LMFDB - Embedded newform 1950.2.z.m.1699.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(1699,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("1950.1699");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.z (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:	$15.5708283941$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1699.3
Root			$-1.35234 + 0.780776i$ of defining polynomial
Character	$\chi$	$=$	1950.1699
Dual form			1950.2.z.m.1849.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(-0.486319 + 0.280776i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(-0.486319 + 0.280776i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.78078 + 3.08440i) q^{11} -1.00000i q^{12} +(1.35234 - 3.34233i) q^{13} -0.561553 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-4.43674 + 2.56155i) q^{17} +1.00000i q^{18} +(-3.28078 - 5.68247i) q^{19} +0.561553 q^{21} +(-3.08440 + 1.78078i) q^{22} +(-4.05703 - 2.34233i) q^{23} +(0.500000 - 0.866025i) q^{24} +(2.84233 - 2.21837i) q^{26} -1.00000i q^{27} +(-0.486319 - 0.280776i) q^{28} +(-3.56155 + 6.16879i) q^{29} +4.00000 q^{31} +(-0.866025 + 0.500000i) q^{32} +(3.08440 - 1.78078i) q^{33} -5.12311 q^{34} +(-0.500000 + 0.866025i) q^{36} +(-3.08440 - 1.78078i) q^{37} -6.56155i q^{38} +(-2.84233 + 2.21837i) q^{39} +(-2.56155 + 4.43674i) q^{41} +(0.486319 + 0.280776i) q^{42} +(3.95042 - 2.28078i) q^{43} -3.56155 q^{44} +(-2.34233 - 4.05703i) q^{46} -4.00000i q^{47} +(0.866025 - 0.500000i) q^{48} +(-3.34233 + 5.78908i) q^{49} +5.12311 q^{51} +(3.57071 - 0.500000i) q^{52} -12.2462i q^{53} +(0.500000 - 0.866025i) q^{54} +(-0.280776 - 0.486319i) q^{56} +6.56155i q^{57} +(-6.16879 + 3.56155i) q^{58} +(3.12311 + 5.40938i) q^{59} +(-5.34233 - 9.25319i) q^{61} +(3.46410 + 2.00000i) q^{62} +(-0.486319 - 0.280776i) q^{63} -1.00000 q^{64} +3.56155 q^{66} +(-7.62775 - 4.40388i) q^{67} +(-4.43674 - 2.56155i) q^{68} +(2.34233 + 4.05703i) q^{69} +(-4.21922 - 7.30791i) q^{71} +(-0.866025 + 0.500000i) q^{72} +9.00000i q^{73} +(-1.78078 - 3.08440i) q^{74} +(3.28078 - 5.68247i) q^{76} -2.00000i q^{77} +(-3.57071 + 0.500000i) q^{78} -4.80776 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-4.43674 + 2.56155i) q^{82} +2.43845i q^{83} +(0.280776 + 0.486319i) q^{84} +4.56155 q^{86} +(6.16879 - 3.56155i) q^{87} +(-3.08440 - 1.78078i) q^{88} +(-3.12311 + 5.40938i) q^{89} +(0.280776 + 2.00514i) q^{91} -4.68466i q^{92} +(-3.46410 - 2.00000i) q^{93} +(2.00000 - 3.46410i) q^{94} +1.00000 q^{96} +(-15.4220 + 8.90388i) q^{97} +(-5.78908 + 3.34233i) q^{98} -3.56155 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} - 4 q^{6} + 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^4 - 4 * q^6 + 4 * q^9	$ 8 q + 4 q^{4} - 4 q^{6} + 4 q^{9} - 6 q^{11} + 12 q^{14} - 4 q^{16} - 18 q^{19} - 12 q^{21} + 4 q^{24} - 2 q^{26} - 12 q^{29} + 32 q^{31} - 8 q^{34} - 4 q^{36} + 2 q^{39} - 4 q^{41} - 12 q^{44} + 6 q^{46} - 2 q^{49} + 8 q^{51} + 4 q^{54} + 6 q^{56} - 8 q^{59} - 18 q^{61} - 8 q^{64} + 12 q^{66} - 6 q^{69} - 42 q^{71} - 6 q^{74} + 18 q^{76} + 44 q^{79} - 4 q^{81} - 6 q^{84} + 20 q^{86} + 8 q^{89} - 6 q^{91} + 16 q^{94} + 8 q^{96} - 12 q^{99}+O(q^{100}) $ 8 * q + 4 * q^4 - 4 * q^6 + 4 * q^9 - 6 * q^11 + 12 * q^14 - 4 * q^16 - 18 * q^19 - 12 * q^21 + 4 * q^24 - 2 * q^26 - 12 * q^29 + 32 * q^31 - 8 * q^34 - 4 * q^36 + 2 * q^39 - 4 * q^41 - 12 * q^44 + 6 * q^46 - 2 * q^49 + 8 * q^51 + 4 * q^54 + 6 * q^56 - 8 * q^59 - 18 * q^61 - 8 * q^64 + 12 * q^66 - 6 * q^69 - 42 * q^71 - 6 * q^74 + 18 * q^76 + 44 * q^79 - 4 * q^81 - 6 * q^84 + 20 * q^86 + 8 * q^89 - 6 * q^91 + 16 * q^94 + 8 * q^96 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	−0.486319	+	0.280776i	−0.183811	+	0.106124i	−0.589082	−	0.808073i	$-0.700511\pi$
$7$	−0.486319	+	0.280776i	−0.183811	+	0.106124i	0.405271	+	0.914197i	$0.367177\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	−1.78078	+	3.08440i	−0.536924	+	0.929980i	0.462143	+	0.886805i	$0.347081\pi$
$11$	−1.78078	+	3.08440i	−0.536924	+	0.929980i	−0.999068	+	0.0431749i	$0.986253\pi$
$12$		−	1.00000i		−	0.288675i
$13$	1.35234	−	3.34233i	0.375073	−	0.926995i
$13$	1.35234	−	3.34233i	0.375073	−	0.926995i
$14$	−0.561553			−0.150081
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−4.43674	+	2.56155i	−1.07607	+	0.621268i	−0.929833	−	0.367982i	$-0.880049\pi$
$17$	−4.43674	+	2.56155i	−1.07607	+	0.621268i	−0.146235	+	0.989250i	$0.546715\pi$
$18$			1.00000i			0.235702i
$19$	−3.28078	−	5.68247i	−0.752662	−	1.30365i	−0.946528	−	0.322620i	$-0.895436\pi$
$19$	−3.28078	−	5.68247i	−0.752662	−	1.30365i	0.193867	−	0.981028i	$-0.437897\pi$
$20$		0			0
$21$	0.561553			0.122541
$22$	−3.08440	+	1.78078i	−0.657595	+	0.379663i
$23$	−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	$0.829089\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$		0			0
$26$	2.84233	−	2.21837i	0.557427	−	0.435058i
$27$		−	1.00000i		−	0.192450i
$28$	−0.486319	−	0.280776i	−0.0919057	−	0.0530618i
$29$	−3.56155	+	6.16879i	−0.661364	+	1.14552i	0.318894	+	0.947790i	$0.396689\pi$
$29$	−3.56155	+	6.16879i	−0.661364	+	1.14552i	−0.980257	+	0.197725i	$0.936645\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	3.08440	−	1.78078i	0.536924	−	0.309993i
$34$	−5.12311			−0.878605
$35$		0			0
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−3.08440	−	1.78078i	−0.507071	−	0.292758i	0.224558	−	0.974461i	$-0.427906\pi$
$37$	−3.08440	−	1.78078i	−0.507071	−	0.292758i	−0.731629	+	0.681703i	$0.761240\pi$
$38$		−	6.56155i		−	1.06442i
$39$	−2.84233	+	2.21837i	−0.455137	+	0.355223i
$40$		0			0
$41$	−2.56155	+	4.43674i	−0.400047	+	0.692902i	−0.993731	−	0.111796i	$-0.964340\pi$
$41$	−2.56155	+	4.43674i	−0.400047	+	0.692902i	0.593684	+	0.804698i	$0.297673\pi$
$42$	0.486319	+	0.280776i	0.0750407	+	0.0433247i
$43$	3.95042	−	2.28078i	0.602433	−	0.347815i	−0.167565	−	0.985861i	$-0.553590\pi$
$43$	3.95042	−	2.28078i	0.602433	−	0.347815i	0.769998	+	0.638046i	$0.220257\pi$
$44$	−3.56155			−0.536924
$45$		0			0
$46$	−2.34233	−	4.05703i	−0.345358	−	0.598177i
$47$		−	4.00000i		−	0.583460i	−0.956501	−	0.291730i	$-0.905769\pi$
$47$		−	4.00000i		−	0.583460i	0.956501	−	0.291730i	$-0.0942309\pi$
$48$	0.866025	−	0.500000i	0.125000	−	0.0721688i
$49$	−3.34233	+	5.78908i	−0.477476	+	0.827012i
$50$		0			0
$51$	5.12311			0.717378
$52$	3.57071	−	0.500000i	0.495169	−	0.0693375i
$53$		−	12.2462i		−	1.68215i	−0.540921	−	0.841073i	$-0.681924\pi$
$53$		−	12.2462i		−	1.68215i	0.540921	−	0.841073i	$-0.318076\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$		0			0
$56$	−0.280776	−	0.486319i	−0.0375203	−	0.0649871i
$57$			6.56155i			0.869099i
$58$	−6.16879	+	3.56155i	−0.810002	+	0.467655i
$59$	3.12311	+	5.40938i	0.406594	+	0.704241i	0.994506	−	0.104684i	$-0.0333831\pi$
$59$	3.12311	+	5.40938i	0.406594	+	0.704241i	−0.587912	+	0.808925i	$0.700050\pi$
$60$		0			0
$61$	−5.34233	−	9.25319i	−0.684015	−	1.18475i	−0.973745	−	0.227641i	$-0.926899\pi$
$61$	−5.34233	−	9.25319i	−0.684015	−	1.18475i	0.289730	−	0.957108i	$-0.406434\pi$
$62$	3.46410	+	2.00000i	0.439941	+	0.254000i
$63$	−0.486319	−	0.280776i	−0.0612704	−	0.0353745i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	3.56155			0.438397
$67$	−7.62775	−	4.40388i	−0.931878	−	0.538020i	−0.0444727	−	0.999011i	$-0.514161\pi$
$67$	−7.62775	−	4.40388i	−0.931878	−	0.538020i	−0.887405	+	0.460991i	$0.847494\pi$
$68$	−4.43674	−	2.56155i	−0.538034	−	0.310634i
$69$	2.34233	+	4.05703i	0.281983	+	0.488409i
$70$		0			0
$71$	−4.21922	−	7.30791i	−0.500730	−	0.867289i	−1.00000		0.000842810i	$-0.999732\pi$
$71$	−4.21922	−	7.30791i	−0.500730	−	0.867289i	0.499270	−	0.866447i	$-0.333602\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$			9.00000i			1.05337i	0.850060	+	0.526685i	$0.176565\pi$
$73$			9.00000i			1.05337i	−0.850060	+	0.526685i	$0.823435\pi$
