LMFDB - Embedded newform 21.8.e.a.16.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,8,Mod(4,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("21.4");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	21.e (of order $3$, degree $2$, 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:	$6.56008553517$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 362x^{6} - 1072x^{5} + 36131x^{4} - 70480x^{3} + 698554x^{2} - 663492x + 2868273 $ x^8 - 4x^7 + 362x^6 - 1072x^5 + 36131x^4 - 70480x^3 + 698554x^2 - 663492*x + 2868273
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{3}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.3
Root			$0.500000 - 12.0633i$ of defining polynomial
Character	$\chi$	$=$	21.16
Dual form			21.8.e.a.4.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.81424 - 4.87440i) q^{2} +(-13.5000 - 23.3827i) q^{3} +(48.1601 + 83.4158i) q^{4} +(-251.471 + 435.561i) q^{5} -151.969 q^{6} +(854.822 - 304.667i) q^{7} +1262.58 q^{8} +(-364.500 + 631.333i) q^{9} +O(q^{10})$	\(q+(2.81424 - 4.87440i) q^{2} +(-13.5000 - 23.3827i) q^{3} +(48.1601 + 83.4158i) q^{4} +(-251.471 + 435.561i) q^{5} -151.969 q^{6} +(854.822 - 304.667i) q^{7} +1262.58 q^{8} +(-364.500 + 631.333i) q^{9} +(1415.40 + 2451.54i) q^{10} +(3100.89 + 5370.90i) q^{11} +(1300.32 - 2252.23i) q^{12} -9719.32 q^{13} +(920.606 - 5024.15i) q^{14} +13579.4 q^{15} +(-2611.29 + 4522.89i) q^{16} +(6954.71 + 12045.9i) q^{17} +(2051.58 + 3553.44i) q^{18} +(5914.28 - 10243.8i) q^{19} -48443.5 q^{20} +(-18664.0 - 15875.0i) q^{21} +34906.6 q^{22} +(1418.72 - 2457.30i) q^{23} +(-17044.8 - 29522.5i) q^{24} +(-87412.9 - 151404. i) q^{25} +(-27352.5 + 47375.9i) q^{26} +19683.0 q^{27} +(66582.4 + 56632.9i) q^{28} -48836.2 q^{29} +(38215.8 - 66191.7i) q^{30} +(-63.0218 - 109.157i) q^{31} +(95502.8 + 165416. i) q^{32} +(83724.0 - 145014. i) q^{33} +78288.8 q^{34} +(-82262.3 + 448942. i) q^{35} -70217.5 q^{36} +(183727. - 318225. i) q^{37} +(-33288.4 - 57657.2i) q^{38} +(131211. + 227264. i) q^{39} +(-317503. + 549931. i) q^{40} -133287. q^{41} +(-129906. + 46299.8i) q^{42} +812254. q^{43} +(-298678. + 517326. i) q^{44} +(-183322. - 317524. i) q^{45} +(-7985.25 - 13830.9i) q^{46} +(552403. - 956790. i) q^{47} +141010. q^{48} +(637900. - 520872. i) q^{49} -984003. q^{50} +(187777. - 325239. i) q^{51} +(-468084. - 810745. i) q^{52} +(386165. + 668858. i) q^{53} +(55392.7 - 95942.9i) q^{54} -3.11914e6 q^{55} +(1.07928e6 - 384666. i) q^{56} -319371. q^{57} +(-137437. + 238047. i) q^{58} +(-356333. - 617187. i) q^{59} +(653987. + 1.13274e6i) q^{60} +(-626610. + 1.08532e6i) q^{61} -709.434 q^{62} +(-119237. + 650728. i) q^{63} +406580. q^{64} +(2.44413e6 - 4.23335e6i) q^{65} +(-471239. - 816209. i) q^{66} +(375109. + 649707. i) q^{67} +(-669879. + 1.16026e6i) q^{68} -76611.0 q^{69} +(1.95682e6 + 1.66441e6i) q^{70} -1.13668e6 q^{71} +(-460211. + 797109. i) q^{72} +(2.08563e6 + 3.61241e6i) q^{73} +(-1.03410e6 - 1.79112e6i) q^{74} +(-2.36015e6 + 4.08790e6i) q^{75} +1.13933e6 q^{76} +(4.28704e6 + 3.64643e6i) q^{77} +1.47703e6 q^{78} +(3.21980e6 - 5.57686e6i) q^{79} +(-1.31333e6 - 2.27475e6i) q^{80} +(-265720. - 460241. i) q^{81} +(-375101. + 649694. i) q^{82} -1.83464e6 q^{83} +(425367. - 2.32142e6i) q^{84} -6.99563e6 q^{85} +(2.28588e6 - 3.95925e6i) q^{86} +(659289. + 1.14192e6i) q^{87} +(3.91513e6 + 6.78120e6i) q^{88} +(-702126. + 1.21612e6i) q^{89} -2.06365e6 q^{90} +(-8.30829e6 + 2.96115e6i) q^{91} +273303. q^{92} +(-1701.59 + 2947.24i) q^{93} +(-3.10919e6 - 5.38527e6i) q^{94} +(2.97454e6 + 5.15206e6i) q^{95} +(2.57858e6 - 4.46622e6i) q^{96} -6.70215e6 q^{97} +(-743737. - 4.57524e6i) q^{98} -4.52110e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 108 q^{3} - 101 q^{4} - 196 q^{5} - 54 q^{6} + 154 q^{7} - 2694 q^{8} - 2916 q^{9}+O(q^{10}) $ 8 * q + q^2 - 108 * q^3 - 101 * q^4 - 196 * q^5 - 54 * q^6 + 154 * q^7 - 2694 * q^8 - 2916 * q^9	\( 8 q + q^{2} - 108 q^{3} - 101 q^{4} - 196 q^{5} - 54 q^{6} + 154 q^{7} - 2694 q^{8} - 2916 q^{9} + 5185 q^{10} + 5210 q^{11} - 2727 q^{12} - 7588 q^{13} - 29932 q^{14} + 10584 q^{15} + 21055 q^{16} + 11436 q^{17} + 729 q^{18} + 69158 q^{19} - 175982 q^{20} - 46872 q^{21} + 114526 q^{22} + 146220 q^{23} + 36369 q^{24} - 6230 q^{25} - 107696 q^{26} + 157464 q^{27} - 19201 q^{28} - 141328 q^{29} + 139995 q^{30} + 288618 q^{31} - 2653 q^{32} + 140670 q^{33} - 991992 q^{34} - 66164 q^{35} + 147258 q^{36} + 448902 q^{37} - 528944 q^{38} + 102438 q^{39} - 767361 q^{40} - 1326632 q^{41} + 899073 q^{42} + 1108 q^{43} + 686635 q^{44} - 142884 q^{45} + 1064964 q^{46} - 762180 q^{47} - 1136970 q^{48} + 5310620 q^{49} - 1050856 q^{50} + 308772 q^{51} - 3423848 q^{52} + 2761920 q^{53} + 19683 q^{54} - 3930112 q^{55} + 5341077 q^{56} - 3734532 q^{57} + 4451395 q^{58} - 3410898 q^{59} + 2375757 q^{60} - 300892 q^{61} - 4132350 q^{62} + 1153278 q^{63} - 5833102 q^{64} + 8019032 q^{65} - 1546101 q^{66} + 4222478 q^{67} - 5770500 q^{68} - 7895880 q^{69} + 7703801 q^{70} - 761928 q^{71} + 981963 q^{72} + 451674 q^{73} + 10091220 q^{74} - 168210 q^{75} - 29495312 q^{76} + 16516528 q^{77} + 5815584 q^{78} + 12154822 q^{79} - 7870085 q^{80} - 2125764 q^{81} - 8814904 q^{82} - 24175956 q^{83} + 3387636 q^{84} - 14751000 q^{85} + 32881826 q^{86} + 1907928 q^{87} + 14439051 q^{88} - 4955752 q^{89} - 7559730 q^{90} + 14146174 q^{91} + 413784 q^{92} + 7792686 q^{93} - 5960646 q^{94} - 8460784 q^{95} - 71631 q^{96} - 45681228 q^{97} + 8665405 q^{98} - 7596180 q^{99}+O(q^{100}) \) 8 * q + q^2 - 108 * q^3 - 101 * q^4 - 196 * q^5 - 54 * q^6 + 154 * q^7 - 2694 * q^8 - 2916 * q^9 + 5185 * q^10 + 5210 * q^11 - 2727 * q^12 - 7588 * q^13 - 29932 * q^14 + 10584 * q^15 + 21055 * q^16 + 11436 * q^17 + 729 * q^18 + 69158 * q^19 - 175982 * q^20 - 46872 * q^21 + 114526 * q^22 + 146220 * q^23 + 36369 * q^24 - 6230 * q^25 - 107696 * q^26 + 157464 * q^27 - 19201 * q^28 - 141328 * q^29 + 139995 * q^30 + 288618 * q^31 - 2653 * q^32 + 140670 * q^33 - 991992 * q^34 - 66164 * q^35 + 147258 * q^36 + 448902 * q^37 - 528944 * q^38 + 102438 * q^39 - 767361 * q^40 - 1326632 * q^41 + 899073 * q^42 + 1108 * q^43 + 686635 * q^44 - 142884 * q^45 + 1064964 * q^46 - 762180 * q^47 - 1136970 * q^48 + 5310620 * q^49 - 1050856 * q^50 + 308772 * q^51 - 3423848 * q^52 + 2761920 * q^53 + 19683 * q^54 - 3930112 * q^55 + 5341077 * q^56 - 3734532 * q^57 + 4451395 * q^58 - 3410898 * q^59 + 2375757 * q^60 - 300892 * q^61 - 4132350 * q^62 + 1153278 * q^63 - 5833102 * q^64 + 8019032 * q^65 - 1546101 * q^66 + 4222478 * q^67 - 5770500 * q^68 - 7895880 * q^69 + 7703801 * q^70 - 761928 * q^71 + 981963 * q^72 + 451674 * q^73 + 10091220 * q^74 - 168210 * q^75 - 29495312 * q^76 + 16516528 * q^77 + 5815584 * q^78 + 12154822 * q^79 - 7870085 * q^80 - 2125764 * q^81 - 8814904 * q^82 - 24175956 * q^83 + 3387636 * q^84 - 14751000 * q^85 + 32881826 * q^86 + 1907928 * q^87 + 14439051 * q^88 - 4955752 * q^89 - 7559730 * q^90 + 14146174 * q^91 + 413784 * q^92 + 7792686 * q^93 - 5960646 * q^94 - 8460784 * q^95 - 71631 * q^96 - 45681228 * q^97 + 8665405 * q^98 - 7596180 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	2.81424	−	4.87440i	0.248746	−	0.430841i	−0.714432	−	0.699705i	$-0.753315\pi$
$2$	2.81424	−	4.87440i	0.248746	−	0.430841i	0.963178	+	0.268864i	$0.0866483\pi$
$3$	−13.5000	−	23.3827i	−0.288675	−	0.500000i
$3$	−13.5000	−	23.3827i	−0.288675	−	0.500000i
$4$	48.1601	+	83.4158i	0.376251	+	0.651686i
$5$	−251.471	+	435.561i	−0.899690	+	1.55831i	−0.0717998	+	0.997419i	$0.522874\pi$
$5$	−251.471	+	435.561i	−0.899690	+	1.55831i	−0.827890	+	0.560890i	$0.810459\pi$
$6$	−151.969			−0.287227
$7$	854.822	−	304.667i	0.941961	−	0.335723i
$7$	854.822	−	304.667i	0.941961	−	0.335723i
$8$	1262.58			0.871855
$9$	−364.500	+	631.333i	−0.166667	+	0.288675i
$10$	1415.40	+	2451.54i	0.447588	+	0.775246i
$11$	3100.89	+	5370.90i	0.702444	+	1.21667i	0.967606	+	0.252465i	$0.0812413\pi$
$11$	3100.89	+	5370.90i	0.702444	+	1.21667i	−0.265162	+	0.964204i	$0.585425\pi$
$12$	1300.32	−	2252.23i	0.217229	−	0.376251i
$13$	−9719.32			−1.22697			−0.613485	−	0.789706i	$-0.710233\pi$
$13$	−9719.32			−1.22697			−0.613485	+	0.789706i	$0.710233\pi$
$14$	920.606	−	5024.15i	0.0896656	−	0.489345i
$15$	13579.4			1.03887
$16$	−2611.29	+	4522.89i	−0.159381	+	0.276055i
$17$	6954.71	+	12045.9i	0.343327	+	0.594659i	0.985048	−	0.172278i	$-0.0551128\pi$
$17$	6954.71	+	12045.9i	0.343327	+	0.594659i	−0.641722	+	0.766938i	$0.721780\pi$
$18$	2051.58	+	3553.44i	0.0829153	+	0.143614i
$19$	5914.28	−	10243.8i	0.197817	−	0.342630i	−0.750003	−	0.661434i	$-0.769948\pi$
$19$	5914.28	−	10243.8i	0.197817	−	0.342630i	0.947820	+	0.318805i	$0.103281\pi$
$20$	−48443.5			−1.35404
$21$	−18664.0	−	15875.0i	−0.439782	−	0.374065i
$22$	34906.6			0.698921
$23$	1418.72	−	2457.30i	0.0243136	−	0.0421125i	−0.853613	−	0.520908i	$-0.825593\pi$
$23$	1418.72	−	2457.30i	0.0243136	−	0.0421125i	0.877926	+	0.478796i	$0.158927\pi$
$24$	−17044.8	−	29522.5i	−0.251683	−	0.435928i
$25$	−87412.9	−	151404.i	−1.11888	−	1.93797i
$26$	−27352.5	+	47375.9i	−0.305204	+	0.528629i
$27$	19683.0			0.192450
$28$	66582.4	+	56632.9i	0.573200	+	0.487546i
$29$	−48836.2			−0.371834			−0.185917	−	0.982565i	$-0.559526\pi$
$29$	−48836.2			−0.371834			−0.185917	+	0.982565i	$0.559526\pi$
$30$	38215.8	−	66191.7i	0.258415	−	0.447588i
$31$	−63.0218	−	109.157i	−0.000379949	−	0.000658091i	0.865835	−	0.500329i	$-0.166788\pi$
$31$	−63.0218	−	109.157i	−0.000379949	−	0.000658091i	−0.866215	+	0.499671i	$0.833454\pi$
$32$	95502.8	+	165416.i	0.515218	+	0.892384i
$33$	83724.0	−	145014.i	0.405556	−	0.702444i
$34$	78288.8			0.341604
$35$	−82262.3	+	448942.i	−0.324312	+	1.76991i
$36$	−70217.5			−0.250834
$37$	183727.	−	318225.i	0.596303	−	1.03283i	−0.397058	−	0.917793i	$-0.629969\pi$
$37$	183727.	−	318225.i	0.596303	−	1.03283i	0.993362	−	0.115034i	$-0.0366977\pi$
