LMFDB - Embedded newform 637.2.e.m.508.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(79,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("637.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.e (of order $3$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 8x^{8} + 7x^{7} + 41x^{6} + 18x^{5} + 58x^{4} + 28x^{3} + 64x^{2} + 16x + 4 $ x^10 - x^9 + 8x^8 + 7x^7 + 41x^6 + 18x^5 + 58x^4 + 28x^3 + 64x^2 + 16x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			508.1
Root			$-0.862625 - 1.49411i$ of defining polynomial
Character	$\chi$	$=$	637.508
Dual form			637.2.e.m.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36263 - 2.36014i) q^{2} +(-0.673208 + 1.16603i) q^{3} +(-2.71349 + 4.69991i) q^{4} +(1.09358 + 1.89414i) q^{5} +3.66932 q^{6} +9.33940 q^{8} +(0.593582 + 1.02811i) q^{9} +O(q^{10})$	\(q+(-1.36263 - 2.36014i) q^{2} +(-0.673208 + 1.16603i) q^{3} +(-2.71349 + 4.69991i) q^{4} +(1.09358 + 1.89414i) q^{5} +3.66932 q^{6} +9.33940 q^{8} +(0.593582 + 1.02811i) q^{9} +(2.98028 - 5.16200i) q^{10} +(0.524077 - 0.907729i) q^{11} +(-3.65349 - 6.32803i) q^{12} -1.00000 q^{13} -2.94483 q^{15} +(-7.29912 - 12.6424i) q^{16} +(-2.64562 + 4.58236i) q^{17} +(1.61766 - 2.80187i) q^{18} +(0.378453 + 0.655500i) q^{19} -11.8697 q^{20} -2.85648 q^{22} +(-0.326792 - 0.566020i) q^{23} +(-6.28736 + 10.8900i) q^{24} +(0.108157 - 0.187333i) q^{25} +(1.36263 + 2.36014i) q^{26} -5.63766 q^{27} -3.10408 q^{29} +(4.01270 + 6.95021i) q^{30} +(0.513956 - 0.890198i) q^{31} +(-10.5525 + 18.2775i) q^{32} +(0.705626 + 1.22218i) q^{33} +14.4200 q^{34} -6.44273 q^{36} +(5.44661 + 9.43381i) q^{37} +(1.03138 - 1.78640i) q^{38} +(0.673208 - 1.16603i) q^{39} +(10.2134 + 17.6901i) q^{40} -7.32040 q^{41} +0.887771 q^{43} +(2.84416 + 4.92623i) q^{44} +(-1.29826 + 2.24865i) q^{45} +(-0.890590 + 1.54255i) q^{46} +(1.16875 + 2.02434i) q^{47} +19.6553 q^{48} -0.589510 q^{50} +(-3.56211 - 6.16976i) q^{51} +(2.71349 - 4.69991i) q^{52} +(-2.44407 + 4.23325i) q^{53} +(7.68202 + 13.3057i) q^{54} +2.29249 q^{55} -1.01911 q^{57} +(4.22970 + 7.32606i) q^{58} +(-0.524077 + 0.907729i) q^{59} +(7.99079 - 13.8404i) q^{60} +(-6.24989 - 10.8251i) q^{61} -2.80132 q^{62} +28.3200 q^{64} +(-1.09358 - 1.89414i) q^{65} +(1.92301 - 3.33075i) q^{66} +(-2.23944 + 3.87883i) q^{67} +(-14.3578 - 24.8684i) q^{68} +0.879996 q^{69} -6.60274 q^{71} +(5.54370 + 9.60197i) q^{72} +(-4.14174 + 7.17370i) q^{73} +(14.8434 - 25.7095i) q^{74} +(0.145624 + 0.252229i) q^{75} -4.10772 q^{76} -3.66932 q^{78} +(-1.07007 - 1.85342i) q^{79} +(15.9644 - 27.6511i) q^{80} +(2.01457 - 3.48935i) q^{81} +(9.97496 + 17.2771i) q^{82} +6.66558 q^{83} -11.5728 q^{85} +(-1.20970 - 2.09526i) q^{86} +(2.08969 - 3.61946i) q^{87} +(4.89457 - 8.47765i) q^{88} +(-2.88388 - 4.99503i) q^{89} +7.07617 q^{90} +3.54699 q^{92} +(0.691998 + 1.19858i) q^{93} +(3.18515 - 5.51684i) q^{94} +(-0.827739 + 1.43369i) q^{95} +(-14.2081 - 24.6091i) q^{96} +2.88777 q^{97} +1.24433 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{2} - 8 q^{4} + 2 q^{5} + 10 q^{6} + 18 q^{8} - 3 q^{9}+O(q^{10}) $ 10 * q - 4 * q^2 - 8 * q^4 + 2 * q^5 + 10 * q^6 + 18 * q^8 - 3 * q^9	$ 10 q - 4 q^{2} - 8 q^{4} + 2 q^{5} + 10 q^{6} + 18 q^{8} - 3 q^{9} - 5 q^{10} - 11 q^{11} + 5 q^{12} - 10 q^{13} - 10 q^{16} - 5 q^{17} - 9 q^{18} + 9 q^{19} - 2 q^{20} + 16 q^{22} - 10 q^{23} - 9 q^{25} + 4 q^{26} - 6 q^{29} + 13 q^{30} - 6 q^{31} - 22 q^{32} + 8 q^{33} + 44 q^{34} + 14 q^{36} - 4 q^{37} - 10 q^{38} + 28 q^{40} - 28 q^{41} + 4 q^{43} - 32 q^{45} - 3 q^{46} + q^{47} + 46 q^{48} + 18 q^{50} + 8 q^{51} + 8 q^{52} - 17 q^{53} + 23 q^{54} - 32 q^{57} + 27 q^{58} + 11 q^{59} + 29 q^{60} - 11 q^{61} + 46 q^{62} + 18 q^{64} - 2 q^{65} + 21 q^{66} - 13 q^{67} - 32 q^{68} - 36 q^{69} + 30 q^{71} + 19 q^{72} + 33 q^{74} - 20 q^{75} - 16 q^{76} - 10 q^{78} - 2 q^{79} + 55 q^{80} + 19 q^{81} + 34 q^{82} - 12 q^{83} - 44 q^{85} - 28 q^{86} - 8 q^{87} + 3 q^{88} - 4 q^{89} + 68 q^{90} + 42 q^{92} - 18 q^{93} + 20 q^{94} + 12 q^{95} - 37 q^{96} + 24 q^{97} + 22 q^{99}+O(q^{100}) $ 10 * q - 4 * q^2 - 8 * q^4 + 2 * q^5 + 10 * q^6 + 18 * q^8 - 3 * q^9 - 5 * q^10 - 11 * q^11 + 5 * q^12 - 10 * q^13 - 10 * q^16 - 5 * q^17 - 9 * q^18 + 9 * q^19 - 2 * q^20 + 16 * q^22 - 10 * q^23 - 9 * q^25 + 4 * q^26 - 6 * q^29 + 13 * q^30 - 6 * q^31 - 22 * q^32 + 8 * q^33 + 44 * q^34 + 14 * q^36 - 4 * q^37 - 10 * q^38 + 28 * q^40 - 28 * q^41 + 4 * q^43 - 32 * q^45 - 3 * q^46 + q^47 + 46 * q^48 + 18 * q^50 + 8 * q^51 + 8 * q^52 - 17 * q^53 + 23 * q^54 - 32 * q^57 + 27 * q^58 + 11 * q^59 + 29 * q^60 - 11 * q^61 + 46 * q^62 + 18 * q^64 - 2 * q^65 + 21 * q^66 - 13 * q^67 - 32 * q^68 - 36 * q^69 + 30 * q^71 + 19 * q^72 + 33 * q^74 - 20 * q^75 - 16 * q^76 - 10 * q^78 - 2 * q^79 + 55 * q^80 + 19 * q^81 + 34 * q^82 - 12 * q^83 - 44 * q^85 - 28 * q^86 - 8 * q^87 + 3 * q^88 - 4 * q^89 + 68 * q^90 + 42 * q^92 - 18 * q^93 + 20 * q^94 + 12 * q^95 - 37 * q^96 + 24 * q^97 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.36263	−	2.36014i	−0.963521	−	1.66887i	−0.713536	−	0.700619i	$-0.752907\pi$
$2$	−1.36263	−	2.36014i	−0.963521	−	1.66887i	−0.249986	−	0.968250i	$-0.580426\pi$
$3$	−0.673208	+	1.16603i	−0.388677	+	0.673208i	−0.992272	−	0.124083i	$-0.960401\pi$
$3$	−0.673208	+	1.16603i	−0.388677	+	0.673208i	0.603595	+	0.797291i	$0.293734\pi$
$4$	−2.71349	+	4.69991i	−1.35675	+	2.34996i
$5$	1.09358	+	1.89414i	0.489065	+	0.847085i	0.999921	−	0.0125813i	$-0.00400485\pi$
$5$	1.09358	+	1.89414i	0.489065	+	0.847085i	−0.510856	+	0.859666i	$0.670672\pi$
$6$	3.66932			1.49799
$7$		0			0
$7$		0			0
$8$	9.33940			3.30198
$9$	0.593582	+	1.02811i	0.197861	+	0.342705i
$10$	2.98028	−	5.16200i	0.942449	−	1.63237i
$11$	0.524077	−	0.907729i	0.158015	−	0.273691i	−0.776138	−	0.630564i	$-0.782824\pi$
$11$	0.524077	−	0.907729i	0.158015	−	0.273691i	0.934153	+	0.356873i	$0.116157\pi$
$12$	−3.65349	−	6.32803i	−1.05467	−	1.82675i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$		0			0
$15$	−2.94483			−0.760352
$16$	−7.29912	−	12.6424i	−1.82478	−	3.16061i
$17$	−2.64562	+	4.58236i	−0.641658	+	1.11138i	0.343404	+	0.939188i	$0.388420\pi$
$17$	−2.64562	+	4.58236i	−0.641658	+	1.11138i	−0.985063	+	0.172197i	$0.944913\pi$
$18$	1.61766	−	2.80187i	0.381286	−	0.660407i
$19$	0.378453	+	0.655500i	0.0868231	+	0.150382i	0.906167	−	0.422921i	$-0.138995\pi$
$19$	0.378453	+	0.655500i	0.0868231	+	0.150382i	−0.819344	+	0.573303i	$0.805662\pi$
$20$	−11.8697			−2.65415
$21$		0			0
$22$	−2.85648			−0.609005
$23$	−0.326792	−	0.566020i	−0.0681408	−	0.118023i	0.829942	−	0.557850i	$-0.188373\pi$
$23$	−0.326792	−	0.566020i	−0.0681408	−	0.118023i	−0.898083	+	0.439826i	$0.855040\pi$
$24$	−6.28736	+	10.8900i	−1.28340	+	2.22292i
$25$	0.108157	−	0.187333i	0.0216314	−	0.0374667i
$26$	1.36263	+	2.36014i	0.267233	+	0.462861i
$27$	−5.63766			−1.08497
$28$		0			0
$29$	−3.10408			−0.576414			−0.288207	−	0.957568i	$-0.593059\pi$
$29$	−3.10408			−0.576414			−0.288207	+	0.957568i	$0.593059\pi$
$30$	4.01270	+	6.95021i	0.732616	+	1.26893i
$31$	0.513956	−	0.890198i	0.0923092	−	0.159884i	−0.816173	−	0.577807i	$-0.803909\pi$
$31$	0.513956	−	0.890198i	0.0923092	−	0.159884i	0.908482	+	0.417923i	$0.137242\pi$
$32$	−10.5525	+	18.2775i	−1.86544	+	3.23104i
$33$	0.705626	+	1.22218i	0.122834	+	0.212754i
$34$	14.4200			2.47301
$35$		0			0
$36$	−6.44273			−1.07379
$37$	5.44661	+	9.43381i	0.895418	+	1.55091i	0.833287	+	0.552841i	$0.186456\pi$
$37$	5.44661	+	9.43381i	0.895418	+	1.55091i	0.0621309	+	0.998068i	$0.480210\pi$
$38$	1.03138	−	1.78640i	0.167312	−	0.289793i
$39$	0.673208	−	1.16603i	0.107800	−	0.186714i
$40$	10.2134	+	17.6901i	1.61488	+	2.79706i
$41$	−7.32040			−1.14325			−0.571627	−	0.820514i	$-0.693688\pi$
$41$	−7.32040			−1.14325			−0.571627	+	0.820514i	$0.693688\pi$
$42$		0			0
$43$	0.887771			0.135384			0.0676919	−	0.997706i	$-0.478437\pi$
$43$	0.887771			0.135384			0.0676919	+	0.997706i	$0.478437\pi$
$44$	2.84416	+	4.92623i	0.428774	+	0.742658i
$45$	−1.29826	+	2.24865i	−0.193533	+	0.335210i
$46$	−0.890590	+	1.54255i	−0.131310	+	0.227436i
$47$	1.16875	+	2.02434i	0.170480	+	0.295281i	0.938588	−	0.345040i	$-0.112135\pi$
$47$	1.16875	+	2.02434i	0.170480	+	0.295281i	−0.768108	+	0.640321i	$0.778801\pi$
$48$	19.6553			2.83700
