LMFDB - Embedded newform 169.4.e.f.147.4

Newspace parameters

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	169.e (of order $6$, degree $2$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$9.97132279097$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.1731891456.1
Defining polynomial:	$ x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 $ x^8 - 9x^6 + 65x^4 - 144*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			147.4
Root			$2.21837 + 1.28078i$ of defining polynomial
Character	$\chi$	$=$	169.147
Dual form			169.4.e.f.23.4

$q$-expansion

$f(q)$	$=$	$q+(2.21837 + 1.28078i) q^{2} +(1.84233 - 3.19101i) q^{3} +(-0.719224 - 1.24573i) q^{4} -0.561553i q^{5} +(8.17394 - 4.71922i) q^{6} +(15.7418 - 9.08854i) q^{7} -24.1771i q^{8} +(6.71165 + 11.6249i) q^{9} +O(q^{10})$	\(q+(2.21837 + 1.28078i) q^{2} +(1.84233 - 3.19101i) q^{3} +(-0.719224 - 1.24573i) q^{4} -0.561553i q^{5} +(8.17394 - 4.71922i) q^{6} +(15.7418 - 9.08854i) q^{7} -24.1771i q^{8} +(6.71165 + 11.6249i) q^{9} +(0.719224 - 1.24573i) q^{10} +(-56.0653 - 32.3693i) q^{11} -5.30019 q^{12} +46.5616 q^{14} +(-1.79192 - 1.03457i) q^{15} +(25.2116 - 43.6679i) q^{16} +(-12.7732 - 22.1238i) q^{17} +34.3845i q^{18} +(93.5045 - 53.9848i) q^{19} +(-0.699544 + 0.403882i) q^{20} -66.9763i q^{21} +(-82.9157 - 143.614i) q^{22} +(36.6307 - 63.4462i) q^{23} +(-77.1493 - 44.5421i) q^{24} +124.685 q^{25} +148.946 q^{27} +(-22.6438 - 13.0734i) q^{28} +(-87.9545 + 152.342i) q^{29} +(-2.65009 - 4.59010i) q^{30} +113.093i q^{31} +(-55.6462 + 32.1274i) q^{32} +(-206.581 + 119.270i) q^{33} -65.4384i q^{34} +(-5.10370 - 8.83986i) q^{35} +(9.65435 - 16.7218i) q^{36} +(-99.4264 - 57.4039i) q^{37} +276.570 q^{38} -13.5767 q^{40} +(-60.3151 - 34.8229i) q^{41} +(85.7817 - 148.578i) q^{42} +(219.151 + 379.581i) q^{43} +93.1231i q^{44} +(6.52800 - 3.76894i) q^{45} +(162.521 - 93.8314i) q^{46} -31.9479i q^{47} +(-92.8963 - 160.901i) q^{48} +(-6.29686 + 10.9065i) q^{49} +(276.597 + 159.693i) q^{50} -94.1298 q^{51} +2.84658 q^{53} +(330.417 + 190.767i) q^{54} +(-18.1771 + 31.4836i) q^{55} +(-219.734 - 380.591i) q^{56} -397.831i q^{57} +(-390.231 + 225.300i) q^{58} +(62.0356 - 35.8163i) q^{59} +2.97633i q^{60} +(460.348 + 797.345i) q^{61} +(-144.847 + 250.882i) q^{62} +(211.307 + 121.998i) q^{63} -567.978 q^{64} -611.032 q^{66} +(-384.758 - 222.140i) q^{67} +(-18.3736 + 31.8240i) q^{68} +(-134.972 - 233.778i) q^{69} -26.1468i q^{70} +(469.142 - 270.859i) q^{71} +(281.056 - 162.268i) q^{72} +764.004i q^{73} +(-147.043 - 254.686i) q^{74} +(229.710 - 397.870i) q^{75} +(-134.501 - 77.6543i) q^{76} -1176.76 q^{77} -421.538 q^{79} +(-24.5218 - 14.1577i) q^{80} +(93.1932 - 161.415i) q^{81} +(-89.2007 - 154.500i) q^{82} -603.797i q^{83} +(-83.4346 + 48.1710i) q^{84} +(-12.4237 + 7.17283i) q^{85} +1122.73i q^{86} +(324.082 + 561.327i) q^{87} +(-782.596 + 1355.50i) q^{88} +(1004.49 + 579.941i) q^{89} +19.3087 q^{90} -105.383 q^{92} +(360.880 + 208.354i) q^{93} +(40.9181 - 70.8722i) q^{94} +(-30.3153 - 52.5077i) q^{95} +236.757i q^{96} +(-505.126 + 291.634i) q^{97} +(-27.9375 + 16.1298i) q^{98} -869.006i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 10 q^{3} - 14 q^{4} - 70 q^{9}+O(q^{10}) $ 8 * q - 10 * q^3 - 14 * q^4 - 70 * q^9	$ 8 q - 10 q^{3} - 14 q^{4} - 70 q^{9} + 14 q^{10} + 172 q^{12} + 356 q^{14} + 78 q^{16} + 38 q^{17} - 284 q^{22} + 392 q^{23} + 948 q^{25} + 1340 q^{27} + 88 q^{29} + 86 q^{30} - 214 q^{35} - 500 q^{36} + 1256 q^{38} - 356 q^{40} - 394 q^{42} + 574 q^{43} - 570 q^{48} + 766 q^{49} - 1924 q^{51} - 472 q^{53} + 36 q^{55} - 2030 q^{56} + 2116 q^{61} - 664 q^{62} - 3076 q^{64} - 3272 q^{66} + 422 q^{68} + 1592 q^{69} - 294 q^{74} - 1032 q^{75} - 3048 q^{77} - 4032 q^{79} - 244 q^{81} + 144 q^{82} + 5116 q^{87} - 2484 q^{88} - 1000 q^{90} - 3152 q^{92} + 1622 q^{94} - 292 q^{95}+O(q^{100}) $ 8 * q - 10 * q^3 - 14 * q^4 - 70 * q^9 + 14 * q^10 + 172 * q^12 + 356 * q^14 + 78 * q^16 + 38 * q^17 - 284 * q^22 + 392 * q^23 + 948 * q^25 + 1340 * q^27 + 88 * q^29 + 86 * q^30 - 214 * q^35 - 500 * q^36 + 1256 * q^38 - 356 * q^40 - 394 * q^42 + 574 * q^43 - 570 * q^48 + 766 * q^49 - 1924 * q^51 - 472 * q^53 + 36 * q^55 - 2030 * q^56 + 2116 * q^61 - 664 * q^62 - 3076 * q^64 - 3272 * q^66 + 422 * q^68 + 1592 * q^69 - 294 * q^74 - 1032 * q^75 - 3048 * q^77 - 4032 * q^79 - 244 * q^81 + 144 * q^82 + 5116 * q^87 - 2484 * q^88 - 1000 * q^90 - 3152 * q^92 + 1622 * q^94 - 292 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	2.21837	+	1.28078i	0.784312	+	0.452823i	0.837956	−	0.545737i	$-0.183750\pi$
$2$	2.21837	+	1.28078i	0.784312	+	0.452823i	−0.0536442	+	0.998560i	$0.517084\pi$
$3$	1.84233	−	3.19101i	0.354556	−	0.614110i	−0.632486	−	0.774572i	$-0.717965\pi$
$3$	1.84233	−	3.19101i	0.354556	−	0.614110i	0.987042	+	0.160462i	$0.0512985\pi$
$4$	−0.719224	−	1.24573i	−0.0899029	−	0.155716i
$5$		−	0.561553i		−	0.0502268i	−0.999685	−	0.0251134i	$-0.992005\pi$
$5$		−	0.561553i		−	0.0502268i	0.999685	−	0.0251134i	$-0.00799469\pi$
$6$	8.17394	−	4.71922i	0.556166	−	0.321102i
$7$	15.7418	−	9.08854i	0.849978	−	0.490735i	−0.0106654	−	0.999943i	$-0.503395\pi$
$7$	15.7418	−	9.08854i	0.849978	−	0.490735i	0.860643	+	0.509208i	$0.170062\pi$
$8$		−	24.1771i		−	1.06849i
$9$	6.71165	+	11.6249i	0.248579	+	0.430552i
$10$	0.719224	−	1.24573i	0.0227438	−	0.0393935i
$11$	−56.0653	−	32.3693i	−1.53676	−	0.887247i	−0.999026	−	0.0441305i	$-0.985948\pi$
$11$	−56.0653	−	32.3693i	−1.53676	−	0.887247i	−0.537731	−	0.843116i	$-0.680718\pi$
$12$	−5.30019			−0.127503
$13$		0			0
$13$		0			0
$14$	46.5616			0.888864
$15$	−1.79192	−	1.03457i	−0.0308448	−	0.0178082i
$16$	25.2116	−	43.6679i	0.393932	−	0.682310i
$17$	−12.7732	−	22.1238i	−0.182233	−	0.315636i	0.760408	−	0.649446i	$-0.224999\pi$
$17$	−12.7732	−	22.1238i	−0.182233	−	0.315636i	−0.942641	+	0.333810i	$0.891666\pi$
$18$			34.3845i			0.450250i
$19$	93.5045	−	53.9848i	1.12902	−	0.651841i	0.185333	−	0.982676i	$-0.440664\pi$
$19$	93.5045	−	53.9848i	1.12902	−	0.651841i	0.943689	+	0.330835i	$0.107330\pi$
$20$	−0.699544	+	0.403882i	−0.00782114	+	0.00451554i
$21$		−	66.9763i		−	0.695973i
$22$	−82.9157	−	143.614i	−0.803531	−	1.39176i
$23$	36.6307	−	63.4462i	0.332088	−	0.575193i	−0.650833	−	0.759221i	$-0.725580\pi$
$23$	36.6307	−	63.4462i	0.332088	−	0.575193i	0.982921	+	0.184027i	$0.0589135\pi$
$24$	−77.1493	−	44.5421i	−0.656168	−	0.378839i
$25$	124.685			0.997477
$26$		0			0
$27$	148.946			1.06165
$28$	−22.6438	−	13.0734i	−0.152831	−	0.0882371i
$29$	−87.9545	+	152.342i	−0.563198	+	0.975488i	0.434017	+	0.900905i	$0.357096\pi$
$29$	−87.9545	+	152.342i	−0.563198	+	0.975488i	−0.997215	+	0.0745830i	$0.976237\pi$
$30$	−2.65009	−	4.59010i	−0.0161280	−	0.0279344i
$31$			113.093i			0.655228i	0.944812	+	0.327614i	$0.106245\pi$
$31$			113.093i			0.655228i	−0.944812	+	0.327614i	$0.893755\pi$
