LMFDB - Embedded newform 60.3.f.b.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,3,Mod(19,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("60.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	60.f (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:	$1.63488158616$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.389136420864.4
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 24x^{4} + 80x^{2} + 256 $ x^8 + 5x^6 + 24x^4 + 80*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.3
Root			$-0.656712 - 1.88911i$ of defining polynomial
Character	$\chi$	$=$	60.19
Dual form			60.3.f.b.19.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.656712 - 1.88911i) q^{2} -1.73205 q^{3} +(-3.13746 + 2.48120i) q^{4} +(-3.27492 - 3.77822i) q^{5} +(1.13746 + 3.27203i) q^{6} -9.55505 q^{7} +(6.74766 + 4.29756i) q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+(-0.656712 - 1.88911i) q^{2} -1.73205 q^{3} +(-3.13746 + 2.48120i) q^{4} +(-3.27492 - 3.77822i) q^{5} +(1.13746 + 3.27203i) q^{6} -9.55505 q^{7} +(6.74766 + 4.29756i) q^{8} +3.00000 q^{9} +(-4.98678 + 8.66787i) q^{10} -9.92480i q^{11} +(5.43424 - 4.29756i) q^{12} +7.55643i q^{13} +(6.27492 + 18.0505i) q^{14} +(5.67232 + 6.54406i) q^{15} +(3.68729 - 15.5693i) q^{16} -17.1903i q^{17} +(-1.97014 - 5.66732i) q^{18} -26.1762i q^{19} +(19.6494 + 3.72827i) q^{20} +16.5498 q^{21} +(-18.7490 + 6.51774i) q^{22} +1.67451 q^{23} +(-11.6873 - 7.44360i) q^{24} +(-3.54983 + 24.7467i) q^{25} +(14.2749 - 4.96240i) q^{26} -5.19615 q^{27} +(29.9786 - 23.7080i) q^{28} -0.350497 q^{29} +(8.63736 - 15.0132i) q^{30} +46.0258i q^{31} +(-31.8336 + 3.25887i) q^{32} +17.1903i q^{33} +(-32.4743 + 11.2890i) q^{34} +(31.2920 + 36.1010i) q^{35} +(-9.41238 + 7.44360i) q^{36} -22.6693i q^{37} +(-49.4498 + 17.1903i) q^{38} -13.0881i q^{39} +(-5.86091 - 39.5683i) q^{40} -77.2990 q^{41} +(-10.8685 - 31.2644i) q^{42} +41.7994 q^{43} +(24.6254 + 31.1386i) q^{44} +(-9.82475 - 11.3346i) q^{45} +(-1.09967 - 3.16332i) q^{46} -14.0866 q^{47} +(-6.38658 + 26.9669i) q^{48} +42.2990 q^{49} +(49.0804 - 9.54543i) q^{50} +29.7744i q^{51} +(-18.7490 - 23.7080i) q^{52} -22.6693i q^{53} +(3.41238 + 9.81609i) q^{54} +(-37.4980 + 32.5029i) q^{55} +(-64.4743 - 41.0634i) q^{56} +45.3386i q^{57} +(0.230175 + 0.662126i) q^{58} -94.7802i q^{59} +(-34.0338 - 6.45756i) q^{60} +38.0000 q^{61} +(86.9478 - 30.2257i) q^{62} -28.6652 q^{63} +(27.0619 + 57.9970i) q^{64} +(28.5498 - 24.7467i) q^{65} +(32.4743 - 11.2890i) q^{66} +29.8477 q^{67} +(42.6525 + 53.9337i) q^{68} -2.90033 q^{69} +(47.6489 - 82.8220i) q^{70} -7.19630i q^{71} +(20.2430 + 12.8927i) q^{72} -34.3805i q^{73} +(-42.8248 + 14.8872i) q^{74} +(6.14849 - 42.8625i) q^{75} +(64.9485 + 82.1269i) q^{76} +94.8320i q^{77} +(-24.7249 + 8.59513i) q^{78} -46.0258i q^{79} +(-70.8999 + 37.0569i) q^{80} +9.00000 q^{81} +(50.7632 + 146.026i) q^{82} -24.1336 q^{83} +(-51.9244 + 41.0634i) q^{84} +(-64.9485 + 56.2967i) q^{85} +(-27.4502 - 78.9636i) q^{86} +0.607078 q^{87} +(42.6525 - 66.9692i) q^{88} +100.199 q^{89} +(-14.9603 + 26.0036i) q^{90} -72.2021i q^{91} +(-5.25370 + 4.15479i) q^{92} -79.7191i q^{93} +(9.25083 + 26.6111i) q^{94} +(-98.8995 + 85.7250i) q^{95} +(55.1375 - 5.64452i) q^{96} -131.861i q^{97} +(-27.7783 - 79.9074i) q^{98} -29.7744i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 10 q^{4} + 4 q^{5} - 6 q^{6} + 24 q^{9}+O(q^{10}) $ 8 * q - 10 * q^4 + 4 * q^5 - 6 * q^6 + 24 * q^9	$ 8 q - 10 q^{4} + 4 q^{5} - 6 q^{6} + 24 q^{9} - 42 q^{10} + 20 q^{14} - 46 q^{16} + 52 q^{20} + 72 q^{21} - 18 q^{24} + 32 q^{25} + 84 q^{26} - 184 q^{29} - 60 q^{30} + 12 q^{34} - 30 q^{36} - 6 q^{40} - 256 q^{41} + 348 q^{44} + 12 q^{45} + 112 q^{46} - 24 q^{49} + 72 q^{50} - 18 q^{54} - 244 q^{56} + 6 q^{60} + 304 q^{61} - 10 q^{64} + 168 q^{65} - 12 q^{66} - 144 q^{69} - 104 q^{70} - 252 q^{74} - 24 q^{76} - 308 q^{80} + 72 q^{81} - 204 q^{84} + 24 q^{85} - 280 q^{86} + 560 q^{89} - 126 q^{90} + 376 q^{94} + 426 q^{96}+O(q^{100}) $ 8 * q - 10 * q^4 + 4 * q^5 - 6 * q^6 + 24 * q^9 - 42 * q^10 + 20 * q^14 - 46 * q^16 + 52 * q^20 + 72 * q^21 - 18 * q^24 + 32 * q^25 + 84 * q^26 - 184 * q^29 - 60 * q^30 + 12 * q^34 - 30 * q^36 - 6 * q^40 - 256 * q^41 + 348 * q^44 + 12 * q^45 + 112 * q^46 - 24 * q^49 + 72 * q^50 - 18 * q^54 - 244 * q^56 + 6 * q^60 + 304 * q^61 - 10 * q^64 + 168 * q^65 - 12 * q^66 - 144 * q^69 - 104 * q^70 - 252 * q^74 - 24 * q^76 - 308 * q^80 + 72 * q^81 - 204 * q^84 + 24 * q^85 - 280 * q^86 + 560 * q^89 - 126 * q^90 + 376 * q^94 + 426 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−0.656712	−	1.88911i	−0.328356	−	0.944554i
$2$	−0.656712	−	1.88911i	−0.328356	−	0.944554i
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	−3.13746	+	2.48120i	−0.784365	+	0.620300i
$5$	−3.27492	−	3.77822i	−0.654983	−	0.755643i
$5$	−3.27492	−	3.77822i	−0.654983	−	0.755643i
$6$	1.13746	+	3.27203i	0.189576	+	0.545339i
$7$	−9.55505			−1.36501			−0.682504	−	0.730882i	$-0.739109\pi$
$7$	−9.55505			−1.36501			−0.682504	+	0.730882i	$0.739109\pi$
$8$	6.74766	+	4.29756i	0.843458	+	0.537196i
$9$	3.00000			0.333333
$10$	−4.98678	+	8.66787i	−0.498678	+	0.866787i
$11$		−	9.92480i		−	0.902255i	−0.892460	−	0.451127i	$-0.851022\pi$
$11$		−	9.92480i		−	0.902255i	0.892460	−	0.451127i	$-0.148978\pi$
$12$	5.43424	−	4.29756i	0.452853	−	0.358130i
$13$			7.55643i			0.581264i	0.956835	+	0.290632i	$0.0938655\pi$
$13$			7.55643i			0.581264i	−0.956835	+	0.290632i	$0.906134\pi$
$14$	6.27492	+	18.0505i	0.448208	+	1.28932i
$15$	5.67232	+	6.54406i	0.378155	+	0.436271i
$16$	3.68729	−	15.5693i	0.230456	−	0.973083i
$17$		−	17.1903i		−	1.01119i	−0.862770	−	0.505596i	$-0.831273\pi$
$17$		−	17.1903i		−	1.01119i	0.862770	−	0.505596i	$-0.168727\pi$
$18$	−1.97014	−	5.66732i	−0.109452	−	0.314851i
$19$		−	26.1762i		−	1.37770i	−0.724905	−	0.688849i	$-0.758116\pi$
$19$		−	26.1762i		−	1.37770i	0.724905	−	0.688849i	$-0.241884\pi$
$20$	19.6494	+	3.72827i	0.982471	+	0.186414i
$21$	16.5498			0.788087
$22$	−18.7490	+	6.51774i	−0.852228	+	0.296261i
$23$	1.67451			0.0728047			0.0364023	−	0.999337i	$-0.488410\pi$
$23$	1.67451			0.0728047			0.0364023	+	0.999337i	$0.488410\pi$
$24$	−11.6873	−	7.44360i	−0.486971	−	0.310150i
$25$	−3.54983	+	24.7467i	−0.141993	+	0.989868i
$26$	14.2749	−	4.96240i	0.549035	−	0.190862i
$27$	−5.19615			−0.192450
$28$	29.9786	−	23.7080i	1.07066	−	0.846714i
$29$	−0.350497			−0.0120861			−0.00604305	−	0.999982i	$-0.501924\pi$
$29$	−0.350497			−0.0120861			−0.00604305	+	0.999982i	$0.501924\pi$
$30$	8.63736	−	15.0132i	0.287912	−	0.500440i
$31$			46.0258i			1.48470i	0.670010	+	0.742352i	$0.266290\pi$
$31$			46.0258i			1.48470i	−0.670010	+	0.742352i	$0.733710\pi$
$32$	−31.8336	+	3.25887i	−0.994801	+	0.101840i
$33$			17.1903i			0.520917i
$34$	−32.4743	+	11.2890i	−0.955125	+	0.332031i
$35$	31.2920	+	36.1010i	0.894057	+	1.03146i
$36$	−9.41238	+	7.44360i	−0.261455	+	0.206767i
$37$		−	22.6693i		−	0.612684i	−0.951922	−	0.306342i	$-0.900895\pi$
$37$		−	22.6693i		−	0.612684i	0.951922	−	0.306342i	$-0.0991051\pi$
$38$	−49.4498	+	17.1903i	−1.30131	+	0.452375i
$39$		−	13.0881i		−	0.335593i
$40$	−5.86091	−	39.5683i	−0.146523	−	0.989207i
$41$	−77.2990			−1.88534			−0.942671	−	0.333724i	$-0.891695\pi$
$41$	−77.2990			−1.88534			−0.942671	+	0.333724i	$0.891695\pi$
$42$	−10.8685	−	31.2644i	−0.258773	−	0.744391i
$43$	41.7994			0.972079			0.486039	−	0.873937i	$-0.338441\pi$
$43$	41.7994			0.972079			0.486039	+	0.873937i	$0.338441\pi$
$44$	24.6254	+	31.1386i	0.559668	+	0.707697i
$45$	−9.82475	−	11.3346i	−0.218328	−	0.251881i
$46$	−1.09967	−	3.16332i	−0.0239058	−	0.0687679i
$47$	−14.0866			−0.299715			−0.149857	−	0.988708i	$-0.547881\pi$
$47$	−14.0866			−0.299715			−0.149857	+	0.988708i	$0.547881\pi$
$48$	−6.38658	+	26.9669i	−0.133054	+	0.561810i
$49$	42.2990			0.863245
$50$	49.0804	−	9.54543i	0.981608	−	0.190909i
$51$			29.7744i			0.583812i
$52$	−18.7490	−	23.7080i	−0.360558	−	0.455923i
$53$		−	22.6693i		−	0.427723i	−0.976864	−	0.213861i	$-0.931396\pi$
$53$		−	22.6693i		−	0.427723i	0.976864	−	0.213861i	$-0.0686041\pi$
$54$	3.41238	+	9.81609i	0.0631921	+	0.181780i
$55$	−37.4980	+	32.5029i	−0.681783	+	0.590962i
$56$	−64.4743	−	41.0634i	−1.15133	−	0.733276i
$57$			45.3386i			0.795414i
$58$	0.230175	+	0.662126i	0.00396854	+	0.0114160i
$59$		−	94.7802i		−	1.60644i	−0.595680	−	0.803222i	$-0.703117\pi$