$49$		0			0
$50$	−0.589510			−0.0833692
$51$	−3.56211	−	6.16976i	−0.498795	−	0.863939i
$52$	2.71349	−	4.69991i	0.376294	−	0.651760i
$53$	−2.44407	+	4.23325i	−0.335719	+	0.581482i	−0.983623	−	0.180240i	$-0.942313\pi$
$53$	−2.44407	+	4.23325i	−0.335719	+	0.581482i	0.647904	+	0.761722i	$0.275646\pi$
$54$	7.68202	+	13.3057i	1.04539	+	1.81067i
$55$	2.29249			0.309119
$56$		0			0
$57$	−1.01911			−0.134985
$58$	4.22970	+	7.32606i	0.555387	+	0.961959i
$59$	−0.524077	+	0.907729i	−0.0682291	+	0.118176i	−0.898122	−	0.439747i	$-0.855068\pi$
$59$	−0.524077	+	0.907729i	−0.0682291	+	0.118176i	0.829893	+	0.557923i	$0.188402\pi$
$60$	7.99079	−	13.8404i	1.03161	−	1.78679i
$61$	−6.24989	−	10.8251i	−0.800217	−	1.38602i	−0.919473	−	0.393153i	$-0.871384\pi$
$61$	−6.24989	−	10.8251i	−0.800217	−	1.38602i	0.119256	−	0.992864i	$-0.461949\pi$
$62$	−2.80132			−0.355768
$63$		0			0
$64$	28.3200			3.54000
$65$	−1.09358	−	1.89414i	−0.135642	−	0.234939i
$66$	1.92301	−	3.33075i	0.236706	−	0.409987i
$67$	−2.23944	+	3.87883i	−0.273592	+	0.473875i	−0.969779	−	0.243986i	$-0.921545\pi$
$67$	−2.23944	+	3.87883i	−0.273592	+	0.473875i	0.696187	+	0.717860i	$0.254878\pi$
$68$	−14.3578	−	24.8684i	−1.74114	−	3.01574i
$69$	0.879996			0.105939
$70$		0			0
$71$	−6.60274			−0.783601			−0.391801	−	0.920050i	$-0.628148\pi$
$71$	−6.60274			−0.783601			−0.391801	+	0.920050i	$0.628148\pi$
$72$	5.54370	+	9.60197i	0.653331	+	1.13160i
$73$	−4.14174	+	7.17370i	−0.484754	+	0.839618i	−0.999847	−	0.0175164i	$-0.994424\pi$
$73$	−4.14174	+	7.17370i	−0.484754	+	0.839618i	0.515093	+	0.857134i	$0.327757\pi$
$74$	14.8434	−	25.7095i	1.72551	−	2.98867i
$75$	0.145624	+	0.252229i	0.0168152	+	0.0291249i
$76$	−4.10772			−0.471188
$77$		0			0
$78$	−3.66932			−0.415469
$79$	−1.07007	−	1.85342i	−0.120392	−	0.208526i	0.799530	−	0.600626i	$-0.205082\pi$
$79$	−1.07007	−	1.85342i	−0.120392	−	0.208526i	−0.919922	+	0.392100i	$0.871749\pi$
$80$	15.9644	−	27.6511i	1.78487	−	3.09149i
$81$	2.01457	−	3.48935i	0.223842	−	0.387705i
$82$	9.97496	+	17.2771i	1.10155	+	1.90794i
$83$	6.66558			0.731642			0.365821	−	0.930685i	$-0.380788\pi$
$83$	6.66558			0.731642			0.365821	+	0.930685i	$0.380788\pi$
$84$		0			0
$85$	−11.5728			−1.25525
$86$	−1.20970	−	2.09526i	−0.130445	−	0.225938i
$87$	2.08969	−	3.61946i	0.224039	−	0.388047i
$88$	4.89457	−	8.47765i	0.521763	−	0.903720i
$89$	−2.88388	−	4.99503i	−0.305691	−	0.529472i	0.671724	−	0.740802i	$-0.265554\pi$
$89$	−2.88388	−	4.99503i	−0.305691	−	0.529472i	−0.977415	+	0.211329i	$0.932221\pi$
$90$	7.07617			0.745894
$91$		0			0
$92$	3.54699			0.369800
$93$	0.691998	+	1.19858i	0.0717569	+	0.124287i
$94$	3.18515	−	5.51684i	0.328523	−	0.569019i
$95$	−0.827739	+	1.43369i	−0.0849242	+	0.147093i
$96$	−14.2081	−	24.6091i	−1.45011	−	2.51166i
$97$	2.88777			0.293209			0.146604	−	0.989195i	$-0.453166\pi$
$97$	2.88777			0.293209			0.146604	+	0.989195i	$0.453166\pi$
$98$		0			0
$99$	1.24433			0.125060
$100$	0.586967	+	1.01666i	0.0586967	+	0.101666i
$101$	−5.62716	+	9.74653i	−0.559924	+	0.969816i	0.437579	+	0.899180i	$0.355836\pi$
$101$	−5.62716	+	9.74653i	−0.559924	+	0.969816i	−0.997502	+	0.0706359i	$0.977497\pi$
$102$	−9.70764	+	16.8141i	−0.961200	+	1.66485i
$103$	10.1167	+	17.5226i	0.996828	+	1.72656i	0.567341	+	0.823483i	$0.307972\pi$
$103$	10.1167	+	17.5226i	0.996828	+	1.72656i	0.429487	+	0.903073i	$0.358694\pi$
$104$	−9.33940			−0.915804
$105$		0			0
$106$	13.3214			1.29389
$107$	−4.52758	−	7.84201i	−0.437698	−	0.758115i	0.559813	−	0.828619i	$-0.310873\pi$
$107$	−4.52758	−	7.84201i	−0.437698	−	0.758115i	−0.997512	+	0.0705034i	$0.977539\pi$
$108$	15.2978	−	26.4965i	1.47203	−	2.54963i
$109$	−7.55070	+	13.0782i	−0.723226	+	1.25266i	0.236474	+	0.971638i	$0.424008\pi$
$109$	−7.55070	+	13.0782i	−0.723226	+	1.25266i	−0.959700	+	0.281026i	$0.909325\pi$
$110$	−3.12380	−	5.41058i	−0.297843	−	0.515879i
$111$	−14.6668			−1.39211
$112$		0			0
$113$	3.10408			0.292008			0.146004	−	0.989284i	$-0.453359\pi$
$113$	3.10408			0.292008			0.146004	+	0.989284i	$0.453359\pi$
$114$	1.38867	+	2.40524i	0.130061	+	0.225271i
$115$	0.714748	−	1.23798i	0.0666506	−	0.115442i
$116$	8.42292	−	14.5889i	0.782048	−	1.35455i
$117$	−0.593582	−	1.02811i	−0.0548767	−	0.0950492i
$118$	2.85648			0.262961
$119$		0			0
$120$	−27.5030			−2.51067
$121$	4.95069	+	8.57484i	0.450062	+	0.779531i
$122$	−17.0325	+	29.5012i	−1.54205	+	2.67091i
$123$	4.92815	−	8.53581i	0.444356	−	0.769648i
$124$	2.78923	+	4.83109i	0.250481	+	0.433845i
$125$	11.4089			1.02045
$126$		0			0
$127$	8.78914			0.779910			0.389955	−	0.920834i	$-0.372491\pi$
$127$	8.78914			0.779910			0.389955	+	0.920834i	$0.372491\pi$
$128$	−17.4846	−	30.2841i	−1.54543	−	2.67676i
$129$	−0.597654	+	1.03517i	−0.0526205	+	0.0911414i
$130$	−2.98028	+	5.16200i	−0.261388	+	0.452738i
$131$	−5.25723	−	9.10580i	−0.459327	−	0.795577i	0.539599	−	0.841922i	$-0.318576\pi$
$131$	−5.25723	−	9.10580i	−0.459327	−	0.795577i	−0.998925	+	0.0463451i	$0.985243\pi$
$132$	−7.65885			−0.666618
$133$		0			0
$134$	12.2061			1.05445
$135$	−6.16525	−	10.6785i	−0.530620	−	0.919061i
$136$	−24.7086	+	42.7965i	−2.11874	+	3.66977i
$137$	−4.36583	+	7.56183i	−0.372998	+	0.646051i	−0.990025	−	0.140891i	$-0.955003\pi$
$137$	−4.36583	+	7.56183i	−0.372998	+	0.646051i	0.617028	+	0.786942i	$0.288337\pi$
$138$	−1.19910	−	2.07691i	−0.102075	−	0.176798i
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$		0			0
$141$	−3.14726			−0.265047
$142$	8.99706	+	15.5834i	0.755016	+	1.30773i
$143$	−0.524077	+	0.907729i	−0.0438256	+	0.0759081i
$144$	8.66525	−	15.0087i	0.722104	−	1.25072i
$145$	−3.39457	−	5.87957i	−0.281904	−	0.488272i
$146$	22.5745			1.86828
$147$		0			0
$148$	−59.1174			−4.85942
$149$	−7.69632	−	13.3304i	−0.630507	−	1.09207i	−0.987448	−	0.157944i	$-0.949514\pi$
$149$	−7.69632	−	13.3304i	−0.630507	−	1.09207i	0.356941	−	0.934127i	$-0.383820\pi$
$150$	0.396863	−	0.687386i	0.0324037	−	0.0561248i
$151$	6.83786	−	11.8435i	0.556457	−	0.963812i	−0.441331	−	0.897344i	$-0.645494\pi$
$151$	6.83786	−	11.8435i	0.556457	−	0.963812i	0.997789	−	0.0664680i	$-0.0211730\pi$
$152$	3.53453	+	6.12198i	0.286688	+	0.496558i
$153$	−6.28158			−0.507836
$154$		0			0
$155$	2.24821			0.180581
$156$	3.65349	+	6.32803i	0.292514	+	0.506648i
$157$	1.69378	−	2.93371i	0.135178	−	0.234136i	−0.790487	−	0.612478i	$-0.790173\pi$
$157$	1.69378	−	2.93371i	0.135178	−	0.234136i	0.925666	+	0.378343i	$0.123506\pi$
$158$	−2.91621	+	5.05102i	−0.232001	+	0.401838i
$159$	−3.29074	−	5.69972i	−0.260972	−	0.452017i
$160$	−46.1602			−3.64928
$161$		0			0
$162$	−10.9804			−0.862705
$163$	6.90502	+	11.9598i	0.540843	+	0.936767i	0.998856	+	0.0478219i	$0.0152280\pi$
$163$	6.90502	+	11.9598i	0.540843	+	0.936767i	−0.458013	+	0.888946i	$0.651439\pi$
$164$	19.8639	−	34.4052i	1.55111	−	2.68660i
$165$	−1.54332	+	2.67311i	−0.120147	+	0.208101i
$166$	−9.08268	−	15.7317i	−0.704953	−	1.22101i
$167$	−16.3783			−1.26739			−0.633695	−	0.773583i	$-0.718462\pi$
$167$	−16.3783			−1.26739			−0.633695	+	0.773583i	$0.718462\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	15.7694	+	27.3134i	1.20946	+	2.09485i
$171$	−0.449286	+	0.778186i	−0.0343578	+	0.0595094i
$172$	−2.40896	+	4.17244i	−0.183682	+	0.318146i
$173$	2.06273	+	3.57275i	0.156826	+	0.271631i	0.933723	−	0.357997i	$-0.116540\pi$
$173$	2.06273	+	3.57275i	0.156826	+	0.271631i	−0.776896	+	0.629629i	$0.783207\pi$
$174$	−11.3899			−0.863465
$175$		0			0
$176$	−15.3012			−1.15337
$177$	−0.705626	−	1.22218i	−0.0530381	−	0.0918647i
$178$	−7.85930	+	13.6127i	−0.589080	+	1.02032i
$179$	−7.20679	+	12.4825i	−0.538661	+	0.932988i	0.460316	+	0.887755i	$0.347736\pi$
$179$	−7.20679	+	12.4825i	−0.538661	+	0.932988i	−0.998976	+	0.0452324i	$0.985597\pi$
$180$	−7.04565	−	12.2034i	−0.525152	−	0.909589i
$181$	−18.1014			−1.34547			−0.672733	−	0.739885i	$-0.734880\pi$
$181$	−18.1014			−1.34547			−0.672733	+	0.739885i	$0.734880\pi$
$182$		0			0
$183$	16.8299			1.24410
$184$	−3.05204	−	5.28629i	−0.225000	−	0.389711i
$185$	−11.9126	+	20.6333i	−0.875834	+	1.51699i
$186$	1.88587	−	3.26642i	0.138279	−	0.239506i
$187$	2.77302	+	4.80302i	0.202784	+	0.351232i
$188$	−12.6856			−0.925195
$189$		0			0
$190$	4.51159			0.327305
$191$	−2.77068	−	4.79895i	−0.200479	−	0.347240i	0.748204	−	0.663469i	$-0.230917\pi$