$32$	−55.6462	+	32.1274i	−0.307405	+	0.177480i
$33$	−206.581	+	119.270i	−1.08973	+	0.629158i
$34$		−	65.4384i		−	0.330077i
$35$	−5.10370	−	8.83986i	−0.0246481	−	0.0426917i
$36$	9.65435	−	16.7218i	0.0446961	−	0.0774158i
$37$	−99.4264	−	57.4039i	−0.441773	−	0.255058i	0.262576	−	0.964911i	$-0.415428\pi$
$37$	−99.4264	−	57.4039i	−0.441773	−	0.255058i	−0.704349	+	0.709853i	$0.748761\pi$
$38$	276.570			1.18067
$39$		0			0
$40$	−13.5767			−0.0536666
$41$	−60.3151	−	34.8229i	−0.229747	−	0.132645i	0.380708	−	0.924695i	$-0.375680\pi$
$41$	−60.3151	−	34.8229i	−0.229747	−	0.132645i	−0.610455	+	0.792051i	$0.709014\pi$
$42$	85.7817	−	148.578i	0.315153	−	0.545860i
$43$	219.151	+	379.581i	0.777214	+	1.34617i	0.933541	+	0.358469i	$0.116701\pi$
$43$	219.151	+	379.581i	0.777214	+	1.34617i	−0.156327	+	0.987705i	$0.549965\pi$
$44$			93.1231i			0.319064i
$45$	6.52800	−	3.76894i	0.0216253	−	0.0124854i
$46$	162.521	−	93.8314i	0.520921	−	0.300754i
$47$		−	31.9479i		−	0.0991506i	−0.998770	−	0.0495753i	$-0.984213\pi$
$47$		−	31.9479i		−	0.0991506i	0.998770	−	0.0495753i	$-0.0157868\pi$
$48$	−92.8963	−	160.901i	−0.279342	−	0.483835i
$49$	−6.29686	+	10.9065i	−0.0183582	+	0.0317973i
$50$	276.597	+	159.693i	0.782334	+	0.451680i
$51$	−94.1298			−0.258447
$52$		0			0
$53$	2.84658			0.00737752			0.00368876	−	0.999993i	$-0.498826\pi$
$53$	2.84658			0.00737752			0.00368876	+	0.999993i	$0.498826\pi$
$54$	330.417	+	190.767i	0.832669	+	0.480741i
$55$	−18.1771	+	31.4836i	−0.0445636	+	0.0771864i
$56$	−219.734	−	380.591i	−0.524344	−	0.908190i
$57$		−	397.831i		−	0.924457i
$58$	−390.231	+	225.300i	−0.883446	+	0.510058i
$59$	62.0356	−	35.8163i	0.136887	−	0.0790319i	−0.429992	−	0.902832i	$-0.641484\pi$
$59$	62.0356	−	35.8163i	0.136887	−	0.0790319i	0.566880	+	0.823801i	$0.308150\pi$
$60$			2.97633i			0.00640405i
$61$	460.348	+	797.345i	0.966253	+	1.67360i	0.706209	+	0.708003i	$0.250404\pi$
$61$	460.348	+	797.345i	0.966253	+	1.67360i	0.260044	+	0.965597i	$0.416263\pi$
$62$	−144.847	+	250.882i	−0.296702	+	0.513903i
$63$	211.307	+	121.998i	0.422574	+	0.243973i
$64$	−567.978			−1.10933
$65$		0			0
$66$	−611.032			−1.13959
$67$	−384.758	−	222.140i	−0.701577	−	0.405056i	0.106357	−	0.994328i	$-0.466081\pi$
$67$	−384.758	−	222.140i	−0.701577	−	0.405056i	−0.807935	+	0.589272i	$0.799415\pi$
$68$	−18.3736	+	31.8240i	−0.0327665	+	0.0567533i
$69$	−134.972	−	233.778i	−0.235488	−	0.407877i
$70$		−	26.1468i		−	0.0446448i
$71$	469.142	−	270.859i	0.784182	−	0.452748i	−0.0537283	−	0.998556i	$-0.517110\pi$
$71$	469.142	−	270.859i	0.784182	−	0.452748i	0.837910	+	0.545808i	$0.183777\pi$
$72$	281.056	−	162.268i	0.460039	−	0.265604i
$73$			764.004i			1.22493i	0.790498	+	0.612465i	$0.209822\pi$
$73$			764.004i			1.22493i	−0.790498	+	0.612465i	$0.790178\pi$
$74$	−147.043	−	254.686i	−0.230992	−	0.400090i
$75$	229.710	−	397.870i	0.353662	−	0.612561i
$76$	−134.501	−	77.6543i	−0.203005	−	0.117205i
$77$	−1176.76			−1.74161
$78$		0			0
$79$	−421.538			−0.600338			−0.300169	−	0.953886i	$-0.597043\pi$
$79$	−421.538			−0.600338			−0.300169	+	0.953886i	$0.597043\pi$
$80$	−24.5218	−	14.1577i	−0.0342703	−	0.0197859i
$81$	93.1932	−	161.415i	0.127837	−	0.221420i
$82$	−89.2007	−	154.500i	−0.120129	−	0.208069i
$83$		−	603.797i		−	0.798498i	−0.916842	−	0.399249i	$-0.869271\pi$
$83$		−	603.797i		−	0.798498i	0.916842	−	0.399249i	$-0.130729\pi$
$84$	−83.4346	+	48.1710i	−0.108374	+	0.0625700i
$85$	−12.4237	+	7.17283i	−0.0158534	+	0.00915297i
$86$			1122.73i			1.40776i
$87$	324.082	+	561.327i	0.399371	+	0.691731i
$88$	−782.596	+	1355.50i	−0.948011	+	1.64200i
$89$	1004.49	+	579.941i	1.19635	+	0.690715i	0.959740	−	0.280889i	$-0.0906292\pi$
$89$	1004.49	+	579.941i	1.19635	+	0.690715i	0.236613	+	0.971604i	$0.423963\pi$
$90$	19.3087			0.0226146
$91$		0			0
$92$	−105.383			−0.119423
$93$	360.880	+	208.354i	0.402382	+	0.232315i
$94$	40.9181	−	70.8722i	0.0448977	−	0.0777650i
$95$	−30.3153	−	52.5077i	−0.0327399	−	0.0567071i
$96$			236.757i			0.251707i
$97$	−505.126	+	291.634i	−0.528740	+	0.305268i	−0.740503	−	0.672053i	$-0.765413\pi$
$97$	−505.126	+	291.634i	−0.528740	+	0.305268i	0.211763	+	0.977321i	$0.432079\pi$
$98$	−27.9375	+	16.1298i	−0.0287971	+	0.0166260i
$99$		−	869.006i		−	0.882206i
$100$	−89.6761	−	155.324i	−0.0896761	−	0.155324i
$101$	460.870	−	798.251i	0.454043	−	0.786425i	−0.544590	−	0.838702i	$-0.683315\pi$
$101$	460.870	−	798.251i	0.454043	−	0.786425i	0.998633	+	0.0522775i	$0.0166480\pi$
$102$	−208.815	−	120.559i	−0.202703	−	0.117031i
$103$	930.712			0.890347			0.445174	−	0.895444i	$-0.353142\pi$
$103$	930.712			0.890347			0.445174	+	0.895444i	$0.353142\pi$
$104$		0			0
$105$	−37.6107			−0.0349565
$106$	6.31478	+	3.64584i	0.00578628	+	0.00334071i
$107$	−428.691	+	742.515i	−0.387319	+	0.670857i	−0.992088	−	0.125545i	$-0.959932\pi$
$107$	−428.691	+	742.515i	−0.387319	+	0.670857i	0.604769	+	0.796401i	$0.293266\pi$
$108$	−107.125	−	185.547i	−0.0954459	−	0.165317i
$109$		−	671.853i		−	0.590384i	−0.955438	−	0.295192i	$-0.904616\pi$
$109$		−	671.853i		−	0.590384i	0.955438	−	0.295192i	$-0.0953836\pi$
$110$	−80.6470	+	46.5616i	−0.0699035	+	0.0403588i
$111$	−366.352	+	211.514i	−0.313267	+	0.180865i
$112$		−	916.548i		−	0.773265i
$113$	−320.737	−	555.532i	−0.267012	−	0.462479i	0.701077	−	0.713086i	$-0.252703\pi$
$113$	−320.737	−	555.532i	−0.267012	−	0.462479i	−0.968089	+	0.250607i	$0.919370\pi$
$114$	509.533	−	882.537i	0.418615	−	0.725063i
$115$	−35.6284	−	20.5701i	−0.0288901	−	0.0166797i
$116$	253.036			0.202533
$117$		0			0
$118$	183.491			0.143150
$119$	−402.147	−	232.179i	−0.309788	−	0.178856i
$120$	−25.0128	+	43.3234i	−0.0190279	+	0.0329572i
$121$	1430.05	+	2476.91i	1.07441	+	1.86094i
$122$			2358.41i			1.75017i
$123$	−222.240	+	128.311i	−0.162917	+	0.0940599i
$124$	140.883	−	81.3390i	0.102030	−	0.0589069i
$125$		−	140.211i		−	0.100327i
$126$	312.505	+	541.274i	0.220953	+	0.382703i
$127$	−276.587	+	479.063i	−0.193253	+	0.334724i	−0.946326	−	0.323212i	$-0.895237\pi$
$127$	−276.587	+	479.063i	−0.193253	+	0.334724i	0.753073	+	0.657937i	$0.228570\pi$
$128$	−814.816	−	470.434i	−0.562658	−	0.324851i
$129$	1614.99			1.10227
$130$		0			0
$131$	2056.40			1.37152			0.685758	−	0.727830i	$-0.259471\pi$
$131$	2056.40			1.37152			0.685758	+	0.727830i	$0.259471\pi$
$132$	297.157	+	171.563i	0.195941	+	0.113126i
$133$	981.287	−	1699.64i	0.639762	−	1.10810i
$134$	−569.024	−	985.578i	−0.366837	−	0.635380i
$135$		−	83.6411i		−	0.0533235i
$136$	−534.890	+	308.819i	−0.337253	+	0.194713i
$137$	−1566.26	+	904.283i	−0.976752	+	0.563928i	−0.901288	−	0.433221i	$-0.857377\pi$
$137$	−1566.26	+	904.283i	−0.976752	+	0.563928i	−0.0754639	+	0.997149i	$0.524044\pi$
$138$		−	691.474i		−	0.426537i
$139$	−746.818	−	1293.53i	−0.455714	−	0.789320i	0.543015	−	0.839723i	$-0.317283\pi$
$139$	−746.818	−	1293.53i	−0.455714	−	0.789320i	−0.998729	+	0.0504032i	$0.983949\pi$
