LMFDB - Embedded newform 177.5.b.a.119.70

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,5,Mod(119,177)]

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([1, 0]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("177.119");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	177.b (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:	$18.2964834658$
Analytic rank:	$0$
Dimension:	$78$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			119.70
Character	$\chi$	$=$	177.119
Dual form			177.5.b.a.119.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+6.47467i q^{2} +(-8.82514 + 1.76549i) q^{3} -25.9214 q^{4} -26.7513i q^{5} +(-11.4310 - 57.1399i) q^{6} -48.5383 q^{7} -64.2378i q^{8} +(74.7661 - 31.1614i) q^{9} +O(q^{10})$	\(q+6.47467i q^{2} +(-8.82514 + 1.76549i) q^{3} -25.9214 q^{4} -26.7513i q^{5} +(-11.4310 - 57.1399i) q^{6} -48.5383 q^{7} -64.2378i q^{8} +(74.7661 - 31.1614i) q^{9} +173.206 q^{10} -66.3235i q^{11} +(228.760 - 45.7639i) q^{12} -17.1474 q^{13} -314.270i q^{14} +(47.2291 + 236.084i) q^{15} +1.17649 q^{16} +329.024i q^{17} +(201.760 + 484.086i) q^{18} +308.577 q^{19} +693.430i q^{20} +(428.357 - 85.6938i) q^{21} +429.423 q^{22} +68.4764i q^{23} +(113.411 + 566.908i) q^{24} -90.6302 q^{25} -111.024i q^{26} +(-604.806 + 407.002i) q^{27} +1258.18 q^{28} -178.384i q^{29} +(-1528.56 + 305.793i) q^{30} +80.5949 q^{31} -1020.19i q^{32} +(117.093 + 585.314i) q^{33} -2130.32 q^{34} +1298.46i q^{35} +(-1938.04 + 807.746i) q^{36} +1120.58 q^{37} +1997.94i q^{38} +(151.328 - 30.2735i) q^{39} -1718.44 q^{40} -426.250i q^{41} +(554.840 + 2773.47i) q^{42} +1032.93 q^{43} +1719.20i q^{44} +(-833.606 - 2000.09i) q^{45} -443.362 q^{46} +574.063i q^{47} +(-10.3827 + 2.07709i) q^{48} -45.0329 q^{49} -586.801i q^{50} +(-580.888 - 2903.68i) q^{51} +444.484 q^{52} -409.120i q^{53} +(-2635.21 - 3915.92i) q^{54} -1774.24 q^{55} +3117.99i q^{56} +(-2723.24 + 544.790i) q^{57} +1154.98 q^{58} +453.188i q^{59} +(-1224.24 - 6119.62i) q^{60} +4085.24 q^{61} +521.826i q^{62} +(-3629.02 + 1512.52i) q^{63} +6624.21 q^{64} +458.714i q^{65} +(-3789.72 + 758.141i) q^{66} +8024.54 q^{67} -8528.76i q^{68} +(-120.894 - 604.313i) q^{69} -8407.11 q^{70} +9533.81i q^{71} +(-2001.74 - 4802.81i) q^{72} +6393.64 q^{73} +7255.40i q^{74} +(799.824 - 160.007i) q^{75} -7998.76 q^{76} +3219.23i q^{77} +(196.011 + 979.799i) q^{78} -2585.51 q^{79} -31.4727i q^{80} +(4618.94 - 4659.63i) q^{81} +2759.83 q^{82} +3769.55i q^{83} +(-11103.6 + 2221.30i) q^{84} +8801.80 q^{85} +6687.86i q^{86} +(314.936 + 1574.27i) q^{87} -4260.48 q^{88} -5967.21i q^{89} +(12949.9 - 5397.33i) q^{90} +832.305 q^{91} -1775.00i q^{92} +(-711.261 + 142.289i) q^{93} -3716.87 q^{94} -8254.84i q^{95} +(1801.13 + 9003.30i) q^{96} +15383.8 q^{97} -291.573i q^{98} +(-2066.73 - 4958.75i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9}+O(q^{10}) $ 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9	$ 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9} - 156 q^{10} - 4 q^{13} + 13 q^{15} + 4948 q^{16} + 22 q^{18} + 812 q^{19} - 173 q^{21} - 1644 q^{22} - 678 q^{24} - 8238 q^{25} + 777 q^{27} - 3764 q^{28} + 1374 q^{30} + 4664 q^{31} - 1042 q^{33} + 3244 q^{34} + 3648 q^{36} - 3960 q^{37} - 7078 q^{39} - 1576 q^{40} + 4934 q^{42} - 1492 q^{43} - 2063 q^{45} - 2036 q^{46} - 2620 q^{48} + 24274 q^{49} + 7300 q^{51} + 8408 q^{52} - 14766 q^{54} + 9780 q^{55} + 6939 q^{57} - 3856 q^{58} + 4712 q^{60} - 212 q^{61} - 7438 q^{63} - 45760 q^{64} + 3048 q^{66} - 12972 q^{67} + 21672 q^{69} + 5828 q^{70} - 866 q^{72} - 5240 q^{73} - 20922 q^{75} + 12368 q^{76} - 16508 q^{78} - 14976 q^{79} + 25524 q^{81} - 14484 q^{82} + 9540 q^{84} + 11572 q^{85} + 5695 q^{87} + 62160 q^{88} - 31672 q^{90} + 8284 q^{91} - 9590 q^{93} - 10992 q^{94} + 34102 q^{96} - 55000 q^{97} - 14254 q^{99}+O(q^{100}) $ 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9 - 156 * q^10 - 4 * q^13 + 13 * q^15 + 4948 * q^16 + 22 * q^18 + 812 * q^19 - 173 * q^21 - 1644 * q^22 - 678 * q^24 - 8238 * q^25 + 777 * q^27 - 3764 * q^28 + 1374 * q^30 + 4664 * q^31 - 1042 * q^33 + 3244 * q^34 + 3648 * q^36 - 3960 * q^37 - 7078 * q^39 - 1576 * q^40 + 4934 * q^42 - 1492 * q^43 - 2063 * q^45 - 2036 * q^46 - 2620 * q^48 + 24274 * q^49 + 7300 * q^51 + 8408 * q^52 - 14766 * q^54 + 9780 * q^55 + 6939 * q^57 - 3856 * q^58 + 4712 * q^60 - 212 * q^61 - 7438 * q^63 - 45760 * q^64 + 3048 * q^66 - 12972 * q^67 + 21672 * q^69 + 5828 * q^70 - 866 * q^72 - 5240 * q^73 - 20922 * q^75 + 12368 * q^76 - 16508 * q^78 - 14976 * q^79 + 25524 * q^81 - 14484 * q^82 + 9540 * q^84 + 11572 * q^85 + 5695 * q^87 + 62160 * q^88 - 31672 * q^90 + 8284 * q^91 - 9590 * q^93 - 10992 * q^94 + 34102 * q^96 - 55000 * q^97 - 14254 * q^99

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 $

$2$			6.47467i			1.61867i	0.587348	+	0.809334i	$0.300172\pi$
$2$			6.47467i			1.61867i	−0.587348	+	0.809334i	$0.699828\pi$
$3$	−8.82514	+	1.76549i	−0.980571	+	0.196165i
$3$	−8.82514	+	1.76549i	−0.980571	+	0.196165i
$4$	−25.9214			−1.62009
$5$		−	26.7513i		−	1.07005i	−0.844836	−	0.535025i	$-0.820302\pi$
$5$		−	26.7513i		−	1.07005i	0.844836	−	0.535025i	$-0.179698\pi$
$6$	−11.4310	−	57.1399i	−0.317527	−	1.58722i
$7$	−48.5383			−0.990578			−0.495289	−	0.868728i	$-0.664938\pi$
$7$	−48.5383			−0.990578			−0.495289	+	0.868728i	$0.664938\pi$
$8$		−	64.2378i		−	1.00372i
$9$	74.7661	−	31.1614i	0.923038	−	0.384708i
$10$	173.206			1.73206
$11$		−	66.3235i		−	0.548128i	−0.961711	−	0.274064i	$-0.911632\pi$
$11$		−	66.3235i		−	0.548128i	0.961711	−	0.274064i	$-0.0883680\pi$
$12$	228.760	−	45.7639i	1.58861	−	0.317805i
$13$	−17.1474			−0.101464			−0.0507319	−	0.998712i	$-0.516155\pi$
$13$	−17.1474			−0.101464			−0.0507319	+	0.998712i	$0.516155\pi$
$14$		−	314.270i		−	1.60342i
$15$	47.2291	+	236.084i	0.209907	+	1.04926i
$16$	1.17649			0.00459568
$17$			329.024i			1.13849i	0.822168	+	0.569245i	$0.192765\pi$
$17$			329.024i			1.13849i	−0.822168	+	0.569245i	$0.807235\pi$
$18$	201.760	+	484.086i	0.622715	+	1.49409i
$19$	308.577			0.854785			0.427393	−	0.904066i	$-0.359432\pi$
$19$	308.577			0.854785			0.427393	+	0.904066i	$0.359432\pi$
$20$			693.430i			1.73358i
$21$	428.357	−	85.6938i	0.971332	−	0.194317i
$22$	429.423			0.887237
$23$			68.4764i			0.129445i	0.997903	+	0.0647225i	$0.0206162\pi$
$23$			68.4764i			0.129445i	−0.997903	+	0.0647225i	$0.979384\pi$
$24$	113.411	+	566.908i	0.196894	+	0.984214i
$25$	−90.6302			−0.145008
$26$		−	111.024i		−	0.164236i
$27$	−604.806	+	407.002i	−0.829638	+	0.558302i
$28$	1258.18			1.60482
$29$		−	178.384i		−	0.212110i	−0.994360	−	0.106055i	$-0.966178\pi$
$29$		−	178.384i		−	0.212110i	0.994360	−	0.106055i	$-0.0338219\pi$
$30$	−1528.56	+	305.793i	−1.69840	+	0.339770i
$31$	80.5949			0.0838656			0.0419328	−	0.999120i	$-0.486648\pi$
$31$	80.5949			0.0838656			0.0419328	+	0.999120i	$0.486648\pi$
$32$		−	1020.19i		−	0.996277i
$33$	117.093	+	585.314i	0.107524	+	0.537478i
$34$	−2130.32			−1.84284
$35$			1298.46i			1.05997i
$36$	−1938.04	+	807.746i	−1.49540	+	0.623261i
$37$	1120.58			0.818541			0.409270	−	0.912413i	$-0.365783\pi$
$37$	1120.58			0.818541			0.409270	+	0.912413i	$0.365783\pi$
$38$			1997.94i			1.38361i
$39$	151.328	−	30.2735i	0.0994924	−	0.0199037i
$40$	−1718.44			−1.07403
$41$		−	426.250i		−	0.253569i	−0.991930	−	0.126785i	$-0.959534\pi$
$41$		−	426.250i		−	0.253569i	0.991930	−	0.126785i	$-0.0404657\pi$
$42$	554.840	+	2773.47i	0.314535	+	1.57226i
$43$	1032.93			0.558640			0.279320	−	0.960198i	$-0.409891\pi$
$43$	1032.93			0.558640			0.279320	+	0.960198i	$0.409891\pi$
$44$			1719.20i			0.888015i
$45$	−833.606	−	2000.09i	−0.411657	−	0.987698i
