LMFDB - Embedded newform 147.4.e.k.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,4,Mod(67,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("147.67");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	147.e (of order $3$, degree $2$, not 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:	$8.67328077084$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	147.79
Dual form			147.4.e.k.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20711 + 2.09077i) q^{2} +(1.50000 + 2.59808i) q^{3} +(1.08579 + 1.88064i) q^{4} +(-9.94975 + 17.2335i) q^{5} -7.24264 q^{6} -24.5563 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(-1.20711 + 2.09077i) q^{2} +(1.50000 + 2.59808i) q^{3} +(1.08579 + 1.88064i) q^{4} +(-9.94975 + 17.2335i) q^{5} -7.24264 q^{6} -24.5563 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-24.0208 - 41.6053i) q^{10} +(-11.9706 - 20.7336i) q^{11} +(-3.25736 + 5.64191i) q^{12} +87.3553 q^{13} -59.6985 q^{15} +(20.9558 - 36.2966i) q^{16} +(2.81981 + 4.88405i) q^{17} +(-10.8640 - 18.8169i) q^{18} +(-32.4437 + 56.1941i) q^{19} -43.2132 q^{20} +57.7990 q^{22} +(12.7990 - 22.1685i) q^{23} +(-36.8345 - 63.7993i) q^{24} +(-135.495 - 234.684i) q^{25} +(-105.447 + 182.640i) q^{26} -27.0000 q^{27} +60.3188 q^{29} +(72.0624 - 124.816i) q^{30} +(61.3553 + 106.271i) q^{31} +(-47.6335 - 82.5037i) q^{32} +(35.9117 - 62.2009i) q^{33} -13.6152 q^{34} -19.5442 q^{36} +(28.0589 - 48.5994i) q^{37} +(-78.3259 - 135.664i) q^{38} +(131.033 + 226.956i) q^{39} +(244.329 - 423.191i) q^{40} -299.713 q^{41} -501.421 q^{43} +(25.9949 - 45.0246i) q^{44} +(-89.5477 - 155.101i) q^{45} +(30.8995 + 53.5195i) q^{46} +(-152.777 + 264.617i) q^{47} +125.735 q^{48} +654.227 q^{50} +(-8.45942 + 14.6521i) q^{51} +(94.8492 + 164.284i) q^{52} +(187.558 + 324.861i) q^{53} +(32.5919 - 56.4508i) q^{54} +476.416 q^{55} -194.662 q^{57} +(-72.8112 + 126.113i) q^{58} +(313.806 + 543.528i) q^{59} +(-64.8198 - 112.271i) q^{60} +(-1.87868 + 3.25397i) q^{61} -296.250 q^{62} +565.288 q^{64} +(-869.164 + 1505.44i) q^{65} +(86.6985 + 150.166i) q^{66} +(406.524 + 704.120i) q^{67} +(-6.12341 + 10.6061i) q^{68} +76.7939 q^{69} +165.902 q^{71} +(110.504 - 191.398i) q^{72} +(-309.550 - 536.156i) q^{73} +(67.7401 + 117.329i) q^{74} +(406.485 - 704.052i) q^{75} -140.908 q^{76} -632.683 q^{78} +(69.1228 - 119.724i) q^{79} +(417.011 + 722.284i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(361.785 - 626.631i) q^{82} +621.137 q^{83} -112.225 q^{85} +(605.269 - 1048.36i) q^{86} +(90.4781 + 156.713i) q^{87} +(293.953 + 509.142i) q^{88} +(-142.709 + 247.180i) q^{89} +432.375 q^{90} +55.5879 q^{92} +(-184.066 + 318.812i) q^{93} +(-368.836 - 638.842i) q^{94} +(-645.612 - 1118.23i) q^{95} +(142.901 - 247.511i) q^{96} -603.114 q^{97} +215.470 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 6 q^{3} + 10 q^{4} - 20 q^{5} - 12 q^{6} - 36 q^{8} - 18 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 6 * q^3 + 10 * q^4 - 20 * q^5 - 12 * q^6 - 36 * q^8 - 18 * q^9	\( 4 q - 2 q^{2} + 6 q^{3} + 10 q^{4} - 20 q^{5} - 12 q^{6} - 36 q^{8} - 18 q^{9} - 48 q^{10} + 20 q^{11} - 30 q^{12} + 208 q^{13} - 120 q^{15} - 18 q^{16} - 116 q^{17} - 18 q^{18} - 192 q^{19} - 88 q^{20} + 152 q^{22} - 28 q^{23} - 54 q^{24} - 146 q^{25} - 204 q^{26} - 108 q^{27} + 592 q^{29} + 144 q^{30} + 104 q^{31} - 18 q^{32} - 60 q^{33} - 128 q^{34} - 180 q^{36} + 248 q^{37} - 104 q^{38} + 312 q^{39} + 488 q^{40} + 40 q^{41} - 1440 q^{43} - 292 q^{44} - 180 q^{45} + 84 q^{46} + 96 q^{47} - 108 q^{48} + 1412 q^{50} + 348 q^{51} + 320 q^{52} - 268 q^{53} + 54 q^{54} + 944 q^{55} - 1152 q^{57} - 48 q^{58} + 616 q^{59} - 132 q^{60} - 16 q^{61} - 608 q^{62} + 236 q^{64} - 1740 q^{65} + 228 q^{66} + 144 q^{67} + 940 q^{68} - 168 q^{69} + 1976 q^{71} + 162 q^{72} - 104 q^{73} + 56 q^{74} + 438 q^{75} - 2272 q^{76} - 1224 q^{78} + 944 q^{79} + 828 q^{80} - 162 q^{81} + 856 q^{82} + 2032 q^{83} - 200 q^{85} + 1120 q^{86} + 888 q^{87} + 876 q^{88} + 388 q^{89} + 864 q^{90} - 728 q^{92} - 312 q^{93} - 904 q^{94} - 1304 q^{95} + 54 q^{96} + 976 q^{97} - 360 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 6 * q^3 + 10 * q^4 - 20 * q^5 - 12 * q^6 - 36 * q^8 - 18 * q^9 - 48 * q^10 + 20 * q^11 - 30 * q^12 + 208 * q^13 - 120 * q^15 - 18 * q^16 - 116 * q^17 - 18 * q^18 - 192 * q^19 - 88 * q^20 + 152 * q^22 - 28 * q^23 - 54 * q^24 - 146 * q^25 - 204 * q^26 - 108 * q^27 + 592 * q^29 + 144 * q^30 + 104 * q^31 - 18 * q^32 - 60 * q^33 - 128 * q^34 - 180 * q^36 + 248 * q^37 - 104 * q^38 + 312 * q^39 + 488 * q^40 + 40 * q^41 - 1440 * q^43 - 292 * q^44 - 180 * q^45 + 84 * q^46 + 96 * q^47 - 108 * q^48 + 1412 * q^50 + 348 * q^51 + 320 * q^52 - 268 * q^53 + 54 * q^54 + 944 * q^55 - 1152 * q^57 - 48 * q^58 + 616 * q^59 - 132 * q^60 - 16 * q^61 - 608 * q^62 + 236 * q^64 - 1740 * q^65 + 228 * q^66 + 144 * q^67 + 940 * q^68 - 168 * q^69 + 1976 * q^71 + 162 * q^72 - 104 * q^73 + 56 * q^74 + 438 * q^75 - 2272 * q^76 - 1224 * q^78 + 944 * q^79 + 828 * q^80 - 162 * q^81 + 856 * q^82 + 2032 * q^83 - 200 * q^85 + 1120 * q^86 + 888 * q^87 + 876 * q^88 + 388 * q^89 + 864 * q^90 - 728 * q^92 - 312 * q^93 - 904 * q^94 - 1304 * q^95 + 54 * q^96 + 976 * q^97 - 360 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.20711	+	2.09077i	−0.426777	+	0.739199i	−0.996585	−	0.0825791i	$-0.973684\pi$
$2$	−1.20711	+	2.09077i	−0.426777	+	0.739199i	0.569808	+	0.821778i	$0.307018\pi$
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$4$	1.08579	+	1.88064i	0.135723	+	0.235080i
$5$	−9.94975	+	17.2335i	−0.889932	+	1.54141i	−0.0499787	+	0.998750i	$0.515915\pi$
$5$	−9.94975	+	17.2335i	−0.889932	+	1.54141i	−0.839954	+	0.542658i	$0.817418\pi$
$6$	−7.24264			−0.492799
$7$		0			0
$7$		0			0
$8$	−24.5563			−1.08525
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	−24.0208	−	41.6053i	−0.759605	−	1.31567i
$11$	−11.9706	−	20.7336i	−0.328115	−	0.568311i	0.654023	−	0.756475i	$-0.273080\pi$
$11$	−11.9706	−	20.7336i	−0.328115	−	0.568311i	−0.982138	+	0.188163i	$0.939747\pi$
$12$	−3.25736	+	5.64191i	−0.0783599	+	0.135723i
$13$	87.3553			1.86369			0.931847	−	0.362852i	$-0.118197\pi$
$13$	87.3553			1.86369			0.931847	+	0.362852i	$0.118197\pi$
$14$		0			0
$15$	−59.6985			−1.02761
$16$	20.9558	−	36.2966i	0.327435	−	0.567134i
$17$	2.81981	+	4.88405i	0.0402296	+	0.0696797i	0.885439	−	0.464755i	$-0.153858\pi$
$17$	2.81981	+	4.88405i	0.0402296	+	0.0696797i	−0.845210	+	0.534435i	$0.820524\pi$
$18$	−10.8640	−	18.8169i	−0.142259	−	0.246400i
$19$	−32.4437	+	56.1941i	−0.391741	+	0.678516i	−0.992679	−	0.120780i	$-0.961460\pi$
$19$	−32.4437	+	56.1941i	−0.391741	+	0.678516i	0.600938	+	0.799296i	$0.294794\pi$
$20$	−43.2132			−0.483138
$21$		0			0
$22$	57.7990			0.560127
$23$	12.7990	−	22.1685i	0.116034	−	0.200976i	−0.802159	−	0.597111i	$-0.796315\pi$
$23$	12.7990	−	22.1685i	0.116034	−	0.200976i	0.918192	+	0.396135i	$0.129649\pi$
$24$	−36.8345	−	63.7993i	−0.313284	−	0.542624i
$25$	−135.495	−	234.684i	−1.08396	−	1.87747i
$26$	−105.447	+	182.640i	−0.795381	+	1.37764i
$27$	−27.0000			−0.192450
$28$		0			0
$29$	60.3188			0.386238			0.193119	−	0.981175i	$-0.438140\pi$
$29$	60.3188			0.386238			0.193119	+	0.981175i	$0.438140\pi$
$30$	72.0624	−	124.816i	0.438558	−	0.759605i
$31$	61.3553	+	106.271i	0.355476	+	0.615702i	0.987199	−	0.159492i	$-0.0509856\pi$
$31$	61.3553	+	106.271i	0.355476	+	0.615702i	−0.631724	+	0.775194i	$0.717652\pi$
$32$	−47.6335	−	82.5037i	−0.263140	−	0.455773i
$33$	35.9117	−	62.2009i	0.189437	−	0.328115i
$34$	−13.6152			−0.0686762
$35$		0			0
$36$	−19.5442			−0.0904822
$37$	28.0589	−	48.5994i	0.124672	−	0.215938i	−0.796933	−	0.604068i	$-0.793546\pi$
$37$	28.0589	−	48.5994i	0.124672	−	0.215938i	0.921605	+	0.388130i	$0.126879\pi$
$38$	−78.3259	−	135.664i	−0.334372	−	0.579149i
$39$	131.033	+	226.956i	0.538002	+	0.931847i
$40$	244.329	−	423.191i	0.965797	−	1.67281i
$41$	−299.713			−1.14164			−0.570820	−	0.821075i	$-0.693375\pi$
$41$	−299.713			−1.14164			−0.570820	+	0.821075i	$0.693375\pi$
$42$		0			0
$43$	−501.421			−1.77828			−0.889140	−	0.457635i	$-0.848697\pi$
$43$	−501.421			−1.77828			−0.889140	+	0.457635i	$0.848697\pi$
$44$	25.9949	−	45.0246i	0.0890656	−	0.154266i
$45$	−89.5477	−	155.101i	−0.296644	−	0.513803i
$46$	30.8995	+	53.5195i	0.0990409	+	0.171544i
$47$	−152.777	+	264.617i	−0.474144	+	0.821242i	−0.999562	−	0.0296028i	$-0.990576\pi$
