LMFDB - Embedded newform 198.6.f.c.163.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [198,6,Mod(37,198)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(198, base_ring=CyclotomicField(10))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("198.37");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 198 = 2 \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	198.f (of order $5$, degree $4$, 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:	$31.7559963230$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 89x^{6} + 22551x^{4} + 4006069x^{2} + 405257161 $ x^8 + 89x^6 + 22551x^4 + 4006069*x^2 + 405257161
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 66)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			163.2
Root			$10.5047 - 7.63209i$ of defining polynomial
Character	$\chi$	$=$	198.163
Dual form			198.6.f.c.181.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23607 + 3.80423i) q^{2} +(-12.9443 - 9.40456i) q^{4} +(9.47098 + 29.1487i) q^{5} +(1.28786 + 0.935685i) q^{7} +(51.7771 - 37.6183i) q^{8} +O(q^{10})$	\(q+(-1.23607 + 3.80423i) q^{2} +(-12.9443 - 9.40456i) q^{4} +(9.47098 + 29.1487i) q^{5} +(1.28786 + 0.935685i) q^{7} +(51.7771 - 37.6183i) q^{8} -122.595 q^{10} +(119.850 - 382.997i) q^{11} +(-289.220 + 890.129i) q^{13} +(-5.15144 + 3.74274i) q^{14} +(79.1084 + 243.470i) q^{16} +(-121.877 - 375.100i) q^{17} +(-1730.20 + 1257.07i) q^{19} +(151.536 - 466.379i) q^{20} +(1308.87 + 929.347i) q^{22} +90.5594 q^{23} +(1768.23 - 1284.70i) q^{25} +(-3028.76 - 2200.52i) q^{26} +(-7.87070 - 24.2235i) q^{28} +(-854.075 - 620.522i) q^{29} +(-1290.47 + 3971.67i) q^{31} -1024.00 q^{32} +1577.61 q^{34} +(-15.0767 + 46.4013i) q^{35} +(-9318.86 - 6770.54i) q^{37} +(-2643.52 - 8135.91i) q^{38} +(1586.90 + 1152.95i) q^{40} +(-1075.99 + 781.752i) q^{41} -17727.1 q^{43} +(-5153.29 + 3830.49i) q^{44} +(-111.938 + 344.508i) q^{46} +(-8078.28 + 5869.21i) q^{47} +(-5192.87 - 15982.0i) q^{49} +(2701.62 + 8314.72i) q^{50} +(12115.0 - 8802.08i) q^{52} +(7853.15 - 24169.5i) q^{53} +(12299.0 - 133.898i) q^{55} +101.880 q^{56} +(3416.30 - 2482.09i) q^{58} +(-6942.17 - 5043.78i) q^{59} +(-12159.0 - 37421.5i) q^{61} +(-13514.0 - 9818.51i) q^{62} +(1265.73 - 3895.53i) q^{64} -28685.3 q^{65} +6661.08 q^{67} +(-1950.04 + 6001.60i) q^{68} +(-157.885 - 114.710i) q^{70} +(-9026.52 - 27780.8i) q^{71} +(-311.338 - 226.200i) q^{73} +(37275.4 - 27082.2i) q^{74} +34218.4 q^{76} +(512.715 - 381.105i) q^{77} +(-7944.07 + 24449.3i) q^{79} +(-6347.61 + 4611.81i) q^{80} +(-1643.97 - 5059.60i) q^{82} +(-31405.1 - 96655.1i) q^{83} +(9779.38 - 7105.14i) q^{85} +(21911.9 - 67437.9i) q^{86} +(-8202.22 - 24339.0i) q^{88} +55800.4 q^{89} +(-1205.36 + 875.742i) q^{91} +(-1172.22 - 851.671i) q^{92} +(-12342.5 - 37986.3i) q^{94} +(-53028.6 - 38527.5i) q^{95} +(-51711.3 + 159151. i) q^{97} +67217.9 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} - 32 q^{4} - 150 q^{5} + 474 q^{7} + 128 q^{8}+O(q^{10}) $ 8 * q + 8 * q^2 - 32 * q^4 - 150 * q^5 + 474 * q^7 + 128 * q^8	$ 8 q + 8 q^{2} - 32 q^{4} - 150 q^{5} + 474 q^{7} + 128 q^{8} - 1200 q^{10} + 582 q^{11} + 510 q^{13} - 1896 q^{14} - 512 q^{16} - 2004 q^{17} - 540 q^{19} - 2400 q^{20} + 672 q^{22} + 9944 q^{23} + 12228 q^{25} + 600 q^{26} - 6496 q^{28} + 11964 q^{29} - 9160 q^{31} - 8192 q^{32} + 2896 q^{34} - 42634 q^{35} - 718 q^{37} - 7560 q^{38} + 1666 q^{41} - 70528 q^{43} + 32 q^{44} + 56664 q^{46} - 51914 q^{47} - 23052 q^{49} + 52888 q^{50} - 2400 q^{52} + 53636 q^{53} + 104980 q^{55} + 8704 q^{56} - 47856 q^{58} + 17600 q^{59} - 10618 q^{61} - 77640 q^{62} - 8192 q^{64} - 116324 q^{65} - 182364 q^{67} - 32064 q^{68} - 79104 q^{70} - 29954 q^{71} + 127228 q^{73} + 2872 q^{74} - 43200 q^{76} + 33046 q^{77} + 39938 q^{79} - 51624 q^{82} - 208842 q^{83} + 125910 q^{85} - 51528 q^{86} + 30592 q^{88} + 344008 q^{89} + 282622 q^{91} + 147104 q^{92} - 106544 q^{94} - 31306 q^{95} - 26202 q^{97} - 323072 q^{98}+O(q^{100}) $ 8 * q + 8 * q^2 - 32 * q^4 - 150 * q^5 + 474 * q^7 + 128 * q^8 - 1200 * q^10 + 582 * q^11 + 510 * q^13 - 1896 * q^14 - 512 * q^16 - 2004 * q^17 - 540 * q^19 - 2400 * q^20 + 672 * q^22 + 9944 * q^23 + 12228 * q^25 + 600 * q^26 - 6496 * q^28 + 11964 * q^29 - 9160 * q^31 - 8192 * q^32 + 2896 * q^34 - 42634 * q^35 - 718 * q^37 - 7560 * q^38 + 1666 * q^41 - 70528 * q^43 + 32 * q^44 + 56664 * q^46 - 51914 * q^47 - 23052 * q^49 + 52888 * q^50 - 2400 * q^52 + 53636 * q^53 + 104980 * q^55 + 8704 * q^56 - 47856 * q^58 + 17600 * q^59 - 10618 * q^61 - 77640 * q^62 - 8192 * q^64 - 116324 * q^65 - 182364 * q^67 - 32064 * q^68 - 79104 * q^70 - 29954 * q^71 + 127228 * q^73 + 2872 * q^74 - 43200 * q^76 + 33046 * q^77 + 39938 * q^79 - 51624 * q^82 - 208842 * q^83 + 125910 * q^85 - 51528 * q^86 + 30592 * q^88 + 344008 * q^89 + 282622 * q^91 + 147104 * q^92 - 106544 * q^94 - 31306 * q^95 - 26202 * q^97 - 323072 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

$n$	$145$	$155$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

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 $

$2$	−1.23607	+	3.80423i	−0.218508	+	0.672499i
$2$	−1.23607	+	3.80423i	−0.218508	+	0.672499i
$3$		0			0
$3$		0			0
$4$	−12.9443	−	9.40456i	−0.404508	−	0.293893i
$5$	9.47098	+	29.1487i	0.169422	+	0.521428i	0.999335	−	0.0364655i	$-0.0116099\pi$
$5$	9.47098	+	29.1487i	0.169422	+	0.521428i	−0.829913	+	0.557893i	$0.811610\pi$
$6$		0			0
$7$	1.28786	+	0.935685i	0.00993398	+	0.00721746i	0.592741	−	0.805393i	$-0.298046\pi$
$7$	1.28786	+	0.935685i	0.00993398	+	0.00721746i	−0.582807	+	0.812610i	$0.698046\pi$
$8$	51.7771	−	37.6183i	0.286031	−	0.207813i
$9$		0			0
$10$	−122.595			−0.387679
$11$	119.850	−	382.997i	0.298645	−	0.954364i
$11$	119.850	−	382.997i	0.298645	−	0.954364i
$12$		0			0
$13$	−289.220	+	890.129i	−0.474647	+	1.46081i	0.371786	+	0.928318i	$0.378745\pi$
$13$	−289.220	+	890.129i	−0.474647	+	1.46081i	−0.846433	+	0.532495i	$0.821255\pi$
$14$	−5.15144	+	3.74274i	−0.00702439	+	0.00510352i
$15$		0			0
$16$	79.1084	+	243.470i	0.0772542	+	0.237764i
$17$	−121.877	−	375.100i	−0.102282	−	0.314793i	0.886801	−	0.462152i	$-0.152923\pi$
$17$	−121.877	−	375.100i	−0.102282	−	0.314793i	−0.989083	+	0.147359i	$0.952923\pi$
$18$		0			0
$19$	−1730.20	+	1257.07i	−1.09955	+	0.798867i	−0.980986	−	0.194080i	$-0.937828\pi$
$19$	−1730.20	+	1257.07i	−1.09955	+	0.798867i	−0.118560	+	0.992947i	$0.537828\pi$
$20$	151.536	−	466.379i	0.0847111	−	0.260714i
$21$		0			0
$22$	1308.87	+	929.347i	0.576552	+	0.409375i
$23$	90.5594			0.0356955			0.0178478	−	0.999841i	$-0.494319\pi$
$23$	90.5594			0.0356955			0.0178478	+	0.999841i	$0.494319\pi$
$24$		0			0
$25$	1768.23	−	1284.70i	0.565834	−	0.411102i
$26$	−3028.76	−	2200.52i	−0.878680	−	0.638399i
$27$		0			0
$28$	−7.87070	−	24.2235i	−0.00189722	−	0.00583905i
$29$	−854.075	−	620.522i	−0.188582	−	0.137013i	0.489488	−	0.872010i	$-0.337184\pi$
$29$	−854.075	−	620.522i	−0.188582	−	0.137013i	−0.678071	+	0.734997i	$0.737184\pi$
$30$		0			0
$31$	−1290.47	+	3971.67i	−0.241182	+	0.742282i	0.755059	+	0.655657i	$0.227608\pi$
$31$	−1290.47	+	3971.67i	−0.241182	+	0.742282i	−0.996241	+	0.0866253i	$0.972392\pi$
$32$	−1024.00			−0.176777
$33$		0			0
$34$	1577.61			0.234047
$35$	−15.0767	+	46.4013i	−0.00208035	+	0.00640265i
$36$		0			0
$37$	−9318.86	−	6770.54i	−1.11907	−	0.813054i	−0.135004	−	0.990845i	$-0.543105\pi$
$37$	−9318.86	−	6770.54i	−1.11907	−	0.813054i	−0.984068	+	0.177791i	$0.943105\pi$
$38$	−2643.52	−	8135.91i	−0.296977	−	0.914002i
$39$		0			0
$40$	1586.90	+	1152.95i	0.156820	+	0.113936i
$41$	−1075.99	+	781.752i	−0.0999651	+	0.0726289i	−0.636645	−	0.771157i	$-0.719678\pi$
$41$	−1075.99	+	781.752i	−0.0999651	+	0.0726289i	0.536680	+	0.843786i	$0.319678\pi$
$42$		0			0
$43$	−17727.1			−1.46206			−0.731032	−	0.682343i	$-0.760961\pi$
$43$	−17727.1			−1.46206			−0.731032	+	0.682343i	$0.760961\pi$
$44$	−5153.29	+	3830.49i	−0.401285	+	0.298279i
$45$		0			0
$46$	−111.938	+	344.508i	−0.00779976	+	0.0240052i
$47$	−8078.28	+	5869.21i	−0.533426	+	0.387557i	−0.821638	−	0.570010i	$-0.806939\pi$