$46$	−443.362			−0.209528
$47$			574.063i			0.259874i	0.991522	+	0.129937i	$0.0414776\pi$
$47$			574.063i			0.259874i	−0.991522	+	0.129937i	$0.958522\pi$
$48$	−10.3827	+	2.07709i	−0.00450639	+	0.000901513i
$49$	−45.0329			−0.0187559
$50$		−	586.801i		−	0.234720i
$51$	−580.888	−	2903.68i	−0.223332	−	1.11637i
$52$	444.484			0.164380
$53$		−	409.120i		−	0.145646i	−0.997345	−	0.0728230i	$-0.976799\pi$
$53$		−	409.120i		−	0.145646i	0.997345	−	0.0728230i	$-0.0232008\pi$
$54$	−2635.21	−	3915.92i	−0.903706	−	1.34291i
$55$	−1774.24			−0.586525
$56$			3117.99i			0.994258i
$57$	−2723.24	+	544.790i	−0.838177	+	0.167679i
$58$	1154.98			0.343335
$59$			453.188i			0.130189i
$59$			453.188i			0.130189i
$60$	−1224.24	−	6119.62i	−0.340068	−	1.69989i
$61$	4085.24			1.09789			0.548944	−	0.835859i	$-0.315030\pi$
$61$	4085.24			1.09789			0.548944	+	0.835859i	$0.315030\pi$
$62$			521.826i			0.135751i
$63$	−3629.02	+	1512.52i	−0.914341	+	0.381083i
$64$	6624.21			1.61724
$65$			458.714i			0.108571i
$66$	−3789.72	+	758.141i	−0.869999	+	0.174045i
$67$	8024.54			1.78760			0.893800	−	0.448466i	$-0.148029\pi$
$67$	8024.54			1.78760			0.893800	+	0.448466i	$0.148029\pi$
$68$		−	8528.76i		−	1.84445i
$69$	−120.894	−	604.313i	−0.0253926	−	0.126930i
$70$	−8407.11			−1.71574
$71$			9533.81i			1.89125i	0.325254	+	0.945627i	$0.394550\pi$
$71$			9533.81i			1.89125i	−0.325254	+	0.945627i	$0.605450\pi$
$72$	−2001.74	−	4802.81i	−0.386138	−	0.926468i
$73$	6393.64			1.19978			0.599891	−	0.800082i	$-0.295211\pi$
$73$	6393.64			1.19978			0.599891	+	0.800082i	$0.295211\pi$
$74$			7255.40i			1.32495i
$75$	799.824	−	160.007i	0.142191	−	0.0284456i
$76$	−7998.76			−1.38483
$77$			3219.23i			0.542963i
$78$	196.011	+	979.799i	0.0322175	+	0.161045i
$79$	−2585.51			−0.414278			−0.207139	−	0.978312i	$-0.566415\pi$
$79$	−2585.51			−0.414278			−0.207139	+	0.978312i	$0.566415\pi$
$80$		−	31.4727i		−	0.00491761i
$81$	4618.94	−	4659.63i	0.703999	−	0.710201i
$82$	2759.83			0.410444
$83$			3769.55i			0.547183i	0.961846	+	0.273592i	$0.0882117\pi$
$83$			3769.55i			0.547183i	−0.961846	+	0.273592i	$0.911788\pi$
$84$	−11103.6	+	2221.30i	−1.57364	+	0.314811i
$85$	8801.80			1.21824
$86$			6687.86i			0.904254i
$87$	314.936	+	1574.27i	0.0416086	+	0.207989i
$88$	−4260.48			−0.550165
$89$		−	5967.21i		−	0.753340i	−0.926347	−	0.376670i	$-0.877069\pi$
$89$		−	5967.21i		−	0.753340i	0.926347	−	0.376670i	$-0.122931\pi$
$90$	12949.9	−	5397.33i	1.59875	−	0.666337i
$91$	832.305			0.100508
$92$		−	1775.00i		−	0.209712i
$93$	−711.261	+	142.289i	−0.0822362	+	0.0164515i
$94$	−3716.87			−0.420651
$95$		−	8254.84i		−	0.914663i
$96$	1801.13	+	9003.30i	0.195435	+	0.976920i
$97$	15383.8			1.63501			0.817503	−	0.575925i	$-0.195358\pi$
$97$	15383.8			1.63501			0.817503	+	0.575925i	$0.195358\pi$
$98$		−	291.573i		−	0.0303595i
$99$	−2066.73	−	4958.75i	−0.210869	−	0.505943i
$100$	2349.26			0.234926
$101$		−	10477.0i		−	1.02706i	−0.858072	−	0.513530i	$-0.828337\pi$
$101$		−	10477.0i		−	1.02706i	0.858072	−	0.513530i	$-0.171663\pi$
$102$	18800.4	−	3761.06i	1.80703	−	0.361501i
$103$	2261.28			0.213148			0.106574	−	0.994305i	$-0.466012\pi$
$103$	2261.28			0.213148			0.106574	+	0.994305i	$0.466012\pi$
$104$			1101.51i			0.101841i
$105$	−2292.42	−	11459.1i	−0.207929	−	1.03937i
$106$	2648.92			0.235753
$107$			21108.2i			1.84368i	0.387576	+	0.921838i	$0.373312\pi$
$107$			21108.2i			1.84368i	−0.387576	+	0.921838i	$0.626688\pi$
$108$	15677.4	−	10550.1i	1.34409	−	0.904498i
$109$	5238.41			0.440906			0.220453	−	0.975398i	$-0.429246\pi$
$109$	5238.41			0.440906			0.220453	+	0.975398i	$0.429246\pi$
$110$		−	11487.6i		−	0.949389i
$111$	−9889.29	+	1978.38i	−0.802637	+	0.160569i
$112$	−57.1050			−0.00455237
$113$		−	10631.5i		−	0.832605i	−0.909226	−	0.416302i	$-0.863326\pi$
$113$		−	10631.5i		−	0.832605i	0.909226	−	0.416302i	$-0.136674\pi$
$114$	−3527.34	−	17632.1i	−0.271417	−	1.35673i
$115$	1831.83			0.138513
$116$			4623.97i			0.343636i
$117$	−1282.04	+	534.336i	−0.0936549	+	0.0390339i
$118$	−2934.24			−0.210733
$119$		−	15970.3i		−	1.12776i
$120$	15165.5	−	3033.89i	1.05316	−	0.210687i
$121$	10242.2			0.699556
$122$			26450.6i			1.77712i
$123$	752.539	+	3761.71i	0.0497415	+	0.248642i
$124$	−2089.13			−0.135870
$125$		−	14295.1i		−	0.914884i
$126$	−9793.07	−	23496.7i	−0.616848	−	1.48001i
$127$	−24055.7			−1.49145			−0.745727	−	0.666252i	$-0.767898\pi$
$127$	−24055.7			−1.49145			−0.745727	+	0.666252i	$0.767898\pi$
$128$			26566.6i			1.62149i
$129$	−9115.71	+	1823.62i	−0.547786	+	0.109586i
$130$	−2970.02			−0.175741
$131$		−	19555.5i		−	1.13953i	−0.821807	−	0.569767i	$-0.807034\pi$
$131$		−	19555.5i		−	1.13953i	0.821807	−	0.569767i	$-0.192966\pi$
$132$	−3035.22	−	15172.2i	−0.174198	−	0.870762i
$133$	−14977.8			−0.846731
$134$			51956.3i			2.89353i
$135$	10887.8	+	16179.3i	0.597411	+	0.887755i
$136$	21135.8			1.14272
$137$		−	10205.1i		−	0.543720i	−0.962337	−	0.271860i	$-0.912361\pi$
$137$		−	10205.1i		−	0.543720i	0.962337	−	0.271860i	$-0.0876388\pi$
$138$	3912.73	−	782.751i	0.205457	−	0.0411022i
$139$	−20686.8			−1.07069			−0.535344	−	0.844634i	$-0.679818\pi$
$139$	−20686.8			−1.07069			−0.535344	+	0.844634i	$0.679818\pi$
$140$		−	33657.9i		−	1.71724i
$141$	−1013.50	−	5066.18i	−0.0509784	−	0.254825i
$142$	−61728.3			−3.06131
$143$			1137.27i			0.0556151i
$144$	87.9618	−	36.6611i	0.00424198	−	0.00176799i
$145$	−4772.01			−0.226968
$146$			41396.7i			1.94205i
$147$	397.421	−	79.5050i	0.0183915	−	0.00367925i
$148$	−29047.1			−1.32611
$149$		−	30863.4i		−	1.39018i	−0.718923	−	0.695090i	$-0.755365\pi$
$149$		−	30863.4i		−	1.39018i	0.718923	−	0.695090i	$-0.244635\pi$
$150$	1035.99	+	5178.60i	0.0460440	+	0.230160i
$151$	20970.3			0.919709			0.459854	−	0.887994i	$-0.347902\pi$
$151$	20970.3			0.919709			0.459854	+	0.887994i	$0.347902\pi$
$152$		−	19822.3i		−	0.857961i
$153$	10252.8	+	24599.8i	0.437987	+	1.05087i
$154$	−20843.5			−0.878878
$155$		−	2156.01i		−	0.0897405i
$156$	−3922.63	+	784.732i	−0.161186	+	0.0322457i
$157$	38969.6			1.58098			0.790490	−	0.612475i	$-0.209826\pi$
$157$	38969.6			1.58098			0.790490	+	0.612475i	$0.209826\pi$
$158$		−	16740.3i		−	0.670578i
$159$	722.297	+	3610.54i	0.0285707	+	0.142816i
$160$	−27291.3			−1.06607
$161$		−	3323.73i		−	0.128225i
$162$	30169.6	+	29906.1i	1.14958	+	1.13954i
$163$	−29092.1			−1.09496			−0.547482	−	0.836818i	$-0.684413\pi$
$163$	−29092.1			−1.09496			−0.547482	+	0.836818i	$0.684413\pi$
$164$			11049.0i			0.410804i
$165$	15657.9	−	3132.40i	0.575129	−	0.115056i
$166$	−24406.6			−0.885709
$167$		−	30094.7i		−	1.07909i	−0.841957	−	0.539545i	$-0.818596\pi$
$167$		−	30094.7i		−	1.07909i	0.841957	−	0.539545i	$-0.181404\pi$
$168$	−5504.79	−	27516.7i	−0.195039	−	0.974941i
$169$	−28267.0			−0.989705
$170$			56988.8i			1.97193i
$171$	23071.1	−	9615.70i	0.788999	−	0.328843i
$172$	−26774.9			−0.905046
$173$			31591.9i			1.05556i	0.849381	+	0.527781i	$0.176976\pi$
$173$			31591.9i			1.05556i	−0.849381	+	0.527781i	$0.823024\pi$
$174$	−10192.9	+	2039.10i	−0.336665	+	0.0673505i
$175$	4399.04			0.143642
$176$		−	78.0291i		−	0.00251902i
$177$	−800.098	−	3999.44i	−0.0255386	−	0.127659i
$178$	38635.7			1.21941
$179$			7027.75i			0.219336i	0.993968	+	0.109668i	$0.0349788\pi$
$179$			7027.75i			0.219336i	−0.993968	+	0.109668i	$0.965021\pi$
$180$	21608.2	+	51845.1i	0.666921	+	1.60016i
$181$	50951.9			1.55526			0.777631	−	0.628721i	$-0.216421\pi$
$181$	50951.9			1.55526			0.777631	+	0.628721i	$0.216421\pi$
$182$			5388.90i			0.162689i
$183$	−36052.8	+	7212.44i	−1.07656	+	0.215368i
$184$	4398.77			0.129926
$185$		−	29977.0i		−	0.875880i
$186$	−921.277	−	4605.18i	−0.0266296	−	0.133113i
$187$	21822.0			0.624038
