LMFDB - Embedded newform 63.4.o.a.20.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,4,Mod(20,63)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("63.20");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			20.8
Character	$\chi$	$=$	63.20
Dual form			63.4.o.a.41.8

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.31807 - 1.33834i) q^{2} +(3.10623 + 4.16549i) q^{3} +(-0.417710 - 0.723496i) q^{4} +(0.223284 + 0.386739i) q^{5} +(-1.62562 - 13.8131i) q^{6} +(18.4159 - 1.96340i) q^{7} +23.6495i q^{8} +(-7.70264 + 25.8780i) q^{9} +O(q^{10})$	\(q+(-2.31807 - 1.33834i) q^{2} +(3.10623 + 4.16549i) q^{3} +(-0.417710 - 0.723496i) q^{4} +(0.223284 + 0.386739i) q^{5} +(-1.62562 - 13.8131i) q^{6} +(18.4159 - 1.96340i) q^{7} +23.6495i q^{8} +(-7.70264 + 25.8780i) q^{9} -1.19532i q^{10} +(34.2729 + 19.7875i) q^{11} +(1.71621 - 3.98731i) q^{12} +(68.4665 - 39.5291i) q^{13} +(-45.3170 - 20.0954i) q^{14} +(-0.917386 + 2.13139i) q^{15} +(28.3094 - 49.0332i) q^{16} +9.74428 q^{17} +(52.4887 - 49.6781i) q^{18} +73.1051i q^{19} +(0.186536 - 0.323090i) q^{20} +(65.3826 + 70.6125i) q^{21} +(-52.9646 - 91.7374i) q^{22} +(-126.471 + 73.0180i) q^{23} +(-98.5119 + 73.4609i) q^{24} +(62.4003 - 108.080i) q^{25} -211.613 q^{26} +(-131.721 + 48.2977i) q^{27} +(-9.11302 - 12.5037i) q^{28} +(-134.097 - 77.4209i) q^{29} +(4.97908 - 3.71293i) q^{30} +(9.87637 - 5.70213i) q^{31} +(32.6028 - 18.8232i) q^{32} +(24.0351 + 204.228i) q^{33} +(-22.5879 - 13.0411i) q^{34} +(4.87129 + 6.68374i) q^{35} +(21.9401 - 5.23667i) q^{36} -337.074 q^{37} +(97.8393 - 169.463i) q^{38} +(377.331 + 162.410i) q^{39} +(-9.14619 + 5.28056i) q^{40} +(53.3244 + 92.3606i) q^{41} +(-57.0580 - 251.188i) q^{42} +(-45.6005 + 78.9824i) q^{43} -33.0617i q^{44} +(-11.7279 + 2.79922i) q^{45} +390.891 q^{46} +(276.698 - 479.254i) q^{47} +(292.183 - 34.3862i) q^{48} +(335.290 - 72.3157i) q^{49} +(-289.296 + 167.025i) q^{50} +(30.2680 + 40.5897i) q^{51} +(-57.1983 - 33.0235i) q^{52} -239.988i q^{53} +(369.976 + 64.3293i) q^{54} +17.6729i q^{55} +(46.4336 + 435.527i) q^{56} +(-304.519 + 227.082i) q^{57} +(207.230 + 358.934i) q^{58} +(126.419 + 218.964i) q^{59} +(1.92525 - 0.226578i) q^{60} +(-342.785 - 197.907i) q^{61} -30.5255 q^{62} +(-91.0421 + 491.689i) q^{63} -553.717 q^{64} +(30.5749 + 17.6524i) q^{65} +(217.611 - 505.581i) q^{66} +(13.5469 + 23.4639i) q^{67} +(-4.07029 - 7.04994i) q^{68} +(-697.004 - 300.003i) q^{69} +(-2.34689 - 22.0128i) q^{70} -348.340i q^{71} +(-612.002 - 182.164i) q^{72} +923.737i q^{73} +(781.360 + 451.119i) q^{74} +(644.038 - 75.7951i) q^{75} +(52.8912 - 30.5368i) q^{76} +(670.017 + 297.112i) q^{77} +(-657.320 - 881.473i) q^{78} +(280.225 - 485.363i) q^{79} +25.2841 q^{80} +(-610.339 - 398.658i) q^{81} -285.464i q^{82} +(-281.406 + 487.409i) q^{83} +(23.7768 - 76.7996i) q^{84} +(2.17574 + 3.76849i) q^{85} +(211.410 - 122.058i) q^{86} +(-94.0401 - 799.067i) q^{87} +(-467.965 + 810.538i) q^{88} -644.990 q^{89} +(30.9323 + 9.20709i) q^{90} +(1183.26 - 862.392i) q^{91} +(105.656 + 61.0008i) q^{92} +(54.4305 + 23.4278i) q^{93} +(-1282.81 + 740.629i) q^{94} +(-28.2726 + 16.3232i) q^{95} +(179.680 + 77.3374i) q^{96} +(427.784 + 246.981i) q^{97} +(-874.008 - 281.098i) q^{98} +(-776.052 + 734.497i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 6 q^{2} + 78 q^{4} + 5 q^{7}+O(q^{10}) $ 44 * q - 6 * q^2 + 78 * q^4 + 5 * q^7	$ 44 q - 6 q^{2} + 78 q^{4} + 5 q^{7} - 18 q^{11} + 204 q^{14} + 66 q^{15} - 242 q^{16} - 210 q^{18} - 57 q^{21} - 34 q^{22} - 102 q^{23} - 352 q^{25} + 300 q^{28} + 246 q^{29} - 144 q^{30} + 1068 q^{32} - 1818 q^{36} + 328 q^{37} - 798 q^{39} - 1158 q^{42} - 170 q^{43} + 968 q^{46} - 79 q^{49} + 288 q^{50} - 204 q^{51} + 1212 q^{56} + 324 q^{57} - 538 q^{58} + 5316 q^{60} + 783 q^{63} - 808 q^{64} + 4350 q^{65} - 590 q^{67} + 384 q^{70} + 4284 q^{72} - 5304 q^{74} - 2787 q^{77} + 612 q^{78} - 302 q^{79} - 3720 q^{81} + 7050 q^{84} - 612 q^{85} - 13692 q^{86} + 1294 q^{88} + 210 q^{91} - 10194 q^{92} - 4266 q^{93} + 6336 q^{95} + 1014 q^{99}+O(q^{100}) $ 44 * q - 6 * q^2 + 78 * q^4 + 5 * q^7 - 18 * q^11 + 204 * q^14 + 66 * q^15 - 242 * q^16 - 210 * q^18 - 57 * q^21 - 34 * q^22 - 102 * q^23 - 352 * q^25 + 300 * q^28 + 246 * q^29 - 144 * q^30 + 1068 * q^32 - 1818 * q^36 + 328 * q^37 - 798 * q^39 - 1158 * q^42 - 170 * q^43 + 968 * q^46 - 79 * q^49 + 288 * q^50 - 204 * q^51 + 1212 * q^56 + 324 * q^57 - 538 * q^58 + 5316 * q^60 + 783 * q^63 - 808 * q^64 + 4350 * q^65 - 590 * q^67 + 384 * q^70 + 4284 * q^72 - 5304 * q^74 - 2787 * q^77 + 612 * q^78 - 302 * q^79 - 3720 * q^81 + 7050 * q^84 - 612 * q^85 - 13692 * q^86 + 1294 * q^88 + 210 * q^91 - 10194 * q^92 - 4266 * q^93 + 6336 * q^95 + 1014 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$10$	$29$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−2.31807	−	1.33834i	−0.819560	−	0.473173i	0.0307044	−	0.999529i	$-0.490225\pi$
$2$	−2.31807	−	1.33834i	−0.819560	−	0.473173i	−0.850265	+	0.526355i	$0.823558\pi$
$3$	3.10623	+	4.16549i	0.597795	+	0.801649i
$3$	3.10623	+	4.16549i	0.597795	+	0.801649i
$4$	−0.417710	−	0.723496i	−0.0522138	−	0.0904369i
$5$	0.223284	+	0.386739i	0.0199711	+	0.0345910i	0.875838	−	0.482605i	$-0.160309\pi$
$5$	0.223284	+	0.386739i	0.0199711	+	0.0345910i	−0.855867	+	0.517196i	$0.826976\pi$
$6$	−1.62562	−	13.8131i	−0.110610	−	0.939861i
$7$	18.4159	−	1.96340i	0.994365	−	0.106014i
$7$	18.4159	−	1.96340i	0.994365	−	0.106014i
$8$			23.6495i			1.04517i
$9$	−7.70264	+	25.8780i	−0.285283	+	0.958443i
$10$		−	1.19532i		−	0.0377992i
$11$	34.2729	+	19.7875i	0.939425	+	0.542377i	0.889780	−	0.456390i	$-0.150858\pi$
$11$	34.2729	+	19.7875i	0.939425	+	0.542377i	0.0496448	+	0.998767i	$0.484191\pi$
$12$	1.71621	−	3.98731i	0.0412856	−	0.0959199i
$13$	68.4665	−	39.5291i	1.46071	−	0.843339i	0.461662	−	0.887056i	$-0.347253\pi$
$13$	68.4665	−	39.5291i	1.46071	−	0.843339i	0.999044	+	0.0437164i	$0.0139198\pi$
$14$	−45.3170	−	20.0954i	−0.865105	−	0.383622i
$15$	−0.917386	+	2.13139i	−0.0157912	+	0.0366881i
$16$	28.3094	−	49.0332i	0.442334	−	0.766144i
$17$	9.74428			0.139020			0.0695099	−	0.997581i	$-0.477856\pi$
$17$	9.74428			0.139020			0.0695099	+	0.997581i	$0.477856\pi$
$18$	52.4887	−	49.6781i	0.687317	−	0.650514i
$19$			73.1051i			0.882709i	0.897333	+	0.441354i	$0.145502\pi$
$19$			73.1051i			0.882709i	−0.897333	+	0.441354i	$0.854498\pi$
$20$	0.186536	−	0.323090i	0.00208553	−	0.00361225i
$21$	65.3826	+	70.6125i	0.679412	+	0.733757i
$22$	−52.9646	−	91.7374i	−0.513277	−	0.889022i
$23$	−126.471	+	73.0180i	−1.14657	+	0.661970i	−0.948048	−	0.318127i	$-0.896946\pi$
$23$	−126.471	+	73.0180i	−1.14657	+	0.661970i	−0.198518	+	0.980097i	$0.563613\pi$
$24$	−98.5119	+	73.4609i	−0.837861	+	0.624798i
$25$	62.4003	−	108.080i	0.499202	−	0.864644i
$26$	−211.613			−1.59618
$27$	−131.721	+	48.2977i	−0.938876	+	0.344255i
$28$	−9.11302	−	12.5037i	−0.0615071	−	0.0843919i
$29$	−134.097	−	77.4209i	−0.858661	−	0.495748i	0.00490247	−	0.999988i	$-0.498439\pi$
$29$	−134.097	−	77.4209i	−0.858661	−	0.495748i	−0.863564	+	0.504240i	$0.831773\pi$
$30$	4.97908	−	3.71293i	0.0303017	−	0.0225962i
$31$	9.87637	−	5.70213i	0.0572209	−	0.0330365i	−0.471117	−	0.882071i	$-0.656149\pi$
$31$	9.87637	−	5.70213i	0.0572209	−	0.0330365i	0.528338	+	0.849034i	$0.322816\pi$
$32$	32.6028	−	18.8232i	0.180107	−	0.103985i
$33$	24.0351	+	204.228i	0.126787	+	1.07732i
$34$	−22.5879	−	13.0411i	−0.113935	−	0.0657804i
$35$	4.87129	+	6.68374i	0.0235257	+	0.0322788i
$36$	21.9401	−	5.23667i	0.101574	−	0.0242438i
$37$	−337.074			−1.49769			−0.748846	−	0.662744i	$-0.769392\pi$
$37$	−337.074			−1.49769			−0.748846	+	0.662744i	$0.769392\pi$
$38$	97.8393	−	169.463i	0.417674	−	0.723433i
$39$	377.331	+	162.410i	1.54926	+	0.666831i
$40$	−9.14619	+	5.28056i	−0.0361535	+	0.0208732i
$41$	53.3244	+	92.3606i	0.203119	+	0.351812i	0.949532	−	0.313671i	$-0.101559\pi$
$41$	53.3244	+	92.3606i	0.203119	+	0.351812i	−0.746413	+	0.665483i	$0.768226\pi$
$42$	−57.0580	−	251.188i	−0.209625	−	0.922838i
$43$	−45.6005	+	78.9824i	−0.161721	+	0.280110i	−0.935486	−	0.353363i	$-0.885038\pi$
$43$	−45.6005	+	78.9824i	−0.161721	+	0.280110i	0.773765	+	0.633473i	$0.218371\pi$
$44$		−	33.0617i		−	0.113278i
$45$	−11.7279	+	2.79922i	−0.0388509	+	0.00927295i
$46$	390.891			1.25291
$47$	276.698	−	479.254i	0.858734	−	1.48737i	−0.0144035	−	0.999896i	$-0.504585\pi$
$47$	276.698	−	479.254i	0.858734	−	1.48737i	0.873137	−	0.487474i	$-0.162082\pi$
$48$	292.183	−	34.3862i	0.878604	−	0.103401i
$49$	335.290	−	72.3157i	0.977522	−	0.210833i
$50$	−289.296	+	167.025i	−0.818253	+	0.472419i
$51$	30.2680	+	40.5897i	0.0831053	+	0.111445i
$52$	−57.1983	−	33.0235i	−0.152538	−	0.0880679i
$53$		−	239.988i		−	0.621979i	−0.950413	−	0.310989i	$-0.899340\pi$
$53$		−	239.988i		−	0.621979i	0.950413	−	0.310989i	$-0.100660\pi$
$54$	369.976	+	64.3293i	0.932358	+	0.162113i
$55$			17.6729i			0.0433275i
$56$	46.4336	+	435.527i	0.110803	+	1.03928i
$57$	−304.519	+	227.082i	−0.707623	+	0.527679i
$58$	207.230	+	358.934i	0.469150	+	0.812591i
$59$	126.419	+	218.964i	0.278955	+	0.483164i	0.971125	−	0.238570i	$-0.0766787\pi$
$59$	126.419	+	218.964i	0.278955	+	0.483164i	−0.692171	+	0.721734i	$0.743345\pi$
$60$	1.92525	−	0.226578i	0.00414248	−	0.000487518i
