LMFDB - Embedded newform 39.4.f.b.8.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [39,4,Mod(5,39)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(39, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("39.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 39 = 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	39.f (of order $4$, 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:	$2.30107449022$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 1316x^{16} + 520390x^{12} + 64668772x^{8} + 2536036097x^{4} + 8509693504 $ x^20 + 1316x^16 + 520390x^12 + 64668772x^8 + 2536036097x^4 + 8509693504
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			8.5
Root			$-0.980238 - 0.980238i$ of defining polynomial
Character	$\chi$	$=$	39.8
Dual form			39.4.f.b.5.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.980238 + 0.980238i) q^{2} +(-2.50090 - 4.55472i) q^{3} +6.07827i q^{4} +(12.5563 - 12.5563i) q^{5} +(6.91619 + 2.01323i) q^{6} +(21.4578 - 21.4578i) q^{7} +(-13.8001 - 13.8001i) q^{8} +(-14.4909 + 22.7818i) q^{9} +O(q^{10})$	\(q+(-0.980238 + 0.980238i) q^{2} +(-2.50090 - 4.55472i) q^{3} +6.07827i q^{4} +(12.5563 - 12.5563i) q^{5} +(6.91619 + 2.01323i) q^{6} +(21.4578 - 21.4578i) q^{7} +(-13.8001 - 13.8001i) q^{8} +(-14.4909 + 22.7818i) q^{9} +24.6163i q^{10} +(-8.34980 - 8.34980i) q^{11} +(27.6848 - 15.2012i) q^{12} +(29.3793 + 36.5220i) q^{13} +42.0674i q^{14} +(-88.5924 - 25.7883i) q^{15} -21.5715 q^{16} -39.5799 q^{17} +(-8.12705 - 36.5362i) q^{18} +(9.15970 + 9.15970i) q^{19} +(76.3204 + 76.3204i) q^{20} +(-151.398 - 44.0703i) q^{21} +16.3696 q^{22} +2.83931 q^{23} +(-28.3428 + 97.3680i) q^{24} -190.320i q^{25} +(-64.5989 - 7.00158i) q^{26} +(140.005 + 9.02699i) q^{27} +(130.426 + 130.426i) q^{28} +175.398i q^{29} +(112.120 - 61.5630i) q^{30} +(95.0010 + 95.0010i) q^{31} +(131.546 - 131.546i) q^{32} +(-17.1489 + 58.9130i) q^{33} +(38.7977 - 38.7977i) q^{34} -538.859i q^{35} +(-138.474 - 88.0799i) q^{36} +(-92.4719 + 92.4719i) q^{37} -17.9574 q^{38} +(92.8728 - 225.152i) q^{39} -346.554 q^{40} +(-187.117 + 187.117i) q^{41} +(191.605 - 105.207i) q^{42} +52.5720i q^{43} +(50.7523 - 50.7523i) q^{44} +(104.103 + 468.007i) q^{45} +(-2.78320 + 2.78320i) q^{46} +(194.887 + 194.887i) q^{47} +(53.9482 + 98.2520i) q^{48} -577.872i q^{49} +(186.559 + 186.559i) q^{50} +(98.9855 + 180.275i) q^{51} +(-221.991 + 178.575i) q^{52} +473.173i q^{53} +(-146.087 + 128.390i) q^{54} -209.685 q^{55} -592.237 q^{56} +(18.8123 - 64.6274i) q^{57} +(-171.932 - 171.932i) q^{58} +(-395.766 - 395.766i) q^{59} +(156.748 - 538.488i) q^{60} +104.515 q^{61} -186.247 q^{62} +(177.904 + 799.791i) q^{63} +85.3201i q^{64} +(827.475 + 89.6862i) q^{65} +(-40.9388 - 74.5588i) q^{66} +(-473.452 - 473.452i) q^{67} -240.577i q^{68} +(-7.10085 - 12.9323i) q^{69} +(528.210 + 528.210i) q^{70} +(313.305 - 313.305i) q^{71} +(514.366 - 114.415i) q^{72} +(-84.4987 + 84.4987i) q^{73} -181.289i q^{74} +(-866.855 + 475.973i) q^{75} +(-55.6751 + 55.6751i) q^{76} -358.336 q^{77} +(129.666 + 311.740i) q^{78} +651.078 q^{79} +(-270.857 + 270.857i) q^{80} +(-309.025 - 660.261i) q^{81} -366.838i q^{82} +(311.890 - 311.890i) q^{83} +(267.871 - 920.238i) q^{84} +(-496.976 + 496.976i) q^{85} +(-51.5330 - 51.5330i) q^{86} +(798.889 - 438.654i) q^{87} +230.455i q^{88} +(617.346 + 617.346i) q^{89} +(-560.804 - 356.713i) q^{90} +(1414.10 + 153.267i) q^{91} +17.2581i q^{92} +(195.114 - 670.291i) q^{93} -382.072 q^{94} +230.023 q^{95} +(-928.136 - 270.170i) q^{96} +(177.855 + 177.855i) q^{97} +(566.452 + 566.452i) q^{98} +(311.220 - 69.2273i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{3} + 44 q^{6} + 44 q^{7} - 112 q^{9}+O(q^{10}) $ 20 * q - 4 * q^3 + 44 * q^6 + 44 * q^7 - 112 * q^9	$ 20 q - 4 q^{3} + 44 q^{6} + 44 q^{7} - 112 q^{9} - 76 q^{13} - 76 q^{15} - 16 q^{16} + 296 q^{18} + 260 q^{19} - 532 q^{21} - 224 q^{22} + 36 q^{24} - 592 q^{27} + 584 q^{28} - 700 q^{31} + 872 q^{33} + 816 q^{34} - 1660 q^{37} + 1016 q^{39} + 3288 q^{40} + 124 q^{42} + 260 q^{45} - 1560 q^{46} - 1084 q^{48} - 3456 q^{52} - 232 q^{54} - 872 q^{55} + 2648 q^{57} - 1352 q^{58} - 1064 q^{60} + 1960 q^{61} + 428 q^{63} - 7664 q^{66} - 916 q^{67} + 1192 q^{70} + 6984 q^{72} + 1964 q^{73} + 1816 q^{76} + 728 q^{78} + 6544 q^{79} + 200 q^{81} + 2612 q^{84} - 8304 q^{85} + 3136 q^{87} + 4580 q^{91} - 2536 q^{93} - 6056 q^{94} - 5956 q^{96} - 2572 q^{97} + 1700 q^{99}+O(q^{100}) $ 20 * q - 4 * q^3 + 44 * q^6 + 44 * q^7 - 112 * q^9 - 76 * q^13 - 76 * q^15 - 16 * q^16 + 296 * q^18 + 260 * q^19 - 532 * q^21 - 224 * q^22 + 36 * q^24 - 592 * q^27 + 584 * q^28 - 700 * q^31 + 872 * q^33 + 816 * q^34 - 1660 * q^37 + 1016 * q^39 + 3288 * q^40 + 124 * q^42 + 260 * q^45 - 1560 * q^46 - 1084 * q^48 - 3456 * q^52 - 232 * q^54 - 872 * q^55 + 2648 * q^57 - 1352 * q^58 - 1064 * q^60 + 1960 * q^61 + 428 * q^63 - 7664 * q^66 - 916 * q^67 + 1192 * q^70 + 6984 * q^72 + 1964 * q^73 + 1816 * q^76 + 728 * q^78 + 6544 * q^79 + 200 * q^81 + 2612 * q^84 - 8304 * q^85 + 3136 * q^87 + 4580 * q^91 - 2536 * q^93 - 6056 * q^94 - 5956 * q^96 - 2572 * q^97 + 1700 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/39\mathbb{Z}\right)^\times$.

$n$	$14$	$28$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.980238	+	0.980238i	−0.346566	+	0.346566i	−0.858829	−	0.512263i	$-0.828807\pi$
$2$	−0.980238	+	0.980238i	−0.346566	+	0.346566i	0.512263	+	0.858829i	$0.328807\pi$
$3$	−2.50090	−	4.55472i	−0.481299	−	0.876556i
$3$	−2.50090	−	4.55472i	−0.481299	−	0.876556i
$4$			6.07827i			0.759783i
$5$	12.5563	−	12.5563i	1.12307	−	1.12307i	0.131790	−	0.991278i	$-0.457928\pi$
$5$	12.5563	−	12.5563i	1.12307	−	1.12307i	0.991278	−	0.131790i	$-0.0420724\pi$
$6$	6.91619	+	2.01323i	0.470587	+	0.136983i
$7$	21.4578	−	21.4578i	1.15861	−	1.15861i	0.173836	−	0.984775i	$-0.444384\pi$
$7$	21.4578	−	21.4578i	1.15861	−	1.15861i	0.984775	−	0.173836i	$-0.0556164\pi$
$8$	−13.8001	−	13.8001i	−0.609882	−	0.609882i
$9$	−14.4909	+	22.7818i	−0.536702	+	0.843772i
$10$			24.6163i			0.778435i
$11$	−8.34980	−	8.34980i	−0.228869	−	0.228869i	0.583351	−	0.812220i	$-0.301741\pi$
$11$	−8.34980	−	8.34980i	−0.228869	−	0.228869i	−0.812220	+	0.583351i	$0.801741\pi$
$12$	27.6848	−	15.2012i	0.665993	−	0.365683i
$13$	29.3793	+	36.5220i	0.626796	+	0.779184i
$13$	29.3793	+	36.5220i	0.626796	+	0.779184i
$14$			42.0674i			0.803071i
$15$	−88.5924	−	25.7883i	−1.52496	−	0.443900i
$16$	−21.5715			−0.337054
$17$	−39.5799			−0.564678			−0.282339	−	0.959315i	$-0.591110\pi$
$17$	−39.5799			−0.564678			−0.282339	+	0.959315i	$0.591110\pi$
$18$	−8.12705	−	36.5362i	−0.106420	−	0.478426i
$19$	9.15970	+	9.15970i	0.110599	+	0.110599i	0.760241	−	0.649642i	$-0.225081\pi$
$19$	9.15970	+	9.15970i	0.110599	+	0.110599i	−0.649642	+	0.760241i	$0.725081\pi$
$20$	76.3204	+	76.3204i	0.853288	+	0.853288i
$21$	−151.398	−	44.0703i	−1.57323	−	0.457949i
$22$	16.3696			0.158637
$23$	2.83931			0.0257408			0.0128704	−	0.999917i	$-0.495903\pi$
$23$	2.83931			0.0257408			0.0128704	+	0.999917i	$0.495903\pi$
$24$	−28.3428	+	97.3680i	−0.241060	+	0.828131i
$25$		−	190.320i		−	1.52256i
$26$	−64.5989	−	7.00158i	−0.487265	−	0.0528124i
$27$	140.005	+	9.02699i	0.997928	+	0.0643424i
$28$	130.426	+	130.426i	0.880293	+	0.880293i
$29$			175.398i			1.12312i	0.827435	+	0.561562i	$0.189799\pi$
$29$			175.398i			1.12312i	−0.827435	+	0.561562i	$0.810201\pi$
$30$	112.120	−	61.5630i	0.682342	−	0.374660i
$31$	95.0010	+	95.0010i	0.550409	+	0.550409i	0.926559	−	0.376150i	$-0.122752\pi$
$31$	95.0010	+	95.0010i	0.550409	+	0.550409i	−0.376150	+	0.926559i	$0.622752\pi$
$32$	131.546	−	131.546i	0.726694	−	0.726694i
$33$	−17.1489	+	58.9130i	−0.0904621	+	0.310771i
$34$	38.7977	−	38.7977i	0.195699	−	0.195699i
$35$		−	538.859i		−	2.60240i
$36$	−138.474	−	88.0799i	−0.641084	−	0.407777i
$37$	−92.4719	+	92.4719i	−0.410873	+	0.410873i	−0.882043	−	0.471170i	$-0.843832\pi$
$37$	−92.4719	+	92.4719i	−0.410873	+	0.410873i	0.471170	+	0.882043i	$0.343832\pi$
$38$	−17.9574			−0.0766597
$39$	92.8728	−	225.152i	0.381322	−	0.924442i
$40$	−346.554			−1.36988
$41$	−187.117	+	187.117i	−0.712749	+	0.712749i	−0.967110	−	0.254360i	$-0.918135\pi$
$41$	−187.117	+	187.117i	−0.712749	+	0.712749i	0.254360	+	0.967110i	$0.418135\pi$
$42$	191.605	−	105.207i	0.703937	−	0.386518i
$43$			52.5720i			0.186445i	0.995645	+	0.0932227i	$0.0297168\pi$
$43$			52.5720i			0.186445i	−0.995645	+	0.0932227i	$0.970283\pi$
$44$	50.7523	−	50.7523i	0.173891	−	0.173891i
$45$	104.103	+	468.007i	0.344861	+	1.55037i
$46$	−2.78320	+	2.78320i	−0.00892089	+	0.00892089i
$47$	194.887	+	194.887i	0.604835	+	0.604835i	0.941592	−	0.336756i	$-0.109330\pi$
$47$	194.887	+	194.887i	0.604835	+	0.604835i	−0.336756	+	0.941592i	$0.609330\pi$
$48$	53.9482	+	98.2520i	0.162224	+	0.295447i
$49$		−	577.872i		−	1.68476i
