LMFDB - Embedded newform 63.4.h.a.25.15

Newspace parameters

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.h (of order $3$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.15
Character	$\chi$	$=$	63.25
Dual form			63.4.h.a.58.15

$q$-expansion

$f(q)$	$=$	$q+1.44809 q^{2} +(0.196108 + 5.19245i) q^{3} -5.90304 q^{4} +(-2.21638 + 3.83887i) q^{5} +(0.283981 + 7.51913i) q^{6} +(9.71690 + 15.7665i) q^{7} -20.1328 q^{8} +(-26.9231 + 2.03656i) q^{9} +O(q^{10})$	\(q+1.44809 q^{2} +(0.196108 + 5.19245i) q^{3} -5.90304 q^{4} +(-2.21638 + 3.83887i) q^{5} +(0.283981 + 7.51913i) q^{6} +(9.71690 + 15.7665i) q^{7} -20.1328 q^{8} +(-26.9231 + 2.03656i) q^{9} +(-3.20951 + 5.55903i) q^{10} +(26.2410 + 45.4507i) q^{11} +(-1.15763 - 30.6512i) q^{12} +(-21.3388 - 36.9599i) q^{13} +(14.0709 + 22.8313i) q^{14} +(-20.3678 - 10.7556i) q^{15} +18.0702 q^{16} +(54.8281 - 94.9651i) q^{17} +(-38.9870 + 2.94912i) q^{18} +(72.6470 + 125.828i) q^{19} +(13.0833 - 22.6610i) q^{20} +(-79.9611 + 53.5465i) q^{21} +(37.9993 + 65.8167i) q^{22} +(18.8228 - 32.6021i) q^{23} +(-3.94820 - 104.539i) q^{24} +(52.6754 + 91.2364i) q^{25} +(-30.9005 - 53.5213i) q^{26} +(-15.8545 - 139.397i) q^{27} +(-57.3593 - 93.0701i) q^{28} +(97.0157 - 168.036i) q^{29} +(-29.4944 - 15.5750i) q^{30} -202.266 q^{31} +187.230 q^{32} +(-230.855 + 145.168i) q^{33} +(79.3960 - 137.518i) q^{34} +(-82.0618 + 2.35755i) q^{35} +(158.928 - 12.0219i) q^{36} +(81.1070 + 140.481i) q^{37} +(105.199 + 182.211i) q^{38} +(187.728 - 118.049i) q^{39} +(44.6219 - 77.2874i) q^{40} +(-52.5349 - 90.9932i) q^{41} +(-115.791 + 77.5400i) q^{42} +(-103.864 + 179.898i) q^{43} +(-154.902 - 268.297i) q^{44} +(51.8536 - 107.868i) q^{45} +(27.2571 - 47.2107i) q^{46} +75.0172 q^{47} +(3.54370 + 93.8285i) q^{48} +(-154.164 + 306.403i) q^{49} +(76.2786 + 132.118i) q^{50} +(503.854 + 266.069i) q^{51} +(125.964 + 218.176i) q^{52} +(-213.185 + 369.248i) q^{53} +(-22.9588 - 201.860i) q^{54} -232.640 q^{55} +(-195.629 - 317.424i) q^{56} +(-639.111 + 401.892i) q^{57} +(140.487 - 243.331i) q^{58} +147.765 q^{59} +(120.232 + 63.4906i) q^{60} -261.037 q^{61} -292.899 q^{62} +(-293.718 - 404.693i) q^{63} +126.564 q^{64} +189.179 q^{65} +(-334.298 + 210.217i) q^{66} +439.129 q^{67} +(-323.653 + 560.583i) q^{68} +(172.976 + 91.3431i) q^{69} +(-118.833 + 3.41394i) q^{70} +356.280 q^{71} +(542.038 - 41.0017i) q^{72} +(190.432 - 329.837i) q^{73} +(117.450 + 203.430i) q^{74} +(-463.410 + 291.406i) q^{75} +(-428.838 - 742.770i) q^{76} +(-461.617 + 855.369i) q^{77} +(271.847 - 170.945i) q^{78} +21.8320 q^{79} +(-40.0503 + 69.3691i) q^{80} +(720.705 - 109.661i) q^{81} +(-76.0752 - 131.766i) q^{82} +(525.566 - 910.307i) q^{83} +(472.013 - 316.087i) q^{84} +(243.039 + 420.957i) q^{85} +(-150.405 + 260.508i) q^{86} +(891.545 + 470.796i) q^{87} +(-528.306 - 915.052i) q^{88} +(-288.820 - 500.251i) q^{89} +(75.0886 - 156.203i) q^{90} +(375.381 - 695.574i) q^{91} +(-111.112 + 192.451i) q^{92} +(-39.6659 - 1050.26i) q^{93} +108.632 q^{94} -644.052 q^{95} +(36.7172 + 972.182i) q^{96} +(564.756 - 978.186i) q^{97} +(-223.243 + 443.698i) q^{98} +(-799.052 - 1170.23i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44q - 2q^{2} - q^{3} + 158q^{4} - 19q^{5} - 20q^{6} - 7q^{7} - 24q^{8} + 11q^{9} + O(q^{10}) $	\( 44q - 2q^{2} - q^{3} + 158q^{4} - 19q^{5} - 20q^{6} - 7q^{7} - 24q^{8} + 11q^{9} - 18q^{10} + 5q^{11} - 62q^{12} - 14q^{13} - 52q^{14} + 119q^{15} + 494q^{16} - 162q^{17} - 188q^{18} + 58q^{19} - 362q^{20} - 59q^{21} - 18q^{22} - 93q^{23} + 30q^{24} - 349q^{25} - 266q^{26} + 272q^{27} - 172q^{28} + 248q^{29} + 85q^{30} - 122q^{31} + 326q^{32} + 77q^{33} + 6q^{34} + 289q^{35} - 806q^{36} - 86q^{37} - 761q^{38} - 256q^{39} - 18q^{40} - 692q^{41} - 364q^{42} - 86q^{43} - 443q^{44} + 527q^{45} - 270q^{46} + 2010q^{47} - 1013q^{48} + 317q^{49} + 239q^{50} + 1209q^{51} - 335q^{52} + 258q^{53} + 577q^{54} - 870q^{55} - 1752q^{56} + 566q^{57} + 237q^{58} + 3330q^{59} + 1669q^{60} - 878q^{61} + 1812q^{62} + 2872q^{63} + 872q^{64} + 1226q^{65} + 1330q^{66} - 590q^{67} - 1374q^{68} + 1389q^{69} + 1251q^{70} + 636q^{71} - 5970q^{72} - 338q^{73} + 1119q^{74} + 2737q^{75} + 1006q^{76} + 2269q^{77} + 157q^{78} - 266q^{79} - 4817q^{80} - 505q^{81} + 6q^{82} - 1356q^{83} - 6013q^{84} + 483q^{85} - 3343q^{86} - 5755q^{87} + 369q^{88} - 2200q^{89} + 2665q^{90} + 1552q^{91} - 396q^{92} - 129q^{93} + 2382q^{94} - 6166q^{95} - 5941q^{96} - 266q^{97} + 3601q^{98} - 5395q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.44809			0.511977			0.255988	−	0.966680i	$-0.417599\pi$
$2$	1.44809			0.511977			0.255988	+	0.966680i	$0.417599\pi$
$3$	0.196108	+	5.19245i	0.0377409	+	0.999288i
$3$	0.196108	+	5.19245i	0.0377409	+	0.999288i
$4$	−5.90304			−0.737880
$5$	−2.21638	+	3.83887i	−0.198239	+	0.343359i	−0.947957	−	0.318397i	$-0.896855\pi$
$5$	−2.21638	+	3.83887i	−0.198239	+	0.343359i	0.749719	+	0.661757i	$0.230189\pi$
$6$	0.283981	+	7.51913i	0.0193225	+	0.511612i
$7$	9.71690	+	15.7665i	0.524664	+	0.851310i
$7$	9.71690	+	15.7665i	0.524664	+	0.851310i
$8$	−20.1328			−0.889754
$9$	−26.9231	+	2.03656i	−0.997151	+	0.0754281i
$10$	−3.20951	+	5.55903i	−0.101494	+	0.175792i
$11$	26.2410	+	45.4507i	0.719269	+	1.24581i	0.961290	+	0.275539i	$0.0888564\pi$
$11$	26.2410	+	45.4507i	0.719269	+	1.24581i	−0.242021	+	0.970271i	$0.577810\pi$
$12$	−1.15763	−	30.6512i	−0.0278483	−	0.737354i
$13$	−21.3388	−	36.9599i	−0.455256	−	0.788526i	0.543447	−	0.839443i	$-0.317119\pi$
$13$	−21.3388	−	36.9599i	−0.455256	−	0.788526i	−0.998703	+	0.0509172i	$0.983786\pi$
$14$	14.0709	+	22.8313i	0.268616	+	0.435851i
$15$	−20.3678	−	10.7556i	−0.350596	−	0.185139i
$16$	18.0702			0.282346
$17$	54.8281	−	94.9651i	0.782222	−	1.35485i	−0.148422	−	0.988924i	$-0.547419\pi$
$17$	54.8281	−	94.9651i	0.782222	−	1.35485i	0.930644	−	0.365925i	$-0.119247\pi$
$18$	−38.9870	+	2.94912i	−0.510518	+	0.0386174i
$19$	72.6470	+	125.828i	0.877178	+	1.51932i	0.854425	+	0.519575i	$0.173910\pi$
$19$	72.6470	+	125.828i	0.877178	+	1.51932i	0.0227527	+	0.999741i	$0.492757\pi$
$20$	13.0833	−	22.6610i	0.146276	−	0.253358i
$21$	−79.9611	+	53.5465i	−0.830902	+	0.556419i
$22$	37.9993	+	65.8167i	0.368249	+	0.637826i
$23$	18.8228	−	32.6021i	0.170645	−	0.295566i	−0.768001	−	0.640449i	$-0.778748\pi$
$23$	18.8228	−	32.6021i	0.170645	−	0.295566i	0.938645	+	0.344884i	$0.112082\pi$
$24$	−3.94820	−	104.539i	−0.0335801	−	0.889120i
$25$	52.6754	+	91.2364i	0.421403	+	0.729891i
$26$	−30.9005	−	53.5213i	−0.233080	−	0.403707i
$27$	−15.8545	−	139.397i	−0.113008	−	0.993594i
$28$	−57.3593	−	93.0701i	−0.387139	−	0.628164i
$29$	97.0157	−	168.036i	0.621220	−	1.07598i	−0.368039	−	0.929810i	$-0.619971\pi$
$29$	97.0157	−	168.036i	0.621220	−	1.07598i	0.989259	−	0.146174i	$-0.0466958\pi$
$30$	−29.4944	−	15.5750i	−0.179497	−	0.0947867i
$31$	−202.266			−1.17187			−0.585936	−	0.810357i	$-0.699273\pi$
$31$	−202.266			−1.17187			−0.585936	+	0.810357i	$0.699273\pi$
$32$	187.230			1.03431
$33$	−230.855	+	145.168i	−1.21778	+	0.765775i
$34$	79.3960	−	137.518i	0.400480	−	0.693651i
$35$	−82.0618	+	2.35755i	−0.396314	+	0.0113857i
$36$	158.928	−	12.0219i	0.735778	−	0.0556568i
$37$	81.1070	+	140.481i	0.360376	+	0.624189i	0.988023	−	0.154309i	$-0.0493151\pi$
