LMFDB - Embedded newform 63.4.o.a.20.20

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			20.20
Character	$\chi$	$=$	63.20
Dual form			63.4.o.a.41.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.92583 + 2.26658i) q^{2} +(3.93727 - 3.39086i) q^{3} +(6.27474 + 10.8682i) q^{4} +(-0.0687529 - 0.119084i) q^{5} +(23.1427 - 4.38780i) q^{6} +(-17.1567 + 6.97489i) q^{7} +20.6235i q^{8} +(4.00416 - 26.7014i) q^{9} +O(q^{10})$	\(q+(3.92583 + 2.26658i) q^{2} +(3.93727 - 3.39086i) q^{3} +(6.27474 + 10.8682i) q^{4} +(-0.0687529 - 0.119084i) q^{5} +(23.1427 - 4.38780i) q^{6} +(-17.1567 + 6.97489i) q^{7} +20.6235i q^{8} +(4.00416 - 26.7014i) q^{9} -0.623335i q^{10} +(8.78077 + 5.06958i) q^{11} +(61.5578 + 21.5142i) q^{12} +(-13.1146 + 7.57170i) q^{13} +(-83.1632 - 11.5047i) q^{14} +(-0.674494 - 0.235732i) q^{15} +(3.45316 - 5.98105i) q^{16} -88.2223 q^{17} +(76.2405 - 95.7495i) q^{18} +66.1014i q^{19} +(0.862814 - 1.49444i) q^{20} +(-43.8995 + 85.6378i) q^{21} +(22.9812 + 39.8046i) q^{22} +(-49.7310 + 28.7122i) q^{23} +(69.9314 + 81.2003i) q^{24} +(62.4905 - 108.237i) q^{25} -68.6473 q^{26} +(-74.7753 - 118.708i) q^{27} +(-183.458 - 142.696i) q^{28} +(102.744 + 59.3195i) q^{29} +(-2.11364 - 2.45424i) q^{30} +(266.140 - 153.656i) q^{31} +(169.997 - 98.1477i) q^{32} +(51.7625 - 9.81404i) q^{33} +(-346.345 - 199.963i) q^{34} +(2.01016 + 1.56353i) q^{35} +(315.321 - 124.027i) q^{36} -337.159 q^{37} +(-149.824 + 259.503i) q^{38} +(-25.9610 + 74.2814i) q^{39} +(2.45592 - 1.41793i) q^{40} +(220.622 + 382.129i) q^{41} +(-366.446 + 236.698i) q^{42} +(46.7113 - 80.9064i) q^{43} +127.241i q^{44} +(-3.45500 + 1.35897i) q^{45} -260.314 q^{46} +(-155.927 + 270.073i) q^{47} +(-6.68487 - 35.2581i) q^{48} +(245.702 - 239.332i) q^{49} +(490.654 - 283.279i) q^{50} +(-347.355 + 299.149i) q^{51} +(-164.581 - 95.0209i) q^{52} +321.580i q^{53} +(-24.4935 - 635.512i) q^{54} -1.39419i q^{55} +(-143.847 - 353.831i) q^{56} +(224.140 + 260.259i) q^{57} +(268.904 + 465.756i) q^{58} +(-287.300 - 497.619i) q^{59} +(-1.67029 - 8.80968i) q^{60} +(634.571 + 366.369i) q^{61} +1393.09 q^{62} +(117.542 + 486.036i) q^{63} +834.587 q^{64} +(1.80333 + 1.04115i) q^{65} +(225.455 + 78.7953i) q^{66} +(31.6068 + 54.7445i) q^{67} +(-553.572 - 958.815i) q^{68} +(-98.4453 + 281.678i) q^{69} +(4.34769 + 10.6943i) q^{70} +621.395i q^{71} +(550.677 + 82.5799i) q^{72} +95.2953i q^{73} +(-1323.63 - 764.196i) q^{74} +(-120.974 - 638.054i) q^{75} +(-718.401 + 414.769i) q^{76} +(-186.008 - 25.7321i) q^{77} +(-270.283 + 232.773i) q^{78} +(425.124 - 736.337i) q^{79} -0.949659 q^{80} +(-696.933 - 213.834i) q^{81} +2000.23i q^{82} +(70.1533 - 121.509i) q^{83} +(-1206.18 + 60.2479i) q^{84} +(6.06554 + 10.5058i) q^{85} +(366.761 - 211.750i) q^{86} +(605.676 - 114.835i) q^{87} +(-104.553 + 181.090i) q^{88} -1223.70 q^{89} +(-16.6439 - 2.49594i) q^{90} +(172.190 - 221.378i) q^{91} +(-624.098 - 360.323i) q^{92} +(526.838 - 1507.43i) q^{93} +(-1224.28 + 706.841i) q^{94} +(7.87159 - 4.54466i) q^{95} +(336.518 - 962.869i) q^{96} +(-671.481 - 387.680i) q^{97} +(1507.05 - 382.673i) q^{98} +(170.525 - 214.160i) 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 $

$2$	3.92583	+	2.26658i	1.38799	+	0.801356i	0.993089	−	0.117368i	$-0.0374456\pi$
$2$	3.92583	+	2.26658i	1.38799	+	0.801356i	0.394901	+	0.918724i	$0.370779\pi$
$3$	3.93727	−	3.39086i	0.757728	−	0.652571i
$3$	3.93727	−	3.39086i	0.757728	−	0.652571i
$4$	6.27474	+	10.8682i	0.784343	+	1.35852i
$5$	−0.0687529	−	0.119084i	−0.00614945	−	0.0106512i	0.862934	−	0.505316i	$-0.168624\pi$
$5$	−0.0687529	−	0.119084i	−0.00614945	−	0.0106512i	−0.869084	+	0.494665i	$0.835291\pi$
$6$	23.1427	−	4.38780i	1.57466	−	0.298552i
$7$	−17.1567	+	6.97489i	−0.926372	+	0.376609i
$7$	−17.1567	+	6.97489i	−0.926372	+	0.376609i
$8$			20.6235i			0.911439i
$9$	4.00416	−	26.7014i	0.148302	−	0.988942i
$10$		−	0.623335i		−	0.0197116i
$11$	8.78077	+	5.06958i	0.240682	+	0.138958i	0.615490	−	0.788145i	$-0.288958\pi$
$11$	8.78077	+	5.06958i	0.240682	+	0.138958i	−0.374808	+	0.927102i	$0.622291\pi$
$12$	61.5578	+	21.5142i	1.48085	+	0.517550i
$13$	−13.1146	+	7.57170i	−0.279794	+	0.161539i	−0.633330	−	0.773882i	$-0.718313\pi$
$13$	−13.1146	+	7.57170i	−0.279794	+	0.161539i	0.353536	+	0.935421i	$0.384979\pi$
$14$	−83.1632	−	11.5047i	−1.58759	−	0.219625i
$15$	−0.674494	−	0.235732i	−0.0116102	−	0.00405772i
$16$	3.45316	−	5.98105i	0.0539556	−	0.0934538i
$17$	−88.2223			−1.25865			−0.629325	−	0.777142i	$-0.716669\pi$
$17$	−88.2223			−1.25865			−0.629325	+	0.777142i	$0.716669\pi$
$18$	76.2405	−	95.7495i	0.998337	−	1.25380i
$19$			66.1014i			0.798142i	0.916920	+	0.399071i	$0.130667\pi$
$19$			66.1014i			0.798142i	−0.916920	+	0.399071i	$0.869333\pi$
$20$	0.862814	−	1.49444i	0.00964655	−	0.0167083i
$21$	−43.8995	+	85.6378i	−0.456174	+	0.889891i
$22$	22.9812	+	39.8046i	0.222709	+	0.385744i
$23$	−49.7310	+	28.7122i	−0.450854	+	0.260300i	−0.708191	−	0.706021i	$-0.750488\pi$
$23$	−49.7310	+	28.7122i	−0.450854	+	0.260300i	0.257337	+	0.966322i	$0.417155\pi$
$24$	69.9314	+	81.2003i	0.594779	+	0.690623i
$25$	62.4905	−	108.237i	0.499924	−	0.865894i
$26$	−68.6473			−0.517802
$27$	−74.7753	−	118.708i	−0.532982	−	0.846127i
$28$	−183.458	−	142.696i	−1.23822	−	0.963106i
$29$	102.744	+	59.3195i	0.657902	+	0.379840i	0.791477	−	0.611199i	$-0.209312\pi$
$29$	102.744	+	59.3195i	0.657902	+	0.379840i	−0.133575	+	0.991039i	$0.542646\pi$
$30$	−2.11364	−	2.45424i	−0.0128632	−	0.0149360i
$31$	266.140	−	153.656i	1.54194	−	0.890238i	0.543221	−	0.839590i	$-0.317204\pi$
$31$	266.140	−	153.656i	1.54194	−	0.890238i	0.998717	−	0.0506486i	$-0.0161289\pi$
$32$	169.997	−	98.1477i	0.939109	−	0.542195i
$33$	51.7625	−	9.81404i	0.273051	−	0.0517699i
$34$	−346.345	−	199.963i	−1.74699	−	1.00863i
$35$	2.01016	+	1.56353i	0.00970800	+	0.00755100i
$36$	315.321	−	124.027i	1.45982	−	0.574198i
$37$	−337.159			−1.49807			−0.749035	−	0.662531i	$-0.769482\pi$
$37$	−337.159			−1.49807			−0.749035	+	0.662531i	$0.769482\pi$
$38$	−149.824	+	259.503i	−0.639596	+	1.10781i
$39$	−25.9610	+	74.2814i	−0.106592	+	0.304988i
$40$	2.45592	−	1.41793i	0.00970788	−	0.00560485i
$41$	220.622	+	382.129i	0.840376	+	1.45557i	0.889577	+	0.456785i	$0.150999\pi$
$41$	220.622	+	382.129i	0.840376	+	1.45557i	−0.0492008	+	0.998789i	$0.515667\pi$
$42$	−366.446	+	236.698i	−1.34628	+	0.869601i
$43$	46.7113	−	80.9064i	0.165661	−	0.286933i	−0.771229	−	0.636558i	$-0.780358\pi$
$43$	46.7113	−	80.9064i	0.165661	−	0.286933i	0.936890	+	0.349625i	$0.113691\pi$
$44$			127.241i			0.435962i
$45$	−3.45500	+	1.35897i	−0.0114454	+	0.00450186i
$46$	−260.314			−0.834373
$47$	−155.927	+	270.073i	−0.483921	+	0.838176i	−0.999829	−	0.0184681i	$-0.994121\pi$
$47$	−155.927	+	270.073i	−0.483921	+	0.838176i	0.515909	+	0.856644i	$0.327454\pi$
$48$	−6.68487	−	35.2581i	−0.0201016	−	0.106022i
$49$	245.702	−	239.332i	0.716332	−	0.697760i
$50$	490.654	−	283.279i	1.38778	−	0.801235i
$51$	−347.355	+	299.149i	−0.953714	+	0.821358i
$52$	−164.581	−	95.0209i	−0.438909	−	0.253404i
$53$			321.580i			0.833441i	0.909035	+	0.416721i	$0.136821\pi$
$53$			321.580i			0.833441i	−0.909035	+	0.416721i	$0.863179\pi$
$54$	−24.4935	−	635.512i	−0.0617248	−	1.60152i
$55$		−	1.39419i		−	0.00341805i
$56$	−143.847	−	353.831i	−0.343256	−	0.844332i
$57$	224.140	+	260.259i	0.520844	+	0.604774i
$58$	268.904	+	465.756i	0.608774	+	1.05443i
$59$	−287.300	−	497.619i	−0.633955	−	1.09804i	−0.986736	−	0.162336i	$-0.948097\pi$
$59$	−287.300	−	497.619i	−0.633955	−	1.09804i	0.352781	−	0.935706i	$-0.385236\pi$
$60$	−1.67029	−	8.80968i	−0.00359390	−	0.0189554i
$61$	634.571	+	366.369i	1.33194	+	0.768997i	0.985597	−	0.169111i	$-0.0540895\pi$
$61$	634.571	+	366.369i	1.33194	+	0.768997i	0.346344	+	0.938107i	$0.387423\pi$
$62$	1393.09			2.85359
$63$	117.542	+	486.036i	0.235061	+	0.971981i
$64$	834.587			1.63005
$65$	1.80333	+	1.04115i	0.00344116	+	0.00198676i
$66$	225.455	+	78.7953i	0.420478	+	0.146955i
$67$	31.6068	+	54.7445i	0.0576325	+	0.0998225i	0.893402	−	0.449258i	$-0.148311\pi$
$67$	31.6068	+	54.7445i	0.0576325	+	0.0998225i	−0.835770	+	0.549080i	$0.814978\pi$
$68$	−553.572	−	958.815i	−0.987213	−	1.70990i
$69$	−98.4453	+	281.678i	−0.171760	+	0.491451i
$70$	4.34769	+	10.6943i	0.00742356	+	0.0182603i
$71$			621.395i			1.03868i	0.854569	+	0.519338i	$0.173822\pi$
$71$			621.395i			1.03868i	−0.854569	+	0.519338i	$0.826178\pi$
$72$	550.677	+	82.5799i	0.901360	+	0.135169i
$73$			95.2953i			0.152787i	0.997078	+	0.0763937i	$0.0243406\pi$
$73$			95.2953i			0.152787i	−0.997078	+	0.0763937i	$0.975659\pi$
$74$	−1323.63	−	764.196i	−2.07930	−	1.20049i
$75$	−120.974	−	638.054i	−0.186251	−	0.982348i
$76$	−718.401	+	414.769i	−1.08429	+	0.626017i
$77$	−186.008	−	25.7321i	−0.275294	−	0.0380837i
$78$	−270.283	+	232.773i	−0.392353	+	0.337903i