$74$	−1.78078	−	3.08440i	−0.207011	−	0.358554i
$75$		0			0
$76$	3.28078	−	5.68247i	0.376331	−	0.651824i
$77$		−	2.00000i		−	0.227921i
$78$	−3.57071	+	0.500000i	−0.404304	+	0.0566139i
$79$	−4.80776			−0.540916			−0.270458	−	0.962732i	$-0.587175\pi$
$79$	−4.80776			−0.540916			−0.270458	+	0.962732i	$0.587175\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−4.43674	+	2.56155i	−0.489956	+	0.282876i
$83$			2.43845i			0.267654i	0.991005	+	0.133827i	$0.0427267\pi$
$83$			2.43845i			0.267654i	−0.991005	+	0.133827i	$0.957273\pi$
$84$	0.280776	+	0.486319i	0.0306352	+	0.0530618i
$85$		0			0
$86$	4.56155			0.491885
$87$	6.16879	−	3.56155i	0.661364	−	0.381839i
$88$	−3.08440	−	1.78078i	−0.328798	−	0.189831i
$89$	−3.12311	+	5.40938i	−0.331049	+	0.573393i	−0.982718	−	0.185110i	$-0.940736\pi$
$89$	−3.12311	+	5.40938i	−0.331049	+	0.573393i	0.651669	+	0.758503i	$0.274069\pi$
$90$		0			0
$91$	0.280776	+	2.00514i	0.0294334	+	0.210196i
$92$		−	4.68466i		−	0.488409i
$93$	−3.46410	−	2.00000i	−0.359211	−	0.207390i
$94$	2.00000	−	3.46410i	0.206284	−	0.357295i
$95$		0			0
$96$	1.00000			0.102062
$97$	−15.4220	+	8.90388i	−1.56586	+	0.904052i	−0.569221	+	0.822184i	$0.692755\pi$
$97$	−15.4220	+	8.90388i	−1.56586	+	0.904052i	−0.996643	+	0.0818678i	$0.973911\pi$
$98$	−5.78908	+	3.34233i	−0.584786	+	0.337626i
$99$	−3.56155			−0.357950
$100$		0			0
$101$	−5.12311	+	8.87348i	−0.509768	+	0.882944i	0.490168	+	0.871628i	$0.336935\pi$
$101$	−5.12311	+	8.87348i	−0.509768	+	0.882944i	−0.999936	+	0.0113162i	$0.996398\pi$
$102$	4.43674	+	2.56155i	0.439303	+	0.253632i
$103$		−	8.56155i		−	0.843595i	−0.906690	−	0.421797i	$-0.861399\pi$
$103$		−	8.56155i		−	0.843595i	0.906690	−	0.421797i	$-0.138601\pi$
$104$	3.34233	+	1.35234i	0.327742	+	0.132608i
$105$		0			0
$106$	6.12311	−	10.6055i	0.594729	−	1.03010i
$107$	−16.7743	−	9.68466i	−1.62163	−	0.936251i	−0.986483	−	0.163864i	$-0.947604\pi$
$107$	−16.7743	−	9.68466i	−1.62163	−	0.936251i	−0.635152	−	0.772387i	$-0.719062\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	−17.8078			−1.70567			−0.852837	−	0.522177i	$-0.825120\pi$
$109$	−17.8078			−1.70567			−0.852837	+	0.522177i	$0.825120\pi$
$110$		0			0
$111$	1.78078	+	3.08440i	0.169024	+	0.292758i
$112$		−	0.561553i		−	0.0530618i
$113$	3.46410	−	2.00000i	0.325875	−	0.188144i	−0.328133	−	0.944632i	$-0.606419\pi$
$113$	3.46410	−	2.00000i	0.325875	−	0.188144i	0.654008	+	0.756487i	$0.273086\pi$
$114$	−3.28078	+	5.68247i	−0.307273	+	0.532212i
$115$		0			0
$116$	−7.12311			−0.661364
$117$	3.57071	−	0.500000i	0.330113	−	0.0462250i
$118$			6.24621i			0.575010i
$119$	1.43845	−	2.49146i	0.131862	−	0.228392i
$120$		0			0
$121$	−0.842329	−	1.45896i	−0.0765754	−	0.132632i
$122$		−	10.6847i		−	0.967344i
$123$	4.43674	−	2.56155i	0.400047	−	0.230967i
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$		0			0
$126$	−0.280776	−	0.486319i	−0.0250136	−	0.0433247i
$127$	1.03251	+	0.596118i	0.0916201	+	0.0528969i	0.545110	−	0.838364i	$-0.316488\pi$
$127$	1.03251	+	0.596118i	0.0916201	+	0.0528969i	−0.453490	+	0.891261i	$0.649821\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−4.56155			−0.401622
$130$		0			0
$131$	9.12311			0.797089			0.398545	−	0.917149i	$-0.369515\pi$
$131$	9.12311			0.797089			0.398545	+	0.917149i	$0.369515\pi$
$132$	3.08440	+	1.78078i	0.268462	+	0.154997i
$133$	3.19101	+	1.84233i	0.276695	+	0.159750i
$134$	−4.40388	−	7.62775i	−0.380437	−	0.658937i
$135$		0			0
$136$	−2.56155	−	4.43674i	−0.219651	−	0.380447i
$137$	14.2829	−	8.24621i	1.22027	−	0.704521i	0.255292	−	0.966864i	$-0.417828\pi$
$137$	14.2829	−	8.24621i	1.22027	−	0.704521i	0.964975	+	0.262343i	$0.0844951\pi$
$138$			4.68466i			0.398785i
$139$	8.71922	+	15.1021i	0.739555	+	1.28095i	0.952696	+	0.303925i	$0.0982973\pi$
$139$	8.71922	+	15.1021i	0.739555	+	1.28095i	−0.213141	+	0.977021i	$0.568369\pi$
$140$		0			0
$141$	−2.00000	+	3.46410i	−0.168430	+	0.291730i
$142$		−	8.43845i		−	0.708139i
$143$	7.90084	+	10.1231i	0.660702	+	0.846537i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	−4.50000	+	7.79423i	−0.372423	+	0.645055i
$147$	5.78908	−	3.34233i	0.477476	−	0.275671i
$148$		−	3.56155i		−	0.292758i
$149$	3.12311	+	5.40938i	0.255855	+	0.443153i	0.965127	−	0.261781i	$-0.0843098\pi$
$149$	3.12311	+	5.40938i	0.255855	+	0.443153i	−0.709273	+	0.704934i	$0.750976\pi$
$150$		0			0
$151$	−4.31534			−0.351178			−0.175589	−	0.984464i	$-0.556183\pi$
$151$	−4.31534			−0.351178			−0.175589	+	0.984464i	$0.556183\pi$
$152$	5.68247	−	3.28078i	0.460909	−	0.266106i
$153$	−4.43674	−	2.56155i	−0.358689	−	0.207089i
$154$	1.00000	−	1.73205i	0.0805823	−	0.139573i
$155$		0			0
$156$	−3.34233	−	1.35234i	−0.267601	−	0.108274i
$157$		−	0.753789i		−	0.0601589i	−0.999548	−	0.0300794i	$-0.990424\pi$
$157$		−	0.753789i		−	0.0601589i	0.999548	−	0.0300794i	$-0.00957603\pi$
$158$	−4.16365	−	2.40388i	−0.331242	−	0.191243i
$159$	−6.12311	+	10.6055i	−0.485594	+	0.841073i
$160$		0			0
$161$	2.63068			0.207327
$162$	−0.866025	+	0.500000i	−0.0680414	+	0.0392837i
$163$	14.2829	−	8.24621i	1.11872	−	0.645893i	0.177646	−	0.984094i	$-0.443152\pi$
$163$	14.2829	−	8.24621i	1.11872	−	0.645893i	0.941074	+	0.338201i	$0.109818\pi$
$164$	−5.12311			−0.400047
$165$		0			0
$166$	−1.21922	+	2.11176i	−0.0946301	+	0.163904i
$167$	9.79937	+	5.65767i	0.758298	+	0.437804i	0.828684	−	0.559716i	$-0.189090\pi$
$167$	9.79937	+	5.65767i	0.758298	+	0.437804i	−0.0703862	+	0.997520i	$0.522423\pi$
$168$			0.561553i			0.0433247i
$169$	−9.34233	−	9.03996i	−0.718641	−	0.695382i
$170$		0			0
$171$	3.28078	−	5.68247i	0.250887	−	0.434549i
$172$	3.95042	+	2.28078i	0.301217	+	0.173908i
$173$	−14.8290	+	8.56155i	−1.12743	+	0.650923i	−0.943288	−	0.331977i	$-0.892285\pi$
$173$	−14.8290	+	8.56155i	−1.12743	+	0.650923i	−0.184144	+	0.982899i	$0.558951\pi$
$174$	7.12311			0.540001
$175$		0			0
$176$	−1.78078	−	3.08440i	−0.134231	−	0.232495i
$177$		−	6.24621i		−	0.469494i
$178$	−5.40938	+	3.12311i	−0.405450	+	0.234087i
$179$	−1.65767	+	2.87117i	−0.123900	+	0.214601i	−0.921302	−	0.388847i	$-0.872874\pi$
$179$	−1.65767	+	2.87117i	−0.123900	+	0.214601i	0.797402	+	0.603448i	$0.206207\pi$
$180$		0			0
$181$	17.4924			1.30020			0.650101	−	0.759848i	$-0.274727\pi$
$181$	17.4924			1.30020			0.650101	+	0.759848i	$0.274727\pi$
$182$	−0.759413	+	1.87689i	−0.0562914	+	0.139125i
$183$			10.6847i			0.789833i
$184$	2.34233	−	4.05703i	0.172679	−	0.299088i
$185$		0			0
$186$	−2.00000	−	3.46410i	−0.146647	−	0.254000i
$187$		−	18.2462i		−	1.33430i
$188$	3.46410	−	2.00000i	0.252646	−	0.145865i
$189$	0.280776	+	0.486319i	0.0204235	+	0.0353745i
$190$		0			0
$191$	6.46543	+	11.1985i	0.467822	+	0.810292i	0.999324	−	0.0367651i	$-0.0117053\pi$
$191$	6.46543	+	11.1985i	0.467822	+	0.810292i	−0.531501	+	0.847057i	$0.678372\pi$
$192$	0.866025	+	0.500000i	0.0625000	+	0.0360844i
$193$	−2.59808	−	1.50000i	−0.187014	−	0.107972i	0.403570	−	0.914949i	$-0.367769\pi$
$193$	−2.59808	−	1.50000i	−0.187014	−	0.107972i	−0.590584	+	0.806976i	$0.701102\pi$
$194$	−17.8078			−1.27852
$195$		0			0
$196$	−6.68466			−0.477476
$197$	−2.70469	−	1.56155i	−0.192701	−	0.111256i	0.400545	−	0.916277i	$-0.368821\pi$
$197$	−2.70469	−	1.56155i	−0.192701	−	0.111256i	−0.593246	+	0.805021i	$0.702154\pi$
$198$	−3.08440	−	1.78078i	−0.219198	−	0.126554i
$199$	−4.28078	−	7.41452i	−0.303456	−	0.525602i	0.673460	−	0.739223i	$-0.264807\pi$
$199$	−4.28078	−	7.41452i	−0.303456	−	0.525602i	−0.976916	+	0.213622i	$0.931474\pi$
$200$		0			0
$201$	4.40388	+	7.62775i	0.310626	+	0.538020i
$202$	−8.87348	+	5.12311i	−0.624336	+	0.360460i
$203$		−	4.00000i		−	0.280745i
$204$	2.56155	+	4.43674i	0.179345	+	0.310634i
$205$		0			0
$206$	4.28078	−	7.41452i	0.298256	−	0.516594i
$207$		−	4.68466i		−	0.325606i
$208$	2.21837	+	2.84233i	0.153816	+	0.197080i