$59$		−	94.7802i		−	1.60644i	0.595680	−	0.803222i	$-0.296883\pi$
$60$	−34.0338	−	6.45756i	−0.567230	−	0.107626i
$61$	38.0000			0.622951			0.311475	−	0.950254i	$-0.399177\pi$
$61$	38.0000			0.622951			0.311475	+	0.950254i	$0.399177\pi$
$62$	86.9478	−	30.2257i	1.40238	−	0.487512i
$63$	−28.6652			−0.455002
$64$	27.0619	+	57.9970i	0.422842	+	0.906203i
$65$	28.5498	−	24.7467i	0.439228	−	0.380718i
$66$	32.4743	−	11.2890i	0.492034	−	0.171046i
$67$	29.8477			0.445488			0.222744	−	0.974877i	$-0.428499\pi$
$67$	29.8477			0.445488			0.222744	+	0.974877i	$0.428499\pi$
$68$	42.6525	+	53.9337i	0.627242	+	0.793143i
$69$	−2.90033			−0.0420338
$70$	47.6489	−	82.8220i	0.680699	−	1.18317i
$71$		−	7.19630i		−	0.101356i	−0.998715	−	0.0506782i	$-0.983862\pi$
$71$		−	7.19630i		−	0.101356i	0.998715	−	0.0506782i	$-0.0161383\pi$
$72$	20.2430	+	12.8927i	0.281153	+	0.179065i
$73$		−	34.3805i		−	0.470966i	−0.971878	−	0.235483i	$-0.924333\pi$
$73$		−	34.3805i		−	0.470966i	0.971878	−	0.235483i	$-0.0756672\pi$
$74$	−42.8248	+	14.8872i	−0.578713	+	0.201178i
$75$	6.14849	−	42.8625i	0.0819799	−	0.571500i
$76$	64.9485	+	82.1269i	0.854586	+	1.08062i
$77$			94.8320i			1.23158i
$78$	−24.7249	+	8.59513i	−0.316986	+	0.110194i
$79$		−	46.0258i		−	0.582606i	−0.956631	−	0.291303i	$-0.905911\pi$
$79$		−	46.0258i		−	0.582606i	0.956631	−	0.291303i	$-0.0940887\pi$
$80$	−70.8999	+	37.0569i	−0.886248	+	0.463211i
$81$	9.00000			0.111111
$82$	50.7632	+	146.026i	0.619063	+	1.78081i
$83$	−24.1336			−0.290767			−0.145383	−	0.989375i	$-0.546442\pi$
$83$	−24.1336			−0.290767			−0.145383	+	0.989375i	$0.546442\pi$
$84$	−51.9244	+	41.0634i	−0.618148	+	0.488851i
$85$	−64.9485	+	56.2967i	−0.764100	+	0.662314i
$86$	−27.4502	−	78.9636i	−0.319188	−	0.918181i
$87$	0.607078			0.00697791
$88$	42.6525	−	66.9692i	0.484687	−	0.761014i
$89$	100.199			1.12584			0.562918	−	0.826513i	$-0.309679\pi$
$89$	100.199			1.12584			0.562918	+	0.826513i	$0.309679\pi$
$90$	−14.9603	+	26.0036i	−0.166226	+	0.288929i
$91$		−	72.2021i		−	0.793430i
$92$	−5.25370	+	4.15479i	−0.0571054	+	0.0451607i
$93$		−	79.7191i		−	0.857195i
$94$	9.25083	+	26.6111i	0.0984131	+	0.283097i
$95$	−98.8995	+	85.7250i	−1.04105	+	0.902369i
$96$	55.1375	−	5.64452i	0.574349	−	0.0587971i
$97$		−	131.861i		−	1.35939i	−0.733494	−	0.679696i	$-0.762112\pi$
$97$		−	131.861i		−	1.35939i	0.733494	−	0.679696i	$-0.237888\pi$
$98$	−27.7783	−	79.9074i	−0.283452	−	0.815382i
$99$		−	29.7744i		−	0.300752i
$100$	−50.2640	−	86.4496i	−0.502640	−	0.864496i
$101$	29.4502			0.291586			0.145793	−	0.989315i	$-0.453427\pi$
$101$	29.4502			0.291586			0.145793	+	0.989315i	$0.453427\pi$
$102$	56.2471	−	19.5532i	0.551442	−	0.191698i
$103$	−143.786			−1.39598			−0.697991	−	0.716107i	$-0.745922\pi$
$103$	−143.786			−1.39598			−0.697991	+	0.716107i	$0.745922\pi$
$104$	−32.4743	+	50.9882i	−0.312252	+	0.490272i
$105$	−54.1993	−	62.5289i	−0.516184	−	0.595513i
$106$	−42.8248	+	14.8872i	−0.404007	+	0.140445i
$107$	35.1014			0.328050			0.164025	−	0.986456i	$-0.447552\pi$
$107$	35.1014			0.328050			0.164025	+	0.986456i	$0.447552\pi$
$108$	16.3027	−	12.8927i	0.150951	−	0.119377i
$109$	−151.498			−1.38989			−0.694947	−	0.719061i	$-0.744572\pi$
$109$	−151.498			−1.38989			−0.694947	+	0.719061i	$0.744572\pi$
$110$	86.0269	+	49.4928i	0.782063	+	0.449935i
$111$			39.2644i			0.353733i
$112$	−35.2323	+	148.766i	−0.314574	+	1.32827i
$113$			32.3031i			0.285868i	0.989732	+	0.142934i	$0.0456537\pi$
$113$			32.3031i			0.285868i	−0.989732	+	0.142934i	$0.954346\pi$
$114$	85.6495	−	29.7744i	0.751311	−	0.261179i
$115$	−5.48387	−	6.32665i	−0.0476858	−	0.0550143i
$116$	1.09967	−	0.869652i	0.00947990	−	0.00749700i
$117$			22.6693i			0.193755i
$118$	−179.050	+	62.2433i	−1.51737	+	0.527486i
$119$			164.254i			1.38028i
$120$	10.1514	+	68.5343i	0.0845949	+	0.571119i
$121$	22.4983			0.185937
$122$	−24.9551	−	71.7861i	−0.204550	−	0.588411i
$123$	133.886			1.08850
$124$	−114.199	−	144.404i	−0.920962	−	1.16455i
$125$	105.124	−	67.6313i	0.840990	−	0.541051i
$126$	18.8248	+	54.1516i	0.149403	+	0.429774i
$127$	192.053			1.51223			0.756116	−	0.654438i	$-0.227095\pi$
$127$	192.053			1.51223			0.756116	+	0.654438i	$0.227095\pi$
$128$	91.7908	−	89.2102i	0.717115	−	0.696954i
$129$	−72.3987			−0.561230
$130$	−65.4982	−	37.6823i	−0.503832	−	0.289864i
$131$		−	42.4277i		−	0.323876i	−0.986801	−	0.161938i	$-0.948226\pi$
$131$		−	42.4277i		−	0.323876i	0.986801	−	0.161938i	$-0.0517744\pi$
$132$	−42.6525	−	53.9337i	−0.323125	−	0.408589i
$133$			250.115i			1.88057i
$134$	−19.6013	−	56.3855i	−0.146279	−	0.420787i
$135$	17.0170	+	19.6322i	0.126052	+	0.145424i
$136$	73.8762	−	115.994i	0.543208	−	0.852897i
$137$			206.854i			1.50988i	0.655791	+	0.754942i	$0.272335\pi$
$137$			206.854i			1.50988i	−0.655791	+	0.754942i	$0.727665\pi$
$138$	1.90468	+	5.47904i	0.0138020	+	0.0397032i
$139$			46.0258i			0.331121i	0.986200	+	0.165561i	$0.0529433\pi$
$139$			46.0258i			0.331121i	−0.986200	+	0.165561i	$0.947057\pi$
$140$	−187.751	−	35.6238i	−1.34108	−	0.254456i
$141$	24.3987			0.173040
$142$	−13.5946	+	4.72590i	−0.0957366	+	0.0332810i
$143$	74.9961			0.524448
$144$	11.0619	−	46.7080i	0.0768186	−	0.324361i
$145$	1.14785	+	1.32425i	0.00791619	+	0.00913277i
$146$	−64.9485	+	22.5781i	−0.444853	+	0.154645i
$147$	−73.2640			−0.498395
$148$	56.2471	+	71.1240i	0.380048	+	0.480567i
$149$	11.6495			0.0781846			0.0390923	−	0.999236i	$-0.487553\pi$
$149$	11.6495			0.0781846			0.0390923	+	0.999236i	$0.487553\pi$
$150$	−85.0097	+	16.5332i	−0.566732	+	0.110221i
$151$			125.424i			0.830624i	0.909679	+	0.415312i	$0.136328\pi$
$151$			125.424i			0.830624i	−0.909679	+	0.415312i	$0.863672\pi$
$152$	112.494	−	176.628i	0.740093	−	1.16203i
$153$		−	51.5708i		−	0.337064i
$154$	179.148	−	62.2773i	1.16330	−	0.404398i
$155$	173.896	−	150.731i	1.12191	−	0.972457i
$156$	32.4743	+	41.0634i	0.208168	+	0.263227i
$157$		−	197.220i		−	1.25618i	−0.778140	−	0.628090i	$-0.783837\pi$
$157$		−	197.220i		−	1.25618i	0.778140	−	0.628090i	$-0.216163\pi$
$158$	−86.9478	+	30.2257i	−0.550303	+	0.191302i
$159$			39.2644i			0.246946i
$160$	116.565	+	109.602i	0.728532	+	0.685011i
$161$	−16.0000			−0.0993789
$162$	−5.91041	−	17.0020i	−0.0364840	−	0.104950i
$163$	18.4196			0.113004			0.0565018	−	0.998402i	$-0.482005\pi$
$163$	18.4196			0.113004			0.0565018	+	0.998402i	$0.482005\pi$
$164$	242.522	−	191.794i	1.47880	−	1.16948i
$165$	64.9485	−	56.2967i	0.393627	−	0.341192i
$166$	15.8488	+	45.5910i	0.0954749	+	0.274645i
$167$	−92.8920			−0.556240			−0.278120	−	0.960546i	$-0.589711\pi$
$167$	−92.8920			−0.556240			−0.278120	+	0.960546i	$0.589711\pi$
$168$	111.673	+	71.1240i	0.664718	+	0.423357i
$169$	111.900			0.662132
$170$	149.003	+	85.7241i	0.876488	+	0.504259i
$171$		−	78.5287i		−	0.459232i
$172$	−131.144	+	103.713i	−0.762464	+	0.602981i
$173$		−	117.501i		−	0.679198i	−0.940570	−	0.339599i	$-0.889709\pi$
$173$		−	117.501i		−	0.679198i	0.940570	−	0.339599i	$-0.110291\pi$
$174$	−0.398675	−	1.14684i	−0.00229124	−	0.00659101i
$175$	33.9189	−	236.456i	0.193822	−	1.35118i
$176$	−154.522	−	36.5956i	−0.877968	−	0.207930i
$177$			164.164i			0.927481i
$178$	−65.8021	−	189.287i	−0.369675	−	1.06341i
$179$			231.988i			1.29602i	0.761631	+	0.648011i	$0.224399\pi$
$179$			231.988i			1.29602i	−0.761631	+	0.648011i	$0.775601\pi$
$180$	58.9483	+	11.1848i	0.327490	+	0.0621379i
$181$	−218.096			−1.20495			−0.602476	−	0.798137i	$-0.705819\pi$
$181$	−218.096			−1.20495			−0.602476	+	0.798137i	$0.705819\pi$
$182$	−136.398	+	47.4160i	−0.749437	+	0.260527i
$183$	−65.8179			−0.359661
$184$	11.2990	+	7.19630i	0.0614076	+	0.0391103i
$185$	−85.6495	+	74.2401i	−0.462970	+	0.401298i
$186$	−150.598	+	52.3525i	−0.809667	+	0.281465i
$187$	−170.610			−0.912352
$188$	44.1961	−	34.9516i	0.235085	−	0.185913i
$189$	49.6495			0.262696
$190$	226.892	+	130.535i	1.19417	+	0.687027i
$191$		−	137.208i		−	0.718366i	−0.933267	−	0.359183i	$-0.883055\pi$
$191$		−	137.208i		−	0.718366i	0.933267	−	0.359183i	$-0.116945\pi$
$192$	−46.8725	−	100.454i	−0.244128	−	0.523197i
$193$		−	37.0290i		−	0.191860i	−0.995388	−	0.0959301i	$-0.969417\pi$
$193$		−	37.0290i		−	0.191860i	0.995388	−	0.0959301i	$-0.0305825\pi$
$194$	−249.100	+	86.5947i	−1.28402	+	0.446364i
$195$	−49.4498	+	42.8625i	−0.253589	+	0.219808i
$196$	−132.711	+	104.952i	−0.677099	+	0.535471i
$197$		−	194.572i		−	0.987674i	−0.869554	−	0.493837i	$-0.835594\pi$
$197$		−	194.572i		−	0.987674i	0.869554	−	0.493837i	$-0.164406\pi$
