LMFDB - Embedded newform 13.4.e.b.4.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [13,4,Mod(4,13)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(13, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("13.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	13.e (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:	$0.767024830075$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	13.4
Dual form			13.4.e.b.10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-2.50000 - 4.33013i) q^{4} -1.73205i q^{5} +(-3.00000 + 1.73205i) q^{6} +(-12.0000 + 6.92820i) q^{7} -22.5167i q^{8} +(11.5000 + 19.9186i) q^{9} +O(q^{10})$	\(q+(1.50000 + 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-2.50000 - 4.33013i) q^{4} -1.73205i q^{5} +(-3.00000 + 1.73205i) q^{6} +(-12.0000 + 6.92820i) q^{7} -22.5167i q^{8} +(11.5000 + 19.9186i) q^{9} +(1.50000 - 2.59808i) q^{10} +(12.0000 + 6.92820i) q^{11} +10.0000 q^{12} +(45.5000 + 11.2583i) q^{13} -24.0000 q^{14} +(3.00000 + 1.73205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-58.5000 - 101.325i) q^{17} +39.8372i q^{18} +(-99.0000 + 57.1577i) q^{19} +(-7.50000 + 4.33013i) q^{20} -27.7128i q^{21} +(12.0000 + 20.7846i) q^{22} +(39.0000 - 67.5500i) q^{23} +(39.0000 + 22.5167i) q^{24} +122.000 q^{25} +(58.5000 + 56.2917i) q^{26} -100.000 q^{27} +(60.0000 + 34.6410i) q^{28} +(70.5000 - 122.110i) q^{29} +(3.00000 + 5.19615i) q^{30} +155.885i q^{31} +(-157.500 + 90.9327i) q^{32} +(-24.0000 + 13.8564i) q^{33} -202.650i q^{34} +(12.0000 + 20.7846i) q^{35} +(57.5000 - 99.5929i) q^{36} +(-124.500 - 71.8801i) q^{37} -198.000 q^{38} +(-65.0000 + 67.5500i) q^{39} -39.0000 q^{40} +(235.500 + 135.966i) q^{41} +(24.0000 - 41.5692i) q^{42} +(-52.0000 - 90.0666i) q^{43} -69.2820i q^{44} +(34.5000 - 19.9186i) q^{45} +(117.000 - 67.5500i) q^{46} +301.377i q^{47} +(-1.00000 - 1.73205i) q^{48} +(-75.5000 + 130.770i) q^{49} +(183.000 + 105.655i) q^{50} +234.000 q^{51} +(-65.0000 - 225.167i) q^{52} +93.0000 q^{53} +(-150.000 - 86.6025i) q^{54} +(12.0000 - 20.7846i) q^{55} +(156.000 + 270.200i) q^{56} -228.631i q^{57} +(211.500 - 122.110i) q^{58} +(-246.000 + 142.028i) q^{59} -17.3205i q^{60} +(-72.5000 - 125.574i) q^{61} +(-135.000 + 233.827i) q^{62} +(-276.000 - 159.349i) q^{63} -307.000 q^{64} +(19.5000 - 78.8083i) q^{65} -48.0000 q^{66} +(-681.000 - 393.176i) q^{67} +(-292.500 + 506.625i) q^{68} +(78.0000 + 135.100i) q^{69} +41.5692i q^{70} +(915.000 - 528.275i) q^{71} +(448.500 - 258.942i) q^{72} +458.993i q^{73} +(-124.500 - 215.640i) q^{74} +(-122.000 + 211.310i) q^{75} +(495.000 + 285.788i) q^{76} -192.000 q^{77} +(-156.000 + 45.0333i) q^{78} +1276.00 q^{79} +(1.50000 + 0.866025i) q^{80} +(-210.500 + 364.597i) q^{81} +(235.500 + 407.898i) q^{82} -789.815i q^{83} +(-120.000 + 69.2820i) q^{84} +(-175.500 + 101.325i) q^{85} -180.133i q^{86} +(141.000 + 244.219i) q^{87} +(156.000 - 270.200i) q^{88} +(-846.000 - 488.438i) q^{89} +69.0000 q^{90} +(-624.000 + 180.133i) q^{91} -390.000 q^{92} +(-270.000 - 155.885i) q^{93} +(-261.000 + 452.065i) q^{94} +(99.0000 + 171.473i) q^{95} -363.731i q^{96} +(174.000 - 100.459i) q^{97} +(-226.500 + 130.770i) q^{98} +318.697i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{2} - 2 q^{3} - 5 q^{4} - 6 q^{6} - 24 q^{7} + 23 q^{9}+O(q^{10}) $ 2 * q + 3 * q^2 - 2 * q^3 - 5 * q^4 - 6 * q^6 - 24 * q^7 + 23 * q^9	\( 2 q + 3 q^{2} - 2 q^{3} - 5 q^{4} - 6 q^{6} - 24 q^{7} + 23 q^{9} + 3 q^{10} + 24 q^{11} + 20 q^{12} + 91 q^{13} - 48 q^{14} + 6 q^{15} - q^{16} - 117 q^{17} - 198 q^{19} - 15 q^{20} + 24 q^{22} + 78 q^{23} + 78 q^{24} + 244 q^{25} + 117 q^{26} - 200 q^{27} + 120 q^{28} + 141 q^{29} + 6 q^{30} - 315 q^{32} - 48 q^{33} + 24 q^{35} + 115 q^{36} - 249 q^{37} - 396 q^{38} - 130 q^{39} - 78 q^{40} + 471 q^{41} + 48 q^{42} - 104 q^{43} + 69 q^{45} + 234 q^{46} - 2 q^{48} - 151 q^{49} + 366 q^{50} + 468 q^{51} - 130 q^{52} + 186 q^{53} - 300 q^{54} + 24 q^{55} + 312 q^{56} + 423 q^{58} - 492 q^{59} - 145 q^{61} - 270 q^{62} - 552 q^{63} - 614 q^{64} + 39 q^{65} - 96 q^{66} - 1362 q^{67} - 585 q^{68} + 156 q^{69} + 1830 q^{71} + 897 q^{72} - 249 q^{74} - 244 q^{75} + 990 q^{76} - 384 q^{77} - 312 q^{78} + 2552 q^{79} + 3 q^{80} - 421 q^{81} + 471 q^{82} - 240 q^{84} - 351 q^{85} + 282 q^{87} + 312 q^{88} - 1692 q^{89} + 138 q^{90} - 1248 q^{91} - 780 q^{92} - 540 q^{93} - 522 q^{94} + 198 q^{95} + 348 q^{97} - 453 q^{98}+O(q^{100}) \) 2 * q + 3 * q^2 - 2 * q^3 - 5 * q^4 - 6 * q^6 - 24 * q^7 + 23 * q^9 + 3 * q^10 + 24 * q^11 + 20 * q^12 + 91 * q^13 - 48 * q^14 + 6 * q^15 - q^16 - 117 * q^17 - 198 * q^19 - 15 * q^20 + 24 * q^22 + 78 * q^23 + 78 * q^24 + 244 * q^25 + 117 * q^26 - 200 * q^27 + 120 * q^28 + 141 * q^29 + 6 * q^30 - 315 * q^32 - 48 * q^33 + 24 * q^35 + 115 * q^36 - 249 * q^37 - 396 * q^38 - 130 * q^39 - 78 * q^40 + 471 * q^41 + 48 * q^42 - 104 * q^43 + 69 * q^45 + 234 * q^46 - 2 * q^48 - 151 * q^49 + 366 * q^50 + 468 * q^51 - 130 * q^52 + 186 * q^53 - 300 * q^54 + 24 * q^55 + 312 * q^56 + 423 * q^58 - 492 * q^59 - 145 * q^61 - 270 * q^62 - 552 * q^63 - 614 * q^64 + 39 * q^65 - 96 * q^66 - 1362 * q^67 - 585 * q^68 + 156 * q^69 + 1830 * q^71 + 897 * q^72 - 249 * q^74 - 244 * q^75 + 990 * q^76 - 384 * q^77 - 312 * q^78 + 2552 * q^79 + 3 * q^80 - 421 * q^81 + 471 * q^82 - 240 * q^84 - 351 * q^85 + 282 * q^87 + 312 * q^88 - 1692 * q^89 + 138 * q^90 - 1248 * q^91 - 780 * q^92 - 540 * q^93 - 522 * q^94 + 198 * q^95 + 348 * q^97 - 453 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.50000	+	0.866025i	0.530330	+	0.306186i	0.741151	−	0.671339i	$-0.234280\pi$
$2$	1.50000	+	0.866025i	0.530330	+	0.306186i	−0.210821	+	0.977525i	$0.567614\pi$
$3$	−1.00000	+	1.73205i	−0.192450	+	0.333333i	−0.946062	−	0.323987i	$-0.894977\pi$
$3$	−1.00000	+	1.73205i	−0.192450	+	0.333333i	0.753612	+	0.657320i	$0.228310\pi$
$4$	−2.50000	−	4.33013i	−0.312500	−	0.541266i
$5$		−	1.73205i		−	0.154919i	−0.996995	−	0.0774597i	$-0.975319\pi$
$5$		−	1.73205i		−	0.154919i	0.996995	−	0.0774597i	$-0.0246809\pi$
$6$	−3.00000	+	1.73205i	−0.204124	+	0.117851i
$7$	−12.0000	+	6.92820i	−0.647939	+	0.374088i	−0.787666	−	0.616102i	$-0.788711\pi$
$7$	−12.0000	+	6.92820i	−0.647939	+	0.374088i	0.139727	+	0.990190i	$0.455377\pi$
$8$		−	22.5167i		−	0.995105i
$9$	11.5000	+	19.9186i	0.425926	+	0.737725i
$10$	1.50000	−	2.59808i	0.0474342	−	0.0821584i
$11$	12.0000	+	6.92820i	0.328921	+	0.189903i	0.655362	−	0.755315i	$-0.272516\pi$
$11$	12.0000	+	6.92820i	0.328921	+	0.189903i	−0.326441	+	0.945218i	$0.605849\pi$
$12$	10.0000			0.240563
$13$	45.5000	+	11.2583i	0.970725	+	0.240192i
$13$	45.5000	+	11.2583i	0.970725	+	0.240192i
$14$	−24.0000			−0.458162
$15$	3.00000	+	1.73205i	0.0516398	+	0.0298142i
$16$	−0.500000	+	0.866025i	−0.00781250	+	0.0135316i
$17$	−58.5000	−	101.325i	−0.834608	−	1.44558i	−0.894349	−	0.447369i	$-0.852361\pi$
$17$	−58.5000	−	101.325i	−0.834608	−	1.44558i	0.0597414	−	0.998214i	$-0.480972\pi$
$18$			39.8372i			0.521651i
$19$	−99.0000	+	57.1577i	−1.19538	+	0.690151i	−0.959521	−	0.281637i	$-0.909123\pi$
$19$	−99.0000	+	57.1577i	−1.19538	+	0.690151i	−0.235856	+	0.971788i	$0.575789\pi$
$20$	−7.50000	+	4.33013i	−0.0838525	+	0.0484123i
$21$		−	27.7128i		−	0.287973i
$22$	12.0000	+	20.7846i	0.116291	+	0.201422i