$38$	−33288.4	−	57657.2i	−0.0984125	−	0.170455i
$39$	131211.	+	227264.i	0.354196	+	0.613485i
$40$	−317503.	+	549931.i	−0.784400	+	1.35862i
$41$	−133287.			−0.302026			−0.151013	−	0.988532i	$-0.548253\pi$
$41$	−133287.			−0.302026			−0.151013	+	0.988532i	$0.548253\pi$
$42$	−129906.	+	46299.8i	−0.270557	+	0.0964289i
$43$	812254.			1.55795			0.778973	−	0.627058i	$-0.215741\pi$
$43$	812254.			1.55795			0.778973	+	0.627058i	$0.215741\pi$
$44$	−298678.	+	517326.i	−0.528591	+	0.915546i
$45$	−183322.	−	317524.i	−0.299897	−	0.519436i
$46$	−7985.25	−	13830.9i	−0.0120958	−	0.0209506i
$47$	552403.	−	956790.i	0.776093	−	1.34423i	−0.158085	−	0.987425i	$-0.550532\pi$
$47$	552403.	−	956790.i	0.776093	−	1.34423i	0.934178	−	0.356807i	$-0.116135\pi$
$48$	141010.			0.184037
$49$	637900.	−	520872.i	0.774580	−	0.632477i
$50$	−984003.			−1.11327
$51$	187777.	−	325239.i	0.198220	−	0.343327i
$52$	−468084.	−	810745.i	−0.461649	−	0.799599i
$53$	386165.	+	668858.i	0.356293	+	0.617118i	0.987338	−	0.158628i	$-0.0507070\pi$
$53$	386165.	+	668858.i	0.356293	+	0.617118i	−0.631045	+	0.775746i	$0.717374\pi$
$54$	55392.7	−	95942.9i	0.0478712	−	0.0829153i
$55$	−3.11914e6			−2.52793
$56$	1.07928e6	−	384666.i	0.821253	−	0.292702i
$57$	−319371.			−0.228420
$58$	−137437.	+	238047.i	−0.0924922	+	0.160201i
$59$	−356333.	−	617187.i	−0.225878	−	0.391232i	0.730704	−	0.682694i	$-0.239192\pi$
$59$	−356333.	−	617187.i	−0.225878	−	0.391232i	−0.956582	+	0.291462i	$0.905858\pi$
$60$	653987.	+	1.13274e6i	0.390877	+	0.677019i
$61$	−626610.	+	1.08532e6i	−0.353462	+	0.612214i	−0.986854	−	0.161617i	$-0.948329\pi$
$61$	−626610.	+	1.08532e6i	−0.353462	+	0.612214i	0.633391	+	0.773832i	$0.281662\pi$
$62$	−709.434			−0.000378043
$63$	−119237.	+	650728.i	−0.0600784	+	0.327875i
$64$	406580.			0.193873
$65$	2.44413e6	−	4.23335e6i	1.10389	−	1.91200i
$66$	−471239.	−	816209.i	−0.201761	−	0.349460i
$67$	375109.	+	649707.i	0.152369	+	0.263910i	0.932098	−	0.362207i	$-0.117977\pi$
$67$	375109.	+	649707.i	0.152369	+	0.263910i	−0.779729	+	0.626117i	$0.784643\pi$
$68$	−669879.	+	1.16026e6i	−0.258354	+	0.447482i
$69$	−76611.0			−0.0280750
$70$	1.95682e6	+	1.66441e6i	0.681879	+	0.579985i
$71$	−1.13668e6			−0.376908			−0.188454	−	0.982082i	$-0.560348\pi$
$71$	−1.13668e6			−0.376908			−0.188454	+	0.982082i	$0.560348\pi$
$72$	−460211.	+	797109.i	−0.145309	+	0.251683i
$73$	2.08563e6	+	3.61241e6i	0.627489	+	1.08684i	0.988054	+	0.154109i	$0.0492507\pi$
$73$	2.08563e6	+	3.61241e6i	0.627489	+	1.08684i	−0.360565	+	0.932734i	$0.617416\pi$
$74$	−1.03410e6	−	1.79112e6i	−0.296656	−	0.513823i
$75$	−2.36015e6	+	4.08790e6i	−0.645988	+	1.11888i
$76$	1.13933e6			0.297716
$77$	4.28704e6	+	3.64643e6i	1.07014	+	0.910227i
$78$	1.47703e6			0.352419
$79$	3.21980e6	−	5.57686e6i	0.734741	−	1.27261i	−0.220096	−	0.975478i	$-0.570637\pi$
$79$	3.21980e6	−	5.57686e6i	0.734741	−	1.27261i	0.954837	−	0.297130i	$-0.0960295\pi$
$80$	−1.31333e6	−	2.27475e6i	−0.286786	−	0.496728i
$81$	−265720.	−	460241.i	−0.0555556	−	0.0962250i
$82$	−375101.	+	649694.i	−0.0751276	+	0.130125i
$83$	−1.83464e6			−0.352191			−0.176095	−	0.984373i	$-0.556347\pi$
$83$	−1.83464e6			−0.352191			−0.176095	+	0.984373i	$0.556347\pi$
$84$	425367.	−	2.32142e6i	0.0783045	−	0.427342i
$85$	−6.99563e6			−1.23555
$86$	2.28588e6	−	3.95925e6i	0.387533	−	0.671226i
$87$	659289.	+	1.14192e6i	0.107339	+	0.185917i
$88$	3.91513e6	+	6.78120e6i	0.612430	+	1.06076i
$89$	−702126.	+	1.21612e6i	−0.105572	+	0.182857i	−0.913972	−	0.405778i	$-0.867001\pi$
$89$	−702126.	+	1.21612e6i	−0.105572	+	0.182857i	0.808400	+	0.588634i	$0.200334\pi$
$90$	−2.06365e6			−0.298392
$91$	−8.30829e6	+	2.96115e6i	−1.15576	+	0.411923i
$92$	273303.			0.0365921
$93$	−1701.59	+	2947.24i	−0.000219364	+	0.000379949i
$94$	−3.10919e6	−	5.38527e6i	−0.386100	−	0.668745i
$95$	2.97454e6	+	5.15206e6i	0.355949	+	0.616521i
$96$	2.57858e6	−	4.46622e6i	0.297461	−	0.515218i
$97$	−6.70215e6			−0.745612			−0.372806	−	0.927909i	$-0.621604\pi$
$97$	−6.70215e6			−0.745612			−0.372806	+	0.927909i	$0.621604\pi$
$98$	−743737.	−	4.57524e6i	−0.0798231	−	0.491046i
$99$	−4.52110e6			−0.468296
$100$	8.41963e6	−	1.45832e7i	0.841963	−	1.45832i
$101$	−191713.	−	332057.i	−0.0185152	−	0.0320692i	0.856619	−	0.515949i	$-0.172561\pi$
$101$	−191713.	−	332057.i	−0.0185152	−	0.0320692i	−0.875135	+	0.483880i	$0.839227\pi$
$102$	−1.05690e6	−	1.83060e6i	−0.0986127	−	0.170802i
$103$	7.52010e6	−	1.30252e7i	0.678099	−	1.17450i	−0.297453	−	0.954736i	$-0.596137\pi$
$103$	7.52010e6	−	1.30252e7i	0.678099	−	1.17450i	0.975553	−	0.219766i	$-0.0705295\pi$
$104$	−1.22714e7			−1.06974
$105$	1.16080e7	−	4.13720e6i	0.978577	−	0.348774i
$106$	4.34705e6			0.354506
$107$	−3.65923e6	+	6.33797e6i	−0.288766	+	0.500158i	−0.973516	−	0.228621i	$-0.926578\pi$
$107$	−3.65923e6	+	6.33797e6i	−0.288766	+	0.500158i	0.684749	+	0.728779i	$0.259912\pi$
$108$	947936.	+	1.64187e6i	0.0724095	+	0.125417i
$109$	6.43172e6	+	1.11401e7i	0.475701	+	0.823938i	0.999613	−	0.0278344i	$-0.00886110\pi$
$109$	6.43172e6	+	1.11401e7i	0.475701	+	0.823938i	−0.523912	+	0.851773i	$0.675528\pi$
$110$	−8.77799e6	+	1.52039e7i	−0.628812	+	1.08913i
$111$	−9.92126e6			−0.688552
$112$	−854217.	+	4.66184e6i	−0.0574520	+	0.313541i
$113$	−900842.			−0.0587319			−0.0293660	−	0.999569i	$-0.509349\pi$
$113$	−900842.			−0.0587319			−0.0293660	+	0.999569i	$0.509349\pi$
$114$	−898787.	+	1.55674e6i	−0.0568185	+	0.0984125i
$115$	713535.	+	1.23588e6i	0.0437495	+	0.0757763i
$116$	−2.35196e6	−	4.07371e6i	−0.139903	−	0.242319i
$117$	3.54269e6	−	6.13612e6i	0.204495	−	0.354196i
$118$	−4.01122e6			−0.224745
$119$	9.61503e6	+	8.17824e6i	0.523041	+	0.444883i
$120$	1.71451e7			0.905747
$121$	−9.48744e6	+	1.64327e7i	−0.486856	+	0.843259i
$122$	3.52686e6	+	6.10870e6i	0.175844	+	0.304572i
$123$	1.79937e6	+	3.11660e6i	0.0871873	+	0.151013i
$124$	6070.28	−	10514.0i	0.000285912	−	0.000495215i
$125$	4.86349e7			2.22722
$126$	2.83635e6	+	2.41251e6i	0.126317	+	0.107442i
$127$	2.48188e6			0.107515			0.0537573	−	0.998554i	$-0.482880\pi$
$127$	2.48188e6			0.107515			0.0537573	+	0.998554i	$0.482880\pi$
$128$	−1.10801e7	+	1.91914e7i	−0.466993	+	0.808856i
$129$	−1.09654e7	−	1.89927e7i	−0.449740	−	0.778973i
$130$	−1.37567e7	−	2.38273e7i	−0.549178	−	0.951204i
$131$	−1.40374e7	+	2.43134e7i	−0.545552	+	0.944923i	0.453020	+	0.891500i	$0.350346\pi$
$131$	−1.40374e7	+	2.43134e7i	−0.545552	+	0.944923i	−0.998572	+	0.0534229i	$0.982987\pi$
$132$	1.61286e7			0.610364
$133$	1.93471e6	−	1.05585e7i	0.0713073	−	0.389156i
$134$	4.22258e6			0.151604
$135$	−4.94970e6	+	8.57314e6i	−0.173145	+	0.299897i
$136$	8.78088e6	+	1.52089e7i	0.299331	+	0.518457i
$137$	−1.09882e7	−	1.90322e7i	−0.365095	−	0.632364i	0.623696	−	0.781667i	$-0.285630\pi$
$137$	−1.09882e7	−	1.90322e7i	−0.365095	−	0.632364i	−0.988791	+	0.149303i	$0.952297\pi$
$138$	−215602.	+	373433.i	−0.00698353	+	0.0120958i
$139$	7.55942e6			0.238746			0.119373	−	0.992849i	$-0.461912\pi$
$139$	7.55942e6			0.238746			0.119373	+	0.992849i	$0.461912\pi$
$140$	−4.14106e7	+	1.47591e7i	−1.27545	+	0.454582i
$141$	−2.98298e7			−0.896155
$142$	−3.19890e6	+	5.54065e6i	−0.0937542	+	0.162387i
$143$	−3.01385e7	−	5.22015e7i	−0.861879	−	1.49282i
$144$	−1.90363e6	−	3.29718e6i	−0.0531268	−	0.0920184i
$145$	1.22809e7	−	2.12711e7i	0.334535	−	0.579432i
$146$	2.34778e7			0.624341
$147$	−2.07910e7	−	7.88404e6i	−0.539840	−	0.204710i
$148$	3.53933e7			0.897439
$149$	2.35900e7	−	4.08591e7i	0.584220	−	1.01190i	−0.410752	−	0.911747i	$-0.634734\pi$
$149$	2.35900e7	−	4.08591e7i	0.584220	−	1.01190i	0.994972	−	0.100152i	$-0.0319328\pi$
$150$	1.32840e7	+	2.30086e7i	0.321374	+	0.556636i
$151$	−2.66686e7	−	4.61913e7i	−0.630348	−	1.09179i	−0.987480	−	0.157741i	$-0.949579\pi$
$151$	−2.66686e7	−	4.61913e7i	−0.630348	−	1.09179i	0.357132	−	0.934054i	$-0.383755\pi$
$152$	7.46726e6	−	1.29337e7i	0.172468	−	0.298724i
$153$	−1.01400e7			−0.228885
$154$	2.98389e7	−	1.06349e7i	0.658356	−	0.234644i
$155$	63392.7			0.00136735
$156$	−1.26383e7	+	2.18901e7i	−0.266533	+	0.461649i
$157$	3.54801e7	+	6.14533e7i	0.731705	+	1.26735i	0.956154	+	0.292864i	$0.0946083\pi$
$157$	3.54801e7	+	6.14533e7i	0.731705	+	1.26735i	−0.224449	+	0.974486i	$0.572058\pi$
$158$	−1.81226e7	−	3.13892e7i	−0.365527	−	0.633112i
$159$	1.04265e7	−	1.80592e7i	0.205706	−	0.356293i
$160$	−9.60648e7			−1.85415
$161$	464099.	−	2.53279e6i	0.00876435	−	0.0478309i
$162$	−2.99120e6			−0.0552769
$163$	−4.91690e7	+	8.51632e7i	−0.889272	+	1.54026i	−0.0485345	+	0.998822i	$0.515455\pi$
$163$	−4.91690e7	+	8.51632e7i	−0.889272	+	1.54026i	−0.840738	+	0.541443i	$0.817878\pi$
$164$	−6.41911e6	−	1.11182e7i	−0.113637	−	0.196826i
$165$	4.21083e7	+	7.29338e7i	0.729750	+	1.26396i
$166$	−5.16312e6	+	8.94279e6i	−0.0876060	+	0.151738i
$167$	7.36791e7			1.22416			0.612078	−	0.790797i	$-0.290334\pi$
$167$	7.36791e7			1.22416			0.612078	+	0.790797i	$0.290334\pi$
$168$	−2.35649e7	−	2.00435e7i	−0.383427	−	0.326131i
$169$	3.17167e7			0.505458
$170$	−1.96874e7	+	3.40995e7i	−0.307338	+	0.532325i
$171$	4.31151e6	+	7.46776e6i	0.0659391	+	0.114210i
$172$	3.91182e7	+	6.77548e7i	0.586178	+	1.01529i
$173$	5.56725e7	−	9.64275e7i	0.817484	−	1.41592i	−0.0900473	−	0.995937i	$-0.528702\pi$
$173$	5.56725e7	−	9.64275e7i	0.817484	−	1.41592i	0.907531	−	0.419986i	$-0.137965\pi$
$174$	7.42159e6			0.106801
$175$	−1.20850e8	−	1.02791e8i	−1.70457	−	1.44985i
$176$	−3.23893e7			−0.447824
$177$	−9.62099e6	+	1.66640e7i	−0.130411	+	0.225878i
$178$	3.95190e6	+	6.84489e6i	0.0525213	+	0.0909696i
$179$	−2.36590e6	−	4.09786e6i	−0.0308326	−	0.0534037i	0.850197	−	0.526464i	$-0.176483\pi$
$179$	−2.36590e6	−	4.09786e6i	−0.0308326	−	0.0534037i	−0.881030	+	0.473060i	$0.843149\pi$
$180$	1.76577e7	−	3.05840e7i	0.225673	−	0.390877i
$181$	1.00313e8			1.25742			0.628710	−	0.777640i	$-0.283583\pi$
$181$	1.00313e8			1.25742			0.628710	+	0.777640i	$0.283583\pi$
$182$	−8.94767e6	+	4.88314e7i	−0.110017	+	0.600412i
$183$	3.38369e7			0.408143
