LMFDB - Embedded newform 56.3.g.b.43.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [56,3,Mod(43,56)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(56, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("56.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 56 = 2^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	56.g (of order $2$, degree $1$, 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:	$1.52588948042$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.292213762624.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} - 2x^{5} + 24x^{4} - 8x^{3} - 32x^{2} - 64x + 256 $ x^8 - x^7 - 2x^6 - 2x^5 + 24x^4 - 8x^3 - 32x^2 - 64x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			43.6
Root			$1.37098 - 1.45617i$ of defining polynomial
Character	$\chi$	$=$	56.43
Dual form			56.3.g.b.43.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37098 + 1.45617i) q^{2} -5.22363 q^{3} +(-0.240837 + 3.99274i) q^{4} +6.26788i q^{5} +(-7.16148 - 7.60647i) q^{6} -2.64575i q^{7} +(-6.14428 + 5.12327i) q^{8} +18.2863 q^{9} +O(q^{10})$	\(q+(1.37098 + 1.45617i) q^{2} -5.22363 q^{3} +(-0.240837 + 3.99274i) q^{4} +6.26788i q^{5} +(-7.16148 - 7.60647i) q^{6} -2.64575i q^{7} +(-6.14428 + 5.12327i) q^{8} +18.2863 q^{9} +(-9.12707 + 8.59313i) q^{10} +9.80688 q^{11} +(1.25804 - 20.8566i) q^{12} +2.41653i q^{13} +(3.85265 - 3.62727i) q^{14} -32.7411i q^{15} +(-15.8840 - 1.92320i) q^{16} +6.89452 q^{17} +(25.0701 + 26.6279i) q^{18} +2.77637 q^{19} +(-25.0260 - 1.50954i) q^{20} +13.8204i q^{21} +(13.4450 + 14.2804i) q^{22} +42.8332i q^{23} +(32.0954 - 26.7620i) q^{24} -14.2863 q^{25} +(-3.51887 + 3.31301i) q^{26} -48.5083 q^{27} +(10.5638 + 0.637195i) q^{28} -37.3505i q^{29} +(47.6764 - 44.8873i) q^{30} -7.16835i q^{31} +(-18.9761 - 25.7664i) q^{32} -51.2275 q^{33} +(9.45224 + 10.0396i) q^{34} +16.5833 q^{35} +(-4.40402 + 73.0126i) q^{36} -0.202653i q^{37} +(3.80634 + 4.04285i) q^{38} -12.6231i q^{39} +(-32.1120 - 38.5116i) q^{40} +63.5494 q^{41} +(-20.1248 + 18.9475i) q^{42} -35.3384 q^{43} +(-2.36186 + 39.1564i) q^{44} +114.616i q^{45} +(-62.3723 + 58.7234i) q^{46} -37.9129i q^{47} +(82.9721 + 10.0461i) q^{48} -7.00000 q^{49} +(-19.5862 - 20.8032i) q^{50} -36.0144 q^{51} +(-9.64858 - 0.581989i) q^{52} -54.6651i q^{53} +(-66.5038 - 70.6361i) q^{54} +61.4684i q^{55} +(13.5549 + 16.2562i) q^{56} -14.5027 q^{57} +(54.3885 - 51.2067i) q^{58} +104.795 q^{59} +(130.727 + 7.88526i) q^{60} +43.7668i q^{61} +(10.4383 - 9.82765i) q^{62} -48.3810i q^{63} +(11.5043 - 62.9575i) q^{64} -15.1465 q^{65} +(-70.2318 - 74.5958i) q^{66} +31.1021 q^{67} +(-1.66046 + 27.5281i) q^{68} -223.745i q^{69} +(22.7353 + 24.1480i) q^{70} +23.1294i q^{71} +(-112.356 + 93.6857i) q^{72} -69.2275 q^{73} +(0.295096 - 0.277832i) q^{74} +74.6264 q^{75} +(-0.668652 + 11.0853i) q^{76} -25.9466i q^{77} +(18.3813 - 17.3059i) q^{78} +19.9328i q^{79} +(12.0544 - 99.5590i) q^{80} +88.8125 q^{81} +(87.1249 + 92.5385i) q^{82} -5.11617 q^{83} +(-55.1814 - 3.32847i) q^{84} +43.2140i q^{85} +(-48.4482 - 51.4585i) q^{86} +195.105i q^{87} +(-60.2562 + 50.2433i) q^{88} -17.9889 q^{89} +(-166.901 + 157.137i) q^{90} +6.39353 q^{91} +(-171.022 - 10.3158i) q^{92} +37.4448i q^{93} +(55.2075 - 51.9778i) q^{94} +17.4019i q^{95} +(99.1242 + 134.594i) q^{96} +12.4864 q^{97} +(-9.59685 - 10.1932i) q^{98} +179.332 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 8 q^{3} + 5 q^{4} - 22 q^{6} + 13 q^{8} + 48 q^{9}+O(q^{10}) $ 8 * q + q^2 - 8 * q^3 + 5 * q^4 - 22 * q^6 + 13 * q^8 + 48 * q^9	$ 8 q + q^{2} - 8 q^{3} + 5 q^{4} - 22 q^{6} + 13 q^{8} + 48 q^{9} + 16 q^{10} - 32 q^{11} + 30 q^{12} + 7 q^{14} - 71 q^{16} - 80 q^{17} - 29 q^{18} + 56 q^{19} - 108 q^{20} + 66 q^{22} + 22 q^{24} - 16 q^{25} + 24 q^{26} - 32 q^{27} + 7 q^{28} + 96 q^{30} - 19 q^{32} + 32 q^{33} + 74 q^{34} + 56 q^{35} - 33 q^{36} - 14 q^{38} + 84 q^{40} + 128 q^{41} - 98 q^{42} + 50 q^{44} - 152 q^{46} + 134 q^{48} - 56 q^{49} + 33 q^{50} - 368 q^{51} + 132 q^{52} - 228 q^{54} - 49 q^{56} + 56 q^{57} + 24 q^{58} + 104 q^{59} + 192 q^{60} + 120 q^{62} - 55 q^{64} - 72 q^{65} - 276 q^{66} + 304 q^{67} - 190 q^{68} + 56 q^{70} - 209 q^{72} - 112 q^{73} + 8 q^{74} + 72 q^{75} + 70 q^{76} - 304 q^{78} + 124 q^{80} + 48 q^{81} + 450 q^{82} + 72 q^{83} + 42 q^{84} + 210 q^{86} - 486 q^{88} - 512 q^{89} - 184 q^{90} - 56 q^{91} - 472 q^{92} + 472 q^{94} + 558 q^{96} + 64 q^{97} - 7 q^{98} + 256 q^{99}+O(q^{100}) $ 8 * q + q^2 - 8 * q^3 + 5 * q^4 - 22 * q^6 + 13 * q^8 + 48 * q^9 + 16 * q^10 - 32 * q^11 + 30 * q^12 + 7 * q^14 - 71 * q^16 - 80 * q^17 - 29 * q^18 + 56 * q^19 - 108 * q^20 + 66 * q^22 + 22 * q^24 - 16 * q^25 + 24 * q^26 - 32 * q^27 + 7 * q^28 + 96 * q^30 - 19 * q^32 + 32 * q^33 + 74 * q^34 + 56 * q^35 - 33 * q^36 - 14 * q^38 + 84 * q^40 + 128 * q^41 - 98 * q^42 + 50 * q^44 - 152 * q^46 + 134 * q^48 - 56 * q^49 + 33 * q^50 - 368 * q^51 + 132 * q^52 - 228 * q^54 - 49 * q^56 + 56 * q^57 + 24 * q^58 + 104 * q^59 + 192 * q^60 + 120 * q^62 - 55 * q^64 - 72 * q^65 - 276 * q^66 + 304 * q^67 - 190 * q^68 + 56 * q^70 - 209 * q^72 - 112 * q^73 + 8 * q^74 + 72 * q^75 + 70 * q^76 - 304 * q^78 + 124 * q^80 + 48 * q^81 + 450 * q^82 + 72 * q^83 + 42 * q^84 + 210 * q^86 - 486 * q^88 - 512 * q^89 - 184 * q^90 - 56 * q^91 - 472 * q^92 + 472 * q^94 + 558 * q^96 + 64 * q^97 - 7 * q^98 + 256 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/56\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$29$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	1.37098	+	1.45617i	0.685489	+	0.728083i
$2$	1.37098	+	1.45617i	0.685489	+	0.728083i
$3$	−5.22363			−1.74121			−0.870605	−	0.491982i	$-0.836272\pi$
$3$	−5.22363			−1.74121			−0.870605	+	0.491982i	$0.836272\pi$
$4$	−0.240837	+	3.99274i	−0.0602092	+	0.998186i
$5$			6.26788i			1.25358i	0.779190	+	0.626788i	$0.215631\pi$
$5$			6.26788i			1.25358i	−0.779190	+	0.626788i	$0.784369\pi$
$6$	−7.16148	−	7.60647i	−1.19358	−	1.26775i
$7$		−	2.64575i		−	0.377964i
$7$		−	2.64575i		−	0.377964i
$8$	−6.14428	+	5.12327i	−0.768035	+	0.640408i
$9$	18.2863			2.03181
$10$	−9.12707	+	8.59313i	−0.912707	+	0.859313i
$11$	9.80688			0.891535			0.445767	−	0.895149i	$-0.352931\pi$
$11$	9.80688			0.891535			0.445767	+	0.895149i	$0.352931\pi$
$12$	1.25804	−	20.8566i	0.104837	−	1.73805i
$13$			2.41653i			0.185887i	0.995671	+	0.0929434i	$0.0296276\pi$
$13$			2.41653i			0.185887i	−0.995671	+	0.0929434i	$0.970372\pi$
$14$	3.85265	−	3.62727i	0.275189	−	0.259091i
$15$		−	32.7411i		−	2.18274i
$16$	−15.8840	−	1.92320i	−0.992750	−	0.120200i
$17$	6.89452			0.405560			0.202780	−	0.979224i	$-0.435002\pi$
$17$	6.89452			0.405560			0.202780	+	0.979224i	$0.435002\pi$
$18$	25.0701	+	26.6279i	1.39279	+	1.47933i
$19$	2.77637			0.146125			0.0730624	−	0.997327i	$-0.476723\pi$
$19$	2.77637			0.146125			0.0730624	+	0.997327i	$0.476723\pi$
$20$	−25.0260	−	1.50954i	−1.25130	−	0.0754769i
$21$			13.8204i			0.658116i
$22$	13.4450	+	14.2804i	0.611137	+	0.649111i
$23$			42.8332i			1.86231i	0.364617	+	0.931157i	$0.381200\pi$
$23$			42.8332i			1.86231i	−0.364617	+	0.931157i	$0.618800\pi$
$24$	32.0954	−	26.7620i	1.33731	−	1.11509i
$25$	−14.2863			−0.571453
$26$	−3.51887	+	3.31301i	−0.135341	+	0.127423i
$27$	−48.5083			−1.79660
$28$	10.5638	+	0.637195i	0.377279	+	0.0227570i
$29$		−	37.3505i		−	1.28795i	−0.765048	−	0.643974i	$-0.777285\pi$
$29$		−	37.3505i		−	1.28795i	0.765048	−	0.643974i	$-0.222715\pi$
$30$	47.6764	−	44.8873i	1.58921	−	1.49624i
$31$		−	7.16835i		−	0.231237i	−0.993294	−	0.115619i	$-0.963115\pi$
$31$		−	7.16835i		−	0.231237i	0.993294	−	0.115619i	$-0.0368850\pi$
$32$	−18.9761	−	25.7664i	−0.593004	−	0.805200i
$33$	−51.2275			−1.55235
$34$	9.45224	+	10.0396i	0.278007	+	0.295281i
$35$	16.5833			0.473807
$36$	−4.40402	+	73.0126i	−0.122334	+	2.02813i
$37$		−	0.202653i		−	0.00547709i	−0.999996	−	0.00273855i	$-0.999128\pi$
$37$		−	0.202653i		−	0.00547709i	0.999996	−	0.00273855i	$-0.000871708\pi$
$38$	3.80634	+	4.04285i	0.100167	+	0.106391i
$39$		−	12.6231i		−	0.323668i
$40$	−32.1120	−	38.5116i	−0.802800	−	0.962790i
$41$	63.5494			1.54999			0.774993	−	0.631970i	$-0.217753\pi$
$41$	63.5494			1.54999			0.774993	+	0.631970i	$0.217753\pi$
$42$	−20.1248	+	18.9475i	−0.479163	+	0.451131i
$43$	−35.3384			−0.821823			−0.410911	−	0.911675i	$-0.634789\pi$
$43$	−35.3384			−0.821823			−0.410911	+	0.911675i	$0.634789\pi$
