LMFDB - Embedded newform 950.2.j.i.349.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(49,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("950.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.j (of order $6$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 8 x^{14} - 36 x^{13} + 67 x^{12} + 34 x^{11} - 24 x^{10} + 182 x^{9} - 495 x^{8} + \cdots + 16 $ x^16 - 4x^15 + 8x^14 - 36x^13 + 67x^12 + 34x^11 - 24x^10 + 182x^9 - 495x^8 - 166x^7 + 258x^6 - 1292x^5 + 2920x^4 + 1176x^3 + 200x^2 + 80*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			349.7
Root			$2.85614 + 0.765301i$ of defining polynomial
Character	$\chi$	$=$	950.349
Dual form			950.2.j.i.49.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(1.47519 - 0.851703i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.851703 - 1.47519i) q^{6} -3.74324i q^{7} -1.00000i q^{8} +(-0.0492032 + 0.0852224i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(1.47519 - 0.851703i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.851703 - 1.47519i) q^{6} -3.74324i q^{7} -1.00000i q^{8} +(-0.0492032 + 0.0852224i) q^{9} +3.64483 q^{11} -1.70341i q^{12} +(-5.23065 - 3.01991i) q^{13} +(-1.87162 - 3.24174i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.54932 + 2.04920i) q^{17} +0.0984064i q^{18} +(0.697500 - 4.30273i) q^{19} +(-3.18813 - 5.52200i) q^{21} +(3.15651 - 1.82241i) q^{22} +(4.05703 + 2.34233i) q^{23} +(-0.851703 - 1.47519i) q^{24} -6.03983 q^{26} +5.27785i q^{27} +(-3.24174 - 1.87162i) q^{28} +(-3.32241 + 5.75459i) q^{29} +10.8416 q^{31} +(-0.866025 - 0.500000i) q^{32} +(5.37683 - 3.10431i) q^{33} +(-2.04920 + 3.54932i) q^{34} +(0.0492032 + 0.0852224i) q^{36} -7.75505i q^{37} +(-1.54731 - 4.07502i) q^{38} -10.2883 q^{39} +(3.99653 + 6.92220i) q^{41} +(-5.52200 - 3.18813i) q^{42} +(3.80018 - 2.19403i) q^{43} +(1.82241 - 3.15651i) q^{44} +4.68466 q^{46} +(-1.50969 - 0.871618i) q^{47} +(-1.47519 - 0.851703i) q^{48} -7.01181 q^{49} +(-3.49063 + 6.04594i) q^{51} +(-5.23065 + 3.01991i) q^{52} +(-1.50969 - 0.871618i) q^{53} +(2.63892 + 4.57075i) q^{54} -3.74324 q^{56} +(-2.63570 - 6.94142i) q^{57} +6.64483i q^{58} +(-3.67412 - 6.36376i) q^{59} +(-1.15420 + 1.99914i) q^{61} +(9.38914 - 5.42082i) q^{62} +(0.319008 + 0.184179i) q^{63} -1.00000 q^{64} +(3.10431 - 5.37683i) q^{66} +(5.83981 + 3.37162i) q^{67} +4.09841i q^{68} +7.97988 q^{69} +(0.994093 + 1.72182i) q^{71} +(0.0852224 + 0.0492032i) q^{72} +(7.95867 - 4.59494i) q^{73} +(-3.87752 - 6.71607i) q^{74} +(-3.37752 - 2.75542i) q^{76} -13.6435i q^{77} +(-8.90992 + 5.14414i) q^{78} +(3.07849 + 5.33210i) q^{79} +(4.34755 + 7.53017i) q^{81} +(6.92220 + 3.99653i) q^{82} +5.69159i q^{83} -6.37625 q^{84} +(2.19403 - 3.80018i) q^{86} +11.3188i q^{87} -3.64483i q^{88} +(-5.53983 + 9.59527i) q^{89} +(-11.3043 + 19.5795i) q^{91} +(4.05703 - 2.34233i) q^{92} +(15.9935 - 9.23386i) q^{93} -1.74324 q^{94} -1.70341 q^{96} +(-1.30356 + 0.752610i) q^{97} +(-6.07241 + 3.50591i) q^{98} +(-0.179337 + 0.310621i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 2 q^{6} + 22 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 + 2 * q^6 + 22 * q^9	$ 16 q + 8 q^{4} + 2 q^{6} + 22 q^{9} + 20 q^{11} + 12 q^{14} - 8 q^{16} - 2 q^{21} - 2 q^{24} - 36 q^{26} - 34 q^{29} + 44 q^{31} - 10 q^{34} - 22 q^{36} + 72 q^{39} + 14 q^{41} + 10 q^{44} - 24 q^{46} - 88 q^{49} - 18 q^{51} + 16 q^{54} + 24 q^{56} - 28 q^{59} - 18 q^{61} - 16 q^{64} - 8 q^{66} - 108 q^{69} + 28 q^{71} - 8 q^{74} + 34 q^{79} - 72 q^{81} - 4 q^{84} - 26 q^{86} - 28 q^{89} - 50 q^{91} + 56 q^{94} - 4 q^{96} + 120 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 2 * q^6 + 22 * q^9 + 20 * q^11 + 12 * q^14 - 8 * q^16 - 2 * q^21 - 2 * q^24 - 36 * q^26 - 34 * q^29 + 44 * q^31 - 10 * q^34 - 22 * q^36 + 72 * q^39 + 14 * q^41 + 10 * q^44 - 24 * q^46 - 88 * q^49 - 18 * q^51 + 16 * q^54 + 24 * q^56 - 28 * q^59 - 18 * q^61 - 16 * q^64 - 8 * q^66 - 108 * q^69 + 28 * q^71 - 8 * q^74 + 34 * q^79 - 72 * q^81 - 4 * q^84 - 26 * q^86 - 28 * q^89 - 50 * q^91 + 56 * q^94 - 4 * q^96 + 120 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	1.47519	−	0.851703i	0.851703	−	0.491731i	−0.00952194	−	0.999955i	$-0.503031\pi$
$3$	1.47519	−	0.851703i	0.851703	−	0.491731i	0.861225	+	0.508224i	$0.169698\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	0.851703	−	1.47519i	0.347706	−	0.602245i
$7$		−	3.74324i		−	1.41481i	−0.706808	−	0.707405i	$-0.749866\pi$
$7$		−	3.74324i		−	1.41481i	0.706808	−	0.707405i	$-0.250134\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.0492032	+	0.0852224i	−0.0164011	+	0.0284075i
$10$		0			0
$11$	3.64483			1.09896			0.549479	−	0.835508i	$-0.314826\pi$
$11$	3.64483			1.09896			0.549479	+	0.835508i	$0.314826\pi$
$12$		−	1.70341i		−	0.491731i
$13$	−5.23065	−	3.01991i	−1.45072	−	0.837574i	−0.452198	−	0.891918i	$-0.649360\pi$
$13$	−5.23065	−	3.01991i	−1.45072	−	0.837574i	−0.998522	+	0.0543441i	$0.982693\pi$
$14$	−1.87162	−	3.24174i	−0.500211	−	0.866391i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.54932	+	2.04920i	−0.860838	+	0.497005i	−0.864293	−	0.502989i	$-0.832234\pi$
$17$	−3.54932	+	2.04920i	−0.860838	+	0.497005i	0.00345514	+	0.999994i	$0.498900\pi$
$18$			0.0984064i			0.0231946i
$19$	0.697500	−	4.30273i	0.160017	−	0.987114i
$19$	0.697500	−	4.30273i	0.160017	−	0.987114i
$20$		0			0
$21$	−3.18813	−	5.52200i	−0.695706	−	1.20500i
$22$	3.15651	−	1.82241i	0.672971	−	0.388540i
$23$	4.05703	+	2.34233i	0.845950	+	0.488409i	0.859282	−	0.511502i	$-0.170911\pi$
$23$	4.05703	+	2.34233i	0.845950	+	0.488409i	−0.0133324	+	0.999911i	$0.504244\pi$
$24$	−0.851703	−	1.47519i	−0.173853	−	0.301123i
$25$		0			0
$26$	−6.03983			−1.18451
$27$			5.27785i			1.01572i
$28$	−3.24174	−	1.87162i	−0.612631	−	0.353703i
$29$	−3.32241	+	5.75459i	−0.616957	+	1.06860i	0.373081	+	0.927799i	$0.378301\pi$
$29$	−3.32241	+	5.75459i	−0.616957	+	1.06860i	−0.990038	+	0.140802i	$0.955032\pi$
$30$		0			0
$31$	10.8416			1.94722			0.973608	−	0.228226i	$-0.0732925\pi$
$31$	10.8416			1.94722			0.973608	+	0.228226i	$0.0732925\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	5.37683	−	3.10431i	0.935986	−	0.540392i
$34$	−2.04920	+	3.54932i	−0.351435	+	0.608704i
$35$		0			0
$36$	0.0492032	+	0.0852224i	0.00820053	+	0.0142037i
$37$		−	7.75505i		−	1.27492i	−0.770483	−	0.637461i	$-0.779985\pi$
$37$		−	7.75505i		−	1.27492i	0.770483	−	0.637461i	$-0.220015\pi$
$38$	−1.54731	−	4.07502i	−0.251007	−	0.661056i
$39$	−10.2883			−1.64744
$40$		0			0
$41$	3.99653	+	6.92220i	0.624154	+	1.08107i	0.988704	+	0.149882i	$0.0478894\pi$
$41$	3.99653	+	6.92220i	0.624154	+	1.08107i	−0.364550	+	0.931184i	$0.618777\pi$
$42$	−5.52200	−	3.18813i	−0.852062	−	0.491939i
$43$	3.80018	−	2.19403i	0.579521	−	0.334587i	−0.181422	−	0.983405i	$-0.558070\pi$
$43$	3.80018	−	2.19403i	0.579521	−	0.334587i	0.760943	+	0.648819i	$0.224737\pi$
$44$	1.82241	−	3.15651i	0.274739	−	0.475863i
$45$		0			0
$46$	4.68466			0.690715
$47$	−1.50969	−	0.871618i	−0.220210	−	0.127139i	0.385837	−	0.922567i	$-0.373913\pi$
$47$	−1.50969	−	0.871618i	−0.220210	−	0.127139i	−0.606048	+	0.795428i	$0.707246\pi$
$48$	−1.47519	−	0.851703i	−0.212926	−	0.122933i
$49$	−7.01181			−1.00169
$50$		0			0
$51$	−3.49063	+	6.04594i	−0.488785	+	0.846601i
$52$	−5.23065	+	3.01991i	−0.725360	+	0.418787i
$53$	−1.50969	−	0.871618i	−0.207371	−	0.119726i	0.392718	−	0.919659i	$-0.371535\pi$
$53$	−1.50969	−	0.871618i	−0.207371	−	0.119726i	−0.600089	+	0.799933i	$0.704868\pi$
$54$	2.63892	+	4.57075i	0.359112	+	0.622000i
$55$		0			0
$56$	−3.74324			−0.500211
$57$	−2.63570	−	6.94142i	−0.349107	−	0.919414i
$58$			6.64483i			0.872509i
$59$	−3.67412	−	6.36376i	−0.478329	−	0.828491i	0.521362	−	0.853336i	$-0.325424\pi$
$59$	−3.67412	−	6.36376i	−0.478329	−	0.828491i	−0.999691	+	0.0248448i	$0.992091\pi$
$60$		0			0
$61$	−1.15420	+	1.99914i	−0.147781	+	0.255963i	−0.930407	−	0.366528i	$-0.880546\pi$