$50$	186.559	+	186.559i	0.527668	+	0.527668i
$51$	98.9855	+	180.275i	0.271779	+	0.494972i
$52$	−221.991	+	178.575i	−0.592011	+	0.476229i
$53$			473.173i			1.22633i	0.789957	+	0.613163i	$0.210103\pi$
$53$			473.173i			1.22633i	−0.789957	+	0.613163i	$0.789897\pi$
$54$	−146.087	+	128.390i	−0.368147	+	0.323549i
$55$	−209.685			−0.514071
$56$	−592.237			−1.41323
$57$	18.8123	−	64.6274i	0.0437150	−	0.150177i
$58$	−171.932	−	171.932i	−0.389237	−	0.389237i
$59$	−395.766	−	395.766i	−0.873294	−	0.873294i	0.119536	−	0.992830i	$-0.461859\pi$
$59$	−395.766	−	395.766i	−0.873294	−	0.873294i	−0.992830	+	0.119536i	$0.961859\pi$
$60$	156.748	−	538.488i	0.337268	−	1.15864i
$61$	104.515			0.219374			0.109687	−	0.993966i	$-0.465015\pi$
$61$	104.515			0.219374			0.109687	+	0.993966i	$0.465015\pi$
$62$	−186.247			−0.381506
$63$	177.904	+	799.791i	0.355775	+	1.59943i
$64$			85.3201i			0.166641i
$65$	827.475	+	89.6862i	1.57901	+	0.171142i
$66$	−40.9388	−	74.5588i	−0.0763517	−	0.139054i
$67$	−473.452	−	473.452i	−0.863305	−	0.863305i	0.128416	−	0.991720i	$-0.459011\pi$
$67$	−473.452	−	473.452i	−0.863305	−	0.863305i	−0.991720	+	0.128416i	$0.959011\pi$
$68$		−	240.577i		−	0.429033i
$69$	−7.10085	−	12.9323i	−0.0123890	−	0.0225632i
$70$	528.210	+	528.210i	0.901903	+	0.901903i
$71$	313.305	−	313.305i	0.523697	−	0.523697i	−0.394989	−	0.918686i	$-0.629252\pi$
$71$	313.305	−	313.305i	0.523697	−	0.523697i	0.918686	+	0.394989i	$0.129252\pi$
$72$	514.366	−	114.415i	0.841926	−	0.187277i
$73$	−84.4987	+	84.4987i	−0.135477	+	0.135477i	−0.771593	−	0.636116i	$-0.780540\pi$
$73$	−84.4987	+	84.4987i	−0.135477	+	0.135477i	0.636116	+	0.771593i	$0.280540\pi$
$74$		−	181.289i		−	0.284789i
$75$	−866.855	+	475.973i	−1.33461	+	0.732808i
$76$	−55.6751	+	55.6751i	−0.0840312	+	0.0840312i
$77$	−358.336			−0.530340
$78$	129.666	+	311.740i	0.188227	+	0.452534i
$79$	651.078			0.927240			0.463620	−	0.886034i	$-0.346550\pi$
$79$	651.078			0.927240			0.463620	+	0.886034i	$0.346550\pi$
$80$	−270.857	+	270.857i	−0.378535	+	0.378535i
$81$	−309.025	−	660.261i	−0.423902	−	0.905708i
$82$		−	366.838i		−	0.494030i
$83$	311.890	−	311.890i	0.412462	−	0.412462i	−0.470133	−	0.882595i	$-0.655794\pi$
$83$	311.890	−	311.890i	0.412462	−	0.412462i	0.882595	+	0.470133i	$0.155794\pi$
$84$	267.871	−	920.238i	0.347942	−	1.19531i
$85$	−496.976	+	496.976i	−0.634172	+	0.634172i
$86$	−51.5330	−	51.5330i	−0.0646157	−	0.0646157i
$87$	798.889	−	438.654i	0.984481	−	0.540559i
$88$			230.455i			0.279166i
$89$	617.346	+	617.346i	0.735264	+	0.735264i	0.971658	−	0.236393i	$-0.0759653\pi$
$89$	617.346	+	617.346i	0.735264	+	0.735264i	−0.236393	+	0.971658i	$0.575965\pi$
$90$	−560.804	−	356.713i	−0.656822	−	0.417787i
$91$	1414.10	+	153.267i	1.62898	+	0.176558i
$92$			17.2581i			0.0195574i
$93$	195.114	−	670.291i	0.217553	−	0.747376i
$94$	−382.072			−0.419231
$95$	230.023			0.248420
$96$	−928.136	−	270.170i	−0.986745	−	0.287231i
$97$	177.855	+	177.855i	0.186169	+	0.186169i	0.794038	−	0.607868i	$-0.207975\pi$
$97$	177.855	+	177.855i	0.186169	+	0.186169i	−0.607868	+	0.794038i	$0.707975\pi$
$98$	566.452	+	566.452i	0.583881	+	0.583881i
$99$	311.220	−	69.2273i	0.315948	−	0.0702788i
$100$	1156.82			1.15682
$101$	−1181.17			−1.16368			−0.581838	−	0.813305i	$-0.697666\pi$
$101$	−1181.17			−1.16368			−0.581838	+	0.813305i	$0.697666\pi$
$102$	−273.742	−	79.6833i	−0.265730	−	0.0773512i
$103$			227.818i			0.217938i	0.994045	+	0.108969i	$0.0347549\pi$
$103$			227.818i			0.217938i	−0.994045	+	0.108969i	$0.965245\pi$
$104$	98.5702	−	909.441i	0.0929385	−	0.857481i
$105$	−2454.35	+	1347.64i	−2.28115	+	1.25253i
$106$	−463.822	−	463.822i	−0.425003	−	0.425003i
$107$			571.489i			0.516336i	0.966100	+	0.258168i	$0.0831188\pi$
$107$			571.489i			0.516336i	−0.966100	+	0.258168i	$0.916881\pi$
$108$	−54.8684	+	850.990i	−0.0488863	+	0.758209i
$109$	−29.9579	−	29.9579i	−0.0263252	−	0.0263252i	0.693822	−	0.720147i	$-0.255926\pi$
$109$	−29.9579	−	29.9579i	−0.0263252	−	0.0263252i	−0.720147	+	0.693822i	$0.755926\pi$
$110$	205.541	−	205.541i	0.178160	−	0.178160i
$111$	652.447	+	189.920i	0.557906	+	0.162400i
$112$	−462.876	+	462.876i	−0.390515	+	0.390515i
$113$		−	18.7115i		−	0.0155773i	−0.999970	−	0.00778864i	$-0.997521\pi$
$113$		−	18.7115i		−	0.0155773i	0.999970	−	0.00778864i	$-0.00247923\pi$
$114$	44.9097	+	81.7908i	0.0368963	+	0.0671966i
$115$	35.6512	−	35.6512i	0.0289086	−	0.0289086i
$116$	−1066.12			−0.853331
$117$	−1257.77	+	140.075i	−0.993856	+	0.110684i
$118$	775.889			0.605309
$119$	−849.296	+	849.296i	−0.654243	+	0.654243i
$120$	866.700	+	1578.46i	0.659321	+	1.20077i
$121$		−	1191.56i		−	0.895238i
$122$	−102.450	+	102.450i	−0.0760277	+	0.0760277i
$123$	1320.23	+	384.303i	0.967811	+	0.281719i
$124$	−577.441	+	577.441i	−0.418192	+	0.418192i
$125$	−820.177	−	820.177i	−0.586871	−	0.586871i
$126$	−958.374	−	609.597i	−0.677609	−	0.431010i
$127$		−	1382.85i		−	0.966207i	−0.875563	−	0.483103i	$-0.839510\pi$
$127$		−	1382.85i		−	0.966207i	0.875563	−	0.483103i	$-0.160490\pi$
$128$	968.731	+	968.731i	0.668941	+	0.668941i
$129$	239.451	−	131.477i	0.163430	−	0.0897360i
$130$	−899.036	+	723.208i	−0.606544	+	0.487920i
$131$		−	1018.32i		−	0.679169i	−0.940576	−	0.339585i	$-0.889714\pi$
$131$		−	1018.32i		−	0.679169i	0.940576	−	0.339585i	$-0.110286\pi$
$132$	−358.089	−	104.236i	−0.236119	−	0.0687316i
$133$	393.093			0.256282
$134$	928.192			0.598385
$135$	1871.29	−	1644.60i	1.19300	−	1.04848i
$136$	546.205	+	546.205i	0.344387	+	0.344387i
$137$	−1113.93	−	1113.93i	−0.694670	−	0.694670i	0.268586	−	0.963256i	$-0.413444\pi$
$137$	−1113.93	−	1113.93i	−0.694670	−	0.694670i	−0.963256	+	0.268586i	$0.913444\pi$
$138$	19.6372	+	5.71618i	0.0121133	+	0.00352604i
$139$	−1755.93			−1.07148			−0.535742	−	0.844382i	$-0.679968\pi$
$139$	−1755.93			−1.07148			−0.535742	+	0.844382i	$0.679968\pi$
$140$	3275.33			1.97726
$141$	400.263	−	1375.05i	0.239065	−	0.821279i
$142$			614.227i			0.362991i
$143$	59.6404	−	550.263i	0.0348768	−	0.321785i
$144$	312.591	−	491.438i	0.180898	−	0.284397i
$145$	2202.35	+	2202.35i	1.26134	+	1.26134i
$146$		−	165.658i		−	0.0939036i
$147$	−2632.05	+	1445.20i	−1.47679	+	0.810873i
$148$	−562.069	−	562.069i	−0.312174	−	0.312174i
$149$	−1917.05	+	1917.05i	−1.05403	+	1.05403i	−0.0555800	+	0.998454i	$0.517701\pi$
$149$	−1917.05	+	1917.05i	−1.05403	+	1.05403i	−0.998454	+	0.0555800i	$0.982299\pi$
$150$	383.158	−	1316.29i	0.208565	−	0.716498i
$151$	969.318	−	969.318i	0.522397	−	0.522397i	−0.395897	−	0.918295i	$-0.629566\pi$
$151$	969.318	−	969.318i	0.522397	−	0.522397i	0.918295	+	0.395897i	$0.129566\pi$
$152$		−	252.809i		−	0.134904i
$153$	573.550	−	901.703i	0.303064	−	0.476460i
$154$	351.255	−	351.255i	0.183798	−	0.183798i
$155$	2385.72			1.23629
$156$	1368.54	+	564.506i	0.702376	+	0.289722i
$157$	−187.932			−0.0955324			−0.0477662	−	0.998859i	$-0.515210\pi$
$157$	−187.932			−0.0955324			−0.0477662	+	0.998859i	$0.515210\pi$
$158$	−638.211	+	638.211i	−0.321350	+	0.321350i
$159$	2155.17	−	1183.36i	1.07494	−	0.590230i
$160$		−	3303.45i		−	1.63225i
$161$	60.9254	−	60.9254i	0.0298235	−	0.0298235i
$162$	950.131	+	344.295i	0.460798	+	0.166978i
$163$	−2353.70	+	2353.70i	−1.13102	+	1.13102i	−0.141010	+	0.990008i	$0.545035\pi$
$163$	−2353.70	+	2353.70i	−1.13102	+	1.13102i	−0.990008	+	0.141010i	$0.954965\pi$
$164$	−1137.35	−	1137.35i	−0.541535	−	0.541535i
$165$	524.402	+	955.055i	0.247422	+	0.450612i
$166$			611.453i			0.285891i
$167$	−1595.37	−	1595.37i	−0.739244	−	0.739244i	0.233188	−	0.972432i	$-0.425084\pi$
$167$	−1595.37	−	1595.37i	−0.739244	−	0.739244i	−0.972432	+	0.233188i	$0.925084\pi$
$168$	1481.13	+	2697.47i	0.680187	+	1.23878i
$169$	−470.716	+	2145.98i	−0.214254	+	0.976778i
$170$		−	974.309i		−	0.439565i
$171$	−341.407	+	75.9421i	−0.152679	+	0.0339616i
$172$	−319.546			−0.141658
$173$	3479.34			1.52907			0.764535	−	0.644582i	$-0.222968\pi$
$173$	3479.34			1.52907			0.764535	+	0.644582i	$0.222968\pi$
$174$	−353.116	+	1213.09i	−0.153849	+	0.528528i
$175$	−4083.85	−	4083.85i	−1.76406	−	1.76406i
$176$	180.118	+	180.118i	0.0771413	+	0.0771413i
$177$	−812.830	+	2792.38i	−0.345175	+	1.18581i
$178$	−1210.29			−0.509636
$179$	−2074.00			−0.866023			−0.433012	−	0.901388i	$-0.642549\pi$
$179$	−2074.00			−0.866023			−0.433012	+	0.901388i	$0.642549\pi$
$180$	−2844.67	+	632.764i	−1.17794	+	0.262019i
$181$		−	4030.51i		−	1.65517i	−0.561341	−	0.827585i	$-0.689714\pi$
$181$		−	4030.51i		−	1.65517i	0.561341	−	0.827585i	$-0.310286\pi$
$182$	−1536.39	+	1235.91i	−0.625740	+	0.503362i
$183$	−261.383	−	476.038i	−0.105585	−	0.192294i
$184$	−39.1827	−	39.1827i	−0.0156988	−	0.0156988i
$185$			2322.21i			0.922876i
$186$	465.786	+	848.303i	0.183619	+	0.334412i
$187$	330.484	+	330.484i	0.129237	+	0.129237i
$188$	−1184.58	+	1184.58i	−0.459544	+	0.459544i
$189$	3197.90	−	2810.51i	1.23076	−	1.08166i
