LMFDB - Embedded newform 63.3.n.b.2.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,3,Mod(2,63)]

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, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("63.2");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	63.n (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:	$1.71662566547$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2.10
Character	$\chi$	$=$	63.2
Dual form			63.3.n.b.32.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.37724 - 1.37250i) q^{2} +(-2.35466 - 1.85892i) q^{3} +(1.76751 - 3.06142i) q^{4} -2.68504i q^{5} +(-8.14895 - 1.18734i) q^{6} +(6.00002 - 3.60552i) q^{7} +1.27635i q^{8} +(2.08880 + 8.75425i) q^{9} +O(q^{10})$	\(q+(2.37724 - 1.37250i) q^{2} +(-2.35466 - 1.85892i) q^{3} +(1.76751 - 3.06142i) q^{4} -2.68504i q^{5} +(-8.14895 - 1.18734i) q^{6} +(6.00002 - 3.60552i) q^{7} +1.27635i q^{8} +(2.08880 + 8.75425i) q^{9} +(-3.68521 - 6.38297i) q^{10} +8.29653i q^{11} +(-9.85284 + 3.92292i) q^{12} +(1.91540 + 3.31756i) q^{13} +(9.31492 - 16.8062i) q^{14} +(-4.99128 + 6.32233i) q^{15} +(8.82185 + 15.2799i) q^{16} +(-14.6266 + 8.44469i) q^{17} +(16.9808 + 17.9441i) q^{18} +(4.77461 - 8.26987i) q^{19} +(-8.22003 - 4.74584i) q^{20} +(-20.8304 - 2.66384i) q^{21} +(11.3870 + 19.7229i) q^{22} -24.4443i q^{23} +(2.37264 - 3.00537i) q^{24} +17.7906 q^{25} +(9.10671 + 5.25776i) q^{26} +(11.3551 - 24.4962i) q^{27} +(-0.432888 - 24.7414i) q^{28} +(-41.1044 - 23.7316i) q^{29} +(-3.18806 + 21.8802i) q^{30} +(-19.6261 + 33.9935i) q^{31} +(37.5219 + 21.6633i) q^{32} +(15.4226 - 19.5355i) q^{33} +(-23.1807 + 40.1501i) q^{34} +(-9.68094 - 16.1103i) q^{35} +(30.4925 + 9.07854i) q^{36} +(-23.3078 + 40.3703i) q^{37} -26.2126i q^{38} +(1.65700 - 11.3723i) q^{39} +3.42705 q^{40} +(-51.2064 + 29.5640i) q^{41} +(-53.1749 + 22.2571i) q^{42} +(28.0196 - 48.5314i) q^{43} +(25.3992 + 14.6642i) q^{44} +(23.5055 - 5.60851i) q^{45} +(-33.5498 - 58.1099i) q^{46} +(18.6551 - 10.7705i) q^{47} +(7.63174 - 52.3780i) q^{48} +(23.0005 - 43.2663i) q^{49} +(42.2925 - 24.4176i) q^{50} +(50.1387 + 7.30546i) q^{51} +13.5420 q^{52} +(-22.2206 + 12.8291i) q^{53} +(-6.62727 - 73.8181i) q^{54} +22.2765 q^{55} +(4.60191 + 7.65814i) q^{56} +(-26.6156 + 10.5971i) q^{57} -130.287 q^{58} +(40.1531 + 23.1824i) q^{59} +(10.5332 + 26.4552i) q^{60} +(-30.1743 - 52.2635i) q^{61} +107.748i q^{62} +(44.0965 + 44.9945i) q^{63} +48.3566 q^{64} +(8.90778 - 5.14291i) q^{65} +(9.85083 - 67.6081i) q^{66} +(32.0411 - 55.4968i) q^{67} +59.7044i q^{68} +(-45.4400 + 57.5578i) q^{69} +(-45.1253 - 25.0109i) q^{70} +49.6536i q^{71} +(-11.1735 + 2.66605i) q^{72} +(58.7013 + 101.674i) q^{73} +127.960i q^{74} +(-41.8907 - 33.0713i) q^{75} +(-16.8784 - 29.2342i) q^{76} +(29.9133 + 49.7794i) q^{77} +(-11.6694 - 29.3089i) q^{78} +(-20.2755 - 35.1182i) q^{79} +(41.0270 - 23.6870i) q^{80} +(-72.2738 + 36.5718i) q^{81} +(-81.1532 + 140.562i) q^{82} +(-64.7120 - 37.3615i) q^{83} +(-44.9731 + 59.0622i) q^{84} +(22.6743 + 39.2730i) q^{85} -153.828i q^{86} +(52.6714 + 132.290i) q^{87} -10.5893 q^{88} +(59.9634 + 34.6199i) q^{89} +(48.1805 - 45.5940i) q^{90} +(23.4539 + 12.9995i) q^{91} +(-74.8342 - 43.2056i) q^{92} +(109.404 - 43.5594i) q^{93} +(29.5651 - 51.2083i) q^{94} +(-22.2049 - 12.8200i) q^{95} +(-48.0807 - 120.760i) q^{96} +(-46.9641 + 81.3442i) q^{97} +(-4.70530 - 134.423i) q^{98} +(-72.6299 + 17.3298i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 6 q^{2} + 8 q^{3} + 12 q^{4} - 8 q^{6} + 3 q^{7} + 20 q^{9}+O(q^{10}) $ 22 * q - 6 * q^2 + 8 * q^3 + 12 * q^4 - 8 * q^6 + 3 * q^7 + 20 * q^9	\( 22 q - 6 q^{2} + 8 q^{3} + 12 q^{4} - 8 q^{6} + 3 q^{7} + 20 q^{9} + 25 q^{10} - 20 q^{12} - 18 q^{13} - 90 q^{14} + 53 q^{15} + 12 q^{16} + 6 q^{17} - 56 q^{18} + 3 q^{19} - 39 q^{20} - 2 q^{21} - 59 q^{22} + 15 q^{24} - 114 q^{25} - 3 q^{26} - 97 q^{27} + 34 q^{28} - 63 q^{29} - 20 q^{30} - 29 q^{31} + 246 q^{32} + 77 q^{33} - 99 q^{34} - 27 q^{35} + 76 q^{36} - 20 q^{37} + 200 q^{39} + 210 q^{40} - 51 q^{41} + 80 q^{42} + 65 q^{43} + 54 q^{44} + 71 q^{45} + 75 q^{46} + 261 q^{47} - 113 q^{48} - 131 q^{49} + 63 q^{50} - 78 q^{51} + 92 q^{52} - 63 q^{53} - 485 q^{54} - 100 q^{55} + 153 q^{56} + 224 q^{57} - 80 q^{58} - 102 q^{59} + 103 q^{60} + 78 q^{61} + 421 q^{63} + 106 q^{64} - 225 q^{65} - 401 q^{66} - 132 q^{67} - 297 q^{69} + 179 q^{70} - 66 q^{72} + q^{73} - 245 q^{75} + 233 q^{76} - 447 q^{77} - 440 q^{78} + 140 q^{79} + 96 q^{80} + 104 q^{81} - 157 q^{82} + 255 q^{83} - 316 q^{84} + 102 q^{85} - 136 q^{87} - 816 q^{88} - 720 q^{89} + 418 q^{90} - 70 q^{91} - 1239 q^{92} + 210 q^{93} + 261 q^{94} + 642 q^{95} + 539 q^{96} + 178 q^{97} + 483 q^{98} - 103 q^{99}+O(q^{100}) \) 22 * q - 6 * q^2 + 8 * q^3 + 12 * q^4 - 8 * q^6 + 3 * q^7 + 20 * q^9 + 25 * q^10 - 20 * q^12 - 18 * q^13 - 90 * q^14 + 53 * q^15 + 12 * q^16 + 6 * q^17 - 56 * q^18 + 3 * q^19 - 39 * q^20 - 2 * q^21 - 59 * q^22 + 15 * q^24 - 114 * q^25 - 3 * q^26 - 97 * q^27 + 34 * q^28 - 63 * q^29 - 20 * q^30 - 29 * q^31 + 246 * q^32 + 77 * q^33 - 99 * q^34 - 27 * q^35 + 76 * q^36 - 20 * q^37 + 200 * q^39 + 210 * q^40 - 51 * q^41 + 80 * q^42 + 65 * q^43 + 54 * q^44 + 71 * q^45 + 75 * q^46 + 261 * q^47 - 113 * q^48 - 131 * q^49 + 63 * q^50 - 78 * q^51 + 92 * q^52 - 63 * q^53 - 485 * q^54 - 100 * q^55 + 153 * q^56 + 224 * q^57 - 80 * q^58 - 102 * q^59 + 103 * q^60 + 78 * q^61 + 421 * q^63 + 106 * q^64 - 225 * q^65 - 401 * q^66 - 132 * q^67 - 297 * q^69 + 179 * q^70 - 66 * q^72 + q^73 - 245 * q^75 + 233 * q^76 - 447 * q^77 - 440 * q^78 + 140 * q^79 + 96 * q^80 + 104 * q^81 - 157 * q^82 + 255 * q^83 - 316 * q^84 + 102 * q^85 - 136 * q^87 - 816 * q^88 - 720 * q^89 + 418 * q^90 - 70 * q^91 - 1239 * q^92 + 210 * q^93 + 261 * q^94 + 642 * q^95 + 539 * q^96 + 178 * q^97 + 483 * q^98 - 103 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	2.37724	−	1.37250i	1.18862	−	0.686250i	0.230627	−	0.973042i	$-0.425922\pi$
$2$	2.37724	−	1.37250i	1.18862	−	0.686250i	0.957993	+	0.286792i	$0.0925889\pi$
$3$	−2.35466	−	1.85892i	−0.784885	−	0.619641i
$3$	−2.35466	−	1.85892i	−0.784885	−	0.619641i
$4$	1.76751	−	3.06142i	0.441878	−	0.765356i
$5$		−	2.68504i		−	0.537007i	−0.963279	−	0.268504i	$-0.913471\pi$
$5$		−	2.68504i		−	0.537007i	0.963279	−	0.268504i	$-0.0865291\pi$
$6$	−8.14895	−	1.18734i	−1.35816	−	0.197891i
$7$	6.00002	−	3.60552i	0.857146	−	0.515074i
$7$	6.00002	−	3.60552i	0.857146	−	0.515074i
$8$			1.27635i			0.159544i
$9$	2.08880	+	8.75425i	0.232089	+	0.972694i
$10$	−3.68521	−	6.38297i	−0.368521	−	0.638297i
$11$			8.29653i			0.754230i	0.926166	+	0.377115i	$0.123084\pi$
$11$			8.29653i			0.754230i	−0.926166	+	0.377115i	$0.876916\pi$
$12$	−9.85284	+	3.92292i	−0.821070	+	0.326910i
$13$	1.91540	+	3.31756i	0.147338	+	0.255197i	0.930243	−	0.366944i	$-0.119596\pi$
$13$	1.91540	+	3.31756i	0.147338	+	0.255197i	−0.782905	+	0.622142i	$0.786263\pi$
$14$	9.31492	−	16.8062i	0.665352	−	1.20044i
$15$	−4.99128	+	6.32233i	−0.332752	+	0.421489i
$16$	8.82185	+	15.2799i	0.551365	+	0.954993i
$17$	−14.6266	+	8.44469i	−0.860390	+	0.496747i	−0.864143	−	0.503246i	$-0.832139\pi$
$17$	−14.6266	+	8.44469i	−0.860390	+	0.496747i	0.00375254	+	0.999993i	$0.498806\pi$
$18$	16.9808	+	17.9441i	0.943378	+	0.996893i
$19$	4.77461	−	8.26987i	0.251295	−	0.435256i	−0.712587	−	0.701583i	$-0.752477\pi$
$19$	4.77461	−	8.26987i	0.251295	−	0.435256i	0.963883	+	0.266327i	$0.0858101\pi$
$20$	−8.22003	−	4.74584i	−0.411001	−	0.237292i
$21$	−20.8304	−	2.66384i	−0.991922	−	0.126849i
$22$	11.3870	+	19.7229i	0.517591	+	0.896493i
$23$		−	24.4443i		−	1.06279i	−0.847123	−	0.531397i	$-0.821667\pi$
$23$		−	24.4443i		−	1.06279i	0.847123	−	0.531397i	$-0.178333\pi$
$24$	2.37264	−	3.00537i	0.0988601	−	0.125224i
$25$	17.7906			0.711623
$26$	9.10671	+	5.25776i	0.350258	+	0.202222i
$27$	11.3551	−	24.4962i	0.420558	−	0.907266i
$28$	−0.432888	−	24.7414i	−0.0154603	−	0.883621i
$29$	−41.1044	−	23.7316i	−1.41739	−	0.818332i	−0.421323	−	0.906911i	$-0.638434\pi$
$29$	−41.1044	−	23.7316i	−1.41739	−	0.818332i	−0.996069	+	0.0885791i	$0.971767\pi$
$30$	−3.18806	+	21.8802i	−0.106269	+	0.729341i
$31$	−19.6261	+	33.9935i	−0.633101	+	1.09656i	0.353813	+	0.935316i	$0.384885\pi$
$31$	−19.6261	+	33.9935i	−0.633101	+	1.09656i	−0.986914	+	0.161247i	$0.948448\pi$
$32$	37.5219	+	21.6633i	1.17256	+	0.676977i
$33$	15.4226	−	19.5355i	0.467352	−	0.591984i
$34$	−23.1807	+	40.1501i	−0.681785	+	1.18089i
$35$	−9.68094	−	16.1103i	−0.276598	−	0.460293i
$36$	30.4925	+	9.07854i	0.847013	+	0.252182i
$37$	−23.3078	+	40.3703i	−0.629941	+	1.09109i	0.357622	+	0.933866i	$0.383588\pi$
$37$	−23.3078	+	40.3703i	−0.629941	+	1.09109i	−0.987563	+	0.157224i	$0.949746\pi$
$38$		−	26.2126i		−	0.689806i
$39$	1.65700	−	11.3723i	0.0424872	−	0.291597i
$40$	3.42705			0.0856763
$41$	−51.2064	+	29.5640i	−1.24894	+	0.721073i	−0.970897	−	0.239496i	$-0.923018\pi$
$41$	−51.2064	+	29.5640i	−1.24894	+	0.721073i	−0.278039	+	0.960570i	$0.589684\pi$
$42$	−53.1749	+	22.2571i	−1.26607	+	0.529931i
$43$	28.0196	−	48.5314i	0.651620	−	1.12864i	−0.331110	−	0.943592i	$-0.607423\pi$
$43$	28.0196	−	48.5314i	0.651620	−	1.12864i	0.982730	−	0.185046i	$-0.0592434\pi$
$44$	25.3992	+	14.6642i	0.577254	+	0.333278i
$45$	23.5055	−	5.60851i	0.522344	−	0.124634i
$46$	−33.5498	−	58.1099i	−0.729343	−	1.26326i
$47$	18.6551	−	10.7705i	0.396917	−	0.229160i	−0.288236	−	0.957559i	$-0.593069\pi$