$47$	−152.777	+	264.617i	−0.474144	+	0.821242i	0.525418	+	0.850844i	$0.323909\pi$
$48$	125.735			0.378089
$49$		0			0
$50$	654.227			1.85043
$51$	−8.45942	+	14.6521i	−0.0232266	+	0.0402296i
$52$	94.8492	+	164.284i	0.252947	+	0.438116i
$53$	187.558	+	324.861i	0.486097	+	0.841944i	0.999872	−	0.0159802i	$-0.00508689\pi$
$53$	187.558	+	324.861i	0.486097	+	0.841944i	−0.513775	+	0.857925i	$0.671754\pi$
$54$	32.5919	−	56.4508i	0.0821332	−	0.142259i
$55$	476.416			1.16800
$56$		0			0
$57$	−194.662			−0.452344
$58$	−72.8112	+	126.113i	−0.164838	+	0.285507i
$59$	313.806	+	543.528i	0.692442	+	1.19934i	0.971035	+	0.238936i	$0.0767985\pi$
$59$	313.806	+	543.528i	0.692442	+	1.19934i	−0.278593	+	0.960409i	$0.589868\pi$
$60$	−64.8198	−	112.271i	−0.139470	−	0.241569i
$61$	−1.87868	+	3.25397i	−0.00394328	+	0.00682997i	−0.867990	−	0.496581i	$-0.834589\pi$
$61$	−1.87868	+	3.25397i	−0.00394328	+	0.00682997i	0.864047	+	0.503411i	$0.167922\pi$
$62$	−296.250			−0.606835
$63$		0			0
$64$	565.288			1.10408
$65$	−869.164	+	1505.44i	−1.65856	+	2.87271i
$66$	86.6985	+	150.166i	0.161695	+	0.280063i
$67$	406.524	+	704.120i	0.741266	+	1.28391i	0.951919	+	0.306349i	$0.0991075\pi$
$67$	406.524	+	704.120i	0.741266	+	1.28391i	−0.210653	+	0.977561i	$0.567559\pi$
$68$	−6.12341	+	10.6061i	−0.0109202	+	0.0189143i
$69$	76.7939			0.133984
$70$		0			0
$71$	165.902			0.277310			0.138655	−	0.990341i	$-0.455722\pi$
$71$	165.902			0.277310			0.138655	+	0.990341i	$0.455722\pi$
$72$	110.504	−	191.398i	0.180875	−	0.313284i
$73$	−309.550	−	536.156i	−0.496302	−	0.859621i	0.503689	−	0.863885i	$-0.331976\pi$
$73$	−309.550	−	536.156i	−0.496302	−	0.859621i	−0.999991	+	0.00426452i	$0.998643\pi$
$74$	67.7401	+	117.329i	0.106414	+	0.184314i
$75$	406.485	−	704.052i	0.625824	−	1.08396i
$76$	−140.908			−0.212674
$77$		0			0
$78$	−632.683			−0.918427
$79$	69.1228	−	119.724i	0.0984421	−	0.170507i	−0.812598	−	0.582825i	$-0.801947\pi$
$79$	69.1228	−	119.724i	0.0984421	−	0.170507i	0.911040	+	0.412318i	$0.135281\pi$
$80$	417.011	+	722.284i	0.582790	+	1.00942i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	361.785	−	626.631i	0.487226	−	0.843900i
$83$	621.137			0.821430			0.410715	−	0.911764i	$-0.365279\pi$
$83$	621.137			0.821430			0.410715	+	0.911764i	$0.365279\pi$
$84$		0			0
$85$	−112.225			−0.143207
$86$	605.269	−	1048.36i	0.758928	−	1.31450i
$87$	90.4781	+	156.713i	0.111497	+	0.193119i
$88$	293.953	+	509.142i	0.356086	+	0.616758i
$89$	−142.709	+	247.180i	−0.169968	+	0.294393i	−0.938408	−	0.345528i	$-0.887700\pi$
$89$	−142.709	+	247.180i	−0.169968	+	0.294393i	0.768440	+	0.639921i	$0.221033\pi$
$90$	432.375			0.506403
$91$		0			0
$92$	55.5879			0.0629939
$93$	−184.066	+	318.812i	−0.205234	+	0.355476i
$94$	−368.836	−	638.842i	−0.404707	−	0.700974i
$95$	−645.612	−	1118.23i	−0.697247	−	1.20767i
$96$	142.901	−	247.511i	0.151924	−	0.263140i
$97$	−603.114			−0.631309			−0.315654	−	0.948874i	$-0.602224\pi$
$97$	−603.114			−0.631309			−0.315654	+	0.948874i	$0.602224\pi$
$98$		0			0
$99$	215.470			0.218743
$100$	294.237	−	509.634i	0.294237	−	0.509634i
$101$	−228.605	−	395.955i	−0.225218	−	0.390089i	0.731167	−	0.682199i	$-0.238976\pi$
$101$	−228.605	−	395.955i	−0.225218	−	0.390089i	−0.956385	+	0.292110i	$0.905643\pi$
$102$	−20.4228	−	35.3734i	−0.0198251	−	0.0343381i
$103$	−393.022	+	680.735i	−0.375977	+	0.651211i	−0.990473	−	0.137709i	$-0.956026\pi$
$103$	−393.022	+	680.735i	−0.375977	+	0.651211i	0.614496	+	0.788920i	$0.289360\pi$
$104$	−2145.13			−2.02257
$105$		0			0
$106$	−905.612			−0.829819
$107$	98.2304	−	170.140i	0.0887504	−	0.153720i	−0.818233	−	0.574887i	$-0.805046\pi$
$107$	98.2304	−	170.140i	0.0887504	−	0.153720i	0.906983	+	0.421167i	$0.138379\pi$
$108$	−29.3162	−	50.7772i	−0.0261200	−	0.0452411i
$109$	153.172	+	265.301i	0.134598	+	0.233130i	0.925444	−	0.378885i	$-0.123692\pi$
$109$	153.172	+	265.301i	0.134598	+	0.233130i	−0.790846	+	0.612015i	$0.790359\pi$
$110$	−575.085	+	996.077i	−0.498475	+	0.863384i
$111$	168.353			0.143958
$112$		0			0
$113$	1997.63			1.66302			0.831508	−	0.555512i	$-0.187478\pi$
$113$	1997.63			1.66302			0.831508	+	0.555512i	$0.187478\pi$
$114$	234.978	−	406.993i	0.193050	−	0.334372i
$115$	254.693	+	441.142i	0.206524	+	0.357710i
$116$	65.4933	+	113.438i	0.0524215	+	0.0907968i
$117$	−393.099	+	680.867i	−0.310616	+	0.538002i
$118$	−1515.19			−1.18207
$119$		0			0
$120$	1465.98			1.11521
$121$	378.911	−	656.294i	0.284682	−	0.493083i
$122$	−4.53553	−	7.85578i	−0.00336580	−	0.00582974i
$123$	−449.569	−	778.677i	−0.329563	−	0.570820i
$124$	−133.238	+	230.774i	−0.0964927	+	0.167130i
$125$	2905.13			2.07874
$126$		0			0
$127$	−2311.40			−1.61499			−0.807494	−	0.589875i	$-0.799177\pi$
$127$	−2311.40			−1.61499			−0.807494	+	0.589875i	$0.799177\pi$
$128$	−301.295	+	521.859i	−0.208055	+	0.360361i
$129$	−752.132	−	1302.73i	−0.513345	−	0.889140i
$130$	−2098.35	−	3634.44i	−1.41567	−	2.45201i
$131$	77.5088	−	134.249i	0.0516945	−	0.0895374i	−0.839020	−	0.544100i	$-0.816871\pi$
$131$	77.5088	−	134.249i	0.0516945	−	0.0895374i	0.890715	+	0.454563i	$0.150204\pi$
$132$	155.970			0.102844
$133$		0			0
$134$	−1962.87			−1.26542
$135$	268.643	−	465.304i	0.171268	−	0.296644i
$136$	−69.2441	−	119.934i	−0.0436591	−	0.0756197i
$137$	−258.468	−	447.680i	−0.161186	−	0.279181i	0.774109	−	0.633053i	$-0.218198\pi$
$137$	−258.468	−	447.680i	−0.161186	−	0.279181i	−0.935294	+	0.353871i	$0.884865\pi$
$138$	−92.6985	+	160.558i	−0.0571813	+	0.0990409i
$139$	958.067			0.584620			0.292310	−	0.956324i	$-0.405576\pi$
$139$	958.067			0.584620			0.292310	+	0.956324i	$0.405576\pi$
$140$		0			0
$141$	−916.660			−0.547494
$142$	−200.262	+	346.864i	−0.118349	+	0.204987i
$143$	−1045.69	−	1811.19i	−0.611505	−	1.05916i
$144$	188.603	+	326.669i	0.109145	+	0.189045i
$145$	−600.156	+	1039.50i	−0.343726	+	0.595351i
$146$	1494.64			0.847241
$147$		0			0
$148$	121.864			0.0676834
$149$	885.313	−	1533.41i	0.486763	−	0.843098i	−0.513121	−	0.858316i	$-0.671511\pi$
$149$	885.313	−	1533.41i	0.486763	−	0.843098i	0.999884	+	0.0152182i	$0.00484428\pi$
$150$	981.341	+	1699.73i	0.534175	+	0.925217i
$151$	1270.12	+	2199.91i	0.684508	+	1.18560i	0.973591	+	0.228299i	$0.0733163\pi$
$151$	1270.12	+	2199.91i	0.684508	+	1.18560i	−0.289083	+	0.957304i	$0.593350\pi$
$152$	796.698	−	1379.92i	0.425136	−	0.736358i
$153$	−50.7565			−0.0268197
$154$		0			0
$155$	−2441.88			−1.26540
$156$	−284.548	+	492.851i	−0.146039	+	0.252947i
$157$	541.672	+	938.203i	0.275351	+	0.476922i	0.970224	−	0.242211i	$-0.0778726\pi$
$157$	541.672	+	938.203i	0.275351	+	0.476922i	−0.694873	+	0.719133i	$0.744539\pi$
$158$	166.877	+	289.040i	0.0840256	+	0.145537i
$159$	−562.675	+	974.582i	−0.280648	+	0.486097i
$160$	1895.77			0.936709
$161$		0			0
$162$	195.551			0.0948393
$163$	−1484.36	+	2570.99i	−0.713277	+	1.23543i	0.250343	+	0.968157i	$0.419457\pi$
$163$	−1484.36	+	2570.99i	−0.713277	+	1.23543i	−0.963620	+	0.267275i	$0.913877\pi$
$164$	−325.424	−	563.651i	−0.154947	−	0.268377i
$165$	714.624	+	1237.77i	0.337172	+	0.584000i
$166$	−749.779	+	1298.65i	−0.350567	+	0.607200i
$167$	−2091.53			−0.969149			−0.484574	−	0.874750i	$-0.661025\pi$
$167$	−2091.53			−0.969149			−0.484574	+	0.874750i	$0.661025\pi$
$168$		0			0
$169$	5433.96			2.47335
$170$	135.468	−	234.638i	0.0611172	−	0.105858i
$171$	−291.993	−	505.746i	−0.130580	−	0.226172i
$172$	−544.437	−	942.992i	−0.241354	−	0.418037i
$173$	235.074	−	407.160i	0.103308	−	0.178935i	−0.809738	−	0.586792i	$-0.800391\pi$
$173$	235.074	−	407.160i	0.103308	−	0.178935i	0.913046	+	0.407857i	$0.133724\pi$
$174$	−436.867			−0.190338
$175$		0			0
$176$	−1003.41			−0.429745
$177$	−941.418	+	1630.58i	−0.399782	+	0.692442i
$178$	−344.530	−	596.744i	−0.145077	−	0.251280i
$179$	−528.230	−	914.922i	−0.220569	−	0.382036i	0.734412	−	0.678704i	$-0.237458\pi$
$179$	−528.230	−	914.922i	−0.220569	−	0.382036i	−0.954981	+	0.296668i	$0.904125\pi$
$180$	194.459	−	336.814i	0.0805231	−	0.139470i
$181$	−406.470			−0.166921			−0.0834605	−	0.996511i	$-0.526597\pi$
$181$	−406.470			−0.166921			−0.0834605	+	0.996511i	$0.526597\pi$
$182$		0			0
$183$	−11.2721			−0.00455331
$184$	−314.296	+	544.377i	−0.125925	+	0.218109i
$185$	558.357	+	967.103i	0.221899	+	0.384340i
$186$	−444.375	−	769.680i	−0.175178	−	0.303417i
$187$	67.5093	−	116.930i	0.0263998	−	0.0457259i
$188$	−663.531			−0.257410
$189$		0			0
$190$	3117.29			1.19027