$190$	−225.478	+	225.478i	−0.0860940	+	0.0860940i
$191$			1624.37i			0.615366i	0.951489	+	0.307683i	$0.0995536\pi$
$191$			1624.37i			0.615366i	−0.951489	+	0.307683i	$0.900446\pi$
$192$	388.609	−	213.377i	0.146070	−	0.0802041i
$193$	589.677	−	589.677i	0.219927	−	0.219927i	−0.588541	−	0.808468i	$-0.700297\pi$
$193$	589.677	−	589.677i	0.219927	−	0.219927i	0.808468	+	0.588541i	$0.200297\pi$
$194$	−348.680			−0.129040
$195$	−1660.94	−	3993.21i	−0.609961	−	1.46646i
$196$	3512.46			1.28005
$197$	3290.58	−	3290.58i	1.19007	−	1.19007i	0.213023	−	0.977047i	$-0.431669\pi$
$197$	3290.58	−	3290.58i	1.19007	−	1.19007i	0.977047	−	0.213023i	$-0.0683309\pi$
$198$	−237.211	+	372.929i	−0.0851406	+	0.133853i
$199$			4033.81i			1.43693i	0.695563	+	0.718466i	$0.255155\pi$
$199$			4033.81i			1.43693i	−0.695563	+	0.718466i	$0.744845\pi$
$200$	−2626.43	+	2626.43i	−0.928582	+	0.928582i
$201$	−972.383	+	3340.50i	−0.341227	+	1.17224i
$202$	1157.83	−	1157.83i	0.403291	−	0.403291i
$203$	3763.65	+	3763.65i	1.30126	+	1.30126i
$204$	−1095.76	+	601.661i	−0.376072	+	0.206493i
$205$			4698.98i			1.60093i
$206$	−223.316	−	223.316i	−0.0755299	−	0.0755299i
$207$	−41.1444	+	64.6848i	−0.0138151	+	0.0217193i
$208$	−633.755	−	787.834i	−0.211264	−	0.262627i
$209$		−	152.963i		−	0.0506253i
$210$	1084.85	−	3726.85i	0.356483	−	1.22465i
$211$	−5146.04			−1.67899			−0.839497	−	0.543364i	$-0.817150\pi$
$211$	−5146.04			−1.67899			−0.839497	+	0.543364i	$0.817150\pi$
$212$	−2876.07			−0.931742
$213$	−2210.56	−	643.471i	−0.711104	−	0.206995i
$214$	−560.196	−	560.196i	−0.178945	−	0.178945i
$215$	660.108	+	660.108i	0.209391	+	0.209391i
$216$	−1807.51	−	2056.65i	−0.569377	−	0.647859i
$217$	4077.02			1.27542
$218$	58.7318			0.0182469
$219$	596.191	+	173.545i	0.183958	+	0.0535483i
$220$		−	1274.52i		−	0.390582i
$221$	−1162.83	−	1445.54i	−0.353938	−	0.439988i
$222$	−825.720	+	453.386i	−0.249634	+	0.137069i
$223$	1830.37	+	1830.37i	0.549645	+	0.549645i	0.926338	−	0.376693i	$-0.122939\pi$
$223$	1830.37	+	1830.37i	0.549645	+	0.549645i	−0.376693	+	0.926338i	$0.622939\pi$
$224$		−	5645.35i		−	1.68391i
$225$	4335.84	+	2757.92i	1.28469	+	0.817161i
$226$	18.3417	+	18.3417i	0.00539856	+	0.00539856i
$227$	2496.64	−	2496.64i	0.729990	−	0.729990i	−0.240628	−	0.970617i	$-0.577353\pi$
$227$	2496.64	−	2496.64i	0.729990	−	0.729990i	0.970617	+	0.240628i	$0.0773533\pi$
$228$	392.823	+	114.346i	0.114102	+	0.0332139i
$229$	−1298.02	+	1298.02i	−0.374565	+	0.374565i	−0.869137	−	0.494572i	$-0.835325\pi$
$229$	−1298.02	+	1298.02i	−0.374565	+	0.374565i	0.494572	+	0.869137i	$0.335325\pi$
$230$			69.8933i			0.0200375i
$231$	896.165	+	1632.12i	0.255252	+	0.464873i
$232$	2420.50	−	2420.50i	0.684973	−	0.684973i
$233$	−374.174			−0.105206			−0.0526028	−	0.998616i	$-0.516752\pi$
$233$	−374.174			−0.105206			−0.0526028	+	0.998616i	$0.516752\pi$
$234$	1095.61	−	1370.22i	0.306078	−	0.382796i
$235$	4894.12			1.35854
$236$	2405.57	−	2405.57i	0.663514	−	0.663514i
$237$	−1628.28	−	2965.48i	−0.446280	−	0.812778i
$238$		−	1665.02i		−	0.453477i
$239$	−14.5400	+	14.5400i	−0.00393522	+	0.00393522i	−0.709072	−	0.705136i	$-0.750886\pi$
$239$	−14.5400	+	14.5400i	−0.00393522	+	0.00393522i	0.705136	+	0.709072i	$0.250886\pi$
$240$	1911.07	+	556.291i	0.513996	+	0.149618i
$241$	−418.110	+	418.110i	−0.111755	+	0.111755i	−0.760773	−	0.649018i	$-0.775180\pi$
$241$	−418.110	+	418.110i	−0.111755	+	0.111755i	0.649018	+	0.760773i	$0.275180\pi$
$242$	1168.01	+	1168.01i	0.310259	+	0.310259i
$243$	−2234.46	+	3058.77i	−0.589880	+	0.807491i
$244$			635.273i			0.166677i
$245$	−7255.92	−	7255.92i	−1.89210	−	1.89210i
$246$	−1670.84	+	917.426i	−0.433045	+	0.237776i
$247$	−65.4253	+	603.636i	−0.0168539	+	0.155500i
$248$		−	2622.04i		−	0.671369i
$249$	−2200.58	−	640.564i	−0.560064	−	0.163029i
$250$	1607.94			0.406780
$251$	−3640.15			−0.915396			−0.457698	−	0.889108i	$-0.651326\pi$
$251$	−3640.15			−0.915396			−0.457698	+	0.889108i	$0.651326\pi$
$252$	−4861.34	+	1081.35i	−1.21522	+	0.270312i
$253$	−23.7077	−	23.7077i	−0.00589127	−	0.00589127i
$254$	1355.52	+	1355.52i	0.334855	+	0.334855i
$255$	3506.48	+	1020.70i	0.861114	+	0.250661i
$256$	−2581.73			−0.630306
$257$	8045.83			1.95286			0.976430	−	0.215832i	$-0.0692464\pi$
$257$	8045.83			1.95286			0.976430	+	0.215832i	$0.0692464\pi$
$258$	−105.839	+	363.598i	−0.0255398	+	0.0877388i
$259$			3968.48i			0.952083i
$260$	−545.137	+	5029.61i	−0.130031	+	1.19971i
$261$	−3995.89	−	2541.68i	−0.947660	−	0.602782i
$262$	998.197	+	998.197i	0.235377	+	0.235377i
$263$			2164.94i			0.507588i	0.967258	+	0.253794i	$0.0816786\pi$
$263$			2164.94i			0.507588i	−0.967258	+	0.253794i	$0.918321\pi$
$264$	1049.66	−	576.347i	0.244705	−	0.134362i
$265$	5941.29	+	5941.29i	1.37725	+	1.37725i
$266$	−385.325	+	385.325i	−0.0888188	+	0.0888188i
$267$	1267.91	−	4355.76i	0.290618	−	0.998383i
$268$	2877.77	−	2877.77i	0.655924	−	0.655924i
$269$			8484.29i			1.92304i	0.274743	+	0.961518i	$0.411407\pi$
$269$			8484.29i			1.92304i	−0.274743	+	0.961518i	$0.588593\pi$
$270$	−222.211	+	3446.41i	−0.0500864	+	0.776822i
$271$	2258.21	−	2258.21i	0.506186	−	0.506186i	−0.407167	−	0.913354i	$-0.633483\pi$
$271$	2258.21	−	2258.21i	0.506186	−	0.506186i	0.913354	+	0.407167i	$0.133483\pi$
$272$	853.797			0.190327
$273$	−2838.43	−	6824.11i	−0.629266	−	1.51287i
$274$	2183.84			0.481498
$275$	−1589.13	+	1589.13i	−0.348467	+	0.348467i
$276$	78.6059	−	43.1609i	0.0171432	−	0.00941297i
$277$		−	7018.23i		−	1.52233i	−0.648559	−	0.761164i	$-0.724628\pi$
$277$		−	7018.23i		−	1.52233i	0.648559	−	0.761164i	$-0.275372\pi$
$278$	1721.23	−	1721.23i	0.371340	−	0.371340i
$279$	−3540.95	+	787.643i	−0.759825	+	0.169014i
$280$	−7436.29	+	7436.29i	−1.58715	+	1.58715i
$281$	98.2745	+	98.2745i	0.0208632	+	0.0208632i	0.717461	−	0.696598i	$-0.245304\pi$
$281$	98.2745	+	98.2745i	0.0208632	+	0.0208632i	−0.696598	+	0.717461i	$0.745304\pi$
$282$	955.526	+	1740.23i	0.201776	+	0.367480i
$283$		−	8008.21i		−	1.68212i	−0.540945	−	0.841058i	$-0.681933\pi$
$283$		−	8008.21i		−	1.68212i	0.540945	−	0.841058i	$-0.318067\pi$
$284$	1904.35	+	1904.35i	0.397896	+	0.397896i
$285$	−575.267	−	1047.69i	−0.119564	−	0.217754i
$286$	480.926	+	597.850i	0.0994328	+	0.123607i
$287$			8030.22i			1.65160i
$288$	1090.63	+	4903.07i	0.223146	+	1.00318i
$289$	−3346.43			−0.681138
$290$	−4317.64			−0.874279
$291$	365.281	−	1254.88i	0.0735847	−	0.252791i
$292$	−513.606	−	513.606i	−0.102933	−	0.102933i
$293$	−5325.57	−	5325.57i	−1.06185	−	1.06185i	−0.997957	−	0.0638968i	$-0.979647\pi$
$293$	−5325.57	−	5325.57i	−1.06185	−	1.06185i	−0.0638968	−	0.997957i	$-0.520353\pi$
$294$	1163.39	−	3996.67i	0.230783	−	0.792826i
$295$	−9938.69			−1.96154
$296$	2552.23			0.501168
$297$	−1093.64	−	1244.39i	−0.213669	−	0.243121i
$298$		−	3758.34i		−	0.730586i
$299$	83.4170	+	103.697i	0.0161342	+	0.0200568i
$300$	−2893.09	−	5268.98i	−0.556775	−	1.01401i
$301$	1128.08	+	1128.08i	0.216018	+	0.216018i
$302$			1900.32i			0.362091i
$303$	2954.01	+	5379.92i	0.560077	+	1.02003i
$304$	−197.588	−	197.588i	−0.0372778	−	0.0372778i
$305$	1312.32	−	1312.32i	0.246372	−	0.246372i
$306$	321.668	+	1446.10i	0.0600932	+	0.270157i
$307$	−4466.27	+	4466.27i	−0.830304	+	0.830304i	−0.987558	−	0.157254i	$-0.949736\pi$
$307$	−4466.27	+	4466.27i	−0.830304	+	0.830304i	0.157254	+	0.987558i	$0.449736\pi$
$308$		−	2178.06i		−	0.402944i
$309$	1037.65	−	569.752i	0.191035	−	0.104893i
$310$	−2338.57	+	2338.57i	−0.428457	+	0.428457i
$311$	−3306.43			−0.602863			−0.301432	−	0.953488i	$-0.597464\pi$
$311$	−3306.43			−0.602863			−0.301432	+	0.953488i	$0.597464\pi$
$312$	−4388.76	+	1825.47i	−0.796362	+	0.331239i
$313$	−572.860			−0.103450			−0.0517252	−	0.998661i	$-0.516472\pi$
$313$	−572.860			−0.103450			−0.0517252	+	0.998661i	$0.516472\pi$
$314$	184.218	−	184.218i	0.0331083	−	0.0331083i
$315$	12276.2	+	7808.58i	2.19583	+	1.39671i
$316$			3957.42i			0.704502i
$317$	2376.21	−	2376.21i	0.421014	−	0.421014i	−0.464539	−	0.885553i	$-0.653780\pi$
$317$	2376.21	−	2376.21i	0.421014	−	0.421014i	0.885553	+	0.464539i	$0.153780\pi$
$318$	−952.604	+	3272.55i	−0.167985	+	0.577093i
$319$	1464.54	−	1464.54i	0.257048	−	0.257048i
$320$	1071.30	+	1071.30i	0.187149	+	0.187149i
$321$	2602.97	−	1429.24i	0.452598	−	0.248512i
$322$			119.443i			0.0206717i
$323$	−362.540	−	362.540i	−0.0624528	−	0.0624528i
$324$	4013.24	−	1878.34i	0.688142	−	0.322074i
$325$	6950.87	−	5591.47i	1.18635	−	0.954335i
$326$		−	4614.37i		−	0.783946i
$327$	−61.5280	+	211.372i	−0.0104052	+	0.0357458i
$328$	5164.44			0.869386
$329$	8363.70			1.40154
$330$	−1450.22	−	422.143i	−0.241915	−	0.0704188i
$331$	−1458.54	−	1458.54i	−0.242201	−	0.242201i	0.575559	−	0.817760i	$-0.304785\pi$
$331$	−1458.54	−	1458.54i	−0.242201	−	0.242201i	−0.817760	+	0.575559i	$0.804785\pi$
$332$	1895.75	+	1895.75i	0.313382	+	0.313382i
$333$	−766.675	−	3446.69i	−0.126167	−	0.567199i
