LMFDB - Embedded newform 100.11.b.e.51.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,11,Mod(51,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("100.51");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	100.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:	$63.5357252674$
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} + 199481 x^{18} + 16413464051 x^{16} + 725560177607766 x^{14} + \cdots + 21\!\cdots\!25 $ x^20 + 199481x^18 + 16413464051x^16 + 725560177607766x^14 + 18834574233849489621x^12 + 294503164498899790078095x^10 + 2731275057520962661290869385x^8 + 14154171070179138865031966998950x^6 + 35770310815174676049504613026680775x^4 + 31929367165777304447910767061760715625*x^2 + 2155644618924695638814066662020965503125
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{97}\cdot 3^{4}\cdot 5^{29} $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.9
Root			$221.211i$ of defining polynomial
Character	$\chi$	$=$	100.51
Dual form			100.11.b.e.51.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.05603 - 31.2124i) q^{2} +442.423i q^{3} +(-924.425 + 440.471i) q^{4} +(13809.1 - 3121.75i) q^{6} -2455.96i q^{7} +(20270.9 + 25745.5i) q^{8} -136689. q^{9} +O(q^{10})$	\(q+(-7.05603 - 31.2124i) q^{2} +442.423i q^{3} +(-924.425 + 440.471i) q^{4} +(13809.1 - 3121.75i) q^{6} -2455.96i q^{7} +(20270.9 + 25745.5i) q^{8} -136689. q^{9} +67384.8i q^{11} +(-194874. - 408986. i) q^{12} +723193. q^{13} +(-76656.3 + 17329.3i) q^{14} +(660547. - 814365. i) q^{16} +817832. q^{17} +(964480. + 4.26638e6i) q^{18} -2.29547e6i q^{19} +1.08657e6 q^{21} +(2.10324e6 - 475469. i) q^{22} -6.87611e6i q^{23} +(-1.13904e7 + 8.96831e6i) q^{24} +(-5.10287e6 - 2.25726e7i) q^{26} -3.43496e7i q^{27} +(1.08178e6 + 2.27035e6i) q^{28} -9.72615e6 q^{29} -3.08049e7i q^{31} +(-3.00791e7 - 1.48710e7i) q^{32} -2.98125e7 q^{33} +(-5.77065e6 - 2.55265e7i) q^{34} +(1.26358e8 - 6.02074e7i) q^{36} +1.03499e8 q^{37} +(-7.16470e7 + 1.61969e7i) q^{38} +3.19957e8i q^{39} +1.28191e8 q^{41} +(-7.66688e6 - 3.39145e7i) q^{42} +7.29658e7i q^{43} +(-2.96810e7 - 6.22921e7i) q^{44} +(-2.14620e8 + 4.85180e7i) q^{46} +1.33904e8i q^{47} +(3.60293e8 + 2.92241e8i) q^{48} +2.76444e8 q^{49} +3.61827e8i q^{51} +(-6.68538e8 + 3.18545e8i) q^{52} -2.17126e8 q^{53} +(-1.07213e9 + 2.42372e8i) q^{54} +(6.32299e7 - 4.97845e7i) q^{56} +1.01557e9 q^{57} +(6.86280e7 + 3.03576e8i) q^{58} -9.48043e8i q^{59} -9.30401e7 q^{61} +(-9.61495e8 + 2.17361e8i) q^{62} +3.35702e8i q^{63} +(-2.51922e8 + 1.04377e9i) q^{64} +(2.10358e8 + 9.30520e8i) q^{66} +1.87893e9i q^{67} +(-7.56024e8 + 3.60231e8i) q^{68} +3.04215e9 q^{69} +5.98404e8i q^{71} +(-2.77081e9 - 3.51912e9i) q^{72} +3.66775e8 q^{73} +(-7.30295e8 - 3.23046e9i) q^{74} +(1.01109e9 + 2.12199e9i) q^{76} +1.65494e8 q^{77} +(9.98662e9 - 2.25763e9i) q^{78} +2.46340e9i q^{79} +7.12570e9 q^{81} +(-9.04519e8 - 4.00114e9i) q^{82} +4.63792e9i q^{83} +(-1.00445e9 + 4.78603e8i) q^{84} +(2.27744e9 - 5.14849e8i) q^{86} -4.30307e9i q^{87} +(-1.73486e9 + 1.36595e9i) q^{88} +2.24892e9 q^{89} -1.77613e9i q^{91} +(3.02873e9 + 6.35644e9i) q^{92} +1.36288e10 q^{93} +(4.17947e9 - 9.44832e8i) q^{94} +(6.57929e9 - 1.33077e10i) q^{96} +6.10089e9 q^{97} +(-1.95059e9 - 8.62846e9i) q^{98} -9.21074e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 22 q^{2} - 644 q^{4} - 14784 q^{6} - 3448 q^{8} - 414868 q^{9}+O(q^{10}) $ 20 * q - 22 * q^2 - 644 * q^4 - 14784 * q^6 - 3448 * q^8 - 414868 * q^9	\( 20 q - 22 q^{2} - 644 q^{4} - 14784 q^{6} - 3448 q^{8} - 414868 q^{9} - 1329640 q^{12} + 278864 q^{13} - 2240504 q^{14} + 4261360 q^{16} + 1921656 q^{17} + 3556082 q^{18} + 4157512 q^{21} + 5811280 q^{22} - 19112144 q^{24} + 25066884 q^{26} + 87415400 q^{28} - 66014888 q^{29} + 33171328 q^{32} - 85980560 q^{33} - 27236084 q^{34} + 355456476 q^{36} + 153620656 q^{37} - 250352720 q^{38} + 477406160 q^{41} + 570662040 q^{42} + 339141040 q^{44} - 897549304 q^{46} + 479727360 q^{48} + 333772012 q^{49} + 110465096 q^{52} + 1669491824 q^{53} + 706139792 q^{54} - 1362290224 q^{56} - 3973032960 q^{57} - 2075027916 q^{58} - 4283166080 q^{61} - 1664032240 q^{62} + 340459456 q^{64} + 1884031760 q^{66} - 3042411896 q^{68} - 5321669928 q^{69} - 1632326712 q^{72} - 2474287656 q^{73} + 188682276 q^{74} + 2323171200 q^{76} - 410885040 q^{77} + 19914223760 q^{78} + 9939722652 q^{81} + 3197757116 q^{82} + 2383099552 q^{84} + 19648321456 q^{86} - 2774318240 q^{88} + 3011851592 q^{89} + 27349072440 q^{92} + 11861394640 q^{93} + 15684681576 q^{94} - 1990377984 q^{96} + 39984502056 q^{97} - 38416891998 q^{98}+O(q^{100}) \) 20 * q - 22 * q^2 - 644 * q^4 - 14784 * q^6 - 3448 * q^8 - 414868 * q^9 - 1329640 * q^12 + 278864 * q^13 - 2240504 * q^14 + 4261360 * q^16 + 1921656 * q^17 + 3556082 * q^18 + 4157512 * q^21 + 5811280 * q^22 - 19112144 * q^24 + 25066884 * q^26 + 87415400 * q^28 - 66014888 * q^29 + 33171328 * q^32 - 85980560 * q^33 - 27236084 * q^34 + 355456476 * q^36 + 153620656 * q^37 - 250352720 * q^38 + 477406160 * q^41 + 570662040 * q^42 + 339141040 * q^44 - 897549304 * q^46 + 479727360 * q^48 + 333772012 * q^49 + 110465096 * q^52 + 1669491824 * q^53 + 706139792 * q^54 - 1362290224 * q^56 - 3973032960 * q^57 - 2075027916 * q^58 - 4283166080 * q^61 - 1664032240 * q^62 + 340459456 * q^64 + 1884031760 * q^66 - 3042411896 * q^68 - 5321669928 * q^69 - 1632326712 * q^72 - 2474287656 * q^73 + 188682276 * q^74 + 2323171200 * q^76 - 410885040 * q^77 + 19914223760 * q^78 + 9939722652 * q^81 + 3197757116 * q^82 + 2383099552 * q^84 + 19648321456 * q^86 - 2774318240 * q^88 + 3011851592 * q^89 + 27349072440 * q^92 + 11861394640 * q^93 + 15684681576 * q^94 - 1990377984 * q^96 + 39984502056 * q^97 - 38416891998 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$1$

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 $

$2$	−7.05603	−	31.2124i	−0.220501	−	0.975387i
$2$	−7.05603	−	31.2124i	−0.220501	−	0.975387i
$3$			442.423i			1.82067i	0.413873	+	0.910335i	$0.364176\pi$
$3$			442.423i			1.82067i	−0.413873	+	0.910335i	$0.635824\pi$
$4$	−924.425	+	440.471i	−0.902759	+	0.430147i
$5$		0			0
$5$		0			0
$6$	13809.1	−	3121.75i	1.77586	−	0.401459i
$7$		−	2455.96i		−	0.146127i	−0.997327	−	0.0730635i	$-0.976722\pi$
$7$		−	2455.96i		−	0.146127i	0.997327	−	0.0730635i	$-0.0232776\pi$
$8$	20270.9	+	25745.5i	0.618619	+	0.785691i
$9$	−136689.			−2.31484
$10$		0			0
$11$			67384.8i			0.418406i	0.977872	+	0.209203i	$0.0670870\pi$
$11$			67384.8i			0.418406i	−0.977872	+	0.209203i	$0.932913\pi$
$12$	−194874.	−	408986.i	−0.783156	−	1.64362i
$13$	723193.			1.94777			0.973884	−	0.227044i	$-0.0729063\pi$
$13$	723193.			1.94777			0.973884	+	0.227044i	$0.0729063\pi$
$14$	−76656.3	+	17329.3i	−0.142530	+	0.0322212i
$15$		0			0
$16$	660547.	−	814365.i	0.629946	−	0.776639i
$17$	817832.			0.575996			0.287998	−	0.957631i	$-0.407010\pi$
$17$	817832.			0.575996			0.287998	+	0.957631i	$0.407010\pi$
$18$	964480.	+	4.26638e6i	0.510424	+	2.25786i
$19$		−	2.29547e6i		−	0.927049i	−0.886084	−	0.463525i	$-0.846585\pi$
$19$		−	2.29547e6i		−	0.927049i	0.886084	−	0.463525i	$-0.153415\pi$
$20$		0			0
$21$	1.08657e6			0.266049
$22$	2.10324e6	−	475469.i	0.408108	−	0.0922590i
$23$		−	6.87611e6i		−	1.06833i	−0.845382	−	0.534163i	$-0.820627\pi$
$23$		−	6.87611e6i		−	1.06833i	0.845382	−	0.534163i	$-0.179373\pi$
$24$	−1.13904e7	+	8.96831e6i	−1.43048	+	1.12630i
$25$		0			0
$26$	−5.10287e6	−	2.25726e7i	−0.429485	−	1.89983i
$27$		−	3.43496e7i		−	2.39388i
$28$	1.08178e6	+	2.27035e6i	0.0628562	+	0.131917i
$29$	−9.72615e6			−0.474188			−0.237094	−	0.971487i	$-0.576195\pi$
$29$	−9.72615e6			−0.474188			−0.237094	+	0.971487i	$0.576195\pi$
$30$		0			0
$31$		−	3.08049e7i		−	1.07600i	−0.842945	−	0.537999i	$-0.819180\pi$
$31$		−	3.08049e7i		−	1.07600i	0.842945	−	0.537999i	$-0.180820\pi$
