LMFDB - Embedded newform 198.6.f.c.37.2

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			37.2
Root			$3.37668 - 10.3924i$ of defining polynomial
Character	$\chi$	$=$	198.37
Dual form			198.6.f.c.91.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.23607 + 2.35114i) q^{2} +(4.94427 + 15.2169i) q^{4} +(2.38251 - 1.73100i) q^{5} +(-19.5441 - 60.1504i) q^{7} +(-19.7771 + 60.8676i) q^{8} +O(q^{10})$	\(q+(3.23607 + 2.35114i) q^{2} +(4.94427 + 15.2169i) q^{4} +(2.38251 - 1.73100i) q^{5} +(-19.5441 - 60.1504i) q^{7} +(-19.7771 + 60.8676i) q^{8} +11.7798 q^{10} +(347.477 + 200.776i) q^{11} +(-19.2535 - 13.9885i) q^{13} +(78.1762 - 240.602i) q^{14} +(-207.108 + 150.473i) q^{16} +(436.239 - 316.946i) q^{17} +(-519.915 + 1600.14i) q^{19} +(38.1202 + 27.6959i) q^{20} +(652.405 + 1466.69i) q^{22} +4776.84 q^{23} +(-962.998 + 2963.80i) q^{25} +(-29.4168 - 90.5355i) q^{26} +(818.672 - 594.800i) q^{28} +(1033.77 + 3181.60i) q^{29} +(-897.700 - 652.217i) q^{31} -1024.00 q^{32} +2156.88 q^{34} +(-150.684 - 109.478i) q^{35} +(639.681 + 1968.73i) q^{37} +(-5444.63 + 3955.75i) q^{38} +(58.2424 + 179.252i) q^{40} +(-4066.14 + 12514.3i) q^{41} +1441.48 q^{43} +(-1337.17 + 6280.21i) q^{44} +(15458.2 + 11231.0i) q^{46} +(-1287.89 + 3963.71i) q^{47} +(10361.0 - 7527.74i) q^{49} +(-10084.6 + 7326.92i) q^{50} +(117.667 - 362.142i) q^{52} +(4578.12 + 3326.20i) q^{53} +(1175.41 - 123.129i) q^{55} +4047.74 q^{56} +(-4135.06 + 12726.4i) q^{58} +(14531.1 + 44722.2i) q^{59} +(2370.73 - 1722.44i) q^{61} +(-1371.56 - 4221.24i) q^{62} +(-3313.73 - 2407.57i) q^{64} -70.0857 q^{65} -29247.5 q^{67} +(6979.82 + 5071.14i) q^{68} +(-230.225 - 708.559i) q^{70} +(16520.7 - 12003.0i) q^{71} +(-479.578 - 1475.99i) q^{73} +(-2558.72 + 7874.94i) q^{74} -26919.7 q^{76} +(5285.66 - 24824.8i) q^{77} +(33803.9 + 24560.0i) q^{79} +(-232.970 + 717.007i) q^{80} +(-42581.1 + 30937.0i) q^{82} +(-13143.3 + 9549.18i) q^{83} +(490.711 - 1510.25i) q^{85} +(4664.73 + 3389.12i) q^{86} +(-19092.8 + 17179.3i) q^{88} -4898.19 q^{89} +(-465.122 + 1431.50i) q^{91} +(23618.0 + 72688.7i) q^{92} +(-13486.9 + 9798.84i) q^{94} +(1531.12 + 4712.31i) q^{95} +(-18314.8 - 13306.5i) q^{97} +51227.8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

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

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 $

$2$	3.23607	+	2.35114i	0.572061	+	0.415627i
$2$	3.23607	+	2.35114i	0.572061	+	0.415627i
$3$		0			0
$3$		0			0
$4$	4.94427	+	15.2169i	0.154508	+	0.475528i
$5$	2.38251	−	1.73100i	0.0426196	−	0.0309650i	−0.566271	−	0.824219i	$-0.691615\pi$
$5$	2.38251	−	1.73100i	0.0426196	−	0.0309650i	0.608891	+	0.793254i	$0.291615\pi$
$6$		0			0
$7$	−19.5441	−	60.1504i	−0.150754	−	0.463974i	0.846952	−	0.531670i	$-0.178435\pi$
$7$	−19.5441	−	60.1504i	−0.150754	−	0.463974i	−0.997706	+	0.0676958i	$0.978435\pi$
$8$	−19.7771	+	60.8676i	−0.109254	+	0.336249i
$9$		0			0
$10$	11.7798			0.0372509
$11$	347.477	+	200.776i	0.865852	+	0.500300i
$11$	347.477	+	200.776i	0.865852	+	0.500300i
$12$		0			0
$13$	−19.2535	−	13.9885i	−0.0315974	−	0.0229569i	0.571874	−	0.820341i	$-0.306216\pi$
$13$	−19.2535	−	13.9885i	−0.0315974	−	0.0229569i	−0.603472	+	0.797384i	$0.706216\pi$
$14$	78.1762	−	240.602i	0.106599	−	0.328079i
$15$		0			0
$16$	−207.108	+	150.473i	−0.202254	+	0.146946i
$17$	436.239	−	316.946i	0.366102	−	0.265989i	−0.389491	−	0.921030i	$-0.627349\pi$
$17$	436.239	−	316.946i	0.366102	−	0.265989i	0.755593	+	0.655042i	$0.227349\pi$
$18$		0			0
$19$	−519.915	+	1600.14i	−0.330407	+	1.01689i	0.638534	+	0.769594i	$0.279541\pi$
$19$	−519.915	+	1600.14i	−0.330407	+	1.01689i	−0.968941	+	0.247293i	$0.920459\pi$
$20$	38.1202	+	27.6959i	0.0213098	+	0.0154825i
$21$		0			0
$22$	652.405	+	1466.69i	0.287383	+	0.646074i
$23$	4776.84			1.88287			0.941437	−	0.337190i	$-0.109477\pi$
$23$	4776.84			1.88287			0.941437	+	0.337190i	$0.109477\pi$
$24$		0			0
$25$	−962.998	+	2963.80i	−0.308159	+	0.948417i
$26$	−29.4168	−	90.5355i	−0.00853417	−	0.0262655i
$27$		0			0
$28$	818.672	−	594.800i	0.197340	−	0.143376i
$29$	1033.77	+	3181.60i	0.228259	+	0.702508i	0.997944	+	0.0640849i	$0.0204128\pi$
$29$	1033.77	+	3181.60i	0.228259	+	0.702508i	−0.769686	+	0.638423i	$0.779587\pi$
$30$		0			0
$31$	−897.700	−	652.217i	−0.167775	−	0.121896i	0.500729	−	0.865604i	$-0.333065\pi$
$31$	−897.700	−	652.217i	−0.167775	−	0.121896i	−0.668504	+	0.743708i	$0.733065\pi$
$32$	−1024.00			−0.176777
$33$		0			0
$34$	2156.88			0.319985
$35$	−150.684	−	109.478i	−0.0207920	−	0.0151063i
$36$		0			0
$37$	639.681	+	1968.73i	0.0768173	+	0.236419i	0.982090	−	0.188411i	$-0.0603337\pi$
$37$	639.681	+	1968.73i	0.0768173	+	0.236419i	−0.905273	+	0.424830i	$0.860334\pi$
$38$	−5444.63	+	3955.75i	−0.611658	+	0.444396i
$39$		0			0
$40$	58.2424	+	179.252i	0.00575559	+	0.0177139i
$41$	−4066.14	+	12514.3i	−0.377765	+	1.16264i	0.563828	+	0.825892i	$0.309328\pi$
$41$	−4066.14	+	12514.3i	−0.377765	+	1.16264i	−0.941594	+	0.336751i	$0.890672\pi$
$42$		0			0
$43$	1441.48			0.118888			0.0594440	−	0.998232i	$-0.481067\pi$
$43$	1441.48			0.118888			0.0594440	+	0.998232i	$0.481067\pi$
$44$	−1337.17	+	6280.21i	−0.104125	+	0.489038i
$45$		0			0
$46$	15458.2	+	11231.0i	1.07712	+	0.782573i
$47$	−1287.89	+	3963.71i	−0.0850420	+	0.261732i	−0.984531	−	0.175211i	$-0.943939\pi$
$47$	−1287.89	+	3963.71i	−0.0850420	+	0.261732i	0.899489	+	0.436944i	$0.143939\pi$
$48$		0			0
$49$	10361.0	−	7527.74i	0.616472	−	0.447893i
$50$	−10084.6	+	7326.92i	−0.570474	+	0.414473i
$51$		0			0
$52$	117.667	−	362.142i	0.00603457	−	0.0185725i
$53$	4578.12	+	3326.20i	0.223871	+	0.162652i	0.694067	−	0.719910i	$-0.255817\pi$
$53$	4578.12	+	3326.20i	0.223871	+	0.162652i	−0.470197	+	0.882562i	$0.655817\pi$
$54$		0			0
$55$	1175.41	−	123.129i	0.0523941	−	0.00548851i
$56$	4047.74			0.172481
$57$		0			0
$58$	−4135.06	+	12726.4i	−0.161403	+	0.496748i
$59$	14531.1	+	44722.2i	0.543462	+	1.67261i	0.724618	+	0.689151i	$0.242016\pi$
$59$	14531.1	+	44722.2i	0.543462	+	1.67261i	−0.181156	+	0.983454i	$0.557984\pi$
$60$		0			0
$61$	2370.73	−	1722.44i	0.0815752	−	0.0592679i	−0.546250	−	0.837622i	$-0.683945\pi$
$61$	2370.73	−	1722.44i	0.0815752	−	0.0592679i	0.627825	+	0.778354i	$0.283945\pi$
$62$	−1371.56	−	4221.24i	−0.0453144	−	0.139464i
$63$		0			0
$64$	−3313.73	−	2407.57i	−0.101127	−	0.0734732i
$65$	−70.0857			−0.00205753
$66$		0			0
$67$	−29247.5			−0.795980			−0.397990	−	0.917390i	$-0.630292\pi$
$67$	−29247.5			−0.795980			−0.397990	+	0.917390i	$0.630292\pi$
$68$	6979.82	+	5071.14i	0.183051	+	0.132994i
$69$		0			0
$70$	−230.225	−	708.559i	−0.00561574	−	0.0172835i
$71$	16520.7	−	12003.0i	0.388940	−	0.282581i	−0.376081	−	0.926587i	$-0.622729\pi$
$71$	16520.7	−	12003.0i	0.388940	−	0.282581i	0.765021	+	0.644006i	$0.222729\pi$
$72$		0			0
$73$	−479.578	−	1475.99i	−0.0105330	−	0.0324172i	0.945652	−	0.325181i	$-0.105425\pi$
$73$	−479.578	−	1475.99i	−0.0105330	−	0.0324172i	−0.956185	+	0.292763i	$0.905425\pi$
$74$	−2558.72	+	7874.94i	−0.0543180	+	0.167174i
$75$		0			0
$76$	−26919.7			−0.534609
$77$	5285.66	−	24824.8i	0.101595	−	0.477155i
$78$		0			0
$79$	33803.9	+	24560.0i	0.609396	+	0.442752i	0.849201	−	0.528069i	$-0.177084\pi$
$79$	33803.9	+	24560.0i	0.609396	+	0.442752i	−0.239806	+	0.970821i	$0.577084\pi$
$80$	−232.970	+	717.007i	−0.00406981	+	0.0125256i
$81$		0			0
$82$	−42581.1	+	30937.0i	−0.699331	+	0.508093i
$83$	−13143.3	+	9549.18i	−0.209416	+	0.152150i	−0.687549	−	0.726138i	$-0.741314\pi$
