LMFDB - Embedded newform 177.4.f.a.2.3

Newspace parameters

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	177.f (of order $58$, degree $28$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$10.4433380710$
Analytic rank:	$0$
Dimension:	$1624$
Relative dimension:	$58$ over $\Q(\zeta_{58})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{58}]$

Embedding invariants

Embedding label			2.3
Character	$\chi$	$=$	177.2
Dual form			177.4.f.a.89.3

$q$-expansion

$f(q)$	$=$	$q+(-0.282358 + 5.20779i) q^{2} +(-0.412985 + 5.17971i) q^{3} +(-19.0882 - 2.07597i) q^{4} +(-2.66012 + 7.89495i) q^{5} +(-26.8583 - 3.61327i) q^{6} +(2.27648 + 3.35756i) q^{7} +(9.45083 - 57.6475i) q^{8} +(-26.6589 - 4.27829i) q^{9} +O(q^{10})$	\(q+(-0.282358 + 5.20779i) q^{2} +(-0.412985 + 5.17971i) q^{3} +(-19.0882 - 2.07597i) q^{4} +(-2.66012 + 7.89495i) q^{5} +(-26.8583 - 3.61327i) q^{6} +(2.27648 + 3.35756i) q^{7} +(9.45083 - 57.6475i) q^{8} +(-26.6589 - 4.27829i) q^{9} +(-40.3641 - 16.0825i) q^{10} +(19.5208 - 4.29684i) q^{11} +(18.6361 - 98.0143i) q^{12} +(-36.1212 + 30.6817i) q^{13} +(-18.1282 + 10.9074i) q^{14} +(-39.7950 - 17.0391i) q^{15} +(147.532 + 32.4743i) q^{16} +(48.1112 + 32.6202i) q^{17} +(29.8078 - 137.626i) q^{18} +(39.6830 - 74.8501i) q^{19} +(67.1667 - 145.178i) q^{20} +(-18.3313 + 10.4049i) q^{21} +(16.8652 + 102.873i) q^{22} +(-107.044 + 101.397i) q^{23} +(294.695 + 72.7601i) q^{24} +(44.2576 + 33.6438i) q^{25} +(-149.584 - 196.775i) q^{26} +(33.1700 - 136.319i) q^{27} +(-36.4838 - 68.8157i) q^{28} +(71.3607 - 3.86907i) q^{29} +(99.9727 - 202.433i) q^{30} +(-242.317 + 128.468i) q^{31} +(-85.7507 + 308.846i) q^{32} +(14.1946 + 102.886i) q^{33} +(-183.464 + 241.342i) q^{34} +(-32.5634 + 9.04119i) q^{35} +(499.990 + 137.008i) q^{36} +(-40.4009 + 6.62339i) q^{37} +(378.599 + 227.795i) q^{38} +(-144.005 - 199.769i) q^{39} +(429.984 + 227.963i) q^{40} +(224.811 - 237.330i) q^{41} +(-49.0105 - 98.4036i) q^{42} +(-76.7406 + 348.636i) q^{43} +(-381.537 + 41.4946i) q^{44} +(104.693 - 199.090i) q^{45} +(-497.830 - 586.091i) q^{46} +(136.613 - 46.0303i) q^{47} +(-229.136 + 750.764i) q^{48} +(120.867 - 303.352i) q^{49} +(-187.706 + 220.985i) q^{50} +(-188.833 + 235.731i) q^{51} +(753.185 - 510.672i) q^{52} +(-251.866 + 100.352i) q^{53} +(700.552 + 211.233i) q^{54} +(-18.0042 + 165.545i) q^{55} +(215.069 - 99.5017i) q^{56} +(371.314 + 236.459i) q^{57} +372.724i q^{58} +(-116.547 - 437.945i) q^{59} +(724.244 + 407.861i) q^{60} +(-778.239 - 42.1949i) q^{61} +(-600.617 - 1298.21i) q^{62} +(-46.3238 - 99.2481i) q^{63} +(-438.941 - 147.896i) q^{64} +(-146.143 - 366.792i) q^{65} +(-539.819 + 44.8719i) q^{66} +(336.138 + 55.1071i) q^{67} +(-850.640 - 722.540i) q^{68} +(-481.000 - 596.331i) q^{69} +(-37.8901 - 172.136i) q^{70} +(-134.699 - 399.772i) q^{71} +(-498.581 + 1496.38i) q^{72} +(-260.421 - 432.823i) q^{73} +(-23.0857 - 212.269i) q^{74} +(-192.543 + 215.348i) q^{75} +(-912.866 + 1346.38i) q^{76} +(58.8655 + 55.7603i) q^{77} +(1081.01 - 693.540i) q^{78} +(-389.756 - 180.320i) q^{79} +(-648.837 + 1078.37i) q^{80} +(692.392 + 228.109i) q^{81} +(1172.49 + 1237.78i) q^{82} +(57.4797 + 207.023i) q^{83} +(371.513 - 160.556i) q^{84} +(-385.516 + 293.062i) q^{85} +(-1793.96 - 498.089i) q^{86} +(-9.43026 + 371.226i) q^{87} +(-63.2149 - 1165.93i) q^{88} +(24.4740 + 451.397i) q^{89} +(1007.26 + 601.432i) q^{90} +(-185.245 - 51.4329i) q^{91} +(2253.77 - 1713.27i) q^{92} +(-565.357 - 1308.19i) q^{93} +(201.142 + 724.449i) q^{94} +(485.376 + 512.406i) q^{95} +(-1564.32 - 571.713i) q^{96} +(-652.015 + 1083.66i) q^{97} +(1545.67 + 715.102i) q^{98} +(-538.785 + 31.0336i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1624q - 21q^{3} - 278q^{4} - 29q^{6} - 42q^{7} - 25q^{9} + O(q^{10}) $	$ 1624q - 21q^{3} - 278q^{4} - 29q^{6} - 42q^{7} - 25q^{9} - 58q^{10} - 57q^{12} - 58q^{13} - 11q^{15} - 926q^{16} - 29q^{18} + 126q^{19} + 159q^{21} + 2q^{22} - 29q^{24} + 656q^{25} - 99q^{27} - 54q^{28} - 29q^{30} - 58q^{31} - 29q^{33} - 58q^{34} + 859q^{36} - 58q^{37} - 29q^{39} - 58q^{40} - 29q^{42} - 58q^{43} + 1703q^{45} + 602q^{46} + 9507q^{48} - 1192q^{49} + 1511q^{51} - 58q^{52} - 7743q^{54} - 58q^{55} - 7441q^{57} - 18722q^{60} - 58q^{61} - 3251q^{63} - 4634q^{64} - 1751q^{66} - 58q^{67} + 6003q^{69} - 58q^{70} + 21547q^{72} - 58q^{73} + 3869q^{75} + 5622q^{76} - 3253q^{78} + 1446q^{79} + 247q^{81} - 58q^{82} + 3303q^{84} + 790q^{85} - 2199q^{87} - 5818q^{88} - 29q^{90} - 58q^{91} - 29q^{93} - 946q^{94} - 29q^{96} - 58q^{97} - 29q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{1}{58}\right)$	$-1$

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 $

$2$	−0.282358	+	5.20779i	−0.0998287	+	1.84123i	0.336784	+	0.941582i	$0.390661\pi$
$2$	−0.282358	+	5.20779i	−0.0998287	+	1.84123i	−0.436613	+	0.899650i	$0.643822\pi$
$3$	−0.412985	+	5.17971i	−0.0794790	+	0.996837i
$3$	−0.412985	+	5.17971i	−0.0794790	+	0.996837i
$4$	−19.0882	−	2.07597i	−2.38603	−	0.259496i
$5$	−2.66012	+	7.89495i	−0.237928	+	0.706146i	0.760460	+	0.649385i	$0.224974\pi$
$5$	−2.66012	+	7.89495i	−0.237928	+	0.706146i	−0.998388	+	0.0567605i	$0.981923\pi$
$6$	−26.8583	−	3.61327i	−1.82747	−	0.245852i
$7$	2.27648	+	3.35756i	0.122918	+	0.181291i	0.884170	−	0.467166i	$-0.154725\pi$
$7$	2.27648	+	3.35756i	0.122918	+	0.181291i	−0.761251	+	0.648457i	$0.775415\pi$
$8$	9.45083	−	57.6475i	0.417671	−	2.54768i
$9$	−26.6589	−	4.27829i	−0.987366	−	0.158455i
$10$	−40.3641	−	16.0825i	−1.27643	−	0.508574i
$11$	19.5208	−	4.29684i	0.535066	−	0.117777i	0.0607858	−	0.998151i	$-0.480639\pi$
$11$	19.5208	−	4.29684i	0.535066	−	0.117777i	0.474280	+	0.880374i	$0.342708\pi$
$12$	18.6361	−	98.0143i	0.448315	−	2.35786i
$13$	−36.1212	+	30.6817i	−0.770633	+	0.654582i	−0.943877	−	0.330297i	$-0.892851\pi$
$13$	−36.1212	+	30.6817i	−0.770633	+	0.654582i	0.173244	+	0.984879i	$0.444575\pi$
$14$	−18.1282	+	10.9074i	−0.346069	+	0.208223i
$15$	−39.7950	−	17.0391i	−0.685002	−	0.293299i
$16$	147.532	+	32.4743i	2.30519	+	0.507411i
$17$	48.1112	+	32.6202i	0.686393	+	0.465386i	0.853868	−	0.520490i	$-0.174251\pi$
$17$	48.1112	+	32.6202i	0.686393	+	0.465386i	−0.167474	+	0.985876i	$0.553561\pi$
$18$	29.8078	−	137.626i	0.390320	−	1.80215i
$19$	39.6830	−	74.8501i	0.479153	−	0.903779i	−0.519627	−	0.854393i	$-0.673929\pi$
$19$	39.6830	−	74.8501i	0.479153	−	0.903779i	0.998780	−	0.0493853i	$-0.0157262\pi$
$20$	67.1667	−	145.178i	0.750946	−	1.62314i
$21$	−18.3313	+	10.4049i	−0.190487	+	0.108121i
$22$	16.8652	+	102.873i	0.163440	+	0.996938i
$23$	−107.044	+	101.397i	−0.970440	+	0.919250i	−0.996762	−	0.0804036i	$-0.974379\pi$
$23$	−107.044	+	101.397i	−0.970440	+	0.919250i	0.0263220	+	0.999654i	$0.491620\pi$
$24$	294.695	+	72.7601i	2.50643	+	0.618838i
$25$	44.2576	+	33.6438i	0.354061	+	0.269150i
$26$	−149.584	−	196.775i	−1.12830	−	1.48426i
$27$	33.1700	−	136.319i	0.236429	−	0.971649i
$28$	−36.4838	−	68.8157i	−0.246242	−	0.464463i
$29$	71.3607	−	3.86907i	0.456943	−	0.0247747i	0.175769	−	0.984431i	$-0.443759\pi$
$29$	71.3607	−	3.86907i	0.456943	−	0.0247747i	0.281174	+	0.959657i	$0.409276\pi$
$30$	99.9727	−	202.433i	0.608415	−	1.23197i
$31$	−242.317	+	128.468i	−1.40392	+	0.744310i	−0.986401	−	0.164358i	$-0.947445\pi$
$31$	−242.317	+	128.468i	−1.40392	+	0.744310i	−0.417518	+	0.908669i	$0.637100\pi$
$32$	−85.7507	+	308.846i	−0.473710	+	1.70615i
$33$	14.1946	+	102.886i	0.0748779	+	0.542734i
$34$	−183.464	+	241.342i	−0.925405	+	1.21735i
$35$	−32.5634	+	9.04119i	−0.157264	+	0.0436640i
$36$	499.990	+	137.008i	2.31477	+	0.634297i
$37$	−40.4009	+	6.62339i	−0.179510	+	0.0294292i	−0.250866	−	0.968022i	$-0.580715\pi$
$37$	−40.4009	+	6.62339i	−0.179510	+	0.0294292i	0.0713565	+	0.997451i	$0.477267\pi$