$61$	−1.15420	+	1.99914i	−0.147781	+	0.255963i	0.782626	+	0.622492i	$0.213880\pi$
$62$	9.38914	−	5.42082i	1.19242	−	0.688445i
$63$	0.319008	+	0.184179i	0.0401912	+	0.0232044i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	3.10431	−	5.37683i	0.382115	−	0.661842i
$67$	5.83981	+	3.37162i	0.713447	+	0.411909i	0.812336	−	0.583190i	$-0.198196\pi$
$67$	5.83981	+	3.37162i	0.713447	+	0.411909i	−0.0988892	+	0.995098i	$0.531529\pi$
$68$			4.09841i			0.497005i
$69$	7.97988			0.960664
$70$		0			0
$71$	0.994093	+	1.72182i	0.117977	+	0.204342i	0.918966	−	0.394337i	$-0.129026\pi$
$71$	0.994093	+	1.72182i	0.117977	+	0.204342i	−0.800989	+	0.598679i	$0.795692\pi$
$72$	0.0852224	+	0.0492032i	0.0100436	+	0.00579865i
$73$	7.95867	−	4.59494i	0.931492	−	0.537797i	0.0442086	−	0.999022i	$-0.485923\pi$
$73$	7.95867	−	4.59494i	0.931492	−	0.537797i	0.887283	+	0.461225i	$0.152590\pi$
$74$	−3.87752	−	6.71607i	−0.450753	−	0.780727i
$75$		0			0
$76$	−3.37752	−	2.75542i	−0.387429	−	0.316068i
$77$		−	13.6435i		−	1.55482i
$78$	−8.90992	+	5.14414i	−1.00885	+	0.582459i
$79$	3.07849	+	5.33210i	0.346357	+	0.599909i	0.985599	−	0.169097i	$-0.0540851\pi$
$79$	3.07849	+	5.33210i	0.346357	+	0.599909i	−0.639242	+	0.769006i	$0.720752\pi$
$80$		0			0
$81$	4.34755	+	7.53017i	0.483061	+	0.836686i
$82$	6.92220	+	3.99653i	0.764429	+	0.441343i
$83$			5.69159i			0.624734i	0.949962	+	0.312367i	$0.101122\pi$
$83$			5.69159i			0.624734i	−0.949962	+	0.312367i	$0.898878\pi$
$84$	−6.37625			−0.695706
$85$		0			0
$86$	2.19403	−	3.80018i	0.236589	−	0.409783i
$87$			11.3188i			1.21351i
$88$		−	3.64483i		−	0.388540i
$89$	−5.53983	+	9.59527i	−0.587221	+	1.01710i	0.407374	+	0.913261i	$0.366445\pi$
$89$	−5.53983	+	9.59527i	−0.587221	+	1.01710i	−0.994595	+	0.103835i	$0.966889\pi$
$90$		0			0
$91$	−11.3043	+	19.5795i	−1.18501	+	2.05249i
$92$	4.05703	−	2.34233i	0.422975	−	0.244205i
$93$	15.9935	−	9.23386i	1.65845	−	0.957507i
$94$	−1.74324			−0.179801
$95$		0			0
$96$	−1.70341			−0.173853
$97$	−1.30356	+	0.752610i	−0.132356	+	0.0764159i	−0.564716	−	0.825285i	$-0.691014\pi$
$97$	−1.30356	+	0.752610i	−0.132356	+	0.0764159i	0.432360	+	0.901701i	$0.357681\pi$
$98$	−6.07241	+	3.50591i	−0.613406	+	0.354150i
$99$	−0.179337	+	0.310621i	−0.0180241	+	0.0312186i
$100$		0			0
$101$	3.91735	−	6.78506i	0.389791	−	0.675138i	−0.602630	−	0.798021i	$-0.705880\pi$
$101$	3.91735	−	6.78506i	0.389791	−	0.675138i	0.992421	+	0.122883i	$0.0392138\pi$
$102$			6.98125i			0.691247i
$103$		−	13.6036i		−	1.34041i	−0.742178	−	0.670203i	$-0.766207\pi$
$103$		−	13.6036i		−	1.34041i	0.742178	−	0.670203i	$-0.233793\pi$
$104$	−3.01991	+	5.23065i	−0.296127	+	0.512907i
$105$		0			0
$106$	−1.74324			−0.169318
$107$			7.24845i			0.700735i	0.936612	+	0.350367i	$0.113943\pi$
$107$			7.24845i			0.700735i	−0.936612	+	0.350367i	$0.886057\pi$
$108$	4.57075	+	2.63892i	0.439820	+	0.253930i
$109$	2.24392	+	3.88659i	0.214929	+	0.372268i	0.953251	−	0.302181i	$-0.0977147\pi$
$109$	2.24392	+	3.88659i	0.214929	+	0.372268i	−0.738322	+	0.674449i	$0.764381\pi$
$110$		0			0
$111$	−6.60500	−	11.4402i	−0.626919	−	1.08586i
$112$	−3.24174	+	1.87162i	−0.306315	+	0.176851i
$113$			13.2813i			1.24940i	0.780863	+	0.624702i	$0.214780\pi$
$113$			13.2813i			1.24940i	−0.780863	+	0.624702i	$0.785220\pi$
$114$	−5.75330	−	4.69360i	−0.538846	−	0.439596i
$115$		0			0
$116$	3.32241	+	5.75459i	0.308478	+	0.534300i
$117$	0.514729	−	0.297179i	0.0475867	−	0.0274742i
$118$	−6.36376	−	3.67412i	−0.585831	−	0.338230i
$119$	7.67065	+	13.2860i	0.703167	+	1.21792i
$120$		0			0
$121$	2.28478			0.207707
$122$			2.30841i			0.208993i
$123$	11.7913	+	6.80772i	1.06319	+	0.613831i
$124$	5.42082	−	9.38914i	0.486804	−	0.843169i
$125$		0			0
$126$	0.368358			0.0328160
$127$	−2.98488	−	1.72332i	−0.264865	−	0.152920i	0.361687	−	0.932300i	$-0.382201\pi$
$127$	−2.98488	−	1.72332i	−0.264865	−	0.152920i	−0.626552	+	0.779380i	$0.715534\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	3.73733	−	6.47324i	0.329053	−	0.569937i
$130$		0			0
$131$	−8.26315	−	14.3122i	−0.721955	−	1.25046i	−0.960215	−	0.279261i	$-0.909911\pi$
$131$	−8.26315	−	14.3122i	−0.721955	−	1.25046i	0.238260	−	0.971201i	$-0.423423\pi$
$132$		−	6.20863i		−	0.540392i
$133$	−16.1061	−	2.61091i	−1.39658	−	0.226394i
$134$	6.74324			0.582527
$135$		0			0
$136$	2.04920	+	3.54932i	0.175718	+	0.304352i
$137$	19.3227	+	11.1560i	1.65085	+	0.953118i	0.976724	+	0.214499i	$0.0688120\pi$
$137$	19.3227	+	11.1560i	1.65085	+	0.953118i	0.674124	+	0.738618i	$0.264521\pi$
$138$	6.91078	−	3.98994i	0.588284	−	0.339646i
$139$	−0.880992	+	1.52592i	−0.0747248	+	0.129427i	−0.900967	−	0.433889i	$-0.857141\pi$
$139$	−0.880992	+	1.52592i	−0.0747248	+	0.129427i	0.826242	+	0.563316i	$0.190474\pi$
$140$		0			0
$141$	−2.96944			−0.250072
$142$	1.72182	+	0.994093i	0.144492	+	0.0834225i
$143$	−19.0648	−	11.0071i	−1.59428	−	0.920458i
$144$	0.0984064			0.00820053
$145$		0			0
$146$	4.59494	−	7.95867i	0.380280	−	0.658664i
$147$	−10.3438	+	5.97198i	−0.853141	+	0.492561i
$148$	−6.71607	−	3.87752i	−0.552057	−	0.318731i
$149$	−1.80713	−	3.13005i	−0.148046	−	0.256424i	0.782459	−	0.622702i	$-0.213965\pi$
$149$	−1.80713	−	3.13005i	−0.148046	−	0.256424i	−0.930505	+	0.366278i	$0.880632\pi$
$150$		0			0
$151$	−18.1711			−1.47875			−0.739373	−	0.673296i	$-0.764878\pi$
$151$	−18.1711			−1.47875			−0.739373	+	0.673296i	$0.764878\pi$
$152$	−4.30273	−	0.697500i	−0.348998	−	0.0565747i
$153$		−	0.403309i		−	0.0326056i
$154$	−6.82173	−	11.8156i	−0.549710	−	0.952126i
$155$		0			0
$156$	−5.14414	+	8.90992i	−0.411861	+	0.713364i
$157$	−6.74033	+	3.89153i	−0.537937	+	0.310578i	−0.744242	−	0.667910i	$-0.767189\pi$
$157$	−6.74033	+	3.89153i	−0.537937	+	0.310578i	0.206305	+	0.978488i	$0.433856\pi$
$158$	5.33210	+	3.07849i	0.424199	+	0.244912i
$159$	−2.96944			−0.235492
$160$		0			0
$161$	8.76789	−	15.1864i	0.691007	−	1.19686i
$162$	7.53017	+	4.34755i	0.591626	+	0.341576i
$163$		−	5.46539i		−	0.428082i	−0.976825	−	0.214041i	$-0.931337\pi$
$163$		−	5.46539i		−	0.428082i	0.976825	−	0.214041i	$-0.0686627\pi$
$164$	7.99307			0.624154
$165$		0			0
$166$	2.84580	+	4.92906i	0.220877	+	0.382570i
$167$	15.9348	+	9.19994i	1.23307	+	0.711913i	0.967668	−	0.252226i	$-0.0811625\pi$
$167$	15.9348	+	9.19994i	1.23307	+	0.711913i	0.265400	+	0.964138i	$0.414496\pi$
$168$	−5.52200	+	3.18813i	−0.426031	+	0.245969i
$169$	11.7398	+	20.3339i	0.903059	+	1.56414i
$170$		0			0
$171$	0.332370	+	0.271151i	0.0254170	+	0.0207354i
$172$		−	4.38806i		−	0.334587i
$173$	−16.8860	+	9.74914i	−1.28382	+	0.741214i	−0.977544	−	0.210729i	$-0.932416\pi$
$173$	−16.8860	+	9.74914i	−1.28382	+	0.741214i	−0.306275	+	0.951943i	$0.599083\pi$
$174$	5.65942	+	9.80241i	0.429040	+	0.743119i
$175$		0			0
$176$	−1.82241	−	3.15651i	−0.137370	−	0.237931i
$177$	−10.8401	−	6.25852i	−0.814789	−	0.470419i
$178$			11.0797i			0.830456i
$179$	23.5661			1.76142			0.880708	−	0.473660i	$-0.157068\pi$
$179$	23.5661			1.76142			0.880708	+	0.473660i	$0.157068\pi$
$180$		0			0
$181$	−7.86746	+	13.6268i	−0.584784	+	1.01288i	0.410118	+	0.912032i	$0.365487\pi$
$181$	−7.86746	+	13.6268i	−0.584784	+	1.01288i	−0.994902	+	0.100843i	$0.967846\pi$
$182$			22.6085i			1.67585i
$183$			3.93215i			0.290673i
$184$	2.34233	−	4.05703i	0.172679	−	0.299088i
$185$		0			0
$186$	9.23386	−	15.9935i	0.677060	−	1.17270i
$187$	−12.9367	+	7.46900i	−0.946024	+	0.546187i
$188$	−1.50969	+	0.871618i	−0.110105	+	0.0635693i
$189$	19.7562			1.43705
$190$		0			0
$191$	6.64483			0.480803			0.240401	−	0.970674i	$-0.422721\pi$
$191$	6.64483			0.480803			0.240401	+	0.970674i	$0.422721\pi$
$192$	−1.47519	+	0.851703i	−0.106463	+	0.0614664i
$193$	−6.92701	+	3.99931i	−0.498617	+	0.287877i	−0.728142	−	0.685426i	$-0.759616\pi$
$193$	−6.92701	+	3.99931i	−0.498617	+	0.287877i	0.229525	+	0.973303i	$0.426283\pi$
$194$	−0.752610	+	1.30356i	−0.0540342	+	0.0935900i
$195$		0			0