$191$	−2.77068	−	4.79895i	−0.200479	−	0.347240i	−0.948683	+	0.316229i	$0.897583\pi$
$192$	−19.0653	+	33.0220i	−1.37592	+	2.38316i
$193$	4.37044	−	7.56983i	0.314591	−	0.544888i	−0.664759	−	0.747058i	$-0.731466\pi$
$193$	4.37044	−	7.56983i	0.314591	−	0.544888i	0.979351	+	0.202170i	$0.0647992\pi$
$194$	−3.93495	−	6.81553i	−0.282513	−	0.489327i
$195$	2.94483			0.210884
$196$		0			0
$197$	−5.46874			−0.389632			−0.194816	−	0.980840i	$-0.562411\pi$
$197$	−5.46874			−0.389632			−0.194816	+	0.980840i	$0.562411\pi$
$198$	−1.69556	−	2.93679i	−0.120498	−	0.208709i
$199$	9.76839	−	16.9193i	0.692463	−	1.19938i	−0.278566	−	0.960417i	$-0.589859\pi$
$199$	9.76839	−	16.9193i	0.692463	−	1.19938i	0.971029	−	0.238963i	$-0.0768075\pi$
$200$	1.01012	−	1.74958i	0.0714264	−	0.123714i
$201$	−3.01522	−	5.22252i	−0.212677	−	0.368368i
$202$	30.6708			2.15799
$203$		0			0
$204$	38.6631			2.70696
$205$	−8.00546	−	13.8659i	−0.559125	−	0.968433i
$206$	27.5705	−	47.7536i	1.92093	−	3.32715i
$207$	0.387956	−	0.671959i	0.0269648	−	0.0467044i
$208$	7.29912	+	12.6424i	0.506103	+	0.876596i
$209$	0.793355			0.0548775
$210$		0			0
$211$	16.6905			1.14902			0.574511	−	0.818497i	$-0.305192\pi$
$211$	16.6905			1.14902			0.574511	+	0.818497i	$0.305192\pi$
$212$	−13.2639	−	22.9738i	−0.910971	−	1.57785i
$213$	4.44502	−	7.69900i	0.304568	−	0.527527i
$214$	−12.3388	+	21.3714i	−0.843463	+	1.46092i
$215$	0.970850	+	1.68156i	0.0662114	+	0.114682i
$216$	−52.6524			−3.58254
$217$		0			0
$218$	41.1551			2.78737
$219$	−5.57650	−	9.65878i	−0.376825	−	0.652680i
$220$	−6.22065	+	10.7745i	−0.419396	+	0.726415i
$221$	2.64562	−	4.58236i	0.177964	−	0.308243i
$222$	19.9854	+	34.6157i	1.34133	+	2.32325i
$223$	5.34217			0.357738			0.178869	−	0.983873i	$-0.442756\pi$
$223$	5.34217			0.357738			0.178869	+	0.983873i	$0.442756\pi$
$224$		0			0
$225$	0.256800			0.0171200
$226$	−4.22970	−	7.32606i	−0.281356	−	0.487322i
$227$	10.0608	−	17.4258i	0.667757	−	1.15659i	−0.310774	−	0.950484i	$-0.600588\pi$
$227$	10.0608	−	17.4258i	0.667757	−	1.15659i	0.978530	−	0.206104i	$-0.0660786\pi$
$228$	2.76535	−	4.78973i	0.183140	−	0.317208i
$229$	12.6249	+	21.8669i	0.834275	+	1.44501i	0.894619	+	0.446829i	$0.147447\pi$
$229$	12.6249	+	21.8669i	0.834275	+	1.44501i	−0.0603445	+	0.998178i	$0.519220\pi$
$230$	−3.89573			−0.256877
$231$		0			0
$232$	−28.9903			−1.90331
$233$	0.396678	+	0.687066i	0.0259872	+	0.0450112i	0.878727	−	0.477326i	$-0.158394\pi$
$233$	0.396678	+	0.687066i	0.0259872	+	0.0450112i	−0.852739	+	0.522337i	$0.825060\pi$
$234$	−1.61766	+	2.80187i	−0.105750	+	0.183164i
$235$	−2.55626	+	4.42757i	−0.166752	+	0.288823i
$236$	−2.84416	−	4.92623i	−0.185139	−	0.320671i
$237$	2.88152			0.187175
$238$		0			0
$239$	20.0488			1.29685			0.648425	−	0.761279i	$-0.275428\pi$
$239$	20.0488			1.29685			0.648425	+	0.761279i	$0.275428\pi$
$240$	21.4947	+	37.2299i	1.38748	+	2.40318i
$241$	6.90602	−	11.9616i	0.444856	−	0.770513i	−0.553186	−	0.833058i	$-0.686588\pi$
$241$	6.90602	−	11.9616i	0.444856	−	0.770513i	0.998042	+	0.0625446i	$0.0199216\pi$
$242$	13.4919	−	23.3686i	0.867289	−	1.50219i
$243$	−5.74404	−	9.94897i	−0.368480	−	0.638227i
$244$	67.8362			4.34277
$245$		0			0
$246$	−26.8609			−1.71259
$247$	−0.378453	−	0.655500i	−0.0240804	−	0.0417085i
$248$	4.80004	−	8.31392i	0.304803	−	0.527934i
$249$	−4.48732	+	7.77227i	−0.284372	+	0.492547i
$250$	−15.5461	−	26.9266i	−0.983222	−	1.70299i
$251$	26.1095			1.64802			0.824010	−	0.566576i	$-0.191732\pi$
$251$	26.1095			1.64802			0.824010	+	0.566576i	$0.191732\pi$
$252$		0			0
$253$	−0.685057			−0.0430692
$254$	−11.9763	−	20.7436i	−0.751460	−	1.30157i
$255$	7.79092	−	13.4943i	0.487886	−	0.845044i
$256$	−19.3298	+	33.4801i	−1.20811	+	2.09251i
$257$	5.30990	+	9.19701i	0.331222	+	0.573694i	0.982752	−	0.184930i	$-0.0592057\pi$
$257$	5.30990	+	9.19701i	0.331222	+	0.573694i	−0.651530	+	0.758623i	$0.725872\pi$
$258$	3.25752			0.202804
$259$		0			0
$260$	11.8697			0.736128
$261$	−1.84253	−	3.19135i	−0.114050	−	0.197540i
$262$	−14.3273	+	24.8156i	−0.885142	+	1.53311i
$263$	−5.17888	+	8.97008i	−0.319343	+	0.553119i	−0.980351	−	0.197260i	$-0.936796\pi$
$263$	−5.17888	+	8.97008i	−0.319343	+	0.553119i	0.661008	+	0.750379i	$0.270129\pi$
$264$	6.59013	+	11.4144i	0.405594	+	0.702510i
$265$	−10.6912			−0.656753
$266$		0			0
$267$	7.76581			0.475260
$268$	−12.1534	−	21.0504i	−0.742389	−	1.28586i
$269$	5.98503	−	10.3664i	0.364914	−	0.632049i	−0.623849	−	0.781545i	$-0.714432\pi$
$269$	5.98503	−	10.3664i	0.364914	−	0.632049i	0.988762	+	0.149496i	$0.0477652\pi$
$270$	−16.8018	+	29.1016i	−1.02253	+	1.77107i
$271$	−1.37845	−	2.38755i	−0.0837351	−	0.145033i	0.821116	−	0.570761i	$-0.193352\pi$
$271$	−1.37845	−	2.38755i	−0.0837351	−	0.145033i	−0.904852	+	0.425727i	$0.860018\pi$
$272$	77.2429			4.68354
$273$		0			0
$274$	23.7959			1.43757
$275$	−0.113365	−	0.196354i	−0.00683618	−	0.0118406i
$276$	−2.38786	+	4.13590i	−0.143733	+	0.248952i
$277$	11.9637	−	20.7218i	0.718831	−	1.24505i	−0.242632	−	0.970118i	$-0.578011\pi$
$277$	11.9637	−	20.7218i	0.718831	−	1.24505i	0.961463	−	0.274933i	$-0.0886558\pi$
$278$	−5.45050	−	9.44054i	−0.326899	−	0.566206i
$279$	1.22030			0.0730574
$280$		0			0
$281$	−3.87870			−0.231384			−0.115692	−	0.993285i	$-0.536909\pi$
$281$	−3.87870			−0.231384			−0.115692	+	0.993285i	$0.536909\pi$
$282$	4.28854	+	7.42796i	0.255379	+	0.442329i
$283$	−3.10499	+	5.37801i	−0.184573	+	0.319689i	−0.943432	−	0.331565i	$-0.892423\pi$
$283$	−3.10499	+	5.37801i	−0.184573	+	0.319689i	0.758860	+	0.651254i	$0.225757\pi$
$284$	17.9165	−	31.0323i	1.06315	−	1.84143i
$285$	−1.11448	−	1.93034i	−0.0660162	−	0.114343i
$286$	2.85648			0.168907
$287$		0			0
$288$	−25.0551			−1.47639
$289$	−5.49866	−	9.52395i	−0.323450	−	0.560232i
$290$	−9.25106	+	16.0233i	−0.543241	+	0.940920i
$291$	−1.94407	+	3.36723i	−0.113963	+	0.197390i
$292$	−22.4772	−	38.9316i	−1.31538	−	2.27830i
$293$	−16.5754			−0.968347			−0.484174	−	0.874972i	$-0.660880\pi$
$293$	−16.5754			−0.968347			−0.484174	+	0.874972i	$0.660880\pi$
$294$		0			0
$295$	−2.29249			−0.133474
$296$	50.8681	+	88.1062i	2.95665	+	5.12107i
$297$	−2.95457	+	5.11747i	−0.171442	+	0.296946i
$298$	−20.9744	+	36.3287i	−1.21501	+	2.10447i
$299$	0.326792	+	0.566020i	0.0188989	+	0.0327338i
$300$	−1.58060			−0.0912561
$301$		0			0
$302$	−37.2698			−2.14463
$303$	−7.57650	−	13.1229i	−0.435259	−	0.753890i
$304$	5.52475	−	9.56914i	0.316866	−	0.548828i
$305$	13.6695	−	23.6763i	0.782716	−	1.35570i
$306$	8.55944	+	14.8254i	0.489311	+	0.847511i
$307$	7.05788			0.402815			0.201407	−	0.979508i	$-0.435449\pi$
$307$	7.05788			0.402815			0.201407	+	0.979508i	$0.435449\pi$
$308$		0			0
$309$	−27.2426			−1.54978
$310$	−3.06347	−	5.30609i	−0.173993	−	0.301365i
$311$	10.5551	−	18.2820i	0.598525	−	1.03668i	−0.394514	−	0.918890i	$-0.629087\pi$
$311$	10.5551	−	18.2820i	0.598525	−	1.03668i	0.993039	−	0.117785i	$-0.0375795\pi$
$312$	6.28736	−	10.8900i	0.355952	−	0.616526i
$313$	0.990260	+	1.71518i	0.0559728	+	0.0969477i	0.892654	−	0.450742i	$-0.148841\pi$
$313$	0.990260	+	1.71518i	0.0559728	+	0.0969477i	−0.836681	+	0.547690i	$0.815507\pi$
$314$	−9.23194			−0.520989
$315$		0			0
$316$	11.6145			0.653368
$317$	9.02297	+	15.6282i	0.506781	+	0.877770i	0.999969	+	0.00784727i	$0.00249789\pi$
$317$	9.02297	+	15.6282i	0.506781	+	0.877770i	−0.493189	+	0.869922i	$0.664169\pi$
$318$	−8.96808	+	15.5332i	−0.502905	+	0.871057i
$319$	−1.62678	+	2.81767i	−0.0910822	+	0.157759i
$320$	30.9703	+	53.6421i	1.73129	+	2.99868i
$321$	12.1920			0.680492
$322$		0			0
$323$	−4.00498			−0.222843
$324$	10.9331	+	18.9366i	0.607393	+	1.05204i
$325$	−0.108157	+	0.187333i	−0.00599947	+	0.0103914i
$326$	18.8179	−	32.5936i	1.04223	−	1.80519i
$327$	−10.1664	−	17.6087i	−0.562202	−	0.973763i
$328$	−68.3682			−3.77500
$329$		0			0
$330$	8.41187			0.463058
$331$	7.33689	+	12.7079i	0.403272	+	0.698488i	0.994119	−	0.108296i	$-0.0345395\pi$
$331$	7.33689	+	12.7079i	0.403272	+	0.698488i	−0.590847	+	0.806784i	$0.701206\pi$
$332$	−18.0870	+	31.3276i	−0.992653	+	1.71933i
$333$	−6.46602	+	11.1995i	−0.354336	+	0.613728i
$334$	22.3175	+	38.6550i	1.22116	+	2.11511i
$335$	−9.79606			−0.535216
$336$		0			0
$337$	12.8080			0.697698			0.348849	−	0.937179i	$-0.386573\pi$
$337$	12.8080			0.697698			0.348849	+	0.937179i	$0.386573\pi$
