LMFDB - Embedded newform 1950.2.bc.k.901.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(751,1950)]

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, 0, 5]))

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

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

chi := DirichletCharacter("1950.751");

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.bc (of order $6$, degree $2$, 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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 87 x^{10} - 380 x^{9} + 2556 x^{8} - 8010 x^{7} + 29687 x^{6} - 62556 x^{5} + \cdots + 14089 $ x^12 - 6x^11 + 87x^10 - 380x^9 + 2556x^8 - 8010x^7 + 29687x^6 - 62556x^5 + 115386x^4 - 135130x^3 + 113253x^2 - 54888*x + 14089
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.2
Root			$0.500000 - 0.414256i$ of defining polynomial
Character	$\chi$	$=$	1950.901
Dual form			1950.2.bc.k.751.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(0.242731 - 0.140141i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(0.242731 - 0.140141i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.663862 + 0.383281i) q^{11} +1.00000 q^{12} +(-2.77303 - 2.30441i) q^{13} -0.280281 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.10917 - 1.92113i) q^{17} +1.00000i q^{18} +(-4.57097 + 2.63905i) q^{19} -0.280281i q^{21} +(-0.383281 - 0.663862i) q^{22} +(-0.725885 + 1.25727i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(1.24931 + 3.38219i) q^{26} -1.00000 q^{27} +(0.242731 + 0.140141i) q^{28} +(-3.03030 + 5.24863i) q^{29} -3.28110i q^{31} +(0.866025 - 0.500000i) q^{32} +(0.663862 - 0.383281i) q^{33} +2.21833i q^{34} +(0.500000 - 0.866025i) q^{36} +(-3.07097 - 1.77303i) q^{37} +5.27811 q^{38} +(-3.38219 + 1.24931i) q^{39} +(1.92113 + 1.10917i) q^{41} +(-0.140141 + 0.242731i) q^{42} +(-1.80441 - 3.12533i) q^{43} +0.766562i q^{44} +(1.25727 - 0.725885i) q^{46} -1.06277i q^{47} +(0.500000 + 0.866025i) q^{48} +(-3.46072 + 5.99414i) q^{49} -2.21833 q^{51} +(0.609166 - 3.55372i) q^{52} +3.28110 q^{53} +(0.866025 + 0.500000i) q^{54} +(-0.140141 - 0.242731i) q^{56} +5.27811i q^{57} +(5.24863 - 3.03030i) q^{58} +(-4.32824 + 2.49891i) q^{59} +(-0.773028 - 1.33892i) q^{61} +(-1.64055 + 2.84152i) q^{62} +(-0.242731 - 0.140141i) q^{63} -1.00000 q^{64} -0.766562 q^{66} +(-6.43963 - 3.71792i) q^{67} +(1.10917 - 1.92113i) q^{68} +(0.725885 + 1.25727i) q^{69} +(-2.09811 + 1.21135i) q^{71} +(-0.866025 + 0.500000i) q^{72} -14.2630i q^{73} +(1.77303 + 3.07097i) q^{74} +(-4.57097 - 2.63905i) q^{76} +0.214853 q^{77} +(3.55372 + 0.609166i) q^{78} -14.4715 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-1.10917 - 1.92113i) q^{82} +4.42419i q^{83} +(0.242731 - 0.140141i) q^{84} +3.60882i q^{86} +(3.03030 + 5.24863i) q^{87} +(0.383281 - 0.663862i) q^{88} +(-4.60275 - 2.65740i) q^{89} +(-0.996041 - 0.170738i) q^{91} -1.45177 q^{92} +(-2.84152 - 1.64055i) q^{93} +(-0.531385 + 0.920385i) q^{94} -1.00000i q^{96} +(1.09737 - 0.633565i) q^{97} +(5.99414 - 3.46072i) q^{98} -0.766562i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} + 6 q^{4} + 6 q^{7} - 6 q^{9}+O(q^{10}) $ 12 * q + 6 * q^3 + 6 * q^4 + 6 * q^7 - 6 * q^9	$ 12 q + 6 q^{3} + 6 q^{4} + 6 q^{7} - 6 q^{9} - 12 q^{11} + 12 q^{12} + 8 q^{14} - 6 q^{16} - 6 q^{19} + 4 q^{22} - 4 q^{23} - 4 q^{26} - 12 q^{27} + 6 q^{28} - 12 q^{33} + 6 q^{36} + 12 q^{37} - 24 q^{38} + 6 q^{39} + 4 q^{42} + 10 q^{43} + 12 q^{46} + 6 q^{48} + 32 q^{49} - 6 q^{52} + 16 q^{53} + 4 q^{56} + 24 q^{61} - 8 q^{62} - 6 q^{63} - 12 q^{64} + 8 q^{66} - 6 q^{67} + 4 q^{69} + 12 q^{71} - 12 q^{74} - 6 q^{76} + 48 q^{77} - 8 q^{78} + 52 q^{79} - 6 q^{81} + 6 q^{84} - 4 q^{88} + 24 q^{89} - 54 q^{91} - 8 q^{92} - 8 q^{94} - 12 q^{97} - 36 q^{98}+O(q^{100}) $ 12 * q + 6 * q^3 + 6 * q^4 + 6 * q^7 - 6 * q^9 - 12 * q^11 + 12 * q^12 + 8 * q^14 - 6 * q^16 - 6 * q^19 + 4 * q^22 - 4 * q^23 - 4 * q^26 - 12 * q^27 + 6 * q^28 - 12 * q^33 + 6 * q^36 + 12 * q^37 - 24 * q^38 + 6 * q^39 + 4 * q^42 + 10 * q^43 + 12 * q^46 + 6 * q^48 + 32 * q^49 - 6 * q^52 + 16 * q^53 + 4 * q^56 + 24 * q^61 - 8 * q^62 - 6 * q^63 - 12 * q^64 + 8 * q^66 - 6 * q^67 + 4 * q^69 + 12 * q^71 - 12 * q^74 - 6 * q^76 + 48 * q^77 - 8 * q^78 + 52 * q^79 - 6 * q^81 + 6 * q^84 - 4 * q^88 + 24 * q^89 - 54 * q^91 - 8 * q^92 - 8 * q^94 - 12 * q^97 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

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
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	0.242731	−	0.140141i	0.0917436	−	0.0529682i	−0.453426	−	0.891294i	$-0.649798\pi$
$7$	0.242731	−	0.140141i	0.0917436	−	0.0529682i	0.545170	+	0.838326i	$0.316465\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	0.663862	+	0.383281i	0.200162	+	0.115564i	0.596731	−	0.802441i	$-0.296466\pi$
$11$	0.663862	+	0.383281i	0.200162	+	0.115564i	−0.396569	+	0.918005i	$0.629799\pi$
$12$	1.00000			0.288675
$13$	−2.77303	−	2.30441i	−0.769100	−	0.639129i
$13$	−2.77303	−	2.30441i	−0.769100	−	0.639129i
$14$	−0.280281			−0.0749083
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.10917	−	1.92113i	−0.269012	−	0.465943i	0.699595	−	0.714540i	$-0.253364\pi$
$17$	−1.10917	−	1.92113i	−0.269012	−	0.465943i	−0.968607	+	0.248597i	$0.920031\pi$
$18$			1.00000i			0.235702i
$19$	−4.57097	+	2.63905i	−1.04865	+	0.605440i	−0.922272	−	0.386541i	$-0.873670\pi$
$19$	−4.57097	+	2.63905i	−1.04865	+	0.605440i	−0.126381	+	0.991982i	$0.540336\pi$
$20$		0			0
$21$		−	0.280281i		−	0.0611624i
$22$	−0.383281	−	0.663862i	−0.0817158	−	0.141536i
$23$	−0.725885	+	1.25727i	−0.151357	+	0.262159i	−0.931727	−	0.363160i	$-0.881698\pi$
$23$	−0.725885	+	1.25727i	−0.151357	+	0.262159i	0.780369	+	0.625319i	$0.215031\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$		0			0
$26$	1.24931	+	3.38219i	0.245009	+	0.663303i
$27$	−1.00000			−0.192450
$28$	0.242731	+	0.140141i	0.0458718	+	0.0264841i
$29$	−3.03030	+	5.24863i	−0.562712	+	0.974646i	0.434546	+	0.900649i	$0.356909\pi$
$29$	−3.03030	+	5.24863i	−0.562712	+	0.974646i	−0.997259	+	0.0739965i	$0.976425\pi$
$30$		0			0
$31$		−	3.28110i		−	0.589303i	−0.955605	−	0.294652i	$-0.904796\pi$
$31$		−	3.28110i		−	0.589303i	0.955605	−	0.294652i	$-0.0952036\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	0.663862	−	0.383281i	0.115564	−	0.0667207i
$34$			2.21833i			0.380441i
$35$		0			0
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−3.07097	−	1.77303i	−0.504865	−	0.291484i	0.225855	−	0.974161i	$-0.427482\pi$
$37$	−3.07097	−	1.77303i	−0.504865	−	0.291484i	−0.730720	+	0.682677i	$0.760816\pi$
$38$	5.27811			0.856222
$39$	−3.38219	+	1.24931i	−0.541584	+	0.200049i
$40$		0			0
$41$	1.92113	+	1.10917i	0.300030	+	0.173223i	0.642457	−	0.766322i	$-0.277915\pi$
$41$	1.92113	+	1.10917i	0.300030	+	0.173223i	−0.342426	+	0.939545i	$0.611249\pi$
$42$	−0.140141	+	0.242731i	−0.0216242	+	0.0374542i
$43$	−1.80441	−	3.12533i	−0.275170	−	0.476609i	0.695008	−	0.719002i	$-0.255401\pi$
$43$	−1.80441	−	3.12533i	−0.275170	−	0.476609i	−0.970178	+	0.242393i	$0.922068\pi$
$44$			0.766562i			0.115564i
$45$		0			0
$46$	1.25727	−	0.725885i	0.185374	−	0.107026i
$47$		−	1.06277i		−	0.155021i	−0.996992	−	0.0775104i	$-0.975303\pi$
$47$		−	1.06277i		−	0.155021i	0.996992	−	0.0775104i	$-0.0246971\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	−3.46072	+	5.99414i	−0.494389	+	0.856306i
$50$		0			0
$51$	−2.21833			−0.310629
$52$	0.609166	−	3.55372i	0.0844761	−	0.492812i
$53$	3.28110			0.450694			0.225347	−	0.974279i	$-0.427648\pi$
$53$	3.28110			0.450694			0.225347	+	0.974279i	$0.427648\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$		0			0
$56$	−0.140141	−	0.242731i	−0.0187271	−	0.0324362i
$57$			5.27811i			0.699102i
$58$	5.24863	−	3.03030i	0.689179	−	0.397898i
$59$	−4.32824	+	2.49891i	−0.563489	+	0.325331i	−0.754545	−	0.656249i	$-0.772142\pi$
$59$	−4.32824	+	2.49891i	−0.563489	+	0.325331i	0.191055	+	0.981579i	$0.438809\pi$
$60$		0			0
$61$	−0.773028	−	1.33892i	−0.0989761	−	0.171432i	0.812285	−	0.583261i	$-0.198223\pi$