$209$	23.3693			1.61649
$210$		0			0
$211$	3.56155	−	6.16879i	0.245187	−	0.424677i	−0.716997	−	0.697076i	$-0.754484\pi$
$211$	3.56155	−	6.16879i	0.245187	−	0.424677i	0.962184	+	0.272399i	$0.0878172\pi$
$212$	10.6055	−	6.12311i	0.728391	−	0.420537i
$213$			8.43845i			0.578193i
$214$	−9.68466	−	16.7743i	−0.662030	−	1.14667i
$215$		0			0
$216$	1.00000			0.0680414
$217$	−1.94528	+	1.12311i	−0.132054	+	0.0762414i
$218$	−15.4220	−	8.90388i	−1.04451	−	0.603047i
$219$	4.50000	−	7.79423i	0.304082	−	0.526685i
$220$		0			0
$221$	2.56155	+	18.2931i	0.172309	+	1.23053i
$222$			3.56155i			0.239036i
$223$	3.95042	+	2.28078i	0.264540	+	0.152732i	0.626404	−	0.779499i	$-0.284526\pi$
$223$	3.95042	+	2.28078i	0.264540	+	0.152732i	−0.361864	+	0.932231i	$0.617860\pi$
$224$	0.280776	−	0.486319i	0.0187602	−	0.0324936i
$225$		0			0
$226$	4.00000			0.266076
$227$	−14.9955	+	8.65767i	−0.995288	+	0.574630i	−0.906851	−	0.421452i	$-0.861521\pi$
$227$	−14.9955	+	8.65767i	−0.995288	+	0.574630i	−0.0884373	+	0.996082i	$0.528187\pi$
$228$	−5.68247	+	3.28078i	−0.376331	+	0.217275i
$229$	23.4924			1.55242			0.776211	−	0.630473i	$-0.217139\pi$
$229$	23.4924			1.55242			0.776211	+	0.630473i	$0.217139\pi$
$230$		0			0
$231$	−1.00000	+	1.73205i	−0.0657952	+	0.113961i
$232$	−6.16879	−	3.56155i	−0.405001	−	0.233827i
$233$		−	0.630683i		−	0.0413174i	−0.999787	−	0.0206587i	$-0.993424\pi$
$233$		−	0.630683i		−	0.0413174i	0.999787	−	0.0206587i	$-0.00657634\pi$
$234$	3.34233	+	1.35234i	0.218495	+	0.0884055i
$235$		0			0
$236$	−3.12311	+	5.40938i	−0.203297	+	0.352120i
$237$	4.16365	+	2.40388i	0.270458	+	0.156149i
$238$	2.49146	−	1.43845i	0.161498	−	0.0932407i
$239$	10.0540			0.650338			0.325169	−	0.945656i	$-0.394579\pi$
$239$	10.0540			0.650338			0.325169	+	0.945656i	$0.394579\pi$
$240$		0			0
$241$	−5.71922	−	9.90599i	−0.368408	−	0.638101i	0.620909	−	0.783883i	$-0.286764\pi$
$241$	−5.71922	−	9.90599i	−0.368408	−	0.638101i	−0.989317	+	0.145782i	$0.953430\pi$
$242$		−	1.68466i		−	0.108294i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	5.34233	−	9.25319i	0.342008	−	0.592375i
$245$		0			0
$246$	5.12311			0.326637
$247$	−23.4294	+	3.28078i	−1.49078	+	0.208751i
$248$			4.00000i			0.254000i
$249$	1.21922	−	2.11176i	0.0772652	−	0.133827i
$250$		0			0
$251$	2.46543	+	4.27026i	0.155617	+	0.269536i	0.933283	−	0.359141i	$-0.116930\pi$
$251$	2.46543	+	4.27026i	0.155617	+	0.269536i	−0.777667	+	0.628677i	$0.783597\pi$
$252$		−	0.561553i		−	0.0353745i
$253$	14.4493	−	8.34233i	0.908422	−	0.524478i
$254$	0.596118	+	1.03251i	0.0374038	+	0.0647852i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	23.9157	+	13.8078i	1.49182	+	0.861305i	0.999956	−	0.00936553i	$-0.00298118\pi$
$257$	23.9157	+	13.8078i	1.49182	+	0.861305i	0.491867	+	0.870670i	$0.336315\pi$
$258$	−3.95042	−	2.28078i	−0.245942	−	0.141995i
$259$	2.00000			0.124274
$260$		0			0
$261$	−7.12311			−0.440909
$262$	7.90084	+	4.56155i	0.488116	+	0.281814i
$263$	−16.1814	−	9.34233i	−0.997787	−	0.576073i	−0.0901944	−	0.995924i	$-0.528749\pi$
$263$	−16.1814	−	9.34233i	−0.997787	−	0.576073i	−0.907593	+	0.419851i	$0.862082\pi$
$264$	1.78078	+	3.08440i	0.109599	+	0.189831i
$265$		0			0
$266$	1.84233	+	3.19101i	0.112960	+	0.195653i
$267$	5.40938	−	3.12311i	0.331049	−	0.191131i
$268$		−	8.80776i		−	0.538020i
$269$	10.6847	+	18.5064i	0.651455	+	1.12835i	0.982770	+	0.184833i	$0.0591745\pi$
$269$	10.6847	+	18.5064i	0.651455	+	1.12835i	−0.331315	+	0.943520i	$0.607492\pi$
$270$		0			0
$271$	9.96543	−	17.2606i	0.605357	−	1.04851i	−0.386638	−	0.922232i	$-0.626364\pi$
$271$	9.96543	−	17.2606i	0.605357	−	1.04851i	0.991995	−	0.126278i	$-0.0403030\pi$
$272$		−	5.12311i		−	0.310634i
$273$	0.759413	−	1.87689i	0.0459618	−	0.113595i
$274$	16.4924			0.996344
$275$		0			0
$276$	−2.34233	+	4.05703i	−0.140992	+	0.244205i
$277$	−4.33013	+	2.50000i	−0.260172	+	0.150210i	−0.624413	−	0.781094i	$-0.714662\pi$
$277$	−4.33013	+	2.50000i	−0.260172	+	0.150210i	0.364241	+	0.931305i	$0.381328\pi$
$278$			17.4384i			1.04589i
$279$	2.00000	+	3.46410i	0.119737	+	0.207390i
$280$		0			0
$281$	−18.2462			−1.08848			−0.544239	−	0.838930i	$-0.683181\pi$
$281$	−18.2462			−1.08848			−0.544239	+	0.838930i	$0.683181\pi$
$282$	−3.46410	+	2.00000i	−0.206284	+	0.119098i
$283$	10.0593	+	5.80776i	0.597966	+	0.345236i	0.768241	−	0.640161i	$-0.221132\pi$
$283$	10.0593	+	5.80776i	0.597966	+	0.345236i	−0.170275	+	0.985397i	$0.554466\pi$
$284$	4.21922	−	7.30791i	0.250365	−	0.433645i
$285$		0			0
$286$	1.78078	+	12.7173i	0.105300	+	0.751989i
$287$		−	2.87689i		−	0.169818i
$288$	−0.866025	−	0.500000i	−0.0510310	−	0.0294628i
$289$	4.62311	−	8.00745i	0.271947	−	0.471027i
$290$		0			0
$291$	17.8078			1.04391
$292$	−7.79423	+	4.50000i	−0.456123	+	0.263343i
$293$	3.25088	−	1.87689i	0.189918	−	0.109649i	−0.402026	−	0.915628i	$-0.631694\pi$
$293$	3.25088	−	1.87689i	0.189918	−	0.109649i	0.591944	+	0.805979i	$0.298361\pi$
$294$	6.68466			0.389857
$295$		0			0
$296$	1.78078	−	3.08440i	0.103506	−	0.179277i
$297$	3.08440	+	1.78078i	0.178975	+	0.103331i
$298$			6.24621i			0.361833i
$299$	−13.3153	+	10.3923i	−0.770046	+	0.601003i
$300$		0			0
$301$	−1.28078	+	2.21837i	−0.0738227	+	0.127865i
$302$	−3.73720	−	2.15767i	−0.215051	−	0.124160i
$303$	8.87348	−	5.12311i	0.509768	−	0.294315i
$304$	6.56155			0.376331
$305$		0			0
$306$	−2.56155	−	4.43674i	−0.146434	−	0.253632i
$307$		−	5.75379i		−	0.328386i	−0.986428	−	0.164193i	$-0.947498\pi$
$307$		−	5.75379i		−	0.328386i	0.986428	−	0.164193i	$-0.0525020\pi$
$308$	1.73205	−	1.00000i	0.0986928	−	0.0569803i
$309$	−4.28078	+	7.41452i	−0.243525	+	0.421797i
$310$		0			0
$311$	−22.6847			−1.28633			−0.643164	−	0.765728i	$-0.722379\pi$
$311$	−22.6847			−1.28633			−0.643164	+	0.765728i	$0.722379\pi$
$312$	−2.21837	−	2.84233i	−0.125590	−	0.160915i
$313$			31.0000i			1.75222i	0.482108	+	0.876112i	$0.339871\pi$
$313$			31.0000i			1.75222i	−0.482108	+	0.876112i	$0.660129\pi$
$314$	0.376894	−	0.652800i	0.0212694	−	0.0368396i
$315$		0			0
$316$	−2.40388	−	4.16365i	−0.135229	−	0.234223i
$317$			0.246211i			0.0138286i	0.999976	+	0.00691430i	$0.00220091\pi$
$317$			0.246211i			0.0138286i	−0.999976	+	0.00691430i	$0.997799\pi$
$318$	−10.6055	+	6.12311i	−0.594729	+	0.343367i
$319$	−12.6847	−	21.9705i	−0.710205	−	1.23011i
$320$		0			0
$321$	9.68466	+	16.7743i	0.540545	+	0.936251i
$322$	2.27824	+	1.31534i	0.126961	+	0.0733011i
$323$	29.1119	+	16.8078i	1.61983	+	0.935209i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	16.4924			0.913431
$327$	15.4220	+	8.90388i	0.852837	+	0.492386i
$328$	−4.43674	−	2.56155i	−0.244978	−	0.141438i
$329$	1.12311	+	1.94528i	0.0619188	+	0.107247i
$330$		0			0
$331$	2.15767	+	3.73720i	0.118596	+	0.205415i	0.919212	−	0.393764i	$-0.128827\pi$
$331$	2.15767	+	3.73720i	0.118596	+	0.205415i	−0.800615	+	0.599179i	$0.795494\pi$
$332$	−2.11176	+	1.21922i	−0.115898	+	0.0669136i
$333$		−	3.56155i		−	0.195172i
$334$	5.65767	+	9.79937i	0.309574	+	0.536198i
$335$		0			0
$336$	−0.280776	+	0.486319i	−0.0153176	+	0.0265309i
$337$			29.0540i			1.58267i	0.611382	+	0.791335i	$0.290614\pi$
$337$			29.0540i			1.58267i	−0.611382	+	0.791335i	$0.709386\pi$
$338$	−3.57071	−	12.5000i	−0.194221	−	0.679910i
$339$	−4.00000			−0.217250
$340$		0			0
$341$	−7.12311	+	12.3376i	−0.385738	+	0.668117i
$342$	5.68247	−	3.28078i	0.307273	−	0.177404i
$343$		−	7.68466i		−	0.414933i
$344$	2.28078	+	3.95042i	0.122971	+	0.212992i
$345$		0			0
$346$	−17.1231			−0.920544
$347$	3.63058	−	2.09612i	0.194900	−	0.112526i	−0.399374	−	0.916788i	$-0.630773\pi$
$347$	3.63058	−	2.09612i	0.194900	−	0.112526i	0.594274	+	0.804262i	$0.297439\pi$
$348$	6.16879	+	3.56155i	0.330682	+	0.190919i
$349$	−1.37689	+	2.38485i	−0.0737035	+	0.127658i	−0.900522	−	0.434811i	$-0.856815\pi$
$349$	−1.37689	+	2.38485i	−0.0737035	+	0.127658i	0.826818	+	0.562469i	$0.190149\pi$