$23$	39.0000	−	67.5500i	0.353568	−	0.612398i	−0.633304	−	0.773903i	$-0.718302\pi$
$23$	39.0000	−	67.5500i	0.353568	−	0.612398i	0.986872	+	0.161506i	$0.0516350\pi$
$24$	39.0000	+	22.5167i	0.331702	+	0.191508i
$25$	122.000			0.976000
$26$	58.5000	+	56.2917i	0.441261	+	0.424604i
$27$	−100.000			−0.712778
$28$	60.0000	+	34.6410i	0.404962	+	0.233805i
$29$	70.5000	−	122.110i	0.451432	−	0.781903i	−0.547043	−	0.837104i	$-0.684247\pi$
$29$	70.5000	−	122.110i	0.451432	−	0.781903i	0.998475	+	0.0552014i	$0.0175801\pi$
$30$	3.00000	+	5.19615i	0.0182574	+	0.0316228i
$31$			155.885i			0.903151i	0.892233	+	0.451576i	$0.149138\pi$
$31$			155.885i			0.903151i	−0.892233	+	0.451576i	$0.850862\pi$
$32$	−157.500	+	90.9327i	−0.870073	+	0.502337i
$33$	−24.0000	+	13.8564i	−0.126602	+	0.0730937i
$34$		−	202.650i		−	1.02218i
$35$	12.0000	+	20.7846i	0.0579534	+	0.100378i
$36$	57.5000	−	99.5929i	0.266204	−	0.461078i
$37$	−124.500	−	71.8801i	−0.553180	−	0.319379i	0.197223	−	0.980359i	$-0.436808\pi$
$37$	−124.500	−	71.8801i	−0.553180	−	0.319379i	−0.750404	+	0.660980i	$0.770141\pi$
$38$	−198.000			−0.845259
$39$	−65.0000	+	67.5500i	−0.266880	+	0.277350i
$40$	−39.0000			−0.154161
$41$	235.500	+	135.966i	0.897047	+	0.517910i	0.876241	−	0.481873i	$-0.160043\pi$
$41$	235.500	+	135.966i	0.897047	+	0.517910i	0.0208059	+	0.999784i	$0.493377\pi$
$42$	24.0000	−	41.5692i	0.0881733	−	0.152721i
$43$	−52.0000	−	90.0666i	−0.184417	−	0.319419i	0.758963	−	0.651134i	$-0.225706\pi$
$43$	−52.0000	−	90.0666i	−0.184417	−	0.319419i	−0.943380	+	0.331714i	$0.892373\pi$
$44$		−	69.2820i		−	0.237379i
$45$	34.5000	−	19.9186i	0.114288	−	0.0659842i
$46$	117.000	−	67.5500i	0.375015	−	0.216515i
$47$			301.377i			0.935326i	0.883907	+	0.467663i	$0.154904\pi$
$47$			301.377i			0.935326i	−0.883907	+	0.467663i	$0.845096\pi$
$48$	−1.00000	−	1.73205i	−0.00300703	−	0.00520833i
$49$	−75.5000	+	130.770i	−0.220117	+	0.381253i
$50$	183.000	+	105.655i	0.517602	+	0.298838i
$51$	234.000			0.642481
$52$	−65.0000	−	225.167i	−0.173344	−	0.600481i
$53$	93.0000			0.241029			0.120514	−	0.992712i	$-0.461546\pi$
$53$	93.0000			0.241029			0.120514	+	0.992712i	$0.461546\pi$
$54$	−150.000	−	86.6025i	−0.378008	−	0.218243i
$55$	12.0000	−	20.7846i	0.0294196	−	0.0509563i
$56$	156.000	+	270.200i	0.372257	+	0.644768i
$57$		−	228.631i		−	0.531279i
$58$	211.500	−	122.110i	0.478816	−	0.276444i
$59$	−246.000	+	142.028i	−0.542822	+	0.313398i	−0.746222	−	0.665698i	$-0.768134\pi$
$59$	−246.000	+	142.028i	−0.542822	+	0.313398i	0.203400	+	0.979096i	$0.434801\pi$
$60$		−	17.3205i		−	0.0372678i
$61$	−72.5000	−	125.574i	−0.152175	−	0.263575i	0.779852	−	0.625964i	$-0.215294\pi$
$61$	−72.5000	−	125.574i	−0.152175	−	0.263575i	−0.932027	+	0.362389i	$0.881961\pi$
$62$	−135.000	+	233.827i	−0.276533	+	0.478968i
$63$	−276.000	−	159.349i	−0.551948	−	0.318667i
$64$	−307.000			−0.599609
$65$	19.5000	−	78.8083i	0.0372104	−	0.150384i
$66$	−48.0000			−0.0895211
$67$	−681.000	−	393.176i	−1.24175	−	0.716926i	−0.272301	−	0.962212i	$-0.587785\pi$
$67$	−681.000	−	393.176i	−1.24175	−	0.716926i	−0.969451	+	0.245286i	$0.921118\pi$
$68$	−292.500	+	506.625i	−0.521630	+	0.903490i
$69$	78.0000	+	135.100i	0.136088	+	0.235712i
$70$			41.5692i			0.0709782i
$71$	915.000	−	528.275i	1.52944	−	0.883025i	0.530059	−	0.847961i	$-0.322170\pi$
$71$	915.000	−	528.275i	1.52944	−	0.883025i	0.999385	−	0.0350641i	$-0.0111635\pi$
$72$	448.500	−	258.942i	0.734114	−	0.423841i
$73$			458.993i			0.735906i	0.929844	+	0.367953i	$0.119941\pi$
$73$			458.993i			0.735906i	−0.929844	+	0.367953i	$0.880059\pi$
$74$	−124.500	−	215.640i	−0.195579	−	0.338752i
$75$	−122.000	+	211.310i	−0.187831	+	0.325333i
$76$	495.000	+	285.788i	0.747110	+	0.431344i
$77$	−192.000			−0.284161
$78$	−156.000	+	45.0333i	−0.226455	+	0.0653720i
$79$	1276.00			1.81723			0.908615	−	0.417634i	$-0.137141\pi$
$79$	1276.00			1.81723			0.908615	+	0.417634i	$0.137141\pi$
$80$	1.50000	+	0.866025i	0.00209631	+	0.00121031i
$81$	−210.500	+	364.597i	−0.288752	+	0.500133i
$82$	235.500	+	407.898i	0.317154	+	0.549327i
$83$		−	789.815i		−	1.04450i	−0.852793	−	0.522250i	$-0.825093\pi$
$83$		−	789.815i		−	1.04450i	0.852793	−	0.522250i	$-0.174907\pi$
$84$	−120.000	+	69.2820i	−0.155870	+	0.0899915i
$85$	−175.500	+	101.325i	−0.223949	+	0.129297i
$86$		−	180.133i		−	0.225864i
$87$	141.000	+	244.219i	0.173756	+	0.300955i
$88$	156.000	−	270.200i	0.188973	−	0.327311i
$89$	−846.000	−	488.438i	−1.00759	−	0.581734i	−0.0971073	−	0.995274i	$-0.530959\pi$
$89$	−846.000	−	488.438i	−1.00759	−	0.581734i	−0.910486	+	0.413540i	$0.864292\pi$
$90$	69.0000			0.0808138
$91$	−624.000	+	180.133i	−0.718824	+	0.207507i
$92$	−390.000			−0.441960
$93$	−270.000	−	155.885i	−0.301050	−	0.173812i
$94$	−261.000	+	452.065i	−0.286384	+	0.496032i
$95$	99.0000	+	171.473i	0.106918	+	0.185187i
$96$		−	363.731i		−	0.386699i
$97$	174.000	−	100.459i	0.182134	−	0.105155i	−0.406161	−	0.913802i	$-0.633133\pi$
$97$	174.000	−	100.459i	0.182134	−	0.105155i	0.588295	+	0.808646i	$0.299799\pi$
$98$	−226.500	+	130.770i	−0.233469	+	0.134793i
$99$			318.697i			0.323538i
$100$	−305.000	−	528.275i	−0.305000	−	0.528275i
$101$	−214.500	+	371.525i	−0.211322	+	0.366021i	−0.952129	−	0.305698i	$-0.901110\pi$
$101$	−214.500	+	371.525i	−0.211322	+	0.366021i	0.740806	+	0.671719i	$0.234444\pi$
$102$	351.000	+	202.650i	0.340727	+	0.196719i
$103$	182.000			0.174107			0.0870534	−	0.996204i	$-0.472255\pi$
$103$	182.000			0.174107			0.0870534	+	0.996204i	$0.472255\pi$
$104$	253.500	−	1024.51i	0.239017	−	0.965974i
$105$	−48.0000			−0.0446126
$106$	139.500	+	80.5404i	0.127825	+	0.0737997i
$107$	753.000	−	1304.23i	0.680330	−	1.17837i	−0.294551	−	0.955636i	$-0.595170\pi$
$107$	753.000	−	1304.23i	0.680330	−	1.17837i	0.974880	−	0.222729i	$-0.0714967\pi$
$108$	250.000	+	433.013i	0.222743	+	0.385802i
$109$			1551.92i			1.36373i	0.731477	+	0.681866i	$0.238831\pi$
$109$			1551.92i			1.36373i	−0.731477	+	0.681866i	$0.761169\pi$
$110$	36.0000	−	20.7846i	0.0312042	−	0.0180158i
$111$	249.000	−	143.760i	0.212919	−	0.122929i
$112$		−	13.8564i		−	0.0116902i
$113$	343.500	+	594.959i	0.285962	+	0.495302i	0.972842	−	0.231470i	$-0.0743534\pi$
$113$	343.500	+	594.959i	0.285962	+	0.495302i	−0.686880	+	0.726771i	$0.741020\pi$
$114$	198.000	−	342.946i	0.162670	−	0.281753i
$115$	−117.000	−	67.5500i	−0.0948722	−	0.0547745i
$116$	−705.000			−0.564290
$117$	299.000	+	1035.77i	0.236261	+	0.818433i
$118$	−492.000			−0.383833
$119$	1404.00	+	810.600i	1.08155	+	0.624433i
$120$	39.0000	−	67.5500i	0.0296683	−	0.0513870i
$121$	−569.500	−	986.403i	−0.427874	−	0.741099i
$122$		−	251.147i		−	0.186376i
$123$	−471.000	+	271.932i	−0.345273	+	0.199344i
$124$	675.000	−	389.711i	0.488845	−	0.282235i
$125$		−	427.817i		−	0.306121i
$126$	−276.000	−	478.046i	−0.195143	−	0.337998i
$127$	−143.000	+	247.683i	−0.0999149	+	0.173058i	−0.911649	−	0.410969i	$-0.865190\pi$
$127$	−143.000	+	247.683i	−0.0999149	+	0.173058i	0.811734	+	0.584027i	$0.198524\pi$
$128$	799.500	+	461.592i	0.552082	+	0.318745i
$129$	208.000			0.141964
$130$	97.5000	−	101.325i	0.0657794	−	0.0683599i
$131$	−1974.00			−1.31656			−0.658279	−	0.752774i	$-0.728715\pi$
$131$	−1974.00			−1.31656			−0.658279	+	0.752774i	$0.728715\pi$
$132$	120.000	+	69.2820i	0.0791262	+	0.0456835i
$133$	792.000	−	1371.78i	0.516354	−	0.894352i
$134$	−681.000	−	1179.53i	−0.439026	−	0.760415i
