LMFDB - Embedded newform 33.7.b.a.23.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,7,Mod(23,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("33.23");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	33.b (of order $2$, degree $1$, 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:	$7.59178475946$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 1026 x^{18} + 441321 x^{16} + 103808124 x^{14} + 14594358456 x^{12} + 1256133373152 x^{10} + \cdots + 32\!\cdots\!64 $ x^20 + 1026x^18 + 441321x^16 + 103808124x^14 + 14594358456x^12 + 1256133373152x^10 + 64843235559312x^8 + 1864534894961472x^6 + 25120735435348224x^4 + 103653954147713024*x^2 + 32367107232497664
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{21}\cdot 3^{17}\cdot 11^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			23.18
Root			$12.6955i$ of defining polynomial
Character	$\chi$	$=$	33.23
Dual form			33.7.b.a.23.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+12.6955i q^{2} +(16.0155 + 21.7372i) q^{3} -97.1752 q^{4} +9.46491i q^{5} +(-275.964 + 203.324i) q^{6} -297.499 q^{7} -421.175i q^{8} +(-216.009 + 696.262i) q^{9} +O(q^{10})$	\(q+12.6955i q^{2} +(16.0155 + 21.7372i) q^{3} -97.1752 q^{4} +9.46491i q^{5} +(-275.964 + 203.324i) q^{6} -297.499 q^{7} -421.175i q^{8} +(-216.009 + 696.262i) q^{9} -120.162 q^{10} -401.312i q^{11} +(-1556.31 - 2112.31i) q^{12} +2805.91 q^{13} -3776.89i q^{14} +(-205.740 + 151.585i) q^{15} -872.197 q^{16} +574.570i q^{17} +(-8839.38 - 2742.33i) q^{18} -1858.10 q^{19} -919.754i q^{20} +(-4764.59 - 6466.78i) q^{21} +5094.84 q^{22} +12721.3i q^{23} +(9155.14 - 6745.32i) q^{24} +15535.4 q^{25} +35622.4i q^{26} +(-18594.3 + 6455.57i) q^{27} +28909.5 q^{28} +41378.4i q^{29} +(-1924.45 - 2611.97i) q^{30} -1792.46 q^{31} -38028.1i q^{32} +(8723.38 - 6427.20i) q^{33} -7294.44 q^{34} -2815.80i q^{35} +(20990.7 - 67659.4i) q^{36} -48308.1 q^{37} -23589.5i q^{38} +(44938.1 + 60992.6i) q^{39} +3986.38 q^{40} +48655.4i q^{41} +(82098.8 - 60488.7i) q^{42} +91123.0 q^{43} +38997.5i q^{44} +(-6590.06 - 2044.50i) q^{45} -161503. q^{46} -156024. i q^{47} +(-13968.7 - 18959.1i) q^{48} -29143.6 q^{49} +197230. i q^{50} +(-12489.5 + 9202.02i) q^{51} -272665. q^{52} +18716.4i q^{53} +(-81956.5 - 236063. i) q^{54} +3798.38 q^{55} +125299. i q^{56} +(-29758.4 - 40389.9i) q^{57} -525318. q^{58} +183868. i q^{59} +(19992.9 - 14730.3i) q^{60} +406626. q^{61} -22756.1i q^{62} +(64262.2 - 207137. i) q^{63} +426965. q^{64} +26557.7i q^{65} +(81596.4 + 110747. i) q^{66} +464104. q^{67} -55833.9i q^{68} +(-276525. + 203738. i) q^{69} +35747.9 q^{70} -581991. i q^{71} +(293248. + 90977.3i) q^{72} +119339. q^{73} -613294. i q^{74} +(248807. + 337696. i) q^{75} +180561. q^{76} +119390. i q^{77} +(-774331. + 570510. i) q^{78} +866139. q^{79} -8255.26i q^{80} +(-438122. - 300797. i) q^{81} -617703. q^{82} +234073. i q^{83} +(462999. + 628410. i) q^{84} -5438.25 q^{85} +1.15685e6i q^{86} +(-899449. + 662695. i) q^{87} -169022. q^{88} +11437.7i q^{89} +(25955.9 - 83664.0i) q^{90} -834756. q^{91} -1.23620e6i q^{92} +(-28707.1 - 38963.0i) q^{93} +1.98080e6 q^{94} -17586.8i q^{95} +(826624. - 609039. i) q^{96} -1.18124e6 q^{97} -369991. i q^{98} +(279418. + 86686.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 16 q^{3} - 772 q^{4} + 286 q^{6} + 160 q^{7} - 1072 q^{9}+O(q^{10}) $ 20 * q + 16 * q^3 - 772 * q^4 + 286 * q^6 + 160 * q^7 - 1072 * q^9	$ 20 q + 16 q^{3} - 772 q^{4} + 286 q^{6} + 160 q^{7} - 1072 q^{9} + 996 q^{10} + 6092 q^{12} + 808 q^{13} - 3032 q^{15} + 28004 q^{16} + 18686 q^{18} + 5920 q^{19} - 20888 q^{21} - 48096 q^{24} - 100612 q^{25} - 17624 q^{27} - 33296 q^{28} + 109582 q^{30} - 90896 q^{31} - 21296 q^{33} + 68928 q^{34} - 28988 q^{36} + 239656 q^{37} - 15416 q^{39} + 34632 q^{40} + 150364 q^{42} - 125840 q^{43} - 242428 q^{45} + 244380 q^{46} + 305492 q^{48} - 186204 q^{49} - 21992 q^{51} - 120368 q^{52} - 777728 q^{54} - 191664 q^{55} - 255840 q^{57} + 601176 q^{58} + 970736 q^{60} + 1108360 q^{61} + 574088 q^{63} - 2533132 q^{64} + 465850 q^{66} + 617728 q^{67} + 323804 q^{69} - 238680 q^{70} - 2031648 q^{72} - 1379960 q^{73} + 2481512 q^{75} + 4678408 q^{76} - 1556840 q^{78} + 347152 q^{79} - 1086136 q^{81} - 1760328 q^{82} - 345760 q^{84} - 4097232 q^{85} - 2983056 q^{87} - 622908 q^{88} - 4093630 q^{90} + 979616 q^{91} + 2363236 q^{93} - 217752 q^{94} + 8811824 q^{96} - 3139256 q^{97} + 212960 q^{99}+O(q^{100}) $ 20 * q + 16 * q^3 - 772 * q^4 + 286 * q^6 + 160 * q^7 - 1072 * q^9 + 996 * q^10 + 6092 * q^12 + 808 * q^13 - 3032 * q^15 + 28004 * q^16 + 18686 * q^18 + 5920 * q^19 - 20888 * q^21 - 48096 * q^24 - 100612 * q^25 - 17624 * q^27 - 33296 * q^28 + 109582 * q^30 - 90896 * q^31 - 21296 * q^33 + 68928 * q^34 - 28988 * q^36 + 239656 * q^37 - 15416 * q^39 + 34632 * q^40 + 150364 * q^42 - 125840 * q^43 - 242428 * q^45 + 244380 * q^46 + 305492 * q^48 - 186204 * q^49 - 21992 * q^51 - 120368 * q^52 - 777728 * q^54 - 191664 * q^55 - 255840 * q^57 + 601176 * q^58 + 970736 * q^60 + 1108360 * q^61 + 574088 * q^63 - 2533132 * q^64 + 465850 * q^66 + 617728 * q^67 + 323804 * q^69 - 238680 * q^70 - 2031648 * q^72 - 1379960 * q^73 + 2481512 * q^75 + 4678408 * q^76 - 1556840 * q^78 + 347152 * q^79 - 1086136 * q^81 - 1760328 * q^82 - 345760 * q^84 - 4097232 * q^85 - 2983056 * q^87 - 622908 * q^88 - 4093630 * q^90 + 979616 * q^91 + 2363236 * q^93 - 217752 * q^94 + 8811824 * q^96 - 3139256 * q^97 + 212960 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$			12.6955i			1.58693i	0.608613	+	0.793467i	$0.291726\pi$
$2$			12.6955i			1.58693i	−0.608613	+	0.793467i	$0.708274\pi$
$3$	16.0155	+	21.7372i	0.593166	+	0.805080i
$3$	16.0155	+	21.7372i	0.593166	+	0.805080i
$4$	−97.1752			−1.51836
$5$			9.46491i			0.0757193i	0.999283	+	0.0378596i	$0.0120540\pi$
$5$			9.46491i			0.0757193i	−0.999283	+	0.0378596i	$0.987946\pi$
$6$	−275.964	+	203.324i	−1.27761	+	0.941316i
$7$	−297.499			−0.867343			−0.433672	−	0.901071i	$-0.642782\pi$
$7$	−297.499			−0.867343			−0.433672	+	0.901071i	$0.642782\pi$
$8$		−	421.175i		−	0.822607i
$9$	−216.009	+	696.262i	−0.296308	+	0.955092i
$10$	−120.162			−0.120162
$11$		−	401.312i		−	0.301511i
$11$		−	401.312i		−	0.301511i
$12$	−1556.31	−	2112.31i	−0.900641	−	1.22240i
$13$	2805.91			1.27716			0.638579	−	0.769557i	$-0.279523\pi$
$13$	2805.91			1.27716			0.638579	+	0.769557i	$0.279523\pi$
$14$		−	3776.89i		−	1.37642i
$15$	−205.740	+	151.585i	−0.0609601	+	0.0449141i
$16$	−872.197			−0.212939
$17$			574.570i			0.116949i	0.998289	+	0.0584744i	$0.0186236\pi$
$17$			574.570i			0.116949i	−0.998289	+	0.0584744i	$0.981376\pi$
$18$	−8839.38	−	2742.33i	−1.51567	−	0.470221i
$19$	−1858.10			−0.270900			−0.135450	−	0.990784i	$-0.543248\pi$
$19$	−1858.10			−0.270900			−0.135450	+	0.990784i	$0.543248\pi$
$20$		−	919.754i		−	0.114969i
$21$	−4764.59	−	6466.78i	−0.514478	−	0.698281i
$22$	5094.84			0.478479
$23$			12721.3i			1.04556i	0.852468	+	0.522779i	$0.175105\pi$
$23$			12721.3i			1.04556i	−0.852468	+	0.522779i	$0.824895\pi$
$24$	9155.14	−	6745.32i	0.662264	−	0.487943i
$25$	15535.4			0.994267
$26$			35622.4i			2.02677i
$27$	−18594.3	+	6455.57i	−0.944686	+	0.327977i
$28$	28909.5			1.31694
$29$			41378.4i			1.69660i	0.529516	+	0.848300i	$0.322374\pi$
$29$			41378.4i			1.69660i	−0.529516	+	0.848300i	$0.677626\pi$
$30$	−1924.45	−	2611.97i	−0.0712758	−	0.0967397i
$31$	−1792.46			−0.0601678			−0.0300839	−	0.999547i	$-0.509577\pi$
$31$	−1792.46			−0.0601678			−0.0300839	+	0.999547i	$0.509577\pi$
$32$		−	38028.1i		−	1.16053i
$33$	8723.38	−	6427.20i	0.242741	−	0.178846i
$34$	−7294.44			−0.185590
$35$		−	2815.80i		−	0.0656746i
$36$	20990.7	−	67659.4i	0.449903	−	1.45018i
$37$	−48308.1			−0.953706			−0.476853	−	0.878983i	$-0.658223\pi$
$37$	−48308.1			−0.953706			−0.476853	+	0.878983i	$0.658223\pi$
$38$		−	23589.5i		−	0.429900i
$39$	44938.1	+	60992.6i	0.757566	+	1.02821i
$40$	3986.38			0.0622872
$41$			48655.4i			0.705959i	0.935631	+	0.352979i	$0.114831\pi$
$41$			48655.4i			0.705959i	−0.935631	+	0.352979i	$0.885169\pi$
$42$	82098.8	−	60488.7i	1.10813	−	0.816444i