$350$		0			0
$351$	−3.34233	−	1.35234i	−0.178400	−	0.0721828i
$352$		−	3.56155i		−	0.189831i
$353$	12.3376	+	7.12311i	0.656663	+	0.379125i	0.791004	−	0.611810i	$-0.209558\pi$
$353$	12.3376	+	7.12311i	0.656663	+	0.379125i	−0.134341	+	0.990935i	$0.542892\pi$
$354$	3.12311	−	5.40938i	0.165991	−	0.287505i
$355$		0			0
$356$	−6.24621			−0.331049
$357$	−2.49146	+	1.43845i	−0.131862	+	0.0761307i
$358$	−2.87117	+	1.65767i	−0.151746	+	0.0876106i
$359$	13.1231			0.692611			0.346306	−	0.938122i	$-0.387436\pi$
$359$	13.1231			0.692611			0.346306	+	0.938122i	$0.387436\pi$
$360$		0			0
$361$	−12.0270	+	20.8314i	−0.632999	+	1.09639i
$362$	15.1489	+	8.74621i	0.796208	+	0.459691i
$363$			1.68466i			0.0884216i
$364$	−1.59612	+	1.24573i	−0.0836593	+	0.0652941i
$365$		0			0
$366$	−5.34233	+	9.25319i	−0.279248	+	0.483672i
$367$	−26.6803	−	15.4039i	−1.39270	−	0.804076i	−0.399087	−	0.916913i	$-0.630673\pi$
$367$	−26.6803	−	15.4039i	−1.39270	−	0.804076i	−0.993614	+	0.112837i	$0.964006\pi$
$368$	4.05703	−	2.34233i	0.211487	−	0.122102i
$369$	−5.12311			−0.266698
$370$		0			0
$371$	3.43845	+	5.95557i	0.178515	+	0.309198i
$372$		−	4.00000i		−	0.207390i
$373$	20.3450	−	11.7462i	1.05343	−	0.608196i	0.129819	−	0.991538i	$-0.458560\pi$
$373$	20.3450	−	11.7462i	1.05343	−	0.608196i	0.923607	+	0.383342i	$0.125227\pi$
$374$	9.12311	−	15.8017i	0.471745	−	0.817086i
$375$		0			0
$376$	4.00000			0.206284
$377$	15.8017	+	20.2462i	0.813828	+	1.04273i
$378$			0.561553i			0.0288832i
$379$	6.52699	−	11.3051i	0.335269	−	0.580703i	−0.648268	−	0.761413i	$-0.724506\pi$
$379$	6.52699	−	11.3051i	0.335269	−	0.580703i	0.983536	+	0.180710i	$0.0578395\pi$
$380$		0			0
$381$	−0.596118	−	1.03251i	−0.0305400	−	0.0528969i
$382$			12.9309i			0.661601i
$383$	−8.28055	+	4.78078i	−0.423116	+	0.244286i	−0.696410	−	0.717644i	$-0.745220\pi$
$383$	−8.28055	+	4.78078i	−0.423116	+	0.244286i	0.273293	+	0.961931i	$0.411887\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$		0			0
$386$	−1.50000	−	2.59808i	−0.0763480	−	0.132239i
$387$	3.95042	+	2.28078i	0.200811	+	0.115938i
$388$	−15.4220	−	8.90388i	−0.782932	−	0.452026i
$389$	13.3693			0.677851			0.338926	−	0.940813i	$-0.389936\pi$
$389$	13.3693			0.677851			0.338926	+	0.940813i	$0.389936\pi$
$390$		0			0
$391$	24.0000			1.21373
$392$	−5.78908	−	3.34233i	−0.292393	−	0.168813i
$393$	−7.90084	−	4.56155i	−0.398545	−	0.230100i
$394$	−1.56155	−	2.70469i	−0.0786699	−	0.136260i
$395$		0			0
$396$	−1.78078	−	3.08440i	−0.0894874	−	0.154997i
$397$	−9.35980	+	5.40388i	−0.469755	+	0.271213i	−0.716137	−	0.697960i	$-0.754091\pi$
$397$	−9.35980	+	5.40388i	−0.469755	+	0.271213i	0.246382	+	0.969173i	$0.420758\pi$
$398$		−	8.56155i		−	0.429152i
$399$	−1.84233	−	3.19101i	−0.0922318	−	0.159750i
$400$		0			0
$401$	18.6847	−	32.3628i	0.933067	−	1.61612i	0.155023	−	0.987911i	$-0.450455\pi$
$401$	18.6847	−	32.3628i	0.933067	−	1.61612i	0.778045	−	0.628209i	$-0.216212\pi$
$402$			8.80776i			0.439291i
$403$	5.40938	−	13.3693i	0.269460	−	0.665973i
$404$	−10.2462			−0.509768
$405$		0			0
$406$	2.00000	−	3.46410i	0.0992583	−	0.171920i
$407$	10.9852	−	6.34233i	0.544518	−	0.314378i
$408$			5.12311i			0.253632i
$409$	−0.123106	−	0.213225i	−0.00608718	−	0.0105433i	0.862966	−	0.505262i	$-0.168604\pi$
$409$	−0.123106	−	0.213225i	−0.00608718	−	0.0105433i	−0.869053	+	0.494719i	$0.835271\pi$
$410$		0			0
$411$	−16.4924			−0.813511
$412$	7.41452	−	4.28078i	0.365287	−	0.210899i
$413$	−3.03765	−	1.75379i	−0.149473	−	0.0862983i
$414$	2.34233	−	4.05703i	0.115119	−	0.199392i
$415$		0			0
$416$	0.500000	+	3.57071i	0.0245145	+	0.175069i
$417$		−	17.4384i		−	0.853964i
$418$	20.2384	+	11.6847i	0.989894	+	0.571515i
$419$	8.46543	−	14.6626i	0.413564	−	0.716313i	−0.581713	−	0.813394i	$-0.697617\pi$
$419$	8.46543	−	14.6626i	0.413564	−	0.716313i	0.995276	+	0.0970811i	$0.0309506\pi$
$420$		0			0
$421$	14.7538			0.719056			0.359528	−	0.933134i	$-0.382938\pi$
$421$	14.7538			0.719056			0.359528	+	0.933134i	$0.382938\pi$
$422$	6.16879	−	3.56155i	0.300292	−	0.173374i
$423$	3.46410	−	2.00000i	0.168430	−	0.0972433i
$424$	12.2462			0.594729
$425$		0			0
$426$	−4.21922	+	7.30791i	−0.204422	+	0.354069i
$427$	5.19615	+	3.00000i	0.251459	+	0.145180i
$428$		−	19.3693i		−	0.936251i
$429$	−1.78078	−	12.7173i	−0.0859767	−	0.613996i
$430$		0			0
$431$	−15.3423	+	26.5737i	−0.739014	+	1.28001i	0.213926	+	0.976850i	$0.431375\pi$
$431$	−15.3423	+	26.5737i	−0.739014	+	1.28001i	−0.952940	+	0.303160i	$0.901958\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$	−1.13912	+	0.657671i	−0.0547426	+	0.0316056i	−0.527121	−	0.849790i	$-0.676729\pi$
$433$	−1.13912	+	0.657671i	−0.0547426	+	0.0316056i	0.472379	+	0.881396i	$0.343395\pi$
$434$	−2.24621			−0.107822
$435$		0			0
$436$	−8.90388	−	15.4220i	−0.426419	−	0.738579i
$437$			30.7386i			1.47043i
$438$	7.79423	−	4.50000i	0.372423	−	0.215018i
$439$	10.9654	−	18.9927i	0.523352	−	0.906472i	−0.476279	−	0.879294i	$-0.658015\pi$
$439$	10.9654	−	18.9927i	0.523352	−	0.906472i	0.999631	−	0.0271774i	$-0.00865191\pi$
$440$		0			0
$441$	−6.68466			−0.318317
$442$	−6.92820	+	17.1231i	−0.329541	+	0.814463i
$443$			17.8078i			0.846072i	0.906113	+	0.423036i	$0.139036\pi$
$443$			17.8078i			0.846072i	−0.906113	+	0.423036i	$0.860964\pi$
$444$	−1.78078	+	3.08440i	−0.0845119	+	0.146379i
$445$		0			0
$446$	2.28078	+	3.95042i	0.107998	+	0.187058i
$447$		−	6.24621i		−	0.295436i
$448$	0.486319	−	0.280776i	0.0229764	−	0.0132654i
$449$	2.56155	+	4.43674i	0.120887	+	0.209383i	0.920118	−	0.391642i	$-0.128093\pi$
$449$	2.56155	+	4.43674i	0.120887	+	0.209383i	−0.799231	+	0.601024i	$0.794759\pi$
$450$		0			0
$451$	−9.12311	−	15.8017i	−0.429590	−	0.744072i
$452$	3.46410	+	2.00000i	0.162938	+	0.0940721i
$453$	3.73720	+	2.15767i	0.175589	+	0.101376i
$454$	−17.3153			−0.812649
$455$		0			0
$456$	−6.56155			−0.307273
$457$	32.4694	+	18.7462i	1.51885	+	0.876911i	0.999754	+	0.0221975i	$0.00706627\pi$
$457$	32.4694	+	18.7462i	1.51885	+	0.876911i	0.519100	+	0.854713i	$0.326267\pi$
$458$	20.3450	+	11.7462i	0.950661	+	0.548864i
$459$	2.56155	+	4.43674i	0.119563	+	0.207089i
$460$		0			0
$461$	−17.6847	−	30.6307i	−0.823657	−	1.42662i	−0.902942	−	0.429763i	$-0.858597\pi$
$461$	−17.6847	−	30.6307i	−0.823657	−	1.42662i	0.0792850	−	0.996852i	$-0.474736\pi$
$462$	−1.73205	+	1.00000i	−0.0805823	+	0.0465242i
$463$			7.19224i			0.334252i	0.985936	+	0.167126i	$0.0534486\pi$
$463$			7.19224i			0.334252i	−0.985936	+	0.167126i	$0.946551\pi$
$464$	−3.56155	−	6.16879i	−0.165341	−	0.286379i
$465$		0			0
$466$	0.315342	−	0.546188i	0.0146079	−	0.0253017i
$467$			7.56155i			0.349907i	0.984577	+	0.174953i	$0.0559775\pi$
$467$			7.56155i			0.349907i	−0.984577	+	0.174953i	$0.944022\pi$
$468$	2.21837	+	2.84233i	0.102544	+	0.131387i
$469$	4.94602			0.228386
$470$		0			0
$471$	−0.376894	+	0.652800i	−0.0173664	+	0.0300794i
$472$	−5.40938	+	3.12311i	−0.248987	+	0.143753i
$473$			16.2462i			0.747002i
$474$	2.40388	+	4.16365i	0.110414	+	0.191243i
$475$		0			0
$476$	2.87689			0.131862
$477$	10.6055	−	6.12311i	0.485594	−	0.280358i
$478$	8.70700	+	5.02699i	0.398249	+	0.229929i
$479$	14.8078	−	25.6478i	0.676584	−	1.17188i	−0.299419	−	0.954122i	$-0.596793\pi$
$479$	14.8078	−	25.6478i	0.676584	−	1.17188i	0.976003	−	0.217756i	$-0.0698738\pi$
$480$		0			0
$481$	−10.1231	+	7.90084i	−0.461574	+	0.360247i
$482$		−	11.4384i		−	0.521007i
$483$	−2.27824	−	1.31534i	−0.103663	−	0.0598501i
$484$	0.842329	−	1.45896i	0.0382877	−	0.0663162i
$485$		0			0
$486$	1.00000			0.0453609
$487$	−26.2539	+	15.1577i	−1.18968	+	0.686860i	−0.958233	−	0.285989i	$-0.907678\pi$
$487$	−26.2539	+	15.1577i	−1.18968	+	0.686860i	−0.231443	+	0.972849i	$0.574345\pi$
$488$	9.25319	−	5.34233i	0.418872	−	0.241836i
$489$	−16.4924			−0.745813
$490$		0			0