$61$	−342.785	−	197.907i	−0.719494	−	0.415400i	0.0950723	−	0.995470i	$-0.469692\pi$
$61$	−342.785	−	197.907i	−0.719494	−	0.415400i	−0.814566	+	0.580070i	$0.803025\pi$
$62$	−30.5255			−0.0625280
$63$	−91.0421	+	491.689i	−0.182067	+	0.983286i
$64$	−553.717			−1.08148
$65$	30.5749	+	17.6524i	0.0583438	+	0.0336848i
$66$	217.611	−	505.581i	0.405849	−	0.942920i
$67$	13.5469	+	23.4639i	0.0247017	+	0.0427846i	0.878112	−	0.478455i	$-0.158803\pi$
$67$	13.5469	+	23.4639i	0.0247017	+	0.0427846i	−0.853410	+	0.521240i	$0.825470\pi$
$68$	−4.07029	−	7.04994i	−0.00725875	−	0.0125725i
$69$	−697.004	−	300.003i	−1.21608	−	0.523422i
$70$	−2.34689	−	22.0128i	−0.00400724	−	0.0375862i
$71$		−	348.340i		−	0.582259i	−0.956684	−	0.291129i	$-0.905969\pi$
$71$		−	348.340i		−	0.582259i	0.956684	−	0.291129i	$-0.0940310\pi$
$72$	−612.002	−	182.164i	−1.00174	−	0.298170i
$73$			923.737i			1.48103i	0.672040	+	0.740515i	$0.265418\pi$
$73$			923.737i			1.48103i	−0.672040	+	0.740515i	$0.734582\pi$
$74$	781.360	+	451.119i	1.22745	+	0.708668i
$75$	644.038	−	75.7951i	0.991562	−	0.116694i
$76$	52.8912	−	30.5368i	0.0798295	−	0.0460896i
$77$	670.017	+	297.112i	0.991630	+	0.439729i
$78$	−657.320	−	881.473i	−0.954190	−	1.27958i
$79$	280.225	−	485.363i	0.399085	−	0.691236i	−0.594528	−	0.804075i	$-0.702661\pi$
$79$	280.225	−	485.363i	0.399085	−	0.691236i	0.993613	+	0.112839i	$0.0359944\pi$
$80$	25.2841			0.0353356
$81$	−610.339	−	398.658i	−0.837227	−	0.546855i
$82$		−	285.464i		−	0.384442i
$83$	−281.406	+	487.409i	−0.372148	+	0.644580i	−0.989896	−	0.141797i	$-0.954712\pi$
$83$	−281.406	+	487.409i	−0.372148	+	0.644580i	0.617748	+	0.786376i	$0.288045\pi$
$84$	23.7768	−	76.7996i	0.0308841	−	0.0997562i
$85$	2.17574	+	3.76849i	0.00277638	+	0.00480883i
$86$	211.410	−	122.058i	0.265081	−	0.153044i
$87$	−94.0401	−	799.067i	−0.115887	−	0.984701i
$88$	−467.965	+	810.538i	−0.566877	+	0.981860i
$89$	−644.990			−0.768188			−0.384094	−	0.923294i	$-0.625486\pi$
$89$	−644.990			−0.768188			−0.384094	+	0.923294i	$0.625486\pi$
$90$	30.9323	+	9.20709i	0.0362284	+	0.0107835i
$91$	1183.26	−	862.392i	1.36307	−	0.993442i
$92$	105.656	+	61.0008i	0.119733	+	0.0691280i
$93$	54.4305	+	23.4278i	0.0606901	+	0.0261221i
$94$	−1282.81	+	740.629i	−1.40757	+	0.812660i
$95$	−28.2726	+	16.3232i	−0.0305338	+	0.0176287i
$96$	179.680	+	77.3374i	0.191026	+	0.0822210i
$97$	427.784	+	246.981i	0.447783	+	0.258527i	0.706893	−	0.707320i	$-0.250096\pi$
$97$	427.784	+	246.981i	0.447783	+	0.258527i	−0.259111	+	0.965848i	$0.583429\pi$
$98$	−874.008	−	281.098i	−0.900899	−	0.289747i
$99$	−776.052	+	734.497i	−0.787840	+	0.745654i
$100$	−104.261			−0.104261
$101$	711.795	−	1232.86i	0.701250	−	1.21460i	−0.266779	−	0.963758i	$-0.585959\pi$
$101$	711.795	−	1232.86i	0.701250	−	1.21460i	0.968028	−	0.250842i	$-0.0807074\pi$
$102$	−15.8405	−	134.598i	−0.0153769	−	0.130659i
$103$	−826.452	+	477.152i	−0.790609	+	0.456458i	−0.840177	−	0.542312i	$-0.817549\pi$
$103$	−826.452	+	477.152i	−0.790609	+	0.456458i	0.0495678	+	0.998771i	$0.484216\pi$
$104$	934.846	+	1619.20i	0.881434	+	1.52669i
$105$	−12.7097	+	41.0526i	−0.0118128	+	0.0381555i
$106$	−321.184	+	556.308i	−0.294304	+	0.509749i
$107$		−	878.606i		−	0.793814i	−0.917859	−	0.396907i	$-0.870084\pi$
$107$		−	878.606i		−	0.793814i	0.917859	−	0.396907i	$-0.129916\pi$
$108$	89.9642	+	75.1249i	0.0801557	+	0.0669342i
$109$	−128.350			−0.112786			−0.0563931	−	0.998409i	$-0.517960\pi$
$109$	−128.350			−0.112786			−0.0563931	+	0.998409i	$0.517960\pi$
$110$	23.6523	−	40.9669i	0.0205014	−	0.0355095i
$111$	−1047.03	−	1404.08i	−0.895313	−	1.20062i
$112$	425.070	−	958.573i	0.358619	−	0.808720i
$113$	−463.489	+	267.596i	−0.385853	+	0.222772i	−0.680362	−	0.732876i	$-0.738177\pi$
$113$	−463.489	+	267.596i	−0.385853	+	0.222772i	0.294509	+	0.955649i	$0.404844\pi$
$114$	1009.81	−	118.841i	0.829623	−	0.0976362i
$115$	−56.4778	−	32.6075i	−0.0457964	−	0.0264406i
$116$			129.358i			0.103540i
$117$	495.561	+	2076.25i	0.391578	+	1.64059i
$118$		−	676.764i		−	0.527976i
$119$	179.450	−	19.1320i	0.138236	−	0.0147380i
$120$	−50.4063	−	21.6958i	−0.0383454	−	0.0165045i
$121$	117.588	+	203.669i	0.0883458	+	0.153019i
$122$	529.733	+	917.524i	0.393113	+	0.680891i
$123$	−219.089	+	509.016i	−0.160607	+	0.373141i
$124$	−8.25092	−	4.76367i	−0.00597544	−	0.00344992i
$125$	111.553			0.0798207
$126$	869.087	−	1017.92i	0.614480	−	0.719713i
$127$	151.161			0.105617			0.0528086	−	0.998605i	$-0.483183\pi$
$127$	151.161			0.105617			0.0528086	+	0.998605i	$0.483183\pi$
$128$	1022.73	+	590.474i	0.706230	+	0.407742i
$129$	−470.647	+	55.3892i	−0.321226	+	0.0378042i
$130$	−47.2498	−	81.8390i	−0.0318775	−	0.0552135i
$131$	−1345.98	−	2331.31i	−0.897702	−	1.55487i	−0.830425	−	0.557131i	$-0.811902\pi$
$131$	−1345.98	−	2331.31i	−0.897702	−	1.55487i	−0.0672769	−	0.997734i	$-0.521431\pi$
$132$	137.718	−	102.697i	0.0908094	−	0.0677171i
$133$	143.535	+	1346.30i	0.0935794	+	0.877734i
$134$		−	72.5210i		−	0.0467527i
$135$	−48.0897	−	40.1574i	−0.0306585	−	0.0256015i
$136$			230.448i			0.145299i
$137$	−1713.35	−	989.205i	−1.06848	−	0.616887i	−0.140713	−	0.990050i	$-0.544940\pi$
$137$	−1713.35	−	989.205i	−1.06848	−	0.616887i	−0.927765	+	0.373164i	$0.878273\pi$
$138$	1214.20	+	1628.25i	0.748981	+	1.00439i
$139$	1065.10	−	614.935i	0.649931	−	0.375238i	−0.138499	−	0.990363i	$-0.544228\pi$
$139$	1065.10	−	614.935i	0.649931	−	0.375238i	0.788430	+	0.615125i	$0.210894\pi$
$140$	2.80087	−	6.31623i	0.00169083	−	0.00381299i
$141$	2855.82	−	336.094i	1.70570	−	0.200739i
$142$	−466.197	+	807.476i	−0.275509	+	0.477196i
$143$	3128.73			1.82963
$144$	1050.82	+	1110.27i	0.608116	+	0.642520i
$145$		−	69.1473i		−	0.0396026i
$146$	1236.27	−	2141.28i	0.700784	−	1.21379i
$147$	1342.72	+	1172.02i	0.753372	+	0.657595i
$148$	140.799	+	243.872i	0.0782002	+	0.135447i
$149$	−1678.18	+	968.895i	−0.922695	+	0.532718i	−0.884494	−	0.466552i	$-0.845496\pi$
$149$	−1678.18	+	968.895i	−0.922695	+	0.532718i	−0.0382010	+	0.999270i	$0.512163\pi$
$150$	−1594.36	−	686.242i	−0.867861	−	0.373543i
$151$	723.386	−	1252.94i	0.389856	−	0.675251i	−0.602574	−	0.798063i	$-0.705858\pi$
$151$	723.386	−	1252.94i	0.389856	−	0.675251i	0.992430	+	0.122812i	$0.0391913\pi$
$152$	−1728.90			−0.922582
$153$	−75.0567	+	252.162i	−0.0396600	+	0.133243i
$154$	−1155.51	−	1585.43i	−0.604633	−	0.829597i
$155$	4.41047	+	2.54638i	0.00228553	+	0.00131955i
$156$	−40.1123	−	340.838i	−0.0205869	−	0.174929i
$157$	−1711.48	+	988.126i	−0.870009	+	0.502300i	−0.867351	−	0.497697i	$-0.834179\pi$
$157$	−1711.48	+	988.126i	−0.870009	+	0.502300i	−0.00265752	+	0.999996i	$0.500846\pi$
$158$	−1299.16	+	750.070i	−0.654149	+	0.377673i
$159$	999.667	−	745.458i	0.498609	−	0.371815i
$160$	14.5594	+	8.40585i	0.00719387	+	0.00415338i
$161$	−2185.71	+	1593.01i	−1.06993	+	0.779792i
$162$	881.268	+	1740.95i	0.427401	+	0.844335i
$163$	890.818			0.428063			0.214031	−	0.976827i	$-0.431340\pi$
$163$	890.818			0.428063			0.214031	+	0.976827i	$0.431340\pi$
$164$	44.5483	−	77.1599i	0.0212112	−	0.0367389i
$165$	−73.6163	+	54.8961i	−0.0347334	+	0.0259009i
$166$	1304.64	−	753.231i	0.609996	−	0.352181i
$167$	−577.006	−	999.403i	−0.267366	−	0.463091i	0.700815	−	0.713343i	$-0.252820\pi$
$167$	−577.006	−	999.403i	−0.267366	−	0.463091i	−0.968181	+	0.250252i	$0.919486\pi$
$168$	−1669.95	+	1546.27i	−0.766902	+	0.710102i
$169$	2026.61	−	3510.18i	0.922442	−	1.59772i
$170$		−	11.6475i		−	0.00525483i
$171$	−1891.81	−	563.103i	−0.846026	−	0.251822i
$172$	76.1913			0.0337763
$173$	−1100.21	+	1905.62i	−0.483512	+	0.837468i	−0.999821	−	0.0189348i	$-0.993972\pi$
$173$	−1100.21	+	1905.62i	−0.483512	+	0.837468i	0.516308	+	0.856403i	$0.327306\pi$
$174$	−851.429	+	1978.15i	−0.370958	+	0.861856i
$175$	936.951	−	2112.92i	0.404725	−	0.912694i
$176$	1940.49	−	1120.34i	0.831078	−	0.479823i
$177$	−519.406	+	1206.75i	−0.220570	+	0.512456i
$178$	1495.13	+	863.213i	0.629577	+	0.363486i
$179$		−	550.246i		−	0.229762i	−0.993379	−	0.114881i	$-0.963351\pi$
$179$		−	550.246i		−	0.229762i	0.993379	−	0.114881i	$-0.0366486\pi$
$180$	6.92408	+	7.31581i	0.00286717	+	0.00302938i
$181$			2053.17i			0.843152i	0.906793	+	0.421576i	$0.138523\pi$
$181$			2053.17i			0.843152i	−0.906793	+	0.421576i	$0.861477\pi$
$182$	−3897.05	+	415.482i	−1.58719	+	0.169218i
$183$	−240.390	−	2042.61i	−0.0971045	−	0.825106i
$184$	−1726.84	−	2990.98i	−0.691872	−	1.19836i
$185$	−75.2632	−	130.360i	−0.0299106	−	0.0518067i
$186$	−94.8191	−	127.154i	−0.0373789	−	0.0501255i
$187$	333.965	+	192.815i	0.130599	+	0.0754011i
$188$	−462.318			−0.179351
$189$	−2330.93	+	1148.07i	−0.897089	+	0.441849i
$190$	87.3837			0.0333657
$191$	−258.109	−	149.020i	−0.0977808	−	0.0564538i	0.450312	−	0.892871i	$-0.351313\pi$
$191$	−258.109	−	149.020i	−0.0977808	−	0.0564538i	−0.548093	+	0.836417i	$0.684646\pi$
$192$	−1719.97	−	2306.50i	−0.646502	−	0.866966i
$193$	−1528.38	−	2647.24i	−0.570028	−	0.987318i	−0.996562	−	0.0828463i	$-0.973599\pi$
$193$	−1528.38	−	2647.24i	−0.570028	−	0.987318i	0.426534	−	0.904471i	$-0.359734\pi$
$194$	−661.088	−	1145.04i	−0.244657	−	0.423758i
$195$	21.4417	+	182.192i	0.00787422	+	0.0669079i
$196$	−192.374	−	212.374i	−0.0701072	−	0.0773957i
$197$			3332.60i			1.20527i	0.798018	+	0.602634i	$0.205882\pi$
