LMFDB - Embedded newform 49.4.e.a.8.7

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			8.7
Character	$\chi$	$=$	49.8
Dual form			49.4.e.a.43.7

$q$-expansion

$f(q)$	$=$	$q+(0.153998 + 0.193108i) q^{2} +(-8.98937 + 4.32905i) q^{3} +(1.76659 - 7.73995i) q^{4} +(14.2902 - 6.88179i) q^{5} +(-2.22032 - 1.06925i) q^{6} +(-13.6848 - 12.4791i) q^{7} +(3.54697 - 1.70813i) q^{8} +(45.2339 - 56.7215i) q^{9} +O(q^{10})$	\(q+(0.153998 + 0.193108i) q^{2} +(-8.98937 + 4.32905i) q^{3} +(1.76659 - 7.73995i) q^{4} +(14.2902 - 6.88179i) q^{5} +(-2.22032 - 1.06925i) q^{6} +(-13.6848 - 12.4791i) q^{7} +(3.54697 - 1.70813i) q^{8} +(45.2339 - 56.7215i) q^{9} +(3.52959 + 1.69976i) q^{10} +(-13.9285 - 17.4658i) q^{11} +(17.6261 + 77.2249i) q^{12} +(-10.6896 - 13.4043i) q^{13} +(0.302377 - 4.56439i) q^{14} +(-98.6682 + 123.726i) q^{15} +(-56.3462 - 27.1349i) q^{16} +(12.1785 + 53.3575i) q^{17} +17.9193 q^{18} +2.07357 q^{19} +(-28.0198 - 122.763i) q^{20} +(177.040 + 52.9370i) q^{21} +(1.22781 - 5.37940i) q^{22} +(22.4625 - 98.4148i) q^{23} +(-24.4904 + 30.7100i) q^{24} +(78.9141 - 98.9552i) q^{25} +(0.942301 - 4.12849i) q^{26} +(-101.129 + 443.074i) q^{27} +(-120.763 + 83.8739i) q^{28} +(-27.8072 - 121.831i) q^{29} -39.0872 q^{30} +155.641 q^{31} +(-10.4455 - 45.7647i) q^{32} +(200.819 + 96.7092i) q^{33} +(-8.42828 + 10.5687i) q^{34} +(-281.436 - 84.1527i) q^{35} +(-359.112 - 450.312i) q^{36} +(47.3283 + 207.359i) q^{37} +(0.319326 + 0.400423i) q^{38} +(154.121 + 74.2207i) q^{39} +(38.9318 - 48.8190i) q^{40} +(11.6961 - 5.63257i) q^{41} +(17.0413 + 42.3400i) q^{42} +(310.966 + 149.753i) q^{43} +(-159.790 + 76.9509i) q^{44} +(256.055 - 1121.85i) q^{45} +(22.4639 - 10.8180i) q^{46} +(-67.8488 - 85.0797i) q^{47} +623.986 q^{48} +(31.5452 + 341.546i) q^{49} +31.2617 q^{50} +(-340.464 - 426.929i) q^{51} +(-122.633 + 59.0569i) q^{52} +(-47.9243 + 209.970i) q^{53} +(-101.135 + 48.7039i) q^{54} +(-319.237 - 153.736i) q^{55} +(-69.8553 - 20.8876i) q^{56} +(-18.6401 + 8.97660i) q^{57} +(19.2443 - 24.1316i) q^{58} +(7.09251 + 3.41558i) q^{59} +(783.326 + 982.260i) q^{60} +(-25.9624 - 113.749i) q^{61} +(23.9684 + 30.0554i) q^{62} +(-1326.85 + 211.743i) q^{63} +(-304.713 + 382.098i) q^{64} +(-245.002 - 117.987i) q^{65} +(12.2505 + 53.6727i) q^{66} +258.343 q^{67} +434.498 q^{68} +(224.119 + 981.929i) q^{69} +(-27.0902 - 67.3069i) q^{70} +(82.2389 - 360.312i) q^{71} +(63.5555 - 278.455i) q^{72} +(113.679 - 142.549i) q^{73} +(-32.7541 + 41.0724i) q^{74} +(-281.006 + 1231.17i) q^{75} +(3.66315 - 16.0493i) q^{76} +(-27.3488 + 412.830i) q^{77} +(9.40176 + 41.1918i) q^{78} +1376.86 q^{79} -991.935 q^{80} +(-573.124 - 2511.02i) q^{81} +(2.88888 + 1.39121i) q^{82} +(-92.9045 + 116.499i) q^{83} +(722.487 - 1276.76i) q^{84} +(541.228 + 678.678i) q^{85} +(18.9697 + 83.1117i) q^{86} +(777.384 + 974.809i) q^{87} +(-79.2378 - 38.1589i) q^{88} +(725.229 - 909.408i) q^{89} +(256.070 - 123.317i) q^{90} +(-20.9892 + 316.831i) q^{91} +(-722.043 - 347.718i) q^{92} +(-1399.11 + 673.777i) q^{93} +(5.98095 - 26.2043i) q^{94} +(29.6317 - 14.2699i) q^{95} +(292.016 + 366.177i) q^{96} -1237.31 q^{97} +(-61.0974 + 58.6892i) q^{98} -1620.73 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 $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{6}{7}\right)$

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 $

$2$	0.153998	+	0.193108i	0.0544466	+	0.0682739i	0.808309	−	0.588758i	$-0.200383\pi$
$2$	0.153998	+	0.193108i	0.0544466	+	0.0682739i	−0.753863	+	0.657032i	$0.771812\pi$
$3$	−8.98937	+	4.32905i	−1.73001	+	0.833127i	−0.743635	+	0.668585i	$0.766900\pi$
$3$	−8.98937	+	4.32905i	−1.73001	+	0.833127i	−0.986370	+	0.164541i	$0.947386\pi$
$4$	1.76659	−	7.73995i	0.220824	−	0.967493i
$5$	14.2902	−	6.88179i	1.27815	−	0.615526i	0.333238	−	0.942843i	$-0.391859\pi$
$5$	14.2902	−	6.88179i	1.27815	−	0.615526i	0.944915	+	0.327317i	$0.106144\pi$
$6$	−2.22032	−	1.06925i	−0.151074	−	0.0727533i
$7$	−13.6848	−	12.4791i	−0.738907	−	0.673807i
$7$	−13.6848	−	12.4791i	−0.738907	−	0.673807i
$8$	3.54697	−	1.70813i	0.156755	−	0.0754894i
$9$	45.2339	−	56.7215i	1.67533	−	2.10080i
$10$	3.52959	+	1.69976i	0.111616	+	0.0537512i
$11$	−13.9285	−	17.4658i	−0.381782	−	0.478739i	0.553396	−	0.832918i	$-0.313332\pi$
$11$	−13.9285	−	17.4658i	−0.381782	−	0.478739i	−0.935178	+	0.354179i	$0.884760\pi$
$12$	17.6261	+	77.2249i	0.424018	+	1.85774i
$13$	−10.6896	−	13.4043i	−0.228059	−	0.285976i	0.654615	−	0.755962i	$-0.272831\pi$
$13$	−10.6896	−	13.4043i	−0.228059	−	0.285976i	−0.882674	+	0.469986i	$0.844259\pi$
$14$	0.302377	−	4.56439i	0.00577241	−	0.0871346i
$15$	−98.6682	+	123.726i	−1.69840	+	2.12973i
$16$	−56.3462	−	27.1349i	−0.880410	−	0.423983i
$17$	12.1785	+	53.3575i	0.173748	+	0.761240i	0.984433	+	0.175758i	$0.0562377\pi$
$17$	12.1785	+	53.3575i	0.173748	+	0.761240i	−0.810685	+	0.585482i	$0.800905\pi$
$18$	17.9193			0.234646
$19$	2.07357			0.0250374			0.0125187	−	0.999922i	$-0.496015\pi$
$19$	2.07357			0.0250374			0.0125187	+	0.999922i	$0.496015\pi$
$20$	−28.0198	−	122.763i	−0.313270	−	1.37253i
$21$	177.040	+	52.9370i	1.83968	+	0.550086i
$22$	1.22781	−	5.37940i	0.0118987	−	0.0521315i
$23$	22.4625	−	98.4148i	0.203642	−	0.892213i	−0.765055	−	0.643965i	$-0.777288\pi$
$23$	22.4625	−	98.4148i	0.203642	−	0.892213i	0.968697	−	0.248248i	$-0.0798547\pi$
$24$	−24.4904	+	30.7100i	−0.208295	+	0.261194i
$25$	78.9141	−	98.9552i	0.631313	−	0.791642i
$26$	0.942301	−	4.12849i	0.00710771	−	0.0311409i
$27$	−101.129	+	443.074i	−0.720823	+	3.15813i
$28$	−120.763	+	83.8739i	−0.815072	+	0.566095i
$29$	−27.8072	−	121.831i	−0.178058	−	0.780122i	−0.982526	−	0.186126i	$-0.940407\pi$
$29$	−27.8072	−	121.831i	−0.178058	−	0.780122i	0.804468	−	0.593996i	$-0.202450\pi$
$30$	−39.0872			−0.237877
$31$	155.641			0.901739			0.450869	−	0.892590i	$-0.351114\pi$
$31$	155.641			0.901739			0.450869	+	0.892590i	$0.351114\pi$
$32$	−10.4455	−	45.7647i	−0.0577037	−	0.252817i
$33$	200.819	+	96.7092i	1.05934	+	0.510149i
$34$	−8.42828	+	10.5687i	−0.0425129	+	0.0533094i
$35$	−281.436	−	84.1527i	−1.35918	−	0.406412i
$36$	−359.112	−	450.312i	−1.66255	−	2.08478i
$37$	47.3283	+	207.359i	0.210290	+	0.921340i	0.964370	+	0.264558i	$0.0852260\pi$
$37$	47.3283	+	207.359i	0.210290	+	0.921340i	−0.754080	+	0.656783i	$0.771917\pi$
$38$	0.319326	+	0.400423i	0.00136320	+	0.00170940i
$39$	154.121	+	74.2207i	0.632797	+	0.304739i
$40$	38.9318	−	48.8190i	0.153892	−	0.192974i
$41$	11.6961	−	5.63257i	0.0445520	−	0.0214551i	−0.411475	−	0.911421i	$-0.634986\pi$
$41$	11.6961	−	5.63257i	0.0445520	−	0.0214551i	0.456027	+	0.889966i	$0.349272\pi$
$42$	17.0413	+	42.3400i	0.0626079	+	0.155553i
$43$	310.966	+	149.753i	1.10283	+	0.531097i	0.894548	−	0.446972i	$-0.147497\pi$
$43$	310.966	+	149.753i	1.10283	+	0.531097i	0.208285	+	0.978068i	$0.433212\pi$
$44$	−159.790	+	76.9509i	−0.547484	+	0.263654i
$45$	256.055	−	1121.85i	0.848232	−	3.71635i
$46$	22.4639	−	10.8180i	0.0720025	−	0.0346746i
$47$	−67.8488	−	85.0797i	−0.210569	−	0.264046i	0.665319	−	0.746559i	$-0.268295\pi$
$47$	−67.8488	−	85.0797i	−0.210569	−	0.264046i	−0.875889	+	0.482513i	$0.839724\pi$
$48$	623.986			1.87634
$49$	31.5452	+	341.546i	0.0919685	+	0.995762i