$191$	−89.7048	+	155.373i	−0.0339833	+	0.0588608i	−0.882517	−	0.470281i	$-0.844153\pi$
$191$	−89.7048	+	155.373i	−0.0339833	+	0.0588608i	0.848534	+	0.529142i	$0.177486\pi$
$192$	847.933	+	1468.66i	0.318720	+	0.552040i
$193$	1194.18	+	2068.39i	0.445385	+	0.771429i	0.998079	−	0.0619551i	$-0.0197336\pi$
$193$	1194.18	+	2068.39i	0.445385	+	0.771429i	−0.552694	+	0.833384i	$0.686400\pi$
$194$	728.023	−	1260.97i	0.269428	−	0.466663i
$195$	−5214.98			−1.91514
$196$		0			0
$197$	−2665.35			−0.963952			−0.481976	−	0.876184i	$-0.660081\pi$
$197$	−2665.35			−0.963952			−0.481976	+	0.876184i	$0.660081\pi$
$198$	−260.095	+	450.499i	−0.0933544	+	0.161695i
$199$	671.153	+	1162.47i	0.239079	+	0.414098i	0.960450	−	0.278451i	$-0.0898211\pi$
$199$	671.153	+	1162.47i	0.239079	+	0.414098i	−0.721371	+	0.692549i	$0.756488\pi$
$200$	3327.26	+	5762.99i	1.17636	+	2.03752i
$201$	−1219.57	+	2112.36i	−0.427970	+	0.741266i
$202$	1103.80			0.384471
$203$		0			0
$204$	−36.7405			−0.0126095
$205$	2982.07	−	5165.09i	1.01598	−	1.75973i
$206$	−948.840	−	1643.44i	−0.320916	−	0.555844i
$207$	115.191	+	199.517i	0.0386779	+	0.0669921i
$208$	1830.60	−	3170.70i	0.610239	−	1.05696i
$209$	1553.48			0.514144
$210$		0			0
$211$	628.442			0.205042			0.102521	−	0.994731i	$-0.467309\pi$
$211$	628.442			0.205042			0.102521	+	0.994731i	$0.467309\pi$
$212$	−407.297	+	705.459i	−0.131949	+	0.228543i
$213$	248.854	+	431.027i	0.0800525	+	0.138655i
$214$	237.149	+	410.755i	0.0757532	+	0.131208i
$215$	4989.02	−	8641.23i	1.58255	−	2.74106i
$216$	663.021			0.208856
$217$		0			0
$218$	−739.578			−0.229773
$219$	928.649	−	1608.47i	0.286540	−	0.496302i
$220$	517.286	+	895.966i	0.158525	+	0.274573i
$221$	246.325	+	426.647i	0.0749756	+	0.129862i
$222$	−203.220	+	351.988i	−0.0614381	+	0.106414i
$223$	−969.970			−0.291273			−0.145637	−	0.989338i	$-0.546523\pi$
$223$	−969.970			−0.291273			−0.145637	+	0.989338i	$0.546523\pi$
$224$		0			0
$225$	2438.91			0.722640
$226$	−2411.35	+	4176.58i	−0.709737	+	1.22930i
$227$	2374.32	+	4112.44i	0.694225	+	1.20243i	0.970441	+	0.241338i	$0.0775862\pi$
$227$	2374.32	+	4112.44i	0.694225	+	1.20243i	−0.276216	+	0.961096i	$0.589080\pi$
$228$	−211.361	−	366.088i	−0.0613936	−	0.106337i
$229$	2401.00	−	4158.65i	0.692848	−	1.20005i	−0.278052	−	0.960566i	$-0.589689\pi$
$229$	2401.00	−	4158.65i	0.692848	−	1.20005i	0.970901	−	0.239482i	$-0.0769778\pi$
$230$	−1229.77			−0.352559
$231$		0			0
$232$	−1481.21			−0.419164
$233$	1577.64	−	2732.56i	0.443583	−	0.768309i	−0.554369	−	0.832271i	$-0.687040\pi$
$233$	1577.64	−	2732.56i	0.443583	−	0.768309i	0.997952	+	0.0639623i	$0.0203737\pi$
$234$	−949.025	−	1643.76i	−0.265127	−	0.459213i
$235$	−3040.18	−	5265.74i	−0.843912	−	1.46170i
$236$	−681.453	+	1180.31i	−0.187961	+	0.325558i
$237$	414.737			0.113671
$238$		0			0
$239$	4241.93			1.14806			0.574032	−	0.818833i	$-0.305378\pi$
$239$	4241.93			1.14806			0.574032	+	0.818833i	$0.305378\pi$
$240$	−1251.03	+	2166.85i	−0.336474	+	0.582790i
$241$	2171.49	+	3761.14i	0.580407	+	1.00530i	0.995431	+	0.0954844i	$0.0304400\pi$
$241$	2171.49	+	3761.14i	0.580407	+	1.00530i	−0.415024	+	0.909811i	$0.636227\pi$
$242$	914.773	+	1584.43i	0.242991	+	0.420873i
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$	−8.15938			−0.00214078
$245$		0			0
$246$	2170.71			0.562600
$247$	−2834.13	+	4908.85i	−0.730086	+	1.26455i
$248$	−1506.66	−	2609.62i	−0.385779	−	0.668189i
$249$	931.706	+	1613.76i	0.237126	+	0.410715i
$250$	−3506.80	+	6073.95i	−0.887157	+	1.53660i
$251$	3003.01			0.755172			0.377586	−	0.925974i	$-0.376754\pi$
$251$	3003.01			0.755172			0.377586	+	0.925974i	$0.376754\pi$
$252$		0			0
$253$	−612.844			−0.152289
$254$	2790.11	−	4832.61i	0.689239	−	1.19380i
$255$	−168.338	−	291.570i	−0.0413402	−	0.0716033i
$256$	1533.76	+	2656.55i	0.374454	+	0.648573i
$257$	−2234.42	+	3870.13i	−0.542332	+	0.939347i	0.456437	+	0.889756i	$0.349125\pi$
$257$	−2234.42	+	3870.13i	−0.542332	+	0.939347i	−0.998770	+	0.0495916i	$0.984208\pi$
$258$	3631.61			0.876335
$259$		0			0
$260$	−3774.90			−0.900422
$261$	−271.434	+	470.138i	−0.0643731	+	0.111497i
$262$	187.123	+	324.106i	0.0441240	+	0.0764250i
$263$	−3080.07	−	5334.83i	−0.722148	−	1.25080i	−0.960137	−	0.279530i	$-0.909821\pi$
$263$	−3080.07	−	5334.83i	−0.722148	−	1.25080i	0.237989	−	0.971268i	$-0.423512\pi$
$264$	−881.860	+	1527.43i	−0.205586	+	0.356086i
$265$	−7464.64			−1.73037
$266$		0			0
$267$	−856.255			−0.196262
$268$	−882.796	+	1529.05i	−0.201214	+	0.348513i
$269$	−2494.45	−	4320.52i	−0.565388	−	0.979281i	−0.997013	−	0.0772281i	$-0.975393\pi$
$269$	−2494.45	−	4320.52i	−0.565388	−	0.979281i	0.431625	−	0.902053i	$-0.357940\pi$
$270$	648.562	+	1123.34i	0.146186	+	0.253202i
$271$	−2216.86	+	3839.72i	−0.496918	+	0.860688i	−0.999994	−	0.00355459i	$-0.998869\pi$
$271$	−2216.86	+	3839.72i	−0.496918	+	0.860688i	0.503075	+	0.864243i	$0.332202\pi$
$272$	236.366			0.0526903
$273$		0			0
$274$	1247.99			0.275161
$275$	−3243.90	+	5618.60i	−0.711326	+	1.23205i
$276$	83.3818	+	144.422i	0.0181848	+	0.0314969i
$277$	−556.184	−	963.339i	−0.120642	−	0.208958i	0.799379	−	0.600827i	$-0.205162\pi$
$277$	−556.184	−	963.339i	−0.120642	−	0.208958i	−0.920021	+	0.391869i	$0.871829\pi$
$278$	−1156.49	+	2003.10i	−0.249502	+	0.432151i
$279$	−1104.40			−0.236984
$280$		0			0
$281$	2813.22			0.597233			0.298616	−	0.954373i	$-0.403475\pi$
$281$	2813.22			0.597233			0.298616	+	0.954373i	$0.403475\pi$
$282$	1106.51	−	1916.53i	0.233658	−	0.404707i
$283$	−1573.77	−	2725.85i	−0.330569	−	0.572562i	0.652055	−	0.758172i	$-0.273907\pi$
$283$	−1573.77	−	2725.85i	−0.330569	−	0.572562i	−0.982623	+	0.185610i	$0.940574\pi$
$284$	180.135	+	312.002i	0.0376374	+	0.0651899i
$285$	1936.84	−	3354.70i	0.402555	−	0.697247i
$286$	5049.05			1.04390
$287$		0			0
$288$	857.403			0.175427
$289$	2440.60	−	4227.24i	0.496763	−	0.860419i
$290$	−1448.91	−	2509.58i	−0.293389	−	0.508164i
$291$	−904.671	−	1566.94i	−0.182243	−	0.315654i
$292$	672.210	−	1164.30i	0.134720	−	0.233341i
$293$	9143.04			1.82301			0.911505	−	0.411289i	$-0.134921\pi$
$293$	9143.04			1.82301			0.911505	+	0.411289i	$0.134921\pi$
$294$		0			0
$295$	−12489.2			−2.46491
$296$	−689.024	+	1193.42i	−0.135300	+	0.234346i
$297$	323.205	+	559.808i	0.0631457	+	0.109372i
$298$	2137.33	+	3701.97i	0.415478	+	0.719629i
$299$	1118.06	−	1936.54i	0.216251	−	0.374558i
$300$	1765.42			0.339756
$301$		0			0
$302$	−6132.67			−1.16853
$303$	685.814	−	1187.86i	0.130030	−	0.225218i
$304$	1359.77	+	2355.19i	0.256540	+	0.444340i
$305$	−37.3848	−	64.7523i	−0.00701851	−	0.0121564i
$306$	61.2685	−	106.120i	0.0114460	−	0.0198251i
$307$	−4648.90			−0.864257			−0.432129	−	0.901812i	$-0.642237\pi$
$307$	−4648.90			−0.864257			−0.432129	+	0.901812i	$0.642237\pi$
$308$		0			0
$309$	−2358.13			−0.434141
$310$	2947.61	−	5105.41i	0.540042	−	0.935380i
$311$	3208.59	+	5557.44i	0.585024	+	1.01329i	0.994872	+	0.101138i	$0.0322482\pi$
$311$	3208.59	+	5557.44i	0.585024	+	1.01329i	−0.409849	+	0.912154i	$0.634418\pi$
$312$	−3217.69	−	5573.21i	−0.583865	−	1.01128i
$313$	−2934.11	+	5082.02i	−0.529858	+	0.917741i	0.469535	+	0.882914i	$0.344422\pi$
$313$	−2934.11	+	5082.02i	−0.529858	+	0.917741i	−0.999393	+	0.0348275i	$0.988912\pi$
$314$	−2615.42			−0.470054
$315$		0			0
$316$	300.210			0.0534435
$317$	1987.26	−	3442.04i	0.352100	−	0.609855i	−0.634517	−	0.772909i	$-0.718801\pi$
$317$	1987.26	−	3442.04i	0.352100	−	0.609855i	0.986617	+	0.163054i	$0.0521344\pi$
$318$	−1358.42	−	2352.85i	−0.239548	−	0.414910i
$319$	−722.049	−	1250.63i	−0.126730	−	0.219504i
$320$	−5624.48	+	9741.88i	−0.982556	+	1.70184i
$321$	589.383			0.102480
$322$		0			0
$323$	−365.939			−0.0630384
$324$	87.9487	−	152.332i	0.0150804	−	0.0261200i
$325$	−11836.2	−	20500.9i	−2.02017	−	3.49903i
$326$	−3583.57	−	6206.92i	−0.608820	−	1.05451i
$327$	−459.515	+	795.903i	−0.0777102	+	0.134598i
$328$	7359.85			1.23896
$329$		0			0
$330$	−3450.51			−0.575589
$331$	4456.41	−	7718.73i	0.740020	−	1.28175i	−0.212466	−	0.977168i	$-0.568149\pi$
$331$	4456.41	−	7718.73i	0.740020	−	1.28175i	0.952486	−	0.304583i	$-0.0985172\pi$
$332$	674.422	+	1168.13i	0.111487	+	0.193101i
$333$	252.530	+	437.395i	0.0415572	+	0.0719792i
$334$	2524.71	−	4372.92i	0.413610	−	0.716394i
$335$	−16179.2			−2.63871
$336$		0			0
$337$	3977.06			0.642862			0.321431	−	0.946933i	$-0.395836\pi$
$337$	3977.06			0.642862			0.321431	+	0.946933i	$0.395836\pi$
