LMFDB - Embedded newform 1950.2.y.m.49.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(49,1950)]

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, 5]))

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

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

chi := DirichletCharacter("1950.49");

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.y (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:	$12$
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			49.5
Root			$0.500000 - 0.414256i$ of defining polynomial
Character	$\chi$	$=$	1950.49
Dual form			1950.2.y.m.199.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(-0.140141 + 0.242731i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(-0.140141 + 0.242731i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(0.663862 - 0.383281i) q^{11} +1.00000i q^{12} +(2.30441 + 2.77303i) q^{13} +0.280281 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.92113 - 1.10917i) q^{17} -1.00000 q^{18} +(4.57097 + 2.63905i) q^{19} +0.280281i q^{21} +(-0.663862 - 0.383281i) q^{22} +(-1.25727 + 0.725885i) q^{23} +(0.866025 - 0.500000i) q^{24} +(1.24931 - 3.38219i) q^{26} -1.00000i q^{27} +(-0.140141 - 0.242731i) q^{28} +(3.03030 + 5.24863i) q^{29} +3.28110i q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.383281 - 0.663862i) q^{33} +2.21833i q^{34} +(0.500000 + 0.866025i) q^{36} +(-1.77303 - 3.07097i) q^{37} -5.27811i q^{38} +(3.38219 + 1.24931i) q^{39} +(1.92113 - 1.10917i) q^{41} +(0.242731 - 0.140141i) q^{42} +(3.12533 + 1.80441i) q^{43} +0.766562i q^{44} +(1.25727 + 0.725885i) q^{46} -1.06277 q^{47} +(-0.866025 - 0.500000i) q^{48} +(3.46072 + 5.99414i) q^{49} -2.21833 q^{51} +(-3.55372 + 0.609166i) q^{52} -3.28110i q^{53} +(-0.866025 + 0.500000i) q^{54} +(-0.140141 + 0.242731i) q^{56} +5.27811 q^{57} +(3.03030 - 5.24863i) q^{58} +(4.32824 + 2.49891i) q^{59} +(-0.773028 + 1.33892i) q^{61} +(2.84152 - 1.64055i) q^{62} +(0.140141 + 0.242731i) q^{63} +1.00000 q^{64} -0.766562 q^{66} +(-3.71792 - 6.43963i) q^{67} +(1.92113 - 1.10917i) q^{68} +(-0.725885 + 1.25727i) q^{69} +(-2.09811 - 1.21135i) q^{71} +(0.500000 - 0.866025i) q^{72} +14.2630 q^{73} +(-1.77303 + 3.07097i) q^{74} +(-4.57097 + 2.63905i) q^{76} +0.214853i q^{77} +(-0.609166 - 3.55372i) q^{78} +14.4715 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-1.92113 - 1.10917i) q^{82} -4.42419 q^{83} +(-0.242731 - 0.140141i) q^{84} -3.60882i q^{86} +(5.24863 + 3.03030i) q^{87} +(0.663862 - 0.383281i) q^{88} +(4.60275 - 2.65740i) q^{89} +(-0.996041 + 0.170738i) q^{91} -1.45177i q^{92} +(1.64055 + 2.84152i) q^{93} +(0.531385 + 0.920385i) q^{94} +1.00000i q^{96} +(-0.633565 + 1.09737i) q^{97} +(3.46072 - 5.99414i) q^{98} -0.766562i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 6 q^{4} + 4 q^{7} + 12 q^{8} + 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^2 - 6 * q^4 + 4 * q^7 + 12 * q^8 + 6 * q^9	$ 12 q - 6 q^{2} - 6 q^{4} + 4 q^{7} + 12 q^{8} + 6 q^{9} - 12 q^{11} - 4 q^{13} - 8 q^{14} - 6 q^{16} - 12 q^{18} + 6 q^{19} + 12 q^{22} - 12 q^{23} - 4 q^{26} + 4 q^{28} - 6 q^{32} - 4 q^{33} + 6 q^{36} + 12 q^{37} - 6 q^{39} + 6 q^{42} - 12 q^{43} + 12 q^{46} - 16 q^{47} - 32 q^{49} + 8 q^{52} + 4 q^{56} - 24 q^{57} + 24 q^{61} - 4 q^{63} + 12 q^{64} + 8 q^{66} - 24 q^{67} - 4 q^{69} + 12 q^{71} + 6 q^{72} + 40 q^{73} + 12 q^{74} - 6 q^{76} + 6 q^{78} - 52 q^{79} - 6 q^{81} - 32 q^{83} - 6 q^{84} - 12 q^{88} - 24 q^{89} - 54 q^{91} + 8 q^{93} + 8 q^{94} - 24 q^{97} - 32 q^{98}+O(q^{100}) $ 12 * q - 6 * q^2 - 6 * q^4 + 4 * q^7 + 12 * q^8 + 6 * q^9 - 12 * q^11 - 4 * q^13 - 8 * q^14 - 6 * q^16 - 12 * q^18 + 6 * q^19 + 12 * q^22 - 12 * q^23 - 4 * q^26 + 4 * q^28 - 6 * q^32 - 4 * q^33 + 6 * q^36 + 12 * q^37 - 6 * q^39 + 6 * q^42 - 12 * q^43 + 12 * q^46 - 16 * q^47 - 32 * q^49 + 8 * q^52 + 4 * q^56 - 24 * q^57 + 24 * q^61 - 4 * q^63 + 12 * q^64 + 8 * q^66 - 24 * q^67 - 4 * q^69 + 12 * q^71 + 6 * q^72 + 40 * q^73 + 12 * q^74 - 6 * q^76 + 6 * q^78 - 52 * q^79 - 6 * q^81 - 32 * q^83 - 6 * q^84 - 12 * q^88 - 24 * q^89 - 54 * q^91 + 8 * q^93 + 8 * q^94 - 24 * q^97 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	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
$6$	−0.866025	−	0.500000i	−0.353553	−	0.204124i
$7$	−0.140141	+	0.242731i	−0.0529682	+	0.0917436i	−0.891294	−	0.453426i	$-0.850202\pi$
$7$	−0.140141	+	0.242731i	−0.0529682	+	0.0917436i	0.838326	+	0.545170i	$0.183535\pi$
$8$	1.00000			0.353553
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	0.663862	−	0.383281i	0.200162	−	0.115564i	−0.396569	−	0.918005i	$-0.629799\pi$
$11$	0.663862	−	0.383281i	0.200162	−	0.115564i	0.596731	+	0.802441i	$0.296466\pi$
$12$			1.00000i			0.288675i
$13$	2.30441	+	2.77303i	0.639129	+	0.769100i
$13$	2.30441	+	2.77303i	0.639129	+	0.769100i
$14$	0.280281			0.0749083
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.92113	−	1.10917i	−0.465943	−	0.269012i	0.248597	−	0.968607i	$-0.420031\pi$
$17$	−1.92113	−	1.10917i	−0.465943	−	0.269012i	−0.714540	+	0.699595i	$0.753364\pi$
$18$	−1.00000			−0.235702
$19$	4.57097	+	2.63905i	1.04865	+	0.605440i	0.922272	−	0.386541i	$-0.126330\pi$
$19$	4.57097	+	2.63905i	1.04865	+	0.605440i	0.126381	+	0.991982i	$0.459664\pi$
$20$		0			0
$21$			0.280281i			0.0611624i
$22$	−0.663862	−	0.383281i	−0.141536	−	0.0817158i
$23$	−1.25727	+	0.725885i	−0.262159	+	0.151357i	−0.625319	−	0.780369i	$-0.715031\pi$
$23$	−1.25727	+	0.725885i	−0.262159	+	0.151357i	0.363160	+	0.931727i	$0.381698\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$		0			0
$26$	1.24931	−	3.38219i	0.245009	−	0.663303i
$27$		−	1.00000i		−	0.192450i
$28$	−0.140141	−	0.242731i	−0.0264841	−	0.0458718i
$29$	3.03030	+	5.24863i	0.562712	+	0.974646i	0.997259	+	0.0739965i	$0.0235754\pi$
$29$	3.03030	+	5.24863i	0.562712	+	0.974646i	−0.434546	+	0.900649i	$0.643091\pi$
$30$		0			0
$31$			3.28110i			0.589303i	0.955605	+	0.294652i	$0.0952036\pi$
$31$			3.28110i			0.589303i	−0.955605	+	0.294652i	$0.904796\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	0.383281	−	0.663862i	0.0667207	−	0.115564i
$34$			2.21833i			0.380441i
$35$		0			0
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	−1.77303	−	3.07097i	−0.291484	−	0.504865i	0.682677	−	0.730720i	$-0.260816\pi$
$37$	−1.77303	−	3.07097i	−0.291484	−	0.504865i	−0.974161	+	0.225855i	$0.927482\pi$
$38$		−	5.27811i		−	0.856222i
$39$	3.38219	+	1.24931i	0.541584	+	0.200049i
$40$		0			0
$41$	1.92113	−	1.10917i	0.300030	−	0.173223i	−0.342426	−	0.939545i	$-0.611249\pi$
$41$	1.92113	−	1.10917i	0.300030	−	0.173223i	0.642457	+	0.766322i	$0.277915\pi$
$42$	0.242731	−	0.140141i	0.0374542	−	0.0216242i
$43$	3.12533	+	1.80441i	0.476609	+	0.275170i	0.719002	−	0.695008i	$-0.244599\pi$
$43$	3.12533	+	1.80441i	0.476609	+	0.275170i	−0.242393	+	0.970178i	$0.577932\pi$
$44$			0.766562i			0.115564i
$45$		0			0
$46$	1.25727	+	0.725885i	0.185374	+	0.107026i
$47$	−1.06277			−0.155021			−0.0775104	−	0.996992i	$-0.524697\pi$
$47$	−1.06277			−0.155021			−0.0775104	+	0.996992i	$0.524697\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	3.46072	+	5.99414i	0.494389	+	0.856306i
$50$		0			0
$51$	−2.21833			−0.310629
$52$	−3.55372	+	0.609166i	−0.492812	+	0.0844761i
$53$		−	3.28110i		−	0.450694i	−0.974279	−	0.225347i	$-0.927648\pi$
$53$		−	3.28110i		−	0.450694i	0.974279	−	0.225347i	$-0.0723515\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$		0			0
$56$	−0.140141	+	0.242731i	−0.0187271	+	0.0324362i
$57$	5.27811			0.699102
$58$	3.03030	−	5.24863i	0.397898	−	0.689179i
$59$	4.32824	+	2.49891i	0.563489	+	0.325331i	0.754545	−	0.656249i	$-0.227858\pi$
$59$	4.32824	+	2.49891i	0.563489	+	0.325331i	−0.191055	+	0.981579i	$0.561191\pi$
$60$		0			0
$61$	−0.773028	+	1.33892i	−0.0989761	+	0.171432i	−0.911261	−	0.411829i	$-0.864890\pi$