$79$	425.124	−	736.337i	0.605446	−	1.04866i	−0.386535	−	0.922275i	$-0.626328\pi$
$79$	425.124	−	736.337i	0.605446	−	1.04866i	0.991981	−	0.126388i	$-0.0403385\pi$
$80$	−0.949659			−0.00132719
$81$	−696.933	−	213.834i	−0.956013	−	0.293325i
$82$			2000.23i			2.69376i
$83$	70.1533	−	121.509i	0.0927750	−	0.160691i	−0.815903	−	0.578189i	$-0.803760\pi$
$83$	70.1533	−	121.509i	0.0927750	−	0.160691i	0.908678	+	0.417498i	$0.137093\pi$
$84$	−1206.18	+	60.2479i	−1.56673	+	0.0782570i
$85$	6.06554	+	10.5058i	0.00774000	+	0.0134061i
$86$	366.761	−	211.750i	0.459871	−	0.265506i
$87$	605.676	−	114.835i	0.746383	−	0.141513i
$88$	−104.553	+	181.090i	−0.126652	+	0.219367i
$89$	−1223.70			−1.45744			−0.728720	−	0.684812i	$-0.759884\pi$
$89$	−1223.70			−1.45744			−0.728720	+	0.684812i	$0.759884\pi$
$90$	−16.6439	−	2.49594i	−0.0194936	−	0.00292327i
$91$	172.190	−	221.378i	0.198357	−	0.255019i
$92$	−624.098	−	360.323i	−0.707247	−	0.408330i
$93$	526.838	−	1507.43i	0.587425	−	1.68078i
$94$	−1224.28	+	706.841i	−1.34335	+	0.775586i
$95$	7.87159	−	4.54466i	0.00850114	−	0.00490813i
$96$	336.518	−	962.869i	0.357768	−	1.02367i
$97$	−671.481	−	387.680i	−0.702872	−	0.405803i	0.105544	−	0.994415i	$-0.466342\pi$
$97$	−671.481	−	387.680i	−0.702872	−	0.405803i	−0.808416	+	0.588611i	$0.799675\pi$
$98$	1507.05	−	382.673i	1.55341	−	0.394447i
$99$	170.525	−	214.160i	0.173115	−	0.217413i
$100$	1568.45			1.56845
$101$	−263.211	+	455.895i	−0.259312	+	0.449141i	−0.966058	−	0.258326i	$-0.916829\pi$
$101$	−263.211	+	455.895i	−0.259312	+	0.449141i	0.706746	+	0.707467i	$0.250162\pi$
$102$	−2041.70	+	387.102i	−1.98194	+	0.375772i
$103$	378.997	−	218.814i	0.362560	−	0.209324i	−0.307643	−	0.951502i	$-0.599540\pi$
$103$	378.997	−	218.814i	0.362560	−	0.209324i	0.670203	+	0.742178i	$0.266207\pi$
$104$	−156.155	−	270.468i	−0.147233	−	0.255015i
$105$	13.2163	−	0.660142i	0.0122836	−	0.000613555i
$106$	−728.886	+	1262.47i	−0.667883	+	1.15681i
$107$		−	1443.67i		−	1.30434i	−0.758071	−	0.652172i	$-0.773858\pi$
$107$		−	1443.67i		−	1.30434i	0.758071	−	0.652172i	$-0.226142\pi$
$108$	820.946	−	1557.53i	0.731441	−	1.38772i
$109$	−1201.61			−1.05590			−0.527950	−	0.849276i	$-0.677039\pi$
$109$	−1201.61			−1.05590			−0.527950	+	0.849276i	$0.677039\pi$
$110$	3.16005	−	5.47336i	0.00273908	−	0.00474422i
$111$	−1327.48	+	1143.26i	−1.13513	+	0.977597i
$112$	−17.5275	+	126.700i	−0.0147874	+	0.106893i
$113$	404.622	−	233.609i	0.336846	−	0.194478i	−0.322030	−	0.946729i	$-0.604365\pi$
$113$	404.622	−	233.609i	0.336846	−	0.194478i	0.658877	+	0.752251i	$0.271032\pi$
$114$	290.040	+	1529.76i	0.238287	+	1.25680i
$115$	6.83830	+	3.94810i	0.00554500	+	0.00320141i
$116$			1488.86i			1.19170i
$117$	149.662	+	380.496i	0.118259	+	0.300657i
$118$		−	2604.75i		−	2.03209i
$119$	1513.60	−	615.341i	1.16598	−	0.474019i
$120$	4.86163	−	13.9104i	0.00369837	−	0.0105820i
$121$	−614.099	−	1063.65i	−0.461381	−	0.799136i
$122$	1660.81	+	2876.61i	1.23248	+	2.13472i
$123$	2164.40	+	756.446i	1.58664	+	0.554524i
$124$	3339.91	+	1928.30i	2.41882	+	1.39650i
$125$	−34.3739			−0.0245959
$126$	−640.190	+	2174.51i	−0.452640	+	1.53747i
$127$	1185.39			0.828237			0.414119	−	0.910223i	$-0.364090\pi$
$127$	1185.39			0.828237			0.414119	+	0.910223i	$0.364090\pi$
$128$	1916.47	+	1106.47i	1.32339	+	0.764058i
$129$	−90.4271	−	476.942i	−0.0617183	−	0.325522i
$130$	4.71970	+	8.17477i	0.00318420	+	0.00551519i
$131$	−693.151	−	1200.57i	−0.462297	−	0.800722i	0.536778	−	0.843723i	$-0.319641\pi$
$131$	−693.151	−	1200.57i	−0.462297	−	0.800722i	−0.999075	+	0.0430017i	$0.986308\pi$
$132$	431.457	+	500.983i	0.284496	+	0.330340i
$133$	−461.050	−	1134.08i	−0.300587	−	0.739377i
$134$			286.557i			0.184737i
$135$	−8.99518	+	17.0660i	−0.00573468	+	0.0108801i
$136$		−	1819.45i		−	1.14718i
$137$	−801.189	−	462.566i	−0.499636	−	0.288465i	0.228927	−	0.973444i	$-0.426478\pi$
$137$	−801.189	−	462.566i	−0.499636	−	0.288465i	−0.728563	+	0.684978i	$0.759812\pi$
$138$	−1024.93	+	882.687i	−0.632228	+	0.544488i
$139$	2339.20	−	1350.54i	1.42740	−	0.824107i	0.430481	−	0.902600i	$-0.358344\pi$
$139$	2339.20	−	1350.54i	1.42740	−	0.824107i	0.996915	+	0.0784926i	$0.0250107\pi$
$140$	−4.37946	+	31.6576i	−0.00264380	+	0.0191111i
$141$	301.854	+	1592.08i	0.180289	+	0.950901i
$142$	−1408.44	+	2439.49i	−0.832350	+	1.44167i
$143$	−153.541			−0.0897886
$144$	−145.875	−	116.153i	−0.0844187	−	0.0672184i
$145$		−	16.3136i		−	0.00934322i
$146$	−215.994	+	374.113i	−0.122437	+	0.212067i
$147$	155.854	−	1775.45i	0.0874464	−	0.996169i
$148$	−2115.58	−	3664.30i	−1.17500	−	2.03516i
$149$	−2532.14	+	1461.93i	−1.39222	+	0.803798i	−0.993561	−	0.113301i	$-0.963858\pi$
$149$	−2532.14	+	1461.93i	−1.39222	+	0.803798i	−0.398659	+	0.917099i	$0.630524\pi$
$150$	971.277	−	2779.08i	0.528696	−	1.51274i
$151$	359.334	−	622.384i	0.193657	−	0.335423i	−0.752803	−	0.658246i	$-0.771299\pi$
$151$	359.334	−	622.384i	0.193657	−	0.335423i	0.946459	+	0.322823i	$0.104632\pi$
$152$	−1363.24			−0.727458
$153$	−353.257	+	2355.66i	−0.186661	+	1.24473i
$154$	−671.913	−	522.622i	−0.351586	−	0.273468i
$155$	−36.5957	−	21.1286i	−0.0189641	−	0.0109489i
$156$	−970.202	+	183.948i	−0.497938	+	0.0944079i
$157$	−1417.53	+	818.411i	−0.720581	+	0.416028i	−0.814966	−	0.579508i	$-0.803245\pi$
$157$	−1417.53	+	818.411i	−0.720581	+	0.416028i	0.0943856	+	0.995536i	$0.469911\pi$
$158$	3337.93	−	1927.15i	1.68070	−	0.970355i
$159$	1090.43	+	1266.15i	0.543880	+	0.631522i
$160$	−23.3756	−	13.4959i	−0.0115500	−	0.00666840i
$161$	652.953	−	839.474i	0.319627	−	0.410931i
$162$	−2251.37	−	2419.13i	−1.09188	−	1.17324i
$163$	−2008.88			−0.965321			−0.482661	−	0.875808i	$-0.660330\pi$
$163$	−2008.88			−0.965321			−0.482661	+	0.875808i	$0.660330\pi$
$164$	−2768.70	+	4795.52i	−1.31829	+	2.28334i
$165$	−4.72751	−	5.48931i	−0.00223052	−	0.00258995i
$166$	550.820	−	318.016i	0.257541	−	0.148692i
$167$	83.5889	+	144.780i	0.0387323	+	0.0670864i	0.884742	−	0.466082i	$-0.154335\pi$
$167$	83.5889	+	144.780i	0.0387323	+	0.0670864i	−0.846009	+	0.533168i	$0.821001\pi$
$168$	−1766.15	−	905.362i	−0.811081	−	0.415775i
$169$	−983.839	+	1704.06i	−0.447810	+	0.775630i
$170$			54.9920i			0.0248100i
$171$	1765.00	+	264.681i	0.789316	+	0.118366i
$172$	1172.41			0.519739
$173$	473.704	−	820.479i	0.208179	−	0.360577i	−0.742962	−	0.669334i	$-0.766580\pi$
$173$	473.704	−	820.479i	0.208179	−	0.360577i	0.951141	+	0.308757i	$0.0999129\pi$
$174$	2638.06	+	921.990i	1.14937	+	0.401701i
$175$	−317.189	+	2292.85i	−0.137013	+	0.990417i
$176$	60.6428	−	35.0121i	0.0259723	−	0.0149951i
$177$	−2818.53	−	985.064i	−1.19691	−	0.418316i
$178$	−4804.04	−	2773.61i	−2.02291	−	1.16793i
$179$			2369.02i			0.989214i	0.869117	+	0.494607i	$0.164688\pi$
$179$			2369.02i			0.989214i	−0.869117	+	0.494607i	$0.835312\pi$
$180$	−36.4488	−	29.0223i	−0.0150929	−	0.0120178i
$181$		−	1499.79i		−	0.615904i	−0.951402	−	0.307952i	$-0.900356\pi$
$181$		−	1499.79i		−	0.615904i	0.951402	−	0.307952i	$-0.0996437\pi$
$182$	1177.76	−	478.808i	0.479677	−	0.195009i
$183$	3740.78	−	709.244i	1.51107	−	0.286496i
$184$	−592.147	−	1025.63i	−0.237248	−	0.410926i
$185$	23.1806	+	40.1501i	0.00921230	+	0.0159562i
$186$	5484.97	−	4723.77i	2.16224	−	1.86217i
$187$	−774.659	−	447.250i	−0.302934	−	0.174899i
$188$	−3913.61			−1.51824
$189$	2110.87	+	1515.09i	0.812399	+	0.583103i
$190$	41.2033			0.0157326
$191$	−685.886	−	395.997i	−0.259838	−	0.150017i	0.364423	−	0.931234i	$-0.381266\pi$
$191$	−685.886	−	395.997i	−0.259838	−	0.150017i	−0.624260	+	0.781216i	$0.714600\pi$
$192$	3285.99	−	2829.97i	1.23514	−	1.06373i
$193$	2170.01	+	3758.56i	0.809330	+	1.40180i	0.913329	+	0.407223i	$0.133503\pi$
$193$	2170.01	+	3758.56i	0.809330	+	1.40180i	−0.103999	+	0.994577i	$0.533164\pi$
$194$	−1757.41	−	3043.93i	−0.650386	−	1.12650i
$195$	10.6306	−	2.01554i	0.00390396	−	0.000740182i
$196$	4142.81	+	1168.58i	1.50977	+	0.425869i
$197$			986.827i			0.356896i	0.983949	+	0.178448i	$0.0571076\pi$
$197$			986.827i			0.356896i	−0.983949	+	0.178448i	$0.942892\pi$
$198$	1154.86	−	454.246i	0.414506	−	0.163040i
$199$			1621.78i			0.577714i	0.957372	+	0.288857i	$0.0932752\pi$
$199$			1621.78i			0.577714i	−0.957372	+	0.288857i	$0.906725\pi$
$200$	2232.22	+	1288.77i	0.789210	+	0.455651i
$201$	310.075	+	108.370i	0.108811	+	0.0380289i
$202$	−2066.64	+	1193.18i	−0.719844	+	0.415602i
$203$	−2176.50	−	301.093i	−0.752513	−	0.104102i
$204$	−5430.77	−	1898.03i	−1.86387	−	0.651414i
$205$	30.3369	−	52.5450i	0.0103357	−	0.0179020i
$206$	1983.84			0.670973
$207$	567.526	+	1442.86i	0.190559	+	0.484471i
$208$			104.585i			0.0348638i
$209$	−335.106	+	580.421i	−0.110908	+	0.192098i
$210$	53.3810	+	27.3641i	0.0175412	+	0.00899191i
$211$	181.071	+	313.625i	0.0590780	+	0.102326i	0.894052	−	0.447964i	$-0.147851\pi$
$211$	181.071	+	313.625i	0.0590780	+	0.102326i	−0.834974	+	0.550290i	$0.814517\pi$
