LMFDB - Embedded newform 177.7.c.a.58.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,7,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, 7, names="a")

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

chi := DirichletCharacter("177.58");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 7 $
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:	$40.7195728007$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			58.3
Character	$\chi$	$=$	177.58
Dual form			177.7.c.a.58.58

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-14.9223i q^{2} -15.5885 q^{3} -158.675 q^{4} +237.797 q^{5} +232.615i q^{6} -568.491 q^{7} +1412.76i q^{8} +243.000 q^{9} +O(q^{10})$	\(q-14.9223i q^{2} -15.5885 q^{3} -158.675 q^{4} +237.797 q^{5} +232.615i q^{6} -568.491 q^{7} +1412.76i q^{8} +243.000 q^{9} -3548.48i q^{10} +416.675i q^{11} +2473.49 q^{12} +2776.81i q^{13} +8483.18i q^{14} -3706.89 q^{15} +10926.5 q^{16} +1573.64 q^{17} -3626.12i q^{18} +5373.33 q^{19} -37732.4 q^{20} +8861.90 q^{21} +6217.74 q^{22} -17579.4i q^{23} -22022.8i q^{24} +40922.4 q^{25} +41436.4 q^{26} -3788.00 q^{27} +90205.1 q^{28} -7605.19 q^{29} +55315.3i q^{30} -36501.6i q^{31} -72631.3i q^{32} -6495.31i q^{33} -23482.3i q^{34} -135185. q^{35} -38558.0 q^{36} +29052.8i q^{37} -80182.4i q^{38} -43286.2i q^{39} +335951. i q^{40} +99324.2 q^{41} -132240. i q^{42} -81683.7i q^{43} -66115.7i q^{44} +57784.7 q^{45} -262324. q^{46} +194198. i q^{47} -170327. q^{48} +205533. q^{49} -610657. i q^{50} -24530.6 q^{51} -440610. i q^{52} -48367.5 q^{53} +56525.6i q^{54} +99084.0i q^{55} -803143. i q^{56} -83762.0 q^{57} +113487. i q^{58} +(142452. - 147946. i) q^{59} +588190. q^{60} -148057. i q^{61} -544688. q^{62} -138143. q^{63} -384530. q^{64} +660318. i q^{65} -96925.0 q^{66} +288192. i q^{67} -249697. q^{68} +274035. i q^{69} +2.01728e6i q^{70} -195515. q^{71} +343302. i q^{72} -231637. i q^{73} +433534. q^{74} -637918. q^{75} -852612. q^{76} -236876. i q^{77} -645929. q^{78} +411213. q^{79} +2.59829e6 q^{80} +59049.0 q^{81} -1.48214e6i q^{82} +585218. i q^{83} -1.40616e6 q^{84} +374207. q^{85} -1.21891e6 q^{86} +118553. q^{87} -588663. q^{88} +251099. i q^{89} -862280. i q^{90} -1.57859e6i q^{91} +2.78940e6i q^{92} +569004. i q^{93} +2.89787e6 q^{94} +1.27776e6 q^{95} +1.13221e6i q^{96} -522437. i q^{97} -3.06702e6i q^{98} +101252. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 1920 q^{4} - 408 q^{7} + 14580 q^{9}+O(q^{10}) $ 60 * q - 1920 * q^4 - 408 * q^7 + 14580 * q^9	$ 60 q - 1920 q^{4} - 408 q^{7} + 14580 q^{9} - 1944 q^{12} - 4536 q^{15} + 56616 q^{16} + 8480 q^{17} + 11376 q^{19} + 40796 q^{20} - 8232 q^{22} + 197940 q^{25} + 147252 q^{26} + 71640 q^{28} + 63456 q^{29} - 364432 q^{35} - 466560 q^{36} + 99632 q^{41} - 470316 q^{46} + 171072 q^{48} + 1737420 q^{49} + 60912 q^{51} + 92240 q^{53} + 186624 q^{57} + 917264 q^{59} + 1063368 q^{60} - 115768 q^{62} - 99144 q^{63} - 1107444 q^{64} + 1172232 q^{66} - 4247232 q^{68} + 1498048 q^{71} + 1161448 q^{74} - 1477440 q^{75} - 1045320 q^{76} - 1060452 q^{78} - 90600 q^{79} + 77096 q^{80} + 3542940 q^{81} - 2225880 q^{84} - 693408 q^{85} - 1567768 q^{86} + 1821528 q^{87} + 62892 q^{88} + 5268696 q^{94} + 296128 q^{95}+O(q^{100}) $ 60 * q - 1920 * q^4 - 408 * q^7 + 14580 * q^9 - 1944 * q^12 - 4536 * q^15 + 56616 * q^16 + 8480 * q^17 + 11376 * q^19 + 40796 * q^20 - 8232 * q^22 + 197940 * q^25 + 147252 * q^26 + 71640 * q^28 + 63456 * q^29 - 364432 * q^35 - 466560 * q^36 + 99632 * q^41 - 470316 * q^46 + 171072 * q^48 + 1737420 * q^49 + 60912 * q^51 + 92240 * q^53 + 186624 * q^57 + 917264 * q^59 + 1063368 * q^60 - 115768 * q^62 - 99144 * q^63 - 1107444 * q^64 + 1172232 * q^66 - 4247232 * q^68 + 1498048 * q^71 + 1161448 * q^74 - 1477440 * q^75 - 1045320 * q^76 - 1060452 * q^78 - 90600 * q^79 + 77096 * q^80 + 3542940 * q^81 - 2225880 * q^84 - 693408 * q^85 - 1567768 * q^86 + 1821528 * q^87 + 62892 * q^88 + 5268696 * q^94 + 296128 * 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 $

$2$		−	14.9223i		−	1.86529i	−0.360800	−	0.932643i	$-0.617496\pi$
$2$		−	14.9223i		−	1.86529i	0.360800	−	0.932643i	$-0.382504\pi$
$3$	−15.5885			−0.577350
$3$	−15.5885			−0.577350
$4$	−158.675			−2.47929
$5$	237.797			1.90238			0.951188	−	0.308611i	$-0.0998642\pi$
$5$	237.797			1.90238			0.951188	+	0.308611i	$0.0998642\pi$
$6$			232.615i			1.07692i
$7$	−568.491			−1.65741			−0.828704	−	0.559687i	$-0.810921\pi$
$7$	−568.491			−1.65741			−0.828704	+	0.559687i	$0.810921\pi$
$8$			1412.76i			2.75930i
$9$	243.000			0.333333
$10$		−	3548.48i		−	3.54848i
$11$			416.675i			0.313054i	0.987674	+	0.156527i	$0.0500298\pi$
$11$			416.675i			0.313054i	−0.987674	+	0.156527i	$0.949970\pi$
$12$	2473.49			1.43142
$13$			2776.81i			1.26391i	0.775005	+	0.631955i	$0.217747\pi$
$13$			2776.81i			1.26391i	−0.775005	+	0.631955i	$0.782253\pi$
$14$			8483.18i			3.09154i
$15$	−3706.89			−1.09834
$16$	10926.5			2.66760
$17$	1573.64			0.320301			0.160150	−	0.987093i	$-0.448802\pi$
$17$	1573.64			0.320301			0.160150	+	0.987093i	$0.448802\pi$
$18$		−	3626.12i		−	0.621762i
$19$	5373.33			0.783399			0.391699	−	0.920093i	$-0.371887\pi$
$19$	5373.33			0.783399			0.391699	+	0.920093i	$0.371887\pi$
$20$	−37732.4			−4.71655
$21$	8861.90			0.956905
$22$	6217.74			0.583935
$23$		−	17579.4i		−	1.44484i	−0.691455	−	0.722419i	$-0.743030\pi$
$23$		−	17579.4i		−	1.44484i	0.691455	−	0.722419i	$-0.256970\pi$
$24$		−	22022.8i		−	1.59308i
$25$	40922.4			2.61904
$26$	41436.4			2.35755
$27$	−3788.00			−0.192450
$28$	90205.1			4.10920
$29$	−7605.19			−0.311828			−0.155914	−	0.987771i	$-0.549832\pi$
$29$	−7605.19			−0.311828			−0.155914	+	0.987771i	$0.549832\pi$
$30$			55315.3i			2.04871i
$31$		−	36501.6i		−	1.22526i	−0.790371	−	0.612628i	$-0.790112\pi$
$31$		−	36501.6i		−	1.22526i	0.790371	−	0.612628i	$-0.209888\pi$
$32$		−	72631.3i		−	2.21653i
$33$		−	6495.31i		−	0.180742i
$34$		−	23482.3i		−	0.597453i
$35$	−135185.			−3.15301
$36$	−38558.0			−0.826431
$37$			29052.8i			0.573565i	0.957996	+	0.286782i	$0.0925857\pi$
$37$			29052.8i			0.573565i	−0.957996	+	0.286782i	$0.907414\pi$
$38$		−	80182.4i		−	1.46126i
$39$		−	43286.2i		−	0.729719i
$40$			335951.i			5.24923i
$41$	99324.2			1.44113			0.720566	−	0.693387i	$-0.243882\pi$
$41$	99324.2			1.44113			0.720566	+	0.693387i	$0.243882\pi$
$42$		−	132240.i		−	1.78490i
$43$		−	81683.7i		−	1.02738i	−0.857977	−	0.513688i	$-0.828279\pi$
$43$		−	81683.7i		−	1.02738i	0.857977	−	0.513688i	$-0.171721\pi$
$44$		−	66115.7i		−	0.776152i
$45$	57784.7			0.634125
$46$	−262324.			−2.69504
$47$			194198.i			1.87047i	0.354028	+	0.935235i	$0.384812\pi$
$47$			194198.i			1.87047i	−0.354028	+	0.935235i	$0.615188\pi$
$48$	−170327.			−1.54014
$49$	205533.			1.74700
$50$		−	610657.i		−	4.88525i
$51$	−24530.6			−0.184926
$52$		−	440610.i		−	3.13360i
$53$	−48367.5			−0.324882			−0.162441	−	0.986718i	$-0.551937\pi$
