LMFDB - Embedded newform 950.2.j.f.349.2

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.1731891456.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 $ x^8 - 9x^6 + 65x^4 - 144*x^2 + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			349.2
Root			$2.21837 - 1.28078i$ of defining polynomial
Character	$\chi$	$=$	950.349
Dual form			950.2.j.f.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(2.21837 - 1.28078i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.28078 + 2.21837i) q^{6} +0.438447i q^{7} +1.00000i q^{8} +(1.78078 - 3.08440i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(2.21837 - 1.28078i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.28078 + 2.21837i) q^{6} +0.438447i q^{7} +1.00000i q^{8} +(1.78078 - 3.08440i) q^{9} +1.00000 q^{11} -2.56155i q^{12} +(-1.73205 - 1.00000i) q^{13} +(-0.219224 - 0.379706i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(4.43674 - 2.56155i) q^{17} +3.56155i q^{18} +(2.50000 - 3.57071i) q^{19} +(0.561553 + 0.972638i) q^{21} +(-0.866025 + 0.500000i) q^{22} +(-4.05703 - 2.34233i) q^{23} +(1.28078 + 2.21837i) q^{24} +2.00000 q^{26} -1.43845i q^{27} +(0.379706 + 0.219224i) q^{28} +(1.00000 - 1.73205i) q^{29} +10.2462 q^{31} +(0.866025 + 0.500000i) q^{32} +(2.21837 - 1.28078i) q^{33} +(-2.56155 + 4.43674i) q^{34} +(-1.78078 - 3.08440i) q^{36} -4.68466i q^{37} +(-0.379706 + 4.34233i) q^{38} -5.12311 q^{39} +(3.06155 + 5.30277i) q^{41} +(-0.972638 - 0.561553i) q^{42} +(-2.70469 + 1.56155i) q^{43} +(0.500000 - 0.866025i) q^{44} +4.68466 q^{46} +(-2.49146 - 1.43845i) q^{47} +(-2.21837 - 1.28078i) q^{48} +6.80776 q^{49} +(6.56155 - 11.3649i) q^{51} +(-1.73205 + 1.00000i) q^{52} +(-6.54850 - 3.78078i) q^{53} +(0.719224 + 1.24573i) q^{54} -0.438447 q^{56} +(0.972638 - 11.1231i) q^{57} +2.00000i q^{58} +(7.28078 + 12.6107i) q^{59} +(-2.56155 + 4.43674i) q^{61} +(-8.87348 + 5.12311i) q^{62} +(1.35234 + 0.780776i) q^{63} -1.00000 q^{64} +(-1.28078 + 2.21837i) q^{66} +(-8.17394 - 4.71922i) q^{67} -5.12311i q^{68} -12.0000 q^{69} +(-8.12311 - 14.0696i) q^{71} +(3.08440 + 1.78078i) q^{72} +(1.45896 - 0.842329i) q^{73} +(2.34233 + 4.05703i) q^{74} +(-1.84233 - 3.95042i) q^{76} +0.438447i q^{77} +(4.43674 - 2.56155i) q^{78} +(-5.56155 - 9.63289i) q^{79} +(3.50000 + 6.06218i) q^{81} +(-5.30277 - 3.06155i) q^{82} +10.8078i q^{83} +1.12311 q^{84} +(1.56155 - 2.70469i) q^{86} -5.12311i q^{87} +1.00000i q^{88} +(-1.34233 + 2.32498i) q^{89} +(0.438447 - 0.759413i) q^{91} +(-4.05703 + 2.34233i) q^{92} +(22.7299 - 13.1231i) q^{93} +2.87689 q^{94} +2.56155 q^{96} +(1.45896 - 0.842329i) q^{97} +(-5.89570 + 3.40388i) q^{98} +(1.78078 - 3.08440i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} - 2 q^{6} + 6 q^{9}+O(q^{10}) $ 8 * q + 4 * q^4 - 2 * q^6 + 6 * q^9	$ 8 q + 4 q^{4} - 2 q^{6} + 6 q^{9} + 8 q^{11} - 10 q^{14} - 4 q^{16} + 20 q^{19} - 12 q^{21} + 2 q^{24} + 16 q^{26} + 8 q^{29} + 16 q^{31} - 4 q^{34} - 6 q^{36} - 8 q^{39} + 8 q^{41} + 4 q^{44} - 12 q^{46} - 28 q^{49} + 36 q^{51} + 14 q^{54} - 20 q^{56} + 50 q^{59} - 4 q^{61} - 8 q^{64} - 2 q^{66} - 96 q^{69} - 32 q^{71} - 6 q^{74} + 10 q^{76} - 28 q^{79} + 28 q^{81} - 24 q^{84} - 4 q^{86} + 14 q^{89} + 20 q^{91} + 56 q^{94} + 4 q^{96} + 6 q^{99}+O(q^{100}) $ 8 * q + 4 * q^4 - 2 * q^6 + 6 * q^9 + 8 * q^11 - 10 * q^14 - 4 * q^16 + 20 * q^19 - 12 * q^21 + 2 * q^24 + 16 * q^26 + 8 * q^29 + 16 * q^31 - 4 * q^34 - 6 * q^36 - 8 * q^39 + 8 * q^41 + 4 * q^44 - 12 * q^46 - 28 * q^49 + 36 * q^51 + 14 * q^54 - 20 * q^56 + 50 * q^59 - 4 * q^61 - 8 * q^64 - 2 * q^66 - 96 * q^69 - 32 * q^71 - 6 * q^74 + 10 * q^76 - 28 * q^79 + 28 * q^81 - 24 * q^84 - 4 * q^86 + 14 * q^89 + 20 * q^91 + 56 * q^94 + 4 * q^96 + 6 * 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
$3$	2.21837	−	1.28078i	1.28078	−	0.739457i	0.303786	−	0.952740i	$-0.401749\pi$
$3$	2.21837	−	1.28078i	1.28078	−	0.739457i	0.976990	+	0.213284i	$0.0684158\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.28078	+	2.21837i	−0.522875	+	0.905646i
$7$			0.438447i			0.165717i	0.996561	+	0.0828587i	$0.0264050\pi$
$7$			0.438447i			0.165717i	−0.996561	+	0.0828587i	$0.973595\pi$
$8$			1.00000i			0.353553i
$9$	1.78078	−	3.08440i	0.593592	−	1.02813i
$10$		0			0
$11$	1.00000			0.301511			0.150756	−	0.988571i	$-0.451829\pi$
$11$	1.00000			0.301511			0.150756	+	0.988571i	$0.451829\pi$
$12$		−	2.56155i		−	0.739457i
$13$	−1.73205	−	1.00000i	−0.480384	−	0.277350i	0.240192	−	0.970725i	$-0.422790\pi$
$13$	−1.73205	−	1.00000i	−0.480384	−	0.277350i	−0.720577	+	0.693375i	$0.756123\pi$
$14$	−0.219224	−	0.379706i	−0.0585900	−	0.101481i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	4.43674	−	2.56155i	1.07607	−	0.621268i	0.146235	−	0.989250i	$-0.453285\pi$
$17$	4.43674	−	2.56155i	1.07607	−	0.621268i	0.929833	+	0.367982i	$0.119951\pi$
$18$			3.56155i			0.839466i
$19$	2.50000	−	3.57071i	0.573539	−	0.819178i
$19$	2.50000	−	3.57071i	0.573539	−	0.819178i
$20$		0			0
$21$	0.561553	+	0.972638i	0.122541	+	0.212247i
$22$	−0.866025	+	0.500000i	−0.184637	+	0.106600i
$23$	−4.05703	−	2.34233i	−0.845950	−	0.488409i	0.0133324	−	0.999911i	$-0.495756\pi$
$23$	−4.05703	−	2.34233i	−0.845950	−	0.488409i	−0.859282	+	0.511502i	$0.829089\pi$
$24$	1.28078	+	2.21837i	0.261437	+	0.452823i
$25$		0			0
$26$	2.00000			0.392232
$27$		−	1.43845i		−	0.276829i
$28$	0.379706	+	0.219224i	0.0717578	+	0.0414294i
$29$	1.00000	−	1.73205i	0.185695	−	0.321634i	−0.758115	−	0.652121i	$-0.773880\pi$
$29$	1.00000	−	1.73205i	0.185695	−	0.321634i	0.943811	+	0.330487i	$0.107213\pi$
$30$		0			0
$31$	10.2462			1.84027			0.920137	−	0.391597i	$-0.128077\pi$
$31$	10.2462			1.84027			0.920137	+	0.391597i	$0.128077\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	2.21837	−	1.28078i	0.386169	−	0.222955i
$34$	−2.56155	+	4.43674i	−0.439303	+	0.760895i
$35$		0			0
$36$	−1.78078	−	3.08440i	−0.296796	−	0.514066i
$37$		−	4.68466i		−	0.770153i	−0.922885	−	0.385077i	$-0.874175\pi$
$37$		−	4.68466i		−	0.770153i	0.922885	−	0.385077i	$-0.125825\pi$
$38$	−0.379706	+	4.34233i	−0.0615965	+	0.704419i
$39$	−5.12311			−0.820353
$40$		0			0
$41$	3.06155	+	5.30277i	0.478134	+	0.828153i	0.999686	−	0.0250670i	$-0.00797991\pi$
$41$	3.06155	+	5.30277i	0.478134	+	0.828153i	−0.521552	+	0.853220i	$0.674647\pi$
$42$	−0.972638	−	0.561553i	−0.150081	−	0.0866495i
$43$	−2.70469	+	1.56155i	−0.412461	+	0.238135i	−0.691847	−	0.722044i	$-0.743203\pi$
$43$	−2.70469	+	1.56155i	−0.412461	+	0.238135i	0.279385	+	0.960179i	$0.409869\pi$
$44$	0.500000	−	0.866025i	0.0753778	−	0.130558i
$45$		0			0
$46$	4.68466			0.690715
$47$	−2.49146	−	1.43845i	−0.363417	−	0.209819i	0.307161	−	0.951657i	$-0.400621\pi$
$47$	−2.49146	−	1.43845i	−0.363417	−	0.209819i	−0.670579	+	0.741838i	$0.733954\pi$
$48$	−2.21837	−	1.28078i	−0.320194	−	0.184864i
$49$	6.80776			0.972538
$50$		0			0
$51$	6.56155	−	11.3649i	0.918801	−	1.59141i
$52$	−1.73205	+	1.00000i	−0.240192	+	0.138675i
$53$	−6.54850	−	3.78078i	−0.899505	−	0.519330i	−0.0224656	−	0.999748i	$-0.507152\pi$
$53$	−6.54850	−	3.78078i	−0.899505	−	0.519330i	−0.877040	+	0.480418i	$0.840485\pi$
$54$	0.719224	+	1.24573i	0.0978739	+	0.169523i
$55$		0			0
$56$	−0.438447			−0.0585900
$57$	0.972638	−	11.1231i	0.128829	−	1.47329i
$58$			2.00000i			0.262613i
$59$	7.28078	+	12.6107i	0.947876	+	1.64177i	0.749887	+	0.661566i	$0.230108\pi$
$59$	7.28078	+	12.6107i	0.947876	+	1.64177i	0.197989	+	0.980204i	$0.436559\pi$
$60$		0			0
$61$	−2.56155	+	4.43674i	−0.327973	+	0.568066i	−0.982110	−	0.188310i	$-0.939699\pi$
$61$	−2.56155	+	4.43674i	−0.327973	+	0.568066i	0.654136	+	0.756377i	$0.273032\pi$
$62$	−8.87348	+	5.12311i	−1.12693	+	0.650635i
$63$	1.35234	+	0.780776i	0.170379	+	0.0983686i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−1.28078	+	2.21837i	−0.157653	+	0.273062i
$67$	−8.17394	−	4.71922i	−0.998605	−	0.576545i	−0.0907698	−	0.995872i	$-0.528933\pi$