$212$	−3494.99	+	2017.83i	−1.13225	+	0.653704i
$213$	2107.06	+	2446.60i	0.677810	+	0.787034i
$214$	3272.19	−	5667.60i	1.04524	−	1.81042i
$215$	−12.8462			−0.00407489
$216$	2448.18	−	1542.13i	0.771193	−	0.485781i
$217$	−3494.33	+	4492.51i	−1.09314	+	1.40540i
$218$	−4717.30	−	2723.53i	−1.46558	−	0.846151i
$219$	323.133	+	375.203i	0.0997046	+	0.115771i
$220$	15.1523	−	8.74820i	0.00464350	−	0.00268093i
$221$	1157.00	−	667.993i	0.352163	−	0.203321i
$222$	−7802.76	+	1479.38i	−2.35895	+	0.447251i
$223$	115.589	+	66.7354i	0.0347104	+	0.0200401i	0.517255	−	0.855831i	$-0.326954\pi$
$223$	115.589	+	66.7354i	0.0347104	+	0.0200401i	−0.482544	+	0.875872i	$0.660287\pi$
$224$	−2232.01	+	2869.60i	−0.665769	+	0.855951i
$225$	−2639.86	−	2101.99i	−0.782179	−	0.622810i
$226$	2117.97			0.623385
$227$	1770.11	−	3065.91i	0.517560	−	0.896439i	−0.482232	−	0.876043i	$-0.660174\pi$
$227$	1770.11	−	3065.91i	0.517560	−	0.896439i	0.999792	−	0.0203961i	$-0.00649274\pi$
$228$	−1422.12	+	4069.06i	−0.413079	+	1.18193i
$229$	2093.97	−	1208.96i	0.604251	−	0.348865i	−0.166461	−	0.986048i	$-0.553234\pi$
$229$	2093.97	−	1208.96i	0.604251	−	0.348865i	0.770712	+	0.637183i	$0.219901\pi$
$230$	17.8973	+	30.9991i	0.00513093	+	0.00888704i
$231$	−819.619	+	529.414i	−0.233450	+	0.150792i
$232$	−1223.38	+	2118.95i	−0.346201	+	0.599638i
$233$		−	4957.61i		−	1.39392i	−0.717110	−	0.696960i	$-0.754535\pi$
$233$		−	4957.61i		−	1.39392i	0.717110	−	0.696960i	$-0.245465\pi$
$234$	−274.875	+	1832.98i	−0.0767913	+	0.512076i
$235$	42.8817			0.0119034
$236$	3605.47	−	6244.86i	0.994475	−	1.72248i
$237$	−822.985	−	4340.69i	−0.225564	−	1.18970i
$238$	7336.85	+	1014.97i	1.99822	+	0.276431i
$239$	−1649.02	+	952.059i	−0.446301	+	0.257672i	−0.706267	−	0.707946i	$-0.749622\pi$
$239$	−1649.02	+	952.059i	−0.446301	+	0.257672i	0.259966	+	0.965618i	$0.416289\pi$
$240$	−3.73906	+	3.22016i	−0.00100565	+	0.000866085i
$241$	−3592.48	−	2074.12i	−0.960216	−	0.554381i	−0.0639765	−	0.997951i	$-0.520378\pi$
$241$	−3592.48	−	2074.12i	−0.960216	−	0.554381i	−0.896240	+	0.443570i	$0.853712\pi$
$242$		−	5567.61i		−	1.47892i
$243$	−3469.09	+	1521.28i	−0.915813	+	0.401606i
$244$			9195.50i			2.41263i
$245$	−45.3932	−	12.8043i	−0.0118370	−	0.00333892i
$246$	6782.50	+	7875.44i	1.75787	+	2.04114i
$247$	−500.500	−	866.891i	−0.128931	−	0.223316i
$248$	3168.92	+	5488.73i	0.811398	+	1.40538i
$249$	−135.808	−	716.294i	−0.0345641	−	0.182302i
$250$	−134.946	−	77.9110i	−0.0341389	−	0.0197101i
$251$	4077.88			1.02547			0.512737	−	0.858546i	$-0.328632\pi$
$251$	4077.88			1.02547			0.512737	+	0.858546i	$0.328632\pi$
$252$	−4544.78	+	4327.21i	−1.13609	+	1.08170i
$253$	−582.235			−0.144683
$254$	4653.62	+	2686.77i	1.14958	+	0.663713i
$255$	59.5054	+	20.7969i	0.0146132	+	0.00510725i
$256$	1677.47	+	2905.46i	0.409538	+	0.709341i
$257$	3830.27	+	6634.22i	0.929671	+	1.61024i	0.783871	+	0.620924i	$0.213242\pi$
$257$	3830.27	+	6634.22i	0.929671	+	1.61024i	0.145801	+	0.989314i	$0.453424\pi$
$258$	726.024	−	2077.35i	0.175195	−	0.501280i
$259$	5784.52	−	2351.65i	1.38777	−	0.564186i
$260$			26.1319i			0.00623319i
$261$	1995.32	−	2505.90i	0.473208	−	0.594296i
$262$		−	6284.32i		−	1.48186i
$263$	2695.92	+	1556.49i	0.632083	+	0.364933i	0.781558	−	0.623832i	$-0.214425\pi$
$263$	2695.92	+	1556.49i	0.632083	+	0.364933i	−0.149475	+	0.988765i	$0.547758\pi$
$264$	202.400	+	1067.52i	0.0471851	+	0.248869i
$265$	38.2949	−	22.1096i	0.00887711	−	0.00512520i
$266$	760.475	−	5497.20i	0.175292	−	1.26712i
$267$	−4818.04	+	4149.40i	−1.10434	+	0.951082i
$268$	−396.648	+	687.015i	−0.0904073	+	0.156590i
$269$	−4950.54			−1.12208			−0.561040	−	0.827789i	$-0.689599\pi$
$269$	−4950.54			−1.12208			−0.561040	+	0.827789i	$0.689599\pi$
$270$	−73.9950	+	46.6101i	−0.0166785	+	0.0105059i
$271$		−	2802.02i		−	0.628084i	−0.949409	−	0.314042i	$-0.898317\pi$
$271$		−	2802.02i		−	0.628084i	0.949409	−	0.314042i	$-0.101683\pi$
$272$	−304.646	+	527.662i	−0.0679112	+	0.117626i
$273$	−72.7008	−	1455.50i	−0.0161174	−	0.322676i
$274$	−2096.88	−	3631.91i	−0.462326	−	0.800773i
$275$	1097.43	−	633.601i	0.240645	−	0.138937i
$276$	−3679.05	+	697.539i	−0.802365	+	0.152127i
$277$	−179.305	+	310.565i	−0.0388930	+	0.0673647i	−0.884817	−	0.465939i	$-0.845716\pi$
$277$	−179.305	+	310.565i	−0.0388930	+	0.0673647i	0.845924	+	0.533304i	$0.179050\pi$
$278$	12244.4			2.64161
$279$	−3037.16	−	7721.57i	−0.651721	−	1.65691i
$280$	−32.2455	+	41.4567i	−0.00688228	+	0.00884825i
$281$	3092.08	+	1785.21i	0.656434	+	0.378993i	0.790917	−	0.611923i	$-0.209604\pi$
$281$	3092.08	+	1785.21i	0.656434	+	0.378993i	−0.134483	+	0.990916i	$0.542937\pi$
$282$	−2423.54	+	6934.40i	−0.511772	+	1.46432i
$283$	626.874	−	361.926i	0.131674	−	0.0760221i	−0.432716	−	0.901530i	$-0.642445\pi$
$283$	626.874	−	361.926i	0.131674	−	0.0760221i	0.564390	+	0.825508i	$0.309111\pi$
$284$	−6753.43	+	3899.10i	−1.41106	+	0.814679i
$285$	15.5822	−	44.5850i	0.00323864	−	0.00926662i
$286$	−602.776	−	348.013i	−0.124626	−	0.0719526i
$287$	−6450.45	−	5017.24i	−1.32668	−	1.03191i
$288$	−1939.99	−	4932.16i	−0.396927	−	1.00913i
$289$	2870.17			0.584199
$290$	36.9759	−	64.0442i	0.00748725	−	0.0129683i
$291$	−3958.37	+	750.498i	−0.797401	+	0.151185i
$292$	−1035.69	+	597.954i	−0.207565	+	0.119838i
$293$	4746.65	+	8221.43i	0.946424	+	1.63925i	0.752876	+	0.658163i	$0.228666\pi$
$293$	4746.65	+	8221.43i	0.946424	+	1.63925i	0.193548	+	0.981091i	$0.438000\pi$
$294$	4636.06	−	6616.86i	0.919661	−	1.31260i
$295$	−39.5055	+	68.4255i	−0.00779694	+	0.0135047i
$296$		−	6953.40i		−	1.36540i
$297$	−54.7837	−	1421.43i	−0.0107033	−	0.277709i
$298$	−13254.3			−2.57651
$299$	434.800	−	753.096i	0.0840975	−	0.145661i
$300$	6175.40	−	5318.39i	1.18846	−	1.02352i
$301$	−237.097	+	1713.89i	−0.0454021	+	0.328196i
$302$	2821.36	−	1628.91i	0.537587	−	0.310376i
$303$	509.543	+	2687.49i	0.0966088	+	0.509546i
$304$	395.355	+	228.259i	0.0745894	+	0.0430642i
$305$		−	100.756i		−	0.0189156i
$306$	−6726.11	+	8447.24i	−1.25656	+	1.57809i
$307$			1940.82i			0.360809i	0.983593	+	0.180405i	$0.0577407\pi$
$307$			1940.82i			0.360809i	−0.983593	+	0.180405i	$0.942259\pi$
$308$	−887.493	−	2183.03i	−0.164187	−	0.403863i
$309$	750.246	−	2146.65i	0.138123	−	0.395207i
$310$	−95.7790	−	165.894i	−0.0175480	−	0.0303940i
$311$	−33.9077	−	58.7299i	−0.00618241	−	0.0107082i	0.862918	−	0.505345i	$-0.168635\pi$
$311$	−33.9077	−	58.7299i	−0.00618241	−	0.0107082i	−0.869100	+	0.494636i	$0.835301\pi$
$312$	−1531.94	−	535.407i	−0.277978	−	0.0971521i
$313$	−5279.91	−	3048.36i	−0.953477	−	0.550490i	−0.0593176	−	0.998239i	$-0.518892\pi$
$313$	−5279.91	−	3048.36i	−0.953477	−	0.550490i	−0.894159	+	0.447749i	$0.852226\pi$
$314$	−7419.97			−1.33354
$315$	49.7976	−	47.4137i	0.00890722	−	0.00848081i
$316$	10670.2			1.89951
$317$	4423.92	+	2554.15i	0.783823	+	0.452541i	0.837784	−	0.546002i	$-0.183851\pi$
$317$	4423.92	+	2554.15i	0.783823	+	0.452541i	−0.0539602	+	0.998543i	$0.517184\pi$
$318$	1411.03	+	7442.22i	0.248826	+	1.31239i
$319$	601.450	+	1041.74i	0.105563	+	0.182841i
$320$	−57.3803	−	99.3856i	−0.0100239	−	0.0173619i
$321$	−4895.28	−	5684.12i	−0.851178	−	0.988338i
$322$	4466.11	−	1815.66i	0.772940	−	0.314232i
$323$		−	5831.62i		−	1.00458i
$324$	−2049.09	−	8916.14i	−0.351354	−	1.52883i
$325$			1892.64i			0.323030i
$326$	−7886.50	−	4553.27i	−1.33986	−	0.773566i
$327$	−4731.05	+	4074.48i	−0.800084	+	0.689049i
$328$	−7880.85	+	4550.01i	−1.32667	+	0.765952i
$329$	791.452	−	5721.13i	0.132627	−	0.958711i
$330$	−6.11744	−	32.2653i	−0.00102047	−	0.00538227i
$331$	1118.47	−	1937.25i	0.185730	−	0.321694i	−0.758092	−	0.652147i	$-0.773868\pi$
$331$	1118.47	−	1937.25i	0.185730	−	0.321694i	0.943822	+	0.330454i	$0.107202\pi$
$332$	1760.78			0.291070
$333$	−1350.04	+	9002.62i	−0.222167	+	1.48150i
$334$			757.842i			0.124154i
$335$	4.34611	−	7.52769i	0.000708816	−	0.00122771i
$336$	360.612	+	558.286i	0.0585505	+	0.0906458i
$337$	−2759.92	−	4780.32i	−0.446120	−	0.772703i	0.552009	−	0.833838i	$-0.313861\pi$
$337$	−2759.92	−	4780.32i	−0.446120	−	0.772703i	−0.998129	+	0.0611353i	$0.980528\pi$
$338$	−7724.76	+	4459.89i	−1.24311	+	0.717711i
$339$	800.972	−	2291.80i	0.128327	−	0.367178i
$340$	−76.1194	+	131.843i	−0.0121416	+	0.0210299i
$341$	3115.88			0.494822
$342$	6329.17	+	5039.60i	1.00071	+	0.796815i
$343$	−2546.11	+	5819.87i	−0.400807	+	0.916162i
$344$	1668.57	+	963.352i	0.261522	+	0.150990i
$345$	40.3117	−	7.64300i	0.00629075	−	0.00119271i
$346$	3719.36	−	2147.37i	0.577901	−	0.333651i
$347$	−7532.59	+	4348.94i	−1.16533	+	0.672805i	−0.952576	−	0.304300i	$-0.901578\pi$
$347$	−7532.59	+	4348.94i	−1.16533	+	0.672805i	−0.212757	+	0.977105i	$0.568244\pi$
$348$	5048.51	+	5862.03i	0.777668	+	0.902983i
$349$	3108.44	+	1794.66i	0.476764	+	0.275260i	0.719067	−	0.694941i	$-0.244569\pi$
$349$	3108.44	+	1794.66i	0.476764	+	0.275260i	−0.242303	+	0.970201i	$0.577903\pi$