$338$	−6559.36	+	11361.2i	−1.05557	+	1.82830i
$339$	2996.44	+	5189.99i	0.480072	+	0.831508i
$340$	−121.853	−	211.055i	−0.0194365	−	0.0336649i
$341$	1468.92	−	2544.24i	0.233273	−	0.404042i
$342$	1409.87			0.222915
$343$		0			0
$344$	12313.1			1.92987
$345$	−764.080	+	1323.43i	−0.119237	+	0.206524i
$346$	567.518	+	982.971i	0.0881791	+	0.152731i
$347$	−3413.21	−	5911.86i	−0.528043	−	0.914597i	−0.999466	−	0.0326898i	$-0.989593\pi$
$347$	−3413.21	−	5911.86i	−0.528043	−	0.914597i	0.471423	−	0.881907i	$-0.343741\pi$
$348$	−196.480	+	340.313i	−0.0302656	+	0.0524215i
$349$	−807.342			−0.123828			−0.0619141	−	0.998081i	$-0.519720\pi$
$349$	−807.342			−0.123828			−0.0619141	+	0.998081i	$0.519720\pi$
$350$		0			0
$351$	−2358.59			−0.358668
$352$	−1140.40	+	1975.23i	−0.172680	+	0.299091i
$353$	3959.60	+	6858.23i	0.597020	+	1.03407i	0.993258	+	0.115922i	$0.0369822\pi$
$353$	3959.60	+	6858.23i	0.597020	+	1.03407i	−0.396238	+	0.918148i	$0.629684\pi$
$354$	−2272.79	−	3936.58i	−0.341235	−	0.591036i
$355$	−1650.69	+	2859.07i	−0.246787	+	0.427448i
$356$	−619.807			−0.0922744
$357$		0			0
$358$	2550.52			0.376534
$359$	4409.61	−	7637.66i	0.648273	−	1.12284i	−0.335262	−	0.942125i	$-0.608825\pi$
$359$	4409.61	−	7637.66i	0.648273	−	1.12284i	0.983535	−	0.180717i	$-0.0578419\pi$
$360$	2198.97	+	3808.72i	0.321932	+	0.557603i
$361$	1324.32	+	2293.79i	0.193078	+	0.334420i
$362$	490.653	−	849.836i	0.0712380	−	0.123388i
$363$	2273.47			0.328722
$364$		0			0
$365$	12319.8			1.76670
$366$	13.6066	−	23.5673i	0.00194325	−	0.00336580i
$367$	5580.89	+	9666.39i	0.793788	+	1.37488i	0.923606	+	0.383344i	$0.125228\pi$
$367$	5580.89	+	9666.39i	0.793788	+	1.37488i	−0.129817	+	0.991538i	$0.541439\pi$
$368$	−536.427	−	929.119i	−0.0759870	−	0.131613i
$369$	1348.71	−	2336.03i	0.190273	−	0.329563i
$370$	−2695.99			−0.378805
$371$		0			0
$372$	−799.426			−0.111420
$373$	−1363.93	+	2362.39i	−0.189334	+	0.327936i	−0.945028	−	0.326988i	$-0.893966\pi$
$373$	−1363.93	+	2362.39i	−0.189334	+	0.327936i	0.755694	+	0.654924i	$0.227300\pi$
$374$	162.982	+	282.293i	0.0225337	+	0.0390295i
$375$	4357.69	+	7547.74i	0.600080	+	1.03937i
$376$	3751.64	−	6498.03i	0.514564	−	0.891250i
$377$	5269.17			0.719830
$378$		0			0
$379$	4086.49			0.553849			0.276924	−	0.960892i	$-0.410685\pi$
$379$	4086.49			0.553849			0.276924	+	0.960892i	$0.410685\pi$
$380$	1401.99	−	2428.32i	0.189265	−	0.327817i
$381$	−3467.10	−	6005.19i	−0.466207	−	0.807494i
$382$	−216.566	−	375.104i	−0.0290066	−	0.0502408i
$383$	−6516.47	+	11286.9i	−0.869389	+	1.50583i	−0.00676631	+	0.999977i	$0.502154\pi$
$383$	−6516.47	+	11286.9i	−0.869389	+	1.50583i	−0.862622	+	0.505848i	$0.831180\pi$
$384$	−1807.77			−0.240241
$385$		0			0
$386$	−5766.03			−0.760319
$387$	2256.40	−	3908.19i	0.296380	−	0.513345i
$388$	−654.853	−	1134.24i	−0.0856833	−	0.148408i
$389$	97.4957	+	168.868i	0.0127075	+	0.0220101i	0.872309	−	0.488955i	$-0.162622\pi$
$389$	97.4957	+	168.868i	0.0127075	+	0.0220101i	−0.859602	+	0.510965i	$0.829288\pi$
$390$	6295.04	−	10903.3i	0.817338	−	1.41567i
$391$	144.363			0.0186719
$392$		0			0
$393$	465.053			0.0596916
$394$	3217.37	−	5572.64i	0.411392	−	0.712553i
$395$	1375.51	+	2382.45i	0.175214	+	0.303479i
$396$	233.955	+	405.221i	0.0296885	+	0.0514220i
$397$	7091.48	−	12282.8i	0.896501	−	1.55279i	0.0645653	−	0.997913i	$-0.479434\pi$
$397$	7091.48	−	12282.8i	0.896501	−	1.55279i	0.831936	−	0.554872i	$-0.187233\pi$
$398$	−3240.61			−0.408134
$399$		0			0
$400$	−11357.6			−1.41971
$401$	−5002.52	+	8664.63i	−0.622978	+	1.07903i	0.365950	+	0.930634i	$0.380744\pi$
$401$	−5002.52	+	8664.63i	−0.622978	+	1.07903i	−0.988928	+	0.148395i	$0.952589\pi$
$402$	−2944.31	−	5099.69i	−0.365295	−	0.632710i
$403$	5359.72	+	9283.30i	0.662498	+	1.14748i
$404$	496.431	−	859.844i	0.0611346	−	0.105888i
$405$	1611.86			0.197763
$406$		0			0
$407$	−1343.52			−0.163626
$408$	207.732	−	359.803i	0.0252066	−	0.0436591i
$409$	−2317.47	−	4013.97i	−0.280174	−	0.485276i	0.691253	−	0.722613i	$-0.257059\pi$
$409$	−2317.47	−	4013.97i	−0.280174	−	0.485276i	−0.971428	+	0.237336i	$0.923726\pi$
$410$	7199.35	+	12469.6i	0.867196	+	1.50203i
$411$	775.404	−	1343.04i	0.0930605	−	0.161186i
$412$	−1706.95			−0.204115
$413$		0			0
$414$	−556.191			−0.0660273
$415$	−6180.16	+	10704.3i	−0.731017	+	1.26616i
$416$	−4161.04	−	7207.14i	−0.490413	−	0.849420i
$417$	1437.10	+	2489.13i	0.168765	+	0.292310i
$418$	−1875.21	+	3247.96i	−0.219425	+	0.380055i
$419$	4998.31			0.582777			0.291388	−	0.956605i	$-0.405883\pi$
$419$	4998.31			0.582777			0.291388	+	0.956605i	$0.405883\pi$
$420$		0			0
$421$	−704.160			−0.0815170			−0.0407585	−	0.999169i	$-0.512977\pi$
$421$	−704.160			−0.0815170			−0.0407585	+	0.999169i	$0.512977\pi$
$422$	−758.597	+	1313.93i	−0.0875069	+	0.151566i
$423$	−1374.99	−	2381.55i	−0.158048	−	0.273747i
$424$	−4605.75	−	7977.39i	−0.527535	−	0.913718i
$425$	764.139	−	1323.53i	0.0872145	−	0.151060i
$426$	−1201.57			−0.136658
$427$		0			0
$428$	426.629			0.0481820
$429$	3137.08	−	5433.58i	0.353053	−	0.611505i
$430$	12044.5	+	20861.8i	1.35079	+	2.33964i
$431$	5166.39	+	8948.45i	0.577393	+	1.00007i	0.995777	+	0.0918037i	$0.0292632\pi$
$431$	5166.39	+	8948.45i	0.577393	+	1.00007i	−0.418384	+	0.908270i	$0.637403\pi$
$432$	−565.808	+	980.008i	−0.0630149	+	0.109145i
$433$	11106.8			1.23270			0.616348	−	0.787474i	$-0.288611\pi$
$433$	11106.8			1.23270			0.616348	+	0.787474i	$0.288611\pi$
$434$		0			0
$435$	−3600.94			−0.396901
$436$	−332.623	+	576.120i	−0.0365362	+	0.0632825i
$437$	830.492	+	1438.45i	0.0909103	+	0.157461i
$438$	2241.96	+	3883.19i	0.244577	+	0.423620i
$439$	3649.64	−	6321.36i	0.396783	−	0.687249i	−0.596544	−	0.802581i	$-0.703460\pi$
$439$	3649.64	−	6321.36i	0.396783	−	0.687249i	0.993327	+	0.115332i	$0.0367931\pi$
$440$	−11699.0			−1.26757
$441$		0			0
$442$	−1189.36			−0.127991
$443$	−8044.83	+	13934.1i	−0.862802	+	1.49442i	0.00641088	+	0.999979i	$0.497959\pi$
$443$	−8044.83	+	13934.1i	−0.862802	+	1.49442i	−0.869213	+	0.494438i	$0.835374\pi$
$444$	182.796	+	316.611i	0.0195385	+	0.0338417i
$445$	−2839.84	−	4918.75i	−0.302520	−	0.523980i
$446$	1170.86	−	2027.98i	0.124309	−	0.215309i
$447$	5311.88			0.562065
$448$		0			0
$449$	13561.7			1.42543			0.712715	−	0.701454i	$-0.247466\pi$
$449$	13561.7			1.42543			0.712715	+	0.701454i	$0.247466\pi$
$450$	−2944.02	+	5099.20i	−0.308406	+	0.534175i
$451$	3587.73	+	6214.13i	0.374589	+	0.648807i
$452$	2169.00	+	3756.81i	0.225710	+	0.390941i
$453$	−3810.35	+	6599.73i	−0.395201	+	0.684508i
$454$	−11464.2			−1.18512
$455$		0			0
$456$	4780.19			0.490905
$457$	−5424.28	+	9395.14i	−0.555224	+	0.961676i	0.442662	+	0.896688i	$0.354034\pi$
$457$	−5424.28	+	9395.14i	−0.555224	+	0.961676i	−0.997886	+	0.0649876i	$0.979299\pi$
$458$	5796.52	+	10039.9i	0.591383	+	1.02431i
$459$	−76.1347	−	131.869i	−0.00774219	−	0.0134099i
$460$	−553.085	+	957.972i	−0.0560603	+	0.0970993i
$461$	−1758.69			−0.177679			−0.0888397	−	0.996046i	$-0.528316\pi$
$461$	−1758.69			−0.177679			−0.0888397	+	0.996046i	$0.528316\pi$
$462$		0			0
$463$	−5411.95			−0.543228			−0.271614	−	0.962406i	$-0.587557\pi$
$463$	−5411.95			−0.543228			−0.271614	+	0.962406i	$0.587557\pi$
$464$	1264.03	−	2189.37i	0.126468	−	0.219049i
$465$	−3662.82	−	6344.19i	−0.365289	−	0.632699i
$466$	3808.77	+	6596.98i	0.378622	+	0.655792i
$467$	−4055.67	+	7024.63i	−0.401872	+	0.696062i	−0.993952	−	0.109817i	$-0.964974\pi$
$467$	−4055.67	+	7024.63i	−0.401872	+	0.696062i	0.592080	+	0.805879i	$0.298307\pi$
$468$	−1707.29			−0.168631
$469$		0			0
$470$	14679.3			1.44065
$471$	−1625.02	+	2814.61i	−0.158974	+	0.275351i
$472$	−7705.93	−	13347.1i	−0.751471	−	1.30159i
$473$	6002.30	+	10396.3i	0.583480	+	1.01062i
$474$	−500.632	+	867.119i	−0.0485122	+	0.0840256i
$475$	17583.8			1.69853
$476$		0			0
$477$	−3376.05			−0.324065
$478$	−5120.46	+	8868.90i	−0.489967	+	0.848648i
$479$	−1047.88	−	1814.98i	−0.0999559	−	0.173129i	0.811710	−	0.584060i	$-0.198537\pi$
$479$	−1047.88	−	1814.98i	−0.0999559	−	0.173129i	−0.911666	+	0.410932i	$0.865203\pi$
$480$	2843.65	+	4925.34i	0.270405	+	0.468355i
$481$	2451.09	−	4245.42i	0.232350	−	0.402441i
$482$	−10484.9			−0.990817
$483$		0			0
$484$	1645.67			0.154552
$485$	6000.83	−	10393.7i	0.561822	−	0.973104i
$486$	293.327	+	508.057i	0.0273777	+	0.0474196i
$487$	−4805.04	−	8322.57i	−0.447099	−	0.774398i	0.551097	−	0.834441i	$-0.314209\pi$