$67$	−8.17394	−	4.71922i	−0.998605	−	0.576545i	−0.907835	+	0.419327i	$0.862266\pi$
$68$		−	5.12311i		−	0.621268i
$69$	−12.0000			−1.44463
$70$		0			0
$71$	−8.12311	−	14.0696i	−0.964035	−	1.66976i	−0.712185	−	0.701992i	$-0.752294\pi$
$71$	−8.12311	−	14.0696i	−0.964035	−	1.66976i	−0.251850	−	0.967766i	$-0.581039\pi$
$72$	3.08440	+	1.78078i	0.363499	+	0.209867i
$73$	1.45896	−	0.842329i	0.170758	−	0.0985872i	−0.412185	−	0.911100i	$-0.635234\pi$
$73$	1.45896	−	0.842329i	0.170758	−	0.0985872i	0.582943	+	0.812513i	$0.301901\pi$
$74$	2.34233	+	4.05703i	0.272290	+	0.471621i
$75$		0			0
$76$	−1.84233	−	3.95042i	−0.211330	−	0.453144i
$77$			0.438447i			0.0499657i
$78$	4.43674	−	2.56155i	0.502362	−	0.290039i
$79$	−5.56155	−	9.63289i	−0.625724	−	1.08379i	−0.988400	−	0.151870i	$-0.951470\pi$
$79$	−5.56155	−	9.63289i	−0.625724	−	1.08379i	0.362677	−	0.931915i	$-0.381863\pi$
$80$		0			0
$81$	3.50000	+	6.06218i	0.388889	+	0.673575i
$82$	−5.30277	−	3.06155i	−0.585592	−	0.338092i
$83$			10.8078i			1.18631i	0.805090	+	0.593153i	$0.202117\pi$
$83$			10.8078i			1.18631i	−0.805090	+	0.593153i	$0.797883\pi$
$84$	1.12311			0.122541
$85$		0			0
$86$	1.56155	−	2.70469i	0.168387	−	0.291654i
$87$		−	5.12311i		−	0.549255i
$88$			1.00000i			0.106600i
$89$	−1.34233	+	2.32498i	−0.142287	+	0.246448i	−0.928357	−	0.371689i	$-0.878779\pi$
$89$	−1.34233	+	2.32498i	−0.142287	+	0.246448i	0.786071	+	0.618137i	$0.212112\pi$
$90$		0			0
$91$	0.438447	−	0.759413i	0.0459618	−	0.0796081i
$92$	−4.05703	+	2.34233i	−0.422975	+	0.244205i
$93$	22.7299	−	13.1231i	2.35698	−	1.36080i
$94$	2.87689			0.296729
$95$		0			0
$96$	2.56155			0.261437
$97$	1.45896	−	0.842329i	0.148135	−	0.0855256i	−0.424101	−	0.905615i	$-0.639410\pi$
$97$	1.45896	−	0.842329i	0.148135	−	0.0855256i	0.572235	+	0.820089i	$0.306076\pi$
$98$	−5.89570	+	3.40388i	−0.595555	+	0.343844i
$99$	1.78078	−	3.08440i	0.178975	−	0.309993i
$100$		0			0
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	−0.999996	−	0.00286291i	$-0.999089\pi$
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	0.502477	+	0.864590i	$0.332422\pi$
$102$			13.1231i			1.29938i
$103$			5.80776i			0.572256i	0.958191	+	0.286128i	$0.0923683\pi$
$103$			5.80776i			0.572256i	−0.958191	+	0.286128i	$0.907632\pi$
$104$	1.00000	−	1.73205i	0.0980581	−	0.169842i
$105$		0			0
$106$	7.56155			0.734443
$107$			2.24621i			0.217149i	0.994088	+	0.108575i	$0.0346287\pi$
$107$			2.24621i			0.217149i	−0.994088	+	0.108575i	$0.965371\pi$
$108$	−1.24573	−	0.719224i	−0.119871	−	0.0692073i
$109$	−7.12311	−	12.3376i	−0.682270	−	1.18173i	−0.974286	−	0.225313i	$-0.927660\pi$
$109$	−7.12311	−	12.3376i	−0.682270	−	1.18173i	0.292017	−	0.956413i	$-0.405674\pi$
$110$		0			0
$111$	−6.00000	−	10.3923i	−0.569495	−	0.986394i
$112$	0.379706	−	0.219224i	0.0358789	−	0.0207147i
$113$			16.8078i			1.58114i	0.612371	+	0.790571i	$0.290216\pi$
$113$			16.8078i			1.58114i	−0.612371	+	0.790571i	$0.709784\pi$
$114$	4.71922	+	10.1192i	0.441996	+	0.947751i
$115$		0			0
$116$	−1.00000	−	1.73205i	−0.0928477	−	0.160817i
$117$	−6.16879	+	3.56155i	−0.570305	+	0.329266i
$118$	−12.6107	−	7.28078i	−1.16091	−	0.670250i
$119$	1.12311	+	1.94528i	0.102955	+	0.178323i
$120$		0			0
$121$	−10.0000			−0.909091
$122$		−	5.12311i		−	0.463824i
$123$	13.5833	+	7.84233i	1.22477	+	0.707119i
$124$	5.12311	−	8.87348i	0.460068	−	0.796862i
$125$		0			0
$126$	−1.56155			−0.139114
$127$	13.4767	+	7.78078i	1.19586	+	0.690432i	0.959630	−	0.281264i	$-0.0907537\pi$
$127$	13.4767	+	7.78078i	1.19586	+	0.690432i	0.236233	+	0.971696i	$0.424087\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−4.00000	+	6.92820i	−0.352180	+	0.609994i
$130$		0			0
$131$	8.06155	+	13.9630i	0.704341	+	1.21995i	0.966929	+	0.255046i	$0.0820908\pi$
$131$	8.06155	+	13.9630i	0.704341	+	1.21995i	−0.262588	+	0.964908i	$0.584576\pi$
$132$		−	2.56155i		−	0.222955i
$133$	1.56557	+	1.09612i	0.135752	+	0.0950455i
$134$	9.43845			0.815358
$135$		0			0
$136$	2.56155	+	4.43674i	0.219651	+	0.380447i
$137$	4.70983	+	2.71922i	0.402388	+	0.232319i	0.687514	−	0.726171i	$-0.258702\pi$
$137$	4.70983	+	2.71922i	0.402388	+	0.232319i	−0.285126	+	0.958490i	$0.592035\pi$
$138$	10.3923	−	6.00000i	0.884652	−	0.510754i
$139$	4.40388	−	7.62775i	0.373532	−	0.646977i	−0.616574	−	0.787297i	$-0.711480\pi$
$139$	4.40388	−	7.62775i	0.373532	−	0.646977i	0.990106	+	0.140320i	$0.0448131\pi$
$140$		0			0
$141$	−7.36932			−0.620608
$142$	14.0696	+	8.12311i	1.18070	+	0.681676i
$143$	−1.73205	−	1.00000i	−0.144841	−	0.0836242i
$144$	−3.56155			−0.296796
$145$		0			0
$146$	−0.842329	+	1.45896i	−0.0697117	+	0.120744i
$147$	15.1021	−	8.71922i	1.24560	−	0.719149i
$148$	−4.05703	−	2.34233i	−0.333486	−	0.192538i
$149$	8.00000	+	13.8564i	0.655386	+	1.13516i	0.981797	+	0.189933i	$0.0608272\pi$
$149$	8.00000	+	13.8564i	0.655386	+	1.13516i	−0.326411	+	0.945228i	$0.605840\pi$
$150$		0			0
$151$	20.4924			1.66765			0.833825	−	0.552029i	$-0.186146\pi$
$151$	20.4924			1.66765			0.833825	+	0.552029i	$0.186146\pi$
$152$	3.57071	+	2.50000i	0.289623	+	0.202777i
$153$		−	18.2462i		−	1.47512i
$154$	−0.219224	−	0.379706i	−0.0176655	−	0.0305976i
$155$		0			0
$156$	−2.56155	+	4.43674i	−0.205088	+	0.355223i
$157$	2.11176	−	1.21922i	0.168537	−	0.0973046i	−0.413359	−	0.910568i	$-0.635645\pi$
$157$	2.11176	−	1.21922i	0.168537	−	0.0973046i	0.581896	+	0.813263i	$0.302311\pi$
$158$	9.63289	+	5.56155i	0.766352	+	0.442453i
$159$	−19.3693			−1.53609
$160$		0			0
$161$	1.02699	−	1.77879i	0.0809380	−	0.140189i
$162$	−6.06218	−	3.50000i	−0.476290	−	0.274986i
$163$		−	17.0540i		−	1.33577i	−0.744264	−	0.667885i	$-0.767200\pi$
$163$		−	17.0540i		−	1.33577i	0.744264	−	0.667885i	$-0.232800\pi$
$164$	6.12311			0.478134
$165$		0			0
$166$	−5.40388	−	9.35980i	−0.419423	−	0.726461i
$167$	−0.592932	−	0.342329i	−0.0458824	−	0.0264902i	0.476883	−	0.878967i	$-0.341766\pi$
$167$	−0.592932	−	0.342329i	−0.0458824	−	0.0264902i	−0.522766	+	0.852476i	$0.675100\pi$
$168$	−0.972638	+	0.561553i	−0.0750407	+	0.0433247i
$169$	−4.50000	−	7.79423i	−0.346154	−	0.599556i
$170$		0			0
$171$	−6.56155	−	14.0696i	−0.501774	−	1.07593i
$172$			3.12311i			0.238135i
$173$	5.02967	−	2.90388i	0.382399	−	0.220778i	−0.296463	−	0.955044i	$-0.595807\pi$
$173$	5.02967	−	2.90388i	0.382399	−	0.220778i	0.678861	+	0.734266i	$0.262474\pi$
$174$	2.56155	+	4.43674i	0.194191	+	0.336348i
$175$		0			0
$176$	−0.500000	−	0.866025i	−0.0376889	−	0.0652791i
$177$	32.3029	+	18.6501i	2.42804	+	1.40183i
$178$		−	2.68466i		−	0.201224i
$179$	−11.4924			−0.858984			−0.429492	−	0.903071i	$-0.641307\pi$
$179$	−11.4924			−0.858984			−0.429492	+	0.903071i	$0.641307\pi$
$180$		0			0
$181$	−10.6847	+	18.5064i	−0.794184	+	1.37557i	0.129171	+	0.991622i	$0.458768\pi$
$181$	−10.6847	+	18.5064i	−0.794184	+	1.37557i	−0.923356	+	0.383945i	$0.874565\pi$
$182$			0.876894i			0.0649997i
$183$			13.1231i			0.970088i
$184$	2.34233	−	4.05703i	0.172679	−	0.299088i
$185$		0			0
$186$	−13.1231	+	22.7299i	−0.962233	+	1.66664i
$187$	4.43674	−	2.56155i	0.324447	−	0.187319i
$188$	−2.49146	+	1.43845i	−0.181709	+	0.104910i
$189$	0.630683			0.0458754
$190$		0			0
$191$	−5.36932			−0.388510			−0.194255	−	0.980951i	$-0.562229\pi$
$191$	−5.36932			−0.388510			−0.194255	+	0.980951i	$0.562229\pi$
$192$	−2.21837	+	1.28078i	−0.160097	+	0.0924321i
$193$	−22.1837	+	12.8078i	−1.59682	+	0.921923i	−0.604722	+	0.796436i	$0.706716\pi$
$193$	−22.1837	+	12.8078i	−1.59682	+	0.921923i	−0.992095	+	0.125487i	$0.959951\pi$
$194$	−0.842329	+	1.45896i	−0.0604757	+	0.104747i
$195$		0			0
$196$	3.40388	−	5.89570i	0.243134	−	0.421121i
$197$			14.4384i			1.02870i	0.857581	+	0.514348i	$0.171966\pi$
$197$			14.4384i			1.02870i	−0.857581	+	0.514348i	$0.828034\pi$
$198$			3.56155i			0.253109i
$199$	−1.43845	+	2.49146i	−0.101969	+	0.176615i	−0.912496	−	0.409086i	$-0.865848\pi$
$199$	−1.43845	+	2.49146i	−0.101969	+	0.176615i	0.810527	+	0.585701i	$0.199181\pi$
$200$		0			0