$43$	91123.0			1.14610			0.573050	−	0.819520i	$-0.305760\pi$
$43$	91123.0			1.14610			0.573050	+	0.819520i	$0.305760\pi$
$44$			38997.5i			0.457803i
$45$	−6590.06	−	2044.50i	−0.0723189	−	0.0224362i
$46$	−161503.			−1.65923
$47$		−	156024.i		−	1.50279i	−0.659852	−	0.751396i	$-0.729381\pi$
$47$		−	156024.i		−	1.50279i	0.659852	−	0.751396i	$-0.270619\pi$
$48$	−13968.7	−	18959.1i	−0.126308	−	0.171433i
$49$	−29143.6			−0.247716
$50$			197230.i			1.57784i
$51$	−12489.5	+	9202.02i	−0.0941532	+	0.0693701i
$52$	−272665.			−1.93919
$53$			18716.4i			0.125717i	0.998022	+	0.0628585i	$0.0200217\pi$
$53$			18716.4i			0.125717i	−0.998022	+	0.0628585i	$0.979978\pi$
$54$	−81956.5	−	236063.i	−0.520478	−	1.49915i
$55$	3798.38			0.0228302
$56$			125299.i			0.713482i
$57$	−29758.4	−	40389.9i	−0.160689	−	0.218096i
$58$	−525318.			−2.69239
$59$			183868.i			0.895263i	0.894218	+	0.447631i	$0.147732\pi$
$59$			183868.i			0.895263i	−0.894218	+	0.447631i	$0.852268\pi$
$60$	19992.9	−	14730.3i	0.0925595	−	0.0681959i
$61$	406626.			1.79145			0.895726	−	0.444607i	$-0.146657\pi$
$61$	406626.			1.79145			0.895726	+	0.444607i	$0.146657\pi$
$62$		−	22756.1i		−	0.0954823i
$63$	64262.2	−	207137.i	0.257001	−	0.828393i
$64$	426965.			1.62874
$65$			26557.7i			0.0967054i
$66$	81596.4	+	110747.i	0.283817	+	0.385214i
$67$	464104.			1.54309			0.771544	−	0.636176i	$-0.219485\pi$
$67$	464104.			1.54309			0.771544	+	0.636176i	$0.219485\pi$
$68$		−	55833.9i		−	0.177571i
$69$	−276525.	+	203738.i	−0.841758	+	0.620190i
$70$	35747.9			0.104221
$71$		−	581991.i		−	1.62608i	−0.582209	−	0.813039i	$-0.697812\pi$
$71$		−	581991.i		−	1.62608i	0.582209	−	0.813039i	$-0.302188\pi$
$72$	293248.	+	90977.3i	0.785666	+	0.243745i
$73$	119339.			0.306772			0.153386	−	0.988166i	$-0.450982\pi$
$73$	119339.			0.306772			0.153386	+	0.988166i	$0.450982\pi$
$74$		−	613294.i		−	1.51347i
$75$	248807.	+	337696.i	0.589765	+	0.800464i
$76$	180561.			0.411324
$77$			119390.i			0.261514i
$78$	−774331.	+	570510.i	−1.63171	+	1.20221i
$79$	866139.			1.75674			0.878368	−	0.477985i	$-0.158633\pi$
$79$	866139.			1.75674			0.878368	+	0.477985i	$0.158633\pi$
$80$		−	8255.26i		−	0.0161236i
$81$	−438122.	−	300797.i	−0.824403	−	0.566003i
$82$	−617703.			−1.12031
$83$			234073.i			0.409370i	0.978828	+	0.204685i	$0.0656170\pi$
$83$			234073.i			0.409370i	−0.978828	+	0.204685i	$0.934383\pi$
$84$	462999.	+	628410.i	0.781165	+	1.06024i
$85$	−5438.25			−0.00885529
$86$			1.15685e6i			1.81879i
$87$	−899449.	+	662695.i	−1.36590	+	1.00637i
$88$	−169022.			−0.248025
$89$			11437.7i			0.0162243i	0.999967	+	0.00811217i	$0.00258221\pi$
$89$			11437.7i			0.0162243i	−0.999967	+	0.00811217i	$0.997418\pi$
$90$	25955.9	−	83664.0i	0.0356048	−	0.114765i
$91$	−834756.			−1.10773
$92$		−	1.23620e6i		−	1.58754i
$93$	−28707.1	−	38963.0i	−0.0356895	−	0.0484399i
$94$	1.98080e6			2.38483
$95$		−	17586.8i		−	0.0205123i
$96$	826624.	−	609039.i	0.934317	−	0.688385i
$97$	−1.18124e6			−1.29427			−0.647134	−	0.762376i	$-0.724033\pi$
$97$	−1.18124e6			−1.29427			−0.647134	+	0.762376i	$0.724033\pi$
$98$		−	369991.i		−	0.393109i
$99$	279418.	+	86686.7i	0.287971	+	0.0893402i
$100$	−1.50966e6			−1.50966
$101$		−	76937.5i		−	0.0746748i	−0.999303	−	0.0373374i	$-0.988112\pi$
$101$		−	76937.5i		−	0.0746748i	0.999303	−	0.0373374i	$-0.0118876\pi$
$102$	−116824.	−	158560.i	−0.110086	−	0.149415i
$103$	−969974.			−0.887664			−0.443832	−	0.896110i	$-0.646381\pi$
$103$	−969974.			−0.887664			−0.443832	+	0.896110i	$0.646381\pi$
$104$		−	1.18178e6i		−	1.05060i
$105$	61207.5	−	45096.4i	0.0528733	−	0.0389559i
$106$	−237613.			−0.199505
$107$		−	776764.i		−	0.634071i	−0.948414	−	0.317035i	$-0.897313\pi$
$107$		−	776764.i		−	0.634071i	0.948414	−	0.317035i	$-0.102687\pi$
$108$	1.80690e6	−	627321.i	1.43438	−	0.497988i
$109$	1.12396e6			0.867902			0.433951	−	0.900936i	$-0.357119\pi$
$109$	1.12396e6			0.867902			0.433951	+	0.900936i	$0.357119\pi$
$110$			48222.2i			0.0362301i
$111$	−773677.	−	1.05008e6i	−0.565706	−	0.767810i
$112$	259477.			0.184691
$113$			750119.i			0.519870i	0.965626	+	0.259935i	$0.0837011\pi$
$113$			750119.i			0.519870i	−0.965626	+	0.259935i	$0.916299\pi$
$114$	512769.	−	377797.i	0.346104	−	0.255002i
$115$	−120406.			−0.0791689
$116$		−	4.02095e6i		−	2.57605i
$117$	−606101.	+	1.95365e6i	−0.378432	+	1.21980i
$118$	−2.33429e6			−1.42072
$119$		−	170934.i		−	0.101435i
$120$	63843.8	+	86652.6i	0.0369467	+	0.0501462i
$121$	−161051.			−0.0909091
$122$			5.16231e6i			2.84292i
$123$	−1.05763e6	+	779239.i	−0.568353	+	0.418751i
$124$	174182.			0.0913565
$125$			294931.i			0.151004i
$126$	2.62970e6	+	815840.i	1.31461	+	0.407843i
$127$	−372084.			−0.181648			−0.0908239	−	0.995867i	$-0.528950\pi$
$127$	−372084.			−0.181648			−0.0908239	+	0.995867i	$0.528950\pi$
$128$			2.98672e6i			1.42418i
$129$	1.45938e6	+	1.98076e6i	0.679828	+	0.922703i
$130$	−337163.			−0.153465
$131$		−	3.85072e6i		−	1.71288i	−0.516244	−	0.856441i	$-0.672670\pi$
$131$		−	3.85072e6i		−	1.71288i	0.516244	−	0.856441i	$-0.327330\pi$
$132$	−847696.	+	624564.i	−0.368568	+	0.271553i
$133$	552783.			0.234963
$134$			5.89202e6i			2.44878i
$135$	−61101.4	−	175993.i	−0.0248342	−	0.0715309i
$136$	241994.			0.0962030
$137$		−	2.37061e6i		−	0.921933i	−0.887418	−	0.460966i	$-0.847503\pi$
$137$		−	2.37061e6i		−	0.921933i	0.887418	−	0.460966i	$-0.152497\pi$
$138$	−2.58655e6	−	3.51062e6i	−0.984201	−	1.33582i
$139$	−3.34452e6			−1.24535			−0.622673	−	0.782482i	$-0.713953\pi$
$139$	−3.34452e6			−1.24535			−0.622673	+	0.782482i	$0.713953\pi$
$140$			273626.i			0.0997178i
$141$	3.39153e6	−	2.49881e6i	1.20987	−	0.891405i
$142$	7.38866e6			2.58048
$143$		−	1.12605e6i		−	0.385077i
$144$	188402.	−	607278.i	0.0630954	−	0.203376i
$145$	−391643.			−0.128465
$146$			1.51507e6i			0.486827i
$147$	−466748.	−	633498.i	−0.146937	−	0.199431i
$148$	4.69435e6			1.44807
$149$		−	438764.i		−	0.132639i	−0.997798	−	0.0663197i	$-0.978874\pi$
$149$		−	438764.i		−	0.132639i	0.997798	−	0.0663197i	$-0.0211257\pi$
$150$	−4.28721e6	+	3.15873e6i	−1.27028	+	0.935919i
$151$	3.78113e6			1.09822			0.549112	−	0.835749i	$-0.314966\pi$
$151$	3.78113e6			1.09822			0.549112	+	0.835749i	$0.314966\pi$
$152$			782586.i			0.222844i
$153$	−400051.	−	124112.i	−0.111697	−	0.0346529i
$154$	−1.51571e6			−0.415005
$155$		−	16965.5i		−	0.00455586i
$156$	−4.36687e6	−	5.92697e6i	−1.15026	−	1.56120i
$157$	7.46553e6			1.92913			0.964565	−	0.263846i	$-0.0849910\pi$
$157$	7.46553e6			1.92913			0.964565	+	0.263846i	$0.0849910\pi$
$158$			1.09961e7i			2.78783i
$159$	−406840.	+	299752.i	−0.101212	+	0.0745710i
$160$	359933.			0.0878742
$161$		−	3.78457e6i		−	0.906858i
$162$	3.81876e6	−	5.56216e6i	0.898210	−	1.30827i
$163$	−7.47919e6			−1.72700			−0.863499	−	0.504351i	$-0.831732\pi$
$163$	−7.47919e6			−1.72700			−0.863499	+	0.504351i	$0.831732\pi$
$164$		−	4.72809e6i		−	1.07190i
$165$	60832.9	+	82566.0i	0.0135421	+	0.0183802i
$166$	−2.97166e6			−0.649644
$167$		−	3.47084e6i		−	0.745220i	−0.927988	−	0.372610i	$-0.878463\pi$
$167$		−	3.47084e6i		−	0.745220i	0.927988	−	0.372610i	$-0.121537\pi$
$168$	−2.72364e6	+	2.00672e6i	−0.574410	+	0.423214i
$169$	3.04635e6			0.631131
$170$		−	69041.2i		−	0.0140528i
$171$	401366.	−	1.29373e6i	0.0802698	−	0.258734i
$172$	−8.85489e6			−1.74020
$173$			5.58560e6i			1.07878i	0.842057	+	0.539388i	$0.181344\pi$
$173$			5.58560e6i			1.07878i	−0.842057	+	0.539388i	$0.818656\pi$
$174$	−8.41323e6	−	1.14189e7i	−1.59704	−	2.16759i
$175$	−4.62177e6			−0.862370
$176$			350023.i			0.0642034i
$177$	−3.99677e6	+	2.94474e6i	−0.720758	+	0.531039i
$178$	−145207.			−0.0257470
$179$			7.43908e6i			1.29706i	0.761189	+	0.648530i	$0.224616\pi$
$179$			7.43908e6i			1.29706i	−0.761189	+	0.648530i	$0.775384\pi$
$180$	640390.	+	198675.i	0.109806	+	0.0340663i
$181$	−2.15664e6			−0.363699			−0.181849	−	0.983326i	$-0.558208\pi$
$181$	−2.15664e6			−0.363699			−0.181849	+	0.983326i	$0.558208\pi$
$182$		−	1.05976e7i		−	1.75790i
$183$	6.51230e6	+	8.83889e6i	1.06263	+	1.44226i
$184$	5.35789e6			0.860083
$185$		−	457232.i		−	0.0722139i
$186$	494653.	−	364450.i	0.0768709	−	0.0566369i