$334$	3127.69			0.512394
$335$	−11889.6			−1.93910
$336$	3265.88	+	950.661i	0.530263	+	0.154354i
$337$			9456.34i			1.52855i	0.644893	+	0.764273i	$0.276902\pi$
$337$			9456.34i			1.52855i	−0.644893	+	0.764273i	$0.723098\pi$
$338$	−1642.16	−	2564.99i	−0.264265	−	0.412772i
$339$	−85.2257	+	46.7957i	−0.0136544	+	0.00749733i
$340$	−3020.75	−	3020.75i	−0.481833	−	0.481833i
$341$		−	1586.48i		−	0.251943i
$342$	260.219	−	409.102i	0.0411434	−	0.0646833i
$343$	−5039.83	−	5039.83i	−0.793368	−	0.793368i
$344$	725.496	−	725.496i	0.113710	−	0.113710i
$345$	−251.542	−	73.2210i	−0.0392537	−	0.0114263i
$346$	−3410.58	+	3410.58i	−0.529925	+	0.529925i
$347$		−	12663.0i		−	1.95903i	−0.201366	−	0.979516i	$-0.564538\pi$
$347$		−	12663.0i		−	1.95903i	0.201366	−	0.979516i	$-0.435462\pi$
$348$	2666.25	+	4855.86i	0.410708	+	0.747992i
$349$	756.113	−	756.113i	0.115971	−	0.115971i	−0.646740	−	0.762711i	$-0.723868\pi$
$349$	756.113	−	756.113i	0.115971	−	0.115971i	0.762711	+	0.646740i	$0.223868\pi$
$350$	8006.28			1.22272
$351$	3783.57	+	5378.49i	0.575363	+	0.817898i
$352$	−2196.76			−0.332635
$353$	3714.43	−	3714.43i	0.560054	−	0.560054i	−0.369268	−	0.929323i	$-0.620392\pi$
$353$	3714.43	−	3714.43i	0.560054	−	0.560054i	0.929323	+	0.369268i	$0.120392\pi$
$354$	−1940.43	−	3533.96i	−0.291335	−	0.530587i
$355$		−	7867.89i		−	1.17629i
$356$	−3752.39	+	3752.39i	−0.558642	+	0.558642i
$357$	5992.32	+	1744.30i	0.888367	+	0.258594i
$358$	2033.01	−	2033.01i	0.300135	−	0.300135i
$359$	−6824.51	−	6824.51i	−1.00330	−	1.00330i	−0.999995	−	0.00330378i	$-0.998948\pi$
$359$	−6824.51	−	6824.51i	−1.00330	−	1.00330i	−0.00330378	−	0.999995i	$-0.501052\pi$
$360$	5021.90	−	7895.15i	0.735215	−	1.15586i
$361$		−	6691.20i		−	0.975536i
$362$	3950.86	+	3950.86i	0.573626	+	0.573626i
$363$	−5427.23	+	2979.98i	−0.784726	+	0.430877i
$364$	−931.600	+	8595.25i	−0.134146	+	1.23767i
$365$			2121.98i			0.304300i
$366$	722.849	+	210.413i	0.103235	+	0.0300505i
$367$	−5558.09			−0.790545			−0.395272	−	0.918564i	$-0.629350\pi$
$367$	−5558.09			−0.790545			−0.395272	+	0.918564i	$0.629350\pi$
$368$	−61.2482			−0.00867604
$369$	−1551.37	−	6974.36i	−0.218864	−	0.983932i
$370$	−2276.31	−	2276.31i	−0.319838	−	0.319838i
$371$	10153.2	+	10153.2i	1.42083	+	1.42083i
$372$	4074.21	+	1185.96i	0.567844	+	0.165293i
$373$	10353.4			1.43721			0.718607	−	0.695416i	$-0.244780\pi$
$373$	10353.4			1.43721			0.718607	+	0.695416i	$0.244780\pi$
$374$	−647.906			−0.0895787
$375$	−1684.49	+	5786.86i	−0.231965	+	0.796886i
$376$		−	5378.91i		−	0.737756i
$377$	−6405.89	+	5153.07i	−0.875119	+	0.703969i
$378$	−379.742	+	5889.67i	−0.0516715	+	0.801407i
$379$	−590.187	−	590.187i	−0.0799891	−	0.0799891i	0.665980	−	0.745969i	$-0.268013\pi$
$379$	−590.187	−	590.187i	−0.0799891	−	0.0799891i	−0.745969	+	0.665980i	$0.768013\pi$
$380$			1398.14i			0.188745i
$381$	−6298.50	+	3458.38i	−0.846934	+	0.465035i
$382$	−1592.26	−	1592.26i	−0.213265	−	0.213265i
$383$	−5620.17	+	5620.17i	−0.749811	+	0.749811i	−0.974443	−	0.224633i	$-0.927882\pi$
$383$	−5620.17	+	5620.17i	−0.749811	+	0.749811i	0.224633	+	0.974443i	$0.427882\pi$
$384$	1989.59	−	6835.00i	0.264404	−	0.908326i
$385$	−4499.37	+	4499.37i	−0.595608	+	0.595608i
$386$			1156.05i			0.152439i
$387$	−1197.69	−	761.818i	−0.157317	−	0.100066i
$388$	−1081.05	+	1081.05i	−0.141448	+	0.141448i
$389$	−907.219			−0.118246			−0.0591232	−	0.998251i	$-0.518830\pi$
$389$	−907.219			−0.118246			−0.0591232	+	0.998251i	$0.518830\pi$
$390$	5542.42	+	2286.18i	0.719618	+	0.296834i
$391$	−112.380			−0.0145353
$392$	−7974.66	+	7974.66i	−1.02750	+	1.02750i
$393$	−4638.17	+	2546.73i	−0.595330	+	0.326884i
$394$			6451.09i			0.824877i
$395$	8175.11	−	8175.11i	1.04135	−	1.04135i
$396$	420.782	+	1891.68i	0.0533967	+	0.240052i
$397$	−39.8753	+	39.8753i	−0.00504102	+	0.00504102i	−0.709623	−	0.704582i	$-0.751135\pi$
$397$	−39.8753	+	39.8753i	−0.00504102	+	0.00504102i	0.704582	+	0.709623i	$0.251135\pi$
$398$	−3954.09	−	3954.09i	−0.497992	−	0.497992i
$399$	−983.089	−	1790.43i	−0.123348	−	0.224646i
$400$			4105.49i			0.513186i
$401$	8973.42	+	8973.42i	1.11748	+	1.11748i	0.992109	+	0.125375i	$0.0400136\pi$
$401$	8973.42	+	8973.42i	1.11748	+	1.11748i	0.125375	+	0.992109i	$0.459986\pi$
$402$	−2321.32	−	4227.65i	−0.288002	−	0.524518i
$403$	−678.567	+	6260.69i	−0.0838755	+	0.773864i
$404$		−	7179.50i		−	0.884142i
$405$	−12170.6	−	4410.22i	−1.49324	−	0.541100i
$406$	−7378.54			−0.901948
$407$	1544.24			0.188072
$408$	1121.80	−	3853.81i	0.136121	−	0.467628i
$409$	1155.75	+	1155.75i	0.139726	+	0.139726i	0.773510	−	0.633784i	$-0.218499\pi$
$409$	1155.75	+	1155.75i	0.139726	+	0.139726i	−0.633784	+	0.773510i	$0.718499\pi$
$410$	−4606.12	−	4606.12i	−0.554829	−	0.554829i
$411$	−2287.81	+	7859.50i	−0.274573	+	0.943261i
$412$	−1384.74			−0.165586
$413$	−16984.5			−2.02362
$414$	−23.0752	−	103.738i	−0.00273934	−	0.0123151i
$415$		−	7832.35i		−	0.926446i
$416$	8669.02	+	939.596i	1.02172	+	0.110739i
$417$	4391.42	+	7997.78i	0.515704	+	0.939215i
$418$	149.940	+	149.940i	0.0175450	+	0.0175450i
$419$		−	1498.58i		−	0.174726i	−0.996177	−	0.0873630i	$-0.972156\pi$
$419$		−	1498.58i		−	0.174726i	0.996177	−	0.0873630i	$-0.0278440\pi$
$420$	−8191.29	−	14918.2i	−0.951653	−	1.73318i
$421$	9941.27	+	9941.27i	1.15085	+	1.15085i	0.986382	+	0.164468i	$0.0525907\pi$
$421$	9941.27	+	9941.27i	1.15085	+	1.15085i	0.164468	+	0.986382i	$0.447409\pi$
$422$	5044.34	−	5044.34i	0.581883	−	0.581883i
$423$	−7264.00	+	1615.79i	−0.834959	+	0.185727i
$424$	6529.81	−	6529.81i	0.747914	−	0.747914i
$425$			7532.85i			0.859757i
$426$	2797.63	−	1536.12i	0.318182	−	0.174708i
$427$	2242.67	−	2242.67i	0.254169	−	0.254169i
$428$	−3473.67			−0.392304
$429$	−2655.45	+	1104.51i	−0.298849	+	0.124303i
$430$	−1294.13			−0.145136
$431$	3711.54	−	3711.54i	0.414800	−	0.414800i	−0.468607	−	0.883407i	$-0.655244\pi$
$431$	3711.54	−	3711.54i	0.414800	−	0.414800i	0.883407	+	0.468607i	$0.155244\pi$
$432$	−3020.12	−	194.725i	−0.336356	−	0.0216869i
$433$		−	5222.54i		−	0.579628i	−0.957083	−	0.289814i	$-0.906407\pi$
$433$		−	5222.54i		−	0.579628i	0.957083	−	0.289814i	$-0.0935935\pi$
$434$	−3996.45	+	3996.45i	−0.442018	+	0.442018i
$435$	4523.21	−	15538.9i	0.498555	−	1.71272i
$436$	182.092	−	182.092i	0.0200015	−	0.0200015i
$437$	26.0073	+	26.0073i	0.00284690	+	0.00284690i
$438$	−754.524	+	414.294i	−0.0823118	+	0.0451958i
$439$			5028.80i			0.546724i	0.961911	+	0.273362i	$0.0881357\pi$
$439$			5028.80i			0.546724i	−0.961911	+	0.273362i	$0.911864\pi$
$440$	2893.66	+	2893.66i	0.313522	+	0.313522i
$441$	13165.0	+	8373.91i	1.42155	+	0.904213i
$442$	2556.82	+	277.122i	0.275148	+	0.0298220i
$443$			14535.3i			1.55890i	0.626466	+	0.779448i	$0.284501\pi$
$443$			14535.3i			1.55890i	−0.626466	+	0.779448i	$0.715499\pi$
$444$	−1154.39	+	3965.75i	−0.123389	+	0.423888i
$445$	15503.1			1.65150
$446$	−3588.40			−0.380977
$447$	13526.0	+	3937.27i	1.43123	+	0.416614i
$448$	1830.78	+	1830.78i	0.193072	+	0.193072i
$449$	1392.85	+	1392.85i	0.146398	+	0.146398i	0.776507	−	0.630109i	$-0.216990\pi$
$449$	1392.85	+	1392.85i	0.146398	+	0.146398i	−0.630109	+	0.776507i	$0.716990\pi$
$450$	−6953.57	+	1546.74i	−0.728432	+	0.162031i
$451$	3124.77			0.326252
$452$	113.734			0.0118354
$453$	−6839.15	−	1990.80i	−0.709340	−	0.206481i
$454$			4894.60i			0.505980i
$455$	19680.2	−	15831.3i	2.02774	−	1.63117i
$456$	−1151.47	+	632.250i	−0.118251	+	0.0649294i
$457$	−1525.73	−	1525.73i	−0.156172	−	0.156172i	0.624696	−	0.780868i	$-0.285223\pi$
$457$	−1525.73	−	1525.73i	−0.156172	−	0.156172i	−0.780868	+	0.624696i	$0.785223\pi$
$458$		−	2544.73i		−	0.259624i
$459$	−5541.40	−	357.287i	−0.563508	−	0.0363328i
$460$	216.698	+	216.698i	0.0219643	+	0.0219643i
$461$	1822.95	−	1822.95i	0.184172	−	0.184172i	−0.608999	−	0.793171i	$-0.708429\pi$
$461$	1822.95	−	1822.95i	0.184172	−	0.184172i	0.793171	+	0.608999i	$0.208429\pi$
$462$	−2478.32	−	721.412i	−0.249571	−	0.0726475i
$463$	11841.6	−	11841.6i	1.18860	−	1.18860i	0.211151	−	0.977454i	$-0.432279\pi$
$463$	11841.6	−	11841.6i	1.18860	−	1.18860i	0.977454	−	0.211151i	$-0.0677211\pi$
$464$		−	3783.59i		−	0.378554i
$465$	−5966.45	−	10866.3i	−0.595027	−	1.08368i
$466$	366.779	−	366.779i	0.0364608	−	0.0364608i
$467$	−9399.73			−0.931408			−0.465704	−	0.884941i	$-0.654199\pi$
$467$	−9399.73			−0.931408			−0.465704	+	0.884941i	$0.654199\pi$
$468$	−851.416	−	7645.08i	−0.0840956	−	0.755115i
$469$	−20318.5			−2.00047
$470$	−4797.40	+	4797.40i	−0.470825	+	0.470825i
$471$	470.000	+	855.977i	0.0459797	+	0.0837396i
$472$			10923.2i			1.06521i
$473$	438.965	−	438.965i	0.0426716	−	0.0426716i
$474$	4502.98	+	1310.77i	0.436347	+	0.127016i
$475$	1743.27	−	1743.27i	0.168394	−	0.168394i
$476$	−5162.25	−	5162.25i	−0.497083	−	0.497083i
$477$	−10779.7	−	6856.72i	−1.03474	−	0.658171i
$478$		−	28.5054i		−	0.00272763i
