LMFDB - Embedded newform 63.4.o.a.20.7

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			20.7
Character	$\chi$	$=$	63.20
Dual form			63.4.o.a.41.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.31807 - 1.33834i) q^{2} +(-3.10623 - 4.16549i) q^{3} +(-0.417710 - 0.723496i) q^{4} +(-0.223284 - 0.386739i) q^{5} +(1.62562 + 13.8131i) q^{6} +(-7.50759 - 16.9303i) q^{7} +23.6495i q^{8} +(-7.70264 + 25.8780i) q^{9} +O(q^{10})$	\(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} +(-7.50759 - 16.9303i) 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} +(-5.25539 + 49.2933i) 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} +(-47.2029 + 83.8623i) 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} +(221.655 - 131.225i) 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} +(-230.272 + 254.212i) 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} +(400.394 - 177.551i) 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} +(495.951 - 63.8728i) 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} +(20.2371 - 8.97393i) 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} +(77.7016 - 728.808i) 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} +(80.3911 - 0.879112i) 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	0.855867	−	0.517196i	$-0.173024\pi$
$5$	−0.223284	−	0.386739i	−0.0199711	−	0.0345910i	−0.875838	+	0.482605i	$0.839691\pi$
$6$	1.62562	+	13.8131i	0.110610	+	0.939861i
$7$	−7.50759	−	16.9303i	−0.405372	−	0.914152i
$7$	−7.50759	−	16.9303i	−0.405372	−	0.914152i
$8$			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	−0.999044	−	0.0437164i	$-0.986080\pi$
$13$	−68.4665	+	39.5291i	−1.46071	+	0.843339i	−0.461662	+	0.887056i	$0.652747\pi$
$14$	−5.25539	+	49.2933i	−0.100326	+	0.941014i
$15$	−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	$-0.522144\pi$
$17$	−9.74428			−0.139020			−0.0695099	+	0.997581i	$0.522144\pi$
$18$	52.4887	−	49.6781i	0.687317	−	0.650514i
$19$		−	73.1051i		−	0.882709i	−0.897333	−	0.441354i	$-0.854498\pi$
$19$		−	73.1051i		−	0.882709i	0.897333	−	0.441354i	$-0.145502\pi$
$20$	−0.186536	+	0.323090i	−0.00208553	+	0.00361225i
$21$	−47.2029	+	83.8623i	−0.490500	+	0.871441i
$22$	−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	−0.528338	−	0.849034i	$-0.677184\pi$
$31$	−9.87637	+	5.70213i	−0.0572209	+	0.0330365i	0.471117	+	0.882071i	$0.343851\pi$
$32$	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	0.746413	−	0.665483i	$-0.231774\pi$
$41$	−53.3244	−	92.3606i	−0.203119	−	0.351812i	−0.949532	+	0.313671i	$0.898441\pi$
$42$	221.655	−	131.225i	0.814337	−	0.482107i
$43$	−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	$0.495415\pi$
$47$	−276.698	+	479.254i	−0.858734	+	1.48737i	−0.873137	+	0.487474i	$0.837918\pi$
$48$	−292.183	+	34.3862i	−0.878604	+	0.103401i
$49$	−230.272	+	254.212i	−0.671348	+	0.741142i
$50$	−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
$56$	400.394	−	177.551i	0.955446	−	0.423683i
$57$	−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	0.692171	−	0.721734i	$-0.256655\pi$
$59$	−126.419	−	218.964i	−0.278955	−	0.483164i	−0.971125	+	0.238570i	$0.923321\pi$
$60$	1.92525	−	0.226578i	0.00414248	−	0.000487518i
$61$	342.785	+	197.907i	0.719494	+	0.415400i	0.814566	−	0.580070i	$-0.196975\pi$
$61$	342.785	+	197.907i	0.719494	+	0.415400i	−0.0950723	+	0.995470i	$0.530308\pi$
$62$	30.5255			0.0625280
$63$	495.951	−	63.8728i	0.991809	−	0.127734i
$64$	−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
$70$	20.2371	−	8.97393i	0.0345542	−	0.0153227i