$187$	230582.			0.0352614
$188$			1.51617e7i			2.28178i
$189$	5.53176e6	−	1.92052e6i	0.819367	−	0.284468i
$190$	223273.			0.0325518
$191$			1.06562e6i			0.152933i	0.997072	+	0.0764664i	$0.0243638\pi$
$191$			1.06562e6i			0.152933i	−0.997072	+	0.0764664i	$0.975636\pi$
$192$	6.83805e6	+	9.28100e6i	0.966114	+	1.31127i
$193$	−509478.			−0.0708686			−0.0354343	−	0.999372i	$-0.511281\pi$
$193$	−509478.			−0.0708686			−0.0354343	+	0.999372i	$0.511281\pi$
$194$		−	1.49965e7i		−	2.05392i
$195$	−577290.	+	425335.i	−0.0778556	+	0.0573624i
$196$	2.83203e6			0.376123
$197$			3.68318e6i			0.481753i	0.970556	+	0.240876i	$0.0774349\pi$
$197$			3.68318e6i			0.481753i	−0.970556	+	0.240876i	$0.922565\pi$
$198$	−1.10053e6	+	3.54735e6i	−0.141777	+	0.456992i
$199$	−1.28675e7			−1.63281			−0.816406	−	0.577478i	$-0.804037\pi$
$199$	−1.28675e7			−1.63281			−0.816406	+	0.577478i	$0.804037\pi$
$200$		−	6.54312e6i		−	0.817891i
$201$	7.43285e6	+	1.00883e7i	0.915308	+	1.24231i
$202$	976759.			0.118504
$203$		−	1.23100e7i		−	1.47153i
$204$	1.21367e6	−	894208.i	0.142959	−	0.105329i
$205$	−460519.			−0.0534547
$206$		−	1.23143e7i		−	1.40866i
$207$	−8.85737e6	−	2.74791e6i	−0.998605	−	0.309807i
$208$	−2.44731e6			−0.271956
$209$			745678.i			0.0816794i
$210$	572520.	+	777058.i	0.0618205	+	0.0839065i
$211$	3.83398e6			0.408134			0.204067	−	0.978957i	$-0.434584\pi$
$211$	3.83398e6			0.408134			0.204067	+	0.978957i	$0.434584\pi$
$212$		−	1.81877e6i		−	0.190884i
$213$	1.26508e7	−	9.32087e6i	1.30912	−	0.964534i
$214$	9.86139e6			1.00623
$215$			862471.i			0.0867819i
$216$	2.71892e6	+	7.83143e6i	0.269796	+	0.777105i
$217$	533254.			0.0521861
$218$			1.42692e7i			1.37730i
$219$	1.91128e6	+	2.59410e6i	0.181967	+	0.246976i
$220$	−369108.			−0.0346645
$221$			1.61219e6i			0.149362i
$222$	1.33313e7	−	9.82220e6i	1.21846	−	0.897739i
$223$	−2.24360e6			−0.202316			−0.101158	−	0.994870i	$-0.532255\pi$
$223$	−2.24360e6			−0.202316			−0.101158	+	0.994870i	$0.532255\pi$
$224$			1.13133e7i			1.00657i
$225$	−3.35578e6	+	1.08167e7i	−0.294609	+	0.949617i
$226$	−9.52312e6			−0.825000
$227$		−	1.25275e7i		−	1.07099i	−0.844537	−	0.535497i	$-0.820124\pi$
$227$		−	1.25275e7i		−	1.07099i	0.844537	−	0.535497i	$-0.179876\pi$
$228$	2.89178e6	+	3.92489e6i	0.243984	+	0.331149i
$229$	1.32159e7			1.10050			0.550251	−	0.835000i	$-0.314532\pi$
$229$	1.32159e7			1.10050			0.550251	+	0.835000i	$0.314532\pi$
$230$		−	1.52861e6i		−	0.125636i
$231$	−2.59519e6	+	1.91208e6i	−0.210540	+	0.155121i
$232$	1.74275e7			1.39563
$233$			2.31985e7i			1.83397i	0.398918	+	0.916987i	$0.369386\pi$
$233$			2.31985e7i			1.83397i	−0.398918	+	0.916987i	$0.630614\pi$
$234$	−2.48026e7	−	7.69475e6i	−1.93575	−	0.600547i
$235$	1.47676e6			0.113790
$236$		−	1.78674e7i		−	1.35933i
$237$	1.38716e7	+	1.88274e7i	1.04204	+	1.41431i
$238$	2.17009e6			0.160970
$239$			7.60325e6i			0.556936i	0.960445	+	0.278468i	$0.0898267\pi$
$239$			7.60325e6i			0.556936i	−0.960445	+	0.278468i	$0.910173\pi$
$240$	179446.	−	132212.i	0.0129808	−	0.00956395i
$241$	−2.79470e6			−0.199657			−0.0998285	−	0.995005i	$-0.531829\pi$
$241$	−2.79470e6			−0.199657			−0.0998285	+	0.995005i	$0.531829\pi$
$242$		−	2.04462e6i		−	0.144267i
$243$	−478252.	−	1.43409e7i	−0.0333302	−	0.999444i
$244$	−3.95139e7			−2.72007
$245$		−	275841.i		−	0.0187569i
$246$	−9.89282e6	−	1.34271e7i	−0.664530	−	0.901939i
$247$	−5.21368e6			−0.345982
$248$			754938.i			0.0494944i
$249$	−5.08807e6	+	3.74878e6i	−0.329576	+	0.242824i
$250$	−3.74428e6			−0.239634
$251$			4.95529e6i			0.313363i	0.987649	+	0.156682i	$0.0500796\pi$
$251$			4.95529e6i			0.313363i	−0.987649	+	0.156682i	$0.949920\pi$
$252$	−6.24469e6	+	2.01286e7i	−0.390220	+	1.25780i
$253$	5.10521e6			0.315248
$254$		−	4.72379e6i		−	0.288263i
$255$	−87096.3	−	118212.i	−0.00525266	−	0.00712922i
$256$	−1.05921e7			−0.631339
$257$		−	1.26574e7i		−	0.745667i	−0.927898	−	0.372833i	$-0.878386\pi$
$257$		−	1.26574e7i		−	0.745667i	0.927898	−	0.372833i	$-0.121614\pi$
$258$	−2.51466e7	+	1.85275e7i	−1.46427	+	1.07884i
$259$	1.43716e7			0.827190
$260$		−	2.58075e6i		−	0.146834i
$261$	−2.88102e7	−	8.93808e6i	−1.62041	−	0.502716i
$262$	4.88867e7			2.71823
$263$		−	3.20086e7i		−	1.75954i	−0.475400	−	0.879770i	$-0.657697\pi$
$263$		−	3.20086e7i		−	1.75954i	0.475400	−	0.879770i	$-0.342303\pi$
$264$	−2.70697e6	−	3.67407e6i	−0.147120	−	0.199680i
$265$	−177149.			−0.00951919
$266$			7.01784e6i			0.372871i
$267$	−248622.	+	183180.i	−0.0130619	+	0.00962373i
$268$	−4.50994e7			−2.34297
$269$		−	2.46124e7i		−	1.26444i	−0.774790	−	0.632219i	$-0.782144\pi$
$269$		−	2.46124e7i		−	1.26444i	0.774790	−	0.632219i	$-0.217856\pi$
$270$	2.23431e6	−	775711.i	0.113515	−	0.0394102i
$271$	9.30356e6			0.467457			0.233728	−	0.972302i	$-0.424907\pi$
$271$	9.30356e6			0.467457			0.233728	+	0.972302i	$0.424907\pi$
$272$		−	501138.i		−	0.0249029i
$273$	−1.33690e7	−	1.81452e7i	−0.657070	−	0.891814i
$274$	3.00961e7			1.46305
$275$		−	6.23454e6i		−	0.299783i
$276$	2.68714e7	−	1.97983e7i	1.27809	−	0.941672i
$277$	7.19972e6			0.338748			0.169374	−	0.985552i	$-0.445825\pi$
$277$	7.19972e6			0.338748			0.169374	+	0.985552i	$0.445825\pi$
$278$		−	4.24603e7i		−	1.97628i
$279$	387186.	−	1.24802e6i	0.0178282	−	0.0574658i
$280$	−1.18594e6			−0.0540244
$281$			383643.i			0.0172905i	0.999963	+	0.00864526i	$0.00275190\pi$
$281$			383643.i			0.0172905i	−0.999963	+	0.00864526i	$0.997248\pi$
$282$	3.17235e7	+	4.30570e7i	1.41460	+	1.91998i
$283$	−2.27753e6			−0.100486			−0.0502430	−	0.998737i	$-0.516000\pi$
$283$	−2.27753e6			−0.100486			−0.0502430	+	0.998737i	$0.516000\pi$
$284$			5.65551e7i			2.46897i
$285$	382287.	−	281661.i	0.0165141	−	0.0121672i
$286$	1.42957e7			0.611093
$287$		−	1.44749e7i		−	0.612308i
$288$	2.64776e7	+	8.21440e6i	1.10841	+	0.343873i
$289$	2.38074e7			0.986323
$290$		−	4.97209e6i		−	0.203866i
$291$	−1.89182e7	−	2.56769e7i	−0.767716	−	1.04199i
$292$	−1.15968e7			−0.465791
$293$			3.42995e7i			1.36359i	0.731542	+	0.681796i	$0.238801\pi$
$293$			3.42995e7i			1.36359i	−0.731542	+	0.681796i	$0.761199\pi$
$294$	8.04256e6	−	5.92559e6i	0.316484	−	0.233179i
$295$	−1.74030e6			−0.0677886
$296$			2.03461e7i			0.784525i
$297$	2.59069e6	+	7.46209e6i	0.0988887	+	0.284833i
$298$	5.57032e6			0.210490
$299$			3.56949e7i			1.33534i
$300$	−2.41779e7	−	3.28157e7i	−0.895477	−	1.21539i
$301$	−2.71090e7			−0.994062
$302$			4.80033e7i			1.74281i
$303$	1.67240e6	−	1.23219e6i	0.0601192	−	0.0442946i
$304$	1.62063e6			0.0576851
$305$			3.84867e6i			0.135647i
$306$	1.57566e6	−	5.07884e6i	0.0549919	−	0.177256i
$307$	−3.73046e7			−1.28928			−0.644640	−	0.764487i	$-0.722993\pi$
$307$	−3.73046e7			−1.28928			−0.644640	+	0.764487i	$0.722993\pi$
$308$		−	1.16017e7i		−	0.397073i
$309$	−1.55346e7	−	2.10845e7i	−0.526532	−	0.714640i
$310$	215385.			0.00722985
$311$			2.73874e6i			0.0910479i	0.998963	+	0.0455239i	$0.0144957\pi$
$311$			2.73874e6i			0.0910479i	−0.998963	+	0.0455239i	$0.985504\pi$
$312$	2.56886e7	−	1.89268e7i	0.845816	−	0.623179i
$313$	−2.70497e7			−0.882124			−0.441062	−	0.897477i	$-0.645398\pi$
$313$	−2.70497e7			−0.882124			−0.441062	+	0.897477i	$0.645398\pi$
$314$			9.47784e7i			3.06140i
$315$	1.96053e6	+	608236.i	0.0627253	+	0.0194599i
$316$	−8.41672e7			−2.66736
$317$			1.20313e7i			0.377690i	0.982007	+	0.188845i	$0.0604744\pi$
$317$			1.20313e7i			0.377690i	−0.982007	+	0.188845i	$0.939526\pi$
$318$	−3.80549e6	−	5.16503e6i	−0.118339	−	0.160617i
$319$	1.66056e7			0.511544
$320$			4.04118e6i			0.123327i
$321$	1.68846e7	−	1.24403e7i	0.510478	−	0.376109i
$322$	4.80469e7			1.43912
$323$		−	1.06761e6i		−	0.0316814i
$324$	4.25745e7	+	2.92300e7i	1.25174	+	0.859398i
$325$	4.35910e7			1.26983
$326$		−	9.49519e7i		−	2.74063i
$327$	1.80007e7	+	2.44317e7i	0.514810	+	0.698731i
$328$	2.04924e7			0.580726
$329$			4.64170e7i			1.30344i
$330$	−1.04821e6	+	772302.i	−0.0291681	+	0.0214905i
$331$	−1.89430e7			−0.522354			−0.261177	−	0.965291i	$-0.584111\pi$
$331$	−1.89430e7			−0.522354			−0.261177	+	0.965291i	$0.584111\pi$
$332$		−	2.27460e7i		−	0.621572i
$333$	1.04350e7	−	3.36351e7i	0.282591	−	0.910877i
$334$	4.40639e7			1.18262