$198$	−56.2471	+	19.5532i	−0.284076	+	0.0987536i
$199$			176.037i			0.884610i	0.896865	+	0.442305i	$0.145839\pi$
$199$			176.037i			0.884610i	−0.896865	+	0.442305i	$0.854161\pi$
$200$	−130.304	+	151.727i	−0.651518	+	0.758633i
$201$	−51.6977			−0.257202
$202$	−19.3403	−	55.6345i	−0.0957440	−	0.275419i
$203$	3.34901			0.0164976
$204$	−73.8762	−	93.4159i	−0.362138	−	0.457921i
$205$	253.148	+	292.052i	1.23487	+	1.42465i
$206$	94.4261	+	271.628i	0.458379	+	1.31858i
$207$	5.02352			0.0242682
$208$	117.649	+	27.8628i	0.565618	+	0.133956i
$209$	−259.794			−1.24303
$210$	−82.5304	+	143.452i	−0.393002	+	0.683104i
$211$		−	20.7193i		−	0.0981955i	−0.998794	−	0.0490978i	$-0.984365\pi$
$211$		−	20.7193i		−	0.0981955i	0.998794	−	0.0490978i	$-0.0156346\pi$
$212$	56.2471	+	71.1240i	0.265316	+	0.335490i
$213$			12.4644i			0.0585181i
$214$	−23.0515	−	66.3103i	−0.107717	−	0.309861i
$215$	−136.890	−	157.927i	−0.636696	−	0.734545i
$216$	−35.0619	−	22.3308i	−0.162324	−	0.103383i
$217$		−	439.779i		−	2.02663i
$218$	99.4908	+	286.197i	0.456380	+	1.31283i
$219$			59.5488i			0.271912i
$220$	37.0024	−	195.017i	0.168193	−	0.886439i
$221$	129.897			0.587769
$222$	74.1746	−	25.7854i	0.334120	−	0.116150i
$223$	−97.0265			−0.435096			−0.217548	−	0.976050i	$-0.569806\pi$
$223$	−97.0265			−0.435096			−0.217548	+	0.976050i	$0.569806\pi$
$224$	304.172	−	31.1386i	1.35791	−	0.139012i
$225$	−10.6495	+	74.2401i	−0.0473311	+	0.329956i
$226$	61.0241	−	21.2138i	0.270018	−	0.0938666i
$227$	−407.256			−1.79408			−0.897040	−	0.441948i	$-0.854287\pi$
$227$	−407.256			−1.79408			−0.897040	+	0.441948i	$0.854287\pi$
$228$	−112.494	−	142.248i	−0.493395	−	0.623895i
$229$	−7.89702			−0.0344848			−0.0172424	−	0.999851i	$-0.505489\pi$
$229$	−7.89702			−0.0344848			−0.0172424	+	0.999851i	$0.505489\pi$
$230$	−8.35040	+	14.5144i	−0.0363061	+	0.0631061i
$231$		−	164.254i		−	0.711055i
$232$	−2.36503	−	1.50628i	−0.0101941	−	0.00649260i
$233$			28.1483i			0.120808i	0.998174	+	0.0604042i	$0.0192390\pi$
$233$			28.1483i			0.120808i	−0.998174	+	0.0604042i	$0.980761\pi$
$234$	42.8248	−	14.8872i	0.183012	−	0.0636205i
$235$	46.1324	+	53.2222i	0.196308	+	0.226477i
$236$	235.169	+	297.369i	0.996477	+	1.26004i
$237$			79.7191i			0.336368i
$238$	310.293	−	107.867i	1.30375	−	0.453225i
$239$		−	296.005i		−	1.23851i	−0.785189	−	0.619257i	$-0.787434\pi$
$239$		−	296.005i		−	1.23851i	0.785189	−	0.619257i	$-0.212566\pi$
$240$	122.802	−	64.1844i	0.511676	−	0.267435i
$241$	465.794			1.93276			0.966378	−	0.257127i	$-0.0827758\pi$
$241$	465.794			1.93276			0.966378	+	0.257127i	$0.0827758\pi$
$242$	−14.7749	−	42.5018i	−0.0610534	−	0.175627i
$243$	−15.5885			−0.0641500
$244$	−119.223	+	94.2856i	−0.488621	+	0.386416i
$245$	−138.526	−	159.815i	−0.565411	−	0.652305i
$246$	−87.9244	−	252.925i	−0.357416	−	1.02815i
$247$	197.799			0.800806
$248$	−197.799	+	310.567i	−0.797577	+	1.25229i
$249$	41.8007			0.167874
$250$	−196.799	−	154.176i	−0.787196	−	0.616703i
$251$			141.676i			0.564445i	0.959349	+	0.282223i	$0.0910716\pi$
$251$			141.676i			0.564445i	−0.959349	+	0.282223i	$0.908928\pi$
$252$	89.9357	−	71.1240i	0.356888	−	0.282238i
$253$		−	16.6191i		−	0.0656883i
$254$	−126.124	−	362.810i	−0.496550	−	1.42838i
$255$	112.494	−	97.5087i	0.441153	−	0.382387i
$256$	−228.808	−	114.817i	−0.893780	−	0.448505i
$257$			41.7549i			0.162470i	0.996695	+	0.0812352i	$0.0258865\pi$
$257$			41.7549i			0.162470i	−0.996695	+	0.0812352i	$0.974113\pi$
$258$	47.5451	+	136.769i	0.184283	+	0.530112i
$259$			216.606i			0.836318i
$260$	−28.1724	+	148.480i	−0.108356	+	0.571075i
$261$	−1.05149			−0.00402870
$262$	−80.1505	+	27.8628i	−0.305918	+	0.106346i
$263$	203.283			0.772939			0.386469	−	0.922302i	$-0.373694\pi$
$263$	203.283			0.772939			0.386469	+	0.922302i	$0.373694\pi$
$264$	−73.8762	+	115.994i	−0.279834	+	0.439371i
$265$	−85.6495	+	74.2401i	−0.323206	+	0.280151i
$266$	472.495	−	164.254i	1.77630	−	0.617495i
$267$	−173.550			−0.650001
$268$	−93.6458	+	74.0580i	−0.349425	+	0.276336i
$269$	−244.048			−0.907242			−0.453621	−	0.891195i	$-0.649868\pi$
$269$	−244.048			−0.907242			−0.453621	+	0.891195i	$0.649868\pi$
$270$	25.9121	−	45.0396i	0.0959706	−	0.166813i
$271$		−	466.585i		−	1.72172i	−0.508845	−	0.860858i	$-0.669927\pi$
$271$		−	466.585i		−	1.72172i	0.508845	−	0.860858i	$-0.330073\pi$
$272$	−267.641	−	63.3855i	−0.983973	−	0.233035i
$273$			125.058i			0.458087i
$274$	390.770	−	135.844i	1.42617	−	0.495780i
$275$	245.606	+	35.2314i	0.893113	+	0.128114i
$276$	9.09967	−	7.19630i	0.0329698	−	0.0260736i
$277$			494.181i			1.78405i	0.451990	+	0.892023i	$0.350714\pi$
$277$			494.181i			1.78405i	−0.451990	+	0.892023i	$0.649286\pi$
$278$	86.9478	−	30.2257i	0.312762	−	0.108726i
$279$			138.078i			0.494902i
$280$	56.0013	+	378.077i	0.200005	+	1.35028i
$281$	−43.4020			−0.154455			−0.0772277	−	0.997013i	$-0.524607\pi$
$281$	−43.4020			−0.154455			−0.0772277	+	0.997013i	$0.524607\pi$
$282$	−16.0229	−	46.0917i	−0.0568188	−	0.163446i
$283$	310.785			1.09818			0.549090	−	0.835763i	$-0.314974\pi$
$283$	310.785			1.09818			0.549090	+	0.835763i	$0.314974\pi$
$284$	17.8555	+	22.5781i	0.0628714	+	0.0795003i
$285$	171.299	−	148.480i	0.601049	−	0.520983i
$286$	−49.2508	−	141.676i	−0.172206	−	0.495370i
$287$	738.596			2.57351
$288$	−95.5009	+	9.77660i	−0.331600	+	0.0339465i
$289$	−6.50497			−0.0225085
$290$	1.74785	−	3.03806i	0.00602707	−	0.0104761i
$291$			228.390i			0.784845i
$292$	85.3049	+	107.867i	0.292140	+	0.369409i
$293$		−	245.207i		−	0.836886i	−0.908243	−	0.418443i	$-0.862576\pi$
$293$		−	245.207i		−	0.836886i	0.908243	−	0.418443i	$-0.137424\pi$
$294$	48.1134	+	138.404i	0.163651	+	0.470761i
$295$	−358.100	+	310.397i	−1.21390	+	1.05219i
$296$	97.4228	−	152.965i	0.329131	−	0.516773i
$297$			51.5708i			0.173639i
$298$	−7.65037	−	22.0072i	−0.0256724	−	0.0738496i
$299$			12.6533i			0.0423187i
$300$	87.0599	+	149.735i	0.290200	+	0.499117i
$301$	−399.395			−1.32689
$302$	236.940	−	82.3676i	0.784569	−	0.272740i
$303$	−51.0092			−0.168347
$304$	−407.547	−	96.5195i	−1.34061	−	0.317498i
$305$	−124.447	−	143.572i	−0.408022	−	0.470729i
$306$	−97.4228	+	33.8671i	−0.318375	+	0.110677i
$307$	−337.514			−1.09939			−0.549697	−	0.835364i	$-0.685257\pi$
$307$	−337.514			−1.09939			−0.549697	+	0.835364i	$0.685257\pi$
$308$	−235.297	−	297.531i	−0.763952	−	0.966011i
$309$	249.045			0.805970
$310$	−398.946	−	229.521i	−1.28692	−	0.740390i
$311$			427.756i			1.37542i	0.725986	+	0.687710i	$0.241384\pi$
$311$			427.756i			1.37542i	−0.725986	+	0.687710i	$0.758616\pi$
$312$	56.2471	−	88.3142i	0.180279	−	0.283058i
$313$			83.8739i			0.267968i	0.990984	+	0.133984i	$0.0427770\pi$
$313$			83.8739i			0.267968i	−0.990984	+	0.133984i	$0.957223\pi$
$314$	−372.571	+	129.517i	−1.18653	+	0.412475i
$315$	93.8760	+	108.303i	0.298019	+	0.343820i
$316$	114.199	+	144.404i	0.361390	+	0.456975i
$317$			112.204i			0.353957i	0.984215	+	0.176978i	$0.0566323\pi$
$317$			112.204i			0.353957i	−0.984215	+	0.176978i	$0.943368\pi$
$318$	74.1746	−	25.7854i	0.233254	−	0.0810861i
$319$			3.47861i			0.0109047i
$320$	130.500	−	292.181i	0.407812	−	0.913066i
$321$	−60.7974			−0.189400
$322$	10.5074	+	30.2257i	0.0326317	+	0.0938687i
$323$	−449.976			−1.39312
$324$	−28.2371	+	22.3308i	−0.0871516	+	0.0689222i
$325$	−186.997	−	26.8241i	−0.575374	−	0.0825356i
$326$	−12.0964	−	34.7966i	−0.0371054	−	0.106738i
$327$	262.403			0.802455
$328$	−521.588	−	332.197i	−1.59021	−	1.01280i
$329$	134.598			0.409113
$330$	−149.003	−	85.7241i	−0.451524	−	0.259770i
$331$			132.621i			0.400666i	0.979728	+	0.200333i	$0.0642025\pi$
$331$			132.621i			0.400666i	−0.979728	+	0.200333i	$0.935798\pi$
$332$	75.7182	−	59.8803i	0.228067	−	0.180362i
$333$		−	68.0079i		−	0.204228i
$334$	61.0033	+	175.483i	0.182645	+	0.525398i
$335$	−97.7487	−	112.771i	−0.291787	−	0.336630i
$336$	61.0241	−	257.670i	0.181619	−	0.766874i
$337$			20.7739i			0.0616437i	0.999525	+	0.0308219i	$0.00981246\pi$
$337$			20.7739i			0.0616437i	−0.999525	+	0.0308219i	$0.990188\pi$
$338$	−73.4863	−	211.392i	−0.217415	−	0.625420i
$339$		−	55.9506i		−	0.165046i
$340$	64.0900	−	337.779i	0.188500	−	0.993467i
$341$	456.797			1.33958
$342$	−148.349	+	51.5708i	−0.433770	+	0.150792i
$343$	64.0283			0.186672
$344$	282.048	+	179.636i	0.819907	+	0.522196i
$345$	9.49834	+	10.9581i	0.0275314	+	0.0317625i
$346$	−221.973	+	77.1645i	−0.641539	+	0.223019i