$201$	−24.1771			−1.70532
$202$		−	10.0000i		−	0.703598i
$203$	0.759413	+	0.438447i	0.0533003	+	0.0307730i
$204$	−6.56155	−	11.3649i	−0.459401	−	0.795705i
$205$		0			0
$206$	−2.90388	−	5.02967i	−0.202323	−	0.350434i
$207$	−14.4493	+	8.34233i	−1.00430	+	0.579832i
$208$			2.00000i			0.138675i
$209$	2.50000	−	3.57071i	0.172929	−	0.246991i
$210$		0			0
$211$	1.65767	+	2.87117i	0.114119	+	0.197659i	0.917427	−	0.397904i	$-0.130262\pi$
$211$	1.65767	+	2.87117i	0.114119	+	0.197659i	−0.803308	+	0.595563i	$0.796929\pi$
$212$	−6.54850	+	3.78078i	−0.449753	+	0.259665i
$213$	−36.0401	−	20.8078i	−2.46943	−	1.42572i
$214$	−1.12311	−	1.94528i	−0.0767739	−	0.132976i
$215$		0			0
$216$	1.43845			0.0978739
$217$			4.49242i			0.304966i
$218$	12.3376	+	7.12311i	0.835606	+	0.482438i
$219$	2.15767	−	3.73720i	0.145802	−	0.252536i
$220$		0			0
$221$	−10.2462			−0.689235
$222$	10.3923	+	6.00000i	0.697486	+	0.402694i
$223$	−9.79937	+	5.65767i	−0.656215	+	0.378866i	−0.790833	−	0.612032i	$-0.790352\pi$
$223$	−9.79937	+	5.65767i	−0.656215	+	0.378866i	0.134619	+	0.990897i	$0.457019\pi$
$224$	−0.219224	+	0.379706i	−0.0146475	+	0.0253702i
$225$		0			0
$226$	−8.40388	−	14.5560i	−0.559018	−	0.968247i
$227$			19.9309i			1.32286i	0.750008	+	0.661429i	$0.230050\pi$
$227$			19.9309i			1.32286i	−0.750008	+	0.661429i	$0.769950\pi$
$228$	−9.14657	−	6.40388i	−0.605747	−	0.424107i
$229$	−12.8769			−0.850929			−0.425465	−	0.904975i	$-0.639889\pi$
$229$	−12.8769			−0.850929			−0.425465	+	0.904975i	$0.639889\pi$
$230$		0			0
$231$	0.561553	+	0.972638i	0.0369475	+	0.0639949i
$232$	1.73205	+	1.00000i	0.113715	+	0.0656532i
$233$	−2.00514	+	1.15767i	−0.131361	+	0.0758415i	−0.564241	−	0.825610i	$-0.690831\pi$
$233$	−2.00514	+	1.15767i	−0.131361	+	0.0758415i	0.432879	+	0.901452i	$0.357498\pi$
$234$	3.56155	−	6.16879i	0.232826	−	0.403266i
$235$		0			0
$236$	14.5616			0.947876
$237$	−24.6752	−	14.2462i	−1.60282	−	0.925391i
$238$	−1.94528	−	1.12311i	−0.126094	−	0.0728001i
$239$	−18.2462			−1.18025			−0.590125	−	0.807312i	$-0.700921\pi$
$239$	−18.2462			−1.18025			−0.590125	+	0.807312i	$0.700921\pi$
$240$		0			0
$241$	4.28078	−	7.41452i	0.275749	−	0.477611i	−0.694575	−	0.719421i	$-0.744407\pi$
$241$	4.28078	−	7.41452i	0.275749	−	0.477611i	0.970324	+	0.241809i	$0.0777408\pi$
$242$	8.66025	−	5.00000i	0.556702	−	0.321412i
$243$	19.2658	+	11.1231i	1.23590	+	0.713548i
$244$	2.56155	+	4.43674i	0.163987	+	0.284033i
$245$		0			0
$246$	−15.6847			−1.00002
$247$	−7.90084	+	3.68466i	−0.502718	+	0.234449i
$248$			10.2462i			0.650635i
$249$	13.8423	+	23.9756i	0.877222	+	1.51939i
$250$		0			0
$251$	−12.9654	+	22.4568i	−0.818371	+	1.41746i	0.0885109	+	0.996075i	$0.471789\pi$
$251$	−12.9654	+	22.4568i	−0.818371	+	1.41746i	−0.906882	+	0.421385i	$0.861544\pi$
$252$	1.35234	−	0.780776i	0.0851897	−	0.0491843i
$253$	−4.05703	−	2.34233i	−0.255063	−	0.147261i
$254$	−15.5616			−0.976419
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−11.3051	−	6.52699i	−0.705191	−	0.407142i	0.104087	−	0.994568i	$-0.466808\pi$
$257$	−11.3051	−	6.52699i	−0.705191	−	0.407142i	−0.809278	+	0.587426i	$0.800141\pi$
$258$		−	8.00000i		−	0.498058i
$259$	2.05398			0.127628
$260$		0			0
$261$	−3.56155	−	6.16879i	−0.220455	−	0.381839i
$262$	−13.9630	−	8.06155i	−0.862638	−	0.498044i
$263$	1.89853	−	1.09612i	0.117068	−	0.0675895i	−0.440322	−	0.897840i	$-0.645136\pi$
$263$	1.89853	−	1.09612i	0.117068	−	0.0675895i	0.557391	+	0.830250i	$0.311803\pi$
$264$	1.28078	+	2.21837i	0.0788263	+	0.136531i
$265$		0			0
$266$	−1.90388	−	0.166481i	−0.116734	−	0.0102076i
$267$			6.87689i			0.420859i
$268$	−8.17394	+	4.71922i	−0.499303	+	0.288272i
$269$	2.00000	+	3.46410i	0.121942	+	0.211210i	0.920534	−	0.390664i	$-0.127754\pi$
$269$	2.00000	+	3.46410i	0.121942	+	0.211210i	−0.798591	+	0.601874i	$0.794421\pi$
$270$		0			0
$271$	4.12311	+	7.14143i	0.250461	+	0.433811i	0.963653	−	0.267158i	$-0.0860845\pi$
$271$	4.12311	+	7.14143i	0.250461	+	0.433811i	−0.713192	+	0.700969i	$0.752751\pi$
$272$	−4.43674	−	2.56155i	−0.269017	−	0.155317i
$273$		−	2.24621i		−	0.135947i
$274$	−5.43845			−0.328549
$275$		0			0
$276$	−6.00000	+	10.3923i	−0.361158	+	0.625543i
$277$			4.24621i			0.255130i	0.991830	+	0.127565i	$0.0407162\pi$
$277$			4.24621i			0.255130i	−0.991830	+	0.127565i	$0.959284\pi$
$278$			8.80776i			0.528255i
$279$	18.2462	−	31.6034i	1.09237	−	1.89204i
$280$		0			0
$281$	−4.18466	+	7.24804i	−0.249636	+	0.432382i	−0.963425	−	0.267979i	$-0.913644\pi$
$281$	−4.18466	+	7.24804i	−0.249636	+	0.432382i	0.713789	+	0.700361i	$0.246978\pi$
$282$	6.38202	−	3.68466i	0.380043	−	0.219418i
$283$	16.8342	−	9.71922i	1.00069	−	0.577748i	0.0922367	−	0.995737i	$-0.470598\pi$
$283$	16.8342	−	9.71922i	1.00069	−	0.577748i	0.908452	+	0.417989i	$0.137265\pi$
$284$	−16.2462			−0.964035
$285$		0			0
$286$	2.00000			0.118262
$287$	−2.32498	+	1.34233i	−0.137239	+	0.0792352i
$288$	3.08440	−	1.78078i	0.181750	−	0.104933i
$289$	4.62311	−	8.00745i	0.271947	−	0.471027i
$290$		0			0
$291$	2.15767	−	3.73720i	0.126485	−	0.219078i
$292$		−	1.68466i		−	0.0985872i
$293$		−	23.5616i		−	1.37648i	−0.725483	−	0.688240i	$-0.758383\pi$
$293$		−	23.5616i		−	1.37648i	0.725483	−	0.688240i	$-0.241617\pi$
$294$	−8.71922	+	15.1021i	−0.508515	+	0.880775i
$295$		0			0
$296$	4.68466			0.272290
$297$		−	1.43845i		−	0.0834672i
$298$	−13.8564	−	8.00000i	−0.802680	−	0.463428i
$299$	4.68466	+	8.11407i	0.270921	+	0.469249i
$300$		0			0
$301$	−0.684658	−	1.18586i	−0.0394631	−	0.0683520i
$302$	−17.7470	+	10.2462i	−1.02122	+	0.589603i
$303$			25.6155i			1.47157i
$304$	−4.34233	−	0.379706i	−0.249050	−	0.0217777i
$305$		0			0
$306$	9.12311	+	15.8017i	0.521533	+	0.903322i
$307$	−20.7247	+	11.9654i	−1.18282	+	0.682903i	−0.956666	−	0.291187i	$-0.905950\pi$
$307$	−20.7247	+	11.9654i	−1.18282	+	0.682903i	−0.226157	+	0.974091i	$0.572616\pi$
$308$	0.379706	+	0.219224i	0.0216358	+	0.0124914i
$309$	7.43845	+	12.8838i	0.423158	+	0.732932i
$310$		0			0
$311$	4.00000			0.226819			0.113410	−	0.993548i	$-0.463823\pi$
$311$	4.00000			0.226819			0.113410	+	0.993548i	$0.463823\pi$
$312$		−	5.12311i		−	0.290039i
$313$	3.73720	+	2.15767i	0.211239	+	0.121959i	0.601887	−	0.798581i	$-0.294416\pi$
$313$	3.73720	+	2.15767i	0.211239	+	0.121959i	−0.390648	+	0.920540i	$0.627749\pi$
$314$	−1.21922	+	2.11176i	−0.0688048	+	0.119173i
$315$		0			0
$316$	−11.1231			−0.625724
$317$	−16.1814	−	9.34233i	−0.908837	−	0.524717i	−0.0287805	−	0.999586i	$-0.509162\pi$
$317$	−16.1814	−	9.34233i	−0.908837	−	0.524717i	−0.880057	+	0.474868i	$0.842496\pi$
$318$	16.7743	−	9.68466i	0.940657	−	0.543089i
$319$	1.00000	−	1.73205i	0.0559893	−	0.0969762i
$320$		0			0
$321$	2.87689	+	4.98293i	0.160573	+	0.278120i
$322$			2.05398i			0.114464i
$323$	1.94528	−	22.2462i	0.108238	−	1.23781i
$324$	7.00000			0.388889
$325$		0			0
$326$	8.52699	+	14.7692i	0.472266	+	0.817989i
$327$	−31.6034	−	18.2462i	−1.74767	−	1.00902i
$328$	−5.30277	+	3.06155i	−0.292796	+	0.169046i
$329$	0.630683	−	1.09238i	0.0347707	−	0.0602246i
$330$		0			0
$331$	23.4924			1.29126			0.645630	−	0.763650i	$-0.276595\pi$
$331$	23.4924			1.29126			0.645630	+	0.763650i	$0.276595\pi$
$332$	9.35980	+	5.40388i	0.513686	+	0.296577i
$333$	−14.4493	−	8.34233i	−0.791819	−	0.457157i
$334$	0.684658			0.0374628
$335$		0			0
$336$	0.561553	−	0.972638i	0.0306352	−	0.0530618i
$337$	18.2333	−	10.5270i	0.993230	−	0.573442i	0.0869917	−	0.996209i	$-0.472275\pi$
$337$	18.2333	−	10.5270i	0.993230	−	0.573442i	0.906238	+	0.422767i	$0.138941\pi$
$338$	7.79423	+	4.50000i	0.423950	+	0.244768i
$339$	21.5270	+	37.2858i	1.16919	+	2.02509i
$340$		0			0
$341$	10.2462			0.554863
$342$	12.7173	+	8.90388i	0.687672	+	0.481467i
$343$			6.05398i			0.326884i
$344$	−1.56155	−	2.70469i	−0.0841933	−	0.145827i
$345$		0			0
$346$	−2.90388	+	5.02967i	−0.156114	+	0.270397i
$347$	1.45896	−	0.842329i	0.0783209	−	0.0452186i	−0.460328	−	0.887749i	$-0.652268\pi$