$350$	−6442.14	+	8282.38i	−0.983848	+	1.26489i
$351$	1879.47	+	990.631i	0.285808	+	0.150644i
$352$	1990.27			0.301369
$353$	−2114.60	+	3662.59i	−0.318834	+	0.552237i	−0.980245	−	0.197786i	$-0.936625\pi$
$353$	−2114.60	+	3662.59i	−0.318834	+	0.552237i	0.661411	+	0.750024i	$0.269958\pi$
$354$	−8832.35	−	10255.6i	−1.32608	−	1.53977i
$355$	73.9979	−	42.7227i	0.0110631	−	0.00638729i
$356$	−7678.41	−	13299.4i	−1.14313	−	1.97996i
$357$	3872.91	−	7555.16i	0.574163	−	1.12006i
$358$	−5369.58	+	9300.38i	−0.792712	+	1.37302i
$359$			5830.19i			0.857119i	0.903513	+	0.428560i	$0.140979\pi$
$359$			5830.19i			0.857119i	−0.903513	+	0.428560i	$0.859021\pi$
$360$	−28.0268	−	71.2542i	−0.00410317	−	0.0104317i
$361$	2489.60			0.362969
$362$	3399.39	−	5887.92i	0.493559	−	0.854868i
$363$	−6024.56	−	2105.55i	−0.871095	−	0.304443i
$364$	3486.42	+	482.306i	0.502028	+	0.0694498i
$365$	11.3481	−	6.55183i	0.00162736	−	0.000939558i
$366$	16293.2	+	5694.40i	2.32694	+	0.813254i
$367$	6038.16	+	3486.13i	0.858826	+	0.495844i	0.863619	−	0.504145i	$-0.168192\pi$
$367$	6038.16	+	3486.13i	0.858826	+	0.495844i	−0.00479270	+	0.999989i	$0.501526\pi$
$368$			396.591i			0.0561787i
$369$	11086.8	−	4360.83i	1.56411	−	0.615218i
$370$			210.163i			0.0295293i
$371$	−2242.99	−	5517.24i	−0.313881	−	0.772077i
$372$	19688.7	−	3732.94i	2.74412	−	0.520279i
$373$	2583.05	+	4473.98i	0.358567	+	0.621056i	0.987722	−	0.156224i	$-0.0499321\pi$
$373$	2583.05	+	4473.98i	0.358567	+	0.621056i	−0.629155	+	0.777280i	$0.716599\pi$
$374$	−2027.45	−	3511.65i	−0.280313	−	0.485516i
$375$	−135.339	+	116.557i	−0.0186370	+	0.0160506i
$376$	−5569.86	−	3215.76i	−0.763946	−	0.441064i
$377$	−1796.60			−0.245436
$378$	4852.85	+	10732.4i	0.660328	+	1.46036i
$379$	12063.2			1.63494			0.817472	−	0.575969i	$-0.195375\pi$
$379$	12063.2			1.63494			0.817472	+	0.575969i	$0.195375\pi$
$380$	98.7844	+	57.0332i	0.0133356	+	0.00769932i
$381$	4667.19	−	4019.48i	0.627578	−	0.540483i
$382$	−1795.11	−	3109.23i	−0.240435	−	0.416445i
$383$	−106.285	−	184.092i	−0.0141800	−	0.0245604i	0.858848	−	0.512230i	$-0.171180\pi$
$383$	−106.285	−	184.092i	−0.0141800	−	0.0245604i	−0.873028	+	0.487670i	$0.837847\pi$
$384$	11297.6	−	2141.99i	1.50137	−	0.284656i
$385$	9.72434	+	23.9197i	0.00128727	+	0.00316639i
$386$			19674.0i			2.59424i
$387$	−1973.28	−	1571.22i	−0.259192	−	0.206382i
$388$		−	9730.36i		−	1.27316i
$389$	12010.6	+	6934.30i	1.56545	+	0.903812i	0.996689	+	0.0813080i	$0.0259097\pi$
$389$	12010.6	+	6934.30i	1.56545	+	0.903812i	0.568759	+	0.822504i	$0.307424\pi$
$390$	46.3022	+	16.1824i	0.00601181	+	0.00210110i
$391$	4387.38	−	2533.06i	0.567467	−	0.327627i
$392$	4935.86	+	5067.23i	0.635966	+	0.652893i
$393$	−6800.10	−	2376.60i	−0.872823	−	0.305048i
$394$	−2236.72	+	3874.11i	−0.286001	+	0.495368i
$395$	−116.914			−0.0148926
$396$	3397.52	+	509.495i	0.431141	+	0.0646542i
$397$		−	13097.7i		−	1.65581i	−0.560869	−	0.827905i	$-0.689533\pi$
$397$		−	13097.7i		−	1.65581i	0.560869	−	0.827905i	$-0.310467\pi$
$398$	−3675.89	+	6366.83i	−0.462954	+	0.801861i
$399$	−5660.78	−	2901.82i	−0.710259	−	0.364092i
$400$	−431.579	−	747.518i	−0.0539474	−	0.0934397i
$401$	10477.0	−	6048.87i	1.30472	−	0.753282i	0.323513	−	0.946224i	$-0.395136\pi$
$401$	10477.0	−	6048.87i	1.30472	−	0.753282i	0.981210	+	0.192941i	$0.0618027\pi$
$402$	971.673	+	1128.25i	0.120554	+	0.139980i
$403$	−2326.87	+	4030.26i	−0.287617	+	0.498167i
$404$	−6606.33			−0.813558
$405$	22.4521	+	97.6950i	0.00275470	+	0.0119864i
$406$	−7862.10	−	6115.24i	−0.961058	−	0.747523i
$407$	−2960.51	−	1709.25i	−0.360558	−	0.208168i
$408$	−6169.51	−	7163.68i	−0.748618	−	0.869252i
$409$	−12143.5	+	7011.04i	−1.46811	+	0.847613i	−0.999362	−	0.0357194i	$-0.988628\pi$
$409$	−12143.5	+	7011.04i	−1.46811	+	0.847613i	−0.468747	+	0.883332i	$0.655294\pi$
$410$	238.194	−	137.522i	0.0286917	−	0.0165651i
$411$	−4722.99	+	895.469i	−0.566832	+	0.107470i
$412$	4756.22	+	2746.00i	0.568743	+	0.328364i
$413$	8399.95	+	6533.59i	1.00081	+	0.778443i
$414$	−1042.34	+	6950.75i	−0.123740	+	0.825147i
$415$	−19.2930			−0.00228206
$416$	−1486.29	+	2574.33i	−0.175172	+	0.303406i
$417$	4630.57	−	13249.3i	0.543789	−	1.55593i
$418$	−2631.14	+	1519.09i	−0.307878	+	0.177754i
$419$	4578.14	+	7929.57i	0.533787	+	0.924546i	0.999221	+	0.0394632i	$0.0125648\pi$
$419$	4578.14	+	7929.57i	0.533787	+	0.924546i	−0.465434	+	0.885082i	$0.654102\pi$
$420$	90.1032	+	139.494i	0.0104681	+	0.0162063i
$421$	−6878.44	+	11913.8i	−0.796281	+	1.37920i	0.125741	+	0.992063i	$0.459869\pi$
$421$	−6878.44	+	11913.8i	−0.796281	+	1.37920i	−0.922022	+	0.387137i	$0.873464\pi$
$422$			1641.65i			0.189370i
$423$	6586.99	+	5244.89i	0.757140	+	0.602873i
$424$	−6632.11			−0.759631
$425$	−5513.06	+	9548.90i	−0.629230	+	1.08986i
$426$	2726.56	+	14380.7i	0.310099	+	1.63556i
$427$	−13442.5	−	1859.61i	−1.52348	−	0.210757i
$428$	15690.1	−	9058.66i	1.77198	−	1.02305i
$429$	−604.533	+	520.637i	−0.0680353	+	0.0585934i
$430$	−50.4318	−	29.1168i	−0.00565590	−	0.00326544i
$431$		−	14429.5i		−	1.61263i	−0.591487	−	0.806314i	$-0.701459\pi$
$431$		−	14429.5i		−	1.61263i	0.591487	−	0.806314i	$-0.298541\pi$
$432$	−968.211	+	37.3161i	−0.107831	+	0.00415595i
$433$		−	11861.6i		−	1.31647i	−0.752814	−	0.658233i	$-0.771304\pi$
$433$		−	11861.6i		−	1.31647i	0.752814	−	0.658233i	$-0.228696\pi$
$434$	−23900.8	+	9716.65i	−2.64349	+	1.07469i
$435$	−55.3169	−	64.2308i	−0.00609711	−	0.00707962i
$436$	−7539.77	−	13059.3i	−0.828187	−	1.43446i
$437$	−1897.92	−	3287.29i	−0.207757	−	0.359845i
$438$	418.137	+	2205.39i	0.0456149	+	0.240588i
$439$	1856.80	+	1072.02i	0.201868	+	0.116549i	0.597527	−	0.801849i	$-0.296150\pi$
$439$	1856.80	+	1072.02i	0.201868	+	0.116549i	−0.395658	+	0.918398i	$0.629484\pi$
$440$	28.7532			0.00311535
$441$	−5406.67	−	7518.91i	−0.583810	−	0.811890i
$442$	6056.23			0.651731
$443$	−3418.13	−	1973.46i	−0.366592	−	0.211652i	0.305376	−	0.952232i	$-0.401218\pi$
$443$	−3418.13	−	1973.46i	−0.366592	−	0.211652i	−0.671969	+	0.740580i	$0.734551\pi$
$444$	−20754.7	−	7253.69i	−2.21842	−	0.775326i
$445$	84.1330	+	145.723i	0.00896244	+	0.0155234i
$446$	302.522	+	523.983i	0.0321184	+	0.0556308i
$447$	−5012.50	+	14342.1i	−0.530388	+	1.51758i
$448$	−14318.7	+	5821.16i	−1.51004	+	0.613892i
$449$		−	1118.30i		−	0.117541i	−0.998272	−	0.0587706i	$-0.981282\pi$
$449$		−	1118.30i		−	0.117541i	0.998272	−	0.0587706i	$-0.0187180\pi$
$450$	−5599.30	−	14235.5i	−0.586564	−	1.49126i
$451$			4473.85i			0.467107i
$452$	5077.80	+	2931.67i	0.528406	+	0.305075i
$453$	−695.623	−	3668.94i	−0.0721484	−	0.380534i
$454$	13898.3	−	8024.16i	1.43673	−	0.829499i
$455$	−38.2010	−	5.28467i	−0.00393603	−	0.000544504i
$456$	−5367.45	+	4622.56i	−0.551215	+	0.474718i
$457$	−153.625	+	266.087i	−0.0157249	+	0.0272363i	−0.873781	−	0.486320i	$-0.838339\pi$
$457$	−153.625	+	266.087i	−0.0157249	+	0.0272363i	0.858056	+	0.513556i	$0.171672\pi$
$458$	10960.8			1.11826
$459$	6596.85	+	10472.7i	0.670838	+	1.06498i
$460$			99.0931i			0.0100440i
$461$	−37.5737	+	65.0796i	−0.00379606	+	0.00657497i	−0.867917	−	0.496709i	$-0.834542\pi$
$461$	−37.5737	+	65.0796i	−0.00379606	+	0.00657497i	0.864121	+	0.503284i	$0.167875\pi$
$462$	−4417.64	+	220.657i	−0.444864	+	0.0222206i
$463$	−8234.32	−	14262.3i	−0.826525	−	1.43158i	−0.900748	−	0.434342i	$-0.856981\pi$
$463$	−8234.32	−	14262.3i	−0.826525	−	1.43158i	0.0742230	−	0.997242i	$-0.476352\pi$
$464$	709.585	−	409.679i	0.0709950	−	0.0409890i
$465$	−215.731	+	40.9021i	−0.0215146	+	0.00407912i
$466$	11236.8	−	19462.7i	1.11703	−	1.93475i
$467$	−8886.59			−0.880561			−0.440281	−	0.897860i	$-0.645121\pi$
$467$	−8886.59			−0.880561			−0.440281	+	0.897860i	$0.645121\pi$
$468$	−3196.20	+	4014.07i	−0.315694	+	0.396475i
$469$	−924.103	−	718.779i	−0.0909832	−	0.0707679i
$470$	168.346	+	97.1947i	0.0165218	+	0.00953885i
$471$	−2806.08	+	8028.95i	−0.274517	+	0.785466i
$472$	10262.6	−	5925.14i	1.00080	−	0.577811i
$473$	820.323	−	473.613i	0.0797431	−	0.0460397i
$474$	6607.62	−	18906.2i	0.640291	−	1.83204i
$475$	7154.60	+	4130.71i	0.691107	+	0.399011i
$476$	16185.1	+	12589.0i	1.55849	+	1.21221i
$477$	8586.65	+	1287.66i	0.824225	+	0.123601i
$478$	−8631.66			−0.825948
$479$	7210.06	−	12488.2i	0.687758	−	1.19123i	−0.284803	−	0.958586i	$-0.591928\pi$
$479$	7210.06	−	12488.2i	0.687758	−	1.19123i	0.972561	−	0.232646i	$-0.0747385\pi$
$480$	−137.798	+	26.1263i	−0.0131034	+	0.00248437i
$481$	4421.69	−	2552.86i	0.419151	−	0.241997i
$482$	−9402.31	−	16285.3i	−0.888513	−	1.53895i
$483$	−275.685	−	5519.31i	−0.0259712	−	0.519953i
$484$	7706.62	−	13348.3i	0.723762	−	1.25359i
$485$			106.616i			0.00998186i
$486$	−17067.2	−	1890.68i	−1.59297	−	0.176467i
$487$	5047.02			0.469615			0.234807	−	0.972042i	$-0.424554\pi$
$487$	5047.02			0.469615			0.234807	+	0.972042i	$0.424554\pi$
$488$	−7555.83	+	13087.1i	−0.700894	+	1.21398i
