89566e10i		−	2.12692i
$137$	−4.49614e10			−0.931617			−0.465808	−	0.884886i	$-0.654236\pi$
$137$	−4.49614e10			−0.931617			−0.465808	+	0.884886i	$0.654236\pi$
$138$	−7.12814e10			−1.42423
$139$	6.54168e10			1.26071			0.630355	−	0.776307i	$-0.282909\pi$
$139$	6.54168e10			1.26071			0.630355	+	0.776307i	$0.282909\pi$
$140$	1.62263e11			3.01703
$141$			4.39305e10i			0.788261i
$142$		−	7.91038e10i		−	1.37011i
$143$	−1.54102e11			−2.57707
$144$	9.63607e10			1.55628
$145$	−1.10325e11			−1.72121
$146$	1.46136e11			2.20289
$147$	6.89727e9			0.100483
$148$		−	1.87563e11i		−	2.64143i
$149$			1.17694e10i			0.160259i	0.996784	+	0.0801296i	$0.0255334\pi$
$149$			1.17694e10i			0.160259i	−0.996784	+	0.0801296i	$0.974467\pi$
$150$			2.44493e10i			0.321967i
$151$			1.26674e11i			1.61363i	0.590806	+	0.806814i	$0.298810\pi$
$151$			1.26674e11i			1.61363i	−0.590806	+	0.806814i	$0.701190\pi$
$152$		−	3.48972e11i		−	4.30103i
$153$	−1.55071e10			−0.184958
$154$	2.62859e11			3.03473
$155$		−	1.51955e11i		−	1.69846i
$156$		−	2.39440e11i		−	2.59163i
$157$		−	7.42949e9i		−	0.0778862i	−0.999241	−	0.0389431i	$-0.987601\pi$
$157$		−	7.42949e9i		−	0.0778862i	0.999241	−	0.0389431i	$-0.0123991\pi$
$158$			7.53667e10i			0.765410i
$159$	1.86263e10			0.183291
$160$		−	6.43983e11i		−	6.14150i
$161$		−	1.22291e11i		−	1.13049i
$162$		−	2.45860e10i		−	0.220349i
$163$	1.39455e11			1.21198			0.605992	−	0.795471i	$-0.292776\pi$
$163$	1.39455e11			1.21198			0.605992	+	0.795471i	$0.292776\pi$
$164$	−2.08205e11			−1.75498
$165$			1.34572e11i			1.10036i
$166$	1.69527e11			1.34492
$167$	5.22512e10			0.402266			0.201133	−	0.979564i	$-0.435538\pi$
$167$	5.22512e10			0.402266			0.201133	+	0.979564i	$0.435538\pi$
$168$			2.69167e11i			2.01129i
$169$	−1.85077e11			−1.34252
$170$			1.76849e11i			1.24554i
$171$	−5.46859e10			−0.374020
$172$			2.86013e11i			1.89996i
$173$		−	7.25153e10i		−	0.467950i	−0.972243	−	0.233975i	$-0.924827\pi$
$173$		−	7.25153e10i		−	0.467950i	0.972243	−	0.233975i	$-0.0751733\pi$
$174$		−	2.77693e11i		−	1.74108i
$175$	−4.19456e10			−0.255562
$176$		−	1.32757e12i		−	7.86130i
$177$	8.07725e10	+	5.94653e10i	0.464940	+	0.342292i
$178$	2.63461e11			1.47440
$179$			1.80016e11i			0.979592i	0.871837	+	0.489796i	$0.162929\pi$
$179$			1.80016e11i			0.979592i	−0.871837	+	0.489796i	$0.837071\pi$
$180$	−2.09094e11			−1.10657
$181$	3.56609e10			0.183569			0.0917844	−	0.995779i	$-0.470743\pi$
$181$	3.56609e10			0.183569			0.0917844	+	0.995779i	$0.470743\pi$
$182$	5.50848e11			2.75851
$183$		−	1.15936e11i		−	0.564887i
$184$	−1.00562e12			−4.76808
$185$			2.20910e11i			1.01943i
$186$	3.82477e11			1.71807
$187$			2.13642e11i			0.934285i
$188$			9.40399e11i			4.00427i
$189$	4.21800e10			0.174903
$190$			6.23659e11i			2.51871i
$191$		−	3.85490e10i		−	0.151651i	−0.997121	−	0.0758257i	$-0.975841\pi$
$191$		−	3.85490e10i		−	0.151651i	0.997121	−	0.0758257i	$-0.0241593\pi$
$192$	9.17614e11			3.51685
$193$	2.29585e11			0.857349			0.428674	−	0.903459i	$-0.358981\pi$
$193$	2.29585e11			0.857349			0.428674	+	0.903459i	$0.358981\pi$
$194$	−4.04587e11			−1.47232
$195$			2.82009e11i			1.00021i
$196$	1.47647e11			0.510438
$197$	−2.59798e11			−0.875599			−0.437799	−	0.899073i	$-0.644242\pi$
$197$	−2.59798e11			−0.875599			−0.437799	+	0.899073i	$0.644242\pi$
$198$	−3.38723e11			−1.11306
$199$	6.07744e11			1.94740			0.973700	−	0.227832i	$-0.0731639\pi$
$199$	6.07744e11			1.94740			0.973700	+	0.227832i	$0.0731639\pi$
$200$			3.44924e11i			1.07789i
$201$			1.80047e10i			0.0548790i
$202$	3.55519e11			1.05708
$203$	4.76414e11			1.38199
$204$	−3.31953e11			−0.939562
$205$	2.45221e11			0.677310
$206$	−5.32678e11			−1.43592
$207$			1.57586e11i			0.414635i
$208$		−	2.78206e12i		−	7.14578i
$209$			7.53413e11i			1.88930i
$210$		−	4.81037e11i		−	1.17783i
$211$			3.48490e11i			0.833255i	0.909077	+	0.416628i	$0.136788\pi$
$211$			3.48490e11i			0.833255i	−0.909077	+	0.416628i	$0.863212\pi$
$212$	3.98724e11			0.931093
$213$	−1.74879e11			−0.398879
$214$		−	1.05351e12i		−	2.34730i
$215$		−	3.36863e11i		−	0.733264i
$216$		−	3.46851e11i		−	0.737691i
$217$			6.56183e11i			1.36372i
$218$	−7.27328e11			−1.47723
$219$		−	3.23072e11i		−	0.641325i
$220$			2.88071e12i			5.58967i
$221$			4.47710e11i			0.849249i
$222$	−5.56040e11			−1.03120
$223$	−9.61110e10			−0.174281			−0.0871403	−	0.996196i	$-0.527773\pi$
$223$	−9.61110e10			−0.174281			−0.0871403	+	0.996196i	$0.527773\pi$
$224$			2.78090e12i			4.93112i
$225$	5.40515e10			0.0937336
$226$	−1.71397e12			−2.90711
$227$			1.97002e11i			0.326845i	0.986556	+	0.163423i	$0.0522534\pi$
$227$			1.97002e11i			0.326845i	−0.986556	+	0.163423i	$0.947747\pi$
$228$	−1.17064e12			−1.89997
$229$			1.93983e11i			0.308026i	0.988069	+	0.154013i	$0.0492197\pi$
$229$			1.93983e11i			0.308026i	−0.988069	+	0.154013i	$0.950780\pi$
$230$	1.79717e12			2.79222
$231$		−	5.81118e11i		−	0.883495i
$232$		−	3.91761e12i		−	5.82883i
$233$		−	4.62830e11i		−	0.673972i	−0.941510	−	0.336986i	$-0.890592\pi$
$233$		−	4.62830e11i		−	0.673972i	0.941510	−	0.336986i	$-0.109408\pi$
$234$	−7.09829e11			−1.01175
$235$		−	1.10759e12i		−	1.54540i
$236$	1.72906e12	+	1.27295e12i	2.36184	+	1.73880i
$237$	1.66617e11			0.222833
$238$		−	7.63682e11i		−	1.00006i
$239$	−1.34407e12			−1.72358			−0.861789	−	0.507267i	$-0.830656\pi$
$239$	−1.34407e12			−1.72358			−0.861789	+	0.507267i	$0.830656\pi$
$240$	−2.42948e12			−3.05110
$241$	3.68238e11			0.452943			0.226471	−	0.974018i	$-0.427281\pi$
$241$	3.68238e11			0.452943			0.226471	+	0.974018i	$0.427281\pi$
$242$			3.02062e12i			3.63931i
$243$	−5.43536e10			−0.0641500
$244$		−	2.48178e12i		−	2.86955i
$245$	−1.73896e11			−0.196997
$246$			6.17232e11i			0.685130i
$247$			1.57885e12i			1.71734i