$184$	1.79125e6	−	3.10254e6i	0.0211980	−	0.0367160i
$185$	9.24041e7	+	1.60049e8i	1.07298	+	1.85845i
$186$	9577.36	+	16588.5i	0.000109132	+	0.000189021i
$187$	−4.31316e7	+	7.47060e7i	−0.482336	+	0.835430i
$188$	1.06415e8			1.16802
$189$	1.68255e7	−	5.99675e6i	0.181280	−	0.0646100i
$190$	3.34843e7			0.354163
$191$	3.23791e7	−	5.60822e7i	0.336238	−	0.582382i	−0.647483	−	0.762079i	$-0.724179\pi$
$191$	3.23791e7	−	5.60822e7i	0.336238	−	0.582382i	0.983722	+	0.179697i	$0.0575119\pi$
$192$	−5.48883e6	−	9.50694e6i	−0.0559662	−	0.0969363i
$193$	−3.83075e7	−	6.63506e7i	−0.383560	−	0.664346i	0.608008	−	0.793931i	$-0.291969\pi$
$193$	−3.83075e7	−	6.63506e7i	−0.383560	−	0.664346i	−0.991568	+	0.129585i	$0.958636\pi$
$194$	−1.88614e7	+	3.26690e7i	−0.185468	+	0.321240i
$195$	−1.31983e8			−1.27467
$196$	7.41702e7	+	2.81256e7i	0.703612	+	0.266813i
$197$	−1.47076e8			−1.37060			−0.685301	−	0.728260i	$-0.740329\pi$
$197$	−1.47076e8			−1.37060			−0.685301	+	0.728260i	$0.740329\pi$
$198$	−1.27234e7	+	2.20377e7i	−0.116487	+	0.201761i
$199$	147032.	+	254667.i	0.00132259	+	0.00229080i	0.866686	−	0.498854i	$-0.166246\pi$
$199$	147032.	+	254667.i	0.00132259	+	0.00229080i	−0.865363	+	0.501145i	$0.832912\pi$
$200$	−1.10366e8	−	1.91159e8i	−0.975506	−	1.68963i
$201$	1.01279e7	−	1.75421e7i	0.0879700	−	0.152369i
$202$	−2.15811e6			−0.0184223
$203$	−4.17463e7	+	1.48788e7i	−0.350253	+	0.124833i
$204$	3.61735e7			0.298322
$205$	3.35178e7	−	5.80545e7i	0.271729	−	0.470649i
$206$	−4.23267e7	−	7.33120e7i	−0.337349	−	0.584305i
$207$	1.03425e6	+	1.79137e6i	0.00810455	+	0.0140375i
$208$	2.53800e7	−	4.39594e7i	0.195555	−	0.338712i
$209$	7.33581e7			0.555823
$210$	1.25013e7	−	6.82252e7i	0.0931511	−	0.508367i
$211$	−1.05229e8			−0.771163			−0.385582	−	0.922674i	$-0.625999\pi$
$211$	−1.05229e8			−0.771163			−0.385582	+	0.922674i	$0.625999\pi$
$212$	−3.71955e7	+	6.44246e7i	−0.268111	+	0.464383i
$213$	1.53452e7	+	2.65787e7i	0.108804	+	0.188454i
$214$	2.05959e7	+	3.56731e7i	0.143659	+	0.248824i
$215$	−2.04258e8	+	3.53786e8i	−1.40167	+	2.42776i
$216$	2.48514e7			0.167789
$217$	−87129.0	−	74109.2i	−0.000578833	−	0.000492338i
$218$	7.24015e7			0.473315
$219$	5.63119e7	−	9.75350e7i	0.362281	−	0.627489i
$220$	−1.50218e8	−	2.60185e8i	−0.951136	−	1.64742i
$221$	−6.75950e7	−	1.17078e8i	−0.421252	−	0.729630i
$222$	−2.79208e7	+	4.83602e7i	−0.171274	+	0.296656i
$223$	3.68334e6			0.0222420			0.0111210	−	0.999938i	$-0.496460\pi$
$223$	3.68334e6			0.0222420			0.0111210	+	0.999938i	$0.496460\pi$
$224$	1.32035e8	+	1.12305e8i	0.784909	+	0.667620i
$225$	1.27448e8			0.745923
$226$	−2.53518e6	+	4.39107e6i	−0.0146093	+	0.0253041i
$227$	3.86092e6	+	6.68731e6i	0.0219079	+	0.0379455i	0.876771	−	0.480907i	$-0.159693\pi$
$227$	3.86092e6	+	6.68731e6i	0.0219079	+	0.0379455i	−0.854864	+	0.518853i	$0.826359\pi$
$228$	−1.53810e7	−	2.66406e7i	−0.0859432	−	0.148858i
$229$	1.47549e8	−	2.55563e8i	0.811920	−	1.40629i	−0.0995986	−	0.995028i	$-0.531756\pi$
$229$	1.47549e8	−	2.55563e8i	0.811920	−	1.40629i	0.911519	−	0.411259i	$-0.134911\pi$
$230$	8.03223e6			0.0435300
$231$	2.73882e7	−	1.49469e8i	0.146191	−	0.797830i
$232$	−6.16597e7			−0.324185
$233$	4.98957e7	−	8.64219e7i	0.258415	−	0.447588i	−0.707403	−	0.706811i	$-0.750133\pi$
$233$	4.98957e7	−	8.64219e7i	0.258415	−	0.447588i	0.965817	+	0.259223i	$0.0834665\pi$
$234$	−1.99400e7	−	3.45370e7i	−0.101735	−	0.176210i
$235$	2.77827e8	+	4.81210e8i	1.39649	+	2.41879i
$236$	3.43221e7	−	5.94476e7i	0.169974	−	0.294403i
$237$	−1.73869e8			−0.848405
$238$	6.69230e7	−	2.38520e7i	0.321778	−	0.114685i
$239$	−1.79058e8			−0.848402			−0.424201	−	0.905568i	$-0.639445\pi$
$239$	−1.79058e8			−0.848402			−0.424201	+	0.905568i	$0.639445\pi$
$240$	−3.54599e7	+	6.14183e7i	−0.165576	+	0.286786i
$241$	3.55400e7	+	6.15570e7i	0.163553	+	0.283281i	0.936140	−	0.351627i	$-0.114371\pi$
$241$	3.55400e7	+	6.15570e7i	0.163553	+	0.283281i	−0.772588	+	0.634908i	$0.781038\pi$
$242$	5.33999e7	+	9.24913e7i	0.242207	+	0.419514i
$243$	−7.17445e6	+	1.24265e7i	−0.0320750	+	0.0555556i
$244$	−1.20710e8			−0.531962
$245$	6.64579e7	+	4.08828e8i	0.288712	+	1.77607i
$246$	2.02554e7			0.0867499
$247$	−5.74828e7	+	9.95632e7i	−0.242716	+	0.420397i
$248$	−79570.2	−	137820.i	−0.000331260	−	0.000573760i
$249$	2.47677e7	+	4.28989e7i	0.101669	+	0.176095i
$250$	1.36870e8	−	2.37066e8i	0.554011	−	0.959576i
$251$	−5.85579e7			−0.233737			−0.116868	−	0.993147i	$-0.537286\pi$
$251$	−5.85579e7			−0.233737			−0.116868	+	0.993147i	$0.537286\pi$
$252$	−6.00235e7	+	2.13929e7i	−0.236276	+	0.0842108i
$253$	1.75972e7			0.0683159
$254$	6.98460e6	−	1.20977e7i	0.0267438	−	0.0463217i
$255$	9.44410e7	+	1.63577e8i	0.356673	+	0.617775i
$256$	8.83855e7	+	1.53088e8i	0.329262	+	0.570298i
$257$	−1.39244e8	+	2.41178e8i	−0.511694	+	0.886280i	0.488214	+	0.872724i	$0.337649\pi$
$257$	−1.39244e8	+	2.41178e8i	−0.511694	+	0.886280i	−0.999908	+	0.0135561i	$0.995685\pi$
$258$	−1.23437e8			−0.447484
$259$	6.01016e7	−	3.28001e8i	0.214950	−	1.17308i
$260$	4.70838e8			1.66136
$261$	1.78008e7	−	3.08319e7i	0.0619723	−	0.107339i
$262$	7.90089e7	+	1.36848e8i	0.271407	+	0.470091i
$263$	−1.24380e7	−	2.15433e7i	−0.0421605	−	0.0730242i	0.844175	−	0.536068i	$-0.180091\pi$
$263$	−1.24380e7	−	2.15433e7i	−0.0421605	−	0.0730242i	−0.886336	+	0.463043i	$0.846757\pi$
$264$	1.05708e8	−	1.83092e8i	0.353586	−	0.612430i
$265$	−3.88438e8			−1.28221
$266$	−4.60219e7	−	3.91448e7i	−0.149927	−	0.127523i
$267$	3.79148e7			0.121904
$268$	−3.61306e7	+	6.25800e7i	−0.114658	+	0.198593i
$269$	−2.27489e8	−	3.94022e8i	−0.712569	−	1.23421i	−0.963890	−	0.266302i	$-0.914198\pi$
$269$	−2.27489e8	−	3.94022e8i	−0.712569	−	1.23421i	0.251320	−	0.967904i	$-0.419135\pi$
$270$	2.78593e7	+	4.82537e7i	0.0861384	+	0.149196i
$271$	−1.37286e8	+	2.37787e8i	−0.419020	+	0.725765i	−0.995841	−	0.0911060i	$-0.970960\pi$
$271$	−1.37286e8	+	2.37787e8i	−0.419020	+	0.725765i	0.576821	+	0.816871i	$0.304293\pi$
$272$	−7.26430e7			−0.218878
$273$	1.81402e8	+	1.54295e8i	0.539600	+	0.458967i
$274$	−1.23694e8			−0.363264
$275$	5.42115e8	−	9.38971e8i	1.57191	−	2.72262i
$276$	−3.68960e6	−	6.39057e6i	−0.0105632	−	0.0182961i
$277$	−2.04311e7	−	3.53877e7i	−0.0577581	−	0.100040i	0.835701	−	0.549185i	$-0.185062\pi$
$277$	−2.04311e7	−	3.53877e7i	−0.0577581	−	0.100040i	−0.893459	+	0.449145i	$0.851729\pi$
$278$	2.12740e7	−	3.68477e7i	0.0593872	−	0.102862i
$279$	91885.8			0.000253299
$280$	−1.03863e8	+	5.66826e8i	−0.282753	+	1.54311i
$281$	−4.08644e8			−1.09868			−0.549342	−	0.835598i	$-0.685122\pi$
$281$	−4.08644e8			−1.09868			−0.549342	+	0.835598i	$0.685122\pi$
$282$	−8.39481e7	+	1.45402e8i	−0.222915	+	0.386100i
$283$	−3.30085e8	−	5.71725e8i	−0.865713	−	1.49946i	−0.866338	−	0.499459i	$-0.833532\pi$
$283$	−3.30085e8	−	5.71725e8i	−0.865713	−	1.49946i	0.000625156	−	1.00000i	$-0.499801\pi$
$284$	−5.47428e7	−	9.48173e7i	−0.141812	−	0.245625i
$285$	8.03126e7	−	1.39106e8i	0.205507	−	0.355949i
$286$	−3.39268e8			−0.857555
$287$	−1.13937e8	+	4.06080e7i	−0.284496	+	0.101397i
$288$	−1.39243e8			−0.343479
$289$	1.08433e8	−	1.87812e8i	0.264253	−	0.457700i
$290$	−6.91227e7	−	1.19724e8i	−0.166429	−	0.288263i
$291$	9.04790e7	+	1.56714e8i	0.215240	+	0.372806i
$292$	−2.00888e8	+	3.47948e8i	−0.472187	+	0.817852i
$293$	6.57223e8			1.52643			0.763213	−	0.646147i	$-0.223621\pi$
$293$	6.57223e8			1.52643			0.763213	+	0.646147i	$0.223621\pi$
$294$	−9.69409e7	+	7.91563e7i	−0.222480	+	0.181664i
$295$	3.58430e8			0.812881
$296$	2.31970e8	−	4.01784e8i	0.519890	−	0.900476i
$297$	6.10348e7	+	1.05715e8i	0.135185	+	0.234148i
$298$	−1.32776e8	−	2.29975e8i	−0.290645	−	0.503411i
$299$	−1.37890e7	+	2.38833e7i	−0.0298321	+	0.0516708i
$300$	−4.54660e8			−0.972215
$301$	6.94333e8	−	2.47467e8i	1.46752	−	0.523039i
$302$	−3.00207e8			−0.627186
$303$	−5.17626e6	+	8.96555e6i	−0.0106897	+	0.0185152i
$304$	3.08878e7	+	5.34993e7i	0.0630565	+	0.109217i
$305$	−3.15148e8	−	5.45853e8i	−0.636013	−	1.10161i
$306$	−2.85363e7	+	4.94263e7i	−0.0569341	+	0.0986127i
$307$	2.21654e8			0.437211			0.218606	−	0.975813i	$-0.429849\pi$
$307$	2.21654e8			0.437211			0.218606	+	0.975813i	$0.429849\pi$
$308$	−9.77050e7	+	5.33219e8i	−0.190541	+	1.03987i
$309$	−4.06085e8			−0.783002
$310$	178402.	−	309002.i	0.000340121	−	0.000589108i
$311$	2.22992e8	+	3.86234e8i	0.420367	+	0.728097i	0.995975	−	0.0896286i	$-0.0285680\pi$
$311$	2.22992e8	+	3.86234e8i	0.420367	+	0.728097i	−0.575608	+	0.817726i	$0.695235\pi$
$312$	1.65664e8	+	2.86939e8i	0.308808	+	0.534871i
$313$	−2.69303e8	+	4.66446e8i	−0.496404	+	0.859797i	−0.999991	−	0.00414734i	$-0.998680\pi$
$313$	−2.69303e8	+	4.66446e8i	−0.496404	+	0.859797i	0.503587	+	0.863944i	$0.332013\pi$
$314$	3.99398e8			0.728034
$315$	−2.53447e8	−	2.15574e8i	−0.456878	−	0.388606i
$316$	6.20264e8			1.10579
$317$	−5.40113e8	+	9.35503e8i	−0.952307	+	1.64944i	−0.211894	+	0.977293i	$0.567963\pi$
$317$	−5.40113e8	+	9.35503e8i	−0.952307	+	1.64944i	−0.740413	+	0.672152i	$0.765370\pi$
$318$	−5.86851e7	−	1.01646e8i	−0.102337	−	0.177253i
$319$	−1.51436e8	−	2.62294e8i	−0.261193	−	0.452399i
$320$	−1.02243e8	+	1.77090e8i	−0.174425	+	0.302113i
$321$	1.97598e8			0.333438
$322$	−1.10398e7	−	9.39008e6i	−0.0184274	−	0.0156738i
$323$	1.64528e8			0.271664
$324$	2.55943e7	−	4.43306e7i	0.0418057	−	0.0724095i
$325$	8.49594e8	+	1.47154e9i	1.37284	+	2.37783i
$326$	2.76747e8	+	4.79339e8i	0.442406	+	0.766269i
$327$	1.73656e8	−	3.00782e8i	0.274646	−	0.475701i
$328$	−1.68285e8			−0.263323
$329$	1.80705e8	−	9.86185e8i	0.279759	−	1.52677i
$330$	4.74012e8			0.726089
$331$	3.86056e7	−	6.68668e7i	0.0585130	−	0.101347i	−0.835285	−	0.549817i	$-0.814697\pi$
$331$	3.86056e7	−	6.68668e7i	0.0585130	−	0.101347i	0.893798	+	0.448470i	$0.148031\pi$
$332$	−8.83566e7	−	1.53038e8i	−0.132512	−	0.229518i
$333$	1.33937e8	+	2.31986e8i	0.198768	+	0.344276i
$334$	2.07351e8	−	3.59142e8i	0.304504	−	0.527416i
$335$	−3.77316e8			−0.548338
$336$	1.20538e8	−	4.29609e7i	0.173355	−	0.0617855i