$489$	−7909.48	+	6811.81i	−0.731450	+	0.629940i
$490$	−149.184	−	153.155i	−0.0137540	−	0.0141200i
$491$	1213.61	−	700.678i	0.111547	−	0.0644015i	−0.443189	−	0.896428i	$-0.646153\pi$
$491$	1213.61	−	700.678i	0.111547	−	0.0644015i	0.554735	+	0.832027i	$0.312819\pi$
$492$	5359.84	+	28269.5i	0.491138	+	2.59042i
$493$	−9064.35	−	5233.30i	−0.828068	−	0.478085i
$494$		−	4537.69i		−	0.413280i
$495$	−37.2270	−	5.58258i	−0.00338026	−	0.000506905i
$496$		−	2122.39i		−	0.192133i
$497$	−4334.16	−	10661.1i	−0.391175	−	0.962202i
$498$	1090.38	−	3119.86i	0.0981145	−	0.280732i
$499$	4556.45	+	7892.00i	0.408767	+	0.708005i	0.994752	−	0.102317i	$-0.0326257\pi$
$499$	4556.45	+	7892.00i	0.408767	+	0.708005i	−0.585985	+	0.810322i	$0.699292\pi$
$500$	−215.687	−	373.581i	−0.0192916	−	0.0334141i
$501$	820.041	+	286.600i	0.0731272	+	0.0255576i
$502$	16009.1	+	9242.84i	1.42335	+	0.821769i
$503$	6606.33			0.585610			0.292805	−	0.956172i	$-0.405411\pi$
$503$	6606.33			0.585610			0.292805	+	0.956172i	$0.405411\pi$
$504$	−10023.8	+	2424.12i	−0.885901	+	0.214244i
$505$	72.3862			0.00637850
$506$	−2285.75	−	1319.68i	−0.200819	−	0.115943i
$507$	1904.58	+	10045.4i	0.166835	+	0.879944i
$508$	7438.00	+	12883.0i	0.649622	+	1.12518i
$509$	−2008.77	−	3479.30i	−0.174926	−	0.302981i	0.765210	−	0.643781i	$-0.222635\pi$
$509$	−2008.77	−	3479.30i	−0.174926	−	0.302981i	−0.940136	+	0.340801i	$0.889302\pi$
$510$	186.470	+	216.518i	0.0161903	+	0.0187992i
$511$	−664.675	−	1634.95i	−0.0575411	−	0.141538i
$512$		−	2495.14i		−	0.215372i
$513$	7846.78	−	4942.75i	0.675329	−	0.425395i
$514$			34726.4i			2.97999i
$515$	−52.1143	−	30.0882i	−0.00445909	−	0.00257446i
$516$	4616.08	−	3975.46i	0.393821	−	0.339167i
$517$	−2738.32	+	1580.97i	−0.232942	+	0.134489i
$518$	28039.2	+	3878.90i	2.37832	+	0.329014i
$519$	−917.028	−	4836.71i	−0.0775589	−	0.409071i
$520$	−21.4722	+	37.1910i	−0.00181081	+	0.00313641i
$521$	1142.40			0.0960645			0.0480323	−	0.998846i	$-0.484705\pi$
$521$	1142.40			0.0960645			0.0480323	+	0.998846i	$0.484705\pi$
$522$	13513.1	−	5315.17i	1.13305	−	0.445668i
$523$			6315.64i			0.528038i	0.964518	+	0.264019i	$0.0850481\pi$
$523$			6315.64i			0.528038i	−0.964518	+	0.264019i	$0.914952\pi$
$524$	8698.69	−	15066.6i	0.725199	−	1.25608i
$525$	6525.86	+	10103.1i	0.542499	+	0.839877i
$526$	7055.82	+	12221.0i	0.584883	+	1.01305i
$527$	−23479.4	+	13555.9i	−1.94076	+	1.12050i
$528$	120.046	−	343.483i	0.00989454	−	0.0283109i
$529$	−4434.72	+	7681.16i	−0.364487	+	0.631311i
$530$	200.452			0.0164285
$531$	−14437.5	+	5678.78i	−1.17992	+	0.464102i
$532$	9432.40	−	12126.8i	0.768696	−	0.988279i
$533$	−5786.73	−	3340.97i	−0.470265	−	0.271508i
$534$	−28319.7	+	5369.35i	−2.29497	+	0.435121i
$535$	−171.917	+	99.2566i	−0.0138928	+	0.00802100i
$536$	−1129.02	+	651.842i	−0.0909821	+	0.0525285i
$537$	8033.03	+	9327.49i	0.645532	+	0.749555i
$538$	−19434.9	−	11220.8i	−1.55744	−	0.899186i
$539$	3370.76	−	855.911i	0.269367	−	0.0683983i
$540$	−241.919	+	9.32388i	−0.0192788	+	0.000743029i
$541$	727.024			0.0577767			0.0288884	−	0.999583i	$-0.490803\pi$
$541$	727.024			0.0577767			0.0288884	+	0.999583i	$0.490803\pi$
$542$	6351.00	−	11000.3i	0.503319	−	0.871774i
$543$	−5085.58	−	5905.08i	−0.401921	−	0.466688i
$544$	−14997.5	+	8658.82i	−1.18201	+	0.682433i
$545$	82.6139	+	143.092i	0.00649320	+	0.0112465i
$546$	3013.58	−	5878.81i	0.236208	−	0.460787i
$547$	455.248	−	788.513i	0.0355850	−	0.0616351i	−0.847684	−	0.530501i	$-0.822004\pi$
$547$	455.248	−	788.513i	0.0355850	−	0.0616351i	0.883269	+	0.468866i	$0.155337\pi$
$548$		−	11609.9i		−	0.905022i
$549$	12323.5	−	15476.9i	0.958023	−	1.20317i
$550$	5744.43			0.445351
$551$	−3921.10	+	6791.55i	−0.303166	+	0.525099i
$552$	−5809.20	−	2030.29i	−0.447927	−	0.156549i
$553$	−2157.84	+	15598.3i	−0.165933	+	1.19947i
$554$	−1407.84	+	812.815i	−0.107966	+	0.0623343i
$555$	227.412	+	79.4793i	0.0173929	+	0.00607875i
$556$	29355.7	+	16948.5i	2.23913	+	1.29276i
$557$			2329.01i			0.177169i	0.996069	+	0.0885847i	$0.0282344\pi$
$557$			2329.01i			0.177169i	−0.996069	+	0.0885847i	$0.971766\pi$
$558$	5578.16	−	37197.5i	0.423194	−	2.82204i
$559$			1414.74i			0.107043i
$560$	16.2930	−	6.62377i	0.00122947	−	0.000499831i
$561$	−4566.60	+	865.817i	−0.343676	+	0.0651601i
$562$	8092.65	+	14016.9i	0.607416	+	1.05208i
$563$	−6684.01	−	11577.0i	−0.500350	−	0.866632i	−1.00000		0.000404657i	$-0.999871\pi$
$563$	−6684.01	−	11577.0i	−0.500350	−	0.866632i	0.499650	−	0.866228i	$-0.333462\pi$
$564$	−15408.9	+	13270.5i	−1.15041	+	0.990759i
$565$	−55.6379	−	32.1225i	−0.00414284	−	0.00239187i
$566$	3281.33			0.243683
$567$	13448.5	−	1192.36i	0.996093	−	0.0883147i
$568$	−12815.4			−0.946691
$569$	6678.40	+	3855.77i	0.492044	+	0.284082i	0.725422	−	0.688304i	$-0.241645\pi$
$569$	6678.40	+	3855.77i	0.492044	+	0.284082i	−0.233378	+	0.972386i	$0.574978\pi$
$570$	162.229	−	139.715i	0.0119211	−	0.0102667i
$571$	−5367.85	−	9297.39i	−0.393411	−	0.681408i	0.599486	−	0.800385i	$-0.295372\pi$
$571$	−5367.85	−	9297.39i	−0.393411	−	0.681408i	−0.992897	+	0.118978i	$0.962038\pi$
$572$	−963.432	−	1668.71i	−0.0704250	−	0.121980i
$573$	−4043.29	+	766.598i	−0.294783	+	0.0558902i
$574$	−13951.4	−	34317.3i	−1.01449	−	2.49543i
$575$			7176.97i			0.520522i
$576$	3341.82	−	22284.7i	0.241741	−	1.61203i
$577$			2233.10i			0.161118i	0.996750	+	0.0805590i	$0.0256705\pi$
$577$			2233.10i			0.161118i	−0.996750	+	0.0805590i	$0.974329\pi$
$578$	11267.8	+	6505.47i	0.810863	+	0.468152i
$579$	21288.7	+	7440.29i	1.52803	+	0.534038i
$580$	177.299	−	102.363i	0.0126930	−	0.00732829i
$581$	−356.083	+	2574.00i	−0.0254266	+	0.183800i
$582$	−17240.9	−	6025.62i	−1.22794	−	0.429158i
$583$	−1630.27	+	2823.72i	−0.115813	+	0.200594i
$584$	−1965.32			−0.139256
$585$	35.0211	−	43.9825i	0.00247512	−	0.00310847i
$586$			43034.6i			3.03369i
$587$	6194.97	−	10730.0i	0.435594	−	0.754471i	−0.561750	−	0.827307i	$-0.689872\pi$
$587$	6194.97	−	10730.0i	0.435594	−	0.754471i	0.997344	+	0.0728359i	$0.0232049\pi$
$588$	20273.9	−	9446.66i	1.42191	−	0.662540i
$589$	10156.9	+	17592.2i	0.710537	+	1.23069i
$590$	−310.183	+	179.084i	−0.0216441	+	0.0124962i
$591$	3346.19	+	3885.40i	0.232900	+	0.270430i
$592$	−1164.26	+	2016.56i	−0.0808292	+	0.140000i
$593$	−16050.0			−1.11146			−0.555729	−	0.831363i	$-0.687561\pi$
$593$	−16050.0			−1.11146			−0.555729	+	0.831363i	$0.687561\pi$
$594$	3006.71	−	5704.45i	0.207688	−	0.394035i
$595$	−177.341	−	137.938i	−0.0122190	−	0.00950407i
$596$	−31777.0	−	18346.5i	−2.18395	−	1.26091i
$597$	5499.23	+	6385.39i	0.376999	+	0.437750i
$598$	3413.90	−	1971.02i	0.233453	−	0.134784i
$599$	−14534.4	+	8391.43i	−0.991417	+	0.572395i	−0.905697	−	0.423925i	$-0.860652\pi$
$599$	−14534.4	+	8391.43i	−0.991417	+	0.572395i	−0.0857192	+	0.996319i	$0.527319\pi$
$600$	13158.9	−	2494.90i	0.895351	−	0.169756i
$601$	−6341.34	−	3661.18i	−0.430397	−	0.248490i	0.269119	−	0.963107i	$-0.413268\pi$
$601$	−6341.34	−	3661.18i	−0.430397	−	0.248490i	−0.699516	+	0.714617i	$0.746601\pi$
$602$	−4815.46	+	6191.04i	−0.326019	+	0.419149i
$603$	1588.32	−	624.740i	0.107266	−	0.0421913i
$604$	9018.90			0.607573
$605$	−84.4422	+	146.258i	−0.00567448	+	0.00982849i
$606$	−4091.04	+	11705.6i	−0.274236	+	0.784663i
$607$	7505.80	−	4333.47i	0.501896	−	0.289770i	−0.227600	−	0.973755i	$-0.573088\pi$
$607$	7505.80	−	4333.47i	0.501896	−	0.289770i	0.729496	+	0.683985i	$0.239755\pi$
$608$	6487.70	+	11237.0i	0.432749	+	0.749543i
$609$	−9590.42	+	6194.71i	−0.638134	+	0.412188i
$610$	228.371	−	395.550i	0.0151581	−	0.0262547i
$611$		−	4722.53i		−	0.312689i
$612$	−27818.3	+	10941.9i	−1.83740	+	0.722714i
$613$	5674.74			0.373900			0.186950	−	0.982369i	$-0.440140\pi$
$613$	5674.74			0.373900			0.186950	+	0.982369i	$0.440140\pi$
$614$	−4399.02	+	7619.32i	−0.289136	+	0.500799i
$615$	−58.7282	−	309.752i	−0.00385065	−	0.0203096i
$616$	530.687	−	3836.15i	0.0347110	−	0.250913i
$617$	−3264.02	+	1884.48i	−0.212973	+	0.122960i	−0.602693	−	0.797974i	$-0.705905\pi$
$617$	−3264.02	+	1884.48i	−0.212973	+	0.122960i	0.389719	+	0.920934i	$0.372572\pi$
$618$	7810.89	−	6726.90i	0.508414	−	0.437857i
$619$	14473.4	+	8356.19i	0.939795	+	0.542591i	0.889896	−	0.456163i	$-0.150777\pi$
$619$	14473.4	+	8356.19i	0.939795	+	0.542591i	0.0498991	+	0.998754i	$0.484110\pi$
$620$		−	530.305i		−	0.0343509i
$621$	7127.03	+	3756.52i	0.460544	+	0.242744i
$622$		−	307.418i		−	0.0198172i
$623$	20994.6	−	8535.18i	1.35013	−	0.548884i
$624$	354.633	+	411.780i	0.0227511	+	0.0264173i
$625$	−7808.95	−	13525.5i	−0.499773	−	0.865632i
$626$	−13818.7	−	23934.7i	−0.882277	−	1.52815i
$627$	648.722	+	3421.57i	0.0413197	+	0.217934i
$628$	−17789.3	−	10270.6i	−1.13036	−	0.652616i
$629$	29744.9			1.88554
$630$	302.963	−	73.2678i	0.0191593	−	0.00463343i
$631$	−19529.4			−1.23210			−0.616049	−	0.787708i	$-0.711268\pi$
$631$	−19529.4			−1.23210			−0.616049	+	0.787708i	$0.711268\pi$