$71$		−	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	$-0.734582\pi$
$73$		−	923.737i		−	1.48103i	0.672040	−	0.740515i	$-0.265418\pi$
$74$	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
$77$	77.7016	−	728.808i	0.114999	−	1.07864i
$78$	−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	−0.617748	−	0.786376i	$-0.711955\pi$
$83$	281.406	−	487.409i	0.372148	−	0.644580i	0.989896	+	0.141797i	$0.0452880\pi$
$84$	80.3911	−	0.879112i	0.104421	−	0.00114189i
$85$	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	$-0.374514\pi$
$89$	644.990			0.768188			0.384094	+	0.923294i	$0.374514\pi$
$90$	−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	0.259111	−	0.965848i	$-0.416571\pi$
$97$	−427.784	−	246.981i	−0.447783	−	0.258527i	−0.706893	+	0.707320i	$0.749904\pi$
$98$	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	$0.414041\pi$
$101$	−711.795	+	1232.86i	−0.701250	+	1.21460i	−0.968028	+	0.250842i	$0.919293\pi$
$102$	−15.8405	−	134.598i	−0.0153769	−	0.130659i
$103$	826.452	−	477.152i	0.790609	−	0.456458i	−0.0495678	−	0.998771i	$-0.515784\pi$
$103$	826.452	−	477.152i	0.790609	−	0.456458i	0.840177	+	0.542312i	$0.182451\pi$
$104$	−934.846	−	1619.20i	−0.881434	−	1.52669i
$105$	42.9724	−	0.469923i	0.0399398	−	0.000436760i
$106$	−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
$112$	−1042.68	−	111.165i	−0.879682	−	0.0937870i
$113$	−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
$119$	73.1560	+	164.974i	0.0563546	+	0.127085i
$120$	−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
$126$	−1235.13	−	515.688i	−0.873287	−	0.364612i
$127$	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	$0.188098\pi$
$131$	1345.98	+	2331.31i	0.897702	+	1.55487i	0.0672769	+	0.997734i	$0.478569\pi$
$132$	−137.718	+	102.697i	−0.0908094	+	0.0677171i
$133$	−1237.69	+	548.843i	−0.806930	+	0.357825i
$134$		−	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	−0.788430	−	0.615125i	$-0.789106\pi$
$139$	−1065.10	+	614.935i	−0.649931	+	0.375238i	0.138499	+	0.990363i	$0.455772\pi$
$140$	6.87045	+	0.732491i	0.00414756	+	0.000442191i
$141$	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
$147$	1774.20	+	169.556i	0.995464	+	0.0951344i
$148$	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	0.00265752	−	0.999996i	$-0.499154\pi$
$157$	1711.48	−	988.126i	0.870009	−	0.502300i	0.867351	+	0.497697i	$0.165821\pi$
$158$	−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	0.968181	−	0.250252i	$-0.0805135\pi$
$167$	577.006	+	999.403i	0.267366	+	0.463091i	−0.700815	+	0.713343i	$0.747180\pi$
$168$	−1983.31	−	1116.33i	−0.910805	−	0.512657i
$169$	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	−0.516308	−	0.856403i	$-0.672694\pi$
$173$	1100.21	−	1905.62i	0.483512	−	0.837468i	0.999821	+	0.0189348i	$0.00602750\pi$
$174$	851.429	−	1978.15i	0.370958	−	0.861856i
$175$	−2298.31	−	245.034i	−0.992778	−	0.105845i
$176$	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	$-0.861477\pi$
$181$		−	2053.17i		−	0.843152i	0.906793	−	0.421576i	$-0.138523\pi$
$182$	−1588.70	−	3582.68i	−0.647047	−	1.45915i
$183$	−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
$189$	−1806.60	−	1867.48i	−0.695295	−	0.718724i
$190$	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
$196$	280.108	+	60.4140i	0.102080	+	0.0220168i
$197$			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	$-0.760610\pi$
$199$		−	3835.52i		−	1.36630i	0.730280	−	0.683148i	$-0.239390\pi$
$200$	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
$203$	−304.017	+	2851.55i	−0.105112	+	0.985909i
