LMFDB - Embedded newform 950.2.j.i.49.7

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			49.7
Root			$2.85614 - 0.765301i$ of defining polynomial
Character	$\chi$	$=$	950.49
Dual form			950.2.j.i.349.7

$q$-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 $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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	0.861225	−	0.508224i	$-0.169698\pi$
$3$	1.47519	+	0.851703i	0.851703	+	0.491731i	−0.00952194	+	0.999955i	$0.503031\pi$
$4$	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	$0.250134\pi$
$7$			3.74324i			1.41481i	−0.706808	+	0.707405i	$0.749866\pi$
$8$			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	−0.998522	−	0.0543441i	$-0.982693\pi$
$13$	−5.23065	+	3.01991i	−1.45072	+	0.837574i	−0.452198	+	0.891918i	$0.649360\pi$
$14$	−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	0.00345514	−	0.999994i	$-0.498900\pi$
$17$	−3.54932	−	2.04920i	−0.860838	−	0.497005i	−0.864293	+	0.502989i	$0.832234\pi$
$18$		−	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	−0.0133324	−	0.999911i	$-0.504244\pi$
$23$	4.05703	−	2.34233i	0.845950	−	0.488409i	0.859282	+	0.511502i	$0.170911\pi$
$24$	−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	−0.990038	−	0.140802i	$-0.955032\pi$
$29$	−3.32241	−	5.75459i	−0.616957	−	1.06860i	0.373081	−	0.927799i	$-0.378301\pi$
$30$		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	$0.220015\pi$
$37$			7.75505i			1.27492i	−0.770483	+	0.637461i	$0.779985\pi$
$38$	−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	−0.364550	−	0.931184i	$-0.618777\pi$
$41$	3.99653	−	6.92220i	0.624154	−	1.08107i	0.988704	−	0.149882i	$-0.0478894\pi$
$42$	−5.52200	+	3.18813i	−0.852062	+	0.491939i
$43$	3.80018	+	2.19403i	0.579521	+	0.334587i	0.760943	−	0.648819i	$-0.224737\pi$
$43$	3.80018	+	2.19403i	0.579521	+	0.334587i	−0.181422	+	0.983405i	$0.558070\pi$
$44$	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	−0.606048	−	0.795428i	$-0.707246\pi$
$47$	−1.50969	+	0.871618i	−0.220210	+	0.127139i	0.385837	+	0.922567i	$0.373913\pi$
$48$	−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	−0.600089	−	0.799933i	$-0.704868\pi$
$53$	−1.50969	+	0.871618i	−0.207371	+	0.119726i	0.392718	+	0.919659i	$0.371535\pi$
$54$	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	−0.999691	−	0.0248448i	$-0.992091\pi$
$59$	−3.67412	+	6.36376i	−0.478329	+	0.828491i	0.521362	+	0.853336i	$0.325424\pi$
$60$		0			0
$61$	−1.15420	−	1.99914i	−0.147781	−	0.255963i	0.782626	−	0.622492i	$-0.213880\pi$
$61$	−1.15420	−	1.99914i	−0.147781	−	0.255963i	−0.930407	+	0.366528i	$0.880546\pi$
$62$	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	−0.0988892	−	0.995098i	$-0.531529\pi$
$67$	5.83981	−	3.37162i	0.713447	−	0.411909i	0.812336	+	0.583190i	$0.198196\pi$
$68$		−	4.09841i		−	0.497005i
$69$	7.97988			0.960664
$70$		0			0
$71$	0.994093	−	1.72182i	0.117977	−	0.204342i	−0.800989	−	0.598679i	$-0.795692\pi$
$71$	0.994093	−	1.72182i	0.117977	−	0.204342i	0.918966	+	0.394337i	$0.129026\pi$
$72$	0.0852224	−	0.0492032i	0.0100436	−	0.00579865i
$73$	7.95867	+	4.59494i	0.931492	+	0.537797i	0.887283	−	0.461225i	$-0.152590\pi$
$73$	7.95867	+	4.59494i	0.931492	+	0.537797i	0.0442086	+	0.999022i	$0.485923\pi$