$248$	5.39587e12			5.75179
$249$		−	3.74782e11i		−	0.391545i
$250$			1.57569e12i			1.61351i
$251$	−4.16900e11			−0.418469			−0.209234	−	0.977866i	$-0.567097\pi$
$251$	−4.16900e11			−0.418469			−0.209234	+	0.977866i	$0.567097\pi$
$252$	9.02928e11			0.888485
$253$	2.17108e12			2.09446
$254$		−	3.80622e11i		−	0.360019i
$255$	3.90969e11			0.362612
$256$	7.81198e12			7.10496
$257$	1.65267e12			1.47407			0.737037	−	0.675852i	$-0.236224\pi$
$257$	1.65267e12			1.47407			0.737037	+	0.675852i	$0.236224\pi$
$258$	8.47899e11			0.741730
$259$		−	9.53949e11i		−	0.818515i
$260$			6.03683e12i			5.08092i
$261$	−6.13912e11			−0.506878
$262$	−2.23835e12			−1.81310
$263$	8.88346e11			0.705998			0.352999	−	0.935624i	$-0.385162\pi$
$263$	8.88346e11			0.705998			0.352999	+	0.935624i	$0.385162\pi$
$264$	−4.77860e12			−3.72633
$265$	−4.69612e11			−0.359343
$266$		−	2.69313e12i		−	2.02232i
$267$		−	5.82448e11i		−	0.429240i
$268$			3.85419e11i			0.278778i
$269$			8.05656e11i			0.571990i	0.958231	+	0.285995i	$0.0923240\pi$
$269$			8.05656e11i			0.571990i	−0.958231	+	0.285995i	$0.907676\pi$
$270$			6.19869e11i			0.431998i
$271$	1.43475e12			0.981587			0.490794	−	0.871276i	$-0.336707\pi$
$271$	1.43475e12			0.981587			0.490794	+	0.871276i	$0.336707\pi$
$272$	−3.85698e12			−2.59061
$273$		−	1.21779e12i		−	0.803082i
$274$			2.85328e12i			1.84753i
$275$		−	7.44673e11i		−	0.473481i
$276$			3.37337e12i			2.10629i
$277$	1.40442e12			0.861191			0.430596	−	0.902545i	$-0.358304\pi$
$277$	1.40442e12			0.861191			0.430596	+	0.902545i	$0.358304\pi$
$278$		−	4.15139e12i		−	2.50017i
$279$		−	8.45564e11i		−	0.500179i
$280$		−	6.78632e12i		−	3.94316i
$281$	−1.17796e12			−0.672355			−0.336177	−	0.941799i	$-0.609134\pi$
$281$	−1.17796e12			−0.672355			−0.336177	+	0.941799i	$0.609134\pi$
$282$	2.78786e12			1.56324
$283$		−	7.49696e11i		−	0.413003i	−0.978446	−	0.206501i	$-0.933792\pi$
$283$		−	7.49696e11i		−	0.413003i	0.978446	−	0.206501i	$-0.0662078\pi$
$284$	−3.74356e12			−2.02625
$285$	1.37876e12			0.733270
$286$			9.77939e12i			5.11071i
$287$	−1.05893e12			−0.543824
$288$		−	3.58350e12i		−	1.80861i
$289$	−1.39530e12			−0.692115
$290$			7.00129e12i			3.41341i
$291$			8.94444e11i			0.428635i
$292$		−	6.91585e12i		−	3.25785i
$293$	3.53806e12			1.63843			0.819213	−	0.573490i	$-0.194411\pi$
$293$	3.53806e12			1.63843			0.819213	+	0.573490i	$0.194411\pi$
$294$		−	4.37705e11i		−	0.199271i
$295$	−2.03646e12	−	1.49926e12i	−0.911520	−	0.671068i
$296$	−7.84444e12			−3.45226
$297$			7.48835e11i			0.324044i
$298$	7.46894e11			0.317817
$299$	4.54972e12			1.90383
$300$	1.15706e12			0.476155
$301$			1.45467e12i			0.588750i
$302$	8.03883e12			3.20006
$303$		−	7.85967e11i		−	0.307745i
$304$	−1.36017e13			−5.23871
$305$			2.92301e12i			1.10747i
$306$			9.84089e11i			0.366798i
$307$	−2.20403e11			−0.0808211			−0.0404106	−	0.999183i	$-0.512867\pi$
$307$	−2.20403e11			−0.0808211			−0.0404106	+	0.999183i	$0.512867\pi$
$308$		−	1.24397e13i		−	4.48804i
$309$			1.17762e12i			0.418036i
$310$	−9.64314e12			−3.36830
$311$	4.06893e12			1.39855			0.699276	−	0.714852i	$-0.253506\pi$
$311$	4.06893e12			1.39855			0.699276	+	0.714852i	$0.253506\pi$
$312$	−1.00141e13			−3.38717
$313$		−	3.98362e12i		−	1.32604i	−0.748602	−	0.663020i	$-0.769275\pi$
$313$		−	3.98362e12i		−	1.32604i	0.748602	−	0.663020i	$-0.230725\pi$
$314$	−4.71480e11			−0.154460
$315$	−1.06346e12			−0.342899
$316$	3.56670e12			1.13196
$317$	−1.46358e12			−0.457216			−0.228608	−	0.973519i	$-0.573417\pi$
$317$	−1.46358e12			−0.457216			−0.228608	+	0.973519i	$0.573417\pi$
$318$		−	1.18204e12i		−	0.363492i
$319$			8.45793e12i			2.56042i
$320$	−2.31352e13			−6.89483
$321$	−2.32905e12			−0.683367
$322$	−7.76069e12			−2.24192
$323$	2.18888e12			0.622601
$324$	−1.16352e12			−0.325874
$325$		−	1.56054e12i		−	0.430386i
$326$		−	8.84993e12i		−	2.40354i
$327$			1.60794e12i			0.430063i
$328$			8.70772e12i			2.29369i
$329$			4.78288e12i			1.24082i
$330$	8.54000e12			2.18217
$331$	3.84998e12			0.968989			0.484495	−	0.874794i	$-0.339003\pi$
$331$	3.84998e12			0.968989			0.484495	+	0.874794i	$0.339003\pi$
$332$		−	8.02279e12i		−	1.98900i
$333$			1.22927e12i			0.300211i
$334$		−	3.31589e12i		−	0.797753i
$335$		−	4.53941e11i		−	0.107591i
$336$	1.04912e13			2.44978
$337$			2.99149e12i			0.688236i	0.938926	+	0.344118i	$0.111822\pi$
$337$			2.99149e12i			0.688236i	−0.938926	+	0.344118i	$0.888178\pi$
$338$			1.17451e13i			2.66240i
$339$			3.78917e12i			0.846342i
$340$	8.36930e12			1.84202
$341$	−1.16494e13			−2.52658
$342$			3.47040e12i			0.741736i
$343$	5.06563e12			1.06700
$344$	1.19619e13			2.48318
$345$		−	3.97311e12i		−	0.812896i
$346$	−4.60187e12			−0.928012
$347$		−	3.80325e12i		−	0.755974i	−0.925811	−	0.377987i	$-0.876616\pi$
$347$		−	3.80325e12i		−	0.755974i	0.925811	−	0.377987i	$-0.123384\pi$
$348$	−1.31417e13			−2.57488
$349$		−	4.05477e12i		−	0.783139i	−0.920148	−	0.391570i	$-0.871932\pi$
$349$		−	4.05477e12i		−	0.783139i	0.920148	−	0.391570i	$-0.128068\pi$
$350$			2.66189e12i			0.506816i
$351$			1.56926e12i			0.294550i
$352$	−4.93702e13			−9.13590
$353$			8.59729e12i			1.56851i	0.620437	+	0.784257i	$0.286955\pi$
$353$			8.59729e12i			1.56851i	−0.620437	+	0.784257i	$0.713045\pi$
$354$	3.77371e12	−	5.12587e12i	0.678815	−	0.922044i
$355$	4.40912e12			0.782006
$356$		−	1.24682e13i		−	2.18049i
$357$	−1.68832e12			−0.291147
$358$	1.14239e13			1.94267
$359$	−4.33032e12			−0.726186			−0.363093	−	0.931753i	$-0.618279\pi$
$359$	−4.33032e12			−0.726186			−0.363093	+	0.931753i	$0.618279\pi$
$360$			8.74493e12i			1.44625i
$361$	1.58805e12			0.259017
$362$		−	2.26306e12i		−	0.364044i
$363$	6.67785e12			1.05951
$364$		−	2.60687e13i		−	4.07955i
$365$			8.14539e12i			1.25733i
$366$	−7.35735e12			−1.12025