$61$	−0.773028	+	1.33892i	−0.0989761	+	0.171432i	0.812285	+	0.583261i	$0.198223\pi$
$62$	2.84152	−	1.64055i	0.360873	−	0.208350i
$63$	0.140141	+	0.242731i	0.0176561	+	0.0305812i
$64$	1.00000			0.125000
$65$		0			0
$66$	−0.766562			−0.0943573
$67$	−3.71792	−	6.43963i	−0.454216	−	0.786726i	0.544426	−	0.838809i	$-0.316747\pi$
$67$	−3.71792	−	6.43963i	−0.454216	−	0.786726i	−0.998643	+	0.0520827i	$0.983414\pi$
$68$	1.92113	−	1.10917i	0.232971	−	0.134506i
$69$	−0.725885	+	1.25727i	−0.0873863	+	0.151357i
$70$		0			0
$71$	−2.09811	−	1.21135i	−0.249000	−	0.143760i	0.370306	−	0.928910i	$-0.379253\pi$
$71$	−2.09811	−	1.21135i	−0.249000	−	0.143760i	−0.619306	+	0.785149i	$0.712586\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	14.2630			1.66936			0.834679	−	0.550737i	$-0.185653\pi$
$73$	14.2630			1.66936			0.834679	+	0.550737i	$0.185653\pi$
$74$	−1.77303	+	3.07097i	−0.206110	+	0.356994i
$75$		0			0
$76$	−4.57097	+	2.63905i	−0.524327	+	0.302720i
$77$			0.214853i			0.0244848i
$78$	−0.609166	−	3.55372i	−0.0689744	−	0.402379i
$79$	14.4715			1.62817			0.814085	−	0.580746i	$-0.197239\pi$
$79$	14.4715			1.62817			0.814085	+	0.580746i	$0.197239\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.92113	−	1.10917i	−0.212153	−	0.122487i
$83$	−4.42419			−0.485617			−0.242809	−	0.970074i	$-0.578069\pi$
$83$	−4.42419			−0.485617			−0.242809	+	0.970074i	$0.578069\pi$
$84$	−0.242731	−	0.140141i	−0.0264841	−	0.0152906i
$85$		0			0
$86$		−	3.60882i		−	0.389150i
$87$	5.24863	+	3.03030i	0.562712	+	0.324882i
$88$	0.663862	−	0.383281i	0.0707679	−	0.0408579i
$89$	4.60275	−	2.65740i	0.487890	−	0.281683i	−0.235809	−	0.971799i	$-0.575774\pi$
$89$	4.60275	−	2.65740i	0.487890	−	0.281683i	0.723699	+	0.690116i	$0.242441\pi$
$90$		0			0
$91$	−0.996041	+	0.170738i	−0.104413	+	0.0178982i
$92$		−	1.45177i		−	0.151357i
$93$	1.64055	+	2.84152i	0.170117	+	0.294652i
$94$	0.531385	+	0.920385i	0.0548081	+	0.0949305i
$95$		0			0
$96$			1.00000i			0.102062i
$97$	−0.633565	+	1.09737i	−0.0643288	+	0.111421i	−0.896396	−	0.443254i	$-0.853824\pi$
$97$	−0.633565	+	1.09737i	−0.0643288	+	0.111421i	0.832067	+	0.554675i	$0.187157\pi$
$98$	3.46072	−	5.99414i	0.349586	−	0.605500i
$99$		−	0.766562i		−	0.0770424i
$100$		0			0
$101$	−2.26374	−	3.92090i	−0.225250	−	0.390145i	0.731144	−	0.682223i	$-0.238987\pi$
$101$	−2.26374	−	3.92090i	−0.225250	−	0.390145i	−0.956394	+	0.292078i	$0.905653\pi$
$102$	1.10917	+	1.92113i	0.109824	+	0.190220i
$103$		−	2.94271i		−	0.289954i	−0.989435	−	0.144977i	$-0.953689\pi$
$103$		−	2.94271i		−	0.289954i	0.989435	−	0.144977i	$-0.0463108\pi$
$104$	2.30441	+	2.77303i	0.225966	+	0.271918i
$105$		0			0
$106$	−2.84152	+	1.64055i	−0.275992	+	0.159344i
$107$	16.4967	−	9.52440i	1.59480	−	0.920758i	0.602333	−	0.798245i	$-0.294238\pi$
$107$	16.4967	−	9.52440i	1.59480	−	0.920758i	0.992467	−	0.122513i	$-0.0390954\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$			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
$112$	0.280281			0.0264841
$113$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$113$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$114$	−2.63905	−	4.57097i	−0.247170	−	0.428111i
$115$		0			0
$116$	−6.06059			−0.562712
$117$	3.55372	−	0.609166i	0.328541	−	0.0563174i
$118$		−	4.99783i		−	0.460087i
$119$	0.538457	−	0.310878i	0.0493603	−	0.0284982i
$120$		0			0
$121$	−5.20619	+	9.01739i	−0.473290	+	0.819763i
$122$	1.54606			0.139973
$123$	1.10917	−	1.92113i	0.100010	−	0.173223i
$124$	−2.84152	−	1.64055i	−0.255176	−	0.147326i
$125$		0			0
$126$	0.140141	−	0.242731i	0.0124847	−	0.0216242i
$127$	−2.74678	+	1.58585i	−0.243737	+	0.140722i	−0.616893	−	0.787047i	$-0.711609\pi$
$127$	−2.74678	+	1.58585i	−0.243737	+	0.140722i	0.373156	+	0.927769i	$0.378276\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	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	$0.264463\pi$
$132$	0.383281	+	0.663862i	0.0333603	+	0.0577818i
$133$	−1.28116	+	0.739677i	−0.111091	+	0.0641381i
$134$	−3.71792	+	6.43963i	−0.321180	+	0.556299i
$135$		0			0
$136$	−1.92113	−	1.10917i	−0.164736	−	0.0951102i
$137$	0.834145	−	1.44478i	0.0712658	−	0.123436i	−0.828191	−	0.560447i	$-0.810629\pi$
$137$	0.834145	−	1.44478i	0.0712658	−	0.123436i	0.899456	+	0.437011i	$0.143963\pi$
$138$	1.45177			0.123583
$139$	1.05395	−	1.82549i	0.0893949	−	0.154836i	−0.817861	−	0.575416i	$-0.804840\pi$
$139$	1.05395	−	1.82549i	0.0893949	−	0.154836i	0.907256	+	0.420580i	$0.138173\pi$
$140$		0			0
$141$	−0.920385	+	0.531385i	−0.0775104	+	0.0447507i
$142$			2.42269i			0.203308i
$143$	2.59266	+	0.957671i	0.216809	+	0.0800844i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	−7.13150	−	12.3521i	−0.590207	−	1.02227i
$147$	5.99414	+	3.46072i	0.494389	+	0.285435i
$148$	3.54606			0.291484
$149$	4.97167	+	2.87039i	0.407295	+	0.235152i	0.689627	−	0.724165i	$-0.257775\pi$
$149$	4.97167	+	2.87039i	0.407295	+	0.235152i	−0.282332	+	0.959317i	$0.591108\pi$
$150$		0			0
$151$			16.1710i			1.31598i	0.753029	+	0.657988i	$0.228592\pi$
$151$			16.1710i			1.31598i	−0.753029	+	0.657988i	$0.771408\pi$
$152$	4.57097	+	2.63905i	0.370755	+	0.214055i
$153$	−1.92113	+	1.10917i	−0.155314	+	0.0896707i
$154$	0.186068	−	0.107426i	0.0149938	−	0.00865667i
$155$		0			0
$156$	−2.77303	+	2.30441i	−0.222020	+	0.184501i
$157$		−	15.8401i		−	1.26418i	−0.774896	−	0.632088i	$-0.782198\pi$
$157$		−	15.8401i		−	1.26418i	0.774896	−	0.632088i	$-0.217802\pi$
$158$	−7.23574	−	12.5327i	−0.575645	−	0.997046i
$159$	−1.64055	−	2.84152i	−0.130104	−	0.225347i
$160$		0			0
$161$		−	0.406904i		−	0.0320685i
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	−5.65740	+	9.79890i	−0.443121	+	0.767509i	−0.997919	−	0.0644763i	$-0.979462\pi$
$163$	−5.65740	+	9.79890i	−0.443121	+	0.767509i	0.554798	+	0.831985i	$0.312796\pi$
$164$			2.21833i			0.173223i
$165$		0			0
$166$	2.21209	+	3.83146i	0.171692	+	0.297379i
$167$	0.725885	+	1.25727i	0.0561707	+	0.0972904i	0.892743	−	0.450565i	$-0.148778\pi$
$167$	0.725885	+	1.25727i	0.0561707	+	0.0972904i	−0.836573	+	0.547856i	$0.815444\pi$
$168$			0.280281i			0.0216242i
$169$	−2.37937	+	12.7804i	−0.183028	+	0.983108i
$170$		0			0
$171$	4.57097	−	2.63905i	0.349551	−	0.201813i
$172$	−3.12533	+	1.80441i	−0.238304	+	0.137585i
$173$	−11.5530	−	6.67010i	−0.878355	−	0.507118i	−0.00823921	−	0.999966i	$-0.502623\pi$
$173$	−11.5530	−	6.67010i	−0.878355	−	0.507118i	−0.870116	+	0.492848i	$0.835956\pi$
$174$		−	6.06059i		−	0.459452i
$175$		0			0
$176$	−0.663862	−	0.383281i	−0.0500405	−	0.0288909i
$177$	4.99783			0.375660
$178$	−4.60275	−	2.65740i	−0.344990	−	0.199180i
$179$	−12.6266	−	21.8699i	−0.943755	−	1.63463i	−0.758226	−	0.651992i	$-0.773933\pi$
$179$	−12.6266	−	21.8699i	−0.943755	−	1.63463i	−0.185529	−	0.982639i	$-0.559400\pi$
$180$		0			0
$181$	−0.314792			−0.0233983			−0.0116992	−	0.999932i	$-0.503724\pi$
$181$	−0.314792			−0.0233983			−0.0116992	+	0.999932i	$0.503724\pi$
$182$	0.645884	+	0.777228i	0.0478761	+	0.0576119i
$183$			1.54606i			0.114288i
$184$	−1.25727	+	0.725885i	−0.0926871	+	0.0535129i
$185$		0			0
$186$	1.64055	−	2.84152i	0.120291	−	0.208350i
$187$	−1.70049			−0.124352
$188$	0.531385	−	0.920385i	0.0387552	−	0.0671260i
$189$	0.242731	+	0.140141i	0.0176561	+	0.0101937i
$190$		0			0
$191$	11.2666	−	19.5143i	0.815223	−	1.41201i	−0.0939445	−	0.995577i	$-0.529948\pi$
$191$	11.2666	−	19.5143i	0.815223	−	1.41201i	0.909168	−	0.416430i	$-0.136719\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	4.89181	+	8.47286i	0.352120	+	0.609890i	0.986621	−	0.163032i	$-0.0521275\pi$
$193$	4.89181	+	8.47286i	0.352120	+	0.609890i	−0.634501	+	0.772922i	$0.718794\pi$
$194$	1.26713			0.0909746
$195$		0			0
$196$	−6.92144			−0.494389
$197$	−6.22862	−	10.7883i	−0.443771	−	0.768634i	0.554195	−	0.832387i	$-0.313026\pi$
