LMFDB - Embedded newform 177.11.c.a.58.82

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			58.82
Character	$\chi$	$=$	177.58
Dual form			177.11.c.a.58.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+45.0342i q^{2} +140.296 q^{3} -1004.08 q^{4} -5626.54 q^{5} +6318.12i q^{6} -22190.3 q^{7} +897.122i q^{8} +19683.0 q^{9} +O(q^{10})$	\(q+45.0342i q^{2} +140.296 q^{3} -1004.08 q^{4} -5626.54 q^{5} +6318.12i q^{6} -22190.3 q^{7} +897.122i q^{8} +19683.0 q^{9} -253387. i q^{10} +28695.6i q^{11} -140868. q^{12} -405198. i q^{13} -999323. i q^{14} -789382. q^{15} -1.06858e6 q^{16} +193238. q^{17} +886408. i q^{18} -1.39719e6 q^{19} +5.64949e6 q^{20} -3.11321e6 q^{21} -1.29228e6 q^{22} -9.59887e6i q^{23} +125863. i q^{24} +2.18923e7 q^{25} +1.82478e7 q^{26} +2.76145e6 q^{27} +2.22808e7 q^{28} -8.13874e6 q^{29} -3.55492e7i q^{30} -8.53152e6i q^{31} -4.72039e7i q^{32} +4.02588e6i q^{33} +8.70231e6i q^{34} +1.24855e8 q^{35} -1.97633e7 q^{36} +3.75479e7i q^{37} -6.29214e7i q^{38} -5.68477e7i q^{39} -5.04769e6i q^{40} -1.74499e8 q^{41} -1.40201e8i q^{42} +1.52269e8i q^{43} -2.88127e7i q^{44} -1.10747e8 q^{45} +4.32278e8 q^{46} -2.46599e8i q^{47} -1.49917e8 q^{48} +2.09935e8 q^{49} +9.85903e8i q^{50} +2.71105e7 q^{51} +4.06851e8i q^{52} -7.65345e8 q^{53} +1.24360e8i q^{54} -1.61457e8i q^{55} -1.99074e7i q^{56} -1.96020e8 q^{57} -3.66521e8i q^{58} +(-3.15700e8 - 6.41444e8i) q^{59} +7.92602e8 q^{60} -2.67620e8i q^{61} +3.84210e8 q^{62} -4.36772e8 q^{63} +1.03157e9 q^{64} +2.27986e9i q^{65} -1.81302e8 q^{66} +1.82349e9i q^{67} -1.94026e8 q^{68} -1.34668e9i q^{69} +5.62273e9i q^{70} +3.31693e9 q^{71} +1.76580e7i q^{72} +3.54365e9i q^{73} -1.69094e9 q^{74} +3.07141e9 q^{75} +1.40289e9 q^{76} -6.36764e8i q^{77} +2.56009e9 q^{78} -4.35656e9 q^{79} +6.01240e9 q^{80} +3.87420e8 q^{81} -7.85841e9i q^{82} +2.12713e9i q^{83} +3.12591e9 q^{84} -1.08726e9 q^{85} -6.85733e9 q^{86} -1.14183e9 q^{87} -2.57434e7 q^{88} +2.36898e9i q^{89} -4.98741e9i q^{90} +8.99147e9i q^{91} +9.63803e9i q^{92} -1.19694e9i q^{93} +1.11054e10 q^{94} +7.86135e9 q^{95} -6.62253e9i q^{96} +1.02166e9i q^{97} +9.45424e9i q^{98} +5.64815e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			45.0342i			1.40732i	0.710537	+	0.703659i	$0.248452\pi$
$2$			45.0342i			1.40732i	−0.710537	+	0.703659i	$0.751548\pi$
$3$	140.296			0.577350
$3$	140.296			0.577350
$4$	−1004.08			−0.980546
$5$	−5626.54			−1.80049			−0.900246	−	0.435381i	$-0.856614\pi$
$5$	−5626.54			−1.80049			−0.900246	+	0.435381i	$0.856614\pi$
$6$			6318.12i			0.812516i
$7$	−22190.3			−1.32030			−0.660151	−	0.751133i	$-0.729508\pi$
$7$	−22190.3			−1.32030			−0.660151	+	0.751133i	$0.729508\pi$
$8$			897.122i			0.0273780i
$9$	19683.0			0.333333
$10$		−	253387.i		−	2.53387i
$11$			28695.6i			0.178177i	0.996024	+	0.0890886i	$0.0283954\pi$
$11$			28695.6i			0.178177i	−0.996024	+	0.0890886i	$0.971605\pi$
$12$	−140868.			−0.566118
$13$		−	405198.i		−	1.09132i	−0.838008	−	0.545658i	$-0.816280\pi$
$13$		−	405198.i		−	1.09132i	0.838008	−	0.545658i	$-0.183720\pi$
$14$		−	999323.i		−	1.85809i
$15$	−789382.			−1.03951
$16$	−1.06858e6			−1.01908
$17$	193238.			0.136097			0.0680484	−	0.997682i	$-0.478323\pi$
$17$	193238.			0.136097			0.0680484	+	0.997682i	$0.478323\pi$
$18$			886408.i			0.469106i
$19$	−1.39719e6			−0.564271			−0.282135	−	0.959375i	$-0.591043\pi$
$19$	−1.39719e6			−0.564271			−0.282135	+	0.959375i	$0.591043\pi$
$20$	5.64949e6			1.76547
$21$	−3.11321e6			−0.762277
$22$	−1.29228e6			−0.250752
$23$		−	9.59887e6i		−	1.49136i	−0.666307	−	0.745678i	$-0.732126\pi$
$23$		−	9.59887e6i		−	1.49136i	0.666307	−	0.745678i	$-0.267874\pi$
$24$			125863.i			0.0158067i
$25$	2.18923e7			2.24177
$26$	1.82478e7			1.53583
$27$	2.76145e6			0.192450
$28$	2.22808e7			1.29462
$29$	−8.13874e6			−0.396796			−0.198398	−	0.980122i	$-0.563574\pi$
$29$	−8.13874e6			−0.396796			−0.198398	+	0.980122i	$0.563574\pi$
$30$		−	3.55492e7i		−	1.46293i
$31$		−	8.53152e6i		−	0.298001i	−0.988837	−	0.149001i	$-0.952394\pi$
$31$		−	8.53152e6i		−	0.298001i	0.988837	−	0.149001i	$-0.0476056\pi$
$32$		−	4.72039e7i		−	1.40679i
$33$			4.02588e6i			0.102871i
$34$			8.70231e6i			0.191531i
$35$	1.24855e8			2.37719
$36$	−1.97633e7			−0.326849
$37$			3.75479e7i			0.541473i	0.962653	+	0.270737i	$0.0872673\pi$
$37$			3.75479e7i			0.541473i	−0.962653	+	0.270737i	$0.912733\pi$
$38$		−	6.29214e7i		−	0.794109i
$39$		−	5.68477e7i		−	0.630071i
$40$		−	5.04769e6i		−	0.0492939i
$41$	−1.74499e8			−1.50617			−0.753083	−	0.657925i	$-0.771434\pi$
$41$	−1.74499e8			−1.50617			−0.753083	+	0.657925i	$0.771434\pi$
$42$		−	1.40201e8i		−	1.07277i
$43$			1.52269e8i			1.03579i	0.855445	+	0.517893i	$0.173284\pi$
$43$			1.52269e8i			1.03579i	−0.855445	+	0.517893i	$0.826716\pi$
$44$		−	2.88127e7i		−	0.174711i
$45$	−1.10747e8			−0.600164
$46$	4.32278e8			2.09881
$47$		−	2.46599e8i		−	1.07523i	−0.843190	−	0.537616i	$-0.819325\pi$
$47$		−	2.46599e8i		−	1.07523i	0.843190	−	0.537616i	$-0.180675\pi$
$48$	−1.49917e8			−0.588364
$49$	2.09935e8			0.743197
$50$			9.85903e8i			3.15489i
$51$	2.71105e7			0.0785755
$52$			4.06851e8i			1.07009i
$53$	−7.65345e8			−1.83011			−0.915057	−	0.403325i	$-0.867854\pi$
$53$	−7.65345e8			−1.83011			−0.915057	+	0.403325i	$0.867854\pi$
$54$			1.24360e8i			0.270839i
$55$		−	1.61457e8i		−	0.320807i
$56$		−	1.99074e7i		−	0.0361472i
$57$	−1.96020e8			−0.325782
$58$		−	3.66521e8i		−	0.558418i
$59$	−3.15700e8	−	6.41444e8i	−0.441585	−	0.897220i
$59$	−3.15700e8	−	6.41444e8i	−0.441585	−	0.897220i
$60$	7.92602e8			1.01929
$61$		−	2.67620e8i		−	0.316862i	−0.987370	−	0.158431i	$-0.949356\pi$
$61$		−	2.67620e8i		−	0.316862i	0.987370	−	0.158431i	$-0.0506435\pi$
$62$	3.84210e8			0.419383
$63$	−4.36772e8			−0.440101
$64$	1.03157e9			0.960721
$65$			2.27986e9i			1.96491i
$66$	−1.81302e8			−0.144772
$67$			1.82349e9i			1.35061i	0.737538	+	0.675306i	$0.235988\pi$
$67$			1.82349e9i			1.35061i	−0.737538	+	0.675306i	$0.764012\pi$
$68$	−1.94026e8			−0.133449
$69$		−	1.34668e9i		−	0.861034i
$70$			5.62273e9i			3.34547i
$71$	3.31693e9			1.83842			0.919210	−	0.393767i	$-0.128828\pi$
$71$	3.31693e9			1.83842			0.919210	+	0.393767i	$0.128828\pi$
$72$			1.76580e7i			0.00912599i
$73$			3.54365e9i			1.70937i	0.519145	+	0.854686i	$0.326251\pi$
$73$			3.54365e9i			1.70937i	−0.519145	+	0.854686i	$0.673749\pi$
$74$	−1.69094e9			−0.762026
$75$	3.07141e9			1.29429
$76$	1.40289e9			0.553294
$77$		−	6.36764e8i		−	0.235248i
$78$	2.56009e9			0.886711
$79$	−4.35656e9			−1.41582			−0.707911	−	0.706302i	$-0.750362\pi$
$79$	−4.35656e9			−1.41582			−0.707911	+	0.706302i	$0.750362\pi$
$80$	6.01240e9			1.83484
$81$	3.87420e8			0.111111
$82$		−	7.85841e9i		−	2.11966i