$338$	−1.36263	−	2.36014i	−0.0741170	−	0.128374i
$339$	−2.08969	+	3.61946i	−0.113497	+	0.196582i
$340$	31.4028	−	54.3913i	1.70306	−	2.94978i
$341$	−0.538705	−	0.933065i	−0.0291725	−	0.0505283i
$342$	2.44883			0.132418
$343$		0			0
$344$	8.29125			0.447034
$345$	0.962348	+	1.66684i	0.0518111	+	0.0897394i
$346$	5.62146	−	9.73665i	0.302211	−	0.523445i
$347$	−10.1027	+	17.4984i	−0.542342	+	0.939363i	0.456428	+	0.889761i	$0.349129\pi$
$347$	−10.1027	+	17.4984i	−0.542342	+	0.939363i	−0.998769	+	0.0496025i	$0.984205\pi$
$348$	11.3408	+	19.6428i	0.607928	+	1.05296i
$349$	18.4434			0.987252			0.493626	−	0.869674i	$-0.335671\pi$
$349$	18.4434			0.987252			0.493626	+	0.869674i	$0.335671\pi$
$350$		0			0
$351$	5.63766			0.300916
$352$	11.0607	+	19.1576i	0.589536	+	1.02111i
$353$	−4.07218	+	7.05322i	−0.216740	+	0.375405i	−0.953810	−	0.300412i	$-0.902876\pi$
$353$	−4.07218	+	7.05322i	−0.216740	+	0.375405i	0.737069	+	0.675817i	$0.236209\pi$
$354$	−1.92301	+	3.33075i	−0.102207	+	0.177027i
$355$	−7.22064	−	12.5065i	−0.383232	−	0.663777i
$356$	31.3016			1.65898
$357$		0			0
$358$	39.2806			2.07604
$359$	16.3050	+	28.2411i	0.860545	+	1.49051i	0.871404	+	0.490566i	$0.163210\pi$
$359$	16.3050	+	28.2411i	0.860545	+	1.49051i	−0.0108595	+	0.999941i	$0.503457\pi$
$360$	−12.1250	+	21.0011i	−0.639043	+	1.10685i
$361$	9.21355	−	15.9583i	0.484923	−	0.839912i
$362$	24.6654	+	42.7218i	1.29639	+	2.24541i
$363$	−13.3314			−0.699715
$364$		0			0
$365$	−18.1173			−0.948304
$366$	−22.9329	−	39.7209i	−1.19872	−	2.07624i
$367$	−1.58006	+	2.73675i	−0.0824786	+	0.142857i	−0.904314	−	0.426868i	$-0.859617\pi$
$367$	−1.58006	+	2.73675i	−0.0824786	+	0.142857i	0.821835	+	0.569725i	$0.192950\pi$
$368$	−4.77059	+	8.26290i	−0.248684	+	0.430733i
$369$	−4.34526	−	7.52621i	−0.226205	−	0.391799i
$370$	64.9298			3.37554
$371$		0			0
$372$	−7.51094			−0.389424
$373$	0.738849	+	1.27972i	0.0382561	+	0.0662616i	0.884520	−	0.466503i	$-0.154486\pi$
$373$	0.738849	+	1.27972i	0.0382561	+	0.0662616i	−0.846263	+	0.532765i	$0.821153\pi$
$374$	7.55718	−	13.0894i	0.390773	−	0.676838i
$375$	−7.68059	+	13.3032i	−0.396624	+	0.686972i
$376$	10.9155	+	18.9061i	0.562922	+	0.975010i
$377$	3.10408			0.159868
$378$		0			0
$379$	10.7254			0.550927			0.275463	−	0.961312i	$-0.411169\pi$
$379$	10.7254			0.550927			0.275463	+	0.961312i	$0.411169\pi$
$380$	−4.49213	−	7.78060i	−0.230441	−	0.399136i
$381$	−5.91692	+	10.2484i	−0.303133	+	0.525042i
$382$	−7.55079	+	13.0784i	−0.386332	+	0.669147i
$383$	−10.7054	−	18.5424i	−0.547023	−	0.947471i	−0.998477	−	0.0551766i	$-0.982428\pi$
$383$	−10.7054	−	18.5424i	−0.547023	−	0.947471i	0.451454	−	0.892294i	$-0.350906\pi$
$384$	47.0830			2.40269
$385$		0			0
$386$	−23.8211			−1.21246
$387$	0.526965	+	0.912730i	0.0267871	+	0.0463967i
$388$	−7.83595	+	13.5723i	−0.397810	+	0.689027i
$389$	−17.3909	+	30.1220i	−0.881755	+	1.52725i	−0.0323675	+	0.999476i	$0.510305\pi$
$389$	−17.3909	+	30.1220i	−0.881755	+	1.52725i	−0.849388	+	0.527769i	$0.823029\pi$
$390$	−4.01270	−	6.95021i	−0.203191	−	0.351937i
$391$	3.45828			0.174893
$392$		0			0
$393$	14.1568			0.714119
$394$	7.45185	+	12.9070i	0.375419	+	0.650244i
$395$	2.34042	−	4.05373i	0.117759	−	0.203965i
$396$	−3.37649	+	5.84825i	−0.169675	+	0.293886i
$397$	2.22605	+	3.85564i	0.111722	+	0.193509i	0.916465	−	0.400115i	$-0.131030\pi$
$397$	2.22605	+	3.85564i	0.111722	+	0.193509i	−0.804742	+	0.593624i	$0.797697\pi$
$398$	−53.2426			−2.66881
$399$		0			0
$400$	−3.15780			−0.157890
$401$	6.87687	+	11.9111i	0.343415	+	0.594811i	0.985064	−	0.172186i	$-0.0550831\pi$
$401$	6.87687	+	11.9111i	0.343415	+	0.594811i	−0.641650	+	0.766998i	$0.721750\pi$
$402$	−8.21724	+	14.2327i	−0.409839	+	0.709861i
$403$	−0.513956	+	0.890198i	−0.0256020	+	0.0443439i
$404$	−30.5385	−	52.8943i	−1.51935	−	2.63159i
$405$	8.81241			0.437892
$406$		0			0
$407$	11.4178			0.565959
$408$	−33.2680	−	57.6219i	−1.64701	−	2.85271i
$409$	−1.74603	+	3.02422i	−0.0863358	+	0.149538i	−0.905960	−	0.423364i	$-0.860849\pi$
$409$	−1.74603	+	3.02422i	−0.0863358	+	0.149538i	0.819624	+	0.572902i	$0.194182\pi$
$410$	−21.8169	+	37.7879i	−1.07746	+	1.86621i
$411$	−5.87822	−	10.1814i	−0.289951	−	0.502210i
$412$	−109.806			−5.40977
$413$		0			0
$414$	−2.11455			−0.103925
$415$	7.28935	+	12.6255i	0.357820	+	0.619763i
$416$	10.5525	−	18.2775i	0.517380	−	0.896128i
$417$	−2.69283	+	4.66412i	−0.131869	+	0.228403i
$418$	−1.08105	−	1.87243i	−0.0528757	−	0.0915834i
$419$	3.56737			0.174278			0.0871388	−	0.996196i	$-0.472228\pi$
$419$	3.56737			0.174278			0.0871388	+	0.996196i	$0.472228\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$	−22.7429	−	39.3919i	−1.10711	−	1.91757i
$423$	−1.38750	+	2.40323i	−0.0674627	+	0.116849i
$424$	−22.8262	+	39.5361i	−1.10854	+	1.92004i
$425$	0.572285	+	0.991227i	0.0277599	+	0.0480816i
$426$	−24.2276			−1.17383
$427$		0			0
$428$	49.1423			2.37538
$429$	−0.705626	−	1.22218i	−0.0340680	−	0.0590074i
$430$	2.64581	−	4.58268i	0.127592	−	0.220996i
$431$	5.68211	−	9.84171i	0.273698	−	0.474059i	−0.696108	−	0.717937i	$-0.745087\pi$
$431$	5.68211	−	9.84171i	0.273698	−	0.474059i	0.969806	+	0.243879i	$0.0784198\pi$
$432$	41.1500	+	71.2738i	1.97983	+	3.42916i
$433$	21.2136			1.01946			0.509731	−	0.860334i	$-0.329745\pi$
$433$	21.2136			1.01946			0.509731	+	0.860334i	$0.329745\pi$
$434$		0			0
$435$	9.14101			0.438278
$436$	−40.9776	−	70.9752i	−1.96247	−	3.39910i
$437$	0.247351	−	0.428424i	0.0118324	−	0.0204943i
$438$	−15.1974	+	26.3226i	−0.726158	+	1.25774i
$439$	−12.2503	−	21.2182i	−0.584676	−	1.01269i	−0.994916	−	0.100711i	$-0.967888\pi$
$439$	−12.2503	−	21.2182i	−0.584676	−	1.01269i	0.410239	−	0.911978i	$-0.365445\pi$
$440$	21.4105			1.02070
$441$		0			0
$442$	−14.4200			−0.685888
$443$	−20.2344	−	35.0470i	−0.961366	−	1.66513i	−0.719077	−	0.694930i	$-0.755435\pi$
$443$	−20.2344	−	35.0470i	−0.961366	−	1.66513i	−0.242288	−	0.970204i	$-0.577898\pi$
$444$	39.7983	−	68.9327i	1.88874	−	3.27140i
$445$	6.30753	−	10.9250i	0.299005	−	0.517893i
$446$	−7.27937	−	12.6082i	−0.344688	−	0.597017i
$447$	20.7249			0.980254
$448$		0			0
$449$	−27.7638			−1.31025			−0.655127	−	0.755519i	$-0.727385\pi$
$449$	−27.7638			−1.31025			−0.655127	+	0.755519i	$0.727385\pi$
$450$	−0.349922	−	0.606083i	−0.0164955	−	0.0285710i
$451$	−3.83646	+	6.64494i	−0.180652	+	0.312898i
$452$	−8.42292	+	14.5889i	−0.396181	+	0.686205i
$453$	9.20661	+	15.9463i	0.432564	+	0.749223i
$454$	−54.8362			−2.57359
$455$		0			0
$456$	−9.51789			−0.445716
$457$	5.59696	+	9.69422i	0.261815	+	0.453476i	0.966724	−	0.255821i	$-0.0823457\pi$
$457$	5.59696	+	9.69422i	0.261815	+	0.453476i	−0.704910	+	0.709297i	$0.749012\pi$
$458$	34.4059	−	59.5928i	1.60768	−	2.78459i
$459$	14.9151	−	25.8338i	0.696179	−	1.20582i
$460$	3.87893	+	6.71850i	0.180856	+	0.313252i
$461$	9.29773			0.433038			0.216519	−	0.976278i	$-0.430530\pi$
$461$	9.29773			0.433038			0.216519	+	0.976278i	$0.430530\pi$
$462$		0			0
$463$	28.2439			1.31260			0.656302	−	0.754499i	$-0.272120\pi$
$463$	28.2439			1.31260			0.656302	+	0.754499i	$0.272120\pi$
$464$	22.6571	+	39.2432i	1.05183	+	1.82182i
$465$	−1.51351	+	2.62148i	−0.0701875	+	0.121568i
$466$	1.08105	−	1.87243i	0.0500785	−	0.0867385i
$467$	11.1303	+	19.2783i	0.515050	+	0.892093i	0.999847	+	0.0174663i	$0.00555997\pi$
$467$	11.1303	+	19.2783i	0.515050	+	0.892093i	−0.484797	+	0.874626i	$0.661107\pi$
$468$	6.44273			0.297815
$469$		0			0
$470$	13.9329			0.642676
$471$	2.28053	+	3.95000i	0.105081	+	0.182006i
$472$	−4.89457	+	8.47765i	−0.225291	+	0.390215i
$473$	0.465261	−	0.805855i	0.0213927	−	0.0370533i
$474$	−3.92643	−	6.80078i	−0.180347	−	0.312370i
$475$	0.163729			0.00751242
$476$		0			0
$477$	−5.80302			−0.265702
$478$	−27.3190	−	47.3179i	−1.24954	−	2.16427i
$479$	−16.4382	+	28.4718i	−0.751081	+	1.30091i	0.196219	+	0.980560i	$0.437134\pi$
$479$	−16.4382	+	28.4718i	−0.751081	+	1.30091i	−0.947299	+	0.320350i	$0.896200\pi$
$480$	31.0754	−	53.8242i	1.41839	−	2.45673i
$481$	−5.44661	−	9.43381i	−0.248344	−	0.430145i
$482$	−37.6413			−1.71451
$483$		0			0
$484$	−53.7346			−2.44248
$485$	3.15801	+	5.46984i	0.143398	+	0.248373i
$486$	−15.6539	+	27.1134i	−0.710078	+	1.22989i
$487$	13.9462	−	24.1555i	0.631962	−	1.09459i	−0.355188	−	0.934795i	$-0.615583\pi$