$135$			173.205i			0.110423i
$136$	−2281.50	+	1317.22i	−1.43851	+	0.830523i
$137$	−733.500	+	423.486i	−0.457424	+	0.264094i	−0.710961	−	0.703232i	$-0.751740\pi$
$137$	−733.500	+	423.486i	−0.457424	+	0.264094i	0.253536	+	0.967326i	$0.418406\pi$
$138$			270.200i			0.166674i
$139$	−118.000	−	204.382i	−0.0720045	−	0.124716i	0.827775	−	0.561060i	$-0.189606\pi$
$139$	−118.000	−	204.382i	−0.0720045	−	0.124716i	−0.899780	+	0.436344i	$0.856273\pi$
$140$	60.0000	−	103.923i	0.0362209	−	0.0627364i
$141$	−522.000	−	301.377i	−0.311775	−	0.180004i
$142$	1830.00			1.08148
$143$	468.000	+	450.333i	0.273679	+	0.263348i
$144$	−23.0000			−0.0133102
$145$	−211.500	−	122.110i	−0.121132	−	0.0699355i
$146$	−397.500	+	688.490i	−0.225324	+	0.390273i
$147$	−151.000	−	261.540i	−0.0847229	−	0.146744i
$148$			718.801i			0.399224i
$149$	−40.5000	+	23.3827i	−0.0222677	+	0.0128563i	−0.511093	−	0.859526i	$-0.670759\pi$
$149$	−40.5000	+	23.3827i	−0.0222677	+	0.0128563i	0.488825	+	0.872382i	$0.337426\pi$
$150$	−366.000	+	211.310i	−0.199225	+	0.115023i
$151$		−	1770.16i		−	0.953995i	−0.878905	−	0.476998i	$-0.841725\pi$
$151$		−	1770.16i		−	0.953995i	0.878905	−	0.476998i	$-0.158275\pi$
$152$	1287.00	+	2229.15i	0.686773	+	1.18953i
$153$	1345.50	−	2330.47i	0.710962	−	1.23142i
$154$	−288.000	−	166.277i	−0.150699	−	0.0870063i
$155$	270.000			0.139916
$156$	455.000	+	112.583i	0.233520	+	0.0577813i
$157$	1211.00			0.615594			0.307797	−	0.951452i	$-0.400408\pi$
$157$	1211.00			0.615594			0.307797	+	0.951452i	$0.400408\pi$
$158$	1914.00	+	1105.05i	0.963732	+	0.556411i
$159$	−93.0000	+	161.081i	−0.0463860	+	0.0803430i
$160$	157.500	+	272.798i	0.0778217	+	0.134791i
$161$			1080.80i			0.529062i
$162$	−631.500	+	364.597i	−0.306267	+	0.176824i
$163$	−870.000	+	502.295i	−0.418059	+	0.241367i	−0.694247	−	0.719737i	$-0.744262\pi$
$163$	−870.000	+	502.295i	−0.418059	+	0.241367i	0.276187	+	0.961104i	$0.410929\pi$
$164$		−	1359.66i		−	0.647388i
$165$	24.0000	+	41.5692i	0.0113236	+	0.0196131i
$166$	684.000	−	1184.72i	0.319811	−	0.553930i
$167$	792.000	+	457.261i	0.366987	+	0.211880i	0.672141	−	0.740423i	$-0.265375\pi$
$167$	792.000	+	457.261i	0.366987	+	0.211880i	−0.305154	+	0.952303i	$0.598708\pi$
$168$	−624.000			−0.286563
$169$	1943.50	+	1024.51i	0.884615	+	0.466321i
$170$	−351.000			−0.158356
$171$	−2277.00	−	1314.63i	−1.01828	−	0.587906i
$172$	−260.000	+	450.333i	−0.115261	+	0.199637i
$173$	−1287.00	−	2229.15i	−0.565600	−	0.979648i	−0.996994	−	0.0774841i	$-0.975311\pi$
$173$	−1287.00	−	2229.15i	−0.565600	−	0.979648i	0.431394	−	0.902164i	$-0.358022\pi$
$174$			488.438i			0.212807i
$175$	−1464.00	+	845.241i	−0.632389	+	0.365110i
$176$	−12.0000	+	6.92820i	−0.00513940	+	0.00296723i
$177$		−	568.113i		−	0.241254i
$178$	−846.000	−	1465.31i	−0.356238	−	0.617022i
$179$	−1872.00	+	3242.40i	−0.781675	+	1.35390i	0.149290	+	0.988793i	$0.452301\pi$
$179$	−1872.00	+	3242.40i	−0.781675	+	1.35390i	−0.930965	+	0.365108i	$0.881032\pi$
$180$	−172.500	−	99.5929i	−0.0714299	−	0.0412401i
$181$	−637.000			−0.261590			−0.130795	−	0.991409i	$-0.541753\pi$
$181$	−637.000			−0.261590			−0.130795	+	0.991409i	$0.541753\pi$
$182$	−1092.00	−	270.200i	−0.444750	−	0.110047i
$183$	290.000			0.117144
$184$	−1521.00	−	878.150i	−0.609400	−	0.351837i
$185$	−124.500	+	215.640i	−0.0494780	+	0.0856983i
$186$	−270.000	−	467.654i	−0.106437	−	0.184355i
$187$		−	1621.20i		−	0.633978i
$188$	1305.00	−	753.442i	0.506260	−	0.292289i
$189$	1200.00	−	692.820i	0.461837	−	0.266642i
$190$			342.946i			0.130947i
$191$	1299.00	+	2249.93i	0.492106	+	0.852353i	0.999959	−	0.00909077i	$-0.00289372\pi$
$191$	1299.00	+	2249.93i	0.492106	+	0.852353i	−0.507852	+	0.861444i	$0.669560\pi$
$192$	307.000	−	531.740i	0.115395	−	0.199870i
$193$	967.500	+	558.586i	0.360840	+	0.208331i	0.669449	−	0.742858i	$-0.266530\pi$
$193$	967.500	+	558.586i	0.360840	+	0.208331i	−0.308609	+	0.951189i	$0.599863\pi$
$194$	348.000			0.128788
$195$	117.000	+	112.583i	0.0429669	+	0.0413449i
$196$	755.000			0.275146
$197$	1776.00	+	1025.37i	0.642308	+	0.370837i	0.785503	−	0.618858i	$-0.212404\pi$
$197$	1776.00	+	1025.37i	0.642308	+	0.370837i	−0.143195	+	0.989695i	$0.545738\pi$
$198$	−276.000	+	478.046i	−0.0990630	+	0.171582i
$199$	1261.00	+	2184.12i	0.449196	+	0.778030i	0.998334	−	0.0577019i	$-0.0183773\pi$
$199$	1261.00	+	2184.12i	0.449196	+	0.778030i	−0.549138	+	0.835732i	$0.685044\pi$
$200$		−	2747.03i		−	0.971223i
$201$	1362.00	−	786.351i	0.477951	−	0.275945i
$202$	−643.500	+	371.525i	−0.224141	+	0.129408i
$203$			1953.75i			0.675500i
$204$	−585.000	−	1013.25i	−0.200775	−	0.347753i
$205$	235.500	−	407.898i	0.0802343	−	0.138970i
$206$	273.000	+	157.617i	0.0923340	+	0.0533091i
$207$	1794.00			0.602375
$208$	−32.5000	+	33.7750i	−0.0108340	+	0.0112590i
$209$	−1584.00			−0.524247
$210$	−72.0000	−	41.5692i	−0.0236594	−	0.0136598i
$211$	−521.000	+	902.398i	−0.169986	+	0.294425i	−0.938415	−	0.345511i	$-0.887706\pi$
$211$	−521.000	+	902.398i	−0.169986	+	0.294425i	0.768428	+	0.639936i	$0.221039\pi$
$212$	−232.500	−	402.702i	−0.0753215	−	0.130461i
$213$			2113.10i			0.679753i
$214$	2259.00	−	1304.23i	0.721598	−	0.416615i
$215$	−156.000	+	90.0666i	−0.0494842	+	0.0285697i
$216$			2251.67i			0.709289i
$217$	−1080.00	−	1870.61i	−0.337858	−	0.585187i
$218$	−1344.00	+	2327.88i	−0.417556	+	0.723228i
$219$	−795.000	−	458.993i	−0.245302	−	0.141625i
$220$	−120.000			−0.0367745
$221$	−1521.00	−	5268.90i	−0.462957	−	1.60373i
$222$	498.000			0.150557
$223$	−2085.00	−	1203.78i	−0.626107	−	0.361483i	0.153136	−	0.988205i	$-0.451063\pi$
$223$	−2085.00	−	1203.78i	−0.626107	−	0.361483i	−0.779243	+	0.626722i	$0.784396\pi$
$224$	1260.00	−	2182.38i	0.375836	−	0.650967i
$225$	1403.00	+	2430.07i	0.415704	+	0.720020i
$226$			1189.92i			0.350231i
$227$	2085.00	−	1203.78i	0.609631	−	0.351971i	−0.163190	−	0.986595i	$-0.552178\pi$
$227$	2085.00	−	1203.78i	0.609631	−	0.351971i	0.772821	+	0.634624i	$0.218845\pi$
$228$	−990.000	+	571.577i	−0.287563	+	0.166025i
$229$			2508.01i			0.723729i	0.932231	+	0.361864i	$0.117860\pi$
$229$			2508.01i			0.723729i	−0.932231	+	0.361864i	$0.882140\pi$
$230$	−117.000	−	202.650i	−0.0335424	−	0.0580971i
$231$	192.000	−	332.554i	0.0546869	−	0.0947205i
$232$	−2749.50	−	1587.42i	−0.778076	−	0.449222i
$233$	−5850.00			−1.64483			−0.822417	−	0.568885i	$-0.807375\pi$
$233$	−5850.00			−1.64483			−0.822417	+	0.568885i	$0.807375\pi$
$234$	−448.500	+	1812.59i	−0.125296	+	0.506379i
$235$	522.000			0.144900
$236$	1230.00	+	710.141i	0.339263	+	0.195874i
$237$	−1276.00	+	2210.10i	−0.349726	+	0.605744i
$238$	1404.00	+	2431.80i	0.382386	+	0.662312i
$239$		−	5383.21i		−	1.45695i	−0.685072	−	0.728475i	$-0.740229\pi$
$239$		−	5383.21i		−	1.45695i	0.685072	−	0.728475i	$-0.259771\pi$
$240$	−3.00000	+	1.73205i	−0.000806872	+	0.000465847i
$241$	4258.50	−	2458.65i	1.13823	−	0.657159i	0.192240	−	0.981348i	$-0.438425\pi$
$241$	4258.50	−	2458.65i	1.13823	−	0.657159i	0.945992	+	0.324189i	$0.105091\pi$
$242$		−	1972.81i		−	0.524036i
$243$	−1771.00	−	3067.46i	−0.467530	−	0.809785i
$244$	−362.500	+	627.868i	−0.0951094	+	0.164734i
$245$	226.500	+	130.770i	0.0590635	+	0.0341003i
$246$	−942.000			−0.244145
$247$	−5148.00	+	1486.10i	−1.32615	+	0.382827i
$248$	3510.00			0.898731
$249$	1368.00	+	789.815i	0.348167	+	0.201014i