$74$	−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	−0.639242	−	0.769006i	$-0.720752\pi$
$79$	3.07849	−	5.33210i	0.346357	−	0.599909i	0.985599	+	0.169097i	$0.0540851\pi$
$80$		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	$-0.898878\pi$
$83$		−	5.69159i		−	0.624734i	0.949962	−	0.312367i	$-0.101122\pi$
$84$	−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	−0.994595	−	0.103835i	$-0.966889\pi$
$89$	−5.53983	−	9.59527i	−0.587221	−	1.01710i	0.407374	−	0.913261i	$-0.366445\pi$
$90$		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	0.432360	−	0.901701i	$-0.357681\pi$
$97$	−1.30356	−	0.752610i	−0.132356	−	0.0764159i	−0.564716	+	0.825285i	$0.691014\pi$
$98$	−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	0.992421	−	0.122883i	$-0.0392138\pi$
$101$	3.91735	+	6.78506i	0.389791	+	0.675138i	−0.602630	+	0.798021i	$0.705880\pi$
$102$		−	6.98125i		−	0.691247i
$103$			13.6036i			1.34041i	0.742178	+	0.670203i	$0.233793\pi$
$103$			13.6036i			1.34041i	−0.742178	+	0.670203i	$0.766207\pi$
$104$	−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	$-0.886057\pi$
$107$		−	7.24845i		−	0.700735i	0.936612	−	0.350367i	$-0.113943\pi$
$108$	4.57075	−	2.63892i	0.439820	−	0.253930i
$109$	2.24392	−	3.88659i	0.214929	−	0.372268i	−0.738322	−	0.674449i	$-0.764381\pi$
$109$	2.24392	−	3.88659i	0.214929	−	0.372268i	0.953251	+	0.302181i	$0.0977147\pi$
$110$		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	$-0.785220\pi$
$113$		−	13.2813i		−	1.24940i	0.780863	−	0.624702i	$-0.214780\pi$
$114$	−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	−0.626552	−	0.779380i	$-0.715534\pi$
$127$	−2.98488	+	1.72332i	−0.264865	+	0.152920i	0.361687	+	0.932300i	$0.382201\pi$
$128$	−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	0.238260	+	0.971201i	$0.423423\pi$
$131$	−8.26315	+	14.3122i	−0.721955	+	1.25046i	−0.960215	+	0.279261i	$0.909911\pi$
$132$			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	0.674124	−	0.738618i	$-0.264521\pi$
$137$	19.3227	−	11.1560i	1.65085	−	0.953118i	0.976724	−	0.214499i	$-0.0688120\pi$
$138$	6.91078	+	3.98994i	0.588284	+	0.339646i
$139$	−0.880992	−	1.52592i	−0.0747248	−	0.129427i	0.826242	−	0.563316i	$-0.190474\pi$
$139$	−0.880992	−	1.52592i	−0.0747248	−	0.129427i	−0.900967	+	0.433889i	$0.857141\pi$
$140$		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	−0.930505	−	0.366278i	$-0.880632\pi$
$149$	−1.80713	+	3.13005i	−0.148046	+	0.256424i	0.782459	+	0.622702i	$0.213965\pi$
$150$		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	0.206305	−	0.978488i	$-0.433856\pi$
$157$	−6.74033	−	3.89153i	−0.537937	−	0.310578i	−0.744242	+	0.667910i	$0.767189\pi$
$158$	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	$0.0686627\pi$
$163$			5.46539i			0.428082i	−0.976825	+	0.214041i	$0.931337\pi$
$164$	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	0.265400	−	0.964138i	$-0.414496\pi$
$167$	15.9348	−	9.19994i	1.23307	−	0.711913i	0.967668	+	0.252226i	$0.0811625\pi$
$168$	−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	−0.306275	−	0.951943i	$-0.599083\pi$
$173$	−16.8860	−	9.74914i	−1.28382	−	0.741214i	−0.977544	+	0.210729i	$0.932416\pi$
$174$	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	−0.994902	−	0.100843i	$-0.967846\pi$