$204$	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
$210$	−100.242	−	56.4223i	−0.0329398	−	0.0185405i
$211$	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	0.316681	−	0.948532i	$-0.397431\pi$
$223$	−1153.65	−	666.060i	−0.346431	−	0.200012i	−0.663112	+	0.748520i	$0.730765\pi$
$224$	−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	−0.957797	−	0.287446i	$-0.907194\pi$
$227$	−786.498	+	1362.25i	−0.229963	+	0.398308i	0.727834	+	0.685754i	$0.240527\pi$
$228$	291.493	+	125.464i	0.0846693	+	0.0364431i
$229$	−5906.31	+	3410.01i	−1.70437	+	0.984017i	−0.763148	+	0.646224i	$0.776347\pi$
$229$	−5906.31	+	3410.01i	−1.70437	+	0.984017i	−0.941220	+	0.337793i	$0.890320\pi$
$230$	−87.2796	−	151.173i	−0.0250219	−	0.0433393i
$231$	−3277.20	+	1940.18i	−0.933438	+	0.552617i
$232$	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
$238$	51.2100	−	480.328i	0.0139473	−	0.130819i
$239$	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	0.878459	−	0.477817i	$-0.158572\pi$
$241$	3381.74	+	1952.45i	0.903887	+	0.521859i	0.0254276	+	0.999677i	$0.491905\pi$
$242$		−	629.491i		−	0.167212i
$243$	235.249	+	3780.68i	0.0621037	+	0.998070i
$244$		−	330.671i		−	0.0867585i
$245$	149.730	+	32.2938i	0.0390444	+	0.00842113i
$246$	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	$-0.727226\pi$
$251$	−5207.34			−1.30950			−0.654750	+	0.755846i	$0.727226\pi$
$252$	−253.376	−	332.138i	−0.0633379	−	0.0830267i
$253$	−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	$-0.878746\pi$
$257$	−3238.89	−	5609.93i	−0.786135	−	1.36163i	0.142184	−	0.989840i	$-0.454587\pi$
$258$	−1165.12	−	501.488i	−0.281152	−	0.121013i
$259$	2530.61	+	5706.78i	0.607122	+	1.36912i
$260$		−	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
$266$	3603.59	+	384.196i	0.830641	+	0.0885586i
$267$	−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	$-0.665397\pi$
$269$	−4381.41			−0.993084			−0.496542	+	0.868013i	$0.665397\pi$
$270$	57.7310	+	157.448i	0.0130126	+	0.0354888i
$271$			2485.08i			0.557040i	0.960430	+	0.278520i	$0.0898438\pi$
$271$			2485.08i			0.557040i	−0.960430	+	0.278520i	$0.910156\pi$
$272$	−275.854	+	477.794i	−0.0614931	+	0.106509i
$273$	−83.1930	−	7607.65i	−0.0184435	−	1.68658i
$274$	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	0.230473	−	0.973079i	$-0.425973\pi$
$283$	5657.83	−	3266.55i	1.18842	−	0.686135i	0.957948	+	0.286944i	$0.0926392\pi$
$284$	−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	$0.147617\pi$
$293$	4185.66	+	7249.78i	0.834569	+	1.44552i	−0.0598110	+	0.998210i	$0.519050\pi$
$294$	−3885.78	−	2767.51i	−0.770828	−	0.548996i
$295$	−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
$301$	1679.55	+	179.065i	0.321620	+	0.0342894i
$302$	−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	$-0.891656\pi$
$307$		−	3591.50i		−	0.667679i	0.942630	−	0.333840i	$-0.108344\pi$
$308$	−559.746	+	248.214i	−0.103554	+	0.0459198i
$309$	−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	0.507815	−	0.861466i	$-0.330453\pi$
$311$	−2699.19	−	4675.13i	−0.492144	−	0.852419i	−0.999959	+	0.00904760i	$0.997120\pi$
$312$	−3840.92	+	8923.70i	−0.696952	+	1.61925i
$313$	2209.23	+	1275.50i	0.398956	+	0.230337i	0.686033	−	0.727570i	$-0.259350\pi$
$313$	2209.23	+	1275.50i	0.398956	+	0.230337i	−0.287077	+	0.957907i	$0.592684\pi$
$314$	−5289.78			−0.950700
$315$	−135.440	−	177.542i	−0.0242259	−	0.0317566i
$316$	−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
$322$	−2934.65	−	6617.91i	−0.507893	−	1.14535i