$197$	−6.22862	−	10.7883i	−0.443771	−	0.768634i	−0.997966	+	0.0637530i	$0.979693\pi$
$198$	−0.663862	+	0.383281i	−0.0471786	+	0.0272386i
$199$	−7.53195	+	13.0457i	−0.533926	+	0.924787i	0.465289	+	0.885159i	$0.345950\pi$
$199$	−7.53195	+	13.0457i	−0.533926	+	0.924787i	−0.999215	+	0.0396276i	$0.987383\pi$
$200$		0			0
$201$	−6.43963	−	3.71792i	−0.454216	−	0.262242i
$202$	−2.26374	+	3.92090i	−0.159276	+	0.275874i
$203$	−1.69867			−0.119223
$204$	1.10917	−	1.92113i	0.0776571	−	0.134506i
$205$		0			0
$206$	−2.54846	+	1.47135i	−0.177560	+	0.102514i
$207$			1.45177i			0.100905i
$208$	1.24931	−	3.38219i	0.0866238	−	0.234513i
$209$	4.04600			0.279867
$210$		0			0
$211$	−7.53876	−	13.0575i	−0.518989	−	0.898916i	−0.999756	−	0.0220676i	$-0.992975\pi$
$211$	−7.53876	−	13.0575i	−0.518989	−	0.898916i	0.480767	−	0.876848i	$-0.340358\pi$
$212$	2.84152	+	1.64055i	0.195156	+	0.112673i
$213$	−2.42269			−0.166000
$214$	−16.4967	−	9.52440i	−1.12769	−	0.651074i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	−0.796424	−	0.459815i	−0.0540648	−	0.0312143i
$218$	7.83362	−	4.52274i	0.530560	−	0.306319i
$219$	12.3521	−	7.13150i	0.834679	−	0.481902i
$220$		0			0
$221$	−1.35133	−	7.88333i	−0.0909004	−	0.530290i
$222$			3.54606i			0.237996i
$223$	2.32817	+	4.03252i	0.155906	+	0.270037i	0.933389	−	0.358867i	$-0.116837\pi$
$223$	2.32817	+	4.03252i	0.155906	+	0.270037i	−0.777482	+	0.628905i	$0.783504\pi$
$224$	−0.140141	−	0.242731i	−0.00936354	−	0.0162181i
$225$		0			0
$226$		0			0
$227$	−3.10218	+	5.37313i	−0.205899	+	0.356627i	−0.950419	−	0.310973i	$-0.899345\pi$
$227$	−3.10218	+	5.37313i	−0.205899	+	0.356627i	0.744520	+	0.667600i	$0.232678\pi$
$228$	−2.63905	+	4.57097i	−0.174776	+	0.302720i
$229$			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
$232$	3.03030	+	5.24863i	0.198949	+	0.344589i
$233$			0.970923i			0.0636073i	0.999494	+	0.0318036i	$0.0101251\pi$
$233$			0.970923i			0.0636073i	−0.999494	+	0.0318036i	$0.989875\pi$
$234$	−2.30441	−	2.77303i	−0.150644	−	0.181279i
$235$		0			0
$236$	−4.32824	+	2.49891i	−0.281745	+	0.162665i
$237$	12.5327	−	7.23574i	0.814085	−	0.470012i
$238$	−0.538457	−	0.310878i	−0.0349030	−	0.0201512i
$239$		−	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	0.559882	−	0.828572i	$-0.310847\pi$
$241$	1.89795	+	1.09578i	0.122258	+	0.0705856i	−0.437624	+	0.899158i	$0.644180\pi$
$242$	10.4124			0.669333
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−0.773028	−	1.33892i	−0.0494880	−	0.0857158i
$245$		0			0
$246$	−2.21833			−0.141436
$247$	3.21524	+	18.7569i	0.204581	+	1.19347i
$248$			3.28110i			0.208350i
$249$	−3.83146	+	2.21209i	−0.242809	+	0.140186i
$250$		0			0
$251$	5.29487	−	9.17098i	0.334209	−	0.578867i	−0.649124	−	0.760683i	$-0.724864\pi$
$251$	5.29487	−	9.17098i	0.334209	−	0.578867i	0.983333	+	0.181816i	$0.0581975\pi$
$252$	−0.280281			−0.0176561
$253$	−0.556436	+	0.963775i	−0.0349828	+	0.0605920i
$254$	2.74678	+	1.58585i	0.172348	+	0.0995053i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.93047	−	3.42396i	0.369933	−	0.213581i	−0.303496	−	0.952833i	$-0.598154\pi$
$257$	5.93047	−	3.42396i	0.369933	−	0.213581i	0.673429	+	0.739252i	$0.264821\pi$
$258$	−1.80441	−	3.12533i	−0.112338	−	0.194575i
$259$	0.993893			0.0617575
$260$		0			0
$261$	6.06059			0.375141
$262$	−7.71724	−	13.3667i	−0.476773	−	0.825795i
$263$	−22.7212	+	13.1181i	−1.40105	+	0.808898i	−0.994501	−	0.104730i	$-0.966602\pi$
$263$	−22.7212	+	13.1181i	−1.40105	+	0.808898i	−0.406551	+	0.913628i	$0.633269\pi$
$264$	0.383281	−	0.663862i	0.0235893	−	0.0408579i
$265$		0			0
$266$	1.28116	+	0.739677i	0.0785529	+	0.0453525i
$267$	2.65740	−	4.60275i	0.162630	−	0.281683i
$268$	7.43584			0.454216
$269$	3.24938	−	5.62808i	0.198118	−	0.343150i	−0.749800	−	0.661664i	$-0.769850\pi$
$269$	3.24938	−	5.62808i	0.198118	−	0.343150i	0.947918	+	0.318514i	$0.103184\pi$
$270$		0			0
$271$	5.35904	−	3.09404i	0.325539	−	0.187950i	−0.328320	−	0.944567i	$-0.606482\pi$
$271$	5.35904	−	3.09404i	0.325539	−	0.187950i	0.653859	+	0.756617i	$0.273149\pi$
$272$			2.21833i			0.134506i
$273$	−0.777228	+	0.645884i	−0.0470400	+	0.0390906i
$274$	−1.66829			−0.100785
$275$		0			0
$276$	−0.725885	−	1.25727i	−0.0436931	−	0.0756787i
$277$	−25.1647	−	14.5289i	−1.51200	−	0.872955i	−0.999902	−	0.0140299i	$-0.995534\pi$
$277$	−25.1647	−	14.5289i	−1.51200	−	0.872955i	−0.512101	−	0.858925i	$-0.671133\pi$
$278$	−2.10790			−0.126423
$279$	2.84152	+	1.64055i	0.170117	+	0.0982172i
$280$		0			0
$281$			14.1438i			0.843746i	0.906655	+	0.421873i	$0.138627\pi$
$281$			14.1438i			0.843746i	−0.906655	+	0.421873i	$0.861373\pi$
$282$	0.920385	+	0.531385i	0.0548081	+	0.0316435i
$283$	7.57409	−	4.37290i	0.450233	−	0.259942i	−0.257696	−	0.966226i	$-0.582963\pi$
$283$	7.57409	−	4.37290i	0.450233	−	0.259942i	0.707928	+	0.706284i	$0.249630\pi$
$284$	2.09811	−	1.21135i	0.124500	−	0.0718802i
$285$		0			0
$286$	−0.466963	−	2.72415i	−0.0276121	−	0.161082i
$287$			0.621757i			0.0367011i
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	−6.03950	−	10.4607i	−0.355265	−	0.615337i
$290$		0			0
$291$			1.26713i			0.0742805i
$292$	−7.13150	+	12.3521i	−0.417339	+	0.722853i
$293$	−15.7500	+	27.2798i	−0.920126	+	1.59371i	−0.120909	+	0.992664i	$0.538581\pi$
$293$	−15.7500	+	27.2798i	−0.920126	+	1.59371i	−0.799217	+	0.601042i	$0.794752\pi$
$294$		−	6.92144i		−	0.403667i
$295$		0			0
$296$	−1.77303	−	3.07097i	−0.103055	−	0.178497i
$297$	−0.383281	−	0.663862i	−0.0222402	−	0.0385212i
$298$		−	5.74079i		−	0.332555i
$299$	−4.91017	−	1.81370i	−0.283962	−	0.104889i
$300$		0			0
$301$	−0.875972	+	0.505743i	−0.0504902	+	0.0291505i
$302$	14.0045	−	8.08549i	0.805867	−	0.465268i
$303$	−3.92090	−	2.26374i	−0.225250	−	0.130048i
$304$		−	5.27811i		−	0.302720i
$305$		0			0
$306$	1.92113	+	1.10917i	0.109824	+	0.0634068i
$307$	−7.03152			−0.401310			−0.200655	−	0.979662i	$-0.564307\pi$
$307$	−7.03152			−0.401310			−0.200655	+	0.979662i	$0.564307\pi$
$308$	−0.186068	−	0.107426i	−0.0106022	−	0.00612119i
$309$	−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	$0.419748\pi$
$312$	3.38219	+	1.24931i	0.191479	+	0.0707280i
$313$		−	9.34134i		−	0.528004i	−0.964522	−	0.264002i	$-0.914958\pi$
$313$		−	9.34134i		−	0.528004i	0.964522	−	0.264002i	$-0.0850425\pi$
$314$	−13.7179	+	7.92004i	−0.774147	+	0.446954i
$315$		0			0
$316$	−7.23574	+	12.5327i	−0.407042	+	0.705018i
$317$	−19.4697			−1.09353			−0.546763	−	0.837287i	$-0.684140\pi$
$317$	−19.4697			−1.09353			−0.546763	+	0.837287i	$0.684140\pi$
$318$	−1.64055	+	2.84152i	−0.0919975	+	0.159344i
$319$	4.02340	+	2.32291i	0.225267	+	0.130058i
$320$		0			0
$321$	9.52440	−	16.4967i	0.531600	−	0.920758i
$322$	−0.352389	+	0.203452i	−0.0196379	+	0.0113379i
$323$	−5.85429	−	10.1399i	−0.325742	−	0.564201i
$324$	1.00000			0.0555556
$325$		0			0
$326$	11.3148			0.626668
$327$	4.52274	+	7.83362i	0.250108	+	0.433200i
$328$	1.92113	−	1.10917i	0.106077	−	0.0612434i
$329$	0.148937	−	0.257967i	0.00821117	−	0.0142222i
$330$		0			0
$331$	16.4081	+	9.47320i	0.901869	+	0.520694i	0.877806	−	0.479016i	$-0.159007\pi$
$331$	16.4081	+	9.47320i	0.901869	+	0.520694i	0.0240626	+	0.999710i	$0.492340\pi$
$332$	2.21209	−	3.83146i	0.121404	−	0.210279i
$333$	−3.54606			−0.194323
$334$	0.725885	−	1.25727i	0.0397186	−	0.0687947i
$335$		0			0
$336$	0.242731	−	0.140141i	0.0132420	−	0.00764530i
$337$		−	2.72966i		−	0.148694i	−0.997232	−	0.0743469i	$-0.976313\pi$
$337$		−	2.72966i		−	0.148694i	0.997232	−	0.0743469i	$-0.0236872\pi$
$338$	12.2578	−	4.32961i	0.666738	−	0.235500i
$339$		0			0
$340$		0			0
$341$	1.25758	+	2.17820i	0.0681020	+	0.117956i
$342$	−4.57097	−	2.63905i	−0.247170	−	0.142704i
$343$	−3.90192			−0.210684
$344$	3.12533	+	1.80441i	0.168507	+	0.0972874i
$345$		0			0
$346$			13.3402i			0.717174i
$347$	10.9916	+	6.34600i	0.590059	+	0.340671i	0.765121	−	0.643887i	$-0.222679\pi$
