LMFDB - Embedded newform 49.4.e.a.36.5

Newspace parameters

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	49.e (of order $7$, degree $6$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$2.89109359028$
Analytic rank:	$0$
Dimension:	$78$
Relative dimension:	$13$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			36.5
Character	$\chi$	$=$	49.36
Dual form			49.4.e.a.15.5

$q$-expansion

$f(q)$	$=$	$q+(-0.424669 - 1.86059i) q^{2} +(0.113640 + 0.142500i) q^{3} +(3.92628 - 1.89080i) q^{4} +(11.1399 + 13.9690i) q^{5} +(0.216876 - 0.271954i) q^{6} +(1.18252 - 18.4825i) q^{7} +(-14.7045 - 18.4389i) q^{8} +(6.00067 - 26.2907i) q^{9} +O(q^{10})$	\(q+(-0.424669 - 1.86059i) q^{2} +(0.113640 + 0.142500i) q^{3} +(3.92628 - 1.89080i) q^{4} +(11.1399 + 13.9690i) q^{5} +(0.216876 - 0.271954i) q^{6} +(1.18252 - 18.4825i) q^{7} +(-14.7045 - 18.4389i) q^{8} +(6.00067 - 26.2907i) q^{9} +(21.2598 - 26.6590i) q^{10} +(4.46612 + 19.5674i) q^{11} +(0.715623 + 0.344626i) q^{12} +(9.93444 + 43.5256i) q^{13} +(-34.8906 + 5.64874i) q^{14} +(-0.724644 + 3.17487i) q^{15} +(-6.32621 + 7.93281i) q^{16} +(9.17124 + 4.41664i) q^{17} -51.4646 q^{18} -51.5845 q^{19} +(70.1508 + 33.7828i) q^{20} +(2.76814 - 1.93184i) q^{21} +(34.5103 - 16.6193i) q^{22} +(-140.115 + 67.4759i) q^{23} +(0.956524 - 4.19080i) q^{24} +(-43.2200 + 189.359i) q^{25} +(76.7647 - 36.9680i) q^{26} +(8.86215 - 4.26779i) q^{27} +(-30.3037 - 74.8033i) q^{28} +(235.771 + 113.541i) q^{29} +6.21489 q^{30} -211.476 q^{31} +(-152.543 - 73.4609i) q^{32} +(-2.28083 + 2.86007i) q^{33} +(4.32283 - 18.9396i) q^{34} +(271.354 - 189.374i) q^{35} +(-26.1500 - 114.571i) q^{36} +(-295.222 - 142.172i) q^{37} +(21.9063 + 95.9779i) q^{38} +(-5.07347 + 6.36193i) q^{39} +(93.7657 - 410.814i) q^{40} +(157.381 + 197.349i) q^{41} +(-4.76992 - 4.32999i) q^{42} +(-12.1868 + 15.2817i) q^{43} +(54.5332 + 68.3825i) q^{44} +(434.100 - 209.052i) q^{45} +(185.048 + 232.042i) q^{46} +(-1.76856 - 7.74855i) q^{47} -1.84934 q^{48} +(-340.203 - 43.7116i) q^{49} +370.675 q^{50} +(0.412850 + 1.80881i) q^{51} +(121.304 + 152.110i) q^{52} +(-233.910 + 112.645i) q^{53} +(-11.7041 - 14.6765i) q^{54} +(-223.584 + 280.365i) q^{55} +(-358.185 + 249.972i) q^{56} +(-5.86208 - 7.35081i) q^{57} +(111.130 - 486.891i) q^{58} +(553.795 - 694.437i) q^{59} +(3.15789 + 13.8356i) q^{60} +(-179.224 - 86.3096i) q^{61} +(89.8072 + 393.471i) q^{62} +(-478.821 - 141.996i) q^{63} +(-89.9630 + 394.154i) q^{64} +(-497.340 + 623.644i) q^{65} +(6.29002 + 3.02911i) q^{66} +454.487 q^{67} +44.3598 q^{68} +(-25.5381 - 12.2985i) q^{69} +(-467.584 - 424.459i) q^{70} +(-9.57888 + 4.61295i) q^{71} +(-573.008 + 275.946i) q^{72} +(-6.65675 + 29.1651i) q^{73} +(-139.152 + 609.665i) q^{74} +(-31.8953 + 15.3600i) q^{75} +(-202.535 + 97.5359i) q^{76} +(366.935 - 59.4063i) q^{77} +(13.9915 + 6.73796i) q^{78} +906.648 q^{79} -181.286 q^{80} +(-654.383 - 315.134i) q^{81} +(300.352 - 376.630i) q^{82} +(-26.1418 + 114.535i) q^{83} +(7.21577 - 12.8190i) q^{84} +(40.4707 + 177.314i) q^{85} +(33.6084 + 16.1850i) q^{86} +(10.6134 + 46.5003i) q^{87} +(295.129 - 370.080i) q^{88} +(-46.7664 + 204.897i) q^{89} +(-573.309 - 718.907i) q^{90} +(816.209 - 132.143i) q^{91} +(-422.548 + 529.858i) q^{92} +(-24.0322 - 30.1354i) q^{93} +(-13.6659 + 6.58114i) q^{94} +(-574.645 - 720.582i) q^{95} +(-6.86683 - 30.0856i) q^{96} +1208.12 q^{97} +(63.1441 + 651.543i) q^{98} +541.239 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q - 5 q^{2} - 5 q^{3} - 53 q^{4} - 23 q^{5} + 19 q^{6} - 31 q^{8} - 174 q^{9}+O(q^{10}) $ 78 * q - 5 * q^2 - 5 * q^3 - 53 * q^4 - 23 * q^5 + 19 * q^6 - 31 * q^8 - 174 * q^9	\( 78 q - 5 q^{2} - 5 q^{3} - 53 q^{4} - 23 q^{5} + 19 q^{6} - 31 q^{8} - 174 q^{9} + 9 q^{10} - 103 q^{11} + 364 q^{12} - 35 q^{13} + 161 q^{14} - 245 q^{15} - 205 q^{16} - 285 q^{17} + 16 q^{18} + 628 q^{19} + 553 q^{20} - 21 q^{21} - 605 q^{22} + 149 q^{23} + 653 q^{24} - 370 q^{25} - 511 q^{26} - 65 q^{27} + 70 q^{28} - 187 q^{29} + 84 q^{30} + 1276 q^{31} + 1399 q^{32} - 23 q^{33} - 765 q^{34} - 805 q^{35} - 1691 q^{36} - 1531 q^{37} - 1041 q^{38} - 1351 q^{39} - 1759 q^{40} - 301 q^{41} + 3395 q^{42} - 257 q^{43} - 883 q^{44} + 3105 q^{45} + 1593 q^{46} + 733 q^{47} - 1948 q^{48} + 1288 q^{49} + 6148 q^{50} + 1197 q^{51} - 1099 q^{52} - 285 q^{53} + 660 q^{54} + 2641 q^{55} - 1988 q^{56} - 2352 q^{57} + 1173 q^{58} - 3603 q^{59} - 175 q^{60} - 2613 q^{61} - 1927 q^{62} - 3066 q^{63} + 1589 q^{64} - 371 q^{65} - 2175 q^{66} + 352 q^{67} + 6076 q^{68} + 5549 q^{69} - 6293 q^{70} - 2623 q^{71} + 6220 q^{72} + 2039 q^{73} - 2411 q^{74} - 3903 q^{75} + 4130 q^{76} + 1029 q^{77} - 3759 q^{78} + 44 q^{79} - 1608 q^{80} + 1394 q^{81} - 10920 q^{82} - 553 q^{83} - 7798 q^{84} + 497 q^{85} - 2985 q^{86} - 4273 q^{87} - 2197 q^{88} - 3957 q^{89} - 2958 q^{90} + 14119 q^{91} - 9136 q^{92} + 6272 q^{93} + 14912 q^{94} + 5866 q^{95} + 21882 q^{96} - 1540 q^{97} - 2303 q^{98} + 10768 q^{99}+O(q^{100}) \) 78 * q - 5 * q^2 - 5 * q^3 - 53 * q^4 - 23 * q^5 + 19 * q^6 - 31 * q^8 - 174 * q^9 + 9 * q^10 - 103 * q^11 + 364 * q^12 - 35 * q^13 + 161 * q^14 - 245 * q^15 - 205 * q^16 - 285 * q^17 + 16 * q^18 + 628 * q^19 + 553 * q^20 - 21 * q^21 - 605 * q^22 + 149 * q^23 + 653 * q^24 - 370 * q^25 - 511 * q^26 - 65 * q^27 + 70 * q^28 - 187 * q^29 + 84 * q^30 + 1276 * q^31 + 1399 * q^32 - 23 * q^33 - 765 * q^34 - 805 * q^35 - 1691 * q^36 - 1531 * q^37 - 1041 * q^38 - 1351 * q^39 - 1759 * q^40 - 301 * q^41 + 3395 * q^42 - 257 * q^43 - 883 * q^44 + 3105 * q^45 + 1593 * q^46 + 733 * q^47 - 1948 * q^48 + 1288 * q^49 + 6148 * q^50 + 1197 * q^51 - 1099 * q^52 - 285 * q^53 + 660 * q^54 + 2641 * q^55 - 1988 * q^56 - 2352 * q^57 + 1173 * q^58 - 3603 * q^59 - 175 * q^60 - 2613 * q^61 - 1927 * q^62 - 3066 * q^63 + 1589 * q^64 - 371 * q^65 - 2175 * q^66 + 352 * q^67 + 6076 * q^68 + 5549 * q^69 - 6293 * q^70 - 2623 * q^71 + 6220 * q^72 + 2039 * q^73 - 2411 * q^74 - 3903 * q^75 + 4130 * q^76 + 1029 * q^77 - 3759 * q^78 + 44 * q^79 - 1608 * q^80 + 1394 * q^81 - 10920 * q^82 - 553 * q^83 - 7798 * q^84 + 497 * q^85 - 2985 * q^86 - 4273 * q^87 - 2197 * q^88 - 3957 * q^89 - 2958 * q^90 + 14119 * q^91 - 9136 * q^92 + 6272 * q^93 + 14912 * q^94 + 5866 * q^95 + 21882 * q^96 - 1540 * q^97 - 2303 * q^98 + 10768 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{7}\right)$

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 $

$2$	−0.424669	−	1.86059i	−0.150143	−	0.657820i	−0.992842	−	0.119435i	$-0.961892\pi$
$2$	−0.424669	−	1.86059i	−0.150143	−	0.657820i	0.842699	−	0.538385i	$-0.180965\pi$
$3$	0.113640	+	0.142500i	0.0218701	+	0.0274242i	0.792646	−	0.609682i	$-0.208703\pi$
$3$	0.113640	+	0.142500i	0.0218701	+	0.0274242i	−0.770776	+	0.637106i	$0.780131\pi$
$4$	3.92628	−	1.89080i	0.490785	−	0.236350i
$5$	11.1399	+	13.9690i	0.996381	+	1.24942i	0.968293	+	0.249817i	$0.0803704\pi$
$5$	11.1399	+	13.9690i	0.996381	+	1.24942i	0.0280878	+	0.999605i	$0.491058\pi$
$6$	0.216876	−	0.271954i	0.0147565	−	0.0185041i
$7$	1.18252	−	18.4825i	0.0638498	−	0.997960i
$7$	1.18252	−	18.4825i	0.0638498	−	0.997960i
$8$	−14.7045	−	18.4389i	−0.649855	−	0.814892i
$9$	6.00067	−	26.2907i	0.222247	−	0.973728i
$10$	21.2598	−	26.6590i	0.672295	−	0.843031i
$11$	4.46612	+	19.5674i	0.122417	+	0.536344i	0.998528	+	0.0542349i	$0.0172720\pi$
$11$	4.46612	+	19.5674i	0.122417	+	0.536344i	−0.876111	+	0.482109i	$0.839871\pi$
$12$	0.715623	+	0.344626i	0.0172152	+	0.00829041i
$13$	9.93444	+	43.5256i	0.211948	+	0.928603i	0.963242	+	0.268636i	$0.0865728\pi$
$13$	9.93444	+	43.5256i	0.211948	+	0.928603i	−0.751294	+	0.659967i	$0.770570\pi$
$14$	−34.8906	+	5.64874i	−0.666064	+	0.107835i
$15$	−0.724644	+	3.17487i	−0.0124735	+	0.0546499i
$16$	−6.32621	+	7.93281i	−0.0988470	+	0.123950i
$17$	9.17124	+	4.41664i	0.130844	+	0.0630113i	0.498161	−	0.867085i	$-0.334009\pi$
$17$	9.17124	+	4.41664i	0.130844	+	0.0630113i	−0.367316	+	0.930096i	$0.619723\pi$
$18$	−51.4646			−0.673906