$83$			2.12713e9i			0.540013i	0.962859	+	0.270006i	$0.0870258\pi$
$83$			2.12713e9i			0.540013i	−0.962859	+	0.270006i	$0.912974\pi$
$84$	3.12591e9			0.747447
$85$	−1.08726e9			−0.245041
$86$	−6.85733e9			−1.45768
$87$	−1.14183e9			−0.229090
$88$	−2.57434e7			−0.00487813
$89$			2.36898e9i			0.424239i	0.977244	+	0.212119i	$0.0680366\pi$
$89$			2.36898e9i			0.424239i	−0.977244	+	0.212119i	$0.931963\pi$
$90$		−	4.98741e9i		−	0.844622i
$91$			8.99147e9i			1.44087i
$92$			9.63803e9i			1.46234i
$93$		−	1.19694e9i		−	0.172051i
$94$	1.11054e10			1.51320
$95$	7.86135e9			1.01597
$96$		−	6.62253e9i		−	0.812208i
$97$			1.02166e9i			0.118973i	0.998229	+	0.0594867i	$0.0189464\pi$
$97$			1.02166e9i			0.118973i	−0.998229	+	0.0594867i	$0.981054\pi$
$98$			9.45424e9i			1.04591i
$99$			5.64815e8i			0.0593924i
$100$	−2.19816e10			−2.19816
$101$			1.13007e10i			1.07522i	0.843192	+	0.537612i	$0.180674\pi$
$101$			1.13007e10i			1.07522i	−0.843192	+	0.537612i	$0.819326\pi$
$102$			1.22090e9i			0.110581i
$103$		−	3.37848e9i		−	0.291431i	−0.989327	−	0.145715i	$-0.953452\pi$
$103$		−	3.37848e9i		−	0.291431i	0.989327	−	0.145715i	$-0.0465484\pi$
$104$	3.63512e8			0.0298780
$105$	1.75166e10			1.37247
$106$		−	3.44667e10i		−	2.57555i
$107$	1.30900e10			0.933299			0.466650	−	0.884442i	$-0.345461\pi$
$107$	1.30900e10			0.933299			0.466650	+	0.884442i	$0.345461\pi$
$108$	−2.77271e9			−0.188706
$109$		−	5.01716e9i		−	0.326081i	−0.986619	−	0.163041i	$-0.947870\pi$
$109$		−	5.01716e9i		−	0.326081i	0.986619	−	0.163041i	$-0.0521302\pi$
$110$	7.27108e9			0.451477
$111$			5.26783e9i			0.312620i
$112$	2.37121e10			1.34549
$113$		−	1.49437e10i		−	0.811085i	−0.914076	−	0.405543i	$-0.867083\pi$
$113$		−	1.49437e10i		−	0.811085i	0.914076	−	0.405543i	$-0.132917\pi$
$114$		−	8.82762e9i		−	0.458479i
$115$			5.40084e10i			2.68517i
$116$	8.17194e9			0.389076
$117$		−	7.97551e9i		−	0.363772i
$118$	2.88869e10	−	1.42173e10i	1.26267	−	0.621450i
$119$	−4.28801e9			−0.179689
$120$		−	7.08171e8i		−	0.0284598i
$121$	2.51140e10			0.968253
$122$	1.20521e10			0.445926
$123$	−2.44815e10			−0.869586
$124$			8.56632e9i			0.292204i
$125$	−6.82313e10			−2.23580
$126$		−	1.96697e10i		−	0.619362i
$127$	−2.45788e10			−0.743946			−0.371973	−	0.928244i	$-0.621319\pi$
$127$	−2.45788e10			−0.743946			−0.371973	+	0.928244i	$0.621319\pi$
$128$		−	1.88104e9i		−	0.0547456i
$129$			2.13628e10i			0.598012i
$130$	−1.02672e11			−2.76525
$131$			6.06689e10i			1.57257i	0.617865	+	0.786284i	$0.287998\pi$
$131$			6.06689e10i			1.57257i	−0.617865	+	0.786284i	$0.712002\pi$
$132$		−	4.04230e9i		−	0.100869i
$133$	3.10041e10			0.745008
$134$	−8.21196e10			−1.90074
$135$	−1.55374e10			−0.346505
$136$			1.73358e8i			0.00372605i
$137$	1.09680e10			0.227261			0.113631	−	0.993523i	$-0.463752\pi$
$137$	1.09680e10			0.227261			0.113631	+	0.993523i	$0.463752\pi$
$138$	6.06469e10			1.21175
$139$	8.72029e9			0.168057			0.0840286	−	0.996463i	$-0.473221\pi$
$139$	8.72029e9			0.168057			0.0840286	+	0.996463i	$0.473221\pi$
$140$	−1.25364e11			−2.33095
$141$		−	3.45969e10i		−	0.620786i
$142$			1.49375e11i			2.58724i
$143$	1.16274e10			0.194447
$144$	−2.10328e10			−0.339692
$145$	4.57929e10			0.714428
$146$	−1.59586e11			−2.40563
$147$	2.94530e10			0.429085
$148$		−	3.77011e10i		−	0.530940i
$149$		−	8.70992e9i		−	0.118600i	−0.998240	−	0.0592998i	$-0.981113\pi$
$149$		−	8.70992e9i		−	0.118600i	0.998240	−	0.0592998i	$-0.0188868\pi$
$150$			1.38318e11i			1.82148i
$151$			1.24128e11i			1.58120i	0.612336	+	0.790598i	$0.290230\pi$
$151$			1.24128e11i			1.58120i	−0.612336	+	0.790598i	$0.709770\pi$
$152$		−	1.25345e9i		−	0.0154486i
$153$	3.80350e9			0.0453656
$154$	2.86762e10			0.331068
$155$			4.80029e10i			0.536549i
$156$			5.70796e10i			0.617814i
$157$		−	1.13466e11i		−	1.18951i	−0.803908	−	0.594754i	$-0.797250\pi$
$157$		−	1.13466e11i		−	1.18951i	0.803908	−	0.594754i	$-0.202750\pi$
$158$		−	1.96194e11i		−	1.99251i
$159$	−1.07375e11			−1.05662
$160$			2.65595e11i			2.53291i
$161$			2.13002e11i			1.96904i
$162$			1.74472e10i			0.156369i
$163$	2.83643e9			0.0246510			0.0123255	−	0.999924i	$-0.496077\pi$
$163$	2.83643e9			0.0246510			0.0123255	+	0.999924i	$0.496077\pi$
$164$	1.75211e11			1.47687
$165$		−	2.26518e10i		−	0.185218i
$166$	−9.57937e10			−0.759970
$167$	−2.06017e10			−0.158607			−0.0793034	−	0.996851i	$-0.525270\pi$
$167$	−2.06017e10			−0.158607			−0.0793034	+	0.996851i	$0.525270\pi$
$168$		−	2.79293e9i		−	0.0208696i
$169$	−2.63269e10			−0.190970
$170$		−	4.89639e10i		−	0.344851i
$171$	−2.75009e10			−0.188090
$172$		−	1.52891e11i		−	1.01564i
$173$			1.10379e11i			0.712289i	0.934431	+	0.356144i	$0.115909\pi$
$173$			1.10379e11i			0.712289i	−0.934431	+	0.356144i	$0.884091\pi$
$174$		−	5.14215e10i		−	0.322403i
$175$	−4.85797e11			−2.95982
$176$		−	3.06635e10i		−	0.181576i
$177$	−4.42914e10	−	8.99921e10i	−0.254949	−	0.518010i
$178$	−1.06685e11			−0.597039
$179$		−	2.16332e11i		−	1.17721i	−0.808420	−	0.588607i	$-0.799677\pi$
$179$		−	2.16332e11i		−	1.17721i	0.808420	−	0.588607i	$-0.200323\pi$
$180$	1.11199e11			0.588489
$181$	−5.36385e9			−0.0276111			−0.0138055	−	0.999905i	$-0.504395\pi$
$181$	−5.36385e9			−0.0276111			−0.0138055	+	0.999905i	$0.504395\pi$
$182$	−4.04924e11			−2.02776
$183$		−	3.75461e10i		−	0.182940i
$184$	8.61136e9			0.0408303
$185$		−	2.11265e11i		−	0.974919i
$186$	5.39032e10			0.242131
$187$			5.54508e9i			0.0242493i
$188$			2.47605e11i			1.05432i
$189$	−6.12774e10			−0.254092
$190$			3.54030e11i			1.42979i
$191$		−	3.93716e11i		−	1.54887i	−0.632651	−	0.774437i	$-0.718033\pi$
$191$		−	3.93716e11i		−	1.54887i	0.632651	−	0.774437i	$-0.281967\pi$
$192$	1.44725e11			0.554672
$193$	−2.89861e10			−0.108244			−0.0541219	−	0.998534i	$-0.517236\pi$
$193$	−2.89861e10			−0.108244			−0.0541219	+	0.998534i	$0.517236\pi$
$194$	−4.60098e10			−0.167433
$195$			3.19856e11i			1.13444i
$196$	−2.10791e11			−0.728738
$197$	−3.75059e11			−1.26406			−0.632031	−	0.774943i	$-0.717778\pi$
$197$	−3.75059e11			−1.26406			−0.632031	+	0.774943i	$0.717778\pi$
$198$	−2.54360e10			−0.0835840
$199$	1.72084e11			0.551409			0.275705	−	0.961242i	$-0.411089\pi$
$199$	1.72084e11			0.551409			0.275705	+	0.961242i	$0.411089\pi$
$200$			1.96401e10i			0.0613752i
$201$			2.55829e11i			0.779776i
$202$	−5.08919e11			−1.51318
$203$	1.80601e11			0.523890
$204$	−2.72211e10			−0.0770469
$205$	9.81824e11			2.71184
$206$	1.52147e11			0.410136
$207$		−	1.88935e11i		−	0.497118i
$208$			4.32986e11i			1.11213i
$209$		−	4.00932e10i		−	0.100540i
$210$			7.88847e11i			1.93151i
$211$		−	2.78128e11i		−	0.665015i	−0.943101	−	0.332508i	$-0.892105\pi$
$211$		−	2.78128e11i		−	0.665015i	0.943101	−	0.332508i	$-0.107895\pi$
$212$	7.68467e11			1.79451
