LMFDB - Embedded newform 21.4.e.a.16.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,4,Mod(4,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("21.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	21.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.23904011012$
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:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	21.16
Dual form			21.4.e.a.4.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 2.59808i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} -9.00000 q^{6} +(-3.50000 + 18.1865i) q^{7} +21.0000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(1.50000 - 2.59808i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} -9.00000 q^{6} +(-3.50000 + 18.1865i) q^{7} +21.0000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-4.50000 - 7.79423i) q^{10} +(7.50000 + 12.9904i) q^{11} +(-1.50000 + 2.59808i) q^{12} -64.0000 q^{13} +(42.0000 + 36.3731i) q^{14} -9.00000 q^{15} +(35.5000 - 61.4878i) q^{16} +(-42.0000 - 72.7461i) q^{17} +(13.5000 + 23.3827i) q^{18} +(8.00000 - 13.8564i) q^{19} -3.00000 q^{20} +(52.5000 - 18.1865i) q^{21} +45.0000 q^{22} +(42.0000 - 72.7461i) q^{23} +(-31.5000 - 54.5596i) q^{24} +(58.0000 + 100.459i) q^{25} +(-96.0000 + 166.277i) q^{26} +27.0000 q^{27} +(17.5000 - 6.06218i) q^{28} -297.000 q^{29} +(-13.5000 + 23.3827i) q^{30} +(126.500 + 219.104i) q^{31} +(-22.5000 - 38.9711i) q^{32} +(22.5000 - 38.9711i) q^{33} -252.000 q^{34} +(42.0000 + 36.3731i) q^{35} +9.00000 q^{36} +(158.000 - 273.664i) q^{37} +(-24.0000 - 41.5692i) q^{38} +(96.0000 + 166.277i) q^{39} +(31.5000 - 54.5596i) q^{40} +360.000 q^{41} +(31.5000 - 163.679i) q^{42} +26.0000 q^{43} +(7.50000 - 12.9904i) q^{44} +(13.5000 + 23.3827i) q^{45} +(-126.000 - 218.238i) q^{46} +(15.0000 - 25.9808i) q^{47} -213.000 q^{48} +(-318.500 - 127.306i) q^{49} +348.000 q^{50} +(-126.000 + 218.238i) q^{51} +(32.0000 + 55.4256i) q^{52} +(-181.500 - 314.367i) q^{53} +(40.5000 - 70.1481i) q^{54} +45.0000 q^{55} +(-73.5000 + 381.917i) q^{56} -48.0000 q^{57} +(-445.500 + 771.629i) q^{58} +(7.50000 + 12.9904i) q^{59} +(4.50000 + 7.79423i) q^{60} +(59.0000 - 102.191i) q^{61} +759.000 q^{62} +(-126.000 - 109.119i) q^{63} +433.000 q^{64} +(-96.0000 + 166.277i) q^{65} +(-67.5000 - 116.913i) q^{66} +(185.000 + 320.429i) q^{67} +(-42.0000 + 72.7461i) q^{68} -252.000 q^{69} +(157.500 - 54.5596i) q^{70} -342.000 q^{71} +(-94.5000 + 163.679i) q^{72} +(-181.000 - 313.501i) q^{73} +(-474.000 - 820.992i) q^{74} +(174.000 - 301.377i) q^{75} -16.0000 q^{76} +(-262.500 + 90.9327i) q^{77} +576.000 q^{78} +(-233.500 + 404.434i) q^{79} +(-106.500 - 184.463i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(540.000 - 935.307i) q^{82} +477.000 q^{83} +(-42.0000 - 36.3731i) q^{84} -252.000 q^{85} +(39.0000 - 67.5500i) q^{86} +(445.500 + 771.629i) q^{87} +(157.500 + 272.798i) q^{88} +(-453.000 + 784.619i) q^{89} +81.0000 q^{90} +(224.000 - 1163.94i) q^{91} -84.0000 q^{92} +(379.500 - 657.313i) q^{93} +(-45.0000 - 77.9423i) q^{94} +(-24.0000 - 41.5692i) q^{95} +(-67.5000 + 116.913i) q^{96} +503.000 q^{97} +(-808.500 + 636.529i) q^{98} -135.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{2} - 3 q^{3} - q^{4} + 3 q^{5} - 18 q^{6} - 7 q^{7} + 42 q^{8} - 9 q^{9}+O(q^{10}) $ 2 * q + 3 * q^2 - 3 * q^3 - q^4 + 3 * q^5 - 18 * q^6 - 7 * q^7 + 42 * q^8 - 9 * q^9	\( 2 q + 3 q^{2} - 3 q^{3} - q^{4} + 3 q^{5} - 18 q^{6} - 7 q^{7} + 42 q^{8} - 9 q^{9} - 9 q^{10} + 15 q^{11} - 3 q^{12} - 128 q^{13} + 84 q^{14} - 18 q^{15} + 71 q^{16} - 84 q^{17} + 27 q^{18} + 16 q^{19} - 6 q^{20} + 105 q^{21} + 90 q^{22} + 84 q^{23} - 63 q^{24} + 116 q^{25} - 192 q^{26} + 54 q^{27} + 35 q^{28} - 594 q^{29} - 27 q^{30} + 253 q^{31} - 45 q^{32} + 45 q^{33} - 504 q^{34} + 84 q^{35} + 18 q^{36} + 316 q^{37} - 48 q^{38} + 192 q^{39} + 63 q^{40} + 720 q^{41} + 63 q^{42} + 52 q^{43} + 15 q^{44} + 27 q^{45} - 252 q^{46} + 30 q^{47} - 426 q^{48} - 637 q^{49} + 696 q^{50} - 252 q^{51} + 64 q^{52} - 363 q^{53} + 81 q^{54} + 90 q^{55} - 147 q^{56} - 96 q^{57} - 891 q^{58} + 15 q^{59} + 9 q^{60} + 118 q^{61} + 1518 q^{62} - 252 q^{63} + 866 q^{64} - 192 q^{65} - 135 q^{66} + 370 q^{67} - 84 q^{68} - 504 q^{69} + 315 q^{70} - 684 q^{71} - 189 q^{72} - 362 q^{73} - 948 q^{74} + 348 q^{75} - 32 q^{76} - 525 q^{77} + 1152 q^{78} - 467 q^{79} - 213 q^{80} - 81 q^{81} + 1080 q^{82} + 954 q^{83} - 84 q^{84} - 504 q^{85} + 78 q^{86} + 891 q^{87} + 315 q^{88} - 906 q^{89} + 162 q^{90} + 448 q^{91} - 168 q^{92} + 759 q^{93} - 90 q^{94} - 48 q^{95} - 135 q^{96} + 1006 q^{97} - 1617 q^{98} - 270 q^{99}+O(q^{100}) \) 2 * q + 3 * q^2 - 3 * q^3 - q^4 + 3 * q^5 - 18 * q^6 - 7 * q^7 + 42 * q^8 - 9 * q^9 - 9 * q^10 + 15 * q^11 - 3 * q^12 - 128 * q^13 + 84 * q^14 - 18 * q^15 + 71 * q^16 - 84 * q^17 + 27 * q^18 + 16 * q^19 - 6 * q^20 + 105 * q^21 + 90 * q^22 + 84 * q^23 - 63 * q^24 + 116 * q^25 - 192 * q^26 + 54 * q^27 + 35 * q^28 - 594 * q^29 - 27 * q^30 + 253 * q^31 - 45 * q^32 + 45 * q^33 - 504 * q^34 + 84 * q^35 + 18 * q^36 + 316 * q^37 - 48 * q^38 + 192 * q^39 + 63 * q^40 + 720 * q^41 + 63 * q^42 + 52 * q^43 + 15 * q^44 + 27 * q^45 - 252 * q^46 + 30 * q^47 - 426 * q^48 - 637 * q^49 + 696 * q^50 - 252 * q^51 + 64 * q^52 - 363 * q^53 + 81 * q^54 + 90 * q^55 - 147 * q^56 - 96 * q^57 - 891 * q^58 + 15 * q^59 + 9 * q^60 + 118 * q^61 + 1518 * q^62 - 252 * q^63 + 866 * q^64 - 192 * q^65 - 135 * q^66 + 370 * q^67 - 84 * q^68 - 504 * q^69 + 315 * q^70 - 684 * q^71 - 189 * q^72 - 362 * q^73 - 948 * q^74 + 348 * q^75 - 32 * q^76 - 525 * q^77 + 1152 * q^78 - 467 * q^79 - 213 * q^80 - 81 * q^81 + 1080 * q^82 + 954 * q^83 - 84 * q^84 - 504 * q^85 + 78 * q^86 + 891 * q^87 + 315 * q^88 - 906 * q^89 + 162 * q^90 + 448 * q^91 - 168 * q^92 + 759 * q^93 - 90 * q^94 - 48 * q^95 - 135 * q^96 + 1006 * q^97 - 1617 * q^98 - 270 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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	−	2.59808i	0.530330	−	0.918559i	−0.469044	−	0.883175i	$-0.655401\pi$
$2$	1.50000	−	2.59808i	0.530330	−	0.918559i	0.999374	−	0.0353837i	$-0.0112653\pi$
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$4$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$5$	1.50000	−	2.59808i	0.134164	−	0.232379i	−0.791114	−	0.611669i	$-0.790498\pi$
$5$	1.50000	−	2.59808i	0.134164	−	0.232379i	0.925278	+	0.379290i	$0.123832\pi$
$6$	−9.00000			−0.612372
$7$	−3.50000	+	18.1865i	−0.188982	+	0.981981i
$7$	−3.50000	+	18.1865i	−0.188982	+	0.981981i
$8$	21.0000			0.928078
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	−4.50000	−	7.79423i	−0.142302	−	0.246475i
$11$	7.50000	+	12.9904i	0.205576	+	0.356068i	0.950316	−	0.311287i	$-0.100760\pi$
$11$	7.50000	+	12.9904i	0.205576	+	0.356068i	−0.744740	+	0.667355i	$0.767427\pi$
$12$	−1.50000	+	2.59808i	−0.0360844	+	0.0625000i
$13$	−64.0000			−1.36542			−0.682708	−	0.730691i	$-0.739198\pi$
$13$	−64.0000			−1.36542			−0.682708	+	0.730691i	$0.739198\pi$
$14$	42.0000	+	36.3731i	0.801784	+	0.694365i
$15$	−9.00000			−0.154919
$16$	35.5000	−	61.4878i	0.554688	−	0.960747i
$17$	−42.0000	−	72.7461i	−0.599206	−	1.03785i	−0.992939	−	0.118630i	$-0.962150\pi$
$17$	−42.0000	−	72.7461i	−0.599206	−	1.03785i	0.393733	−	0.919225i	$-0.371183\pi$
$18$	13.5000	+	23.3827i	0.176777	+	0.306186i
$19$	8.00000	−	13.8564i	0.0965961	−	0.167309i	−0.813678	−	0.581317i	$-0.802538\pi$
$19$	8.00000	−	13.8564i	0.0965961	−	0.167309i	0.910274	+	0.414007i	$0.135871\pi$
$20$	−3.00000			−0.0335410
$21$	52.5000	−	18.1865i	0.545545	−	0.188982i
$22$	45.0000			0.436092
$23$	42.0000	−	72.7461i	0.380765	−	0.659505i	−0.610406	−	0.792088i	$-0.708994\pi$
$23$	42.0000	−	72.7461i	0.380765	−	0.659505i	0.991172	+	0.132583i	$0.0423272\pi$
$24$	−31.5000	−	54.5596i	−0.267913	−	0.464039i
$25$	58.0000	+	100.459i	0.464000	+	0.803672i
$26$	−96.0000	+	166.277i	−0.724121	+	1.25421i
$27$	27.0000			0.192450
$28$	17.5000	−	6.06218i	0.118114	−	0.0409159i
$29$	−297.000			−1.90178			−0.950888	−	0.309535i	$-0.899827\pi$
$29$	−297.000			−1.90178			−0.950888	+	0.309535i	$0.899827\pi$
$30$	−13.5000	+	23.3827i	−0.0821584	+	0.142302i
$31$	126.500	+	219.104i	0.732906	+	1.26943i	0.955636	+	0.294550i	$0.0951696\pi$
$31$	126.500	+	219.104i	0.732906	+	1.26943i	−0.222731	+	0.974880i	$0.571497\pi$
$32$	−22.5000	−	38.9711i	−0.124296	−	0.215287i
$33$	22.5000	−	38.9711i	0.118689	−	0.205576i
$34$	−252.000			−1.27111
$35$	42.0000	+	36.3731i	0.202837	+	0.175662i
$36$	9.00000			0.0416667
$37$	158.000	−	273.664i	0.702028	−	1.21595i	−0.265725	−	0.964049i	$-0.585611\pi$
$37$	158.000	−	273.664i	0.702028	−	1.21595i	0.967753	−	0.251900i	$-0.0810553\pi$
$38$	−24.0000	−	41.5692i	−0.102456	−	0.177458i
$39$	96.0000	+	166.277i	0.394162	+	0.682708i
$40$	31.5000	−	54.5596i	0.124515	−	0.215666i
$41$	360.000			1.37128			0.685641	−	0.727940i	$-0.259522\pi$
$41$	360.000			1.37128			0.685641	+	0.727940i	$0.259522\pi$
$42$	31.5000	−	163.679i	0.115728	−	0.601338i
$43$	26.0000			0.0922084			0.0461042	−	0.998937i	$-0.485319\pi$
$43$	26.0000			0.0922084			0.0461042	+	0.998937i	$0.485319\pi$
$44$	7.50000	−	12.9904i	0.0256970	−	0.0445085i
$45$	13.5000	+	23.3827i	0.0447214	+	0.0774597i