$53$	−48367.5			−0.324882			−0.162441	+	0.986718i	$0.551937\pi$
$54$			56525.6i			0.358974i
$55$			99084.0i			0.595546i
$56$		−	803143.i		−	4.57329i
$57$	−83762.0			−0.452296
$58$			113487.i			0.581649i
$59$	142452.	−	147946.i	0.693605	−	0.720355i
$59$	142452.	−	147946.i	0.693605	−	0.720355i
$60$	588190.			2.72310
$61$		−	148057.i		−	0.652288i	−0.945320	−	0.326144i	$-0.894250\pi$
$61$		−	148057.i		−	0.652288i	0.945320	−	0.326144i	$-0.105750\pi$
$62$	−544688.			−2.28545
$63$	−138143.			−0.552469
$64$	−384530.			−1.46687
$65$			660318.i			2.40443i
$66$	−96925.0			−0.337135
$67$			288192.i			0.958204i	0.877759	+	0.479102i	$0.159038\pi$
$67$			288192.i			0.958204i	−0.877759	+	0.479102i	$0.840962\pi$
$68$	−249697.			−0.794120
$69$			274035.i			0.834178i
$70$			2.01728e6i			5.88127i
$71$	−195515.			−0.546266			−0.273133	−	0.961976i	$-0.588060\pi$
$71$	−195515.			−0.546266			−0.273133	+	0.961976i	$0.588060\pi$
$72$			343302.i			0.919768i
$73$		−	231637.i		−	0.595442i	−0.954653	−	0.297721i	$-0.903773\pi$
$73$		−	231637.i		−	0.595442i	0.954653	−	0.297721i	$-0.0962266\pi$
$74$	433534.			1.06986
$75$	−637918.			−1.51210
$76$	−852612.			−1.94227
$77$		−	236876.i		−	0.518858i
$78$	−645929.			−1.36113
$79$	411213.			0.834038			0.417019	−	0.908898i	$-0.363075\pi$
$79$	411213.			0.834038			0.417019	+	0.908898i	$0.363075\pi$
$80$	2.59829e6			5.07478
$81$	59049.0			0.111111
$82$		−	1.48214e6i		−	2.68812i
$83$			585218.i			1.02349i	0.859138	+	0.511745i	$0.171001\pi$
$83$			585218.i			1.02349i	−0.859138	+	0.511745i	$0.828999\pi$
$84$	−1.40616e6			−2.37245
$85$	374207.			0.609333
$86$	−1.21891e6			−1.91635
$87$	118553.			0.180034
$88$	−588663.			−0.863811
$89$			251099.i			0.356185i	0.984014	+	0.178092i	$0.0569926\pi$
$89$			251099.i			0.356185i	−0.984014	+	0.178092i	$0.943007\pi$
$90$		−	862280.i		−	1.18283i
$91$		−	1.57859e6i		−	2.09481i
$92$			2.78940e6i			3.58218i
$93$			569004.i			0.707402i
$94$	2.89787e6			3.48896
$95$	1.27776e6			1.49032
$96$			1.13221e6i			1.27971i
$97$		−	522437.i		−	0.572425i	−0.958166	−	0.286213i	$-0.907604\pi$
$97$		−	522437.i		−	0.572425i	0.958166	−	0.286213i	$-0.0923963\pi$
$98$		−	3.06702e6i		−	3.25866i
$99$			101252.i			0.104351i
$100$	−6.49336e6			−6.49336
$101$		−	1.18118e6i		−	1.14644i	−0.819401	−	0.573220i	$-0.805694\pi$
$101$		−	1.18118e6i		−	1.14644i	0.819401	−	0.573220i	$-0.194306\pi$
$102$			366053.i			0.344940i
$103$		−	910974.i		−	0.833670i	−0.908982	−	0.416835i	$-0.863139\pi$
$103$		−	910974.i		−	0.833670i	0.908982	−	0.416835i	$-0.136861\pi$
$104$	−3.92298e6			−3.48751
$105$	2.10733e6			1.82039
$106$			721753.i			0.605998i
$107$	115592.			0.0943578			0.0471789	−	0.998886i	$-0.484977\pi$
$107$	115592.			0.0943578			0.0471789	+	0.998886i	$0.484977\pi$
$108$	601059.			0.477140
$109$			980508.i			0.757132i	0.925574	+	0.378566i	$0.123583\pi$
$109$			980508.i			0.757132i	−0.925574	+	0.378566i	$0.876417\pi$
$110$	1.47856e6			1.11086
$111$		−	452888.i		−	0.331148i
$112$	−6.21161e6			−4.42130
$113$		−	821694.i		−	0.569475i	−0.958606	−	0.284737i	$-0.908094\pi$
$113$		−	821694.i		−	0.569475i	0.958606	−	0.284737i	$-0.0919064\pi$
$114$			1.24992e6i			0.843661i
$115$		−	4.18032e6i		−	2.74863i
$116$	1.20675e6			0.773114
$117$			674765.i			0.421303i
$118$	−2.20769e6	−	2.12571e6i	−1.34367	−	1.29377i
$119$	−894599.			−0.530869
$120$		−	5.23696e6i		−	3.03065i
$121$	1.59794e6			0.901997
$122$	−2.20935e6			−1.21670
$123$	−1.54831e6			−0.832038
$124$			5.79188e6i			3.03777i
$125$	6.01566e6			3.08002
$126$			2.06141e6i			1.03051i
$127$	1.80210e6			0.879766			0.439883	−	0.898055i	$-0.355020\pi$
$127$	1.80210e6			0.879766			0.439883	+	0.898055i	$0.355020\pi$
$128$			1.08967e6i			0.519594i
$129$			1.27332e6i			0.593156i
$130$	9.85345e6			4.48496
$131$		−	1.05222e6i		−	0.468048i	−0.972231	−	0.234024i	$-0.924810\pi$
$131$		−	1.05222e6i		−	0.468048i	0.972231	−	0.234024i	$-0.0751895\pi$
$132$			1.03064e6i			0.448112i
$133$	−3.05469e6			−1.29841
$134$	4.30049e6			1.78732
$135$	−900774.			−0.366113
$136$			2.22318e6i			0.883808i
$137$	2.66845e6			1.03776			0.518880	−	0.854847i	$-0.326349\pi$
$137$	2.66845e6			1.03776			0.518880	+	0.854847i	$0.326349\pi$
$138$	4.08923e6			1.55598
$139$	−1.59715e6			−0.594705			−0.297353	−	0.954768i	$-0.596104\pi$
$139$	−1.59715e6			−0.594705			−0.297353	+	0.954768i	$0.596104\pi$
$140$	2.14505e7			7.81724
$141$		−	3.02724e6i		−	1.07992i
$142$			2.91753e6i			1.01894i
$143$	−1.15703e6			−0.395672
$144$	2.65514e6			0.889200
$145$	−1.80849e6			−0.593215
$146$	−3.45656e6			−1.11067
$147$	−3.20394e6			−1.00863
$148$		−	4.60994e6i		−	1.42204i
$149$		−	6.57201e6i		−	1.98673i	−0.114995	−	0.993366i	$-0.536685\pi$
$149$		−	6.57201e6i		−	1.98673i	0.114995	−	0.993366i	$-0.463315\pi$
$150$			9.51919e6i			2.82050i
$151$			1.47674e6i			0.428918i	0.976733	+	0.214459i	$0.0687988\pi$
$151$			1.47674e6i			0.428918i	−0.976733	+	0.214459i	$0.931201\pi$
$152$			7.59125e6i			2.16164i
$153$	382394.			0.106767
$154$	−3.53473e6			−0.967818
$155$		−	8.67998e6i		−	2.33090i
$156$			6.86843e6i			1.80919i
$157$			2.33787e6i			0.604117i	0.953289	+	0.302058i	$0.0976738\pi$
$157$			2.33787e6i			0.604117i	−0.953289	+	0.302058i	$0.902326\pi$
$158$		−	6.13624e6i		−	1.55572i
$159$	753974.			0.187571
$160$		−	1.72715e7i		−	4.21668i
$161$			9.99370e6i			2.39469i
$162$		−	881146.i		−	0.207254i
$163$	1.65292e6			0.381670			0.190835	−	0.981622i	$-0.438880\pi$
$163$	1.65292e6			0.381670			0.190835	+	0.981622i	$0.438880\pi$
$164$	−1.57602e7			−3.57299
$165$		−	1.54457e6i		−	0.343839i
$166$	8.73279e6			1.90910
$167$	7.33918e6			1.57579			0.787895	−	0.615810i	$-0.211171\pi$
$167$	7.33918e6			1.57579			0.787895	+	0.615810i	$0.211171\pi$
$168$			1.25198e7i			2.64039i
$169$	−2.88387e6			−0.597470
$170$		−	5.58402e6i		−	1.13658i
$171$	1.30572e6			0.261133
$172$			1.29611e7i			2.54717i
$173$			9.58118e6i			1.85046i	0.379401	+	0.925232i	$0.376130\pi$
$173$			9.58118e6i			1.85046i	−0.379401	+	0.925232i	$0.623870\pi$
$174$		−	1.76908e6i		−	0.335815i
$175$	−2.32640e7			−4.34081
$176$			4.55279e6i			0.835102i
$177$	−2.22061e6	+	2.30625e6i	−0.400453	+	0.415897i
$178$	3.74698e6			0.664387
$179$		−	5.21840e6i		−	0.909867i	−0.890525	−	0.454934i	$-0.849663\pi$
$179$		−	5.21840e6i		−	0.909867i	0.890525	−	0.454934i	$-0.150337\pi$
$180$	−9.16897e6			−1.57218
$181$	937112.			0.158036			0.0790179	−	0.996873i	$-0.474822\pi$
$181$	937112.			0.158036			0.0790179	+	0.996873i	$0.474822\pi$
$182$	−2.35562e7			−3.90743
$183$			2.30798e6i			0.376599i
$184$	2.48355e7			3.98675
$185$			6.90867e6i			1.09114i
$186$	8.49084e6			1.31951
$187$			655695.i			0.100271i
$188$		−	3.08143e7i		−	4.63744i
$189$	2.15344e6			0.318968
$190$		−	1.90671e7i		−	2.77987i
$191$			4.78038e6i			0.686061i	0.939324	+	0.343031i	$0.111453\pi$
$191$			4.78038e6i			0.686061i	−0.939324	+	0.343031i	$0.888547\pi$
$192$	5.99423e6			0.846895
$193$	7.50133e6			1.04344			0.521719	−	0.853118i	$-0.325291\pi$