$487$	13.9462	−	24.1555i	0.631962	−	1.09459i	0.987150	−	0.159796i	$-0.0510836\pi$
$488$	−58.3703	−	101.100i	−2.64230	−	4.57660i
$489$	−18.5941			−0.840852
$490$		0			0
$491$	10.6571			0.480948			0.240474	−	0.970656i	$-0.422697\pi$
$491$	10.6571			0.480948			0.240474	+	0.970656i	$0.422697\pi$
$492$	26.7450	+	46.3237i	1.20576	+	2.08844i
$493$	8.21224	−	14.2240i	0.369861	−	0.640618i
$494$	−1.03138	+	1.78640i	−0.0464040	+	0.0803740i
$495$	1.36078	+	2.35694i	0.0611625	+	0.105936i
$496$	−15.0057			−0.673776
$497$		0			0
$498$	24.4581			1.09600
$499$	12.2557	+	21.2275i	0.548641	+	0.950274i	0.998368	+	0.0571077i	$0.0181878\pi$
$499$	12.2557	+	21.2275i	0.548641	+	0.950274i	−0.449727	+	0.893166i	$0.648479\pi$
$500$	−30.9581	+	53.6210i	−1.38449	+	2.39800i
$501$	11.0260	−	19.0976i	0.492605	−	0.853217i
$502$	−35.5775	−	61.6221i	−1.58790	−	2.75033i
$503$	38.0054			1.69458			0.847288	−	0.531134i	$-0.178234\pi$
$503$	38.0054			1.69458			0.847288	+	0.531134i	$0.178234\pi$
$504$		0			0
$505$	−24.6151			−1.09536
$506$	0.933476	+	1.61683i	0.0414981	+	0.0718768i
$507$	−0.673208	+	1.16603i	−0.0298982	+	0.0517852i
$508$	−23.8493	+	41.3082i	−1.05814	+	1.83275i
$509$	19.9250	+	34.5112i	0.883161	+	1.52968i	0.847807	+	0.530305i	$0.177923\pi$
$509$	19.9250	+	34.5112i	0.883161	+	1.52968i	0.0353545	+	0.999375i	$0.488744\pi$
$510$	−42.4644			−1.88036
$511$		0			0
$512$	35.4186			1.56530
$513$	−2.13359	−	3.69549i	−0.0942004	−	0.163160i
$514$	14.4708	−	25.0642i	0.638279	−	1.10553i
$515$	−22.1269	+	38.3249i	−0.975027	+	1.68880i
$516$	−3.24346	−	5.61784i	−0.142786	−	0.247312i
$517$	2.45007			0.107754
$518$		0			0
$519$	−5.55459			−0.243819
$520$	−10.2134	−	17.6901i	−0.447887	−	0.775764i
$521$	−9.81670	+	17.0030i	−0.430077	+	0.744916i	−0.996880	−	0.0789382i	$-0.974847\pi$
$521$	−9.81670	+	17.0030i	−0.430077	+	0.744916i	0.566802	+	0.823854i	$0.308180\pi$
$522$	−5.02135	+	8.69724i	−0.219779	+	0.380668i
$523$	11.4162	+	19.7734i	0.499195	+	0.864632i	1.00000		0.000928862i	$-0.000295666\pi$
$523$	11.4162	+	19.7734i	0.499195	+	0.864632i	−0.500804	+	0.865561i	$0.666962\pi$
$524$	57.0619			2.49276
$525$		0			0
$526$	28.2275			1.23078
$527$	2.71947	+	4.71026i	0.118462	+	0.205182i
$528$	10.3009	−	17.8417i	0.448289	−	0.776459i
$529$	11.2864	−	19.5486i	0.490714	−	0.849941i
$530$	14.5681	+	25.2326i	0.632796	+	1.09603i
$531$	−1.24433			−0.0539994
$532$		0			0
$533$	7.32040			0.317082
$534$	−10.5819	−	18.3284i	−0.457923	−	0.793146i
$535$	9.90257	−	17.1518i	0.428125	−	0.741535i
$536$	−20.9151	+	36.2260i	−0.903394	+	1.56472i
$537$	−9.70333	−	16.8067i	−0.418730	−	0.725261i
$538$	−32.6214			−1.40641
$539$		0			0
$540$	66.9175			2.87967
$541$	4.82334	+	8.35427i	0.207372	+	0.359178i	0.950886	−	0.309542i	$-0.100176\pi$
$541$	4.82334	+	8.35427i	0.207372	+	0.359178i	−0.743514	+	0.668720i	$0.766842\pi$
$542$	−3.75663	+	6.50667i	−0.161361	+	0.279486i
$543$	12.1860	−	21.1068i	0.522952	−	0.905779i
$544$	−55.8360	−	96.7108i	−2.39395	−	4.14644i
$545$	−33.0292			−1.41482
$546$		0			0
$547$	−43.8570			−1.87519			−0.937596	−	0.347728i	$-0.886953\pi$
$547$	−43.8570			−1.87519			−0.937596	+	0.347728i	$0.886953\pi$
$548$	−23.6933	−	41.0380i	−1.01213	−	1.75306i
$549$	7.41965	−	12.8512i	0.316663	−	0.548476i
$550$	−0.308949	+	0.535115i	−0.0131736	+	0.0228174i
$551$	−1.17475	−	2.03473i	−0.0500461	−	0.0866823i
$552$	8.21864			0.349808
$553$		0			0
$554$	−65.2083			−2.77044
$555$	−16.0394	−	27.7810i	−0.680833	−	1.17924i
$556$	−10.8540	+	18.7996i	−0.460311	+	0.797282i
$557$	−7.45977	+	12.9207i	−0.316080	+	0.547467i	−0.979667	−	0.200633i	$-0.935700\pi$
$557$	−7.45977	+	12.9207i	−0.316080	+	0.547467i	0.663586	+	0.748100i	$0.269034\pi$
$558$	−1.66281	−	2.88007i	−0.0703924	−	0.121923i
$559$	−0.887771			−0.0375487
$560$		0			0
$561$	−7.46729			−0.315269
$562$	5.28521	+	9.15426i	0.222943	+	0.386149i
$563$	−8.63486	+	14.9560i	−0.363916	+	0.630321i	−0.988602	−	0.150555i	$-0.951894\pi$
$563$	−8.63486	+	14.9560i	−0.363916	+	0.630321i	0.624686	+	0.780876i	$0.285227\pi$
$564$	8.54007	−	14.7918i	0.359602	−	0.622849i
$565$	3.39457	+	5.87957i	0.142811	+	0.247355i
$566$	16.9238			0.711359
$567$		0			0
$568$	−61.6657			−2.58743
$569$	−13.2662	−	22.9777i	−0.556148	−	0.963277i	−0.997813	−	0.0660972i	$-0.978945\pi$
$569$	−13.2662	−	22.9777i	−0.556148	−	0.963277i	0.441665	−	0.897180i	$-0.354388\pi$
$570$	−3.03724	+	5.26065i	−0.127216	+	0.220345i
$571$	0.992844	−	1.71966i	0.0415492	−	0.0719654i	−0.844503	−	0.535551i	$-0.820104\pi$
$571$	0.992844	−	1.71966i	0.0415492	−	0.0719654i	0.886052	+	0.463586i	$0.153437\pi$
$572$	−2.84416	−	4.92623i	−0.118920	−	0.205976i
$573$	7.46097			0.311686
$574$		0			0
$575$	−0.141379			−0.00589593
$576$	16.8103	+	29.1162i	0.700428	+	1.21318i
$577$	5.94915	−	10.3042i	0.247666	−	0.428971i	−0.715212	−	0.698908i	$-0.753670\pi$
$577$	5.94915	−	10.3042i	0.247666	−	0.428971i	0.962878	+	0.269937i	$0.0870030\pi$
$578$	−14.9852	+	25.9551i	−0.623303	+	1.07959i
$579$	5.88443	+	10.1921i	0.244549	+	0.423571i
$580$	36.8446			1.52989
$581$		0			0
$582$	10.5962			0.439225
$583$	2.56176	+	4.43711i	0.106097	+	0.183766i
$584$	−38.6814	+	66.9981i	−1.60065	+	2.77240i
$585$	1.29826	−	2.24865i	0.0536765	−	0.0929704i
$586$	22.5861	+	39.1203i	0.933024	+	1.61604i
$587$	−33.5122			−1.38320			−0.691598	−	0.722283i	$-0.743093\pi$
$587$	−33.5122			−1.38320			−0.691598	+	0.722283i	$0.743093\pi$
$588$		0			0
$589$	0.778033			0.0320583
$590$	3.12380	+	5.41058i	0.128605	+	0.222750i
$591$	3.68160	−	6.37672i	0.151441	−	0.262303i
$592$	79.5109	−	137.717i	3.26788	−	5.66013i
$593$	17.6408	+	30.5547i	0.724419	+	1.25473i	0.959213	+	0.282686i	$0.0912253\pi$
$593$	17.6408	+	30.5547i	0.724419	+	1.25473i	−0.234793	+	0.972045i	$0.575441\pi$
$594$	16.1039			0.660751
$595$		0			0
$596$	83.5357			3.42176
$597$	13.1523	+	22.7805i	0.538288	+	0.932343i
$598$	0.890590	−	1.54255i	0.0364189	−	0.0630794i
$599$	12.5034	−	21.6565i	0.510876	−	0.884863i	−0.489045	−	0.872259i	$-0.662655\pi$
$599$	12.5034	−	21.6565i	0.510876	−	0.884863i	0.999921	−	0.0126040i	$-0.00401207\pi$
$600$	1.36004	+	2.35566i	0.0555236	+	0.0961696i
$601$	28.4688			1.16127			0.580634	−	0.814165i	$-0.302805\pi$
$601$	28.4688			1.16127			0.580634	+	0.814165i	$0.302805\pi$
$602$		0			0
$603$	−5.31717			−0.216532
$604$	37.1090	+	64.2747i	1.50994	+	2.61530i
$605$	−10.8280	+	18.7546i	−0.440219	+	0.762482i
$606$	−20.6479	+	35.7631i	−0.838762	+	1.45278i
$607$	18.0234	+	31.2175i	0.731549	+	1.26708i	0.956221	+	0.292646i	$0.0945356\pi$
$607$	18.0234	+	31.2175i	0.731549	+	1.26708i	−0.224672	+	0.974434i	$0.572131\pi$
$608$	−15.9745			−0.647853
$609$		0			0
$610$	−74.5058			−3.01665
$611$	−1.16875	−	2.02434i	−0.0472827	−	0.0818961i
$612$	17.0450	−	29.5229i	0.689005	−	1.19339i
$613$	−9.16264	+	15.8702i	−0.370075	+	0.640989i	−0.989577	−	0.144006i	$-0.954001\pi$
$613$	−9.16264	+	15.8702i	−0.370075	+	0.640989i	0.619501	+	0.784996i	$0.287335\pi$
$614$	−9.61725	−	16.6576i	−0.388121	−	0.672245i
$615$	21.5573			0.869276
$616$		0			0
$617$	44.3782			1.78660			0.893299	−	0.449463i	$-0.148385\pi$
$617$	44.3782			1.78660			0.893299	+	0.449463i	$0.148385\pi$
$618$	37.1214	+	64.2962i	1.49324	+	2.58637i
$619$	−12.5043	+	21.6580i	−0.502588	+	0.870509i	0.497407	+	0.867517i	$0.334286\pi$
$619$	−12.5043	+	21.6580i	−0.502588	+	0.870509i	−0.999996	+	0.00299144i	$0.999048\pi$
$620$	−6.10051	+	10.5664i	−0.245002	+	0.424357i
$621$	1.84234	+	3.19103i	0.0739307	+	0.128052i
$622$	−57.5306			−2.30677
$623$		0			0
$624$	−19.6553			−0.786842
$625$	11.9358	+	20.6734i	0.477433	+	0.826938i
$626$	2.69871	−	4.67429i	0.107862	−	0.186822i
$627$	−0.534093	+	0.925076i	−0.0213296	+	0.0369440i
$628$	9.19212	+	15.9212i	0.366806	+	0.635326i
$629$	−57.6388			−2.29821
$630$		0			0
$631$	−18.4638			−0.735032			−0.367516	−	0.930017i	$-0.619792\pi$
$631$	−18.4638			−0.735032			−0.367516	+	0.930017i	$0.619792\pi$
$632$	−9.99382	−	17.3098i	−0.397533	−	0.688547i
$633$	−11.2362	+	19.4616i	−0.446598	+	0.773531i
$634$	24.5899	−	42.5909i	0.976588	−	1.69150i
$635$	9.61165	+	16.6479i	0.381427	+	0.660650i
$636$	35.7176			1.41629
$637$		0			0
$638$	8.86677			0.351039
$639$	−3.91927	−	6.78837i	−0.155044	−	0.268544i
$640$	38.2416	−	66.2364i	1.51163	−	2.61822i
$641$	10.6284	−	18.4088i	0.419795	−	0.727106i	−0.576124	−	0.817362i	$-0.695435\pi$