$335$			4.39270e6i			0.116842i
$336$	4.15565e6	+	5.64030e6i	0.109552	+	0.148691i
$337$	−4.28451e7			−1.11947			−0.559733	−	0.828673i	$-0.689096\pi$
$337$	−4.28451e7			−1.11947			−0.559733	+	0.828673i	$0.689096\pi$
$338$			3.86748e7i			1.00156i
$339$	−1.63055e7	+	1.20135e7i	−0.418537	+	0.308369i
$340$	528463.			0.0134455
$341$			719334.i			0.0181413i
$342$	1.64245e7	+	5.09553e6i	0.410595	+	0.127383i
$343$	4.36706e7			1.08220
$344$		−	3.83787e7i		−	0.942790i
$345$	−1.92836e6	−	2.61729e6i	−0.0469603	−	0.0637373i
$346$	−7.09118e7			−1.71195
$347$		−	1.05723e7i		−	0.253036i	−0.991964	−	0.126518i	$-0.959620\pi$
$347$		−	1.05723e7i		−	0.253036i	0.991964	−	0.126518i	$-0.0403802\pi$
$348$	8.74041e7	−	6.43975e7i	2.07393	−	1.52803i
$349$	3.43535e7			0.808155			0.404077	−	0.914725i	$-0.367593\pi$
$349$	3.43535e7			0.808155			0.404077	+	0.914725i	$0.367593\pi$
$350$		−	5.86755e7i		−	1.36853i
$351$	−5.21739e7	+	1.81138e7i	−1.20651	+	0.418878i
$352$	−1.52611e7			−0.349912
$353$		−	5.00716e7i		−	1.13833i	−0.822224	−	0.569164i	$-0.807267\pi$
$353$		−	5.00716e7i		−	1.13833i	0.822224	−	0.569164i	$-0.192733\pi$
$354$	−3.73848e7	−	5.07409e7i	−0.842725	−	1.14380i
$355$	5.50849e6			0.123125
$356$		−	1.11146e6i		−	0.0246344i
$357$	3.71562e6	−	2.73759e6i	0.0816631	−	0.0601677i
$358$	−9.44426e7			−2.05835
$359$		−	4.45700e7i		−	0.963294i	−0.876365	−	0.481647i	$-0.840039\pi$
$359$		−	4.45700e7i		−	0.963294i	0.876365	−	0.481647i	$-0.159961\pi$
$360$	−861092.	+	2.77557e6i	−0.0184562	+	0.0594900i
$361$	−4.35933e7			−0.926613
$362$		−	2.73796e7i		−	0.577166i
$363$	−2.57931e6	−	3.50079e6i	−0.0539242	−	0.0731891i
$364$	8.11175e7			1.68194
$365$			1.12954e6i			0.0232285i
$366$	−1.12214e8	+	8.26768e7i	−2.28878	+	1.68632i
$367$	6.68109e6			0.135160			0.0675801	−	0.997714i	$-0.478472\pi$
$367$	6.68109e6			0.135160			0.0675801	+	0.997714i	$0.478472\pi$
$368$		−	1.10955e7i		−	0.222640i
$369$	−3.38769e7	−	1.05100e7i	−0.674256	−	0.209181i
$370$	5.80477e6			0.114599
$371$		−	5.56809e6i		−	0.109040i
$372$	2.78962e6	+	3.78623e6i	0.0541896	+	0.0735493i
$373$	2.06336e6			0.0397601			0.0198801	−	0.999802i	$-0.493672\pi$
$373$	2.06336e6			0.0397601			0.0198801	+	0.999802i	$0.493672\pi$
$374$			2.92734e6i			0.0559576i
$375$	−6.41095e6	+	4.72346e6i	−0.121571	+	0.0895707i
$376$	−6.57135e7			−1.23621
$377$			1.16104e8i			2.16683i
$378$	2.43820e7	+	7.02284e7i	0.451433	+	1.30028i
$379$	2.29200e7			0.421015			0.210507	−	0.977592i	$-0.432488\pi$
$379$	2.29200e7			0.421015			0.210507	+	0.977592i	$0.432488\pi$
$380$			1.70900e6i			0.0311452i
$381$	−5.95911e6	−	8.08806e6i	−0.107747	−	0.146241i
$382$	−1.35285e7			−0.242695
$383$			1.98522e7i			0.353356i	0.984269	+	0.176678i	$0.0565351\pi$
$383$			1.98522e7i			0.353356i	−0.984269	+	0.176678i	$0.943465\pi$
$384$	−6.49229e7	+	4.78338e7i	−1.14658	+	0.844775i
$385$	−1.13001e6			−0.0198016
$386$		−	6.46807e6i		−	0.112464i
$387$	−1.96833e7	+	6.34455e7i	−0.339599	+	1.09463i
$388$	1.14788e8			1.96517
$389$			1.50591e7i			0.255829i	0.991785	+	0.127915i	$0.0408284\pi$
$389$			1.50591e7i			0.255829i	−0.991785	+	0.127915i	$0.959172\pi$
$390$	−5.39983e6	−	7.32897e6i	−0.0910304	−	0.123552i
$391$	−7.30928e6			−0.122277
$392$			1.22745e7i			0.203773i
$393$	8.37037e7	−	6.16711e7i	1.37901	−	1.01602i
$394$	−4.67597e7			−0.764511
$395$			8.19793e6i			0.133019i
$396$	−2.71525e7	−	8.42380e6i	−0.437245	−	0.135651i
$397$	7.19453e7			1.14982			0.574911	−	0.818216i	$-0.305037\pi$
$397$	7.19453e7			1.14982			0.574911	+	0.818216i	$0.305037\pi$
$398$		−	1.63360e8i		−	2.59117i
$399$	8.85309e6	+	1.20159e7i	0.139372	+	0.189164i
$400$	−1.35499e7			−0.211718
$401$			8.41217e7i			1.30459i	0.757964	+	0.652296i	$0.226194\pi$
$401$			8.41217e7i			1.30459i	−0.757964	+	0.652296i	$0.773806\pi$
$402$	−1.28076e8	+	9.43636e7i	−1.97146	+	1.45253i
$403$	−5.02948e6			−0.0768437
$404$			7.47642e6i			0.113383i
$405$	2.84702e6	−	4.14678e6i	0.0428573	−	0.0624232i
$406$	1.56281e8			2.33523
$407$			1.93866e7i			0.287553i
$408$	3.87566e6	+	5.26027e6i	0.0570643	+	0.0774511i
$409$	−2.60990e6			−0.0381464			−0.0190732	−	0.999818i	$-0.506072\pi$
$409$	−2.60990e6			−0.0381464			−0.0190732	+	0.999818i	$0.506072\pi$
$410$		−	5.84651e6i		−	0.0848291i
$411$	5.15304e7	−	3.79665e7i	0.742230	−	0.546859i
$412$	9.42574e7			1.34779
$413$		−	5.47005e7i		−	0.776500i
$414$	3.48860e7	−	1.12449e8i	0.491644	−	1.58472i
$415$	−2.21548e6			−0.0309972
$416$		−	1.06704e8i		−	1.48217i
$417$	−5.35642e7	−	7.27004e7i	−0.738697	−	1.00260i
$418$	−9.46674e6			−0.129620
$419$		−	2.57612e7i		−	0.350206i	−0.984550	−	0.175103i	$-0.943974\pi$
$419$		−	2.57612e7i		−	0.350206i	0.984550	−	0.175103i	$-0.0560258\pi$
$420$	−5.94785e6	+	4.38225e6i	−0.0802808	+	0.0591492i
$421$	−7.65386e6			−0.102573			−0.0512866	−	0.998684i	$-0.516332\pi$
$421$	−7.65386e6			−0.102573			−0.0512866	+	0.998684i	$0.516332\pi$
$422$			4.86742e7i			0.647681i
$423$	1.08634e8	+	3.37026e7i	1.43530	+	0.445289i
$424$	7.88286e6			0.103416
$425$			8.92618e6i			0.116278i
$426$	1.18333e8	+	1.60608e8i	1.53065	+	2.07749i
$427$	−1.20971e8			−1.55380
$428$			7.54822e7i			0.962749i
$429$	2.44770e7	−	1.80342e7i	0.310018	−	0.228415i
$430$	−1.09495e7			−0.137717
$431$			5.12277e7i			0.639842i	0.947444	+	0.319921i	$0.103656\pi$
$431$			5.12277e7i			0.639842i	−0.947444	+	0.319921i	$0.896344\pi$
$432$	1.62178e7	−	5.63052e6i	0.201160	−	0.0698389i
$433$	9.50929e7			1.17134			0.585672	−	0.810548i	$-0.300831\pi$
$433$	9.50929e7			1.17134			0.585672	+	0.810548i	$0.300831\pi$
$434$			6.76991e6i			0.0828159i
$435$	−6.27235e6	−	8.51320e6i	−0.0762013	−	0.103425i
$436$	−1.09221e8			−1.31779
$437$		−	2.36375e7i		−	0.283242i
$438$	−3.29334e7	+	2.42646e7i	−0.391935	+	0.288769i
$439$	8.28520e7			0.979286			0.489643	−	0.871923i	$-0.337127\pi$
$439$	8.28520e7			0.979286			0.489643	+	0.871923i	$0.337127\pi$
$440$		−	1.59978e6i		−	0.0187803i
$441$	6.29526e6	−	2.02916e7i	0.0734003	−	0.236592i
$442$	−2.04676e7			−0.237028
$443$		−	3.87774e7i		−	0.446033i	−0.974815	−	0.223017i	$-0.928410\pi$
$443$		−	3.87774e7i		−	0.446033i	0.974815	−	0.223017i	$-0.0715904\pi$
$444$	7.51822e7	+	1.02042e8i	0.858947	+	1.16581i
$445$	−108256.			−0.00122850
$446$		−	2.84835e7i		−	0.321062i
$447$	9.53749e6	−	7.02702e6i	0.106785	−	0.0786772i
$448$	−1.27021e8			−1.41268
$449$		−	1.35174e8i		−	1.49333i	−0.665200	−	0.746665i	$-0.731654\pi$
$449$		−	1.35174e8i		−	1.49333i	0.665200	−	0.746665i	$-0.268346\pi$
$450$	−1.37324e8	−	4.26033e7i	−1.50698	−	0.467525i
$451$	1.95260e7			0.212855
$452$		−	7.28929e7i		−	0.789351i
$453$	6.05567e7	+	8.21911e7i	0.651429	+	0.884158i
$454$	1.59043e8			1.69960
$455$		−	7.90089e6i		−	0.0838768i
$456$	−1.70112e7	+	1.25335e7i	−0.179407	+	0.132184i
$457$	−5.43242e7			−0.569174			−0.284587	−	0.958650i	$-0.591856\pi$
$457$	−5.43242e7			−0.569174			−0.284587	+	0.958650i	$0.591856\pi$
$458$			1.67782e8i			1.74642i
$459$	−3.70917e6	−	1.06837e7i	−0.0383565	−	0.110480i
$460$	1.17005e7			0.120207
$461$			4.41749e7i			0.450893i	0.974256	+	0.225446i	$0.0723840\pi$
$461$			4.41749e7i			0.450893i	−0.974256	+	0.225446i	$0.927616\pi$
$462$	−2.42748e7	−	3.29472e7i	−0.246167	−	0.334113i
$463$	−6.41757e7			−0.646588			−0.323294	−	0.946299i	$-0.604790\pi$
$463$	−6.41757e7			−0.646588			−0.323294	+	0.946299i	$0.604790\pi$
$464$		−	3.60901e7i		−	0.361272i
$465$	368781.	−	271710.i	0.00366783	−	0.00270238i
$466$	−2.94517e8			−2.91040
$467$			8.24472e7i			0.809516i	0.914424	+	0.404758i	$0.132644\pi$
$467$			8.24472e7i			0.809516i	−0.914424	+	0.404758i	$0.867356\pi$
$468$	5.88980e7	−	1.89847e8i	0.574597	−	1.85210i
$469$	−1.38070e8			−1.33839
$470$			1.87481e7i			0.180578i
$471$	1.19564e8	+	1.62279e8i	1.14429	+	1.55310i
$472$	7.74406e7			0.736449
$473$		−	3.65687e7i		−	0.345562i
$474$	−2.39023e8	+	1.76107e8i	−2.24442	+	1.65364i
$475$	−2.88664e7			−0.269347
$476$			1.66105e7i			0.154015i
$477$	−1.30315e7	−	4.04289e6i	−0.120071	−	0.0372509i
$478$	−9.65269e7			−0.883822
$479$		−	1.28589e8i		−	1.17003i	−0.811024	−	0.585013i	$-0.801089\pi$
$479$		−	1.28589e8i		−	1.17003i	0.811024	−	0.585013i	$-0.198911\pi$
$480$	5.76450e6	+	7.82392e6i	0.0521240	+	0.0707458i