$213$	4.65353e11			1.06141
$214$			5.89498e11i			1.31345i
$215$		−	8.56750e11i		−	1.86493i
$216$			2.47736e9i			0.00526890i
$217$			1.89317e11i			0.393451i
$218$	2.25944e11			0.458900
$219$			4.97161e11i			0.986907i
$220$			1.62116e11i			0.314566i
$221$		−	7.82996e10i		−	0.148525i
$222$	−2.37232e11			−0.439956
$223$	8.44345e11			1.53107			0.765536	−	0.643393i	$-0.222474\pi$
$223$	8.44345e11			1.53107			0.765536	+	0.643393i	$0.222474\pi$
$224$			1.04747e12i			1.85738i
$225$	4.30907e11			0.747258
$226$	6.72979e11			1.14146
$227$		−	4.73535e11i		−	0.785639i	−0.919616	−	0.392819i	$-0.871500\pi$
$227$		−	4.73535e11i		−	0.785639i	0.919616	−	0.392819i	$-0.128500\pi$
$228$	1.96820e11			0.319444
$229$		−	8.37316e11i		−	1.32957i	−0.747034	−	0.664786i	$-0.768523\pi$
$229$		−	8.37316e11i		−	1.32957i	0.747034	−	0.664786i	$-0.231477\pi$
$230$	−2.43223e12			−3.77890
$231$		−	8.93356e10i		−	0.135820i
$232$		−	7.30144e9i		−	0.0108635i
$233$			4.53701e11i			0.660678i	0.943862	+	0.330339i	$0.107163\pi$
$233$			4.53701e11i			0.660678i	−0.943862	+	0.330339i	$0.892837\pi$
$234$	3.59171e11			0.511943
$235$			1.38750e12i			1.93595i
$236$	3.16987e11	+	6.44061e11i	0.432994	+	0.879765i
$237$	−6.11209e11			−0.817425
$238$		−	1.93107e11i		−	0.252879i
$239$	−2.54511e11			−0.326375			−0.163187	−	0.986595i	$-0.552178\pi$
$239$	−2.54511e11			−0.326375			−0.163187	+	0.986595i	$0.552178\pi$
$240$	8.43516e11			1.05934
$241$	1.20698e12			1.48461			0.742307	−	0.670060i	$-0.233732\pi$
$241$	1.20698e12			1.48461			0.742307	+	0.670060i	$0.233732\pi$
$242$			1.13099e12i			1.36264i
$243$	5.43536e10			0.0641500
$244$			2.68712e11i			0.310698i
$245$	−1.18121e12			−1.33812
$246$		−	1.10250e12i		−	1.22378i
$247$			5.66139e11i			0.615798i
$248$	7.65381e9			0.00815867
$249$			2.98428e11i			0.311777i
$250$		−	3.07274e12i		−	3.14649i
$251$	−1.28580e12			−1.29064			−0.645319	−	0.763913i	$-0.723275\pi$
$251$	−1.28580e12			−1.29064			−0.645319	+	0.763913i	$0.723275\pi$
$252$	4.38554e11			0.431539
$253$	2.75445e11			0.265725
$254$		−	1.10689e12i		−	1.04697i
$255$	−1.52538e11			−0.141475
$256$	1.14104e12			1.03777
$257$	1.40208e12			1.25057			0.625283	−	0.780398i	$-0.284984\pi$
$257$	1.40208e12			1.25057			0.625283	+	0.780398i	$0.284984\pi$
$258$	−9.62057e11			−0.841593
$259$		−	8.33200e11i		−	0.714908i
$260$		−	2.28916e12i		−	1.92668i
$261$	−1.60195e11			−0.132265
$262$	−2.73217e12			−2.21310
$263$	−3.94685e11			−0.313669			−0.156835	−	0.987625i	$-0.550129\pi$
$263$	−3.94685e11			−0.313669			−0.156835	+	0.987625i	$0.550129\pi$
$264$	−3.61171e9			−0.00281639
$265$	4.30624e12			3.29511
$266$			1.39624e12i			1.04846i
$267$			3.32358e11i			0.244934i
$268$		−	1.83093e12i		−	1.32434i
$269$		−	8.99702e11i		−	0.638759i	−0.947627	−	0.319380i	$-0.896525\pi$
$269$		−	8.99702e11i		−	0.638759i	0.947627	−	0.319380i	$-0.103475\pi$
$270$		−	6.99714e11i		−	0.487643i
$271$	2.66302e12			1.82192			0.910958	−	0.412500i	$-0.135344\pi$
$271$	2.66302e12			1.82192			0.910958	+	0.412500i	$0.135344\pi$
$272$	−2.06490e11			−0.138693
$273$			1.26147e12i			0.831884i
$274$			4.93936e11i			0.319829i
$275$			6.28213e11i			0.399433i
$276$			1.35218e12i			0.844284i
$277$	1.10030e12			0.674700			0.337350	−	0.941379i	$-0.390469\pi$
$277$	1.10030e12			0.674700			0.337350	+	0.941379i	$0.390469\pi$
$278$			3.92711e11i			0.236510i
$279$		−	1.67926e11i		−	0.0993337i
$280$			1.12010e11i			0.0650828i
$281$	−1.67835e12			−0.957967			−0.478984	−	0.877824i	$-0.658995\pi$
$281$	−1.67835e12			−0.957967			−0.478984	+	0.877824i	$0.658995\pi$
$282$	1.55804e12			0.873644
$283$		−	1.13383e12i		−	0.624620i	−0.949980	−	0.312310i	$-0.898897\pi$
$283$		−	1.13383e12i		−	0.624620i	0.949980	−	0.312310i	$-0.101103\pi$
$284$	−3.33046e12			−1.80266
$285$	1.10292e12			0.586568
$286$			5.23631e11i			0.273650i
$287$	3.87218e12			1.98859
$288$		−	9.29115e11i		−	0.468929i
$289$	−1.97865e12			−0.981478
$290$			2.06225e12i			1.00543i
$291$			1.43336e11i			0.0686893i
$292$		−	3.55811e12i		−	1.67612i
$293$	8.14054e11			0.376977			0.188489	−	0.982075i	$-0.439641\pi$
$293$	8.14054e11			0.376977			0.188489	+	0.982075i	$0.439641\pi$
$294$			1.32639e12i			0.603859i
$295$	1.77630e12	+	3.60911e12i	0.795070	+	1.61544i
$296$	−3.36850e10			−0.0148244
$297$			7.92414e10i			0.0342902i
$298$	3.92244e11			0.166907
$299$	−3.88944e12			−1.62754
$300$	−3.08394e12			−1.26911
$301$		−	3.37891e12i		−	1.36755i
$302$	−5.59001e12			−2.22525
$303$			1.58545e12i			0.620781i
$304$	1.49301e12			0.575035
$305$			1.50578e12i			0.570507i
$306$			1.71288e11i			0.0638438i
$307$	−2.37197e12			−0.869796			−0.434898	−	0.900480i	$-0.643216\pi$
$307$	−2.37197e12			−0.869796			−0.434898	+	0.900480i	$0.643216\pi$
$308$			6.39362e11i			0.230671i
$309$		−	4.73988e11i		−	0.168258i
$310$	−2.16177e12			−0.755095
$311$	2.97835e11			0.102370			0.0511851	−	0.998689i	$-0.483700\pi$
$311$	2.97835e11			0.102370			0.0511851	+	0.998689i	$0.483700\pi$
$312$	5.09993e10			0.0172501
$313$		−	2.87994e12i		−	0.958652i	−0.877637	−	0.479326i	$-0.840881\pi$
$313$		−	2.87994e12i		−	0.958652i	0.877637	−	0.479326i	$-0.159119\pi$
$314$	5.10985e12			1.67402
$315$	2.45751e12			0.792398
$316$	4.37433e12			1.38828
$317$	−1.12526e12			−0.351526			−0.175763	−	0.984432i	$-0.556239\pi$
$317$	−1.12526e12			−0.351526			−0.175763	+	0.984432i	$0.556239\pi$
$318$		−	4.83554e12i		−	1.48700i
$319$		−	2.33546e11i		−	0.0706999i
$320$	−5.80415e12			−1.72977
$321$	1.83648e12			0.538841
$322$	−9.59237e12			−2.77106
$323$	−2.69990e11			−0.0767954
$324$	−3.89001e11			−0.108950
$325$		−	8.87072e12i		−	2.44648i
$326$			1.27736e11i			0.0346918i
$327$		−	7.03889e11i		−	0.188263i
$328$		−	1.56547e11i		−	0.0412358i
$329$			5.47211e12i			1.41963i
$330$	1.02010e12			0.260660
$331$	4.32711e12			1.08907			0.544537	−	0.838737i	$-0.316705\pi$
$331$	4.32711e12			1.08907			0.544537	+	0.838737i	$0.316705\pi$
$332$		−	2.13581e12i		−	0.529508i
$333$			7.39055e11i			0.180491i
$334$		−	9.27783e11i		−	0.223210i
$335$		−	1.02600e13i		−	2.43177i
$336$	3.32671e12			0.776817
$337$		−	2.09082e12i		−	0.481023i	−0.970646	−	0.240512i	$-0.922685\pi$
$337$		−	2.09082e12i		−	0.481023i	0.970646	−	0.240512i	$-0.0773152\pi$
$338$		−	1.18561e12i		−	0.268756i
$339$		−	2.09655e12i		−	0.468280i
$340$	1.09170e12			0.240274
$341$	2.44817e11			0.0530970
$342$		−	1.23848e12i		−	0.264703i
$343$	1.60970e12			0.339058
$344$	−1.36604e11			−0.0283578
$345$			7.57717e12i			1.55029i
$346$	−4.97083e12			−1.00242
$347$			7.74052e12i			1.53859i	0.638895	+	0.769294i	$0.279392\pi$
$347$			7.74052e12i			1.53859i	−0.638895	+	0.769294i	$0.720608\pi$
$348$	1.14649e12			0.224633
$349$			1.01012e13i			1.95095i	0.220099	+	0.975477i	$0.429362\pi$