$19$	−51.5845			−0.622858			−0.311429	−	0.950269i	$-0.600808\pi$
$19$	−51.5845			−0.622858			−0.311429	+	0.950269i	$0.600808\pi$
$20$	70.1508	+	33.7828i	0.784310	+	0.377704i
$21$	2.76814	−	1.93184i	0.0287647	−	0.0200744i
$22$	34.5103	−	16.6193i	0.334438	−	0.161057i
$23$	−140.115	+	67.4759i	−1.27026	+	0.611726i	−0.942869	−	0.333163i	$-0.891884\pi$
$23$	−140.115	+	67.4759i	−1.27026	+	0.611726i	−0.327392	+	0.944889i	$0.606170\pi$
$24$	0.956524	−	4.19080i	0.00813540	−	0.0356435i
$25$	−43.2200	+	189.359i	−0.345760	+	1.51487i
$26$	76.7647	−	36.9680i	0.579031	−	0.278847i
$27$	8.86215	−	4.26779i	0.0631675	−	0.0304199i
$28$	−30.3037	−	74.8033i	−0.204531	−	0.504875i
$29$	235.771	+	113.541i	1.50971	+	0.727037i	0.991728	−	0.128356i	$-0.0409700\pi$
$29$	235.771	+	113.541i	1.50971	+	0.727037i	0.517980	+	0.855393i	$0.326684\pi$
$30$	6.21489			0.0378226
$31$	−211.476			−1.22523			−0.612616	−	0.790381i	$-0.709883\pi$
$31$	−211.476			−1.22523			−0.612616	+	0.790381i	$0.709883\pi$
$32$	−152.543	−	73.4609i	−0.842689	−	0.405818i
$33$	−2.28083	+	2.86007i	−0.0120315	+	0.0150871i
$34$	4.32283	−	18.9396i	0.0218047	−	0.0955326i
$35$	271.354	−	189.374i	1.31049	−	0.914572i
$36$	−26.1500	−	114.571i	−0.121065	−	0.530420i
$37$	−295.222	−	142.172i	−1.31174	−	0.631699i	−0.358388	−	0.933573i	$-0.616674\pi$
$37$	−295.222	−	142.172i	−1.31174	−	0.631699i	−0.953348	+	0.301874i	$0.902388\pi$
$38$	21.9063	+	95.9779i	0.0935178	+	0.409728i
$39$	−5.07347	+	6.36193i	−0.0208309	+	0.0261211i
$40$	93.7657	−	410.814i	0.370641	−	1.62389i
$41$	157.381	+	197.349i	0.599481	+	0.751726i	0.985297	−	0.170850i	$-0.0546514\pi$
$41$	157.381	+	197.349i	0.599481	+	0.751726i	−0.385816	+	0.922576i	$0.626080\pi$
$42$	−4.76992	−	4.32999i	−0.0175242	−	0.0159079i
$43$	−12.1868	+	15.2817i	−0.0432201	+	0.0541963i	−0.802972	−	0.596017i	$-0.796749\pi$
$43$	−12.1868	+	15.2817i	−0.0432201	+	0.0541963i	0.759752	+	0.650213i	$0.225320\pi$
$44$	54.5332	+	68.3825i	0.186845	+	0.234296i
$45$	434.100	−	209.052i	1.43804	−	0.692524i
$46$	185.048	+	232.042i	0.593126	+	0.743756i
$47$	−1.76856	−	7.74855i	−0.00548874	−	0.0240477i	0.972109	−	0.234528i	$-0.0753544\pi$
$47$	−1.76856	−	7.74855i	−0.00548874	−	0.0240477i	−0.977598	+	0.210480i	$0.932497\pi$
$48$	−1.84934			−0.00556103
$49$	−340.203	−	43.7116i	−0.991846	−	0.127439i
$50$	370.675			1.04843
$51$	0.412850	+	1.80881i	0.00113354	+	0.00496636i
$52$	121.304	+	152.110i	0.323496	+	0.405651i
$53$	−233.910	+	112.645i	−0.606228	+	0.291944i	−0.711706	−	0.702478i	$-0.752077\pi$
$53$	−233.910	+	112.645i	−0.606228	+	0.291944i	0.105478	+	0.994422i	$0.466363\pi$
$54$	−11.7041	−	14.6765i	−0.0294949	−	0.0369855i
$55$	−223.584	+	280.365i	−0.548146	+	0.687353i
$56$	−358.185	+	249.972i	−0.854723	+	0.596498i
$57$	−5.86208	−	7.35081i	−0.0136220	−	0.0170814i
$58$	111.130	−	486.891i	0.251587	−	1.10227i
$59$	553.795	−	694.437i	1.22200	−	1.53234i	0.455295	−	0.890341i	$-0.349534\pi$
$59$	553.795	−	694.437i	1.22200	−	1.53234i	0.766705	−	0.641999i	$-0.221895\pi$
$60$	3.15789	+	13.8356i	0.00679469	+	0.0297695i
$61$	−179.224	−	86.3096i	−0.376184	−	0.181161i	0.236231	−	0.971697i	$-0.424088\pi$
$61$	−179.224	−	86.3096i	−0.376184	−	0.181161i	−0.612416	+	0.790536i	$0.709802\pi$
$62$	89.8072	+	393.471i	0.183960	+	0.805981i
$63$	−478.821	−	141.996i	−0.957551	−	0.283966i
$64$	−89.9630	+	394.154i	−0.175709	+	0.769832i
$65$	−497.340	+	623.644i	−0.949037	+	1.19005i
$66$	6.29002	+	3.02911i	0.0117310	+	0.00564936i
$67$	454.487			0.828723			0.414362	−	0.910112i	$-0.364005\pi$
$67$	454.487			0.828723			0.414362	+	0.910112i	$0.364005\pi$
$68$	44.3598			0.0791091
$69$	−25.5381	−	12.2985i	−0.0445568	−	0.0214574i
$70$	−467.584	−	424.459i	−0.798385	−	0.724750i
$71$	−9.57888	+	4.61295i	−0.0160113	+	0.00771065i	−0.441872	−	0.897078i	$-0.645686\pi$
$71$	−9.57888	+	4.61295i	−0.0160113	+	0.00771065i	0.425861	+	0.904789i	$0.359971\pi$
$72$	−573.008	+	275.946i	−0.937912	+	0.451675i
$73$	−6.65675	+	29.1651i	−0.0106728	+	0.0467605i	−0.979984	−	0.199077i	$-0.936206\pi$
$73$	−6.65675	+	29.1651i	−0.0106728	+	0.0467605i	0.969311	+	0.245837i	$0.0790629\pi$
$74$	−139.152	+	609.665i	−0.218596	+	0.957731i
$75$	−31.8953	+	15.3600i	−0.0491060	+	0.0236482i
$76$	−202.535	+	97.5359i	−0.305689	+	0.147212i
$77$	366.935	−	59.4063i	0.543066	−	0.0879217i
$78$	13.9915	+	6.73796i	0.0203106	+	0.00978107i
$79$	906.648			1.29121			0.645607	−	0.763670i	$-0.276604\pi$
$79$	906.648			1.29121			0.645607	+	0.763670i	$0.276604\pi$
$80$	−181.286			−0.253355
$81$	−654.383	−	315.134i	−0.897645	−	0.432283i
$82$	300.352	−	376.630i	0.404492	−	0.507217i
$83$	−26.1418	+	114.535i	−0.0345715	+	0.151468i	−0.989268	−	0.146115i	$-0.953323\pi$
$83$	−26.1418	+	114.535i	−0.0345715	+	0.151468i	0.954696	+	0.297582i	$0.0961803\pi$
$84$	7.21577	−	12.8190i	0.00937268	−	0.0166507i
$85$	40.4707	+	177.314i	0.0516431	+	0.226263i
$86$	33.6084	+	16.1850i	0.0421406	+	0.0202938i
$87$	10.6134	+	46.5003i	0.0130790	+	0.0573029i
$88$	295.129	−	370.080i	0.357509	−	0.448302i
$89$	−46.7664	+	204.897i	−0.0556992	+	0.244034i	−0.995112	−	0.0987542i	$-0.968514\pi$
$89$	−46.7664	+	204.897i	−0.0556992	+	0.244034i	0.939413	+	0.342788i	$0.111371\pi$
$90$	−573.309	−	718.907i	−0.671468	−	0.841994i
$91$	816.209	−	132.143i	0.940241	−	0.152224i
$92$	−422.548	+	529.858i	−0.478844	+	0.600452i
$93$	−24.0322	−	30.1354i	−0.0267959	−	0.0336010i
$94$	−13.6659	+	6.58114i	−0.0149950	+	0.00722119i
$95$	−574.645	−	720.582i	−0.620604	−	0.778212i
$96$	−6.86683	−	30.0856i	−0.00730045	−	0.0319854i
$97$	1208.12			1.26460			0.632298	−	0.774726i	$-0.282112\pi$
$97$	1208.12			1.26460			0.632298	+	0.774726i	$0.282112\pi$
$98$	63.1441	+	651.543i	0.0650869	+	0.671590i
$99$	541.239			0.549460
$100$	188.346	+	825.197i	0.188346	+	0.825197i
$101$	1057.44	+	1325.99i	1.04177	+	1.30634i	0.950570	+	0.310510i	$0.100500\pi$
$101$	1057.44	+	1325.99i	1.04177	+	1.30634i	0.0912033	+	0.995832i	$0.470929\pi$
$102$	3.19014	−	1.53629i	0.00309678	−	0.00149133i
$103$	−1135.31	−	1423.63i	−1.08607	−	1.36189i	−0.927189	−	0.374594i	$-0.877782\pi$
$103$	−1135.31	−	1423.63i	−1.08607	−	1.36189i	−0.158883	−	0.987297i	$-0.550789\pi$
$104$	656.484	−	823.205i	0.618976	−	0.776172i
$105$	57.8226	+	17.1476i	0.0537420	+	0.0159374i
$106$	308.922	+	387.376i	0.283067	+	0.354955i
$107$	170.878	−	748.666i	0.154387	−	0.676413i	−0.837192	−	0.546909i	$-0.815804\pi$
$107$	170.878	−	748.666i	0.154387	−	0.676413i	0.991579	−	0.129504i	$-0.0413386\pi$
$108$	26.7258	−	33.5131i	0.0238119	−	0.0298592i
$109$	−108.098	−	473.609i	−0.0949901	−	0.416179i	0.904967	−	0.425483i	$-0.139896\pi$
$109$	−108.098	−	473.609i	−0.0949901	−	0.416179i	−0.999957	+	0.00930378i	$0.997038\pi$
$110$	616.595	+	296.937i	0.534455	+	0.257380i
$111$	−13.2896	−	58.2257i	−0.0113639	−	0.0497886i
$112$	139.137	+	126.305i	0.117386	+	0.106559i
$113$	226.713	−	993.294i	0.188738	−	0.826914i	−0.788546	−	0.614976i	$-0.789166\pi$
$113$	226.713	−	993.294i	0.188738	−	0.826914i	0.977283	−	0.211937i	$-0.0679773\pi$
$114$	−11.1874	+	14.0286i	−0.00919123	+	0.0115254i
$115$	−2503.43	−	1205.59i	−2.02997	−	0.977581i
$116$	1140.39			0.912777
$117$	1203.93			0.951312
$118$	−1527.25	−	735.483i	−1.19148	−	0.573786i
$119$	92.4755	−	164.284i	0.0712371	−	0.126554i
$120$	69.1968	−	33.3234i	0.0526398	−	0.0253500i
$121$	836.254	−	402.719i	0.628290	−	0.302568i
$122$	−84.4765	+	370.116i	−0.0626897	+	0.274662i
$123$	−10.2375	+	44.8536i	−0.00750478	+	0.0328806i
$124$	−830.314	+	399.858i	−0.601326	+	0.289583i
$125$	−1114.42	+	536.675i	−0.797412	+	0.384014i
$126$	−60.8577	+	951.192i	−0.0430288	+	0.672531i
$127$	−1151.59	−	554.576i	−0.804622	−	0.387485i	−0.0140857	−	0.999901i	$-0.504484\pi$
$127$	−1151.59	−	554.576i	−0.804622	−	0.387485i	−0.790536	+	0.612415i	$0.790198\pi$
$128$	−582.915			−0.402523
$129$	−3.56256			−0.00243152
$130$	1371.55	+	660.506i	0.925333	+	0.445617i
$131$	−933.095	+	1170.06i	−0.622327	+	0.780374i	−0.988670	−	0.150106i	$-0.952038\pi$
$131$	−933.095	+	1170.06i	−0.622327	+	0.780374i	0.366343	+	0.930480i	$0.380610\pi$