$323$			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
$329$	10191.3	+	1086.54i	1.70779	+	0.182075i
$330$	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
$336$	2775.76	+	4688.60i	0.450685	+	0.761262i
$337$	−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	0.0470151	−	0.998894i	$-0.485029\pi$
$349$	−5180.32	−	2990.86i	−0.794545	−	0.458731i	−0.841560	+	0.540163i	$0.818362\pi$
$350$	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	−0.714588	−	0.699545i	$-0.753386\pi$
$353$	1648.31	−	2854.96i	0.248530	−	0.430466i	0.963118	+	0.269079i	$0.0867194\pi$
$354$	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
$357$	459.958	−	817.178i	0.0681892	−	0.121147i
$358$	−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
$364$	129.677	−	1216.31i	0.0186728	−	0.175143i
$365$	−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	0.491816	−	0.870699i	$-0.336333\pi$
$367$	−114.764	−	66.2588i	−0.0163232	−	0.00942421i	−0.508139	+	0.861275i	$0.669667\pi$
$368$			8268.37i			1.17125i
$369$	2800.84	−	668.507i	0.395138	−	0.0943118i
$370$		−	402.910i		−	0.0566116i
$371$	−4063.07	+	1801.73i	−0.568583	+	0.252132i
$372$	−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
$378$	1688.51	+	6746.77i	0.229755	+	0.918033i
$379$	−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	0.938537	−	0.345178i	$-0.112181\pi$
$383$	1276.74	+	2211.38i	0.170336	+	0.295030i	−0.768202	+	0.640208i	$0.778848\pi$
$384$	−717.225	−	6094.32i	−0.0953144	−	0.809895i
$385$	−299.208	+	132.681i	−0.0396079	+	0.0175637i
$386$			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
$392$	−6011.99	−	5445.83i	−0.774621	−	0.701674i
$393$	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	$0.119081\pi$
$397$			5781.38i			0.730880i	−0.930835	+	0.365440i	$0.880919\pi$
$398$	−5133.22	+	8891.00i	−0.646495	+	1.11976i
$399$	6130.77	+	3450.77i	0.769229	+	0.432969i
$400$	−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	−0.834307	−	0.551300i	$-0.814132\pi$
$409$	−6402.33	+	3696.39i	−0.774021	+	0.446882i	0.0602858	+	0.998181i	$0.480799\pi$
$410$	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	0.620997	−	0.783813i	$-0.286728\pi$
$419$	−3158.84	−	5471.26i	−0.368304	−	0.637921i	−0.989300	+	0.145892i	$0.953395\pi$
$420$	−18.2900	−	30.8941i	−0.00212491	−	0.00358923i
$421$	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
$427$	777.144	−	7289.27i	0.0880764	−	0.826118i
$428$	−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	$0.185889\pi$
$433$			9935.59i			1.10271i	−0.834270	+	0.551355i	$0.814111\pi$
$434$	−229.172	−	516.806i	−0.0253471	−	0.0571601i
$435$	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	0.652553	−	0.757743i	$-0.273698\pi$
$439$	2967.35	+	1713.20i	0.322606	+	0.186256i	−0.329948	+	0.943999i	$0.607031\pi$
$440$	417.956			0.0452847
$441$	−4804.78	−	7917.08i	−0.518819	−	0.854884i
$442$	−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
$448$	4157.08	+	9374.61i	0.438401	+	0.988636i
$449$			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
$455$	69.3177	−	650.170i	0.00714212	−	0.0669900i
$456$	−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	−0.710820	−	0.703374i	$-0.751676\pi$
$461$	2511.44	−	4349.95i	0.253730	−	0.439473i	0.964550	+	0.263901i	$0.0850092\pi$
$462$	10193.4	−	111.469i	1.02649	−	0.0112251i
$463$	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	$-0.855874\pi$
$467$	−18150.0			−1.79846			−0.899232	+	0.437471i	$0.855874\pi$
$468$	−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	−0.814903	−	0.579597i	$-0.803210\pi$