$38$	378.599	+	227.795i	1.61623	+	0.972455i
$39$	−144.005	−	199.769i	−0.591262	−	0.820221i
$40$	429.984	+	227.963i	1.69966	+	0.901103i
$41$	224.811	−	237.330i	0.856332	−	0.904019i	−0.139951	−	0.990158i	$-0.544695\pi$
$41$	224.811	−	237.330i	0.856332	−	0.904019i	0.996283	+	0.0861399i	$0.0274532\pi$
$42$	−49.0105	−	98.4036i	−0.180059	−	0.361524i
$43$	−76.7406	+	348.636i	−0.272159	+	1.23643i	0.619961	+	0.784632i	$0.287148\pi$
$43$	−76.7406	+	348.636i	−0.272159	+	1.23643i	−0.892120	+	0.451798i	$0.850783\pi$
$44$	−381.537	+	41.4946i	−1.30725	+	0.142172i
$45$	104.693	−	199.090i	0.346815	−	0.659523i
$46$	−497.830	−	586.091i	−1.59567	−	1.87857i
$47$	136.613	−	46.0303i	0.423980	−	0.142856i	−0.0992197	−	0.995066i	$-0.531635\pi$
$47$	136.613	−	46.0303i	0.423980	−	0.142856i	0.523200	+	0.852210i	$0.324738\pi$
$48$	−229.136	+	750.764i	−0.689021	+	2.25757i
$49$	120.867	−	303.352i	0.352381	−	0.884409i
$50$	−187.706	+	220.985i	−0.530913	+	0.625040i
$51$	−188.833	+	235.731i	−0.518468	+	0.647233i
$52$	753.185	−	510.672i	2.00861	−	1.36187i
$53$	−251.866	+	100.352i	−0.652762	+	0.260084i	−0.672923	−	0.739712i	$-0.734962\pi$
$53$	−251.866	+	100.352i	−0.652762	+	0.260084i	0.0201607	+	0.999797i	$0.493582\pi$
$54$	700.552	+	211.233i	1.76543	+	0.532319i
$55$	−18.0042	+	165.545i	−0.0441396	+	0.405857i
$56$	215.069	−	99.5017i	0.513211	−	0.237437i
$57$	371.314	+	236.459i	0.862837	+	0.549469i
$58$			372.724i			0.843812i
$59$	−116.547	−	437.945i	−0.257171	−	0.966366i
$59$	−116.547	−	437.945i	−0.257171	−	0.966366i
$60$	724.244	+	407.861i	1.55832	+	0.877576i
$61$	−778.239	−	42.1949i	−1.63350	−	0.0885656i	−0.785603	−	0.618731i	$-0.787647\pi$
$61$	−778.239	−	42.1949i	−1.63350	−	0.0885656i	−0.847894	+	0.530165i	$0.822130\pi$
$62$	−600.617	−	1298.21i	−1.23030	−	2.65924i
$63$	−46.3238	−	99.2481i	−0.0926389	−	0.198478i
$64$	−438.941	−	147.896i	−0.857307	−	0.288860i
$65$	−146.143	−	366.792i	−0.278875	−	0.699923i
$66$	−539.819	+	44.8719i	−1.00677	+	0.0836870i
$67$	336.138	+	55.1071i	0.612923	+	0.100484i	0.460244	−	0.887792i	$-0.347762\pi$
$67$	336.138	+	55.1071i	0.612923	+	0.100484i	0.152679	+	0.988276i	$0.451210\pi$
$68$	−850.640	−	722.540i	−1.51699	−	1.28854i
$69$	−481.000	−	596.331i	−0.839212	−	1.04043i
$70$	−37.8901	−	172.136i	−0.0646962	−	0.293918i
$71$	−134.699	−	399.772i	−0.225153	−	0.668229i	−0.999376	−	0.0353169i	$-0.988756\pi$
$71$	−134.699	−	399.772i	−0.225153	−	0.668229i	0.774224	−	0.632912i	$-0.218141\pi$
$72$	−498.581	+	1496.38i	−0.816088	+	2.44931i
$73$	−260.421	−	432.823i	−0.417533	−	0.693946i	0.574696	−	0.818367i	$-0.305120\pi$
$73$	−260.421	−	432.823i	−0.417533	−	0.693946i	−0.992230	+	0.124421i	$0.960293\pi$
$74$	−23.0857	−	212.269i	−0.0362656	−	0.333457i
$75$	−192.543	+	215.348i	−0.296439	+	0.331549i
$76$	−912.866	+	1346.38i	−1.37780	+	2.03210i
$77$	58.8655	+	55.7603i	0.0871214	+	0.0825257i
$78$	1081.01	−	693.540i	1.56924	−	1.00677i
$79$	−389.756	−	180.320i	−0.555076	−	0.256806i	0.122236	−	0.992501i	$-0.460993\pi$
$79$	−389.756	−	180.320i	−0.555076	−	0.256806i	−0.677312	+	0.735696i	$0.736855\pi$
$80$	−648.837	+	1078.37i	−0.906777	+	1.50707i
$81$	692.392	+	228.109i	0.949784	+	0.312907i
$82$	1172.49	+	1237.78i	1.57902	+	1.66695i
$83$	57.4797	+	207.023i	0.0760146	+	0.273780i	0.991784	−	0.127925i	$-0.0408316\pi$
$83$	57.4797	+	207.023i	0.0760146	+	0.273780i	−0.915769	+	0.401705i	$0.868418\pi$
$84$	371.513	−	160.556i	0.482564	−	0.208548i
$85$	−385.516	+	293.062i	−0.491943	+	0.373965i
$86$	−1793.96	−	498.089i	−2.24939	−	0.624539i
$87$	−9.43026	+	371.226i	−0.0116210	+	0.457467i
$88$	−63.2149	−	1165.93i	−0.0765765	−	1.41237i
$89$	24.4740	+	451.397i	0.0291488	+	0.537618i	0.976245	+	0.216669i	$0.0695191\pi$
$89$	24.4740	+	451.397i	0.0291488	+	0.537618i	−0.947096	+	0.320949i	$0.895998\pi$
$90$	1007.26	+	601.432i	1.17971	+	0.704405i
$91$	−185.245	−	51.4329i	−0.213395	−	0.0592487i
$92$	2253.77	−	1713.27i	2.55404	−	1.94153i
$93$	−565.357	−	1308.19i	−0.630374	−	1.45863i
$94$	201.142	+	724.449i	0.220705	+	0.794907i
$95$	485.376	+	512.406i	0.524195	+	0.553386i
$96$	−1564.32	−	571.713i	−1.66310	−	0.607814i
$97$	−652.015	+	1083.66i	−0.682496	+	1.13432i	0.301042	+	0.953611i	$0.402666\pi$
$97$	−652.015	+	1083.66i	−0.682496	+	1.13432i	−0.983537	+	0.180705i	$0.942162\pi$
$98$	1545.67	+	715.102i	1.59322	+	0.737104i
$99$	−538.785	+	31.0336i	−0.546969	+	0.0315050i
$100$	−774.957	−	734.078i	−0.774957	−	0.734078i
$101$	−1007.18	+	1485.48i	−0.992259	+	1.46347i	−0.109308	+	0.994008i	$0.534864\pi$
$101$	−1007.18	+	1485.48i	−0.992259	+	1.46347i	−0.882951	+	0.469465i	$0.844447\pi$
$102$	−1174.32	−	1049.96i	−1.13995	−	1.01923i
$103$	76.2944	+	701.515i	0.0729855	+	0.671091i	0.972292	+	0.233771i	$0.0751066\pi$
$103$	76.2944	+	701.515i	0.0729855	+	0.671091i	−0.899306	+	0.437320i	$0.855928\pi$
$104$	1427.34	+	2372.27i	1.34580	+	2.23673i
$105$	−33.3826	−	172.403i	−0.0310267	−	0.160236i
$106$	−451.498	−	1340.00i	−0.413711	−	1.22785i
$107$	−157.944	−	717.546i	−0.142701	−	0.648297i	−0.992608	−	0.121365i	$-0.961273\pi$
$107$	−157.944	−	717.546i	−0.142701	−	0.648297i	0.849907	−	0.526933i	$-0.176658\pi$
$108$	−916.151	+	2533.22i	−0.816266	+	2.25703i
$109$	−1216.10	−	1032.96i	−1.06863	−	0.907704i	−0.0726583	−	0.997357i	$-0.523148\pi$
$109$	−1216.10	−	1032.96i	−1.06863	−	0.907704i	−0.995973	+	0.0896532i	$0.971424\pi$
$110$	−857.042	−	140.505i	−0.742871	−	0.121787i
$111$	−17.6223	−	212.000i	−0.0150688	−	0.181281i
$112$	226.820	+	569.275i	0.191361	+	0.480281i
$113$	1922.03	+	647.608i	1.60008	+	0.539131i	0.971179	−	0.238350i	$-0.0766067\pi$
$113$	1922.03	+	647.608i	1.60008	+	0.539131i	0.628906	+	0.777482i	$0.283503\pi$
$114$	−1336.27	+	1866.96i	−1.09784	+	1.53383i
$115$	−515.776	−	1114.83i	−0.418229	−	0.903988i
$116$	−1370.18	−	74.2891i	−1.09671	−	0.0594618i
$117$	1094.22	−	663.402i	0.864619	−	0.524201i
$118$	2313.63	−	483.294i	1.80498	−	0.377041i
$119$			235.795i			0.181641i
$120$	−1358.36	+	2133.05i	−1.03334	+	1.62266i
$121$	−845.386	+	391.117i	−0.635151	+	0.293852i
$122$	439.484	−	4040.99i	0.326140	−	2.99880i
$123$	1136.46	+	1262.47i	0.833098	+	0.925473i
$124$	4892.11	−	1949.19i	3.54294	−	1.41163i
$125$	−1245.29	+	844.325i	−0.891055	+	0.604150i
$126$	529.943	−	213.221i	0.374691	−	0.150756i
$127$	410.996	−	483.861i	0.287165	−	0.338077i	−0.599598	−	0.800301i	$-0.704673\pi$
$127$	410.996	−	483.861i	0.287165	−	0.338077i	0.886763	+	0.462225i	$0.152949\pi$
$128$	−54.9687	+	137.961i	−0.0379578	+	0.0952668i
$129$	−1774.14	−	541.476i	−1.21089	−	0.369568i
$130$	1951.44	−	657.517i	1.31656	−	0.443600i
$131$	1139.36	+	1341.35i	0.759893	+	0.894615i	0.997042	−	0.0768579i	$-0.0244888\pi$
$131$	1139.36	+	1341.35i	0.759893	+	0.894615i	−0.237149	+	0.971473i	$0.576213\pi$
$132$	−57.3613	−	1993.39i	−0.0378232	−	1.31441i
$133$	341.651	−	37.1568i	0.222744	−	0.0242248i
$134$	−381.897	+	1734.98i	−0.246201	+	1.11850i
$135$	987.992	+	624.499i	0.629873	+	0.398136i
$136$	2335.16	−	2465.20i	1.47234	−	1.55433i
$137$	371.136	+	196.764i	0.231447	+	0.122706i	0.580097	−	0.814548i	$-0.303015\pi$
$137$	371.136	+	196.764i	0.231447	+	0.122706i	−0.348649	+	0.937253i	$0.613360\pi$
$138$	3241.38	−	2336.57i	1.99945	−	1.44132i
$139$	2324.40	+	1398.54i	1.41836	+	0.853402i	0.998530	−	0.0541988i	$-0.0172605\pi$
$139$	2324.40	+	1398.54i	1.41836	+	0.853402i	0.419835	+	0.907601i	$0.362088\pi$
$140$	640.348	−	104.980i	0.386566	−	0.0633743i
$141$	182.005	+	726.627i	0.108706	+	0.433993i
$142$	2119.96	−	588.605i	1.25284	−	0.347850i
$143$	−573.279	+	754.136i	−0.335245	+	0.441007i
$144$	−3794.11	−	1496.92i	−2.19567	−	0.866271i
$145$	−159.282	+	573.681i	−0.0912251	+	0.328563i
$146$	2327.58	−	1234.01i	1.31940	−	0.699500i