$347$	−8.89616			−0.0256374			−0.0128187	−	0.999918i	$-0.504080\pi$
$347$	−8.89616			−0.0256374			−0.0128187	+	0.999918i	$0.504080\pi$
$348$	−1.90468	+	1.50628i	−0.00547323	+	0.00432840i
$349$	19.4020			0.0555931			0.0277965	−	0.999614i	$-0.491151\pi$
$349$	19.4020			0.0555931			0.0277965	+	0.999614i	$0.491151\pi$
$350$	−468.966	+	91.2071i	−1.33990	+	0.260592i
$351$		−	39.2644i		−	0.111864i
$352$	32.3436	+	315.942i	0.0918853	+	0.897564i
$353$			80.2902i			0.227451i	0.993512	+	0.113726i	$0.0362784\pi$
$353$			80.2902i			0.227451i	−0.993512	+	0.113726i	$0.963722\pi$
$354$	310.124	−	107.809i	0.876056	−	0.304544i
$355$	−27.1892	+	23.5673i	−0.0765892	+	0.0663867i
$356$	−314.371	+	248.615i	−0.883065	+	0.698356i
$357$		−	284.496i		−	0.796907i
$358$	438.251	−	152.349i	1.22416	−	0.425557i
$359$		−	314.115i		−	0.874972i	−0.899225	−	0.437486i	$-0.855869\pi$
$359$		−	314.115i		−	0.874972i	0.899225	−	0.437486i	$-0.144131\pi$
$360$	−17.5827	−	118.705i	−0.0488409	−	0.329736i
$361$	−324.196			−0.898050
$362$	143.227	+	412.008i	0.395653	+	1.13814i
$363$	−38.9683			−0.107351
$364$	179.148	+	226.531i	0.492164	+	0.622338i
$365$	−129.897	+	112.593i	−0.355882	+	0.308475i
$366$	43.2234	+	124.337i	0.118097	+	0.339719i
$367$	476.800			1.29918			0.649592	−	0.760283i	$-0.274940\pi$
$367$	476.800			1.29918			0.649592	+	0.760283i	$0.274940\pi$
$368$	6.17440	−	26.0709i	0.0167783	−	0.0708450i
$369$	−231.897			−0.628447
$370$	196.495	+	113.047i	0.531066	+	0.305532i
$371$			216.606i			0.583844i
$372$	197.799	+	250.115i	0.531718	+	0.672353i
$373$		−	86.1333i		−	0.230920i	−0.993312	−	0.115460i	$-0.963166\pi$
$373$		−	86.1333i		−	0.230920i	0.993312	−	0.115460i	$-0.0368343\pi$
$374$	112.042	+	322.300i	0.299576	+	0.861766i
$375$	−182.080	+	117.141i	−0.485546	+	0.312376i
$376$	−95.0515	−	60.5380i	−0.252797	−	0.161005i
$377$		−	2.64850i		−	0.00702521i
$378$	−32.6054	−	93.7933i	−0.0862577	−	0.248130i
$379$		−	638.035i		−	1.68347i	−0.539891	−	0.841735i	$-0.681534\pi$
$379$		−	638.035i		−	1.68347i	0.539891	−	0.841735i	$-0.318466\pi$
$380$	97.5922	−	514.348i	0.256822	−	1.35355i
$381$	−332.646			−0.873087
$382$	−259.201	+	90.1061i	−0.678535	+	0.235880i
$383$	−216.742			−0.565907			−0.282953	−	0.959134i	$-0.591314\pi$
$383$	−216.742			−0.565907			−0.282953	+	0.959134i	$0.591314\pi$
$384$	−158.986	+	154.517i	−0.414027	+	0.402387i
$385$	358.296	−	310.567i	0.930638	−	0.806667i
$386$	−69.9518	+	24.3174i	−0.181222	+	0.0629985i
$387$	125.398			0.324026
$388$	327.174	+	413.708i	0.843231	+	1.06626i
$389$	476.640			1.22529			0.612647	−	0.790356i	$-0.290105\pi$
$389$	476.640			1.22529			0.612647	+	0.790356i	$0.290105\pi$
$390$	113.446	+	65.2676i	0.290888	+	0.167353i
$391$		−	28.7852i		−	0.0736195i
$392$	285.419	+	181.783i	0.728111	+	0.463731i
$393$			73.4869i			0.186990i
$394$	−367.567	+	127.778i	−0.932912	+	0.324309i
$395$	−173.896	+	150.731i	−0.440242	+	0.381597i
$396$	73.8762	+	93.4159i	0.186556	+	0.235899i
$397$			43.0792i			0.108512i	0.998527	+	0.0542559i	$0.0172787\pi$
$397$			43.0792i			0.108512i	−0.998527	+	0.0542559i	$0.982721\pi$
$398$	332.554	−	115.606i	0.835562	−	0.290467i
$399$		−	433.213i		−	1.08575i
$400$	372.200	+	146.517i	0.930500	+	0.366292i
$401$	−168.694			−0.420684			−0.210342	−	0.977628i	$-0.567458\pi$
$401$	−168.694			−0.420684			−0.210342	+	0.977628i	$0.567458\pi$
$402$	33.9505	+	97.6625i	0.0844540	+	0.242942i
$403$	−347.791			−0.863005
$404$	−92.3987	+	73.0718i	−0.228710	+	0.180871i
$405$	−29.4743	−	34.0039i	−0.0727759	−	0.0839604i
$406$	−2.19934	−	6.32665i	−0.00541709	−	0.0155829i
$407$	−224.988			−0.552797
$408$	−127.957	+	200.908i	−0.313621	+	0.492421i
$409$	373.890			0.914157			0.457079	−	0.889426i	$-0.348896\pi$
$409$	373.890			0.914157			0.457079	+	0.889426i	$0.348896\pi$
$410$	385.473	−	670.018i	0.940179	−	1.63419i
$411$		−	358.282i		−	0.871732i
$412$	451.123	−	356.762i	1.09496	−	0.865927i
$413$			905.630i			2.19281i
$414$	−3.29901	−	9.48997i	−0.00796862	−	0.0229226i
$415$	79.0356	+	91.1820i	0.190447	+	0.219716i
$416$	−24.6254	−	240.549i	−0.0591957	−	0.578242i
$417$		−	79.7191i		−	0.191173i
$418$	170.610	+	490.779i	0.408158	+	1.17411i
$419$		−	87.5839i		−	0.209031i	−0.994523	−	0.104515i	$-0.966671\pi$
$419$		−	87.5839i		−	0.209031i	0.994523	−	0.104515i	$-0.0333291\pi$
$420$	325.195	+	61.7023i	0.774273	+	0.146910i
$421$	70.3023			0.166989			0.0834944	−	0.996508i	$-0.473392\pi$
$421$	70.3023			0.166989			0.0834944	+	0.996508i	$0.473392\pi$
$422$	−39.1409	+	13.6066i	−0.0927510	+	0.0322431i
$423$	−42.2597			−0.0999048
$424$	97.4228	−	152.965i	0.229771	−	0.360766i
$425$	425.402	+	61.0226i	1.00095	+	0.143583i
$426$	23.5465	−	8.18550i	0.0552735	−	0.0192148i
$427$	−363.092			−0.850332
$428$	−110.129	+	87.0935i	−0.257311	+	0.203490i
$429$	−129.897			−0.302790
$430$	−208.444	+	362.312i	−0.484754	+	0.842586i
$431$		−	247.370i		−	0.573944i	−0.957939	−	0.286972i	$-0.907351\pi$
$431$		−	247.370i		−	0.573944i	0.957939	−	0.286972i	$-0.0926487\pi$
$432$	−19.1597	+	80.9006i	−0.0443512	+	0.187270i
$433$		−	636.247i		−	1.46939i	−0.678397	−	0.734696i	$-0.737325\pi$
$433$		−	636.247i		−	1.46939i	0.678397	−	0.734696i	$-0.262675\pi$
$434$	−830.791	+	288.808i	−1.91426	+	0.665457i
$435$	−1.98813	−	2.29367i	−0.00457041	−	0.00527281i
$436$	475.320	−	375.898i	1.09018	−	0.862151i
$437$		−	43.8323i		−	0.100303i
$438$	112.494	−	39.1064i	0.256836	−	0.0892840i
$439$		−	769.786i		−	1.75350i	−0.480947	−	0.876750i	$-0.659707\pi$
$439$		−	769.786i		−	1.75350i	0.480947	−	0.876750i	$-0.340293\pi$
$440$	−392.707	+	58.1683i	−0.892517	+	0.132201i
$441$	126.897			0.287748
$442$	−85.3049	−	245.390i	−0.192998	−	0.555180i
$443$	612.214			1.38197			0.690986	−	0.722868i	$-0.257177\pi$
$443$	612.214			1.38197			0.690986	+	0.722868i	$0.257177\pi$
$444$	−97.4228	−	123.190i	−0.219421	−	0.277456i
$445$	−328.145	−	378.575i	−0.737403	−	0.850730i
$446$	63.7185	+	183.294i	0.142867	+	0.410972i
$447$	−20.1775			−0.0451399
$448$	−258.578	−	554.165i	−0.577182	−	1.23697i
$449$	175.897			0.391753			0.195876	−	0.980629i	$-0.437245\pi$
$449$	175.897			0.391753			0.195876	+	0.980629i	$0.437245\pi$
$450$	147.241	−	28.6363i	0.327203	−	0.0636362i
$451$			767.177i			1.70106i
$452$	−80.1505	−	101.350i	−0.177324	−	0.224225i
$453$		−	217.241i		−	0.479561i
$454$	267.450	+	769.351i	0.589097	+	1.69461i
$455$	−272.795	+	236.456i	−0.599550	+	0.519683i
$456$	−194.846	+	305.929i	−0.427293	+	0.670898i
$457$			365.357i			0.799469i	0.916631	+	0.399734i	$0.130898\pi$
$457$			365.357i			0.799469i	−0.916631	+	0.399734i	$0.869102\pi$
$458$	5.18607	+	14.9183i	0.0113233	+	0.0325728i
$459$			89.3232i			0.194604i
$460$	32.9031	+	6.24302i	0.0715285	+	0.0135718i
$461$	308.350			0.668873			0.334437	−	0.942418i	$-0.391454\pi$
$461$	308.350			0.668873			0.334437	+	0.942418i	$0.391454\pi$
$462$	−310.293	+	107.867i	−0.671630	+	0.233479i
$463$	92.6302			0.200065			0.100033	−	0.994984i	$-0.468105\pi$
$463$	92.6302			0.200065			0.100033	+	0.994984i	$0.468105\pi$
$464$	−1.29238	+	5.45700i	−0.00278531	+	0.0117608i
$465$	−301.196	+	261.073i	−0.647733	+	0.561448i
$466$	53.1752	−	18.4854i	0.114110	−	0.0396681i
$467$	−606.103			−1.29786			−0.648932	−	0.760846i	$-0.724784\pi$
$467$	−606.103			−1.29786			−0.648932	+	0.760846i	$0.724784\pi$
$468$	−56.2471	−	71.1240i	−0.120186	−	0.151974i
$469$	−285.196			−0.608094
$470$	70.2467	−	122.101i	0.149461	−	0.259789i
$471$			341.596i			0.725256i
$472$	407.324	−	639.545i	0.862975	−	1.35497i
$473$		−	414.851i		−	0.877063i
$474$	150.598	−	52.3525i	0.317717	−	0.110448i
$475$	647.776	+	92.9214i	1.36374	+	0.195624i
$476$	−407.547	−	515.339i	−0.856190	−	1.08265i
$477$		−	68.0079i		−	0.142574i
$478$	−559.185	+	194.390i	−1.16984	+	0.406673i
$479$			138.947i			0.290078i	0.989426	+	0.145039i	$0.0463307\pi$
$479$			138.947i			0.290078i	−0.989426	+	0.145039i	$0.953669\pi$
$480$	−201.897	−	189.836i	−0.420618	−	0.395491i
$481$	171.299			0.356131
$482$	−305.893	−	879.935i	−0.634632	−	1.82559i
$483$	27.7128			0.0573764
$484$	−70.5876	+	55.8229i	−0.145842	+	0.115337i
$485$	−498.199	+	431.834i	−1.02722	+	0.890379i
$486$	10.2371	+	29.4483i	0.0210640	+	0.0605932i
$487$	201.243			0.413230			0.206615	−	0.978422i	$-0.433755\pi$
$487$	201.243			0.413230			0.206615	+	0.978422i	$0.433755\pi$
$488$	256.411	+	163.307i	0.525433	+	0.334646i
$489$	−31.9036			−0.0652426
$490$	−210.936	+	366.642i	−0.430481	+	0.748250i
$491$		−	347.368i		−	0.707470i	−0.935346	−	0.353735i	$-0.884911\pi$