$193$	7.50133e6			1.04344			0.521719	+	0.853118i	$0.325291\pi$
$194$	−7.79595e6			−1.06774
$195$		−	1.02933e7i		−	1.38820i
$196$	−3.26129e7			−4.33132
$197$	1.17472e7			1.53651			0.768254	−	0.640146i	$-0.221126\pi$
$197$	1.17472e7			1.53651			0.768254	+	0.640146i	$0.221126\pi$
$198$	1.51091e6			0.194645
$199$	1.30642e7			1.65777			0.828883	−	0.559422i	$-0.188977\pi$
$199$	1.30642e7			1.65777			0.828883	+	0.559422i	$0.188977\pi$
$200$			5.78137e7i			7.22672i
$201$		−	4.49247e6i		−	0.553219i
$202$	−1.76259e7			−2.13844
$203$	4.32348e6			0.516827
$204$	3.89239e6			0.458485
$205$	2.36190e7			2.74157
$206$	−1.35938e7			−1.55503
$207$		−	4.27178e6i		−	0.481613i
$208$			3.03408e7i			3.37161i
$209$			2.23893e6i			0.245246i
$210$		−	3.14462e7i		−	3.39555i
$211$		−	1.79409e7i		−	1.90984i	−0.296868	−	0.954919i	$-0.595942\pi$
$211$		−	1.79409e7i		−	1.90984i	0.296868	−	0.954919i	$-0.404058\pi$
$212$	7.67469e6			0.805477
$213$	3.04777e6			0.315387
$214$		−	1.72490e6i		−	0.176004i
$215$		−	1.94241e7i		−	1.95446i
$216$		−	5.35154e6i		−	0.531028i
$217$			2.07508e7i			2.03075i
$218$	1.46314e7			1.41227
$219$			3.61087e6i			0.343779i
$220$		−	1.57221e7i		−	1.47653i
$221$			4.36970e6i			0.404832i
$222$	−6.75813e6			−0.617685
$223$	4.56125e6			0.411310			0.205655	−	0.978625i	$-0.434068\pi$
$223$	4.56125e6			0.411310			0.205655	+	0.978625i	$0.434068\pi$
$224$			4.12902e7i			3.67370i
$225$	9.94415e6			0.873012
$226$	−1.22615e7			−1.06223
$227$			5.19345e6i			0.443995i	0.975047	+	0.221998i	$0.0712578\pi$
$227$			5.19345e6i			0.443995i	−0.975047	+	0.221998i	$0.928742\pi$
$228$	1.32909e7			1.12137
$229$			1.07784e7i			0.897525i	0.893651	+	0.448762i	$0.148135\pi$
$229$			1.07784e7i			0.897525i	−0.893651	+	0.448762i	$0.851865\pi$
$230$	−6.23799e7			−5.12698
$231$			3.69253e6i			0.299563i
$232$		−	1.07443e7i		−	0.860429i
$233$			6.65739e6i			0.526303i	0.964754	+	0.263152i	$0.0847620\pi$
$233$			6.65739e6i			0.526303i	−0.964754	+	0.263152i	$0.915238\pi$
$234$	1.00690e7			0.785852
$235$			4.61797e7i			3.55834i
$236$	−2.26035e7	+	2.34753e7i	−1.71965	+	1.78597i
$237$	−6.41018e6			−0.481532
$238$			1.33495e7i			0.990223i
$239$	−1.00785e7			−0.738247			−0.369123	−	0.929380i	$-0.620342\pi$
$239$	−1.00785e7			−0.738247			−0.369123	+	0.929380i	$0.620342\pi$
$240$	−4.05033e7			−2.92992
$241$	−5.64758e6			−0.403470			−0.201735	−	0.979440i	$-0.564658\pi$
$241$	−5.64758e6			−0.403470			−0.201735	+	0.979440i	$0.564658\pi$
$242$		−	2.38450e7i		−	1.68248i
$243$	−920483.			−0.0641500
$244$			2.34929e7i			1.61721i
$245$	4.88751e7			3.32345
$246$			2.31044e7i			1.55199i
$247$			1.49207e7i			0.990146i
$248$	5.15681e7			3.38085
$249$		−	9.12264e6i		−	0.590912i
$250$		−	8.97674e7i		−	5.74511i
$251$	−1.14392e7			−0.723393			−0.361697	−	0.932296i	$-0.617802\pi$
$251$	−1.14392e7			−0.723393			−0.361697	+	0.932296i	$0.617802\pi$
$252$	2.19198e7			1.36973
$253$	7.32487e6			0.452312
$254$		−	2.68914e7i		−	1.64102i
$255$	−5.83330e6			−0.351799
$256$	−8.34960e6			−0.497675
$257$	−7.49665e6			−0.441639			−0.220820	−	0.975315i	$-0.570873\pi$
$257$	−7.49665e6			−0.441639			−0.220820	+	0.975315i	$0.570873\pi$
$258$	1.90009e7			1.10641
$259$		−	1.65162e7i		−	0.950631i
$260$		−	1.04776e8i		−	5.96129i
$261$	−1.84806e6			−0.103943
$262$	−1.57015e7			−0.873044
$263$	5.41778e6			0.297820			0.148910	−	0.988851i	$-0.452424\pi$
$263$	5.41778e6			0.297820			0.148910	+	0.988851i	$0.452424\pi$
$264$	9.17634e6			0.498721
$265$	−1.15016e7			−0.618048
$266$			4.55830e7i			2.42191i
$267$		−	3.91425e6i		−	0.205643i
$268$		−	4.57288e7i		−	2.37567i
$269$			2.76710e7i			1.42157i	0.703409	+	0.710785i	$0.251660\pi$
$269$			2.76710e7i			1.42157i	−0.703409	+	0.710785i	$0.748340\pi$
$270$			1.34416e7i			0.682905i
$271$	2.37766e7			1.19465			0.597327	−	0.801998i	$-0.296230\pi$
$271$	2.37766e7			1.19465			0.597327	+	0.801998i	$0.296230\pi$
$272$	1.71943e7			0.854434
$273$			2.46078e7i			1.20944i
$274$		−	3.98193e7i		−	1.93572i
$275$			1.70513e7i			0.819899i
$276$		−	4.34824e7i		−	2.06817i
$277$	1.81769e7			0.855226			0.427613	−	0.903962i	$-0.359355\pi$
$277$	1.81769e7			0.855226			0.427613	+	0.903962i	$0.359355\pi$
$278$			2.38332e7i			1.10930i
$279$		−	8.86989e6i		−	0.408419i
$280$		−	1.90985e8i		−	8.70012i
$281$	−2.61915e7			−1.18043			−0.590217	−	0.807245i	$-0.700958\pi$
$281$	−2.61915e7			−1.18043			−0.590217	+	0.807245i	$0.700958\pi$
$282$	−4.51734e7			−2.01435
$283$		−	3.33164e7i		−	1.46994i	−0.678101	−	0.734969i	$-0.737197\pi$
$283$		−	3.33164e7i		−	1.46994i	0.678101	−	0.734969i	$-0.262803\pi$
$284$	3.10232e7			1.35435
$285$	−1.99183e7			−0.860436
$286$			1.72655e7i			0.738041i
$287$	−5.64649e7			−2.38854
$288$		−	1.76494e7i		−	0.738844i
$289$	−2.16612e7			−0.897407
$290$			2.69868e7i			1.10652i
$291$			8.14398e6i			0.330490i
$292$			3.67550e7i			1.47628i
$293$	1.78407e7			0.709267			0.354633	−	0.935005i	$-0.384606\pi$
$293$	1.78407e7			0.709267			0.354633	+	0.935005i	$0.384606\pi$
$294$			4.78101e7i			1.88139i
$295$	3.38746e7	−	3.51811e7i	1.31950	−	1.37039i
$296$	−4.10447e7			−1.58264
$297$		−	1.57836e6i		−	0.0602472i
$298$	−9.80694e7			−3.70582
$299$	4.88145e7			1.82615
$300$	1.01221e8			3.74894
$301$			4.64364e7i			1.70278i
$302$	2.20364e7			0.800055
$303$			1.84128e7i			0.661898i
$304$	5.87116e7			2.08979
$305$		−	3.52075e7i		−	1.24090i
$306$		−	5.70620e6i		−	0.199151i
$307$	−2.29419e7			−0.792892			−0.396446	−	0.918058i	$-0.629757\pi$
$307$	−2.29419e7			−0.792892			−0.396446	+	0.918058i	$0.629757\pi$
$308$			3.75862e7i			1.28640i
$309$			1.42007e7i			0.481320i
$310$	−1.29525e8			−4.34779
$311$	−5.79269e7			−1.92575			−0.962874	−	0.269951i	$-0.912992\pi$
$311$	−5.79269e7			−1.92575			−0.962874	+	0.269951i	$0.912992\pi$
$312$	6.11532e7			2.01352
$313$		−	1.90759e7i		−	0.622087i	−0.950396	−	0.311043i	$-0.899322\pi$
$313$		−	1.90759e7i		−	0.622087i	0.950396	−	0.311043i	$-0.100678\pi$
$314$	3.48863e7			1.12685
$315$	−3.28501e7			−1.05100
$316$	−6.52491e7			−2.06782
$317$	3.26544e6			0.102509			0.0512547	−	0.998686i	$-0.483678\pi$
$317$	3.26544e6			0.102509			0.0512547	+	0.998686i	$0.483678\pi$
$318$		−	1.12510e7i		−	0.349873i
$319$		−	3.16889e6i		−	0.0976191i
$320$	−9.14401e7			−2.79053
$321$	−1.80191e6			−0.0544775
$322$	1.49129e8			4.46678
$323$	8.45568e6			0.250923
$324$	−9.36958e6			−0.275477
$325$			1.13634e8i			3.31023i
$326$		−	2.46653e7i		−	0.711924i
$327$		−	1.52846e7i		−	0.437131i
$328$			1.40322e8i			3.97652i
$329$		−	1.10400e8i		−	3.10013i
$330$	−2.30485e7			−0.641358
$331$	8.69953e6			0.239890			0.119945	−	0.992781i	$-0.461728\pi$
$331$	8.69953e6			0.239890			0.119945	+	0.992781i	$0.461728\pi$
$332$		−	9.28593e7i		−	2.53753i
$333$			7.05983e6i			0.191188i
$334$		−	1.09517e8i		−	2.93930i
$335$			6.85313e7i			1.82286i
$336$	9.68293e7			2.55264
$337$		−	4.16849e7i		−	1.08915i	−0.838711	−	0.544576i	$-0.816691\pi$
$337$		−	4.16849e7i		−	1.08915i	0.838711	−	0.544576i	$-0.183309\pi$