$147$	1521.36	+	751.334i	0.853604	+	0.421558i
$148$	784.932	−	42.5578i	0.435953	−	0.0236367i
$149$	554.596	+	1046.08i	0.304928	+	0.575155i	0.987864	−	0.155323i	$-0.0496419\pi$
$149$	554.596	+	1046.08i	0.304928	+	0.575155i	−0.682936	+	0.730479i	$0.739297\pi$
$150$	−1067.12	−	1063.53i	−0.580866	−	0.578911i
$151$	−1128.40	−	1484.38i	−0.608130	−	0.799981i	0.384246	−	0.923231i	$-0.374462\pi$
$151$	−1128.40	−	1484.38i	−0.608130	−	0.799981i	−0.992376	+	0.123250i	$0.960668\pi$
$152$	−3939.88	−	2995.02i	−2.10241	−	1.59821i
$153$	−1143.03	−	1075.45i	−0.603979	−	0.568269i
$154$	−307.009	+	290.815i	−0.160646	+	0.152172i
$155$	−369.660	−	2254.82i	−0.191560	−	1.16846i
$156$	2334.08	+	4112.18i	1.19792	+	2.11050i
$157$	−1541.55	+	3332.01i	−0.783626	+	1.69378i	−0.0655135	+	0.997852i	$0.520869\pi$
$157$	−1541.55	+	3332.01i	−0.783626	+	1.69378i	−0.718112	+	0.695927i	$0.754994\pi$
$158$	1049.12	−	1978.85i	0.528251	−	0.996387i
$159$	−415.780	−	1346.04i	−0.207381	−	0.671369i
$160$	−2210.22	−	1498.56i	−1.09208	−	0.740449i
$161$	−584.129	−	128.576i	−0.285937	−	0.0629394i
$162$	−1383.45	+	3541.43i	−0.670949	+	1.71754i
$163$	−518.196	+	311.788i	−0.249008	+	0.149823i	−0.634586	−	0.772852i	$-0.718829\pi$
$163$	−518.196	+	311.788i	−0.249008	+	0.149823i	0.385579	+	0.922675i	$0.374002\pi$
$164$	−4783.94	+	4063.52i	−2.27782	+	1.93480i
$165$	−850.043	−	161.624i	−0.401065	−	0.0762571i
$166$	−1094.36	+	240.887i	−0.511681	+	0.112629i
$167$	985.190	+	392.536i	0.456505	+	0.181888i	0.587044	−	0.809555i	$-0.300292\pi$
$167$	985.190	+	392.536i	0.456505	+	0.181888i	−0.130539	+	0.991443i	$0.541671\pi$
$168$	426.570	+	1155.09i	0.195896	+	0.530459i
$169$	7.94476	−	48.4609i	0.00361619	−	0.0220578i
$170$	−1417.35	−	2090.44i	−0.639446	−	0.943113i
$171$	−1378.14	+	1825.65i	−0.616308	+	0.816436i
$172$	2188.60	−	6495.54i	0.970229	−	2.87954i
$173$	3432.46	+	373.302i	1.50847	+	0.164056i	0.824669	−	0.565616i	$-0.191361\pi$
$173$	3432.46	+	373.302i	1.50847	+	0.164056i	0.683798	+	0.729671i	$0.260327\pi$
$174$	−1930.60	−	153.929i	−0.841142	−	0.0670653i
$175$	−12.2093	+	225.187i	−0.00527391	+	0.0972716i
$176$	3019.48			1.29319
$177$	2316.56	−	422.814i	0.983749	−	0.179552i
$178$	−2357.69			−0.992789
$179$	−126.757	+	2337.89i	−0.0529288	+	0.976214i	0.844639	+	0.535337i	$0.179815\pi$
$179$	−126.757	+	2337.89i	−0.0529288	+	0.976214i	−0.897567	+	0.440877i	$0.854667\pi$
$180$	−2411.70	+	3582.93i	−0.998654	+	1.48365i
$181$	−119.159	−	12.9593i	−0.0489337	−	0.00532186i	0.0836194	−	0.996498i	$-0.473352\pi$
$181$	−119.159	−	12.9593i	−0.0489337	−	0.00532186i	−0.132553	+	0.991176i	$0.542318\pi$
$182$	320.157	−	950.193i	0.130394	−	0.386994i
$183$	539.959	−	4013.63i	0.218114	−	1.62129i
$184$	4833.64	+	7129.08i	1.93663	+	2.85632i
$185$	55.1798	−	336.582i	0.0219292	−	0.133762i
$186$	6972.41	−	2574.88i	2.74861	−	1.01505i
$187$	1079.33	+	430.045i	0.422078	+	0.168171i
$188$	−2703.26	+	595.033i	−1.04870	+	0.230836i
$189$	533.208	−	198.956i	0.205213	−	0.0765710i
$190$	−2805.55	+	2383.06i	−1.07124	+	0.909921i
$191$	−313.688	+	188.740i	−0.118836	+	0.0715012i	−0.573731	−	0.819044i	$-0.694504\pi$
$191$	−313.688	+	188.740i	−0.118836	+	0.0715012i	0.454895	+	0.890545i	$0.349677\pi$
$192$	947.338	−	2212.51i	0.356084	−	0.831636i
$193$	−3882.31	−	854.561i	−1.44795	−	0.318718i	−0.579695	−	0.814833i	$-0.696828\pi$
$193$	−3882.31	−	854.561i	−1.44795	−	0.318718i	−0.868257	+	0.496115i	$0.834759\pi$
$194$	−5459.36	−	3701.53i	−2.02041	−	1.36987i
$195$	1960.23	−	605.501i	0.719873	−	0.222363i
$196$	−2936.88	+	5539.54i	−1.07029	+	2.01878i
$197$	357.616	−	772.975i	0.129336	−	0.279554i	−0.832079	−	0.554657i	$-0.812850\pi$
$197$	357.616	−	772.975i	0.129336	−	0.279554i	0.961415	+	0.275102i	$0.0887117\pi$
$198$	−9.48623	−	2814.64i	−0.00340483	−	1.01024i
$199$	537.977	+	3281.52i	0.191639	+	1.16895i	0.890941	+	0.454120i	$0.150046\pi$
$199$	537.977	+	3281.52i	0.191639	+	1.16895i	−0.699301	+	0.714827i	$0.746505\pi$
$200$	2357.75	−	2233.38i	0.833591	−	0.789619i
$201$	−424.259	+	1718.34i	−0.148880	+	0.602998i
$202$	−7451.68	−	5664.62i	−2.59554	−	1.97308i
$203$	175.442	+	230.790i	0.0606581	+	0.0797944i
$204$	4093.85	−	4107.67i	1.40503	−	1.40978i
$205$	1275.69	+	2406.20i	0.434623	+	0.819787i
$206$	−3674.88	+	199.246i	−1.24292	+	0.0673891i
$207$	3287.47	−	2245.17i	1.10384	−	0.753865i
$208$	−6325.42	+	3353.52i	−2.10860	+	1.11791i
$209$	453.023	−	1631.64i	0.149934	−	0.540015i
$210$	907.265	−	125.170i	0.298130	−	0.0411312i
$211$	3262.25	−	4291.41i	1.06437	−	1.40016i	0.153167	−	0.988200i	$-0.451053\pi$
$211$	3262.25	−	4291.41i	1.06437	−	1.40016i	0.911204	−	0.411955i	$-0.135154\pi$
$212$	5016.00	−	1392.69i	1.62500	−	0.451179i
$213$	2126.34	−	532.602i	0.684010	−	0.171330i
$214$	3781.43	−	619.933i	1.20791	−	0.198027i
$215$	−2548.33	−	1533.28i	−0.808346	−	0.486366i
$216$	−7544.94	−	3200.49i	−2.37670	−	1.00818i
$217$	−982.970	−	521.138i	−0.307504	−	0.163028i
$218$	5722.82	−	6041.50i	1.77797	−	1.87698i
$219$	2349.45	−	1170.16i	0.724936	−	0.361058i
$220$	687.335	−	3122.59i	0.210637	−	0.956933i
$221$	−2738.68	+	297.849i	−0.833590	+	0.0906584i
$222$	1109.03	−	31.9132i	0.335285	−	0.00964808i
$223$	451.079	+	531.052i	0.135455	+	0.159470i	0.825707	−	0.564099i	$-0.190776\pi$
$223$	451.079	+	531.052i	0.135455	+	0.159470i	−0.690252	+	0.723569i	$0.742500\pi$
$224$	−1232.18	+	415.169i	−0.367537	+	0.123838i
$225$	−1035.92	−	1086.25i	−0.306940	−	0.321853i
$226$	−3915.31	+	9826.68i	−1.15240	+	2.89231i
$227$	−2099.54	+	2471.77i	−0.613882	+	0.722717i	−0.977993	−	0.208638i	$-0.933097\pi$
$227$	−2099.54	+	2471.77i	−0.613882	+	0.722717i	0.364111	+	0.931355i	$0.381373\pi$
$228$	−6596.84	−	5284.42i	−1.91617	−	1.53495i
$229$	1456.23	−	987.349i	0.420220	−	0.284916i	−0.332694	−	0.943035i	$-0.607958\pi$
$229$	1456.23	−	987.349i	0.420220	−	0.284916i	0.752914	+	0.658118i	$0.228647\pi$
$230$	5951.44	−	2371.27i	1.70620	−	0.679813i
$231$	−313.133	+	281.878i	−0.0891890	+	0.0802867i
$232$	451.376	−	4150.33i	0.127734	−	1.17449i
$233$	−3119.51	+	1443.24i	−0.877108	+	0.405793i	−0.806168	−	0.591687i	$-0.798462\pi$
$233$	−3119.51	+	1443.24i	−0.877108	+	0.405793i	−0.0709404	+	0.997481i	$0.522600\pi$
$234$	3145.89	+	5885.77i	0.878861	+	1.64429i
$235$			1201.00i			0.333381i
$236$	1315.51	+	8601.55i	0.362850	+	2.37251i
$237$	1094.97	−	1944.36i	0.300110	−	0.532909i
$238$	−1227.97	−	66.5787i	−0.334444	−	0.0181330i
$239$	1860.23	+	4020.82i	0.503466	+	1.08822i	0.978118	+	0.208050i	$0.0667116\pi$
$239$	1860.23	+	4020.82i	0.503466	+	1.08822i	−0.474653	+	0.880173i	$0.657426\pi$
$240$	−5317.71	−	3806.14i	−1.43024	−	1.02369i
$241$	−5824.02	−	1962.34i	−1.55667	−	0.524504i	−0.596189	−	0.802844i	$-0.703319\pi$
$241$	−5824.02	−	1962.34i	−1.55667	−	0.524504i	−0.960483	+	0.278340i	$0.910216\pi$
$242$	−1798.15	−	4513.03i	−0.477644	−	1.19879i
$243$	−1467.49	+	3492.19i	−0.387405	+	0.921910i
$244$	14767.6	+	2421.03i	3.87459	+	0.635207i
$245$	2073.43	+	1761.19i	0.540680	+	0.459258i
$246$	−6895.57	+	5561.97i	−1.78718	+	1.44154i
$247$	863.126	+	3921.22i	0.222346	+	1.01013i
$248$	5115.79	+	15183.1i	1.30989	+	3.88762i
$249$	−1096.06	+	212.231i	−0.278955	+	0.0540144i
$250$	−4045.45	−	6723.59i	−1.02343	−	1.70095i
$251$	824.467	+	7580.85i	0.207330	+	1.90637i	0.386062	+	0.922473i	$0.373835\pi$
$251$	824.467	+	7580.85i	0.207330	+	1.90637i	−0.178732	+	0.983898i	$0.557200\pi$
$252$	678.204	+	1990.64i	0.169535	+	0.497613i
$253$	−1653.88	+	2439.30i	−0.410983	+	0.606155i
$254$	2403.80	+	2277.00i	0.593810	+	0.562487i
$255$	−1358.76	−	2117.90i	−0.333683	−	0.520109i
$256$	−4065.97	−	1881.12i	−0.992669	−	0.459258i
$257$	965.673	−	1604.96i	0.234385	−	0.389551i	−0.717233	−	0.696833i	$-0.754592\pi$
$257$	965.673	−	1604.96i	0.234385	−	0.389551i	0.951619	+	0.307282i	$0.0994194\pi$