$197$			3332.60i			1.20527i	−0.798018	+	0.602634i	$0.794118\pi$
$198$	2781.94	−	663.996i	0.998506	−	0.238324i
$199$			3835.52i			1.36630i	0.730280	+	0.683148i	$0.239390\pi$
$199$			3835.52i			1.36630i	−0.730280	+	0.683148i	$0.760610\pi$
$200$	2556.05	+	1475.74i	0.903701	+	0.521752i
$201$	−55.6588	+	129.314i	−0.0195317	+	0.0453785i
$202$	−3299.97	+	1905.24i	−1.14943	+	0.663625i
$203$	−2621.52	−	1162.49i	−0.906379	−	0.401925i
$204$	16.7232	−	38.8535i	0.00573951	−	0.0133348i
$205$	−23.8129	+	41.2452i	−0.00811302	+	0.0140522i
$206$	2554.36			0.863936
$207$	−915.398	−	3835.24i	−0.307365	−	1.28777i
$208$		−	4476.18i		−	1.49215i
$209$	−1446.57	+	2505.53i	−0.478761	+	0.829238i
$210$	84.4041	−	78.1528i	0.0277354	−	0.0256812i
$211$	2890.75	+	5006.93i	0.943164	+	1.63361i	0.759386	+	0.650640i	$0.225499\pi$
$211$	2890.75	+	5006.93i	0.943164	+	1.63361i	0.183777	+	0.982968i	$0.441167\pi$
$212$	−173.630	+	100.245i	−0.0562498	+	0.0324759i
$213$	1451.01	−	1082.03i	0.466767	−	0.348071i
$214$	−1175.87	+	2036.67i	−0.375611	+	0.650578i
$215$	−40.7274			−0.0129190
$216$	−1142.22	−	3115.13i	−0.359806	−	0.981287i
$217$	170.687	−	124.401i	0.0533961	−	0.0389166i
$218$	297.524	+	171.775i	0.0924351	+	0.0533674i
$219$	−3847.82	+	2869.34i	−1.18727	+	0.885352i
$220$	12.7863	−	7.38215i	0.00391841	−	0.00226229i
$221$	667.157	−	385.183i	0.203067	−	0.117241i
$222$	547.956	+	4656.03i	0.165659	+	1.40762i
$223$	1153.65	+	666.060i	0.346431	+	0.200012i	0.663112	−	0.748520i	$-0.269235\pi$
$223$	1153.65	+	666.060i	0.346431	+	0.200012i	−0.316681	+	0.948532i	$0.602569\pi$
$224$	563.452	−	410.659i	0.168068	−	0.122493i
$225$	2316.26	+	2447.30i	0.686298	+	0.725125i
$226$	1432.53			0.421640
$227$	786.498	−	1362.25i	0.229963	−	0.398308i	−0.727834	−	0.685754i	$-0.759473\pi$
$227$	786.498	−	1362.25i	0.229963	−	0.398308i	0.957797	+	0.287446i	$0.0928060\pi$
$228$	291.493	+	125.464i	0.0846693	+	0.0364431i
$229$	5906.31	−	3410.01i	1.70437	−	0.984017i	0.763148	−	0.646224i	$-0.223653\pi$
$229$	5906.31	−	3410.01i	1.70437	−	0.984017i	0.941220	−	0.337793i	$-0.109680\pi$
$230$	87.2796	+	151.173i	0.0250219	+	0.0433393i
$231$	843.609	+	3713.85i	0.240283	+	1.05781i
$232$	1830.97	−	3171.33i	0.518142	−	0.897448i
$233$			1585.11i			0.445683i	0.974855	+	0.222841i	$0.0715332\pi$
$233$			1585.11i			0.445683i	−0.974855	+	0.222841i	$0.928467\pi$
$234$	1629.98	−	5476.12i	0.455364	−	1.52985i
$235$	247.128			0.0685995
$236$	105.613	−	182.927i	0.0291306	−	0.0504556i
$237$	2892.22	−	340.378i	0.792700	−	0.0932907i
$238$	−441.581	−	195.815i	−0.120267	−	0.0533310i
$239$	5706.02	−	3294.37i	1.54432	−	0.891612i	0.545758	−	0.837943i	$-0.316242\pi$
$239$	5706.02	−	3294.37i	1.54432	−	0.891612i	0.998559	−	0.0536684i	$-0.0170914\pi$
$240$	78.5382	+	105.321i	0.0211234	+	0.0283267i
$241$	−3381.74	−	1952.45i	−0.903887	−	0.521859i	−0.0254276	−	0.999677i	$-0.508095\pi$
$241$	−3381.74	−	1952.45i	−0.903887	−	0.521859i	−0.878459	+	0.477817i	$0.841428\pi$
$242$		−	629.491i		−	0.167212i
$243$	−235.249	−	3780.68i	−0.0621037	−	0.998070i
$244$			330.671i			0.0867585i
$245$	102.832	+	113.523i	0.0268151	+	0.0296029i
$246$	1189.10	−	886.717i	0.308187	−	0.229817i
$247$	2889.78	+	5005.25i	0.744423	+	1.28938i
$248$	134.853	+	233.572i	0.0345288	+	0.0598057i
$249$	−2904.41	+	341.812i	−0.739195	+	0.0869939i
$250$	−258.587	−	149.295i	−0.0654179	−	0.0377690i
$251$	5207.34			1.30950			0.654750	−	0.755846i	$-0.272774\pi$
$251$	5207.34			1.30950			0.654750	+	0.755846i	$0.272774\pi$
$252$	393.764	−	139.515i	0.0984318	−	0.0348755i
$253$	−5779.37			−1.43615
$254$	−350.402	−	202.305i	−0.0865597	−	0.0499753i
$255$	−8.93927	+	20.7688i	−0.00219529	+	0.00510037i
$256$	634.363	+	1098.75i	0.154874	+	0.268249i
$257$	3238.89	+	5609.93i	0.786135	+	1.36163i	0.928319	+	0.371785i	$0.121254\pi$
$257$	3238.89	+	5609.93i	0.786135	+	1.36163i	−0.142184	+	0.989840i	$0.545413\pi$
$258$	1165.12	+	501.488i	0.281152	+	0.121013i
$259$	−6207.52	+	661.813i	−1.48925	+	0.158776i
$260$		−	29.4944i		−	0.00703525i
$261$	3036.40	−	2873.81i	0.720108	−	0.681550i
$262$			7205.50i			1.69907i
$263$	−3268.22	−	1886.91i	−0.766263	−	0.442402i	0.0652767	−	0.997867i	$-0.479207\pi$
$263$	−3268.22	−	1886.91i	−0.766263	−	0.442402i	−0.831540	+	0.555465i	$0.812540\pi$
$264$	−4829.90	+	568.418i	−1.12598	+	0.132514i
$265$	92.8126	−	53.5854i	0.0215148	−	0.0124216i
$266$	1469.07	−	3312.90i	0.338627	−	0.763636i
$267$	−2003.49	−	2686.70i	−0.459219	−	0.615818i
$268$	11.3173	−	19.6022i	0.00257954	−	0.00446789i
$269$	4381.41			0.993084			0.496542	−	0.868013i	$-0.334603\pi$
$269$	4381.41			0.993084			0.496542	+	0.868013i	$0.334603\pi$
$270$	57.7310	+	157.448i	0.0130126	+	0.0354888i
$271$		−	2485.08i		−	0.557040i	−0.960430	−	0.278520i	$-0.910156\pi$
$271$		−	2485.08i		−	0.557040i	0.960430	−	0.278520i	$-0.0898438\pi$
$272$	275.854	−	477.794i	0.0614931	−	0.106509i
$273$	7267.76	+	2250.07i	1.61123	+	0.498829i
$274$	2647.78	+	4586.09i	0.583789	+	1.01115i
$275$	4277.28	−	2469.49i	0.937926	−	0.541512i
$276$	74.0952	+	629.594i	0.0161595	+	0.137308i
$277$	−3013.11	+	5218.87i	−0.653576	+	1.13203i	0.328673	+	0.944444i	$0.393399\pi$
$277$	−3013.11	+	5218.87i	−0.653576	+	1.13203i	−0.982249	+	0.187583i	$0.939935\pi$
$278$	−3291.96			−0.710210
$279$	71.4853	+	299.502i	0.0153395	+	0.0642678i
$280$	−158.067	+	115.204i	−0.0337369	+	0.0245884i
$281$	−3454.28	−	1994.33i	−0.733327	−	0.423387i	0.0863108	−	0.996268i	$-0.472492\pi$
$281$	−3454.28	−	1994.33i	−0.733327	−	0.423387i	−0.819638	+	0.572881i	$0.805826\pi$
$282$	−7069.78	−	3042.96i	−1.49291	−	0.642572i
$283$	−5657.83	+	3266.55i	−1.18842	+	0.686135i	−0.957948	−	0.286944i	$-0.907361\pi$
$283$	−5657.83	+	3266.55i	−1.18842	+	0.686135i	−0.230473	+	0.973079i	$0.574027\pi$
$284$	−252.023	+	145.505i	−0.0526577	+	0.0304020i
$285$	−155.815	−	67.0656i	−0.0323849	−	0.0139390i
$286$	−7252.60	−	4187.29i	−1.49949	−	0.865733i
$287$	1163.36	+	1596.20i	0.239271	+	0.328296i
$288$	235.980	+	988.684i	0.0482820	+	0.202287i
$289$	−4818.05			−0.980674
$290$	−92.5424	+	160.288i	−0.0187389	+	0.0324567i
$291$	299.998	+	2549.11i	0.0604337	+	0.513511i
$292$	668.319	−	385.854i	0.133940	−	0.0773302i
$293$	−4185.66	−	7249.78i	−0.834569	−	1.44552i	−0.894380	−	0.447307i	$-0.852383\pi$
$293$	−4185.66	−	7249.78i	−0.834569	−	1.44552i	0.0598110	−	0.998210i	$-0.480950\pi$
$294$	−1543.96	−	4513.83i	−0.306277	−	0.895414i
$295$	−56.4545	+	97.7821i	−0.0111421	+	0.0192986i
$296$		−	7971.64i		−	1.56535i
$297$	−5470.14	−	951.117i	−1.06872	−	0.185823i
$298$	5186.83			1.00827
$299$	−5772.68	+	9998.58i	−1.11653	+	1.93389i
$300$	−323.859	−	434.298i	−0.0623267	−	0.0835807i
$301$	−684.700	+	1544.06i	−0.131114	+	0.295676i
$302$	−3353.71	+	1936.27i	−0.639022	+	0.368939i
$303$	7346.48	−	864.588i	1.39289	−	0.163925i
$304$	3584.58	+	2069.56i	0.676282	+	0.390452i
$305$		−	176.758i		−	0.0331840i
$306$	511.464	−	484.078i	0.0955506	−	0.0904343i
$307$			3591.50i			0.667679i	0.942630	+	0.333840i	$0.108344\pi$
$307$			3591.50i			0.667679i	−0.942630	+	0.333840i	$0.891656\pi$
$308$	−64.9136	−	608.861i	−0.0120091	−	0.112640i
$309$	−4554.73	−	1960.43i	−0.838542	−	0.360923i
$310$	−6.81584	−	11.8054i	−0.00124875	−	0.00216290i
$311$	2699.19	+	4675.13i	0.492144	+	0.852419i	0.999959	−	0.00904760i	$-0.00287998\pi$
$311$	2699.19	+	4675.13i	0.492144	+	0.852419i	−0.507815	+	0.861466i	$0.669547\pi$
$312$	−3840.92	+	8923.70i	−0.696952	+	1.61925i
$313$	−2209.23	−	1275.50i	−0.398956	−	0.230337i	0.287077	−	0.957907i	$-0.407316\pi$
$313$	−2209.23	−	1275.50i	−0.398956	−	0.230337i	−0.686033	+	0.727570i	$0.740650\pi$
$314$	5289.78			0.950700
$315$	−210.484	+	74.5767i	−0.0376489	+	0.0133394i
$316$	−468.211			−0.0833510
$317$	7748.08	+	4473.35i	1.37279	+	0.792582i	0.991279	−	0.131781i	$-0.0420695\pi$
$317$	7748.08	+	4473.35i	1.37279	+	0.792582i	0.381514	+	0.924363i	$0.375403\pi$
$318$	−3314.97	+	390.130i	−0.584573	+	0.0687969i
$319$	−3063.93	−	5306.88i	−0.537765	−	0.931436i
$320$	−123.636	−	214.144i	−0.0215983	−	0.0374094i
$321$	3659.83	−	2729.15i	0.636360	−	0.474537i
$322$	7198.60	−	767.477i	1.24585	−	0.132826i
$323$			712.357i			0.122714i
$324$	−33.4822	+	608.101i	−0.00574112	+	0.104270i
$325$		−	9866.52i		−	1.68399i
$326$	−2064.98	−	1192.21i	−0.350823	−	0.202548i
$327$	−398.685	−	534.641i	−0.0674230	−	0.0904150i
$328$	−2184.28	+	1261.10i	−0.367704	+	0.212294i
$329$	4154.66	−	9369.16i	0.696213	−	1.57003i
$330$	244.117	−	28.7295i	0.0407218	−	0.00479244i
$331$	1235.22	−	2139.46i	0.205117	−	0.355274i	−0.745053	−	0.667006i	$-0.767576\pi$
$331$	1235.22	−	2139.46i	0.205117	−	0.355274i	0.950170	+	0.311732i	$0.100909\pi$
$332$	470.185			0.0777251
$333$	2596.36	−	8722.79i	0.427266	−	1.43545i
$334$			3088.91i			0.506041i
$335$	−6.04959	+	10.4782i	−0.000986640	+	0.00170891i
$336$	5313.30	−	1206.93i	0.862691	−	0.195962i
$337$	−2669.18	−	4623.15i	−0.431452	−	0.747297i	0.565546	−	0.824716i	$-0.308665\pi$
$337$	−2669.18	−	4623.15i	−0.431452	−	0.747297i	−0.996999	+	0.0774194i	$0.975332\pi$
$338$	−9395.62	+	5424.56i	−1.51199	+	0.872950i
$339$	−2554.37	−	1099.45i	−0.409246	−	0.176147i
$340$	1.81766	−	3.14828i	0.000289930	−	0.000502174i
$341$	451.323			0.0716730
$342$	3631.73	+	3837.19i	0.574214	+	0.606700i
$343$	6032.68	−	1990.07i	0.949662	−	0.313276i
$344$	−1867.90	−	1078.43i	−0.292763	−	0.169027i