$250$	370.500	−	641.725i	0.0937299	−	0.162345i
$251$	1989.00	+	3445.05i	0.500178	+	0.866333i	1.00000		0.000205037i	$6.52654e-5\pi$
$251$	1989.00	+	3445.05i	0.500178	+	0.866333i	−0.499822	+	0.866128i	$0.666601\pi$
$252$			1593.49i			0.398334i
$253$	936.000	−	540.400i	0.232592	−	0.134287i
$254$	−429.000	+	247.683i	−0.105976	+	0.0611852i
$255$		−	405.300i		−	0.0995328i
$256$	2027.50	+	3511.73i	0.494995	+	0.857357i
$257$	−1033.50	+	1790.07i	−0.250848	+	0.434482i	−0.963760	−	0.266772i	$-0.914043\pi$
$257$	−1033.50	+	1790.07i	−0.250848	+	0.434482i	0.712911	+	0.701254i	$0.247376\pi$
$258$	312.000	+	180.133i	0.0752879	+	0.0434675i
$259$	1992.00			0.477903
$260$	−390.000	+	112.583i	−0.0930261	+	0.0268543i
$261$	3243.00			0.769106
$262$	−2961.00	−	1709.53i	−0.698211	−	0.403112i
$263$	1026.00	−	1777.08i	0.240555	−	0.416653i	−0.720318	−	0.693644i	$-0.756004\pi$
$263$	1026.00	−	1777.08i	0.240555	−	0.416653i	0.960872	+	0.276991i	$0.0893373\pi$
$264$	312.000	+	540.400i	0.0727359	+	0.125982i
$265$		−	161.081i		−	0.0373400i
$266$	2376.00	−	1371.78i	0.547676	−	0.316201i
$267$	1692.00	−	976.877i	0.387823	−	0.223910i
$268$			3931.76i			0.896157i
$269$	−1665.00	−	2883.86i	−0.377386	−	0.653652i	0.613295	−	0.789854i	$-0.289844\pi$
$269$	−1665.00	−	2883.86i	−0.377386	−	0.653652i	−0.990681	+	0.136202i	$0.956510\pi$
$270$	−150.000	+	259.808i	−0.0338100	+	0.0585607i
$271$	2430.00	+	1402.96i	0.544694	+	0.314479i	0.746979	−	0.664848i	$-0.231504\pi$
$271$	2430.00	+	1402.96i	0.544694	+	0.314479i	−0.202285	+	0.979327i	$0.564837\pi$
$272$	117.000			0.0260815
$273$	312.000	−	1260.93i	0.0691689	−	0.279543i
$274$	−1467.00			−0.323448
$275$	1464.00	+	845.241i	0.321027	+	0.185345i
$276$	390.000	−	675.500i	0.0850552	−	0.147320i
$277$	−188.500	−	326.492i	−0.0408876	−	0.0708194i	0.844857	−	0.534992i	$-0.179685\pi$
$277$	−188.500	−	326.492i	−0.0408876	−	0.0708194i	−0.885745	+	0.464172i	$0.846352\pi$
$278$		−	408.764i		−	0.0881872i
$279$	−3105.00	+	1792.67i	−0.666278	+	0.384676i
$280$	468.000	−	270.200i	0.0998870	−	0.0576698i
$281$		−	36.3731i		−	0.00772183i	−0.999993	−	0.00386092i	$-0.998771\pi$
$281$		−	36.3731i		−	0.00772183i	0.999993	−	0.00386092i	$-0.00122897\pi$
$282$	−522.000	−	904.131i	−0.110229	−	0.190923i
$283$	3562.00	−	6169.56i	0.748194	−	1.29591i	−0.200493	−	0.979695i	$-0.564255\pi$
$283$	3562.00	−	6169.56i	0.748194	−	1.29591i	0.948688	−	0.316215i	$-0.102412\pi$
$284$	−4575.00	−	2641.38i	−0.955902	−	0.551891i
$285$	−396.000			−0.0823053
$286$	312.000	+	1080.80i	0.0645068	+	0.223458i
$287$	−3768.00			−0.774976
$288$	−3622.50	−	2091.45i	−0.741173	−	0.427917i
$289$	−4388.00	+	7600.24i	−0.893141	+	1.54696i
$290$	−211.500	−	366.329i	−0.0428266	−	0.0741778i
$291$			401.836i			0.0809486i
$292$	1987.50	−	1147.48i	0.398321	−	0.229971i
$293$	−7207.50	+	4161.25i	−1.43709	+	0.829703i	−0.997646	−	0.0685685i	$-0.978157\pi$
$293$	−7207.50	+	4161.25i	−1.43709	+	0.829703i	−0.439441	+	0.898271i	$0.644823\pi$
$294$		−	523.079i		−	0.103764i
$295$	246.000	+	426.084i	0.0485514	+	0.0840936i
$296$	−1618.50	+	2803.32i	−0.317816	+	0.550473i
$297$	−1200.00	−	692.820i	−0.234448	−	0.135359i
$298$	−81.0000			−0.0157457
$299$	2535.00	−	2634.45i	0.490310	−	0.509546i
$300$	1220.00			0.234789
$301$	1248.00	+	720.533i	0.238982	+	0.137976i
$302$	1533.00	−	2655.23i	0.292100	−	0.505932i
$303$	−429.000	−	743.050i	−0.0813380	−	0.140882i
$304$		−	114.315i		−	0.0215672i
$305$	−217.500	+	125.574i	−0.0408328	+	0.0235748i
$306$	4036.50	−	2330.47i	0.754089	−	0.435374i
$307$		−	2220.49i		−	0.412801i	−0.978468	−	0.206401i	$-0.933825\pi$
$307$		−	2220.49i		−	0.412801i	0.978468	−	0.206401i	$-0.0661750\pi$
$308$	480.000	+	831.384i	0.0888004	+	0.153807i
$309$	−182.000	+	315.233i	−0.0335069	+	0.0580356i
$310$	405.000	+	233.827i	0.0742015	+	0.0428402i
$311$	4914.00			0.895972			0.447986	−	0.894041i	$-0.352141\pi$
$311$	4914.00			0.895972			0.447986	+	0.894041i	$0.352141\pi$
$312$	1521.00	+	1463.58i	0.275993	+	0.265574i
$313$	−518.000			−0.0935434			−0.0467717	−	0.998906i	$-0.514893\pi$
$313$	−518.000			−0.0935434			−0.0467717	+	0.998906i	$0.514893\pi$
$314$	1816.50	+	1048.76i	0.326468	+	0.188487i
$315$	−276.000	+	478.046i	−0.0493677	+	0.0855074i
$316$	−3190.00	−	5525.24i	−0.567885	−	0.983605i
$317$			3916.17i			0.693861i	0.937891	+	0.346930i	$0.112776\pi$
$317$			3916.17i			0.693861i	−0.937891	+	0.346930i	$0.887224\pi$
$318$	−279.000	+	161.081i	−0.0491998	+	0.0284055i
$319$	1692.00	−	976.877i	0.296971	−	0.171456i
$320$			531.740i			0.0928911i
$321$	1506.00	+	2608.47i	0.261859	+	0.453553i
$322$	−936.000	+	1621.20i	−0.161991	+	0.280577i
$323$	11583.0	+	6687.45i	1.99534	+	1.15201i
$324$	2105.00			0.360940
$325$	5551.00	+	1373.52i	0.947428	+	0.234428i
$326$	−1740.00			−0.295613
$327$	−2688.00	−	1551.92i	−0.454577	−	0.262450i
$328$	3061.50	−	5302.67i	0.515375	−	0.892656i
$329$	−2088.00	−	3616.52i	−0.349894	−	0.606034i
$330$			83.1384i			0.0138685i
$331$	−6456.00	+	3727.37i	−1.07207	+	0.618958i	−0.928745	−	0.370719i	$-0.879111\pi$
$331$	−6456.00	+	3727.37i	−1.07207	+	0.618958i	−0.143321	+	0.989676i	$0.545778\pi$
$332$	−3420.00	+	1974.54i	−0.565352	+	0.326406i
$333$		−	3306.48i		−	0.544127i
$334$	792.000	+	1371.78i	0.129749	+	0.224733i
$335$	−681.000	+	1179.53i	−0.111066	+	0.192371i
$336$	24.0000	+	13.8564i	0.00389675	+	0.00224979i
$337$	−3575.00			−0.577871			−0.288936	−	0.957349i	$-0.593301\pi$
$337$	−3575.00			−0.577871			−0.288936	+	0.957349i	$0.593301\pi$
$338$	2028.00	+	3219.88i	0.326357	+	0.518161i
$339$	−1374.00			−0.220134
$340$	877.500	+	506.625i	0.139968	+	0.0808106i
$341$	−1080.00	+	1870.61i	−0.171511	+	0.297066i
$342$	−2277.00	−	3943.88i	−0.360018	−	0.623569i
$343$		−	6845.06i		−	1.07755i
$344$	−2028.00	+	1170.87i	−0.317856	+	0.183514i
$345$	234.000	−	135.100i	0.0365163	−	0.0210827i
$346$		−	4458.30i		−	0.692716i
$347$	3483.00	+	6032.73i	0.538839	+	0.933297i	0.998967	+	0.0454442i	$0.0144703\pi$
$347$	3483.00	+	6032.73i	0.538839	+	0.933297i	−0.460128	+	0.887853i	$0.652196\pi$
$348$	705.000	−	1221.10i	0.108598	−	0.188097i
$349$	−5760.00	−	3325.54i	−0.883455	−	0.510063i	−0.0116588	−	0.999932i	$-0.503711\pi$
$349$	−5760.00	−	3325.54i	−0.883455	−	0.510063i	−0.871796	+	0.489869i	$0.837045\pi$
$350$	−2928.00			−0.447166
$351$	−4550.00	−	1125.83i	−0.691912	−	0.171204i
$352$	−2520.00			−0.381581
$353$	4876.50	+	2815.45i	0.735269	+	0.424508i	0.820347	−	0.571867i	$-0.193781\pi$
$353$	4876.50	+	2815.45i	0.735269	+	0.424508i	−0.0850777	+	0.996374i	$0.527114\pi$
$354$	492.000	−	852.169i	0.0738687	−	0.127944i
$355$	−915.000	−	1584.83i	−0.136798	−	0.236940i
$356$			4884.38i			0.727168i
$357$	−2808.00	+	1621.20i	−0.416289	+	0.240344i
$358$	−5616.00	+	3242.40i	−0.829092	+	0.478676i
$359$		−	7129.12i		−	1.04808i	−0.851694	−	0.524040i	$-0.824424\pi$
$359$		−	7129.12i		−	1.04808i	0.851694	−	0.524040i	$-0.175576\pi$
$360$	−448.500	−	776.825i	−0.0656612	−	0.113729i
$361$	3104.50	−	5377.15i	0.452617	−	0.783956i
$362$	−955.500	−	551.658i	−0.138729	−	0.0800953i
$363$	2278.00			0.329377
$364$	2340.00	+	2251.67i	0.336949	+	0.324229i
$365$	795.000			0.114006
$366$	435.000	+	251.147i	0.0621252	+	0.0358680i
$367$	−1.00000	+	1.73205i	−0.000142233	+	0.000246355i	−0.866097	−	0.499877i	$-0.833379\pi$
$367$	−1.00000	+	1.73205i	−0.000142233	+	0.000246355i	0.865954	+	0.500123i	$0.166712\pi$