$258$	3320.84	−	9086.47i	0.801342	−	2.19263i
$259$	−114.210	−	120.570i	−0.0274003	−	0.0289261i
$260$	2028.17	+	7304.81i	0.483776	+	1.74240i
$261$	−1918.95	−	202.157i	−0.455096	−	0.0479433i
$262$	−7307.19	+	5554.78i	−1.72305	+	1.30983i
$263$	−1839.66	−	510.780i	−0.431325	−	0.119757i	0.0450788	−	0.998983i	$-0.485646\pi$
$263$	−1839.66	−	510.780i	−0.431325	−	0.119757i	−0.476404	+	0.879227i	$0.658060\pi$
$264$	6065.30	+	154.077i	1.41399	+	0.0359196i
$265$	−122.285	−	2255.42i	−0.0283468	−	0.522827i
$266$	97.0368	+	1789.74i	0.0223673	+	0.412541i
$267$	−2348.21	−	59.6517i	−0.538234	−	0.0136728i
$268$	−6301.89	−	1749.71i	−1.43638	−	0.398808i
$269$	6848.74	−	5206.27i	1.55232	−	1.18005i	0.641591	−	0.767047i	$-0.278275\pi$
$269$	6848.74	−	5206.27i	1.55232	−	1.18005i	0.910732	−	0.412998i	$-0.135519\pi$
$270$	−3531.23	+	4968.92i	−0.795940	+	1.12000i
$271$	−974.291	−	3509.08i	−0.218391	−	0.786574i	−0.988828	−	0.149058i	$-0.952376\pi$
$271$	−974.291	−	3509.08i	−0.218391	−	0.786574i	0.770437	−	0.637516i	$-0.220038\pi$
$272$	6038.64	+	6374.92i	1.34613	+	1.42109i
$273$	342.911	−	938.273i	0.0760217	−	0.208011i
$274$	−1129.50	+	1877.24i	−0.249035	+	0.413899i
$275$	1008.50	+	466.584i	0.221146	+	0.102313i
$276$	7943.49	+	12381.4i	1.73240	+	2.70027i
$277$	3830.89	+	3628.81i	0.830960	+	0.787127i	0.979429	−	0.201790i	$-0.0646759\pi$
$277$	3830.89	+	3628.81i	0.830960	+	0.787127i	−0.148469	+	0.988917i	$0.547435\pi$
$278$	−7939.63	+	11710.1i	−1.71290	+	2.52634i
$279$	7009.53	−	2388.12i	1.50412	−	0.512449i
$280$	213.451	+	1962.65i	0.0455576	+	0.418895i
$281$	−416.295	−	691.887i	−0.0883774	−	0.146884i	0.809515	−	0.587099i	$-0.199730\pi$
$281$	−416.295	−	691.887i	−0.0883774	−	0.146884i	−0.897893	+	0.440214i	$0.854902\pi$
$282$	−3835.51	+	742.673i	−0.809934	+	0.156828i
$283$	−187.706	−	557.092i	−0.0394275	−	0.117017i	0.926132	−	0.377201i	$-0.123113\pi$
$283$	−187.706	−	557.092i	−0.0394275	−	0.117017i	−0.965559	+	0.260184i	$0.916217\pi$
$284$	1741.25	+	7910.58i	0.363818	+	1.65284i
$285$	−2854.57	+	2302.50i	−0.593298	+	0.478555i
$286$	−3765.51	−	3198.46i	−0.778529	−	0.661289i
$287$	1308.63	+	214.539i	0.269149	+	0.0441248i
$288$	3607.35	−	7866.62i	0.738073	−	1.60953i
$289$	−567.878	−	1425.27i	−0.115587	−	0.290101i
$290$	−2942.64	−	991.490i	−0.595854	−	0.200767i
$291$	−5343.76	−	3824.78i	−1.07648	−	0.770491i
$292$	4072.44	+	8802.45i	0.816171	+	1.76412i
$293$	−3719.64	−	201.673i	−0.741652	−	0.0402112i	−0.320559	−	0.947229i	$-0.603871\pi$
$293$	−3719.64	−	201.673i	−0.741652	−	0.0402112i	−0.421093	+	0.907017i	$0.638353\pi$
$294$	−4342.36	+	7710.79i	−0.861400	+	1.52960i
$295$	3767.58	+	244.854i	0.743583	+	0.0483253i
$296$			2391.61i			0.469626i
$297$	61.7648	−	2803.57i	0.0120672	−	0.547742i
$298$	−5604.36	+	2592.85i	−1.08943	+	0.504026i
$299$	755.517	−	6946.86i	0.146129	−	1.34364i
$300$	4122.36	−	3710.89i	0.793349	−	0.714161i
$301$	−1345.26	+	536.002i	−0.257607	+	0.102640i
$302$	8048.95	−	5457.33i	1.53366	−	1.03985i
$303$	−7278.41	−	5830.39i	−1.37998	−	1.10544i
$304$	8285.24	−	9754.13i	1.56313	−	1.84026i
$305$	2403.33	−	6031.92i	0.451195	−	1.13241i
$306$	5923.47	−	5649.01i	1.10661	−	1.05533i
$307$	2491.67	−	839.541i	0.463215	−	0.156075i	−0.0780107	−	0.996953i	$-0.524857\pi$
$307$	2491.67	−	839.541i	0.463215	−	0.156075i	0.541226	+	0.840877i	$0.317960\pi$
$308$	−1007.88	−	1186.57i	−0.186459	−	0.219517i
$309$	−3665.16	+	105.468i	−0.674768	+	0.0194170i
$310$	11847.0	−	1288.44i	2.17053	−	0.236060i
$311$	2256.66	−	10252.1i	0.411458	−	1.86927i	−0.0775424	−	0.996989i	$-0.524707\pi$
$311$	2256.66	−	10252.1i	0.411458	−	1.86927i	0.489000	−	0.872284i	$-0.337362\pi$
$312$	−12877.1	+	6413.53i	−2.33662	+	1.16376i
$313$	−2813.29	+	2969.95i	−0.508040	+	0.536331i	−0.928673	−	0.370900i	$-0.879049\pi$
$313$	−2813.29	+	2969.95i	−0.508040	+	0.536331i	0.420633	+	0.907231i	$0.361808\pi$
$314$	−16917.1	−	8968.90i	−3.04041	−	1.61192i
$315$	906.786	−	101.712i	0.162196	−	0.0181931i
$316$	7065.42	+	4251.12i	1.25779	+	0.756786i
$317$	−3216.11	+	527.254i	−0.569826	+	0.0934182i	−0.439805	−	0.898093i	$-0.644953\pi$
$317$	−3216.11	+	527.254i	−0.569826	+	0.0934182i	−0.130020	+	0.991511i	$0.541504\pi$
$318$	7127.27	−	1785.23i	1.25685	−	0.314814i
$319$	1376.39	−	382.153i	0.241577	−	0.0670735i
$320$	2335.27	−	3072.00i	0.407955	−	0.536656i
$321$	3781.91	−	521.768i	0.657588	−	0.0907236i
$322$	834.533	−	3005.72i	0.144431	−	0.520192i
$323$	4350.83	−	2306.66i	0.749494	−	0.397356i
$324$	−12743.0	−	5791.58i	−2.18501	−	0.993070i
$325$	−2630.89	+	142.643i	−0.449032	+	0.0243458i
$326$	−1477.41	−	2786.69i	−0.251001	−	0.473437i
$327$	5852.67	−	5872.43i	0.989766	−	0.993107i
$328$	−11556.8	−	15202.8i	−1.94549	−	2.55925i
$329$	465.546	+	353.899i	0.0780134	+	0.0593042i
$330$	1081.72	−	4381.21i	0.180445	−	0.730841i
$331$	2410.51	−	2283.36i	0.400284	−	0.379169i	−0.460909	−	0.887447i	$-0.652477\pi$
$331$	2410.51	−	2283.36i	0.400284	−	0.379169i	0.861193	+	0.508279i	$0.169718\pi$
$332$	−667.412	−	4071.03i	−0.110328	−	0.672973i
$333$	1105.38	−	3.72548i	0.181905	−	0.000613078i
$334$	−2322.42	+	5019.83i	−0.380470	+	0.822373i
$335$	−1329.24	+	2507.20i	−0.216788	+	0.408905i
$336$	−3042.36	+	939.761i	−0.493971	+	0.152584i
$337$	−691.454	−	468.817i	−0.111768	−	0.0757807i	0.504022	−	0.863691i	$-0.331853\pi$
$337$	−691.454	−	468.817i	−0.111768	−	0.0757807i	−0.615791	+	0.787910i	$0.711163\pi$
$338$	250.131	+	55.0580i	0.0402525	+	0.00886024i
$339$	−4148.20	+	9688.13i	−0.664599	+	1.55217i
$340$	7967.22	−	4793.72i	1.27083	−	0.764635i
$341$	−4178.21	+	3549.00i	−0.663527	+	0.563605i
$342$	−9118.45	−	7692.53i	−1.44172	−	1.21627i
$343$	2652.54	−	583.867i	0.417561	−	0.0919122i
$344$	19372.7	+	7718.80i	3.03636	+	1.20980i
$345$	5987.52	−	2211.16i	0.934368	−	0.345058i
$346$	−2913.26	+	17770.1i	−0.452653	+	2.76106i
$347$	−4470.38	−	6593.32i	−0.691592	−	1.02002i	−0.997684	−	0.0680202i	$-0.978332\pi$
$347$	−4470.38	−	6593.32i	−0.691592	−	1.02002i	0.306092	−	0.952002i	$-0.400979\pi$
$348$	950.662	−	7066.47i	0.146439	−	1.08851i
$349$	3383.54	−	10042.0i	0.518960	−	1.54022i	−0.292769	−	0.956183i	$-0.594577\pi$
$349$	3383.54	−	10042.0i	0.518960	−	1.54022i	0.811729	−	0.584034i	$-0.198527\pi$
$350$	−1169.28	−	127.167i	−0.178573	−	0.0194210i
$351$	2984.34	+	5941.71i	0.453824	+	0.903547i
$352$	−346.855	+	6397.36i	−0.0525211	+	0.968695i
$353$	3298.94			0.497408			0.248704	−	0.968580i	$-0.419995\pi$
$353$	3298.94			0.497408			0.248704	+	0.968580i	$0.419995\pi$
$354$	1547.83	+	12183.6i	0.232390	+	1.82923i
$355$	3514.50			0.525437
$356$	469.921	−	8667.18i	0.0699600	−	1.29034i
$357$	−1221.35	−	97.3800i	−0.181067	−	0.0144367i
$358$	−12139.5	−	1320.25i	−1.79215	−	0.194908i
$359$	423.664	−	1257.39i	0.0622844	−	0.184854i	−0.911993	−	0.410206i	$-0.865457\pi$
$359$	423.664	−	1257.39i	0.0622844	−	0.184854i	0.974277	+	0.225352i	$0.0723533\pi$
$360$	−10487.6	−	7916.83i	−1.53540	−	1.15904i
$361$	−178.616	−	263.439i	−0.0260411	−	0.0384078i
$362$	101.135	−	616.895i	0.0146838	−	0.0895670i
$363$	−1676.74	−	4540.38i	−0.242441	−	0.656497i
$364$	3429.22	+	1366.33i	0.493791	+	0.196744i
$365$	4109.86	−	904.649i	0.589370	−	0.129730i
$366$	20749.7	+	3945.27i	2.96340	+	0.563450i
$367$	−150.886	+	128.164i	−0.0214610	+	0.0182292i	−0.658053	−	0.752972i	$-0.728620\pi$
$367$	−150.886	+	128.164i	−0.0214610	+	0.0182292i	0.636592	+	0.771201i	$0.280344\pi$
$368$	−19085.2	+	11483.2i	−2.70349	+	1.62664i
$369$	−7008.58	+	5365.15i	−0.988760	+	0.756907i
$370$	1737.27	+	382.401i	0.244098	+	0.0537300i
$371$	−910.306	−	617.203i	−0.127387	−	0.0863708i
$372$	8075.90	+	26144.7i	1.12558	+	3.64392i
$373$	−1351.08	+	2548.41i	−0.187550	+	0.353757i	−0.959401	−	0.282047i	$-0.908987\pi$