$47$	−8078.28	+	5869.21i	−0.533426	+	0.387557i	0.288212	+	0.957567i	$0.406939\pi$
$48$		0			0
$49$	−5192.87	−	15982.0i	−0.308970	−	0.950913i
$50$	2701.62	+	8314.72i	0.152827	+	0.470352i
$51$		0			0
$52$	12115.0	−	8802.08i	0.621321	−	0.451416i
$53$	7853.15	−	24169.5i	0.384020	−	1.18189i	−0.553168	−	0.833070i	$-0.686581\pi$
$53$	7853.15	−	24169.5i	0.384020	−	1.18189i	0.937189	−	0.348823i	$-0.113419\pi$
$54$		0			0
$55$	12299.0	−	133.898i	0.548229	−	0.00596851i
$56$	101.880			0.00434131
$57$		0			0
$58$	3416.30	−	2482.09i	0.133348	−	0.0968829i
$59$	−6942.17	−	5043.78i	−0.259636	−	0.188637i	0.450350	−	0.892852i	$-0.351299\pi$
$59$	−6942.17	−	5043.78i	−0.259636	−	0.188637i	−0.709987	+	0.704215i	$0.751299\pi$
$60$		0			0
$61$	−12159.0	−	37421.5i	−0.418382	−	1.28765i	−0.909191	−	0.416380i	$-0.863299\pi$
$61$	−12159.0	−	37421.5i	−0.418382	−	1.28765i	0.490809	−	0.871267i	$-0.336701\pi$
$62$	−13514.0	−	9818.51i	−0.446484	−	0.324389i
$63$		0			0
$64$	1265.73	−	3895.53i	0.0386271	−	0.118882i
$65$	−28685.3			−0.842124
$66$		0			0
$67$	6661.08			0.181283			0.0906417	−	0.995884i	$-0.471108\pi$
$67$	6661.08			0.181283			0.0906417	+	0.995884i	$0.471108\pi$
$68$	−1950.04	+	6001.60i	−0.0511412	+	0.157396i
$69$		0			0
$70$	−157.885	−	114.710i	−0.00385120	−	0.00279806i
$71$	−9026.52	−	27780.8i	−0.212508	−	0.654031i	−0.999321	−	0.0368403i	$-0.988271\pi$
$71$	−9026.52	−	27780.8i	−0.212508	−	0.654031i	0.786814	−	0.617191i	$-0.211729\pi$
$72$		0			0
$73$	−311.338	−	226.200i	−0.00683793	−	0.00496804i	0.584361	−	0.811494i	$-0.301345\pi$
$73$	−311.338	−	226.200i	−0.00683793	−	0.00496804i	−0.591199	+	0.806526i	$0.701345\pi$
$74$	37275.4	−	27082.2i	0.791304	−	0.574916i
$75$		0			0
$76$	34218.4			0.679557
$77$	512.715	−	381.105i	0.00985482	−	0.00732518i
$78$		0			0
$79$	−7944.07	+	24449.3i	−0.143211	+	0.440757i	−0.996777	−	0.0802278i	$-0.974435\pi$
$79$	−7944.07	+	24449.3i	−0.143211	+	0.440757i	0.853566	+	0.520985i	$0.174435\pi$
$80$	−6347.61	+	4611.81i	−0.110888	+	0.0805650i
$81$		0			0
$82$	−1643.97	−	5059.60i	−0.0269996	−	0.0830963i
$83$	−31405.1	−	96655.1i	−0.500386	−	1.54003i	−0.808391	−	0.588646i	$-0.799661\pi$
$83$	−31405.1	−	96655.1i	−0.500386	−	1.54003i	0.308004	−	0.951385i	$-0.400339\pi$
$84$		0			0
$85$	9779.38	−	7105.14i	0.146813	−	0.106666i
$86$	21911.9	−	67437.9i	0.319473	−	0.983236i
$87$		0			0
$88$	−8202.22	−	24339.0i	−0.112908	−	0.335040i
$89$	55800.4			0.746728			0.373364	−	0.927685i	$-0.378204\pi$
$89$	55800.4			0.746728			0.373364	+	0.927685i	$0.378204\pi$
$90$		0			0
$91$	−1205.36	+	875.742i	−0.0152585	+	0.0110859i
$92$	−1172.22	−	851.671i	−0.0144391	−	0.0104907i
$93$		0			0
$94$	−12342.5	−	37986.3i	−0.144073	−	0.443412i
$95$	−53028.6	−	38527.5i	−0.602839	−	0.437988i
$96$		0			0
$97$	−51711.3	+	159151.i	−0.558028	+	1.71743i	0.129780	+	0.991543i	$0.458573\pi$
$97$	−51711.3	+	159151.i	−0.558028	+	1.71743i	−0.687809	+	0.725892i	$0.741427\pi$
$98$	67217.9			0.707000
$99$		0			0
$100$	−34970.5			−0.349705
$101$	11435.6	−	35195.1i	0.111546	−	0.343304i	−0.879665	−	0.475594i	$-0.842233\pi$
$101$	11435.6	−	35195.1i	0.111546	−	0.343304i	0.991211	+	0.132290i	$0.0422332\pi$
$102$		0			0
$103$	−63969.1	−	46476.3i	−0.594124	−	0.431657i	0.249664	−	0.968333i	$-0.419680\pi$
$103$	−63969.1	−	46476.3i	−0.594124	−	0.431657i	−0.843789	+	0.536676i	$0.819680\pi$
$104$	18510.1	+	56968.3i	0.167813	+	0.516475i
$105$		0			0
$106$	82239.2	+	59750.3i	0.710910	+	0.516506i
$107$	−143789.	+	104469.i	−1.21413	+	0.882120i	−0.995600	−	0.0937094i	$-0.970128\pi$
$107$	−143789.	+	104469.i	−1.21413	+	0.882120i	−0.218534	+	0.975829i	$0.570128\pi$
$108$		0			0
$109$	19984.5			0.161112			0.0805560	−	0.996750i	$-0.474330\pi$
$109$	19984.5			0.161112			0.0805560	+	0.996750i	$0.474330\pi$
$110$	−14693.0	+	46953.6i	−0.115779	+	0.369987i
$111$		0			0
$112$	−125.931	+	387.576i	−0.000948611	+	0.00291952i
$113$	−169582.	+	123208.i	−1.24935	+	0.907703i	−0.998184	−	0.0602416i	$-0.980813\pi$
$113$	−169582.	+	123208.i	−1.24935	+	0.907703i	−0.251163	+	0.967945i	$0.580813\pi$
$114$		0			0
$115$	857.686	+	2639.69i	0.00604761	+	0.0186126i
$116$	5219.64	+	16064.4i	0.0360160	+	0.110846i
$117$		0			0
$118$	27768.7	−	20175.1i	0.183591	−	0.133386i
$119$	194.015	−	597.115i	0.00125593	−	0.00386537i
$120$		0			0
$121$	−132323.	−	91804.3i	−0.821622	−	0.570033i
$122$	157389.			0.957361
$123$		0			0
$124$	54056.1	−	39274.1i	0.315712	−	0.229378i
$125$	131680.	+	95670.8i	0.753778	+	0.547652i
$126$		0			0
$127$	35056.5	+	107893.i	0.192868	+	0.593585i	0.999995	+	0.00320783i	$0.00102109\pi$
$127$	35056.5	+	107893.i	0.192868	+	0.593585i	−0.807127	+	0.590377i	$0.798979\pi$
$128$	13254.9	+	9630.27i	0.0715077	+	0.0519534i
$129$		0			0
$130$	35457.0	−	109125.i	0.184011	−	0.566327i
$131$	−30840.5			−0.157015			−0.0785077	−	0.996914i	$-0.525016\pi$
$131$	−30840.5			−0.157015			−0.0785077	+	0.996914i	$0.525016\pi$
$132$		0			0
$133$	−3404.48			−0.0166887
$134$	−8233.55	+	25340.3i	−0.0396119	+	0.121913i
$135$		0			0
$136$	−20421.1	−	14836.8i	−0.0946741	−	0.0687848i
$137$	86723.1	+	266906.i	0.394760	+	1.21495i	0.929148	+	0.369708i	$0.120542\pi$
$137$	86723.1	+	266906.i	0.394760	+	1.21495i	−0.534388	+	0.845239i	$0.679458\pi$
$138$		0			0
$139$	165065.	+	119927.i	0.724633	+	0.526477i	0.887861	−	0.460111i	$-0.152191\pi$
$139$	165065.	+	119927.i	0.724633	+	0.526477i	−0.163228	+	0.986588i	$0.552191\pi$
$140$	631.541	−	458.841i	0.00272321	−	0.00197853i
$141$		0			0
$142$	116842.			0.486269
$143$	306254.	+	217452.i	1.25240	+	0.889251i
$144$		0			0
$145$	9998.47	−	30772.1i	0.0394924	−	0.121545i
$146$	1245.35	−	904.800i	0.00483514	−	0.00351294i
$147$		0			0
$148$	56951.8	+	175280.i	0.213724	+	0.657774i
$149$	74110.4	+	228088.i	0.273472	+	0.841661i	0.989620	+	0.143712i	$0.0459039\pi$
$149$	74110.4	+	228088.i	0.273472	+	0.841661i	−0.716147	+	0.697949i	$0.754096\pi$
$150$		0			0
$151$	−387792.	+	281748.i	−1.38407	+	1.00558i	−0.387579	+	0.921836i	$0.626689\pi$
$151$	−387792.	+	281748.i	−1.38407	+	1.00558i	−0.996487	+	0.0837468i	$0.973311\pi$
$152$	−42296.3	+	130175.i	−0.148489	+	0.457001i
$153$		0			0
$154$	816.060	+	2421.55i	0.00277281	+	0.00822796i
$155$	−127991.			−0.427908
$156$		0			0
$157$	111107.	−	80724.3i	0.359744	−	0.261370i	−0.393201	−	0.919453i	$-0.628632\pi$
$157$	111107.	−	80724.3i	0.359744	−	0.261370i	0.752945	+	0.658083i	$0.228632\pi$
$158$	−83191.4	−	60442.1i	−0.265116	−	0.192618i
$159$		0			0
$160$	−9698.29	−	29848.3i	−0.0299499	−	0.0921763i
$161$	116.628	+	84.7350i	0.000354599	+	0.000257631i
$162$		0			0
$163$	−61790.6	+	190172.i	−0.182160	+	0.560631i	−0.999888	−	0.0149741i	$-0.995233\pi$
$163$	−61790.6	+	190172.i	−0.182160	+	0.560631i	0.817728	+	0.575605i	$0.195233\pi$
$164$	21279.9			0.0617818
$165$		0			0
$166$	406517.			1.14501
$167$	19433.2	−	59809.3i	0.0539205	−	0.165950i	−0.920470	−	0.390814i	$-0.872194\pi$
$167$	19433.2	−	59809.3i	0.0539205	−	0.165950i	0.974390	+	0.224864i	$0.0721936\pi$
$168$		0			0
$169$	−408299.	−	296647.i	−1.09967	−	0.798955i
$170$	14941.6	+	45985.4i	0.0396528	+	0.122039i
$171$		0			0
$172$	229464.	+	166716.i	0.591418	+	0.429690i
$173$	485344.	−	352623.i	1.23292	−	0.895767i	0.235812	−	0.971799i	$-0.424225\pi$
$173$	485344.	−	352623.i	1.23292	−	0.895767i	0.997105	+	0.0760314i	$0.0242249\pi$
$174$		0			0
$175$	3479.30			0.00858810
$176$	102730.	−	1118.41i	0.249985	−	0.00272156i
$177$		0			0
$178$	−68973.1	+	212277.i	−0.163166	+	0.502173i
$179$	−86352.3	+	62738.6i	−0.201438	+	0.146353i	−0.683931	−	0.729546i	$-0.739731\pi$
$179$	−86352.3	+	62738.6i	−0.201438	+	0.146353i	0.482493	+	0.875900i	$0.339731\pi$
$180$		0			0
$181$	−56138.5	−	172777.i	−0.127369	−	0.392002i	0.866956	−	0.498385i	$-0.166073\pi$
$181$	−56138.5	−	172777.i	−0.127369	−	0.392002i	−0.994325	+	0.106382i	$0.966073\pi$
$182$	−1841.62	−	5667.92i	−0.00412118	−	0.0126837i
$183$		0			0
$184$	4688.90	−	3406.69i	0.0102100	−	0.00741801i
$185$	109094.	−	335756.i	0.234353	−	0.721265i
$186$		0			0
$187$	−158269.	+	1723.06i	−0.330973	+	0.00360327i
$188$	159765.			0.329675
$189$		0			0
$190$	212114.	−	154110.i	0.426271	−	0.309704i