$46$	−126.000	−	218.238i	−0.403863	−	0.699511i
$47$	15.0000	−	25.9808i	0.0465527	−	0.0806316i	−0.841810	−	0.539774i	$-0.818510\pi$
$47$	15.0000	−	25.9808i	0.0465527	−	0.0806316i	0.888363	+	0.459142i	$0.151843\pi$
$48$	−213.000			−0.640498
$49$	−318.500	−	127.306i	−0.928571	−	0.371154i
$50$	348.000			0.984293
$51$	−126.000	+	218.238i	−0.345952	+	0.599206i
$52$	32.0000	+	55.4256i	0.0853385	+	0.147811i
$53$	−181.500	−	314.367i	−0.470395	−	0.814748i	0.529032	−	0.848602i	$-0.322555\pi$
$53$	−181.500	−	314.367i	−0.470395	−	0.814748i	−0.999427	+	0.0338538i	$0.989222\pi$
$54$	40.5000	−	70.1481i	0.102062	−	0.176777i
$55$	45.0000			0.110324
$56$	−73.5000	+	381.917i	−0.175390	+	0.911354i
$57$	−48.0000			−0.111540
$58$	−445.500	+	771.629i	−1.00857	+	1.74689i
$59$	7.50000	+	12.9904i	0.0165494	+	0.0286645i	0.874182	−	0.485599i	$-0.161399\pi$
$59$	7.50000	+	12.9904i	0.0165494	+	0.0286645i	−0.857632	+	0.514264i	$0.828065\pi$
$60$	4.50000	+	7.79423i	0.00968246	+	0.0167705i
$61$	59.0000	−	102.191i	0.123839	−	0.214495i	−0.797440	−	0.603399i	$-0.793813\pi$
$61$	59.0000	−	102.191i	0.123839	−	0.214495i	0.921279	+	0.388903i	$0.127146\pi$
$62$	759.000			1.55473
$63$	−126.000	−	109.119i	−0.251976	−	0.218218i
$64$	433.000			0.845703
$65$	−96.0000	+	166.277i	−0.183190	+	0.317294i
$66$	−67.5000	−	116.913i	−0.125889	−	0.218046i
$67$	185.000	+	320.429i	0.337334	+	0.584279i	0.983930	−	0.178553i	$-0.0571417\pi$
$67$	185.000	+	320.429i	0.337334	+	0.584279i	−0.646597	+	0.762832i	$0.723808\pi$
$68$	−42.0000	+	72.7461i	−0.0749007	+	0.129732i
$69$	−252.000			−0.439670
$70$	157.500	−	54.5596i	0.268926	−	0.0931589i
$71$	−342.000			−0.571661			−0.285831	−	0.958280i	$-0.592269\pi$
$71$	−342.000			−0.571661			−0.285831	+	0.958280i	$0.592269\pi$
$72$	−94.5000	+	163.679i	−0.154680	+	0.267913i
$73$	−181.000	−	313.501i	−0.290198	−	0.502638i	0.683658	−	0.729802i	$-0.260388\pi$
$73$	−181.000	−	313.501i	−0.290198	−	0.502638i	−0.973856	+	0.227165i	$0.927054\pi$
$74$	−474.000	−	820.992i	−0.744613	−	1.28971i
$75$	174.000	−	301.377i	0.267891	−	0.464000i
$76$	−16.0000			−0.0241490
$77$	−262.500	+	90.9327i	−0.388502	+	0.134581i
$78$	576.000			0.836143
$79$	−233.500	+	404.434i	−0.332542	+	0.575979i	−0.983010	−	0.183555i	$-0.941240\pi$
$79$	−233.500	+	404.434i	−0.332542	+	0.575979i	0.650468	+	0.759534i	$0.274573\pi$
$80$	−106.500	−	184.463i	−0.148838	−	0.257795i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	540.000	−	935.307i	0.727232	−	1.25960i
$83$	477.000			0.630814			0.315407	−	0.948957i	$-0.397859\pi$
$83$	477.000			0.630814			0.315407	+	0.948957i	$0.397859\pi$
$84$	−42.0000	−	36.3731i	−0.0545545	−	0.0472456i
$85$	−252.000			−0.321568
$86$	39.0000	−	67.5500i	0.0489009	−	0.0846989i
$87$	445.500	+	771.629i	0.548996	+	0.950888i
$88$	157.500	+	272.798i	0.190790	+	0.330459i
$89$	−453.000	+	784.619i	−0.539527	+	0.934488i	0.459402	+	0.888228i	$0.348064\pi$
$89$	−453.000	+	784.619i	−0.539527	+	0.934488i	−0.998929	+	0.0462600i	$0.985270\pi$
$90$	81.0000			0.0948683
$91$	224.000	−	1163.94i	0.258039	−	1.34081i
$92$	−84.0000			−0.0951914
$93$	379.500	−	657.313i	0.423143	−	0.732906i
$94$	−45.0000	−	77.9423i	−0.0493765	−	0.0855227i
$95$	−24.0000	−	41.5692i	−0.0259195	−	0.0448938i
$96$	−67.5000	+	116.913i	−0.0717624	+	0.124296i
$97$	503.000			0.526515			0.263257	−	0.964726i	$-0.415203\pi$
$97$	503.000			0.526515			0.263257	+	0.964726i	$0.415203\pi$
$98$	−808.500	+	636.529i	−0.833376	+	0.656113i
$99$	−135.000			−0.137051
$100$	58.0000	−	100.459i	0.0580000	−	0.100459i
$101$	543.000	+	940.504i	0.534956	+	0.926570i	0.999165	+	0.0408451i	$0.0130050\pi$
$101$	543.000	+	940.504i	0.534956	+	0.926570i	−0.464210	+	0.885725i	$0.653662\pi$
$102$	378.000	+	654.715i	0.366937	+	0.635554i
$103$	−868.000	+	1503.42i	−0.830355	+	1.43822i	0.0674017	+	0.997726i	$0.478529\pi$
$103$	−868.000	+	1503.42i	−0.830355	+	1.43822i	−0.897757	+	0.440491i	$0.854804\pi$
$104$	−1344.00			−1.26721
$105$	31.5000	−	163.679i	0.0292770	−	0.152128i
$106$	−1089.00			−0.997859
$107$	676.500	−	1171.73i	0.611212	−	1.05865i	−0.379824	−	0.925059i	$-0.624015\pi$
$107$	676.500	−	1171.73i	0.611212	−	1.05865i	0.991036	−	0.133592i	$-0.0426512\pi$
$108$	−13.5000	−	23.3827i	−0.0120281	−	0.0208333i
$109$	185.000	+	320.429i	0.162567	+	0.281574i	0.935789	−	0.352562i	$-0.114689\pi$
$109$	185.000	+	320.429i	0.162567	+	0.281574i	−0.773222	+	0.634136i	$0.781356\pi$
$110$	67.5000	−	116.913i	0.0585079	−	0.101339i
$111$	−948.000			−0.810632
$112$	994.000	+	860.829i	0.838609	+	0.726256i
$113$	−648.000			−0.539458			−0.269729	−	0.962936i	$-0.586934\pi$
$113$	−648.000			−0.539458			−0.269729	+	0.962936i	$0.586934\pi$
$114$	−72.0000	+	124.708i	−0.0591528	+	0.102456i
$115$	−126.000	−	218.238i	−0.102170	−	0.176964i
$116$	148.500	+	257.210i	0.118861	+	0.205873i
$117$	288.000	−	498.831i	0.227569	−	0.394162i
$118$	45.0000			0.0351067
$119$	1470.00	−	509.223i	1.13239	−	0.392272i
$120$	−189.000			−0.143777
$121$	553.000	−	957.824i	0.415477	−	0.719627i
$122$	−177.000	−	306.573i	−0.131351	−	0.227507i
$123$	−540.000	−	935.307i	−0.395855	−	0.685641i
$124$	126.500	−	219.104i	0.0916132	−	0.158679i
$125$	723.000			0.517337
$126$	−472.500	+	163.679i	−0.334077	+	0.115728i
$127$	377.000			0.263412			0.131706	−	0.991289i	$-0.457954\pi$
$127$	377.000			0.263412			0.131706	+	0.991289i	$0.457954\pi$
$128$	829.500	−	1436.74i	0.572798	−	0.992115i
$129$	−39.0000	−	67.5500i	−0.0266183	−	0.0461042i
$130$	288.000	+	498.831i	0.194302	+	0.336541i
$131$	325.500	−	563.783i	0.217092	−	0.376015i	−0.736826	−	0.676083i	$-0.763676\pi$
$131$	325.500	−	563.783i	0.217092	−	0.376015i	0.953918	+	0.300068i	$0.0970095\pi$
$132$	−45.0000			−0.0296723
$133$	224.000	+	193.990i	0.146040	+	0.126474i
$134$	1110.00			0.715593
$135$	40.5000	−	70.1481i	0.0258199	−	0.0447214i
$136$	−882.000	−	1527.67i	−0.556109	−	0.963210i
$137$	885.000	+	1532.86i	0.551903	+	0.955923i	0.998137	+	0.0610074i	$0.0194313\pi$
$137$	885.000	+	1532.86i	0.551903	+	0.955923i	−0.446235	+	0.894916i	$0.647235\pi$
$138$	−378.000	+	654.715i	−0.233170	+	0.403863i
$139$	−1558.00			−0.950704			−0.475352	−	0.879796i	$-0.657679\pi$
$139$	−1558.00			−0.950704			−0.475352	+	0.879796i	$0.657679\pi$
$140$	10.5000	−	54.5596i	0.00633866	−	0.0329366i
$141$	−90.0000			−0.0537544
$142$	−513.000	+	888.542i	−0.303169	+	0.525104i
$143$	−480.000	−	831.384i	−0.280697	−	0.486181i
$144$	319.500	+	553.390i	0.184896	+	0.320249i
$145$	−445.500	+	771.629i	−0.255150	+	0.441933i
$146$	−1086.00			−0.615603
$147$	147.000	+	1018.45i	0.0824786	+	0.571429i
$148$	−316.000			−0.175507
$149$	−1227.00	+	2125.23i	−0.674629	+	1.16849i	0.301948	+	0.953324i	$0.402363\pi$
$149$	−1227.00	+	2125.23i	−0.674629	+	1.16849i	−0.976577	+	0.215168i	$0.930970\pi$
$150$	−522.000	−	904.131i	−0.284141	−	0.492146i
$151$	−629.500	−	1090.33i	−0.339258	−	0.587612i	0.645035	−	0.764153i	$-0.276843\pi$
$151$	−629.500	−	1090.33i	−0.339258	−	0.587612i	−0.984293	+	0.176540i	$0.943509\pi$
$152$	168.000	−	290.985i	0.0896487	−	0.155276i
$153$	756.000			0.399470
$154$	−157.500	+	818.394i	−0.0824137	+	0.428234i
$155$	759.000			0.393318
$156$	96.0000	−	166.277i	0.0492702	−	0.0853385i
$157$	98.0000	+	169.741i	0.0498169	+	0.0862854i	0.889859	−	0.456236i	$-0.150803\pi$
$157$	98.0000	+	169.741i	0.0498169	+	0.0862854i	−0.840042	+	0.542522i	$0.817470\pi$
$158$	700.500	+	1213.30i	0.352714	+	0.610918i
$159$	−544.500	+	943.102i	−0.271583	+	0.470395i
$160$	−135.000			−0.0667043
$161$	1176.00	+	1018.45i	0.575663	+	0.498539i
$162$	−243.000			−0.117851
$163$	626.000	−	1084.26i	0.300810	−	0.521019i	−0.675509	−	0.737351i	$-0.736076\pi$
$163$	626.000	−	1084.26i	0.300810	−	0.521019i	0.976320	+	0.216332i	$0.0694095\pi$
$164$	−180.000	−	311.769i	−0.0857051	−	0.148446i
$165$	−67.5000	−	116.913i	−0.0318477	−	0.0551618i
$166$	715.500	−	1239.28i	0.334540	−	0.579440i
$167$	−2646.00			−1.22607			−0.613035	−	0.790056i	$-0.710051\pi$
$167$	−2646.00			−1.22607			−0.613035	+	0.790056i	$0.710051\pi$
$168$	1102.50	−	381.917i	0.506308	−	0.175390i
$169$	1899.00			0.864360
$170$	−378.000	+	654.715i	−0.170537	+	0.295379i
$171$	72.0000	+	124.708i	0.0321987	+	0.0557698i
$172$	−13.0000	−	22.5167i	−0.00576303	−	0.00998186i
$173$	393.000	−	680.696i	0.172712	−	0.299147i	−0.766655	−	0.642059i	$-0.778080\pi$
$173$	393.000	−	680.696i	0.172712	−	0.299147i	0.939367	+	0.342913i	$0.111414\pi$
$174$	2673.00			1.16460
$175$	−2030.00	+	703.213i	−0.876878	+	0.303759i
$176$	1065.00			0.456122
$177$	22.5000	−	38.9711i	0.00955482	−	0.0165494i
$178$	1359.00	+	2353.86i	0.572255	+	0.991174i
$179$	−1446.00	−	2504.55i	−0.603794	−	1.04580i	−0.992241	−	0.124331i	$-0.960322\pi$
$179$	−1446.00	−	2504.55i	−0.603794	−	1.04580i	0.388447	−	0.921471i	$-0.373012\pi$
$180$	13.5000	−	23.3827i	0.00559017	−	0.00968246i
$181$	1352.00			0.555212			0.277606	−	0.960695i	$-0.410459\pi$
$181$	1352.00			0.555212			0.277606	+	0.960695i	$0.410459\pi$
$182$	−2688.00	−	2327.88i	−1.09477	−	0.948097i
$183$	−354.000			−0.142997
$184$	882.000	−	1527.67i	0.353380	−	0.612072i
$185$	−474.000	−	820.992i	−0.188374	−	0.326273i
$186$	−1138.50	−	1971.94i	−0.448811	−	0.777364i
$187$	630.000	−	1091.19i	0.246365	−	0.426716i
$188$	−30.0000			−0.0116382
$189$	−94.5000	+	491.036i	−0.0363696	+	0.188982i