$132$	−3.54736	+	15.5420i	−0.00233908	+	0.0102482i
$133$	−60.9995	+	953.409i	−0.0397694	+	0.621587i
$134$	−193.006	−	845.616i	−0.124427	−	0.545150i
$135$	158.340	+	76.2525i	0.100946	+	0.0486131i
$136$	−53.4209	−	234.052i	−0.0336824	−	0.147572i
$137$	−786.111	+	985.751i	−0.490233	+	0.614733i	−0.963995	−	0.265920i	$-0.914324\pi$
$137$	−786.111	+	985.751i	−0.490233	+	0.614733i	0.473762	+	0.880653i	$0.342896\pi$
$138$	−12.0373	+	52.7387i	−0.00742522	+	0.0325320i
$139$	1291.21	+	1619.12i	0.787905	+	0.988002i	0.999942	+	0.0107404i	$0.00341883\pi$
$139$	1291.21	+	1619.12i	0.787905	+	0.988002i	−0.212037	+	0.977262i	$0.568010\pi$
$140$	707.345	−	1256.61i	0.427011	−	0.758593i
$141$	0.903193	−	1.13257i	0.000539451	−	0.000676450i
$142$	12.6507	+	15.8634i	0.00747620	+	0.00937486i
$143$	−807.314	+	388.782i	−0.472105	+	0.227354i
$144$	170.597	+	213.922i	0.0987253	+	0.123798i
$145$	1040.40	+	4558.31i	0.595868	+	2.61067i
$146$	57.0914			0.0323624
$147$	−32.4319	−	53.4465i	−0.0181968	−	0.0299877i
$148$	−1427.94			−0.793082
$149$	−337.671	−	1479.43i	−0.185658	−	0.813421i	−0.978871	−	0.204477i	$-0.934451\pi$
$149$	−337.671	−	1479.43i	−0.185658	−	0.813421i	0.793213	−	0.608944i	$-0.208407\pi$
$150$	42.1236	+	52.8213i	0.0229292	+	0.0287523i
$151$	1393.21	−	670.937i	0.750849	−	0.361590i	−0.0189971	−	0.999820i	$-0.506047\pi$
$151$	1393.21	−	670.937i	0.750849	−	0.361590i	0.769846	+	0.638230i	$0.220333\pi$
$152$	758.526	+	951.162i	0.404767	+	0.507562i
$153$	171.150	−	214.615i	0.0904357	−	0.113403i
$154$	−266.357	−	657.489i	−0.139374	−	0.344039i
$155$	−2355.82	−	2954.10i	−1.22080	−	1.53083i
$156$	−7.89075	+	34.5716i	−0.00404978	+	0.0177432i
$157$	−1870.40	+	2345.41i	−0.950793	+	1.19226i	0.0304601	+	0.999536i	$0.490303\pi$
$157$	−1870.40	+	2345.41i	−0.950793	+	1.19226i	−0.981254	+	0.192721i	$0.938269\pi$
$158$	−385.025	−	1686.90i	−0.193867	−	0.849386i
$159$	−42.6337	−	20.5313i	−0.0212646	−	0.0102405i
$160$	−673.139	−	2949.21i	−0.332602	−	1.45722i
$161$	1081.43	+	2669.46i	0.529371	+	1.30673i
$162$	−308.441	+	1351.37i	−0.149589	+	0.655392i
$163$	1448.32	−	1816.13i	0.695957	−	0.872703i	−0.300757	−	0.953701i	$-0.597239\pi$
$163$	1448.32	−	1816.13i	0.695957	−	0.872703i	0.996714	+	0.0809981i	$0.0258108\pi$
$164$	991.068	+	477.273i	0.471887	+	0.227249i
$165$	−65.3603			−0.0308381
$166$	224.204			0.104829
$167$	289.999	+	139.656i	0.134376	+	0.0647121i	0.499864	−	0.866104i	$-0.333383\pi$
$167$	289.999	+	139.656i	0.134376	+	0.0647121i	−0.365488	+	0.930816i	$0.619098\pi$
$168$	−76.3253	−	22.6346i	−0.0350513	−	0.0103946i
$169$	183.640	−	88.4363i	0.0835866	−	0.0402532i
$170$	312.722	−	150.599i	0.141086	−	0.0679436i
$171$	−309.542	+	1356.19i	−0.138428	+	0.606494i
$172$	−18.9540	+	83.0431i	−0.00840251	+	0.0368138i
$173$	−2138.92	+	1030.05i	−0.939993	+	0.452677i	−0.840167	−	0.542328i	$-0.817543\pi$
$173$	−2138.92	+	1030.05i	−0.939993	+	0.452677i	−0.0998263	+	0.995005i	$0.531829\pi$
$174$	82.0110	−	39.4944i	0.0357313	−	0.0172073i
$175$	3448.72	+	1022.73i	1.48971	+	0.441779i
$176$	−183.478	−	88.3583i	−0.0785805	−	0.0378424i
$177$	161.891			0.0687485
$178$	401.091			0.168893
$179$	−1872.58	−	901.785i	−0.781916	−	0.376551i	−5.20429e−5	−	1.00000i	$-0.500017\pi$
$179$	−1872.58	−	901.785i	−0.781916	−	0.376551i	−0.781864	+	0.623449i	$0.785731\pi$
$180$	1309.13	−	1641.59i	0.542091	−	0.679761i
$181$	269.745	−	1181.83i	0.110773	−	0.485330i	−0.888858	−	0.458183i	$-0.848501\pi$
$181$	269.745	−	1181.83i	0.110773	−	0.485330i	0.999631	−	0.0271472i	$-0.00864227\pi$
$182$	−592.484	−	1462.52i	−0.241307	−	0.595654i
$183$	−8.06788	−	35.3477i	−0.00325899	−	0.0142786i
$184$	3304.51	+	1591.37i	1.32398	+	0.637593i
$185$	−1302.75	−	5707.72i	−0.517730	−	2.26832i
$186$	−45.8640	+	57.5117i	−0.0180802	+	0.0226718i
$187$	−45.4621	+	199.182i	−0.0177782	+	0.0778912i
$188$	−21.5948	−	27.0790i	−0.00837746	−	0.0105050i
$189$	−68.3996	−	168.841i	−0.0263246	−	0.0649809i
$190$	−1096.68	+	1375.19i	−0.418744	+	0.525088i
$191$	685.201	+	859.215i	0.259578	+	0.325500i	0.894493	−	0.447081i	$-0.147536\pi$
$191$	685.201	+	859.215i	0.259578	+	0.325500i	−0.634915	+	0.772582i	$0.718965\pi$
$192$	−66.3905	+	31.9720i	−0.0249548	+	0.0120176i
$193$	−2281.93	−	2861.45i	−0.851073	−	1.06721i	−0.996960	−	0.0779111i	$-0.975175\pi$
$193$	−2281.93	−	2861.45i	−0.851073	−	1.06721i	0.145887	−	0.989301i	$-0.453396\pi$
$194$	−513.049	−	2247.82i	−0.189870	−	0.831875i
$195$	−145.387			−0.0533918
$196$	−1418.38	+	471.631i	−0.516904	+	0.171877i
$197$	3701.09			1.33854			0.669269	−	0.743020i	$-0.266607\pi$
$197$	3701.09			1.33854			0.669269	+	0.743020i	$0.266607\pi$
$198$	−229.847	−	1007.03i	−0.0824976	−	0.361446i
$199$	426.520	+	534.839i	0.151936	+	0.190521i	0.851974	−	0.523584i	$-0.175405\pi$
$199$	426.520	+	534.839i	0.151936	+	0.190521i	−0.700039	+	0.714105i	$0.746834\pi$
$200$	4127.10	−	1987.51i	1.45915	−	0.702691i
$201$	51.6480	+	64.7646i	0.0181242	+	0.0227271i
$202$	2018.06	−	2530.57i	0.702923	−	0.881437i
$203$	2377.32	−	4223.36i	0.821948	−	1.46021i
$204$	5.04107	+	6.32130i	0.00173012	+	0.00216951i
$205$	−1003.56	+	4396.89i	−0.341911	+	1.49801i
$206$	−2166.68	+	2716.92i	−0.732813	+	0.918918i
$207$	933.201	+	4088.62i	0.313343	+	1.37284i
$208$	−408.128	−	196.544i	−0.136051	−	0.0655187i
$209$	−230.383	−	1009.37i	−0.0762484	−	0.334066i
$210$	7.34920	−	114.866i	0.00241497	−	0.0377454i
$211$	−430.597	+	1886.57i	−0.140491	+	0.615530i	0.854830	+	0.518907i	$0.173661\pi$
$211$	−430.597	+	1886.57i	−0.140491	+	0.615530i	−0.995321	+	0.0966224i	$0.969196\pi$
$212$	−705.409	+	884.555i	−0.228527	+	0.286563i
$213$	−1.74589	−	0.840778i	−0.000561627	−	0.000270465i
$214$	−1465.53			−0.468138
$215$	−349.229			−0.110778
$216$	−209.007	−	100.653i	−0.0658386	−	0.0317062i
$217$	−250.073	+	3908.60i	−0.0782308	+	1.22273i
$218$	−835.288	+	402.253i	−0.259508	+	0.124973i
$219$	−4.91251	+	2.36574i	−0.00151579	+	0.000729964i
$220$	−347.739	+	1523.54i	−0.106566	+	0.466897i
$221$	−101.126	+	443.061i	−0.0307804	+	0.134858i
$222$	−102.691	+	49.4532i	−0.0310457	+	0.0149508i
$223$	−386.484	+	186.121i	−0.116058	+	0.0558905i	−0.491012	−	0.871153i	$-0.663373\pi$
$223$	−386.484	+	186.121i	−0.116058	+	0.0558905i	0.374954	+	0.927043i	$0.377659\pi$
$224$	−1538.12	+	2732.50i	−0.458795	+	0.815059i
$225$	4719.03	+	2272.56i	1.39823	+	0.673352i
$226$	−1944.40			−0.572298
$227$	833.226			0.243626			0.121813	−	0.992553i	$-0.461129\pi$
$227$	833.226			0.243626			0.121813	+	0.992553i	$0.461129\pi$
$228$	−36.9151	−	17.7774i	−0.0107226	−	0.00516375i
$229$	−989.141	+	1240.34i	−0.285433	+	0.357922i	−0.903791	−	0.427975i	$-0.859227\pi$
$229$	−989.141	+	1240.34i	−0.285433	+	0.357922i	0.618357	+	0.785897i	$0.287799\pi$
$230$	−1179.98	+	5169.85i	−0.338286	+	1.48213i
$231$	50.1640	+	45.5374i	0.0142881	+	0.0129703i
$232$	−1373.32	−	6016.93i	−0.388634	−	1.70272i
$233$	−2055.45	−	989.853i	−0.577927	−	0.278315i	0.121999	−	0.992530i	$-0.461070\pi$
$233$	−2055.45	−	989.853i	−0.577927	−	0.278315i	−0.699926	+	0.714215i	$0.746784\pi$
$234$	−511.272	−	2240.03i	−0.142833	−	0.625792i
$235$	88.5378	−	111.023i	0.0245769	−	0.0308184i
$236$	861.316	−	3773.67i	0.237572	−	1.04087i
$237$	103.032	+	129.198i	0.0282389	+	0.0354105i
$238$	−344.938	−	102.293i	−0.0939455	−	0.0278600i
$239$	−2379.98	+	2984.40i	−0.644133	+	0.807718i	−0.991513	−	0.130007i	$-0.958500\pi$
$239$	−2379.98	+	2984.40i	−0.644133	+	0.807718i	0.347380	+	0.937725i	$0.387071\pi$
$240$	−20.6014	−	25.8334i	−0.00554090	−	0.00694807i
$241$	4071.99	−	1960.97i	1.08838	−	0.524137i	0.198394	−	0.980122i	$-0.436427\pi$
$241$	4071.99	−	1960.97i	1.08838	−	0.524137i	0.889987	+	0.455985i	$0.150713\pi$
$242$	−1104.43	−	1384.91i	−0.293369	−	0.367873i
$243$	−88.5543	−	387.982i	−0.0233776	−	0.102424i
$244$	−866.877			−0.227443
$245$	−3179.22	−	5239.23i	−0.829032	−	1.36621i
$246$	87.8020			0.0227563
$247$	−512.464	−	2245.25i	−0.132013	−	0.578388i
$248$	3109.65	+	3899.38i	0.796223	+	0.998432i