$481$	−1.35548e8			−1.21803
$482$		−	3.54801e7i		−	0.316843i
$483$	8.22658e7	−	6.06117e7i	0.730093	−	0.537917i
$484$	1.56502e7			0.138033
$485$		−	1.11804e7i		−	0.0980011i
$486$	1.82065e8	−	6.07164e6i	1.58605	−	0.0528929i
$487$	1.22214e8			1.05812			0.529061	−	0.848584i	$-0.322544\pi$
$487$	1.22214e8			1.05812			0.529061	+	0.848584i	$0.322544\pi$
$488$		−	1.71260e8i		−	1.47366i
$489$	−1.19783e8	−	1.62576e8i	−1.02440	−	1.39037i
$490$	3.50194e6			0.0297660
$491$			1.16766e8i			0.986446i	0.869903	+	0.493223i	$0.164181\pi$
$491$			1.16766e8i			0.986446i	−0.869903	+	0.493223i	$0.835819\pi$
$492$	1.02775e8	−	7.57227e7i	0.862966	−	0.635815i
$493$	−2.37748e7			−0.198416
$494$		−	6.61901e7i		−	0.549051i
$495$	−820482.	+	2.64467e6i	−0.00676478	+	0.0218050i
$496$	1.56338e6			0.0128120
$497$			1.73142e8i			1.41037i
$498$	−4.75926e7	−	6.45955e7i	−0.385347	−	0.523015i
$499$	7.46207e7			0.600562			0.300281	−	0.953851i	$-0.402920\pi$
$499$	7.46207e7			0.600562			0.300281	+	0.953851i	$0.402920\pi$
$500$		−	2.86599e7i		−	0.229279i
$501$	7.54461e7	−	5.55871e7i	0.599962	−	0.442039i
$502$	−6.29098e7			−0.497287
$503$			1.33260e8i			1.04712i	0.851989	+	0.523560i	$0.175397\pi$
$503$			1.33260e8i			1.04712i	−0.851989	+	0.523560i	$0.824603\pi$
$504$	−8.72409e7	−	2.70656e7i	−0.681442	−	0.211411i
$505$	728207.			0.00565432
$506$			6.48131e7i			0.500277i
$507$	4.87887e7	+	6.62190e7i	0.374365	+	0.508111i
$508$	3.61574e7			0.275807
$509$		−	1.33322e8i		−	1.01099i	−0.862828	−	0.505497i	$-0.831309\pi$
$509$		−	1.33322e8i		−	1.01099i	0.862828	−	0.505497i	$-0.168691\pi$
$510$	1.50076e6	−	1.10573e6i	0.0113136	−	0.00833562i
$511$	−3.55033e7			−0.266076
$512$			5.66782e7i			0.422286i
$513$	3.45500e7	−	1.19951e7i	0.255915	−	0.0888489i
$514$	1.60692e8			1.18332
$515$		−	9.18072e6i		−	0.0672133i
$516$	−1.41815e8	−	1.92480e8i	−1.03222	−	1.40100i
$517$	−6.26144e7			−0.453109
$518$			1.82454e8i			1.31270i
$519$	−1.21415e8	+	8.94560e7i	−0.868501	+	0.639893i
$520$	1.11854e7			0.0795506
$521$		−	1.27099e8i		−	0.898732i	−0.893348	−	0.449366i	$-0.851650\pi$
$521$		−	1.27099e8i		−	0.898732i	0.893348	−	0.449366i	$-0.148350\pi$
$522$	1.13473e8	−	3.65759e8i	0.797778	−	2.57148i
$523$	1.62159e8			1.13353			0.566767	−	0.823878i	$-0.308194\pi$
$523$	1.62159e8			1.13353			0.566767	+	0.823878i	$0.308194\pi$
$524$			3.74194e8i			2.60078i
$525$	−7.40198e7	−	1.00464e8i	−0.511529	−	0.694277i
$526$	4.06364e8			2.79227
$527$		−	1.02989e6i		−	0.00703655i
$528$	−7.60850e6	+	5.60578e6i	−0.0516889	+	0.0380833i
$529$	−1.37958e7			−0.0931920
$530$		−	2.24899e6i		−	0.0151063i
$531$	−1.28020e8	−	3.97171e7i	−0.855059	−	0.265273i
$532$	−5.37168e7			−0.356759
$533$			1.36523e8i			0.901620i
$534$	−2.32555e6	−	3.15638e6i	−0.0152722	−	0.0207284i
$535$	7.35200e6			0.0480114
$536$		−	1.95469e8i		−	1.26936i
$537$	−1.61704e8	+	1.19140e8i	−1.04424	+	0.769372i
$538$	3.12466e8			2.00658
$539$			1.16956e7i			0.0746892i
$540$	5.93754e6	+	1.71021e7i	0.0377073	+	0.108610i
$541$	−2.62665e8			−1.65886			−0.829431	−	0.558609i	$-0.811335\pi$
$541$	−2.62665e8			−1.65886			−0.829431	+	0.558609i	$0.811335\pi$
$542$			1.18113e8i			0.741823i
$543$	−3.45396e7	−	4.68792e7i	−0.215734	−	0.292806i
$544$	2.18498e7			0.135722
$545$			1.06382e7i			0.0657170i
$546$	2.30362e8	−	1.69726e8i	1.41525	−	1.04273i
$547$	−5.01073e7			−0.306153			−0.153077	−	0.988214i	$-0.548918\pi$
$547$	−5.01073e7			−0.306153			−0.153077	+	0.988214i	$0.548918\pi$
$548$			2.30365e8i			1.39983i
$549$	−8.78346e7	+	2.83118e8i	−0.530821	+	1.71100i
$550$	7.91505e7			0.475736
$551$		−	7.68853e7i		−	0.459609i
$552$	8.58092e7	+	1.16465e8i	0.510172	+	0.692436i
$553$	−2.57675e8			−1.52369
$554$			9.14039e7i			0.537571i
$555$	9.93892e6	−	7.32279e6i	0.0581380	−	0.0428349i
$556$	3.25005e8			1.89088
$557$			1.09524e8i			0.633787i	0.948461	+	0.316893i	$0.102640\pi$
$557$			1.09524e8i			0.633787i	−0.948461	+	0.316893i	$0.897360\pi$
$558$	1.58442e7	+	4.91551e6i	0.0911945	+	0.0282922i
$559$	2.55683e8			1.46375
$560$			2.45593e6i			0.0139847i
$561$	3.69288e6	+	5.01219e6i	0.0209159	+	0.0283883i
$562$	−4.87053e6			−0.0274389
$563$		−	3.24618e8i		−	1.81906i	−0.415637	−	0.909530i	$-0.636441\pi$
$563$		−	3.24618e8i		−	1.81906i	0.415637	−	0.909530i	$-0.363559\pi$
$564$	−3.29572e8	+	2.42822e8i	−1.83702	+	1.35348i
$565$	−7.09981e6			−0.0393642
$566$		−	2.89144e7i		−	0.159465i
$567$	1.30341e8	+	8.94868e7i	0.715040	+	0.490919i
$568$	−2.45120e8			−1.33762
$569$		−	2.73474e8i		−	1.48450i	−0.670124	−	0.742249i	$-0.733759\pi$
$569$		−	2.73474e8i		−	1.48450i	0.670124	−	0.742249i	$-0.266241\pi$
$570$	3.57582e6	+	4.85331e6i	0.0193086	+	0.0262068i
$571$	−8.88382e7			−0.477190			−0.238595	−	0.971119i	$-0.576687\pi$
$571$	−8.88382e7			−0.477190			−0.238595	+	0.971119i	$0.576687\pi$
$572$			1.09424e8i			0.584687i
$573$	−2.31635e7	+	1.70664e7i	−0.123123	+	0.0907146i
$574$	1.83766e8			0.971693
$575$			1.97631e8i			1.03956i
$576$	−9.22280e7	+	2.97280e8i	−0.482609	+	1.55560i
$577$	1.87886e8			0.978065			0.489032	−	0.872266i	$-0.337350\pi$
$577$	1.87886e8			0.978065			0.489032	+	0.872266i	$0.337350\pi$
$578$			3.02247e8i			1.56523i
$579$	−8.15954e6	−	1.10746e7i	−0.0420369	−	0.0570549i
$580$	3.80579e7			0.195057
$581$		−	6.96363e7i		−	0.355064i
$582$	3.25980e8	−	2.40175e8i	1.65357	−	1.21832i
$583$	7.51109e6			0.0379051
$584$		−	5.02628e7i		−	0.252353i
$585$	−1.84911e7	−	5.73670e6i	−0.0923626	−	0.0286546i
$586$	−4.35448e8			−2.16393
$587$		−	2.96662e8i		−	1.46672i	−0.679840	−	0.733361i	$-0.737951\pi$
$587$		−	2.96662e8i		−	1.46672i	0.679840	−	0.733361i	$-0.262049\pi$
$588$	4.53563e7	+	6.15603e7i	0.223103	+	0.302809i
$589$	3.33057e6			0.0162994
$590$		−	2.20939e7i		−	0.107576i
$591$	−8.00619e7	+	5.89879e7i	−0.387850	+	0.285760i
$592$	4.21341e7			0.203081
$593$			6.25208e7i			0.299820i	0.988700	+	0.149910i	$0.0478983\pi$
$593$			6.25208e7i			0.299820i	−0.988700	+	0.149910i	$0.952102\pi$
$594$	−9.47348e7	+	3.28901e7i	−0.452012	+	0.156930i
$595$	1.61787e6			0.00768057
$596$			4.26370e7i			0.201395i
$597$	−2.06080e8	−	2.79704e8i	−0.968529	−	1.31455i
$598$	−4.53164e8			−2.11910
$599$		−	9.11542e7i		−	0.424127i	−0.977256	−	0.212064i	$-0.931982\pi$
$599$		−	9.11542e7i		−	0.424127i	0.977256	−	0.212064i	$-0.0680184\pi$
$600$	1.42229e8	−	1.04791e8i	0.658467	−	0.485145i
$601$	3.48927e8			1.60735			0.803677	−	0.595066i	$-0.202874\pi$
$601$	3.48927e8			1.60735			0.803677	+	0.595066i	$0.202874\pi$
$602$		−	3.44161e8i		−	1.57751i
$603$	−1.00250e8	+	3.23138e8i	−0.457229	+	1.47379i
$604$	−3.67432e8			−1.66750
$605$		−	1.52433e6i		−	0.00688357i
$606$	1.56433e7	+	2.12320e7i	0.0702926	+	0.0954052i
$607$	−1.64684e8			−0.736351			−0.368176	−	0.929756i	$-0.620017\pi$
$607$	−1.64684e8			−0.736351			−0.368176	+	0.929756i	$0.620017\pi$
$608$			7.06602e7i			0.314387i
$609$	2.67585e8	−	1.97151e8i	1.18470	−	0.872864i
$610$	−4.88608e7			−0.215264
$611$		−	4.37791e8i		−	1.91930i
$612$	3.88751e7	+	1.20606e7i	0.169597	+	0.0526156i
$613$	−2.39331e7			−0.103901			−0.0519503	−	0.998650i	$-0.516544\pi$
$613$	−2.39331e7			−0.103901			−0.0519503	+	0.998650i	$0.516544\pi$
$614$		−	4.73599e8i		−	2.04600i
$615$	−7.37543e6	−	1.00104e7i	−0.0317075	−	0.0430353i
$616$	5.02839e7			0.215123
$617$			3.86885e8i			1.64712i	0.567227	+	0.823562i	$0.308016\pi$
$617$			3.86885e8i			1.64712i	−0.567227	+	0.823562i	$0.691984\pi$
$618$	2.67678e8	−	1.97219e8i	1.13409	−	0.835572i
$619$	1.29316e8			0.545233			0.272616	−	0.962123i	$-0.412111\pi$
$619$	1.29316e8			0.545233			0.272616	+	0.962123i	$0.412111\pi$
$620$			1.64862e6i			0.00691745i
$621$	−8.21232e7	−	2.36543e8i	−0.342919	−	0.987724i
$622$	−3.47696e7			−0.144487
$623$		−	3.40269e6i		−	0.0140721i
$624$	−3.91948e7	−	5.31976e7i	−0.161315	−	0.218946i
$625$	2.39949e8			0.982833
$626$		−	3.43409e8i		−	1.39987i
$627$	−1.62089e7	+	1.19424e7i	−0.0657585	+	0.0484494i
$628$	−7.25464e8			−2.92912
$629$		−	2.77564e7i		−	0.111535i
$630$	−7.72185e6	+	2.48899e7i	−0.0308816	+	0.0995410i
$631$	2.83022e8			1.12650			0.563252	−	0.826285i	$-0.309550\pi$
$631$	2.83022e8			1.12650			0.563252	+	0.826285i	$0.309550\pi$
$632$		−	3.64796e8i		−	1.44510i