$373$	−1351.08	+	2548.41i	−0.187550	+	0.353757i	0.771850	+	0.635804i	$0.219331\pi$
$374$	−2544.34	+	5499.50i	−0.351777	+	0.760354i
$375$	−3859.08	−	6798.92i	−0.531419	−	0.936253i
$376$	−1362.43	−	8310.43i	−0.186866	−	1.13983i
$377$	−2458.93	+	2329.22i	−0.335918	+	0.318199i
$378$	885.566	+	2833.01i	0.120499	+	0.385488i
$379$	5556.29	+	4223.78i	0.753054	+	0.572457i	0.909733	−	0.415193i	$-0.136286\pi$
$379$	5556.29	+	4223.78i	0.753054	+	0.572457i	−0.156680	+	0.987649i	$0.550079\pi$
$380$	−8201.24	−	10788.5i	−1.10714	−	1.45642i
$381$	2336.53	+	2328.67i	0.314184	+	0.313127i
$382$	−894.345	−	1686.91i	−0.119787	−	0.225942i
$383$	6912.27	−	374.773i	0.922195	−	0.0499999i	0.413076	−	0.910696i	$-0.364454\pi$
$383$	6912.27	−	374.773i	0.922195	−	0.0499999i	0.509118	+	0.860696i	$0.329972\pi$
$384$	−691.898	−	341.698i	−0.0919486	−	0.0454094i
$385$	−596.814	+	316.411i	−0.0790038	+	0.0418852i
$386$	5546.57	−	19977.0i	0.731381	−	2.63420i
$387$	3537.39	−	8965.93i	0.464639	−	1.17768i
$388$	14695.5	−	19331.5i	1.92281	−	2.52941i
$389$	−13627.4	+	3783.64i	−1.77619	+	0.493157i	−0.991876	−	0.127206i	$-0.959399\pi$
$389$	−13627.4	+	3783.64i	−1.77619	+	0.493157i	−0.784315	+	0.620363i	$0.786985\pi$
$390$	2599.83	+	10379.5i	0.337558	+	1.34765i
$391$	−8457.59	+	1386.55i	−1.09391	+	0.179337i
$392$	−16345.2	−	9834.58i	−2.10601	−	1.26715i
$393$	−7418.37	+	5347.58i	−0.952181	+	0.686386i
$394$	3924.51	+	2080.65i	0.501813	+	0.266044i
$395$	2460.42	−	2597.43i	0.313410	−	0.330863i
$396$	10348.9	+	526.125i	1.31326	+	0.0667645i
$397$	1767.06	−	8027.83i	0.223391	−	1.01487i	−0.722748	−	0.691112i	$-0.757121\pi$
$397$	1767.06	−	8027.83i	0.223391	−	1.01487i	0.946138	−	0.323762i	$-0.104948\pi$
$398$	−17241.3	+	1875.11i	−2.17143	+	0.236158i
$399$	51.3648	+	1785.00i	0.00644475	+	0.223964i
$400$	5436.87	+	6400.78i	0.679609	+	0.800098i
$401$	−4081.23	+	1375.13i	−0.508247	+	0.171248i	−0.561730	−	0.827320i	$-0.689864\pi$
$401$	−4081.23	+	1375.13i	−0.508247	+	0.171248i	0.0534833	+	0.998569i	$0.482968\pi$
$402$	−8828.97	−	2694.64i	−1.09540	−	0.334319i
$403$	4811.17	−	12075.1i	0.594694	−	1.49257i
$404$	22309.1	−	26264.3i	2.74733	−	3.23440i
$405$	−3642.75	+	4859.61i	−0.446938	+	0.596237i
$406$	−1251.44	+	848.499i	−0.152975	+	0.103720i
$407$	−760.196	+	302.890i	−0.0925836	+	0.0368887i
$408$	11804.7	+	13113.6i	1.43240	+	1.59122i
$409$	−231.054	+	2124.51i	−0.0279337	+	0.256847i	0.971841	+	0.235636i	$0.0757174\pi$
$409$	−231.054	+	2124.51i	−0.0279337	+	0.256847i	−0.999775	+	0.0212102i	$0.993248\pi$
$410$	−12891.2	+	5964.09i	−1.55280	+	0.718404i
$411$	−1172.45	+	1841.12i	−0.140713	+	0.220963i
$412$		−	13549.1i		−	1.62018i
$413$	1205.11	−	1388.29i	0.143582	−	0.165407i
$414$	10764.1	+	17754.4i	1.27785	+	2.10768i
$415$	−1787.34	−	96.9067i	−0.211415	−	0.0114626i
$416$	−6378.49	−	13786.9i	−0.751757	−	1.62490i
$417$	−8203.99	+	11462.1i	−0.963432	+	1.34605i
$418$	8369.33	+	2819.96i	0.979324	+	0.329973i
$419$	1474.06	+	3699.62i	0.171868	+	0.431356i	0.989527	−	0.144346i	$-0.0461080\pi$
$419$	1474.06	+	3699.62i	0.171868	+	0.431356i	−0.817659	+	0.575702i	$0.804729\pi$
$420$	279.311	+	3360.17i	0.0324499	+	0.390380i
$421$	6105.25	+	1000.90i	0.706773	+	0.115870i	0.504440	−	0.863447i	$-0.331699\pi$
$421$	6105.25	+	1000.90i	0.706773	+	0.115870i	0.202334	+	0.979317i	$0.435147\pi$
$422$	21427.6	+	18200.8i	2.47176	+	2.09953i
$423$	−3838.88	+	642.646i	−0.441260	+	0.0738689i
$424$	3404.73	+	15467.8i	0.389972	+	1.77166i
$425$	1031.82	+	3062.34i	0.117766	+	0.349518i
$426$	2173.29	+	11223.9i	0.247175	+	1.27652i
$427$	−1629.97	−	2709.04i	−0.184731	−	0.307025i
$428$	1525.27	+	14024.6i	0.172258	+	1.58389i
$429$	−3669.45	−	3280.87i	−0.412967	−	0.369235i
$430$	8704.52	−	12838.2i	0.976208	−	1.43980i
$431$	−3436.07	−	3254.82i	−0.384013	−	0.363756i	0.471206	−	0.882023i	$-0.343819\pi$
$431$	−3436.07	−	3254.82i	−0.384013	−	0.363756i	−0.855219	+	0.518267i	$0.826577\pi$
$432$	9320.51	−	19034.2i	1.03804	−	2.11987i
$433$	6380.18	+	2951.79i	0.708111	+	0.327607i	0.740676	−	0.671863i	$-0.234506\pi$
$433$	6380.18	+	2951.79i	0.708111	+	0.327607i	−0.0325650	+	0.999470i	$0.510368\pi$
$434$	2991.53	−	4971.96i	0.330871	−	0.549911i
$435$	−2905.73	−	1061.96i	−0.320273	−	0.117050i
$436$	21068.7	+	22242.0i	2.31424	+	2.44311i
$437$	3341.77	+	12036.0i	0.365809	+	1.31752i
$438$	5430.54	+	12565.8i	0.592423	+	1.37082i
$439$	2357.20	−	1791.89i	0.256271	−	0.194812i	−0.469148	−	0.883119i	$-0.655439\pi$
$439$	2357.20	−	1791.89i	0.256271	−	0.194812i	0.725419	+	0.688307i	$0.241646\pi$
$440$	9373.13	+	2602.44i	1.01556	+	0.281969i
$441$	−4520.00	+	7569.93i	−0.488068	+	0.817399i
$442$	−777.848	−	14346.6i	−0.0837069	−	1.54388i
$443$	328.255	+	6054.31i	0.0352051	+	0.649320i	0.961883	+	0.273463i	$0.0881690\pi$
$443$	328.255	+	6054.31i	0.0352051	+	0.649320i	−0.926677	+	0.375857i	$0.877348\pi$
$444$	−103.728	+	4083.30i	−0.0110872	+	0.436452i
$445$	−3628.86	−	1007.55i	−0.386572	−	0.107331i
$446$	−2892.97	+	2199.18i	−0.307144	+	0.233485i
$447$	−5647.43	+	2440.63i	−0.597571	+	0.258251i
$448$	−502.670	−	1810.45i	−0.0530110	−	0.190928i
$449$	7264.55	+	7669.09i	0.763553	+	0.806073i	0.985623	−	0.168958i	$-0.0540402\pi$
$449$	7264.55	+	7669.09i	0.763553	+	0.806073i	−0.222071	+	0.975031i	$0.571282\pi$
$450$	5949.48	−	5088.15i	0.623247	−	0.533017i
$451$	3368.71	−	5598.84i	0.351722	−	0.584566i
$452$	−35343.8	−	16351.8i	−3.67795	−	1.70160i
$453$	8154.68	−	5231.75i	0.845784	−	0.542624i
$454$	−12279.6	−	11631.9i	−1.26941	−	1.20245i
$455$	898.833	−	1325.68i	0.0926108	−	0.136591i
$456$	17140.5	−	19170.6i	1.76025	−	1.96874i
$457$	577.989	+	5314.52i	0.0591623	+	0.543988i	0.985787	+	0.168001i	$0.0537311\pi$
$457$	577.989	+	5314.52i	0.0591623	+	0.543988i	−0.926625	+	0.375988i	$0.877303\pi$
$458$	4730.73	+	7862.53i	0.482647	+	0.802166i
$459$	6042.59	−	5476.44i	0.614475	−	0.556902i
$460$	7530.90	+	22350.9i	0.763326	+	2.26547i
$461$	2176.89	+	9889.70i	0.219930	+	0.999152i	0.949138	+	0.314860i	$0.101958\pi$
$461$	2176.89	+	9889.70i	0.219930	+	0.999152i	−0.729208	+	0.684292i	$0.760111\pi$
$462$	−1379.55	−	1710.32i	−0.138923	−	0.172232i
$463$	11904.2	+	10111.5i	1.19489	+	1.01495i	0.999413	+	0.0342455i	$0.0109028\pi$
$463$	11904.2	+	10111.5i	1.19489	+	1.01495i	0.195481	+	0.980707i	$0.437373\pi$
$464$	10653.7	+	1746.58i	1.06591	+	0.174748i
$465$	11832.0	−	983.523i	1.17999	−	0.0980855i
$466$	−6635.27	−	16653.3i	−0.659599	−	1.65547i
$467$	18579.2	+	6260.08i	1.84100	+	0.620304i	0.996388	+	0.0849183i	$0.0270629\pi$
$467$	18579.2	+	6260.08i	1.84100	+	0.620304i	0.844608	+	0.535385i	$0.179834\pi$
$468$	−22263.9	+	10391.6i	−2.19903	+	1.02639i
$469$	580.187	+	1254.05i	0.0571227	+	0.123469i
$470$	−6254.55	−	339.112i	−0.613832	−	0.0332810i
$471$	−16622.2	−	9360.87i	−1.62614	−	0.915767i
$472$	−26347.9	+	2579.69i	−2.56941	+	0.251567i
$473$			7135.38i			0.693626i
$474$	9816.62	+	6251.39i	0.951250	+	0.605772i
$475$	4274.52	−	1977.60i	0.412902	−	0.191029i
$476$	489.504	−	4500.92i	0.0471353	−	0.433402i
$477$	7143.80	−	1597.73i	0.685727	−	0.153365i
$478$	−21464.8	+	8552.37i	−2.05393	+	0.818361i
$479$	921.453	−	624.761i	0.0878962	−	0.0595951i	−0.516447	−	0.856319i	$-0.672746\pi$
$479$	921.453	−	624.761i	0.0878962	−	0.0595951i	0.604344	+	0.796724i	$0.293435\pi$
$480$	8674.92	−	10829.4i	0.824904	−	1.02978i
$481$	1256.11	−	1478.81i	0.119072	−	0.140183i
$482$	11863.9	−	29776.2i	1.12113	−	2.81383i
$483$	907.226	−	2972.52i	0.0854663	−	0.280030i
$484$	16948.9	−	5710.74i	1.59174	−	0.536321i
$485$	−6820.98	−	8030.28i	−0.638608	−	0.751827i
$486$	−17772.2	−	8628.41i	−1.65878	−	0.805335i
$487$	7776.25	−	845.718i	0.723564	−	0.0786923i	0.261076	−	0.965318i	$-0.415923\pi$