$83$	−13143.3	+	9549.18i	−0.209416	+	0.152150i	0.478133	+	0.878287i	$0.341314\pi$
$84$		0			0
$85$	490.711	−	1510.25i	0.00736680	−	0.0226727i
$86$	4664.73	+	3389.12i	0.0680112	+	0.0494130i
$87$		0			0
$88$	−19092.8	+	17179.3i	−0.262823	+	0.236482i
$89$	−4898.19			−0.0655482			−0.0327741	−	0.999463i	$-0.510434\pi$
$89$	−4898.19			−0.0655482			−0.0327741	+	0.999463i	$0.510434\pi$
$90$		0			0
$91$	−465.122	+	1431.50i	−0.00588795	+	0.0181212i
$92$	23618.0	+	72688.7i	0.290920	+	0.895359i
$93$		0			0
$94$	−13486.9	+	9798.84i	−0.157432	+	0.114381i
$95$	1531.12	+	4712.31i	0.0174061	+	0.0535704i
$96$		0			0
$97$	−18314.8	−	13306.5i	−0.197639	−	0.143593i	0.484564	−	0.874756i	$-0.338978\pi$
$97$	−18314.8	−	13306.5i	−0.197639	−	0.143593i	−0.682203	+	0.731162i	$0.738978\pi$
$98$	51227.8			0.538816
$99$		0			0
$100$	−49861.2			−0.498612
$101$	−52570.2	−	38194.5i	−0.512786	−	0.372561i	0.301093	−	0.953595i	$-0.402648\pi$
$101$	−52570.2	−	38194.5i	−0.512786	−	0.372561i	−0.813879	+	0.581034i	$0.802648\pi$
$102$		0			0
$103$	−54484.5	−	167686.i	−0.506034	−	1.55741i	−0.799026	−	0.601297i	$-0.794651\pi$
$103$	−54484.5	−	167686.i	−0.506034	−	1.55741i	0.292992	−	0.956115i	$-0.405349\pi$
$104$	1232.23	−	895.264i	0.0111714	−	0.00811648i
$105$		0			0
$106$	6994.74	+	21527.6i	0.0604654	+	0.186093i
$107$	−9406.77	+	28951.1i	−0.0794294	+	0.244459i	−0.982884	−	0.184225i	$-0.941022\pi$
$107$	−9406.77	+	28951.1i	−0.0794294	+	0.244459i	0.903455	+	0.428684i	$0.141022\pi$
$108$		0			0
$109$	134312.			1.08280			0.541400	−	0.840765i	$-0.317895\pi$
$109$	134312.			1.08280			0.541400	+	0.840765i	$0.317895\pi$
$110$	4093.20	+	2365.10i	0.0322538	+	0.0186366i
$111$		0			0
$112$	13098.8	+	9516.80i	0.0986700	+	0.0716879i
$113$	55512.9	−	170851.i	0.408976	−	1.25870i	−0.508553	−	0.861030i	$-0.669820\pi$
$113$	55512.9	−	170851.i	0.408976	−	1.25870i	0.917529	−	0.397668i	$-0.130180\pi$
$114$		0			0
$115$	11380.9	−	8268.69i	0.0802474	−	0.0583031i
$116$	−43302.9	+	31461.4i	−0.298794	+	0.217087i
$117$		0			0
$118$	−58124.5	+	178889.i	−0.384286	+	1.18271i
$119$	−27590.3	−	20045.5i	−0.178603	−	0.129763i
$120$		0			0
$121$	80428.9	+	139530.i	0.499400	+	0.866371i
$122$	11721.6			0.0712993
$123$		0			0
$124$	5486.25	−	16885.0i	0.0320421	−	0.0986156i
$125$	5679.85	+	17480.8i	0.0325133	+	0.100066i
$126$		0			0
$127$	251196.	−	182505.i	1.38199	−	1.00407i	0.385296	−	0.922793i	$-0.374099\pi$
$127$	251196.	−	182505.i	1.38199	−	1.00407i	0.996691	−	0.0812796i	$-0.0259007\pi$
$128$	−5062.93	−	15582.1i	−0.0273135	−	0.0840623i
$129$		0			0
$130$	−226.802	−	164.781i	−0.00117703	−	0.000855165i
$131$	−219752.			−1.11880			−0.559402	−	0.828896i	$-0.688969\pi$
$131$	−219752.			−1.11880			−0.559402	+	0.828896i	$0.688969\pi$
$132$		0			0
$133$	106410.			0.521619
$134$	−94647.0	−	68765.1i	−0.455350	−	0.330831i
$135$		0			0
$136$	10664.2	+	32821.1i	0.0494404	+	0.152162i
$137$	182567.	−	132642.i	0.831036	−	0.603783i	−0.0888162	−	0.996048i	$-0.528308\pi$
$137$	182567.	−	132642.i	0.831036	−	0.603783i	0.919852	+	0.392265i	$0.128308\pi$
$138$		0			0
$139$	−86532.5	−	266320.i	−0.379876	−	1.16914i	−0.940129	−	0.340818i	$-0.889296\pi$
$139$	−86532.5	−	266320.i	−0.379876	−	1.16914i	0.560253	−	0.828321i	$-0.310704\pi$
$140$	920.899	−	2834.24i	0.00397093	−	0.0122213i
$141$		0			0
$142$	81682.8			0.339946
$143$	−3881.59	−	8726.32i	−0.0158734	−	0.0356855i
$144$		0			0
$145$	7970.30	+	5790.76i	0.0314814	+	0.0228726i
$146$	1918.31	−	5903.96i	0.00744796	−	0.0229225i
$147$		0			0
$148$	−26795.3	+	19467.9i	−0.100555	+	0.0730576i
$149$	−33455.4	+	24306.8i	−0.123453	+	0.0896937i	−0.647798	−	0.761812i	$-0.724310\pi$
$149$	−33455.4	+	24306.8i	−0.123453	+	0.0896937i	0.524345	+	0.851506i	$0.324310\pi$
$150$		0			0
$151$	−6886.82	+	21195.5i	−0.0245797	+	0.0756485i	−0.962594	−	0.270948i	$-0.912663\pi$
$151$	−6886.82	+	21195.5i	−0.0245797	+	0.0756485i	0.938014	+	0.346597i	$0.112663\pi$
$152$	−87114.0	−	63292.0i	−0.305829	−	0.222198i
$153$		0			0
$154$	75471.5	−	67907.5i	0.256437	−	0.230736i
$155$	−3267.76			−0.0109250
$156$		0			0
$157$	6989.70	−	21512.1i	0.0226313	−	0.0696520i	−0.939103	−	0.343636i	$-0.888341\pi$
$157$	6989.70	−	21512.1i	0.0226313	−	0.0696520i	0.961734	+	0.273984i	$0.0883415\pi$
$158$	51647.8	+	158956.i	0.164592	+	0.506562i
$159$		0			0
$160$	−2439.69	+	1772.54i	−0.00753416	+	0.00547389i
$161$	−93358.8	−	287329.i	−0.283851	−	0.873604i
$162$		0			0
$163$	−345217.	−	250815.i	−1.01771	−	0.739409i	−0.0518971	−	0.998652i	$-0.516527\pi$
$163$	−345217.	−	250815.i	−1.01771	−	0.739409i	−0.965812	+	0.259244i	$0.916527\pi$
$164$	−210533.			−0.611237
$165$		0			0
$166$	−64984.1			−0.183036
$167$	330673.	+	240248.i	0.917503	+	0.666605i	0.942901	−	0.333073i	$-0.108085\pi$
$167$	330673.	+	240248.i	0.917503	+	0.666605i	−0.0253985	+	0.999677i	$0.508085\pi$
$168$		0			0
$169$	−114561.	−	352582.i	−0.308546	−	0.949606i
$170$	5138.80	−	3733.55i	0.0136376	−	0.00990832i
$171$		0			0
$172$	7127.07	+	21934.9i	0.0183692	+	0.0565346i
$173$	219015.	−	674059.i	0.556364	−	1.71231i	−0.135951	−	0.990716i	$-0.543409\pi$
$173$	219015.	−	674059.i	0.556364	−	1.71231i	0.692315	−	0.721596i	$-0.256591\pi$
$174$		0			0
$175$	197095.			0.486497
$176$	−102177.	+	10703.4i	−0.248640	+	0.0260461i
$177$		0			0
$178$	−15850.9	−	11516.3i	−0.0374976	−	0.0272436i
$179$	233988.	−	720142.i	0.545835	−	1.67991i	−0.173161	−	0.984893i	$-0.555398\pi$
$179$	233988.	−	720142.i	0.545835	−	1.67991i	0.718996	−	0.695014i	$-0.244602\pi$
$180$		0			0
$181$	−522345.	+	379506.i	−1.18512	+	0.861038i	−0.992740	−	0.120283i	$-0.961620\pi$
$181$	−522345.	+	379506.i	−1.18512	+	0.861038i	−0.192377	+	0.981321i	$0.561620\pi$
$182$	−4870.83	+	3538.86i	−0.0108999	+	0.00791927i
$183$		0			0
$184$	−94472.0	+	290755.i	−0.205711	+	0.633115i
$185$	4931.92	+	3583.25i	0.0105946	+	0.00769746i
$186$		0			0
$187$	215218.	−	22545.0i	0.450064	−	0.0471462i
$188$	−66683.1			−0.137601
$189$		0			0
$190$	−6124.49	+	18849.2i	−0.0123080	+	0.0378800i
$191$	171377.	+	527444.i	0.339914	+	1.04615i	0.964251	+	0.264992i	$0.0853693\pi$
$191$	171377.	+	527444.i	0.339914	+	1.04615i	−0.624337	+	0.781155i	$0.714631\pi$
$192$		0			0
$193$	−166272.	+	120803.i	−0.321310	+	0.233446i	−0.736734	−	0.676182i	$-0.763633\pi$
$193$	−166272.	+	120803.i	−0.321310	+	0.233446i	0.415424	+	0.909628i	$0.363633\pi$
$194$	−27982.5	−	86121.4i	−0.0533805	−	0.164288i
$195$		0			0
$196$	165777.	+	120444.i	0.308236	+	0.223947i
$197$	−439037.			−0.806001			−0.403001	−	0.915200i	$-0.632033\pi$
$197$	−439037.			−0.806001			−0.403001	+	0.915200i	$0.632033\pi$
$198$		0			0
$199$	−660644.			−1.18259			−0.591296	−	0.806455i	$-0.701383\pi$
$199$	−660644.			−1.18259			−0.591296	+	0.806455i	$0.701383\pi$
$200$	−161354.	−	117231.i	−0.285237	−	0.207237i
$201$		0			0
$202$	−80320.1	−	247200.i	−0.138499	−	0.426255i
$203$	171171.	−	124363.i	0.291534	−	0.211812i
$204$		0			0
$205$	11974.5	+	36853.9i	0.0199010	+	0.0612489i
$206$	217938.	−	670744.i	0.357820	−	1.10126i
$207$		0			0
$208$	6092.46			0.00976414
$209$	−501927.	+	451623.i	−0.794832	+	0.715172i
$210$		0			0
$211$	−648691.	−	471302.i	−1.00307	−	0.728774i	−0.0403267	−	0.999187i	$-0.512840\pi$
$211$	−648691.	−	471302.i	−1.00307	−	0.728774i	−0.962745	+	0.270413i	$0.912840\pi$
$212$	−27979.0	+	86110.4i	−0.0427555	+	0.131588i
$213$		0			0
$214$	−98509.0	+	71571.0i	−0.147042	+	0.106832i
$215$	3434.34	−	2495.20i	0.00506696	−	0.00368136i
$216$		0			0
$217$	−21686.4	+	66744.0i	−0.0312636	+	0.0962194i
$218$	434642.	+	315786.i	0.619428	+	0.450041i