$347$	1.45896	−	0.842329i	0.0783209	−	0.0452186i	0.538649	+	0.842530i	$0.318935\pi$
$348$	−4.43674	−	2.56155i	−0.237834	−	0.137314i
$349$	14.2462			0.762582			0.381291	−	0.924455i	$-0.375480\pi$
$349$	14.2462			0.762582			0.381291	+	0.924455i	$0.375480\pi$
$350$		0			0
$351$	−1.43845	+	2.49146i	−0.0767786	+	0.132984i
$352$	0.866025	+	0.500000i	0.0461593	+	0.0266501i
$353$		−	24.1771i		−	1.28682i	−0.765523	−	0.643408i	$-0.777520\pi$
$353$		−	24.1771i		−	1.28682i	0.765523	−	0.643408i	$-0.222480\pi$
$354$	−37.3002			−1.98248
$355$		0			0
$356$	1.34233	+	2.32498i	0.0711433	+	0.123224i
$357$	4.98293	+	2.87689i	0.263724	+	0.152261i
$358$	9.95273	−	5.74621i	0.526018	−	0.303697i
$359$	7.56155	+	13.0970i	0.399083	+	0.691233i	0.993613	−	0.112841i	$-0.0359950\pi$
$359$	7.56155	+	13.0970i	0.399083	+	0.691233i	−0.594530	+	0.804074i	$0.702662\pi$
$360$		0			0
$361$	−6.50000	−	17.8536i	−0.342105	−	0.939662i
$362$		−	21.3693i		−	1.12315i
$363$	−22.1837	+	12.8078i	−1.16434	+	0.672233i
$364$	−0.438447	−	0.759413i	−0.0229809	−	0.0398040i
$365$		0			0
$366$	−6.56155	−	11.3649i	−0.342978	−	0.594055i
$367$	15.3752	+	8.87689i	0.802581	+	0.463370i	0.844373	−	0.535756i	$-0.179973\pi$
$367$	15.3752	+	8.87689i	0.802581	+	0.463370i	−0.0417921	+	0.999126i	$0.513307\pi$
$368$			4.68466i			0.244205i
$369$	21.8078			1.13527
$370$		0			0
$371$	1.65767	−	2.87117i	0.0860620	−	0.149064i
$372$		−	26.2462i		−	1.36080i
$373$			35.8078i			1.85406i	0.374992	+	0.927028i	$0.377645\pi$
$373$			35.8078i			1.85406i	−0.374992	+	0.927028i	$0.622355\pi$
$374$	−2.56155	+	4.43674i	−0.132455	+	0.229418i
$375$		0			0
$376$	1.43845	−	2.49146i	0.0741822	−	0.128487i
$377$	−3.46410	+	2.00000i	−0.178410	+	0.103005i
$378$	−0.546188	+	0.315342i	−0.0280929	+	0.0162194i
$379$	0.492423			0.0252940			0.0126470	−	0.999920i	$-0.495974\pi$
$379$	0.492423			0.0252940			0.0126470	+	0.999920i	$0.495974\pi$
$380$		0			0
$381$	39.8617			2.04218
$382$	4.64996	−	2.68466i	0.237913	−	0.137359i
$383$	−4.43674	+	2.56155i	−0.226707	+	0.130889i	−0.609052	−	0.793130i	$-0.708450\pi$
$383$	−4.43674	+	2.56155i	−0.226707	+	0.130889i	0.382345	+	0.924020i	$0.375117\pi$
$384$	1.28078	−	2.21837i	0.0653593	−	0.113206i
$385$		0			0
$386$	12.8078	−	22.1837i	0.651898	−	1.12912i
$387$			11.1231i			0.565419i
$388$		−	1.68466i		−	0.0855256i
$389$	−9.56155	+	16.5611i	−0.484790	+	0.839681i	−0.999847	−	0.0174749i	$-0.994437\pi$
$389$	−9.56155	+	16.5611i	−0.484790	+	0.839681i	0.515057	+	0.857156i	$0.327771\pi$
$390$		0			0
$391$	−24.0000			−1.21373
$392$			6.80776i			0.343844i
$393$	35.7670	+	20.6501i	1.80421	+	1.04166i
$394$	−7.21922	−	12.5041i	−0.363699	−	0.629946i
$395$		0			0
$396$	−1.78078	−	3.08440i	−0.0894874	−	0.154997i
$397$	24.5087	−	14.1501i	1.23006	−	0.710173i	0.263014	−	0.964792i	$-0.415283\pi$
$397$	24.5087	−	14.1501i	1.23006	−	0.710173i	0.967041	+	0.254619i	$0.0819501\pi$
$398$		−	2.87689i		−	0.144206i
$399$	4.87689	+	0.426450i	0.244150	+	0.0213492i
$400$		0			0
$401$	−13.9654	−	24.1888i	−0.697401	−	1.20793i	−0.969365	−	0.245626i	$-0.921007\pi$
$401$	−13.9654	−	24.1888i	−0.697401	−	1.20793i	0.271964	−	0.962307i	$-0.412327\pi$
$402$	20.9380	−	12.0885i	1.04429	−	0.602922i
$403$	−17.7470	−	10.2462i	−0.884039	−	0.510400i
$404$	5.00000	+	8.66025i	0.248759	+	0.430864i
$405$		0			0
$406$	−0.876894			−0.0435195
$407$		−	4.68466i		−	0.232210i
$408$	11.3649	+	6.56155i	0.562649	+	0.324845i
$409$	10.5000	−	18.1865i	0.519192	−	0.899266i	−0.480560	−	0.876962i	$-0.659566\pi$
$409$	10.5000	−	18.1865i	0.519192	−	0.899266i	0.999751	−	0.0223042i	$-0.00710022\pi$
$410$		0			0
$411$	13.9309			0.687159
$412$	5.02967	+	2.90388i	0.247794	+	0.143064i
$413$	−5.52911	+	3.19224i	−0.272070	+	0.157080i
$414$	8.34233	−	14.4493i	0.410003	−	0.710146i
$415$		0			0
$416$	−1.00000	−	1.73205i	−0.0490290	−	0.0849208i
$417$		−	22.5616i		−	1.10484i
$418$	−0.379706	+	4.34233i	−0.0185720	+	0.212390i
$419$	17.5616			0.857938			0.428969	−	0.903319i	$-0.358877\pi$
$419$	17.5616			0.857938			0.428969	+	0.903319i	$0.358877\pi$
$420$		0			0
$421$	−16.2462	−	28.1393i	−0.791792	−	1.37142i	−0.924856	−	0.380316i	$-0.875815\pi$
$421$	−16.2462	−	28.1393i	−0.791792	−	1.37142i	0.133065	−	0.991107i	$-0.457518\pi$
$422$	−2.87117	−	1.65767i	−0.139766	−	0.0806942i
$423$	−8.87348	+	5.12311i	−0.431443	+	0.249094i
$424$	3.78078	−	6.54850i	0.183611	−	0.318023i
$425$		0			0
$426$	41.6155			2.01628
$427$	−1.94528	−	1.12311i	−0.0941385	−	0.0543509i
$428$	1.94528	+	1.12311i	0.0940285	+	0.0542874i
$429$	−5.12311			−0.247346
$430$		0			0
$431$	3.68466	−	6.38202i	0.177484	−	0.307411i	−0.763534	−	0.645767i	$-0.776538\pi$
$431$	3.68466	−	6.38202i	0.177484	−	0.307411i	0.941018	+	0.338356i	$0.109871\pi$
$432$	−1.24573	+	0.719224i	−0.0599353	+	0.0346037i
$433$	−31.8166	−	18.3693i	−1.52901	−	0.882773i	−0.999404	−	0.0345280i	$-0.989007\pi$
$433$	−31.8166	−	18.3693i	−1.52901	−	0.882773i	−0.529604	−	0.848245i	$-0.677659\pi$
$434$	−2.24621	−	3.89055i	−0.107822	−	0.186752i
$435$		0			0
$436$	−14.2462			−0.682270
$437$	−18.5064	+	8.63068i	−0.885280	+	0.412862i
$438$			4.31534i			0.206195i
$439$	−8.24621	−	14.2829i	−0.393570	−	0.681684i	0.599347	−	0.800489i	$-0.295427\pi$
$439$	−8.24621	−	14.2829i	−0.393570	−	0.681684i	−0.992918	+	0.118806i	$0.962094\pi$
$440$		0			0
$441$	12.1231	−	20.9978i	0.577291	−	0.999897i
$442$	8.87348	−	5.12311i	0.422068	−	0.243681i
$443$	29.3850	+	16.9654i	1.39612	+	0.806052i	0.993984	−	0.109526i	$-0.0349334\pi$
$443$	29.3850	+	16.9654i	1.39612	+	0.806052i	0.402139	+	0.915578i	$0.368267\pi$
$444$	−12.0000			−0.569495
$445$		0			0
$446$	5.65767	−	9.79937i	0.267898	−	0.464014i
$447$	35.4939	+	20.4924i	1.67880	+	0.969258i
$448$		−	0.438447i		−	0.0207147i
$449$	−29.0000			−1.36859			−0.684297	−	0.729203i	$-0.739891\pi$
$449$	−29.0000			−1.36859			−0.684297	+	0.729203i	$0.739891\pi$
$450$		0			0
$451$	3.06155	+	5.30277i	0.144163	+	0.249697i
$452$	14.5560	+	8.40388i	0.684654	+	0.395285i
$453$	45.4598	−	26.2462i	2.13589	−	1.23315i
$454$	−9.96543	−	17.2606i	−0.467701	−	0.810082i
$455$		0			0
$456$	11.1231	+	0.972638i	0.520887	+	0.0455479i
$457$			7.05398i			0.329971i	0.986296	+	0.164986i	$0.0527577\pi$
$457$			7.05398i			0.329971i	−0.986296	+	0.164986i	$0.947242\pi$
$458$	11.1517	−	6.43845i	0.521086	−	0.300849i
$459$	−3.68466	−	6.38202i	−0.171985	−	0.297887i
$460$		0			0
$461$	19.4924	+	33.7619i	0.907853	+	1.57245i	0.817042	+	0.576579i	$0.195613\pi$
$461$	19.4924	+	33.7619i	0.907853	+	1.57245i	0.0908110	+	0.995868i	$0.471054\pi$
$462$	−0.972638	−	0.561553i	−0.0452512	−	0.0261258i
$463$			19.5616i			0.909102i	0.890721	+	0.454551i	$0.150200\pi$
$463$			19.5616i			0.909102i	−0.890721	+	0.454551i	$0.849800\pi$
$464$	−2.00000			−0.0928477
$465$		0			0
$466$	1.15767	−	2.00514i	0.0536281	−	0.0928865i
$467$			16.5616i			0.766377i	0.923670	+	0.383189i	$0.125174\pi$
$467$			16.5616i			0.766377i	−0.923670	+	0.383189i	$0.874826\pi$
$468$			7.12311i			0.329266i
$469$	2.06913	−	3.58384i	0.0955436	−	0.165486i
$470$		0			0
$471$	3.12311	−	5.40938i	0.143905	−	0.249251i
$472$	−12.6107	+	7.28078i	−0.580453	+	0.335125i
$473$	−2.70469	+	1.56155i	−0.124362	+	0.0718003i
$474$	28.4924			1.30870
$475$		0			0
$476$	2.24621			0.102955
$477$	−23.3228	+	13.4654i	−1.06788	+	0.616540i
$478$	15.8017	−	9.12311i	0.722752	−	0.417281i
$479$	14.6847	−	25.4346i	0.670959	−	1.16214i	−0.306673	−	0.951815i	$-0.599216\pi$
$479$	14.6847	−	25.4346i	0.670959	−	1.16214i	0.977632	−	0.210321i	$-0.0674508\pi$
$480$		0			0
$481$	−4.68466	+	8.11407i	−0.213602	+	0.369970i
$482$			8.56155i			0.389968i
$483$		−	5.26137i		−	0.239400i
$484$	−5.00000	+	8.66025i	−0.227273	+	0.393648i
$485$		0			0
$486$	−22.2462			−1.00911
$487$		−	6.93087i		−	0.314068i	−0.987593	−	0.157034i	$-0.949807\pi$
$487$		−	6.93087i		−	0.314068i	0.987593	−	0.157034i	$-0.0501932\pi$
$488$	−4.43674	−	2.56155i	−0.200842	−	0.115956i
$489$	−21.8423	−	37.8320i	−0.987744	−	1.71082i
$490$		0			0