$44$	−2.36186	+	39.1564i	−0.0536786	+	0.889917i
$45$			114.616i			2.54703i
$46$	−62.3723	+	58.7234i	−1.35592	+	1.27660i
$47$		−	37.9129i		−	0.806657i	−0.915055	−	0.403329i	$-0.867853\pi$
$47$		−	37.9129i		−	0.806657i	0.915055	−	0.403329i	$-0.132147\pi$
$48$	82.9721	+	10.0461i	1.72859	+	0.209294i
$49$	−7.00000			−0.142857
$50$	−19.5862	−	20.8032i	−0.391725	−	0.416065i
$51$	−36.0144			−0.706165
$52$	−9.64858	−	0.581989i	−0.185550	−	0.0111921i
$53$		−	54.6651i		−	1.03142i	−0.856764	−	0.515709i	$-0.827529\pi$
$53$		−	54.6651i		−	1.03142i	0.856764	−	0.515709i	$-0.172471\pi$
$54$	−66.5038	−	70.6361i	−1.23155	−	1.30808i
$55$			61.4684i			1.11761i
$56$	13.5549	+	16.2562i	0.242052	+	0.290290i
$57$	−14.5027			−0.254434
$58$	54.3885	−	51.2067i	0.937732	−	0.882874i
$59$	104.795			1.77619			0.888093	−	0.459665i	$-0.152030\pi$
$59$	104.795			1.77619			0.888093	+	0.459665i	$0.152030\pi$
$60$	130.727	+	7.88526i	2.17878	+	0.131421i
$61$			43.7668i			0.717489i	0.933436	+	0.358745i	$0.116795\pi$
$61$			43.7668i			0.717489i	−0.933436	+	0.358745i	$0.883205\pi$
$62$	10.4383	−	9.82765i	0.168360	−	0.158511i
$63$		−	48.3810i		−	0.767953i
$64$	11.5043	−	62.9575i	0.179755	−	0.983711i
$65$	−15.1465			−0.233023
$66$	−70.2318	−	74.5958i	−1.06412	−	1.13024i
$67$	31.1021			0.464210			0.232105	−	0.972691i	$-0.425439\pi$
$67$	31.1021			0.464210			0.232105	+	0.972691i	$0.425439\pi$
$68$	−1.66046	+	27.5281i	−0.0244185	+	0.404824i
$69$		−	223.745i		−	3.24268i
$70$	22.7353	+	24.1480i	0.324790	+	0.344971i
$71$			23.1294i			0.325766i	0.986645	+	0.162883i	$0.0520794\pi$
$71$			23.1294i			0.325766i	−0.986645	+	0.162883i	$0.947921\pi$
$72$	−112.356	+	93.6857i	−1.56050	+	1.30119i
$73$	−69.2275			−0.948322			−0.474161	−	0.880438i	$-0.657249\pi$
$73$	−69.2275			−0.948322			−0.474161	+	0.880438i	$0.657249\pi$
$74$	0.295096	−	0.277832i	0.00398778	−	0.00375449i
$75$	74.6264			0.995019
$76$	−0.668652	+	11.0853i	−0.00879806	+	0.145860i
$77$		−	25.9466i		−	0.336968i
$78$	18.3813	−	17.3059i	0.235657	−	0.221871i
$79$			19.9328i			0.252315i	0.992010	+	0.126157i	$0.0402644\pi$
$79$			19.9328i			0.252315i	−0.992010	+	0.126157i	$0.959736\pi$
$80$	12.0544	−	99.5590i	0.150680	−	1.24449i
$81$	88.8125			1.09645
$82$	87.1249	+	92.5385i	1.06250	+	1.12852i
$83$	−5.11617			−0.0616406			−0.0308203	−	0.999525i	$-0.509812\pi$
$83$	−5.11617			−0.0616406			−0.0308203	+	0.999525i	$0.509812\pi$
$84$	−55.1814	−	3.32847i	−0.656922	−	0.0396246i
$85$			43.2140i			0.508400i
$86$	−48.4482	−	51.4585i	−0.563351	−	0.598355i
$87$			195.105i			2.24259i
$88$	−60.2562	+	50.2433i	−0.684730	+	0.570946i
$89$	−17.9889			−0.202122			−0.101061	−	0.994880i	$-0.532224\pi$
$89$	−17.9889			−0.202122			−0.101061	+	0.994880i	$0.532224\pi$
$90$	−166.901	+	157.137i	−1.85445	+	1.74596i
$91$	6.39353			0.0702586
$92$	−171.022	−	10.3158i	−1.85894	−	0.112129i
$93$			37.4448i			0.402632i
$94$	55.2075	−	51.9778i	0.587313	−	0.552955i
$95$			17.4019i			0.183178i
$96$	99.1242	+	134.594i	1.03254	+	1.40202i
$97$	12.4864			0.128726			0.0643629	−	0.997927i	$-0.479498\pi$
$97$	12.4864			0.128726			0.0643629	+	0.997927i	$0.479498\pi$
$98$	−9.59685	−	10.1932i	−0.0979270	−	0.104012i
$99$	179.332			1.81143
$100$	3.44067	−	57.0416i	0.0344067	−	0.570416i
$101$		−	68.0753i		−	0.674013i	−0.941502	−	0.337006i	$-0.890586\pi$
$101$		−	68.0753i		−	0.674013i	0.941502	−	0.337006i	$-0.109414\pi$
$102$	−49.3750	−	52.4430i	−0.484069	−	0.514147i
$103$		−	58.2931i		−	0.565952i	−0.959127	−	0.282976i	$-0.908678\pi$
$103$		−	58.2931i		−	0.565952i	0.959127	−	0.282976i	$-0.0913217\pi$
$104$	−12.3805	−	14.8478i	−0.119043	−	0.142768i
$105$	−86.6248			−0.824998
$106$	79.6015	−	74.9447i	0.750957	−	0.707026i
$107$	135.868			1.26979			0.634897	−	0.772597i	$-0.281043\pi$
$107$	135.868			1.26979			0.634897	+	0.772597i	$0.281043\pi$
$108$	11.6826	−	193.681i	0.108172	−	1.79334i
$109$			44.4981i			0.408239i	0.978946	+	0.204120i	$0.0654332\pi$
$109$			44.4981i			0.408239i	−0.978946	+	0.204120i	$0.934567\pi$
$110$	−89.5081	+	84.2718i	−0.813710	+	0.766107i
$111$			1.05858i			0.00953677i
$112$	−5.08831	+	42.0251i	−0.0454313	+	0.375224i
$113$	−133.391			−1.18045			−0.590224	−	0.807240i	$-0.700961\pi$
$113$	−133.391			−1.18045			−0.590224	+	0.807240i	$0.700961\pi$
$114$	−19.8829	−	21.1184i	−0.174412	−	0.185249i
$115$	−268.474			−2.33455
$116$	149.131	+	8.99537i	1.28561	+	0.0775463i
$117$			44.1894i			0.377687i
$118$	143.672	+	152.599i	1.21756	+	1.29321i
$119$		−	18.2412i		−	0.153287i
$120$	167.741	+	201.170i	1.39784	+	1.67642i
$121$	−24.8251			−0.205166
$122$	−63.7318	+	60.0034i	−0.522392	+	0.491831i
$123$	−331.959			−2.69885
$124$	28.6214	+	1.72640i	0.230818	+	0.0139226i
$125$			67.1521i			0.537217i
$126$	70.4508	−	66.3294i	0.559133	−	0.526424i
$127$		−	130.977i		−	1.03131i	−0.856795	−	0.515657i	$-0.827548\pi$
$127$		−	130.977i		−	1.03131i	0.856795	−	0.515657i	$-0.172452\pi$
$128$	107.449	−	69.5612i	0.839443	−	0.543447i
$129$	184.595			1.43097
$130$	−20.7655	−	22.0558i	−0.159735	−	0.169660i
$131$	−53.3311			−0.407108			−0.203554	−	0.979064i	$-0.565249\pi$
$131$	−53.3311			−0.407108			−0.203554	+	0.979064i	$0.565249\pi$
$132$	12.3375	−	204.538i	0.0934658	−	1.54953i
$133$		−	7.34558i		−	0.0552299i
$134$	42.6403	+	45.2898i	0.318211	+	0.337983i
$135$		−	304.044i		−	2.25218i
$136$	−42.3619	+	35.3225i	−0.311484	+	0.259724i
$137$	−57.7179			−0.421299			−0.210649	−	0.977562i	$-0.567558\pi$
$137$	−57.7179			−0.421299			−0.210649	+	0.977562i	$0.567558\pi$
$138$	325.810	−	306.750i	2.36094	−	2.22282i
$139$	−172.422			−1.24045			−0.620224	−	0.784425i	$-0.712958\pi$
$139$	−172.422			−1.24045			−0.620224	+	0.784425i	$0.712958\pi$
$140$	−3.99386	+	66.2127i	−0.0285276	+	0.472948i
$141$			198.043i			1.40456i
$142$	−33.6803	+	31.7099i	−0.237185	+	0.223309i
$143$			23.6986i			0.165725i
$144$	−290.460	−	35.1682i	−2.01708	−	0.244224i
$145$	234.108			1.61454
$146$	−94.9094	−	100.807i	−0.650065	−	0.690457i
$147$	36.5654			0.248744
$148$	0.809139	+	0.0488062i	0.00546716	+	0.000329772i
$149$			219.529i			1.47335i	0.676249	+	0.736673i	$0.263604\pi$
$149$			219.529i			1.47335i	−0.676249	+	0.736673i	$0.736396\pi$
$150$	102.311	+	108.668i	0.682075	+	0.724456i
$151$		−	185.668i		−	1.22959i	−0.788687	−	0.614795i	$-0.789239\pi$
$151$		−	185.668i		−	1.22959i	0.788687	−	0.614795i	$-0.210761\pi$
$152$	−17.0588	+	14.2241i	−0.112229	+	0.0935795i
$153$	126.075			0.824022
$154$	37.7825	−	35.5722i	0.245341	−	0.230988i
$155$	44.9304			0.289873
$156$	50.4006	+	3.04010i	0.323081	+	0.0194878i
$157$		−	188.182i		−	1.19861i	−0.800521	−	0.599305i	$-0.795444\pi$
$157$		−	188.182i		−	1.19861i	0.800521	−	0.599305i	$-0.204556\pi$
$158$	−29.0255	+	27.3275i	−0.183706	+	0.172959i
$159$			285.550i			1.79591i
$160$	161.501	−	118.940i	1.00938	−	0.743375i
$161$	113.326			0.703889
$162$	121.760	+	129.326i	0.751605	+	0.798307i
$163$	54.5154			0.334450			0.167225	−	0.985919i	$-0.446519\pi$
$163$	54.5154			0.334450			0.167225	+	0.985919i	$0.446519\pi$
$164$	−15.3050	+	253.736i	−0.0933235	+	1.54717i
$165$		−	321.088i		−	1.94599i
$166$	−7.01416	−	7.45000i	−0.0422540	−	0.0448795i
$167$			266.435i			1.59542i	0.603042	+	0.797709i	$0.293955\pi$
$167$			266.435i			1.59542i	−0.603042	+	0.797709i	$0.706045\pi$
$168$	−70.8057	−	84.9165i	−0.421463	−	0.505456i
$169$	163.160			0.965446
$170$	−62.9268	+	59.2455i	−0.370158	+	0.348503i
$171$	50.7696			0.296898
$172$	8.51079	−	141.097i	0.0494813	−	0.820332i
$173$			114.835i			0.663786i	0.943317	+	0.331893i	$0.107687\pi$
$173$			114.835i			0.663786i	−0.943317	+	0.331893i	$0.892313\pi$
$174$	−284.105	+	267.485i	−1.63279	+	1.53727i
$175$			37.7980i			0.215989i
$176$	−155.772	−	18.8606i	−0.885071	−	0.107162i
$177$	−547.410			−3.09271
$178$	−24.6624	−	26.1948i	−0.138553	−	0.147162i
$179$	112.849			0.630439			0.315220	−	0.949019i	$-0.397922\pi$
$179$	112.849			0.630439			0.315220	+	0.949019i	$0.397922\pi$
$180$	−457.634	−	27.6039i	−2.54241	−	0.153355i
$181$			60.9470i			0.336724i	0.985725	+	0.168362i	$0.0538477\pi$
$181$			60.9470i			0.336724i	−0.985725	+	0.168362i	$0.946152\pi$
$182$	8.76539	+	9.31004i	0.0481615	+	0.0511541i
$183$		−	228.622i		−	1.24930i
$184$	−219.446	−	263.179i	−1.19264	−	1.43032i
$185$	1.27020			0.00686595
$186$	−54.5258	+	51.3360i	−0.293150	+	0.276000i
$187$	67.6138			0.361571
$188$	151.376	+	9.13083i	0.805194	+	0.0485682i
$189$			128.341i			0.679052i