$190$	−144.000			−0.0549835
$191$	−1956.00	+	3387.89i	−0.741001	+	1.28345i	0.211039	+	0.977478i	$0.432315\pi$
$191$	−1956.00	+	3387.89i	−0.741001	+	1.28345i	−0.952040	+	0.305974i	$0.901018\pi$
$192$	−649.500	−	1124.97i	−0.244133	−	0.422852i
$193$	−746.500	−	1292.98i	−0.278416	−	0.482230i	0.692575	−	0.721345i	$-0.256476\pi$
$193$	−746.500	−	1292.98i	−0.278416	−	0.482230i	−0.970991	+	0.239115i	$0.923143\pi$
$194$	754.500	−	1306.83i	0.279227	−	0.483635i
$195$	576.000			0.211529
$196$	49.0000	+	339.482i	0.0178571	+	0.123718i
$197$	−4086.00			−1.47774			−0.738872	−	0.673846i	$-0.764641\pi$
$197$	−4086.00			−1.47774			−0.738872	+	0.673846i	$0.764641\pi$
$198$	−202.500	+	350.740i	−0.0726821	+	0.125889i
$199$	1778.00	+	3079.59i	0.633362	+	1.09702i	0.986860	+	0.161580i	$0.0516590\pi$
$199$	1778.00	+	3079.59i	0.633362	+	1.09702i	−0.353497	+	0.935436i	$0.615008\pi$
$200$	1218.00	+	2109.64i	0.430628	+	0.745870i
$201$	555.000	−	961.288i	0.194760	−	0.337334i
$202$	3258.00			1.13481
$203$	1039.50	−	5401.40i	0.359402	−	1.86751i
$204$	252.000			0.0864879
$205$	540.000	−	935.307i	0.183977	−	0.318657i
$206$	2604.00	+	4510.26i	0.880725	+	1.52546i
$207$	378.000	+	654.715i	0.126922	+	0.219835i
$208$	−2272.00	+	3935.22i	−0.757379	+	1.31182i
$209$	240.000			0.0794313
$210$	−378.000	−	327.358i	−0.124212	−	0.107571i
$211$	1250.00			0.407837			0.203918	−	0.978988i	$-0.434632\pi$
$211$	1250.00			0.407837			0.203918	+	0.978988i	$0.434632\pi$
$212$	−181.500	+	314.367i	−0.0587994	+	0.101844i
$213$	513.000	+	888.542i	0.165024	+	0.285831i
$214$	−2029.50	−	3515.20i	−0.648289	−	1.12287i
$215$	39.0000	−	67.5500i	0.0123711	−	0.0214273i
$216$	567.000			0.178609
$217$	−4427.50	+	1533.73i	−1.38506	+	0.479799i
$218$	1110.00			0.344856
$219$	−543.000	+	940.504i	−0.167546	+	0.290198i
$220$	−22.5000	−	38.9711i	−0.00689523	−	0.0119429i
$221$	2688.00	+	4655.75i	0.818165	+	1.41710i
$222$	−1422.00	+	2462.98i	−0.429903	+	0.744613i
$223$	425.000			0.127624			0.0638119	−	0.997962i	$-0.479674\pi$
$223$	425.000			0.127624			0.0638119	+	0.997962i	$0.479674\pi$
$224$	787.500	−	272.798i	0.234898	−	0.0813709i
$225$	−1044.00			−0.309333
$226$	−972.000	+	1683.55i	−0.286091	+	0.495523i
$227$	−1927.50	−	3338.53i	−0.563580	−	0.976149i	−0.997180	−	0.0750439i	$-0.976090\pi$
$227$	−1927.50	−	3338.53i	−0.563580	−	0.976149i	0.433600	−	0.901105i	$-0.357243\pi$
$228$	24.0000	+	41.5692i	0.00697122	+	0.0120745i
$229$	1094.00	−	1894.86i	0.315692	−	0.546795i	−0.663892	−	0.747828i	$-0.731097\pi$
$229$	1094.00	−	1894.86i	0.315692	−	0.546795i	0.979584	+	0.201033i	$0.0644299\pi$
$230$	−756.000			−0.216735
$231$	630.000	+	545.596i	0.179441	+	0.155401i
$232$	−6237.00			−1.76500
$233$	−426.000	+	737.854i	−0.119778	+	0.207461i	−0.919679	−	0.392670i	$-0.871551\pi$
$233$	−426.000	+	737.854i	−0.119778	+	0.207461i	0.799902	+	0.600131i	$0.204885\pi$
$234$	−864.000	−	1496.49i	−0.241374	−	0.418072i
$235$	−45.0000	−	77.9423i	−0.0124914	−	0.0216357i
$236$	7.50000	−	12.9904i	0.00206868	−	0.00358306i
$237$	1401.00			0.383986
$238$	882.000	−	4583.01i	0.240217	−	1.24820i
$239$	5508.00			1.49072			0.745362	−	0.666660i	$-0.232277\pi$
$239$	5508.00			1.49072			0.745362	+	0.666660i	$0.232277\pi$
$240$	−319.500	+	553.390i	−0.0859318	+	0.148838i
$241$	−395.500	−	685.026i	−0.105711	−	0.183097i	0.808317	−	0.588747i	$-0.200379\pi$
$241$	−395.500	−	685.026i	−0.105711	−	0.183097i	−0.914029	+	0.405650i	$0.867045\pi$
$242$	−1659.00	−	2873.47i	−0.440680	−	0.763280i
$243$	−121.500	+	210.444i	−0.0320750	+	0.0555556i
$244$	−118.000			−0.0309597
$245$	−808.500	+	636.529i	−0.210829	+	0.165985i
$246$	−3240.00			−0.839735
$247$	−512.000	+	886.810i	−0.131894	+	0.228447i
$248$	2656.50	+	4601.19i	0.680193	+	1.17813i
$249$	−715.500	−	1239.28i	−0.182100	−	0.315407i
$250$	1084.50	−	1878.41i	0.274359	−	0.475204i
$251$	5265.00			1.32400			0.662000	−	0.749504i	$-0.269708\pi$
$251$	5265.00			1.32400			0.662000	+	0.749504i	$0.269708\pi$
$252$	−31.5000	+	163.679i	−0.00787426	+	0.0409159i
$253$	1260.00			0.313105
$254$	565.500	−	979.475i	0.139695	−	0.241959i
$255$	378.000	+	654.715i	0.0928285	+	0.160784i
$256$	−756.500	−	1310.30i	−0.184692	−	0.319897i
$257$	3435.00	−	5949.59i	0.833733	−	1.44407i	−0.0613246	−	0.998118i	$-0.519532\pi$
$257$	3435.00	−	5949.59i	0.833733	−	1.44407i	0.895058	−	0.445950i	$-0.147134\pi$
$258$	−234.000			−0.0564659
$259$	4424.00	+	3831.30i	1.06137	+	0.919171i
$260$	192.000			0.0457974
$261$	1336.50	−	2314.89i	0.316963	−	0.548996i
$262$	−976.500	−	1691.35i	−0.230261	−	0.398824i
$263$	111.000	+	192.258i	0.0260249	+	0.0450765i	0.878745	−	0.477292i	$-0.158382\pi$
$263$	111.000	+	192.258i	0.0260249	+	0.0450765i	−0.852720	+	0.522369i	$0.825048\pi$
$264$	472.500	−	818.394i	0.110153	−	0.190790i
$265$	−1089.00			−0.252441
$266$	840.000	−	290.985i	0.193623	−	0.0670730i
$267$	2718.00			0.622992
$268$	185.000	−	320.429i	0.0421667	−	0.0730349i
$269$	−3925.50	−	6799.17i	−0.889747	−	1.54109i	−0.840174	−	0.542317i	$-0.817547\pi$
$269$	−3925.50	−	6799.17i	−0.889747	−	1.54109i	−0.0495729	−	0.998771i	$-0.515786\pi$
$270$	−121.500	−	210.444i	−0.0273861	−	0.0474342i
$271$	−2591.50	+	4488.61i	−0.580895	+	1.00614i	0.414479	+	0.910059i	$0.363964\pi$
$271$	−2591.50	+	4488.61i	−0.580895	+	1.00614i	−0.995374	+	0.0960800i	$0.969370\pi$
$272$	−5964.00			−1.32949
$273$	−3360.00	+	1163.94i	−0.744895	+	0.258039i
$274$	5310.00			1.17076
$275$	−870.000	+	1506.88i	−0.190774	+	0.330431i
$276$	126.000	+	218.238i	0.0274794	+	0.0475957i
$277$	2480.00	+	4295.49i	0.537938	+	0.931736i	0.999015	+	0.0443755i	$0.0141298\pi$
$277$	2480.00	+	4295.49i	0.537938	+	0.931736i	−0.461077	+	0.887360i	$0.652537\pi$
$278$	−2337.00	+	4047.80i	−0.504187	+	0.873277i
$279$	−2277.00			−0.488604
$280$	882.000	+	763.834i	0.188249	+	0.163028i
$281$	−774.000			−0.164317			−0.0821583	−	0.996619i	$-0.526181\pi$
$281$	−774.000			−0.164317			−0.0821583	+	0.996619i	$0.526181\pi$
$282$	−135.000	+	233.827i	−0.0285076	+	0.0493765i
$283$	−1849.00	−	3202.56i	−0.388380	−	0.672695i	0.603852	−	0.797097i	$-0.293632\pi$
$283$	−1849.00	−	3202.56i	−0.388380	−	0.672695i	−0.992232	+	0.124402i	$0.960299\pi$
$284$	171.000	+	296.181i	0.0357288	+	0.0618841i
$285$	−72.0000	+	124.708i	−0.0149646	+	0.0259195i
$286$	−2880.00			−0.595447
$287$	−1260.00	+	6547.15i	−0.259148	+	1.34657i
$288$	405.000			0.0828641
$289$	−1071.50	+	1855.89i	−0.218095	+	0.377751i
$290$	1336.50	+	2314.89i	0.270628	+	0.468741i
$291$	−754.500	−	1306.83i	−0.151992	−	0.263257i
$292$	−181.000	+	313.501i	−0.0362747	+	0.0628297i
$293$	−6273.00			−1.25076			−0.625380	−	0.780321i	$-0.715056\pi$
$293$	−6273.00			−1.25076			−0.625380	+	0.780321i	$0.715056\pi$
$294$	2866.50	+	1145.75i	0.568632	+	0.227284i
$295$	45.0000			0.00888136
$296$	3318.00	−	5746.94i	0.651537	−	1.12849i
$297$	202.500	+	350.740i	0.0395631	+	0.0685253i
$298$	3681.00	+	6375.68i	0.715552	+	1.23937i
$299$	−2688.00	+	4655.75i	−0.519903	+	0.900499i
$300$	−348.000			−0.0669726
$301$	−91.0000	+	472.850i	−0.0174258	+	0.0905469i
$302$	−3777.00			−0.719675
$303$	1629.00	−	2821.51i	0.308857	−	0.534956i
$304$	−568.000	−	983.805i	−0.107161	−	0.185609i
$305$	−177.000	−	306.573i	−0.0332295	−	0.0575551i
$306$	1134.00	−	1964.15i	0.211851	−	0.366937i
$307$	−1684.00			−0.313065			−0.156533	−	0.987673i	$-0.550032\pi$
$307$	−1684.00			−0.313065			−0.156533	+	0.987673i	$0.550032\pi$
$308$	210.000	+	181.865i	0.0388502	+	0.0336453i
$309$	5208.00			0.958812
$310$	1138.50	−	1971.94i	0.208589	−	0.361286i
$311$	660.000	+	1143.15i	0.120338	+	0.208432i	0.919901	−	0.392151i	$-0.128269\pi$
$311$	660.000	+	1143.15i	0.120338	+	0.208432i	−0.799563	+	0.600582i	$0.794935\pi$
$312$	2016.00	+	3491.81i	0.365813	+	0.633606i
$313$	4251.50	−	7363.81i	0.767760	−	1.32980i	−0.171014	−	0.985269i	$-0.554704\pi$
$313$	4251.50	−	7363.81i	0.767760	−	1.32980i	0.938775	−	0.344531i	$-0.111962\pi$
$314$	588.000			0.105678
$315$	−472.500	+	163.679i	−0.0845154	+	0.0292770i
$316$	467.000			0.0831355
$317$	1288.50	−	2231.75i	0.228295	−	0.395418i	−0.729008	−	0.684505i	$-0.760018\pi$
$317$	1288.50	−	2231.75i	0.228295	−	0.395418i	0.957303	+	0.289087i	$0.0933517\pi$
$318$	1633.50	+	2829.30i	0.288057	+	0.498929i
$319$	−2227.50	−	3858.14i	−0.390959	−	0.677162i
$320$	649.500	−	1124.97i	0.113463	−	0.196524i
$321$	−4059.00			−0.705767
$322$	4410.00	−	1527.67i	0.763229	−	0.264390i
$323$	−1344.00			−0.231524
$324$	−40.5000	+	70.1481i	−0.00694444	+	0.0120281i
$325$	−3712.00	−	6429.37i	−0.633553	−	1.09735i
$326$	−1878.00	−	3252.79i	−0.319058	−	0.552624i
$327$	555.000	−	961.288i	0.0938580	−	0.162567i
$328$	7560.00			1.27266
$329$	420.000	+	363.731i	0.0703810	+	0.0609517i
$330$	−405.000			−0.0675591
$331$	242.000	−	419.156i	0.0401859	−	0.0696040i	−0.845233	−	0.534398i	$-0.820538\pi$
$331$	242.000	−	419.156i	0.0401859	−	0.0696040i	0.885419	+	0.464794i	$0.153872\pi$
$332$	−238.500	−	413.094i	−0.0394259	−	0.0682876i
$333$	1422.00	+	2462.98i	0.234009	+	0.405316i
$334$	−3969.00	+	6874.51i	−0.650222	+	1.12622i
$335$	1110.00			0.181032
$336$	745.500	−	3873.73i	0.121043	−	0.628957i
$337$	−8359.00			−1.35117			−0.675584	−	0.737283i	$-0.736109\pi$
$337$	−8359.00			−1.35117			−0.675584	+	0.737283i	$0.736109\pi$
$338$	2848.50	−	4933.75i	0.458396	−	0.793966i