$37$	81.1070	+	140.481i	0.360376	+	0.624189i	−0.627647	+	0.778498i	$0.715982\pi$
$38$	105.199	+	182.211i	0.449094	+	0.777854i
$39$	187.728	−	118.049i	0.770783	−	0.484691i
$40$	44.6219	−	77.2874i	0.176384	−	0.305505i
$41$	−52.5349	−	90.9932i	−0.200112	−	0.346603i	0.748453	−	0.663188i	$-0.230797\pi$
$41$	−52.5349	−	90.9932i	−0.200112	−	0.346603i	−0.948564	+	0.316585i	$0.897464\pi$
$42$	−115.791	+	77.5400i	−0.425402	+	0.284874i
$43$	−103.864	+	179.898i	−0.368352	+	0.638004i	−0.989308	−	0.145841i	$-0.953411\pi$
$43$	−103.864	+	179.898i	−0.368352	+	0.638004i	0.620956	+	0.783845i	$0.286745\pi$
$44$	−154.902	−	268.297i	−0.530734	−	0.919258i
$45$	51.8536	−	107.868i	0.171775	−	0.357334i
$46$	27.2571	−	47.2107i	0.0873662	−	0.151323i
$47$	75.0172			0.232817			0.116408	−	0.993201i	$-0.462862\pi$
$47$	75.0172			0.232817			0.116408	+	0.993201i	$0.462862\pi$
$48$	3.54370	+	93.8285i	0.0106560	+	0.282145i
$49$	−154.164	+	306.403i	−0.449456	+	0.893302i
$50$	76.2786	+	132.118i	0.215748	+	0.373687i
$51$	503.854	+	266.069i	1.38341	+	0.730532i
$52$	125.964	+	218.176i	0.335924	+	0.581838i
$53$	−213.185	+	369.248i	−0.552514	+	0.956983i	0.445578	+	0.895243i	$0.352998\pi$
$53$	−213.185	+	369.248i	−0.552514	+	0.956983i	−0.998092	+	0.0617395i	$0.980335\pi$
$54$	−22.9588	−	201.860i	−0.0578573	−	0.508697i
$55$	−232.640			−0.570348
$56$	−195.629	−	317.424i	−0.466821	−	0.757456i
$57$	−639.111	+	401.892i	−1.48513	+	0.933893i
$58$	140.487	−	243.331i	0.318050	−	0.550879i
$59$	147.765			0.326057			0.163028	−	0.986621i	$-0.447874\pi$
$59$	147.765			0.326057			0.163028	+	0.986621i	$0.447874\pi$
$60$	120.232	+	63.4906i	0.258698	+	0.136610i
$61$	−261.037			−0.547908			−0.273954	−	0.961743i	$-0.588332\pi$
$61$	−261.037			−0.547908			−0.273954	+	0.961743i	$0.588332\pi$
$62$	−292.899			−0.599971
$63$	−293.718	−	404.693i	−0.587382	−	0.809310i
$64$	126.564			0.247196
$65$	189.179			0.360997
$66$	−334.298	+	210.217i	−0.623473	+	0.392059i
$67$	439.129			0.800719			0.400359	−	0.916358i	$-0.368885\pi$
$67$	439.129			0.800719			0.400359	+	0.916358i	$0.368885\pi$
$68$	−323.653	+	560.583i	−0.577186	+	0.999716i
$69$	172.976	+	91.3431i	0.301795	+	0.159368i
$70$	−118.833	+	3.41394i	−0.202903	+	0.00582920i
$71$	356.280			0.595531			0.297766	−	0.954639i	$-0.403759\pi$
$71$	356.280			0.595531			0.297766	+	0.954639i	$0.403759\pi$
$72$	542.038	−	41.0017i	0.887219	−	0.0671124i
$73$	190.432	−	329.837i	0.305320	−	0.528829i	−0.672013	−	0.740539i	$-0.734570\pi$
$73$	190.432	−	329.837i	0.305320	−	0.528829i	0.977332	+	0.211710i	$0.0679034\pi$
$74$	117.450	+	203.430i	0.184504	+	0.319570i
$75$	−463.410	+	291.406i	−0.713467	+	0.448649i
$76$	−428.838	−	742.770i	−0.647252	−	1.12107i
$77$	−461.617	+	855.369i	−0.683196	+	1.26595i
$78$	271.847	−	170.945i	0.394623	−	0.248151i
$79$	21.8320			0.0310923			0.0155462	−	0.999879i	$-0.495051\pi$
$79$	21.8320			0.0310923			0.0155462	+	0.999879i	$0.495051\pi$
$80$	−40.0503	+	69.3691i	−0.0559720	+	0.0969463i
$81$	720.705	−	109.661i	0.988621	−	0.150426i
$82$	−76.0752	−	131.766i	−0.102452	−	0.177453i
$83$	525.566	−	910.307i	0.695040	−	1.20384i	−0.275127	−	0.961408i	$-0.588720\pi$
$83$	525.566	−	910.307i	0.695040	−	1.20384i	0.970167	−	0.242437i	$-0.0779468\pi$
$84$	472.013	−	316.087i	0.613106	−	0.410570i
$85$	243.039	+	420.957i	0.310133	+	0.537167i
$86$	−150.405	+	260.508i	−0.188588	+	0.326643i
$87$	891.545	+	470.796i	1.09866	+	0.580168i
$88$	−528.306	−	915.052i	−0.639972	−	1.10846i
$89$	−288.820	−	500.251i	−0.343987	−	0.595803i	0.641182	−	0.767389i	$-0.278444\pi$
$89$	−288.820	−	500.251i	−0.343987	−	0.595803i	−0.985169	+	0.171586i	$0.945111\pi$
$90$	75.0886	−	156.203i	0.0879448	−	0.182947i
$91$	375.381	−	695.574i	0.432424	−	0.801275i
$92$	−111.112	+	192.451i	−0.125915	+	0.218092i
$93$	−39.6659	−	1050.26i	−0.0442275	−	1.17104i
$94$	108.632			0.119197
$95$	−644.052			−0.695562
$96$	36.7172	+	972.182i	0.0390358	+	1.03357i
$97$	564.756	−	978.186i	0.591157	−	1.02391i	−0.402920	−	0.915235i	$-0.632005\pi$
$97$	564.756	−	978.186i	0.591157	−	1.02391i	0.994077	−	0.108679i	$-0.0346621\pi$
$98$	−223.243	+	443.698i	−0.230111	+	0.457350i
$99$	−799.052	−	1170.23i	−0.811189	−	1.18801i
$100$	−310.945	−	538.572i	−0.310945	−	0.538572i
$101$	−369.355	−	639.742i	−0.363884	−	0.630265i	0.624713	−	0.780855i	$-0.285216\pi$
$101$	−369.355	−	639.742i	−0.363884	−	0.630265i	−0.988596	+	0.150590i	$0.951883\pi$
$102$	729.625	+	385.292i	0.708271	+	0.374015i
$103$	198.856	−	344.429i	0.190232	−	0.329491i	−0.755095	−	0.655615i	$-0.772409\pi$
$103$	198.856	−	344.429i	0.190232	−	0.329491i	0.945327	+	0.326124i	$0.105743\pi$
$104$	429.611	+	744.108i	0.405066	+	0.701594i
$105$	−28.3344	−	425.640i	−0.0263348	−	0.395602i
$106$	−308.711	+	534.704i	−0.282874	+	0.489953i
$107$	−263.679	−	456.706i	−0.238232	−	0.412630i	0.721975	−	0.691919i	$-0.243235\pi$
$107$	−263.679	−	456.706i	−0.238232	−	0.412630i	−0.960207	+	0.279289i	$0.909901\pi$
$108$	93.5900	+	822.868i	0.0833861	+	0.733153i
$109$	−0.0844665	+	0.146300i	−7.42241e−5	+	0.000128560i	−0.866063	−	0.499936i	$-0.833357\pi$
$109$	−0.0844665	+	0.146300i	−7.42241e−5	+	0.000128560i	0.865988	+	0.500064i	$0.166690\pi$
$110$	−336.883			−0.292005
$111$	−713.537	+	448.693i	−0.610144	+	0.383677i
$112$	175.586	+	284.903i	0.148137	+	0.240364i
$113$	149.961	+	259.741i	0.124842	+	0.216233i	0.921671	−	0.387972i	$-0.126824\pi$
$113$	149.961	+	259.741i	0.124842	+	0.216233i	−0.796829	+	0.604205i	$0.793491\pi$
$114$	−925.489	+	581.975i	−0.760351	+	0.478131i
$115$	83.4369	+	144.517i	0.0676568	+	0.117185i
$116$	−572.687	+	991.924i	−0.458385	+	0.793947i
$117$	649.778	+	951.618i	0.513436	+	0.751941i
$118$	213.977			0.166933
$119$	2030.03	−	58.3205i	1.56380	−	0.0449263i
$120$	410.062	+	216.540i	0.311945	+	0.164728i
$121$	−711.680	+	1232.67i	−0.534696	+	0.926120i
$122$	−378.005			−0.280516
$123$	462.175	−	290.629i	0.338804	−	0.213050i
$124$	1193.98			0.864701
$125$	−1021.09			−0.730631
$126$	−425.330	−	586.032i	−0.300726	−	0.414348i
$127$	−1116.82			−0.780330			−0.390165	−	0.920745i	$-0.627582\pi$
$127$	−1116.82			−0.780330			−0.390165	+	0.920745i	$0.627582\pi$
$128$	−1314.56			−0.907750
$129$	−954.480	−	504.030i	−0.651452	−	0.344011i
$130$	273.949			0.184822
$131$	334.249	−	578.937i	0.222927	−	0.386122i	−0.732768	−	0.680478i	$-0.761772\pi$
$131$	334.249	−	578.937i	0.222927	−	0.386122i	0.955696	+	0.294357i	$0.0951054\pi$
$132$	1362.74	−	856.934i	0.898573	−	0.565050i
$133$	−1277.97	+	2368.05i	−0.833185	+	1.54388i
$134$	635.898			0.409949
$135$	570.269	+	248.093i	0.363562	+	0.158166i
$136$	−1103.85	+	1911.92i	−0.695985	+	1.20548i
$137$	1163.25	+	2014.82i	0.725427	+	1.25648i	0.958798	+	0.284089i	$0.0916910\pi$
$137$	1163.25	+	2014.82i	0.725427	+	1.25648i	−0.233371	+	0.972388i	$0.574976\pi$
$138$	250.485	+	132.273i	0.154512	+	0.0815929i
$139$	119.539	+	207.047i	0.0729433	+	0.126342i	0.900190	−	0.435497i	$-0.143427\pi$
$139$	119.539	+	207.047i	0.0729433	+	0.126342i	−0.827247	+	0.561839i	$0.810094\pi$
$140$	484.414	−	13.9167i	0.292432	−	0.00840125i
$141$	14.7114	+	389.523i	0.00878672	+	0.232651i
$142$	515.926			0.304898
$143$	1119.90	−	1939.73i	0.654903	−	1.13432i
$144$	−486.505	+	36.8010i	−0.281542	+	0.0212968i
$145$	430.046	+	744.862i	0.246299	+	0.426603i
$146$	275.762	−	477.633i	0.156317	−	0.270748i