$61$	−0.773028	−	1.33892i	−0.0989761	−	0.171432i	−0.911261	+	0.411829i	$0.864890\pi$
$62$	−1.64055	+	2.84152i	−0.208350	+	0.360873i
$63$	−0.242731	−	0.140141i	−0.0305812	−	0.0176561i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−0.766562			−0.0943573
$67$	−6.43963	−	3.71792i	−0.786726	−	0.454216i	0.0520827	−	0.998643i	$-0.483414\pi$
$67$	−6.43963	−	3.71792i	−0.786726	−	0.454216i	−0.838809	+	0.544426i	$0.816747\pi$
$68$	1.10917	−	1.92113i	0.134506	−	0.232971i
$69$	0.725885	+	1.25727i	0.0873863	+	0.151357i
$70$		0			0
$71$	−2.09811	+	1.21135i	−0.249000	+	0.143760i	−0.619306	−	0.785149i	$-0.712586\pi$
$71$	−2.09811	+	1.21135i	−0.249000	+	0.143760i	0.370306	+	0.928910i	$0.379253\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$		−	14.2630i		−	1.66936i	−0.550737	−	0.834679i	$-0.685653\pi$
$73$		−	14.2630i		−	1.66936i	0.550737	−	0.834679i	$-0.314347\pi$
$74$	1.77303	+	3.07097i	0.206110	+	0.356994i
$75$		0			0
$76$	−4.57097	−	2.63905i	−0.524327	−	0.302720i
$77$	0.214853			0.0244848
$78$	3.55372	+	0.609166i	0.402379	+	0.0689744i
$79$	−14.4715			−1.62817			−0.814085	−	0.580746i	$-0.802761\pi$
$79$	−14.4715			−1.62817			−0.814085	+	0.580746i	$0.802761\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−1.10917	−	1.92113i	−0.122487	−	0.212153i
$83$			4.42419i			0.485617i	0.970074	+	0.242809i	$0.0780687\pi$
$83$			4.42419i			0.485617i	−0.970074	+	0.242809i	$0.921931\pi$
$84$	0.242731	−	0.140141i	0.0264841	−	0.0152906i
$85$		0			0
$86$			3.60882i			0.389150i
$87$	3.03030	+	5.24863i	0.324882	+	0.562712i
$88$	0.383281	−	0.663862i	0.0408579	−	0.0707679i
$89$	−4.60275	−	2.65740i	−0.487890	−	0.281683i	0.235809	−	0.971799i	$-0.424226\pi$
$89$	−4.60275	−	2.65740i	−0.487890	−	0.281683i	−0.723699	+	0.690116i	$0.757559\pi$
$90$		0			0
$91$	−0.996041	−	0.170738i	−0.104413	−	0.0178982i
$92$	−1.45177			−0.151357
$93$	−2.84152	−	1.64055i	−0.294652	−	0.170117i
$94$	−0.531385	+	0.920385i	−0.0548081	+	0.0949305i
$95$		0			0
$96$		−	1.00000i		−	0.102062i
$97$	1.09737	−	0.633565i	0.111421	−	0.0643288i	−0.443254	−	0.896396i	$-0.646176\pi$
$97$	1.09737	−	0.633565i	0.111421	−	0.0643288i	0.554675	+	0.832067i	$0.312843\pi$
$98$	5.99414	−	3.46072i	0.605500	−	0.349586i
$99$		−	0.766562i		−	0.0770424i
$100$		0			0
$101$	−2.26374	+	3.92090i	−0.225250	+	0.390145i	−0.956394	−	0.292078i	$-0.905653\pi$
$101$	−2.26374	+	3.92090i	−0.225250	+	0.390145i	0.731144	+	0.682223i	$0.238987\pi$
$102$	1.92113	+	1.10917i	0.190220	+	0.109824i
$103$	2.94271			0.289954			0.144977	−	0.989435i	$-0.453689\pi$
$103$	2.94271			0.289954			0.144977	+	0.989435i	$0.453689\pi$
$104$	−2.30441	+	2.77303i	−0.225966	+	0.271918i
$105$		0			0
$106$	−2.84152	−	1.64055i	−0.275992	−	0.159344i
$107$	−9.52440	+	16.4967i	−0.920758	+	1.59480i	−0.122513	+	0.992467i	$0.539095\pi$
$107$	−9.52440	+	16.4967i	−0.920758	+	1.59480i	−0.798245	+	0.602333i	$0.794238\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$			9.04549i			0.866401i	0.901298	+	0.433200i	$0.142616\pi$
$109$			9.04549i			0.866401i	−0.901298	+	0.433200i	$0.857384\pi$
$110$		0			0
$111$	−3.07097	+	1.77303i	−0.291484	+	0.168288i
$112$			0.280281i			0.0264841i
$113$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$113$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$114$	2.63905	−	4.57097i	0.247170	−	0.428111i
$115$		0			0
$116$	−6.06059			−0.562712
$117$	−0.609166	+	3.55372i	−0.0563174	+	0.328541i
$118$	4.99783			0.460087
$119$	−0.538457	−	0.310878i	−0.0493603	−	0.0284982i
$120$		0			0
$121$	−5.20619	−	9.01739i	−0.473290	−	0.819763i
$122$			1.54606i			0.139973i
$123$	1.92113	−	1.10917i	0.173223	−	0.100010i
$124$	2.84152	−	1.64055i	0.255176	−	0.147326i
$125$		0			0
$126$	0.140141	+	0.242731i	0.0124847	+	0.0216242i
$127$	1.58585	−	2.74678i	0.140722	−	0.243737i	−0.787047	−	0.616893i	$-0.788391\pi$
$127$	1.58585	−	2.74678i	0.140722	−	0.243737i	0.927769	+	0.373156i	$0.121724\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−3.60882			−0.317739
$130$		0			0
$131$	15.4345			1.34852			0.674259	−	0.738495i	$-0.264463\pi$
$131$	15.4345			1.34852			0.674259	+	0.738495i	$0.264463\pi$
$132$	0.663862	+	0.383281i	0.0577818	+	0.0333603i
$133$	−0.739677	+	1.28116i	−0.0641381	+	0.111091i
$134$	3.71792	+	6.43963i	0.321180	+	0.556299i
$135$		0			0
$136$	−1.92113	+	1.10917i	−0.164736	+	0.0951102i
$137$	−1.44478	+	0.834145i	−0.123436	+	0.0712658i	−0.560447	−	0.828191i	$-0.689371\pi$
$137$	−1.44478	+	0.834145i	−0.123436	+	0.0712658i	0.437011	+	0.899456i	$0.356037\pi$
$138$		−	1.45177i		−	0.123583i
$139$	−1.05395	−	1.82549i	−0.0893949	−	0.154836i	0.817861	−	0.575416i	$-0.195160\pi$
$139$	−1.05395	−	1.82549i	−0.0893949	−	0.154836i	−0.907256	+	0.420580i	$0.861827\pi$
$140$		0			0
$141$	−0.920385	−	0.531385i	−0.0775104	−	0.0447507i
$142$	2.42269			0.203308
$143$	−0.957671	−	2.59266i	−0.0800844	−	0.216809i
$144$	1.00000			0.0833333
$145$		0			0
$146$	−7.13150	+	12.3521i	−0.590207	+	1.02227i
$147$	3.46072	+	5.99414i	0.285435	+	0.494389i
$148$		−	3.54606i		−	0.291484i
$149$	−4.97167	+	2.87039i	−0.407295	+	0.235152i	−0.689627	−	0.724165i	$-0.742225\pi$
$149$	−4.97167	+	2.87039i	−0.407295	+	0.235152i	0.282332	+	0.959317i	$0.408892\pi$
$150$		0			0
$151$		−	16.1710i		−	1.31598i	−0.753029	−	0.657988i	$-0.771408\pi$
$151$		−	16.1710i		−	1.31598i	0.753029	−	0.657988i	$-0.228592\pi$
$152$	2.63905	+	4.57097i	0.214055	+	0.370755i
$153$	−1.10917	+	1.92113i	−0.0896707	+	0.155314i
$154$	−0.186068	−	0.107426i	−0.0149938	−	0.00865667i
$155$		0			0
$156$	−2.77303	−	2.30441i	−0.222020	−	0.184501i
$157$	−15.8401			−1.26418			−0.632088	−	0.774896i	$-0.717802\pi$
$157$	−15.8401			−1.26418			−0.632088	+	0.774896i	$0.717802\pi$
$158$	12.5327	+	7.23574i	0.997046	+	0.575645i
$159$	1.64055	−	2.84152i	0.130104	−	0.225347i
$160$		0			0
$161$			0.406904i			0.0320685i
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$	−9.79890	+	5.65740i	−0.767509	+	0.443121i	−0.831985	−	0.554798i	$-0.812796\pi$
$163$	−9.79890	+	5.65740i	−0.767509	+	0.443121i	0.0644763	+	0.997919i	$0.479462\pi$
$164$			2.21833i			0.173223i
$165$		0			0
$166$	2.21209	−	3.83146i	0.171692	−	0.297379i
$167$	1.25727	+	0.725885i	0.0972904	+	0.0561707i	0.547856	−	0.836573i	$-0.315444\pi$
$167$	1.25727	+	0.725885i	0.0972904	+	0.0561707i	−0.450565	+	0.892743i	$0.648778\pi$
$168$	−0.280281			−0.0216242
$169$	2.37937	+	12.7804i	0.183028	+	0.983108i
$170$		0			0
$171$	4.57097	+	2.63905i	0.349551	+	0.201813i
$172$	1.80441	−	3.12533i	0.137585	−	0.238304i
$173$	6.67010	+	11.5530i	0.507118	+	0.878355i	0.999966	+	0.00823921i	$0.00262265\pi$
$173$	6.67010	+	11.5530i	0.507118	+	0.878355i	−0.492848	+	0.870116i	$0.664044\pi$
$174$		−	6.06059i		−	0.459452i
$175$		0			0
$176$	−0.663862	+	0.383281i	−0.0500405	+	0.0288909i
$177$			4.99783i			0.375660i
$178$	2.65740	+	4.60275i	0.199180	+	0.344990i
$179$	12.6266	−	21.8699i	0.943755	−	1.63463i	0.185529	−	0.982639i	$-0.440600\pi$
$179$	12.6266	−	21.8699i	0.943755	−	1.63463i	0.758226	−	0.651992i	$-0.226067\pi$
$180$		0			0
$181$	−0.314792			−0.0233983			−0.0116992	−	0.999932i	$-0.503724\pi$
$181$	−0.314792			−0.0233983			−0.0116992	+	0.999932i	$0.503724\pi$
$182$	0.777228	+	0.645884i	0.0576119	+	0.0478761i
$183$	−1.54606			−0.114288
$184$	1.25727	+	0.725885i	0.0926871	+	0.0535129i
$185$		0			0
$186$	1.64055	+	2.84152i	0.120291	+	0.208350i
$187$		−	1.70049i		−	0.124352i
$188$	0.920385	−	0.531385i	0.0671260	−	0.0387552i
$189$	−0.242731	+	0.140141i	−0.0176561	+	0.0101937i
$190$		0			0
$191$	11.2666	+	19.5143i	0.815223	+	1.41201i	0.909168	+	0.416430i	$0.136719\pi$
$191$	11.2666	+	19.5143i	0.815223	+	1.41201i	−0.0939445	+	0.995577i	$0.529948\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−8.47286	−	4.89181i	−0.609890	−	0.352120i	0.163032	−	0.986621i	$-0.447872\pi$
$193$	−8.47286	−	4.89181i	−0.609890	−	0.352120i	−0.772922	+	0.634501i	$0.781206\pi$
$194$	−1.26713			−0.0909746
$195$		0			0
$196$	−6.92144			−0.494389