$249$	−19.2920	+	9.29053i	−0.00490996	+	0.00236451i
$250$	1471.79	+	1845.57i	0.372337	+	0.466896i
$251$	−1965.50	+	2464.65i	−0.494267	+	0.619791i	−0.964925	−	0.262524i	$-0.915445\pi$
$251$	−1965.50	+	2464.65i	−0.494267	+	0.619791i	0.470658	+	0.882316i	$0.344016\pi$
$252$	−2148.47	+	347.835i	−0.537067	+	0.0869506i
$253$	−1946.10	−	2440.33i	−0.483597	−	0.606411i
$254$	−542.797	+	2378.15i	−0.134087	+	0.587474i
$255$	−20.6682	+	25.9170i	−0.00507565	+	0.00636466i
$256$	967.250	+	4237.80i	0.236145	+	1.03462i
$257$	−2685.65	−	1293.34i	−0.651853	−	0.313916i	0.0785723	−	0.996908i	$-0.474964\pi$
$257$	−2685.65	−	1293.34i	−0.651853	−	0.313916i	−0.730425	+	0.682993i	$0.760678\pi$
$258$	1.51291	+	6.62848i	0.000365076	+	0.00159950i
$259$	−2976.79	+	5288.32i	−0.714164	+	1.26873i
$260$	−773.511	+	3388.97i	−0.184504	+	0.808366i
$261$	4399.86	−	5517.25i	1.04346	−	1.30846i
$262$	2573.27	+	1239.22i	0.606783	+	0.292211i
$263$	1107.38			0.259635			0.129818	−	0.991538i	$-0.458561\pi$
$263$	1107.38			0.259635			0.129818	+	0.991538i	$0.458561\pi$
$264$	86.2750			0.0201131
$265$	−4179.27	−	2012.63i	−0.968795	−	0.466547i
$266$	1799.81	−	291.388i	0.414863	−	0.0671659i
$267$	−34.5125	+	16.6203i	−0.00791059	+	0.00380954i
$268$	1784.44	−	859.343i	0.406725	−	0.195868i
$269$	52.6293	−	230.584i	0.0119289	−	0.0522638i	−0.968613	−	0.248573i	$-0.920038\pi$
$269$	52.6293	−	230.584i	0.0119289	−	0.0522638i	0.980542	+	0.196309i	$0.0628956\pi$
$270$	74.6330	−	326.988i	0.0168223	−	0.0737032i
$271$	3180.72	−	1531.76i	0.712971	−	0.343349i	−0.0419902	−	0.999118i	$-0.513370\pi$
$271$	3180.72	−	1531.76i	0.712971	−	0.343349i	0.754961	+	0.655769i	$0.227656\pi$
$272$	−93.0555	+	44.8132i	−0.0207438	+	0.00998970i
$273$	111.585	+	101.293i	0.0247378	+	0.0224562i
$274$	2167.92	+	1044.02i	0.477989	+	0.230187i
$275$	−3898.29			−0.854820
$276$	−123.524			−0.0269393
$277$	2527.81	+	1217.33i	0.548309	+	0.264052i	0.687463	−	0.726219i	$-0.258724\pi$
$277$	2527.81	+	1217.33i	0.548309	+	0.264052i	−0.139154	+	0.990271i	$0.544438\pi$
$278$	2464.20	−	3090.01i	0.531629	−	0.666641i
$279$	−1269.00	+	5559.84i	−0.272304	+	1.19304i
$280$	−7481.98	−	2218.82i	−1.59691	−	0.473570i
$281$	−53.7927	−	235.681i	−0.0114199	−	0.0500340i	0.968897	−	0.247465i	$-0.0795974\pi$
$281$	−53.7927	−	235.681i	−0.0114199	−	0.0500340i	−0.980317	+	0.197431i	$0.936740\pi$
$282$	−2.49081	−	1.19951i	−0.000525977	−	0.000253297i
$283$	−1867.07	−	8180.16i	−0.392176	−	1.71823i	−0.656959	−	0.753926i	$-0.728158\pi$
$283$	−1867.07	−	8180.16i	−0.392176	−	1.71823i	0.264783	−	0.964308i	$-0.414700\pi$
$284$	−28.8872	+	36.2234i	−0.00603571	+	0.00756854i
$285$	37.3804	−	163.774i	0.00776921	−	0.0340391i
$286$	1066.21	+	1336.98i	0.220441	+	0.276424i
$287$	3833.60	−	2675.41i	0.788469	−	0.550260i
$288$	−2846.70	+	3569.64i	−0.582442	+	0.730359i
$289$	−2998.60	−	3760.13i	−0.610340	−	0.765342i
$290$	8039.34	−	3871.54i	1.62788	−	0.783947i
$291$	137.291	+	172.157i	0.0276568	+	0.0346805i
$292$	29.0091	+	127.097i	0.00581379	+	0.0254719i
$293$	4575.19			0.912237			0.456118	−	0.889919i	$-0.349239\pi$
$293$	4575.19			0.912237			0.456118	+	0.889919i	$0.349239\pi$
$294$	−85.6695	+	83.0396i	−0.0169944	+	0.0164727i
$295$	15869.8			3.13212
$296$	1719.62	+	7534.14i	0.337672	+	1.47944i
$297$	123.089	+	154.349i	0.0240483	+	0.0301556i
$298$	−2609.22	+	1256.54i	−0.507209	+	0.244259i
$299$	−4328.90	−	5428.26i	−0.837279	−	1.04992i
$300$	−96.1873	+	120.615i	−0.0185113	+	0.0232124i
$301$	268.033	+	243.312i	0.0513261	+	0.0465924i
$302$	−1840.00	−	2307.28i	−0.350596	−	0.439633i
$303$	−68.7860	+	301.371i	−0.0130417	+	0.0571396i
$304$	326.334	−	409.210i	0.0615676	−	0.0772033i
$305$	−790.875	−	3465.05i	−0.148477	−	0.650518i
$306$	−471.994	−	227.300i	−0.0881768	−	0.0424637i
$307$	−7.22642	−	31.6610i	−0.00134343	−	0.00588596i	0.974252	−	0.225463i	$-0.0723894\pi$
$307$	−7.22642	−	31.6610i	−0.00134343	−	0.00588596i	−0.975595	+	0.219577i	$0.929532\pi$
$308$	1328.36	−	927.045i	0.245748	−	0.171504i
$309$	73.8514	−	323.564i	0.0135963	−	0.0595693i
$310$	−4495.94	+	5637.73i	−0.823717	+	1.03291i
$311$	3207.32	+	1544.56i	0.584792	+	0.281621i	0.702795	−	0.711392i	$-0.251935\pi$
$311$	3207.32	+	1544.56i	0.584792	+	0.281621i	−0.118003	+	0.993013i	$0.537649\pi$
$312$	191.910			0.0348230
$313$	7720.29			1.39417			0.697087	−	0.716986i	$-0.254479\pi$
$313$	7720.29			1.39417			0.697087	+	0.716986i	$0.254479\pi$
$314$	5158.17	+	2484.04i	0.927045	+	0.446441i
$315$	−3350.46	−	8270.45i	−0.599292	−	1.47932i
$316$	3559.76	−	1714.29i	0.633709	−	0.305178i
$317$	−1002.73	+	482.892i	−0.177663	+	0.0855580i	−0.520601	−	0.853800i	$-0.674292\pi$
$317$	−1002.73	+	482.892i	−0.177663	+	0.0855580i	0.342938	+	0.939358i	$0.388578\pi$
$318$	−20.0952	+	88.0429i	−0.00354366	+	0.0155258i
$319$	−1168.72	+	5120.50i	−0.205128	+	0.898724i
$320$	−6508.10	+	3134.13i	−1.13692	+	0.547511i
$321$	126.104	−	60.7284i	0.0219266	−	0.0105593i
$322$	4507.54	−	3145.74i	0.780110	−	0.544427i
$323$	−473.094	−	227.830i	−0.0814974	−	0.0392471i
$324$	−3165.15			−0.542721
$325$	−8671.34			−1.48000
$326$	−3994.14	−	1923.48i	−0.678574	−	0.326784i
$327$	55.2051	−	69.2250i	0.00933593	−	0.0117069i
$328$	1324.69	−	5803.85i	0.223000	−	0.977025i
$329$	−145.304	+	23.5245i	−0.0243491	+	0.00394209i
$330$	27.7565	+	121.609i	0.00463013	+	0.0202859i
$331$	−4529.01	−	2181.05i	−0.752075	−	0.362180i	0.0182487	−	0.999833i	$-0.494191\pi$
$331$	−4529.01	−	2181.05i	−0.752075	−	0.362180i	−0.770323	+	0.637653i	$0.779905\pi$
$332$	113.922	+	499.124i	0.0188321	+	0.0825090i
$333$	−5509.32	+	6908.46i	−0.906633	+	1.13688i
$334$	136.690	−	598.878i	0.0223933	−	0.0981113i
$335$	5062.93	+	6348.72i	0.825724	+	1.03543i
$336$	−2.18687	+	34.1804i	−0.000355071	+	0.00554968i
$337$	−1694.51	+	2124.85i	−0.273905	+	0.343466i	−0.899690	−	0.436530i	$-0.856207\pi$
$337$	−1694.51	+	2124.85i	−0.273905	+	0.343466i	0.625785	+	0.779996i	$0.284779\pi$
$338$	−242.530	−	304.123i	−0.0390293	−	0.0489412i
$339$	167.309	−	80.5715i	0.0268052	−	0.0129087i
$340$	494.163	+	619.661i	0.0788228	+	0.0988407i
$341$	−944.477	−	4138.03i	−0.149989	−	0.657146i
$342$	2654.77			0.419748
$343$	−1210.19	+	6236.11i	−0.190508	+	0.981686i
$344$	460.979			0.0722510
$345$	−112.694	−	493.744i	−0.0175862	−	0.0770500i
$346$	2824.83	+	3542.23i	0.438913	+	0.550380i
$347$	−5930.65	+	2856.05i	−0.917504	+	0.441846i	−0.832179	−	0.554507i	$-0.812907\pi$
$347$	−5930.65	+	2856.05i	−0.917504	+	0.441846i	−0.0853244	+	0.996353i	$0.527193\pi$
$348$	129.594	+	162.505i	0.0199625	+	0.0250322i
$349$	6125.71	−	7681.40i	0.939547	−	1.17816i	−0.0442771	−	0.999019i	$-0.514098\pi$
$349$	6125.71	−	7681.40i	0.939547	−	1.17816i	0.983824	−	0.179136i	$-0.0573301\pi$
$350$	438.329	−	6850.98i	0.0669419	−	1.04629i
$351$	273.799	+	343.333i	0.0416362	+	0.0522101i
$352$	756.160	−	3312.95i	0.114498	−	0.501650i
$353$	−966.715	+	1212.22i	−0.145759	+	0.182777i	−0.849352	−	0.527827i	$-0.823007\pi$
$353$	−966.715	+	1212.22i	−0.145759	+	0.182777i	0.703592	+	0.710604i	$0.251578\pi$
$354$	−68.7501	−	301.214i	−0.0103221	−	0.0452241i
$355$	−171.146	−	82.4194i	−0.0255872	−	0.0123222i
$356$	203.801	+	892.909i	0.0303411	+	0.132933i
$357$	33.9195	−	5.49154i	0.00502861	−	0.000814126i
$358$	−882.633	+	3867.07i	−0.130303	+	0.570896i
$359$	−4575.39	+	5737.36i	−0.672646	+	0.843472i	−0.994654	−	0.103265i	$-0.967071\pi$
$359$	−4575.39	+	5737.36i	−0.672646	+	0.843472i	0.322008	+	0.946737i	$0.395642\pi$
$360$	−10237.9	−	4930.32i	−1.49885	−	0.721808i
$361$	−4198.04			−0.612048
$362$	−2313.46			−0.335891
$363$	152.420	+	73.4015i	0.0220385	+	0.0106132i
$364$	2954.81	−	2062.12i	0.425478	−	0.296935i
$365$	−481.562	+	231.908i	−0.0690578	+	0.0332565i
$366$	−62.3416	+	30.0221i	−0.00890341	+	0.00428765i
$367$	−728.198	+	3190.44i	−0.103574	+	0.453787i	0.896371	+	0.443304i	$0.146194\pi$
$367$	−728.198	+	3190.44i	−0.103574	+	0.453787i	−0.999945	+	0.0104825i	$0.996663\pi$
$368$	351.124	−	1538.37i	0.0497380	−	0.217916i
$369$	6132.83	−	2953.41i	0.865210	−	0.416663i