$339$	972.000	+	1683.55i	0.155728	+	0.269729i
$340$	126.000	+	218.238i	0.0200980	+	0.0348107i
$341$	−1897.50	+	3286.57i	−0.301335	+	0.521928i
$342$	432.000			0.0683038
$343$	3430.00	−	5346.84i	0.539949	−	0.841698i
$344$	546.000			0.0855766
$345$	−378.000	+	654.715i	−0.0589879	+	0.102170i
$346$	−1179.00	−	2042.09i	−0.183189	−	0.317293i
$347$	930.000	+	1610.81i	0.143876	+	0.249201i	0.928953	−	0.370197i	$-0.120710\pi$
$347$	930.000	+	1610.81i	0.143876	+	0.249201i	−0.785077	+	0.619398i	$0.787377\pi$
$348$	445.500	−	771.629i	0.0686244	−	0.118861i
$349$	−1918.00			−0.294178			−0.147089	−	0.989123i	$-0.546990\pi$
$349$	−1918.00			−0.294178			−0.147089	+	0.989123i	$0.546990\pi$
$350$	−1218.00	+	6328.91i	−0.186014	+	0.966556i
$351$	−1728.00			−0.262774
$352$	337.500	−	584.567i	0.0511046	−	0.0885157i
$353$	1524.00	+	2639.65i	0.229786	+	0.398000i	0.957744	−	0.287620i	$-0.0928642\pi$
$353$	1524.00	+	2639.65i	0.229786	+	0.398000i	−0.727959	+	0.685621i	$0.759531\pi$
$354$	−67.5000	−	116.913i	−0.0101344	−	0.0175533i
$355$	−513.000	+	888.542i	−0.0766964	+	0.132842i
$356$	906.000			0.134882
$357$	−3528.00	−	3055.34i	−0.523030	−	0.452957i
$358$	−8676.00			−1.28084
$359$	15.0000	−	25.9808i	0.00220521	−	0.00381953i	−0.864921	−	0.501909i	$-0.832631\pi$
$359$	15.0000	−	25.9808i	0.00220521	−	0.00381953i	0.867126	+	0.498089i	$0.165965\pi$
$360$	283.500	+	491.036i	0.0415049	+	0.0718886i
$361$	3301.50	+	5718.37i	0.481338	+	0.833703i
$362$	2028.00	−	3512.60i	0.294446	−	0.509995i
$363$	−3318.00			−0.479752
$364$	−1120.00	+	387.979i	−0.161275	+	0.0558672i
$365$	−1086.00			−0.155737
$366$	−531.000	+	919.719i	−0.0758356	+	0.131351i
$367$	5655.50	+	9795.61i	0.804400	+	1.39326i	0.916696	+	0.399586i	$0.130846\pi$
$367$	5655.50	+	9795.61i	0.804400	+	1.39326i	−0.112296	+	0.993675i	$0.535820\pi$
$368$	−2982.00	−	5164.98i	−0.422412	−	0.731638i
$369$	−1620.00	+	2805.92i	−0.228547	+	0.395855i
$370$	−2844.00			−0.399601
$371$	6352.50	−	2200.57i	0.888963	−	0.307946i
$372$	−759.000			−0.105786
$373$	−604.000	+	1046.16i	−0.0838443	+	0.145223i	−0.904898	−	0.425628i	$-0.860053\pi$
$373$	−604.000	+	1046.16i	−0.0838443	+	0.145223i	0.821054	+	0.570851i	$0.193387\pi$
$374$	−1890.00	−	3273.58i	−0.261309	−	0.452600i
$375$	−1084.50	−	1878.41i	−0.149342	−	0.258668i
$376$	315.000	−	545.596i	0.0432045	−	0.0748324i
$377$	19008.0			2.59672
$378$	1134.00	+	982.073i	0.154303	+	0.133631i
$379$	7640.00			1.03546			0.517731	−	0.855543i	$-0.326777\pi$
$379$	7640.00			1.03546			0.517731	+	0.855543i	$0.326777\pi$
$380$	−24.0000	+	41.5692i	−0.00323993	+	0.00561173i
$381$	−565.500	−	979.475i	−0.0760405	−	0.131706i
$382$	5868.00	+	10163.7i	0.785950	+	1.36131i
$383$	−6375.00	+	11041.8i	−0.850515	+	1.47314i	0.0302291	+	0.999543i	$0.490376\pi$
$383$	−6375.00	+	11041.8i	−0.850515	+	1.47314i	−0.880744	+	0.473592i	$0.842957\pi$
$384$	−4977.00			−0.661410
$385$	−157.500	+	818.394i	−0.0208492	+	0.108336i
$386$	−4479.00			−0.590609
$387$	−117.000	+	202.650i	−0.0153681	+	0.0266183i
$388$	−251.500	−	435.611i	−0.0329072	−	0.0569969i
$389$	−1563.00	−	2707.20i	−0.203720	−	0.352854i	0.746004	−	0.665942i	$-0.231970\pi$
$389$	−1563.00	−	2707.20i	−0.203720	−	0.352854i	−0.949724	+	0.313087i	$0.898637\pi$
$390$	864.000	−	1496.49i	0.112180	−	0.194302i
$391$	−7056.00			−0.912627
$392$	−6688.50	−	2673.42i	−0.861786	−	0.344459i
$393$	−1953.00			−0.250676
$394$	−6129.00	+	10615.7i	−0.783692	+	1.35739i
$395$	700.500	+	1213.30i	0.0892303	+	0.154551i
$396$	67.5000	+	116.913i	0.00856566	+	0.0148362i
$397$	2966.00	−	5137.26i	0.374960	−	0.649450i	−0.615361	−	0.788246i	$-0.710990\pi$
$397$	2966.00	−	5137.26i	0.374960	−	0.649450i	0.990321	+	0.138795i	$0.0443230\pi$
$398$	10668.0			1.34356
$399$	168.000	−	872.954i	0.0210790	−	0.109530i
$400$	8236.00			1.02950
$401$	−804.000	+	1392.57i	−0.100124	+	0.173420i	−0.911736	−	0.410777i	$-0.865257\pi$
$401$	−804.000	+	1392.57i	−0.100124	+	0.173420i	0.811611	+	0.584198i	$0.198591\pi$
$402$	−1665.00	−	2883.86i	−0.206574	−	0.357796i
$403$	−8096.00	−	14022.7i	−1.00072	−	1.73330i
$404$	543.000	−	940.504i	0.0668695	−	0.115821i
$405$	−243.000			−0.0298142
$406$	−12474.0	−	10802.8i	−1.52481	−	1.32053i
$407$	4740.00			0.577280
$408$	−2646.00	+	4583.01i	−0.321070	+	0.556109i
$409$	2232.50	+	3866.80i	0.269902	+	0.467484i	0.968836	−	0.247702i	$-0.0796753\pi$
$409$	2232.50	+	3866.80i	0.269902	+	0.467484i	−0.698934	+	0.715186i	$0.746342\pi$
$410$	−1620.00	−	2805.92i	−0.195137	−	0.337987i
$411$	2655.00	−	4598.59i	0.318641	−	0.551903i
$412$	1736.00			0.207589
$413$	−262.500	+	90.9327i	−0.0312755	+	0.0108342i
$414$	2268.00			0.269242
$415$	715.500	−	1239.28i	0.0846326	−	0.146588i
$416$	1440.00	+	2494.15i	0.169716	+	0.293957i
$417$	2337.00	+	4047.80i	0.274445	+	0.475352i
$418$	360.000	−	623.538i	0.0421248	−	0.0729623i
$419$	−1584.00			−0.184686			−0.0923430	−	0.995727i	$-0.529436\pi$
$419$	−1584.00			−0.184686			−0.0923430	+	0.995727i	$0.529436\pi$
$420$	−157.500	+	54.5596i	−0.0182981	+	0.00633866i
$421$	−1330.00			−0.153967			−0.0769837	−	0.997032i	$-0.524529\pi$
$421$	−1330.00			−0.153967			−0.0769837	+	0.997032i	$0.524529\pi$
$422$	1875.00	−	3247.60i	0.216288	−	0.374622i
$423$	135.000	+	233.827i	0.0155176	+	0.0268772i
$424$	−3811.50	−	6601.71i	−0.436563	−	0.756150i
$425$	4872.00	−	8438.55i	0.556063	−	0.963129i
$426$	3078.00			0.350069
$427$	1652.00	+	1430.67i	0.187227	+	0.162143i
$428$	−1353.00			−0.152803
$429$	−1440.00	+	2494.15i	−0.162060	+	0.280697i
$430$	−117.000	−	202.650i	−0.0131215	−	0.0227271i
$431$	−4794.00	−	8303.45i	−0.535775	−	0.927989i	−0.999125	−	0.0418139i	$-0.986686\pi$
$431$	−4794.00	−	8303.45i	−0.535775	−	0.927989i	0.463351	−	0.886175i	$-0.346647\pi$
$432$	958.500	−	1660.17i	0.106750	−	0.184896i
$433$	494.000			0.0548271			0.0274135	−	0.999624i	$-0.491273\pi$
$433$	494.000			0.0548271			0.0274135	+	0.999624i	$0.491273\pi$
$434$	−2656.50	+	13803.6i	−0.293816	+	1.52671i
$435$	2673.00			0.294622
$436$	185.000	−	320.429i	0.0203209	−	0.0351968i
$437$	−672.000	−	1163.94i	−0.0735609	−	0.127411i
$438$	1629.00	+	2821.51i	0.177709	+	0.307801i
$439$	8004.50	−	13864.2i	0.870237	−	1.50729i	0.00848508	−	0.999964i	$-0.497299\pi$
$439$	8004.50	−	13864.2i	0.870237	−	1.50729i	0.861752	−	0.507330i	$-0.169368\pi$
$440$	945.000			0.102389
$441$	2425.50	−	1909.59i	0.261905	−	0.206197i
$442$	16128.0			1.73559
$443$	−3886.50	+	6731.62i	−0.416824	+	0.721961i	−0.995618	−	0.0935130i	$-0.970190\pi$
$443$	−3886.50	+	6731.62i	−0.416824	+	0.721961i	0.578794	+	0.815474i	$0.303524\pi$
$444$	474.000	+	820.992i	0.0506645	+	0.0877535i
$445$	1359.00	+	2353.86i	0.144770	+	0.250749i
$446$	637.500	−	1104.18i	0.0676827	−	0.117230i
$447$	7362.00			0.778995
$448$	−1515.50	+	7874.77i	−0.159823	+	0.830464i
$449$	864.000			0.0908122			0.0454061	−	0.998969i	$-0.485542\pi$
$449$	864.000			0.0908122			0.0454061	+	0.998969i	$0.485542\pi$
$450$	−1566.00	+	2712.39i	−0.164049	+	0.284141i
$451$	2700.00	+	4676.54i	0.281903	+	0.488269i
$452$	324.000	+	561.184i	0.0337161	+	0.0583980i
$453$	−1888.50	+	3270.98i	−0.195871	+	0.339258i
$454$	−11565.0			−1.19553
$455$	−2688.00	−	2327.88i	−0.276957	−	0.239852i
$456$	−1008.00			−0.103517
$457$	−1259.50	+	2181.52i	−0.128921	+	0.223298i	−0.923259	−	0.384179i	$-0.874485\pi$
$457$	−1259.50	+	2181.52i	−0.128921	+	0.223298i	0.794338	+	0.607476i	$0.207818\pi$
$458$	−3282.00	−	5684.59i	−0.334842	−	0.579964i
$459$	−1134.00	−	1964.15i	−0.115317	−	0.199735i
$460$	−126.000	+	218.238i	−0.0127713	+	0.0221205i
$461$	−342.000			−0.0345521			−0.0172761	−	0.999851i	$-0.505499\pi$
$461$	−342.000			−0.0345521			−0.0172761	+	0.999851i	$0.505499\pi$
$462$	2362.50	−	818.394i	0.237908	−	0.0824137i
$463$	−4336.00			−0.435229			−0.217614	−	0.976035i	$-0.569828\pi$
$463$	−4336.00			−0.435229			−0.217614	+	0.976035i	$0.569828\pi$
$464$	−10543.5	+	18261.9i	−1.05489	+	1.82713i
$465$	−1138.50	−	1971.94i	−0.113541	−	0.196659i
$466$	1278.00	+	2213.56i	0.127043	+	0.220046i
$467$	−9318.00	+	16139.2i	−0.923310	+	1.59922i	−0.129052	+	0.991638i	$0.541194\pi$
$467$	−9318.00	+	16139.2i	−0.923310	+	1.59922i	−0.794257	+	0.607581i	$0.792140\pi$
$468$	−576.000			−0.0568923
$469$	−6475.00	+	2243.01i	−0.637500	+	0.220837i
$470$	−270.000			−0.0264982
$471$	294.000	−	509.223i	0.0287618	−	0.0498169i
$472$	157.500	+	272.798i	0.0153592	+	0.0266029i
$473$	195.000	+	337.750i	0.0189558	+	0.0328325i
$474$	2101.50	−	3639.90i	0.203639	−	0.352714i
$475$	1856.00			0.179282
$476$	−1176.00	−	1018.45i	−0.113239	−	0.0980680i
$477$	3267.00			0.313597
$478$	8262.00	−	14310.2i	0.790575	−	1.36932i
$479$	−7539.00	−	13057.9i	−0.719135	−	1.24558i	−0.961343	−	0.275354i	$-0.911205\pi$
$479$	−7539.00	−	13057.9i	−0.719135	−	1.24558i	0.242208	−	0.970224i	$-0.422128\pi$
$480$	202.500	+	350.740i	0.0192559	+	0.0333521i
$481$	−10112.0	+	17514.5i	−0.958560	+	1.66028i
$482$	−2373.00			−0.224247
$483$	882.000	−	4583.01i	0.0830898	−	0.431747i
$484$	−1106.00			−0.103869
$485$	754.500	−	1306.83i	0.0706393	−	0.122351i
$486$	364.500	+	631.333i	0.0340207	+	0.0589256i
$487$	−3110.50	−	5387.54i	−0.289425	−	0.501300i	0.684247	−	0.729250i	$-0.260131\pi$
$487$	−3110.50	−	5387.54i	−0.289425	−	0.501300i	−0.973673	+	0.227950i	$0.926798\pi$