$181$	−7.86746	−	13.6268i	−0.584784	−	1.01288i	0.410118	−	0.912032i	$-0.365487\pi$
$182$		−	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	0.229525	−	0.973303i	$-0.426283\pi$
$193$	−6.92701	−	3.99931i	−0.498617	−	0.287877i	−0.728142	+	0.685426i	$0.759616\pi$
$194$	−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	$-0.994539\pi$
$197$		−	0.481593i		−	0.0343121i	0.999853	−	0.0171560i	$-0.00546121\pi$
$198$		−	0.358674i		−	0.0254899i
$199$	11.6793	+	20.2292i	0.827926	+	1.43401i	0.899662	+	0.436587i	$0.143813\pi$
$199$	11.6793	+	20.2292i	0.827926	+	1.43401i	−0.0717359	+	0.997424i	$0.522854\pi$
$200$		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	−0.748074	−	0.663616i	$-0.769021\pi$
$211$	2.91491	−	5.04878i	0.200671	−	0.347572i	0.948745	+	0.316043i	$0.102354\pi$
$212$	−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	0.899209	−	0.437520i	$-0.144143\pi$
$223$	14.4838	+	8.36224i	0.969909	+	0.559977i	0.0707005	+	0.997498i	$0.477477\pi$
$224$	−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	$0.0441048\pi$
$227$			4.16186i			0.276232i	−0.990416	+	0.138116i	$0.955895\pi$
$228$	−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	0.0765832	−	0.997063i	$-0.475599\pi$
$233$	−11.4270	−	6.59738i	−0.748607	−	0.432209i	−0.825190	+	0.564855i	$0.808932\pi$
$234$	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	−0.975790	−	0.218711i	$-0.929815\pi$
$241$	−10.5146	−	18.2118i	−0.677304	−	1.17313i	0.298485	−	0.954414i	$-0.403519\pi$
$242$	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	−0.872329	−	0.488919i	$-0.837391\pi$
$251$	−13.6183	−	23.5876i	−0.859581	−	1.48884i	0.0127485	−	0.999919i	$-0.495942\pi$
$252$	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	−0.877094	−	0.480318i	$-0.840521\pi$
$257$	−14.4229	+	8.32705i	−0.899674	+	0.519427i	−0.0225796	+	0.999745i	$0.507188\pi$
$258$			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	0.552146	−	0.833748i	$-0.313809\pi$
$263$	1.72182	+	0.994093i	0.106172	+	0.0612984i	−0.445974	+	0.895046i	$0.647143\pi$
$264$	−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	−0.736333	−	0.676620i	$-0.763444\pi$
$269$	3.57224	−	6.18731i	0.217804	−	0.377247i	0.954136	+	0.299373i	$0.0967775\pi$
$270$		0			0
$271$	−5.47940	+	9.49060i	−0.332850	+	0.576513i	−0.983069	−	0.183234i	$-0.941344\pi$
$271$	−5.47940	+	9.49060i	−0.332850	+	0.576513i	0.650220	+	0.759746i	$0.274677\pi$
$272$	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	$-0.879846\pi$
$277$		−	12.2686i		−	0.737147i	0.929599	−	0.368574i	$-0.120154\pi$
$278$		−	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	0.999940	+	0.0109390i	$0.00348205\pi$
$281$	8.53983	+	14.7914i	0.509443	+	0.882382i	−0.490497	+	0.871443i	$0.663185\pi$
$282$	−2.57161	−	1.48472i	−0.153137	−	0.0884138i
$283$	−25.9918	−	15.0064i	−1.54505	−	0.892037i	−0.998508	−	0.0546077i	$-0.982609\pi$
$283$	−25.9918	−	15.0064i	−1.54505	−	0.892037i	−0.546546	−	0.837429i	$-0.684057\pi$
$284$	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	$0.227875\pi$
$293$			22.4677i			1.31258i	−0.754509	+	0.656289i	$0.772125\pi$
$294$	−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	0.847019	−	0.531563i	$-0.178395\pi$
$307$	14.1955	+	8.19578i	0.810181	+	0.467758i	−0.0368378	+	0.999321i	$0.511729\pi$