$190$	−25.3401	+	23.8577i	−0.133369	+	0.125567i
$191$		−	178.459i		−	0.934342i	−0.884167	−	0.467171i	$-0.845273\pi$
$191$		−	178.459i		−	0.934342i	0.884167	−	0.467171i	$-0.154727\pi$
$192$	−60.0942	+	328.867i	−0.312991	+	1.71285i
$193$	221.588			1.14812			0.574062	−	0.818812i	$-0.305367\pi$
$193$	221.588			1.14812			0.574062	+	0.818812i	$0.305367\pi$
$194$	17.1186	+	18.1823i	0.0882402	+	0.0937231i
$195$	79.1198			0.405742
$196$	1.68586	−	27.9492i	0.00860132	−	0.142598i
$197$		−	242.298i		−	1.22994i	−0.788550	−	0.614970i	$-0.789168\pi$
$197$		−	242.298i		−	1.22994i	0.788550	−	0.614970i	$-0.210832\pi$
$198$	245.860	+	261.137i	1.24172	+	1.31887i
$199$		−	297.047i		−	1.49270i	−0.665555	−	0.746349i	$-0.731805\pi$
$199$		−	297.047i		−	1.49270i	0.665555	−	0.746349i	$-0.268195\pi$
$200$	87.7791	−	73.1926i	0.438895	−	0.365963i
$201$	−162.466			−0.808287
$202$	99.1289	−	93.3297i	0.490737	−	0.462028i
$203$	−98.8201			−0.486798
$204$	8.67361	−	143.796i	0.0425177	−	0.704884i
$205$			398.320i			1.94302i
$206$	84.8844	−	79.9186i	0.412060	−	0.387954i
$207$			783.262i			3.78388i
$208$	4.64747	−	38.3841i	0.0223436	−	0.184539i
$209$	27.2275			0.130275
$210$	−118.761	−	126.140i	−0.565527	−	0.600667i
$211$	−141.020			−0.668341			−0.334171	−	0.942513i	$-0.608456\pi$
$211$	−141.020			−0.668341			−0.334171	+	0.942513i	$0.608456\pi$
$212$	218.264	+	13.1654i	1.02955	+	0.0621009i
$213$		−	120.820i		−	0.567228i
$214$	186.272	+	197.846i	0.870430	+	0.924515i
$215$		−	221.497i		−	1.03022i
$216$	298.048	−	248.521i	1.37985	−	1.15056i
$217$	−18.9657			−0.0873994
$218$	−64.7966	+	61.0059i	−0.297232	+	0.279844i
$219$	361.619			1.65123
$220$	−245.427	−	14.8039i	−1.11558	−	0.0672902i
$221$			16.6608i			0.0753883i
$222$	−1.54147	+	1.45129i	−0.00694356	+	0.00653735i
$223$		−	40.8267i		−	0.183079i	−0.995801	−	0.0915396i	$-0.970821\pi$
$223$		−	40.8267i		−	0.183079i	0.995801	−	0.0915396i	$-0.0291788\pi$
$224$	−68.1715	+	50.2061i	−0.304337	+	0.224134i
$225$	−261.244			−1.16108
$226$	−182.876	−	194.239i	−0.809184	−	0.859464i
$227$	8.18598			0.0360616			0.0180308	−	0.999837i	$-0.494260\pi$
$227$	8.18598			0.0360616			0.0180308	+	0.999837i	$0.494260\pi$
$228$	3.49279	−	57.9057i	0.0153193	−	0.253972i
$229$		−	332.252i		−	1.45088i	−0.688285	−	0.725440i	$-0.741636\pi$
$229$		−	332.252i		−	1.45088i	0.688285	−	0.725440i	$-0.258364\pi$
$230$	−368.071	−	390.942i	−1.60031	−	1.69975i
$231$			135.535i			0.586733i
$232$	191.356	+	229.492i	0.824812	+	0.989188i
$233$	329.260			1.41314			0.706568	−	0.707646i	$-0.250243\pi$
$233$	329.260			1.41314			0.706568	+	0.707646i	$0.250243\pi$
$234$	−64.3471	+	60.5827i	−0.274988	+	0.258900i
$235$	237.633			1.01121
$236$	−25.2385	+	418.419i	−0.106943	+	1.77296i
$237$		−	104.122i		−	0.439333i
$238$	26.5622	−	25.0083i	0.111606	−	0.105077i
$239$			137.719i			0.576230i	0.957596	+	0.288115i	$0.0930286\pi$
$239$			137.719i			0.576230i	−0.957596	+	0.288115i	$0.906971\pi$
$240$	−62.9677	+	520.059i	−0.262365	+	2.16691i
$241$	201.854			0.837567			0.418783	−	0.908086i	$-0.362457\pi$
$241$	201.854			0.837567			0.418783	+	0.908086i	$0.362457\pi$
$242$	−34.0346	−	36.1494i	−0.140639	−	0.149378i
$243$	−27.3492			−0.112548
$244$	−174.750	−	10.5407i	−0.716188	−	0.0431995i
$245$		−	43.8752i		−	0.179082i
$246$	−455.108	−	483.387i	−1.85003	−	1.96499i
$247$			6.70917i			0.0271627i
$248$	36.7254	+	44.0443i	0.148086	+	0.177598i
$249$	26.7250			0.107329
$250$	−97.7846	+	92.0640i	−0.391138	+	0.368256i
$251$	−269.203			−1.07252			−0.536261	−	0.844052i	$-0.680164\pi$
$251$	−269.203			−1.07252			−0.536261	+	0.844052i	$0.680164\pi$
$252$	193.173	+	11.6519i	0.766560	+	0.0462379i
$253$			420.061i			1.66032i
$254$	190.724	−	179.566i	0.750881	−	0.706954i
$255$		−	225.734i		−	0.885232i
$256$	248.603	+	61.0962i	0.971104	+	0.238657i
$257$	−242.359			−0.943032			−0.471516	−	0.881858i	$-0.656293\pi$
$257$	−242.359			−0.943032			−0.471516	+	0.881858i	$0.656293\pi$
$258$	253.075	+	268.800i	0.980912	+	1.04186i
$259$	−0.536168			−0.00207015
$260$	3.64784	−	60.4761i	0.0140302	−	0.232600i
$261$		−	683.002i		−	2.61687i
$262$	−73.1158	−	77.6589i	−0.279068	−	0.296408i
$263$		−	33.8470i		−	0.128696i	−0.997928	−	0.0643479i	$-0.979503\pi$
$263$		−	33.8470i		−	0.128696i	0.997928	−	0.0643479i	$-0.0204967\pi$
$264$	314.756	−	262.452i	1.19226	−	0.994137i
$265$	342.634			1.29296
$266$	10.6964	−	10.0706i	0.0402120	−	0.0378595i
$267$	93.9673			0.351937
$268$	−7.49053	+	124.183i	−0.0279497	+	0.463368i
$269$		−	165.598i		−	0.615606i	−0.951450	−	0.307803i	$-0.900406\pi$
$269$		−	165.598i		−	0.615606i	0.951450	−	0.307803i	$-0.0995938\pi$
$270$	442.739	−	416.838i	1.63977	−	1.54384i
$271$		−	148.308i		−	0.547263i	−0.961835	−	0.273632i	$-0.911775\pi$
$271$		−	148.308i		−	0.547263i	0.961835	−	0.273632i	$-0.0882249\pi$
$272$	−109.513	−	13.2595i	−0.402620	−	0.0487483i
$273$	−33.3975			−0.122335
$274$	−79.1300	−	84.0468i	−0.288796	−	0.306740i
$275$	−140.104			−0.509470
$276$	893.356	+	53.8861i	3.23680	+	0.195239i
$277$			478.358i			1.72693i	0.504413	+	0.863463i	$0.331709\pi$
$277$			478.358i			1.72693i	−0.504413	+	0.863463i	$0.668291\pi$
$278$	−236.387	−	251.075i	−0.850314	−	0.903149i
$279$		−	131.083i		−	0.469830i
$280$	−101.892	+	84.9604i	−0.363900	+	0.303430i
$281$	−226.066			−0.804506			−0.402253	−	0.915528i	$-0.631773\pi$
$281$	−226.066			−0.804506			−0.402253	+	0.915528i	$0.631773\pi$
$282$	−288.383	+	271.513i	−1.02264	+	0.962811i
$283$	−254.628			−0.899745			−0.449873	−	0.893093i	$-0.648531\pi$
$283$	−254.628			−0.899745			−0.449873	+	0.893093i	$0.648531\pi$
$284$	−92.3498	−	5.57042i	−0.325175	−	0.0196142i
$285$		−	90.9014i		−	0.318952i
$286$	−34.5091	+	32.4903i	−0.120661	+	0.113602i
$287$		−	168.136i		−	0.585840i
$288$	−347.003	−	471.172i	−1.20487	−	1.63602i
$289$	−241.466			−0.835521
$290$	320.957	+	340.900i	1.10675	+	1.17552i
$291$	−65.2244			−0.224139
$292$	16.6725	−	276.408i	0.0570978	−	0.946602i
$293$			149.558i			0.510437i	0.966883	+	0.255218i	$0.0821474\pi$
$293$			149.558i			0.510437i	−0.966883	+	0.255218i	$0.917853\pi$
$294$	50.1304	+	53.2453i	0.170512	+	0.181106i
$295$			656.842i			2.22658i
$296$	1.03824	+	1.24515i	0.00350758	+	0.00420660i
$297$	−475.715			−1.60173
$298$	−319.670	+	300.969i	−1.07272	+	1.00996i
$299$	−103.508			−0.346180
$300$	−17.9728	+	297.964i	−0.0599094	+	0.993214i
$301$			93.4966i			0.310620i
$302$	270.363	−	254.547i	0.895243	−	0.842870i
$303$			355.600i			1.17360i
$304$	−44.0998	−	5.33951i	−0.145065	−	0.0175642i
$305$	−274.325			−0.899427
$306$	172.847	+	183.587i	0.564858	+	0.599957i
$307$	271.779			0.885272			0.442636	−	0.896701i	$-0.354043\pi$
$307$	271.779			0.885272			0.442636	+	0.896701i	$0.354043\pi$
$308$	103.598	+	6.24889i	0.336357	+	0.0202886i
$309$			304.502i			0.985442i
$310$	61.5985	+	65.4260i	0.198705	+	0.211052i
$311$			534.180i			1.71762i	0.512293	+	0.858811i	$0.328796\pi$
$311$			534.180i			1.71762i	−0.512293	+	0.858811i	$0.671204\pi$
$312$	64.6712	+	77.5595i	0.207280	+	0.248588i
$313$	−556.232			−1.77710			−0.888550	−	0.458780i	$-0.848287\pi$
$313$	−556.232			−1.77710			−0.888550	+	0.458780i	$0.848287\pi$
$314$	274.024	−	257.993i	0.872688	−	0.821634i
$315$	303.247			0.962688
$316$	−79.5867	−	4.80057i	−0.251857	−	0.0151917i
$317$		−	387.459i		−	1.22227i	−0.791527	−	0.611134i	$-0.790714\pi$
$317$		−	387.459i		−	1.22227i	0.791527	−	0.611134i	$-0.209286\pi$
$318$	−415.809	+	391.483i	−1.30757	+	1.23108i
$319$		−	366.292i		−	1.14825i
$320$	394.610	+	72.1076i	1.23316	+	0.225336i
$321$	−709.724			−2.21098
$322$	155.368	+	165.022i	0.482508	+	0.512489i
$323$	19.1417			0.0592624
$324$	−21.3893	+	354.606i	−0.0660165	+	1.09446i
$325$		−	34.5233i		−	0.106225i
$326$	74.7394	+	79.3834i	0.229262	+	0.243507i
$327$		−	232.442i		−	0.710830i
$328$	−390.465	+	325.581i	−1.19044	+	0.992624i
$329$	−100.308			−0.304888
$330$	467.557	−	440.205i	1.41684	−	1.33395i
$331$	−383.205			−1.15772			−0.578860	−	0.815427i	$-0.696502\pi$
$331$	−383.205			−1.15772			−0.578860	+	0.815427i	$0.696502\pi$
$332$	1.23216	−	20.4276i	0.00371134	−	0.0615288i
$333$		−	3.70577i		−	0.0111284i
$334$	−387.973	+	365.276i	−1.16160	+	1.09364i
$335$			194.944i			0.581923i
$336$	26.5795	−	219.524i	0.0791055	−	0.653344i
$337$	563.726			1.67278			0.836388	−	0.548138i	$-0.184663\pi$
$337$	563.726			1.67278			0.836388	+	0.548138i	$0.184663\pi$
$338$	223.689	+	237.589i	0.661803	+	0.702925i
$339$	696.783			2.05541