$345$	−39.6070	−	336.544i	−0.00618078	−	0.0525187i
$346$	5100.73	−	2944.91i	0.792535	−	0.457570i
$347$	1017.68	−	587.557i	0.157440	−	0.0908982i	−0.419210	−	0.907889i	$-0.637693\pi$
$347$	1017.68	−	587.557i	0.157440	−	0.0908982i	0.576650	+	0.816991i	$0.304360\pi$
$348$	−538.840	+	401.816i	−0.0830025	+	0.0618954i
$349$	5180.32	+	2990.86i	0.794545	+	0.458731i	0.841560	−	0.540163i	$-0.181638\pi$
$349$	5180.32	+	2990.86i	0.794545	+	0.458731i	−0.0470151	+	0.998894i	$0.514971\pi$
$350$	−4999.71	+	3643.92i	−0.763559	+	0.556502i
$351$	−7109.28	+	8513.58i	−1.08110	+	1.29465i
$352$	1489.86			0.225596
$353$	−1648.31	+	2854.96i	−0.248530	+	0.430466i	−0.963118	−	0.269079i	$-0.913281\pi$
$353$	−1648.31	+	2854.96i	−0.248530	+	0.430466i	0.714588	+	0.699545i	$0.246614\pi$
$354$	2819.05	−	2102.18i	0.423251	−	0.315621i
$355$	134.717	−	77.7787i	0.0201409	−	0.0116284i
$356$	269.419	+	466.647i	0.0401100	+	0.0694726i
$357$	637.106	+	688.068i	0.0944517	+	0.102007i
$358$	−736.414	+	1275.51i	−0.108717	+	0.188303i
$359$			1871.57i			0.275146i	0.990492	+	0.137573i	$0.0439302\pi$
$359$			1871.57i			0.275146i	−0.990492	+	0.137573i	$0.956070\pi$
$360$	−66.2002	−	277.359i	−0.00969183	−	0.0406059i
$361$	1514.64			0.220825
$362$	2747.83	−	4759.37i	0.398957	−	0.691014i
$363$	−483.124	+	1122.46i	−0.0698553	+	0.162297i
$364$	−1118.20	−	495.853i	−0.161015	−	0.0714004i
$365$	−357.245	+	206.255i	−0.0512303	+	0.0295778i
$366$	−2176.47	+	5056.64i	−0.310835	+	0.722171i
$367$	114.764	+	66.2588i	0.0163232	+	0.00942421i	0.508139	−	0.861275i	$-0.330333\pi$
$367$	114.764	+	66.2588i	0.0163232	+	0.00942421i	−0.491816	+	0.870699i	$0.663667\pi$
$368$			8268.37i			1.17125i
$369$	−2800.84	+	668.507i	−0.395138	+	0.0943118i
$370$			402.910i			0.0566116i
$371$	−471.193	−	4419.59i	−0.0659384	−	0.618473i
$372$	−5.78624	−	49.1662i	−0.000806459	−	0.00685256i
$373$	−943.284	−	1633.82i	−0.130942	−	0.226798i	0.793098	−	0.609094i	$-0.208467\pi$
$373$	−943.284	−	1633.82i	−0.130942	−	0.226798i	−0.924040	+	0.382296i	$0.875134\pi$
$374$	−516.102	−	893.915i	−0.0713556	−	0.123592i
$375$	346.509	+	464.672i	0.0477164	+	0.0639882i
$376$	11334.1	+	6543.77i	1.55456	+	0.897524i
$377$	−12241.5			−1.67234
$378$	6939.74	+	458.269i	0.944290	+	0.0623567i
$379$	−6290.03			−0.852499			−0.426249	−	0.904606i	$-0.640165\pi$
$379$	−6290.03			−0.852499			−0.426249	+	0.904606i	$0.640165\pi$
$380$	23.6195	+	13.6367i	0.00318857	+	0.00184092i
$381$	469.542	+	629.661i	0.0631374	+	0.0846680i
$382$	398.877	+	690.874i	0.0534249	+	0.0925346i
$383$	−1276.74	−	2211.38i	−0.170336	−	0.295030i	0.768202	−	0.640208i	$-0.221152\pi$
$383$	−1276.74	−	2211.38i	−0.170336	−	0.295030i	−0.938537	+	0.345178i	$0.887819\pi$
$384$	717.225	+	6094.32i	0.0953144	+	0.809895i
$385$	34.6990	+	325.462i	0.00459332	+	0.0430833i
$386$			8181.97i			1.07889i
$387$	−1692.66	−	1788.42i	−0.222333	−	0.234911i
$388$		−	412.667i		−	0.0539948i
$389$	11399.3	+	6581.36i	1.48577	+	0.857810i	0.999869	−	0.0162025i	$-0.00515763\pi$
$389$	11399.3	+	6581.36i	1.48577	+	0.857810i	0.485903	+	0.874013i	$0.338491\pi$
$390$	194.131	−	451.030i	0.0252057	−	0.0585610i
$391$	−1232.37	+	711.508i	−0.159395	+	0.0920269i
$392$	1710.23	+	7929.45i	0.220357	+	1.02168i
$393$	5530.11	−	12848.3i	0.709815	−	1.64913i
$394$	4460.14	−	7725.18i	0.570301	−	0.987790i
$395$	250.278			0.0318807
$396$	855.571	+	254.663i	0.108571	+	0.0323164i
$397$		−	5781.38i		−	0.730880i	−0.930835	−	0.365440i	$-0.880919\pi$
$397$		−	5781.38i		−	0.730880i	0.930835	−	0.365440i	$-0.119081\pi$
$398$	5133.22	−	8891.00i	0.646495	−	1.11976i
$399$	−5162.13	+	4779.80i	−0.647694	+	0.599723i
$400$	−3533.02	−	6119.38i	−0.441628	−	0.764922i
$401$	−9010.34	+	5202.12i	−1.12208	+	0.647835i	−0.941932	−	0.335804i	$-0.890992\pi$
$401$	−9010.34	+	5202.12i	−1.12208	+	0.647835i	−0.180151	+	0.983639i	$0.557659\pi$
$402$	302.086	−	225.267i	0.0374793	−	0.0279485i
$403$	450.800	−	780.809i	0.0557220	−	0.0965133i
$404$	−1189.30			−0.146460
$405$	17.8977	−	325.055i	0.00219591	−	0.0398818i
$406$	4521.07	+	6203.21i	0.552652	+	0.758276i
$407$	−11552.5	−	6669.84i	−1.40697	−	0.812314i
$408$	−959.928	+	715.824i	−0.116479	+	0.0868593i
$409$	6402.33	−	3696.39i	0.774021	−	0.446882i	−0.0602858	−	0.998181i	$-0.519201\pi$
$409$	6402.33	−	3696.39i	0.774021	−	0.446882i	0.834307	+	0.551300i	$0.185868\pi$
$410$	110.400	−	63.7395i	0.0132982	−	0.00767773i
$411$	−1201.55	−	10209.7i	−0.144204	−	1.22532i
$412$	690.435	+	398.623i	0.0825614	+	0.0476669i
$413$	2758.03	+	3784.20i	0.328605	+	0.450868i
$414$	−3010.89	+	10115.5i	−0.357433	+	1.20084i
$415$	−251.333			−0.0297288
$416$	1488.13	−	2577.52i	0.175389	−	0.303782i
$417$	5869.95	+	2526.53i	0.689335	+	0.296702i
$418$	6706.47	−	3871.98i	0.784747	−	0.453074i
$419$	3158.84	+	5471.26i	0.368304	+	0.637921i	0.989300	−	0.145892i	$-0.0466054\pi$
$419$	3158.84	+	5471.26i	0.368304	+	0.637921i	−0.620997	+	0.783813i	$0.713272\pi$
$420$	35.0103	−	7.95268i	0.00406745	−	0.000923931i
$421$	655.795	−	1135.87i	0.0759180	−	0.131494i	−0.825567	−	0.564304i	$-0.809145\pi$
$421$	655.795	−	1135.87i	0.0759180	−	0.131494i	0.901485	+	0.432810i	$0.142478\pi$
$422$		−	15475.2i		−	1.78512i
$423$	10270.8	+	10851.9i	1.18058	+	1.24737i
$424$	5675.60			0.650074
$425$	608.046	−	1053.17i	0.0693990	−	0.120203i
$426$	−4811.65	+	566.270i	−0.547242	+	0.0644035i
$427$	−6701.27	−	2971.61i	−0.759478	−	0.336783i
$428$	−635.668	+	367.003i	−0.0717901	+	0.0414480i
$429$	9718.55	+	13032.7i	1.09374	+	1.46672i
$430$	94.4089	+	54.5070i	0.0105879	+	0.00611293i
$431$		−	10904.1i		−	1.21863i	−0.792927	−	0.609317i	$-0.791444\pi$
$431$		−	10904.1i		−	1.21863i	0.792927	−	0.609317i	$-0.208556\pi$
$432$	−1360.74	+	7825.97i	−0.151547	+	0.871590i
$433$		−	9935.59i		−	1.10271i	−0.834270	−	0.551355i	$-0.814111\pi$
$433$		−	9935.59i		−	1.10271i	0.834270	−	0.551355i	$-0.185889\pi$
$434$	−562.153	+	59.9338i	−0.0621756	+	0.00662884i
$435$	288.033	−	214.788i	0.0317474	−	0.0236742i
$436$	53.6131	+	92.8606i	0.00588899	+	0.0102000i
$437$	−5337.99	−	9245.68i	−0.584327	−	1.01208i
$438$	12759.6	−	1501.65i	1.39196	−	0.163816i
$439$	−2967.35	−	1713.20i	−0.322606	−	0.186256i	0.329948	−	0.943999i	$-0.392969\pi$
$439$	−2967.35	−	1713.20i	−0.322606	−	0.186256i	−0.652553	+	0.757743i	$0.726302\pi$
$440$	−417.956			−0.0452847
$441$	−711.236	+	9233.65i	−0.0767991	+	0.997047i
$442$	−2062.02			−0.221901
$443$	1658.53	+	957.551i	0.177876	+	0.102697i	0.586294	−	0.810098i	$-0.300586\pi$
$443$	1658.53	+	957.551i	0.177876	+	0.102697i	−0.408418	+	0.912795i	$0.633920\pi$
$444$	−578.490	+	1344.02i	−0.0618331	+	0.143659i
$445$	−144.016	−	249.443i	−0.0153416	−	0.0265724i
$446$	−1782.82	−	3087.94i	−0.189281	−	0.327844i
$447$	−9248.73	−	3980.81i	−0.978635	−	0.421222i
$448$	−10197.2	+	1087.17i	−1.07538	+	0.114652i
$449$			3077.07i			0.323421i	0.986838	+	0.161711i	$0.0517011\pi$
$449$			3077.07i			0.323421i	−0.986838	+	0.161711i	$0.948299\pi$
$450$	−2093.93	−	8772.93i	−0.219353	−	0.919022i
$451$			4220.62i			0.440668i
$452$	387.209	+	223.555i	0.0402937	+	0.0232636i
$453$	7466.12	−	878.668i	0.774369	−	0.0911334i
$454$	−3646.31	+	2105.20i	−0.376938	+	0.217625i
$455$	597.723	+	265.054i	0.0615861	+	0.0273098i
$456$	−5370.37	−	7201.73i	−0.551515	−	0.739587i
$457$	−6115.64	+	10592.6i	−0.625990	+	1.08425i	0.362358	+	0.932039i	$0.381972\pi$
$457$	−6115.64	+	10592.6i	−0.625990	+	1.08425i	−0.988349	+	0.152208i	$0.951362\pi$
$458$	−18255.0			−1.86244
$459$	−1283.52	+	470.626i	−0.130522	+	0.0478583i
$460$			54.4819i			0.00552225i
$461$	−2511.44	+	4349.95i	−0.253730	+	0.439473i	−0.964550	−	0.263901i	$-0.914991\pi$
$461$	−2511.44	+	4349.95i	−0.253730	+	0.439473i	0.710820	+	0.703374i	$0.248324\pi$
$462$	3014.84	−	9737.99i	0.303600	−	0.980632i
$463$	2690.92	+	4660.82i	0.270103	+	0.467833i	0.968888	−	0.247499i	$-0.0796088\pi$
$463$	2690.92	+	4660.82i	0.270103	+	0.467833i	−0.698785	+	0.715332i	$0.746275\pi$
$464$	−7592.40	+	4383.47i	−0.759630	+	0.438572i
$465$	3.09299	+	26.2814i	0.000308460	+	0.00262101i
$466$	2121.41	−	3674.39i	0.210885	−	0.365264i
$467$	18150.0			1.79846			0.899232	−	0.437471i	$-0.144126\pi$
$467$	18150.0			1.79846			0.899232	+	0.437471i	$0.144126\pi$
$468$	1295.16	−	1225.81i	0.127925	−	0.121075i
$469$	295.547	+	405.510i	0.0290982	+	0.0399247i
$470$	−572.860	−	330.741i	−0.0562214	−	0.0324594i
$471$	−9432.30	−	4059.83i	−0.922755	−	0.397170i
$472$	−5178.39	+	2989.75i	−0.504989	+	0.291555i
$473$	−3125.73	+	1804.64i	−0.303850	+	0.175428i
$474$	−7159.90	−	3081.74i	−0.693808	−	0.298627i
$475$	7901.24	+	4561.78i	0.763229	+	0.440650i
$476$	−88.7999	−	121.839i	−0.00855070	−	0.0117321i
$477$	6210.40	+	1848.54i	0.596131	+	0.177440i
$478$	−17635.9			−1.68755
$479$	−990.626	+	1715.81i	−0.0944945	+	0.163669i	−0.909398	−	0.415928i	$-0.863457\pi$
$479$	−990.626	+	1715.81i	−0.0944945	+	0.163669i	0.814903	+	0.579597i	$0.196790\pi$
$480$	10.2103	+	86.7574i	0.000970900	+	0.00824983i
$481$	−23078.3	+	13324.2i	−2.18769	+	1.26306i
$482$	5226.06	+	9051.80i	0.493860	+	0.855390i
$483$	−13425.0	−	4156.32i	−1.26472	−	0.391551i
$484$	98.2357	−	170.149i	0.00922574	−	0.0159794i
$485$			220.588i			0.0206523i
$486$	−4514.50	+	9078.72i	−0.421362	+	0.847364i
$487$	6722.00			0.625468			0.312734	−	0.949841i	$-0.398755\pi$
$487$	6722.00			0.625468			0.312734	+	0.949841i	$0.398755\pi$