$50$	31.2617			0.0884214
$51$	−340.464	−	426.929i	−0.934795	−	1.17220i
$52$	−122.633	+	59.0569i	−0.327041	+	0.157495i
$53$	−47.9243	+	209.970i	−0.124206	+	0.544181i	0.874087	+	0.485770i	$0.161461\pi$
$53$	−47.9243	+	209.970i	−0.124206	+	0.544181i	−0.998293	+	0.0584113i	$0.981397\pi$
$54$	−101.135	+	48.7039i	−0.254864	+	0.122736i
$55$	−319.237	−	153.736i	−0.782652	−	0.376905i
$56$	−69.8553	−	20.8876i	−0.166693	−	0.0498432i
$57$	−18.6401	+	8.97660i	−0.0433148	+	0.0208593i
$58$	19.2443	−	24.1316i	0.0435673	−	0.0546317i
$59$	7.09251	+	3.41558i	0.0156503	+	0.00753678i	0.441693	−	0.897166i	$-0.354378\pi$
$59$	7.09251	+	3.41558i	0.0156503	+	0.00753678i	−0.426042	+	0.904703i	$0.640093\pi$
$60$	783.326	+	982.260i	1.68545	+	2.11349i
$61$	−25.9624	−	113.749i	−0.0544941	−	0.238754i	0.940345	−	0.340224i	$-0.110503\pi$
$61$	−25.9624	−	113.749i	−0.0544941	−	0.238754i	−0.994839	+	0.101469i	$0.967646\pi$
$62$	23.9684	+	30.0554i	0.0490966	+	0.0615652i
$63$	−1326.85	+	211.743i	−2.65344	+	0.423446i
$64$	−304.713	+	382.098i	−0.595143	+	0.746286i
$65$	−245.002	−	117.987i	−0.467520	−	0.225146i
$66$	12.2505	+	53.6727i	0.0228474	+	0.100101i
$67$	258.343			0.471068			0.235534	−	0.971866i	$-0.424316\pi$
$67$	258.343			0.471068			0.235534	+	0.971866i	$0.424316\pi$
$68$	434.498			0.774863
$69$	224.119	+	981.929i	0.391025	+	1.71319i
$70$	−27.0902	−	67.3069i	−0.0462556	−	0.114924i
$71$	82.2389	−	360.312i	0.137464	−	0.602270i	−0.858523	−	0.512775i	$-0.828617\pi$
$71$	82.2389	−	360.312i	0.137464	−	0.602270i	0.995987	−	0.0894952i	$-0.0285254\pi$
$72$	63.5555	−	278.455i	0.104029	−	0.455781i
$73$	113.679	−	142.549i	0.182262	−	0.228549i	−0.682304	−	0.731069i	$-0.739022\pi$
$73$	113.679	−	142.549i	0.182262	−	0.228549i	0.864566	+	0.502519i	$0.167593\pi$
$74$	−32.7541	+	41.0724i	−0.0514539	+	0.0645212i
$75$	−281.006	+	1231.17i	−0.432637	+	1.89551i
$76$	3.66315	−	16.0493i	0.00552885	−	0.0242235i
$77$	−27.3488	+	412.830i	−0.0404764	+	0.610991i
$78$	9.40176	+	41.1918i	0.0136479	+	0.0597956i
$79$	1376.86			1.96087			0.980433	−	0.196853i	$-0.0630721\pi$
$79$	1376.86			1.96087			0.980433	+	0.196853i	$0.0630721\pi$
$80$	−991.935			−1.38627
$81$	−573.124	−	2511.02i	−0.786179	−	3.44447i
$82$	2.88888	+	1.39121i	0.00389053	+	0.00187358i
$83$	−92.9045	+	116.499i	−0.122863	+	0.154065i	−0.839459	−	0.543424i	$-0.817128\pi$
$83$	−92.9045	+	116.499i	−0.122863	+	0.154065i	0.716596	+	0.697488i	$0.245699\pi$
$84$	722.487	−	1276.76i	0.938450	−	1.65841i
$85$	541.228	+	678.678i	0.690640	+	0.866035i
$86$	18.9697	+	83.1117i	0.0237855	+	0.104211i
$87$	777.384	+	974.809i	0.957981	+	1.20127i
$88$	−79.2378	−	38.1589i	−0.0959861	−	0.0462245i
$89$	725.229	−	909.408i	0.863754	−	1.08311i	−0.132017	−	0.991247i	$-0.542145\pi$
$89$	725.229	−	909.408i	0.863754	−	1.08311i	0.995771	−	0.0918661i	$-0.0292832\pi$
$90$	256.070	−	123.317i	0.299913	−	0.144431i
$91$	−20.9892	+	316.831i	−0.0241787	+	0.364978i
$92$	−722.043	−	347.718i	−0.818241	−	0.394044i
$93$	−1399.11	+	673.777i	−1.56001	+	0.751263i
$94$	5.98095	−	26.2043i	0.00656264	−	0.0287528i
$95$	29.6317	−	14.2699i	0.0320016	−	0.0154111i
$96$	292.016	+	366.177i	0.310456	+	0.389300i
$97$	−1237.31			−1.29515			−0.647574	−	0.762003i	$-0.724216\pi$
$97$	−1237.31			−1.29515			−0.647574	+	0.762003i	$0.724216\pi$
$98$	−61.0974	+	58.6892i	−0.0629772	+	0.0604949i
$99$	−1620.73			−1.64534
$100$	−626.499	−	785.605i	−0.626499	−	0.785605i
$101$	−1121.89	+	540.272i	−1.10527	+	0.532268i	−0.895310	−	0.445443i	$-0.853046\pi$
$101$	−1121.89	+	540.272i	−1.10527	+	0.532268i	−0.209955	+	0.977711i	$0.567332\pi$
$102$	30.0123	−	131.493i	0.0291340	−	0.127644i
$103$	−596.511	+	287.265i	−0.570641	+	0.274806i	−0.696873	−	0.717195i	$-0.745426\pi$
$103$	−596.511	+	287.265i	−0.570641	+	0.274806i	0.126232	+	0.992001i	$0.459712\pi$
$104$	−60.8120	−	29.2855i	−0.0573376	−	0.0276123i
$105$	2894.24	−	461.872i	2.68999	−	0.429277i
$106$	−47.9271	+	23.0805i	−0.0439159	+	0.0211488i
$107$	1169.97	−	1467.09i	1.05706	−	1.32551i	0.113777	−	0.993506i	$-0.463705\pi$
$107$	1169.97	−	1467.09i	1.05706	−	1.32551i	0.943279	−	0.332000i	$-0.107724\pi$
$108$	3250.71	+	1565.46i	2.89630	+	1.39478i
$109$	650.311	+	815.465i	0.571454	+	0.716581i	0.980629	−	0.195875i	$-0.0627547\pi$
$109$	650.311	+	815.465i	0.571454	+	0.716581i	−0.409175	+	0.912456i	$0.634183\pi$
$110$	−19.4742	−	85.3222i	−0.0168800	−	0.0739560i
$111$	−1323.12	−	1659.14i	−1.13140	−	1.41873i
$112$	432.466	+	1074.48i	0.364859	+	0.906510i
$113$	1055.25	−	1323.24i	0.878493	−	1.10160i	−0.115625	−	0.993293i	$-0.536887\pi$
$113$	1055.25	−	1323.24i	0.878493	−	1.10160i	0.994118	−	0.108302i	$-0.0345414\pi$
$114$	−4.60400	−	2.21717i	−0.00378249	−	0.00182155i
$115$	−356.276	−	1560.95i	−0.288895	−	1.26573i
$116$	−992.093			−0.794082
$117$	−1243.85			−0.982852
$118$	0.432661	+	1.89561i	0.000337540	+	0.00147886i
$119$	499.192	−	882.160i	0.384545	−	0.679559i
$120$	−138.633	+	607.390i	−0.105462	+	0.462057i
$121$	185.125	−	811.085i	0.139087	−	0.609380i
$122$	17.9676	−	22.5306i	0.0133337	−	0.0167199i
$123$	−80.7573	+	101.267i	−0.0592004	+	0.0742349i
$124$	274.954	−	1204.65i	0.199126	−	0.872426i
$125$	5.53571	−	24.2535i	0.00396103	−	0.0173544i
$126$	−245.221	−	223.616i	−0.173381	−	0.158106i
$127$	340.190	+	1490.47i	0.237693	+	1.04140i	0.943077	+	0.332575i	$0.107918\pi$
$127$	340.190	+	1490.47i	0.237693	+	1.04140i	−0.705384	+	0.708826i	$0.749225\pi$
$128$	−496.244			−0.342674
$129$	−3443.68			−2.35038
$130$	−14.9458	−	65.4816i	−0.0100833	−	0.0441778i
$131$	1969.64	+	948.527i	1.31365	+	0.632619i	0.953814	−	0.300397i	$-0.0971192\pi$
$131$	1969.64	+	948.527i	1.31365	+	0.632619i	0.359834	+	0.933016i	$0.382833\pi$
$132$	1103.29	−	1383.48i	0.727492	−	0.912247i
$133$	−28.3763	−	25.8762i	−0.0185003	−	0.0168703i
$134$	39.7843	+	49.8880i	0.0256481	+	0.0321617i
$135$	1603.99	+	7027.55i	1.02259	+	4.48026i
$136$	134.338	+	168.455i	0.0847015	+	0.106212i
$137$	−1280.84	−	616.822i	−0.798759	−	0.384662i	−0.0104527	−	0.999945i	$-0.503327\pi$
$137$	−1280.84	−	616.822i	−0.798759	−	0.384662i	−0.788306	+	0.615284i	$0.789042\pi$
$138$	−155.104	+	194.494i	−0.0956764	+	0.119974i
$139$	−69.4787	+	33.4592i	−0.0423964	+	0.0204170i	−0.454962	−	0.890511i	$-0.650347\pi$
$139$	−69.4787	+	33.4592i	−0.0423964	+	0.0204170i	0.412565	+	0.910928i	$0.364633\pi$
$140$	−1148.52	+	2029.64i	−0.693341	+	1.22525i
$141$	978.233	+	471.092i	0.584270	+	0.281370i
$142$	82.2438	−	39.6065i	0.0486038	−	0.0234064i
$143$	−85.2272	+	373.405i	−0.0498395	+	0.218361i
$144$	−4087.89	+	1968.62i	−2.36568	+	1.13925i
$145$	−1235.79	−	1549.63i	−0.707770	−	0.887516i
$146$	45.0337			0.0255275
$147$	−1762.14	−	2933.73i	−0.988702	−	1.64605i
$148$	1688.56			0.937828
$149$	560.342	+	702.647i	0.308087	+	0.386329i	0.911637	−	0.410996i	$-0.134819\pi$
$149$	560.342	+	702.647i	0.308087	+	0.386329i	−0.603550	+	0.797325i	$0.706248\pi$
$150$	−281.023	+	135.333i	−0.152969	+	0.0736662i
$151$	−459.745	+	2014.28i	−0.247772	+	1.08556i	0.685975	+	0.727625i	$0.259376\pi$
$151$	−459.745	+	2014.28i	−0.247772	+	1.08556i	−0.933747	+	0.357934i	$0.883481\pi$
$152$	7.35489	−	3.54193i	0.00392474	−	0.00189005i
$153$	3577.40	+	1722.78i	1.89030	+	0.910319i