$196$	−3.50591	+	6.07241i	−0.250422	+	0.433743i
$197$			0.481593i			0.0343121i	0.999853	+	0.0171560i	$0.00546121\pi$
$197$			0.481593i			0.0343121i	−0.999853	+	0.0171560i	$0.994539\pi$
$198$			0.358674i			0.0254899i
$199$	11.6793	−	20.2292i	0.827926	−	1.43401i	−0.0717359	−	0.997424i	$-0.522854\pi$
$199$	11.6793	−	20.2292i	0.827926	−	1.43401i	0.899662	−	0.436587i	$-0.143813\pi$
$200$		0			0
$201$	11.4865			0.810193
$202$		−	7.83471i		−	0.551248i
$203$	21.5408	+	12.4366i	1.51187	+	0.872877i
$204$	3.49063	+	6.04594i	0.244393	+	0.423301i
$205$		0			0
$206$	−6.80181	−	11.7811i	−0.473905	−	0.820827i
$207$	−0.399238	+	0.230500i	−0.0277490	+	0.0160209i
$208$			6.03983i			0.418787i
$209$	2.54227	−	15.6827i	0.175852	−	1.08480i
$210$		0			0
$211$	2.91491	+	5.04878i	0.200671	+	0.347572i	0.948745	−	0.316043i	$-0.102354\pi$
$211$	2.91491	+	5.04878i	0.200671	+	0.347572i	−0.748074	+	0.663616i	$0.769021\pi$
$212$	−1.50969	+	0.871618i	−0.103686	+	0.0598630i
$213$	2.93296	+	1.69335i	0.200963	+	0.116026i
$214$	3.62423	+	6.27735i	0.247747	+	0.429111i
$215$		0			0
$216$	5.27785			0.359112
$217$		−	40.5828i		−	2.75494i
$218$	3.88659	+	2.24392i	0.263233	+	0.151978i
$219$	7.82705	−	13.5568i	0.528903	−	0.916087i
$220$		0			0
$221$	24.7537			1.66511
$222$	−11.4402	−	6.60500i	−0.767816	−	0.443299i
$223$	14.4838	−	8.36224i	0.969909	−	0.559977i	0.0707005	−	0.997498i	$-0.477477\pi$
$223$	14.4838	−	8.36224i	0.969909	−	0.559977i	0.899209	+	0.437520i	$0.144143\pi$
$224$	−1.87162	+	3.24174i	−0.125053	+	0.216598i
$225$		0			0
$226$	6.64067	+	11.5020i	0.441731	+	0.765101i
$227$		−	4.16186i		−	0.276232i	−0.990416	−	0.138116i	$-0.955895\pi$
$227$		−	4.16186i		−	0.276232i	0.990416	−	0.138116i	$-0.0441048\pi$
$228$	−7.32930	−	1.18813i	−0.485395	−	0.0786856i
$229$	5.49828			0.363337			0.181668	−	0.983360i	$-0.441850\pi$
$229$	5.49828			0.363337			0.181668	+	0.983360i	$0.441850\pi$
$230$		0			0
$231$	−11.6202	−	20.1267i	−0.764551	−	1.32424i
$232$	5.75459	+	3.32241i	0.377807	+	0.218127i
$233$	−11.4270	+	6.59738i	−0.748607	+	0.432209i	−0.825190	−	0.564855i	$-0.808932\pi$
$233$	−11.4270	+	6.59738i	−0.748607	+	0.432209i	0.0765832	+	0.997063i	$0.475599\pi$
$234$	0.297179	−	0.514729i	0.0194272	−	0.0336489i
$235$		0			0
$236$	−7.34824			−0.478329
$237$	9.08274	+	5.24392i	0.589987	+	0.340629i
$238$	13.2860	+	7.67065i	0.861201	+	0.497214i
$239$	−8.47720			−0.548345			−0.274172	−	0.961681i	$-0.588404\pi$
$239$	−8.47720			−0.548345			−0.274172	+	0.961681i	$0.588404\pi$
$240$		0			0
$241$	−10.5146	+	18.2118i	−0.677304	+	1.17313i	0.298485	+	0.954414i	$0.403519\pi$
$241$	−10.5146	+	18.2118i	−0.677304	+	1.17313i	−0.975790	+	0.218711i	$0.929815\pi$
$242$	1.97868	−	1.14239i	0.127194	−	0.0734356i
$243$	−0.885296	−	0.511126i	−0.0567918	−	0.0327887i
$244$	1.15420	+	1.99914i	0.0738903	+	0.127982i
$245$		0			0
$246$	13.6154			0.868089
$247$	−16.6423	+	20.3997i	−1.05892	+	1.29800i
$248$		−	10.8416i		−	0.688445i
$249$	4.84755	+	8.39620i	0.307201	+	0.532088i
$250$		0			0
$251$	−13.6183	+	23.5876i	−0.859581	+	1.48884i	0.0127485	+	0.999919i	$0.495942\pi$
$251$	−13.6183	+	23.5876i	−0.859581	+	1.48884i	−0.872329	+	0.488919i	$0.837391\pi$
$252$	0.319008	−	0.184179i	0.0200956	−	0.0116022i
$253$	14.7872	+	8.53739i	0.929663	+	0.536741i
$254$	−3.44664			−0.216262
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−14.4229	−	8.32705i	−0.899674	−	0.519427i	−0.0225796	−	0.999745i	$-0.507188\pi$
$257$	−14.4229	−	8.32705i	−0.899674	−	0.519427i	−0.877094	+	0.480318i	$0.840521\pi$
$258$		−	7.47466i		−	0.465352i
$259$	−29.0290			−1.80377
$260$		0			0
$261$	−0.326947	−	0.566288i	−0.0202375	−	0.0350524i
$262$	−14.3122	−	8.26315i	−0.884210	−	0.510499i
$263$	1.72182	−	0.994093i	0.106172	−	0.0612984i	−0.445974	−	0.895046i	$-0.647143\pi$
$263$	1.72182	−	0.994093i	0.106172	−	0.0612984i	0.552146	+	0.833748i	$0.313809\pi$
$264$	−3.10431	−	5.37683i	−0.191057	−	0.330921i
$265$		0			0
$266$	−15.2538	+	5.79196i	−0.935269	+	0.355128i
$267$			18.8732i			1.15502i
$268$	5.83981	−	3.37162i	0.356723	−	0.205954i
$269$	3.57224	+	6.18731i	0.217804	+	0.377247i	0.954136	−	0.299373i	$-0.0967775\pi$
$269$	3.57224	+	6.18731i	0.217804	+	0.377247i	−0.736333	+	0.676620i	$0.763444\pi$
$270$		0			0
$271$	−5.47940	−	9.49060i	−0.332850	−	0.576513i	0.650220	−	0.759746i	$-0.274677\pi$
$271$	−5.47940	−	9.49060i	−0.332850	−	0.576513i	−0.983069	+	0.183234i	$0.941344\pi$
$272$	3.54932	+	2.04920i	0.215209	+	0.124251i
$273$			38.5115i			2.33082i
$274$	22.3119			1.34791
$275$		0			0
$276$	3.98994	−	6.91078i	0.240166	−	0.415980i
$277$			12.2686i			0.737147i	0.929599	+	0.368574i	$0.120154\pi$
$277$			12.2686i			0.737147i	−0.929599	+	0.368574i	$0.879846\pi$
$278$			1.76198i			0.105677i
$279$	−0.533443	+	0.923951i	−0.0319364	+	0.0553155i
$280$		0			0
$281$	8.53983	−	14.7914i	0.509443	−	0.882382i	−0.490497	−	0.871443i	$-0.663185\pi$
$281$	8.53983	−	14.7914i	0.509443	−	0.882382i	0.999940	−	0.0109390i	$-0.00348205\pi$
$282$	−2.57161	+	1.48472i	−0.153137	+	0.0884138i
$283$	−25.9918	+	15.0064i	−1.54505	+	0.892037i	−0.546546	+	0.837429i	$0.684057\pi$
$283$	−25.9918	+	15.0064i	−1.54505	+	0.892037i	−0.998508	+	0.0546077i	$0.982609\pi$
$284$	1.98819			0.117977
$285$		0			0
$286$	−22.0141			−1.30172
$287$	25.9114	−	14.9600i	1.52950	−	0.883059i
$288$	0.0852224	−	0.0492032i	0.00502178	−	0.00289933i
$289$	−0.101533	+	0.175860i	−0.00597251	+	0.0103447i
$290$		0			0
$291$	−1.28200	+	2.22049i	−0.0751522	+	0.130167i
$292$		−	9.18988i		−	0.537797i
$293$		−	22.4677i		−	1.31258i	−0.754509	−	0.656289i	$-0.772125\pi$
$293$		−	22.4677i		−	1.31258i	0.754509	−	0.656289i	$-0.227875\pi$
$294$	−5.97198	+	10.3438i	−0.348293	+	0.603261i
$295$		0			0
$296$	−7.75505			−0.450753
$297$			19.2368i			1.11624i
$298$	−3.13005	−	1.80713i	−0.181319	−	0.104684i
$299$	−14.1473	−	24.5038i	−0.818158	−	1.41709i
$300$		0			0
$301$	−8.21278	−	14.2250i	−0.473377	−	0.819913i
$302$	−15.7367	+	9.08556i	−0.905543	+	0.522816i
$303$		−	13.3457i		−	0.766690i
$304$	−4.07502	+	1.54731i	−0.233719	+	0.0887445i
$305$		0			0
$306$	−0.201655	−	0.349276i	−0.0115278	−	0.0199668i
$307$	14.1955	−	8.19578i	0.810181	−	0.467758i	−0.0368378	−	0.999321i	$-0.511729\pi$
$307$	14.1955	−	8.19578i	0.810181	−	0.467758i	0.847019	+	0.531563i	$0.178395\pi$
$308$	−11.8156	−	6.82173i	−0.673255	−	0.388704i
$309$	−11.5863	−	20.0680i	−0.659119	−	1.14163i
$310$		0			0
$311$	−18.0197			−1.02180			−0.510902	−	0.859639i	$-0.670688\pi$
$311$	−18.0197			−1.02180			−0.510902	+	0.859639i	$0.670688\pi$
$312$			10.2883i			0.582459i
$313$	15.5975	+	9.00522i	0.881623	+	0.509005i	0.871193	−	0.490941i	$-0.163347\pi$
$313$	15.5975	+	9.00522i	0.881623	+	0.509005i	0.0104296	+	0.999946i	$0.496680\pi$
$314$	−3.89153	+	6.74033i	−0.219612	+	0.380379i
$315$		0			0
$316$	6.15698			0.346357
$317$	−20.1398	−	11.6277i	−1.13116	−	0.653076i	−0.186935	−	0.982372i	$-0.559855\pi$
$317$	−20.1398	−	11.6277i	−1.13116	−	0.653076i	−0.944227	+	0.329296i	$0.893189\pi$
$318$	−2.57161	+	1.48472i	−0.144209	+	0.0832589i
$319$	−12.1096	+	20.9745i	−0.678009	+	1.17435i
$320$		0			0
$321$	6.17353	+	10.6929i	0.344573	+	0.596818i
$322$		−	17.5358i		−	0.977231i
$323$	6.34152	+	16.7011i	0.352851	+	0.929274i
$324$	8.69510			0.483061
$325$		0			0
$326$	−2.73270	−	4.73317i	−0.151350	−	0.262146i
$327$	6.62044	+	3.82231i	0.366111	+	0.211374i
$328$	6.92220	−	3.99653i	0.382214	−	0.220672i
$329$	−3.26267	+	5.65111i	−0.179877	+	0.311556i
$330$		0			0
$331$	7.38319			0.405817			0.202908	−	0.979198i	$-0.434961\pi$
$331$	7.38319			0.405817			0.202908	+	0.979198i	$0.434961\pi$
$332$	4.92906	+	2.84580i	0.270518	+	0.156183i
$333$	0.660904	+	0.381573i	0.0362173	+	0.0209101i
$334$	18.3999			1.00680
$335$		0			0
$336$	−3.18813	+	5.52200i	−0.173927	+	0.301250i
$337$	−26.7429	+	15.4400i	−1.45678	+	0.841073i	−0.998851	−	0.0479153i	$-0.984742\pi$
$337$	−26.7429	+	15.4400i	−1.45678	+	0.841073i	−0.457930	+	0.888988i	$0.651409\pi$