$491$		−	347.368i		−	0.707470i	0.935346	−	0.353735i	$-0.115089\pi$
$492$	−420.061	+	332.197i	−0.853783	+	0.675198i
$493$			6.02513i			0.0122214i
$494$	−129.897	−	373.664i	−0.262949	−	0.756404i
$495$	−112.494	+	97.5087i	−0.227261	+	0.196987i
$496$	716.591	+	169.711i	1.44474	+	0.342159i
$497$			68.7610i			0.138352i
$498$	−27.4510	−	78.9660i	−0.0551225	−	0.158566i
$499$			672.277i			1.34725i	0.739074	+	0.673625i	$0.235264\pi$
$499$			672.277i			1.34725i	−0.739074	+	0.673625i	$0.764736\pi$
$500$	−162.015	+	473.024i	−0.324029	+	0.946047i
$501$	160.894			0.321145
$502$	267.641	−	93.0401i	0.533149	−	0.185339i
$503$	−436.350			−0.867496			−0.433748	−	0.901034i	$-0.642809\pi$
$503$	−436.350			−0.867496			−0.433748	+	0.901034i	$0.642809\pi$
$504$	−193.423	−	123.190i	−0.383775	−	0.244425i
$505$	−96.4469	−	111.269i	−0.190984	−	0.220335i
$506$	−31.3954	+	10.9140i	−0.0620462	+	0.0215692i
$507$	−193.817			−0.382282
$508$	−602.559	+	476.523i	−1.18614	+	0.938037i
$509$	−109.547			−0.215219			−0.107610	−	0.994193i	$-0.534320\pi$
$509$	−109.547			−0.215219			−0.107610	+	0.994193i	$0.534320\pi$
$510$	−258.081	−	148.478i	−0.506041	−	0.291134i
$511$			328.508i			0.642872i
$512$	−66.6415	+	507.644i	−0.130159	+	0.991493i
$513$			136.016i			0.265138i
$514$	78.8796	−	27.4210i	0.153462	−	0.0533482i
$515$	470.888	+	543.255i	0.914345	+	1.05486i
$516$	227.148	−	179.636i	0.440209	−	0.348131i
$517$			139.807i			0.270419i
$518$	409.193	−	142.248i	0.789947	−	0.274610i
$519$			203.518i			0.392135i
$520$	298.995	−	44.2875i	0.574991	−	0.0851683i
$521$	−743.100			−1.42629			−0.713147	−	0.701014i	$-0.752731\pi$
$521$	−743.100			−1.42629			−0.713147	+	0.701014i	$0.752731\pi$
$522$	0.690526	+	1.98638i	0.00132285	+	0.00380532i
$523$	366.211			0.700212			0.350106	−	0.936710i	$-0.386146\pi$
$523$	366.211			0.700212			0.350106	+	0.936710i	$0.386146\pi$
$524$	105.272	+	133.115i	0.200900	+	0.254037i
$525$	−58.7492	+	409.554i	−0.111903	+	0.780102i
$526$	−133.498	−	384.023i	−0.253799	−	0.730083i
$527$	791.196			1.50132
$528$	267.641	+	63.3855i	0.506895	+	0.120048i
$529$	−526.196			−0.994699
$530$	196.495	+	113.047i	0.370744	+	0.213296i
$531$		−	284.341i		−	0.535481i
$532$	−620.586	−	784.727i	−1.16652	−	1.47505i
$533$		−	584.105i		−	1.09588i
$534$	113.973	+	327.855i	0.213432	+	0.613961i
$535$	−114.954	−	132.621i	−0.214867	−	0.247889i
$536$	201.402	+	128.272i	0.375750	+	0.239314i
$537$		−	401.815i		−	0.748259i
$538$	160.269	+	461.033i	0.297898	+	0.856939i
$539$		−	419.809i		−	0.778867i
$540$	−102.101	−	19.3727i	−0.189077	−	0.0358753i
$541$	170.688			0.315504			0.157752	−	0.987479i	$-0.449575\pi$
$541$	170.688			0.315504			0.157752	+	0.987479i	$0.449575\pi$
$542$	−881.430	+	306.412i	−1.62625	+	0.565336i
$543$	377.754			0.695680
$544$	56.0208	+	547.228i	0.102979	+	1.00593i
$545$	496.145	+	572.393i	0.910357	+	1.05026i
$546$	236.248	−	82.1269i	0.432688	−	0.150416i
$547$	−507.600			−0.927971			−0.463986	−	0.885843i	$-0.653581\pi$
$547$	−507.600			−0.927971			−0.463986	+	0.885843i	$0.653581\pi$
$548$	−513.247	−	648.997i	−0.936581	−	1.18430i
$549$	114.000			0.207650
$550$	−94.7365	−	487.113i	−0.172248	−	0.885660i
$551$			9.17469i			0.0166510i
$552$	−19.5705	−	12.4644i	−0.0354537	−	0.0225804i
$553$			439.779i			0.795261i
$554$	933.561	−	324.534i	1.68513	−	0.585802i
$555$	148.349	−	128.588i	0.267296	−	0.231689i
$556$	−114.199	−	144.404i	−0.205394	−	0.259720i
$557$		−	788.492i		−	1.41561i	−0.706410	−	0.707803i	$-0.749686\pi$
$557$		−	788.492i		−	1.41561i	0.706410	−	0.707803i	$-0.250314\pi$
$558$	260.843	−	90.6772i	0.467461	−	0.162504i
$559$			315.854i			0.565035i
$560$	677.452	−	354.080i	1.20974	−	0.632286i
$561$	295.505			0.526747
$562$	28.5026	+	81.9910i	0.0507164	+	0.145892i
$563$	936.102			1.66270			0.831351	−	0.555747i	$-0.187568\pi$
$563$	936.102			1.66270			0.831351	+	0.555747i	$0.187568\pi$
$564$	−76.5498	+	60.5380i	−0.135727	+	0.107337i
$565$	122.048	−	105.790i	0.216014	−	0.187239i
$566$	−204.096	−	587.107i	−0.360594	−	1.03729i
$567$	−85.9955			−0.151667
$568$	30.9266	−	48.5582i	0.0544482	−	0.0854898i
$569$	−95.4983			−0.167835			−0.0839177	−	0.996473i	$-0.526743\pi$
$569$	−95.4983			−0.167835			−0.0839177	+	0.996473i	$0.526743\pi$
$570$	−392.989	−	226.094i	−0.689455	−	0.396656i
$571$		−	889.123i		−	1.55713i	−0.627562	−	0.778566i	$-0.715947\pi$
$571$		−	889.123i		−	1.55713i	0.627562	−	0.778566i	$-0.284053\pi$
$572$	−235.297	+	186.080i	−0.411359	+	0.325315i
$573$			237.651i			0.414749i
$574$	−485.045	−	1395.29i	−0.845026	−	2.43081i
$575$	−5.94422	+	41.4385i	−0.0103378	+	0.0720670i
$576$	81.1856	+	173.991i	0.140947	+	0.302068i
$577$			522.147i			0.904934i	0.891781	+	0.452467i	$0.149456\pi$
$577$			522.147i			0.904934i	−0.891781	+	0.452467i	$0.850544\pi$
$578$	4.27189	+	12.2886i	0.00739081	+	0.0212605i
$579$			64.1361i			0.110771i
$580$	−6.88706	−	1.30675i	−0.0118742	−	0.00225301i
$581$	230.598			0.396898
$582$	431.453	−	149.986i	0.741329	−	0.257709i
$583$	−224.988			−0.385915
$584$	147.752	−	231.988i	0.253001	−	0.397240i
$585$	85.6495	−	74.2401i	0.146409	−	0.126906i
$586$	−463.223	+	161.031i	−0.790484	+	0.274796i
$587$	−95.8440			−0.163278			−0.0816388	−	0.996662i	$-0.526015\pi$
$587$	−95.8440			−0.163278			−0.0816388	+	0.996662i	$0.526015\pi$
$588$	229.863	−	181.783i	0.390923	−	0.309154i
$589$	1204.78			2.04547
$590$	821.543	+	472.648i	1.39245	+	0.801098i
$591$			337.008i			0.570234i
$592$	−352.946	−	83.5883i	−0.596192	−	0.141197i
$593$			878.624i			1.48166i	0.671693	+	0.740829i	$0.265567\pi$
$593$			878.624i			1.48166i	−0.671693	+	0.740829i	$0.734433\pi$
$594$	97.4228	−	33.8671i	0.164011	−	0.0570154i
$595$	620.586	−	537.918i	1.04300	−	0.904063i
$596$	−36.5498	+	28.9047i	−0.0613252	+	0.0484979i
$597$		−	304.906i		−	0.510730i
$598$	23.9034	−	8.30957i	0.0399723	−	0.0138956i
$599$			967.652i			1.61545i	0.589563	+	0.807723i	$0.299300\pi$
$599$			967.652i			1.61545i	−0.589563	+	0.807723i	$0.700700\pi$
$600$	225.692	−	262.798i	0.376154	−	0.437997i
$601$	279.704			0.465398			0.232699	−	0.972549i	$-0.425244\pi$
$601$	279.704			0.465398			0.232699	+	0.972549i	$0.425244\pi$
$602$	262.288	+	754.501i	0.435694	+	1.25332i
$603$	89.5430			0.148496
$604$	−311.203	−	393.513i	−0.515236	−	0.651512i
$605$	−73.6802	−	85.0036i	−0.121785	−	0.140502i
$606$	33.4983	+	96.3619i	0.0552778	+	0.159013i
$607$	−747.564			−1.23157			−0.615786	−	0.787914i	$-0.711161\pi$
$607$	−747.564			−1.23157			−0.615786	+	0.787914i	$0.711161\pi$
$608$	85.3049	+	833.285i	0.140304	+	1.37053i
$609$	−5.80066			−0.00952490
$610$	−189.498	+	329.379i	−0.310652	+	0.539966i
$611$		−	106.444i		−	0.174213i
$612$	127.957	+	161.801i	0.209081	+	0.264381i
$613$			457.152i			0.745761i	0.927879	+	0.372881i	$0.121630\pi$
$613$			457.152i			0.745761i	−0.927879	+	0.372881i	$0.878370\pi$
$614$	221.650	+	637.600i	0.360993	+	1.03844i
$615$	−438.465	−	505.850i	−0.712951	−	0.822520i
$616$	−407.547	+	639.894i	−0.661601	+	1.03879i
$617$		−	764.888i		−	1.23969i	−0.784725	−	0.619844i	$-0.787196\pi$
$617$		−	764.888i		−	1.23969i	0.784725	−	0.619844i	$-0.212804\pi$
$618$	−163.551	−	470.473i	−0.264645	−	0.761283i
$619$		−	365.359i		−	0.590240i	−0.955460	−	0.295120i	$-0.904640\pi$
$619$		−	365.359i		−	0.590240i	0.955460	−	0.295120i	$-0.0953597\pi$
$620$	−171.597	+	904.382i	−0.276769	+	1.45868i
$621$	−8.70099			−0.0140113
$622$	808.077	−	280.912i	1.29916	−	0.451627i
$623$	−957.410			−1.53677
$624$	−203.773	−	48.2598i	−0.326560	−	0.0773393i
$625$	−599.797	−	175.693i	−0.959676	−	0.281109i
$626$	158.447	−	55.0810i	0.253110	−	0.0879888i
$627$	449.976			0.717666
$628$	489.343	+	618.771i	0.779209	+	0.985304i
$629$	−389.691			−0.619541
$630$	142.947	−	248.466i	0.226900	−	0.394390i
$631$			62.1578i			0.0985067i	0.998786	+	0.0492534i	$0.0156842\pi$
$631$			62.1578i			0.0985067i	−0.998786	+	0.0492534i	$0.984316\pi$
$632$	197.799	−	310.567i	0.312973	−	0.491403i
$633$			35.8868i			0.0566932i
$634$	211.966	−	73.6859i	0.334331	−	0.116224i
$635$	−628.959	−	725.619i	−0.990486	−	1.14271i
$636$	−97.4228	−	123.190i	−0.153180	−	0.193696i
$637$			319.630i			0.501773i
$638$	6.57147	−	2.28444i	0.0103001	−	0.00358063i
$639$		−	21.5889i		−	0.0337855i
$640$	−637.662	−	54.6495i	−0.996348	−	0.0853899i
$641$	−1111.69			−1.73431			−0.867154	−	0.498041i	$-0.834053\pi$
$641$	−1111.69			−1.73431			−0.867154	+	0.498041i	$0.834053\pi$
$642$	39.9264	+	114.853i	0.0621906	+	0.178898i