$349$			1.01012e13i			1.95095i	−0.220099	+	0.975477i	$0.570638\pi$
$350$		−	2.18775e13i		−	4.16541i
$351$		−	1.11893e12i		−	0.210024i
$352$	1.35454e12			0.250657
$353$		−	6.56754e12i		−	1.19820i	−0.800675	−	0.599100i	$-0.795525\pi$
$353$		−	6.56754e12i		−	1.19820i	0.800675	−	0.599100i	$-0.204475\pi$
$354$	4.05272e12	−	1.99463e12i	0.729005	−	0.358794i
$355$	−1.86628e13			−3.31006
$356$		−	2.37864e12i		−	0.415986i
$357$	−6.01591e11			−0.103743
$358$	9.74233e12			1.65671
$359$	−1.83840e12			−0.308296			−0.154148	−	0.988048i	$-0.549263\pi$
$359$	−1.83840e12			−0.308296			−0.154148	+	0.988048i	$0.549263\pi$
$360$		−	9.93537e10i		−	0.0164313i
$361$	−4.17892e12			−0.681598
$362$		−	2.41557e11i		−	0.0388576i
$363$	3.52339e12			0.559021
$364$		−	9.02815e12i		−	1.41284i
$365$		−	1.99385e13i		−	3.07771i
$366$	1.69086e12			0.257455
$367$			4.47888e12i			0.672728i	0.941732	+	0.336364i	$0.109197\pi$
$367$			4.47888e12i			0.672728i	−0.941732	+	0.336364i	$0.890803\pi$
$368$			1.02571e13i			1.51980i
$369$	−3.43466e12			−0.502056
$370$	9.51414e12			1.37202
$371$	1.69832e13			2.41630
$372$			1.20182e12i			0.168704i
$373$	2.05362e12			0.284430			0.142215	−	0.989836i	$-0.454578\pi$
$373$	2.05362e12			0.284430			0.142215	+	0.989836i	$0.454578\pi$
$374$	−2.49718e11			−0.0341265
$375$	−9.57259e12			−1.29084
$376$	2.21230e11			0.0294377
$377$			3.29780e12i			0.433029i
$378$		−	2.75958e12i		−	0.357589i
$379$	5.75685e12			0.736188			0.368094	−	0.929789i	$-0.380011\pi$
$379$	5.75685e12			0.736188			0.368094	+	0.929789i	$0.380011\pi$
$380$	−7.89342e12			−0.996201
$381$	−3.44831e12			−0.429517
$382$	1.77307e13			2.17976
$383$	1.33107e13			1.61513			0.807567	−	0.589776i	$-0.200784\pi$
$383$	1.33107e13			1.61513			0.807567	+	0.589776i	$0.200784\pi$
$384$		−	2.63903e11i		−	0.0316074i
$385$			3.58278e12i			0.423561i
$386$		−	1.30537e12i		−	0.152334i
$387$			2.99712e12i			0.345262i
$388$		−	1.02583e12i		−	0.116659i
$389$	−9.51362e12			−1.06807			−0.534033	−	0.845464i	$-0.679324\pi$
$389$	−9.51362e12			−1.06807			−0.534033	+	0.845464i	$0.679324\pi$
$390$	−1.44045e13			−1.59652
$391$		−	1.85487e12i		−	0.202969i
$392$			1.88337e11i			0.0203472i
$393$			8.51161e12i			0.907922i
$394$		−	1.68905e13i		−	1.77894i
$395$	2.45124e13			2.54918
$396$		−	5.67119e11i		−	0.0582369i
$397$			1.37121e13i			1.39043i	0.718799	+	0.695217i	$0.244692\pi$
$397$			1.37121e13i			1.39043i	−0.718799	+	0.695217i	$0.755308\pi$
$398$			7.74964e12i			0.776008i
$399$	4.34975e12			0.430130
$400$	−2.33937e13			−2.28454
$401$		−	5.09480e12i		−	0.491366i	−0.969350	−	0.245683i	$-0.920988\pi$
$401$		−	5.09480e12i		−	0.491366i	0.969350	−	0.245683i	$-0.0790122\pi$
$402$	−1.15211e13			−1.09739
$403$	−3.45695e12			−0.325213
$404$		−	1.13468e13i		−	1.05431i
$405$	−2.17984e12			−0.200055
$406$			8.13323e12i			0.737280i
$407$	−1.07746e12			−0.0964782
$408$			2.43214e10i			0.00215124i
$409$			1.87597e13i			1.63911i	0.572999	+	0.819556i	$0.305780\pi$
$409$			1.87597e13i			1.63911i	−0.572999	+	0.819556i	$0.694220\pi$
$410$			4.42157e13i			3.81643i
$411$	1.53877e12			0.131209
$412$			3.39226e12i			0.285761i
$413$	7.00547e12	+	1.42338e13i	0.583025	+	1.18460i
$414$	8.50852e12			0.699604
$415$		−	1.19684e13i		−	0.972289i
$416$	−1.91269e13			−1.53525
$417$	1.22342e12			0.0970279
$418$	1.80557e12			0.141492
$419$		−	5.45055e12i		−	0.422056i	−0.977480	−	0.211028i	$-0.932319\pi$
$419$		−	5.45055e12i		−	0.422056i	0.977480	−	0.211028i	$-0.0676811\pi$
$420$	−1.75881e13			−1.34577
$421$			8.20035e11i			0.0620043i	0.999519	+	0.0310022i	$0.00986987\pi$
$421$			8.20035e11i			0.0620043i	−0.999519	+	0.0310022i	$0.990130\pi$
$422$	1.25253e13			0.935889
$423$		−	4.85381e12i		−	0.358411i
$424$		−	6.86608e11i		−	0.0501048i
$425$	4.23043e12			0.305098
$426$			2.09568e13i			1.49375i
$427$			5.93858e12i			0.418353i
$428$	−1.31434e13			−0.915143
$429$	1.63128e12			0.112264
$430$	3.85830e13			2.62455
$431$			2.14838e13i			1.44452i	0.691620	+	0.722262i	$0.256897\pi$
$431$			2.14838e13i			1.44452i	−0.691620	+	0.722262i	$0.743103\pi$
$432$	−2.95082e12			−0.196121
$433$	5.73747e12			0.376948			0.188474	−	0.982078i	$-0.439646\pi$
$433$	5.73747e12			0.376948			0.188474	+	0.982078i	$0.439646\pi$
$434$	−8.52574e12			−0.553711
$435$	6.42457e12			0.412475
$436$			5.03763e12i			0.319738i
$437$			1.34115e13i			0.841528i
$438$	−2.23892e13			−1.38889
$439$	9.11837e12			0.559235			0.279618	−	0.960111i	$-0.409792\pi$
$439$	9.11837e12			0.559235			0.279618	+	0.960111i	$0.409792\pi$
$440$	1.44847e11			0.00878304
$441$	4.13214e12			0.247732
$442$	3.52616e12			0.209021
$443$			2.76185e13i			1.61876i	0.587288	+	0.809378i	$0.300196\pi$
$443$			2.76185e13i			1.61876i	−0.587288	+	0.809378i	$0.699804\pi$
$444$		−	5.28931e12i		−	0.306538i
$445$		−	1.33291e13i		−	0.763839i
$446$			3.80244e13i			2.15471i
$447$		−	1.22197e12i		−	0.0684735i
$448$	−2.28908e13			−1.26844
$449$	3.20562e13			1.75663			0.878314	−	0.478084i	$-0.158669\pi$
$449$	3.20562e13			1.75663			0.878314	+	0.478084i	$0.158669\pi$
$450$			1.94055e13i			1.05163i
$451$		−	5.00735e12i		−	0.268364i
$452$			1.50047e13i			0.795306i
$453$			1.74147e13i			0.912903i
$454$	2.13253e13			1.10564
$455$		−	5.05909e13i		−	2.59427i
$456$		−	1.75854e11i		−	0.00891925i
$457$			5.98878e12i			0.300440i	0.988653	+	0.150220i	$0.0479981\pi$
$457$			5.98878e12i			0.300440i	−0.988653	+	0.150220i	$0.952002\pi$
$458$	3.77079e13			1.87113
$459$	5.33617e11			0.0261918
$460$		−	5.42287e13i		−	2.63294i
$461$	2.61854e13			1.25763			0.628817	−	0.777553i	$-0.283539\pi$
$461$	2.61854e13			1.25763			0.628817	+	0.777553i	$0.283539\pi$
$462$	4.02316e12			0.191142
$463$			3.74521e12i			0.176024i	0.996119	+	0.0880118i	$0.0280513\pi$
$463$			3.74521e12i			0.176024i	−0.996119	+	0.0880118i	$0.971949\pi$
$464$	8.69688e12			0.404365
$465$			6.73462e12i			0.309777i
$466$	−2.04320e13			−0.929784
$467$			3.53965e13i			1.59359i	0.604250	+	0.796794i	$0.293473\pi$
$467$			3.53965e13i			1.59359i	−0.604250	+	0.796794i	$0.706527\pi$
$468$			8.00804e12i			0.356695i
$469$		−	4.04639e13i		−	1.78321i
$470$	−6.24850e13			−2.72450
$471$		−	1.59188e13i		−	0.686762i
$472$	5.75453e11	−	2.83221e11i	0.0245641	−	0.0120897i
$473$	−4.36946e12			−0.184553
$474$		−	2.75253e13i		−	1.15038i
$475$	−3.05877e13			−1.26497
$476$	4.30550e12			0.176193
$477$	−1.50643e13			−0.610038
$478$		−	1.14617e13i		−	0.459313i
$479$	1.25567e13			0.497964			0.248982	−	0.968508i	$-0.419904\pi$
$479$	1.25567e13			0.497964			0.248982	+	0.968508i	$0.419904\pi$
$480$			3.72619e13i			1.46238i
$481$	1.52143e13			0.590918
$482$			5.43552e13i			2.08932i
$483$			2.98833e13i			1.13682i
$484$	−2.52164e13			−0.949417
$485$		−	5.74844e12i		−	0.214211i
$486$			2.44777e12i			0.0902795i
