LMFDB - Embedded newform 33.7.b.a.23.20

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			23.20
Root			$15.8546i$ of defining polynomial
Character	$\chi$	$=$	33.23
Dual form			33.7.b.a.23.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+15.8546i q^{2} +(10.1117 - 25.0350i) q^{3} -187.368 q^{4} -128.653i q^{5} +(396.920 + 160.317i) q^{6} +185.193 q^{7} -1955.95i q^{8} +(-524.506 - 506.295i) q^{9} +O(q^{10})$	\(q+15.8546i q^{2} +(10.1117 - 25.0350i) q^{3} -187.368 q^{4} -128.653i q^{5} +(396.920 + 160.317i) q^{6} +185.193 q^{7} -1955.95i q^{8} +(-524.506 - 506.295i) q^{9} +2039.74 q^{10} -401.312i q^{11} +(-1894.61 + 4690.76i) q^{12} -1345.24 q^{13} +2936.16i q^{14} +(-3220.83 - 1300.90i) q^{15} +19019.2 q^{16} -3331.63i q^{17} +(8027.10 - 8315.82i) q^{18} -5146.77 q^{19} +24105.4i q^{20} +(1872.62 - 4636.32i) q^{21} +6362.63 q^{22} -1970.59i q^{23} +(-48967.2 - 19778.0i) q^{24} -926.572 q^{25} -21328.2i q^{26} +(-17978.8 + 8011.51i) q^{27} -34699.3 q^{28} -34167.5i q^{29} +(20625.3 - 51064.9i) q^{30} -1277.35 q^{31} +176361. i q^{32} +(-10046.8 - 4057.95i) q^{33} +52821.6 q^{34} -23825.6i q^{35} +(98275.6 + 94863.4i) q^{36} +28407.2 q^{37} -81599.9i q^{38} +(-13602.7 + 33678.1i) q^{39} -251638. q^{40} -41104.9i q^{41} +(73506.9 + 29689.7i) q^{42} +33139.3 q^{43} +75192.9i q^{44} +(-65136.3 + 67479.2i) q^{45} +31242.8 q^{46} +50398.2i q^{47} +(192317. - 476146. i) q^{48} -83352.5 q^{49} -14690.4i q^{50} +(-83407.4 - 33688.5i) q^{51} +252055. q^{52} +191289. i q^{53} +(-127019. - 285046. i) q^{54} -51629.9 q^{55} -362228. i q^{56} +(-52042.7 + 128850. i) q^{57} +541712. q^{58} +297868. i q^{59} +(603480. + 243747. i) q^{60} +11454.4 q^{61} -20251.8i q^{62} +(-97134.9 - 93762.4i) q^{63} -1.57890e6 q^{64} +173069. i q^{65} +(64337.2 - 159289. i) q^{66} +80004.0 q^{67} +624240. i q^{68} +(-49333.7 - 19926.0i) q^{69} +377746. q^{70} -515460. i q^{71} +(-990286. + 1.02591e6i) q^{72} +540021. q^{73} +450385. i q^{74} +(-9369.24 + 23196.8i) q^{75} +964340. q^{76} -74320.2i q^{77} +(-533953. - 215665. i) q^{78} +97148.4 q^{79} -2.44687e6i q^{80} +(18771.9 + 531109. i) q^{81} +651702. q^{82} -354258. i q^{83} +(-350870. + 868697. i) q^{84} -428623. q^{85} +525410. i q^{86} +(-855385. - 345493. i) q^{87} -784944. q^{88} -310319. i q^{89} +(-1.06985e6 - 1.03271e6i) q^{90} -249129. q^{91} +369225. i q^{92} +(-12916.2 + 31978.5i) q^{93} -799043. q^{94} +662147. i q^{95} +(4.41519e6 + 1.78331e6i) q^{96} -74273.0 q^{97} -1.32152e6i q^{98} +(-203182. + 210490. i) 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 $

$2$			15.8546i			1.98182i	0.134515	+	0.990912i	$0.457052\pi$
$2$			15.8546i			1.98182i	−0.134515	+	0.990912i	$0.542948\pi$
$3$	10.1117	−	25.0350i	0.374508	−	0.927224i
$3$	10.1117	−	25.0350i	0.374508	−	0.927224i
$4$	−187.368			−2.92762
$5$		−	128.653i		−	1.02922i	−0.857423	−	0.514612i	$-0.827936\pi$
$5$		−	128.653i		−	1.02922i	0.857423	−	0.514612i	$-0.172064\pi$
$6$	396.920	+	160.317i	1.83759	+	0.742210i
$7$	185.193			0.539922			0.269961	−	0.962871i	$-0.412989\pi$
$7$	185.193			0.539922			0.269961	+	0.962871i	$0.412989\pi$
$8$		−	1955.95i		−	3.82021i
$9$	−524.506	−	506.295i	−0.719487	−	0.694506i
$10$	2039.74			2.03974
$11$		−	401.312i		−	0.301511i
$11$		−	401.312i		−	0.301511i
$12$	−1894.61	+	4690.76i	−1.09642	+	2.71456i
$13$	−1345.24			−0.612308			−0.306154	−	0.951982i	$-0.599042\pi$
$13$	−1345.24			−0.612308			−0.306154	+	0.951982i	$0.599042\pi$
$14$			2936.16i			1.07003i
$15$	−3220.83	−	1300.90i	−0.954320	−	0.385453i
$16$	19019.2			4.64335
$17$		−	3331.63i		−	0.678125i	−0.940764	−	0.339062i	$-0.889890\pi$
$17$		−	3331.63i		−	0.678125i	0.940764	−	0.339062i	$-0.110110\pi$
$18$	8027.10	−	8315.82i	1.37639	−	1.42590i
$19$	−5146.77			−0.750368			−0.375184	−	0.926950i	$-0.622420\pi$
$19$	−5146.77			−0.750368			−0.375184	+	0.926950i	$0.622420\pi$
$20$			24105.4i			3.01318i
$21$	1872.62	−	4636.32i	0.202205	−	0.500628i
$22$	6362.63			0.597542
$23$		−	1970.59i		−	0.161962i	−0.996716	−	0.0809808i	$-0.974195\pi$
$23$		−	1970.59i		−	0.161962i	0.996716	−	0.0809808i	$-0.0258052\pi$
$24$	−48967.2	−	19778.0i	−3.54219	−	1.43070i
$25$	−926.572			−0.0593006
$26$		−	21328.2i		−	1.21349i
$27$	−17978.8	+	8011.51i	−0.913416	+	0.407027i
$28$	−34699.3			−1.58069
$29$		−	34167.5i		−	1.40094i	−0.713682	−	0.700470i	$-0.752974\pi$
$29$		−	34167.5i		−	1.40094i	0.713682	−	0.700470i	$-0.247026\pi$
$30$	20625.3	−	51064.9i	0.763899	−	1.89129i
$31$	−1277.35			−0.0428770			−0.0214385	−	0.999770i	$-0.506825\pi$
$31$	−1277.35			−0.0428770			−0.0214385	+	0.999770i	$0.506825\pi$
$32$			176361.i			5.38210i
$33$	−10046.8	−	4057.95i	−0.279568	−	0.112919i
$34$	52821.6			1.34392
$35$		−	23825.6i		−	0.555700i
$36$	98275.6	+	94863.4i	2.10639	+	2.03325i
$37$	28407.2			0.560821			0.280410	−	0.959880i	$-0.409529\pi$
$37$	28407.2			0.560821			0.280410	+	0.959880i	$0.409529\pi$
$38$		−	81599.9i		−	1.48710i
$39$	−13602.7	+	33678.1i	−0.229315	+	0.567746i
$40$	−251638.			−3.93185
$41$		−	41104.9i		−	0.596406i	−0.954502	−	0.298203i	$-0.903613\pi$
$41$		−	41104.9i		−	0.596406i	0.954502	−	0.298203i	$-0.0963873\pi$
$42$	73506.9	+	29689.7i	0.992157	+	0.400735i
$43$	33139.3			0.416810			0.208405	−	0.978043i	$-0.433173\pi$
$43$	33139.3			0.416810			0.208405	+	0.978043i	$0.433173\pi$
$44$			75192.9i			0.882712i
$45$	−65136.3	+	67479.2i	−0.714802	+	0.740513i
$46$	31242.8			0.320979
$47$			50398.2i			0.485424i	0.970098	+	0.242712i	$0.0780370\pi$
$47$			50398.2i			0.485424i	−0.970098	+	0.242712i	$0.921963\pi$
$48$	192317.	−	476146.i	1.73898	−	4.30543i
$49$	−83352.5			−0.708484
$50$		−	14690.4i		−	0.117523i
$51$	−83407.4	−	33688.5i	−0.628773	−	0.253963i
$52$	252055.			1.79261
$53$			191289.i			1.28488i	0.766337	+	0.642438i	$0.222077\pi$
$53$			191289.i			1.28488i	−0.766337	+	0.642438i	$0.777923\pi$
$54$	−127019.	−	285046.i	−0.806655	−	1.81023i
$55$	−51629.9			−0.310322
$56$		−	362228.i		−	2.06261i
$57$	−52042.7	+	128850.i	−0.281019	+	0.695758i
$58$	541712.			2.77642
$59$			297868.i			1.45033i	0.688574	+	0.725166i	$0.258237\pi$
$59$			297868.i			1.45033i	−0.688574	+	0.725166i	$0.741763\pi$
$60$	603480.	+	243747.i	2.79389	+	1.12846i
$61$	11454.4			0.0504642			0.0252321	−	0.999682i	$-0.491968\pi$
$61$	11454.4			0.0504642			0.0252321	+	0.999682i	$0.491968\pi$
$62$		−	20251.8i		−	0.0849746i
$63$	−97134.9	−	93762.4i	−0.388467	−	0.374979i
$64$	−1.57890e6			−6.02301
$65$			173069.i			0.630202i
$66$	64337.2	−	159289.i	0.223785	−	0.554055i
$67$	80004.0			0.266003			0.133002	−	0.991116i	$-0.457538\pi$
$67$	80004.0			0.266003			0.133002	+	0.991116i	$0.457538\pi$
$68$			624240.i			1.98529i
$69$	−49333.7	−	19926.0i	−0.150175	−	0.0606560i
$70$	377746.			1.10130
$71$		−	515460.i		−	1.44019i	−0.693875	−	0.720095i	$-0.744098\pi$
$71$		−	515460.i		−	1.44019i	0.693875	−	0.720095i	$-0.255902\pi$
$72$	−990286.	+	1.02591e6i	−2.65316	+	2.74859i
$73$	540021.			1.38817			0.694084	−	0.719894i	$-0.255810\pi$
$73$	540021.			1.38817			0.694084	+	0.719894i	$0.255810\pi$
$74$			450385.i			1.11145i
$75$	−9369.24	+	23196.8i	−0.0222086	+	0.0549849i
$76$	964340.			2.19679
$77$		−	74320.2i		−	0.162793i
$78$	−533953.	−	215665.i	−1.12517	−	0.454461i
$79$	97148.4			0.197040			0.0985200	−	0.995135i	$-0.468589\pi$
$79$	97148.4			0.197040			0.0985200	+	0.995135i	$0.468589\pi$
$80$		−	2.44687e6i		−	4.77905i
$81$	18771.9	+	531109.i	0.0353227	+	0.999376i
$82$	651702.			1.18197