$632$	15185.9	+	8767.56i	0.955793	+	0.551827i
$633$	1776.38	+	620.838i	0.111540	+	0.0389828i
$634$	11578.4	+	20054.3i	0.725292	+	1.25624i
$635$	−81.4988	−	141.160i	−0.00509320	−	0.00882168i
$636$	−6918.52	+	19795.7i	−0.431348	+	1.23420i
$637$	−1410.12	+	4999.11i	−0.0877099	+	0.310945i
$638$			5452.93i			0.338375i
$639$	16592.1	+	2488.17i	1.02719	+	0.154038i
$640$		−	304.293i		−	0.0187941i
$641$	−15018.7	−	8671.07i	−0.925436	−	0.534301i	−0.0400707	−	0.999197i	$-0.512758\pi$
$641$	−15018.7	−	8671.07i	−0.925436	−	0.534301i	−0.885365	+	0.464896i	$0.846092\pi$
$642$	−6334.54	−	33410.4i	−0.389415	−	2.05390i
$643$	247.186	−	142.713i	0.0151603	−	0.00875278i	−0.492401	−	0.870369i	$-0.663881\pi$
$643$	247.186	−	142.713i	0.0151603	−	0.00875278i	0.507561	+	0.861616i	$0.330547\pi$
$644$	13220.7	+	1828.93i	0.808955	+	0.111910i
$645$	−50.5788	+	43.5595i	−0.00308766	+	0.00265915i
$646$	13217.8	−	22893.9i	0.805027	−	1.39435i
$647$	−24266.2			−1.47450			−0.737252	−	0.675617i	$-0.763877\pi$
$647$	−24266.2			−1.47450			−0.737252	+	0.675617i	$0.763877\pi$
$648$	4410.01	−	14373.2i	0.267348	−	0.871347i
$649$		−	5825.97i		−	0.352372i
$650$	−4289.81	+	7430.17i	−0.258862	+	0.448362i
$651$	1475.35	+	29537.0i	0.0888226	+	1.77826i
$652$	−12605.2	−	21832.8i	−0.757143	−	1.31141i
$653$	19796.2	−	11429.4i	1.18635	−	0.684939i	0.228875	−	0.973456i	$-0.426495\pi$
$653$	19796.2	−	11429.4i	1.18635	−	0.684939i	0.957475	+	0.288517i	$0.0931621\pi$
$654$	−27808.4	+	5272.41i	−1.66268	+	0.315241i
$655$	−95.3123	+	165.086i	−0.00568574	+	0.00984799i
$656$	3047.38			0.181372
$657$	2544.52	+	381.578i	0.151098	+	0.0226587i
$658$	16074.5	−	20666.3i	0.952354	−	1.22440i
$659$	−2687.96	−	1551.89i	−0.158889	−	0.0917346i	0.418447	−	0.908241i	$-0.362574\pi$
$659$	−2687.96	−	1551.89i	−0.158889	−	0.0917346i	−0.577336	+	0.816506i	$0.695908\pi$
$660$	29.9949	−	85.8234i	0.00176901	−	0.00506162i
$661$	20614.8	−	11901.9i	1.21304	−	0.700351i	0.249622	−	0.968343i	$-0.419694\pi$
$661$	20614.8	−	11901.9i	1.21304	−	0.700351i	0.963421	+	0.267993i	$0.0863603\pi$
$662$	8781.83	−	5070.19i	0.515582	−	0.297672i
$663$	2290.34	−	6553.28i	0.134162	−	0.383874i
$664$	2505.94	+	1446.81i	0.146460	+	0.0845588i
$665$	−103.352	+	132.875i	−0.00602677	+	0.00774836i
$666$	−25705.2	+	32282.8i	−1.49558	+	1.87828i
$667$	−6812.78			−0.395490
$668$	−1049.00	+	1816.92i	−0.0607589	+	0.105237i
$669$	681.395	−	129.191i	0.0393786	−	0.00746609i
$670$	34.1242	−	19.7016i	0.00196766	−	0.00113603i
$671$	3714.68	+	6434.01i	0.213716	+	0.370167i
$672$	942.381	+	18866.8i	0.0540969	+	1.08304i
$673$	7675.47	−	13294.3i	0.439625	−	0.761453i	−0.558035	−	0.829817i	$-0.688445\pi$
$673$	7675.47	−	13294.3i	0.439625	−	0.761453i	0.997660	+	0.0683640i	$0.0217779\pi$
$674$		−	25022.3i		−	1.43000i
$675$	−17521.4	+	675.296i	−0.999107	+	0.0385069i
$676$	−24693.3			−1.40495
$677$	−7096.57	+	12291.6i	−0.402871	+	0.697793i	−0.994071	−	0.108732i	$-0.965321\pi$
$677$	−7096.57	+	12291.6i	−0.402871	+	0.697793i	0.591200	+	0.806525i	$0.298654\pi$
$678$	8339.01	−	7181.73i	0.472356	−	0.406803i
$679$	14224.4	+	1967.78i	0.803950	+	0.111217i
$680$	−216.667	+	125.093i	−0.0122188	+	0.00705454i
$681$	−3426.69	−	18073.5i	−0.192821	−	1.01700i
$682$	12232.4	+	7062.38i	0.686808	+	0.396529i
$683$			2156.60i			0.120820i	0.998174	+	0.0604100i	$0.0192408\pi$
$683$			2156.60i			0.120820i	−0.998174	+	0.0604100i	$0.980759\pi$
$684$	8198.34	+	20843.2i	0.458291	+	1.16514i
$685$			127.211i			0.00709560i
$686$	−23186.8	+	17076.9i	−1.29049	+	0.950434i
$687$	4145.13	−	11860.3i	0.230199	−	0.658661i
$688$	−322.603	−	558.765i	−0.0178766	−	0.0309633i
$689$	−2434.91	−	4217.38i	−0.134634	−	0.233192i
$690$	175.580	+	61.3644i	0.00968727	+	0.00338566i
$691$	−2822.31	−	1629.46i	−0.155377	−	0.0897071i	0.420295	−	0.907387i	$-0.361926\pi$
$691$	−2822.31	−	1629.46i	−0.155377	−	0.0897071i	−0.575673	+	0.817680i	$0.695260\pi$
$692$	11889.5			0.653136
$693$	−1431.89	+	4863.65i	−0.0784893	+	0.266602i
$694$	−39428.9			−2.15663
$695$	−321.653	−	185.706i	−0.0175554	−	0.0101356i
$696$	2368.30	+	12491.2i	0.128980	+	0.680283i
$697$	−19463.8	−	33712.3i	−1.05774	−	1.83206i
$698$	8135.45	+	14091.0i	0.441163	+	0.764116i
$699$	−16810.5	−	19519.4i	−0.909632	−	1.05621i
$700$	−26909.3	+	10939.8i	−1.45297	+	0.590691i
$701$			23138.1i			1.24667i	0.781956	+	0.623334i	$0.214222\pi$
$701$			23138.1i			1.24667i	−0.781956	+	0.623334i	$0.785778\pi$
$702$	5133.13	+	8149.01i	0.275979	+	0.438126i
$703$		−	22286.7i		−	1.19567i
$704$	7328.32	+	4231.00i	0.392324	+	0.226509i
$705$	168.837	−	145.406i	0.00901952	−	0.00776780i
$706$	−16603.1	+	9585.79i	−0.885078	+	0.511000i
$707$	1336.01	−	9657.51i	0.0710688	−	0.513731i
$708$	−6979.72	−	36813.3i	−0.370500	−	1.95414i
$709$	3118.01	−	5400.55i	0.165161	−	0.286067i	−0.771551	−	0.636167i	$-0.780519\pi$
$709$	3118.01	−	5400.55i	0.165161	−	0.286067i	0.936712	+	0.350100i	$0.113852\pi$
$710$	387.337			0.0204740
$711$	−17959.0	−	14299.8i	−0.947278	−	0.754270i
$712$		−	25237.0i		−	1.32837i
$713$	−8823.59	+	15282.9i	−0.463459	+	0.802734i
$714$	32328.7	−	20882.0i	1.69450	−	1.09452i
$715$	10.5564	+	18.2842i	0.000552150	+	0.000956352i
$716$	−25747.0	+	14865.0i	−1.34387	+	0.775883i
$717$	−3264.32	+	9340.09i	−0.170025	+	0.486488i
$718$	−13214.6	+	22888.3i	−0.686858	+	1.18967i
$719$	−26084.5			−1.35297			−0.676486	−	0.736455i	$-0.736498\pi$
$719$	−26084.5			−1.35297			−0.676486	+	0.736455i	$0.736498\pi$
$720$	−3.80259	+	25.3572i	−0.000196825	+	0.00131251i
$721$	−4976.12	+	6397.58i	−0.257032	+	0.330455i
$722$	9773.76	+	5642.88i	0.503797	+	0.290867i
$723$	−21177.6	+	4015.23i	−1.08936	+	0.206539i
$724$	16300.0	−	9410.81i	0.836719	−	0.483080i
$725$	12841.1	−	7413.82i	0.657802	−	0.379782i
$726$	−18879.0	−	21921.2i	−0.965102	−	1.12062i
$727$	−5419.16	−	3128.75i	−0.276459	−	0.159614i	0.355360	−	0.934729i	$-0.384358\pi$
$727$	−5419.16	−	3128.75i	−0.276459	−	0.159614i	−0.631819	+	0.775116i	$0.717691\pi$
$728$	4565.59	+	3551.17i	0.232434	+	0.180790i
$729$	−8500.31	+	17752.9i	−0.431860	+	0.901941i
$730$	59.4009			0.00301168
$731$	−4120.98	+	7137.75i	−0.208509	+	0.361148i
$732$	31180.6	+	36205.1i	1.57441	+	1.82812i
$733$	−5690.16	+	3285.22i	−0.286727	+	0.165542i	−0.636465	−	0.771306i	$-0.719604\pi$
$733$	−5690.16	+	3285.22i	−0.286727	+	0.165542i	0.349738	+	0.936848i	$0.386271\pi$
$734$	15803.2	+	27371.9i	0.794695	+	1.37645i
$735$	−222.143	+	103.508i	−0.0111481	+	0.00519448i
$736$	−5636.08	+	9761.97i	−0.282267	+	0.488901i
$737$			640.932i			0.0320339i
$738$	53409.0	+	8009.25i	2.66397	+	0.399491i
$739$	22303.3			1.11020			0.555101	−	0.831783i	$-0.312680\pi$
$739$	22303.3			1.11020			0.555101	+	0.831783i	$0.312680\pi$
$740$	−290.905	+	503.863i	−0.0144512	+	0.0250302i
$741$	−4910.11	−	1716.06i	−0.243424	−	0.0850756i
$742$	3699.67	−	26743.6i	0.183045	−	1.32317i
$743$	20415.4	−	11786.8i	1.00803	−	0.581988i	0.0974173	−	0.995244i	$-0.468942\pi$
$743$	20415.4	−	11786.8i	1.00803	−	0.581988i	0.910615	+	0.413256i	$0.135609\pi$
$744$	31088.4	+	10865.3i	1.53193	+	0.535402i
$745$	348.183	+	201.024i	0.0171228	+	0.00988583i
$746$			23418.8i			1.14936i
$747$	−2963.56	−	2359.74i	−0.145155	−	0.115580i
$748$		−	11225.5i		−	0.548724i
$749$	10069.4	+	24768.6i	0.491228	+	1.20831i
$750$	−795.503	+	150.826i	−0.0387302	+	0.00734316i
$751$	87.9670	+	152.363i	0.00427425	+	0.00740322i	0.868155	−	0.496294i	$-0.165306\pi$
$751$	87.9670	+	152.363i	0.00427425	+	0.00740322i	−0.863880	+	0.503697i	$0.831973\pi$
$752$	1076.88	+	1865.21i	0.0522205	+	0.0904485i
$753$	16055.7	−	13827.5i	0.777029	−	0.669194i
$754$	−7053.13	−	4072.13i	−0.340663	−	0.196682i
$755$	−98.8209			−0.00476352
$756$	−3221.05	+	32448.1i	−0.154958	+	1.56101i
$757$	6273.79			0.301221			0.150611	−	0.988593i	$-0.451876\pi$
$757$	6273.79			0.301221			0.150611	+	0.988593i	$0.451876\pi$
$758$	47357.9	+	27342.1i	2.26928	+	1.31017i
$759$	−2292.42	+	1974.28i	−0.109630	+	0.0944159i
$760$	93.7269	+	162.340i	0.00447346	+	0.00774827i
$761$	482.344	+	835.445i	0.0229763	+	0.0397961i	0.877285	−	0.479970i	$-0.159352\pi$
$761$	482.344	+	835.445i	0.0229763	+	0.0397961i	−0.854309	+	0.519766i	$0.826019\pi$
$762$	27433.0	−	5201.24i	1.30419	−	0.247272i
$763$	20615.5	−	8381.07i	0.978156	−	0.397661i
$764$		−	9939.11i		−	0.470660i
$765$	304.808	−	119.892i	0.0144057	−	0.00566626i
$766$		−	963.616i		−	0.0454528i
$767$	7535.64	+	4350.70i	0.354754	+	0.204817i
$768$	16456.6	+	5751.52i	0.773214	+	0.270235i
$769$	−382.458	+	220.812i	−0.0179347	+	0.0103546i	−0.508941	−	0.860802i	$-0.669963\pi$
$769$	−382.458	+	220.812i	−0.0179347	+	0.0103546i	0.491006	+	0.871156i	$0.336629\pi$
$770$	−16.0397	+	115.946i	−0.000750690	+	0.00542648i
$771$	37576.5	+	13132.8i	1.75523	+	0.613445i
$772$	−27232.5	+	47168.0i	−1.26958	+	2.19898i
$773$	−6634.17			−0.308686			−0.154343	−	0.988017i	$-0.549326\pi$