$191$	−299996.	−	217960.i	−0.595021	−	0.432308i	0.249087	−	0.968481i	$-0.419869\pi$
$191$	−299996.	−	217960.i	−0.595021	−	0.432308i	−0.844108	+	0.536173i	$0.819869\pi$
$192$		0			0
$193$	62200.3	+	191433.i	0.120199	+	0.369933i	0.992996	−	0.118150i	$-0.0376963\pi$
$193$	62200.3	+	191433.i	0.120199	+	0.369933i	−0.872797	+	0.488083i	$0.837696\pi$
$194$	−541528.	−	393443.i	−1.03304	−	0.750546i
$195$		0			0
$196$	−83085.8	+	255712.i	−0.154485	+	0.475457i
$197$	−329001.			−0.603992			−0.301996	−	0.953309i	$-0.597653\pi$
$197$	−329001.			−0.603992			−0.301996	+	0.953309i	$0.597653\pi$
$198$		0			0
$199$	729463.			1.30578			0.652891	−	0.757452i	$-0.273556\pi$
$199$	729463.			1.30578			0.652891	+	0.757452i	$0.273556\pi$
$200$	43225.9	−	133036.i	0.0764133	−	0.235176i
$201$		0			0
$202$	119755.	+	87007.0i	0.206497	+	0.150029i
$203$	−519.316	−	1598.29i	−0.000884487	−	0.00272217i
$204$		0			0
$205$	−32977.7	−	23959.7i	−0.0548070	−	0.0398196i
$206$	255877.	−	185905.i	0.420109	−	0.305227i
$207$		0			0
$208$	−239600.			−0.383997
$209$	274089.	+	813323.i	0.434036	+	1.28794i
$210$		0			0
$211$	−182726.	+	562372.i	−0.282549	+	0.869595i	0.704574	+	0.709630i	$0.251138\pi$
$211$	−182726.	+	562372.i	−0.282549	+	0.869595i	−0.987123	+	0.159965i	$0.948862\pi$
$212$	−328957.	+	239001.i	−0.502689	+	0.365225i
$213$		0			0
$214$	−219690.	−	676137.i	−0.327926	−	1.00925i
$215$	−167893.	−	516722.i	−0.247706	−	0.762361i
$216$		0			0
$217$	−5378.18	+	3907.48i	−0.00775329	+	0.00563310i
$218$	−24702.2	+	76025.7i	−0.0352043	+	0.108348i
$219$		0			0
$220$	−160460.	−	113933.i	−0.223517	−	0.158706i
$221$	369137.			0.508402
$222$		0			0
$223$	518643.	−	376816.i	0.698404	−	0.507420i	−0.181008	−	0.983482i	$-0.557936\pi$
$223$	518643.	−	376816.i	0.698404	−	0.507420i	0.879412	+	0.476062i	$0.157936\pi$
$224$	−1318.77	−	958.141i	−0.00175610	−	0.00127588i
$225$		0			0
$226$	−259098.	−	797421.i	−0.337437	−	1.03852i
$227$	−325100.	−	236199.i	−0.418748	−	0.304238i	0.358386	−	0.933574i	$-0.383327\pi$
$227$	−325100.	−	236199.i	−0.418748	−	0.304238i	−0.777134	+	0.629335i	$0.783327\pi$
$228$		0			0
$229$	104660.	−	322111.i	0.131884	−	0.405898i	−0.863208	−	0.504848i	$-0.831548\pi$
$229$	104660.	−	322111.i	0.131884	−	0.405898i	0.995092	+	0.0989502i	$0.0315484\pi$
$230$	−11102.1			−0.0138384
$231$		0			0
$232$	−67564.5			−0.0824135
$233$	−359299.	+	1.10581e6i	−0.433577	+	1.33441i	0.460960	+	0.887421i	$0.347505\pi$
$233$	−359299.	+	1.10581e6i	−0.433577	+	1.33441i	−0.894537	+	0.446993i	$0.852495\pi$
$234$		0			0
$235$	−247589.	−	179884.i	−0.292457	−	0.212482i
$236$	42426.8	+	130576.i	0.0495861	+	0.152610i
$237$		0			0
$238$	2031.75	+	1476.15i	0.00232502	+	0.00168923i
$239$	868453.	−	630968.i	0.983449	−	0.714517i	0.0249720	−	0.999688i	$-0.492050\pi$
$239$	868453.	−	630968.i	0.983449	−	0.714517i	0.958477	+	0.285171i	$0.0920503\pi$
$240$		0			0
$241$	859568.			0.953318			0.476659	−	0.879088i	$-0.341848\pi$
$241$	859568.			0.953318			0.476659	+	0.879088i	$0.341848\pi$
$242$	512805.	−	389910.i	0.562877	−	0.427983i
$243$		0			0
$244$	−194544.	+	598744.i	−0.209191	+	0.643824i
$245$	416673.	−	302731.i	0.443486	−	0.322211i
$246$		0			0
$247$	−618541.	−	1.90367e6i	−0.645099	−	1.98541i
$248$	82590.4	+	254187.i	0.0852708	+	0.262436i
$249$		0			0
$250$	−526718.	+	382683.i	−0.533001	+	0.387248i
$251$	262893.	−	809101.i	0.263387	−	0.810622i	−0.728674	−	0.684861i	$-0.759863\pi$
$251$	262893.	−	809101.i	0.263387	−	0.810622i	0.992061	−	0.125761i	$-0.0401371\pi$
$252$		0			0
$253$	10853.5	−	34684.0i	0.0106603	−	0.0340665i
$254$	−453781.			−0.441328
$255$		0			0
$256$	−53019.7	+	38521.1i	−0.0505636	+	0.0367366i
$257$	−1.57308e6	−	1.14291e6i	−1.48566	−	1.07939i	−0.975678	−	0.219210i	$-0.929652\pi$
$257$	−1.57308e6	−	1.14291e6i	−1.48566	−	1.07939i	−0.509982	−	0.860185i	$-0.670348\pi$
$258$		0			0
$259$	−5666.28	−	17439.0i	−0.00524866	−	0.0161537i
$260$	371310.	+	269773.i	0.340646	+	0.247494i
$261$		0			0
$262$	38120.9	−	117324.i	0.0343091	−	0.105593i
$263$	−2.00871e6			−1.79072			−0.895360	−	0.445342i	$-0.853082\pi$
$263$	−2.00871e6			−1.79072			−0.895360	+	0.445342i	$0.853082\pi$
$264$		0			0
$265$	778887.			0.681333
$266$	4208.17	−	12951.4i	0.00364661	−	0.0112231i
$267$		0			0
$268$	−86222.9	−	62644.6i	−0.0733307	−	0.0532778i
$269$	549282.	+	1.69052e6i	0.462822	+	1.42442i	0.861701	+	0.507417i	$0.169400\pi$
$269$	549282.	+	1.69052e6i	0.462822	+	1.42442i	−0.398878	+	0.917004i	$0.630600\pi$
$270$		0			0
$271$	−149494.	−	108614.i	−0.123652	−	0.0898383i	0.524240	−	0.851570i	$-0.324349\pi$
$271$	−149494.	−	108614.i	−0.123652	−	0.0898383i	−0.647892	+	0.761732i	$0.724349\pi$
$272$	81684.3	−	59347.1i	0.0669447	−	0.0486382i
$273$		0			0
$274$	−1.12257e6			−0.903309
$275$	−280113.	−	831198.i	−0.223358	−	0.662786i
$276$		0			0
$277$	−444058.	+	1.36667e6i	−0.347729	+	1.07020i	0.612378	+	0.790565i	$0.290213\pi$
$277$	−444058.	+	1.36667e6i	−0.347729	+	1.07020i	−0.960107	+	0.279634i	$0.909787\pi$
$278$	−660261.	+	479707.i	−0.512393	+	0.372275i
$279$		0			0
$280$	964.908	+	2969.68i	0.000735514	+	0.00226368i
$281$	61549.6	+	189430.i	0.0465007	+	0.143114i	0.971611	−	0.236584i	$-0.0760278\pi$
$281$	61549.6	+	189430.i	0.0465007	+	0.143114i	−0.925110	+	0.379698i	$0.876028\pi$
$282$		0			0
$283$	−1.12417e6	+	816760.i	−0.834386	+	0.606217i	−0.920797	−	0.390043i	$-0.872460\pi$
$283$	−1.12417e6	+	816760.i	−0.834386	+	0.606217i	0.0864107	+	0.996260i	$0.472460\pi$
$284$	−144424.	+	444492.i	−0.106254	+	0.327016i
$285$		0			0
$286$	−1.20579e6	+	896274.i	−0.871679	+	0.647926i
$287$	−2117.20			−0.00151725
$288$		0			0
$289$	1.02284e6	−	743138.i	0.720384	−	0.523390i
$290$	104705.	+	76072.9i	0.0731095	+	0.0531172i
$291$		0			0
$292$	1902.73	+	5855.99i	0.00130593	+	0.00401923i
$293$	−1.83865e6	−	1.33586e6i	−1.25121	−	0.909057i	−0.252918	−	0.967488i	$-0.581390\pi$
$293$	−1.83865e6	−	1.33586e6i	−1.25121	−	0.909057i	−0.998291	+	0.0584304i	$0.981390\pi$
$294$		0			0
$295$	81270.5	−	250125.i	0.0543723	−	0.167341i
$296$	−737199.			−0.489053
$297$		0			0
$298$	−959305.			−0.625772
$299$	−26191.6	+	80609.5i	−0.0169428	+	0.0521445i
$300$		0			0
$301$	−22830.0	−	16587.0i	−0.0145241	−	0.0105524i
$302$	−592494.	−	1.82351e6i	−0.373824	−	1.15051i
$303$		0			0
$304$	−442932.	−	321809.i	−0.274886	−	0.199717i
$305$	975631.	−	708837.i	0.600532	−	0.436312i
$306$		0			0
$307$	2.98610e6			1.80825			0.904125	−	0.427268i	$-0.140524\pi$
$307$	2.98610e6			1.80825			0.904125	+	0.427268i	$0.140524\pi$
$308$	−10220.8	+	111.273i	−0.00613917	+	6.68366e-5i
$309$		0			0
$310$	158206.	−	486907.i	0.0935014	−	0.287768i
$311$	706342.	−	513187.i	0.414108	−	0.300867i	−0.361155	−	0.932506i	$-0.617617\pi$
$311$	706342.	−	513187.i	0.414108	−	0.300867i	0.775263	+	0.631639i	$0.217617\pi$
$312$		0			0
$313$	153869.	+	473561.i	0.0887750	+	0.273221i	0.985581	−	0.169202i	$-0.0541189\pi$
$313$	153869.	+	473561.i	0.0887750	+	0.273221i	−0.896806	+	0.442423i	$0.854119\pi$
$314$	169757.	+	522459.i	0.0971636	+	0.299039i
$315$		0			0
$316$	332765.	−	241768.i	0.187465	−	0.136201i
$317$	847270.	−	2.60763e6i	0.473559	−	1.45746i	−0.374333	−	0.927294i	$-0.622128\pi$
$317$	847270.	−	2.60763e6i	0.473559	−	1.45746i	0.847892	−	0.530169i	$-0.177872\pi$
$318$		0			0
$319$	−340019.	+	252739.i	−0.187080	+	0.139058i
$320$	125537.			0.0685327
$321$		0			0
$322$	−466.511	+	338.940i	−0.000250739	+	0.000182173i
$323$	682399.	+	495792.i	0.363942	+	0.264419i
$324$		0			0
$325$	632136.	+	1.94551e6i	0.331972	+	1.02171i
$326$	−647079.	−	470130.i	−0.337220	−	0.245005i
$327$		0			0
$328$	−26303.4	+	80953.7i	−0.0134998	+	0.0415482i
$329$	−15895.4			−0.00809622
$330$		0			0
$331$	−3.59901e6			−1.80557			−0.902783	−	0.430097i	$-0.858479\pi$
$331$	−3.59901e6			−1.80557			−0.902783	+	0.430097i	$0.858479\pi$
$332$	−502482.	+	1.54648e6i	−0.250193	+	0.770016i
$333$		0			0
$334$	203507.	+	147857.i	0.0998192	+	0.0725229i
$335$	63087.0	+	194162.i	0.0307134	+	0.0945262i
$336$		0			0
$337$	1.12157e6	+	814866.i	0.537961	+	0.390851i	0.823327	−	0.567567i	$-0.192115\pi$
$337$	1.12157e6	+	814866.i	0.537961	+	0.390851i	−0.285366	+	0.958418i	$0.592115\pi$