$140$	−7.34140	+	12.7157i	−0.00443187	+	0.00767622i
$141$	−101.946	−	58.8585i	−0.0608894	−	0.0351545i
$142$	1387.64			0.820058
$143$		0			0
$144$	676.847			0.391694
$145$	85.5479	+	49.3911i	0.0489956	+	0.0282876i
$146$	−978.518	+	1694.84i	−0.554676	+	0.960727i
$147$	23.2018	+	40.1867i	0.0130180	+	0.0225479i
$148$			165.145i			0.0917218i
$149$	2389.38	−	1379.51i	1.31373	−	0.758482i	0.331018	−	0.943625i	$-0.392608\pi$
$149$	2389.38	−	1379.51i	1.31373	−	0.758482i	0.982712	+	0.185143i	$0.0592747\pi$
$150$	1019.16	−	588.415i	0.554763	−	0.320292i
$151$		−	976.355i		−	0.526190i	−0.964770	−	0.263095i	$-0.915257\pi$
$151$		−	976.355i		−	0.526190i	0.964770	−	0.263095i	$-0.0847432\pi$
$152$	−1305.20	−	2260.67i	−0.696483	−	1.20634i
$153$	171.458	−	296.975i	0.0905986	−	0.156921i
$154$	−2610.49	−	1507.17i	−1.36597	−	0.788642i
$155$	63.5076			0.0329100
$156$		0			0
$157$	−564.875			−0.287146			−0.143573	−	0.989640i	$-0.545859\pi$
$157$	−564.875			−0.287146			−0.143573	+	0.989640i	$0.545859\pi$
$158$	−935.127	−	539.896i	−0.470853	−	0.271847i
$159$	5.24435	−	9.08347i	0.00261575	−	0.00453061i
$160$	18.0412	+	31.2483i	0.00891427	+	0.0154400i
$161$		−	1331.68i		−	0.651869i
$162$	413.474	−	238.719i	0.200528	−	0.115775i
$163$	1306.43	−	754.266i	0.627775	−	0.362446i	−0.152115	−	0.988363i	$-0.548608\pi$
$163$	1306.43	−	754.266i	0.627775	−	0.362446i	0.779890	+	0.625917i	$0.215275\pi$
$164$			100.182i			0.0477005i
$165$	66.9763	+	116.006i	0.0316006	+	0.0547339i
$166$	773.329	−	1339.45i	0.361578	−	0.626272i
$167$	−513.138	−	296.260i	−0.237771	−	0.137277i	0.376381	−	0.926465i	$-0.377168\pi$
$167$	−513.138	−	296.260i	−0.237771	−	0.137277i	−0.614152	+	0.789188i	$0.710502\pi$
$168$	−1619.29			−0.743638
$169$		0			0
$170$	−36.7471			−0.0165787
$171$	1255.14	+	724.654i	0.561303	+	0.324068i
$172$	315.237	−	546.007i	0.139748	−	0.242050i
$173$	−2247.78	−	3893.28i	−0.987838	−	1.71099i	−0.628576	−	0.777748i	$-0.716362\pi$
$173$	−2247.78	−	3893.28i	−0.987838	−	1.71099i	−0.359262	−	0.933237i	$-0.616972\pi$
$174$			1660.31i			0.723377i
$175$	1962.76	−	1133.20i	0.847834	−	0.489497i
$176$	−2827.00	+	1632.17i	−1.21076	+	0.699030i
$177$		−	263.941i		−	0.112085i
$178$	1485.55	+	2573.05i	0.625543	+	1.08347i
$179$	−77.1425	+	133.615i	−0.0322117	+	0.0557924i	−0.881682	−	0.471844i	$-0.843588\pi$
$179$	−77.1425	+	133.615i	−0.0322117	+	0.0557924i	0.849470	+	0.527637i	$0.176922\pi$
$180$	−9.39019	−	5.42143i	−0.00388835	−	0.00224494i
$181$	−1071.35			−0.439959			−0.219979	−	0.975505i	$-0.570599\pi$
$181$	−1071.35			−0.439959			−0.219979	+	0.975505i	$0.570599\pi$
$182$		0			0
$183$	3392.45			1.37037
$184$	−1533.94	−	885.623i	−0.614586	−	0.354831i
$185$	−32.2353	+	55.8332i	−0.0128107	+	0.0221889i
$186$	533.710	+	924.413i	0.210395	+	0.364415i
$187$			1653.84i			0.646742i
$188$	−39.7985	+	22.9777i	−0.0154394	+	0.00891393i
$189$	2344.68	−	1353.70i	0.902383	−	0.520991i
$190$		−	155.309i		−	0.0593015i
$191$	−338.601	−	586.475i	−0.128274	−	0.222177i	0.794734	−	0.606958i	$-0.207610\pi$
$191$	−338.601	−	586.475i	−0.128274	−	0.222177i	−0.923008	+	0.384781i	$0.874277\pi$
$192$	−1046.40	+	1812.42i	−0.393321	+	0.681252i
$193$	−1144.61	−	660.840i	−0.426895	−	0.246468i	0.271128	−	0.962543i	$-0.412603\pi$
$193$	−1144.61	−	660.840i	−0.426895	−	0.246468i	−0.698023	+	0.716075i	$0.745937\pi$
$194$	−1494.07			−0.552929
$195$		0			0
$196$	18.1154			0.00660183
$197$	1097.57	+	633.683i	0.396948	+	0.229178i	0.685166	−	0.728387i	$-0.259730\pi$
$197$	1097.57	+	633.683i	0.396948	+	0.229178i	−0.288218	+	0.957565i	$0.593063\pi$
$198$	1113.00	−	1927.78i	0.399483	−	0.691925i
$199$	1198.12	+	2075.21i	0.426796	+	0.739233i	0.996586	−	0.0825573i	$-0.0263088\pi$
$199$	1198.12	+	2075.21i	0.426796	+	0.739233i	−0.569790	+	0.821790i	$0.692975\pi$
$200$		−	3014.51i		−	1.06579i
$201$	−1417.70	+	818.510i	−0.497497	+	0.287230i
$202$	2044.76	−	1180.54i	0.712222	−	0.411202i
$203$			3197.51i			1.10552i
$204$	67.7003	+	117.260i	0.0232352	+	0.0402445i
$205$	−19.5549	+	33.8701i	−0.00666231	+	0.0115395i
$206$	2064.66	+	1192.03i	0.698310	+	0.403170i
$207$	983.409			0.330201
$208$		0			0
$209$	−6989.81			−2.31337
$210$	−83.4346	−	48.1710i	−0.0274168	−	0.0158291i
$211$	45.7769	−	79.2880i	0.0149356	−	0.0258692i	−0.858461	−	0.512879i	$-0.828579\pi$
$211$	45.7769	−	79.2880i	0.0149356	−	0.0258692i	0.873397	+	0.487010i	$0.161912\pi$
$212$	−2.04733	−	3.54608i	−0.000663261	−	0.00114880i
$213$		−	1996.05i		−	0.642099i
$214$	−1901.99	+	1098.12i	−0.607558	+	0.350774i
$215$	213.155	−	123.065i	0.0676141	−	0.0390370i
$216$		−	3601.08i		−	1.13436i
$217$	1027.85	+	1780.29i	0.321543	+	0.556929i
$218$	860.494	−	1490.42i	0.267339	−	0.463045i
$219$	2437.94	+	1407.55i	0.752241	+	0.434307i
$220$	52.2935			0.0160256
$221$		0			0
$222$	−1083.61			−0.327599
$223$	1069.90	+	617.709i	0.321282	+	0.185493i	0.651964	−	0.758250i	$-0.273945\pi$
$223$	1069.90	+	617.709i	0.321282	+	0.185493i	−0.330682	+	0.943742i	$0.607279\pi$
$224$	−583.982	+	1011.49i	−0.174192	+	0.301709i
$225$	836.839	+	1449.45i	0.247952	+	0.429466i
$226$		−	1643.17i		−	0.483637i
$227$	−2859.32	+	1650.83i	−0.836035	+	0.482685i	−0.855914	−	0.517118i	$-0.827005\pi$
$227$	−2859.32	+	1650.83i	−0.836035	+	0.482685i	0.0198797	+	0.999802i	$0.493672\pi$
$228$	−495.591	+	286.130i	−0.143953	+	0.0831114i
$229$			211.283i			0.0609694i	0.999535	+	0.0304847i	$0.00970508\pi$
$229$			211.283i			0.0609694i	−0.999535	+	0.0304847i	$0.990295\pi$
$230$	−52.6913	−	91.2640i	−0.0151059	−	0.0261642i
$231$	−2167.98	+	3755.05i	−0.617500	+	1.06954i
$232$	3683.18	+	2126.48i	1.04230	+	0.601769i
$233$	256.724			0.0721827			0.0360913	−	0.999348i	$-0.488509\pi$
$233$	256.724			0.0721827			0.0360913	+	0.999348i	$0.488509\pi$
$234$		0			0
$235$	−17.9404			−0.00498002
$236$	−89.2349	−	51.5198i	−0.0246131	−	0.0142104i
$237$	−776.612	+	1345.13i	−0.212854	+	0.368674i
$238$	−594.740	−	1030.12i	−0.161980	−	0.280558i
$239$			3549.62i			0.960694i	0.877078	+	0.480347i	$0.159489\pi$
$239$			3549.62i			0.960694i	−0.877078	+	0.480347i	$0.840511\pi$
$240$	−90.3545	+	52.1662i	−0.0243015	+	0.0140305i
$241$	−4356.19	+	2515.05i	−1.16434	+	0.672235i	−0.952341	−	0.305034i	$-0.901332\pi$
$241$	−4356.19	+	2515.05i	−1.16434	+	0.672235i	−0.212003	+	0.977269i	$0.567999\pi$
$242$			7326.27i			1.94608i
$243$	1667.39	+	2888.00i	0.440176	+	0.762408i
$244$	662.186	−	1146.94i	0.173738	−	0.300923i
$245$	6.12457	+	3.53602i	0.00159708	+	0.000922074i
$246$	−657.349			−0.170370
$247$		0			0
$248$	2734.25			0.700102
$249$	−1926.72	−	1112.39i	−0.490366	−	0.283113i
$250$	179.579	−	311.040i	0.0454303	−	0.0786876i
$251$	−359.392	−	622.485i	−0.0903770	−	0.156538i	0.817293	−	0.576223i	$-0.195474\pi$
$251$	−359.392	−	622.485i	−0.0903770	−	0.156538i	−0.907670	+	0.419685i	$0.862141\pi$
$252$		−	350.976i		−	0.0877357i
$253$	−4107.42	+	2371.42i	−1.02068	+	0.589288i