$488$	4680.41	−	8106.71i	0.434164	−	0.751995i
$489$	2767.09	+	3710.70i	0.255894	+	0.343156i
$490$	−86.4401	−	400.777i	−0.00796931	−	0.0369495i
$491$	2394.40	−	1382.41i	0.220077	−	0.127062i	−0.385909	−	0.922537i	$-0.626112\pi$
$491$	2394.40	−	1382.41i	0.220077	−	0.127062i	0.605986	+	0.795475i	$0.292779\pi$
$492$	459.786	−	54.1111i	0.0421317	−	0.00495836i
$493$	−1306.68	−	754.411i	−0.119371	−	0.0689188i
$494$		−	15470.0i		−	1.40896i
$495$	−457.338	−	136.128i	−0.0415269	−	0.0123606i
$496$		−	645.694i		−	0.0584526i
$497$	−683.933	−	6415.00i	−0.0617275	−	0.578978i
$498$	7190.08	+	3094.73i	0.646978	+	0.278471i
$499$	1527.72	+	2646.09i	0.137054	+	0.237385i	0.926380	−	0.376589i	$-0.122903\pi$
$499$	1527.72	+	2646.09i	0.137054	+	0.237385i	−0.789326	+	0.613974i	$0.789570\pi$
$500$	−46.5968	−	80.7080i	−0.00416774	−	0.00721874i
$501$	2370.69	−	5507.89i	0.211407	−	0.491167i
$502$	−12071.0	−	6969.18i	−1.07321	−	0.619621i
$503$	−15649.8			−1.38726			−0.693630	−	0.720331i	$-0.743990\pi$
$503$	−15649.8			−1.38726			−0.693630	+	0.720331i	$0.743990\pi$
$504$	−11628.2	−	2153.10i	−1.02770	−	0.190291i
$505$	635.729			0.0560189
$506$	13397.0	+	7734.74i	1.17701	+	0.679548i
$507$	20916.8	−	2461.64i	1.83224	−	0.215631i
$508$	−63.1416	−	109.365i	−0.00551468	−	0.00955170i
$509$	5822.79	+	10085.4i	0.507054	+	0.878243i	0.999967	+	0.00816434i	$0.00259882\pi$
$509$	5822.79	+	10085.4i	0.507054	+	0.878243i	−0.492913	+	0.870079i	$0.664068\pi$
$510$	48.5175	−	36.1798i	0.00421253	−	0.00314131i
$511$	1813.67	+	17011.4i	0.157010	+	1.47268i
$512$		−	12843.5i		−	1.10861i
$513$	−3530.81	−	9629.46i	−0.303877	−	0.828754i
$514$		−	17338.9i		−	1.48791i
$515$	−369.067	−	213.081i	−0.0315787	−	0.0182320i
$516$	236.668	+	317.374i	0.0201913	+	0.0270768i
$517$	18966.5	−	10950.3i	1.61343	−	0.931515i
$518$	15275.2	+	6773.62i	1.29566	+	0.574548i
$519$	−11355.4	+	1336.38i	−0.960397	+	0.113027i
$520$	−417.472	+	723.082i	−0.0352064	+	0.0609793i
$521$	−3960.23			−0.333015			−0.166508	−	0.986040i	$-0.553249\pi$
$521$	−3960.23			−0.333015			−0.166508	+	0.986040i	$0.553249\pi$
$522$	−10884.7	+	2597.97i	−0.912663	+	0.217835i
$523$			19478.4i			1.62855i	0.580481	+	0.814274i	$0.302865\pi$
$523$			19478.4i			1.62855i	−0.580481	+	0.814274i	$0.697135\pi$
$524$	−1124.46	+	1947.62i	−0.0937448	+	0.162371i
$525$	11711.7	−	2660.34i	0.973603	−	0.221156i
$526$	5050.64	+	8747.96i	0.418666	+	0.725151i
$527$	96.2381	−	55.5631i	0.00795484	−	0.00459273i
$528$	10694.4	+	4603.05i	0.881464	+	0.379398i
$529$	4579.77	−	7932.39i	0.376409	−	0.651960i
$530$	−286.861			−0.0235103
$531$	−6640.10	+	1584.86i	−0.542666	+	0.129524i
$532$	914.083	−	666.209i	0.0744935	−	0.0542929i
$533$	7301.87	+	4215.74i	0.593394	+	0.342596i
$534$	1048.51	+	8909.29i	0.0849691	+	0.721990i
$535$	339.791	−	196.178i	0.0274588	−	0.0158533i
$536$	−554.909	+	320.377i	−0.0447172	+	0.0258175i
$537$	2292.04	−	1709.19i	0.184188	−	0.137350i
$538$	−10156.4	−	5863.81i	−0.813892	−	0.469901i
$539$	12922.3	+	4156.07i	1.03266	+	0.332124i
$540$	−8.96615	+	51.5668i	−0.000714522	+	0.00410941i
$541$	17325.2			1.37684			0.688420	−	0.725312i	$-0.258305\pi$
$541$	17325.2			1.37684			0.688420	+	0.725312i	$0.258305\pi$
$542$	−3325.87	+	5760.58i	−0.263576	+	0.456528i
$543$	−8552.44	+	6377.61i	−0.675912	+	0.504032i
$544$	317.691	−	183.419i	0.0250384	−	0.0144559i
$545$	−28.6585	−	49.6379i	−0.00225246	−	0.00390138i
$546$	−13835.8	−	14942.5i	−1.08447	−	1.17121i
$547$	1586.64	−	2748.14i	0.124021	−	0.214812i	−0.797329	−	0.603546i	$-0.793754\pi$
$547$	1586.64	−	2748.14i	0.124021	−	0.214812i	0.921350	+	0.388734i	$0.127087\pi$
$548$			1652.80i			0.128840i
$549$	7761.79	−	7346.18i	0.603397	−	0.571088i
$550$	−13220.0			−1.02492
$551$	5659.87	−	9803.17i	0.437601	−	0.757948i
$552$	7094.93	−	16483.8i	0.547065	−	1.27101i
$553$	4207.62	−	9488.59i	0.323556	−	0.729649i
$554$	13969.2	−	8065.12i	1.07129	−	0.618509i
$555$	309.227	−	718.435i	0.0236504	−	0.0549475i
$556$	−889.805	−	513.729i	−0.0678707	−	0.0391852i
$557$			11046.4i			0.840304i	0.907454	+	0.420152i	$0.138023\pi$
$557$			11046.4i			0.840304i	−0.907454	+	0.420152i	$0.861977\pi$
$558$	235.127	−	789.937i	0.0178382	−	0.0599295i
$559$			7210.20i			0.545544i
$560$	465.629	−	49.6429i	0.0351364	−	0.00374606i
$561$	234.204	+	1990.06i	0.0176259	+	0.149769i
$562$	5338.17	+	9245.98i	0.400671	+	0.693982i
$563$	2213.27	+	3833.50i	0.165681	+	0.286968i	0.936897	−	0.349606i	$-0.113684\pi$
$563$	2213.27	+	3833.50i	0.165681	+	0.286968i	−0.771216	+	0.636574i	$0.780351\pi$
$564$	−1436.07	−	1925.78i	−0.107215	−	0.143777i
$565$	−206.979	−	119.500i	−0.0154118	−	0.00889802i
$566$	17487.0			1.29864
$567$	−12022.7	−	6143.29i	−0.890483	−	0.455016i
$568$	8238.09			0.608561
$569$	9164.47	+	5291.11i	0.675210	+	0.389833i	0.798048	−	0.602594i	$-0.205866\pi$
$569$	9164.47	+	5291.11i	0.675210	+	0.389833i	−0.122838	+	0.992427i	$0.539199\pi$
$570$	271.434	+	363.996i	0.0199458	+	0.0267476i
$571$	11167.7	+	19343.0i	0.818480	+	1.41765i	0.906802	+	0.421557i	$0.138516\pi$
$571$	11167.7	+	19343.0i	0.818480	+	1.41765i	−0.0883214	+	0.996092i	$0.528150\pi$
$572$	−1306.90	−	2263.62i	−0.0955320	−	0.165466i
$573$	−181.008	−	1538.04i	−0.0131967	−	0.112134i
$574$	−560.481	−	5257.07i	−0.0407562	−	0.382275i
$575$			18225.4i			1.32183i
$576$	4265.08	−	14329.1i	0.308528	−	1.03654i
$577$		−	6646.62i		−	0.479553i	−0.970828	−	0.239777i	$-0.922926\pi$
$577$		−	6646.62i		−	0.479553i	0.970828	−	0.239777i	$-0.0770742\pi$
$578$	11168.6	+	6448.17i	0.803721	+	0.464029i
$579$	6279.53	−	14589.4i	0.450723	−	1.04718i
$580$	−50.0278	+	28.8836i	−0.00358154	+	0.00206780i
$581$	−4225.36	+	9528.59i	−0.301717	+	0.680400i
$582$	2716.15	−	6310.51i	0.193451	−	0.449449i
$583$	4748.75	−	8225.08i	0.337347	−	0.584302i
$584$	−21845.9			−1.54793
$585$	−692.317	+	655.246i	−0.0489295	+	0.0463096i
$586$			22407.3i			1.57958i
$587$	57.5485	−	99.6770i	0.00404648	−	0.00700870i	−0.863995	−	0.503500i	$-0.832045\pi$
$587$	57.5485	−	99.6770i	0.00404648	−	0.00700870i	0.868042	+	0.496492i	$0.165379\pi$
$588$	287.083	−	1461.02i	0.0201345	−	0.102468i
$589$	416.855	+	722.013i	0.0291616	+	0.0505094i
$590$	261.731	−	151.110i	0.0182632	−	0.0105443i
$591$	−13881.9	+	10351.8i	−0.966202	+	0.720503i
$592$	−9542.35	+	16527.8i	−0.662480	+	1.14745i
$593$	−13996.5			−0.969251			−0.484625	−	0.874722i	$-0.661044\pi$
$593$	−13996.5			−0.969251			−0.484625	+	0.874722i	$0.661044\pi$
$594$	11407.2	+	9525.64i	0.787954	+	0.657983i
$595$	47.4673	+	65.1283i	0.00327053	+	0.00448739i
$596$	1401.98	+	809.435i	0.0963548	+	0.0556305i
$597$	−15976.8	+	11914.0i	−1.09529	+	0.816765i
$598$	26762.9	−	15451.6i	1.83013	−	1.05663i
$599$	−7820.94	+	4515.42i	−0.533481	+	0.308005i	−0.742433	−	0.669921i	$-0.766328\pi$
$599$	−7820.94	+	4515.42i	−0.533481	+	0.308005i	0.208952	+	0.977926i	$0.432995\pi$
$600$	1792.52	+	15231.2i	0.121966	+	1.03635i
$601$	854.920	+	493.588i	0.0580248	+	0.0335006i	0.528732	−	0.848789i	$-0.322668\pi$
$601$	854.920	+	493.588i	0.0580248	+	0.0335006i	−0.470707	+	0.882290i	$0.656001\pi$
$602$	3653.66	−	2662.89i	0.247362	−	0.180284i
$603$	−711.543	+	169.832i	−0.0480536	+	0.0114694i
$604$	−1208.66			−0.0814235
$605$	−52.5111	+	90.9519i	−0.00352873	+	0.00611193i
$606$	−18186.8	−	7827.90i	−1.21912	−	0.524730i
$607$	−24746.4	+	14287.4i	−1.65474	+	0.955364i	−0.679654	+	0.733533i	$0.737870\pi$
$607$	−24746.4	+	14287.4i	−1.65474	+	0.955364i	−0.975085	+	0.221832i	$0.928796\pi$
$608$	1376.08	+	2383.43i	0.0917882	+	0.158982i
$609$	−3300.72	−	14530.9i	−0.219626	−	0.966866i
$610$	−236.561	+	409.736i	−0.0157018	+	0.0271963i
$611$		−	43750.5i		−	2.89682i
$612$	213.790	−	51.0276i	0.0141208	−	0.00337037i
$613$	−25910.7			−1.70722			−0.853609	−	0.520915i	$-0.825591\pi$
$613$	−25910.7			−1.70722			−0.853609	+	0.520915i	$0.825591\pi$
$614$	4806.63	−	8325.33i	0.315928	−	0.547203i
$615$	−245.775	+	28.9246i	−0.0161148	+	0.00189651i
$616$	−7026.57	+	15845.6i	−0.459592	+	1.03642i
$617$	16717.2	−	9651.66i	1.09077	−	0.629759i	0.156991	−	0.987600i	$-0.449820\pi$
$617$	16717.2	−	9651.66i	1.09077	−	0.629759i	0.933782	+	0.357841i	$0.116487\pi$
$618$	7934.44	+	10640.2i	0.516456	+	0.692574i
$619$	−8336.56	−	4813.12i	−0.541316	−	0.312529i	0.204296	−	0.978909i	$-0.434510\pi$
$619$	−8336.56	−	4813.12i	−0.541316	−	0.312529i	−0.745612	+	0.666380i	$0.767843\pi$
$620$		−	4.25460i		−	0.000275595i
$621$	13132.2	−	15726.2i	0.848597	−	1.01622i
$622$		−	14449.7i		−	0.931478i
$623$	−11878.1	+	1266.38i	−0.763859	+	0.0814387i
$624$	18645.5	−	13904.0i	1.19618	−	0.891999i
$625$	−7775.13	−	13466.9i	−0.497608	−	0.861883i
$626$	3414.10	+	5913.39i	0.217979	+	0.377551i
$627$	−14930.1	+	1757.09i	−0.950959	+	0.111916i
$628$	1429.81	+	825.501i	0.0908529	+	0.0524540i
$629$	−3284.54			−0.208209
$630$	587.724	+	108.824i	0.0371674	+	0.00688199i
$631$	9205.14			0.580746			0.290373	−	0.956914i	$-0.406221\pi$
$631$	9205.14			0.580746			0.290373	+	0.956914i	$0.406221\pi$
$632$	11478.6	+	6627.18i	0.722460	+	0.417113i
$633$	−11877.0	+	27594.1i	−0.745762	+	1.73265i
$634$	−11973.7	−	20739.1i	−0.750058	−	1.29914i
$635$	33.7519	+	58.4599i	0.00210929	+	0.00365340i
$636$	−956.907	−	411.869i	−0.0596601	−	0.0256787i
$637$	20097.6	−	18204.9i	1.25007	−	1.13235i
$638$			16402.3i			1.01782i