$147$	−1621.21	−	740.399i	−0.909629	−	0.415422i
$148$	−478.778	−	829.267i	−0.265914	−	0.460577i
$149$	996.454	−	1725.91i	0.547871	−	0.948940i	−0.450550	−	0.892751i	$-0.648772\pi$
$149$	996.454	−	1725.91i	0.547871	−	0.948940i	0.998420	−	0.0561883i	$-0.0178947\pi$
$150$	−671.060	+	421.982i	−0.365279	+	0.229698i
$151$	−1180.35	−	2044.43i	−0.636129	−	1.10181i	−0.986275	−	0.165113i	$-0.947201\pi$
$151$	−1180.35	−	2044.43i	−0.636129	−	1.10181i	0.350146	−	0.936695i	$-0.386132\pi$
$152$	−1462.59	−	2533.28i	−0.780472	−	1.35182i
$153$	−1282.74	+	2668.42i	−0.677800	+	1.40999i
$154$	−668.462	+	1238.65i	−0.349781	+	0.648138i
$155$	448.297	−	776.474i	0.232310	−	0.402373i
$156$	−1108.17	+	696.847i	−0.568745	+	0.357644i
$157$	2262.73			1.15023			0.575113	−	0.818074i	$-0.304958\pi$
$157$	2262.73			1.15023			0.575113	+	0.818074i	$0.304958\pi$
$158$	31.6147			0.0159185
$159$	−1959.11	−	1034.54i	−0.977153	−	0.516003i
$160$	−414.972	+	718.752i	−0.205040	+	0.355140i
$161$	696.920	−	20.0218i	0.341149	−	0.00980084i
$162$	1043.64	−	158.799i	0.506151	−	0.0770148i
$163$	1085.74	+	1880.56i	0.521728	+	0.903659i	0.999681	+	0.0252736i	$0.00804570\pi$
$163$	1085.74	+	1880.56i	0.521728	+	0.903659i	−0.477953	+	0.878386i	$0.658621\pi$
$164$	310.116	+	537.136i	0.147658	+	0.255752i
$165$	−45.6224	−	1207.97i	−0.0215254	−	0.569941i
$166$	761.066	−	1318.20i	0.355844	−	0.616341i
$167$	−17.1772	−	29.7518i	−0.00795937	−	0.0137860i	0.862018	−	0.506877i	$-0.169200\pi$
$167$	−17.1772	−	29.7518i	−0.00795937	−	0.0137860i	−0.869978	+	0.493091i	$0.835867\pi$
$168$	1609.84	−	1078.04i	0.739298	−	0.495076i
$169$	187.809	−	325.295i	0.0854842	−	0.148063i
$170$	351.943	+	609.583i	0.158781	+	0.275017i
$171$	−2212.14	−	3239.74i	−0.989278	−	1.44882i
$172$	613.114	−	1061.94i	0.271799	−	0.470770i
$173$	100.393			0.0441200			0.0220600	−	0.999757i	$-0.492978\pi$
$173$	100.393			0.0441200			0.0220600	+	0.999757i	$0.492978\pi$
$174$	1291.04	+	681.755i	0.562490	+	0.297033i
$175$	−926.635	+	1717.04i	−0.400269	+	0.741692i
$176$	474.179	+	821.303i	0.203083	+	0.351750i
$177$	28.9778	+	767.262i	0.0123057	+	0.325824i
$178$	−418.237	−	724.408i	−0.176113	−	0.305037i
$179$	−987.721	+	1710.78i	−0.412434	+	0.714357i	−0.995155	−	0.0983150i	$-0.968655\pi$
$179$	−987.721	+	1710.78i	−0.412434	+	0.714357i	0.582721	+	0.812672i	$0.301988\pi$
$180$	−306.094	+	636.750i	−0.126749	+	0.263670i
$181$	2193.67			0.900850			0.450425	−	0.892814i	$-0.351272\pi$
$181$	2193.67			0.900850			0.450425	+	0.892814i	$0.351272\pi$
$182$	543.584	−	1007.25i	0.221391	−	0.410234i
$183$	−51.1914	−	1355.42i	−0.0206785	−	0.547518i
$184$	−378.957	+	656.373i	−0.151832	+	0.262981i
$185$	−719.054			−0.285762
$186$	−57.4397	−	1520.86i	−0.0226435	−	0.599544i
$187$	5754.98			2.25051
$188$	−442.829			−0.171791
$189$	2043.75	−	1604.48i	0.786565	−	0.617507i
$190$	−932.645			−0.356112
$191$	−1072.32			−0.406231			−0.203116	−	0.979155i	$-0.565107\pi$
$191$	−1072.32			−0.406231			−0.203116	+	0.979155i	$0.565107\pi$
$192$	24.8202	+	657.178i	0.00932939	+	0.247019i
$193$	−5258.54			−1.96123			−0.980616	−	0.195941i	$-0.937224\pi$
$193$	−5258.54			−1.96123			−0.980616	+	0.195941i	$0.937224\pi$
$194$	817.817	−	1416.50i	0.302659	−	0.524220i
$195$	37.0995	+	982.305i	0.0136244	+	0.360740i
$196$	910.033	−	1808.71i	0.331645	−	0.659150i
$197$	4365.42			1.57880			0.789399	−	0.613880i	$-0.210392\pi$
$197$	4365.42			1.57880			0.789399	+	0.613880i	$0.210392\pi$
$198$	−1157.10	−	1694.60i	−0.415310	−	0.608233i
$199$	−81.1941	+	140.632i	−0.0289231	+	0.0500963i	−0.880125	−	0.474743i	$-0.842541\pi$
$199$	−81.1941	+	140.632i	−0.0289231	+	0.0500963i	0.851202	+	0.524839i	$0.175874\pi$
$200$	−1060.50	−	1836.85i	−0.374945	−	0.649424i
$201$	86.1165	+	2280.16i	0.0302199	+	0.800148i
$202$	−534.860	−	926.404i	−0.186300	−	0.322681i
$203$	3592.03	−	103.195i	1.24193	−	0.0356792i
$204$	−2974.27	−	1570.62i	−1.02079	−	0.539045i
$205$	465.748			0.158679
$206$	287.961	−	498.764i	0.0973942	−	0.168692i
$207$	−440.373	+	916.083i	−0.147865	+	0.307595i
$208$	−385.596	−	667.872i	−0.128540	−	0.222638i
$209$	−3812.66	+	6603.72i	−1.26185	+	2.18559i
$210$	−41.0307	−	616.364i	−0.0134828	−	0.202539i
$211$	948.694	+	1643.19i	0.309530	+	0.536121i	0.978260	−	0.207384i	$-0.0664951\pi$
$211$	948.694	+	1643.19i	0.309530	+	0.536121i	−0.668730	+	0.743505i	$0.733162\pi$
$212$	1258.44	−	2179.68i	0.407689	−	0.706138i
$213$	69.8693	+	1849.97i	0.0224759	+	0.595107i
$214$	−381.831	−	661.351i	−0.121969	−	0.211257i
$215$	−460.404	−	797.443i	−0.146043	−	0.252954i
$216$	319.197	+	2806.46i	0.100549	+	0.884054i
$217$	−1965.40	−	3189.02i	−0.614839	−	0.997626i
$218$	−0.122315	+	0.211856i	−3.80010e−5	+	6.58197e-5i
$219$	1750.01	+	924.123i	0.539975	+	0.285144i
$220$	1373.28			0.420848
$221$	−4679.87			−1.42445
$222$	−1033.27	+	649.748i	−0.312379	+	0.196433i
$223$	−2214.51	+	3835.64i	−0.664998	+	1.15181i	0.314288	+	0.949328i	$0.398234\pi$
$223$	−2214.51	+	3835.64i	−0.664998	+	1.15181i	−0.979286	+	0.202482i	$0.935099\pi$
$224$	1819.30	+	2951.96i	0.542664	+	0.880517i
$225$	−1603.99	−	2349.09i	−0.475257	−	0.696026i
$226$	217.158	+	376.128i	0.0639164	+	0.110706i
$227$	−1443.96	−	2501.01i	−0.422198	−	0.731269i	0.573956	−	0.818886i	$-0.305408\pi$
$227$	−1443.96	−	2501.01i	−0.422198	−	0.731269i	−0.996154	+	0.0876174i	$0.972075\pi$
$228$	3772.70	−	2372.38i	1.09585	−	0.689101i
$229$	246.093	−	426.246i	0.0710144	−	0.123001i	−0.828332	−	0.560238i	$-0.810710\pi$
$229$	246.093	−	426.246i	0.0710144	−	0.123001i	0.899346	+	0.437237i	$0.144043\pi$
$230$	120.824	+	209.273i	0.0346387	+	0.0599960i
$231$	−4531.99	−	2229.18i	−1.29083	−	0.634931i
$232$	−1953.20	+	3383.04i	−0.552733	+	0.957361i
$233$	2390.19	+	4139.94i	0.672046	+	1.16402i	0.977323	+	0.211754i	$0.0679177\pi$
$233$	2390.19	+	4139.94i	0.672046	+	1.16402i	−0.305277	+	0.952264i	$0.598749\pi$
$234$	940.936	+	1378.03i	0.262867	+	0.384976i
$235$	−166.266	+	287.982i	−0.0461533	+	0.0799398i
$236$	−872.262			−0.240591
$237$	4.28142	+	113.362i	0.00117345	+	0.0310702i
$238$	2939.66	−	84.4532i	0.800629	−	0.0230012i
$239$	−2954.59	−	5117.51i	−0.799652	−	1.38504i	−0.919843	−	0.392287i	$-0.871684\pi$
$239$	−2954.59	−	5117.51i	−0.799652	−	1.38504i	0.120191	−	0.992751i	$-0.461649\pi$
$240$	−368.050	−	194.355i	−0.0989897	−	0.0522733i
$241$	−75.8276	−	131.337i	−0.0202676	−	0.0351045i	0.855714	−	0.517450i	$-0.173118\pi$
$241$	−75.8276	−	131.337i	−0.0202676	−	0.0351045i	−0.875981	+	0.482345i	$0.839785\pi$
$242$	−1030.58	+	1785.01i	−0.273752	+	0.474152i
$243$	710.744	+	3720.72i	0.187631	+	0.982240i
$244$	1540.91			0.404290
$245$	−834.557	−	1270.92i	−0.217624	−	0.331412i
$246$	669.270	−	420.857i	0.173460	−	0.109077i
$247$	3100.41	−	5370.06i	0.798680	−	1.38336i
$248$	4072.19			1.04268
$249$	4829.79	+	2550.46i	1.22922	+	0.649111i
$250$	−1478.63			−0.374066
$251$	−29.8186			−0.00749854			−0.00374927	−	0.999993i	$-0.501193\pi$
$251$	−29.8186			−0.00749854			−0.00374927	+	0.999993i	$0.501193\pi$
$252$	1733.83	+	2388.92i	0.433417	+	0.597174i
$253$	1975.72			0.490958
$254$	−1617.26			−0.399511
$255$	−2138.14	+	1344.52i	−0.525079	+	0.330186i
$256$	−2916.12			−0.711943
$257$	−301.982	+	523.049i	−0.0732963	+	0.126953i	−0.900344	−	0.435179i	$-0.856685\pi$
$257$	−301.982	+	523.049i	−0.0732963	+	0.126953i	0.827048	+	0.562132i	$0.190019\pi$
