LMFDB - Embedded newform 177.7.c.a.58.2

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			58.2
Character	$\chi$	$=$	177.58
Dual form			177.7.c.a.58.59

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-15.1313i q^{2} +15.5885 q^{3} -164.955 q^{4} -92.6753 q^{5} -235.873i q^{6} -595.836 q^{7} +1527.58i q^{8} +243.000 q^{9} +O(q^{10})$	\(q-15.1313i q^{2} +15.5885 q^{3} -164.955 q^{4} -92.6753 q^{5} -235.873i q^{6} -595.836 q^{7} +1527.58i q^{8} +243.000 q^{9} +1402.29i q^{10} -1188.16i q^{11} -2571.39 q^{12} +1180.06i q^{13} +9015.75i q^{14} -1444.67 q^{15} +12557.0 q^{16} +7501.19 q^{17} -3676.90i q^{18} -6572.73 q^{19} +15287.3 q^{20} -9288.16 q^{21} -17978.3 q^{22} +10020.3i q^{23} +23812.6i q^{24} -7036.28 q^{25} +17855.7 q^{26} +3788.00 q^{27} +98286.1 q^{28} -28197.5 q^{29} +21859.6i q^{30} -24653.7i q^{31} -92238.9i q^{32} -18521.5i q^{33} -113502. i q^{34} +55219.3 q^{35} -40084.1 q^{36} -38798.6i q^{37} +99453.6i q^{38} +18395.2i q^{39} -141569. i q^{40} +61352.8 q^{41} +140542. i q^{42} -19526.7i q^{43} +195993. i q^{44} -22520.1 q^{45} +151620. q^{46} -60661.5i q^{47} +195745. q^{48} +237372. q^{49} +106468. i q^{50} +116932. q^{51} -194656. i q^{52} +128781. q^{53} -57317.1i q^{54} +110113. i q^{55} -910185. i q^{56} -102459. q^{57} +426664. i q^{58} +(65188.5 + 194759. i) q^{59} +238305. q^{60} +200868. i q^{61} -373041. q^{62} -144788. q^{63} -592041. q^{64} -109362. i q^{65} -280254. q^{66} -526100. i q^{67} -1.23736e6 q^{68} +156201. i q^{69} -835538. i q^{70} +123865. q^{71} +371201. i q^{72} +618533. i q^{73} -587072. q^{74} -109685. q^{75} +1.08420e6 q^{76} +707947. i q^{77} +278343. q^{78} +63990.6 q^{79} -1.16373e6 q^{80} +59049.0 q^{81} -928345. i q^{82} -513107. i q^{83} +1.53213e6 q^{84} -695175. q^{85} -295464. q^{86} -439556. q^{87} +1.81500e6 q^{88} -297297. i q^{89} +340758. i q^{90} -703120. i q^{91} -1.65290e6i q^{92} -384313. i q^{93} -917885. q^{94} +609130. q^{95} -1.43786e6i q^{96} +1.39038e6i q^{97} -3.59173e6i q^{98} -288722. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	15.1313i		−	1.89141i	−0.325030	−	0.945704i	$-0.605374\pi$
$2$		−	15.1313i		−	1.89141i	0.325030	−	0.945704i	$-0.394626\pi$
$3$	15.5885			0.577350
$3$	15.5885			0.577350
$4$	−164.955			−2.57742
$5$	−92.6753			−0.741403			−0.370701	−	0.928752i	$-0.620883\pi$
$5$	−92.6753			−0.741403			−0.370701	+	0.928752i	$0.620883\pi$
$6$		−	235.873i		−	1.09200i
$7$	−595.836			−1.73713			−0.868566	−	0.495574i	$-0.834958\pi$
$7$	−595.836			−1.73713			−0.868566	+	0.495574i	$0.834958\pi$
$8$			1527.58i			2.98355i
$9$	243.000			0.333333
$10$			1402.29i			1.40229i
$11$		−	1188.16i		−	0.892680i	−0.894863	−	0.446340i	$-0.852727\pi$
$11$		−	1188.16i		−	0.892680i	0.894863	−	0.446340i	$-0.147273\pi$
$12$	−2571.39			−1.48808
$13$			1180.06i			0.537121i	0.963263	+	0.268561i	$0.0865480\pi$
$13$			1180.06i			0.537121i	−0.963263	+	0.268561i	$0.913452\pi$
$14$			9015.75i			3.28562i
$15$	−1444.67			−0.428049
$16$	12557.0			3.06568
$17$	7501.19			1.52680			0.763402	−	0.645924i	$-0.223528\pi$
$17$	7501.19			1.52680			0.763402	+	0.645924i	$0.223528\pi$
$18$		−	3676.90i		−	0.630469i
$19$	−6572.73			−0.958263			−0.479132	−	0.877743i	$-0.659048\pi$
$19$	−6572.73			−0.958263			−0.479132	+	0.877743i	$0.659048\pi$
$20$	15287.3			1.91091
$21$	−9288.16			−1.00293
$22$	−17978.3			−1.68842
$23$			10020.3i			0.823565i	0.911282	+	0.411782i	$0.135094\pi$
$23$			10020.3i			0.823565i	−0.911282	+	0.411782i	$0.864906\pi$
$24$			23812.6i			1.72255i
$25$	−7036.28			−0.450322
$26$	17855.7			1.01592
$27$	3788.00			0.192450
$28$	98286.1			4.47732
$29$	−28197.5			−1.15616			−0.578078	−	0.815981i	$-0.696197\pi$
$29$	−28197.5			−1.15616			−0.578078	+	0.815981i	$0.696197\pi$
$30$			21859.6i			0.809615i
$31$		−	24653.7i		−	0.827554i	−0.910378	−	0.413777i	$-0.864209\pi$
$31$		−	24653.7i		−	0.827554i	0.910378	−	0.413777i	$-0.135791\pi$
$32$		−	92238.9i		−	2.81491i
$33$		−	18521.5i		−	0.515389i
$34$		−	113502.i		−	2.88781i
$35$	55219.3			1.28791
$36$	−40084.1			−0.859141
$37$		−	38798.6i		−	0.765969i	−0.923755	−	0.382984i	$-0.874896\pi$
$37$		−	38798.6i		−	0.765969i	0.923755	−	0.382984i	$-0.125104\pi$
$38$			99453.6i			1.81247i
$39$			18395.2i			0.310107i
$40$		−	141569.i		−	2.21201i
$41$	61352.8			0.890190			0.445095	−	0.895483i	$-0.353170\pi$
$41$	61352.8			0.890190			0.445095	+	0.895483i	$0.353170\pi$
$42$			140542.i			1.89696i
$43$		−	19526.7i		−	0.245597i	−0.992432	−	0.122799i	$-0.960813\pi$
$43$		−	19526.7i		−	0.245597i	0.992432	−	0.122799i	$-0.0391869\pi$
$44$			195993.i			2.30081i
$45$	−22520.1			−0.247134
$46$	151620.			1.55770
$47$		−	60661.5i		−	0.584278i	−0.956376	−	0.292139i	$-0.905633\pi$
$47$		−	60661.5i		−	0.584278i	0.956376	−	0.292139i	$-0.0943670\pi$
$48$	195745.			1.76997
$49$	237372.			2.01762
$50$			106468.i			0.851742i
$51$	116932.			0.881501
$52$		−	194656.i		−	1.38439i
$53$	128781.			0.865018			0.432509	−	0.901630i	$-0.357628\pi$
$53$	128781.			0.865018			0.432509	+	0.901630i	$0.357628\pi$
$54$		−	57317.1i		−	0.364002i
$55$			110113.i			0.661836i
$56$		−	910185.i		−	5.18282i
$57$	−102459.			−0.553253
$58$			426664.i			2.18676i
$59$	65188.5	+	194759.i	0.317406	+	0.948290i
$59$	65188.5	+	194759.i	0.317406	+	0.948290i
$60$	238305.			1.10326
$61$			200868.i			0.884955i	0.896780	+	0.442477i	$0.145900\pi$
$61$			200868.i			0.884955i	−0.896780	+	0.442477i	$0.854100\pi$
$62$	−373041.			−1.56524
$63$	−144788.			−0.579044
$64$	−592041.			−2.25846
$65$		−	109362.i		−	0.398223i
$66$	−280254.			−0.974811
$67$		−	526100.i		−	1.74922i	−0.484829	−	0.874609i	$-0.661118\pi$
$67$		−	526100.i		−	1.74922i	0.484829	−	0.874609i	$-0.338882\pi$
$68$	−1.23736e6			−3.93522
$69$			156201.i			0.475485i
$70$		−	835538.i		−	2.43597i
$71$	123865.			0.346079			0.173039	−	0.984915i	$-0.444641\pi$
$71$	123865.			0.346079			0.173039	+	0.984915i	$0.444641\pi$
$72$			371201.i			0.994516i
$73$			618533.i			1.58999i	0.606616	+	0.794995i	$0.292526\pi$
$73$			618533.i			1.58999i	−0.606616	+	0.794995i	$0.707474\pi$
$74$	−587072.			−1.44876
$75$	−109685.			−0.259993
$76$	1.08420e6			2.46985
$77$			707947.i			1.55070i
$78$	278343.			0.586539
$79$	63990.6			0.129788			0.0648941	−	0.997892i	$-0.479329\pi$
$79$	63990.6			0.129788			0.0648941	+	0.997892i	$0.479329\pi$
$80$	−1.16373e6			−2.27291
$81$	59049.0			0.111111
$82$		−	928345.i		−	1.68371i
$83$		−	513107.i		−	0.897374i	−0.893689	−	0.448687i	$-0.851892\pi$
$83$		−	513107.i		−	0.897374i	0.893689	−	0.448687i	$-0.148108\pi$