$83$		−	354258.i		−	0.619563i	−0.950808	−	0.309781i	$-0.899744\pi$
$83$		−	354258.i		−	0.619563i	0.950808	−	0.309781i	$-0.100256\pi$
$84$	−350870.	+	868697.i	−0.591981	+	1.46565i
$85$	−428623.			−0.697942
$86$			525410.i			0.826044i
$87$	−855385.	−	345493.i	−1.29898	−	0.524664i
$88$	−784944.			−1.15184
$89$		−	310319.i		−	0.440188i	−0.975479	−	0.220094i	$-0.929364\pi$
$89$		−	310319.i		−	0.440188i	0.975479	−	0.220094i	$-0.0706365\pi$
$90$	−1.06985e6	−	1.03271e6i	−1.46757	−	1.41661i
$91$	−249129.			−0.330599
$92$			369225.i			0.474162i
$93$	−12916.2	+	31978.5i	−0.0160578	+	0.0397566i
$94$	−799043.			−0.962025
$95$			662147.i			0.772296i
$96$	4.41519e6	+	1.78331e6i	4.99041	+	2.01564i
$97$	−74273.0			−0.0813796			−0.0406898	−	0.999172i	$-0.512956\pi$
$97$	−74273.0			−0.0813796			−0.0406898	+	0.999172i	$0.512956\pi$
$98$		−	1.32152e6i		−	1.40409i
$99$	−203182.	+	210490.i	−0.209401	+	0.216933i
$100$	173610.			0.173610
$101$		−	221232.i		−	0.214726i	−0.994220	−	0.107363i	$-0.965759\pi$
$101$		−	221232.i		−	0.214726i	0.994220	−	0.107363i	$-0.0342407\pi$
$102$	534117.	−	1.32239e6i	0.503311	−	1.24612i
$103$	2.09784e6			1.91982			0.959910	−	0.280308i	$-0.0904365\pi$
$103$	2.09784e6			1.91982			0.959910	+	0.280308i	$0.0904365\pi$
$104$			2.63122e6i			2.33914i
$105$	−596476.	−	240918.i	−0.515258	−	0.208114i
$106$	−3.03280e6			−2.54640
$107$		−	2.03845e6i		−	1.66399i	−0.554786	−	0.831993i	$-0.687200\pi$
$107$		−	2.03845e6i		−	1.66399i	0.554786	−	0.831993i	$-0.312800\pi$
$108$	3.36864e6	−	1.50110e6i	2.67414	−	1.19162i
$109$	1.11566e6			0.861495			0.430748	−	0.902472i	$-0.358250\pi$
$109$	1.11566e6			0.861495			0.430748	+	0.902472i	$0.358250\pi$
$110$		−	818571.i		−	0.615004i
$111$	287246.	−	711176.i	0.210032	−	0.520006i
$112$	3.52222e6			2.50705
$113$			1.09073e6i			0.755931i	0.925820	+	0.377965i	$0.123376\pi$
$113$			1.09073e6i			0.755931i	−0.925820	+	0.377965i	$0.876624\pi$
$114$	−2.04286e6	−	825116.i	−1.37887	−	0.556930i
$115$	−253522.			−0.166695
$116$			6.40190e6i			4.10142i
$117$	705587.	+	681089.i	0.440548	+	0.425252i
$118$	−4.72257e6			−2.87430
$119$		−	616995.i		−	0.366134i
$120$	−2.54450e6	+	6.29977e6i	−1.47251	+	3.64570i
$121$	−161051.			−0.0909091
$122$			181605.i			0.100011i
$123$	−1.02906e6	−	415642.i	−0.553002	−	0.223359i
$124$	239334.			0.125528
$125$		−	1.89100e6i		−	0.968190i
$126$	1.48656e6	−	1.54003e6i	0.743142	−	0.769872i
$127$	945966.			0.461811			0.230905	−	0.972976i	$-0.425831\pi$
$127$	945966.			0.461811			0.230905	+	0.972976i	$0.425831\pi$
$128$		−	1.37457e7i		−	6.55445i
$129$	335096.	−	829644.i	0.156099	−	0.386476i
$130$	−2.74394e6			−1.24895
$131$		−	1.10072e6i		−	0.489623i	−0.969571	−	0.244812i	$-0.921274\pi$
$131$		−	1.10072e6i		−	0.489623i	0.969571	−	0.244812i	$-0.0787261\pi$
$132$	1.88246e6	+	760330.i	0.818471	+	0.330583i
$133$	−953147.			−0.405140
$134$			1.26843e6i			0.527172i
$135$	1.03070e6	+	2.31302e6i	0.418921	+	0.940109i
$136$	−6.51648e6			−2.59058
$137$			1.83112e6i			0.712124i	0.934462	+	0.356062i	$0.115881\pi$
$137$			1.83112e6i			0.712124i	−0.934462	+	0.356062i	$0.884119\pi$
$138$	315919.	−	782165.i	0.120209	−	0.297619i
$139$	4.38797e6			1.63388			0.816939	−	0.576725i	$-0.195669\pi$
$139$	4.38797e6			1.63388			0.816939	+	0.576725i	$0.195669\pi$
$140$			4.46416e6i			1.62688i
$141$	1.26172e6	+	509613.i	0.450097	+	0.181795i
$142$	8.17241e6			2.85420
$143$			539861.i			0.184618i
$144$	−9.97567e6	−	9.62931e6i	−3.34083	−	3.22484i
$145$	−4.39575e6			−1.44188
$146$			8.56181e6i			2.75110i
$147$	−842838.	+	2.08673e6i	−0.265333	+	0.656923i
$148$	−5.32261e6			−1.64187
$149$		−	2.55775e6i		−	0.773212i	−0.922245	−	0.386606i	$-0.873647\pi$
$149$		−	2.55775e6i		−	0.773212i	0.922245	−	0.386606i	$-0.126353\pi$
$150$	−367775.	−	148545.i	−0.108970	−	0.0440135i
$151$	2.51872e6			0.731559			0.365779	−	0.930702i	$-0.380802\pi$
$151$	2.51872e6			0.731559			0.365779	+	0.930702i	$0.380802\pi$
$152$			1.00668e7i			2.86656i
$153$	−1.68679e6	+	1.74746e6i	−0.470962	+	0.487902i
$154$	1.17832e6			0.322626
$155$			164335.i			0.0441300i
$156$	2.54871e6	−	6.31020e6i	0.671347	−	1.66215i
$157$	−3.97012e6			−1.02590			−0.512950	−	0.858419i	$-0.671447\pi$
$157$	−3.97012e6			−1.02590			−0.512950	+	0.858419i	$0.671447\pi$
$158$			1.54025e6i			0.390498i
$159$	4.78892e6	+	1.93426e6i	1.19137	+	0.481197i
$160$	2.26893e7			5.53938
$161$		−	364939.i		−	0.0874466i
$162$	−8.42052e6	+	297621.i	−1.98059	+	0.0700033i
$163$	2.27088e6			0.524363			0.262181	−	0.965019i	$-0.415558\pi$
$163$	2.27088e6			0.524363			0.262181	+	0.965019i	$0.415558\pi$
$164$			7.70174e6i			1.74605i
$165$	−522068.	+	1.29256e6i	−0.116218	+	0.287738i
$166$	5.61661e6			1.22786
$167$			2.93117e6i			0.629348i	0.949200	+	0.314674i	$0.101895\pi$
$167$			2.93117e6i			0.629348i	−0.949200	+	0.314674i	$0.898105\pi$
$168$	−9.06839e6	−	3.66275e6i	−1.91250	−	0.772466i
$169$	−3.01714e6			−0.625079
$170$		−	6.79565e6i		−	1.38320i
$171$	2.69951e6	+	2.60578e6i	0.539880	+	0.521135i
$172$	−6.20924e6			−1.22026
$173$		−	1.30228e6i		−	0.251515i	−0.992061	−	0.125758i	$-0.959864\pi$
$173$		−	1.30228e6i		−	0.251515i	0.992061	−	0.125758i	$-0.0401362\pi$
$174$	5.47764e6	−	1.35618e7i	1.03979	−	2.57436i
$175$	−171595.			−0.0320177
$176$		−	7.63262e6i		−	1.40002i
$177$	7.45713e6	+	3.01196e6i	1.34478	+	0.543162i
$178$	4.91998e6			0.872376
$179$		−	4.31869e6i		−	0.752996i	−0.926417	−	0.376498i	$-0.877128\pi$
$179$		−	4.31869e6i		−	0.752996i	0.926417	−	0.376498i	$-0.122872\pi$
$180$	1.22045e7	−	1.26434e7i	2.09267	−	2.16794i
$181$	−8.23223e6			−1.38829			−0.694147	−	0.719833i	$-0.744218\pi$
$181$	−8.23223e6			−1.38829			−0.694147	+	0.719833i	$0.744218\pi$
$182$		−	3.94984e6i		−	0.655188i
$183$	115824.	−	286762.i	0.0188993	−	0.0467916i
$184$	−3.85436e6			−0.618727
$185$		−	3.65467e6i		−	0.577210i
$186$	−507005.	−	204781.i	−0.0787905	−	0.0318237i
$187$	−1.33702e6			−0.204462
$188$		−	9.44300e6i		−	1.42114i
$189$	−3.32955e6	+	1.48368e6i	−0.493173	+	0.219763i
$190$	−1.04981e7			−1.53055
$191$			5.83873e6i			0.837951i	0.907998	+	0.418976i	$0.137611\pi$
$191$			5.83873e6i			0.837951i	−0.907998	+	0.418976i	$0.862389\pi$
$192$	−1.59654e7	+	3.95277e7i	−2.25567	+	5.58468i
$193$	−1.17612e7			−1.63598			−0.817991	−	0.575232i	$-0.804912\pi$
$193$	−1.17612e7			−1.63598			−0.817991	+	0.575232i	$0.804912\pi$
$194$		−	1.17757e6i		−	0.161280i
$195$	4.33279e6	+	1.75003e6i	0.584338	+	0.236016i
$196$	1.56176e7			2.07418
$197$		−	4.57928e6i		−	0.598961i	−0.954102	−	0.299480i	$-0.903187\pi$
$197$		−	4.57928e6i		−	0.598961i	0.954102	−	0.299480i	$-0.0968133\pi$
$198$	−3.33724e6	−	3.22137e6i	−0.429924	−	0.414997i
$199$	9.25354e6			1.17422			0.587109	−	0.809508i	$-0.300266\pi$
$199$	9.25354e6			1.17422			0.587109	+	0.809508i	$0.300266\pi$
$200$			1.81232e6i			0.226541i
$201$	808979.	−	2.00290e6i	0.0996205	−	0.246645i
$202$	3.50755e6			0.425549
$203$		−	6.32759e6i		−	0.756398i
$204$	1.56279e7	+	6.31214e6i	1.84081	+	0.743509i
$205$	−5.28827e6			−0.613835
$206$			3.32604e7i			3.80474i
$207$	−997698.	+	1.03358e6i	−0.112483	+	0.116529i
$208$	−2.55854e7			−2.84316
$209$			2.06546e6i			0.226244i
$210$	3.81966e6	−	9.45688e6i	0.412446	−	1.02115i
$211$	−1.12218e7			−1.19458			−0.597291	−	0.802024i	$-0.703756\pi$
$211$	−1.12218e7			−1.19458			−0.597291	+	0.802024i	$0.703756\pi$
$212$		−	3.58413e7i		−	3.76164i
$213$	−1.29046e7	−	5.21219e6i	−1.33538	−	0.539364i
$214$	3.23189e7			3.29773
$215$		−	4.26347e6i		−	0.428991i
$216$	1.56701e7	+	3.51655e7i	1.55493	+	3.48944i