$491$	4.58854	+	7.94759i	0.207078	+	0.358670i	0.950793	−	0.309827i	$-0.100271\pi$
$491$	4.58854	+	7.94759i	0.207078	+	0.358670i	−0.743715	+	0.668497i	$0.766938\pi$
$492$	13.5833	−	7.84233i	0.612383	−	0.353560i
$493$		−	10.2462i		−	0.461466i
$494$	5.00000	−	7.14143i	0.224961	−	0.321308i
$495$		0			0
$496$	−5.12311	−	8.87348i	−0.230034	−	0.398431i
$497$	6.16879	−	3.56155i	0.276708	−	0.159757i
$498$	−23.9756	−	13.8423i	−1.07437	−	0.620290i
$499$	14.5000	+	25.1147i	0.649109	+	1.12429i	0.983336	+	0.181797i	$0.0581915\pi$
$499$	14.5000	+	25.1147i	0.649109	+	1.12429i	−0.334227	+	0.942493i	$0.608475\pi$
$500$		0			0
$501$	−1.75379			−0.0783535
$502$		−	25.9309i		−	1.15735i
$503$	23.7493	+	13.7116i	1.05893	+	0.611372i	0.925135	−	0.379637i	$-0.123951\pi$
$503$	23.7493	+	13.7116i	1.05893	+	0.611372i	0.133792	+	0.991009i	$0.457285\pi$
$504$	−0.780776	+	1.35234i	−0.0347785	+	0.0602382i
$505$		0			0
$506$	4.68466			0.208258
$507$	−19.9653	−	11.5270i	−0.886691	−	0.511931i
$508$	13.4767	−	7.78078i	0.597932	−	0.345216i
$509$	−0.438447	+	0.759413i	−0.0194338	+	0.0336604i	−0.875579	−	0.483075i	$-0.839520\pi$
$509$	−0.438447	+	0.759413i	−0.0194338	+	0.0336604i	0.856145	+	0.516736i	$0.172853\pi$
$510$		0			0
$511$	0.369317	+	0.639676i	0.0163376	+	0.0282976i
$512$		−	1.00000i		−	0.0441942i
$513$	−5.13628	−	3.59612i	−0.226772	−	0.158772i
$514$	13.0540			0.575786
$515$		0			0
$516$	4.00000	+	6.92820i	0.176090	+	0.304997i
$517$	−2.49146	−	1.43845i	−0.109574	−	0.0632628i
$518$	−1.77879	+	1.02699i	−0.0781558	+	0.0451232i
$519$	7.43845	−	12.8838i	0.326512	−	0.565535i
$520$		0			0
$521$	−22.8078			−0.999226			−0.499613	−	0.866249i	$-0.666524\pi$
$521$	−22.8078			−0.999226			−0.499613	+	0.866249i	$0.666524\pi$
$522$	6.16879	+	3.56155i	0.270001	+	0.155885i
$523$	12.6705	+	7.31534i	0.554044	+	0.319878i	0.750752	−	0.660585i	$-0.229692\pi$
$523$	12.6705	+	7.31534i	0.554044	+	0.319878i	−0.196707	+	0.980462i	$0.563025\pi$
$524$	16.1231			0.704341
$525$		0			0
$526$	−1.09612	+	1.89853i	−0.0477930	+	0.0827799i
$527$	45.4598	−	26.2462i	1.98026	−	1.14330i
$528$	−2.21837	−	1.28078i	−0.0965422	−	0.0557386i
$529$	−0.526988	−	0.912769i	−0.0229125	−	0.0396856i
$530$		0			0
$531$	51.8617			2.25061
$532$	1.73205	−	0.807764i	0.0750939	−	0.0350210i
$533$		−	12.2462i		−	0.530442i
$534$	−3.43845	−	5.95557i	−0.148796	−	0.257723i
$535$		0			0
$536$	4.71922	−	8.17394i	0.203839	−	0.353060i
$537$	−25.4944	+	14.7192i	−1.10017	+	0.635181i
$538$	−3.46410	−	2.00000i	−0.149348	−	0.0862261i
$539$	6.80776			0.293231
$540$		0			0
$541$	14.2462	−	24.6752i	0.612492	−	1.06087i	−0.378326	−	0.925672i	$-0.623500\pi$
$541$	14.2462	−	24.6752i	0.612492	−	1.06087i	0.990819	−	0.135196i	$-0.0431664\pi$
$542$	−7.14143	−	4.12311i	−0.306751	−	0.177103i
$543$			54.7386i			2.34906i
$544$	5.12311			0.219651
$545$		0			0
$546$	1.12311	+	1.94528i	0.0480645	+	0.0832501i
$547$	4.22351	+	2.43845i	0.180584	+	0.104260i	0.587567	−	0.809175i	$-0.300086\pi$
$547$	4.22351	+	2.43845i	0.180584	+	0.104260i	−0.406983	+	0.913436i	$0.633419\pi$
$548$	4.70983	−	2.71922i	0.201194	−	0.116159i
$549$	9.12311	+	15.8017i	0.389365	+	0.674399i
$550$		0			0
$551$	−3.68466	−	7.90084i	−0.156972	−	0.336587i
$552$		−	12.0000i		−	0.510754i
$553$	4.22351	−	2.43845i	0.179602	−	0.103693i
$554$	−2.12311	−	3.67733i	−0.0902021	−	0.156235i
$555$		0			0
$556$	−4.40388	−	7.62775i	−0.186766	−	0.323489i
$557$	−36.0868	−	20.8348i	−1.52905	−	0.882797i	−0.999402	−	0.0345785i	$-0.988991\pi$
$557$	−36.0868	−	20.8348i	−1.52905	−	0.882797i	−0.529647	−	0.848218i	$-0.677676\pi$
$558$			36.4924i			1.54485i
$559$	6.24621			0.264187
$560$		0			0
$561$	6.56155	−	11.3649i	0.277029	−	0.479828i
$562$		−	8.36932i		−	0.353038i
$563$		−	21.3002i		−	0.897696i	−0.893608	−	0.448848i	$-0.851834\pi$
$563$		−	21.3002i		−	0.897696i	0.893608	−	0.448848i	$-0.148166\pi$
$564$	−3.68466	+	6.38202i	−0.155152	+	0.268731i
$565$		0			0
$566$	−9.71922	+	16.8342i	−0.408529	+	0.707594i
$567$	−2.65794	+	1.53457i	−0.111623	+	0.0644457i
$568$	14.0696	−	8.12311i	0.590349	−	0.340838i
$569$	11.1771			0.468568			0.234284	−	0.972168i	$-0.424726\pi$
$569$	11.1771			0.468568			0.234284	+	0.972168i	$0.424726\pi$
$570$		0			0
$571$	−4.80776			−0.201199			−0.100599	−	0.994927i	$-0.532076\pi$
$571$	−4.80776			−0.201199			−0.100599	+	0.994927i	$0.532076\pi$
$572$	−1.73205	+	1.00000i	−0.0724207	+	0.0418121i
$573$	−11.9111	+	6.87689i	−0.497595	+	0.287286i
$574$	1.34233	−	2.32498i	0.0560277	−	0.0970429i
$575$		0			0
$576$	−1.78078	+	3.08440i	−0.0741990	+	0.128516i
$577$		−	16.3153i		−	0.679217i	−0.940567	−	0.339608i	$-0.889705\pi$
$577$		−	16.3153i		−	0.679217i	0.940567	−	0.339608i	$-0.110295\pi$
$578$			9.24621i			0.384592i
$579$	−32.8078	+	56.8247i	−1.36344	+	2.36155i
$580$		0			0
$581$	−4.73863			−0.196592
$582$			4.31534i			0.178877i
$583$	−6.54850	−	3.78078i	−0.271211	−	0.156584i
$584$	0.842329	+	1.45896i	0.0348558	+	0.0603721i
$585$		0			0
$586$	11.7808	+	20.4049i	0.486659	+	0.842919i
$587$	23.1563	−	13.3693i	0.955764	−	0.551811i	0.0608975	−	0.998144i	$-0.480604\pi$
$587$	23.1563	−	13.3693i	0.955764	−	0.551811i	0.894867	+	0.446333i	$0.147270\pi$
$588$		−	17.4384i		−	0.719149i
$589$	25.6155	−	36.5863i	1.05547	−	1.50751i
$590$		0			0
$591$	18.4924	+	32.0298i	0.760677	+	1.31753i
$592$	−4.05703	+	2.34233i	−0.166743	+	0.0962691i
$593$	22.1238	+	12.7732i	0.908517	+	0.524532i	0.879954	−	0.475060i	$-0.157573\pi$
$593$	22.1238	+	12.7732i	0.908517	+	0.524532i	0.0285632	+	0.999592i	$0.490907\pi$
$594$	0.719224	+	1.24573i	0.0295101	+	0.0511130i
$595$		0			0
$596$	16.0000			0.655386
$597$			7.36932i			0.301606i
$598$	−8.11407	−	4.68466i	−0.331809	−	0.191570i
$599$	−16.2462	+	28.1393i	−0.663802	+	1.14974i	0.315806	+	0.948824i	$0.397725\pi$
$599$	−16.2462	+	28.1393i	−0.663802	+	1.14974i	−0.979609	+	0.200915i	$0.935608\pi$
$600$		0			0
$601$	−11.6307			−0.474425			−0.237213	−	0.971458i	$-0.576234\pi$
$601$	−11.6307			−0.474425			−0.237213	+	0.971458i	$0.576234\pi$
$602$	1.18586	+	0.684658i	0.0483322	+	0.0279046i
$603$	−29.1119	+	16.8078i	−1.18553	+	0.684465i
$604$	10.2462	−	17.7470i	0.416912	−	0.722113i
$605$		0			0
$606$	−12.8078	−	22.1837i	−0.520280	−	0.901151i
$607$			10.1922i			0.413690i	0.978374	+	0.206845i	$0.0663196\pi$
$607$			10.1922i			0.413690i	−0.978374	+	0.206845i	$0.933680\pi$
$608$	3.95042	−	1.84233i	0.160211	−	0.0747163i
$609$	2.24621			0.0910211
$610$		0			0
$611$	2.87689	+	4.98293i	0.116387	+	0.201588i
$612$	−15.8017	−	9.12311i	−0.638745	−	0.368780i
$613$	−26.5737	+	15.3423i	−1.07330	+	0.619671i	−0.929082	−	0.369875i	$-0.879401\pi$
$613$	−26.5737	+	15.3423i	−1.07330	+	0.619671i	−0.144220	+	0.989546i	$0.546067\pi$
$614$	11.9654	−	20.7247i	0.482886	−	0.836382i
$615$		0			0
$616$	−0.438447			−0.0176655
$617$	−6.22866	−	3.59612i	−0.250756	−	0.144774i	0.369354	−	0.929289i	$-0.379579\pi$
$617$	−6.22866	−	3.59612i	−0.250756	−	0.144774i	−0.620111	+	0.784514i	$0.712912\pi$
$618$	−12.8838	−	7.43845i	−0.518261	−	0.299218i
$619$	−26.0540			−1.04720			−0.523599	−	0.851965i	$-0.675411\pi$
$619$	−26.0540			−1.04720			−0.523599	+	0.851965i	$0.675411\pi$
$620$		0			0
$621$	−3.36932	+	5.83583i	−0.135206	+	0.234184i
$622$	−3.46410	+	2.00000i	−0.138898	+	0.0801927i
$623$	−1.01938	−	0.588540i	−0.0408407	−	0.0235794i
$624$	2.56155	+	4.43674i	0.102544	+	0.177612i
$625$		0			0
$626$	−4.31534			−0.172476
$627$	0.972638	−	11.1231i	0.0388434	−	0.444214i
$628$		−	2.43845i		−	0.0973046i
$629$	−12.0000	−	20.7846i	−0.478471	−	0.828737i
$630$		0			0
$631$	−2.12311	+	3.67733i	−0.0845195	+	0.146392i	−0.905186	−	0.425015i	$-0.860269\pi$
$631$	−2.12311	+	3.67733i	−0.0845195	+	0.146392i	0.820667	+	0.571407i	$0.193602\pi$
$632$	9.63289	−	5.56155i	0.383176	−	0.221227i
$633$	7.35465	+	4.24621i	0.292321	+	0.168772i
$634$	18.6847			0.742063
$635$		0			0
$636$	−9.68466	+	16.7743i	−0.384022	+	0.665145i
$637$	−11.7914	−	6.80776i	−0.467192	−	0.269733i