$197$	−10.7883	−	6.22862i	−0.768634	−	0.443771i	0.0637530	−	0.997966i	$-0.479693\pi$
$197$	−10.7883	−	6.22862i	−0.768634	−	0.443771i	−0.832387	+	0.554195i	$0.813026\pi$
$198$	−0.383281	+	0.663862i	−0.0272386	+	0.0471786i
$199$	7.53195	+	13.0457i	0.533926	+	0.924787i	0.999215	+	0.0396276i	$0.0126171\pi$
$199$	7.53195	+	13.0457i	0.533926	+	0.924787i	−0.465289	+	0.885159i	$0.654050\pi$
$200$		0			0
$201$	−6.43963	+	3.71792i	−0.454216	+	0.262242i
$202$	3.92090	−	2.26374i	0.275874	−	0.159276i
$203$			1.69867i			0.119223i
$204$	−1.10917	−	1.92113i	−0.0776571	−	0.134506i
$205$		0			0
$206$	−2.54846	−	1.47135i	−0.177560	−	0.102514i
$207$	1.45177			0.100905
$208$	3.38219	−	1.24931i	0.234513	−	0.0866238i
$209$	−4.04600			−0.279867
$210$		0			0
$211$	−7.53876	+	13.0575i	−0.518989	+	0.898916i	0.480767	+	0.876848i	$0.340358\pi$
$211$	−7.53876	+	13.0575i	−0.518989	+	0.898916i	−0.999756	+	0.0220676i	$0.992975\pi$
$212$	1.64055	+	2.84152i	0.112673	+	0.195156i
$213$			2.42269i			0.166000i
$214$	16.4967	−	9.52440i	1.12769	−	0.651074i
$215$		0			0
$216$			1.00000i			0.0680414i
$217$	−0.459815	−	0.796424i	−0.0312143	−	0.0540648i
$218$	4.52274	−	7.83362i	0.306319	−	0.530560i
$219$	−12.3521	−	7.13150i	−0.834679	−	0.481902i
$220$		0			0
$221$	−1.35133	+	7.88333i	−0.0909004	+	0.530290i
$222$	3.54606			0.237996
$223$	−4.03252	−	2.32817i	−0.270037	−	0.155906i	0.358867	−	0.933389i	$-0.383163\pi$
$223$	−4.03252	−	2.32817i	−0.270037	−	0.155906i	−0.628905	+	0.777482i	$0.716496\pi$
$224$	0.140141	−	0.242731i	0.00936354	−	0.0162181i
$225$		0			0
$226$		0			0
$227$	5.37313	−	3.10218i	0.356627	−	0.205899i	−0.310973	−	0.950419i	$-0.600655\pi$
$227$	5.37313	−	3.10218i	0.356627	−	0.205899i	0.667600	+	0.744520i	$0.267322\pi$
$228$	−4.57097	+	2.63905i	−0.302720	+	0.174776i
$229$			12.8610i			0.849878i	0.905222	+	0.424939i	$0.139704\pi$
$229$			12.8610i			0.849878i	−0.905222	+	0.424939i	$0.860296\pi$
$230$		0			0
$231$	0.107426	−	0.186068i	0.00706814	−	0.0122424i
$232$	5.24863	+	3.03030i	0.344589	+	0.198949i
$233$	−0.970923			−0.0636073			−0.0318036	−	0.999494i	$-0.510125\pi$
$233$	−0.970923			−0.0636073			−0.0318036	+	0.999494i	$0.510125\pi$
$234$	2.30441	−	2.77303i	0.150644	−	0.181279i
$235$		0			0
$236$	−4.32824	−	2.49891i	−0.281745	−	0.162665i
$237$	−7.23574	+	12.5327i	−0.470012	+	0.814085i
$238$	0.310878	+	0.538457i	0.0201512	+	0.0349030i
$239$		−	14.7984i		−	0.957231i	−0.878025	−	0.478616i	$-0.841139\pi$
$239$		−	14.7984i		−	0.957231i	0.878025	−	0.478616i	$-0.158861\pi$
$240$		0			0
$241$	1.89795	−	1.09578i	0.122258	−	0.0705856i	−0.437624	−	0.899158i	$-0.644180\pi$
$241$	1.89795	−	1.09578i	0.122258	−	0.0705856i	0.559882	+	0.828572i	$0.310847\pi$
$242$			10.4124i			0.669333i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	0.773028	−	1.33892i	0.0494880	−	0.0857158i
$245$		0			0
$246$	−2.21833			−0.141436
$247$	18.7569	+	3.21524i	1.19347	+	0.204581i
$248$	−3.28110			−0.208350
$249$	3.83146	+	2.21209i	0.242809	+	0.140186i
$250$		0			0
$251$	5.29487	+	9.17098i	0.334209	+	0.578867i	0.983333	−	0.181816i	$-0.0581975\pi$
$251$	5.29487	+	9.17098i	0.334209	+	0.578867i	−0.649124	+	0.760683i	$0.724864\pi$
$252$		−	0.280281i		−	0.0176561i
$253$	−0.963775	+	0.556436i	−0.0605920	+	0.0349828i
$254$	−2.74678	+	1.58585i	−0.172348	+	0.0995053i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.42396	+	5.93047i	−0.213581	+	0.369933i	−0.952833	−	0.303496i	$-0.901846\pi$
$257$	−3.42396	+	5.93047i	−0.213581	+	0.369933i	0.739252	+	0.673429i	$0.235179\pi$
$258$	3.12533	+	1.80441i	0.194575	+	0.112338i
$259$	−0.993893			−0.0617575
$260$		0			0
$261$	6.06059			0.375141
$262$	−13.3667	−	7.71724i	−0.825795	−	0.476773i
$263$	−13.1181	+	22.7212i	−0.808898	+	1.40105i	0.104730	+	0.994501i	$0.466602\pi$
$263$	−13.1181	+	22.7212i	−0.808898	+	1.40105i	−0.913628	+	0.406551i	$0.866731\pi$
$264$	−0.383281	−	0.663862i	−0.0235893	−	0.0408579i
$265$		0			0
$266$	1.28116	−	0.739677i	0.0785529	−	0.0453525i
$267$	−4.60275	+	2.65740i	−0.281683	+	0.162630i
$268$		−	7.43584i		−	0.454216i
$269$	−3.24938	−	5.62808i	−0.198118	−	0.343150i	0.749800	−	0.661664i	$-0.230150\pi$
$269$	−3.24938	−	5.62808i	−0.198118	−	0.343150i	−0.947918	+	0.318514i	$0.896816\pi$
$270$		0			0
$271$	5.35904	+	3.09404i	0.325539	+	0.187950i	0.653859	−	0.756617i	$-0.273149\pi$
$271$	5.35904	+	3.09404i	0.325539	+	0.187950i	−0.328320	+	0.944567i	$0.606482\pi$
$272$	2.21833			0.134506
$273$	−0.645884	+	0.777228i	−0.0390906	+	0.0470400i
$274$	1.66829			0.100785
$275$		0			0
$276$	−0.725885	+	1.25727i	−0.0436931	+	0.0756787i
$277$	−14.5289	−	25.1647i	−0.872955	−	1.51200i	−0.858925	−	0.512101i	$-0.828867\pi$
$277$	−14.5289	−	25.1647i	−0.872955	−	1.51200i	−0.0140299	−	0.999902i	$-0.504466\pi$
$278$			2.10790i			0.126423i
$279$	−2.84152	+	1.64055i	−0.170117	+	0.0982172i
$280$		0			0
$281$		−	14.1438i		−	0.843746i	−0.906655	−	0.421873i	$-0.861373\pi$
$281$		−	14.1438i		−	0.843746i	0.906655	−	0.421873i	$-0.138627\pi$
$282$	0.531385	+	0.920385i	0.0316435	+	0.0548081i
$283$	4.37290	−	7.57409i	0.259942	−	0.450233i	−0.706284	−	0.707928i	$-0.749630\pi$
$283$	4.37290	−	7.57409i	0.259942	−	0.450233i	0.966226	+	0.257696i	$0.0829632\pi$
$284$	−2.09811	−	1.21135i	−0.124500	−	0.0718802i
$285$		0			0
$286$	−0.466963	+	2.72415i	−0.0276121	+	0.161082i
$287$	0.621757			0.0367011
$288$	−0.866025	−	0.500000i	−0.0510310	−	0.0294628i
$289$	6.03950	−	10.4607i	0.355265	−	0.615337i
$290$		0			0
$291$		−	1.26713i		−	0.0742805i
$292$	12.3521	−	7.13150i	0.722853	−	0.417339i
$293$	−27.2798	+	15.7500i	−1.59371	+	0.920126i	−0.601042	+	0.799217i	$0.705248\pi$
$293$	−27.2798	+	15.7500i	−1.59371	+	0.920126i	−0.992664	+	0.120909i	$0.961419\pi$
$294$		−	6.92144i		−	0.403667i
$295$		0			0
$296$	−1.77303	+	3.07097i	−0.103055	+	0.178497i
$297$	−0.663862	−	0.383281i	−0.0385212	−	0.0222402i
$298$	5.74079			0.332555
$299$	4.91017	−	1.81370i	0.283962	−	0.104889i
$300$		0			0
$301$	−0.875972	−	0.505743i	−0.0504902	−	0.0291505i
$302$	−8.08549	+	14.0045i	−0.465268	+	0.805867i
$303$	2.26374	+	3.92090i	0.130048	+	0.225250i
$304$		−	5.27811i		−	0.302720i
$305$		0			0
$306$	1.92113	−	1.10917i	0.109824	−	0.0634068i
$307$		−	7.03152i		−	0.401310i	−0.979662	−	0.200655i	$-0.935693\pi$
$307$		−	7.03152i		−	0.401310i	0.979662	−	0.200655i	$-0.0643070\pi$
$308$	0.107426	+	0.186068i	0.00612119	+	0.0106022i
$309$	1.47135	−	2.54846i	0.0837025	−	0.144977i
$310$		0			0
$311$	8.79844			0.498914			0.249457	−	0.968386i	$-0.419748\pi$
$311$	8.79844			0.498914			0.249457	+	0.968386i	$0.419748\pi$
$312$	1.24931	+	3.38219i	0.0707280	+	0.191479i
$313$	9.34134			0.528004			0.264002	−	0.964522i	$-0.414958\pi$
$313$	9.34134			0.528004			0.264002	+	0.964522i	$0.414958\pi$
$314$	13.7179	+	7.92004i	0.774147	+	0.446954i
$315$		0			0
$316$	−7.23574	−	12.5327i	−0.407042	−	0.705018i
$317$		−	19.4697i		−	1.09353i	−0.837287	−	0.546763i	$-0.815860\pi$
$317$		−	19.4697i		−	1.09353i	0.837287	−	0.546763i	$-0.184140\pi$
$318$	−2.84152	+	1.64055i	−0.159344	+	0.0919975i
$319$	−4.02340	+	2.32291i	−0.225267	+	0.130058i
$320$		0			0
$321$	9.52440	+	16.4967i	0.531600	+	0.920758i
$322$	0.203452	−	0.352389i	0.0113379	−	0.0196379i
$323$	10.1399	+	5.85429i	0.564201	+	0.325742i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	11.3148			0.626668
$327$	7.83362	+	4.52274i	0.433200	+	0.250108i
$328$	1.10917	−	1.92113i	0.0612434	−	0.106077i
$329$	−0.148937	−	0.257967i	−0.00821117	−	0.0142222i
$330$		0			0
$331$	16.4081	−	9.47320i	0.901869	−	0.520694i	0.0240626	−	0.999710i	$-0.492340\pi$
$331$	16.4081	−	9.47320i	0.901869	−	0.520694i	0.877806	+	0.479016i	$0.159007\pi$
$332$	−3.83146	+	2.21209i	−0.210279	+	0.121404i
$333$			3.54606i			0.194323i
$334$	−0.725885	−	1.25727i	−0.0397186	−	0.0687947i
$335$		0			0
$336$	0.242731	+	0.140141i	0.0132420	+	0.00764530i
$337$	−2.72966			−0.148694			−0.0743469	−	0.997232i	$-0.523687\pi$
$337$	−2.72966			−0.148694			−0.0743469	+	0.997232i	$0.523687\pi$
$338$	4.32961	−	12.2578i	0.235500	−	0.666738i
$339$		0			0