$367$		−	3.71511e12i		−	0.558009i	−0.960290	−	0.279004i	$-0.909996\pi$
$367$		−	3.71511e12i		−	0.558009i	0.960290	−	0.279004i	$-0.0900044\pi$
$368$			3.91954e13i			5.80758i
$369$	1.36455e12			0.199461
$370$	1.40191e13			2.02167
$371$	2.02792e12			0.288523
$372$		−	1.81006e13i		−	2.54085i
$373$	−5.40807e12			−0.749028			−0.374514	−	0.927221i	$-0.622190\pi$
$373$	−5.40807e12			−0.749028			−0.374514	+	0.927221i	$0.622190\pi$
$374$	1.35579e13			1.85282
$375$	3.48347e12			0.469738
$376$	3.93302e13			5.23344
$377$			1.77245e13i			2.32737i
$378$		−	2.67677e12i		−	0.346858i
$379$	−5.39111e12			−0.689418			−0.344709	−	0.938710i	$-0.612022\pi$
$379$	−5.39111e12			−0.689418			−0.344709	+	0.938710i	$0.612022\pi$
$380$	2.95144e13			3.72492
$381$	−8.41462e11			−0.104812
$382$	−2.44635e12			−0.300747
$383$	2.79998e12			0.339752			0.169876	−	0.985465i	$-0.445663\pi$
$383$	2.79998e12			0.339752			0.169876	+	0.985465i	$0.445663\pi$
$384$		−	3.20770e13i		−	3.84183i
$385$			1.46513e13i			1.73210i
$386$		−	1.45696e13i		−	1.70025i
$387$		−	1.87450e12i		−	0.215939i
$388$			1.91469e13i			2.17741i
$389$	−6.90292e12			−0.774970			−0.387485	−	0.921876i	$-0.626656\pi$
$389$	−6.90292e12			−0.774970			−0.387485	+	0.921876i	$0.626656\pi$
$390$	1.78964e13			1.98355
$391$		−	6.30761e12i		−	0.690209i
$392$		−	6.17501e12i		−	0.667125i
$393$			4.94846e12i			0.527846i
$394$			1.64870e13i			1.73644i
$395$	−4.20081e12			−0.436866
$396$			1.60300e13i			1.64610i
$397$			5.45035e12i			0.552678i	0.961060	+	0.276339i	$0.0891212\pi$
$397$			5.45035e12i			0.552678i	−0.961060	+	0.276339i	$0.910879\pi$
$398$		−	3.85678e13i		−	3.86198i
$399$	−5.95386e12			−0.588755
$400$	1.34439e13			1.31288
$401$			1.49009e12i			0.143711i	0.997415	+	0.0718557i	$0.0228921\pi$
$401$			1.49009e12i			0.143711i	−0.997415	+	0.0718557i	$0.977108\pi$
$402$	1.14259e12			0.108833
$403$	−2.44126e13			−2.29662
$404$		−	1.68248e13i		−	1.56331i
$405$	1.37038e12			0.125767
$406$		−	3.02335e13i		−	2.74068i
$407$	1.69358e13			1.51647
$408$			1.38832e13i			1.22798i
$409$		−	8.65719e12i		−	0.756415i	−0.925721	−	0.378208i	$-0.876541\pi$
$409$		−	8.65719e12i		−	0.756415i	0.925721	−	0.378208i	$-0.123459\pi$
$410$		−	1.55619e13i		−	1.34320i
$411$	6.30792e12			0.537869
$412$			2.52088e13i			2.12357i
$413$	8.79401e12	+	6.47422e12i	0.731875	+	0.538812i
$414$	1.00005e13			0.822281
$415$			9.44913e12i			0.767629i
$416$	−1.03460e14			−8.30438
$417$	−9.17773e12			−0.727872
$418$	4.78121e13			3.74676
$419$		−	1.38750e13i		−	1.07439i	−0.843458	−	0.537196i	$-0.819484\pi$
$419$		−	1.38750e13i		−	1.07439i	0.843458	−	0.537196i	$-0.180516\pi$
$420$	−2.27649e13			−1.74188
$421$			1.17891e13i			0.891397i	0.895183	+	0.445699i	$0.147045\pi$
$421$			1.17891e13i			0.891397i	−0.895183	+	0.445699i	$0.852955\pi$
$422$	2.21154e13			1.65247
$423$		−	6.16327e12i		−	0.455103i
$424$		−	1.66758e13i		−	1.21691i
$425$	−2.16349e12			−0.156031
$426$			1.10980e13i			0.791034i
$427$		−	1.26224e13i		−	0.889204i
$428$	−4.98570e13			−3.47142
$429$	2.16199e13			1.48787
$430$	−2.13775e13			−1.45417
$431$			8.12118e12i			0.546051i	0.962007	+	0.273025i	$0.0880243\pi$
$431$			8.12118e12i			0.546051i	−0.962007	+	0.273025i	$0.911976\pi$
$432$	−1.35190e13			−0.898518
$433$	−1.62737e13			−1.06917			−0.534585	−	0.845114i	$-0.679532\pi$
$433$	−1.62737e13			−1.06917			−0.534585	+	0.845114i	$0.679532\pi$
$434$	4.16418e13			2.70446
$435$	1.54782e13			0.993740
$436$			3.44205e13i			2.18467i
$437$		−	2.22438e13i		−	1.39573i
$438$	−2.05023e13			−1.27184
$439$	2.87183e11			0.0176131			0.00880655	−	0.999961i	$-0.497197\pi$
$439$	2.87183e11			0.0176131			0.00880655	+	0.999961i	$0.497197\pi$
$440$	1.20480e14			7.30551
$441$	−9.67660e11			−0.0580136
$442$	2.84120e13			1.68418
$443$			2.13237e13i			1.24981i	0.780700	+	0.624906i	$0.214863\pi$
$443$			2.13237e13i			1.24981i	−0.780700	+	0.624906i	$0.785137\pi$
$444$			2.63144e13i			1.52503i
$445$			1.46849e13i			0.841530i
$446$			6.09927e12i			0.345624i
$447$		−	1.65120e12i		−	0.0925257i
$448$	9.99043e13			5.53597
$449$	−6.85125e12			−0.375438			−0.187719	−	0.982223i	$-0.560109\pi$
$449$	−6.85125e12			−0.375438			−0.187719	+	0.982223i	$0.560109\pi$
$450$		−	3.43015e12i		−	0.185887i
$451$		−	1.87995e13i		−	1.00755i
$452$			8.11130e13i			4.29931i
$453$		−	1.77719e13i		−	0.931629i
$454$	1.25019e13			0.648181
$455$			3.07034e13i			1.57445i
$456$			4.89593e13i			2.48320i
$457$			2.16366e13i			1.08544i	0.839912	+	0.542722i	$0.182606\pi$
$457$			2.16366e13i			1.08544i	−0.839912	+	0.542722i	$0.817394\pi$
$458$	1.23103e13			0.610860
$459$	2.17558e12			0.106785
$460$		−	8.50505e13i		−	4.12941i
$461$	−2.85231e13			−1.36991			−0.684954	−	0.728586i	$-0.740178\pi$
$461$	−2.85231e13			−1.36991			−0.684954	+	0.728586i	$0.740178\pi$
$462$	−3.68781e13			−1.75210
$463$			2.28437e13i			1.07365i	0.843695	+	0.536823i	$0.180376\pi$
$463$			2.28437e13i			1.07365i	−0.843695	+	0.536823i	$0.819624\pi$
$464$	−1.52695e14			−7.09959
$465$			2.13187e13i			0.980607i
$466$	−2.93715e13			−1.33658
$467$			2.57417e13i			1.15892i	0.815001	+	0.579460i	$0.196736\pi$
$467$			2.57417e13i			1.15892i	−0.815001	+	0.579460i	$0.803264\pi$
$468$			3.35924e13i			1.49628i
$469$			1.96025e12i			0.0863866i
$470$	−7.02884e13			−3.06474
$471$			1.04233e12i			0.0449676i
$472$	5.32383e13	−	7.23143e13i	2.27255	−	3.08684i
$473$	−2.58252e13			−1.09078
$474$		−	1.05737e13i		−	0.441910i
$475$	−7.62958e12			−0.315524
$476$	−3.61410e13			−1.47899
$477$	−2.61319e12			−0.105823
$478$			8.52953e13i			3.41811i
$479$	2.39832e13			0.951109			0.475554	−	0.879686i	$-0.342247\pi$
$479$	2.39832e13			0.951109			0.475554	+	0.879686i	$0.342247\pi$
$480$			9.03483e13i			3.54580i
$481$	3.54906e13			1.37844
$482$		−	2.33686e13i		−	0.898252i