$217$	−236556.			−0.0231502
$218$			1.76883e7i			1.70733i
$219$	5.46054e6	−	1.35194e7i	0.519881	−	1.28714i
$220$	9.67379e6			0.908507
$221$			4.48184e6i			0.415221i
$222$	1.12754e7	+	4.55417e6i	1.03056	+	0.416246i
$223$	−1.76329e7			−1.59005			−0.795023	−	0.606579i	$-0.792541\pi$
$223$	−1.76329e7			−1.59005			−0.795023	+	0.606579i	$0.792541\pi$
$224$			3.26608e7i			2.90591i
$225$	485992.	+	469118.i	0.0426660	+	0.0411846i
$226$	−1.72931e7			−1.49812
$227$		−	1.52434e7i		−	1.30318i	−0.758572	−	0.651590i	$-0.774102\pi$
$227$		−	1.52434e7i		−	1.30318i	0.758572	−	0.651590i	$-0.225898\pi$
$228$	9.75114e6	−	2.41423e7i	0.822718	−	2.03692i
$229$	1.71986e6			0.143214			0.0716071	−	0.997433i	$-0.477187\pi$
$229$	1.71986e6			0.143214			0.0716071	+	0.997433i	$0.477187\pi$
$230$		−	4.01948e6i		−	0.330359i
$231$	−1.86061e6	−	751506.i	−0.150945	−	0.0609672i
$232$	−6.68299e7			−5.35188
$233$			1.88276e7i			1.48843i	0.667943	+	0.744213i	$0.267175\pi$
$233$			1.88276e7i			1.48843i	−0.667943	+	0.744213i	$0.732825\pi$
$234$	−1.07984e7	+	1.11868e7i	−0.842774	+	0.873087i
$235$	6.48388e6			0.499610
$236$		−	5.58109e7i		−	4.24603i
$237$	982338.	−	2.43211e6i	0.0737931	−	0.182700i
$238$	9.78219e6			0.725614
$239$		−	1.84413e6i		−	0.135082i	−0.997717	−	0.0675409i	$-0.978485\pi$
$239$		−	1.84413e6i		−	0.135082i	0.997717	−	0.0675409i	$-0.0215153\pi$
$240$	−6.12575e7	−	2.47421e7i	−4.43125	−	1.78979i
$241$	1.68939e7			1.20692			0.603460	−	0.797393i	$-0.293788\pi$
$241$	1.68939e7			1.20692			0.603460	+	0.797393i	$0.293788\pi$
$242$		−	2.55340e6i		−	0.180166i
$243$	1.34862e7	+	4.90048e6i	0.939874	+	0.341523i
$244$	−2.14619e6			−0.147740
$245$			1.07235e7i			0.729189i
$246$	6.58983e6	−	1.63154e7i	0.442659	−	1.09595i
$247$	6.92365e6			0.459456
$248$			2.49843e6i			0.163799i
$249$	−8.86886e6	−	3.58216e6i	−0.574473	−	0.232031i
$250$	2.99810e7			1.91878
$251$		−	1.63058e7i		−	1.03115i	−0.856844	−	0.515575i	$-0.827578\pi$
$251$		−	1.63058e7i		−	1.03115i	0.856844	−	0.515575i	$-0.172422\pi$
$252$	1.82000e7	+	1.75681e7i	1.13728	+	1.09780i
$253$	−790819.			−0.0488333
$254$			1.49979e7i			0.915228i
$255$	−4.33412e6	+	1.07306e7i	−0.261385	+	0.647148i
$256$	1.16883e8			6.96675
$257$			4.56355e6i			0.268846i	0.990924	+	0.134423i	$0.0429181\pi$
$257$			4.56355e6i			0.268846i	−0.990924	+	0.134423i	$0.957082\pi$
$258$	1.31537e7	+	5.31280e6i	0.765927	+	0.309360i
$259$	5.26083e6			0.302799
$260$		−	3.24276e7i		−	1.84499i
$261$	−1.72988e7	+	1.79211e7i	−0.972961	+	1.00796i
$262$	1.74514e7			0.970346
$263$			1.01280e6i			0.0556743i	0.999612	+	0.0278371i	$0.00886198\pi$
$263$			1.01280e6i			0.0556743i	−0.999612	+	0.0278371i	$0.991138\pi$
$264$	−7.93714e6	+	1.96511e7i	−0.431372	+	1.06801i
$265$	2.46098e7			1.32243
$266$		−	1.51118e7i		−	0.802916i
$267$	−7.76885e6	−	3.13786e6i	−0.408153	−	0.164854i
$268$	−1.49902e7			−0.778758
$269$			8.62511e6i			0.443106i	0.975148	+	0.221553i	$0.0711126\pi$
$269$			8.62511e6i			0.443106i	−0.975148	+	0.221553i	$0.928887\pi$
$270$	−3.66720e7	+	1.63414e7i	−1.86313	+	0.830228i
$271$	1.74663e6			0.0877594			0.0438797	−	0.999037i	$-0.486028\pi$
$271$	1.74663e6			0.0877594			0.0438797	+	0.999037i	$0.486028\pi$
$272$		−	6.33648e7i		−	3.14877i
$273$	−2.51913e6	+	6.23696e6i	−0.123812	+	0.306539i
$274$	−2.90317e7			−1.41130
$275$			371844.i			0.0178798i
$276$	9.24355e6	+	3.73350e6i	0.439655	+	0.177578i
$277$	−3.65231e7			−1.71841			−0.859207	−	0.511627i	$-0.829043\pi$
$277$	−3.65231e7			−1.71841			−0.859207	+	0.511627i	$0.829043\pi$
$278$			6.95695e7i			3.23806i
$279$	669977.	+	646715.i	0.0308494	+	0.0297783i
$280$	−4.66017e7			−2.12289
$281$			3.91564e7i			1.76475i	0.470543	+	0.882377i	$0.344058\pi$
$281$			3.91564e7i			1.76475i	−0.470543	+	0.882377i	$0.655942\pi$
$282$	−8.07970e6	+	2.00041e7i	−0.360286	+	0.892012i
$283$	2.03435e7			0.897567			0.448784	−	0.893640i	$-0.351857\pi$
$283$	2.03435e7			0.897567			0.448784	+	0.893640i	$0.351857\pi$
$284$			9.65807e7i			4.21634i
$285$	1.65769e7	+	6.69545e6i	0.716091	+	0.289231i
$286$	−8.55927e6			−0.365880
$287$		−	7.61235e6i		−	0.322013i
$288$	8.92905e7	−	9.25022e7i	3.73790	−	3.87235i
$289$	1.30378e7			0.540147
$290$		−	6.96928e7i		−	2.85755i
$291$	−751028.	+	1.85943e6i	−0.0304774	+	0.0754571i
$292$	−1.01183e8			−4.06403
$293$		−	1.02903e7i		−	0.409094i	−0.978857	−	0.204547i	$-0.934428\pi$
$293$		−	1.02903e7i		−	0.409094i	0.978857	−	0.204547i	$-0.0655722\pi$
$294$	−3.30843e7	−	1.33628e7i	−1.30191	−	0.525844i
$295$	3.83216e7			1.49272
$296$		−	5.55631e7i		−	2.14245i
$297$	3.21511e6	+	7.21509e6i	0.122723	+	0.275405i
$298$	4.05520e7			1.53237
$299$			2.65091e6i			0.0991704i
$300$	1.75549e6	−	4.34633e6i	0.0650183	−	0.160975i
$301$	6.13718e6			0.225045
$302$			3.99333e7i			1.44982i
$303$	−5.53856e6	−	2.23704e6i	−0.199099	−	0.0804167i
$304$	−9.78874e7			−3.48422
$305$		−	1.47364e6i		−	0.0519389i
$306$	−2.77052e7	−	2.67433e7i	−0.966935	−	0.933363i
$307$	2.59469e7			0.896749			0.448375	−	0.893846i	$-0.352003\pi$
$307$	2.59469e7			0.896749			0.448375	+	0.893846i	$0.352003\pi$
$308$			1.39252e7i			0.476595i
$309$	2.12128e7	−	5.25195e7i	0.718989	−	1.78010i
$310$	−2.60546e6			−0.0874579
$311$		−	7.33036e6i		−	0.243693i	−0.992549	−	0.121847i	$-0.961118\pi$
$311$		−	7.33036e6i		−	0.243693i	0.992549	−	0.121847i	$-0.0388816\pi$
$312$	6.58727e7	+	2.66062e7i	2.16891	+	0.876029i
$313$	4.32409e7			1.41014			0.705069	−	0.709139i	$-0.250916\pi$
$313$	4.32409e7			1.41014			0.705069	+	0.709139i	$0.250916\pi$
$314$		−	6.29446e7i		−	2.03315i
$315$	−1.20628e7	+	1.24967e7i	−0.385937	+	0.399819i
$316$	−1.82025e7			−0.576859
$317$		−	3.44820e7i		−	1.08247i	−0.840872	−	0.541234i	$-0.817957\pi$
$317$		−	3.44820e7i		−	1.08247i	0.840872	−	0.541234i	$-0.182043\pi$
$318$	−3.06669e7	+	7.59263e7i	−0.953648	+	2.36108i
$319$	−1.37118e7			−0.422399
$320$			2.03130e8i			6.19903i
$321$	−5.10328e7	−	2.06123e7i	−1.54289	−	0.623177i
$322$	5.78596e6			0.173304
$323$			1.71471e7i			0.508843i
$324$	−3.51725e6	−	9.95128e7i	−0.103411	−	2.92580i
$325$	1.24646e6			0.0363102
$326$			3.60039e7i			1.03919i
$327$	1.12813e7	−	2.79306e7i	0.322637	−	0.798799i
$328$	−8.03990e7			−2.27840
$329$			9.33341e6i			0.262091i
$330$	−2.04929e7	−	8.27716e6i	−0.570246	−	0.230324i
$331$	−6.26596e6			−0.172784			−0.0863920	−	0.996261i	$-0.527534\pi$
$331$	−6.26596e6			−0.172784			−0.0863920	+	0.996261i	$0.527534\pi$
$332$			6.63766e7i			1.81385i
$333$	−1.48998e7	−	1.43824e7i	−0.403503	−	0.389493i
$334$	−4.64724e7			−1.24726
$335$		−	1.02927e7i		−	0.273777i
$336$	3.56158e7	−	8.81790e7i	0.938911	−	2.32459i
$337$	3.30030e7			0.862311			0.431155	−	0.902278i	$-0.358106\pi$
$337$	3.30030e7			0.862311			0.431155	+	0.902278i	$0.358106\pi$
$338$		−	4.78354e7i		−	1.23880i
$339$	2.73065e7	+	1.10292e7i	0.700917	+	0.283102i
$340$	8.03103e7			2.04331
$341$			512615.i			0.0129279i
$342$	−4.13136e7	+	4.27996e7i	−1.03280	+	1.06995i
$343$	−3.72241e7			−0.922448
$344$		−	6.48187e7i		−	1.59230i
$345$	−2.56354e6	+	6.34692e6i	−0.0624285	+	0.154563i
$346$	2.06470e7			0.498459
$347$			1.33343e7i			0.319141i	0.987187	+	0.159571i	$0.0510110\pi$
$347$			1.33343e7i			0.319141i	−0.987187	+	0.159571i	$0.948989\pi$
$348$	1.60272e8	+	6.47342e7i	3.80294	+	1.53602i
$349$	−4.08627e7			−0.961281			−0.480641	−	0.876918i	$-0.659596\pi$
$349$	−4.08627e7			−0.961281			−0.480641	+	0.876918i	$0.659596\pi$
$350$		−	2.72056e6i		−	0.0634534i
$351$	2.41858e7	−	1.07774e7i	0.559292	−	0.249226i