$188$		−	14880.5i		−	0.421019i
$189$	29356.3	−	19755.2i	0.821821	−	0.553041i
$190$	53447.4			1.48054
$191$		−	36553.1i		−	1.00198i	−0.865454	−	0.500988i	$-0.832970\pi$
$191$		−	36553.1i		−	1.00198i	0.865454	−	0.500988i	$-0.167030\pi$
$192$	−58459.5	+	11695.0i	−1.58582	+	0.317246i
$193$	−34412.9			−0.923862			−0.461931	−	0.886916i	$-0.652843\pi$
$193$	−34412.9			−0.923862			−0.461931	+	0.886916i	$0.652843\pi$
$194$			99604.9i			2.64653i
$195$	−809.855	−	4048.21i	−0.0212980	−	0.106462i
$196$	1167.31			0.0303862
$197$			20824.8i			0.536597i	0.963336	+	0.268298i	$0.0864613\pi$
$197$			20824.8i			0.536597i	−0.963336	+	0.268298i	$0.913539\pi$
$198$	32106.3	−	13381.4i	0.818954	−	0.341328i
$199$	−67155.1			−1.69579			−0.847897	−	0.530161i	$-0.822131\pi$
$199$	−67155.1			−1.69579			−0.847897	+	0.530161i	$0.822131\pi$
$200$			5821.88i			0.145547i
$201$	−70817.6	+	14167.2i	−1.75287	+	0.350665i
$202$	67835.4			1.66247
$203$			8658.47i			0.210111i
$204$	15057.4	+	75267.4i	0.361818	+	1.80862i
$205$	−11402.7			−0.271332
$206$			14641.1i			0.345015i
$207$	2133.82	+	5119.71i	0.0497985	+	0.119483i
$208$	−20.1738			−0.000466295
$209$		−	20465.9i		−	0.468532i
$210$	74193.9	−	14842.7i	1.68240	−	0.336568i
$211$	63630.6			1.42923			0.714613	−	0.699520i	$-0.246603\pi$
$211$	63630.6			1.42923			0.714613	+	0.699520i	$0.246603\pi$
$212$			10605.0i			0.235959i
$213$	−16831.8	−	84137.2i	−0.370999	−	1.85451i
$214$	−136669.			−2.98430
$215$		−	27632.1i		−	0.597773i
$216$	26144.9	+	38851.4i	0.560376	+	0.832721i
$217$	−3911.94			−0.0830754
$218$			33917.0i			0.713681i
$219$	−56424.7	+	11287.9i	−1.17647	+	0.235356i
$220$	45990.7			0.950221
$221$		−	5641.89i		−	0.115516i
$222$	−12809.3	−	64029.9i	−0.259909	−	1.29920i
$223$	60412.0			1.21482			0.607412	−	0.794387i	$-0.292208\pi$
$223$	60412.0			1.21482			0.607412	+	0.794387i	$0.292208\pi$
$224$			49518.2i			0.986890i
$225$	−6776.06	+	2824.16i	−0.133848	+	0.0557859i
$226$	68835.7			1.34771
$227$			45524.1i			0.883466i	0.897147	+	0.441733i	$0.145636\pi$
$227$			45524.1i			0.883466i	−0.897147	+	0.441733i	$0.854364\pi$
$228$	70590.1	−	14121.7i	1.35792	−	0.271655i
$229$	19054.3			0.363348			0.181674	−	0.983359i	$-0.441848\pi$
$229$	19054.3			0.363348			0.181674	+	0.983359i	$0.441848\pi$
$230$			11860.5i			0.224206i
$231$	−5683.51	−	28410.1i	−0.106511	−	0.532414i
$232$	−11459.0			−0.212898
$233$			84699.7i			1.56016i	0.625678	+	0.780081i	$0.284822\pi$
$233$			84699.7i			1.56016i	−0.625678	+	0.780081i	$0.715178\pi$
$234$	−3459.65	−	8300.81i	−0.0631830	−	0.151596i
$235$	15356.9			0.278079
$236$		−	11747.3i		−	0.210917i
$237$	22817.5	−	4564.68i	0.406229	−	0.0812670i
$238$	103402.			1.82547
$239$			102141.i			1.78815i	0.447918	+	0.894075i	$0.352166\pi$
$239$			102141.i			1.78815i	−0.447918	+	0.894075i	$0.647834\pi$
$240$	55.5647	+	277.751i	0.000964664	+	0.00482206i
$241$	8557.27			0.147333			0.0736667	−	0.997283i	$-0.476530\pi$
$241$	8557.27			0.147333			0.0736667	+	0.997283i	$0.476530\pi$
$242$			66314.9i			1.13235i
$243$	−32536.2	+	49276.5i	−0.551004	+	0.834502i
$244$	−105895.			−1.77867
$245$			1204.69i			0.0200697i
$246$	−24355.9	+	4872.44i	−0.402470	+	0.0805150i
$247$	−5291.29			−0.0867297
$248$		−	5177.24i		−	0.0841773i
$249$	−6655.09	−	33266.8i	−0.107338	−	0.536552i
$250$	92555.9			1.48089
$251$		−	43678.6i		−	0.693300i	−0.937995	−	0.346650i	$-0.887319\pi$
$251$		−	43678.6i		−	0.693300i	0.937995	−	0.346650i	$-0.112681\pi$
$252$	94069.3	−	39206.6i	1.48131	−	0.617388i
$253$	4541.59			0.0709524
$254$		−	155753.i		−	2.41417i
$255$	−77677.1	+	15539.5i	−1.19457	+	0.238977i
$256$	−66022.6			−1.00742
$257$			49137.2i			0.743951i	0.928243	+	0.371976i	$0.121319\pi$
$257$			49137.2i			0.743951i	−0.928243	+	0.371976i	$0.878681\pi$
$258$	−11807.3	−	59021.3i	−0.177383	−	0.886685i
$259$	−54391.2			−0.810828
$260$		−	11890.5i		−	0.175895i
$261$	−5558.70	−	13337.1i	−0.0816004	−	0.195785i
$262$	126616.			1.84453
$263$		−	102582.i		−	1.48306i	−0.670919	−	0.741531i	$-0.734100\pi$
$263$		−	102582.i		−	1.48306i	0.670919	−	0.741531i	$-0.265900\pi$
$264$	37599.3	−	7521.82i	0.539475	−	0.107923i
$265$	−10944.5			−0.155849
$266$		−	96976.5i		−	1.37058i
$267$	10535.0	+	52661.4i	0.147779	+	0.738703i
$268$	−208007.			−2.89607
$269$		−	19982.6i		−	0.276151i	−0.990422	−	0.138076i	$-0.955908\pi$
$269$		−	19982.6i		−	0.276151i	0.990422	−	0.138076i	$-0.0440917\pi$
$270$	−104756.	+	70495.1i	−1.43698	+	0.967011i
$271$	926.550			0.0126162			0.00630812	−	0.999980i	$-0.497992\pi$
$271$	926.550			0.0126162			0.00630812	+	0.999980i	$0.497992\pi$
$272$			387.094i			0.00523213i
$273$	−7345.20	+	1469.42i	−0.0985550	+	0.0197161i
$274$	66074.6			0.880103
$275$			6010.91i			0.0794831i
$276$	3133.75	+	15664.6i	0.0411383	+	0.205638i
$277$	−127962.			−1.66771			−0.833857	−	0.551981i	$-0.813872\pi$
$277$	−127962.			−1.66771			−0.833857	+	0.551981i	$0.813872\pi$
$278$		−	133940.i		−	1.73309i
$279$	6025.76	−	2511.45i	0.0774112	−	0.0322638i
$280$	83410.3			1.06391
$281$		−	77722.8i		−	0.984319i	−0.870505	−	0.492160i	$-0.836208\pi$
$281$		−	77722.8i		−	0.984319i	0.870505	−	0.492160i	$-0.163792\pi$
$282$	32801.9	−	6562.09i	0.412478	−	0.0825171i
$283$	14238.3			0.177781			0.0888907	−	0.996041i	$-0.471668\pi$
$283$	14238.3			0.177781			0.0888907	+	0.996041i	$0.471668\pi$
$284$		−	247130.i		−	3.06400i
$285$	14573.8	+	72850.1i	0.179425	+	0.896892i
$286$	−7363.48			−0.0900224
$287$			20689.4i			0.251180i
$288$	−31790.4	−	76275.4i	−0.383276	−	0.919602i
$289$	−24735.6			−0.296161
$290$		−	30897.2i		−	0.367386i
$291$	−135764.	+	27159.9i	−1.60324	+	0.320732i
$292$	−165732.			−1.94375
$293$		−	94699.3i		−	1.10309i	−0.834145	−	0.551546i	$-0.814038\pi$
$293$		−	94699.3i		−	1.10309i	0.834145	−	0.551546i	$-0.185962\pi$
$294$	514.769	+	2573.17i	0.00595549	+	0.0297697i
$295$	12123.3			0.139309
$296$		−	71983.7i		−	0.821582i
$297$	26993.8	+	40112.8i	0.306021	+	0.454748i
$298$	199830.			2.25024
$299$		−	1174.19i		−	0.0131340i
$300$	−20732.5	+	4147.59i	−0.230362	+	0.0460844i
$301$	−50136.5			−0.553377
$302$			135776.i			1.48870i
$303$	18497.1	+	92461.3i	0.201474	+	1.00711i
$304$	363.039			0.00392832
$305$		−	109285.i		−	1.17480i
$306$	−159276.	+	66383.7i	−1.70101	+	0.708955i
$307$	118694.			1.25937			0.629685	−	0.776850i	$-0.283184\pi$
$307$	118694.			1.25937			0.629685	+	0.776850i	$0.283184\pi$
$308$		−	83446.9i		−	0.879648i
$309$	−19956.1	+	3992.27i	−0.209006	+	0.0418122i
$310$	13959.5			0.145260
$311$			11227.5i			0.116082i	0.998314	+	0.0580409i	$0.0184854\pi$
$311$			11227.5i			0.116082i	−0.998314	+	0.0580409i	$0.981515\pi$
$312$	−1944.70	−	9720.98i	−0.0199776	−	0.0998621i
$313$	43090.7			0.439840			0.219920	−	0.975518i	$-0.429420\pi$
$313$	43090.7			0.439840			0.219920	+	0.975518i	$0.429420\pi$
$314$			252315.i			2.55908i
$315$	40461.8	+	97080.9i	0.407778	+	0.978391i
$316$	67020.0			0.671166
$317$			34372.0i			0.342047i	0.985267	+	0.171024i	$0.0547075\pi$
$317$			34372.0i			0.342047i	−0.985267	+	0.171024i	$0.945293\pi$
$318$	−23377.1	+	4676.63i	−0.231172	+	0.0462465i
$319$	−11831.1			−0.116263
$320$		−	177206.i		−	1.73053i
$321$	−37266.4	−	186283.i	−0.361665	−	1.80785i
$322$	21520.0			0.207554
$323$			101529.i			0.973165i
$324$	−119729.	+	120784.i	−1.14054	+	1.15059i
$325$	1554.07			0.0147131
$326$		−	188362.i		−	1.77238i
$327$	−46229.7	+	9248.35i	−0.432340	+	0.0864906i
$328$	−27381.3			−0.254511
$329$		−	27864.0i		−	0.257426i
$330$	20281.2	+	101380.i	0.186237	+	0.930943i
$331$	−75885.6			−0.692633			−0.346317	−	0.938118i	$-0.612568\pi$
$331$	−75885.6			−0.692633			−0.346317	+	0.938118i	$0.612568\pi$
$332$		−	97711.9i		−	0.886485i
$333$	83781.6	−	34918.9i	0.755544	−	0.314899i