$254$	−1227.14	+	708.492i	−0.303141	+	0.175019i
$255$			52.8588i			0.0129810i
$256$	1066.87	+	1847.87i	0.260466	+	0.451141i
$257$	640.397	−	1109.20i	0.155435	−	0.269222i	−0.777782	−	0.628534i	$-0.783655\pi$
$257$	640.397	−	1109.20i	0.155435	−	0.269222i	0.933217	+	0.359312i	$0.116989\pi$
$258$	3582.65	+	2068.45i	0.864520	+	0.499131i
$259$	−2086.87			−0.500663
$260$		0			0
$261$	−2361.28			−0.559998
$262$	4561.86	+	2633.79i	1.07570	+	0.621054i
$263$	−2612.77	+	4525.46i	−0.612587	+	1.06103i	0.378215	+	0.925718i	$0.376538\pi$
$263$	−2612.77	+	4525.46i	−0.612587	+	1.06103i	−0.990803	+	0.135315i	$0.956795\pi$
$264$	2883.60	+	4994.54i	0.672247	+	1.16437i
$265$		−	1.59851i		−	0.000370549i
$266$	4353.71	−	2513.62i	1.00355	−	0.579398i
$267$	3701.19	−	2136.89i	0.848350	−	0.489795i
$268$			639.074i			0.145663i
$269$	−3221.90	−	5580.50i	−0.730270	−	1.26487i	−0.956768	−	0.290854i	$-0.906061\pi$
$269$	−3221.90	−	5580.50i	−0.730270	−	1.26487i	0.226497	−	0.974012i	$-0.427273\pi$
$270$	107.125	−	185.547i	0.0241461	−	0.0418223i
$271$	3403.42	+	1964.97i	0.762890	+	0.440455i	0.830332	−	0.557269i	$-0.188151\pi$
$271$	3403.42	+	1964.97i	0.762890	+	0.440455i	−0.0674426	+	0.997723i	$0.521484\pi$
$272$	−1288.13			−0.287149
$273$		0			0
$274$	−4632.74			−1.02144
$275$	−6990.48	−	4035.96i	−1.53288	−	0.885009i
$276$	−194.149	+	336.277i	−0.0423421	+	0.0733387i
$277$	−2942.20	−	5096.04i	−0.638194	−	1.10538i	−0.985829	−	0.167754i	$-0.946348\pi$
$277$	−2942.20	−	5096.04i	−0.638194	−	1.10538i	0.347635	−	0.937630i	$-0.386985\pi$
$278$		−	3826.03i		−	0.825431i
$279$	−1314.69	+	759.039i	−0.282110	+	0.162876i
$280$	−213.722	+	123.392i	−0.0456155	+	0.0263361i
$281$			3529.79i			0.749358i	0.927155	+	0.374679i	$0.122247\pi$
$281$			3529.79i			0.749358i	−0.927155	+	0.374679i	$0.877753\pi$
$282$	−150.769	−	261.140i	−0.0318375	−	0.0551442i
$283$	−1305.50	+	2261.19i	−0.274219	+	0.474961i	−0.969938	−	0.243353i	$-0.921753\pi$
$283$	−1305.50	+	2261.19i	−0.274219	+	0.474961i	0.695719	+	0.718314i	$0.255086\pi$
$284$	−674.836	−	389.617i	−0.141001	−	0.0814067i
$285$	−223.403			−0.0464325
$286$		0			0
$287$	−1265.96			−0.260373
$288$	−746.955	−	431.255i	−0.152829	−	0.0882359i
$289$	2130.19	−	3689.60i	0.433582	−	0.750987i
$290$	126.518	+	219.136i	0.0256186	+	0.0443727i
$291$			2149.15i			0.432939i
$292$	951.744	−	549.490i	0.190742	−	0.110125i
$293$	−4755.37	+	2745.51i	−0.948163	+	0.547422i	−0.892510	−	0.451028i	$-0.851057\pi$
$293$	−4755.37	+	2745.51i	−0.948163	+	0.547422i	−0.0556531	+	0.998450i	$0.517724\pi$
$294$			118.865i			0.0235795i
$295$	−20.1127	−	34.8363i	−0.00396952	−	0.00687541i
$296$	−1387.86	+	2403.84i	−0.272526	+	0.472028i
$297$	−8350.70	−	4821.28i	−1.63150	−	0.941950i
$298$	7067.37			1.37383
$299$		0			0
$300$	−660.852			−0.127181
$301$	6899.67	+	3983.53i	1.32123	+	0.762813i
$302$	1250.49	−	2165.92i	0.238271	−	0.412697i
$303$	−1698.15	−	2941.28i	−0.321967	−	0.557664i
$304$		−	5444.19i		−	1.02712i
$305$	447.751	−	258.509i	0.0840596	−	0.0485318i
$306$	760.716	−	439.200i	0.142115	−	0.0820502i
$307$		−	7307.59i		−	1.35852i	−0.733897	−	0.679261i	$-0.762300\pi$
$307$		−	7307.59i		−	1.35852i	0.733897	−	0.679261i	$-0.237700\pi$
$308$	846.353	+	1465.93i	0.156576	+	0.271198i
$309$	1714.68	−	2969.91i	0.315678	−	0.546771i
$310$	140.883	+	81.3390i	0.0258117	+	0.0149024i
$311$	−7904.92			−1.44131			−0.720654	−	0.693295i	$-0.756158\pi$
$311$	−7904.92			−1.44131			−0.720654	+	0.693295i	$0.756158\pi$
$312$		0			0
$313$	10002.4			1.80629			0.903145	−	0.429336i	$-0.141252\pi$
$313$	10002.4			1.80629			0.903145	+	0.429336i	$0.141252\pi$
$314$	−1253.10	−	723.478i	−0.225212	−	0.130026i
$315$	68.5084	−	118.660i	0.0122540	−	0.0212246i
$316$	303.180	+	525.123i	0.0539722	+	0.0934825i
$317$			6230.81i			1.10397i	0.833856	+	0.551983i	$0.186129\pi$
$317$			6230.81i			1.10397i	−0.833856	+	0.551983i	$0.813871\pi$
$318$	23.2678	−	13.4337i	0.00410312	−	0.00236894i
$319$	9862.40	−	5694.06i	1.73100	−	0.999392i
$320$			318.950i			0.0557182i
$321$	1579.58	+	2735.91i	0.274653	+	0.475713i
$322$	1705.58	−	2954.15i	0.295181	−	0.511269i
$323$	−2388.70	−	1379.12i	−0.411489	−	0.237573i
$324$	−268.107			−0.0459717
$325$		0			0
$326$	3864.19			0.656495
$327$	−2143.89	−	1237.77i	−0.362561	−	0.209324i
$328$	−841.917	+	1458.24i	−0.141729	+	0.245482i
$329$	−290.360	−	502.918i	−0.0486567	−	0.0842758i
$330$			343.127i			0.0572379i
$331$	4013.60	−	2317.25i	0.666488	−	0.384797i	−0.128257	−	0.991741i	$-0.540938\pi$
$331$	4013.60	−	2317.25i	0.666488	−	0.384797i	0.794745	+	0.606944i	$0.207605\pi$
$332$	−752.170	+	434.265i	−0.124339	+	0.0717874i
$333$		−	1541.10i		−	0.253609i
$334$	−758.886	−	1314.43i	−0.124325	−	0.215337i
$335$	−124.743	+	216.062i	−0.0203447	+	0.0352380i
$336$	−2924.71	−	1688.58i	−0.474870	−	0.274166i
$337$	−3029.82			−0.489747			−0.244874	−	0.969555i	$-0.578746\pi$
$337$	−3029.82			−0.489747			−0.244874	+	0.969555i	$0.578746\pi$
$338$		0			0
$339$	−2363.61			−0.378684
$340$	17.8708	+	10.3177i	0.00285054	+	0.00164576i
$341$	3660.74	−	6340.58i	0.581349	−	1.00693i
$342$	1856.24	+	3215.10i	0.293491	+	0.508342i
$343$			6463.66i			1.01751i
$344$	9177.15	−	5298.43i	1.43837	−	0.830443i
$345$	−131.278	+	75.7937i	−0.0204864	+	0.0118278i
$346$		−	11515.6i		−	1.78926i
$347$	−1420.80	−	2460.90i	−0.219805	−	0.380714i	0.734943	−	0.678129i	$-0.237209\pi$
$347$	−1420.80	−	2460.90i	−0.219805	−	0.380714i	−0.954748	+	0.297415i	$0.903876\pi$
$348$	466.175	−	807.440i	0.0718093	−	0.124377i
$349$	−6552.07	−	3782.84i	−1.00494	−	0.580202i	−0.0952339	−	0.995455i	$-0.530360\pi$
$349$	−6552.07	−	3782.84i	−1.00494	−	0.580202i	−0.909706	+	0.415252i	$0.863693\pi$
$350$	5805.51			0.886622
$351$		0			0
$352$	4159.76			0.629875
$353$	−2026.01	−	1169.72i	−0.305478	−	0.176368i	0.339423	−	0.940634i	$-0.389768\pi$
$353$	−2026.01	−	1169.72i	−0.305478	−	0.176368i	−0.644901	+	0.764266i	$0.723101\pi$
$354$	338.050	−	585.520i	0.0507547	−	0.0879097i
$355$	−152.102	−	263.448i	−0.0227401	−	0.0393870i
$356$		−	1668.43i		−	0.248389i
$357$	−1481.77	+	855.502i	−0.219674	+	0.126829i
$358$	−342.261	+	197.605i	−0.0505281	+	0.0291724i
$359$		−	2531.68i		−	0.372192i	−0.982532	−	0.186096i	$-0.940417\pi$
$359$		−	2531.68i		−	0.372192i	0.982532	−	0.186096i	$-0.0595835\pi$
$360$	−91.1221	−	157.828i	−0.0133404	−	0.0231063i
$361$	2399.23	−	4155.58i	0.349793	−	0.605858i
$362$	−2376.64	−	1372.16i	−0.345065	−	0.199223i
$363$	10538.5			1.52376
$364$		0			0
$365$	429.028			0.0615243
$366$	7525.70	+	4344.97i	1.07479	+	0.620533i
$367$	−3288.91	+	5696.55i	−0.467792	+	0.810239i	−0.999323	−	0.0368000i	$-0.988284\pi$
$367$	−3288.91	+	5696.55i	−0.467792	+	0.810239i	0.531531	+	0.847039i	$0.321617\pi$
$368$	−1847.04	−	3199.17i	−0.261640	−	0.453174i
$369$		−	934.876i		−	0.131891i
$370$	−143.020	+	82.5725i	−0.0200952	+	0.0116020i
$371$	44.8104	−	25.8713i	0.00627073	−	0.00362041i
