LMFDB - Embedded newform 177.11.c.a.58.5

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			58.5
Character	$\chi$	$=$	177.58
Dual form			177.11.c.a.58.96

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-58.9981i q^{2} -140.296 q^{3} -2456.77 q^{4} +878.334 q^{5} +8277.20i q^{6} -5578.77 q^{7} +84530.8i q^{8} +19683.0 q^{9} +O(q^{10})$	\(q-58.9981i q^{2} -140.296 q^{3} -2456.77 q^{4} +878.334 q^{5} +8277.20i q^{6} -5578.77 q^{7} +84530.8i q^{8} +19683.0 q^{9} -51820.0i q^{10} -8137.20i q^{11} +344676. q^{12} +545367. i q^{13} +329136. i q^{14} -123227. q^{15} +2.47142e6 q^{16} +193046. q^{17} -1.16126e6i q^{18} +3.36874e6 q^{19} -2.15787e6 q^{20} +782679. q^{21} -480079. q^{22} -5.01255e6i q^{23} -1.18593e7i q^{24} -8.99415e6 q^{25} +3.21756e7 q^{26} -2.76145e6 q^{27} +1.37058e7 q^{28} +1.17377e7 q^{29} +7.27014e6i q^{30} +3.31260e7i q^{31} -5.92495e7i q^{32} +1.14162e6i q^{33} -1.13893e7i q^{34} -4.90002e6 q^{35} -4.83567e7 q^{36} -6.48748e7i q^{37} -1.98749e8i q^{38} -7.65128e7i q^{39} +7.42463e7i q^{40} -4.00314e7 q^{41} -4.61766e7i q^{42} -2.00048e8i q^{43} +1.99913e7i q^{44} +1.72882e7 q^{45} -2.95731e8 q^{46} -1.47000e8i q^{47} -3.46731e8 q^{48} -2.51353e8 q^{49} +5.30638e8i q^{50} -2.70836e7 q^{51} -1.33984e9i q^{52} +4.79174e7 q^{53} +1.62920e8i q^{54} -7.14718e6i q^{55} -4.71578e8i q^{56} -4.72621e8 q^{57} -6.92502e8i q^{58} +(1.12376e8 + 7.06037e8i) q^{59} +3.02740e8 q^{60} -5.55854e8i q^{61} +1.95437e9 q^{62} -1.09807e8 q^{63} -9.64871e8 q^{64} +4.79014e8i q^{65} +6.73533e7 q^{66} -8.19852e8i q^{67} -4.74270e8 q^{68} +7.03241e8i q^{69} +2.89092e8i q^{70} +3.33641e8 q^{71} +1.66382e9i q^{72} +2.91990e9i q^{73} -3.82749e9 q^{74} +1.26184e9 q^{75} -8.27623e9 q^{76} +4.53956e7i q^{77} -4.51411e9 q^{78} -3.70815e9 q^{79} +2.17073e9 q^{80} +3.87420e8 q^{81} +2.36177e9i q^{82} +5.07449e9i q^{83} -1.92286e9 q^{84} +1.69559e8 q^{85} -1.18024e10 q^{86} -1.64675e9 q^{87} +6.87845e8 q^{88} -1.18443e9i q^{89} -1.01997e9i q^{90} -3.04247e9i q^{91} +1.23147e10i q^{92} -4.64745e9i q^{93} -8.67271e9 q^{94} +2.95888e9 q^{95} +8.31247e9i q^{96} -1.13463e9i q^{97} +1.48293e10i q^{98} -1.60165e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	58.9981i		−	1.84369i	−0.387559	−	0.921845i	$-0.626682\pi$
$2$		−	58.9981i		−	1.84369i	0.387559	−	0.921845i	$-0.373318\pi$
$3$	−140.296			−0.577350
$3$	−140.296			−0.577350
$4$	−2456.77			−2.39919
$5$	878.334			0.281067			0.140533	−	0.990076i	$-0.455118\pi$
$5$	878.334			0.281067			0.140533	+	0.990076i	$0.455118\pi$
$6$			8277.20i			1.06445i
$7$	−5578.77			−0.331931			−0.165966	−	0.986132i	$-0.553074\pi$
$7$	−5578.77			−0.331931			−0.165966	+	0.986132i	$0.553074\pi$
$8$			84530.8i			2.57968i
$9$	19683.0			0.333333
$10$		−	51820.0i		−	0.518200i
$11$		−	8137.20i		−	0.0505256i	−0.999681	−	0.0252628i	$-0.991958\pi$
$11$		−	8137.20i		−	0.0505256i	0.999681	−	0.0252628i	$-0.00804226\pi$
$12$	344676.			1.38517
$13$			545367.i			1.46883i	0.678700	+	0.734416i	$0.262544\pi$
$13$			545367.i			1.46883i	−0.678700	+	0.734416i	$0.737456\pi$
$14$			329136.i			0.611978i
$15$	−123227.			−0.162274
$16$	2.47142e6			2.35693
$17$	193046.			0.135962			0.0679808	−	0.997687i	$-0.478344\pi$
$17$	193046.			0.135962			0.0679808	+	0.997687i	$0.478344\pi$
$18$		−	1.16126e6i		−	0.614563i
$19$	3.36874e6			1.36050			0.680251	−	0.732979i	$-0.261871\pi$
$19$	3.36874e6			1.36050			0.680251	+	0.732979i	$0.261871\pi$
$20$	−2.15787e6			−0.674333
$21$	782679.			0.191640
$22$	−480079.			−0.0931536
$23$		−	5.01255e6i		−	0.778788i	−0.921071	−	0.389394i	$-0.872684\pi$
$23$		−	5.01255e6i		−	0.778788i	0.921071	−	0.389394i	$-0.127316\pi$
$24$		−	1.18593e7i		−	1.48938i
$25$	−8.99415e6			−0.921001
$26$	3.21756e7			2.70807
$27$	−2.76145e6			−0.192450
$28$	1.37058e7			0.796366
$29$	1.17377e7			0.572260			0.286130	−	0.958191i	$-0.407631\pi$
$29$	1.17377e7			0.572260			0.286130	+	0.958191i	$0.407631\pi$
$30$			7.27014e6i			0.299183i
$31$			3.31260e7i			1.15707i	0.815657	+	0.578536i	$0.196376\pi$
$31$			3.31260e7i			1.15707i	−0.815657	+	0.578536i	$0.803624\pi$
$32$		−	5.92495e7i		−	1.76577i
$33$			1.14162e6i			0.0291710i
$34$		−	1.13893e7i		−	0.250671i
$35$	−4.90002e6			−0.0932948
$36$	−4.83567e7			−0.799731
$37$		−	6.48748e7i		−	0.935550i	−0.883848	−	0.467775i	$-0.845056\pi$
$37$		−	6.48748e7i		−	0.935550i	0.883848	−	0.467775i	$-0.154944\pi$
$38$		−	1.98749e8i		−	2.50835i
$39$		−	7.65128e7i		−	0.848030i
$40$			7.42463e7i			0.725061i
$41$	−4.00314e7			−0.345526			−0.172763	−	0.984963i	$-0.555270\pi$
$41$	−4.00314e7			−0.345526			−0.172763	+	0.984963i	$0.555270\pi$
$42$		−	4.61766e7i		−	0.353326i
$43$		−	2.00048e8i		−	1.36079i	−0.732845	−	0.680396i	$-0.761808\pi$
$43$		−	2.00048e8i		−	1.36079i	0.732845	−	0.680396i	$-0.238192\pi$
$44$			1.99913e7i			0.121221i
$45$	1.72882e7			0.0936889
$46$	−2.95731e8			−1.43584
$47$		−	1.47000e8i		−	0.640955i	−0.947256	−	0.320478i	$-0.896157\pi$
$47$		−	1.47000e8i		−	0.640955i	0.947256	−	0.320478i	$-0.103843\pi$
$48$	−3.46731e8			−1.36077
$49$	−2.51353e8			−0.889822
$50$			5.30638e8i			1.69804i
$51$	−2.70836e7			−0.0784974
$52$		−	1.33984e9i		−	3.52401i
$53$	4.79174e7			0.114581			0.0572907	−	0.998358i	$-0.481754\pi$
$53$	4.79174e7			0.114581			0.0572907	+	0.998358i	$0.481754\pi$
$54$			1.62920e8i			0.354818i
$55$		−	7.14718e6i		−	0.0142011i
$56$		−	4.71578e8i		−	0.856275i
$57$	−4.72621e8			−0.785487
$58$		−	6.92502e8i		−	1.05507i
$59$	1.12376e8	+	7.06037e8i	0.157186	+	0.987569i
$59$	1.12376e8	+	7.06037e8i	0.157186	+	0.987569i
$60$	3.02740e8			0.389326
$61$		−	5.55854e8i		−	0.658130i	−0.944307	−	0.329065i	$-0.893266\pi$
$61$		−	5.55854e8i		−	0.658130i	0.944307	−	0.329065i	$-0.106734\pi$
$62$	1.95437e9			2.13328
$63$	−1.09807e8			−0.110644
$64$	−9.64871e8			−0.898606
$65$			4.79014e8i			0.412840i
$66$	6.73533e7			0.0537823
$67$		−	8.19852e8i		−	0.607241i	−0.952793	−	0.303621i	$-0.901804\pi$
$67$		−	8.19852e8i		−	0.607241i	0.952793	−	0.303621i	$-0.0981955\pi$
$68$	−4.74270e8			−0.326198
$69$			7.03241e8i			0.449633i
$70$			2.89092e8i			0.172007i
$71$	3.33641e8			0.184922			0.0924609	−	0.995716i	$-0.470527\pi$
$71$	3.33641e8			0.184922			0.0924609	+	0.995716i	$0.470527\pi$
$72$			1.66382e9i			0.859892i
$73$			2.91990e9i			1.40849i	0.709958	+	0.704244i	$0.248714\pi$
$73$			2.91990e9i			1.40849i	−0.709958	+	0.704244i	$0.751286\pi$
$74$	−3.82749e9			−1.72486
$75$	1.26184e9			0.531740
$76$	−8.27623e9			−3.26411
$77$			4.53956e7i			0.0167710i
$78$	−4.51411e9			−1.56350
$79$	−3.70815e9			−1.20510			−0.602548	−	0.798083i	$-0.705848\pi$
$79$	−3.70815e9			−1.20510			−0.602548	+	0.798083i	$0.705848\pi$
$80$	2.17073e9			0.662455
$81$	3.87420e8			0.111111
$82$			2.36177e9i			0.637043i