$487$	−1.22247e13			−0.446265			−0.223133	−	0.974788i	$-0.571628\pi$
$487$	−1.22247e13			−0.446265			−0.223133	+	0.974788i	$0.571628\pi$
$488$	2.40088e11			0.00867504
$489$	3.97940e11			0.0142323
$490$		−	5.31946e13i		−	1.88316i
$491$	−4.44368e13			−1.55717			−0.778583	−	0.627541i	$-0.784061\pi$
$491$	−4.44368e13			−1.55717			−0.778583	+	0.627541i	$0.784061\pi$
$492$	2.45814e13			0.852669
$493$	−1.57271e12			−0.0540026
$494$	−2.54956e13			−0.866624
$495$		−	3.17796e12i		−	0.106936i
$496$			9.11659e12i			0.303686i
$497$	−7.36038e13			−2.42727
$498$	−1.34395e13			−0.438769
$499$	−9.54778e12			−0.308603			−0.154301	−	0.988024i	$-0.549313\pi$
$499$	−9.54778e12			−0.308603			−0.154301	+	0.988024i	$0.549313\pi$
$500$	6.85097e13			2.19231
$501$	−2.89034e12			−0.0915716
$502$		−	5.79049e13i		−	1.81634i
$503$		−	4.02782e13i		−	1.25092i	−0.780256	−	0.625461i	$-0.784911\pi$
$503$		−	4.02782e13i		−	1.25092i	0.780256	−	0.625461i	$-0.215089\pi$
$504$		−	3.91838e11i		−	0.0120491i
$505$		−	6.35839e13i		−	1.93593i
$506$			1.24045e13i			0.373960i
$507$	−3.69356e12			−0.110257
$508$	2.46790e13			0.729473
$509$		−	2.69555e13i		−	0.788966i	−0.918903	−	0.394483i	$-0.870924\pi$
$509$		−	2.69555e13i		−	0.788966i	0.918903	−	0.394483i	$-0.129076\pi$
$510$		−	6.86945e12i		−	0.199100i
$511$		−	7.86347e13i		−	2.25689i
$512$			4.94594e13i			1.40572i
$513$	−3.85827e12			−0.108594
$514$			6.31415e13i			1.75994i
$515$			1.90092e13i			0.524719i
$516$		−	2.14499e13i		−	0.586378i
$517$	7.07631e12			0.191582
$518$	3.75225e13			1.00610
$519$			1.54858e13i			0.411240i
$520$	−2.04531e12			−0.0537952
$521$	9.50332e12			0.247564			0.123782	−	0.992309i	$-0.460498\pi$
$521$	9.50332e12			0.247564			0.123782	+	0.992309i	$0.460498\pi$
$522$		−	7.21424e12i		−	0.186139i
$523$	2.38341e13			0.609103			0.304551	−	0.952496i	$-0.401493\pi$
$523$	2.38341e13			0.609103			0.304551	+	0.952496i	$0.401493\pi$
$524$		−	6.09163e13i		−	1.54198i
$525$	−6.81555e13			−1.70885
$526$		−	1.77743e13i		−	0.441433i
$527$		−	1.64861e12i		−	0.0405570i
$528$		−	4.30197e12i		−	0.104833i
$529$	−5.07118e13			−1.22414
$530$			1.93928e14i			4.63726i
$531$	−6.21391e12	−	1.26255e13i	−0.147195	−	0.299073i
$532$	−3.11306e13			−0.730514
$533$			7.07065e13i			1.64370i
$534$	−1.49675e13			−0.344701
$535$	−7.36514e13			−1.68040
$536$	−1.63590e12			−0.0369770
$537$		−	3.03505e13i		−	0.679664i
$538$	4.05174e13			0.898938
$539$			6.02420e12i			0.132421i
$540$	1.56008e13			0.339764
$541$			5.05282e13i			1.09030i	0.838337	+	0.545152i	$0.183528\pi$
$541$			5.05282e13i			1.09030i	−0.838337	+	0.545152i	$0.816472\pi$
$542$			1.19927e14i			2.56402i
$543$	−7.52527e11			−0.0159413
$544$		−	9.12159e12i		−	0.191459i
$545$			2.82293e13i			0.587107i
$546$	−5.68092e13			−1.17073
$547$	7.08827e13			1.44745			0.723725	−	0.690089i	$-0.242429\pi$
$547$	7.08827e13			1.44745			0.723725	+	0.690089i	$0.242429\pi$
$548$	−1.10128e13			−0.222840
$549$		−	5.26757e12i		−	0.105621i
$550$	−2.82911e13			−0.562129
$551$	1.13714e13			0.223900
$552$	1.20814e12			0.0235734
$553$	9.66734e13			1.86931
$554$			4.95509e13i			0.949518i
$555$		−	2.96396e13i		−	0.562870i
$556$	−8.75586e12			−0.164788
$557$	8.11846e12			0.151425			0.0757125	−	0.997130i	$-0.475877\pi$
$557$	8.11846e12			0.151425			0.0757125	+	0.997130i	$0.475877\pi$
$558$	7.56241e12			0.139794
$559$	6.16992e13			1.13037
$560$	−1.33417e14			−2.42254
$561$			7.77953e11i			0.0140004i
$562$		−	7.55831e13i		−	1.34816i
$563$		−	8.26188e13i		−	1.46062i	−0.683117	−	0.730309i	$-0.739376\pi$
$563$		−	8.26188e13i		−	1.46062i	0.683117	−	0.730309i	$-0.260624\pi$
$564$			3.47380e13i			0.608709i
$565$			8.40814e13i			1.46035i
$566$	5.10612e13			0.879040
$567$	−8.59698e12			−0.146700
$568$			2.97569e12i			0.0503322i
$569$		−	9.00309e13i		−	1.50949i	−0.656018	−	0.754745i	$-0.727761\pi$
$569$		−	9.00309e13i		−	1.50949i	0.656018	−	0.754745i	$-0.272239\pi$
$570$			4.96690e13i			0.825488i
$571$		−	6.91183e13i		−	1.13871i	−0.822093	−	0.569354i	$-0.807193\pi$
$571$		−	6.91183e13i		−	1.13871i	0.822093	−	0.569354i	$-0.192807\pi$
$572$	−1.16748e13			−0.190665
$573$		−	5.52368e13i		−	0.894243i
$574$			1.74381e14i			2.79859i
$575$		−	2.10142e14i		−	3.34328i
$576$	2.03043e13			0.320240
$577$	−3.78206e13			−0.591356			−0.295678	−	0.955288i	$-0.595546\pi$
$577$	−3.78206e13			−0.591356			−0.295678	+	0.955288i	$0.595546\pi$
$578$		−	8.91071e13i		−	1.38125i
$579$	−4.06664e12			−0.0624946
$580$	−4.59797e13			−0.700529
$581$		−	4.72017e13i		−	0.712980i
$582$	−6.45500e12			−0.0966677
$583$		−	2.19620e13i		−	0.326084i
$584$	−3.17909e12			−0.0467992
$585$			4.48745e13i			0.654969i
$586$			3.66603e13i			0.530527i
$587$		−	2.91118e13i		−	0.417713i	−0.977946	−	0.208857i	$-0.933026\pi$
$587$		−	2.91118e13i		−	0.417713i	0.977946	−	0.208857i	$-0.0669742\pi$
$588$	−2.95732e13			−0.420737
$589$			1.19202e13i			0.168153i
$590$	−1.62533e14	+	7.99941e13i	−2.27344	+	1.11892i
$591$	−5.26193e13			−0.729806
$592$		−	4.01229e13i		−	0.551802i
$593$	−4.78928e13			−0.653126			−0.326563	−	0.945175i	$-0.605891\pi$
$593$	−4.78928e13			−0.653126			−0.326563	+	0.945175i	$0.605891\pi$
$594$	−3.56857e12			−0.0482572
$595$	2.41267e13			0.323528
$596$			8.74545e12i			0.116292i
$597$	2.41427e13			0.318356
$598$		−	1.75158e14i		−	2.29047i
$599$	8.90386e13			1.15463			0.577317	−	0.816520i	$-0.304100\pi$
$599$	8.90386e13			1.15463			0.577317	+	0.816520i	$0.304100\pi$
$600$			2.75543e12i			0.0354350i
$601$			5.52898e13i			0.705135i	0.935786	+	0.352568i	$0.114691\pi$
$601$			5.52898e13i			0.705135i	−0.935786	+	0.352568i	$0.885309\pi$
$602$	1.52166e14			1.92458
$603$			3.58918e13i			0.450204i
$604$		−	1.24634e14i		−	1.55043i
$605$	−1.41305e14			−1.74333
$606$	−7.13993e13			−0.873637
$607$	9.75041e13			1.18326			0.591629	−	0.806210i	$-0.298485\pi$
$607$	9.75041e13			1.18326			0.591629	+	0.806210i	$0.298485\pi$
$608$			6.59529e13i			0.793809i
$609$	2.53376e13			0.302468
$610$	−6.78114e13			−0.802886
$611$	−9.99215e13			−1.17342
$612$	−3.81902e12			−0.0444830
$613$			1.20146e14i			1.38806i	0.719947	+	0.694029i	$0.244166\pi$
$613$			1.20146e14i			1.38806i	−0.719947	+	0.694029i	$0.755834\pi$
$614$		−	1.06820e14i		−	1.22408i
$615$	1.37746e14			1.56568
$616$	5.71255e11			0.00644060
$617$	5.83950e13			0.653055			0.326527	−	0.945188i	$-0.394121\pi$
$617$	5.83950e13			0.653055			0.326527	+	0.945188i	$0.394121\pi$
$618$	2.13457e13			0.236792
$619$	−9.32857e13			−1.02651			−0.513253	−	0.858237i	$-0.671560\pi$
$619$	−9.32857e13			−1.02651			−0.513253	+	0.858237i	$0.671560\pi$
$620$		−	4.81987e13i		−	0.526111i
$621$		−	2.65068e13i		−	0.287011i
$622$			1.34128e13i			0.144067i
$623$		−	5.25683e13i		−	0.560123i
$624$			6.07462e13i			0.642090i