$347$	10.9916	+	6.34600i	0.590059	+	0.340671i	−0.175062	+	0.984557i	$0.556012\pi$
$348$	−5.24863	+	3.03030i	−0.281356	+	0.162441i
$349$	−1.04906	+	0.605676i	−0.0561549	+	0.0324211i	−0.527815	−	0.849360i	$-0.676988\pi$
$349$	−1.04906	+	0.605676i	−0.0561549	+	0.0324211i	0.471660	+	0.881781i	$0.343655\pi$
$350$		0			0
$351$	2.77303	−	2.30441i	0.148013	−	0.123000i
$352$			0.766562i			0.0408579i
$353$	16.7901	+	29.0813i	0.893647	+	1.54784i	0.835471	+	0.549535i	$0.185195\pi$
$353$	16.7901	+	29.0813i	0.893647	+	1.54784i	0.0581762	+	0.998306i	$0.481471\pi$
$354$	−2.49891	−	4.32824i	−0.132816	−	0.230044i
$355$		0			0
$356$			5.31479i			0.281683i
$357$	0.310878	−	0.538457i	0.0164534	−	0.0284982i
$358$	−12.6266	+	21.8699i	−0.667335	+	1.15586i
$359$		−	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
$362$	0.157396	+	0.272618i	0.00827256	+	0.0143285i
$363$			10.4124i			0.546508i
$364$	0.350157	−	0.947965i	0.0183532	−	0.0496869i
$365$		0			0
$366$	1.33892	−	0.773028i	0.0699867	−	0.0404068i
$367$	−8.36421	+	4.82908i	−0.436608	+	0.252076i	−0.702158	−	0.712021i	$-0.747780\pi$
$367$	−8.36421	+	4.82908i	−0.436608	+	0.252076i	0.265550	+	0.964097i	$0.414447\pi$
$368$	1.25727	+	0.725885i	0.0655397	+	0.0378394i
$369$		−	2.21833i		−	0.115482i
$370$		0			0
$371$	0.796424	+	0.459815i	0.0413483	+	0.0238724i
$372$	−3.28110			−0.170117
$373$	10.6028	+	6.12153i	0.548992	+	0.316961i	0.748715	−	0.662892i	$-0.230671\pi$
$373$	10.6028	+	6.12153i	0.548992	+	0.316961i	−0.199723	+	0.979852i	$0.564004\pi$
$374$	0.850244	+	1.47267i	0.0439651	+	0.0761498i
$375$		0			0
$376$	−1.06277			−0.0548081
$377$	−7.57154	+	20.4981i	−0.389954	+	1.05571i
$378$		−	0.280281i		−	0.0144161i
$379$	−11.7669	+	6.79362i	−0.604425	+	0.348965i	−0.770780	−	0.637101i	$-0.780133\pi$
$379$	−11.7669	+	6.79362i	−0.604425	+	0.348965i	0.166355	+	0.986066i	$0.446800\pi$
$380$		0			0
$381$	−1.58585	+	2.74678i	−0.0812458	+	0.140722i
$382$	−22.5332			−1.15290
$383$	−7.70686	+	13.3487i	−0.393802	+	0.682086i	−0.992948	−	0.118555i	$-0.962174\pi$
$383$	−7.70686	+	13.3487i	−0.393802	+	0.682086i	0.599145	+	0.800640i	$0.295507\pi$
$384$	−0.866025	−	0.500000i	−0.0441942	−	0.0255155i
$385$		0			0
$386$	4.89181	−	8.47286i	0.248987	−	0.431257i
$387$	3.12533	−	1.80441i	0.158870	−	0.0917234i
$388$	−0.633565	−	1.09737i	−0.0321644	−	0.0557103i
$389$	−6.06059			−0.307284			−0.153642	−	0.988127i	$-0.549100\pi$
$389$	−6.06059			−0.307284			−0.153642	+	0.988127i	$0.549100\pi$
$390$		0			0
$391$	3.22051			0.162868
$392$	3.46072	+	5.99414i	0.174793	+	0.302750i
$393$	13.3667	−	7.71724i	0.674259	−	0.389283i
$394$	−6.22862	+	10.7883i	−0.313794	+	0.543506i
$395$		0			0
$396$	0.663862	+	0.383281i	0.0333603	+	0.0192606i
$397$	−8.49464	+	14.7131i	−0.426334	+	0.738432i	−0.996544	−	0.0830670i	$-0.973528\pi$
$397$	−8.49464	+	14.7131i	−0.426334	+	0.738432i	0.570210	+	0.821499i	$0.306862\pi$
$398$	15.0639			0.755085
$399$	−0.739677	+	1.28116i	−0.0370302	+	0.0641381i
$400$		0			0
$401$	−16.8156	+	9.70852i	−0.839733	+	0.484820i	−0.857174	−	0.515028i	$-0.827782\pi$
$401$	−16.8156	+	9.70852i	−0.839733	+	0.484820i	0.0174403	+	0.999848i	$0.494448\pi$
$402$			7.43584i			0.370866i
$403$	−9.09858	+	7.56101i	−0.453233	+	0.376641i
$404$	4.52747			0.225250
$405$		0			0
$406$	0.849335	+	1.47109i	0.0421518	+	0.0730091i
$407$	−2.35409	−	1.35914i	−0.116688	−	0.0673699i
$408$	−2.21833			−0.109824
$409$	0.803328	+	0.463802i	0.0397220	+	0.0229335i	0.519730	−	0.854331i	$-0.326033\pi$
$409$	0.803328	+	0.463802i	0.0397220	+	0.0229335i	−0.480007	+	0.877264i	$0.659366\pi$
$410$		0			0
$411$		−	1.66829i		−	0.0822907i
$412$	2.54846	+	1.47135i	0.125554	+	0.0724885i
$413$	−1.21313	+	0.700398i	−0.0596940	+	0.0344643i
$414$	1.25727	−	0.725885i	0.0617914	−	0.0356753i
$415$		0			0
$416$	−3.55372	+	0.609166i	−0.174235	+	0.0298668i
$417$		−	2.10790i		−	0.103224i
$418$	−2.02300	−	3.50393i	−0.0989481	−	0.171383i
$419$	−12.5907	−	21.8077i	−0.615096	−	1.06538i	−0.990368	−	0.138463i	$-0.955784\pi$
$419$	−12.5907	−	21.8077i	−0.615096	−	1.06538i	0.375271	−	0.926915i	$-0.377550\pi$
$420$		0			0
$421$			27.6912i			1.34958i	0.738008	+	0.674792i	$0.235767\pi$
$421$			27.6912i			1.34958i	−0.738008	+	0.674792i	$0.764233\pi$
$422$	−7.53876	+	13.0575i	−0.366981	+	0.635630i
$423$	−0.531385	+	0.920385i	−0.0258368	+	0.0447507i
$424$		−	3.28110i		−	0.159344i
$425$		0			0
$426$	1.21135	+	2.09811i	0.0586899	+	0.101654i
$427$	−0.216665	−	0.375275i	−0.0104852	−	0.0181608i
$428$			19.0488i			0.920758i
$429$	2.72415	−	0.466963i	0.131523	−	0.0225452i
$430$		0			0
$431$	0.0798174	−	0.0460826i	0.00384467	−	0.00221972i	−0.498076	−	0.867133i	$-0.665960\pi$
$431$	0.0798174	−	0.0460826i	0.00384467	−	0.00221972i	0.501921	+	0.864913i	$0.332627\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	−3.48337	−	2.01113i	−0.167400	−	0.0966486i	0.413959	−	0.910295i	$-0.364146\pi$
$433$	−3.48337	−	2.01113i	−0.167400	−	0.0966486i	−0.581359	+	0.813647i	$0.697479\pi$
$434$			0.919631i			0.0441437i
$435$		0			0
$436$	−7.83362	−	4.52274i	−0.375162	−	0.216600i
$437$	−7.66259			−0.366552
$438$	−12.3521	−	7.13150i	−0.590207	−	0.340756i
$439$	−12.9742	−	22.4719i	−0.619223	−	1.07253i	−0.989628	−	0.143656i	$-0.954114\pi$
$439$	−12.9742	−	22.4719i	−0.619223	−	1.07253i	0.370404	−	0.928871i	$-0.379219\pi$
$440$		0			0
$441$	6.92144			0.329592
$442$	−6.15150	+	5.11195i	−0.292597	+	0.243151i
$443$		−	15.0646i		−	0.715740i	−0.933771	−	0.357870i	$-0.883503\pi$
$443$		−	15.0646i		−	0.715740i	0.933771	−	0.357870i	$-0.116497\pi$
$444$	3.07097	−	1.77303i	0.145742	−	0.0841442i
$445$		0			0
$446$	2.32817	−	4.03252i	0.110242	−	0.190945i
$447$	5.74079			0.271530
$448$	−0.140141	+	0.242731i	−0.00662102	+	0.0114679i
$449$	−29.8460	−	17.2316i	−1.40852	−	0.813208i	−0.413273	−	0.910607i	$-0.635614\pi$
$449$	−29.8460	−	17.2316i	−1.40852	−	0.813208i	−0.995245	+	0.0973991i	$0.968948\pi$
$450$		0			0
$451$	0.850244	−	1.47267i	0.0400364	−	0.0693451i
$452$		0			0
$453$	8.08549	+	14.0045i	0.379889	+	0.657988i
$454$	6.20436			0.291185
$455$		0			0
$456$	5.27811			0.247170
$457$	−20.8149	−	36.0525i	−0.973680	−	1.68646i	−0.684223	−	0.729273i	$-0.739859\pi$
$457$	−20.8149	−	36.0525i	−0.973680	−	1.68646i	−0.289457	−	0.957191i	$-0.593475\pi$
$458$	11.1379	−	6.43049i	0.520442	−	0.300477i
$459$	−1.10917	+	1.92113i	−0.0517714	+	0.0896707i
$460$		0			0
$461$	6.02737	+	3.47990i	0.280722	+	0.162075i	0.633750	−	0.773538i	$-0.281515\pi$
$461$	6.02737	+	3.47990i	0.280722	+	0.162075i	−0.353028	+	0.935613i	$0.614848\pi$
$462$	0.107426	−	0.186068i	0.00499793	−	0.00865667i
$463$	11.9289			0.554382			0.277191	−	0.960815i	$-0.410597\pi$
$463$	11.9289			0.554382			0.277191	+	0.960815i	$0.410597\pi$
$464$	3.03030	−	5.24863i	0.140678	−	0.243661i
$465$		0			0
$466$	0.840844	−	0.485461i	0.0389513	−	0.0224886i
$467$			34.4406i			1.59372i	0.604164	+	0.796860i	$0.293507\pi$
$467$			34.4406i			1.59372i	−0.604164	+	0.796860i	$0.706493\pi$
$468$	−1.24931	+	3.38219i	−0.0577492	+	0.156342i
$469$	2.08413			0.0962361
$470$		0			0
$471$	−7.92004	−	13.7179i	−0.364936	−	0.632088i
$472$	4.32824	+	2.49891i	0.199224	+	0.115022i
$473$	2.76639			0.127199
$474$	−12.5327	−	7.23574i	−0.575645	−	0.332349i
$475$		0			0
$476$			0.621757i			0.0284982i
$477$	−2.84152	−	1.64055i	−0.130104	−	0.0751156i
$478$	−12.8158	+	7.39922i	−0.586182	+	0.338432i
$479$	11.8896	−	6.86444i	0.543248	−	0.313644i	−0.203146	−	0.979148i	$-0.565117\pi$
$479$	11.8896	−	6.86444i	0.543248	−	0.313644i	0.746394	+	0.665504i	$0.231783\pi$
$480$		0			0
$481$	4.43011	−	11.9934i	0.201996	−	0.546854i
$482$		−	2.19157i		−	0.0998231i
$483$	−0.203452	−	0.352389i	−0.00925738	−	0.0160343i
$484$	−5.20619	−	9.01739i	−0.236645	−	0.409881i
$485$		0			0
$486$			1.00000i			0.0453609i
$487$	−4.76489	+	8.25303i	−0.215918	+	0.373981i	−0.953556	−	0.301215i	$-0.902608\pi$