$488$	1239.00	−	2146.01i	0.114932	−	0.199068i
$489$	−3756.00			−0.347346
$490$	441.000	+	3055.34i	0.0406579	+	0.281686i
$491$	−7371.00			−0.677492			−0.338746	−	0.940878i	$-0.610003\pi$
$491$	−7371.00			−0.677492			−0.338746	+	0.940878i	$0.610003\pi$
$492$	−540.000	+	935.307i	−0.0494819	+	0.0857051i
$493$	12474.0	+	21605.6i	1.13956	+	1.97377i
$494$	1536.00	+	2660.43i	0.139895	+	0.242304i
$495$	−202.500	+	350.740i	−0.0183873	+	0.0318477i
$496$	17963.0			1.62613
$497$	1197.00	−	6219.79i	0.108034	−	0.561360i
$498$	−4293.00			−0.386293
$499$	−2137.00	+	3701.39i	−0.191714	+	0.332058i	−0.945818	−	0.324696i	$-0.894738\pi$
$499$	−2137.00	+	3701.39i	−0.191714	+	0.332058i	0.754104	+	0.656755i	$0.228071\pi$
$500$	−361.500	−	626.136i	−0.0323335	−	0.0560033i
$501$	3969.00	+	6874.51i	0.353936	+	0.613035i
$502$	7897.50	−	13678.9i	0.702157	−	1.21617i
$503$	−2520.00			−0.223382			−0.111691	−	0.993743i	$-0.535627\pi$
$503$	−2520.00			−0.223382			−0.111691	+	0.993743i	$0.535627\pi$
$504$	−2646.00	−	2291.50i	−0.233854	−	0.202523i
$505$	3258.00			0.287087
$506$	1890.00	−	3273.58i	0.166049	−	0.287605i
$507$	−2848.50	−	4933.75i	−0.249519	−	0.432180i
$508$	−188.500	−	326.492i	−0.0164633	−	0.0285152i
$509$	7138.50	−	12364.2i	0.621628	−	1.07669i	−0.367555	−	0.930002i	$-0.619805\pi$
$509$	7138.50	−	12364.2i	0.621628	−	1.07669i	0.989183	−	0.146689i	$-0.0468616\pi$
$510$	2268.00			0.196919
$511$	6335.00	−	2194.51i	0.548423	−	0.189979i
$512$	8733.00			0.753804
$513$	216.000	−	374.123i	0.0185899	−	0.0321987i
$514$	−10305.0	−	17848.8i	−0.884308	−	1.53167i
$515$	2604.00	+	4510.26i	0.222808	+	0.385914i
$516$	−39.0000	+	67.5500i	−0.00332729	+	0.00576303i
$517$	450.000			0.0382804
$518$	16590.0	−	5746.94i	1.40719	−	0.487464i
$519$	−2358.00			−0.199431
$520$	−2016.00	+	3491.81i	−0.170014	+	0.294473i
$521$	3153.00	+	5461.16i	0.265135	+	0.459228i	0.967599	−	0.252492i	$-0.0812501\pi$
$521$	3153.00	+	5461.16i	0.265135	+	0.459228i	−0.702464	+	0.711719i	$0.747917\pi$
$522$	−4009.50	−	6944.66i	−0.336190	−	0.582298i
$523$	−4036.00	+	6990.56i	−0.337442	+	0.584466i	−0.983951	−	0.178440i	$-0.942895\pi$
$523$	−4036.00	+	6990.56i	−0.337442	+	0.584466i	0.646509	+	0.762906i	$0.276228\pi$
$524$	−651.000			−0.0542730
$525$	4872.00	+	4219.28i	0.405012	+	0.350751i
$526$	666.000			0.0552072
$527$	10626.0	−	18404.8i	0.878322	−	1.52130i
$528$	−1597.50	−	2766.95i	−0.131671	−	0.228061i
$529$	2555.50	+	4426.26i	0.210035	+	0.363792i
$530$	−1633.50	+	2829.30i	−0.133877	+	0.231881i
$531$	−135.000			−0.0110330
$532$	56.0000	−	290.985i	0.00456374	−	0.0237139i
$533$	−23040.0			−1.87237
$534$	4077.00	−	7061.57i	0.330391	−	0.572255i
$535$	−2029.50	−	3515.20i	−0.164005	−	0.284066i
$536$	3885.00	+	6729.02i	0.313072	+	0.542256i
$537$	−4338.00	+	7513.64i	−0.348601	+	0.603794i
$538$	−23553.0			−1.88744
$539$	−735.000	−	5092.23i	−0.0587360	−	0.406935i
$540$	−81.0000			−0.00645497
$541$	11429.0	−	19795.6i	0.908264	−	1.57316i	0.0917903	−	0.995778i	$-0.470741\pi$
$541$	11429.0	−	19795.6i	0.908264	−	1.57316i	0.816474	−	0.577382i	$-0.195926\pi$
$542$	7774.50	+	13465.8i	0.616132	+	1.06717i
$543$	−2028.00	−	3512.60i	−0.160276	−	0.277606i
$544$	−1890.00	+	3273.58i	−0.148958	+	0.258003i
$545$	1110.00			0.0872425
$546$	−2016.00	+	10475.4i	−0.158016	+	0.821076i
$547$	−24724.0			−1.93258			−0.966291	−	0.257454i	$-0.917116\pi$
$547$	−24724.0			−1.93258			−0.966291	+	0.257454i	$0.917116\pi$
$548$	885.000	−	1532.86i	0.0689878	−	0.119490i
$549$	531.000	+	919.719i	0.0412796	+	0.0714985i
$550$	2610.00	+	4520.65i	0.202347	+	0.350475i
$551$	−2376.00	+	4115.35i	−0.183704	+	0.318185i
$552$	−5292.00			−0.408048
$553$	−6538.00	−	5662.07i	−0.502756	−	0.435399i
$554$	14880.0			1.14114
$555$	−1422.00	+	2462.98i	−0.108758	+	0.188374i
$556$	779.000	+	1349.27i	0.0594190	+	0.102917i
$557$	4921.50	+	8524.29i	0.374382	+	0.648448i	0.990234	−	0.139413i	$-0.0445216\pi$
$557$	4921.50	+	8524.29i	0.374382	+	0.648448i	−0.615853	+	0.787861i	$0.711188\pi$
$558$	−3415.50	+	5915.82i	−0.259121	+	0.448811i
$559$	−1664.00			−0.125903
$560$	3727.50	−	1291.24i	0.281278	−	0.0974375i
$561$	−3780.00			−0.284477
$562$	−1161.00	+	2010.91i	−0.0871420	+	0.150934i
$563$	6685.50	+	11579.6i	0.500462	+	0.866826i	1.00000		0.000533812i	$0.000169918\pi$
$563$	6685.50	+	11579.6i	0.500462	+	0.866826i	−0.499538	+	0.866292i	$0.666497\pi$
$564$	45.0000	+	77.9423i	0.00335965	+	0.00581908i
$565$	−972.000	+	1683.55i	−0.0723758	+	0.125359i
$566$	−11094.0			−0.823879
$567$	1417.50	−	491.036i	0.104990	−	0.0363696i
$568$	−7182.00			−0.530546
$569$	2616.00	−	4531.04i	0.192739	−	0.333834i	−0.753418	−	0.657542i	$-0.771596\pi$
$569$	2616.00	−	4531.04i	0.192739	−	0.333834i	0.946157	+	0.323708i	$0.104930\pi$
$570$	216.000	+	374.123i	0.0158724	+	0.0274917i
$571$	7199.00	+	12469.0i	0.527616	+	0.913858i	0.999482	+	0.0321874i	$0.0102474\pi$
$571$	7199.00	+	12469.0i	0.527616	+	0.913858i	−0.471866	+	0.881670i	$0.656419\pi$
$572$	−480.000	+	831.384i	−0.0350871	+	0.0607726i
$573$	11736.0			0.855634
$574$	15120.0	+	13094.3i	1.09947	+	0.952170i
$575$	9744.00			0.706701
$576$	−1948.50	+	3374.90i	−0.140951	+	0.244133i
$577$	−9935.50	−	17208.8i	−0.716846	−	1.24161i	−0.962243	−	0.272191i	$-0.912252\pi$
$577$	−9935.50	−	17208.8i	−0.716846	−	1.24161i	0.245397	−	0.969423i	$-0.421082\pi$
$578$	3214.50	+	5567.68i	0.231325	+	0.400666i
$579$	−2239.50	+	3878.93i	−0.160743	+	0.278416i
$580$	891.000			0.0637875
$581$	−1669.50	+	8674.98i	−0.119213	+	0.619447i
$582$	−4527.00			−0.322423
$583$	2722.50	−	4715.51i	0.193404	−	0.334985i
$584$	−3801.00	−	6583.53i	−0.269326	−	0.466487i
$585$	−864.000	−	1496.49i	−0.0610633	−	0.105765i
$586$	−9409.50	+	16297.7i	−0.663315	+	1.14890i
$587$	−16137.0			−1.13466			−0.567330	−	0.823491i	$-0.692024\pi$
$587$	−16137.0			−1.13466			−0.567330	+	0.823491i	$0.692024\pi$
$588$	808.500	−	636.529i	0.0567040	−	0.0446429i
$589$	4048.00			0.283183
$590$	67.5000	−	116.913i	0.00471005	−	0.00815805i
$591$	6129.00	+	10615.7i	0.426588	+	0.738872i
$592$	−11218.0	−	19430.1i	−0.778812	−	1.34894i
$593$	10662.0	−	18467.1i	0.738340	−	1.27884i	−0.214902	−	0.976636i	$-0.568943\pi$
$593$	10662.0	−	18467.1i	0.738340	−	1.27884i	0.953242	−	0.302207i	$-0.0977235\pi$
$594$	1215.00			0.0839260
$595$	882.000	−	4583.01i	0.0607705	−	0.315773i
$596$	2454.00			0.168657
$597$	5334.00	−	9238.76i	0.365672	−	0.633362i
$598$	8064.00	+	13967.3i	0.551441	+	0.955123i
$599$	4323.00	+	7487.66i	0.294880	+	0.510747i	0.974957	−	0.222394i	$-0.0713871\pi$
$599$	4323.00	+	7487.66i	0.294880	+	0.510747i	−0.680077	+	0.733141i	$0.738054\pi$
$600$	3654.00	−	6328.91i	0.248623	−	0.430628i
$601$	11195.0			0.759823			0.379911	−	0.925023i	$-0.375954\pi$
$601$	11195.0			0.759823			0.379911	+	0.925023i	$0.375954\pi$
$602$	1092.00	+	945.700i	0.0739312	+	0.0640263i
$603$	−3330.00			−0.224889
$604$	−629.500	+	1090.33i	−0.0424073	+	0.0734515i
$605$	−1659.00	−	2873.47i	−0.111484	−	0.193096i
$606$	−4887.00	−	8464.53i	−0.327592	−	0.567406i
$607$	4485.50	−	7769.11i	0.299935	−	0.519503i	−0.676185	−	0.736731i	$-0.736368\pi$
$607$	4485.50	−	7769.11i	0.299935	−	0.519503i	0.976121	+	0.217228i	$0.0697015\pi$
$608$	−720.000			−0.0480261
$609$	−15592.5	+	5401.40i	−1.03750	+	0.359402i
$610$	−1062.00			−0.0704904
$611$	−960.000	+	1662.77i	−0.0635637	+	0.110096i
$612$	−378.000	−	654.715i	−0.0249669	−	0.0432439i
$613$	6386.00	+	11060.9i	0.420764	+	0.728784i	0.996014	−	0.0891932i	$-0.0284288\pi$
$613$	6386.00	+	11060.9i	0.420764	+	0.728784i	−0.575251	+	0.817977i	$0.695096\pi$
$614$	−2526.00	+	4375.16i	−0.166028	+	0.287569i
$615$	−3240.00			−0.212438
$616$	−5512.50	+	1909.59i	−0.360560	+	0.124902i
$617$	12762.0			0.832705			0.416352	−	0.909203i	$-0.363308\pi$
$617$	12762.0			0.832705			0.416352	+	0.909203i	$0.363308\pi$
$618$	7812.00	−	13530.8i	0.508487	−	0.880725i
$619$	−6421.00	−	11121.5i	−0.416933	−	0.722150i	0.578696	−	0.815543i	$-0.303562\pi$
$619$	−6421.00	−	11121.5i	−0.416933	−	0.722150i	−0.995629	+	0.0933936i	$0.970229\pi$
$620$	−379.500	−	657.313i	−0.0245824	−	0.0425780i
$621$	1134.00	−	1964.15i	0.0732783	−	0.126922i
$622$	3960.00			0.255276
$623$	−12684.0	−	10984.7i	−0.815688	−	0.706407i
$624$	13632.0			0.874546
$625$	−6165.50	+	10679.0i	−0.394592	+	0.683453i
$626$	−12754.5	−	22091.4i	−0.814333	−	1.41047i
$627$	−360.000	−	623.538i	−0.0229298	−	0.0397157i
$628$	98.0000	−	169.741i	0.00622711	−	0.0107857i
$629$	−26544.0			−1.68264
$630$	−283.500	+	1473.11i	−0.0179284	+	0.0931589i
$631$	21365.0			1.34790			0.673952	−	0.738775i	$-0.264596\pi$
$631$	21365.0			1.34790			0.673952	+	0.738775i	$0.264596\pi$
$632$	−4903.50	+	8493.11i	−0.308625	+	0.534554i
$633$	−1875.00	−	3247.60i	−0.117732	−	0.203918i
$634$	−3865.50	−	6695.24i	−0.242143	−	0.419404i
$635$	565.500	−	979.475i	0.0353404	−	0.0612114i
$636$	1089.00			0.0678957
$637$	20384.0	+	8147.57i	1.26789	+	0.506779i
$638$	−13365.0			−0.829350
$639$	1539.00	−	2665.63i	0.0952768	−	0.165024i
$640$	−2488.50	−	4310.21i	−0.153698	−	0.266212i
$641$	−4137.00	−	7165.49i	−0.254917	−	0.441529i	0.709956	−	0.704246i	$-0.248715\pi$
$641$	−4137.00	−	7165.49i	−0.254917	−	0.441529i	−0.964873	+	0.262717i	$0.915381\pi$
$642$	−6088.50	+	10545.6i	−0.374290	+	0.648289i
$643$	27998.0			1.71716			0.858580	−	0.512680i	$-0.171347\pi$