$337$	−1.16026e9			−1.65139			−0.825697	−	0.564114i	$-0.809218\pi$
$337$	−1.16026e9			−1.65139			−0.825697	+	0.564114i	$0.809218\pi$
$338$	8.92584e7	−	1.54600e8i	0.125731	−	0.217772i
$339$	1.21614e7	+	2.10641e7i	0.0169544	+	0.0293660i
$340$	−3.36910e8	−	5.83546e8i	−0.464877	−	0.805191i
$341$	390848.	−	676968.i	0.000533786	−	0.000924544i
$342$	4.85345e7			0.0656083
$343$	3.86599e8	−	6.39599e8i	0.517286	−	0.855813i
$344$	1.02554e9			1.35830
$345$	1.92654e7	−	3.33687e7i	0.0252588	−	0.0437495i
$346$	−3.13351e8	−	5.42740e8i	−0.406691	−	0.704410i
$347$	4.28904e8	+	7.42883e8i	0.551070	+	0.954481i	0.998198	+	0.0600112i	$0.0191136\pi$
$347$	4.28904e8	+	7.42883e8i	0.551070	+	0.954481i	−0.447128	+	0.894470i	$0.647553\pi$
$348$	−6.35029e7	+	1.09990e8i	−0.0807730	+	0.139903i
$349$	−2.41142e7			−0.0303657			−0.0151829	−	0.999885i	$-0.504833\pi$
$349$	−2.41142e7			−0.0303657			−0.0151829	+	0.999885i	$0.504833\pi$
$350$	−8.41147e8	+	2.99793e8i	−1.04866	+	0.373752i
$351$	−1.91305e8			−0.236131
$352$	−5.92287e8	+	1.02587e9i	−0.723824	+	1.25370i
$353$	−3.19711e8	−	5.53755e8i	−0.386853	−	0.670048i	0.605172	−	0.796095i	$-0.293104\pi$
$353$	−3.19711e8	−	5.53755e8i	−0.386853	−	0.670048i	−0.992024	+	0.126047i	$0.959771\pi$
$354$	5.41515e7	+	9.37932e7i	0.0648783	+	0.112372i
$355$	2.85843e8	−	4.95094e8i	0.339100	−	0.587339i
$356$	−1.35258e8			−0.158887
$357$	6.14265e7	−	3.35231e8i	0.0714524	−	0.389947i
$358$	−2.66328e7			−0.0306779
$359$	−5.24301e8	+	9.08117e8i	−0.598068	+	1.03588i	0.395038	+	0.918665i	$0.370731\pi$
$359$	−5.24301e8	+	9.08117e8i	−0.598068	+	1.03588i	−0.993106	+	0.117219i	$0.962602\pi$
$360$	−2.31459e8	−	4.00900e8i	−0.261467	−	0.452873i
$361$	3.76978e8	+	6.52946e8i	0.421737	+	0.730469i
$362$	2.82304e8	−	4.88964e8i	0.312778	−	0.541748i
$363$	5.12322e8			0.562173
$364$	−6.47135e8	−	5.50433e8i	−0.703299	−	0.598205i
$365$	−2.09790e9			−2.25818
$366$	9.52252e7	−	1.64935e8i	0.101524	−	0.175844i
$367$	−4.54436e7	−	7.87106e7i	−0.0479889	−	0.0831193i	0.841033	−	0.540984i	$-0.181948\pi$
$367$	−4.54436e7	−	7.87106e7i	−0.0479889	−	0.0831193i	−0.889022	+	0.457864i	$0.848615\pi$
$368$	7.40939e6	+	1.28334e7i	0.00775024	+	0.0134238i
$369$	4.85830e7	−	8.41483e7i	0.0503376	−	0.0871873i
$370$	1.04019e9			1.06759
$371$	5.33882e8	+	4.54103e8i	0.542795	+	0.461685i
$372$	−327795.			−0.000330143
$373$	6.25483e8	−	1.08337e9i	0.624072	−	1.08092i	−0.364648	−	0.931145i	$-0.618811\pi$
$373$	6.25483e8	−	1.08337e9i	0.624072	−	1.08092i	0.988720	−	0.149778i	$-0.0478560\pi$
$374$	2.42765e8	+	4.20481e8i	0.239958	+	0.415620i
$375$	−6.56571e8	−	1.13721e9i	−0.642942	−	1.11361i
$376$	6.97454e8	−	1.20803e9i	0.676641	−	1.17198i
$377$	4.74655e8			0.456229
$378$	1.81203e7	−	9.88904e7i	0.0172561	−	0.0941744i
$379$	7.56067e8			0.713384			0.356692	−	0.934222i	$-0.383905\pi$
$379$	7.56067e8			0.713384			0.356692	+	0.934222i	$0.383905\pi$
$380$	−2.86509e8	+	4.96247e8i	−0.267852	+	0.463933i
$381$	−3.35054e7	−	5.80330e7i	−0.0310368	−	0.0537573i
$382$	−1.82245e8	−	3.15657e8i	−0.167276	−	0.289730i
$383$	−2.86932e8	+	4.96980e8i	−0.260965	+	0.452005i	−0.966499	−	0.256671i	$-0.917374\pi$
$383$	−2.86932e8	+	4.96980e8i	−0.260965	+	0.452005i	0.705533	+	0.708677i	$0.250707\pi$
$384$	5.98328e8			0.539237
$385$	−2.66631e9	+	9.50296e8i	−2.38121	+	0.848685i
$386$	−4.31226e8			−0.381636
$387$	−2.96067e8	+	5.12802e8i	−0.259658	+	0.449740i
$388$	−3.22776e8	−	5.59065e8i	−0.280537	−	0.485905i
$389$	−1.05986e9	−	1.83572e9i	−0.912899	−	1.58119i	−0.809948	−	0.586502i	$-0.800505\pi$
$389$	−1.05986e9	−	1.83572e9i	−0.912899	−	1.58119i	−0.102952	−	0.994686i	$-0.532829\pi$
$390$	−3.71431e8	+	6.43338e8i	−0.317068	+	0.549178i
$391$	3.94672e7			0.0333901
$392$	8.05400e8	−	6.57643e8i	0.675321	−	0.551428i
$393$	7.58017e8			0.629949
$394$	−4.13908e8	+	7.16910e8i	−0.340932	+	0.590511i
$395$	1.61937e9	+	2.80484e9i	1.32208	+	2.28991i
$396$	−2.17737e8	−	3.77131e8i	−0.176197	−	0.305182i
$397$	−6.92743e8	+	1.19987e9i	−0.555655	+	0.962423i	0.442197	+	0.896918i	$0.354199\pi$
$397$	−6.92743e8	+	1.19987e9i	−0.555655	+	0.962423i	−0.997852	+	0.0655049i	$0.979134\pi$
$398$	1.65513e6			0.00131596
$399$	−2.73006e8	+	9.73017e7i	−0.215162	+	0.0766859i
$400$	9.13042e8			0.713314
$401$	−2.20004e8	+	3.81058e8i	−0.170382	+	0.295111i	−0.938554	−	0.345133i	$-0.887834\pi$
$401$	−2.20004e8	+	3.81058e8i	−0.170382	+	0.295111i	0.768171	+	0.640245i	$0.221167\pi$
$402$	−5.70048e7	−	9.87353e7i	−0.0437644	−	0.0758021i
$403$	612530.	+	1.06093e6i	0.000466186	+	0.000807458i
$404$	1.84659e7	−	3.19838e7i	0.0139327	−	0.0241321i
$405$	2.67284e8			0.199931
$406$	−4.49589e7	+	2.45361e8i	−0.0333407	+	0.181955i
$407$	2.27887e9			1.67548
$408$	2.37084e8	−	4.10641e8i	0.172819	−	0.299331i
$409$	3.60756e7	+	6.24848e7i	0.0260725	+	0.0451589i	0.878767	−	0.477251i	$-0.158367\pi$
$409$	3.60756e7	+	6.24848e7i	0.0260725	+	0.0451589i	−0.852695	+	0.522409i	$0.825033\pi$
$410$	−1.88654e8	−	3.26758e8i	−0.135183	−	0.234144i
$411$	−2.96683e8	+	5.13869e8i	−0.210788	+	0.365095i
$412$	1.44868e9			1.02054
$413$	−4.92638e8	−	4.19022e8i	−0.344114	−	0.292693i
$414$	1.16425e7			0.00806389
$415$	4.61359e8	−	7.99098e8i	0.316863	−	0.548822i
$416$	−9.28223e8	−	1.60773e9i	−0.632158	−	1.09493i
$417$	−1.02052e8	−	1.76760e8i	−0.0689201	−	0.119373i
$418$	2.06447e8	−	3.57577e8i	0.138259	−	0.239471i
$419$	1.18463e9			0.786745			0.393373	−	0.919379i	$-0.371308\pi$
$419$	1.18463e9			0.786745			0.393373	+	0.919379i	$0.371308\pi$
$420$	9.04151e8	+	7.69043e8i	0.595482	+	0.506498i
$421$	−2.28422e8			−0.149194			−0.0745969	−	0.997214i	$-0.523767\pi$
$421$	−2.28422e8			−0.149194			−0.0745969	+	0.997214i	$0.523767\pi$
$422$	−2.96139e8	+	5.12928e8i	−0.191824	+	0.332248i
$423$	4.02702e8	+	6.97500e8i	0.258698	+	0.448077i
$424$	4.87565e8	+	8.44488e8i	0.310636	+	0.538038i
$425$	1.21586e9	−	2.10593e9i	0.768286	−	1.33071i
$426$	1.72740e8			0.108258
$427$	−2.04979e8	+	1.11866e9i	−0.127413	+	0.695347i
$428$	−7.04916e8			−0.434594
$429$	−8.13741e8	+	1.40944e9i	−0.497606	+	0.861879i
$430$	1.14966e9	+	1.99128e9i	0.697318	+	1.20779i
$431$	2.66068e8	+	4.60843e8i	0.160074	+	0.277257i	0.934895	−	0.354924i	$-0.115493\pi$
$431$	2.66068e8	+	4.60843e8i	0.160074	+	0.277257i	−0.774821	+	0.632181i	$0.782160\pi$
$432$	−5.13980e7	+	8.90240e7i	−0.0306728	+	0.0531268i
$433$	−3.55195e8			−0.210261			−0.105131	−	0.994458i	$-0.533526\pi$
$433$	−3.55195e8			−0.210261			−0.105131	+	0.994458i	$0.533526\pi$
$434$	−606440.	+	216141.i	−0.000356102	+	0.000126918i
$435$	−6.63168e8			−0.386288
$436$	−6.19504e8	+	1.07301e9i	−0.357966	+	0.620015i
$437$	−1.67814e7	−	2.90663e7i	−0.00961932	−	0.0166612i
$438$	−3.16950e8	−	5.48974e8i	−0.180232	−	0.312171i
$439$	2.86605e8	−	4.96415e8i	0.161681	−	0.280039i	−0.773791	−	0.633441i	$-0.781642\pi$
$439$	2.86605e8	−	4.96415e8i	0.161681	−	0.280039i	0.935472	+	0.353402i	$0.114975\pi$
$440$	−3.93816e9			−2.20399
$441$	9.63288e7	+	5.92584e8i	0.0534837	+	0.329015i
$442$	−7.60914e8			−0.419139
$443$	−8.04540e8	+	1.39350e9i	−0.439678	+	0.761544i	−0.997664	−	0.0683058i	$-0.978241\pi$
$443$	−8.04540e8	+	1.39350e9i	−0.439678	+	0.761544i	0.557987	+	0.829850i	$0.311574\pi$
$444$	−4.77809e8	−	8.27590e8i	−0.259068	−	0.448719i
$445$	−3.53129e8	−	6.11637e8i	−0.189965	−	0.329028i
$446$	1.03658e7	−	1.79541e7i	0.00553262	−	0.00958277i
$447$	−1.27386e9			−0.674599
$448$	3.47554e8	−	1.23871e8i	0.182620	−	0.0650876i
$449$	2.60121e9			1.35616			0.678082	−	0.734986i	$-0.262811\pi$
$449$	2.60121e9			1.35616			0.678082	+	0.734986i	$0.262811\pi$
$450$	3.58669e8	−	6.21233e8i	0.185545	−	0.321374i
$451$	−4.13308e8	−	7.15870e8i	−0.212156	−	0.367465i
$452$	−4.33847e7	−	7.51444e7i	−0.0220979	−	0.0382747i
$453$	−7.20051e8	+	1.24717e9i	−0.363932	+	0.630348i
$454$	4.34622e7			0.0217980
$455$	7.99534e8	−	4.36341e9i	0.397921	−	2.17163i
$456$	−4.03232e8			−0.199149
$457$	1.39615e9	−	2.41820e9i	0.684267	−	1.18519i	−0.289400	−	0.957208i	$-0.593456\pi$
$457$	1.39615e9	−	2.41820e9i	0.684267	−	1.18519i	0.973667	−	0.227977i	$-0.0732110\pi$
$458$	−8.30478e8	−	1.43843e9i	−0.403924	−	0.699616i
$459$	1.36890e8	+	2.37100e8i	0.0660733	+	0.114442i
$460$	−6.87279e7	+	1.19040e8i	−0.0329216	+	0.0570218i
$461$	−2.44371e9			−1.16171			−0.580854	−	0.814008i	$-0.697281\pi$
$461$	−2.44371e9			−1.16171			−0.580854	+	0.814008i	$0.697281\pi$
$462$	−6.51497e8	−	5.54143e8i	−0.307373	−	0.261442i
$463$	−5.78623e8			−0.270933			−0.135467	−	0.990782i	$-0.543253\pi$
$463$	−5.78623e8			−0.270933			−0.135467	+	0.990782i	$0.543253\pi$
$464$	1.27526e8	−	2.20881e8i	0.0592631	−	0.102647i
$465$	−855801.	−	1.48229e6i	−0.000394719	−	0.000683673i
$466$	−2.80837e8	−	4.86424e8i	−0.128559	−	0.222671i
$467$	1.93660e9	−	3.35430e9i	0.879897	−	1.52403i	0.0284440	−	0.999595i	$-0.490945\pi$
$467$	1.93660e9	−	3.35430e9i	0.879897	−	1.52403i	0.851453	−	0.524431i	$-0.175722\pi$
$468$	6.82466e8			0.307766
$469$	5.18595e8	+	4.41101e8i	0.232126	+	0.197439i
$470$	3.12748e9			1.38948
$471$	9.57962e8	−	1.65924e9i	0.422450	−	0.731705i
$472$	−4.49899e8	−	7.79249e8i	−0.196933	−	0.341098i
$473$	2.51871e9	+	4.36253e9i	1.09437	+	1.89550i
$474$	−4.89309e8	+	8.47509e8i	−0.211037	+	0.365527i
$475$	−2.06794e9			−0.885339
$476$	−2.19134e8	+	1.19591e9i	−0.0931290	+	0.508246i
$477$	−5.63029e8			−0.237529
$478$	−5.03913e8	+	8.72803e8i	−0.211037	+	0.365526i
$479$	−1.00117e9	−	1.73408e9i	−0.416232	−	0.720935i	0.579325	−	0.815097i	$-0.303316\pi$
$479$	−1.00117e9	−	1.73408e9i	−0.416232	−	0.720935i	−0.995557	+	0.0941618i	$0.969983\pi$
$480$	1.29687e9	+	2.24625e9i	0.535246	+	0.927073i
$481$	−1.78570e9	+	3.09293e9i	−0.731647	+	1.26725i
$482$	4.00072e8			0.162732
$483$	−6.54888e7	+	2.33408e7i	−0.0264455	+	0.00942543i
$484$	−1.82767e9			−0.732720
$485$	1.68540e9	−	2.91919e9i	0.670820	−	1.16189i
$486$	4.03812e7	+	6.99424e7i	0.0159571	+	0.0276384i
$487$	−2.16847e9	−	3.75591e9i	−0.850751	−	1.47354i	−0.880531	−	0.473988i	$-0.842814\pi$