$258$	−1382.17	−	729.880i	−0.333528	−	0.176125i
$259$	−1426.79	+	2643.82i	−0.342302	+	0.634281i
$260$	−1116.73			−0.266373
$261$	−2269.75	+	4721.63i	−0.538290	+	1.11978i
$262$	484.023	−	838.352i	0.114134	−	0.197685i
$263$	1360.86	+	2357.08i	0.319066	+	0.552638i	0.980293	−	0.197547i	$-0.0632975\pi$
$263$	1360.86	+	2357.08i	0.319066	+	0.552638i	−0.661228	+	0.750185i	$0.729964\pi$
$264$	4647.76	−	2922.65i	1.08352	−	0.681351i
$265$	−944.997	−	1636.78i	−0.219059	−	0.379422i
$266$	−1850.61	+	3429.15i	−0.426572	+	0.790430i
$267$	2540.89	−	1597.79i	0.582396	−	0.366228i
$268$	−2592.20			−0.590834
$269$	−1346.22	+	2331.72i	−0.305131	+	0.528503i	−0.977291	−	0.211904i	$-0.932034\pi$
$269$	−1346.22	+	2331.72i	−0.305131	+	0.528503i	0.672159	+	0.740407i	$0.265367\pi$
$270$	825.800	+	359.261i	0.186135	+	0.0809776i
$271$	−595.824	−	1032.00i	−0.133556	−	0.231326i	0.791489	−	0.611184i	$-0.209306\pi$
$271$	−595.824	−	1032.00i	−0.133556	−	0.231326i	−0.925045	+	0.379857i	$0.875973\pi$
$272$	990.754	−	1716.04i	0.220858	−	0.382537i
$273$	3685.35	+	1812.74i	0.817024	+	0.401875i
$274$	1684.50	+	2917.63i	0.371402	+	0.643287i
$275$	−2764.51	+	4788.27i	−0.606204	+	1.04998i
$276$	−1021.08	−	539.202i	−0.222689	−	0.117595i
$277$	−3490.45	−	6045.64i	−0.757115	−	1.31136i	−0.944316	−	0.329041i	$-0.893275\pi$
$277$	−3490.45	−	6045.64i	−0.757115	−	1.31136i	0.187200	−	0.982322i	$-0.440059\pi$
$278$	173.102	+	299.822i	0.0373453	+	0.0646839i
$279$	5445.62	−	411.926i	1.16853	−	0.0883921i
$280$	1652.14	−	47.4641i	0.352622	−	0.0101304i
$281$	−3073.57	+	5323.59i	−0.652506	+	1.13017i	0.330007	+	0.943978i	$0.392949\pi$
$281$	−3073.57	+	5323.59i	−0.652506	+	1.13017i	−0.982513	+	0.186195i	$0.940385\pi$
$282$	21.3035	+	564.064i	0.00449859	+	0.119112i
$283$	−4784.78			−1.00504			−0.502519	−	0.864566i	$-0.667593\pi$
$283$	−4784.78			−1.00504			−0.502519	+	0.864566i	$0.667593\pi$
$284$	−2103.14			−0.439430
$285$	−126.304	−	3344.21i	−0.0262511	−	0.695066i
$286$	1621.72	−	2808.90i	0.335295	−	0.580748i
$287$	924.165	−	1712.46i	0.190076	−	0.352207i
$288$	−5040.81	+	381.305i	−1.03136	+	0.0780159i
$289$	−3555.75	−	6158.74i	−0.723743	−	1.25356i
$290$	622.745	+	1078.63i	0.126100	+	0.218411i
$291$	5189.93	+	2740.64i	1.04550	+	0.552093i
$292$	−1124.12	+	1947.04i	−0.225289	+	0.390212i
$293$	−4130.04	−	7153.44i	−0.823480	−	1.42631i	−0.903075	−	0.429482i	$-0.858696\pi$
$293$	−4130.04	−	7153.44i	−0.823480	−	1.42631i	0.0795955	−	0.996827i	$-0.474637\pi$
$294$	−2347.66	−	1072.16i	−0.465709	−	0.212686i
$295$	−327.502	+	567.251i	−0.0646370	+	0.111955i
$296$	−1632.91	−	2828.29i	−0.320646	−	0.555375i
$297$	5919.68	−	4378.53i	1.15655	−	0.855448i
$298$	1442.95	−	2499.27i	0.280497	−	0.485835i
$299$	−1606.63			−0.310748
$300$	2735.53	−	1720.18i	0.526453	−	0.331049i
$301$	−3845.60	+	110.480i	−0.736400	+	0.0211560i
$302$	−1709.25	−	2960.51i	−0.325683	−	0.564100i
$303$	3249.40	−	2043.32i	0.616083	−	0.387411i
$304$	1312.74	+	2273.74i	0.247668	+	0.428974i
$305$	578.556	−	1002.09i	0.108617	−	0.188129i
$306$	−1857.52	+	3864.10i	−0.347018	+	0.721882i
$307$	1586.28			0.294899			0.147449	−	0.989070i	$-0.452894\pi$
$307$	1586.28			0.294899			0.147449	+	0.989070i	$0.452894\pi$
$308$	2724.94	−	5049.27i	0.504117	−	0.934120i
$309$	1827.43	+	965.005i	0.336436	+	0.177661i
$310$	649.174	−	1124.40i	0.118938	−	0.206006i
$311$	−2809.95			−0.512339			−0.256170	−	0.966632i	$-0.582461\pi$
$311$	−2809.95			−0.512339			−0.256170	+	0.966632i	$0.582461\pi$
$312$	−3779.50	+	2376.66i	−0.685807	+	0.431256i
$313$	4537.47			0.819403			0.409701	−	0.912220i	$-0.365633\pi$
$313$	4537.47			0.819403			0.409701	+	0.912220i	$0.365633\pi$
$314$	3276.64			0.588889
$315$	2204.56	−	230.596i	0.394326	−	0.0412464i
$316$	−128.875			−0.0229424
$317$	−2187.89			−0.387647			−0.193823	−	0.981036i	$-0.562089\pi$
$317$	−2187.89			−0.387647			−0.193823	+	0.981036i	$0.562089\pi$
$318$	−2836.96	−	1498.11i	−0.500280	−	0.264182i
$319$	10183.2			1.78730
$320$	−280.514	+	485.864i	−0.0490037	+	0.0848769i
$321$	2319.71	−	1458.71i	0.403345	−	0.253636i
$322$	1009.20	−	28.9933i	0.174660	−	0.00501780i
$323$	15932.4			2.74459
$324$	−4254.35	+	647.332i	−0.729484	+	0.110997i
$325$	2248.06	−	3893.76i	0.383692	−	0.664574i
$326$	1572.25	+	2723.21i	0.267113	+	0.462652i
$327$	−0.776222	−	0.409898i	−0.000131270	−	6.93192e-5i
$328$	1057.68	+	1831.95i	0.178050	+	0.308392i
$329$	728.935	+	1182.76i	0.122150	+	0.198199i
$330$	−66.0653	−	1749.25i	−0.0110205	−	0.291797i
$331$	−1808.57			−0.300325			−0.150163	−	0.988661i	$-0.547980\pi$
$331$	−1808.57			−0.300325			−0.150163	+	0.988661i	$0.547980\pi$
$332$	−3102.43	+	5373.57i	−0.512856	+	0.888293i
$333$	−2469.75	−	3617.01i	−0.406431	−	0.595229i
$334$	−24.8742	−	43.0833i	−0.00407501	−	0.00705813i
$335$	−973.275	+	1685.76i	−0.158733	+	0.274934i
$336$	−1444.91	+	967.594i	−0.234602	+	0.157103i
$337$	−845.218	−	1463.96i	−0.136623	−	0.236638i	0.789593	−	0.613631i	$-0.210292\pi$
$337$	−845.218	−	1463.96i	−0.136623	−	0.236638i	−0.926216	+	0.376992i	$0.876958\pi$
$338$	271.964	−	471.055i	0.0437659	−	0.0758048i
$339$	−1319.28	+	829.605i	−0.211368	+	0.132914i
$340$	−1434.67	−	2484.92i	−0.228841	−	0.396364i
$341$	−5307.66	−	9193.14i	−0.842892	−	1.45993i
$342$	−3203.37	−	4691.43i	−0.506487	−	0.741764i
$343$	−6328.88	+	546.670i	−0.996290	+	0.0860565i
$344$	2091.08	−	3621.86i	0.327743	−	0.567667i
$345$	−734.035	+	461.583i	−0.114548	+	0.0720313i
$346$	145.379			0.0225884
$347$	8614.10			1.33265			0.666324	−	0.745662i	$-0.267867\pi$
$347$	8614.10			1.33265			0.666324	+	0.745662i	$0.267867\pi$
$348$	−5262.82	−	2779.13i	−0.810681	−	0.428094i
$349$	3434.46	−	5948.67i	0.526770	−	0.912392i	−0.472744	−	0.881200i	$-0.656736\pi$
$349$	3434.46	−	5948.67i	0.526770	−	0.912392i	0.999513	−	0.0311920i	$-0.00993032\pi$
$350$	−1341.85	+	2486.43i	−0.204928	+	0.379729i
$351$	−4813.80	+	3560.56i	−0.732028	+	0.541449i
$352$	4913.10	+	8509.74i	0.743946	+	1.28855i
$353$	19.1346	+	33.1422i	0.00288508	+	0.00499711i	0.867464	−	0.497499i	$-0.165748\pi$
$353$	19.1346	+	33.1422i	0.00288508	+	0.00499711i	−0.864579	+	0.502496i	$0.832415\pi$
$354$	41.9624	+	1111.06i	0.00630022	+	0.166814i
$355$	−789.651	+	1367.72i	−0.118057	+	0.204481i
$356$	1704.92	+	2953.00i	0.253821	+	0.439631i
$357$	700.929	+	10529.4i	0.103913	+	1.56099i
$358$	−1430.31	+	2477.37i	−0.211157	+	0.365734i
$359$	402.050	+	696.371i	0.0591070	+	0.102376i	0.894065	−	0.447938i	$-0.147841\pi$
$359$	402.050	+	696.371i	0.0591070	+	0.102376i	−0.834958	+	0.550314i	$0.814508\pi$
$360$	−1043.96	+	2171.69i	−0.152837	+	0.317939i
$361$	−7125.68	+	12342.0i	−1.03888	+	1.79939i
$362$	3176.62			0.461214
$363$	−6540.12	−	3453.63i	−0.945640	−	0.499362i
$364$	−2215.89	+	4106.00i	−0.319077	+	0.591244i
$365$	844.136	+	1462.09i	0.121052	+	0.209669i
$366$	−74.1296	−	1962.77i	−0.0105869	−	0.280316i
$367$	4198.26	+	7271.60i	0.597132	+	1.03426i	0.993242	+	0.116059i	$0.0370263\pi$
$367$	4198.26	+	7271.60i	0.597132	+	1.03426i	−0.396111	+	0.918203i	$0.629640\pi$
$368$	340.132	−	589.126i	0.0481810	−	0.0834519i
$369$	1599.71	+	2342.83i	0.225685	+	0.330522i
$370$	−1041.25			−0.146303
$371$	−7893.24	+	226.764i	−1.10457	+	0.0317332i
$372$	234.149	+	6199.70i	0.0326346	+	0.864085i
$373$	1978.22	−	3426.37i	0.274606	−	0.475632i	−0.695429	−	0.718594i	$-0.744786\pi$