$47$	18.6551	−	10.7705i	0.396917	−	0.229160i	0.685153	+	0.728399i	$0.259735\pi$
$48$	7.63174	−	52.3780i	0.158994	−	1.09121i
$49$	23.0005	−	43.2663i	0.469398	−	0.882986i
$50$	42.2925	−	24.4176i	0.845850	−	0.488352i
$51$	50.1387	+	7.30546i	0.983112	+	0.143244i
$52$	13.5420			0.260422
$53$	−22.2206	+	12.8291i	−0.419257	+	0.242058i	−0.694759	−	0.719242i	$-0.744489\pi$
$53$	−22.2206	+	12.8291i	−0.419257	+	0.242058i	0.275502	+	0.961300i	$0.411156\pi$
$54$	−6.62727	−	73.8181i	−0.122727	−	1.36700i
$55$	22.2765			0.405027
$56$	4.60191	+	7.65814i	0.0821769	+	0.136753i
$57$	−26.6156	+	10.5971i	−0.466941	+	0.185913i
$58$	−130.287			−2.24632
$59$	40.1531	+	23.1824i	0.680560	+	0.392922i	0.800066	−	0.599912i	$-0.204798\pi$
$59$	40.1531	+	23.1824i	0.680560	+	0.392922i	−0.119506	+	0.992834i	$0.538131\pi$
$60$	10.5332	+	26.4552i	0.175553	+	0.440920i
$61$	−30.1743	−	52.2635i	−0.494661	−	0.856778i	0.505320	−	0.862932i	$-0.331375\pi$
$61$	−30.1743	−	52.2635i	−0.494661	−	0.856778i	−0.999981	+	0.00615380i	$0.998041\pi$
$62$			107.748i			1.73786i
$63$	44.0965	+	44.9945i	0.699944	+	0.714198i
$64$	48.3566			0.755572
$65$	8.90778	−	5.14291i	0.137043	−	0.0791216i
$66$	9.85083	−	67.6081i	0.149255	−	1.02436i
$67$	32.0411	−	55.4968i	0.478225	−	0.828311i	−0.521463	−	0.853274i	$-0.674614\pi$
$67$	32.0411	−	55.4968i	0.478225	−	0.828311i	0.999688	+	0.0249632i	$0.00794684\pi$
$68$			59.7044i			0.878006i
$69$	−45.4400	+	57.5578i	−0.658551	+	0.834171i
$70$	−45.1253	−	25.0109i	−0.644646	−	0.357298i
$71$			49.6536i			0.699346i	0.936872	+	0.349673i	$0.113707\pi$
$71$			49.6536i			0.699346i	−0.936872	+	0.349673i	$0.886293\pi$
$72$	−11.1735	+	2.66605i	−0.155188	+	0.0370285i
$73$	58.7013	+	101.674i	0.804128	+	1.39279i	0.916878	+	0.399167i	$0.130701\pi$
$73$	58.7013	+	101.674i	0.804128	+	1.39279i	−0.112750	+	0.993623i	$0.535966\pi$
$74$			127.960i			1.72919i
$75$	−41.8907	−	33.0713i	−0.558543	−	0.440951i
$76$	−16.8784	−	29.2342i	−0.222084	−	0.384661i
$77$	29.9133	+	49.7794i	0.388484	+	0.646485i
$78$	−11.6694	−	29.3089i	−0.149608	−	0.375755i
$79$	−20.2755	−	35.1182i	−0.256652	−	0.444534i	0.708691	−	0.705519i	$-0.249286\pi$
$79$	−20.2755	−	35.1182i	−0.256652	−	0.444534i	−0.965343	+	0.260985i	$0.915953\pi$
$80$	41.0270	−	23.6870i	0.512838	−	0.296087i
$81$	−72.2738	+	36.5718i	−0.892269	+	0.451504i
$82$	−81.1532	+	140.562i	−0.989673	+	1.71416i
$83$	−64.7120	−	37.3615i	−0.779663	−	0.450139i	0.0566477	−	0.998394i	$-0.481959\pi$
$83$	−64.7120	−	37.3615i	−0.779663	−	0.450139i	−0.836311	+	0.548255i	$0.815292\pi$
$84$	−44.9731	+	59.0622i	−0.535394	+	0.703121i
$85$	22.6743	+	39.2730i	0.266756	+	0.462036i
$86$		−	153.828i		−	1.78870i
$87$	52.6714	+	132.290i	0.605418	+	1.52057i
$88$	−10.5893			−0.120333
$89$	59.9634	+	34.6199i	0.673747	+	0.388988i	0.797495	−	0.603326i	$-0.206158\pi$
$89$	59.9634	+	34.6199i	0.673747	+	0.388988i	−0.123748	+	0.992314i	$0.539492\pi$
$90$	48.1805	−	45.5940i	0.535338	−	0.506601i
$91$	23.4539	+	12.9995i	0.257736	+	0.142851i
$92$	−74.8342	−	43.2056i	−0.813416	−	0.469626i
$93$	109.404	−	43.5594i	1.17639	−	0.468381i
$94$	29.5651	−	51.2083i	0.314522	−	0.544769i
$95$	−22.2049	−	12.8200i	−0.233736	−	0.134947i
$96$	−48.0807	−	120.760i	−0.500841	−	1.25792i
$97$	−46.9641	+	81.3442i	−0.484166	+	0.838600i	−0.999835	−	0.0181878i	$-0.994210\pi$
$97$	−46.9641	+	81.3442i	−0.484166	+	0.838600i	0.515668	+	0.856788i	$0.327544\pi$
$98$	−4.70530	−	134.423i	−0.0480132	−	1.37166i
$99$	−72.6299	+	17.3298i	−0.733636	+	0.175049i
$100$	31.4451	−	54.4645i	0.314451	−	0.544645i
$101$		−	130.200i		−	1.28911i	−0.764558	−	0.644555i	$-0.777043\pi$
$101$		−	130.200i		−	1.28911i	0.764558	−	0.644555i	$-0.222957\pi$
$102$	129.219	−	51.4486i	1.26685	−	0.504398i
$103$	96.5836			0.937705			0.468853	−	0.883276i	$-0.344668\pi$
$103$	96.5836			0.937705			0.468853	+	0.883276i	$0.344668\pi$
$104$	−4.23438	+	2.44472i	−0.0407152	+	0.0235069i
$105$	−7.15250	+	55.9303i	−0.0681190	+	0.532669i
$106$	−35.2158	+	60.9956i	−0.332225	+	0.575430i
$107$	7.05070	+	4.07073i	0.0658944	+	0.0380442i	0.532585	−	0.846376i	$-0.321221\pi$
$107$	7.05070	+	4.07073i	0.0658944	+	0.0380442i	−0.466691	+	0.884421i	$0.654554\pi$
$108$	−54.9229	−	78.0600i	−0.508545	−	0.722778i
$109$	−91.4455	−	158.388i	−0.838950	−	1.45310i	−0.890774	−	0.454447i	$-0.849837\pi$
$109$	−91.4455	−	158.388i	−0.838950	−	1.45310i	0.0518242	−	0.998656i	$-0.483496\pi$
$110$	52.9566	−	30.5745i	0.481423	−	0.277950i
$111$	129.927	−	51.7308i	1.17052	−	0.466043i
$112$	108.023	+	59.8724i	0.964492	+	0.534575i
$113$	65.5463	−	37.8432i	0.580056	−	0.334896i	−0.181100	−	0.983465i	$-0.557966\pi$
$113$	65.5463	−	37.8432i	0.580056	−	0.334896i	0.761156	+	0.648569i	$0.224632\pi$
$114$	−48.7273	+	61.7217i	−0.427432	+	0.541418i
$115$	−65.6337			−0.570728
$116$	−145.305	+	83.8919i	−1.25263	+	0.723206i
$117$	−25.0419	+	23.6976i	−0.214033	+	0.202544i
$118$	127.271			1.07857
$119$	−57.3127	+	103.405i	−0.481619	+	0.868949i
$120$	−8.06952	−	6.37063i	−0.0672460	−	0.0530886i
$121$	52.1675			0.431137
$122$	−143.463	−	82.8286i	−1.17593	−	0.678923i
$123$	175.531	+	25.5757i	1.42708	+	0.207932i
$124$	69.3789	+	120.168i	0.559507	+	0.969095i
$125$		−	114.894i		−	0.919154i
$126$	166.583	+	46.4403i	1.32209	+	0.368574i
$127$	−38.6425			−0.304271			−0.152136	−	0.988360i	$-0.548615\pi$
$127$	−38.6425			−0.304271			−0.152136	+	0.988360i	$0.548615\pi$
$128$	−35.1323	+	20.2837i	−0.274471	+	0.158466i
$129$	−156.193	+	62.1884i	−1.21080	+	0.482081i
$130$	14.1173	−	24.4518i	0.108594	−	0.188091i
$131$		−	5.60734i		−	0.0428041i	−0.999771	−	0.0214021i	$-0.993187\pi$
$131$		−	5.60734i		−	0.0428041i	0.999771	−	0.0214021i	$-0.00681301\pi$
$132$	−32.5467	−	81.7444i	−0.246566	−	0.619276i
$133$	−1.16937	−	66.8343i	−0.00879224	−	0.502514i
$134$		−	175.906i		−	1.31273i
$135$	−65.7731	−	30.4888i	−0.487208	−	0.225843i
$136$	−10.7784	−	18.6687i	−0.0792530	−	0.137270i
$137$		−	119.913i		−	0.875274i	−0.899152	−	0.437637i	$-0.855815\pi$
$137$		−	119.913i		−	0.875274i	0.899152	−	0.437637i	$-0.144185\pi$
$138$	−29.0237	+	199.195i	−0.210317	+	1.44344i
$139$	−77.4562	−	134.158i	−0.557239	−	0.965166i	−0.997726	−	0.0674071i	$-0.978527\pi$
$139$	−77.4562	−	134.158i	−0.557239	−	0.965166i	0.440487	−	0.897759i	$-0.354806\pi$
$140$	−66.4315	+	1.16232i	−0.474511	+	0.00830228i
$141$	−63.9479	−	9.31753i	−0.453531	−	0.0660818i
$142$	68.1495	+	118.038i	0.479926	+	0.831256i
$143$	−27.5243	+	15.8912i	−0.192477	+	0.111127i
$144$	−115.337	+	109.145i	−0.800950	+	0.757954i
$145$	−63.7202	+	110.367i	−0.439450	+	0.761150i
$146$	279.094	+	161.135i	1.91160	+	1.10367i
$147$	−134.587	+	59.1211i	−0.915559	+	0.402184i
$148$	82.3938	+	142.710i	0.556715	+	0.964258i
$149$			190.151i			1.27618i	0.769961	+	0.638090i	$0.220275\pi$
$149$			190.151i			1.27618i	−0.769961	+	0.638090i	$0.779725\pi$
$150$	−144.975	−	21.1235i	−0.966498	−	0.140824i
$151$	57.8161			0.382888			0.191444	−	0.981504i	$-0.438683\pi$
$151$	57.8161			0.382888			0.191444	+	0.981504i	$0.438683\pi$
$152$	10.5553	+	6.09409i	0.0694425	+	0.0400927i
$153$	−104.479	−	110.406i	−0.682870	−	0.721607i
$154$	139.433	+	77.2816i	0.905411	+	0.501828i
$155$	91.2737	+	52.6969i	0.588862	+	0.339980i
$156$	−31.8866	−	25.1735i	−0.204402	−	0.161368i
$157$	−71.4749	+	123.798i	−0.455254	+	0.788523i	−0.998703	−	0.0509191i	$-0.983785\pi$
$157$	−71.4749	+	123.798i	−0.455254	+	0.788523i	0.543449	+	0.839442i	$0.317118\pi$
$158$	−96.3995	−	55.6563i	−0.610123	−	0.352255i
$159$	76.1702	+	11.0984i	0.479058	+	0.0698011i
$160$	58.1666	−	100.748i	0.363541	−	0.629672i
$161$	−88.1342	−	146.666i	−0.547417	−	0.910970i
$162$	−121.617	+	186.136i	−0.750724	+	1.14899i
$163$	36.5916	−	63.3785i	0.224488	−	0.388825i	−0.731677	−	0.681651i	$-0.761262\pi$
$163$	36.5916	−	63.3785i	0.224488	−	0.388825i	0.956166	+	0.292826i	$0.0945956\pi$
$164$			209.019i			1.27451i
$165$	−52.4534	−	41.4103i	−0.317900	−	0.250971i
$166$	−205.115			−1.23563
$167$	192.478	−	111.127i	1.15256	−	0.665433i	0.203053	−	0.979168i	$-0.434914\pi$
$167$	192.478	−	111.127i	1.15256	−	0.665433i	0.949510	+	0.313735i	$0.101580\pi$
$168$	3.39999	−	26.5869i	0.0202381	−	0.158255i
$169$	77.1625	−	133.649i	0.456583	−	0.790825i
$170$	107.805	+	62.2410i	0.634144	+	0.366123i
$171$	82.3697	+	24.5240i	0.481694	+	0.143415i
$172$	−99.0502	−	171.560i	−0.575873	−	0.997441i
$173$	210.928	−	121.779i	1.21923	−	0.703926i	0.254481	−	0.967078i	$-0.418095\pi$
$173$	210.928	−	121.779i	1.21923	−	0.703926i	0.964754	+	0.263152i	$0.0847622\pi$
$174$	306.780	+	242.193i	1.76310	+	1.39191i
$175$	106.744	−	64.1442i	0.609965	−	0.366538i
$176$	−126.770	+	73.1907i	−0.720285	+	0.415857i
$177$	−51.4523	−	129.228i	−0.290691	−	0.730102i
$178$	190.063			1.06777
$179$	−125.271	+	72.3251i	−0.699837	+	0.404051i	−0.807287	−	0.590159i	$-0.799065\pi$
$179$	−125.271	+	72.3251i	−0.699837	+	0.404051i	0.107450	+	0.994211i	$0.465732\pi$
$180$	24.3762	−	81.8733i	0.135423	−	0.454852i
$181$	16.9989			0.0939167			0.0469584	−	0.998897i	$-0.485047\pi$
$181$	16.9989			0.0939167			0.0469584	+	0.998897i	$0.485047\pi$
$182$	73.5974	−	1.28770i	0.404381	−	0.00707526i
$183$	−26.1037	+	179.154i	−0.142643	+	0.978985i
$184$	31.1995			0.169562
$185$	108.396	+	62.5823i	0.585923	+	0.338283i
$186$	200.294	−	253.708i	1.07685	−	1.36402i
$187$	−70.0617	−	121.350i	−0.374661	−	0.648933i
$188$		−	76.1482i		−	0.405044i
$189$	−20.1907	−	187.918i	−0.106829	−	0.994277i
$190$	−70.3818			−0.370431
$191$	−61.8161	+	35.6895i	−0.323644	+	0.186856i	−0.653016	−	0.757344i	$-0.726496\pi$