$638$			2.00000i			0.0791808i
$639$	−57.8617			−2.28898
$640$		0			0
$641$	−3.71922	−	6.44188i	−0.146900	−	0.254439i	0.783180	−	0.621795i	$-0.213596\pi$
$641$	−3.71922	−	6.44188i	−0.146900	−	0.254439i	−0.930080	+	0.367356i	$0.880263\pi$
$642$	−4.98293	−	2.87689i	−0.196660	−	0.113542i
$643$	19.5389	−	11.2808i	0.770538	−	0.444870i	−0.0625284	−	0.998043i	$-0.519916\pi$
$643$	19.5389	−	11.2808i	0.770538	−	0.444870i	0.833067	+	0.553173i	$0.186583\pi$
$644$	−1.02699	−	1.77879i	−0.0404690	−	0.0700943i
$645$		0			0
$646$	9.43845	+	20.2384i	0.371351	+	0.796270i
$647$			3.17708i			0.124904i	0.998048	+	0.0624520i	$0.0198920\pi$
$647$			3.17708i			0.124904i	−0.998048	+	0.0624520i	$0.980108\pi$
$648$	−6.06218	+	3.50000i	−0.238145	+	0.137493i
$649$	7.28078	+	12.6107i	0.285795	+	0.495012i
$650$		0			0
$651$	5.75379	+	9.96585i	0.225509	+	0.390593i
$652$	−14.7692	−	8.52699i	−0.578406	−	0.333943i
$653$			5.06913i			0.198370i	0.995069	+	0.0991852i	$0.0316236\pi$
$653$			5.06913i			0.198370i	−0.995069	+	0.0991852i	$0.968376\pi$
$654$	36.4924			1.42697
$655$		0			0
$656$	3.06155	−	5.30277i	0.119534	−	0.207038i
$657$		−	6.00000i		−	0.234082i
$658$			1.26137i			0.0491732i
$659$	9.46543	−	16.3946i	0.368721	−	0.638643i	−0.620645	−	0.784092i	$-0.713129\pi$
$659$	9.46543	−	16.3946i	0.368721	−	0.638643i	0.989366	+	0.145448i	$0.0464624\pi$
$660$		0			0
$661$	19.9309	−	34.5213i	0.775221	−	1.34272i	−0.159449	−	0.987206i	$-0.550972\pi$
$661$	19.9309	−	34.5213i	0.775221	−	1.34272i	0.934670	−	0.355516i	$-0.115695\pi$
$662$	−20.3450	+	11.7462i	−0.790732	+	0.456529i
$663$	−22.7299	+	13.1231i	−0.882756	+	0.509659i
$664$	−10.8078			−0.419423
$665$		0			0
$666$	16.6847			0.646517
$667$	−8.11407	+	4.68466i	−0.314178	+	0.181391i
$668$	−0.592932	+	0.342329i	−0.0229412	+	0.0132451i
$669$	−14.4924	+	25.1016i	−0.560309	+	0.970484i
$670$		0			0
$671$	−2.56155	+	4.43674i	−0.0988876	+	0.171278i
$672$			1.12311i			0.0433247i
$673$		−	46.1080i		−	1.77733i	−0.458556	−	0.888665i	$-0.651633\pi$
$673$		−	46.1080i		−	1.77733i	0.458556	−	0.888665i	$-0.348367\pi$
$674$	−10.5270	+	18.2333i	−0.405484	+	0.702320i
$675$		0			0
$676$	−9.00000			−0.346154
$677$		−	23.1771i		−	0.890768i	−0.895340	−	0.445384i	$-0.853067\pi$
$677$		−	23.1771i		−	0.890768i	0.895340	−	0.445384i	$-0.146933\pi$
$678$	−37.2858	−	21.5270i	−1.43195	−	0.826739i
$679$	0.369317	+	0.639676i	0.0141731	+	0.0245485i
$680$		0			0
$681$	25.5270	+	44.2140i	0.978196	+	1.69429i
$682$	−8.87348	+	5.12311i	−0.339783	+	0.196174i
$683$		−	28.0000i		−	1.07139i	−0.844411	−	0.535695i	$-0.820050\pi$
$683$		−	28.0000i		−	1.07139i	0.844411	−	0.535695i	$-0.179950\pi$
$684$	−15.4654	−	1.35234i	−0.591336	−	0.0517082i
$685$		0			0
$686$	−3.02699	−	5.24290i	−0.115571	−	0.200175i
$687$	−28.5657	+	16.4924i	−1.08985	+	0.629225i
$688$	2.70469	+	1.56155i	0.103115	+	0.0595336i
$689$	7.56155	+	13.0970i	0.288072	+	0.498956i
$690$		0			0
$691$	−21.0691			−0.801507			−0.400754	−	0.916186i	$-0.631252\pi$
$691$	−21.0691			−0.801507			−0.400754	+	0.916186i	$0.631252\pi$
$692$		−	5.80776i		−	0.220778i
$693$	1.35234	+	0.780776i	0.0513713	+	0.0296592i
$694$	−0.842329	+	1.45896i	−0.0319744	+	0.0553813i
$695$		0			0
$696$	5.12311			0.194191
$697$	27.1666	+	15.6847i	1.02901	+	0.594099i
$698$	−12.3376	+	7.12311i	−0.466984	+	0.269614i
$699$	−2.96543	+	5.13628i	−0.112163	+	0.194272i
$700$		0			0
$701$	−3.24621	−	5.62260i	−0.122608	−	0.212363i	0.798188	−	0.602409i	$-0.205792\pi$
$701$	−3.24621	−	5.62260i	−0.122608	−	0.212363i	−0.920795	+	0.390046i	$0.872459\pi$
$702$		−	2.87689i		−	0.108581i
$703$	−16.7276	−	11.7116i	−0.630892	−	0.441713i
$704$	−1.00000			−0.0376889
$705$		0			0
$706$	12.0885	+	20.9380i	0.454958	+	0.788011i
$707$	−3.79706	−	2.19224i	−0.142803	−	0.0824475i
$708$	32.3029	−	18.6501i	1.21402	−	0.700913i
$709$	−20.0000	+	34.6410i	−0.751116	+	1.30097i	0.196167	+	0.980571i	$0.437151\pi$
$709$	−20.0000	+	34.6410i	−0.751116	+	1.30097i	−0.947282	+	0.320400i	$0.896183\pi$
$710$		0			0
$711$	−39.6155			−1.48570
$712$	−2.32498	−	1.34233i	−0.0871324	−	0.0503059i
$713$	−41.5692	−	24.0000i	−1.55678	−	0.898807i
$714$	−5.75379			−0.215330
$715$		0			0
$716$	−5.74621	+	9.95273i	−0.214746	+	0.371951i
$717$	−40.4768	+	23.3693i	−1.51164	+	0.872743i
$718$	−13.0970	−	7.56155i	−0.488775	−	0.282195i
$719$	7.43845	+	12.8838i	0.277407	+	0.480483i	0.970740	−	0.240134i	$-0.0771915\pi$
$719$	7.43845	+	12.8838i	0.277407	+	0.480483i	−0.693332	+	0.720618i	$0.743858\pi$
$720$		0			0
$721$	−2.54640			−0.0948328
$722$	14.5560	+	12.2116i	0.541716	+	0.454470i
$723$		−	21.9309i		−	0.815618i
$724$	10.6847	+	18.5064i	0.397092	+	0.687784i
$725$		0			0
$726$	12.8078	−	22.1837i	0.475341	−	0.823314i
$727$	−6.92820	+	4.00000i	−0.256953	+	0.148352i	−0.622944	−	0.782267i	$-0.714063\pi$
$727$	−6.92820	+	4.00000i	−0.256953	+	0.148352i	0.365991	+	0.930618i	$0.380730\pi$
$728$	0.759413	+	0.438447i	0.0281457	+	0.0162499i
$729$	35.9848			1.33277
$730$		0			0
$731$	−8.00000	+	13.8564i	−0.295891	+	0.512498i
$732$	11.3649	+	6.56155i	0.420060	+	0.242522i
$733$			26.9309i			0.994714i	0.867546	+	0.497357i	$0.165696\pi$
$733$			26.9309i			0.994714i	−0.867546	+	0.497357i	$0.834304\pi$
$734$	−17.7538			−0.655304
$735$		0			0
$736$	−2.34233	−	4.05703i	−0.0863394	−	0.149544i
$737$	−8.17394	−	4.71922i	−0.301091	−	0.173835i
$738$	−18.8861	+	10.9039i	−0.695206	+	0.401377i
$739$	9.37689	+	16.2413i	0.344935	+	0.597444i	0.985342	−	0.170591i	$-0.0545677\pi$
$739$	9.37689	+	16.2413i	0.344935	+	0.597444i	−0.640407	+	0.768036i	$0.721234\pi$
$740$		0			0
$741$	−12.8078	+	18.2931i	−0.470505	+	0.672016i
$742$			3.31534i			0.121710i
$743$	15.9682	−	9.21922i	0.585815	−	0.338221i	−0.177626	−	0.984098i	$-0.556842\pi$
$743$	15.9682	−	9.21922i	0.585815	−	0.338221i	0.763441	+	0.645878i	$0.223508\pi$
$744$	13.1231	+	22.7299i	0.481116	+	0.833318i
$745$		0			0
$746$	−17.9039	−	31.0104i	−0.655508	−	1.13537i
$747$	33.3354	+	19.2462i	1.21968	+	0.704182i
$748$		−	5.12311i		−	0.187319i
$749$	−0.984845			−0.0359855
$750$		0			0
$751$	17.4384	−	30.2043i	0.636338	−	1.10217i	−0.349892	−	0.936790i	$-0.613782\pi$
$751$	17.4384	−	30.2043i	0.636338	−	1.10217i	0.986230	−	0.165380i	$-0.0528849\pi$
$752$			2.87689i			0.104910i
$753$			66.4233i			2.42060i
$754$	2.00000	−	3.46410i	0.0728357	−	0.126155i
$755$		0			0
$756$	0.315342	−	0.546188i	0.0114689	−	0.0198647i
$757$	−16.9408	+	9.78078i	−0.615724	+	0.355488i	−0.775202	−	0.631713i	$-0.782352\pi$
$757$	−16.9408	+	9.78078i	−0.615724	+	0.355488i	0.159478	+	0.987201i	$0.449019\pi$
$758$	−0.426450	+	0.246211i	−0.0154894	+	0.00894280i
$759$	−12.0000			−0.435572
$760$		0			0
$761$	−51.9848			−1.88445			−0.942225	−	0.334982i	$-0.891270\pi$
$761$	−51.9848			−1.88445			−0.942225	+	0.334982i	$0.891270\pi$
$762$	−34.5213	+	19.9309i	−1.25057	+	0.722019i
$763$	5.40938	−	3.12311i	0.195833	−	0.113064i
$764$	−2.68466	+	4.64996i	−0.0971275	+	0.168230i
$765$		0			0
$766$	2.56155	−	4.43674i	0.0925527	−	0.160306i
$767$		−	29.1231i		−	1.05157i
$768$			2.56155i			0.0924321i
$769$	13.2462	−	22.9431i	0.477671	−	0.827350i	−0.522002	−	0.852944i	$-0.674815\pi$
$769$	13.2462	−	22.9431i	0.477671	−	0.827350i	0.999672	+	0.0255946i	$0.00814792\pi$
$770$		0			0
$771$	−33.4384			−1.20426
$772$			25.6155i			0.921923i
$773$	−12.3843	−	7.15009i	−0.445433	−	0.257171i	0.260466	−	0.965483i	$-0.416124\pi$
$773$	−12.3843	−	7.15009i	−0.445433	−	0.257171i	−0.705900	+	0.708312i	$0.749457\pi$
$774$	−5.56155	−	9.63289i	−0.199906	−	0.346247i
$775$		0			0
$776$	0.842329	+	1.45896i	0.0302379	+	0.0523735i
$777$	4.55648	−	2.63068i	0.163463	−	0.0943752i
$778$		−	19.1231i		−	0.685597i
$779$	26.5885	+	2.32498i	0.952633	+	0.0833011i
$780$		0			0
$781$	−8.12311	−	14.0696i	−0.290668	−	0.503451i
$782$	20.7846	−	12.0000i	0.743256	−	0.429119i
$783$	−2.49146	−	1.43845i	−0.0890376	−	0.0514059i
$784$	−3.40388	−	5.89570i	−0.121567	−	0.210561i
$785$		0			0
$786$	−41.3002			−1.47313