$633$	6.14030e7	+	8.33398e7i	0.242091	+	0.328580i
$634$	−1.52744e8			−0.599370
$635$		−	3.52175e6i		−	0.0137542i
$636$	3.95348e7	−	2.91284e7i	0.153677	−	0.113226i
$637$	−8.17743e7			−0.316372
$638$			2.10816e8i			0.811787i
$639$	4.05219e8	+	1.25715e8i	1.55305	+	0.481820i
$640$	−2.82691e7			−0.107838
$641$		−	3.29490e7i		−	0.125103i	−0.998042	−	0.0625516i	$-0.980076\pi$
$641$		−	3.29490e7i		−	0.125103i	0.998042	−	0.0625516i	$-0.0199238\pi$
$642$	1.57935e8	+	2.14359e8i	0.596861	+	0.810095i
$643$	−4.45315e7			−0.167507			−0.0837537	−	0.996486i	$-0.526691\pi$
$643$	−4.45315e7			−0.167507			−0.0837537	+	0.996486i	$0.526691\pi$
$644$			3.67766e8i			1.37694i
$645$	−1.87477e7	+	1.38129e7i	−0.0698664	+	0.0514761i
$646$	1.35538e7			0.0502764
$647$			2.33818e8i			0.863308i	0.902039	+	0.431654i	$0.142070\pi$
$647$			2.33818e8i			0.863308i	−0.902039	+	0.431654i	$0.857930\pi$
$648$	−1.26688e8	+	1.84526e8i	−0.465598	+	0.678160i
$649$	7.37884e7			0.269932
$650$			5.53409e8i			2.01515i
$651$	8.54032e6	+	1.15914e7i	0.0309550	+	0.0420140i
$652$	7.26792e8			2.62221
$653$			1.34079e8i			0.481528i	0.970584	+	0.240764i	$0.0773981\pi$
$653$			1.34079e8i			0.481528i	−0.970584	+	0.240764i	$0.922602\pi$
$654$	−3.10172e8	+	2.28528e8i	−1.10884	+	0.816970i
$655$	3.64467e7			0.129698
$656$		−	4.24370e7i		−	0.150326i
$657$	−2.57783e7	+	8.30916e7i	−0.0908990	+	0.292995i
$658$	−5.89286e8			−2.06847
$659$			1.61429e8i			0.564059i	0.959406	+	0.282029i	$0.0910076\pi$
$659$			1.61429e8i			0.564059i	−0.959406	+	0.282029i	$0.908992\pi$
$660$	−5.91144e6	−	8.02336e6i	−0.0205618	−	0.0279077i
$661$	3.93652e7			0.136304			0.0681519	−	0.997675i	$-0.478290\pi$
$661$	3.93652e7			0.136304			0.0681519	+	0.997675i	$0.478290\pi$
$662$		−	2.40491e8i		−	0.828942i
$663$	−3.50445e7	+	2.58201e7i	−0.120248	+	0.0885966i
$664$	9.85854e7			0.336751
$665$			5.23204e6i			0.0177912i
$666$	4.27014e8	+	1.32477e8i	1.44550	+	0.448453i
$667$	−5.26387e8			−1.77389
$668$			3.37279e8i			1.13151i
$669$	−3.59323e7	−	4.87694e7i	−0.120007	−	0.162881i
$670$	−5.57675e7			−0.185420
$671$		−	1.63184e8i		−	0.540143i
$672$	−2.45919e8	+	1.81188e8i	−0.810373	+	0.597066i
$673$	−1.81232e8			−0.594553			−0.297277	−	0.954791i	$-0.596078\pi$
$673$	−1.81232e8			−0.594553			−0.297277	+	0.954791i	$0.596078\pi$
$674$		−	5.43939e8i		−	1.77652i
$675$	−2.88869e8	+	1.00290e8i	−0.939270	+	0.326096i
$676$	−2.96029e8			−0.958285
$677$		−	2.85711e8i		−	0.920790i	−0.887714	−	0.460395i	$-0.847708\pi$
$677$		−	2.85711e8i		−	0.920790i	0.887714	−	0.460395i	$-0.152292\pi$
$678$	−1.52517e8	−	2.07006e8i	−0.489362	−	0.664191i
$679$	3.51418e8			1.12257
$680$			2.29045e6i			0.00728442i
$681$	2.72312e8	−	2.00634e8i	0.862236	−	0.635277i
$682$	−9.13229e6			−0.0287890
$683$		−	5.51690e8i		−	1.73154i	−0.500439	−	0.865772i	$-0.666828\pi$
$683$		−	5.51690e8i		−	1.73154i	0.500439	−	0.865772i	$-0.333172\pi$
$684$	−3.90028e7	+	1.25718e8i	−0.121879	+	0.392853i
$685$	2.24377e7			0.0698081
$686$			5.54419e8i			1.71738i
$687$	2.11659e8	+	2.87276e8i	0.652780	+	0.885992i
$688$	−7.94772e7			−0.244049
$689$			5.25165e7i			0.160560i
$690$	3.32277e7	−	2.44815e7i	0.101147	−	0.0745230i
$691$	2.58702e8			0.784090			0.392045	−	0.919946i	$-0.371768\pi$
$691$	2.58702e8			0.784090			0.392045	+	0.919946i	$0.371768\pi$
$692$		−	5.42781e8i		−	1.63797i
$693$	−8.31265e7	−	2.57892e7i	−0.249770	−	0.0774886i
$694$	1.34221e8			0.401552
$695$		−	3.16556e7i		−	0.0942966i
$696$	2.79110e8	+	3.78825e8i	0.827843	+	1.12360i
$697$	−2.79559e7			−0.0825611
$698$			4.36134e8i			1.28249i
$699$	−5.04271e8	+	3.71536e8i	−1.47650	+	1.08785i
$700$	4.49121e8			1.30939
$701$			5.09615e8i			1.47941i	0.672932	+	0.739705i	$0.265035\pi$
$701$			5.09615e8i			1.47941i	−0.672932	+	0.739705i	$0.734965\pi$
$702$	−2.29963e8	−	6.62372e8i	−0.664732	−	1.91466i
$703$	8.97613e7			0.258359
$704$		−	1.71346e8i		−	0.491084i
$705$	2.36510e7	+	3.21005e7i	0.0674966	+	0.0916103i
$706$	6.35684e8			1.80645
$707$			2.28888e7i			0.0647687i
$708$	3.88387e8	−	2.86155e8i	1.09437	−	0.806310i
$709$	6.51470e8			1.82791			0.913957	−	0.405811i	$-0.133011\pi$
$709$	6.51470e8			1.82791			0.913957	+	0.405811i	$0.133011\pi$
$710$			6.99330e7i			0.195392i
$711$	−1.87093e8	+	6.03060e8i	−0.520535	+	1.67785i
$712$	4.81725e6			0.0133463
$713$		−	2.28024e7i		−	0.0629089i
$714$	3.47550e7	+	4.71715e7i	0.0954822	+	0.129594i
$715$	1.06579e7			0.0291578
$716$		−	7.22893e8i		−	1.96941i
$717$	−1.65273e8	+	1.21770e8i	−0.448378	+	0.330356i
$718$	5.65837e8			1.52869
$719$			3.32202e7i			0.0893749i	0.999001	+	0.0446875i	$0.0142292\pi$
$719$			3.32202e7i			0.0893749i	−0.999001	+	0.0446875i	$0.985771\pi$
$720$	5.74783e6	+	1.78321e6i	0.0153995	+	0.00477754i
$721$	2.88566e8			0.769909
$722$		−	5.53438e8i		−	1.47047i
$723$	−4.47585e7	−	6.07489e7i	−0.118430	−	0.160740i
$724$	2.09572e8			0.552226
$725$			6.42830e8i			1.68687i
$726$	4.44442e7	−	3.27456e7i	0.116146	−	0.0855742i
$727$	2.33749e8			0.608341			0.304171	−	0.952618i	$-0.401621\pi$
$727$	2.33749e8			0.608341			0.304171	+	0.952618i	$0.401621\pi$
$728$			3.51578e8i			0.911229i
$729$	3.04072e8	−	2.40073e8i	0.784862	−	0.619670i
$730$	−1.43400e7			−0.0368622
$731$			5.23565e7i			0.134035i
$732$	−6.32834e8	−	8.58920e8i	−1.61345	−	2.18988i
$733$	−7.53193e7			−0.191247			−0.0956234	−	0.995418i	$-0.530484\pi$
$733$	−7.53193e7			−0.191247			−0.0956234	+	0.995418i	$0.530484\pi$
$734$			8.48196e7i			0.214491i
$735$	5.99600e6	−	4.41773e6i	0.0151008	−	0.0111259i
$736$	4.83768e8			1.21340
$737$		−	1.86250e8i		−	0.465259i
$738$	1.33429e8	−	4.30084e8i	0.331957	−	1.07000i
$739$	−7.23910e8			−1.79371			−0.896853	−	0.442329i	$-0.854152\pi$
$739$	−7.23910e8			−1.79371			−0.896853	+	0.442329i	$0.854152\pi$
$740$			4.44316e7i			0.109647i
$741$	−8.34996e7	−	1.13331e8i	−0.205225	−	0.278543i
$742$	7.06896e7			0.173039
$743$		−	6.68484e8i		−	1.62976i	−0.579627	−	0.814882i	$-0.696802\pi$
$743$		−	6.68484e8i		−	1.62976i	0.579627	−	0.814882i	$-0.303198\pi$
$744$	−1.64102e7	+	1.20907e7i	−0.0398470	+	0.0293584i
$745$	4.15287e6			0.0100434
$746$			2.61953e7i			0.0630967i
$747$	−1.62976e8	−	5.05617e7i	−0.390986	−	0.121300i
$748$	−2.24068e7			−0.0535396
$749$			2.31086e8i			0.549957i
$750$	−5.99665e7	−	8.13901e7i	−0.142143	−	0.192925i
$751$	−5.27966e8			−1.24648			−0.623241	−	0.782030i	$-0.714184\pi$
$751$	−5.27966e8			−1.24648			−0.623241	+	0.782030i	$0.714184\pi$
$752$			1.36084e8i			0.320002i
$753$	−1.07714e8	+	7.93613e7i	−0.252282	+	0.185876i
$754$	−1.47400e9			−3.43861
$755$			3.57881e7i			0.0831568i
$756$	−5.37550e8	+	1.86627e8i	−1.24410	+	0.431926i
$757$	−6.37097e8			−1.46865			−0.734325	−	0.678798i	$-0.762501\pi$
$757$	−6.37097e8			−1.46865			−0.734325	+	0.678798i	$0.762501\pi$
$758$			2.90981e8i			0.668123i
$759$	8.17624e7	+	1.10973e8i	0.186994	+	0.253800i
$760$	−7.40710e6			−0.0168736
$761$			4.58701e8i			1.04082i	0.853916	+	0.520410i	$0.174221\pi$
$761$			4.58701e8i			1.04082i	−0.853916	+	0.520410i	$0.825779\pi$
$762$	1.02682e8	−	7.56538e7i	0.232075	−	0.170988i
$763$	−3.34376e8			−0.752769
$764$		−	1.03551e8i		−	0.232208i
$765$	1.17471e6	−	3.78645e6i	0.00262389	−	0.00845762i
$766$	−2.52033e8			−0.560753
$767$			5.15918e8i			1.14339i
$768$	−1.69638e8	−	2.30243e8i	−0.374489	−	0.508279i
$769$	2.94569e8			0.647750			0.323875	−	0.946100i	$-0.395014\pi$
$769$	2.94569e8			0.647750			0.323875	+	0.946100i	$0.395014\pi$
$770$		−	1.43460e7i		−	0.0314239i
$771$	2.75136e8	−	2.02714e8i	0.600321	−	0.442304i
$772$	4.95087e7			0.107604
$773$			7.18654e8i			1.55590i	0.628327	+	0.777949i	$0.283740\pi$
$773$			7.18654e8i			1.55590i	−0.628327	+	0.777949i	$0.716260\pi$
$774$	−8.05471e8	−	2.49889e8i	−1.73711	−	0.538921i
$775$	−2.78466e7			−0.0598228
$776$			4.97510e8i			1.06467i
$777$	2.30168e8	+	3.12398e8i	0.490661	+	0.665954i
$778$	−1.91183e8			−0.405984
$779$		−	9.04067e7i		−	0.191244i
$780$	5.60982e7	−	4.13320e7i	0.118213	−	0.0870969i
$781$	−2.33560e8			−0.490281
$782$		−	9.27948e7i		−	0.194045i
$783$	−2.67121e8	−	7.69400e8i	−0.556445	−	1.60275i
$784$	2.54189e7			0.0527483
$785$			7.06605e7i			0.146072i
$786$	7.82944e8	+	1.06266e9i	1.61236	+	2.18840i