$625$	1.70114e14			1.78378
$626$	1.29696e14			1.34913
$627$		−	5.62492e12i		−	0.0580469i
$628$			1.13929e14i			1.16637i
$629$			7.25568e12i			0.0736928i
$630$			1.10672e14i			1.11516i
$631$	1.09580e14			1.09543			0.547717	−	0.836664i	$-0.315497\pi$
$631$	1.09580e14			1.09543			0.547717	+	0.836664i	$0.315497\pi$
$632$		−	3.90837e12i		−	0.0387623i
$633$		−	3.90202e13i		−	0.383947i
$634$		−	5.06753e13i		−	0.494710i
$635$	1.38293e14			1.33947
$636$	1.07813e14			1.03606
$637$		−	8.50651e13i		−	0.811062i
$638$	1.05176e13			0.0994973
$639$	6.52872e13			0.612807
$640$			1.05838e13i			0.0985691i
$641$	−5.54416e13			−0.512325			−0.256162	−	0.966634i	$-0.582458\pi$
$641$	−5.54416e13			−0.512325			−0.256162	+	0.966634i	$0.582458\pi$
$642$			8.27043e13i			0.758320i
$643$	8.60177e13			0.782588			0.391294	−	0.920266i	$-0.372028\pi$
$643$	8.60177e13			0.782588			0.391294	+	0.920266i	$0.372028\pi$
$644$		−	2.13871e14i		−	1.93073i
$645$		−	1.20199e14i		−	1.07672i
$646$		−	1.21588e13i		−	0.108076i
$647$	−1.11602e14			−0.984353			−0.492177	−	0.870495i	$-0.663799\pi$
$647$	−1.11602e14			−0.984353			−0.492177	+	0.870495i	$0.663799\pi$
$648$			3.47563e11i			0.00304200i
$649$	1.84066e13	−	9.05919e12i	0.159864	−	0.0786803i
$650$	3.99486e14			3.44298
$651$			2.65604e13i			0.227159i
$652$	−2.84800e12			−0.0241714
$653$	6.79967e13			0.572693			0.286347	−	0.958126i	$-0.407559\pi$
$653$	6.79967e13			0.572693			0.286347	+	0.958126i	$0.407559\pi$
$654$	3.16991e13			0.264946
$655$		−	3.41356e14i		−	2.83140i
$656$	1.86466e14			1.53490
$657$			6.97497e13i			0.569791i
$658$	−2.46432e14			−1.99787
$659$		−	1.24712e14i		−	1.00341i	−0.865038	−	0.501707i	$-0.832706\pi$
$659$		−	1.24712e14i		−	1.00341i	0.865038	−	0.501707i	$-0.167294\pi$
$660$			2.27442e13i			0.181615i
$661$	−1.82791e14			−1.44860			−0.724300	−	0.689485i	$-0.757837\pi$
$661$	−1.82791e14			−1.44860			−0.724300	+	0.689485i	$0.757837\pi$
$662$			1.94868e14i			1.53267i
$663$		−	1.09851e13i		−	0.0857507i
$664$	−1.90830e12			−0.0147845
$665$	−1.74446e14			−1.34138
$666$	−3.32828e13			−0.254009
$667$			7.81227e13i			0.591763i
$668$	2.06858e13			0.155521
$669$	1.18458e14			0.883965
$670$	4.62049e14			3.42227
$671$	7.67953e12			0.0564575
$672$			1.46956e14i			1.07236i
$673$			2.27493e14i			1.64775i	0.566769	+	0.823877i	$0.308193\pi$
$673$			2.27493e14i			1.64775i	−0.566769	+	0.823877i	$0.691807\pi$
$674$	9.41582e13			0.676953
$675$	6.04545e13			0.431430
$676$	2.64343e13			0.187255
$677$	6.74546e13			0.474317			0.237158	−	0.971471i	$-0.423784\pi$
$677$	6.74546e13			0.474317			0.237158	+	0.971471i	$0.423784\pi$
$678$	9.44163e13			0.659020
$679$		−	2.26711e13i		−	0.157081i
$680$		−	9.75405e11i		−	0.00670873i
$681$		−	6.64351e13i		−	0.453589i
$682$			1.10251e13i			0.0747244i
$683$		−	1.46199e14i		−	0.983651i	−0.870694	−	0.491825i	$-0.836330\pi$
$683$		−	1.46199e14i		−	0.983651i	0.870694	−	0.491825i	$-0.163670\pi$
$684$	2.76131e13			0.184431
$685$	−6.17120e13			−0.409182
$686$			7.24915e13i			0.477163i
$687$		−	1.17472e14i		−	0.767629i
$688$		−	1.62712e14i		−	1.05554i
$689$			3.10116e14i			1.99723i
$690$	−3.41232e14			−2.18175
$691$		−	1.79039e14i		−	1.13647i	−0.822868	−	0.568233i	$-0.807627\pi$
$691$		−	1.79039e14i		−	1.13647i	0.822868	−	0.568233i	$-0.192373\pi$
$692$		−	1.10829e14i		−	0.698432i
$693$		−	1.25334e13i		−	0.0784158i
$694$	−3.48588e14			−2.16528
$695$	−4.90651e13			−0.302586
$696$		−	1.02436e12i		−	0.00627203i
$697$	−3.37198e13			−0.204984
$698$	−4.54901e14			−2.74562
$699$			6.36524e13i			0.381442i
$700$	4.87779e14			2.90224
$701$			2.73394e14i			1.61510i	0.589801	+	0.807548i	$0.299206\pi$
$701$			2.73394e14i			1.61510i	−0.589801	+	0.807548i	$0.700794\pi$
$702$	5.03903e13			0.295570
$703$		−	5.24616e13i		−	0.305538i
$704$			2.96014e13i			0.171178i
$705$			1.94661e14i			1.11772i
$706$	2.95764e14			1.68625
$707$		−	2.50766e14i		−	1.41962i
$708$	4.44721e13	+	9.03592e13i	0.249989	+	0.507933i
$709$	−1.22783e14			−0.685341			−0.342670	−	0.939456i	$-0.611331\pi$
$709$	−1.22783e14			−0.685341			−0.342670	+	0.939456i	$0.611331\pi$
$710$		−	8.40466e14i		−	4.65831i
$711$	−8.57502e13			−0.471940
$712$	−2.12526e12			−0.0116148
$713$	−8.18930e13			−0.444425
$714$		−	2.70922e13i		−	0.146000i
$715$	−6.54220e13			−0.350101
$716$			2.17214e14i			1.15431i
$717$	−3.57069e13			−0.188433
$718$		−	8.27910e13i		−	0.433871i
$719$			1.35503e14i			0.705188i	0.935776	+	0.352594i	$0.114700\pi$
$719$			1.35503e14i			0.705188i	−0.935776	+	0.352594i	$0.885300\pi$
$720$	1.18342e14			0.611613
$721$			7.49696e13i			0.384777i
$722$		−	1.88195e14i		−	0.959226i
$723$	1.69334e14			0.857142
$724$	5.38573e12			0.0270739
$725$	−1.78176e14			−0.889526
$726$			1.58673e14i			0.786721i
$727$	−8.06261e13			−0.397012			−0.198506	−	0.980100i	$-0.563609\pi$
$727$	−8.06261e13			−0.397012			−0.198506	+	0.980100i	$0.563609\pi$
$728$	−8.06644e12			−0.0394480
$729$	7.62560e12			0.0370370
$730$	8.97914e14			4.33132
$731$			2.94242e13i			0.140967i
$732$			3.76992e13i			0.179381i
$733$	1.43569e14			0.678487			0.339243	−	0.940699i	$-0.389829\pi$
$733$	1.43569e14			0.678487			0.339243	+	0.940699i	$0.389829\pi$
$734$	−2.01703e14			−0.946743
$735$	−1.65719e14			−0.772564
$736$	−4.53104e14			−2.09802
$737$	−5.23263e13			−0.240648
$738$		−	1.54677e14i		−	0.706552i
$739$		−	2.12888e14i		−	0.965893i	−0.875650	−	0.482947i	$-0.839566\pi$
$739$		−	2.12888e14i		−	0.965893i	0.875650	−	0.482947i	$-0.160434\pi$
$740$			2.12127e14i			0.955953i
$741$			7.94271e13i			0.355531i
$742$			7.64827e14i			3.40051i
$743$	−4.45283e14			−1.96649			−0.983245	−	0.182288i	$-0.941650\pi$
$743$	−4.45283e14			−1.96649			−0.983245	+	0.182288i	$0.941650\pi$
$744$	1.07380e12			0.00471041
$745$			4.90067e13i			0.213538i
$746$			9.24831e13i			0.400284i
$747$			4.18684e13i			0.180004i
$748$		−	5.56770e12i		−	0.0237776i
$749$	−2.90471e14			−1.23224
$750$		−	4.31094e14i		−	1.81663i
$751$			4.39685e12i			0.0184053i	0.999958	+	0.00920263i	$0.00292933\pi$
$751$			4.39685e12i			0.0184053i	−0.999958	+	0.00920263i	$0.997071\pi$
$752$			2.63511e14i			1.09574i
$753$	−1.80393e14			−0.745150
$754$	−1.48514e14			−0.609411
$755$		−	6.98412e14i		−	2.84693i
$756$	6.15274e13			0.249149
$757$	−4.84573e12			−0.0194931			−0.00974653	−	0.999953i	$-0.503102\pi$
$757$	−4.84573e12			−0.0194931			−0.00974653	+	0.999953i	$0.503102\pi$
$758$			2.59255e14i			1.03605i
$759$	3.86439e13			0.153417
$760$			7.05259e12i			0.0278151i
$761$	1.51033e13			0.0591762			0.0295881	−	0.999562i	$-0.490580\pi$
$761$	1.51033e13			0.0591762			0.0295881	+	0.999562i	$0.490580\pi$
$762$		−	1.55292e14i		−	0.604468i
$763$			1.11332e14i			0.430526i
$764$			3.95322e14i			1.51874i
$765$	−2.14006e13			−0.0816804