$340$		0			0
$341$	1.25758	−	2.17820i	0.0681020	−	0.117956i
$342$	−2.63905	−	4.57097i	−0.142704	−	0.247170i
$343$			3.90192i			0.210684i
$344$	−3.12533	+	1.80441i	−0.168507	+	0.0972874i
$345$		0			0
$346$		−	13.3402i		−	0.717174i
$347$	6.34600	+	10.9916i	0.340671	+	0.590059i	0.984557	−	0.175062i	$-0.0560125\pi$
$347$	6.34600	+	10.9916i	0.340671	+	0.590059i	−0.643887	+	0.765121i	$0.722679\pi$
$348$	−3.03030	+	5.24863i	−0.162441	+	0.281356i
$349$	1.04906	+	0.605676i	0.0561549	+	0.0324211i	0.527815	−	0.849360i	$-0.323012\pi$
$349$	1.04906	+	0.605676i	0.0561549	+	0.0324211i	−0.471660	+	0.881781i	$0.656345\pi$
$350$		0			0
$351$	2.77303	+	2.30441i	0.148013	+	0.123000i
$352$	0.766562			0.0408579
$353$	−29.0813	−	16.7901i	−1.54784	−	0.893647i	−0.998306	−	0.0581762i	$-0.981471\pi$
$353$	−29.0813	−	16.7901i	−1.54784	−	0.893647i	−0.549535	−	0.835471i	$-0.685195\pi$
$354$	2.49891	−	4.32824i	0.132816	−	0.230044i
$355$		0			0
$356$		−	5.31479i		−	0.281683i
$357$	−0.538457	+	0.310878i	−0.0284982	+	0.0164534i
$358$	−21.8699	+	12.6266i	−1.15586	+	0.667335i
$359$		−	22.0423i		−	1.16335i	−0.813423	−	0.581673i	$-0.802398\pi$
$359$		−	22.0423i		−	1.16335i	0.813423	−	0.581673i	$-0.197602\pi$
$360$		0			0
$361$	4.42920	−	7.67161i	0.233116	−	0.403769i
$362$	0.272618	+	0.157396i	0.0143285	+	0.00827256i
$363$	−10.4124			−0.546508
$364$	−0.350157	−	0.947965i	−0.0183532	−	0.0496869i
$365$		0			0
$366$	1.33892	+	0.773028i	0.0699867	+	0.0404068i
$367$	4.82908	−	8.36421i	0.252076	−	0.436608i	−0.712021	−	0.702158i	$-0.752220\pi$
$367$	4.82908	−	8.36421i	0.252076	−	0.436608i	0.964097	+	0.265550i	$0.0855534\pi$
$368$	−0.725885	−	1.25727i	−0.0378394	−	0.0655397i
$369$		−	2.21833i		−	0.115482i
$370$		0			0
$371$	0.796424	−	0.459815i	0.0413483	−	0.0238724i
$372$		−	3.28110i		−	0.170117i
$373$	−6.12153	−	10.6028i	−0.316961	−	0.548992i	0.662892	−	0.748715i	$-0.269329\pi$
$373$	−6.12153	−	10.6028i	−0.316961	−	0.548992i	−0.979852	+	0.199723i	$0.935996\pi$
$374$	−0.850244	+	1.47267i	−0.0439651	+	0.0761498i
$375$		0			0
$376$	−1.06277			−0.0548081
$377$	20.4981	−	7.57154i	1.05571	−	0.389954i
$378$	0.280281			0.0144161
$379$	11.7669	+	6.79362i	0.604425	+	0.348965i	0.770780	−	0.637101i	$-0.219867\pi$
$379$	11.7669	+	6.79362i	0.604425	+	0.348965i	−0.166355	+	0.986066i	$0.553200\pi$
$380$		0			0
$381$	−1.58585	−	2.74678i	−0.0812458	−	0.140722i
$382$		−	22.5332i		−	1.15290i
$383$	−13.3487	+	7.70686i	−0.682086	+	0.393802i	−0.800640	−	0.599145i	$-0.795507\pi$
$383$	−13.3487	+	7.70686i	−0.682086	+	0.393802i	0.118555	+	0.992948i	$0.462174\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$		0			0
$386$	4.89181	+	8.47286i	0.248987	+	0.431257i
$387$	−1.80441	+	3.12533i	−0.0917234	+	0.158870i
$388$	1.09737	+	0.633565i	0.0557103	+	0.0321644i
$389$	6.06059			0.307284			0.153642	−	0.988127i	$-0.450900\pi$
$389$	6.06059			0.307284			0.153642	+	0.988127i	$0.450900\pi$
$390$		0			0
$391$	3.22051			0.162868
$392$	5.99414	+	3.46072i	0.302750	+	0.174793i
$393$	7.71724	−	13.3667i	0.389283	−	0.674259i
$394$	6.22862	+	10.7883i	0.313794	+	0.543506i
$395$		0			0
$396$	0.663862	−	0.383281i	0.0333603	−	0.0192606i
$397$	14.7131	−	8.49464i	0.738432	−	0.426334i	−0.0830670	−	0.996544i	$-0.526472\pi$
$397$	14.7131	−	8.49464i	0.738432	−	0.426334i	0.821499	+	0.570210i	$0.193138\pi$
$398$		−	15.0639i		−	0.755085i
$399$	0.739677	+	1.28116i	0.0370302	+	0.0641381i
$400$		0			0
$401$	−16.8156	−	9.70852i	−0.839733	−	0.484820i	0.0174403	−	0.999848i	$-0.494448\pi$
$401$	−16.8156	−	9.70852i	−0.839733	−	0.484820i	−0.857174	+	0.515028i	$0.827782\pi$
$402$	7.43584			0.370866
$403$	−7.56101	+	9.09858i	−0.376641	+	0.453233i
$404$	−4.52747			−0.225250
$405$		0			0
$406$	0.849335	−	1.47109i	0.0421518	−	0.0730091i
$407$	−1.35914	−	2.35409i	−0.0673699	−	0.116688i
$408$			2.21833i			0.109824i
$409$	−0.803328	+	0.463802i	−0.0397220	+	0.0229335i	−0.519730	−	0.854331i	$-0.673967\pi$
$409$	−0.803328	+	0.463802i	−0.0397220	+	0.0229335i	0.480007	+	0.877264i	$0.340634\pi$
$410$		0			0
$411$			1.66829i			0.0822907i
$412$	1.47135	+	2.54846i	0.0724885	+	0.125554i
$413$	−0.700398	+	1.21313i	−0.0344643	+	0.0596940i
$414$	−1.25727	−	0.725885i	−0.0617914	−	0.0356753i
$415$		0			0
$416$	−3.55372	−	0.609166i	−0.174235	−	0.0298668i
$417$	−2.10790			−0.103224
$418$	3.50393	+	2.02300i	0.171383	+	0.0989481i
$419$	12.5907	−	21.8077i	0.615096	−	1.06538i	−0.375271	−	0.926915i	$-0.622450\pi$
$419$	12.5907	−	21.8077i	0.615096	−	1.06538i	0.990368	−	0.138463i	$-0.0442163\pi$
$420$		0			0
$421$		−	27.6912i		−	1.34958i	−0.738008	−	0.674792i	$-0.764233\pi$
$421$		−	27.6912i		−	1.34958i	0.738008	−	0.674792i	$-0.235767\pi$
$422$	13.0575	−	7.53876i	0.635630	−	0.366981i
$423$	−0.920385	+	0.531385i	−0.0447507	+	0.0258368i
$424$		−	3.28110i		−	0.159344i
$425$		0			0
$426$	1.21135	−	2.09811i	0.0586899	−	0.101654i
$427$	−0.375275	−	0.216665i	−0.0181608	−	0.0104852i
$428$	−19.0488			−0.920758
$429$	−2.72415	−	0.466963i	−0.131523	−	0.0225452i
$430$		0			0
$431$	0.0798174	+	0.0460826i	0.00384467	+	0.00221972i	0.501921	−	0.864913i	$-0.332627\pi$
$431$	0.0798174	+	0.0460826i	0.00384467	+	0.00221972i	−0.498076	+	0.867133i	$0.665960\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	2.01113	+	3.48337i	0.0966486	+	0.167400i	0.910295	−	0.413959i	$-0.135854\pi$
$433$	2.01113	+	3.48337i	0.0966486	+	0.167400i	−0.813647	+	0.581359i	$0.802521\pi$
$434$			0.919631i			0.0441437i
$435$		0			0
$436$	−7.83362	+	4.52274i	−0.375162	+	0.216600i
$437$		−	7.66259i		−	0.366552i
$438$	7.13150	+	12.3521i	0.340756	+	0.590207i
$439$	12.9742	−	22.4719i	0.619223	−	1.07253i	−0.370404	−	0.928871i	$-0.620781\pi$
$439$	12.9742	−	22.4719i	0.619223	−	1.07253i	0.989628	−	0.143656i	$-0.0458858\pi$
$440$		0			0
$441$	6.92144			0.329592
$442$	5.11195	−	6.15150i	0.243151	−	0.292597i
$443$	15.0646			0.715740			0.357870	−	0.933771i	$-0.383503\pi$
$443$	15.0646			0.715740			0.357870	+	0.933771i	$0.383503\pi$
$444$	−3.07097	−	1.77303i	−0.145742	−	0.0841442i
$445$		0			0
$446$	2.32817	+	4.03252i	0.110242	+	0.190945i
$447$			5.74079i			0.271530i
$448$	−0.242731	+	0.140141i	−0.0114679	+	0.00662102i
$449$	29.8460	−	17.2316i	1.40852	−	0.813208i	0.413273	−	0.910607i	$-0.364386\pi$
$449$	29.8460	−	17.2316i	1.40852	−	0.813208i	0.995245	+	0.0973991i	$0.0310523\pi$
$450$		0			0
$451$	0.850244	+	1.47267i	0.0400364	+	0.0693451i
$452$		0			0
$453$	−14.0045	−	8.08549i	−0.657988	−	0.379889i
$454$	−6.20436			−0.291185
$455$		0			0
$456$	5.27811			0.247170
$457$	−36.0525	−	20.8149i	−1.68646	−	0.973680i	−0.957191	−	0.289457i	$-0.906525\pi$
$457$	−36.0525	−	20.8149i	−1.68646	−	0.973680i	−0.729273	−	0.684223i	$-0.760141\pi$
$458$	6.43049	−	11.1379i	0.300477	−	0.520442i
$459$	1.10917	+	1.92113i	0.0517714	+	0.0896707i
$460$		0			0
$461$	6.02737	−	3.47990i	0.280722	−	0.162075i	−0.353028	−	0.935613i	$-0.614848\pi$
$461$	6.02737	−	3.47990i	0.280722	−	0.162075i	0.633750	+	0.773538i	$0.281515\pi$
$462$	−0.186068	+	0.107426i	−0.00865667	+	0.00499793i
$463$		−	11.9289i		−	0.554382i	−0.960815	−	0.277191i	$-0.910597\pi$
$463$		−	11.9289i		−	0.554382i	0.960815	−	0.277191i	$-0.0894035\pi$
$464$	−3.03030	−	5.24863i	−0.140678	−	0.243661i
$465$		0			0
$466$	0.840844	+	0.485461i	0.0389513	+	0.0224886i
$467$	34.4406			1.59372			0.796860	−	0.604164i	$-0.206493\pi$
$467$	34.4406			1.59372			0.796860	+	0.604164i	$0.206493\pi$
$468$	−3.38219	+	1.24931i	−0.156342	+	0.0577492i
$469$	−2.08413			−0.0962361
$470$		0			0
$471$	−7.92004	+	13.7179i	−0.364936	+	0.632088i
$472$	2.49891	+	4.32824i	0.115022	+	0.199224i
$473$		−	2.76639i		−	0.127199i
$474$	12.5327	−	7.23574i	0.575645	−	0.332349i
$475$		0			0
$476$		−	0.621757i		−	0.0284982i
$477$	−1.64055	−	2.84152i	−0.0751156	−	0.130104i
$478$	−7.39922	+	12.8158i	−0.338432	+	0.586182i
$479$	−11.8896	−	6.86444i	−0.543248	−	0.313644i	0.203146	−	0.979148i	$-0.434883\pi$
$479$	−11.8896	−	6.86444i	−0.543248	−	0.313644i	−0.746394	+	0.665504i	$0.768217\pi$
$480$		0			0