$368$	39.0000	+	67.5500i	0.00552450	+	0.00956871i
$369$			6254.44i			0.882366i
$370$	−373.500	+	215.640i	−0.0524793	+	0.0302989i
$371$	−1116.00	+	644.323i	−0.156172	+	0.0901660i
$372$			1558.85i			0.217264i
$373$	−1749.50	−	3030.22i	−0.242857	−	0.420641i	0.718670	−	0.695351i	$-0.244751\pi$
$373$	−1749.50	−	3030.22i	−0.242857	−	0.420641i	−0.961527	+	0.274711i	$0.911418\pi$
$374$	1404.00	−	2431.80i	0.194115	−	0.336218i
$375$	741.000	+	427.817i	0.102040	+	0.0589129i
$376$	6786.00			0.930748
$377$	4582.50	−	4762.27i	0.626023	−	0.650582i
$378$	2400.00			0.326568
$379$	4779.00	+	2759.16i	0.647706	+	0.373953i	0.787577	−	0.616216i	$-0.211335\pi$
$379$	4779.00	+	2759.16i	0.647706	+	0.373953i	−0.139871	+	0.990170i	$0.544669\pi$
$380$	495.000	−	857.365i	0.0668236	−	0.115742i
$381$	−286.000	−	495.367i	−0.0384573	−	0.0666100i
$382$			4499.87i			0.602705i
$383$	−6378.00	+	3682.34i	−0.850915	+	0.491276i	−0.860960	−	0.508673i	$-0.830136\pi$
$383$	−6378.00	+	3682.34i	−0.850915	+	0.491276i	0.0100443	+	0.999950i	$0.496803\pi$
$384$	−1599.00	+	923.183i	−0.212496	+	0.122685i
$385$			332.554i			0.0440221i
$386$	967.500	+	1675.76i	0.127576	+	0.220969i
$387$	1196.00	−	2071.53i	0.157096	−	0.272098i
$388$	−870.000	−	502.295i	−0.113834	−	0.0657220i
$389$	−1209.00			−0.157580			−0.0787901	−	0.996891i	$-0.525106\pi$
$389$	−1209.00			−0.157580			−0.0787901	+	0.996891i	$0.525106\pi$
$390$	78.0000	+	270.200i	0.0101274	+	0.0350823i
$391$	−9126.00			−1.18036
$392$	2944.50	+	1700.01i	0.379387	+	0.219039i
$393$	1974.00	−	3419.07i	0.253372	−	0.438853i
$394$	1776.00	+	3076.12i	0.227090	+	0.393332i
$395$		−	2210.10i		−	0.281524i
$396$	1380.00	−	796.743i	0.175120	−	0.101106i
$397$	10128.0	−	5847.40i	1.28038	−	0.739226i	0.303460	−	0.952844i	$-0.401858\pi$
$397$	10128.0	−	5847.40i	1.28038	−	0.739226i	0.976917	+	0.213618i	$0.0685248\pi$
$398$			4368.23i			0.550150i
$399$	1584.00	+	2743.57i	0.198745	+	0.344236i
$400$	−61.0000	+	105.655i	−0.00762500	+	0.0132069i
$401$	−2581.50	−	1490.43i	−0.321481	−	0.185607i	0.330571	−	0.943781i	$-0.392759\pi$
$401$	−2581.50	−	1490.43i	−0.321481	−	0.185607i	−0.652053	+	0.758174i	$0.726092\pi$
$402$	2724.00			0.337962
$403$	−1755.00	+	7092.75i	−0.216930	+	0.876712i
$404$	2145.00			0.264153
$405$	631.500	+	364.597i	0.0774802	+	0.0447332i
$406$	−1692.00	+	2930.63i	−0.206829	+	0.358238i
$407$	−996.000	−	1725.12i	−0.121302	−	0.210101i
$408$		−	5268.90i		−	0.639337i
$409$	37.5000	−	21.6506i	0.00453363	−	0.00261749i	−0.497731	−	0.867331i	$-0.665833\pi$
$409$	37.5000	−	21.6506i	0.00453363	−	0.00261749i	0.502265	+	0.864714i	$0.332500\pi$
$410$	706.500	−	407.898i	0.0851013	−	0.0491333i
$411$		−	1693.95i		−	0.203300i
$412$	−455.000	−	788.083i	−0.0544084	−	0.0942380i
$413$	1968.00	−	3408.68i	0.234477	−	0.406126i
$414$	2691.00	+	1553.65i	0.319458	+	0.184439i
$415$	−1368.00			−0.161813
$416$	−8190.00	+	2364.25i	−0.965259	+	0.278646i
$417$	472.000			0.0554291
$418$	−2376.00	−	1371.78i	−0.278024	−	0.160517i
$419$	4731.00	−	8194.33i	0.551610	−	0.955416i	−0.446549	−	0.894759i	$-0.647347\pi$
$419$	4731.00	−	8194.33i	0.551610	−	0.955416i	0.998159	−	0.0606569i	$-0.0193195\pi$
$420$	120.000	+	207.846i	0.0139414	+	0.0241473i
$421$			7068.50i			0.818284i	0.912471	+	0.409142i	$0.134172\pi$
$421$			7068.50i			0.818284i	−0.912471	+	0.409142i	$0.865828\pi$
$422$	−1563.00	+	902.398i	−0.180298	+	0.104095i
$423$	−6003.00	+	3465.83i	−0.690014	+	0.398380i
$424$		−	2094.05i		−	0.239849i
$425$	−7137.00	−	12361.6i	−0.814577	−	1.41089i
$426$	−1830.00	+	3169.65i	−0.208131	+	0.360493i
$427$	1740.00	+	1004.59i	0.197200	+	0.113854i
$428$	−7530.00			−0.850412
$429$	−1248.00	+	360.267i	−0.140452	+	0.0405451i
$430$	−312.000			−0.0349906
$431$	−8598.00	−	4964.06i	−0.960907	−	0.554780i	−0.0644552	−	0.997921i	$-0.520531\pi$
$431$	−8598.00	−	4964.06i	−0.960907	−	0.554780i	−0.896452	+	0.443140i	$0.853864\pi$
$432$	50.0000	−	86.6025i	0.00556858	−	0.00964506i
$433$	3308.50	+	5730.49i	0.367197	+	0.636004i	0.989126	−	0.147070i	$-0.0469841\pi$
$433$	3308.50	+	5730.49i	0.367197	+	0.636004i	−0.621929	+	0.783074i	$0.713651\pi$
$434$		−	3741.23i		−	0.413790i
$435$	423.000	−	244.219i	0.0466237	−	0.0269182i
$436$	6720.00	−	3879.79i	0.738141	−	0.426166i
$437$			8916.60i			0.976061i
$438$	−795.000	−	1376.98i	−0.0867273	−	0.150216i
$439$	−6994.00	+	12114.0i	−0.760377	+	1.31701i	0.182280	+	0.983247i	$0.441652\pi$
$439$	−6994.00	+	12114.0i	−0.760377	+	1.31701i	−0.942656	+	0.333765i	$0.891681\pi$
$440$	−468.000	−	270.200i	−0.0507069	−	0.0292756i
$441$	−3473.00			−0.375013
$442$	2281.50	−	9220.57i	0.245520	−	0.992258i
$443$	2004.00			0.214928			0.107464	−	0.994209i	$-0.465727\pi$
$443$	2004.00			0.214928			0.107464	+	0.994209i	$0.465727\pi$
$444$	−1245.00	−	718.801i	−0.133075	−	0.0768306i
$445$	−846.000	+	1465.31i	−0.0901219	+	0.156096i
$446$	−2085.00	−	3611.33i	−0.221362	−	0.383411i
$447$		−	93.5307i		−	0.00989676i
$448$	3684.00	−	2126.96i	0.388510	−	0.224307i
$449$	7866.00	−	4541.44i	0.826769	−	0.477336i	−0.0259758	−	0.999663i	$-0.508269\pi$
$449$	7866.00	−	4541.44i	0.826769	−	0.477336i	0.852745	+	0.522327i	$0.174936\pi$
$450$			4860.13i			0.509131i
$451$	1884.00	+	3263.18i	0.196705	+	0.340704i
$452$	1717.50	−	2974.80i	0.178727	−	0.309563i
$453$	3066.00	+	1770.16i	0.317998	+	0.183596i
$454$	4170.00			0.431074
$455$	312.000	+	1080.80i	0.0321468	+	0.111360i
$456$	−5148.00			−0.528678
$457$	2185.50	+	1261.80i	0.223705	+	0.129156i	0.607665	−	0.794194i	$-0.292106\pi$
$457$	2185.50	+	1261.80i	0.223705	+	0.129156i	−0.383959	+	0.923350i	$0.625440\pi$
$458$	−2172.00	+	3762.01i	−0.221596	+	0.383815i
$459$	5850.00	+	10132.5i	0.594890	+	1.03038i
$460$			675.500i			0.0684681i
$461$	16963.5	−	9793.88i	1.71382	−	0.989472i	0.784545	−	0.620072i	$-0.212897\pi$
$461$	16963.5	−	9793.88i	1.71382	−	0.989472i	0.929270	−	0.369400i	$-0.120437\pi$
$462$	576.000	−	332.554i	0.0580042	−	0.0334887i
$463$			8632.54i			0.866497i	0.901274	+	0.433249i	$0.142633\pi$
$463$			8632.54i			0.866497i	−0.901274	+	0.433249i	$0.857367\pi$
$464$	70.5000	+	122.110i	0.00705362	+	0.0122172i
$465$	−270.000	+	467.654i	−0.0269268	+	0.0466385i
$466$	−8775.00	−	5066.25i	−0.872305	−	0.503625i
$467$	5460.00			0.541025			0.270512	−	0.962716i	$-0.412807\pi$
$467$	5460.00			0.541025			0.270512	+	0.962716i	$0.412807\pi$
$468$	3737.50	−	3884.12i	0.369158	−	0.383640i
$469$	10896.0			1.07277
$470$	783.000	+	452.065i	0.0768449	+	0.0443664i
$471$	−1211.00	+	2097.51i	−0.118471	+	0.205198i
$472$	3198.00	+	5539.10i	0.311864	+	0.540165i
$473$		−	1441.07i		−	0.140085i
$474$	−3828.00	+	2210.10i	−0.370941	+	0.214163i
$475$	−12078.0	+	6973.24i	−1.16669	+	0.673587i
$476$		−	8106.00i		−	0.780542i
$477$	1069.50	+	1852.43i	0.102660	+	0.177813i
$478$	4662.00	−	8074.82i	0.446098	−	0.772665i
$479$	−2211.00	−	1276.52i	−0.210904	−	0.121766i	0.390827	−	0.920464i	$-0.372189\pi$
$479$	−2211.00	−	1276.52i	−0.210904	−	0.121766i	−0.601732	+	0.798698i	$0.705522\pi$
$480$	−630.000			−0.0599072
$481$	−4855.50	−	4672.21i	−0.460274	−	0.442899i
$482$	8517.00			0.804852
$483$	−1872.00	−	1080.80i	−0.176354	−	0.101818i
$484$	−2847.50	+	4932.01i	−0.267421	+	0.463187i
$485$	−174.000	−	301.377i	−0.0162906	−	0.0282161i
$486$		−	6134.92i		−	0.572605i
$487$	9378.00	−	5414.39i	0.872603	−	0.503798i	0.00439074	−	0.999990i	$-0.498602\pi$