$334$	194854.			1.74669
$335$		−	214666.i		−	1.91282i
$336$	503.959	−	100.818i	0.00446392	−	0.000893018i
$337$	142500.			1.25474			0.627371	−	0.778721i	$-0.284131\pi$
$337$	142500.			1.25474			0.627371	+	0.778721i	$0.284131\pi$
$338$		−	183019.i		−	1.60200i
$339$	18769.9	+	93824.7i	0.163328	+	0.816428i
$340$	−228155.			−1.97366
$341$		−	5345.33i		−	0.0459691i
$342$	62258.5	+	149378.i	0.532288	+	1.27713i
$343$	118726.			1.00916
$344$		−	66352.9i		−	0.560716i
$345$	−16166.1	+	3234.07i	−0.135821	+	0.0271714i
$346$	−204547.			−1.70860
$347$			184710.i			1.53402i	0.641635	+	0.767010i	$0.278256\pi$
$347$			184710.i			1.53402i	−0.641635	+	0.767010i	$0.721744\pi$
$348$	−8163.57	−	40807.2i	−0.0674096	−	0.336960i
$349$	−68094.4			−0.559062			−0.279531	−	0.960137i	$-0.590179\pi$
$349$	−68094.4			−0.559062			−0.279531	+	0.960137i	$0.590179\pi$
$350$			28482.3i			0.232509i
$351$	10370.8	−	6979.02i	0.0841782	−	0.0566474i
$352$	−67662.4			−0.546087
$353$		−	2116.15i		−	0.0169823i	−0.999964	−	0.00849116i	$-0.997297\pi$
$353$		−	2116.15i		−	0.0169823i	0.999964	−	0.00849116i	$-0.00270285\pi$
$354$	25895.1	−	5180.37i	0.206638	−	0.0413385i
$355$	255041.			2.02374
$356$			154678.i			1.22048i
$357$	28195.3	+	140940.i	0.221228	+	1.10585i
$358$	−45502.4			−0.355033
$359$			102400.i			0.794532i	0.917704	+	0.397266i	$0.130041\pi$
$359$			102400.i			0.794532i	−0.917704	+	0.397266i	$0.869959\pi$
$360$	−128481.	+	53549.0i	−0.991368	+	0.413187i
$361$	−35100.9			−0.269342
$362$			329897.i			2.51745i
$363$	−90388.8	+	18082.5i	−0.685964	+	0.137229i
$364$	−21574.5			−0.162831
$365$		−	171038.i		−	1.28383i
$366$	−46698.2	−	233430.i	−0.348609	−	1.74259i
$367$	204790.			1.52047			0.760233	−	0.649650i	$-0.225085\pi$
$367$	204790.			1.52047			0.760233	+	0.649650i	$0.225085\pi$
$368$			80.5619i			0.000594887i
$369$	−13282.5	−	31869.0i	−0.0975501	−	0.234054i
$370$	194091.			1.41776
$371$			19858.0i			0.144274i
$372$	18436.9	−	3688.34i	0.133230	−	0.0266529i
$373$	−37570.6			−0.270042			−0.135021	−	0.990843i	$-0.543110\pi$
$373$	−37570.6			−0.270042			−0.135021	+	0.990843i	$0.543110\pi$
$374$			141290.i			1.01011i
$375$	25237.8	+	126156.i	0.179469	+	0.897109i
$376$	36876.5			0.260840
$377$			3058.82i			0.0215215i
$378$	127908.	+	190072.i	0.895191	+	1.33026i
$379$	127620.			0.888465			0.444233	−	0.895911i	$-0.353476\pi$
$379$	127620.			0.888465			0.444233	+	0.895911i	$0.353476\pi$
$380$			213977.i			1.48183i
$381$	212295.	−	42470.0i	1.46248	−	0.292572i
$382$	236669.			1.62187
$383$			67921.4i			0.463030i	0.972831	+	0.231515i	$0.0743682\pi$
$383$			67921.4i			0.463030i	−0.972831	+	0.231515i	$0.925632\pi$
$384$	−46903.0	−	234454.i	−0.318081	−	1.58999i
$385$	86118.5			0.580998
$386$		−	222812.i		−	1.49543i
$387$	77227.8	−	32187.4i	0.515646	−	0.214914i
$388$	−398769.			−2.64885
$389$		−	81552.6i		−	0.538938i	−0.963009	−	0.269469i	$-0.913152\pi$
$389$		−	81552.6i		−	0.538938i	0.963009	−	0.269469i	$-0.0868481\pi$
$390$	26210.9	−	5243.54i	0.172327	−	0.0344743i
$391$	−22530.3			−0.147372
$392$			2892.81i			0.0188256i
$393$	34525.1	+	172580.i	0.223537	+	1.11739i
$394$	−134834.			−0.868572
$395$			69165.6i			0.443298i
$396$	53572.5	+	128538.i	0.341627	+	0.819672i
$397$	−20135.3			−0.127754			−0.0638772	−	0.997958i	$-0.520347\pi$
$397$	−20135.3			−0.127754			−0.0638772	+	0.997958i	$0.520347\pi$
$398$		−	434808.i		−	2.74493i
$399$	132181.	−	26443.2i	0.830280	−	0.166099i
$400$	−106.626			−0.000666411
$401$			188063.i			1.16954i	0.811199	+	0.584770i	$0.198815\pi$
$401$			188063.i			1.16954i	−0.811199	+	0.584770i	$0.801185\pi$
$402$	−91728.2	−	458521.i	−0.567611	−	2.83731i
$403$	−1381.99			−0.00850932
$404$			271580.i			1.66393i
$405$	−124651.	−	123562.i	−0.759951	−	0.753315i
$406$	−56060.8			−0.340100
$407$		−	74320.9i		−	0.448665i
$408$	−186526.	+	37315.0i	−1.12052	+	0.224162i
$409$	19089.1			0.114114			0.0570571	−	0.998371i	$-0.481828\pi$
$409$	19089.1			0.114114			0.0570571	+	0.998371i	$0.481828\pi$
$410$		−	73828.9i		−	0.439196i
$411$	18017.0	+	90061.3i	0.106659	+	0.533156i
$412$	−58615.6			−0.345318
$413$		−	21997.0i		−	0.128962i
$414$	−33148.4	+	13815.8i	−0.193403	+	0.0806073i
$415$	100840.			0.585514
$416$			17493.5i			0.101086i
$417$	182563.	−	36522.2i	1.04989	−	0.210032i
$418$	132510.			0.758397
$419$		−	152039.i		−	0.866018i	−0.901390	−	0.433009i	$-0.857452\pi$
$419$		−	152039.i		−	0.866018i	0.901390	−	0.433009i	$-0.142548\pi$
$420$	59422.7	+	297036.i	0.336863	+	1.68388i
$421$	166921.			0.941776			0.470888	−	0.882193i	$-0.343934\pi$
$421$	166921.			0.941776			0.470888	+	0.882193i	$0.343934\pi$
$422$			411987.i			2.31344i
$423$	17888.6	+	42920.4i	0.0999758	+	0.239874i
$424$	−26281.0			−0.146187
$425$		−	29819.5i		−	0.165091i
$426$	544761.	−	108981.i	3.00183	−	0.600524i
$427$	−198291.			−1.08754
$428$		−	547155.i		−	2.98692i
$429$	−2007.84	−	10036.6i	−0.0109098	−	0.0545346i
$430$	178909.			0.967597
$431$			1348.54i			0.00725954i	0.999993	+	0.00362977i	$0.00115539\pi$
$431$			1348.54i			0.00725954i	−0.999993	+	0.00362977i	$0.998845\pi$
$432$	−711.550	+	478.835i	−0.00381275	+	0.00256577i
$433$	293401.			1.56490			0.782449	−	0.622715i	$-0.213970\pi$
$433$	293401.			1.56490			0.782449	+	0.622715i	$0.213970\pi$
$434$		−	25328.5i		−	0.134472i
$435$	42113.6	−	8424.92i	0.222558	−	0.0445233i
$436$	−135787.			−0.714307
$437$			21130.3i			0.110648i
$438$	−73085.5	−	365332.i	−0.380963	−	1.90432i
$439$	−258719.			−1.34245			−0.671227	−	0.741252i	$-0.734233\pi$
$439$	−258719.			−1.34245			−0.671227	+	0.741252i	$0.734233\pi$
$440$			113973.i			0.588704i
$441$	−3366.93	+	1403.29i	−0.0173124	+	0.00721554i
$442$	36529.4			0.186981
$443$			89500.4i			0.456056i	0.973655	+	0.228028i	$0.0732277\pi$
$443$			89500.4i			0.456056i	−0.973655	+	0.228028i	$0.926772\pi$
$444$	256344.	−	51282.3i	1.30034	−	0.260136i
$445$	−159630.			−0.806112
$446$			391148.i			1.96640i
$447$	54489.0	+	272374.i	0.272705	+	1.36317i
$448$	−321528.			−1.60200
$449$			14364.7i			0.0712532i	0.999365	+	0.0356266i	$0.0113427\pi$
$449$			14364.7i			0.0712532i	−0.999365	+	0.0356266i	$0.988657\pi$
$450$	−18285.5	−	43872.8i	−0.0902988	−	0.216656i
$451$	−28270.4			−0.138988
$452$			275584.i			1.34889i
$453$	−185066.	+	37022.8i	−0.901839	+	0.180415i
$454$	−294754.			−1.43004
$455$		−	22265.2i		−	0.107548i
$456$	34996.1	+	174935.i	0.168302	+	0.841292i
$457$	−223969.			−1.07240			−0.536198	−	0.844092i	$-0.680140\pi$
$457$	−223969.			−1.07240			−0.536198	+	0.844092i	$0.680140\pi$
$458$			123371.i			0.588140i
$459$	−133913.	−	198996.i	−0.635621	−	0.944535i
$460$	−47483.6			−0.224403
$461$			293479.i			1.38094i	0.723361	+	0.690470i	$0.242596\pi$
$461$			293479.i			1.38094i	−0.723361	+	0.690470i	$0.757404\pi$
$462$	183946.	−	36798.9i	0.861802	−	0.172405i
$463$	−197511.			−0.921361			−0.460680	−	0.887566i	$-0.652395\pi$
$463$	−197511.			−0.921361			−0.460680	+	0.887566i	$0.652395\pi$
$464$		−	209.868i		−	0.000974788i
$465$	3806.42	+	19027.1i	0.0176040	+	0.0879969i
$466$	−548403.			−2.52539
$467$			368870.i			1.69137i	0.533680	+	0.845686i	$0.320809\pi$
$467$			368870.i			1.69137i	−0.533680	+	0.845686i	$0.679191\pi$
$468$	33232.3	−	13850.7i	0.151729	−	0.0632384i
$469$	−389497.			−1.77076
$470$			99430.9i			0.450117i
$471$	−343912.	+	68800.4i	−1.55026	+	0.310134i
$472$	29111.8			0.130673
$473$		−	68507.3i		−	0.306206i
$474$	29554.8	+	147736.i	0.131544	+	0.657549i
$475$	−27966.4			−0.123951
$476$			413971.i			1.82707i
$477$	−12748.7	−	30588.3i	−0.0560312	−	0.134437i
$478$	−661329.			−2.89442
$479$			329730.i			1.43710i	0.695475	+	0.718550i	$0.255194\pi$
$479$			329730.i			1.43710i	−0.695475	+	0.718550i	$0.744806\pi$
$480$	240850.	−	48182.5i	1.04535	−	0.209125i