$481$	4.43011	+	11.9934i	0.201996	+	0.546854i
$482$	−2.19157			−0.0998231
$483$	0.352389	+	0.203452i	0.0160343	+	0.00925738i
$484$	5.20619	−	9.01739i	0.236645	−	0.409881i
$485$		0			0
$486$		−	1.00000i		−	0.0453609i
$487$	8.25303	−	4.76489i	0.373981	−	0.215918i	−0.301215	−	0.953556i	$-0.597392\pi$
$487$	8.25303	−	4.76489i	0.373981	−	0.215918i	0.675196	+	0.737638i	$0.264059\pi$
$488$	−1.33892	+	0.773028i	−0.0606102	+	0.0349933i
$489$			11.3148i			0.511673i
$490$		0			0
$491$	16.7409	−	28.9960i	0.755505	−	1.30857i	−0.189618	−	0.981858i	$-0.560725\pi$
$491$	16.7409	−	28.9960i	0.755505	−	1.30857i	0.945123	−	0.326715i	$-0.105942\pi$
$492$	1.92113	+	1.10917i	0.0866113	+	0.0500051i
$493$	13.4444			0.605506
$494$	−14.6363	−	12.1629i	−0.658520	−	0.547236i
$495$		0			0
$496$	2.84152	+	1.64055i	0.127588	+	0.0736629i
$497$	−0.339518	+	0.588062i	−0.0152294	+	0.0263782i
$498$	−2.21209	−	3.83146i	−0.0991262	−	0.171692i
$499$			15.0882i			0.675439i	0.941247	+	0.337720i	$0.109656\pi$
$499$			15.0882i			0.675439i	−0.941247	+	0.337720i	$0.890344\pi$
$500$		0			0
$501$	1.25727	−	0.725885i	0.0561707	−	0.0324301i
$502$		−	10.5897i		−	0.472643i
$503$	9.74919	+	16.8861i	0.434695	+	0.752914i	0.997271	−	0.0738319i	$-0.0235228\pi$
$503$	9.74919	+	16.8861i	0.434695	+	0.752914i	−0.562576	+	0.826746i	$0.690189\pi$
$504$	−0.140141	+	0.242731i	−0.00624236	+	0.0108121i
$505$		0			0
$506$	1.11287			0.0494732
$507$	12.2578	+	4.32961i	0.544390	+	0.192285i
$508$	3.17171			0.140722
$509$	29.5101	+	17.0377i	1.30801	+	0.755181i	0.981764	−	0.190103i	$-0.0608821\pi$
$509$	29.5101	+	17.0377i	1.30801	+	0.755181i	0.326248	+	0.945284i	$0.394215\pi$
$510$		0			0
$511$	−1.99883	−	3.46207i	−0.0884228	−	0.153153i
$512$			1.00000i			0.0441942i
$513$	4.57097	−	2.63905i	0.201813	−	0.116517i
$514$	5.93047	−	3.42396i	0.261582	−	0.151024i
$515$		0			0
$516$	−1.80441	−	3.12533i	−0.0794348	−	0.137585i
$517$	0.407339	−	0.705532i	0.0179148	−	0.0310293i
$518$	0.860736	+	0.496946i	0.0378186	+	0.0218346i
$519$	13.3402			0.585570
$520$		0			0
$521$	−1.10626			−0.0484660			−0.0242330	−	0.999706i	$-0.507714\pi$
$521$	−1.10626			−0.0484660			−0.0242330	+	0.999706i	$0.507714\pi$
$522$	−5.24863	−	3.03030i	−0.229726	−	0.132633i
$523$	−5.32920	+	9.23044i	−0.233030	+	0.403619i	−0.958698	−	0.284425i	$-0.908197\pi$
$523$	−5.32920	+	9.23044i	−0.233030	+	0.403619i	0.725669	+	0.688044i	$0.241531\pi$
$524$	7.71724	+	13.3667i	0.337129	+	0.583925i
$525$		0			0
$526$	22.7212	−	13.1181i	0.990693	−	0.571977i
$527$	−6.30343	+	3.63928i	−0.274582	+	0.158530i
$528$			0.766562i			0.0333603i
$529$	10.4462	+	18.0933i	0.454182	+	0.786666i
$530$		0			0
$531$	4.32824	+	2.49891i	0.187830	+	0.108444i
$532$	−1.47935			−0.0641381
$533$	−2.77138	−	7.50283i	−0.120042	−	0.324983i
$534$	5.31479			0.229994
$535$		0			0
$536$	−3.71792	+	6.43963i	−0.160590	+	0.278150i
$537$	−12.6266	−	21.8699i	−0.544877	−	0.943755i
$538$			6.49875i			0.280181i
$539$	−4.59488	+	2.65286i	−0.197916	+	0.114267i
$540$		0			0
$541$		−	38.1486i		−	1.64013i	−0.572267	−	0.820067i	$-0.693936\pi$
$541$		−	38.1486i		−	1.64013i	0.572267	−	0.820067i	$-0.306064\pi$
$542$	−3.09404	−	5.35904i	−0.132901	−	0.230191i
$543$	−0.157396	+	0.272618i	−0.00675452	+	0.0116992i
$544$	−1.92113	−	1.10917i	−0.0823678	−	0.0475551i
$545$		0			0
$546$	0.947965	−	0.350157i	0.0405692	−	0.0149853i
$547$	26.9609			1.15277			0.576383	−	0.817180i	$-0.304464\pi$
$547$	26.9609			1.15277			0.576383	+	0.817180i	$0.304464\pi$
$548$	−1.44478	−	0.834145i	−0.0617180	−	0.0356329i
$549$	−0.773028	+	1.33892i	−0.0329920	+	0.0571439i
$550$		0			0
$551$		−	31.9885i		−	1.36275i
$552$	1.25727	−	0.725885i	0.0535129	−	0.0308957i
$553$	−3.51267	+	2.02804i	−0.149374	+	0.0862411i
$554$			29.0577i			1.23454i
$555$		0			0
$556$	1.05395	−	1.82549i	0.0446974	−	0.0774182i
$557$	30.5249	+	17.6236i	1.29338	+	0.746735i	0.979252	−	0.202645i	$-0.0649539\pi$
$557$	30.5249	+	17.6236i	1.29338	+	0.746735i	0.314130	+	0.949380i	$0.398287\pi$
$558$	3.28110			0.138900
$559$	−2.19837	+	12.8247i	−0.0929812	+	0.542429i
$560$		0			0
$561$	−1.47267	−	0.850244i	−0.0621760	−	0.0358973i
$562$	−7.07188	+	12.2489i	−0.298309	+	0.516687i
$563$	8.50830	+	14.7368i	0.358582	+	0.621082i	0.987724	−	0.156208i	$-0.0499270\pi$
$563$	8.50830	+	14.7368i	0.358582	+	0.621082i	−0.629142	+	0.777290i	$0.716594\pi$
$564$		−	1.06277i		−	0.0447507i
$565$		0			0
$566$	−7.57409	+	4.37290i	−0.318363	+	0.183807i
$567$			0.280281i			0.0117707i
$568$	1.21135	+	2.09811i	0.0508270	+	0.0880349i
$569$	17.6968	−	30.6518i	0.741889	−	1.28499i	−0.209746	−	0.977756i	$-0.567264\pi$
$569$	17.6968	−	30.6518i	0.741889	−	1.28499i	0.951634	−	0.307233i	$-0.0994030\pi$
$570$		0			0
$571$	−17.5185			−0.733125			−0.366563	−	0.930393i	$-0.619465\pi$
$571$	−17.5185			−0.733125			−0.366563	+	0.930393i	$0.619465\pi$
$572$	1.76647	−	2.12570i	0.0738600	−	0.0888799i
$573$	22.5332			0.941339
$574$	−0.538457	−	0.310878i	−0.0224748	−	0.0129758i
$575$		0			0
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$		−	26.6215i		−	1.10827i	−0.832428	−	0.554133i	$-0.813050\pi$
$577$		−	26.6215i		−	1.10827i	0.832428	−	0.554133i	$-0.186950\pi$
$578$	−10.4607	+	6.03950i	−0.435109	+	0.251210i
$579$	−8.47286	+	4.89181i	−0.352120	+	0.203297i
$580$		0			0
$581$	0.620008	+	1.07389i	0.0257223	+	0.0445523i
$582$	−0.633565	+	1.09737i	−0.0262621	+	0.0454873i
$583$	2.17820	+	1.25758i	0.0902118	+	0.0520838i
$584$	−14.2630			−0.590207
$585$		0			0
$586$	31.5001			1.30126
$587$	−14.4115	−	8.32051i	−0.594828	−	0.343424i	0.172176	−	0.985066i	$-0.444920\pi$
$587$	−14.4115	−	8.32051i	−0.594828	−	0.343424i	−0.767004	+	0.641642i	$0.778254\pi$
$588$	−3.46072	+	5.99414i	−0.142718	+	0.247194i
$589$	8.65900	+	14.9978i	0.356788	+	0.617975i
$590$		0			0
$591$	−10.7883	+	6.22862i	−0.443771	+	0.256211i
$592$	3.07097	−	1.77303i	0.126216	−	0.0728710i
$593$		−	24.7460i		−	1.01620i	−0.861300	−	0.508098i	$-0.830349\pi$
$593$		−	24.7460i		−	1.01620i	0.861300	−	0.508098i	$-0.169651\pi$
$594$	0.383281	+	0.663862i	0.0157262	+	0.0272386i
$595$		0			0
$596$	−4.97167	−	2.87039i	−0.203647	−	0.117576i
$597$	15.0639			0.616524
$598$	−5.15918	−	0.884368i	−0.210975	−	0.0361645i
$599$	−23.2517			−0.950037			−0.475019	−	0.879976i	$-0.657559\pi$
$599$	−23.2517			−0.950037			−0.475019	+	0.879976i	$0.657559\pi$
$600$		0			0
$601$	−16.5985	+	28.7494i	−0.677067	+	1.17271i	0.298793	+	0.954318i	$0.403416\pi$
$601$	−16.5985	+	28.7494i	−0.677067	+	1.17271i	−0.975860	+	0.218396i	$0.929917\pi$
$602$	0.505743	+	0.875972i	0.0206125	+	0.0357020i
$603$			7.43584i			0.302811i
$604$	14.0045	−	8.08549i	0.569834	−	0.328994i
$605$		0			0
$606$		−	4.52747i		−	0.183916i
$607$	19.7130	+	34.1440i	0.800128	+	1.38586i	0.919532	+	0.393016i	$0.128568\pi$
$607$	19.7130	+	34.1440i	0.800128	+	1.38586i	−0.119404	+	0.992846i	$0.538098\pi$
$608$	−2.63905	+	4.57097i	−0.107028	+	0.185377i
$609$	1.47109	+	0.849335i	0.0596117	+	0.0344168i
$610$		0			0
$611$	−2.44906	+	2.94709i	−0.0990783	+	0.119226i
$612$	−2.21833			−0.0896707
$613$	−9.03087	−	5.21398i	−0.364753	−	0.210591i	0.306410	−	0.951899i	$-0.400872\pi$
$613$	−9.03087	−	5.21398i	−0.364753	−	0.210591i	−0.671164	+	0.741309i	$0.734205\pi$
$614$	−3.51576	+	6.08947i	−0.141884	+	0.245751i
$615$		0			0
$616$		−	0.214853i		−	0.00865667i
$617$	17.5464	−	10.1304i	0.706393	−	0.407836i	−0.103331	−	0.994647i	$-0.532950\pi$
$617$	17.5464	−	10.1304i	0.706393	−	0.407836i	0.809724	+	0.586811i	$0.199617\pi$
$618$	−2.54846	+	1.47135i	−0.102514	+	0.0591866i
$619$		−	27.8009i		−	1.11741i	−0.829365	−	0.558707i	$-0.811298\pi$
$619$		−	27.8009i		−	1.11741i	0.829365	−	0.558707i	$-0.188702\pi$
$620$		0			0
$621$	0.725885	−	1.25727i	0.0291288	−	0.0504525i
$622$	−7.61967	−	4.39922i	−0.305521	−	0.176393i
$623$	−1.48964			−0.0596810
$624$	0.609166	−	3.55372i	0.0243861	−	0.142263i
$625$		0			0
$626$	−8.08984	−	4.67067i	−0.323335	−	0.186677i
$627$	−2.02300	+	3.50393i	−0.0807907	+	0.139934i
$628$	−7.92004	−	13.7179i	−0.316044	−	0.547405i
$629$			7.86633i			0.313651i