$84$	1.53213e6			2.58498
$85$	−695175.			−1.13198
$86$	−295464.			−0.464525
$87$	−439556.			−0.667508
$88$	1.81500e6			2.66336
$89$		−	297297.i		−	0.421716i	−0.977517	−	0.210858i	$-0.932374\pi$
$89$		−	297297.i		−	0.421716i	0.977517	−	0.210858i	$-0.0676258\pi$
$90$			340758.i			0.467432i
$91$		−	703120.i		−	0.933050i
$92$		−	1.65290e6i		−	2.12267i
$93$		−	384313.i		−	0.477789i
$94$	−917885.			−1.10511
$95$	609130.			0.710459
$96$		−	1.43786e6i		−	1.62519i
$97$			1.39038e6i			1.52341i	0.647924	+	0.761705i	$0.275638\pi$
$97$			1.39038e6i			1.52341i	−0.647924	+	0.761705i	$0.724362\pi$
$98$		−	3.59173e6i		−	3.81615i
$99$		−	288722.i		−	0.297560i
$100$	1.16067e6			1.16067
$101$			1.40220e6i			1.36097i	0.732764	+	0.680483i	$0.238230\pi$
$101$			1.40220e6i			1.36097i	−0.732764	+	0.680483i	$0.761770\pi$
$102$		−	1.76933e6i		−	1.66728i
$103$			1.73005e6i			1.58324i	0.611014	+	0.791619i	$0.290762\pi$
$103$			1.73005e6i			1.58324i	−0.611014	+	0.791619i	$0.709238\pi$
$104$	−1.80263e6			−1.60253
$105$	860784.			0.743577
$106$		−	1.94862e6i		−	1.63610i
$107$	719986.			0.587723			0.293862	−	0.955848i	$-0.405059\pi$
$107$	719986.			0.587723			0.293862	+	0.955848i	$0.405059\pi$
$108$	−624849.			−0.496025
$109$			1.47588e6i			1.13965i	0.821767	+	0.569823i	$0.192988\pi$
$109$			1.47588e6i			1.13965i	−0.821767	+	0.569823i	$0.807012\pi$
$110$	1.66615e6			1.25180
$111$		−	604811.i		−	0.442232i
$112$	−7.48194e6			−5.32549
$113$		−	130130.i		−	0.0901868i	−0.998983	−	0.0450934i	$-0.985641\pi$
$113$		−	130130.i		−	0.0901868i	0.998983	−	0.0450934i	$-0.0143585\pi$
$114$			1.55033e6i			1.04643i
$115$		−	928636.i		−	0.610593i
$116$	4.65132e6			2.97990
$117$			286754.i			0.179040i
$118$	2.94695e6	−	986384.i	1.79360	−	0.600344i
$119$	−4.46948e6			−2.65226
$120$		−	2.20684e6i		−	1.27711i
$121$	359843.			0.203122
$122$	3.03939e6			1.67381
$123$	956395.			0.513952
$124$			4.06675e6i			2.13296i
$125$	2.10014e6			1.07527
$126$			2.19083e6i			1.09521i
$127$	3.38640e6			1.65321			0.826603	−	0.562785i	$-0.190270\pi$
$127$	3.38640e6			1.65321			0.826603	+	0.562785i	$0.190270\pi$
$128$			3.05503e6i			1.45675i
$129$		−	304391.i		−	0.141796i
$130$	−1.65479e6			−0.753203
$131$			1.57313e6i			0.699761i	0.936794	+	0.349881i	$0.113778\pi$
$131$			1.57313e6i			0.699761i	−0.936794	+	0.349881i	$0.886222\pi$
$132$			3.05522e6i			1.32838i
$133$	3.91627e6			1.66463
$134$	−7.96056e6			−3.30848
$135$	−351054.			−0.142683
$136$			1.14586e7i			4.55529i
$137$	−3.59610e6			−1.39853			−0.699263	−	0.714865i	$-0.746488\pi$
$137$	−3.59610e6			−1.39853			−0.699263	+	0.714865i	$0.746488\pi$
$138$	2.36352e6			0.899337
$139$	−3.36752e6			−1.25391			−0.626954	−	0.779056i	$-0.715699\pi$
$139$	−3.36752e6			−1.25391			−0.626954	+	0.779056i	$0.715699\pi$
$140$	−9.10870e6			−3.31950
$141$		−	945620.i		−	0.337333i
$142$		−	1.87424e6i		−	0.654576i
$143$	1.40209e6			0.479478
$144$	3.05136e6			1.02189
$145$	2.61321e6			0.857178
$146$	9.35918e6			3.00732
$147$	3.70026e6			1.16488
$148$			6.40003e6i			1.97423i
$149$			3.49052e6i			1.05519i	0.849495	+	0.527596i	$0.176906\pi$
$149$			3.49052e6i			1.05519i	−0.849495	+	0.527596i	$0.823094\pi$
$150$			1.65967e6i			0.491754i
$151$			6.31660e6i			1.83465i	0.398142	+	0.917324i	$0.369655\pi$
$151$			6.31660e6i			1.83465i	−0.398142	+	0.917324i	$0.630345\pi$
$152$		−	1.00403e7i		−	2.85902i
$153$	1.82279e6			0.508935
$154$	1.07121e7			2.93301
$155$			2.28479e6i			0.613551i
$156$		−	3.03439e6i		−	0.799277i
$157$		−	1.08459e6i		−	0.280264i	−0.990133	−	0.140132i	$-0.955247\pi$
$157$		−	1.08459e6i		−	0.280264i	0.990133	−	0.140132i	$-0.0447528\pi$
$158$		−	968259.i		−	0.245482i
$159$	2.00750e6			0.499418
$160$			8.54827e6i			2.08698i
$161$		−	5.97046e6i		−	1.43064i
$162$		−	893486.i		−	0.210156i
$163$	3.99116e6			0.921588			0.460794	−	0.887507i	$-0.347565\pi$
$163$	3.99116e6			0.921588			0.460794	+	0.887507i	$0.347565\pi$
$164$	−1.01205e7			−2.29440
$165$			1.71649e6i			0.382111i
$166$	−7.76395e6			−1.69730
$167$	−119449.			−0.0256469			−0.0128234	−	0.999918i	$-0.504082\pi$
$167$	−119449.			−0.0256469			−0.0128234	+	0.999918i	$0.504082\pi$
$168$		−	1.41884e7i		−	2.99230i
$169$	3.43428e6			0.711501
$170$			1.05189e7i			2.14103i
$171$	−1.59717e6			−0.319421
$172$			3.22103e6i			0.633008i
$173$		−	4.96046e6i		−	0.958040i	−0.877804	−	0.479020i	$-0.840992\pi$
$173$		−	4.96046e6i		−	0.958040i	0.877804	−	0.479020i	$-0.159008\pi$
$174$			6.65103e6i			1.26253i
$175$	4.19247e6			0.782268
$176$		−	1.49197e7i		−	2.73668i
$177$	1.01619e6	+	3.03599e6i	0.183254	+	0.547495i
$178$	−4.49847e6			−0.797637
$179$		−	9.53711e6i		−	1.66287i	−0.555624	−	0.831434i	$-0.687520\pi$
$179$		−	9.53711e6i		−	1.66287i	0.555624	−	0.831434i	$-0.312480\pi$
$180$	3.71481e6			0.636969
$181$	−6.69436e6			−1.12895			−0.564473	−	0.825452i	$-0.690921\pi$
$181$	−6.69436e6			−1.12895			−0.564473	+	0.825452i	$0.690921\pi$
$182$	−1.06391e7			−1.76478
$183$			3.13122e6i			0.510929i
$184$	−1.53068e7			−2.45715
$185$			3.59568e6i			0.567892i
$186$	−5.81513e6			−0.903693
$187$		−	8.91259e6i		−	1.36295i
$188$			1.00064e7i			1.50593i
$189$	−2.25702e6			−0.334311
$190$		−	9.21690e6i		−	1.34377i
$191$			8.32841e6i			1.19526i	0.801773	+	0.597629i	$0.203891\pi$
$191$			8.32841e6i			1.19526i	−0.801773	+	0.597629i	$0.796109\pi$
$192$	−9.22900e6			−1.30392
$193$	9.49958e6			1.32140			0.660698	−	0.750652i	$-0.270261\pi$
$193$	9.49958e6			1.32140			0.660698	+	0.750652i	$0.270261\pi$
$194$	2.10381e7			2.88139
$195$		−	1.70479e6i		−	0.229914i
$196$	−3.91556e7			−5.20027
$197$	2.34210e6			0.306342			0.153171	−	0.988200i	$-0.451051\pi$
$197$	2.34210e6			0.306342			0.153171	+	0.988200i	$0.451051\pi$
$198$	−4.36873e6			−0.562807
$199$	−7.24381e6			−0.919196			−0.459598	−	0.888127i	$-0.652006\pi$
$199$	−7.24381e6			−0.919196			−0.459598	+	0.888127i	$0.652006\pi$
$200$		−	1.07485e7i		−	1.34356i
$201$		−	8.20109e6i		−	1.00991i
$202$	2.12171e7			2.57414
$203$	1.68011e7			2.00840
$204$	−1.92885e7			−2.27200
$205$	−5.68589e6			−0.659990
$206$	2.61778e7			2.99455
$207$			2.43494e6i			0.274522i
$208$			1.48180e7i			1.64664i
$209$			7.80944e6i			0.855423i
$210$		−	1.30247e7i		−	1.40641i
$211$		−	8.80392e6i		−	0.937192i	−0.883413	−	0.468596i	$-0.844760\pi$
$211$		−	8.80392e6i		−	0.937192i	0.883413	−	0.468596i	$-0.155240\pi$
$212$	−2.12431e7			−2.22952
$213$	1.93087e6			0.199809
$214$		−	1.08943e7i		−	1.11162i
$215$			1.80964e6i			0.182087i
$216$			5.78645e6i			0.574184i