$340$	−172.543	−	10.4075i	−0.507478	−	0.0306104i
$341$		−	70.2992i		−	0.206156i
$342$	69.6040	+	73.9289i	0.203520	+	0.216166i
$343$			18.5203i			0.0539949i
$344$	217.129	−	181.048i	0.631188	−	0.526302i
$345$	1402.41			4.06495
$346$	−167.219	+	157.436i	−0.483291	+	0.455018i
$347$	51.5890			0.148671			0.0743357	−	0.997233i	$-0.476316\pi$
$347$	51.5890			0.148671			0.0743357	+	0.997233i	$0.476316\pi$
$348$	−779.004	−	46.9885i	−2.23852	−	0.135024i
$349$		−	586.383i		−	1.68018i	−0.542447	−	0.840090i	$-0.682502\pi$
$349$		−	586.383i		−	1.68018i	0.542447	−	0.840090i	$-0.317498\pi$
$350$	−55.0402	+	51.8203i	−0.157258	+	0.148058i
$351$		−	117.222i		−	0.333965i
$352$	−186.097	−	252.688i	−0.528683	−	0.717864i
$353$	303.844			0.860746			0.430373	−	0.902651i	$-0.358382\pi$
$353$	303.844			0.860746			0.430373	+	0.902651i	$0.358382\pi$
$354$	−750.487	−	797.120i	−2.12002	−	2.25175i
$355$	−144.972			−0.408373
$356$	4.33239	−	71.8250i	0.0121696	−	0.201756i
$357$			95.2852i			0.266905i
$358$	154.713	+	164.326i	0.432159	+	0.459012i
$359$			116.130i			0.323481i	0.986833	+	0.161741i	$0.0517108\pi$
$359$			116.130i			0.323481i	−0.986833	+	0.161741i	$0.948289\pi$
$360$	−587.210	−	704.235i	−1.63114	−	1.95621i
$361$	−353.292			−0.978648
$362$	−88.7489	+	83.5570i	−0.245163	+	0.230820i
$363$	129.677			0.357237
$364$	−1.53980	+	25.5277i	−0.00423022	+	0.0701311i
$365$		−	433.910i		−	1.18879i
$366$	332.911	−	313.436i	0.909594	−	0.856381i
$367$		−	476.288i		−	1.29779i	−0.760879	−	0.648894i	$-0.775232\pi$
$367$		−	476.288i		−	1.29779i	0.760879	−	0.648894i	$-0.224768\pi$
$368$	82.3769	−	680.363i	0.223850	−	1.84881i
$369$	1162.08			3.14928
$370$	1.74142	+	1.84962i	0.00470654	+	0.00499898i
$371$	−144.630			−0.389839
$372$	−149.507	−	9.01809i	−0.401902	−	0.0242422i
$373$			49.2857i			0.132133i	0.997815	+	0.0660666i	$0.0210450\pi$
$373$			49.2857i			0.132133i	−0.997815	+	0.0660666i	$0.978955\pi$
$374$	92.6970	+	98.4568i	0.247853	+	0.263254i
$375$		−	350.778i		−	0.935407i
$376$	194.238	+	232.947i	0.516590	+	0.619541i
$377$	90.2585			0.239412
$378$	−186.886	+	175.953i	−0.494406	+	0.465483i
$379$	167.511			0.441983			0.220991	−	0.975276i	$-0.429071\pi$
$379$	167.511			0.441983			0.220991	+	0.975276i	$0.429071\pi$
$380$	−69.4815	−	4.19103i	−0.182846	−	0.0110290i
$381$			684.174i			1.79573i
$382$	259.866	−	244.664i	0.680278	−	0.640481i
$383$		−	513.207i		−	1.33997i	−0.742376	−	0.669983i	$-0.766301\pi$
$383$		−	513.207i		−	1.33997i	0.742376	−	0.669983i	$-0.233699\pi$
$384$	−561.273	+	363.362i	−1.46165	+	0.946256i
$385$	162.630			0.422416
$386$	303.792	+	322.668i	0.787026	+	0.835929i
$387$	−646.209			−1.66979
$388$	−3.00719	+	49.8550i	−0.00775049	+	0.128492i
$389$			709.398i			1.82365i	0.410584	+	0.911823i	$0.365325\pi$
$389$			709.398i			1.82365i	−0.410584	+	0.911823i	$0.634675\pi$
$390$	108.471	+	115.211i	0.278132	+	0.295414i
$391$			295.315i			0.755281i
$392$	43.0099	−	35.8629i	0.109719	−	0.0914869i
$393$	278.582			0.708860
$394$	352.826	−	332.186i	0.895498	−	0.843111i
$395$	−124.937			−0.316295
$396$	−43.1897	+	716.026i	−0.109065	+	1.80815i
$397$			309.404i			0.779355i	0.920951	+	0.389677i	$0.127413\pi$
$397$			309.404i			0.779355i	−0.920951	+	0.389677i	$0.872587\pi$
$398$	432.549	−	407.245i	1.08681	−	1.02323i
$399$			38.3706i			0.0961669i
$400$	226.924	+	27.4754i	0.567309	+	0.0686886i
$401$	−528.073			−1.31689			−0.658445	−	0.752629i	$-0.728785\pi$
$401$	−528.073			−1.31689			−0.658445	+	0.752629i	$0.728785\pi$
$402$	−222.737	−	236.577i	−0.554072	−	0.588500i
$403$	17.3225			0.0429839
$404$	271.807	+	16.3950i	0.672790	+	0.0405818i
$405$			556.666i			1.37448i
$406$	−135.480	−	143.898i	−0.333695	−	0.354429i
$407$		−	1.98739i		−	0.00488302i
$408$	221.283	−	184.512i	0.542360	−	0.452234i
$409$	−612.830			−1.49836			−0.749181	−	0.662366i	$-0.769552\pi$
$409$	−612.830			−1.49836			−0.749181	+	0.662366i	$0.769552\pi$
$410$	−580.020	+	546.088i	−1.41468	+	1.33192i
$411$	301.497			0.733569
$412$	232.749	+	14.0391i	0.564926	+	0.0340756i
$413$		−	277.261i		−	0.671335i
$414$	−1140.56	+	1073.84i	−2.75497	+	2.59381i
$415$		−	32.0676i		−	0.0772712i
$416$	62.2652	−	45.8563i	0.149676	−	0.110232i
$417$	900.670			2.15988
$418$	37.3283	+	39.6478i	0.0893023	+	0.0948512i
$419$	−237.642			−0.567165			−0.283583	−	0.958948i	$-0.591523\pi$
$419$	−237.642			−0.567165			−0.283583	+	0.958948i	$0.591523\pi$
$420$	20.8624	−	345.870i	0.0496725	−	0.823501i
$421$		−	394.516i		−	0.937092i	−0.883439	−	0.468546i	$-0.844778\pi$
$421$		−	394.516i		−	0.937092i	0.883439	−	0.468546i	$-0.155222\pi$
$422$	−193.335	−	205.348i	−0.458141	−	0.486608i
$423$		−	693.287i		−	1.63898i
$424$	280.064	+	335.878i	0.660528	+	0.792164i
$425$	−98.4973			−0.231758
$426$	175.933	−	165.641i	0.412989	−	0.388829i
$427$	115.796			0.271185
$428$	−32.7220	+	542.486i	−0.0764533	+	1.26749i
$429$		−	123.793i		−	0.288561i
$430$	322.536	−	303.667i	0.750084	−	0.706203i
$431$		−	363.359i		−	0.843059i	−0.906815	−	0.421530i	$-0.861493\pi$
$431$		−	363.359i		−	0.843059i	0.906815	−	0.421530i	$-0.138507\pi$
$432$	770.505	+	93.2912i	1.78358	+	0.215952i
$433$	119.733			0.276520			0.138260	−	0.990396i	$-0.455849\pi$
$433$	119.733			0.276520			0.138260	+	0.990396i	$0.455849\pi$
$434$	−26.0015	−	27.6172i	−0.0599113	−	0.0636340i
$435$	−1222.89			−2.81125
$436$	−177.669	−	10.7168i	−0.407499	−	0.0245798i
$437$			118.921i			0.272130i
$438$	495.772	+	526.577i	1.13190	+	1.20223i
$439$			871.477i			1.98514i	0.121672	+	0.992570i	$0.461174\pi$
$439$			871.477i			1.98514i	−0.121672	+	0.992570i	$0.538826\pi$
$440$	−314.919	−	377.679i	−0.715724	−	0.858361i
$441$	−128.004			−0.290259
$442$	−24.2609	+	22.8416i	−0.0548889	+	0.0516778i
$443$	−343.956			−0.776424			−0.388212	−	0.921570i	$-0.626907\pi$
$443$	−343.956			−0.776424			−0.388212	+	0.921570i	$0.626907\pi$
$444$	−4.22665	−	0.254946i	−0.00951947	−	0.000574202i
$445$		−	112.752i		−	0.253376i
$446$	59.4504	−	55.9725i	0.133297	−	0.125499i
$447$		−	1146.74i		−	2.56541i
$448$	−166.570	−	30.4375i	−0.371808	−	0.0679409i
$449$	−242.849			−0.540866			−0.270433	−	0.962739i	$-0.587167\pi$
$449$	−242.849			−0.540866			−0.270433	+	0.962739i	$0.587167\pi$
$450$	−358.160	−	380.415i	−0.795911	−	0.845366i
$451$	623.222			1.38187
$452$	32.1254	−	532.594i	0.0710739	−	1.17831i
$453$			969.861i			2.14097i
$454$	11.2228	+	11.9201i	0.0247198	+	0.0262558i
$455$			40.0739i			0.0880745i
$456$	89.1088	−	74.3013i	0.195414	−	0.162942i
$457$	−42.2571			−0.0924662			−0.0462331	−	0.998931i	$-0.514722\pi$
$457$	−42.2571			−0.0924662			−0.0462331	+	0.998931i	$0.514722\pi$
$458$	483.814	−	455.510i	1.05636	−	0.994563i
$459$	−334.441			−0.728631
$460$	64.6584	−	1071.95i	0.140562	−	2.33032i
$461$			816.370i			1.77087i	0.464766	+	0.885434i	$0.346139\pi$
$461$			816.370i			1.77087i	−0.464766	+	0.885434i	$0.653861\pi$
$462$	−197.362	+	185.816i	−0.427190	+	0.402199i
$463$			115.161i			0.248727i	0.992237	+	0.124363i	$0.0396889\pi$
$463$			115.161i			0.248727i	−0.992237	+	0.124363i	$0.960311\pi$
$464$	−71.8324	+	593.275i	−0.154811	+	1.27861i
$465$	−234.700			−0.504730
$466$	451.409	+	479.458i	0.968689	+	1.02888i
$467$	603.424			1.29213			0.646064	−	0.763283i	$-0.276414\pi$
$467$	603.424			1.29213			0.646064	+	0.763283i	$0.276414\pi$
$468$	−176.437	−	10.6424i	−0.377002	−	0.0227403i
$469$		−	82.2884i		−	0.175455i
$470$	325.790	+	346.034i	0.693171	+	0.736242i
$471$			982.992i			2.08703i
$472$	−643.889	+	536.892i	−1.36417	+	1.13748i
$473$	−346.559			−0.732684
$474$	151.619	−	142.749i	0.319871	−	0.301158i
$475$	−39.6641			−0.0835034
$476$	72.8324	+	4.39315i	0.153009	+	0.00922931i
$477$		−	999.624i		−	2.09565i
$478$	−200.542	+	188.810i	−0.419543	+	0.395000i
$479$			158.595i			0.331097i	0.986202	+	0.165548i	$0.0529394\pi$
$479$			158.595i			0.331097i	−0.986202	+	0.165548i	$0.947061\pi$
$480$	−843.620	+	621.299i	−1.75754	+	1.29437i
$481$	0.489715			0.00101812
$482$	276.737	+	293.932i	0.574143	+	0.609818i
$483$	−591.974			−1.22562
$484$	5.97880	−	99.1201i	0.0123529	−	0.204794i
$485$			78.2633i			0.161368i
$486$	−37.4952	−	39.8250i	−0.0771505	−	0.0819444i
$487$		−	106.987i		−	0.219687i	−0.993949	−	0.109843i	$-0.964965\pi$
$487$		−	106.987i		−	0.219687i	0.993949	−	0.109843i	$-0.0350349\pi$
$488$	−224.229	−	268.916i	−0.459486	−	0.551057i
$489$	−284.768			−0.582348
$490$	63.8895	−	60.1519i	0.130387	−	0.122759i