$481$	−19215.0			−0.0830522
$482$			55405.5i			0.238484i
$483$	5868.00	+	29332.3i	0.0251534	+	0.125734i
$484$	−265492.			−1.13334
$485$		−	411535.i		−	1.74954i
$486$	−319049.	−	210662.i	−1.35078	−	0.891893i
$487$	−87884.6			−0.370557			−0.185279	−	0.982686i	$-0.559319\pi$
$487$	−87884.6			−0.370557			−0.185279	+	0.982686i	$0.559319\pi$
$488$		−	262427.i		−	1.10197i
$489$	256742.	−	51361.7i	1.07369	−	0.214794i
$490$	−7799.95			−0.0324862
$491$			18504.7i			0.0767570i	0.999263	+	0.0383785i	$0.0122193\pi$
$491$			18504.7i			0.0767570i	−0.999263	+	0.0383785i	$0.987781\pi$
$492$	−19506.9	−	97508.8i	−0.0805856	−	0.402822i
$493$	58692.7			0.241485
$494$		−	34259.4i		−	0.140387i
$495$	−132653.	+	55287.6i	−0.541385	+	0.225641i
$496$	94.8193			0.000385419
$497$		−	462755.i		−	1.87343i
$498$	215391.	−	43089.6i	0.868500	−	0.173745i
$499$	171794.			0.689934			0.344967	−	0.938615i	$-0.387890\pi$
$499$	171794.			0.689934			0.344967	+	0.938615i	$0.387890\pi$
$500$			370548.i			1.48219i
$501$	53131.9	+	265590.i	0.211680	+	1.05812i
$502$	282805.			1.12222
$503$		−	256618.i		−	1.01426i	−0.861868	−	0.507132i	$-0.830706\pi$
$503$		−	256618.i		−	1.01426i	0.861868	−	0.507132i	$-0.169294\pi$
$504$	97161.0	+	233120.i	0.382499	+	0.917739i
$505$	−280274.			−1.09901
$506$			29405.3i			0.114848i
$507$	249460.	−	49905.0i	0.970476	−	0.194146i
$508$	623556.			2.41629
$509$			482881.i			1.86382i	0.362688	+	0.931911i	$0.381859\pi$
$509$			482881.i			1.86382i	−0.362688	+	0.931911i	$0.618141\pi$
$510$	−100613.	−	502934.i	−0.386825	−	1.93362i
$511$	−310336.			−1.18848
$512$		−	2409.45i		−	0.00919132i
$513$	−186630.	+	125592.i	−0.709162	+	0.477228i
$514$	−318148.			−1.20421
$515$		−	60492.2i		−	0.228079i
$516$	236292.	−	47270.8i	0.887462	−	0.177539i
$517$	38073.8			0.142444
$518$		−	352165.i		−	1.31246i
$519$	−55775.1	−	278803.i	−0.207065	−	1.03505i
$520$	29466.8			0.108975
$521$			55186.5i			0.203309i	0.994820	+	0.101655i	$0.0324137\pi$
$521$			55186.5i			0.203309i	−0.994820	+	0.101655i	$0.967586\pi$
$522$	86353.4	−	35990.8i	0.316912	−	0.132084i
$523$	−20140.8			−0.0736330			−0.0368165	−	0.999322i	$-0.511722\pi$
$523$	−20140.8			−0.0736330			−0.0368165	+	0.999322i	$0.511722\pi$
$524$			506907.i			1.84614i
$525$	−38822.1	+	7766.45i	−0.140851	+	0.0281776i
$526$	664184.			2.40059
$527$			26517.6i			0.0954802i
$528$	137.760	+	688.618i	0.000494144	+	0.00247008i
$529$	275152.			0.983244
$530$		−	70861.9i		−	0.252267i
$531$	14121.9	+	33883.1i	0.0500847	+	0.120169i
$532$	388246.			1.37178
$533$			7309.06i			0.0257281i
$534$	−340965.	+	68210.9i	−1.19572	+	0.239206i
$535$	564672.			1.97283
$536$		−	515479.i		−	1.79424i
$537$	−12407.4	−	62020.9i	−0.0430262	−	0.215075i
$538$	129381.			0.446997
$539$			2986.74i			0.0102806i
$540$	−282228.	−	419391.i	−0.967858	−	1.43824i
$541$	−169569.			−0.579366			−0.289683	−	0.957123i	$-0.593550\pi$
$541$	−169569.			−0.579366			−0.289683	+	0.957123i	$0.593550\pi$
$542$			5999.11i			0.0204215i
$543$	−449658.	+	89955.0i	−1.52504	+	0.305088i
$544$	335666.			1.13425
$545$		−	140134.i		−	0.471792i
$546$	−9514.05	−	47557.8i	−0.0319139	−	0.159528i
$547$	−395041.			−1.32029			−0.660143	−	0.751140i	$-0.729504\pi$
$547$	−395041.			−1.32029			−0.660143	+	0.751140i	$0.729504\pi$
$548$			264530.i			0.880874i
$549$	305437.	−	127302.i	1.01339	−	0.422366i
$550$	−38918.7			−0.128657
$551$		−	55045.4i		−	0.181308i
$552$	−38819.8	+	7765.98i	−0.127402	+	0.0254870i
$553$	125496.			0.410374
$554$		−	828512.i		−	2.69948i
$555$	52924.0	+	264551.i	0.171817	+	0.858862i
$556$	536230.			1.73461
$557$		−	322463.i		−	1.03937i	−0.854358	−	0.519684i	$-0.826050\pi$
$557$		−	322463.i		−	1.03937i	0.854358	−	0.519684i	$-0.173950\pi$
$558$	16260.8	+	39014.9i	0.0522244	+	0.125303i
$559$	−17712.0			−0.0566818
$560$			1527.63i			0.00487127i
$561$	−192582.	+	38526.5i	−0.611914	+	0.122415i
$562$	503230.			1.59329
$563$		−	434134.i		−	1.36964i	−0.728711	−	0.684821i	$-0.759880\pi$
$563$		−	434134.i		−	1.36964i	0.728711	−	0.684821i	$-0.240120\pi$
$564$	26271.4	+	131323.i	0.0825894	+	0.412839i
$565$	−284407.			−0.890929
$566$			92188.5i			0.287769i
$567$	−224195.	+	226170.i	−0.697366	+	0.703509i
$568$	612431.			1.89828
$569$		−	32540.0i		−	0.100506i	−0.998737	−	0.0502531i	$-0.983997\pi$
$569$		−	32540.0i		−	0.100506i	0.998737	−	0.0502531i	$-0.0160028\pi$
$570$	−471680.	+	94360.8i	−1.45177	+	0.290430i
$571$	−42779.4			−0.131209			−0.0656043	−	0.997846i	$-0.520898\pi$
$571$	−42779.4			−0.131209			−0.0656043	+	0.997846i	$0.520898\pi$
$572$		−	29479.7i		−	0.0901014i
$573$	64534.1	+	322586.i	0.196553	+	0.982509i
$574$	−133957.			−0.406577
$575$		−	6206.02i		−	0.0187706i
$576$	495266.	−	206419.i	1.49277	−	0.622165i
$577$	625011.			1.87731			0.938655	−	0.344858i	$-0.112073\pi$
$577$	625011.			1.87731			0.938655	+	0.344858i	$0.112073\pi$
$578$		−	160155.i		−	0.479386i
$579$	303699.	−	60755.6i	0.905912	−	0.181230i
$580$	123697.			0.367708
$581$		−	182967.i		−	0.542028i
$582$	−175851.	−	879027.i	−0.519158	−	2.59511i
$583$	−27134.3			−0.0798327
$584$		−	410713.i		−	1.20424i
$585$	14294.2	+	34296.3i	0.0417683	+	0.100216i
$586$	613147.			1.78554
$587$		−	161202.i		−	0.467838i	−0.972256	−	0.233919i	$-0.924845\pi$
$587$		−	161202.i		−	0.467838i	0.972256	−	0.233919i	$-0.0751551\pi$
$588$	−10301.7	+	2060.88i	−0.0297958	+	0.00596071i
$589$	24869.8			0.0716871
$590$			78494.7i			0.225495i
$591$	−36765.9	−	183782.i	−0.105262	−	0.526171i
$592$	1318.36			0.00376175
$593$		−	57859.8i		−	0.164539i	−0.996610	−	0.0822693i	$-0.973783\pi$
$593$		−	57859.8i		−	0.164539i	0.996610	−	0.0822693i	$-0.0262168\pi$
$594$	−259718.	+	174776.i	−0.736086	+	0.495346i
$595$	−427225.			−1.20676
$596$			800022.i			2.25221i
$597$	592653.	−	118562.i	1.66285	−	0.332656i
$598$	7602.50			0.0212595
$599$		−	290228.i		−	0.808882i	−0.914564	−	0.404441i	$-0.867466\pi$
$599$		−	290228.i		−	0.808882i	0.914564	−	0.404441i	$-0.132534\pi$
$600$	−10278.5	−	51378.9i	−0.0285513	−	0.142719i
$601$	−385928.			−1.06846			−0.534229	−	0.845340i	$-0.679398\pi$
$601$	−385928.			−1.06846			−0.534229	+	0.845340i	$0.679398\pi$
$602$		−	324617.i		−	0.895733i
$603$	599963.	−	250056.i	1.65002	−	0.687704i
$604$	−543579.			−1.49001
$605$		−	273992.i		−	0.748560i
$606$	−598657.	+	119763.i	−1.63017	+	0.326119i
$607$	508784.			1.38088			0.690440	−	0.723389i	$-0.257417\pi$
$607$	508784.			1.38088			0.690440	+	0.723389i	$0.257417\pi$
$608$		−	314807.i		−	0.851603i
$609$	−15286.4	−	76412.2i	−0.0412166	−	0.206029i
$610$	707587.			1.90160
$611$		−	9843.67i		−	0.0263678i
$612$	−265768.	−	637662.i	−0.709577	−	1.70250i
$613$	−293162.			−0.780167			−0.390083	−	0.920780i	$-0.627554\pi$
$613$	−293162.			−0.780167			−0.390083	+	0.920780i	$0.627554\pi$
$614$			768508.i			2.03850i
$615$	100631.	−	20131.4i	0.266060	−	0.0532259i
$616$	206796.			0.544981
$617$			124210.i			0.326276i	0.986603	+	0.163138i	$0.0521615\pi$
$617$			124210.i			0.326276i	−0.986603	+	0.163138i	$0.947838\pi$
$618$	−25848.6	−	129209.i	−0.0676801	−	0.338312i
$619$	326503.			0.852131			0.426065	−	0.904692i	$-0.359899\pi$
$619$	326503.			0.852131			0.426065	+	0.904692i	$0.359899\pi$
$620$			55886.9i			0.145387i
$621$	−27870.0	−	41414.9i	−0.0722693	−	0.107392i
$622$	−72694.6			−0.187898
$623$			289638.i			0.746242i
$624$	178.036	−	35.6166i	0.000457235	−	9.14709e-5i
$625$	−439055.			−1.12398
$626$			278998.i			0.711955i
$627$	36132.4	+	180615.i	0.0919097	+	0.459428i
$628$	−1.01015e6			−2.56133
$629$			368698.i			0.931901i
$630$	−628567.	+	261977.i	−1.58369	+	0.660058i
$631$	−421608.			−1.05889			−0.529445	−	0.848345i	$-0.677600\pi$
$631$	−421608.			−1.05889			−0.529445	+	0.848345i	$0.677600\pi$