$83$			5.07449e9i			1.28826i	0.764918	+	0.644128i	$0.222780\pi$
$83$			5.07449e9i			1.28826i	−0.764918	+	0.644128i	$0.777220\pi$
$84$	−1.92286e9			−0.459782
$85$	1.69559e8			0.0382143
$86$	−1.18024e10			−2.50888
$87$	−1.64675e9			−0.330394
$88$	6.87845e8			0.130340
$89$		−	1.18443e9i		−	0.212110i	−0.994360	−	0.106055i	$-0.966178\pi$
$89$		−	1.18443e9i		−	0.212110i	0.994360	−	0.106055i	$-0.0338219\pi$
$90$		−	1.01997e9i		−	0.172733i
$91$		−	3.04247e9i		−	0.487551i
$92$			1.23147e10i			1.86846i
$93$		−	4.64745e9i		−	0.668036i
$94$	−8.67271e9			−1.18172
$95$	2.95888e9			0.382392
$96$			8.31247e9i			1.01947i
$97$		−	1.13463e9i		−	0.132128i	−0.997815	−	0.0660640i	$-0.978956\pi$
$97$		−	1.13463e9i		−	0.132128i	0.997815	−	0.0660640i	$-0.0210442\pi$
$98$			1.48293e10i			1.64056i
$99$		−	1.60165e8i		−	0.0168419i
$100$	2.20966e10			2.20966
$101$		−	2.89566e9i		−	0.275512i	−0.990466	−	0.137756i	$-0.956011\pi$
$101$		−	2.89566e9i		−	0.275512i	0.990466	−	0.137756i	$-0.0439890\pi$
$102$			1.59788e9i			0.144725i
$103$		−	1.48531e10i		−	1.28124i	−0.767858	−	0.640621i	$-0.778677\pi$
$103$		−	1.48531e10i		−	1.28124i	0.767858	−	0.640621i	$-0.221323\pi$
$104$	−4.61003e10			−3.78911
$105$	6.87454e8			0.0538638
$106$		−	2.82704e9i		−	0.211253i
$107$	1.76146e10			1.25590			0.627948	−	0.778256i	$-0.283895\pi$
$107$	1.76146e10			1.25590			0.627948	+	0.778256i	$0.283895\pi$
$108$	6.78425e9			0.461725
$109$		−	1.79260e10i		−	1.16506i	−0.812808	−	0.582532i	$-0.802062\pi$
$109$		−	1.79260e10i		−	1.16506i	0.812808	−	0.582532i	$-0.197938\pi$
$110$	−4.21670e8			−0.0261824
$111$			9.10168e9i			0.540140i
$112$	−1.37875e10			−0.782338
$113$			1.41136e10i			0.766030i	0.923742	+	0.383015i	$0.125114\pi$
$113$			1.41136e10i			0.766030i	−0.923742	+	0.383015i	$0.874886\pi$
$114$			2.78837e10i			1.44819i
$115$		−	4.40269e9i		−	0.218891i
$116$	−2.88369e10			−1.37296
$117$			1.07345e10i			0.489610i
$118$	4.16548e10	−	6.62996e9i	1.82077	−	0.289801i
$119$	−1.07696e9			−0.0451299
$120$		−	1.04165e10i		−	0.418614i
$121$	2.58712e10			0.997447
$122$	−3.27943e10			−1.21339
$123$	5.61624e9			0.199490
$124$		−	8.13830e10i		−	2.77604i
$125$	−1.64773e10			−0.539930
$126$			6.47839e9i			0.203993i
$127$	−1.92944e10			−0.584001			−0.292000	−	0.956418i	$-0.594321\pi$
$127$	−1.92944e10			−0.584001			−0.292000	+	0.956418i	$0.594321\pi$
$128$		−	3.74596e9i		−	0.109022i
$129$			2.80660e10i			0.785654i
$130$	2.82609e10			0.761148
$131$		−	3.30391e10i		−	0.856389i	−0.903687	−	0.428195i	$-0.859150\pi$
$131$		−	3.30391e10i		−	0.856389i	0.903687	−	0.428195i	$-0.140850\pi$
$132$		−	2.80470e9i		−	0.0699868i
$133$	−1.87934e10			−0.451593
$134$	−4.83697e10			−1.11956
$135$	−2.42547e9			−0.0540913
$136$			1.63183e10i			0.350737i
$137$	−1.61857e10			−0.335373			−0.167687	−	0.985840i	$-0.553630\pi$
$137$	−1.61857e10			−0.335373			−0.167687	+	0.985840i	$0.553630\pi$
$138$	4.14899e10			0.828985
$139$	3.74958e10			0.722618			0.361309	−	0.932446i	$-0.382330\pi$
$139$	3.74958e10			0.722618			0.361309	+	0.932446i	$0.382330\pi$
$140$	1.20382e10			0.223832
$141$			2.06235e10i			0.370056i
$142$		−	1.96842e10i		−	0.340939i
$143$	4.43776e9			0.0742136
$144$	4.86450e10			0.785643
$145$	1.03096e10			0.160843
$146$	1.72268e11			2.59682
$147$	3.52638e10			0.513739
$148$			1.59383e11i			2.24456i
$149$			7.52577e10i			1.02475i	0.858761	+	0.512377i	$0.171235\pi$
$149$			7.52577e10i			1.02475i	−0.858761	+	0.512377i	$0.828765\pi$
$150$		−	7.44464e10i		−	0.980364i
$151$			2.90345e10i			0.369853i	0.982752	+	0.184926i	$0.0592047\pi$
$151$			2.90345e10i			0.369853i	−0.982752	+	0.184926i	$0.940795\pi$
$152$			2.84762e11i			3.50966i
$153$	3.79972e9			0.0453205
$154$	2.67825e9			0.0309206
$155$			2.90957e10i			0.325214i
$156$			1.87975e11i			2.03459i
$157$		−	6.67856e10i		−	0.700140i	−0.936724	−	0.350070i	$-0.886158\pi$
$157$		−	6.67856e10i		−	0.700140i	0.936724	−	0.350070i	$-0.113842\pi$
$158$			2.18774e11i			2.22182i
$159$	−6.72263e9			−0.0661536
$160$		−	5.20408e10i		−	0.496300i
$161$			2.79638e10i			0.258504i
$162$		−	2.28571e10i		−	0.204854i
$163$	7.80950e10			0.678711			0.339356	−	0.940658i	$-0.389791\pi$
$163$	7.80950e10			0.678711			0.339356	+	0.940658i	$0.389791\pi$
$164$	9.83479e10			0.828984
$165$			1.00272e9i			0.00819900i
$166$	2.99385e11			2.37514
$167$	5.27454e10			0.406071			0.203035	−	0.979171i	$-0.434919\pi$
$167$	5.27454e10			0.406071			0.203035	+	0.979171i	$0.434919\pi$
$168$			6.61605e10i			0.494370i
$169$	−1.59566e11			−1.15747
$170$		−	1.00036e10i		−	0.0704553i
$171$	6.63069e10			0.453501
$172$			4.91472e11i			3.26480i
$173$		−	1.11742e11i		−	0.721085i	−0.932743	−	0.360542i	$-0.882592\pi$
$173$		−	1.11742e11i		−	0.721085i	0.932743	−	0.360542i	$-0.117408\pi$
$174$			9.71553e10i			0.609145i
$175$	5.01763e10			0.305709
$176$		−	2.01105e10i		−	0.119085i
$177$	−1.57659e10	−	9.90543e10i	−0.0907511	−	0.570173i
$178$	−6.98793e10			−0.391065
$179$		−	3.34656e11i		−	1.82110i	−0.413403	−	0.910548i	$-0.635660\pi$
$179$		−	3.34656e11i		−	1.82110i	0.413403	−	0.910548i	$-0.364340\pi$
$180$	−4.24733e10			−0.224778
$181$	−3.32967e11			−1.71399			−0.856996	−	0.515324i	$-0.827672\pi$
$181$	−3.32967e11			−1.71399			−0.856996	+	0.515324i	$0.827672\pi$
$182$	−1.79500e11			−0.898892
$183$			7.79842e10i			0.379972i
$184$	4.23715e11			2.00902
$185$		−	5.69817e10i		−	0.262952i
$186$	−2.74190e11			−1.23165
$187$		−	1.57085e9i		−	0.00686954i
$188$			3.61145e11i			1.53777i
$189$	1.54055e10			0.0638802
$190$		−	1.74568e11i		−	0.705013i
$191$			4.09885e11i			1.61248i	0.591587	+	0.806241i	$0.298502\pi$
$191$			4.09885e11i			1.61248i	−0.591587	+	0.806241i	$0.701498\pi$
$192$	1.35368e11			0.518810
$193$	−2.89215e11			−1.08002			−0.540012	−	0.841657i	$-0.681580\pi$
$193$	−2.89215e11			−1.08002			−0.540012	+	0.841657i	$0.681580\pi$
$194$	−6.69409e10			−0.243603
$195$		−	6.72038e10i		−	0.238353i
$196$	6.17516e11			2.13485
$197$	−3.80310e9			−0.0128176			−0.00640880	−	0.999979i	$-0.502040\pi$
$197$	−3.80310e9			−0.0128176			−0.00640880	+	0.999979i	$0.502040\pi$
$198$	−9.44940e9			−0.0310512
$199$	−1.29787e11			−0.415879			−0.207939	−	0.978142i	$-0.566676\pi$
$199$	−1.29787e11			−0.415879			−0.207939	+	0.978142i	$0.566676\pi$
$200$		−	7.60283e11i		−	2.37589i
$201$			1.15022e11i			0.350591i
$202$	−1.70838e11			−0.507959
$203$	−6.54819e10			−0.189951
$204$	6.65382e10			0.188330
$205$	−3.51609e10			−0.0971159
$206$	−8.76304e11			−2.36221
$207$		−	9.86620e10i		−	0.259596i
$208$			1.34783e12i			3.46193i
$209$		−	2.74121e10i		−	0.0687403i
$210$		−	4.05584e10i		−	0.0993081i
$211$			6.14086e11i			1.46831i	0.678984	+	0.734153i	$0.262421\pi$
$211$			6.14086e11i			1.46831i	−0.678984	+	0.734153i	$0.737579\pi$
$212$	−1.17722e11			−0.274903
$213$	−4.68086e10			−0.106765