$372$		−	599.413i		−	0.0835433i
$373$	−1451.36	−	2513.83i	−0.201471	−	0.348958i	0.747532	−	0.664226i	$-0.231239\pi$
$373$	−1451.36	−	2513.83i	−0.201471	−	0.348958i	−0.949003	+	0.315268i	$0.897905\pi$
$374$	−2118.20	+	3668.83i	−0.292859	+	0.507247i
$375$	−447.415	−	258.315i	−0.0616117	−	0.0355716i
$376$	−772.407			−0.105941
$377$		0			0
$378$	6935.16			0.943667
$379$	−1615.77	−	932.867i	−0.218989	−	0.126433i	0.386493	−	0.922292i	$-0.373686\pi$
$379$	−1615.77	−	932.867i	−0.218989	−	0.126433i	−0.605482	+	0.795859i	$0.707020\pi$
$380$	−43.6070	+	75.5296i	−0.00588682	+	0.0101963i
$381$	1019.13	+	1765.18i	0.137038	+	0.237357i
$382$		−	1734.69i		−	0.232342i
$383$	−9384.24	+	5417.99i	−1.25199	+	0.722837i	−0.971504	−	0.237021i	$-0.923829\pi$
$383$	−9384.24	+	5417.99i	−1.25199	+	0.722837i	−0.280486	+	0.959858i	$0.590496\pi$
$384$	−3002.32	+	1733.39i	−0.398988	+	0.230356i
$385$			660.813i			0.0874757i
$386$	−1692.78	−	2931.97i	−0.223213	−	0.386616i
$387$	−2941.73	+	5095.22i	−0.386399	+	0.669263i
$388$	726.597	+	419.501i	0.0950705	+	0.0548890i
$389$	9520.34			1.24088			0.620438	−	0.784256i	$-0.286955\pi$
$389$	9520.34			1.24088			0.620438	+	0.784256i	$0.286955\pi$
$390$		0			0
$391$	−1871.56			−0.242069
$392$	263.687	+	152.240i	0.0339750	+	0.0196155i
$393$	3788.57	−	6561.99i	0.486280	−	0.842261i
$394$	1623.21	+	2811.49i	0.207554	+	0.359494i
$395$			236.716i			0.0301531i
$396$	−1082.55	+	625.009i	−0.137374	+	0.0793129i
$397$	−8754.51	+	5054.42i	−1.10674	+	0.638978i	−0.937983	−	0.346680i	$-0.887309\pi$
$397$	−8754.51	+	5054.42i	−1.10674	+	0.638978i	−0.168758	+	0.985657i	$0.553976\pi$
$398$			6138.10i			0.773053i
$399$	−3615.71	−	6262.59i	−0.453664	−	0.785768i
$400$	3143.51	−	5444.71i	0.392938	−	0.680589i
$401$	−1805.12	−	1042.19i	−0.224797	−	0.129787i	0.383373	−	0.923594i	$-0.374763\pi$
$401$	−1805.12	−	1042.19i	−0.224797	−	0.129787i	−0.608169	+	0.793807i	$0.708096\pi$
$402$	−4193.32			−0.520258
$403$		0			0
$404$	−1325.88			−0.163279
$405$	−90.6432	−	52.3329i	−0.0111212	−	0.00642084i
$406$	−4095.30	+	7093.27i	−0.500607	+	0.867076i
$407$	3716.25	+	6436.73i	0.452599	+	0.783924i
$408$			2275.78i			0.276147i
$409$	8414.76	−	4858.26i	1.01732	−	0.587349i	0.103992	−	0.994578i	$-0.466838\pi$
$409$	8414.76	−	4858.26i	1.01732	−	0.587349i	0.913326	+	0.407229i	$0.133505\pi$
$410$	−86.7600	+	50.0909i	−0.0104507	+	0.00603369i
$411$			6663.95i			0.799777i
$412$	−669.390	−	1159.42i	−0.0800449	−	0.138642i
$413$	651.035	−	1127.63i	0.0775674	−	0.134351i
$414$	2181.56	+	1259.53i	0.258981	+	0.149523i
$415$	−339.064			−0.0401060
$416$		0			0
$417$	−5503.54			−0.646305
$418$	−15506.0	−	8952.38i	−1.81441	−	1.04755i
$419$	−6690.94	+	11589.1i	−0.780129	+	1.35122i	0.151737	+	0.988421i	$0.451513\pi$
$419$	−6690.94	+	11589.1i	−0.780129	+	1.35122i	−0.931866	+	0.362802i	$0.881820\pi$
$420$	27.0505	+	46.8529i	0.00314269	+	0.00544330i
$421$			9463.37i			1.09553i	0.836633	+	0.547763i	$0.184521\pi$
$421$			9463.37i			1.09553i	−0.836633	+	0.547763i	$0.815479\pi$
$422$	203.100	−	117.260i	0.0234284	−	0.0135264i
$423$	371.391	−	214.423i	0.0426895	−	0.0246468i
$424$		−	68.8221i		−	0.00788278i
$425$	−1592.62	−	2758.50i	−0.181773	−	0.314840i
$426$	2556.49	−	4427.97i	0.290757	−	0.503606i
$427$	14493.4	+	8367.77i	1.64259	+	0.948349i
$428$	1233.30			0.139285
$429$		0			0
$430$	630.474			0.0707074
$431$	4202.20	+	2426.14i	0.469635	+	0.271144i	0.716087	−	0.698011i	$-0.245931\pi$
$431$	4202.20	+	2426.14i	0.469635	+	0.271144i	−0.246452	+	0.969155i	$0.579265\pi$
$432$	3755.17	−	6504.15i	0.418220	−	0.724378i
$433$	−4104.00	−	7108.33i	−0.455486	−	0.788925i	0.543230	−	0.839584i	$-0.317201\pi$
$433$	−4104.00	−	7108.33i	−0.455486	−	0.788925i	−0.998716	+	0.0506587i	$0.983868\pi$
$434$			5265.78i			0.582409i
$435$	315.215	−	181.989i	0.0347434	−	0.0200591i
$436$	−836.949	+	483.213i	−0.0919325	+	0.0530773i
$437$		−	7910.01i		−	0.865874i
$438$	3605.50	+	6244.92i	0.393328	+	0.681264i
$439$	−1496.90	+	2592.71i	−0.162741	+	0.281875i	−0.935851	−	0.352397i	$-0.885367\pi$
$439$	−1496.90	+	2592.71i	−0.162741	+	0.281875i	0.773110	+	0.634272i	$0.218700\pi$
$440$	761.182	+	439.469i	0.0824726	+	0.0476156i
$441$	−169.049			−0.0182539
$442$		0			0
$443$	9743.67			1.04500			0.522501	−	0.852639i	$-0.324999\pi$
$443$	9743.67			1.04500			0.522501	+	0.852639i	$0.324999\pi$
$444$	526.979	+	304.251i	0.0563273	+	0.0325206i
$445$	325.668	−	564.073i	0.0346924	−	0.0600890i
$446$	1582.29	+	2740.61i	0.167990	+	0.290968i
$447$		−	10166.0i		−	1.07570i
$448$	−8941.01	+	5162.09i	−0.942908	+	0.544388i
$449$	−486.237	+	280.729i	−0.0511068	+	0.0295065i	−0.525336	−	0.850895i	$-0.676060\pi$
$449$	−486.237	+	280.729i	−0.0511068	+	0.0295065i	0.474229	+	0.880402i	$0.342727\pi$
$450$			4287.22i			0.449114i
$451$	2254.39	+	3904.71i	0.235377	+	0.407685i
$452$	−461.363	+	799.104i	−0.0480104	+	0.0831564i
$453$	−3115.56	−	1798.77i	−0.323138	−	0.186564i
$454$	−8457.38			−0.874283
$455$		0			0
$456$	−9618.40			−0.987770
$457$	11915.1	+	6879.20i	1.21962	+	0.704148i	0.964837	−	0.262851i	$-0.0846627\pi$
$457$	11915.1	+	6879.20i	1.21962	+	0.704148i	0.254783	+	0.966998i	$0.417996\pi$
$458$	−270.606	+	468.704i	−0.0276083	+	0.0478190i
$459$	−1902.52	−	3295.26i	−0.193468	−	0.335097i
$460$			59.1779i			0.00599823i
$461$	−10400.3	+	6004.62i	−1.05074	+	0.606644i	−0.922856	−	0.385145i	$-0.874151\pi$
$461$	−10400.3	+	6004.62i	−1.05074	+	0.606644i	−0.127882	+	0.991789i	$0.540818\pi$
$462$	−9618.75	+	5553.39i	−0.968625	+	0.559236i
$463$			13635.7i			1.36870i	0.729156	+	0.684348i	$0.239913\pi$
$463$			13635.7i			1.36870i	−0.729156	+	0.684348i	$0.760087\pi$
$464$	4434.96	+	7681.57i	0.443724	+	0.768552i
$465$	117.002	−	202.653i	0.0116685	−	0.0202104i
$466$	569.509	+	328.806i	0.0566138	+	0.0326860i
$467$	−8821.95			−0.874157			−0.437079	−	0.899423i	$-0.643987\pi$
$467$	−8821.95			−0.874157			−0.437079	+	0.899423i	$0.643987\pi$
$468$		0			0
$469$	−8075.72			−0.795100
$470$	−39.7985	−	22.9777i	−0.00390589	−	0.00225507i
$471$	−1040.69	+	1802.52i	−0.101809	+	0.176339i
$472$	−865.933	−	1499.84i	−0.0844445	−	0.146262i
$473$		−	28375.1i		−	2.75832i
$474$	−3445.62	+	1989.33i	−0.333888	+	0.192770i
$475$	11658.6	−	6731.08i	1.12617	−	0.650196i
$476$			667.956i			0.0643187i
$477$	19.1053	+	33.0913i	0.00183390	+	0.00317641i
$478$	−4546.27	+	7874.37i	−0.435024	+	0.753484i
$479$	12661.3	+	7310.02i	1.20775	+	0.697293i	0.962267	−	0.272109i	$-0.0877210\pi$
$479$	12661.3	+	7310.02i	1.20775	+	0.697293i	0.245480	+	0.969402i	$0.421054\pi$
$480$	132.951			0.0126424
$481$		0			0
$482$	−12884.9			−1.21761
$483$	−4249.39	−	2453.39i	−0.400319	−	0.231124i
$484$	2057.04	−	3562.91i	0.193186	−	0.334608i
$485$	163.768	+	283.655i	0.0153326	+	0.0265569i
$486$			8542.20i			0.797288i
$487$	8486.06	−	4899.43i	0.789610	−	0.455882i	−0.0502150	−	0.998738i	$-0.515991\pi$