$352$	7.07756e7			1.62276
$353$		−	4.75983e7i		−	1.08210i	−0.840990	−	0.541050i	$-0.818027\pi$
$353$		−	4.75983e7i		−	1.08210i	0.840990	−	0.541050i	$-0.181973\pi$
$354$	−4.77533e7	+	1.18230e8i	−1.07645	+	2.66512i
$355$	−6.63154e7			−1.48228
$356$			5.81438e7i			1.28871i
$357$	−1.54465e7	−	6.23888e6i	−0.339488	−	0.137120i
$358$	6.84710e7			1.49231
$359$			1.43224e7i			0.309550i	0.987950	+	0.154775i	$0.0494653\pi$
$359$			1.43224e7i			0.309550i	−0.987950	+	0.154775i	$0.950535\pi$
$360$	1.31986e8	+	1.27403e8i	2.82891	+	2.73069i
$361$	−2.05566e7			−0.436949
$362$		−	1.30519e8i		−	2.75135i
$363$	−1.62850e6	+	4.03192e6i	−0.0340462	+	0.0842930i
$364$	4.66789e7			0.967868
$365$		−	6.94753e7i		−	1.42873i
$366$	4.54649e6	+	1.83634e6i	0.0927327	+	0.0374550i
$367$	9.85151e6			0.199299			0.0996494	−	0.995023i	$-0.468228\pi$
$367$	9.85151e6			0.199299			0.0996494	+	0.995023i	$0.468228\pi$
$368$		−	3.74789e7i		−	0.752045i
$369$	−2.08112e7	+	2.15598e7i	−0.414208	+	0.429107i
$370$	5.79434e7			1.14393
$371$			3.54254e7i			0.693733i
$372$	2.42008e6	−	5.99174e6i	0.0470112	−	0.116392i
$373$	−5.01962e7			−0.967262			−0.483631	−	0.875272i	$-0.660682\pi$
$373$	−5.01962e7			−0.967262			−0.483631	+	0.875272i	$0.660682\pi$
$374$		−	2.11979e7i		−	0.405208i
$375$	−4.73411e7	−	1.91212e7i	−0.897728	−	0.362595i
$376$	9.85762e7			1.85442
$377$			4.59636e7i			0.857807i
$378$	−2.35231e7	−	5.27886e7i	−0.435531	−	0.977383i
$379$	7.20877e7			1.32417			0.662085	−	0.749429i	$-0.269672\pi$
$379$	7.20877e7			1.32417			0.662085	+	0.749429i	$0.269672\pi$
$380$		−	1.24065e8i		−	2.26099i
$381$	9.56535e6	−	2.36823e7i	0.172952	−	0.428202i
$382$	−9.25707e7			−1.66067
$383$		−	3.85458e7i		−	0.686090i	−0.939319	−	0.343045i	$-0.888542\pi$
$383$		−	3.85458e7i		−	0.686090i	0.939319	−	0.343045i	$-0.111458\pi$
$384$	−3.44124e8	−	1.38993e8i	−6.07744	−	2.45470i
$385$	−9.56151e6			−0.167550
$386$		−	1.86468e8i		−	3.24223i
$387$	−1.73818e7	−	1.67783e7i	−0.299889	−	0.289477i
$388$	1.39164e7			0.238249
$389$			9.92963e7i			1.68688i	0.537223	+	0.843440i	$0.319473\pi$
$389$			9.92963e7i			1.68688i	−0.537223	+	0.843440i	$0.680527\pi$
$390$	−2.77460e7	+	6.86946e7i	−0.467742	+	1.15805i
$391$	−6.56526e6			−0.109830
$392$			1.63033e8i			2.70656i
$393$	−2.75565e7	−	1.11302e7i	−0.453990	−	0.183368i
$394$	7.26026e7			1.18703
$395$		−	1.24984e7i		−	0.202798i
$396$	3.80698e7	−	3.94391e7i	0.613049	−	0.635099i
$397$	6.44801e7			1.03051			0.515257	−	0.857036i	$-0.327696\pi$
$397$	6.44801e7			1.03051			0.515257	+	0.857036i	$0.327696\pi$
$398$			1.46711e8i			2.32709i
$399$	−9.63796e6	+	2.38621e7i	−0.151728	+	0.375655i
$400$	−1.76226e7			−0.275354
$401$			4.53947e7i			0.703999i	0.936000	+	0.351999i	$0.114498\pi$
$401$			4.53947e7i			0.703999i	−0.936000	+	0.351999i	$0.885502\pi$
$402$	3.17552e7	+	1.28260e7i	0.488806	+	0.197430i
$403$	1.71834e6			0.0262539
$404$			4.14518e7i			0.628637i
$405$	6.83288e7	−	2.41506e6i	1.02858	−	0.0363549i
$406$	1.00321e8			1.49905
$407$		−	1.14002e7i		−	0.169094i
$408$	−6.58929e7	+	1.63140e8i	−0.970193	+	2.40204i
$409$	8.79754e6			0.128585			0.0642927	−	0.997931i	$-0.479521\pi$
$409$	8.79754e6			0.128585			0.0642927	+	0.997931i	$0.479521\pi$
$410$		−	8.38433e7i		−	1.21651i
$411$	4.58422e7	+	1.85158e7i	0.660298	+	0.266696i
$412$	−3.93068e8			−5.62051
$413$			5.51631e7i			0.783066i
$414$	−1.63871e7	−	1.58181e7i	−0.230940	−	0.222922i
$415$	−4.55763e7			−0.637668
$416$		−	2.37247e8i		−	3.29550i
$417$	4.43700e7	−	1.09853e8i	0.611901	−	1.51497i
$418$	−3.27470e7			−0.448376
$419$			9.18249e7i			1.24830i	0.781305	+	0.624149i	$0.214554\pi$
$419$			9.18249e7i			1.24830i	−0.781305	+	0.624149i	$0.785446\pi$
$420$	1.11760e8	+	4.51404e7i	1.50848	+	0.609281i
$421$	−4.07931e7			−0.546689			−0.273345	−	0.961916i	$-0.588130\pi$
$421$	−4.07931e7			−0.546689			−0.273345	+	0.961916i	$0.588130\pi$
$422$		−	1.77917e8i		−	2.36745i
$423$	2.55164e7	−	2.64342e7i	0.337130	−	0.349256i
$424$	3.74150e8			4.90850
$425$			3.08699e6i			0.0402132i
$426$	8.26371e7	−	2.04596e8i	1.06892	−	2.64648i
$427$	2.12128e6			0.0272467
$428$			3.81941e8i			4.87152i
$429$	1.35154e7	+	5.45892e6i	0.171182	+	0.0691409i
$430$	6.75956e7			0.850184
$431$			6.18380e7i			0.772367i	0.922422	+	0.386183i	$0.126207\pi$
$431$			6.18380e7i			0.772367i	−0.922422	+	0.386183i	$0.873793\pi$
$432$	−3.41941e8	+	1.52372e8i	−4.24132	+	1.88997i
$433$	8.88585e7			1.09455			0.547274	−	0.836953i	$-0.315665\pi$
$433$	8.88585e7			1.09455			0.547274	+	0.836953i	$0.315665\pi$
$434$		−	3.75050e6i		−	0.0458797i
$435$	−4.44486e7	+	1.10048e8i	−0.539996	+	1.33695i
$436$	−2.09039e8			−2.52213
$437$			1.01422e7i			0.121531i
$438$	2.14345e8	+	8.65747e7i	2.55089	+	1.03031i
$439$	−9.10548e7			−1.07624			−0.538120	−	0.842868i	$-0.680865\pi$
$439$	−9.10548e7			−1.07624			−0.538120	+	0.842868i	$0.680865\pi$
$440$			1.00985e8i			1.18550i
$441$	4.37189e7	+	4.22009e7i	0.509745	+	0.492047i
$442$	−7.10577e7			−0.822895
$443$			9.28671e7i			1.06820i	0.845423	+	0.534098i	$0.179349\pi$
$443$			9.28671e7i			1.06820i	−0.845423	+	0.534098i	$0.820651\pi$
$444$	−5.38207e7	+	1.33252e8i	−0.614895	+	1.52238i
$445$	−3.99235e7			−0.453052
$446$		−	2.79563e8i		−	3.15119i
$447$	−6.40332e7	−	2.58632e7i	−0.716940	−	0.289574i
$448$	−2.92401e8			−3.25196
$449$			2.83109e7i			0.312763i	0.987697	+	0.156381i	$0.0499829\pi$
$449$			2.83109e7i			0.312763i	−0.987697	+	0.156381i	$0.950017\pi$
$450$	−7.43768e6	+	7.70521e6i	−0.0816206	+	0.0845564i
$451$	−1.64959e7			−0.179823
$452$		−	2.04368e8i		−	2.21308i
$453$	2.54686e7	−	6.30563e7i	0.273975	−	0.678319i
$454$	2.41678e8			2.58267
$455$			3.20512e7i			0.340260i
$456$	2.52023e8	+	1.01793e8i	2.65794	+	1.07355i
$457$	−3.80742e7			−0.398917			−0.199458	−	0.979906i	$-0.563918\pi$
$457$	−3.80742e7			−0.398917			−0.199458	+	0.979906i	$0.563918\pi$
$458$			2.72676e7i			0.283825i
$459$	2.66913e7	+	5.98985e7i	0.276015	+	0.619410i
$460$	4.75018e7			0.488019
$461$			2.77698e7i			0.283446i	0.989906	+	0.141723i	$0.0452642\pi$
$461$			2.77698e7i			0.283446i	−0.989906	+	0.141723i	$0.954736\pi$
$462$	1.19148e7	−	2.94992e7i	0.120826	−	0.299147i
$463$	−6.60376e7			−0.665347			−0.332674	−	0.943042i	$-0.607951\pi$
$463$	−6.60376e7			−0.665347			−0.332674	+	0.943042i	$0.607951\pi$
$464$		−	6.49838e8i		−	6.50506i
$465$	4.11412e6	+	1.66171e6i	0.0409184	+	0.0165271i
$466$	−2.98504e8			−2.94980
$467$		−	1.25595e8i		−	1.23316i	−0.787291	−	0.616581i	$-0.788517\pi$
$467$		−	1.25595e8i		−	1.23316i	0.787291	−	0.616581i	$-0.211483\pi$
$468$	−1.32204e8	−	1.27614e8i	−1.28976	−	1.24498i
$469$	1.48162e7			0.143621
$470$			1.02799e8i			0.990139i
$471$	−4.01448e7	+	9.93922e7i	−0.384208	+	0.951238i
$472$	5.82613e8			5.54057
$473$		−	1.32992e7i		−	0.125673i
$474$	3.85602e7	+	1.55746e7i	0.362079	+	0.146245i
$475$	4.76885e6			0.0444972
$476$			1.15605e8i			1.07190i
$477$	9.68485e7	−	1.00332e8i	0.892355	−	0.924452i
$478$	2.92379e7			0.267708
$479$		−	1.17909e7i		−	0.107286i	−0.998560	−	0.0536428i	$-0.982917\pi$
$479$		−	1.17909e7i		−	0.107286i	0.998560	−	0.0536428i	$-0.0170832\pi$
$480$	2.29428e8	−	5.68028e8i	2.07455	−	5.13624i
$481$	−3.82146e7			−0.343395
$482$			2.67846e8i			2.39190i
$483$	−9.13627e6	−	3.69017e6i	−0.0810825	−	0.0327495i
$484$	3.01758e7			0.266148
$485$			9.55544e6i			0.0837578i
$486$	−7.76950e7	+	2.13817e8i	−0.676838	+	1.86266i
$487$	−1.38318e8			−1.19754			−0.598772	−	0.800920i	$-0.704344\pi$
$487$	−1.38318e8			−1.19754			−0.598772	+	0.800920i	$0.704344\pi$