$214$		−	1.03923e12i		−	2.31548i
$215$		−	1.75709e11i		−	0.382474i
$216$		−	2.33428e11i		−	0.496459i
$217$		−	1.84802e11i		−	0.384068i
$218$	−1.05760e12			−2.14802
$219$		−	4.09650e11i		−	0.813191i
$220$			1.75590e10i			0.0340711i
$221$			1.05281e11i			0.199705i
$222$	5.36981e11			0.995851
$223$	−3.91815e11			−0.710487			−0.355244	−	0.934774i	$-0.615602\pi$
$223$	−3.91815e11			−0.710487			−0.355244	+	0.934774i	$0.615602\pi$
$224$			3.30539e11i			0.586115i
$225$	−1.77032e11			−0.307000
$226$	8.32675e11			1.41232
$227$		−	8.46193e10i		−	0.140391i	−0.997533	−	0.0701956i	$-0.977638\pi$
$227$		−	8.46193e10i		−	0.140391i	0.997533	−	0.0701956i	$-0.0223624\pi$
$228$	1.16112e12			1.88453
$229$		−	4.23162e11i		−	0.671938i	−0.941873	−	0.335969i	$-0.890936\pi$
$229$		−	4.23162e11i		−	0.671938i	0.941873	−	0.335969i	$-0.109064\pi$
$230$	−2.59750e11			−0.403568
$231$		−	6.36882e9i		−	0.00968276i
$232$			9.92198e11i			1.47624i
$233$		−	1.16336e11i		−	0.169408i	−0.996406	−	0.0847038i	$-0.973006\pi$
$233$		−	1.16336e11i		−	0.169408i	0.996406	−	0.0847038i	$-0.0269944\pi$
$234$	6.33312e11			0.902690
$235$		−	1.29115e11i		−	0.180151i
$236$	−2.76082e11	−	1.73457e12i	−0.377118	−	2.36937i
$237$	5.20239e11			0.695762
$238$			6.35385e10i			0.0832055i
$239$	−5.97628e11			−0.766376			−0.383188	−	0.923670i	$-0.625174\pi$
$239$	−5.97628e11			−0.766376			−0.383188	+	0.923670i	$0.625174\pi$
$240$	−3.04545e11			−0.382468
$241$	8.42531e11			1.03634			0.518168	−	0.855279i	$-0.326614\pi$
$241$	8.42531e11			1.03634			0.518168	+	0.855279i	$0.326614\pi$
$242$		−	1.52635e12i		−	1.83898i
$243$	−5.43536e10			−0.0641500
$244$			1.36561e12i			1.57898i
$245$	−2.20771e11			−0.250099
$246$		−	3.31348e11i		−	0.367797i
$247$			1.83720e12i			1.99835i
$248$	−2.80017e12			−2.98487
$249$		−	7.11931e11i		−	0.743775i
$250$			9.72132e11i			0.995463i
$251$	−1.56342e12			−1.56930			−0.784651	−	0.619937i	$-0.787158\pi$
$251$	−1.56342e12			−1.56930			−0.784651	+	0.619937i	$0.787158\pi$
$252$	2.69770e11			0.265455
$253$	−4.07881e10			−0.0393488
$254$			1.13833e12i			1.07672i
$255$	−2.37884e10			−0.0220630
$256$	−1.20903e12			−1.09961
$257$	−1.50581e12			−1.34309			−0.671545	−	0.740963i	$-0.734369\pi$
$257$	−1.50581e12			−1.34309			−0.671545	+	0.740963i	$0.734369\pi$
$258$	1.65584e12			1.44850
$259$			3.61921e11i			0.310538i
$260$		−	1.17683e12i		−	0.990482i
$261$	2.31033e11			0.190753
$262$	−1.94924e12			−1.57892
$263$	−1.97250e12			−1.56761			−0.783806	−	0.621005i	$-0.786725\pi$
$263$	−1.97250e12			−1.56761			−0.783806	+	0.621005i	$0.786725\pi$
$264$	−9.65019e10			−0.0752517
$265$	4.20875e10			0.0322050
$266$			1.10877e12i			0.832598i
$267$			1.66171e11i			0.122462i
$268$			2.01419e12i			1.45689i
$269$		−	1.72362e11i		−	0.122372i	−0.998126	−	0.0611858i	$-0.980512\pi$
$269$		−	1.72362e11i		−	0.122372i	0.998126	−	0.0611858i	$-0.0194882\pi$
$270$			1.43098e11i			0.0997276i
$271$	6.13704e11			0.419868			0.209934	−	0.977716i	$-0.432675\pi$
$271$	6.13704e11			0.419868			0.209934	+	0.977716i	$0.432675\pi$
$272$	4.77098e11			0.320452
$273$			4.26847e11i			0.281488i
$274$			9.54924e11i			0.618324i
$275$			7.31873e10i			0.0465342i
$276$		−	1.72770e12i		−	1.07876i
$277$	−1.33413e12			−0.818085			−0.409042	−	0.912515i	$-0.634137\pi$
$277$	−1.33413e12			−0.818085			−0.409042	+	0.912515i	$0.634137\pi$
$278$		−	2.21218e12i		−	1.33228i
$279$			6.52019e11i			0.385691i
$280$		−	4.14203e11i		−	0.240670i
$281$	−6.02278e11			−0.343768			−0.171884	−	0.985117i	$-0.554985\pi$
$281$	−6.02278e11			−0.343768			−0.171884	+	0.985117i	$0.554985\pi$
$282$	1.21675e12			0.682268
$283$		−	4.75465e10i		−	0.0261931i	−0.999914	−	0.0130965i	$-0.995831\pi$
$283$		−	4.75465e10i		−	0.0261931i	0.999914	−	0.0130965i	$-0.00416887\pi$
$284$	−8.19681e11			−0.443663
$285$	−4.15119e11			−0.220774
$286$		−	2.61819e11i		−	0.136827i
$287$	2.23326e11			0.114691
$288$		−	1.16621e12i		−	0.588591i
$289$	−1.97873e12			−0.981514
$290$		−	6.08248e11i		−	0.296545i
$291$			1.59184e11i			0.0762842i
$292$		−	7.17352e12i		−	3.37923i
$293$	−2.20283e12			−1.02010			−0.510050	−	0.860145i	$-0.670373\pi$
$293$	−2.20283e12			−1.02010			−0.510050	+	0.860145i	$0.670373\pi$
$294$		−	2.08050e12i		−	0.947175i
$295$	9.87035e10	+	6.20136e11i	0.0441797	+	0.277573i
$296$	5.48392e12			2.41342
$297$			2.24705e10i			0.00972366i
$298$	4.44006e12			1.88933
$299$	2.73368e12			1.14391
$300$	−3.10007e12			−1.27575
$301$			1.11602e12i			0.451689i
$302$	1.71298e12			0.681894
$303$			4.06250e11i			0.159067i
$304$	8.32557e12			3.20661
$305$		−	4.88226e11i		−	0.184979i
$306$		−	2.24176e11i		−	0.0835570i
$307$	3.22845e12			1.18387			0.591933	−	0.805987i	$-0.298365\pi$
$307$	3.22845e12			1.18387			0.591933	+	0.805987i	$0.298365\pi$
$308$		−	1.11527e11i		−	0.0402369i
$309$			2.08383e12i			0.739725i
$310$	1.71659e12			0.599595
$311$	8.05238e11			0.276772			0.138386	−	0.990378i	$-0.455809\pi$
$311$	8.05238e11			0.276772			0.138386	+	0.990378i	$0.455809\pi$
$312$	6.46769e12			2.18764
$313$		−	1.45199e12i		−	0.483330i	−0.970360	−	0.241665i	$-0.922307\pi$
$313$		−	1.45199e12i		−	0.483330i	0.970360	−	0.241665i	$-0.0776934\pi$
$314$	−3.94022e12			−1.29084
$315$	−9.64471e10			−0.0310983
$316$	9.11007e12			2.89126
$317$	2.50893e12			0.783775			0.391888	−	0.920013i	$-0.371822\pi$
$317$	2.50893e12			0.783775			0.391888	+	0.920013i	$0.371822\pi$
$318$			3.96622e11i			0.121967i
$319$		−	9.55121e10i		−	0.0289138i
$320$	−8.47478e11			−0.252568
$321$	−2.47126e12			−0.725091
$322$	1.64981e12			0.476601
$323$	6.50322e11			0.184976
$324$	−9.51804e11			−0.266577
$325$		−	4.90511e12i		−	1.35280i
$326$		−	4.60745e12i		−	1.25133i
$327$			2.51494e12i			0.672650i
$328$		−	3.38388e12i		−	0.891346i
$329$			8.20078e11i			0.212753i
$330$	5.91586e10			0.0151164
$331$	−7.32593e12			−1.84384			−0.921919	−	0.387382i	$-0.873379\pi$
$331$	−7.32593e12			−1.84384			−0.921919	+	0.387382i	$0.873379\pi$
$332$		−	1.24669e13i		−	3.09077i
$333$		−	1.27693e12i		−	0.311850i
$334$		−	3.11187e12i		−	0.748669i
$335$		−	7.20103e11i		−	0.170675i
$336$	1.93433e12			0.451683
$337$		−	1.61710e12i		−	0.372038i	−0.982546	−	0.186019i	$-0.940441\pi$
$337$		−	1.61710e12i		−	0.372038i	0.982546	−	0.186019i	$-0.0595586\pi$
$338$			9.41412e12i			2.13401i
$339$		−	1.98008e12i		−	0.442267i
$340$	−4.16567e11			−0.0916834
$341$	2.69553e11			0.0584618
$342$		−	3.91198e12i		−	0.836115i
$343$	2.97810e12			0.627291
$344$	1.69102e13			3.51040
$345$			6.17680e11i			0.126377i
$346$	−6.59257e12			−1.32946
$347$		−	5.66931e12i		−	1.12689i	−0.826152	−	0.563447i	$-0.809475\pi$
$347$		−	5.66931e12i		−	1.12689i	0.826152	−	0.563447i	$-0.190525\pi$
$348$	4.04570e12			0.792679
$349$		−	2.94604e12i		−	0.568998i	−0.958676	−	0.284499i	$-0.908173\pi$