$219$		0			0
$220$	7685.19	+	17277.3i	0.0107053	+	0.0240668i
$221$	−12832.7			−0.0176741
$222$		0			0
$223$	108293.	−	333291.i	0.145827	−	0.448808i	−0.851290	−	0.524696i	$-0.824179\pi$
$223$	108293.	−	333291.i	0.145827	−	0.448808i	0.997116	+	0.0758876i	$0.0241790\pi$
$224$	20013.1	+	61594.0i	0.0266498	+	0.0820198i
$225$		0			0
$226$	581339.	−	422367.i	0.757108	−	0.550071i
$227$	175924.	+	541439.i	0.226601	+	0.697405i	0.998125	+	0.0612055i	$0.0194945\pi$
$227$	175924.	+	541439.i	0.226601	+	0.697405i	−0.771525	+	0.636200i	$0.780505\pi$
$228$		0			0
$229$	1.08805e6	+	790518.i	1.37108	+	0.996146i	0.997652	+	0.0684851i	$0.0218165\pi$
$229$	1.08805e6	+	790518.i	1.37108	+	0.996146i	0.373425	+	0.927661i	$0.378183\pi$
$230$	56270.1			0.0701388
$231$		0			0
$232$	−214102.			−0.261156
$233$	327862.	+	238206.i	0.395641	+	0.287450i	0.767763	−	0.640734i	$-0.221370\pi$
$233$	327862.	+	238206.i	0.395641	+	0.287450i	−0.372122	+	0.928184i	$0.621370\pi$
$234$		0			0
$235$	3792.76	+	11672.9i	0.00448008	+	0.0137883i
$236$	−608688.	+	442238.i	−0.711402	+	0.516863i
$237$		0			0
$238$	−42154.2	−	129737.i	−0.0482391	−	0.148465i
$239$	−394301.	+	1.21353e6i	−0.446512	+	1.37422i	0.434305	+	0.900766i	$0.356994\pi$
$239$	−394301.	+	1.21353e6i	−0.446512	+	1.37422i	−0.880817	+	0.473457i	$0.843006\pi$
$240$		0			0
$241$	1.05184e6			1.16656			0.583278	−	0.812273i	$-0.301770\pi$
$241$	1.05184e6			1.16656			0.583278	+	0.812273i	$0.301770\pi$
$242$	−67781.1	+	640628.i	−0.0743996	+	0.703182i
$243$		0			0
$244$	37931.7	+	27559.0i	0.0407876	+	0.0296339i
$245$	11654.8	−	35869.8i	0.0124048	−	0.0381781i
$246$		0			0
$247$	32393.7	−	23535.4i	0.0337845	−	0.0245459i
$248$	57452.8	−	41741.9i	0.0593174	−	0.0430966i
$249$		0			0
$250$	−22719.4	+	69923.1i	−0.0229904	+	0.0707572i
$251$	−608155.	−	441851.i	−0.609299	−	0.442681i	0.239869	−	0.970805i	$-0.422896\pi$
$251$	−608155.	−	441851.i	−0.609299	−	0.442681i	−0.849167	+	0.528124i	$0.822896\pi$
$252$		0			0
$253$	1.65984e6	+	959075.i	1.63029	+	0.942001i
$254$	1.24198e6			1.20790
$255$		0			0
$256$	20251.7	−	62328.4i	0.0193136	−	0.0594410i
$257$	599032.	+	1.84363e6i	0.565741	+	1.74117i	0.665741	+	0.746183i	$0.268116\pi$
$257$	599032.	+	1.84363e6i	0.565741	+	1.74117i	−0.100000	+	0.994987i	$0.531884\pi$
$258$		0			0
$259$	105918.	−	76954.1i	0.0981118	−	0.0712824i
$260$	−346.523	−	1066.49i	−0.000317906	−	0.000978414i
$261$		0			0
$262$	−711132.	−	516667.i	−0.640025	−	0.465005i
$263$	−1.35587e6			−1.20873			−0.604365	−	0.796707i	$-0.706573\pi$
$263$	−1.35587e6			−1.20873			−0.604365	+	0.796707i	$0.706573\pi$
$264$		0			0
$265$	16665.0			0.0145778
$266$	344350.	+	250185.i	0.298398	+	0.216799i
$267$		0			0
$268$	−144608.	−	445057.i	−0.122986	−	0.378511i
$269$	−208686.	+	151619.i	−0.175838	+	0.127754i	−0.672223	−	0.740349i	$-0.734660\pi$
$269$	−208686.	+	151619.i	−0.175838	+	0.127754i	0.496385	+	0.868102i	$0.334660\pi$
$270$		0			0
$271$	640286.	+	1.97060e6i	0.529603	+	1.62995i	0.755029	+	0.655691i	$0.227623\pi$
$271$	640286.	+	1.97060e6i	0.529603	+	1.62995i	−0.225426	+	0.974260i	$0.572377\pi$
$272$	−42656.9	+	131284.i	−0.0349596	+	0.107595i
$273$		0			0
$274$	902659.			0.726352
$275$	−929680.	+	836505.i	−0.741313	+	0.667017i
$276$		0			0
$277$	−1.21229e6	−	880778.i	−0.949306	−	0.689711i	0.00133682	−	0.999999i	$-0.499574\pi$
$277$	−1.21229e6	−	880778.i	−0.949306	−	0.689711i	−0.950643	+	0.310288i	$0.899574\pi$
$278$	346130.	−	1.06528e6i	0.268613	−	0.826706i
$279$		0			0
$280$	9643.78	−	7006.61i	0.00735110	−	0.00534088i
$281$	899238.	−	653334.i	0.679374	−	0.493594i	−0.193776	−	0.981046i	$-0.562074\pi$
$281$	899238.	−	653334.i	0.679374	−	0.493594i	0.873150	+	0.487452i	$0.162074\pi$
$282$		0			0
$283$	−706009.	+	2.17287e6i	−0.524015	+	1.61275i	0.242240	+	0.970216i	$0.422118\pi$
$283$	−706009.	+	2.17287e6i	−0.524015	+	1.61275i	−0.766255	+	0.642537i	$0.777882\pi$
$284$	264331.	+	192048.i	0.194470	+	0.141291i
$285$		0			0
$286$	7955.72	−	37365.1i	0.00575128	−	0.0270117i
$287$	832208.			0.596386
$288$		0			0
$289$	−348910.	+	1.07384e6i	−0.245736	+	0.756299i
$290$	12177.5	+	37478.6i	0.00850285	+	0.0261691i
$291$		0			0
$292$	20088.8	−	14595.4i	0.0137879	−	0.0100175i
$293$	−89403.8	−	275157.i	−0.0608397	−	0.187245i	0.916017	−	0.401139i	$-0.131385\pi$
$293$	−89403.8	−	275157.i	−0.0608397	−	0.187245i	−0.976857	+	0.213893i	$0.931385\pi$
$294$		0			0
$295$	112035.	+	81397.9i	0.0749544	+	0.0544575i
$296$	−132483.			−0.0878884
$297$		0			0
$298$	−165413.			−0.107902
$299$	−91971.0	−	66820.8i	−0.0594940	−	0.0432249i
$300$		0			0
$301$	−28172.4	−	86705.7i	−0.0179229	−	0.0551609i
$302$	−72119.7	+	52398.0i	−0.0455026	+	0.0330596i
$303$		0			0
$304$	−133098.	−	409635.i	−0.0826016	−	0.254222i
$305$	2666.76	−	8207.46i	0.00164148	−	0.00505195i
$306$		0			0
$307$	−2.29491e6			−1.38970			−0.694848	−	0.719157i	$-0.744528\pi$
$307$	−2.29491e6			−1.38970			−0.694848	+	0.719157i	$0.744528\pi$
$308$	403891.	−	42309.3i	0.242598	−	0.0254132i
$309$		0			0
$310$	−10574.7	−	7682.97i	−0.00624977	−	0.00454072i
$311$	−107177.	+	329858.i	−0.0628351	+	0.193387i	−0.977546	−	0.210722i	$-0.932418\pi$
$311$	−107177.	+	329858.i	−0.0628351	+	0.193387i	0.914711	+	0.404109i	$0.132418\pi$
$312$		0			0
$313$	523448.	−	380307.i	0.302004	−	0.219419i	−0.426454	−	0.904509i	$-0.640237\pi$
$313$	523448.	−	380307.i	0.302004	−	0.219419i	0.728458	+	0.685091i	$0.240237\pi$
$314$	73197.1	−	53180.8i	0.0418957	−	0.0304390i
$315$		0			0
$316$	−206591.	+	635822.i	−0.116384	+	0.358194i
$317$	1.66102e6	+	1.20680e6i	0.928382	+	0.674509i	0.945596	−	0.325343i	$-0.105480\pi$
$317$	1.66102e6	+	1.20680e6i	0.928382	+	0.674509i	−0.0172141	+	0.999852i	$0.505480\pi$
$318$		0			0
$319$	−279581.	+	1.31309e6i	−0.153826	+	0.722466i
$320$	−12062.5			−0.00658510
$321$		0			0
$322$	373435.	−	1.14932e6i	0.200713	−	0.617731i
$323$	280349.	+	862826.i	0.149518	+	0.460169i
$324$		0			0
$325$	60000.3	−	43592.8i	0.0315097	−	0.0228932i
$326$	−527445.	−	1.62331e6i	−0.274874	−	0.845975i
$327$		0			0
$328$	−681298.	−	494992.i	−0.349665	−	0.254047i
$329$	263590.			0.134257
$330$		0			0
$331$	327883.			0.164493			0.0822467	−	0.996612i	$-0.473790\pi$
$331$	327883.			0.164493			0.0822467	+	0.996612i	$0.473790\pi$
$332$	−210293.	−	152787.i	−0.104708	−	0.0760748i
$333$		0			0
$334$	505223.	+	1.55492e6i	0.247809	+	0.762678i
$335$	−69682.6	+	50627.4i	−0.0339244	+	0.0246475i
$336$		0			0
$337$	−252520.	−	777178.i	−0.121122	−	0.372774i	0.872053	−	0.489412i	$-0.162788\pi$
$337$	−252520.	−	777178.i	−0.121122	−	0.372774i	−0.993175	+	0.116638i	$0.962788\pi$
$338$	458243.	−	1.41033e6i	0.218175	−	0.671473i
$339$		0			0
$340$	25407.6			0.0119197
$341$	−180980.	−	406867.i	−0.0842839	−	0.189481i
$342$		0			0
$343$	−1.51526e6	−	1.10090e6i	−0.695426	−	0.505257i
$344$	−28508.3	+	87739.5i	−0.0129890	+	0.0399760i
$345$		0			0
$346$	2.29356e6	−	1.66637e6i	1.02996	−	0.748307i
$347$	1.83385e6	−	1.33237e6i	0.817600	−	0.594021i	−0.0984238	−	0.995145i	$-0.531380\pi$
$347$	1.83385e6	−	1.33237e6i	0.817600	−	0.594021i	0.916024	+	0.401123i	$0.131380\pi$
$348$		0			0
$349$	258755.	−	796366.i	0.113717	−	0.349985i	−0.877960	−	0.478733i	$-0.841096\pi$
$349$	258755.	−	796366.i	0.113717	−	0.349985i	0.991677	+	0.128749i	$0.0410961\pi$
$350$	637813.	+	463398.i	0.278306	+	0.202201i
$351$		0			0
$352$	−355816.	−	205595.i	−0.153063	−	0.0884413i
$353$	−1.30266e6			−0.556410			−0.278205	−	0.960522i	$-0.589739\pi$
$353$	−1.30266e6			−0.556410			−0.278205	+	0.960522i	$0.589739\pi$