$338$	1.63320e6	−	1.18659e6i	0.777583	−	0.564947i
$339$		0			0
$340$	−193408.			−0.0907353
$341$	1.36648e6	+	970253.i	0.636380	+	0.451855i
$342$		0			0
$343$	16534.1	−	50886.7i	0.00758832	−	0.0233544i
$344$	−917858.	+	666863.i	−0.418195	+	0.303837i
$345$		0			0
$346$	741539.	+	2.28222e6i	0.333000	+	1.02487i
$347$	406747.	+	1.25184e6i	0.181343	+	0.558116i	0.999866	−	0.0163575i	$-0.00520698\pi$
$347$	406747.	+	1.25184e6i	0.181343	+	0.558116i	−0.818523	+	0.574473i	$0.805207\pi$
$348$		0			0
$349$	1.62828e6	−	1.18301e6i	0.715592	−	0.519908i	−0.169381	−	0.985551i	$-0.554177\pi$
$349$	1.62828e6	−	1.18301e6i	0.715592	−	0.519908i	0.884973	+	0.465643i	$0.154177\pi$
$350$	−4300.66	+	13236.1i	−0.00187657	+	0.00577549i
$351$		0			0
$352$	−122726.	+	392189.i	−0.0527935	+	0.168709i
$353$	1.49229e6			0.637407			0.318703	−	0.947854i	$-0.396753\pi$
$353$	1.49229e6			0.637407			0.318703	+	0.947854i	$0.396753\pi$
$354$		0			0
$355$	724283.	−	526222.i	0.305026	−	0.221615i
$356$	−722296.	−	524778.i	−0.302058	−	0.219458i
$357$		0			0
$358$	−131935.	−	406053.i	−0.0544065	−	0.167446i
$359$	3.42308e6	+	2.48702e6i	1.40178	+	1.01846i	0.994454	+	0.105176i	$0.0335405\pi$
$359$	3.42308e6	+	2.48702e6i	1.40178	+	1.01846i	0.407331	+	0.913281i	$0.366460\pi$
$360$		0			0
$361$	648232.	−	1.99505e6i	0.261796	−	0.805724i
$362$	726672.			0.291452
$363$		0			0
$364$	23838.4			0.00943027
$365$	3644.76	−	11217.4i	0.00143198	−	0.00440718i
$366$		0			0
$367$	−2.75186e6	−	1.99934e6i	−1.06650	−	0.774858i	−0.0912208	−	0.995831i	$-0.529077\pi$
$367$	−2.75186e6	−	1.99934e6i	−1.06650	−	0.774858i	−0.975280	+	0.220972i	$0.929077\pi$
$368$	7164.00	+	22048.5i	0.00275763	+	0.00848711i
$369$		0			0
$370$	1.14245e6	+	830035.i	0.433841	+	0.315204i
$371$	32728.8	−	23778.9i	0.0123451	−	0.00896925i
$372$		0			0
$373$	3.01172e6			1.12084			0.560418	−	0.828210i	$-0.310640\pi$
$373$	3.01172e6			1.12084			0.560418	+	0.828210i	$0.310640\pi$
$374$	189077.	−	604222.i	0.0698971	−	0.223366i
$375$		0			0
$376$	−197480.	+	607781.i	−0.0720367	+	0.221706i
$377$	799361.	−	580769.i	0.289661	−	0.210451i
$378$		0			0
$379$	−550858.	−	1.69537e6i	−0.196989	−	0.606270i	−0.999948	−	0.0102349i	$-0.996742\pi$
$379$	−550858.	−	1.69537e6i	−0.196989	−	0.606270i	0.802959	−	0.596035i	$-0.203258\pi$
$380$	324082.	+	997422.i	0.115132	+	0.354340i
$381$		0			0
$382$	1.19998e6	−	871840.i	0.420743	−	0.305688i
$383$	−1.68093e6	+	5.17336e6i	−0.585533	+	1.80209i	0.0115841	+	0.999933i	$0.496313\pi$
$383$	−1.68093e6	+	5.17336e6i	−0.585533	+	1.80209i	−0.597118	+	0.802154i	$0.703687\pi$
$384$		0			0
$385$	15964.6	+	11335.5i	0.00548918	+	0.00389753i
$386$	−805138.			−0.275044
$387$		0			0
$388$	2.16611e6	−	1.57377e6i	0.730469	−	0.530716i
$389$	2.90304e6	+	2.10918e6i	0.972699	+	0.706707i	0.956065	−	0.293154i	$-0.0947050\pi$
$389$	2.90304e6	+	2.10918e6i	0.972699	+	0.706707i	0.0166339	+	0.999862i	$0.494705\pi$
$390$		0			0
$391$	−11037.1	−	33968.8i	−0.00365102	−	0.0112367i
$392$	−870086.	−	632155.i	−0.285988	−	0.207782i
$393$		0			0
$394$	406667.	−	1.25159e6i	0.131977	−	0.406184i
$395$	−787904.			−0.254086
$396$		0			0
$397$	5.21167e6			1.65959			0.829795	−	0.558069i	$-0.188457\pi$
$397$	5.21167e6			1.65959			0.829795	+	0.558069i	$0.188457\pi$
$398$	−901666.	+	2.77504e6i	−0.285324	+	0.878137i
$399$		0			0
$400$	452667.	+	328882.i	0.141459	+	0.102776i
$401$	198319.	+	610364.i	0.0615891	+	0.189552i	0.977117	−	0.212703i	$-0.0682266\pi$
$401$	198319.	+	610364.i	0.0615891	+	0.189552i	−0.915528	+	0.402255i	$0.868227\pi$
$402$		0			0
$403$	−3.16207e6	−	2.29738e6i	−0.969859	−	0.704644i
$404$	−479019.	+	348028.i	−0.146016	+	0.106087i
$405$		0			0
$406$	6722.17			0.00202392
$407$	−3.70996e6	+	2.75765e6i	−1.11016	+	0.825188i
$408$		0			0
$409$	−1.57118e6	+	4.83560e6i	−0.464428	+	1.42936i	0.395273	+	0.918564i	$0.370650\pi$
$409$	−1.57118e6	+	4.83560e6i	−0.464428	+	1.42936i	−0.859701	+	0.510798i	$0.829350\pi$
$410$	131911.	−	95838.9i	0.0387544	−	0.0281567i
$411$		0			0
$412$	390945.	+	1.20320e6i	0.113468	+	0.349218i
$413$	−4221.15	−	12991.4i	−0.00121774	−	0.00374783i
$414$		0			0
$415$	2.51993e6	−	1.83084e6i	0.718238	−	0.521831i
$416$	296162.	−	911492.i	0.0839065	−	0.258238i
$417$		0			0
$418$	−3.43286e6	+	37373.1i	−0.960981	+	0.0104621i
$419$	2.44419e6			0.680143			0.340072	−	0.940400i	$-0.389549\pi$
$419$	2.44419e6			0.680143			0.340072	+	0.940400i	$0.389549\pi$
$420$		0			0
$421$	−4.33962e6	+	3.15292e6i	−1.19329	+	0.866977i	−0.993608	−	0.112884i	$-0.963991\pi$
$421$	−4.33962e6	+	3.15292e6i	−1.19329	+	0.866977i	−0.199683	+	0.979861i	$0.563991\pi$
$422$	−1.91353e6	−	1.39026e6i	−0.523062	−	0.380027i
$423$		0			0
$424$	−502601.	−	1.54685e6i	−0.135772	−	0.417862i
$425$	−697397.	−	506689.i	−0.187287	−	0.136072i
$426$		0			0
$427$	19355.7	−	59570.6i	0.00513734	−	0.0158111i
$428$	2.84373e6			0.750376
$429$		0			0
$430$	2.17325e6			0.566812
$431$	−1.69723e6	+	5.22353e6i	−0.440095	+	1.35447i	0.447679	+	0.894194i	$0.352251\pi$
$431$	−1.69723e6	+	5.22353e6i	−0.440095	+	1.35447i	−0.887774	+	0.460280i	$0.847749\pi$
$432$		0			0
$433$	85891.1	+	62403.5i	0.0220155	+	0.0159952i	0.598739	−	0.800945i	$-0.295669\pi$
$433$	85891.1	+	62403.5i	0.0220155	+	0.0159952i	−0.576723	+	0.816940i	$0.695669\pi$
$434$	−8217.13	−	25289.7i	−0.00209409	−	0.00644496i
$435$		0			0
$436$	−258685.	−	187946.i	−0.0651712	−	0.0473496i
$437$	−156686.	+	113839.i	−0.0392489	+	0.0285160i
$438$		0			0
$439$	−4.59366e6			−1.13762			−0.568811	−	0.822469i	$-0.692596\pi$
$439$	−4.59366e6			−1.13762			−0.568811	+	0.822469i	$0.692596\pi$
$440$	631768.	−	469599.i	0.155570	−	0.115637i
$441$		0			0
$442$	−456279.	+	1.40428e6i	−0.111090	+	0.341899i
$443$	4.03165e6	−	2.92917e6i	0.976053	−	0.709144i	0.0192303	−	0.999815i	$-0.493878\pi$
$443$	4.03165e6	−	2.92917e6i	0.976053	−	0.709144i	0.956823	+	0.290671i	$0.0938784\pi$
$444$		0			0
$445$	528485.	+	1.62651e6i	0.126512	+	0.389365i
$446$	792416.	+	2.43881e6i	0.188632	+	0.580551i
$447$		0			0
$448$	5275.07	−	3832.56i	0.00124175	−	0.000902183i
$449$	1.94826e6	−	5.99612e6i	0.456069	−	1.40364i	−0.413806	−	0.910365i	$-0.635801\pi$
$449$	1.94826e6	−	5.99612e6i	0.456069	−	1.40364i	0.869875	−	0.493271i	$-0.164199\pi$
$450$		0			0
$451$	170452.	+	505794.i	0.0394603	+	0.117093i
$452$	3.35383e6			0.772139
$453$		0			0
$454$	1.30040e6	−	944797.i	0.296099	−	0.215129i
$455$	−36942.6	−	26840.4i	−0.00836565	−	0.00607800i
$456$		0			0
$457$	2.48617e6	+	7.65166e6i	0.556854	+	1.71382i	0.690997	+	0.722857i	$0.257172\pi$
$457$	2.48617e6	+	7.65166e6i	0.556854	+	1.71382i	−0.134144	+	0.990962i	$0.542828\pi$
$458$	1.09602e6	+	796302.i	0.244148	+	0.177384i
$459$		0			0
$460$	13723.0	−	42235.0i	0.00302381	−	0.00930632i
$461$	−1.76141e6			−0.386018			−0.193009	−	0.981197i	$-0.561825\pi$
$461$	−1.76141e6			−0.386018			−0.193009	+	0.981197i	$0.561825\pi$
$462$		0			0
$463$	−2.64405e6			−0.573214			−0.286607	−	0.958048i	$-0.592527\pi$
$463$	−2.64405e6			−0.573214			−0.286607	+	0.958048i	$0.592527\pi$
$464$	83514.3	−	257031.i	0.0180080	−	0.0554230i
$465$		0			0
$466$	−3.76263e6	−	2.73371e6i	−0.802651	−	0.583160i
$467$	−2.51159e6	−	7.72987e6i	−0.532912	−	1.64014i	−0.748117	−	0.663567i	$-0.769042\pi$
$467$	−2.51159e6	−	7.72987e6i	−0.532912	−	1.64014i	0.215205	−	0.976569i	$-0.430958\pi$
$468$		0			0
$469$	8578.54	+	6232.67i	0.00180087	+	0.00130841i
$470$	990356.	−	719536.i	0.206798	−	0.150248i
$471$		0			0
$472$	−549184.			−0.113465
$473$	−2.12459e6	+	6.78943e6i	−0.436639	+	1.39534i
$474$		0			0
$475$	−1.44445e6	+	4.44557e6i	−0.293744	+	0.904052i
$476$	−8126.99	+	5904.60i	−0.00164404	+	0.00119446i
$477$		0			0
$478$	1.32688e6	+	4.08371e6i	0.265620	+	0.817496i
$479$	−1.73466e6	−	5.33873e6i	−0.345442	−	1.06316i	−0.961347	−	0.275340i	$-0.911209\pi$
$479$	−1.73466e6	−	5.33873e6i	−0.345442	−	1.06316i	0.615905	−	0.787821i	$-0.288791\pi$
$480$		0			0
$481$	8.72186e6	−	6.33680e6i	1.71888	−	1.24884i
$482$	−1.06248e6	+	3.26999e6i	−0.208308	+	0.641105i
$483$		0			0
$484$	849446.	+	2.43278e6i	0.164825	+	0.472052i
$485$	−5.12880e6			−0.990060
$486$		0			0