$349$		−	2.94604e12i		−	0.568998i	0.958676	−	0.284499i	$-0.0918273\pi$
$350$		−	2.96030e12i		−	0.563633i
$351$		−	1.50600e12i		−	0.282677i
$352$	−4.82125e11			−0.0892168
$353$		−	3.12828e12i		−	0.570732i	−0.958419	−	0.285366i	$-0.907885\pi$
$353$		−	3.12828e12i		−	0.570732i	0.958419	−	0.285366i	$-0.0921152\pi$
$354$	−5.84401e12	+	9.30157e11i	−1.05122	+	0.167317i
$355$	2.93049e11			0.0519754
$356$			2.90988e12i			0.508892i
$357$	1.51093e11			0.0260557
$358$	−1.97440e13			−3.35754
$359$	−1.08107e13			−1.81293			−0.906465	−	0.422281i	$-0.861229\pi$
$359$	−1.08107e13			−1.81293			−0.906465	+	0.422281i	$0.861229\pi$
$360$			1.46139e12i			0.241687i
$361$	5.21734e12			0.850968
$362$			1.96444e13i			3.16007i
$363$	−3.62963e12			−0.575876
$364$			7.47467e12i			1.16973i
$365$			2.56464e12i			0.395879i
$366$	4.60092e12			0.700550
$367$			1.20760e11i			0.0181381i	0.999959	+	0.00906904i	$0.00288680\pi$
$367$			1.20760e11i			0.0181381i	−0.999959	+	0.00906904i	$0.997113\pi$
$368$		−	1.23881e13i		−	1.83555i
$369$	−7.87937e11			−0.115175
$370$	−3.36181e12			−0.484802
$371$	−2.67320e11			−0.0380331
$372$			1.14177e13i			1.60275i
$373$	−1.97848e12			−0.274024			−0.137012	−	0.990569i	$-0.543750\pi$
$373$	−1.97848e12			−0.274024			−0.137012	+	0.990569i	$0.543750\pi$
$374$	−9.26774e10			−0.0126653
$375$	2.31171e12			0.311729
$376$	1.24260e13			1.65346
$377$			6.40135e12i			0.840553i
$378$		−	9.08893e11i		−	0.117775i
$379$	−1.30205e12			−0.166506			−0.0832530	−	0.996528i	$-0.526531\pi$
$379$	−1.30205e12			−0.166506			−0.0832530	+	0.996528i	$0.526531\pi$
$380$	−7.26929e12			−0.917432
$381$	2.70693e12			0.337173
$382$	2.41824e13			2.97292
$383$	−9.48784e12			−1.15126			−0.575630	−	0.817710i	$-0.695243\pi$
$383$	−9.48784e12			−1.15126			−0.575630	+	0.817710i	$0.695243\pi$
$384$			5.25544e11i			0.0629438i
$385$			3.98724e10i			0.00471378i
$386$			1.70631e13i			1.99123i
$387$		−	3.93754e12i		−	0.453597i
$388$			2.78752e12i			0.317001i
$389$	−4.80814e12			−0.539795			−0.269898	−	0.962889i	$-0.586990\pi$
$389$	−4.80814e12			−0.539795			−0.269898	+	0.962889i	$0.586990\pi$
$390$	−3.96490e12			−0.439449
$391$		−	9.67652e11i		−	0.105885i
$392$		−	2.12470e13i		−	2.29545i
$393$			4.63525e12i			0.494437i
$394$			2.24376e11i			0.0236317i
$395$	−3.25699e12			−0.338712
$396$			3.93488e11i			0.0404069i
$397$		−	7.74867e12i		−	0.785732i	−0.919596	−	0.392866i	$-0.871484\pi$
$397$		−	7.74867e12i		−	0.785732i	0.919596	−	0.392866i	$-0.128516\pi$
$398$			7.65720e12i			0.766752i
$399$	2.63664e12			0.260727
$400$	−2.22283e13			−2.17074
$401$			1.99175e11i			0.0192094i	0.999954	+	0.00960469i	$0.00305732\pi$
$401$			1.99175e11i			0.0192094i	−0.999954	+	0.00960469i	$0.996943\pi$
$402$	6.78608e12			0.646381
$403$	−1.80658e13			−1.69954
$404$			7.11398e12i			0.661006i
$405$	3.40284e11			0.0312296
$406$			3.86331e12i			0.350210i
$407$	−5.27899e11			−0.0472693
$408$		−	2.28940e12i		−	0.202498i
$409$		−	3.39310e12i		−	0.296469i	−0.988952	−	0.148235i	$-0.952641\pi$
$409$		−	3.39310e12i		−	0.296469i	0.988952	−	0.148235i	$-0.0473591\pi$
$410$			2.07442e12i			0.179052i
$411$	2.27079e12			0.193628
$412$			3.64907e13i			3.07394i
$413$	−6.26918e11	−	3.93882e12i	−0.0521748	−	0.327805i
$414$	−5.82087e12			−0.478615
$415$			4.45710e12i			0.362086i
$416$	3.23127e13			2.59362
$417$	−5.26052e12			−0.417204
$418$	−1.61726e12			−0.126736
$419$			7.11612e12i			0.551028i	0.961297	+	0.275514i	$0.0888480\pi$
$419$			7.11612e12i			0.551028i	−0.961297	+	0.275514i	$0.911152\pi$
$420$	−1.68892e12			−0.129230
$421$		−	1.08044e13i		−	0.816937i	−0.912772	−	0.408469i	$-0.866063\pi$
$421$		−	1.08044e13i		−	0.816937i	0.912772	−	0.408469i	$-0.133937\pi$
$422$	3.62299e13			2.70710
$423$		−	2.89340e12i		−	0.213652i
$424$			4.05050e12i			0.295583i
$425$	−1.73629e12			−0.125221
$426$			2.76162e12i			0.196841i
$427$			3.10098e12i			0.218454i
$428$	−4.32750e13			−3.01313
$429$	−6.22601e11			−0.0428473
$430$	−1.03665e13			−0.705163
$431$		−	1.42715e13i		−	0.959586i	−0.877382	−	0.479793i	$-0.840712\pi$
$431$		−	1.42715e13i		−	0.959586i	0.877382	−	0.479793i	$-0.159288\pi$
$432$	−6.82470e12			−0.453591
$433$	2.64948e10			0.00174069			0.000870344	−	1.00000i	$-0.499723\pi$
$433$	2.64948e10			0.00174069			0.000870344		1.00000i	$0.499723\pi$
$434$	−1.09030e13			−0.708102
$435$	−1.44640e12			−0.0928629
$436$			4.40400e13i			2.79521i
$437$		−	1.68860e13i		−	1.05954i
$438$	−2.41686e13			−1.49927
$439$	−1.87522e13			−1.15008			−0.575042	−	0.818124i	$-0.695014\pi$
$439$	−1.87522e13			−1.15008			−0.575042	+	0.818124i	$0.695014\pi$
$440$	6.04157e11			0.0366342
$441$	−4.94737e12			−0.296607
$442$	6.21137e12			0.368193
$443$		−	1.85113e13i		−	1.08497i	−0.840064	−	0.542487i	$-0.817483\pi$
$443$		−	1.85113e13i		−	1.08497i	0.840064	−	0.542487i	$-0.182517\pi$
$444$		−	2.23607e13i		−	1.29590i
$445$		−	1.04033e12i		−	0.0596170i
$446$			2.31163e13i			1.30992i
$447$		−	1.05584e13i		−	0.591642i
$448$	5.38279e12			0.298275
$449$	−1.42119e13			−0.778788			−0.389394	−	0.921071i	$-0.627316\pi$
$449$	−1.42119e13			−0.778788			−0.389394	+	0.921071i	$0.627316\pi$
$450$			1.04445e13i			0.566014i
$451$			3.25743e11i			0.0174579i
$452$		−	3.46739e13i		−	1.83785i
$453$		−	4.07342e12i		−	0.213535i
$454$	−4.99238e12			−0.258838
$455$		−	2.67231e12i		−	0.137034i
$456$		−	3.99510e13i		−	2.02630i
$457$		−	1.91190e13i		−	0.959146i	−0.877502	−	0.479573i	$-0.840792\pi$
$457$		−	1.91190e13i		−	0.959146i	0.877502	−	0.479573i	$-0.159208\pi$
$458$	−2.49658e13			−1.23885
$459$	−5.33087e11			−0.0261658
$460$			1.08164e13i			0.525163i
$461$	2.60561e13			1.25143			0.625713	−	0.780053i	$-0.284808\pi$
$461$	2.60561e13			1.25143			0.625713	+	0.780053i	$0.284808\pi$
$462$	−3.75748e11			−0.0178520
$463$			1.34310e13i			0.631253i	0.948884	+	0.315626i	$0.102215\pi$
$463$			1.34310e13i			0.631253i	−0.948884	+	0.315626i	$0.897785\pi$
$464$	2.90088e13			1.34878
$465$		−	4.08201e12i		−	0.187763i
$466$	−6.86357e12			−0.312335
$467$			2.92825e12i			0.131833i	0.997825	+	0.0659164i	$0.0209971\pi$
$467$			2.92825e12i			0.131833i	−0.997825	+	0.0659164i	$0.979003\pi$
$468$		−	2.63721e13i		−	1.17467i
$469$			4.57376e12i			0.201562i
$470$	−7.61753e12			−0.332143
$471$			9.36976e12i			0.404226i
$472$	−5.96819e13	+	9.49922e12i	−2.54761	+	0.405488i
$473$	−1.62783e12			−0.0687549
$474$		−	3.06931e13i		−	1.28277i
$475$	−3.02990e13			−1.25303
$476$	2.64584e12			0.108275
$477$	9.43159e11			0.0381938
$478$			3.52589e13i			1.41296i
$479$	1.37810e13			0.546515			0.273258	−	0.961941i	$-0.411899\pi$
$479$	1.37810e13			0.546515			0.273258	+	0.961941i	$0.411899\pi$
$480$			7.30112e12i			0.286539i
$481$	3.53805e13			1.37417
$482$		−	4.97077e13i		−	1.91068i
$483$		−	3.92322e12i		−	0.149247i