$483$			1.71570e13i			0.652688i
$484$	1.42950e14			5.38216
$485$		−	2.25510e13i		−	0.840344i
$486$			3.44931e12i			0.127219i
$487$	−4.35984e13			−1.59157			−0.795785	−	0.605579i	$-0.792942\pi$
$487$	−4.35984e13			−1.59157			−0.795785	+	0.605579i	$0.792942\pi$
$488$	−1.03795e14			−3.75041
$489$	−1.95650e13			−0.699740
$490$			1.10356e13i			0.390674i
$491$	1.82138e13			0.638253			0.319126	−	0.947712i	$-0.396611\pi$
$491$	1.82138e13			0.638253			0.319126	+	0.947712i	$0.396611\pi$
$492$	2.92103e13			1.01324
$493$	2.45727e13			0.843760
$494$	1.00195e14			3.40574
$495$		−	1.88799e13i		−	0.635291i
$496$		−	2.10312e14i		−	7.00576i
$497$	−1.90398e13			−0.627886
$498$	−2.37839e13			−0.776491
$499$	−1.37633e13			−0.444858			−0.222429	−	0.974949i	$-0.571399\pi$
$499$	−1.37633e13			−0.444858			−0.222429	+	0.974949i	$0.571399\pi$
$500$	7.45690e13			2.38621
$501$	−7.33064e12			−0.232249
$502$			2.64567e13i			0.829884i
$503$		−	5.90065e13i		−	1.83257i	−0.400529	−	0.916284i	$-0.631173\pi$
$503$		−	5.90065e13i		−	1.83257i	0.400529	−	0.916284i	$-0.368827\pi$
$504$		−	3.77630e13i		−	1.16122i
$505$			1.98161e13i			0.603337i
$506$		−	1.37778e14i		−	4.15362i
$507$	2.59656e13			0.775102
$508$	−1.80128e13			−0.532430
$509$			2.78998e13i			0.816606i	0.912846	+	0.408303i	$0.133879\pi$
$509$			2.78998e13i			0.816606i	−0.912846	+	0.408303i	$0.866121\pi$
$510$		−	2.48112e13i		−	0.719112i
$511$		−	3.51741e13i		−	1.00953i
$512$		−	2.61628e14i		−	7.43593i
$513$	7.67221e12			0.215940
$514$		−	1.04879e14i		−	2.92330i
$515$		−	2.96906e13i		−	0.819564i
$516$		−	4.01266e13i		−	1.09694i
$517$	−8.49120e13			−2.29888
$518$	−6.05382e13			−1.62323
$519$			1.01736e13i			0.270171i
$520$	2.52478e14			6.64058
$521$	−2.12484e12			−0.0553526			−0.0276763	−	0.999617i	$-0.508811\pi$
$521$	−2.12484e12			−0.0553526			−0.0276763	+	0.999617i	$0.508811\pi$
$522$			3.89593e13i			1.00521i
$523$	6.37536e12			0.162928			0.0814641	−	0.996676i	$-0.474040\pi$
$523$	6.37536e12			0.162928			0.0814641	+	0.996676i	$0.474040\pi$
$524$			1.05929e14i			2.68139i
$525$	5.88480e12			0.147549
$526$		−	5.63750e13i		−	1.40010i
$527$			3.38450e13i			0.832609i
$528$			1.86253e14i			4.53872i
$529$	−2.26726e13			−0.547298
$530$			2.98019e13i			0.712630i
$531$	−1.13321e13	−	8.34275e12i	−0.268433	−	0.197623i
$532$	−1.27452e14			−2.99080
$533$		−	3.93964e13i		−	0.915841i
$534$	−3.69625e13			−0.851246
$535$	5.87209e13			1.33975
$536$	1.61193e13			0.364354
$537$		−	2.52555e13i		−	0.565567i
$538$	5.11274e13			1.13434
$539$			1.33315e13i			0.293047i
$540$	2.93351e13			0.638879
$541$			2.78098e13i			0.600084i	0.953926	+	0.300042i	$0.0970007\pi$
$541$			2.78098e13i			0.600084i	−0.953926	+	0.300042i	$0.902999\pi$
$542$		−	9.10500e13i		−	1.94663i
$543$	−5.00308e12			−0.105984
$544$			1.43435e14i			3.01065i
$545$		−	4.05400e13i		−	0.843144i
$546$	−7.72819e13			−1.59263
$547$	2.91420e13			0.595090			0.297545	−	0.954708i	$-0.403832\pi$
$547$	2.91420e13			0.595090			0.297545	+	0.954708i	$0.403832\pi$
$548$	1.35031e14			2.73231
$549$			1.62653e13i			0.326138i
$550$	−4.72575e13			−0.938981
$551$	8.66560e13			1.70624
$552$	1.41084e14			2.75285
$553$	1.81403e13			0.350767
$554$		−	8.91257e13i		−	1.70787i
$555$		−	3.09927e13i		−	0.588566i
$556$	−1.96463e14			−3.69750
$557$	−1.00678e14			−1.87784			−0.938918	−	0.344141i	$-0.888170\pi$
$557$	−1.00678e14			−1.87784			−0.938918	+	0.344141i	$0.888170\pi$
$558$	−5.36601e13			−0.991928
$559$	−5.41193e13			−0.991501
$560$	−2.64507e14			−4.80282
$561$		−	2.99732e13i		−	0.539410i
$562$			7.47540e13i			1.33338i
$563$			8.71239e13i			1.54027i	0.637884	+	0.770133i	$0.279810\pi$
$563$			8.71239e13i			1.54027i	−0.637884	+	0.770133i	$0.720190\pi$
$564$		−	1.31934e14i		−	2.31186i
$565$		−	9.55338e13i		−	1.65926i
$566$	−4.75762e13			−0.819044
$567$	−5.91769e12			−0.100980
$568$			1.56567e14i			2.64824i
$569$		−	3.85604e13i		−	0.646517i	−0.946311	−	0.323258i	$-0.895222\pi$
$569$		−	3.85604e13i		−	0.646517i	0.946311	−	0.323258i	$-0.104778\pi$
$570$		−	8.74969e13i		−	1.45418i
$571$		−	2.61452e13i		−	0.430736i	−0.976533	−	0.215368i	$-0.930905\pi$
$571$		−	2.61452e13i		−	0.430736i	0.976533	−	0.215368i	$-0.0690952\pi$
$572$	4.62806e14			7.55821
$573$			5.40828e12i			0.0875560i
$574$			6.72004e13i			1.07848i
$575$			2.19858e13i			0.349787i
$576$	−1.28738e14			−2.03046
$577$	3.06953e13			0.479947			0.239973	−	0.970779i	$-0.422861\pi$
$577$	3.06953e13			0.479947			0.239973	+	0.970779i	$0.422861\pi$
$578$			8.85467e13i			1.37257i
$579$	−3.22099e13			−0.494991
$580$	3.31334e14			5.04807
$581$		−	4.08040e13i		−	0.616342i
$582$	5.67620e13			0.850046
$583$			3.60022e13i			0.534548i
$584$	−2.89241e14			−4.25790
$585$		−	3.95647e13i		−	0.577469i
$586$		−	2.24527e14i		−	3.24924i
$587$			2.54401e13i			0.365029i	0.983203	+	0.182515i	$0.0584237\pi$
$587$			2.54401e13i			0.365029i	−0.983203	+	0.182515i	$0.941576\pi$
$588$	−2.07143e13			−0.294702
$589$			1.19355e14i			1.68369i
$590$	−9.51439e13	+	1.29235e14i	−1.33082	+	1.80768i
$591$	3.64487e13			0.505527
$592$			3.05748e14i			4.20490i
$593$	1.36225e13			0.185773			0.0928864	−	0.995677i	$-0.470391\pi$
$593$	1.36225e13			0.185773			0.0928864	+	0.995677i	$0.470391\pi$
$594$	4.75215e13			0.642626
$595$	4.25664e13			0.570797
$596$		−	3.53465e13i		−	0.470019i
$597$	−8.52641e13			−1.12433
$598$		−	2.88728e14i		−	3.77557i
$599$	1.16474e14			1.51041			0.755205	−	0.655489i	$-0.227537\pi$
$599$	1.16474e14			1.51041			0.755205	+	0.655489i	$0.227537\pi$
$600$		−	4.83915e13i		−	0.622318i
$601$			1.07353e14i			1.36912i	0.728956	+	0.684560i	$0.240006\pi$
$601$			1.07353e14i			1.36912i	−0.728956	+	0.684560i	$0.759994\pi$
$602$	9.23141e13			1.16758
$603$		−	2.52599e12i		−	0.0316844i