$217$			1.46895e7i			1.43757i
$218$	2.23319e7			2.15554
$219$			9.64197e6i			0.917981i
$220$		−	1.81637e7i		−	1.70583i
$221$			8.85182e6i			0.820079i
$222$	−9.15155e6			−0.836442
$223$	−5.42731e6			−0.489407			−0.244703	−	0.969598i	$-0.578691\pi$
$223$	−5.42731e6			−0.489407			−0.244703	+	0.969598i	$0.578691\pi$
$224$			5.49593e7i			4.88987i
$225$	−1.70982e6			−0.150107
$226$	−1.96903e6			−0.170580
$227$			3.67832e6i			0.314464i	0.987562	+	0.157232i	$0.0502571\pi$
$227$			3.67832e6i			0.314464i	−0.987562	+	0.157232i	$0.949743\pi$
$228$	1.69011e7			1.42597
$229$		−	1.67437e7i		−	1.39426i	−0.716943	−	0.697132i	$-0.754459\pi$
$229$		−	1.67437e7i		−	1.39426i	0.716943	−	0.697132i	$-0.245541\pi$
$230$	−1.40514e7			−1.15488
$231$			1.10358e7i			0.895299i
$232$		−	4.30739e7i		−	3.44945i
$233$			1.79137e7i			1.41618i	0.706124	+	0.708088i	$0.250442\pi$
$233$			1.79137e7i			1.41618i	−0.706124	+	0.708088i	$0.749558\pi$
$234$	4.33894e6			0.338638
$235$			5.62183e6i			0.433186i
$236$	−1.07532e7	−	3.21264e7i	−0.818089	−	2.44414i
$237$	997515.			0.0749332
$238$			6.76288e7i			5.01650i
$239$	7.08766e6			0.519170			0.259585	−	0.965720i	$-0.416414\pi$
$239$	7.08766e6			0.519170			0.259585	+	0.965720i	$0.416414\pi$
$240$	−1.81407e7			−1.31226
$241$	−1.91122e7			−1.36540			−0.682699	−	0.730700i	$-0.739194\pi$
$241$	−1.91122e7			−1.36540			−0.682699	+	0.730700i	$0.739194\pi$
$242$		−	5.44487e6i		−	0.384186i
$243$	920483.			0.0641500
$244$		−	3.31342e7i		−	2.28090i
$245$	−2.19985e7			−1.49587
$246$		−	1.44715e7i		−	0.972092i
$247$		−	7.75618e6i		−	0.514704i
$248$	3.76604e7			2.46905
$249$		−	7.99854e6i		−	0.518099i
$250$		−	3.17778e7i		−	2.03378i
$251$	−1.00728e7			−0.636984			−0.318492	−	0.947926i	$-0.603176\pi$
$251$	−1.00728e7			−0.636984			−0.318492	+	0.947926i	$0.603176\pi$
$252$	2.38835e7			1.49244
$253$	1.19057e7			0.735180
$254$		−	5.12405e7i		−	3.12689i
$255$	−1.08367e7			−0.653547
$256$	8.33583e6			0.496854
$257$	−2.64289e7			−1.55697			−0.778483	−	0.627666i	$-0.784011\pi$
$257$	−2.64289e7			−1.55697			−0.778483	+	0.627666i	$0.784011\pi$
$258$	−4.60582e6			−0.268193
$259$			2.31176e7i			1.33059i
$260$			1.80398e7i			1.02639i
$261$	−6.85200e6			−0.385386
$262$	2.38034e7			1.32353
$263$	−9.07873e6			−0.499066			−0.249533	−	0.968366i	$-0.580277\pi$
$263$	−9.07873e6			−0.499066			−0.249533	+	0.968366i	$0.580277\pi$
$264$	2.82931e7			1.53769
$265$	−1.19349e7			−0.641327
$266$		−	5.92581e7i		−	3.14849i
$267$		−	4.63440e6i		−	0.243478i
$268$			8.67828e7i			4.50847i
$269$		−	3.68828e6i		−	0.189482i	−0.995502	−	0.0947409i	$-0.969798\pi$
$269$		−	3.68828e6i		−	0.189482i	0.995502	−	0.0947409i	$-0.0302023\pi$
$270$			5.31189e6i			0.269872i
$271$	2.96429e7			1.48941			0.744703	−	0.667396i	$-0.232591\pi$
$271$	2.96429e7			1.48941			0.744703	+	0.667396i	$0.232591\pi$
$272$	9.41927e7			4.68070
$273$		−	1.09606e7i		−	0.538697i
$274$			5.44136e7i			2.64518i
$275$			8.36021e6i			0.401994i
$276$		−	2.57662e7i		−	1.22553i
$277$	−3.08538e7			−1.45167			−0.725837	−	0.687867i	$-0.758547\pi$
$277$	−3.08538e7			−1.45167			−0.725837	+	0.687867i	$0.758547\pi$
$278$			5.09548e7i			2.37165i
$279$		−	5.99084e6i		−	0.275851i
$280$			8.43517e7i			3.84255i
$281$	3.94507e7			1.77802			0.889008	−	0.457892i	$-0.151396\pi$
$281$	3.94507e7			1.77802			0.889008	+	0.457892i	$0.151396\pi$
$282$	−1.43084e7			−0.638035
$283$		−	2.68048e7i		−	1.18264i	−0.806436	−	0.591322i	$-0.798606\pi$
$283$		−	2.68048e7i		−	1.18264i	0.806436	−	0.591322i	$-0.201394\pi$
$284$	−2.04322e7			−0.891991
$285$	9.49539e6			0.410184
$286$		−	2.12154e7i		−	0.906888i
$287$	−3.65562e7			−1.54638
$288$		−	2.24141e7i		−	0.938303i
$289$	3.21302e7			1.33113
$290$		−	3.95412e7i		−	1.62127i
$291$			2.16738e7i			0.879542i
$292$		−	1.02030e8i		−	4.09807i
$293$	1.18646e7			0.471683			0.235842	−	0.971792i	$-0.424215\pi$
$293$	1.18646e7			0.471683			0.235842	+	0.971792i	$0.424215\pi$
$294$		−	5.59895e7i		−	2.20326i
$295$	−6.04137e6	−	1.80493e7i	−0.235326	−	0.703065i
$296$	5.92679e7			2.28531
$297$		−	4.50074e6i		−	0.171796i
$298$	5.28160e7			1.99580
$299$	−1.18245e7			−0.442354
$300$	1.80931e7			0.670113
$301$			1.16347e7i			0.426635i
$302$	9.55781e7			3.47007
$303$			2.18582e7i			0.785754i
$304$	−8.25340e7			−2.93773
$305$		−	1.86155e7i		−	0.656108i
$306$		−	2.75811e7i		−	0.962603i
$307$	2.24412e7			0.775587			0.387793	−	0.921746i	$-0.373237\pi$
$307$	2.24412e7			0.775587			0.387793	+	0.921746i	$0.373237\pi$
$308$		−	1.16779e8i		−	3.99682i
$309$			2.69688e7i			0.914083i
$310$	3.45717e7			1.16047
$311$	−4.88319e7			−1.62339			−0.811695	−	0.584082i	$-0.801455\pi$
$311$	−4.88319e7			−1.62339			−0.811695	+	0.584082i	$0.801455\pi$
$312$	−2.81002e7			−0.925220
$313$		−	3.07669e7i		−	1.00335i	−0.865057	−	0.501674i	$-0.832718\pi$
$313$		−	3.07669e7i		−	1.00335i	0.865057	−	0.501674i	$-0.167282\pi$
$314$	−1.64113e7			−0.530094
$315$	1.34183e7			0.429305
$316$	−1.05556e7			−0.334519
$317$	5.20357e6			0.163352			0.0816759	−	0.996659i	$-0.473973\pi$
$317$	5.20357e6			0.163352			0.0816759	+	0.996659i	$0.473973\pi$
$318$		−	3.03760e7i		−	0.944604i
$319$			3.35031e7i			1.03208i
$320$	5.48676e7			1.67443
$321$	1.12235e7			0.339322
$322$	−9.03406e7			−2.70592
$323$	−4.93033e7			−1.46308
$324$	−9.74043e6			−0.286380
$325$		−	8.30320e6i		−	0.241878i
$326$		−	6.03914e7i		−	1.74310i
$327$			2.30066e7i			0.657975i
$328$			9.37211e7i			2.65593i
$329$			3.61443e7i			1.01497i
$330$	2.59727e7			0.722728
$331$	7.01782e6			0.193517			0.0967583	−	0.995308i	$-0.469153\pi$
$331$	7.01782e6			0.193517			0.0967583	+	0.995308i	$0.469153\pi$
$332$			8.46395e7i			2.31291i
$333$		−	9.42807e6i		−	0.255323i
$334$			1.80742e6i			0.0485087i
$335$			4.87565e7i			1.29687i
$336$	−1.16632e8			−3.07468
$337$			5.80128e7i			1.51577i	0.652387	+	0.757886i	$0.273768\pi$
$337$			5.80128e7i			1.51577i	−0.652387	+	0.757886i	$0.726232\pi$
$338$		−	5.19649e7i		−	1.34574i
$339$		−	2.02853e6i		−	0.0520694i
$340$	1.14673e8			2.91758
$341$	−2.92924e7			−0.738741
$342$			2.41672e7i			0.604155i
$343$	−7.13350e7			−1.76775
$344$	2.98285e7			0.732751
$345$		−	1.44760e7i		−	0.352526i
$346$	−7.50580e7			−1.81204
$347$			1.15980e7i			0.277585i	0.990322	+	0.138792i	$0.0443220\pi$
$347$			1.15980e7i			0.277585i	−0.990322	+	0.138792i	$0.955678\pi$
$348$	7.25069e7			1.72045
$349$			536779.i			0.0126275i	0.999980	+	0.00631377i	$0.00200975\pi$
$349$			536779.i			0.0126275i	−0.999980	+	0.00631377i	$0.997990\pi$
$350$		−	6.34373e7i		−	1.47959i