$484$	−6.35597e13			−2.39307
$485$		−	9.96583e11i		−	0.0371368i
$486$			3.20676e12i			0.118273i
$487$	−1.30167e13			−0.475178			−0.237589	−	0.971366i	$-0.576357\pi$
$487$	−1.30167e13			−0.475178			−0.237589	+	0.971366i	$0.576357\pi$
$488$	4.69868e13			1.69776
$489$	−1.09564e13			−0.391854
$490$			1.30251e13i			0.461106i
$491$	4.71076e13			1.65076			0.825380	−	0.564578i	$-0.190961\pi$
$491$	4.71076e13			1.65076			0.825380	+	0.564578i	$0.190961\pi$
$492$	−1.37978e13			−0.478614
$493$	2.26592e12			0.0778053
$494$	1.08391e14			3.68434
$495$		−	1.40678e11i		−	0.00473369i
$496$			8.18682e13i			2.72714i
$497$	−1.86131e12			−0.0613813
$498$	−4.20026e13			−1.37129
$499$	−7.09676e12			−0.229381			−0.114691	−	0.993401i	$-0.536588\pi$
$499$	−7.09676e12			−0.229381			−0.114691	+	0.993401i	$0.536588\pi$
$500$	4.04811e13			1.29540
$501$	−7.39997e12			−0.234445
$502$			9.22387e13i			2.89331i
$503$			3.49998e13i			1.08699i	0.839413	+	0.543495i	$0.182899\pi$
$503$			3.49998e13i			1.08699i	−0.839413	+	0.543495i	$0.817101\pi$
$504$		−	9.28206e12i		−	0.285425i
$505$		−	2.54336e12i		−	0.0774373i
$506$			2.40642e12i			0.0725469i
$507$	2.23866e13			0.668263
$508$	4.74020e13			1.40113
$509$		−	2.08317e13i		−	0.609728i	−0.952396	−	0.304864i	$-0.901389\pi$
$509$		−	2.08317e13i		−	0.609728i	0.952396	−	0.304864i	$-0.0986111\pi$
$510$			1.40347e12i			0.0406774i
$511$		−	1.62894e13i		−	0.467521i
$512$			6.74947e13i			1.91831i
$513$	−9.30260e12			−0.261829
$514$			8.88400e13i			2.47624i
$515$		−	1.30460e13i		−	0.360114i
$516$		−	6.89517e13i		−	1.88493i
$517$	−1.19617e12			−0.0323847
$518$	2.13526e13			0.572536
$519$			1.56770e13i			0.416319i
$520$	−4.04915e13			−1.06499
$521$	3.85247e13			1.00358			0.501789	−	0.864990i	$-0.332676\pi$
$521$	3.85247e13			1.00358			0.501789	+	0.864990i	$0.332676\pi$
$522$		−	1.36305e13i		−	0.351690i
$523$	4.12615e12			0.105448			0.0527238	−	0.998609i	$-0.483210\pi$
$523$	4.12615e12			0.105448			0.0527238	+	0.998609i	$0.483210\pi$
$524$			8.11695e13i			2.05464i
$525$	−7.03954e12			−0.176501
$526$			1.16374e14i			2.89019i
$527$			6.39484e12i			0.157317i
$528$			2.82142e12i			0.0687540i
$529$	1.63009e13			0.393489
$530$		−	2.48308e12i		−	0.0593761i
$531$	2.21189e12	+	1.38969e13i	0.0523952	+	0.329190i
$532$	4.61711e13			1.08346
$533$		−	2.18318e13i		−	0.507520i
$534$	9.80380e12			0.225781
$535$	1.54715e13			0.352990
$536$	6.93027e13			1.56649
$537$			4.69509e13i			1.05141i
$538$	−1.01690e13			−0.225615
$539$			2.04531e12i			0.0449588i
$540$	5.95884e12			0.129775
$541$		−	5.42521e13i		−	1.17066i	−0.810796	−	0.585329i	$-0.800965\pi$
$541$		−	5.42521e13i		−	1.17066i	0.810796	−	0.585329i	$-0.199035\pi$
$542$		−	3.62073e13i		−	0.774105i
$543$	4.67140e13			0.989573
$544$		−	1.14379e13i		−	0.240077i
$545$		−	1.57450e13i		−	0.327461i
$546$	2.51832e13			0.518976
$547$	−3.18411e13			−0.650207			−0.325104	−	0.945678i	$-0.605399\pi$
$547$	−3.18411e13			−0.650207			−0.325104	+	0.945678i	$0.605399\pi$
$548$	3.97645e13			0.804624
$549$		−	1.09409e13i		−	0.219377i
$550$	4.31791e12			0.0857946
$551$	3.95413e13			0.778561
$552$	−5.94455e13			−1.15991
$553$	2.06869e13			0.400009
$554$			7.87109e13i			1.50829i
$555$			7.99431e12i			0.151815i
$556$	−9.21187e13			−1.73370
$557$	−1.04334e14			−1.94603			−0.973017	−	0.230734i	$-0.925887\pi$
$557$	−1.04334e14			−1.94603			−0.973017	+	0.230734i	$0.925887\pi$
$558$	3.84678e13			0.711094
$559$	1.09100e14			1.99877
$560$	−1.21100e13			−0.219889
$561$			2.20385e11i			0.00396613i
$562$			3.55332e13i			0.633801i
$563$		−	5.93567e13i		−	1.04937i	−0.851297	−	0.524684i	$-0.824184\pi$
$563$		−	5.93567e13i		−	1.04937i	0.851297	−	0.524684i	$-0.175816\pi$
$564$		−	5.06673e13i		−	0.887834i
$565$			1.23965e13i			0.215306i
$566$	−2.80515e12			−0.0482919
$567$	−2.16133e12			−0.0368812
$568$			2.82030e13i			0.477038i
$569$			3.20243e12i			0.0536931i	0.999640	+	0.0268465i	$0.00854654\pi$
$569$			3.20243e12i			0.0536931i	−0.999640	+	0.0268465i	$0.991453\pi$
$570$			2.44912e13i			0.407039i
$571$		−	7.95421e13i		−	1.31044i	−0.755439	−	0.655219i	$-0.772576\pi$
$571$		−	7.95421e13i		−	1.31044i	0.755439	−	0.655219i	$-0.227424\pi$
$572$	−1.09026e13			−0.178053
$573$		−	5.75053e13i		−	0.930967i
$574$		−	1.31758e13i		−	0.211454i
$575$			4.50836e13i			0.717265i
$576$	−1.89915e13			−0.299535
$577$	9.22842e13			1.44294			0.721470	−	0.692446i	$-0.243467\pi$
$577$	9.22842e13			1.44294			0.721470	+	0.692446i	$0.243467\pi$
$578$			1.16741e14i			1.80961i
$579$	4.05757e13			0.623553
$580$	−2.53284e13			−0.385894
$581$		−	2.83094e13i		−	0.427612i
$582$	9.39155e12			0.140644
$583$		−	3.89914e11i		−	0.00578930i
$584$	−2.46821e14			−3.63344
$585$			9.42843e12i			0.137613i
$586$			1.29963e14i			1.88075i
$587$			7.51498e13i			1.07830i	0.842211	+	0.539148i	$0.181253\pi$
$587$			7.51498e13i			1.07830i	−0.842211	+	0.539148i	$0.818747\pi$
$588$	−8.66351e13			−1.23256
$589$			1.11593e14i			1.57420i
$590$	3.65868e13	−	5.82331e12i	0.511758	−	0.0814536i
$591$	5.33560e11			0.00740024
$592$		−	1.60333e14i		−	2.20503i
$593$	−1.12517e14			−1.53442			−0.767211	−	0.641394i	$-0.778356\pi$
$593$	−1.12517e14			−1.53442			−0.767211	+	0.641394i	$0.778356\pi$
$594$	1.32571e12			0.0179274
$595$	−9.45929e11			−0.0126845
$596$		−	1.84891e14i		−	2.45858i
$597$	1.82087e13			0.240108
$598$		−	1.61282e14i		−	2.10901i
$599$	−9.96471e13			−1.29220			−0.646101	−	0.763252i	$-0.723602\pi$
$599$	−9.96471e13			−1.29220			−0.646101	+	0.763252i	$0.723602\pi$
$600$			1.06665e14i			1.37172i
$601$			3.86261e12i			0.0492616i	0.999697	+	0.0246308i	$0.00784102\pi$
$601$			3.86261e12i			0.0492616i	−0.999697	+	0.0246308i	$0.992159\pi$
$602$	6.58431e13			0.832775
$603$		−	1.61371e13i		−	0.202414i
$604$		−	7.13311e13i		−	0.887348i
$605$	2.27236e13			0.280349
$606$	2.39680e13			0.293270
$607$	1.06519e14			1.29266			0.646331	−	0.763057i	$-0.276303\pi$
$607$	1.06519e14			1.29266			0.646331	+	0.763057i	$0.276303\pi$
$608$		−	1.99596e14i		−	2.40234i
$609$	9.18686e12			0.109668
$610$	−2.88044e13			−0.341043
$611$	8.01688e13			0.941455
$612$	−9.33506e12			−0.108733
$613$		−	9.28471e13i		−	1.07267i	−0.844005	−	0.536335i	$-0.819808\pi$
$613$		−	9.28471e13i		−	1.07267i	0.844005	−	0.536335i	$-0.180192\pi$
$614$		−	1.90473e14i		−	2.18268i
$615$	4.93294e12			0.0560699
$616$	−3.83732e12			−0.0432638
$617$	1.55222e14			1.73591			0.867953	−	0.496646i	$-0.165435\pi$
$617$	1.55222e14			1.73591			0.867953	+	0.496646i	$0.165435\pi$
$618$	1.22942e14			1.36382
$619$	−9.06182e13			−0.997154			−0.498577	−	0.866845i	$-0.666144\pi$
$619$	−9.06182e13			−0.997154			−0.498577	+	0.866845i	$0.666144\pi$
$620$		−	7.14814e13i		−	0.780252i
$621$			1.38419e13i			0.149878i
$622$		−	4.75075e13i		−	0.510282i
$623$			6.60768e12i			0.0704058i