$487$	−3.89340e6	+	2.82872e6i	−0.743886	+	0.540465i	−0.893926	−	0.448215i	$-0.852060\pi$
$487$	−3.89340e6	+	2.82872e6i	−0.743886	+	0.540465i	0.150040	+	0.988680i	$0.452060\pi$
$488$	−2.03729e6	−	1.48018e6i	−0.387261	−	0.281361i
$489$		0			0
$490$	636619.	+	1.95931e6i	0.119781	+	0.368649i
$491$	−3.15250e6	−	2.29042e6i	−0.590134	−	0.428758i	0.252229	−	0.967668i	$-0.418836\pi$
$491$	−3.15250e6	−	2.29042e6i	−0.590134	−	0.428758i	−0.842363	+	0.538910i	$0.818836\pi$
$492$		0			0
$493$	−128665.	+	395991.i	−0.0238421	+	0.0733784i
$494$	8.00657e6			1.47614
$495$		0			0
$496$	−1.06907e6			−0.195120
$497$	14369.2	−	44223.7i	0.00260940	−	0.00803090i
$498$		0			0
$499$	−6.68808e6	−	4.85918e6i	−1.20240	−	0.873598i	−0.207885	−	0.978153i	$-0.566658\pi$
$499$	−6.68808e6	−	4.85918e6i	−1.20240	−	0.873598i	−0.994519	+	0.104556i	$0.966658\pi$
$500$	−804754.	−	2.47678e6i	−0.143959	−	0.443060i
$501$		0			0
$502$	2.75305e6	+	2.00021e6i	0.487590	+	0.354255i
$503$	−4.38776e6	+	3.18790e6i	−0.773256	+	0.561803i	−0.902947	−	0.429751i	$-0.858601\pi$
$503$	−4.38776e6	+	3.18790e6i	−0.773256	+	0.561803i	0.129691	+	0.991554i	$0.458601\pi$
$504$		0			0
$505$	1.13420e6			0.197906
$506$	118530.	+	84161.0i	0.0205803	+	0.0146128i
$507$		0			0
$508$	560904.	−	1.72628e6i	0.0964338	−	0.296793i
$509$	3.34715e6	−	2.43185e6i	0.572639	−	0.416047i	−0.263424	−	0.964680i	$-0.584852\pi$
$509$	3.34715e6	−	2.43185e6i	0.572639	−	0.416047i	0.836063	+	0.548634i	$0.184852\pi$
$510$		0			0
$511$	−189.307	−	582.628i	−3.20712e−5	−	9.87049e-5i
$512$	−81007.0	−	249314.i	−0.0136568	−	0.0420312i
$513$		0			0
$514$	6.29234e6	−	4.57165e6i	1.05052	−	0.763248i
$515$	748873.	−	2.30479e6i	0.124420	−	0.382925i
$516$		0			0
$517$	1.27971e6	+	3.79738e6i	0.210565	+	0.624825i
$518$	73345.9			0.0120102
$519$		0			0
$520$	−1.48524e6	+	1.07909e6i	−0.240873	+	0.175005i
$521$	−4.82766e6	−	3.50750e6i	−0.779188	−	0.566113i	0.125547	−	0.992088i	$-0.459931\pi$
$521$	−4.82766e6	−	3.50750e6i	−0.779188	−	0.566113i	−0.904735	+	0.425974i	$0.859931\pi$
$522$		0			0
$523$	1.77441e6	+	5.46108e6i	0.283661	+	0.873020i	0.986797	+	0.161964i	$0.0517828\pi$
$523$	1.77441e6	+	5.46108e6i	0.283661	+	0.873020i	−0.703135	+	0.711056i	$0.748217\pi$
$524$	399207.	+	290041.i	0.0635141	+	0.0461457i
$525$		0			0
$526$	2.48290e6	−	7.64159e6i	0.391287	−	1.20426i
$527$	1.64706e6			0.258334
$528$		0			0
$529$	−6.42814e6			−0.998726
$530$	−962757.	+	2.96306e6i	−0.148877	+	0.458196i
$531$		0			0
$532$	44068.5	+	32017.6i	0.00675070	+	0.00490467i
$533$	−384662.	−	1.18387e6i	−0.0586491	−	0.180503i
$534$		0			0
$535$	−4.40696e6	−	3.20184e6i	−0.665663	−	0.483632i
$536$	344892.	−	250578.i	0.0518526	−	0.0376731i
$537$		0			0
$538$	−7.11005e6			−1.05905
$539$	−6.74343e6	+	73415.0i	−0.999790	+	0.0108846i
$540$		0			0
$541$	1.81565e6	−	5.58800e6i	0.266710	−	0.820849i	−0.724584	−	0.689186i	$-0.757968\pi$
$541$	1.81565e6	−	5.58800e6i	0.266710	−	0.820849i	0.991295	−	0.131663i	$-0.0420317\pi$
$542$	597976.	−	434455.i	0.0874350	−	0.0635253i
$543$		0			0
$544$	124803.	+	384103.i	0.0180812	+	0.0556481i
$545$	189273.	+	582523.i	0.0272959	+	0.0840082i
$546$		0			0
$547$	−5.94812e6	+	4.32156e6i	−0.849985	+	0.617550i	−0.925142	−	0.379621i	$-0.876054\pi$
$547$	−5.94812e6	+	4.32156e6i	−0.849985	+	0.617550i	0.0751567	+	0.997172i	$0.476054\pi$
$548$	1.38757e6	−	4.27050e6i	0.197380	−	0.607474i
$549$		0			0
$550$	3.50831e6	−	38194.6i	0.494528	−	0.00538387i
$551$	2.25776e6			0.316810
$552$		0			0
$553$	−33107.7	+	24054.2i	−0.00460380	+	0.00334486i
$554$	−4.65024e6	−	3.37860e6i	−0.643726	−	0.467694i
$555$		0			0
$556$	−1.00879e6	−	3.10473e6i	−0.138393	−	0.425929i
$557$	6.64030e6	+	4.82446e6i	0.906880	+	0.658887i	0.940224	−	0.340557i	$-0.110616\pi$
$557$	6.64030e6	+	4.82446e6i	0.906880	+	0.658887i	−0.0333437	+	0.999444i	$0.510616\pi$
$558$		0			0
$559$	5.12704e6	−	1.57794e7i	0.693964	−	2.13580i
$560$	−12490.0			−0.00168304
$561$		0			0
$562$	−796715.			−0.106405
$563$	−216678.	+	666868.i	−0.0288101	+	0.0886684i	−0.964428	−	0.264347i	$-0.914844\pi$
$563$	−216678.	+	666868.i	−0.0288101	+	0.0886684i	0.935618	+	0.353015i	$0.114844\pi$
$564$		0			0
$565$	−5.19747e6	−	3.77618e6i	−0.684969	−	0.497659i
$566$	−1.71758e6	−	5.28618e6i	−0.225360	−	0.693587i
$567$		0			0
$568$	−1.51243e6	−	1.09885e6i	−0.196700	−	0.142911i
$569$	−6.22955e6	+	4.52603e6i	−0.806633	+	0.586053i	−0.912852	−	0.408290i	$-0.866125\pi$
$569$	−6.22955e6	+	4.52603e6i	−0.806633	+	0.586053i	0.106219	+	0.994343i	$0.466125\pi$
$570$		0			0
$571$	9.38506e6			1.20461			0.602306	−	0.798266i	$-0.294249\pi$
$571$	9.38506e6			1.20461			0.602306	+	0.798266i	$0.294249\pi$
$572$	−1.91919e6	−	5.69495e6i	−0.245261	−	0.727780i
$573$		0			0
$574$	2617.00	−	8054.29i	0.000331531	−	0.00102035i
$575$	160130.	−	116341.i	0.0201977	−	0.0146745i
$576$		0			0
$577$	3.56102e6	+	1.09597e7i	0.445282	+	1.37044i	0.882174	+	0.470923i	$0.156079\pi$
$577$	3.56102e6	+	1.09597e7i	0.445282	+	1.37044i	−0.436892	+	0.899514i	$0.643921\pi$
$578$	1.56276e6	+	4.80969e6i	0.194569	+	0.598822i
$579$		0			0
$580$	−418821.	+	304292.i	−0.0516962	+	0.0375595i
$581$	49993.3	−	153863.i	0.00614428	−	0.0189102i
$582$		0			0
$583$	−8.31566e6	−	5.90445e6i	−1.01327	−	0.719462i
$584$	−24629.4			−0.00298828
$585$		0			0
$586$	7.35460e6	−	5.34343e6i	0.884739	−	0.642800i
$587$	−1.05188e7	−	7.64233e6i	−1.26000	−	0.915441i	−0.261239	−	0.965274i	$-0.584131\pi$
$587$	−1.05188e7	−	7.64233e6i	−1.26000	−	0.915441i	−0.998758	+	0.0498333i	$0.984131\pi$
$588$		0			0
$589$	−2.75987e6	−	8.49402e6i	−0.327794	−	1.00885i
$590$	851076.	+	618343.i	0.100656	+	0.0731306i
$591$		0			0
$592$	911228.	−	2.80447e6i	0.106862	−	0.328887i
$593$	5.36206e6			0.626173			0.313087	−	0.949725i	$-0.398637\pi$
$593$	5.36206e6			0.626173			0.313087	+	0.949725i	$0.398637\pi$
$594$		0			0
$595$	19242.6			0.00222829
$596$	1.18577e6	−	3.64941e6i	0.136736	−	0.420831i
$597$		0			0
$598$	−274282.	−	199278.i	−0.0313650	−	0.0227880i
$599$	2.27155e6	+	6.99110e6i	0.258675	+	0.796120i	0.993083	+	0.117412i	$0.0374598\pi$
$599$	2.27155e6	+	6.99110e6i	0.258675	+	0.796120i	−0.734408	+	0.678708i	$0.762540\pi$
$600$		0			0
$601$	−1.10155e7	−	8.00324e6i	−1.24400	−	0.903816i	−0.246138	−	0.969235i	$-0.579162\pi$
$601$	−1.10155e7	−	8.00324e6i	−1.24400	−	0.903816i	−0.997858	+	0.0654192i	$0.979162\pi$
$602$	91320.1	−	66347.9i	0.0102701	−	0.00746167i
$603$		0			0
$604$	7.66940e6			0.855400
$605$	1.42275e6	−	4.72652e6i	0.158030	−	0.524993i
$606$		0			0
$607$	−69336.6	+	213396.i	−0.00763820	+	0.0235080i	−0.954803	−	0.297239i	$-0.903934\pi$
$607$	−69336.6	+	213396.i	−0.00763820	+	0.0235080i	0.947165	+	0.320747i	$0.103934\pi$
$608$	1.77173e6	−	1.28724e6i	0.194374	−	0.141221i
$609$		0			0
$610$	1.49063e6	+	4.58769e6i	0.162198	+	0.499194i
$611$	−2.88795e6	−	8.88821e6i	−0.312959	−	0.963188i
$612$		0			0
$613$	8.41246e6	−	6.11201e6i	0.904216	−	0.656951i	−0.0353296	−	0.999376i	$-0.511248\pi$
$613$	8.41246e6	−	6.11201e6i	0.904216	−	0.656951i	0.939545	+	0.342424i	$0.111248\pi$
$614$	−3.69102e6	+	1.13598e7i	−0.395117	+	1.21605i
$615$		0			0
$616$	12210.4	−	39019.9i	0.00129651	−	0.00414319i
$617$	5.76529e6			0.609688			0.304844	−	0.952402i	$-0.401396\pi$
$617$	5.76529e6			0.609688			0.304844	+	0.952402i	$0.401396\pi$
$618$		0			0
$619$	−9.55842e6	+	6.94460e6i	−1.00267	+	0.728485i	−0.962660	−	0.270714i	$-0.912740\pi$
$619$	−9.55842e6	+	6.94460e6i	−1.00267	+	0.728485i	−0.0400135	+	0.999199i	$0.512740\pi$
$620$	1.65675e6	+	1.20370e6i	0.173093	+	0.125759i
$621$		0			0
$622$	1.07919e6	+	3.32142e6i	0.111847	+	0.344229i
$623$	71863.1	+	52211.6i	0.00741798	+	0.00538948i
$624$		0			0
$625$	569094.	−	1.75149e6i	0.0582752	−	0.179353i
$626$	−1.99172e6			−0.203139
$627$		0			0
$628$	−2.19738e6			−0.222334
$629$	−1.40387e6	+	4.32068e6i	−0.141482	+	0.435437i
$630$		0			0
$631$	−8.15428e6	−	5.92443e6i	−0.815290	−	0.592343i	0.100069	−	0.994980i	$-0.468094\pi$
$631$	−8.15428e6	−	5.92443e6i	−0.815290	−	0.592343i	−0.915360	+	0.402637i	$0.868094\pi$
$632$	508420.	+	1.56476e6i	0.0506326	+	0.155831i
$633$		0			0
$634$	8.87273e6	+	6.44641e6i	0.876666	+	0.636935i