$354$		0			0
$355$	18583.6	−	57194.5i	0.00782635	−	0.0240870i
$356$	−24218.0	−	74535.4i	−0.0101278	−	0.0311700i
$357$		0			0
$358$	2.45036e6	−	1.78029e6i	1.01047	−	0.734146i
$359$	−1.23379e6	−	3.79723e6i	−0.505250	−	1.55500i	−0.800349	−	0.599534i	$-0.795353\pi$
$359$	−1.23379e6	−	3.79723e6i	−0.505250	−	1.55500i	0.295099	−	0.955467i	$-0.404647\pi$
$360$		0			0
$361$	−286914.	−	208455.i	−0.115873	−	0.0841870i
$362$	−2.58262e6			−1.03583
$363$		0			0
$364$	−24082.7			−0.00952690
$365$	−3697.53	−	2686.41i	−0.00145271	−	0.00105546i
$366$		0			0
$367$	−1.11663e6	−	3.43665e6i	−0.432759	−	1.33189i	−0.895366	−	0.445331i	$-0.853086\pi$
$367$	−1.11663e6	−	3.43665e6i	−0.432759	−	1.33189i	0.462607	−	0.886563i	$-0.346914\pi$
$368$	−989323.	+	718785.i	−0.380819	+	0.276681i
$369$		0			0
$370$	7535.30	+	23191.3i	0.00286152	+	0.00880684i
$371$	110597.	−	340383.i	0.0417166	−	0.128391i
$372$		0			0
$373$	−1.73947e6			−0.647357			−0.323678	−	0.946167i	$-0.604920\pi$
$373$	−1.73947e6			−0.647357			−0.323678	+	0.946167i	$0.604920\pi$
$374$	749466.	+	433051.i	0.277060	+	0.160088i
$375$		0			0
$376$	−215791.	−	156781.i	−0.0787162	−	0.0571906i
$377$	24602.2	−	75717.9i	0.00891500	−	0.0274375i
$378$		0			0
$379$	−3.21375e6	+	2.33492e6i	−1.14925	+	0.834977i	−0.988381	−	0.151999i	$-0.951429\pi$
$379$	−3.21375e6	+	2.33492e6i	−1.14925	+	0.834977i	−0.160867	+	0.986976i	$0.551429\pi$
$380$	−64136.5	+	46597.9i	−0.0227848	+	0.0165542i
$381$		0			0
$382$	−685507.	+	2.10977e6i	−0.240355	+	0.739738i
$383$	−3.52699e6	−	2.56251e6i	−1.22859	−	0.892625i	−0.231808	−	0.972761i	$-0.574464\pi$
$383$	−3.52699e6	−	2.56251e6i	−1.22859	−	0.892625i	−0.996784	+	0.0801369i	$0.974464\pi$
$384$		0			0
$385$	−30378.5	−	68294.9i	−0.0104452	−	0.0234821i
$386$	−822092.			−0.280835
$387$		0			0
$388$	111930.	−	344485.i	0.0377457	−	0.116169i
$389$	227129.	+	699031.i	0.0761024	+	0.234219i	0.981870	−	0.189556i	$-0.0607048\pi$
$389$	227129.	+	699031.i	0.0761024	+	0.234219i	−0.905768	+	0.423775i	$0.860705\pi$
$390$		0			0
$391$	2.08384e6	−	1.51400e6i	0.689323	−	0.500823i
$392$	253284.	+	779529.i	0.0832517	+	0.256222i
$393$		0			0
$394$	−1.42075e6	−	1.03224e6i	−0.461082	−	0.334996i
$395$	123051.			0.0396820
$396$		0			0
$397$	4.38966e6			1.39783			0.698915	−	0.715205i	$-0.253667\pi$
$397$	4.38966e6			1.39783			0.698915	+	0.715205i	$0.253667\pi$
$398$	−2.13789e6	−	1.55327e6i	−0.676515	−	0.491517i
$399$		0			0
$400$	−246528.	−	758734.i	−0.0770398	−	0.237104i
$401$	2.13286e6	−	1.54962e6i	0.662373	−	0.481242i	−0.205091	−	0.978743i	$-0.565749\pi$
$401$	2.13286e6	−	1.54962e6i	0.662373	−	0.481242i	0.867463	+	0.497501i	$0.165749\pi$
$402$		0			0
$403$	8160.34	+	25115.0i	0.00250291	+	0.00770317i
$404$	321280.	−	988800.i	0.0979334	−	0.301408i
$405$		0			0
$406$	846315.			0.254810
$407$	−173001.	+	812522.i	−0.0517681	+	0.243136i
$408$		0			0
$409$	−905649.	−	657993.i	−0.267702	−	0.194497i	0.445834	−	0.895116i	$-0.352907\pi$
$409$	−905649.	−	657993.i	−0.267702	−	0.194497i	−0.713536	+	0.700619i	$0.752907\pi$
$410$	−47898.2	+	147415.i	−0.0140721	+	0.0433095i
$411$		0			0
$412$	2.28227e6	−	1.65817e6i	0.662407	−	0.481267i
$413$	2.40606e6	−	1.74811e6i	0.694116	−	0.504305i
$414$		0			0
$415$	−14784.5	+	45502.0i	−0.00421392	+	0.0129691i
$416$	19715.6	+	14324.2i	0.00558569	+	0.00405824i
$417$		0			0
$418$	−2.68610e6	+	281381.i	−0.751937	+	0.0787686i
$419$	−2.22354e6			−0.618743			−0.309371	−	0.950941i	$-0.600119\pi$
$419$	−2.22354e6			−0.618743			−0.309371	+	0.950941i	$0.600119\pi$
$420$		0			0
$421$	1.72045e6	−	5.29500e6i	0.473082	−	1.45600i	−0.375444	−	0.926845i	$-0.622510\pi$
$421$	1.72045e6	−	5.29500e6i	0.473082	−	1.45600i	0.848526	−	0.529153i	$-0.177490\pi$
$422$	−991112.	−	3.05033e6i	−0.270920	−	0.833807i
$423$		0			0
$424$	−292999.	+	212877.i	−0.0791502	+	0.0575060i
$425$	519269.	+	1.59814e6i	0.139450	+	0.429184i
$426$		0			0
$427$	−149939.	−	108937.i	−0.0397965	−	0.0289139i
$428$	−487055.			−0.128519
$429$		0			0
$430$	16980.3			0.00442869
$431$	−4.60151e6	−	3.34319e6i	−1.19318	−	0.866898i	−0.199585	−	0.979880i	$-0.563959\pi$
$431$	−4.60151e6	−	3.34319e6i	−1.19318	−	0.866898i	−0.993597	+	0.112983i	$0.963959\pi$
$432$		0			0
$433$	777366.	+	2.39249e6i	0.199254	+	0.613239i	0.999901	+	0.0141030i	$0.00448926\pi$
$433$	777366.	+	2.39249e6i	0.199254	+	0.613239i	−0.800647	+	0.599136i	$0.795511\pi$
$434$	−227103.	+	165000.i	−0.0578761	+	0.0420494i
$435$		0			0
$436$	664074.	+	2.04381e6i	0.167302	+	0.514902i
$437$	−2.48355e6	+	7.64359e6i	−0.622114	+	1.91467i
$438$		0			0
$439$	−1.23688e6			−0.306312			−0.153156	−	0.988202i	$-0.548944\pi$
$439$	−1.23688e6			−0.306312			−0.153156	+	0.988202i	$0.548944\pi$
$440$	−15751.6	+	73979.5i	−0.00387876	+	0.0182171i
$441$		0			0
$442$	−41527.6	−	30171.6i	−0.0101107	−	0.00734585i
$443$	1.59899e6	−	4.92120e6i	0.387113	−	1.19141i	−0.547823	−	0.836594i	$-0.684543\pi$
$443$	1.59899e6	−	4.92120e6i	0.387113	−	1.19141i	0.934936	−	0.354816i	$-0.115457\pi$
$444$		0			0
$445$	−11670.0	+	8478.75i	−0.00279364	+	0.00202970i
$446$	1.13406e6	−	823940.i	0.269959	−	0.196136i
$447$		0			0
$448$	−80052.5	+	246376.i	−0.0188443	+	0.0579967i
$449$	−1.09519e6	−	795705.i	−0.256375	−	0.186267i	0.452173	−	0.891930i	$-0.350649\pi$
$449$	−1.09519e6	−	795705.i	−0.256375	−	0.186267i	−0.708547	+	0.705663i	$0.750649\pi$
$450$		0			0
$451$	−3.92545e6	+	3.53204e6i	−0.908759	+	0.817681i
$452$	2.87430e6			0.661737
$453$		0			0
$454$	−703697.	+	2.16576e6i	−0.160231	+	0.493140i
$455$	1369.76	+	4215.69i	0.000310182	+	0.000954641i
$456$		0			0
$457$	4.72087e6	−	3.42992e6i	1.05738	−	0.768233i	0.0837799	−	0.996484i	$-0.473301\pi$
$457$	4.72087e6	−	3.42992e6i	1.05738	−	0.768233i	0.973602	+	0.228251i	$0.0733007\pi$
$458$	1.66240e6	+	5.11634e6i	0.370315	+	1.13971i
$459$		0			0
$460$	182094.	+	132299.i	0.0401237	+	0.0291516i
$461$	3.90242e6			0.855228			0.427614	−	0.903961i	$-0.359354\pi$
$461$	3.90242e6			0.855228			0.427614	+	0.903961i	$0.359354\pi$
$462$		0			0
$463$	5.38828e6			1.16815			0.584073	−	0.811701i	$-0.301458\pi$
$463$	5.38828e6			1.16815			0.584073	+	0.811701i	$0.301458\pi$
$464$	−692847.	−	503383.i	−0.149397	−	0.108543i
$465$		0			0
$466$	500929.	+	1.54170e6i	0.106859	+	0.328878i
$467$	3.92185e6	−	2.84939e6i	0.832145	−	0.604589i	−0.0880204	−	0.996119i	$-0.528054\pi$
$467$	3.92185e6	−	2.84939e6i	0.832145	−	0.604589i	0.920165	+	0.391530i	$0.128054\pi$
$468$		0			0
$469$	571616.	+	1.75925e6i	0.119997	+	0.369314i
$470$	−15171.0	+	46691.7i	−0.00316789	+	0.00974978i
$471$		0			0
$472$	−3.00952e6			−0.621788
$473$	500881.	+	289415.i	0.102939	+	0.0594796i
$474$		0			0
$475$	−4.24181e6	−	3.08185e6i	−0.862615	−	0.626727i
$476$	168617.	−	518950.i	0.0341102	−	0.104980i
$477$		0			0
$478$	−4.12918e6	+	3.00002e6i	−0.826597	+	0.600558i
$479$	2.59202e6	−	1.88322e6i	0.516179	−	0.375026i	−0.298984	−	0.954258i	$-0.596648\pi$
$479$	2.59202e6	−	1.88322e6i	0.516179	−	0.375026i	0.815163	+	0.579232i	$0.196648\pi$
$480$		0			0
$481$	15223.5	−	46853.2i	0.00300022	−	0.00923373i
$482$	3.40381e6	+	2.47301e6i	0.667341	+	0.484852i
$483$		0			0
$484$	−1.72555e6	+	1.91375e6i	−0.334822	+	0.371341i
$485$	−66668.7			−0.0128697
$486$		0			0
$487$	825334.	−	2.54012e6i	0.157691	−	0.485323i	−0.840732	−	0.541451i	$-0.817875\pi$
$487$	825334.	−	2.54012e6i	0.157691	−	0.485323i	0.998424	+	0.0561273i	$0.0178753\pi$
$488$	57954.5	+	178366.i	0.0110164	+	0.0339049i
$489$		0			0
$490$	122051.	−	88675.1i	0.0229642	−	0.0166844i