$624$		−	1.89095e14i		−	1.99875i
$625$	7.33609e13			0.769245
$626$	−8.56649e13			−0.891110
$627$			3.84581e12i			0.0396872i
$628$			1.64077e14i			1.67977i
$629$		−	1.25238e13i		−	0.127199i
$630$			5.69019e12i			0.0573356i
$631$	1.77515e14			1.77455			0.887277	−	0.461238i	$-0.152595\pi$
$631$	1.77515e14			1.77455			0.887277	+	0.461238i	$0.152595\pi$
$632$		−	3.13453e14i		−	3.10876i
$633$		−	8.61538e13i		−	0.847727i
$634$		−	1.48022e14i		−	1.44504i
$635$	−1.69470e13			−0.164143
$636$	1.65160e13			0.158715
$637$		−	1.37079e14i		−	1.30700i
$638$	−5.63503e12			−0.0533080
$639$	6.56706e12			0.0616406
$640$		−	3.29021e12i		−	0.0306424i
$641$	−2.06098e14			−1.90451			−0.952256	−	0.305300i	$-0.901243\pi$
$641$	−2.06098e14			−1.90451			−0.952256	+	0.305300i	$0.901243\pi$
$642$			1.45799e14i			1.33684i
$643$	−1.15575e14			−1.05150			−0.525749	−	0.850640i	$-0.676215\pi$
$643$	−1.15575e14			−1.05150			−0.525749	+	0.850640i	$0.676215\pi$
$644$		−	6.87008e13i		−	0.620201i
$645$			2.46513e13i			0.220821i
$646$		−	3.83677e13i		−	0.341039i
$647$	8.52398e13			0.751833			0.375916	−	0.926654i	$-0.377328\pi$
$647$	8.52398e13			0.751833			0.375916	+	0.926654i	$0.377328\pi$
$648$			3.27490e13i			0.286631i
$649$	5.74517e12	−	9.14425e11i	0.0498976	−	0.00794190i
$650$	−2.89392e14			−2.49414
$651$			2.59270e13i			0.221742i
$652$	−1.91862e14			−1.62836
$653$	−2.95306e13			−0.248718			−0.124359	−	0.992237i	$-0.539687\pi$
$653$	−2.95306e13			−0.248718			−0.124359	+	0.992237i	$0.539687\pi$
$654$	1.48377e14			1.24016
$655$		−	2.90193e13i		−	0.240703i
$656$	−9.89343e13			−0.814381
$657$			5.74723e13i			0.469496i
$658$	4.83830e13			0.392250
$659$		−	2.36748e13i		−	0.190484i	−0.995454	−	0.0952421i	$-0.969637\pi$
$659$		−	2.36748e13i		−	0.190484i	0.995454	−	0.0952421i	$-0.0303625\pi$
$660$		−	2.46346e12i		−	0.0196710i
$661$	1.92368e14			1.52450			0.762248	−	0.647285i	$-0.224096\pi$
$661$	1.92368e14			1.52450			0.762248	+	0.647285i	$0.224096\pi$
$662$			4.32216e14i			3.39947i
$663$		−	1.47705e13i		−	0.115300i
$664$	−4.28951e14			−3.32328
$665$	−1.65069e13			−0.126928
$666$	−7.53364e13			−0.574955
$667$		−	5.88358e13i		−	0.445669i
$668$	−1.29583e14			−0.974242
$669$	5.49701e13			0.410200
$670$	−4.24847e13			−0.314672
$671$	−4.52310e12			−0.0332524
$672$		−	4.63733e13i		−	0.338393i
$673$			4.95325e13i			0.358769i	0.983779	+	0.179385i	$0.0574106\pi$
$673$			4.95325e13i			0.358769i	−0.983779	+	0.179385i	$0.942589\pi$
$674$	−9.54057e13			−0.685922
$675$	2.48369e13			0.177247
$676$	3.92019e14			2.77698
$677$	1.47697e14			1.03855			0.519277	−	0.854606i	$-0.326201\pi$
$677$	1.47697e14			1.03855			0.519277	+	0.854606i	$0.326201\pi$
$678$	−1.16821e14			−0.815404
$679$			6.32983e12i			0.0438574i
$680$			1.43329e13i			0.0985805i
$681$			1.18718e13i			0.0810549i
$682$		−	1.59031e13i		−	0.107785i
$683$			1.28534e14i			0.864799i	0.901682	+	0.432400i	$0.142333\pi$
$683$			1.28534e14i			0.864799i	−0.901682	+	0.432400i	$0.857667\pi$
$684$	−1.62901e14			−1.08804
$685$	−1.42164e13			−0.0942622
$686$		−	1.75702e14i		−	1.15653i
$687$			5.93680e13i			0.387944i
$688$		−	4.94403e14i		−	3.20729i
$689$			2.61326e13i			0.168301i
$690$	3.64419e13			0.233000
$691$			3.89661e12i			0.0247341i	0.999924	+	0.0123671i	$0.00393666\pi$
$691$			3.89661e12i			0.0247341i	−0.999924	+	0.0123671i	$0.996063\pi$
$692$			2.74525e14i			1.73002i
$693$			8.93521e11i			0.00559034i
$694$	−3.34478e14			−2.07764
$695$	3.29338e13			0.203104
$696$		−	1.39201e14i		−	0.852310i
$697$	−7.72789e12			−0.0469783
$698$	−1.73810e14			−1.04906
$699$			1.63214e13i			0.0978075i
$700$	−1.23272e14			−0.733455
$701$		−	1.98299e14i		−	1.17147i	−0.810504	−	0.585733i	$-0.800807\pi$
$701$		−	1.98299e14i		−	1.17147i	0.810504	−	0.585733i	$-0.199193\pi$
$702$	−8.88512e13			−0.521168
$703$		−	2.18546e14i		−	1.27282i
$704$			7.85135e12i			0.0454026i
$705$			1.81143e13i			0.104010i
$706$	−1.84563e14			−1.05225
$707$			1.61542e13i			0.0914510i
$708$	3.87332e13	+	2.43354e14i	0.217729	+	1.36796i
$709$	−2.33879e14			−1.30545			−0.652726	−	0.757594i	$-0.726375\pi$
$709$	−2.33879e14			−1.30545			−0.652726	+	0.757594i	$0.726375\pi$
$710$		−	1.72893e13i		−	0.0958265i
$711$	−7.29875e13			−0.401699
$712$	1.00121e14			0.547175
$713$	1.66046e14			0.901114
$714$		−	8.91420e12i		−	0.0480387i
$715$	3.89784e12			0.0208590
$716$			8.22172e14i			4.36916i
$717$	8.38449e13			0.442467
$718$			6.37810e14i			3.34248i
$719$		−	3.09647e14i		−	1.61147i	−0.592277	−	0.805735i	$-0.701771\pi$
$719$		−	3.09647e14i		−	1.61147i	0.592277	−	0.805735i	$-0.298229\pi$
$720$	4.27265e13			0.220818
$721$			8.28620e13i			0.425284i
$722$		−	3.07813e14i		−	1.56892i
$723$	−1.18204e14			−0.598329
$724$	8.18025e14			4.11219
$725$	−1.05571e14			−0.527052
$726$			2.14141e14i			1.06174i
$727$	1.40474e14			0.691712			0.345856	−	0.938288i	$-0.387589\pi$
$727$	1.40474e14			0.691712			0.345856	+	0.938288i	$0.387589\pi$
$728$	2.57183e14			1.25772
$729$	7.62560e12			0.0370370
$730$	1.51309e14			0.729879
$731$		−	3.86185e13i		−	0.185015i
$732$		−	1.91589e14i		−	0.911625i
$733$	7.94185e13			0.375320			0.187660	−	0.982234i	$-0.439910\pi$
$733$	7.94185e13			0.375320			0.187660	+	0.982234i	$0.439910\pi$
$734$	7.12458e12			0.0334410
$735$	3.09734e13			0.144395
$736$	−2.96991e14			−1.37516
$737$	−6.67130e12			−0.0306812
$738$			4.64868e13i			0.212348i
$739$			3.40946e13i			0.154690i	0.997004	+	0.0773451i	$0.0246443\pi$
$739$			3.40946e13i			0.154690i	−0.997004	+	0.0773451i	$0.975356\pi$
$740$			1.39991e14i			0.630873i
$741$		−	2.57752e14i		−	1.15375i
$742$			1.57714e13i			0.0701213i
$743$	4.85674e13			0.214487			0.107243	−	0.994233i	$-0.465798\pi$
$743$	4.85674e13			0.214487			0.107243	+	0.994233i	$0.465798\pi$
$744$	3.92852e14			1.72332
$745$			6.61014e13i			0.288024i
$746$			1.16727e14i			0.505215i
$747$			9.98812e13i			0.429419i
$748$			3.85923e12i			0.0164814i
$749$	−9.82676e13			−0.416871
$750$		−	1.36386e14i		−	0.574731i
$751$			3.59154e14i			1.50342i	0.659494	+	0.751710i	$0.270771\pi$
$751$			3.59154e14i			1.50342i	−0.659494	+	0.751710i	$0.729229\pi$
$752$		−	3.63298e14i		−	1.51069i
$753$	2.19342e14			0.906037
$754$	3.77668e14			1.54972
$755$			2.55019e13i			0.103953i
$756$	−3.78477e13			−0.153261
$757$	−1.69304e12			−0.00681065			−0.00340532	−	0.999994i	$-0.501084\pi$
$757$	−1.69304e12			−0.00681065			−0.00340532	+	0.999994i	$0.501084\pi$
$758$			7.68182e13i			0.306986i
$759$	5.72241e12			0.0227180
$760$			2.50116e14i			0.986448i
$761$	−2.82739e14			−1.10780			−0.553902	−	0.832582i	$-0.686862\pi$
$761$	−2.82739e14			−1.10780			−0.553902	+	0.832582i	$0.686862\pi$
$762$		−	1.59704e14i		−	0.621643i
$763$			1.00005e14i			0.386721i
$764$		−	1.00699e15i		−	3.86866i
$765$	3.33743e12			0.0127381