$191$	−61.8161	+	35.6895i	−0.323644	+	0.186856i	0.329372	+	0.944200i	$0.393163\pi$
$192$	−113.863	−	89.8912i	−0.593037	−	0.468183i
$193$	−164.087	+	284.206i	−0.850190	+	1.47257i	0.0308465	+	0.999524i	$0.490180\pi$
$193$	−164.087	+	284.206i	−0.850190	+	1.47257i	−0.881037	+	0.473048i	$0.843154\pi$
$194$			257.833i			1.32904i
$195$	−30.5350	−	4.44910i	−0.156590	−	0.0228159i
$196$	−91.8028	−	146.888i	−0.468382	−	0.749429i
$197$			171.288i			0.869481i	0.900556	+	0.434741i	$0.143160\pi$
$197$			171.288i			0.869481i	−0.900556	+	0.434741i	$0.856840\pi$
$198$	−148.874	+	140.882i	−0.751887	+	0.711524i
$199$	−139.848	−	242.224i	−0.702755	−	1.21721i	−0.967496	−	0.252888i	$-0.918620\pi$
$199$	−139.848	−	242.224i	−0.702755	−	1.21721i	0.264740	−	0.964320i	$-0.414714\pi$
$200$			22.7071i			0.113535i
$201$	−178.610	+	71.1139i	−0.888608	+	0.353801i
$202$	−178.700	−	309.517i	−0.884652	−	1.53226i
$203$	−332.192	+	5.81220i	−1.63641	+	0.0286315i
$204$	110.986	−	140.583i	0.544049	−	0.689134i
$205$	79.3804	+	137.491i	0.387222	+	0.670687i
$206$	229.603	−	132.561i	1.11458	−	0.643500i
$207$	213.991	−	51.0593i	1.03377	−	0.246663i
$208$	−33.7947	+	58.5341i	−0.162474	+	0.281414i
$209$	68.6113	+	39.6127i	0.328284	+	0.189535i
$210$	59.7611	+	142.776i	0.284577	+	0.679888i
$211$	−17.0206	−	29.4806i	−0.0806664	−	0.139718i	0.822870	−	0.568230i	$-0.192372\pi$
$211$	−17.0206	−	29.4806i	−0.0806664	−	0.139718i	−0.903536	+	0.428511i	$0.859038\pi$
$212$			90.7023i			0.427841i
$213$	92.3022	−	116.917i	0.433344	−	0.548906i
$214$	22.3483			0.104431
$215$	−130.309	−	75.2337i	−0.606087	−	0.349924i
$216$	31.2657	+	14.4931i	0.144749	+	0.0670975i
$217$	4.80671	+	274.724i	0.0221507	+	1.26601i
$218$	−434.776	−	251.018i	−1.99438	−	1.15146i
$219$	50.7822	−	348.528i	0.231882	−	1.59145i
$220$	39.3740	−	68.1977i	0.178973	−	0.309990i
$221$	−56.0316	−	32.3499i	−0.253537	−	0.146380i
$222$	237.868	−	301.302i	1.07148	−	1.35721i
$223$	−175.785	+	304.469i	−0.788274	+	1.36533i	0.138750	+	0.990327i	$0.455692\pi$
$223$	−175.785	+	304.469i	−0.788274	+	1.36533i	−0.927024	+	0.375003i	$0.877642\pi$
$224$	303.239	−	5.30563i	1.35375	−	0.0236858i
$225$	37.1611	+	155.743i	0.165160	+	0.692192i
$226$	103.880	−	179.925i	0.459644	−	0.796127i
$227$			233.614i			1.02914i	0.857450	+	0.514568i	$0.172048\pi$
$227$			233.614i			1.02914i	−0.857450	+	0.514568i	$0.827952\pi$
$228$	−14.6014	+	100.212i	−0.0640412	+	0.439527i
$229$	−50.8143			−0.221897			−0.110948	−	0.993826i	$-0.535389\pi$
$229$	−50.8143			−0.221897			−0.110948	+	0.993826i	$0.535389\pi$
$230$	−156.027	+	90.0823i	−0.678379	+	0.391662i
$231$	22.1006	−	172.820i	0.0956737	−	0.748138i
$232$	30.2899	−	52.4637i	0.130560	−	0.226136i
$233$	13.2624	+	7.65706i	0.0569203	+	0.0328629i	0.528190	−	0.849126i	$-0.322871\pi$
$233$	13.2624	+	7.65706i	0.0569203	+	0.0328629i	−0.471270	+	0.881989i	$0.656204\pi$
$234$	−27.0056	+	90.7049i	−0.115409	+	0.387628i
$235$	−28.9192	−	50.0896i	−0.123061	−	0.213147i
$236$	141.942	−	81.9503i	0.601450	−	0.347247i
$237$	−17.5402	+	120.382i	−0.0740095	+	0.507941i
$238$	5.67727	+	324.480i	0.0238541	+	1.36336i
$239$	214.220	−	123.680i	0.896316	−	0.517488i	0.0203128	−	0.999794i	$-0.493534\pi$
$239$	214.220	−	123.680i	0.896316	−	0.517488i	0.876003	+	0.482305i	$0.160200\pi$
$240$	−140.637	−	20.4915i	−0.585987	−	0.0853812i
$241$	−3.21213			−0.0133283			−0.00666417	−	0.999978i	$-0.502121\pi$
$241$	−3.21213			−0.0133283			−0.00666417	+	0.999978i	$0.502121\pi$
$242$	124.015	−	71.5999i	0.512458	−	0.295868i
$243$	238.164	+	48.2374i	0.980099	+	0.198508i
$244$	−213.334			−0.874320
$245$	−116.172	−	61.7572i	−0.474170	−	0.252070i
$246$	452.381	−	180.116i	1.83895	−	0.732180i
$247$	36.5811			0.148102
$248$	−43.3876	−	25.0499i	−0.174950	−	0.101008i
$249$	82.9224	+	208.268i	0.333021	+	0.836419i
$250$	−157.692	−	273.131i	−0.630769	−	1.09252i
$251$			91.5892i			0.364897i	0.983215	+	0.182449i	$0.0584023\pi$
$251$			91.5892i			0.364897i	−0.983215	+	0.182449i	$0.941598\pi$
$252$	215.688	−	55.4696i	0.855905	−	0.220117i
$253$	202.803			0.801592
$254$	−91.8624	+	53.0368i	−0.361663	+	0.208806i
$255$	19.6154	−	134.624i	0.0769232	−	0.527938i
$256$	−152.392	+	263.950i	−0.595281	+	1.03106i
$257$			116.231i			0.452262i	0.974097	+	0.226131i	$0.0726077\pi$
$257$			116.231i			0.452262i	−0.974097	+	0.226131i	$0.927392\pi$
$258$	−285.954	+	362.212i	−1.10835	+	1.40392i
$259$	5.70840	+	326.260i	0.0220402	+	1.25969i
$260$		−	36.3606i		−	0.139849i
$261$	121.894	−	409.409i	0.467025	−	1.56862i
$262$	−7.69608	−	13.3300i	−0.0293743	−	0.0508778i
$263$		−	41.0283i		−	0.156001i	−0.996953	−	0.0780005i	$-0.975146\pi$
$263$		−	41.0283i		−	0.156001i	0.996953	−	0.0780005i	$-0.0248536\pi$
$264$	24.9342	+	19.6847i	0.0944475	+	0.0745633i
$265$	34.4465	+	59.6632i	0.129987	+	0.225144i
$266$	−94.5100	−	157.276i	−0.355301	−	0.591264i
$267$	−76.8375	−	192.985i	−0.287781	−	0.722792i
$268$	−113.266	−	196.183i	−0.422635	−	0.732025i
$269$	320.521	−	185.053i	1.19153	−	0.687930i	0.232876	−	0.972506i	$-0.425186\pi$
$269$	320.521	−	185.053i	1.19153	−	0.687930i	0.958653	+	0.284577i	$0.0918531\pi$
$270$	−198.204	+	17.7945i	−0.734090	+	0.0659054i
$271$	−88.3608	+	153.045i	−0.326055	+	0.564743i	−0.981725	−	0.190304i	$-0.939053\pi$
$271$	−88.3608	+	153.045i	−0.326055	+	0.564743i	0.655671	+	0.755047i	$0.272386\pi$
$272$	−258.068	−	148.996i	−0.948779	−	0.547778i
$273$	−31.0610	−	74.2084i	−0.113776	−	0.271826i
$274$	−164.580	−	285.061i	−0.600657	−	1.04037i
$275$			147.600i			0.536728i
$276$	95.8930	+	240.845i	0.347438	+	0.872628i
$277$	197.918			0.714504			0.357252	−	0.934008i	$-0.383714\pi$
$277$	197.918			0.714504			0.357252	+	0.934008i	$0.383714\pi$
$278$	−368.264	−	212.617i	−1.32469	−	0.764811i
$279$	−338.582	−	100.806i	−1.21356	−	0.361313i
$280$	20.5624	−	12.3563i	0.0734371	−	0.0441296i
$281$	327.590	+	189.134i	1.16580	+	0.673076i	0.952688	−	0.303951i	$-0.0983059\pi$
$281$	327.590	+	189.134i	1.16580	+	0.673076i	0.213115	+	0.977027i	$0.431639\pi$
$282$	−164.808	+	65.6185i	−0.584425	+	0.232690i
$283$	−119.321	+	206.669i	−0.421628	+	0.730281i	−0.996099	−	0.0882441i	$-0.971874\pi$
$283$	−119.321	+	206.669i	−0.421628	+	0.730281i	0.574471	+	0.818525i	$0.305208\pi$
$284$	152.011	+	87.7633i	0.535248	+	0.309026i
$285$	28.4535	+	71.4639i	0.0998367	+	0.250750i
$286$	−43.6212	+	75.5542i	−0.152522	+	0.264175i
$287$	−200.646	+	362.010i	−0.699114	+	1.26136i
$288$	−111.270	+	373.726i	−0.386353	+	1.29766i
$289$	−1.87430	+	3.24638i	−0.00648546	+	0.0112331i
$290$			349.824i			1.20629i
$291$	261.797	−	104.235i	0.899646	−	0.358196i
$292$	415.022			1.42131
$293$	154.593	−	89.2544i	0.527622	−	0.304622i	−0.212426	−	0.977177i	$-0.568136\pi$
$293$	154.593	−	89.2544i	0.527622	−	0.304622i	0.740047	+	0.672555i	$0.234803\pi$
$294$	−238.802	+	325.266i	−0.812252	+	1.10635i
$295$	62.2455	−	107.812i	0.211002	−	0.365466i
$296$	−51.5268	−	29.7490i	−0.174077	−	0.100503i
$297$	203.233	+	94.2077i	0.684287	+	0.317198i
$298$	260.982	+	452.034i	0.875779	+	1.51689i
$299$	81.0954	−	46.8205i	0.271222	−	0.156590i
$300$	−175.288	+	69.7911i	−0.584292	+	0.232637i
$301$	−6.86239	−	392.215i	−0.0227986	−	1.30304i
$302$	137.443	−	79.3525i	0.455108	−	0.262757i
$303$	−242.032	+	306.576i	−0.798786	+	1.01180i
$304$	168.484			0.554222
$305$	−140.329	+	81.0191i	−0.460096	+	0.265637i
$306$	−399.904	−	119.064i	−1.30688	−	0.389097i
$307$	29.6153			0.0964667			0.0482333	−	0.998836i	$-0.484641\pi$
$307$	29.6153			0.0964667			0.0482333	+	0.998836i	$0.484641\pi$
$308$	205.268	−	3.59147i	0.666454	−	0.0116606i
$309$	−227.421	−	179.542i	−0.735991	−	0.581041i
$310$	289.306			0.933245
$311$	−179.860	−	103.842i	−0.578328	−	0.333898i	0.182141	−	0.983272i	$-0.441697\pi$
$311$	−179.860	−	103.842i	−0.578328	−	0.333898i	−0.760469	+	0.649375i	$0.775031\pi$
$312$	14.5151	+	2.11492i	0.0465226	+	0.00677858i
$313$	71.6556	+	124.111i	0.228932	+	0.396521i	0.957492	−	0.288461i	$-0.0931435\pi$
$313$	71.6556	+	124.111i	0.228932	+	0.396521i	−0.728560	+	0.684982i	$0.759810\pi$
$314$			392.397i			1.24967i
$315$	120.812	−	118.401i	0.383529	−	0.375875i
$316$	−143.349			−0.453636
$317$	63.4074	−	36.6083i	0.200023	−	0.115484i	−0.396643	−	0.917973i	$-0.629825\pi$
$317$	63.4074	−	36.6083i	0.200023	−	0.115484i	0.596666	+	0.802489i	$0.296492\pi$
$318$	196.307	−	78.1601i	0.617319	−	0.245787i
$319$	196.890	−	341.024i	0.617211	−	1.06904i
$320$		−	129.839i		−	0.405747i
$321$	−9.03481	−	22.6919i	−0.0281458	−	0.0706912i
$322$	−410.815	−	227.696i	−1.27582	−	0.707132i
$323$			161.281i			0.499321i
$324$	−15.7830	+	285.902i	−0.0487131	+	0.882413i
$325$	34.0760	+	59.0214i	0.104849	+	0.181604i
$326$		−	200.888i		−	0.616221i
$327$	−79.1091	+	542.940i	−0.241924	+	1.66037i
$328$	−37.7341	−	65.3574i	−0.115043	−	0.199260i
$329$	73.0977	−	131.885i	0.222182	−	0.400865i
$330$	−181.530	−	26.4498i	−0.550091	−	0.0801510i
$331$	−21.6068	−	37.4241i	−0.0652773	−	0.113064i	0.831540	−	0.555465i	$-0.187460\pi$
$331$	−21.6068	−	37.4241i	−0.0652773	−	0.113064i	−0.896817	+	0.442402i	$0.854127\pi$
$332$	−228.759	+	132.074i	−0.689032	+	0.397813i
$333$	−402.098	−	119.717i	−1.20750	−	0.359510i
$334$	305.044	−	528.352i	0.913306	−	1.58189i
$335$	−149.011	−	86.0315i	−0.444809	−	0.256810i
$336$	−143.059	−	341.786i	−0.425771	−	1.01722i
$337$	23.8185	+	41.2549i	0.0706781	+	0.122418i	0.899199	−	0.437541i	$-0.144150\pi$
$337$	23.8185	+	41.2549i	0.0706781	+	0.122418i	−0.828521	+	0.559959i	$0.810817\pi$
$338$		−	423.622i		−	1.25332i
$339$	−224.687	−	32.7380i	−0.662792	−	0.0965721i