$639$	9014.34	+	2683.14i	0.558062	+	0.166109i
$640$			527.373i			0.0325723i
$641$	−15509.1	−	8954.17i	−0.955651	−	0.551745i	−0.0608189	−	0.998149i	$-0.519371\pi$
$641$	−15509.1	−	8954.17i	−0.955651	−	0.551745i	−0.894832	+	0.446404i	$0.852705\pi$
$642$	−12136.2	+	1428.28i	−0.746074	+	0.0878035i
$643$	8189.11	−	4727.98i	0.502250	−	0.289974i	−0.227392	−	0.973803i	$-0.573020\pi$
$643$	8189.11	−	4727.98i	0.502250	−	0.289974i	0.729642	+	0.683829i	$0.239687\pi$
$644$	2065.53	+	915.937i	0.126387	+	0.0560450i
$645$	−126.509	−	169.650i	−0.00772292	−	0.0103565i
$646$	953.373	−	1651.29i	0.0580650	−	0.100571i
$647$	−2719.32			−0.165235			−0.0826177	−	0.996581i	$-0.526328\pi$
$647$	−2719.32			−0.165235			−0.0826177	+	0.996581i	$0.526328\pi$
$648$	9428.06	−	14434.2i	0.571558	−	0.875046i
$649$			10006.0i			0.605194i
$650$	−13204.7	+	22871.3i	−0.796818	+	1.38013i
$651$	1048.38	+	324.575i	0.0631173	+	0.0195409i
$652$	−372.104	−	644.503i	−0.0223508	−	0.0387127i
$653$	−18950.9	+	10941.3i	−1.13569	+	0.655692i	−0.945360	−	0.326028i	$-0.894289\pi$
$653$	−18950.9	+	10941.3i	−1.13569	+	0.655692i	−0.190331	+	0.981720i	$0.560956\pi$
$654$	208.649	+	1772.91i	0.0124752	+	0.106003i
$655$	601.071	−	1041.09i	0.0358562	−	0.0621047i
$656$	6038.32			0.359385
$657$	−23904.4	−	7115.21i	−1.41948	−	0.422513i
$658$	−22169.9	+	16158.0i	−1.31348	+	0.957302i
$659$	−12468.9	−	7198.91i	−0.737054	−	0.425538i	0.0839434	−	0.996471i	$-0.473248\pi$
$659$	−12468.9	−	7198.91i	−0.737054	−	0.425538i	−0.820997	+	0.570932i	$0.806582\pi$
$660$	70.4674	+	30.3304i	0.00415597	+	0.00178880i
$661$	97.0927	−	56.0565i	0.00571326	−	0.00329855i	−0.497141	−	0.867670i	$-0.665617\pi$
$661$	97.0927	−	56.0565i	0.00571326	−	0.00329855i	0.502854	+	0.864371i	$0.332283\pi$
$662$	−5726.65	+	3306.28i	−0.336212	+	0.194112i
$663$	3676.82	+	1582.57i	0.215378	+	0.0927026i
$664$	−11527.0	−	6655.12i	−0.673696	−	0.388959i
$665$	−488.616	+	356.117i	−0.0284928	+	0.0207663i
$666$	−17692.6	+	16745.2i	−1.02939	+	0.974270i
$667$	22612.5			1.31268
$668$	−482.043	+	834.922i	−0.0279203	+	0.0483595i
$669$	809.037	+	6874.46i	0.0467551	+	0.397282i
$670$	28.0467	−	16.1928i	0.00161722	−	0.000933703i
$671$	−7832.16	−	13565.7i	−0.450607	−	0.780474i
$672$	3460.81	+	1071.45i	0.198666	+	0.0615062i
$673$	407.222	−	705.330i	0.0233243	−	0.0403989i	−0.854128	−	0.520063i	$-0.825908\pi$
$673$	407.222	−	705.330i	0.0233243	−	0.0403989i	0.877452	+	0.479665i	$0.159242\pi$
$674$			14289.0i			0.816607i
$675$	−2999.37	+	17250.2i	−0.171031	+	0.983646i
$676$	−3386.14			−0.192657
$677$	12060.1	−	20888.6i	0.684647	−	1.18584i	−0.288901	−	0.957359i	$-0.593290\pi$
$677$	12060.1	−	20888.6i	0.684647	−	1.18584i	0.973548	−	0.228484i	$-0.0733769\pi$
$678$	4449.78	+	5967.20i	0.252054	+	0.338007i
$679$	8362.95	+	3708.47i	0.472667	+	0.209599i
$680$	−89.1231	+	51.4552i	−0.00502605	+	0.00290179i
$681$	8117.50	−	955.327i	0.456774	−	0.0537566i
$682$	−1046.20	−	604.022i	−0.0587403	−	0.0339138i
$683$		−	2642.57i		−	0.148046i	−0.997257	−	0.0740228i	$-0.976416\pi$
$683$		−	2642.57i		−	0.148046i	0.997257	−	0.0740228i	$-0.0235838\pi$
$684$	382.827	+	1603.93i	0.0214002	+	0.0896606i
$685$		−	883.493i		−	0.0492796i
$686$	−16647.5	−	3460.65i	−0.926539	−	0.192607i
$687$	32550.8	+	14010.4i	1.80770	+	0.778065i
$688$	2581.84	+	4471.88i	0.143070	+	0.247804i
$689$	−9486.51	−	16431.1i	−0.524539	−	0.908528i
$690$	−358.598	+	833.140i	−0.0197849	+	0.0459668i
$691$	−12315.9	−	7110.57i	−0.678029	−	0.391460i	0.121083	−	0.992642i	$-0.461363\pi$
$691$	−12315.9	−	7110.57i	−0.678029	−	0.391460i	−0.799112	+	0.601182i	$0.794697\pi$
$692$	1838.28			0.100984
$693$	−12849.6	+	15050.1i	−0.704350	+	0.824974i
$694$	−3145.39			−0.172043
$695$	475.638	+	274.610i	0.0259597	+	0.0149878i
$696$	18897.6	−	2224.00i	1.02918	−	0.121122i
$697$	519.608	+	899.987i	0.0282375	+	0.0489088i
$698$	−8005.55	−	13866.0i	−0.434118	−	0.751915i
$699$	−6602.76	+	4923.72i	−0.357281	+	0.266427i
$700$	−1920.06	+	204.707i	−0.103673	+	0.0110531i
$701$		−	5049.19i		−	0.272048i	−0.990706	−	0.136024i	$-0.956568\pi$
$701$		−	5049.19i		−	0.272048i	0.990706	−	0.136024i	$-0.0434324\pi$
$702$	27873.8	−	10220.4i	1.49862	−	0.549494i
$703$		−	24641.8i		−	1.32203i
$704$	−18977.5	−	10956.7i	−1.01597	−	0.586569i
$705$	767.638	+	1029.41i	0.0410084	+	0.0549927i
$706$	7641.81	−	4412.00i	0.407370	−	0.235195i
$707$	10687.7	−	24101.8i	0.568533	−	1.28210i
$708$	1090.04	−	128.284i	0.0578618	−	0.00680960i
$709$	−8032.47	+	13912.6i	−0.425481	+	0.736954i	−0.996465	−	0.0840068i	$-0.973228\pi$
$709$	−8032.47	+	13912.6i	−0.425481	+	0.736954i	0.570985	+	0.820961i	$0.306562\pi$
$710$	−416.376			−0.0220089
$711$	10401.7	+	10990.2i	0.548658	+	0.579698i
$712$		−	15253.7i		−	0.802889i
$713$	−832.716	+	1442.31i	−0.0437384	+	0.0757571i
$714$	−555.989	−	2447.65i	−0.0291420	−	0.128293i
$715$	698.594	+	1210.00i	0.0365398	+	0.0632887i
$716$	−398.101	+	229.843i	−0.0207789	+	0.0119967i
$717$	31446.9	+	13535.3i	1.63794	+	0.705000i
$718$	2504.79	−	4338.42i	0.130192	−	0.225499i
$719$	26291.7			1.36372			0.681860	−	0.731482i	$-0.261171\pi$
$719$	26291.7			1.36372			0.681860	+	0.731482i	$0.261171\pi$
$720$	−194.754	+	654.301i	−0.0100806	+	0.0338671i
$721$	−14283.0	+	10409.8i	−0.737763	+	0.537702i
$722$	−3511.04	−	2027.10i	−0.180980	−	0.104489i
$723$	−2371.56	−	20151.3i	−0.121991	−	1.03656i
$724$	1485.46	−	857.628i	0.0762521	−	0.0440242i
$725$	−16735.4	+	9662.17i	−0.857291	+	0.494957i
$726$	2622.14	−	1955.34i	0.134045	−	0.0999582i
$727$	29281.6	+	16905.8i	1.49380	+	0.862448i	0.999975	−	0.00711022i	$-0.00226327\pi$
$727$	29281.6	+	16905.8i	1.49380	+	0.862448i	0.493830	+	0.869559i	$0.335597\pi$
$728$	20395.2	+	27983.5i	1.03832	+	1.42464i
$729$	15017.7	−	12723.6i	0.762977	−	0.646426i
$730$	1104.16			0.0559817
$731$	−444.344	+	769.627i	−0.0224825	+	0.0389408i
$732$	−1377.41	+	1027.14i	−0.0695499	+	0.0518638i
$733$	9659.36	−	5576.83i	0.486735	−	0.281016i	−0.236484	−	0.971635i	$-0.575995\pi$
$733$	9659.36	−	5576.83i	0.486735	−	0.281016i	0.723219	+	0.690619i	$0.242662\pi$
$734$	−177.353	−	307.185i	−0.00891857	−	0.0154474i
$735$	−153.458	+	780.974i	−0.00770119	+	0.0391928i
$736$	−2748.87	+	4761.19i	−0.137670	+	0.238451i
$737$			1072.23i			0.0535905i
$738$	7387.23	+	2198.83i	0.368466	+	0.109675i
$739$	10412.2			0.518291			0.259146	−	0.965838i	$-0.416559\pi$
$739$	10412.2			0.518291			0.259146	+	0.965838i	$0.416559\pi$
$740$	−62.8764	+	108.905i	−0.00312349	+	0.00541004i
$741$	−11873.0	+	27584.8i	−0.588617	+	1.36755i
$742$	−4822.64	+	10875.5i	−0.238605	+	0.538077i
$743$	−3776.55	+	2180.39i	−0.186471	+	0.107659i	−0.590330	−	0.807162i	$-0.701002\pi$
$743$	−3776.55	+	2180.39i	−0.186471	+	0.107659i	0.403858	+	0.914822i	$0.367669\pi$
$744$	−554.057	+	1287.25i	−0.0273020	+	0.0634315i
$745$	−749.419	−	432.677i	−0.0368545	−	0.0212779i
$746$			5049.73i			0.247833i
$747$	−10445.6	−	11036.6i	−0.511625	−	0.540571i
$748$		−	322.163i		−	0.0157479i
$749$	−1725.06	−	16180.3i	−0.0841553	−	0.789340i
$750$	−181.343	−	1540.89i	−0.00882894	−	0.0750203i
$751$	−19401.4	−	33604.1i	−0.942697	−	1.63280i	−0.760298	−	0.649574i	$-0.774947\pi$
$751$	−19401.4	−	33604.1i	−0.942697	−	1.63280i	−0.182399	−	0.983225i	$-0.558386\pi$
$752$	−15666.3	−	27134.8i	−0.759694	−	1.31583i
$753$	16175.2	+	21691.1i	0.782812	+	1.04976i
$754$	28376.7	+	16383.3i	1.37058	+	0.791305i
$755$	646.081			0.0311435
$756$	1804.27	+	1206.86i	0.0867999	+	0.0580594i
$757$	26111.4			1.25368			0.626840	−	0.779148i	$-0.284348\pi$
$757$	26111.4			1.25368			0.626840	+	0.779148i	$0.284348\pi$
$758$	14580.7	+	8418.18i	0.698674	+	0.403380i
$759$	−17952.1	−	24073.9i	−0.858523	−	1.15129i
$760$	−386.036	−	668.634i	−0.0184250	−	0.0319130i
$761$	11401.0	+	19747.0i	0.543081	+	0.940644i	0.998725	+	0.0504816i	$0.0160756\pi$
$761$	11401.0	+	19747.0i	0.543081	+	0.940644i	−0.455644	+	0.890162i	$0.650591\pi$
$762$	−245.731	−	2088.00i	−0.0116823	−	0.0992655i
$763$	−2363.68	+	252.003i	−0.112151	+	0.0119569i
$764$			248.988i			0.0117907i
$765$	−114.280	+	27.2764i	−0.00540104	+	0.00128912i
$766$			6834.85i			0.322393i
$767$	17310.9	+	9994.45i	0.814942	+	0.470507i
$768$	−2606.35	+	6055.40i	−0.122459	+	0.284512i
$769$	−1260.21	+	727.581i	−0.0590952	+	0.0341187i	−0.529257	−	0.848462i	$-0.677529\pi$
$769$	−1260.21	+	727.581i	−0.0590952	+	0.0341187i	0.470161	+	0.882581i	$0.344196\pi$
$770$	355.143	−	800.882i	0.0166214	−	0.0374828i
$771$	−13307.4	+	30917.3i	−0.621599	+	1.44418i
$772$	−1276.84	+	2211.56i	−0.0595267	+	0.103103i
$773$	−281.797			−0.0131120			−0.00655598	−	0.999979i	$-0.502087\pi$
$773$	−281.797			−0.0131120			−0.00655598	+	0.999979i	$0.502087\pi$
$774$	1530.19	+	6411.03i	0.0710614	+	0.297726i
$775$		−	1423.26i		−	0.0659676i
$776$	−5840.99	+	10116.9i	−0.270205	+	0.468010i
$777$	−22038.8	−	23801.6i	−1.01755	−	1.09894i
$778$	−17616.2	−	30512.1i	−0.811786	−	1.40606i
$779$	−6752.03	+	3898.29i	−0.310548	+	0.179295i
$780$	122.859	−	91.6165i	0.00563981	−	0.00420564i
$781$	6892.77	−	11938.6i	0.315804	−	0.546988i
$782$	3808.95			0.174179
$783$	21402.6	+	3721.36i	0.976841	+	0.169848i
$784$	5945.97	−	18487.6i	0.270862	−	0.842182i
$785$	−764.293	−	441.265i	−0.0347501	−	0.0200630i
$786$	−30014.5	+	22382.0i	−1.36206	+	1.01570i
$787$	3285.92	−	1897.13i	0.148832	−	0.0859280i	−0.423735	−	0.905786i	$-0.639281\pi$