$491$	616.591			1.25579			0.627893	−	0.778299i	$-0.283917\pi$
$491$	616.591			1.25579			0.627893	+	0.778299i	$0.283917\pi$
$492$	79.9479	−	1325.43i	0.162496	−	2.69395i
$493$		−	257.514i		−	0.522340i
$494$	−9.76967	+	9.19813i	−0.0197767	+	0.0186197i
$495$			1124.03i			2.27077i
$496$	−13.7862	+	113.862i	−0.0277947	+	0.229561i
$497$	61.1947			0.123128
$498$	36.6394	+	38.9160i	0.0735731	+	0.0781446i
$499$	554.090			1.11040			0.555200	−	0.831717i	$-0.312642\pi$
$499$	554.090			1.11040			0.555200	+	0.831717i	$0.312642\pi$
$500$	−268.121	−	16.1727i	−0.536242	−	0.0323454i
$501$		−	1391.76i		−	2.77796i
$502$	−369.072	−	392.004i	−0.735202	−	0.780885i
$503$			148.158i			0.294548i	0.989096	+	0.147274i	$0.0470499\pi$
$503$			148.158i			0.294548i	−0.989096	+	0.147274i	$0.952950\pi$
$504$	247.869	+	297.267i	0.491803	+	0.589815i
$505$	426.688			0.844926
$506$	−611.678	+	575.894i	−1.20885	+	1.13813i
$507$	−852.290			−1.68104
$508$	522.957	+	31.5440i	1.02944	+	0.0620946i
$509$		−	182.889i		−	0.359310i	−0.983730	−	0.179655i	$-0.942502\pi$
$509$		−	182.889i		−	0.359310i	0.983730	−	0.179655i	$-0.0574981\pi$
$510$	328.706	−	309.477i	0.644522	−	0.606817i
$511$			183.159i			0.358432i
$512$	251.863	+	445.768i	0.491919	+	0.870641i
$513$	−134.677			−0.262528
$514$	−332.269	−	352.915i	−0.646438	−	0.686605i
$515$	365.374			0.709464
$516$	−44.4572	+	737.039i	−0.0861574	+	1.42837i
$517$		−	371.807i		−	0.719163i
$518$	−0.735075	−	0.780750i	−0.00141906	−	0.00150724i
$519$		−	599.856i		−	1.15579i
$520$	93.0644	−	77.5996i	0.178970	−	0.149230i
$521$	98.2461			0.188572			0.0942861	−	0.995545i	$-0.469943\pi$
$521$	98.2461			0.188572			0.0942861	+	0.995545i	$0.469943\pi$
$522$	994.565	−	936.382i	1.90530	−	1.79383i
$523$	−574.764			−1.09898			−0.549488	−	0.835502i	$-0.685177\pi$
$523$	−574.764			−1.09898			−0.549488	+	0.835502i	$0.685177\pi$
$524$	12.8441	−	212.937i	0.0245116	−	0.406369i
$525$		−	197.443i		−	0.376082i
$526$	49.2868	−	46.4035i	0.0937012	−	0.0882196i
$527$		−	49.4223i		−	0.0937805i
$528$	813.698	+	98.5208i	1.54109	+	0.186592i
$529$	−1305.69			−2.46822
$530$	469.744	+	498.933i	0.886310	+	0.941382i
$531$	1916.31			3.60888
$532$	29.3290	+	1.76909i	0.0551297	+	0.00332535i
$533$			153.569i			0.288122i
$534$	128.827	+	136.832i	0.241249	+	0.256240i
$535$			851.604i			1.59178i
$536$	−191.100	+	159.344i	−0.356529	+	0.297284i
$537$	−589.480			−1.09773
$538$	241.138	−	227.031i	0.448212	−	0.421991i
$539$	−68.6482			−0.127362
$540$	1213.97	+	73.2251i	2.24809	+	0.135602i
$541$		−	370.654i		−	0.685128i	−0.939495	−	0.342564i	$-0.888705\pi$
$541$		−	370.654i		−	0.685128i	0.939495	−	0.342564i	$-0.111295\pi$
$542$	215.962	−	203.328i	0.398453	−	0.375143i
$543$		−	318.365i		−	0.586307i
$544$	−130.831	−	177.647i	−0.240499	−	0.326557i
$545$	−278.909			−0.511759
$546$	−45.7872	−	48.6322i	−0.0838593	−	0.0890700i
$547$	−56.5966			−0.103467			−0.0517336	−	0.998661i	$-0.516475\pi$
$547$	−56.5966			−0.103467			−0.0517336	+	0.998661i	$0.516475\pi$
$548$	13.9006	−	230.453i	0.0253661	−	0.420534i
$549$			800.334i			1.45780i
$550$	−192.080	−	204.015i	−0.349236	−	0.370936i
$551$		−	103.699i		−	0.188201i
$552$	1146.31	+	1374.75i	2.07664	+	2.49049i
$553$	52.7374			0.0953659
$554$	−696.569	+	655.819i	−1.25734	+	1.18379i
$555$	−6.63506			−0.0119551
$556$	41.5257	−	688.438i	0.0746864	−	1.23820i
$557$		−	151.525i		−	0.272037i	−0.990706	−	0.136019i	$-0.956569\pi$
$557$		−	151.525i		−	0.272037i	0.990706	−	0.136019i	$-0.0434307\pi$
$558$	190.878	−	179.712i	0.342076	−	0.322064i
$559$		−	85.3962i		−	0.152766i
$560$	−263.408	−	31.8929i	−0.470372	−	0.0569516i
$561$	−353.189			−0.629571
$562$	−309.932	−	329.190i	−0.551480	−	0.585747i
$563$	−318.048			−0.564917			−0.282458	−	0.959280i	$-0.591150\pi$
$563$	−318.048			−0.564917			−0.282458	+	0.959280i	$0.591150\pi$
$564$	−790.735	−	47.6961i	−1.40201	−	0.0845675i
$565$		−	836.076i		−	1.47978i
$566$	−349.089	−	370.780i	−0.616766	−	0.655089i
$567$		−	234.976i		−	0.414419i
$568$	−118.498	−	142.114i	−0.208624	−	0.250200i
$569$	356.654			0.626808			0.313404	−	0.949620i	$-0.398531\pi$
$569$	356.654			0.626808			0.313404	+	0.949620i	$0.398531\pi$
$570$	132.367	−	124.624i	0.232224	−	0.218638i
$571$	831.014			1.45537			0.727683	−	0.685914i	$-0.240597\pi$
$571$	831.014			1.45537			0.727683	+	0.685914i	$0.240597\pi$
$572$	−94.6224	−	5.70750i	−0.165424	−	0.00997815i
$573$			932.205i			1.62689i
$574$	244.834	−	230.511i	0.426540	−	0.401587i
$575$		−	611.929i		−	1.06422i
$576$	210.371	−	1151.26i	0.365228	−	1.99872i
$577$	771.483			1.33706			0.668530	−	0.743685i	$-0.266924\pi$
$577$	771.483			1.33706			0.668530	+	0.743685i	$0.266924\pi$
$578$	−331.044	−	351.614i	−0.572741	−	0.608328i
$579$	−1157.49			−1.99912
$580$	−56.3819	+	934.734i	−0.0972102	+	1.61161i
$581$			13.5361i			0.0232980i
$582$	−89.4212	−	94.9775i	−0.153645	−	0.163192i
$583$		−	536.094i		−	0.919544i
$584$	425.353	−	354.671i	0.728344	−	0.607313i
$585$	−276.974			−0.473460
$586$	−217.781	+	205.041i	−0.371640	+	0.349899i
$587$	144.376			0.245956			0.122978	−	0.992409i	$-0.460756\pi$
$587$	144.376			0.245956			0.122978	+	0.992409i	$0.460756\pi$
$588$	−8.80630	+	145.996i	−0.0149767	+	0.248293i
$589$		−	19.9020i		−	0.0337894i
$590$	−956.471	+	900.516i	−1.62114	+	1.52630i
$591$			1265.68i			2.14158i
$592$	−0.389741	+	3.21893i	−0.000658347	+	0.00543738i
$593$	838.926			1.41471			0.707357	−	0.706856i	$-0.249887\pi$
$593$	838.926			1.41471			0.707357	+	0.706856i	$0.249887\pi$
$594$	−652.195	−	692.720i	−1.09797	−	1.16620i
$595$	114.334			0.192157
$596$	−876.521	−	52.8706i	−1.47067	−	0.0887090i
$597$			1551.66i			2.59910i
$598$	−141.907	−	150.724i	−0.237302	−	0.252048i
$599$			711.341i			1.18755i	0.804632	+	0.593774i	$0.202363\pi$
$599$			711.341i			1.18755i	−0.804632	+	0.593774i	$0.797637\pi$
$600$	−458.526	+	382.331i	−0.764209	+	0.637218i
$601$	−356.394			−0.593002			−0.296501	−	0.955033i	$-0.595820\pi$
$601$	−356.394			−0.593002			−0.296501	+	0.955033i	$0.595820\pi$
$602$	−136.147	+	128.182i	−0.226157	+	0.212927i
$603$	568.742			0.943188
$604$	741.324	+	44.7157i	1.22736	+	0.0740326i
$605$		−	155.601i		−	0.257191i
$606$	−517.813	+	487.520i	−0.854476	+	0.804488i
$607$			60.3719i			0.0994595i	0.998763	+	0.0497298i	$0.0158360\pi$
$607$			60.3719i			0.0994595i	−0.998763	+	0.0497298i	$0.984164\pi$
$608$	−52.6847	−	71.5370i	−0.0866525	−	0.117660i
$609$	516.199			0.847618
$610$	−376.094	−	399.463i	−0.616548	−	0.654858i
$611$	91.6176			0.149947
$612$	−30.3636	+	503.387i	−0.0496138	+	0.822527i
$613$			482.989i			0.787911i	0.919130	+	0.393955i	$0.128894\pi$
$613$			482.989i			0.787911i	−0.919130	+	0.393955i	$0.871106\pi$
$614$	372.603	+	395.755i	0.606845	+	0.644552i
$615$		−	2080.68i		−	3.38321i
$616$	132.931	+	159.423i	0.215797	+	0.258803i
$617$	712.490			1.15476			0.577382	−	0.816474i	$-0.304074\pi$
$617$	712.490			1.15476			0.577382	+	0.816474i	$0.304074\pi$
$618$	−443.405	+	417.465i	−0.717483	+	0.675510i
$619$	−93.0817			−0.150374			−0.0751872	−	0.997169i	$-0.523955\pi$
$619$	−93.0817			−0.150374			−0.0751872	+	0.997169i	$0.523955\pi$
$620$	−10.8209	+	179.395i	−0.0174530	+	0.289347i
$621$		−	2077.77i		−	3.34584i
$622$	−777.855	+	732.350i	−1.25057	+	1.17741i
$623$			47.5941i			0.0763951i
$624$	−24.2767	+	200.504i	−0.0389049	+	0.321321i
$625$	−778.059			−1.24489
$626$	−762.582	−	809.966i	−1.21818	−	1.29388i
$627$	−142.227			−0.226837
$628$	751.362	+	45.3211i	1.19644	+	0.0721674i
$629$		−	1.39719i		−	0.00222129i
$630$	415.744	+	441.577i	0.659912	+	0.700916i
$631$			610.573i			0.967628i	0.875171	+	0.483814i	$0.160749\pi$
$631$			610.573i			0.967628i	−0.875171	+	0.483814i	$0.839251\pi$
$632$	−102.121	−	122.473i	−0.161584	−	0.193786i
$633$	736.636			1.16372
$634$	564.205	−	531.198i	0.889912	−	0.837852i
$635$	820.947			1.29283
$636$	−1140.13	−	68.7711i	−1.79266	−	0.108131i
$637$		−	16.9157i		−	0.0265553i
$638$	533.381	−	502.178i	0.836021	−	0.787113i
$639$			422.952i			0.661897i
$640$	436.002	+	673.476i	0.681252	+	1.05231i
$641$	590.153			0.920676			0.460338	−	0.887744i	$-0.347728\pi$
$641$	590.153			0.920676			0.460338	+	0.887744i	$0.347728\pi$
$642$	−973.016	−	1033.48i	−1.51560	−	1.60977i
$643$	−257.971			−0.401199			−0.200600	−	0.979673i	$-0.564289\pi$
$643$	−257.971			−0.401199			−0.200600	+	0.979673i	$0.564289\pi$
$644$	−27.2931	+	452.482i	−0.0423806	+	0.702612i
$645$			1157.02i			1.79383i