$370$	−10066.5	+	4847.78i	−1.41441	+	0.681146i
$371$	1805.36	+	4456.45i	0.252641	+	0.623631i
$372$	−151.337	−	72.8801i	−0.0210926	−	0.0101577i
$373$	11240.2			1.56032			0.780158	−	0.625583i	$-0.215139\pi$
$373$	11240.2			1.56032			0.780158	+	0.625583i	$0.215139\pi$
$374$	389.904			0.0539076
$375$	−203.119	−	97.8170i	−0.0279707	−	0.0134700i
$376$	−116.869	+	146.549i	−0.0160294	+	0.0201003i
$377$	−2599.70	+	11390.0i	−0.355150	+	1.55601i
$378$	−285.098	+	198.966i	−0.0387933	+	0.0270732i
$379$	−1577.42	−	6911.12i	−0.213790	−	0.936676i	−0.961965	−	0.273174i	$-0.911927\pi$
$379$	−1577.42	−	6911.12i	−0.213790	−	0.936676i	0.748174	−	0.663502i	$-0.230931\pi$
$380$	−3618.69	−	1742.67i	−0.488513	−	0.235256i
$381$	−51.8396	−	227.124i	−0.00697066	−	0.0305405i
$382$	1307.67	−	1639.76i	0.175147	−	0.219627i
$383$	−2725.71	+	11942.1i	−0.363649	+	1.59325i	0.380202	+	0.924903i	$0.375854\pi$
$383$	−2725.71	+	11942.1i	−0.363649	+	1.59325i	−0.743851	+	0.668346i	$0.767003\pi$
$384$	−66.2427	−	83.0657i	−0.00880321	−	0.0110389i
$385$	4917.45	+	4463.92i	0.650952	+	0.590915i
$386$	−4354.94	+	5460.92i	−0.574250	+	0.720087i
$387$	328.638	+	412.099i	0.0431669	+	0.0541296i
$388$	4743.41	−	2284.31i	0.620645	−	0.298887i
$389$	7340.31	+	9204.46i	0.956732	+	1.19970i	0.979802	+	0.199970i	$0.0640844\pi$
$389$	7340.31	+	9204.46i	0.956732	+	1.19970i	−0.0230704	+	0.999734i	$0.507344\pi$
$390$	61.7415	+	270.507i	0.00801641	+	0.0351222i
$391$	−1583.05			−0.204752
$392$	4196.54	+	6915.74i	0.540707	+	0.891065i
$393$	−272.772			−0.0350115
$394$	−1571.74	−	6886.24i	−0.200972	−	0.880517i
$395$	10099.9	+	12664.9i	1.28654	+	1.61327i
$396$	2125.06	−	1023.37i	0.269667	−	0.129865i
$397$	1019.22	+	1278.06i	0.128850	+	0.161572i	0.842071	−	0.539366i	$-0.181336\pi$
$397$	1019.22	+	1278.06i	0.128850	+	0.161572i	−0.713222	+	0.700938i	$0.752765\pi$
$398$	813.989	−	1020.71i	0.102517	−	0.128552i
$399$	−142.793	+	99.6532i	−0.0179163	+	0.0125035i
$400$	−1228.73	−	1540.78i	−0.153591	−	0.192598i
$401$	1802.03	−	7895.22i	0.224412	−	0.983214i	−0.729701	−	0.683767i	$-0.760341\pi$
$401$	1802.03	−	7895.22i	0.224412	−	0.983214i	0.954113	−	0.299447i	$-0.0968022\pi$
$402$	98.5674	−	123.600i	0.0122291	−	0.0153348i
$403$	−2100.90	−	9204.62i	−0.259685	−	1.13775i
$404$	6658.98	+	3206.79i	0.820041	+	0.394911i
$405$	−2887.65	−	12651.6i	−0.354292	−	1.55226i
$406$	−8867.54	−	2629.71i	−1.08396	−	0.321454i
$407$	1463.42	−	6411.68i	0.178229	−	0.780872i
$408$	27.2818	−	34.2103i	0.00331041	−	0.00415113i
$409$	−13043.4	−	6281.39i	−1.57691	−	0.759400i	−0.578496	−	0.815685i	$-0.696360\pi$
$409$	−13043.4	−	6281.39i	−1.57691	−	0.759400i	−0.998415	+	0.0562846i	$0.982075\pi$
$410$	8607.01			1.03676
$411$	−229.804			−0.0275800
$412$	−7149.35	−	3442.95i	−0.854911	−	0.411703i
$413$	−12180.0	−	11056.7i	−1.45119	−	1.31735i
$414$	7210.96	−	3472.62i	0.856037	−	0.412246i
$415$	−1891.15	+	910.728i	−0.223693	+	0.107725i
$416$	1682.00	−	7369.33i	0.198238	−	0.868536i
$417$	−83.9925	+	367.995i	−0.00986363	+	0.0432154i
$418$	−1780.20	+	857.298i	−0.208307	+	0.100315i
$419$	−2141.25	+	1031.17i	−0.249658	+	0.120229i	−0.554528	−	0.832165i	$-0.687101\pi$
$419$	−2141.25	+	1031.17i	−0.249658	+	0.120229i	0.304870	+	0.952394i	$0.401387\pi$
$420$	259.450	−	42.0047i	0.0301426	−	0.00488005i
$421$	471.014	+	226.828i	0.0545268	+	0.0262587i	0.460948	−	0.887427i	$-0.347509\pi$
$421$	471.014	+	226.828i	0.0545268	+	0.0262587i	−0.406422	+	0.913686i	$0.633224\pi$
$422$	3693.00			0.426001
$423$	−214.327			−0.0246358
$424$	5516.60	+	2656.66i	0.631863	+	0.304289i
$425$	−1232.71	+	1545.77i	−0.140695	+	0.176426i
$426$	−0.822921	+	3.60545i	−9.35931e−5	+	0.000410058i
$427$	−1807.15	+	3210.44i	−0.204811	+	0.363850i
$428$	−744.660	−	3262.57i	−0.0840993	−	0.368463i
$429$	−147.145	−	70.8613i	−0.0165600	−	0.00797486i
$430$	148.307	+	649.774i	0.0166325	+	0.0728718i
$431$	10033.1	−	12581.2i	1.12130	−	1.40606i	0.218587	−	0.975818i	$-0.429855\pi$
$431$	10033.1	−	12581.2i	1.12130	−	1.40606i	0.902712	−	0.430246i	$-0.141573\pi$
$432$	−22.2082	+	97.3007i	−0.00247337	+	0.0108365i
$433$	7527.87	+	9439.65i	0.835488	+	1.04767i	0.998139	+	0.0609852i	$0.0194242\pi$
$433$	7527.87	+	9439.65i	0.835488	+	1.04767i	−0.162651	+	0.986684i	$0.552004\pi$
$434$	7378.51	−	1194.57i	0.816083	−	0.132123i
$435$	−531.329	+	666.265i	−0.0585638	+	0.0734367i
$436$	−1319.92	−	1655.13i	−0.144983	−	0.181804i
$437$	7227.77	−	3480.71i	0.791192	−	0.381018i
$438$	6.48788	+	8.13554i	0.000707769	+	0.000887514i
$439$	231.831	+	1015.72i	0.0252043	+	0.110427i	0.985965	−	0.166950i	$-0.0533919\pi$
$439$	231.831	+	1015.72i	0.0252043	+	0.110427i	−0.960761	+	0.277378i	$0.910535\pi$
$440$	8457.32			0.916334
$441$	−3190.66	+	8681.87i	−0.344526	+	0.937466i
$442$	867.302			0.0933334
$443$	3037.91	+	13310.0i	0.325814	+	1.42748i	0.827028	+	0.562160i	$0.190030\pi$
$443$	3037.91	+	13310.0i	0.325814	+	1.42748i	−0.501215	+	0.865323i	$0.667113\pi$
$444$	−162.272	−	203.482i	−0.0173448	−	0.0217497i
$445$	−3383.17	+	1629.25i	−0.360399	+	0.173559i
$446$	510.423	+	640.050i	0.0541911	+	0.0679535i
$447$	172.447	−	216.241i	0.0182471	−	0.0228811i
$448$	7178.55	+	2128.83i	0.757042	+	0.224504i
$449$	−10331.0	−	12954.7i	−1.08586	−	1.36162i	−0.927320	−	0.374269i	$-0.877894\pi$
$449$	−10331.0	−	12954.7i	−1.08586	−	1.36162i	−0.158537	−	0.987353i	$-0.550678\pi$
$450$	2224.30	−	9745.29i	0.233010	−	1.02088i
$451$	−3158.72	+	3960.91i	−0.329797	+	0.413552i
$452$	−987.979	−	4328.62i	−0.102811	−	0.450445i
$453$	253.934	+	122.288i	0.0263374	+	0.0126834i
$454$	−353.845	−	1550.30i	−0.0365788	−	0.160262i
$455$	10938.4	+	9929.54i	1.12703	+	1.02309i
$456$	−49.3418	+	216.181i	−0.00506720	+	0.0222008i
$457$	6164.66	−	7730.24i	0.631008	−	0.791259i	−0.358839	−	0.933400i	$-0.616827\pi$
$457$	6164.66	−	7730.24i	0.631008	−	0.791259i	0.989846	+	0.142141i	$0.0453986\pi$
$458$	2727.83	+	1313.66i	0.278304	+	0.134024i
$459$	100.126			0.0101819
$460$	−12108.7			−1.22733
$461$	−14797.3	−	7126.03i	−1.49497	−	0.719940i	−0.505252	−	0.862972i	$-0.668600\pi$
$461$	−14797.3	−	7126.03i	−1.49497	−	0.719940i	−0.989718	+	0.143032i	$0.954315\pi$
$462$	63.4235	−	112.673i	0.00638686	−	0.0113464i
$463$	−13009.9	+	6265.22i	−1.30587	+	0.628875i	−0.951908	−	0.306383i	$-0.900881\pi$
$463$	−13009.9	+	6265.22i	−1.30587	+	0.628875i	−0.353965	+	0.935259i	$0.615167\pi$
$464$	−2392.24	+	1152.04i	−0.239346	+	0.115263i
$465$	153.245	−	671.409i	0.0152829	−	0.0669588i
$466$	−968.830	+	4244.72i	−0.0963094	+	0.421959i
$467$	2791.59	−	1344.36i	0.276615	−	0.133211i	−0.290434	−	0.956895i	$-0.593800\pi$
$467$	2791.59	−	1344.36i	0.276615	−	0.133211i	0.567048	+	0.823684i	$0.308085\pi$
$468$	4726.97	−	2276.39i	0.466890	−	0.224842i
$469$	537.438	−	8400.05i	0.0529138	−	0.827032i
$470$	−244.168	−	117.585i	−0.0239630	−	0.0115400i
$471$	−546.776			−0.0534906
$472$	−20948.0			−2.04281
$473$	−353.451	−	170.213i	−0.0343587	−	0.0165463i
$474$	196.630	−	246.567i	0.0190539	−	0.0238928i
$475$	2229.48	−	9768.00i	0.215359	−	0.943551i
$476$	52.4562	−	819.880i	0.00505111	−	0.0789477i
$477$	1557.90	+	6825.61i	0.149542	+	0.655185i
$478$	6563.45	+	3160.79i	0.628045	+	0.302450i
$479$	3295.63	+	14439.1i	0.314366	+	1.37733i	0.847275	+	0.531155i	$0.178242\pi$
$479$	3295.63	+	14439.1i	0.314366	+	1.37733i	−0.532908	+	0.846173i	$0.678901\pi$
$480$	343.768	−	431.072i	0.0326892	−	0.0409910i
$481$	3255.24	−	14262.1i	0.308578	−	1.35197i
$482$	−5377.81	−	6743.56i	−0.508200	−	0.637263i
$483$	−257.505	+	457.463i	−0.0242586	+	0.0430958i
$484$	2521.91	−	3162.37i	0.236843	−	0.296992i
$485$	13458.3	+	16876.1i	1.26002	+	1.58001i
$486$	−684.271	+	329.527i	−0.0638666	+	0.0307565i
$487$	1176.11	+	1474.80i	0.109435	+	0.137227i	0.833532	−	0.552471i	$-0.186315\pi$
$487$	1176.11	+	1474.80i	0.109435	+	0.137227i	−0.724098	+	0.689697i	$0.757744\pi$
$488$	1043.95	+	4573.83i	0.0968387	+	0.424278i
$489$	423.387			0.0391538
$490$	−8397.97	+	8140.17i	−0.774248	+	0.750481i
$491$	−3139.09			−0.288524			−0.144262	−	0.989540i	$-0.546081\pi$