$630$		0			0
$631$	−31.6461	+	18.2709i	−1.25981	+	0.727352i	−0.973038	−	0.230646i	$-0.925916\pi$
$631$	−31.6461	+	18.2709i	−1.25981	+	0.727352i	−0.286773	+	0.957999i	$0.592583\pi$
$632$			14.4715i			0.575645i
$633$	7.53876	+	13.0575i	0.299639	+	0.518989i
$634$	−9.73484	+	16.8612i	−0.386620	+	0.669645i
$635$		0			0
$636$	3.28110			0.130104
$637$	23.4097	−	8.64700i	0.927524	−	0.342607i
$638$	4.64582			0.183930
$639$	2.09811	+	1.21135i	0.0830001	+	0.0479201i
$640$		0			0
$641$	−21.9295	−	37.9830i	−0.866163	−	1.50024i	−0.865888	−	0.500238i	$-0.833246\pi$
$641$	−21.9295	−	37.9830i	−0.866163	−	1.50024i	−0.000274574	−	1.00000i	$-0.500087\pi$
$642$		−	19.0488i		−	0.751796i
$643$	14.4213	−	8.32615i	0.568721	−	0.328351i	−0.187917	−	0.982185i	$-0.560174\pi$
$643$	14.4213	−	8.32615i	0.568721	−	0.328351i	0.756638	+	0.653834i	$0.226840\pi$
$644$	−0.352389	+	0.203452i	−0.0138861	+	0.00801713i
$645$		0			0
$646$	−5.85429	−	10.1399i	−0.230334	−	0.398950i
$647$	4.69543	−	8.13271i	0.184596	−	0.319730i	−0.758844	−	0.651272i	$-0.774236\pi$
$647$	4.69543	−	8.13271i	0.184596	−	0.319730i	0.943440	+	0.331542i	$0.107569\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	−3.83114			−0.150386
$650$		0			0
$651$	−0.919631			−0.0360432
$652$	−9.79890	−	5.65740i	−0.383754	−	0.221561i
$653$	−20.5572	+	35.6061i	−0.804465	+	1.39337i	0.112187	+	0.993687i	$0.464214\pi$
$653$	−20.5572	+	35.6061i	−0.804465	+	1.39337i	−0.916652	+	0.399686i	$0.869119\pi$
$654$	−4.52274	−	7.83362i	−0.176853	−	0.306319i
$655$		0			0
$656$	−1.92113	+	1.10917i	−0.0750076	+	0.0433056i
$657$	−12.3521	+	7.13150i	−0.481902	+	0.278226i
$658$			0.297874i			0.0116123i
$659$	1.72663	+	2.99061i	0.0672600	+	0.116498i	0.897694	−	0.440619i	$-0.145241\pi$
$659$	1.72663	+	2.99061i	0.0672600	+	0.116498i	−0.830434	+	0.557117i	$0.811908\pi$
$660$		0			0
$661$	21.3306	+	12.3152i	0.829665	+	0.479007i	0.853738	−	0.520703i	$-0.174330\pi$
$661$	21.3306	+	12.3152i	0.829665	+	0.479007i	−0.0240732	+	0.999710i	$0.507663\pi$
$662$	−18.9464			−0.736373
$663$	6.15150	+	5.11195i	0.238904	+	0.198532i
$664$	4.42419			0.171692
$665$		0			0
$666$	1.77303	−	3.07097i	0.0687034	−	0.118998i
$667$	−4.39929	−	7.61980i	−0.170341	−	0.295040i
$668$			1.45177i			0.0561707i
$669$	−4.03252	+	2.32817i	−0.155906	+	0.0900124i
$670$		0			0
$671$		−	1.18515i		−	0.0457521i
$672$	−0.140141	−	0.242731i	−0.00540604	−	0.00936354i
$673$	8.52052	−	14.7580i	0.328442	−	0.568878i	−0.653761	−	0.756701i	$-0.726810\pi$
$673$	8.52052	−	14.7580i	0.328442	−	0.568878i	0.982203	+	0.187823i	$0.0601431\pi$
$674$	2.36395	+	1.36483i	0.0910560	+	0.0525712i
$675$		0			0
$676$	−9.87847	+	8.45079i	−0.379941	+	0.325030i
$677$	−16.6324			−0.639236			−0.319618	−	0.947546i	$-0.603555\pi$
$677$	−16.6324			−0.639236			−0.319618	+	0.947546i	$0.603555\pi$
$678$		0			0
$679$	0.177576	−	0.307571i	0.00681475	−	0.0118035i
$680$		0			0
$681$		−	6.20436i		−	0.237752i
$682$	−2.17820	+	1.25758i	−0.0834075	+	0.0481554i
$683$	42.3252	−	24.4365i	1.61953	−	0.935035i	0.632486	−	0.774572i	$-0.282035\pi$
$683$	42.3252	−	24.4365i	1.61953	−	0.935035i	0.987042	−	0.160463i	$-0.0512987\pi$
$684$			5.27811i			0.201813i
$685$		0			0
$686$	1.95096	−	3.37916i	0.0744880	−	0.129017i
$687$	11.1379	+	6.43049i	0.424939	+	0.245339i
$688$	3.60882			0.137585
$689$	−9.09858	−	7.56101i	−0.346628	−	0.288051i
$690$		0			0
$691$	31.0699	+	17.9382i	1.18195	+	0.682401i	0.956466	−	0.291845i	$-0.0942690\pi$
$691$	31.0699	+	17.9382i	1.18195	+	0.682401i	0.225488	+	0.974246i	$0.427602\pi$
$692$	−6.67010	+	11.5530i	−0.253559	+	0.439177i
$693$	−0.107426	−	0.186068i	−0.00408079	−	0.00706814i
$694$		−	12.6920i		−	0.481781i
$695$		0			0
$696$	5.24863	−	3.03030i	0.198949	−	0.114863i
$697$		−	4.92099i		−	0.186396i
$698$	−0.605676	−	1.04906i	−0.0229252	−	0.0397075i
$699$	−0.485461	+	0.840844i	−0.0183618	+	0.0318036i
$700$		0			0
$701$	−31.0288			−1.17194			−0.585971	−	0.810332i	$-0.699287\pi$
$701$	−31.0288			−1.17194			−0.585971	+	0.810332i	$0.699287\pi$
$702$	−1.24931	−	3.38219i	−0.0471520	−	0.127653i
$703$	18.7165			0.705905
$704$	−0.663862	−	0.383281i	−0.0250202	−	0.0144454i
$705$		0			0
$706$	16.7901	+	29.0813i	0.631904	+	1.09449i
$707$			1.26896i			0.0477243i
$708$	−4.32824	+	2.49891i	−0.162665	+	0.0939149i
$709$	9.78339	−	5.64844i	0.367423	−	0.212132i	−0.304909	−	0.952381i	$-0.598626\pi$
$709$	9.78339	−	5.64844i	0.367423	−	0.212132i	0.672332	+	0.740250i	$0.265293\pi$
$710$		0			0
$711$	7.23574	+	12.5327i	0.271362	+	0.470012i
$712$	−2.65740	+	4.60275i	−0.0995901	+	0.172495i
$713$	4.12523	+	2.38170i	0.154491	+	0.0891954i
$714$	0.621757			0.0232687
$715$		0			0
$716$	25.2532			0.943755
$717$	−12.8158	−	7.39922i	−0.478616	−	0.276329i
$718$	−11.0211	+	19.0892i	−0.411305	+	0.712401i
$719$	−6.01084	−	10.4111i	−0.224167	−	0.388268i	0.731902	−	0.681409i	$-0.238633\pi$
$719$	−6.01084	−	10.4111i	−0.224167	−	0.388268i	−0.956069	+	0.293141i	$0.905299\pi$
$720$		0			0
$721$	0.714286	−	0.412393i	0.0266014	−	0.0153583i
$722$	−7.67161	+	4.42920i	−0.285508	+	0.164838i
$723$		−	2.19157i		−	0.0815052i
$724$	−0.157396	−	0.272618i	−0.00584958	−	0.0101318i
$725$		0			0
$726$	9.01739	+	5.20619i	0.334667	+	0.193220i
$727$	−4.18908			−0.155364			−0.0776822	−	0.996978i	$-0.524752\pi$
$727$	−4.18908			−0.155364			−0.0776822	+	0.996978i	$0.524752\pi$
$728$	−0.170738	+	0.996041i	−0.00632796	+	0.0369157i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−4.00278	+	6.93303i	−0.148048	+	0.256427i
$732$	−0.773028	−	1.33892i	−0.0285719	−	0.0494880i
$733$		−	11.3923i		−	0.420783i	−0.977617	−	0.210391i	$-0.932526\pi$
$733$		−	11.3923i		−	0.420783i	0.977617	−	0.210391i	$-0.0674738\pi$
$734$	−8.36421	+	4.82908i	−0.308729	+	0.178244i
$735$		0			0
$736$			1.45177i			0.0535129i
$737$	−2.85002	−	4.93637i	−0.104982	−	0.181834i
$738$	−1.10917	+	1.92113i	−0.0408290	+	0.0707178i
$739$	−17.6996	−	10.2189i	−0.651090	−	0.375907i	0.137783	−	0.990462i	$-0.456002\pi$
$739$	−17.6996	−	10.2189i	−0.651090	−	0.375907i	−0.788874	+	0.614555i	$0.789336\pi$
$740$		0			0
$741$	12.1629	−	14.6363i	0.446817	−	0.537679i
$742$	−0.919631			−0.0337607
$743$	−8.79255	−	5.07638i	−0.322567	−	0.186234i	0.329969	−	0.943992i	$-0.392962\pi$
$743$	−8.79255	−	5.07638i	−0.322567	−	0.186234i	−0.652536	+	0.757757i	$0.726295\pi$
$744$	−1.64055	+	2.84152i	−0.0601455	+	0.104175i
$745$		0			0
$746$			12.2431i			0.448250i
$747$	3.83146	−	2.21209i	0.140186	−	0.0809362i
$748$	1.47267	−	0.850244i	0.0538460	−	0.0310880i
$749$			5.33902i			0.195083i
$750$		0			0
$751$	−8.99084	+	15.5726i	−0.328080	+	0.568252i	−0.982131	−	0.188199i	$-0.939735\pi$
$751$	−8.99084	+	15.5726i	−0.328080	+	0.568252i	0.654051	+	0.756451i	$0.273068\pi$
$752$	0.920385	+	0.531385i	0.0335630	+	0.0193776i
$753$	10.5897			0.385911
$754$	−21.5376	−	3.69191i	−0.784355	−	0.134451i
$755$		0			0
$756$	−0.242731	−	0.140141i	−0.00882803	−	0.00509686i
$757$	−22.4916	+	38.9566i	−0.817470	+	1.41590i	0.0900700	+	0.995935i	$0.471291\pi$
$757$	−22.4916	+	38.9566i	−0.817470	+	1.41590i	−0.907540	+	0.419965i	$0.862042\pi$
$758$	−6.79362	−	11.7669i	−0.246755	−	0.427393i
$759$			1.11287i			0.0403947i
$760$		0			0
$761$	−39.1697	+	22.6146i	−1.41990	+	0.819779i	−0.996289	−	0.0860657i	$-0.972571\pi$
$761$	−39.1697	+	22.6146i	−1.41990	+	0.819779i	−0.423610	+	0.905845i	$0.639237\pi$
$762$			3.17171i			0.114899i
$763$	1.26764	+	2.19562i	0.0458917	+	0.0794867i
$764$	−11.2666	+	19.5143i	−0.407612	+	0.706004i
$765$		0			0
$766$	15.4137			0.556921
$767$	17.7609	+	3.04450i	0.641308	+	0.109931i
$768$	−1.00000			−0.0360844
$769$	31.3010	+	18.0716i	1.12874	+	0.651680i	0.943619	−	0.331035i	$-0.107398\pi$
$769$	31.3010	+	18.0716i	1.12874	+	0.651680i	0.185125	+	0.982715i	$0.440731\pi$
$770$		0			0
$771$	3.42396	+	5.93047i	0.123311	+	0.213581i
$772$		−	9.78362i		−	0.352120i
$773$	14.1829	−	8.18850i	0.510123	−	0.294520i	−0.222761	−	0.974873i	$-0.571507\pi$
$773$	14.1829	−	8.18850i	0.510123	−	0.294520i	0.732884	+	0.680353i	$0.238174\pi$