$488$		−	2.24042e7i		−	0.192784i
$489$	2.29625e7	−	5.68516e7i	0.196378	−	0.486202i
$490$	−1.70017e8			−1.44512
$491$		−	2.06775e8i		−	1.74684i	−0.486969	−	0.873419i	$-0.661898\pi$
$491$		−	2.06775e8i		−	1.74684i	0.486969	−	0.873419i	$-0.338102\pi$
$492$	1.92813e8	+	7.78779e7i	1.61898	+	0.653912i
$493$	−1.13833e8			−0.950012
$494$			1.09772e8i			0.910561i
$495$	2.70802e7	+	2.61400e7i	0.223273	+	0.215521i
$496$	−2.42941e7			−0.199093
$497$		−	9.54597e7i		−	0.777590i
$498$	5.67937e7	−	1.40612e8i	0.459845	−	1.13850i
$499$	−1.14110e8			−0.918378			−0.459189	−	0.888339i	$-0.651860\pi$
$499$	−1.14110e8			−0.918378			−0.459189	+	0.888339i	$0.651860\pi$
$500$			3.54312e8i			2.83449i
$501$	7.33818e7	+	2.96391e7i	0.583546	+	0.235696i
$502$	2.58522e8			2.04356
$503$		−	1.23308e8i		−	0.968920i	−0.874813	−	0.484460i	$-0.839016\pi$
$503$		−	1.23308e8i		−	0.968920i	0.874813	−	0.484460i	$-0.160984\pi$
$504$	−1.83394e8	+	1.89991e8i	−1.43250	+	1.48402i
$505$	−2.84622e7			−0.221001
$506$		−	1.25381e7i		−	0.0967789i
$507$	−3.05085e7	+	7.55341e7i	−0.234097	+	0.579588i
$508$	−1.77244e8			−1.35201
$509$		−	1.79367e7i		−	0.136016i	−0.997685	−	0.0680079i	$-0.978336\pi$
$509$		−	1.79367e7i		−	0.136016i	0.997685	−	0.0680079i	$-0.0216643\pi$
$510$	−1.70129e8	−	6.87157e7i	−1.28253	−	0.518019i
$511$	1.00008e8			0.749502
$512$			9.73402e8i			7.25241i
$513$	9.25326e7	−	4.12334e7i	0.685398	−	0.305420i
$514$	−7.23532e7			−0.532805
$515$		−	2.69893e8i		−	1.97592i
$516$	−6.27862e7	+	1.55449e8i	−0.456999	+	1.13146i
$517$	2.02254e7			0.146361
$518$			8.34083e7i			0.600095i
$519$	−3.26025e7	−	1.31683e7i	−0.233211	−	0.0941946i
$520$	3.38514e8			2.40750
$521$			1.48311e7i			0.104872i	0.998624	+	0.0524360i	$0.0166986\pi$
$521$			1.48311e7i			0.104872i	−0.998624	+	0.0524360i	$0.983301\pi$
$522$	−2.84131e8	−	2.74266e8i	−1.99759	−	1.92824i
$523$	2.24477e8			1.56916			0.784581	−	0.620027i	$-0.212878\pi$
$523$	2.24477e8			1.56916			0.784581	+	0.620027i	$0.212878\pi$
$524$			2.06239e8i			1.43343i
$525$	−1.73512e6	+	4.29588e6i	−0.0119909	+	0.0296875i
$526$	−1.60575e7			−0.110337
$527$			4.25565e6i			0.0290760i
$528$	−1.91083e8	−	7.71790e7i	−1.29814	−	0.524321i
$529$	1.44153e8			0.973768
$530$			3.90179e8i			2.62081i
$531$	1.50809e8	−	1.56233e8i	1.00726	−	1.04349i
$532$	1.78589e8			1.18610
$533$			5.52960e7i			0.365184i
$534$	4.97495e7	−	1.23172e8i	0.326712	−	0.808887i
$535$	−2.62253e8			−1.71261
$536$		−	1.56484e8i		−	1.01619i
$537$	−1.08119e8	−	4.36694e7i	−0.698196	−	0.282004i
$538$	−1.36747e8			−0.878158
$539$			3.34503e7i			0.213616i
$540$	−1.93121e8	−	4.33386e8i	−1.22644	−	2.75229i
$541$	2.83695e8			1.79168			0.895838	−	0.444380i	$-0.146576\pi$
$541$	2.83695e8			1.79168			0.895838	+	0.444380i	$0.146576\pi$
$542$			2.76921e7i			0.173924i
$543$	−8.32420e7	+	2.06094e8i	−0.519928	+	1.28726i
$544$	5.87568e8			3.64973
$545$		−	1.43533e8i		−	0.886671i
$546$	−9.88845e7	−	3.99398e7i	−0.607506	−	0.245373i
$547$	2.19148e8			1.33898			0.669492	−	0.742819i	$-0.266512\pi$
$547$	2.19148e8			1.33898			0.669492	+	0.742819i	$0.266512\pi$
$548$		−	3.43093e8i		−	2.08483i
$549$	−6.00791e6	−	5.79931e6i	−0.0363083	−	0.0350477i
$550$	−5.89543e6			−0.0354346
$551$			1.75852e8i			1.05122i
$552$	−3.89743e7	+	9.64941e7i	−0.231718	+	0.573698i
$553$	1.79912e7			0.106386
$554$		−	5.79058e8i		−	3.40559i
$555$	−9.14949e7	−	3.69551e7i	−0.535202	−	0.216170i
$556$	−8.22165e8			−4.78338
$557$			6.89999e7i			0.399285i	0.979869	+	0.199642i	$0.0639780\pi$
$557$			6.89999e7i			0.399285i	−0.979869	+	0.199642i	$0.936022\pi$
$558$	−1.02534e7	+	1.06222e7i	−0.0590154	+	0.0611381i
$559$	−4.45804e7			−0.255216
$560$		−	4.53144e8i		−	2.58031i
$561$	−1.35196e7	+	3.34723e7i	−0.0765728	+	0.189582i
$562$	−6.20809e8			−3.49743
$563$		−	2.31527e8i		−	1.29741i	−0.761041	−	0.648704i	$-0.775311\pi$
$563$		−	2.31527e8i		−	1.29741i	0.761041	−	0.648704i	$-0.224689\pi$
$564$	−2.36406e8	−	9.54851e7i	−1.31771	−	0.532229i
$565$	1.40326e8			0.778022
$566$			3.22538e8i			1.77882i
$567$	3.47643e6	+	9.83579e7i	0.0190715	+	0.539585i
$568$	−1.00821e9			−5.50183
$569$			3.34075e8i			1.81346i	0.421715	+	0.906728i	$0.361428\pi$
$569$			3.34075e8i			1.81346i	−0.421715	+	0.906728i	$0.638572\pi$
$570$	−1.06154e8	+	2.62819e8i	−0.573205	+	1.41917i
$571$	−8.53238e7			−0.458313			−0.229156	−	0.973390i	$-0.573597\pi$
$571$	−8.53238e7			−0.458313			−0.229156	+	0.973390i	$0.573597\pi$
$572$		−	1.01153e8i		−	0.540491i
$573$	1.46173e8	+	5.90397e7i	0.776968	+	0.313820i
$574$	1.20691e8			0.638173
$575$			1.82589e6i			0.00960442i
$576$	8.28141e8	+	7.99388e8i	4.33348	+	4.18302i
$577$	−1.64072e8			−0.854095			−0.427048	−	0.904229i	$-0.640446\pi$
$577$	−1.64072e8			−0.854095			−0.427048	+	0.904229i	$0.640446\pi$
$578$			2.06709e8i			1.07048i
$579$	−1.18926e8	+	2.94441e8i	−0.612689	+	1.51692i
$580$	8.23623e8			4.22128
$581$		−	6.56062e7i		−	0.334515i
$582$	−2.94804e7	−	1.19072e7i	−0.149543	−	0.0604007i
$583$	7.67663e7			0.387405
$584$		−	1.05625e9i		−	5.30309i
$585$	8.76240e7	−	9.07758e7i	0.437679	−	0.453422i
$586$	1.63148e8			0.810753
$587$		−	4.37424e7i		−	0.216266i	−0.994136	−	0.108133i	$-0.965513\pi$
$587$		−	4.37424e7i		−	0.216266i	0.994136	−	0.108133i	$-0.0344872\pi$
$588$	1.57921e8	−	3.90987e8i	0.776796	−	1.92322i
$589$	6.57422e6			0.0321735
$590$			6.07572e8i			2.95830i
$591$	−1.14642e8	−	4.63044e7i	−0.555370	−	0.224316i
$592$	5.40282e8			2.60409
$593$		−	2.29706e8i		−	1.10156i	−0.834651	−	0.550780i	$-0.814330\pi$
$593$		−	2.29706e8i		−	1.10156i	0.834651	−	0.550780i	$-0.185670\pi$
$594$	−1.14392e8	+	5.09742e7i	−0.545805	+	0.243216i
$595$	−7.93782e7			−0.376834
$596$			4.79239e8i			2.26367i
$597$	9.35693e7	−	2.31663e8i	0.439755	−	1.08876i
$598$	−4.20291e7			−0.196538
$599$			3.30491e8i			1.53773i	0.639413	+	0.768864i	$0.279177\pi$
$599$			3.30491e8i			1.53773i	−0.639413	+	0.768864i	$0.720823\pi$
$600$	4.53716e7	+	1.83257e7i	0.210054	+	0.0848414i
$601$	3.26450e8			1.50381			0.751906	−	0.659271i	$-0.229135\pi$
$601$	3.26450e8			1.50381			0.751906	+	0.659271i	$0.229135\pi$
$602$			9.73024e7i			0.445999i
$603$	−4.19626e7	−	4.05056e7i	−0.191386	−	0.184741i
$604$	−4.71928e8			−2.14173
$605$			2.07197e7i			0.0935658i
$606$	3.54674e7	−	8.78116e7i	0.159372	−	0.394579i
$607$	−6.54783e7			−0.292773			−0.146387	−	0.989227i	$-0.546764\pi$
$607$	−6.54783e7			−0.292773			−0.146387	+	0.989227i	$0.546764\pi$
$608$		−	9.07688e8i		−	4.03855i
$609$	−1.58412e8	−	6.39829e7i	−0.701350	−	0.283278i
$610$	2.33640e7			0.102934
$611$		−	6.77977e7i		−	0.297229i
$612$	3.16049e8	−	3.27417e8i	1.37880	−	1.42839i
$613$	2.91321e8			1.26471			0.632354	−	0.774680i	$-0.282089\pi$
$613$	2.91321e8			1.26471			0.632354	+	0.774680i	$0.282089\pi$
$614$			4.11378e8i			1.77720i
$615$	−5.34735e7	+	1.32392e8i	−0.229887	+	0.569163i
$616$	−1.45366e8			−0.621902
$617$			1.60188e8i			0.681986i	0.940066	+	0.340993i	$0.110763\pi$
$617$			1.60188e8i			0.681986i	−0.940066	+	0.340993i	$0.889237\pi$
$618$	8.32675e8	+	3.36320e8i	3.52785	+	1.42491i
$619$	2.89751e8			1.22167			0.610834	−	0.791758i	$-0.290834\pi$
$619$	2.89751e8			1.22167			0.610834	+	0.791758i	$0.290834\pi$
$620$		−	3.07910e7i		−	0.129196i
$621$	1.57874e7	+	3.54287e7i	0.0659227	+	0.147938i
$622$	1.16220e8			0.482957
$623$		−	5.74690e7i		−	0.237667i
$624$	−2.58712e8	+	6.40531e8i	−1.06479	+	2.63625i
$625$	−2.57760e8			−1.05578
$626$			6.85566e8i			2.79464i
$627$	5.17088e7	+	2.08854e7i	0.209779	+	0.0847304i