$338$			4.30340e7i			1.11445i
$339$			1.28089e7i			0.328786i
$340$	−5.93771e7			−1.51071
$341$	1.52093e7			0.383571
$342$		−	1.94843e7i		−	0.487088i
$343$	−4.99611e7			−1.23808
$344$	1.15400e8			2.83484
$345$			6.51647e7i			1.58692i
$346$	1.42973e8			3.45165
$347$			6.07357e6i			0.145364i	0.997355	+	0.0726818i	$0.0231558\pi$
$347$			6.07357e6i			0.145364i	−0.997355	+	0.0726818i	$0.976844\pi$
$348$	−1.88114e7			−0.446358
$349$			2.69330e7i			0.633591i	0.948494	+	0.316795i	$0.102607\pi$
$349$			2.69330e7i			0.633591i	−0.948494	+	0.316795i	$0.897393\pi$
$350$			3.47153e8i			8.09685i
$351$		−	1.05185e7i		−	0.243240i
$352$	3.02636e7			0.693893
$353$		−	2.66019e7i		−	0.604768i	−0.953186	−	0.302384i	$-0.902217\pi$
$353$		−	2.66019e7i		−	0.604768i	0.953186	−	0.302384i	$-0.0977826\pi$
$354$	3.44145e7	+	3.31365e7i	0.775768	+	0.746960i
$355$	−4.64928e7			−1.03920
$356$		−	3.98431e7i		−	0.883087i
$357$	1.39454e7			0.306498
$358$	−7.78704e7			−1.69716
$359$	3.78830e7			0.818768			0.409384	−	0.912362i	$-0.365744\pi$
$359$	3.78830e7			0.818768			0.409384	+	0.912362i	$0.365744\pi$
$360$			8.16361e7i			1.74974i
$361$	−1.81732e7			−0.386286
$362$		−	1.39838e7i		−	0.294782i
$363$	−2.49095e7			−0.520768
$364$			2.50483e8i			5.19366i
$365$		−	5.50826e7i		−	1.13276i
$366$	3.44404e7			0.702465
$367$			4.23690e7i			0.857137i	0.903509	+	0.428569i	$0.140982\pi$
$367$			4.23690e7i			0.857137i	−0.903509	+	0.428569i	$0.859018\pi$
$368$		−	1.92080e8i		−	3.85425i
$369$	2.41358e7			0.480377
$370$	1.03093e8			2.03528
$371$	2.74965e7			0.538462
$372$		−	9.02865e7i		−	1.75386i
$373$	2.26006e7			0.435505			0.217753	−	0.976004i	$-0.430127\pi$
$373$	2.26006e7			0.435505			0.217753	+	0.976004i	$0.430127\pi$
$374$	9.78448e6			0.187035
$375$	−9.37748e7			−1.77825
$376$	−2.74355e8			−5.16119
$377$		−	2.11182e7i		−	0.394123i
$378$		−	3.21343e7i		−	0.594967i
$379$	−3.95902e7			−0.727227			−0.363613	−	0.931550i	$-0.618457\pi$
$379$	−3.95902e7			−0.727227			−0.363613	+	0.931550i	$0.618457\pi$
$380$	−2.02749e8			−3.69494
$381$	−2.80919e7			−0.507933
$382$	7.13343e7			1.27970
$383$	−1.05831e7			−0.188372			−0.0941858	−	0.995555i	$-0.530025\pi$
$383$	−1.05831e7			−0.188372			−0.0941858	+	0.995555i	$0.530025\pi$
$384$		−	1.69862e7i		−	0.299988i
$385$		−	5.63283e7i		−	0.987063i
$386$		−	1.11937e8i		−	1.94631i
$387$		−	1.98491e7i		−	0.342459i
$388$			8.28975e7i			1.41921i
$389$	−3.28357e7			−0.557824			−0.278912	−	0.960317i	$-0.589974\pi$
$389$	−3.28357e7			−0.557824			−0.278912	+	0.960317i	$0.589974\pi$
$390$	−1.53600e8			−2.58939
$391$		−	2.76635e7i		−	0.462783i
$392$			2.90369e8i			4.82050i
$393$			1.64024e7i			0.270228i
$394$		−	1.75295e8i		−	2.86603i
$395$	9.77853e7			1.58665
$396$		−	1.60661e7i		−	0.258717i
$397$			4.64196e7i			0.741874i	0.928658	+	0.370937i	$0.120963\pi$
$397$			4.64196e7i			0.741874i	−0.928658	+	0.370937i	$0.879037\pi$
$398$		−	1.94948e8i		−	3.09221i
$399$	4.76179e7			0.749638
$400$	4.47138e8			6.98654
$401$			3.20229e7i			0.496624i	0.968680	+	0.248312i	$0.0798758\pi$
$401$			3.20229e7i			0.496624i	−0.968680	+	0.248312i	$0.920124\pi$
$402$	−6.70380e7			−1.03191
$403$	1.01358e8			1.54861
$404$			1.87423e8i			2.84236i
$405$	1.40417e7			0.211375
$406$		−	6.45162e7i		−	0.964030i
$407$	−1.21056e7			−0.179557
$408$		−	3.46559e7i		−	0.510267i
$409$			6.55020e7i			0.957380i	0.877984	+	0.478690i	$0.158888\pi$
$409$			6.55020e7i			0.957380i	−0.877984	+	0.478690i	$0.841112\pi$
$410$		−	3.52450e8i		−	5.11382i
$411$	−4.15970e7			−0.599151
$412$			1.44548e8i			2.06691i
$413$	−8.09826e7	+	8.41059e7i	−1.14959	+	1.19392i
$414$	−6.37448e7			−0.898346
$415$			1.39163e8i			1.94706i
$416$	2.01683e8			2.80150
$417$	2.48971e7			0.343353
$418$	3.34100e7			0.457454
$419$		−	1.79347e7i		−	0.243810i	−0.992542	−	0.121905i	$-0.961100\pi$
$419$		−	1.79347e7i		−	0.243810i	0.992542	−	0.121905i	$-0.0389003\pi$
$420$	−3.34380e8			−4.51329
$421$			1.27320e7i			0.170629i	0.996354	+	0.0853143i	$0.0271894\pi$
$421$			1.27320e7i			0.170629i	−0.996354	+	0.0853143i	$0.972811\pi$
$422$	−2.67719e8			−3.56239
$423$			4.71901e7i			0.623490i
$424$		−	6.83318e7i		−	0.896448i
$425$	6.43971e7			0.838880
$426$		−	4.54797e7i		−	0.588287i
$427$			8.41691e7i			1.08111i
$428$	−1.83416e7			−0.233941
$429$	1.80363e7			0.228441
$430$	−2.89853e8			−3.64562
$431$		−	5.74355e7i		−	0.717379i	−0.933457	−	0.358689i	$-0.883224\pi$
$431$		−	5.74355e7i		−	0.717379i	0.933457	−	0.358689i	$-0.116776\pi$
$432$	−4.13895e7			−0.513380
$433$	−9.16313e7			−1.12870			−0.564352	−	0.825534i	$-0.690874\pi$
$433$	−9.16313e7			−1.12870			−0.564352	+	0.825534i	$0.690874\pi$
$434$	3.09650e8			3.78793
$435$	2.81916e7			0.342493
$436$		−	1.55582e8i		−	1.87715i
$437$		−	9.44597e7i		−	1.13188i
$438$	5.38824e7			0.641246
$439$	2.60876e7			0.308348			0.154174	−	0.988044i	$-0.450728\pi$
$439$	2.60876e7			0.308348			0.154174	+	0.988044i	$0.450728\pi$
$440$	−1.39982e8			−1.64329
$441$	4.99445e7			0.582333
$442$	6.52059e7			0.755127
$443$			1.18657e7i			0.136484i	0.997669	+	0.0682422i	$0.0217391\pi$
$443$			1.18657e7i			0.136484i	−0.997669	+	0.0682422i	$0.978261\pi$
$444$			7.18619e7i			0.821012i
$445$			5.97107e7i			0.677598i
$446$		−	6.80643e7i		−	0.767211i
$447$			1.02447e8i			1.14704i
$448$	2.18602e8			2.43119
$449$	4.68237e7			0.517282			0.258641	−	0.965974i	$-0.416725\pi$
$449$	4.68237e7			0.517282			0.258641	+	0.965974i	$0.416725\pi$
$450$		−	1.48390e8i		−	1.62842i
$451$			4.13859e7i			0.451152i
$452$			1.30382e8i			1.41189i
$453$		−	2.30202e7i		−	0.247636i
$454$	7.74982e7			0.828179
$455$		−	3.75384e8i		−	3.98513i
$456$		−	1.18336e8i		−	1.24802i
$457$		−	3.74987e7i		−	0.392887i	−0.980515	−	0.196443i	$-0.937061\pi$
$457$		−	3.74987e7i		−	0.392887i	0.980515	−	0.196443i	$-0.0629392\pi$
$458$	1.60838e8			1.67414
$459$	−5.96094e6			−0.0616420
$460$			6.63311e8i			6.81465i
$461$	−3.39765e7			−0.346797			−0.173399	−	0.984852i	$-0.555475\pi$
$461$	−3.39765e7			−0.346797			−0.173399	+	0.984852i	$0.555475\pi$
$462$	5.51010e7			0.558770
$463$			1.00232e8i			1.00987i	0.863159	+	0.504933i	$0.168483\pi$
$463$			1.00232e8i			1.00987i	−0.863159	+	0.504933i	$0.831517\pi$
$464$	−8.30979e7			−0.831833
$465$			1.35307e8i			1.34574i
$466$	9.93435e7			0.981706
$467$			1.69289e8i			1.66218i	0.556140	+	0.831089i	$0.312282\pi$
$467$			1.69289e8i			1.66218i	−0.556140	+	0.831089i	$0.687718\pi$
$468$		−	1.07068e8i		−	1.04453i
$469$		−	1.63835e8i		−	1.58813i
$470$	6.89106e8			6.63732
$471$		−	3.64438e7i		−	0.348787i
$472$	2.09013e8	+	2.01251e8i	1.98768	+	1.91387i
$473$	3.40355e7			0.321624
$474$			9.56545e7i			0.898195i
$475$	2.19890e8			2.05175
$476$	1.41950e8			1.31618
$477$	−1.17533e7			−0.108294
$478$			1.50394e8i			1.37704i
$479$	−1.74885e6			−0.0159127			−0.00795637	−	0.999968i	$-0.502533\pi$
$479$	−1.74885e6			−0.0159127			−0.00795637	+	0.999968i	$0.502533\pi$
$480$			2.69236e8i			2.43450i