$32$	−3.00791e7	−	1.48710e7i	−0.896427	−	0.443192i
$33$	−2.98125e7			−0.761780
$34$	−5.77065e6	−	2.55265e7i	−0.127008	−	0.561819i
$35$		0			0
$36$	1.26358e8	−	6.02074e7i	2.08974	−	0.995721i
$37$	1.03499e8			1.49255			0.746275	−	0.665637i	$-0.231840\pi$
$37$	1.03499e8			1.49255			0.746275	+	0.665637i	$0.231840\pi$
$38$	−7.16470e7	+	1.61969e7i	−0.904232	+	0.204415i
$39$			3.19957e8i			3.54624i
$40$		0			0
$41$	1.28191e8			1.10647			0.553233	−	0.833027i	$-0.313394\pi$
$41$	1.28191e8			1.10647			0.553233	+	0.833027i	$0.313394\pi$
$42$	−7.66688e6	−	3.39145e7i	−0.0586641	−	0.259501i
$43$			7.29658e7i			0.496337i	0.968717	+	0.248169i	$0.0798287\pi$
$43$			7.29658e7i			0.496337i	−0.968717	+	0.248169i	$0.920171\pi$
$44$	−2.96810e7	−	6.22921e7i	−0.179976	−	0.377720i
$45$		0			0
$46$	−2.14620e8	+	4.85180e7i	−1.04203	+	0.235567i
$47$			1.33904e8i			0.583855i	0.956441	+	0.291927i	$0.0942965\pi$
$47$			1.33904e8i			0.583855i	−0.956441	+	0.291927i	$0.905703\pi$
$48$	3.60293e8	+	2.92241e8i	1.41400	+	1.14692i
$49$	2.76444e8			0.978647
$50$		0			0
$51$			3.61827e8i			1.04870i
$52$	−6.68538e8	+	3.18545e8i	−1.75837	+	0.837828i
$53$	−2.17126e8			−0.519197			−0.259598	−	0.965717i	$-0.583590\pi$
$53$	−2.17126e8			−0.519197			−0.259598	+	0.965717i	$0.583590\pi$
$54$	−1.07213e9	+	2.42372e8i	−2.33496	+	0.527853i
$55$		0			0
$56$	6.32299e7	−	4.97845e7i	0.114811	−	0.0903970i
$57$	1.01557e9			1.68785
$58$	6.86280e7	+	3.03576e8i	0.104559	+	0.462517i
$59$		−	9.48043e8i		−	1.32607i	−0.748586	−	0.663037i	$-0.769267\pi$
$59$		−	9.48043e8i		−	1.32607i	0.748586	−	0.663037i	$-0.230733\pi$
$60$		0			0
$61$	−9.30401e7			−0.110159			−0.0550797	−	0.998482i	$-0.517541\pi$
$61$	−9.30401e7			−0.110159			−0.0550797	+	0.998482i	$0.517541\pi$
$62$	−9.61495e8	+	2.17361e8i	−1.04951	+	0.237259i
$63$			3.35702e8i			0.338260i
$64$	−2.51922e8	+	1.04377e9i	−0.234620	+	0.972087i
$65$		0			0
$66$	2.10358e8	+	9.30520e8i	0.167973	+	0.743030i
$67$			1.87893e9i			1.39167i	0.718200	+	0.695836i	$0.244966\pi$
$67$			1.87893e9i			1.39167i	−0.718200	+	0.695836i	$0.755034\pi$
$68$	−7.56024e8	+	3.60231e8i	−0.519985	+	0.247763i
$69$	3.04215e9			1.94507
$70$		0			0
$71$			5.98404e8i			0.331667i	0.986154	+	0.165834i	$0.0530315\pi$
$71$			5.98404e8i			0.331667i	−0.986154	+	0.165834i	$0.946969\pi$
$72$	−2.77081e9	−	3.51912e9i	−1.43200	−	1.81875i
$73$	3.66775e8			0.176923			0.0884617	−	0.996080i	$-0.471805\pi$
$73$	3.66775e8			0.176923			0.0884617	+	0.996080i	$0.471805\pi$
$74$	−7.30295e8	−	3.23046e9i	−0.329109	−	1.45581i
$75$		0			0
$76$	1.01109e9	+	2.12199e9i	0.398768	+	0.836902i