$351$			4.47005e6i			0.103369i
$352$	−1.09594e8			−2.51281
$353$		−	6.84752e7i		−	1.55672i	−0.627821	−	0.778358i	$-0.716053\pi$
$353$		−	6.84752e7i		−	1.55672i	0.627821	−	0.778358i	$-0.283947\pi$
$354$	4.59383e7	−	1.53762e7i	1.03554	−	0.346609i
$355$	−1.14793e7			−0.256584
$356$			4.90406e7i			1.08694i
$357$	−6.96723e7			−1.53128
$358$	−1.44309e8			−3.14516
$359$	−1.42567e6			−0.0308131			−0.0154066	−	0.999881i	$-0.504904\pi$
$359$	−1.42567e6			−0.0308131			−0.0154066	+	0.999881i	$0.504904\pi$
$360$		−	3.44012e7i		−	0.737337i
$361$	−3.84514e6			−0.0817317
$362$			1.01294e8i			2.13530i
$363$	5.60939e6			0.117272
$364$			1.15983e8i			2.40486i
$365$		−	5.73228e7i		−	1.17882i
$366$	4.73793e7			0.966375
$367$			5.92009e7i			1.19765i	0.800880	+	0.598826i	$0.204366\pi$
$367$			5.92009e7i			1.19765i	−0.800880	+	0.598826i	$0.795634\pi$
$368$			1.25825e8i			2.52479i
$369$	1.49087e7			0.296730
$370$	5.44071e7			1.07411
$371$	−7.67325e7			−1.50265
$372$			6.33943e7i			1.23146i
$373$	4.76153e7			0.917530			0.458765	−	0.888558i	$-0.348292\pi$
$373$	4.76153e7			0.917530			0.458765	+	0.888558i	$0.348292\pi$
$374$	−1.34859e8			−2.57789
$375$	3.27380e7			0.620809
$376$	9.26651e7			1.74322
$377$		−	3.32746e7i		−	0.620997i
$378$			3.41516e7i			0.632318i
$379$	4.30636e7			0.791029			0.395515	−	0.918460i	$-0.370566\pi$
$379$	4.30636e7			0.791029			0.395515	+	0.918460i	$0.370566\pi$
$380$	−1.00479e8			−1.83115
$381$	5.27888e7			0.954479
$382$	1.26019e8			2.26072
$383$	−5.11356e7			−0.910180			−0.455090	−	0.890446i	$-0.650393\pi$
$383$	−5.11356e7			−0.910180			−0.455090	+	0.890446i	$0.650393\pi$
$384$			4.76232e7i			0.841056i
$385$		−	6.56092e7i		−	1.14970i
$386$		−	1.43741e8i		−	2.49930i
$387$		−	4.74499e6i		−	0.0818658i
$388$		−	2.29349e8i		−	3.92647i
$389$	−8.81530e7			−1.49757			−0.748787	−	0.662811i	$-0.769363\pi$
$389$	−8.81530e7			−1.49757			−0.748787	+	0.662811i	$0.769363\pi$
$390$	−2.57956e7			−0.434862
$391$			7.51642e7i			1.25742i
$392$			3.62603e8i			6.01968i
$393$			2.45226e7i			0.404007i
$394$		−	3.54389e7i		−	0.579418i
$395$	−5.93035e6			−0.0962253
$396$			4.76262e7i			0.766938i
$397$			1.55026e7i			0.247762i	0.992297	+	0.123881i	$0.0395341\pi$
$397$			1.55026e7i			0.247762i	−0.992297	+	0.123881i	$0.960466\pi$
$398$			1.09608e8i			1.73857i
$399$	6.10486e7			0.961074
$400$	−8.83548e7			−1.38054
$401$		−	2.07907e7i		−	0.322430i	−0.986919	−	0.161215i	$-0.948459\pi$
$401$		−	2.07907e7i		−	0.322430i	0.986919	−	0.161215i	$-0.0515413\pi$
$402$	−1.24093e8			−1.91015
$403$	2.90927e7			0.444497
$404$		−	2.31301e8i		−	3.50778i
$405$	−5.47239e6			−0.0823781
$406$		−	2.54222e8i		−	3.79870i
$407$	−4.60989e7			−0.683765
$408$			1.78623e8i			2.63000i
$409$		−	6.42981e7i		−	0.939784i	−0.882724	−	0.469892i	$-0.844293\pi$
$409$		−	6.42981e7i		−	0.939784i	0.882724	−	0.469892i	$-0.155707\pi$
$410$			8.60347e7i			1.24831i
$411$	−5.60577e7			−0.807439
$412$		−	2.85380e8i		−	4.08068i
$413$	−3.88416e7	−	1.16044e8i	−0.551376	−	1.64730i
$414$	3.68436e7			0.519232
$415$			4.75523e7i			0.665315i
$416$	1.08847e8			1.51195
$417$	−5.24945e7			−0.723945
$418$	1.18167e8			1.61795
$419$			1.31802e8i			1.79176i	0.444293	+	0.895882i	$0.353455\pi$
$419$			1.31802e8i			1.79176i	−0.444293	+	0.895882i	$0.646545\pi$
$420$	−1.41991e8			−1.91651
$421$			1.19244e8i			1.59805i	0.601297	+	0.799026i	$0.294651\pi$
$421$			1.19244e8i			1.59805i	−0.601297	+	0.799026i	$0.705349\pi$
$422$	−1.33214e8			−1.77261
$423$		−	1.47408e7i		−	0.194759i
$424$			1.96723e8i			2.58082i
$425$	−5.27804e7			−0.687553
$426$		−	2.92165e7i		−	0.377920i
$427$		−	1.19684e8i		−	1.53728i
$428$	−1.18765e8			−1.51481
$429$	2.18565e7			0.276827
$430$	2.73822e7			0.344400
$431$		−	3.54230e7i		−	0.442439i	−0.975224	−	0.221219i	$-0.928996\pi$
$431$		−	3.54230e7i		−	0.442439i	0.975224	−	0.221219i	$-0.0710037\pi$
$432$	4.75660e7			0.589991
$433$	7.84185e7			0.965950			0.482975	−	0.875634i	$-0.339556\pi$
$433$	7.84185e7			0.965950			0.482975	+	0.875634i	$0.339556\pi$
$434$	2.22271e8			2.71903
$435$	4.07360e7			0.494892
$436$		−	2.43453e8i		−	2.93735i
$437$		−	6.58608e7i		−	0.789192i
$438$	1.45895e8			1.73628
$439$	−2.27293e7			−0.268654			−0.134327	−	0.990937i	$-0.542887\pi$
$439$	−2.27293e7			−0.268654			−0.134327	+	0.990937i	$0.542887\pi$
$440$	−1.68206e8			−1.97462
$441$	5.76813e7			0.672542
$442$	1.33939e8			1.55110
$443$		−	2.48221e7i		−	0.285514i	−0.989758	−	0.142757i	$-0.954403\pi$
$443$		−	2.48221e7i		−	0.285514i	0.989758	−	0.142757i	$-0.0455968\pi$
$444$			9.97666e7i			1.13982i
$445$			2.75521e7i			0.312662i
$446$			8.21221e7i			0.925668i
$447$			5.44118e7i			0.609215i
$448$	3.52759e8			3.92323
$449$	1.38674e8			1.53199			0.765995	−	0.642846i	$-0.222247\pi$
$449$	1.38674e8			1.53199			0.765995	+	0.642846i	$0.222247\pi$
$450$			2.58717e7i			0.283914i
$451$		−	7.28968e7i		−	0.794655i
$452$			2.14656e7i			0.232449i
$453$			9.84661e7i			1.05923i
$454$	5.56576e7			0.594780
$455$			6.51619e7i			0.691766i
$456$		−	1.56513e8i		−	1.65066i
$457$			3.89150e7i			0.407726i	0.978999	+	0.203863i	$0.0653498\pi$
$457$			3.89150e7i			0.407726i	−0.978999	+	0.203863i	$0.934650\pi$
$458$	−2.53353e8			−2.63712
$459$	2.84145e7			0.293834
$460$			1.53183e8i			1.57376i
$461$	1.46047e8			1.49070			0.745349	−	0.666675i	$-0.232283\pi$
$461$	1.46047e8			1.49070			0.745349	+	0.666675i	$0.232283\pi$
$462$	1.66986e8			1.69337
$463$		−	8.54558e7i		−	0.860991i	−0.902593	−	0.430496i	$-0.858339\pi$
$463$		−	8.54558e7i		−	0.860991i	0.902593	−	0.430496i	$-0.141661\pi$
$464$	−3.54077e8			−3.54441
$465$			3.56163e7i			0.354234i
$466$	2.71057e8			2.67857
$467$			1.88192e8i			1.84778i	0.382656	+	0.923891i	$0.375009\pi$
$467$			1.88192e8i			1.84778i	−0.382656	+	0.923891i	$0.624991\pi$
$468$		−	4.73014e7i		−	0.461463i
$469$			3.13469e8i			3.03862i
$470$	8.50653e7			0.819330
$471$		−	1.69071e7i		−	0.161811i
$472$	−2.97509e8	+	9.95804e7i	−2.82927	+	0.946996i
$473$	−2.32008e7			−0.219240
$474$		−	1.50937e7i		−	0.141729i
$475$	4.62475e7			0.431527
$476$	7.37263e8			6.83599
$477$	3.12939e7			0.288339
$478$		−	1.07245e8i		−	0.981962i
$479$	1.84353e8			1.67743			0.838713	−	0.544573i	$-0.183308\pi$
$479$	1.84353e8			1.67743			0.838713	+	0.544573i	$0.183308\pi$
$480$			1.33254e8i			1.20492i
$481$	4.57845e7			0.411418
$482$			2.89191e8i			2.58252i
$483$		−	9.30703e7i		−	0.825980i
$484$	−5.93578e7			−0.523531
$485$		−	1.28854e8i		−	1.12946i
$486$		−	1.39281e7i		−	0.121334i