$774$	3.12533	−	1.80441i	0.112338	−	0.0648583i
$775$		0			0
$776$	−0.633565	−	1.09737i	−0.0227437	−	0.0393932i
$777$	−0.496946	+	0.860736i	−0.0178279	+	0.0308787i
$778$	−5.24863	−	3.03030i	−0.188172	−	0.108641i
$779$	−11.7086			−0.419504
$780$		0			0
$781$	−1.85714			−0.0664538
$782$	−2.78904	−	1.61025i	−0.0997359	−	0.0575825i
$783$	3.03030	−	5.24863i	0.108294	−	0.187571i
$784$	−3.46072	−	5.99414i	−0.123597	−	0.214077i
$785$		0			0
$786$	−13.3667	+	7.71724i	−0.476773	+	0.275265i
$787$	−39.1108	+	22.5807i	−1.39415	+	0.804913i	−0.993772	−	0.111436i	$-0.964455\pi$
$787$	−39.1108	+	22.5807i	−1.39415	+	0.804913i	−0.400379	+	0.916350i	$0.631122\pi$
$788$		−	12.4572i		−	0.443771i
$789$	13.1181	+	22.7212i	0.467017	+	0.808898i
$790$		0			0
$791$		0			0
$792$	−0.766562			−0.0272386
$793$	−0.941804	+	5.49425i	−0.0334444	+	0.195106i
$794$	−16.9893			−0.602927
$795$		0			0
$796$	−7.53195	+	13.0457i	−0.266963	+	0.462393i
$797$	−13.4818	−	23.3511i	−0.477549	−	0.827139i	0.522120	−	0.852872i	$-0.325141\pi$
$797$	−13.4818	−	23.3511i	−0.477549	−	0.827139i	−0.999669	+	0.0257329i	$0.991808\pi$
$798$		−	1.47935i		−	0.0523686i
$799$	−2.04172	+	1.17879i	−0.0722308	+	0.0417025i
$800$		0			0
$801$			5.31479i			0.187789i
$802$	9.70852	+	16.8156i	0.342820	+	0.593781i
$803$	5.46674	−	9.46867i	0.192917	−	0.334142i
$804$	−6.43963	−	3.71792i	−0.227108	−	0.131121i
$805$		0			0
$806$	11.0973	−	4.09910i	0.390886	−	0.144385i
$807$	−6.49875			−0.228767
$808$	3.92090	+	2.26374i	0.137937	+	0.0796379i
$809$	5.02204	−	8.69843i	0.176566	−	0.305821i	−0.764136	−	0.645055i	$-0.776835\pi$
$809$	5.02204	−	8.69843i	0.176566	−	0.305821i	0.940702	+	0.339234i	$0.110168\pi$
$810$		0			0
$811$			26.8449i			0.942652i	0.881959	+	0.471326i	$0.156224\pi$
$811$			26.8449i			0.942652i	−0.881959	+	0.471326i	$0.843776\pi$
$812$	−1.47109	+	0.849335i	−0.0516252	+	0.0298058i
$813$	5.35904	−	3.09404i	0.187950	−	0.108513i
$814$			2.71827i			0.0952754i
$815$		0			0
$816$	1.10917	−	1.92113i	0.0388286	−	0.0672531i
$817$	16.4958	+	9.52388i	0.577117	+	0.333198i
$818$	0.927603			0.0324329
$819$	0.350157	+	0.947965i	0.0122355	+	0.0331246i
$820$		0			0
$821$	−28.4214	−	16.4091i	−0.991912	−	0.572681i	−0.0860669	−	0.996289i	$-0.527430\pi$
$821$	−28.4214	−	16.4091i	−0.991912	−	0.572681i	−0.905845	+	0.423609i	$0.860763\pi$
$822$	0.834145	−	1.44478i	0.0290941	−	0.0503925i
$823$	−4.43549	−	7.68249i	−0.154611	−	0.267795i	0.778306	−	0.627885i	$-0.216079\pi$
$823$	−4.43549	−	7.68249i	−0.154611	−	0.267795i	−0.932917	+	0.360090i	$0.882746\pi$
$824$		−	2.94271i		−	0.102514i
$825$		0			0
$826$	1.21313	−	0.700398i	0.0422100	−	0.0243700i
$827$		−	0.892425i		−	0.0310327i	−0.999880	−	0.0155163i	$-0.995061\pi$
$827$		−	0.892425i		−	0.0310327i	0.999880	−	0.0155163i	$-0.00493920\pi$
$828$	0.725885	+	1.25727i	0.0252262	+	0.0436931i
$829$	−5.74291	+	9.94701i	−0.199459	+	0.345474i	−0.948353	−	0.317216i	$-0.897252\pi$
$829$	−5.74291	+	9.94701i	−0.199459	+	0.345474i	0.748894	+	0.662690i	$0.230585\pi$
$830$		0			0
$831$	−29.0577			−1.00800
$832$	2.77303	+	2.30441i	0.0961374	+	0.0798911i
$833$	15.3541			0.531986
$834$	1.82549	+	1.05395i	0.0632117	+	0.0364953i
$835$		0			0
$836$	−2.02300	−	3.50393i	−0.0699668	−	0.121186i
$837$			3.28110i			0.113411i
$838$	−21.8077	+	12.5907i	−0.753336	+	0.434939i
$839$	24.1738	−	13.9568i	0.834573	−	0.481841i	−0.0208426	−	0.999783i	$-0.506635\pi$
$839$	24.1738	−	13.9568i	0.834573	−	0.481841i	0.855416	+	0.517942i	$0.173302\pi$
$840$		0			0
$841$	−3.86540	−	6.69507i	−0.133290	−	0.230865i
$842$	−13.8456	+	23.9812i	−0.477150	+	0.826448i
$843$	−12.2489	−	7.07188i	−0.421873	−	0.243568i
$844$	−15.0775			−0.518989
$845$		0			0
$846$	1.06277			0.0365388
$847$	−2.52740	−	1.45920i	−0.0868426	−	0.0501386i
$848$	−1.64055	+	2.84152i	−0.0563367	+	0.0975781i
$849$	−4.37290	−	7.57409i	−0.150078	−	0.259942i
$850$		0			0
$851$	4.45835	−	2.57403i	0.152830	−	0.0882365i
$852$	−2.09811	+	1.21135i	−0.0718802	+	0.0415000i
$853$			41.6937i			1.42757i	0.700367	+	0.713783i	$0.253020\pi$
$853$			41.6937i			1.42757i	−0.700367	+	0.713783i	$0.746980\pi$
$854$	0.216665	+	0.375275i	0.00741413	+	0.0128417i
$855$		0			0
$856$	16.4967	+	9.52440i	0.563847	+	0.325537i
$857$	4.57772			0.156372			0.0781860	−	0.996939i	$-0.475087\pi$
$857$	4.57772			0.156372			0.0781860	+	0.996939i	$0.475087\pi$
$858$	2.12570	+	1.76647i	0.0725701	+	0.0603065i
$859$	−32.0617			−1.09393			−0.546966	−	0.837155i	$-0.684217\pi$
$859$	−32.0617			−1.09393			−0.546966	+	0.837155i	$0.684217\pi$
$860$		0			0
$861$	0.310878	−	0.538457i	0.0105947	−	0.0183506i
$862$	−0.0460826	−	0.0798174i	−0.00156958	−	0.00271859i
$863$		−	30.7876i		−	1.04802i	−0.851711	−	0.524011i	$-0.824435\pi$
$863$		−	30.7876i		−	1.04802i	0.851711	−	0.524011i	$-0.175565\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$		0			0
$866$		−	4.02225i		−	0.136682i
$867$	−6.03950	−	10.4607i	−0.205112	−	0.355265i
$868$	0.459815	−	0.796424i	0.0156072	−	0.0270324i
$869$	−9.60707	−	5.54664i	−0.325898	−	0.188157i
$870$		0			0
$871$	9.28965	+	25.1495i	0.314768	+	0.852157i
$872$	9.04549			0.306319
$873$	−1.09737	−	0.633565i	−0.0371402	−	0.0214429i
$874$	−3.83130	+	6.63600i	−0.129596	+	0.224466i
$875$		0			0
$876$		−	14.2630i		−	0.481902i
$877$	−35.3169	+	20.3902i	−1.19257	+	0.688529i	−0.958888	−	0.283785i	$-0.908410\pi$
$877$	−35.3169	+	20.3902i	−1.19257	+	0.688529i	−0.233679	+	0.972314i	$0.575076\pi$
$878$	−22.4719	+	12.9742i	−0.758391	+	0.437857i
$879$			31.5001i			1.06247i
$880$		0			0
$881$	−21.4928	+	37.2265i	−0.724109	+	1.25419i	0.235230	+	0.971940i	$0.424416\pi$
$881$	−21.4928	+	37.2265i	−0.724109	+	1.25419i	−0.959340	+	0.282254i	$0.908918\pi$
$882$	−5.99414	−	3.46072i	−0.201833	−	0.116529i
$883$	29.9139			1.00668			0.503341	−	0.864088i	$-0.332104\pi$
$883$	29.9139			1.00668			0.503341	+	0.864088i	$0.332104\pi$
$884$	−7.50283	+	2.77138i	−0.252347	+	0.0932115i
$885$		0			0
$886$	−13.0463	−	7.53229i	−0.438299	−	0.253052i
$887$	−23.4471	+	40.6116i	−0.787278	+	1.36360i	0.140351	+	0.990102i	$0.455177\pi$
$887$	−23.4471	+	40.6116i	−0.787278	+	1.36360i	−0.927629	+	0.373503i	$0.878157\pi$
$888$	1.77303	+	3.07097i	0.0594989	+	0.103055i
$889$		−	0.888970i		−	0.0298151i
$890$		0			0
$891$	−0.663862	+	0.383281i	−0.0222402	+	0.0128404i
$892$		−	4.65635i		−	0.155906i
$893$	2.80470	+	4.85789i	0.0938558	+	0.162563i
$894$	2.87039	−	4.97167i	0.0960004	−	0.166277i
$895$		0			0
$896$	0.280281			0.00936354
$897$	0.884368	−	5.15918i	0.0295282	−	0.172260i
$898$	−34.4631			−1.15005
$899$	17.2213	+	9.94271i	0.574362	+	0.331608i
$900$		0			0
$901$	−3.63928	−	6.30343i	−0.121242	−	0.209998i
$902$		−	1.70049i		−	0.0566201i
$903$	−0.875972	+	0.505743i	−0.0291505	+	0.0168301i
$904$		0			0
$905$		0			0
$906$	8.08549	+	14.0045i	0.268622	+	0.465268i
$907$	−13.3523	+	23.1269i	−0.443356	+	0.767915i	−0.997936	−	0.0642155i	$-0.979546\pi$
$907$	−13.3523	+	23.1269i	−0.443356	+	0.767915i	0.554580	+	0.832130i	$0.312879\pi$
$908$	5.37313	+	3.10218i	0.178314	+	0.102949i
$909$	4.52747			0.150167
$910$		0			0
$911$	28.8401			0.955515			0.477758	−	0.878492i	$-0.341450\pi$
$911$	28.8401			0.955515			0.477758	+	0.878492i	$0.341450\pi$
$912$	−4.57097	−	2.63905i	−0.151360	−	0.0873878i
$913$	−1.69571	+	2.93705i	−0.0561197	+	0.0972021i
$914$	20.8149	+	36.0525i	0.688496	+	1.19251i
$915$		0			0
$916$	−11.1379	+	6.43049i	−0.368008	+	0.212469i
$917$	3.74642	−	2.16300i	0.123718	−	0.0714285i
$918$		−	2.21833i		−	0.0732158i
$919$	−14.4493	−	25.0269i	−0.476637	−	0.825560i	0.523005	−	0.852330i	$-0.324811\pi$
$919$	−14.4493	−	25.0269i	−0.476637	−	0.825560i	−0.999642	+	0.0267702i	$0.991478\pi$
$920$		0			0
$921$	−6.08947	−	3.51576i	−0.200655	−	0.115848i
$922$	−6.95980			−0.229209
$923$	8.60957	+	1.47582i	0.283387	+	0.0485772i
$924$	0.214853			0.00706814
$925$		0			0
$926$	−5.96444	+	10.3307i	−0.196004	+	0.339488i
$927$	−1.47135	−	2.54846i	−0.0483256	−	0.0837025i
$928$			6.06059i			0.198949i
$929$	−37.8896	+	21.8756i	−1.24312	+	0.717715i	−0.969728	−	0.244188i	$-0.921479\pi$