$766$			5.59764e14i			2.12257i
$767$	−3.85049e14	+	6.12860e13i	−1.45057	+	0.230879i
$768$	1.69622e14			0.634859
$769$			2.52231e14i			0.937923i	0.883219	+	0.468962i	$0.155372\pi$
$769$			2.52231e14i			0.937923i	−0.883219	+	0.468962i	$0.844628\pi$
$770$	2.35240e12			0.00869075
$771$	2.11260e14			0.775434
$772$	7.10535e14			2.59119
$773$			3.63335e13i			0.131647i	0.997831	+	0.0658234i	$0.0209674\pi$
$773$			3.63335e13i			0.131647i	−0.997831	+	0.0658234i	$0.979033\pi$
$774$	−2.32308e14			−0.836293
$775$		−	2.97940e14i		−	1.06566i
$776$	9.59111e13			0.340848
$777$		−	5.07761e13i		−	0.179289i
$778$			2.83671e14i			0.995215i
$779$	−1.34855e14			−0.470089
$780$			1.65104e14i			0.571855i
$781$		−	2.71491e12i		−	0.00934329i
$782$	−5.70896e13			−0.195220
$783$	−3.24131e13			−0.110131
$784$	−6.21198e14			−2.09725
$785$		−	5.86601e13i		−	0.196786i
$786$	2.73471e14			0.911588
$787$	−1.58878e14			−0.526246			−0.263123	−	0.964762i	$-0.584753\pi$
$787$	−1.58878e14			−0.526246			−0.263123	+	0.964762i	$0.584753\pi$
$788$	9.34335e12			0.0307519
$789$	2.76734e14			0.905062
$790$			1.92156e14i			0.624480i
$791$		−	7.87365e13i		−	0.254269i
$792$	1.35388e13			0.0434466
$793$	3.03144e14			0.966682
$794$	−4.57156e14			−1.44865
$795$	−5.90471e12			−0.0185936
$796$	3.18858e14			0.997773
$797$			2.96105e13i			0.0920776i	0.998940	+	0.0460388i	$0.0146598\pi$
$797$			2.96105e13i			0.0920776i	−0.998940	+	0.0460388i	$0.985340\pi$
$798$		−	1.55557e14i		−	0.480701i
$799$		−	2.83777e13i		−	0.0871452i
$800$			5.32899e14i			1.62628i
$801$		−	2.33132e13i		−	0.0707033i
$802$	1.17510e13			0.0354161
$803$	2.37598e13			0.0711648
$804$		−	2.82583e14i		−	0.841135i
$805$			2.45616e13i			0.0726569i
$806$			1.06585e15i			3.13343i
$807$			2.41817e13i			0.0706513i
$808$	2.44773e14			0.710732
$809$		−	5.69842e14i		−	1.64442i	−0.569187	−	0.822208i	$-0.692742\pi$
$809$		−	5.69842e14i		−	1.64442i	0.569187	−	0.822208i	$-0.307258\pi$
$810$		−	2.00761e13i		−	0.0575778i
$811$		−	3.71311e14i		−	1.05836i	−0.848509	−	0.529181i	$-0.822499\pi$
$811$		−	3.71311e14i		−	1.05836i	0.848509	−	0.529181i	$-0.177501\pi$
$812$	1.60874e14			0.455728
$813$	−8.61002e13			−0.242411
$814$			3.11450e13i			0.0871499i
$815$	6.85935e13			0.190763
$816$	−6.69350e13			−0.185013
$817$		−	6.73910e14i		−	1.85136i
$818$	−2.00186e14			−0.546598
$819$		−	5.98850e13i		−	0.162517i
$820$	8.63823e13			0.233000
$821$		−	2.78691e14i		−	0.747148i	−0.927600	−	0.373574i	$-0.878132\pi$
$821$		−	2.78691e14i		−	0.747148i	0.927600	−	0.373574i	$-0.121868\pi$
$822$		−	1.33972e14i		−	0.356989i
$823$		−	1.92849e14i		−	0.510762i	−0.966841	−	0.255381i	$-0.917799\pi$
$823$		−	1.92849e14i		−	0.510762i	0.966841	−	0.255381i	$-0.0822008\pi$
$824$	1.25554e15			3.30519
$825$		−	1.02679e13i		−	0.0268665i
$826$	−2.32383e14	+	3.69870e13i	−0.604370	+	0.0961941i
$827$	−6.02172e14			−1.55666			−0.778329	−	0.627857i	$-0.783932\pi$
$827$	−6.02172e14			−1.55666			−0.778329	+	0.627857i	$0.783932\pi$
$828$			2.42390e14i			0.622821i
$829$	4.65163e14			1.18804			0.594022	−	0.804449i	$-0.297539\pi$
$829$	4.65163e14			1.18804			0.594022	+	0.804449i	$0.297539\pi$
$830$	2.62960e14			0.667574
$831$	1.87173e14			0.472321
$832$		−	5.26208e14i		−	1.31990i
$833$	−4.85226e13			−0.120982
$834$			3.10360e14i			0.769194i
$835$	4.63280e13			0.114133
$836$			6.73453e13i			0.164921i
$837$		−	9.14757e13i		−	0.222679i
$838$	4.19838e14			1.01592
$839$		−	1.92671e14i		−	0.463453i	−0.972781	−	0.231727i	$-0.925563\pi$
$839$		−	1.92671e14i		−	0.463453i	0.972781	−	0.231727i	$-0.0744375\pi$
$840$			5.81110e13i			0.138951i
$841$	−2.82934e14			−0.672519
$842$	−6.37437e14			−1.50618
$843$	8.44972e13			0.198474
$844$		−	1.50867e15i		−	3.52275i
$845$	−1.40153e14			−0.325325
$846$	−1.70705e14			−0.393907
$847$	−1.44329e14			−0.331084
$848$	1.18424e14			0.270060
$849$			6.67059e12i			0.0151226i
$850$			1.02437e14i			0.230868i
$851$	−3.25188e14			−0.728595
$852$	1.14998e14			0.256149
$853$	6.20276e14			1.37353			0.686767	−	0.726877i	$-0.259029\pi$
$853$	6.20276e14			1.37353			0.686767	+	0.726877i	$0.259029\pi$
$854$	1.82952e14			0.402761
$855$	5.82396e13			0.127464
$856$			1.48897e15i			3.23980i
$857$			1.76342e14i			0.381462i	0.981642	+	0.190731i	$0.0610858\pi$
$857$			1.76342e14i			0.381462i	−0.981642	+	0.190731i	$0.938914\pi$
$858$			3.67322e13i			0.0789971i
$859$			4.16931e14i			0.891453i	0.895169	+	0.445727i	$0.147055\pi$
$859$			4.16931e14i			0.891453i	−0.895169	+	0.445727i	$0.852945\pi$
$860$			4.31677e14i			0.917627i
$861$	−3.13317e13			−0.0662168
$862$	−8.41992e14			−1.76918
$863$		−	4.95912e14i		−	1.03598i	−0.855387	−	0.517989i	$-0.826681\pi$
$863$		−	4.95912e14i		−	1.03598i	0.855387	−	0.517989i	$-0.173319\pi$
$864$			1.63614e14i			0.339823i
$865$		−	9.81469e13i		−	0.202673i
$866$		−	1.56314e12i		−	0.00320929i
$867$	2.77608e14			0.566678
$868$			4.54017e14i			0.921453i
$869$			3.01739e13i			0.0608882i
$870$			8.53348e13i			0.171210i
$871$	4.47120e14			0.891935
$872$	1.51530e15			3.00549
$873$		−	2.23329e13i		−	0.0440427i
$874$	−9.96239e14			−1.95347
$875$	9.19233e13			0.179219
$876$			1.00642e15i			1.95100i
$877$	1.48560e14			0.286354			0.143177	−	0.989697i	$-0.454268\pi$
$877$	1.48560e14			0.286354			0.143177	+	0.989697i	$0.454268\pi$
$878$			1.10634e15i			2.12040i
$879$	3.09048e14			0.588955
$880$		−	1.76637e13i		−	0.0334709i
$881$			7.63417e14i			1.43841i	0.694798	+	0.719205i	$0.255494\pi$
$881$			7.63417e14i			1.43841i	−0.694798	+	0.719205i	$0.744506\pi$
$882$			2.91886e14i			0.546852i
$883$	−3.07333e14			−0.572541			−0.286270	−	0.958149i	$-0.592416\pi$
$883$	−3.07333e14			−0.572541			−0.286270	+	0.958149i	$0.592416\pi$
$884$		−	2.58651e14i		−	0.479130i
$885$	−1.38477e13	−	8.70027e13i	−0.0255071	−	0.160257i
$886$	−1.09213e15			−2.00035
$887$			5.45475e14i			0.993474i	0.867901	+	0.496737i	$0.165469\pi$
$887$			5.45475e14i			0.993474i	−0.867901	+	0.496737i	$0.834531\pi$
$888$	−7.69372e14			−1.39339
$889$	1.07639e14			0.193848
$890$	−6.13774e13			−0.109915
$891$		−	3.15252e12i		−	0.00561396i
$892$	9.62599e14			1.70460
$893$		−	4.95204e14i		−	0.872021i
$894$	−6.22923e14			−1.09080
$895$		−	2.93939e14i		−	0.511850i
$896$			2.08978e13i			0.0361877i
$897$	−3.83524e14			−0.660436
$898$			8.38473e14i			1.43584i
$899$			3.88823e14i			0.662145i
$900$	4.34927e14			0.736553
$901$	9.25027e12			0.0155787
$902$	1.92182e13			0.0321870
$903$		−	1.56573e14i		−	0.260783i
$904$	−1.19303e15			−1.97611
$905$	−2.92456e14			−0.481746
$906$	−2.40324e14			−0.393692
$907$	−4.42978e13			−0.0721682			−0.0360841	−	0.999349i	$-0.511488\pi$
$907$	−4.42978e13			−0.0721682			−0.0360841	+	0.999349i	$0.511488\pi$
$908$			2.07890e14i			0.336826i
$909$		−	5.69953e13i		−	0.0918374i
$910$	−1.57661e14			−0.252649