$487$	4.40439e6			0.0381328			0.0190664	−	0.999818i	$-0.493931\pi$
$487$	4.40439e6			0.0381328			0.0190664	+	0.999818i	$0.493931\pi$
$488$	−3.06841e8			−2.64031
$489$	6.22161e7			0.532079
$490$			3.32865e8i			2.82931i
$491$	−1.86538e8			−1.57588			−0.787941	−	0.615751i	$-0.788853\pi$
$491$	−1.86538e8			−1.57588			−0.787941	+	0.615751i	$0.788853\pi$
$492$	−1.57762e8			−1.32467
$493$	−2.11515e8			−1.76522
$494$	−1.17361e8			−0.973514
$495$			2.67574e7i			0.220612i
$496$		−	3.09577e8i		−	2.53702i
$497$	−7.38034e7			−0.601184
$498$	−1.21028e8			−0.979936
$499$	1.68862e8			1.35904			0.679518	−	0.733659i	$-0.262189\pi$
$499$	1.68862e8			1.35904			0.679518	+	0.733659i	$0.262189\pi$
$500$	−3.46429e8			−2.77143
$501$	−1.86203e6			−0.0148072
$502$			1.52414e8i			1.20480i
$503$			5.98804e7i			0.470523i	0.971932	+	0.235262i	$0.0755947\pi$
$503$			5.98804e7i			0.470523i	−0.971932	+	0.235262i	$0.924405\pi$
$504$		−	2.21175e8i		−	1.72761i
$505$		−	1.29950e8i		−	1.00902i
$506$		−	1.80148e8i		−	1.39053i
$507$	5.35351e7			0.410785
$508$	−5.58604e8			−4.26101
$509$			9.59701e7i			0.727751i	0.931448	+	0.363875i	$0.118547\pi$
$509$			9.59701e7i			0.727751i	−0.931448	+	0.363875i	$0.881453\pi$
$510$			1.63973e8i			1.23612i
$511$		−	3.68544e8i		−	2.76202i
$512$			6.93902e7i			0.516997i
$513$	−2.48975e7			−0.184418
$514$			3.99902e8i			2.94486i
$515$		−	1.60333e8i		−	1.17382i
$516$			5.02109e7i			0.365467i
$517$	−7.20755e7			−0.521574
$518$	3.49799e8			2.51669
$519$		−	7.73259e7i		−	0.553125i
$520$	1.67059e8			1.18812
$521$	4.20956e7			0.297662			0.148831	−	0.988863i	$-0.452449\pi$
$521$	4.20956e7			0.297662			0.148831	+	0.988863i	$0.452449\pi$
$522$			1.03679e8i			0.728921i
$523$	−7.93657e7			−0.554789			−0.277395	−	0.960756i	$-0.589471\pi$
$523$	−7.93657e7			−0.554789			−0.277395	+	0.960756i	$0.589471\pi$
$524$		−	2.59495e8i		−	1.80358i
$525$	6.53541e7			0.451643
$526$			1.37373e8i			0.943936i
$527$		−	1.84932e8i		−	1.26351i
$528$		−	2.32576e8i		−	1.58002i
$529$	4.76292e7			0.321741
$530$			1.80589e8i			1.21301i
$531$	1.58408e7	+	4.73264e7i	0.105802	+	0.316097i
$532$	−6.46008e8			−4.29045
$533$			7.23997e7i			0.478140i
$534$	−7.01243e7			−0.460516
$535$	−6.67250e7			−0.435740
$536$	8.03658e8			5.21888
$537$		−	1.48669e8i		−	0.960057i
$538$	−5.58084e7			−0.358387
$539$		−	2.82035e8i		−	1.80109i
$540$	5.79081e7			0.367754
$541$			9.87052e7i			0.623373i	0.950185	+	0.311687i	$0.100894\pi$
$541$			9.87052e7i			0.623373i	−0.950185	+	0.311687i	$0.899106\pi$
$542$		−	4.48535e8i		−	2.81707i
$543$	−1.04355e8			−0.651797
$544$		−	6.91901e8i		−	4.29781i
$545$		−	1.36777e8i		−	0.844937i
$546$	−1.65847e8			−1.01890
$547$	2.02839e8			1.23934			0.619670	−	0.784863i	$-0.287267\pi$
$547$	2.02839e8			1.23934			0.619670	+	0.784863i	$0.287267\pi$
$548$	5.93195e8			3.60459
$549$			4.88109e7i			0.294985i
$550$	1.26500e8			0.760334
$551$	1.85335e8			1.10790
$552$	−2.38609e8			−1.41863
$553$	−3.81279e7			−0.225459
$554$			4.66857e8i			2.74571i
$555$			5.60510e7i			0.327872i
$556$	5.55490e8			3.23185
$557$	−1.45125e8			−0.839799			−0.419900	−	0.907571i	$-0.637935\pi$
$557$	−1.45125e8			−0.839799			−0.419900	+	0.907571i	$0.637935\pi$
$558$	−9.06490e7			−0.521747
$559$	2.30426e7			0.131916
$560$	6.93391e8			3.94834
$561$		−	1.38934e8i		−	0.786898i
$562$		−	5.96938e8i		−	3.36295i
$563$			5.96255e7i			0.334123i	0.985946	+	0.167062i	$0.0534279\pi$
$563$			5.96255e7i			0.334123i	−0.985946	+	0.167062i	$0.946572\pi$
$564$			1.55985e8i			0.869450i
$565$			1.20599e7i			0.0668647i
$566$	−4.05591e8			−2.23686
$567$	−3.51835e7			−0.193015
$568$			1.89214e8i			1.03254i
$569$			1.89340e8i			1.02779i	0.857853	+	0.513895i	$0.171798\pi$
$569$			1.89340e8i			1.02779i	−0.857853	+	0.513895i	$0.828202\pi$
$570$		−	1.43677e8i		−	0.775825i
$571$		−	1.06328e8i		−	0.571134i	−0.958359	−	0.285567i	$-0.907818\pi$
$571$		−	1.06328e8i		−	0.571134i	0.958359	−	0.285567i	$-0.0921819\pi$
$572$	−2.31282e8			−1.23582
$573$			1.29827e8i			0.690083i
$574$			5.53141e8i			2.92483i
$575$		−	7.05057e7i		−	0.370869i
$576$	−1.43866e8			−0.752818
$577$	5.19980e7			0.270682			0.135341	−	0.990799i	$-0.456787\pi$
$577$	5.19980e7			0.270682			0.135341	+	0.990799i	$0.456787\pi$
$578$		−	4.86171e8i		−	2.51771i
$579$	1.48084e8			0.762908
$580$	−4.31063e8			−2.20931
$581$			3.05727e8i			1.55886i
$582$	3.27952e8			1.66357
$583$		−	1.53012e8i		−	0.772185i
$584$	−9.44857e8			−4.74381
$585$		−	2.65750e7i		−	0.132741i
$586$		−	1.79526e8i		−	0.892145i
$587$			1.55758e8i			0.770079i	0.922900	+	0.385040i	$0.125812\pi$
$587$			1.55758e8i			0.770079i	−0.922900	+	0.385040i	$0.874188\pi$
$588$	−6.10376e8			−3.00238
$589$			1.62042e8i			0.793015i
$590$	−2.73109e8	+	9.14135e7i	−1.32978	+	0.445096i
$591$	3.65097e7			0.176867
$592$		−	4.87196e8i		−	2.34822i
$593$	−2.00518e8			−0.961590			−0.480795	−	0.876833i	$-0.659652\pi$
$593$	−2.00518e8			−0.961590			−0.480795	+	0.876833i	$0.659652\pi$
$594$	−6.81018e7			−0.324937
$595$	4.14210e8			1.96639
$596$		−	5.75779e8i		−	2.71967i
$597$	−1.12920e8			−0.530698
$598$			1.78920e8i			0.836672i
$599$	1.37449e8			0.639532			0.319766	−	0.947497i	$-0.396396\pi$
$599$	1.37449e8			0.639532			0.319766	+	0.947497i	$0.396396\pi$
$600$		−	1.67552e8i		−	0.775703i
$601$			8.17326e7i			0.376506i	0.982121	+	0.188253i	$0.0602825\pi$
$601$			8.17326e7i			0.376506i	−0.982121	+	0.188253i	$0.939717\pi$
$602$	1.76048e8			0.806940
$603$		−	1.27842e8i		−	0.583073i
$604$		−	1.04196e9i		−	4.72866i
$605$	−3.33485e7			−0.150595
$606$	3.30742e8			1.48618
$607$	2.19240e8			0.980287			0.490144	−	0.871642i	$-0.336944\pi$
$607$	2.19240e8			0.980287			0.490144	+	0.871642i	$0.336944\pi$
$608$			6.06261e8i			2.69742i
$609$	2.61903e8			1.15955
$610$	−2.81676e8			−1.24097
$611$	7.15840e7			0.313828
$612$	−3.00678e8			−1.31174
$613$			2.72141e8i			1.18144i	0.806875	+	0.590722i	$0.201157\pi$
$613$			2.72141e8i			1.18144i	−0.806875	+	0.590722i	$0.798843\pi$
$614$		−	3.39563e8i		−	1.46695i
$615$	−8.86343e7			−0.381045
$616$	−1.08144e9			−4.62660
$617$	2.19651e8			0.935141			0.467570	−	0.883956i	$-0.345129\pi$
$617$	2.19651e8			0.935141			0.467570	+	0.883956i	$0.345129\pi$
$618$	4.08072e8			1.72890
$619$	−1.55922e7			−0.0657407			−0.0328703	−	0.999460i	$-0.510465\pi$
$619$	−1.55922e7			−0.0657407			−0.0328703	+	0.999460i	$0.510465\pi$
$620$		−	3.76887e8i		−	1.58138i
$621$			3.79569e7i			0.158495i
$622$			7.38889e8i			3.07049i
$623$			1.77140e8i			0.732576i
$624$			2.30990e8i			0.950690i
$625$	−8.46895e7			−0.346888