$604$		−	3.80435e14i		−	4.73255i
$605$	−1.68364e14			−2.07717
$606$	−4.98780e13			−0.610303
$607$	−8.44133e13			−1.02440			−0.512198	−	0.858868i	$-0.671168\pi$
$607$	−8.44133e13			−1.02440			−0.512198	+	0.858868i	$0.671168\pi$
$608$			5.05824e14i			6.08810i
$609$	−6.68390e13			−0.797891
$610$	1.85496e14			2.19627
$611$	−1.77942e14			−2.08964
$612$	4.65717e13			0.542456
$613$		−	9.06076e13i		−	1.04680i	−0.852088	−	0.523398i	$-0.824664\pi$
$613$		−	9.06076e13i		−	1.04680i	0.852088	−	0.523398i	$-0.175336\pi$
$614$			1.39869e13i			0.160280i
$615$	−3.44035e13			−0.391045
$616$	−5.20265e14			−5.86572
$617$	−1.24220e14			−1.38920			−0.694599	−	0.719397i	$-0.744418\pi$
$617$	−1.24220e14			−1.38920			−0.694599	+	0.719397i	$0.744418\pi$
$618$	7.47327e13			0.829026
$619$	−2.99465e13			−0.329528			−0.164764	−	0.986333i	$-0.552686\pi$
$619$	−2.99465e13			−0.329528			−0.164764	+	0.986333i	$0.552686\pi$
$620$			4.56359e14i			4.98136i
$621$		−	2.21087e13i		−	0.239389i
$622$		−	2.58217e14i		−	2.77353i
$623$		−	6.34133e13i		−	0.675679i
$624$			3.90312e14i			4.12562i
$625$	−1.14644e14			−1.20213
$626$	−2.52803e14			−2.62973
$627$		−	1.05701e14i		−	1.09079i
$628$			2.23126e13i			0.228430i
$629$		−	4.92033e13i		−	0.499737i
$630$			6.74876e13i			0.680019i
$631$	7.50471e13			0.750218			0.375109	−	0.926981i	$-0.377605\pi$
$631$	7.50471e13			0.750218			0.375109	+	0.926981i	$0.377605\pi$
$632$		−	1.49170e14i		−	1.47943i
$633$		−	4.88918e13i		−	0.481080i
$634$			9.28800e13i			0.906726i
$635$	2.12152e13			0.205484
$636$	−5.59394e13			−0.537567
$637$			2.79376e13i			0.266374i
$638$	5.36746e14			5.07768
$639$	2.45349e13			0.230293
$640$			8.08736e14i			7.53194i
$641$	1.27671e14			1.17978			0.589890	−	0.807484i	$-0.299171\pi$
$641$	1.27671e14			1.17978			0.589890	+	0.807484i	$0.299171\pi$
$642$			1.47803e14i			1.35522i
$643$	−1.71159e14			−1.55720			−0.778599	−	0.627522i	$-0.784069\pi$
$643$	−1.71159e14			−1.55720			−0.778599	+	0.627522i	$0.784069\pi$
$644$			3.67272e14i			3.31557i
$645$			4.72605e13i			0.423350i
$646$		−	1.38908e14i		−	1.23471i
$647$	−2.06196e14			−1.81869			−0.909346	−	0.416041i	$-0.863417\pi$
$647$	−2.06196e14			−1.81869			−0.909346	+	0.416041i	$0.863417\pi$
$648$			4.86619e13i			0.425906i
$649$	−1.14939e14	+	1.56123e14i	−0.998259	+	1.35595i
$650$	−9.90329e13			−0.853518
$651$		−	9.20599e13i		−	0.787346i
$652$	−4.18820e14			−3.55459
$653$	6.59315e13			0.555299			0.277650	−	0.960682i	$-0.410445\pi$
$653$	6.59315e13			0.555299			0.277650	+	0.960682i	$0.410445\pi$
$654$	1.02041e14			0.852878
$655$		−	1.24762e14i		−	1.03485i
$656$	3.39396e14			2.79375
$657$			4.53257e13i			0.370269i
$658$	3.03525e14			2.46073
$659$			4.23653e13i			0.340866i	0.985369	+	0.170433i	$0.0545166\pi$
$659$			4.23653e13i			0.340866i	−0.985369	+	0.170433i	$0.945483\pi$
$660$		−	4.04153e14i		−	3.22720i
$661$	5.82687e13			0.461772			0.230886	−	0.972981i	$-0.425837\pi$
$661$	5.82687e13			0.461772			0.230886	+	0.972981i	$0.425837\pi$
$662$		−	2.44323e14i		−	1.92165i
$663$		−	6.28119e13i		−	0.490314i
$664$	−3.35536e14			−2.59955
$665$	1.50111e14			1.15426
$666$	7.80102e13			0.595361
$667$		−	2.49713e14i		−	1.89152i
$668$	−1.56924e14			−1.17979
$669$	1.34840e13			0.100621
$670$	−2.88074e13			−0.213368
$671$	2.24089e14			1.64743
$672$		−	3.90149e14i		−	2.84698i
$673$		−	2.60802e13i		−	0.188901i	−0.995530	−	0.0944507i	$-0.969891\pi$
$673$		−	2.60802e13i		−	0.188901i	0.995530	−	0.0944507i	$-0.0301095\pi$
$674$	1.89842e14			1.36487
$675$	−7.58322e12			−0.0541171
$676$	5.55834e14			3.93742
$677$	3.97353e13			0.279405			0.139702	−	0.990194i	$-0.455385\pi$
$677$	3.97353e13			0.279405			0.139702	+	0.990194i	$0.455385\pi$
$678$	2.40463e14			1.67842
$679$			9.73816e13i			0.674727i
$680$		−	3.50028e14i		−	2.40746i
$681$		−	2.76387e13i		−	0.188704i
$682$			7.39280e14i			5.01057i
$683$		−	9.13519e13i		−	0.614630i	−0.951608	−	0.307315i	$-0.900569\pi$
$683$		−	9.13519e13i		−	0.614630i	0.951608	−	0.307315i	$-0.0994306\pi$
$684$	1.64236e14			1.09695
$685$	−1.59037e14			−1.05450
$686$		−	3.21468e14i		−	2.11601i
$687$		−	2.72151e13i		−	0.177839i
$688$		−	4.66233e14i		−	3.02455i
$689$			7.54464e13i			0.485895i
$690$	−2.52136e14			−1.61209
$691$			1.66013e13i			0.105378i	0.998611	+	0.0526892i	$0.0167793\pi$
$691$			1.66013e13i			0.105378i	−0.998611	+	0.0526892i	$0.983221\pi$
$692$			2.17782e14i			1.37243i
$693$			8.15286e13i			0.510086i
$694$	−2.41356e14			−1.49921
$695$	2.31392e14			1.42700
$696$			5.49625e14i			3.36528i
$697$	−5.46181e13			−0.332027
$698$	−2.57318e14			−1.55308
$699$			6.49333e13i			0.389118i
$700$	1.25973e14			0.749529
$701$			7.36214e13i			0.434924i	0.976069	+	0.217462i	$0.0697779\pi$
$701$			7.36214e13i			0.434924i	−0.976069	+	0.217462i	$0.930222\pi$
$702$	9.95863e13			0.584136
$703$		−	1.73516e14i		−	1.01056i
$704$			1.77363e15i			10.2565i
$705$			1.55391e14i			0.892234i
$706$	5.45590e14			3.11059
$707$		−	8.55713e13i		−	0.484430i
$708$	−2.42580e14	−	1.78589e14i	−1.36361	−	1.00390i
$709$	−7.87948e13			−0.439811			−0.219906	−	0.975521i	$-0.570575\pi$
$709$	−7.87948e13			−0.439811			−0.219906	+	0.975521i	$0.570575\pi$
$710$		−	2.79806e14i		−	1.55083i
$711$	−2.33758e13			−0.128652
$712$	−5.21456e14			−2.84982
$713$	3.43939e14			1.86653
$714$			1.07142e14i			0.577387i
$715$	−5.45087e14			−2.91699
$716$		−	5.40633e14i		−	2.87301i
$717$	1.88567e14			0.995108
$718$			2.74805e14i			1.44013i
$719$		−	7.23964e12i		−	0.0376767i	−0.999823	−	0.0188383i	$-0.994003\pi$
$719$		−	7.23964e12i		−	0.0376767i	0.999823	−	0.0188383i	$-0.00599678\pi$
$720$	3.40846e14			1.76155
$721$			1.28212e14i			0.658042i
$722$		−	1.00779e14i		−	0.513669i
$723$	−5.16624e13			−0.261507
$724$	−1.07099e14			−0.538383
$725$	−8.56509e13			−0.427604