$487$	−2.16847e9	−	3.75591e9i	−0.850751	−	1.47354i	0.0297798	−	0.999556i	$-0.490519\pi$
$488$	−7.91146e8	+	1.37030e9i	−0.308168	+	0.533762i
$489$	2.65513e9			1.02684
$490$	2.17982e9	+	8.26597e8i	0.837018	+	0.317400i
$491$	−4.62835e9			−1.76458			−0.882289	−	0.470709i	$-0.843998\pi$
$491$	−4.62835e9			−1.76458			−0.882289	+	0.470709i	$0.843998\pi$
$492$	−1.73316e8	+	3.00192e8i	−0.0656086	+	0.113637i
$493$	−3.39642e8	−	5.88277e8i	−0.127661	−	0.221115i
$494$	3.23541e8	+	5.60389e8i	0.120749	+	0.209144i
$495$	1.13692e9	−	1.96921e9i	0.421321	−	0.729750i
$496$	658273.			0.000242226
$497$	−9.71662e8	+	3.46309e8i	−0.355032	+	0.126537i
$498$	2.78809e8			0.101159
$499$	−1.25641e9	+	2.17616e9i	−0.452666	+	0.784041i	−0.998551	−	0.0538194i	$-0.982860\pi$
$499$	−1.25641e9	+	2.17616e9i	−0.452666	+	0.784041i	0.545884	+	0.837861i	$0.316194\pi$
$500$	2.34226e9	+	4.05692e9i	0.837993	+	1.45145i
$501$	−9.94668e8	−	1.72282e9i	−0.353383	−	0.612078i
$502$	−1.64796e8	+	2.85435e8i	−0.0581411	+	0.100703i
$503$	1.12749e9			0.395025			0.197512	−	0.980300i	$-0.436714\pi$
$503$	1.12749e9			0.395025			0.197512	+	0.980300i	$0.436714\pi$
$504$	−1.50546e8	+	8.21597e8i	−0.0523797	+	0.285859i
$505$	1.92841e8			0.0666316
$506$	4.95227e7	−	8.57759e7i	0.0169933	−	0.0294333i
$507$	−4.28176e8	−	7.41622e8i	−0.145913	−	0.252729i
$508$	1.19528e8	+	2.07028e8i	0.0404525	+	0.0700658i
$509$	−1.32335e9	+	2.29211e9i	−0.444798	+	0.770413i	−0.998038	−	0.0626088i	$-0.980058\pi$
$509$	−1.32335e9	+	2.29211e9i	−0.444798	+	0.770413i	0.553240	+	0.833022i	$0.313391\pi$
$510$	1.06312e9			0.354884
$511$	2.88342e9	+	2.45255e9i	0.955949	+	0.813101i
$512$	−1.84157e9			−0.606376
$513$	1.16411e8	−	2.01629e8i	0.0380700	−	0.0659391i
$514$	7.83731e8	+	1.35746e9i	0.254564	+	0.440917i
$515$	3.78218e9	+	6.55092e9i	1.22016	+	2.11338i
$516$	1.05619e9	−	1.82938e9i	0.338430	−	0.586178i
$517$	6.85177e9			2.18065
$518$	−1.42967e9	−	1.21603e9i	−0.451941	−	0.384407i
$519$	−3.00631e9			−0.943949
$520$	3.08591e9	−	5.34495e9i	0.962436	−	1.66699i
$521$	−2.49556e9	−	4.32244e9i	−0.773101	−	1.33905i	−0.935856	−	0.352384i	$-0.885371\pi$
$521$	−2.49556e9	−	4.32244e9i	−0.773101	−	1.33905i	0.162755	−	0.986667i	$-0.447962\pi$
$522$	−1.00191e8	−	1.73537e8i	−0.0308307	−	0.0534004i
$523$	−9.79195e8	+	1.69602e9i	−0.299304	+	0.518411i	−0.975977	−	0.217874i	$-0.930088\pi$
$523$	−9.79195e8	+	1.69602e9i	−0.299304	+	0.518411i	0.676673	+	0.736284i	$0.263421\pi$
$524$	−2.70416e9			−0.821057
$525$	−7.72062e8	+	4.21348e9i	−0.232860	+	1.27082i
$526$	−1.40014e8			−0.0419490
$527$	876597.	−	1.51831e6i	0.000260893	−	0.000451880i
$528$	4.37255e8	+	7.57349e8i	0.129276	+	0.223912i
$529$	1.69839e9	+	2.94169e9i	0.498818	+	0.863978i
$530$	−1.09316e9	+	1.89340e9i	−0.318946	+	0.552430i
$531$	5.19533e8			0.150585
$532$	9.73925e8	−	3.47116e8i	0.280437	−	0.0999502i
$533$	1.29546e9			0.370577
$534$	1.06701e8	−	1.84812e8i	0.0303232	−	0.0525213i
$535$	−1.84038e9	−	3.18763e9i	−0.519600	−	0.899974i
$536$	4.73605e8	+	8.20308e8i	0.132843	+	0.230091i
$537$	−6.38792e7	+	1.10642e8i	−0.0178012	+	0.0308326i
$538$	−2.56083e9			−0.708995
$539$	4.77560e9	+	1.81093e9i	1.31361	+	0.498127i
$540$	−9.53513e8			−0.260585
$541$	2.02416e9	−	3.50595e9i	0.549610	−	0.951952i	−0.448692	−	0.893687i	$-0.648110\pi$
$541$	2.02416e9	−	3.50595e9i	0.549610	−	0.951952i	0.998301	−	0.0582650i	$-0.0185568\pi$
$542$	7.72714e8	+	1.33838e9i	0.208459	+	0.361062i
$543$	−1.35422e9	−	2.34558e9i	−0.362986	−	0.628710i
$544$	−1.32839e9	+	2.30084e9i	−0.353776	+	0.612759i
$545$	−6.46956e9			−1.71193
$546$	1.26260e9	−	4.50003e8i	0.331965	−	0.118315i
$547$	3.15001e9			0.822917			0.411458	−	0.911429i	$-0.365020\pi$
$547$	3.15001e9			0.822917			0.411458	+	0.911429i	$0.365020\pi$
$548$	1.05839e9	−	1.83319e9i	0.274735	−	0.475855i
$549$	−4.56799e8	−	7.91198e8i	−0.117821	−	0.204071i
$550$	−3.05128e9	−	5.28498e9i	−0.782011	−	1.35448i
$551$	−2.88831e8	+	5.00270e8i	−0.0735552	+	0.127401i
$552$	−9.67276e7			−0.0244773
$553$	1.05327e9	−	5.74819e9i	0.264852	−	1.44542i
$554$	−2.29992e8			−0.0574683
$555$	2.49491e9	−	4.32131e9i	0.619483	−	1.07298i
$556$	3.64063e8	+	6.30575e8i	0.0898285	+	0.155588i
$557$	−1.28499e8	−	2.22567e8i	−0.0315071	−	0.0545718i	0.849842	−	0.527038i	$-0.176697\pi$
$557$	−1.28499e8	−	2.22567e8i	−0.0315071	−	0.0545718i	−0.881349	+	0.472466i	$0.843364\pi$
$558$	258589.	−	447889.i	6.30072e−5	−	0.000109132i
$559$	−7.89456e9			−1.91155
$560$	−1.81570e9	−	1.54438e9i	−0.436905	−	0.371618i
$561$	2.32910e9			0.556953
$562$	−1.15002e9	+	1.99190e9i	−0.273293	+	0.473358i
$563$	2.33078e9	+	4.03703e9i	0.550455	+	0.953415i	0.998242	+	0.0592751i	$0.0188789\pi$
$563$	2.33078e9	+	4.03703e9i	0.550455	+	0.953415i	−0.447787	+	0.894140i	$0.647788\pi$
$564$	−1.43661e9	−	2.48827e9i	−0.337179	−	0.584011i
$565$	2.26536e8	−	3.92371e8i	0.0528405	−	0.0915225i
$566$	−3.71576e9			−0.861370
$567$	−3.67364e8	−	3.12468e8i	−0.0846361	−	0.0719889i
$568$	−1.43515e9			−0.328609
$569$	−1.41323e9	+	2.44779e9i	−0.321604	+	0.557034i	−0.980819	−	0.194920i	$-0.937555\pi$
$569$	−1.41323e9	+	2.44779e9i	−0.321604	+	0.557034i	0.659215	+	0.751954i	$0.270889\pi$
$570$	−4.52038e8	−	7.82952e8i	−0.102238	−	0.177082i
$571$	2.18958e9	+	3.79246e9i	0.492191	+	0.852500i	0.999960	−	0.00899348i	$-0.00286275\pi$
$571$	2.18958e9	+	3.79246e9i	0.492191	+	0.852500i	−0.507768	+	0.861494i	$0.669529\pi$
$572$	2.90295e9	−	5.02806e9i	0.648565	−	1.12335i
$573$	−1.74847e9			−0.388255
$574$	−1.22705e8	+	6.69653e8i	−0.0270813	+	0.147795i
$575$	−4.96058e8			−0.108817
$576$	−1.48199e8	+	2.56687e8i	−0.0323121	+	0.0559662i
$577$	−1.27067e9	−	2.20087e9i	−0.275371	−	0.476957i	0.694857	−	0.719148i	$-0.255467\pi$
$577$	−1.27067e9	−	2.20087e9i	−0.275371	−	0.476957i	−0.970229	+	0.242190i	$0.922134\pi$
$578$	−6.10315e8	−	1.05710e9i	−0.131464	−	0.227702i
$579$	−1.03430e9	+	1.79147e9i	−0.221449	+	0.383560i
$580$	2.36580e9			0.503477
$581$	−1.56829e9	+	5.58954e8i	−0.331750	+	0.118239i
$582$	1.01852e9			0.214160
$583$	−2.39491e9	+	4.14811e9i	−0.500553	+	0.866982i
$584$	2.63327e9	+	4.56096e9i	0.547080	+	0.947570i
$585$	1.78177e9	+	3.08612e9i	0.367965	+	0.637333i
$586$	1.84958e9	−	3.20357e9i	0.379692	−	0.657646i
$587$	−1.61818e9			−0.330213			−0.165106	−	0.986276i	$-0.552797\pi$
$587$	−1.61818e9			−0.330213			−0.165106	+	0.986276i	$0.552797\pi$
$588$	−3.43645e8	−	2.11400e9i	−0.0697091	−	0.428828i
$589$	−1.49092e6			−0.000300642
$590$	1.00871e9	−	1.74713e9i	0.202201	−	0.350222i
$591$	1.98553e9	+	3.43904e9i	0.395659	+	0.685301i
$592$	9.59529e8	+	1.66195e9i	0.190078	+	0.329225i
$593$	1.13749e9	−	1.97018e9i	0.224003	−	0.387985i	−0.732017	−	0.681287i	$-0.761421\pi$
$593$	1.13749e9	−	1.97018e9i	0.224003	−	0.387985i	0.956020	+	0.293302i	$0.0947540\pi$
$594$	6.87066e8			0.134507
$595$	−5.98002e9	+	2.13133e9i	−1.16384	+	0.414803i
$596$	4.54439e9			0.879253
$597$	3.96986e6	−	6.87600e6i	0.000763599	−	0.00132259i
$598$	7.76112e7	+	1.34427e8i	0.0148412	+	0.0257058i
$599$	−2.61737e9	−	4.53342e9i	−0.497589	−	0.861850i	0.502407	−	0.864631i	$-0.332448\pi$
$599$	−2.61737e9	−	4.53342e9i	−0.497589	−	0.861850i	−0.999996	+	0.00278122i	$0.999115\pi$
$600$	−2.97988e9	+	5.16130e9i	−0.563208	+	0.975506i
$601$	5.20968e9			0.978926			0.489463	−	0.872024i	$-0.337193\pi$
$601$	5.20968e9			0.978926			0.489463	+	0.872024i	$0.337193\pi$
$602$	7.47766e8	−	4.08089e9i	0.139694	−	0.762372i
$603$	−5.46908e8			−0.101579
$604$	2.56872e9	−	4.44916e9i	0.474338	−	0.821578i
$605$	−4.77163e9	−	8.26471e9i	−0.876039	−	1.51734i
$606$	2.91345e7	+	5.04624e7i	0.00531806	+	0.00921114i
$607$	3.04091e9	−	5.26701e9i	0.551878	−	0.955881i	−0.446261	−	0.894903i	$-0.647245\pi$
$607$	3.04091e9	−	5.26701e9i	0.551878	−	0.955881i	0.998139	−	0.0609780i	$-0.0194219\pi$
$608$	2.25932e9			0.407676
$609$	9.11480e8	+	7.75277e8i	0.163526	+	0.139090i
$610$	−3.54761e9			−0.632822
$611$	−5.36899e9	+	9.29936e9i	−0.952243	+	1.64933i
$612$	−4.88342e8	−	8.45833e8i	−0.0861180	−	0.149161i
$613$	2.69788e9	+	4.67287e9i	0.473055	+	0.819355i	0.999524	−	0.0308387i	$-0.00981783\pi$
$613$	2.69788e9	+	4.67287e9i	0.473055	+	0.819355i	−0.526469	+	0.850194i	$0.676484\pi$
$614$	6.23787e8	−	1.08043e9i	0.108754	−	0.188368i
$615$	−1.80996e9			−0.313766
$616$	5.41274e9	+	4.60391e9i	0.933007	+	0.793587i
$617$	9.38467e9			1.60850			0.804249	−	0.594292i	$-0.202568\pi$
$617$	9.38467e9			1.60850			0.804249	+	0.594292i	$0.202568\pi$
$618$	−1.14282e9	+	1.97942e9i	−0.194768	+	0.337349i
$619$	1.03338e9	+	1.78987e9i	0.175123	+	0.303322i	0.940204	−	0.340613i	$-0.110634\pi$
$619$	1.03338e9	+	1.78987e9i	0.175123	+	0.303322i	−0.765081	+	0.643934i	$0.777301\pi$
$620$	3.05300e6	+	5.28795e6i	0.000514465	+	0.000891079i
$621$	2.79247e7	−	4.83670e7i	0.00467916	−	0.00810455i
$622$	2.51021e9			0.418258
$623$	−2.29682e8	+	1.25348e9i	−0.0380557	+	0.207687i
$624$	−1.37052e9			−0.225808
$625$	−5.40113e9	+	9.35503e9i	−0.884921	+	1.53273i
$626$	1.51576e9	+	2.62538e9i	0.246957	+	0.427742i
$627$	−9.90335e8	−	1.71531e9i	−0.160452	−	0.277911i
$628$	−3.41745e9	+	5.91920e9i	−0.550609	+	0.953683i
$629$	5.11107e9			0.818907
$630$	−1.76406e9	+	6.28726e8i	−0.281074	+	0.100177i
$631$	−2.45121e9			−0.388399			−0.194200	−	0.980962i	$-0.562211\pi$
$631$	−2.45121e9			−0.388399			−0.194200	+	0.980962i	$0.562211\pi$
$632$	4.06526e9	−	7.04124e9i	0.640588	−	1.10953i
$633$	1.42059e9	+	2.46053e9i	0.222616	+	0.385582i
$634$	3.04001e9	+	5.26546e9i	0.473765	+	0.820585i
$635$	−6.24121e8	+	1.08101e9i	−0.0967299	+	0.167541i
$636$	2.00856e9			0.309588
$637$	−6.19995e9	+	5.06252e9i	−0.950387	+	0.776030i
$638$	−1.70470e9			−0.259882
$639$	4.14321e8	−	7.17625e8i	0.0628179	−	0.108804i
$640$	−5.57267e9	−	9.65215e9i	−0.840298	−	1.45544i
$641$	−3.63409e9	−	6.29443e9i	−0.544995	−	0.943959i	−0.998607	−	0.0527601i	$-0.983198\pi$
$641$	−3.63409e9	−	6.29443e9i	−0.544995	−	0.943959i	0.453612	−	0.891199i	$-0.350135\pi$
$642$	5.56089e8	−	9.63174e8i	0.0829414	−	0.143659i
$643$	8.55284e9			1.26874			0.634369	−	0.773030i	$-0.281260\pi$