$154$	−83.9323	+	58.2939i	−0.0439186	+	0.0305029i
$155$	2224.14	−	1071.09i	1.15256	−	0.555044i
$156$	846.733	−	1061.77i	0.434570	−	0.544933i
$157$	−499.417	−	240.507i	−0.253871	−	0.122258i	0.302620	−	0.953111i	$-0.402139\pi$
$157$	−499.417	−	240.507i	−0.253871	−	0.122258i	−0.556492	+	0.830853i	$0.687853\pi$
$158$	212.034	+	265.882i	0.106763	+	0.133876i
$159$	−478.162	−	2094.96i	−0.238495	−	1.04492i
$160$	−464.211	−	582.102i	−0.229369	−	0.287620i
$161$	−1535.52	+	1066.47i	−0.751652	+	0.522048i
$162$	396.638	−	497.368i	0.192363	−	0.241215i
$163$	−1722.39	−	829.462i	−0.827659	−	0.398579i	−0.0284221	−	0.999596i	$-0.509048\pi$
$163$	−1722.39	−	829.462i	−0.827659	−	0.398579i	−0.799237	+	0.601017i	$0.794763\pi$
$164$	−22.9335	−	100.478i	−0.0109195	−	0.0478416i
$165$	3535.27			1.66800
$166$	−36.8039			−0.0172081
$167$	−514.433	−	2253.88i	−0.238371	−	1.04437i	−0.942475	−	0.334276i	$-0.891508\pi$
$167$	−514.433	−	2253.88i	−0.238371	−	1.04437i	0.704104	−	0.710097i	$-0.251349\pi$
$168$	718.379	−	114.641i	0.329905	−	0.0526474i
$169$	423.470	−	1855.34i	0.192749	−	0.844489i
$170$	−47.7099	+	209.031i	−0.0215246	+	0.0943054i
$171$	93.7957	−	117.616i	0.0419458	−	0.0525984i
$172$	1708.43	−	2142.31i	0.757364	−	0.949705i
$173$	−401.320	+	1758.30i	−0.176369	+	0.772722i	0.806919	+	0.590662i	$0.201133\pi$
$173$	−401.320	+	1758.30i	−0.176369	+	0.772722i	−0.983288	+	0.182060i	$0.941724\pi$
$174$	−68.5273	+	300.238i	−0.0298566	+	0.130810i
$175$	−2314.79	+	369.402i	−0.999896	+	0.159567i
$176$	310.886	+	1362.08i	0.133147	+	0.583356i
$177$	−78.5435			−0.0333542
$178$	287.298			0.120977
$179$	797.111	+	3492.37i	0.332843	+	1.45828i	0.813599	+	0.581426i	$0.197505\pi$
$179$	797.111	+	3492.37i	0.332843	+	1.45828i	−0.480757	+	0.876854i	$0.659638\pi$
$180$	−8230.72	−	3963.71i	−3.40823	−	1.64132i
$181$	1034.61	−	1297.36i	0.424872	−	0.532772i	−0.522614	−	0.852569i	$-0.675043\pi$
$181$	1034.61	−	1297.36i	0.424872	−	0.532772i	0.947486	+	0.319797i	$0.103615\pi$
$182$	−64.4149	+	44.7383i	−0.0262349	+	0.0182210i
$183$	725.809	+	910.136i	0.293188	+	0.367646i
$184$	−88.4314	−	387.443i	−0.0354307	−	0.155232i
$185$	2103.33	+	2637.49i	0.835892	+	1.04818i
$186$	−345.573	−	166.419i	−0.136229	−	0.0656045i
$187$	762.302	−	955.896i	0.298102	−	0.373808i
$188$	−778.373	+	374.845i	−0.301961	+	0.145417i
$189$	6913.07	−	4801.36i	2.66059	−	1.84787i
$190$	7.31886	+	3.52458i	0.00279456	+	0.00134579i
$191$	−2588.23	+	1246.43i	−0.980514	+	0.472190i	−0.854282	−	0.519810i	$-0.826003\pi$
$191$	−2588.23	+	1246.43i	−0.980514	+	0.472190i	−0.126232	+	0.992001i	$0.540288\pi$
$192$	1085.06	−	4753.95i	0.407850	−	1.78691i
$193$	−131.941	+	63.5394i	−0.0492089	+	0.0236978i	−0.458326	−	0.888784i	$-0.651551\pi$
$193$	−131.941	+	63.5394i	−0.0492089	+	0.0236978i	0.409117	+	0.912482i	$0.365837\pi$
$194$	−190.543	−	238.933i	−0.0705164	−	0.0884248i
$195$	2713.19			0.996387
$196$	2699.28	+	359.215i	0.983702	+	0.130909i
$197$	3039.31			1.09920			0.549599	−	0.835429i	$-0.314781\pi$
$197$	3039.31			1.09920			0.549599	+	0.835429i	$0.314781\pi$
$198$	−249.589	−	312.975i	−0.0895835	−	0.112334i
$199$	−3539.19	+	1704.38i	−1.26074	+	0.607138i	−0.940369	−	0.340155i	$-0.889520\pi$
$199$	−3539.19	+	1704.38i	−1.26074	+	0.607138i	−0.320367	+	0.947294i	$0.603806\pi$
$200$	110.878	−	485.787i	0.0392012	−	0.171752i
$201$	−2322.34	+	1118.38i	−0.814950	+	0.392459i
$202$	−277.099	−	133.444i	−0.0965180	−	0.0464806i
$203$	−1139.81	+	2014.24i	−0.394083	+	0.696414i
$204$	−3905.87	+	1880.97i	−1.34052	+	0.645559i
$205$	128.378	−	160.981i	0.0437381	−	0.0548458i
$206$	−147.335	−	70.9527i	−0.0498316	−	0.0239976i
$207$	−4566.17	−	5725.79i	−1.53319	−	1.92256i
$208$	238.593	+	1045.34i	0.0795359	+	0.348469i
$209$	−28.8817	−	36.2165i	−0.00955881	−	0.0119864i
$210$	534.899	+	487.772i	0.175769	+	0.160283i
$211$	−2317.44	+	2905.97i	−0.756108	+	0.948130i	−0.999764	−	0.0217320i	$-0.993082\pi$
$211$	−2317.44	+	2905.97i	−0.756108	+	0.948130i	0.243655	+	0.969862i	$0.421653\pi$
$212$	1540.49	+	741.863i	0.499064	+	0.240336i
$213$	820.535	+	3595.00i	0.263954	+	1.15646i
$214$	463.480			0.148051
$215$	5474.33			1.73649
$216$	398.127	+	1744.31i	0.125413	+	0.549469i
$217$	−2129.91	−	1942.25i	−0.666302	−	0.607598i
$218$	−57.3257	+	251.160i	−0.0178100	+	0.0780309i
$219$	−404.801	+	1773.55i	−0.124904	+	0.547239i
$220$	−1753.87	+	2199.29i	−0.537482	+	0.673981i
$221$	585.038	−	733.615i	0.178072	−	0.223295i
$222$	116.635	−	511.010i	0.0352613	−	0.154490i
$223$	363.330	−	1591.85i	0.109105	−	0.478020i	−0.890624	−	0.454740i	$-0.849732\pi$
$223$	363.330	−	1591.85i	0.109105	−	0.478020i	0.999729	−	0.0232796i	$-0.00741079\pi$
$224$	−428.157	+	756.629i	−0.127712	+	0.225689i
$225$	−2043.29	−	8952.26i	−0.605421	−	2.65252i
$226$	418.036			0.123041
$227$	4417.04			1.29149			0.645747	−	0.763552i	$-0.276546\pi$
$227$	4417.04			1.29149			0.645747	+	0.763552i	$0.276546\pi$
$228$	36.5489	+	160.131i	0.0106163	+	0.0465130i
$229$	4118.80	+	1983.51i	1.18855	+	0.572375i	0.920391	−	0.391000i	$-0.127871\pi$
$229$	4118.80	+	1983.51i	1.18855	+	0.572375i	0.268158	+	0.963375i	$0.413585\pi$
$230$	246.565	−	309.183i	0.0706871	−	0.0886388i
$231$	−1541.31	−	3829.48i	−0.439009	−	1.09074i
$232$	−306.735	−	384.634i	−0.0868024	−	0.108847i
$233$	−262.249	−	1148.99i	−0.0737360	−	0.323058i	0.924585	−	0.380975i	$-0.124411\pi$
$233$	−262.249	−	1148.99i	−0.0737360	−	0.323058i	−0.998321	+	0.0579163i	$0.981554\pi$
$234$	−191.550	−	240.196i	−0.0535130	−	0.0671031i
$235$	−1555.07	−	748.883i	−0.431667	−	0.207880i
$236$	38.9660	−	48.8618i	0.0107477	−	0.0134772i
$237$	−12377.1	+	5960.48i	−3.39231	+	1.63365i
$238$	247.227	−	39.4533i	0.0673333	−	0.0107453i
$239$	1059.49	+	510.225i	0.286749	+	0.138091i	0.571729	−	0.820442i	$-0.306273\pi$
$239$	1059.49	+	510.225i	0.286749	+	0.138091i	−0.284980	+	0.958533i	$0.591987\pi$
$240$	8916.87	−	4294.14i	2.39826	−	1.15494i
$241$	−640.169	+	2804.76i	−0.171108	+	0.749671i	0.814437	+	0.580253i	$0.197046\pi$
$241$	−640.169	+	2804.76i	−0.171108	+	0.749671i	−0.985544	+	0.169419i	$0.945811\pi$
$242$	185.136	−	89.1567i	0.0491776	−	0.0236827i
$243$	8371.75	+	10497.8i	2.21008	+	2.77135i
$244$	−926.273			−0.243027
$245$	2801.24	+	4663.67i	0.730467	+	1.21613i
$246$	−31.9918			−0.00829157
$247$	−22.1656	−	27.7948i	−0.00570998	−	0.00716009i
$248$	552.053	−	265.855i	0.141352	−	0.0680717i
$249$	330.825	−	1449.44i	0.0841975	−	0.368893i
$250$	5.53604	−	2.66601i	0.00140052	−	0.000674454i
$251$	−2625.82	−	1264.53i	−0.660321	−	0.317994i	0.0735414	−	0.997292i	$-0.476570\pi$
$251$	−2625.82	−	1264.53i	−0.660321	−	0.317994i	−0.733862	+	0.679298i	$0.762284\pi$
$252$	−705.120	+	10643.8i	−0.176263	+	2.66070i
$253$	−2031.76	+	978.445i	−0.504884	+	0.243139i
$254$	−235.433	+	295.223i	−0.0581589	+	0.0729290i
$255$	−7803.33	−	3757.89i	−1.91633	−	0.922855i
$256$	2361.29	+	2960.96i	0.576486	+	0.722890i
$257$	−772.118	−	3382.87i	−0.187406	−	0.821081i	−0.977977	−	0.208711i	$-0.933073\pi$
$257$	−772.118	−	3382.87i	−0.187406	−	0.821081i	0.790571	−	0.612370i	$-0.209784\pi$
$258$	−530.321	−	665.001i	−0.127970	−	0.160470i
$259$	1939.97	−	3428.27i	0.465421	−	0.822480i
$260$	−1346.03	+	1687.87i	−0.321067	+	0.402605i