$635$	−2.81291e6	+	2.04370e6i	−0.276836	+	0.201133i
$636$		0			0
$637$	1.57279e7			1.53576
$638$	−541190.	−	1.60591e6i	−0.0526379	−	0.156196i
$639$		0			0
$640$	−155173.	+	477572.i	−0.0149749	+	0.0460881i
$641$	444511.	−	322956.i	0.0427305	−	0.0310455i	−0.566215	−	0.824258i	$-0.691593\pi$
$641$	444511.	−	322956.i	0.0427305	−	0.0310455i	0.608945	+	0.793212i	$0.291593\pi$
$642$		0			0
$643$	4.96547e6	+	1.52821e7i	0.473623	+	1.45766i	0.847806	+	0.530307i	$0.177923\pi$
$643$	4.96547e6	+	1.52821e7i	0.473623	+	1.45766i	−0.374183	+	0.927355i	$0.622077\pi$
$644$	−712.765	−	2193.67i	−6.77223e−5	−	0.000208428i
$645$		0			0
$646$	−2.72960e6	+	1.98317e6i	−0.257346	+	0.186973i
$647$	4.18779e6	−	1.28887e7i	0.393300	−	1.21045i	−0.536977	−	0.843597i	$-0.680434\pi$
$647$	4.18779e6	−	1.28887e7i	0.393300	−	1.21045i	0.930277	−	0.366857i	$-0.119566\pi$
$648$		0			0
$649$	−2.76377e6	+	2.05434e6i	−0.257567	+	0.191452i
$650$	−8.18254e6			−0.759635
$651$		0			0
$652$	2.58832e6	−	1.88052e6i	0.238451	−	0.173244i
$653$	3.23232e6	+	2.34842e6i	0.296641	+	0.215522i	0.726143	−	0.687543i	$-0.241311\pi$
$653$	3.23232e6	+	2.34842e6i	0.296641	+	0.215522i	−0.429502	+	0.903066i	$0.641311\pi$
$654$		0			0
$655$	−292089.	−	898959.i	−0.0266019	−	0.0818722i
$656$	−275453.	−	200128.i	−0.0249913	−	0.0181572i
$657$		0			0
$658$	19647.8	−	60469.8i	0.00176909	−	0.00544469i
$659$	2.14695e7			1.92578			0.962892	−	0.269889i	$-0.0869868\pi$
$659$	2.14695e7			1.92578			0.962892	+	0.269889i	$0.0869868\pi$
$660$		0			0
$661$	6.17516e6			0.549724			0.274862	−	0.961484i	$-0.411368\pi$
$661$	6.17516e6			0.549724			0.274862	+	0.961484i	$0.411368\pi$
$662$	4.44862e6	−	1.36914e7i	0.394530	−	1.21424i
$663$		0			0
$664$	−5.26206e6	−	3.82311e6i	−0.463165	−	0.336509i
$665$	−32243.8	−	99236.1i	−0.00282743	−	0.00870193i
$666$		0			0
$667$	−77344.5	−	56194.1i	−0.00673155	−	0.00489075i
$668$	−814030.	+	591427.i	−0.0705828	+	0.0512814i
$669$		0			0
$670$	−816616.			−0.0702798
$671$	−1.57896e7	+	171900.i	−1.35383	+	0.0147390i
$672$		0			0
$673$	−7.18765e6	+	2.21213e7i	−0.611715	+	1.88267i	−0.170207	+	0.985408i	$0.554444\pi$
$673$	−7.18765e6	+	2.21213e7i	−0.611715	+	1.88267i	−0.441508	+	0.897257i	$0.645556\pi$
$674$	−4.48627e6	+	3.25946e6i	−0.380396	+	0.276374i
$675$		0			0
$676$	2.49530e6	+	7.67975e6i	0.210018	+	0.646369i
$677$	548695.	+	1.68871e6i	0.0460108	+	0.141607i	0.971423	−	0.237356i	$-0.0762808\pi$
$677$	548695.	+	1.68871e6i	0.0460108	+	0.141607i	−0.925412	+	0.378963i	$0.876281\pi$
$678$		0			0
$679$	−215512.	+	156579.i	−0.0179390	+	0.0130334i
$680$	239065.	−	735767.i	0.0198264	−	0.0610194i
$681$		0			0
$682$	−5.38012e6	+	3.99909e6i	−0.442926	+	0.329231i
$683$	−4.78941e6			−0.392853			−0.196426	−	0.980519i	$-0.562934\pi$
$683$	−4.78941e6			−0.392853			−0.196426	+	0.980519i	$0.562934\pi$
$684$		0			0
$685$	−6.95862e6	+	5.05573e6i	−0.566626	+	0.411678i
$686$	173147.	+	125799.i	0.0140477	+	0.0102063i
$687$		0			0
$688$	−1.40236e6	−	4.31603e6i	−0.112951	−	0.347627i
$689$	1.92427e7	+	1.39806e7i	1.54425	+	1.12196i
$690$		0			0
$691$	1.54728e6	−	4.76203e6i	0.123274	−	0.379400i	−0.870308	−	0.492507i	$-0.836081\pi$
$691$	1.54728e6	−	4.76203e6i	0.123274	−	0.379400i	0.993583	+	0.113108i	$0.0360805\pi$
$692$	−9.59868e6			−0.761985
$693$		0			0
$694$	−5.26504e6			−0.414957
$695$	−1.93238e6	+	5.94726e6i	−0.151751	+	0.467041i
$696$		0			0
$697$	424374.	+	308326.i	0.0330877	+	0.0240396i
$698$	2.48779e6	+	7.65663e6i	0.193275	+	0.594839i
$699$		0			0
$700$	−45037.0	−	32721.3i	−0.00347396	−	0.00252398i
$701$	3.05642e6	−	2.22062e6i	0.234919	−	0.170679i	−0.464098	−	0.885784i	$-0.653621\pi$
$701$	3.05642e6	−	2.22062e6i	0.234919	−	0.170679i	0.699017	+	0.715105i	$0.253621\pi$
$702$		0			0
$703$	2.46345e7			1.87999
$704$	−1.34028e6	−	951651.i	−0.101921	−	0.0723679i
$705$		0			0
$706$	−1.84457e6	+	5.67701e6i	−0.139278	+	0.428655i
$707$	47658.9	−	34626.2i	0.00358588	−	0.00260529i
$708$		0			0
$709$	617866.	+	1.90160e6i	0.0461614	+	0.142070i	0.971481	−	0.237119i	$-0.0762030\pi$
$709$	617866.	+	1.90160e6i	0.0461614	+	0.142070i	−0.925319	+	0.379189i	$0.876203\pi$
$710$	1.10661e6	+	3.40578e6i	0.0823848	+	0.253554i
$711$		0			0
$712$	2.88918e6	−	2.09911e6i	0.213587	−	0.155180i
$713$	−116865.	+	359672.i	−0.00860912	+	0.0264962i
$714$		0			0
$715$	−3.43793e6	+	1.09864e7i	−0.251496	+	0.803693i
$716$	1.70780e6			0.124496
$717$		0			0
$718$	−1.36923e7	+	9.94806e6i	−0.991212	+	0.720157i
$719$	7.86754e6	+	5.71610e6i	0.567566	+	0.412361i	0.834220	−	0.551431i	$-0.185918\pi$
$719$	7.86754e6	+	5.71610e6i	0.567566	+	0.412361i	−0.266654	+	0.963792i	$0.585918\pi$
$720$		0			0
$721$	−38896.1	−	119710.i	−0.00278656	−	0.00857614i
$722$	6.78838e6	+	4.93204e6i	0.484644	+	0.352114i
$723$		0			0
$724$	−898216.	+	2.76443e6i	−0.0636846	+	0.196001i
$725$	−2.30738e6			−0.163033
$726$		0			0
$727$	−4.16302e6			−0.292127			−0.146064	−	0.989275i	$-0.546660\pi$
$727$	−4.16302e6			−0.292127			−0.146064	+	0.989275i	$0.546660\pi$
$728$	−29465.9	+	90686.7i	−0.00206059	+	0.00634184i
$729$		0			0
$730$	38168.4	+	27731.0i	0.00265092	+	0.00192601i
$731$	2.16053e6	+	6.64944e6i	0.149544	+	0.460248i
$732$		0			0
$733$	−7.37146e6	−	5.35568e6i	−0.506749	−	0.368175i	0.304840	−	0.952404i	$-0.401397\pi$
$733$	−7.37146e6	−	5.35568e6i	−0.506749	−	0.368175i	−0.811589	+	0.584229i	$0.801397\pi$
$734$	1.10074e7	−	7.99737e6i	0.754130	−	0.547908i
$735$		0			0
$736$	−92732.8			−0.00631014
$737$	798330.	−	2.55118e6i	0.0541394	−	0.173010i
$738$		0			0
$739$	−3.50280e6	+	1.07805e7i	−0.235942	+	0.726154i	0.761053	+	0.648689i	$0.224683\pi$
$739$	−3.50280e6	+	1.07805e7i	−0.235942	+	0.726154i	−0.996995	+	0.0774647i	$0.975317\pi$
$740$	−4.56978e6	+	3.32014e6i	−0.306772	+	0.222883i
$741$		0			0
$742$	50005.1	+	153900.i	0.00333430	+	0.0102619i
$743$	3.77186e6	+	1.16086e7i	0.250659	+	0.771449i	0.994654	+	0.103264i	$0.0329286\pi$
$743$	3.77186e6	+	1.16086e7i	0.250659	+	0.771449i	−0.743995	+	0.668185i	$0.767071\pi$
$744$		0			0
$745$	−5.94658e6	+	4.32044e6i	−0.392533	+	0.285192i
$746$	−3.72269e6	+	1.14573e7i	−0.244912	+	0.753761i
$747$		0			0
$748$	2.06489e6	+	1.46615e6i	0.134940	+	0.0958131i
$749$	−282930.			−0.0184278
$750$		0			0
$751$	1.67934e7	−	1.22011e7i	1.08652	−	0.789404i	0.107713	−	0.994182i	$-0.465647\pi$
$751$	1.67934e7	−	1.22011e7i	1.08652	−	0.789404i	0.978808	+	0.204778i	$0.0656473\pi$
$752$	−2.06804e6	−	1.50252e6i	−0.133356	−	0.0968891i
$753$		0			0
$754$	1.22131e6	+	3.75882e6i	0.0782346	+	0.240781i
$755$	−1.18854e7	−	8.63521e6i	−0.758830	−	0.551323i
$756$		0			0
$757$	5.56063e6	−	1.71139e7i	0.352683	−	1.08545i	−0.604658	−	0.796485i	$-0.706690\pi$
$757$	5.56063e6	−	1.71139e7i	0.352683	−	1.08545i	0.957341	−	0.288961i	$-0.0933097\pi$
$758$	7.13046e6			0.450759
$759$		0			0
$760$	−4.19500e6			−0.263450
$761$	−5.15403e6	+	1.58625e7i	−0.322616	+	0.992909i	0.649890	+	0.760029i	$0.274815\pi$
$761$	−5.15403e6	+	1.58625e7i	−0.322616	+	0.992909i	−0.972505	+	0.232881i	$0.925185\pi$
$762$		0			0
$763$	25737.3	+	18699.2i	0.00160048	+	0.00116282i
$764$	1.83341e6	+	5.64267e6i	0.113639	+	0.349745i
$765$		0			0
$766$	−1.76029e7	−	1.27892e7i	−1.08396	−	0.787541i
$767$	6.49744e6	−	4.72066e6i	0.398799	−	0.289744i
$768$		0			0
$769$	1.10319e7			0.672718			0.336359	−	0.941734i	$-0.390804\pi$
$769$	1.10319e7			0.672718			0.336359	+	0.941734i	$0.390804\pi$
$770$	−62856.2	+	46721.6i	−0.00382051	+	0.00283982i
$771$		0			0
$772$	995205.	−	3.06293e6i	0.0600993	−	0.184967i
$773$	−2.77975e6	+	2.01961e6i	−0.167324	+	0.121568i	−0.668296	−	0.743896i	$-0.732976\pi$
$773$	−2.77975e6	+	2.01961e6i	−0.167324	+	0.121568i	0.500972	+	0.865463i	$0.332976\pi$
$774$		0			0
$775$	2.82053e6	+	8.68070e6i	0.168685	+	0.519159i
$776$	3.30952e6	+	1.01857e7i	0.197293	+	0.607205i
$777$		0			0
$778$	−1.16121e7	+	8.43672e6i	−0.687802	+	0.499717i
$779$	878966.	−	2.70518e6i	0.0518954	−	0.159718i
$780$		0			0
$781$	−1.17218e7	+	127614.i	−0.687648	+	0.00748635i
$782$	142868.			0.00835444
$783$		0			0
$784$	3.48035e6	−	2.52862e6i	0.202224	−	0.146924i
$785$	3.40530e6	+	2.47410e6i	0.197234	+	0.143299i
$786$		0			0