$487$	7776.25	−	845.718i	0.723564	−	0.0786923i	0.462487	+	0.886626i	$0.346957\pi$
$488$	−9787.43	+	44464.8i	−0.907902	+	4.12464i
$489$	−1400.97	−	2812.87i	−0.129558	−	0.260128i
$490$	−9757.35	+	10300.7i	−0.899575	+	0.949670i
$491$	−2022.64	−	1072.34i	−0.185907	−	0.0985619i	0.372855	−	0.927890i	$-0.378379\pi$
$491$	−2022.64	−	1072.34i	−0.185907	−	0.0985619i	−0.558763	+	0.829328i	$0.688724\pi$
$492$	−19072.2	−	26457.6i	−1.74764	−	2.42439i
$493$	3559.46	+	2141.66i	0.325173	+	0.195650i
$494$	−20664.6	+	3387.79i	−1.88207	+	0.308550i
$495$	1188.22	−	4336.23i	0.107892	−	0.393735i
$496$	−39921.6	+	11084.2i	−3.61397	+	1.00341i
$497$	1035.62	−	1362.33i	0.0934685	−	0.122956i
$498$	−795.773	−	5767.97i	−0.0716053	−	0.519014i
$499$	−5003.55	+	18021.2i	−0.448877	+	1.61671i	0.299956	+	0.953953i	$0.403028\pi$
$499$	−5003.55	+	18021.2i	−0.448877	+	1.61671i	−0.748834	+	0.662758i	$0.769386\pi$
$500$	25523.1	−	13531.5i	2.28286	−	1.21029i
$501$	−2440.09	+	4940.89i	−0.217595	+	0.440604i
$502$	−39712.3	+	2153.14i	−3.53077	+	0.191433i
$503$	5768.16	+	10879.9i	0.511311	+	0.964436i	0.995966	+	0.0897300i	$0.0286004\pi$
$503$	5768.16	+	10879.9i	0.511311	+	0.964436i	−0.484655	+	0.874706i	$0.661055\pi$
$504$	−6159.20	+	1732.47i	−0.544351	+	0.153116i
$505$	−9048.57	−	11903.2i	−0.797339	−	1.04888i
$506$	−12236.4	−	9301.83i	−1.07504	−	0.817227i
$507$	247.733	+	61.1653i	0.0217006	+	0.00535788i
$508$	−8849.66	+	8382.85i	−0.772914	+	0.732143i
$509$	3267.08	+	19928.3i	0.284501	+	1.73538i	0.612295	+	0.790629i	$0.290246\pi$
$509$	3267.08	+	19928.3i	0.284501	+	1.73538i	−0.327795	+	0.944749i	$0.606305\pi$
$510$	11413.2	−	6478.16i	0.990952	−	0.562466i
$511$	860.384	−	1859.69i	0.0744836	−	0.160994i
$512$	10388.0	−	19593.9i	0.896661	−	1.69128i
$513$	−8887.17	−	7892.31i	−0.764870	−	0.679248i
$514$	8085.63	+	5482.20i	0.693856	+	0.470446i
$515$	−5741.38	−	1263.77i	−0.491253	−	0.108133i
$516$	32741.2	+	14018.9i	2.79331	+	1.19602i
$517$	2469.01	−	1485.55i	0.210032	−	0.126372i
$518$	660.153	−	560.739i	0.0559951	−	0.0475626i
$519$	−3351.15	+	17625.0i	−0.283428	+	1.49066i
$520$	−22525.8	+	4958.31i	−1.89966	+	0.418147i
$521$	1409.92	+	561.763i	0.118560	+	0.0472385i	0.428664	−	0.903464i	$-0.358985\pi$
$521$	1409.92	+	561.763i	0.118560	+	0.0472385i	−0.310104	+	0.950703i	$0.600364\pi$
$522$	1594.62	−	9936.41i	0.133706	−	0.833151i
$523$	2548.00	−	15542.1i	0.213033	−	1.29944i	−0.636241	−	0.771490i	$-0.719512\pi$
$523$	2548.00	−	15542.1i	0.213033	−	1.29944i	0.849274	−	0.527952i	$-0.177040\pi$
$524$	−18963.7	−	27969.4i	−1.58098	−	2.33177i
$525$	−1161.36	−	156.239i	−0.0965447	−	0.0129883i
$526$	3179.48	−	9436.35i	0.263559	−	0.782214i
$527$	−15848.8	−	1723.67i	−1.31003	−	0.142475i
$528$	−1247.00	+	15640.0i	−0.102782	+	1.28910i
$529$	518.255	−	9558.65i	0.0425951	−	0.785621i
$530$	11780.3			0.965475
$531$	1233.35	+	12173.7i	0.100797	+	0.994907i
$532$	−6598.65			−0.537759
$533$	−838.772	+	15470.2i	−0.0681637	+	1.25721i
$534$	973.691	−	12212.2i	0.0789059	−	0.989648i
$535$	6085.14	+	661.799i	0.491745	+	0.0534805i
$536$	6353.57	−	18856.7i	0.512001	−	1.51956i
$537$	−12057.3	−	1622.08i	−0.968919	−	0.130350i
$538$	25179.4	+	37136.8i	2.01777	+	2.97599i
$539$	1055.95	−	6441.01i	0.0843840	−	0.514720i
$540$	−17562.6	−	13971.6i	−1.39958	−	1.11341i
$541$	18593.7	+	7408.42i	1.47765	+	0.588748i	0.963203	−	0.268776i	$-0.0866193\pi$
$541$	18593.7	+	7408.42i	1.47765	+	0.588748i	0.514443	+	0.857524i	$0.327999\pi$
$542$	18549.7	−	4083.09i	1.47007	−	0.323586i
$543$	116.336	−	611.856i	0.00919423	−	0.0483559i
$544$	−14200.2	+	12061.8i	−1.11917	+	0.950631i
$545$	11390.1	−	6853.21i	0.895229	−	0.538641i
$546$	4789.51	+	2050.74i	0.375406	+	0.160739i
$547$	−6861.19	−	1510.26i	−0.536313	−	0.118052i	−0.0614486	−	0.998110i	$-0.519572\pi$
$547$	−6861.19	−	1510.26i	−0.536313	−	0.118052i	−0.474865	+	0.880059i	$0.657503\pi$
$548$	−6675.86	−	4526.34i	−0.520399	−	0.352839i
$549$	20566.5	+	4454.40i	1.59883	+	0.346283i
$550$	−2714.63	+	5120.33i	−0.210459	+	0.396967i
$551$	2542.21	−	5494.90i	0.196555	−	0.424846i
$552$	−38922.8	+	22092.7i	−3.00120	+	1.70349i
$553$	−281.836	−	1719.12i	−0.0216725	−	0.132196i
$554$	−19979.8	+	18925.8i	−1.53224	+	1.45141i
$555$	1720.61	+	424.819i	0.131596	+	0.0324911i
$556$	−41465.3	−	31521.1i	−3.16281	−	2.40430i
$557$	4693.62	+	6174.35i	0.357047	+	0.469687i	0.939189	−	0.343400i	$-0.111579\pi$
$557$	4693.62	+	6174.35i	0.357047	+	0.469687i	−0.582143	+	0.813087i	$0.697785\pi$
$558$	10457.6	+	37178.5i	0.793382	+	2.82059i
$559$	−7924.77	−	14947.7i	−0.599610	−	1.13098i
$560$	−5097.77	+	276.393i	−0.384679	+	0.0208567i
$561$	−2673.26	+	5413.02i	−0.201185	+	0.407376i
$562$	3720.75	−	1972.61i	0.279271	−	0.148060i
$563$	−3147.27	+	11335.5i	−0.235598	+	0.848548i	0.747314	+	0.664471i	$0.231343\pi$
$563$	−3147.27	+	11335.5i	−0.235598	+	0.848548i	−0.982912	+	0.184077i	$0.941071\pi$
$564$	−1965.69	−	14247.9i	−0.146756	−	1.06373i
$565$	−10225.7	+	13451.6i	−0.761411	+	1.00162i
$566$	2954.22	−	820.235i	0.219391	−	0.0609135i
$567$	810.329	+	2844.03i	0.0600187	+	0.210649i
$568$	−24318.9	+	3986.88i	−1.79648	+	0.294517i
$569$	158.038	+	95.0886i	0.0116438	+	0.00700584i	0.521364	−	0.853334i	$-0.325423\pi$
$569$	158.038	+	95.0886i	0.0116438	+	0.00700584i	−0.509720	+	0.860340i	$0.670251\pi$
$570$	−11184.9	−	15516.1i	−0.821902	−	1.14017i
$571$	16889.1	+	8954.04i	1.23781	+	0.656243i	0.953182	−	0.302397i	$-0.0977867\pi$
$571$	16889.1	+	8954.04i	1.23781	+	0.656243i	0.284623	+	0.958639i	$0.408132\pi$
$572$	12508.5	−	13205.0i	0.914344	−	0.965262i
$573$	−848.070	−	1702.76i	−0.0618301	−	0.124143i
$574$	−1486.77	+	6754.48i	−0.108113	+	0.491161i
$575$	−8148.88	+	886.244i	−0.591012	+	0.0642764i
$576$	11068.9	+	5820.67i	0.800704	+	0.421056i
$577$	−9233.94	−	10871.0i	−0.666229	−	0.784345i	0.320408	−	0.947280i	$-0.396180\pi$
$577$	−9233.94	−	10871.0i	−0.666229	−	0.784345i	−0.986637	+	0.162934i	$0.947904\pi$
$578$	7582.83	−	2554.95i	0.545682	−	0.183862i
$579$	6029.72	−	19756.3i	0.432792	−	1.41804i
$580$	4231.36	−	10619.9i	0.302927	−	0.760289i
$581$	−564.240	+	664.275i	−0.0402903	+	0.0474333i
$582$	21427.5	−	26749.2i	1.52612	−	1.90514i
$583$	−4485.41	+	3041.18i	−0.318639	+	0.216043i
$584$	−27412.3	+	10922.1i	−1.94235	+	0.773901i
$585$	2326.78	+	10403.5i	0.164445	+	0.735269i
$586$	2100.54	−	19314.2i	0.148076	−	1.36154i
$587$	21726.6	−	10051.8i	1.52769	−	0.706783i	0.537081	−	0.843531i	$-0.319527\pi$
$587$	21726.6	−	10051.8i	1.52769	−	0.706783i	0.990606	+	0.136748i	$0.0436650\pi$
$588$	−27480.4	−	17499.9i	−1.92733	−	1.22736i
$589$			23235.5i			1.62547i
$590$	−2338.96	+	19551.6i	−0.163209	+	1.36428i
$591$	3856.10	+	2171.58i	0.268390	+	0.151145i
$592$	−6175.53	−	334.827i	−0.428738	−	0.0232455i
$593$	−8610.94	−	18612.3i	−0.596305	−	1.28889i	−0.937200	−	0.348792i	$-0.886592\pi$
$593$	−8610.94	−	18612.3i	−0.596305	−	1.28889i	0.340895	−	0.940101i	$-0.389270\pi$
$594$	14582.9	+	1113.27i	1.00732	+	0.0768989i
$595$	−1861.59	−	627.244i	−0.128265	−	0.0432176i
$596$	−8414.63	−	21119.1i	−0.578317	−	1.45147i
$597$	−17219.5	+	1431.35i	−1.18048	+	0.0981261i
$598$	35964.5	+	5896.07i	2.45936	+	0.403191i
$599$	−220.551	−	187.338i	−0.0150442	−	0.0127787i	0.639833	−	0.768514i	$-0.279004\pi$
$599$	−220.551	−	187.338i	−0.0150442	−	0.0127787i	−0.654877	+	0.755736i	$0.727280\pi$
$600$	10594.6	+	13134.8i	0.720868	+	0.893712i
$601$	−602.952	−	2739.24i	−0.0409233	−	0.185917i	0.951725	−	0.306953i	$-0.0993093\pi$
$601$	−602.952	−	2739.24i	−0.0409233	−	0.185917i	−0.992648	+	0.121036i	$0.961378\pi$
$602$	−2411.54	−	7157.20i	−0.163267	−	0.484561i
$603$	−8725.31	−	2907.19i	−0.589257	−	0.196335i
$604$	18457.6	+	30676.7i	1.24342	+	2.06659i
$605$	−839.024	−	7714.70i	−0.0563821	−	0.518425i
$606$	32418.6	−	36258.2i	2.17312	−	2.43051i