$628$	7.43873e8			3.00345
$629$		−	9.46423e7i		−	0.380306i
$630$	−1.98130e8	−	1.91251e8i	−0.792371	−	0.764859i
$631$	1.58941e8			0.632625			0.316313	−	0.948655i	$-0.397555\pi$
$631$	1.58941e8			0.632625			0.316313	+	0.948655i	$0.397555\pi$
$632$		−	1.90017e8i		−	0.752734i
$633$	−1.13472e8	+	2.80939e8i	−0.447381	+	1.10764i
$634$	5.46699e8			2.14526
$635$		−	1.21701e8i		−	0.475307i
$636$	−8.97289e8	−	3.62418e8i	−3.48788	−	1.40876i
$637$	1.12129e8			0.433811
$638$		−	2.17395e8i		−	0.837121i
$639$	−2.60975e8	+	2.70362e8i	−1.00022	+	1.03620i
$640$	−1.76842e9			−6.74599
$641$			1.32811e7i			0.0504266i	0.999682	+	0.0252133i	$0.00802649\pi$
$641$			1.32811e7i			0.0504266i	−0.999682	+	0.0252133i	$0.991974\pi$
$642$	3.26799e8	−	8.09104e8i	1.23503	−	3.05773i
$643$	−1.13651e8			−0.427505			−0.213752	−	0.976888i	$-0.568569\pi$
$643$	−1.13651e8			−0.427505			−0.213752	+	0.976888i	$0.568569\pi$
$644$			6.83779e7i			0.256011i
$645$	−1.06736e8	−	4.31110e7i	−0.397770	−	0.160661i
$646$	−2.71860e8			−1.00844
$647$		−	3.63017e8i		−	1.34034i	−0.742209	−	0.670168i	$-0.766222\pi$
$647$		−	3.63017e8i		−	1.34034i	0.742209	−	0.670168i	$-0.233778\pi$
$648$	1.03882e9	−	3.67169e7i	3.81782	−	0.134940i
$649$	1.19538e8			0.437292
$650$			1.97621e7i			0.0719604i
$651$	−2.39199e6	+	5.92220e6i	−0.00866996	+	0.0214654i
$652$	−4.25491e8			−1.53514
$653$			4.69750e8i			1.68705i	0.537093	+	0.843523i	$0.319522\pi$
$653$			4.69750e8i			1.68705i	−0.537093	+	0.843523i	$0.680478\pi$
$654$	4.42828e8	+	1.78860e8i	1.58308	+	0.639410i
$655$	−1.41610e8			−0.503932
$656$		−	7.81782e8i		−	2.76933i
$657$	−2.83244e8	−	2.73410e8i	−0.998768	−	0.964091i
$658$	−1.47977e8			−0.519418
$659$		−	4.11301e7i		−	0.143716i	−0.997415	−	0.0718578i	$-0.977107\pi$
$659$		−	4.11301e7i		−	0.143716i	0.997415	−	0.0718578i	$-0.0228928\pi$
$660$	9.78187e7	−	2.42184e8i	0.340244	−	0.842389i
$661$	−4.86133e8			−1.68326			−0.841629	−	0.540056i	$-0.818403\pi$
$661$	−4.86133e8			−1.68326			−0.841629	+	0.540056i	$0.818403\pi$
$662$		−	9.93442e7i		−	0.342427i
$663$	1.12203e8	+	4.53191e7i	0.385003	+	0.155504i
$664$	−6.92910e8			−2.36686
$665$			1.22625e8i			0.416979i
$666$	2.28028e8	−	2.36230e8i	0.771907	−	0.799672i
$667$	−6.73301e7			−0.226898
$668$		−	5.49206e8i		−	1.84249i
$669$	−1.78299e8	+	4.41441e8i	−0.595486	+	1.47433i
$670$	1.63187e8			0.542577
$671$		−	4.59679e6i		−	0.0152155i
$672$	8.17664e8	+	3.30257e8i	2.69443	+	1.08829i
$673$	1.70921e8			0.560725			0.280363	−	0.959894i	$-0.409545\pi$
$673$	1.70921e8			0.560725			0.280363	+	0.959894i	$0.409545\pi$
$674$			5.23249e8i			1.70895i
$675$	1.66586e7	−	7.42323e6i	0.0541661	−	0.0241369i
$676$	5.65314e8			1.83000
$677$		−	1.65301e8i		−	0.532734i	−0.963872	−	0.266367i	$-0.914177\pi$
$677$		−	1.65301e8i		−	0.532734i	0.963872	−	0.266367i	$-0.0858233\pi$
$678$	−1.74863e8	+	4.32933e8i	−0.561059	+	1.38909i
$679$	−1.37549e7			−0.0439387
$680$			8.38365e8i			2.66628i
$681$	−3.81619e8	−	1.54137e8i	−1.20834	−	0.488052i
$682$	−8.12730e6			−0.0256208
$683$			5.29470e7i			0.166180i	0.996542	+	0.0830901i	$0.0264789\pi$
$683$			5.29470e7i			0.166180i	−0.996542	+	0.0830901i	$0.973521\pi$
$684$	−5.05802e8	−	4.88240e8i	−1.58056	−	1.52569i
$685$	2.35579e8			0.732935
$686$		−	5.90173e8i		−	1.82813i
$687$	1.73907e7	−	4.30567e7i	0.0536349	−	0.132791i
$688$	6.30283e8			1.93540
$689$		−	2.57329e8i		−	0.786740i
$690$	−1.00628e8	−	4.06439e7i	−0.306317	−	0.123722i
$691$	3.86846e8			1.17248			0.586238	−	0.810139i	$-0.300608\pi$
$691$	3.86846e8			1.17248			0.586238	+	0.810139i	$0.300608\pi$
$692$			2.44005e8i			0.736342i
$693$	−3.76279e7	+	3.89814e7i	−0.113060	+	0.117127i
$694$	−2.11410e8			−0.632482
$695$		−	5.64525e8i		−	1.68162i
$696$	−6.75765e8	+	1.67309e9i	−2.00433	+	4.96239i
$697$	−1.36946e8			−0.404438
$698$		−	6.47861e8i		−	1.90509i
$699$	4.71349e8	+	1.90379e8i	1.38010	+	0.557428i
$700$	3.21514e7			0.0937357
$701$			4.44973e8i			1.29175i	0.763442	+	0.645877i	$0.223508\pi$
$701$			4.44973e8i			1.29175i	−0.763442	+	0.645877i	$0.776492\pi$
$702$	1.70871e8	+	3.83455e8i	0.493921	+	1.10842i
$703$	−1.46206e8			−0.420822
$704$			6.33630e8i			1.81601i
$705$	6.55632e7	−	1.62324e8i	0.187108	−	0.463250i
$706$	7.54652e8			2.14453
$707$		−	4.09707e7i		−	0.115935i
$708$	−1.39723e9	−	5.64344e8i	−3.93702	−	1.59017i
$709$	−3.83387e8			−1.07572			−0.537860	−	0.843034i	$-0.680767\pi$
$709$	−3.83387e8			−1.07572			−0.537860	+	0.843034i	$0.680767\pi$
$710$		−	1.05140e9i		−	2.93761i
$711$	−5.09549e7	−	4.91857e7i	−0.141768	−	0.136845i
$712$	−6.06968e8			−1.68161
$713$			2.51713e6i			0.00694443i
$714$	9.89149e7	−	2.44898e8i	0.271748	−	0.672806i
$715$	6.94547e7			0.190013
$716$			8.09184e8i			2.20449i
$717$	−4.61678e7	−	1.86473e7i	−0.125251	−	0.0505893i
$718$	−2.27075e8			−0.613474
$719$			6.93991e8i			1.86710i	0.358451	+	0.933548i	$0.383305\pi$
$719$			6.93991e8i			1.86710i	−0.358451	+	0.933548i	$0.616695\pi$
$720$	−1.23884e9	+	1.28340e9i	−3.31908	+	3.43846i
$721$	3.88506e8			1.03655
$722$		−	3.25917e8i		−	0.865955i
$723$	1.70827e8	−	4.22939e8i	0.452002	−	1.11909i
$724$	1.54245e9			4.06440
$725$			3.16587e7i			0.0830766i
$726$	−6.39244e7	−	2.58193e7i	−0.167054	−	0.0674736i
$727$	−5.61057e8			−1.46017			−0.730085	−	0.683356i	$-0.760520\pi$
$727$	−5.61057e8			−1.46017			−0.730085	+	0.683356i	$0.760520\pi$
$728$			4.87284e8i			1.26296i
$729$	2.59052e8	−	2.88074e8i	0.668658	−	0.743570i
$730$	1.10150e9			2.83150
$731$		−	1.10408e8i		−	0.282649i
$732$	−2.17017e7	+	5.37299e7i	−0.0553300	+	0.136988i
$733$	−5.79420e8			−1.47123			−0.735616	−	0.677398i	$-0.763107\pi$
$733$	−5.79420e8			−1.47123			−0.735616	+	0.677398i	$0.763107\pi$
$734$			1.56192e8i			0.394975i
$735$	2.68464e8	+	1.08433e8i	0.676121	+	0.273087i
$736$	3.47534e8			0.871693
$737$		−	3.21065e7i		−	0.0802030i
$738$	−3.41821e8	−	3.29953e8i	−0.850413	−	0.820887i
$739$	−1.31471e8			−0.325759			−0.162879	−	0.986646i	$-0.552078\pi$
$739$	−1.31471e8			−0.325759			−0.162879	+	0.986646i	$0.552078\pi$
$740$			6.84769e8i			1.68985i
$741$	7.00100e7	−	1.73334e8i	0.172070	−	0.426018i
$742$	−5.61654e8			−1.37486
$743$		−	2.64972e8i		−	0.646003i	−0.946399	−	0.323001i	$-0.895308\pi$
$743$		−	2.64972e8i		−	0.646003i	0.946399	−	0.323001i	$-0.104692\pi$
$744$	6.25482e7	+	2.52634e7i	0.151878	+	0.0613441i
$745$	−3.29061e8			−0.795808
$746$		−	7.95840e8i		−	1.91694i
$747$	−1.79359e8	+	1.85810e8i	−0.430290	+	0.445767i
$748$	2.50515e8			0.598588
$749$		−	3.77508e8i		−	0.898423i
$750$	3.03159e8	−	7.50574e8i	0.718600	−	1.77914i
$751$	3.40897e8			0.804828			0.402414	−	0.915458i	$-0.368171\pi$
$751$	3.40897e8			0.804828			0.402414	+	0.915458i	$0.368171\pi$
$752$			9.58532e8i			2.25400i
$753$	−4.08217e8	−	1.64880e8i	−0.956107	−	0.386174i
$754$	−7.28733e8			−1.70002
$755$		−	3.24041e8i		−	0.752938i
$756$	6.23850e8	−	2.77993e8i	1.44383	−	0.643382i
$757$	−4.88346e8			−1.12574			−0.562872	−	0.826544i	$-0.690304\pi$
$757$	−4.88346e8			−1.12574			−0.562872	+	0.826544i	$0.690304\pi$
$758$			1.14292e9i			2.62427i
$759$	−7.99655e6	+	1.97982e7i	−0.0182885	+	0.0452793i
$760$	1.29512e9			2.95033
$761$		−	1.56828e8i		−	0.355852i	−0.984044	−	0.177926i	$-0.943061\pi$
$761$		−	1.56828e8i		−	0.355852i	0.984044	−	0.177926i	$-0.0569387\pi$
$762$	3.75473e8	+	1.51655e8i	0.848621	+	0.342761i
$763$	2.06613e8			0.465140
$764$		−	1.09399e9i		−	2.45320i
$765$	2.24816e8	+	2.17010e8i	0.502160	+	0.484725i
$766$	6.11128e8			1.35971
$767$		−	4.00704e8i		−	0.888050i