$487$	−4805.04	−	8322.57i	−0.447099	−	0.774398i	−0.998196	+	0.0600435i	$0.980876\pi$
$488$	46.1335	−	79.9056i	0.00427944	−	0.00741221i
$489$	−8906.17			−0.823622
$490$		0			0
$491$	−11717.3			−1.07698			−0.538488	−	0.842633i	$-0.681004\pi$
$491$	−11717.3			−1.07698			−0.538488	+	0.842633i	$0.681004\pi$
$492$	976.272	−	1690.95i	0.0894588	−	0.154947i
$493$	170.087	+	294.600i	0.0155382	+	0.0269130i
$494$	−6842.19	−	11851.0i	−0.623167	−	1.07936i
$495$	−2143.87	+	3713.30i	−0.194667	+	0.337172i
$496$	5143.01			0.465581
$497$		0			0
$498$	−4498.67			−0.404800
$499$	4597.59	−	7963.26i	0.412458	−	0.714398i	−0.582700	−	0.812687i	$-0.698004\pi$
$499$	4597.59	−	7963.26i	0.412458	−	0.714398i	0.995158	+	0.0982893i	$0.0313370\pi$
$500$	3154.35	+	5463.49i	0.282133	+	0.488669i
$501$	−3137.30	−	5433.97i	−0.279769	−	0.484574i
$502$	−3624.95	+	6278.60i	−0.322290	+	0.558222i
$503$	16118.8			1.42883			0.714414	−	0.699724i	$-0.246693\pi$
$503$	16118.8			1.42883			0.714414	+	0.699724i	$0.246693\pi$
$504$		0			0
$505$	9098.23			0.801715
$506$	739.769	−	1281.32i	0.0649935	−	0.112572i
$507$	8150.93	+	14117.8i	0.713995	+	1.23668i
$508$	−2509.69	−	4346.90i	−0.219192	−	0.379651i
$509$	−2459.39	+	4259.79i	−0.214166	+	0.370947i	−0.953014	−	0.302925i	$-0.902037\pi$
$509$	−2459.39	+	4259.79i	−0.214166	+	0.370947i	0.738848	+	0.673872i	$0.235370\pi$
$510$	812.808			0.0705721
$511$		0			0
$512$	−12226.4			−1.05534
$513$	875.979	−	1517.24i	0.0753906	−	0.130580i
$514$	−5394.37	−	9343.33i	−0.462910	−	0.801783i
$515$	−7820.95	−	13546.3i	−0.669188	−	1.15907i
$516$	1633.31	−	2828.98i	0.139346	−	0.241354i
$517$	7315.29			0.622294
$518$		0			0
$519$	1410.44			0.119290
$520$	21343.5	−	36968.0i	1.79995	−	3.11760i
$521$	−6981.69	−	12092.6i	−0.587089	−	1.01687i	−0.994611	−	0.103673i	$-0.966940\pi$
$521$	−6981.69	−	12092.6i	−0.587089	−	1.01687i	0.407522	−	0.913195i	$-0.366393\pi$
$522$	−655.301	−	1135.01i	−0.0549458	−	0.0951690i
$523$	6877.63	−	11912.4i	0.575024	−	0.995972i	−0.421015	−	0.907054i	$-0.638326\pi$
$523$	6877.63	−	11912.4i	0.575024	−	0.995972i	0.996039	−	0.0889177i	$-0.0283408\pi$
$524$	336.632			0.0280646
$525$		0			0
$526$	14871.9			1.23278
$527$	−346.020	+	599.325i	−0.0286013	+	0.0495389i
$528$	−1505.12	−	2606.94i	−0.124057	−	0.214872i
$529$	5755.87	+	9969.46i	0.473072	+	0.819385i
$530$	9010.61	−	15606.8i	0.738483	−	1.27909i
$531$	−5648.51			−0.461628
$532$		0			0
$533$	−26181.5			−2.12767
$534$	1033.59	−	1790.23i	0.0837601	−	0.145077i
$535$	1954.74	+	3385.70i	0.157964	+	0.273601i
$536$	−9982.74	−	17290.6i	−0.804457	−	1.39336i
$537$	1584.69	−	2744.77i	0.127345	−	0.220569i
$538$	12044.3			0.965178
$539$		0			0
$540$	1166.76			0.0929800
$541$	−7231.34	+	12525.1i	−0.574676	+	0.995368i	0.421401	+	0.906875i	$0.361539\pi$
$541$	−7231.34	+	12525.1i	−0.574676	+	0.995368i	−0.996077	+	0.0884937i	$0.971795\pi$
$542$	−5351.98	−	9269.91i	−0.424146	−	0.734643i
$543$	−609.706	−	1056.04i	−0.0481860	−	0.0834605i
$544$	268.634	−	465.289i	0.0211721	−	0.0366711i
$545$	−6096.07			−0.479132
$546$		0			0
$547$	13682.5			1.06951			0.534755	−	0.845007i	$-0.320404\pi$
$547$	13682.5			1.06951			0.534755	+	0.845007i	$0.320404\pi$
$548$	561.282	−	972.169i	0.0437533	−	0.0757829i
$549$	−16.9081	−	29.2857i	−0.00131443	−	0.00227666i
$550$	−7831.47	−	13564.5i	−0.607155	−	1.05162i
$551$	−1956.96	+	3389.56i	−0.151306	+	0.262069i
$552$	−1885.78			−0.145406
$553$		0			0
$554$	2685.49			0.205949
$555$	−1675.07	+	2901.31i	−0.128113	+	0.221899i
$556$	1040.26	+	1801.78i	0.0793466	+	0.137432i
$557$	3831.56	+	6636.46i	0.291470	+	0.504840i	0.974157	−	0.225870i	$-0.0725225\pi$
$557$	3831.56	+	6636.46i	0.291470	+	0.504840i	−0.682688	+	0.730710i	$0.739189\pi$
$558$	1333.12	−	2309.04i	0.101139	−	0.175178i
$559$	−43801.8			−3.31417
$560$		0			0
$561$	405.056			0.0304839
$562$	−3395.85	+	5881.79i	−0.254885	+	0.441474i
$563$	−8735.24	−	15129.9i	−0.653902	−	1.13259i	−0.982168	−	0.188006i	$-0.939798\pi$
$563$	−8735.24	−	15129.9i	−0.653902	−	1.13259i	0.328266	−	0.944585i	$-0.393536\pi$
$564$	−995.297	−	1723.91i	−0.0743078	−	0.128705i
$565$	−19875.9	+	34426.0i	−1.47997	+	2.56339i
$566$	7598.83			0.564316
$567$		0			0
$568$	−4073.96			−0.300950
$569$	6936.96	−	12015.2i	0.511094	−	0.885240i	−0.488824	−	0.872383i	$-0.662574\pi$
$569$	6936.96	−	12015.2i	0.511094	−	0.885240i	0.999917	−	0.0128577i	$-0.00409284\pi$
$570$	4675.94	+	8098.96i	0.343603	+	0.595137i
$571$	1888.76	+	3271.43i	0.138428	+	0.239764i	0.926902	−	0.375305i	$-0.122462\pi$
$571$	1888.76	+	3271.43i	0.138428	+	0.239764i	−0.788474	+	0.615068i	$0.789129\pi$
$572$	2270.80	−	3933.14i	0.165991	−	0.287505i
$573$	−538.229			−0.0392405
$574$		0			0
$575$	−6936.79			−0.503103
$576$	−2543.80	+	4405.99i	−0.184013	+	0.318720i
$577$	−6940.23	−	12020.8i	−0.500738	−	0.867303i	−1.00000		0.000852075i	$-0.999729\pi$
$577$	−6940.23	−	12020.8i	−0.500738	−	0.867303i	0.499262	−	0.866451i	$-0.333605\pi$
$578$	5892.12	+	10205.5i	0.424014	+	0.734414i
$579$	−3582.55	+	6205.16i	−0.257143	+	0.445385i
$580$	−2606.57			−0.186607
$581$		0			0
$582$	4368.14			0.311108
$583$	4490.36	−	7777.53i	0.318991	−	0.552509i
$584$	7601.41	+	13166.0i	0.538611	+	0.932901i
$585$	−7822.47	−	13548.9i	−0.552854	−	0.957571i
$586$	−11036.6	+	19116.0i	−0.778018	+	1.34757i
$587$	−2395.61			−0.168445			−0.0842227	−	0.996447i	$-0.526841\pi$
$587$	−2395.61			−0.168445			−0.0842227	+	0.996447i	$0.526841\pi$
$588$		0			0
$589$	−7962.36			−0.557018
$590$	15075.8	−	26112.0i	1.05196	−	1.82206i
$591$	−3998.03	−	6924.79i	−0.278269	−	0.481976i
$592$	−1175.99	−	2036.88i	−0.0816437	−	0.141411i
$593$	−3301.75	+	5718.80i	−0.228645	+	0.396025i	−0.957407	−	0.288742i	$-0.906763\pi$
$593$	−3301.75	+	5718.80i	−0.228645	+	0.396025i	0.728762	+	0.684767i	$0.240096\pi$
$594$	−1560.57			−0.107796
$595$		0			0
$596$	3845.04			0.264260
$597$	−2013.46	+	3487.41i	−0.138033	+	0.239079i
$598$	2699.24	+	4675.21i	0.184582	+	0.319705i
$599$	−8626.05	−	14940.8i	−0.588399	−	1.01914i	−0.994442	−	0.105283i	$-0.966425\pi$
$599$	−8626.05	−	14940.8i	−0.588399	−	1.01914i	0.406044	−	0.913854i	$-0.366908\pi$
$600$	−9981.78	+	17289.0i	−0.679174	+	1.17636i
$601$	12833.1			0.871005			0.435503	−	0.900187i	$-0.356571\pi$
$601$	12833.1			0.871005			0.435503	+	0.900187i	$0.356571\pi$
$602$		0			0
$603$	−7317.43			−0.494177
$604$	−2758.15	+	4777.26i	−0.185807	+	0.321828i
$605$	7540.14	+	13059.9i	0.506695	+	0.877621i
$606$	1655.70	+	2867.76i	0.110987	+	0.192235i
$607$	−4310.08	+	7465.28i	−0.288206	+	0.499187i	−0.973381	−	0.229191i	$-0.926392\pi$
$607$	−4310.08	+	7465.28i	−0.288206	+	0.499187i	0.685176	+	0.728378i	$0.259725\pi$
$608$	6181.62			0.412332
$609$		0			0
$610$	180.510			0.0119813
$611$	−13345.9	+	23115.7i	−0.883659	+	1.53054i
$612$	−55.1107	−	95.4546i	−0.00364006	−	0.00630477i
$613$	−2568.37	−	4448.54i	−0.169226	−	0.293107i	0.768922	−	0.639342i	$-0.220793\pi$
$613$	−2568.37	−	4448.54i	−0.169226	−	0.293107i	−0.938148	+	0.346235i	$0.887460\pi$
$614$	5611.72	−	9719.79i	0.368845	−	0.638858i
$615$	17892.4			1.17316
$616$		0			0
$617$	−1759.82			−0.114826			−0.0574131	−	0.998351i	$-0.518285\pi$
$617$	−1759.82			−0.114826			−0.0574131	+	0.998351i	$0.518285\pi$
$618$	2846.52	−	4930.32i	0.185281	−	0.320916i
$619$	1780.12	+	3083.26i	0.115588	+	0.200205i	0.918015	−	0.396546i	$-0.129791\pi$
$619$	1780.12	+	3083.26i	0.115588	+	0.200205i	−0.802427	+	0.596751i	$0.796458\pi$
$620$	−2651.36	−	4592.29i	−0.171744	−	0.297469i
$621$	−345.573	+	598.550i	−0.0223307	+	0.0386779i
$622$	−15492.4			−0.998698
$623$		0			0
$624$	10983.6			0.704643
$625$	−11968.4	+	20729.9i	−0.765977	+	1.32671i
$626$	−7083.56	−	12269.1i	−0.452262	−	0.783341i
$627$	2330.21	+	4036.05i	0.148421	+	0.257072i
$628$	−1176.28	+	2037.38i	−0.0747431	+	0.129459i
$629$	316.482			0.0200620
$630$		0			0
$631$	−27321.4			−1.72369			−0.861845	−	0.507172i	$-0.830691\pi$
$631$	−27321.4			−1.72369			−0.861845	+	0.507172i	$0.830691\pi$
$632$	−1697.40	+	2939.99i	−0.106834	+	0.185042i
$633$	942.664	+	1632.74i	0.0591904	+	0.102521i
$634$	4797.67	+	8309.81i	0.300536	+	0.520544i
$635$	22997.8	−	39833.4i	1.43723	−	2.48936i
$636$	−2443.78			−0.152362
$637$		0			0
$638$	3486.36			0.216342
$639$	−746.561	+	1293.08i	−0.0462183	+	0.0800525i
$640$	−5995.63	−	10384.7i	−0.370309	−	0.641395i
$641$	10963.5	+	18989.4i	0.675558	+	1.17010i	0.976306	+	0.216397i	$0.0694305\pi$