$773$	−6634.17			−0.308686			−0.154343	+	0.988017i	$0.549326\pi$
$774$	−4185.45	−	10640.9i	−0.194371	−	0.494161i
$775$		−	38408.1i		−	1.78021i
$776$	7995.32	−	13848.3i	0.369865	−	0.640625i
$777$	14801.1	−	28873.5i	0.683380	−	1.33312i
$778$	31434.2	+	54445.7i	1.44855	+	2.50896i
$779$	−25259.3	+	14583.4i	−1.16176	+	0.670740i
$780$	88.6094	+	102.888i	0.00406760	+	0.00472306i
$781$	−3150.21	+	5456.33i	−0.144332	+	0.249991i
$782$	22965.5			1.05018
$783$	−641.028	−	16632.2i	−0.0292573	−	0.759116i
$784$	−583.006	−	2296.00i	−0.0265582	−	0.104592i
$785$	194.919	+	112.536i	0.00886235	+	0.00511668i
$786$	−21309.2	−	24743.1i	−0.967017	−	1.12284i
$787$	−6336.06	+	3658.13i	−0.286984	+	0.165690i	−0.636581	−	0.771210i	$-0.719652\pi$
$787$	−6336.06	+	3658.13i	−0.286984	+	0.165690i	0.349597	+	0.936900i	$0.386318\pi$
$788$	−10725.0	+	6192.09i	−0.484851	+	0.279929i
$789$	15892.4	−	3013.17i	0.717092	−	0.135959i
$790$	−458.985	−	264.995i	−0.0206708	−	0.0119343i
$791$	−5312.57	+	6830.14i	−0.238803	+	0.307019i
$792$	4416.72	+	3516.82i	0.198158	+	0.157784i
$793$	−11096.2			−0.496893
$794$	29687.0	−	51419.4i	1.32689	−	2.29825i
$795$	75.8068	−	216.904i	0.00338188	−	0.00967646i
$796$	−17625.8	+	10176.3i	−0.784837	+	0.453126i
$797$	−14429.9	−	24993.3i	−0.641322	−	1.11080i	−0.985138	−	0.171765i	$-0.945053\pi$
$797$	−14429.9	−	24993.3i	−0.641322	−	1.11080i	0.343816	−	0.939037i	$-0.388280\pi$
$798$	−15646.0	−	24222.6i	−0.694065	−	1.07453i
$799$	13756.2	−	23826.5i	0.609087	−	1.05497i
$800$		−	24533.2i		−	1.08423i
$801$	−4899.90	+	32674.6i	−0.216142	+	1.44132i
$802$	54840.9			2.41459
$803$	−483.107	+	836.766i	−0.0212310	+	0.0367731i
$804$	767.860	+	4049.94i	0.0336820	+	0.177650i
$805$	−144.860	−	20.0397i	−0.00634241	−	0.000877400i
$806$	−18269.8	+	10548.1i	−0.798418	+	0.460967i
$807$	−19491.6	+	16786.6i	−0.850231	+	0.732237i
$808$	−9402.16	−	5428.34i	−0.409365	−	0.236347i
$809$		−	9191.53i		−	0.399452i	−0.979852	−	0.199726i	$-0.935995\pi$
$809$		−	9191.53i		−	0.399452i	0.979852	−	0.199726i	$-0.0640053\pi$
$810$	−133.290	+	434.423i	−0.00578190	+	0.0188445i
$811$			31228.1i			1.35212i	0.736848	+	0.676058i	$0.236313\pi$
$811$			31228.1i			1.35212i	−0.736848	+	0.676058i	$0.763687\pi$
$812$	−10384.6	−	25543.8i	−0.448804	−	1.10396i
$813$	−9501.26	−	11032.3i	−0.409869	−	0.475917i
$814$	−7748.31	−	13420.5i	−0.333634	−	0.577871i
$815$	138.116	+	239.224i	0.00593619	+	0.0102818i
$816$	589.754	+	3110.55i	0.0253009	+	0.133445i
$817$	5348.03	+	3087.68i	0.229013	+	0.132221i
$818$	−63564.3			−2.71696
$819$	−5221.62	−	5484.16i	−0.222782	−	0.233983i
$820$	761.424			0.0324269
$821$	−18611.4	−	10745.3i	−0.791160	−	0.456776i	0.0492107	−	0.998788i	$-0.484329\pi$
$821$	−18611.4	−	10745.3i	−0.791160	−	0.456776i	−0.840371	+	0.542012i	$0.817663\pi$
$822$	−20571.3	−	7189.57i	−0.872879	−	0.305067i
$823$	−13576.6	−	23515.4i	−0.575032	−	0.995984i	−0.996038	−	0.0889267i	$-0.971656\pi$
$823$	−13576.6	−	23515.4i	−0.575032	−	0.995984i	0.421006	−	0.907058i	$-0.361677\pi$
$824$	4512.71	+	7816.25i	0.190786	+	0.330451i
$825$	2172.42	−	6215.89i	0.0916777	−	0.262314i
$826$	18167.9	+	44688.9i	0.765304	+	1.88248i
$827$		−	14491.9i		−	0.609349i	−0.952457	−	0.304675i	$-0.901452\pi$
$827$		−	14491.9i		−	0.609349i	0.952457	−	0.304675i	$-0.0985477\pi$
$828$	−12120.1	+	15221.5i	−0.508701	+	0.638871i
$829$			12056.9i			0.505129i	0.967580	+	0.252565i	$0.0812741\pi$
$829$			12056.9i			0.505129i	−0.967580	+	0.252565i	$0.918726\pi$
$830$	−75.7409	−	43.7290i	−0.00316748	−	0.00182874i
$831$	347.110	+	1830.77i	0.0144899	+	0.0764246i
$832$	−10945.2	+	6319.24i	−0.456080	+	0.263318i
$833$	−21676.4	+	21114.4i	−0.901611	+	0.878235i
$834$	48209.4	−	41518.9i	2.00162	−	1.72384i
$835$	11.4940	−	19.9081i	0.000476365	−	0.000825088i
$836$	−8410.82			−0.347960
$837$	−38140.9	−	20103.3i	−1.57508	−	0.830194i
$838$			41506.8i			1.71101i
$839$	15546.1	−	26926.7i	0.639704	−	1.10800i	−0.345794	−	0.938311i	$-0.612390\pi$
$839$	15546.1	−	26926.7i	0.639704	−	1.10800i	0.985498	−	0.169689i	$-0.0542764\pi$
$840$	13.6144	+	272.566i	0.000559218	+	0.0111957i
$841$	−5156.89	−	8932.00i	−0.211443	−	0.366231i
$842$	−54007.1	+	31181.0i	−2.21046	+	1.27621i
$843$	18227.8	−	3455.94i	0.744718	−	0.141197i
$844$	−2272.35	+	3935.83i	−0.0926749	+	0.160518i
$845$	270.567			0.0110151
$846$	13971.4	+	35520.5i	0.567787	+	1.44352i
$847$	17954.7	+	13965.4i	0.728373	+	0.566537i
$848$	1923.38	+	1110.47i	0.0778883	+	0.0449688i
$849$	1240.93	−	3550.64i	0.0501633	−	0.143531i
$850$	−43286.6	+	24991.5i	−1.74673	+	1.00847i
$851$	16767.2	−	9680.57i	0.675410	−	0.389948i
$852$	−13368.8	+	38251.7i	−0.537567	+	1.53812i
$853$	33795.3	+	19511.7i	1.35654	+	0.783198i	0.989156	−	0.146871i	$-0.0469203\pi$
$853$	33795.3	+	19511.7i	1.35654	+	0.783198i	0.367384	+	0.930070i	$0.380254\pi$
$854$	−48558.0	−	37769.0i	−1.94569	−	1.51338i
$855$	−89.8299	−	228.380i	−0.00359312	−	0.00913502i
$856$	29773.6			1.18883
$857$	−8986.51	+	15565.1i	−0.358195	+	0.620412i	−0.987659	−	0.156617i	$-0.949941\pi$
$857$	−8986.51	+	15565.1i	−0.358195	+	0.620412i	0.629464	+	0.777030i	$0.283274\pi$
$858$	−3553.35	+	673.708i	−0.141386	+	0.0268065i
$859$	16462.0	−	9504.31i	0.653870	−	0.377512i	−0.136067	−	0.990700i	$-0.543446\pi$
$859$	16462.0	−	9504.31i	0.653870	−	0.377512i	0.789937	+	0.613187i	$0.210113\pi$
$860$	−80.6063	−	139.614i	−0.00319611	−	0.00553582i
$861$	−42409.9	+	2118.34i	−1.67866	+	0.0838477i
$862$	32705.5	−	56647.6i	1.29229	−	2.23831i
$863$			5497.42i			0.216842i	0.994105	+	0.108421i	$0.0345794\pi$
$863$			5497.42i			0.216842i	−0.994105	+	0.108421i	$0.965421\pi$
$864$	−24362.5	−	12841.0i	−0.959294	−	0.505625i
$865$	−130.274			−0.00512075
$866$	26885.1	−	46566.4i	1.05496	−	1.82724i
$867$	11300.6	−	9732.35i	0.442664	−	0.381232i
$868$	−70751.4	−	9787.65i	−2.76666	−	0.382735i
$869$	7465.83	−	4310.40i	0.291440	−	0.168263i
$870$	−71.5806	−	377.539i	−0.00278944	−	0.0147124i
$871$	−829.018	−	478.634i	−0.0322505	−	0.0186198i
$872$		−	24781.3i		−	0.962388i
$873$	−13040.3	+	16377.2i	−0.505553	+	0.634918i
$874$		−	17207.1i		−	0.665948i
$875$	589.740	−	239.754i	0.0227850	−	0.00926304i
$876$	−2050.20	+	5866.17i	−0.0790751	+	0.226255i
$877$	9852.44	+	17064.9i	0.379354	+	0.657060i	0.990968	−	0.134096i	$-0.0428130\pi$
$877$	9852.44	+	17064.9i	0.379354	+	0.657060i	−0.611615	+	0.791156i	$0.709480\pi$
$878$	4859.65	+	8417.15i	0.186794	+	0.323537i
$879$	46566.5	+	16274.8i	1.78686	+	0.624499i
$880$	−8.33873	−	4.81437i	−0.000319430	−	0.000184423i
$881$	−16133.0			−0.616952			−0.308476	−	0.951232i	$-0.599819\pi$
$881$	−16133.0			−0.616952			−0.308476	+	0.951232i	$0.599819\pi$
$882$	−4183.45	−	41772.6i	−0.159710	−	1.59473i
$883$	21767.7			0.829605			0.414803	−	0.909911i	$-0.363851\pi$
$883$	21767.7			0.829605			0.414803	+	0.909911i	$0.363851\pi$
$884$	14519.7	+	8382.96i	0.552433	+	0.318947i
$885$	76.4775	+	403.367i	0.00290482	+	0.0153209i
$886$	−8945.99	−	15494.9i	−0.339217	−	0.587542i
$887$	9673.92	+	16755.7i	0.366199	+	0.634275i	0.988968	−	0.148131i	$-0.0473256\pi$
$887$	9673.92	+	16755.7i	0.366199	+	0.634275i	−0.622769	+	0.782406i	$0.713992\pi$
$888$	−23578.0	−	27377.4i	−0.891020	−	1.03460i
$889$	−20337.3	+	8267.95i	−0.767256	+	0.311921i
$890$			762.776i			0.0287284i
$891$	−5035.56	−	5410.78i	−0.189335	−	0.203443i
$892$			1674.99i			0.0628731i
$893$	−17852.2	−	10307.0i	−0.668983	−	0.386238i
$894$	−52185.8	+	44943.5i	−1.95230	+	1.68136i
$895$	282.112	−	162.877i	0.0105363	−	0.00608312i
$896$	−40597.7	−	5616.23i	−1.51370	−	0.209403i
$897$	−841.717	−	4439.49i	−0.0313312	−	0.165251i
$898$	2534.72	−	4390.26i	0.0941923	−	0.163146i
$899$	36459.1			1.35259
$900$	6280.32	−	41879.8i	0.232605	−	1.55110i
$901$		−	28370.5i		−	1.04901i
$902$	−10140.3	+	17563.6i	−0.374319	+	0.648340i
$903$	4878.04	+	7552.01i	0.179769	+	0.278311i
$904$	4817.83	+	8344.73i	0.177255	+	0.307015i
$905$	−178.601	+	103.115i	−0.00656009	+	0.00378747i
$906$	5585.04	−	15980.3i	0.204802	−	0.585994i
$907$	−11279.6	+	19536.8i	−0.412935	+	0.715225i	−0.995209	−	0.0977677i	$-0.968830\pi$
$907$	−11279.6	+	19536.8i	−0.412935	+	0.715225i	0.582274	+	0.812993i	$0.302163\pi$
$908$	44427.8			1.62378
$909$	11119.1	+	8853.60i	0.405718	+	0.323053i
$910$	−137.992	−	107.332i	−0.00502682	−	0.00390992i
$911$	8494.79	+	4904.47i	0.308941	+	0.178367i	0.646452	−	0.762954i	$-0.276252\pi$
$911$	8494.79	+	4904.47i	0.308941	+	0.178367i	−0.337512	+	0.941321i	$0.609585\pi$
$912$	2330.61	−	441.879i	0.0846210	−	0.0160439i
$913$	1232.00	−	711.295i	0.0446585	−	0.0257836i
$914$	−1206.21	+	696.407i	−0.0436520	+	0.0252025i
$915$	−341.649	−	396.703i	−0.0123438	−	0.0143329i
$916$	26278.3	+	15171.8i	0.947881	+	0.547259i
$917$	20266.0	+	15763.2i	0.729818	+	0.567662i
$918$	2160.87	+	56066.3i	0.0776899	+	2.01576i
$919$	−38354.6			−1.37672			−0.688358	−	0.725371i	$-0.741668\pi$
$919$	−38354.6			−1.37672			−0.688358	+	0.725371i	$0.741668\pi$