$643$	8.55284e9			1.26874			0.634369	+	0.773030i	$0.281260\pi$
$644$	2.33626e8	−	8.32664e7i	0.0344683	−	0.0122848i
$645$	1.10299e10			1.61851
$646$	4.63022e8	−	8.01978e8i	0.0675753	−	0.117044i
$647$	3.30445e8	+	5.72348e8i	0.0479661	+	0.0830797i	0.889012	−	0.457885i	$-0.151393\pi$
$647$	3.30445e8	+	5.72348e8i	0.0479661	+	0.0830797i	−0.841046	+	0.540964i	$0.818059\pi$
$648$	−3.35494e8	−	5.81092e8i	−0.0484364	−	0.0838943i
$649$	2.20990e9	−	3.82766e9i	0.317333	−	0.549638i
$650$	9.56384e9			1.36595
$651$	−556631.	+	3.03778e6i	−7.90741e−5	+	0.000431542i
$652$	−9.47194e9			−1.33836
$653$	8.64218e8	−	1.49687e9i	0.121458	−	0.210372i	−0.798885	−	0.601484i	$-0.794576\pi$
$653$	8.64218e8	−	1.49687e9i	0.121458	−	0.210372i	0.920343	+	0.391112i	$0.127910\pi$
$654$	−9.77421e8	−	1.69294e9i	−0.136634	−	0.236657i
$655$	−7.05998e9	−	1.22282e10i	−0.981655	−	1.70028i
$656$	3.48051e8	−	6.02841e8i	0.0481370	−	0.0833757i
$657$	−3.04084e9			−0.418326
$658$	−4.29852e9	−	3.65619e9i	−0.588204	−	0.500308i
$659$	−4.19192e9			−0.570576			−0.285288	−	0.958442i	$-0.592089\pi$
$659$	−4.19192e9			−0.570576			−0.285288	+	0.958442i	$0.592089\pi$
$660$	−4.05588e9	+	7.02500e9i	−0.549138	+	0.951136i
$661$	3.78878e9	+	6.56236e9i	0.510263	+	0.883802i	0.999929	+	0.0118920i	$0.00378543\pi$
$661$	3.78878e9	+	6.56236e9i	0.510263	+	0.883802i	−0.489666	+	0.871910i	$0.662881\pi$
$662$	−2.17291e8	−	3.76358e8i	−0.0291097	−	0.0504195i
$663$	−1.82507e9	+	3.16111e9i	−0.243210	+	0.421252i
$664$	−2.31639e9			−0.307059
$665$	4.11236e9	+	3.49785e9i	0.542270	+	0.461238i
$666$	1.50772e9			0.197771
$667$	−6.92850e7	+	1.20005e8i	−0.00904064	+	0.0156588i
$668$	3.54840e9	+	6.14600e9i	0.460590	+	0.797765i
$669$	−4.97251e7	−	8.61264e7i	−0.00642073	−	0.0111210i
$670$	−1.06186e9	+	1.83919e9i	−0.136397	+	0.236246i
$671$	−7.77219e9			−0.993149
$672$	8.43515e8	−	4.60343e9i	0.107226	−	0.585180i
$673$	5.50701e9			0.696407			0.348203	−	0.937419i	$-0.386792\pi$
$673$	5.50701e9			0.696407			0.348203	+	0.937419i	$0.386792\pi$
$674$	−3.26525e9	+	5.65558e9i	−0.410777	+	0.711487i
$675$	−1.72055e9	−	2.98008e9i	−0.215329	−	0.372962i
$676$	1.52748e9	+	2.64567e9i	0.190179	+	0.329400i
$677$	4.86653e9	−	8.42908e9i	0.602781	−	1.04405i	−0.389617	−	0.920977i	$-0.627393\pi$
$677$	4.86653e9	−	8.42908e9i	0.602781	−	1.04405i	0.992398	−	0.123070i	$-0.0392740\pi$
$678$	1.36900e8			0.0168694
$679$	−5.72914e9	+	2.04192e9i	−0.702337	+	0.250319i
$680$	−8.83255e9			−1.07722
$681$	1.04245e8	−	1.80557e8i	0.0126485	−	0.0219079i
$682$	−2.19988e6	−	3.81030e6i	−0.000265554	−	0.000459953i
$683$	−4.84040e9	−	8.38382e9i	−0.581311	−	1.00686i	−0.995324	−	0.0965899i	$-0.969206\pi$
$683$	−4.84040e9	−	8.38382e9i	−0.581311	−	1.00686i	0.414013	−	0.910271i	$-0.364127\pi$
$684$	−4.15286e8	+	7.19296e8i	−0.0496193	+	0.0859432i
$685$	1.10529e10			1.31389
$686$	−2.02969e9	−	3.68442e9i	−0.240046	−	0.435748i
$687$	−7.96767e9			−0.937524
$688$	−2.12103e9	+	3.67373e9i	−0.248306	+	0.430079i
$689$	−3.75327e9	−	6.50085e9i	−0.437162	−	0.757186i
$690$	−1.08435e8	−	1.87815e8i	−0.0125660	−	0.0217650i
$691$	2.76919e9	−	4.79637e9i	0.319285	−	0.553019i	−0.661054	−	0.750339i	$-0.729890\pi$
$691$	2.76919e9	−	4.79637e9i	0.319285	−	0.553019i	0.980339	+	0.197320i	$0.0632238\pi$
$692$	1.07248e10			1.23032
$693$	−3.86473e9	+	1.37743e9i	−0.441117	+	0.157218i
$694$	4.82815e9			0.548306
$695$	−1.90097e9	+	3.29258e9i	−0.214798	+	0.372040i
$696$	8.32406e8	+	1.44177e9i	0.0935843	+	0.162093i
$697$	−9.26971e8	−	1.60556e9i	−0.103693	−	0.179602i
$698$	−6.78631e7	+	1.17542e8i	−0.00755335	+	0.0130828i
$699$	−2.69437e9			−0.298392
$700$	2.75427e9	−	1.50312e10i	0.303503	−	1.65635i
$701$	−1.27820e10			−1.40148			−0.700738	−	0.713419i	$-0.747146\pi$
$701$	−1.27820e10			−1.40148			−0.700738	+	0.713419i	$0.747146\pi$
$702$	−5.38379e8	+	9.32500e8i	−0.0587365	+	0.101735i
$703$	−2.17323e9	−	3.76414e9i	−0.235918	−	0.408622i
$704$	1.26076e9	+	2.18370e9i	0.136185	+	0.235879i
$705$	7.50132e9	−	1.29927e10i	0.806262	−	1.39649i
$706$	−3.59897e9			−0.384912
$707$	−2.65048e8	−	2.25441e8i	−0.0282069	−	0.0239920i
$708$	−1.85339e9			−0.196269
$709$	−1.87549e9	+	3.24845e9i	−0.197630	+	0.342306i	−0.947760	−	0.318985i	$-0.896658\pi$
$709$	−1.87549e9	+	3.24845e9i	−0.197630	+	0.342306i	0.750129	+	0.661291i	$0.229991\pi$
$710$	−1.60886e9	−	2.78663e9i	−0.168700	−	0.292196i
$711$	2.34723e9	+	4.06553e9i	0.244914	+	0.424203i
$712$	−8.86491e8	+	1.53545e9i	−0.0920437	+	0.159424i
$713$	−357642.			−3.69518e−5
$714$	−1.46118e9	−	1.24284e9i	−0.150232	−	0.127782i
$715$	3.03159e10			3.10169
$716$	2.27884e8	−	3.94706e8i	0.0232016	−	0.0401864i
$717$	2.41729e9	+	4.18686e9i	0.244913	+	0.424201i
$718$	2.95102e9	+	5.11131e9i	0.297534	+	0.515344i
$719$	−7.78801e9	+	1.34892e10i	−0.781403	+	1.35343i	0.149721	+	0.988728i	$0.452162\pi$
$719$	−7.78801e9	+	1.34892e10i	−0.781403	+	1.35343i	−0.931124	+	0.364702i	$0.881171\pi$
$720$	1.91483e9			0.191191
$721$	2.46001e9	−	1.34254e10i	0.244435	−	1.33399i
$722$	4.24363e9			0.419621
$723$	9.59579e8	−	1.66204e9i	0.0944271	−	0.163553i
$724$	4.83107e9	+	8.36766e9i	0.473106	+	0.819443i
$725$	4.26891e9	+	7.39398e9i	0.416039	+	0.720601i
$726$	1.44180e9	−	2.49726e9i	0.139838	−	0.242207i
$727$	−2.04219e10			−1.97118			−0.985589	−	0.169158i	$-0.945895\pi$
$727$	−2.04219e10			−1.97118			−0.985589	+	0.169158i	$0.945895\pi$
$728$	−1.04899e10	+	3.73870e9i	−1.00765	+	0.359137i
$729$	3.87420e8			0.0370370
$730$	−5.90398e9	+	1.02260e10i	−0.561714	+	0.972917i
$731$	5.64899e9	+	9.78433e9i	0.534884	+	0.926447i
$732$	1.62959e9	+	2.82253e9i	0.153564	+	0.265981i
$733$	−1.13462e9	+	1.96521e9i	−0.106411	+	0.184309i	−0.914314	−	0.405007i	$-0.867269\pi$
$733$	−1.13462e9	+	1.96521e9i	−0.106411	+	0.184309i	0.807903	+	0.589315i	$0.200602\pi$
$734$	−5.11556e8			−0.0477482
$735$	8.66232e9	−	7.07314e9i	0.804690	−	0.657063i
$736$	5.41968e8			0.0501073
$737$	−2.32634e9	+	4.02934e9i	−0.214061	+	0.370764i
$738$	−2.73449e8	−	4.73627e8i	−0.0250425	−	0.0433749i
$739$	−9.23031e9	−	1.59874e10i	−0.841319	−	1.45721i	−0.888780	−	0.458334i	$-0.848446\pi$
$739$	−9.23031e9	−	1.59874e10i	−0.841319	−	1.45721i	0.0474611	−	0.998873i	$-0.484887\pi$
$740$	−8.90038e9	+	1.54159e10i	−0.807417	+	1.39849i
$741$	3.10407e9			0.280264
$742$	3.71595e9	−	1.32440e9i	0.333931	−	0.119016i
$743$	1.77069e10			1.58373			0.791866	−	0.610695i	$-0.209110\pi$
$743$	1.77069e10			1.58373			0.791866	+	0.610695i	$0.209110\pi$
$744$	−2.14840e6	+	3.72113e6i	−0.000191253	+	0.000331260i
$745$	1.18644e10	+	2.05498e10i	1.05123	+	1.82079i
$746$	−3.52052e9	−	6.09771e9i	−0.310471	−	0.537751i
$747$	6.68727e8	−	1.15827e9i	0.0586985	−	0.101669i
$748$	−8.30888e9			−0.725917
$749$	−1.19702e9	+	6.53268e9i	−0.104092	+	0.568074i
$750$	−7.39099e9			−0.639717
$751$	8.13389e9	−	1.40883e10i	0.700742	−	1.21372i	−0.267464	−	0.963568i	$-0.586186\pi$
$751$	8.13389e9	−	1.40883e10i	0.700742	−	1.21372i	0.968206	−	0.250153i	$-0.0804810\pi$
$752$	2.88497e9	+	4.99692e9i	0.247388	+	0.428489i
$753$	7.90531e8	+	1.36924e9i	0.0674740	+	0.116868i
$754$	1.33579e9	−	2.31366e9i	0.113485	−	0.196562i
$755$	2.68255e10			2.26847
$756$	1.31054e9	+	1.11471e9i	0.110312	+	0.0938283i
$757$	−2.16032e10			−1.81002			−0.905008	−	0.425394i	$-0.860135\pi$
$757$	−2.16032e10			−1.81002			−0.905008	+	0.425394i	$0.860135\pi$
$758$	2.12775e9	−	3.68538e9i	0.177451	−	0.307355i
$759$	−2.37562e8	−	4.11470e8i	−0.0197211	−	0.0341580i
$760$	3.75560e9	+	6.50489e9i	0.310336	+	0.537517i
$761$	2.78515e9	−	4.82401e9i	0.229088	−	0.396791i	−0.728450	−	0.685099i	$-0.759759\pi$
$761$	2.78515e9	−	4.82401e9i	0.229088	−	0.396791i	0.957538	+	0.288307i	$0.0930924\pi$
$762$	−3.77168e8			−0.0308811
$763$	8.89198e9	+	7.56324e9i	0.724707	+	0.616413i
$764$	6.23752e9			0.506040
$765$	2.54991e9	−	4.41657e9i	0.205925	−	0.356673i
$766$	1.61499e9	+	2.79724e9i	0.129828	+	0.224869i
$767$	3.46331e9	+	5.99864e9i	0.277146	+	0.480031i
$768$	2.38641e9	−	4.13338e9i	0.190099	−	0.329262i
$769$	−2.06958e10			−1.64112			−0.820558	−	0.571563i	$-0.806337\pi$
$769$	−2.06958e10			−1.64112			−0.820558	+	0.571563i	$0.806337\pi$
$770$	−2.87149e9	+	1.56710e10i	−0.226668	+	1.23703i
$771$	7.51917e9			0.590853
$772$	3.68979e9	−	6.39091e9i	0.288630	−	0.499922i
$773$	−8.11373e9	−	1.40534e10i	−0.631819	−	1.09434i	−0.987180	−	0.159613i	$-0.948975\pi$
$773$	−8.11373e9	−	1.40534e10i	−0.631819	−	1.09434i	0.355361	−	0.934729i	$-0.384358\pi$
$774$	1.66640e9	+	2.88630e9i	0.129178	+	0.223742i
$775$	−1.10178e7	+	1.90835e7i	−0.000850238	+	0.00147266i
$776$	−8.46200e9			−0.650066
$777$	−8.48092e9	+	3.02268e9i	−0.648588	+	0.231163i
$778$	−1.19307e10			−0.908320
$779$	−7.88296e8	+	1.36537e9i	−0.0597459	+	0.103483i
$780$	−6.35631e9	−	1.10095e10i	−0.479595	−	0.830682i
$781$	−3.52473e9	−	6.10501e9i	−0.264757	−	0.458572i
$782$	1.11070e8	−	1.92379e8i	0.00830565	−	0.0143858i
$783$	−9.61243e8			−0.0715595
$784$	6.90103e8	+	4.24529e9i	0.0511455	+	0.314631i
$785$	−3.56889e10			−2.63323
$786$	2.13324e9	−	3.69488e9i	0.156697	−	0.271407i
$787$	−4.10073e9	−	7.10268e9i	−0.299882	−	0.519410i	0.676227	−	0.736693i	$-0.263614\pi$
$787$	−4.10073e9	−	7.10268e9i	−0.299882	−	0.519410i	−0.976109	+	0.217283i	$0.930281\pi$
$788$	−7.08322e9	−	1.22685e10i	−0.515690	−	0.893202i
$789$	−3.35826e8	+	5.81668e8i	−0.0243414	+	0.0421605i
$790$	1.82292e10			1.31545
$791$	−7.70060e8	+	2.74456e8i	−0.0553231	+	0.0197177i
$792$	−5.70825e9			−0.408287
$793$	6.09022e9	−	1.05486e10i	0.433688	−	0.751169i
$794$	3.89909e9	+	6.75342e9i	0.276434	+	0.478797i
$795$	5.24391e9	+	9.08272e9i	0.370144	+	0.641107i
$796$	−1.41621e7	+	2.45296e7i	−0.000995253	+	0.00172383i
$797$	1.97600e10			1.38255			0.691276	−	0.722590i	$-0.257049\pi$
$797$	1.97600e10			1.38255			0.691276	+	0.722590i	$0.257049\pi$
$798$	−2.94015e8	+	1.60457e9i	−0.0204814	+	0.111776i
$799$	1.53672e10			1.06581
$800$	1.66963e10	−	2.89189e10i	1.15294	−	1.99695i
$801$	−5.11850e8	−	8.86550e8i	−0.0351908	−	0.0609522i