$487$	8486.06	−	4899.43i	0.789610	−	0.455882i	0.839825	+	0.542857i	$0.182657\pi$
$488$	19277.5	−	11129.9i	1.78822	−	1.03243i
$489$		−	5558.43i		−	0.514030i
$490$	9.05771	+	15.6884i	0.000835072	+	0.00144639i
$491$	−5418.03	+	9384.31i	−0.497989	+	0.862542i	−0.999997	−	0.00232091i	$-0.999261\pi$
$491$	−5418.03	+	9384.31i	−0.497989	+	0.862542i	0.502009	+	0.864863i	$0.332595\pi$
$492$	319.681	+	184.568i	0.0292934	+	0.0169125i
$493$	4493.84			0.410532
$494$		0			0
$495$	−487.993			−0.0443104
$496$	4938.52	+	2851.26i	0.447069	+	0.258115i
$497$	4923.43	−	8527.63i	0.444358	−	0.769651i
$498$	−2849.45	−	4935.40i	−0.256400	−	0.444098i
$499$		−	2589.96i		−	0.232349i	−0.993229	−	0.116175i	$-0.962937\pi$
$499$		−	2589.96i		−	0.232349i	0.993229	−	0.116175i	$-0.0370633\pi$
$500$	−174.665	+	100.843i	−0.0156226	+	0.00901969i
$501$	−1890.74	+	1091.62i	−0.168607	+	0.0973451i
$502$		−	1841.20i		−	0.163699i
$503$	8533.73	+	14780.9i	0.756462	+	1.31023i	0.944644	+	0.328096i	$0.106407\pi$
$503$	8533.73	+	14780.9i	0.756462	+	1.31023i	−0.188183	+	0.982134i	$0.560260\pi$
$504$	2949.56	−	5108.79i	0.260682	−	0.451515i
$505$	−448.260	−	258.803i	−0.0394996	−	0.0228051i
$506$	−12149.0			−1.06737
$507$		0			0
$508$	795.712			0.0694961
$509$	−877.192	−	506.447i	−0.0763867	−	0.0441019i	0.461320	−	0.887234i	$-0.347376\pi$
$509$	−877.192	−	506.447i	−0.0763867	−	0.0441019i	−0.537707	+	0.843132i	$0.680709\pi$
$510$	−67.7003	+	117.260i	−0.00587808	+	0.0101811i
$511$	6943.68	+	12026.8i	0.601116	+	1.04116i
$512$			12992.6i			1.12148i
$513$	13927.1	−	8040.83i	1.19863	−	0.692030i
$514$	2841.28	−	1640.41i	0.243820	−	0.140769i
$515$		−	522.644i		−	0.0447193i
$516$	−1161.54	−	2011.85i	−0.0990969	−	0.171641i
$517$	−1034.13	+	1791.17i	−0.0879711	+	0.152370i
$518$	−4629.45	−	2672.81i	−0.392676	−	0.226712i
$519$	−16564.6			−1.40098
$520$		0			0
$521$	−14367.7			−1.20818			−0.604089	−	0.796917i	$-0.706463\pi$
$521$	−14367.7			−1.20818			−0.604089	+	0.796917i	$0.706463\pi$
$522$	−5238.19	−	3024.27i	−0.439213	−	0.253580i
$523$	8109.96	−	14046.9i	0.678057	−	1.17443i	−0.297509	−	0.954719i	$-0.596156\pi$
$523$	8109.96	−	14046.9i	0.678057	−	1.17443i	0.975565	−	0.219709i	$-0.0705109\pi$
$524$	−1479.01	−	2561.72i	−0.123303	−	0.213568i
$525$		−	8350.92i		−	0.694217i
$526$	−11592.2	+	6692.76i	−0.960919	+	0.554787i
$527$	2502.05	−	1444.56i	0.206814	−	0.119404i
$528$			12028.0i			0.991382i
$529$	3399.89	+	5888.78i	0.279435	+	0.483996i
$530$	2.04733	−	3.54608i	0.000167793	−	0.000290626i
$531$	832.722	+	480.772i	0.0680547	+	0.0392914i
$532$	−2823.06			−0.230066
$533$		0			0
$534$	10947.5			0.887161
$535$	416.961	+	240.733i	0.0336950	+	0.0194538i
$536$	−5370.70	+	9302.32i	−0.432796	+	0.749625i
$537$	284.244	+	492.325i	0.0228418	+	0.0395631i
$538$		−	16506.1i		−	1.32273i
$539$	706.071	−	407.650i	0.0564242	−	0.0325765i
$540$	−104.194	+	60.1566i	−0.00830335	+	0.00479394i
$541$			17592.2i			1.39806i	0.715094	+	0.699029i	$0.246384\pi$
$541$			17592.2i			1.39806i	−0.715094	+	0.699029i	$0.753616\pi$
$542$	5033.36	+	8718.04i	0.398896	+	0.690908i
$543$	−1973.77	+	3418.67i	−0.155990	+	0.270183i
$544$	1421.56	+	820.738i	0.112038	+	0.0646854i
$545$	−377.281			−0.0296531
$546$		0			0
$547$	10504.6			0.821103			0.410552	−	0.911837i	$-0.365336\pi$
$547$	10504.6			0.821103			0.410552	+	0.911837i	$0.365336\pi$
$548$	2252.99	+	1300.76i	0.175626	+	0.101398i
$549$	−6179.38	+	10703.0i	−0.480382	+	0.832045i
$550$	−10338.3	−	17906.5i	−0.801504	−	1.38825i
$551$			18992.8i			1.46846i
$552$	−5652.06	+	3263.22i	−0.435811	+	0.251616i
$553$	−6635.77	+	3831.16i	−0.510274	+	0.294607i
$554$		−	15073.2i		−	1.15596i
$555$	118.776	+	205.726i	0.00908426	+	0.0157344i
$556$	−1074.26	+	1860.67i	−0.0819401	+	0.141924i
$557$	439.558	+	253.779i	0.0334375	+	0.0193051i	0.516626	−	0.856211i	$-0.327188\pi$
$557$	439.558	+	253.779i	0.0334375	+	0.0193051i	−0.483188	+	0.875517i	$0.660521\pi$
$558$	−3888.64			−0.295016
$559$		0			0
$560$	−514.690			−0.0388386
$561$	5277.41	+	3046.92i	0.397170	+	0.229306i
$562$	−4520.87	+	7830.38i	−0.339327	+	0.587731i
$563$	−1721.57	−	2981.85i	−0.128873	−	0.223215i	0.794367	−	0.607438i	$-0.207803\pi$
$563$	−1721.57	−	2981.85i	−0.128873	−	0.223215i	−0.923240	+	0.384223i	$0.874469\pi$
$564$			169.330i			0.0126420i
$565$	−311.961	+	180.111i	−0.0232288	+	0.0134112i
$566$	−5792.16	+	3344.11i	−0.430146	+	0.248345i
$567$		−	3387.96i		−	0.250936i
$568$	−6548.59	−	11342.5i	−0.483755	−	0.837888i
$569$	11986.1	−	20760.5i	0.883098	−	1.52957i	0.0352188	−	0.999380i	$-0.488787\pi$
$569$	11986.1	−	20760.5i	0.883098	−	1.52957i	0.847879	−	0.530190i	$-0.177879\pi$
$570$	−495.591	−	286.130i	−0.0364176	−	0.0210257i
$571$	7458.32			0.546622			0.273311	−	0.961926i	$-0.411881\pi$
$571$	7458.32			0.546622			0.273311	+	0.961926i	$0.411881\pi$
$572$		0			0
$573$	−2495.26			−0.181922
$574$	−2808.36	−	1621.41i	−0.204214	−	0.117903i
$575$	4567.28	−	7910.77i	0.331250	−	0.573742i
$576$	−3812.07	−	6602.70i	−0.275757	−	0.477626i
$577$		−	5669.57i		−	0.409059i	−0.978860	−	0.204530i	$-0.934434\pi$
$577$		−	5669.57i		−	0.409059i	0.978860	−	0.204530i	$-0.0655665\pi$
$578$	9451.10	−	5456.60i	0.680128	−	0.392672i
$579$	−4217.49	+	2434.97i	−0.302717	+	0.174774i
$580$		−	142.093i		−	0.0101726i
$581$	−5487.64	−	9504.87i	−0.391851	−	0.678706i
$582$	−2752.58	+	4767.60i	−0.196045	+	0.339559i
$583$	−159.595	−	92.1420i	−0.0113375	−	0.00654568i
$584$	18471.4			1.30882
$585$		0			0
$586$	−14065.6			−0.991541
$587$	881.087	+	508.696i	0.0619529	+	0.0357685i	0.530657	−	0.847587i	$-0.321945\pi$
$587$	881.087	+	508.696i	0.0619529	+	0.0357685i	−0.468704	+	0.883355i	$0.655279\pi$
$588$	33.3746	−	57.8064i	0.00234072	−	0.00405425i
$589$	6105.30	+	10574.7i	0.427104	+	0.739766i
$590$		−	103.040i		−	0.00718996i
$591$	4044.18	−	2334.91i	0.281481	−	0.162513i
$592$	−5013.41	+	2894.49i	−0.348057	+	0.200951i
$593$		−	10198.2i		−	0.706221i	−0.935582	−	0.353111i	$-0.885124\pi$
$593$		−	10198.2i		−	0.706221i	0.935582	−	0.353111i	$-0.114876\pi$
$594$	−12350.0	−	21390.8i	−0.853073	−	1.47757i
$595$	−130.381	+	225.827i	−0.00898336	+	0.0155596i
$596$	−3437.00	−	1984.35i	−0.236216	−	0.136380i
$597$	8829.33			0.605294
$598$		0			0
$599$	12516.3			0.853763			0.426881	−	0.904308i	$-0.359612\pi$
$599$	12516.3			0.853763			0.426881	+	0.904308i	$0.359612\pi$
$600$	−9619.33	−	5553.72i	−0.654512	−	0.377883i
$601$	−4813.73	+	8337.63i	−0.326716	+	0.565888i	−0.981858	−	0.189617i	$-0.939275\pi$
$601$	−4813.73	+	8337.63i	−0.326716	+	0.565888i	0.655142	+	0.755505i	$0.272609\pi$
$602$	10204.0	+	17673.9i	0.690838	+	1.19657i
$603$		−	5963.70i		−	0.402754i
$604$	−1216.28	+	702.218i	−0.0819364	+	0.0473060i
$605$	1390.92	−	803.046i	0.0934691	−	0.0539644i
$606$		−	8699.80i		−	0.583177i
$607$	−3333.60	−	5773.96i	−0.222910	−	0.386092i	0.732780	−	0.680466i	$-0.238222\pi$
$607$	−3333.60	−	5773.96i	−0.222910	−	0.386092i	−0.955690	+	0.294373i	$0.904889\pi$