$261$	−8168.29	−	3933.64i	−1.93718	−	0.932898i
$262$	120.153	+	526.424i	0.0283323	+	0.124132i
$263$	−868.871			−0.203714			−0.101857	−	0.994799i	$-0.532478\pi$
$263$	−868.871			−0.203714			−0.101857	+	0.994799i	$0.532478\pi$
$264$	877.490			0.204567
$265$	760.123	+	3330.31i	0.176204	+	0.771998i
$266$	0.627001	−	9.46459i	0.000144526	−	0.00218162i
$267$	−2582.48	+	11314.6i	−0.591929	+	2.59341i
$268$	456.386	−	1999.56i	0.104023	−	0.455755i
$269$	2394.93	−	3003.14i	0.542830	−	0.680687i	−0.432451	−	0.901658i	$-0.642351\pi$
$269$	2394.93	−	3003.14i	0.542830	−	0.680687i	0.975280	+	0.220971i	$0.0709225\pi$
$270$	−1110.06	+	1391.97i	−0.250208	+	0.313751i
$271$	255.953	−	1121.40i	0.0573727	−	0.251366i	−0.938106	−	0.346347i	$-0.887422\pi$
$271$	255.953	−	1121.40i	0.0573727	−	0.251366i	0.995479	+	0.0949809i	$0.0302790\pi$
$272$	761.638	−	3336.95i	0.169783	−	0.743869i
$273$	−1182.90	−	2938.98i	−0.262243	−	0.651557i
$274$	−78.1347	−	342.331i	−0.0172273	−	0.0754779i
$275$	−2827.49			−0.620014
$276$	7996.00			1.74385
$277$	1131.60	+	4957.87i	0.245456	+	1.07541i	0.935966	+	0.352091i	$0.114529\pi$
$277$	1131.60	+	4957.87i	0.245456	+	1.07541i	−0.690510	+	0.723323i	$0.742614\pi$
$278$	−17.1608	−	8.26422i	−0.00370230	−	0.00178293i
$279$	7040.24	−	8828.18i	1.51071	−	1.89437i
$280$	−1141.99	+	182.243i	−0.243739	+	0.0388967i
$281$	−2112.47	−	2648.96i	−0.448468	−	0.562362i	0.505285	−	0.862953i	$-0.331387\pi$
$281$	−2112.47	−	2648.96i	−0.448468	−	0.562362i	−0.953753	+	0.300591i	$0.902816\pi$
$282$	59.6747	+	261.452i	0.0126013	+	0.0552100i
$283$	−4411.62	−	5532.00i	−0.926657	−	1.16199i	−0.986496	−	0.163783i	$-0.947630\pi$
$283$	−4411.62	−	5532.00i	−0.926657	−	1.16199i	0.0598398	−	0.998208i	$-0.480941\pi$
$284$	−2643.51	−	1273.05i	−0.552337	−	0.265992i
$285$	−204.595	+	256.555i	−0.0425235	+	0.0533227i
$286$	−85.2322	+	41.0457i	−0.0176220	+	0.00848630i
$287$	−230.348	−	68.8768i	−0.0473764	−	0.0141661i
$288$	−3068.33	−	1477.63i	−0.627789	−	0.302327i
$289$	1727.76	−	832.044i	0.351670	−	0.169356i
$290$	108.936	−	477.281i	0.0220585	−	0.0966445i
$291$	11122.6	−	5356.36i	2.24061	−	1.07902i
$292$	−902.498	−	1131.70i	−0.180872	−	0.226807i
$293$	−5500.06			−1.09665			−0.548323	−	0.836267i	$-0.684734\pi$
$293$	−5500.06			−1.09665			−0.548323	+	0.836267i	$0.684734\pi$
$294$	295.158	−	792.073i	0.0585509	−	0.157125i
$295$	124.859			0.0246425
$296$	522.068	+	654.653i	0.102516	+	0.128550i
$297$	9147.20	−	4405.06i	1.78712	−	0.860631i
$298$	−49.3948	+	216.413i	−0.00960190	+	0.0420687i
$299$	−1559.30	+	750.920i	−0.301594	+	0.145240i
$300$	9032.76	+	4349.95i	1.73836	+	0.837148i
$301$	−2386.71	−	5929.90i	−0.457035	−	1.13553i
$302$	−459.772	+	221.415i	−0.0876057	+	0.0421887i
$303$	7746.18	−	9713.41i	1.46867	−	1.84165i
$304$	−116.838	−	56.2661i	−0.0220431	−	0.0106154i
$305$	−1153.80	−	1446.82i	−0.216611	−	0.271622i
$306$	218.230	+	956.129i	0.0407692	+	0.178622i
$307$	3902.06	+	4893.03i	0.725415	+	0.909642i	0.998631	−	0.0523107i	$-0.0166586\pi$
$307$	3902.06	+	4893.03i	0.725415	+	0.909642i	−0.273215	+	0.961953i	$0.588087\pi$
$308$	3146.97	+	940.980i	0.582192	+	0.174082i
$309$	4118.68	−	5164.66i	0.758264	−	0.950832i
$310$	549.348	+	264.552i	0.100648	+	0.0484695i
$311$	−1774.32	−	7773.82i	−0.323514	−	1.41741i	−0.831253	−	0.555895i	$-0.812376\pi$
$311$	−1774.32	−	7773.82i	−0.323514	−	1.41741i	0.507739	−	0.861511i	$-0.330481\pi$
$312$	673.441			0.122199
$313$	1547.88			0.279525			0.139763	−	0.990185i	$-0.455366\pi$
$313$	1547.88			0.279525			0.139763	+	0.990185i	$0.455366\pi$
$314$	−30.4657	−	133.479i	−0.00547541	−	0.0239893i
$315$	−17503.7	+	12156.9i	−3.13087	+	2.17449i
$316$	2432.34	−	10656.8i	0.433006	−	1.89712i
$317$	−1432.36	+	6275.58i	−0.253783	+	1.11190i	0.673986	+	0.738744i	$0.264581\pi$
$317$	−1432.36	+	6275.58i	−0.253783	+	1.11190i	−0.927770	+	0.373154i	$0.878276\pi$
$318$	330.918	−	414.958i	0.0583552	−	0.0731751i
$319$	−1740.57	+	2182.60i	−0.305496	+	0.383079i
$320$	−1724.89	+	7557.23i	−0.301326	+	1.32019i
$321$	−4166.15	+	18253.1i	−0.724398	+	3.17380i
$322$	−442.411	−	132.286i	−0.0765672	−	0.0228945i
$323$	25.2530	+	110.640i	0.00435019	+	0.0190594i
$324$	−20447.6			−3.50611
$325$	−2169.99			−0.370367
$326$	−105.070	−	460.344i	−0.0178506	−	0.0782088i
$327$	−9376.08	−	4515.28i	−1.58562	−	0.763595i
$328$	31.8647	−	39.9571i	0.00536413	−	0.00672641i
$329$	−133.222	+	2010.99i	−0.0223245	+	0.336988i
$330$	544.426	+	682.688i	0.0908171	+	0.113881i
$331$	248.134	+	1087.15i	0.0412045	+	0.180529i	0.991343	−	0.131301i	$-0.0419154\pi$
$331$	248.134	+	1087.15i	0.0412045	+	0.180529i	−0.950138	+	0.311829i	$0.899058\pi$
$332$	737.568	+	924.882i	0.121926	+	0.152890i
$333$	13902.6	+	6695.12i	2.28785	+	1.10177i
$334$	356.020	−	446.434i	0.0583249	−	0.0731371i
$335$	3691.76	−	1777.86i	0.602097	−	0.289955i
$336$	−8539.09	−	7786.76i	−1.38645	−	1.26429i
$337$	−4816.18	−	2319.35i	−0.778499	−	0.374905i	0.00205180	−	0.999998i	$-0.499347\pi$
$337$	−4816.18	−	2319.35i	−0.778499	−	0.374905i	−0.780551	+	0.625093i	$0.785061\pi$
$338$	423.495	−	203.944i	0.0681511	−	0.0328199i
$339$	−3757.66	+	16463.4i	−0.602029	+	2.63766i
$340$	6209.06	−	2990.13i	0.990393	−	0.476948i
$341$	−2167.84	−	2718.39i	−0.344268	−	0.431698i
$342$	37.1570			0.00587491
$343$	3830.50	−	5067.63i	0.602995	−	0.797745i
$344$	1358.78			0.212967
$345$	9960.13	+	12489.6i	1.55431	+	1.94904i
$346$	−401.344	+	193.277i	−0.0623594	+	0.0300307i
$347$	1497.62	−	6561.52i	0.231691	−	1.01510i	−0.716547	−	0.697539i	$-0.754278\pi$
$347$	1497.62	−	6561.52i	0.231691	−	1.01510i	0.948237	−	0.317563i	$-0.102865\pi$
$348$	8918.29	−	4294.82i	1.37377	−	0.661571i
$349$	9787.76	+	4713.54i	1.50122	+	0.722951i	0.990592	−	0.136849i	$-0.0436974\pi$
$349$	9787.76	+	4713.54i	1.50122	+	0.722951i	0.510631	+	0.859800i	$0.329412\pi$
$350$	−427.808	−	390.117i	−0.0653352	−	0.0595789i
$351$	7020.13	−	3380.72i	1.06754	−	0.514101i
$352$	−653.826	+	819.872i	−0.0990030	+	0.124146i
$353$	902.225	+	434.488i	0.136036	+	0.0655113i	0.500663	−	0.865642i	$-0.333089\pi$
$353$	902.225	+	434.488i	0.136036	+	0.0655113i	−0.364628	+	0.931153i	$0.618804\pi$
$354$	−12.0956	−	15.1674i	−0.00181602	−	0.00227722i
$355$	−1304.38	−	5714.88i	−0.195013	−	0.854407i
$356$	−5757.59	−	7219.79i	−0.857167	−	1.07485i
$357$	−668.506	+	10091.1i	−0.0991066	+	1.49602i
$358$	−551.650	+	691.748i	−0.0814403	+	0.102123i
$359$	−11337.8	−	5459.98i	−1.66681	−	0.802693i	−0.998256	−	0.0590270i	$-0.981200\pi$
$359$	−11337.8	−	5459.98i	−1.66681	−	0.802693i	−0.668552	−	0.743666i	$-0.733086\pi$
$360$	−1008.05	−	4416.55i	−0.147580	−	0.646590i
$361$	−6854.70			−0.999373
$362$	409.858			0.0595073
$363$	1847.07	+	8092.56i	0.267069	+	1.17011i
$364$	2415.18	+	722.167i	0.347774	+	0.103989i
$365$	643.503	−	2819.37i	0.0922807	−	0.404308i
$366$	−63.9809	+	280.319i	−0.00913753	+	0.0400342i
$367$	4890.84	−	6132.92i	0.695639	−	0.872304i	−0.301050	−	0.953608i	$-0.597337\pi$
$367$	4890.84	−	6132.92i	0.695639	−	0.872304i	0.996689	+	0.0813041i	$0.0259085\pi$
$368$	−3936.15	+	4935.78i	−0.557571	+	0.699172i
$369$	209.575	−	918.206i	0.0295664	−	0.129539i
$370$	−185.411	+	812.339i	−0.0260515	+	0.114139i
$371$	3276.06	−	2275.34i	0.458449	−	0.318409i
$372$	2743.34	+	12019.3i	0.382353	+	1.67520i