$768$	1.18189e9	−	2.92616e9i	2.60911	−	6.45973i
$769$	−2.03685e8			−0.447898			−0.223949	−	0.974601i	$-0.571895\pi$
$769$	−2.03685e8			−0.447898			−0.223949	+	0.974601i	$0.571895\pi$
$770$		−	1.51594e8i		−	0.332054i
$771$	1.14249e8	+	4.61454e7i	0.249280	+	0.100685i
$772$	2.20366e9			4.78954
$773$			1.83062e8i			0.396332i	0.980168	+	0.198166i	$0.0634985\pi$
$773$			1.83062e8i			0.396332i	−0.980168	+	0.198166i	$0.936501\pi$
$774$	2.66013e8	−	2.75581e8i	0.573693	−	0.594328i
$775$	1.18356e6			0.00254263
$776$			1.45274e8i			0.310887i
$777$	5.31961e7	−	1.31705e8i	0.113401	−	0.280763i
$778$	−1.57430e9			−3.34310
$779$			2.11558e8i			0.447524i
$780$	−8.11826e8	−	3.27899e8i	−1.71072	−	0.690965i
$781$	−2.06860e8			−0.434234
$782$		−	1.04089e8i		−	0.217664i
$783$	2.73733e8	+	6.14290e8i	0.570220	+	1.27964i
$784$	−1.58530e9			−3.28974
$785$			5.10768e8i			1.05588i
$786$	1.76464e8	−	4.36897e8i	0.363403	−	0.899728i
$787$	2.05821e8			0.422247			0.211123	−	0.977459i	$-0.432288\pi$
$787$	2.05821e8			0.422247			0.211123	+	0.977459i	$0.432288\pi$
$788$			8.58010e8i			1.75353i
$789$	2.53554e7	+	1.02411e7i	0.0516225	+	0.0208505i
$790$	1.98157e8			0.401910
$791$			2.01996e8i			0.408144i
$792$	4.11708e8	+	3.97413e8i	0.828731	+	0.799957i
$793$	−1.54090e7			−0.0308996
$794$			1.02230e9i			2.04230i
$795$	2.48848e8	−	6.16108e8i	0.495259	−	1.22618i
$796$	−1.73382e9			−3.43767
$797$			5.46988e8i			1.08045i	0.841522	+	0.540223i	$0.181660\pi$
$797$			5.46988e8i			1.08045i	−0.841522	+	0.540223i	$0.818340\pi$
$798$	−3.78323e8	−	1.52806e8i	−0.744482	−	0.300699i
$799$	1.67908e8			0.329178
$800$		−	1.63411e8i		−	0.319162i
$801$	−1.57113e8	+	1.62764e8i	−0.305713	+	0.316710i
$802$	−7.19714e8			−1.39520
$803$		−	2.16717e8i		−	0.418548i
$804$	−1.51577e8	+	3.75280e8i	−0.291651	+	0.722082i
$805$	−4.69505e7			−0.0900021
$806$			2.72436e7i			0.0520307i
$807$	2.15930e8	+	8.72147e7i	0.410858	+	0.165947i
$808$	−4.32719e8			−0.820298
$809$		−	1.05172e8i		−	0.198634i	−0.995056	−	0.0993171i	$-0.968334\pi$
$809$		−	1.05172e8i		−	0.198634i	0.995056	−	0.0993171i	$-0.0316658\pi$
$810$	3.82898e7	+	1.08332e9i	0.0720490	+	2.03847i
$811$	4.53936e8			0.851005			0.425503	−	0.904957i	$-0.360097\pi$
$811$	4.53936e8			0.851005			0.425503	+	0.904957i	$0.360097\pi$
$812$			1.18559e9i			2.21445i
$813$	1.76615e7	−	4.37270e7i	0.0328666	−	0.0813726i
$814$	1.80745e8			0.335114
$815$		−	2.92156e8i		−	0.539686i
$816$	−1.58634e9	−	6.40728e8i	−2.91962	−	1.17924i
$817$	−1.70560e8			−0.312761
$818$			1.39481e8i			0.254833i
$819$	1.30670e8	+	1.26133e8i	0.237861	+	0.229603i
$820$	9.90852e8			1.79708
$821$		−	2.93586e8i		−	0.530526i	−0.964176	−	0.265263i	$-0.914541\pi$
$821$		−	2.93586e8i		−	0.530526i	0.964176	−	0.265263i	$-0.0854588\pi$
$822$	−2.93560e8	+	7.26809e8i	−0.528545	+	1.30859i
$823$	−5.30156e8			−0.951051			−0.475526	−	0.879702i	$-0.657742\pi$
$823$	−5.30156e8			−0.951051			−0.475526	+	0.879702i	$0.657742\pi$
$824$		−	4.10326e9i		−	7.33411i
$825$	9.30913e6	+	3.75998e6i	0.0165786	+	0.00669614i
$826$	−8.74588e8			−1.55190
$827$			7.00285e7i			0.123811i	0.998082	+	0.0619053i	$0.0197177\pi$
$827$			7.00285e7i			0.123811i	−0.998082	+	0.0619053i	$0.980282\pi$
$828$	1.86937e8	−	1.93660e8i	0.329309	−	0.341154i
$829$	5.36209e8			0.941175			0.470587	−	0.882353i	$-0.344042\pi$
$829$	5.36209e8			0.941175			0.470587	+	0.882353i	$0.344042\pi$
$830$		−	7.22593e8i		−	1.26375i
$831$	−3.69311e8	+	9.14356e8i	−0.643561	+	1.59335i
$832$	2.12400e9			3.68794
$833$			2.77699e8i			0.480441i
$834$	1.74167e9	+	7.03468e8i	3.00240	+	1.21268i
$835$	3.77103e8			0.647740
$836$		−	3.87001e8i		−	0.662358i
$837$	2.29652e7	−	1.02335e7i	0.0391646	−	0.0174521i
$838$	−1.45585e9			−2.47391
$839$			3.00251e8i			0.508392i	0.967153	+	0.254196i	$0.0818108\pi$
$839$			3.00251e8i			0.508392i	−0.967153	+	0.254196i	$0.918189\pi$
$840$	−4.71224e8	+	1.16668e9i	−0.795040	+	1.96839i
$841$	−5.72597e8			−0.962633
$842$		−	6.46758e8i		−	1.08344i
$843$	9.80283e8	+	3.95939e8i	1.63632	+	0.660916i
$844$	2.10261e9			3.49729
$845$			3.88163e8i			0.643346i
$846$	4.19103e8	+	4.04551e8i	0.692164	+	0.668132i
$847$	−2.98256e7			−0.0490838
$848$			3.63815e9i			5.96614i
$849$	2.05708e8	−	5.09301e8i	0.336146	−	0.832245i
$850$	−4.89430e7			−0.0796954
$851$		−	5.59789e7i		−	0.0908314i
$852$	2.41790e9	+	9.76597e8i	3.90949	+	1.57905i
$853$	8.66835e8			1.39666			0.698328	−	0.715778i	$-0.253928\pi$
$853$	8.66835e8			1.39666			0.698328	+	0.715778i	$0.253928\pi$
$854$			3.36320e7i			0.0539982i
$855$	3.35242e8	−	3.47300e8i	0.536364	−	0.555657i
$856$	−3.98711e9			−6.35677
$857$		−	6.92610e8i		−	1.10039i	−0.835036	−	0.550195i	$-0.814554\pi$
$857$		−	6.92610e8i		−	1.10039i	0.835036	−	0.550195i	$-0.185446\pi$
$858$	−8.65490e7	+	2.14282e8i	−0.137025	+	0.339252i
$859$	8.37000e7			0.132052			0.0660262	−	0.997818i	$-0.478968\pi$
$859$	8.37000e7			0.132052			0.0660262	+	0.997818i	$0.478968\pi$
$860$			7.98837e8i			1.25592i
$861$	−1.90576e8	−	7.69741e7i	−0.298578	−	0.120597i
$862$	−9.80416e8			−1.53069
$863$			1.12003e9i			1.74260i	0.490749	+	0.871301i	$0.336723\pi$
$863$			1.12003e9i			1.74260i	−0.490749	+	0.871301i	$0.663277\pi$
$864$	−1.41291e9	−	3.17075e9i	−2.19066	−	4.91610i
$865$	−1.67542e8			−0.258865
$866$			1.40881e9i			2.16920i
$867$	1.31835e8	−	3.26403e8i	0.202290	−	0.500837i
$868$	4.43231e7			0.0677752
$869$		−	3.89868e7i		−	0.0594098i
$870$	−1.74476e9	−	7.04715e8i	−2.64959	−	1.07018i
$871$	−1.07625e8			−0.162876
$872$		−	2.18217e9i		−	3.29109i
$873$	3.89566e7	+	3.76040e7i	0.0585516	+	0.0565187i
$874$	−1.60800e8			−0.240852
$875$		−	3.50200e8i		−	0.522747i
$876$	−1.02313e9	+	2.53311e9i	−1.52201	+	3.76827i
$877$	−3.43690e8			−0.509527			−0.254764	−	0.967003i	$-0.581998\pi$
$877$	−3.43690e8			−0.509527			−0.254764	+	0.967003i	$0.581998\pi$
$878$		−	1.44364e9i		−	2.13292i
$879$	−2.57617e8	−	1.04052e8i	−0.379322	−	0.153209i
$880$	−9.81958e8			−1.44094
$881$			1.05473e9i			1.54245i	0.636561	+	0.771226i	$0.280356\pi$
$881$			1.05473e9i			1.54245i	−0.636561	+	0.771226i	$0.719644\pi$
$882$	−6.69078e8	+	6.93144e8i	−0.975149	+	1.01022i
$883$	2.92243e8			0.424484			0.212242	−	0.977217i	$-0.431923\pi$
$883$	2.92243e8			0.424484			0.212242	+	0.977217i	$0.431923\pi$
$884$		−	8.39753e8i		−	1.21561i
$885$	3.87497e8	−	9.59381e8i	0.559035	−	1.38408i
$886$	−1.47237e9			−2.11697
$887$		−	6.77345e8i		−	0.970597i	−0.874349	−	0.485298i	$-0.838711\pi$
$887$		−	6.77345e8i		−	0.970597i	0.874349	−	0.485298i	$-0.161289\pi$
$888$	−1.39102e9	−	5.61839e8i	−1.98653	−	0.802366i
$889$	1.75186e8			0.249342
$890$		−	6.32970e8i		−	0.897869i
$891$	2.13140e8	−	7.53339e6i	0.301323	−	0.0106502i
$892$	3.30384e9			4.65506
$893$		−	2.59388e8i		−	0.364247i
$894$	4.10051e8	−	1.01522e9i	0.573885	−	1.42085i
$895$	−5.55612e8			−0.775002
$896$		−	2.54561e9i		−	3.53889i
$897$	6.63657e7	+	2.68053e7i	0.0919531	+	0.0371401i
$898$	−4.48858e8			−0.619841
$899$			4.36439e7i			0.0600681i
$900$	−9.10593e7	−	8.78977e7i	−0.124910	−	0.120573i
$901$	6.37302e8			0.871307
$902$		−	2.61535e8i		−	0.356378i
$903$	6.20575e7	−	1.53644e8i	0.0842812	−	0.208667i
$904$	2.13341e9			2.88781
$905$			1.05910e9i			1.42886i
$906$	9.99731e8	+	4.03795e8i	1.34431	+	0.542970i
$907$	1.05336e9			1.41174			0.705870	−	0.708341i	$-0.250556\pi$
$907$	1.05336e9			1.41174			0.705870	+	0.708341i	$0.250556\pi$
$908$			2.85612e9i			3.81522i
$909$	−1.12009e8	+	1.16038e8i	−0.149129	+	0.154493i
$910$	−5.08159e8			−0.674335