$338$	20.3339	+	11.7398i	1.10602	+	0.638559i
$339$	11.3118	+	19.5926i	0.614371	+	1.06412i
$340$		0			0
$341$	39.5159			2.13991
$342$	0.423416	+	0.0686384i	0.0228957	+	0.00371154i
$343$			0.0442191i			0.00238761i
$344$	−2.19403	−	3.80018i	−0.118294	−	0.204892i
$345$		0			0
$346$	−9.74914	+	16.8860i	−0.524117	+	0.907797i
$347$	−7.89771	+	4.55974i	−0.423971	+	0.244780i	−0.696775	−	0.717290i	$-0.745382\pi$
$347$	−7.89771	+	4.55974i	−0.423971	+	0.244780i	0.272804	+	0.962070i	$0.412049\pi$
$348$	9.80241	+	5.65942i	0.525464	+	0.303377i
$349$	14.2508			0.762827			0.381414	−	0.924404i	$-0.375437\pi$
$349$	14.2508			0.762827			0.381414	+	0.924404i	$0.375437\pi$
$350$		0			0
$351$	15.9386	−	27.6065i	0.850742	−	1.47353i
$352$	−3.15651	−	1.82241i	−0.168243	−	0.0971350i
$353$		−	7.77613i		−	0.413882i	−0.978353	−	0.206941i	$-0.933649\pi$
$353$		−	7.77613i		−	0.413882i	0.978353	−	0.206941i	$-0.0663508\pi$
$354$	−12.5170			−0.665273
$355$		0			0
$356$	5.53983	+	9.59527i	0.293610	+	0.508548i
$357$	22.6314	+	13.0662i	1.19778	+	0.691539i
$358$	20.4089	−	11.7831i	1.07864	−	0.622754i
$359$	2.90437	+	5.03052i	0.153287	+	0.265501i	0.932434	−	0.361340i	$-0.117681\pi$
$359$	2.90437	+	5.03052i	0.153287	+	0.265501i	−0.779147	+	0.626841i	$0.784347\pi$
$360$		0			0
$361$	−18.0270	−	6.00231i	−0.948789	−	0.315911i
$362$			15.7349i			0.827009i
$363$	3.37049	−	1.94595i	0.176905	−	0.102136i
$364$	11.3043	+	19.5795i	0.592504	+	1.02625i
$365$		0			0
$366$	1.96608	+	3.40535i	0.102769	+	0.178000i
$367$	−19.2974	−	11.1414i	−1.00732	−	0.581574i	−0.0969115	−	0.995293i	$-0.530896\pi$
$367$	−19.2974	−	11.1414i	−1.00732	−	0.581574i	−0.910405	+	0.413719i	$0.864230\pi$
$368$		−	4.68466i		−	0.244205i
$369$	−0.786568			−0.0409471
$370$		0			0
$371$	−3.26267	+	5.65111i	−0.169389	+	0.293391i
$372$		−	18.4677i		−	0.957507i
$373$			17.0609i			0.883380i	0.897168	+	0.441690i	$0.145621\pi$
$373$			17.0609i			0.883380i	−0.897168	+	0.441690i	$0.854379\pi$
$374$	−7.46900	+	12.9367i	−0.386213	+	0.668940i
$375$		0			0
$376$	−0.871618	+	1.50969i	−0.0449503	+	0.0778561i
$377$	34.7567	−	20.0668i	1.79006	−	1.03349i
$378$	17.1094	−	9.87811i	0.880012	−	0.508075i
$379$	10.0329			0.515355			0.257678	−	0.966231i	$-0.417043\pi$
$379$	10.0329			0.515355			0.257678	+	0.966231i	$0.417043\pi$
$380$		0			0
$381$	−5.87103			−0.300782
$382$	5.75459	−	3.32241i	0.294430	−	0.169990i
$383$	1.72182	−	0.994093i	0.0879809	−	0.0507958i	−0.455364	−	0.890305i	$-0.650491\pi$
$383$	1.72182	−	0.994093i	0.0879809	−	0.0507958i	0.543345	+	0.839510i	$0.317158\pi$
$384$	−0.851703	+	1.47519i	−0.0434633	+	0.0752806i
$385$		0			0
$386$	−3.99931	+	6.92701i	−0.203560	+	0.352576i
$387$			0.431814i			0.0219503i
$388$			1.50522i			0.0764159i
$389$	4.43854	−	7.68778i	0.225043	−	0.389786i	−0.731289	−	0.682067i	$-0.761081\pi$
$389$	4.43854	−	7.68778i	0.225043	−	0.389786i	0.956332	+	0.292282i	$0.0944144\pi$
$390$		0			0
$391$	−19.1996			−0.970967
$392$			7.01181i			0.354150i
$393$	−24.3795	−	14.0755i	−1.22978	−	0.710015i
$394$	0.240797	+	0.417072i	0.0121312	+	0.0210118i
$395$		0			0
$396$	0.179337	+	0.310621i	0.00901203	+	0.0156093i
$397$	18.2840	−	10.5563i	0.917648	−	0.529804i	0.0347640	−	0.999396i	$-0.488932\pi$
$397$	18.2840	−	10.5563i	0.917648	−	0.529804i	0.882884	+	0.469591i	$0.155599\pi$
$398$		−	23.3587i		−	1.17086i
$399$	−25.9834	+	9.86606i	−1.30080	+	0.493921i
$400$		0			0
$401$	−14.9806	−	25.9471i	−0.748094	−	1.29574i	−0.948735	−	0.316072i	$-0.897636\pi$
$401$	−14.9806	−	25.9471i	−0.748094	−	1.29574i	0.200642	−	0.979665i	$-0.435697\pi$
$402$	9.94758	−	5.74324i	0.496140	−	0.286447i
$403$	−56.7088	−	32.7408i	−2.82487	−	1.63094i
$404$	−3.91735	−	6.78506i	−0.194896	−	0.337569i
$405$		0			0
$406$	24.8732			1.23443
$407$		−	28.2658i		−	1.40109i
$408$	6.04594	+	3.49063i	0.299319	+	0.172812i
$409$	−2.09772	+	3.63336i	−0.103726	+	0.179658i	−0.913217	−	0.407474i	$-0.866410\pi$
$409$	−2.09772	+	3.63336i	−0.103726	+	0.179658i	0.809491	+	0.587132i	$0.199743\pi$
$410$		0			0
$411$	38.0063			1.87471
$412$	−11.7811	−	6.80181i	−0.580412	−	0.335101i
$413$	−23.8210	+	13.7531i	−1.17216	+	0.676745i
$414$	−0.230500	+	0.399238i	−0.0113285	+	0.0196215i
$415$		0			0
$416$	3.01991	+	5.23065i	0.148063	+	0.256453i
$417$			3.00137i			0.146978i
$418$	−5.63969	−	14.8528i	−0.275846	−	0.726473i
$419$	−12.5326			−0.612255			−0.306128	−	0.951990i	$-0.599033\pi$
$419$	−12.5326			−0.612255			−0.306128	+	0.951990i	$0.599033\pi$
$420$		0			0
$421$	13.2883	+	23.0160i	0.647631	+	1.12173i	0.983687	+	0.179888i	$0.0575736\pi$
$421$	13.2883	+	23.0160i	0.647631	+	1.12173i	−0.336056	+	0.941842i	$0.609093\pi$
$422$	5.04878	+	2.91491i	0.245771	+	0.141896i
$423$	0.148563	−	0.0857727i	0.00722337	−	0.00417041i
$424$	−0.871618	+	1.50969i	−0.0423295	+	0.0733169i
$425$		0			0
$426$	3.38669			0.164086
$427$	7.48325	+	4.32045i	0.362140	+	0.209081i
$428$	6.27735	+	3.62423i	0.303427	+	0.175184i
$429$	−37.4990			−1.81047
$430$		0			0
$431$	0.0903049	−	0.156413i	0.00434983	−	0.00753413i	−0.863842	−	0.503762i	$-0.831949\pi$
$431$	0.0903049	−	0.156413i	0.00434983	−	0.00753413i	0.868192	+	0.496228i	$0.165282\pi$
$432$	4.57075	−	2.63892i	0.219910	−	0.126965i
$433$	10.4013	+	6.00522i	0.499857	+	0.288592i	0.728654	−	0.684882i	$-0.240146\pi$
$433$	10.4013	+	6.00522i	0.499857	+	0.288592i	−0.228798	+	0.973474i	$0.573479\pi$
$434$	−20.2914	−	35.1458i	−0.974019	−	1.68705i
$435$		0			0
$436$	4.48785			0.214929
$437$	12.9082	−	15.8225i	0.617483	−	0.756895i
$438$		−	15.6541i		−	0.747982i
$439$	−14.2544	−	24.6893i	−0.680324	−	1.17835i	−0.974882	−	0.222722i	$-0.928506\pi$
$439$	−14.2544	−	24.6893i	−0.680324	−	1.17835i	0.294559	−	0.955633i	$-0.404827\pi$
$440$		0			0
$441$	0.345004	−	0.597564i	0.0164287	−	0.0284554i
$442$	21.4373	−	12.3768i	1.01967	−	0.588706i
$443$	−7.40142	−	4.27321i	−0.351652	−	0.203026i	0.313761	−	0.949502i	$-0.398411\pi$
$443$	−7.40142	−	4.27321i	−0.351652	−	0.203026i	−0.665413	+	0.746476i	$0.731744\pi$
$444$	−13.2100			−0.626919
$445$		0			0
$446$	8.36224	−	14.4838i	0.395964	−	0.685829i
$447$	−5.33174	−	3.07828i	−0.252183	−	0.145598i
$448$			3.74324i			0.176851i
$449$	4.24612			0.200387			0.100193	−	0.994968i	$-0.468054\pi$
$449$	4.24612			0.200387			0.100193	+	0.994968i	$0.468054\pi$
$450$		0			0
$451$	14.5667	+	25.2302i	0.685918	+	1.18805i
$452$	11.5020	+	6.64067i	0.541008	+	0.312351i
$453$	−26.8059	+	15.4764i	−1.25945	+	0.727145i
$454$	−2.08093	−	3.60428i	−0.0976629	−	0.169157i
$455$		0			0
$456$	−6.94142	+	2.63570i	−0.325062	+	0.123428i
$457$		−	18.2204i		−	0.852316i	−0.904649	−	0.426158i	$-0.859867\pi$
$457$		−	18.2204i		−	0.852316i	0.904649	−	0.426158i	$-0.140133\pi$
$458$	4.76165	−	2.74914i	0.222497	−	0.128459i
$459$	−10.8154	−	18.7328i	−0.504819	−	0.874371i
$460$		0			0
$461$	−15.0140	−	26.0050i	−0.699272	−	1.21117i	−0.968719	−	0.248160i	$-0.920174\pi$
$461$	−15.0140	−	26.0050i	−0.699272	−	1.21117i	0.269447	−	0.963015i	$-0.413159\pi$
$462$	−20.1267	−	11.6202i	−0.936380	−	0.540619i
$463$		−	10.1656i		−	0.472434i	−0.971700	−	0.236217i	$-0.924092\pi$
$463$		−	10.1656i		−	0.472434i	0.971700	−	0.236217i	$-0.0759076\pi$
$464$	6.64483			0.308478
$465$		0			0
$466$	−6.59738	+	11.4270i	−0.305618	+	0.529345i
$467$			13.6129i			0.629930i	0.949103	+	0.314965i	$0.101993\pi$
$467$			13.6129i			0.629930i	−0.949103	+	0.314965i	$0.898007\pi$
$468$		−	0.594358i		−	0.0274742i
$469$	12.6208	−	21.8598i	0.582773	−	1.00939i
$470$		0			0
$471$	−6.62886	+	11.4815i	−0.305442	+	0.529041i
$472$	−6.36376	+	3.67412i	−0.292916	+	0.169115i
$473$	13.8510	−	7.99687i	0.636869	−	0.367697i
$474$	10.4878			0.481723
$475$		0			0
$476$	15.3413			0.703167
$477$	0.148563	−	0.0857727i	0.00680222	−	0.00392726i
$478$	−7.34147	+	4.23860i	−0.335791	+	0.193869i
$479$	2.71463	−	4.70188i	0.124035	−	0.214835i	−0.797320	−	0.603556i	$-0.793750\pi$
$479$	2.71463	−	4.70188i	0.124035	−	0.214835i	0.921355	+	0.388722i	$0.127083\pi$