$643$	−468.983			−0.729367			−0.364683	−	0.931132i	$-0.618823\pi$
$643$	−468.983			−0.729367			−0.364683	+	0.931132i	$0.618823\pi$
$644$	50.1993	−	39.6992i	0.0779493	−	0.0616447i
$645$	237.100	+	273.538i	0.367596	+	0.424090i
$646$	295.505	+	850.054i	0.457438	+	1.31587i
$647$	96.7647			0.149559			0.0747795	−	0.997200i	$-0.476175\pi$
$647$	96.7647			0.149559			0.0747795	+	0.997200i	$0.476175\pi$
$648$	60.7290	+	38.6781i	0.0937175	+	0.0596884i
$649$	−940.675			−1.44942
$650$	72.1294	+	370.873i	0.110968	+	0.570573i
$651$			761.720i			1.17008i
$652$	−57.7907	+	45.7027i	−0.0886360	+	0.0700961i
$653$		−	920.353i		−	1.40942i	−0.709494	−	0.704712i	$-0.751076\pi$
$653$		−	920.353i		−	1.40942i	0.709494	−	0.704712i	$-0.248924\pi$
$654$	−172.323	−	495.707i	−0.263491	−	0.757962i
$655$	−160.301	+	138.947i	−0.244734	+	0.212133i
$656$	−285.024	+	1203.49i	−0.434488	+	1.83459i
$657$		−	103.142i		−	0.156989i
$658$	−88.3921	−	254.270i	−0.134335	−	0.386429i
$659$		−	591.020i		−	0.896844i	−0.893822	−	0.448422i	$-0.851986\pi$
$659$		−	591.020i		−	0.896844i	0.893822	−	0.448422i	$-0.148014\pi$
$660$	−64.0900	+	337.779i	−0.0971060	+	0.511786i
$661$	−306.193			−0.463226			−0.231613	−	0.972808i	$-0.574400\pi$
$661$	−306.193			−0.463226			−0.231613	+	0.972808i	$0.574400\pi$
$662$	250.535	−	87.0935i	0.378451	−	0.131561i
$663$	−224.988			−0.339349
$664$	−162.846	−	103.716i	−0.245249	−	0.156198i
$665$	944.990	−	819.107i	1.42104	−	1.23174i
$666$	−128.474	+	44.6616i	−0.192904	+	0.0670595i
$667$	−0.586909			−0.000879924
$668$	291.445	−	230.484i	0.436295	−	0.345035i
$669$	168.055			0.251203
$670$	−148.844	+	258.716i	−0.222155	+	0.386143i
$671$		−	377.142i		−	0.562060i
$672$	−526.841	+	53.9337i	−0.783990	+	0.0802585i
$673$		−	556.892i		−	0.827476i	−0.910396	−	0.413738i	$-0.864223\pi$
$673$		−	556.892i		−	0.827476i	0.910396	−	0.413738i	$-0.135777\pi$
$674$	39.2442	−	13.6425i	0.0582258	−	0.0202411i
$675$	18.4455	−	128.588i	0.0273266	−	0.190500i
$676$	−351.083	+	277.647i	−0.519353	+	0.410721i
$677$		−	58.1920i		−	0.0859557i	−0.999076	−	0.0429779i	$-0.986316\pi$
$677$		−	58.1920i		−	0.0859557i	0.999076	−	0.0429779i	$-0.0136845\pi$
$678$	−105.697	+	36.7435i	−0.155895	+	0.0541939i
$679$			1259.94i			1.85558i
$680$	−680.189	+	100.750i	−1.00028	+	0.148162i
$681$	705.389			1.03581
$682$	−299.984	−	862.940i	−0.439860	−	1.26531i
$683$	357.274			0.523096			0.261548	−	0.965191i	$-0.415767\pi$
$683$	357.274			0.523096			0.261548	+	0.965191i	$0.415767\pi$
$684$	194.846	+	246.381i	0.284862	+	0.360206i
$685$	781.540	−	677.430i	1.14093	−	0.988949i
$686$	−42.0482	−	120.956i	−0.0612947	−	0.176321i
$687$	13.6780			0.0199098
$688$	154.127	−	650.788i	0.224021	−	0.945913i
$689$	171.299			0.248620
$690$	14.4633	−	25.1397i	0.0209613	−	0.0364343i
$691$		−	614.707i		−	0.889590i	−0.895632	−	0.444795i	$-0.853276\pi$
$691$		−	614.707i		−	0.889590i	0.895632	−	0.444795i	$-0.146724\pi$
$692$	291.544	+	368.655i	0.421307	+	0.532739i
$693$			284.496i			0.410528i
$694$	5.84222	+	16.8058i	0.00841818	+	0.0242159i
$695$	173.896	−	150.731i	0.250210	−	0.216879i
$696$	4.09636	+	2.60896i	0.00588557	+	0.00374850i
$697$			1328.79i			1.90644i
$698$	−12.7415	−	36.6524i	−0.0182543	−	0.0525107i
$699$		−	48.7543i		−	0.0697487i
$700$	480.275	+	826.030i	0.686108	+	1.18004i
$701$	−886.028			−1.26395			−0.631975	−	0.774989i	$-0.717755\pi$
$701$	−886.028			−1.26395			−0.631975	+	0.774989i	$0.717755\pi$
$702$	−74.1746	+	25.7854i	−0.105662	+	0.0367313i
$703$	−593.397			−0.844093
$704$	575.609	−	268.584i	0.817626	−	0.381511i
$705$	−79.9036	−	92.1835i	−0.113338	−	0.130757i
$706$	151.677	−	52.7276i	0.214840	−	0.0746849i
$707$	−281.398			−0.398017
$708$	−407.324	−	515.058i	−0.575316	−	0.727483i
$709$	−760.887			−1.07318			−0.536592	−	0.843842i	$-0.680288\pi$
$709$	−760.887			−1.07318			−0.536592	+	0.843842i	$0.680288\pi$
$710$	62.3766	+	35.8864i	0.0878544	+	0.0505442i
$711$		−	138.078i		−	0.194202i
$712$	676.111	+	430.613i	0.949594	+	0.604794i
$713$			77.0706i			0.108093i
$714$	−537.444	+	186.832i	−0.752722	+	0.261669i
$715$	−245.606	−	283.351i	−0.343505	−	0.396296i
$716$	−575.609	−	727.853i	−0.803923	−	1.01655i
$717$			512.695i			0.715056i
$718$	−593.397	+	206.283i	−0.826458	+	0.287302i
$719$			575.877i			0.800942i	0.916309	+	0.400471i	$0.131154\pi$
$719$			575.877i			0.800942i	−0.916309	+	0.400471i	$0.868846\pi$
$720$	−212.700	+	111.171i	−0.295416	+	0.154404i
$721$	1373.88			1.90553
$722$	212.903	+	612.441i	0.294880	+	0.848257i
$723$	−806.779			−1.11588
$724$	684.268	−	541.141i	0.945122	−	0.747432i
$725$	1.24421	−	8.67363i	0.00171615	−	0.0119636i
$726$	25.5909	+	73.6153i	0.0352492	+	0.101398i
$727$	327.332			0.450250			0.225125	−	0.974330i	$-0.427721\pi$
$727$	327.332			0.450250			0.225125	+	0.974330i	$0.427721\pi$
$728$	310.293	−	487.195i	0.426227	−	0.669224i
$729$	27.0000			0.0370370
$730$	298.006	+	171.448i	0.408227	+	0.234860i
$731$		−	718.542i		−	0.982958i
$732$	206.501	−	163.307i	0.282105	−	0.223098i
$733$		−	947.567i		−	1.29272i	−0.763031	−	0.646362i	$-0.776290\pi$
$733$		−	947.567i		−	1.29272i	0.763031	−	0.646362i	$-0.223710\pi$
$734$	−313.120	−	900.727i	−0.426595	−	1.22715i
$735$	239.934	+	276.807i	0.326440	+	0.376609i
$736$	−53.3056	+	5.45700i	−0.0724261	+	0.00741440i
$737$		−	296.232i		−	0.401943i
$738$	152.290	+	438.079i	0.206354	+	0.593602i
$739$		−	183.234i		−	0.247948i	−0.992285	−	0.123974i	$-0.960436\pi$
$739$		−	183.234i		−	0.247948i	0.992285	−	0.123974i	$-0.0395640\pi$
$740$	84.5173	−	445.439i	0.114213	−	0.601944i
$741$	−342.598			−0.462345
$742$	409.193	−	142.248i	0.551473	−	0.191709i
$743$	183.712			0.247258			0.123629	−	0.992329i	$-0.460547\pi$
$743$	183.712			0.247258			0.123629	+	0.992329i	$0.460547\pi$
$744$	342.598	−	537.918i	0.460481	−	0.723008i
$745$	−38.1512	−	44.0143i	−0.0512096	−	0.0590797i
$746$	−162.715	+	56.5648i	−0.218117	+	0.0758241i
$747$	−72.4009			−0.0969222
$748$	535.281	−	423.317i	0.715617	−	0.565932i
$749$	−335.395			−0.447791
$750$	340.866	+	267.040i	0.454488	+	0.356054i
$751$			345.748i			0.460384i	0.973145	+	0.230192i	$0.0739354\pi$
$751$			345.748i			0.460384i	−0.973145	+	0.230192i	$0.926065\pi$
$752$	−51.9414	+	219.319i	−0.0690710	+	0.291647i
$753$		−	245.390i		−	0.325882i
$754$	−5.00331	+	1.73930i	−0.00663569	+	0.00230677i
$755$	473.880	−	410.754i	0.627656	−	0.544045i
$756$	−155.773	+	123.190i	−0.206049	+	0.162950i
$757$			549.335i			0.725674i	0.931853	+	0.362837i	$0.118192\pi$
$757$			549.335i			0.725674i	−0.931853	+	0.362837i	$0.881808\pi$
$758$	−1205.32	+	419.005i	−1.59013	+	0.552778i
$759$			28.7852i			0.0379252i
$760$	−1035.75	+	153.417i	−1.36283	+	0.201864i
$761$	251.485			0.330467			0.165233	−	0.986255i	$-0.447162\pi$
$761$	251.485			0.330467			0.165233	+	0.986255i	$0.447162\pi$
$762$	218.453	+	628.405i	0.286683	+	0.824678i
$763$	1447.57			1.89721
$764$	340.440	+	430.484i	0.445602	+	0.563461i
$765$	−194.846	+	168.890i	−0.254700	+	0.220771i
$766$	142.337	+	409.450i	0.185819	+	0.534529i
$767$	716.200			0.933768
$768$	396.307	+	198.869i	0.516024	+	0.258945i
$769$	583.691			0.759026			0.379513	−	0.925186i	$-0.376092\pi$
$769$	583.691			0.759026			0.379513	+	0.925186i	$0.376092\pi$
$770$	−821.991	−	472.906i	−1.06752	−	0.614164i
$771$		−	72.3216i		−	0.0938024i
$772$	91.8764	+	116.177i	0.119011	+	0.150488i
$773$			1328.04i			1.71803i	0.511951	+	0.859015i	$0.328923\pi$
$773$			1328.04i			1.71803i	−0.511951	+	0.859015i	$0.671077\pi$
$774$	−82.3505	−	236.891i	−0.106396	−	0.306060i
$775$	−1138.99	−	163.384i	−1.46966	−	0.210818i
$776$	566.681	−	889.753i	0.730259	−	1.14659i
$777$		−	375.173i		−	0.482848i
$778$	−313.015	−	900.424i	−0.402333	−	1.15736i
$779$			2023.40i			2.59743i
$780$	48.7961	−	257.174i	0.0625591	−	0.329710i
$781$	−71.4219			−0.0914492
$782$	−54.3784	+	18.9036i	−0.0695376	+	0.0241734i
$783$	1.82123			0.00232597
$784$	155.969	−	658.567i	0.198940	−	0.840009i
$785$	−745.141	+	645.880i	−0.949224	+	0.822778i
$786$	138.825	−	48.2598i	0.176622	−	0.0613992i
$787$	1318.83			1.67577			0.837883	−	0.545850i	$-0.183793\pi$
$787$	1318.83			1.67577			0.837883	+	0.545850i	$0.183793\pi$
$788$	482.772	+	610.461i	0.612654	+	0.774697i
$789$	−352.096			−0.446256
$790$	398.946	+	229.521i	0.504995	+	0.290533i
$791$		−	308.658i		−	0.390212i
$792$	127.957	−	200.908i	0.161562	−	0.253671i
$793$			287.144i			0.362099i
$794$	81.3812	−	28.2906i	0.102495	−	0.0356305i
$795$	148.349	−	128.588i	0.186603	−	0.161745i