$479$	4069.42	+	4069.42i	0.388177	+	0.388177i	0.874037	−	0.485860i	$-0.161494\pi$
$479$	4069.42	+	4069.42i	0.388177	+	0.388177i	−0.485860	+	0.874037i	$0.661494\pi$
$480$	−15046.3	+	8261.60i	−1.43076	+	0.785602i
$481$	−6094.02	−	660.503i	−0.577679	−	0.0626119i
$482$		−	819.695i		−	0.0774607i
$483$	−429.866	−	125.129i	−0.0404961	−	0.0117880i
$484$	7242.63			0.680187
$485$	4466.39			0.418161
$486$	−808.019	−	5188.63i	−0.0754166	−	0.484282i
$487$	9498.10	+	9498.10i	0.883778	+	0.883778i	0.993916	−	0.110138i	$-0.0351294\pi$
$487$	9498.10	+	9498.10i	0.883778	+	0.883778i	−0.110138	+	0.993916i	$0.535129\pi$
$488$	−1442.32	−	1442.32i	−0.133792	−	0.133792i
$489$	16606.8	+	4834.06i	1.53576	+	0.447043i
$490$	14225.1			1.31147
$491$	10110.3			0.929269			0.464634	−	0.885503i	$-0.346186\pi$
$491$	10110.3			0.929269			0.464634	+	0.885503i	$0.346186\pi$
$492$	−2335.90	+	8024.68i	−0.214045	+	0.735327i
$493$		−	6942.23i		−	0.634204i
$494$	−527.574	−	655.839i	−0.0480500	−	0.0597320i
$495$	3038.53	−	4777.01i	0.275903	−	0.433758i
$496$	−2049.31	−	2049.31i	−0.185518	−	0.185518i
$497$		−	13445.7i		−	1.21352i
$498$	2785.00	−	1529.19i	0.250600	−	0.137599i
$499$	859.012	+	859.012i	0.0770635	+	0.0770635i	0.744588	−	0.667524i	$-0.232646\pi$
$499$	859.012	+	859.012i	0.0770635	+	0.0770635i	−0.667524	+	0.744588i	$0.732646\pi$
$500$	4985.26	−	4985.26i	0.445895	−	0.445895i
$501$	−3276.60	+	11256.4i	−0.292191	+	1.00379i
$502$	3568.21	−	3568.21i	0.317245	−	0.317245i
$503$		−	5309.97i		−	0.470695i	−0.971911	−	0.235348i	$-0.924377\pi$
$503$		−	5309.97i		−	0.470695i	0.971911	−	0.235348i	$-0.0756229\pi$
$504$	8582.07	−	13492.2i	0.758484	−	1.19245i
$505$	−14831.2	+	14831.2i	−1.30689	+	1.30689i
$506$	46.4784			0.00408343
$507$	10951.6	−	3222.92i	0.959321	−	0.282317i
$508$	8405.34			0.734108
$509$	−11449.6	+	11449.6i	−0.997046	+	0.997046i	−0.999996	−	0.00294997i	$-0.999061\pi$
$509$	−11449.6	+	11449.6i	−0.997046	+	0.997046i	0.00294997	+	0.999996i	$0.499061\pi$
$510$	−4437.71	+	2436.66i	−0.385304	+	0.211563i
$511$			3626.31i			0.313930i
$512$	−5219.13	+	5219.13i	−0.450499	+	0.450499i
$513$	1199.72	+	1365.09i	0.103254	+	0.117486i
$514$	−7886.83	+	7886.83i	−0.676796	+	0.676796i
$515$	2860.55	+	2860.55i	0.244759	+	0.244759i
$516$	799.155	+	1455.44i	0.0681799	+	0.124171i
$517$		−	3254.54i		−	0.276856i
$518$	−3890.06	−	3890.06i	−0.329960	−	0.329960i
$519$	−8701.50	−	15847.4i	−0.735941	−	1.34032i
$520$	−10181.5	−	12656.9i	−0.858633	−	1.06739i
$521$		−	4751.09i		−	0.399518i	−0.979845	−	0.199759i	$-0.935984\pi$
$521$		−	4751.09i		−	0.399518i	0.979845	−	0.199759i	$-0.0640160\pi$
$522$	6408.38	−	1425.47i	0.537331	−	0.119523i
$523$	−13699.2			−1.14536			−0.572682	−	0.819778i	$-0.694097\pi$
$523$	−13699.2			−1.14536			−0.572682	+	0.819778i	$0.694097\pi$
$524$	6189.63			0.516021
$525$	−8387.46	+	28814.1i	−0.697255	+	2.39533i
$526$	−2122.15	−	2122.15i	−0.175913	−	0.175913i
$527$	−3760.13	−	3760.13i	−0.310804	−	0.310804i
$528$	369.928	−	1270.84i	0.0304906	−	0.104747i
$529$	−12158.9			−0.999337
$530$	−11647.7			−0.954615
$531$	14751.3	−	3281.25i	1.20556	−	0.268162i
$532$			2389.33i			0.194719i
$533$	−12331.2	−	1336.53i	−1.00211	−	0.108614i
$534$	3026.82	+	5512.54i	0.245287	+	0.446725i
$535$	7175.78	+	7175.78i	0.579880	+	0.579880i
$536$			13067.3i			1.05303i
$537$	5186.88	+	9446.50i	0.416816	+	0.759118i
$538$	−8316.62	−	8316.62i	−0.666459	−	0.666459i
$539$	−4825.12	+	4825.12i	−0.385589	+	0.385589i
$540$	9996.33	+	11374.2i	0.796617	+	0.906423i
$541$	7488.89	−	7488.89i	0.595143	−	0.595143i	−0.343873	−	0.939016i	$-0.611739\pi$
$541$	7488.89	−	7488.89i	0.595143	−	0.595143i	0.939016	+	0.343873i	$0.111739\pi$
$542$			4427.17i			0.350854i
$543$	−18357.9	+	10079.9i	−1.45085	+	0.796632i
$544$	−5206.56	+	5206.56i	−0.410348	+	0.410348i
$545$	−752.320			−0.0591300
$546$	9471.59	+	3906.92i	0.742393	+	0.306228i
$547$	−3941.66			−0.308105			−0.154052	−	0.988063i	$-0.549232\pi$
$547$	−3941.66			−0.308105			−0.154052	+	0.988063i	$0.549232\pi$
$548$	6770.79	−	6770.79i	0.527799	−	0.527799i
$549$	−1514.53	+	2381.05i	−0.117739	+	0.185102i
$550$		−	3115.46i		−	0.241534i
$551$	−1606.59	+	1606.59i	−0.124216	+	0.124216i
$552$	−80.4740	+	276.458i	−0.00620507	+	0.0213167i
$553$	13970.7	−	13970.7i	1.07431	−	1.07431i
$554$	6879.54	+	6879.54i	0.527588	+	0.527588i
$555$	10577.0	−	5807.62i	0.808952	−	0.444179i
$556$		−	10673.0i		−	0.814095i
$557$	9204.93	+	9204.93i	0.700225	+	0.700225i	0.964459	−	0.264234i	$-0.0851190\pi$
$557$	9204.93	+	9204.93i	0.700225	+	0.700225i	−0.264234	+	0.964459i	$0.585119\pi$
$558$	2698.90	−	4243.05i	0.204755	−	0.321904i
$559$	−1920.03	+	1544.53i	−0.145275	+	0.116863i
$560$			11624.0i			0.877149i
$561$	678.753	−	2331.77i	0.0510820	−	0.175486i
$562$	−192.665			−0.0144610
$563$	−18033.2			−1.34993			−0.674963	−	0.737852i	$-0.735840\pi$
$563$	−18033.2			−1.34993			−0.674963	+	0.737852i	$0.735840\pi$
$564$	8357.94	+	2432.90i	0.623994	+	0.181638i
$565$	−234.947	−	234.947i	−0.0174943	−	0.0174943i
$566$	7849.95	+	7849.95i	0.582965	+	0.582965i
$567$	−20798.7	−	7536.75i	−1.54050	−	0.558225i
$568$	−8647.25			−0.638786
$569$	11148.1			0.821361			0.410680	−	0.911779i	$-0.365291\pi$
$569$	11148.1			0.821361			0.410680	+	0.911779i	$0.365291\pi$
$570$	1590.89	+	463.089i	0.116903	+	0.0340293i
$571$			5351.31i			0.392199i	0.980584	+	0.196099i	$0.0628275\pi$
$571$			5351.31i			0.392199i	−0.980584	+	0.196099i	$0.937173\pi$
$572$	3344.64	+	362.511i	0.244487	+	0.0264988i
$573$	7398.53	−	4062.38i	0.539403	−	0.296175i
$574$	−7871.52	−	7871.52i	−0.572388	−	0.572388i
$575$		−	540.379i		−	0.0391919i
$576$	−1943.75	−	1236.37i	−0.140607	−	0.0894364i
$577$	−13728.6	−	13728.6i	−0.990515	−	0.990515i	0.00944038	−	0.999955i	$-0.496995\pi$
$577$	−13728.6	−	13728.6i	−0.990515	−	0.990515i	−0.999955	+	0.00944038i	$0.996995\pi$
$578$	3280.30	−	3280.30i	0.236060	−	0.236060i
$579$	−4160.54	−	1211.09i	−0.298629	−	0.0869276i
$580$	−13386.4	+	13386.4i	−0.958348	+	0.958348i
$581$		−	13384.9i		−	0.955767i
$582$	872.015	+	1588.14i	0.0621069	+	0.113111i
$583$	3950.90	−	3950.90i	0.280668	−	0.280668i
$584$	2332.17			0.165250
$585$	−14034.1	+	17551.8i	−0.991862	+	1.24047i
$586$	10440.6			0.736005
$587$	1912.64	−	1912.64i	0.134486	−	0.134486i	−0.636659	−	0.771145i	$-0.719684\pi$
$587$	1912.64	−	1912.64i	0.134486	−	0.134486i	0.771145	+	0.636659i	$0.219684\pi$
$588$	−8784.33	−	15998.3i	−0.616088	−	1.12204i
$589$			1740.36i			0.121749i
$590$	9742.28	−	9742.28i	0.679802	−	0.679802i
$591$	−23217.1	−	6758.23i	−1.61594	−	0.470383i
$592$	1994.76	−	1994.76i	0.138486	−	0.138486i
$593$	11122.4	+	11122.4i	0.770223	+	0.770223i	0.978145	−	0.207922i	$-0.0666701\pi$
$593$	11122.4	+	11122.4i	0.770223	+	0.770223i	−0.207922	+	0.978145i	$0.566670\pi$
$594$	2291.83	+	147.768i	0.158308	+	0.0102071i
$595$			21328.0i			1.46952i
$596$	−11652.4	−	11652.4i	−0.800838	−	0.800838i
$597$	18372.9	−	10088.2i	1.25955	−	0.691594i
$598$	−183.417	−	19.8797i	−0.0125426	−	0.00135943i
$599$		−	6287.08i		−	0.428853i	−0.976740	−	0.214427i	$-0.931212\pi$
$599$		−	6287.08i		−	0.428853i	0.976740	−	0.214427i	$-0.0687882\pi$
$600$	18531.1	+	5394.20i	1.26088	+	0.367029i
$601$	−4651.42			−0.315700			−0.157850	−	0.987463i	$-0.550456\pi$
$601$	−4651.42			−0.315700			−0.157850	+	0.987463i	$0.550456\pi$
$602$	−2211.57			−0.149729
$603$	17646.9	−	3925.34i	1.19177	−	0.265095i
$604$	5891.78	+	5891.78i	0.396909	+	0.396909i
$605$	−14961.6	−	14961.6i	−1.00541	−	1.00541i
$606$	−8169.23	−	2377.97i	−0.547611	−	0.159404i
$607$	5225.96			0.349448			0.174724	−	0.984617i	$-0.444097\pi$
$607$	5225.96			0.349448			0.174724	+	0.984617i	$0.444097\pi$
$608$	2409.84			0.160743
$609$	7729.84	−	26554.9i	0.514333	−	1.76693i
$610$			2572.78i			0.170769i
$611$	−1392.03	+	12843.3i	−0.0921694	+	0.850386i
$612$	5480.79	+	3486.19i	0.362006	+	0.230263i
$613$	−9977.15	−	9977.15i	−0.657379	−	0.657379i	0.297380	−	0.954759i	$-0.403887\pi$
$613$	−9977.15	−	9977.15i	−0.657379	−	0.657379i	−0.954759	+	0.297380i	$0.903887\pi$
$614$		−	8756.01i		−	0.575511i
$615$	21402.5	−	11751.7i	1.40331	−	0.770527i
$616$	4945.06	+	4945.06i	0.323445	+	0.323445i
$617$	−3883.63	+	3883.63i	−0.253402	+	0.253402i	−0.822364	−	0.568962i	$-0.807345\pi$
$617$	−3883.63	+	3883.63i	−0.253402	+	0.253402i	0.568962	+	0.822364i	$0.307345\pi$
$618$	−458.650	+	1575.63i	−0.0298537	+	0.102559i
$619$	−11697.3	+	11697.3i	−0.759537	+	0.759537i	−0.976238	−	0.216701i	$-0.930470\pi$
$619$	−11697.3	+	11697.3i	−0.759537	+	0.759537i	0.216701	+	0.976238i	$0.430470\pi$
$620$			14501.0i			0.939315i
$621$	397.519	+	25.6305i	0.0256874	+	0.00165622i
$622$	3241.09	−	3241.09i	0.208932	−	0.208932i
$623$	26493.7			1.70377
$624$	−2003.40	+	4856.87i	−0.128526	+	0.311587i
$625$	3193.27			0.204369
$626$	561.539	−	561.539i	0.0358524	−	0.0358524i
$627$	−696.705	+	382.547i	−0.0443759	+	0.0243659i
$628$		−	1142.30i		−	0.0725840i