$373$	−5554.72			−0.771080			−0.385540	−	0.922691i	$-0.625985\pi$
$373$	−5554.72			−0.771080			−0.385540	+	0.922691i	$0.625985\pi$
$374$	301.984			0.0417520
$375$	55.2323	+	241.988i	0.00760582	+	0.0333233i
$376$	−385.985	−	185.880i	−0.0529405	−	0.0254948i
$377$	−1335.82	+	1675.07i	−0.182489	+	0.228834i
$378$	1991.78	+	595.566i	0.271022	+	0.0810387i
$379$	4093.93	+	5133.63i	0.554858	+	0.695769i	0.977598	−	0.210481i	$-0.0675031\pi$
$379$	4093.93	+	5133.63i	0.554858	+	0.695769i	−0.422740	+	0.906251i	$0.638932\pi$
$380$	−58.1010	−	254.557i	−0.00784346	−	0.0343645i
$381$	−9510.42	−	11925.7i	−1.27883	−	1.60360i
$382$	−639.279	−	307.860i	−0.0856240	−	0.0412343i
$383$	−5982.55	+	7501.89i	−0.798157	+	1.00086i	0.201614	+	0.979465i	$0.435381\pi$
$383$	−5982.55	+	7501.89i	−0.798157	+	1.00086i	−0.999771	+	0.0213924i	$0.993190\pi$
$384$	4460.93	−	2148.27i	0.592827	−	0.285491i
$385$	2450.19	+	6087.62i	0.324346	+	0.805855i
$386$	−32.5887	−	15.6939i	−0.00429720	−	0.00206942i
$387$	22560.4	−	10864.5i	2.96333	−	1.42707i
$388$	−2185.81	+	9576.68i	−0.286000	+	1.25305i
$389$	−3904.58	+	1880.35i	−0.508921	+	0.245083i	−0.670680	−	0.741747i	$-0.733998\pi$
$389$	−3904.58	+	1880.35i	−0.508921	+	0.245083i	0.161759	+	0.986830i	$0.448283\pi$
$390$	417.826	+	523.938i	0.0542499	+	0.0680272i
$391$	5524.72			0.714571
$392$	695.295	+	1157.57i	0.0895860	+	0.149148i
$393$	−21812.0			−2.79967
$394$	468.049	+	586.915i	0.0598476	+	0.0750466i
$395$	19675.5	−	9475.24i	2.50629	−	1.20696i
$396$	−2863.16	+	12544.3i	−0.363332	+	1.59186i
$397$	−12903.9	+	6214.18i	−1.63130	+	0.785594i	−0.631353	+	0.775496i	$0.717500\pi$
$397$	−12903.9	+	6214.18i	−1.63130	+	0.785594i	−0.999949	+	0.0100981i	$0.996786\pi$
$398$	−874.159	−	420.973i	−0.110095	−	0.0530187i
$399$	367.105	+	109.769i	0.0460607	+	0.0137727i
$400$	−7131.65	+	3434.42i	−0.891457	+	0.429303i
$401$	−1505.72	+	1888.11i	−0.187511	+	0.235132i	−0.866697	−	0.498835i	$-0.833762\pi$
$401$	−1505.72	+	1888.11i	−0.187511	+	0.235132i	0.679186	+	0.733966i	$0.262333\pi$
$402$	−573.604	−	276.233i	−0.0711660	−	0.0342718i
$403$	−1663.74	−	2086.26i	−0.205649	−	0.257876i
$404$	2199.76	+	9637.77i	0.270896	+	1.18687i
$405$	−25470.4	−	31938.8i	−3.12502	−	3.91865i
$406$	−564.494	+	90.0840i	−0.0690034	+	0.0110118i
$407$	2962.47	−	3714.82i	0.360797	−	0.452425i
$408$	−1936.87	−	932.746i	−0.235022	−	0.113181i
$409$	2495.01	+	10931.4i	0.301639	+	1.32157i	0.867653	+	0.497170i	$0.165628\pi$
$409$	2495.01	+	10931.4i	0.301639	+	1.32157i	−0.566014	+	0.824396i	$0.691515\pi$
$410$	50.8567			0.00612593
$411$	14184.2			1.70233
$412$	1169.62	+	5124.45i	0.139862	+	0.612775i
$413$	−54.4361	−	135.249i	−0.00648578	−	0.0161143i
$414$	402.513	−	1763.53i	0.0477837	−	0.209354i
$415$	−525.904	+	2304.14i	−0.0622063	+	0.272544i
$416$	−501.787	+	629.221i	−0.0591398	+	0.0741589i
$417$	479.723	−	601.554i	0.0563361	−	0.0706432i
$418$	2.54596	−	11.1546i	0.000297911	−	0.00130523i
$419$	2504.32	−	10972.2i	0.291991	−	1.27930i	−0.589759	−	0.807579i	$-0.700777\pi$
$419$	2504.32	−	10972.2i	0.291991	−	1.27930i	0.881750	−	0.471717i	$-0.156366\pi$
$420$	1538.07	−	23217.2i	0.178691	−	2.69734i
$421$	2514.46	+	11016.6i	0.291086	+	1.27533i	0.883017	+	0.469342i	$0.155509\pi$
$421$	2514.46	+	11016.6i	0.291086	+	1.27533i	−0.591931	+	0.805989i	$0.701634\pi$
$422$	−918.047			−0.105900
$423$	−7894.91			−0.907479
$424$	188.670	+	826.618i	0.0216100	+	0.0946795i
$425$	6241.05	+	3005.53i	0.712319	+	0.343035i
$426$	−567.861	+	712.075i	−0.0645844	+	0.0809863i
$427$	−1064.19	+	1880.61i	−0.120608	+	0.213136i
$428$	−9288.36	−	11647.2i	−1.04900	−	1.31540i
$429$	−850.350	−	3725.63i	−0.0956999	−	0.419289i
$430$	843.038	+	1057.14i	0.0945462	+	0.118557i
$431$	−6735.18	−	3243.49i	−0.752719	−	0.362491i	0.0178550	−	0.999841i	$-0.494316\pi$
$431$	−6735.18	−	3243.49i	−0.752719	−	0.362491i	−0.770574	+	0.637350i	$0.780031\pi$
$432$	17721.0	−	22221.4i	1.97361	−	2.47483i
$433$	−5425.62	+	2612.84i	−0.602168	+	0.289989i	−0.710024	−	0.704178i	$-0.751316\pi$
$433$	−5425.62	+	2612.84i	−0.602168	+	0.289989i	0.107856	+	0.994167i	$0.465602\pi$
$434$	47.0623	−	710.405i	0.00520521	−	0.0785727i
$435$	17817.4	+	8580.41i	1.96386	+	0.945745i
$436$	7460.49	−	3592.78i	0.819478	−	0.394640i
$437$	46.5776	−	204.070i	0.00509865	−	0.0223387i
$438$	−404.825	+	194.954i	−0.0441628	+	0.0212677i
$439$	9848.98	+	12350.2i	1.07077	+	1.34270i	0.936071	+	0.351810i	$0.114434\pi$
$439$	9848.98	+	12350.2i	1.07077	+	1.34270i	0.134694	+	0.990887i	$0.456995\pi$
$440$	−1394.92			−0.151137
$441$	20799.9	+	13660.2i	2.24597	+	1.47502i
$442$	231.762			0.0249407
$443$	1548.60	+	1941.88i	0.166086	+	0.208265i	0.857909	−	0.513802i	$-0.171764\pi$
$443$	1548.60	+	1941.88i	0.166086	+	0.208265i	−0.691823	+	0.722067i	$0.743192\pi$
$444$	−15179.1	+	7309.85i	−1.62245	+	0.781329i
$445$	4105.30	−	17986.5i	0.437325	−	1.91605i
$446$	363.352	−	174.981i	0.0385767	−	0.0185776i
$447$	−8078.92	−	3890.60i	−0.854854	−	0.411676i
$448$	8938.17	−	1426.38i	0.942609	−	0.150425i
$449$	13042.1	−	6280.73i	1.37081	−	0.660147i	0.403790	−	0.914852i	$-0.367693\pi$
$449$	13042.1	−	6280.73i	1.37081	−	0.660147i	0.967019	+	0.254705i	$0.0819783\pi$
$450$	1414.09	−	1773.21i	0.148135	−	0.185755i
$451$	−261.287	−	125.829i	−0.0272805	−	0.0131376i
$452$	−8377.63	−	10505.2i	−0.871794	−	1.09319i
$453$	−4587.09	−	20097.3i	−0.475762	−	2.08445i
$454$	680.216	+	852.964i	0.0703175	+	0.0881753i
$455$	1880.43	+	4672.02i	0.193749	+	0.481380i
$456$	−50.7826	+	63.6794i	−0.00521517	+	0.00653961i
$457$	13202.4	+	6357.95i	1.35138	+	0.650793i	0.962698	−	0.270577i	$-0.0872146\pi$
$457$	13202.4	+	6357.95i	1.35138	+	0.650793i	0.388687	+	0.921370i	$0.372929\pi$
$458$	251.257	+	1100.83i	0.0256342	+	0.112311i
$459$	−24872.9			−2.52934
$460$	−12711.1			−1.28838
$461$	−201.738	−	883.872i	−0.0203815	−	0.0892973i	0.963714	−	0.266936i	$-0.0860113\pi$
$461$	−201.738	−	883.872i	−0.0203815	−	0.0892973i	−0.984096	+	0.177639i	$0.943154\pi$
$462$	502.142	−	887.373i	0.0505666	−	0.0893600i
$463$	1090.46	−	4777.63i	0.109456	−	0.479558i	−0.890254	−	0.455465i	$-0.849473\pi$
$463$	1090.46	−	4777.63i	0.109456	−	0.479558i	0.999710	−	0.0240933i	$-0.00766987\pi$
$464$	−1739.05	+	7619.28i	−0.173995	+	0.762320i
$465$	−15356.8	+	19256.8i	−1.53151	+	1.92046i
$466$	181.492	−	227.584i	0.0180418	−	0.0226237i
$467$	−697.977	+	3058.04i	−0.0691617	+	0.303017i	−0.997664	−	0.0683089i	$-0.978240\pi$
$467$	−697.977	+	3058.04i	−0.0691617	+	0.303017i	0.928503	+	0.371326i	$0.121097\pi$
$468$	−2197.37	+	9627.30i	−0.217037	+	0.950902i
$469$	−3535.35	−	3223.88i	−0.348076	−	0.317409i
$470$	−94.8633	−	415.623i	−0.00931004	−	0.0407900i
$471$	5530.61			0.541055
$472$	30.9912			0.00302221
$473$	−1715.73	−	7517.10i	−0.166785	−	0.730733i
$474$	−3057.06	−	1472.20i	−0.296236	−	0.142660i
$475$	163.634	−	205.191i	0.0158064	−	0.0198206i
$476$	−5946.00	−	5422.14i	−0.572552	−	0.522108i
$477$	9742.01	+	12216.1i	0.935128	+	1.17261i
$478$	64.6318	+	283.170i	0.00618449	+	0.0270960i
$479$	6661.33	+	8353.05i	0.635416	+	0.796786i	0.990421	−	0.138078i	$-0.0440925\pi$
$479$	6661.33	+	8353.05i	0.635416	+	0.796786i	−0.355006	+	0.934864i	$0.615521\pi$
$480$	6692.92	+	3223.14i	0.636434	+	0.306491i