$726$		−	4.23781e14i		−	2.10116i
$727$	−1.20450e14			−0.593111			−0.296555	−	0.955016i	$-0.595838\pi$
$727$	−1.20450e14			−0.593111			−0.296555	+	0.955016i	$0.595838\pi$
$728$	−1.09027e15			−5.33184
$729$	7.62560e12			0.0370370
$730$	5.16912e14			2.49346
$731$			7.50296e13i			0.359456i
$732$			3.48184e14i			1.65674i
$733$	2.09581e14			0.990449			0.495224	−	0.868765i	$-0.335086\pi$
$733$	2.09581e14			0.990449			0.495224	+	0.868765i	$0.335086\pi$
$734$	−2.35763e14			−1.10661
$735$	2.43970e13			0.113736
$736$	1.45761e15			6.74921
$737$	−3.48009e13			−0.160049
$738$		−	8.65952e13i		−	0.395560i
$739$		−	1.83607e14i		−	0.833041i	−0.909126	−	0.416521i	$-0.863249\pi$
$739$		−	1.83607e14i		−	0.833041i	0.909126	−	0.416521i	$-0.136751\pi$
$740$		−	6.63448e14i		−	2.98984i
$741$		−	2.21507e14i		−	0.991509i
$742$		−	1.28693e14i		−	0.572183i
$743$	1.11239e14			0.491261			0.245631	−	0.969364i	$-0.421005\pi$
$743$	1.11239e14			0.491261			0.245631	+	0.969364i	$0.421005\pi$
$744$	−7.57020e14			−3.32080
$745$			4.16306e13i			0.181398i
$746$			3.43200e14i			1.48543i
$747$			5.25805e13i			0.226059i
$748$		−	6.41623e14i		−	2.74013i
$749$	−2.53573e14			−1.07571
$750$		−	2.21063e14i		−	0.931558i
$751$			2.25353e12i			0.00943331i	0.999989	+	0.00471665i	$0.00150136\pi$
$751$			2.25353e12i			0.00943331i	−0.999989	+	0.00471665i	$0.998499\pi$
$752$		−	1.53295e15i		−	6.37440i
$753$	5.84894e13			0.241603
$754$	1.12481e15			4.61552
$755$			4.48071e14i			1.82647i
$756$	−1.26677e14			−0.512967
$757$	−2.44932e14			−0.985294			−0.492647	−	0.870229i	$-0.663971\pi$
$757$	−2.44932e14			−0.985294			−0.492647	+	0.870229i	$0.663971\pi$
$758$			3.42124e14i			1.36722i
$759$	−3.04594e14			−1.20924
$760$		−	1.23438e15i		−	4.86834i
$761$	−1.44245e14			−0.565167			−0.282584	−	0.959243i	$-0.591191\pi$
$761$	−1.44245e14			−0.565167			−0.282584	+	0.959243i	$0.591191\pi$
$762$			5.33997e13i			0.207857i
$763$			1.75063e14i			0.676975i
$764$			1.15773e14i			0.444773i
$765$	−5.48515e13			−0.209354
$766$		−	1.77689e14i		−	0.673777i
$767$	−2.40866e14	+	3.27172e14i	−0.907401	+	1.23253i
$768$	−1.09599e15			−4.10205
$769$			3.66398e14i			1.36245i	0.732073	+	0.681227i	$0.238553\pi$
$769$			3.66398e14i			1.36245i	−0.732073	+	0.681227i	$0.761447\pi$
$770$	9.29783e14			3.43501
$771$	−2.31863e14			−0.851057
$772$	−6.89503e14			−2.51449
$773$		−	8.64869e13i		−	0.313367i	−0.987649	−	0.156683i	$-0.949920\pi$
$773$		−	8.64869e13i		−	0.313367i	0.987649	−	0.156683i	$-0.0500802\pi$
$774$	−1.18957e14			−0.428238
$775$		−	1.17970e14i		−	0.421953i
$776$	8.00780e14			2.84580
$777$			1.33835e14i			0.472570i
$778$			4.38064e14i			1.53688i
$779$	−1.92611e14			−0.671421
$780$		−	8.46944e14i		−	2.93347i
$781$		−	3.38020e14i		−	1.16329i
$782$	−4.00285e14			−1.36879
$783$	8.61295e13			0.292646
$784$	−2.40680e14			−0.812568
$785$		−	2.62795e13i		−	0.0881595i
$786$	3.14032e14			1.04679
$787$	−2.41866e14			−0.801128			−0.400564	−	0.916269i	$-0.631186\pi$
$787$	−2.41866e14			−0.801128			−0.400564	+	0.916269i	$0.631186\pi$
$788$	7.80241e14			2.56801
$789$	−1.24632e14			−0.407608
$790$			2.66586e14i			0.866368i
$791$			4.12542e14i			1.33225i
$792$	6.70419e14			2.15140
$793$	4.69601e14			1.49749
$794$	3.45883e14			1.09604
$795$	6.58847e13			0.207467
$796$	−1.82521e15			−5.71146
$797$			1.49789e14i			0.465788i	0.972502	+	0.232894i	$0.0748195\pi$
$797$			1.49789e14i			0.465788i	−0.972502	+	0.232894i	$0.925181\pi$
$798$			3.77836e14i			1.16759i
$799$			2.46694e14i			0.757574i
$800$		−	4.99957e14i		−	1.52575i
$801$			8.17151e13i			0.247822i
$802$	9.45622e13			0.285001
$803$	6.24457e14			1.87036
$804$		−	5.40728e13i		−	0.160953i
$805$		−	4.32568e14i		−	1.27960i
$806$			1.54924e15i			4.55452i
$807$		−	1.13030e14i		−	0.330238i
$808$	−7.03663e14			−2.04319
$809$			5.91611e13i			0.170724i	0.996350	+	0.0853618i	$0.0272046\pi$
$809$			5.91611e13i			0.170724i	−0.996350	+	0.0853618i	$0.972795\pi$
$810$		−	8.69653e13i		−	0.249414i
$811$		−	5.27501e14i		−	1.50356i	−0.659417	−	0.751778i	$-0.729197\pi$
$811$		−	5.27501e14i		−	1.50356i	0.659417	−	0.751778i	$-0.270803\pi$
$812$	−1.43079e15			−4.05319
$813$	−2.01289e14			−0.566720
$814$		−	1.07475e15i		−	3.00737i
$815$	4.93280e14			1.37185
$816$	5.41119e14			1.49569
$817$			2.64593e14i			0.726888i
$818$	−5.49391e14			−1.50008
$819$			1.70852e14i			0.463660i
$820$	−7.36460e14			−1.98646
$821$			2.45054e14i			0.656971i	0.944509	+	0.328485i	$0.106538\pi$
$821$			2.45054e14i			0.656971i	−0.944509	+	0.328485i	$0.893462\pi$
$822$		−	4.00304e14i		−	1.06667i
$823$		−	2.80071e14i		−	0.741770i	−0.928679	−	0.370885i	$-0.879054\pi$
$823$		−	2.80071e14i		−	0.741770i	0.928679	−	0.370885i	$-0.120946\pi$
$824$	1.05431e15			2.77543
$825$			1.04475e14i			0.273364i
$826$	4.10858e14	−	5.58074e14i	1.06854	−	1.45141i
$827$	9.63150e13			0.248981			0.124491	−	0.992221i	$-0.460270\pi$
$827$	9.63150e13			0.248981			0.124491	+	0.992221i	$0.460270\pi$
$828$		−	4.73271e14i		−	1.21607i
$829$	2.75833e14			0.704488			0.352244	−	0.935908i	$-0.385419\pi$
$829$	2.75833e14			0.704488			0.352244	+	0.935908i	$0.385419\pi$
$830$	5.99648e14			1.52232
$831$	−1.97035e14			−0.497209
$832$			3.71683e15i			9.32301i
$833$	3.87320e13			0.0965706
$834$			5.82424e14i			1.44348i
$835$	1.84823e14			0.455326
$836$		−	2.26269e15i		−	5.54107i
$837$			1.18629e14i			0.288779i
$838$	−8.80516e14			−2.13068
$839$			3.50659e13i			0.0843482i	0.999110	+	0.0421741i	$0.0134284\pi$
$839$			3.50659e13i			0.0843482i	−0.999110	+	0.0421741i	$0.986572\pi$
$840$			9.52094e14i			2.27658i
$841$	5.52107e14			1.31233
$842$	7.48146e14			1.76777
$843$	1.65263e14			0.388184
$844$		−	1.04660e15i		−	2.44383i
$845$	−6.54654e14			−1.51960
$846$	−3.91125e14			−0.902535
$847$	7.27044e14			1.66780