$491$	11.1501	−	19.3125i	0.503197	−	0.871562i	−0.496797	−	0.867867i	$-0.665490\pi$
$491$	11.1501	−	19.3125i	0.503197	−	0.871562i	0.999993	−	0.00369513i	$-0.00117620\pi$
$492$	4.43674	+	2.56155i	0.200024	+	0.115484i
$493$		−	36.4924i		−	1.64354i
$494$	−21.9309	−	8.87348i	−0.986716	−	0.399237i
$495$		0			0
$496$	−2.00000	+	3.46410i	−0.0898027	+	0.155543i
$497$	4.10378	+	2.36932i	0.184080	+	0.106278i
$498$	2.11176	−	1.21922i	0.0946301	−	0.0546347i
$499$	31.0540			1.39017			0.695083	−	0.718929i	$-0.255367\pi$
$499$	31.0540			1.39017			0.695083	+	0.718929i	$0.255367\pi$
$500$		0			0
$501$	−5.65767	−	9.79937i	−0.252766	−	0.437804i
$502$			4.93087i			0.220075i
$503$	−31.7698	+	18.3423i	−1.41655	+	0.817844i	−0.995994	−	0.0894236i	$-0.971498\pi$
$503$	−31.7698	+	18.3423i	−1.41655	+	0.817844i	−0.420554	+	0.907268i	$0.638164\pi$
$504$	0.280776	−	0.486319i	0.0125068	−	0.0216624i
$505$		0			0
$506$	16.6847			0.741724
$507$	3.57071	+	12.5000i	0.158581	+	0.555144i
$508$			1.19224i			0.0528969i
$509$	0.123106	−	0.213225i	0.00545656	−	0.00945104i	−0.863284	−	0.504718i	$-0.831596\pi$
$509$	0.123106	−	0.213225i	0.00545656	−	0.00945104i	0.868741	+	0.495267i	$0.164930\pi$
$510$		0			0
$511$	−2.52699	−	4.37687i	−0.111787	−	0.193621i
$512$		−	1.00000i		−	0.0441942i
$513$	−5.68247	+	3.28078i	−0.250887	+	0.144850i
$514$	13.8078	+	23.9157i	0.609034	+	1.05488i
$515$		0			0
$516$	−2.28078	−	3.95042i	−0.100406	−	0.173908i
$517$	12.3376	+	7.12311i	0.542606	+	0.313274i
$518$	1.73205	+	1.00000i	0.0761019	+	0.0439375i
$519$	17.1231			0.751621
$520$		0			0
$521$	−14.7386			−0.645711			−0.322856	−	0.946448i	$-0.604643\pi$
$521$	−14.7386			−0.645711			−0.322856	+	0.946448i	$0.604643\pi$
$522$	−6.16879	−	3.56155i	−0.270001	−	0.155885i
$523$	3.40423	+	1.96543i	0.148857	+	0.0859425i	0.572578	−	0.819850i	$-0.305943\pi$
$523$	3.40423	+	1.96543i	0.148857	+	0.0859425i	−0.423722	+	0.905792i	$0.639277\pi$
$524$	4.56155	+	7.90084i	0.199272	+	0.345150i
$525$		0			0
$526$	−9.34233	−	16.1814i	−0.407345	−	0.705542i
$527$	−17.7470	+	10.2462i	−0.773070	+	0.446332i
$528$			3.56155i			0.154997i
$529$	−0.526988	−	0.912769i	−0.0229125	−	0.0396856i
$530$		0			0
$531$	−3.12311	+	5.40938i	−0.135531	+	0.234747i
$532$			3.68466i			0.159750i
$533$	11.3649	+	14.5616i	0.492270	+	0.630731i
$534$	6.24621			0.270300
$535$		0			0
$536$	4.40388	−	7.62775i	0.190219	−	0.329469i
$537$	2.87117	−	1.65767i	0.123900	−	0.0715338i
$538$			21.3693i			0.921297i
$539$	−11.9039	−	20.6181i	−0.512736	−	0.888086i
$540$		0			0
$541$	−34.6847			−1.49121			−0.745605	−	0.666388i	$-0.767839\pi$
$541$	−34.6847			−1.49121			−0.745605	+	0.666388i	$0.767839\pi$
$542$	17.2606	−	9.96543i	0.741408	−	0.428052i
$543$	−15.1489	−	8.74621i	−0.650101	−	0.375336i
$544$	2.56155	−	4.43674i	0.109826	−	0.190224i
$545$		0			0
$546$	1.59612	−	1.24573i	0.0683075	−	0.0533124i
$547$			2.06913i			0.0884696i	0.999021	+	0.0442348i	$0.0140850\pi$
$547$			2.06913i			0.0884696i	−0.999021	+	0.0442348i	$0.985915\pi$
$548$	14.2829	+	8.24621i	0.610133	+	0.352261i
$549$	5.34233	−	9.25319i	0.228005	−	0.394916i
$550$		0			0
$551$	46.7386			1.99113
$552$	−4.05703	+	2.34233i	−0.172679	+	0.0996962i
$553$	2.33811	−	1.34991i	0.0994264	−	0.0574039i
$554$	−5.00000			−0.212430
$555$		0			0
$556$	−8.71922	+	15.1021i	−0.369777	+	0.640473i
$557$	8.32729	+	4.80776i	0.352839	+	0.203712i	0.665935	−	0.746010i	$-0.268033\pi$
$557$	8.32729	+	4.80776i	0.352839	+	0.203712i	−0.313096	+	0.949721i	$0.601366\pi$
$558$			4.00000i			0.169334i
$559$	−2.28078	−	16.2880i	−0.0964666	−	0.688909i
$560$		0			0
$561$	−9.12311	+	15.8017i	−0.385178	+	0.667148i
$562$	−15.8017	−	9.12311i	−0.666554	−	0.384835i
$563$	0.166481	−	0.0961180i	0.00701635	−	0.00405089i	−0.496488	−	0.868044i	$-0.665377\pi$
$563$	0.166481	−	0.0961180i	0.00701635	−	0.00405089i	0.503504	+	0.863993i	$0.332044\pi$
$564$	−4.00000			−0.168430
$565$		0			0
$566$	5.80776	+	10.0593i	0.244119	+	0.422826i
$567$		−	0.561553i		−	0.0235830i
$568$	7.30791	−	4.21922i	0.306633	−	0.177035i
$569$	−22.2462	+	38.5316i	−0.932610	+	1.61533i	−0.153768	+	0.988107i	$0.549141\pi$
$569$	−22.2462	+	38.5316i	−0.932610	+	1.61533i	−0.778842	+	0.627220i	$0.784193\pi$
$570$		0			0
$571$	−40.4233			−1.69166			−0.845831	−	0.533451i	$-0.820895\pi$
$571$	−40.4233			−1.69166			−0.845831	+	0.533451i	$0.820895\pi$
$572$	−4.81645	+	11.9039i	−0.201386	+	0.497726i
$573$		−	12.9309i		−	0.540195i
$574$	1.43845	−	2.49146i	0.0600396	−	0.103992i
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$		−	23.0000i		−	0.957503i	−0.877951	−	0.478751i	$-0.841090\pi$
$577$		−	23.0000i		−	0.957503i	0.877951	−	0.478751i	$-0.158910\pi$
$578$	8.00745	−	4.62311i	0.333066	−	0.192296i
$579$	1.50000	+	2.59808i	0.0623379	+	0.107972i
$580$		0			0
$581$	−0.684658	−	1.18586i	−0.0284044	−	0.0491979i
$582$	15.4220	+	8.90388i	0.639261	+	0.369078i
$583$	37.7722	+	21.8078i	1.56436	+	0.903185i
$584$	−9.00000			−0.372423
$585$		0			0
$586$	3.75379			0.155068
$587$	9.46641	+	5.46543i	0.390721	+	0.225583i	0.682472	−	0.730911i	$-0.260905\pi$
$587$	9.46641	+	5.46543i	0.390721	+	0.225583i	−0.291752	+	0.956494i	$0.594238\pi$
$588$	5.78908	+	3.34233i	0.238738	+	0.137835i
$589$	−13.1231	−	22.7299i	−0.540728	−	0.936569i
$590$		0			0
$591$	1.56155	+	2.70469i	0.0642337	+	0.111256i
$592$	3.08440	−	1.78078i	0.126768	−	0.0731895i
$593$			26.9848i			1.10813i	0.832472	+	0.554067i	$0.186925\pi$
$593$			26.9848i			1.10813i	−0.832472	+	0.554067i	$0.813075\pi$
$594$	1.78078	+	3.08440i	0.0730661	+	0.126554i
$595$		0			0
$596$	−3.12311	+	5.40938i	−0.127927	+	0.221577i
$597$			8.56155i			0.350401i
$598$	−16.7276	+	2.34233i	−0.684041	+	0.0957850i
$599$	30.6847			1.25374			0.626871	−	0.779123i	$-0.284335\pi$
$599$	30.6847			1.25374			0.626871	+	0.779123i	$0.284335\pi$
$600$		0			0
$601$	−7.40388	+	12.8239i	−0.302011	+	0.523098i	−0.976591	−	0.215103i	$-0.930991\pi$
$601$	−7.40388	+	12.8239i	−0.302011	+	0.523098i	0.674581	+	0.738201i	$0.264324\pi$
$602$	−2.21837	+	1.28078i	−0.0904140	+	0.0522005i
$603$		−	8.80776i		−	0.358680i
$604$	−2.15767	−	3.73720i	−0.0877944	−	0.152064i
$605$		0			0
$606$	10.2462			0.416224
$607$	12.6705	−	7.31534i	0.514281	−	0.296921i	−0.220310	−	0.975430i	$-0.570707\pi$
$607$	12.6705	−	7.31534i	0.514281	−	0.296921i	0.734592	+	0.678509i	$0.237374\pi$
$608$	5.68247	+	3.28078i	0.230455	+	0.133053i
$609$	−2.00000	+	3.46410i	−0.0810441	+	0.140372i
$610$		0			0
$611$	−13.3693	−	5.40938i	−0.540865	−	0.218840i
$612$		−	5.12311i		−	0.207089i
$613$	−29.0520	−	16.7732i	−1.17340	−	0.677463i	−0.218922	−	0.975742i	$-0.570254\pi$
$613$	−29.0520	−	16.7732i	−1.17340	−	0.677463i	−0.954479	+	0.298279i	$0.903587\pi$
$614$	2.87689	−	4.98293i	0.116102	−	0.201095i
$615$		0			0
$616$	2.00000			0.0805823
$617$	−19.5987	+	11.3153i	−0.789016	+	0.455538i	−0.839616	−	0.543180i	$-0.817220\pi$
$617$	−19.5987	+	11.3153i	−0.789016	+	0.455538i	0.0506001	+	0.998719i	$0.483887\pi$
$618$	−7.41452	+	4.28078i	−0.298256	+	0.172198i
$619$	−41.3002			−1.65999			−0.829997	−	0.557767i	$-0.811658\pi$
$619$	−41.3002			−1.65999			−0.829997	+	0.557767i	$0.811658\pi$
$620$		0			0
$621$	−2.34233	+	4.05703i	−0.0939944	+	0.162803i
$622$	−19.6455	−	11.3423i	−0.787712	−	0.454786i
$623$		−	3.50758i		−	0.140528i
$624$	−0.500000	−	3.57071i	−0.0200160	−	0.142943i
$625$		0			0
$626$	−15.5000	+	26.8468i	−0.619505	+	1.07301i
$627$	−20.2384	−	11.6847i	−0.808245	−	0.466640i
$628$	0.652800	−	0.376894i	0.0260496	−	0.0150397i
$629$	18.2462			0.727524
$630$		0			0
$631$	−2.03457	−	3.52397i	−0.0809948	−	0.140287i	0.822683	−	0.568501i	$-0.192476\pi$
$631$	−2.03457	−	3.52397i	−0.0809948	−	0.140287i	−0.903677	+	0.428214i	$0.859143\pi$
$632$		−	4.80776i		−	0.191243i
$633$	−6.16879	+	3.56155i	−0.245187	+	0.141559i
$634$	−0.123106	+	0.213225i	−0.00488915	+	0.00846825i