$641$	10963.5	+	18989.4i	0.675558	+	1.17010i	−0.300748	+	0.953704i	$0.597236\pi$
$642$	−711.448	+	1232.26i	−0.0437361	+	0.0757532i
$643$	−5826.04			−0.357320			−0.178660	−	0.983911i	$-0.557176\pi$
$643$	−5826.04			−0.357320			−0.178660	+	0.983911i	$0.557176\pi$
$644$		0			0
$645$	29934.1			1.82737
$646$	441.728	−	765.095i	0.0269033	−	0.0465979i
$647$	−12105.4	−	20967.1i	−0.735565	−	1.27404i	−0.954475	−	0.298291i	$-0.903583\pi$
$647$	−12105.4	−	20967.1i	−0.735565	−	1.27404i	0.218910	−	0.975745i	$-0.429750\pi$
$648$	994.532	+	1722.58i	0.0602915	+	0.104428i
$649$	7512.87	−	13012.7i	0.454401	−	0.787045i
$650$	57150.3			3.44864
$651$		0			0
$652$	−6446.80			−0.387233
$653$	12811.7	−	22190.4i	0.767778	−	1.32983i	−0.170988	−	0.985273i	$-0.554696\pi$
$653$	12811.7	−	22190.4i	0.767778	−	1.32983i	0.938765	−	0.344557i	$-0.111971\pi$
$654$	−1109.37	−	1921.48i	−0.0663298	−	0.114887i
$655$	1542.39	+	2671.49i	0.0920092	+	0.159365i
$656$	−6280.73	+	10878.6i	−0.373813	+	0.647463i
$657$	5571.90			0.330868
$658$		0			0
$659$	−23273.7			−1.37574			−0.687871	−	0.725833i	$-0.741455\pi$
$659$	−23273.7			−1.37574			−0.687871	+	0.725833i	$0.741455\pi$
$660$	−1551.86	+	2687.90i	−0.0915243	+	0.158525i
$661$	10018.2	+	17352.1i	0.589508	+	1.02106i	0.994297	+	0.106647i	$0.0340116\pi$
$661$	10018.2	+	17352.1i	0.589508	+	1.02106i	−0.404789	+	0.914410i	$0.632655\pi$
$662$	10758.7	+	18634.7i	0.631646	+	1.09404i
$663$	−738.975	+	1279.94i	−0.0432872	+	0.0749756i
$664$	−15252.9			−0.891454
$665$		0			0
$666$	−1219.32			−0.0709426
$667$	772.019	−	1337.18i	0.0448166	−	0.0776247i
$668$	−2270.96	−	3933.42i	−0.131536	−	0.227827i
$669$	−1454.95	−	2520.06i	−0.0840834	−	0.145637i
$670$	19530.1	−	33827.1i	1.12614	−	1.95053i
$671$	89.9554			0.00517540
$672$		0			0
$673$	−18127.8			−1.03830			−0.519149	−	0.854684i	$-0.673751\pi$
$673$	−18127.8			−1.03830			−0.519149	+	0.854684i	$0.673751\pi$
$674$	−4800.74	+	8315.12i	−0.274358	+	0.475203i
$675$	3658.36	+	6336.47i	0.208608	+	0.361320i
$676$	5900.11	+	10219.3i	0.335692	+	0.581435i
$677$	−6907.73	+	11964.5i	−0.392150	+	0.679224i	−0.992733	−	0.120339i	$-0.961602\pi$
$677$	−6907.73	+	11964.5i	−0.392150	+	0.679224i	0.600583	+	0.799563i	$0.294935\pi$
$678$	−14468.1			−0.819533
$679$		0			0
$680$	2755.85			0.155415
$681$	−7122.96	+	12337.3i	−0.400811	+	0.694225i
$682$	3546.28	+	6142.33i	0.199111	+	0.344871i
$683$	2302.11	+	3987.38i	0.128972	+	0.223386i	0.923279	−	0.384131i	$-0.125499\pi$
$683$	2302.11	+	3987.38i	0.128972	+	0.223386i	−0.794306	+	0.607517i	$0.792166\pi$
$684$	634.084	−	1098.27i	0.0354456	−	0.0613936i
$685$	10286.8			0.573777
$686$		0			0
$687$	14406.0			0.800032
$688$	−10507.7	+	18199.9i	−0.582271	+	1.00852i
$689$	16384.2	+	28378.3i	0.905935	+	1.56913i
$690$	−1844.65	−	3195.03i	−0.101775	−	0.176279i
$691$	−8956.83	+	15513.7i	−0.493103	+	0.854079i	−0.999968	−	0.00794632i	$-0.997471\pi$
$691$	−8956.83	+	15513.7i	−0.493103	+	0.854079i	0.506866	+	0.862025i	$0.330804\pi$
$692$	1020.96			0.0560854
$693$		0			0
$694$	16480.5			0.901426
$695$	−9532.53	+	16510.8i	−0.520272	+	0.901138i
$696$	−2221.81	−	3848.29i	−0.121002	−	0.209582i
$697$	−845.132	−	1463.81i	−0.0459278	−	0.0795492i
$698$	974.548	−	1687.97i	0.0528470	−	0.0915336i
$699$	9465.86			0.512206
$700$		0			0
$701$	11303.7			0.609035			0.304518	−	0.952507i	$-0.401505\pi$
$701$	11303.7			0.609035			0.304518	+	0.952507i	$0.401505\pi$
$702$	2847.07	−	4931.28i	0.153071	−	0.265127i
$703$	1820.66	+	3153.48i	0.0976780	+	0.169183i
$704$	−6766.82	−	11720.5i	−0.362264	−	0.627460i
$705$	9120.54	−	15797.2i	0.487233	−	0.843912i
$706$	−19118.6			−1.01918
$707$		0			0
$708$	−4088.72			−0.217039
$709$	8023.15	−	13896.5i	0.424987	−	0.736099i	−0.571432	−	0.820649i	$-0.693612\pi$
$709$	8023.15	−	13896.5i	0.424987	−	0.736099i	0.996419	+	0.0845505i	$0.0269454\pi$
$710$	−3985.11	−	6902.42i	−0.210646	−	0.364849i
$711$	622.105	+	1077.52i	0.0328140	+	0.0568355i
$712$	3504.42	−	6069.83i	0.184457	−	0.319489i
$713$	3141.15			0.164989
$714$		0			0
$715$	41617.5			2.17679
$716$	1147.09	−	1986.82i	0.0598726	−	0.103702i
$717$	6362.89	+	11020.9i	0.331418	+	0.574032i
$718$	10645.7	+	18438.9i	0.553336	+	0.958406i
$719$	12595.2	−	21815.6i	0.653300	−	1.13155i	−0.329017	−	0.944324i	$-0.606717\pi$
$719$	12595.2	−	21815.6i	0.653300	−	1.13155i	0.982317	−	0.187225i	$-0.0599493\pi$
$720$	−7506.19			−0.388527
$721$		0			0
$722$	−6394.38			−0.329604
$723$	−6514.48	+	11283.4i	−0.335098	+	0.580407i
$724$	−441.340	−	764.424i	−0.0226551	−	0.0392397i
$725$	−8172.89	−	14155.9i	−0.418667	−	0.725152i
$726$	−2744.32	+	4753.30i	−0.140291	+	0.242991i
$727$	11277.2			0.575307			0.287653	−	0.957735i	$-0.407125\pi$
$727$	11277.2			0.575307			0.287653	+	0.957735i	$0.407125\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$	−14871.3	+	25757.8i	−0.753987	+	1.30594i
$731$	−1413.91	−	2448.96i	−0.0715395	−	0.123910i
$732$	−12.2391	−	21.1987i	−0.000617990	−	0.00107039i
$733$	−11860.0	+	20542.2i	−0.597626	+	1.03512i	0.395544	+	0.918447i	$0.370556\pi$
$733$	−11860.0	+	20542.2i	−0.597626	+	1.03512i	−0.993171	+	0.116672i	$0.962777\pi$
$734$	−26946.9			−1.35508
$735$		0			0
$736$	−2438.64			−0.122133
$737$	9732.64	−	16857.4i	0.486440	−	0.842539i
$738$	3256.07	+	5639.67i	0.162409	+	0.281300i
$739$	−4062.36	−	7036.21i	−0.202214	−	0.350245i	0.747027	−	0.664793i	$-0.231480\pi$
$739$	−4062.36	−	7036.21i	−0.202214	−	0.350245i	−0.949242	+	0.314548i	$0.898147\pi$
$740$	−1212.51	+	2100.14i	−0.0602336	+	0.104328i
$741$	−17004.8			−0.843030
$742$		0			0
$743$	20955.3			1.03469			0.517346	−	0.855777i	$-0.326920\pi$
$743$	20955.3			1.03469			0.517346	+	0.855777i	$0.326920\pi$
$744$	4519.99	−	7828.85i	0.222730	−	0.385779i
$745$	17617.3	+	30514.0i	0.866372	+	1.50060i
$746$	−3292.81	−	5703.32i	−0.161607	−	0.279911i
$747$	−2795.12	+	4841.28i	−0.136905	+	0.237126i
$748$	293.203			0.0143323
$749$		0			0
$750$	−21040.8			−1.02440
$751$	19104.0	−	33089.2i	0.928251	−	1.60778i	0.142004	−	0.989866i	$-0.454645\pi$
$751$	19104.0	−	33089.2i	0.928251	−	1.60778i	0.786247	−	0.617912i	$-0.212021\pi$
$752$	6403.13	+	11090.5i	0.310503	+	0.537807i
$753$	4504.51	+	7802.04i	0.217999	+	0.377586i
$754$	−6360.45	+	11016.6i	−0.307207	+	0.532097i
$755$	−50549.4			−2.43666
$756$		0			0
$757$	30958.1			1.48638			0.743191	−	0.669079i	$-0.233311\pi$
$757$	30958.1			1.48638			0.743191	+	0.669079i	$0.233311\pi$
$758$	−4932.82	+	8543.90i	−0.236370	+	0.409404i
$759$	−919.267	−	1592.22i	−0.0439621	−	0.0761447i
$760$	15853.9	+	27459.7i	0.756685	+	1.31062i
$761$	20024.7	−	34683.8i	0.953871	−	1.65215i	0.216939	−	0.976185i	$-0.430393\pi$
$761$	20024.7	−	34683.8i	0.953871	−	1.65215i	0.736932	−	0.675967i	$-0.236274\pi$
$762$	16740.6			0.795865
$763$		0			0
$764$	−389.601			−0.0184493
$765$	505.014	−	874.710i	0.0238678	−	0.0413402i
$766$	−15732.1	−	27248.9i	−0.742070	−	1.28530i
$767$	27412.6	+	47480.1i	1.29050	+	2.23521i
$768$	−4601.29	+	7969.66i	−0.216191	+	0.374454i
$769$	−8002.01			−0.375240			−0.187620	−	0.982242i	$-0.560077\pi$
$769$	−8002.01			−0.375240			−0.187620	+	0.982242i	$0.560077\pi$
$770$		0			0
$771$	−13406.5			−0.626231
$772$	−2593.26	+	4491.65i	−0.120898	+	0.209402i
$773$	6966.68	+	12066.6i	0.324158	+	0.561458i	0.981342	−	0.192273i	$-0.0615858\pi$
$773$	6966.68	+	12066.6i	0.324158	+	0.561458i	−0.657184	+	0.753730i	$0.728252\pi$
$774$	5447.42	+	9435.21i	0.252976	+	0.438168i
$775$	16626.7	−	28798.2i	0.770642	−	1.33479i
$776$	14810.3			0.685126
$777$		0			0
$778$	−470.751			−0.0216931
$779$	9723.78	−	16842.1i	0.447228	−	0.774621i
$780$	−5662.36	−	9807.49i	−0.259929	−	0.450211i
$781$	−1985.95	−	3439.76i	−0.0909894	−	0.157598i
$782$	−174.261	+	301.829i	−0.00796875	+	0.0138023i
$783$	−1628.61			−0.0743316
$784$		0			0
$785$	−21558.0			−0.980175
$786$	−561.368	+	972.319i	−0.0254750	+	0.0441240i
$787$	−18790.9	−	32546.7i	−0.851108	−	1.47416i	−0.880209	−	0.474586i	$-0.842598\pi$
$787$	−18790.9	−	32546.7i	−0.851108	−	1.47416i	0.0291013	−	0.999576i	$-0.490735\pi$
$788$	−2894.01	−	5012.56i	−0.130831	−	0.226606i
$789$	9240.20	−	16004.5i	0.416933	−	0.722148i
$790$	−6641.54			−0.299108
$791$		0			0
$792$	−5291.16			−0.237390
$793$	−164.113	+	284.252i	−0.00734907	+	0.0127290i
$794$	17120.3	+	29653.3i	0.765212	+	1.32539i
$795$	−11197.0	−	19393.7i	−0.499516	−	0.865187i
$796$	−1457.46	+	2524.39i	−0.0648973	+	0.112405i
$797$	−9458.78			−0.420385			−0.210193	−	0.977660i	$-0.567409\pi$