$340$	160.309			0.471496
$341$	−282.028	−	162.829i	−0.827061	−	0.477504i
$342$	229.472	−	54.7530i	0.670970	−	0.160097i
$343$	−17.9938	−	342.528i	−0.0524601	−	0.998623i
$344$	61.9432	+	35.7629i	0.180067	+	0.103962i
$345$	154.545	+	122.008i	0.447956	+	0.353647i
$346$	334.284	−	578.996i	0.966138	−	1.67340i
$347$	278.468	+	160.774i	0.802502	+	0.463325i	0.844345	−	0.535799i	$-0.179990\pi$
$347$	278.468	+	160.774i	0.802502	+	0.463325i	−0.0418432	+	0.999124i	$0.513323\pi$
$348$	498.092	+	72.5745i	1.43130	+	0.208547i
$349$	−7.57794	+	13.1254i	−0.0217133	+	0.0376085i	−0.876678	−	0.481078i	$-0.840245\pi$
$349$	−7.57794	+	13.1254i	−0.0217133	+	0.0376085i	0.854965	+	0.518686i	$0.173579\pi$
$350$	165.718	−	298.992i	0.473480	−	0.854264i
$351$	103.017	−	9.24871i	0.293496	−	0.0263496i
$352$	−179.730	+	311.302i	−0.510597	+	0.884379i
$353$		−	351.929i		−	0.996965i	−0.866900	−	0.498482i	$-0.833891\pi$
$353$		−	351.929i		−	0.996965i	0.866900	−	0.498482i	$-0.166109\pi$
$354$	−299.680	−	236.588i	−0.846554	−	0.668327i
$355$	133.322			0.375554
$356$	211.972	−	122.382i	0.595428	−	0.343770i
$357$	327.173	−	136.943i	0.916452	−	0.383594i
$358$	−198.533	+	343.868i	−0.554560	+	0.960526i
$359$	−20.3965	−	11.7759i	−0.0568147	−	0.0328020i	0.471324	−	0.881960i	$-0.343776\pi$
$359$	−20.3965	−	11.7759i	−0.0568147	−	0.0328020i	−0.528138	+	0.849158i	$0.677110\pi$
$360$	7.15844	+	30.0013i	0.0198846	+	0.0833368i
$361$	134.906	+	233.664i	0.373701	+	0.647270i
$362$	40.4105	−	23.3310i	0.111631	−	0.0644504i
$363$	−122.837	−	96.9755i	−0.338393	−	0.267150i
$364$	81.2520	−	48.8257i	0.223220	−	0.134137i
$365$	272.997	−	157.615i	0.747938	−	0.431822i
$366$	183.835	+	461.720i	0.502280	+	1.26153i
$367$	−332.892			−0.907062			−0.453531	−	0.891240i	$-0.649836\pi$
$367$	−332.892			−0.907062			−0.453531	+	0.891240i	$0.649836\pi$
$368$	373.506	−	215.644i	1.01496	−	0.585988i
$369$	−365.771	−	386.520i	−0.991249	−	1.04748i
$370$	343.577			0.928587
$371$	−87.0688	+	157.092i	−0.234687	+	0.423427i
$372$	60.0194	−	411.924i	0.161342	−	1.10732i
$373$	−82.2838			−0.220600			−0.110300	−	0.993898i	$-0.535181\pi$
$373$	−82.2838			−0.220600			−0.110300	+	0.993898i	$0.535181\pi$
$374$	−333.107	−	192.319i	−0.890660	−	0.514223i
$375$	−213.580	+	270.536i	−0.569546	+	0.721430i
$376$	13.7470	+	23.8105i	0.0365611	+	0.0633257i
$377$		−	181.822i		−	0.482286i
$378$	−305.916	−	419.016i	−0.809302	−	1.10851i
$379$	−182.889			−0.482557			−0.241278	−	0.970456i	$-0.577567\pi$
$379$	−182.889			−0.482557			−0.241278	+	0.970456i	$0.577567\pi$
$380$	−78.4949	+	45.3190i	−0.206565	+	0.119261i
$381$	90.9897	+	71.8334i	0.238818	+	0.188539i
$382$	−97.9677	+	169.685i	−0.256460	+	0.444202i
$383$		−	128.598i		−	0.335765i	−0.985807	−	0.167883i	$-0.946307\pi$
$383$		−	128.598i		−	0.335765i	0.985807	−	0.167883i	$-0.0536930\pi$
$384$	120.430	+	17.5473i	0.313621	+	0.0456961i
$385$	133.659	−	80.3182i	0.347167	−	0.208619i
$386$			900.836i			2.33377i
$387$	483.384	+	143.918i	1.24905	+	0.371882i
$388$	166.019	+	287.554i	0.427885	+	0.741119i
$389$		−	474.365i		−	1.21945i	−0.792614	−	0.609724i	$-0.791280\pi$
$389$		−	474.365i		−	1.21945i	0.792614	−	0.609724i	$-0.208720\pi$
$390$	−78.6955	+	31.3327i	−0.201783	+	0.0803403i
$391$	206.424	+	357.537i	0.527940	+	0.914418i
$392$	55.2231	+	29.3568i	0.140875	+	0.0748897i
$393$	−10.4236	+	13.2034i	−0.0265232	+	0.0335963i
$394$	235.092	+	407.192i	0.596681	+	1.03348i
$395$	−94.2936	+	54.4405i	−0.238718	+	0.137824i
$396$	−75.3204	+	252.982i	−0.190203	+	0.638843i
$397$	123.800	−	214.429i	0.311840	−	0.540122i	−0.666921	−	0.745129i	$-0.732388\pi$
$397$	123.800	−	214.429i	0.311840	−	0.540122i	0.978761	+	0.205006i	$0.0657214\pi$
$398$	−664.906	−	383.884i	−1.67062	−	0.964532i
$399$	−121.486	+	159.546i	−0.304477	+	0.399864i
$400$	156.946	+	271.838i	0.392365	+	0.679595i
$401$			395.840i			0.987132i	0.869708	+	0.493566i	$0.164307\pi$
$401$			395.840i			0.987132i	−0.869708	+	0.493566i	$0.835693\pi$
$402$	−326.995	+	414.197i	−0.813421	+	1.03034i
$403$	−150.367			−0.373120
$404$	−398.598	−	230.130i	−0.986628	−	0.569630i
$405$	98.1967	+	194.058i	0.242461	+	0.479155i
$406$	−781.722	+	469.750i	−1.92542	+	1.15702i
$407$	−334.934	−	193.374i	−0.822933	−	0.475121i
$408$	−9.32434	+	63.9947i	−0.0228538	+	0.156850i
$409$	−236.650	+	409.890i	−0.578607	+	1.00218i	0.417033	+	0.908891i	$0.363070\pi$
$409$	−236.650	+	409.890i	−0.578607	+	1.00218i	−0.995639	+	0.0932846i	$0.970263\pi$
$410$	377.413	+	217.899i	0.920519	+	0.531462i
$411$	−222.908	+	282.353i	−0.542356	+	0.686990i
$412$	170.713	−	295.683i	0.414352	−	0.717678i
$413$	324.504	−	5.67768i	0.785723	−	0.0137474i
$414$	438.630	−	415.083i	1.05949	−	1.00262i
$415$	−100.317	+	173.754i	−0.241728	+	0.418685i
$416$			165.975i			0.398978i
$417$	−67.0070	+	459.881i	−0.160688	+	1.10283i
$418$	217.474			0.520272
$419$	−126.657	+	73.1253i	−0.302283	+	0.174523i	−0.643468	−	0.765473i	$-0.722505\pi$
$419$	−126.657	+	73.1253i	−0.302283	+	0.174523i	0.341185	+	0.939996i	$0.389172\pi$
$420$	158.584	+	120.754i	0.377581	+	0.287510i
$421$	−246.784	+	427.443i	−0.586186	+	1.01530i	0.408540	+	0.912740i	$0.366038\pi$
$421$	−246.784	+	427.443i	−0.586186	+	1.01530i	−0.994726	+	0.102564i	$0.967295\pi$
$422$	−80.9242	−	46.7216i	−0.191763	−	0.110715i
$423$	133.255	+	140.814i	0.315023	+	0.332893i
$424$	−16.3744	−	28.3613i	−0.0386189	−	0.0668900i
$425$	−260.216	+	150.236i	−0.612274	+	0.353497i
$426$	58.9558	−	404.625i	0.138394	−	0.949823i
$427$	−369.483	−	204.788i	−0.865301	−	0.479597i
$428$	24.9244	−	14.3901i	0.0582346	−	0.0336218i
$429$	94.3506	+	13.7474i	0.219932	+	0.0320451i
$430$	−413.033			−0.960542
$431$	−68.6770	+	39.6507i	−0.159343	+	0.0919969i	−0.577551	−	0.816354i	$-0.695992\pi$
$431$	−68.6770	+	39.6507i	−0.159343	+	0.0919969i	0.418208	+	0.908351i	$0.362658\pi$
$432$	474.471	−	42.5973i	1.09831	−	0.0986049i
$433$	707.731			1.63448			0.817241	−	0.576296i	$-0.195503\pi$
$433$	707.731			1.63448			0.817241	+	0.576296i	$0.195503\pi$
$434$	388.485	+	646.487i	0.895127	+	1.48960i
$435$	355.202	−	141.424i	0.816557	−	0.325114i
$436$	−646.525			−1.48285
$437$	−202.151	−	116.712i	−0.462588	−	0.267075i
$438$	−357.633	−	898.233i	−0.816514	−	2.05076i
$439$	3.27233	+	5.66785i	0.00745407	+	0.0129108i	0.869728	−	0.493531i	$-0.164294\pi$
$439$	3.27233	+	5.66785i	0.00745407	+	0.0129108i	−0.862274	+	0.506442i	$0.830961\pi$
$440$			28.4326i			0.0646196i
$441$	426.808	+	110.977i	0.967818	+	0.251649i
$442$	−177.601			−0.401812
$443$	−147.306	+	85.0470i	−0.332518	+	0.191980i	−0.656959	−	0.753927i	$-0.728157\pi$
$443$	−147.306	+	85.0470i	−0.332518	+	0.191980i	0.324440	+	0.945906i	$0.394824\pi$
$444$	71.2784	−	489.197i	0.160537	−	1.10180i
$445$	92.9557	−	161.004i	0.208889	−	0.361807i
$446$			965.060i			2.16381i
$447$	353.476	−	447.740i	0.790774	−	1.00166i
$448$	290.141	−	174.350i	0.647635	−	0.389175i
$449$		−	0.562541i		−	0.00125288i	−1.00000		0.000626438i	$-0.999801\pi$
$449$		−	0.562541i		−	0.00125288i	1.00000		0.000626438i	$-0.000199401\pi$
$450$	302.098	+	319.235i	0.671330	+	0.709412i
$451$	−245.279	−	424.835i	−0.543855	−	0.941985i
$452$		−	267.553i		−	0.591932i
$453$	−136.137	−	107.476i	−0.300523	−	0.237253i
$454$	320.635	+	555.356i	0.706245	+	1.22325i
$455$	34.9040	−	62.9747i	0.0767121	−	0.138406i
$456$	−13.5256	−	33.9709i	−0.0296613	−	0.0744976i
$457$	−368.848	−	638.864i	−0.807108	−	1.39795i	−0.914859	−	0.403774i	$-0.867698\pi$
$457$	−368.848	−	638.864i	−0.807108	−	1.39795i	0.107751	−	0.994178i	$-0.465635\pi$
$458$	−120.798	+	69.7426i	−0.263751	+	0.152276i
$459$	40.7762	+	454.187i	0.0888370	+	0.989514i
$460$	−116.008	+	200.933i	−0.252192	+	0.436810i
$461$	−18.3873	−	10.6159i	−0.0398857	−	0.0230280i	0.479925	−	0.877310i	$-0.340664\pi$
$461$	−18.3873	−	10.6159i	−0.0398857	−	0.0230280i	−0.519810	+	0.854282i	$0.673997\pi$
$462$	−184.657	−	441.167i	−0.399690	−	0.954907i
$463$	−256.649	−	444.530i	−0.554318	−	0.960108i	−0.997956	−	0.0639015i	$-0.979646\pi$
$463$	−256.649	−	444.530i	−0.554318	−	0.960108i	0.443638	−	0.896206i	$-0.353688\pi$
$464$		−	837.427i		−	1.80480i
$465$	−116.959	−	293.754i	−0.251524	−	0.631728i
$466$	42.0373			0.0902087
$467$	391.478	+	226.020i	0.838282	+	0.483982i	0.856680	−	0.515848i	$-0.172523\pi$
$467$	391.478	+	226.020i	0.838282	+	0.483982i	−0.0183979	+	0.999831i	$0.505857\pi$
$468$	28.2865	+	118.550i	0.0604412	+	0.253311i
$469$	−7.84730	−	448.507i	−0.0167320	−	0.956305i
$470$	−137.496	−	79.3833i	−0.292545	−	0.168901i
$471$	398.430	−	158.636i	0.845924	−	0.336806i
$472$	−29.5889	+	51.2494i	−0.0626883	+	0.108579i
$473$	402.643	+	232.466i	0.851253	+	0.491471i
$474$	123.527	+	310.251i	0.260605	+	0.654537i
$475$	84.9431	−	147.126i	0.178828	−	0.309739i
$476$	215.265	+	358.228i	0.452238	+	0.752580i
$477$	−158.724	−	167.727i	−0.332754	−	0.351630i
$478$	339.501	−	588.033i	0.710253	−	1.23019i
$479$			150.185i			0.313539i	0.987635	+	0.156770i	$0.0501080\pi$
$479$			150.185i			0.313539i	−0.987635	+	0.156770i	$0.949892\pi$
$480$	−324.244	+	129.098i	−0.675509	+	0.268955i
$481$	−178.575			−0.371258
$482$	−7.63600	+	4.40865i	−0.0158423	+	0.00914657i
$483$	−65.1156	+	509.183i	−0.134815	+	1.05421i
$484$	92.2068	−	159.707i	0.190510	−	0.329973i
$485$	218.412	+	126.100i	0.450334	+	0.260001i
$486$	632.379	−	212.208i	1.30119	−	0.436643i
$487$	−78.8441	−	136.562i	−0.161897	−	0.280415i	0.773652	−	0.633611i	$-0.218428\pi$
$487$	−78.8441	−	136.562i	−0.161897	−	0.280415i	−0.935549	+	0.353196i	$0.885095\pi$