$643$	27998.0			1.71716			0.858580	+	0.512680i	$0.171347\pi$
$644$	294.000	−	1527.67i	0.0179895	−	0.0934761i
$645$	−234.000			−0.0142849
$646$	−2016.00	+	3491.81i	−0.122784	+	0.212668i
$647$	8733.00	+	15126.0i	0.530649	+	0.919110i	0.999360	+	0.0357592i	$0.0113849\pi$
$647$	8733.00	+	15126.0i	0.530649	+	0.919110i	−0.468712	+	0.883351i	$0.655282\pi$
$648$	−850.500	−	1473.11i	−0.0515599	−	0.0893043i
$649$	−112.500	+	194.856i	−0.00680433	+	0.0117854i
$650$	−22272.0			−1.34397
$651$	10626.0	+	9202.39i	0.639732	+	0.554024i
$652$	−1252.00			−0.0752026
$653$	−1078.50	+	1868.02i	−0.0646324	+	0.111947i	−0.896531	−	0.442981i	$-0.853921\pi$
$653$	−1078.50	+	1868.02i	−0.0646324	+	0.111947i	0.831898	+	0.554928i	$0.187254\pi$
$654$	−1665.00	−	2883.86i	−0.0995515	−	0.172428i
$655$	−976.500	−	1691.35i	−0.0582519	−	0.100895i
$656$	12780.0	−	22135.6i	0.760633	−	1.31745i
$657$	3258.00			0.193465
$658$	1575.00	−	545.596i	0.0933129	−	0.0323245i
$659$	19944.0			1.17892			0.589460	−	0.807798i	$-0.299341\pi$
$659$	19944.0			1.17892			0.589460	+	0.807798i	$0.299341\pi$
$660$	−67.5000	+	116.913i	−0.00398096	+	0.00689523i
$661$	−13753.0	−	23820.9i	−0.809273	−	1.40170i	−0.913368	−	0.407135i	$-0.866528\pi$
$661$	−13753.0	−	23820.9i	−0.809273	−	1.40170i	0.104095	−	0.994567i	$-0.466806\pi$
$662$	−726.000	−	1257.47i	−0.0426236	−	0.0738262i
$663$	8064.00	−	13967.3i	0.472368	−	0.818165i
$664$	10017.0			0.585444
$665$	840.000	−	290.985i	0.0489832	−	0.0169683i
$666$	8532.00			0.496409
$667$	−12474.0	+	21605.6i	−0.724131	+	1.25423i
$668$	1323.00	+	2291.50i	0.0766294	+	0.132726i
$669$	−637.500	−	1104.18i	−0.0368418	−	0.0638119i
$670$	1665.00	−	2883.86i	0.0960068	−	0.166289i
$671$	1770.00			0.101833
$672$	−1890.00	−	1636.79i	−0.108495	−	0.0939590i
$673$	−19123.0			−1.09530			−0.547650	−	0.836707i	$-0.684478\pi$
$673$	−19123.0			−1.09530			−0.547650	+	0.836707i	$0.684478\pi$
$674$	−12538.5	+	21717.3i	−0.716565	+	1.24113i
$675$	1566.00	+	2712.39i	0.0892968	+	0.154667i
$676$	−949.500	−	1644.58i	−0.0540225	−	0.0935698i
$677$	−6928.50	+	12000.5i	−0.393329	+	0.681266i	−0.992886	−	0.119066i	$-0.962010\pi$
$677$	−6928.50	+	12000.5i	−0.393329	+	0.681266i	0.599557	+	0.800332i	$0.295343\pi$
$678$	5832.00			0.330349
$679$	−1760.50	+	9147.83i	−0.0995019	+	0.517027i
$680$	−5292.00			−0.298440
$681$	−5782.50	+	10015.6i	−0.325383	+	0.563580i
$682$	5692.50	+	9859.70i	0.319615	+	0.553589i
$683$	11122.5	+	19264.7i	0.623120	+	1.07927i	0.988901	+	0.148574i	$0.0474683\pi$
$683$	11122.5	+	19264.7i	0.623120	+	1.07927i	−0.365782	+	0.930701i	$0.619198\pi$
$684$	72.0000	−	124.708i	0.00402484	−	0.00697122i
$685$	5310.00			0.296182
$686$	−8746.50	−	16931.7i	−0.486797	−	0.942353i
$687$	−6564.00			−0.364530
$688$	923.000	−	1598.68i	0.0511469	−	0.0885890i
$689$	11616.0	+	20119.5i	0.642285	+	1.11247i
$690$	1134.00	+	1964.15i	0.0625661	+	0.108368i
$691$	320.000	−	554.256i	0.0176170	−	0.0305136i	−0.857082	−	0.515179i	$-0.827725\pi$
$691$	320.000	−	554.256i	0.0176170	−	0.0305136i	0.874700	+	0.484666i	$0.161059\pi$
$692$	−786.000			−0.0431781
$693$	472.500	−	2455.18i	0.0259001	−	0.134581i
$694$	5580.00			0.305207
$695$	−2337.00	+	4047.80i	−0.127550	+	0.220924i
$696$	9355.50	+	16204.2i	0.509511	+	0.882498i
$697$	−15120.0	−	26188.6i	−0.821680	−	1.42319i
$698$	−2877.00	+	4983.11i	−0.156012	+	0.270220i
$699$	2556.00			0.138307
$700$	1624.00	+	1406.43i	0.0876878	+	0.0759398i
$701$	−15561.0			−0.838418			−0.419209	−	0.907890i	$-0.637693\pi$
$701$	−15561.0			−0.838418			−0.419209	+	0.907890i	$0.637693\pi$
$702$	−2592.00	+	4489.48i	−0.139357	+	0.241374i
$703$	−2528.00	−	4378.62i	−0.135626	−	0.234912i
$704$	3247.50	+	5624.83i	0.173856	+	0.301128i
$705$	−135.000	+	233.827i	−0.00721191	+	0.0124914i
$706$	9144.00			0.487449
$707$	−19005.0	+	6583.53i	−1.01097	+	0.350211i
$708$	−45.0000			−0.00238871
$709$	−2767.00	+	4792.58i	−0.146568	+	0.253864i	−0.929957	−	0.367668i	$-0.880156\pi$
$709$	−2767.00	+	4792.58i	−0.146568	+	0.253864i	0.783389	+	0.621532i	$0.213489\pi$
$710$	1539.00	+	2665.63i	0.0813488	+	0.140900i
$711$	−2101.50	−	3639.90i	−0.110847	−	0.191993i
$712$	−9513.00	+	16477.0i	−0.500723	+	0.867278i
$713$	21252.0			1.11626
$714$	−13230.0	+	4583.01i	−0.693446	+	0.240217i
$715$	−2880.00			−0.150638
$716$	−1446.00	+	2504.55i	−0.0754742	+	0.130725i
$717$	−8262.00	−	14310.2i	−0.430335	−	0.745362i
$718$	−45.0000	−	77.9423i	−0.00233898	−	0.00405123i
$719$	10923.0	−	18919.2i	0.566564	−	0.981317i	−0.430339	−	0.902667i	$-0.641606\pi$
$719$	10923.0	−	18919.2i	0.566564	−	0.981317i	0.996902	−	0.0786494i	$-0.0250607\pi$
$720$	1917.00			0.0992255
$721$	−24304.0	−	21047.9i	−1.25538	−	1.08719i
$722$	19809.0			1.02107
$723$	−1186.50	+	2055.08i	−0.0610324	+	0.105711i
$724$	−676.000	−	1170.87i	−0.0347007	−	0.0601035i
$725$	−17226.0	−	29836.3i	−0.882424	−	1.52840i
$726$	−4977.00	+	8620.42i	−0.254427	+	0.440680i
$727$	−11089.0			−0.565706			−0.282853	−	0.959163i	$-0.591281\pi$
$727$	−11089.0			−0.565706			−0.282853	+	0.959163i	$0.591281\pi$
$728$	4704.00	−	24442.7i	0.239481	−	1.24438i
$729$	729.000			0.0370370
$730$	−1629.00	+	2821.51i	−0.0825918	+	0.143053i
$731$	−1092.00	−	1891.40i	−0.0552518	−	0.0956990i
$732$	177.000	+	306.573i	0.00893731	+	0.0154799i
$733$	−5881.00	+	10186.2i	−0.296343	+	0.513282i	−0.975296	−	0.220900i	$-0.929101\pi$
$733$	−5881.00	+	10186.2i	−0.296343	+	0.513282i	0.678953	+	0.734182i	$0.262434\pi$
$734$	33933.0			1.70639
$735$	2866.50	+	1145.75i	0.143854	+	0.0574989i
$736$	−3780.00			−0.189311
$737$	−2775.00	+	4806.44i	−0.138695	+	0.240227i
$738$	4860.00	+	8417.77i	0.242411	+	0.419868i
$739$	11363.0	+	19681.3i	0.565622	+	0.979686i	0.996992	+	0.0775108i	$0.0246972\pi$
$739$	11363.0	+	19681.3i	0.565622	+	0.979686i	−0.431369	+	0.902175i	$0.641969\pi$
$740$	−474.000	+	820.992i	−0.0235467	+	0.0407841i
$741$	3072.00			0.152298
$742$	3811.50	−	19805.1i	0.188578	−	0.979878i
$743$	6678.00			0.329734			0.164867	−	0.986316i	$-0.447281\pi$
$743$	6678.00			0.329734			0.164867	+	0.986316i	$0.447281\pi$
$744$	7969.50	−	13803.6i	0.392710	−	0.680193i
$745$	3681.00	+	6375.68i	0.181022	+	0.313539i
$746$	1812.00	+	3138.48i	0.0889303	+	0.154032i
$747$	−2146.50	+	3717.85i	−0.105136	+	0.182100i
$748$	−1260.00			−0.0615911
$749$	18942.0	+	16404.3i	0.924066	+	0.800265i
$750$	−6507.00			−0.316803
$751$	9993.50	−	17309.2i	0.485577	−	0.841043i	−0.514286	−	0.857619i	$-0.671943\pi$
$751$	9993.50	−	17309.2i	0.485577	−	0.841043i	0.999863	+	0.0165754i	$0.00527637\pi$
$752$	−1065.00	−	1844.63i	−0.0516444	−	0.0894506i
$753$	−7897.50	−	13678.9i	−0.382206	−	0.662000i
$754$	28512.0	−	49384.2i	1.37712	−	2.38524i
$755$	−3777.00			−0.182065
$756$	472.500	−	163.679i	0.0227310	−	0.00787426i
$757$	314.000			0.0150760			0.00753799	−	0.999972i	$-0.497601\pi$
$757$	314.000			0.0150760			0.00753799	+	0.999972i	$0.497601\pi$
$758$	11460.0	−	19849.3i	0.549137	−	0.951133i
$759$	−1890.00	−	3273.58i	−0.0903856	−	0.156552i
$760$	−504.000	−	872.954i	−0.0240553	−	0.0416649i
$761$	5748.00	−	9955.83i	0.273804	−	0.474242i	−0.696029	−	0.718014i	$-0.745051\pi$
$761$	5748.00	−	9955.83i	0.273804	−	0.474242i	0.969833	+	0.243772i	$0.0783847\pi$
$762$	−3393.00			−0.161306
$763$	−6475.00	+	2243.01i	−0.307222	+	0.106425i
$764$	3912.00			0.185250
$765$	1134.00	−	1964.15i	0.0535946	−	0.0928285i
$766$	19125.0	+	33125.5i	0.902107	+	1.56250i
$767$	−480.000	−	831.384i	−0.0225969	−	0.0391389i
$768$	−2269.50	+	3930.89i	−0.106632	+	0.184692i
$769$	2765.00			0.129660			0.0648299	−	0.997896i	$-0.479350\pi$
$769$	2765.00			0.129660			0.0648299	+	0.997896i	$0.479350\pi$
$770$	1890.00	+	1636.79i	0.0884557	+	0.0766049i
$771$	−20610.0			−0.962712
$772$	−746.500	+	1292.98i	−0.0348020	+	0.0602788i
$773$	7023.00	+	12164.2i	0.326778	+	0.565997i	0.981871	−	0.189552i	$-0.0607036\pi$
$773$	7023.00	+	12164.2i	0.326778	+	0.565997i	−0.655092	+	0.755549i	$0.727370\pi$
$774$	351.000	+	607.950i	0.0163003	+	0.0282330i
$775$	−14674.0	+	25416.1i	−0.680136	+	1.17803i
$776$	10563.0			0.488646
$777$	3318.00	−	17240.8i	0.153195	−	0.796025i
$778$	−9378.00			−0.432156
$779$	2880.00	−	4988.31i	0.132460	−	0.229428i
$780$	−288.000	−	498.831i	−0.0132206	−	0.0228987i
$781$	−2565.00	−	4442.71i	−0.117520	−	0.203550i
$782$	−10584.0	+	18332.0i	−0.483994	+	0.838302i
$783$	−8019.00			−0.365997
$784$	−19134.5	+	15064.5i	−0.871652	+	0.686248i
$785$	588.000			0.0267345
$786$	−2929.50	+	5074.04i	−0.132941	+	0.230261i
$787$	9257.00	+	16033.6i	0.419284	+	0.726221i	0.995868	−	0.0908171i	$-0.0289479\pi$
$787$	9257.00	+	16033.6i	0.419284	+	0.726221i	−0.576584	+	0.817038i	$0.695615\pi$
$788$	2043.00	+	3538.58i	0.0923590	+	0.159970i
$789$	333.000	−	576.773i	0.0150255	−	0.0260249i
$790$	4203.00			0.189286
$791$	2268.00	−	11784.9i	0.101948	−	0.529737i
$792$	−2835.00			−0.127194
$793$	−3776.00	+	6540.22i	−0.169092	+	0.292875i
$794$	−8898.00	−	15411.8i	−0.397706	−	0.688846i
$795$	1633.50	+	2829.30i	0.0728733	+	0.126220i
$796$	1778.00	−	3079.59i	0.0791703	−	0.137127i
$797$	−27495.0			−1.22199			−0.610993	−	0.791636i	$-0.709230\pi$
$797$	−27495.0			−1.22199			−0.610993	+	0.791636i	$0.709230\pi$
$798$	−2016.00	−	1745.91i	−0.0894306	−	0.0774492i
$799$	−2520.00			−0.111578