$487$	9378.00	−	5414.39i	0.872603	−	0.503798i	0.868212	+	0.496193i	$0.165269\pi$
$488$	−2827.50	+	1632.46i	−0.262285	+	0.151430i
$489$		−	2009.18i		−	0.185804i
$490$	226.500	+	392.310i	0.0208821	+	0.0361689i
$491$	−5694.00	+	9862.30i	−0.523354	+	0.906475i	0.476277	+	0.879295i	$0.341986\pi$
$491$	−5694.00	+	9862.30i	−0.523354	+	0.906475i	−0.999631	+	0.0271797i	$0.991347\pi$
$492$	2355.00	+	1359.66i	0.215796	+	0.124590i
$493$	−16497.0			−1.50707
$494$	−9009.00	−	2229.15i	−0.820514	−	0.203025i
$495$	552.000			0.0501223
$496$	−135.000	−	77.9423i	−0.0122211	−	0.00705587i
$497$	−7320.00	+	12678.6i	−0.660658	+	1.14429i
$498$	1368.00	+	2369.45i	0.123095	+	0.213208i
$499$		−	17677.3i		−	1.58586i	−0.609311	−	0.792931i	$-0.708554\pi$
$499$		−	17677.3i		−	1.58586i	0.609311	−	0.792931i	$-0.291446\pi$
$500$	−1852.50	+	1069.54i	−0.165693	+	0.0956627i
$501$	−1584.00	+	914.523i	−0.141253	+	0.0815526i
$502$			6890.10i			0.612590i
$503$	−1938.00	−	3356.71i	−0.171792	−	0.297552i	0.767255	−	0.641343i	$-0.221622\pi$
$503$	−1938.00	−	3356.71i	−0.171792	−	0.297552i	−0.939046	+	0.343791i	$0.888289\pi$
$504$	−3588.00	+	6214.60i	−0.317108	+	0.549246i
$505$	643.500	+	371.525i	0.0567037	+	0.0327379i
$506$	1872.00			0.164467
$507$	−3718.00	+	2341.73i	−0.325685	+	0.205128i
$508$	1430.00			0.124894
$509$	−14779.5	−	8532.95i	−1.28701	−	0.743058i	−0.308893	−	0.951097i	$-0.599958\pi$
$509$	−14779.5	−	8532.95i	−1.28701	−	0.743058i	−0.978120	+	0.208039i	$0.933292\pi$
$510$	351.000	−	607.950i	0.0304756	−	0.0527852i
$511$	−3180.00	−	5507.92i	−0.275293	−	0.476822i
$512$		−	361.999i		−	0.0312465i
$513$	9900.00	−	5715.77i	0.852038	−	0.491925i
$514$	−3100.50	+	1790.07i	−0.266065	+	0.153612i
$515$		−	315.233i		−	0.0269725i
$516$	−520.000	−	900.666i	−0.0443638	−	0.0768404i
$517$	−2088.00	+	3616.52i	−0.177621	+	0.307649i
$518$	2988.00	+	1725.12i	0.253446	+	0.146327i
$519$	5148.00			0.435399
$520$	−1774.50	−	439.075i	−0.149648	−	0.0370283i
$521$	2121.00			0.178355			0.0891773	−	0.996016i	$-0.471576\pi$
$521$	2121.00			0.178355			0.0891773	+	0.996016i	$0.471576\pi$
$522$	4864.50	+	2808.52i	0.407880	+	0.235490i
$523$	5732.00	−	9928.12i	0.479241	−	0.830069i	−0.520476	−	0.853876i	$-0.674245\pi$
$523$	5732.00	−	9928.12i	0.479241	−	0.830069i	0.999717	+	0.0238072i	$0.00757878\pi$
$524$	4935.00	+	8547.67i	0.411425	+	0.712608i
$525$		−	3380.96i		−	0.281062i
$526$	3078.00	−	1777.08i	0.255147	−	0.147309i
$527$	15795.0	−	9119.25i	1.30558	−	0.753777i
$528$		−	27.7128i		−	0.00228418i
$529$	3041.50	+	5268.03i	0.249979	+	0.432977i
$530$	139.500	−	241.621i	0.0114330	−	0.0198025i
$531$	−5658.00	−	3266.65i	−0.462404	−	0.266969i
$532$	−7920.00			−0.645443
$533$	9184.50	+	8837.79i	0.746388	+	0.718212i
$534$	3384.00			0.274232
$535$	−2259.00	−	1304.23i	−0.182552	−	0.105396i
$536$	−8853.00	+	15333.8i	−0.713417	+	1.23567i
$537$	−3744.00	−	6484.80i	−0.300867	−	0.521117i
$538$		−	5767.73i		−	0.462202i
$539$	−1812.00	+	1046.16i	−0.144802	+	0.0836016i
$540$	750.000	−	433.013i	0.0597683	−	0.0345072i
$541$		−	4764.87i		−	0.378665i	−0.981913	−	0.189333i	$-0.939368\pi$
$541$		−	4764.87i		−	0.378665i	0.981913	−	0.189333i	$-0.0606324\pi$
$542$	2430.00	+	4208.88i	0.192578	+	0.333555i
$543$	637.000	−	1103.32i	0.0503431	−	0.0871968i
$544$	18427.5	+	10639.1i	1.45234	+	0.838508i
$545$	2688.00			0.211268
$546$	1560.00	−	1621.20i	0.122274	−	0.127071i
$547$	6554.00			0.512301			0.256151	−	0.966637i	$-0.417546\pi$
$547$	6554.00			0.512301			0.256151	+	0.966637i	$0.417546\pi$
$548$	3667.50	+	2117.43i	0.285890	+	0.165059i
$549$	1667.50	−	2888.19i	0.129631	−	0.224527i
$550$	1464.00	+	2535.72i	0.113500	+	0.196588i
$551$			16118.5i			1.24622i
$552$	3042.00	−	1756.30i	0.234558	−	0.135422i
$553$	−15312.0	+	8840.39i	−1.17745	+	0.679804i
$554$		−	652.983i		−	0.0500769i
$555$	−249.000	−	431.281i	−0.0190441	−	0.0329853i
$556$	−590.000	+	1021.91i	−0.0450028	+	0.0779472i
$557$	−15685.5	−	9056.03i	−1.19321	−	0.688898i	−0.234174	−	0.972195i	$-0.575239\pi$
$557$	−15685.5	−	9056.03i	−1.19321	−	0.688898i	−0.959032	+	0.283297i	$0.908572\pi$
$558$	−6210.00			−0.471130
$559$	−1352.00	−	4683.47i	−0.102296	−	0.354364i
$560$	−24.0000			−0.00181104
$561$	2808.00	+	1621.20i	0.211326	+	0.122009i
$562$	31.5000	−	54.5596i	0.00236432	−	0.00409512i
$563$	6084.00	+	10537.8i	0.455435	+	0.788837i	0.998713	−	0.0507160i	$-0.0161503\pi$
$563$	6084.00	+	10537.8i	0.455435	+	0.788837i	−0.543278	+	0.839553i	$0.682817\pi$
$564$			3013.77i			0.225005i
$565$	1030.50	−	594.959i	0.0767318	−	0.0443011i
$566$	10686.0	−	6169.56i	0.793580	−	0.458173i
$567$		−	5833.55i		−	0.432074i
$568$	−11895.0	−	20602.7i	−0.878703	−	1.52196i
$569$	3861.00	−	6687.45i	0.284467	−	0.492711i	−0.688013	−	0.725698i	$-0.741517\pi$
$569$	3861.00	−	6687.45i	0.284467	−	0.492711i	0.972480	+	0.232988i	$0.0748502\pi$
$570$	−594.000	−	342.946i	−0.0436490	−	0.0252008i
$571$	11440.0			0.838440			0.419220	−	0.907885i	$-0.362304\pi$
$571$	11440.0			0.838440			0.419220	+	0.907885i	$0.362304\pi$
$572$	780.000	−	3152.33i	0.0570165	−	0.230429i
$573$	−5196.00			−0.378824
$574$	−5652.00	−	3263.18i	−0.410993	−	0.237287i
$575$	4758.00	−	8241.10i	0.345082	−	0.597700i
$576$	−3530.50	−	6115.01i	−0.255389	−	0.442347i
$577$			15444.7i			1.11433i	0.830400	+	0.557167i	$0.188112\pi$
$577$			15444.7i			1.11433i	−0.830400	+	0.557167i	$0.811888\pi$
$578$	−13164.0	+	7600.24i	−0.947319	+	0.546935i
$579$	−1935.00	+	1117.17i	−0.138887	+	0.0801867i
$580$			1221.10i			0.0874194i
$581$	5472.00	+	9477.78i	0.390735	+	0.676772i
$582$	−348.000	+	602.754i	−0.0247853	+	0.0429295i
$583$	1116.00	+	644.323i	0.0792796	+	0.0457721i
$584$	10335.0			0.732304
$585$	1794.00	−	517.883i	0.126791	−	0.0366014i
$586$	−14415.0			−1.01617
$587$	−12186.0	−	7035.59i	−0.856848	−	0.494702i	0.00610719	−	0.999981i	$-0.498056\pi$
$587$	−12186.0	−	7035.59i	−0.856848	−	0.494702i	−0.862956	+	0.505280i	$0.831389\pi$
$588$	−755.000	+	1307.70i	−0.0529518	+	0.0917153i
$589$	−8910.00	−	15432.6i	−0.623311	−	1.07961i
$590$			852.169i			0.0594631i
$591$	−3552.00	+	2050.75i	−0.247225	+	0.142735i
$592$	124.500	−	71.8801i	0.00864344	−	0.00499029i
$593$			26938.6i			1.86549i	0.360538	+	0.932745i	$0.382593\pi$
$593$			26938.6i			1.86549i	−0.360538	+	0.932745i	$0.617407\pi$
$594$	−1200.00	−	2078.46i	−0.0828899	−	0.143570i
$595$	1404.00	−	2431.80i	0.0967368	−	0.167553i
$596$	202.500	+	116.913i	0.0139173	+	0.00803517i
$597$	−5044.00			−0.345791
$598$	6084.00	−	1756.30i	0.416042	−	0.120101i
$599$	−10554.0			−0.719908			−0.359954	−	0.932970i	$-0.617208\pi$
$599$	−10554.0			−0.719908			−0.359954	+	0.932970i	$0.617208\pi$
$600$	4758.00	+	2747.03i	0.323741	+	0.186912i
$601$	7415.50	−	12844.0i	0.503302	−	0.871745i	−0.496691	−	0.867928i	$-0.665452\pi$
$601$	7415.50	−	12844.0i	0.503302	−	0.871745i	0.999993	−	0.00381713i	$-0.00121503\pi$
$602$	1248.00	+	2161.60i	0.0844928	+	0.146346i
$603$		−	18086.1i		−	1.22143i
$604$	−7665.00	+	4425.39i	−0.516365	+	0.298123i
$605$	−1708.50	+	986.403i	−0.114811	+	0.0662859i
$606$		−	1486.10i		−	0.0996183i
$607$	3977.00	+	6888.37i	0.265933	+	0.460610i	0.967808	−	0.251691i	$-0.0809866\pi$
$607$	3977.00	+	6888.37i	0.265933	+	0.460610i	−0.701874	+	0.712301i	$0.747653\pi$
$608$	10395.0	−	18004.7i	0.693377	−	1.20096i
$609$	−3384.00	−	1953.75i	−0.225167	−	0.130000i
$610$	−435.000			−0.0288732