$481$	−8.06741e7			−0.724935
$482$			8.42748e7i			0.752587i
$483$		−	1.55786e8i		−	1.38257i
$484$	−2.53553e8			−2.23632
$485$		−	1.24234e8i		−	1.08897i
$486$			1.37357e7i			0.119658i
$487$	−8.62647e7			−0.746872			−0.373436	−	0.927656i	$-0.621821\pi$
$487$	−8.62647e7			−0.746872			−0.373436	+	0.927656i	$0.621821\pi$
$488$	2.09170e8			1.79986
$489$	−2.57664e7			−0.220357
$490$		−	7.29328e8i		−	6.19919i
$491$	2.23878e8			1.89132			0.945662	−	0.325150i	$-0.105415\pi$
$491$	2.23878e8			1.89132			0.945662	+	0.325150i	$0.105415\pi$
$492$	2.45678e8			2.06286
$493$	−1.19678e7			−0.0998790
$494$	2.22651e8			1.84691
$495$			2.40774e7i			0.198515i
$496$		−	3.98834e8i		−	3.26849i
$497$	1.11148e8			0.905385
$498$	−1.36131e8			−1.10222
$499$	2.25336e8			1.81355			0.906774	−	0.421616i	$-0.138537\pi$
$499$	2.25336e8			1.81355			0.906774	+	0.421616i	$0.138537\pi$
$500$	−9.54533e8			−7.63626
$501$	−1.14407e8			−0.909783
$502$			1.70699e8i			1.34934i
$503$			1.53443e8i			1.20571i	0.797851	+	0.602854i	$0.205970\pi$
$503$			1.53443e8i			1.20571i	−0.797851	+	0.602854i	$0.794030\pi$
$504$		−	1.95164e8i		−	1.52443i
$505$		−	2.80881e8i		−	2.18096i
$506$		−	1.09304e8i		−	0.843692i
$507$	4.49551e7			0.344949
$508$	−2.85947e8			−2.18120
$509$		−	1.46180e7i		−	0.110849i	−0.998463	−	0.0554247i	$-0.982349\pi$
$509$		−	1.46180e7i		−	0.110849i	0.998463	−	0.0554247i	$-0.0176513\pi$
$510$			8.70463e7i			0.656205i
$511$			1.31684e8i			0.986891i
$512$			1.94334e8i			1.44790i
$513$	−2.03542e7			−0.150765
$514$			1.11867e8i			0.823784i
$515$		−	2.16627e8i		−	1.58595i
$516$		−	2.02044e8i		−	1.47061i
$517$	−8.09173e7			−0.585558
$518$	−2.46460e8			−1.77320
$519$		−	1.49356e8i		−	1.06837i
$520$	−9.32873e8			−6.63456
$521$	−2.03766e8			−1.44085			−0.720423	−	0.693535i	$-0.756052\pi$
$521$	−2.03766e8			−1.44085			−0.720423	+	0.693535i	$0.756052\pi$
$522$			2.75773e7i			0.193883i
$523$	−1.03055e8			−0.720385			−0.360193	−	0.932878i	$-0.617289\pi$
$523$	−1.03055e8			−0.720385			−0.360193	+	0.932878i	$0.617289\pi$
$524$			1.66960e8i			1.16043i
$525$	3.62650e8			2.50617
$526$		−	8.08457e7i		−	0.555520i
$527$		−	5.74403e7i		−	0.392451i
$528$		−	7.09709e7i		−	0.482146i
$529$	−1.60998e8			−1.08756
$530$			1.71631e8i			1.15284i
$531$	3.46158e7	−	3.59508e7i	0.231202	−	0.240118i
$532$	4.84702e8			3.21914
$533$			2.75805e8i			1.82146i
$534$	−5.84096e7			−0.383584
$535$	2.74875e7			0.179504
$536$	−4.07148e8			−2.64398
$537$			8.13467e7i			0.525312i
$538$	4.12915e8			2.65164
$539$			8.56403e7i			0.546905i
$540$	1.42930e8			0.907700
$541$		−	8.57244e7i		−	0.541393i	−0.962665	−	0.270697i	$-0.912746\pi$
$541$		−	8.57244e7i		−	0.541393i	0.962665	−	0.270697i	$-0.0872540\pi$
$542$		−	3.54801e8i		−	2.22837i
$543$	−1.46081e7			−0.0912420
$544$		−	1.14295e8i		−	0.709957i
$545$			2.33162e8i			1.44035i
$546$	3.67205e8			2.25596
$547$	−2.50356e8			−1.52966			−0.764832	−	0.644230i	$-0.777178\pi$
$547$	−2.50356e8			−1.52966			−0.764832	+	0.644230i	$0.777178\pi$
$548$	−4.23415e8			−2.57291
$549$		−	3.59779e7i		−	0.217429i
$550$	2.54445e8			1.52935
$551$	−4.08652e7			−0.244286
$552$	−3.87147e8			−2.30175
$553$	−2.33771e8			−1.38234
$554$		−	2.71241e8i		−	1.59524i
$555$		−	1.07695e8i		−	0.629968i
$556$	2.53427e8			1.47445
$557$	2.40770e8			1.39328			0.696638	−	0.717423i	$-0.254679\pi$
$557$	2.40770e8			1.39328			0.696638	+	0.717423i	$0.254679\pi$
$558$	−1.32359e8			−0.761818
$559$	2.26820e8			1.29851
$560$	−1.47710e9			−8.41097
$561$		−	1.02213e7i		−	0.0578917i
$562$			3.90837e8i			2.20185i
$563$			2.33540e8i			1.30869i	0.756198	+	0.654343i	$0.227055\pi$
$563$			2.33540e8i			1.30869i	−0.756198	+	0.654343i	$0.772945\pi$
$564$			4.80347e8i			2.67743i
$565$		−	1.95396e8i		−	1.08336i
$566$	−4.97157e8			−2.74186
$567$	−3.35688e7			−0.184156
$568$		−	2.76216e8i		−	1.50731i
$569$		−	2.43872e8i		−	1.32381i	−0.749589	−	0.661904i	$-0.769749\pi$
$569$		−	2.43872e8i		−	1.32381i	0.749589	−	0.661904i	$-0.230251\pi$
$570$			2.97227e8i			1.60496i
$571$		−	3.01057e8i		−	1.61712i	−0.588417	−	0.808558i	$-0.700249\pi$
$571$		−	3.01057e8i		−	1.61712i	0.588417	−	0.808558i	$-0.299751\pi$
$572$	1.83591e8			0.980987
$573$		−	7.45188e7i		−	0.396098i
$574$			8.42586e8i			4.45532i
$575$		−	7.19390e8i		−	3.78408i
$576$	−9.34408e7			−0.488955
$577$	7.05247e7			0.367125			0.183563	−	0.983008i	$-0.441237\pi$
$577$	7.05247e7			0.367125			0.183563	+	0.983008i	$0.441237\pi$
$578$			3.23235e8i			1.67392i
$579$	−1.16934e8			−0.602429
$580$	2.86962e8			1.47075
$581$		−	3.32691e8i		−	1.69634i
$582$	1.21527e8			0.616458
$583$		−	2.01535e7i		−	0.101706i
$584$	3.27249e8			1.64301
$585$			1.60457e8i			0.801478i
$586$		−	2.66224e8i		−	1.32299i
$587$			1.98624e8i			0.982014i	0.871156	+	0.491007i	$0.163371\pi$
$587$			1.98624e8i			0.982014i	−0.871156	+	0.491007i	$0.836629\pi$
$588$	5.08384e8			2.50069
$589$		−	1.96135e8i		−	0.959864i
$590$	−5.24982e8	−	5.05487e8i	−2.55616	−	2.46124i
$591$	−1.83120e8			−0.887103
$592$			3.17445e8i			1.53004i
$593$	2.54012e8			1.21812			0.609060	−	0.793124i	$-0.291547\pi$
$593$	2.54012e8			1.21812			0.609060	+	0.793124i	$0.291547\pi$
$594$	−2.35528e7			−0.112378
$595$	−2.12733e8			−1.00991
$596$			1.04281e9i			4.92569i
$597$	−2.03651e8			−0.957112
$598$		−	7.28425e8i		−	3.40629i
$599$	2.12333e8			0.987955			0.493978	−	0.869475i	$-0.335542\pi$
$599$	2.12333e8			0.987955			0.493978	+	0.869475i	$0.335542\pi$
$600$		−	9.01227e8i		−	4.17235i
$601$		−	5.30450e7i		−	0.244355i	−0.992508	−	0.122178i	$-0.961012\pi$
$601$		−	5.30450e7i		−	0.244355i	0.992508	−	0.122178i	$-0.0389877\pi$
$602$	6.92937e8			3.17618
$603$			7.00307e7i			0.319401i
$604$		−	2.34322e8i		−	1.06341i
$605$	3.79986e8			1.71594
$606$	2.74761e8			1.23463
$607$	1.69882e7			0.0759594			0.0379797	−	0.999279i	$-0.487908\pi$
$607$	1.69882e7			0.0759594			0.0379797	+	0.999279i	$0.487908\pi$
$608$		−	3.90272e8i		−	1.73643i
$609$	−6.73964e7			−0.298390
$610$	−5.25377e8			−2.31463
$611$	−5.39250e8			−2.36411
$612$	−6.06763e7			−0.264707
$613$			3.39053e8i			1.47192i	0.677022	+	0.735962i	$0.263270\pi$
$613$			3.39053e8i			1.47192i	−0.677022	+	0.735962i	$0.736730\pi$
$614$			3.42346e8i			1.47897i
$615$	−3.68184e8			−1.58285
$616$	3.34649e8			1.43169
$617$	4.28788e7			0.182552			0.0912760	−	0.995826i	$-0.470905\pi$
$617$	4.28788e7			0.182552			0.0912760	+	0.995826i	$0.470905\pi$
$618$	2.11907e8			0.897799
$619$	−2.18000e7			−0.0919148			−0.0459574	−	0.998943i	$-0.514634\pi$
$619$	−2.18000e7			−0.0919148			−0.0459574	+	0.998943i	$0.514634\pi$
$620$			1.37729e9i			5.77898i
$621$			6.65905e7i			0.278059i
$622$			8.64403e8i			3.59207i
$623$		−	1.42748e8i		−	0.590344i
$624$		−	4.72966e8i		−	1.94660i
$625$	7.91092e8			3.24031
$626$	−2.84655e8			−1.16037
$627$		−	3.49015e7i		−	0.141593i
$628$		−	3.70961e8i		−	1.49778i
$629$			4.57186e7i			0.183713i
$630$			4.90198e8i			1.96042i
$631$	−3.17528e8			−1.26385			−0.631924	−	0.775031i	$-0.717734\pi$