$481$	2273.59	−	2850.99i	0.215523	−	0.270258i
$482$	−640.207	+	308.307i	−0.0604992	+	0.0291349i
$483$	9186.55	−	16234.3i	0.865430	−	1.52937i
$484$	−5950.71	−	2865.71i	−0.558857	−	0.269131i
$485$	−17681.3	+	8514.88i	−1.65540	+	0.797197i
$486$	−737.980	+	3233.30i	−0.0688795	+	0.301781i
$487$	−1319.15	+	635.271i	−0.122745	+	0.0591107i	−0.494248	−	0.869321i	$-0.664557\pi$
$487$	−1319.15	+	635.271i	−0.122745	+	0.0591107i	0.371504	+	0.928431i	$0.378842\pi$
$488$	−286.385	−	359.116i	−0.0265657	−	0.0333123i
$489$	19074.0			1.76392
$490$	−469.206	+	1259.14i	−0.0432583	+	0.116086i
$491$	−7285.35			−0.669620			−0.334810	−	0.942286i	$-0.608672\pi$
$491$	−7285.35			−0.669620			−0.334810	+	0.942286i	$0.608672\pi$
$492$	641.132	+	803.954i	0.0587489	+	0.0736688i
$493$	6161.96	−	2967.45i	0.562923	−	0.271089i
$494$	1.95393	−	8.56072i	0.000177958	−	0.000779686i
$495$	−23160.5	+	11153.5i	−2.10300	+	1.01275i
$496$	−8769.77	−	4223.30i	−0.793899	−	0.382322i
$497$	−5621.78	+	3904.52i	−0.507387	+	0.352398i
$498$	330.844	−	159.326i	0.0297700	−	0.0143365i
$499$	1040.75	−	1305.05i	0.0933671	−	0.117079i	−0.732953	−	0.680279i	$-0.761859\pi$
$499$	1040.75	−	1305.05i	0.0933671	−	0.117079i	0.826320	+	0.563200i	$0.190430\pi$
$500$	−177.942	−	85.6922i	−0.0159156	−	0.00766454i
$501$	14381.6	+	18033.9i	1.28248	+	1.60818i
$502$	−160.182	−	701.803i	−0.0142416	−	0.0623964i
$503$	4974.64	+	6238.00i	0.440970	+	0.552959i	0.951799	−	0.306723i	$-0.0992327\pi$
$503$	4974.64	+	6238.00i	0.440970	+	0.552959i	−0.510828	+	0.859683i	$0.670661\pi$
$504$	−4344.60	+	3017.47i	−0.383976	+	0.266684i
$505$	−12313.9	+	15441.2i	−1.08507	+	1.36064i
$506$	−501.833	−	241.670i	−0.0440893	−	0.0212323i
$507$	4225.15	+	18511.6i	0.370109	+	1.62156i
$508$	12137.1			1.06004
$509$	2176.61			0.189541			0.0947705	−	0.995499i	$-0.469788\pi$
$509$	2176.61			0.189541			0.0947705	+	0.995499i	$0.469788\pi$
$510$	−476.023	−	2085.59i	−0.0413307	−	0.181082i
$511$	−3334.55	+	532.139i	−0.288673	+	0.0460674i
$512$	−1091.55	+	4782.39i	−0.0942189	+	0.412800i
$513$	−209.697	+	918.745i	−0.0180475	+	0.0790713i
$514$	534.354	−	670.059i	0.0458548	−	0.0575000i
$515$	−6547.36	+	8210.13i	−0.560216	+	0.702489i
$516$	−6083.57	+	26653.9i	−0.519020	+	2.27398i
$517$	−540.952	+	2370.06i	−0.0460175	+	0.201616i
$518$	960.778	−	153.324i	0.0814945	−	0.0130052i
$519$	−4004.15	−	17543.3i	−0.338656	−	1.48375i
$520$	−1070.55			−0.0902823
$521$	12665.4			1.06503			0.532515	−	0.846420i	$-0.321247\pi$
$521$	12665.4			1.06503			0.532515	+	0.846420i	$0.321247\pi$
$522$	−498.286	−	2183.13i	−0.0417805	−	0.183052i
$523$	−19095.6	−	9195.95i	−1.59654	−	0.768855i	−0.597098	−	0.802168i	$-0.703680\pi$
$523$	−19095.6	−	9195.95i	−1.59654	−	0.768855i	−0.999445	+	0.0333133i	$0.989394\pi$
$524$	10821.1	−	13569.2i	0.902140	−	1.13125i
$525$	19209.4	−	13341.5i	1.59689	−	1.10909i
$526$	−133.805	−	167.786i	−0.0110916	−	0.0139084i
$527$	1895.47	+	8304.60i	0.156675	+	0.686440i
$528$	−8691.18	−	10898.4i	−0.716354	−	0.898280i
$529$	1781.18	+	857.772i	0.146395	+	0.0704999i
$530$	−526.052	+	659.648i	−0.0431137	+	0.0540628i
$531$	514.559	−	247.798i	0.0420526	−	0.0202515i
$532$	−250.410	+	173.918i	−0.0204073	+	0.0141735i
$533$	−200.528	−	96.5692i	−0.0162961	−	0.00784780i
$534$	−2582.63	+	1243.73i	−0.209291	+	0.100789i
$535$	6622.83	−	29016.5i	0.535196	−	2.34485i
$536$	916.333	−	441.283i	0.0738424	−	0.0355606i
$537$	−22284.2	−	27943.5i	−1.79075	−	2.24553i
$538$	948.745			0.0760284
$539$	5526.00	−	5308.19i	0.441598	−	0.424193i
$540$	57226.5			4.56044
$541$	3658.71	+	4587.87i	0.290758	+	0.364599i	0.905660	−	0.424004i	$-0.139376\pi$
$541$	3658.71	+	4587.87i	0.290758	+	0.364599i	−0.614902	+	0.788603i	$0.710804\pi$
$542$	255.968	−	123.268i	0.0202855	−	0.00976899i
$543$	−3684.15	+	16141.3i	−0.291164	+	1.27567i
$544$	2314.68	−	1114.69i	0.182428	−	0.0878528i
$545$	14904.9	+	7177.83i	1.17148	+	0.564155i
$546$	385.375	−	681.025i	0.0302061	−	0.0533795i
$547$	3781.64	−	1821.14i	0.295596	−	0.142352i	−0.280208	−	0.959939i	$-0.590403\pi$
$547$	3781.64	−	1821.14i	0.295596	−	0.142352i	0.575804	+	0.817588i	$0.304689\pi$
$548$	−7036.90	+	8823.99i	−0.548543	+	0.687851i
$549$	−7626.37	−	3672.67i	−0.592870	−	0.285511i
$550$	−435.428	−	546.010i	−0.0337577	−	0.0423308i
$551$	−57.6602	−	252.626i	−0.00445809	−	0.0195322i
$552$	2472.20	+	3100.05i	0.190623	+	0.239034i
$553$	−18841.9	−	17181.9i	−1.44890	−	1.32125i
$554$	−783.139	+	982.025i	−0.0600585	+	0.0753109i
$555$	−30325.5	−	14604.0i	−2.31936	−	1.11695i
$556$	136.232	+	596.870i	0.0103912	+	0.0455268i
$557$	−2751.46			−0.209305			−0.104653	−	0.994509i	$-0.533373\pi$
$557$	−2751.46			−0.209305			−0.104653	+	0.994509i	$0.533373\pi$
$558$	2788.97			0.211589
$559$	−1316.76	−	5769.09i	−0.0996295	−	0.436506i
$560$	13574.4	+	12378.4i	1.02433	+	0.934079i
$561$	−2714.49	+	11893.0i	−0.204288	+	0.895046i
$562$	186.217	−	815.870i	0.0139770	−	0.0612374i
$563$	−7375.66	+	9248.79i	−0.552126	+	0.692344i	−0.977080	−	0.212870i	$-0.931719\pi$
$563$	−7375.66	+	9248.79i	−0.552126	+	0.692344i	0.424954	+	0.905215i	$0.360290\pi$
$564$	5374.37	−	6739.24i	0.401244	−	0.503144i
$565$	5973.45	−	26171.4i	0.444788	−	1.94874i
$566$	388.890	−	1703.84i	0.0288803	−	0.126533i
$567$	−23492.2	+	41514.8i	−1.74000	+	3.07488i
$568$	−323.761	−	1418.49i	−0.0239168	−	0.104786i
$569$	960.148			0.0707408			0.0353704	−	0.999374i	$-0.488739\pi$
$569$	960.148			0.0707408			0.0353704	+	0.999374i	$0.488739\pi$
$570$	−81.0500			−0.00595581
$571$	−603.477	−	2644.01i	−0.0442290	−	0.193780i	0.947987	−	0.318309i	$-0.103115\pi$
$571$	−603.477	−	2644.01i	−0.0442290	−	0.193780i	−0.992216	+	0.124529i	$0.960258\pi$
$572$	2739.57	+	1319.31i	0.200257	+	0.0964388i
$573$	17870.8	−	22409.2i	1.30290	−	1.63378i
$574$	−22.1726	−	55.0890i	−0.00161231	−	0.00400587i
$575$	−7966.04	−	9989.10i	−0.577751	−	0.724477i
$576$	7889.83	+	34567.6i	0.570734	+	2.50055i
$577$	1267.51	+	1589.41i	0.0914510	+	0.114676i	0.825452	−	0.564473i	$-0.190921\pi$
$577$	1267.51	+	1589.41i	0.0914510	+	0.114676i	−0.734001	+	0.679149i	$0.762349\pi$
$578$	426.746	+	205.510i	0.0307098	+	0.0147891i
$579$	911.001	−	1142.36i	0.0653885	−	0.0819945i
$580$	−14177.2	+	6827.37i	−1.01496	+	0.488778i
$581$	2725.17	−	434.892i	0.194594	−	0.0310540i
$582$	2747.22	+	1322.99i	0.195663	+	0.0942263i
$583$	4334.80	−	2087.53i	0.307940	−	0.148296i
$584$	159.724	−	699.796i	0.0113175	−	0.0495852i
$585$	−17774.8	+	8559.89i	−1.25623	+	0.604971i
$586$	−847.001	−	1062.11i	−0.0597087	−	0.0748723i
$587$	−16417.0			−1.15435			−0.577173	−	0.816622i	$-0.695844\pi$
$587$	−16417.0			−1.15435			−0.577173	+	0.816622i	$0.695844\pi$
$588$	−25819.9	+	8456.20i	−1.81087	+	0.593075i
$589$	322.732			0.0225772
$590$	19.2280	+	24.1112i	0.00134170	+	0.00168244i
$591$	−27321.5	+	13157.3i	−1.90162	+	0.915771i
$592$	2959.89	−	12968.1i	0.205491	−	0.900316i
$593$	23458.3	−	11296.9i	1.62448	−	0.782309i	0.624483	−	0.781038i	$-0.285310\pi$
$593$	23458.3	−	11296.9i	1.62448	−	0.782309i	0.999999	−	0.00127109i	$-0.000404601\pi$
$594$	2259.31	+	1088.02i	0.156061	+	0.0751552i
$595$	1062.71	−	16041.6i	0.0732214	−	1.10528i
$596$	6428.35	−	3095.73i	0.441804	−	0.212762i
$597$	24436.7	−	30642.7i	1.67526	−	2.10071i