$800$	2610.00	−	4520.65i	0.115347	−	0.199787i
$801$	−4077.00	−	7061.57i	−0.179842	−	0.311496i
$802$	2412.00	+	4177.71i	0.106198	+	0.183940i
$803$	2715.00	−	4702.52i	0.119315	−	0.206660i
$804$	−1110.00			−0.0486899
$805$	4410.00	−	1527.67i	0.193083	−	0.0668860i
$806$	−48576.0			−2.12285
$807$	−11776.5	+	20397.5i	−0.513696	+	0.889747i
$808$	11403.0	+	19750.6i	0.496480	+	0.859929i
$809$	3972.00	+	6879.71i	0.172618	+	0.298983i	0.939334	−	0.343003i	$-0.111444\pi$
$809$	3972.00	+	6879.71i	0.172618	+	0.298983i	−0.766716	+	0.641986i	$0.778111\pi$
$810$	−364.500	+	631.333i	−0.0158114	+	0.0273861i
$811$	−28942.0			−1.25313			−0.626567	−	0.779368i	$-0.715540\pi$
$811$	−28942.0			−1.25313			−0.626567	+	0.779368i	$0.715540\pi$
$812$	−5197.50	+	1800.47i	−0.224626	+	0.0778128i
$813$	15549.0			0.670759
$814$	7110.00	−	12314.9i	0.306149	−	0.530266i
$815$	−1878.00	−	3252.79i	−0.0807159	−	0.139804i
$816$	8946.00	+	15494.9i	0.383790	+	0.664744i
$817$	208.000	−	360.267i	0.00890698	−	0.0154273i
$818$	13395.0			0.572549
$819$	8064.00	+	6983.63i	0.344052	+	0.297958i
$820$	−1080.00			−0.0459942
$821$	−4093.50	+	7090.15i	−0.174012	+	0.301398i	−0.939819	−	0.341673i	$-0.889007\pi$
$821$	−4093.50	+	7090.15i	−0.174012	+	0.301398i	0.765807	+	0.643071i	$0.222340\pi$
$822$	−7965.00	−	13795.8i	−0.337970	−	0.585381i
$823$	140.000	+	242.487i	0.00592964	+	0.0102704i	0.868975	−	0.494856i	$-0.164779\pi$
$823$	140.000	+	242.487i	0.00592964	+	0.0102704i	−0.863045	+	0.505126i	$0.831446\pi$
$824$	−18228.0	+	31571.8i	−0.770634	+	1.33478i
$825$	5220.00			0.220287
$826$	−157.500	+	818.394i	−0.00663453	+	0.0344741i
$827$	25317.0			1.06452			0.532260	−	0.846581i	$-0.321343\pi$
$827$	25317.0			1.06452			0.532260	+	0.846581i	$0.321343\pi$
$828$	378.000	−	654.715i	0.0158652	−	0.0274794i
$829$	−7660.00	−	13267.5i	−0.320920	−	0.555850i	0.659758	−	0.751478i	$-0.270659\pi$
$829$	−7660.00	−	13267.5i	−0.320920	−	0.555850i	−0.980678	+	0.195628i	$0.937325\pi$
$830$	−2146.50	−	3717.85i	−0.0897664	−	0.155480i
$831$	7440.00	−	12886.5i	0.310579	−	0.537938i
$832$	−27712.0			−1.15474
$833$	4116.00	+	28516.5i	0.171202	+	1.18612i
$834$	14022.0			0.582185
$835$	−3969.00	+	6874.51i	−0.164495	+	0.284913i
$836$	−120.000	−	207.846i	−0.00496446	−	0.00859869i
$837$	3415.50	+	5915.82i	0.141048	+	0.244302i
$838$	−2376.00	+	4115.35i	−0.0979446	+	0.169645i
$839$	34092.0			1.40284			0.701422	−	0.712746i	$-0.252549\pi$
$839$	34092.0			1.40284			0.701422	+	0.712746i	$0.252549\pi$
$840$	661.500	−	3437.25i	0.0271713	−	0.141186i
$841$	63820.0			2.61675
$842$	−1995.00	+	3455.44i	−0.0816535	+	0.141428i
$843$	1161.00	+	2010.91i	0.0474341	+	0.0821583i
$844$	−625.000	−	1082.53i	−0.0254898	−	0.0441496i
$845$	2848.50	−	4933.75i	0.115966	−	0.200859i
$846$	810.000			0.0329177
$847$	15484.0	+	13409.5i	0.628142	+	0.543987i
$848$	−25773.0			−1.04369
$849$	−5547.00	+	9607.69i	−0.224232	+	0.388380i
$850$	−14616.0	−	25315.7i	−0.589794	−	1.02155i
$851$	−13272.0	−	22987.8i	−0.534616	−	0.925982i
$852$	513.000	−	888.542i	0.0206280	−	0.0357288i
$853$	−7378.00			−0.296152			−0.148076	−	0.988976i	$-0.547308\pi$
$853$	−7378.00			−0.296152			−0.148076	+	0.988976i	$0.547308\pi$
$854$	6195.00	−	2146.01i	0.248230	−	0.0859894i
$855$	432.000			0.0172796
$856$	14206.5	−	24606.4i	0.567253	−	0.982510i
$857$	7797.00	+	13504.8i	0.310782	+	0.538291i	0.978532	−	0.206095i	$-0.0660757\pi$
$857$	7797.00	+	13504.8i	0.310782	+	0.538291i	−0.667750	+	0.744386i	$0.732742\pi$
$858$	4320.00	+	7482.46i	0.171891	+	0.297724i
$859$	15269.0	−	26446.7i	0.606486	−	1.05046i	−0.385329	−	0.922779i	$-0.625912\pi$
$859$	15269.0	−	26446.7i	0.606486	−	1.05046i	0.991815	−	0.127685i	$-0.0407548\pi$
$860$	−78.0000			−0.00309277
$861$	18900.0	−	6547.15i	0.748096	−	0.259148i
$862$	−28764.0			−1.13655
$863$	411.000	−	711.873i	0.0162116	−	0.0280793i	−0.857806	−	0.513974i	$-0.828173\pi$
$863$	411.000	−	711.873i	0.0162116	−	0.0280793i	0.874017	+	0.485895i	$0.161506\pi$
$864$	−607.500	−	1052.22i	−0.0239208	−	0.0414320i
$865$	−1179.00	−	2042.09i	−0.0463436	−	0.0802694i
$866$	741.000	−	1283.45i	0.0290764	−	0.0503619i
$867$	6429.00			0.251834
$868$	3542.00	+	3067.46i	0.138506	+	0.119950i
$869$	−7005.00			−0.273450
$870$	4009.50	−	6944.66i	0.156247	−	0.270628i
$871$	−11840.0	−	20507.5i	−0.460601	−	0.797784i
$872$	3885.00	+	6729.02i	0.150875	+	0.261323i
$873$	−2263.50	+	3920.50i	−0.0877524	+	0.151992i
$874$	−4032.00			−0.156046
$875$	−2530.50	+	13148.9i	−0.0977674	+	0.508015i
$876$	1086.00			0.0418865
$877$	20912.0	−	36220.6i	0.805186	−	1.39462i	−0.110980	−	0.993823i	$-0.535399\pi$
$877$	20912.0	−	36220.6i	0.805186	−	1.39462i	0.916165	−	0.400800i	$-0.131268\pi$
$878$	−24013.5	−	41592.6i	−0.923025	−	1.59873i
$879$	9409.50	+	16297.7i	0.361063	+	0.625380i
$880$	1597.50	−	2766.95i	0.0611951	−	0.105993i
$881$	−46098.0			−1.76286			−0.881431	−	0.472313i	$-0.843419\pi$
$881$	−46098.0			−1.76286			−0.881431	+	0.472313i	$0.843419\pi$
$882$	−1323.00	−	9166.01i	−0.0505076	−	0.349927i
$883$	21008.0			0.800652			0.400326	−	0.916373i	$-0.368897\pi$
$883$	21008.0			0.800652			0.400326	+	0.916373i	$0.368897\pi$
$884$	2688.00	−	4655.75i	0.102271	−	0.177138i
$885$	−67.5000	−	116.913i	−0.00256383	−	0.00444068i
$886$	11659.5	+	20194.8i	0.442109	+	0.765755i
$887$	−12018.0	+	20815.8i	−0.454932	+	0.787966i	−0.998684	−	0.0512801i	$-0.983670\pi$
$887$	−12018.0	+	20815.8i	−0.454932	+	0.787966i	0.543752	+	0.839246i	$0.317003\pi$
$888$	−19908.0			−0.752330
$889$	−1319.50	+	6856.32i	−0.0497802	+	0.258666i
$890$	8154.00			0.307104
$891$	607.500	−	1052.22i	0.0228418	−	0.0395631i
$892$	−212.500	−	368.061i	−0.00797649	−	0.0138157i
$893$	−240.000	−	415.692i	−0.00899361	−	0.0155774i
$894$	11043.0	−	19127.0i	0.413124	−	0.715552i
$895$	−8676.00			−0.324030
$896$	23226.0	+	20114.3i	0.865989	+	0.749969i
$897$	16128.0			0.600332
$898$	1296.00	−	2244.74i	0.0481604	−	0.0834163i
$899$	−37570.5	−	65074.0i	−1.39382	−	2.41417i
$900$	522.000	+	904.131i	0.0193333	+	0.0334863i
$901$	−15246.0	+	26406.8i	−0.563727	+	0.976404i
$902$	16200.0			0.598006
$903$	1365.00	−	472.850i	0.0503038	−	0.0174258i
$904$	−13608.0			−0.500659
$905$	2028.00	−	3512.60i	0.0744895	−	0.129020i
$906$	5665.50	+	9812.93i	0.207752	+	0.359838i
$907$	−6646.00	−	11511.2i	−0.243304	−	0.421415i	0.718349	−	0.695683i	$-0.244898\pi$
$907$	−6646.00	−	11511.2i	−0.243304	−	0.421415i	−0.961653	+	0.274268i	$0.911565\pi$
$908$	−1927.50	+	3338.53i	−0.0704475	+	0.122019i
$909$	−9774.00			−0.356637
$910$	−10080.0	+	3491.81i	−0.367196	+	0.127201i
$911$	−9306.00			−0.338443			−0.169221	−	0.985578i	$-0.554125\pi$
$911$	−9306.00			−0.338443			−0.169221	+	0.985578i	$0.554125\pi$
$912$	−1704.00	+	2951.41i	−0.0618696	+	0.107161i
$913$	3577.50	+	6196.41i	0.129680	+	0.224613i
$914$	3778.50	+	6544.55i	0.136741	+	0.236843i
$915$	−531.000	+	919.719i	−0.0191850	+	0.0332295i
$916$	−2188.00			−0.0789231
$917$	9114.00	+	7892.96i	0.328212	+	0.284240i
$918$	−6804.00			−0.244625
$919$	−8248.00	+	14286.0i	−0.296057	+	0.512786i	−0.975230	−	0.221192i	$-0.929005\pi$
$919$	−8248.00	+	14286.0i	−0.296057	+	0.512786i	0.679173	+	0.733978i	$0.262339\pi$
$920$	−2646.00	−	4583.01i	−0.0948218	−	0.164236i
$921$	2526.00	+	4375.16i	0.0903741	+	0.156533i
$922$	−513.000	+	888.542i	−0.0183240	+	0.0317382i
$923$	21888.0			0.780555
$924$	157.500	−	818.394i	0.00560754	−	0.0291376i
$925$	36656.0			1.30296
$926$	−6504.00	+	11265.3i	−0.230815	+	0.399783i
$927$	−7812.00	−	13530.8i	−0.276785	−	0.479406i
$928$	6682.50	+	11574.4i	0.236383	+	0.409428i
$929$	−7077.00	+	12257.7i	−0.249934	+	0.432899i	−0.963507	−	0.267682i	$-0.913742\pi$
$929$	−7077.00	+	12257.7i	−0.249934	+	0.432899i	0.713573	+	0.700581i	$0.247076\pi$
$930$	−6831.00			−0.240857
$931$	−4312.00	+	3394.82i	−0.151794	+	0.119507i
$932$	852.000			0.0299444
$933$	1980.00	−	3429.46i	0.0694773	−	0.120338i
$934$	27954.0	+	48417.7i	0.979318	+	1.69623i
$935$	−1890.00	−	3273.58i	−0.0661065	−	0.114500i
$936$	6048.00	−	10475.4i	0.211202	−	0.365813i
$937$	−3781.00			−0.131825			−0.0659124	−	0.997825i	$-0.520996\pi$
$937$	−3781.00			−0.131825			−0.0659124	+	0.997825i	$0.520996\pi$
$938$	−3885.00	+	20187.1i	−0.135234	+	0.702698i
$939$	−25509.0			−0.886533
$940$	−45.0000	+	77.9423i	−0.00156142	+	0.00270446i
$941$	12931.5	+	22398.0i	0.447986	+	0.775935i	0.998255	−	0.0590530i	$-0.0188081\pi$
$941$	12931.5	+	22398.0i	0.447986	+	0.775935i	−0.550269	+	0.834988i	$0.685475\pi$
$942$	−882.000	−	1527.67i	−0.0305065	−	0.0528388i
$943$	15120.0	−	26188.6i	0.522137	−	0.904367i
$944$	1065.00			0.0367191
$945$	1134.00	+	982.073i	0.0390360	+	0.0338062i
$946$	1170.00			0.0402114
$947$	21192.0	−	36705.6i	0.727188	−	1.25953i	−0.230878	−	0.972983i	$-0.574160\pi$
$947$	21192.0	−	36705.6i	0.727188	−	1.25953i	0.958067	−	0.286545i	$-0.0925067\pi$
$948$	−700.500	−	1213.30i	−0.0239991	−	0.0415677i
$949$	11584.0	+	20064.1i	0.396241	+	0.686309i
$950$	2784.00	−	4822.03i	0.0950788	−	0.164681i
$951$	−7731.00			−0.263612
$952$	30870.0	−	10693.7i	1.05095	−	0.364059i
$953$	10530.0			0.357923			0.178961	−	0.983856i	$-0.442726\pi$
$953$	10530.0			0.357923			0.178961	+	0.983856i	$0.442726\pi$
$954$	4900.50	−	8487.91i	0.166310	−	0.288057i
$955$	5868.00	+	10163.7i	0.198831	+	0.344386i