$787$	−7.09022e8			−1.45457			−0.727286	−	0.686334i	$-0.759219\pi$
$787$	−7.09022e8			−1.45457			−0.727286	+	0.686334i	$0.759219\pi$
$788$		−	3.57914e8i		−	0.731475i
$789$	6.95775e8	−	5.12633e8i	1.41657	−	1.04370i
$790$	−1.04077e8			−0.211092
$791$		−	2.23159e8i		−	0.450906i
$792$	3.65103e7	−	1.17684e8i	0.0734919	−	0.236887i
$793$	1.14096e9			2.28797
$794$			9.13380e8i			1.82469i
$795$	−2.83712e6	−	3.85071e6i	−0.00564646	−	0.00766371i
$796$	1.25041e9			2.47920
$797$		−	4.95174e8i		−	0.978099i	−0.872256	−	0.489050i	$-0.837344\pi$
$797$		−	4.95174e8i		−	0.978099i	0.872256	−	0.489050i	$-0.162656\pi$
$798$	−1.52548e8	+	1.12394e8i	−0.300191	+	0.221175i
$799$	8.96469e7			0.175750
$800$		−	5.90783e8i		−	1.15387i
$801$	−7.96361e6	−	2.47063e6i	−0.0154958	−	0.00480740i
$802$	−1.06797e9			−2.07030
$803$		−	4.78923e7i		−	0.0924952i
$804$	−7.22288e8	−	9.80332e8i	−1.38977	−	1.88628i
$805$	3.58206e7			0.0686666
$806$		−	6.38517e7i		−	0.121946i
$807$	5.35004e8	−	3.94180e8i	1.01797	−	0.750021i
$808$	−3.24041e7			−0.0614280
$809$			9.14294e7i			0.172679i	0.996266	+	0.0863396i	$0.0275170\pi$
$809$			9.14294e7i			0.172679i	−0.996266	+	0.0863396i	$0.972483\pi$
$810$	5.26454e7	+	3.61443e7i	0.0990616	+	0.0680118i
$811$	1.77641e8			0.333027			0.166514	−	0.986039i	$-0.446749\pi$
$811$	1.77641e8			0.333027			0.166514	+	0.986039i	$0.446749\pi$
$812$			1.19623e9i			2.23432i
$813$	1.49001e8	+	2.02233e8i	0.277279	+	0.376340i
$814$	−2.46122e8			−0.456328
$815$		−	7.07899e7i		−	0.130767i
$816$	1.08933e7	−	8.02597e6i	0.0200489	−	0.0147716i
$817$	−1.69316e8			−0.310478
$818$		−	3.31339e7i		−	0.0605358i
$819$	1.80314e8	−	5.81209e8i	0.328230	−	1.05799i
$820$	4.47510e7			0.0811636
$821$		−	8.83675e8i		−	1.59685i	−0.602096	−	0.798423i	$-0.705668\pi$
$821$		−	8.83675e8i		−	1.59685i	0.602096	−	0.798423i	$-0.294332\pi$
$822$	4.82003e8	+	6.54204e8i	0.867830	+	1.17787i
$823$	−6.78430e8			−1.21704			−0.608521	−	0.793538i	$-0.708237\pi$
$823$	−6.78430e8			−1.21704			−0.608521	+	0.793538i	$0.708237\pi$
$824$			4.08529e8i			0.730198i
$825$	1.35521e8	−	9.98492e7i	0.241349	−	0.177821i
$826$	6.94449e8			1.23225
$827$		−	6.21613e8i		−	1.09901i	−0.835489	−	0.549507i	$-0.814815\pi$
$827$		−	6.21613e8i		−	1.09901i	0.835489	−	0.549507i	$-0.185185\pi$
$828$	8.60716e8	+	2.67029e8i	1.51624	+	0.470400i
$829$	3.01308e8			0.528867			0.264433	−	0.964404i	$-0.414815\pi$
$829$	3.01308e8			0.528867			0.264433	+	0.964404i	$0.414815\pi$
$830$		−	2.81265e7i		−	0.0491906i
$831$	1.15307e8	+	1.56502e8i	0.200934	+	0.272719i
$832$	1.19803e9			2.08016
$833$		−	1.67450e7i		−	0.0289701i
$834$	9.22967e8	−	6.80023e8i	1.59107	−	1.17226i
$835$	3.28512e7			0.0564275
$836$		−	7.24614e7i		−	0.124019i
$837$	3.33294e7	−	1.15713e7i	0.0568396	−	0.0197336i
$838$	3.27050e8			0.555754
$839$			2.55425e8i			0.432491i	0.976339	+	0.216246i	$0.0693812\pi$
$839$			2.55425e8i			0.432491i	−0.976339	+	0.216246i	$0.930619\pi$
$840$	−1.89935e7	−	2.57790e7i	−0.0320454	−	0.0434939i
$841$	−1.11735e9			−1.87845
$842$		−	9.71694e7i		−	0.162777i
$843$	−8.33930e6	+	6.14422e6i	−0.0139202	+	0.0102561i
$844$	−3.72568e8			−0.619695
$845$			2.88334e7i			0.0477888i
$846$	−4.27870e8	+	1.37916e9i	−0.706645	+	2.27774i
$847$	4.79125e7			0.0788494
$848$		−	1.63243e7i		−	0.0267700i
$849$	−3.64758e7	−	4.95071e7i	−0.0596049	−	0.0808993i
$850$	−1.13322e8			−0.184526
$851$		−	6.14542e8i		−	0.997155i
$852$	−1.22935e9	+	9.05757e8i	−1.98772	+	1.46451i
$853$	6.38017e8			1.02798			0.513991	−	0.857796i	$-0.328167\pi$
$853$	6.38017e8			1.02798			0.513991	+	0.857796i	$0.328167\pi$
$854$		−	1.53578e9i		−	2.46578i
$855$	1.22450e7	+	3.79889e6i	0.0195912	+	0.00607797i
$856$	−3.27153e8			−0.521591
$857$			1.15803e8i			0.183982i	0.995760	+	0.0919912i	$0.0293232\pi$
$857$			1.15803e8i			0.183982i	−0.995760	+	0.0919912i	$0.970677\pi$
$858$	2.28952e8	+	3.10748e8i	0.362479	+	0.491979i
$859$	−9.03582e8			−1.42557			−0.712785	−	0.701383i	$-0.752566\pi$
$859$	−9.03582e8			−1.42557			−0.712785	+	0.701383i	$0.752566\pi$
$860$		−	8.38108e7i		−	0.131766i
$861$	3.14643e8	−	2.31823e8i	0.492957	−	0.363200i
$862$	−6.50360e8			−1.01539
$863$			6.01900e8i			0.936466i	0.883605	+	0.468233i	$0.155109\pi$
$863$			6.01900e8i			0.936466i	−0.883605	+	0.468233i	$0.844891\pi$
$864$	2.45493e8	+	7.07105e8i	0.380626	+	1.09633i
$865$	−5.28672e7			−0.0816841
$866$			1.20725e9i			1.85885i
$867$	3.81288e8	+	5.17506e8i	0.585053	+	0.794069i
$868$	−5.18190e7			−0.0792374
$869$		−	3.47592e8i		−	0.529676i
$870$	1.08079e8	−	7.96304e7i	0.164129	−	0.120926i
$871$	1.30224e9			1.97077
$872$		−	4.73383e8i		−	0.713942i
$873$	2.55159e8	−	8.22455e8i	0.383502	−	1.23615i
$874$	3.00089e8			0.449486
$875$		−	8.77414e7i		−	0.130973i
$876$	−1.85729e8	−	2.52082e8i	−0.276291	−	0.374999i
$877$	−3.57282e8			−0.529678			−0.264839	−	0.964293i	$-0.585319\pi$
$877$	−3.57282e8			−0.529678			−0.264839	+	0.964293i	$0.585319\pi$
$878$			1.05185e9i			1.55406i
$879$	−7.45573e8	+	5.49323e8i	−1.09780	+	0.808837i
$880$	−3.31293e6			−0.00486144
$881$			8.68132e8i			1.26957i	0.772687	+	0.634787i	$0.218912\pi$
$881$			8.68132e8i			1.26957i	−0.772687	+	0.634787i	$0.781088\pi$
$882$	2.57611e8	+	7.99213e7i	0.375456	+	0.116481i
$883$	−6.71764e8			−0.975741			−0.487871	−	0.872916i	$-0.662226\pi$
$883$	−6.71764e8			−0.975741			−0.487871	+	0.872916i	$0.662226\pi$
$884$		−	1.56665e8i		−	0.226786i
$885$	−2.78717e7	−	3.78291e7i	−0.0402099	−	0.0545753i
$886$	4.92297e8			0.707826
$887$		−	3.54182e7i		−	0.0507522i	−0.999678	−	0.0253761i	$-0.991922\pi$
$887$		−	3.54182e7i		−	0.0507522i	0.999678	−	0.0253761i	$-0.00807833\pi$
$888$	−4.42267e8	+	3.25853e8i	−0.631606	+	0.465354i
$889$	1.10695e8			0.157551
$890$		−	1.37437e6i		−	0.00194954i
$891$	−1.20713e8	+	1.75823e8i	−0.170656	+	0.248567i
$892$	2.18022e8			0.307189
$893$			2.89909e8i			0.407106i
$894$	8.92114e7	+	1.21083e8i	0.124856	+	0.169461i
$895$	−7.04102e7			−0.0982124
$896$		−	8.88546e8i		−	1.23525i
$897$	−7.75906e8	+	5.71671e8i	−1.07506	+	0.792080i
$898$	1.71610e9			2.36982
$899$		−	7.41690e7i		−	0.102081i
$900$	3.26099e8	−	1.05112e9i	0.447323	−	1.44186i
$901$	−1.07539e7			−0.0147025
$902$			2.47891e8i			0.337786i
$903$	−4.34163e8	−	5.89272e8i	−0.589644	−	0.800300i
$904$	3.15931e8			0.427649
$905$		−	2.04124e7i		−	0.0275390i
$906$	−1.04346e9	+	7.68796e8i	−1.40310	+	1.03378i
$907$	−3.54547e8			−0.475173			−0.237586	−	0.971366i	$-0.576356\pi$
$907$	−3.54547e8			−0.475173			−0.237586	+	0.971366i	$0.576356\pi$
$908$			1.21736e9i			1.62616i
$909$	5.35687e7	+	1.66192e7i	0.0713213	+	0.0221267i
$910$	1.00306e8			0.133107
$911$			1.98413e8i			0.262431i	0.991354	+	0.131216i	$0.0418880\pi$
$911$			1.98413e8i			0.262431i	−0.991354	+	0.131216i	$0.958112\pi$
$912$	2.59552e7	+	3.52279e7i	0.0342168	+	0.0464411i
$913$	9.39360e7			0.123430
$914$		−	6.89672e8i		−	0.903241i
$915$	−8.36593e7	+	6.16384e7i	−0.109207	+	0.0804615i
$916$	−1.28426e9			−1.67096
$917$			1.14558e9i			1.48566i
$918$	1.35635e8	−	4.70897e7i	0.175324	−	0.0608693i
$919$	1.17227e9			1.51036			0.755180	−	0.655517i	$-0.227549\pi$
$919$	1.17227e9			1.51036			0.755180	+	0.655517i	$0.227549\pi$
$920$			5.07120e7i			0.0651249i
$921$	−5.97451e8	−	8.10896e8i	−0.764757	−	1.03797i
$922$	−5.60822e8			−0.715537
$923$		−	1.63302e9i		−	2.07676i
$924$	2.52188e8	−	1.85807e8i	0.319675	−	0.235530i
$925$	−7.50486e8			−0.948238
$926$		−	8.14741e8i		−	1.02609i
$927$	2.09523e8	−	6.75356e8i	0.263022	−	0.847801i
$928$	1.57354e9			1.96895
$929$			5.20749e8i			0.649503i	0.945799	+	0.324752i	$0.105281\pi$
$929$			5.20749e8i			0.649503i	−0.945799	+	0.324752i	$0.894719\pi$
$930$	3.44949e6	+	4.68185e6i	0.00428850	+	0.00582061i
$931$	5.41517e7			0.0671063
$932$		−	2.25432e9i		−	2.78464i
$933$	−5.95325e7	+	4.38623e7i	−0.0733008	+	0.0540065i
$934$	−1.04671e9			−1.28465
$935$			2.18243e6i			0.00266997i
$936$	8.22829e8	+	2.55275e8i	1.00342	+	0.311301i
$937$	−3.73345e8			−0.453829			−0.226914	−	0.973915i	$-0.572864\pi$
$937$	−3.73345e8			−0.453829			−0.226914	+	0.973915i	$0.572864\pi$
$938$		−	1.75287e9i		−	2.12393i
$939$	−4.33214e8	−	5.87984e8i	−0.523246	−	0.710181i
$940$	−1.43504e8			−0.172775