$611$	−3393.00	+	13712.6i	−0.224658	+	0.907945i
$612$	−13455.0			−0.888703
$613$	21841.5	+	12610.2i	1.43910	+	0.830866i	0.997787	−	0.0664859i	$-0.0211787\pi$
$613$	21841.5	+	12610.2i	1.43910	+	0.830866i	0.441315	+	0.897352i	$0.354512\pi$
$614$	1923.00	−	3330.73i	0.126394	−	0.218921i
$615$	471.000	+	815.796i	0.0308822	+	0.0534895i
$616$			4323.20i			0.282771i
$617$	−15055.5	+	8692.30i	−0.982353	+	0.567162i	−0.902980	−	0.429683i	$-0.858625\pi$
$617$	−15055.5	+	8692.30i	−0.982353	+	0.567162i	−0.0793731	+	0.996845i	$0.525292\pi$
$618$	−546.000	+	315.233i	−0.0355394	+	0.0205187i
$619$		−	8209.92i		−	0.533093i	−0.963822	−	0.266547i	$-0.914117\pi$
$619$		−	8209.92i		−	0.533093i	0.963822	−	0.266547i	$-0.0858826\pi$
$620$	−675.000	−	1169.13i	−0.0437236	−	0.0757316i
$621$	−3900.00	+	6755.00i	−0.252015	+	0.436504i
$622$	7371.00	+	4255.65i	0.475161	+	0.274334i
$623$	13536.0			0.870479
$624$	−26.0000	−	90.0666i	−0.00166800	−	0.00577813i
$625$	14509.0			0.928576
$626$	−777.000	−	448.601i	−0.0496089	−	0.0286417i
$627$	1584.00	−	2743.57i	0.100891	−	0.174749i
$628$	−3027.50	−	5243.78i	−0.192373	−	0.333200i
$629$			16819.9i			1.06622i
$630$	−828.000	+	478.046i	−0.0523624	+	0.0302314i
$631$	11142.0	−	6432.84i	0.702941	−	0.405843i	−0.105501	−	0.994419i	$-0.533645\pi$
$631$	11142.0	−	6432.84i	0.702941	−	0.405843i	0.808442	+	0.588576i	$0.200311\pi$
$632$		−	28731.3i		−	1.80834i
$633$	−1042.00	−	1804.80i	−0.0654278	−	0.113324i
$634$	−3391.50	+	5874.25i	−0.212451	+	0.367975i
$635$	429.000	+	247.683i	0.0268100	+	0.0154788i
$636$	930.000			0.0579825
$637$	−4907.50	+	5100.02i	−0.305247	+	0.317222i
$638$	3384.00			0.209990
$639$	21045.0	+	12150.3i	1.30286	+	0.752206i
$640$	799.500	−	1384.77i	0.0493797	−	0.0855282i
$641$	−3100.50	−	5370.22i	−0.191049	−	0.330907i	0.754549	−	0.656244i	$-0.227856\pi$
$641$	−3100.50	−	5370.22i	−0.191049	−	0.330907i	−0.945598	+	0.325337i	$0.894522\pi$
$642$			5216.94i			0.320710i
$643$	−14568.0	+	8410.84i	−0.893477	+	0.515849i	−0.875078	−	0.483981i	$-0.839190\pi$
$643$	−14568.0	+	8410.84i	−0.893477	+	0.515849i	−0.0183989	+	0.999831i	$0.505857\pi$
$644$	4680.00	−	2702.00i	0.286363	−	0.165332i
$645$		−	360.267i		−	0.0219930i
$646$	11583.0	+	20062.3i	0.705460	+	1.22189i
$647$	6747.00	−	11686.1i	0.409972	−	0.710092i	−0.584914	−	0.811095i	$-0.698872\pi$
$647$	6747.00	−	11686.1i	0.409972	−	0.710092i	0.994886	+	0.101003i	$0.0322051\pi$
$648$	8209.50	+	4739.76i	0.497685	+	0.287338i
$649$	−3936.00			−0.238061
$650$	7137.00	+	6867.58i	0.430671	+	0.414413i
$651$	4320.00			0.260083
$652$	4350.00	+	2511.47i	0.261287	+	0.150854i
$653$	5667.00	−	9815.53i	0.339612	−	0.588226i	−0.644747	−	0.764396i	$-0.723037\pi$
$653$	5667.00	−	9815.53i	0.339612	−	0.588226i	0.984360	+	0.176170i	$0.0563708\pi$
$654$	−2688.00	−	4655.75i	−0.160717	−	0.278371i
$655$			3419.07i			0.203960i
$656$	−235.500	+	135.966i	−0.0140164	+	0.00809235i
$657$	−9142.50	+	5278.42i	−0.542896	+	0.313441i
$658$		−	7233.04i		−	0.428531i
$659$	−6618.00	−	11462.7i	−0.391200	−	0.677578i	0.601408	−	0.798942i	$-0.294607\pi$
$659$	−6618.00	−	11462.7i	−0.391200	−	0.677578i	−0.992608	+	0.121364i	$0.961273\pi$
$660$	120.000	−	207.846i	0.00707726	−	0.0122582i
$661$	−10264.5	−	5926.21i	−0.603998	−	0.348718i	0.166615	−	0.986022i	$-0.446716\pi$
$661$	−10264.5	−	5926.21i	−0.603998	−	0.348718i	−0.770613	+	0.637304i	$0.780050\pi$
$662$	−12912.0			−0.758065
$663$	10647.0	+	2634.45i	0.623673	+	0.154319i
$664$	−17784.0			−1.03939
$665$	−2376.00	−	1371.78i	−0.138552	−	0.0799932i
$666$	2863.50	−	4959.73i	0.166604	−	0.288567i
$667$	−5499.00	−	9524.55i	−0.319224	−	0.552911i
$668$		−	4572.61i		−	0.264850i
$669$	4170.00	−	2407.55i	0.240989	−	0.139135i
$670$	−2043.00	+	1179.53i	−0.117803	+	0.0680136i
$671$		−	2009.18i		−	0.115594i
$672$	2520.00	+	4364.77i	0.144659	+	0.250557i
$673$	−4010.50	+	6946.39i	−0.229708	+	0.397866i	−0.957722	−	0.287697i	$-0.907110\pi$
$673$	−4010.50	+	6946.39i	−0.229708	+	0.397866i	0.728014	+	0.685563i	$0.240444\pi$
$674$	−5362.50	−	3096.04i	−0.306463	−	0.176936i
$675$	−12200.0			−0.695671
$676$	−422.500	−	10976.9i	−0.0240385	−	0.624538i
$677$	−21630.0			−1.22793			−0.613965	−	0.789333i	$-0.710426\pi$
$677$	−21630.0			−1.22793			−0.613965	+	0.789333i	$0.710426\pi$
$678$	−2061.00	−	1189.92i	−0.116744	−	0.0674020i
$679$	−1392.00	+	2411.01i	−0.0786746	+	0.136268i
$680$	2281.50	+	3951.67i	0.128664	+	0.222853i
$681$			4815.10i			0.270947i
$682$	−3240.00	+	1870.61i	−0.181915	+	0.105029i
$683$	−22983.0	+	13269.2i	−1.28758	+	0.743387i	−0.978223	−	0.207557i	$-0.933449\pi$
$683$	−22983.0	+	13269.2i	−1.28758	+	0.743387i	−0.309361	+	0.950945i	$0.600115\pi$
$684$			13146.3i			0.734883i
$685$	733.500	+	1270.46i	0.0409133	+	0.0708639i
$686$	5928.00	−	10267.6i	0.329930	−	0.571456i
$687$	−4344.00	−	2508.01i	−0.241243	−	0.139282i
$688$	104.000			0.00576303
$689$	4231.50	+	1047.02i	0.233973	+	0.0578933i
$690$	468.000			0.0258210
$691$	−720.000	−	415.692i	−0.0396383	−	0.0228852i	0.480050	−	0.877241i	$-0.340619\pi$
$691$	−720.000	−	415.692i	−0.0396383	−	0.0228852i	−0.519688	+	0.854356i	$0.673952\pi$
$692$	−6435.00	+	11145.7i	−0.353500	+	0.612280i
$693$	−2208.00	−	3824.37i	−0.121032	−	0.209633i
$694$			12065.5i			0.659941i
$695$	−354.000	+	204.382i	−0.0193208	+	0.0111549i
$696$	5499.00	−	3174.85i	0.299481	−	0.172906i
$697$		−	31816.0i		−	1.72901i
$698$	−5760.00	−	9976.61i	−0.312348	−	0.541003i
$699$	5850.00	−	10132.5i	0.316548	−	0.548278i
$700$	7320.00	+	4226.20i	0.395243	+	0.228194i
$701$	30186.0			1.62640			0.813202	−	0.581981i	$-0.197722\pi$
$701$	30186.0			1.62640			0.813202	+	0.581981i	$0.197722\pi$
$702$	−5850.00	−	5629.17i	−0.314521	−	0.302648i
$703$	16434.0			0.881679
$704$	−3684.00	−	2126.96i	−0.197224	−	0.113868i
$705$	−522.000	+	904.131i	−0.0278860	+	0.0483000i
$706$	4876.50	+	8446.35i	0.259957	+	0.450258i
$707$		−	5944.40i		−	0.316212i
$708$	−2460.00	+	1420.28i	−0.130583	+	0.0753919i
$709$	−10288.5	+	5940.07i	−0.544983	+	0.314646i	−0.747096	−	0.664716i	$-0.768552\pi$
$709$	−10288.5	+	5940.07i	−0.544983	+	0.314646i	0.202113	+	0.979362i	$0.435219\pi$
$710$		−	3169.65i		−	0.167542i
$711$	14674.0	+	25416.1i	0.774006	+	1.34062i
$712$	−10998.0	+	19049.1i	−0.578887	+	1.00266i
$713$	10530.0	+	6079.50i	0.553088	+	0.319325i
$714$	−5616.00			−0.294361
$715$	780.000	−	810.600i	0.0407977	−	0.0423982i
$716$	18720.0			0.977094
$717$	9324.00	+	5383.21i	0.485650	+	0.280390i
$718$	6174.00	−	10693.7i	0.320908	−	0.555828i
$719$	−9204.00	−	15941.8i	−0.477401	−	0.826883i	0.522264	−	0.852784i	$-0.325088\pi$
$719$	−9204.00	−	15941.8i	−0.477401	−	0.826883i	−0.999665	+	0.0259014i	$0.991754\pi$
$720$			39.8372i			0.00206201i
$721$	−2184.00	+	1260.93i	−0.112811	+	0.0651312i
$722$	9313.50	−	5377.15i	0.480073	−	0.277170i
$723$			9834.58i			0.505881i
$724$	1592.50	+	2758.29i	0.0817470	+	0.141590i
$725$	8601.00	−	14897.4i	0.440597	−	0.763137i
$726$	3417.00	+	1972.81i	0.174679	+	0.100851i
$727$	21112.0			1.07703			0.538515	−	0.842616i	$-0.318986\pi$
$727$	21112.0			1.07703			0.538515	+	0.842616i	$0.318986\pi$
$728$	4056.00	+	14050.4i	0.206491	+	0.715305i
$729$	−4283.00			−0.217599
$730$	1192.50	+	688.490i	0.0604608	+	0.0349071i
$731$	−6084.00	+	10537.8i	−0.307832	+	0.533180i
$732$	−725.000	−	1255.74i	−0.0366076	−	0.0634062i