$635$		0			0
$636$	−12.2462			−0.485594
$637$	14.8290	+	19.0000i	0.587548	+	0.752807i
$638$		−	25.3693i		−	1.00438i
$639$	4.21922	−	7.30791i	0.166910	−	0.289096i
$640$		0			0
$641$	−10.8769	−	18.8393i	−0.429611	−	0.744109i	0.567227	−	0.823561i	$-0.308016\pi$
$641$	−10.8769	−	18.8393i	−0.429611	−	0.744109i	−0.996839	+	0.0794524i	$0.974683\pi$
$642$			19.3693i			0.764446i
$643$	−39.4443	+	22.7732i	−1.55553	+	0.898087i	−0.557858	+	0.829937i	$0.688377\pi$
$643$	−39.4443	+	22.7732i	−1.55553	+	0.898087i	−0.997675	+	0.0681507i	$0.978290\pi$
$644$	1.31534	+	2.27824i	0.0518317	+	0.0897752i
$645$		0			0
$646$	16.8078	+	29.1119i	0.661293	+	1.14539i
$647$	−25.4813	−	14.7116i	−1.00177	−	0.578374i	−0.0930013	−	0.995666i	$-0.529646\pi$
$647$	−25.4813	−	14.7116i	−1.00177	−	0.578374i	−0.908773	+	0.417291i	$0.862979\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	−22.2462			−0.873240
$650$		0			0
$651$	2.24621			0.0880360
$652$	14.2829	+	8.24621i	0.559360	+	0.322947i
$653$	−3.13114	−	1.80776i	−0.122531	−	0.0707433i	0.437482	−	0.899227i	$-0.355870\pi$
$653$	−3.13114	−	1.80776i	−0.122531	−	0.0707433i	−0.560013	+	0.828484i	$0.689204\pi$
$654$	8.90388	+	15.4220i	0.348169	+	0.603047i
$655$		0			0
$656$	−2.56155	−	4.43674i	−0.100012	−	0.173226i
$657$	−7.79423	+	4.50000i	−0.304082	+	0.175562i
$658$			2.24621i			0.0875664i
$659$	15.3423	+	26.5737i	0.597652	+	1.03516i	0.993167	+	0.116704i	$0.0372330\pi$
$659$	15.3423	+	26.5737i	0.597652	+	1.03516i	−0.395514	+	0.918460i	$0.629434\pi$
$660$		0			0
$661$	−10.7732	+	18.6597i	−0.419029	+	0.725779i	−0.995842	−	0.0910968i	$-0.970963\pi$
$661$	−10.7732	+	18.6597i	−0.419029	+	0.725779i	0.576813	+	0.816876i	$0.304296\pi$
$662$			4.31534i			0.167721i
$663$	6.92820	−	17.1231i	0.269069	−	0.665006i
$664$	−2.43845			−0.0946301
$665$		0			0
$666$	1.78078	−	3.08440i	0.0690037	−	0.119518i
$667$	28.8987	−	16.6847i	1.11896	−	0.646033i
$668$			11.3153i			0.437804i
$669$	−2.28078	−	3.95042i	−0.0881799	−	0.152732i
$670$		0			0
$671$	38.0540			1.46906
$672$	−0.486319	+	0.280776i	−0.0187602	+	0.0108312i
$673$	−39.1844	−	22.6231i	−1.51045	−	0.872057i	−0.999926	−	0.0121912i	$-0.996119\pi$
$673$	−39.1844	−	22.6231i	−1.51045	−	0.872057i	−0.510521	−	0.859865i	$-0.670547\pi$
$674$	−14.5270	+	25.1615i	−0.559559	+	0.969184i
$675$		0			0
$676$	3.15767	−	12.6107i	0.121449	−	0.485026i
$677$			29.6155i			1.13822i	0.822262	+	0.569109i	$0.192712\pi$
$677$			29.6155i			1.13822i	−0.822262	+	0.569109i	$0.807288\pi$
$678$	−3.46410	−	2.00000i	−0.133038	−	0.0768095i
$679$	5.00000	−	8.66025i	0.191882	−	0.332350i
$680$		0			0
$681$	17.3153			0.663525
$682$	−12.3376	+	7.12311i	−0.472430	+	0.272758i
$683$	16.9408	−	9.78078i	0.648222	−	0.374251i	−0.139553	−	0.990215i	$-0.544567\pi$
$683$	16.9408	−	9.78078i	0.648222	−	0.374251i	0.787775	+	0.615964i	$0.211233\pi$
$684$	6.56155			0.250887
$685$		0			0
$686$	3.84233	−	6.65511i	0.146701	−	0.254093i
$687$	−20.3450	−	11.7462i	−0.776211	−	0.448146i
$688$			4.56155i			0.173908i
$689$	−40.9309	−	16.5611i	−1.55934	−	0.630927i
$690$		0			0
$691$	25.0885	−	43.4546i	0.954413	−	1.65309i	0.218707	−	0.975790i	$-0.429816\pi$
$691$	25.0885	−	43.4546i	0.954413	−	1.65309i	0.735706	−	0.677301i	$-0.236851\pi$
$692$	−14.8290	−	8.56155i	−0.563716	−	0.325461i
$693$	1.73205	−	1.00000i	0.0657952	−	0.0379869i
$694$	4.19224			0.159135
$695$		0			0
$696$	3.56155	+	6.16879i	0.135000	+	0.233827i
$697$		−	26.2462i		−	0.994146i
$698$	−2.38485	+	1.37689i	−0.0902679	+	0.0521162i
$699$	−0.315342	+	0.546188i	−0.0119273	+	0.0206587i
$700$		0			0
$701$	−9.12311			−0.344575			−0.172287	−	0.985047i	$-0.555116\pi$
$701$	−9.12311			−0.344575			−0.172287	+	0.985047i	$0.555116\pi$
$702$	−2.21837	−	2.84233i	−0.0837270	−	0.107277i
$703$			23.3693i			0.881390i
$704$	1.78078	−	3.08440i	0.0671155	−	0.116248i
$705$		0			0
$706$	7.12311	+	12.3376i	0.268082	+	0.464331i
$707$		−	5.75379i		−	0.216393i
$708$	5.40938	−	3.12311i	0.203297	−	0.117373i
$709$	−22.6231	−	39.1844i	−0.849629	−	1.47160i	−0.881540	−	0.472109i	$-0.843493\pi$
$709$	−22.6231	−	39.1844i	−0.849629	−	1.47160i	0.0319115	−	0.999491i	$-0.489841\pi$
$710$		0			0
$711$	−2.40388	−	4.16365i	−0.0901526	−	0.156149i
$712$	−5.40938	−	3.12311i	−0.202725	−	0.117043i
$713$	−16.2281	−	9.36932i	−0.607748	−	0.350884i
$714$	−2.87689			−0.107665
$715$		0			0
$716$	−3.31534			−0.123900
$717$	−8.70700	−	5.02699i	−0.325169	−	0.187736i
$718$	11.3649	+	6.56155i	0.424136	+	0.244875i
$719$	−10.7808	−	18.6729i	−0.402055	−	0.696380i	0.591919	−	0.805998i	$-0.298371\pi$
$719$	−10.7808	−	18.6729i	−0.402055	−	0.696380i	−0.993974	+	0.109618i	$0.965037\pi$
$720$		0			0
$721$	2.40388	+	4.16365i	0.0895252	+	0.155062i
$722$	−20.8314	+	12.0270i	−0.775263	+	0.447598i
$723$			11.4384i			0.425400i
$724$	8.74621	+	15.1489i	0.325050	+	0.563004i
$725$		0			0
$726$	−0.842329	+	1.45896i	−0.0312618	+	0.0541470i
$727$		−	35.7926i		−	1.32747i	−0.747966	−	0.663737i	$-0.768969\pi$
$727$		−	35.7926i		−	1.32747i	0.747966	−	0.663737i	$-0.231031\pi$
$728$	−2.00514	+	0.280776i	−0.0743156	+	0.0104063i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−11.6847	+	20.2384i	−0.432173	+	0.748545i
$732$	−9.25319	+	5.34233i	−0.342008	+	0.197458i
$733$			17.9848i			0.664285i	0.943229	+	0.332143i	$0.107772\pi$
$733$			17.9848i			0.664285i	−0.943229	+	0.332143i	$0.892228\pi$
$734$	−15.4039	−	26.6803i	−0.568568	−	0.984788i
$735$		0			0
$736$	4.68466			0.172679
$737$	27.1666	−	15.6847i	1.00070	−	0.577752i
$738$	−4.43674	−	2.56155i	−0.163319	−	0.0942921i
$739$	−2.43845	+	4.22351i	−0.0896997	+	0.155364i	−0.907384	−	0.420302i	$-0.861924\pi$
$739$	−2.43845	+	4.22351i	−0.0896997	+	0.155364i	0.817684	+	0.575667i	$0.195257\pi$
$740$		0			0
$741$	21.9309	+	8.87348i	0.805651	+	0.325975i
$742$			6.87689i			0.252459i
$743$	−2.49146	−	1.43845i	−0.0914029	−	0.0527715i	0.453602	−	0.891204i	$-0.350139\pi$
$743$	−2.49146	−	1.43845i	−0.0914029	−	0.0527715i	−0.545005	+	0.838433i	$0.683472\pi$
$744$	2.00000	−	3.46410i	0.0733236	−	0.127000i
$745$		0			0
$746$	23.4924			0.860119
$747$	−2.11176	+	1.21922i	−0.0772652	+	0.0446091i
$748$	15.8017	−	9.12311i	0.577767	−	0.333574i
$749$	10.8769			0.397433
$750$		0			0
$751$	−16.8769	+	29.2316i	−0.615847	+	1.06668i	0.374389	+	0.927272i	$0.377853\pi$
$751$	−16.8769	+	29.2316i	−0.615847	+	1.06668i	−0.990235	+	0.139406i	$0.955481\pi$
$752$	3.46410	+	2.00000i	0.126323	+	0.0729325i
$753$		−	4.93087i		−	0.179691i
$754$	3.56155	+	25.4346i	0.129704	+	0.926273i
$755$		0			0
$756$	−0.280776	+	0.486319i	−0.0102117	+	0.0176873i
$757$	−15.8616	−	9.15767i	−0.576498	−	0.332841i	0.183243	−	0.983068i	$-0.441341\pi$
$757$	−15.8616	−	9.15767i	−0.576498	−	0.332841i	−0.759740	+	0.650227i	$0.774674\pi$
$758$	11.3051	−	6.52699i	0.410619	−	0.237071i
$759$	−16.6847			−0.605615
$760$		0			0
$761$	−21.4924	−	37.2260i	−0.779100	−	1.34944i	−0.932461	−	0.361270i	$-0.882343\pi$
$761$	−21.4924	−	37.2260i	−0.779100	−	1.34944i	0.153361	−	0.988170i	$-0.450990\pi$
$762$		−	1.19224i		−	0.0431902i
$763$	8.66025	−	5.00000i	0.313522	−	0.181012i
$764$	−6.46543	+	11.1985i	−0.233911	+	0.405146i
$765$		0			0
$766$	−9.56155			−0.345473
$767$	22.3034	−	3.12311i	0.805330	−	0.112769i
$768$			1.00000i			0.0360844i
$769$	−10.8423	+	18.7795i	−0.390984	+	0.677205i	−0.992580	−	0.121596i	$-0.961199\pi$
$769$	−10.8423	+	18.7795i	−0.390984	+	0.677205i	0.601595	+	0.798801i	$0.294532\pi$
$770$		0			0
$771$	−13.8078	−	23.9157i	−0.497274	−	0.861305i
$772$		−	3.00000i		−	0.107972i
$773$	10.0593	−	5.80776i	0.361809	−	0.208891i	−0.308065	−	0.951365i	$-0.599681\pi$
$773$	10.0593	−	5.80776i	0.361809	−	0.208891i	0.669874	+	0.742475i	$0.266348\pi$
$774$	2.28078	+	3.95042i	0.0819808	+	0.141995i
$775$		0			0
$776$	−8.90388	−	15.4220i	−0.319631	−	0.553617i
$777$	−1.73205	−	1.00000i	−0.0621370	−	0.0358748i