$480$		0			0
$481$	−23.4196	+	40.5639i	−1.06784	+	1.84956i
$482$			21.0292i			0.957853i
$483$		−	29.8706i		−	1.35916i
$484$	1.14239	−	1.97868i	0.0519268	−	0.0899399i
$485$		0			0
$486$	−1.02225			−0.0463703
$487$			32.5569i			1.47529i	0.675188	+	0.737646i	$0.264063\pi$
$487$			32.5569i			1.47529i	−0.675188	+	0.737646i	$0.735937\pi$
$488$	1.99914	+	1.15420i	0.0904968	+	0.0522483i
$489$	−4.65489	−	8.06251i	−0.210501	−	0.364599i
$490$		0			0
$491$	−15.3410	−	26.5713i	−0.692328	−	1.19915i	−0.971073	−	0.238782i	$-0.923252\pi$
$491$	−15.3410	−	26.5713i	−0.692328	−	1.19915i	0.278746	−	0.960365i	$-0.410081\pi$
$492$	11.7913	−	6.80772i	0.531594	−	0.306916i
$493$		−	27.2332i		−	1.22652i
$494$	−4.21278	+	25.9878i	−0.189542	+	1.16924i
$495$		0			0
$496$	−5.42082	−	9.38914i	−0.243402	−	0.421585i
$497$	6.44518	−	3.72113i	0.289106	−	0.166915i
$498$	8.39620	+	4.84755i	0.376243	+	0.217224i
$499$	−4.91213	−	8.50807i	−0.219897	−	0.380873i	0.734879	−	0.678198i	$-0.237239\pi$
$499$	−4.91213	−	8.50807i	−0.219897	−	0.380873i	−0.954776	+	0.297325i	$0.903906\pi$
$500$		0			0
$501$	31.3425			1.40028
$502$			27.2366i			1.21563i
$503$	13.1203	+	7.57502i	0.585006	+	0.337754i	0.763121	−	0.646256i	$-0.223666\pi$
$503$	13.1203	+	7.57502i	0.585006	+	0.337754i	−0.178114	+	0.984010i	$0.557000\pi$
$504$	0.184179	−	0.319008i	0.00820399	−	0.0142097i
$505$		0			0
$506$	17.0748			0.759067
$507$	34.6369	+	19.9976i	1.53828	+	0.888124i
$508$	−2.98488	+	1.72332i	−0.132433	+	0.0764600i
$509$	−1.12110	+	1.94180i	−0.0496919	+	0.0860690i	−0.889801	−	0.456348i	$-0.849157\pi$
$509$	−1.12110	+	1.94180i	−0.0496919	+	0.0860690i	0.840110	+	0.542417i	$0.182491\pi$
$510$		0			0
$511$	−17.1999	−	29.7912i	−0.760881	−	1.31788i
$512$			1.00000i			0.0441942i
$513$	22.7091	+	3.68130i	1.00263	+	0.162533i
$514$	−16.6541			−0.734581
$515$		0			0
$516$	−3.73733	−	6.47324i	−0.164527	−	0.284969i
$517$	−5.50255	−	3.17690i	−0.242002	−	0.139720i
$518$	−25.1398	+	14.5145i	−1.10458	+	0.637730i
$519$	−16.6068	+	28.7637i	−0.728956	+	1.26259i
$520$		0			0
$521$	−7.06785			−0.309648			−0.154824	−	0.987942i	$-0.549481\pi$
$521$	−7.06785			−0.309648			−0.154824	+	0.987942i	$0.549481\pi$
$522$	−0.566288	−	0.326947i	−0.0247858	−	0.0143101i
$523$	−30.3057	−	17.4970i	−1.32518	−	0.765091i	−0.340627	−	0.940199i	$-0.610639\pi$
$523$	−30.3057	−	17.4970i	−1.32518	−	0.765091i	−0.984549	+	0.175108i	$0.943973\pi$
$524$	−16.5263			−0.721955
$525$		0			0
$526$	0.994093	−	1.72182i	0.0433445	−	0.0750749i
$527$	−38.4805	+	22.2167i	−1.67624	+	0.967776i
$528$	−5.37683	−	3.10431i	−0.233996	−	0.135098i
$529$	−0.526988	−	0.912769i	−0.0229125	−	0.0396856i
$530$		0			0
$531$	0.723113			0.0313804
$532$	−10.3142	+	12.6429i	−0.447176	+	0.548138i
$533$		−	48.2767i		−	2.09110i
$534$	9.43658	+	16.3446i	0.408361	+	0.707302i
$535$		0			0
$536$	3.37162	−	5.83981i	0.145632	−	0.252242i
$537$	34.7646	−	20.0713i	1.50020	−	0.866143i
$538$	6.18731	+	3.57224i	0.266754	+	0.154010i
$539$	−25.5569			−1.10081
$540$		0			0
$541$	14.4090	−	24.9571i	0.619492	−	1.07299i	−0.370087	−	0.928997i	$-0.620672\pi$
$541$	14.4090	−	24.9571i	0.619492	−	1.07299i	0.989579	−	0.143994i	$-0.0459946\pi$
$542$	−9.49060	−	5.47940i	−0.407656	−	0.235360i
$543$			26.8030i			1.15023i
$544$	4.09841			0.175718
$545$		0			0
$546$	19.2557	+	33.3519i	0.824069	+	1.42733i
$547$	−27.7778	−	16.0375i	−1.18769	−	0.685715i	−0.229912	−	0.973211i	$-0.573844\pi$
$547$	−27.7778	−	16.0375i	−1.18769	−	0.685715i	−0.957782	+	0.287496i	$0.907177\pi$
$548$	19.3227	−	11.1560i	0.825424	−	0.476559i
$549$	−0.113581	−	0.196728i	−0.00484752	−	0.00839615i
$550$		0			0
$551$	22.4431	+	18.3093i	0.956107	+	0.780002i
$552$		−	7.97988i		−	0.339646i
$553$	19.9593	−	11.5235i	0.848757	−	0.490030i
$554$	6.13429	+	10.6249i	0.260621	+	0.451409i
$555$		0			0
$556$	0.880992	+	1.52592i	0.0373624	+	0.0647135i
$557$	8.98610	+	5.18813i	0.380753	+	0.219828i	0.678146	−	0.734927i	$-0.262784\pi$
$557$	8.98610	+	5.18813i	0.380753	+	0.219828i	−0.297393	+	0.954755i	$0.596117\pi$
$558$			1.06689i			0.0451649i
$559$	−26.5032			−1.12096
$560$		0			0
$561$	−12.7227	+	22.0364i	−0.537154	+	0.930379i
$562$		−	17.0797i		−	0.720462i
$563$			8.44664i			0.355984i	0.984032	+	0.177992i	$0.0569600\pi$
$563$			8.44664i			0.355984i	−0.984032	+	0.177992i	$0.943040\pi$
$564$	−1.48472	+	2.57161i	−0.0625180	+	0.108284i
$565$		0			0
$566$	−15.0064	+	25.9918i	−0.630765	+	1.09252i
$567$	28.1872	−	16.2739i	1.18375	−	0.683440i
$568$	1.72182	−	0.994093i	0.0722460	−	0.0417112i
$569$	−1.80181			−0.0755359			−0.0377680	−	0.999287i	$-0.512025\pi$
$569$	−1.80181			−0.0755359			−0.0377680	+	0.999287i	$0.512025\pi$
$570$		0			0
$571$	2.70574			0.113232			0.0566158	−	0.998396i	$-0.481969\pi$
$571$	2.70574			0.113232			0.0566158	+	0.998396i	$0.481969\pi$
$572$	−19.0648	+	11.0071i	−0.797140	+	0.460229i
$573$	9.80241	−	5.65942i	0.409501	−	0.236426i
$574$	14.9600	−	25.9114i	0.624417	−	1.08152i
$575$		0			0
$576$	0.0492032	−	0.0852224i	0.00205013	−	0.00355093i
$577$		−	6.61544i		−	0.275404i	−0.990474	−	0.137702i	$-0.956028\pi$
$577$		−	6.61544i		−	0.275404i	0.990474	−	0.137702i	$-0.0439717\pi$
$578$			0.203065i			0.00844640i
$579$	−6.81246	+	11.7995i	−0.283116	+	0.490371i
$580$		0			0
$581$	21.3050			0.883879
$582$			2.56400i			0.106281i
$583$	−5.50255	−	3.17690i	−0.227892	−	0.131574i
$584$	−4.59494	−	7.95867i	−0.190140	−	0.329332i
$585$		0			0
$586$	−11.2339	−	19.4576i	−0.464067	−	0.803787i
$587$	−12.4961	+	7.21463i	−0.515770	+	0.297780i	−0.735202	−	0.677848i	$-0.762913\pi$
$587$	−12.4961	+	7.21463i	−0.515770	+	0.297780i	0.219432	+	0.975628i	$0.429579\pi$
$588$			11.9440i			0.492561i
$589$	7.56204	−	46.6487i	0.311589	−	1.92212i
$590$		0			0
$591$	0.410174	+	0.710443i	0.0168723	+	0.0292237i
$592$	−6.71607	+	3.87752i	−0.276029	+	0.159365i
$593$	−17.9652	−	10.3722i	−0.737742	−	0.425935i	0.0835060	−	0.996507i	$-0.473388\pi$
$593$	−17.9652	−	10.3722i	−0.737742	−	0.425935i	−0.821248	+	0.570572i	$0.806722\pi$
$594$	9.61842	+	16.6596i	0.394649	+	0.683552i
$595$		0			0
$596$	−3.61427			−0.148046
$597$		−	39.7893i		−	1.62847i
$598$	−24.5038	−	14.1473i	−1.00203	−	0.578525i
$599$	−9.41389	+	16.3053i	−0.384641	+	0.666218i	−0.991719	−	0.128424i	$-0.959008\pi$
$599$	−9.41389	+	16.3053i	−0.384641	+	0.666218i	0.607078	+	0.794642i	$0.292341\pi$
$600$		0			0
$601$	−23.0999			−0.942263			−0.471131	−	0.882063i	$-0.656154\pi$
$601$	−23.0999			−0.942263			−0.471131	+	0.882063i	$0.656154\pi$
$602$	−14.2250	−	8.21278i	−0.579766	−	0.334728i
$603$	−0.574675	+	0.331789i	−0.0234026	+	0.0135115i
$604$	−9.08556	+	15.7367i	−0.369686	+	0.640316i
$605$		0			0
$606$	−6.67285	−	11.5577i	−0.271066	−	0.469500i
$607$			28.6025i			1.16094i	0.814281	+	0.580470i	$0.197131\pi$
$607$			28.6025i			1.16094i	−0.814281	+	0.580470i	$0.802869\pi$
$608$	−2.75542	+	3.37752i	−0.111747	+	0.136977i
$609$	42.3691			1.71688
$610$		0			0
$611$	5.26442	+	9.11825i	0.212976	+	0.368885i
$612$	−0.349276	−	0.201655i	−0.0141186	−	0.00815141i
$613$	−6.45202	+	3.72507i	−0.260594	+	0.150454i	−0.624606	−	0.780940i	$-0.714740\pi$
$613$	−6.45202	+	3.72507i	−0.260594	+	0.150454i	0.364011	+	0.931395i	$0.381407\pi$
$614$	8.19578	−	14.1955i	0.330755	−	0.572884i
$615$		0			0
$616$	−13.6435			−0.549710
$617$	−27.1432	−	15.6711i	−1.09274	−	0.630896i	−0.158438	−	0.987369i	$-0.550646\pi$
$617$	−27.1432	−	15.6711i	−1.09274	−	0.630896i	−0.934306	+	0.356473i	$0.883979\pi$
$618$	−20.0680	−	11.5863i	−0.807252	−	0.466067i
$619$	−1.60012			−0.0643143			−0.0321572	−	0.999483i	$-0.510238\pi$
$619$	−1.60012			−0.0643143			−0.0321572	+	0.999483i	$0.510238\pi$
$620$		0			0
$621$	−12.3625	+	21.4124i	−0.496088	+	0.859250i
$622$	−15.6055	+	9.00985i	−0.625724	+	0.361262i
$623$	35.9173	+	20.7369i	1.43900	+	0.830806i
$624$	5.14414	+	8.90992i	0.205930	+	0.356682i
$625$		0			0
$626$	18.0104			0.719842
$627$	−9.60669	−	25.3003i	−0.383654	−	1.01040i