$641$	10.6284	−	18.4088i	0.419795	−	0.727106i	0.995919	+	0.0902567i	$0.0287687\pi$
$642$	−16.6132	−	28.7748i	−0.655669	−	1.13565i
$643$	36.0554			1.42188			0.710942	−	0.703251i	$-0.248269\pi$
$643$	36.0554			1.42188			0.710942	+	0.703251i	$0.248269\pi$
$644$		0			0
$645$	−2.61434			−0.102939
$646$	5.45729	+	9.45230i	0.214714	+	0.371896i
$647$	19.9117	−	34.4881i	0.782809	−	1.35587i	−0.147490	−	0.989064i	$-0.547119\pi$
$647$	19.9117	−	34.4881i	0.782809	−	1.35587i	0.930299	−	0.366802i	$-0.119547\pi$
$648$	18.8149	−	32.5884i	0.739120	−	1.28019i
$649$	0.549314	+	0.951440i	0.0215625	+	0.0373473i
$650$	0.589510			0.0231225
$651$		0			0
$652$	−74.9469			−2.93515
$653$	16.2335	+	28.1172i	0.635265	+	1.10031i	0.986459	+	0.164008i	$0.0524423\pi$
$653$	16.2335	+	28.1172i	0.635265	+	1.10031i	−0.351195	+	0.936303i	$0.614224\pi$
$654$	−27.7059	+	47.9881i	−1.08339	+	1.87648i
$655$	11.4984	−	19.9159i	0.449281	−	0.778177i
$656$	53.4324	+	92.5477i	2.08619	+	3.61338i
$657$	−9.83384			−0.383655
$658$		0			0
$659$	23.5230			0.916327			0.458164	−	0.888868i	$-0.348507\pi$
$659$	23.5230			0.916327			0.458164	+	0.888868i	$0.348507\pi$
$660$	−8.37558	−	14.5069i	−0.326019	−	0.564682i
$661$	7.01944	−	12.1580i	0.273025	−	0.472893i	−0.696610	−	0.717450i	$-0.745309\pi$
$661$	7.01944	−	12.1580i	0.273025	−	0.472893i	0.969635	+	0.244557i	$0.0786426\pi$
$662$	19.9949	−	34.6321i	0.777122	−	1.34602i
$663$	3.56211	+	6.16976i	0.138341	+	0.239614i
$664$	62.2525			2.41587
$665$		0			0
$666$	35.2431			1.36564
$667$	1.01439	+	1.75698i	0.0392773	+	0.0680303i
$668$	44.4424	−	76.9765i	1.71953	−	2.97831i
$669$	−3.59639	+	6.22913i	−0.139044	+	0.240832i
$670$	13.3484	+	23.1200i	0.515692	+	0.893205i
$671$	−13.1017			−0.505786
$672$		0			0
$673$	−47.1937			−1.81918			−0.909592	−	0.415502i	$-0.863606\pi$
$673$	−47.1937			−1.81918			−0.909592	+	0.415502i	$0.863606\pi$
$674$	−17.4526	−	30.2287i	−0.672247	−	1.16437i
$675$	−0.609753	+	1.05612i	−0.0234694	+	0.0406502i
$676$	−2.71349	+	4.69991i	−0.104365	+	0.180766i
$677$	−4.79438	−	8.30411i	−0.184263	−	0.319153i	0.759065	−	0.651015i	$-0.225656\pi$
$677$	−4.79438	−	8.30411i	−0.184263	−	0.319153i	−0.943328	+	0.331862i	$0.892323\pi$
$678$	11.3899			0.437426
$679$		0			0
$680$	−108.083			−4.14481
$681$	13.5460	+	23.4623i	0.519083	+	0.899078i
$682$	−1.46811	+	2.54284i	−0.0562167	+	0.0973702i
$683$	−23.6581	+	40.9769i	−0.905250	+	1.56794i	−0.0846691	+	0.996409i	$0.526983\pi$
$683$	−23.6581	+	40.9769i	−0.905250	+	1.56794i	−0.820581	+	0.571530i	$0.806350\pi$
$684$	−2.43827	−	4.22321i	−0.0932296	−	0.161478i
$685$	−19.0976			−0.729680
$686$		0			0
$687$	−33.9967			−1.29705
$688$	−6.47994	−	11.2236i	−0.247045	−	0.427895i
$689$	2.44407	−	4.23325i	0.0931117	−	0.161274i
$690$	2.62264	−	4.54254i	0.0998421	−	0.172932i
$691$	−13.5559	−	23.4796i	−0.515692	−	0.893205i	−0.999834	−	0.0182158i	$-0.994201\pi$
$691$	−13.5559	−	23.4796i	−0.515692	−	0.893205i	0.484142	−	0.874990i	$-0.339132\pi$
$692$	−22.3888			−0.851095
$693$		0			0
$694$	55.0648			2.09023
$695$	4.37433	+	7.57656i	0.165928	+	0.287395i
$696$	19.5165	−	33.8036i	0.739771	−	1.28132i
$697$	19.3670	−	33.5447i	0.733578	−	1.27059i
$698$	−25.1314	−	43.5289i	−0.951238	−	1.64759i
$699$	−1.06819			−0.0404025
$700$		0			0
$701$	−1.79821			−0.0679176			−0.0339588	−	0.999423i	$-0.510811\pi$
$701$	−1.79821			−0.0679176			−0.0339588	+	0.999423i	$0.510811\pi$
$702$	−7.68202	−	13.3057i	−0.289939	−	0.502190i
$703$	−4.12258	+	7.14051i	−0.155486	+	0.269310i
$704$	14.8419	−	25.7069i	0.559375	−	0.968866i
$705$	−3.44179	−	5.96135i	−0.129625	−	0.224517i
$706$	22.1954			0.835336
$707$		0			0
$708$	7.65885			0.287837
$709$	14.1615	+	24.5284i	0.531846	+	0.921185i	0.999309	+	0.0371721i	$0.0118350\pi$
$709$	14.1615	+	24.5284i	0.531846	+	0.921185i	−0.467462	+	0.884013i	$0.654832\pi$
$710$	−19.6780	+	34.0834i	−0.738504	+	1.27913i
$711$	1.27035	−	2.20031i	0.0476418	−	0.0825180i
$712$	−26.9337	−	46.6506i	−1.00938	−	1.74831i
$713$	−0.671827			−0.0251601
$714$		0			0
$715$	−2.29249			−0.0857341
$716$	−39.1112	−	67.7425i	−1.46165	−	2.53166i
$717$	−13.4970	+	23.3775i	−0.504055	+	0.873050i
$718$	44.4352	−	76.9640i	1.65831	−	2.87227i
$719$	−20.9485	−	36.2839i	−0.781249	−	1.35316i	−0.931215	−	0.364471i	$-0.881250\pi$
$719$	−20.9485	−	36.2839i	−0.781249	−	1.35316i	0.149966	−	0.988691i	$-0.452084\pi$
$720$	37.9046			1.41262
$721$		0			0
$722$	−50.2184			−1.86894
$723$	9.29838	+	16.1053i	0.345810	+	0.598961i
$724$	49.1180	−	85.0749i	1.82546	−	3.16179i
$725$	−0.335728	+	0.581499i	−0.0124686	+	0.0215963i
$726$	18.1657	+	31.4638i	0.674191	+	1.16773i
$727$	−19.5123			−0.723670			−0.361835	−	0.932242i	$-0.617850\pi$
$727$	−19.5123			−0.723670			−0.361835	+	0.932242i	$0.617850\pi$
$728$		0			0
$729$	27.5552			1.02056
$730$	24.6871	+	42.7593i	0.913711	+	1.58259i
$731$	−2.34871	+	4.06808i	−0.0868701	+	0.150463i
$732$	−45.6679	+	79.0991i	−1.68793	+	2.92359i
$733$	8.87698	+	15.3754i	0.327879	+	0.567902i	0.982091	−	0.188409i	$-0.0603330\pi$
$733$	8.87698	+	15.3754i	0.327879	+	0.567902i	−0.654212	+	0.756311i	$0.727000\pi$
$734$	8.61213			0.317880
$735$		0			0
$736$	13.7939			0.508450
$737$	2.34728	+	4.06562i	0.0864633	+	0.149759i
$738$	−11.8419	+	20.5108i	−0.435907	+	0.755013i
$739$	−22.1571	+	38.3772i	−0.815061	+	1.41173i	0.0942227	+	0.995551i	$0.469963\pi$
$739$	−22.1571	+	38.3772i	−0.815061	+	1.41173i	−0.909284	+	0.416176i	$0.863370\pi$
$740$	−64.6497	−	111.977i	−2.37657	−	4.11634i
$741$	1.01911			0.0374380
$742$		0			0
$743$	−7.16727			−0.262941			−0.131471	−	0.991320i	$-0.541970\pi$
$743$	−7.16727			−0.262941			−0.131471	+	0.991320i	$0.541970\pi$
$744$	6.46285	+	11.1940i	0.236940	+	0.410392i
$745$	16.8331	−	29.1558i	0.616718	−	1.06819i
$746$	2.01355	−	3.48757i	0.0737212	−	0.127689i
$747$	3.95657	+	6.85297i	0.144763	+	0.250737i
$748$	−30.0983			−1.10050
$749$		0			0
$750$	41.8630			1.52862
$751$	16.9532	+	29.3639i	0.618632	+	1.07150i	0.989736	+	0.142911i	$0.0456462\pi$
$751$	16.9532	+	29.3639i	0.618632	+	1.07150i	−0.371103	+	0.928592i	$0.621020\pi$
$752$	17.0618	−	29.5518i	0.622178	−	1.07764i
$753$	−17.5772	+	30.4445i	−0.640547	+	1.10946i
$754$	−4.22970	−	7.32606i	−0.154037	−	0.266799i
$755$	29.9110			1.08857
$756$		0			0
$757$	−0.906670			−0.0329535			−0.0164767	−	0.999864i	$-0.505245\pi$
$757$	−0.906670			−0.0329535			−0.0164767	+	0.999864i	$0.505245\pi$
$758$	−14.6147	−	25.3134i	−0.530830	−	0.919424i
$759$	0.461186	−	0.798798i	0.0167400	−	0.0289945i
$760$	−7.73059	+	13.3898i	−0.280418	+	0.485698i
$761$	10.1247	+	17.5365i	0.367020	+	0.635697i	0.989098	−	0.147258i	$-0.0470449\pi$
$761$	10.1247	+	17.5365i	0.367020	+	0.635697i	−0.622079	+	0.782955i	$0.713712\pi$
$762$	32.2502			1.16830
$763$		0			0
$764$	30.0729			1.08800
$765$	−6.86942	−	11.8982i	−0.248364	−	0.430180i
$766$	−29.1750	+	50.5326i	−1.05414	+	1.82582i
$767$	0.524077	−	0.907729i	0.0189233	−	0.0327762i
$768$	−26.0259	−	45.0782i	−0.939129	−	1.62662i
$769$	36.9094			1.33099			0.665494	−	0.746403i	$-0.268221\pi$
$769$	36.9094			1.33099			0.665494	+	0.746403i	$0.268221\pi$
$770$		0			0
$771$	−14.2987			−0.514954
$772$	23.7183	+	41.0814i	0.853642	+	1.47855i
$773$	−4.94018	+	8.55665i	−0.177686	+	0.307761i	−0.941088	−	0.338163i	$-0.890194\pi$
$773$	−4.94018	+	8.55665i	−0.177686	+	0.307761i	0.763402	+	0.645924i	$0.223528\pi$
$774$	1.43611	−	2.48742i	0.0516199	−	0.0894083i
$775$	−0.111176	−	0.192562i	−0.00399355	−	0.00691704i
$776$	26.9701			0.968169
$777$		0			0
$778$	94.7893			3.39836
$779$	−2.77043	−	4.79852i	−0.0992609	−	0.171925i
$780$	−7.99079	+	13.8404i	−0.286116	+	0.495568i
$781$	−3.46035	+	5.99350i	−0.123821	+	0.214464i
$782$	−4.71233	−	8.16200i	−0.168513	−	0.291873i
$783$	17.4998			0.625391
$784$		0			0
$785$	7.40915			0.264444
$786$	−19.2905	−	33.4121i	−0.688069	−	1.19177i
$787$	18.8411	−	32.6337i	0.671611	−	1.16326i	−0.305836	−	0.952084i	$-0.598936\pi$
$787$	18.8411	−	32.6337i	0.671611	−	1.16326i	0.977447	−	0.211180i	$-0.0677307\pi$
$788$	14.8394	−	25.7026i	0.528632	−	0.915617i
$789$	−6.97292	−	12.0775i	−0.248243	−	0.429969i
$790$	−12.7565			−0.453854
$791$		0			0
$792$	11.6213			0.412945
$793$	6.24989	+	10.8251i	0.221940	+	0.384412i
$794$	6.06656	−	10.5076i	0.215294	−	0.372900i
$795$	7.19738	−	12.4662i	0.255265	−	0.442131i