$373$	1978.22	−	3426.37i	0.274606	−	0.475632i	0.970036	+	0.242962i	$0.0781192\pi$
$374$	8333.72			1.15221
$375$	−200.243	−	5301.95i	−0.0275747	−	0.730110i
$376$	−1510.31			−0.207150
$377$	−8280.81			−1.13126
$378$	2959.53	−	2323.43i	0.402703	−	0.316149i
$379$	−2203.21			−0.298605			−0.149303	−	0.988792i	$-0.547703\pi$
$379$	−2203.21			−0.298605			−0.149303	+	0.988792i	$0.547703\pi$
$380$	3801.87			0.513241
$381$	−219.017	−	5799.04i	−0.0294504	−	0.779774i
$382$	−1552.81			−0.207981
$383$	−4009.18	+	6944.11i	−0.534882	+	0.926442i	0.464287	+	0.885685i	$0.346310\pi$
$383$	−4009.18	+	6944.11i	−0.534882	+	0.926442i	−0.999169	+	0.0407576i	$0.987023\pi$
$384$	−257.796	−	6825.80i	−0.0342593	−	0.907104i
$385$	−2260.54	−	3667.91i	−0.299241	−	0.485542i
$386$	−7614.83			−1.00410
$387$	2429.97	−	5054.93i	0.319179	−	0.663971i
$388$	−3333.78	+	5774.27i	−0.436203	+	0.755526i
$389$	2496.84	+	4324.65i	0.325436	+	0.563672i	0.981601	−	0.190946i	$-0.0611556\pi$
$389$	2496.84	+	4324.65i	0.325436	+	0.563672i	−0.656164	+	0.754618i	$0.727822\pi$
$390$	53.7234	+	1422.46i	0.00697536	+	0.184690i
$391$	−2064.04	−	3575.03i	−0.266964	−	0.462396i
$392$	3103.75	−	6168.75i	0.399906	−	0.794819i
$393$	3071.65	+	1622.04i	0.394260	+	0.208196i
$394$	6321.51			0.808308
$395$	−48.3879	+	83.8103i	−0.00616370	+	0.0106758i
$396$	4716.83	+	6907.93i	0.598560	+	0.876607i
$397$	1821.32	+	3154.62i	0.230250	+	0.398805i	0.957882	−	0.287163i	$-0.0927122\pi$
$397$	1821.32	+	3154.62i	0.230250	+	0.398805i	−0.727631	+	0.685968i	$0.759379\pi$
$398$	−117.576	+	203.648i	−0.0148079	+	0.0256481i
$399$	−12546.6	−	6171.38i	−1.57422	−	0.774324i
$400$	951.853	+	1648.66i	0.118982	+	0.206082i
$401$	5351.45	−	9268.99i	0.666431	−	1.15429i	−0.312464	−	0.949930i	$-0.601154\pi$
$401$	5351.45	−	9268.99i	0.666431	−	1.15429i	0.978895	−	0.204363i	$-0.0655122\pi$
$402$	124.704	+	3301.87i	0.0154719	+	0.409657i
$403$	4316.12	+	7475.74i	0.533502	+	0.924052i
$404$	2180.32	+	3776.42i	0.268502	+	0.465060i
$405$	−1176.38	+	3009.75i	−0.144333	+	0.369273i
$406$	5201.58	−	149.436i	0.635838	−	0.0182669i
$407$	−4256.66	+	7372.75i	−0.518414	+	0.897920i
$408$	−10144.0	−	5356.72i	−1.23089	−	0.649994i
$409$	4918.40			0.594619			0.297310	−	0.954781i	$-0.403911\pi$
$409$	4918.40			0.594619			0.297310	+	0.954781i	$0.403911\pi$
$410$	674.445			0.0812402
$411$	−10233.7	+	6435.26i	−1.22820	+	0.772331i
$412$	−1173.86	+	2033.18i	−0.140368	+	0.243125i
$413$	1435.82	+	2329.73i	0.171070	+	0.277575i
$414$	−637.699	+	1326.57i	−0.0757033	+	0.157481i
$415$	2329.70	+	4035.16i	0.275568	+	0.477297i
$416$	−3995.27	−	6920.00i	−0.470875	−	0.815580i
$417$	−1051.64	+	661.301i	−0.123499	+	0.0776596i
$418$	−5521.07	+	9562.78i	−0.646039	+	1.11897i
$419$	−2009.53	−	3480.60i	−0.234300	−	0.405820i	0.724769	−	0.688992i	$-0.241947\pi$
$419$	−2009.53	−	3480.60i	−0.234300	−	0.405820i	−0.959069	+	0.283172i	$0.908613\pi$
$420$	167.259	+	2512.57i	0.0194319	+	0.291906i
$421$	6249.87	−	10825.1i	0.723516	−	1.25317i	−0.236066	−	0.971737i	$-0.575858\pi$
$421$	6249.87	−	10825.1i	0.723516	−	1.25317i	0.959582	−	0.281429i	$-0.0908084\pi$
$422$	1373.79	+	2379.48i	0.158472	+	0.274482i
$423$	−2019.69	+	152.777i	−0.232153	+	0.0175609i
$424$	4292.02	−	7434.00i	0.491602	−	0.851479i
$425$	11552.4			1.31852
$426$	101.177	+	2678.92i	0.0115071	+	0.304681i
$427$	−2536.47	−	4115.64i	−0.287467	−	0.466439i
$428$	1556.51	+	2695.95i	0.175787	+	0.304472i
$429$	10291.6	+	5434.65i	1.15823	+	0.611626i
$430$	−666.706	−	1154.77i	−0.0747707	−	0.129507i
$431$	7811.23	−	13529.4i	0.872978	−	1.51204i	0.0140778	−	0.999901i	$-0.495519\pi$
$431$	7811.23	−	13529.4i	0.872978	−	1.51204i	0.858901	−	0.512142i	$-0.171148\pi$
$432$	−286.494	−	2518.94i	−0.0319073	−	0.280538i
$433$	383.001			0.0425077			0.0212539	−	0.999774i	$-0.493234\pi$
$433$	383.001			0.0425077			0.0212539	+	0.999774i	$0.493234\pi$
$434$	−2846.07	−	4617.99i	−0.314783	−	0.510761i
$435$	−3783.33	+	2379.07i	−0.417004	+	0.262224i
$436$	0.498609	−	0.863616i	5.47684e−5	−	9.48617e-5i
$437$	5469.69			0.598743
$438$	2534.17	+	1338.21i	0.276455	+	0.145987i
$439$	−13784.6			−1.49864			−0.749318	−	0.662211i	$-0.769618\pi$
$439$	−13784.6			−1.49864			−0.749318	+	0.662211i	$0.769618\pi$
$440$	4683.69			0.507469
$441$	3526.55	−	8563.27i	0.380796	−	0.924659i
$442$	−6776.87			−0.729283
$443$	8074.79			0.866015			0.433008	−	0.901390i	$-0.357452\pi$
$443$	8074.79			0.866015			0.433008	+	0.901390i	$0.357452\pi$
$444$	4212.04	−	2648.65i	0.450213	−	0.283107i
$445$	2560.53			0.272766
$446$	−3206.81	+	5554.35i	−0.340463	+	0.589700i
$447$	9157.11	+	4835.58i	0.968941	+	0.511666i
$448$	1229.81	+	1995.47i	0.129695	+	0.210440i
$449$	−17506.7			−1.84007			−0.920037	−	0.391832i	$-0.871842\pi$
$449$	−17506.7			−1.84007			−0.920037	+	0.391832i	$0.871842\pi$
$450$	−2322.72	−	3401.69i	−0.243320	−	0.356349i
$451$	2757.14	−	4775.50i	0.287868	−	0.498602i
$452$	−885.228	−	1533.26i	−0.0921187	−	0.159554i
$453$	10384.1	−	6529.83i	1.07701	−	0.677259i
$454$	−2090.98	−	3621.69i	−0.216156	−	0.374393i
$455$	1838.24	+	2982.69i	0.189402	+	0.307320i
$456$	12867.1	−	8091.23i	1.32140	−	0.830935i
$457$	1323.72			0.135495			0.0677474	−	0.997703i	$-0.478419\pi$
$457$	1323.72			0.135495			0.0677474	+	0.997703i	$0.478419\pi$
$458$	356.365	−	617.242i	0.0363577	−	0.0629734i
$459$	−14107.2	−	6137.27i	−1.43457	−	0.624103i
$460$	−492.531	−	853.089i	−0.0499226	−	0.0864685i
$461$	7172.07	−	12422.4i	0.724591	−	1.25503i	−0.234551	−	0.972104i	$-0.575362\pi$
$461$	7172.07	−	12422.4i	0.724591	−	1.25503i	0.959142	−	0.282925i	$-0.0913048\pi$
$462$	−6562.72	−	3228.05i	−0.660877	−	0.325070i
$463$	1972.13	+	3415.83i	0.197954	+	0.342866i	0.947865	−	0.318673i	$-0.103237\pi$
$463$	1972.13	+	3415.83i	0.197954	+	0.342866i	−0.749911	+	0.661539i	$0.769904\pi$
$464$	1753.09	−	3036.44i	0.175399	−	0.303800i
$465$	4119.72	+	2175.49i	0.410854	+	0.216959i
$466$	3461.21	+	5995.00i	0.344072	+	0.595950i
$467$	−7039.21	−	12192.3i	−0.697507	−	1.20812i	−0.969328	−	0.245769i	$-0.920959\pi$
$467$	−7039.21	−	12192.3i	−0.697507	−	1.20812i	0.271822	−	0.962348i	$-0.412374\pi$
$468$	−3835.67	−	5617.44i	−0.378854	−	0.554842i
$469$	4266.97	+	6923.52i	0.420108	+	0.681660i
$470$	−240.768	+	417.023i	−0.0236294	+	0.0409273i
$471$	443.739	+	11749.1i	0.0434106	+	1.14941i
$472$	−2974.93			−0.290110
$473$	−10902.0			−1.05978
$474$	6.19988	+	164.158i	0.000600780	+	0.0159072i
$475$	−7653.42	+	13256.1i	−0.739290	+	1.28049i
$476$	−11983.3	+	344.268i	−1.15390	+	0.0331502i
$477$	4987.61	−	10375.5i	0.478757	−	0.995931i
$478$	−4278.51	−	7410.61i	−0.409403	−	0.709107i
$479$	−4988.58	−	8640.48i	−0.475854	−	0.824204i	0.523763	−	0.851864i	$-0.324528\pi$
$479$	−4988.58	−	8640.48i	−0.475854	−	0.824204i	−0.999617	+	0.0276601i	$0.991194\pi$
$480$	−3813.46	−	2013.77i	−0.362625	−	0.191491i
$481$	3461.46	−	5995.42i	0.328126	−	0.568332i
$482$	−109.805	−	190.188i	−0.0103765	−	0.0179727i
$483$	240.633	+	3614.80i	0.0226691	+	0.340536i
$484$	4201.08	−	7276.48i	0.394541	−	0.683365i
$485$	2503.42	+	4336.05i	0.234380	+	0.405959i
$486$	1029.22	+	5387.93i	0.0960625	+	0.502884i
$487$	−1115.24	+	1931.66i	−0.103771	+	0.179737i	−0.913235	−	0.407432i	$-0.866424\pi$
$487$	−1115.24	+	1931.66i	−0.103771	+	0.179737i	0.809464	+	0.587169i	$0.199758\pi$
$488$	5255.42			0.487503