$766$			5.99439e14i			2.27301i
$767$	−2.59912e14	+	1.27921e14i	−0.979150	+	0.481908i
$768$	1.60083e14			0.599154
$769$		−	3.43597e14i		−	1.27767i	−0.769346	−	0.638833i	$-0.779418\pi$
$769$		−	3.43597e14i		−	1.27767i	0.769346	−	0.638833i	$-0.220582\pi$
$770$	−1.61348e14			−0.596086
$771$	1.96706e14			0.722014
$772$	2.91043e13			0.106138
$773$		−	2.71018e14i		−	0.981975i	−0.871167	−	0.490987i	$-0.836636\pi$
$773$		−	2.71018e14i		−	0.981975i	0.871167	−	0.490987i	$-0.163364\pi$
$774$	−1.34973e14			−0.485894
$775$		−	1.86775e14i		−	0.668051i
$776$	−9.16558e11			−0.00325725
$777$		−	1.16895e14i		−	0.412752i
$778$		−	4.28438e14i		−	1.50311i
$779$	2.43808e14			0.849886
$780$		−	3.21161e14i		−	1.11237i
$781$			9.51814e13i			0.327564i
$782$	8.35324e13			0.285641
$783$	−2.24747e13			−0.0763634
$784$	−2.24332e14			−0.757373
$785$			6.38420e14i			2.14170i
$786$	−3.83313e14			−1.27774
$787$	2.21727e14			0.734421			0.367210	−	0.930138i	$-0.380313\pi$
$787$	2.21727e14			0.734421			0.367210	+	0.930138i	$0.380313\pi$
$788$	3.76589e14			1.23947
$789$	−5.53728e13			−0.181097
$790$			1.10389e15i			3.58750i
$791$			3.31606e14i			1.07088i
$792$	−5.06708e11			−0.00162604
$793$	−1.08439e14			−0.345796
$794$	−6.17512e14			−1.95679
$795$	6.04149e14			1.90243
$796$	−1.72785e14			−0.540682
$797$		−	3.07757e14i		−	0.957009i	−0.878085	−	0.478505i	$-0.841179\pi$
$797$		−	3.07757e14i		−	0.957009i	0.878085	−	0.478505i	$-0.158821\pi$
$798$			1.95888e14i			0.605331i
$799$		−	4.76523e13i		−	0.146336i
$800$		−	1.03340e15i		−	3.15370i
$801$			4.66285e13i			0.141413i
$802$	2.29440e14			0.691508
$803$	−1.01687e14			−0.304571
$804$		−	2.56873e14i		−	0.764606i
$805$		−	1.19846e15i		−	3.54524i
$806$		−	1.55681e14i		−	0.457679i
$807$		−	1.26225e14i		−	0.368788i
$808$	−1.01381e13			−0.0294375
$809$		−	4.81189e14i		−	1.38859i	−0.719691	−	0.694294i	$-0.755717\pi$
$809$		−	4.81189e14i		−	1.38859i	0.719691	−	0.694294i	$-0.244283\pi$
$810$		−	9.81672e13i		−	0.281541i
$811$			2.23309e14i			0.636504i	0.948006	+	0.318252i	$0.103096\pi$
$811$			2.23309e14i			0.636504i	−0.948006	+	0.318252i	$0.896904\pi$
$812$	−1.81338e14			−0.513698
$813$	3.73612e14			1.05188
$814$		−	4.85225e13i		−	0.135776i
$815$	−1.59593e13			−0.0443839
$816$	−2.89697e13			−0.0800744
$817$		−	2.12749e14i		−	0.584464i
$818$	−8.44827e14			−2.30675
$819$			1.76979e14i			0.480289i
$820$	−9.85829e14			−2.65909
$821$			3.99764e14i			1.07174i	0.844302	+	0.535868i	$0.180015\pi$
$821$			3.99764e14i			1.07174i	−0.844302	+	0.535868i	$0.819985\pi$
$822$			6.92973e13i			0.184653i
$823$		−	6.18165e12i		−	0.0163721i	−0.999966	−	0.00818607i	$-0.997394\pi$
$823$		−	6.18165e12i		−	0.0163721i	0.999966	−	0.00818607i	$-0.00260574\pi$
$824$	3.03091e12			0.00797879
$825$			8.81359e13i			0.230613i
$826$	−6.41010e14	+	3.15486e14i	−1.66711	+	0.820502i
$827$	−4.82983e14			−1.24854			−0.624272	−	0.781207i	$-0.714604\pi$
$827$	−4.82983e14			−1.24854			−0.624272	+	0.781207i	$0.714604\pi$
$828$			1.89705e14i			0.487447i
$829$	6.85246e14			1.75014			0.875072	−	0.483993i	$-0.160814\pi$
$829$	6.85246e14			1.75014			0.875072	+	0.483993i	$0.160814\pi$
$830$	5.38987e14			1.36832
$831$	1.54367e14			0.389538
$832$		−	4.17988e14i		−	1.04845i
$833$	4.05673e13			0.101147
$834$			5.50959e13i			0.136549i
$835$	1.15917e14			0.285570
$836$			4.02568e13i			0.0985842i
$837$		−	2.35593e13i		−	0.0573503i
$838$	2.45461e14			0.593967
$839$			4.07238e14i			0.979576i	0.871841	+	0.489788i	$0.162926\pi$
$839$			4.07238e14i			0.979576i	−0.871841	+	0.489788i	$0.837074\pi$
$840$			1.57145e13i			0.0375756i
$841$	−3.54468e14			−0.842553
$842$	−3.69296e13			−0.0872598
$843$	−2.35466e14			−0.553083
$844$			2.79262e14i			0.652078i
$845$	1.48129e14			0.343841
$846$	2.18588e14			0.504398
$847$	−5.57287e14			−1.27839
$848$	8.17831e14			1.86502
$849$		−	1.59072e14i		−	0.360625i
$850$			1.90514e14i			0.429370i
$851$	3.60418e14			0.807529
$852$	−4.67251e14			−1.04076
$853$	4.86162e14			1.07655			0.538277	−	0.842768i	$-0.319076\pi$
$853$	4.86162e14			1.07655			0.538277	+	0.842768i	$0.319076\pi$
$854$	−2.67439e14			−0.588756
$855$	1.54735e14			0.338655
$856$			1.17433e13i			0.0255519i
$857$			3.02831e14i			0.655083i	0.944837	+	0.327541i	$0.106220\pi$
$857$			3.02831e14i			0.655083i	−0.944837	+	0.327541i	$0.893780\pi$
$858$			7.34633e13i			0.157992i
$859$			1.11886e14i			0.239226i	0.992821	+	0.119613i	$0.0381655\pi$
$859$			1.11886e14i			0.239226i	−0.992821	+	0.119613i	$0.961835\pi$
$860$			8.60245e14i			1.82865i
$861$	5.43252e14			1.14812
$862$	−9.67506e14			−2.03291
$863$			8.71907e14i			1.82144i	0.413019	+	0.910722i	$0.364474\pi$
$863$			8.71907e14i			1.82144i	−0.413019	+	0.910722i	$0.635526\pi$
$864$		−	1.30351e14i		−	0.270736i
$865$		−	6.21052e14i		−	1.28247i
$866$			2.58382e14i			0.530485i
$867$	−2.77597e14			−0.566656
$868$		−	1.90089e14i		−	0.385797i
$869$		−	1.25014e14i		−	0.252267i
$870$			2.89325e14i			0.580484i
$871$	7.38876e14			1.47394
$872$	4.50101e12			0.00892745
$873$			2.01094e13i			0.0396578i
$874$	−6.03974e14			−1.18430
$875$	1.51407e15			2.95194
$876$		−	4.99189e14i		−	0.967708i
$877$	−6.68413e14			−1.28839			−0.644194	−	0.764862i	$-0.722807\pi$
$877$	−6.68413e14			−1.28839			−0.644194	+	0.764862i	$0.722807\pi$
$878$			4.10638e14i			0.787022i
$879$	1.14209e14			0.217648
$880$			1.72529e14i			0.326926i
$881$			5.32606e14i			1.00352i	0.865007	+	0.501761i	$0.167314\pi$
$881$			5.32606e14i			1.00352i	−0.865007	+	0.501761i	$0.832686\pi$
$882$			1.86088e14i			0.348638i
$883$	4.44418e14			0.827920			0.413960	−	0.910295i	$-0.364145\pi$
$883$	4.44418e14			0.827920			0.413960	+	0.910295i	$0.364145\pi$
$884$			7.86190e13i			0.145635i
$885$	2.49207e14	+	5.06344e14i	0.459034	+	0.932673i
$886$	−1.24378e15			−2.27811
$887$		−	4.92366e14i		−	0.896747i	−0.893846	−	0.448373i	$-0.852003\pi$
$887$		−	4.92366e14i		−	0.896747i	0.893846	−	0.448373i	$-0.147997\pi$
$888$	−4.72588e12			−0.00855890
$889$	5.45410e14			0.982233
$890$	6.00267e14			1.07497
$891$			1.11173e13i			0.0197975i
$892$	−8.47789e14			−1.50129
$893$			3.44546e14i			0.606723i
$894$	5.50304e13			0.0963640
$895$			1.21720e15i			2.11956i
$896$			4.17410e13i			0.0722807i
$897$	−5.45674e14			−0.939660
$898$			1.44362e15i			2.47214i
$899$			6.94358e13i			0.118246i
$900$	−4.32664e14			−0.732721
$901$	−1.47894e14			−0.249072
$902$	2.25502e14			0.377674
$903$		−	4.74047e14i		−	0.789556i
$904$	1.34063e13			0.0222059
$905$	3.01799e13			0.0497136
$906$	−7.84257e14			−1.28475
$907$	−6.61841e14			−1.07824			−0.539122	−	0.842227i	$-0.681244\pi$
$907$	−6.61841e14			−1.07824			−0.539122	+	0.842227i	$0.681244\pi$
$908$			4.75467e14i			0.770355i
$909$			2.22432e14i			0.358408i
$910$	2.27832e15			3.65096