$733$		−	23959.5i		−	1.20732i	−0.797243	−	0.603658i	$-0.793709\pi$
$733$		−	23959.5i		−	1.20732i	0.797243	−	0.603658i	$-0.206291\pi$
$734$	−3.00000	+	1.73205i	−0.000150861	+	8.70997e-5i
$735$	−453.000	+	261.540i	−0.0227335	+	0.0131252i
$736$			14185.5i			0.710441i
$737$	−5448.00	−	9436.21i	−0.272293	−	0.471625i
$738$	−5416.50	+	9381.65i	−0.270168	+	0.467945i
$739$	2742.00	+	1583.09i	0.136490	+	0.0788025i	0.566690	−	0.823931i	$-0.308224\pi$
$739$	2742.00	+	1583.09i	0.136490	+	0.0788025i	−0.430200	+	0.902734i	$0.641557\pi$
$740$	1245.00			0.0618474
$741$	2574.00	−	10402.7i	0.127609	−	0.515726i
$742$	−2232.00			−0.110430
$743$	−26070.0	−	15051.5i	−1.28723	−	0.743185i	−0.309075	−	0.951038i	$-0.600019\pi$
$743$	−26070.0	−	15051.5i	−1.28723	−	0.743185i	−0.978160	+	0.207852i	$0.933353\pi$
$744$	−3510.00	+	6079.50i	−0.172961	+	0.299577i
$745$	40.5000	+	70.1481i	0.00199168	+	0.00344970i
$746$		−	6060.45i		−	0.297438i
$747$	15732.0	−	9082.87i	0.770554	−	0.444880i
$748$	−7020.00	+	4053.00i	−0.343151	+	0.198118i
$749$			20867.7i			1.01801i
$750$	741.000	+	1283.45i	0.0360767	+	0.0624866i
$751$	−14248.0	+	24678.3i	−0.692299	+	1.19910i	0.278783	+	0.960354i	$0.410069\pi$
$751$	−14248.0	+	24678.3i	−0.692299	+	1.19910i	−0.971083	+	0.238744i	$0.923264\pi$
$752$	−261.000	−	150.688i	−0.0126565	−	0.00730724i
$753$	−7956.00			−0.385037
$754$	10998.0	−	3174.85i	0.531198	−	0.153344i
$755$	−3066.00			−0.147792
$756$	−6000.00	−	3464.10i	−0.288648	−	0.166651i
$757$	−8711.00	+	15087.9i	−0.418239	+	0.724411i	−0.995762	−	0.0919633i	$-0.970686\pi$
$757$	−8711.00	+	15087.9i	−0.418239	+	0.724411i	0.577524	+	0.816374i	$0.304019\pi$
$758$	4779.00	+	8277.47i	0.228999	+	0.396638i
$759$			2161.60i			0.103374i
$760$	3861.00	−	2229.15i	0.184281	−	0.106394i
$761$	35790.0	−	20663.4i	1.70484	−	0.984292i	0.764149	−	0.645040i	$-0.223159\pi$
$761$	35790.0	−	20663.4i	1.70484	−	0.984292i	0.940695	−	0.339252i	$-0.110174\pi$
$762$		−	990.733i		−	0.0471004i
$763$	−10752.0	−	18623.0i	−0.510155	−	0.883615i
$764$	6495.00	−	11249.7i	0.307567	−	0.532721i

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:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	13.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-2.50000 - 4.33013i) q^{4} -1.73205i q^{5} +(-3.00000 + 1.73205i) q^{6} +(-12.0000 + 6.92820i) q^{7} -22.5167i q^{8} +(11.5000 + 19.9186i) q^{9} +O(q^{10})\)	\(q+(1.50000 + 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-2.50000 - 4.33013i) q^{4} -1.73205i q^{5} +(-3.00000 + 1.73205i) q^{6} +(-12.0000 + 6.92820i) q^{7} -22.5167i q^{8} +(11.5000 + 19.9186i) q^{9} +(1.50000 - 2.59808i) q^{10} +(12.0000 + 6.92820i) q^{11} +10.0000 q^{12} +(45.5000 + 11.2583i) q^{13} -24.0000 q^{14} +(3.00000 + 1.73205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-58.5000 - 101.325i) q^{17} +39.8372i q^{18} +(-99.0000 + 57.1577i) q^{19} +(-7.50000 + 4.33013i) q^{20} -27.7128i q^{21} +(12.0000 + 20.7846i) q^{22} +(39.0000 - 67.5500i) q^{23} +(39.0000 + 22.5167i) q^{24} +122.000 q^{25} +(58.5000 + 56.2917i) q^{26} -100.000 q^{27} +(60.0000 + 34.6410i) q^{28} +(70.5000 - 122.110i) q^{29} +(3.00000 + 5.19615i) q^{30} +155.885i q^{31} +(-157.500 + 90.9327i) q^{32} +(-24.0000 + 13.8564i) q^{33} -202.650i q^{34} +(12.0000 + 20.7846i) q^{35} +(57.5000 - 99.5929i) q^{36} +(-124.500 - 71.8801i) q^{37} -198.000 q^{38} +(-65.0000 + 67.5500i) q^{39} -39.0000 q^{40} +(235.500 + 135.966i) q^{41} +(24.0000 - 41.5692i) q^{42} +(-52.0000 - 90.0666i) q^{43} -69.2820i q^{44} +(34.5000 - 19.9186i) q^{45} +(117.000 - 67.5500i) q^{46} +301.377i q^{47} +(-1.00000 - 1.73205i) q^{48} +(-75.5000 + 130.770i) q^{49} +(183.000 + 105.655i) q^{50} +234.000 q^{51} +(-65.0000 - 225.167i) q^{52} +93.0000 q^{53} +(-150.000 - 86.6025i) q^{54} +(12.0000 - 20.7846i) q^{55} +(156.000 + 270.200i) q^{56} -228.631i q^{57} +(211.500 - 122.110i) q^{58} +(-246.000 + 142.028i) q^{59} -17.3205i q^{60} +(-72.5000 - 125.574i) q^{61} +(-135.000 + 233.827i) q^{62} +(-276.000 - 159.349i) q^{63} -307.000 q^{64} +(19.5000 - 78.8083i) q^{65} -48.0000 q^{66} +(-681.000 - 393.176i) q^{67} +(-292.500 + 506.625i) q^{68} +(78.0000 + 135.100i) q^{69} +41.5692i q^{70} +(915.000 - 528.275i) q^{71} +(448.500 - 258.942i) q^{72} +458.993i q^{73} +(-124.500 - 215.640i) q^{74} +(-122.000 + 211.310i) q^{75} +(495.000 + 285.788i) q^{76} -192.000 q^{77} +(-156.000 + 45.0333i) q^{78} +1276.00 q^{79} +(1.50000 + 0.866025i) q^{80} +(-210.500 + 364.597i) q^{81} +(235.500 + 407.898i) q^{82} -789.815i q^{83} +(-120.000 + 69.2820i) q^{84} +(-175.500 + 101.325i) q^{85} -180.133i q^{86} +(141.000 + 244.219i) q^{87} +(156.000 - 270.200i) q^{88} +(-846.000 - 488.438i) q^{89} +69.0000 q^{90} +(-624.000 + 180.133i) q^{91} -390.000 q^{92} +(-270.000 - 155.885i) q^{93} +(-261.000 + 452.065i) q^{94} +(99.0000 + 171.473i) q^{95} -363.731i q^{96} +(174.000 - 100.459i) q^{97} +(-226.500 + 130.770i) q^{98} +318.697i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} - 2 q^{3} - 5 q^{4} - 6 q^{6} - 24 q^{7} + 23 q^{9}+O(q^{10}) \) 2 * q + 3 * q^2 - 2 * q^3 - 5 * q^4 - 6 * q^6 - 24 * q^7 + 23 * q^9	\( 2 q + 3 q^{2} - 2 q^{3} - 5 q^{4} - 6 q^{6} - 24 q^{7} + 23 q^{9} + 3 q^{10} + 24 q^{11} + 20 q^{12} + 91 q^{13} - 48 q^{14} + 6 q^{15} - q^{16} - 117 q^{17} - 198 q^{19} - 15 q^{20} + 24 q^{22} + 78 q^{23} + 78 q^{24} + 244 q^{25} + 117 q^{26} - 200 q^{27} + 120 q^{28} + 141 q^{29} + 6 q^{30} - 315 q^{32} - 48 q^{33} + 24 q^{35} + 115 q^{36} - 249 q^{37} - 396 q^{38} - 130 q^{39} - 78 q^{40} + 471 q^{41} + 48 q^{42} - 104 q^{43} + 69 q^{45} + 234 q^{46} - 2 q^{48} - 151 q^{49} + 366 q^{50} + 468 q^{51} - 130 q^{52} + 186 q^{53} - 300 q^{54} + 24 q^{55} + 312 q^{56} + 423 q^{58} - 492 q^{59} - 145 q^{61} - 270 q^{62} - 552 q^{63} - 614 q^{64} + 39 q^{65} - 96 q^{66} - 1362 q^{67} - 585 q^{68} + 156 q^{69} + 1830 q^{71} + 897 q^{72} - 249 q^{74} - 244 q^{75} + 990 q^{76} - 384 q^{77} - 312 q^{78} + 2552 q^{79} + 3 q^{80} - 421 q^{81} + 471 q^{82} - 240 q^{84} - 351 q^{85} + 282 q^{87} + 312 q^{88} - 1692 q^{89} + 138 q^{90} - 1248 q^{91} - 780 q^{92} - 540 q^{93} - 522 q^{94} + 198 q^{95} + 348 q^{97} - 453 q^{98}+O(q^{100}) \) 2 * q + 3 * q^2 - 2 * q^3 - 5 * q^4 - 6 * q^6 - 24 * q^7 + 23 * q^9 + 3 * q^10 + 24 * q^11 + 20 * q^12 + 91 * q^13 - 48 * q^14 + 6 * q^15 - q^16 - 117 * q^17 - 198 * q^19 - 15 * q^20 + 24 * q^22 + 78 * q^23 + 78 * q^24 + 244 * q^25 + 117 * q^26 - 200 * q^27 + 120 * q^28 + 141 * q^29 + 6 * q^30 - 315 * q^32 - 48 * q^33 + 24 * q^35 + 115 * q^36 - 249 * q^37 - 396 * q^38 - 130 * q^39 - 78 * q^40 + 471 * q^41 + 48 * q^42 - 104 * q^43 + 69 * q^45 + 234 * q^46 - 2 * q^48 - 151 * q^49 + 366 * q^50 + 468 * q^51 - 130 * q^52 + 186 * q^53 - 300 * q^54 + 24 * q^55 + 312 * q^56 + 423 * q^58 - 492 * q^59 - 145 * q^61 - 270 * q^62 - 552 * q^63 - 614 * q^64 + 39 * q^65 - 96 * q^66 - 1362 * q^67 - 585 * q^68 + 156 * q^69 + 1830 * q^71 + 897 * q^72 - 249 * q^74 - 244 * q^75 + 990 * q^76 - 384 * q^77 - 312 * q^78 + 2552 * q^79 + 3 * q^80 - 421 * q^81 + 471 * q^82 - 240 * q^84 - 351 * q^85 + 282 * q^87 + 312 * q^88 - 1692 * q^89 + 138 * q^90 - 1248 * q^91 - 780 * q^92 - 540 * q^93 - 522 * q^94 + 198 * q^95 + 348 * q^97 - 453 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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