$802$	1.23829e9	+	2.14478e9i	0.0847639	+	0.146815i
$803$	−1.29346e10	+	2.24034e10i	−0.881552	+	1.52689i
$804$	1.95105e9			0.132395
$805$	9.86477e8	+	8.39067e8i	0.0666502	+	0.0566906i
$806$	6.89522e6			0.000463848
$807$	−6.14220e9	+	1.06386e10i	−0.411402	+	0.712569i
$808$	−2.42054e8	−	4.19249e8i	−0.0161425	−	0.0279597i
$809$	5.83956e8	+	1.01144e9i	0.0387757	+	0.0671615i	0.884762	−	0.466043i	$-0.154321\pi$
$809$	5.83956e8	+	1.01144e9i	0.0387757	+	0.0671615i	−0.845986	+	0.533205i	$0.820988\pi$
$810$	7.52201e8	−	1.30285e9i	0.0497321	−	0.0861384i
$811$	−1.21328e10			−0.798711			−0.399356	−	0.916796i	$-0.630766\pi$
$811$	−1.21328e10			−0.798711			−0.399356	+	0.916796i	$0.630766\pi$
$812$	−3.25163e9	−	2.76574e9i	−0.213135	−	0.181286i
$813$	7.41347e9			0.483843
$814$	6.41328e9	−	1.11081e10i	0.416769	−	0.721864i
$815$	−2.47292e10	−	4.28321e10i	−1.60014	−	2.77152i
$816$	9.80681e8	+	1.69859e9i	0.0631847	+	0.109439i
$817$	4.80390e9	−	8.32060e9i	0.308189	−	0.533798i
$818$	4.06102e8			0.0259417
$819$	1.15890e9	−	6.32464e9i	0.0737145	−	0.402292i
$820$	6.45688e9			0.408954
$821$	−9.54695e7	+	1.65358e8i	−0.00602093	+	0.0104286i	−0.869020	−	0.494777i	$-0.835250\pi$
$821$	−9.54695e7	+	1.65358e8i	−0.00602093	+	0.0104286i	0.862999	+	0.505205i	$0.168583\pi$
$822$	1.66987e9	+	2.89230e9i	0.104865	+	0.181632i
$823$	5.70929e9	+	9.88878e9i	0.357012	+	0.618362i	0.987460	−	0.157869i	$-0.0504623\pi$
$823$	5.70929e9	+	9.88878e9i	0.357012	+	0.618362i	−0.630448	+	0.776231i	$0.717129\pi$
$824$	9.49474e9	−	1.64454e10i	0.591205	−	1.02400i
$825$	−2.92742e10			−1.81508
$826$	−3.42888e9	+	1.22209e9i	−0.211701	+	0.0754521i
$827$	−1.33839e9			−0.0822834			−0.0411417	−	0.999153i	$-0.513100\pi$
$827$	−1.33839e9			−0.0822834			−0.0411417	+	0.999153i	$0.513100\pi$
$828$	−9.96191e7	+	1.72545e8i	−0.00609869	+	0.0105632i
$829$	1.01269e8	+	1.75402e8i	0.00617353	+	0.0106929i	0.869096	−	0.494644i	$-0.164702\pi$
$829$	1.01269e8	+	1.75402e8i	0.00617353	+	0.0106929i	−0.862922	+	0.505337i	$0.831368\pi$
$830$	−2.59675e9	−	4.49770e9i	−0.157637	−	0.273035i
$831$	−5.51640e8	+	9.55468e8i	−0.0333466	+	0.0577581i
$832$	−3.95169e9			−0.237876
$833$	1.07108e10	+	4.06157e9i	0.642042	+	0.243465i
$834$	−1.14880e9			−0.0685744
$835$	−1.85282e10	+	3.20917e10i	−1.10136	+	1.90761i
$836$	3.53294e9	+	6.11923e9i	0.209129	+	0.362222i
$837$	−1.24046e6	−	2.14854e6i	−7.31212e−5	−	0.000126650i
$838$	3.33384e9	−	5.77437e9i	0.195700	−	0.338962i
$839$	2.24187e10			1.31052			0.655259	−	0.755405i	$-0.272560\pi$
$839$	2.24187e10			1.31052			0.655259	+	0.755405i	$0.272560\pi$
$840$	1.46561e10	−	5.22355e9i	0.853178	−	0.304080i
$841$	−1.48649e10			−0.861739
$842$	−6.42834e8	+	1.11342e9i	−0.0371113	+	0.0642787i
$843$	5.51669e9	+	9.55519e9i	0.317163	+	0.549342i
$844$	−5.06784e9	−	8.77775e9i	−0.290151	−	0.502556i
$845$	−7.97584e9	+	1.38146e10i	−0.454755	+	0.787659i
$846$	4.53320e9			0.257400
$847$	−3.10357e9	+	1.69376e10i	−0.175497	+	0.957766i
$848$	−4.03356e9			−0.227145
$849$	−8.91231e9	+	1.54366e10i	−0.499819	+	0.865713i
$850$	−6.84345e9	−	1.18532e10i	−0.382216	−	0.662018i
$851$	−5.21315e8	−	9.02945e8i	−0.0289966	−	0.0502236i
$852$	−1.47805e9	+	2.56007e9i	−0.0818751	+	0.141812i
$853$	−1.43556e10			−0.791952			−0.395976	−	0.918261i	$-0.629594\pi$
$853$	−1.43556e10			−0.791952			−0.395976	+	0.918261i	$0.629594\pi$
$854$	4.87595e9	+	4.14734e9i	0.267890	+	0.227859i
$855$	−4.33688e9			−0.237299
$856$	−4.62007e9	+	8.00220e9i	−0.251762	+	0.436065i
$857$	4.29142e9	+	7.43295e9i	0.232899	+	0.403393i	0.958660	−	0.284554i	$-0.0918455\pi$
$857$	4.29142e9	+	7.43295e9i	0.232899	+	0.403393i	−0.725761	+	0.687947i	$0.758512\pi$
$858$	4.58012e9	+	7.93300e9i	0.247555	+	0.428778i
$859$	−5.04094e9	+	8.73117e9i	−0.271354	+	0.469998i	−0.969209	−	0.246241i	$-0.920805\pi$
$859$	−5.04094e9	+	8.73117e9i	−0.271354	+	0.469998i	0.697855	+	0.716239i	$0.254138\pi$
$860$	−3.93484e10			−2.10952
$861$	2.48767e9	+	2.11593e9i	0.132825	+	0.112977i
$862$	2.99511e9			0.159271
$863$	1.70490e10	−	2.95298e10i	0.902946	−	1.56395i	0.0792950	−	0.996851i	$-0.474733\pi$
$863$	1.70490e10	−	2.95298e10i	0.902946	−	1.56395i	0.823651	−	0.567097i	$-0.191934\pi$
$864$	1.87978e9	+	3.25588e9i	0.0991538	+	0.171739i
$865$	2.80000e10	+	4.84975e10i	1.47096	+	2.54778i
$866$	−9.99604e8	+	1.73136e9i	−0.0523016	+	0.0905891i
$867$	−5.85540e9			−0.305134
$868$	1.98574e6	−	1.08370e7i	0.000103063	−	0.000562460i
$869$	3.99370e10			2.06446
$870$	−1.86631e9	+	3.23255e9i	−0.0960876	+	0.166429i
$871$	−3.64580e9	−	6.31471e9i	−0.186952	−	0.323810i
$872$	8.12056e9	+	1.40652e10i	0.414742	+	0.718355i
$873$	2.44293e9	−	4.23128e9i	0.124269	−	0.215240i
$874$	−1.88908e8			−0.00957107
$875$	4.15742e10	−	1.48174e10i	2.09795	−	0.747729i
$876$	1.08479e10			0.545234
$877$	1.38568e10	−	2.40006e10i	0.693687	−	1.20150i	−0.276934	−	0.960889i	$-0.589318\pi$
$877$	1.38568e10	−	2.40006e10i	0.693687	−	1.20150i	0.970621	−	0.240612i	$-0.0773483\pi$
$878$	−1.61315e9	−	2.79406e9i	−0.0804349	−	0.139317i
$879$	−8.87251e9	−	1.53676e10i	−0.440641	−	0.763213i
$880$	8.14497e9	−	1.41075e10i	0.402903	−	0.697848i
$881$	−1.61765e10			−0.797020			−0.398510	−	0.917164i	$-0.630473\pi$
$881$	−1.61765e10			−0.797020			−0.398510	+	0.917164i	$0.630473\pi$
$882$	3.15959e9	+	1.19813e9i	0.155057	+	0.0587981i
$883$	2.67909e10			1.30956			0.654780	−	0.755820i	$-0.272761\pi$
$883$	2.67909e10			1.30956			0.654780	+	0.755820i	$0.272761\pi$
$884$	6.51077e9	−	1.12770e10i	0.316993	−	0.549048i
$885$	−4.83880e9	−	8.38105e9i	−0.234658	−	0.406440i
$886$	4.52833e9	+	7.84330e9i	0.218736	+	0.378862i
$887$	−1.74706e9	+	3.02600e9i	−0.0840573	+	0.145591i	−0.904989	−	0.425435i	$-0.860121\pi$
$887$	−1.74706e9	+	3.02600e9i	−0.0840573	+	0.145591i	0.820932	+	0.571026i	$0.193455\pi$
$888$	−1.25264e10			−0.600317
$889$	2.12157e9	−	7.56146e8i	0.101275	−	0.0360952i
$890$	−3.97515e9			−0.189012
$891$	1.64794e9	−	2.85432e9i	0.0780494	−	0.135185i
$892$	1.77390e8	+	3.07249e8i	0.00836859	+	0.0144948i
$893$	−6.53414e9	−	1.13175e10i	−0.307049	−	0.531825i
$894$	−3.58495e9	+	6.20932e9i	−0.167804	+	0.290645i
$895$	2.37982e9			0.110959
$896$	−3.62458e9	+	1.97810e10i	−0.168337	+	0.918691i
$897$	7.44607e8			0.0344472
$898$	7.32041e9	−	1.26793e10i	0.337340	−	0.584291i
$899$	3.07775e6	+	5.33082e6i	0.000141278	+	0.000244701i
$900$	6.13791e9	+	1.06312e10i	0.280654	+	0.486107i
$901$	−5.37133e9	+	9.30342e9i	−0.244650	+	0.423746i
$902$	−4.65259e9			−0.211092
$903$	−1.51599e10	−	1.28946e10i	−0.685157	−	0.582773i
$904$	−1.13739e9			−0.0512057
$905$	−2.52257e10	+	4.36922e10i	−1.13129	+	1.95945i
$906$	4.05279e9	+	7.01964e9i	0.181053	+	0.313593i
$907$	1.40268e10	+	2.42952e10i	0.624215	+	1.08117i	0.988692	+	0.149959i	$0.0479143\pi$
$907$	1.40268e10	+	2.42952e10i	0.624215	+	1.08117i	−0.364477	+	0.931212i	$0.618752\pi$
$908$	−3.71885e8	+	6.44123e8i	−0.0164857	+	0.0285541i
$909$	2.79518e8			0.0123434
$910$	−1.90189e10	−	1.61769e10i	−0.836646	−	0.711625i
$911$	−2.81753e10			−1.23468			−0.617341	−	0.786696i	$-0.711790\pi$
$911$	−2.81753e10			−1.23468			−0.617341	+	0.786696i	$0.711790\pi$
$912$	8.33971e8	−	1.44448e9i	0.0364057	−	0.0630565i
$913$	−5.68902e9	−	9.85368e9i	−0.247394	−	0.428500i
$914$	−7.85820e9	−	1.36108e10i	−0.340417	−	0.589620i
$915$	−8.50901e9	+	1.47380e10i	−0.367202	+	0.636013i
$916$	2.84240e10			1.22194
$917$	−4.59196e9	+	2.50604e10i	−0.196655	+	1.07323i
$918$	1.54096e9			0.0657418
$919$	1.41657e10	−	2.45357e10i	0.602052	−	1.04278i	−0.390458	−	0.920621i	$-0.627683\pi$
$919$	1.41657e10	−	2.45357e10i	0.602052	−	1.04278i	0.992510	−	0.122163i	$-0.0389832\pi$
$920$	9.00896e8	+	1.56040e9i	0.0381432	+	0.0660660i
$921$	−2.99233e9	−	5.18287e9i	−0.126212	−	0.218606i
$922$	−6.87719e9	+	1.19116e10i	−0.288970	+	0.500511i
$923$	1.10478e10			0.462455
$924$	1.37871e10	−	4.91386e9i	0.574939	−	0.204913i
$925$	−6.42404e10			−2.66878
$926$	−1.62838e9	+	2.82044e9i	−0.0673935	+	0.116729i
$927$	5.48215e9	+	9.49537e9i	0.226033	+	0.391501i
$928$	−4.66400e9	−	8.07828e9i	−0.191576	−	0.331819i
$929$	2.01385e10	−	3.48810e10i	0.824086	−	1.42736i	−0.0785291	−	0.996912i	$-0.525022\pi$
$929$	2.01385e10	−	3.48810e10i	0.824086	−	1.42736i	0.902616	−	0.430448i	$-0.141644\pi$
$930$	−9.63371e6			−0.000392738
$931$	−1.56301e9	−	9.61512e9i	−0.0634800	−	0.390509i
$932$	9.61193e9			0.388915
$933$	6.02079e9	−	1.04283e10i	0.242699	−	0.420367i
$934$	−1.09001e10	−	1.88796e10i	−0.437742	−	0.758191i
$935$	−2.16927e10	−	3.75728e10i	−0.867906	−	1.50326i
$936$	4.47294e9	−	7.74736e9i	0.178290	−	0.308808i
$937$	−2.09269e10			−0.831029			−0.415514	−	0.909587i	$-0.636398\pi$
$937$	−2.09269e10			−0.831029			−0.415514	+	0.909587i	$0.636398\pi$
$938$	3.60956e9	−	1.28648e9i	0.142805	−	0.0508971i
$939$	1.45423e10			0.573198
$940$	−2.67603e10	+	4.63503e10i	−1.05086	+	1.82014i
$941$	8.70847e8	+	1.50835e9i	0.0340705	+	0.0590118i	0.882558	−	0.470204i	$-0.155820\pi$
$941$	8.70847e8	+	1.50835e9i	0.0340705	+	0.0590118i	−0.848487	+	0.529216i	$0.822486\pi$
$942$	−5.39187e9	−	9.33899e9i	−0.210165	−	0.364017i
$943$	−1.89097e8	+	3.27526e8i	−0.00734334	+	0.0127190i
$944$	3.72196e9			0.144002
$945$	−1.61917e9	+	8.83652e9i	−0.0624138	+	0.340620i
$946$	2.83530e10			1.08888
$947$	1.29476e10	−	2.24258e10i	0.495408	−	0.858072i	−0.504578	−	0.863366i	$-0.668352\pi$
$947$	1.29476e10	−	2.24258e10i	0.495408	−	0.858072i	0.999986	+	0.00529407i	$0.00168516\pi$
$948$	−8.37356e9	−	1.45034e10i	−0.319213	−	0.552894i
$949$	−2.02709e10	−	3.51102e10i	−0.769911	−	1.33352i
$950$	−5.81967e9	+	1.00800e10i	−0.220225	+	0.381440i
$951$	2.91661e10			1.09963
$952$	1.21398e10	+	1.03257e10i	0.456016	+	0.387873i
$953$	−3.87113e9			−0.144881			−0.0724407	−	0.997373i	$-0.523079\pi$
$953$	−3.87113e9			−0.144881			−0.0724407	+	0.997373i	$0.523079\pi$
$954$	−1.58450e9	+	2.74443e9i	−0.0590844	+	0.102337i
$955$	1.62848e10	+	2.82061e10i	0.605021	+	1.04793i
$956$	−8.62347e9	−	1.49363e10i	−0.319212	−	0.552892i
$957$	−4.08876e9	+	7.08195e9i	−0.150800	+	0.261193i