$487$	−4.76489	+	8.25303i	−0.215918	+	0.373981i	0.737638	+	0.675196i	$0.235941\pi$
$488$	−0.773028	+	1.33892i	−0.0349933	+	0.0606102i
$489$			11.3148i			0.511673i
$490$		0			0
$491$	16.7409	+	28.9960i	0.755505	+	1.30857i	0.945123	+	0.326715i	$0.105942\pi$
$491$	16.7409	+	28.9960i	0.755505	+	1.30857i	−0.189618	+	0.981858i	$0.560725\pi$
$492$	1.10917	+	1.92113i	0.0500051	+	0.0866113i
$493$		−	13.4444i		−	0.605506i
$494$	14.6363	−	12.1629i	0.658520	−	0.547236i
$495$		0			0
$496$	2.84152	−	1.64055i	0.127588	−	0.0736629i
$497$	0.588062	−	0.339518i	0.0263782	−	0.0152294i
$498$	3.83146	+	2.21209i	0.171692	+	0.0991262i
$499$			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
$502$	−10.5897			−0.472643
$503$	−16.8861	−	9.74919i	−0.752914	−	0.434695i	0.0738319	−	0.997271i	$-0.476477\pi$
$503$	−16.8861	−	9.74919i	−0.752914	−	0.434695i	−0.826746	+	0.562576i	$0.809811\pi$
$504$	0.140141	+	0.242731i	0.00624236	+	0.0108121i
$505$		0			0
$506$	1.11287			0.0494732
$507$	4.32961	+	12.2578i	0.192285	+	0.544390i
$508$		−	3.17171i		−	0.140722i
$509$	−29.5101	+	17.0377i	−1.30801	+	0.755181i	−0.981764	−	0.190103i	$-0.939118\pi$
$509$	−29.5101	+	17.0377i	−1.30801	+	0.755181i	−0.326248	+	0.945284i	$0.605785\pi$
$510$		0			0
$511$	−1.99883	+	3.46207i	−0.0884228	+	0.153153i
$512$	1.00000			0.0441942
$513$	2.63905	−	4.57097i	0.116517	−	0.201813i
$514$	−5.93047	−	3.42396i	−0.261582	−	0.151024i
$515$		0			0
$516$	−1.80441	+	3.12533i	−0.0794348	+	0.137585i
$517$	−0.705532	+	0.407339i	−0.0310293	+	0.0179148i
$518$	−0.496946	−	0.860736i	−0.0218346	−	0.0378186i
$519$	−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	$0.507714\pi$
$522$	−3.03030	−	5.24863i	−0.132633	−	0.229726i
$523$	−9.23044	+	5.32920i	−0.403619	+	0.233030i	−0.688044	−	0.725669i	$-0.741531\pi$
$523$	−9.23044	+	5.32920i	−0.403619	+	0.233030i	0.284425	+	0.958698i	$0.408197\pi$
$524$	−7.71724	+	13.3667i	−0.337129	+	0.583925i
$525$		0			0
$526$	22.7212	+	13.1181i	0.990693	+	0.571977i
$527$	3.63928	−	6.30343i	0.158530	−	0.274582i
$528$	−0.766562			−0.0333603
$529$	−10.4462	+	18.0933i	−0.454182	+	0.786666i
$530$		0			0
$531$	4.32824	−	2.49891i	0.187830	−	0.108444i
$532$		−	1.47935i		−	0.0641381i
$533$	7.50283	+	2.77138i	0.324983	+	0.120042i
$534$	−5.31479			−0.229994
$535$		0			0
$536$	−3.71792	−	6.43963i	−0.160590	−	0.278150i
$537$	−21.8699	−	12.6266i	−0.943755	−	0.544877i
$538$	−6.49875			−0.280181
$539$	4.59488	+	2.65286i	0.197916	+	0.114267i
$540$		0			0
$541$			38.1486i			1.64013i	0.572267	+	0.820067i	$0.306064\pi$
$541$			38.1486i			1.64013i	−0.572267	+	0.820067i	$0.693936\pi$
$542$	−5.35904	−	3.09404i	−0.230191	−	0.132901i
$543$	−0.272618	+	0.157396i	−0.0116992	+	0.00675452i
$544$	1.92113	−	1.10917i	0.0823678	−	0.0475551i
$545$		0			0
$546$	0.947965	+	0.350157i	0.0405692	+	0.0149853i
$547$			26.9609i			1.15277i	0.817180	+	0.576383i	$0.195536\pi$
$547$			26.9609i			1.15277i	−0.817180	+	0.576383i	$0.804464\pi$
$548$	0.834145	+	1.44478i	0.0356329	+	0.0617180i
$549$	0.773028	+	1.33892i	0.0329920	+	0.0571439i
$550$		0			0
$551$			31.9885i			1.36275i
$552$	−0.725885	+	1.25727i	−0.0308957	+	0.0535129i
$553$	−2.02804	+	3.51267i	−0.0862411	+	0.149374i
$554$			29.0577i			1.23454i
$555$		0			0
$556$	1.05395	+	1.82549i	0.0446974	+	0.0774182i
$557$	17.6236	+	30.5249i	0.746735	+	1.29338i	0.949380	+	0.314130i	$0.101713\pi$
$557$	17.6236	+	30.5249i	0.746735	+	1.29338i	−0.202645	+	0.979252i	$0.564954\pi$
$558$		−	3.28110i		−	0.138900i
$559$	2.19837	+	12.8247i	0.0929812	+	0.542429i
$560$		0			0
$561$	−1.47267	+	0.850244i	−0.0621760	+	0.0358973i
$562$	12.2489	−	7.07188i	0.516687	−	0.298309i
$563$	−14.7368	−	8.50830i	−0.621082	−	0.358582i	0.156208	−	0.987724i	$-0.450073\pi$
$563$	−14.7368	−	8.50830i	−0.621082	−	0.358582i	−0.777290	+	0.629142i	$0.783406\pi$
$564$		−	1.06277i		−	0.0447507i
$565$		0			0
$566$	−7.57409	−	4.37290i	−0.318363	−	0.183807i
$567$	0.280281			0.0117707
$568$	−2.09811	−	1.21135i	−0.0880349	−	0.0508270i
$569$	−17.6968	−	30.6518i	−0.741889	−	1.28499i	−0.951634	−	0.307233i	$-0.900597\pi$
$569$	−17.6968	−	30.6518i	−0.741889	−	1.28499i	0.209746	−	0.977756i	$-0.432736\pi$
$570$		0			0
$571$	−17.5185			−0.733125			−0.366563	−	0.930393i	$-0.619465\pi$
$571$	−17.5185			−0.733125			−0.366563	+	0.930393i	$0.619465\pi$
$572$	−2.12570	+	1.76647i	−0.0888799	+	0.0738600i
$573$		−	22.5332i		−	0.941339i
$574$	0.538457	−	0.310878i	0.0224748	−	0.0129758i
$575$		0			0
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−26.6215			−1.10827			−0.554133	−	0.832428i	$-0.686950\pi$
$577$	−26.6215			−1.10827			−0.554133	+	0.832428i	$0.686950\pi$
$578$	−6.03950	+	10.4607i	−0.251210	+	0.435109i
$579$	8.47286	+	4.89181i	0.352120	+	0.203297i
$580$		0			0
$581$	0.620008	−	1.07389i	0.0257223	−	0.0445523i
$582$	1.09737	−	0.633565i	0.0454873	−	0.0262621i
$583$	−1.25758	−	2.17820i	−0.0520838	−	0.0902118i
$584$	14.2630			0.590207
$585$		0			0
$586$	31.5001			1.30126
$587$	−8.32051	−	14.4115i	−0.343424	−	0.594828i	0.641642	−	0.767004i	$-0.278254\pi$
$587$	−8.32051	−	14.4115i	−0.343424	−	0.594828i	−0.985066	+	0.172176i	$0.944920\pi$
$588$	−5.99414	+	3.46072i	−0.247194	+	0.142718i
$589$	−8.65900	+	14.9978i	−0.356788	+	0.617975i
$590$		0			0
$591$	−10.7883	−	6.22862i	−0.443771	−	0.256211i
$592$	−1.77303	+	3.07097i	−0.0728710	+	0.126216i
$593$	24.7460			1.01620			0.508098	−	0.861300i	$-0.330349\pi$
$593$	24.7460			1.01620			0.508098	+	0.861300i	$0.330349\pi$
$594$	−0.383281	+	0.663862i	−0.0157262	+	0.0272386i
$595$		0			0
$596$	−4.97167	+	2.87039i	−0.203647	+	0.117576i
$597$			15.0639i			0.616524i
$598$	0.884368	+	5.15918i	0.0361645	+	0.210975i
$599$	23.2517			0.950037			0.475019	−	0.879976i	$-0.342441\pi$
$599$	23.2517			0.950037			0.475019	+	0.879976i	$0.342441\pi$
$600$		0			0
$601$	−16.5985	−	28.7494i	−0.677067	−	1.17271i	−0.975860	−	0.218396i	$-0.929917\pi$
$601$	−16.5985	−	28.7494i	−0.677067	−	1.17271i	0.298793	−	0.954318i	$-0.403416\pi$
$602$	0.875972	+	0.505743i	0.0357020	+	0.0206125i
$603$	−7.43584			−0.302811
$604$	−14.0045	−	8.08549i	−0.569834	−	0.328994i
$605$		0			0
$606$			4.52747i			0.183916i
$607$	34.1440	+	19.7130i	1.38586	+	0.800128i	0.992846	−	0.119404i	$-0.0380984\pi$
$607$	34.1440	+	19.7130i	1.38586	+	0.800128i	0.393016	+	0.919532i	$0.371432\pi$
$608$	−4.57097	+	2.63905i	−0.185377	+	0.107028i
$609$	−1.47109	+	0.849335i	−0.0596117	+	0.0344168i
$610$		0			0
$611$	−2.44906	−	2.94709i	−0.0990783	−	0.119226i
$612$		−	2.21833i		−	0.0896707i
$613$	5.21398	+	9.03087i	0.210591	+	0.364753i	0.951899	−	0.306410i	$-0.0991280\pi$
$613$	5.21398	+	9.03087i	0.210591	+	0.364753i	−0.741309	+	0.671164i	$0.765795\pi$
$614$	3.51576	+	6.08947i	0.141884	+	0.245751i
$615$		0			0
$616$			0.214853i			0.00865667i
$617$	−10.1304	+	17.5464i	−0.407836	+	0.706393i	−0.994647	−	0.103331i	$-0.967050\pi$
$617$	−10.1304	+	17.5464i	−0.407836	+	0.706393i	0.586811	+	0.809724i	$0.300383\pi$
$618$	−1.47135	+	2.54846i	−0.0591866	+	0.102514i
$619$		−	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
$622$	−4.39922	−	7.61967i	−0.176393	−	0.305521i
$623$			1.48964i			0.0596810i
$624$	−0.609166	−	3.55372i	−0.0243861	−	0.142263i
$625$		0			0
$626$	−8.08984	+	4.67067i	−0.323335	+	0.186677i
$627$	3.50393	−	2.02300i	0.139934	−	0.0807907i
$628$	13.7179	+	7.92004i	0.547405	+	0.316044i
$629$			7.86633i			0.313651i
$630$		0			0
$631$	−31.6461	−	18.2709i	−1.25981	−	0.727352i	−0.286773	−	0.957999i	$-0.592583\pi$
$631$	−31.6461	−	18.2709i	−1.25981	−	0.727352i	−0.973038	+	0.230646i	$0.925916\pi$
$632$	14.4715			0.575645
$633$	−13.0575	−	7.53876i	−0.518989	−	0.299639i
$634$	9.73484	+	16.8612i	0.386620	+	0.669645i
$635$		0			0
$636$	3.28110			0.130104
$637$	−8.64700	+	23.4097i	−0.342607	+	0.927524i
$638$		−	4.64582i		−	0.183930i
$639$	−2.09811	+	1.21135i	−0.0830001	+	0.0479201i