$607$	−1674.11	+	2469.13i	−0.111944	+	0.165105i	−0.879534	−	0.475836i	$-0.842146\pi$
$607$	−1674.11	+	2469.13i	−0.111944	+	0.165105i	0.767590	+	0.640942i	$0.221456\pi$
$608$	19714.3	+	18674.4i	1.31500	+	1.24564i
$609$	−1267.88	+	813.426i	−0.0843630	+	0.0541243i
$610$	30734.3	+	14219.2i	2.04000	+	0.943802i
$611$	−3522.35	+	5854.19i	−0.233223	+	0.387619i
$612$	19585.9	+	22901.4i	1.29365	+	1.51264i
$613$	−7509.97	−	7928.18i	−0.494820	−	0.522376i	0.429975	−	0.902841i	$-0.358522\pi$
$613$	−7509.97	−	7928.18i	−0.494820	−	0.522376i	−0.924795	+	0.380465i	$0.875764\pi$
$614$	3668.61	+	13213.1i	0.241129	+	0.868468i
$615$	−12990.3	+	5613.97i	−0.851737	+	0.368093i
$616$	3770.77	−	2866.47i	0.246638	−	0.187489i
$617$	−27746.9	−	7703.89i	−1.81045	−	0.502669i	−0.813561	−	0.581480i	$-0.802474\pi$
$617$	−27746.9	−	7703.89i	−1.81045	−	0.502669i	−0.996890	+	0.0788113i	$0.974888\pi$
$618$	485.633	−	19117.1i	0.0316101	−	1.24434i
$619$	−467.423	−	8621.10i	−0.0303511	−	0.559792i	−0.973678	−	0.227928i	$-0.926805\pi$
$619$	−467.423	−	8621.10i	−0.0303511	−	0.559792i	0.943327	−	0.331865i	$-0.107678\pi$
$620$	2375.20	+	43808.0i	0.153855	+	2.83770i
$621$	10271.7	+	17955.4i	0.663748	+	1.16026i
$622$	52753.6	+	14647.0i	3.40069	+	0.944196i
$623$	−1459.88	+	1109.77i	−0.0938823	+	0.0713675i
$624$	−14758.0	−	34148.8i	−0.946783	−	2.19078i
$625$	−1494.19	−	5381.58i	−0.0956281	−	0.344421i
$626$	−14672.5	−	15489.6i	−0.936793	−	0.988960i
$627$	8264.35	+	3020.38i	0.526390	+	0.192380i
$628$	36342.7	−	60402.0i	2.30928	−	3.83806i
$629$	−2159.79	−	999.226i	−0.136910	−	0.0633414i
$630$	273.658	+	4751.07i	0.0173060	+	0.300456i
$631$	−12206.3	−	11562.4i	−0.770086	−	0.729464i	0.197968	−	0.980209i	$-0.436566\pi$
$631$	−12206.3	−	11562.4i	−0.770086	−	0.729464i	−0.968053	+	0.250745i	$0.919325\pi$
$632$	−14078.5	+	20764.3i	−0.886098	+	1.30690i
$633$	20881.0	+	18669.8i	1.31113	+	1.17229i
$634$	−1837.73	−	16897.7i	−0.115120	−	1.05851i
$635$	2726.76	+	4531.92i	0.170407	+	0.283218i
$636$	5142.18	+	26556.6i	0.320599	+	1.65572i
$637$	4941.50	+	14665.8i	0.307362	+	0.912216i
$638$	1601.54	+	7275.85i	0.0993816	+	0.451495i
$639$	1880.58	+	11233.8i	0.116424	+	0.695463i
$640$	−942.972	−	800.968i	−0.0582410	−	0.0494704i
$641$	11519.8	+	1888.58i	0.709837	+	0.116372i	0.505875	−	0.862607i	$-0.331170\pi$
$641$	11519.8	+	1888.58i	0.709837	+	0.116372i	0.203962	+	0.978979i	$0.434618\pi$
$642$	1649.41	+	19842.7i	0.101397	+	1.21983i
$643$	2512.08	+	6304.84i	0.154069	+	0.386685i	0.985669	−	0.168690i	$-0.0539538\pi$
$643$	2512.08	+	6304.84i	0.154069	+	0.386685i	−0.831600	+	0.555376i	$0.812574\pi$
$644$	10883.1	+	3666.93i	0.665921	+	0.224375i
$645$	8994.36	−	12566.4i	0.549073	−	0.767133i
$646$	10784.1	+	23309.5i	0.656804	+	1.41966i
$647$	7320.25	+	396.892i	0.444805	+	0.0241166i	0.275181	−	0.961392i	$-0.411262\pi$
$647$	7320.25	+	396.892i	0.444805	+	0.0241166i	0.169623	+	0.985509i	$0.445745\pi$
$648$	19693.6	−	37758.9i	1.19388	−	2.28906i
$649$	−4156.86	−	8048.23i	−0.251419	−	0.486781i
$650$		−	13741.4i		−	0.829202i
$651$	3105.30	−	4876.28i	0.186953	−	0.293574i
$652$	10538.7	−	4875.73i	0.633018	−	0.292865i
$653$	3014.33	−	27716.3i	0.180643	−	1.66098i	−0.456115	−	0.889921i	$-0.650760\pi$
$653$	3014.33	−	27716.3i	0.180643	−	1.66098i	0.636758	−	0.771063i	$-0.280275\pi$
$654$	28929.8	+	32137.6i	1.72973	+	1.92153i
$655$	−13620.7	+	5427.00i	−0.812529	+	0.323741i
$656$	40874.1	−	27713.3i	2.43272	−	1.64942i
$657$	5090.79	+	12652.7i	0.302299	+	0.751339i
$658$	−1974.48	+	2324.54i	−0.116981	+	0.137720i
$659$	4121.87	−	10345.1i	0.243650	−	0.611515i	−0.755392	−	0.655273i	$-0.772554\pi$
$659$	4121.87	−	10345.1i	0.243650	−	0.611515i	0.999042	+	0.0437577i	$0.0139330\pi$
$660$	15890.3	+	4849.78i	0.937165	+	0.286027i
$661$	−13864.1	+	4671.36i	−0.815811	+	0.274879i	−0.696113	−	0.717932i	$-0.745089\pi$
$661$	−13864.1	+	4671.36i	−0.815811	+	0.274879i	−0.119697	+	0.992810i	$0.538192\pi$
$662$	11210.6	+	13198.2i	0.658178	+	0.774867i
$663$	−411.741	−	14308.6i	−0.0241187	−	0.838159i
$664$	12477.6	−	1357.02i	0.729254	−	0.0793111i
$665$	−615.481	+	2796.16i	−0.0358907	+	0.163053i
$666$	−292.711	+	5757.64i	−0.0170305	+	0.334991i
$667$	−7246.40	+	7649.93i	−0.420662	+	0.444087i
$668$	−17990.7	−	9538.04i	−1.04203	−	0.552452i
$669$	−2936.98	+	2117.15i	−0.169732	+	0.122352i
$670$	−12681.7	−	7630.31i	−0.731247	−	0.439977i
$671$	−15373.1	+	2520.30i	−0.884460	+	0.145000i
$672$	−1641.59	−	6553.79i	−0.0942344	−	0.376217i
$673$	−25837.2	+	7173.68i	−1.47987	+	0.410884i	−0.911297	−	0.411749i	$-0.864918\pi$
$673$	−25837.2	+	7173.68i	−1.47987	+	0.410884i	−0.568573	+	0.822633i	$0.692504\pi$
$674$	2636.74	−	3468.57i	0.150688	−	0.198226i
$675$	6054.30	−	4917.17i	0.345230	−	0.280388i
$676$	−252.255	+	908.540i	−0.0143522	+	0.0516921i
$677$	−16483.6	+	8739.06i	−0.935771	+	0.496114i	−0.865219	−	0.501394i	$-0.832821\pi$
$677$	−16483.6	+	8739.06i	−0.935771	+	0.496114i	−0.0705517	+	0.997508i	$0.522476\pi$
$678$	−49282.4	−	24338.4i	−2.79156	−	1.37863i
$679$	−5122.74	+	277.747i	−0.289533	+	0.0156980i
$680$	13250.8	+	24993.7i	0.747274	+	1.40951i
$681$	−11936.0	−	11895.8i	−0.671640	−	0.669381i
$682$	−17302.7	−	22761.3i	−0.971487	−	1.27797i
$683$	3917.17	+	2977.75i	0.219453	+	0.166824i	0.709125	−	0.705083i	$-0.249090\pi$
$683$	3917.17	+	2977.75i	0.219453	+	0.166824i	−0.489672	+	0.871907i	$0.662883\pi$
$684$	30096.2	−	31987.4i	1.68239	−	1.78811i
$685$	−2540.71	+	2406.69i	−0.141716	+	0.134240i
$686$	2291.69	+	13978.7i	0.127547	+	0.778002i
$687$	4512.78	+	7950.62i	0.250616	+	0.441536i
$688$	−22643.4	+	48943.0i	−1.25476	+	2.71211i
$689$	6018.72	−	11352.5i	0.332794	−	0.627716i
$690$	9824.65	+	31806.1i	0.542055	+	1.75484i
$691$	16943.8	+	11488.2i	0.932811	+	0.632461i	0.930010	−	0.367535i	$-0.119798\pi$
$691$	16943.8	+	11488.2i	0.932811	+	0.632461i	0.00280101	+	0.999996i	$0.499108\pi$
$692$	−64744.6	−	14251.4i	−3.55668	−	0.782883i
$693$	−1330.73	−	1738.35i	−0.0729440	−	0.0952879i
$694$	35598.8	−	21419.1i	1.94714	−	1.17155i
$695$	−17224.6	+	14630.7i	−0.940095	+	0.798524i
$696$	21311.1	+	4052.02i	1.16063	+	0.220678i
$697$	18557.7	−	4084.86i	1.00850	−	0.221987i
$698$	51341.2	+	20456.2i	2.78409	+	1.10928i
$699$	−6187.26	−	16754.2i	−0.334798	−	0.906585i
$700$	700.535	−	4273.07i	0.0378253	−	0.230724i
$701$	4587.74	+	6766.41i	0.247185	+	0.364570i	0.930959	−	0.365123i	$-0.118973\pi$
$701$	4587.74	+	6766.41i	0.247185	+	0.364570i	−0.683774	+	0.729693i	$0.739663\pi$
$702$	−31785.8	+	13864.1i	−1.70894	+	0.745394i
$703$	−1107.47	+	3286.85i	−0.0594153	+	0.176338i
$704$	−9203.95	−	1000.99i	−0.492737	−	0.0535884i
$705$	−6220.83	−	495.995i	−0.332327	−	0.0264968i
$706$	−931.484	+	17180.2i	−0.0496556	+	0.915843i
$707$	−7280.41			−0.387281
$708$	−45096.8	+	3261.67i	−2.39385	+	0.173137i
$709$	−20528.0			−1.08737			−0.543686	−	0.839289i	$-0.682972\pi$
$709$	−20528.0			−1.08737			−0.543686	+	0.839289i	$0.682972\pi$
$710$	−992.347	+	18302.8i	−0.0524537	+	0.967452i
$711$	9619.00	+	6474.63i	0.507371	+	0.341516i
$712$	26253.2	+	2855.21i	1.38185	+	0.150286i
$713$	12912.2	−	38322.0i	0.678212	−	2.01286i
$714$	851.993	−	6333.05i	0.0446569	−	0.331945i
$715$	−4428.88	−	6532.10i	−0.231651	−	0.341660i
$716$	7272.97	−	44363.1i	0.379614	−	2.31554i
$717$	−21595.0	+	7974.92i	−1.12480	+	0.415382i
$718$	6428.59	+	2561.38i	0.334141	+	0.133134i
$719$	−1208.84	+	266.085i	−0.0627010	+	0.0138015i	−0.246210	−	0.969216i	$-0.579185\pi$
$719$	−1208.84	+	266.085i	−0.0627010	+	0.0138015i	0.183509	+	0.983018i	$0.441254\pi$
$720$	21910.9	−	25972.4i	1.13412	−	1.34435i
$721$	−2181.69	+	1853.15i	−0.112691	+	0.0957209i
$722$	1422.37	−	855.811i	0.0733173	−	0.0441136i
$723$	12569.6	−	29356.3i	0.646567	−	1.51006i