$308$	−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	0.0104296	−	0.999946i	$-0.496680\pi$
$313$	15.5975	−	9.00522i	0.881623	−	0.509005i	0.871193	+	0.490941i	$0.163347\pi$
$314$	−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	−0.944227	−	0.329296i	$-0.893189\pi$
$317$	−20.1398	+	11.6277i	−1.13116	+	0.653076i	−0.186935	+	0.982372i	$0.559855\pi$
$318$	−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	−0.457930	−	0.888988i	$-0.651409\pi$
$337$	−26.7429	−	15.4400i	−1.45678	−	0.841073i	−0.998851	+	0.0479153i	$0.984742\pi$
$338$	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	0.272804	−	0.962070i	$-0.412049\pi$
$347$	−7.89771	−	4.55974i	−0.423971	−	0.244780i	−0.696775	+	0.717290i	$0.745382\pi$
$348$	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	$0.0663508\pi$
$353$			7.77613i			0.413882i	−0.978353	+	0.206941i	$0.933649\pi$
$354$	−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	−0.779147	−	0.626841i	$-0.784347\pi$
$359$	2.90437	−	5.03052i	0.153287	−	0.265501i	0.932434	+	0.361340i	$0.117681\pi$
$360$		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	−0.910405	−	0.413719i	$-0.864230\pi$
$367$	−19.2974	+	11.1414i	−1.00732	+	0.581574i	−0.0969115	+	0.995293i	$0.530896\pi$
$368$			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	$-0.854379\pi$
$373$		−	17.0609i		−	0.883380i	0.897168	−	0.441690i	$-0.145621\pi$
$374$	−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	0.543345	−	0.839510i	$-0.317158\pi$
$383$	1.72182	+	0.994093i	0.0879809	+	0.0507958i	−0.455364	+	0.890305i	$0.650491\pi$
$384$	−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	0.956332	−	0.292282i	$-0.0944144\pi$
$389$	4.43854	+	7.68778i	0.225043	+	0.389786i	−0.731289	+	0.682067i	$0.761081\pi$
$390$		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	0.882884	−	0.469591i	$-0.155599\pi$
$397$	18.2840	+	10.5563i	0.917648	+	0.529804i	0.0347640	+	0.999396i	$0.488932\pi$
$398$			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	0.200642	+	0.979665i	$0.435697\pi$
$401$	−14.9806	+	25.9471i	−0.748094	+	1.29574i	−0.948735	+	0.316072i	$0.897636\pi$
$402$	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	0.809491	−	0.587132i	$-0.199743\pi$
$409$	−2.09772	−	3.63336i	−0.103726	−	0.179658i	−0.913217	+	0.407474i	$0.866410\pi$
$410$		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	−0.336056	−	0.941842i	$-0.609093\pi$
$421$	13.2883	−	23.0160i	0.647631	−	1.12173i	0.983687	−	0.179888i	$-0.0575736\pi$
$422$	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	0.868192	−	0.496228i	$-0.165282\pi$
$431$	0.0903049	+	0.156413i	0.00434983	+	0.00753413i	−0.863842	+	0.503762i	$0.831949\pi$
$432$	4.57075	+	2.63892i	0.219910	+	0.126965i
$433$	10.4013	−	6.00522i	0.499857	−	0.288592i	−0.228798	−	0.973474i	$-0.573479\pi$
$433$	10.4013	−	6.00522i	0.499857	−	0.288592i	0.728654	+	0.684882i	$0.240146\pi$
$434$	−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	0.294559	+	0.955633i	$0.404827\pi$
$439$	−14.2544	+	24.6893i	−0.680324	+	1.17835i	−0.974882	+	0.222722i	$0.928506\pi$
$440$		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	−0.665413	−	0.746476i	$-0.731744\pi$
$443$	−7.40142	+	4.27321i	−0.351652	+	0.203026i	0.313761	+	0.949502i	$0.398411\pi$