$632$			166087.i			0.415817i
$633$	−561549.	+	112339.i	−1.40146	+	0.280365i
$634$	−222547.			−0.553661
$635$			643519.i			1.59593i
$636$	−18722.9	−	93590.2i	−0.0462871	−	0.231375i
$637$	772.195			0.00190304
$638$		−	76602.3i		−	0.188192i
$639$	297086.	+	712806.i	0.727581	+	1.74570i
$640$	710689.			1.73508
$641$			135933.i			0.330834i	0.986224	+	0.165417i	$0.0528970\pi$
$641$			135933.i			0.330834i	−0.986224	+	0.165417i	$0.947103\pi$
$642$	1.20612e6	−	241288.i	2.92632	−	0.585416i
$643$	−293832.			−0.710686			−0.355343	−	0.934736i	$-0.615636\pi$
$643$	−293832.			−0.710686			−0.355343	+	0.934736i	$0.615636\pi$
$644$			86155.6i			0.207736i
$645$	48784.1	+	243857.i	0.117262	+	0.586159i
$646$	−657369.			−1.57523
$647$		−	585214.i		−	1.39800i	−0.715123	−	0.698999i	$-0.753629\pi$
$647$		−	585214.i		−	1.39800i	0.715123	−	0.698999i	$-0.246371\pi$
$648$	−299324.	−	296710.i	−0.712840	−	0.706615i
$649$	30057.0			0.0713602
$650$			10062.1i			0.0238156i
$651$	34523.4	−	6906.48i	0.0814613	−	0.0162965i
$652$	754107.			1.77394
$653$			449055.i			1.05311i	0.850142	+	0.526554i	$0.176516\pi$
$653$			449055.i			1.05311i	−0.850142	+	0.526554i	$0.823484\pi$
$654$	−59880.0	−	299322.i	−0.140000	−	0.699815i
$655$	−523135.			−1.21936
$656$		−	501.480i		−	0.00116532i
$657$	478027.	−	199235.i	1.10744	−	0.461566i
$658$	180410.			0.416687
$659$			394456.i			0.908297i	0.890926	+	0.454149i	$0.150056\pi$
$659$			394456.i			0.908297i	−0.890926	+	0.454149i	$0.849944\pi$
$660$	−405874.	+	81196.1i	−0.931759	+	0.186401i
$661$	61363.2			0.140445			0.0702223	−	0.997531i	$-0.477629\pi$
$661$	61363.2			0.140445			0.0702223	+	0.997531i	$0.477629\pi$
$662$		−	491335.i		−	1.12114i
$663$	9960.70	+	49790.5i	0.0226602	+	0.113271i
$664$	242147.			0.549217
$665$			400676.i			0.906045i
$666$	226088.	+	542458.i	0.509718	+	1.22298i
$667$	12215.1			0.0274565
$668$			780097.i			1.74822i
$669$	−533144.	+	106657.i	−1.19122	+	0.238307i
$670$	1.38990e6			3.09623
$671$		−	270947.i		−	0.601783i
$672$	−87423.8	−	437005.i	−0.193594	−	0.967715i
$673$	678204.			1.49737			0.748687	−	0.662924i	$-0.230685\pi$
$673$	678204.			1.49737			0.748687	+	0.662924i	$0.230685\pi$
$674$			922639.i			2.03101i
$675$	54813.7	−	36886.7i	0.120304	−	0.0809584i
$676$	732719.			1.60341
$677$		−	84970.9i		−	0.185393i	−0.995694	−	0.0926964i	$-0.970451\pi$
$677$		−	84970.9i		−	0.185393i	0.995694	−	0.0926964i	$-0.0295486\pi$
$678$	−607484.	+	121529.i	−1.32153	+	0.264374i
$679$	−746702.			−1.61960
$680$		−	565408.i		−	1.22277i
$681$	−80372.3	−	401757.i	−0.173305	−	0.866301i
$682$	34609.3			0.0744087
$683$		−	368714.i		−	0.790403i	−0.918594	−	0.395201i	$-0.870675\pi$
$683$		−	368714.i		−	0.790403i	0.918594	−	0.395201i	$-0.129325\pi$
$684$	−598036.	+	249252.i	−1.27825	+	0.532754i
$685$	−272999.			−0.581808
$686$			768714.i			1.63349i
$687$	−168157.	+	33640.2i	−0.356288	+	0.0712763i
$688$	1215.23			0.00256733
$689$			7015.33i			0.0147778i
$690$	−20939.6	−	104670.i	−0.0439815	−	0.219850i
$691$	431721.			0.904164			0.452082	−	0.891976i	$-0.350681\pi$
$691$	431721.			0.904164			0.452082	+	0.891976i	$0.350681\pi$
$692$		−	818906.i		−	1.71010i
$693$	100316.	+	240689.i	0.208882	+	0.501176i
$694$	−1.19594e6			−2.48307
$695$			553397.i			1.14569i
$696$	101127.	−	20230.8i	0.208761	−	0.0417632i
$697$	140246.			0.288686
$698$		−	440889.i		−	0.904937i
$699$	−149536.	−	747486.i	−0.306050	−	1.52985i
$700$	−114029.			−0.232713
$701$		−	165775.i		−	0.337351i	−0.985672	−	0.168676i	$-0.946051\pi$
$701$		−	165775.i		−	0.337351i	0.985672	−	0.168676i	$-0.0539490\pi$
$702$	45186.9	+	67147.8i	0.0916934	+	0.136257i
$703$	345786.			0.699676
$704$		−	439340.i		−	0.886453i
$705$	−135527.	+	27112.4i	−0.272676	+	0.0545495i
$706$	13701.4			0.0274887
$707$			508538.i			1.01738i
$708$	20739.7	+	103671.i	0.0413747	+	0.206819i
$709$	−156571.			−0.311472			−0.155736	−	0.987799i	$-0.549775\pi$
$709$	−156571.			−0.311472			−0.155736	+	0.987799i	$0.549775\pi$
$710$			1.65131e6i			3.27576i
$711$	−193308.	+	80567.9i	−0.382394	+	0.159376i
$712$	−383320.			−0.756139
$713$			5518.84i			0.0108560i
$714$	−912539.	+	182555.i	−1.79001	+	0.358095i
$715$	30423.5			0.0595110
$716$		−	182169.i		−	0.355344i
$717$	−180329.	−	901407.i	−0.350773	−	1.75341i
$718$	−663007.			−1.28608
$719$		−	731807.i		−	1.41559i	−0.706416	−	0.707797i	$-0.749689\pi$
$719$		−	731807.i		−	1.41559i	0.706416	−	0.707797i	$-0.250311\pi$
$720$	−980.731	−	2353.09i	−0.00189184	−	0.00453914i
$721$	−109759.			−0.211139
$722$		−	227267.i		−	0.435976i
$723$	−75519.1	+	15107.8i	−0.144471	+	0.0289017i
$724$	−1.32074e6			−2.51966
$725$			16167.0i			0.0307577i
$726$	−117078.	−	585238.i	−0.222128	−	1.11035i
$727$	−131366.			−0.248549			−0.124275	−	0.992248i	$-0.539660\pi$
$727$	−131366.			−0.248549			−0.124275	+	0.992248i	$0.539660\pi$
$728$		−	53465.4i		−	0.100881i
$729$	200140.	−	492315.i	0.376598	−	0.926377i
$730$	1.10741e6			2.07809
$731$			339857.i			0.636007i
$732$	934539.	−	186957.i	1.74412	−	0.348914i
$733$	145629.			0.271044			0.135522	−	0.990774i	$-0.456729\pi$
$733$	145629.			0.271044			0.135522	+	0.990774i	$0.456729\pi$
$734$			1.32595e6i			2.46113i
$735$	−2126.86	−	10631.5i	−0.00393699	−	0.0196798i
$736$	69858.7			0.128963
$737$		−	532215.i		−	0.979834i
$738$	206342.	−	86000.0i	0.378856	−	0.157901i
$739$	711310.			1.30248			0.651238	−	0.758873i	$-0.274250\pi$
$739$	711310.			1.30248			0.651238	+	0.758873i	$0.274250\pi$
$740$			777045.i			1.41900i
$741$	46696.4	−	9341.72i	0.0850446	−	0.0170134i
$742$	−128574.			−0.233531
$743$		−	356613.i		−	0.645981i	−0.946402	−	0.322991i	$-0.895312\pi$
$743$		−	356613.i		−	0.645981i	0.946402	−	0.322991i	$-0.104688\pi$
$744$	9140.36	+	45689.8i	0.0165127	+	0.0825418i
$745$	−825635.			−1.48756
$746$		−	243258.i		−	0.437108i
$747$	117464.	+	281834.i	0.210506	+	0.505071i
$748$	−565657.			−1.01100
$749$		−	1.02456e6i		−	1.82630i
$750$	−816819.	+	163406.i	−1.45212	+	0.290500i
$751$	−747008.			−1.32448			−0.662240	−	0.749292i	$-0.730394\pi$
$751$	−747008.			−1.32448			−0.662240	+	0.749292i	$0.730394\pi$
$752$			675.381i			0.00119430i
$753$	77114.1	+	385470.i	0.136002	+	0.679830i
$754$	−19804.9			−0.0348361
$755$		−	560981.i		−	0.984135i
$756$	−760955.	+	512082.i	−1.33142	+	0.895975i
$757$	−376457.			−0.656937			−0.328469	−	0.944515i	$-0.606533\pi$
$757$	−376457.			−0.656937			−0.328469	+	0.944515i	$0.606533\pi$
$758$			826298.i			1.43813i
$759$	−40080.2	+	8018.13i	−0.0695738	+	0.0139184i
$760$	−530273.			−0.918062
$761$		−	1.05381e6i		−	1.81968i	−0.414965	−	0.909838i	$-0.636206\pi$
$761$		−	1.05381e6i		−	1.81968i	0.414965	−	0.909838i	$-0.363794\pi$
$762$	274979.	+	1.37454e6i	0.473577	+	2.36726i
$763$	−254263.			−0.436752
$764$			947508.i			1.62329i
$765$	658076.	−	274276.i	1.12448	−	0.468668i
$766$	−439769.			−0.749492
$767$		−	7770.98i		−	0.0132095i
$768$	582658.	−	116562.i	0.987851	−	0.197622i
$769$	321414.			0.543515			0.271758	−	0.962366i	$-0.412395\pi$
$769$	321414.			0.543515			0.271758	+	0.962366i	$0.412395\pi$
$770$			557589.i			0.940443i
$771$	−86751.2	−	433643.i	−0.145938	−	0.729497i
$772$	892031.			1.49674
$773$		−	618982.i		−	1.03590i	−0.855410	−	0.517951i	$-0.826695\pi$
$773$		−	618982.i		−	1.03590i	0.855410	−	0.517951i	$-0.173305\pi$
$774$	208403.	+	500025.i	0.347874	+	0.834661i
$775$	−7304.33			−0.0121612
$776$		−	988219.i		−	1.64108i
$777$	480009.	−	96027.0i	0.795074	−	0.159056i
$778$	528026.			0.872361
$779$		−	131531.i		−	0.216747i
$780$	20992.6	+	104935.i	0.0345045	+	0.172478i
$781$	632315.			1.03665
$782$		−	145877.i		−	0.238546i
$783$	72602.8	+	107888.i	0.118421	+	0.175974i
$784$	−52.9808			−8.61959e−5
$785$		−	1.04249e6i		−	1.69173i