$640$		0			0
$641$	−21.9295	+	37.9830i	−0.866163	+	1.50024i	−0.000274574		1.00000i	$0.500087\pi$
$641$	−21.9295	+	37.9830i	−0.866163	+	1.50024i	−0.865888	+	0.500238i	$0.833246\pi$
$642$	−19.0488			−0.751796
$643$	8.32615	−	14.4213i	0.328351	−	0.568721i	−0.653834	−	0.756638i	$-0.726840\pi$
$643$	8.32615	−	14.4213i	0.328351	−	0.568721i	0.982185	+	0.187917i	$0.0601737\pi$
$644$	0.352389	+	0.203452i	0.0138861	+	0.00801713i
$645$		0			0
$646$	−5.85429	+	10.1399i	−0.230334	+	0.398950i
$647$	−8.13271	+	4.69543i	−0.319730	+	0.184596i	−0.651272	−	0.758844i	$-0.725764\pi$
$647$	−8.13271	+	4.69543i	−0.319730	+	0.184596i	0.331542	+	0.943440i	$0.392431\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	3.83114			0.150386
$650$		0			0
$651$	−0.919631			−0.0360432
$652$	−5.65740	−	9.79890i	−0.221561	−	0.383754i
$653$	−35.6061	+	20.5572i	−1.39337	+	0.804465i	−0.993687	−	0.112187i	$-0.964214\pi$
$653$	−35.6061	+	20.5572i	−1.39337	+	0.804465i	−0.399686	+	0.916652i	$0.630881\pi$
$654$	4.52274	−	7.83362i	0.176853	−	0.306319i
$655$		0			0
$656$	−1.92113	−	1.10917i	−0.0750076	−	0.0433056i
$657$	7.13150	−	12.3521i	0.278226	−	0.481902i
$658$	−0.297874			−0.0116123
$659$	−1.72663	+	2.99061i	−0.0672600	+	0.116498i	−0.897694	−	0.440619i	$-0.854759\pi$
$659$	−1.72663	+	2.99061i	−0.0672600	+	0.116498i	0.830434	+	0.557117i	$0.188092\pi$
$660$		0			0
$661$	21.3306	−	12.3152i	0.829665	−	0.479007i	−0.0240732	−	0.999710i	$-0.507663\pi$
$661$	21.3306	−	12.3152i	0.829665	−	0.479007i	0.853738	+	0.520703i	$0.174330\pi$
$662$		−	18.9464i		−	0.736373i
$663$	−5.11195	−	6.15150i	−0.198532	−	0.238904i
$664$	−4.42419			−0.171692
$665$		0			0
$666$	1.77303	+	3.07097i	0.0687034	+	0.118998i
$667$	−7.61980	−	4.39929i	−0.295040	−	0.170341i
$668$	−1.45177			−0.0561707
$669$	4.03252	+	2.32817i	0.155906	+	0.0900124i
$670$		0			0
$671$			1.18515i			0.0457521i
$672$	−0.242731	−	0.140141i	−0.00936354	−	0.00540604i
$673$	14.7580	−	8.52052i	0.568878	−	0.328442i	−0.187823	−	0.982203i	$-0.560143\pi$
$673$	14.7580	−	8.52052i	0.568878	−	0.328442i	0.756701	+	0.653761i	$0.226810\pi$
$674$	−2.36395	+	1.36483i	−0.0910560	+	0.0525712i
$675$		0			0
$676$	−9.87847	−	8.45079i	−0.379941	−	0.325030i
$677$		−	16.6324i		−	0.639236i	−0.947546	−	0.319618i	$-0.896445\pi$
$677$		−	16.6324i		−	0.639236i	0.947546	−	0.319618i	$-0.103555\pi$
$678$		0			0
$679$	−0.177576	−	0.307571i	−0.00681475	−	0.0118035i
$680$		0			0
$681$			6.20436i			0.237752i
$682$	1.25758	−	2.17820i	0.0481554	−	0.0834075i
$683$	24.4365	−	42.3252i	0.935035	−	1.61953i	0.160463	−	0.987042i	$-0.448701\pi$
$683$	24.4365	−	42.3252i	0.935035	−	1.61953i	0.774572	−	0.632486i	$-0.217965\pi$
$684$			5.27811i			0.201813i
$685$		0			0
$686$	1.95096	+	3.37916i	0.0744880	+	0.129017i
$687$	6.43049	+	11.1379i	0.245339	+	0.424939i
$688$		−	3.60882i		−	0.137585i
$689$	9.09858	−	7.56101i	0.346628	−	0.288051i
$690$		0			0
$691$	31.0699	−	17.9382i	1.18195	−	0.682401i	0.225488	−	0.974246i	$-0.427602\pi$
$691$	31.0699	−	17.9382i	1.18195	−	0.682401i	0.956466	+	0.291845i	$0.0942690\pi$
$692$	11.5530	−	6.67010i	0.439177	−	0.253559i
$693$	0.186068	+	0.107426i	0.00706814	+	0.00408079i
$694$		−	12.6920i		−	0.481781i
$695$		0			0
$696$	5.24863	+	3.03030i	0.198949	+	0.114863i
$697$	−4.92099			−0.186396
$698$	1.04906	+	0.605676i	0.0397075	+	0.0229252i
$699$	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	$0.699287\pi$
$702$	−3.38219	−	1.24931i	−0.127653	−	0.0471520i
$703$		−	18.7165i		−	0.705905i
$704$	0.663862	−	0.383281i	0.0250202	−	0.0144454i
$705$		0			0
$706$	16.7901	−	29.0813i	0.631904	−	1.09449i
$707$	1.26896			0.0477243
$708$	−2.49891	+	4.32824i	−0.0939149	+	0.162665i
$709$	−9.78339	−	5.64844i	−0.367423	−	0.212132i	0.304909	−	0.952381i	$-0.401374\pi$
$709$	−9.78339	−	5.64844i	−0.367423	−	0.212132i	−0.672332	+	0.740250i	$0.734707\pi$
$710$		0			0
$711$	7.23574	−	12.5327i	0.271362	−	0.470012i
$712$	4.60275	−	2.65740i	0.172495	−	0.0995901i
$713$	−2.38170	−	4.12523i	−0.0891954	−	0.154491i
$714$	−0.621757			−0.0232687
$715$		0			0
$716$	25.2532			0.943755
$717$	−7.39922	−	12.8158i	−0.276329	−	0.478616i
$718$	−19.0892	+	11.0211i	−0.712401	+	0.411305i
$719$	6.01084	−	10.4111i	0.224167	−	0.388268i	−0.731902	−	0.681409i	$-0.761367\pi$
$719$	6.01084	−	10.4111i	0.224167	−	0.388268i	0.956069	+	0.293141i	$0.0947007\pi$
$720$		0			0
$721$	0.714286	+	0.412393i	0.0266014	+	0.0153583i
$722$	4.42920	−	7.67161i	0.164838	−	0.285508i
$723$	2.19157			0.0815052
$724$	0.157396	−	0.272618i	0.00584958	−	0.0101318i
$725$		0			0
$726$	9.01739	−	5.20619i	0.334667	−	0.193220i
$727$		−	4.18908i		−	0.155364i	−0.996978	−	0.0776822i	$-0.975248\pi$
$727$		−	4.18908i		−	0.155364i	0.996978	−	0.0776822i	$-0.0247519\pi$
$728$	−0.996041	+	0.170738i	−0.0369157	+	0.00632796i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−4.00278	−	6.93303i	−0.148048	−	0.256427i
$732$	−1.33892	−	0.773028i	−0.0494880	−	0.0285719i
$733$	11.3923			0.420783			0.210391	−	0.977617i	$-0.432526\pi$
$733$	11.3923			0.420783			0.210391	+	0.977617i	$0.432526\pi$
$734$	8.36421	+	4.82908i	0.308729	+	0.178244i
$735$		0			0
$736$		−	1.45177i		−	0.0535129i
$737$	−4.93637	−	2.85002i	−0.181834	−	0.104982i
$738$	−1.92113	+	1.10917i	−0.0707178	+	0.0408290i
$739$	17.6996	−	10.2189i	0.651090	−	0.375907i	−0.137783	−	0.990462i	$-0.543998\pi$
$739$	17.6996	−	10.2189i	0.651090	−	0.375907i	0.788874	+	0.614555i	$0.210664\pi$
$740$		0			0
$741$	12.1629	+	14.6363i	0.446817	+	0.537679i
$742$		−	0.919631i		−	0.0337607i
$743$	5.07638	+	8.79255i	0.186234	+	0.322567i	0.943992	−	0.329969i	$-0.107038\pi$
$743$	5.07638	+	8.79255i	0.186234	+	0.322567i	−0.757757	+	0.652536i	$0.773705\pi$
$744$	1.64055	+	2.84152i	0.0601455	+	0.104175i
$745$		0			0
$746$		−	12.2431i		−	0.448250i
$747$	−2.21209	+	3.83146i	−0.0809362	+	0.140186i
$748$	0.850244	−	1.47267i	0.0310880	−	0.0538460i
$749$			5.33902i			0.195083i
$750$		0			0
$751$	−8.99084	−	15.5726i	−0.328080	−	0.568252i	0.654051	−	0.756451i	$-0.273068\pi$
$751$	−8.99084	−	15.5726i	−0.328080	−	0.568252i	−0.982131	+	0.188199i	$0.939735\pi$
$752$	0.531385	+	0.920385i	0.0193776	+	0.0335630i
$753$		−	10.5897i		−	0.385911i
$754$	21.5376	−	3.69191i	0.784355	−	0.134451i
$755$		0			0
$756$	−0.242731	+	0.140141i	−0.00882803	+	0.00509686i
$757$	38.9566	−	22.4916i	1.41590	−	0.817470i	0.419965	−	0.907540i	$-0.362042\pi$
$757$	38.9566	−	22.4916i	1.41590	−	0.817470i	0.995935	+	0.0900700i	$0.0287091\pi$
$758$	11.7669	+	6.79362i	0.427393	+	0.246755i
$759$			1.11287i			0.0403947i
$760$		0			0
$761$	−39.1697	−	22.6146i	−1.41990	−	0.819779i	−0.423610	−	0.905845i	$-0.639237\pi$
$761$	−39.1697	−	22.6146i	−1.41990	−	0.819779i	−0.996289	+	0.0860657i	$0.972571\pi$
$762$	3.17171			0.114899
$763$	−2.19562	−	1.26764i	−0.0794867	−	0.0458917i
$764$	11.2666	+	19.5143i	0.407612	+	0.706004i
$765$		0			0
$766$	15.4137			0.556921
$767$	3.04450	+	17.7609i	0.109931	+	0.641308i
$768$			1.00000i			0.0360844i
$769$	−31.3010	+	18.0716i	−1.12874	+	0.651680i	−0.943619	−	0.331035i	$-0.892602\pi$
$769$	−31.3010	+	18.0716i	−1.12874	+	0.651680i	−0.185125	+	0.982715i	$0.559269\pi$
$770$		0			0
$771$	3.42396	−	5.93047i	0.123311	−	0.213581i
$772$	−9.78362			−0.352120
$773$	8.18850	−	14.1829i	0.294520	−	0.510123i	−0.680353	−	0.732884i	$-0.738174\pi$
$773$	8.18850	−	14.1829i	0.294520	−	0.510123i	0.974873	+	0.222761i	$0.0715070\pi$
$774$	−3.12533	−	1.80441i	−0.112338	−	0.0648583i
$775$		0			0
$776$	−0.633565	+	1.09737i	−0.0227437	+	0.0393932i
$777$	0.860736	−	0.496946i	0.0308787	−	0.0178279i
$778$	3.03030	+	5.24863i	0.108641	+	0.188172i
$779$	11.7086			0.419504
$780$		0			0
$781$	−1.85714			−0.0664538
$782$	−1.61025	−	2.78904i	−0.0575825	−	0.0997359i
$783$	5.24863	−	3.03030i	0.187571	−	0.108294i
$784$	3.46072	−	5.99414i	0.123597	−	0.214077i
$785$		0			0