$444$	−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	$0.140133\pi$
$457$			18.2204i			0.852316i	−0.904649	+	0.426158i	$0.859867\pi$
$458$	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	0.269447	+	0.963015i	$0.413159\pi$
$461$	−15.0140	+	26.0050i	−0.699272	+	1.21117i	−0.968719	+	0.248160i	$0.920174\pi$
$462$	−20.1267	+	11.6202i	−0.936380	+	0.540619i
$463$			10.1656i			0.472434i	0.971700	+	0.236217i	$0.0759076\pi$
$463$			10.1656i			0.472434i	−0.971700	+	0.236217i	$0.924092\pi$
$464$	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	$-0.898007\pi$
$467$		−	13.6129i		−	0.629930i	0.949103	−	0.314965i	$-0.101993\pi$
$468$			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	0.921355	−	0.388722i	$-0.127083\pi$
$479$	2.71463	+	4.70188i	0.124035	+	0.214835i	−0.797320	+	0.603556i	$0.793750\pi$
$480$		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	$-0.735937\pi$
$487$		−	32.5569i		−	1.47529i	0.675188	−	0.737646i	$-0.264063\pi$
$488$	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	0.278746	+	0.960365i	$0.410081\pi$
$491$	−15.3410	+	26.5713i	−0.692328	+	1.19915i	−0.971073	+	0.238782i	$0.923252\pi$
$492$	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	−0.954776	−	0.297325i	$-0.903906\pi$
$499$	−4.91213	+	8.50807i	−0.219897	+	0.380873i	0.734879	+	0.678198i	$0.237239\pi$
$500$		0			0
$501$	31.3425			1.40028
$502$		−	27.2366i		−	1.21563i
$503$	13.1203	−	7.57502i	0.585006	−	0.337754i	−0.178114	−	0.984010i	$-0.557000\pi$
$503$	13.1203	−	7.57502i	0.585006	−	0.337754i	0.763121	+	0.646256i	$0.223666\pi$
$504$	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	0.840110	−	0.542417i	$-0.182491\pi$
$509$	−1.12110	−	1.94180i	−0.0496919	−	0.0860690i	−0.889801	+	0.456348i	$0.849157\pi$
$510$		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	−0.984549	−	0.175108i	$-0.943973\pi$
$523$	−30.3057	+	17.4970i	−1.32518	+	0.765091i	−0.340627	+	0.940199i	$0.610639\pi$
$524$	−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	0.989579	+	0.143994i	$0.0459946\pi$
$541$	14.4090	+	24.9571i	0.619492	+	1.07299i	−0.370087	+	0.928997i	$0.620672\pi$
$542$	−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	−0.957782	−	0.287496i	$-0.907177\pi$
$547$	−27.7778	+	16.0375i	−1.18769	+	0.685715i	−0.229912	+	0.973211i	$0.573844\pi$
$548$	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	−0.297393	−	0.954755i	$-0.596117\pi$
$557$	8.98610	−	5.18813i	0.380753	−	0.219828i	0.678146	+	0.734927i	$0.262784\pi$
$558$		−	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	$-0.943040\pi$
$563$		−	8.44664i		−	0.355984i	0.984032	−	0.177992i	$-0.0569600\pi$
$564$	−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	$0.0439717\pi$
$577$			6.61544i			0.275404i	−0.990474	+	0.137702i	$0.956028\pi$
$578$		−	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	0.219432	−	0.975628i	$-0.429579\pi$
$587$	−12.4961	−	7.21463i	−0.515770	−	0.297780i	−0.735202	+	0.677848i	$0.762913\pi$
$588$		−	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	−0.821248	−	0.570572i	$-0.806722\pi$
$593$	−17.9652	+	10.3722i	−0.737742	+	0.425935i	0.0835060	+	0.996507i	$0.473388\pi$
$594$	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	0.607078	−	0.794642i	$-0.292341\pi$