$489$	−9551.77	+	6006.44i	−0.883325	+	0.555461i
$490$	−1208.51	−	1840.40i	−0.111418	−	0.169675i
$491$	2482.38	+	4299.61i	0.228163	+	0.395191i	0.957264	−	0.289216i	$-0.0933946\pi$
$491$	2482.38	+	4299.61i	0.228163	+	0.395191i	−0.729100	+	0.684407i	$0.760061\pi$
$492$	−2728.24	+	1715.60i	−0.249997	+	0.157205i
$493$	−10638.4	−	18426.2i	−0.971863	−	1.68332i
$494$	4489.66	−	7776.32i	0.408906	−	0.708246i
$495$	6263.38	−	473.784i	0.568723	−	0.0430202i
$496$	−3654.98			−0.330874
$497$	3461.94	+	5617.29i	0.312453	+	0.506981i
$498$	6993.96	+	3693.29i	0.629331	+	0.332330i
$499$	−6132.96	+	10622.6i	−0.550198	+	0.952971i	0.448062	+	0.894003i	$0.352114\pi$
$499$	−6132.96	+	10622.6i	−0.550198	+	0.952971i	−0.998260	+	0.0589685i	$0.981219\pi$
$500$	6027.52			0.539118
$501$	151.116	−	95.0265i	0.0134758	−	0.00847399i
$502$	−43.1800			−0.00383908
$503$	16083.2			1.42567			0.712836	−	0.701331i	$-0.247411\pi$
$503$	16083.2			1.42567			0.712836	+	0.701331i	$0.247411\pi$
$504$	5913.38	+	8147.62i	0.522625	+	0.720087i
$505$	3274.52			0.288543
$506$	2861.02			0.251359
$507$	1725.91	+	911.396i	0.151184	+	0.0798353i
$508$	6592.64			0.575790
$509$	−10632.4	+	18415.9i	−0.925882	+	1.60368i	−0.135746	+	0.990744i	$0.543343\pi$
$509$	−10632.4	+	18415.9i	−0.925882	+	1.60368i	−0.790136	+	0.612932i	$0.789990\pi$
$510$	−3096.21	+	1946.99i	−0.268828	+	0.169047i
$511$	7050.77	−	202.561i	0.610387	−	0.0175358i
$512$	6293.71			0.543252
$513$	16388.4	−	12121.8i	1.41046	−	1.04325i
$514$	−437.297	+	757.421i	−0.0375260	+	0.0649969i
$515$	881.479	+	1526.77i	0.0754226	+	0.130636i
$516$	5634.33	+	2975.31i	0.480693	+	0.253839i
$517$	1968.53	+	3409.59i	0.167458	+	0.290045i
$518$	−2066.12	+	3828.48i	−0.175251	+	0.324737i
$519$	19.6879	+	521.288i	0.00166513	+	0.0440886i
$520$	−3808.72			−0.321199
$521$	−10110.9	+	17512.6i	−0.850224	+	1.47263i	0.0307825	+	0.999526i	$0.490200\pi$
$521$	−10110.9	+	17512.6i	−0.850224	+	1.47263i	−0.881006	+	0.473105i	$0.843133\pi$
$522$	−3286.80	+	6837.34i	−0.275592	+	0.573299i
$523$	−3623.07	−	6275.34i	−0.302917	−	0.524668i	0.673878	−	0.738842i	$-0.264627\pi$
$523$	−3623.07	−	6275.34i	−0.302917	−	0.524668i	−0.976795	+	0.214175i	$0.931294\pi$
$524$	−1973.09	+	3417.48i	−0.164494	+	0.284911i
$525$	−9097.37	−	4474.78i	−0.756270	−	0.371991i
$526$	1970.65	+	3413.26i	0.163354	+	0.282938i
$527$	−11089.9	+	19208.2i	−0.916665	+	1.58771i
$528$	−4171.58	+	2623.22i	−0.343835	+	0.216214i
$529$	5374.90	+	9309.60i	0.441761	+	0.765152i
$530$	−1368.44	−	2370.21i	−0.112153	−	0.194255i
$531$	−3978.29	+	300.932i	−0.325128	+	0.0245938i
$532$	7543.88	−	13978.7i	0.614791	−	1.13920i
$533$	−2242.07	+	3883.37i	−0.182204	+	0.315587i
$534$	3679.43	−	2313.74i	0.298173	−	0.187500i
$535$	2337.65			0.188907
$536$	−8840.91			−0.712443
$537$	−9076.86	−	4793.20i	−0.729414	−	0.385180i
$538$	−1949.44	+	3376.53i	−0.156220	+	0.270581i
$539$	−17971.6	+	1033.46i	−1.43617	+	0.0825871i
$540$	−3366.32	−	1464.50i	−0.268265	−	0.116708i
$541$	−5211.51	−	9026.60i	−0.414160	−	0.717346i	0.581180	−	0.813775i	$-0.302591\pi$
$541$	−5211.51	−	9026.60i	−0.414160	−	0.717346i	−0.995340	+	0.0964293i	$0.969258\pi$
$542$	−862.807	−	1494.42i	−0.0683777	−	0.118434i
$543$	430.195	+	11390.5i	0.0339989	+	0.900208i
$544$	10265.5	−	17780.3i	0.809059	−	1.40133i
$545$	−0.374419	−	0.648513i	−2.94282e−5	−	5.09711e-5i
$546$	5336.71	+	2625.01i	0.418297	+	0.205751i
$547$	3552.96	−	6153.91i	0.277721	−	0.481028i	−0.693097	−	0.720845i	$-0.743754\pi$
$547$	3552.96	−	6153.91i	0.277721	−	0.481028i	0.970818	+	0.239817i	$0.0770874\pi$
$548$	−6866.73	−	11893.5i	−0.535278	−	0.927129i
$549$	7027.93	−	531.617i	0.546347	−	0.0413276i
$550$	−4003.25	+	6933.84i	−0.310362	+	0.537563i
$551$	28191.6			2.17968
$552$	−3482.50	−	1839.00i	−0.268524	−	0.141799i
$553$	212.139	+	344.214i	0.0163130	+	0.0264692i
$554$	−5054.49	−	8754.63i	−0.387625	−	0.671387i
$555$	−141.012	−	3733.65i	−0.0107849	−	0.285558i
$556$	−705.640	−	1222.21i	−0.0538234	−	0.0932249i
$557$	−47.2835	+	81.8974i	−0.00359689	+	0.00622999i	−0.867818	−	0.496882i	$-0.834478\pi$
$557$	−47.2835	+	81.8974i	−0.00359689	+	0.00622999i	0.864221	+	0.503112i	$0.167812\pi$
$558$	7885.75	−	596.506i	0.598262	−	0.0452547i
$559$	8865.36			0.670777
$560$	−1482.87	+	42.6013i	−0.111898	+	0.00321470i
$561$	1128.60	+	29882.5i	0.0849364	+	2.24891i
$562$	−4450.81	+	7709.03i	−0.334068	+	0.578622i
$563$	−10193.1			−0.763031			−0.381515	−	0.924363i	$-0.624598\pi$
$563$	−10193.1			−0.763031			−0.381515	+	0.924363i	$0.624598\pi$
$564$	−86.8422	−	2299.37i	−0.00648354	−	0.171668i
$565$	−1329.48			−0.0989943
$566$	−6928.78			−0.514556
$567$	8731.98	+	10297.4i	0.646753	+	0.762700i
$568$	−7172.94			−0.529876
$569$	−16381.8			−1.20696			−0.603479	−	0.797379i	$-0.706219\pi$
$569$	−16381.8			−1.20696			−0.603479	+	0.797379i	$0.706219\pi$
$570$	−182.899	−	4842.71i	−0.0134400	−	0.355858i
$571$	8838.50			0.647776			0.323888	−	0.946096i	$-0.395010\pi$
$571$	8838.50			0.647776			0.323888	+	0.946096i	$0.395010\pi$
$572$	−6610.84	+	11450.3i	−0.483240	+	0.836996i
$573$	−210.290	−	5567.95i	−0.0153315	−	0.405942i
$574$	1338.27	−	2479.80i	0.0973143	−	0.180322i
$575$	3966.00			0.287641
$576$	−3407.50	+	257.755i	−0.246491	+	0.0186455i
$577$	784.410	−	1358.64i	0.0565952	−	0.0980257i	−0.836340	−	0.548211i	$-0.815309\pi$
$577$	784.410	−	1358.64i	0.0565952	−	0.0980257i	0.892935	+	0.450186i	$0.148642\pi$
$578$	−5149.04	−	8918.41i	−0.370540	−	0.641794i
$579$	−1031.24	−	27304.7i	−0.0740187	−	1.95983i
$580$	−2538.58	−	4396.95i	−0.181739	−	0.314782i
$581$	19459.2	−	559.042i	1.38951	−	0.0399190i
$582$	7515.49	+	3968.69i	0.535270	+	0.282659i
$583$	−22376.8			−1.58963
$584$	−3833.93	+	6640.56i	−0.271659	+	0.470528i
$585$	−5093.29	+	385.275i	−0.359969	+	0.0272293i
$586$	−5980.67	−	10358.8i	−0.421603	−	0.730237i
$587$	−3938.28	+	6821.29i	−0.276917	+	0.479634i	−0.970617	−	0.240630i	$-0.922646\pi$
$587$	−3938.28	+	6821.29i	−0.276917	+	0.479634i	0.693700	+	0.720264i	$0.255979\pi$
$588$	9570.09	+	4370.60i	0.671197	+	0.306532i
$589$	−14694.0	−	25450.8i	−1.02794	−	1.78044i
$590$	−474.252	+	821.429i	−0.0330927	+	0.0573182i
$591$	856.092	+	22667.2i	0.0595853	+	1.57767i
$592$	1465.62	+	2538.52i	0.101751	+	0.176238i
$593$	11693.9	+	20254.4i	0.809797	+	1.40261i	0.913004	+	0.407950i	$0.133756\pi$
$593$	11693.9	+	20254.4i	0.809797	+	1.40261i	−0.103207	+	0.994660i	$0.532910\pi$
$594$	8572.22	−	6340.50i	0.592125	−	0.437969i
$595$	−4275.41	+	7922.27i	−0.294580	+	0.545851i
$596$	−5882.11	+	10188.1i	−0.404263	+	0.700203i
$597$	−746.149	−	394.017i	−0.0511522	−	0.0270118i
$598$	−2326.54			−0.159096
$599$	5493.80			0.374742			0.187371	−	0.982289i	$-0.440003\pi$
$599$	5493.80			0.374742			0.187371	+	0.982289i	$0.440003\pi$
$600$	9329.77	−	5866.84i	0.634810	−	0.399188i
$601$	4107.69	−	7114.73i	0.278796	−	0.482888i	−0.692290	−	0.721619i	$-0.743398\pi$
$601$	4107.69	−	7114.73i	0.278796	−	0.482888i	0.971086	+	0.238731i	$0.0767314\pi$
$602$	−5568.76	+	159.985i	−0.377020	+	0.0108314i
$603$	−11822.7	+	894.312i	−0.798438	+	0.0603967i
$604$	6967.65	+	12068.3i	0.469387	+	0.813002i
$605$	−3154.70	−	5464.10i	−0.211995	−	0.367186i
$606$	4705.42	−	2958.91i	0.315420	−	0.198345i
$607$	−11482.1	+	19887.6i	−0.767783	+	1.32984i	0.170979	+	0.985275i	$0.445307\pi$
$607$	−11482.1	+	19887.6i	−0.767783	+	1.32984i	−0.938763	+	0.344565i	$0.888026\pi$