$628$			7.78306i			0.310578i
$629$	15.8917	+	27.5252i	0.633642	+	1.09750i
$630$		0			0
$631$	6.44386	−	11.1611i	0.256526	−	0.444316i	−0.708783	−	0.705427i	$-0.750755\pi$
$631$	6.44386	−	11.1611i	0.256526	−	0.444316i	0.965309	+	0.261111i	$0.0840887\pi$
$632$	5.33210	−	3.07849i	0.212100	−	0.122456i
$633$	8.60012	+	4.96528i	0.341824	+	0.197352i
$634$	−23.2554			−0.923590
$635$		0			0
$636$	−1.48472	+	2.57161i	−0.0588730	+	0.101971i
$637$	36.6763	+	21.1751i	1.45317	+	0.838987i
$638$			24.2193i			0.958850i
$639$	−0.195650			−0.00773980
$640$		0			0
$641$	13.9086	+	24.0903i	0.549355	+	0.951511i	0.998319	+	0.0579612i	$0.0184600\pi$
$641$	13.9086	+	24.0903i	0.549355	+	0.951511i	−0.448964	+	0.893550i	$0.648207\pi$
$642$	10.6929	+	6.17353i	0.422014	+	0.243650i
$643$	−14.7275	+	8.50292i	−0.580795	+	0.335322i	−0.761449	−	0.648224i	$-0.775512\pi$
$643$	−14.7275	+	8.50292i	−0.580795	+	0.335322i	0.180654	+	0.983547i	$0.442179\pi$
$644$	−8.76789	−	15.1864i	−0.345503	−	0.598429i
$645$		0			0
$646$	13.8425	+	11.2928i	0.544625	+	0.444310i
$647$		−	42.3379i		−	1.66447i	−0.554420	−	0.832237i	$-0.687060\pi$
$647$		−	42.3379i		−	1.66447i	0.554420	−	0.832237i	$-0.312940\pi$
$648$	7.53017	−	4.34755i	0.295813	−	0.170788i
$649$	−13.3915	−	23.1948i	−0.525664	−	0.910476i
$650$		0			0
$651$	−34.5645	−	59.8675i	−1.35469	−	2.34639i
$652$	−4.73317	−	2.73270i	−0.185365	−	0.107021i
$653$			48.6365i			1.90329i	0.307194	+	0.951647i	$0.400610\pi$
$653$			48.6365i			1.90329i	−0.307194	+	0.951647i	$0.599390\pi$
$654$	7.64463			0.298929
$655$		0			0
$656$	3.99653	−	6.92220i	0.156038	−	0.270266i
$657$			0.904342i			0.0352818i
$658$			6.52534i			0.254384i
$659$	5.47593	−	9.48459i	0.213312	−	0.369467i	−0.739437	−	0.673226i	$-0.764908\pi$
$659$	5.47593	−	9.48459i	0.213312	−	0.369467i	0.952749	+	0.303758i	$0.0982416\pi$
$660$		0			0
$661$	12.3214	−	21.3413i	0.479246	−	0.830079i	−0.520470	−	0.853880i	$-0.674243\pi$
$661$	12.3214	−	21.3413i	0.479246	−	0.830079i	0.999717	+	0.0238007i	$0.00757670\pi$
$662$	6.39403	−	3.69159i	0.248511	−	0.143478i
$663$	36.5165	−	21.0828i	1.41818	−	0.818788i
$664$	5.69159			0.220877
$665$		0			0
$666$	0.763146			0.0295713
$667$	−26.9583	+	15.5644i	−1.04383	+	0.602655i
$668$	15.9348	−	9.19994i	0.616534	−	0.355956i
$669$	14.2443	−	24.6719i	0.550716	−	0.953869i
$670$		0			0
$671$	−4.20687	+	7.28652i	−0.162405	+	0.281293i
$672$			6.37625i			0.245969i
$673$		−	5.18012i		−	0.199679i	−0.995004	−	0.0998395i	$-0.968167\pi$
$673$		−	5.18012i		−	0.199679i	0.995004	−	0.0998395i	$-0.0318329\pi$
$674$	−15.4400	+	26.7429i	−0.594728	+	1.03010i
$675$		0			0
$676$	23.4795			0.903059
$677$		−	45.4548i		−	1.74697i	−0.486851	−	0.873485i	$-0.661854\pi$
$677$		−	45.4548i		−	1.74697i	0.486851	−	0.873485i	$-0.338146\pi$
$678$	19.5926	+	11.3118i	0.752448	+	0.434426i
$679$	2.81720	+	4.87953i	0.108114	+	0.187259i
$680$		0			0
$681$	−3.54467	−	6.13955i	−0.135832	−	0.235268i
$682$	34.2218	−	19.7580i	1.31042	−	0.756572i
$683$		−	3.24495i		−	0.124165i	−0.998071	−	0.0620823i	$-0.980226\pi$
$683$		−	3.24495i		−	0.124165i	0.998071	−	0.0620823i	$-0.0197741\pi$
$684$	0.401008	−	0.152265i	0.0153329	−	0.00582201i
$685$		0			0
$686$	0.0221096	+	0.0382949i	0.000844147	+	0.00146211i
$687$	8.11103	−	4.68291i	0.309455	−	0.178664i
$688$	−3.80018	−	2.19403i	−0.144880	−	0.0836467i
$689$	5.26442	+	9.11825i	0.200559	+	0.347378i
$690$		0			0
$691$	44.0806			1.67691			0.838453	−	0.544974i	$-0.183461\pi$
$691$	44.0806			1.67691			0.838453	+	0.544974i	$0.183461\pi$
$692$			19.4983i			0.741214i
$693$	1.16273	+	0.671301i	0.0441684	+	0.0255006i
$694$	−4.55974	+	7.89771i	−0.173086	+	0.299793i
$695$		0			0
$696$	11.3188			0.429040
$697$	−28.3700	−	16.3794i	−1.07459	−	0.620415i
$698$	12.3415	−	7.12539i	0.467134	−	0.269700i
$699$	−11.2380	+	19.4648i	−0.425061	+	0.736227i
$700$		0			0
$701$	−25.7667	−	44.6292i	−0.973193	−	1.68562i	−0.685773	−	0.727815i	$-0.740536\pi$
$701$	−25.7667	−	44.6292i	−0.973193	−	1.68562i	−0.287420	−	0.957805i	$-0.592797\pi$
$702$		−	31.8773i		−	1.20313i
$703$	−33.3679	−	5.40915i	−1.25849	−	0.204010i
$704$	−3.64483			−0.137370
$705$		0			0
$706$	−3.88806	−	6.73433i	−0.146329	−	0.253450i
$707$	−25.3981	−	14.6636i	−0.955192	−	0.551481i
$708$	−10.8401	+	6.25852i	−0.407395	+	0.235209i
$709$	4.42556	−	7.66530i	0.166205	−	0.287876i	−0.770877	−	0.636984i	$-0.780182\pi$
$709$	4.42556	−	7.66530i	0.166205	−	0.287876i	0.937083	+	0.349107i	$0.113515\pi$
$710$		0			0
$711$	−0.605886			−0.0227225
$712$	9.59527	+	5.53983i	0.359598	+	0.207614i
$713$	43.9849	+	25.3947i	1.64725	+	0.951039i
$714$	26.1325			0.977983
$715$		0			0
$716$	11.7831	−	20.4089i	0.440354	−	0.762715i
$717$	−12.5055	+	7.22006i	−0.467027	+	0.269638i
$718$	5.03052	+	2.90437i	0.187737	+	0.108390i
$719$	23.5785	+	40.8392i	0.879331	+	1.52305i	0.852077	+	0.523417i	$0.175343\pi$
$719$	23.5785	+	40.8392i	0.879331	+	1.52305i	0.0272540	+	0.999629i	$0.491324\pi$
$720$		0			0
$721$	−50.9216			−1.89642
$722$	−18.6130	+	3.81534i	−0.692704	+	0.141992i
$723$			35.8213i			1.33221i
$724$	7.86746	+	13.6268i	0.292392	+	0.506438i
$725$		0			0
$726$	1.94595	−	3.37049i	0.0722212	−	0.125091i
$727$	11.2960	−	6.52177i	0.418947	−	0.241879i	−0.275680	−	0.961250i	$-0.588903\pi$
$727$	11.2960	−	6.52177i	0.418947	−	0.241879i	0.694627	+	0.719371i	$0.255570\pi$
$728$	19.5795	+	11.3043i	0.725666	+	0.418963i
$729$	−27.8266			−1.03061
$730$		0			0
$731$	−8.99204	+	15.5747i	−0.332582	+	0.576050i
$732$	3.40535	+	1.96608i	0.125865	+	0.0726683i
$733$		−	13.9861i		−	0.516590i	−0.966066	−	0.258295i	$-0.916839\pi$
$733$		−	13.9861i		−	0.516590i	0.966066	−	0.258295i	$-0.0831606\pi$
$734$	−22.2827			−0.822470
$735$		0			0
$736$	−2.34233	−	4.05703i	−0.0863394	−	0.149544i
$737$	21.2851	+	12.2890i	0.784048	+	0.452670i
$738$	−0.681188	+	0.393284i	−0.0250749	+	0.0144770i
$739$	0.534508	+	0.925795i	0.0196622	+	0.0340559i	0.875689	−	0.482875i	$-0.160408\pi$
$739$	0.534508	+	0.925795i	0.0196622	+	0.0340559i	−0.856027	+	0.516931i	$0.827074\pi$
$740$		0			0
$741$	−7.17608	+	44.2677i	−0.263620	+	1.62622i
$742$			6.52534i			0.239553i
$743$	8.67048	−	5.00591i	0.318089	−	0.183649i	−0.332451	−	0.943120i	$-0.607876\pi$
$743$	8.67048	−	5.00591i	0.318089	−	0.183649i	0.650541	+	0.759472i	$0.274542\pi$
$744$	−9.23386	−	15.9935i	−0.338530	−	0.586351i
$745$		0			0
$746$	8.53046	+	14.7752i	0.312322	+	0.540958i
$747$	−0.485051	−	0.280045i	−0.0177471	−	0.0102463i
$748$			14.9380i			0.546187i
$749$	27.1327			0.991406
$750$		0			0
$751$	−17.3070	+	29.9767i	−0.631543	+	1.09386i	0.355694	+	0.934603i	$0.384245\pi$
$751$	−17.3070	+	29.9767i	−0.631543	+	1.09386i	−0.987236	+	0.159261i	$0.949089\pi$
$752$			1.74324i			0.0635693i
$753$			46.3951i			1.69073i
$754$	20.0668	−	34.7567i	0.730790	−	1.26577i
$755$		0			0
$756$	9.87811	−	17.1094i	0.359263	−	0.622262i
$757$	2.90364	−	1.67642i	0.105535	−	0.0609305i	−0.446304	−	0.894882i	$-0.647260\pi$
$757$	2.90364	−	1.67642i	0.105535	−	0.0609305i	0.551838	+	0.833951i	$0.313927\pi$
$758$	8.68874	−	5.01645i	0.315589	−	0.182206i
$759$	29.0853			1.05573
$760$		0			0
$761$	27.5087			0.997190			0.498595	−	0.866835i	$-0.333849\pi$
$761$	27.5087			0.997190			0.498595	+	0.866835i	$0.333849\pi$
$762$	−5.08446	+	2.93552i	−0.184191	+	0.106343i
$763$	14.5484	−	8.39953i	0.526688	−	0.304083i
$764$	3.32241	−	5.75459i	0.120201	−	0.208194i
$765$		0			0
$766$	0.994093	−	1.72182i	0.0359181	−	0.0622119i
$767$			44.3821i			1.60254i
$768$			1.70341i			0.0614664i
$769$	−17.1306	+	29.6711i	−0.617746	+	1.06997i	0.372150	+	0.928172i	$0.378621\pi$
$769$	−17.1306	+	29.6711i	−0.617746	+	1.06997i	−0.989896	+	0.141795i	$0.954713\pi$
$770$		0			0
$771$	−28.3687			−1.02167
$772$			7.99863i			0.287877i
$773$	−10.3608	−	5.98184i	−0.372654	−	0.215152i	0.301963	−	0.953320i	$-0.402358\pi$
$773$	−10.3608	−	5.98184i	−0.372654	−	0.215152i	−0.674617	+	0.738168i	$0.735691\pi$
$774$	0.215907	+	0.373961i	0.00776061	+	0.0134418i