$626$	−4.65543e8			−1.89774
$627$			1.21737e8i			0.493879i
$628$			1.78909e8i			0.722360i
$629$		−	2.91036e8i		−	1.16948i
$630$		−	2.03036e8i		−	0.811990i
$631$	2.72913e8			1.08627			0.543133	−	0.839647i	$-0.317238\pi$
$631$	2.72913e8			1.08627			0.543133	+	0.839647i	$0.317238\pi$
$632$			9.77506e7i			0.387229i
$633$		−	1.37239e8i		−	0.541088i
$634$		−	7.87366e7i		−	0.308965i
$635$	−3.13836e8			−1.22569
$636$	−3.31148e8			−1.28721
$637$			2.80112e8i			1.08371i
$638$	5.06944e8			1.95208
$639$	3.00993e7			0.115360
$640$		−	2.83126e8i		−	1.08004i
$641$	−1.14939e8			−0.436408			−0.218204	−	0.975903i	$-0.570020\pi$
$641$	−1.14939e8			−0.436408			−0.218204	+	0.975903i	$0.570020\pi$
$642$		−	1.69825e8i		−	0.641797i
$643$	6.33589e7			0.238328			0.119164	−	0.992875i	$-0.461979\pi$
$643$	6.33589e7			0.238328			0.119164	+	0.992875i	$0.461979\pi$
$644$			9.84858e8i			3.68736i
$645$			2.82096e7i			0.105128i
$646$			7.46020e8i			2.76728i
$647$	−1.82038e8			−0.672124			−0.336062	−	0.941840i	$-0.609095\pi$
$647$	−1.82038e8			−0.672124			−0.336062	+	0.941840i	$0.609095\pi$
$648$			9.02019e7i			0.331505i
$649$	2.31404e8	−	7.74542e7i	0.846520	−	0.283342i
$650$	−1.25638e8			−0.457489
$651$			2.28987e8i			0.829981i
$652$	−6.58363e8			−2.37532
$653$	1.02226e8			0.367133			0.183567	−	0.983007i	$-0.441236\pi$
$653$	1.02226e8			0.367133			0.183567	+	0.983007i	$0.441236\pi$
$654$	3.48119e8			1.24450
$655$		−	1.45790e8i		−	0.518805i
$656$	7.70410e8			2.72904
$657$			1.50304e8i			0.529997i
$658$	5.46909e8			1.91972
$659$		−	1.72924e8i		−	0.604224i	−0.953272	−	0.302112i	$-0.902308\pi$
$659$		−	1.72924e8i		−	0.604224i	0.953272	−	0.302112i	$-0.0976917\pi$
$660$		−	2.83144e8i		−	0.984862i
$661$	−3.09634e8			−1.07212			−0.536061	−	0.844179i	$-0.680088\pi$
$661$	−3.09634e8			−1.07212			−0.536061	+	0.844179i	$0.680088\pi$
$662$		−	1.06188e8i		−	0.366019i
$663$			1.37986e8i			0.473473i
$664$	7.83810e8			2.67736
$665$	−3.62941e8			−1.23416
$666$	−1.42659e8			−0.482920
$667$		−	2.82548e8i		−	0.952170i
$668$	1.97038e7			0.0661028
$669$	−8.46034e7			−0.282559
$670$	7.37747e8			2.45292
$671$	2.38663e8			0.789982
$672$			8.56730e8i			2.82317i
$673$			1.81697e7i			0.0596077i	0.999556	+	0.0298039i	$0.00948827\pi$
$673$			1.81697e7i			0.0596077i	−0.999556	+	0.0298039i	$0.990512\pi$
$674$	8.77806e8			2.86694
$675$	−2.66534e7			−0.0866645
$676$	−5.66501e8			−1.83384
$677$	1.33288e8			0.429560			0.214780	−	0.976662i	$-0.431096\pi$
$677$	1.33288e8			0.429560			0.214780	+	0.976662i	$0.431096\pi$
$678$	−3.06942e7			−0.0984844
$679$		−	8.28436e8i		−	2.64636i
$680$		−	1.06193e9i		−	3.37731i
$681$			5.73393e7i			0.181556i
$682$			4.43231e8i			1.39726i
$683$			6.18392e8i			1.94089i	0.241314	+	0.970447i	$0.422422\pi$
$683$			6.18392e8i			1.94089i	−0.241314	+	0.970447i	$0.577578\pi$
$684$	2.63462e8			0.823283
$685$	3.33270e8			1.03687
$686$			1.07939e9i			3.34353i
$687$		−	2.61008e8i		−	0.804979i
$688$		−	2.45198e8i		−	0.752924i
$689$			1.51969e8i			0.464620i
$690$	−2.19040e8			−0.666771
$691$		−	3.88370e8i		−	1.17709i	−0.808463	−	0.588547i	$-0.799700\pi$
$691$		−	3.88370e8i		−	1.17709i	0.808463	−	0.588547i	$-0.200300\pi$
$692$			8.18253e8i			2.46927i
$693$			1.72031e8i			0.516901i
$694$	1.75493e8			0.525026
$695$	3.12086e8			0.929651
$696$		−	6.71455e8i		−	1.99154i
$697$	4.60219e8			1.35915
$698$	8.12214e6			0.0238838
$699$			2.79247e8i			0.817630i
$700$	−6.91569e8			−2.01624
$701$		−	1.30199e8i		−	0.377968i	−0.981980	−	0.188984i	$-0.939481\pi$
$701$		−	1.30199e8i		−	0.377968i	0.981980	−	0.188984i	$-0.0605194\pi$
$702$	6.76374e7			0.195513
$703$			2.55013e8i			0.734000i
$704$			7.03437e8i			2.01608i
$705$			8.76356e7i			0.250100i
$706$	−1.03612e9			−2.94438
$707$		−	8.35484e8i		−	2.36418i
$708$	−1.67625e8	−	5.00802e8i	−0.472324	−	1.41113i
$709$	3.25855e8			0.914292			0.457146	−	0.889392i	$-0.348872\pi$
$709$	3.25855e8			0.914292			0.457146	+	0.889392i	$0.348872\pi$
$710$			1.73696e8i			0.485304i
$711$	1.55497e7			0.0432627
$712$	4.54144e8			1.25821
$713$	2.47037e8			0.681544
$714$			1.05423e9i			2.89628i
$715$	−1.29939e8			−0.355486
$716$			1.57319e9i			4.28591i
$717$	1.10486e8			0.299743
$718$			2.15722e7i			0.0582801i
$719$			6.80856e8i			1.83176i	0.401453	+	0.915880i	$0.368505\pi$
$719$			6.80856e8i			1.83176i	−0.401453	+	0.915880i	$0.631495\pi$
$720$	−2.82786e8			−0.757635
$721$		−	1.03082e9i		−	2.75029i
$722$			5.81818e7i			0.154588i
$723$	−2.97929e8			−0.788313
$724$	1.10427e9			2.90977
$725$	1.98406e8			0.520643
$726$		−	8.48771e7i		−	0.221810i
$727$	−5.81108e8			−1.51236			−0.756178	−	0.654367i	$-0.772935\pi$
$727$	−5.81108e8			−1.51236			−0.756178	+	0.654367i	$0.772935\pi$
$728$	1.07407e9			2.78380
$729$	1.43489e7			0.0370370
$730$	−8.67366e8			−2.22963
$731$		−	1.46473e8i		−	0.374979i
$732$		−	5.16511e8i		−	1.31688i
$733$	−6.55023e8			−1.66320			−0.831601	−	0.555374i	$-0.812575\pi$
$733$	−6.55023e8			−1.66320			−0.831601	+	0.555374i	$0.812575\pi$
$734$	8.95785e8			2.26525
$735$	−3.42923e8			−0.863643
$736$	9.24263e8			2.31826
$737$	−6.25090e8			−1.56149
$738$		−	2.25588e8i		−	0.561237i
$739$			9.21054e7i			0.228219i	0.993468	+	0.114109i	$0.0364015\pi$
$739$			9.21054e7i			0.228219i	−0.993468	+	0.114109i	$0.963599\pi$
$740$		−	5.93125e8i		−	1.46370i
$741$		−	1.20907e8i		−	0.297164i
$742$			1.16106e9i			2.84212i
$743$	−1.08383e8			−0.264237			−0.132118	−	0.991234i	$-0.542178\pi$
$743$	−1.08383e8			−0.264237			−0.132118	+	0.991234i	$0.542178\pi$
$744$	5.87067e8			1.42551
$745$		−	3.23485e8i		−	0.782322i
$746$		−	7.20480e8i		−	1.73542i
$747$		−	1.24685e8i		−	0.299125i
$748$			1.47018e9i			3.51289i
$749$	−4.28994e8			−1.02095
$750$		−	4.95367e8i		−	1.17420i
$751$		−	2.13766e8i		−	0.504684i	−0.967638	−	0.252342i	$-0.918799\pi$
$751$		−	2.13766e8i		−	0.504684i	0.967638	−	0.252342i	$-0.0812008\pi$
$752$		−	7.61729e8i		−	1.79121i
$753$	−1.57019e8			−0.367763
$754$	−5.03487e8			−1.17456
$755$		−	5.85393e8i		−	1.36021i
$756$	3.72307e8			0.861661
$757$	1.56480e7			0.0360721			0.0180360	−	0.999837i	$-0.494259\pi$
$757$	1.56480e7			0.0360721			0.0180360	+	0.999837i	$0.494259\pi$
$758$		−	6.51606e8i		−	1.49616i
$759$	1.85592e8			0.424456
$760$			9.30493e8i			2.11969i
$761$	−3.91353e8			−0.888005			−0.444002	−	0.896026i	$-0.646442\pi$
$761$	−3.91353e8			−0.888005			−0.444002	+	0.896026i	$0.646442\pi$
$762$		−	7.98761e8i		−	1.80531i
$763$		−	8.79380e8i		−	1.97972i
$764$		−	1.37381e9i		−	3.08069i
$765$	−1.68928e8			−0.377326