$787$	3285.92	−	1897.13i	0.148832	−	0.0859280i	0.572566	+	0.819858i	$0.305948\pi$
$788$	2411.12	−	1392.06i	0.109001	−	0.0629316i
$789$	−2291.95	−	19474.9i	−0.103417	−	0.878740i
$790$	−580.162	−	334.957i	−0.0261282	−	0.0150851i
$791$	−8010.17	+	5838.03i	−0.360062	+	0.262423i
$792$	−17370.5	−	18353.3i	−0.779337	−	0.823428i
$793$	−31292.4			−1.40129
$794$	−7737.44	+	13401.6i	−0.345833	+	0.599000i
$795$	511.507	+	220.162i	0.0228192	+	0.00982179i
$796$	2774.98	−	1602.14i	0.123564	−	0.0713395i
$797$	−2.60409	−	4.51042i	−0.000115736	−	0.000200461i	0.865968	−	0.500100i	$-0.166704\pi$
$797$	−2.60409	−	4.51042i	−0.000115736	−	0.000200461i	−0.866083	+	0.499900i	$0.833370\pi$
$798$	18363.2	−	4171.23i	0.814597	−	0.185038i
$799$	2696.22	−	4669.99i	0.119381	−	0.206774i
$800$		−	4698.30i		−	0.207638i
$801$	4968.13	−	16691.0i	0.219151	−	0.736265i
$802$	27848.8			1.22615
$803$	−18278.4	+	31659.1i	−0.803277	+	1.39132i
$804$	116.807	−	13.7467i	0.00512371	−	0.000602996i
$805$	−1104.11	−	489.607i	−0.0483414	−	0.0214365i
$806$	−2089.97	+	1206.64i	−0.0913351	+	0.0527323i
$807$	13609.7	+	18250.7i	0.593660	+	0.796105i
$808$	29156.7	+	16833.6i	1.26947	+	0.732926i
$809$		−	3739.33i		−	0.162506i	−0.996693	−	0.0812532i	$-0.974108\pi$
$809$		−	3739.33i		−	0.162506i	0.996693	−	0.0812532i	$-0.0258923\pi$
$810$	−476.521	+	729.547i	−0.0206707	+	0.0316465i
$811$		−	14932.6i		−	0.646554i	−0.946304	−	0.323277i	$-0.895215\pi$
$811$		−	14932.6i		−	0.646554i	0.946304	−	0.323277i	$-0.104785\pi$
$812$	253.982	+	2382.24i	0.0109766	+	0.102956i
$813$	10351.6	−	7719.23i	0.446550	−	0.332995i
$814$	17853.0	+	30922.3i	0.768731	+	1.33148i
$815$	198.905	+	344.514i	0.00854889	+	0.0148071i
$816$	2847.11	−	335.069i	0.122143	−	0.0143747i
$817$	−5774.02	−	3333.63i	−0.247255	−	0.142753i
$818$	−19788.0			−0.845810
$819$	13202.7	+	37263.0i	0.563297	+	1.58984i
$820$	39.7877			0.00169445
$821$	−20015.6	−	11556.0i	−0.850852	−	0.491240i	0.0100864	−	0.999949i	$-0.496789\pi$
$821$	−20015.6	−	11556.0i	−0.850852	−	0.491240i	−0.860938	+	0.508710i	$0.830123\pi$
$822$	−10878.7	+	25274.7i	−0.461603	+	1.07245i
$823$	201.466	+	348.950i	0.00853301	+	0.0147796i	0.870260	−	0.492592i	$-0.163950\pi$
$823$	201.466	+	348.950i	0.00853301	+	0.0147796i	−0.861727	+	0.507372i	$0.830617\pi$
$824$	−11284.4	−	19545.2i	−0.477077	−	0.826322i
$825$	23572.9	+	10146.2i	0.994790	+	0.428175i
$826$	−1328.76	−	12463.2i	−0.0559728	−	0.525000i
$827$			25979.2i			1.09236i	0.837666	+	0.546182i	$0.183919\pi$
$827$			25979.2i			1.09236i	−0.837666	+	0.546182i	$0.816081\pi$
$828$	−2392.41	+	2264.31i	−0.100413	+	0.0950364i
$829$			13552.1i			0.567771i	0.958858	+	0.283886i	$0.0916236\pi$
$829$			13552.1i			0.567771i	−0.958858	+	0.283886i	$0.908376\pi$
$830$	582.608	+	336.369i	0.0243646	+	0.0140669i
$831$	−31098.6	+	3659.91i	−1.29819	+	0.152781i
$832$	−37911.1	+	21888.0i	−1.57972	+	0.912053i
$833$	3267.16	−	704.665i	0.135895	−	0.0293099i
$834$	−10225.6	−	13712.6i	−0.424560	−	0.569340i
$835$	257.672	−	446.301i	0.0106792	−	0.0184969i
$836$	2416.98			0.0999917
$837$	−1025.52	+	1228.09i	−0.0423504	+	0.0507158i
$838$		−	16910.3i		−	0.697086i
$839$	21098.2	−	36543.2i	0.868166	−	1.50371i	0.00429755	−	0.999991i	$-0.498632\pi$
$839$	21098.2	−	36543.2i	0.868166	−	1.50371i	0.863869	−	0.503717i	$-0.168035\pi$
$840$	−970.875	−	300.579i	−0.0398790	−	0.0123464i
$841$	−206.506	−	357.679i	−0.00846719	−	0.0146656i
$842$	−3040.35	+	1755.35i	−0.124439	+	0.0718448i
$843$	−2422.43	−	20583.6i	−0.0989715	−	0.840970i
$844$	2414.99	−	4182.89i	0.0984923	−	0.170594i
$845$	1810.03			0.0736888
$846$	−9284.97	−	38901.2i	−0.377333	−	1.58091i
$847$	2565.38	+	3519.87i	0.104070	+	0.142791i
$848$	−11767.4	−	6793.90i	−0.476525	−	0.275122i
$849$	−31181.3	−	13421.0i	−1.26047	−	0.542529i
$850$	−2818.98	+	1627.54i	−0.113753	+	0.0656755i
$851$	42630.1	−	24612.5i	1.71720	−	0.991428i
$852$	−1388.94	−	597.825i	−0.0558502	−	0.0240389i
$853$	−15800.4	−	9122.36i	−0.634227	−	0.366171i	0.148161	−	0.988963i	$-0.452665\pi$
$853$	−15800.4	−	9122.36i	−0.634227	−	0.366171i	−0.782387	+	0.622792i	$0.785998\pi$
$854$	11557.0	+	15856.9i	0.463081	+	0.635379i
$855$	−204.637	−	857.369i	−0.00818532	−	0.0342940i
$856$	20778.6			0.829671
$857$	−11224.4	+	19441.2i	−0.447396	+	0.774913i	−0.998216	−	0.0597116i	$-0.980982\pi$
$857$	−11224.4	+	19441.2i	−0.447396	+	0.774913i	0.550820	+	0.834624i	$0.314315\pi$
$858$	−5086.13	−	43217.3i	−0.202375	−	1.71960i
$859$	4483.49	−	2588.54i	0.178084	−	0.102817i	−0.408308	−	0.912844i	$-0.633881\pi$
$859$	4483.49	−	2588.54i	0.178084	−	0.102817i	0.586392	+	0.810027i	$0.300548\pi$
$860$	17.0123	+	29.4661i	0.000674551	+	0.00116836i
$861$	−3035.32	+	9804.14i	−0.120143	+	0.388065i
$862$	−14593.3	+	25276.4i	−0.576625	+	0.998744i
$863$			8172.68i			0.322365i	0.986925	+	0.161183i	$0.0515309\pi$
$863$			8172.68i			0.322365i	−0.986925	+	0.161183i	$0.948469\pi$
$864$	−3385.35	+	4054.05i	−0.133301	+	0.159632i
$865$	−982.639			−0.0386251
$866$	−13297.2	+	23031.4i	−0.521774	+	0.903738i
$867$	−14966.0	−	20069.5i	−0.586241	−	0.786156i
$868$	−161.301	−	71.5274i	−0.00630751	−	0.00279700i
$869$	19208.2	−	11089.9i	0.749821	−	0.432909i
$870$	−955.137	+	112.408i	−0.0372209	+	0.00438043i
$871$	1855.01	+	1070.99i	0.0721638	+	0.0416638i
$872$		−	3035.42i		−	0.117881i
$873$	−9686.44	+	9167.78i	−0.375529	+	0.355421i
$874$			28576.1i			1.10595i
$875$	2054.34	−	219.023i	0.0793709	−	0.00846210i
$876$	3683.23	+	1585.33i	0.142060	+	0.0611452i
$877$	−3903.08	−	6760.33i	−0.150282	−	0.260297i	0.781049	−	0.624470i	$-0.214685\pi$
$877$	−3903.08	−	6760.33i	−0.150282	−	0.260297i	−0.931331	+	0.364173i	$0.881352\pi$
$878$	4585.68	+	7942.62i	0.176263	+	0.305297i
$879$	17197.2	−	39954.8i	0.659896	−	1.53315i
$880$	866.559	+	500.308i	0.0331951	+	0.0191652i
$881$	13545.7			0.518009			0.259005	−	0.965876i	$-0.416606\pi$
$881$	13545.7			0.518009			0.259005	+	0.965876i	$0.416606\pi$
$882$	14006.4	−	20452.3i	0.534717	−	0.780801i
$883$	−22881.0			−0.872035			−0.436018	−	0.899938i	$-0.643611\pi$
$883$	−22881.0			−0.872035			−0.436018	+	0.899938i	$0.643611\pi$
$884$	−557.357	−	321.790i	−0.0212058	−	0.0122432i
$885$	−582.671	+	68.5731i	−0.0221314	+	0.00260459i
$886$	−2563.05	−	4439.34i	−0.0971867	−	0.168332i
$887$	13466.2	+	23324.2i	0.509754	+	0.882921i	0.999936	+	0.0113003i	$0.00359707\pi$
$887$	13466.2	+	23324.2i	0.509754	+	0.882921i	−0.490182	+	0.871620i	$0.663070\pi$
$888$	33205.8	−	24761.8i	1.25486	−	0.935756i
$889$	2783.77	−	296.791i	0.105022	−	0.0111969i
$890$			770.966i			0.0290369i
$891$	−13029.7	−	25740.2i	−0.489910	−	0.967822i
$892$		−	1112.88i		−	0.0417735i
$893$	35035.9	+	20228.0i	1.31292	+	0.758012i
$894$	16111.5	+	21605.7i	0.602740	+	0.808281i
$895$	212.801	−	122.861i	0.00794767	−	0.00458859i
$896$	19993.8	+	8866.07i	0.745477	+	0.330574i
$897$	−59580.3	+	7011.85i	−2.21776	+	0.261002i
$898$	4118.16	−	7132.86i	0.153034	−	0.265063i
$899$	−1765.85			−0.0655112
$900$	803.085	−	2698.06i	0.0297439	−	0.0999282i
$901$		−	2338.51i		−	0.0864673i
$902$	5648.61	−	9783.68i	0.208512	−	0.361154i
$903$	−8558.62	+	1944.11i	−0.315408	+	0.0716456i
$904$	−6328.51	−	10961.3i	−0.232835	−	0.403283i
$905$	−794.039	+	458.438i	−0.0291655	+	0.0168387i
$906$	−18482.9	−	7955.37i	−0.677764	−	0.291721i
$907$	−2467.59	+	4273.99i	−0.0903362	+	0.156467i	−0.907653	−	0.419722i	$-0.862127\pi$
$907$	−2467.59	+	4273.99i	−0.0903362	+	0.156467i	0.817316	+	0.576189i	$0.195461\pi$
$908$	−1314.11			−0.0480290
$909$	26421.3	+	27916.1i	0.964070	+	1.01861i
$910$	−1030.83	−	1414.37i	−0.0375513	−	0.0515229i
$911$	−21835.9	−	12607.0i	−0.794134	−	0.458493i	0.0472820	−	0.998882i	$-0.484944\pi$
$911$	−21835.9	−	12607.0i	−0.794134	−	0.458493i	−0.841416	+	0.540388i	$0.818277\pi$
$912$	2513.81	+	21360.1i	0.0912726	+	0.775551i
$913$	−19289.2	+	11136.6i	−0.699210	+	0.403689i
$914$	28352.9	−	16369.6i	1.02607	−	0.592404i
$915$	736.283	−	549.051i	0.0266019	−	0.0198372i
$916$	−4934.26	−	2848.80i	−0.177983	−	0.102759i
$917$	−29364.7	−	40290.4i	−1.05748	−	1.45093i
$918$	3605.15	+	626.843i	0.129616	+	0.0225369i
$919$	−2976.03			−0.106823			−0.0534114	−	0.998573i	$-0.517009\pi$
$919$	−2976.03			−0.106823			−0.0534114	+	0.998573i	$0.517009\pi$
$920$	771.152	−	1335.67i	0.0276349	−	0.0478651i
$921$	−14960.3	+	11156.0i	−0.535245	+	0.399135i
$922$	11643.4	−	6722.31i	0.415894	−	0.240117i
$923$	−13769.6	−	23849.6i	−0.491042	−	0.850509i
$924$	2334.57	−	2161.66i	0.0831187	−	0.0769626i
$925$	−21033.5	+	36431.1i	−0.747652	+	1.29497i
$926$		−	14405.4i		−	0.511223i
$927$	−5981.87	−	25062.2i	−0.211942	−	0.887974i
$928$	−5829.25			−0.206201
$929$	−20451.6	+	35423.2i	−0.722276	+	1.25102i	0.237809	+	0.971312i	$0.423571\pi$
$929$	−20451.6	+	35423.2i	−0.722276	+	1.25102i	−0.960085	+	0.279707i	$0.909763\pi$
$930$	28.0036	−	65.0616i	0.000987393	−	0.00229403i
$931$	5286.65	+	24511.4i	0.186104	+	0.862867i
$932$	1146.82	−	662.117i	0.0403062	−	0.0232708i
$933$	−11089.9	+	25765.5i	−0.389140	+	0.904098i
$934$	−42073.0	−	24290.8i	−1.47395	−	0.850986i
$935$			172.210i			0.00602337i
$936$	−49102.4	+	11719.8i	−1.71470	+	0.409266i
$937$			5474.97i			0.190885i	0.995435	+	0.0954426i	$0.0304267\pi$
$937$			5474.97i			0.190885i	−0.995435	+	0.0954426i	$0.969573\pi$
$938$	−142.388	−	1335.54i	−0.00495644	−	0.0464892i