$786$	−13.3667	−	7.71724i	−0.476773	−	0.275265i
$787$	22.5807	−	39.1108i	0.804913	−	1.39415i	−0.111436	−	0.993772i	$-0.535545\pi$
$787$	22.5807	−	39.1108i	0.804913	−	1.39415i	0.916350	−	0.400379i	$-0.131122\pi$
$788$	12.4572			0.443771
$789$	−13.1181	+	22.7212i	−0.467017	+	0.808898i
$790$		0			0
$791$		0			0
$792$		−	0.766562i		−	0.0272386i
$793$	−5.49425	+	0.941804i	−0.195106	+	0.0334444i
$794$	16.9893			0.602927
$795$		0			0
$796$	−7.53195	−	13.0457i	−0.266963	−	0.462393i
$797$	−23.3511	−	13.4818i	−0.827139	−	0.477549i	0.0257329	−	0.999669i	$-0.491808\pi$
$797$	−23.3511	−	13.4818i	−0.827139	−	0.477549i	−0.852872	+	0.522120i	$0.825141\pi$
$798$	1.47935			0.0523686
$799$	2.04172	+	1.17879i	0.0722308	+	0.0417025i
$800$		0			0
$801$		−	5.31479i		−	0.187789i
$802$	16.8156	+	9.70852i	0.593781	+	0.342820i
$803$	9.46867	−	5.46674i	0.334142	−	0.192917i
$804$	6.43963	−	3.71792i	0.227108	−	0.131121i
$805$		0			0
$806$	11.0973	+	4.09910i	0.390886	+	0.144385i
$807$		−	6.49875i		−	0.228767i
$808$	−2.26374	−	3.92090i	−0.0796379	−	0.137937i
$809$	−5.02204	−	8.69843i	−0.176566	−	0.305821i	0.764136	−	0.645055i	$-0.223165\pi$
$809$	−5.02204	−	8.69843i	−0.176566	−	0.305821i	−0.940702	+	0.339234i	$0.889832\pi$
$810$		0			0
$811$		−	26.8449i		−	0.942652i	−0.881959	−	0.471326i	$-0.843776\pi$
$811$		−	26.8449i		−	0.942652i	0.881959	−	0.471326i	$-0.156224\pi$
$812$	0.849335	−	1.47109i	0.0298058	−	0.0516252i
$813$	3.09404	−	5.35904i	0.108513	−	0.187950i
$814$			2.71827i			0.0952754i
$815$		0			0
$816$	1.10917	+	1.92113i	0.0388286	+	0.0672531i
$817$	9.52388	+	16.4958i	0.333198	+	0.577117i
$818$		−	0.927603i		−	0.0324329i
$819$	−0.350157	+	0.947965i	−0.0122355	+	0.0331246i
$820$		0			0
$821$	−28.4214	+	16.4091i	−0.991912	+	0.572681i	−0.905845	−	0.423609i	$-0.860763\pi$
$821$	−28.4214	+	16.4091i	−0.991912	+	0.572681i	−0.0860669	+	0.996289i	$0.527430\pi$
$822$	−1.44478	+	0.834145i	−0.0503925	+	0.0290941i
$823$	7.68249	+	4.43549i	0.267795	+	0.154611i	0.627885	−	0.778306i	$-0.283921\pi$
$823$	7.68249	+	4.43549i	0.267795	+	0.154611i	−0.360090	+	0.932917i	$0.617254\pi$
$824$		−	2.94271i		−	0.102514i
$825$		0			0
$826$	1.21313	+	0.700398i	0.0422100	+	0.0243700i
$827$	−0.892425			−0.0310327			−0.0155163	−	0.999880i	$-0.504939\pi$
$827$	−0.892425			−0.0310327			−0.0155163	+	0.999880i	$0.504939\pi$
$828$	−1.25727	−	0.725885i	−0.0436931	−	0.0252262i
$829$	5.74291	+	9.94701i	0.199459	+	0.345474i	0.948353	−	0.317216i	$-0.102748\pi$
$829$	5.74291	+	9.94701i	0.199459	+	0.345474i	−0.748894	+	0.662690i	$0.769415\pi$
$830$		0			0
$831$	−29.0577			−1.00800
$832$	2.30441	+	2.77303i	0.0798911	+	0.0961374i
$833$		−	15.3541i		−	0.531986i
$834$	−1.82549	+	1.05395i	−0.0632117	+	0.0364953i
$835$		0			0
$836$	−2.02300	+	3.50393i	−0.0699668	+	0.121186i
$837$	3.28110			0.113411
$838$	−12.5907	+	21.8077i	−0.434939	+	0.753336i
$839$	−24.1738	−	13.9568i	−0.834573	−	0.481841i	0.0208426	−	0.999783i	$-0.493365\pi$
$839$	−24.1738	−	13.9568i	−0.834573	−	0.481841i	−0.855416	+	0.517942i	$0.826698\pi$
$840$		0			0
$841$	−3.86540	+	6.69507i	−0.133290	+	0.230865i
$842$	23.9812	−	13.8456i	0.826448	−	0.477150i
$843$	7.07188	+	12.2489i	0.243568	+	0.421873i
$844$	15.0775			0.518989
$845$		0			0
$846$	1.06277			0.0365388
$847$	−1.45920	−	2.52740i	−0.0501386	−	0.0868426i
$848$	−2.84152	+	1.64055i	−0.0975781	+	0.0563367i
$849$	4.37290	−	7.57409i	0.150078	−	0.259942i
$850$		0			0
$851$	4.45835	+	2.57403i	0.152830	+	0.0882365i
$852$	1.21135	−	2.09811i	0.0415000	−	0.0718802i
$853$	−41.6937			−1.42757			−0.713783	−	0.700367i	$-0.753020\pi$
$853$	−41.6937			−1.42757			−0.713783	+	0.700367i	$0.753020\pi$
$854$	−0.216665	+	0.375275i	−0.00741413	+	0.0128417i
$855$		0			0
$856$	16.4967	−	9.52440i	0.563847	−	0.325537i
$857$			4.57772i			0.156372i	0.996939	+	0.0781860i	$0.0249128\pi$
$857$			4.57772i			0.156372i	−0.996939	+	0.0781860i	$0.975087\pi$
$858$	−1.76647	−	2.12570i	−0.0603065	−	0.0725701i
$859$	32.0617			1.09393			0.546966	−	0.837155i	$-0.315783\pi$
$859$	32.0617			1.09393			0.546966	+	0.837155i	$0.315783\pi$
$860$		0			0
$861$	0.310878	+	0.538457i	0.0105947	+	0.0183506i
$862$	−0.0798174	−	0.0460826i	−0.00271859	−	0.00156958i
$863$	30.7876			1.04802			0.524011	−	0.851711i	$-0.324435\pi$
$863$	30.7876			1.04802			0.524011	+	0.851711i	$0.324435\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$		0			0
$866$			4.02225i			0.136682i
$867$	−10.4607	−	6.03950i	−0.355265	−	0.205112i
$868$	0.796424	−	0.459815i	0.0270324	−	0.0156072i
$869$	9.60707	−	5.54664i	0.325898	−	0.188157i
$870$		0			0
$871$	9.28965	−	25.1495i	0.314768	−	0.852157i
$872$			9.04549i			0.306319i
$873$	0.633565	+	1.09737i	0.0214429	+	0.0371402i
$874$	3.83130	+	6.63600i	0.129596	+	0.224466i
$875$		0			0
$876$			14.2630i			0.481902i
$877$	20.3902	−	35.3169i	0.688529	−	1.19257i	−0.283785	−	0.958888i	$-0.591590\pi$
$877$	20.3902	−	35.3169i	0.688529	−	1.19257i	0.972314	−	0.233679i	$-0.0750764\pi$
$878$	−12.9742	+	22.4719i	−0.437857	+	0.758391i
$879$			31.5001i			1.06247i
$880$		0			0
$881$	−21.4928	−	37.2265i	−0.724109	−	1.25419i	−0.959340	−	0.282254i	$-0.908918\pi$
$881$	−21.4928	−	37.2265i	−0.724109	−	1.25419i	0.235230	−	0.971940i	$-0.424416\pi$
$882$	−3.46072	−	5.99414i	−0.116529	−	0.201833i
$883$		−	29.9139i		−	1.00668i	−0.864088	−	0.503341i	$-0.832104\pi$
$883$		−	29.9139i		−	1.00668i	0.864088	−	0.503341i	$-0.167896\pi$
$884$	7.50283	+	2.77138i	0.252347	+	0.0932115i
$885$		0			0
$886$	−13.0463	+	7.53229i	−0.438299	+	0.253052i
$887$	40.6116	−	23.4471i	1.36360	−	0.787278i	0.373503	−	0.927629i	$-0.378157\pi$
$887$	40.6116	−	23.4471i	1.36360	−	0.787278i	0.990102	+	0.140351i	$0.0448232\pi$
$888$	−3.07097	−	1.77303i	−0.103055	−	0.0594989i
$889$		−	0.888970i		−	0.0298151i
$890$		0			0
$891$	−0.663862	−	0.383281i	−0.0222402	−	0.0128404i
$892$	−4.65635			−0.155906
$893$	−4.85789	−	2.80470i	−0.162563	−	0.0938558i
$894$	−2.87039	−	4.97167i	−0.0960004	−	0.166277i
$895$		0			0
$896$	0.280281			0.00936354
$897$	−5.15918	+	0.884368i	−0.172260	+	0.0295282i
$898$			34.4631i			1.15005i
$899$	−17.2213	+	9.94271i	−0.574362	+	0.331608i
$900$		0			0
$901$	−3.63928	+	6.30343i	−0.121242	+	0.209998i
$902$	−1.70049			−0.0566201
$903$	−0.505743	+	0.875972i	−0.0168301	+	0.0291505i
$904$		0			0
$905$		0			0
$906$	8.08549	−	14.0045i	0.268622	−	0.465268i
$907$	23.1269	−	13.3523i	0.767915	−	0.443356i	−0.0642155	−	0.997936i	$-0.520454\pi$
$907$	23.1269	−	13.3523i	0.767915	−	0.443356i	0.832130	+	0.554580i	$0.187121\pi$
$908$	−3.10218	−	5.37313i	−0.102949	−	0.178314i
$909$	−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	$0.341450\pi$
$912$	−2.63905	−	4.57097i	−0.0873878	−	0.151360i
$913$	−2.93705	+	1.69571i	−0.0972021	+	0.0561197i
$914$	−20.8149	+	36.0525i	−0.688496	+	1.19251i
$915$		0			0
$916$	−11.1379	−	6.43049i	−0.368008	−	0.212469i
$917$	−2.16300	+	3.74642i	−0.0714285	+	0.123718i
$918$	2.21833			0.0732158
$919$	14.4493	−	25.0269i	0.476637	−	0.825560i	−0.523005	−	0.852330i	$-0.675189\pi$
$919$	14.4493	−	25.0269i	0.476637	−	0.825560i	0.999642	+	0.0267702i	$0.00852225\pi$
$920$		0			0
$921$	−6.08947	+	3.51576i	−0.200655	+	0.115848i
$922$		−	6.95980i		−	0.229209i
$923$	−1.47582	−	8.60957i	−0.0485772	−	0.283387i
$924$	−0.214853			−0.00706814
$925$		0			0
$926$	−5.96444	−	10.3307i	−0.196004	−	0.339488i
$927$	−2.54846	−	1.47135i	−0.0837025	−	0.0483256i
$928$	−6.06059			−0.198949
$929$	37.8896	+	21.8756i	1.24312	+	0.717715i	0.969728	−	0.244188i	$-0.0785215\pi$
$929$	37.8896	+	21.8756i	1.24312	+	0.717715i	0.273391	+	0.961903i	$0.411855\pi$
$930$		0			0
$931$			36.5321i			1.19729i
$932$	−0.840844	−	0.485461i	−0.0275428	−	0.0159018i
$933$	7.61967	−	4.39922i	0.249457	−	0.144024i
$934$	29.8264	−	17.2203i	0.975950	−	0.563465i
$935$		0			0
$936$	3.55372	−	0.609166i	0.116157	−	0.0199112i