$488$	66.7066	−	38.5131i	0.136694	−	0.0789202i
$489$	−203.976	+	81.2136i	−0.417130	+	0.166081i
$490$	−360.930	+	12.6339i	−0.736591	+	0.0257834i
$491$	−327.632	+	189.158i	−0.667274	+	0.385251i	−0.795043	−	0.606553i	$-0.792552\pi$
$491$	−327.632	+	189.158i	−0.667274	+	0.385251i	0.127769	+	0.991804i	$0.459218\pi$
$492$	388.551	−	492.168i	0.789737	−	1.00034i
$493$	801.625			1.62601
$494$	86.9620	−	50.2076i	0.176037	−	0.101635i
$495$	46.5312	+	195.014i	0.0940025	+	0.393968i
$496$	−692.555			−1.39628
$497$	179.027	+	297.922i	0.360215	+	0.599441i
$498$	482.975	+	381.293i	0.969828	+	0.765648i
$499$	−769.555			−1.54219			−0.771097	−	0.636717i	$-0.780292\pi$
$499$	−769.555			−1.54219			−0.771097	+	0.636717i	$0.780292\pi$
$500$	−351.740	−	203.077i	−0.703480	−	0.406154i
$501$	−659.796	−	96.1356i	−1.31696	−	0.191887i
$502$	125.706	+	217.729i	0.250411	+	0.433724i
$503$		−	313.393i		−	0.623047i	−0.950238	−	0.311524i	$-0.899161\pi$
$503$		−	313.393i		−	0.623047i	0.950238	−	0.311524i	$-0.100839\pi$
$504$	−57.4288	+	56.2826i	−0.113946	+	0.111672i
$505$	−349.592			−0.692261
$506$	482.111	−	278.347i	0.952788	−	0.550092i
$507$	−430.135	+	171.259i	−0.848393	+	0.337789i
$508$	−68.3011	+	118.301i	−0.134451	+	0.232876i
$509$		−	105.381i		−	0.207035i	−0.994628	−	0.103517i	$-0.966990\pi$
$509$		−	105.381i		−	0.207035i	0.994628	−	0.103517i	$-0.0330098\pi$
$510$	−138.141	−	346.956i	−0.270865	−	0.680307i
$511$	718.795	+	398.396i	1.40664	+	0.779640i
$512$			674.362i			1.31711i
$513$	−148.364	−	210.865i	−0.289209	−	0.411042i
$514$	159.527	+	276.310i	0.310365	+	0.537567i
$515$		−	259.331i		−	0.503554i
$516$	−85.6878	+	588.091i	−0.166062	+	1.13971i
$517$	89.3581	+	154.773i	0.172840	+	0.299367i
$518$	461.362	+	767.763i	0.890659	+	1.48217i
$519$	−723.040	−	105.351i	−1.39314	−	0.202988i
$520$	6.56416	+	11.3695i	0.0126234	+	0.0218643i
$521$	446.856	−	257.992i	0.857689	−	0.495187i	−0.00554870	−	0.999985i	$-0.501766\pi$
$521$	446.856	−	257.992i	0.857689	−	0.495187i	0.863238	+	0.504798i	$0.168433\pi$
$522$	−272.143	−	1140.56i	−0.521347	−	2.18498i
$523$	361.692	−	626.468i	0.691571	−	1.19784i	−0.279752	−	0.960072i	$-0.590252\pi$
$523$	361.692	−	626.468i	0.691571	−	1.19784i	0.971323	−	0.237764i	$-0.0764144\pi$
$524$	−17.1664	−	9.91105i	−0.0327604	−	0.0189142i
$525$	−370.584	−	47.3912i	−0.705875	−	0.0902690i
$526$	−56.3113	−	97.5341i	−0.107056	−	0.185426i
$527$		−	662.947i		−	1.25796i
$528$	434.556	+	63.3170i	0.823023	+	0.119918i
$529$	−68.5222			−0.129532
$530$	163.775	+	94.5558i	0.309010	+	0.178407i
$531$	−119.072	+	399.933i	−0.224242	+	0.753170i
$532$	−206.675	−	114.551i	−0.388487	−	0.215321i
$533$	−196.161	−	113.254i	−0.368032	−	0.212483i
$534$	−447.534	−	353.313i	−0.838078	−	0.661635i
$535$	10.9300	−	18.9314i	0.0204300	−	0.0353858i
$536$	70.8335	+	40.8957i	0.132152	+	0.0762980i
$537$	429.417	+	62.5681i	0.799658	+	0.116514i
$538$	507.971	−	879.831i	0.944183	−	1.63537i
$539$	358.961	+	190.825i	0.665975	+	0.354035i
$540$	−209.594	+	147.470i	−0.388137	+	0.273092i
$541$	−285.742	+	494.920i	−0.528174	+	0.914825i	0.471286	+	0.881980i	$0.343790\pi$
$541$	−285.742	+	494.920i	−0.528174	+	0.914825i	−0.999460	+	0.0328442i	$0.989543\pi$
$542$			485.101i			0.895020i
$543$	−40.0266	−	31.5997i	−0.0737139	−	0.0581947i
$544$	−731.759			−1.34514
$545$	−425.278	+	245.534i	−0.780327	+	0.450522i
$546$	−175.690	−	133.780i	−0.321777	−	0.245018i
$547$	441.232	−	764.235i	0.806639	−	1.39714i	−0.108540	−	0.994092i	$-0.534618\pi$
$547$	441.232	−	764.235i	0.806639	−	1.39714i	0.915179	−	0.403048i	$-0.132049\pi$
$548$	−367.103	−	211.947i	−0.669896	−	0.386765i
$549$	394.499	−	373.322i	0.718578	−	0.680003i
$550$	202.581	+	350.881i	0.368330	+	0.637966i
$551$	−392.515	+	226.619i	−0.712368	+	0.411286i
$552$	−73.4641	−	57.9975i	−0.133087	−	0.105068i
$553$	−248.273	−	137.606i	−0.448956	−	0.248836i
$554$	470.497	−	271.642i	0.849273	−	0.490328i
$555$	−138.899	−	348.859i	−0.250268	−	0.628575i
$556$	−547.620			−0.984927
$557$	−139.724	+	80.6697i	−0.250851	+	0.144829i	−0.620154	−	0.784480i	$-0.712930\pi$
$557$	−139.724	+	80.6697i	−0.250851	+	0.144829i	0.369303	+	0.929309i	$0.379597\pi$
$558$	−943.249	+	225.063i	−1.69041	+	0.403340i
$559$	214.675			0.384034
$560$	160.759	−	290.046i	0.287070	−	0.517939i
$561$	−60.6100	+	415.978i	−0.108039	+	0.741493i
$562$	1038.35			1.84759
$563$	423.928	+	244.755i	0.752980	+	0.434733i	0.826770	−	0.562541i	$-0.190176\pi$
$563$	423.928	+	244.755i	0.752980	+	0.434733i	−0.0737897	+	0.997274i	$0.523509\pi$
$564$	−141.554	+	179.303i	−0.250982	+	0.317913i
$565$	−101.610	−	175.994i	−0.179841	−	0.311494i
$566$			655.071i			1.15737i
$567$	−301.784	+	480.016i	−0.532247	+	0.846589i
$568$	−63.3754			−0.111576
$569$	−173.416	+	100.122i	−0.304774	+	0.175961i	−0.644585	−	0.764532i	$-0.722970\pi$
$569$	−173.416	+	100.122i	−0.304774	+	0.175961i	0.339812	+	0.940493i	$0.389637\pi$
$570$	165.725	+	130.834i	0.290745	+	0.229534i
$571$	44.2456	−	76.6356i	0.0774878	−	0.134213i	−0.824678	−	0.565603i	$-0.808643\pi$
$571$	44.2456	−	76.6356i	0.0774878	−	0.134213i	0.902165	+	0.431390i	$0.141977\pi$
$572$			112.351i			0.196418i
$573$	211.900	+	30.8748i	0.369807	+	0.0538828i
$574$	19.8755	+	1135.97i	0.0346264	+	1.97904i
$575$		−	434.878i		−	0.756309i
$576$	101.007	+	423.326i	0.175360	+	0.734940i
$577$	−91.3150	−	158.162i	−0.158258	−	0.274111i	0.775982	−	0.630755i	$-0.217255\pi$
$577$	−91.3150	−	158.162i	−0.158258	−	0.274111i	−0.934241	+	0.356643i	$0.883921\pi$
$578$			10.2899i			0.0178026i
$579$	914.686	−	364.184i	1.57977	−	0.628987i
$580$	225.253	+	390.149i	0.388367	+	0.672671i
$581$	−522.981	+	9.15034i	−0.900140	+	0.0157493i
$582$	479.292	−	607.108i	0.823526	−	1.04314i
$583$	−106.437	−	184.354i	−0.182568	−	0.316216i
$584$	−129.771	+	74.9236i	−0.222211	+	0.128294i
$585$	63.6289	+	67.2384i	0.108767	+	0.114937i
$586$	245.003	−	424.358i	0.418094	−	0.724161i
$587$	540.196	+	311.882i	0.920266	+	0.531316i	0.883720	−	0.468016i	$-0.155031\pi$
$587$	540.196	+	311.882i	0.920266	+	0.531316i	0.0365462	+	0.999332i	$0.488364\pi$
$588$	−56.8898	+	516.525i	−0.0967514	+	0.878445i
$589$	187.414	+	324.611i	0.318191	+	0.551123i
$590$		−	341.728i		−	0.579200i
$591$	318.411	−	403.324i	0.538766	−	0.682443i
$592$	−822.472			−1.38931
$593$	−940.956	−	543.261i	−1.58677	−	0.916124i	−0.993834	−	0.110876i	$-0.964634\pi$
$593$	−940.956	−	543.261i	−1.58677	−	0.916124i	−0.592939	−	0.805247i	$-0.702032\pi$
$594$	612.434	−	54.9834i	1.03103	−	0.0925647i
$595$	277.646	+	153.887i	0.466632	+	0.258633i
$596$	582.132	+	336.094i	0.976732	+	0.563917i
$597$	−120.982	+	830.322i	−0.202650	+	1.39082i
$598$	128.522	−	222.607i	0.214920	−	0.372252i
$599$	−952.684	−	550.032i	−1.59046	−	0.918251i	−0.993228	−	0.116180i	$-0.962935\pi$
$599$	−952.684	−	550.032i	−1.59046	−	0.918251i	−0.597229	−	0.802071i	$-0.703732\pi$
$600$	42.2107	−	53.4673i	0.0703511	−	0.0891121i
$601$	−359.808	+	623.206i	−0.598683	+	1.03695i	0.394333	+	0.918968i	$0.370976\pi$
$601$	−359.808	+	623.206i	−0.598683	+	1.03695i	−0.993016	+	0.117982i	$0.962358\pi$
$602$	−554.629	−	922.970i	−0.921310	−	1.53317i
$603$	552.761	+	164.574i	0.916684	+	0.272925i
$604$	102.191	−	176.999i	0.169190	−	0.293045i
$605$		−	140.072i		−	0.231523i
$606$	−154.592	+	1060.99i	−0.255103	+	1.75082i
$607$	894.431			1.47353			0.736764	−	0.676150i	$-0.236353\pi$
$607$	894.431			1.47353			0.736764	+	0.676150i	$0.236353\pi$
$608$	358.305	−	206.867i	0.589317	−	0.340242i
$609$	793.002	+	603.834i	1.30214	+	0.991516i
$610$	−222.398	+	385.204i	−0.364586	+	0.631482i
$611$	71.4638	+	41.2597i	0.116962	+	0.0675281i
$612$	−522.668	+	124.711i	−0.854032	+	0.203776i
$613$	187.261	+	324.346i	0.305483	+	0.529113i	0.977369	−	0.211542i	$-0.0678486\pi$
$613$	187.261	+	324.346i	0.305483	+	0.529113i	−0.671885	+	0.740655i	$0.734515\pi$
$614$	70.4026	−	40.6470i	0.114662	−	0.0662003i
$615$	68.6716	−	471.306i	0.111661	−	0.766351i
$616$	−63.5360	+	38.1799i	−0.103143	+	0.0619803i
$617$	−753.256	+	434.892i	−1.22084	+	0.704850i	−0.965096	−	0.261896i	$-0.915652\pi$
$617$	−753.256	+	434.892i	−1.22084	+	0.704850i	−0.255740	+	0.966746i	$0.582319\pi$
$618$	−787.056	−	114.678i	−1.27355	−	0.185563i
$619$	16.9707			0.0274163			0.0137082	−	0.999906i	$-0.495636\pi$
$619$	16.9707			0.0274163			0.0137082	+	0.999906i	$0.495636\pi$
$620$	322.655	−	186.285i	0.520411	−	0.300459i
$621$	−598.791	−	277.566i	−0.964237	−	0.446967i
$622$	−570.094			−0.916550
$623$	484.605	−	8.47889i	0.777856	−	0.0136098i
$624$	188.385	−	75.0059i	0.301899	−	0.120202i
$625$	136.270			0.218031
$626$	340.685	+	196.695i	0.544225	+	0.314209i
$627$	−87.9188	−	220.817i	−0.140221	−	0.352181i
$628$	252.666	+	437.630i	0.402334	+	0.696863i
$629$		−	787.310i		−	1.25168i
$630$	124.694	−	447.281i	0.197927	−	0.709969i
$631$	638.650			1.01212			0.506062	−	0.862497i	$-0.331101\pi$
$631$	638.650			1.01212			0.506062	+	0.862497i	$0.331101\pi$
$632$	44.8232	−	25.8787i	0.0709228	−	0.0409473i
$633$	−14.7244	+	101.057i	−0.0232614	+	0.159647i
$634$	100.490	−	174.053i	0.158501	−	0.274532i
$635$			103.756i			0.163396i
$636$	168.609	−	213.573i	0.265108	−	0.335806i
$637$	187.594	−	6.56649i	0.294496	−	0.0103085i
$638$		−	1080.93i		−	1.69424i
$639$	−434.680	+	103.717i	−0.680250	+	0.162311i
$640$	54.4623	+	94.3316i	0.0850974	+	0.147393i
$641$			639.194i			0.997182i	0.866837	+	0.498591i	$0.166149\pi$
$641$			639.194i			0.997182i	−0.866837	+	0.498591i	$0.833851\pi$
$642$	−52.6225	−	41.5438i	−0.0819665	−	0.0647099i