$646$	26.2429	+	27.8735i	0.0406237	+	0.0431479i
$647$			379.964i			0.587271i	0.955918	+	0.293635i	$0.0948651\pi$
$647$			379.964i			0.587271i	−0.955918	+	0.293635i	$0.905135\pi$
$648$	−545.689	+	455.010i	−0.842112	+	0.702176i
$649$	1027.71			1.58353
$650$	50.2716	−	47.3307i	0.0773410	−	0.0728164i
$651$	99.0696			0.152181
$652$	−13.1293	+	217.666i	−0.0201370	+	0.333843i
$653$		−	952.773i		−	1.45907i	−0.683943	−	0.729535i	$-0.739736\pi$
$653$		−	952.773i		−	1.45907i	0.683943	−	0.729535i	$-0.260264\pi$
$654$	338.473	−	318.672i	0.517543	−	0.487267i
$655$		−	334.273i		−	0.510340i
$656$	−1009.42	−	122.218i	−1.53875	−	0.186308i
$657$	−1265.92			−1.92681
$658$	−137.520	−	146.065i	−0.208997	−	0.221984i
$659$	−963.119			−1.46149			−0.730743	−	0.682653i	$-0.760826\pi$
$659$	−963.119			−1.46149			−0.730743	+	0.682653i	$0.760826\pi$
$660$	1282.02	+	77.3299i	1.94246	+	0.117166i
$661$			71.6817i			0.108444i	0.998529	+	0.0542222i	$0.0172679\pi$
$661$			71.6817i			0.108444i	−0.998529	+	0.0542222i	$0.982732\pi$
$662$	−525.366	−	558.010i	−0.793604	−	0.842915i
$663$		−	87.0299i		−	0.131267i
$664$	31.4352	−	26.2115i	0.0473422	−	0.0394752i
$665$	46.0412			0.0692349
$666$	5.39621	−	5.08053i	0.00810242	−	0.00762842i
$667$	1599.84			2.39856
$668$	−1063.81	−	64.1674i	−1.59252	−	0.0960589i
$669$			213.263i			0.318779i
$670$	−283.871	+	267.264i	−0.423688	+	0.398902i
$671$			429.216i			0.639667i
$672$	356.103	−	262.258i	0.529915	−	0.390265i
$673$	−712.783			−1.05911			−0.529556	−	0.848275i	$-0.677642\pi$
$673$	−712.783			−1.05911			−0.529556	+	0.848275i	$0.677642\pi$
$674$	772.856	+	820.878i	1.14667	+	1.21792i
$675$	693.005			1.02667
$676$	−39.2951	+	651.458i	−0.0581288	+	0.963695i
$677$			767.527i			1.13372i	0.823815	+	0.566859i	$0.191841\pi$
$677$			767.527i			1.13372i	−0.823815	+	0.566859i	$0.808159\pi$
$678$	955.275	+	1014.63i	1.40896	+	1.49651i
$679$		−	33.0359i		−	0.0486538i
$680$	−221.397	−	265.519i	−0.325584	−	0.390469i
$681$	−42.7605			−0.0627908
$682$	102.367	−	96.3786i	0.150099	−	0.141318i
$683$	−484.354			−0.709156			−0.354578	−	0.935026i	$-0.615375\pi$
$683$	−484.354			−0.709156			−0.354578	+	0.935026i	$0.615375\pi$
$684$	−12.2272	+	202.710i	−0.0178760	+	0.296359i
$685$		−	361.769i		−	0.528130i
$686$	−26.9686	+	25.3909i	−0.0393128	+	0.0370129i
$687$			1735.56i			2.52629i
$688$	561.315	+	67.9628i	0.815864	+	0.0987831i
$689$	132.100			0.191727
$690$	1922.67	+	2042.14i	2.78648	+	2.95962i
$691$	−574.851			−0.831912			−0.415956	−	0.909385i	$-0.636553\pi$
$691$	−574.851			−0.831912			−0.415956	+	0.909385i	$0.636553\pi$
$692$	−458.507	−	27.6565i	−0.662582	−	0.0399661i
$693$		−	474.467i		−	0.684657i
$694$	70.7274	+	75.1221i	0.101913	+	0.108245i
$695$		−	1080.72i		−	1.55500i
$696$	−999.575	−	1198.78i	−1.43617	−	1.72238i
$697$	438.143			0.628612
$698$	853.871	−	803.918i	1.22331	−	1.15175i
$699$	−1719.94			−2.46057
$700$	−150.918	−	9.10317i	−0.215597	−	0.0130045i
$701$		−	143.138i		−	0.204191i	−0.994775	−	0.102096i	$-0.967445\pi$
$701$		−	143.138i		−	0.204191i	0.994775	−	0.102096i	$-0.0325548\pi$
$702$	170.694	−	160.708i	0.243154	−	0.228929i
$703$		−	0.562638i		−	0.000800339i
$704$	112.821	−	617.417i	0.160258	−	0.877013i
$705$	−1241.31			−1.76072
$706$	416.563	+	442.446i	0.590032	+	0.626695i
$707$	−180.110			−0.254753
$708$	131.837	−	2185.67i	0.186210	−	3.08710i
$709$			255.311i			0.360101i	0.983657	+	0.180050i	$0.0576261\pi$
$709$			255.311i			0.360101i	−0.983657	+	0.180050i	$0.942374\pi$
$710$	−198.754	−	211.104i	−0.279935	−	0.297329i
$711$			364.498i			0.512656i
$712$	110.529	−	92.1618i	0.155237	−	0.129441i
$713$	307.044			0.430636
$714$	−138.751	+	130.634i	−0.194329	+	0.182961i
$715$	−148.540			−0.207748
$716$	−27.1781	+	450.576i	−0.0379583	+	0.629296i
$717$		−	719.393i		−	1.00334i
$718$	−169.104	+	159.211i	−0.235521	+	0.221743i
$719$		−	415.630i		−	0.578067i	−0.957319	−	0.289034i	$-0.906666\pi$
$719$		−	415.630i		−	0.578067i	0.957319	−	0.289034i	$-0.0933340\pi$
$720$	220.430	−	1820.57i	0.306153	−	2.52857i
$721$	−154.229			−0.213910
$722$	−484.355	−	514.451i	−0.670852	−	0.712537i
$723$	−1054.41			−1.45838
$724$	−243.346	−	14.6783i	−0.336113	−	0.0202739i
$725$			533.601i			0.736001i
$726$	177.784	+	188.831i	0.244882	+	0.260098i
$727$		−	896.838i		−	1.23361i	−0.787114	−	0.616807i	$-0.788426\pi$
$727$		−	896.838i		−	1.23361i	0.787114	−	0.616807i	$-0.211574\pi$
$728$	−39.2836	+	32.7558i	−0.0539610	+	0.0449942i
$729$	−656.451			−0.900481
$730$	631.845	−	594.881i	0.865541	−	0.814905i
$731$	−243.641			−0.333299
$732$	912.828	+	55.0606i	1.24703	+	0.0752194i
$733$			509.059i			0.694487i	0.937775	+	0.347244i	$0.112882\pi$
$733$			509.059i			0.694487i	−0.937775	+	0.347244i	$0.887118\pi$
$734$	693.555	−	652.981i	0.944898	−	0.889620i
$735$			229.188i			0.311820i
$736$	1103.66	−	812.808i	1.49954	−	1.10436i
$737$	305.014			0.413859
$738$	1593.19	+	1692.19i	2.15880	+	2.29294i
$739$	741.427			1.00328			0.501642	−	0.865075i	$-0.332729\pi$
$739$	741.427			1.00328			0.501642	+	0.865075i	$0.332729\pi$
$740$	−0.305911	+	5.07159i	−0.000413394	+	0.00685350i
$741$		−	35.0463i		−	0.0472959i
$742$	−198.285	−	210.606i	−0.267231	−	0.283835i
$743$		−	1344.98i		−	1.81021i	−0.425191	−	0.905104i	$-0.639793\pi$
$743$		−	1344.98i		−	1.81021i	0.425191	−	0.905104i	$-0.360207\pi$
$744$	−191.840	−	230.071i	−0.257849	−	0.309236i
$745$	−1375.98			−1.84695
$746$	−71.7681	+	67.5696i	−0.0962039	+	0.0905759i
$747$	−93.5560			−0.125242
$748$	−16.2839	+	269.964i	−0.0217699	+	0.360915i
$749$		−	359.473i		−	0.479937i
$750$	510.790	−	480.909i	0.681054	−	0.641211i
$751$		−	27.6931i		−	0.0368749i	−0.999830	−	0.0184375i	$-0.994131\pi$
$751$		−	27.6931i		−	0.0368749i	0.999830	−	0.0184375i	$-0.00586916\pi$
$752$	−72.9141	+	602.208i	−0.0969602	+	0.800809i
$753$	1406.22			1.86749
$754$	123.742	+	131.431i	0.164115	+	0.174312i
$755$	1163.74			1.54138
$756$	−512.432	−	30.9092i	−0.677820	−	0.0408852i
$757$		−	1341.69i		−	1.77238i	−0.463318	−	0.886192i	$-0.653341\pi$
$757$		−	1341.69i		−	1.77238i	0.463318	−	0.886192i	$-0.346659\pi$
$758$	229.654	+	243.924i	0.302974	+	0.321800i
$759$		−	2194.24i		−	2.89096i
$760$	−89.1548	−	106.922i	−0.117309	−	0.140687i
$761$	−112.001			−0.147176			−0.0735881	−	0.997289i	$-0.523445\pi$
$761$	−112.001			−0.147176			−0.0735881	+	0.997289i	$0.523445\pi$
$762$	−996.271	+	937.988i	−1.30744	+	1.23096i
$763$	117.731			0.154300
$764$	712.542	+	42.9796i	0.932647	+	0.0562560i
$765$			790.226i			1.03297i
$766$	747.314	−	703.596i	0.975606	−	0.918532i
$767$			253.240i			0.330169i
$768$	−1298.61	−	319.144i	−1.69090	−	0.415552i
$769$	140.749			0.183028			0.0915142	−	0.995804i	$-0.470829\pi$
$769$	140.749			0.183028			0.0915142	+	0.995804i	$0.470829\pi$
$770$	222.962	+	236.816i	0.289561	+	0.307553i
$771$	1265.99			1.64202
$772$	−53.3665	+	884.743i	−0.0691276	+	1.14604i
$773$			1325.14i			1.71428i	0.515087	+	0.857138i	$0.327760\pi$
$773$			1325.14i			1.71428i	−0.515087	+	0.857138i	$0.672240\pi$
$774$	−885.938	−	940.987i	−1.14462	−	1.21575i
$775$			102.409i			0.132141i
$776$	−76.7200	+	63.9712i	−0.0988660	+	0.0824371i
$777$	2.80074			0.00360456
$778$	−1033.00	+	972.570i	−1.32777	+	1.25009i
$779$	176.437			0.226491
$780$	−19.0550	+	315.905i	−0.0244294	+	0.405006i
$781$			226.827i			0.290432i
$782$	−430.027	+	404.870i	−0.549907	+	0.517737i
$783$			1811.81i			2.31393i
$784$	111.188	+	13.4624i	0.141821	+	0.0171714i
$785$	1179.50			1.50255
$786$	381.930	+	405.661i	0.485916	+	0.516109i
$787$	−327.801			−0.416519			−0.208260	−	0.978074i	$-0.566780\pi$
$787$	−327.801			−0.416519			−0.208260	+	0.978074i	$0.566780\pi$
$788$	967.434	+	58.3544i	1.22771	+	0.0740538i
$789$			176.804i			0.224086i
$790$	−171.285	−	181.929i	−0.216817	−	0.230289i
$791$			352.918i			0.446167i
$792$	−1101.86	+	918.764i	−1.39124	+	1.16006i
$793$	−105.764			−0.133372
$794$	−450.543	+	424.186i	−0.567435	+	0.534239i
$795$	−1789.80			−2.25132
$796$	1186.03	+	71.5399i	1.48999	+	0.0898742i
$797$		−	393.650i		−	0.493915i	−0.969026	−	0.246958i	$-0.920569\pi$
$797$		−	393.650i		−	0.493915i	0.969026	−	0.246958i	$-0.0794308\pi$
$798$	−55.8740	+	52.6053i	−0.0700175	+	0.0659214i
$799$		−	261.391i		−	0.327148i
$800$	271.099	+	368.107i	0.338873	+	0.460134i
$801$	−328.950			−0.410675
$802$	−723.976	−	768.961i	−0.902713	−	0.958804i
$803$	−678.906			−0.845462
$804$	39.1278	−	648.684i	0.0486664	−	0.806821i
$805$			710.314i			0.882378i