$491$	1.10859e6	+	3.41188e6i	0.207523	+	0.638689i	0.999600	+	0.0282690i	$0.00899949\pi$
$491$	1.10859e6	+	3.41188e6i	0.207523	+	0.638689i	−0.792078	+	0.610420i	$0.791001\pi$
$492$		0			0
$493$	1.45937e6	+	1.06029e6i	0.270425	+	0.196475i
$494$	160163.			0.0295288
$495$		0			0
$496$	284062.			0.0518453
$497$	−1.04487e6	−	759139.i	−0.189745	−	0.137858i
$498$		0			0
$499$	1.82173e6	+	5.60671e6i	0.327516	+	1.00799i	0.970292	+	0.241937i	$0.0777827\pi$
$499$	1.82173e6	+	5.60671e6i	0.327516	+	1.00799i	−0.642776	+	0.766054i	$0.722217\pi$
$500$	−237920.	+	172859.i	−0.0425605	+	0.0309220i
$501$		0			0
$502$	−929179.	−	2.85972e6i	−0.164566	−	0.506482i
$503$	−2.71431e6	+	8.35377e6i	−0.478342	+	1.47219i	0.363054	+	0.931768i	$0.381734\pi$
$503$	−2.71431e6	+	8.35377e6i	−0.478342	+	1.47219i	−0.841397	+	0.540418i	$0.818266\pi$
$504$		0			0
$505$	−191364.			−0.0333911
$506$	3.11643e6	+	7.00615e6i	0.541105	+	1.21647i
$507$		0			0
$508$	4.01914e6	+	2.92008e6i	0.690994	+	0.502036i
$509$	1.58098e6	−	4.86576e6i	0.270478	−	0.832446i	−0.719902	−	0.694075i	$-0.755813\pi$
$509$	1.58098e6	−	4.86576e6i	0.270478	−	0.832446i	0.990381	−	0.138371i	$-0.0441865\pi$
$510$		0			0
$511$	−79408.5	+	57693.7i	−0.0134529	+	0.00977408i
$512$	212079.	−	154084.i	0.0357538	−	0.0259767i
$513$		0			0
$514$	−2.39613e6	+	7.37453e6i	−0.400039	+	1.23119i
$515$	−420073.	−	305201.i	−0.0697922	−	0.0507070i
$516$		0			0
$517$	−1.24333e6	+	1.11872e6i	−0.204578	+	0.184075i
$518$	523689.			0.0857529
$519$		0			0
$520$	1386.09	−	4265.95i	0.000224793	−	0.000691843i
$521$	−502811.	−	1.54749e6i	−0.0811542	−	0.249767i	0.902245	−	0.431225i	$-0.141918\pi$
$521$	−502811.	−	1.54749e6i	−0.0811542	−	0.249767i	−0.983399	+	0.181458i	$0.941918\pi$
$522$		0			0
$523$	−8.89989e6	+	6.46615e6i	−1.42276	+	1.03369i	−0.431447	+	0.902138i	$0.641997\pi$
$523$	−8.89989e6	+	6.46615e6i	−1.42276	+	1.03369i	−0.991309	+	0.131555i	$0.958003\pi$
$524$	−1.08651e6	−	3.34394e6i	−0.172865	−	0.532023i
$525$		0			0
$526$	−4.38770e6	−	3.18785e6i	−0.691468	−	0.502381i
$527$	−598329.			−0.0938455
$528$		0			0
$529$	1.63818e7			2.54521
$530$	53929.2	+	39181.9i	0.00833939	+	0.00605892i
$531$		0			0
$532$	526120.	+	1.61923e6i	0.0805946	+	0.248045i
$533$	253343.	−	184065.i	0.0386271	−	0.0280642i
$534$		0			0
$535$	27702.4	+	85259.3i	0.00418440	+	0.0128783i
$536$	578431.	−	1.78023e6i	0.0869641	−	0.267648i
$537$		0			0
$538$	−1.03180e6			−0.153688
$539$	5.11161e6	−	535463.i	0.757855	−	0.0793885i
$540$		0			0
$541$	924559.	+	671732.i	0.135813	+	0.0986740i	0.653618	−	0.756825i	$-0.273251\pi$
$541$	924559.	+	671732.i	0.135813	+	0.0986740i	−0.517804	+	0.855499i	$0.673251\pi$
$542$	−2.56114e6	+	7.88239e6i	−0.374486	+	1.15255i
$543$		0			0
$544$	−446709.	+	324553.i	−0.0647183	+	0.0470206i
$545$	319999.	−	232493.i	0.0461485	−	0.0335289i
$546$		0			0
$547$	3.72371e6	−	1.14604e7i	0.532118	−	1.63769i	−0.217677	−	0.976021i	$-0.569848\pi$
$547$	3.72371e6	−	1.14604e7i	0.532118	−	1.63769i	0.749795	−	0.661670i	$-0.230152\pi$
$548$	2.92107e6	+	2.12228e6i	0.415518	+	0.301892i
$549$		0			0
$550$	−4.97525e6	+	521179.i	−0.701307	+	0.0734649i
$551$	−5.62847e6			−0.789789
$552$		0			0
$553$	816628.	−	2.51332e6i	0.113556	−	0.349490i
$554$	−1.85221e6	−	5.70052e6i	−0.256399	−	0.789114i
$555$		0			0
$556$	3.62472e6	−	2.63351e6i	0.497265	−	0.361284i
$557$	2.70551e6	+	8.32671e6i	0.369498	+	1.13720i	0.947116	+	0.320890i	$0.103982\pi$
$557$	2.70551e6	+	8.32671e6i	0.369498	+	1.13720i	−0.577619	+	0.816307i	$0.696018\pi$
$558$		0			0
$559$	−27753.6	−	20164.2i	−0.00375655	−	0.00272930i
$560$	47681.5			0.00642509
$561$		0			0
$562$	4.44608e6			0.593794
$563$	−5.36894e6	−	3.90076e6i	−0.713867	−	0.518655i	0.170552	−	0.985349i	$-0.445445\pi$
$563$	−5.36894e6	−	3.90076e6i	−0.713867	−	0.518655i	−0.884419	+	0.466694i	$0.845445\pi$
$564$		0			0
$565$	−163482.	−	503147.i	−0.0215452	−	0.0663092i
$566$	−7.39342e6	+	5.37163e6i	−0.970073	+	0.704799i
$567$		0			0
$568$	403862.	+	1.24296e6i	0.0525245	+	0.161654i
$569$	−2.10832e6	+	6.48873e6i	−0.272995	+	0.840194i	0.716747	+	0.697333i	$0.245630\pi$
$569$	−2.10832e6	+	6.48873e6i	−0.272995	+	0.840194i	−0.989743	+	0.142861i	$0.954370\pi$
$570$		0			0
$571$	−6.97441e6			−0.895194			−0.447597	−	0.894235i	$-0.647720\pi$
$571$	−6.97441e6			−0.895194			−0.447597	+	0.894235i	$0.647720\pi$
$572$	113596.	−	102211.i	0.0145169	−	0.0130620i
$573$		0			0
$574$	2.69308e6	+	1.95664e6i	0.341169	+	0.247874i
$575$	−4.60009e6	+	1.41576e7i	−0.580225	+	1.78575i
$576$		0			0
$577$	6.11937e6	−	4.44599e6i	0.765187	−	0.555941i	−0.135310	−	0.990803i	$-0.543203\pi$
$577$	6.11937e6	−	4.44599e6i	0.765187	−	0.555941i	0.900497	+	0.434863i	$0.143203\pi$
$578$	−3.65384e6	+	2.65467e6i	−0.454914	+	0.330515i
$579$		0			0
$580$	−48710.1	+	149914.i	−0.00601242	+	0.0185043i
$581$	831261.	+	603946.i	0.102164	+	0.0742263i
$582$		0			0
$583$	922967.	+	2.07495e6i	0.112464	+	0.252835i
$584$	99324.6			0.0120510
$585$		0			0
$586$	357615.	−	1.10063e6i	0.0430201	−	0.132402i
$587$	−122288.	−	376365.i	−0.0146484	−	0.0450831i	0.943465	−	0.331472i	$-0.107545\pi$
$587$	−122288.	−	376365.i	−0.0146484	−	0.0450831i	−0.958114	+	0.286389i	$0.907545\pi$
$588$		0			0
$589$	1.51036e6	−	1.09734e6i	0.179388	−	0.130333i
$590$	171174.	+	526818.i	0.0202445	+	0.0623061i
$591$		0			0
$592$	−428725.	−	311487.i	−0.0502776	−	0.0365288i
$593$	7.07407e6			0.826100			0.413050	−	0.910708i	$-0.364464\pi$
$593$	7.07407e6			0.826100			0.413050	+	0.910708i	$0.364464\pi$
$594$		0			0
$595$	−100433.			−0.0116301
$596$	−535287.	−	388909.i	−0.0617264	−	0.0448469i
$597$		0			0
$598$	−140519.	−	432473.i	−0.0160688	−	0.0494546i
$599$	−5.20483e6	+	3.78153e6i	−0.592707	+	0.430627i	−0.843283	−	0.537470i	$-0.819380\pi$
$599$	−5.20483e6	+	3.78153e6i	−0.592707	+	0.430627i	0.250576	+	0.968097i	$0.419380\pi$
$600$		0			0
$601$	399453.	+	1.22939e6i	0.0451107	+	0.138837i	0.971075	−	0.238774i	$-0.0767457\pi$
$601$	399453.	+	1.22939e6i	0.0451107	+	0.138837i	−0.925964	+	0.377611i	$0.876746\pi$
$602$	112690.	−	346823.i	0.0126734	−	0.0390046i
$603$		0			0
$604$	−356579.			−0.0397708
$605$	433148.	+	193210.i	0.0481114	+	0.0214605i
$606$		0			0
$607$	−1.01936e7	−	7.40606e6i	−1.12294	−	0.815860i	−0.138284	−	0.990393i	$-0.544159\pi$
$607$	−1.01936e7	−	7.40606e6i	−1.12294	−	0.815860i	−0.984651	+	0.174533i	$0.944159\pi$
$608$	532393.	−	1.63854e6i	0.0584082	−	0.179762i
$609$		0			0
$610$	27926.7	−	20289.9i	0.00303875	−	0.00220778i
$611$	80242.8	−	58299.8i	0.00869567	−	0.00631777i
$612$		0			0
$613$	−4.07956e6	+	1.25556e7i	−0.438492	+	1.34954i	0.450973	+	0.892538i	$0.351077\pi$
$613$	−4.07956e6	+	1.25556e7i	−0.438492	+	1.34954i	−0.889465	+	0.457003i	$0.848923\pi$
$614$	−7.42649e6	−	5.39566e6i	−0.794991	−	0.577595i
$615$		0			0
$616$	1.40649e6	+	812689.i	0.149343	+	0.0862924i
$617$	4.10212e6			0.433805			0.216903	−	0.976193i	$-0.430405\pi$
$617$	4.10212e6			0.433805			0.216903	+	0.976193i	$0.430405\pi$
$618$		0			0
$619$	5.35713e6	−	1.64875e7i	0.561960	−	1.72953i	−0.114857	−	0.993382i	$-0.536641\pi$
$619$	5.35713e6	−	1.64875e7i	0.561960	−	1.72953i	0.676816	−	0.736152i	$-0.263359\pi$
$620$	−16156.7	−	49725.3i	−0.00168801	−	0.00519515i
$621$		0			0
$622$	−1.12238e6	+	815455.i	−0.116322	+	0.0845131i
$623$	95730.6	+	294629.i	0.00988168	+	0.0304127i
$624$		0			0
$625$	−7.83484e6	−	5.69234e6i	−0.802288	−	0.582896i
$626$	2.58807e6			0.263961
$627$		0			0
$628$	361906.			0.0366182
$629$	903036.	+	656094.i	0.0910078	+	0.0661210i
$630$		0			0