$797$	−9458.78			−0.420385			−0.210193	+	0.977660i	$0.567409\pi$
$798$		0			0
$799$	−1723.20			−0.0762985
$800$	−12908.2	+	22357.7i	−0.570467	+	0.988078i
$801$	−1284.38	−	2224.62i	−0.0566560	−	0.0981310i
$802$	−12077.2	−	20918.3i	−0.531745	−	0.921009i
$803$	−7410.97	+	12836.2i	−0.325688	+	0.564108i
$804$	−5296.78			−0.232342
$805$		0			0
$806$	−25879.0			−1.13095
$807$	7483.36	−	12961.6i	0.326427	−	0.565388i
$808$	5613.69	+	9723.20i	0.244417	+	0.423343i
$809$	954.968	+	1654.05i	0.0415017	+	0.0718831i	0.886030	−	0.463628i	$-0.153452\pi$
$809$	954.968	+	1654.05i	0.0415017	+	0.0718831i	−0.844528	+	0.535511i	$0.820119\pi$
$810$	−1945.69	+	3370.03i	−0.0844005	+	0.146186i
$811$	43110.6			1.86661			0.933303	−	0.359091i	$-0.116913\pi$
$811$	43110.6			1.86661			0.933303	+	0.359091i	$0.116913\pi$
$812$		0			0
$813$	−13301.2			−0.573792
$814$	1621.77	−	2809.00i	0.0698319	−	0.120952i
$815$	−29538.0	−	51161.4i	−1.26954	−	2.19890i
$816$	354.548	+	614.096i	0.0152104	+	0.0263452i
$817$	16267.9	−	28176.9i	0.696626	−	1.20659i
$818$	11189.7			0.478287
$819$		0			0
$820$	12951.5			0.551570
$821$	−2013.28	+	3487.10i	−0.0855834	+	0.148235i	−0.905640	−	0.424048i	$-0.860609\pi$
$821$	−2013.28	+	3487.10i	−0.0855834	+	0.148235i	0.820056	+	0.572283i	$0.193942\pi$
$822$	1871.99	+	3242.38i	0.0794321	+	0.137580i
$823$	−19834.0	−	34353.5i	−0.840062	−	1.45503i	−0.889842	−	0.456269i	$-0.849185\pi$
$823$	−19834.0	−	34353.5i	−0.840062	−	1.45503i	0.0497799	−	0.998760i	$-0.484148\pi$
$824$	9651.19	−	16716.4i	0.408028	−	0.706726i
$825$	−19463.4			−0.821368
$826$		0			0
$827$	30137.7			1.26722			0.633611	−	0.773652i	$-0.281572\pi$
$827$	30137.7			1.26722			0.633611	+	0.773652i	$0.281572\pi$
$828$	−250.145	+	433.265i	−0.0104990	+	0.0181848i
$829$	−11639.0	−	20159.3i	−0.487622	−	0.844587i	0.512276	−	0.858821i	$-0.328802\pi$
$829$	−11639.0	−	20159.3i	−0.487622	−	0.844587i	−0.999899	+	0.0142341i	$0.995469\pi$
$830$	−14920.2	−	25842.6i	−0.623962	−	1.08073i
$831$	1668.55	−	2890.02i	0.0696528	−	0.120642i
$832$	49381.0			2.05766
$833$		0			0
$834$	−6938.94			−0.288100
$835$	20810.2	−	36044.4i	0.862477	−	1.49385i
$836$	1686.74	+	2921.52i	0.0697813	+	0.120865i
$837$	−1656.59	−	2869.31i	−0.0684113	−	0.118492i
$838$	−6033.49	+	10450.3i	−0.248716	+	0.430788i
$839$	−9494.43			−0.390684			−0.195342	−	0.980735i	$-0.562582\pi$
$839$	−9494.43			−0.390684			−0.195342	+	0.980735i	$0.562582\pi$
$840$		0			0
$841$	−20750.6			−0.850820
$842$	849.996	−	1472.24i	0.0347896	−	0.0602573i
$843$	4219.83	+	7308.95i	0.172406	+	0.298616i
$844$	682.354	+	1181.87i	0.0278289	+	0.0482011i
$845$	−54066.5	+	93645.9i	−2.20112	+	3.81245i
$846$	6639.04			0.269805
$847$		0			0
$848$	15721.8			0.636661
$849$	4721.31	−	8177.55i	0.190854	−	0.330569i
$850$	1844.79	+	3195.28i	0.0744423	+	0.128938i
$851$	−718.251	−	1244.05i	−0.0289322	−	0.0501121i
$852$	−540.404	+	936.007i	−0.0217300	+	0.0376374i
$853$	−12692.4			−0.509471			−0.254736	−	0.967011i	$-0.581988\pi$
$853$	−12692.4			−0.509471			−0.254736	+	0.967011i	$0.581988\pi$
$854$		0			0
$855$	11621.0			0.464831
$856$	−2412.18	+	4178.02i	−0.0963162	+	0.166825i
$857$	−11103.0	−	19231.0i	−0.442557	−	0.766531i	0.555322	−	0.831636i	$-0.312595\pi$
$857$	−11103.0	−	19231.0i	−0.442557	−	0.766531i	−0.997878	+	0.0651047i	$0.979262\pi$
$858$	7573.58	+	13117.8i	0.301349	+	0.521952i
$859$	−9910.24	+	17165.0i	−0.393636	+	0.681797i	−0.992926	−	0.118735i	$-0.962116\pi$
$859$	−9910.24	+	17165.0i	−0.393636	+	0.681797i	0.599290	+	0.800532i	$0.295450\pi$
$860$	21668.0			0.859155
$861$		0			0
$862$	−24945.5			−0.985671
$863$	−18206.9	+	31535.3i	−0.718157	+	1.24389i	0.243572	+	0.969883i	$0.421681\pi$
$863$	−18206.9	+	31535.3i	−0.718157	+	1.24389i	−0.961729	+	0.274002i	$0.911652\pi$
$864$	1286.10	+	2227.60i	0.0506414	+	0.0877135i
$865$	4677.85	+	8102.27i	0.183875	+	0.318480i
$866$	−13407.1	+	23221.7i	−0.526086	+	0.911208i
$867$	14643.6			0.573613
$868$		0			0
$869$	−3309.76			−0.129201
$870$	4346.72	−	7528.74i	0.169388	−	0.293389i
$871$	35512.0	+	61508.7i	1.38149	+	2.39281i
$872$	−3761.33	−	6514.82i	−0.146072	−	0.253004i
$873$	2714.01	−	4700.81i	0.105218	−	0.182243i
$874$	−4009.97			−0.155194
$875$		0			0
$876$	4033.26			0.155561
$877$	−9721.31	+	16837.8i	−0.374305	+	0.648315i	−0.990223	−	0.139496i	$-0.955452\pi$
$877$	−9721.31	+	16837.8i	−0.374305	+	0.648315i	0.615918	+	0.787810i	$0.288785\pi$
$878$	8811.01	+	15261.1i	0.338676	+	0.586603i
$879$	13714.6	+	23754.3i	0.526258	+	0.911505i
$880$	9983.71	−	17292.3i	0.382444	−	0.662412i
$881$	−25184.2			−0.963082			−0.481541	−	0.876423i	$-0.659923\pi$
$881$	−25184.2			−0.963082			−0.481541	+	0.876423i	$0.659923\pi$
$882$		0			0
$883$	−4050.03			−0.154354			−0.0771769	−	0.997017i	$-0.524591\pi$
$883$	−4050.03			−0.154354			−0.0771769	+	0.997017i	$0.524591\pi$
$884$	−534.913	+	926.496i	−0.0203519	+	0.0352505i
$885$	−18733.8	−	32447.8i	−0.711557	−	1.23245i
$886$	−19421.9	−	33639.8i	−0.736448	−	1.27556i
$887$	−20802.1	+	36030.3i	−0.787447	+	1.36390i	0.140080	+	0.990140i	$0.455264\pi$
$887$	−20802.1	+	36030.3i	−0.787447	+	1.36390i	−0.927526	+	0.373758i	$0.878069\pi$
$888$	−4134.14			−0.156231
$889$		0			0
$890$	13712.0			0.516434
$891$	−969.616	+	1679.42i	−0.0364572	+	0.0631457i
$892$	−1053.18	−	1824.16i	−0.0395326	−	0.0684725i
$893$	−9913.27	−	17170.3i	−0.371484	−	0.643428i
$894$	−6412.00	+	11105.9i	−0.239876	+	0.415478i
$895$	21023.0			0.785165
$896$		0			0
$897$	6708.36			0.249705
$898$	−16370.5	+	28354.5i	−0.608340	+	1.05368i
$899$	3700.88	+	6410.11i	0.137298	+	0.237808i
$900$	2648.13	+	4586.70i	0.0980791	+	0.169878i
$901$	−1057.76	+	1832.09i	−0.0391110	+	0.0677422i
$902$	−17323.1			−0.639463
$903$		0			0
$904$	−49054.4			−1.80478
$905$	4044.28	−	7004.90i	0.148548	−	0.257294i
$906$	−9199.01	−	15933.1i	−0.337325	−	0.584264i
$907$	1786.30	+	3093.96i	0.0653949	+	0.113267i	0.896869	−	0.442296i	$-0.145836\pi$
$907$	1786.30	+	3093.96i	0.0653949	+	0.113267i	−0.831474	+	0.555563i	$0.812503\pi$
$908$	−5156.01	+	8930.47i	−0.188445	+	0.326397i
$909$	4114.88			0.150145
$910$		0			0
$911$	29457.7			1.07133			0.535663	−	0.844432i	$-0.320062\pi$
$911$	29457.7			1.07133			0.535663	+	0.844432i	$0.320062\pi$
$912$	−4079.30	+	7065.56i	−0.148113	+	0.256540i
$913$	−7435.36	−	12878.4i	−0.269523	−	0.466828i
$914$	−13095.4	−	22681.9i	−0.473913	−	0.820842i
$915$	112.154	−	194.257i	0.00405214	−	0.00701851i
$916$	10427.9			0.376143
$917$		0			0
$918$	367.611			0.0132167
$919$	1655.32	−	2867.10i	0.0594168	−	0.102913i	−0.834787	−	0.550573i	$-0.814409\pi$
$919$	1655.32	−	2867.10i	0.0594168	−	0.102913i	0.894204	+	0.447660i	$0.147743\pi$
$920$	−6254.34	−	10832.8i	−0.224130	−	0.388204i
$921$	−6973.36	−	12078.2i	−0.249490	−	0.432129i
$922$	2122.92	−	3677.01i	0.0758295	−	0.131340i
$923$	14492.5			0.516820
$924$		0			0
$925$	−15207.3			−0.540556
$926$	6532.80	−	11315.1i	0.231837	−	0.401554i
$927$	−3537.20	−	6126.61i	−0.125326	−	0.217070i
$928$	−2873.19	−	4976.52i	−0.101635	−	0.176037i
$929$	15733.8	−	27251.7i	0.555660	−	0.962431i	−0.442192	−	0.896920i	$-0.645799\pi$
$929$	15733.8	−	27251.7i	0.555660	−	0.962431i	0.997852	−	0.0655103i	$-0.0208675\pi$
$930$	17685.7			0.623587
$931$		0			0
$932$	6851.94			0.240818
$933$	−9625.77	+	16672.3i	−0.337764	+	0.585024i
$934$	−9791.26	−	16959.0i	−0.343019	−	0.594126i
$935$	1343.40	+	2326.84i	0.0469881	+	0.0813859i
$936$	9653.08	−	16719.6i	0.337095	−	0.583865i
$937$	−17363.4			−0.605375			−0.302688	−	0.953090i	$-0.597884\pi$
$937$	−17363.4			−0.605375			−0.302688	+	0.953090i	$0.597884\pi$
$938$		0			0
$939$	−17604.6			−0.611828
$940$	6601.97	−	11434.9i	0.229077	−	0.396773i
$941$	2773.89	+	4804.51i	0.0960958	+	0.166443i	0.910065	−	0.414465i	$-0.136031\pi$
$941$	2773.89	+	4804.51i	0.0960958	+	0.166443i	−0.813970	+	0.580907i	$0.802698\pi$
$942$	−3923.13	−	6795.07i	−0.135693	−	0.235027i
$943$	−3836.02	+	6644.18i	−0.132469	+	0.229443i
$944$	26304.3			0.906919
$945$		0			0
$946$	−28981.6			−0.996062
$947$	18980.1	−	32874.6i	0.651290	−	1.12807i	−0.331520	−	0.943448i	$-0.607562\pi$
$947$	18980.1	−	32874.6i	0.651290	−	1.12807i	0.982810	−	0.184619i	$-0.0591052\pi$
$948$	450.316	+	779.969i	0.0154278	+	0.0267218i
$949$	−27040.8	−	46836.1i	−0.924955	−	1.60207i
$950$	−21225.5	+	36763.7i	−0.724892	+	1.25555i
$951$	11923.6			0.406570
$952$		0			0
$953$	−10019.3			−0.340563			−0.170282	−	0.985395i	$-0.554468\pi$