$956$	−2754.00	−	4770.07i	−0.0931702	−	0.161376i
$957$	−6682.50	+	11574.4i	−0.225721	+	0.390959i
$958$	−45234.0			−1.52552
$959$	−30975.0	+	10730.1i	−1.04300	+	0.361305i
$960$	−3897.00			−0.131016
$961$	−17109.0	+	29633.7i	−0.574301	+	0.994718i
$962$	30336.0	+	52543.5i	1.01671	+	1.76099i
$963$	6088.50	+	10545.6i	0.203737	+	0.352884i
$964$	−395.500	+	685.026i	−0.0132139	+	0.0228871i
$965$	−4479.00			−0.149414
$966$	−10584.0	−	9166.01i	−0.352520	−	0.305292i
$967$	−38341.0			−1.27504			−0.637520	−	0.770434i	$-0.720040\pi$
$967$	−38341.0			−1.27504			−0.637520	+	0.770434i	$0.720040\pi$
$968$	11613.0	−	20114.3i	0.385595	−	0.667870i
$969$	2016.00	+	3491.81i	0.0668351	+	0.115762i
$970$	−2263.50	−	3920.50i	−0.0749243	−	0.129773i
$971$	−961.500	+	1665.37i	−0.0317776	+	0.0550403i	−0.881477	−	0.472227i	$-0.843450\pi$
$971$	−961.500	+	1665.37i	−0.0317776	+	0.0550403i	0.849699	+	0.527268i	$0.176783\pi$
$972$	243.000			0.00801875
$973$	5453.00	−	28334.6i	0.179666	−	0.933573i
$974$	−18663.0			−0.613964
$975$	−11136.0	+	19288.1i	−0.365782	+	0.633553i
$976$	−4189.00	−	7255.56i	−0.137384	−	0.237956i
$977$	−28545.0	−	49441.4i	−0.934734	−	1.61901i	−0.775107	−	0.631830i	$-0.782304\pi$
$977$	−28545.0	−	49441.4i	−0.934734	−	1.61901i	−0.159627	−	0.987177i	$-0.551029\pi$
$978$	−5634.00	+	9758.37i	−0.184208	+	0.319058i
$979$	−13590.0			−0.443655
$980$	955.500	+	381.917i	0.0311452	+	0.0124489i
$981$	−3330.00			−0.108378
$982$	−11056.5	+	19150.4i	−0.359294	+	0.622316i
$983$	−2742.00	−	4749.28i	−0.0889687	−	0.154098i	0.818107	−	0.575066i	$-0.195024\pi$
$983$	−2742.00	−	4749.28i	−0.0889687	−	0.154098i	−0.907075	+	0.420968i	$0.861690\pi$
$984$	−11340.0	−	19641.5i	−0.367384	−	0.636328i
$985$	−6129.00	+	10615.7i	−0.198260	+	0.343397i
$986$	74844.0			2.41736
$987$	315.000	−	1636.79i	0.0101586	−	0.0527858i
$988$	1024.00			0.0329735
$989$	1092.00	−	1891.40i	0.0351098	−	0.0608119i
$990$	607.500	+	1052.22i	0.0195026	+	0.0337796i
$991$	11232.5	+	19455.3i	0.360053	+	0.623629i	0.987969	−	0.154651i	$-0.0494254\pi$
$991$	11232.5	+	19455.3i	0.360053	+	0.623629i	−0.627917	+	0.778281i	$0.716092\pi$
$992$	5692.50	−	9859.70i	0.182195	−	0.315570i
$993$	−1452.00			−0.0464026
$994$	−14364.0	−	12439.6i	−0.458349	−	0.396941i
$995$	10668.0			0.339898
$996$	−715.500	+	1239.28i	−0.0227625	+	0.0394259i
$997$	−14683.0	−	25431.7i	−0.466415	−	0.807854i	0.532850	−	0.846210i	$-0.321121\pi$
$997$	−14683.0	−	25431.7i	−0.466415	−	0.807854i	−0.999264	+	0.0383563i	$0.987788\pi$
$998$	6411.00	+	11104.2i	0.203343	+	0.352201i
$999$	4266.00	−	7388.93i	0.135105	−	0.234009i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.4.e.a.16.1	yes	2
3.2	odd	2		63.4.e.a.37.1		2
4.3	odd	2		336.4.q.e.289.1		2
7.2	even	3		147.4.a.b.1.1		1
7.3	odd	6		147.4.e.h.67.1		2
7.4	even	3	inner	21.4.e.a.4.1	✓	2
7.5	odd	6		147.4.a.a.1.1		1
7.6	odd	2		147.4.e.h.79.1		2
21.2	odd	6		441.4.a.l.1.1		1
21.5	even	6		441.4.a.k.1.1		1
21.11	odd	6		63.4.e.a.46.1		2
21.17	even	6		441.4.e.c.361.1		2
21.20	even	2		441.4.e.c.226.1		2
28.11	odd	6		336.4.q.e.193.1		2
28.19	even	6		2352.4.a.bd.1.1		1
28.23	odd	6		2352.4.a.i.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.e.a.4.1	✓	2	7.4	even	3	inner
21.4.e.a.16.1	yes	2	1.1	even	1	trivial
63.4.e.a.37.1		2	3.2	odd	2
63.4.e.a.46.1		2	21.11	odd	6
147.4.a.a.1.1		1	7.5	odd	6
147.4.a.b.1.1		1	7.2	even	3
147.4.e.h.67.1		2	7.3	odd	6
147.4.e.h.79.1		2	7.6	odd	2
336.4.q.e.193.1		2	28.11	odd	6
336.4.q.e.289.1		2	4.3	odd	2
441.4.a.k.1.1		1	21.5	even	6
441.4.a.l.1.1		1	21.2	odd	6
441.4.e.c.226.1		2	21.20	even	2
441.4.e.c.361.1		2	21.17	even	6
2352.4.a.i.1.1		1	28.23	odd	6
2352.4.a.bd.1.1		1	28.19	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	21.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 2.59808i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} -9.00000 q^{6} +(-3.50000 + 18.1865i) q^{7} +21.0000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.50000 - 2.59808i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} -9.00000 q^{6} +(-3.50000 + 18.1865i) q^{7} +21.0000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-4.50000 - 7.79423i) q^{10} +(7.50000 + 12.9904i) q^{11} +(-1.50000 + 2.59808i) q^{12} -64.0000 q^{13} +(42.0000 + 36.3731i) q^{14} -9.00000 q^{15} +(35.5000 - 61.4878i) q^{16} +(-42.0000 - 72.7461i) q^{17} +(13.5000 + 23.3827i) q^{18} +(8.00000 - 13.8564i) q^{19} -3.00000 q^{20} +(52.5000 - 18.1865i) q^{21} +45.0000 q^{22} +(42.0000 - 72.7461i) q^{23} +(-31.5000 - 54.5596i) q^{24} +(58.0000 + 100.459i) q^{25} +(-96.0000 + 166.277i) q^{26} +27.0000 q^{27} +(17.5000 - 6.06218i) q^{28} -297.000 q^{29} +(-13.5000 + 23.3827i) q^{30} +(126.500 + 219.104i) q^{31} +(-22.5000 - 38.9711i) q^{32} +(22.5000 - 38.9711i) q^{33} -252.000 q^{34} +(42.0000 + 36.3731i) q^{35} +9.00000 q^{36} +(158.000 - 273.664i) q^{37} +(-24.0000 - 41.5692i) q^{38} +(96.0000 + 166.277i) q^{39} +(31.5000 - 54.5596i) q^{40} +360.000 q^{41} +(31.5000 - 163.679i) q^{42} +26.0000 q^{43} +(7.50000 - 12.9904i) q^{44} +(13.5000 + 23.3827i) q^{45} +(-126.000 - 218.238i) q^{46} +(15.0000 - 25.9808i) q^{47} -213.000 q^{48} +(-318.500 - 127.306i) q^{49} +348.000 q^{50} +(-126.000 + 218.238i) q^{51} +(32.0000 + 55.4256i) q^{52} +(-181.500 - 314.367i) q^{53} +(40.5000 - 70.1481i) q^{54} +45.0000 q^{55} +(-73.5000 + 381.917i) q^{56} -48.0000 q^{57} +(-445.500 + 771.629i) q^{58} +(7.50000 + 12.9904i) q^{59} +(4.50000 + 7.79423i) q^{60} +(59.0000 - 102.191i) q^{61} +759.000 q^{62} +(-126.000 - 109.119i) q^{63} +433.000 q^{64} +(-96.0000 + 166.277i) q^{65} +(-67.5000 - 116.913i) q^{66} +(185.000 + 320.429i) q^{67} +(-42.0000 + 72.7461i) q^{68} -252.000 q^{69} +(157.500 - 54.5596i) q^{70} -342.000 q^{71} +(-94.5000 + 163.679i) q^{72} +(-181.000 - 313.501i) q^{73} +(-474.000 - 820.992i) q^{74} +(174.000 - 301.377i) q^{75} -16.0000 q^{76} +(-262.500 + 90.9327i) q^{77} +576.000 q^{78} +(-233.500 + 404.434i) q^{79} +(-106.500 - 184.463i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(540.000 - 935.307i) q^{82} +477.000 q^{83} +(-42.0000 - 36.3731i) q^{84} -252.000 q^{85} +(39.0000 - 67.5500i) q^{86} +(445.500 + 771.629i) q^{87} +(157.500 + 272.798i) q^{88} +(-453.000 + 784.619i) q^{89} +81.0000 q^{90} +(224.000 - 1163.94i) q^{91} -84.0000 q^{92} +(379.500 - 657.313i) q^{93} +(-45.0000 - 77.9423i) q^{94} +(-24.0000 - 41.5692i) q^{95} +(-67.5000 + 116.913i) q^{96} +503.000 q^{97} +(-808.500 + 636.529i) q^{98} -135.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} - 3 q^{3} - q^{4} + 3 q^{5} - 18 q^{6} - 7 q^{7} + 42 q^{8} - 9 q^{9}+O(q^{10}) \) 2 * q + 3 * q^2 - 3 * q^3 - q^4 + 3 * q^5 - 18 * q^6 - 7 * q^7 + 42 * q^8 - 9 * q^9	\( 2 q + 3 q^{2} - 3 q^{3} - q^{4} + 3 q^{5} - 18 q^{6} - 7 q^{7} + 42 q^{8} - 9 q^{9} - 9 q^{10} + 15 q^{11} - 3 q^{12} - 128 q^{13} + 84 q^{14} - 18 q^{15} + 71 q^{16} - 84 q^{17} + 27 q^{18} + 16 q^{19} - 6 q^{20} + 105 q^{21} + 90 q^{22} + 84 q^{23} - 63 q^{24} + 116 q^{25} - 192 q^{26} + 54 q^{27} + 35 q^{28} - 594 q^{29} - 27 q^{30} + 253 q^{31} - 45 q^{32} + 45 q^{33} - 504 q^{34} + 84 q^{35} + 18 q^{36} + 316 q^{37} - 48 q^{38} + 192 q^{39} + 63 q^{40} + 720 q^{41} + 63 q^{42} + 52 q^{43} + 15 q^{44} + 27 q^{45} - 252 q^{46} + 30 q^{47} - 426 q^{48} - 637 q^{49} + 696 q^{50} - 252 q^{51} + 64 q^{52} - 363 q^{53} + 81 q^{54} + 90 q^{55} - 147 q^{56} - 96 q^{57} - 891 q^{58} + 15 q^{59} + 9 q^{60} + 118 q^{61} + 1518 q^{62} - 252 q^{63} + 866 q^{64} - 192 q^{65} - 135 q^{66} + 370 q^{67} - 84 q^{68} - 504 q^{69} + 315 q^{70} - 684 q^{71} - 189 q^{72} - 362 q^{73} - 948 q^{74} + 348 q^{75} - 32 q^{76} - 525 q^{77} + 1152 q^{78} - 467 q^{79} - 213 q^{80} - 81 q^{81} + 1080 q^{82} + 954 q^{83} - 84 q^{84} - 504 q^{85} + 78 q^{86} + 891 q^{87} + 315 q^{88} - 906 q^{89} + 162 q^{90} + 448 q^{91} - 168 q^{92} + 759 q^{93} - 90 q^{94} - 48 q^{95} - 135 q^{96} + 1006 q^{97} - 1617 q^{98} - 270 q^{99}+O(q^{100}) \) 2 * q + 3 * q^2 - 3 * q^3 - q^4 + 3 * q^5 - 18 * q^6 - 7 * q^7 + 42 * q^8 - 9 * q^9 - 9 * q^10 + 15 * q^11 - 3 * q^12 - 128 * q^13 + 84 * q^14 - 18 * q^15 + 71 * q^16 - 84 * q^17 + 27 * q^18 + 16 * q^19 - 6 * q^20 + 105 * q^21 + 90 * q^22 + 84 * q^23 - 63 * q^24 + 116 * q^25 - 192 * q^26 + 54 * q^27 + 35 * q^28 - 594 * q^29 - 27 * q^30 + 253 * q^31 - 45 * q^32 + 45 * q^33 - 504 * q^34 + 84 * q^35 + 18 * q^36 + 316 * q^37 - 48 * q^38 + 192 * q^39 + 63 * q^40 + 720 * q^41 + 63 * q^42 + 52 * q^43 + 15 * q^44 + 27 * q^45 - 252 * q^46 + 30 * q^47 - 426 * q^48 - 637 * q^49 + 696 * q^50 - 252 * q^51 + 64 * q^52 - 363 * q^53 + 81 * q^54 + 90 * q^55 - 147 * q^56 - 96 * q^57 - 891 * q^58 + 15 * q^59 + 9 * q^60 + 118 * q^61 + 1518 * q^62 - 252 * q^63 + 866 * q^64 - 192 * q^65 - 135 * q^66 + 370 * q^67 - 84 * q^68 - 504 * q^69 + 315 * q^70 - 684 * q^71 - 189 * q^72 - 362 * q^73 - 948 * q^74 + 348 * q^75 - 32 * q^76 - 525 * q^77 + 1152 * q^78 - 467 * q^79 - 213 * q^80 - 81 * q^81 + 1080 * q^82 + 954 * q^83 - 84 * q^84 - 504 * q^85 + 78 * q^86 + 891 * q^87 + 315 * q^88 - 906 * q^89 + 162 * q^90 + 448 * q^91 - 168 * q^92 + 759 * q^93 - 90 * q^94 - 48 * q^95 - 135 * q^96 + 1006 * q^97 - 1617 * q^98 - 270 * q^99

Introduction

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