$631$	−2.11432e6	−	6.50721e6i	−0.211396	−	0.650612i	−0.999390	−	0.0349278i	$-0.988880\pi$
$631$	−2.11432e6	−	6.50721e6i	−0.211396	−	0.650612i	0.787993	−	0.615684i	$-0.211120\pi$
$632$	−2.16345e6	+	1.57184e6i	−0.215454	+	0.156536i
$633$		0			0
$634$	2.53781e6	+	7.81058e6i	0.250747	+	0.771721i
$635$	282563.	−	869639.i	0.0278087	−	0.0855864i
$636$		0			0
$637$	−304788.			−0.0297612
$638$	−3.99200e6	+	3.59191e6i	−0.388274	+	0.349360i
$639$		0			0
$640$	−39035.1	−	28360.6i	−0.00376708	−	0.00273694i
$641$	5.06121e6	−	1.55768e7i	0.486530	−	1.49738i	−0.343224	−	0.939254i	$-0.611519\pi$
$641$	5.06121e6	−	1.55768e7i	0.486530	−	1.49738i	0.829753	−	0.558130i	$-0.188481\pi$
$642$		0			0
$643$	−1.16988e7	+	8.49970e6i	−1.11587	+	0.810730i	−0.983579	−	0.180480i	$-0.942235\pi$
$643$	−1.16988e7	+	8.49970e6i	−1.11587	+	0.810730i	−0.132296	+	0.991210i	$0.542235\pi$
$644$	3.91067e6	−	2.84126e6i	0.371566	−	0.269958i
$645$		0			0
$646$	−1.12140e6	+	3.45130e6i	−0.105725	+	0.325388i
$647$	−1.92256e6	−	1.39682e6i	−0.180559	−	0.131184i	0.493834	−	0.869556i	$-0.335595\pi$
$647$	−1.92256e6	−	1.39682e6i	−0.180559	−	0.131184i	−0.674394	+	0.738372i	$0.735595\pi$
$648$		0			0
$649$	−3.92993e6	+	1.84574e7i	−0.366246	+	1.72012i
$650$	296658.			0.0275405
$651$		0			0
$652$	2.10978e6	−	6.49324e6i	0.194365	−	0.598194i
$653$	−5.16542e6	−	1.58975e7i	−0.474048	−	1.45897i	−0.847237	−	0.531215i	$-0.821736\pi$
$653$	−5.16542e6	−	1.58975e7i	−0.474048	−	1.45897i	0.373188	−	0.927756i	$-0.378264\pi$
$654$		0			0
$655$	−523561.	+	380389.i	−0.0476830	+	0.0346438i
$656$	−1.04093e6	−	3.20366e6i	−0.0944414	−	0.290661i
$657$		0			0
$658$	852994.	+	619736.i	0.0768035	+	0.0558010i
$659$	1.05919e7			0.950076			0.475038	−	0.879965i	$-0.342434\pi$
$659$	1.05919e7			0.950076			0.475038	+	0.879965i	$0.342434\pi$
$660$		0			0
$661$	1.18987e7			1.05924			0.529621	−	0.848234i	$-0.322334\pi$
$661$	1.18987e7			1.05924			0.529621	+	0.848234i	$0.322334\pi$
$662$	1.06105e6	+	770898.i	0.0941003	+	0.0683679i
$663$		0			0
$664$	−321299.	−	988857.i	−0.0282806	−	0.0870389i
$665$	253523.	−	184195.i	0.0222312	−	0.0161519i
$666$		0			0
$667$	4.93813e6	+	1.51980e7i	0.429782	+	1.32273i
$668$	−2.02089e6	+	6.21967e6i	−0.175227	+	0.539295i
$669$		0			0
$670$	−344530.			−0.0296510
$671$	1.16960e6	−	122521.i	0.100284	−	0.0105052i
$672$		0			0
$673$	−1.02873e7	−	7.47417e6i	−0.875516	−	0.636100i	0.0565453	−	0.998400i	$-0.481991\pi$
$673$	−1.02873e7	−	7.47417e6i	−0.875516	−	0.636100i	−0.932061	+	0.362300i	$0.881991\pi$
$674$	1.01008e6	−	3.10871e6i	0.0856459	−	0.263591i
$675$		0			0
$676$	4.79879e6	−	3.48652e6i	0.403891	−	0.293444i
$677$	1.06593e7	−	7.74441e6i	0.893832	−	0.649407i	−0.0430424	−	0.999073i	$-0.513705\pi$
$677$	1.06593e7	−	7.74441e6i	0.893832	−	0.649407i	0.936874	+	0.349666i	$0.113705\pi$
$678$		0			0
$679$	−442445.	+	1.36171e6i	−0.0368286	+	0.113347i
$680$	82220.7	+	59736.9i	0.00681882	+	0.00495416i
$681$		0			0
$682$	370937.	−	1.74216e6i	0.0305379	−	0.143426i
$683$	1.82149e7			1.49409			0.747044	−	0.664775i	$-0.231473\pi$
$683$	1.82149e7			1.49409			0.747044	+	0.664775i	$0.231473\pi$
$684$		0			0
$685$	205363.	−	632044.i	0.0167223	−	0.0514660i
$686$	−2.31511e6	−	7.12517e6i	−0.187828	−	0.578076i
$687$		0			0
$688$	−298543.	+	216904.i	−0.0240456	+	0.0174701i
$689$	−41616.4	−	128082.i	−0.00333977	−	0.0102787i
$690$		0			0
$691$	−9.29945e6	−	6.75644e6i	−0.740904	−	0.538298i	0.152090	−	0.988367i	$-0.451400\pi$
$691$	−9.29945e6	−	6.75644e6i	−0.740904	−	0.538298i	−0.892994	+	0.450068i	$0.851400\pi$
$692$	1.13400e7			0.900215
$693$		0			0
$694$	9.06707e6			0.714609
$695$	−667163.	−	484722.i	−0.0523926	−	0.0380654i
$696$		0			0
$697$	2.19254e6	+	6.74796e6i	0.170949	+	0.526127i
$698$	2.70972e6	−	1.96872e6i	0.210516	−	0.152949i
$699$		0			0
$700$	974491.	+	2.99917e6i	0.0751679	+	0.231343i
$701$	−3.48214e6	+	1.07169e7i	−0.267640	+	0.823711i	0.723434	+	0.690394i	$0.242563\pi$
$701$	−3.48214e6	+	1.07169e7i	−0.267640	+	0.823711i	−0.991073	+	0.133317i	$0.957437\pi$
$702$		0			0
$703$	−3.48282e6			−0.265793
$704$	−668063.	−	1.50189e6i	−0.0508026	−	0.114211i
$705$		0			0
$706$	−4.21550e6	−	3.06274e6i	−0.318301	−	0.231259i
$707$	−1.26998e6	+	3.90859e6i	−0.0955538	+	0.294085i
$708$		0			0
$709$	7.06470e6	−	5.13280e6i	0.527811	−	0.383477i	−0.291728	−	0.956501i	$-0.594230\pi$
$709$	7.06470e6	−	5.13280e6i	0.527811	−	0.383477i	0.819538	+	0.573025i	$0.194230\pi$
$710$	194610.	−	141392.i	0.0144884	−	0.0105264i
$711$		0			0
$712$	96872.0	−	298141.i	0.00716141	−	0.0220405i
$713$	−4.28817e6	−	3.11554e6i	−0.315899	−	0.229514i
$714$		0			0
$715$	−24353.2	−	14071.5i	−0.00178152	−	0.00102938i
$716$	1.21152e7			0.883180
$717$		0			0
$718$	4.93518e6	−	1.51889e7i	0.357266	−	1.09955i
$719$	−532458.	−	1.63874e6i	−0.0384117	−	0.118219i	0.930012	−	0.367529i	$-0.119796\pi$
$719$	−532458.	−	1.63874e6i	−0.0384117	−	0.118219i	−0.968424	+	0.249310i	$0.919796\pi$
$720$		0			0
$721$	−9.02153e6	+	6.55453e6i	−0.646312	+	0.469573i
$722$	−438366.	−	1.34915e6i	−0.0312964	−	0.0963203i
$723$		0			0
$724$	−8.35752e6	−	6.07210e6i	−0.592558	−	0.430519i
$725$	−1.04252e7			−0.736610
$726$		0			0
$727$	1.88729e7			1.32435			0.662174	−	0.749350i	$-0.269634\pi$
$727$	1.88729e7			1.32435			0.662174	+	0.749350i	$0.269634\pi$
$728$	−77933.2	−	56621.8i	−0.00544997	−	0.00395963i
$729$		0			0
$730$	−5649.32	−	17386.8i	−0.000392364	−	0.00120757i
$731$	628830.	−	456872.i	0.0435251	−	0.0316228i
$732$		0			0
$733$	4.72240e6	+	1.45341e7i	0.324641	+	0.999142i	0.971602	+	0.236619i	$0.0760394\pi$
$733$	4.72240e6	+	1.45341e7i	0.324641	+	0.999142i	−0.646961	+	0.762523i	$0.723961\pi$
$734$	4.46654e6	−	1.37466e7i	0.306007	−	0.941792i
$735$		0			0
$736$	−4.89148e6			−0.332848
$737$	−1.01628e7	−	5.87221e6i	−0.689202	−	0.398229i
$738$		0			0
$739$	−4.88497e6	−	3.54914e6i	−0.329041	−	0.239063i	0.410982	−	0.911643i	$-0.365186\pi$
$739$	−4.88497e6	−	3.54914e6i	−0.329041	−	0.239063i	−0.740024	+	0.672581i	$0.765186\pi$
$740$	−30141.2	+	92765.0i	−0.00202340	+	0.00622737i
$741$		0			0
$742$	1.15819e6	−	841473.i	0.0772270	−	0.0561087i
$743$	−1.76918e7	+	1.28539e7i	−1.17571	+	0.854204i	−0.991681	−	0.128716i	$-0.958914\pi$
$743$	−1.76918e7	+	1.28539e7i	−1.17571	+	0.854204i	−0.184030	+	0.982921i	$0.558914\pi$
$744$		0			0
$745$	−37633.0	+	115822.i	−0.00248415	+	0.00764543i
$746$	−5.62903e6	−	4.08973e6i	−0.370328	−	0.269059i
$747$		0			0
$748$	1.40716e6	+	3.16348e6i	0.0919581	+	0.206734i
$749$	1.92527e6			0.125397
$750$		0			0
$751$	3.30904e6	−	1.01842e7i	0.214093	−	0.658911i	−0.785124	−	0.619339i	$-0.787401\pi$
$751$	3.30904e6	−	1.01842e7i	0.214093	−	0.658911i	0.999217	−	0.0395717i	$-0.0125994\pi$
$752$	−329699.	−	1.01471e6i	−0.0212605	−	0.0654331i
$753$		0			0
$754$	257638.	−	187185.i	0.0165037	−	0.0119906i
$755$	20281.3	+	62419.4i	0.00129488	+	0.00398522i
$756$		0			0
$757$	−1.76824e6	−	1.28470e6i	−0.112151	−	0.0814822i	0.530296	−	0.847812i	$-0.322081\pi$
$757$	−1.76824e6	−	1.28470e6i	−0.112151	−	0.0814822i	−0.642447	+	0.766330i	$0.722081\pi$
$758$	−1.58896e7			−1.00448
$759$		0			0
$760$	−317108.			−0.0199147
$761$	−7.59275e6	−	5.51646e6i	−0.475267	−	0.345302i	0.324224	−	0.945980i	$-0.394897\pi$
$761$	−7.59275e6	−	5.51646e6i	−0.475267	−	0.345302i	−0.799490	+	0.600679i	$0.794897\pi$
$762$		0			0
$763$	−2.62500e6	−	8.07892e6i	−0.163237	−	0.502391i
$764$	−7.17873e6	+	5.21565e6i	−0.444953	+	0.323277i
$765$		0			0
$766$	−5.38877e6	−	1.65849e7i	−0.331831	−	1.02127i
$767$	345822.	−	1.06433e6i	0.0212258	−	0.0653262i
$768$		0			0