$629$	3660.03	−	3660.03i	0.232011	−	0.232011i
$630$	−19687.9	+	4379.34i	−1.24505	+	0.276948i
$631$	16669.7	−	16669.7i	1.05168	−	1.05168i	0.0530933	−	0.998590i	$-0.483092\pi$
$631$	16669.7	−	16669.7i	1.05168	−	1.05168i	0.998590	−	0.0530933i	$-0.0169081\pi$
$632$	−8984.90	−	8984.90i	−0.565507	−	0.565507i
$633$	12869.8	+	23438.8i	0.808099	+	1.47173i
$634$			4658.51i			0.291818i
$635$	−17363.5	−	17363.5i	−1.08512	−	1.08512i
$636$	7192.78	+	13099.7i	0.448447	+	0.816724i
$637$	21105.1	−	16977.5i	1.31274	−	1.05600i
$638$			2871.19i			0.178169i
$639$	2597.58	+	11677.8i	0.160812	+	0.722949i
$640$	24327.3			1.50253
$641$	−16769.7			−1.03333			−0.516663	−	0.856189i	$-0.672826\pi$
$641$	−16769.7			−1.03333			−0.516663	+	0.856189i	$0.672826\pi$
$642$	−1150.54	+	3952.53i	−0.0707292	+	0.242981i
$643$	9637.04	+	9637.04i	0.591054	+	0.591054i	0.937916	−	0.346862i	$-0.112753\pi$
$643$	9637.04	+	9637.04i	0.591054	+	0.591054i	−0.346862	+	0.937916i	$0.612753\pi$
$644$	370.321	+	370.321i	0.0226594	+	0.0226594i
$645$	1355.74	−	4657.47i	0.0827631	−	0.284322i
$646$	710.751			0.0432881
$647$	15564.9			0.945781			0.472890	−	0.881121i	$-0.343211\pi$
$647$	15564.9			0.945781			0.472890	+	0.881121i	$0.343211\pi$
$648$	−4847.08	+	13376.2i	−0.293844	+	0.810905i
$649$			6609.13i			0.399740i
$650$	−1332.54	+	12294.5i	−0.0804102	+	0.741891i
$651$	−10196.2	−	18569.7i	−0.613859	−	1.11798i
$652$	−14306.4	−	14306.4i	−0.859329	−	0.859329i
$653$			26562.0i			1.59181i	0.605424	+	0.795903i	$0.293004\pi$
$653$			26562.0i			1.59181i	−0.605424	+	0.795903i	$0.706996\pi$
$654$	−146.883	−	267.507i	−0.00878221	−	0.0159944i
$655$	−12786.3	−	12786.3i	−0.762753	−	0.762753i
$656$	4036.38	−	4036.38i	0.240235	−	0.240235i
$657$	−700.570	−	3149.50i	−0.0416010	−	0.187023i
$658$	−8198.42	+	8198.42i	−0.485726	+	0.485726i
$659$		−	16494.7i		−	0.975026i	−0.873116	−	0.487513i	$-0.837904\pi$
$659$		−	16494.7i		−	0.975026i	0.873116	−	0.487513i	$-0.162096\pi$
$660$	−5805.08	+	3187.45i	−0.342367	+	0.187987i
$661$	−22055.3	+	22055.3i	−1.29781	+	1.29781i	−0.367968	+	0.929839i	$0.619946\pi$
$661$	−22055.3	+	22055.3i	−1.29781	+	1.29781i	−0.929839	+	0.367968i	$0.880054\pi$
$662$	2859.43			0.167878
$663$	−3675.89	+	8911.51i	−0.215324	+	0.522013i
$664$	−8608.19			−0.503107
$665$	4935.79	−	4935.79i	0.287822	−	0.287822i
$666$	4130.10	+	2627.05i	0.240297	+	0.152847i
$667$			498.010i			0.0289101i
$668$	9697.11	−	9697.11i	0.561665	−	0.561665i
$669$	3759.25	−	12914.4i	0.217251	−	0.746338i
$670$	11654.6	−	11654.6i	0.672026	−	0.672026i
$671$	−872.683	−	872.683i	−0.0502080	−	0.0502080i
$672$	−25713.0	+	14118.5i	−1.47604	+	0.810465i
$673$			19116.7i			1.09494i	0.836825	+	0.547471i	$0.184409\pi$
$673$			19116.7i			1.09494i	−0.836825	+	0.547471i	$0.815591\pi$
$674$	−9269.46	−	9269.46i	−0.529742	−	0.529742i
$675$	1718.02	−	26645.8i	0.0979652	−	1.51941i
$676$	−13043.8	−	2861.14i	−0.742140	−	0.162787i
$677$		−	10209.1i		−	0.579567i	−0.957092	−	0.289783i	$-0.906417\pi$
$677$		−	10209.1i		−	0.579567i	0.957092	−	0.289783i	$-0.0935833\pi$
$678$	37.6705	−	129.412i	0.00213382	−	0.00733046i
$679$	7632.73			0.431395
$680$	13716.6			0.773540
$681$	−17615.3	−	5127.63i	−0.991221	−	0.288533i
$682$	1555.13	+	1555.13i	0.0873150	+	0.0873150i
$683$	3196.97	+	3196.97i	0.179105	+	0.179105i	0.790966	−	0.611861i	$-0.209579\pi$
$683$	3196.97	+	3196.97i	0.179105	+	0.179105i	−0.611861	+	0.790966i	$0.709579\pi$
$684$	−461.596	−	2075.17i	−0.0258035	−	0.116003i
$685$	−27973.7			−1.56032
$686$	9880.47			0.549910
$687$	9158.33	+	2665.89i	0.508606	+	0.148050i
$688$		−	1134.05i		−	0.0628422i
$689$	−17281.2	+	13901.5i	−0.955533	+	0.768656i
$690$	318.345	−	174.797i	0.0175640	−	0.00964405i
$691$	23607.5	+	23607.5i	1.29967	+	1.29967i	0.928608	+	0.371063i	$0.121007\pi$
$691$	23607.5	+	23607.5i	1.29967	+	1.29967i	0.371063	+	0.928608i	$0.378993\pi$
$692$			21148.4i			1.16176i
$693$	5192.63	−	8163.56i	0.284635	−	0.447486i
$694$	12412.7	+	12412.7i	0.678935	+	0.678935i
$695$	−22048.0	+	22048.0i	−1.20335	+	1.20335i
$696$	−17078.1	−	4971.26i	−0.930094	−	0.270740i
$697$	7406.06	−	7406.06i	0.402474	−	0.402474i
$698$			1482.34i			0.0803832i
$699$	935.772	+	1704.26i	0.0506354	+	0.0922187i
$700$	24822.7	−	24822.7i	1.34030	−	1.34030i
$701$	−23768.5			−1.28063			−0.640316	−	0.768111i	$-0.721197\pi$
$701$	−23768.5			−1.28063			−0.640316	+	0.768111i	$0.721197\pi$
$702$	−8981.00	−	1563.39i	−0.482857	−	0.0840548i
$703$	−1694.03			−0.0908841
$704$	712.406	−	712.406i	0.0381389	−	0.0381389i
$705$	−12239.7	−	22291.4i	−0.653865	−	1.19084i
$706$			7282.05i			0.388192i
$707$	−25345.4	+	25345.4i	−1.34825	+	1.34825i
$708$	−16972.8	−	4940.60i	−0.900956	−	0.262259i
$709$	−6842.97	+	6842.97i	−0.362473	+	0.362473i	−0.864723	−	0.502250i	$-0.832506\pi$
$709$	−6842.97	+	6842.97i	−0.362473	+	0.362473i	0.502250	+	0.864723i	$0.332506\pi$
$710$	7712.40	+	7712.40i	0.407664	+	0.407664i
$711$	−9434.73	+	14832.7i	−0.497651	+	0.782379i
$712$		−	17038.8i		−	0.896849i
$713$	269.738	+	269.738i	0.0141680	+	0.0141680i
$714$	−7583.72	+	4164.07i	−0.397498	+	0.218258i
$715$	−6160.39	−	7658.11i	−0.322217	−	0.400555i
$716$		−	12606.3i		−	0.657990i
$717$	102.589	+	29.8626i	0.00534346	+	0.00155542i
$718$	13379.3			0.695419
$719$	14543.7			0.754365			0.377183	−	0.926139i	$-0.376893\pi$
$719$	14543.7			0.754365			0.377183	+	0.926139i	$0.376893\pi$
$720$	−2245.65	−	10095.6i	−0.116237	−	0.522557i
$721$	4888.47	+	4888.47i	0.252505	+	0.252505i
$722$	6558.97	+	6558.97i	0.338088	+	0.338088i
$723$	2950.03	+	858.721i	0.151747	+	0.0441718i
$724$	24498.5			1.25757
$725$	33381.8			1.71002
$726$	2398.88	−	8241.07i	0.122632	−	0.421287i
$727$			37001.0i			1.88761i	0.330508	+	0.943803i	$0.392780\pi$
$727$			37001.0i			1.88761i	−0.330508	+	0.943803i	$0.607220\pi$
$728$	−17399.5	−	21629.7i	−0.885808	−	1.10117i
$729$	19520.0	+	2527.65i	0.991720	+	0.128418i
$730$	−2080.04	−	2080.04i	−0.105460	−	0.105460i
$731$		−	2080.79i		−	0.105282i
$732$	2893.49	−	1588.76i	0.146102	−	0.0802215i
$733$	−25498.3	−	25498.3i	−1.28486	−	1.28486i	−0.937870	−	0.346987i	$-0.887205\pi$
$733$	−25498.3	−	25498.3i	−1.28486	−	1.28486i	−0.346987	−	0.937870i	$-0.612795\pi$
$734$	5448.25	−	5448.25i	0.273976	−	0.273976i
$735$	−14902.3	+	51195.1i	−0.747864	+	2.56919i
$736$	373.499	−	373.499i	0.0187057	−	0.0187057i
$737$			7906.46i			0.395167i
$738$	8357.24	+	5315.83i	0.416849	+	0.265147i
$739$	19940.2	−	19940.2i	0.992574	−	0.992574i	−0.00739871	−	0.999973i	$-0.502355\pi$
$739$	19940.2	−	19940.2i	0.992574	−	0.992574i	0.999973	+	0.00739871i	$0.00235511\pi$
$740$	−14115.0			−0.701186
$741$	2913.02	−	1211.64i	0.144416	−	0.0600685i
$742$	−19905.2			−0.984827
$743$	14891.9	−	14891.9i	0.735302	−	0.735302i	−0.236363	−	0.971665i	$-0.575955\pi$
$743$	14891.9	−	14891.9i	0.735302	−	0.735302i	0.971665	+	0.236363i	$0.0759555\pi$
$744$	−11942.6	+	6557.46i	−0.588492	+	0.323129i
$745$			48142.1i			2.36750i
$746$	−10148.8	+	10148.8i	−0.498090	+	0.498090i
$747$	2585.85	+	11625.0i	0.126655	+	0.569393i
$748$	−2008.77	+	2008.77i	−0.0981924	+	0.0981924i
$749$	12262.9	+	12262.9i	0.598233	+	0.598233i
$750$	−4021.30	−	7323.71i	−0.195783	−	0.356565i
$751$		−	29500.0i		−	1.43338i	−0.697391	−	0.716691i	$-0.745656\pi$
$751$		−	29500.0i		−	1.43338i	0.697391	−	0.716691i	$-0.254344\pi$
$752$	−4204.01	−	4204.01i	−0.203862	−	0.203862i
$753$	9103.67	+	16579.9i	0.440579	+	0.802396i
$754$	1228.06	−	11330.5i	0.0593149	−	0.547259i
$755$		−	24342.1i		−	1.17337i
$756$	17083.0	+	19437.7i	0.821829	+	0.935109i
$757$	33559.2			1.61127			0.805634	−	0.592414i	$-0.201825\pi$
$757$	33559.2			1.61127			0.805634	+	0.592414i	$0.201825\pi$
$758$	1157.05			0.0554431
$759$	−48.6912	+	167.273i	−0.00232856	+	0.00799949i
$760$	−3174.33	−	3174.33i	−0.151507	−	0.151507i
$761$	−7495.37	−	7495.37i	−0.357039	−	0.357039i	0.505681	−	0.862720i	$-0.331241\pi$
$761$	−7495.37	−	7495.37i	−0.357039	−	0.357039i	−0.862720	+	0.505681i	$0.831241\pi$
$762$	2783.99	−	9564.06i	0.132354	−	0.454684i
$763$	−1285.66			−0.0610014
$764$	−9873.33			−0.467545
$765$	−4120.38	−	18523.7i	−0.194735	−	0.875458i
$766$		−	11018.2i		−	0.519718i
$767$	2826.85	−	26081.5i	0.133079	−	1.22783i
$768$	6456.67	+	11759.1i	0.303366	+	0.552499i
$769$	3499.00	+	3499.00i	0.164080	+	0.164080i	0.784371	−	0.620292i	$-0.212986\pi$
$769$	3499.00	+	3499.00i	0.164080	+	0.164080i	−0.620292	+	0.784371i	$0.712986\pi$
$770$		−	8820.90i		−	0.412835i
$771$	−20121.9	−	36646.5i	−0.939911	−	1.71179i
$772$	3584.22	+	3584.22i	0.167097	+	0.167097i
$773$	21389.3	−	21389.3i	0.995240	−	0.995240i	−0.00474920	−	0.999989i	$-0.501512\pi$
$773$	21389.3	−	21389.3i	0.995240	−	0.995240i	0.999989	+	0.00474920i	$0.00151172\pi$
$774$	1920.78	−	427.255i	0.0892003	−	0.0198416i
$775$	18080.6	−	18080.6i	0.838031	−	0.838031i
$776$		−	4908.81i		−	0.227082i
$777$	18075.3	−	9924.80i	0.834554	−	0.458237i