$786$	−1.11740e6	+	223539.i	−1.80869	+	0.361832i
$787$	402088.			0.649190			0.324595	−	0.945853i	$-0.394772\pi$
$787$	402088.			0.649190			0.324595	+	0.945853i	$0.394772\pi$
$788$		−	539807.i		−	0.869333i
$789$	181107.	+	905299.i	0.290925	+	1.45425i
$790$	−447825.			−0.717553
$791$			516037.i			0.824760i
$792$	−318539.	+	132762.i	−0.507823	+	0.211653i
$793$	−70051.1			−0.111396
$794$		−	130369.i		−	0.206792i
$795$	96586.5	−	19322.3i	0.152821	−	0.0305721i
$796$	1.74075e6			2.74733
$797$		−	99124.1i		−	0.156050i	−0.996951	−	0.0780248i	$-0.975139\pi$
$797$		−	99124.1i		−	0.156050i	0.996951	−	0.0780248i	$-0.0248613\pi$
$798$	171211.	+	855831.i	0.268860	+	1.34395i
$799$	−188880.			−0.295865
$800$			92459.8i			0.144468i
$801$	−185946.	−	446145.i	−0.289816	−	0.695362i
$802$	−1.21765e6			−1.89310
$803$		−	424048.i		−	0.657634i
$804$	1.83569e6	−	367234.i	2.83980	−	0.568108i
$805$	−88913.9			−0.137207
$806$		−	8947.94i		−	0.0137738i
$807$	35279.0	+	176349.i	0.0541713	+	0.270786i
$808$	−673022.			−1.03088
$809$		−	63839.2i		−	0.0975418i	−0.998810	−	0.0487709i	$-0.984470\pi$
$809$		−	63839.2i		−	0.0975418i	0.998810	−	0.0487709i	$-0.0155304\pi$
$810$	800027.	−	807074.i	1.21937	−	1.23011i
$811$	−10598.6			−0.0161141			−0.00805707	−	0.999968i	$-0.502565\pi$
$811$	−10598.6			−0.0161141			−0.00805707	+	0.999968i	$0.502565\pi$
$812$		−	224440.i		−	0.340398i
$813$	−8176.93	+	1635.81i	−0.0123711	+	0.00247487i
$814$	481204.			0.726240
$815$			778250.i			1.17167i
$816$	−683.410	−	3416.16i	−0.00102636	−	0.00513048i
$817$	318738.			0.477518
$818$			123596.i			0.184713i
$819$	62228.2	−	25935.7i	0.0927725	−	0.0386662i
$820$	295574.			0.439581
$821$			1.05519e6i			1.56546i	0.622360	+	0.782731i	$0.286174\pi$
$821$			1.05519e6i			1.56546i	−0.622360	+	0.782731i	$0.713826\pi$
$822$	−583117.	+	116654.i	−0.863003	+	0.172646i
$823$	−380641.			−0.561974			−0.280987	−	0.959712i	$-0.590662\pi$
$823$	−380641.			−0.561974			−0.280987	+	0.959712i	$0.590662\pi$
$824$		−	145260.i		−	0.213940i
$825$	−10612.2	−	53047.1i	−0.0155918	−	0.0779388i
$826$	142423.			0.208747
$827$			365073.i			0.533787i	0.963726	+	0.266894i	$0.0859973\pi$
$827$			365073.i			0.533787i	−0.963726	+	0.266894i	$0.914003\pi$
$828$	−55311.5	−	132710.i	−0.0806779	−	0.193572i
$829$	864659.			1.25816			0.629080	−	0.777341i	$-0.283432\pi$
$829$	864659.			1.25816			0.629080	+	0.777341i	$0.283432\pi$
$830$			652907.i			0.947753i
$831$	1.12928e6	−	225916.i	1.63531	−	0.327148i
$832$	−113588.			−0.164091
$833$		−	14816.9i		−	0.0213534i
$834$	236470.	+	1.18204e6i	0.339972	+	1.69942i
$835$	−805072.			−1.15468
$836$			530506.i			0.759062i
$837$	−48744.3	+	32802.3i	−0.0695781	+	0.0468223i
$838$	984403.			1.40180
$839$		−	802316.i		−	1.13978i	−0.821720	−	0.569891i	$-0.806985\pi$
$839$		−	802316.i		−	1.13978i	0.821720	−	0.569891i	$-0.193015\pi$
$840$	−736107.	+	147260.i	−1.04324	+	0.208702i
$841$	675460.			0.955009
$842$			1.08076e6i			1.52442i
$843$	137219.	+	685914.i	0.193089	+	0.965194i
$844$	−1.64939e6			−2.31547
$845$			756177.i			1.05903i
$846$	−277896.	+	115823.i	−0.388277	+	0.161828i
$847$	−497139.			−0.692964
$848$		−	481.327i		−	0.000669342i
$849$	−125655.	+	25137.6i	−0.174327	+	0.0348746i
$850$	193071.			0.267227
$851$			76733.4i			0.105956i
$852$	436305.	+	2.18095e6i	0.601050	+	3.00446i
$853$	264679.			0.363765			0.181882	−	0.983320i	$-0.441781\pi$
$853$	264679.			0.363765			0.181882	+	0.983320i	$0.441781\pi$
$854$		−	1.28387e6i		−	1.76037i
$855$	−257232.	−	617182.i	−0.351879	−	0.844269i
$856$	1.35595e6			1.85053
$857$			604516.i			0.823088i	0.911390	+	0.411544i	$0.135010\pi$
$857$			604516.i			0.823088i	−0.911390	+	0.411544i	$0.864990\pi$
$858$	64983.7	−	13000.1i	0.0882734	−	0.0176593i
$859$	−444881.			−0.602917			−0.301459	−	0.953479i	$-0.597474\pi$
$859$	−444881.			−0.602917			−0.301459	+	0.953479i	$0.597474\pi$
$860$			716262.i			0.968445i
$861$	−36527.0	−	182587.i	−0.0492728	−	0.246300i
$862$	−8731.36			−0.0117508
$863$			92519.9i			0.124226i	0.998069	+	0.0621132i	$0.0197840\pi$
$863$			92519.9i			0.124226i	−0.998069	+	0.0621132i	$0.980216\pi$
$864$	415218.	+	617016.i	0.556223	+	0.826549i
$865$	845123.			1.12950
$866$			1.89968e6i			2.53305i
$867$	218295.	−	43670.5i	0.290406	−	0.0580965i
$868$	101403.			0.134589
$869$			171480.i			0.227077i
$870$	54548.6	+	272672.i	0.0720685	+	0.360248i
$871$	−137600.			−0.181377
$872$		−	336504.i		−	0.442545i
$873$	1.15018e6	−	479379.i	1.50917	−	0.629000i
$874$	−136812.			−0.179102
$875$			693858.i			0.906264i
$876$	1.46261e6	−	292598.i	1.90599	−	0.381297i
$877$	−1.19525e6			−1.55403			−0.777014	−	0.629483i	$-0.783267\pi$
$877$	−1.19525e6			−1.55403			−0.777014	+	0.629483i	$0.783267\pi$
$878$		−	1.67512e6i		−	2.17299i
$879$	167191.	+	835735.i	0.216388	+	1.08166i
$880$	−2087.38			−0.00269548
$881$		−	1.52256e6i		−	1.96166i	−0.194870	−	0.980829i	$-0.562429\pi$
$881$		−	1.52256e6i		−	1.96166i	0.194870	−	0.980829i	$-0.437571\pi$
$882$	−9085.82	−	21799.8i	−0.0116796	−	0.0280230i
$883$	1.38373e6			1.77471			0.887357	−	0.461083i	$-0.152539\pi$
$883$	1.38373e6			1.77471			0.887357	+	0.461083i	$0.152539\pi$
$884$			146246.i			0.187145i
$885$	−106990.	+	21403.6i	−0.136602	+	0.0273276i
$886$	−579486.			−0.738203
$887$			952113.i			1.21016i	0.796166	+	0.605078i	$0.206858\pi$
$887$			952113.i			1.21016i	−0.796166	+	0.605078i	$0.793142\pi$
$888$	127087.	+	635266.i	0.161166	+	0.805620i
$889$	1.16762e6			1.47740
$890$		−	1.03355e6i		−	1.30483i
$891$	−309043.	−	306344.i	−0.389281	−	0.385882i
$892$	−1.56596e6			−1.96812
$893$			177143.i			0.222137i
$894$	−1.76353e6	+	352798.i	−2.20652	+	0.441419i
$895$	188001.			0.234701
$896$		−	1.28950e6i		−	1.60622i
$897$	2073.02	+	10362.4i	0.00257643	+	0.0128788i
$898$	−93006.9			−0.115335
$899$		−	14376.9i		−	0.0177887i
$900$	175645.	−	73206.2i	0.216846	−	0.0903780i
$901$	134610.			0.165817
$902$		−	183041.i		−	0.224976i
$903$	442461.	−	88515.4i	0.542625	−	0.108553i
$904$	−682946.			−0.835699
$905$		−	1.36303e6i		−	1.66421i
$906$	−239710.	−	1.19824e6i	−0.292032	−	1.45978i
$907$	727198.			0.883972			0.441986	−	0.897022i	$-0.354274\pi$
$907$	727198.			0.883972			0.441986	+	0.897022i	$0.354274\pi$
$908$		−	1.18005e6i		−	1.43129i
$909$	−326479.	−	783327.i	−0.395119	−	0.948016i
$910$	144160.			0.174085
$911$			748391.i			0.901762i	0.892584	+	0.450881i	$0.148890\pi$
$911$			748391.i			0.901762i	−0.892584	+	0.450881i	$0.851110\pi$
$912$	−3203.87	+	640.942i	−0.00385199	+	0.000770600i
$913$	250009.			0.299927
$914$		−	1.45012e6i		−	1.73585i
$915$	192942.	+	964458.i	0.230454	+	1.15197i
$916$	−493915.			−0.588655
$917$			949192.i			1.12880i
$918$	1.28843e6	−	867045.i	1.52889	−	1.02886i
$919$	908418.			1.07561			0.537805	−	0.843069i	$-0.319254\pi$
$919$	908418.			1.07561			0.537805	+	0.843069i	$0.319254\pi$
$920$		−	117673.i		−	0.139027i
$921$	−1.04749e6	+	209554.i	−1.23490	+	0.247045i
$922$	−1.90018e6			−2.23528
$923$		−	163480.i		−	0.191894i
$924$	147325.	+	736431.i	0.172557	+	0.862557i
$925$	−101559.			−0.118695
$926$		−	1.27882e6i		−	1.49138i
$927$	169067.	−	70464.6i	0.196743	−	0.0819996i
$928$	−181985.			−0.211320
$929$			301938.i			0.349853i	0.984581	+	0.174927i	$0.0559688\pi$
$929$			301938.i			0.349853i	−0.984581	+	0.174927i	$0.944031\pi$
$930$	−123194.	+	24645.3i	−0.142438	+	0.0284950i
$931$	−13896.1			−0.0160322
$932$		−	2.19553e6i		−	2.52760i
$933$	−19822.1	−	99084.6i	−0.0227712	−	0.113826i
$934$	−2.38831e6			−2.73777
$935$		−	583766.i		−	0.667753i
$936$	34324.6	+	82355.6i	0.0391790	+	0.0940029i
$937$	−788069.			−0.897604			−0.448802	−	0.893631i	$-0.648149\pi$
$937$	−788069.			−0.897604			−0.448802	+	0.893631i	$0.648149\pi$
$938$		−	2.52187e6i		−	2.86627i