$479$	990.626	−	1715.81i	0.0944945	−	0.163669i	0.909398	+	0.415928i	$0.136543\pi$
$480$	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
$483$	−153.674	−	14052.8i	−0.0144770	−	1.32386i
$484$	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
$490$	−303.863	−	275.248i	−0.0280146	−	0.0253764i
$491$	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
$497$	−5897.52	+	2615.20i	−0.532273	+	0.236031i
$498$	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	$-0.256010\pi$
$503$	15649.8			1.38726			0.693630	+	0.720331i	$0.256010\pi$
$504$	1510.56	+	11729.0i	0.133504	+	1.03661i
$505$	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	$-0.997401\pi$
$509$	−5822.79	−	10085.4i	−0.507054	−	0.878243i	0.492913	−	0.870079i	$-0.335932\pi$
$510$	−48.5175	+	36.1798i	−0.00421253	+	0.00314131i
$511$	−15639.2	+	6935.03i	−1.35389	+	0.600368i
$512$		−	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
$518$	1771.46	−	16615.5i	0.150257	−	1.40935i
$519$	−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	$-0.446751\pi$
$521$	3960.23			0.333015			0.166508	+	0.986040i	$0.446751\pi$
$522$	−10884.7	+	2597.97i	−0.912663	+	0.217835i
$523$		−	19478.4i		−	1.62855i	−0.580481	−	0.814274i	$-0.697135\pi$
$523$		−	19478.4i		−	1.62855i	0.580481	−	0.814274i	$-0.302865\pi$
$524$	1124.46	−	1947.62i	0.0937448	−	0.162371i
$525$	6118.41	+	10334.7i	0.508627	+	0.859133i
$526$	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
$546$	−9988.74	+	17746.4i	−0.782928	+	1.39098i
$547$	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
$553$	−10321.2	−	1100.39i	−0.793672	−	0.0846172i
$554$	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
$560$	189.822	+	428.068i	0.0143240	+	0.0323021i
$561$	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	0.771216	−	0.636574i	$-0.219649\pi$
$563$	−2213.27	−	3833.50i	−0.165681	−	0.286968i	−0.936897	+	0.349606i	$0.886316\pi$
$564$	−1436.07	−	1925.78i	−0.107215	−	0.143777i
$565$	206.979	+	119.500i	0.0154118	+	0.00889802i
$566$	−17487.0			−1.29864
$567$	−2167.23	+	13326.2i	−0.160521	+	0.987032i
$568$	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
$574$	4833.00	−	2143.15i	0.351438	−	0.155842i
$575$			18225.4i			1.32183i
$576$	4265.08	−	14329.1i	0.308528	−	1.03654i
$577$			6646.62i			0.479553i	0.970828	+	0.239777i	$0.0770742\pi$
$577$			6646.62i			0.479553i	−0.970828	+	0.239777i	$0.922926\pi$
$578$	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
$581$	−10364.7	−	1105.03i	−0.740102	−	0.0789058i
$582$	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	−0.868042	−	0.496492i	$-0.834621\pi$
$587$	−57.5485	+	99.6770i	−0.00404648	+	0.00700870i	0.863995	+	0.503500i	$0.167955\pi$
$588$	−618.427	−	1354.45i	−0.0433733	−	0.0949941i
$589$	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	$-0.338956\pi$
$593$	13996.5			0.969251			0.484625	+	0.874722i	$0.338956\pi$
$594$	−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	0.470707	−	0.882290i	$-0.343999\pi$
$601$	−854.920	−	493.588i	−0.0580248	−	0.0335006i	−0.528732	+	0.848789i	$0.677332\pi$
$602$	−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	$-0.262130\pi$
$607$	24746.4	−	14287.4i	1.65474	−	0.955364i	0.975085	−	0.221832i	$-0.0712035\pi$
$608$	−1376.08	−	2383.43i	−0.0917882	−	0.158982i
$609$	12822.5	−	7591.20i	0.853189	−	0.505108i
$610$	−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
$616$	17236.0	+	1837.61i	1.12737	+	0.120194i
$617$	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	0.745612	−	0.666380i	$-0.232157\pi$
$619$	8336.56	+	4813.12i	0.541316	+	0.312529i	−0.204296	+	0.978909i	$0.565490\pi$