$724$	2247.63	+	494.740i	0.115376	+	0.0253962i
$725$	3288.43	+	2229.61i	0.168454	+	0.114215i
$726$	24118.8	−	7450.11i	1.23297	−	0.380854i
$727$	−448.702	+	846.341i	−0.0228905	+	0.0431761i	−0.894694	−	0.446681i	$-0.852606\pi$
$727$	−448.702	+	846.341i	−0.0228905	+	0.0431761i	0.871803	+	0.489857i	$0.162951\pi$
$728$	−4715.69	+	10192.8i	−0.240076	+	0.518916i
$729$	−17482.5	−	9043.38i	−0.888203	−	0.459452i
$730$	3550.77	+	21658.7i	0.180027	+	1.09812i
$731$	−15064.7	+	14270.0i	−0.762226	+	0.722019i
$732$	−18639.0	+	75492.2i	−0.941146	+	3.81185i
$733$	−16530.7	−	12566.3i	−0.832981	−	0.633216i	0.0992565	−	0.995062i	$-0.468354\pi$
$733$	−16530.7	−	12566.3i	−0.832981	−	0.633216i	−0.932238	+	0.361846i	$0.882147\pi$
$734$	−624.847	−	821.972i	−0.0314217	−	0.0413345i
$735$	−9978.75	+	10012.4i	−0.500778	+	0.502468i
$736$	−22137.0	−	41754.8i	−1.10867	−	2.09117i
$737$	6798.46	−	368.602i	0.339789	−	0.0184228i
$738$	−25961.7	−	38014.1i	−1.29493	−	1.89610i
$739$	−15194.8	+	8055.80i	−0.756362	+	0.400998i	−0.801509	−	0.597983i	$-0.795969\pi$
$739$	−15194.8	+	8055.80i	−0.756362	+	0.400998i	0.0451472	+	0.998980i	$0.485624\pi$
$740$	−1752.02	+	6310.21i	−0.0870345	+	0.313470i
$741$	−20667.3	+	2851.34i	−1.02460	+	0.141358i
$742$	3471.29	−	4566.41i	0.171746	−	0.225927i
$743$	14877.0	−	4130.58i	0.734569	−	0.203952i	0.119954	−	0.992779i	$-0.461725\pi$
$743$	14877.0	−	4130.58i	0.734569	−	0.203952i	0.614615	+	0.788827i	$0.289311\pi$
$744$	−80757.0	+	20227.9i	−3.97943	+	0.996763i
$745$	−9734.03	+	1595.81i	−0.478695	+	0.0784780i
$746$	−12890.1	−	7755.70i	−0.632626	−	0.380639i
$747$	−646.640	−	5764.92i	−0.0316724	−	0.282366i
$748$	−19709.8	−	10449.5i	−0.963450	−	0.510789i
$749$	2049.65	−	2163.78i	0.0999899	−	0.105558i
$750$	36497.0	−	18177.5i	1.77691	−	0.885000i
$751$	1060.58	−	4818.27i	0.0515329	−	0.234116i	−0.943813	−	0.330479i	$-0.892790\pi$
$751$	1060.58	−	4818.27i	0.0515329	−	0.234116i	0.995346	+	0.0963626i	$0.0307208\pi$
$752$	21649.7	−	2354.54i	1.04984	−	0.114177i
$753$	−39607.1	+	1139.73i	−1.91682	+	0.0551579i
$754$	−11435.8	−	13463.3i	−0.552343	−	0.650269i
$755$	14720.8	−	4960.01i	0.709595	−	0.239090i
$756$	−10591.0	+	2690.80i	−0.509513	+	0.129449i
$757$	6104.70	−	15321.6i	0.293103	−	0.735633i	−0.706507	−	0.707706i	$-0.749730\pi$
$757$	6104.70	−	15321.6i	0.293103	−	0.735633i	0.999610	−	0.0279269i	$-0.00889058\pi$
$758$	−23565.4	+	27743.4i	−1.12920	+	1.32940i
$759$	−11951.8	−	9574.04i	−0.571573	−	0.457860i
$760$	34126.1	−	23138.1i	1.62879	−	1.10435i
$761$	−9922.98	+	3953.68i	−0.472678	+	0.188332i	−0.594298	−	0.804245i	$-0.702570\pi$
$761$	−9922.98	+	3953.68i	−0.472678	+	0.188332i	0.121621	+	0.992577i	$0.461191\pi$
$762$	−12786.9	+	11510.6i	−0.607903	+	0.547226i
$763$	699.807	−	6434.62i	0.0332041	−	0.305307i
$764$	6379.57	−	2951.50i	0.302101	−	0.139767i
$765$	11531.2	−	6163.36i	0.544984	−	0.291290i
$766$			36103.5i			1.70297i
$767$	17646.7	+	12243.3i	0.830750	+	0.576374i
$768$	11422.8	−	20283.7i	0.536701	−	0.953027i
$769$	−5859.56	−	317.696i	−0.274774	−	0.0148978i	−0.0837629	−	0.996486i	$-0.526694\pi$
$769$	−5859.56	−	317.696i	−0.274774	−	0.0148978i	−0.191011	+	0.981588i	$0.561177\pi$
$770$	−1479.29	−	3197.42i	−0.0692335	−	0.149646i
$771$	7914.43	+	5664.74i	0.369690	+	0.264605i
$772$	72332.4	+	24371.6i	3.37215	+	1.13621i
$773$	−2491.22	−	6252.48i	−0.115916	−	0.290926i	0.859560	−

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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	177.f (of order \(58\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.282358 + 5.20779i) q^{2} +(-0.412985 + 5.17971i) q^{3} +(-19.0882 - 2.07597i) q^{4} +(-2.66012 + 7.89495i) q^{5} +(-26.8583 - 3.61327i) q^{6} +(2.27648 + 3.35756i) q^{7} +(9.45083 - 57.6475i) q^{8} +(-26.6589 - 4.27829i) q^{9} +O(q^{10})\)	\(q+(-0.282358 + 5.20779i) q^{2} +(-0.412985 + 5.17971i) q^{3} +(-19.0882 - 2.07597i) q^{4} +(-2.66012 + 7.89495i) q^{5} +(-26.8583 - 3.61327i) q^{6} +(2.27648 + 3.35756i) q^{7} +(9.45083 - 57.6475i) q^{8} +(-26.6589 - 4.27829i) q^{9} +(-40.3641 - 16.0825i) q^{10} +(19.5208 - 4.29684i) q^{11} +(18.6361 - 98.0143i) q^{12} +(-36.1212 + 30.6817i) q^{13} +(-18.1282 + 10.9074i) q^{14} +(-39.7950 - 17.0391i) q^{15} +(147.532 + 32.4743i) q^{16} +(48.1112 + 32.6202i) q^{17} +(29.8078 - 137.626i) q^{18} +(39.6830 - 74.8501i) q^{19} +(67.1667 - 145.178i) q^{20} +(-18.3313 + 10.4049i) q^{21} +(16.8652 + 102.873i) q^{22} +(-107.044 + 101.397i) q^{23} +(294.695 + 72.7601i) q^{24} +(44.2576 + 33.6438i) q^{25} +(-149.584 - 196.775i) q^{26} +(33.1700 - 136.319i) q^{27} +(-36.4838 - 68.8157i) q^{28} +(71.3607 - 3.86907i) q^{29} +(99.9727 - 202.433i) q^{30} +(-242.317 + 128.468i) q^{31} +(-85.7507 + 308.846i) q^{32} +(14.1946 + 102.886i) q^{33} +(-183.464 + 241.342i) q^{34} +(-32.5634 + 9.04119i) q^{35} +(499.990 + 137.008i) q^{36} +(-40.4009 + 6.62339i) q^{37} +(378.599 + 227.795i) q^{38} +(-144.005 - 199.769i) q^{39} +(429.984 + 227.963i) q^{40} +(224.811 - 237.330i) q^{41} +(-49.0105 - 98.4036i) q^{42} +(-76.7406 + 348.636i) q^{43} +(-381.537 + 41.4946i) q^{44} +(104.693 - 199.090i) q^{45} +(-497.830 - 586.091i) q^{46} +(136.613 - 46.0303i) q^{47} +(-229.136 + 750.764i) q^{48} +(120.867 - 303.352i) q^{49} +(-187.706 + 220.985i) q^{50} +(-188.833 + 235.731i) q^{51} +(753.185 - 510.672i) q^{52} +(-251.866 + 100.352i) q^{53} +(700.552 + 211.233i) q^{54} +(-18.0042 + 165.545i) q^{55} +(215.069 - 99.5017i) q^{56} +(371.314 + 236.459i) q^{57} +372.724i q^{58} +(-116.547 - 437.945i) q^{59} +(724.244 + 407.861i) q^{60} +(-778.239 - 42.1949i) q^{61} +(-600.617 - 1298.21i) q^{62} +(-46.3238 - 99.2481i) q^{63} +(-438.941 - 147.896i) q^{64} +(-146.143 - 366.792i) q^{65} +(-539.819 + 44.8719i) q^{66} +(336.138 + 55.1071i) q^{67} +(-850.640 - 722.540i) q^{68} +(-481.000 - 596.331i) q^{69} +(-37.8901 - 172.136i) q^{70} +(-134.699 - 399.772i) q^{71} +(-498.581 + 1496.38i) q^{72} +(-260.421 - 432.823i) q^{73} +(-23.0857 - 212.269i) q^{74} +(-192.543 + 215.348i) q^{75} +(-912.866 + 1346.38i) q^{76} +(58.8655 + 55.7603i) q^{77} +(1081.01 - 693.540i) q^{78} +(-389.756 - 180.320i) q^{79} +(-648.837 + 1078.37i) q^{80} +(692.392 + 228.109i) q^{81} +(1172.49 + 1237.78i) q^{82} +(57.4797 + 207.023i) q^{83} +(371.513 - 160.556i) q^{84} +(-385.516 + 293.062i) q^{85} +(-1793.96 - 498.089i) q^{86} +(-9.43026 + 371.226i) q^{87} +(-63.2149 - 1165.93i) q^{88} +(24.4740 + 451.397i) q^{89} +(1007.26 + 601.432i) q^{90} +(-185.245 - 51.4329i) q^{91} +(2253.77 - 1713.27i) q^{92} +(-565.357 - 1308.19i) q^{93} +(201.142 + 724.449i) q^{94} +(485.376 + 512.406i) q^{95} +(-1564.32 - 571.713i) q^{96} +(-652.015 + 1083.66i) q^{97} +(1545.67 + 715.102i) q^{98} +(-538.785 + 31.0336i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1624q - 21q^{3} - 278q^{4} - 29q^{6} - 42q^{7} - 25q^{9} + O(q^{10}) \)	\( 1624q - 21q^{3} - 278q^{4} - 29q^{6} - 42q^{7} - 25q^{9} - 58q^{10} - 57q^{12} - 58q^{13} - 11q^{15} - 926q^{16} - 29q^{18} + 126q^{19} + 159q^{21} + 2q^{22} - 29q^{24} + 656q^{25} - 99q^{27} - 54q^{28} - 29q^{30} - 58q^{31} - 29q^{33} - 58q^{34} + 859q^{36} - 58q^{37} - 29q^{39} - 58q^{40} - 29q^{42} - 58q^{43} + 1703q^{45} + 602q^{46} + 9507q^{48} - 1192q^{49} + 1511q^{51} - 58q^{52} - 7743q^{54} - 58q^{55} - 7441q^{57} - 18722q^{60} - 58q^{61} - 3251q^{63} - 4634q^{64} - 1751q^{66} - 58q^{67} + 6003q^{69} - 58q^{70} + 21547q^{72} - 58q^{73} + 3869q^{75} + 5622q^{76} - 3253q^{78} + 1446q^{79} + 247q^{81} - 58q^{82} + 3303q^{84} + 790q^{85} - 2199q^{87} - 5818q^{88} - 29q^{90} - 58q^{91} - 29q^{93} - 946q^{94} - 29q^{96} - 58q^{97} - 29q^{99} + O(q^{100}) \)

Introduction

L-functions

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