$911$		−	1.25004e9i		−	1.65337i	−0.562665	−	0.826685i	$-0.690224\pi$
$911$		−	1.25004e9i		−	1.65337i	0.562665	−	0.826685i	$-0.309776\pi$
$912$	−9.89810e8	+	2.45061e9i	−1.30487	+	3.23065i
$913$	−1.42168e8			−0.186805
$914$		−	6.03650e8i		−	0.790582i
$915$	−3.68927e7	−	1.49011e7i	−0.0481590	−	0.0194516i
$916$	−3.22246e8			−0.419277
$917$		−	2.03845e8i		−	0.264358i
$918$	−9.49667e8	+	4.23180e8i	−1.22756	+	0.547013i
$919$	−2.81054e8			−0.362112			−0.181056	−	0.983473i	$-0.557952\pi$
$919$	−2.81054e8			−0.362112			−0.181056	+	0.983473i	$0.557952\pi$
$920$			4.95875e8i			0.636808i
$921$	2.62368e8	−	6.49583e8i	0.335840	−	0.831487i
$922$	−4.40278e8			−0.561739
$923$			6.93418e8i			0.881840i
$924$	3.48618e8	+	1.40808e8i	0.441910	+	0.178489i
$925$	−2.63213e7			−0.0332570
$926$		−	1.04700e9i		−	1.31860i
$927$	−1.10033e9	−	1.06213e9i	−1.38129	−	1.33333i
$928$	6.02581e9			7.54000
$929$			1.06474e9i			1.32799i	0.747735	+	0.663997i	$0.231141\pi$
$929$			1.06474e9i			1.32799i	−0.747735	+	0.663997i	$0.768859\pi$
$930$	−2.63457e7	+	6.52277e7i	−0.0327537	+	0.0810930i
$931$	4.28996e8			0.531624
$932$		−	3.52769e9i		−	4.35755i
$933$	−1.83516e8	−	7.41226e7i	−0.225958	−	0.0912653i
$934$	1.99125e9			2.44391
$935$			1.72012e8i			0.210437i
$936$	1.33217e9	−	1.38009e9i	1.62455	−	1.68298i
$937$	−1.46662e8			−0.178279			−0.0891394	−	0.996019i	$-0.528412\pi$
$937$	−1.46662e8			−0.178279			−0.0891394	+	0.996019i	$0.528412\pi$
$938$			2.34905e8i			0.284632i
$939$	4.37240e8	−	1.08254e9i	0.528108	−	1.30751i
$940$	−1.21487e9			−1.46267
$941$		−	2.60104e8i		−	0.312160i	−0.987744	−	0.156080i	$-0.950114\pi$
$941$		−	2.60104e8i		−	0.312160i	0.987744	−	0.156080i	$-0.0498858\pi$
$942$	−1.57582e9	−	6.36479e8i	−1.88519	−	0.761433i
$943$	−8.10008e7			−0.0965949
$944$			5.66520e9i			6.73441i
$945$	1.90879e8	+	4.28356e8i	0.226185	+	0.507586i
$946$	2.10853e8			0.249062
$947$		−	6.06936e8i		−	0.714649i	−0.933980	−	0.357324i	$-0.883689\pi$
$947$		−	6.06936e8i		−	0.714649i	0.933980	−	0.357324i	$-0.116311\pi$
$948$	−1.84059e8	+	4.55700e8i	−0.216039	+	0.534877i
$949$	−7.26458e8			−0.849986
$950$			7.56082e7i			0.0881856i
$951$	−8.63259e8	−	3.48673e8i	−1.00369	−	0.405394i
$952$	−1.20681e9			−1.39871
$953$			6.25077e8i			0.722196i	0.932528	+	0.361098i	$0.117598\pi$
$953$			6.25077e8i			0.722196i	−0.932528	+	0.361098i	$0.882402\pi$
$954$	1.59072e9	+	1.53549e9i	1.83210	+	1.76849i
$955$	7.51170e8			0.862439
$956$			3.45530e8i			0.395469i
$957$	−1.38650e8	+	3.43276e8i	−0.158192	+	0.391659i
$958$	1.86940e8			0.212621
$959$			3.39111e8i			0.384491i
$960$	5.08536e9	+	2.05399e9i	5.74788	+	2.32159i
$961$	−8.85872e8			−0.998162
$962$		−	6.05876e8i		−	0.680548i
$963$	−1.03206e9	+	1.06918e9i	−1.15565	+	1.19722i
$964$	−3.16537e9			−3.53341
$965$			1.51311e9i			1.68379i
$966$	5.85061e7	−	1.44852e8i	0.0649037	−	0.160691i
$967$	−1.59781e9			−1.76704			−0.883521	−	0.468392i	$-0.844833\pi$
$967$	−1.59781e9			−1.76704			−0.883521	+	0.468392i	$0.844833\pi$
$968$			3.15007e8i			0.347292i
$969$	4.29279e8	+	1.73387e8i	0.471811	+	0.190566i
$970$	−1.51498e8			−0.165993
$971$			3.10777e8i			0.339462i	0.985490	+	0.169731i	$0.0542899\pi$
$971$			3.10777e8i			0.339462i	−0.985490	+	0.169731i	$0.945710\pi$
$972$	−2.52687e9	−	9.18192e8i	−2.75160	−	0.999850i
$973$	8.12623e8			0.882166
$974$		−	2.19297e9i		−	2.37332i
$975$	1.26039e7	−	3.12052e7i	0.0135985	−	0.0336677i
$976$	2.17854e8			0.234323
$977$		−	4.68001e8i		−	0.501838i	−0.968008	−	0.250919i	$-0.919267\pi$
$977$		−	4.68001e8i		−	0.501838i	0.968008	−	0.250919i	$-0.0807327\pi$
$978$	9.01359e8	+	3.64062e8i	0.963566	+	0.389187i
$979$	−1.24535e8			−0.132722
$980$		−	2.00925e9i		−	2.13479i
$981$	−5.85171e8	−	5.64854e8i	−0.619834	−	0.598314i
$982$	3.27833e9			3.46192
$983$		−	9.25224e8i		−	0.974061i	−0.873385	−	0.487031i	$-0.838080\pi$
$983$		−	9.25224e8i		−	0.974061i	0.873385	−	0.487031i	$-0.161920\pi$
$984$	−8.12973e8	+	2.01279e9i	−0.853279	+	2.11258i
$985$	−5.89137e8			−0.616464
$986$		−	1.80478e9i		−	1.88276i
$987$	2.33662e8	+	9.43769e7i	0.243017	+	0.0981554i
$988$	−1.29727e9			−1.34511
$989$		−	6.53039e7i		−	0.0675072i
$990$	−4.14438e8	+	4.29345e8i	−0.427124	+	0.442488i
$991$	7.58329e8			0.779178			0.389589	−	0.920989i	$-0.372617\pi$
$991$	7.58329e8			0.779178			0.389589	+	0.920989i	$0.372617\pi$
$992$		−	2.25274e8i		−	0.230768i
$993$	−6.33597e7	+	1.56868e8i	−0.0647091	+	0.160209i
$994$	1.51347e9			1.54105
$995$		−	1.19050e9i		−	1.20853i
$996$	1.66174e9	+	6.71182e8i	1.68184	+	0.679301i
$997$	−1.02173e9			−1.03098			−0.515490	−	0.856896i	$-0.672390\pi$
$997$	−1.02173e9			−1.03098			−0.515490	+	0.856896i	$0.672390\pi$
$998$		−	1.80916e9i		−	1.82006i
$999$	−5.10727e8	+	2.27585e8i	−0.512263	+	0.228269i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.7.b.a.23.20	yes	20
3.2	odd	2	inner	33.7.b.a.23.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.7.b.a.23.1	✓	20	3.2	odd	2	inner
33.7.b.a.23.20	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)

\(f(q)\)	\(=\)	\(q+15.8546i q^{2} +(10.1117 - 25.0350i) q^{3} -187.368 q^{4} -128.653i q^{5} +(396.920 + 160.317i) q^{6} +185.193 q^{7} -1955.95i q^{8} +(-524.506 - 506.295i) q^{9} +O(q^{10})\)	\(q+15.8546i q^{2} +(10.1117 - 25.0350i) q^{3} -187.368 q^{4} -128.653i q^{5} +(396.920 + 160.317i) q^{6} +185.193 q^{7} -1955.95i q^{8} +(-524.506 - 506.295i) q^{9} +2039.74 q^{10} -401.312i q^{11} +(-1894.61 + 4690.76i) q^{12} -1345.24 q^{13} +2936.16i q^{14} +(-3220.83 - 1300.90i) q^{15} +19019.2 q^{16} -3331.63i q^{17} +(8027.10 - 8315.82i) q^{18} -5146.77 q^{19} +24105.4i q^{20} +(1872.62 - 4636.32i) q^{21} +6362.63 q^{22} -1970.59i q^{23} +(-48967.2 - 19778.0i) q^{24} -926.572 q^{25} -21328.2i q^{26} +(-17978.8 + 8011.51i) q^{27} -34699.3 q^{28} -34167.5i q^{29} +(20625.3 - 51064.9i) q^{30} -1277.35 q^{31} +176361. i q^{32} +(-10046.8 - 4057.95i) q^{33} +52821.6 q^{34} -23825.6i q^{35} +(98275.6 + 94863.4i) q^{36} +28407.2 q^{37} -81599.9i q^{38} +(-13602.7 + 33678.1i) q^{39} -251638. q^{40} -41104.9i q^{41} +(73506.9 + 29689.7i) q^{42} +33139.3 q^{43} +75192.9i q^{44} +(-65136.3 + 67479.2i) q^{45} +31242.8 q^{46} +50398.2i q^{47} +(192317. - 476146. i) q^{48} -83352.5 q^{49} -14690.4i q^{50} +(-83407.4 - 33688.5i) q^{51} +252055. q^{52} +191289. i q^{53} +(-127019. - 285046. i) q^{54} -51629.9 q^{55} -362228. i q^{56} +(-52042.7 + 128850. i) q^{57} +541712. q^{58} +297868. i q^{59} +(603480. + 243747. i) q^{60} +11454.4 q^{61} -20251.8i q^{62} +(-97134.9 - 93762.4i) q^{63} -1.57890e6 q^{64} +173069. i q^{65} +(64337.2 - 159289. i) q^{66} +80004.0 q^{67} +624240. i q^{68} +(-49333.7 - 19926.0i) q^{69} +377746. q^{70} -515460. i q^{71} +(-990286. + 1.02591e6i) q^{72} +540021. q^{73} +450385. i q^{74} +(-9369.24 + 23196.8i) q^{75} +964340. q^{76} -74320.2i q^{77} +(-533953. - 215665. i) q^{78} +97148.4 q^{79} -2.44687e6i q^{80} +(18771.9 + 531109. i) q^{81} +651702. q^{82} -354258. i q^{83} +(-350870. + 868697. i) q^{84} -428623. q^{85} +525410. i q^{86} +(-855385. - 345493. i) q^{87} -784944. q^{88} -310319. i q^{89} +(-1.06985e6 - 1.03271e6i) q^{90} -249129. q^{91} +369225. i q^{92} +(-12916.2 + 31978.5i) q^{93} -799043. q^{94} +662147. i q^{95} +(4.41519e6 + 1.78331e6i) q^{96} -74273.0 q^{97} -1.32152e6i q^{98} +(-203182. + 210490. i) 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

Varieties

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Database

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