$778$	889.290	−	889.290i	0.0409802	−	0.0409802i
$779$	−3427.86			−0.157659
$780$	24271.8	−	10095.6i	1.11419	−	0.463438i
$781$	−5232.07			−0.239716
$782$	110.159	−	110.159i	0.00503743	−	0.00503743i
$783$	−1583.32	+	24556.7i	−0.0722645	+	1.12080i
$784$			12465.6i			0.567855i
$785$	−2359.72	+	2359.72i	−0.107289	+	0.107289i
$786$	2050.11	−	7042.91i	0.0930345	−	0.319608i
$787$	−18104.8	+	18104.8i	−0.820033	+	0.820033i	−0.986112	−	0.166079i	$-0.946889\pi$
$787$	−18104.8	+	18104.8i	−0.820033	+	0.820033i	0.166079	+	0.986112i	$0.446889\pi$
$788$	20001.0	+	20001.0i	0.904196	+	0.904196i
$789$	9860.68	−	5414.30i	0.444930	−	0.244302i
$790$			16027.1i			0.721796i
$791$	−401.508	−	401.508i	−0.0180480	−	0.0180480i
$792$	−5250.20	−	3339.52i	−0.235553	−	0.149829i
$793$	3070.59	+	3817.11i	0.137503	+	0.170933i
$794$		−	78.1746i		−	0.00349409i
$795$	12202.3	−	41919.5i	0.544366	−	1.87010i
$796$	−24518.6			−1.09176
$797$	33484.2			1.48817			0.744086	−	0.668084i	$-0.232885\pi$
$797$	33484.2			1.48817			0.744086	+	0.668084i	$0.232885\pi$
$798$	2718.71	+	791.386i	0.120603	+	0.0351062i
$799$	−7713.62	−	7713.62i	−0.341537	−	0.341537i
$800$	−25035.8	−	25035.8i	−1.10644	−	1.10644i
$801$	−23010.2	+	5118.35i	−1.01501	+	0.225778i
$802$	−17592.2			−0.774565
$803$	1411.09			0.0620130
$804$	−20304.5	−	5910.41i	−0.890651	−	0.259259i
$805$		−	1529.99i		−	0.0669877i
$806$	−5471.80	−	6802.12i	−0.239127	−	0.297264i
$807$	38643.6	−	21218.4i	1.68565	−	0.925556i
$808$	16300.3	+	16300.3i	0.709705	+	0.709705i
$809$		−	17431.9i		−	0.757568i	−0.925485	−	0.378784i	$-0.876342\pi$
$809$		−	17431.9i		−	0.757568i	0.925485	−	0.378784i	$-0.123658\pi$
$810$	16253.2	−	7607.04i	0.705035	−	0.329980i
$811$	27929.2	+	27929.2i	1.20928	+	1.20928i	0.971261	+	0.238019i	$0.0764980\pi$
$811$	27929.2	+	27929.2i	1.20928	+	1.20928i	0.238019	+	0.971261i	$0.423502\pi$
$812$	−22876.5	+	22876.5i	−0.988678	+	0.988678i
$813$	−15933.1	−	4637.95i	−0.687328	−	0.200074i
$814$	−1513.73	+	1513.73i	−0.0651795	+	0.0651795i
$815$			59107.4i			2.54042i
$816$	−2135.26	−	3888.81i	−0.0916044	−	0.166833i
$817$	−481.543	+	481.543i	−0.0206206	+	0.0206206i
$818$	−2265.82			−0.0968489
$819$	−23983.3	+	29994.7i	−1.02325	+	1.27973i
$820$	−28561.6			−1.21636
$821$	−977.281	+	977.281i	−0.0415437	+	0.0415437i	−0.727573	−	0.686030i	$-0.759352\pi$
$821$	−977.281	+	977.281i	−0.0415437	+	0.0415437i	0.686030	+	0.727573i	$0.259352\pi$
$822$	−5461.58	−	9946.78i	−0.231745	−	0.422060i
$823$		−	18625.0i		−	0.788856i	−0.918927	−	0.394428i	$-0.870943\pi$
$823$		−	18625.0i		−	0.788856i	0.918927	−	0.394428i	$-0.129057\pi$
$824$	3143.90	−	3143.90i	0.132916	−	0.132916i
$825$	11212.3	+	3263.79i	0.473168	+	0.137734i
$826$	16648.9	−	16648.9i	0.701317	−	0.701317i
$827$	−18545.6	−	18545.6i	−0.779799	−	0.779799i	0.199997	−	0.979796i	$-0.435907\pi$
$827$	−18545.6	−	18545.6i	−0.779799	−	0.779799i	−0.979796	+	0.199997i	$0.935907\pi$
$828$	−393.172	−	250.086i	−0.0165020	−	0.0104965i
$829$			30011.6i			1.25735i	0.777667	+	0.628676i	$0.216403\pi$
$829$			30011.6i			1.25735i	−0.777667	+	0.628676i	$0.783597\pi$
$830$	7677.57	+	7677.57i	0.321075	+	0.321075i
$831$	−31966.1	+	17551.9i	−1.33441	+	0.732696i
$832$	−3116.06	+	2506.64i	−0.129844	+	0.104450i
$833$			22872.1i			0.951347i
$834$	−12144.4	−	3535.09i	−0.504226	−	0.146775i
$835$	−40063.9			−1.66044
$836$	929.752			0.0384643
$837$	12443.1	+	14158.2i	0.513854	+	0.584683i
$838$	1468.96	+	1468.96i	0.0605542	+	0.0605542i
$839$	29877.0	+	29877.0i	1.22940	+	1.22940i	0.964190	+	0.265211i	$0.0854415\pi$
$839$	29877.0	+	29877.0i	1.22940	+	1.22940i	0.265211	+	0.964190i	$0.414558\pi$
$840$	52467.7	+	15272.8i	2.15513	+	0.627334i
$841$	−6375.44			−0.261407
$842$	−19489.6			−0.797692
$843$	201.838	−	693.388i	0.00824633	−	0.0283293i
$844$		−	31279.0i		−	1.27567i
$845$	21035.1	+	32856.0i	0.856366	+	1.33761i
$846$	5536.59	−	8704.31i	0.225002	−	0.353736i
$847$	−25568.3	−	25568.3i	−1.03723	−	1.03723i
$848$		−	10207.0i		−	0.413338i
$849$	−36475.2	+	20027.8i	−1.47447	+	0.809601i
$850$	−7383.98	−	7383.98i	−0.297963	−	0.297963i
$851$	−262.557	+	262.557i	−0.0105762	+	0.0105762i
$852$	3911.19	−	13436.4i	0.157271	−	0.540285i
$853$	−2542.34	+	2542.34i	−0.102049	+	0.102049i	−0.756288	−	0.654239i	$-0.772989\pi$
$853$	−2542.34	+	2542.34i	−0.102049	+	0.102049i	0.654239	+	0.756288i	$0.272989\pi$
$854$			4396.70i			0.176173i
$855$	−3333.26	+	5240.36i	−0.133327	+	0.209610i
$856$	7886.58	−	7886.58i	0.314904	−	0.314904i
$857$	−670.949			−0.0267435			−0.0133717	−	0.999911i	$-0.504256\pi$
$857$	−670.949			−0.0267435			−0.0133717	+	0.999911i	$0.504256\pi$
$858$	1520.29	−	3685.65i	0.0604916	−	0.146650i
$859$	−21485.2			−0.853396			−0.426698	−	0.904394i	$-0.640323\pi$
$859$	−21485.2			−0.853396			−0.426698	+	0.904394i	$0.640323\pi$
$860$	−4012.31	+	4012.31i	−0.159092	+	0.159092i
$861$	36575.4	−	20082.8i	1.44772	−	0.794913i
$862$			7276.39i			0.287511i
$863$	5985.24	−	5985.24i	0.236084	−	0.236084i	−0.579143	−	0.815226i	$-0.696613\pi$
$863$	5985.24	−	5985.24i	0.236084	−	0.236084i	0.815226	+	0.579143i	$0.196613\pi$
$864$	19604.6	−	17229.6i	0.771945	−	0.678431i
$865$	43687.5	−	43687.5i	1.71725	−	1.71725i
$866$	5119.33	+	5119.33i	0.200880	+	0.200880i
$867$	8369.11	+	15242.1i	0.327831	+	0.597056i
$868$			24781.2i			0.969043i
$869$	−5436.37	−	5436.37i	−0.212216	−	0.212216i
$870$	10798.0	+	19665.7i	0.420790	+	0.766354i
$871$	3381.75	−	31201.1i	0.131557	−	1.21379i
$872$			826.842i			0.0321105i
$873$	−6629.14	+	1474.58i	−0.257002	+	0.0571670i
$874$	−50.9866			−0.00197328
$875$	−35198.4			−1.35991
$876$	−1054.85	+	3623.81i	−0.0406851	+	0.139768i
$877$	−15989.8	−	15989.8i	−0.615664	−	0.615664i	0.328752	−	0.944416i	$-0.393372\pi$
$877$	−15989.8	−	15989.8i	−0.615664	−	0.615664i	−0.944416	+	0.328752i	$0.893372\pi$
$878$	−4929.42	−	4929.42i	−0.189476	−	0.189476i
$879$	−10937.7	+	37575.2i	−0.419705	+	1.44184i
$880$	4523.21			0.173270
$881$	4784.23			0.182957			0.0914784	−	0.995807i	$-0.470841\pi$
$881$	4784.23			0.182957			0.0914784	+	0.995807i	$0.470841\pi$
$882$	−21113.3	+	4696.39i	−0.806032	+	0.179292i
$883$			14740.6i			0.561792i	0.959738	+	0.280896i	$0.0906316\pi$
$883$			14740.6i			0.561792i	−0.959738	+	0.280896i	$0.909368\pi$
$884$	8786.36	−	7067.98i	0.334296	−	0.268916i
$885$	24855.7	+	45268.0i	0.944086	+	1.71940i
$886$	−14248.0	−	14248.0i	−0.540261	−	0.540261i
$887$		−	33315.4i		−	1.26113i	−0.776137	−	0.630564i	$-0.782824\pi$
$887$		−	33315.4i		−	1.26113i	0.776137	−	0.630564i	$-0.217176\pi$
$888$	−6382.90	−	11624.7i	−0.241212	−	0.439302i
$889$	−29672.9	−	29672.9i	−1.11946	−	1.11946i
$890$	−15196.8	+	15196.8i	−0.572356	+	0.572356i
$891$	−2932.75	+	8093.34i	−0.110270	+	0.304307i
$892$	−11125.5	+	11125.5i	−0.417611	+	0.417611i
$893$			3570.22i			0.133788i
$894$	−17118.2	+	9399.24i	−0.640400	+	0.351630i
$895$	−26041.7	+	26041.7i	−0.972603	+	0.972603i
$896$	41573.6			1.55009
$897$	263.695	−	639.279i	0.00981552	−	0.0237959i
$898$	−2730.65			−0.101473
$899$	−16663.0	+	16663.0i	−0.618177	+	0.618177i
$900$	−16763.4	+	26354.4i	−0.620866	+	0.976089i
$901$		−	18728.1i		−	0.692480i
$902$	−3063.02	+	3063.02i	−0.113068	+	0.113068i
$903$	2316.86	−	7959.29i	0.0853824	−	0.293321i
$904$	−258.220	+	258.220i	−0.00950030	+	0.00950030i
$905$	−50608.2	−	50608.2i	−1.85887	−	1.85887i
$906$	8655.45	−	4752.53i	0.317393	−	0.174274i
$907$			1739.58i			0.0636844i	0.999493	+	0.0318422i	$0.0101374\pi$
$907$			1739.58i			0.0636844i	−0.999493	+	0.0318422i	$0.989863\pi$
$908$	15175.2	+	15175.2i	0.554634	+	0.554634i
$909$	17116.3	−	26909.3i	0.624547	−	0.981877i
$910$	−3772.87	+	34809.8i	−0.137439	+	1.26806i
$911$		−	20866.1i		−	0.758864i	−0.925220	−	0.379432i	$-0.876119\pi$
$911$		−	20866.1i		−	0.758864i	0.925220	−	0.379432i	$-0.123881\pi$
$912$	−405.810	+	1394.11i	−0.0147343	+	0.0506179i
$913$	−5208.44			−0.188800
$914$	2991.16			0.108248
$915$	−9259.27	−	2695.27i	−0.334538	−	0.0973803i
$916$	−7889.70	−	7889.70i	−0.284589	−	0.284589i
$917$	−21850.9	−	21850.9i	−0.786893	−	0.786893i
$918$	5782.12	−	5081.66i	0.207885	−	0.182701i
$919$	36900.1			1.32451			0.662254	−	0.749280i	$-0.269600\pi$
$919$	36900.1			1.32451			0.662254	+	0.749280i	$0.269600\pi$
$920$	−983.977			−0.0352617
$921$	31512.3	+	9172.89i	1.12743	+	0.328184i
$922$			3573.85i			0.127656i
$923$	20647.2	+	2237.86i	0.736307	+	0.0798049i
$924$	−9920.47	+	5447.13i	−0.353203	+	0.193937i
$925$	17599.3	+	17599.3i	0.625579	+	0.625579i
$926$			23215.1i			0.823861i
$927$	−5190.12	−	3301.30i	−0.183890	−	0.116968i
$928$	23072.8	+	23072.8i	0.816167	+	0.816167i
$929$	13969.2	−	13969.2i	0.493340	−	0.493340i	−0.416017	−	0.909357i	$-0.636574\pi$
$929$	13969.2	−	13969.2i	0.493340	−	0.493340i	0.909357	+	0.416017i	$0.136574\pi$
$930$	16500.1	+	4802.99i	0.581783	+	0.169351i
$931$	5293.13	−	5293.13i	0.186332	−	0.186332i
$932$		−	2274.33i		−	0.0799335i
$933$	8269.07	+	15059.9i	0.290158	+	0.528444i