$598$	−385.138	−	185.473i	−0.0263369	−	0.0126832i
$599$	11360.8	+	14246.0i	0.774944	+	0.971749i	0.999997	−	0.00259795i	$-0.000826954\pi$
$599$	11360.8	+	14246.0i	0.774944	+	0.971749i	−0.225053	+	0.974347i	$0.572256\pi$
$600$	1106.28	+	4846.91i	0.0752726	+	0.329791i
$601$	13346.8	+	16736.4i	0.905869	+	1.13592i	0.990224	+	0.139488i	$0.0445456\pi$
$601$	13346.8	+	16736.4i	0.905869	+	1.13592i	−0.0843551	+	0.996436i	$0.526883\pi$
$602$	777.561	−	1374.09i	0.0526429	−	0.0930293i
$603$	11685.8	−	14653.6i	0.789194	−	0.989618i
$604$	14778.2	+	7116.81i	0.995557	+	0.479435i
$605$	−2936.25	−	12864.5i	−0.197315	−	0.864493i
$606$	3068.63			0.205701
$607$	−15396.6			−1.02954			−0.514769	−	0.857329i	$-0.672122\pi$
$607$	−15396.6			−1.02954			−0.514769	+	0.857329i	$0.672122\pi$
$608$	−21.6595	−	94.8963i	−0.00144475	−	0.00632986i
$609$	1526.40	−	23041.1i	0.101565	−	1.53312i
$610$	101.709	−	445.616i	0.00675094	−	0.0295778i
$611$	−415.160	+	1818.94i	−0.0274887	+	0.120436i
$612$	19654.1	−	24645.4i	1.29815	−	1.62783i
$613$	−12995.5	+	16295.8i	−0.856251	+	1.07370i	0.140249	+	0.990116i	$0.455210\pi$
$613$	−12995.5	+	16295.8i	−0.856251	+	1.07370i	−0.996500	+	0.0835886i	$0.973362\pi$
$614$	−343.972	+	1507.04i	−0.0226084	+	0.0990539i
$615$	−457.143	+	2002.87i	−0.0299736	+	0.131323i
$616$	608.162	+	1511.01i	0.0397785	+	0.0988317i
$617$	−4133.09	−	18108.3i	−0.269679	−	1.18154i	−0.910387	−	0.413757i	$-0.864216\pi$
$617$	−4133.09	−	18108.3i	−0.269679	−	1.18154i	0.640708	−	0.767784i	$-0.278641\pi$
$618$	1631.61			0.106202
$619$	−1570.70			−0.101990			−0.0509949	−	0.998699i	$-0.516239\pi$
$619$	−1570.70			−0.101990			−0.0509949	+	0.998699i	$0.516239\pi$
$620$	−4361.02	−	19106.9i	−0.282488	−	1.23766i
$621$	41333.4	+	19905.1i	2.67094	+	1.28626i
$622$	1227.94	−	1539.79i	0.0791576	−	0.0992605i
$623$	−21273.2	+	3394.84i	−1.36804	+	0.218317i
$624$	−6670.16	−	8364.11i	−0.427917	−	0.536590i
$625$	3432.72	+	15039.7i	0.219694	+	0.962541i
$626$	238.371	+	298.908i	0.0152192	+	0.0190843i
$627$	416.412	+	200.533i	0.0265230	+	0.0127728i
$628$	−2743.77	+	3440.58i	−0.174345	+	0.218621i
$629$	−10487.8	+	5050.64i	−0.664824	+	0.320162i
$630$	−5043.14	−	1507.96i	−0.318926	−	0.0953627i
$631$	24.4838	+	11.7908i	0.00154466	+	0.000743871i	0.434656	−	0.900597i	$-0.356870\pi$
$631$	24.4838	+	11.7908i	0.00154466	+	0.000743871i	−0.433111	+	0.901340i	$0.642584\pi$
$632$	4883.67	−	2351.85i	0.307376	−	0.148025i
$633$	8252.18	−	36155.2i	0.518159	−	2.27020i
$634$	−1432.44	+	689.829i	−0.0897313	+	0.0432123i
$635$	15118.5	+	18958.0i	0.944817	+	1.18476i
$636$	−17059.6			−1.06361
$637$	4241.00	−	4073.84i	0.263790	−	0.253393i
$638$	−689.522			−0.0427875
$639$	−16717.5	−	20963.0i	−1.03495	−	1.29779i
$640$	−7091.43	+	3415.05i	−0.437989	+	0.210925i
$641$	690.621	−	3025.81i	0.0425552	−	0.186447i	−0.949183	−	0.314725i	$-0.898088\pi$
$641$	690.621	−	3025.81i	0.0425552	−	0.186447i	0.991738	+	0.128278i	$0.0409450\pi$
$642$	−4166.40	+	2006.43i	−0.256129	+	0.123345i
$643$	2348.38	+	1130.92i	0.144030	+	0.0693611i	0.504510	−	0.863406i	$-0.331673\pi$
$643$	2348.38	+	1130.92i	0.144030	+	0.0693611i	−0.360481	+	0.932767i	$0.617387\pi$
$644$	5541.79	+	13768.9i	0.339095	+	0.842499i
$645$	−49210.8	+	23698.7i	−3.00414	+	1.44672i
$646$	−17.4766	+	21.9150i	−0.00106441	+	0.00133473i
$647$	26461.3	+	12743.1i	1.60788	+	0.774316i	0.999809	−	0.0195623i	$-0.00622727\pi$
$647$	26461.3	+	12743.1i	1.60788	+	0.774316i	0.608076	+	0.793879i	$0.291942\pi$
$648$	−6322.00	−	7927.54i	−0.383259	−	0.480592i
$649$	−39.1324	−	171.450i	−0.00236684	−	0.0103698i
$650$	−334.175	−	419.042i	−0.0201653	−	0.0252864i
$651$	27554.6	+	8239.16i	1.65891	+	0.496034i
$652$	−9462.76	+	11865.9i	−0.568390	+	0.712738i
$653$	5591.70	+	2692.82i	0.335100	+	0.161376i	0.593865	−	0.804565i	$-0.297601\pi$
$653$	5591.70	+	2692.82i	0.335100	+	0.161376i	−0.258765	+	0.965940i	$0.583316\pi$
$654$	−571.965	−	2505.94i	−0.0341981	−	0.149832i
$655$	34674.0			2.06844
$656$	−811.873			−0.0483206
$657$	−2943.45	−	12896.1i	−0.174787	−	0.765791i
$658$	−408.853	+	283.962i	−0.0242230	+	0.0168237i
$659$	−2500.74	+	10956.5i	−0.147822	+	0.647653i	0.845665	+	0.533714i	$0.179204\pi$
$659$	−2500.74	+	10956.5i	−0.147822	+	0.647653i	−0.993488	+	0.113939i	$0.963653\pi$
$660$	6245.38	−	27362.8i	0.368335	−	1.61378i
$661$	−5305.30	+	6652.64i	−0.312182	+	0.391464i	−0.913025	−	0.407903i	$-0.866260\pi$
$661$	−5305.30	+	6652.64i	−0.312182	+	0.391464i	0.600843	+	0.799367i	$0.294832\pi$
$662$	−171.724	+	215.335i	−0.0100819	+	0.0126424i
$663$	−2083.27	+	9127.40i	−0.122032	+	0.534659i
$664$	−130.535	+	571.910i	−0.00762911	+	0.0334253i
$665$	−583.578	−	174.497i	−0.0340303	−	0.0101755i
$666$	848.091	+	3715.73i	0.0493436	+	0.216189i
$667$	−12614.6			−0.732295
$668$	−18353.7			−1.06306
$669$	3625.11	+	15882.6i	0.209499	+	0.917875i
$670$	911.844	+	439.121i	0.0525785	+	0.0253205i
$671$	−1625.09	+	2037.80i	−0.0934962	+	0.117241i
$672$	573.377	−	8655.13i	0.0329144	−	0.496844i
$673$	11165.4	+	14001.0i	0.639518	+	0.801930i	0.990943	−	0.134286i	$-0.0428741\pi$
$673$	11165.4	+	14001.0i	0.639518	+	0.801930i	−0.351425	+	0.936216i	$0.614303\pi$
$674$	−293.799	−	1287.22i	−0.0167904	−	0.0735635i
$675$	35864.0	+	44972.0i	2.04504	+	2.56440i
$676$	−13612.2	−	6555.27i	−0.774474	−	0.372967i
$677$	−4151.85	+	5206.26i	−0.235700	+	0.295558i	−0.885588	−	0.464472i	$-0.846244\pi$
$677$	−4151.85	+	5206.26i	−0.235700	+	0.295558i	0.649888	+	0.760030i	$0.274816\pi$
$678$	−3757.88	+	1809.70i	−0.212862	+	0.102509i
$679$	16932.2	+	15440.4i	0.956994	+	0.872680i
$680$	3078.99	+	1482.76i	0.173638	+	0.0836197i
$681$	−39706.4	+	19121.6i	−2.23429	+	1.07598i
$682$	191.098	−	837.254i	0.0107295	−	0.0470090i
$683$	−29390.6	+	14153.8i	−1.64656	+	0.792941i	−0.647023	+	0.762471i	$0.723986\pi$
$683$	−29390.6	+	14153.8i	−1.64656	+	0.792941i	−0.999536	+	0.0304702i	$0.990300\pi$
$684$	−744.643	−	933.753i	−0.0416259	−	0.0521973i
$685$	−22548.3			−1.25771
$686$	1568.49	−	40.7087i	0.0872962	−	0.00226569i
$687$	−45612.1			−2.53306
$688$	−13458.2	−	16876.1i	−0.745769	−	0.935165i
$689$	3326.80	−	1602.10i	0.183949	−	0.0885852i
$690$	−877.997	+	3846.76i	−0.0484417	+	0.212237i
$691$	−17034.8	+	8203.51i	−0.937819	+	0.451630i	−0.839399	−	0.543515i	$-0.817093\pi$
$691$	−17034.8	+	8203.51i	−0.937819	+	0.451630i	−0.0984195	+	0.995145i	$0.531379\pi$
$692$	12900.2	+	6212.39i	0.708657	+	0.341271i
$693$	22179.2	+	20225.2i	1.21576	+	1.10864i
$694$	1497.71	−	721.260i	0.0819198	−	0.0394505i
$695$	−762.604	+	956.276i	−0.0416219	+	0.0521922i
$696$	4422.46	+	2129.74i	0.240852	+	0.115988i
$697$	442.981	+	555.481i	0.0240733	+	0.0301870i
$698$	597.078	+	2615.97i	0.0323779	+	0.141857i
$699$	7331.47	+	9193.38i	0.396712	+	0.497461i
$700$	−1230.14	+	18568.9i	−0.0664212	+	1.00263i
$701$	12369.6	−	15510.9i	0.666465	−	0.835720i	−0.327565	−	0.944829i	$-0.606228\pi$
$701$	12369.6	−	15510.9i	0.666465	−	0.835720i	0.994030	+	0.109108i	$0.0347996\pi$
$702$	1733.93	+	835.018i	0.0932237	+	0.0448942i
$703$	98.1386	+	429.973i	0.00526510	+	0.0230679i
$704$	10917.9			0.584491
$705$	17221.1			0.919977
$706$	55.0380	+	241.137i	0.00293397	+	0.0128546i
$707$	22094.8	+	6606.61i	1.17533	+	0.351439i