$766$			7.73746e8i			1.72152i
$767$	−2.29826e8	+	7.69260e7i	−0.509347	+	0.170485i
$768$	1.29943e8			0.286859
$769$		−	4.26822e8i		−	0.938573i	−0.883046	−	0.469286i	$-0.844511\pi$
$769$		−	4.26822e8i		−	0.938573i	0.883046	−	0.469286i	$-0.155489\pi$
$770$	−9.92751e8			−2.17454
$771$	−4.11985e8			−0.898915
$772$	−1.56700e9			−3.40579
$773$			4.13804e8i			0.895892i	0.894061	+	0.447946i	$0.147844\pi$
$773$			4.13804e8i			0.895892i	−0.894061	+	0.447946i	$0.852156\pi$
$774$	−7.17977e7			−0.154842
$775$			1.73470e8i			0.372666i
$776$	−2.12391e9			−4.54517
$777$			3.60368e8i			0.768216i
$778$			1.33387e9i			2.83252i
$779$	−4.03255e8			−0.853036
$780$			2.81213e8i			0.592586i
$781$		−	1.47172e8i		−	0.308938i
$782$	1.13733e9			2.37830
$783$	−1.06812e8			−0.222503
$784$	2.98068e9			6.18540
$785$			1.00515e8i			0.207789i
$786$	3.71058e8			0.764143
$787$	1.69453e8			0.347637			0.173819	−	0.984778i	$-0.444389\pi$
$787$	1.69453e8			0.347637			0.173819	+	0.984778i	$0.444389\pi$
$788$	−3.86341e8			−0.789573
$789$	−1.41523e8			−0.288136
$790$			8.97337e7i			0.182001i
$791$			7.75363e7i			0.156666i
$792$	4.41045e8			0.887785
$793$	−2.37035e8			−0.475328
$794$	2.34574e8			0.468618
$795$	−1.86046e8			−0.370270
$796$	1.19490e9			2.36916
$797$			5.90958e8i			1.16730i	0.812006	+	0.583648i	$0.198375\pi$
$797$			5.90958e8i			1.16730i	−0.812006	+	0.583648i	$0.801625\pi$
$798$		−	9.23742e8i		−	1.81778i
$799$		−	4.55033e8i		−	0.892078i
$800$			6.49019e8i			1.26761i
$801$		−	7.22431e7i		−	0.140572i
$802$	−3.14589e8			−0.609847
$803$	7.34915e8			1.41935
$804$			1.35281e9i			2.60297i
$805$			5.53315e8i			1.06068i
$806$		−	4.40209e8i		−	0.840725i
$807$		−	5.74947e7i		−	0.109397i
$808$	−2.14198e9			−4.06051
$809$			1.81338e8i			0.342487i	0.985229	+	0.171243i	$0.0547784\pi$
$809$			1.81338e8i			0.342487i	−0.985229	+	0.171243i	$0.945222\pi$
$810$			8.28041e7i			0.155811i
$811$		−	4.74521e8i		−	0.889596i	−0.895631	−	0.444798i	$-0.853275\pi$
$811$		−	4.74521e8i		−	0.889596i	0.895631	−	0.444798i	$-0.146725\pi$
$812$	−2.77142e9			−5.17649
$813$	4.62087e8			0.859909
$814$			6.97534e8i			1.29328i
$815$	−3.69883e8			−0.683268
$816$	1.46832e9			2.70240
$817$			1.28344e8i			0.235347i
$818$	−9.72911e8			−1.77751
$819$		−	1.70858e8i		−	0.311017i
$820$	9.37917e8			1.70107
$821$		−	3.97234e8i		−	0.717822i	−0.933372	−	0.358911i	$-0.883148\pi$
$821$		−	3.97234e8i		−	0.717822i	0.933372	−	0.358911i	$-0.116852\pi$
$822$			8.48224e8i			1.52720i
$823$			2.57711e8i			0.462310i	0.972917	+	0.231155i	$0.0742504\pi$
$823$			2.57711e8i			0.462310i	−0.972917	+	0.231155i	$0.925750\pi$
$824$	−2.64278e9			−4.72367
$825$			1.30323e8i			0.232091i
$826$	−1.75590e9	+	5.87723e8i	−3.11572	+	1.04288i
$827$	1.89323e8			0.334724			0.167362	−	0.985895i	$-0.446475\pi$
$827$	1.89323e8			0.334724			0.167362	+	0.985895i	$0.446475\pi$
$828$		−	4.01655e8i		−	0.707558i
$829$	−1.73548e8			−0.304618			−0.152309	−	0.988333i	$-0.548671\pi$
$829$	−1.73548e8			−0.304618			−0.152309	+	0.988333i	$0.548671\pi$
$830$	7.19527e8			1.25838
$831$	−4.80963e8			−0.838124
$832$		−	6.98641e8i		−	1.21306i
$833$	1.78057e9			3.08052
$834$			7.94307e8i			1.36927i
$835$	1.10700e7			0.0190147
$836$		−	1.28821e9i		−	2.20479i
$837$		−	9.33880e7i		−	0.159263i
$838$	1.99433e9			3.38895
$839$			1.36767e8i			0.231576i	0.993274	+	0.115788i	$0.0369394\pi$
$839$			1.36767e8i			0.231576i	−0.993274	+	0.115788i	$0.963061\pi$
$840$			1.31491e9i			2.21850i
$841$	2.00276e8			0.336699
$842$	1.80431e9			3.02257
$843$	6.14975e8			1.02654
$844$			1.45225e9i			2.41554i
$845$	−3.18273e8			−0.527509
$846$	−2.23046e8			−0.368369
$847$	−2.14407e8			−0.352849
$848$	1.61711e9			2.65187
$849$		−	4.17846e8i		−	0.682799i
$850$			7.98635e8i			1.30044i
$851$	3.88774e8			0.630825
$852$	−3.18507e8			−0.514991
$853$	−6.10143e8			−0.983069			−0.491535	−	0.870858i	$-0.663564\pi$
$853$	−6.10143e8			−0.983069			−0.491535	+	0.870858i	$0.663564\pi$
$854$	−1.81098e9			−2.90763
$855$	1.48019e8			0.236820
$856$			1.09983e9i			1.75350i
$857$			7.28112e7i			0.115679i	0.998326	+	0.0578396i	$0.0184212\pi$
$857$			7.28112e7i			0.115679i	−0.998326	+	0.0578396i	$0.981579\pi$
$858$		−	3.30716e8i		−	0.523592i
$859$		−	8.01836e8i		−	1.26505i	−0.774542	−	0.632523i	$-0.782019\pi$
$859$		−	8.01836e8i		−	1.26505i	0.774542	−	0.632523i	$-0.217981\pi$
$860$		−	2.98510e8i		−	0.469314i
$861$	−5.69855e8			−0.892801
$862$	−5.35994e8			−0.836832
$863$			5.48768e7i			0.0853801i	0.999088	+	0.0426900i	$0.0135928\pi$
$863$			5.48768e7i			0.0853801i	−0.999088	+	0.0426900i	$0.986407\pi$
$864$		−	3.49401e8i		−	0.541729i
$865$			4.59712e8i			0.710293i
$866$		−	1.18657e9i		−	1.82701i
$867$	5.00861e8			0.768528
$868$		−	2.42311e9i		−	3.70523i
$869$		−	7.60310e7i		−	0.115859i
$870$		−	6.16387e8i		−	0.936042i
$871$	6.20827e8			0.939542
$872$	−2.25451e9			−3.40019
$873$			3.37861e8i			0.507804i
$874$	−9.96557e8			−1.49268
$875$	−1.25134e9			−1.86789
$876$		−	1.59049e9i		−	2.36602i
$877$	−3.97650e7			−0.0589526			−0.0294763	−	0.999565i	$-0.509384\pi$
$877$	−3.97650e7			−0.0589526			−0.0294763	+	0.999565i	$0.509384\pi$
$878$			3.43923e8i			0.508133i
$879$	1.84951e8			0.272326
$880$			1.38269e9i			2.02898i
$881$			2.80407e8i			0.410073i	0.978754	+	0.205036i	$0.0657313\pi$
$881$			2.80407e8i			0.410073i	−0.978754	+	0.205036i	$0.934269\pi$
$882$		−	8.72791e8i		−	1.27205i
$883$	−5.64252e8			−0.819579			−0.409789	−	0.912180i	$-0.634398\pi$
$883$	−5.64252e8			−0.819579			−0.409789	+	0.912180i	$0.634398\pi$
$884$		−	1.46015e9i		−	2.11369i
$885$	−9.41756e7	−	2.81361e8i	−0.135865	−	0.405915i
$886$	−3.75590e8			−0.540023
$887$		−	7.71283e8i		−	1.10520i	−0.833445	−	0.552602i	$-0.813635\pi$
$887$		−	7.71283e8i		−	1.10520i	0.833445	−	0.552602i	$-0.186365\pi$
$888$	9.23895e8			1.31942
$889$	−2.01774e9			−2.87184
$890$	4.16898e8			0.591370
$891$		−	7.01595e7i		−	0.0991867i
$892$	8.95262e8			1.26141
$893$			3.98712e8i			0.559892i
$894$	8.23320e8			1.15227
$895$			8.83855e8i			1.23285i
$896$		−	1.82030e9i		−	2.53057i
$897$	−1.84326e8			−0.255393
$898$		−	2.09831e9i		−	2.89762i
$899$			6.95172e8i			0.956782i
$900$	2.82043e8			0.386890
$901$	9.66013e8			1.32071
$902$	−1.10302e9			−1.50302
$903$			1.81367e8i			0.246318i
$904$	1.98784e8			0.269077
$905$	6.20402e8			0.837004
$906$	1.48992e9			2.00344
$907$	2.13827e8			0.286577			0.143288	−	0.989681i	$-0.454232\pi$
$907$	2.13827e8			0.286577			0.143288	+	0.989681i	$0.454232\pi$
$908$		−	6.06757e8i		−	0.810508i
$909$			3.40736e8i			0.453655i