$643$	362.332	+	627.578i	0.563503	+	0.976015i	0.997187	+	0.0749505i	$0.0238799\pi$
$643$	362.332	+	627.578i	0.563503	+	0.976015i	−0.433685	+	0.901065i	$0.642787\pi$
$644$	−604.785	+	10.5816i	−0.939108	+	0.0164311i
$645$	166.978	+	419.383i	0.258881	+	0.650207i
$646$	221.358	+	383.403i	0.342659	+	0.593502i
$647$	−220.212	+	127.140i	−0.340359	+	0.196506i	−0.660431	−	0.750887i	$-0.729626\pi$
$647$	−220.212	+	127.140i	−0.340359	+	0.196506i	0.320072	+	0.947393i	$0.396293\pi$
$648$	−46.6785	−	92.2468i	−0.0720348	−	0.142356i
$649$	−192.333	+	333.131i	−0.296353	+	0.513299i
$650$	162.014	+	93.5387i	0.249252	+	0.143906i
$651$	499.373	−	655.815i	0.767085	−	1.00740i
$652$	−129.352	−	224.045i	−0.198393	−	0.343627i
$653$			817.624i			1.25210i	0.779781	+	0.626052i	$0.215330\pi$
$653$			817.624i			1.25210i	−0.779781	+	0.626052i	$0.784670\pi$
$654$	557.124	+	1399.28i	0.851872	+	2.13957i
$655$	−15.0559			−0.0229861
$656$	−903.470	−	521.618i	−1.37724	−	0.795150i
$657$	−767.461	+	726.263i	−1.16813	+	1.10542i
$658$	−7.24090	−	413.848i	−0.0110044	−	0.628948i
$659$	−771.870	−	445.640i	−1.17128	−	0.676236i	−0.217295	−	0.976106i	$-0.569723\pi$
$659$	−771.870	−	445.640i	−1.17128	−	0.676236i	−0.953980	+	0.299870i	$0.903057\pi$
$660$	−219.487	+	87.3889i	−0.332555	+	0.132407i
$661$	246.530	−	427.003i	0.372965	−	0.645995i	−0.617055	−	0.786920i	$-0.711674\pi$
$661$	246.530	−	427.003i	0.372965	−	0.645995i	0.990020	+	0.140925i	$0.0450077\pi$
$662$	−102.729	−	59.3106i	−0.155180	−	0.0895931i
$663$	71.7992	+	180.331i	0.108294	+	0.271993i
$664$	47.6865	−	82.5954i	0.0718169	−	0.124391i
$665$	−179.453	+	3.13979i	−0.269853	+	0.00472149i
$666$	−1120.19	+	267.283i	−1.68197	+	0.401326i
$667$	−580.102	+	1004.77i	−0.869718	+	1.50640i
$668$		−	785.675i		−	1.17616i
$669$	979.897	−	390.148i	1.46472	−	0.583181i
$670$	−472.313			−0.704945
$671$	433.606	−	250.342i	0.646208	−	0.373088i
$672$	−723.887	−	551.206i	−1.07721	−	0.820247i
$673$	−442.879	+	767.089i	−0.658067	+	1.13981i	0.323048	+	0.946383i	$0.395292\pi$
$673$	−442.879	+	767.089i	−0.658067	+	1.13981i	−0.981115	+	0.193423i	$0.938041\pi$
$674$	113.245	+	65.3819i	0.168019	+	0.0970057i
$675$	202.013	−	435.801i	0.299279	−	0.645631i
$676$	−272.772	−	472.454i	−0.403508	−	0.698897i
$677$	887.269	−	512.265i	1.31059	−	0.756669i	0.328396	−	0.944540i	$-0.393492\pi$
$677$	887.269	−	512.265i	1.31059	−	0.756669i	0.982194	+	0.187871i	$0.0601586\pi$
$678$	−579.067	+	230.556i	−0.854081	+	0.340054i
$679$	11.5022	+	657.397i	0.0169398	+	0.968184i
$680$	−50.1262	+	28.9404i	−0.0737150	+	0.0425594i
$681$	434.270	−	550.080i	0.637695	−	0.807754i
$682$	−893.931			−1.31075
$683$	263.216	−	151.968i	0.385382	−	0.222500i	−0.294775	−	0.955567i	$-0.595245\pi$
$683$	263.216	−	151.968i	0.385382	−	0.222500i	0.680157	+	0.733066i	$0.261911\pi$
$684$	220.668	−	208.822i	0.322614	−	0.305295i
$685$	−321.969			−0.470028
$686$	−512.895	−	789.574i	−0.747660	−	1.15098i
$687$	119.650	+	94.4599i	0.174163	+	0.137496i
$688$	988.740			1.43712
$689$	−85.1226	−	49.1456i	−0.123545	−	0.0713288i
$690$	534.846	+	77.9297i	0.775139	+	0.112942i
$691$	308.726	+	534.729i	0.446781	+	0.773848i	0.998174	−	0.0603976i	$-0.0192369\pi$
$691$	308.726	+	534.729i	0.446781	+	0.773848i	−0.551393	+	0.834246i	$0.685904\pi$
$692$		−	860.985i		−	1.24420i
$693$	−373.298	+	365.848i	−0.538670	+	0.527919i
$694$	882.648			1.27183
$695$	−360.219	+	207.973i	−0.518301	+	0.299241i
$696$	−168.848	+	67.2272i	−0.242598	+	0.0965908i
$697$	499.318	−	864.844i	0.716382	−	1.24081i
$698$			41.6029i			0.0596030i
$699$	−16.9945	−	42.6836i	−0.0243126	−	0.0610638i
$700$	−7.70133	−	440.164i	−0.0110019	−	0.628806i
$701$			793.809i			1.13239i	0.824270	+	0.566197i	$0.191586\pi$
$701$			793.809i			1.13239i	−0.824270	+	0.566197i	$0.808414\pi$
$702$	232.202	−	163.377i	0.330773	−	0.232731i
$703$	222.572	+	385.505i	0.316603	+	0.548372i
$704$			401.192i			0.569875i
$705$	−25.0179	+	171.702i	−0.0354864	+	0.243550i
$706$	−483.022	−	836.619i	−0.684167	−	1.18501i
$707$	−469.438	−	781.203i	−0.663986	−	1.10496i
$708$	−486.564	−	70.8948i	−0.687238	−	0.100134i
$709$	−434.595	−	752.740i	−0.612969	−	1.06169i	−0.990737	−	0.135793i	$-0.956642\pi$
$709$	−434.595	−	752.740i	−0.612969	−	1.06169i	0.377769	−	0.925900i	$-0.376691\pi$
$710$	316.937	−	182.984i	0.446391	−	0.257724i
$711$	265.082	−	250.852i	0.372830	−	0.352816i
$712$	−44.1872	+	76.5345i	−0.0620607	+	0.107492i
$713$	830.945	+	479.747i	1.16542	+	0.672856i
$714$	589.815	−	774.592i	0.826072	−	1.08486i
$715$	42.6683	+	73.9037i	0.0596759	+	0.103362i
$716$			511.343i			0.714166i
$717$	−734.324	−	106.995i	−1.02416	−	0.149226i
$718$	−64.6498			−0.0900415
$719$	1146.88	+	662.152i	1.59510	+	0.920934i	0.992412	+	0.122961i	$0.0392390\pi$
$719$	1146.88	+	662.152i	1.59510	+	0.920934i	0.602693	+	0.797973i	$0.294094\pi$
$720$	293.059	+	309.683i	0.407027	+	0.430116i
$721$	579.504	−	348.234i	0.803750	−	0.482987i
$722$	641.409	+	370.317i	0.888378	+	0.512905i
$723$	7.56346	+	5.97110i	0.0104612	+	0.00825879i
$724$	30.0458	−	52.0409i	0.0414998	−	0.0718797i
$725$	−731.271	−	422.199i	−1.00865	−	0.582344i
$726$	−425.111	−	61.9408i	−0.585552	−	0.0853178i
$727$	413.149	−	715.595i	0.568293	−	0.984313i	−0.428442	−	0.903569i	$-0.640937\pi$
$727$	413.149	−	715.595i	0.568293	−	0.984313i	0.996735	−	0.0807432i	$-0.0257294\pi$
$728$	−16.5919	+	29.9355i	−0.0227911	+	0.0411202i
$729$	−471.125	−	556.311i	−0.646262	−	0.763116i
$730$	432.654	−	749.378i	0.592676	−	1.02655i
$731$			946.469i			1.29476i
$732$	502.328	+	396.572i	0.686241	+	0.541765i
$733$	−61.7846			−0.0842900			−0.0421450	−	0.999112i	$-0.513419\pi$
$733$	−61.7846			−0.0842900			−0.0421450	+	0.999112i	$0.513419\pi$
$734$	−791.364	+	456.894i	−1.07815	+	0.622472i
$735$	158.742	+	361.371i	0.215976	+	0.491661i
$736$	529.543	−	917.195i	0.719487	−	1.24619i
$737$	460.431	+	265.830i	0.624737	+	0.360692i
$738$	−1400.02	−	416.830i	−1.89705	−	0.564810i
$739$	659.374	+	1142.07i	0.892252	+	1.54543i	0.837169	+	0.546945i	$0.184209\pi$
$739$	659.374	+	1142.07i	0.892252	+	1.54543i	0.0550835	+	0.998482i	$0.482457\pi$
$740$	383.182	−	221.230i	0.517813	−	0.298960i
$741$	−86.1359	−	68.0015i	−0.116243	−	0.0917699i
$742$	8.62484	+	492.946i	0.0116238	+	0.664348i
$743$	1171.10	−	676.136i	1.57618	−	0.910008i	0.580795	−	0.814050i	$-0.302742\pi$
$743$	1171.10	−	676.136i	1.57618	−	0.910008i	0.995385	−	0.0959588i	$-0.0305917\pi$
$744$	55.5971	+	139.638i	0.0747273	+	0.187686i
$745$	510.562			0.685318
$746$	−195.608	+	112.935i	−0.262210	+	0.151387i
$747$	191.901	−	644.546i	0.256896	−	0.862846i
$748$	−495.340			−0.662219
$749$	56.9814	−	0.996976i	0.0760767	−	0.00133108i
$750$	−136.419	+	936.268i	−0.181892	+	1.24836i
$751$	857.117			1.14130			0.570650	−	0.821193i	$-0.306691\pi$
$751$	857.117			1.14130			0.570650	+	0.821193i	$0.306691\pi$
$752$	329.145	+	190.032i	0.437693	+	0.252702i
$753$	170.257	−	215.661i	0.226105	−	0.286402i
$754$	−249.550	−	432.234i	−0.330969	−	0.573255i
$755$		−	155.238i		−	0.205613i
$756$	−610.985	−	270.336i	−0.808181	−	0.357588i
$757$	−903.868			−1.19401			−0.597007	−	0.802236i	$-0.703643\pi$
$757$	−903.868			−1.19401			−0.597007	+	0.802236i	$0.703643\pi$
$758$	−434.771	+	251.015i	−0.573576	+	0.331154i
$759$	−477.530	−	376.995i	−0.629157	−	0.496699i
$760$	16.3628	−	28.3413i	0.0215300	−	0.0372911i
$761$		−	685.917i		−	0.901336i	−0.892692	−	0.450668i	$-0.851186\pi$
$761$		−	685.917i		−	0.901336i	0.892692	−	0.450668i	$-0.148814\pi$
$762$	314.896	+	45.8819i	0.413249	+	0.0602124i
$763$	−1119.75	−	620.625i	−1.46756	−	0.813401i
$764$			252.327i			0.330271i
$765$	−296.444	+	280.530i	−0.387508	+	0.366706i
$766$	−176.501	−	305.709i	−0.230419	−	0.399097i
$767$			177.614i			0.231569i
$768$	849.494	−	338.227i	1.10611	−	0.440400i
$769$	−700.427	−	1213.17i	−0.910828	−	1.57760i	−0.812897	−	0.582407i	$-0.802111\pi$
$769$	−700.427	−	1213.17i	−0.910828	−	1.57760i	−0.0979303	−	0.995193i	$-0.531222\pi$
$770$	207.504	−	374.383i	0.269485	−	0.486212i
$771$	216.065	−	273.685i	0.280240	−	0.354973i
$772$	580.051	+	1004.68i	0.751361	+	1.30140i
$773$	−884.334	+	510.570i	−1.14403	+	0.660505i	−0.947425	−	0.319978i	$-0.896324\pi$
$773$	−884.334	+	510.570i	−1.14403	+	0.660505i	−0.196603	+	0.980483i	$0.562991\pi$
$774$	1346.65	−	321.316i	1.73985	−	0.415137i
$775$	−349.160	+	604.764i	−0.450530	+	0.780340i
$776$	−103.824	−	59.9428i	−0.133794	−	0.0772458i
$777$	593.050	−	778.840i	0.763257	−	1.00237i
$778$	−651.067	−	1127.68i	−0.836846	−	1.44946i
$779$			564.627i			0.724810i
$780$	−67.5916	+	85.6167i	−0.0866559	+	0.109765i
$781$	−411.952			−0.527468
$782$	981.440	+	566.635i	1.25504	+	0.724597i
$783$	−1048.08	+	737.425i	−1.33854	+	0.941795i
$784$	864.012	−	30.2436i	1.10206	−	0.0385761i
$785$	332.402	+	191.913i	0.423443	+	0.244475i
$786$	−6.65784	+	45.6940i	−0.00847053	+	0.0581348i
$787$	−56.8686	+	98.4993i	−0.0722600	+	0.125158i	−0.899891	−	0.436114i	$-0.856354\pi$
$787$	−56.8686	+	98.4993i	−0.0722600	+	0.125158i	0.827631	+	0.561272i	$0.189688\pi$
$788$	524.384	+	302.753i	0.665462	+	0.384205i
$789$	−76.2684	+	96.6075i	−0.0966647	+	0.122443i
$790$	−149.439	+	258.836i	−0.189163	+	0.327641i
$791$	256.835	−	463.388i	0.324697	−	0.585826i
$792$	−22.1190	−	92.7014i	−0.0279280	−	0.117047i
$793$	115.592	−	200.211i	0.145765	−	0.252472i
$794$		−	679.664i		−	0.856000i
$795$	29.7995	−	204.520i	0.0374837	−	0.257257i
$796$	−988.735			−1.24213
$797$	20.9995	−	12.1241i	0.0263482	−	0.0152121i	−0.486768	−	0.873531i	$-0.661824\pi$