$920$	−81.4236	+	141.030i	−0.00291789	+	0.00505393i
$921$	6581.04	+	7641.52i	0.235453	+	0.273395i
$922$	−295.016	+	170.328i	−0.0105378	+	0.00608399i
$923$	−4705.02	−	8149.33i	−0.167787	−	0.290616i
$924$	−10896.7	−	5585.82i	−0.387958	−	0.198875i
$925$	−21069.2	+	36493.0i	−0.748921	+	1.29717i
$926$		−	74654.8i		−	2.64936i
$927$	−4325.08	−	10995.9i	−0.153241	−	0.389594i
$928$	23288.3			0.823789
$929$	−1824.39	+	3159.94i	−0.0644310	+	0.111598i	−0.896441	−	0.443162i	$-0.853857\pi$
$929$	−1824.39	+	3159.94i	−0.0644310	+	0.111598i	0.832010	+	0.554760i	$0.187190\pi$
$930$	−939.631	−	328.397i	−0.0331309	−	0.0115791i
$931$	15820.2	+	16241.2i	0.556912	+	0.571735i
$932$	53880.1	−	31107.7i	1.89367	−	1.09331i
$933$	−332.648	−	116.259i	−0.0116725	−	0.00407948i
$934$	−34887.2	−	20142.1i	−1.22221	−	0.705643i
$935$			122.999i			0.00430213i
$936$	−7847.17	+	3086.56i	−0.274031	+	0.107786i
$937$			22851.6i			0.796724i	0.917228	+	0.398362i	$0.130421\pi$
$937$			22851.6i			0.796724i	−0.917228	+	0.398362i	$0.869579\pi$
$938$	−1998.70	−	4916.35i	−0.0695735	−	0.171135i
$939$	−31125.0	+	5901.23i	−1.08171	+	0.205090i
$940$	269.072	+	466.046i	0.00933633	+	0.0161710i
$941$	23868.9	+	41342.2i	0.826892	+	1.43222i	0.900465	+	0.434928i	$0.143226\pi$
$941$	23868.9	+	41342.2i	0.826892	+	1.43222i	−0.0735735	+	0.997290i	$0.523440\pi$
$942$	−29214.4	+	25160.1i	−1.01046	+	0.870232i
$943$	−21943.5	−	12669.1i	−0.757773	−	0.437501i
$944$	−3968.37			−0.136822
$945$	35.2934	−	355.537i	0.00121491	−	0.0122387i
$946$	4293.93			0.147577
$947$	40970.4	+	23654.2i	1.40587	+	0.811679i	0.994986	−	0.100010i	$-0.0318874\pi$
$947$	40970.4	+	23654.2i	1.40587	+	0.811679i	0.410882	+	0.911688i	$0.365221\pi$
$948$	42011.4	−	36181.1i	1.43931	−	1.23956i
$949$	−721.548	−	1249.76i	−0.0246812	−	0.0427490i
$950$	18725.2	+	32432.9i	0.639499	+	1.10765i
$951$	26078.9	−	4944.50i	0.889239	−	0.168598i
$952$	12690.5	+	31215.7i	0.432039	+	1.06272i
$953$			29971.1i			1.01874i	0.860548	+	0.509370i	$0.170121\pi$
$953$			29971.1i			1.01874i	−0.860548	+	0.509370i	$0.829879\pi$
$954$	30791.1	+	24517.4i	1.04497	+	0.832055i
$955$			108.904i			0.00369009i
$956$	−20694.3	−	11947.9i	−0.700106	−	0.404206i
$957$	5900.47	+	2062.18i	0.199305	+	0.0696562i
$958$	56610.9	−	32684.3i	1.90920	−	1.10228i
$959$	16972.1	+	2347.89i	0.571488	+	0.0790587i
$960$	−562.924	−	196.739i	−0.0189253	−	0.00661431i
$961$	32324.7	−	55988.0i	1.08505	−	1.87936i
$962$	23145.1			0.775703
$963$	−38548.1	−	5780.69i	−1.28992	−	0.193437i
$964$		−	52058.3i		−	1.73930i
$965$	298.389	−	516.824i	0.00995386	−	0.0172406i
$966$	11427.6	−	22292.7i	0.380619	−	0.742501i
$967$	27462.8	+	47567.0i	0.913284	+	1.58185i	0.809395	+	0.587265i	$0.199795\pi$
$967$	27462.8	+	47567.0i	0.913284	+	1.58185i	0.103889	+	0.994589i	$0.466871\pi$
$968$	21936.2	−	12664.9i	0.728364	−	0.420521i
$969$	−19774.2	−	22960.6i	−0.655561	−	0.761199i
$970$	−241.654	+	418.558i	−0.00799902	+	0.0138547i
$971$	38391.4			1.26884			0.634418	−	0.772990i	$-0.281240\pi$
$971$	38391.4			1.26884			0.634418	+	0.772990i	$0.281240\pi$
$972$	−38301.2	−	28157.1i	−1.26390	−	0.929155i
$973$	−30712.9	+	39486.3i	−1.01193	+	1.30100i
$974$	19813.7	+	11439.5i	0.651821	+	0.376329i
$975$	6417.67	+	7451.82i	0.210800	+	0.244769i
$976$	4382.54	−	2530.26i	0.143731	−	0.0829834i
$977$	12928.6	−	7464.33i	0.423360	−	0.244427i	−0.273154	−	0.961970i	$-0.588067\pi$
$977$	12928.6	−	7464.33i	0.423360	−	0.244427i	0.696514	+	0.717543i	$0.254734\pi$
$978$	−46490.8	+	8814.54i	−1.52005	+	0.288198i
$979$	−10745.0	−	6203.65i	−0.350779	−	0.202522i
$980$	−145.671	−	573.684i	−0.00474826	−	0.0186997i
$981$	−4811.43	+	32084.6i	−0.156592	+	1.04422i
$982$	6352.56			0.206434
$983$	−25253.7	+	43740.8i	−0.819399	+	1.41924i	0.0867264	+	0.996232i	$0.472359\pi$
$983$	−25253.7	+	43740.8i	−0.819399	+	1.41924i	−0.906126	+	0.423009i	$0.860974\pi$
$984$	−15600.6	+	44637.4i	−0.505415	+	1.44613i
$985$	117.515	−	67.8472i	0.00380136	−	0.00219471i
$986$	−23723.4	−	41090.1i	−0.766233	−	1.32715i
$987$	−16283.4	−	25209.3i	−0.525132	−	0.812991i
$988$	6281.02	−	10879.0i	0.202253	−	0.350312i
$989$			5364.74i			0.172486i
$990$	−133.493	−	106.294i	−0.00428555	−	0.00341237i
$991$	−4236.35			−0.135794			−0.0678971	−	0.997692i	$-0.521629\pi$
$991$	−4236.35			−0.135794			−0.0678971	+	0.997692i	$0.521629\pi$
$992$	30161.9	−	52242.0i	0.965365	−	1.67206i
$993$	−2165.21	−	11420.0i	−0.0691953	−	0.364958i
$994$	7148.95	−	51677.2i	0.228120	−	1.64900i
$995$	193.127	−	111.502i	0.00615332	−	0.00355262i
$996$	6932.65	−	5970.54i	0.220552	−	0.189944i
$997$	−19233.0	−	11104.2i	−0.610948	−	0.352731i	0.162388	−	0.986727i	$-0.448080\pi$
$997$	−19233.0	−	11104.2i	−0.610948	−	0.352731i	−0.773336	+	0.633996i	$0.781414\pi$
$998$			41310.1i			1.31027i
$999$	25211.2	+	40023.5i	0.798444	+	1.26756i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.o.a.20.20	yes	44
3.2	odd	2		189.4.o.a.62.4		44
7.6	odd	2	inner	63.4.o.a.20.19	✓	44
9.2	odd	6		567.4.c.c.566.28		44
9.4	even	3		189.4.o.a.125.3		44
9.5	odd	6	inner	63.4.o.a.41.19	yes	44
9.7	even	3		567.4.c.c.566.17		44
21.20	even	2		189.4.o.a.62.3		44
63.13	odd	6		189.4.o.a.125.4		44
63.20	even	6		567.4.c.c.566.18		44
63.34	odd	6		567.4.c.c.566.27		44
63.41	even	6	inner	63.4.o.a.41.20	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.o.a.20.19	✓	44	7.6	odd	2	inner
63.4.o.a.20.20	yes	44	1.1	even	1	trivial
63.4.o.a.41.19	yes	44	9.5	odd	6	inner
63.4.o.a.41.20	yes	44	63.41	even	6	inner
189.4.o.a.62.3		44	21.20	even	2
189.4.o.a.62.4		44	3.2	odd	2
189.4.o.a.125.3		44	9.4	even	3
189.4.o.a.125.4		44	63.13	odd	6
567.4.c.c.566.17		44	9.7	even	3
567.4.c.c.566.18		44	63.20	even	6
567.4.c.c.566.27		44	63.34	odd	6
567.4.c.c.566.28		44	9.2	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)

\(f(q)\)	\(=\)	\(q+(3.92583 + 2.26658i) q^{2} +(3.93727 - 3.39086i) q^{3} +(6.27474 + 10.8682i) q^{4} +(-0.0687529 - 0.119084i) q^{5} +(23.1427 - 4.38780i) q^{6} +(-17.1567 + 6.97489i) q^{7} +20.6235i q^{8} +(4.00416 - 26.7014i) q^{9} +O(q^{10})\)	\(q+(3.92583 + 2.26658i) q^{2} +(3.93727 - 3.39086i) q^{3} +(6.27474 + 10.8682i) q^{4} +(-0.0687529 - 0.119084i) q^{5} +(23.1427 - 4.38780i) q^{6} +(-17.1567 + 6.97489i) q^{7} +20.6235i q^{8} +(4.00416 - 26.7014i) q^{9} -0.623335i q^{10} +(8.78077 + 5.06958i) q^{11} +(61.5578 + 21.5142i) q^{12} +(-13.1146 + 7.57170i) q^{13} +(-83.1632 - 11.5047i) q^{14} +(-0.674494 - 0.235732i) q^{15} +(3.45316 - 5.98105i) q^{16} -88.2223 q^{17} +(76.2405 - 95.7495i) q^{18} +66.1014i q^{19} +(0.862814 - 1.49444i) q^{20} +(-43.8995 + 85.6378i) q^{21} +(22.9812 + 39.8046i) q^{22} +(-49.7310 + 28.7122i) q^{23} +(69.9314 + 81.2003i) q^{24} +(62.4905 - 108.237i) q^{25} -68.6473 q^{26} +(-74.7753 - 118.708i) q^{27} +(-183.458 - 142.696i) q^{28} +(102.744 + 59.3195i) q^{29} +(-2.11364 - 2.45424i) q^{30} +(266.140 - 153.656i) q^{31} +(169.997 - 98.1477i) q^{32} +(51.7625 - 9.81404i) q^{33} +(-346.345 - 199.963i) q^{34} +(2.01016 + 1.56353i) q^{35} +(315.321 - 124.027i) q^{36} -337.159 q^{37} +(-149.824 + 259.503i) q^{38} +(-25.9610 + 74.2814i) q^{39} +(2.45592 - 1.41793i) q^{40} +(220.622 + 382.129i) q^{41} +(-366.446 + 236.698i) q^{42} +(46.7113 - 80.9064i) q^{43} +127.241i q^{44} +(-3.45500 + 1.35897i) q^{45} -260.314 q^{46} +(-155.927 + 270.073i) q^{47} +(-6.68487 - 35.2581i) q^{48} +(245.702 - 239.332i) q^{49} +(490.654 - 283.279i) q^{50} +(-347.355 + 299.149i) q^{51} +(-164.581 - 95.0209i) q^{52} +321.580i q^{53} +(-24.4935 - 635.512i) q^{54} -1.39419i q^{55} +(-143.847 - 353.831i) q^{56} +(224.140 + 260.259i) q^{57} +(268.904 + 465.756i) q^{58} +(-287.300 - 497.619i) q^{59} +(-1.67029 - 8.80968i) q^{60} +(634.571 + 366.369i) q^{61} +1393.09 q^{62} +(117.542 + 486.036i) q^{63} +834.587 q^{64} +(1.80333 + 1.04115i) q^{65} +(225.455 + 78.7953i) q^{66} +(31.6068 + 54.7445i) q^{67} +(-553.572 - 958.815i) q^{68} +(-98.4453 + 281.678i) q^{69} +(4.34769 + 10.6943i) q^{70} +621.395i q^{71} +(550.677 + 82.5799i) q^{72} +95.2953i q^{73} +(-1323.63 - 764.196i) q^{74} +(-120.974 - 638.054i) q^{75} +(-718.401 + 414.769i) q^{76} +(-186.008 - 25.7321i) q^{77} +(-270.283 + 232.773i) q^{78} +(425.124 - 736.337i) q^{79} -0.949659 q^{80} +(-696.933 - 213.834i) q^{81} +2000.23i q^{82} +(70.1533 - 121.509i) q^{83} +(-1206.18 + 60.2479i) q^{84} +(6.06554 + 10.5058i) q^{85} +(366.761 - 211.750i) q^{86} +(605.676 - 114.835i) q^{87} +(-104.553 + 181.090i) q^{88} -1223.70 q^{89} +(-16.6439 - 2.49594i) q^{90} +(172.190 - 221.378i) q^{91} +(-624.098 - 360.323i) q^{92} +(526.838 - 1507.43i) q^{93} +(-1224.28 + 706.841i) q^{94} +(7.87159 - 4.54466i) q^{95} +(336.518 - 962.869i) q^{96} +(-671.481 - 387.680i) q^{97} +(1507.05 - 382.673i) q^{98} +(170.525 - 214.160i) 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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