$599$	−9.41389	−	16.3053i	−0.384641	−	0.666218i	−0.991719	+	0.128424i	$0.959008\pi$
$600$		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	$-0.802869\pi$
$607$		−	28.6025i		−	1.16094i	0.814281	−	0.580470i	$-0.197131\pi$
$608$	−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	0.364011	−	0.931395i	$-0.381407\pi$
$613$	−6.45202	−	3.72507i	−0.260594	−	0.150454i	−0.624606	+	0.780940i	$0.714740\pi$
$614$	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	−0.934306	−	0.356473i	$-0.883979\pi$
$617$	−27.1432	+	15.6711i	−1.09274	+	0.630896i	−0.158438	+	0.987369i	$0.550646\pi$
$618$	−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	0.965309	−	0.261111i	$-0.0840887\pi$
$631$	6.44386	+	11.1611i	0.256526	+	0.444316i	−0.708783	+	0.705427i	$0.750755\pi$
$632$	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	−0.448964	−	0.893550i	$-0.648207\pi$
$641$	13.9086	−	24.0903i	0.549355	−	0.951511i	0.998319	−	0.0579612i	$-0.0184600\pi$
$642$	10.6929	−	6.17353i	0.422014	−	0.243650i
$643$	−14.7275	−	8.50292i	−0.580795	−	0.335322i	0.180654	−	0.983547i	$-0.442179\pi$
$643$	−14.7275	−	8.50292i	−0.580795	−	0.335322i	−0.761449	+	0.648224i	$0.775512\pi$
$644$	−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	$0.312940\pi$
$647$			42.3379i			1.66447i	−0.554420	+	0.832237i	$0.687060\pi$
$648$	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	$-0.599390\pi$
$653$		−	48.6365i		−	1.90329i	0.307194	−	0.951647i	$-0.400610\pi$
$654$	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	0.952749	−	0.303758i	$-0.0982416\pi$
$659$	5.47593	+	9.48459i	0.213312	+	0.369467i	−0.739437	+	0.673226i	$0.764908\pi$
$660$		0			0
$661$	12.3214	+	21.3413i	0.479246	+	0.830079i	0.999717	−	0.0238007i	$-0.00757670\pi$
$661$	12.3214	+	21.3413i	0.479246	+	0.830079i	−0.520470	+	0.853880i	$0.674243\pi$
$662$	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	$0.0318329\pi$
$673$			5.18012i			0.199679i	−0.995004	+	0.0998395i	$0.968167\pi$
$674$	−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	$0.338146\pi$
$677$			45.4548i			1.74697i	−0.486851	+	0.873485i	$0.661854\pi$
$678$	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	$0.0197741\pi$
$683$			3.24495i			0.124165i	−0.998071	+	0.0620823i	$0.980226\pi$
$684$	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	−0.287420	+	0.957805i	$0.592797\pi$
$701$	−25.7667	+	44.6292i	−0.973193	+	1.68562i	−0.685773	+	0.727815i	$0.740536\pi$
$702$			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	0.937083	−	0.349107i	$-0.113515\pi$
$709$	4.42556	+	7.66530i	0.166205	+	0.287876i	−0.770877	+	0.636984i	$0.780182\pi$
$710$		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	0.0272540	−	0.999629i	$-0.491324\pi$
$719$	23.5785	−	40.8392i	0.879331	−	1.52305i	0.852077	−	0.523417i	$-0.175343\pi$
$720$		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	0.694627	−	0.719371i	$-0.255570\pi$
$727$	11.2960	+	6.52177i	0.418947	+	0.241879i	−0.275680	+	0.961250i	$0.588903\pi$
$728$	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	$0.0831606\pi$
$733$			13.9861i			0.516590i	−0.966066	+	0.258295i	$0.916839\pi$
$734$	−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	−0.856027	−	0.516931i	$-0.827074\pi$
$739$	0.534508	−	0.925795i	0.0196622	−	0.0340559i	0.875689	+	0.482875i	$0.160408\pi$