$806$	23.7488	+	25.2245i	0.0294650	+	0.0312959i
$807$			865.023i			1.07190i
$808$	348.768	+	418.273i	0.431643	+	0.517665i
$809$	416.641			0.515008			0.257504	−	0.966277i	$-0.417100\pi$
$809$	416.641			0.515008			0.257504	+	0.966277i	$0.417100\pi$
$810$	−810.598	+	763.177i	−1.00074	+	0.942194i
$811$	−748.707			−0.923190			−0.461595	−	0.887091i	$-0.652723\pi$
$811$	−748.707			−0.923190			−0.461595	+	0.887091i	$0.652723\pi$
$812$	23.7995	−	394.563i	0.0293098	−	0.485915i
$813$			774.708i			0.952901i
$814$	2.89397	−	2.72467i	0.00355524	−	0.00334726i
$815$			341.696i			0.419259i
$816$	572.053	+	69.2630i	0.701046	+	0.0848811i
$817$	−98.1124			−0.120089
$818$	−840.176	−	892.382i	−1.02711	−	1.09093i
$819$	116.914			0.142752
$820$	−1590.39	−	95.9302i	−1.93950	−	0.116988i
$821$		−	554.169i		−	0.674993i	−0.941327	−	0.337496i	$-0.890420\pi$
$821$		−	554.169i		−	0.674993i	0.941327	−	0.337496i	$-0.109580\pi$
$822$	413.346	+	439.030i	0.502854	+	0.534099i
$823$		−	121.452i		−	0.147572i	−0.997274	−	0.0737861i	$-0.976492\pi$
$823$		−	121.452i		−	0.147572i	0.997274	−	0.0737861i	$-0.0235082\pi$
$824$	298.651	+	358.169i	0.362441	+	0.434671i
$825$	731.853			0.887094
$826$	403.738	−	380.119i	0.488787	−	0.460193i
$827$	−1516.61			−1.83386			−0.916932	−	0.399043i	$-0.869343\pi$
$827$	−1516.61			−1.83386			−0.916932	+	0.399043i	$0.869343\pi$
$828$	−3127.36	−	188.638i	−3.77701	−	0.227824i
$829$			325.042i			0.392089i	0.980595	+	0.196044i	$0.0628097\pi$
$829$			325.042i			0.392089i	−0.980595	+	0.196044i	$0.937190\pi$
$830$	46.6957	−	43.9639i	0.0562599	−	0.0529686i
$831$		−	2498.77i		−	3.00694i
$832$	152.139	+	27.8005i	0.182859	+	0.0334140i
$833$	−48.2617			−0.0579372
$834$	1234.80	+	1311.53i	1.48057	+	1.57257i
$835$	−1669.98			−1.99998
$836$	−6.55740	+	108.713i	−0.00784377	+	0.130039i
$837$			347.724i			0.415441i
$838$	−325.802	−	346.046i	−0.388785	−	0.412943i
$839$			1165.70i			1.38939i	0.719303	+	0.694696i	$0.244461\pi$
$839$			1165.70i			1.38939i	−0.719303	+	0.694696i	$0.755539\pi$
$840$	532.247	−	443.802i	0.633627	−	0.528335i
$841$	−554.058			−0.658808
$842$	574.480	−	540.872i	0.682280	−	0.642366i
$843$	1180.89			1.40081
$844$	33.9628	−	563.057i	0.0402403	−	0.667129i
$845$			1022.67i			1.21026i
$846$	1009.54	−	950.482i	1.19331	−	1.12350i
$847$			65.6810i			0.0775454i
$848$	−105.132	+	868.301i	−0.123976	+	1.02394i
$849$	1330.08			1.56665
$850$	−135.038	−	143.428i	−0.158868	−	0.168739i
$851$	8.68026			0.0102001
$852$	482.401	+	29.0978i	0.566199	+	0.0341524i
$853$			151.949i			0.178134i	0.996026	+	0.0890672i	$0.0283886\pi$
$853$			151.949i			0.178134i	−0.996026	+	0.0890672i	$0.971611\pi$
$854$	158.754	+	168.618i	0.185895	+	0.197445i
$855$			318.218i			0.372184i
$856$	−834.810	+	696.087i	−0.975246	+	0.813186i
$857$	412.018			0.480768			0.240384	−	0.970678i	$-0.422727\pi$
$857$	412.018			0.480768			0.240384	+	0.970678i	$0.422727\pi$
$858$	180.263	−	169.717i	0.210096	−	0.197806i
$859$	159.993			0.186255			0.0931274	−	0.995654i	$-0.470314\pi$
$859$	159.993			0.186255			0.0931274	+	0.995654i	$0.470314\pi$
$860$	884.380	+	53.3446i	1.02835	+	0.0620286i
$861$			878.280i			1.02007i
$862$	529.110	−	498.157i	0.613817	−	0.577908i
$863$		−	992.910i		−	1.15053i	−0.817966	−	0.575266i	$-0.804898\pi$
$863$		−	992.910i		−	1.15053i	0.817966	−	0.575266i	$-0.195102\pi$
$864$	920.499	+	1249.88i	1.06539	+	1.44662i
$865$	−719.772			−0.832107
$866$	164.152	+	174.352i	0.189552	+	0.201330i
$867$	1261.33			1.45482
$868$	4.56763	−	75.7250i	0.00526225	−	0.0872408i
$869$			195.479i			0.224947i
$870$	−1676.56	−	1780.74i	−1.92708	−	2.04682i
$871$			75.1590i			0.0862905i
$872$	−227.975	−	273.409i	−0.261440	−	0.313542i
$873$	228.330			0.261547
$874$	−173.169	+	163.038i	−0.198133	+	0.186542i
$875$	177.668			0.203049
$876$	−87.0912	+	1443.85i	−0.0994192	+	1.64823i
$877$			825.096i			0.940817i	0.882449	+	0.470408i	$0.155893\pi$
$877$			825.096i			0.940817i	−0.882449	+	0.470408i	$0.844107\pi$
$878$	−1269.01	+	1194.78i	−1.44535	+	1.36079i
$879$		−	781.236i		−	0.888778i
$880$	118.216	−	976.363i	0.134336	−	1.10950i
$881$	1352.83			1.53556			0.767780	−	0.640714i	$-0.221361\pi$
$881$	1352.83			1.53556			0.767780	+	0.640714i	$0.221361\pi$
$882$	−175.491	−	186.395i	−0.198969	−	0.211333i
$883$	−1013.40			−1.14768			−0.573838	−	0.818969i	$-0.694546\pi$
$883$	−1013.40			−1.14768			−0.573838	+	0.818969i	$0.694546\pi$
$884$	−66.5223	−	4.01254i	−0.0752515	−	0.00453907i
$885$		−	3431.10i		−	3.87695i
$886$	−471.556	−	500.857i	−0.532230	−	0.565301i
$887$			233.760i			0.263540i	0.991280	+	0.131770i	$0.0420661\pi$
$887$			233.760i			0.263540i	−0.991280	+	0.131770i	$0.957934\pi$
$888$	−5.42340	−	6.50422i	−0.00610743	−	0.00732457i
$889$	−346.532			−0.389800
$890$	164.186	−	154.581i	0.184478	−	0.173686i
$891$	870.974			0.977524
$892$	163.010	+	9.83257i	0.182747	+	0.0110231i
$893$		−	105.260i		−	0.117873i
$894$	1669.84	−	1572.15i	1.86783	−	1.75856i
$895$			707.322i			0.790304i
$896$	−184.042	−	284.283i	−0.205404	−	0.317280i
$897$	540.686			0.602772
$898$	−332.941	−	353.628i	−0.370758	−	0.393795i
$899$	−267.741			−0.297821
$900$	62.9172	−	1043.08i	0.0699080	−	1.15898i
$901$		−	376.890i		−	0.418302i
$902$	854.423	+	907.514i	0.947254	+	1.00611i
$903$		−	488.392i		−	0.540854i
$904$	819.589	−	683.396i	0.906625	−	0.755968i
$905$	−382.008			−0.422109
$906$	−1412.28	+	1329.66i	−1.55881	+	1.46761i
$907$	−203.590			−0.224465			−0.112233	−	0.993682i	$-0.535800\pi$
$907$	−203.590			−0.224465			−0.112233	+	0.993682i	$0.535800\pi$
$908$	−1.97149	+	32.6845i	−0.00217124	+	0.0359961i
$909$		−	1244.85i		−	1.36947i
$910$	−58.3542	+	54.9404i	−0.0641255	+	0.0603741i
$911$		−	712.022i		−	0.781583i	−0.920479	−	0.390792i	$-0.872201\pi$
$911$		−	712.022i		−	0.781583i	0.920479	−	0.390792i	$-0.127799\pi$
$912$	230.361	+	27.8917i	0.252589	+	0.0305830i
$913$	−50.1737			−0.0549548
$914$	−57.9335	−	61.5333i	−0.0633846	−	0.0673231i
$915$	1432.97			1.56609
$916$	1326.60	+	80.0185i	1.44825	+	0.0873564i
$917$			141.101i			0.153872i
$918$	−458.512	−	487.002i	−0.499468	−	0.530503i
$919$			786.783i			0.856129i	0.903748	+	0.428065i	$0.140804\pi$
$919$			786.783i			0.856129i	−0.903748	+	0.428065i	$0.859196\pi$
$920$	1649.58	−	1375.46i	1.79302	−	1.49507i
$921$	−1419.67			−1.54145
$922$	−1188.77	+	1119.23i	−1.28934	+	1.21391i
$923$	−55.8929			−0.0605557
$924$	−541.158	−	32.6419i	−0.585668	−	0.0353267i
$925$			2.89516i			0.00312990i
$926$	−167.693	+	157.883i	−0.181094	+	0.170500i
$927$		−	1065.97i		−	1.14991i
$928$	−962.387	+	708.767i	−1.03705	+	0.763757i
$929$	−1657.99			−1.78471			−0.892353	−	0.451338i	$-0.850947\pi$
$929$	−1657.99			−1.78471			−0.892353	+	0.451338i	$0.850947\pi$
$930$	−321.768	−	341.761i	−0.345987	−	0.367485i
$931$	−19.4346			−0.0208750
$932$	−79.2981	+	1314.65i	−0.0850838	+	1.41057i
$933$		−	2790.36i		−	2.99074i
$934$	827.281	+	878.685i	0.885740	+	0.940776i
$935$			423.795i			0.453257i
$936$	−226.394	−	271.512i	−0.241874	−	0.290077i
$937$	333.736			0.356175			0.178088	−	0.984015i	$-0.443009\pi$
$937$	333.736			0.356175			0.178088	+	0.984015i	$0.443009\pi$
$938$	119.825	−	112.816i	0.127746	−	0.120272i
$939$	2905.55			3.09430
$940$	−57.2309	+	948.809i	−0.0608840	+	1.00937i
$941$		−	543.324i		−	0.577390i	−0.957421	−	0.288695i	$-0.906779\pi$
$941$		−	543.324i		−	0.577390i	0.957421	−	0.288695i	$-0.0932214\pi$
$942$	−1431.40	+	1347.66i	−1.51953	+	1.43064i
$943$			2722.03i			2.88656i
$944$	−1664.56	−	201.542i	−1.76331	−	0.213497i
$945$	−804.425			−0.851243
$946$	−475.125	−	504.648i	−0.502247	−	0.533454i
$947$	−359.728			−0.379861			−0.189930	−	0.981798i	$-0.560826\pi$
$947$	−359.728			−0.379861			−0.189930	+	0.981798i	$0.560826\pi$
$948$	415.732	+	25.0764i	0.438536	+	0.0264519i
$949$		−	167.290i		−	0.176281i
$950$	−54.3786	−	57.7575i	−0.0572406	−	0.0607974i
$951$			2023.94i			2.12823i
$952$	93.4545	+	112.079i	0.0981665	+	0.117730i
$953$	−904.225			−0.948820			−0.474410	−	0.880304i	$-0.657339\pi$
$953$	−904.225			−0.948820			−0.474410	+	0.880304i	$0.657339\pi$
$954$	1455.62	−	1370.46i	1.52580	−	1.43654i
$955$	1118.56			1.17127
$956$	−549.877	−	33.1678i	−0.575185	−	0.0346944i
$957$			1913.37i			1.99934i
$958$	−230.941	+	217.431i	−0.241066	+	0.226963i
$959$			152.707i			0.159236i
$960$	−2061.30	−	376.663i	−2.14719	−	0.392358i
$961$	909.615			0.946529
$962$	0.671389	+	0.713107i	0.000697910	+	0.000741275i
$963$	2484.52			2.57998