$929$	−37.8896	+	21.8756i	−1.24312	+	0.717715i	−0.273391	+	0.961903i	$0.588145\pi$
$930$		0			0
$931$		−	36.5321i		−	1.19729i
$932$	−0.485461	−	0.840844i	−0.0159018	−	0.0275428i
$933$	4.39922	−	7.61967i	0.144024	−	0.249457i
$934$	−29.8264	−	17.2203i	−0.975950	−	0.563465i
$935$		0			0
$936$	3.55372	+	0.609166i	0.116157	+	0.0199112i
$937$	6.71836			0.219479			0.109740	−	0.993960i	$-0.464998\pi$
$937$	6.71836			0.219479			0.109740	+	0.993960i	$0.464998\pi$
$938$	1.80491	+	1.04206i	0.0589323	+	0.0340246i
$939$	4.67067	−	8.08984i	0.152422	−	0.264002i
$940$		0			0
$941$		−	33.9654i		−	1.10724i	−0.832769	−	0.553621i	$-0.813246\pi$
$941$		−	33.9654i		−	1.10724i	0.832769	−	0.553621i	$-0.186754\pi$
$942$	13.7179	−	7.92004i	0.446954	−	0.258049i
$943$	−2.78904	+	1.61025i	−0.0908236	+	0.0524371i
$944$		−	4.99783i		−	0.162665i
$945$		0			0
$946$	−1.38319	+	2.39576i	−0.0449715	+	0.0778929i
$947$	35.2907	+	20.3751i	1.14679	+	0.662101i	0.948104	−	0.317962i	$-0.102998\pi$
$947$	35.2907	+	20.3751i	1.14679	+	0.662101i	0.198689	+	0.980063i	$0.436332\pi$
$948$	−14.4715			−0.470012
$949$	−32.8678	+	39.5517i	−1.06694	+	1.28390i
$950$		0			0
$951$	−16.8612	−	9.73484i	−0.546763	−	0.315674i
$952$	−0.310878	+	0.538457i	−0.0100756	+	0.0174515i
$953$	3.02309	+	5.23614i	0.0979274	+	0.169615i	0.910827	−	0.412789i	$-0.135445\pi$
$953$	3.02309	+	5.23614i	0.0979274	+	0.169615i	−0.812899	+	0.582404i	$0.802112\pi$
$954$			3.28110i			0.106230i
$955$		0			0
$956$	12.8158	−	7.39922i	0.414493	−	0.239308i
$957$			4.64582i			0.150178i
$958$	6.86444	+	11.8896i	0.221780	+	0.384134i
$959$	−0.233795	+	0.404945i	−0.00754964	+	0.0130764i
$960$		0			0
$961$	20.2344			0.652722
$962$	2.16014	−	12.6017i	0.0696456	−	0.406295i
$963$	19.0488			0.613839
$964$	1.89795	+	1.09578i	0.0611289	+	0.0352928i
$965$		0			0
$966$	−0.203452	−	0.352389i	−0.00654596	−	0.0113379i
$967$			39.8852i			1.28262i	0.767282	+	0.641310i	$0.221609\pi$
$967$			39.8852i			1.28262i	−0.767282	+	0.641310i	$0.778391\pi$
$968$	−9.01739	+	5.20619i	−0.289830	+	0.167333i
$969$	10.1399	−	5.85429i	0.325742	−	0.188067i
$970$		0			0
$971$	19.5176	+	33.8055i	0.626349	+	1.08487i	0.988278	+	0.152663i	$0.0487849\pi$
$971$	19.5176	+	33.8055i	0.626349	+	1.08487i	−0.361929	+	0.932206i	$0.617882\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	−0.511652	−	0.295402i	−0.0164028	−	0.00947017i
$974$	−9.52978			−0.305354
$975$		0			0
$976$	1.54606			0.0494880
$977$	−36.4159	−	21.0247i	−1.16505	−	0.672641i	−0.212539	−	0.977153i	$-0.568173\pi$
$977$	−36.4159	−	21.0247i	−1.16505	−	0.672641i	−0.952509	+	0.304512i	$0.901507\pi$
$978$	5.65740	−	9.79890i	0.180904	−	0.313334i
$979$	−2.03706	−	3.52829i	−0.0651047	−	0.112765i
$980$		0			0
$981$	7.83362	−	4.52274i	0.250108	−	0.144400i
$982$	−28.9960	+	16.7409i	−0.925301	+	0.534223i
$983$		−	27.5124i		−	0.877508i	−0.898607	−	0.438754i	$-0.855420\pi$
$983$		−	27.5124i		−	0.877508i	0.898607	−	0.438754i	$-0.144580\pi$
$984$	−1.10917	−	1.92113i	−0.0353589	−	0.0612434i
$985$		0			0
$986$	−11.6432	−	6.72220i	−0.370795	−	0.214079i
$987$	−0.297874			−0.00948144
$988$	6.59397	+	17.8516i	0.209782	+	0.567934i
$989$	5.23918			0.166596
$990$		0			0
$991$	−27.9614	+	48.4306i	−0.888224	+	1.53845i	−0.0462506	+	0.998930i	$0.514727\pi$
$991$	−27.9614	+	48.4306i	−0.888224	+	1.53845i	−0.841973	+	0.539519i	$0.818606\pi$
$992$	−1.64055	−	2.84152i	−0.0520875	−	0.0902182i
$993$		−	18.9464i		−	0.601246i
$994$	0.588062	−	0.339518i	0.0186522	−	0.0107688i
$995$		0			0
$996$			4.42419i			0.140186i
$997$	14.8283	+	25.6834i	0.469618	+	0.813403i	0.999397	−	0.0347335i	$-0.0110582\pi$
$997$	14.8283	+	25.6834i	0.469618	+	0.813403i	−0.529778	+	0.848136i	$0.677725\pi$
$998$	7.54409	−	13.0667i	0.238804	−	0.413620i
$999$	3.07097	+	1.77303i	0.0971613	+	0.0560961i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.bc.k.901.2	yes	12
5.2	odd	4		1950.2.y.n.199.2		12
5.3	odd	4		1950.2.y.m.199.5		12
5.4	even	2		1950.2.bc.h.901.5	yes	12
13.10	even	6	inner	1950.2.bc.k.751.2	yes	12
65.23	odd	12		1950.2.y.n.49.2		12
65.49	even	6		1950.2.bc.h.751.5	✓	12
65.62	odd	12		1950.2.y.m.49.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1950.2.y.m.49.5		12	65.62	odd	12
1950.2.y.m.199.5		12	5.3	odd	4
1950.2.y.n.49.2		12	65.23	odd	12
1950.2.y.n.199.2		12	5.2	odd	4
1950.2.bc.h.751.5	✓	12	65.49	even	6
1950.2.bc.h.901.5	yes	12	5.4	even	2
1950.2.bc.k.751.2	yes	12	13.10	even	6	inner
1950.2.bc.k.901.2	yes	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(0.242731 - 0.140141i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(0.242731 - 0.140141i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.663862 + 0.383281i) q^{11} +1.00000 q^{12} +(-2.77303 - 2.30441i) q^{13} -0.280281 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.10917 - 1.92113i) q^{17} +1.00000i q^{18} +(-4.57097 + 2.63905i) q^{19} -0.280281i q^{21} +(-0.383281 - 0.663862i) q^{22} +(-0.725885 + 1.25727i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(1.24931 + 3.38219i) q^{26} -1.00000 q^{27} +(0.242731 + 0.140141i) q^{28} +(-3.03030 + 5.24863i) q^{29} -3.28110i q^{31} +(0.866025 - 0.500000i) q^{32} +(0.663862 - 0.383281i) q^{33} +2.21833i q^{34} +(0.500000 - 0.866025i) q^{36} +(-3.07097 - 1.77303i) q^{37} +5.27811 q^{38} +(-3.38219 + 1.24931i) q^{39} +(1.92113 + 1.10917i) q^{41} +(-0.140141 + 0.242731i) q^{42} +(-1.80441 - 3.12533i) q^{43} +0.766562i q^{44} +(1.25727 - 0.725885i) q^{46} -1.06277i q^{47} +(0.500000 + 0.866025i) q^{48} +(-3.46072 + 5.99414i) q^{49} -2.21833 q^{51} +(0.609166 - 3.55372i) q^{52} +3.28110 q^{53} +(0.866025 + 0.500000i) q^{54} +(-0.140141 - 0.242731i) q^{56} +5.27811i q^{57} +(5.24863 - 3.03030i) q^{58} +(-4.32824 + 2.49891i) q^{59} +(-0.773028 - 1.33892i) q^{61} +(-1.64055 + 2.84152i) q^{62} +(-0.242731 - 0.140141i) q^{63} -1.00000 q^{64} -0.766562 q^{66} +(-6.43963 - 3.71792i) q^{67} +(1.10917 - 1.92113i) q^{68} +(0.725885 + 1.25727i) q^{69} +(-2.09811 + 1.21135i) q^{71} +(-0.866025 + 0.500000i) q^{72} -14.2630i q^{73} +(1.77303 + 3.07097i) q^{74} +(-4.57097 - 2.63905i) q^{76} +0.214853 q^{77} +(3.55372 + 0.609166i) q^{78} -14.4715 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-1.10917 - 1.92113i) q^{82} +4.42419i q^{83} +(0.242731 - 0.140141i) q^{84} +3.60882i q^{86} +(3.03030 + 5.24863i) q^{87} +(0.383281 - 0.663862i) q^{88} +(-4.60275 - 2.65740i) q^{89} +(-0.996041 - 0.170738i) q^{91} -1.45177 q^{92} +(-2.84152 - 1.64055i) q^{93} +(-0.531385 + 0.920385i) q^{94} -1.00000i q^{96} +(1.09737 - 0.633565i) q^{97} +(5.99414 - 3.46072i) q^{98} -0.766562i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} + 6 q^{4} + 6 q^{7} - 6 q^{9}+O(q^{10}) \) 12 * q + 6 * q^3 + 6 * q^4 + 6 * q^7 - 6 * q^9	\( 12 q + 6 q^{3} + 6 q^{4} + 6 q^{7} - 6 q^{9} - 12 q^{11} + 12 q^{12} + 8 q^{14} - 6 q^{16} - 6 q^{19} + 4 q^{22} - 4 q^{23} - 4 q^{26} - 12 q^{27} + 6 q^{28} - 12 q^{33} + 6 q^{36} + 12 q^{37} - 24 q^{38} + 6 q^{39} + 4 q^{42} + 10 q^{43} + 12 q^{46} + 6 q^{48} + 32 q^{49} - 6 q^{52} + 16 q^{53} + 4 q^{56} + 24 q^{61} - 8 q^{62} - 6 q^{63} - 12 q^{64} + 8 q^{66} - 6 q^{67} + 4 q^{69} + 12 q^{71} - 12 q^{74} - 6 q^{76} + 48 q^{77} - 8 q^{78} + 52 q^{79} - 6 q^{81} + 6 q^{84} - 4 q^{88} + 24 q^{89} - 54 q^{91} - 8 q^{92} - 8 q^{94} - 12 q^{97} - 36 q^{98}+O(q^{100}) \) 12 * q + 6 * q^3 + 6 * q^4 + 6 * q^7 - 6 * q^9 - 12 * q^11 + 12 * q^12 + 8 * q^14 - 6 * q^16 - 6 * q^19 + 4 * q^22 - 4 * q^23 - 4 * q^26 - 12 * q^27 + 6 * q^28 - 12 * q^33 + 6 * q^36 + 12 * q^37 - 24 * q^38 + 6 * q^39 + 4 * q^42 + 10 * q^43 + 12 * q^46 + 6 * q^48 + 32 * q^49 - 6 * q^52 + 16 * q^53 + 4 * q^56 + 24 * q^61 - 8 * q^62 - 6 * q^63 - 12 * q^64 + 8 * q^66 - 6 * q^67 + 4 * q^69 + 12 * q^71 - 12 * q^74 - 6 * q^76 + 48 * q^77 - 8 * q^78 + 52 * q^79 - 6 * q^81 + 6 * q^84 - 4 * q^88 + 24 * q^89 - 54 * q^91 - 8 * q^92 - 8 * q^94 - 12 * q^97 - 36 * q^98

Introduction

L-functions

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