$77$	1.65494e8			0.0611405
$78$	9.98662e9	−	2.25763e9i	3.45896	−	0.781950i
$79$			2.46340e9i			0.800571i	0.916390	+	0.400286i	$0.131089\pi$
$79$			2.46340e9i			0.800571i	−0.916390	+	0.400286i	$0.868911\pi$
$80$		0			0
$81$	7.12570e9			2.04363
$82$	−9.04519e8	−	4.00114e9i	−0.243977	−	1.07923i
$83$			4.63792e9i			1.17743i	0.808342	+	0.588713i	$0.200365\pi$
$83$			4.63792e9i			1.17743i	−0.808342	+	0.588713i	$0.799635\pi$
$84$	−1.00445e9	+	4.78603e8i	−0.240178	+	0.114440i
$85$		0			0
$86$	2.27744e9	−	5.14849e8i	0.484121	−	0.109443i
$87$		−	4.30307e9i		−	0.863340i
$88$	−1.73486e9	+	1.36595e9i	−0.328738	+	0.258834i
$89$	2.24892e9			0.402740			0.201370	−	0.979515i	$-0.435461\pi$
$89$	2.24892e9			0.402740			0.201370	+	0.979515i	$0.435461\pi$
$90$		0			0
$91$		−	1.77613e9i		−	0.284622i
$92$	3.02873e9	+	6.35644e9i	0.459537	+	0.964440i
$93$	1.36288e10			1.95904
$94$	4.17947e9	−	9.44832e8i	0.569484	−	0.128741i
$95$		0			0
$96$	6.57929e9	−	1.33077e10i	0.806906	−	1.63210i
$97$	6.10089e9			0.710452			0.355226	−	0.934780i	$-0.384404\pi$
$97$	6.10089e9			0.710452			0.355226	+	0.934780i	$0.384404\pi$
$98$	−1.95059e9	−	8.62846e9i	−0.215793	−	0.954559i
$99$		−	9.21074e9i		−	0.968542i
$100$		0			0
$101$	−6.57079e9			−0.625188			−0.312594	−	0.949887i	$-0.601198\pi$
$101$	−6.57079e9			−0.625188			−0.312594	+	0.949887i	$0.601198\pi$
$102$	1.12935e10	−	2.55306e9i	1.02289	−	0.231239i
$103$		−	1.86346e10i		−	1.60743i	−0.595012	−	0.803717i	$-0.702853\pi$
$103$		−	1.86346e10i		−	1.60743i	0.595012	−	0.803717i	$-0.297147\pi$
$104$	1.46598e10	+	1.86190e10i	1.20493	+	1.53034i
$105$		0			0
$106$	1.53205e9	+	6.77701e9i	0.114483	+	0.506418i
$107$		−	1.66388e9i		−	0.118632i	−0.998239	−	0.0593162i	$-0.981108\pi$
$107$		−	1.66388e9i		−	0.118632i	0.998239	−	0.0593162i	$-0.0188920\pi$
$108$	1.51300e10	+	3.17536e10i	1.02972	+	2.16110i
$109$	−1.74212e10			−1.13226			−0.566129	−	0.824317i	$-0.691559\pi$
$109$	−1.74212e10			−1.13226			−0.566129	+	0.824317i	$0.691559\pi$
$110$		0			0
$111$			4.57905e10i			2.71744i
$112$	−2.00005e9	−	1.62227e9i	−0.113488	−	0.0920522i
$113$	2.08179e10			1.12991			0.564956	−	0.825121i	$-0.308893\pi$
$113$	2.08179e10			1.12991			0.564956	+	0.825121i	$0.308893\pi$
$114$	−7.16587e9	−	3.16982e10i	−0.372173	−	1.64631i
$115$		0			0
$116$	8.99109e9	−	4.28409e9i	0.428078	−	0.203971i
$117$	−9.88523e10			−4.50877
$118$	−2.95907e10	+	6.68942e9i	−1.29344	+	0.292401i
$119$		−	2.00856e9i		−	0.0841686i
$120$		0			0
$121$	2.13967e10			0.824936
$122$	6.56494e8	+	2.90400e9i	0.0242902	+	0.107448i
$123$			5.67146e10i			2.01451i
$124$	1.35687e10	+	2.84768e10i	0.462838	+	0.971367i