$740$		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	0.650541	−	0.759472i	$-0.274542\pi$
$743$	8.67048	+	5.00591i	0.318089	+	0.183649i	−0.332451	+	0.943120i	$0.607876\pi$
$744$	−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	−0.987236	−	0.159261i	$-0.949089\pi$
$751$	−17.3070	−	29.9767i	−0.631543	−	1.09386i	0.355694	−	0.934603i	$-0.384245\pi$
$752$		−	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	0.551838	−	0.833951i	$-0.313927\pi$
$757$	2.90364	+	1.67642i	0.105535	+	0.0609305i	−0.446304	+	0.894882i	$0.647260\pi$
$758$	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	−0.989896	−	0.141795i	$-0.954713\pi$
$769$	−17.1306	−	29.6711i	−0.617746	−	1.06997i	0.372150	−	0.928172i	$-0.378621\pi$
$770$		0			0
$771$	−28.3687			−1.02167
$772$		−	7.99863i		−	0.287877i
$773$	−10.3608	+	5.98184i	−0.372654	+	0.215152i	−0.674617	−	0.738168i	$-0.735691\pi$
$773$	−10.3608	+	5.98184i	−0.372654	+	0.215152i	0.301963	+	0.953320i	$0.402358\pi$
$774$	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	$-0.805237\pi$
$787$		−	32.2277i		−	1.14879i	0.818578	−	0.574396i	$-0.194763\pi$
$788$	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	$-0.750103\pi$
$797$		−	39.9120i		−	1.41376i	0.707335	−	0.706878i	$-0.249897\pi$
$798$	−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	0.620556	−	0.784162i	$-0.286907\pi$
$811$	−10.5035	−	18.1925i	−0.368827	−	0.638826i	−0.989382	+	0.145336i	$0.953574\pi$
$812$	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	−0.978278	−	0.207299i	$-0.933533\pi$
$821$	−19.1593	−	33.1849i	−0.668665	−	1.15816i	0.309613	−	0.950863i	$-0.399801\pi$
$822$	32.9144	+	19.0031i	1.14802	+	0.662810i
$823$	46.3479	−	26.7590i	1.61559	−	0.932760i	0.627545	−	0.778580i	$-0.284060\pi$
$823$	46.3479	−	26.7590i	1.61559	−	0.932760i	0.988043	−	0.154179i	$-0.0492734\pi$
$824$	−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	−0.780308	−	0.625396i	$-0.784938\pi$
$827$	−18.0843	+	10.4410i	−0.628853	+	0.363068i	0.151455	+	0.988464i	$0.451604\pi$
$828$		−	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	−0.996941	−	0.0781610i	$-0.975095\pi$
$839$	−12.4778	+	21.6122i	−0.430781	+	0.746135i	0.566160	+	0.824296i	$0.308429\pi$
$840$		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	0.0300087	−	0.999550i	$-0.490447\pi$
$853$	−23.9672	−	13.8375i	−0.820622	−	0.473787i	−0.850631	+	0.525763i	$0.823780\pi$
$854$	8.64091			0.295686
$855$		0			0
$856$	7.24845			0.247747
$857$	18.1865	+	10.5000i	0.621240	+	0.358673i	0.777352	−	0.629066i	$-0.216563\pi$
$857$	18.1865	+	10.5000i	0.621240	+	0.358673i	−0.156112	+	0.987739i	$0.549896\pi$
$858$	−32.4751	−	18.7495i	−1.10868	−	0.640098i
$859$	11.0617	+	19.1594i	0.377420	+	0.653711i	0.990686	−	0.136165i	$-0.0434778\pi$
$859$	11.0617	+	19.1594i	0.377420	+	0.653711i	−0.613266	+	0.789877i	$0.710144\pi$
$860$		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	$-0.821987\pi$
$863$		−	31.1716i		−	1.06109i	0.847655	−	0.530547i	$-0.178013\pi$
$864$	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	0.166457	−	0.986049i	$-0.446767\pi$
$877$	−17.8946	−	10.3314i	−0.604257	−	0.348868i	−0.770715	+	0.637180i	$0.780101\pi$
$878$	−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	−0.739727	−	0.672908i	$-0.765045\pi$