$491$	−3139.09			−0.288524			−0.144262	+	0.989540i	$0.546081\pi$
$492$	44.6136	+	195.465i	0.00408808	+	0.0179111i
$493$	1660.84	+	2082.63i	0.151725	+	0.190257i
$494$	−3959.87	+	1906.97i	−0.360654	+	0.173682i
$495$	6029.34	+	7560.55i	0.547472	+	0.686508i
$496$	1337.84	−	1677.60i	0.121110	−	0.151868i
$497$	73.9314	+	182.496i	0.00667259	+	0.0164710i
$498$	25.4786	+	31.9492i	0.00229262	+	0.00287485i
$499$	−372.771	+	1633.22i	−0.0334419	+	0.146519i	−0.988893	−	0.148632i	$-0.952513\pi$
$499$	−372.771	+	1633.22i	−0.0334419	+	0.146519i	0.955451	+	0.295151i	$0.0953700\pi$
$500$	−3360.77	+	4214.28i	−0.300597	+	0.376936i
$501$	13.0545	+	57.1955i	0.00116414	+	0.00510042i
$502$	5420.41	+	2610.33i	0.481922	+	0.232081i
$503$	−760.973	−	3334.04i	−0.0674555	−	0.295542i	0.929936	−	0.367721i	$-0.119862\pi$
$503$	−760.973	−	3334.04i	−0.0674555	−	0.295542i	−0.997392	+	0.0721791i	$0.977005\pi$
$504$	4422.58	+	10916.9i	0.390867	+	0.964838i
$505$	−6742.92	+	29542.7i	−0.594170	+	2.60323i
$506$	−3714.01	+	4657.23i	−0.326301	+	0.409168i
$507$	33.4711	+	16.1188i	0.00293196	+	0.00141196i
$508$	−5570.05			−0.486479
$509$	−16653.8			−1.45023			−0.725114	−	0.688629i	$-0.758213\pi$
$509$	−16653.8			−1.45023			−0.725114	+	0.688629i	$0.758213\pi$
$510$	56.9982	+	27.4489i	0.00494887	+	0.00238325i
$511$	531.172	+	157.521i	0.0459836	+	0.0136367i
$512$	3272.56	−	1575.98i	0.282477	−	0.136034i
$513$	−457.150	+	220.152i	−0.0393444	+	0.0189472i
$514$	−1265.87	+	5546.15i	−0.108629	+	0.475934i
$515$	7239.48	−	31718.2i	0.619436	−	2.71393i
$516$	−13.9876	+	6.73608i	−0.00119335	+	0.000574689i
$517$	143.720	−	69.2120i	0.0122259	−	0.00588770i
$518$	11103.6	+	3292.81i	0.941819	+	0.279301i
$519$	−389.849	−	187.742i	−0.0329720	−	0.0158785i
$520$	18812.5			1.58650
$521$	−9695.11			−0.815260			−0.407630	−	0.913147i	$-0.633645\pi$
$521$	−9695.11			−0.815260			−0.407630	+	0.913147i	$0.633645\pi$
$522$	−12133.8	−	5843.35i	−1.01740	−	0.489955i
$523$	−8774.61	+	11003.0i	−0.733627	+	0.919939i	−0.999023	−	0.0442006i	$-0.985926\pi$
$523$	−8774.61	+	11003.0i	−0.733627	+	0.919939i	0.265396	+	0.964140i	$0.414497\pi$
$524$	−1451.24	+	6358.29i	−0.120988	+	0.530083i
$525$	246.173	+	607.667i	0.0204645	+	0.0505157i
$526$	−470.270	−	2060.39i	−0.0389824	−	0.170793i
$527$	−1939.50	−	934.012i	−0.160315	−	0.0772034i
$528$	−8.25938	−	36.1867i	−0.000680764	−	0.00298262i
$529$	7493.24	−	9396.23i	0.615866	−	0.772271i
$530$	−1969.89	+	8630.63i	−0.161446	+	0.707341i
$531$	−14934.1	−	18726.7i	−1.22050	−	1.53045i
$532$	1563.20	+	3858.69i	0.127394	+	0.314465i
$533$	−7026.26	+	8810.65i	−0.570996	+	0.716007i
$534$	45.5800	+	57.1556i	0.00369371	+	0.00463177i
$535$	12361.6	−	5953.05i	0.998954	−	0.481071i
$536$	−6683.02	−	8380.25i	−0.538550	−	0.675320i
$537$	−84.2954	−	369.322i	−0.00677395	−	0.0296786i
$538$	−451.374			−0.0361712
$539$	−664.069	−	6852.11i	−0.0530677	−	0.547572i
$540$	765.865			0.0610325
$541$	588.469	+	2578.25i	0.0467658	+	0.204894i	0.992913	−	0.118842i	$-0.0379182\pi$
$541$	588.469	+	2578.25i	0.0467658	+	0.204894i	−0.946147	+	0.323736i	$0.895061\pi$
$542$	−4200.73	−	5267.55i	−0.332909	−	0.417455i
$543$	199.065	−	95.8647i	0.0157324	−	0.00757633i
$544$	−1074.56	−	1347.45i	−0.0846900	−	0.106198i
$545$	5411.62	−	6785.96i	0.425337	−	0.533355i
$546$	141.079	−	250.630i	0.0110579	−	0.0196446i
$547$	−68.4828	−	85.8748i	−0.00535304	−	0.00671250i	0.779148	−	0.626840i	$-0.215652\pi$
$547$	−68.4828	−	85.8748i	−0.00535304	−	0.00671250i	−0.784501	+	0.620128i	$0.787081\pi$
$548$	−1222.63	+	5356.71i	−0.0953073	+	0.417568i
$549$	−3344.60	+	4194.00i	−0.260007	+	0.326039i
$550$	1655.48	+	7253.13i	0.128345	+	0.562317i
$551$	−12162.1	−	5856.97i	−0.940333	−	0.452841i
$552$	148.755	+	651.737i	0.0114700	+	0.0502532i
$553$	1072.13	−	16757.1i	0.0824438	−	1.28858i
$554$	1191.48	−	5220.20i	0.0913736	−	0.400334i
$555$	665.308	−	834.269i	0.0508842	−	0.0638068i
$556$	8131.08	+	3915.72i	0.620206	+	0.298676i
$557$	748.378			0.0569296			0.0284648	−	0.999595i	$-0.490938\pi$
$557$	748.378			0.0569296			0.0284648	+	0.999595i	$0.490938\pi$
$558$	10883.5			0.825692
$559$	−786.216	−	378.622i	−0.0594873	−	0.0286476i
$560$	−214.374	+	3350.62i	−0.0161767	+	0.252838i
$561$	−33.5499	+	16.1568i	−0.00252491	+	0.00121593i
$562$	−415.663	+	200.173i	−0.0311987	+	0.0150245i
$563$	1622.88	−	7110.28i	0.121485	−	0.532260i	−0.877159	−	0.480200i	$-0.840564\pi$
$563$	1622.88	−	7110.28i	0.121485	−	0.532260i	0.998644	−	0.0520604i	$-0.0165788\pi$
$564$	1.40473	−	6.15454i	0.000104876	−	0.000459491i
$565$	16400.8	−	7898.23i	1.22122	−	0.588108i
$566$	−14427.1	+	6947.72i	−1.07141	+	0.515962i
$567$	−6598.28	+	11722.0i	−0.488715	+	0.868212i
$568$	225.911	+	108.793i	0.0166884	+	0.00803670i
$569$	−9917.94			−0.730723			−0.365362	−	0.930866i	$-0.619055\pi$
$569$	−9917.94			−0.730723			−0.365362	+	0.930866i	$0.619055\pi$
$570$	−320.592			−0.0235581
$571$	22221.7	+	10701.4i	1.62864	+	0.784309i	0.999978	+	0.00662684i	$0.00210940\pi$
$571$	22221.7	+	10701.4i	1.62864	+	0.784309i	0.628657	+	0.777683i	$0.283605\pi$
$572$	−2434.63	+	3052.93i	−0.177967	+	0.223164i
$573$	−44.5720	+	195.283i	−0.00324960	+	0.0142374i
$574$	−6605.87	−	5996.62i	−0.480355	−	0.436052i
$575$	−6721.40	−	29448.4i	−0.487481	−	2.13579i
$576$	9822.73	+	4730.38i	0.710556	+	0.342186i
$577$	−3972.47	−	17404.5i	−0.286614	−	1.25574i	−0.889139	−	0.457637i	$-0.848696\pi$
$577$	−3972.47	−	17404.5i	−0.286614	−	1.25574i	0.602525	−	0.798100i	$-0.294161\pi$
$578$	−5722.66	+	7175.99i	−0.411819	+	0.516404i
$579$	148.439	−	650.353i	0.0106544	−	0.0466800i
$580$	12703.8	+	15930.0i	0.909474	+	1.14044i
$581$	2085.97	+	618.604i	0.148951	+	0.0441721i
$582$	262.012	−	328.552i	0.0186611	−	0.0234002i
$583$	−3248.85	−	4073.92i	−0.230795	−	0.289408i
$584$	635.657	−	306.116i	0.0450405	−	0.0216904i
$585$	13411.7	+	16817.7i	0.947869	+	1.18859i
$586$	−1942.94	−	8512.57i	−0.136966	−	0.600087i
$587$	14869.5			1.04554			0.522768	−	0.852475i	$-0.324899\pi$
$587$	14869.5			1.04554			0.522768	+	0.852475i	$0.324899\pi$
$588$	−228.393	−	148.524i	−0.0160183	−	0.0104167i
$589$	10908.9			0.763145
$590$	−6739.40	−	29527.2i	−0.470266	−	2.06037i
$591$	420.593	+	527.407i	0.0292739	+	0.0367084i
$592$	2995.46	−	1442.54i	0.207960	−	0.100148i
$593$	13332.3	+	16718.1i	0.923255	+	1.15772i	0.987155	+	0.159769i	$0.0510748\pi$
$593$	13332.3	+	16718.1i	0.923255	+	1.15772i	−0.0638997	+	0.997956i	$0.520354\pi$
$594$	234.908	−	294.565i	0.0162263	−	0.0203471i
$595$	3325.05	−	538.322i	0.229099	−	0.0370908i
$596$	−4123.10	−	5170.20i	−0.283370	−	0.355335i
$597$	−27.7449	+	121.558i	−0.00190205	+	0.00833343i
$598$	−8261.45	+	10359.5i	−0.564943	+	0.708416i
$599$	860.853	+	3771.65i	0.0587204	+	0.257271i	0.995765	−	0.0919400i	$-0.0293068\pi$
$599$	860.853	+	3771.65i	0.0587204	+	0.257271i	−0.937044	+	0.349211i	$0.886450\pi$
$600$	752.226	+	362.253i	0.0511825	+	0.0246482i
$601$	1348.05	+	5906.18i	0.0914942	+	0.400862i	0.999850	−	0.0173365i	$-0.00551865\pi$
$601$	1348.05	+	5906.18i	0.0914942	+	0.400862i	−0.908355	+	0.418199i	$0.862662\pi$
$602$	338.881	−	602.028i	0.0229431	−	0.0407589i
$603$	2727.23	−	11948.8i	0.184181	−	0.806951i
$604$	4201.55	−	5268.57i	0.283044	−	0.354926i
$605$	14941.3	+	7195.36i	1.00405	+	0.483526i
$606$	589.940			0.0395457
$607$	−4622.27			−0.309081			−0.154540	−	0.987986i	$-0.549390\pi$
$607$	−4622.27			−0.309081			−0.154540	+	0.987986i	$0.549390\pi$
$608$	7868.86	+	3789.44i	0.524876	+	0.252767i
$609$	871.990	−	141.174i	0.0580211	−	0.00939355i
$610$	−6111.19	+	2943.00i	−0.405631	+	0.195342i
$611$	319.691	−	153.955i	0.0211675	−	0.0101937i
$612$	266.189	−	1166.25i	0.0175818	−	0.0770308i
$613$	−2373.77	+	10400.2i	−0.156404	+	0.685251i	0.834537	+	0.550952i	$0.185735\pi$
$613$	−2373.77	+	10400.2i	−0.156404	+	0.685251i	−0.990941	+	0.134299i	$0.957122\pi$
$614$	−55.8395	+	26.8909i	−0.00367019	+	0.00176747i
$615$	−740.604	+	356.656i	−0.0485594	+	0.0233850i
$616$	−6490.99	−	5892.33i	−0.424561	−	0.385404i
$617$	3042.11	+	1465.00i	0.198494	+	0.0955897i	0.530490	−	0.847691i	$-0.322008\pi$