$620$		−	4.25460i		−	0.000275595i
$621$	−13132.2	+	15726.2i	−0.848597	+	1.01622i
$622$			14449.7i			0.931478i
$623$	−4842.32	−	10919.9i	−0.311402	−	0.702241i
$624$	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
$630$	76.3481	+	592.818i	0.00482823	+	0.0374896i
$631$	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
$637$	5717.15	−	26507.5i	0.355607	−	1.64877i
$638$			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	−0.729642	−	0.683829i	$-0.760313\pi$
$643$	−8189.11	+	4727.98i	−0.502250	+	0.289974i	0.227392	+	0.973803i	$0.426980\pi$
$644$	239.539	−	2246.77i	0.0146570	−	0.137477i
$645$	−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	$-0.473672\pi$
$647$	2719.32			0.165235			0.0826177	+	0.996581i	$0.473672\pi$
$648$	9428.06	−	14434.2i	0.571558	−	0.875046i
$649$		−	10006.0i		−	0.605194i
$650$	13204.7	−	22871.3i	0.796818	−	1.38013i
$651$	−12.0007	−	1097.41i	−0.000722494	−	0.0660691i
$652$	−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	−0.502854	−	0.864371i	$-0.667717\pi$
$661$	−97.0927	+	56.0565i	−0.00571326	+	0.00329855i	0.497141	+	0.867670i	$0.334383\pi$
$662$	−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
$672$	39.6154	+	3622.66i	0.00227410	+	0.207957i
$673$	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	$0.406710\pi$
$677$	−12060.1	+	20888.6i	−0.684647	+	1.18584i	−0.973548	+	0.228484i	$0.926623\pi$
$678$	−4449.78	−	5967.20i	−0.252054	−	0.338007i
$679$	−969.849	+	9096.76i	−0.0548150	+	0.514141i
$680$	−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
$686$	−11320.8	−	12686.9i	−0.630072	−	0.706103i
$687$	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	0.799112	−	0.601182i	$-0.205303\pi$
$691$	12315.9	+	7110.57i	0.678029	+	0.391460i	−0.121083	+	0.992642i	$0.538637\pi$
$692$	−1838.28			−0.100984
$693$	18261.6	+	7624.51i	1.00101	+	0.417938i
$694$	−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
$700$	782.748	+	1765.17i	0.0422644	+	0.0953104i
$701$		−	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
$707$	26216.7	+	2795.08i	1.39460	+	0.148684i
$708$	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
$714$	−2159.87	+	1278.70i	−0.113209	+	0.0670224i
$715$	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	$-0.738829\pi$
$719$	−26291.7			−1.36372			−0.681860	+	0.731482i	$0.738829\pi$
$720$	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	−0.493830	−	0.869559i	$-0.664403\pi$
$727$	−29281.6	−	16905.8i	−1.49380	−	0.862448i	−0.999975	+	0.00711022i	$0.997737\pi$
$728$	−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	−0.723219	−	0.690619i	$-0.757338\pi$
$733$	−9659.36	+	5576.83i	−0.486735	+	0.281016i	0.236484	+	0.971635i	$0.424005\pi$
$734$	177.353	+	307.185i	0.00891857	+	0.0154474i
$735$	−330.575	−	724.010i	−0.0165897	−	0.0363340i
$736$	−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
$742$	11829.8	+	1261.23i	0.585290	+	0.0624006i
$743$	−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
$749$	−14875.1	+	6596.21i	−0.725666	+	0.321789i
$750$	−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
$756$	−596.475	+	2087.13i	−0.0286952	+	0.100408i
$757$	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	$-0.983924\pi$
$761$	−11401.0	−	19747.0i	−0.543081	−	0.940644i	0.455644	−	0.890162i	$-0.349409\pi$
$762$	245.731	+	2088.00i	0.0116823	+	0.0992655i
$763$	963.598	+	2173.01i	0.0457203	+	0.103104i
$764$			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	−0.470161	−	0.882581i	$-0.655804\pi$