$911$	−1.75413e14			−0.279556			−0.139778	−	0.990183i	$-0.544639\pi$
$911$	−1.75413e14			−0.279556			−0.139778	+	0.990183i	$0.544639\pi$
$912$	2.09463e14			0.331996
$913$	−6.10394e13			−0.0962179
$914$	−2.69700e14			−0.422814
$915$			2.11255e14i			0.329383i
$916$			8.40731e14i			1.30371i
$917$		−	1.34626e15i		−	2.07626i
$918$			2.40310e13i			0.0368603i
$919$			6.06410e14i			0.925101i	0.886593	+	0.462550i	$0.153066\pi$
$919$			6.06410e14i			0.925101i	−0.886593	+	0.462550i	$0.846934\pi$
$920$	−4.84521e13			−0.0735146
$921$	−3.32778e14			−0.502177
$922$			1.17924e15i			1.76989i
$923$		−	1.34401e15i		−	2.00630i
$924$			8.97000e13i			0.133178i
$925$			8.22011e14i			1.21386i
$926$	−1.68662e14			−0.247721
$927$		−	6.64987e13i		−	0.0971436i
$928$			3.84180e14i			0.558207i
$929$			2.38947e14i			0.345320i	0.984981	+	0.172660i	$0.0552362\pi$
$929$			2.38947e14i			0.345320i	−0.984981	+	0.172660i	$0.944764\pi$
$930$	−3.03288e14			−0.435954
$931$	−2.93319e14			−0.419364
$932$		−	4.55551e14i		−	0.647825i
$933$	4.17851e13			0.0591034
$934$	−1.59405e15			−2.24269
$935$		−	3.11996e13i		−	0.0436607i
$936$	7.15500e12			0.00995934
$937$			9.34429e13i			0.129374i	0.997906	+	0.0646872i	$0.0206050\pi$
$937$			9.34429e13i			0.129374i	−0.997906	+	0.0646872i	$0.979395\pi$
$938$	1.82226e15			2.50955
$939$		−	4.04044e14i		−	0.553478i
$940$		−	1.39316e15i		−	1.89829i
$941$		−	1.26396e15i		−	1.71311i	−0.516053	−	0.856557i	$-0.672599\pi$
$941$		−	1.26396e15i		−	1.71311i	0.516053	−	0.856557i	$-0.327401\pi$
$942$	7.16892e14			0.966494
$943$			1.67499e15i			2.24623i
$944$	3.37350e14	+	6.85433e14i	0.450008	+	0.914335i
$945$	3.44780e14			0.457491
$946$		−	1.96775e14i		−	0.259726i
$947$	6.61481e14			0.868495			0.434248	−	0.900794i	$-0.357014\pi$
$947$	6.61481e14			0.868495			0.434248	+	0.900794i	$0.357014\pi$
$948$	6.13702e14			0.801522
$949$	1.43588e15			1.86547
$950$		−	1.37749e15i		−	1.78021i
$951$	−1.57870e14			−0.202954
$952$		−	3.84687e12i		−	0.00491952i
$953$	−1.50978e15			−1.92065			−0.960327	−	0.278876i	$-0.910038\pi$
$953$	−1.50978e15			−1.92065			−0.960327	+	0.278876i	$0.910038\pi$
$954$		−	6.78408e14i		−	0.858518i
$955$			2.21526e15i			2.78874i
$956$	2.55549e14			0.320026
$957$		−	3.27656e13i		−	0.0408186i
$958$			5.65480e14i			0.700793i
$959$	−2.43384e14			−0.300053
$960$	−8.14299e14			−0.998684
$961$	7.46841e14			0.911195
$962$			6.85165e14i			0.831611i
$963$	2.57651e14			0.311100
$964$	−1.21190e15			−1.45573
$965$	1.63091e14			0.194892
$966$	−1.34577e15			−1.59988
$967$		−	1.54678e15i		−	1.82935i	−0.404192	−	0.914674i	$-0.632447\pi$
$967$		−	1.54678e15i		−	1.82935i	0.404192	−	0.914674i	$-0.367553\pi$
$968$			2.25303e13i			0.0265088i
$969$	−3.78786e13			−0.0443379
$970$	2.58876e14			0.301463
$971$	−1.91897e13			−0.0222317			−0.0111158	−	0.999938i	$-0.503538\pi$
$971$	−1.91897e13			−0.0222317			−0.0111158	+	0.999938i	$0.503538\pi$
$972$	−5.45753e13			−0.0629021
$973$	−1.93506e14			−0.221886
$974$		−	5.50529e14i		−	0.628038i
$975$		−	1.24453e15i		−	1.41248i
$976$			2.85973e14i			0.322906i
$977$			7.31465e14i			0.821715i	0.911700	+	0.410857i	$0.134771\pi$
$977$			7.31465e14i			0.821715i	−0.911700	+	0.410857i	$0.865229\pi$
$978$			1.79209e13i			0.0200293i
$979$	−6.79792e13			−0.0755897
$980$	1.18602e15			1.31209
$981$		−	9.87528e13i		−	0.108694i
$982$		−	2.00117e15i		−	2.19143i
$983$		−	8.36951e14i		−	0.911869i	−0.890013	−	0.455934i	$-0.849305\pi$
$983$		−	8.36951e14i		−	0.911869i	0.890013	−	0.455934i	$-0.150695\pi$
$984$		−	2.19629e13i		−	0.0238075i
$985$	2.11028e15			2.27593
$986$		−	7.08259e13i		−	0.0759989i
$987$			7.67716e14i			0.819625i
$988$		−	5.68448e14i		−	0.603818i
$989$	1.46161e15			1.54473
$990$	1.43117e14			0.150492
$991$		−	1.17534e15i		−	1.22969i	−0.788648	−	0.614845i	$-0.789218\pi$
$991$		−	1.17534e15i		−	1.22969i	0.788648	−	0.614845i	$-0.210782\pi$
$992$	−4.02721e14			−0.419224
$993$	6.07076e14			0.628777
$994$		−	3.31469e15i		−	3.41594i
$995$	−9.68235e14			−0.992808
$996$		−	2.99646e14i		−	0.305711i
$997$	1.20743e15			1.22571			0.612854	−	0.790196i	$-0.290021\pi$
$997$	1.20743e15			1.22571			0.612854	+	0.790196i	$0.290021\pi$
$998$		−	4.29977e14i		−	0.434302i
$999$			1.03687e14i			0.104207i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.11.c.a.58.82	yes	100
59.58	odd	2	inner	177.11.c.a.58.19	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.11.c.a.58.19	✓	100	59.58	odd	2	inner
177.11.c.a.58.82	yes	100	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	177.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+45.0342i q^{2} +140.296 q^{3} -1004.08 q^{4} -5626.54 q^{5} +6318.12i q^{6} -22190.3 q^{7} +897.122i q^{8} +19683.0 q^{9} +O(q^{10})\)	\(q+45.0342i q^{2} +140.296 q^{3} -1004.08 q^{4} -5626.54 q^{5} +6318.12i q^{6} -22190.3 q^{7} +897.122i q^{8} +19683.0 q^{9} -253387. i q^{10} +28695.6i q^{11} -140868. q^{12} -405198. i q^{13} -999323. i q^{14} -789382. q^{15} -1.06858e6 q^{16} +193238. q^{17} +886408. i q^{18} -1.39719e6 q^{19} +5.64949e6 q^{20} -3.11321e6 q^{21} -1.29228e6 q^{22} -9.59887e6i q^{23} +125863. i q^{24} +2.18923e7 q^{25} +1.82478e7 q^{26} +2.76145e6 q^{27} +2.22808e7 q^{28} -8.13874e6 q^{29} -3.55492e7i q^{30} -8.53152e6i q^{31} -4.72039e7i q^{32} +4.02588e6i q^{33} +8.70231e6i q^{34} +1.24855e8 q^{35} -1.97633e7 q^{36} +3.75479e7i q^{37} -6.29214e7i q^{38} -5.68477e7i q^{39} -5.04769e6i q^{40} -1.74499e8 q^{41} -1.40201e8i q^{42} +1.52269e8i q^{43} -2.88127e7i q^{44} -1.10747e8 q^{45} +4.32278e8 q^{46} -2.46599e8i q^{47} -1.49917e8 q^{48} +2.09935e8 q^{49} +9.85903e8i q^{50} +2.71105e7 q^{51} +4.06851e8i q^{52} -7.65345e8 q^{53} +1.24360e8i q^{54} -1.61457e8i q^{55} -1.99074e7i q^{56} -1.96020e8 q^{57} -3.66521e8i q^{58} +(-3.15700e8 - 6.41444e8i) q^{59} +7.92602e8 q^{60} -2.67620e8i q^{61} +3.84210e8 q^{62} -4.36772e8 q^{63} +1.03157e9 q^{64} +2.27986e9i q^{65} -1.81302e8 q^{66} +1.82349e9i q^{67} -1.94026e8 q^{68} -1.34668e9i q^{69} +5.62273e9i q^{70} +3.31693e9 q^{71} +1.76580e7i q^{72} +3.54365e9i q^{73} -1.69094e9 q^{74} +3.07141e9 q^{75} +1.40289e9 q^{76} -6.36764e8i q^{77} +2.56009e9 q^{78} -4.35656e9 q^{79} +6.01240e9 q^{80} +3.87420e8 q^{81} -7.85841e9i q^{82} +2.12713e9i q^{83} +3.12591e9 q^{84} -1.08726e9 q^{85} -6.85733e9 q^{86} -1.14183e9 q^{87} -2.57434e7 q^{88} +2.36898e9i q^{89} -4.98741e9i q^{90} +8.99147e9i q^{91} +9.63803e9i q^{92} -1.19694e9i q^{93} +1.11054e10 q^{94} +7.86135e9 q^{95} -6.62253e9i q^{96} +1.02166e9i q^{97} +9.45424e9i q^{98} +5.64815e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 51200 q^{4} + 18392 q^{7} + 1968300 q^{9}+O(q^{10}) \) 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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