$608$	13601.7	+	23558.8i	0.907273	+	1.57144i
$609$	1240.26	+	18631.2i	0.0825253	+	1.23970i
$610$	837.801	−	1451.11i	0.0556091	−	0.0963178i
$611$	−1600.78	−	2772.63i	−0.105991	−	0.183582i
$612$	7572.07	−	15751.8i	0.500135	−	1.04040i
$613$	9736.80	−	16864.6i	0.641542	−	1.11118i	−0.343546	−	0.939136i	$-0.611628\pi$
$613$	9736.80	−	16864.6i	0.641542	−	1.11118i	0.985089	−	0.172048i	$-0.0550385\pi$
$614$	2297.08			0.150981
$615$	91.3368	+	2418.38i	0.00598871	+	0.158566i
$616$	9293.66	−	17221.0i	0.607877	−	1.12639i
$617$	−13722.0	−	23767.1i	−0.895341	−	1.55078i	−0.833382	−	0.552697i	$-0.813599\pi$
$617$	−13722.0	−	23767.1i	−0.895341	−	1.55078i	−0.0619588	−	0.998079i	$-0.519735\pi$
$618$	2646.28	+	1397.41i	0.172247	+	0.0909583i
$619$	4280.39	+	7413.85i	0.277938	+	0.481402i	0.970872	−	0.239598i	$-0.0770158\pi$
$619$	4280.39	+	7413.85i	0.277938	+	0.481402i	−0.692934	+	0.721001i	$0.743682\pi$
$620$	−2646.32	+	4583.55i	−0.171417	+	0.296903i
$621$	−4843.08	−	2106.96i	−0.312956	−	0.136151i
$622$	−4069.05			−0.262306
$623$	5080.76	−	9414.56i	0.326736	−	0.605436i
$624$	3392.28	−	2133.16i	0.217628	−	0.136851i
$625$	−4321.31	+	7484.72i	−0.276564	+	0.479022i
$626$	6570.66			0.419515
$627$	−35037.2	−	18502.0i	−2.23166	−	1.17847i
$628$	−13357.0			−0.848729
$629$	17787.8			1.12758
$630$	3192.39	−	333.924i	0.201886	−	0.0211172i
$631$	20165.6			1.27224			0.636118	−	0.771592i	$-0.280539\pi$
$631$	20165.6			1.27224			0.636118	+	0.771592i	$0.280539\pi$
$632$	−439.540			−0.0276645
$633$	−8346.11	+	5248.29i	−0.524057	+	0.329543i
$634$	−3168.26			−0.198466
$635$	2475.30	−	4287.34i	0.154692	−	0.267934i
$636$	11564.7	+	6106.94i	0.721022	+	0.380748i
$637$	14614.3	−	840.399i	0.909010	−	0.0522729i
$638$	14746.1			0.915054
$639$	−9592.17	+	725.586i	−0.593835	+	0.0449198i
$640$	2913.57	−	5046.44i	0.179951	−	0.311685i
$641$	−4245.54	−	7353.49i	−0.261605	−	0.453113i	0.705064	−	0.709144i	$-0.250918\pi$
$641$	−4245.54	−	7353.49i	−0.261605	−	0.453113i	−0.966669	+	0.256031i	$0.917585\pi$
$642$	3359.15	−	2112.34i	0.206503	−	0.129855i
$643$	10428.6	+	18062.8i	0.639599	+	1.10782i	0.985521	+	0.169555i	$0.0542329\pi$
$643$	10428.6	+	18062.8i	0.639599	+	1.10782i	−0.345922	+	0.938263i	$0.612434\pi$
$644$	−4113.95	+	118.189i	−0.251727	+	0.00723185i
$645$	4050.39	−	2547.01i	0.247262	−	0.155486i
$646$	23071.5			1.40517
$647$	1920.65	−	3326.66i	0.116705	−	0.202140i	−0.801755	−	0.597653i	$-0.796100\pi$
$647$	1920.65	−	3326.66i	0.116705	−	0.202140i	0.918460	+	0.395513i	$0.129433\pi$
$648$	−14509.8	+	2207.78i	−0.879630	+	0.133842i
$649$	3877.50	+	6716.02i	0.234522	+	0.406205i
$650$	3255.39	−	5638.50i	0.196442	−	0.340247i
$651$	16173.4	−	10830.6i	0.973711	−	0.652052i
$652$	−6409.16	−	11101.0i	−0.384972	−	0.666792i
$653$	3356.42	−	5813.48i	0.201144	−	0.348391i	−0.747754	−	0.663976i	$-0.768868\pi$
$653$	3356.42	−	5813.48i	0.201144	−	0.348391i	0.948897	+	0.315585i	$0.102201\pi$
$654$	−1.12404	−	0.593568i	−6.72070e−5	−	3.54898e-5i
$655$	1481.64	+	2566.28i	0.0883856	+	0.153088i
$656$	−949.315	−	1644.26i	−0.0565008	−	0.0978623i
$657$	−4455.27	+	9268.06i	−0.264561	+	0.550352i
$658$	1055.56	+	1712.74i	0.0625382	+	0.101473i
$659$	3122.01	−	5407.48i	0.184547	−	0.319644i	−0.758877	−	0.651234i	$-0.774252\pi$
$659$	3122.01	−	5407.48i	0.184547	−	0.319644i	0.943424	+	0.331590i	$0.107585\pi$
$660$	269.311	+	7130.69i	0.0158832	+	0.420548i
$661$	−10122.8			−0.595662			−0.297831	−	0.954619i	$-0.596263\pi$
$661$	−10122.8			−0.595662			−0.297831	+	0.954619i	$0.596263\pi$
$662$	−2618.96			−0.153760
$663$	−917.759	−	24300.0i	−0.0537599	−	1.42343i
$664$	−10581.1	+	18327.1i	−0.618415	+	1.07113i
$665$	−6258.20	−	10154.4i	−0.364936	−	0.592139i
$666$	−3576.42	−	5237.76i	−0.208083	−	0.304743i
$667$	−3652.22	−	6325.83i	−0.212016	−	0.367222i
$668$	101.398	+	175.626i	0.00587306	+	0.0101724i
$669$	−20350.7	−	10746.5i	−1.17609	−	0.621054i
$670$	−1409.39	+	2441.13i	−0.0812678	+	0.140760i
$671$	−6849.88	−	11864.3i	−0.394093	−	0.682589i
$672$	−14971.1	+	10025.5i	−0.859409	+	0.575509i
$673$	−13958.8	+	24177.4i	−0.799515	+	1.38480i	0.120417	+	0.992723i	$0.461577\pi$
$673$	−13958.8	+	24177.4i	−0.799515	+	1.38480i	−0.919932	+	0.392077i	$0.871757\pi$
$674$	−1223.95	−	2119.95i	−0.0699478	−	0.121153i
$675$	11883.0	−	8789.32i	0.677594	−	0.501187i
$676$	−1108.64	+	1920.23i	−0.0630771	+	0.109253i
$677$	3273.96			0.185862			0.0929309	−	0.995673i	$-0.470376\pi$
$677$	3273.96			0.185862			0.0929309	+	0.995673i	$0.470376\pi$
$678$	−1910.44	+	1201.34i	−0.108215	+	0.0680490i
$679$	20910.2	−	600.728i	1.18183	−	0.0339526i
$680$	−4893.07	−	8475.05i	−0.275942	−	0.477946i
$681$	12703.2	−	7988.16i	0.714814	−	0.449496i
$682$	−7685.97	−	13312.5i	−0.431541	−	0.747451i
$683$	14977.3	−	25941.4i	0.839077	−	1.45332i	−0.0515911	−	0.998668i	$-0.516429\pi$
$683$	14977.3	−	25941.4i	0.839077	−	1.45332i	0.890668	−	0.454655i	$-0.150237\pi$
$684$	13058.3	+	19124.3i	0.729968	+	1.06906i
$685$	−10312.8			−0.575231
$686$	−9164.79	+	791.626i	−0.510077	+	0.0440589i
$687$	2261.52	+	1194.24i	0.125593	+	0.0663216i
$688$	−1876.84	+	3250.79i	−0.104003	+	0.180138i
$689$	18196.5			1.00614
$690$	−1062.95	+	668.413i	−0.0586460	+	0.0368783i
$691$	23976.9			1.32001			0.660003	−	0.751263i	$-0.270555\pi$
$691$	23976.9			1.32001			0.660003	+	0.751263i	$0.270555\pi$
$692$	−592.626			−0.0325553
$693$	10686.1	−	23969.3i	0.585762	−	1.31388i
$694$	12474.0			0.682285
$695$	−1059.77			−0.0578407
$696$	−17949.3	−	9478.46i	−0.977539	−	0.516207i
$697$	−11521.6			−0.626127
$698$	4973.41	−	8614.20i	0.269694	−	0.467123i
$699$	−21027.7	+	13222.8i	−1.13783	+	0.715499i
$700$	5469.96	−	10135.8i	0.295350	−	0.547279i
$701$	−17256.4			−0.929762			−0.464881	−	0.885373i	$-0.653903\pi$
$701$	−17256.4			−0.929762			−0.464881	+	0.885373i	$0.653903\pi$
$702$	−6970.81	+	5156.01i	−0.374781	+	0.277209i
$703$	−11784.4	+	20411.1i	−0.632227	+	1.09505i
$704$	3321.17	+	5752.43i	0.177800	+	0.307959i
$705$	−1527.94	−	806.854i	−0.0816247	−	0.0431034i
$706$	27.7086	+	47.9928i	0.00147709	+	0.00255840i
$707$	6497.49	−	12039.8i	0.345634	−	0.640455i
$708$	−171.057	−	4529.17i	−0.00908011	−	0.240419i
$709$	−25346.9			−1.34263			−0.671314	−	0.741173i	$-0.734270\pi$
$709$	−25346.9			−1.34263			−0.671314	+	0.741173i	$0.734270\pi$
$710$	−1143.49	+	1980.57i	−0.0604426	+	0.104690i
$711$	−587.785	+	44.4621i	−0.0310037	+	0.00234523i
$712$	5814.77	+	10071.5i	0.306064	+	0.530118i
$713$	−3807.22	+	6594.30i	−0.199974	+	0.346365i
$714$	1015.01	+	15247.5i	0.0532013	+	0.799190i
$715$	4964.26	+	8598.34i	0.259654	+	0.449734i
$716$	5830.56	−	10098.8i	0.304327	−	0.527110i
$717$	25993.0	−	16345.2i	1.35387	−	0.851355i
$718$	582.204	+	1008.41i	0.0302614	+	0.0524143i
$719$	−6056.07	−	10489.4i	−0.314121	−	0.544074i	0.665129	−	0.746728i	$-0.268377\pi$
$719$	−6056.07	−	10489.4i	−0.314121	−	0.544074i	−0.979250	+	0.202654i	$0.935043\pi$
$720$	937.003	−	1949.20i	0.0485001	−	0.100892i
$721$	7362.69	−	211.522i	0.380307	−	0.0109258i
$722$	−10318.6	+	17872.4i	−0.531883	+	0.921248i
$723$	667.092	−	419.487i	0.0343145	−	0.0215780i
$724$	−12949.3			−0.664719
$725$	20441.4			1.04713
$726$	−9470.68	−	5001.16i	−0.484146	−	0.255662i
$727$	8747.77	−	15151.6i	0.446268	−	0.772959i	−0.551871	−	0.833929i	$-0.686086\pi$