$848$	−6.49963e14			−1.48221
$849$			1.05179e14i			0.238447i
$850$			1.37297e14i			0.309432i
$851$	−5.00014e14			−1.12030
$852$	5.25207e14			1.16986
$853$	−6.23367e14			−1.38038			−0.690190	−	0.723628i	$-0.742473\pi$
$853$	−6.23367e14			−1.38038			−0.690190	+	0.723628i	$0.742473\pi$
$854$	−8.01024e14			−1.76342
$855$	−1.93434e14			−0.423354
$856$			2.08516e15i			4.53703i
$857$			1.22523e14i			0.265041i	0.991180	+	0.132520i	$0.0423070\pi$
$857$			1.22523e14i			0.265041i	−0.991180	+	0.132520i	$0.957693\pi$
$858$		−	1.37201e15i		−	2.95067i
$859$		−	5.99314e14i		−	1.28141i	−0.767787	−	0.640705i	$-0.778642\pi$
$859$		−	5.99314e14i		−	1.28141i	0.767787	−	0.640705i	$-0.221358\pi$
$860$			1.01168e15i			2.15057i
$861$	1.48564e14			0.313977
$862$	5.15376e14			1.08290
$863$		−	3.52693e14i		−	0.736789i	−0.929670	−	0.368395i	$-0.879908\pi$
$863$		−	3.52693e14i		−	0.736789i	0.929670	−	0.368395i	$-0.120092\pi$
$864$			5.02751e14i			1.04420i
$865$		−	2.56501e14i		−	0.529673i
$866$			1.03274e15i			2.12032i
$867$	1.95755e14			0.399593
$868$		−	1.97068e15i		−	3.99962i
$869$			3.22050e14i			0.649868i
$870$		−	9.82254e14i		−	1.97073i
$871$	−7.29288e13			−0.145482
$872$	1.43957e15			2.85528
$873$		−	1.25487e14i		−	0.247473i
$874$	−1.41161e15			−2.76794
$875$	3.79259e14			0.739427
$876$			9.70267e14i			1.88092i
$877$	−6.80335e14			−1.31137			−0.655684	−	0.755035i	$-0.727620\pi$
$877$	−6.80335e14			−1.31137			−0.655684	+	0.755035i	$0.727620\pi$
$878$		−	1.82248e13i		−	0.0349293i
$879$	−4.96376e14			−0.945945
$880$		−	4.69587e15i		−	8.89821i
$881$		−	8.57109e13i		−	0.161494i	−0.996735	−	0.0807470i	$-0.974269\pi$
$881$		−	8.57109e13i		−	0.161494i	0.996735	−	0.0807470i	$-0.0257306\pi$
$882$			6.14083e13i			0.115049i
$883$	−4.71583e14			−0.878525			−0.439263	−	0.898359i	$-0.644760\pi$
$883$	−4.71583e14			−0.878525			−0.439263	+	0.898359i	$0.644760\pi$
$884$		−	1.34459e15i		−	2.49073i
$885$	2.85708e14	+	2.10340e14i	0.526266	+	0.387441i
$886$	1.35322e15			2.47856
$887$			3.52580e14i			0.642154i	0.947053	+	0.321077i	$0.104045\pi$
$887$			3.52580e14i			0.642154i	−0.947053	+	0.321077i	$0.895955\pi$
$888$	1.10054e15			1.99316
$889$	−9.16133e13			−0.164987
$890$	9.31911e14			1.66888
$891$		−	1.05059e14i		−	0.187087i
$892$	2.88646e14			0.511141
$893$			8.69969e14i			1.53196i
$894$	−1.04786e14			−0.183492
$895$			6.36750e14i			1.10880i
$896$		−	3.49235e15i		−	6.04753i
$897$	−6.38307e14			−1.09918
$898$			4.34785e14i			0.744548i
$899$			1.33989e15i			2.28177i
$900$	−1.62331e14			−0.274908
$901$	1.04597e14			0.176155
$902$	−1.19303e15			−1.99811
$903$		−	2.04084e14i		−	0.339915i
$904$	3.39238e15			5.61905
$905$	1.26139e14			0.207782
$906$	−1.12782e15			−1.84755
$907$	−1.17675e15			−1.91712			−0.958560	−	0.284890i	$-0.908043\pi$
$907$	−1.17675e15			−1.91712			−0.958560	+	0.284890i	$0.908043\pi$
$908$		−	5.91648e14i		−	0.958593i
$909$			1.10268e14i			0.177677i
$910$	1.94846e15			3.12237
$911$	−3.77793e14			−0.602091			−0.301045	−	0.953610i	$-0.597336\pi$
$911$	−3.77793e14			−0.602091			−0.301045	+	0.953610i	$0.597336\pi$
$912$	1.90826e15			3.02457
$913$	7.24406e14			1.14190
$914$	1.37307e15			2.15259
$915$		−	4.10087e14i		−	0.639396i
$916$		−	5.82581e14i		−	0.903398i
$917$			5.38758e14i			0.830897i
$918$		−	1.38064e14i		−	0.211771i
$919$		−	1.02406e15i		−	1.56225i	−0.624377	−	0.781123i	$-0.714647\pi$
$919$		−	1.02406e15i		−	1.56225i	0.624377	−	0.781123i	$-0.285353\pi$
$920$	−3.55706e15			−5.39699
$921$	3.09216e13			0.0466621
$922$			1.81009e15i			2.71673i
$923$		−	7.08355e14i		−	1.05741i
$924$			1.74524e15i			2.59117i
$925$			1.71503e14i			0.253258i
$926$	1.44967e15			2.12919
$927$		−	1.65216e14i		−	0.241353i
$928$			5.67846e15i			8.25070i
$929$		−	5.61053e14i		−	0.810822i	−0.914135	−	0.405411i	$-0.867128\pi$
$929$		−	5.61053e14i		−	0.810822i	0.914135	−	0.405411i	$-0.132872\pi$
$930$	1.35290e15			1.94469
$931$	1.36589e14			0.195284
$932$			1.39000e15i			1.97667i
$933$	−5.70855e14			−0.807454
$934$	1.63359e15			2.29831
$935$			7.55694e14i			1.05752i
$936$	1.40493e15			1.95558
$937$			1.45287e14i			0.201154i	0.994929	+	0.100577i	$0.0320689\pi$
$937$			1.45287e14i			0.201154i	−0.994929	+	0.100577i	$0.967931\pi$
$938$	1.24398e14			0.171317
$939$			5.58887e14i			0.765589i
$940$			3.32637e15i			4.53244i
$941$		−	9.26253e14i		−	1.25540i	−0.778456	−	0.627699i	$-0.783997\pi$
$941$		−	9.26253e14i		−	1.25540i	0.778456	−	0.627699i	$-0.216003\pi$
$942$	6.61468e13			0.0891773
$943$			5.55040e14i			0.744330i
$944$	−2.81855e15	−	2.07504e15i	−3.75981	−	2.76800i
$945$	1.49199e14			0.197973
$946$			1.63888e15i			2.16318i
$947$	1.28749e15			1.69041			0.845206	−	0.534440i	$-0.179477\pi$
$947$	1.28749e15			1.69041			0.845206	+	0.534440i	$0.179477\pi$
$948$	−5.00395e14			−0.653538
$949$	1.30861e15			1.70012
$950$			4.84178e14i			0.625730i
$951$	2.05335e14			0.263974
$952$			1.51152e15i			1.93299i
$953$	−1.38865e15			−1.76656			−0.883278	−	0.468849i	$-0.844669\pi$
$953$	−1.38865e15			−1.76656			−0.883278	+	0.468849i	$0.844669\pi$
$954$			1.65835e14i			0.209862i
$955$		−	1.36355e14i		−	0.171655i
$956$	4.03657e15			5.05502
$957$		−	1.18661e15i		−	1.47826i
$958$		−	1.52199e15i		−	1.88619i
$959$	6.86767e14			0.846675
$960$	3.24578e15			3.98073
$961$	−1.02586e15			−1.25161
$962$		−	2.25226e15i		−	2.73365i
$963$	3.26757e14			0.394542
$964$	−1.10591e15			−1.32842
$965$	8.12087e14			0.970434
$966$	1.08879e15			1.29438
$967$			1.54240e15i			1.82417i	0.410005	+	0.912083i	$0.365527\pi$
$967$			1.54240e15i			1.82417i	−0.410005	+	0.912083i	$0.634473\pi$
$968$		−	5.97857e15i		−	7.03429i
$969$	−3.07092e14			−0.359459
$970$	−1.43110e15			−1.66652
$971$	−1.47299e15			−1.70649			−0.853246	−	0.521508i	$-0.825370\pi$