$708$	−138.754	+	607.922i	−0.00736540	+	0.0322699i
$709$	6163.71	−	27005.0i	0.326492	−	1.43046i	−0.499275	−	0.866444i	$-0.666400\pi$
$709$	6163.71	−	27005.0i	0.326492	−	1.43046i	0.825767	−	0.564011i	$-0.190743\pi$
$710$	902.715	−	1131.97i	0.0477159	−	0.0598338i
$711$	62280.6	−	78097.4i	3.28510	−	4.11938i
$712$	1018.98	−	4464.43i	0.0536345	−	0.234988i
$713$	3496.09	−	15317.4i	0.183632	−	0.804543i
$714$	−2051.62	+	1424.92i	−0.107535	+	0.0746866i
$715$	1351.78	+	5922.54i	0.0707045	+	0.309777i
$716$	28438.9			1.48438
$717$	−11733.0			−0.611124
$718$	−691.632	−	3030.24i	−0.0359491	−	0.157503i
$719$	−5998.04	−	2888.51i	−0.311112	−	0.149823i	0.271812	−	0.962350i	$-0.412377\pi$
$719$	−5998.04	−	2888.51i	−0.311112	−	0.149823i	−0.582924	+	0.812527i	$0.698091\pi$
$720$	−44869.1	+	56264.0i	−2.32246	+	2.91227i
$721$	11747.9	+	3512.76i	0.606817	+	0.181445i
$722$	−1055.61	−	1323.70i	−0.0544125	−	0.0682311i
$723$	−6387.26	−	27984.4i	−0.328554	−	1.43949i
$724$	−8213.74	−	10299.7i	−0.421632	−	0.528710i
$725$	−14250.2	−	6862.55i	−0.729987	−	0.351543i
$726$	−1278.29	+	1602.92i	−0.0653468	+	0.0819423i
$727$	13986.2	−	6735.38i	0.713504	−	0.343606i	−0.0416683	−	0.999132i	$-0.513267\pi$
$727$	13986.2	−	6735.38i	0.713504	−	0.343606i	0.755173	+	0.655526i	$0.227553\pi$
$728$	466.742	+	1159.64i	0.0237618	+	0.0590374i
$729$	−58048.2	−	27954.5i	−2.94915	−	1.42024i
$730$	643.541	−	309.913i	0.0326281	−	0.0157129i
$731$	−4203.36	+	18416.1i	−0.212677	+	0.931798i
$732$	8326.61	−	4009.89i	0.420438	−	0.202472i
$733$	20008.2	+	25089.5i	1.00821	+	1.26426i	0.964186	+	0.265228i	$0.0854471\pi$
$733$	20008.2	+	25089.5i	1.00821	+	1.26426i	0.0440262	+	0.999030i	$0.485981\pi$
$734$	1937.50			0.0974309
$735$	−45370.7	−	29796.8i	−2.27690	−	1.49533i
$736$	−4738.55			−0.237317
$737$	−3598.32	−	4512.15i	−0.179845	−	0.225519i
$738$	209.587	−	100.932i	0.0104539	−	0.00503435i
$739$	−3541.52	+	15516.4i	−0.176288	+	0.772368i	0.807035	+	0.590503i	$0.201071\pi$
$739$	−3541.52	+	15516.4i	−0.176288	+	0.772368i	−0.983323	+	0.181865i	$0.941787\pi$
$740$	24129.8	−	11620.3i	1.19869	−	0.577257i
$741$	319.581	+	153.902i	0.0158436	+	0.00762986i
$742$	943.894	+	282.235i	0.0467000	+	0.0139639i
$743$	30843.0	−	14853.2i	1.52291	−	0.733393i	0.529530	−	0.848291i	$-0.322368\pi$
$743$	30843.0	−	14853.2i	1.52291	−	0.733393i	0.993377	+	0.114898i	$0.0366540\pi$
$744$	−3811.71	+	4779.73i	−0.187828	+	0.235529i
$745$	12842.9	+	6184.80i	0.631579	+	0.304152i
$746$	−855.418	−	1072.66i	−0.0419827	−	0.0526446i
$747$	2405.54	+	10539.4i	0.117824	+	0.516219i
$748$	−6051.91	−	7588.86i	−0.295829	−	0.370957i
$749$	−34318.7	+	5476.69i	−1.67420	+	0.267175i
$750$	−38.2242	+	47.9316i	−0.00186100	+	0.00233362i
$751$	−19904.3	−	9585.40i	−0.967134	−	0.465747i	−0.117473	−	0.993076i	$-0.537479\pi$
$751$	−19904.3	−	9585.40i	−0.967134	−	0.465747i	−0.849661	+	0.527329i	$0.823194\pi$
$752$	1514.39	+	6634.99i	0.0734365	+	0.321746i
$753$	29078.7			1.40729
$754$	−529.183			−0.0255593
$755$	7291.98	+	31948.2i	0.351500	+	1.54002i
$756$	−24949.7	−	61988.9i	−1.20028	−	2.98216i
$757$	5978.29	−	26192.6i	0.287034	−	1.25758i	−0.601539	−	0.798843i	$-0.705446\pi$
$757$	5978.29	−	26192.6i	0.287034	−	1.25758i	0.888573	−	0.458735i	$-0.151697\pi$
$758$	−360.885	+	1581.14i	−0.0172928	+	0.0757646i
$759$	14028.5	−	17591.2i	0.670887	−	0.841265i
$760$	80.7279	−	101.230i	0.00385304	−	0.00483156i
$761$	−3482.77	+	15259.0i	−0.165900	+	0.726857i	0.821707	+	0.569911i	$0.193022\pi$
$761$	−3482.77	+	15259.0i	−0.165900	+	0.726857i	−0.987607	+	0.156947i	$0.949835\pi$
$762$	838.355	−	3673.07i	0.0398562	−	0.174621i
$763$	1276.89	−	19274.7i	0.0605854	−	0.914537i
$764$	5074.93	+	22234.7i	0.240320	+	1.05291i
$765$	62977.5			2.97641
$766$	−2369.98			−0.111789
$767$	−30.0326	−	131.582i	−0.00141384	−	0.00619444i
$768$	−34044.6	−	16395.0i	−1.59958	−	0.770319i
$769$	−4026.14	+	5048.62i	−0.188799	+	0.236746i	−0.867218	−	0.497929i	$-0.834094\pi$
$769$	−4026.14	+	5048.62i	−0.188799	+	0.236746i	0.678419	+	0.734675i	$0.262665\pi$
$770$	−798.243	+	1410.63i

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)

\(f(q)\)	\(=\)	\(q+(0.153998 + 0.193108i) q^{2} +(-8.98937 + 4.32905i) q^{3} +(1.76659 - 7.73995i) q^{4} +(14.2902 - 6.88179i) q^{5} +(-2.22032 - 1.06925i) q^{6} +(-13.6848 - 12.4791i) q^{7} +(3.54697 - 1.70813i) q^{8} +(45.2339 - 56.7215i) q^{9} +O(q^{10})\)	\(q+(0.153998 + 0.193108i) q^{2} +(-8.98937 + 4.32905i) q^{3} +(1.76659 - 7.73995i) q^{4} +(14.2902 - 6.88179i) q^{5} +(-2.22032 - 1.06925i) q^{6} +(-13.6848 - 12.4791i) q^{7} +(3.54697 - 1.70813i) q^{8} +(45.2339 - 56.7215i) q^{9} +(3.52959 + 1.69976i) q^{10} +(-13.9285 - 17.4658i) q^{11} +(17.6261 + 77.2249i) q^{12} +(-10.6896 - 13.4043i) q^{13} +(0.302377 - 4.56439i) q^{14} +(-98.6682 + 123.726i) q^{15} +(-56.3462 - 27.1349i) q^{16} +(12.1785 + 53.3575i) q^{17} +17.9193 q^{18} +2.07357 q^{19} +(-28.0198 - 122.763i) q^{20} +(177.040 + 52.9370i) q^{21} +(1.22781 - 5.37940i) q^{22} +(22.4625 - 98.4148i) q^{23} +(-24.4904 + 30.7100i) q^{24} +(78.9141 - 98.9552i) q^{25} +(0.942301 - 4.12849i) q^{26} +(-101.129 + 443.074i) q^{27} +(-120.763 + 83.8739i) q^{28} +(-27.8072 - 121.831i) q^{29} -39.0872 q^{30} +155.641 q^{31} +(-10.4455 - 45.7647i) q^{32} +(200.819 + 96.7092i) q^{33} +(-8.42828 + 10.5687i) q^{34} +(-281.436 - 84.1527i) q^{35} +(-359.112 - 450.312i) q^{36} +(47.3283 + 207.359i) q^{37} +(0.319326 + 0.400423i) q^{38} +(154.121 + 74.2207i) q^{39} +(38.9318 - 48.8190i) q^{40} +(11.6961 - 5.63257i) q^{41} +(17.0413 + 42.3400i) q^{42} +(310.966 + 149.753i) q^{43} +(-159.790 + 76.9509i) q^{44} +(256.055 - 1121.85i) q^{45} +(22.4639 - 10.8180i) q^{46} +(-67.8488 - 85.0797i) q^{47} +623.986 q^{48} +(31.5452 + 341.546i) q^{49} +31.2617 q^{50} +(-340.464 - 426.929i) q^{51} +(-122.633 + 59.0569i) q^{52} +(-47.9243 + 209.970i) q^{53} +(-101.135 + 48.7039i) q^{54} +(-319.237 - 153.736i) q^{55} +(-69.8553 - 20.8876i) q^{56} +(-18.6401 + 8.97660i) q^{57} +(19.2443 - 24.1316i) q^{58} +(7.09251 + 3.41558i) q^{59} +(783.326 + 982.260i) q^{60} +(-25.9624 - 113.749i) q^{61} +(23.9684 + 30.0554i) q^{62} +(-1326.85 + 211.743i) q^{63} +(-304.713 + 382.098i) q^{64} +(-245.002 - 117.987i) q^{65} +(12.2505 + 53.6727i) q^{66} +258.343 q^{67} +434.498 q^{68} +(224.119 + 981.929i) q^{69} +(-27.0902 - 67.3069i) q^{70} +(82.2389 - 360.312i) q^{71} +(63.5555 - 278.455i) q^{72} +(113.679 - 142.549i) q^{73} +(-32.7541 + 41.0724i) q^{74} +(-281.006 + 1231.17i) q^{75} +(3.66315 - 16.0493i) q^{76} +(-27.3488 + 412.830i) q^{77} +(9.40176 + 41.1918i) q^{78} +1376.86 q^{79} -991.935 q^{80} +(-573.124 - 2511.02i) q^{81} +(2.88888 + 1.39121i) q^{82} +(-92.9045 + 116.499i) q^{83} +(722.487 - 1276.76i) q^{84} +(541.228 + 678.678i) q^{85} +(18.9697 + 83.1117i) q^{86} +(777.384 + 974.809i) q^{87} +(-79.2378 - 38.1589i) q^{88} +(725.229 - 909.408i) q^{89} +(256.070 - 123.317i) q^{90} +(-20.9892 + 316.831i) q^{91} +(-722.043 - 347.718i) q^{92} +(-1399.11 + 673.777i) q^{93} +(5.98095 - 26.2043i) q^{94} +(29.6317 - 14.2699i) q^{95} +(292.016 + 366.177i) q^{96} -1237.31 q^{97} +(-61.0974 + 58.6892i) q^{98} -1620.73 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more