$787$			8.56155i			0.305186i	0.988289	+	0.152593i	$0.0487624\pi$
$787$			8.56155i			0.305186i	−0.988289	+	0.152593i	$0.951238\pi$
$788$	12.5041	+	7.21922i	0.445439	+	0.257174i
$789$	2.80776	−	4.86319i	0.0999590	−	0.173134i
$790$		0			0
$791$	−7.36932			−0.262023
$792$	3.08440	+	1.78078i	0.109599	+	0.0632771i
$793$	8.87348	−	5.12311i	0.315106	−	0.181927i
$794$	−14.1501	+	24.5087i	−0.502168	+	0.869781i
$795$		0			0
$796$	1.43845	+	2.49146i	0.0509844	+	0.0883076i
$797$		−	4.19224i		−	0.148497i	−0.997240	−	0.0742483i	$-0.976344\pi$
$797$		−	4.19224i		−	0.148497i	0.997240	−	0.0742483i	$-0.0236557\pi$
$798$	−4.43674	+	2.06913i	−0.157059	+	0.0732464i
$799$	−14.7386			−0.521415
$800$		0			0
$801$	4.78078	+	8.28055i	0.168920	+	0.292579i
$802$	24.1888	+	13.9654i	0.854138	+	0.493137i
$803$	1.45896	−	0.842329i	0.0514855	−	0.0297252i
$804$	−12.0885	+	20.9380i	−0.426330	+	0.738425i
$805$		0			0
$806$	20.4924			0.721815
$807$	8.87348	+	5.12311i	0.312361	+	0.180342i
$808$	−8.66025	−	5.00000i	−0.304667	−	0.175899i
$809$	−23.4384			−0.824052			−0.412026	−	0.911172i	$-0.635179\pi$
$809$	−23.4384			−0.824052			−0.412026	+	0.911172i	$0.635179\pi$
$810$		0			0
$811$	4.58854	−	7.94759i	0.161125	−	0.279077i	−0.774147	−	0.633006i	$-0.781821\pi$
$811$	4.58854	−	7.94759i	0.161125	−	0.279077i	0.935273	+	0.353928i	$0.115154\pi$
$812$	0.759413	−	0.438447i	0.0266502	−	0.0153865i
$813$	18.2931	+	10.5616i	0.641569	+	0.370410i
$814$	2.34233	+	4.05703i	0.0820986	+	0.142199i
$815$		0			0
$816$	−13.1231			−0.459401
$817$	−1.18586	+	13.5616i	−0.0414881	+	0.474459i
$818$			21.0000i			0.734248i
$819$	−1.56155	−	2.70469i	−0.0545651	−	0.0945095i
$820$		0			0
$821$	7.00000	−	12.1244i	0.244302	−	0.423143i	−0.717633	−	0.696421i	$-0.754775\pi$
$821$	7.00000	−	12.1244i	0.244302	−	0.423143i	0.961935	+	0.273278i	$0.0881079\pi$
$822$	−12.0645	+	6.96543i	−0.420797	+	0.242947i
$823$	−23.5360	−	13.5885i	−0.820415	−	0.473667i	0.0301446	−	0.999546i	$-0.490403\pi$
$823$	−23.5360	−	13.5885i	−0.820415	−	0.473667i	−0.850560	+	0.525879i	$0.823737\pi$
$824$	−5.80776			−0.202323
$825$		0			0
$826$	3.19224	−	5.52911i	0.111072	−	0.192383i
$827$	27.6529	+	15.9654i	0.961587	+	0.555173i	0.896661	−	0.442718i	$-0.145986\pi$
$827$	27.6529	+	15.9654i	0.961587	+	0.555173i	0.0649260	+	0.997890i	$0.479319\pi$
$828$			16.6847i			0.579832i
$829$	−26.7386			−0.928671			−0.464336	−	0.885659i	$-0.653707\pi$
$829$	−26.7386			−0.928671			−0.464336	+	0.885659i	$0.653707\pi$
$830$		0			0
$831$	5.43845	+	9.41967i	0.188658	+	0.326765i
$832$	1.73205	+	1.00000i	0.0600481	+	0.0346688i
$833$	30.2043	−	17.4384i	1.04652	−	0.604206i
$834$	11.2808	+	19.5389i	0.390621	+	0.676576i
$835$		0			0
$836$	−1.84233	−	3.95042i	−0.0637183	−	0.136628i
$837$		−	14.7386i		−	0.509442i
$838$	−15.2088	+	8.78078i	−0.525378	+	0.303327i
$839$	1.24621	+	2.15850i	0.0430240	+	0.0745197i	0.886735	−	0.462277i	$-0.152967\pi$
$839$	1.24621	+	2.15850i	0.0430240	+	0.0745197i	−0.843712	+	0.536797i	$0.819634\pi$
$840$		0			0
$841$	12.5000	+	21.6506i	0.431034	+	0.746574i
$842$	28.1393	+	16.2462i	0.969743	+	0.559881i
$843$			21.4384i			0.738379i
$844$	3.31534			0.114119
$845$		0			0
$846$	5.12311	−	8.87348i	0.176136	−	0.305077i
$847$		−	4.38447i		−	0.150652i
$848$			7.56155i			0.259665i
$849$	24.8963	−	43.1217i	0.854439	−	1.47993i
$850$		0			0
$851$	−10.9730	+	19.0058i	−0.376150	+	0.651511i
$852$	−36.0401	+	20.8078i	−1.23471	+	0.712862i
$853$	−0.639676	+	0.369317i	−0.0219021	+	0.0126452i	−0.510911	−	0.859634i	$-0.670692\pi$
$853$	−0.639676	+	0.369317i	−0.0219021	+	0.0126452i	0.489009	+	0.872279i	$0.337359\pi$
$854$	2.24621			0.0768638
$855$		0			0
$856$	−2.24621			−0.0767739
$857$	25.8012	−	14.8963i	0.881351	−	0.508848i	0.0102472	−	0.999947i	$-0.496738\pi$
$857$	25.8012	−	14.8963i	0.881351	−	0.508848i	0.871104	+	0.491099i	$0.163405\pi$
$858$	4.43674	−	2.56155i	0.151468	−	0.0874500i
$859$	23.7462	−	41.1296i	0.810210	−	1.40333i	−0.102506	−	0.994732i	$-0.532686\pi$
$859$	23.7462	−	41.1296i	0.810210	−	1.40333i	0.912717	−	0.408593i	$-0.133980\pi$
$860$		0			0
$861$	−3.43845	+	5.95557i	−0.117182	+	0.202965i
$862$			7.36932i			0.251000i
$863$		−	52.3002i		−	1.78032i	−0.455649	−	0.890160i	$-0.650593\pi$
$863$		−	52.3002i		−	1.78032i	0.455649	−	0.890160i	$-0.349407\pi$
$864$	0.719224	−	1.24573i	0.0244685	−	0.0423807i
$865$		0			0
$866$	36.7386			1.24843
$867$		−	23.6847i		−	0.804373i
$868$	3.89055	+	2.24621i	0.132054	+	0.0762414i
$869$	−5.56155	−	9.63289i	−0.188663	−	0.326773i
$870$		0			0
$871$	9.43845	+	16.3479i	0.319810	+	0.553926i
$872$	12.3376	−	7.12311i	0.417803	−	0.241219i
$873$		−	6.00000i		−	0.203069i
$874$	11.7116	−	16.7276i	0.396152	−	0.565819i
$875$		0			0
$876$	−2.15767	−	3.73720i	−0.0729009	−	0.126268i
$877$	15.4220	−	8.90388i	0.520763	−	0.300663i	−0.216484	−	0.976286i	$-0.569459\pi$
$877$	15.4220	−	8.90388i	0.520763	−	0.300663i	0.737247	+	0.675623i	$0.236125\pi$
$878$	14.2829	+	8.24621i	0.482023	+	0.278296i
$879$	−30.1771	−	52.2682i	−1.01785	−	1.76296i
$880$		0			0
$881$	−24.1231			−0.812728			−0.406364	−	0.913711i	$-0.633204\pi$
$881$	−24.1231			−0.812728			−0.406364	+	0.913711i	$0.633204\pi$
$882$			24.2462i			0.816412i
$883$	−7.62775	−	4.40388i	−0.256694	−	0.148202i	0.366131	−	0.930563i	$-0.380682\pi$
$883$	−7.62775	−	4.40388i	−0.256694	−	0.148202i	−0.622826	+	0.782361i	$0.714015\pi$
$884$	−5.12311	+	8.87348i	−0.172309	+	0.298447i
$885$		0			0
$886$	−33.9309			−1.13993
$887$	22.7299	+	13.1231i	0.763195	+	0.440631i	0.830442	−	0.557106i	$-0.188088\pi$
$887$	22.7299	+	13.1231i	0.763195	+	0.440631i	−0.0672468	+	0.997736i	$0.521421\pi$
$888$	10.3923	−	6.00000i	0.348743	−	0.201347i
$889$	−3.41146	+	5.90882i	−0.114417	+	0.198176i
$890$		0			0
$891$	3.50000	+	6.06218i	0.117254	+	0.203091i
$892$			11.3153i			0.378866i
$893$	−11.3649	+	5.30019i	−0.380313	+	0.177364i
$894$	−40.9848			−1.37074
$895$		0			0
$896$	0.219224	+	0.379706i	0.00732375	+	0.0126851i
$897$	20.7846	+	12.0000i	0.693978	+	0.400668i
$898$	25.1147	−	14.5000i	0.838090	−	0.483871i
$899$	10.2462	−	17.7470i	0.341730	−	0.591894i
$900$		0			0
$901$	−38.7386			−1.29057
$902$	−5.30277	−	3.06155i	−0.176563	−	0.101939i
$903$	−3.03765	−	1.75379i	−0.101087	−	0.0583624i
$904$	−16.8078			−0.559018
$905$		0			0
$906$	−26.2462	+	45.4598i	−0.871972	+	1.51030i
$907$	−43.4546	+	25.0885i	−1.44289	+	0.833051i	−0.998041	−	0.0625559i	$-0.980075\pi$
$907$	−43.4546	+	25.0885i	−1.44289	+	0.833051i	−0.444846	+	0.895607i	$0.646741\pi$
$908$	17.2606	+	9.96543i	0.572814	+	0.330715i
$909$	17.8078	+	30.8440i	0.590646	+	1.02303i
$910$		0			0
$911$	12.3845			0.410316			0.205158	−	0.978729i	$-0.434229\pi$
$911$	12.3845			0.410316			0.205158	+	0.978729i	$0.434229\pi$
$912$	−10.1192	+	4.71922i	−0.335081	+	0.156269i
$913$			10.8078i			0.357685i
$914$	−3.52699	−	6.10892i	−0.116662	−	0.202065i
$915$		0			0
$916$	−6.43845	+	11.1517i	−0.212732	+	0.368463i
$917$	−6.12205	+	3.53457i	−0.202168	+	0.116722i
$918$	6.38202	+	3.68466i	0.210638	+	0.121612i
$919$	−20.2462			−0.667861			−0.333930	−	0.942598i	$-0.608375\pi$
$919$	−20.2462			−0.667861			−0.333930	+	0.942598i	$0.608375\pi$
$920$		0			0
$921$	−30.6501	+	53.0875i	−1.00995	+	1.74929i
$922$	−33.7619	−	19.4924i	−1.11189	−	0.641949i
$923$			32.4924i			1.06950i
$924$	1.12311			0.0369475
$925$		0			0
$926$	−9.78078	−	16.9408i	−0.321416	−	0.556709i
$927$	17.9134	+	10.3423i	0.588355	+	0.339687i
$928$	1.73205	−	1.00000i	0.0568574	−	0.0328266i
$929$	−17.9924	−	31.1638i	−0.590312	−	1.02245i	−0.994190	−	0.107638i	$-0.965671\pi$
$929$	−17.9924	−	31.1638i	−0.590312	−	1.02245i	0.403878	−	0.914813i	$-0.367662\pi$
$930$		0			0
$931$	17.0194	−	24.3086i	0.557789	−	0.796682i
$932$			2.31534i			0.0758415i
$933$	8.87348	−	5.12311i	0.290505	−	0.167723i
$934$	−8.28078	−	14.3427i	−0.270955	−	0.469308i
$935$		0			0
$936$	−3.56155	−	6.16879i	−0.116413	−	0.201633i
$937$	43.4546	+	25.0885i	1.41960	+	0.819607i	0.996264	−	0.0863653i	$-0.0275252\pi$