$608$	−3468.78	+	6008.11i	−0.231378	+	0.400758i
$609$	10203.3	+	5890.87i	0.678913	+	0.391971i
$610$	1324.37			0.0879053
$611$		0			0
$612$	−493.268			−0.0325803
$613$	−19992.5	−	11542.7i	−1.31728	−	0.760530i	−0.333987	−	0.942578i	$-0.608394\pi$
$613$	−19992.5	−	11542.7i	−1.31728	−	0.760530i	−0.983290	+	0.182047i	$0.941728\pi$
$614$	9359.39	−	16210.9i	0.615170	−	1.06551i
$615$	72.0532	+	124.800i	0.00472433	+	0.00818278i
$616$			28450.6i			1.86089i
$617$	−2640.72	+	1524.62i	−0.172304	+	0.0994796i	−0.583672	−	0.811990i	$-0.698384\pi$
$617$	−2640.72	+	1524.62i	−0.172304	+	0.0994796i	0.411368	+	0.911469i	$0.365051\pi$
$618$	7607.58	−	4392.24i	0.495181	−	0.285893i
$619$			7296.58i			0.473787i	0.971536	+	0.236894i	$0.0761293\pi$
$619$			7296.58i			0.473787i	−0.971536	+	0.236894i	$0.923871\pi$
$620$	−45.6761	−	79.1134i	−0.00295871	−	0.00512463i
$621$	5455.99	−	9450.06i	0.352563	−	0.610657i
$622$	−17536.0	−	10124.4i	−1.13044	−	0.652657i
$623$	21083.3			1.35583
$624$		0			0
$625$	15506.8			0.992438
$626$	22189.0	+	12810.8i	1.41670	+	0.817929i
$627$	−12877.5	+	22304.5i	−0.820222	+	1.42067i
$628$	406.271	+	703.683i	0.0258153	+	0.0447134i
$629$			2932.92i			0.185920i
$630$	303.954	−	175.488i	0.0192219	−	0.0110978i
$631$	−20637.0	+	11914.8i	−1.30197	+	0.751694i	−0.980742	−	0.195307i	$-0.937430\pi$
$631$	−20637.0	+	11914.8i	−1.30197	+	0.751694i	−0.321230	+	0.947001i	$0.604096\pi$
$632$			10191.6i			0.641453i
$633$	−168.672	−	292.149i	−0.0105910	−	0.0183442i
$634$	−7980.27	+	13822.2i	−0.499901	+	0.865853i
$635$	269.019	+	155.318i	0.0168121	+	0.00970648i
$636$	−15.0874			−0.000940653
$637$		0			0
$638$	29171.3			1.81019
$639$	6297.43	+	3635.82i	0.389863	+	0.225088i
$640$	−264.174	+	457.562i	−0.0163162	+	0.0282605i
$641$	6702.63	+	11609.3i	0.413008	+	0.715351i	0.995217	−	0.0976883i	$-0.0311448\pi$
$641$	6702.63	+	11609.3i	0.413008	+	0.715351i	−0.582209	+	0.813039i	$0.697812\pi$
$642$			8092.36i			0.497477i
$643$	−4547.94	+	2625.76i	−0.278932	+	0.161042i	−0.632940	−	0.774201i	$-0.718152\pi$
$643$	−4547.94	+	2625.76i	−0.278932	+	0.161042i	0.354008	+	0.935243i	$0.384819\pi$
$644$	−1658.91	+	957.774i	−0.101507	+	0.0586049i
$645$		−	906.904i		−	0.0553633i
$646$	−3532.68	−	6118.79i	−0.215157	−	0.372663i
$647$	10805.7	−	18716.1i	0.656595	−	1.13726i	−0.324897	−	0.945749i	$-0.605330\pi$
$647$	10805.7	−	18716.1i	0.656595	−	1.13726i	0.981492	−	0.191506i	$-0.0613370\pi$
$648$	−3902.55	−	2253.14i	−0.236584	−	0.136592i
$649$	−4637.39			−0.280483
$650$		0			0
$651$	7574.54			0.456021
$652$	−1879.23	−	1084.97i	−0.112878	−	0.0651699i
$653$	10797.9	−	18702.6i	0.647099	−	1.12081i	−0.336714	−	0.941607i	$-0.609316\pi$
$653$	10797.9	−	18702.6i	0.647099	−	1.12081i	0.983813	−	0.179201i	$-0.0573512\pi$
$654$	−3170.63	−	5491.68i	−0.189574	−	0.328351i
$655$		−	1154.78i		−	0.0688869i
$656$	−3041.28	+	1755.89i	−0.181009	+	0.104506i
$657$	−8881.48	+	5127.72i	−0.527396	+	0.304492i
$658$		−	1487.54i		−	0.0881314i
$659$	8321.30	+	14412.9i	0.491884	+	0.851968i	0.999956	−	0.00934609i	$-0.00297500\pi$
$659$	8321.30	+	14412.9i	0.491884	+	0.851968i	−0.508072	+	0.861315i	$0.669642\pi$
$660$	96.3419	−	166.869i	0.00568198	−	0.00984147i
$661$	−23366.3	−	13490.6i	−1.37495	−	0.793831i	−0.383408	−	0.923579i	$-0.625250\pi$
$661$	−23366.3	−	13490.6i	−1.37495	−	0.793831i	−0.991547	+	0.129748i	$0.958583\pi$
$662$	11871.5			0.696980
$663$		0			0
$664$	−14598.1			−0.853185
$665$	−954.437	−	551.044i	−0.0556564	−	0.0321332i
$666$	1973.80	−	3418.73i	0.114840	−	0.198908i
$667$	6443.67	+	11160.8i	0.374063	+	0.647896i
$668$			852.310i			0.0493665i
$669$	3942.23	−	2276.05i	0.227826	−	0.131535i
$670$	−553.454	+	319.537i	−0.0319131	+	0.0184251i
$671$		−	59604.5i		−	3.42922i
$672$	2151.77	+	3726.98i	0.123521	+	0.213945i
$673$	5574.62	−	9655.53i	0.319296	−	0.553036i	−0.661046	−	0.750346i	$-0.729887\pi$
$673$	5574.62	−	9655.53i	0.319296	−	0.553036i	0.980341	+	0.197309i	$0.0632204\pi$
$674$	−6721.26	−	3880.52i	−0.384115	−	0.221769i
$675$	18571.3			1.05898
$676$		0			0
$677$	3314.33			0.188154			0.0940769	−	0.995565i	$-0.470010\pi$
$677$	3314.33			0.188154			0.0940769	+	0.995565i	$0.470010\pi$
$678$	−5243.36	−	3027.26i	−0.297006	−	0.171477i
$679$	−5301.06	+	9181.71i	−0.299611	+	0.518942i
$680$	173.418	+	300.369i	0.00977982	+	0.0169391i
$681$			12165.5i			0.684556i
$682$	16241.7	−	9377.17i	0.911918	−	0.526496i
$683$	21222.2	−	12252.6i	1.18894	−	0.686433i	0.230872	−	0.972984i	$-0.425842\pi$
$683$	21222.2	−	12252.6i	1.18894	−	0.686433i	0.958065	+	0.286552i	$0.0925090\pi$
$684$		−	2084.75i		−	0.116539i
$685$	507.803	+	879.540i	0.0283243	+	0.0490591i
$686$	−8278.50	+	14338.8i	−0.460750	+	0.798042i
$687$	674.206	+	389.253i	0.0374419	+	0.0216171i
$688$	22100.6			1.22468
$689$		0			0
$690$	−388.299			−0.0214236
$691$	−18838.5	−	10876.4i	−1.03712	−	0.598782i	−0.118105	−	0.993001i	$-0.537682\pi$
$691$	−18838.5	−	10876.4i	−1.03712	−	0.598782i	−0.919017	+	0.394219i	$0.871015\pi$
$692$	−3233.32	+	5600.27i	−0.177619	+	0.307645i
$693$	−7897.99	−	13679.7i	−0.432929	−	0.749855i
$694$		−	7278.90i		−	0.398132i
$695$	−726.383	+	419.378i	−0.0396450	+	0.0228891i
$696$	13571.3	−	7835.37i	0.739105	−	0.426722i
$697$			1779.20i			0.0966887i
$698$	−9689.94	−	16783.5i	−0.525458	−	0.910120i
$699$	472.971	−	819.209i	0.0255928	−	0.0443281i
$700$	−2823.33	−	1630.05i	−0.152446	−	0.0880145i
$701$	−34250.9			−1.84542			−0.922709	−	0.385496i	$-0.874030\pi$
$701$	−34250.9			−1.84542			−0.922709	+	0.385496i	$0.874030\pi$
$702$		0			0
$703$	−12395.8			−0.665028
$704$	31843.9	+	18385.1i	1.70477	+	0.984252i
$705$	−33.0522	+	57.2480i	−0.00176570	+	0.00305828i
$706$	−2996.30	−	5189.74i	−0.159727	−	0.276655i
$707$		−	16754.6i		−	0.891259i
$708$	−328.800	+	189.833i	−0.0174535	+	0.0100768i
$709$	−4786.62	+	2763.56i	−0.253548	+	0.146386i	−0.621388	−	0.783503i	$-0.713431\pi$
$709$	−4786.62	+	2763.56i	−0.253548	+	0.146386i	0.367840	+	0.929889i	$0.380097\pi$
$710$		−	779.234i		−	0.0411889i
$711$	−2829.21	−	4900.34i	−0.149232	−	0.258477i
$712$	14021.3	−	24285.6i	0.738020	−	1.27829i
$713$	7175.31	+	4142.67i	0.376883	+	0.217593i
$714$	−4382.83			−0.229724
$715$		0			0
$716$	221.931			0.0115837
$717$	11326.9	+	6539.57i	0.589972	+	0.340620i
$718$	3242.51	−	5616.19i	0.168537	−	0.291914i
$719$	−1888.89	−	3271.65i	−0.0979745	−	0.169697i	0.812872	−	0.582443i	$-0.197903\pi$
$719$	−1888.89	−	3271.65i	−0.0979745	−	0.169697i	−0.910846	+	0.412746i	$0.864570\pi$
$720$		−	380.085i		−	0.0196735i
$721$	14651.1	−	8458.81i	0.756776	−	0.436925i
$722$	10644.7	−	6145.75i	0.548693	−	0.316788i
$723$			18534.2i			0.953380i
$724$	770.538	+	1334.61i	0.0395536	+	0.0685088i
$725$	−10966.6	+	18994.7i	−0.561777	+	0.973027i
$726$	23378.2	+	13497.4i	1.19510	+	0.689994i
$727$	−19076.8			−0.973204			−0.486602	−	0.873624i	$-0.661764\pi$
$727$	−19076.8			−0.973204			−0.486602	+	0.873624i	$0.661764\pi$