$775$		0			0
$776$	0.752610	+	1.30356i	0.0270171	+	0.0467950i
$777$	−42.8233	+	24.7241i	−1.53628	+	0.886971i
$778$		−	8.87708i		−	0.318259i
$779$	32.5719	−	12.3678i	1.16701	−	0.443121i
$780$		0			0
$781$	3.62330	+	6.27574i	0.129652	+	0.224564i
$782$	−16.6274	+	9.59982i	−0.594594	+	0.343289i
$783$	−30.3718	−	17.5352i	−1.08540	−	0.626657i
$784$	3.50591	+	6.07241i	0.125211	+	0.216872i
$785$		0			0
$786$	−28.1510			−1.00411
$787$			32.2277i			1.14879i	0.818578	+	0.574396i	$0.194763\pi$
$787$			32.2277i			1.14879i	−0.818578	+	0.574396i	$0.805237\pi$
$788$	0.417072	+	0.240797i	0.0148576	+	0.00857802i
$789$	1.69335	−	2.93296i	0.0602847	−	0.104416i
$790$		0			0
$791$	49.7152			1.76767
$792$	0.310621	+	0.179337i	0.0110374	+	0.00637247i
$793$	12.0745	−	6.97119i	0.428777	−	0.247554i
$794$	10.5563	−	18.2840i	0.374628	−	0.648875i
$795$		0			0
$796$	−11.6793	−	20.2292i	−0.413963	−	0.717005i
$797$			39.9120i			1.41376i	0.707335	+	0.706878i	$0.249897\pi$
$797$			39.9120i			1.41376i	−0.707335	+	0.706878i	$0.750103\pi$
$798$	−17.5692	+	21.5359i	−0.621944	+	0.762364i
$799$	7.14449			0.252754
$800$		0			0
$801$	−0.545154	−	0.944235i	−0.0192621	−	0.0333629i
$802$	−25.9471	−	14.9806i	−0.916224	−	0.528982i
$803$	29.0080	−	16.7478i	1.02367	−	0.591016i
$804$	5.74324	−	9.94758i	0.202548	−	0.350824i
$805$		0			0
$806$	−65.4817			−2.30649
$807$	10.5395	+	6.08498i	0.371008	+	0.214202i
$808$	−6.78506	−	3.91735i	−0.238697	−	0.137812i
$809$	22.1075			0.777257			0.388629	−	0.921394i	$-0.372949\pi$
$809$	22.1075			0.777257			0.388629	+	0.921394i	$0.372949\pi$
$810$		0			0
$811$	−10.5035	+	18.1925i	−0.368827	+	0.638826i	−0.989382	−	0.145336i	$-0.953574\pi$
$811$	−10.5035	+	18.1925i	−0.368827	+	0.638826i	0.620556	+	0.784162i	$0.286907\pi$
$812$	21.5408	−	12.4366i	0.755934	−	0.436438i
$813$	−16.1663	−	9.33364i	−0.566978	−	0.327345i
$814$	−14.1329	−	24.4789i	−0.495358	−	0.857986i
$815$		0			0
$816$	6.98125			0.244393
$817$	−6.78971	−	17.8815i	−0.237542	−	0.625593i
$818$			4.19544i			0.146690i
$819$	−1.11241	−	1.92675i	−0.0388708	−	0.0673261i
$820$		0			0
$821$	−19.1593	+	33.1849i	−0.668665	+	1.15816i	0.309613	+	0.950863i	$0.399801\pi$
$821$	−19.1593	+	33.1849i	−0.668665	+	1.15816i	−0.978278	+	0.207299i	$0.933533\pi$
$822$	32.9144	−	19.0031i	1.14802	−	0.662810i
$823$	46.3479	+	26.7590i	1.61559	+	0.932760i	0.988043	+	0.154179i	$0.0492734\pi$
$823$	46.3479	+	26.7590i	1.61559	+	0.932760i	0.627545	+	0.778580i	$0.284060\pi$
$824$	−13.6036			−0.473905
$825$		0			0
$826$	−13.7531	+	23.8210i	−0.478531	+	0.828840i
$827$	−18.0843	−	10.4410i	−0.628853	−	0.363068i	0.151455	−	0.988464i	$-0.451604\pi$
$827$	−18.0843	−	10.4410i	−0.628853	−	0.363068i	−0.780308	+	0.625396i	$0.784938\pi$
$828$			0.461000i			0.0160209i
$829$	57.1594			1.98523			0.992614	−	0.121317i	$-0.0387117\pi$
$829$	57.1594			1.98523			0.992614	+	0.121317i	$0.0387117\pi$
$830$		0			0
$831$	10.4492	+	18.0985i	0.362478	+	0.627831i
$832$	5.23065	+	3.01991i	0.181340	+	0.104697i
$833$	24.8872	−	14.3686i	0.862290	−	0.497844i
$834$	1.50069	+	2.59927i	0.0519645	+	0.0900052i
$835$		0			0
$836$	−12.3105	−	10.0430i	−0.425768	−	0.347345i
$837$			57.2205i			1.97783i
$838$	−10.8535	+	6.26628i	−0.374928	+	0.216465i
$839$	−12.4778	−	21.6122i	−0.430781	−	0.746135i	0.566160	−	0.824296i	$-0.308429\pi$
$839$	−12.4778	−	21.6122i	−0.430781	−	0.746135i	−0.996941	+	0.0781610i	$0.975095\pi$
$840$		0			0
$841$	−7.57688	−	13.1235i	−0.261272	−	0.452536i
$842$	23.0160	+	13.2883i	0.793183	+	0.457945i
$843$		−	29.0936i		−	1.00204i
$844$	5.82983			0.200671
$845$		0			0
$846$	0.0857727	−	0.148563i	0.00294893	−	0.00510769i
$847$		−	8.55247i		−	0.293866i
$848$			1.74324i			0.0598630i
$849$	−25.5620	+	44.2746i	−0.877285	+	1.51950i
$850$		0			0
$851$	18.1649	−	31.4625i	0.622684	−	1.07852i
$852$	2.93296	−	1.69335i	0.100482	−	0.0580131i
$853$	−23.9672	+	13.8375i	−0.820622	+	0.473787i	−0.850631	−	0.525763i	$-0.823780\pi$
$853$	−23.9672	+	13.8375i	−0.820622	+	0.473787i	0.0300087	+	0.999550i	$0.490447\pi$
$854$	8.64091			0.295686
$855$		0			0
$856$	7.24845			0.247747
$857$	18.1865	−	10.5000i	0.621240	−	0.358673i	−0.156112	−	0.987739i	$-0.549896\pi$
$857$	18.1865	−	10.5000i	0.621240	−	0.358673i	0.777352	+	0.629066i	$0.216563\pi$
$858$	−32.4751	+	18.7495i	−1.10868	+	0.640098i
$859$	11.0617	−	19.1594i	0.377420	−	0.653711i	−0.613266	−	0.789877i	$-0.710144\pi$
$859$	11.0617	−	19.1594i	0.377420	−	0.653711i	0.990686	+	0.136165i	$0.0434778\pi$
$860$		0			0
$861$	25.4829	−	44.1377i	0.868455	−	1.50421i
$862$		−	0.180610i		−	0.00615159i
$863$			31.1716i			1.06109i	0.847655	+	0.530547i	$0.178013\pi$
$863$			31.1716i			1.06109i	−0.847655	+	0.530547i	$0.821987\pi$
$864$	2.63892	−	4.57075i	0.0897780	−	0.155500i
$865$		0			0
$866$	12.0104			0.408131
$867$			0.345903i			0.0117475i
$868$	−35.1458	−	20.2914i	−1.19292	−	0.688735i
$869$	11.2206	+	19.4346i	0.380632	+	0.659274i
$870$		0			0
$871$	−20.3640	−	35.2715i	−0.690008	−	1.19513i
$872$	3.88659	−	2.24392i	0.131616	−	0.0759888i
$873$		−	0.148123i		−	0.00501321i
$874$	3.26755	−	20.1568i	0.110526	−	0.681815i
$875$		0			0
$876$	−7.82705	−	13.5568i	−0.264451	−	0.458043i
$877$	−17.8946	+	10.3314i	−0.604257	+	0.348868i	−0.770715	−	0.637180i	$-0.780101\pi$
$877$	−17.8946	+	10.3314i	−0.604257	+	0.348868i	0.166457	+	0.986049i	$0.446767\pi$
$878$	−24.6893	−	14.2544i	−0.833223	−	0.481061i
$879$	−19.1358	−	33.1442i	−0.645436	−	1.11793i
$880$		0			0
$881$	35.5613			1.19809			0.599045	−	0.800716i	$-0.295547\pi$
$881$	35.5613			1.19809			0.599045	+	0.800716i	$0.295547\pi$
$882$		−	0.690007i		−	0.0232337i
$883$	−15.6551	−	9.03845i	−0.526835	−	0.304168i	0.212892	−	0.977076i	$-0.431712\pi$
$883$	−15.6551	−	9.03845i	−0.526835	−	0.304168i	−0.739727	+	0.672908i	$0.765045\pi$
$884$	12.3768	−	21.4373i	0.416278	−	0.721015i
$885$		0			0
$886$	−8.54642			−0.287123
$887$	40.7620	+	23.5340i	1.36865	+	0.790193i	0.990756	−	0.135654i	$-0.0433136\pi$
$887$	40.7620	+	23.5340i	1.36865	+	0.790193i	0.377898	+	0.925847i	$0.376647\pi$
$888$	−11.4402	+	6.60500i	−0.383908	+	0.221649i
$889$	−6.45080	+	11.1731i	−0.216353	+	0.374734i
$890$		0			0
$891$	15.8461	+	27.4462i	0.530863	+	0.919482i
$892$		−	16.7245i		−	0.559977i
$893$	−4.80334	+	5.88782i	−0.160738	+	0.197028i
$894$	−6.15657			−0.205906
$895$		0			0
$896$	1.87162	+	3.24174i	0.0625264	+	0.108299i
$897$	−41.7399	−	24.0985i	−1.39366	−	0.804627i
$898$	3.67725	−	2.12306i	0.122711	−	0.0708475i
$899$	−36.0204	+	62.3892i	−1.20135	+	2.08080i
$900$		0			0
$901$	7.14449			0.238017
$902$	25.2302	+	14.5667i	0.840075	+	0.485017i
$903$	−24.2309	−	13.9897i	−0.806353	−	0.465548i
$904$	13.2813			0.441731
$905$		0			0
$906$	−15.4764	+	26.8059i	−0.514169	+	0.890567i
$907$	−17.3869	+	10.0383i	−0.577322	+	0.333317i	−0.760068	−	0.649843i	$-0.774835\pi$
$907$	−17.3869	+	10.0383i	−0.577322	+	0.333317i	0.182746	+	0.983160i	$0.441501\pi$
$908$	−3.60428	−	2.08093i	−0.119612	−	0.0690581i
$909$	0.385493	+	0.667693i	0.0127860	+	0.0221460i
$910$		0			0
$911$	−29.6273			−0.981595			−0.490797	−	0.871274i	$-0.663294\pi$
$911$	−29.6273			−0.981595			−0.490797	+	0.871274i	$0.663294\pi$
$912$	−4.69360	+	5.75330i	−0.155421	+	0.190511i
$913$			20.7449i			0.686556i
$914$	−9.11022	−	15.7794i	−0.301339	−	0.521935i
$915$		0			0
$916$	2.74914	−	4.76165i	0.0908342	−	0.157329i
$917$	−53.5739	+	30.9309i	−1.76917	+	1.02143i
$918$	−18.7328	−	10.8154i	−0.618274	−	0.356961i
$919$	55.4525			1.82921			0.914604	−	0.404350i	$-0.132502\pi$
$919$	55.4525			1.82921			0.914604	+	0.404350i	$0.132502\pi$
$920$		0			0
$921$	13.9608	−	24.1807i	0.460022	−	0.796782i
$922$	−26.0050	−	15.0140i	−0.856430	−	0.494460i
$923$		−	12.0083i		−	0.395258i
$924$	−23.2403			−0.764551
$925$		0			0
$926$	−5.08278	−	8.80364i	−0.167031	−	0.289306i
$927$	1.15933	+	0.669342i	0.0380775	+	0.0219841i
$928$	5.75459	−	3.32241i	0.188904	−	0.109064i