$937$			6.71836i			0.219479i	0.993960	+	0.109740i	$0.0350017\pi$
$937$			6.71836i			0.219479i	−0.993960	+	0.109740i	$0.964998\pi$
$938$	−1.04206	−	1.80491i	−0.0340246	−	0.0589323i
$939$	−4.67067	−	8.08984i	−0.152422	−	0.264002i
$940$		0			0
$941$			33.9654i			1.10724i	0.832769	+	0.553621i	$0.186754\pi$
$941$			33.9654i			1.10724i	−0.832769	+	0.553621i	$0.813246\pi$
$942$	−7.92004	+	13.7179i	−0.258049	+	0.446954i
$943$	−1.61025	+	2.78904i	−0.0524371	+	0.0908236i
$944$		−	4.99783i		−	0.162665i
$945$		0			0
$946$	−1.38319	−	2.39576i	−0.0449715	−	0.0778929i
$947$	20.3751	+	35.2907i	0.662101	+	1.14679i	0.980063	+	0.198689i	$0.0636683\pi$
$947$	20.3751	+	35.2907i	0.662101	+	1.14679i	−0.317962	+	0.948104i	$0.602998\pi$
$948$			14.4715i			0.470012i
$949$	32.8678	+	39.5517i	1.06694	+	1.28390i
$950$		0			0
$951$	−16.8612	+	9.73484i	−0.546763	+	0.315674i
$952$	0.538457	−	0.310878i	0.0174515	−	0.0100756i
$953$	−5.23614	−	3.02309i	−0.169615	−	0.0979274i	0.412789	−	0.910827i	$-0.364555\pi$
$953$	−5.23614	−	3.02309i	−0.169615	−	0.0979274i	−0.582404	+	0.812899i	$0.697888\pi$
$954$			3.28110i			0.106230i
$955$		0			0
$956$	12.8158	+	7.39922i	0.414493	+	0.239308i
$957$	4.64582			0.150178
$958$	−11.8896	−	6.86444i	−0.384134	−	0.221780i
$959$	0.233795	+	0.404945i	0.00754964	+	0.0130764i
$960$		0			0
$961$	20.2344			0.652722
$962$	−12.6017	+	2.16014i	−0.406295	+	0.0696456i
$963$		−	19.0488i		−	0.613839i
$964$	−1.89795	+	1.09578i	−0.0611289	+	0.0352928i
$965$		0			0
$966$	−0.203452	+	0.352389i	−0.00654596	+	0.0113379i
$967$	39.8852			1.28262			0.641310	−	0.767282i	$-0.278391\pi$
$967$	39.8852			1.28262			0.641310	+	0.767282i	$0.278391\pi$
$968$	−5.20619	+	9.01739i	−0.167333	+	0.289830i
$969$	−10.1399	−	5.85429i	−0.325742	−	0.188067i
$970$		0			0
$971$	19.5176	−	33.8055i	0.626349	−	1.08487i	−0.361929	−	0.932206i	$-0.617882\pi$
$971$	19.5176	−	33.8055i	0.626349	−	1.08487i	0.988278	−	0.152663i	$-0.0487849\pi$
$972$	0.866025	−	0.500000i	0.0277778	−	0.0160375i
$973$	0.295402	+	0.511652i	0.00947017	+	0.0164028i
$974$	9.52978			0.305354
$975$		0			0
$976$	1.54606			0.0494880
$977$	−21.0247	−	36.4159i	−0.672641	−	1.16505i	−0.977153	−	0.212539i	$-0.931827\pi$
$977$	−21.0247	−	36.4159i	−0.672641	−	1.16505i	0.304512	−	0.952509i	$-0.401507\pi$
$978$	9.79890	−	5.65740i	0.313334	−	0.180904i
$979$	2.03706	−	3.52829i	0.0651047	−	0.112765i
$980$		0			0
$981$	7.83362	+	4.52274i	0.250108	+	0.144400i
$982$	16.7409	−	28.9960i	0.534223	−	0.925301i
$983$	27.5124			0.877508			0.438754	−	0.898607i	$-0.355420\pi$
$983$	27.5124			0.877508			0.438754	+	0.898607i	$0.355420\pi$
$984$	1.10917	−	1.92113i	0.0353589	−	0.0612434i
$985$		0			0
$986$	−11.6432	+	6.72220i	−0.370795	+	0.214079i
$987$		−	0.297874i		−	0.00948144i
$988$	−17.8516	−	6.59397i	−0.567934	−	0.209782i
$989$	−5.23918			−0.166596
$990$		0			0
$991$	−27.9614	−	48.4306i	−0.888224	−	1.53845i	−0.841973	−	0.539519i	$-0.818606\pi$
$991$	−27.9614	−	48.4306i	−0.888224	−	1.53845i	−0.0462506	−	0.998930i	$-0.514727\pi$
$992$	−2.84152	−	1.64055i	−0.0902182	−	0.0520875i
$993$	18.9464			0.601246
$994$	−0.588062	−	0.339518i	−0.0186522	−	0.0107688i
$995$		0			0
$996$		−	4.42419i		−	0.140186i
$997$	25.6834	+	14.8283i	0.813403	+	0.469618i	0.848136	−	0.529778i	$-0.177725\pi$
$997$	25.6834	+	14.8283i	0.813403	+	0.469618i	−0.0347335	+	0.999397i	$0.511058\pi$
$998$	13.0667	−	7.54409i	0.413620	−	0.238804i
$999$	−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.y.m.49.5		12
5.2	odd	4		1950.2.bc.h.751.5	✓	12
5.3	odd	4		1950.2.bc.k.751.2	yes	12
5.4	even	2		1950.2.y.n.49.2		12
13.4	even	6		1950.2.y.n.199.2		12
65.4	even	6	inner	1950.2.y.m.199.5		12
65.17	odd	12		1950.2.bc.h.901.5	yes	12
65.43	odd	12		1950.2.bc.k.901.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1950.2.y.m.49.5		12	1.1	even	1	trivial
1950.2.y.m.199.5		12	65.4	even	6	inner
1950.2.y.n.49.2		12	5.4	even	2
1950.2.y.n.199.2		12	13.4	even	6
1950.2.bc.h.751.5	✓	12	5.2	odd	4
1950.2.bc.h.901.5	yes	12	65.17	odd	12
1950.2.bc.k.751.2	yes	12	5.3	odd	4
1950.2.bc.k.901.2	yes	12	65.43	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.y (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(-0.140141 + 0.242731i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(-0.140141 + 0.242731i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(0.663862 - 0.383281i) q^{11} +1.00000i q^{12} +(2.30441 + 2.77303i) q^{13} +0.280281 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.92113 - 1.10917i) q^{17} -1.00000 q^{18} +(4.57097 + 2.63905i) q^{19} +0.280281i q^{21} +(-0.663862 - 0.383281i) q^{22} +(-1.25727 + 0.725885i) q^{23} +(0.866025 - 0.500000i) q^{24} +(1.24931 - 3.38219i) q^{26} -1.00000i q^{27} +(-0.140141 - 0.242731i) q^{28} +(3.03030 + 5.24863i) q^{29} +3.28110i q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.383281 - 0.663862i) q^{33} +2.21833i q^{34} +(0.500000 + 0.866025i) q^{36} +(-1.77303 - 3.07097i) q^{37} -5.27811i q^{38} +(3.38219 + 1.24931i) q^{39} +(1.92113 - 1.10917i) q^{41} +(0.242731 - 0.140141i) q^{42} +(3.12533 + 1.80441i) q^{43} +0.766562i q^{44} +(1.25727 + 0.725885i) q^{46} -1.06277 q^{47} +(-0.866025 - 0.500000i) q^{48} +(3.46072 + 5.99414i) q^{49} -2.21833 q^{51} +(-3.55372 + 0.609166i) q^{52} -3.28110i q^{53} +(-0.866025 + 0.500000i) q^{54} +(-0.140141 + 0.242731i) q^{56} +5.27811 q^{57} +(3.03030 - 5.24863i) q^{58} +(4.32824 + 2.49891i) q^{59} +(-0.773028 + 1.33892i) q^{61} +(2.84152 - 1.64055i) q^{62} +(0.140141 + 0.242731i) q^{63} +1.00000 q^{64} -0.766562 q^{66} +(-3.71792 - 6.43963i) q^{67} +(1.92113 - 1.10917i) q^{68} +(-0.725885 + 1.25727i) q^{69} +(-2.09811 - 1.21135i) q^{71} +(0.500000 - 0.866025i) q^{72} +14.2630 q^{73} +(-1.77303 + 3.07097i) q^{74} +(-4.57097 + 2.63905i) q^{76} +0.214853i q^{77} +(-0.609166 - 3.55372i) q^{78} +14.4715 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-1.92113 - 1.10917i) q^{82} -4.42419 q^{83} +(-0.242731 - 0.140141i) q^{84} -3.60882i q^{86} +(5.24863 + 3.03030i) q^{87} +(0.663862 - 0.383281i) q^{88} +(4.60275 - 2.65740i) q^{89} +(-0.996041 + 0.170738i) q^{91} -1.45177i q^{92} +(1.64055 + 2.84152i) q^{93} +(0.531385 + 0.920385i) q^{94} +1.00000i q^{96} +(-0.633565 + 1.09737i) q^{97} +(3.46072 - 5.99414i) q^{98} -0.766562i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 6 q^{4} + 4 q^{7} + 12 q^{8} + 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^2 - 6 * q^4 + 4 * q^7 + 12 * q^8 + 6 * q^9	\( 12 q - 6 q^{2} - 6 q^{4} + 4 q^{7} + 12 q^{8} + 6 q^{9} - 12 q^{11} - 4 q^{13} - 8 q^{14} - 6 q^{16} - 12 q^{18} + 6 q^{19} + 12 q^{22} - 12 q^{23} - 4 q^{26} + 4 q^{28} - 6 q^{32} - 4 q^{33} + 6 q^{36} + 12 q^{37} - 6 q^{39} + 6 q^{42} - 12 q^{43} + 12 q^{46} - 16 q^{47} - 32 q^{49} + 8 q^{52} + 4 q^{56} - 24 q^{57} + 24 q^{61} - 4 q^{63} + 12 q^{64} + 8 q^{66} - 24 q^{67} - 4 q^{69} + 12 q^{71} + 6 q^{72} + 40 q^{73} + 12 q^{74} - 6 q^{76} + 6 q^{78} - 52 q^{79} - 6 q^{81} - 32 q^{83} - 6 q^{84} - 12 q^{88} - 24 q^{89} - 54 q^{91} + 8 q^{93} + 8 q^{94} - 24 q^{97} - 32 q^{98}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^4 + 4 * q^7 + 12 * q^8 + 6 * q^9 - 12 * q^11 - 4 * q^13 - 8 * q^14 - 6 * q^16 - 12 * q^18 + 6 * q^19 + 12 * q^22 - 12 * q^23 - 4 * q^26 + 4 * q^28 - 6 * q^32 - 4 * q^33 + 6 * q^36 + 12 * q^37 - 6 * q^39 + 6 * q^42 - 12 * q^43 + 12 * q^46 - 16 * q^47 - 32 * q^49 + 8 * q^52 + 4 * q^56 - 24 * q^57 + 24 * q^61 - 4 * q^63 + 12 * q^64 + 8 * q^66 - 24 * q^67 - 4 * q^69 + 12 * q^71 + 6 * q^72 + 40 * q^73 + 12 * q^74 - 6 * q^76 + 6 * q^78 - 52 * q^79 - 6 * q^81 - 32 * q^83 - 6 * q^84 - 12 * q^88 - 24 * q^89 - 54 * q^91 + 8 * q^93 + 8 * q^94 - 24 * q^97 - 32 * q^98

Introduction

L-functions

Modular forms

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Database

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