$910$	9.85981e8			1.30841
$911$	1.28553e8			0.170031			0.0850155	−	0.996380i	$-0.472906\pi$
$911$	1.28553e8			0.170031			0.0850155	+	0.996380i	$0.472906\pi$
$912$	−1.28658e9			−1.69610
$913$	−6.09651e8			−0.801068
$914$	5.88834e8			0.771177
$915$		−	2.90187e8i		−	0.378804i
$916$			2.76196e9i			3.59361i
$917$		−	9.37326e8i		−	1.21558i
$918$		−	4.29947e8i		−	0.555759i
$919$			7.76012e8i			0.999820i	0.866077	+	0.499910i	$0.166634\pi$
$919$			7.76012e8i			0.999820i	−0.866077	+	0.499910i	$0.833366\pi$
$920$	1.41856e9			1.82173
$921$	3.49823e8			0.447785
$922$		−	2.20987e9i		−	2.81952i
$923$			1.46168e8i			0.185886i
$924$		−	1.82041e9i		−	2.30756i
$925$			2.72998e8i			0.344933i
$926$	−1.29305e9			−1.62849
$927$			4.20402e8i			0.527746i
$928$			2.60091e9i			3.25448i
$929$			1.65318e8i			0.206193i	0.994671	+	0.103096i	$0.0328750\pi$
$929$			1.65318e8i			0.206193i	−0.994671	+	0.103096i	$0.967125\pi$
$930$	5.38920e8			0.670000
$931$	−1.56018e9			−1.93342
$932$		−	2.95495e9i		−	3.65009i
$933$	−7.61214e8			−0.937264
$934$	2.84758e9			3.49491
$935$			8.25978e8i			1.01049i
$936$	−4.38038e8			−0.534176
$937$			1.04565e9i			1.27106i	0.772076	+	0.635530i	$0.219219\pi$
$937$			1.04565e9i			1.27106i	−0.772076	+	0.635530i	$0.780781\pi$
$938$	4.74319e9			5.74727
$939$		−	4.79609e8i		−	0.579283i
$940$		−	9.27349e8i		−	1.11650i
$941$		−	1.90709e8i		−	0.228877i	−0.993430	−	0.114439i	$-0.963493\pi$
$941$		−	1.90709e8i		−	0.228877i	0.993430	−	0.114439i	$-0.0365070\pi$
$942$	−2.55826e8			−0.306050
$943$			6.14774e8i			0.733129i
$944$	8.18574e8	+	2.44559e9i	0.973066	+	2.90716i
$945$	2.09170e8			0.247859
$946$			3.51057e8i			0.414672i
$947$	1.62274e8			0.191073			0.0955363	−	0.995426i	$-0.469543\pi$
$947$	1.62274e8			0.191073			0.0955363	+	0.995426i	$0.469543\pi$
$948$	−1.64545e8			−0.193135
$949$	−7.29903e8			−0.854017
$950$		−	6.99784e8i		−	0.816193i
$951$	8.11157e7			0.0943112
$952$		−	6.82747e9i		−	7.91314i
$953$	2.63837e8			0.304830			0.152415	−	0.988317i	$-0.451295\pi$
$953$	2.63837e8			0.304830			0.152415	+	0.988317i	$0.451295\pi$
$954$		−	4.73516e8i		−	0.545367i
$955$		−	7.71838e8i		−	0.886168i
$956$	−1.16915e9			−1.33812
$957$			5.22261e8i			0.595871i
$958$		−	2.78949e9i		−	3.17270i
$959$	2.14269e9			2.42942
$960$	8.55301e8			0.966730
$961$	2.79701e8			0.315154
$962$		−	6.92778e8i		−	0.778160i
$963$	1.74957e8			0.195908
$964$	3.15265e9			3.51921
$965$	−8.80377e8			−0.979686
$966$	−1.40827e9			−1.56227
$967$		−	1.48620e9i		−	1.64361i	−0.569769	−	0.821805i	$-0.692967\pi$
$967$		−	1.48620e9i		−	1.64361i	0.569769	−	0.821805i	$-0.307033\pi$
$968$			5.49687e8i			0.606024i
$969$	−7.68562e8			−0.844710
$970$	−1.94972e9			−2.13627
$971$	4.03325e8			0.440552			0.220276	−	0.975438i	$-0.429304\pi$
$971$	4.03325e8			0.440552			0.220276	+	0.975438i	$0.429304\pi$
$972$	−1.51838e8			−0.165342
$973$	2.00649e9			2.17820
$974$		−	6.66439e7i		−	0.0721246i
$975$		−	1.29434e8i		−	0.139648i
$976$			2.52231e9i			2.71299i
$977$		−	5.94187e8i		−	0.637147i	−0.947898	−	0.318573i	$-0.896796\pi$
$977$		−	5.94187e8i		−	0.637147i	0.947898	−	0.318573i	$-0.103204\pi$
$978$		−	9.41408e8i		−	1.00638i
$979$	−3.53235e8			−0.376458
$980$	3.62876e9			3.85550
$981$			3.58638e8i			0.379882i
$982$			2.82256e9i			2.98063i
$983$		−	2.16494e8i		−	0.227921i	−0.993485	−	0.113961i	$-0.963646\pi$
$983$		−	2.16494e8i		−	0.227921i	0.993485	−	0.113961i	$-0.0363538\pi$
$984$			1.46097e9i			1.53340i
$985$	−2.17055e8			−0.227123
$986$			3.20049e9i			3.33876i
$987$			5.63434e8i			0.585992i
$988$			1.27942e9i			1.32661i
$989$	1.95664e8			0.202265
$990$	4.04874e8			0.417267
$991$		−	2.67690e7i		−	0.0275050i	−0.999905	−	0.0137525i	$-0.995622\pi$
$991$		−	2.67690e7i		−	0.0275050i	0.999905	−	0.0137525i	$-0.00437769\pi$
$992$	−2.27403e9			−2.32949
$993$	1.09397e8			0.111727
$994$			1.11674e9i			1.13708i
$995$	6.71323e8			0.681494
$996$			1.31940e9i			1.33536i
$997$	1.23355e9			1.24472			0.622358	−	0.782733i	$-0.286175\pi$
$997$	1.23355e9			1.24472			0.622358	+	0.782733i	$0.286175\pi$
$998$		−	2.55510e9i		−	2.57049i
$999$		−	1.46969e8i		−	0.147411i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.7.c.a.58.2	✓	60
59.58	odd	2	inner	177.7.c.a.58.59	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.7.c.a.58.2	✓	60	1.1	even	1	trivial
177.7.c.a.58.59	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)

\(f(q)\)	\(=\)	\(q-15.1313i q^{2} +15.5885 q^{3} -164.955 q^{4} -92.6753 q^{5} -235.873i q^{6} -595.836 q^{7} +1527.58i q^{8} +243.000 q^{9} +O(q^{10})\)	\(q-15.1313i q^{2} +15.5885 q^{3} -164.955 q^{4} -92.6753 q^{5} -235.873i q^{6} -595.836 q^{7} +1527.58i q^{8} +243.000 q^{9} +1402.29i q^{10} -1188.16i q^{11} -2571.39 q^{12} +1180.06i q^{13} +9015.75i q^{14} -1444.67 q^{15} +12557.0 q^{16} +7501.19 q^{17} -3676.90i q^{18} -6572.73 q^{19} +15287.3 q^{20} -9288.16 q^{21} -17978.3 q^{22} +10020.3i q^{23} +23812.6i q^{24} -7036.28 q^{25} +17855.7 q^{26} +3788.00 q^{27} +98286.1 q^{28} -28197.5 q^{29} +21859.6i q^{30} -24653.7i q^{31} -92238.9i q^{32} -18521.5i q^{33} -113502. i q^{34} +55219.3 q^{35} -40084.1 q^{36} -38798.6i q^{37} +99453.6i q^{38} +18395.2i q^{39} -141569. i q^{40} +61352.8 q^{41} +140542. i q^{42} -19526.7i q^{43} +195993. i q^{44} -22520.1 q^{45} +151620. q^{46} -60661.5i q^{47} +195745. q^{48} +237372. q^{49} +106468. i q^{50} +116932. q^{51} -194656. i q^{52} +128781. q^{53} -57317.1i q^{54} +110113. i q^{55} -910185. i q^{56} -102459. q^{57} +426664. i q^{58} +(65188.5 + 194759. i) q^{59} +238305. q^{60} +200868. i q^{61} -373041. q^{62} -144788. q^{63} -592041. q^{64} -109362. i q^{65} -280254. q^{66} -526100. i q^{67} -1.23736e6 q^{68} +156201. i q^{69} -835538. i q^{70} +123865. q^{71} +371201. i q^{72} +618533. i q^{73} -587072. q^{74} -109685. q^{75} +1.08420e6 q^{76} +707947. i q^{77} +278343. q^{78} +63990.6 q^{79} -1.16373e6 q^{80} +59049.0 q^{81} -928345. i q^{82} -513107. i q^{83} +1.53213e6 q^{84} -695175. q^{85} -295464. q^{86} -439556. q^{87} +1.81500e6 q^{88} -297297. i q^{89} +340758. i q^{90} -703120. i q^{91} -1.65290e6i q^{92} -384313. i q^{93} -917885. q^{94} +609130. q^{95} -1.43786e6i q^{96} +1.39038e6i q^{97} -3.59173e6i q^{98} -288722. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 1920 q^{4} - 408 q^{7} + 14580 q^{9}+O(q^{10}) \) 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

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Database

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