$778$	11.5782	+	6.68466i	0.415097	+	0.239657i
$779$	33.6155			1.20440
$780$		0			0
$781$	30.0540			1.07542
$782$	20.7846	+	12.0000i	0.743256	+	0.429119i
$783$	6.16879	+	3.56155i	0.220455	+	0.127280i
$784$	−3.34233	−	5.78908i	−0.119369	−	0.206753i
$785$		0			0
$786$	−4.56155	−	7.90084i	−0.162705	−	0.281814i
$787$	10.3923	−	6.00000i	0.370446	−	0.213877i	−0.303207	−	0.952925i	$-0.598058\pi$
$787$	10.3923	−	6.00000i	0.370446	−	0.213877i	0.673653	+	0.739048i	$0.264724\pi$
$788$		−	3.12311i		−	0.111256i
$789$	9.34233	+	16.1814i	0.332596	+	0.576073i
$790$		0			0
$791$	−1.12311	+	1.94528i	−0.0399330	+	0.0691661i
$792$		−	3.56155i		−	0.126554i
$793$	−38.1519	+	5.34233i	−1.35481	+	0.189712i
$794$	−10.8078			−0.383553
$795$		0			0
$796$	4.28078	−	7.41452i	0.151728	−	0.262801i
$797$	8.44703	−	4.87689i	0.299209	−	0.172748i	−0.342878	−	0.939380i	$-0.611402\pi$
$797$	8.44703	−	4.87689i	0.299209	−	0.172748i	0.642088	+	0.766631i	$0.278069\pi$
$798$		−	3.68466i		−	0.130435i
$799$	10.2462	+	17.7470i	0.362485	+	0.627842i
$800$		0			0
$801$	−6.24621			−0.220699
$802$	32.3628	−	18.6847i	1.14277	−	0.659778i
$803$	−27.7596	−	16.0270i	−0.979613	−	0.565580i
$804$	−4.40388	+	7.62775i	−0.155313	+	0.269010i
$805$		0			0
$806$	11.3693	−	8.87348i	0.400467	−	0.312555i
$807$		−	21.3693i		−	0.752236i
$808$	−8.87348	−	5.12311i	−0.312168	−	0.180230i
$809$	−4.80776	+	8.32729i	−0.169032	+	0.292772i	−0.938080	−	0.346419i	$-0.887397\pi$
$809$	−4.80776	+	8.32729i	−0.169032	+	0.292772i	0.769048	+	0.639191i	$0.220731\pi$
$810$		0			0
$811$	11.9309			0.418949			0.209475	−	0.977814i	$-0.432825\pi$
$811$	11.9309			0.418949			0.209475	+	0.977814i	$0.432825\pi$
$812$	3.46410	−	2.00000i	0.121566	−	0.0701862i
$813$	−17.2606	+	9.96543i	−0.605357	+	0.349503i
$814$	12.6847			0.444597
$815$		0			0
$816$	−2.56155	+	4.43674i	−0.0896723	+	0.155317i
$817$	−25.9209	−	14.9654i	−0.906857	−	0.523574i
$818$		−	0.246211i		−	0.00860857i
$819$	−1.59612	+	1.24573i	−0.0557729	+	0.0435294i
$820$		0			0
$821$	13.4924	−	23.3696i	0.470889	−	0.815603i	−0.528557	−	0.848898i	$-0.677267\pi$
$821$	13.4924	−	23.3696i	0.470889	−	0.815603i	0.999446	+	0.0332946i	$0.0106000\pi$
$822$	−14.2829	−	8.24621i	−0.498172	−	0.287620i
$823$	−30.9973	+	17.8963i	−1.08050	+	0.623826i	−0.931031	−	0.364941i	$-0.881089\pi$
$823$	−30.9973	+	17.8963i	−1.08050	+	0.623826i	−0.149467	+	0.988767i	$0.547756\pi$
$824$	8.56155			0.298256
$825$		0			0
$826$	−1.75379	−	3.03765i	−0.0610221	−	0.105693i
$827$		−	34.9309i		−	1.21467i	−0.794448	−	0.607333i	$-0.792240\pi$
$827$		−	34.9309i		−	1.21467i	0.794448	−	0.607333i	$-0.207760\pi$
$828$	4.05703	−	2.34233i	0.140992	−	0.0814016i
$829$	−28.7732	+	49.8366i	−0.999335	+	1.73090i	−0.468078	+	0.883687i	$0.655053\pi$
$829$	−28.7732	+	49.8366i	−0.999335	+	1.73090i	−0.531257	+	0.847211i	$0.678280\pi$
$830$		0			0
$831$	5.00000			0.173448
$832$	−1.35234	+	3.34233i	−0.0468841	+	0.115874i
$833$		−	34.2462i		−	1.18656i
$834$	8.71922	−	15.1021i	0.301922	−	0.522944i
$835$		0			0
$836$	11.6847	+	20.2384i	0.404122	+	0.699960i
$837$		−	4.00000i		−	0.138260i
$838$	14.6626	−	8.46543i	0.506510	−	0.292434i
$839$	0.657671	+	1.13912i	0.0227053	+	0.0393268i	0.877155	−	0.480208i	$-0.159439\pi$
$839$	0.657671	+	1.13912i	0.0227053	+	0.0393268i	−0.854449	+	0.519534i	$0.826105\pi$
$840$		0			0
$841$	−10.8693	−	18.8262i	−0.374804	−	0.649180i
$842$	12.7772	+	7.37689i	0.440330	+	0.254225i
$843$	15.8017	+	9.12311i	0.544239	+	0.314216i
$844$	7.12311			0.245187
$845$		0			0
$846$	4.00000			0.137523
$847$	0.819281	+	0.473012i	0.0281508	+	0.0162529i
$848$	10.6055	+	6.12311i	0.364195	+	0.210268i
$849$	−5.80776	−	10.0593i	−0.199322	−	0.345236i
$850$		0			0
$851$	8.34233	+	14.4493i	0.285971	+	0.495317i
$852$	−7.30791	+	4.21922i	−0.250365	+	0.144548i
$853$		−	46.9848i		−	1.60873i	−0.594135	−	0.804365i	$-0.702506\pi$
$853$		−	46.9848i		−	1.60873i	0.594135	−	0.804365i	$-0.297494\pi$
$854$	3.00000	+	5.19615i	0.102658	+	0.177809i
$855$		0			0
$856$	9.68466	−	16.7743i	0.331015	−	0.573334i
$857$			39.7538i			1.35796i	0.734155	+	0.678982i	$0.237578\pi$
$857$			39.7538i			1.35796i	−0.734155	+	0.678982i	$0.762422\pi$
$858$	4.81645	−	11.9039i	0.164431	−	0.406392i
$859$	34.4233			1.17451			0.587254	−	0.809403i	$-0.300209\pi$
$859$	34.4233			1.17451			0.587254	+	0.809403i	$0.300209\pi$
$860$		0			0
$861$	−1.43845	+	2.49146i	−0.0490221	+	0.0849089i
$862$	−26.5737	+	15.3423i	−0.905104	+	0.522562i
$863$			30.9309i			1.05290i	0.850206	+	0.526450i	$0.176477\pi$
$863$			30.9309i			1.05290i	−0.850206	+	0.526450i	$0.823523\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$		0			0
$866$	−1.31534			−0.0446971
$867$	−8.00745	+	4.62311i	−0.271947	+	0.157009i
$868$	−1.94528	−	1.12311i	−0.0660270	−	0.0381207i
$869$	8.56155	−	14.8290i	0.290431	−	0.503041i
$870$		0			0
$871$	−25.0346	+	19.5389i	−0.848264	+	0.662050i
$872$		−	17.8078i		−	0.603047i
$873$	−15.4220	−	8.90388i	−0.521955	−	0.301351i
$874$	−15.3693	+	26.6204i	−0.519875	+	0.900450i
$875$		0			0
$876$	9.00000			0.304082
$877$	−9.09983	+	5.25379i	−0.307279	+	0.177408i	−0.645708	−	0.763584i	$-0.723438\pi$
$877$	−9.09983	+	5.25379i	−0.307279	+	0.177408i	0.338429	+	0.940992i	$0.390105\pi$
$878$	18.9927	−	10.9654i	0.640972	−	0.370066i
$879$	−3.75379			−0.126612
$880$		0			0
$881$	−20.4384	+	35.4004i	−0.688589	+	1.19267i	0.283706	+	0.958911i	$0.408436\pi$
$881$	−20.4384	+	35.4004i	−0.688589	+	1.19267i	−0.972294	+	0.233759i	$0.924897\pi$
$882$	−5.78908	−	3.34233i	−0.194929	−	0.112542i
$883$			17.7538i			0.597463i	0.954337	+	0.298731i	$0.0965634\pi$
$883$			17.7538i			0.597463i	−0.954337	+	0.298731i	$0.903437\pi$
$884$	−14.5616	+	11.3649i	−0.489758	+	0.382244i
$885$		0			0
$886$	−8.90388	+	15.4220i	−0.299132	+	0.518111i
$887$	−14.4026	−	8.31534i	−0.483592	−	0.279202i	0.238320	−	0.971187i	$-0.423403\pi$
$887$	−14.4026	−	8.31534i	−0.483592	−	0.279202i	−0.721912	+	0.691985i	$0.756737\pi$
$888$	−3.08440	+	1.78078i	−0.103506	+	0.0597589i
$889$	−0.669503			−0.0224544
$890$		0			0
$891$	−1.78078	−	3.08440i	−0.0596583	−	0.103331i
$892$			4.56155i			0.152732i
$893$	−22.7299	+	13.1231i	−0.760627	+	0.439148i
$894$	3.12311	−	5.40938i	0.104452	−	0.180917i
$895$		0			0
$896$	0.561553			0.0187602
$897$	16.7276	−	2.34233i	0.558518	−	0.0782081i
$898$			5.12311i			0.170960i
$899$	−14.2462	+	24.6752i	−0.475138	+	0.822963i
$900$		0			0
$901$	31.3693	+	54.3333i	1.04506	+	1.81010i
$902$		−	18.2462i		−	0.607532i
$903$	2.21837	−	1.28078i	0.0738227	−	0.0426216i
$904$	2.00000	+	3.46410i	0.0665190	+	0.115214i
$905$		0			0
$906$	2.15767	+	3.73720i	0.0716838	+	0.124160i
$907$	46.6456	+	26.9309i	1.54884	+	0.894225i	0.998230	+	0.0594638i	$0.0189391\pi$
$907$	46.6456	+	26.9309i	1.54884	+	0.894225i	0.550612	+	0.834761i	$0.314394\pi$
$908$	−14.9955	−	8.65767i	−0.497644	−	0.287315i
$909$	−10.2462			−0.339845
$910$		0			0
$911$	27.3153			0.904998			0.452499	−	0.891765i	$-0.350533\pi$
$911$	27.3153			0.904998			0.452499	+	0.891765i	$0.350533\pi$
$912$	−5.68247	−	3.28078i	−0.188165	−	0.108637i
$913$	−7.52113	−	4.34233i	−0.248913	−	0.143710i
$914$	18.7462	+	32.4694i	0.620070	+	1.07399i
$915$		0			0
$916$	11.7462	+	20.3450i	0.388106	+	0.672219i
$917$	−4.43674	+	2.56155i	−0.146514	+	0.0845899i
$918$			5.12311i			0.169088i
$919$	19.8423	+	34.3679i	0.654538	+	1.13369i	0.982009	+	0.188832i	$0.0604702\pi$
$919$	19.8423	+	34.3679i	0.654538	+	1.13369i	−0.327471	+	0.944861i	$0.606196\pi$
$920$		0			0
$921$	−2.87689	+	4.98293i	−0.0947969	+	0.164193i
$922$		−	35.3693i		−	1.16483i
$923$	−30.1313	+	4.21922i	−0.991783	+	0.138877i
$924$	−2.00000			−0.0657952
$925$		0			0
$926$	−3.59612	+	6.22866i	−0.118176	+	0.204686i
$927$	7.41452	−	4.28078i	0.243525	−	0.140599i
$928$		−	7.12311i		−	0.233827i
$929$	3.93087	+	6.80847i	0.128968	+	0.223379i	0.923277	−	0.384135i	$-0.125500\pi$