$941$			2.81555e8i			0.337905i	0.985624	+	0.168953i	$0.0540384\pi$
$941$			2.81555e8i			0.337905i	−0.985624	+	0.168953i	$0.945962\pi$
$942$	−2.06021e9	+	1.51792e9i	−2.46467	+	1.81592i
$943$	−6.18960e8			−0.738121
$944$		−	1.60369e8i		−	0.190636i
$945$	1.81776e7	+	5.23577e7i	0.0215397	+	0.0620419i
$946$	4.64257e8			0.548385
$947$			3.45676e8i			0.407023i	0.979073	+	0.203511i	$0.0652354\pi$
$947$			3.45676e8i			0.407023i	−0.979073	+	0.203511i	$0.934765\pi$
$948$	−1.34798e9	−	1.82956e9i	−1.58219	−	2.14744i
$949$	3.34856e8			0.391796
$950$		−	3.66473e8i		−	0.427436i
$951$	−2.61527e8	+	1.92688e8i	−0.304071	+	0.224033i
$952$	−7.19930e7			−0.0834410
$953$			8.21696e7i			0.0949363i	0.998873	+	0.0474682i	$0.0151153\pi$
$953$			8.21696e7i			0.0949363i	−0.998873	+	0.0474682i	$0.984885\pi$
$954$	5.13265e7	−	1.65441e8i	0.0591148	−	0.190545i
$955$	−1.00860e7			−0.0115800
$956$		−	7.38847e8i		−	0.845631i
$957$	2.65947e8	+	3.60959e8i	0.303431	+	0.411834i
$958$	1.63249e9			1.85676
$959$			7.05255e8i			0.799632i
$960$	−8.78439e7	+	6.47215e7i	−0.0992882	+	0.0731535i
$961$	−8.84291e8			−0.996380
$962$		−	1.72085e9i		−	1.93294i
$963$	5.40832e8	+	1.67788e8i	0.605596	+	0.187880i
$964$	2.71576e8			0.303152
$965$		−	4.82217e6i		−	0.00536612i
$966$	7.69495e8	+	1.04440e9i	0.853639	+	1.15861i
$967$	6.02998e8			0.666863			0.333431	−	0.942774i	$-0.391793\pi$
$967$	6.02998e8			0.666863			0.333431	+	0.942774i	$0.391793\pi$
$968$			6.78306e7i			0.0747824i
$969$	2.32068e7	−	1.70983e7i	0.0255061	−	0.0187924i
$970$	1.41940e8			0.155521
$971$		−	5.33976e7i		−	0.0583263i	−0.999575	−	0.0291631i	$-0.990716\pi$
$971$		−	5.33976e7i		−	0.0583263i	0.999575	−	0.0291631i	$-0.00928423\pi$
$972$	4.64742e7	+	1.39358e9i	0.0506073	+	1.51752i
$973$	9.94991e8			1.08014
$974$			1.55157e9i			1.67917i
$975$	6.98132e8	+	9.47546e8i	0.753223	+	1.02232i
$976$	−3.54657e8			−0.381469
$977$		−	8.28819e8i		−	0.888743i	−0.895843	−	0.444371i	$-0.853427\pi$
$977$		−	8.28819e8i		−	0.888743i	0.895843	−	0.444371i	$-0.146573\pi$
$978$	2.06398e9	−	1.52070e9i	2.20643	−	1.62565i
$979$	4.59007e6			0.00489183
$980$			2.68049e7i			0.0284797i
$981$	−2.42785e8	+	7.82570e8i	−0.257166	+	0.828927i
$982$	−1.48240e9			−1.56542
$983$			5.79129e8i			0.609698i	0.952401	+	0.304849i	$0.0986061\pi$
$983$			5.79129e8i			0.609698i	−0.952401	+	0.304849i	$0.901394\pi$
$984$	3.28196e8	+	4.45447e8i	0.344467	+	0.467531i
$985$	−3.48610e7			−0.0364780
$986$		−	3.01832e8i		−	0.314872i
$987$	−1.00897e9	+	7.43391e8i	−1.04937	+	0.773154i
$988$	5.06640e8			0.525326
$989$			1.15920e9i			1.19831i
$990$	−3.35753e7	−	1.04164e7i	−0.0346031	−	0.0107353i
$991$	2.78169e8			0.285817			0.142909	−	0.989736i	$-0.454355\pi$
$991$	2.78169e8			0.285817			0.142909	+	0.989736i	$0.454355\pi$
$992$			6.81638e7i			0.0698263i
$993$	−3.03382e8	−	4.11768e8i	−0.309843	−	0.420537i
$994$	−2.19812e9			−2.23816
$995$		−	1.21790e8i		−	0.123635i
$996$	4.94434e8	−	3.64289e8i	0.500415	−	0.368696i
$997$	−4.68940e8			−0.473185			−0.236593	−	0.971609i	$-0.576031\pi$
$997$	−4.68940e8			−0.473185			−0.236593	+	0.971609i	$0.576031\pi$
$998$			9.47346e8i			0.953053i
$999$	8.98252e8	−	3.11856e8i	0.900953	−	0.312793i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.7.b.a.23.18	yes	20
3.2	odd	2	inner	33.7.b.a.23.3	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.7.b.a.23.3	✓	20	3.2	odd	2	inner
33.7.b.a.23.18	yes	20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	33.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+12.6955i q^{2} +(16.0155 + 21.7372i) q^{3} -97.1752 q^{4} +9.46491i q^{5} +(-275.964 + 203.324i) q^{6} -297.499 q^{7} -421.175i q^{8} +(-216.009 + 696.262i) q^{9} +O(q^{10})\)	\(q+12.6955i q^{2} +(16.0155 + 21.7372i) q^{3} -97.1752 q^{4} +9.46491i q^{5} +(-275.964 + 203.324i) q^{6} -297.499 q^{7} -421.175i q^{8} +(-216.009 + 696.262i) q^{9} -120.162 q^{10} -401.312i q^{11} +(-1556.31 - 2112.31i) q^{12} +2805.91 q^{13} -3776.89i q^{14} +(-205.740 + 151.585i) q^{15} -872.197 q^{16} +574.570i q^{17} +(-8839.38 - 2742.33i) q^{18} -1858.10 q^{19} -919.754i q^{20} +(-4764.59 - 6466.78i) q^{21} +5094.84 q^{22} +12721.3i q^{23} +(9155.14 - 6745.32i) q^{24} +15535.4 q^{25} +35622.4i q^{26} +(-18594.3 + 6455.57i) q^{27} +28909.5 q^{28} +41378.4i q^{29} +(-1924.45 - 2611.97i) q^{30} -1792.46 q^{31} -38028.1i q^{32} +(8723.38 - 6427.20i) q^{33} -7294.44 q^{34} -2815.80i q^{35} +(20990.7 - 67659.4i) q^{36} -48308.1 q^{37} -23589.5i q^{38} +(44938.1 + 60992.6i) q^{39} +3986.38 q^{40} +48655.4i q^{41} +(82098.8 - 60488.7i) q^{42} +91123.0 q^{43} +38997.5i q^{44} +(-6590.06 - 2044.50i) q^{45} -161503. q^{46} -156024. i q^{47} +(-13968.7 - 18959.1i) q^{48} -29143.6 q^{49} +197230. i q^{50} +(-12489.5 + 9202.02i) q^{51} -272665. q^{52} +18716.4i q^{53} +(-81956.5 - 236063. i) q^{54} +3798.38 q^{55} +125299. i q^{56} +(-29758.4 - 40389.9i) q^{57} -525318. q^{58} +183868. i q^{59} +(19992.9 - 14730.3i) q^{60} +406626. q^{61} -22756.1i q^{62} +(64262.2 - 207137. i) q^{63} +426965. q^{64} +26557.7i q^{65} +(81596.4 + 110747. i) q^{66} +464104. q^{67} -55833.9i q^{68} +(-276525. + 203738. i) q^{69} +35747.9 q^{70} -581991. i q^{71} +(293248. + 90977.3i) q^{72} +119339. q^{73} -613294. i q^{74} +(248807. + 337696. i) q^{75} +180561. q^{76} +119390. i q^{77} +(-774331. + 570510. i) q^{78} +866139. q^{79} -8255.26i q^{80} +(-438122. - 300797. i) q^{81} -617703. q^{82} +234073. i q^{83} +(462999. + 628410. i) q^{84} -5438.25 q^{85} +1.15685e6i q^{86} +(-899449. + 662695. i) q^{87} -169022. q^{88} +11437.7i q^{89} +(25955.9 - 83664.0i) q^{90} -834756. q^{91} -1.23620e6i q^{92} +(-28707.1 - 38963.0i) q^{93} +1.98080e6 q^{94} -17586.8i q^{95} +(826624. - 609039. i) q^{96} -1.18124e6 q^{97} -369991. i q^{98} +(279418. + 86686.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 16 q^{3} - 772 q^{4} + 286 q^{6} + 160 q^{7} - 1072 q^{9}+O(q^{10}) \) 20 * q + 16 * q^3 - 772 * q^4 + 286 * q^6 + 160 * q^7 - 1072 * q^9	\( 20 q + 16 q^{3} - 772 q^{4} + 286 q^{6} + 160 q^{7} - 1072 q^{9} + 996 q^{10} + 6092 q^{12} + 808 q^{13} - 3032 q^{15} + 28004 q^{16} + 18686 q^{18} + 5920 q^{19} - 20888 q^{21} - 48096 q^{24} - 100612 q^{25} - 17624 q^{27} - 33296 q^{28} + 109582 q^{30} - 90896 q^{31} - 21296 q^{33} + 68928 q^{34} - 28988 q^{36} + 239656 q^{37} - 15416 q^{39} + 34632 q^{40} + 150364 q^{42} - 125840 q^{43} - 242428 q^{45} + 244380 q^{46} + 305492 q^{48} - 186204 q^{49} - 21992 q^{51} - 120368 q^{52} - 777728 q^{54} - 191664 q^{55} - 255840 q^{57} + 601176 q^{58} + 970736 q^{60} + 1108360 q^{61} + 574088 q^{63} - 2533132 q^{64} + 465850 q^{66} + 617728 q^{67} + 323804 q^{69} - 238680 q^{70} - 2031648 q^{72} - 1379960 q^{73} + 2481512 q^{75} + 4678408 q^{76} - 1556840 q^{78} + 347152 q^{79} - 1086136 q^{81} - 1760328 q^{82} - 345760 q^{84} - 4097232 q^{85} - 2983056 q^{87} - 622908 q^{88} - 4093630 q^{90} + 979616 q^{91} + 2363236 q^{93} - 217752 q^{94} + 8811824 q^{96} - 3139256 q^{97} + 212960 q^{99}+O(q^{100}) \) 20 * q + 16 * q^3 - 772 * q^4 + 286 * q^6 + 160 * q^7 - 1072 * q^9 + 996 * q^10 + 6092 * q^12 + 808 * q^13 - 3032 * q^15 + 28004 * q^16 + 18686 * q^18 + 5920 * q^19 - 20888 * q^21 - 48096 * q^24 - 100612 * q^25 - 17624 * q^27 - 33296 * q^28 + 109582 * q^30 - 90896 * q^31 - 21296 * q^33 + 68928 * q^34 - 28988 * q^36 + 239656 * q^37 - 15416 * q^39 + 34632 * q^40 + 150364 * q^42 - 125840 * q^43 - 242428 * q^45 + 244380 * q^46 + 305492 * q^48 - 186204 * q^49 - 21992 * q^51 - 120368 * q^52 - 777728 * q^54 - 191664 * q^55 - 255840 * q^57 + 601176 * q^58 + 970736 * q^60 + 1108360 * q^61 + 574088 * q^63 - 2533132 * q^64 + 465850 * q^66 + 617728 * q^67 + 323804 * q^69 - 238680 * q^70 - 2031648 * q^72 - 1379960 * q^73 + 2481512 * q^75 + 4678408 * q^76 - 1556840 * q^78 + 347152 * q^79 - 1086136 * q^81 - 1760328 * q^82 - 345760 * q^84 - 4097232 * q^85 - 2983056 * q^87 - 622908 * q^88 - 4093630 * q^90 + 979616 * q^91 + 2363236 * q^93 - 217752 * q^94 + 8811824 * q^96 - 3139256 * q^97 + 212960 * q^99

Introduction

L-functions

Modular forms

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