$787$	3.53686e6	+	1.08853e7i	0.203555	+	0.626477i	0.999770	+	0.0214632i	$0.00683247\pi$
$787$	3.53686e6	+	1.08853e7i	0.203555	+	0.626477i	−0.796215	+	0.605014i	$0.793168\pi$
$788$	4.25867e6	+	3.09411e6i	0.244320	+	0.177509i
$789$		0			0
$790$	973903.	−	2.99737e6i	0.0555198	−	0.170872i
$791$	−333682.			−0.0189623
$792$		0			0
$793$	3.68266e7			2.07960
$794$	−6.44198e6	+	1.98264e7i	−0.362634	+	1.11607i
$795$		0			0
$796$	−9.44237e6	−	6.86029e6i	−0.528200	−	0.383760i
$797$	9.75593e6	+	3.00257e7i	0.544030	+	1.67435i	0.723285	+	0.690550i	$0.242631\pi$
$797$	9.75593e6	+	3.00257e7i	0.544030	+	1.67435i	−0.179254	+	0.983803i	$0.557369\pi$
$798$		0			0
$799$	3.18610e6	+	2.31484e6i	0.176560	+	0.128278i
$800$	−1.81067e6	+	1.31553e6i	−0.100026	+	0.0726733i
$801$		0			0
$802$	−2.56710e6			−0.140931
$803$	−123948.	+	92131.5i	−0.00678344	+	0.00504219i
$804$		0			0
$805$	−1365.34	+	4202.07i	−7.42591e−5	+	0.000228546i
$806$	1.26483e7	−	9.18951e6i	0.685794	−	0.498259i
$807$		0			0
$808$	−731876.	−	2.25248e6i	−0.0394375	−	0.121376i
$809$	1.02411e6	+	3.15188e6i	0.0550142	+	0.169316i	0.974788	−	0.223132i	$-0.0716281\pi$
$809$	1.02411e6	+	3.15188e6i	0.0550142	+	0.169316i	−0.919774	+	0.392448i	$0.871628\pi$
$810$		0			0
$811$	6.16149e6	−	4.47659e6i	0.328953	−	0.238998i	−0.411033	−	0.911620i	$-0.634832\pi$
$811$	6.16149e6	−	4.47659e6i	0.328953	−	0.238998i	0.739986	+	0.672622i	$0.234832\pi$
$812$	−8309.05	+	25572.6i	−0.000442244	+	0.00136109i
$813$		0			0
$814$	−5.90495e6	−	1.75222e7i	−0.312360	−	0.926888i
$815$	−6.12848e6			−0.323190
$816$		0			0
$817$	3.06715e7	−	2.22841e7i	1.60761	−	1.16799i
$818$	−1.64536e7	−	1.19543e7i	−0.859763	−	0.624654i
$819$		0			0
$820$	201542.	+	620282.i	0.0104672	+	0.0322147i
$821$	−2.52833e7	−	1.83694e7i	−1.30911	−	0.951122i	−1.00000		9.54010e-5i	$-0.999970\pi$
$821$	−2.52833e7	−	1.83694e7i	−1.30911	−	0.951122i	−0.309108	−	0.951027i	$-0.600030\pi$
$822$		0			0
$823$	3.84034e6	−	1.18194e7i	0.197638	−	0.608267i	−0.802298	−	0.596924i	$-0.796389\pi$
$823$	3.84034e6	−	1.18194e7i	0.197638	−	0.608267i	0.999936	−	0.0113430i	$-0.00361067\pi$
$824$	−5.06049e6			−0.259642
$825$		0			0
$826$	54639.7			0.00278650
$827$	8.60743e6	−	2.64909e7i	0.437632	−	1.34689i	−0.452732	−	0.891646i	$-0.649551\pi$
$827$	8.60743e6	−	2.64909e7i	0.437632	−	1.34689i	0.890365	−	0.455248i	$-0.150449\pi$
$828$		0			0
$829$	−588896.	−	427858.i	−0.0297613	−	0.0216229i	0.572805	−	0.819692i	$-0.305855\pi$
$829$	−588896.	−	427858.i	−0.0297613	−	0.0216229i	−0.602566	+	0.798069i	$0.705855\pi$
$830$	3.85011e6	+	1.18494e7i	0.193990	+	0.597038i
$831$		0			0
$832$	3.10145e6	+	2.25333e6i	0.155330	+	0.112854i
$833$	−5.36196e6	+	3.89569e6i	−0.267739	+	0.194523i
$834$		0			0
$835$	1.92742e6			0.0956664
$836$	4.10107e6	−	1.31056e7i	0.202946	−	0.648545i
$837$		0			0
$838$	−3.02119e6	+	9.29826e6i	−0.148617	+	0.457395i
$839$	−1.01777e7	+	7.39450e6i	−0.499164	+	0.362664i	−0.808697	−	0.588225i	$-0.799827\pi$
$839$	−1.01777e7	+	7.39450e6i	−0.499164	+	0.362664i	0.309534	+	0.950888i	$0.399827\pi$
$840$		0			0
$841$	−5.99390e6	−	1.84473e7i	−0.292226	−	0.899380i
$842$	−6.63035e6	−	2.04061e7i	−0.322297	−	0.991928i
$843$		0			0
$844$	7.65411e6	−	5.56104e6i	0.369861	−	0.268720i
$845$	4.77987e6	−	1.47109e7i	0.230289	−	0.708758i
$846$		0			0
$847$	−84513.6	−	242044.i	−0.00404779	−	0.0115927i
$848$	6.50581e6			0.310679
$849$		0			0
$850$	2.78959e6	−	2.02675e6i	0.132432	−	0.0962174i
$851$	−843910.	−	613136.i	−0.0399459	−	0.0290224i
$852$		0			0
$853$	764502.	+	2.35289e6i	0.0359754	+	0.110721i	0.967432	−	0.253133i	$-0.0814609\pi$
$853$	764502.	+	2.35289e6i	0.0359754	+	0.110721i	−0.931456	+	0.363854i	$0.881461\pi$
$854$	202695.	+	147267.i	0.00951040	+	0.00690971i
$855$		0			0
$856$	−3.51504e6	+	1.08182e7i	−0.163963	+	0.504627i
$857$	3.29116e7			1.53072			0.765362	−	0.643600i	$-0.222560\pi$
$857$	3.29116e7			1.53072			0.765362	+	0.643600i	$0.222560\pi$
$858$		0			0
$859$	−1.12463e7			−0.520028			−0.260014	−	0.965605i	$-0.583727\pi$
$859$	−1.12463e7			−0.520028			−0.260014	+	0.965605i	$0.583727\pi$
$860$	−2.68629e6	+	8.26755e6i	−0.123853	+	0.381180i
$861$		0			0
$862$	−1.77736e7	−	1.29133e7i	−0.814717	−	0.591927i
$863$	6.23301e6	+	1.91832e7i	0.284886	+	0.876788i	0.986433	+	0.164165i	$0.0524930\pi$
$863$	6.23301e6	+	1.91832e7i	0.284886	+	0.876788i	−0.701547	+	0.712623i	$0.747507\pi$
$864$		0			0
$865$	1.48752e7	+	1.08074e7i	0.675961	+	0.491115i
$866$	−343564.	+	249614.i	−0.0155673	+	0.0113103i
$867$		0			0
$868$	106365.			0.00479180
$869$	8.41194e6	+	5.97281e6i	0.377874	+	0.268305i
$870$		0			0
$871$	−1.92652e6	+	5.92923e6i	−0.0860456	+	0.264821i
$872$	1.03474e6	−	751783.i	0.0460830	−	0.0334812i
$873$		0			0
$874$	−239395.	−	736782.i	−0.0106008	−	0.0326258i
$875$	80067.1	+	246421.i	0.00353536	+	0.0108807i
$876$		0			0
$877$	−1.65220e7	+	1.20039e7i	−0.725375	+	0.527016i	−0.888097	−	0.459656i	$-0.847973\pi$
$877$	−1.65220e7	+	1.20039e7i	−0.725375	+	0.527016i	0.162722	+	0.986672i	$0.447973\pi$
$878$	5.67808e6	−	1.74753e7i	0.248579	−	0.765049i
$879$		0			0
$880$	1.00555e6	+	2.98384e6i	0.0437721	+	0.129888i
$881$	−4.49818e6			−0.195253			−0.0976263	−	0.995223i	$-0.531125\pi$
$881$	−4.49818e6			−0.195253			−0.0976263	+	0.995223i	$0.531125\pi$
$882$		0			0
$883$	−3.08903e6	+	2.24431e6i	−0.133327	+	0.0968681i	−0.652450	−	0.757832i	$-0.726259\pi$
$883$	−3.08903e6	+	2.24431e6i	−0.133327	+	0.0968681i	0.519123	+	0.854700i	$0.326259\pi$
$884$	−4.77821e6	−	3.47157e6i	−0.205653	−	0.149416i
$885$		0			0
$886$	6.15981e6	+	1.89580e7i	0.263623	+	0.811348i
$887$	−1.74286e7	−	1.26626e7i	−0.743794	−	0.540398i	0.150103	−	0.988670i	$-0.452039\pi$
$887$	−1.74286e7	−	1.26626e7i	−0.743794	−	0.540398i	−0.893897	+	0.448273i	$0.852039\pi$
$888$		0			0
$889$	−55805.8	+	171753.i	−0.00236824	+	0.00728868i
$890$	−6.84085e6			−0.289491
$891$		0			0
$892$	−1.02573e7			−0.431637
$893$	6.59908e6	−	2.03099e7i	0.276920	−	0.852272i
$894$		0			0
$895$	−2.64659e6	−	1.92286e6i	−0.110441	−	0.0802399i
$896$	8059.59	+	24804.9i	0.000335385	+	0.00103221i
$897$		0			0
$898$	2.04024e7	+	1.48232e7i	0.844289	+	0.613412i
$899$	3.56667e6	−	2.59134e6i	0.147185	−	0.106936i
$900$		0			0
$901$	−1.00231e7			−0.411330
$902$	−2.13484e6	+	23241.8i	−0.0873675	+	0.000951161i
$903$		0			0
$904$	−4.14556e6	+	1.27587e7i	−0.168718	+	0.519262i
$905$	4.50453e6	−	3.27273e6i	0.182822	−	0.132828i
$906$		0			0
$907$	−2.04718e6	−	6.30057e6i	−0.0826300	−	0.254309i	0.901203	−	0.433397i	$-0.142685\pi$
$907$	−2.04718e6	−	6.30057e6i	−0.0826300	−	0.254309i	−0.983833	+	0.179088i	$0.942685\pi$
$908$	1.98684e6	+	6.11485e6i	0.0799737	+	0.246134i
$909$		0			0
$910$	147771.	−	107362.i	0.00591540	−	0.00429779i
$911$	9.43049e6	−	2.90241e7i	0.376477	−	1.15868i	−0.566000	−	0.824405i	$-0.691510\pi$
$911$	9.43049e6	−	2.90241e7i	0.376477	−	1.15868i	0.942477	−	0.334271i	$-0.108490\pi$
$912$		0			0
$913$	−4.07825e7	+	443995.i	−1.61919	+	0.0176279i
$914$	−3.21817e7			−1.27422
$915$		0			0
$916$	−4.38407e6	+	3.18521e6i	−0.172639	+	0.125429i
$917$	−39718.2	−	28856.9i	−0.00155979	−	0.00113325i
$918$		0			0
$919$	−4.79890e6	−	1.47695e7i	−0.187436	−	0.576869i	0.812546	−	0.582897i	$-0.198081\pi$
$919$	−4.79890e6	−	1.47695e7i	−0.187436	−	0.576869i	−0.999982	+	0.00602850i	$0.998081\pi$
$920$	143709.	+	104411.i	0.00559776	+	0.00406701i
$921$		0			0
$922$	2.17722e6	−	6.70080e6i	0.0843481	−	0.259597i
$923$	2.73391e7			1.05628
$924$		0			0
$925$	−2.51760e7			−0.967458
$926$	3.26823e6	−	1.00586e7i	0.125252	−	0.385486i
$927$		0			0
$928$	874573.	+	635414.i	0.0333370	+	0.0242207i
$929$	−1.47381e7	−	4.53592e7i	−0.560276	−	1.72435i	−0.681587	−	0.731738i	$-0.738710\pi$
$929$	−1.47381e7	−	4.53592e7i	−0.560276	−	1.72435i	0.121311	−	0.992615i	$-0.461290\pi$
$930$		0			0
$931$	2.90752e7	+	2.11243e7i	1.09938	+	0.798746i
$932$	1.50505e7	−	1.09348e7i	0.567560	−	0.412357i
$933$		0			0
$934$	3.25106e7			1.21943
$935$	−1.54919e6	−	4.59703e6i	−0.0579530	−	0.171968i
$936$		0			0
$937$	4.43316e6	−	1.36439e7i	0.164955	−	0.507678i	−0.834078	−	0.551646i	$-0.814000\pi$
$937$	4.43316e6	−	1.36439e7i	0.164955	−	0.507678i	0.999033	+	0.0439678i	$0.0139999\pi$