$964$	−48.6138	+	805.949i	−0.0504293	+	0.836047i
$965$			1388.89i			1.43926i
$966$	−811.583	−	862.012i	−0.840148	−	0.892352i
$967$			920.961i			0.952390i	0.879340	+	0.476195i	$0.157984\pi$
$967$			920.961i			0.952390i	−0.879340	+	0.476195i	$0.842016\pi$
$968$	152.532	−	127.185i	0.157575	−	0.131390i
$969$	−99.9894			−0.103188
$970$	−113.964	+	107.297i	−0.117489	+	0.110616i
$971$	1327.31			1.36695			0.683476	−	0.729973i	$-0.260468\pi$
$971$	1327.31			1.36695			0.683476	+	0.729973i	$0.260468\pi$
$972$	6.58670	−	109.198i	0.00677644	−	0.112344i
$973$			456.186i			0.468845i
$974$	155.791	−	146.677i	0.159950	−	0.150593i
$975$			180.337i			0.184961i
$976$	84.1724	−	695.192i	0.0862422	−	0.712287i
$977$	−688.490			−0.704698			−0.352349	−	0.935869i	$-0.614617\pi$
$977$	−688.490			−0.704698			−0.352349	+	0.935869i	$0.614617\pi$
$978$	−390.411	−	414.670i	−0.399193	−	0.423998i
$979$	−176.415			−0.180199
$980$	175.182	+	10.5668i	0.178757	+	0.0107824i
$981$			813.706i			0.829466i
$982$	845.333	+	897.859i	0.860828	+	0.914317i
$983$		−	1687.08i		−	1.71625i	−0.513438	−	0.858127i	$-0.671628\pi$
$983$		−	1687.08i		−	1.71625i	0.513438	−	0.858127i	$-0.328372\pi$
$984$	2039.65	−	1700.71i	2.07281	−	1.72837i
$985$	1518.70			1.54182
$986$	374.983	−	353.046i	0.380307	−	0.358058i
$987$	523.972			0.530874
$988$	−26.7880	−	1.61582i	−0.0271134	−	0.00163544i
$989$		−	1513.66i		−	1.53049i
$990$	−1636.77	+	1541.02i	−1.65331	+	1.55659i
$991$		−	1139.22i		−	1.14957i	−0.818304	−	0.574785i	$-0.805086\pi$
$991$		−	1139.22i		−	1.14957i	0.818304	−	0.574785i	$-0.194914\pi$
$992$	−184.703	+	136.027i	−0.186192	+	0.137124i
$993$	2001.72			2.01583
$994$	83.8966	+	89.1096i	0.0844030	+	0.0896475i
$995$	1861.85			1.87121
$996$	−6.43637	+	106.706i	−0.00646222	+	0.107135i
$997$			206.085i			0.206705i	0.994645	+	0.103353i	$0.0329570\pi$
$997$			206.085i			0.206705i	−0.994645	+	0.103353i	$0.967043\pi$
$998$	759.645	+	806.847i	0.761168	+	0.808464i
$999$			9.83033i			0.00984017i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	56.3.g.b.43.6	yes	8
3.2	odd	2		504.3.g.b.379.3		8
4.3	odd	2		224.3.g.b.15.8		8
7.2	even	3		392.3.k.o.67.6		16
7.3	odd	6		392.3.k.n.275.1		16
7.4	even	3		392.3.k.o.275.1		16
7.5	odd	6		392.3.k.n.67.6		16
7.6	odd	2		392.3.g.m.99.6		8
8.3	odd	2	inner	56.3.g.b.43.5	✓	8
8.5	even	2		224.3.g.b.15.7		8
12.11	even	2		2016.3.g.b.1135.1		8
16.3	odd	4		1792.3.d.j.1023.16		16
16.5	even	4		1792.3.d.j.1023.15		16
16.11	odd	4		1792.3.d.j.1023.1		16
16.13	even	4		1792.3.d.j.1023.2		16
24.5	odd	2		2016.3.g.b.1135.8		8
24.11	even	2		504.3.g.b.379.4		8
28.27	even	2		1568.3.g.m.687.1		8
56.3	even	6		392.3.k.n.275.6		16
56.11	odd	6		392.3.k.o.275.6		16
56.13	odd	2		1568.3.g.m.687.2		8
56.19	even	6		392.3.k.n.67.1		16
56.27	even	2		392.3.g.m.99.5		8
56.51	odd	6		392.3.k.o.67.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.g.b.43.5	✓	8	8.3	odd	2	inner
56.3.g.b.43.6	yes	8	1.1	even	1	trivial
224.3.g.b.15.7		8	8.5	even	2
224.3.g.b.15.8		8	4.3	odd	2
392.3.g.m.99.5		8	56.27	even	2
392.3.g.m.99.6		8	7.6	odd	2
392.3.k.n.67.1		16	56.19	even	6
392.3.k.n.67.6		16	7.5	odd	6
392.3.k.n.275.1		16	7.3	odd	6
392.3.k.n.275.6		16	56.3	even	6
392.3.k.o.67.1		16	56.51	odd	6
392.3.k.o.67.6		16	7.2	even	3
392.3.k.o.275.1		16	7.4	even	3
392.3.k.o.275.6		16	56.11	odd	6
504.3.g.b.379.3		8	3.2	odd	2
504.3.g.b.379.4		8	24.11	even	2
1568.3.g.m.687.1		8	28.27	even	2
1568.3.g.m.687.2		8	56.13	odd	2
1792.3.d.j.1023.1		16	16.11	odd	4
1792.3.d.j.1023.2		16	16.13	even	4
1792.3.d.j.1023.15		16	16.5	even	4
1792.3.d.j.1023.16		16	16.3	odd	4
2016.3.g.b.1135.1		8	12.11	even	2
2016.3.g.b.1135.8		8	24.5	odd	2

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:	\( N \)	\(=\)	\( 56 = 2^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	56.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37098 + 1.45617i) q^{2} -5.22363 q^{3} +(-0.240837 + 3.99274i) q^{4} +6.26788i q^{5} +(-7.16148 - 7.60647i) q^{6} -2.64575i q^{7} +(-6.14428 + 5.12327i) q^{8} +18.2863 q^{9} +O(q^{10})\)	\(q+(1.37098 + 1.45617i) q^{2} -5.22363 q^{3} +(-0.240837 + 3.99274i) q^{4} +6.26788i q^{5} +(-7.16148 - 7.60647i) q^{6} -2.64575i q^{7} +(-6.14428 + 5.12327i) q^{8} +18.2863 q^{9} +(-9.12707 + 8.59313i) q^{10} +9.80688 q^{11} +(1.25804 - 20.8566i) q^{12} +2.41653i q^{13} +(3.85265 - 3.62727i) q^{14} -32.7411i q^{15} +(-15.8840 - 1.92320i) q^{16} +6.89452 q^{17} +(25.0701 + 26.6279i) q^{18} +2.77637 q^{19} +(-25.0260 - 1.50954i) q^{20} +13.8204i q^{21} +(13.4450 + 14.2804i) q^{22} +42.8332i q^{23} +(32.0954 - 26.7620i) q^{24} -14.2863 q^{25} +(-3.51887 + 3.31301i) q^{26} -48.5083 q^{27} +(10.5638 + 0.637195i) q^{28} -37.3505i q^{29} +(47.6764 - 44.8873i) q^{30} -7.16835i q^{31} +(-18.9761 - 25.7664i) q^{32} -51.2275 q^{33} +(9.45224 + 10.0396i) q^{34} +16.5833 q^{35} +(-4.40402 + 73.0126i) q^{36} -0.202653i q^{37} +(3.80634 + 4.04285i) q^{38} -12.6231i q^{39} +(-32.1120 - 38.5116i) q^{40} +63.5494 q^{41} +(-20.1248 + 18.9475i) q^{42} -35.3384 q^{43} +(-2.36186 + 39.1564i) q^{44} +114.616i q^{45} +(-62.3723 + 58.7234i) q^{46} -37.9129i q^{47} +(82.9721 + 10.0461i) q^{48} -7.00000 q^{49} +(-19.5862 - 20.8032i) q^{50} -36.0144 q^{51} +(-9.64858 - 0.581989i) q^{52} -54.6651i q^{53} +(-66.5038 - 70.6361i) q^{54} +61.4684i q^{55} +(13.5549 + 16.2562i) q^{56} -14.5027 q^{57} +(54.3885 - 51.2067i) q^{58} +104.795 q^{59} +(130.727 + 7.88526i) q^{60} +43.7668i q^{61} +(10.4383 - 9.82765i) q^{62} -48.3810i q^{63} +(11.5043 - 62.9575i) q^{64} -15.1465 q^{65} +(-70.2318 - 74.5958i) q^{66} +31.1021 q^{67} +(-1.66046 + 27.5281i) q^{68} -223.745i q^{69} +(22.7353 + 24.1480i) q^{70} +23.1294i q^{71} +(-112.356 + 93.6857i) q^{72} -69.2275 q^{73} +(0.295096 - 0.277832i) q^{74} +74.6264 q^{75} +(-0.668652 + 11.0853i) q^{76} -25.9466i q^{77} +(18.3813 - 17.3059i) q^{78} +19.9328i q^{79} +(12.0544 - 99.5590i) q^{80} +88.8125 q^{81} +(87.1249 + 92.5385i) q^{82} -5.11617 q^{83} +(-55.1814 - 3.32847i) q^{84} +43.2140i q^{85} +(-48.4482 - 51.4585i) q^{86} +195.105i q^{87} +(-60.2562 + 50.2433i) q^{88} -17.9889 q^{89} +(-166.901 + 157.137i) q^{90} +6.39353 q^{91} +(-171.022 - 10.3158i) q^{92} +37.4448i q^{93} +(55.2075 - 51.9778i) q^{94} +17.4019i q^{95} +(99.1242 + 134.594i) q^{96} +12.4864 q^{97} +(-9.59685 - 10.1932i) q^{98} +179.332 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 8 q^{3} + 5 q^{4} - 22 q^{6} + 13 q^{8} + 48 q^{9}+O(q^{10}) \) 8 * q + q^2 - 8 * q^3 + 5 * q^4 - 22 * q^6 + 13 * q^8 + 48 * q^9	\( 8 q + q^{2} - 8 q^{3} + 5 q^{4} - 22 q^{6} + 13 q^{8} + 48 q^{9} + 16 q^{10} - 32 q^{11} + 30 q^{12} + 7 q^{14} - 71 q^{16} - 80 q^{17} - 29 q^{18} + 56 q^{19} - 108 q^{20} + 66 q^{22} + 22 q^{24} - 16 q^{25} + 24 q^{26} - 32 q^{27} + 7 q^{28} + 96 q^{30} - 19 q^{32} + 32 q^{33} + 74 q^{34} + 56 q^{35} - 33 q^{36} - 14 q^{38} + 84 q^{40} + 128 q^{41} - 98 q^{42} + 50 q^{44} - 152 q^{46} + 134 q^{48} - 56 q^{49} + 33 q^{50} - 368 q^{51} + 132 q^{52} - 228 q^{54} - 49 q^{56} + 56 q^{57} + 24 q^{58} + 104 q^{59} + 192 q^{60} + 120 q^{62} - 55 q^{64} - 72 q^{65} - 276 q^{66} + 304 q^{67} - 190 q^{68} + 56 q^{70} - 209 q^{72} - 112 q^{73} + 8 q^{74} + 72 q^{75} + 70 q^{76} - 304 q^{78} + 124 q^{80} + 48 q^{81} + 450 q^{82} + 72 q^{83} + 42 q^{84} + 210 q^{86} - 486 q^{88} - 512 q^{89} - 184 q^{90} - 56 q^{91} - 472 q^{92} + 472 q^{94} + 558 q^{96} + 64 q^{97} - 7 q^{98} + 256 q^{99}+O(q^{100}) \) 8 * q + q^2 - 8 * q^3 + 5 * q^4 - 22 * q^6 + 13 * q^8 + 48 * q^9 + 16 * q^10 - 32 * q^11 + 30 * q^12 + 7 * q^14 - 71 * q^16 - 80 * q^17 - 29 * q^18 + 56 * q^19 - 108 * q^20 + 66 * q^22 + 22 * q^24 - 16 * q^25 + 24 * q^26 - 32 * q^27 + 7 * q^28 + 96 * q^30 - 19 * q^32 + 32 * q^33 + 74 * q^34 + 56 * q^35 - 33 * q^36 - 14 * q^38 + 84 * q^40 + 128 * q^41 - 98 * q^42 + 50 * q^44 - 152 * q^46 + 134 * q^48 - 56 * q^49 + 33 * q^50 - 368 * q^51 + 132 * q^52 - 228 * q^54 - 49 * q^56 + 56 * q^57 + 24 * q^58 + 104 * q^59 + 192 * q^60 + 120 * q^62 - 55 * q^64 - 72 * q^65 - 276 * q^66 + 304 * q^67 - 190 * q^68 + 56 * q^70 - 209 * q^72 - 112 * q^73 + 8 * q^74 + 72 * q^75 + 70 * q^76 - 304 * q^78 + 124 * q^80 + 48 * q^81 + 450 * q^82 + 72 * q^83 + 42 * q^84 + 210 * q^86 - 486 * q^88 - 512 * q^89 - 184 * q^90 - 56 * q^91 - 472 * q^92 + 472 * q^94 + 558 * q^96 + 64 * q^97 - 7 * q^98 + 256 * q^99

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