$796$	−436.784	−	552.310i	−0.548724	−	0.693857i
$797$			1277.40i			1.60276i	0.598154	+	0.801381i	$0.295901\pi$
$797$			1277.40i			1.60276i	−0.598154	+	0.801381i	$0.704099\pi$
$798$	−818.385	+	284.496i	−1.02555	+	0.356511i
$799$			242.152i			0.303069i
$800$	32.3579	−	799.345i	0.0404474	−	0.999182i
$801$	300.598			0.375278
$802$	110.784	+	318.682i	0.138134	+	0.397359i
$803$	−341.220			−0.424931
$804$	162.199	−	128.272i	0.201740	−	0.159543i
$805$	52.3987	+	60.4515i	0.0650915	+	0.0750950i
$806$	228.399	+	657.015i	0.283373	+	0.815155i
$807$	422.704			0.523797
$808$	198.720	+	126.564i	0.245940	+	0.156639i
$809$	321.093			0.396901			0.198451	−	0.980111i	$-0.436409\pi$
$809$	321.093			0.396901			0.198451	+	0.980111i	$0.436409\pi$
$810$	−44.8810	+	78.0109i	−0.0554087	+	0.0963097i
$811$			946.932i			1.16761i	0.811894	+	0.583805i	$0.198437\pi$
$811$			946.932i			1.16761i	−0.811894	+	0.583805i	$0.801563\pi$
$812$	−10.5074	+	8.30957i	−0.0129401	+	0.0102335i
$813$			808.149i			0.994033i
$814$	147.752	+	425.027i	0.181514	+	0.522146i
$815$	−60.3226	−	69.5931i	−0.0740154	−	0.0853904i
$816$	463.567	+	109.787i	0.568097	+	0.134543i
$817$		−	1094.15i		−	1.33923i
$818$	−245.538	−	706.319i	−0.300169	−	0.863471i
$819$		−	216.606i		−	0.264477i
$820$	−1518.88	−	288.192i	−1.85229	−	0.351453i
$821$	1169.34			1.42429			0.712144	−	0.702033i	$-0.247724\pi$
$821$	1169.34			1.42429			0.712144	+	0.702033i	$0.247724\pi$
$822$	−676.833	+	235.288i	−0.823398	+	0.286239i
$823$	1251.71			1.52091			0.760457	−	0.649389i	$-0.224975\pi$
$823$	1251.71			1.52091			0.760457	+	0.649389i	$0.224975\pi$
$824$	−970.220	−	617.930i	−1.17745	−	0.749915i
$825$	−425.402	−	61.0226i	−0.515639	−	0.0739668i
$826$	1710.83	−	594.738i	2.07123	−	0.720022i
$827$	892.104			1.07872			0.539362	−	0.842074i	$-0.318666\pi$
$827$	892.104			1.07872			0.539362	+	0.842074i	$0.318666\pi$
$828$	−15.7611	+	12.4644i	−0.0190351	+	0.0150536i
$829$	998.688			1.20469			0.602345	−	0.798236i	$-0.294233\pi$
$829$	998.688			1.20469			0.602345	+	0.798236i	$0.294233\pi$
$830$	120.349	−	209.187i	0.144999	−	0.252033i
$831$		−	855.946i		−	1.03002i
$832$	−438.251	+	204.491i	−0.526743	+	0.245783i
$833$		−	727.131i		−	0.872906i
$834$	−150.598	+	52.3525i	−0.180573	+	0.0627728i
$835$	304.214	+	350.966i	0.364328	+	0.420319i
$836$	815.093	−	644.601i	0.974992	−	0.771054i
$837$		−	239.157i		−	0.285732i
$838$	−165.455	+	57.5174i	−0.197441	+	0.0686365i
$839$		−	610.359i		−	0.727484i	−0.931500	−	0.363742i	$-0.881499\pi$
$839$		−	610.359i		−	0.727484i	0.931500	−	0.363742i	$-0.118501\pi$
$840$	−96.9970	−	654.849i	−0.115473	−	0.779582i
$841$	−840.877			−0.999854
$842$	−46.1684	−	132.809i	−0.0548318	−	0.157730i
$843$	75.1744			0.0891749
$844$	51.4086	+	65.0058i	0.0609107	+	0.0770211i
$845$	−366.464	−	422.784i	−0.433686	−	0.500336i
$846$	27.7525	+	79.8332i	0.0328044	+	0.0943655i
$847$	−214.973			−0.253805
$848$	−352.946	−	83.5883i	−0.416209	−	0.0985712i
$849$	−538.296			−0.634035
$850$	−164.088	−	843.705i	−0.193045	−	0.992594i
$851$		−	37.9599i		−	0.0446062i
$852$	−30.9266	−	39.1064i	−0.0362988	−	0.0458995i
$853$		−	832.689i		−	0.976189i	−0.872791	−	0.488094i	$-0.837692\pi$
$853$		−	832.689i		−	0.976189i	0.872791	−	0.488094i	$-0.162308\pi$
$854$	238.447	+	685.920i	0.279212	+	0.803185i
$855$	−296.699	+	257.175i	−0.347016	+	0.300790i
$856$	236.852	+	150.850i	0.276696	+	0.176227i
$857$		−	149.415i		−	0.174347i	−0.996193	−	0.0871735i	$-0.972217\pi$
$857$		−	149.415i		−	0.174347i	0.996193	−	0.0871735i	$-0.0277834\pi$
$858$	85.3049	+	245.390i	0.0994230	+	0.286002i
$859$			394.144i			0.458840i	0.973327	+	0.229420i	$0.0736830\pi$
$859$			394.144i			0.458840i	−0.973327	+	0.229420i	$0.926317\pi$
$860$	821.334	+	155.840i	0.955040	+	0.181209i
$861$	−1279.29			−1.48581
$862$	−467.308	+	162.451i	−0.542121	+	0.188458i
$863$	−1409.58			−1.63335			−0.816677	−	0.577095i	$-0.804186\pi$
$863$	−1409.58			−1.63335			−0.816677	+	0.577095i	$0.804186\pi$
$864$	165.412	−	16.9336i	0.191450	−	0.0195990i
$865$	−443.945	+	384.807i	−0.513231	+	0.444864i
$866$	−1201.94	+	417.831i	−1.38792	+	0.482484i
$867$	11.2669			0.0129953
$868$	1091.18	+	1379.79i	1.25712	+	1.58962i
$869$	−456.797			−0.525659
$870$	−3.02737	+	5.26208i	−0.00347973	+	0.00604836i
$871$			225.542i			0.258946i
$872$	−1022.26	−	651.074i	−1.17232	−	0.746644i
$873$		−	395.583i		−	0.453131i
$874$	−82.8040	+	28.7852i	−0.0947414	+	0.0329350i
$875$	−1004.46	+	646.221i	−1.14796	+	0.738538i
$876$	−147.752	−	186.832i	−0.168667	−	0.213278i
$877$		−	872.780i		−	0.995189i	−0.867410	−	0.497594i	$-0.834217\pi$
$877$		−	872.780i		−	0.995189i	0.867410	−	0.497594i	$-0.165783\pi$
$878$	−1454.21	+	505.528i	−1.65627	+	0.575772i
$879$			424.712i			0.483176i
$880$	367.782	+	703.667i	0.417934	+	0.799621i
$881$	1103.38			1.25241			0.626206	−	0.779657i	$-0.284607\pi$
$881$	1103.38			1.25241			0.626206	+	0.779657i	$0.284607\pi$
$882$	−83.3348	−	239.722i	−0.0944839	−	0.271794i
$883$	−536.884			−0.608023			−0.304011	−	0.952668i	$-0.598326\pi$
$883$	−536.884			−0.608023			−0.304011	+	0.952668i	$0.598326\pi$
$884$	−407.547	+	322.300i	−0.461025	+	0.364593i
$885$	620.248	−	537.624i	0.700845	−	0.607485i
$886$	−402.048	−	1156.54i	−0.453779	−	1.30535i
$887$	−888.945			−1.00219			−0.501096	−	0.865392i	$-0.667070\pi$
$887$	−888.945			−1.00219			−0.501096	+	0.865392i	$0.667070\pi$
$888$	−168.741	+	264.943i	−0.190024	+	0.298359i
$889$	−1835.08			−2.06421
$890$	−499.672	+	868.515i	−0.561429	+	0.975860i
$891$		−	89.3232i		−	0.100251i
$892$	304.417	−	240.742i	0.341274	−	0.269890i
$893$			368.734i			0.412916i
$894$	13.2508	+	38.1175i	0.0148220	+	0.0426371i
$895$	876.501	−	759.742i	0.979331	−	0.848874i
$896$	−877.066	+	852.408i	−0.978868	+	0.951348i
$897$		−	21.9162i		−	0.0244327i
$898$	−115.514	−	332.288i	−0.128634	−	0.370032i
$899$		−	16.1319i		−	0.0179443i
$900$	−150.792	−	259.349i	−0.167547	−	0.288165i
$901$	−389.691			−0.432510
$902$	1449.28	−	503.814i	1.60674	−	0.558553i
$903$	691.773			0.766083
$904$	−138.825	+	217.971i	−0.153567	+	0.241118i
$905$	714.248	+	824.015i	0.789224	+	0.910514i
$906$	−410.392	+	142.665i	−0.452971	+	0.157467i
$907$	−1668.40			−1.83947			−0.919734	−	0.392543i	$-0.871595\pi$
$907$	−1668.40			−1.83947			−0.919734	+	0.392543i	$0.871595\pi$
$908$	1277.75	−	1010.48i	1.40721	−	1.11287i
$909$	88.3505			0.0971953
$910$	625.839	+	360.056i	0.687735	+	0.395666i
$911$			1498.13i			1.64449i	0.569131	+	0.822247i	$0.307280\pi$
$911$			1498.13i			1.64449i	−0.569131	+	0.822247i	$0.692720\pi$
$912$	705.891	+	167.177i	0.774004	+	0.183308i
$913$			239.521i			0.262345i
$914$	690.199	−	239.935i	0.755142	−	0.262510i
$915$	215.548	+	248.674i	0.235572	+	0.271775i
$916$	24.7766	−	19.5941i	0.0270487	−	0.0213909i
$917$			405.399i			0.442093i
$918$	168.741	−	58.6596i	0.183814	−	0.0638994i
$919$		−	1094.82i		−	1.19131i	−0.803240	−	0.595656i	$-0.796892\pi$
$919$		−	1094.82i		−	1.19131i	0.803240	−	0.595656i	$-0.203108\pi$
$920$	−9.81413	−	66.2574i	−0.0106675	−	0.0720189i
$921$	584.591			0.634735
$922$	−202.497	−	582.507i	−0.219629	−	0.631787i
$923$	54.3784			0.0589148
$924$	407.547	+	515.339i	0.441068	+	0.557727i
$925$	560.990	+	80.4723i	0.606476	+	0.0869970i
$926$	−60.8314	−	174.988i	−0.0656926	−	0.188972i
$927$	−431.358			−0.465327
$928$	11.1576	−	1.14222i	0.0120233	−	0.00123084i
$929$	1145.90			1.23348			0.616740	−	0.787167i	$-0.288453\pi$
$929$	1145.90			1.23348			0.616740	+	0.787167i	$0.288453\pi$
$930$	690.995	+	397.542i	0.743005	+	0.427464i
$931$		−	1107.23i		−	1.18929i
$932$	−69.8417	−	88.3142i	−0.0749374	−	0.0947578i
$933$		−	740.894i		−	0.794099i
$934$	398.035	+	1144.99i	0.426162	+	1.22590i
$935$	558.733	+	644.601i	0.597576	+	0.689413i
$936$	−97.4228	+	152.965i	−0.104084	+	0.163424i
$937$			1272.49i			1.35805i	0.734115	+	0.679025i	$0.237597\pi$
$937$			1272.49i			1.35805i	−0.734115	+	0.679025i	$0.762403\pi$
$938$	187.292	+	538.766i	0.199671	+	0.574378i
$939$		−	145.274i		−	0.154711i
$940$	−276.793	−	52.5186i	−0.294461	−	0.0558709i
$941$	707.360			0.751711			0.375856	−	0.926678i	$-0.377349\pi$
$941$	707.360			0.751711			0.375856	+	0.926678i	$0.377349\pi$
$942$	645.311	−	224.330i	0.685044	−	0.238142i
$943$	−129.438			−0.137262
$944$	−1475.66	−	349.482i	−1.56320	−	0.370214i
$945$	−162.598	−	187.587i	−0.172061	−	0.198504i
$946$	−783.698	+	272.437i	−0.828433	+	0.287989i
$947$	−284.977			−0.300926			−0.150463	−	0.988616i	$-0.548076\pi$