$631$	−3.17528e8			−1.26385			−0.631924	+	0.775031i	$0.717734\pi$
$632$			5.80947e8i			2.30136i
$633$			2.79671e8i			1.10265i
$634$		−	4.87278e7i		−	0.191209i
$635$	4.28533e8			1.67365
$636$	−1.19637e8			−0.465043
$637$			5.70726e8i			2.20805i
$638$	−4.72871e7			−0.182088
$639$	−4.75100e7			−0.182089
$640$			2.59120e8i			0.988463i
$641$	−1.98433e7			−0.0753425			−0.0376712	−	0.999290i	$-0.511994\pi$
$641$	−1.98433e7			−0.0753425			−0.0376712	+	0.999290i	$0.511994\pi$
$642$			2.68886e7i			0.101616i
$643$	−1.33186e8			−0.500985			−0.250493	−	0.968119i	$-0.580593\pi$
$643$	−1.33186e8			−0.500985			−0.250493	+	0.968119i	$0.580593\pi$
$644$		−	1.58575e9i		−	5.93713i
$645$			3.02792e8i			1.12841i
$646$		−	1.26178e8i		−	0.468044i
$647$	8.23746e7			0.304145			0.152072	−	0.988369i	$-0.451405\pi$
$647$	8.23746e7			0.304145			0.152072	+	0.988369i	$0.451405\pi$
$648$			8.34223e7i			0.306589i
$649$	6.16453e7	+	5.93561e7i	0.225510	+	0.217136i
$650$	1.69568e9			6.17452
$651$		−	3.23473e8i		−	1.17245i
$652$	−2.62276e8			−0.946272
$653$	7.86537e7			0.282475			0.141237	−	0.989976i	$-0.454892\pi$
$653$	7.86537e7			0.282475			0.141237	+	0.989976i	$0.454892\pi$
$654$	−2.28081e8			−0.815373
$655$		−	2.50214e8i		−	0.890404i
$656$	1.08526e9			3.84436
$657$		−	5.62878e7i		−	0.198481i
$658$	−1.64742e9			−5.78263
$659$		−	4.32893e8i		−	1.51260i	−0.654224	−	0.756301i	$-0.727004\pi$
$659$		−	4.32893e8i		−	1.51260i	0.654224	−	0.756301i	$-0.272996\pi$
$660$			2.45084e8i			0.852477i
$661$	2.67269e8			0.925430			0.462715	−	0.886507i	$-0.346875\pi$
$661$	2.67269e8			0.925430			0.462715	+	0.886507i	$0.346875\pi$
$662$		−	1.29817e8i		−	0.447463i
$663$		−	6.81168e7i		−	0.233730i
$664$	−8.26774e8			−2.82412
$665$	−7.26396e8			−2.47007
$666$	1.05349e8			0.356621
$667$			1.33694e8i			0.450542i
$668$	−1.16454e9			−3.90684
$669$	−7.11029e7			−0.237470
$670$	1.02264e9			3.40016
$671$	6.16916e7			0.204201
$672$		−	6.43651e8i		−	2.12101i
$673$			9.44890e7i			0.309982i	0.987916	+	0.154991i	$0.0495348\pi$
$673$			9.44890e7i			0.309982i	−0.987916	+	0.154991i	$0.950465\pi$
$674$	−6.22034e8			−2.03158
$675$	−1.55014e8			−0.504034
$676$	4.57598e8			1.48130
$677$	−5.98234e8			−1.92799			−0.963995	−	0.265920i	$-0.914324\pi$
$677$	−5.98234e8			−1.92799			−0.963995	+	0.265920i	$0.914324\pi$
$678$	1.91139e8			0.613281
$679$			2.97001e8i			0.948742i
$680$			5.28666e8i			1.68133i
$681$		−	8.09579e7i		−	0.256341i
$682$		−	2.26957e8i		−	0.715470i
$683$			1.94951e8i			0.611876i	0.952051	+	0.305938i	$0.0989700\pi$
$683$			1.94951e8i			0.611876i	−0.952051	+	0.305938i	$0.901030\pi$
$684$	−2.07185e8			−0.647425
$685$	6.34549e8			1.97421
$686$			7.45535e8i			2.30938i
$687$		−	1.68018e8i		−	0.518186i
$688$		−	8.92515e8i		−	2.74063i
$689$		−	1.34307e8i		−	0.410622i
$690$	9.72407e8			2.96006
$691$			3.82858e8i			1.16039i	0.814478	+	0.580195i	$0.197024\pi$
$691$			3.82858e8i			1.16039i	−0.814478	+	0.580195i	$0.802976\pi$
$692$		−	1.52029e9i		−	4.58784i
$693$		−	5.75608e7i		−	0.172953i
$694$	9.06316e7			0.271145
$695$	−3.79798e8			−1.13135
$696$			1.67487e8i			0.496769i
$697$	1.56300e8			0.461596
$698$	4.01902e8			1.18183
$699$		−	1.03778e8i		−	0.303861i
$700$	3.69141e9			10.7621
$701$		−	2.40447e8i		−	0.698016i	−0.937120	−	0.349008i	$-0.886519\pi$
$701$		−	2.40447e8i		−	0.698016i	0.937120	−	0.349008i	$-0.113481\pi$
$702$	−1.56961e8			−0.453712
$703$			1.56110e8i			0.449330i
$704$		−	1.60224e8i		−	0.459208i
$705$		−	7.19870e8i		−	2.05441i
$706$	−3.96962e8			−1.12807
$707$			6.71490e8i			1.90012i
$708$	3.52354e8	−	3.65943e8i	0.992840	−	1.03113i
$709$	3.37545e8			0.947093			0.473546	−	0.880769i	$-0.342974\pi$
$709$	3.37545e8			0.947093			0.473546	+	0.880769i	$0.342974\pi$
$710$			6.93779e8i			1.93841i
$711$	9.99248e7			0.278013
$712$	−3.54744e8			−0.982822
$713$	−6.41675e8			−1.77030
$714$		−	2.08098e8i		−	0.571706i
$715$	−2.75138e8			−0.752717
$716$			8.28028e8i			2.25583i
$717$	1.57108e8			0.426227
$718$		−	5.65301e8i		−	1.52724i
$719$			1.76060e8i			0.473667i	0.971550	+	0.236834i	$0.0761097\pi$
$719$			1.76060e8i			0.473667i	−0.971550	+	0.236834i	$0.923890\pi$
$720$	6.31383e8			1.69159
$721$			5.17880e8i			1.38173i
$722$			2.71185e8i			0.720534i
$723$	8.80370e7			0.232943
$724$	−1.48696e8			−0.391817
$725$	−3.11223e8			−0.816690
$726$			3.71706e8i			0.971382i
$727$	−2.54718e7			−0.0662914			−0.0331457	−	0.999451i	$-0.510553\pi$
$727$	−2.54718e7			−0.0662914			−0.0331457	+	0.999451i	$0.510553\pi$
$728$	2.23018e9			5.78023
$729$	1.43489e7			0.0370370
$730$	−8.21959e8			−2.11291
$731$		−	1.28541e8i		−	0.329070i
$732$		−	3.66218e8i		−	0.933699i
$733$	−5.53773e7			−0.140611			−0.0703056	−	0.997525i	$-0.522397\pi$
$733$	−5.53773e7			−0.140611			−0.0703056	+	0.997525i	$0.522397\pi$
$734$	6.32243e8			1.59881
$735$	−7.61887e8			−1.91880
$736$	−1.27681e9			−3.20253
$737$	−1.20082e8			−0.299969
$738$		−	3.60161e8i		−	0.896041i
$739$		−	1.60876e8i		−	0.398618i	−0.979937	−	0.199309i	$-0.936130\pi$
$739$		−	1.60876e8i		−	0.398618i	0.979937	−	0.199309i	$-0.0638698\pi$
$740$		−	1.09623e9i		−	2.70525i
$741$		−	2.32591e8i		−	0.571661i
$742$		−	4.10310e8i		−	1.00439i
$743$	2.88499e8			0.703359			0.351680	−	0.936120i	$-0.385611\pi$
$743$	2.88499e8			0.703359			0.351680	+	0.936120i	$0.385611\pi$
$744$	−8.03868e8			−1.95194
$745$		−	1.56280e9i		−	3.77951i
$746$		−	3.37253e8i		−	0.812342i
$747$			1.42208e8i			0.341163i
$748$		−	1.04042e8i		−	0.248602i
$749$	−6.57132e7			−0.156389
$750$			1.39933e9i			3.31694i
$751$		−	7.51038e7i		−	0.177314i	−0.996062	−	0.0886568i	$-0.971743\pi$
$751$		−	7.51038e7i		−	0.177314i	0.996062	−	0.0886568i	$-0.0282574\pi$
$752$			2.12190e9i			4.98966i
$753$	1.78319e8			0.417651
$754$	−3.15131e8			−0.735153
$755$			3.51165e8i			0.815964i
$756$	−3.41697e8			−0.790816
$757$	−3.66017e8			−0.843749			−0.421874	−	0.906654i	$-0.638628\pi$
$757$	−3.66017e8			−0.843749			−0.421874	+	0.906654i	$0.638628\pi$
$758$			5.90776e8i			1.35649i
$759$	−1.14183e8			−0.261143
$760$			1.80518e9i			4.11224i
$761$	−1.74119e8			−0.395088			−0.197544	−	0.980294i	$-0.563296\pi$
$761$	−1.74119e8			−0.395088			−0.197544	+	0.980294i	$0.563296\pi$
$762$			4.19196e8i			0.947441i
$763$		−	5.57410e8i		−	1.25488i
$764$		−	7.58526e8i		−	1.70095i
$765$	9.09322e7			0.203111
$766$			1.57924e8i			0.351367i
$767$	4.10818e8	+	3.95562e8i	0.910465	+	0.876655i
$768$	1.30157e8			0.287333
$769$			4.02756e8i			0.885653i	0.896607	+	0.442826i	$0.146024\pi$
$769$			4.02756e8i			0.885653i	−0.896607	+	0.442826i	$0.853976\pi$
$770$	−8.40548e8			−1.84115
$771$	1.16861e8			0.254981
$772$	−1.19027e9			−2.58699
$773$			2.63971e8i			0.571502i	0.958304	+	0.285751i	$0.0922429\pi$
$773$			2.63971e8i			0.571502i	−0.958304	+	0.285751i	$0.907757\pi$
$774$	−2.96194e8			−0.638784
$775$		−	1.49373e9i		−	3.20899i
$776$	7.38080e8			1.57949
$777$			2.57463e8i			0.548847i
$778$			4.89983e8i			1.04050i
$779$	5.33702e8			1.12898
$780$			1.63329e9i			3.44175i