$796$	53.0129	+	91.8211i	1.87899	+	3.25451i
$797$	−28.3837			−1.00540			−0.502701	−	0.864460i	$-0.667660\pi$
$797$	−28.3837			−1.00540			−0.502701	+	0.864460i	$0.667660\pi$
$798$		0			0
$799$	−12.3683			−0.437560
$800$	2.28266	+	3.95368i	0.0807041	+	0.139784i
$801$	3.42364	−	5.92992i	0.120968	−	0.209524i
$802$	18.7412	−	32.4607i	0.661775	−	1.14623i
$803$	4.34118	+	7.51915i	0.153197	+	0.265345i
$804$	32.7272			1.15420
$805$		0			0
$806$	2.80132			0.0986722
$807$	8.05834	+	13.9574i	0.283667	+	0.491325i
$808$	−52.5543	+	91.0268i	−1.84886	+	3.20231i
$809$	5.87327	−	10.1728i	0.206493	−	0.357657i	−0.744114	−	0.668052i	$-0.767128\pi$
$809$	5.87327	−	10.1728i	0.206493	−	0.357657i	0.950607	+	0.310396i	$0.100461\pi$
$810$	−12.0080	−	20.7985i	−0.421919	−	0.730784i
$811$	−2.01940			−0.0709108			−0.0354554	−	0.999371i	$-0.511288\pi$
$811$	−2.01940			−0.0709108			−0.0354554	+	0.999371i	$0.511288\pi$
$812$		0			0
$813$	3.71194			0.130184
$814$	−15.5582	−	26.9475i	−0.545313	−	0.944511i
$815$	−15.1024	+	26.1581i	−0.529014	+	0.916280i
$816$	−52.0005	+	90.0676i	−1.82038	+	3.15300i
$817$	0.335980	+	0.581934i	0.0117544	+	0.0203593i
$818$	9.51676			0.332746
$819$		0			0
$820$	86.8910			3.03437
$821$	7.54208	+	13.0633i	0.263220	+	0.455911i	0.967096	−	0.254412i	$-0.0818820\pi$
$821$	7.54208	+	13.0633i	0.263220	+	0.455911i	−0.703875	+	0.710323i	$0.748549\pi$
$822$	−16.0196	+	27.7468i	−0.558748	+	0.967780i
$823$	7.38828	−	12.7969i	0.257539	−	0.446071i	−0.708043	−	0.706170i	$-0.750422\pi$
$823$	7.38828	−	12.7969i	0.257539	−	0.446071i	0.965582	+	0.260098i	$0.0837550\pi$
$824$	94.4839	+	163.651i	3.29150	+	5.70105i
$825$	0.305274			0.0106283
$826$		0			0
$827$	13.0407			0.453471			0.226736	−	0.973956i	$-0.427195\pi$
$827$	13.0407			0.453471			0.226736	+	0.973956i	$0.427195\pi$
$828$	2.10543	+	3.64671i	0.0731688	+	0.126732i
$829$	−12.7291	+	22.0474i	−0.442099	+	0.765738i	−0.997845	−	0.0656144i	$-0.979099\pi$
$829$	−12.7291	+	22.0474i	−0.442099	+	0.765738i	0.555746	+	0.831352i	$0.312433\pi$
$830$	19.8653	−	34.4077i	0.689535	−	1.19431i
$831$	16.1082	+	27.9002i	0.558786	+	0.967845i
$832$	−28.3200			−0.981820
$833$		0			0
$834$	14.6773			0.508233
$835$	−17.9110	−	31.0228i	−0.619835	−	1.07359i
$836$	−2.15277	+	3.72870i	−0.0744549	+	0.128960i
$837$	−2.89751	+	5.01864i	−0.100153	+	0.173469i
$838$	−4.86099	−	8.41948i	−0.167920	−	0.290846i
$839$	−32.1703			−1.11064			−0.555321	−	0.831636i	$-0.687404\pi$
$839$	−32.1703			−1.11064			−0.555321	+	0.831636i	$0.687404\pi$
$840$		0			0
$841$	−19.3647			−0.667747
$842$	13.6263	+	23.6014i	0.469592	+	0.813357i
$843$	2.61117	−	4.52268i	0.0899335	−	0.155769i
$844$	−45.2896	+	78.4439i	−1.55893	+	2.70015i
$845$	1.09358	+	1.89414i	0.0376204	+	0.0651604i
$846$	7.56259			0.260007
$847$		0			0
$848$	71.3582			2.45045
$849$	−4.18061	−	7.24104i	−0.143478	−	0.248512i
$850$	1.55962	−	2.70134i	0.0534946	−	0.0926553i
$851$	3.55982	−	6.16579i	0.122029	−	0.211360i
$852$	24.1231	+	41.7824i	0.826442	+	1.43144i
$853$	19.3910			0.663934			0.331967	−	0.943291i	$-0.392288\pi$
$853$	19.3910			0.663934			0.331967	+	0.943291i	$0.392288\pi$
$854$		0			0
$855$	−1.96532			−0.0672127
$856$	−42.2849	−	73.2396i	−1.44527	−	2.50328i
$857$	8.71210	−	15.0898i	0.297600	−	0.515458i	−0.677987	−	0.735074i	$-0.737147\pi$
$857$	8.71210	−	15.0898i	0.297600	−	0.515458i	0.975586	+	0.219616i	$0.0704806\pi$
$858$	−1.92301	+	3.33075i	−0.0656504	+	0.113710i
$859$	−17.7459	−	30.7367i	−0.605481	−	1.04872i	−0.991975	−	0.126432i	$-0.959648\pi$
$859$	−17.7459	−	30.7367i	−0.605481	−	1.04872i	0.386495	−	0.922292i	$-0.373686\pi$
$860$	−10.5376			−0.359329
$861$		0			0
$862$	−30.9704			−1.05486
$863$	−28.0010	−	48.4991i	−0.953164	−	1.65093i	−0.738516	−	0.674236i	$-0.764473\pi$
$863$	−28.0010	−	48.4991i	−0.953164	−	1.65093i	−0.214648	−	0.976691i	$-0.568860\pi$
$864$	59.4916	−	103.042i	2.02394	−	3.50557i
$865$	−4.51153	+	7.81420i	−0.153397	+	0.265691i
$866$	−28.9062	−	50.0670i	−0.982273	−	1.70135i
$867$	14.8070			0.502871
$868$		0			0
$869$	−2.24320			−0.0760953
$870$	−12.4558	−	21.5740i	−0.422290	−	0.731428i
$871$	2.23944	−	3.87883i	0.0758807	−	0.131429i
$872$	−70.5190	+	122.143i	−2.38808	+	4.13627i
$873$	1.71413	+	2.96896i	0.0580145	+	0.100484i
$874$	−1.34819			−0.0456031
$875$		0			0
$876$	60.5272			2.04503
$877$	−12.6031	−	21.8292i	−0.425577	−	0.737120i	0.570898	−	0.821021i	$-0.306595\pi$
$877$	−12.6031	−	21.8292i	−0.425577	−	0.737120i	−0.996474	+	0.0839011i	$0.973262\pi$
$878$	−33.3852	+	57.8249i	−1.12670	+	1.95150i
$879$	11.1587	−	19.3275i	0.376374	−	0.651899i
$880$	−16.7331	−	28.9826i	−0.564074	−	0.977004i
$881$	18.6082			0.626925			0.313463	−	0.949601i	$-0.398511\pi$
$881$	18.6082			0.626925			0.313463	+	0.949601i	$0.398511\pi$
$882$		0			0
$883$	−11.2552			−0.378768			−0.189384	−	0.981903i	$-0.560649\pi$
$883$	−11.2552			−0.378768			−0.189384	+	0.981903i	$0.560649\pi$
$884$	14.3578	+	24.8684i	0.482904	+	0.836415i
$885$	1.54332	−	2.67311i	0.0518781	−	0.0898556i
$886$	−55.1438	+	95.5119i	−1.85259	+	3.20879i
$887$	−19.6056	−	33.9579i	−0.658292	−	1.14020i	−0.981057	−	0.193717i	$-0.937946\pi$
$887$	−19.6056	−	33.9579i	−0.658292	−	1.14020i	0.322765	−	0.946479i	$-0.395388\pi$
$888$	−136.979			−4.59672
$889$		0			0
$890$	−34.3792			−1.15239
$891$	−2.11159	−	3.65738i	−0.0707408	−	0.122527i
$892$	−14.4959	+	25.1077i	−0.485360	+	0.840668i
$893$	−0.884638	+	1.53224i	−0.0296033	+	0.0512744i
$894$	−28.2403	−	48.9136i	−0.944496	−	1.63592i
$895$	−31.5249			−1.05376
$896$		0			0
$897$	−0.879996			−0.0293822
$898$	37.8316	+	65.5263i	1.26246	+	2.18664i
$899$	−1.59536	+	2.76325i	−0.0532083	+	0.0921595i
$900$	−0.696826	+	1.20694i	−0.0232275	+	0.0402312i
$901$	−12.9322	−	22.3992i	−0.430834	−	0.746226i
$902$	20.9106			0.696247
$903$		0			0
$904$	28.9903			0.964203
$905$	−19.7954	−	34.2866i	−0.658020	−	1.13972i
$906$	25.0903	−	43.4577i	0.833570	−	1.44378i
$907$	−10.7985	+	18.7035i	−0.358558	+	0.621040i	−0.987720	−	0.156234i	$-0.950065\pi$
$907$	−10.7985	+	18.7035i	−0.358558	+	0.621040i	0.629162	+	0.777274i	$0.283398\pi$
$908$	54.5997	+	94.5694i	1.81195	+	3.13840i
$909$	−13.3607			−0.443147
$910$		0			0
$911$	−32.4434			−1.07490			−0.537449	−	0.843297i	$-0.680612\pi$
$911$	−32.4434			−1.07490			−0.537449	+	0.843297i	$0.680612\pi$
$912$	7.43861	+	12.8840i	0.246317	+	0.426634i
$913$	3.49328	−	6.05054i	0.115611	−	0.200244i
$914$	15.2531	−	26.4192i	0.504528	−	0.873868i
$915$	18.4049	+	31.8782i	0.608447	+	1.05386i
$916$	−137.030			−4.52760
$917$		0			0
$918$	−81.2950			−2.68313
$919$	−17.8686	−	30.9493i	−0.589430	−	1.02092i	−0.994307	−	0.106552i	$-0.966019\pi$
$919$	−17.8686	−	30.9493i	−0.589430	−	1.02092i	0.404877	−	0.914371i	$-0.367314\pi$
$920$	6.67532	−	11.5620i	0.220079	−	0.381187i
$921$	−4.75142	+	8.22971i	−0.156565	+	0.271178i
$922$	−12.6693	−	21.9439i	−0.417242	−	0.722684i
$923$	6.60274			0.217332
$924$		0			0
$925$	2.35636			0.0774765
$926$	−38.4858	−	66.6594i	−1.26472	−	2.19056i
$927$	−12.0102	+	20.8022i	−0.394466	+	0.683235i
$928$	32.7559	−	56.7349i	1.07527	−	1.86241i
$929$	5.88847	+	10.1991i	0.193194	+	0.334622i	0.946307	−	0.323269i	$-0.104782\pi$
$929$	5.88847	+	10.1991i	0.193194	+	0.334622i	−0.753113	+	0.657891i	$0.771449\pi$
$930$	8.24941			0.270509
$931$		0			0
$932$	−4.30553			−0.141032
$933$	14.2116	+	24.6151i	0.465265	+	0.805863i
$934$	30.3329	−	52.5382i	0.992523	−	1.71910i
$935$	−6.06506	+	10.5050i	−0.198349	+	0.343550i
$936$	−5.54370	−	9.60197i	−0.181202	−	0.313850i
$937$	−18.9937			−0.620497			−0.310248	−	0.950655i	$-0.600412\pi$
$937$	−18.9937			−0.620497			−0.310248	+	0.950655i	$0.600412\pi$
$938$		0			0
$939$	−2.66660			−0.0870213
$940$	−13.8728	−	24.0284i	−0.452480	−	0.783719i
$941$	3.40932	−	5.90511i	0.111141	−	0.192501i	−0.805090	−	0.593153i	$-0.797883\pi$
$941$	3.40932	−	5.90511i	0.111141	−	0.192501i	0.916230	+	0.400652i	$0.131216\pi$
$942$	6.21502	−	10.7647i	0.202496	−	0.350734i
$943$	2.39225	+	4.14349i	0.0779023	+	0.134931i
$944$	15.3012			0.498012
$945$		0			0
$946$	−2.53590			−0.0824493
$947$	−0.529958	−	0.917914i	−0.0172213	−	0.0298282i	0.857286	−	0.514840i	$-0.172149\pi$
$947$	−0.529958	−	0.917914i	−0.0172213	−	0.0298282i	−0.874508	+	0.485012i	$0.838815\pi$
$948$	−7.81899	+	13.5429i	−0.253949	+	0.439853i