$929$	3.61925	+	6.26873i	0.118744	+	0.205670i	0.919270	−	0.393627i	$-0.128780\pi$
$929$	3.61925	+	6.26873i	0.118744	+	0.205670i	−0.800526	+	0.599298i	$0.795447\pi$
$930$		0			0
$931$	−4.89074	+	30.1699i	−0.160288	+	0.988780i
$932$			13.1948i			0.432209i
$933$	−26.5826	+	15.3474i	−0.870274	+	0.502453i
$934$	6.80645	+	11.7891i	0.222714	+	0.385752i
$935$		0			0
$936$	−0.297179	−	0.514729i	−0.00971359	−	0.0168244i
$937$	32.5974	+	18.8201i	1.06491	+	0.614826i	0.926786	−	0.375589i	$-0.122559\pi$
$937$	32.5974	+	18.8201i	1.06491	+	0.614826i	0.138124	+	0.990415i	$0.455893\pi$
$938$		−	25.2415i		−	0.824165i
$939$	30.6791			1.00117
$940$		0			0
$941$	12.9631	−	22.4527i	0.422585	−	0.731938i	−0.573607	−	0.819131i	$-0.694456\pi$
$941$	12.9631	−	22.4527i	0.422585	−	0.731938i	0.996191	+	0.0871927i	$0.0277896\pi$
$942$			13.2577i			0.431960i
$943$			37.4448i			1.21937i
$944$	−3.67412	+	6.36376i	−0.119582	+	0.207123i
$945$		0			0
$946$	7.99687	−	13.8510i	0.260001	−	0.450335i
$947$	35.5953	−	20.5510i	1.15669	−	0.667816i	0.206183	−	0.978513i	$-0.433896\pi$
$947$	35.5953	−	20.5510i	1.15669	−	0.667816i	0.950509	+	0.310697i	$0.100563\pi$
$948$	9.08274	−	5.24392i	0.294994	−	0.170315i
$949$	−55.5053			−1.80178
$950$		0			0
$951$	−39.6134			−1.28455
$952$	13.2860	−	7.67065i	0.430600	−	0.248607i
$953$	11.8400	−	6.83584i	0.383536	−	0.221435i	−0.295820	−	0.955244i	$-0.595593\pi$
$953$	11.8400	−	6.83584i	0.383536	−	0.221435i	0.679356	+	0.733809i	$0.262259\pi$
$954$	0.0857727	−	0.148563i	0.00277700	−	0.00480990i
$955$		0			0
$956$	−4.23860	+	7.34147i	−0.137086	+	0.237440i
$957$			41.2553i			1.33359i
$958$		−	5.42927i		−	0.175412i
$959$	41.7594	−	72.3293i	1.34848	−	2.33564i
$960$		0			0
$961$	86.5412			2.79165
$962$			46.8392i			1.51016i
$963$	−0.617731	−	0.356647i	−0.0199061	−	0.0114928i
$964$	10.5146	+	18.2118i	0.338652	+	0.586563i
$965$		0			0
$966$	−14.9353	−	25.8687i	−0.480535	−	0.832311i
$967$	41.1289	−	23.7458i	1.32262	−	0.763614i	0.338472	−	0.940976i	$-0.390090\pi$
$967$	41.1289	−	23.7458i	1.32262	−	0.763614i	0.984146	+	0.177363i	$0.0567566\pi$
$968$		−	2.28478i		−	0.0734356i
$969$	23.5793	+	19.2363i	0.757478	+	0.617958i
$970$		0			0
$971$	−4.83017	−	8.36611i	−0.155008	−	0.268481i	0.778054	−	0.628197i	$-0.216207\pi$
$971$	−4.83017	−	8.36611i	−0.155008	−	0.268481i	−0.933062	+	0.359716i	$0.882874\pi$
$972$	−0.885296	+	0.511126i	−0.0283959	+	0.0163944i
$973$	5.71189	+	3.29776i	0.183115	+	0.105721i
$974$	16.2784	+	28.1951i	0.521595	+	0.903428i
$975$		0			0
$976$	2.30841			0.0738903
$977$			38.8232i			1.24206i	0.783786	+	0.621032i	$0.213286\pi$
$977$			38.8232i			1.24206i	−0.783786	+	0.621032i	$0.786714\pi$
$978$	−8.06251	−	4.65489i	−0.257811	−	0.148847i
$979$	−20.1917	+	34.9731i	−0.645331	+	1.11775i
$980$		0			0
$981$	−0.441633			−0.0141002
$982$	−26.5713	−	15.3410i	−0.847925	−	0.489550i
$983$	−41.2505	+	23.8160i	−1.31569	+	0.759611i	−0.983031	−	0.183438i	$-0.941277\pi$
$983$	−41.2505	+	23.8160i	−1.31569	+	0.759611i	−0.332654	+	0.943049i	$0.607944\pi$
$984$	6.80772	−	11.7913i	0.217022	−	0.375893i
$985$		0			0
$986$	−13.6166	−	23.5847i	−0.433641	−	0.751088i
$987$			11.1153i			0.353804i
$988$	9.34551	+	24.6125i	0.297320	+	0.783026i
$989$	20.5566			0.653661
$990$		0			0
$991$	3.04886	+	5.28078i	0.0968503	+	0.167750i	0.910379	−	0.413775i	$-0.135790\pi$
$991$	3.04886	+	5.28078i	0.0968503	+	0.167750i	−0.813529	+	0.581524i	$0.802457\pi$
$992$	−9.38914	−	5.42082i	−0.298105	−	0.172111i
$993$	10.8916	−	6.28828i	0.345635	−	0.199553i
$994$	3.72113	−	6.44518i	0.118027	−	0.204429i
$995$		0			0
$996$	9.69510			0.307201
$997$	16.0170	+	9.24743i	0.507264	+	0.292869i	0.731708	−	0.681618i	$-0.238723\pi$
$997$	16.0170	+	9.24743i	0.507264	+	0.292869i	−0.224444	+	0.974487i	$0.572057\pi$
$998$	−8.50807	−	4.91213i	−0.269318	−	0.155491i
$999$	40.9299			1.29497

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.j.i.349.7		16
5.2	odd	4		950.2.e.m.501.2	yes	8
5.3	odd	4		950.2.e.l.501.3	yes	8
5.4	even	2	inner	950.2.j.i.349.2		16
19.11	even	3	inner	950.2.j.i.49.2		16
95.49	even	6	inner	950.2.j.i.49.7		16
95.68	odd	12		950.2.e.l.201.3	✓	8
95.87	odd	12		950.2.e.m.201.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.e.l.201.3	✓	8	95.68	odd	12
950.2.e.l.501.3	yes	8	5.3	odd	4
950.2.e.m.201.2	yes	8	95.87	odd	12
950.2.e.m.501.2	yes	8	5.2	odd	4
950.2.j.i.49.2		16	19.11	even	3	inner
950.2.j.i.49.7		16	95.49	even	6	inner
950.2.j.i.349.2		16	5.4	even	2	inner
950.2.j.i.349.7		16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(1.47519 - 0.851703i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.851703 - 1.47519i) q^{6} -3.74324i q^{7} -1.00000i q^{8} +(-0.0492032 + 0.0852224i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(1.47519 - 0.851703i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.851703 - 1.47519i) q^{6} -3.74324i q^{7} -1.00000i q^{8} +(-0.0492032 + 0.0852224i) q^{9} +3.64483 q^{11} -1.70341i q^{12} +(-5.23065 - 3.01991i) q^{13} +(-1.87162 - 3.24174i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.54932 + 2.04920i) q^{17} +0.0984064i q^{18} +(0.697500 - 4.30273i) q^{19} +(-3.18813 - 5.52200i) q^{21} +(3.15651 - 1.82241i) q^{22} +(4.05703 + 2.34233i) q^{23} +(-0.851703 - 1.47519i) q^{24} -6.03983 q^{26} +5.27785i q^{27} +(-3.24174 - 1.87162i) q^{28} +(-3.32241 + 5.75459i) q^{29} +10.8416 q^{31} +(-0.866025 - 0.500000i) q^{32} +(5.37683 - 3.10431i) q^{33} +(-2.04920 + 3.54932i) q^{34} +(0.0492032 + 0.0852224i) q^{36} -7.75505i q^{37} +(-1.54731 - 4.07502i) q^{38} -10.2883 q^{39} +(3.99653 + 6.92220i) q^{41} +(-5.52200 - 3.18813i) q^{42} +(3.80018 - 2.19403i) q^{43} +(1.82241 - 3.15651i) q^{44} +4.68466 q^{46} +(-1.50969 - 0.871618i) q^{47} +(-1.47519 - 0.851703i) q^{48} -7.01181 q^{49} +(-3.49063 + 6.04594i) q^{51} +(-5.23065 + 3.01991i) q^{52} +(-1.50969 - 0.871618i) q^{53} +(2.63892 + 4.57075i) q^{54} -3.74324 q^{56} +(-2.63570 - 6.94142i) q^{57} +6.64483i q^{58} +(-3.67412 - 6.36376i) q^{59} +(-1.15420 + 1.99914i) q^{61} +(9.38914 - 5.42082i) q^{62} +(0.319008 + 0.184179i) q^{63} -1.00000 q^{64} +(3.10431 - 5.37683i) q^{66} +(5.83981 + 3.37162i) q^{67} +4.09841i q^{68} +7.97988 q^{69} +(0.994093 + 1.72182i) q^{71} +(0.0852224 + 0.0492032i) q^{72} +(7.95867 - 4.59494i) q^{73} +(-3.87752 - 6.71607i) q^{74} +(-3.37752 - 2.75542i) q^{76} -13.6435i q^{77} +(-8.90992 + 5.14414i) q^{78} +(3.07849 + 5.33210i) q^{79} +(4.34755 + 7.53017i) q^{81} +(6.92220 + 3.99653i) q^{82} +5.69159i q^{83} -6.37625 q^{84} +(2.19403 - 3.80018i) q^{86} +11.3188i q^{87} -3.64483i q^{88} +(-5.53983 + 9.59527i) q^{89} +(-11.3043 + 19.5795i) q^{91} +(4.05703 - 2.34233i) q^{92} +(15.9935 - 9.23386i) q^{93} -1.74324 q^{94} -1.70341 q^{96} +(-1.30356 + 0.752610i) q^{97} +(-6.07241 + 3.50591i) q^{98} +(-0.179337 + 0.310621i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 2 q^{6} + 22 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 + 2 * q^6 + 22 * q^9	\( 16 q + 8 q^{4} + 2 q^{6} + 22 q^{9} + 20 q^{11} + 12 q^{14} - 8 q^{16} - 2 q^{21} - 2 q^{24} - 36 q^{26} - 34 q^{29} + 44 q^{31} - 10 q^{34} - 22 q^{36} + 72 q^{39} + 14 q^{41} + 10 q^{44} - 24 q^{46} - 88 q^{49} - 18 q^{51} + 16 q^{54} + 24 q^{56} - 28 q^{59} - 18 q^{61} - 16 q^{64} - 8 q^{66} - 108 q^{69} + 28 q^{71} - 8 q^{74} + 34 q^{79} - 72 q^{81} - 4 q^{84} - 26 q^{86} - 28 q^{89} - 50 q^{91} + 56 q^{94} - 4 q^{96} + 120 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 2 * q^6 + 22 * q^9 + 20 * q^11 + 12 * q^14 - 8 * q^16 - 2 * q^21 - 2 * q^24 - 36 * q^26 - 34 * q^29 + 44 * q^31 - 10 * q^34 - 22 * q^36 + 72 * q^39 + 14 * q^41 + 10 * q^44 - 24 * q^46 - 88 * q^49 - 18 * q^51 + 16 * q^54 + 24 * q^56 - 28 * q^59 - 18 * q^61 - 16 * q^64 - 8 * q^66 - 108 * q^69 + 28 * q^71 - 8 * q^74 + 34 * q^79 - 72 * q^81 - 4 * q^84 - 26 * q^86 - 28 * q^89 - 50 * q^91 + 56 * q^94 - 4 * q^96 + 120 * q^99

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