$953$	−10019.3			−0.340563			−0.170282	+	0.985395i	$0.554468\pi$
$954$	4075.26	−	7058.55i	0.138303	−	0.239548i
$955$	−1785.08	−	3091.85i	−0.0604857	−	0.104764i
$956$	4605.83	+	7977.53i	0.155819	+	0.269887i
$957$	2166.15	−	3751.88i	0.0731679	−	0.126730i
$958$	5059.61			0.170635
$959$		0			0
$960$	−33746.9			−1.13456
$961$	7366.54	−	12759.2i	0.247274	−	0.428291i
$962$	5917.46	+	10249.3i	0.198323	+	0.343505i
$963$	884.074	+	1531.26i	0.0295835	+	0.0512401i
$964$	−4715.56	+	8167.58i	−0.157550	+	0.272884i
$965$	−47527.3			−1.58545
$966$		0			0
$967$	27834.4			0.925641			0.462820	−	0.886452i	$-0.346837\pi$
$967$	27834.4			0.925641			0.462820	+	0.886452i	$0.346837\pi$
$968$	−9304.68	+	16116.2i	−0.308950	+	0.535117i
$969$	−548.909	−	950.738i	−0.0181976	−	0.0315192i
$970$	14487.3	+	25092.7i	0.479545	+	0.830597i
$971$	9137.67	−	15826.9i	0.302000	−	0.523079i	−0.674589	−	0.738193i	$-0.735679\pi$
$971$	9137.67	−	15826.9i	0.302000	−	0.523079i	0.976589	+	0.215115i	$0.0690125\pi$
$972$	527.692			0.0174133
$973$		0			0
$974$	23200.8			0.763245
$975$	35508.6	−	61502.7i	1.16634	−	2.02017i
$976$	78.7386	+	136.379i	0.00258234	+	0.00447274i
$977$	21514.5	+	37264.2i	0.704513	+	1.22025i	0.966867	+	0.255280i	$0.0821677\pi$
$977$	21514.5	+	37264.2i	0.704513	+	1.22025i	−0.262354	+	0.964972i	$0.584499\pi$
$978$	10750.7	−	18620.8i	0.351502	−	0.608820i
$979$	6833.24			0.223076
$980$		0			0
$981$	−2757.09			−0.0897320
$982$	14144.0	−	24498.2i	0.459628	−	0.796099i
$983$	−15279.6	−	26465.1i	−0.495772	−	0.858702i	0.504216	−	0.863577i	$-0.331781\pi$
$983$	−15279.6	−	26465.1i	−0.495772	−	0.858702i	−0.999988	+	0.00487535i	$0.998448\pi$
$984$	11039.8	+	19121.5i	0.357658	+	0.619481i
$985$	26519.6	−	45933.3i	0.857853	−	1.48584i
$986$	−821.253			−0.0265254
$987$		0			0
$988$	−12309.0			−0.396358
$989$	−6417.69	+	11115.8i	−0.206340	+	0.357392i
$990$	−5175.77	−	8964.69i	−0.166158	−	0.287795i
$991$	22473.0	+	38924.3i	0.720360	+	1.24770i	0.960855	+	0.277050i	$0.0893569\pi$
$991$	22473.0	+	38924.3i	0.720360	+	1.24770i	−0.240495	+	0.970650i	$0.577310\pi$
$992$	5845.14	−	10124.1i	0.187080	−	0.324032i
$993$	26738.5			0.854501
$994$		0			0
$995$	−26711.2			−0.851058
$996$	−2023.27	+	3504.40i	−0.0643671	+	0.111487i
$997$	−14503.1	−	25120.0i	−0.460698	−	0.797953i	0.538297	−	0.842755i	$-0.319068\pi$
$997$	−14503.1	−	25120.0i	−0.460698	−	0.797953i	−0.998996	+	0.0448018i	$0.985734\pi$
$998$	11099.6	+	19225.0i	0.352055	+	0.609777i
$999$	−757.590	+	1312.18i	−0.0239931	+	0.0415572i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.4.e.k.79.1		4
3.2	odd	2		441.4.e.v.226.2		4
7.2	even	3		147.4.a.j.1.2	✓	2
7.3	odd	6		147.4.e.j.67.1		4
7.4	even	3	inner	147.4.e.k.67.1		4
7.5	odd	6		147.4.a.k.1.2	yes	2
7.6	odd	2		147.4.e.j.79.1		4
21.2	odd	6		441.4.a.n.1.1		2
21.5	even	6		441.4.a.o.1.1		2
21.11	odd	6		441.4.e.v.361.2		4
21.17	even	6		441.4.e.u.361.2		4
21.20	even	2		441.4.e.u.226.2		4
28.19	even	6		2352.4.a.bl.1.1		2
28.23	odd	6		2352.4.a.cf.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.4.a.j.1.2	✓	2	7.2	even	3
147.4.a.k.1.2	yes	2	7.5	odd	6
147.4.e.j.67.1		4	7.3	odd	6
147.4.e.j.79.1		4	7.6	odd	2
147.4.e.k.67.1		4	7.4	even	3	inner
147.4.e.k.79.1		4	1.1	even	1	trivial
441.4.a.n.1.1		2	21.2	odd	6
441.4.a.o.1.1		2	21.5	even	6
441.4.e.u.226.2		4	21.20	even	2
441.4.e.u.361.2		4	21.17	even	6
441.4.e.v.226.2		4	3.2	odd	2
441.4.e.v.361.2		4	21.11	odd	6
2352.4.a.bl.1.1		2	28.19	even	6
2352.4.a.cf.1.2		2	28.23	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	147.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.20711 + 2.09077i) q^{2} +(1.50000 + 2.59808i) q^{3} +(1.08579 + 1.88064i) q^{4} +(-9.94975 + 17.2335i) q^{5} -7.24264 q^{6} -24.5563 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(-1.20711 + 2.09077i) q^{2} +(1.50000 + 2.59808i) q^{3} +(1.08579 + 1.88064i) q^{4} +(-9.94975 + 17.2335i) q^{5} -7.24264 q^{6} -24.5563 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-24.0208 - 41.6053i) q^{10} +(-11.9706 - 20.7336i) q^{11} +(-3.25736 + 5.64191i) q^{12} +87.3553 q^{13} -59.6985 q^{15} +(20.9558 - 36.2966i) q^{16} +(2.81981 + 4.88405i) q^{17} +(-10.8640 - 18.8169i) q^{18} +(-32.4437 + 56.1941i) q^{19} -43.2132 q^{20} +57.7990 q^{22} +(12.7990 - 22.1685i) q^{23} +(-36.8345 - 63.7993i) q^{24} +(-135.495 - 234.684i) q^{25} +(-105.447 + 182.640i) q^{26} -27.0000 q^{27} +60.3188 q^{29} +(72.0624 - 124.816i) q^{30} +(61.3553 + 106.271i) q^{31} +(-47.6335 - 82.5037i) q^{32} +(35.9117 - 62.2009i) q^{33} -13.6152 q^{34} -19.5442 q^{36} +(28.0589 - 48.5994i) q^{37} +(-78.3259 - 135.664i) q^{38} +(131.033 + 226.956i) q^{39} +(244.329 - 423.191i) q^{40} -299.713 q^{41} -501.421 q^{43} +(25.9949 - 45.0246i) q^{44} +(-89.5477 - 155.101i) q^{45} +(30.8995 + 53.5195i) q^{46} +(-152.777 + 264.617i) q^{47} +125.735 q^{48} +654.227 q^{50} +(-8.45942 + 14.6521i) q^{51} +(94.8492 + 164.284i) q^{52} +(187.558 + 324.861i) q^{53} +(32.5919 - 56.4508i) q^{54} +476.416 q^{55} -194.662 q^{57} +(-72.8112 + 126.113i) q^{58} +(313.806 + 543.528i) q^{59} +(-64.8198 - 112.271i) q^{60} +(-1.87868 + 3.25397i) q^{61} -296.250 q^{62} +565.288 q^{64} +(-869.164 + 1505.44i) q^{65} +(86.6985 + 150.166i) q^{66} +(406.524 + 704.120i) q^{67} +(-6.12341 + 10.6061i) q^{68} +76.7939 q^{69} +165.902 q^{71} +(110.504 - 191.398i) q^{72} +(-309.550 - 536.156i) q^{73} +(67.7401 + 117.329i) q^{74} +(406.485 - 704.052i) q^{75} -140.908 q^{76} -632.683 q^{78} +(69.1228 - 119.724i) q^{79} +(417.011 + 722.284i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(361.785 - 626.631i) q^{82} +621.137 q^{83} -112.225 q^{85} +(605.269 - 1048.36i) q^{86} +(90.4781 + 156.713i) q^{87} +(293.953 + 509.142i) q^{88} +(-142.709 + 247.180i) q^{89} +432.375 q^{90} +55.5879 q^{92} +(-184.066 + 318.812i) q^{93} +(-368.836 - 638.842i) q^{94} +(-645.612 - 1118.23i) q^{95} +(142.901 - 247.511i) q^{96} -603.114 q^{97} +215.470 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 6 q^{3} + 10 q^{4} - 20 q^{5} - 12 q^{6} - 36 q^{8} - 18 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 6 * q^3 + 10 * q^4 - 20 * q^5 - 12 * q^6 - 36 * q^8 - 18 * q^9	\( 4 q - 2 q^{2} + 6 q^{3} + 10 q^{4} - 20 q^{5} - 12 q^{6} - 36 q^{8} - 18 q^{9} - 48 q^{10} + 20 q^{11} - 30 q^{12} + 208 q^{13} - 120 q^{15} - 18 q^{16} - 116 q^{17} - 18 q^{18} - 192 q^{19} - 88 q^{20} + 152 q^{22} - 28 q^{23} - 54 q^{24} - 146 q^{25} - 204 q^{26} - 108 q^{27} + 592 q^{29} + 144 q^{30} + 104 q^{31} - 18 q^{32} - 60 q^{33} - 128 q^{34} - 180 q^{36} + 248 q^{37} - 104 q^{38} + 312 q^{39} + 488 q^{40} + 40 q^{41} - 1440 q^{43} - 292 q^{44} - 180 q^{45} + 84 q^{46} + 96 q^{47} - 108 q^{48} + 1412 q^{50} + 348 q^{51} + 320 q^{52} - 268 q^{53} + 54 q^{54} + 944 q^{55} - 1152 q^{57} - 48 q^{58} + 616 q^{59} - 132 q^{60} - 16 q^{61} - 608 q^{62} + 236 q^{64} - 1740 q^{65} + 228 q^{66} + 144 q^{67} + 940 q^{68} - 168 q^{69} + 1976 q^{71} + 162 q^{72} - 104 q^{73} + 56 q^{74} + 438 q^{75} - 2272 q^{76} - 1224 q^{78} + 944 q^{79} + 828 q^{80} - 162 q^{81} + 856 q^{82} + 2032 q^{83} - 200 q^{85} + 1120 q^{86} + 888 q^{87} + 876 q^{88} + 388 q^{89} + 864 q^{90} - 728 q^{92} - 312 q^{93} - 904 q^{94} - 1304 q^{95} + 54 q^{96} + 976 q^{97} - 360 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 6 * q^3 + 10 * q^4 - 20 * q^5 - 12 * q^6 - 36 * q^8 - 18 * q^9 - 48 * q^10 + 20 * q^11 - 30 * q^12 + 208 * q^13 - 120 * q^15 - 18 * q^16 - 116 * q^17 - 18 * q^18 - 192 * q^19 - 88 * q^20 + 152 * q^22 - 28 * q^23 - 54 * q^24 - 146 * q^25 - 204 * q^26 - 108 * q^27 + 592 * q^29 + 144 * q^30 + 104 * q^31 - 18 * q^32 - 60 * q^33 - 128 * q^34 - 180 * q^36 + 248 * q^37 - 104 * q^38 + 312 * q^39 + 488 * q^40 + 40 * q^41 - 1440 * q^43 - 292 * q^44 - 180 * q^45 + 84 * q^46 + 96 * q^47 - 108 * q^48 + 1412 * q^50 + 348 * q^51 + 320 * q^52 - 268 * q^53 + 54 * q^54 + 944 * q^55 - 1152 * q^57 - 48 * q^58 + 616 * q^59 - 132 * q^60 - 16 * q^61 - 608 * q^62 + 236 * q^64 - 1740 * q^65 + 228 * q^66 + 144 * q^67 + 940 * q^68 - 168 * q^69 + 1976 * q^71 + 162 * q^72 - 104 * q^73 + 56 * q^74 + 438 * q^75 - 2272 * q^76 - 1224 * q^78 + 944 * q^79 + 828 * q^80 - 162 * q^81 + 856 * q^82 + 2032 * q^83 - 200 * q^85 + 1120 * q^86 + 888 * q^87 + 876 * q^88 + 388 * q^89 + 864 * q^90 - 728 * q^92 - 312 * q^93 - 904 * q^94 - 1304 * q^95 + 54 * q^96 + 976 * q^97 - 360 * q^99

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