$727$	8747.77	−	15151.6i	0.446268	−	0.772959i	0.998140	+	0.0609701i	$0.0194194\pi$
$728$	−7557.48	+	14003.9i	−0.384751	+	0.712937i
$729$	−19180.3	+	4420.16i	−0.974459	+	0.224568i
$730$	1222.38	+	2117.23i	0.0619759	+	0.107345i
$731$	11389.4	+	19726.9i	0.576266	+	0.998122i
$732$	302.185	+	8001.11i	0.0152583	+	0.404002i
$733$	−9869.33	+	17094.2i	−0.497315	+	0.861375i	−0.999995	−	0.00309747i	$-0.999014\pi$
$733$	−9869.33	+	17094.2i	−0.497315	+	0.861375i	0.502680	+	0.864473i	$0.332347\pi$
$734$	6079.45	+	10529.9i	0.305717	+	0.529518i
$735$	6435.51	−	4582.63i	0.322963	−	0.229977i
$736$	3524.20	−	6104.09i	0.176499	−	0.305706i
$737$	11523.2	+	19958.7i	0.575932	+	0.997544i
$738$	2316.53	+	3392.62i	0.115546	+	0.169220i
$739$	−19917.8	+	34498.7i	−0.991460	+	1.71726i	−0.382791	+	0.923835i	$0.625037\pi$
$739$	−19917.8	+	34498.7i	−0.991460	+	1.71726i	−0.608669	+	0.793424i	$0.708296\pi$
$740$	4244.60			0.210858
$741$	28491.8	+	15045.6i	1.41251	+	0.745902i
$742$	−11430.1	+	328.375i	−0.565515	+	0.0162467i
$743$	−5385.11	−	9327.28i	−0.265896	−	0.460545i	0.701902	−	0.712273i	$-0.252334\pi$
$743$	−5385.11	−	9327.28i	−0.265896	−	0.460545i	−0.967798	+	0.251729i	$0.919001\pi$
$744$	798.587	+	21144.6i	0.0393516	+	1.04194i
$745$	4417.03	+	7650.53i	0.217218	+	0.376233i
$746$	2864.63	−	4961.69i	0.140592	−	0.243513i
$747$	−12296.0	+	25578.6i	−0.602256	+	1.25284i
$748$	−33971.9			−1.66061
$749$	4638.50	−	8595.06i	0.226284	−	0.419301i
$750$	−289.970	−	7677.69i	−0.0141176	−	0.373799i
$751$	19140.0	−	33151.5i	0.929998	−	1.61080i	0.146680	−	0.989184i	$-0.453141\pi$
$751$	19140.0	−	33151.5i	0.929998	−	1.61080i	0.783319	−	0.621620i	$-0.213525\pi$
$752$	1355.57			0.0657350
$753$	−5.84766	−	154.832i	−0.000283002	−	0.00749320i
$754$	−11991.3			−0.579176
$755$	10464.4			0.504421
$756$	−12064.3	+	9471.32i	−0.580391	+	0.455646i
$757$	14993.2			0.719862			0.359931	−	0.932979i	$-0.382800\pi$
$757$	14993.2			0.719862			0.359931	+	0.932979i	$0.382800\pi$
$758$	−3190.45			−0.152879
$759$	387.454	+	10258.8i	0.0185292	+	0.490608i
$760$	12966.6			0.618879
$761$	5633.54	−	9757.58i	0.268352	−	0.464799i	−0.700085	−	0.714060i	$-0.746854\pi$
$761$	5633.54	−	9757.58i	0.268352	−	0.464799i	0.968436	+	0.249261i	$0.0801877\pi$
$762$	−317.156	−	8397.53i	−0.0150779	−	0.399226i
$763$	−3.12739	+	0.0898466i	−0.000148387	+	4.26300e-6i
$764$	6329.93			0.299750
$765$	−7400.68	−	10838.5i	−0.349767	−	0.512244i
$766$	−5805.65	+	10055.7i	−0.273847	+	0.474317i
$767$	−3153.13	−	5461.38i	−0.148439	−	0.257104i
$768$	−571.873	−	15141.8i	−0.0268694	−	0.711436i
$769$	10254.7	+	17761.7i	0.480878	+	0.832905i	0.999759	−	0.0219410i	$-0.00698459\pi$
$769$	10254.7	+	17761.7i	0.480878	+	0.832905i	−0.518881	+	0.854846i	$0.673651\pi$
$770$	−3273.46	−	5311.46i	−0.153204	−	0.248586i
$771$	−2775.13	−	1465.45i	−0.129629	−	0.0684527i
$772$	31041.3			1.44715
$773$	−9879.14	+	17111.2i	−0.459674	+	0.796178i	−0.998944	−	0.0459548i

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.44809 q^{2} +(0.196108 + 5.19245i) q^{3} -5.90304 q^{4} +(-2.21638 + 3.83887i) q^{5} +(0.283981 + 7.51913i) q^{6} +(9.71690 + 15.7665i) q^{7} -20.1328 q^{8} +(-26.9231 + 2.03656i) q^{9} +O(q^{10})\)	\(q+1.44809 q^{2} +(0.196108 + 5.19245i) q^{3} -5.90304 q^{4} +(-2.21638 + 3.83887i) q^{5} +(0.283981 + 7.51913i) q^{6} +(9.71690 + 15.7665i) q^{7} -20.1328 q^{8} +(-26.9231 + 2.03656i) q^{9} +(-3.20951 + 5.55903i) q^{10} +(26.2410 + 45.4507i) q^{11} +(-1.15763 - 30.6512i) q^{12} +(-21.3388 - 36.9599i) q^{13} +(14.0709 + 22.8313i) q^{14} +(-20.3678 - 10.7556i) q^{15} +18.0702 q^{16} +(54.8281 - 94.9651i) q^{17} +(-38.9870 + 2.94912i) q^{18} +(72.6470 + 125.828i) q^{19} +(13.0833 - 22.6610i) q^{20} +(-79.9611 + 53.5465i) q^{21} +(37.9993 + 65.8167i) q^{22} +(18.8228 - 32.6021i) q^{23} +(-3.94820 - 104.539i) q^{24} +(52.6754 + 91.2364i) q^{25} +(-30.9005 - 53.5213i) q^{26} +(-15.8545 - 139.397i) q^{27} +(-57.3593 - 93.0701i) q^{28} +(97.0157 - 168.036i) q^{29} +(-29.4944 - 15.5750i) q^{30} -202.266 q^{31} +187.230 q^{32} +(-230.855 + 145.168i) q^{33} +(79.3960 - 137.518i) q^{34} +(-82.0618 + 2.35755i) q^{35} +(158.928 - 12.0219i) q^{36} +(81.1070 + 140.481i) q^{37} +(105.199 + 182.211i) q^{38} +(187.728 - 118.049i) q^{39} +(44.6219 - 77.2874i) q^{40} +(-52.5349 - 90.9932i) q^{41} +(-115.791 + 77.5400i) q^{42} +(-103.864 + 179.898i) q^{43} +(-154.902 - 268.297i) q^{44} +(51.8536 - 107.868i) q^{45} +(27.2571 - 47.2107i) q^{46} +75.0172 q^{47} +(3.54370 + 93.8285i) q^{48} +(-154.164 + 306.403i) q^{49} +(76.2786 + 132.118i) q^{50} +(503.854 + 266.069i) q^{51} +(125.964 + 218.176i) q^{52} +(-213.185 + 369.248i) q^{53} +(-22.9588 - 201.860i) q^{54} -232.640 q^{55} +(-195.629 - 317.424i) q^{56} +(-639.111 + 401.892i) q^{57} +(140.487 - 243.331i) q^{58} +147.765 q^{59} +(120.232 + 63.4906i) q^{60} -261.037 q^{61} -292.899 q^{62} +(-293.718 - 404.693i) q^{63} +126.564 q^{64} +189.179 q^{65} +(-334.298 + 210.217i) q^{66} +439.129 q^{67} +(-323.653 + 560.583i) q^{68} +(172.976 + 91.3431i) q^{69} +(-118.833 + 3.41394i) q^{70} +356.280 q^{71} +(542.038 - 41.0017i) q^{72} +(190.432 - 329.837i) q^{73} +(117.450 + 203.430i) q^{74} +(-463.410 + 291.406i) q^{75} +(-428.838 - 742.770i) q^{76} +(-461.617 + 855.369i) q^{77} +(271.847 - 170.945i) q^{78} +21.8320 q^{79} +(-40.0503 + 69.3691i) q^{80} +(720.705 - 109.661i) q^{81} +(-76.0752 - 131.766i) q^{82} +(525.566 - 910.307i) q^{83} +(472.013 - 316.087i) q^{84} +(243.039 + 420.957i) q^{85} +(-150.405 + 260.508i) q^{86} +(891.545 + 470.796i) q^{87} +(-528.306 - 915.052i) q^{88} +(-288.820 - 500.251i) q^{89} +(75.0886 - 156.203i) q^{90} +(375.381 - 695.574i) q^{91} +(-111.112 + 192.451i) q^{92} +(-39.6659 - 1050.26i) q^{93} +108.632 q^{94} -644.052 q^{95} +(36.7172 + 972.182i) q^{96} +(564.756 - 978.186i) q^{97} +(-223.243 + 443.698i) q^{98} +(-799.052 - 1170.23i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44q - 2q^{2} - q^{3} + 158q^{4} - 19q^{5} - 20q^{6} - 7q^{7} - 24q^{8} + 11q^{9} + O(q^{10}) \)	\( 44q - 2q^{2} - q^{3} + 158q^{4} - 19q^{5} - 20q^{6} - 7q^{7} - 24q^{8} + 11q^{9} - 18q^{10} + 5q^{11} - 62q^{12} - 14q^{13} - 52q^{14} + 119q^{15} + 494q^{16} - 162q^{17} - 188q^{18} + 58q^{19} - 362q^{20} - 59q^{21} - 18q^{22} - 93q^{23} + 30q^{24} - 349q^{25} - 266q^{26} + 272q^{27} - 172q^{28} + 248q^{29} + 85q^{30} - 122q^{31} + 326q^{32} + 77q^{33} + 6q^{34} + 289q^{35} - 806q^{36} - 86q^{37} - 761q^{38} - 256q^{39} - 18q^{40} - 692q^{41} - 364q^{42} - 86q^{43} - 443q^{44} + 527q^{45} - 270q^{46} + 2010q^{47} - 1013q^{48} + 317q^{49} + 239q^{50} + 1209q^{51} - 335q^{52} + 258q^{53} + 577q^{54} - 870q^{55} - 1752q^{56} + 566q^{57} + 237q^{58} + 3330q^{59} + 1669q^{60} - 878q^{61} + 1812q^{62} + 2872q^{63} + 872q^{64} + 1226q^{65} + 1330q^{66} - 590q^{67} - 1374q^{68} + 1389q^{69} + 1251q^{70} + 636q^{71} - 5970q^{72} - 338q^{73} + 1119q^{74} + 2737q^{75} + 1006q^{76} + 2269q^{77} + 157q^{78} - 266q^{79} - 4817q^{80} - 505q^{81} + 6q^{82} - 1356q^{83} - 6013q^{84} + 483q^{85} - 3343q^{86} - 5755q^{87} + 369q^{88} - 2200q^{89} + 2665q^{90} + 1552q^{91} - 396q^{92} - 129q^{93} + 2382q^{94} - 6166q^{95} - 5941q^{96} - 266q^{97} + 3601q^{98} - 5395q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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