$929$	3.93087	+	6.80847i	0.128968	+	0.223379i	−0.794309	+	0.607514i	$0.792167\pi$
$930$		0			0
$931$	43.8617			1.43751
$932$	0.546188	−	0.315342i	0.0178910	−	0.0103294i
$933$	19.6455	+	11.3423i	0.643164	+	0.371331i
$934$	−3.78078	+	6.54850i	−0.123711	+	0.214273i
$935$		0			0
$936$	0.500000	+	3.57071i	0.0163430	+	0.116712i
$937$		−	5.24621i		−	0.171386i	−0.996322	−	0.0856931i	$-0.972690\pi$
$937$		−	5.24621i		−	0.171386i	0.996322	−	0.0856931i	$-0.0273105\pi$
$938$	4.28338	+	2.47301i	0.139857	+	0.0807467i
$939$	15.5000	−	26.8468i	0.505823	−	0.876112i
$940$		0			0
$941$	59.3693			1.93538			0.967692	−	0.252134i	$-0.0811325\pi$
$941$	59.3693			1.93538			0.967692	+	0.252134i	$0.0811325\pi$
$942$	−0.652800	+	0.376894i	−0.0212694	+	0.0122799i
$943$	20.7846	−	12.0000i	0.676840	−	0.390774i
$944$	−6.24621			−0.203297
$945$		0			0
$946$	−8.12311	+	14.0696i	−0.264105	+	0.457443i
$947$	−27.4266	−	15.8348i	−0.891245	−	0.514560i	−0.0168952	−	0.999857i	$-0.505378\pi$
$947$	−27.4266	−	15.8348i	−0.891245	−	0.514560i	−0.874349	+	0.485297i	$0.838711\pi$
$948$			4.80776i			0.156149i
$949$	30.0810	+	12.1711i	0.976469	+	0.395091i
$950$		0			0
$951$	0.123106	−	0.213225i	0.00399197	−	0.00691430i
$952$	2.49146	+	1.43845i	0.0807488	+	0.0466203i
$953$	7.14143	−	4.12311i	0.231334	−	0.133560i	−0.379854	−	0.925047i	$-0.624026\pi$
$953$	7.14143	−	4.12311i	0.231334	−	0.133560i	0.611187	+	0.791486i	$0.290692\pi$
$954$	12.2462			0.396486
$955$		0			0
$956$	5.02699	+	8.70700i	0.162584	+	0.281604i
$957$			25.3693i			0.820074i
$958$	25.6478	−	14.8078i	0.828643	−	0.478417i
$959$	−4.63068	+	8.02058i	−0.149533	+	0.258998i
$960$		0			0
$961$	−15.0000			−0.483871
$962$	−12.7173	+	1.78078i	−0.410022	+	0.0574145i
$963$		−	19.3693i		−	0.624168i
$964$	5.71922	−	9.90599i	0.184204	−	0.319050i
$965$		0			0
$966$	−1.31534	−	2.27824i	−0.0423204	−	0.0733011i
$967$		−	41.3693i		−	1.33035i	−0.746689	−	0.665174i	$-0.768357\pi$
$967$		−	41.3693i		−	1.33035i	0.746689	−	0.665174i	$-0.231643\pi$
$968$	1.45896	−	0.842329i	0.0468927	−	0.0270735i
$969$	−16.8078	−	29.1119i	−0.539943	−	0.935209i
$970$		0			0
$971$	−19.6847	−	34.0948i	−0.631711	−	1.09416i	−0.987202	−	0.159475i	$-0.949020\pi$
$971$	−19.6847	−	34.0948i	−0.631711	−	1.09416i	0.355491	−	0.934680i	$-0.384314\pi$
$972$	0.866025	+	0.500000i	0.0277778	+	0.0160375i
$973$	−8.48065	−	4.89630i	−0.271877	−	0.156968i
$974$	−30.3153			−0.971366
$975$		0			0
$976$	10.6847			0.342008
$977$	−25.7675	−	14.8769i	−0.824377	−	0.475954i	0.0275468	−	0.999621i	$-0.491230\pi$
$977$	−25.7675	−	14.8769i	−0.824377	−	0.475954i	−0.851923	+	0.523666i	$0.824564\pi$
$978$	−14.2829	−	8.24621i	−0.456715	−	0.263685i
$979$	−11.1231	−	19.2658i	−0.355496	−	0.615737i
$980$		0			0
$981$	−8.90388	−	15.4220i	−0.284279	−	0.492386i
$982$	19.3125	−	11.1501i	0.616288	−	0.355814i
$983$		−	5.75379i		−	0.183517i	−0.995781	−	0.0917587i	$-0.970751\pi$
$983$		−	5.75379i		−	0.183517i	0.995781	−	0.0917587i	$-0.0292488\pi$
$984$	2.56155	+	4.43674i	0.0816593	+	0.141438i
$985$		0			0
$986$	18.2462	−	31.6034i	0.581078	−	1.00646i
$987$		−	2.24621i		−	0.0714977i
$988$	−14.5560	−	18.6501i	−0.463086	−	0.593339i
$989$	−21.3693			−0.679505
$990$		0			0
$991$	28.5270	−	49.4102i	0.906190	−	1.56957i	0.0868773	−	0.996219i	$-0.472311\pi$
$991$	28.5270	−	49.4102i	0.906190	−	1.56957i	0.819312	−	0.573347i	$-0.194355\pi$
$992$	−3.46410	+	2.00000i	−0.109985	+	0.0635001i
$993$		−	4.31534i		−	0.136943i
$994$	2.36932	+	4.10378i	0.0751502	+	0.130164i
$995$		0			0
$996$	2.43845			0.0772652
$997$	43.8811	−	25.3348i	1.38973	−	0.802360i	0.396443	−	0.918059i	$-0.370244\pi$
$997$	43.8811	−	25.3348i	1.38973	−	0.802360i	0.993284	+	0.115700i	$0.0369110\pi$
$998$	26.8935	+	15.5270i	0.851300	+	0.491498i
$999$	−1.78078	+	3.08440i	−0.0563413	+	0.0975859i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.z.m.1699.3		8
5.2	odd	4		1950.2.i.z.451.1	✓	4
5.3	odd	4		1950.2.i.bg.451.2	yes	4
5.4	even	2	inner	1950.2.z.m.1699.2		8
13.3	even	3	inner	1950.2.z.m.1849.2		8
65.3	odd	12		1950.2.i.bg.601.2	yes	4
65.29	even	6	inner	1950.2.z.m.1849.3		8
65.42	odd	12		1950.2.i.z.601.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1950.2.i.z.451.1	✓	4	5.2	odd	4
1950.2.i.z.601.1	yes	4	65.42	odd	12
1950.2.i.bg.451.2	yes	4	5.3	odd	4
1950.2.i.bg.601.2	yes	4	65.3	odd	12
1950.2.z.m.1699.2		8	5.4	even	2	inner
1950.2.z.m.1699.3		8	1.1	even	1	trivial
1950.2.z.m.1849.2		8	13.3	even	3	inner
1950.2.z.m.1849.3		8	65.29	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:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.z (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(-0.486319 + 0.280776i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(-0.486319 + 0.280776i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.78078 + 3.08440i) q^{11} -1.00000i q^{12} +(1.35234 - 3.34233i) q^{13} -0.561553 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-4.43674 + 2.56155i) q^{17} +1.00000i q^{18} +(-3.28078 - 5.68247i) q^{19} +0.561553 q^{21} +(-3.08440 + 1.78078i) q^{22} +(-4.05703 - 2.34233i) q^{23} +(0.500000 - 0.866025i) q^{24} +(2.84233 - 2.21837i) q^{26} -1.00000i q^{27} +(-0.486319 - 0.280776i) q^{28} +(-3.56155 + 6.16879i) q^{29} +4.00000 q^{31} +(-0.866025 + 0.500000i) q^{32} +(3.08440 - 1.78078i) q^{33} -5.12311 q^{34} +(-0.500000 + 0.866025i) q^{36} +(-3.08440 - 1.78078i) q^{37} -6.56155i q^{38} +(-2.84233 + 2.21837i) q^{39} +(-2.56155 + 4.43674i) q^{41} +(0.486319 + 0.280776i) q^{42} +(3.95042 - 2.28078i) q^{43} -3.56155 q^{44} +(-2.34233 - 4.05703i) q^{46} -4.00000i q^{47} +(0.866025 - 0.500000i) q^{48} +(-3.34233 + 5.78908i) q^{49} +5.12311 q^{51} +(3.57071 - 0.500000i) q^{52} -12.2462i q^{53} +(0.500000 - 0.866025i) q^{54} +(-0.280776 - 0.486319i) q^{56} +6.56155i q^{57} +(-6.16879 + 3.56155i) q^{58} +(3.12311 + 5.40938i) q^{59} +(-5.34233 - 9.25319i) q^{61} +(3.46410 + 2.00000i) q^{62} +(-0.486319 - 0.280776i) q^{63} -1.00000 q^{64} +3.56155 q^{66} +(-7.62775 - 4.40388i) q^{67} +(-4.43674 - 2.56155i) q^{68} +(2.34233 + 4.05703i) q^{69} +(-4.21922 - 7.30791i) q^{71} +(-0.866025 + 0.500000i) q^{72} +9.00000i q^{73} +(-1.78078 - 3.08440i) q^{74} +(3.28078 - 5.68247i) q^{76} -2.00000i q^{77} +(-3.57071 + 0.500000i) q^{78} -4.80776 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-4.43674 + 2.56155i) q^{82} +2.43845i q^{83} +(0.280776 + 0.486319i) q^{84} +4.56155 q^{86} +(6.16879 - 3.56155i) q^{87} +(-3.08440 - 1.78078i) q^{88} +(-3.12311 + 5.40938i) q^{89} +(0.280776 + 2.00514i) q^{91} -4.68466i q^{92} +(-3.46410 - 2.00000i) q^{93} +(2.00000 - 3.46410i) q^{94} +1.00000 q^{96} +(-15.4220 + 8.90388i) q^{97} +(-5.78908 + 3.34233i) q^{98} -3.56155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} - 4 q^{6} + 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^4 - 4 * q^6 + 4 * q^9	\( 8 q + 4 q^{4} - 4 q^{6} + 4 q^{9} - 6 q^{11} + 12 q^{14} - 4 q^{16} - 18 q^{19} - 12 q^{21} + 4 q^{24} - 2 q^{26} - 12 q^{29} + 32 q^{31} - 8 q^{34} - 4 q^{36} + 2 q^{39} - 4 q^{41} - 12 q^{44} + 6 q^{46} - 2 q^{49} + 8 q^{51} + 4 q^{54} + 6 q^{56} - 8 q^{59} - 18 q^{61} - 8 q^{64} + 12 q^{66} - 6 q^{69} - 42 q^{71} - 6 q^{74} + 18 q^{76} + 44 q^{79} - 4 q^{81} - 6 q^{84} + 20 q^{86} + 8 q^{89} - 6 q^{91} + 16 q^{94} + 8 q^{96} - 12 q^{99}+O(q^{100}) \) 8 * q + 4 * q^4 - 4 * q^6 + 4 * q^9 - 6 * q^11 + 12 * q^14 - 4 * q^16 - 18 * q^19 - 12 * q^21 + 4 * q^24 - 2 * q^26 - 12 * q^29 + 32 * q^31 - 8 * q^34 - 4 * q^36 + 2 * q^39 - 4 * q^41 - 12 * q^44 + 6 * q^46 - 2 * q^49 + 8 * q^51 + 4 * q^54 + 6 * q^56 - 8 * q^59 - 18 * q^61 - 8 * q^64 + 12 * q^66 - 6 * q^69 - 42 * q^71 - 6 * q^74 + 18 * q^76 + 44 * q^79 - 4 * q^81 - 6 * q^84 + 20 * q^86 + 8 * q^89 - 6 * q^91 + 16 * q^94 + 8 * q^96 - 12 * q^99

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