$937$	43.4546	+	25.0885i	1.41960	+	0.819607i	0.423337	+	0.905972i	$0.360859\pi$
$938$			4.13826i			0.135119i
$939$	11.0540			0.360733
$940$		0			0
$941$	8.12311	−	14.0696i	0.264806	−	0.458657i	−0.702707	−	0.711479i	$-0.748026\pi$
$941$	8.12311	−	14.0696i	0.264806	−	0.458657i	0.967513	+	0.252822i	$0.0813589\pi$
$942$			6.24621i			0.203513i
$943$		−	28.6847i		−	0.934101i
$944$	7.28078	−	12.6107i	0.236969	−	0.410442i
$945$		0			0
$946$	1.56155	−	2.70469i	0.0507705	−	0.0879370i
$947$	48.9239	−	28.2462i	1.58981	−	0.917879i	0.596475	−	0.802631i	$-0.296567\pi$
$947$	48.9239	−	28.2462i	1.58981	−	0.917879i	0.993337	−	0.115247i	$-0.0367660\pi$
$948$	−24.6752	+	14.2462i	−0.801412	+	0.462695i
$949$	−3.36932			−0.109373
$950$		0			0
$951$	−47.8617			−1.55202
$952$	−1.94528	+	1.12311i	−0.0630468	+	0.0364001i
$953$	13.5833	−	7.84233i	0.440007	−	0.254038i	−0.263594	−	0.964634i	$-0.584908\pi$
$953$	13.5833	−	7.84233i	0.440007	−	0.254038i	0.703600	+	0.710596i	$0.251575\pi$
$954$	13.4654	−	23.3228i	0.435960	−	0.755104i
$955$		0			0
$956$	−9.12311	+	15.8017i	−0.295062	+	0.511063i
$957$		−	5.12311i		−	0.165606i
$958$			29.3693i			0.948880i
$959$	−1.19224	+	2.06501i	−0.0384993	+	0.0666828i
$960$		0			0
$961$	73.9848			2.38661
$962$		−	9.36932i		−	0.302079i
$963$	6.92820	+	4.00000i	0.223258	+	0.128898i
$964$	−4.28078	−	7.41452i	−0.137875	−	0.238806i
$965$		0			0
$966$	2.63068	+	4.55648i	0.0846408	+	0.146602i
$967$	25.2213	−	14.5616i	0.811064	−	0.468268i	−0.0362613	−	0.999342i	$-0.511545\pi$
$967$	25.2213	−	14.5616i	0.811064	−	0.468268i	0.847325	+	0.531074i	$0.178212\pi$
$968$		−	10.0000i		−	0.321412i
$969$	−24.1771	−	51.8418i	−0.776680	−	1.66540i
$970$		0			0
$971$	−8.96543	−	15.5286i	−0.287714	−	0.498336i	0.685549	−	0.728026i	$-0.259562\pi$
$971$	−8.96543	−	15.5286i	−0.287714	−	0.498336i	−0.973264	+	0.229690i	$0.926229\pi$
$972$	19.2658	−	11.1231i	0.617950	−	0.356774i
$973$	3.34436	+	1.93087i	0.107215	+	0.0619008i
$974$	3.46543	+	6.00231i	0.111040	+	0.192326i
$975$		0			0
$976$	5.12311			0.163987
$977$		−	30.3153i		−	0.969874i	−0.874549	−	0.484937i	$-0.838843\pi$
$977$		−	30.3153i		−	0.969874i	0.874549	−	0.484937i	$-0.161157\pi$
$978$	37.8320	+	21.8423i	1.20973	+	0.698441i
$979$	−1.34233	+	2.32498i	−0.0429010	+	0.0743068i
$980$		0			0
$981$	−50.7386			−1.61996
$982$	−7.94759	−	4.58854i	−0.253618	−	0.146426i
$983$	−35.9934	+	20.7808i	−1.14801	+	0.662804i	−0.948401	−	0.317072i	$-0.897300\pi$
$983$	−35.9934	+	20.7808i	−1.14801	+	0.662804i	−0.199608	+	0.979876i	$0.563967\pi$
$984$	−7.84233	+	13.5833i	−0.250004	+	0.433020i
$985$		0			0
$986$	5.12311	+	8.87348i	0.163153	+	0.282589i
$987$		−	3.23106i		−	0.102846i
$988$	−0.759413	+	8.68466i	−0.0241601	+	0.276296i
$989$	14.6307			0.465229
$990$		0			0
$991$	4.19224	+	7.26117i	0.133171	+	0.230659i	0.924897	−	0.380217i	$-0.124151\pi$
$991$	4.19224	+	7.26117i	0.133171	+	0.230659i	−0.791726	+	0.610876i	$0.790817\pi$
$992$	8.87348	+	5.12311i	0.281733	+	0.162659i
$993$	52.1149	−	30.0885i	1.65382	−	0.954831i
$994$	−3.56155	+	6.16879i	−0.112966	+	0.195662i
$995$		0			0
$996$	27.6847			0.877222
$997$	2.32498	+	1.34233i	0.0736329	+	0.0425120i	0.536364	−	0.843986i	$-0.319797\pi$
$997$	2.32498	+	1.34233i	0.0736329	+	0.0425120i	−0.462732	+	0.886498i	$0.653131\pi$
$998$	−25.1147	−	14.5000i	−0.794993	−	0.458989i
$999$	−6.73863			−0.213201

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.j.f.349.2		8
5.2	odd	4		950.2.e.h.501.1		4
5.3	odd	4		190.2.e.c.121.2	yes	4
5.4	even	2	inner	950.2.j.f.349.3		8
15.8	even	4		1710.2.l.m.1261.1		4
19.11	even	3	inner	950.2.j.f.49.3		8
20.3	even	4		1520.2.q.h.881.1		4
95.49	even	6	inner	950.2.j.f.49.2		8
95.68	odd	12		190.2.e.c.11.2	✓	4
95.83	odd	12		3610.2.a.k.1.1		2
95.87	odd	12		950.2.e.h.201.1		4
95.88	even	12		3610.2.a.u.1.2		2
285.68	even	12		1710.2.l.m.1531.1		4
380.163	even	12		1520.2.q.h.961.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.e.c.11.2	✓	4	95.68	odd	12
190.2.e.c.121.2	yes	4	5.3	odd	4
950.2.e.h.201.1		4	95.87	odd	12
950.2.e.h.501.1		4	5.2	odd	4
950.2.j.f.49.2		8	95.49	even	6	inner
950.2.j.f.49.3		8	19.11	even	3	inner
950.2.j.f.349.2		8	1.1	even	1	trivial
950.2.j.f.349.3		8	5.4	even	2	inner
1520.2.q.h.881.1		4	20.3	even	4
1520.2.q.h.961.1		4	380.163	even	12
1710.2.l.m.1261.1		4	15.8	even	4
1710.2.l.m.1531.1		4	285.68	even	12
3610.2.a.k.1.1		2	95.83	odd	12
3610.2.a.u.1.2		2	95.88	even	12

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)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(2.21837 - 1.28078i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.28078 + 2.21837i) q^{6} +0.438447i q^{7} +1.00000i q^{8} +(1.78078 - 3.08440i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(2.21837 - 1.28078i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.28078 + 2.21837i) q^{6} +0.438447i q^{7} +1.00000i q^{8} +(1.78078 - 3.08440i) q^{9} +1.00000 q^{11} -2.56155i q^{12} +(-1.73205 - 1.00000i) q^{13} +(-0.219224 - 0.379706i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(4.43674 - 2.56155i) q^{17} +3.56155i q^{18} +(2.50000 - 3.57071i) q^{19} +(0.561553 + 0.972638i) q^{21} +(-0.866025 + 0.500000i) q^{22} +(-4.05703 - 2.34233i) q^{23} +(1.28078 + 2.21837i) q^{24} +2.00000 q^{26} -1.43845i q^{27} +(0.379706 + 0.219224i) q^{28} +(1.00000 - 1.73205i) q^{29} +10.2462 q^{31} +(0.866025 + 0.500000i) q^{32} +(2.21837 - 1.28078i) q^{33} +(-2.56155 + 4.43674i) q^{34} +(-1.78078 - 3.08440i) q^{36} -4.68466i q^{37} +(-0.379706 + 4.34233i) q^{38} -5.12311 q^{39} +(3.06155 + 5.30277i) q^{41} +(-0.972638 - 0.561553i) q^{42} +(-2.70469 + 1.56155i) q^{43} +(0.500000 - 0.866025i) q^{44} +4.68466 q^{46} +(-2.49146 - 1.43845i) q^{47} +(-2.21837 - 1.28078i) q^{48} +6.80776 q^{49} +(6.56155 - 11.3649i) q^{51} +(-1.73205 + 1.00000i) q^{52} +(-6.54850 - 3.78078i) q^{53} +(0.719224 + 1.24573i) q^{54} -0.438447 q^{56} +(0.972638 - 11.1231i) q^{57} +2.00000i q^{58} +(7.28078 + 12.6107i) q^{59} +(-2.56155 + 4.43674i) q^{61} +(-8.87348 + 5.12311i) q^{62} +(1.35234 + 0.780776i) q^{63} -1.00000 q^{64} +(-1.28078 + 2.21837i) q^{66} +(-8.17394 - 4.71922i) q^{67} -5.12311i q^{68} -12.0000 q^{69} +(-8.12311 - 14.0696i) q^{71} +(3.08440 + 1.78078i) q^{72} +(1.45896 - 0.842329i) q^{73} +(2.34233 + 4.05703i) q^{74} +(-1.84233 - 3.95042i) q^{76} +0.438447i q^{77} +(4.43674 - 2.56155i) q^{78} +(-5.56155 - 9.63289i) q^{79} +(3.50000 + 6.06218i) q^{81} +(-5.30277 - 3.06155i) q^{82} +10.8078i q^{83} +1.12311 q^{84} +(1.56155 - 2.70469i) q^{86} -5.12311i q^{87} +1.00000i q^{88} +(-1.34233 + 2.32498i) q^{89} +(0.438447 - 0.759413i) q^{91} +(-4.05703 + 2.34233i) q^{92} +(22.7299 - 13.1231i) q^{93} +2.87689 q^{94} +2.56155 q^{96} +(1.45896 - 0.842329i) q^{97} +(-5.89570 + 3.40388i) q^{98} +(1.78078 - 3.08440i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} - 2 q^{6} + 6 q^{9}+O(q^{10}) \) 8 * q + 4 * q^4 - 2 * q^6 + 6 * q^9	\( 8 q + 4 q^{4} - 2 q^{6} + 6 q^{9} + 8 q^{11} - 10 q^{14} - 4 q^{16} + 20 q^{19} - 12 q^{21} + 2 q^{24} + 16 q^{26} + 8 q^{29} + 16 q^{31} - 4 q^{34} - 6 q^{36} - 8 q^{39} + 8 q^{41} + 4 q^{44} - 12 q^{46} - 28 q^{49} + 36 q^{51} + 14 q^{54} - 20 q^{56} + 50 q^{59} - 4 q^{61} - 8 q^{64} - 2 q^{66} - 96 q^{69} - 32 q^{71} - 6 q^{74} + 10 q^{76} - 28 q^{79} + 28 q^{81} - 24 q^{84} - 4 q^{86} + 14 q^{89} + 20 q^{91} + 56 q^{94} + 4 q^{96} + 6 q^{99}+O(q^{100}) \) 8 * q + 4 * q^4 - 2 * q^6 + 6 * q^9 + 8 * q^11 - 10 * q^14 - 4 * q^16 + 20 * q^19 - 12 * q^21 + 2 * q^24 + 16 * q^26 + 8 * q^29 + 16 * q^31 - 4 * q^34 - 6 * q^36 - 8 * q^39 + 8 * q^41 + 4 * q^44 - 12 * q^46 - 28 * q^49 + 36 * q^51 + 14 * q^54 - 20 * q^56 + 50 * q^59 - 4 * q^61 - 8 * q^64 - 2 * q^66 - 96 * q^69 - 32 * q^71 - 6 * q^74 + 10 * q^76 - 28 * q^79 + 28 * q^81 - 24 * q^84 - 4 * q^86 + 14 * q^89 + 20 * q^91 + 56 * q^94 + 4 * q^96 + 6 * q^99

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