$781$		−	8.14660e7i		−	0.171011i
$782$	−4.12803e8			−0.863223
$783$	2.88084e7			0.0600114
$784$	2.24575e9			4.66030
$785$			5.55938e8i			1.14926i
$786$	2.44762e8			0.504052
$787$	−7.55689e8			−1.55031			−0.775156	−	0.631770i	$-0.782329\pi$
$787$	−7.55689e8			−1.55031			−0.775156	+	0.631770i	$0.782329\pi$
$788$	−1.86398e9			−3.80945
$789$	−8.44548e7			−0.171947
$790$		−	1.45918e9i		−	2.95956i
$791$			4.67125e8i			0.943852i
$792$	−1.43045e8			−0.287937
$793$	4.11127e8			0.824434
$794$	6.92687e8			1.38381
$795$	1.79293e8			0.356830
$796$	−2.07296e9			−4.11009
$797$		−	4.33414e8i		−	0.856107i	−0.903753	−	0.428054i	$-0.859199\pi$
$797$		−	4.33414e8i		−	0.856107i	0.903753	−	0.428054i	$-0.140801\pi$
$798$		−	7.10568e8i		−	1.39829i
$799$			3.05597e8i			0.599113i
$800$		−	2.97225e9i		−	5.80517i
$801$			6.10171e7i			0.118728i
$802$	4.77855e8			0.926346
$803$	9.65173e7			0.186406
$804$			7.12842e8i			1.37159i
$805$			2.37647e9i			4.55560i
$806$		−	1.51249e9i		−	2.88861i
$807$		−	4.31349e8i		−	0.820744i
$808$	1.66873e9			3.16338
$809$		−	4.64580e8i		−	0.877434i	−0.898625	−	0.438717i	$-0.855433\pi$
$809$		−	4.64580e8i		−	0.877434i	0.898625	−	0.438717i	$-0.144567\pi$
$810$		−	2.09534e8i		−	0.394275i
$811$			7.91081e8i			1.48306i	0.670920	+	0.741530i	$0.265899\pi$
$811$			7.91081e8i			1.48306i	−0.670920	+	0.741530i	$0.734101\pi$
$812$	−6.86027e8			−1.28137
$813$	−3.70641e8			−0.689734
$814$			1.80643e8i			0.334925i
$815$	3.93059e8			0.726080
$816$	−2.68033e8			−0.493308
$817$		−	4.38913e8i		−	0.804846i
$818$	9.77439e8			1.78579
$819$		−	3.83598e8i		−	0.698272i
$820$	−3.74774e9			−6.79717
$821$		−	1.05880e9i		−	1.91331i	−0.291220	−	0.956656i	$-0.594061\pi$
$821$		−	1.05880e9i		−	1.91331i	0.291220	−	0.956656i	$-0.405939\pi$
$822$			6.20722e8i			1.11759i
$823$		−	5.10302e8i		−	0.915435i	−0.889098	−	0.457718i	$-0.848667\pi$
$823$		−	5.10302e8i		−	0.915435i	0.889098	−	0.457718i	$-0.151333\pi$
$824$	1.28699e9			2.30035
$825$		−	2.65804e8i		−	0.473369i
$826$	1.25505e9	+	1.20845e9i	2.22701	+	2.14431i
$827$	−9.12307e8			−1.61296			−0.806481	−	0.591260i	$-0.798631\pi$
$827$	−9.12307e8			−1.61296			−0.806481	+	0.591260i	$0.798631\pi$
$828$			6.77824e8i			1.19406i
$829$	1.55032e8			0.272119			0.136059	−	0.990701i	$-0.456556\pi$
$829$	1.55032e8			0.272119			0.136059	+	0.990701i	$0.456556\pi$
$830$	2.07663e9			3.63183
$831$	−2.83350e8			−0.493765
$832$		−	1.06777e9i		−	1.85399i
$833$	3.23434e8			0.559566
$834$		−	3.71522e8i		−	0.640452i
$835$	1.74524e9			2.99774
$836$		−	3.55262e8i		−	0.608037i
$837$			1.38268e8i			0.235801i
$838$	−2.67626e8			−0.454775
$839$		−	1.52642e7i		−	0.0258458i	−0.999916	−	0.0129229i	$-0.995886\pi$
$839$		−	1.52642e7i		−	0.0258458i	0.999916	−	0.0129229i	$-0.00411360\pi$
$840$			2.97716e9i			5.02302i
$841$	−5.36984e8			−0.902763
$842$	1.89991e8			0.318271
$843$	4.08285e8			0.681523
$844$			2.84676e9i			4.73504i
$845$	−6.85776e8			−1.13661
$846$	7.04184e8			1.16299
$847$	−9.08416e8			−1.49498
$848$	−5.28486e8			−0.866655
$849$			5.19352e8i			0.848669i
$850$		−	9.60953e8i		−	1.56475i
$851$	5.10729e8			0.828709
$852$	−4.83604e8			−0.781936
$853$	7.76971e8			1.25186			0.625932	−	0.779877i	$-0.284719\pi$
$853$	7.76971e8			1.25186			0.625932	+	0.779877i	$0.284719\pi$
$854$	1.25600e9			2.01658
$855$	3.10496e8			0.496773
$856$			1.63305e8i			0.260362i
$857$		−	7.73590e8i		−	1.22905i	−0.788899	−	0.614523i	$-0.789348\pi$
$857$		−	7.73590e8i		−	1.22905i	0.788899	−	0.614523i	$-0.210652\pi$
$858$		−	2.69142e8i		−	0.426108i
$859$			1.26771e7i			0.0200004i	0.999950	+	0.0100002i	$0.00318322\pi$
$859$			1.26771e7i			0.0200004i	−0.999950	+	0.0100002i	$0.996817\pi$
$860$			3.08212e9i			4.84567i
$861$	8.80201e8			1.37903
$862$	−8.57069e8			−1.33812
$863$			2.36038e8i			0.367239i	0.982997	+	0.183620i	$0.0587815\pi$
$863$			2.36038e8i			0.367239i	−0.982997	+	0.183620i	$0.941219\pi$
$864$			2.75127e8i			0.426572i
$865$			2.27838e9i			3.52028i
$866$			1.36735e9i			2.10536i
$867$	3.37665e8			0.518118
$868$		−	3.29263e9i		−	5.03482i
$869$			1.71342e8i			0.261099i
$870$		−	4.20683e8i		−	0.638847i
$871$	−8.00256e8			−1.21108
$872$	−1.38523e9			−2.08916
$873$		−	1.26952e8i		−	0.190808i
$874$	−1.40955e9			−2.11129
$875$	−3.41985e9			−5.10484
$876$		−	5.72953e8i		−	0.852328i
$877$	−1.66206e8			−0.246404			−0.123202	−	0.992382i	$-0.539316\pi$
$877$	−1.66206e8			−0.246404			−0.123202	+	0.992382i	$0.539316\pi$
$878$		−	3.89287e8i		−	0.575157i
$879$	−2.78109e8			−0.409495
$880$			1.08264e9i			1.58868i
$881$			1.02212e9i			1.49476i	0.664395	+	0.747382i	$0.268689\pi$
$881$			1.02212e9i			1.49476i	−0.664395	+	0.747382i	$0.731311\pi$
$882$		−	7.45286e8i		−	1.08622i
$883$	−2.59307e8			−0.376644			−0.188322	−	0.982107i	$-0.560305\pi$
$883$	−2.59307e8			−0.376644			−0.188322	+	0.982107i	$0.560305\pi$
$884$		−	6.93361e8i		−	1.00370i
$885$	−5.28053e8	+	5.48419e8i	−0.761813	+	0.791193i
$886$	1.77064e8			0.254583
$887$		−	1.23046e9i		−	1.76318i	−0.472016	−	0.881590i	$-0.656473\pi$
$887$		−	1.23046e9i		−	1.76318i	0.472016	−	0.881590i	$-0.343527\pi$
$888$	6.39824e8			0.913737
$889$	−1.02448e9			−1.45813
$890$	8.91020e8			1.26391
$891$			2.46042e7i			0.0347838i
$892$	−7.23755e8			−1.01976
$893$			1.04349e9i			1.46532i
$894$	1.52875e9			2.13956
$895$		−	1.24092e9i		−	1.73091i
$896$		−	6.19466e8i		−	0.861179i
$897$	−7.60943e8			−1.05433
$898$		−	6.98717e8i		−	0.964878i
$899$			2.77601e8i			0.382070i
$900$	−1.57789e9			−2.16445
$901$	−7.61129e7			−0.104060
$902$	6.17572e8			0.841527
$903$		−	7.23872e8i		−	0.983102i
$904$	1.16086e9			1.57135
$905$	2.22842e8			0.300644
$906$	−3.43513e8			−0.461912
$907$	−2.77299e8			−0.371643			−0.185822	−	0.982583i	$-0.559495\pi$
$907$	−2.77299e8			−0.371643			−0.185822	+	0.982583i	$0.559495\pi$
$908$		−	8.24069e8i		−	1.10079i
$909$		−	2.87027e8i		−	0.382147i
$910$	−5.60160e9			−7.43340
$911$	−3.75767e8			−0.497009			−0.248504	−	0.968631i	$-0.579939\pi$
$911$	−3.75767e8			−0.497009			−0.248504	+	0.968631i	$0.579939\pi$
$912$	−9.15224e8			−1.20654
$913$	−2.43845e8			−0.320407
$914$	−5.59566e8			−0.732847
$915$			5.48831e8i			0.716433i
$916$		−	1.71025e9i		−	2.22523i
$917$			5.98175e8i			0.775747i
$918$			8.89508e7i			0.114980i
$919$			9.80786e8i			1.26365i	0.775110	+	0.631827i	$0.217695\pi$
$919$			9.80786e8i			1.26365i	−0.775110	+	0.631827i	$0.782305\pi$
$920$	5.90580e9			7.58430
$921$	3.57629e8			0.457777
$922$			5.07007e8i			0.646876i
$923$		−	5.42907e8i		−	0.690431i
$924$		−	5.85911e8i		−	0.742703i
$925$			1.18891e9i			1.50219i
$926$	1.49569e9			1.88369
$927$		−	2.21367e8i		−	0.277890i
$928$			5.52374e8i			0.691177i
$929$		−	1.39384e8i		−	0.173846i	−0.996215	−	0.0869231i	$-0.972297\pi$
$929$		−	1.39384e8i		−	0.173846i	0.996215	−	0.0869231i	$-0.0277034\pi$
$930$	2.01910e9			2.51020
$931$	1.10440e9			1.36860
$932$		−	1.05636e9i		−	1.30486i
$933$	9.02992e8			1.11183
$934$	2.52618e9			3.10044