$617$	3042.11	+	1465.00i	0.198494	+	0.0955897i	−0.331996	+	0.943281i	$0.607722\pi$
$618$	−633.384			−0.0412273
$619$	15534.0			1.00867			0.504333	−	0.863509i	$-0.331738\pi$
$619$	15534.0			1.00867			0.504333	+	0.863509i	$0.331738\pi$
$620$	−14835.2	−	7144.25i	−0.960961	−	0.462774i
$621$	−953.748	+	1195.96i	−0.0616306	+	0.0772823i
$622$	1511.76	−	6623.45i	0.0974534	−	0.426971i
$623$	3731.70	+	1106.65i	0.239980	+	0.0711671i
$624$	−18.3722	−	80.4937i	−0.00117865	−	0.00516399i
$625$	1963.00	+	945.329i	0.125632	+	0.0605011i
$626$	−3278.57	−	14364.3i	−0.209326	−	0.917116i
$627$	117.655	−	147.535i	0.00749394	−	0.00939710i
$628$	−2909.03	+	12745.3i	−0.184846	+	0.809862i
$629$	−2079.63	−	2607.78i	−0.131829	−	0.165308i
$630$	−13965.1	+	9746.05i	−0.883149	+	0.616336i
$631$	−4162.42	+	5219.51i	−0.262604	+	0.329295i	−0.895600	−	0.444860i	$-0.853254\pi$
$631$	−4162.42	+	5219.51i	−0.262604	+	0.329295i	0.632996	+	0.774155i	$0.281825\pi$
$632$	−13331.8	−	16717.6i	−0.839101	−	1.05220i
$633$	−317.770	+	153.030i	−0.0199530	+	0.00960884i
$634$	1324.30	+	1660.61i	0.0829566	+	0.104024i
$635$	−5081.71	−	22264.4i	−0.317577	−	1.39140i
$636$	−206.212			−0.0128567
$637$	−1477.15	−	15241.8i	−0.0918791	−	0.948042i
$638$	10023.5			0.621997
$639$	63.7977	+	279.516i	0.00394960	+	0.0173043i
$640$	−6493.61	−	8142.72i	−0.401066	−	0.502921i
$641$	6414.46	−	3089.04i	0.395251	−	0.190343i	−0.225692	−	0.974199i	$-0.572464\pi$
$641$	6414.46	−	3089.04i	0.395251	−	0.190343i	0.620943	+	0.783856i	$0.286750\pi$
$642$	−166.543	−	208.839i	−0.0102382	−	0.0128383i
$643$	−9911.95	+	12429.2i	−0.607915	+	0.762301i	−0.986588	−	0.163229i	$-0.947809\pi$
$643$	−9911.95	+	12429.2i	−0.607915	+	0.762301i	0.378673	+	0.925530i	$0.376380\pi$
$644$	9293.42	+	8436.30i	0.568652	+	0.516206i
$645$	−39.6865	−	49.7653i	−0.00242272	−	0.00303799i
$646$	−222.991	+	976.989i	−0.0135812	+	0.0595033i
$647$	−6367.66	+	7984.80i	−0.386922	+	0.485185i	−0.936704	−	0.350124i	$-0.886140\pi$
$647$	−6367.66	+	7984.80i	−0.386922	+	0.485185i	0.549781	+	0.835309i	$0.314711\pi$
$648$	3811.67	+	16700.0i	0.231075	+	1.01240i
$649$	16061.6	+	7734.87i	0.971455	+	0.467828i
$650$	3682.45	+	16133.9i	0.222212	+	0.973572i
$651$	−585.395	+	408.538i	−0.0352434	+	0.0245958i
$652$	2252.56	−	9869.13i	0.135302	−	0.592799i
$653$	−5470.36	+	6859.62i	−0.327828	+	0.411083i	−0.918244	−	0.396016i	$-0.870392\pi$
$653$	−5470.36	+	6859.62i	−0.327828	+	0.411083i	0.590415	+	0.807099i	$0.298964\pi$
$654$	−152.244	−	73.3167i	−0.00910275	−	0.00438365i
$655$	−26739.1			−1.59509
$656$	−2561.16			−0.152433
$657$	726.825	+	350.021i	0.0431600	+	0.0207848i
$658$	105.476	+	260.361i	0.00624903	+	0.0154254i
$659$	4155.12	−	2001.00i	0.245615	−	0.118282i	−0.307026	−	0.951701i	$-0.599334\pi$
$659$	4155.12	−	2001.00i	0.245615	−	0.118282i	0.552642	+	0.833419i	$0.313620\pi$
$660$	−256.623	+	123.583i	−0.0151349	+	0.00728858i
$661$	−2994.45	+	13119.5i	−0.176204	+	0.771999i	0.807157	+	0.590336i	$0.201005\pi$
$661$	−2994.45	+	13119.5i	−0.176204	+	0.771999i	−0.983361	+	0.181662i	$0.941852\pi$
$662$	−2134.73	+	9352.87i	−0.125330	+	0.549108i
$663$	−74.6283	+	35.9391i	−0.00437153	+	0.00210522i
$664$	2496.30	−	1202.15i	0.145896	−	0.0702599i
$665$	−13997.7	+	9768.76i	−0.816250	+	0.569649i
$666$	15193.5	+	7316.80i	0.883987	+	0.425706i
$667$	−40696.3			−2.36247
$668$	1402.68			0.0812445
$669$	−70.4424	−	33.9233i	−0.00407094	−	0.00196046i
$670$	9662.32	−	12116.2i	0.557146	−	0.698639i
$671$	888.417	−	3892.41i	0.0511132	−	0.223941i
$672$	−564.176	+	91.3394i	−0.0323862	+	0.00524329i
$673$	5408.30	+	23695.3i	0.309769	+	1.35719i	0.854881	+	0.518824i	$0.173630\pi$
$673$	5408.30	+	23695.3i	0.309769	+	1.35719i	−0.545112	+	0.838363i	$0.683513\pi$
$674$	4673.09	+	2250.44i	0.267063	+	0.128611i
$675$	425.122	+	1862.58i	0.0242414	+	0.106209i
$676$	553.807	−	694.451i	0.0315092	−	0.0395113i
$677$	−603.660	+	2644.81i	−0.0342696	+	0.150145i	−0.989168	−	0.146788i	$-0.953107\pi$
$677$	−603.660	+	2644.81i	−0.0342696	+	0.150145i	0.954898	+	0.296933i	$0.0959637\pi$
$678$	−220.962	−	277.077i	−0.0125162	−	0.0156948i
$679$	1428.62	−	22329.0i	0.0807442	−	1.26201i
$680$	2674.37	−	3353.55i	0.150819	−	0.189122i
$681$	94.6881	+	118.735i	0.00532813	+	0.00668126i
$682$	−7298.10	+	3514.58i	−0.409763	+	0.197332i
$683$	−9971.74	−	12504.2i	−0.558650	−	0.700525i	0.419657	−	0.907683i	$-0.362150\pi$
$683$	−9971.74	−	12504.2i	−0.558650	−	0.700525i	−0.978308	+	0.207157i	$0.933579\pi$
$684$	1348.93	+	5910.07i	0.0754062	+	0.330376i
$685$	−22527.1			−1.25652
$686$	12116.8	−	396.598i	0.674375	−	0.0220732i
$687$	−289.156			−0.0160582
$688$	−44.1310	−	193.351i	−0.00244547	−	0.0107143i
$689$	−7226.73	−	9062.03i	−0.399589	−	0.501068i
$690$	−870.799	+	419.355i	−0.0480446	+	0.0231371i
$691$	−12035.1	−	15091.6i	−0.662572	−	0.830839i	0.331048	−	0.943614i	$-0.392598\pi$
$691$	−12035.1	−	15091.6i	−0.662572	−	0.830839i	−0.993621	+	0.112775i	$0.964026\pi$
$692$	−6450.38	+	8088.52i	−0.354345	+	0.444334i
$693$	640.023	−	10003.4i	0.0350829	−	0.548339i
$694$	7832.51	+	9821.65i	0.428412	+	0.537212i
$695$	−8233.58	+	36073.7i	−0.449378	+	1.96885i
$696$	701.349	−	879.464i	0.0381962	−	0.0478966i
$697$	571.757	+	2505.03i	0.0310715	+	0.136133i
$698$	−16893.4	−	8135.42i	−0.916080	−	0.441161i
$699$	−92.5275	−	405.390i	−0.00500674	−	0.0219360i
$700$	15474.4	−	2505.29i	0.835540	−	0.135273i
$701$	698.114	−	3058.64i	0.0376140	−	0.164798i	−0.952633	−	0.304124i	$-0.901636\pi$
$701$	698.114	−	3058.64i	0.0376140	−	0.164798i	0.990247	+	0.139326i	$0.0444936\pi$
$702$	522.529	−	655.231i	0.0280935	−	0.0352281i
$703$	15228.9	+	7333.85i	0.817025	+	0.393459i
$704$	−8114.34			−0.434404
$705$	25.8823			0.00138267
$706$	2665.99	+	1283.87i	0.142119	+	0.0684408i
$707$	25757.9	−	17976.1i	1.37019	−	0.956238i
$708$	635.630	−	306.103i	0.0337407	−	0.0162487i
$709$	15886.5	−	7650.52i	0.841508	−	0.405249i	0.0370896	−	0.999312i	$-0.488191\pi$
$709$	15886.5	−	7650.52i	0.841508	−	0.405249i	0.804419	+	0.594063i	$0.202477\pi$
$710$	−80.6689	+	353.434i	−0.00426401	+	0.0186819i
$711$	5440.50	−	23836.4i	0.286969	−	1.25729i
$712$	4465.76	−	2150.59i	0.235058	−	0.113198i
$713$	29631.0	−	14269.5i	1.55636	−	0.749506i
$714$	−24.6221	−	60.7784i	−0.00129056	−	0.00318568i
$715$	−14424.3	−	6946.36i	−0.754457	−	0.363327i
$716$	−9057.36			−0.472750
$717$	−695.739			−0.0362383
$718$	12617.9	+	6076.48i	0.655845	+	0.315838i
$719$	2339.85	−	2934.08i	0.121365	−	0.152187i	−0.717437	−	0.696623i	$-0.754685\pi$
$719$	2339.85	−	2934.08i	0.121365	−	0.152187i	0.838802	+	0.544436i	$0.183256\pi$
$720$	−1087.84	+	4766.14i	−0.0563075	+	0.246699i
$721$	−27654.8	+	19299.9i	−1.42846	+	0.996899i
$722$	1782.77	+	7810.85i	0.0918948	+	0.402617i
$723$	742.181	+	357.415i	0.0381770	+	0.0183851i
$724$	−1175.51	−	5150.23i	−0.0603416	−	0.264374i
$725$	−31690.1	+	39738.1i	−1.62337	+	2.03564i
$726$	71.8425	−	314.763i	0.00367262	−	0.0160908i
$727$	21783.8	+	27316.0i	1.11130	+	1.39353i	0.910305	+	0.413937i	$0.135847\pi$
$727$	21783.8	+	27316.0i	1.11130	+	1.39353i	0.200997	+	0.979592i	$0.435582\pi$
$728$	−14438.6	−	13106.9i	−0.735067	−	0.667272i
$729$	−12181.6	+	15275.3i	−0.618892	+	0.776066i
$730$	635.991	+	797.507i	0.0322453	+	0.0404343i
$731$	−179.262	+	86.3279i	−0.00907009	+	0.00436792i
$732$	−98.5121	−	123.530i	−0.00497420	−	0.00623745i
$733$	601.404	+	2634.92i	0.0303047	+	0.132774i	0.987817	−	0.155618i	$-0.0497368\pi$
$733$	601.404	+	2634.92i	0.0303047	+	0.132774i	−0.957513	+	0.288391i	$0.906880\pi$
$734$	6245.36			0.314061
$735$	385.305	−	1048.43i	0.0193363	−	0.0526147i
$736$	26330.4			1.31868
$737$	2029.80	+	8893.12i	0.101450	+	0.444481i
$738$	−8099.53	−	10156.5i	−0.403994	−	0.506593i
$739$	−27915.4	+	13443.3i	−1.38956	+	0.669176i	−0.971015	−	0.239020i	$-0.923174\pi$
$739$	−27915.4	+	13443.3i	−1.38956	+	0.669176i	−0.418544	+	0.908196i	$0.637459\pi$
$740$	−15907.1	−	19946.9i	−0.790212	−	0.990895i
$741$	261.712	−	328.177i	0.0129747	−	0.0162697i