$971$	−1.47299e15			−1.70649			−0.853246	+	0.521508i	$0.825370\pi$
$972$	1.63238e14			0.188143
$973$	−9.99215e14			−1.14576
$974$			2.76678e15i			3.15632i
$975$			2.18938e14i			0.248483i
$976$			4.04557e15i			4.56805i
$977$			1.92591e14i			0.216354i	0.994132	+	0.108177i	$0.0345013\pi$
$977$			1.92591e14i			0.216354i	−0.994132	+	0.108177i	$0.965499\pi$
$978$			1.24161e15i			1.38769i
$979$	1.12580e15			1.25183
$980$	5.22255e14			0.577766
$981$		−	2.25588e14i		−	0.248297i
$982$		−	1.15586e15i		−	1.26575i
$983$			1.33915e15i			1.45902i	0.683970	+	0.729510i	$0.260252\pi$
$983$			1.33915e15i			1.45902i	−0.683970	+	0.729510i	$0.739748\pi$
$984$		−	1.22166e15i		−	1.32426i
$985$	−9.18957e14			−0.991092
$986$		−	1.55940e15i		−	1.67330i
$987$		−	6.71020e14i		−	0.716390i
$988$		−	4.74170e15i		−	5.03674i
$989$	7.62466e14			0.805821
$990$	−1.19813e15			−1.25988
$991$			1.70616e15i			1.78506i	0.450992	+	0.892528i	$0.351070\pi$
$991$			1.70616e15i			1.78506i	−0.450992	+	0.892528i	$0.648930\pi$
$992$	−7.82116e15			−8.14166
$993$	−5.40138e14			−0.559446
$994$			1.20828e15i			1.24519i
$995$	2.14971e15			2.20427
$996$			1.12557e15i			1.14835i
$997$	1.52311e14			0.154616			0.0773080	−	0.997007i	$-0.475368\pi$
$997$	1.52311e14			0.154616			0.0773080	+	0.997007i	$0.475368\pi$
$998$			8.73431e14i			0.882218i
$999$		−	1.72462e14i		−	0.173327i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.11.c.a.58.2	✓	100
59.58	odd	2	inner	177.11.c.a.58.99	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.11.c.a.58.2	✓	100	1.1	even	1	trivial
177.11.c.a.58.99	yes	100	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:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	177.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-63.4607i q^{2} -140.296 q^{3} -3003.25 q^{4} +3537.19 q^{5} +8903.28i q^{6} -15274.6 q^{7} +125605. i q^{8} +19683.0 q^{9} +O(q^{10})\)	\(q-63.4607i q^{2} -140.296 q^{3} -3003.25 q^{4} +3537.19 q^{5} +8903.28i q^{6} -15274.6 q^{7} +125605. i q^{8} +19683.0 q^{9} -224473. i q^{10} -271175. i q^{11} +421345. q^{12} -568274. i q^{13} +969335. i q^{14} -496254. q^{15} +4.89563e6 q^{16} -787841. q^{17} -1.24910e6i q^{18} -2.77833e6 q^{19} -1.06231e7 q^{20} +2.14297e6 q^{21} -1.72089e7 q^{22} +8.00619e6i q^{23} -1.76219e7i q^{24} +2.74610e6 q^{25} -3.60631e7 q^{26} -2.76145e6 q^{27} +4.58735e7 q^{28} -3.11900e7 q^{29} +3.14926e7i q^{30} -4.29591e7i q^{31} -1.82061e8i q^{32} +3.80447e7i q^{33} +4.99969e7i q^{34} -5.40291e7 q^{35} -5.91131e7 q^{36} +6.24534e7i q^{37} +1.76315e8i q^{38} +7.97267e7i q^{39} +4.44288e8i q^{40} +6.93263e7 q^{41} -1.35994e8i q^{42} -9.52345e7i q^{43} +8.14406e8i q^{44} +6.96226e7 q^{45} +5.08078e8 q^{46} -3.13127e8i q^{47} -6.86838e8 q^{48} -4.91622e7 q^{49} -1.74269e8i q^{50} +1.10531e8 q^{51} +1.70667e9i q^{52} -1.32764e8 q^{53} +1.75243e8i q^{54} -9.59197e8i q^{55} -1.91856e9i q^{56} +3.89789e8 q^{57} +1.97934e9i q^{58} +(-5.75728e8 - 4.23855e8i) q^{59} +1.49038e9 q^{60} +8.26364e8i q^{61} -2.72621e9 q^{62} -3.00650e8 q^{63} -6.54056e9 q^{64} -2.01010e9i q^{65} +2.41434e9 q^{66} -1.28334e8i q^{67} +2.36609e9 q^{68} -1.12324e9i q^{69} +3.42873e9i q^{70} +1.24650e9 q^{71} +2.47228e9i q^{72} +2.30278e9i q^{73} +3.96333e9 q^{74} -3.85268e8 q^{75} +8.34403e9 q^{76} +4.14208e9i q^{77} +5.05951e9 q^{78} -1.18761e9 q^{79} +1.73168e10 q^{80} +3.87420e8 q^{81} -4.39949e9i q^{82} +2.67136e9i q^{83} -6.43587e9 q^{84} -2.78674e9 q^{85} -6.04364e9 q^{86} +4.37583e9 q^{87} +3.40608e10 q^{88} +4.15156e9i q^{89} -4.41829e9i q^{90} +8.68016e9i q^{91} -2.40446e10i q^{92} +6.02700e9i q^{93} -1.98712e10 q^{94} -9.82749e9 q^{95} +2.55424e10i q^{96} -6.37540e9i q^{97} +3.11987e9i q^{98} -5.33753e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 51200 q^{4} + 18392 q^{7} + 1968300 q^{9}+O(q^{10}) \) 100 * q - 51200 * q^4 + 18392 * q^7 + 1968300 * q^9	\( 100 q - 51200 q^{4} + 18392 q^{7} + 1968300 q^{9} + 620136 q^{12} + 662904 q^{15} + 27925160 q^{16} - 2053136 q^{17} - 5169828 q^{19} - 1076324 q^{20} - 1829224 q^{22} + 215378180 q^{25} - 22082700 q^{26} - 102921320 q^{28} - 112503588 q^{29} - 76491392 q^{35} - 1007769600 q^{36} + 473464516 q^{41} + 1215405588 q^{46} - 1676272320 q^{48} + 1975297276 q^{49} + 733970808 q^{51} + 3267506728 q^{53} + 591502824 q^{57} + 508142200 q^{59} + 1264196808 q^{60} - 6538206968 q^{62} + 362009736 q^{63} - 10324137972 q^{64} - 2764346616 q^{66} + 9997685952 q^{68} + 14908523204 q^{71} + 4863508712 q^{74} + 1890481680 q^{75} + 2044437240 q^{76} - 758396196 q^{78} - 3599839500 q^{79} - 23217941144 q^{80} + 38742048900 q^{81} - 13094894808 q^{84} + 23360564412 q^{85} + 12186923752 q^{86} + 7965322272 q^{87} + 32415437996 q^{88} - 22098322280 q^{94} + 7834510028 q^{95}+O(q^{100}) \) 100 * q - 51200 * q^4 + 18392 * q^7 + 1968300 * q^9 + 620136 * q^12 + 662904 * q^15 + 27925160 * q^16 - 2053136 * q^17 - 5169828 * q^19 - 1076324 * q^20 - 1829224 * q^22 + 215378180 * q^25 - 22082700 * q^26 - 102921320 * q^28 - 112503588 * q^29 - 76491392 * q^35 - 1007769600 * q^36 + 473464516 * q^41 + 1215405588 * q^46 - 1676272320 * q^48 + 1975297276 * q^49 + 733970808 * q^51 + 3267506728 * q^53 + 591502824 * q^57 + 508142200 * q^59 + 1264196808 * q^60 - 6538206968 * q^62 + 362009736 * q^63 - 10324137972 * q^64 - 2764346616 * q^66 + 9997685952 * q^68 + 14908523204 * q^71 + 4863508712 * q^74 + 1890481680 * q^75 + 2044437240 * q^76 - 758396196 * q^78 - 3599839500 * q^79 - 23217941144 * q^80 + 38742048900 * q^81 - 13094894808 * q^84 + 23360564412 * q^85 + 12186923752 * q^86 + 7965322272 * q^87 + 32415437996 * q^88 - 22098322280 * q^94 + 7834510028 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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