$949$	4.14174	−	7.17370i	0.134446	−	0.232868i
$950$	−0.223102	−	0.386424i	−0.00723838	−	0.0125372i
$951$	−24.2973			−0.787895
$952$		0			0
$953$	−40.4127			−1.30910			−0.654548	−	0.756020i	$-0.727141\pi$
$953$	−40.4127			−1.30910			−0.654548	+	0.756020i	$0.727141\pi$
$954$	7.90735	+	13.6959i	0.256010	+	0.443422i
$955$	6.05993	−	10.4961i	0.196095	−	0.339646i
$956$	−54.4023	+	94.2276i	−1.75950	+	3.04754i
$957$	−2.19032	−	3.79375i	−0.0708031	−	0.122635i
$958$	89.5964			2.89473
$959$		0			0
$960$	−83.3978			−2.69165
$961$	14.9717	+	25.9317i	0.482958	+	0.836508i
$962$	−14.8434	+	25.7095i	−0.478570	+	0.828907i
$963$	5.37498	−	9.30975i	0.173206	−	0.300002i
$964$	37.4789	+	64.9154i	1.20711	+	2.09078i
$965$	19.1177			0.615422
$966$		0			0
$967$	−36.2949			−1.16717			−0.583583	−	0.812053i	$-0.698350\pi$
$967$	−36.2949			−1.16717			−0.583583	+	0.812053i	$0.698350\pi$
$968$	46.2365	+	80.0839i	1.48610	+	2.57399i
$969$	2.69618	−	4.66993i	0.0866139	−	0.150020i
$970$	8.60638	−	14.9067i	0.276334	−	0.478625i
$971$	−10.7218	−	18.5708i	−0.344080	−	0.595964i	0.641106	−	0.767452i	$-0.278476\pi$
$971$	−10.7218	−	18.5708i	−0.344080	−	0.595964i	−0.985186	+	0.171488i	$0.945142\pi$
$972$	62.3457			1.99974
$973$		0			0
$974$	−76.0137			−2.43564
$975$	−0.145624	−	0.252229i	−0.00466371	−	0.00807778i
$976$	−91.2374	+	158.028i	−2.92044	+	5.05835i
$977$	19.9138	−	34.4918i	0.637100	−	1.10349i	−0.348966	−	0.937135i	$-0.613467\pi$
$977$	19.9138	−	34.4918i	0.637100	−	1.10349i	0.986066	−	0.166354i	$-0.0531994\pi$
$978$	25.3367	+	43.8845i	0.810179	+	1.40327i
$979$	−6.04551			−0.193215
$980$		0			0
$981$	−17.9278			−0.572392
$982$	−14.5216	−	25.1522i	−0.463403	−	0.802638i
$983$	7.94071	−	13.7537i	0.253269	−	0.438675i	−0.711155	−	0.703036i	$-0.751827\pi$
$983$	7.94071	−	13.7537i	0.253269	−	0.438675i	0.964424	+	0.264360i	$0.0851608\pi$
$984$	46.0260	−	79.7194i	1.46725	−	2.54136i
$985$	−5.98052	−	10.3586i	−0.190555	−	0.330051i
$986$	−44.7608			−1.42548
$987$		0			0
$988$	4.10772			0.130684
$989$	−0.290116	−	0.502496i	−0.00922516	−	0.0159785i
$990$	3.70846	−	6.42325i	0.117863	−	0.204144i
$991$	8.83435	−	15.3016i	0.280633	−	0.486070i	−0.690908	−	0.722943i	$-0.742789\pi$
$991$	8.83435	−	15.3016i	0.280633	−	0.486070i	0.971541	+	0.236873i	$0.0761225\pi$
$992$	10.8471	+	18.7877i	0.344394	+	0.596509i
$993$	−19.7570			−0.626970
$994$		0			0
$995$	42.7301			1.35464
$996$	−24.3526	−	42.1800i	−0.771643	−	1.33652i
$997$	−12.4304	+	21.5301i	−0.393675	+	0.681865i	−0.992931	−	0.118692i	$-0.962130\pi$
$997$	−12.4304	+	21.5301i	−0.393675	+	0.681865i	0.599256	+	0.800558i	$0.295463\pi$
$998$	33.3999	−	57.8503i	1.05725	−	1.83122i
$999$	−30.7062	−	53.1847i	−0.971500	−	1.68269i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.e.m.508.1		10
7.2	even	3	inner	637.2.e.m.79.1		10
7.3	odd	6		637.2.a.l.1.5		5
7.4	even	3		637.2.a.k.1.5		5
7.5	odd	6		91.2.e.c.79.1	yes	10
7.6	odd	2		91.2.e.c.53.1	✓	10
21.5	even	6		819.2.j.h.352.5		10
21.11	odd	6		5733.2.a.bm.1.1		5
21.17	even	6		5733.2.a.bl.1.1		5
21.20	even	2		819.2.j.h.235.5		10
28.19	even	6		1456.2.r.p.625.2		10
28.27	even	2		1456.2.r.p.417.2		10
91.12	odd	6		1183.2.e.f.170.5		10
91.25	even	6		8281.2.a.bx.1.1		5
91.38	odd	6		8281.2.a.bw.1.1		5
91.90	odd	2		1183.2.e.f.508.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.e.c.53.1	✓	10	7.6	odd	2
91.2.e.c.79.1	yes	10	7.5	odd	6
637.2.a.k.1.5		5	7.4	even	3
637.2.a.l.1.5		5	7.3	odd	6
637.2.e.m.79.1		10	7.2	even	3	inner
637.2.e.m.508.1		10	1.1	even	1	trivial
819.2.j.h.235.5		10	21.20	even	2
819.2.j.h.352.5		10	21.5	even	6
1183.2.e.f.170.5		10	91.12	odd	6
1183.2.e.f.508.5		10	91.90	odd	2
1456.2.r.p.417.2		10	28.27	even	2
1456.2.r.p.625.2		10	28.19	even	6
5733.2.a.bl.1.1		5	21.17	even	6
5733.2.a.bm.1.1		5	21.11	odd	6
8281.2.a.bw.1.1		5	91.38	odd	6
8281.2.a.bx.1.1		5	91.25	even	6

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.36263 - 2.36014i) q^{2} +(-0.673208 + 1.16603i) q^{3} +(-2.71349 + 4.69991i) q^{4} +(1.09358 + 1.89414i) q^{5} +3.66932 q^{6} +9.33940 q^{8} +(0.593582 + 1.02811i) q^{9} +O(q^{10})\)	\(q+(-1.36263 - 2.36014i) q^{2} +(-0.673208 + 1.16603i) q^{3} +(-2.71349 + 4.69991i) q^{4} +(1.09358 + 1.89414i) q^{5} +3.66932 q^{6} +9.33940 q^{8} +(0.593582 + 1.02811i) q^{9} +(2.98028 - 5.16200i) q^{10} +(0.524077 - 0.907729i) q^{11} +(-3.65349 - 6.32803i) q^{12} -1.00000 q^{13} -2.94483 q^{15} +(-7.29912 - 12.6424i) q^{16} +(-2.64562 + 4.58236i) q^{17} +(1.61766 - 2.80187i) q^{18} +(0.378453 + 0.655500i) q^{19} -11.8697 q^{20} -2.85648 q^{22} +(-0.326792 - 0.566020i) q^{23} +(-6.28736 + 10.8900i) q^{24} +(0.108157 - 0.187333i) q^{25} +(1.36263 + 2.36014i) q^{26} -5.63766 q^{27} -3.10408 q^{29} +(4.01270 + 6.95021i) q^{30} +(0.513956 - 0.890198i) q^{31} +(-10.5525 + 18.2775i) q^{32} +(0.705626 + 1.22218i) q^{33} +14.4200 q^{34} -6.44273 q^{36} +(5.44661 + 9.43381i) q^{37} +(1.03138 - 1.78640i) q^{38} +(0.673208 - 1.16603i) q^{39} +(10.2134 + 17.6901i) q^{40} -7.32040 q^{41} +0.887771 q^{43} +(2.84416 + 4.92623i) q^{44} +(-1.29826 + 2.24865i) q^{45} +(-0.890590 + 1.54255i) q^{46} +(1.16875 + 2.02434i) q^{47} +19.6553 q^{48} -0.589510 q^{50} +(-3.56211 - 6.16976i) q^{51} +(2.71349 - 4.69991i) q^{52} +(-2.44407 + 4.23325i) q^{53} +(7.68202 + 13.3057i) q^{54} +2.29249 q^{55} -1.01911 q^{57} +(4.22970 + 7.32606i) q^{58} +(-0.524077 + 0.907729i) q^{59} +(7.99079 - 13.8404i) q^{60} +(-6.24989 - 10.8251i) q^{61} -2.80132 q^{62} +28.3200 q^{64} +(-1.09358 - 1.89414i) q^{65} +(1.92301 - 3.33075i) q^{66} +(-2.23944 + 3.87883i) q^{67} +(-14.3578 - 24.8684i) q^{68} +0.879996 q^{69} -6.60274 q^{71} +(5.54370 + 9.60197i) q^{72} +(-4.14174 + 7.17370i) q^{73} +(14.8434 - 25.7095i) q^{74} +(0.145624 + 0.252229i) q^{75} -4.10772 q^{76} -3.66932 q^{78} +(-1.07007 - 1.85342i) q^{79} +(15.9644 - 27.6511i) q^{80} +(2.01457 - 3.48935i) q^{81} +(9.97496 + 17.2771i) q^{82} +6.66558 q^{83} -11.5728 q^{85} +(-1.20970 - 2.09526i) q^{86} +(2.08969 - 3.61946i) q^{87} +(4.89457 - 8.47765i) q^{88} +(-2.88388 - 4.99503i) q^{89} +7.07617 q^{90} +3.54699 q^{92} +(0.691998 + 1.19858i) q^{93} +(3.18515 - 5.51684i) q^{94} +(-0.827739 + 1.43369i) q^{95} +(-14.2081 - 24.6091i) q^{96} +2.88777 q^{97} +1.24433 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} - 8 q^{4} + 2 q^{5} + 10 q^{6} + 18 q^{8} - 3 q^{9}+O(q^{10}) \) 10 * q - 4 * q^2 - 8 * q^4 + 2 * q^5 + 10 * q^6 + 18 * q^8 - 3 * q^9	\( 10 q - 4 q^{2} - 8 q^{4} + 2 q^{5} + 10 q^{6} + 18 q^{8} - 3 q^{9} - 5 q^{10} - 11 q^{11} + 5 q^{12} - 10 q^{13} - 10 q^{16} - 5 q^{17} - 9 q^{18} + 9 q^{19} - 2 q^{20} + 16 q^{22} - 10 q^{23} - 9 q^{25} + 4 q^{26} - 6 q^{29} + 13 q^{30} - 6 q^{31} - 22 q^{32} + 8 q^{33} + 44 q^{34} + 14 q^{36} - 4 q^{37} - 10 q^{38} + 28 q^{40} - 28 q^{41} + 4 q^{43} - 32 q^{45} - 3 q^{46} + q^{47} + 46 q^{48} + 18 q^{50} + 8 q^{51} + 8 q^{52} - 17 q^{53} + 23 q^{54} - 32 q^{57} + 27 q^{58} + 11 q^{59} + 29 q^{60} - 11 q^{61} + 46 q^{62} + 18 q^{64} - 2 q^{65} + 21 q^{66} - 13 q^{67} - 32 q^{68} - 36 q^{69} + 30 q^{71} + 19 q^{72} + 33 q^{74} - 20 q^{75} - 16 q^{76} - 10 q^{78} - 2 q^{79} + 55 q^{80} + 19 q^{81} + 34 q^{82} - 12 q^{83} - 44 q^{85} - 28 q^{86} - 8 q^{87} + 3 q^{88} - 4 q^{89} + 68 q^{90} + 42 q^{92} - 18 q^{93} + 20 q^{94} + 12 q^{95} - 37 q^{96} + 24 q^{97} + 22 q^{99}+O(q^{100}) \) 10 * q - 4 * q^2 - 8 * q^4 + 2 * q^5 + 10 * q^6 + 18 * q^8 - 3 * q^9 - 5 * q^10 - 11 * q^11 + 5 * q^12 - 10 * q^13 - 10 * q^16 - 5 * q^17 - 9 * q^18 + 9 * q^19 - 2 * q^20 + 16 * q^22 - 10 * q^23 - 9 * q^25 + 4 * q^26 - 6 * q^29 + 13 * q^30 - 6 * q^31 - 22 * q^32 + 8 * q^33 + 44 * q^34 + 14 * q^36 - 4 * q^37 - 10 * q^38 + 28 * q^40 - 28 * q^41 + 4 * q^43 - 32 * q^45 - 3 * q^46 + q^47 + 46 * q^48 + 18 * q^50 + 8 * q^51 + 8 * q^52 - 17 * q^53 + 23 * q^54 - 32 * q^57 + 27 * q^58 + 11 * q^59 + 29 * q^60 - 11 * q^61 + 46 * q^62 + 18 * q^64 - 2 * q^65 + 21 * q^66 - 13 * q^67 - 32 * q^68 - 36 * q^69 + 30 * q^71 + 19 * q^72 + 33 * q^74 - 20 * q^75 - 16 * q^76 - 10 * q^78 - 2 * q^79 + 55 * q^80 + 19 * q^81 + 34 * q^82 - 12 * q^83 - 44 * q^85 - 28 * q^86 - 8 * q^87 + 3 * q^88 - 4 * q^89 + 68 * q^90 + 42 * q^92 - 18 * q^93 + 20 * q^94 + 12 * q^95 - 37 * q^96 + 24 * q^97 + 22 * q^99

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