$769$	1.82299e7			1.11165			0.555825	−	0.831299i	$-0.312402\pi$
$769$	1.82299e7			1.11165			0.555825	+	0.831299i	$0.312402\pi$
$770$	62264.0	−	292431.i	0.00378451	−	0.0177745i
$771$		0			0
$772$	−2.66034e6	−	1.93285e6i	−0.160655	−	0.116723i
$773$	3.68451e6	−	1.13398e7i	0.221784	−	0.682582i	−0.776818	−	0.629726i	$-0.783167\pi$
$773$	3.68451e6	−	1.13398e7i	0.221784	−	0.682582i	0.998602	−	0.0528567i	$-0.0168327\pi$
$774$		0			0
$775$	2.79753e6	−	2.03252e6i	0.167309	−	0.121557i
$776$	1.17215e6	−	851615.i	0.0698760	−	0.0507679i
$777$		0			0
$778$	−908516.	+	2.79612e6i	−0.0538125	+	0.165618i
$779$	−1.79105e7	−	1.30127e7i	−1.05746	−	0.768289i
$780$		0			0
$781$	8.15046e6	−	853796.i	0.478140	−	0.0500872i
$782$	1.03031e7			0.602491
$783$		0			0
$784$	−1.01314e6	+	3.11812e6i	−0.0588678	+	0.181177i
$785$	−20584.3	−	63351.9i	−0.00119223	−	0.00366932i
$786$		0			0
$787$	4.72971e6	−	3.43633e6i	0.272206	−	0.197769i	−0.443305	−	0.896371i	$-0.646194\pi$
$787$	4.72971e6	−	3.43633e6i	0.272206	−	0.197769i	0.715511	+	0.698602i	$0.246194\pi$
$788$	−2.17072e6	−	6.68079e6i	−0.124534	−	0.383276i
$789$		0			0
$790$	398203.	+	289311.i	0.0227006	+	0.0164929i
$791$	−1.13617e7			−0.645658
$792$		0			0
$793$	−69739.3			−0.00393817
$794$	1.42052e7	+	1.03207e7i	0.799645	+	0.580976i
$795$		0			0
$796$	−3.26640e6	−	1.00530e7i	−0.182720	−	0.562356i
$797$	2.73160e6	−	1.98463e6i	0.152325	−	0.110671i	−0.509012	−	0.860759i	$-0.669989\pi$
$797$	2.73160e6	−	1.98463e6i	0.152325	−	0.110671i	0.661337	+	0.750089i	$0.269989\pi$
$798$		0			0
$799$	694456.	+	2.13732e6i	0.0384838	+	0.118441i
$800$	986110.	−	3.03493e6i	0.0544754	−	0.167658i
$801$		0			0
$802$	1.05455e7			0.578935
$803$	129701.	−	609160.i	0.00709832	−	0.0333382i
$804$		0			0
$805$	−719793.	−	522960.i	−0.0391488	−	0.0284432i
$806$	−32641.4	+	100460.i	−0.00176983	+	0.00544697i
$807$		0			0
$808$	3.36449e6	−	2.44445e6i	0.181297	−	0.131720i
$809$	−2.29499e7	+	1.66741e7i	−1.23285	+	0.895716i	−0.997100	−	0.0760982i	$-0.975754\pi$
$809$	−2.29499e7	+	1.66741e7i	−1.23285	+	0.895716i	−0.235747	+	0.971814i	$0.575754\pi$
$810$		0			0
$811$	−1.00477e7	+	3.09236e7i	−0.536430	+	1.65096i	0.204108	+	0.978948i	$0.434571\pi$
$811$	−1.00477e7	+	3.09236e7i	−0.536430	+	1.65096i	−0.740538	+	0.672014i	$0.765429\pi$
$812$	2.73873e6	+	1.98981e6i	0.145767	+	0.105906i
$813$		0			0
$814$	−2.47020e6	+	2.22263e6i	−0.130668	+	0.117572i
$815$	−1.25664e6			−0.0662702
$816$		0			0
$817$	−749448.	+	2.30656e6i	−0.0392813	+	0.120896i
$818$	−1.38371e6	−	4.25862e6i	−0.0723039	−	0.222528i
$819$		0			0
$820$	−501596.	+	364431.i	−0.0260507	+	0.0189270i
$821$	1.86294e6	+	5.73353e6i	0.0964584	+	0.296868i	0.987631	−	0.156796i	$-0.0501165\pi$
$821$	1.86294e6	+	5.73353e6i	0.0964584	+	0.296868i	−0.891173	+	0.453664i	$0.850117\pi$
$822$		0			0
$823$	−1.01406e7	−	7.36760e6i	−0.521874	−	0.379164i	0.295435	−	0.955363i	$-0.404535\pi$
$823$	−1.01406e7	−	7.36760e6i	−0.521874	−	0.379164i	−0.817309	+	0.576199i	$0.804535\pi$
$824$	1.12842e7			0.578965
$825$		0			0
$826$	1.18962e7			0.606680
$827$	3.06969e6	+	2.23026e6i	0.156074	+	0.113394i	0.663081	−	0.748547i	$-0.269248\pi$
$827$	3.06969e6	+	2.23026e6i	0.156074	+	0.113394i	−0.507007	+	0.861942i	$0.669248\pi$
$828$		0			0
$829$	−1.55707e6	−	4.79218e6i	−0.0786906	−	0.242185i	0.903971	−	0.427594i	$-0.140639\pi$
$829$	−1.55707e6	−	4.79218e6i	−0.0786906	−	0.242185i	−0.982661	+	0.185410i	$0.940639\pi$
$830$	−154825.	+	112487.i	−0.00780094	+	0.00566771i
$831$		0			0
$832$	30122.8	+	92708.3i	0.00150864	+	0.00464313i
$833$	2.13400e6	−	6.56778e6i	0.106557	−	0.327949i
$834$		0			0
$835$	1.20370e6			0.0597450
$836$	−9.35397e6	−	5.40483e6i	−0.462893	−	0.267465i
$837$		0			0
$838$	−7.19553e6	−	5.22786e6i	−0.353959	−	0.257166i
$839$	1.57913e6	−	4.86007e6i	0.0774487	−	0.238362i	−0.904835	−	0.425762i	$-0.860006\pi$
$839$	1.57913e6	−	4.86007e6i	0.0774487	−	0.238362i	0.982284	+	0.187400i	$0.0600060\pi$
$840$		0			0
$841$	7.53994e6	−	5.47809e6i	0.367602	−	0.267078i
$842$	1.80168e7	−	1.30900e7i	0.875784	−	0.636294i
$843$		0			0
$844$	3.96445e6	−	1.22013e7i	0.191570	−	0.589590i
$845$	−883260.	−	641726.i	−0.0425546	−	0.0309177i
$846$		0			0
$847$	6.82088e6	−	7.56482e6i	0.326687	−	0.362318i
$848$	−1.44867e6			−0.0691798
$849$		0			0
$850$	−2.07707e6	+	6.39258e6i	−0.0986063	+	0.303479i
$851$	3.05565e6	+	9.40433e6i	0.144637	+	0.445147i
$852$		0			0
$853$	−9.61608e6	+	6.98649e6i	−0.452507	+	0.328766i	−0.790585	−	0.612353i	$-0.790223\pi$
$853$	−9.61608e6	+	6.98649e6i	−0.452507	+	0.328766i	0.338078	+	0.941118i	$0.390223\pi$
$854$	−229087.	−	705056.i	−0.0107487	−	0.0330810i
$855$		0			0
$856$	−1.57614e6	−	1.14514e6i	−0.0735210	−	0.0534162i
$857$	933996.			0.0434403			0.0217201	−	0.999764i	$-0.493086\pi$
$857$	933996.			0.0434403			0.0217201	+	0.999764i	$0.493086\pi$
$858$		0			0
$859$	−2.01632e7			−0.932345			−0.466172	−	0.884694i	$-0.654367\pi$
$859$	−2.01632e7			−0.932345			−0.466172	+	0.884694i	$0.654367\pi$
$860$	54949.5	+	39923.1i	0.00253348	+	0.00184068i
$861$		0			0
$862$	−7.03047e6	−	2.16376e7i	−0.322267	−	0.991837i
$863$	1.28275e7	−	9.31970e6i	0.586292	−	0.425966i	−0.254695	−	0.967021i	$-0.581975\pi$
$863$	1.28275e7	−	9.31970e6i	0.586292	−	0.425966i	0.840987	+	0.541055i	$0.181975\pi$
$864$		0			0
$865$	−644987.	−	1.98507e6i	−0.0293097	−	0.0902059i
$866$	−3.10947e6	+	9.56995e6i	−0.140894	+	0.433626i
$867$		0			0
$868$	−1.12286e6			−0.0505856
$869$	6.81501e6	+	1.53210e7i	0.306138	+	0.688238i
$870$		0			0
$871$	563118.	+	409129.i	0.0251509	+	0.0182732i
$872$	−2.65630e6	+	8.17524e6i	−0.118300	+	0.364091i
$873$		0			0
$874$	−2.60081e7	+	1.88960e7i	−1.15168	+	0.836741i
$875$	940468.	−	683290.i	0.0415264	−	0.0301707i
$876$		0			0
$877$	−1.29390e7	+	3.98222e7i	−0.568070	+	1.74834i	0.0905789	+	0.995889i	$0.471128\pi$
$877$	−1.29390e7	+	3.98222e7i	−0.568070	+	1.74834i	−0.658649	+	0.752450i	$0.728872\pi$
$878$	−4.00261e6	−	2.90807e6i	−0.175230	−	0.127312i
$879$		0			0
$880$	−224909.	+	202368.i	−0.00979041	+	0.00880919i
$881$	2.32138e7			1.00764			0.503820	−	0.863808i	$-0.331927\pi$
$881$	2.32138e7			1.00764			0.503820	+	0.863808i	$0.331927\pi$
$882$		0			0
$883$	375047.	−	1.15428e6i	0.0161877	−	0.0498205i	−0.942636	−	0.333821i	$-0.891662\pi$
$883$	375047.	−	1.15428e6i	0.0161877	−	0.0498205i	0.958824	+	0.284001i	$0.0916618\pi$
$884$	−63448.5	−	195274.i	−0.00273081	−	0.00840456i
$885$		0			0
$886$	1.67449e7	−	1.21659e7i	0.716634	−	0.520665i
$887$	9.89380e6	+	3.04500e7i	0.422235	+	1.29951i	0.905617	+	0.424096i	$0.139408\pi$
$887$	9.89380e6	+	3.04500e7i	0.422235	+	1.29951i	−0.483382	+	0.875409i	$0.660592\pi$
$888$		0			0
$889$	−1.58871e7	−	1.15427e7i	−0.674204	−	0.489838i
$890$	−57699.7			−0.00244173
$891$		0			0
$892$	5.60708e6			0.235952
$893$	−5.67288e6	−	4.12159e6i	−0.238054	−	0.172956i
$894$		0			0
$895$	−689082.	−	2.12078e6i	−0.0287550	−	0.0884988i
$896$	−838320.	+	609075.i	−0.0348851	+	0.0253455i
$897$		0			0
$898$	−1.67331e6	−	5.14991e6i	−0.0692444	−	0.213112i
$899$	1.14709e6	−	3.53036e6i	0.0473365	−	0.145687i
$900$		0			0
$901$	3.05138e6			0.125223
$902$	−2.10074e7	+	2.20061e6i	−0.859716	+	0.0900590i
$903$		0			0
$904$	9.30142e6	+	6.75788e6i	0.378554	+	0.275036i
$905$	−587570.	+	1.80835e6i	−0.0238472	+	0.0733943i
$906$		0			0
$907$	−8.52957e6	+	6.19710e6i	−0.344278	+	0.250132i	−0.746465	−	0.665425i	$-0.768250\pi$
$907$	−8.52957e6	+	6.19710e6i	−0.344278	+	0.250132i	0.402187	+	0.915558i	$0.368250\pi$
$908$	−7.36921e6	+	5.35405e6i	−0.296624	+	0.215510i
$909$		0			0