$883$	−15.6551	+	9.03845i	−0.526835	+	0.304168i	0.212892	+	0.977076i	$0.431712\pi$
$884$	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	0.377898	−	0.925847i	$-0.376647\pi$
$887$	40.7620	−	23.5340i	1.36865	−	0.790193i	0.990756	+	0.135654i	$0.0433136\pi$
$888$	−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	0.182746	−	0.983160i	$-0.441501\pi$
$907$	−17.3869	−	10.0383i	−0.577322	−	0.333317i	−0.760068	+	0.649843i	$0.774835\pi$
$908$	−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	−0.800526	−	0.599298i	$-0.795447\pi$
$929$	3.61925	−	6.26873i	0.118744	−	0.205670i	0.919270	+	0.393627i	$0.128780\pi$
$930$		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	0.138124	−	0.990415i	$-0.455893\pi$
$937$	32.5974	−	18.8201i	1.06491	−	0.614826i	0.926786	+	0.375589i	$0.122559\pi$
$938$			25.2415i			0.824165i
$939$	30.6791			1.00117
$940$		0			0
$941$	12.9631	+	22.4527i	0.422585	+	0.731938i	0.996191	−	0.0871927i	$-0.0277896\pi$
$941$	12.9631	+	22.4527i	0.422585	+	0.731938i	−0.573607	+	0.819131i	$0.694456\pi$
$942$		−	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	0.950509	−	0.310697i	$-0.100563\pi$
$947$	35.5953	+	20.5510i	1.15669	+	0.667816i	0.206183	+	0.978513i	$0.433896\pi$
$948$	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	0.679356	−	0.733809i	$-0.262259\pi$
$953$	11.8400	+	6.83584i	0.383536	+	0.221435i	−0.295820	+	0.955244i	$0.595593\pi$
$954$	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	0.984146	−	0.177363i	$-0.0567566\pi$
$967$	41.1289	+	23.7458i	1.32262	+	0.763614i	0.338472	+	0.940976i	$0.390090\pi$
$968$			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	−0.933062	−	0.359716i	$-0.882874\pi$
$971$	−4.83017	+	8.36611i	−0.155008	+	0.268481i	0.778054	+	0.628197i	$0.216207\pi$
$972$	−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	$-0.786714\pi$
$977$		−	38.8232i		−	1.24206i	0.783786	−	0.621032i	$-0.213286\pi$
$978$	−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	−0.332654	−	0.943049i	$-0.607944\pi$
$983$	−41.2505	−	23.8160i	−1.31569	−	0.759611i	−0.983031	+	0.183438i	$0.941277\pi$
$984$	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	−0.813529	−	0.581524i	$-0.802457\pi$
$991$	3.04886	−	5.28078i	0.0968503	−	0.167750i	0.910379	+	0.413775i	$0.135790\pi$
$992$	−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	−0.224444	−	0.974487i	$-0.572057\pi$
$997$	16.0170	−	9.24743i	0.507264	−	0.292869i	0.731708	+	0.681618i	$0.238723\pi$
$998$	−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.49.7		16
5.2	odd	4		950.2.e.l.201.3	✓	8
5.3	odd	4		950.2.e.m.201.2	yes	8
5.4	even	2	inner	950.2.j.i.49.2		16
19.7	even	3	inner	950.2.j.i.349.2		16
95.7	odd	12		950.2.e.l.501.3	yes	8
95.64	even	6	inner	950.2.j.i.349.7		16
95.83	odd	12		950.2.e.m.501.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.e.l.201.3	✓	8	5.2	odd	4
950.2.e.l.501.3	yes	8	95.7	odd	12
950.2.e.m.201.2	yes	8	5.3	odd	4
950.2.e.m.501.2	yes	8	95.83	odd	12
950.2.j.i.49.2		16	5.4	even	2	inner
950.2.j.i.49.7		16	1.1	even	1	trivial
950.2.j.i.349.2		16	19.7	even	3	inner
950.2.j.i.349.7		16	95.64	even	6	inner

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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