$939$	−380281.	+	76076.2i	−0.431294	+	0.0862815i
$940$	−398072.			−0.450512
$941$		−	347979.i		−	0.392983i	−0.980506	−	0.196491i	$-0.937045\pi$
$941$		−	347979.i		−	0.392983i	0.980506	−	0.196491i	$-0.0629548\pi$
$942$	−445460.	−	2.22672e6i	−0.502004	−	2.50936i
$943$	29188.0			0.0328232
$944$			533.172i			0.000598306i
$945$	−528476.	−	785317.i	−0.591782	−	0.879390i
$946$	443562.			0.495647
$947$			704206.i			0.785236i	0.919702	+	0.392618i	$0.128430\pi$
$947$			704206.i			0.785236i	−0.919702	+	0.392618i	$0.871570\pi$
$948$	−591460.	+	118323.i	−0.658126	+	0.131660i
$949$	−109634.			−0.121734
$950$		−	181074.i		−	0.200635i
$951$	−60683.4	−	303338.i	−0.0670979	−	0.335402i
$952$	−1.02589e6			−1.13195
$953$		−	885025.i		−	0.974473i	−0.873270	−	0.487236i	$-0.838005\pi$
$953$		−	885025.i		−	0.974473i	0.873270	−	0.487236i	$-0.161995\pi$
$954$	198049.	−	82543.9i	0.217609	−	0.0906960i
$955$	−977842.			−1.07217
$956$		−	2.64763e6i		−	2.89696i
$957$	104411.	−	20887.6i	0.114004	−	0.0228068i
$958$	−2.13489e6			−2.32619
$959$			495338.i			0.538597i
$960$	312855.	+	1.56387e6i	0.339469	+	1.69690i
$961$	−917025.			−0.992967
$962$		−	124411.i		−	0.134434i
$963$	657762.	+	1.57818e6i	0.709277	+	1.70178i
$964$	−221816.			−0.238693
$965$			920589.i			0.988579i
$966$	−189917.	+	37993.4i	−0.203522	+	0.0407149i
$967$	565109.			0.604337			0.302169	−	0.953254i	$-0.402289\pi$
$967$	565109.			0.604337			0.302169	+	0.953254i	$0.402289\pi$
$968$		−	657936.i		−	0.702155i
$969$	−179249.	−	896010.i	−0.190901	−	0.954257i
$970$	2.66456e6			2.83192
$971$		−	1.67113e6i		−	1.77244i	−0.463268	−	0.886218i	$-0.653323\pi$
$971$		−	1.67113e6i		−	1.77244i	0.463268	−	0.886218i	$-0.346677\pi$
$972$	843385.	−	1.27732e6i	0.892675	−	1.35197i
$973$	1.00410e6			1.06060
$974$		−	569024.i		−	0.599809i
$975$	−13714.9	+	2743.69i	−0.0144272	+	0.00288620i
$976$	4806.25			0.00504553
$977$		−	57680.8i		−	0.0604285i	−0.999543	−	0.0302143i	$-0.990381\pi$
$977$		−	57680.8i		−	0.0604285i	0.999543	−	0.0302143i	$-0.00961896\pi$
$978$	332551.	+	1.66232e6i	0.347680	+	1.73795i
$979$	−395766.			−0.412927
$980$		−	31227.1i		−	0.0325147i
$981$	391655.	−	163236.i	0.406973	−	0.169620i
$982$	−119812.			−0.124244
$983$			704181.i			0.728748i	0.931253	+	0.364374i	$0.118717\pi$
$983$			704181.i			0.728748i	−0.931253	+	0.364374i	$0.881283\pi$
$984$	241644.	−	48341.5i	0.249566	−	0.0499263i
$985$	557089.			0.574186
$986$			380016.i			0.390884i
$987$	49193.6	+	245904.i	0.0504981	+	0.252424i
$988$	137158.			0.140510
$989$			70731.0i			0.0723131i
$990$	−357969.	−	858883.i	−0.365238	−	0.876322i
$991$	880717.			0.896786			0.448393	−	0.893836i	$-0.351996\pi$
$991$	880717.			0.896786			0.448393	+	0.893836i	$0.351996\pi$
$992$		−	82221.9i		−	0.0835534i
$993$	669701.	−	133975.i	0.679176	−	0.135871i
$994$	2.99619e6			3.03247
$995$			1.79648e6i			1.81459i
$996$	172509.	+	862321.i	0.173898	+	0.869261i
$997$	275274.			0.276933			0.138466	−	0.990367i	$-0.455783\pi$
$997$	275274.			0.276933			0.138466	+	0.990367i	$0.455783\pi$
$998$			1.11231e6i			1.11677i
$999$	−677735.	+	456079.i	−0.679092	+	0.456993i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.5.b.a.119.70	yes	78
3.2	odd	2	inner	177.5.b.a.119.9	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.5.b.a.119.9	✓	78	3.2	odd	2	inner
177.5.b.a.119.70	yes	78	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	177.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+6.47467i q^{2} +(-8.82514 + 1.76549i) q^{3} -25.9214 q^{4} -26.7513i q^{5} +(-11.4310 - 57.1399i) q^{6} -48.5383 q^{7} -64.2378i q^{8} +(74.7661 - 31.1614i) q^{9} +O(q^{10})\)	\(q+6.47467i q^{2} +(-8.82514 + 1.76549i) q^{3} -25.9214 q^{4} -26.7513i q^{5} +(-11.4310 - 57.1399i) q^{6} -48.5383 q^{7} -64.2378i q^{8} +(74.7661 - 31.1614i) q^{9} +173.206 q^{10} -66.3235i q^{11} +(228.760 - 45.7639i) q^{12} -17.1474 q^{13} -314.270i q^{14} +(47.2291 + 236.084i) q^{15} +1.17649 q^{16} +329.024i q^{17} +(201.760 + 484.086i) q^{18} +308.577 q^{19} +693.430i q^{20} +(428.357 - 85.6938i) q^{21} +429.423 q^{22} +68.4764i q^{23} +(113.411 + 566.908i) q^{24} -90.6302 q^{25} -111.024i q^{26} +(-604.806 + 407.002i) q^{27} +1258.18 q^{28} -178.384i q^{29} +(-1528.56 + 305.793i) q^{30} +80.5949 q^{31} -1020.19i q^{32} +(117.093 + 585.314i) q^{33} -2130.32 q^{34} +1298.46i q^{35} +(-1938.04 + 807.746i) q^{36} +1120.58 q^{37} +1997.94i q^{38} +(151.328 - 30.2735i) q^{39} -1718.44 q^{40} -426.250i q^{41} +(554.840 + 2773.47i) q^{42} +1032.93 q^{43} +1719.20i q^{44} +(-833.606 - 2000.09i) q^{45} -443.362 q^{46} +574.063i q^{47} +(-10.3827 + 2.07709i) q^{48} -45.0329 q^{49} -586.801i q^{50} +(-580.888 - 2903.68i) q^{51} +444.484 q^{52} -409.120i q^{53} +(-2635.21 - 3915.92i) q^{54} -1774.24 q^{55} +3117.99i q^{56} +(-2723.24 + 544.790i) q^{57} +1154.98 q^{58} +453.188i q^{59} +(-1224.24 - 6119.62i) q^{60} +4085.24 q^{61} +521.826i q^{62} +(-3629.02 + 1512.52i) q^{63} +6624.21 q^{64} +458.714i q^{65} +(-3789.72 + 758.141i) q^{66} +8024.54 q^{67} -8528.76i q^{68} +(-120.894 - 604.313i) q^{69} -8407.11 q^{70} +9533.81i q^{71} +(-2001.74 - 4802.81i) q^{72} +6393.64 q^{73} +7255.40i q^{74} +(799.824 - 160.007i) q^{75} -7998.76 q^{76} +3219.23i q^{77} +(196.011 + 979.799i) q^{78} -2585.51 q^{79} -31.4727i q^{80} +(4618.94 - 4659.63i) q^{81} +2759.83 q^{82} +3769.55i q^{83} +(-11103.6 + 2221.30i) q^{84} +8801.80 q^{85} +6687.86i q^{86} +(314.936 + 1574.27i) q^{87} -4260.48 q^{88} -5967.21i q^{89} +(12949.9 - 5397.33i) q^{90} +832.305 q^{91} -1775.00i q^{92} +(-711.261 + 142.289i) q^{93} -3716.87 q^{94} -8254.84i q^{95} +(1801.13 + 9003.30i) q^{96} +15383.8 q^{97} -291.573i q^{98} +(-2066.73 - 4958.75i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9}+O(q^{10}) \) 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9	\( 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9} - 156 q^{10} - 4 q^{13} + 13 q^{15} + 4948 q^{16} + 22 q^{18} + 812 q^{19} - 173 q^{21} - 1644 q^{22} - 678 q^{24} - 8238 q^{25} + 777 q^{27} - 3764 q^{28} + 1374 q^{30} + 4664 q^{31} - 1042 q^{33} + 3244 q^{34} + 3648 q^{36} - 3960 q^{37} - 7078 q^{39} - 1576 q^{40} + 4934 q^{42} - 1492 q^{43} - 2063 q^{45} - 2036 q^{46} - 2620 q^{48} + 24274 q^{49} + 7300 q^{51} + 8408 q^{52} - 14766 q^{54} + 9780 q^{55} + 6939 q^{57} - 3856 q^{58} + 4712 q^{60} - 212 q^{61} - 7438 q^{63} - 45760 q^{64} + 3048 q^{66} - 12972 q^{67} + 21672 q^{69} + 5828 q^{70} - 866 q^{72} - 5240 q^{73} - 20922 q^{75} + 12368 q^{76} - 16508 q^{78} - 14976 q^{79} + 25524 q^{81} - 14484 q^{82} + 9540 q^{84} + 11572 q^{85} + 5695 q^{87} + 62160 q^{88} - 31672 q^{90} + 8284 q^{91} - 9590 q^{93} - 10992 q^{94} + 34102 q^{96} - 55000 q^{97} - 14254 q^{99}+O(q^{100}) \) 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9 - 156 * q^10 - 4 * q^13 + 13 * q^15 + 4948 * q^16 + 22 * q^18 + 812 * q^19 - 173 * q^21 - 1644 * q^22 - 678 * q^24 - 8238 * q^25 + 777 * q^27 - 3764 * q^28 + 1374 * q^30 + 4664 * q^31 - 1042 * q^33 + 3244 * q^34 + 3648 * q^36 - 3960 * q^37 - 7078 * q^39 - 1576 * q^40 + 4934 * q^42 - 1492 * q^43 - 2063 * q^45 - 2036 * q^46 - 2620 * q^48 + 24274 * q^49 + 7300 * q^51 + 8408 * q^52 - 14766 * q^54 + 9780 * q^55 + 6939 * q^57 - 3856 * q^58 + 4712 * q^60 - 212 * q^61 - 7438 * q^63 - 45760 * q^64 + 3048 * q^66 - 12972 * q^67 + 21672 * q^69 + 5828 * q^70 - 866 * q^72 - 5240 * q^73 - 20922 * q^75 + 12368 * q^76 - 16508 * q^78 - 14976 * q^79 + 25524 * q^81 - 14484 * q^82 + 9540 * q^84 + 11572 * q^85 + 5695 * q^87 + 62160 * q^88 - 31672 * q^90 + 8284 * q^91 - 9590 * q^93 - 10992 * q^94 + 34102 * q^96 - 55000 * q^97 - 14254 * q^99

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