$947$	−284.977			−0.300926			−0.150463	+	0.988616i	$0.548076\pi$
$948$	−197.799	−	250.115i	−0.208649	−	0.263835i
$949$	259.794			0.273756
$950$	−249.864	−	1284.74i	−0.263014	−	1.35236i
$951$		−	194.343i		−	0.204357i
$952$	−705.891	+	1108.33i	−0.741482	+	1.16421i
$953$		−	295.247i		−	0.309808i	−0.987930	−	0.154904i	$-0.950493\pi$
$953$		−	295.247i		−	0.309808i	0.987930	−	0.154904i	$-0.0495068\pi$
$954$	−128.474	+	44.6616i	−0.134669	+	0.0468151i
$955$	−518.401	+	449.344i	−0.542828	+	0.470518i
$956$	734.447	+	928.702i	0.768250	+	0.971446i
$957$		−	6.02513i		−	0.00629585i
$958$	262.486	−	91.2483i	0.273994	−	0.0952487i
$959$		−	1976.50i		−	2.06100i
$960$	−226.032	+	506.072i	−0.235450	+	0.527159i
$961$	−1157.38			−1.20435
$962$	−112.494	−	323.602i	−0.116938	−	0.336385i
$963$	105.304			0.109350
$964$	−1461.41	+	1155.73i	−1.51598	+	1.19889i
$965$	−139.904	+	121.267i	−0.144978	+	0.125665i
$966$	−18.1993	−	52.3525i	−0.0188399	−	0.0541951i
$967$	−348.013			−0.359889			−0.179945	−	0.983677i	$-0.557592\pi$
$967$	−348.013			−0.359889			−0.179945	+	0.983677i	$0.557592\pi$
$968$	151.811	+	96.6881i	0.156830	+	0.0998844i
$969$	779.382			0.804316
$970$	1142.95	+	657.562i	1.17830	+	0.677899i
$971$			798.691i			0.822545i	0.911513	+	0.411272i	$0.134915\pi$
$971$			798.691i			0.822545i	−0.911513	+	0.411272i	$0.865085\pi$
$972$	48.9081	−	38.6781i	0.0503170	−	0.0397923i
$973$		−	439.779i		−	0.451983i
$974$	−132.159	−	380.170i	−0.135687	−	0.390318i
$975$	323.888	+	46.4607i	0.332193	+	0.0476520i
$976$	140.117	−	591.634i	0.143563	−	0.606183i
$977$			721.834i			0.738827i	0.929265	+	0.369413i	$0.120441\pi$
$977$			721.834i			0.738827i	−0.929265	+	0.369413i	$0.879559\pi$
$978$	20.9515	+	60.2694i	0.0214228	+	0.0616252i
$979$		−	994.458i		−	1.01579i
$980$	831.151	+	157.702i	0.848114	+	0.160921i
$981$	−454.495			−0.463298
$982$	−656.216	+	228.121i	−0.668244	+	0.232302i
$983$	1717.25			1.74695			0.873474	−	0.486870i	$-0.161861\pi$
$983$	1717.25			1.74695			0.873474	+	0.486870i	$0.161861\pi$
$984$	903.416	+	575.383i	0.918106	+	0.584739i
$985$	−735.135	+	637.207i	−0.746330	+	0.646910i
$986$	11.3821	−	3.95677i	0.0115437	−	0.00401296i
$987$	−233.131			−0.236201
$988$	−620.586	+	490.779i	−0.628124	+	0.496740i
$989$	69.9934			0.0707719
$990$	258.081	+	148.478i	0.260688	+	0.149978i
$991$		−	342.270i		−	0.345378i	−0.984976	−	0.172689i	$-0.944754\pi$
$991$		−	342.270i		−	0.345378i	0.984976	−	0.172689i	$-0.0552456\pi$
$992$	−149.992	−	1465.17i	−0.151202	−	1.47699i
$993$		−	229.706i		−	0.231325i
$994$	129.897	−	45.1562i	0.130681	−	0.0454288i
$995$	665.108	−	576.508i	0.668450	−	0.579405i
$996$	−131.148	+	103.716i	−0.131675	+	0.104132i
$997$		−	1586.05i		−	1.59082i	−0.606072	−	0.795410i	$-0.707256\pi$
$997$		−	1586.05i		−	1.59082i	0.606072	−	0.795410i	$-0.292744\pi$
$998$	1270.00	−	441.493i	1.27255	−	0.442377i
$999$			117.793i			0.117911i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.3.f.b.19.3	✓	8
3.2	odd	2		180.3.f.h.19.6		8
4.3	odd	2	inner	60.3.f.b.19.5	yes	8
5.2	odd	4		300.3.c.f.151.7		8
5.3	odd	4		300.3.c.f.151.2		8
5.4	even	2	inner	60.3.f.b.19.6	yes	8
8.3	odd	2		960.3.j.e.319.4		8
8.5	even	2		960.3.j.e.319.8		8
12.11	even	2		180.3.f.h.19.4		8
15.2	even	4		900.3.c.r.451.2		8
15.8	even	4		900.3.c.r.451.7		8
15.14	odd	2		180.3.f.h.19.3		8
20.3	even	4		300.3.c.f.151.1		8
20.7	even	4		300.3.c.f.151.8		8
20.19	odd	2	inner	60.3.f.b.19.4	yes	8
40.19	odd	2		960.3.j.e.319.7		8
40.29	even	2		960.3.j.e.319.3		8
60.23	odd	4		900.3.c.r.451.8		8
60.47	odd	4		900.3.c.r.451.1		8
60.59	even	2		180.3.f.h.19.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.f.b.19.3	✓	8	1.1	even	1	trivial
60.3.f.b.19.4	yes	8	20.19	odd	2	inner
60.3.f.b.19.5	yes	8	4.3	odd	2	inner
60.3.f.b.19.6	yes	8	5.4	even	2	inner
180.3.f.h.19.3		8	15.14	odd	2
180.3.f.h.19.4		8	12.11	even	2
180.3.f.h.19.5		8	60.59	even	2
180.3.f.h.19.6		8	3.2	odd	2
300.3.c.f.151.1		8	20.3	even	4
300.3.c.f.151.2		8	5.3	odd	4
300.3.c.f.151.7		8	5.2	odd	4
300.3.c.f.151.8		8	20.7	even	4
900.3.c.r.451.1		8	60.47	odd	4
900.3.c.r.451.2		8	15.2	even	4
900.3.c.r.451.7		8	15.8	even	4
900.3.c.r.451.8		8	60.23	odd	4
960.3.j.e.319.3		8	40.29	even	2
960.3.j.e.319.4		8	8.3	odd	2
960.3.j.e.319.7		8	40.19	odd	2
960.3.j.e.319.8		8	8.5	even	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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	60.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.656712 - 1.88911i) q^{2} -1.73205 q^{3} +(-3.13746 + 2.48120i) q^{4} +(-3.27492 - 3.77822i) q^{5} +(1.13746 + 3.27203i) q^{6} -9.55505 q^{7} +(6.74766 + 4.29756i) q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+(-0.656712 - 1.88911i) q^{2} -1.73205 q^{3} +(-3.13746 + 2.48120i) q^{4} +(-3.27492 - 3.77822i) q^{5} +(1.13746 + 3.27203i) q^{6} -9.55505 q^{7} +(6.74766 + 4.29756i) q^{8} +3.00000 q^{9} +(-4.98678 + 8.66787i) q^{10} -9.92480i q^{11} +(5.43424 - 4.29756i) q^{12} +7.55643i q^{13} +(6.27492 + 18.0505i) q^{14} +(5.67232 + 6.54406i) q^{15} +(3.68729 - 15.5693i) q^{16} -17.1903i q^{17} +(-1.97014 - 5.66732i) q^{18} -26.1762i q^{19} +(19.6494 + 3.72827i) q^{20} +16.5498 q^{21} +(-18.7490 + 6.51774i) q^{22} +1.67451 q^{23} +(-11.6873 - 7.44360i) q^{24} +(-3.54983 + 24.7467i) q^{25} +(14.2749 - 4.96240i) q^{26} -5.19615 q^{27} +(29.9786 - 23.7080i) q^{28} -0.350497 q^{29} +(8.63736 - 15.0132i) q^{30} +46.0258i q^{31} +(-31.8336 + 3.25887i) q^{32} +17.1903i q^{33} +(-32.4743 + 11.2890i) q^{34} +(31.2920 + 36.1010i) q^{35} +(-9.41238 + 7.44360i) q^{36} -22.6693i q^{37} +(-49.4498 + 17.1903i) q^{38} -13.0881i q^{39} +(-5.86091 - 39.5683i) q^{40} -77.2990 q^{41} +(-10.8685 - 31.2644i) q^{42} +41.7994 q^{43} +(24.6254 + 31.1386i) q^{44} +(-9.82475 - 11.3346i) q^{45} +(-1.09967 - 3.16332i) q^{46} -14.0866 q^{47} +(-6.38658 + 26.9669i) q^{48} +42.2990 q^{49} +(49.0804 - 9.54543i) q^{50} +29.7744i q^{51} +(-18.7490 - 23.7080i) q^{52} -22.6693i q^{53} +(3.41238 + 9.81609i) q^{54} +(-37.4980 + 32.5029i) q^{55} +(-64.4743 - 41.0634i) q^{56} +45.3386i q^{57} +(0.230175 + 0.662126i) q^{58} -94.7802i q^{59} +(-34.0338 - 6.45756i) q^{60} +38.0000 q^{61} +(86.9478 - 30.2257i) q^{62} -28.6652 q^{63} +(27.0619 + 57.9970i) q^{64} +(28.5498 - 24.7467i) q^{65} +(32.4743 - 11.2890i) q^{66} +29.8477 q^{67} +(42.6525 + 53.9337i) q^{68} -2.90033 q^{69} +(47.6489 - 82.8220i) q^{70} -7.19630i q^{71} +(20.2430 + 12.8927i) q^{72} -34.3805i q^{73} +(-42.8248 + 14.8872i) q^{74} +(6.14849 - 42.8625i) q^{75} +(64.9485 + 82.1269i) q^{76} +94.8320i q^{77} +(-24.7249 + 8.59513i) q^{78} -46.0258i q^{79} +(-70.8999 + 37.0569i) q^{80} +9.00000 q^{81} +(50.7632 + 146.026i) q^{82} -24.1336 q^{83} +(-51.9244 + 41.0634i) q^{84} +(-64.9485 + 56.2967i) q^{85} +(-27.4502 - 78.9636i) q^{86} +0.607078 q^{87} +(42.6525 - 66.9692i) q^{88} +100.199 q^{89} +(-14.9603 + 26.0036i) q^{90} -72.2021i q^{91} +(-5.25370 + 4.15479i) q^{92} -79.7191i q^{93} +(9.25083 + 26.6111i) q^{94} +(-98.8995 + 85.7250i) q^{95} +(55.1375 - 5.64452i) q^{96} -131.861i q^{97} +(-27.7783 - 79.9074i) q^{98} -29.7744i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 10 q^{4} + 4 q^{5} - 6 q^{6} + 24 q^{9}+O(q^{10}) \) 8 * q - 10 * q^4 + 4 * q^5 - 6 * q^6 + 24 * q^9	\( 8 q - 10 q^{4} + 4 q^{5} - 6 q^{6} + 24 q^{9} - 42 q^{10} + 20 q^{14} - 46 q^{16} + 52 q^{20} + 72 q^{21} - 18 q^{24} + 32 q^{25} + 84 q^{26} - 184 q^{29} - 60 q^{30} + 12 q^{34} - 30 q^{36} - 6 q^{40} - 256 q^{41} + 348 q^{44} + 12 q^{45} + 112 q^{46} - 24 q^{49} + 72 q^{50} - 18 q^{54} - 244 q^{56} + 6 q^{60} + 304 q^{61} - 10 q^{64} + 168 q^{65} - 12 q^{66} - 144 q^{69} - 104 q^{70} - 252 q^{74} - 24 q^{76} - 308 q^{80} + 72 q^{81} - 204 q^{84} + 24 q^{85} - 280 q^{86} + 560 q^{89} - 126 q^{90} + 376 q^{94} + 426 q^{96}+O(q^{100}) \) 8 * q - 10 * q^4 + 4 * q^5 - 6 * q^6 + 24 * q^9 - 42 * q^10 + 20 * q^14 - 46 * q^16 + 52 * q^20 + 72 * q^21 - 18 * q^24 + 32 * q^25 + 84 * q^26 - 184 * q^29 - 60 * q^30 + 12 * q^34 - 30 * q^36 - 6 * q^40 - 256 * q^41 + 348 * q^44 + 12 * q^45 + 112 * q^46 - 24 * q^49 + 72 * q^50 - 18 * q^54 - 244 * q^56 + 6 * q^60 + 304 * q^61 - 10 * q^64 + 168 * q^65 - 12 * q^66 - 144 * q^69 - 104 * q^70 - 252 * q^74 - 24 * q^76 - 308 * q^80 + 72 * q^81 - 204 * q^84 + 24 * q^85 - 280 * q^86 + 560 * q^89 - 126 * q^90 + 376 * q^94 + 426 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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