$797$	20.9995	−	12.1241i	0.0263482	−	0.0152121i	0.513116	+	0.858319i	$0.328491\pi$
$798$	−69.8262	+	546.018i	−0.0875015	+	0.684234i
$799$	−181.908	+	315.073i	−0.227669	+	0.394334i
$800$	667.536	+	385.402i	0.834420	+	0.481753i
$801$	−177.819	+	597.249i	−0.221997	+	0.745629i
$802$	543.290	+	941.006i	0.677419	+	1.17332i
$803$	−843.539	+	487.018i	−1.05048	+	0.606498i
$804$	−97.9860	+	672.496i	−0.121873	+	0.836438i
$805$	−393.804	+	236.643i	−0.489197	+	0.293967i
$806$	−357.459	+	206.379i	−0.443498	+	0.256054i
$807$	−1098.72	−	160.088i	−1.36148	−	0.198375i
$808$	166.181			0.205670
$809$	−828.117	+	478.113i	−1.02363	+	0.590993i	−0.915153	−	0.403106i	$-0.867931\pi$
$809$	−828.117	+	478.113i	−1.02363	+	0.590993i	−0.108477	+	0.994099i	$0.534597\pi$
$810$	499.781	+	326.547i	0.617014	+	0.403144i
$811$	−1352.18			−1.66730			−0.833650	−	0.552293i	$-0.813753\pi$
$811$	−1352.18			−1.66730			−0.833650	+	0.552293i	$0.813753\pi$
$812$	−569.360	+	1027.25i	−0.701182	+	1.26509i
$813$	492.559	−	196.113i	0.605854	−	0.241222i
$814$	−1061.62			−1.30421
$815$	−170.174	−	98.2498i	−0.208802	−	0.120552i
$816$	330.690	+	830.562i	0.405257	+	1.01785i
$817$	−267.566	−	463.438i	−0.327498	−	0.567243i
$818$			1299.21i			1.58828i
$819$	−64.8099	+	232.475i	−0.0791329	+	0.283852i
$820$	561.224			0.684419
$821$	−626.856	+	361.915i	−0.763527	+	0.440823i	−0.830561	−	0.556928i	$-0.811980\pi$
$821$	−626.856	+	361.915i	−0.763527	+	0.440823i	0.0670336	+	0.997751i	$0.478647\pi$
$822$	−142.377	+	977.162i	−0.173208	+	1.18876i
$823$	47.1543	−	81.6737i	0.0572957	−	0.0992390i	−0.835955	−	0.548798i	$-0.815086\pi$
$823$	47.1543	−	81.6737i	0.0572957	−	0.0992390i	0.893251	+	0.449559i	$0.148419\pi$
$824$			123.275i			0.149605i
$825$	274.378	−	347.548i	0.332579	−	0.421270i
$826$	763.630	−	458.879i	0.924492	−	0.555543i
$827$		−	838.852i		−	1.01433i	−0.861849	−	0.507166i	$-0.830693\pi$
$827$		−	838.852i		−	1.01433i	0.861849	−	0.507166i	$-0.169307\pi$
$828$	221.918	−	745.366i	0.268017	−	0.900200i
$829$	−249.593	−	432.307i	−0.301077	−	0.521481i	0.675303	−	0.737540i	$-0.264013\pi$
$829$	−249.593	−	432.307i	−0.301077	−	0.521481i	−0.976380	+	0.216060i	$0.930679\pi$
$830$			550.740i			0.663543i
$831$	−466.028	−	367.914i	−0.560803	−	0.442736i
$832$	92.6220	+	160.426i	0.111325	+	0.192820i
$833$	28.9507	+	827.073i	0.0347547	+	0.992885i
$834$	471.896	+	1185.22i	0.565822	+	1.42112i
$835$	−298.381	−	516.810i	−0.357342	−	0.618934i
$836$	242.543	−	140.032i	0.290123	−	0.167502i
$837$	609.854	+	866.763i	0.728618	+	1.03556i
$838$	−200.729	+	347.673i	−0.239533	+	0.414884i
$839$	419.220	+	242.037i	0.499667	+	0.288483i	0.728576	−	0.684965i	$-0.240183\pi$
$839$	419.220	+	242.037i	0.499667	+	0.288483i	−0.228909	+	0.973448i	$0.573516\pi$
$840$	−71.3867	−	9.12911i	−0.0849842	−	0.0108680i
$841$	705.879	+	1222.62i	0.839333	+	1.45377i
$842$			1354.85i			1.60908i
$843$	−419.776	−	1054.31i	−0.497955	−	1.25067i
$844$	−120.337			−0.142579
$845$	−358.853	−	207.184i	−0.424679	−	0.245188i
$846$	510.046	+	151.856i	0.602891	+	0.179499i
$847$	313.006	−	188.091i	0.369547	−	0.222067i
$848$	−392.054	−	226.352i	−0.462328	−	0.266925i
$849$	665.142	−	264.827i	0.783442	−	0.311929i
$850$	−412.398	+	714.294i	−0.485174	+	0.840346i
$851$	986.823	+	569.743i	1.15960	+	0.669498i
$852$	−194.787	−	489.228i	−0.228623	−	0.574212i
$853$	83.1713	−	144.057i	0.0975045	−	0.168883i	−0.813147	−	0.582059i	$-0.802247\pi$
$853$	83.1713	−	144.057i	0.0975045	−	0.168883i	0.910651	+	0.413176i	$0.135581\pi$
$854$	−1159.42	+	20.2858i	−1.35764	+	0.0237539i
$855$	65.8478	−	221.166i	0.0770150	−	0.258673i
$856$	−5.19568	+	8.99918i	−0.00606972	+	0.0105131i
$857$		−	784.284i		−	0.915150i	−0.889171	−	0.457575i	$-0.848718\pi$
$857$		−	784.284i		−	0.915150i	0.889171	−	0.457575i	$-0.151282\pi$
$858$	243.162	−	96.8155i	0.283406	−	0.112839i
$859$	−1421.63			−1.65498			−0.827492	−	0.561478i	$-0.810233\pi$
$859$	−1421.63			−1.65498			−0.827492	+	0.561478i	$0.810233\pi$
$860$	−460.644	+	265.953i	−0.535633	+	0.309248i
$861$	1145.40	−	479.424i	1.33031	−	0.556822i
$862$	−108.841	+	188.518i	−0.126266	+	0.218699i
$863$	710.341	+	410.116i	0.823107	+	0.475221i	0.851487	−	0.524376i	$-0.175702\pi$
$863$	710.341	+	410.116i	0.823107	+	0.475221i	−0.0283800	+	0.999597i	$0.509035\pi$
$864$	956.731	−	673.154i	1.10733	−	0.779114i
$865$	−326.981	−	566.348i	−0.378013	−	0.654738i
$866$	1682.45	−	971.360i	1.94278	−	1.12166i
$867$	10.4481	−	4.15993i	0.0120509	−	0.00479807i
$868$	849.542	+	470.863i	0.978735	+	0.542469i
$869$	291.359	−	168.216i	0.335281	−	0.193575i
$870$	650.296	−	823.715i	0.747467	−	0.946799i
$871$	245.486			0.281843
$872$	202.159	−	116.717i	0.231834	−	0.133849i
$873$	−810.207	−	241.223i	−0.928072	−	0.276316i
$874$	−640.748			−0.733122
$875$	−414.253	−	689.368i	−0.473432	−	0.787849i
$876$	−977.233	−	771.493i	−1.11556	−	0.880700i
$877$	679.973			0.775340			0.387670	−	0.921798i	$-0.373280\pi$
$877$	679.973			0.775340			0.387670	+	0.921798i	$0.373280\pi$
$878$	15.5583	+	8.98256i	0.0177201	+	0.0102307i
$879$	−529.931	−	77.2135i	−0.602879	−	0.0878425i
$880$	196.520	+	340.382i	0.223318	+	0.386798i
$881$		−	169.140i		−	0.191986i	−0.995382	−	0.0959932i	$-0.969397\pi$
$881$		−	169.140i		−	0.191986i	0.995382	−	0.0959932i	$-0.0306027\pi$
$882$	1166.94	−	321.974i	1.32306	−	0.365050i
$883$	−118.699			−0.134427			−0.0672135	−	0.997739i	$-0.521411\pi$
$883$	−118.699			−0.134427			−0.0672135	+	0.997739i	$0.521411\pi$
$884$	−198.073	+	114.358i	−0.224065	+	0.129364i
$885$	−346.982	+	138.151i	−0.392070	+	0.156103i
$886$	−233.454	+	404.354i	−0.263492	+	0.456382i
$887$		−	924.427i		−	1.04219i	−0.853497	−	0.521097i	$-0.825523\pi$
$887$		−	924.427i		−	1.04219i	0.853497	−	0.521097i	$-0.174477\pi$
$888$	66.0267	+	165.833i	0.0743544	+	0.186749i
$889$	−231.856	+	139.326i	−0.260805	+	0.156722i
$890$		−	510.327i		−	0.573401i
$891$	−303.419	−	599.622i	−0.340538	−	0.672976i
$892$	621.405	+	1076.30i	0.696642	+	1.20662i
$893$		−	205.700i		−	0.230348i
$894$	225.774	−	1549.53i	0.252544	−	1.73326i
$895$	194.196	+	336.357i	0.216978	+	0.375817i
$896$	−137.662	+	248.373i	−0.153640	+	0.277202i
$897$	−277.987	−	40.5042i	−0.309908	−	0.0451551i
$898$	−0.772088	−	1.33730i	−0.000859786	−	0.00148919i
$899$	1613.44	−	931.520i	1.79471	−	1.03617i
$900$	542.479	+	161.513i	0.602754	+	0.179458i
$901$	216.675	−	375.293i	0.240483	−	0.416529i
$902$	−1166.17	−	673.290i	−1.29288	−	0.746442i
$903$	−712.939	+	936.288i	−0.789523	+	1.03686i
$904$	48.3012	+	83.6602i	0.0534306	+	0.0925445i
$905$		−	45.6427i		−	0.0504340i
$906$	−471.140	−	68.6475i	−0.520022	−	0.0757699i
$907$	−412.168			−0.454430			−0.227215	−	0.973845i	$-0.572962\pi$
$907$	−412.168			−0.454430			−0.227215	+	0.973845i	$0.572962\pi$
$908$	715.191	+	412.916i	0.787655	+	0.454753i
$909$	1139.80	−	271.963i	1.25391	−	0.299189i
$910$	−3.45751	−	197.612i	−0.00379947	−	0.217156i
$911$	−487.377	−	281.387i	−0.534991	−	0.308877i	0.208056	−	0.978117i	$-0.433287\pi$
$911$	−487.377	−	281.387i	−0.534991	−	0.308877i	−0.743046	+	0.669240i	$0.766620\pi$
$912$	−396.721	−	313.198i	−0.435001	−	0.343419i
$913$	309.971	−	536.886i	0.339508	−	0.588046i
$914$	−1753.68	−	1012.49i	−1.91869	−	1.10776i
$915$	481.036	+	70.0893i	0.525722	+	0.0766003i
$916$	−89.8149	+	155.564i	−0.0980513	+	0.169830i
$917$	−20.2173	−	33.6442i	−0.0220473	−	0.0366894i
$918$	720.306	+	1023.75i	0.784647	+	1.11519i
$919$	230.981	−	400.070i	0.251339	−	0.435332i	−0.712556	−	0.701616i	$-0.752462\pi$
$919$	230.981	−	400.070i	0.251339	−	0.435332i	0.963895	+	0.266284i	$0.0857957\pi$
$920$		−	83.7717i		−	0.0910562i
$921$	−69.7338	−	55.0525i	−0.0757153	−	0.0597747i
$922$	−58.2813			−0.0632119
$923$	−164.729	+	95.1062i	−0.178471	+	0.103040i
$924$	−490.011	−	373.121i	−0.530315	−	0.403810i
$925$	−414.660	+	718.212i	−0.448281	+	0.776445i
$926$	−1220.23	−	704.503i	−1.31775	−	0.760802i
$927$	201.744	+	845.517i	0.217631	+	0.912101i
$928$	−1028.21	−	1780.91i	−1.10798	−	1.91908i
$929$	−464.074	+	267.933i	−0.499541	+	0.288410i	−0.728524	−	0.685020i	$-0.759793\pi$
$929$	−464.074	+	267.933i	−0.499541	+	0.288410i	0.228983	+	0.973430i	$0.426460\pi$
$930$	−681.216	−	537.798i	−0.732490	−	0.578277i
$931$	−247.988	−	396.791i	−0.266368	−	0.426199i
$932$	46.8830	−	27.0679i	0.0503037	−	0.0290428i
$933$	230.474	+	578.859i	0.247024	+	0.620427i
$934$	1240.85			1.32853
$935$	−325.830	+	188.118i	−0.348481	+	0.201196i
$936$	−30.2465	−	31.9623i	−0.0323146	−	0.0341477i
$937$	−449.946			−0.480199			−0.240099	−	0.970748i	$-0.577180\pi$
$937$	−449.946			−0.480199			−0.240099	+	0.970748i	$0.577180\pi$
$938$	−634.231	−	1055.44i	−0.676152	−	1.12520i
$939$	61.9889	−	425.441i	0.0660159	−	0.453079i
$940$	−204.461			−0.217511
$941$	1477.01	+	852.751i	1.56962	+	0.906218i	0.996213	+	0.0869448i	$0.0277104\pi$
$941$	1477.01	+	852.751i	1.56962	+	0.906218i	0.573403	+	0.819273i	$0.305623\pi$
$942$	729.437	−	923.960i	0.774349	−	0.980850i
$943$	722.671	+	1251.70i	0.766353	+	1.32736i
$944$			818.046i			0.866574i
$945$	−504.568	+	54.2126i	−0.533934	+	0.0573679i
$946$	1276.24			1.34909
$947$	1519.45	−	877.258i	1.60449	−	0.926354i	0.613920	−	0.789368i	$-0.289592\pi$
$947$	1519.45	−	877.258i	1.60449	−	0.926354i	0.990573	−	0.136986i	$-0.0437415\pi$
$948$	337.537	+	266.475i	0.356052	+	0.281092i
$949$	−224.873	+	389.491i	−0.236957	+	0.410422i
$950$		−	466.338i		−	0.490882i
$951$	−217.355	−	31.6696i	−0.228554	−	0.0333014i
$952$	−131.981	−	73.1512i	−0.138636	−	0.0768395i
$953$		−	946.668i		−	0.993356i	−0.867935	−	0.496678i	$-0.834553\pi$