$742$	7524.96	−	5251.56i	0.372305	−	0.259826i
$743$	9356.93	+	11733.2i	0.462009	+	0.579340i	0.957194	−	0.289447i	$-0.0934713\pi$
$743$	9356.93	+	11733.2i	0.462009	+	0.579340i	−0.495186	+	0.868787i	$0.664900\pi$
$744$	−202.282	+	886.254i	−0.00996775	+	0.0436716i
$745$	16904.5	−	21197.6i	0.831320	−	1.04244i
$746$	−4773.38	−	20913.5i	−0.234270	−	1.02641i
$747$	2854.32	+	1374.57i	0.139805	+	0.0673265i
$748$	198.117	+	868.006i	0.00968431	+	0.0424297i
$749$	−13635.1	−	4043.56i	−0.665176	−	0.197261i
$750$	−95.7395	+	419.462i	−0.00466122	+	0.0204221i
$751$	−3154.59	+	3955.73i	−0.153279	+	0.192206i	−0.852542	−	0.522659i	$-0.824940\pi$
$751$	−3154.59	+	3955.73i	−0.153279	+	0.192206i	0.699263	+	0.714865i	$0.253512\pi$
$752$	72.6561	+	34.9893i	0.00352326	+	0.00169671i
$753$	−574.574			−0.0278070
$754$	22296.3			1.07690
$755$	24892.5	+	11987.6i	1.19991	+	0.577846i
$756$	−587.801	−	533.588i	−0.0282779	−	0.0256699i
$757$	36125.8	−	17397.3i	1.73450	−	0.835289i	0.749655	−	0.661829i	$-0.230219\pi$
$757$	36125.8	−	17397.3i	1.73450	−	0.835289i	0.984841	−	0.173460i	$-0.0554948\pi$
$758$	−12188.9	+	5869.87i	−0.584065	+	0.281271i
$759$	126.593	−	554.639i	0.00605405	−	0.0265245i
$760$	−4836.86	+	21191.7i	−0.230857	+	1.01145i
$761$	6966.39	−	3354.84i	0.331842	−	0.159807i	−0.260542	−	0.965463i	$-0.583901\pi$
$761$	6966.39	−	3354.84i	0.331842	−	0.159807i	0.592384	+	0.805656i	$0.298187\pi$
$762$	−400.571	+	192.905i	−0.0190435	+	0.00917087i
$763$	−8881.29	+	1437.87i	−0.421395	+	0.0682233i
$764$	4314.89	+	2077.94i	0.204329	+	0.0983996i
$765$	4904.54			0.231796
$766$	23377.0			1.10267
$767$	35727.5	+	17205.5i	1.68194	+	0.809978i
$768$	−493.970	+	619.418i	−0.0232091	+	0.0291033i
$769$	859.833	−	3767.17i	0.0403204	−	0.176655i	−0.950758	−	0.309933i	$-0.899693\pi$
$769$	859.833	−	3767.17i	0.0403204	−	0.176655i	0.991079	+	0.133278i	$0.0425504\pi$

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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	49.e (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.424669 - 1.86059i) q^{2} +(0.113640 + 0.142500i) q^{3} +(3.92628 - 1.89080i) q^{4} +(11.1399 + 13.9690i) q^{5} +(0.216876 - 0.271954i) q^{6} +(1.18252 - 18.4825i) q^{7} +(-14.7045 - 18.4389i) q^{8} +(6.00067 - 26.2907i) q^{9} +O(q^{10})\)	\(q+(-0.424669 - 1.86059i) q^{2} +(0.113640 + 0.142500i) q^{3} +(3.92628 - 1.89080i) q^{4} +(11.1399 + 13.9690i) q^{5} +(0.216876 - 0.271954i) q^{6} +(1.18252 - 18.4825i) q^{7} +(-14.7045 - 18.4389i) q^{8} +(6.00067 - 26.2907i) q^{9} +(21.2598 - 26.6590i) q^{10} +(4.46612 + 19.5674i) q^{11} +(0.715623 + 0.344626i) q^{12} +(9.93444 + 43.5256i) q^{13} +(-34.8906 + 5.64874i) q^{14} +(-0.724644 + 3.17487i) q^{15} +(-6.32621 + 7.93281i) q^{16} +(9.17124 + 4.41664i) q^{17} -51.4646 q^{18} -51.5845 q^{19} +(70.1508 + 33.7828i) q^{20} +(2.76814 - 1.93184i) q^{21} +(34.5103 - 16.6193i) q^{22} +(-140.115 + 67.4759i) q^{23} +(0.956524 - 4.19080i) q^{24} +(-43.2200 + 189.359i) q^{25} +(76.7647 - 36.9680i) q^{26} +(8.86215 - 4.26779i) q^{27} +(-30.3037 - 74.8033i) q^{28} +(235.771 + 113.541i) q^{29} +6.21489 q^{30} -211.476 q^{31} +(-152.543 - 73.4609i) q^{32} +(-2.28083 + 2.86007i) q^{33} +(4.32283 - 18.9396i) q^{34} +(271.354 - 189.374i) q^{35} +(-26.1500 - 114.571i) q^{36} +(-295.222 - 142.172i) q^{37} +(21.9063 + 95.9779i) q^{38} +(-5.07347 + 6.36193i) q^{39} +(93.7657 - 410.814i) q^{40} +(157.381 + 197.349i) q^{41} +(-4.76992 - 4.32999i) q^{42} +(-12.1868 + 15.2817i) q^{43} +(54.5332 + 68.3825i) q^{44} +(434.100 - 209.052i) q^{45} +(185.048 + 232.042i) q^{46} +(-1.76856 - 7.74855i) q^{47} -1.84934 q^{48} +(-340.203 - 43.7116i) q^{49} +370.675 q^{50} +(0.412850 + 1.80881i) q^{51} +(121.304 + 152.110i) q^{52} +(-233.910 + 112.645i) q^{53} +(-11.7041 - 14.6765i) q^{54} +(-223.584 + 280.365i) q^{55} +(-358.185 + 249.972i) q^{56} +(-5.86208 - 7.35081i) q^{57} +(111.130 - 486.891i) q^{58} +(553.795 - 694.437i) q^{59} +(3.15789 + 13.8356i) q^{60} +(-179.224 - 86.3096i) q^{61} +(89.8072 + 393.471i) q^{62} +(-478.821 - 141.996i) q^{63} +(-89.9630 + 394.154i) q^{64} +(-497.340 + 623.644i) q^{65} +(6.29002 + 3.02911i) q^{66} +454.487 q^{67} +44.3598 q^{68} +(-25.5381 - 12.2985i) q^{69} +(-467.584 - 424.459i) q^{70} +(-9.57888 + 4.61295i) q^{71} +(-573.008 + 275.946i) q^{72} +(-6.65675 + 29.1651i) q^{73} +(-139.152 + 609.665i) q^{74} +(-31.8953 + 15.3600i) q^{75} +(-202.535 + 97.5359i) q^{76} +(366.935 - 59.4063i) q^{77} +(13.9915 + 6.73796i) q^{78} +906.648 q^{79} -181.286 q^{80} +(-654.383 - 315.134i) q^{81} +(300.352 - 376.630i) q^{82} +(-26.1418 + 114.535i) q^{83} +(7.21577 - 12.8190i) q^{84} +(40.4707 + 177.314i) q^{85} +(33.6084 + 16.1850i) q^{86} +(10.6134 + 46.5003i) q^{87} +(295.129 - 370.080i) q^{88} +(-46.7664 + 204.897i) q^{89} +(-573.309 - 718.907i) q^{90} +(816.209 - 132.143i) q^{91} +(-422.548 + 529.858i) q^{92} +(-24.0322 - 30.1354i) q^{93} +(-13.6659 + 6.58114i) q^{94} +(-574.645 - 720.582i) q^{95} +(-6.86683 - 30.0856i) q^{96} +1208.12 q^{97} +(63.1441 + 651.543i) q^{98} +541.239 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q - 5 q^{2} - 5 q^{3} - 53 q^{4} - 23 q^{5} + 19 q^{6} - 31 q^{8} - 174 q^{9}+O(q^{10}) \) 78 * q - 5 * q^2 - 5 * q^3 - 53 * q^4 - 23 * q^5 + 19 * q^6 - 31 * q^8 - 174 * q^9	\( 78 q - 5 q^{2} - 5 q^{3} - 53 q^{4} - 23 q^{5} + 19 q^{6} - 31 q^{8} - 174 q^{9} + 9 q^{10} - 103 q^{11} + 364 q^{12} - 35 q^{13} + 161 q^{14} - 245 q^{15} - 205 q^{16} - 285 q^{17} + 16 q^{18} + 628 q^{19} + 553 q^{20} - 21 q^{21} - 605 q^{22} + 149 q^{23} + 653 q^{24} - 370 q^{25} - 511 q^{26} - 65 q^{27} + 70 q^{28} - 187 q^{29} + 84 q^{30} + 1276 q^{31} + 1399 q^{32} - 23 q^{33} - 765 q^{34} - 805 q^{35} - 1691 q^{36} - 1531 q^{37} - 1041 q^{38} - 1351 q^{39} - 1759 q^{40} - 301 q^{41} + 3395 q^{42} - 257 q^{43} - 883 q^{44} + 3105 q^{45} + 1593 q^{46} + 733 q^{47} - 1948 q^{48} + 1288 q^{49} + 6148 q^{50} + 1197 q^{51} - 1099 q^{52} - 285 q^{53} + 660 q^{54} + 2641 q^{55} - 1988 q^{56} - 2352 q^{57} + 1173 q^{58} - 3603 q^{59} - 175 q^{60} - 2613 q^{61} - 1927 q^{62} - 3066 q^{63} + 1589 q^{64} - 371 q^{65} - 2175 q^{66} + 352 q^{67} + 6076 q^{68} + 5549 q^{69} - 6293 q^{70} - 2623 q^{71} + 6220 q^{72} + 2039 q^{73} - 2411 q^{74} - 3903 q^{75} + 4130 q^{76} + 1029 q^{77} - 3759 q^{78} + 44 q^{79} - 1608 q^{80} + 1394 q^{81} - 10920 q^{82} - 553 q^{83} - 7798 q^{84} + 497 q^{85} - 2985 q^{86} - 4273 q^{87} - 2197 q^{88} - 3957 q^{89} - 2958 q^{90} + 14119 q^{91} - 9136 q^{92} + 6272 q^{93} + 14912 q^{94} + 5866 q^{95} + 21882 q^{96} - 1540 q^{97} - 2303 q^{98} + 10768 q^{99}+O(q^{100}) \) 78 * q - 5 * q^2 - 5 * q^3 - 53 * q^4 - 23 * q^5 + 19 * q^6 - 31 * q^8 - 174 * q^9 + 9 * q^10 - 103 * q^11 + 364 * q^12 - 35 * q^13 + 161 * q^14 - 245 * q^15 - 205 * q^16 - 285 * q^17 + 16 * q^18 + 628 * q^19 + 553 * q^20 - 21 * q^21 - 605 * q^22 + 149 * q^23 + 653 * q^24 - 370 * q^25 - 511 * q^26 - 65 * q^27 + 70 * q^28 - 187 * q^29 + 84 * q^30 + 1276 * q^31 + 1399 * q^32 - 23 * q^33 - 765 * q^34 - 805 * q^35 - 1691 * q^36 - 1531 * q^37 - 1041 * q^38 - 1351 * q^39 - 1759 * q^40 - 301 * q^41 + 3395 * q^42 - 257 * q^43 - 883 * q^44 + 3105 * q^45 + 1593 * q^46 + 733 * q^47 - 1948 * q^48 + 1288 * q^49 + 6148 * q^50 + 1197 * q^51 - 1099 * q^52 - 285 * q^53 + 660 * q^54 + 2641 * q^55 - 1988 * q^56 - 2352 * q^57 + 1173 * q^58 - 3603 * q^59 - 175 * q^60 - 2613 * q^61 - 1927 * q^62 - 3066 * q^63 + 1589 * q^64 - 371 * q^65 - 2175 * q^66 + 352 * q^67 + 6076 * q^68 + 5549 * q^69 - 6293 * q^70 - 2623 * q^71 + 6220 * q^72 + 2039 * q^73 - 2411 * q^74 - 3903 * q^75 + 4130 * q^76 + 1029 * q^77 - 3759 * q^78 + 44 * q^79 - 1608 * q^80 + 1394 * q^81 - 10920 * q^82 - 553 * q^83 - 7798 * q^84 + 497 * q^85 - 2985 * q^86 - 4273 * q^87 - 2197 * q^88 - 3957 * q^89 - 2958 * q^90 + 14119 * q^91 - 9136 * q^92 + 6272 * q^93 + 14912 * q^94 + 5866 * q^95 + 21882 * q^96 - 1540 * q^97 - 2303 * q^98 + 10768 * q^99

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