$934$	9213.97	−	9213.97i	0.322795	−	0.322795i
$935$	8299.30			0.290285
$936$	19290.4	+	15424.3i	0.673638	+	0.538631i
$937$	13597.8			0.474088			0.237044	−	0.971499i	$-0.423821\pi$
$937$	13597.8			0.474088			0.237044	+	0.971499i	$0.423821\pi$
$938$	19916.9	−	19916.9i	0.693295	−	0.693295i
$939$	1432.67	+	2609.22i	0.0497906	+	0.0906801i
$940$			29747.8i			1.03220i
$941$	−18089.6	+	18089.6i	−0.626678	+	0.626678i	−0.947231	−	0.320553i	$-0.896131\pi$
$941$	−18089.6	+	18089.6i	−0.626678	+	0.626678i	0.320553	+	0.947231i	$0.396131\pi$
$942$	−1299.77	−	378.349i	−0.0449563	−	0.0130863i
$943$	−531.283	+	531.283i	−0.0183467	+	0.0183467i
$944$	8537.26	+	8537.26i	0.294347	+	0.294347i
$945$	4864.28	−	75443.2i	0.167444	−	2.59700i
$946$			860.581i			0.0295771i
$947$	1830.89	+	1830.89i	0.0628257	+	0.0628257i	0.737822	−	0.674996i	$-0.235855\pi$
$947$	1830.89	+	1830.89i	0.0628257	+	0.0628257i	−0.674996	+	0.737822i	$0.735855\pi$
$948$	18025.0	−	9897.14i	0.617535	−	0.339076i
$949$	−5568.58	−	603.552i	−0.190478	−	0.0206450i
$950$			3417.65i			0.116719i
$951$	−16765.7	−	4880.30i	−0.571676	−	0.166409i
$952$	23440.7			0.798021
$953$	10645.7			0.361855			0.180927	−	0.983496i	$-0.442090\pi$
$953$	10645.7			0.361855			0.180927	+	0.983496i	$0.442090\pi$
$954$	17287.9	−	3845.50i	0.586706	−	0.130506i
$955$	20396.0	+	20396.0i	0.691098	+	0.691098i
$956$	−88.3783	−	88.3783i	−0.00298991	−	0.00298991i
$957$	−10333.2	−	3007.89i	−0.349034	−	0.101600i
$958$	−7978.00			−0.269058
$959$	−47805.1			−1.60970
$960$	2200.26	−	7558.71i	0.0739719	−	0.254121i
$961$		−	11740.6i		−	0.394100i
$962$	6621.04	−	5326.14i	0.221903	−	0.178505i
$963$	−13019.6	−	8281.42i	−0.435670	−	0.277119i
$964$	−2541.39	−	2541.39i	−0.0849093	−	0.0849093i
$965$		−	14808.3i		−	0.493985i
$966$	544.028	−	298.715i	0.0181199	−	0.00994927i
$967$	2868.25	+	2868.25i	0.0953843	+	0.0953843i	0.753189	−	0.657804i	$-0.228515\pi$
$967$	2868.25	+	2868.25i	0.0953843	+	0.0953843i	−0.657804	+	0.753189i	$0.728515\pi$
$968$	−16443.6	+	16443.6i	−0.545989	+	0.545989i
$969$	−744.590	+	2557.95i	−0.0246849	+	0.0848019i
$970$	−4378.12	+	4378.12i	−0.144921	+	0.144921i
$971$		−	28264.0i		−	0.934123i	−0.884225	−	0.467062i	$-0.845313\pi$
$971$		−	28264.0i		−	0.934123i	0.884225	−	0.467062i	$-0.154687\pi$
$972$	−18592.0	−	13581.7i	−0.613518	−	0.448181i
$973$	−37678.4	+	37678.4i	−1.24143	+	1.24143i
$974$	−18620.8			−0.612575
$975$	−42851.0	−	17675.6i	−1.40752	−	0.580586i
$976$	−2254.55			−0.0739410
$977$	9578.62	−	9578.62i	0.313661	−	0.313661i	−0.532665	−	0.846326i	$-0.678809\pi$
$977$	9578.62	−	9578.62i	0.313661	−	0.313661i	0.846326	+	0.532665i	$0.178809\pi$
$978$	−21017.2	+	11540.1i	−0.687173	+	0.377313i
$979$		−	10309.4i		−	0.336559i
$980$	44103.4	−	44103.4i	1.43758	−	1.43758i
$981$	1116.62	−	248.378i	0.0363413	−	0.00808369i
$982$	−9910.49	+	9910.49i	−0.322053	+	0.322053i
$983$	3628.32	+	3628.32i	0.117727	+	0.117727i	0.763516	−	0.645789i	$-0.223471\pi$
$983$	3628.32	+	3628.32i	0.117727	+	0.117727i	−0.645789	+	0.763516i	$0.723471\pi$
$984$	−12915.8	−	23522.6i	−0.418435	−	0.762065i
$985$		−	82634.8i		−	2.67306i
$986$	6805.04	+	6805.04i	0.219794	+	0.219794i
$987$	−20916.8	−	38094.3i	−0.674559	−	1.22853i
$988$	−3669.06	−	397.673i	−0.118146	−	0.0128053i
$989$			149.268i			0.00479925i
$990$	1704.12	+	7661.08i	0.0547075	+	0.245945i
$991$	−5968.73			−0.191325			−0.0956624	−	0.995414i	$-0.530497\pi$
$991$	−5968.73			−0.191325			−0.0956624	+	0.995414i	$0.530497\pi$
$992$	24993.9			0.799957
$993$	−2995.57	+	10290.9i	−0.0957317	+	0.328874i
$994$	13179.9	+	13179.9i	0.420566	+	0.420566i
$995$	50649.6	+	50649.6i	1.61377	+	1.61377i
$996$	3893.52	−	13375.7i	0.123866	−	0.425528i
$997$	7785.95			0.247325			0.123663	−	0.992324i	$-0.460536\pi$
$997$	7785.95			0.247325			0.123663	+	0.992324i	$0.460536\pi$
$998$	−1684.07			−0.0534152
$999$	−13781.3	+	12111.8i	−0.436458	+	0.383585i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	39.4.f.b.8.5	yes	20
3.2	odd	2	inner	39.4.f.b.8.6	yes	20
13.5	odd	4	inner	39.4.f.b.5.6	yes	20
39.5	even	4	inner	39.4.f.b.5.5	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.f.b.5.5	✓	20	39.5	even	4	inner
39.4.f.b.5.6	yes	20	13.5	odd	4	inner
39.4.f.b.8.5	yes	20	1.1	even	1	trivial
39.4.f.b.8.6	yes	20	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 39 = 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	39.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.980238 + 0.980238i) q^{2} +(-2.50090 - 4.55472i) q^{3} +6.07827i q^{4} +(12.5563 - 12.5563i) q^{5} +(6.91619 + 2.01323i) q^{6} +(21.4578 - 21.4578i) q^{7} +(-13.8001 - 13.8001i) q^{8} +(-14.4909 + 22.7818i) q^{9} +O(q^{10})\)	\(q+(-0.980238 + 0.980238i) q^{2} +(-2.50090 - 4.55472i) q^{3} +6.07827i q^{4} +(12.5563 - 12.5563i) q^{5} +(6.91619 + 2.01323i) q^{6} +(21.4578 - 21.4578i) q^{7} +(-13.8001 - 13.8001i) q^{8} +(-14.4909 + 22.7818i) q^{9} +24.6163i q^{10} +(-8.34980 - 8.34980i) q^{11} +(27.6848 - 15.2012i) q^{12} +(29.3793 + 36.5220i) q^{13} +42.0674i q^{14} +(-88.5924 - 25.7883i) q^{15} -21.5715 q^{16} -39.5799 q^{17} +(-8.12705 - 36.5362i) q^{18} +(9.15970 + 9.15970i) q^{19} +(76.3204 + 76.3204i) q^{20} +(-151.398 - 44.0703i) q^{21} +16.3696 q^{22} +2.83931 q^{23} +(-28.3428 + 97.3680i) q^{24} -190.320i q^{25} +(-64.5989 - 7.00158i) q^{26} +(140.005 + 9.02699i) q^{27} +(130.426 + 130.426i) q^{28} +175.398i q^{29} +(112.120 - 61.5630i) q^{30} +(95.0010 + 95.0010i) q^{31} +(131.546 - 131.546i) q^{32} +(-17.1489 + 58.9130i) q^{33} +(38.7977 - 38.7977i) q^{34} -538.859i q^{35} +(-138.474 - 88.0799i) q^{36} +(-92.4719 + 92.4719i) q^{37} -17.9574 q^{38} +(92.8728 - 225.152i) q^{39} -346.554 q^{40} +(-187.117 + 187.117i) q^{41} +(191.605 - 105.207i) q^{42} +52.5720i q^{43} +(50.7523 - 50.7523i) q^{44} +(104.103 + 468.007i) q^{45} +(-2.78320 + 2.78320i) q^{46} +(194.887 + 194.887i) q^{47} +(53.9482 + 98.2520i) q^{48} -577.872i q^{49} +(186.559 + 186.559i) q^{50} +(98.9855 + 180.275i) q^{51} +(-221.991 + 178.575i) q^{52} +473.173i q^{53} +(-146.087 + 128.390i) q^{54} -209.685 q^{55} -592.237 q^{56} +(18.8123 - 64.6274i) q^{57} +(-171.932 - 171.932i) q^{58} +(-395.766 - 395.766i) q^{59} +(156.748 - 538.488i) q^{60} +104.515 q^{61} -186.247 q^{62} +(177.904 + 799.791i) q^{63} +85.3201i q^{64} +(827.475 + 89.6862i) q^{65} +(-40.9388 - 74.5588i) q^{66} +(-473.452 - 473.452i) q^{67} -240.577i q^{68} +(-7.10085 - 12.9323i) q^{69} +(528.210 + 528.210i) q^{70} +(313.305 - 313.305i) q^{71} +(514.366 - 114.415i) q^{72} +(-84.4987 + 84.4987i) q^{73} -181.289i q^{74} +(-866.855 + 475.973i) q^{75} +(-55.6751 + 55.6751i) q^{76} -358.336 q^{77} +(129.666 + 311.740i) q^{78} +651.078 q^{79} +(-270.857 + 270.857i) q^{80} +(-309.025 - 660.261i) q^{81} -366.838i q^{82} +(311.890 - 311.890i) q^{83} +(267.871 - 920.238i) q^{84} +(-496.976 + 496.976i) q^{85} +(-51.5330 - 51.5330i) q^{86} +(798.889 - 438.654i) q^{87} +230.455i q^{88} +(617.346 + 617.346i) q^{89} +(-560.804 - 356.713i) q^{90} +(1414.10 + 153.267i) q^{91} +17.2581i q^{92} +(195.114 - 670.291i) q^{93} -382.072 q^{94} +230.023 q^{95} +(-928.136 - 270.170i) q^{96} +(177.855 + 177.855i) q^{97} +(566.452 + 566.452i) q^{98} +(311.220 - 69.2273i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{3} + 44 q^{6} + 44 q^{7} - 112 q^{9}+O(q^{10}) \) 20 * q - 4 * q^3 + 44 * q^6 + 44 * q^7 - 112 * q^9	\( 20 q - 4 q^{3} + 44 q^{6} + 44 q^{7} - 112 q^{9} - 76 q^{13} - 76 q^{15} - 16 q^{16} + 296 q^{18} + 260 q^{19} - 532 q^{21} - 224 q^{22} + 36 q^{24} - 592 q^{27} + 584 q^{28} - 700 q^{31} + 872 q^{33} + 816 q^{34} - 1660 q^{37} + 1016 q^{39} + 3288 q^{40} + 124 q^{42} + 260 q^{45} - 1560 q^{46} - 1084 q^{48} - 3456 q^{52} - 232 q^{54} - 872 q^{55} + 2648 q^{57} - 1352 q^{58} - 1064 q^{60} + 1960 q^{61} + 428 q^{63} - 7664 q^{66} - 916 q^{67} + 1192 q^{70} + 6984 q^{72} + 1964 q^{73} + 1816 q^{76} + 728 q^{78} + 6544 q^{79} + 200 q^{81} + 2612 q^{84} - 8304 q^{85} + 3136 q^{87} + 4580 q^{91} - 2536 q^{93} - 6056 q^{94} - 5956 q^{96} - 2572 q^{97} + 1700 q^{99}+O(q^{100}) \) 20 * q - 4 * q^3 + 44 * q^6 + 44 * q^7 - 112 * q^9 - 76 * q^13 - 76 * q^15 - 16 * q^16 + 296 * q^18 + 260 * q^19 - 532 * q^21 - 224 * q^22 + 36 * q^24 - 592 * q^27 + 584 * q^28 - 700 * q^31 + 872 * q^33 + 816 * q^34 - 1660 * q^37 + 1016 * q^39 + 3288 * q^40 + 124 * q^42 + 260 * q^45 - 1560 * q^46 - 1084 * q^48 - 3456 * q^52 - 232 * q^54 - 872 * q^55 + 2648 * q^57 - 1352 * q^58 - 1064 * q^60 + 1960 * q^61 + 428 * q^63 - 7664 * q^66 - 916 * q^67 + 1192 * q^70 + 6984 * q^72 + 1964 * q^73 + 1816 * q^76 + 728 * q^78 + 6544 * q^79 + 200 * q^81 + 2612 * q^84 - 8304 * q^85 + 3136 * q^87 + 4580 * q^91 - 2536 * q^93 - 6056 * q^94 - 5956 * q^96 - 2572 * q^97 + 1700 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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