$953$		−	946.668i		−	0.993356i	0.867935	−	0.496678i	$-0.165447\pi$
$954$	−607.530	−	180.880i	−0.636824	−	0.189602i
$955$	95.8276	+	165.978i	0.100343	+	0.173799i
$956$		−	874.422i		−	0.914667i
$957$	−1097.55	+	436.990i	−1.14686	+	0.456625i
$958$	206.129	+	357.026i	0.215166	+	0.372679i
$959$	−432.347	−	719.478i	−0.450831	−	0.750238i
$960$	−241.361	+	305.726i	−0.251418	+	0.318465i
$961$	−289.871	−	502.070i	−0.301634	−	0.522446i
$962$	−424.515	+	245.094i	−0.441284	+	0.254776i
$963$	−20.9086	+	70.2266i	−0.0217119	+	0.0729248i
$964$	−5.67748	+	9.83369i	−0.00588950	+	0.0102009i
$965$	763.104	+	440.579i	0.790782	+	0.456558i
$966$	544.058	+	1299.82i	0.563207	+	1.34557i
$967$	269.581	+	466.929i	0.278781	+	0.482863i	0.971082	−	0.238746i	$-0.0767362\pi$
$967$	269.581	+	466.929i	0.278781	+	0.482863i	−0.692301	+	0.721609i	$0.743403\pi$
$968$			66.5841i			0.0687853i
$969$	299.808	−	379.760i	0.309400	−	0.391909i
$970$	692.291			0.713702
$971$	1150.15	+	664.038i	1.18450	+	0.683870i	0.957051	−	0.289921i	$-0.0936289\pi$
$971$	1150.15	+	664.038i	1.18450	+	0.683870i	0.227447	+	0.973790i	$0.426962\pi$
$972$	568.633	−	643.861i	0.585014	−	0.662408i
$973$	−948.448	−	525.682i	−0.974767	−	0.540269i
$974$	−374.863	−	216.427i	−0.384869	−	0.222204i
$975$	29.4790	−	202.320i	0.0302349	−	0.207507i
$976$	532.387	−	922.121i	0.545478	−	0.944796i
$977$	90.4855	+	52.2418i	0.0926157	+	0.0534717i	0.545593	−	0.838051i	$-0.316305\pi$
$977$	90.4855	+	52.2418i	0.0926157	+	0.0534717i	−0.452977	+	0.891522i	$0.649638\pi$
$978$	−373.435	+	473.022i	−0.381836	+	0.483662i
$979$	−287.225	+	497.489i	−0.293386	+	0.508160i
$980$	−394.400	+	246.494i	−0.402449	+	0.251524i
$981$	1195.56	−	1131.38i	1.21871	−	1.15329i
$982$	−519.239	+	899.349i	−0.528757	+	0.915834i
$983$			966.334i			0.983046i	0.870865	+	0.491523i	$0.163560\pi$
$983$			966.334i			0.983046i	−0.870865	+	0.491523i	$0.836440\pi$
$984$	−32.6436	+	224.039i	−0.0331744	+	0.227682i
$985$	459.914			0.466917
$986$	1905.65	−	1100.23i	1.93271	−	1.11585i
$987$	−417.283	+	174.660i	−0.422780	+	0.176960i
$988$	64.6576	−	111.990i	0.0654429	−	0.113350i
$989$	−1186.32	−	684.920i	−1.19951	−	0.692537i
$990$	378.273	+	399.731i	0.382093	+	0.403768i
$991$	−408.045	−	706.755i	−0.411751	−	0.713174i	0.583330	−	0.812235i	$-0.301749\pi$
$991$	−408.045	−	706.755i	−0.411751	−	0.713174i	−0.995081	+	0.0990613i	$0.968416\pi$
$992$	−1472.82	+	850.333i	−1.48470	+	0.857190i
$993$	−18.6919	+	128.286i	−0.0188237	+	0.129190i
$994$	834.488	+	462.519i	0.839525	+	0.465311i
$995$	−650.381	+	375.498i	−0.653649	+	0.377384i
$996$	784.164	+	114.257i	0.787313	+	0.114715i
$997$	88.5286			0.0887950			0.0443975	−	0.999014i	$-0.485863\pi$
$997$	88.5286			0.0887950			0.0443975	+	0.999014i	$0.485863\pi$
$998$	−1829.42	+	1056.21i	−1.83308	+	1.05833i
$999$	724.257	+	1029.36i	0.724982	+	1.03039i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.3.n.b.2.10	yes	22
3.2	odd	2		189.3.n.b.170.2		22
7.2	even	3		441.3.r.g.344.2		22
7.3	odd	6		441.3.j.f.263.10		22
7.4	even	3		63.3.j.b.11.10	✓	22
7.5	odd	6		441.3.r.f.344.2		22
7.6	odd	2		441.3.n.f.128.10		22
9.4	even	3		189.3.j.b.44.10		22
9.5	odd	6		63.3.j.b.23.2	yes	22
21.11	odd	6		189.3.j.b.116.2		22
63.4	even	3		189.3.n.b.179.2		22
63.5	even	6		441.3.r.f.50.2		22
63.23	odd	6		441.3.r.g.50.2		22
63.32	odd	6	inner	63.3.n.b.32.10	yes	22
63.41	even	6		441.3.j.f.275.2		22
63.59	even	6		441.3.n.f.410.10		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.j.b.11.10	✓	22	7.4	even	3
63.3.j.b.23.2	yes	22	9.5	odd	6
63.3.n.b.2.10	yes	22	1.1	even	1	trivial
63.3.n.b.32.10	yes	22	63.32	odd	6	inner
189.3.j.b.44.10		22	9.4	even	3
189.3.j.b.116.2		22	21.11	odd	6
189.3.n.b.170.2		22	3.2	odd	2
189.3.n.b.179.2		22	63.4	even	3
441.3.j.f.263.10		22	7.3	odd	6
441.3.j.f.275.2		22	63.41	even	6
441.3.n.f.128.10		22	7.6	odd	2
441.3.n.f.410.10		22	63.59	even	6
441.3.r.f.50.2		22	63.5	even	6
441.3.r.f.344.2		22	7.5	odd	6
441.3.r.g.50.2		22	63.23	odd	6
441.3.r.g.344.2		22	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(2.37724 - 1.37250i) q^{2} +(-2.35466 - 1.85892i) q^{3} +(1.76751 - 3.06142i) q^{4} -2.68504i q^{5} +(-8.14895 - 1.18734i) q^{6} +(6.00002 - 3.60552i) q^{7} +1.27635i q^{8} +(2.08880 + 8.75425i) q^{9} +O(q^{10})\)	\(q+(2.37724 - 1.37250i) q^{2} +(-2.35466 - 1.85892i) q^{3} +(1.76751 - 3.06142i) q^{4} -2.68504i q^{5} +(-8.14895 - 1.18734i) q^{6} +(6.00002 - 3.60552i) q^{7} +1.27635i q^{8} +(2.08880 + 8.75425i) q^{9} +(-3.68521 - 6.38297i) q^{10} +8.29653i q^{11} +(-9.85284 + 3.92292i) q^{12} +(1.91540 + 3.31756i) q^{13} +(9.31492 - 16.8062i) q^{14} +(-4.99128 + 6.32233i) q^{15} +(8.82185 + 15.2799i) q^{16} +(-14.6266 + 8.44469i) q^{17} +(16.9808 + 17.9441i) q^{18} +(4.77461 - 8.26987i) q^{19} +(-8.22003 - 4.74584i) q^{20} +(-20.8304 - 2.66384i) q^{21} +(11.3870 + 19.7229i) q^{22} -24.4443i q^{23} +(2.37264 - 3.00537i) q^{24} +17.7906 q^{25} +(9.10671 + 5.25776i) q^{26} +(11.3551 - 24.4962i) q^{27} +(-0.432888 - 24.7414i) q^{28} +(-41.1044 - 23.7316i) q^{29} +(-3.18806 + 21.8802i) q^{30} +(-19.6261 + 33.9935i) q^{31} +(37.5219 + 21.6633i) q^{32} +(15.4226 - 19.5355i) q^{33} +(-23.1807 + 40.1501i) q^{34} +(-9.68094 - 16.1103i) q^{35} +(30.4925 + 9.07854i) q^{36} +(-23.3078 + 40.3703i) q^{37} -26.2126i q^{38} +(1.65700 - 11.3723i) q^{39} +3.42705 q^{40} +(-51.2064 + 29.5640i) q^{41} +(-53.1749 + 22.2571i) q^{42} +(28.0196 - 48.5314i) q^{43} +(25.3992 + 14.6642i) q^{44} +(23.5055 - 5.60851i) q^{45} +(-33.5498 - 58.1099i) q^{46} +(18.6551 - 10.7705i) q^{47} +(7.63174 - 52.3780i) q^{48} +(23.0005 - 43.2663i) q^{49} +(42.2925 - 24.4176i) q^{50} +(50.1387 + 7.30546i) q^{51} +13.5420 q^{52} +(-22.2206 + 12.8291i) q^{53} +(-6.62727 - 73.8181i) q^{54} +22.2765 q^{55} +(4.60191 + 7.65814i) q^{56} +(-26.6156 + 10.5971i) q^{57} -130.287 q^{58} +(40.1531 + 23.1824i) q^{59} +(10.5332 + 26.4552i) q^{60} +(-30.1743 - 52.2635i) q^{61} +107.748i q^{62} +(44.0965 + 44.9945i) q^{63} +48.3566 q^{64} +(8.90778 - 5.14291i) q^{65} +(9.85083 - 67.6081i) q^{66} +(32.0411 - 55.4968i) q^{67} +59.7044i q^{68} +(-45.4400 + 57.5578i) q^{69} +(-45.1253 - 25.0109i) q^{70} +49.6536i q^{71} +(-11.1735 + 2.66605i) q^{72} +(58.7013 + 101.674i) q^{73} +127.960i q^{74} +(-41.8907 - 33.0713i) q^{75} +(-16.8784 - 29.2342i) q^{76} +(29.9133 + 49.7794i) q^{77} +(-11.6694 - 29.3089i) q^{78} +(-20.2755 - 35.1182i) q^{79} +(41.0270 - 23.6870i) q^{80} +(-72.2738 + 36.5718i) q^{81} +(-81.1532 + 140.562i) q^{82} +(-64.7120 - 37.3615i) q^{83} +(-44.9731 + 59.0622i) q^{84} +(22.6743 + 39.2730i) q^{85} -153.828i q^{86} +(52.6714 + 132.290i) q^{87} -10.5893 q^{88} +(59.9634 + 34.6199i) q^{89} +(48.1805 - 45.5940i) q^{90} +(23.4539 + 12.9995i) q^{91} +(-74.8342 - 43.2056i) q^{92} +(109.404 - 43.5594i) q^{93} +(29.5651 - 51.2083i) q^{94} +(-22.2049 - 12.8200i) q^{95} +(-48.0807 - 120.760i) q^{96} +(-46.9641 + 81.3442i) q^{97} +(-4.70530 - 134.423i) q^{98} +(-72.6299 + 17.3298i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 6 q^{2} + 8 q^{3} + 12 q^{4} - 8 q^{6} + 3 q^{7} + 20 q^{9}+O(q^{10}) \) 22 * q - 6 * q^2 + 8 * q^3 + 12 * q^4 - 8 * q^6 + 3 * q^7 + 20 * q^9	\( 22 q - 6 q^{2} + 8 q^{3} + 12 q^{4} - 8 q^{6} + 3 q^{7} + 20 q^{9} + 25 q^{10} - 20 q^{12} - 18 q^{13} - 90 q^{14} + 53 q^{15} + 12 q^{16} + 6 q^{17} - 56 q^{18} + 3 q^{19} - 39 q^{20} - 2 q^{21} - 59 q^{22} + 15 q^{24} - 114 q^{25} - 3 q^{26} - 97 q^{27} + 34 q^{28} - 63 q^{29} - 20 q^{30} - 29 q^{31} + 246 q^{32} + 77 q^{33} - 99 q^{34} - 27 q^{35} + 76 q^{36} - 20 q^{37} + 200 q^{39} + 210 q^{40} - 51 q^{41} + 80 q^{42} + 65 q^{43} + 54 q^{44} + 71 q^{45} + 75 q^{46} + 261 q^{47} - 113 q^{48} - 131 q^{49} + 63 q^{50} - 78 q^{51} + 92 q^{52} - 63 q^{53} - 485 q^{54} - 100 q^{55} + 153 q^{56} + 224 q^{57} - 80 q^{58} - 102 q^{59} + 103 q^{60} + 78 q^{61} + 421 q^{63} + 106 q^{64} - 225 q^{65} - 401 q^{66} - 132 q^{67} - 297 q^{69} + 179 q^{70} - 66 q^{72} + q^{73} - 245 q^{75} + 233 q^{76} - 447 q^{77} - 440 q^{78} + 140 q^{79} + 96 q^{80} + 104 q^{81} - 157 q^{82} + 255 q^{83} - 316 q^{84} + 102 q^{85} - 136 q^{87} - 816 q^{88} - 720 q^{89} + 418 q^{90} - 70 q^{91} - 1239 q^{92} + 210 q^{93} + 261 q^{94} + 642 q^{95} + 539 q^{96} + 178 q^{97} + 483 q^{98} - 103 q^{99}+O(q^{100}) \) 22 * q - 6 * q^2 + 8 * q^3 + 12 * q^4 - 8 * q^6 + 3 * q^7 + 20 * q^9 + 25 * q^10 - 20 * q^12 - 18 * q^13 - 90 * q^14 + 53 * q^15 + 12 * q^16 + 6 * q^17 - 56 * q^18 + 3 * q^19 - 39 * q^20 - 2 * q^21 - 59 * q^22 + 15 * q^24 - 114 * q^25 - 3 * q^26 - 97 * q^27 + 34 * q^28 - 63 * q^29 - 20 * q^30 - 29 * q^31 + 246 * q^32 + 77 * q^33 - 99 * q^34 - 27 * q^35 + 76 * q^36 - 20 * q^37 + 200 * q^39 + 210 * q^40 - 51 * q^41 + 80 * q^42 + 65 * q^43 + 54 * q^44 + 71 * q^45 + 75 * q^46 + 261 * q^47 - 113 * q^48 - 131 * q^49 + 63 * q^50 - 78 * q^51 + 92 * q^52 - 63 * q^53 - 485 * q^54 - 100 * q^55 + 153 * q^56 + 224 * q^57 - 80 * q^58 - 102 * q^59 + 103 * q^60 + 78 * q^61 + 421 * q^63 + 106 * q^64 - 225 * q^65 - 401 * q^66 - 132 * q^67 - 297 * q^69 + 179 * q^70 - 66 * q^72 + q^73 - 245 * q^75 + 233 * q^76 - 447 * q^77 - 440 * q^78 + 140 * q^79 + 96 * q^80 + 104 * q^81 - 157 * q^82 + 255 * q^83 - 316 * q^84 + 102 * q^85 - 136 * q^87 - 816 * q^88 - 720 * q^89 + 418 * q^90 - 70 * q^91 - 1239 * q^92 + 210 * q^93 + 261 * q^94 + 642 * q^95 + 539 * q^96 + 178 * q^97 + 483 * q^98 - 103 * q^99

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