$911$	−3.51924e14			−0.560864			−0.280432	−	0.959874i	$-0.590478\pi$
$911$	−3.51924e14			−0.560864			−0.280432	+	0.959874i	$0.590478\pi$
$912$	−1.16805e15			−1.85134
$913$	4.12922e13			0.0650899
$914$	−1.12799e15			−1.76837
$915$			6.84961e13i			0.106797i
$916$			1.03961e15i			1.61211i
$917$			1.84317e14i			0.284262i
$918$			3.14511e13i			0.0482416i
$919$			7.64582e14i			1.16640i	0.812330	+	0.583198i	$0.198199\pi$
$919$			7.64582e14i			1.16640i	−0.812330	+	0.583198i	$0.801801\pi$
$920$	3.72163e14			0.564669
$921$	−4.52940e14			−0.683506
$922$		−	1.53726e15i		−	2.30724i
$923$			1.81957e14i			0.271619i
$924$			1.56467e13i			0.0232308i
$925$			5.83494e14i			0.861643i
$926$	7.92403e14			1.16383
$927$		−	2.92354e14i		−	0.427080i
$928$		−	6.95453e14i		−	1.01048i
$929$		−	1.17645e15i		−	1.70019i	−0.526632	−	0.850093i	$-0.676546\pi$
$929$		−	1.17645e15i		−	1.70019i	0.526632	−	0.850093i	$-0.323454\pi$
$930$	−2.40831e14			−0.346176
$931$	−8.46742e14			−1.21061
$932$			2.85810e14i			0.406441i
$933$	−1.12972e14			−0.159795
$934$	1.72761e14			0.243059
$935$		−	1.37973e12i		−	0.00193080i
$936$	−9.07392e14			−1.26304
$937$		−	1.28020e15i		−	1.77248i	−0.463229	−	0.886238i	$-0.653309\pi$
$937$		−	1.28020e15i		−	1.77248i	0.463229	−	0.886238i	$-0.346691\pi$
$938$	2.69843e14			0.371618
$939$			2.03709e14i			0.279050i
$940$			3.17206e14i			0.432217i
$941$			4.59722e14i			0.623085i	0.950232	+	0.311542i	$0.100846\pi$
$941$			4.59722e14i			0.623085i	−0.950232	+	0.311542i	$0.899154\pi$
$942$	5.52798e14			0.745267
$943$			2.00659e14i			0.269092i
$944$	2.77728e14	+	1.74491e15i	0.370475	+	2.32763i
$945$	1.35311e13			0.0179546
$946$			9.60389e13i			0.126763i
$947$	−3.78787e14			−0.497331			−0.248665	−	0.968589i	$-0.579992\pi$
$947$	−3.78787e14			−0.497331			−0.248665	+	0.968589i	$0.579992\pi$
$948$	−1.27811e15			−1.66927
$949$	−1.59242e15			−2.06883
$950$			1.78758e15i			2.31019i
$951$	−3.51992e14			−0.452513
$952$		−	9.10362e13i		−	0.116420i
$953$	−4.07818e14			−0.518803			−0.259401	−	0.965770i	$-0.583525\pi$
$953$	−4.07818e14			−0.518803			−0.259401	+	0.965770i	$0.583525\pi$
$954$		−	5.56445e13i		−	0.0704175i
$955$			3.60016e14i			0.453215i
$956$	1.46824e15			1.83868
$957$			1.34000e13i			0.0166934i
$958$		−	8.13051e14i		−	1.00760i
$959$	9.02961e13			0.111321
$960$	1.18898e14			0.145820
$961$	−2.77702e14			−0.338815
$962$		−	2.08738e15i		−	2.53354i
$963$	3.46708e14			0.418632
$964$	−2.06991e15			−2.48637
$965$	−2.54027e14			−0.303559
$966$	−2.31462e14			−0.275166
$967$		−	1.08565e15i		−	1.28398i	−0.766713	−	0.641990i	$-0.778109\pi$
$967$		−	1.08565e15i		−	1.28398i	0.766713	−	0.641990i	$-0.221891\pi$
$968$			2.18691e15i			2.57309i
$969$	−9.12376e13			−0.106796
$970$	−5.87964e13			−0.0684688
$971$	−3.68899e13			−0.0427377			−0.0213689	−	0.999772i	$-0.506802\pi$
$971$	−3.68899e13			−0.0427377			−0.0213689	+	0.999772i	$0.506802\pi$
$972$	1.33534e14			0.153908
$973$	−2.09180e14			−0.239859
$974$			7.67961e14i			0.876082i
$975$			6.88168e14i			0.781037i
$976$		−	1.37375e15i		−	1.55117i
$977$		−	1.16341e15i		−	1.30696i	−0.756945	−	0.653478i	$-0.773309\pi$
$977$		−	1.16341e15i		−	1.30696i	0.756945	−	0.653478i	$-0.226691\pi$
$978$			6.46408e14i			0.722458i
$979$	−9.63798e12			−0.0107170
$980$	5.42385e14			0.600036
$981$		−	3.52837e14i		−	0.388355i
$982$		−	2.77926e15i		−	3.04349i
$983$			1.37712e14i			0.150039i	0.997182	+	0.0750194i	$0.0239019\pi$
$983$			1.37712e14i			0.150039i	−0.997182	+	0.0750194i	$0.976098\pi$
$984$			4.74746e14i			0.514619i
$985$	−3.34039e12			−0.00360260
$986$		−	1.33685e14i		−	0.143449i
$987$		−	1.15054e14i		−	0.122833i
$988$		−	4.51358e15i		−	4.79442i
$989$	−1.00275e15			−1.05977
$990$	−8.29973e12			−0.00872746
$991$			1.13165e15i			1.18398i	0.805947	+	0.591988i	$0.201657\pi$
$991$			1.13165e15i			1.18398i	−0.805947	+	0.591988i	$0.798343\pi$
$992$	1.96270e15			2.04312
$993$	1.02780e15			1.06454
$994$			1.09814e14i			0.113168i
$995$	−1.13997e14			−0.116890
$996$			1.74905e15i			1.78446i
$997$	9.08116e14			0.921862			0.460931	−	0.887436i	$-0.347516\pi$
$997$	9.08116e14			0.921862			0.460931	+	0.887436i	$0.347516\pi$
$998$			4.18695e14i			0.422907i
$999$			1.79148e14i			0.180047i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.11.c.a.58.5	✓	100
59.58	odd	2	inner	177.11.c.a.58.96	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.11.c.a.58.5	✓	100	1.1	even	1	trivial
177.11.c.a.58.96	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)

\(f(q)\)	\(=\)	\(q-58.9981i q^{2} -140.296 q^{3} -2456.77 q^{4} +878.334 q^{5} +8277.20i q^{6} -5578.77 q^{7} +84530.8i q^{8} +19683.0 q^{9} +O(q^{10})\)	\(q-58.9981i q^{2} -140.296 q^{3} -2456.77 q^{4} +878.334 q^{5} +8277.20i q^{6} -5578.77 q^{7} +84530.8i q^{8} +19683.0 q^{9} -51820.0i q^{10} -8137.20i q^{11} +344676. q^{12} +545367. i q^{13} +329136. i q^{14} -123227. q^{15} +2.47142e6 q^{16} +193046. q^{17} -1.16126e6i q^{18} +3.36874e6 q^{19} -2.15787e6 q^{20} +782679. q^{21} -480079. q^{22} -5.01255e6i q^{23} -1.18593e7i q^{24} -8.99415e6 q^{25} +3.21756e7 q^{26} -2.76145e6 q^{27} +1.37058e7 q^{28} +1.17377e7 q^{29} +7.27014e6i q^{30} +3.31260e7i q^{31} -5.92495e7i q^{32} +1.14162e6i q^{33} -1.13893e7i q^{34} -4.90002e6 q^{35} -4.83567e7 q^{36} -6.48748e7i q^{37} -1.98749e8i q^{38} -7.65128e7i q^{39} +7.42463e7i q^{40} -4.00314e7 q^{41} -4.61766e7i q^{42} -2.00048e8i q^{43} +1.99913e7i q^{44} +1.72882e7 q^{45} -2.95731e8 q^{46} -1.47000e8i q^{47} -3.46731e8 q^{48} -2.51353e8 q^{49} +5.30638e8i q^{50} -2.70836e7 q^{51} -1.33984e9i q^{52} +4.79174e7 q^{53} +1.62920e8i q^{54} -7.14718e6i q^{55} -4.71578e8i q^{56} -4.72621e8 q^{57} -6.92502e8i q^{58} +(1.12376e8 + 7.06037e8i) q^{59} +3.02740e8 q^{60} -5.55854e8i q^{61} +1.95437e9 q^{62} -1.09807e8 q^{63} -9.64871e8 q^{64} +4.79014e8i q^{65} +6.73533e7 q^{66} -8.19852e8i q^{67} -4.74270e8 q^{68} +7.03241e8i q^{69} +2.89092e8i q^{70} +3.33641e8 q^{71} +1.66382e9i q^{72} +2.91990e9i q^{73} -3.82749e9 q^{74} +1.26184e9 q^{75} -8.27623e9 q^{76} +4.53956e7i q^{77} -4.51411e9 q^{78} -3.70815e9 q^{79} +2.17073e9 q^{80} +3.87420e8 q^{81} +2.36177e9i q^{82} +5.07449e9i q^{83} -1.92286e9 q^{84} +1.69559e8 q^{85} -1.18024e10 q^{86} -1.64675e9 q^{87} +6.87845e8 q^{88} -1.18443e9i q^{89} -1.01997e9i q^{90} -3.04247e9i q^{91} +1.23147e10i q^{92} -4.64745e9i q^{93} -8.67271e9 q^{94} +2.95888e9 q^{95} +8.31247e9i q^{96} -1.13463e9i q^{97} +1.48293e10i q^{98} -1.60165e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 51200 q^{4} + 18392 q^{7} + 1968300 q^{9}+O(q^{10}) \) 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

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Database

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