$938$	−34314.2	+	24930.7i	−0.00127340	+	0.000925182i
$939$		0			0
$940$	1.51313e6	+	4.65694e6i	0.0558543	+	0.171902i
$941$	−9.12708e6	−	2.80903e7i	−0.336014	−	1.03415i	−0.966220	−	0.257718i	$-0.917029\pi$
$941$	−9.12708e6	−	2.80903e7i	−0.336014	−	1.03415i	0.630206	−	0.776428i	$-0.282971\pi$
$942$		0			0
$943$	−97440.9	+	70794.9i	−0.00356831	+	0.00259253i
$944$	678829.	−	2.08922e6i	0.0247931	−	0.0763052i
$945$		0			0
$946$	−2.32024e7	−	1.64746e7i	−0.842956	−	0.598532i
$947$	−1.69481e7			−0.614109			−0.307054	−	0.951692i	$-0.599343\pi$
$947$	−1.69481e7			−0.614109			−0.307054	+	0.951692i	$0.599343\pi$
$948$		0			0
$949$	291392.	−	211709.i	0.0105030	−	0.00763087i
$950$	−1.51265e7	−	1.09901e7i	−0.543788	−	0.395085i
$951$		0			0
$952$	−12416.9	−	38215.4i	−0.000444040	−	0.00136661i
$953$	−2.82219e7	−	2.05044e7i	−1.00659	−	0.731333i	−0.0431019	−	0.999071i	$-0.513724\pi$
$953$	−2.82219e7	−	2.05044e7i	−1.00659	−	0.731333i	−0.963492	+	0.267737i	$0.913724\pi$
$954$		0			0
$955$	3.51199e6	−	1.08088e7i	0.124608	−	0.383503i
$956$	−1.71755e7			−0.607805
$957$		0			0
$958$	2.24539e7			0.790456
$959$	−138053.	+	424883.i	−0.00484729	+	0.0149184i
$960$		0			0
$961$	9.05261e6	+	6.57711e6i	0.316203	+	0.229735i
$962$	1.33258e7	+	4.10127e7i	0.464255	+	1.42883i
$963$		0			0
$964$	−1.11265e7	−	8.08386e6i	−0.385625	−	0.280173i
$965$	−4.99092e6	+	3.62612e6i	−0.172529	+	0.125350i
$966$		0			0
$967$	4.59896e6			0.158159			0.0790794	−	0.996868i	$-0.474802\pi$
$967$	4.59896e6			0.158159			0.0790794	+	0.996868i	$0.474802\pi$
$968$	−1.03048e7	+	224402.i	−0.353470	+	0.00769729i
$969$		0			0
$970$	6.33955e6	−	1.95111e7i	0.216336	−	0.665814i
$971$	−1.96705e7	+	1.42914e7i	−0.669525	+	0.486438i	−0.869866	−	0.493288i	$-0.835795\pi$
$971$	−1.96705e7	+	1.42914e7i	−0.669525	+	0.486438i	0.200341	+	0.979726i	$0.435795\pi$
$972$		0			0
$973$	100367.	+	308898.i	0.00339867	+	0.0104600i
$974$	−5.94858e6	−	1.83079e7i	−0.200917	−	0.618358i
$975$		0			0
$976$	8.14916e6	−	5.92071e6i	0.273835	−	0.198952i
$977$	−1.29140e6	+	3.97452e6i	−0.0432836	+	0.133213i	−0.970363	−	0.241652i	$-0.922311\pi$
$977$	−1.29140e6	+	3.97452e6i	−0.0432836	+	0.133213i	0.927079	+	0.374865i	$0.122311\pi$
$978$		0			0
$979$	6.68767e6	−	2.13714e7i	0.223007	−	0.712650i
$980$	−8.24057e6			−0.274089
$981$		0			0
$982$	1.26100e7	−	9.16169e6i	0.417288	−	0.303177i
$983$	3.02818e7	+	2.20010e7i	0.999534	+	0.726204i	0.961988	−	0.273091i	$-0.0880459\pi$
$983$	3.02818e7	+	2.20010e7i	0.999534	+	0.726204i	0.0375461	+	0.999295i	$0.488046\pi$
$984$		0			0
$985$	−3.11596e6	−	9.58994e6i	−0.102330	−	0.314938i
$986$	−1.34740e6	−	978944.i	−0.0441372	−	0.0320675i
$987$		0			0
$988$	−9.89666e6	+	3.04588e7i	−0.322549	+	0.992705i
$989$	−1.60535e6			−0.0521892
$990$		0			0
$991$	−4.60166e7			−1.48844			−0.744218	−	0.667937i	$-0.767178\pi$
$991$	−4.60166e7			−1.48844			−0.744218	+	0.667937i	$0.767178\pi$
$992$	1.32145e6	−	4.06699e6i	0.0426354	−	0.131218i
$993$		0			0
$994$	150476.	+	109327.i	0.00483059	+	0.00350963i
$995$	6.90874e6	+	2.12629e7i	0.221228	+	0.680871i
$996$		0			0
$997$	−2.01777e7	−	1.46600e7i	−0.642887	−	0.467085i	0.217954	−	0.975959i	$-0.430062\pi$
$997$	−2.01777e7	−	1.46600e7i	−0.642887	−	0.467085i	−0.860841	+	0.508874i	$0.830062\pi$
$998$	2.67523e7	−	1.94367e7i	0.850228	−	0.617727i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.6.f.c.163.2		8
3.2	odd	2		66.6.e.a.31.1	✓	8
11.5	even	5	inner	198.6.f.c.181.2		8
33.5	odd	10		66.6.e.a.49.1	yes	8
33.26	odd	10		726.6.a.be.1.2		4
33.29	even	10		726.6.a.bb.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.6.e.a.31.1	✓	8	3.2	odd	2
66.6.e.a.49.1	yes	8	33.5	odd	10
198.6.f.c.163.2		8	1.1	even	1	trivial
198.6.f.c.181.2		8	11.5	even	5	inner
726.6.a.bb.1.2		4	33.29	even	10
726.6.a.be.1.2		4	33.26	odd	10

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:	\( N \)	\(=\)	\( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	198.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23607 + 3.80423i) q^{2} +(-12.9443 - 9.40456i) q^{4} +(9.47098 + 29.1487i) q^{5} +(1.28786 + 0.935685i) q^{7} +(51.7771 - 37.6183i) q^{8} +O(q^{10})\)	\(q+(-1.23607 + 3.80423i) q^{2} +(-12.9443 - 9.40456i) q^{4} +(9.47098 + 29.1487i) q^{5} +(1.28786 + 0.935685i) q^{7} +(51.7771 - 37.6183i) q^{8} -122.595 q^{10} +(119.850 - 382.997i) q^{11} +(-289.220 + 890.129i) q^{13} +(-5.15144 + 3.74274i) q^{14} +(79.1084 + 243.470i) q^{16} +(-121.877 - 375.100i) q^{17} +(-1730.20 + 1257.07i) q^{19} +(151.536 - 466.379i) q^{20} +(1308.87 + 929.347i) q^{22} +90.5594 q^{23} +(1768.23 - 1284.70i) q^{25} +(-3028.76 - 2200.52i) q^{26} +(-7.87070 - 24.2235i) q^{28} +(-854.075 - 620.522i) q^{29} +(-1290.47 + 3971.67i) q^{31} -1024.00 q^{32} +1577.61 q^{34} +(-15.0767 + 46.4013i) q^{35} +(-9318.86 - 6770.54i) q^{37} +(-2643.52 - 8135.91i) q^{38} +(1586.90 + 1152.95i) q^{40} +(-1075.99 + 781.752i) q^{41} -17727.1 q^{43} +(-5153.29 + 3830.49i) q^{44} +(-111.938 + 344.508i) q^{46} +(-8078.28 + 5869.21i) q^{47} +(-5192.87 - 15982.0i) q^{49} +(2701.62 + 8314.72i) q^{50} +(12115.0 - 8802.08i) q^{52} +(7853.15 - 24169.5i) q^{53} +(12299.0 - 133.898i) q^{55} +101.880 q^{56} +(3416.30 - 2482.09i) q^{58} +(-6942.17 - 5043.78i) q^{59} +(-12159.0 - 37421.5i) q^{61} +(-13514.0 - 9818.51i) q^{62} +(1265.73 - 3895.53i) q^{64} -28685.3 q^{65} +6661.08 q^{67} +(-1950.04 + 6001.60i) q^{68} +(-157.885 - 114.710i) q^{70} +(-9026.52 - 27780.8i) q^{71} +(-311.338 - 226.200i) q^{73} +(37275.4 - 27082.2i) q^{74} +34218.4 q^{76} +(512.715 - 381.105i) q^{77} +(-7944.07 + 24449.3i) q^{79} +(-6347.61 + 4611.81i) q^{80} +(-1643.97 - 5059.60i) q^{82} +(-31405.1 - 96655.1i) q^{83} +(9779.38 - 7105.14i) q^{85} +(21911.9 - 67437.9i) q^{86} +(-8202.22 - 24339.0i) q^{88} +55800.4 q^{89} +(-1205.36 + 875.742i) q^{91} +(-1172.22 - 851.671i) q^{92} +(-12342.5 - 37986.3i) q^{94} +(-53028.6 - 38527.5i) q^{95} +(-51711.3 + 159151. i) q^{97} +67217.9 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 32 q^{4} - 150 q^{5} + 474 q^{7} + 128 q^{8}+O(q^{10}) \) 8 * q + 8 * q^2 - 32 * q^4 - 150 * q^5 + 474 * q^7 + 128 * q^8	\( 8 q + 8 q^{2} - 32 q^{4} - 150 q^{5} + 474 q^{7} + 128 q^{8} - 1200 q^{10} + 582 q^{11} + 510 q^{13} - 1896 q^{14} - 512 q^{16} - 2004 q^{17} - 540 q^{19} - 2400 q^{20} + 672 q^{22} + 9944 q^{23} + 12228 q^{25} + 600 q^{26} - 6496 q^{28} + 11964 q^{29} - 9160 q^{31} - 8192 q^{32} + 2896 q^{34} - 42634 q^{35} - 718 q^{37} - 7560 q^{38} + 1666 q^{41} - 70528 q^{43} + 32 q^{44} + 56664 q^{46} - 51914 q^{47} - 23052 q^{49} + 52888 q^{50} - 2400 q^{52} + 53636 q^{53} + 104980 q^{55} + 8704 q^{56} - 47856 q^{58} + 17600 q^{59} - 10618 q^{61} - 77640 q^{62} - 8192 q^{64} - 116324 q^{65} - 182364 q^{67} - 32064 q^{68} - 79104 q^{70} - 29954 q^{71} + 127228 q^{73} + 2872 q^{74} - 43200 q^{76} + 33046 q^{77} + 39938 q^{79} - 51624 q^{82} - 208842 q^{83} + 125910 q^{85} - 51528 q^{86} + 30592 q^{88} + 344008 q^{89} + 282622 q^{91} + 147104 q^{92} - 106544 q^{94} - 31306 q^{95} - 26202 q^{97} - 323072 q^{98}+O(q^{100}) \) 8 * q + 8 * q^2 - 32 * q^4 - 150 * q^5 + 474 * q^7 + 128 * q^8 - 1200 * q^10 + 582 * q^11 + 510 * q^13 - 1896 * q^14 - 512 * q^16 - 2004 * q^17 - 540 * q^19 - 2400 * q^20 + 672 * q^22 + 9944 * q^23 + 12228 * q^25 + 600 * q^26 - 6496 * q^28 + 11964 * q^29 - 9160 * q^31 - 8192 * q^32 + 2896 * q^34 - 42634 * q^35 - 718 * q^37 - 7560 * q^38 + 1666 * q^41 - 70528 * q^43 + 32 * q^44 + 56664 * q^46 - 51914 * q^47 - 23052 * q^49 + 52888 * q^50 - 2400 * q^52 + 53636 * q^53 + 104980 * q^55 + 8704 * q^56 - 47856 * q^58 + 17600 * q^59 - 10618 * q^61 - 77640 * q^62 - 8192 * q^64 - 116324 * q^65 - 182364 * q^67 - 32064 * q^68 - 79104 * q^70 - 29954 * q^71 + 127228 * q^73 + 2872 * q^74 - 43200 * q^76 + 33046 * q^77 + 39938 * q^79 - 51624 * q^82 - 208842 * q^83 + 125910 * q^85 - 51528 * q^86 + 30592 * q^88 + 344008 * q^89 + 282622 * q^91 + 147104 * q^92 - 106544 * q^94 - 31306 * q^95 - 26202 * q^97 - 323072 * q^98

Introduction

L-functions

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