$910$	−5479.04	+	16862.7i	−0.000219331	+	0.000675033i
$911$	−5.48046e6	−	3.98178e6i	−0.218787	−	0.158958i	0.472994	−	0.881066i	$-0.343173\pi$
$911$	−5.48046e6	−	3.98178e6i	−0.218787	−	0.158958i	−0.691780	+	0.722108i	$0.743173\pi$
$912$		0			0
$913$	−6.48424e6	+	679252.i	−0.257444	+	0.0269683i
$914$	2.33413e7			0.924186
$915$		0			0
$916$	−6.64959e6	+	2.04653e7i	−0.261852	+	0.805899i
$917$	4.29484e6	+	1.32182e7i	0.168665	+	0.519096i
$918$		0			0
$919$	2.40291e7	−	1.74582e7i	0.938533	−	0.681884i	−0.00953398	−	0.999955i	$-0.503035\pi$
$919$	2.40291e7	−	1.74582e7i	0.938533	−	0.681884i	0.948067	+	0.318070i	$0.103035\pi$
$920$	278215.	+	856257.i	0.0108370	+	0.0333530i
$921$		0			0
$922$	1.26285e7	+	9.17515e6i	0.489243	+	0.355456i
$923$	−485985.			−0.0187767
$924$		0			0
$925$	−6.45095e6			−0.247896
$926$	1.74368e7	+	1.26686e7i	0.668252	+	0.485513i
$927$		0			0
$928$	−1.05858e6	−	3.25796e6i	−0.0403508	−	0.124187i
$929$	2.55110e7	−	1.85348e7i	0.969813	−	0.704610i	0.0144042	−	0.999896i	$-0.495415\pi$
$929$	2.55110e7	−	1.85348e7i	0.969813	−	0.704610i	0.955409	+	0.295286i	$0.0954149\pi$
$930$		0			0
$931$	6.65853e6	+	2.04929e7i	0.251770	+	0.774869i
$932$	−2.00372e6	+	6.16680e6i	−0.0755608	+	0.232552i
$933$		0			0
$934$	1.93907e7			0.727321
$935$	473734.	−	426255.i	0.0177217	−	0.0159456i
$936$		0			0
$937$	−2.81010e7	−	2.04166e7i	−1.04562	−	0.759686i	−0.0742434	−	0.997240i	$-0.523654\pi$
$937$	−2.81010e7	−	2.04166e7i	−1.04562	−	0.759686i	−0.971374	+	0.237555i	$0.923654\pi$
$938$	−2.28646e6	+	7.03701e6i	−0.0848510	+	0.261145i
$939$		0			0
$940$	−158873.	+	115428.i	−0.00586450	+	0.00426081i
$941$	−3.95599e7	+	2.87419e7i	−1.45640	+	1.05814i	−0.472118	+	0.881536i	$0.656510\pi$
$941$	−3.95599e7	+	2.87419e7i	−1.45640	+	1.05814i	−0.984283	+	0.176601i	$0.943490\pi$
$942$		0			0
$943$	−1.94233e7	+	5.97787e7i	−0.711284	+	2.18911i
$944$	−9.73901e6	−	7.07580e6i	−0.355701	−	0.258432i
$945$		0			0
$946$	940429.	+	2.11421e6i	0.0341663	+	0.0768103i
$947$	3.45436e7			1.25168			0.625838	−	0.779953i	$-0.284757\pi$
$947$	3.45436e7			1.25168			0.625838	+	0.779953i	$0.284757\pi$
$948$		0			0
$949$	−11413.3	+	35126.6i	−0.000411383	+	0.00126611i
$950$	−6.48091e6	−	1.99462e7i	−0.232984	−	0.717052i
$951$		0			0
$952$	1.76578e6	−	1.28291e6i	0.0631458	−	0.0458781i
$953$	1.35426e7	+	4.16798e7i	0.483025	+	1.48660i	0.834821	+	0.550522i	$0.185571\pi$
$953$	1.35426e7	+	4.16798e7i	0.483025	+	1.48660i	−0.351796	+	0.936077i	$0.614429\pi$
$954$		0			0
$955$	1.32131e6	+	959988.i	0.0468809	+	0.0340610i
$956$	−2.04158e7			−0.722472
$957$		0			0
$958$	1.28157e7			0.451157
$959$	−1.15466e7	−	8.38909e6i	−0.405422	−	0.294556i
$960$		0			0
$961$	−8.46642e6	−	2.60570e7i	−0.295727	−	0.910154i
$962$	159423.	−	115828.i	0.00555409	−	0.00403529i
$963$		0			0
$964$	5.20056e6	+	1.60057e7i	0.180243	+	0.554730i
$965$	−187034.	+	575630.i	−0.00646549	+	0.0198987i
$966$		0			0
$967$	2.24734e7			0.772865			0.386432	−	0.922318i	$-0.373707\pi$
$967$	2.24734e7			0.772865			0.386432	+	0.922318i	$0.373707\pi$
$968$	−1.00835e7	+	2.13602e6i	−0.345878	+	0.0732685i
$969$		0			0
$970$	−215744.	−	156747.i	−0.00736224	−	0.00534898i
$971$	1.02058e7	−	3.14101e7i	0.347374	−	1.06911i	−0.612927	−	0.790139i	$-0.710008\pi$
$971$	1.02058e7	−	3.14101e7i	0.347374	−	1.06911i	0.960301	−	0.278967i	$-0.0899919\pi$
$972$		0			0
$973$	−1.43280e7	+	1.04099e7i	−0.485182	+	0.352505i
$974$	8.64301e6	−	6.27951e6i	0.291922	−	0.212094i
$975$		0			0
$976$	−231818.	+	713463.i	−0.00778974	+	0.0239743i
$977$	1.37751e7	+	1.00082e7i	0.461699	+	0.335444i	0.794197	−	0.607660i	$-0.207892\pi$
$977$	1.37751e7	+	1.00082e7i	0.461699	+	0.335444i	−0.332499	+	0.943104i	$0.607892\pi$
$978$		0			0
$979$	−1.70201e6	−	983440.i	−0.0567551	−	0.0327938i
$980$	603452.			0.0200714
$981$		0			0
$982$	−4.43434e6	+	1.36475e7i	−0.146741	+	0.451622i
$983$	1.22946e7	+	3.78390e7i	0.405818	+	1.24898i	0.920210	+	0.391425i	$0.128018\pi$
$983$	1.22946e7	+	3.78390e7i	0.405818	+	1.24898i	−0.514392	+	0.857555i	$0.671982\pi$
$984$		0			0
$985$	−1.04601e6	+	759971.i	−0.0343515	+	0.0249578i
$986$	2.22971e6	+	6.86235e6i	0.0730393	+	0.224792i
$987$		0			0
$988$	518299.	+	376566.i	0.0168923	+	0.0122730i
$989$	6.88572e6			0.223851
$990$		0			0
$991$	2.71153e7			0.877060			0.438530	−	0.898716i	$-0.355499\pi$
$991$	2.71153e7			0.877060			0.438530	+	0.898716i	$0.355499\pi$
$992$	919245.	+	667870.i	0.0296587	+	0.0215483i
$993$		0			0
$994$	−1.59641e6	−	4.91325e6i	−0.0512483	−	0.157726i
$995$	−1.57399e6	+	1.14357e6i	−0.0504016	+	0.0366189i
$996$		0			0
$997$	5.44410e6	+	1.67552e7i	0.173455	+	0.533841i	0.999560	−	0.0296766i	$-0.00944773\pi$
$997$	5.44410e6	+	1.67552e7i	0.173455	+	0.533841i	−0.826104	+	0.563518i	$0.809448\pi$
$998$	−7.28692e6	+	2.24268e7i	−0.231589	+	0.712758i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.6.f.c.37.2		8
3.2	odd	2		66.6.e.a.37.1	yes	8
11.3	even	5	inner	198.6.f.c.91.2		8
33.5	odd	10		726.6.a.be.1.4		4
33.14	odd	10		66.6.e.a.25.1	✓	8
33.17	even	10		726.6.a.bb.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.6.e.a.25.1	✓	8	33.14	odd	10
66.6.e.a.37.1	yes	8	3.2	odd	2
198.6.f.c.37.2		8	1.1	even	1	trivial
198.6.f.c.91.2		8	11.3	even	5	inner
726.6.a.bb.1.4		4	33.17	even	10
726.6.a.be.1.4		4	33.5	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)

\(f(q)\)	\(=\)	\(q+(3.23607 + 2.35114i) q^{2} +(4.94427 + 15.2169i) q^{4} +(2.38251 - 1.73100i) q^{5} +(-19.5441 - 60.1504i) q^{7} +(-19.7771 + 60.8676i) q^{8} +O(q^{10})\)	\(q+(3.23607 + 2.35114i) q^{2} +(4.94427 + 15.2169i) q^{4} +(2.38251 - 1.73100i) q^{5} +(-19.5441 - 60.1504i) q^{7} +(-19.7771 + 60.8676i) q^{8} +11.7798 q^{10} +(347.477 + 200.776i) q^{11} +(-19.2535 - 13.9885i) q^{13} +(78.1762 - 240.602i) q^{14} +(-207.108 + 150.473i) q^{16} +(436.239 - 316.946i) q^{17} +(-519.915 + 1600.14i) q^{19} +(38.1202 + 27.6959i) q^{20} +(652.405 + 1466.69i) q^{22} +4776.84 q^{23} +(-962.998 + 2963.80i) q^{25} +(-29.4168 - 90.5355i) q^{26} +(818.672 - 594.800i) q^{28} +(1033.77 + 3181.60i) q^{29} +(-897.700 - 652.217i) q^{31} -1024.00 q^{32} +2156.88 q^{34} +(-150.684 - 109.478i) q^{35} +(639.681 + 1968.73i) q^{37} +(-5444.63 + 3955.75i) q^{38} +(58.2424 + 179.252i) q^{40} +(-4066.14 + 12514.3i) q^{41} +1441.48 q^{43} +(-1337.17 + 6280.21i) q^{44} +(15458.2 + 11231.0i) q^{46} +(-1287.89 + 3963.71i) q^{47} +(10361.0 - 7527.74i) q^{49} +(-10084.6 + 7326.92i) q^{50} +(117.667 - 362.142i) q^{52} +(4578.12 + 3326.20i) q^{53} +(1175.41 - 123.129i) q^{55} +4047.74 q^{56} +(-4135.06 + 12726.4i) q^{58} +(14531.1 + 44722.2i) q^{59} +(2370.73 - 1722.44i) q^{61} +(-1371.56 - 4221.24i) q^{62} +(-3313.73 - 2407.57i) q^{64} -70.0857 q^{65} -29247.5 q^{67} +(6979.82 + 5071.14i) q^{68} +(-230.225 - 708.559i) q^{70} +(16520.7 - 12003.0i) q^{71} +(-479.578 - 1475.99i) q^{73} +(-2558.72 + 7874.94i) q^{74} -26919.7 q^{76} +(5285.66 - 24824.8i) q^{77} +(33803.9 + 24560.0i) q^{79} +(-232.970 + 717.007i) q^{80} +(-42581.1 + 30937.0i) q^{82} +(-13143.3 + 9549.18i) q^{83} +(490.711 - 1510.25i) q^{85} +(4664.73 + 3389.12i) q^{86} +(-19092.8 + 17179.3i) q^{88} -4898.19 q^{89} +(-465.122 + 1431.50i) q^{91} +(23618.0 + 72688.7i) q^{92} +(-13486.9 + 9798.84i) q^{94} +(1531.12 + 4712.31i) q^{95} +(-18314.8 - 13306.5i) q^{97} +51227.8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 32 q^{4} - 150 q^{5} + 474 q^{7} + 128 q^{8}+O(q^{10}) \) 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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