$958$	−1.12702e10			−0.414144
$959$	−1.51915e10	−	1.29214e10i	−0.556205	−	0.473091i
$960$	5.52113e9			0.201409
$961$	1.37563e10	−	2.38266e10i	0.500000	−	0.866025i
$962$	1.00508e10	+	1.74085e10i	0.363988	+	0.630446i
$963$	−2.66758e9	−	4.62038e9i	−0.0962554	−	0.166719i
$964$	−3.42322e9	+	5.92919e9i	−0.123074	+	0.213170i
$965$	3.85329e10			1.38034
$966$	−7.05285e7	+	3.84905e8i	−0.00251736	+	0.0137383i
$967$	−1.34763e9			−0.0479266			−0.0239633	−	0.999713i	$-0.507628\pi$
$967$	−1.34763e9			−0.0479266			−0.0239633	+	0.999713i	$0.507628\pi$
$968$	−1.19787e10	+	2.07477e10i	−0.424468	+	0.735200i
$969$	−2.22113e9	−	3.84712e9i	−0.0784226	−	0.135832i
$970$	−9.48621e9	−	1.64306e10i	−0.333727	−	0.578033i
$971$	−2.62011e10	+	4.53816e10i	−0.918443	+	1.59079i	−0.116662	+	0.993172i	$0.537220\pi$
$971$	−2.62011e10	+	4.53816e10i	−0.918443	+	1.59079i	−0.801781	+	0.597618i	$0.796114\pi$
$972$	−1.38209e9			−0.0482730
$973$	6.46196e9	−	2.30310e9i	0.224890	−	0.0801527i
$974$	−2.44104e10			−0.846484
$975$	2.29390e10	−	3.97316e10i	0.792609	−	1.37284i
$976$	−3.27252e9	−	5.66817e9i	−0.112670	−	0.195150i
$977$	2.55095e10	+	4.41838e10i	0.875128	+	1.51577i	0.856626	+	0.515938i	$0.172556\pi$
$977$	2.55095e10	+	4.41838e10i	0.875128	+	1.51577i	0.0185021	+	0.999829i	$0.494110\pi$
$978$	7.47216e9	−	1.29422e10i	0.255423	−	0.442406i
$979$	−8.70886e9			−0.296635
$980$	−3.09021e10	+	2.52328e10i	−1.04881	+	0.856397i
$981$	−9.37744e9			−0.317134
$982$	−1.30253e10	+	2.25604e10i	−0.438931	+	0.760251i
$983$	2.19807e10	+	3.80717e10i	0.738082	+	1.27840i	0.953358	+	0.301842i	$0.0976015\pi$
$983$	2.19807e10	+	3.80717e10i	0.738082	+	1.27840i	−0.215276	+	0.976553i	$0.569065\pi$
$984$	2.27185e9	+	3.93497e9i	0.0760147	+	0.131661i
$985$	3.69855e10	−	6.40607e10i	1.23312	−	2.13582i
$986$	−3.82333e9			−0.127020
$987$	−2.54992e10	+	9.08814e9i	−0.844143	+	0.300860i
$988$	−1.10735e10			−0.365289
$989$	1.15236e9	−	1.99595e9i	0.0378793	−	0.0656089i
$990$	−6.39916e9	−	1.10837e10i	−0.209604	−	0.363045i
$991$	−6.08355e9	−	1.05370e10i	−0.198563	−	0.343922i	0.749500	−	0.662005i	$-0.230294\pi$
$991$	−6.08355e9	−	1.05370e10i	−0.198563	−	0.343922i	−0.948063	+	0.318083i	$0.896961\pi$
$992$	1.20375e7	−	2.08496e7i	0.000391513	−	0.000678121i
$993$	−2.08470e9			−0.0675650
$994$	−1.04644e9	+	5.71087e9i	−0.0337956	+	0.184438i
$995$	−1.47897e8			−0.00475969
$996$	−2.38563e9	+	4.13203e9i	−0.0765059	+	0.132512i
$997$	2.00273e9	+	3.46883e9i	0.0640013	+	0.110853i	0.896251	−	0.443548i	$-0.146280\pi$
$997$	2.00273e9	+	3.46883e9i	0.0640013	+	0.110853i	−0.832249	+	0.554402i	$0.812947\pi$
$998$	7.07165e9	+	1.22485e10i	0.225198	+	0.390054i
$999$	3.61630e9	−	6.26362e9i	0.114759	−	0.198768i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.8.e.a.16.3	yes	8
3.2	odd	2		63.8.e.c.37.2		8
7.2	even	3		147.8.a.i.1.2		4
7.3	odd	6		147.8.e.k.67.3		8
7.4	even	3	inner	21.8.e.a.4.3	✓	8
7.5	odd	6		147.8.a.h.1.2		4
7.6	odd	2		147.8.e.k.79.3		8
21.2	odd	6		441.8.a.q.1.3		4
21.5	even	6		441.8.a.r.1.3		4
21.11	odd	6		63.8.e.c.46.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.8.e.a.4.3	✓	8	7.4	even	3	inner
21.8.e.a.16.3	yes	8	1.1	even	1	trivial
63.8.e.c.37.2		8	3.2	odd	2
63.8.e.c.46.2		8	21.11	odd	6
147.8.a.h.1.2		4	7.5	odd	6
147.8.a.i.1.2		4	7.2	even	3
147.8.e.k.67.3		8	7.3	odd	6
147.8.e.k.79.3		8	7.6	odd	2
441.8.a.q.1.3		4	21.2	odd	6
441.8.a.r.1.3		4	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	21.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.81424 - 4.87440i) q^{2} +(-13.5000 - 23.3827i) q^{3} +(48.1601 + 83.4158i) q^{4} +(-251.471 + 435.561i) q^{5} -151.969 q^{6} +(854.822 - 304.667i) q^{7} +1262.58 q^{8} +(-364.500 + 631.333i) q^{9} +O(q^{10})\)	\(q+(2.81424 - 4.87440i) q^{2} +(-13.5000 - 23.3827i) q^{3} +(48.1601 + 83.4158i) q^{4} +(-251.471 + 435.561i) q^{5} -151.969 q^{6} +(854.822 - 304.667i) q^{7} +1262.58 q^{8} +(-364.500 + 631.333i) q^{9} +(1415.40 + 2451.54i) q^{10} +(3100.89 + 5370.90i) q^{11} +(1300.32 - 2252.23i) q^{12} -9719.32 q^{13} +(920.606 - 5024.15i) q^{14} +13579.4 q^{15} +(-2611.29 + 4522.89i) q^{16} +(6954.71 + 12045.9i) q^{17} +(2051.58 + 3553.44i) q^{18} +(5914.28 - 10243.8i) q^{19} -48443.5 q^{20} +(-18664.0 - 15875.0i) q^{21} +34906.6 q^{22} +(1418.72 - 2457.30i) q^{23} +(-17044.8 - 29522.5i) q^{24} +(-87412.9 - 151404. i) q^{25} +(-27352.5 + 47375.9i) q^{26} +19683.0 q^{27} +(66582.4 + 56632.9i) q^{28} -48836.2 q^{29} +(38215.8 - 66191.7i) q^{30} +(-63.0218 - 109.157i) q^{31} +(95502.8 + 165416. i) q^{32} +(83724.0 - 145014. i) q^{33} +78288.8 q^{34} +(-82262.3 + 448942. i) q^{35} -70217.5 q^{36} +(183727. - 318225. i) q^{37} +(-33288.4 - 57657.2i) q^{38} +(131211. + 227264. i) q^{39} +(-317503. + 549931. i) q^{40} -133287. q^{41} +(-129906. + 46299.8i) q^{42} +812254. q^{43} +(-298678. + 517326. i) q^{44} +(-183322. - 317524. i) q^{45} +(-7985.25 - 13830.9i) q^{46} +(552403. - 956790. i) q^{47} +141010. q^{48} +(637900. - 520872. i) q^{49} -984003. q^{50} +(187777. - 325239. i) q^{51} +(-468084. - 810745. i) q^{52} +(386165. + 668858. i) q^{53} +(55392.7 - 95942.9i) q^{54} -3.11914e6 q^{55} +(1.07928e6 - 384666. i) q^{56} -319371. q^{57} +(-137437. + 238047. i) q^{58} +(-356333. - 617187. i) q^{59} +(653987. + 1.13274e6i) q^{60} +(-626610. + 1.08532e6i) q^{61} -709.434 q^{62} +(-119237. + 650728. i) q^{63} +406580. q^{64} +(2.44413e6 - 4.23335e6i) q^{65} +(-471239. - 816209. i) q^{66} +(375109. + 649707. i) q^{67} +(-669879. + 1.16026e6i) q^{68} -76611.0 q^{69} +(1.95682e6 + 1.66441e6i) q^{70} -1.13668e6 q^{71} +(-460211. + 797109. i) q^{72} +(2.08563e6 + 3.61241e6i) q^{73} +(-1.03410e6 - 1.79112e6i) q^{74} +(-2.36015e6 + 4.08790e6i) q^{75} +1.13933e6 q^{76} +(4.28704e6 + 3.64643e6i) q^{77} +1.47703e6 q^{78} +(3.21980e6 - 5.57686e6i) q^{79} +(-1.31333e6 - 2.27475e6i) q^{80} +(-265720. - 460241. i) q^{81} +(-375101. + 649694. i) q^{82} -1.83464e6 q^{83} +(425367. - 2.32142e6i) q^{84} -6.99563e6 q^{85} +(2.28588e6 - 3.95925e6i) q^{86} +(659289. + 1.14192e6i) q^{87} +(3.91513e6 + 6.78120e6i) q^{88} +(-702126. + 1.21612e6i) q^{89} -2.06365e6 q^{90} +(-8.30829e6 + 2.96115e6i) q^{91} +273303. q^{92} +(-1701.59 + 2947.24i) q^{93} +(-3.10919e6 - 5.38527e6i) q^{94} +(2.97454e6 + 5.15206e6i) q^{95} +(2.57858e6 - 4.46622e6i) q^{96} -6.70215e6 q^{97} +(-743737. - 4.57524e6i) q^{98} -4.52110e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 108 q^{3} - 101 q^{4} - 196 q^{5} - 54 q^{6} + 154 q^{7} - 2694 q^{8} - 2916 q^{9}+O(q^{10}) \) 8 * q + q^2 - 108 * q^3 - 101 * q^4 - 196 * q^5 - 54 * q^6 + 154 * q^7 - 2694 * q^8 - 2916 * q^9	\( 8 q + q^{2} - 108 q^{3} - 101 q^{4} - 196 q^{5} - 54 q^{6} + 154 q^{7} - 2694 q^{8} - 2916 q^{9} + 5185 q^{10} + 5210 q^{11} - 2727 q^{12} - 7588 q^{13} - 29932 q^{14} + 10584 q^{15} + 21055 q^{16} + 11436 q^{17} + 729 q^{18} + 69158 q^{19} - 175982 q^{20} - 46872 q^{21} + 114526 q^{22} + 146220 q^{23} + 36369 q^{24} - 6230 q^{25} - 107696 q^{26} + 157464 q^{27} - 19201 q^{28} - 141328 q^{29} + 139995 q^{30} + 288618 q^{31} - 2653 q^{32} + 140670 q^{33} - 991992 q^{34} - 66164 q^{35} + 147258 q^{36} + 448902 q^{37} - 528944 q^{38} + 102438 q^{39} - 767361 q^{40} - 1326632 q^{41} + 899073 q^{42} + 1108 q^{43} + 686635 q^{44} - 142884 q^{45} + 1064964 q^{46} - 762180 q^{47} - 1136970 q^{48} + 5310620 q^{49} - 1050856 q^{50} + 308772 q^{51} - 3423848 q^{52} + 2761920 q^{53} + 19683 q^{54} - 3930112 q^{55} + 5341077 q^{56} - 3734532 q^{57} + 4451395 q^{58} - 3410898 q^{59} + 2375757 q^{60} - 300892 q^{61} - 4132350 q^{62} + 1153278 q^{63} - 5833102 q^{64} + 8019032 q^{65} - 1546101 q^{66} + 4222478 q^{67} - 5770500 q^{68} - 7895880 q^{69} + 7703801 q^{70} - 761928 q^{71} + 981963 q^{72} + 451674 q^{73} + 10091220 q^{74} - 168210 q^{75} - 29495312 q^{76} + 16516528 q^{77} + 5815584 q^{78} + 12154822 q^{79} - 7870085 q^{80} - 2125764 q^{81} - 8814904 q^{82} - 24175956 q^{83} + 3387636 q^{84} - 14751000 q^{85} + 32881826 q^{86} + 1907928 q^{87} + 14439051 q^{88} - 4955752 q^{89} - 7559730 q^{90} + 14146174 q^{91} + 413784 q^{92} + 7792686 q^{93} - 5960646 q^{94} - 8460784 q^{95} - 71631 q^{96} - 45681228 q^{97} + 8665405 q^{98} - 7596180 q^{99}+O(q^{100}) \) 8 * q + q^2 - 108 * q^3 - 101 * q^4 - 196 * q^5 - 54 * q^6 + 154 * q^7 - 2694 * q^8 - 2916 * q^9 + 5185 * q^10 + 5210 * q^11 - 2727 * q^12 - 7588 * q^13 - 29932 * q^14 + 10584 * q^15 + 21055 * q^16 + 11436 * q^17 + 729 * q^18 + 69158 * q^19 - 175982 * q^20 - 46872 * q^21 + 114526 * q^22 + 146220 * q^23 + 36369 * q^24 - 6230 * q^25 - 107696 * q^26 + 157464 * q^27 - 19201 * q^28 - 141328 * q^29 + 139995 * q^30 + 288618 * q^31 - 2653 * q^32 + 140670 * q^33 - 991992 * q^34 - 66164 * q^35 + 147258 * q^36 + 448902 * q^37 - 528944 * q^38 + 102438 * q^39 - 767361 * q^40 - 1326632 * q^41 + 899073 * q^42 + 1108 * q^43 + 686635 * q^44 - 142884 * q^45 + 1064964 * q^46 - 762180 * q^47 - 1136970 * q^48 + 5310620 * q^49 - 1050856 * q^50 + 308772 * q^51 - 3423848 * q^52 + 2761920 * q^53 + 19683 * q^54 - 3930112 * q^55 + 5341077 * q^56 - 3734532 * q^57 + 4451395 * q^58 - 3410898 * q^59 + 2375757 * q^60 - 300892 * q^61 - 4132350 * q^62 + 1153278 * q^63 - 5833102 * q^64 + 8019032 * q^65 - 1546101 * q^66 + 4222478 * q^67 - 5770500 * q^68 - 7895880 * q^69 + 7703801 * q^70 - 761928 * q^71 + 981963 * q^72 + 451674 * q^73 + 10091220 * q^74 - 168210 * q^75 - 29495312 * q^76 + 16516528 * q^77 + 5815584 * q^78 + 12154822 * q^79 - 7870085 * q^80 - 2125764 * q^81 - 8814904 * q^82 - 24175956 * q^83 + 3387636 * q^84 - 14751000 * q^85 + 32881826 * q^86 + 1907928 * q^87 + 14439051 * q^88 - 4955752 * q^89 - 7559730 * q^90 + 14146174 * q^91 + 413784 * q^92 + 7792686 * q^93 - 5960646 * q^94 - 8460784 * q^95 - 71631 * q^96 - 45681228 * q^97 + 8665405 * q^98 - 7596180 * q^99

Introduction

L-functions

Modular forms

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