$939$	−1549.30	−	13164.5i	−0.0538440	−	0.457517i
$940$	−103.228	−	178.796i	−0.00358184	−	0.00620393i
$941$	22644.7	+	39221.7i	0.784479	+	1.35876i	0.929310	+	0.369301i	$0.120403\pi$
$941$	22644.7	+	39221.7i	0.784479	+	1.35876i	−0.144831	+	0.989456i	$0.546264\pi$
$942$	16431.3	+	22034.5i	0.568323	+	0.762128i
$943$	−13488.0	−	7787.29i	−0.465778	−	0.268917i
$944$	14315.3			0.493564
$945$	−964.459	−	645.115i	−0.0331999	−	0.0222070i
$946$	9660.86			0.332031
$947$	1734.42	+	1001.37i	0.0595153	+	0.0343612i	0.529462	−	0.848333i	$-0.322394\pi$
$947$	1734.42	+	1001.37i	0.0595153	+	0.0343612i	−0.469947	+	0.882695i	$0.655727\pi$
$948$	−1454.37	−	1950.33i	−0.0498268	−	0.0668183i
$949$	36514.5	+	63245.0i	1.24901	+	2.16335i
$950$	−12210.4	−	21149.0i	−0.417008	−	0.722279i
$951$	5433.61	+	46169.8i	0.185275	+	1.57430i
$952$	452.462	+	4243.90i	0.0154038	+	0.144481i
$953$		−	18814.3i		−	0.639513i	−0.947500	−	0.319756i	$-0.896399\pi$
$953$		−	18814.3i		−	0.639513i	0.947500	−	0.319756i	$-0.103601\pi$
$954$	−11922.1	−	12596.6i	−0.404606	−	0.427496i
$955$		−	133.095i		−	0.00450978i
$956$	−4766.93	−	2752.19i	−0.161269	−	0.0931088i
$957$	12588.5	−	29247.2i	0.425212	−	0.987907i
$958$	4592.67	−	2651.58i	0.154888	−	0.0894245i
$959$	−33495.1	−	14853.1i	−1.12786	−	0.500137i
$960$	507.972	−	1180.19i	0.0170779	−	0.0396774i
$961$	−14830.5	+	25687.1i	−0.497817	+	0.862245i
$962$	71329.3			2.39059
$963$	22736.5	+	6767.59i	0.760825	+	0.226462i
$964$			3262.23i			0.108993i
$965$	682.526	−	1182.17i	0.0227682	−	0.0394357i
$966$	25557.5	+	27601.8i	0.851240	+	0.919329i
$967$	−5039.39	−	8728.48i	−0.167586	−	0.290268i	0.769984	−	0.638063i	$-0.220264\pi$
$967$	−5039.39	−	8728.48i	−0.167586	−	0.290268i	−0.937571	+	0.347795i	$0.886931\pi$
$968$	−4816.67	+	2780.91i	−0.159932	+	0.0923365i
$969$	−2967.32	+	2212.75i	−0.0983735	+	0.0733577i
$970$	295.221	−	511.337i	0.00977212	−	0.0169258i
$971$	30488.8			1.00766			0.503828	−	0.863804i	$-0.331925\pi$
$971$	30488.8			1.00766			0.503828	+	0.863804i	$0.331925\pi$
$972$	−2637.04	+	1749.43i	−0.0870197	+	0.0577295i
$973$	18407.4	−	13415.8i	0.606488	−	0.442025i
$974$	−15582.0	−	8996.29i	−0.512609	−	0.295955i
$975$	41098.9	−	30647.7i	1.34997	−	1.00668i
$976$	−19408.1	+	11205.2i	−0.636513	+	0.367491i
$977$	−39269.5	+	22672.2i	−1.28592	+	0.742425i	−0.977924	−	0.208963i	$-0.932991\pi$
$977$	−39269.5	+	22672.2i	−1.28592	+	0.742425i	−0.307995	+	0.951388i	$0.599658\pi$
$978$	−1448.14	−	12304.9i	−0.0473479	−	0.402320i
$979$	−22105.7	−	12762.7i	−0.721655	−	0.416648i
$980$	39.1792	−	121.818i	0.00127707	−	0.00397076i
$981$	988.634	−	3321.44i	0.0321760	−	0.108099i
$982$	−7400.52			−0.240489
$983$	976.252	−	1690.92i	0.0316761	−	0.0548646i	−0.849753	−	0.527181i	$-0.823249\pi$
$983$	976.252	−	1690.92i	0.0316761	−	0.0548646i	0.881429	+	0.472317i	$0.156582\pi$
$984$	−12038.0	−	5181.36i	−0.389997	−	0.167861i
$985$	−1288.84	+	744.115i	−0.0416914	+	0.0240705i
$986$	2019.31	+	3497.55i	0.0652211	+	0.112966i
$987$	51932.5	−	11796.6i	1.67480	−	0.380435i
$988$	2414.18	−	4181.49i	0.0777383	−	0.134647i
$989$		−	13318.6i		−	0.428219i
$990$	877.956	+	927.626i	0.0281851	+	0.0297797i
$991$	−32006.2			−1.02594			−0.512972	−	0.858405i	$-0.671456\pi$
$991$	−32006.2			−1.02594			−0.512972	+	0.858405i	$0.671456\pi$
$992$	214.665	−	371.811i	0.00687059	−	0.0119002i
$993$	12748.8	−	1500.37i	0.407423	−	0.0479485i
$994$	−7000.02	+	15785.7i	−0.223367	+	0.503715i
$995$	−1483.35	+	856.410i	−0.0472615	+	0.0272865i
$996$	1460.50	+	1958.55i	0.0464636	+	0.0623083i
$997$	28451.4	+	16426.4i	0.903775	+	0.521795i	0.878423	−	0.477884i	$-0.158596\pi$
$997$	28451.4	+	16426.4i	0.903775	+	0.521795i	0.0253520	+	0.999679i	$0.491929\pi$
$998$		−	8178.42i		−	0.259402i
$999$	44399.6	−	16279.9i	1.40615	−	0.515589i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.o.a.20.8	yes	44
3.2	odd	2		189.4.o.a.62.15		44
7.6	odd	2	inner	63.4.o.a.20.7	✓	44
9.2	odd	6		567.4.c.c.566.21		44
9.4	even	3		189.4.o.a.125.16		44
9.5	odd	6	inner	63.4.o.a.41.7	yes	44
9.7	even	3		567.4.c.c.566.24		44
21.20	even	2		189.4.o.a.62.16		44
63.13	odd	6		189.4.o.a.125.15		44
63.20	even	6		567.4.c.c.566.23		44
63.34	odd	6		567.4.c.c.566.22		44
63.41	even	6	inner	63.4.o.a.41.8	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.o.a.20.7	✓	44	7.6	odd	2	inner
63.4.o.a.20.8	yes	44	1.1	even	1	trivial
63.4.o.a.41.7	yes	44	9.5	odd	6	inner
63.4.o.a.41.8	yes	44	63.41	even	6	inner
189.4.o.a.62.15		44	3.2	odd	2
189.4.o.a.62.16		44	21.20	even	2
189.4.o.a.125.15		44	63.13	odd	6
189.4.o.a.125.16		44	9.4	even	3
567.4.c.c.566.21		44	9.2	odd	6
567.4.c.c.566.22		44	63.34	odd	6
567.4.c.c.566.23		44	63.20	even	6
567.4.c.c.566.24		44	9.7	even	3

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.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.31807 - 1.33834i) q^{2} +(3.10623 + 4.16549i) q^{3} +(-0.417710 - 0.723496i) q^{4} +(0.223284 + 0.386739i) q^{5} +(-1.62562 - 13.8131i) q^{6} +(18.4159 - 1.96340i) q^{7} +23.6495i q^{8} +(-7.70264 + 25.8780i) q^{9} +O(q^{10})\)	\(q+(-2.31807 - 1.33834i) q^{2} +(3.10623 + 4.16549i) q^{3} +(-0.417710 - 0.723496i) q^{4} +(0.223284 + 0.386739i) q^{5} +(-1.62562 - 13.8131i) q^{6} +(18.4159 - 1.96340i) q^{7} +23.6495i q^{8} +(-7.70264 + 25.8780i) q^{9} -1.19532i q^{10} +(34.2729 + 19.7875i) q^{11} +(1.71621 - 3.98731i) q^{12} +(68.4665 - 39.5291i) q^{13} +(-45.3170 - 20.0954i) q^{14} +(-0.917386 + 2.13139i) q^{15} +(28.3094 - 49.0332i) q^{16} +9.74428 q^{17} +(52.4887 - 49.6781i) q^{18} +73.1051i q^{19} +(0.186536 - 0.323090i) q^{20} +(65.3826 + 70.6125i) q^{21} +(-52.9646 - 91.7374i) q^{22} +(-126.471 + 73.0180i) q^{23} +(-98.5119 + 73.4609i) q^{24} +(62.4003 - 108.080i) q^{25} -211.613 q^{26} +(-131.721 + 48.2977i) q^{27} +(-9.11302 - 12.5037i) q^{28} +(-134.097 - 77.4209i) q^{29} +(4.97908 - 3.71293i) q^{30} +(9.87637 - 5.70213i) q^{31} +(32.6028 - 18.8232i) q^{32} +(24.0351 + 204.228i) q^{33} +(-22.5879 - 13.0411i) q^{34} +(4.87129 + 6.68374i) q^{35} +(21.9401 - 5.23667i) q^{36} -337.074 q^{37} +(97.8393 - 169.463i) q^{38} +(377.331 + 162.410i) q^{39} +(-9.14619 + 5.28056i) q^{40} +(53.3244 + 92.3606i) q^{41} +(-57.0580 - 251.188i) q^{42} +(-45.6005 + 78.9824i) q^{43} -33.0617i q^{44} +(-11.7279 + 2.79922i) q^{45} +390.891 q^{46} +(276.698 - 479.254i) q^{47} +(292.183 - 34.3862i) q^{48} +(335.290 - 72.3157i) q^{49} +(-289.296 + 167.025i) q^{50} +(30.2680 + 40.5897i) q^{51} +(-57.1983 - 33.0235i) q^{52} -239.988i q^{53} +(369.976 + 64.3293i) q^{54} +17.6729i q^{55} +(46.4336 + 435.527i) q^{56} +(-304.519 + 227.082i) q^{57} +(207.230 + 358.934i) q^{58} +(126.419 + 218.964i) q^{59} +(1.92525 - 0.226578i) q^{60} +(-342.785 - 197.907i) q^{61} -30.5255 q^{62} +(-91.0421 + 491.689i) q^{63} -553.717 q^{64} +(30.5749 + 17.6524i) q^{65} +(217.611 - 505.581i) q^{66} +(13.5469 + 23.4639i) q^{67} +(-4.07029 - 7.04994i) q^{68} +(-697.004 - 300.003i) q^{69} +(-2.34689 - 22.0128i) q^{70} -348.340i q^{71} +(-612.002 - 182.164i) q^{72} +923.737i q^{73} +(781.360 + 451.119i) q^{74} +(644.038 - 75.7951i) q^{75} +(52.8912 - 30.5368i) q^{76} +(670.017 + 297.112i) q^{77} +(-657.320 - 881.473i) q^{78} +(280.225 - 485.363i) q^{79} +25.2841 q^{80} +(-610.339 - 398.658i) q^{81} -285.464i q^{82} +(-281.406 + 487.409i) q^{83} +(23.7768 - 76.7996i) q^{84} +(2.17574 + 3.76849i) q^{85} +(211.410 - 122.058i) q^{86} +(-94.0401 - 799.067i) q^{87} +(-467.965 + 810.538i) q^{88} -644.990 q^{89} +(30.9323 + 9.20709i) q^{90} +(1183.26 - 862.392i) q^{91} +(105.656 + 61.0008i) q^{92} +(54.4305 + 23.4278i) q^{93} +(-1282.81 + 740.629i) q^{94} +(-28.2726 + 16.3232i) q^{95} +(179.680 + 77.3374i) q^{96} +(427.784 + 246.981i) q^{97} +(-874.008 - 281.098i) q^{98} +(-776.052 + 734.497i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 6 q^{2} + 78 q^{4} + 5 q^{7}+O(q^{10}) \) 44 * q - 6 * q^2 + 78 * q^4 + 5 * q^7	\( 44 q - 6 q^{2} + 78 q^{4} + 5 q^{7} - 18 q^{11} + 204 q^{14} + 66 q^{15} - 242 q^{16} - 210 q^{18} - 57 q^{21} - 34 q^{22} - 102 q^{23} - 352 q^{25} + 300 q^{28} + 246 q^{29} - 144 q^{30} + 1068 q^{32} - 1818 q^{36} + 328 q^{37} - 798 q^{39} - 1158 q^{42} - 170 q^{43} + 968 q^{46} - 79 q^{49} + 288 q^{50} - 204 q^{51} + 1212 q^{56} + 324 q^{57} - 538 q^{58} + 5316 q^{60} + 783 q^{63} - 808 q^{64} + 4350 q^{65} - 590 q^{67} + 384 q^{70} + 4284 q^{72} - 5304 q^{74} - 2787 q^{77} + 612 q^{78} - 302 q^{79} - 3720 q^{81} + 7050 q^{84} - 612 q^{85} - 13692 q^{86} + 1294 q^{88} + 210 q^{91} - 10194 q^{92} - 4266 q^{93} + 6336 q^{95} + 1014 q^{99}+O(q^{100}) \) 44 * q - 6 * q^2 + 78 * q^4 + 5 * q^7 - 18 * q^11 + 204 * q^14 + 66 * q^15 - 242 * q^16 - 210 * q^18 - 57 * q^21 - 34 * q^22 - 102 * q^23 - 352 * q^25 + 300 * q^28 + 246 * q^29 - 144 * q^30 + 1068 * q^32 - 1818 * q^36 + 328 * q^37 - 798 * q^39 - 1158 * q^42 - 170 * q^43 + 968 * q^46 - 79 * q^49 + 288 * q^50 - 204 * q^51 + 1212 * q^56 + 324 * q^57 - 538 * q^58 + 5316 * q^60 + 783 * q^63 - 808 * q^64 + 4350 * q^65 - 590 * q^67 + 384 * q^70 + 4284 * q^72 - 5304 * q^74 - 2787 * q^77 + 612 * q^78 - 302 * q^79 - 3720 * q^81 + 7050 * q^84 - 612 * q^85 - 13692 * q^86 + 1294 * q^88 + 210 * q^91 - 10194 * q^92 - 4266 * q^93 + 6336 * q^95 + 1014 * q^99

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