$728$		0			0
$729$	17319.9			0.879944
$730$	951.744	+	549.490i	0.0482543	+	0.0278596i
$731$	5598.52	−	9696.92i	0.283268	−	0.490634i
$732$	−2439.93	−	4226.08i	−0.123200	−	0.213388i
$733$		−	7997.30i		−	0.402984i	−0.979490	−	0.201492i	$-0.935421\pi$
$733$		−	7997.30i		−	0.402984i	0.979490	−	0.201492i	$-0.0645790\pi$
$734$	−14592.0	+	8424.71i	−0.733789	+	0.423653i
$735$	22.5669	−	13.0290i	0.00113251	−	0.000653855i
$736$			4707.39i			0.235756i
$737$	14381.0	+	24908.7i	0.718769	+	1.24494i
$738$	1197.37	−	2073.90i	0.0597232	−	0.103444i
$739$	−25100.6	−	14491.8i	−1.24944	−	0.721367i	−0.278445	−	0.960452i	$-0.589819\pi$
$739$	−25100.6	−	14491.8i	−1.24944	−	0.721367i	−0.970998	+	0.239086i	$0.923152\pi$
$740$	92.7376			0.00460689
$741$		0			0
$742$	132.541			0.00655761
$743$	−16580.4	−	9572.69i	−0.818674	−	0.472662i	0.0312847	−	0.999511i	$-0.490040\pi$
$743$	−16580.4	−	9572.69i	−0.818674	−	0.472662i	−0.849959	+	0.526849i	$0.823373\pi$
$744$	5037.40	−	8725.02i	0.248226	−	0.429939i
$745$	−774.667	−	1341.76i	−0.0380961	−	0.0659844i
$746$		−	7435.47i		−	0.364922i
$747$	7019.09	−	4052.47i	0.343795	−	0.198490i
$748$	2060.24	−	1189.48i	0.100708	−	0.0581440i
$749$			15584.7i			0.760284i
$750$	−661.688	−	1146.08i	−0.0322152	−	0.0557984i
$751$	−12758.4	+	22098.3i	−0.619923	+	1.07374i	0.369576	+	0.929200i	$0.379503\pi$
$751$	−12758.4	+	22098.3i	−0.619923	+	1.07374i	−0.989499	+	0.144538i	$0.953830\pi$
$752$	−1395.10	−	805.459i	−0.0676515	−	0.0390586i
$753$	−2648.47			−0.128175
$754$		0			0
$755$	−548.275			−0.0264288
$756$	−3372.70	−	1947.23i	−0.162254	−	0.0936773i
$757$	8615.31	−	14922.2i	0.413645	−	0.716453i	−0.581641	−	0.813446i	$-0.697589\pi$
$757$	8615.31	−	14922.2i	0.413645	−	0.716453i	0.995285	+	0.0969925i	$0.0309223\pi$
$758$	−2389.59	−	4138.89i	−0.114504	−	0.198326i
$759$			17475.7i			0.835744i
$760$	−1269.48	+	732.936i	−0.0605908	+	0.0349821i
$761$	−2029.15	+	1171.53i	−0.0966576	+	0.0558053i	−0.547550	−	0.836773i	$-0.684439\pi$
$761$	−2029.15	+	1171.53i	−0.0966576	+	0.0558053i	0.450892	+	0.892579i	$0.351106\pi$
$762$			5221.11i			0.248216i
$763$	−6106.17	−	10576.2i	−0.289722	−	0.501814i
$764$	−487.060	+	843.613i	−0.0230644	+	0.0399488i
$765$	−166.767	−	96.2829i	−0.00788166	−	0.00455048i
$766$	−27756.9			−1.30927
$767$		0			0
$768$	7862.11			0.369400
$769$	−6148.93	−	3550.09i	−0.288344	−	0.166475i	0.348851	−	0.937178i	$-0.386572\pi$
$769$	−6148.93	−	3550.09i	−0.288344	−	0.166475i	−0.637195	+	0.770703i	$0.719905\pi$
$770$	−846.353	+	1465.93i	−0.0396110	+	0.0686082i
$771$	−2359.65	−	4087.03i	−0.110221	−	0.190909i
$772$			1901.17i			0.0886328i
$773$	−10626.5	+	6135.22i	−0.494449	+	0.285470i	−0.726418	−	0.687253i	$-0.758816\pi$
$773$	−10626.5	+	6135.22i	−0.494449	+	0.285470i	0.231969	+

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	169.e (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.21837 + 1.28078i) q^{2} +(1.84233 - 3.19101i) q^{3} +(-0.719224 - 1.24573i) q^{4} -0.561553i q^{5} +(8.17394 - 4.71922i) q^{6} +(15.7418 - 9.08854i) q^{7} -24.1771i q^{8} +(6.71165 + 11.6249i) q^{9} +O(q^{10})\)	\(q+(2.21837 + 1.28078i) q^{2} +(1.84233 - 3.19101i) q^{3} +(-0.719224 - 1.24573i) q^{4} -0.561553i q^{5} +(8.17394 - 4.71922i) q^{6} +(15.7418 - 9.08854i) q^{7} -24.1771i q^{8} +(6.71165 + 11.6249i) q^{9} +(0.719224 - 1.24573i) q^{10} +(-56.0653 - 32.3693i) q^{11} -5.30019 q^{12} +46.5616 q^{14} +(-1.79192 - 1.03457i) q^{15} +(25.2116 - 43.6679i) q^{16} +(-12.7732 - 22.1238i) q^{17} +34.3845i q^{18} +(93.5045 - 53.9848i) q^{19} +(-0.699544 + 0.403882i) q^{20} -66.9763i q^{21} +(-82.9157 - 143.614i) q^{22} +(36.6307 - 63.4462i) q^{23} +(-77.1493 - 44.5421i) q^{24} +124.685 q^{25} +148.946 q^{27} +(-22.6438 - 13.0734i) q^{28} +(-87.9545 + 152.342i) q^{29} +(-2.65009 - 4.59010i) q^{30} +113.093i q^{31} +(-55.6462 + 32.1274i) q^{32} +(-206.581 + 119.270i) q^{33} -65.4384i q^{34} +(-5.10370 - 8.83986i) q^{35} +(9.65435 - 16.7218i) q^{36} +(-99.4264 - 57.4039i) q^{37} +276.570 q^{38} -13.5767 q^{40} +(-60.3151 - 34.8229i) q^{41} +(85.7817 - 148.578i) q^{42} +(219.151 + 379.581i) q^{43} +93.1231i q^{44} +(6.52800 - 3.76894i) q^{45} +(162.521 - 93.8314i) q^{46} -31.9479i q^{47} +(-92.8963 - 160.901i) q^{48} +(-6.29686 + 10.9065i) q^{49} +(276.597 + 159.693i) q^{50} -94.1298 q^{51} +2.84658 q^{53} +(330.417 + 190.767i) q^{54} +(-18.1771 + 31.4836i) q^{55} +(-219.734 - 380.591i) q^{56} -397.831i q^{57} +(-390.231 + 225.300i) q^{58} +(62.0356 - 35.8163i) q^{59} +2.97633i q^{60} +(460.348 + 797.345i) q^{61} +(-144.847 + 250.882i) q^{62} +(211.307 + 121.998i) q^{63} -567.978 q^{64} -611.032 q^{66} +(-384.758 - 222.140i) q^{67} +(-18.3736 + 31.8240i) q^{68} +(-134.972 - 233.778i) q^{69} -26.1468i q^{70} +(469.142 - 270.859i) q^{71} +(281.056 - 162.268i) q^{72} +764.004i q^{73} +(-147.043 - 254.686i) q^{74} +(229.710 - 397.870i) q^{75} +(-134.501 - 77.6543i) q^{76} -1176.76 q^{77} -421.538 q^{79} +(-24.5218 - 14.1577i) q^{80} +(93.1932 - 161.415i) q^{81} +(-89.2007 - 154.500i) q^{82} -603.797i q^{83} +(-83.4346 + 48.1710i) q^{84} +(-12.4237 + 7.17283i) q^{85} +1122.73i q^{86} +(324.082 + 561.327i) q^{87} +(-782.596 + 1355.50i) q^{88} +(1004.49 + 579.941i) q^{89} +19.3087 q^{90} -105.383 q^{92} +(360.880 + 208.354i) q^{93} +(40.9181 - 70.8722i) q^{94} +(-30.3153 - 52.5077i) q^{95} +236.757i q^{96} +(-505.126 + 291.634i) q^{97} +(-27.9375 + 16.1298i) q^{98} -869.006i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 10 q^{3} - 14 q^{4} - 70 q^{9}+O(q^{10}) \) 8 * q - 10 * q^3 - 14 * q^4 - 70 * q^9	\( 8 q - 10 q^{3} - 14 q^{4} - 70 q^{9} + 14 q^{10} + 172 q^{12} + 356 q^{14} + 78 q^{16} + 38 q^{17} - 284 q^{22} + 392 q^{23} + 948 q^{25} + 1340 q^{27} + 88 q^{29} + 86 q^{30} - 214 q^{35} - 500 q^{36} + 1256 q^{38} - 356 q^{40} - 394 q^{42} + 574 q^{43} - 570 q^{48} + 766 q^{49} - 1924 q^{51} - 472 q^{53} + 36 q^{55} - 2030 q^{56} + 2116 q^{61} - 664 q^{62} - 3076 q^{64} - 3272 q^{66} + 422 q^{68} + 1592 q^{69} - 294 q^{74} - 1032 q^{75} - 3048 q^{77} - 4032 q^{79} - 244 q^{81} + 144 q^{82} + 5116 q^{87} - 2484 q^{88} - 1000 q^{90} - 3152 q^{92} + 1622 q^{94} - 292 q^{95}+O(q^{100}) \) 8 * q - 10 * q^3 - 14 * q^4 - 70 * q^9 + 14 * q^10 + 172 * q^12 + 356 * q^14 + 78 * q^16 + 38 * q^17 - 284 * q^22 + 392 * q^23 + 948 * q^25 + 1340 * q^27 + 88 * q^29 + 86 * q^30 - 214 * q^35 - 500 * q^36 + 1256 * q^38 - 356 * q^40 - 394 * q^42 + 574 * q^43 - 570 * q^48 + 766 * q^49 - 1924 * q^51 - 472 * q^53 + 36 * q^55 - 2030 * q^56 + 2116 * q^61 - 664 * q^62 - 3076 * q^64 - 3272 * q^66 + 422 * q^68 + 1592 * q^69 - 294 * q^74 - 1032 * q^75 - 3048 * q^77 - 4032 * q^79 - 244 * q^81 + 144 * q^82 + 5116 * q^87 - 2484 * q^88 - 1000 * q^90 - 3152 * q^92 + 1622 * q^94 - 292 * q^95

Introduction

L-functions

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