$769$	1260.21	−	727.581i	0.0590952	−	0.0341187i	0.529257	+	0.848462i	$0.322471\pi$
$770$	871.155	+	92.8780i	0.0407718	+	0.00434687i
$771$	−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	$-0.497913\pi$
$773$	281.797			0.0131120			0.00655598	+	0.999979i	$0.497913\pi$
$774$	1530.19	+	6411.03i	0.0710614	+	0.297726i
$775$			1423.26i			0.0659676i
$776$	5840.99	−	10116.9i	0.270205	−	0.468010i
$777$	15910.9	−	28267.8i	0.734619	−	1.30515i
$778$	−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	−0.572566	−	0.819858i	$-0.694052\pi$
$787$	−3285.92	+	1897.13i	−0.148832	+	0.0859280i	0.423735	+	0.905786i	$0.360719\pi$
$788$	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	0.866083	−	0.499900i	$-0.166630\pi$
$797$	2.60409	+	4.51042i	0.000115736	+	0.000200461i	−0.865968	+	0.500100i	$0.833296\pi$
$798$	−9593.24	−	16204.1i	−0.425560	−	0.718823i
$799$	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
$805$	128.043	−	1200.99i	0.00560613	−	0.0525831i
$806$	−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	$0.104785\pi$
$811$			14932.6i			0.646554i	−0.946304	+	0.323277i	$0.895215\pi$
$812$	2190.07	−	971.167i	0.0946509	−	0.0419720i
$813$	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
$819$	−31431.2	+	23977.7i	−1.34102	+	1.02301i
$820$	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
$826$	11457.8	−	5080.86i	0.482650	−	0.214026i
$827$			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	$-0.908376\pi$
$829$		−	13552.1i		−	0.567771i	0.958858	−	0.283886i	$-0.0916236\pi$
$830$	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
$833$	2243.84	−	2477.11i	0.0933306	−	0.103033i
$834$	−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	$0.501368\pi$
$839$	−21098.2	+	36543.2i	−0.868166	+	1.50371i	−0.863869	+	0.503717i	$0.831965\pi$
$840$	11.1135	+	1016.28i	0.000456489	+	0.0417440i
$841$	−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	0.782387	−	0.622792i	$-0.214002\pi$
$853$	15800.4	+	9122.36i	0.634227	+	0.366171i	−0.148161	+	0.988963i	$0.547335\pi$
$854$	−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	−0.550820	−	0.834624i	$-0.685685\pi$
$857$	11224.4	−	19441.2i	0.447396	−	0.774913i	0.998216	+	0.0597116i	$0.0190181\pi$
$858$	−5086.13	−	43217.3i	−0.202375	−	1.71960i
$859$	−4483.49	+	2588.54i	−0.178084	+	0.102817i	−0.586392	−	0.810027i	$-0.699452\pi$
$859$	−4483.49	+	2588.54i	−0.178084	+	0.102817i	0.408308	+	0.912844i	$0.366119\pi$
$860$	−17.0123	−	29.4661i	−0.000674551	−	0.00116836i
$861$	10262.6	−	112.226i	0.406213	−	0.00444212i
$862$	−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
$868$	18.7060	−	175.455i	0.000731480	−	0.00686096i
$869$	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
$875$	837.493	+	1888.63i	0.0323570	+	0.0729683i
$876$	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	$-0.583394\pi$
$881$	−13545.7			−0.518009			−0.259005	+	0.965876i	$0.583394\pi$
$882$	542.085	+	24782.7i	0.0206950	+	0.946121i
$883$	−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	$-0.996403\pi$
$887$	−13466.2	−	23324.2i	−0.509754	−	0.882921i	0.490182	−	0.871620i	$-0.336930\pi$
$888$	−33205.8	+	24761.8i	−1.25486	+	0.935756i
$889$	−1134.86	−	2559.21i	−0.0428142	−	0.0965503i
$890$			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
$896$	2318.68	−	21748.2i	0.0864527	−	0.810889i
$897$	−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
$903$	−4471.18	−	7552.36i	−0.164775	−	0.278324i
$904$	−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
$924$	2772.63	+	1560.61i	0.0987153	+	0.0555630i