$935$			1.55922e8i			0.190754i
$936$	−9.53284e8			−1.16250
$937$			2.12553e8i			0.258373i	0.991620	+	0.129187i	$0.0412366\pi$
$937$			2.12553e8i			0.258373i	−0.991620	+	0.129187i	$0.958763\pi$
$938$	−2.44479e9			−2.96233
$939$			2.97363e8i			0.359162i
$940$		−	7.32754e9i		−	8.82216i
$941$		−	3.13084e8i		−	0.375744i	−0.982193	−	0.187872i	$-0.939841\pi$
$941$		−	3.13084e8i		−	0.375744i	0.982193	−	0.187872i	$-0.0601591\pi$
$942$	−5.43824e8			−0.650588
$943$		−	1.74606e9i		−	2.08220i
$944$	1.55650e9	−	1.61653e9i	1.85026	−	1.92162i
$945$	5.12082e8			0.606798
$946$		−	5.07888e8i		−	0.599921i
$947$	−7.62049e8			−0.897290			−0.448645	−	0.893710i	$-0.648093\pi$
$947$	−7.62049e8			−0.897290			−0.448645	+	0.893710i	$0.648093\pi$
$948$	1.01713e9			1.19386
$949$	6.43213e8			0.752586
$950$		−	3.28126e9i		−	3.82710i
$951$	−5.09032e7			−0.0591838
$952$		−	1.26386e9i		−	1.46483i
$953$	−1.08825e9			−1.25733			−0.628665	−	0.777676i	$-0.716398\pi$
$953$	−1.08825e9			−1.25733			−0.628665	+	0.777676i	$0.716398\pi$
$954$			1.75386e8i			0.201999i
$955$			1.13676e9i			1.30515i
$956$	1.59920e9			1.83033
$957$			4.93981e7i			0.0563604i
$958$			2.60968e7i			0.0296818i
$959$	−1.51699e9			−1.71999
$960$	1.42541e9			1.61111
$961$	−4.44864e8			−0.501253
$962$			1.20384e9i			1.35221i
$963$	2.80890e7			0.0314526
$964$	8.96128e8			1.00032
$965$	1.78379e9			1.98501
$966$	−2.32469e9			−2.57889
$967$			7.34053e8i			0.811799i	0.913918	+	0.405899i	$0.133042\pi$
$967$			7.34053e8i			0.811799i	−0.913918	+	0.405899i	$0.866958\pi$
$968$			2.25752e9i			2.48888i
$969$	−1.31811e8			−0.144871
$970$	−1.85385e9			−2.03124
$971$	5.73521e8			0.626458			0.313229	−	0.949678i	$-0.398589\pi$
$971$	5.73521e8			0.626458			0.313229	+	0.949678i	$0.398589\pi$
$972$	1.46057e8			0.159047
$973$	9.07966e8			0.985669
$974$			1.28727e9i			1.39313i
$975$		−	1.77138e9i		−	1.91116i
$976$		−	1.61774e9i		−	1.74004i
$977$			9.91194e8i			1.06286i	0.847103	+	0.531429i	$0.178345\pi$
$977$			9.91194e8i			1.06286i	−0.847103	+	0.531429i	$0.821655\pi$
$978$			3.84494e8i			0.411030i
$979$	−1.04627e8			−0.111505
$980$	−7.75524e9			−8.23981
$981$			2.38263e8i			0.252377i
$982$		−	3.34077e9i		−	3.52786i
$983$			2.93331e8i			0.308814i	0.988007	+	0.154407i	$0.0493467\pi$
$983$			2.93331e8i			0.308814i	−0.988007	+	0.154407i	$0.950653\pi$
$984$		−	2.18740e9i		−	2.29584i
$985$	2.79344e9			2.92302
$986$			1.78587e8i			0.186303i
$987$			1.72096e9i			1.78986i
$988$		−	2.36754e9i		−	2.45486i
$989$	−1.43595e9			−1.48439
$990$	3.59290e8			0.370288
$991$			7.26894e8i			0.746879i	0.927654	+	0.373440i	$0.121822\pi$
$991$			7.26894e8i			0.746879i	−0.927654	+	0.373440i	$0.878178\pi$
$992$	−2.65116e9			−2.71582
$993$	−1.35612e8			−0.138500
$994$		−	1.65859e9i		−	1.68880i
$995$	3.10663e9			3.15370
$996$			1.44753e9i			1.46504i
$997$	−5.32048e8			−0.536865			−0.268433	−	0.963298i	$-0.586506\pi$
$997$	−5.32048e8			−0.536865			−0.268433	+	0.963298i	$0.586506\pi$
$998$		−	3.36253e9i		−	3.38279i
$999$		−	1.10052e8i		−	0.110383i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.7.c.a.58.3	✓	60
59.58	odd	2	inner	177.7.c.a.58.58	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.7.c.a.58.3	✓	60	1.1	even	1	trivial
177.7.c.a.58.58	yes	60	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:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	177.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-14.9223i q^{2} -15.5885 q^{3} -158.675 q^{4} +237.797 q^{5} +232.615i q^{6} -568.491 q^{7} +1412.76i q^{8} +243.000 q^{9} +O(q^{10})\)	\(q-14.9223i q^{2} -15.5885 q^{3} -158.675 q^{4} +237.797 q^{5} +232.615i q^{6} -568.491 q^{7} +1412.76i q^{8} +243.000 q^{9} -3548.48i q^{10} +416.675i q^{11} +2473.49 q^{12} +2776.81i q^{13} +8483.18i q^{14} -3706.89 q^{15} +10926.5 q^{16} +1573.64 q^{17} -3626.12i q^{18} +5373.33 q^{19} -37732.4 q^{20} +8861.90 q^{21} +6217.74 q^{22} -17579.4i q^{23} -22022.8i q^{24} +40922.4 q^{25} +41436.4 q^{26} -3788.00 q^{27} +90205.1 q^{28} -7605.19 q^{29} +55315.3i q^{30} -36501.6i q^{31} -72631.3i q^{32} -6495.31i q^{33} -23482.3i q^{34} -135185. q^{35} -38558.0 q^{36} +29052.8i q^{37} -80182.4i q^{38} -43286.2i q^{39} +335951. i q^{40} +99324.2 q^{41} -132240. i q^{42} -81683.7i q^{43} -66115.7i q^{44} +57784.7 q^{45} -262324. q^{46} +194198. i q^{47} -170327. q^{48} +205533. q^{49} -610657. i q^{50} -24530.6 q^{51} -440610. i q^{52} -48367.5 q^{53} +56525.6i q^{54} +99084.0i q^{55} -803143. i q^{56} -83762.0 q^{57} +113487. i q^{58} +(142452. - 147946. i) q^{59} +588190. q^{60} -148057. i q^{61} -544688. q^{62} -138143. q^{63} -384530. q^{64} +660318. i q^{65} -96925.0 q^{66} +288192. i q^{67} -249697. q^{68} +274035. i q^{69} +2.01728e6i q^{70} -195515. q^{71} +343302. i q^{72} -231637. i q^{73} +433534. q^{74} -637918. q^{75} -852612. q^{76} -236876. i q^{77} -645929. q^{78} +411213. q^{79} +2.59829e6 q^{80} +59049.0 q^{81} -1.48214e6i q^{82} +585218. i q^{83} -1.40616e6 q^{84} +374207. q^{85} -1.21891e6 q^{86} +118553. q^{87} -588663. q^{88} +251099. i q^{89} -862280. i q^{90} -1.57859e6i q^{91} +2.78940e6i q^{92} +569004. i q^{93} +2.89787e6 q^{94} +1.27776e6 q^{95} +1.13221e6i q^{96} -522437. i q^{97} -3.06702e6i q^{98} +101252. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 1920 q^{4} - 408 q^{7} + 14580 q^{9}+O(q^{10}) \) 60 * q - 1920 * q^4 - 408 * q^7 + 14580 * q^9	\( 60 q - 1920 q^{4} - 408 q^{7} + 14580 q^{9} - 1944 q^{12} - 4536 q^{15} + 56616 q^{16} + 8480 q^{17} + 11376 q^{19} + 40796 q^{20} - 8232 q^{22} + 197940 q^{25} + 147252 q^{26} + 71640 q^{28} + 63456 q^{29} - 364432 q^{35} - 466560 q^{36} + 99632 q^{41} - 470316 q^{46} + 171072 q^{48} + 1737420 q^{49} + 60912 q^{51} + 92240 q^{53} + 186624 q^{57} + 917264 q^{59} + 1063368 q^{60} - 115768 q^{62} - 99144 q^{63} - 1107444 q^{64} + 1172232 q^{66} - 4247232 q^{68} + 1498048 q^{71} + 1161448 q^{74} - 1477440 q^{75} - 1045320 q^{76} - 1060452 q^{78} - 90600 q^{79} + 77096 q^{80} + 3542940 q^{81} - 2225880 q^{84} - 693408 q^{85} - 1567768 q^{86} + 1821528 q^{87} + 62892 q^{88} + 5268696 q^{94} + 296128 q^{95}+O(q^{100}) \) 60 * q - 1920 * q^4 - 408 * q^7 + 14580 * q^9 - 1944 * q^12 - 4536 * q^15 + 56616 * q^16 + 8480 * q^17 + 11376 * q^19 + 40796 * q^20 - 8232 * q^22 + 197940 * q^25 + 147252 * q^26 + 71640 * q^28 + 63456 * q^29 - 364432 * q^35 - 466560 * q^36 + 99632 * q^41 - 470316 * q^46 + 171072 * q^48 + 1737420 * q^49 + 60912 * q^51 + 92240 * q^53 + 186624 * q^57 + 917264 * q^59 + 1063368 * q^60 - 115768 * q^62 - 99144 * q^63 - 1107444 * q^64 + 1172232 * q^66 - 4247232 * q^68 + 1498048 * q^71 + 1161448 * q^74 - 1477440 * q^75 - 1045320 * q^76 - 1060452 * q^78 - 90600 * q^79 + 77096 * q^80 + 3542940 * q^81 - 2225880 * q^84 - 693408 * q^85 - 1567768 * q^86 + 1821528 * q^87 + 62892 * q^88 + 5268696 * q^94 + 296128 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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