$925$	−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	$-0.576429\pi$
$929$	20451.6	−	35423.2i	0.722276	−	1.25102i	0.960085	−	0.279707i	$-0.0902375\pi$
$930$	−28.0036	+	65.0616i	−0.000987393	+	0.00229403i
$931$	18584.2	+	16834.1i	0.654213	+	0.592605i
$932$	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	$-0.969573\pi$
$937$		−	5474.97i		−	0.190885i	0.995435	−	0.0954426i	$-0.0304267\pi$
$938$	−1227.81	+	544.458i	−0.0427391	+	0.0189522i
$939$	−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	$-0.879597\pi$
$941$	−22644.7	−	39221.7i	−0.784479	−	1.35876i	0.144831	−	0.989456i	$-0.453736\pi$
$942$	16431.3	+	22034.5i	0.568323	+	0.762128i
$943$	13488.0	+	7787.29i	0.465778	+	0.268917i
$944$	−14315.3			−0.493564
$945$	−318.841	+	1115.66i	−0.0109755	+	0.0384047i
$946$	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
$952$	−3901.56	+	1730.11i	−0.132826	+	0.0589003i
$953$		−	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
$959$	−3884.42	+	36434.2i	−0.130797	+	1.22682i
$960$	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
$966$	−18451.2	+	32781.0i	−0.614551	+	1.09183i
$967$	−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	$-0.668075\pi$
$971$	−30488.8			−1.00766			−0.503828	+	0.863804i	$0.668075\pi$
$972$	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	−0.881429	−	0.472317i	$-0.843418\pi$
$983$	−976.252	+	1690.92i	−0.0316761	+	0.0548646i	0.849753	+	0.527181i	$0.176751\pi$
$984$	−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
$987$	−27130.5	−	45826.7i	−0.874947	−	1.47789i
$988$	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
$994$	17170.8	+	1830.67i	0.547914	+	0.0584157i
$995$	−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	−0.0253520	−	0.999679i	$-0.508071\pi$
$997$	−28451.4	−	16426.4i	−0.903775	−	0.521795i	−0.878423	+	0.477884i	$0.841404\pi$
$998$		−	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.20.7	✓	44
3.2	odd	2		189.4.o.a.62.16		44
7.6	odd	2	inner	63.4.o.a.20.8	yes	44
9.2	odd	6		567.4.c.c.566.23		44
9.4	even	3		189.4.o.a.125.15		44
9.5	odd	6	inner	63.4.o.a.41.8	yes	44
9.7	even	3		567.4.c.c.566.22		44
21.20	even	2		189.4.o.a.62.15		44
63.13	odd	6		189.4.o.a.125.16		44
63.20	even	6		567.4.c.c.566.21		44
63.34	odd	6		567.4.c.c.566.24		44
63.41	even	6	inner	63.4.o.a.41.7	yes	44

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

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)

\(f(q)\)	\(=\)	\(q+(-2.31807 - 1.33834i) q^{2} +(-3.10623 - 4.16549i) q^{3} +(-0.417710 - 0.723496i) q^{4} +(-0.223284 - 0.386739i) q^{5} +(1.62562 + 13.8131i) q^{6} +(-7.50759 - 16.9303i) q^{7} +23.6495i q^{8} +(-7.70264 + 25.8780i) q^{9} +O(q^{10})\)	\(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} +(-7.50759 - 16.9303i) 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} +(-5.25539 + 49.2933i) 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} +(-47.2029 + 83.8623i) 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} +(221.655 - 131.225i) 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} +(-230.272 + 254.212i) 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} +(400.394 - 177.551i) 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} +(495.951 - 63.8728i) 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} +(20.2371 - 8.97393i) 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} +(77.7016 - 728.808i) 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} +(80.3911 - 0.879112i) 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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