$125$		0			0
$126$	1.04781e10	−	2.36872e9i	0.329935	−	0.0745867i
$127$			2.11654e10i			0.640632i	0.947311	+	0.320316i	$0.103789\pi$
$127$			2.11654e10i			0.640632i	−0.947311	+	0.320316i	$0.896211\pi$
$128$	3.43561e10	+	4.98200e8i	0.999895	+	0.0144995i
$129$	−3.22817e10			−0.903666
$130$		0			0
$131$			2.07233e10i			0.537159i	0.963258	+	0.268579i	$0.0865542\pi$
$131$			2.07233e10i			0.537159i	−0.963258	+	0.268579i	$0.913446\pi$
$132$	2.75595e10	−	1.31316e10i	0.687703	−	0.327678i
$133$	−5.63757e9			−0.135467
$134$	5.86460e10	−	1.32578e10i	1.35742	−	0.306865i
$135$		0			0
$136$	1.65782e10	+	2.10555e10i	0.356322	+	0.452555i
$137$	6.69834e10			1.38792			0.693960	−	0.720013i	$-0.255864\pi$
$137$	6.69834e10			1.38792			0.693960	+	0.720013i	$0.255864\pi$
$138$	−2.14655e10	−	9.49526e10i	−0.428889	−	1.89719i
$139$			6.96773e9i			0.134282i	0.997743	+	0.0671410i	$0.0213877\pi$
$139$			6.96773e9i			0.134282i	−0.997743	+	0.0671410i	$0.978612\pi$
$140$		0			0
$141$	−5.92422e10			−1.06301
$142$	1.86776e10	−	4.22236e9i	0.323504	−	0.0731330i
$143$			4.87322e10i			0.814959i
$144$	−9.02893e10	+	1.11314e11i	−1.45822	+	1.79779i
$145$		0			0
$146$	−2.58797e9	−	1.14479e10i	−0.0390118	−	0.172569i
$147$			1.22305e11i			1.78179i
$148$	−9.56774e10	+	4.55885e10i	−1.34741	+	0.642017i
$149$	−4.07677e10			−0.555118			−0.277559	−	0.960709i	$-0.589525\pi$
$149$	−4.07677e10			−0.555118			−0.277559	+	0.960709i	$0.589525\pi$
$150$		0			0
$151$		−	7.69203e10i		−	0.979843i	−0.871767	−	0.489921i	$-0.837025\pi$
$151$		−	7.69203e10i		−	0.979843i	0.871767	−	0.489921i	$-0.162975\pi$
$152$	5.90980e10	−	4.65312e10i	0.728374	−	0.573491i
$153$	−1.11788e11			−1.33334
$154$	−1.16773e9	−	5.16547e9i	−0.0134815	−	0.0596356i
$155$		0			0
$156$	−1.40932e11	−	2.95776e11i	−1.52541	−	3.20140i
$157$	−1.86695e10			−0.195720			−0.0978600	−	0.995200i	$-0.531200\pi$
$157$	−1.86695e10			−0.195720			−0.0978600	+	0.995200i	$0.531200\pi$
$158$	7.68887e10	−	1.73818e10i	0.780867	−	0.176527i
$159$		−	9.60614e10i		−	0.945286i
$160$		0			0
$161$	−1.68874e10			−0.156111
$162$	−5.02792e10	−	2.22410e11i	−0.450623	−	1.99333i
$163$		−	2.00550e11i		−	1.74295i	−0.490442	−	0.871474i	$-0.663165\pi$
$163$		−	2.00550e11i		−	1.74295i	0.490442	−	0.871474i	$-0.336835\pi$
$164$	−1.18503e11	+	5.64644e10i	−0.998872	+	0.475944i
$165$		0			0
$166$	1.44761e11	−	3.27253e10i	1.14844	−	0.259623i
$167$			8.39156e10i			0.646041i	0.946392	+	0.323021i	$0.104698\pi$
$167$			8.39156e10i			0.646041i	−0.946392	+	0.323021i	$0.895302\pi$
$168$	2.20258e10	+	2.79743e10i	0.164583	+	0.209032i
$169$	3.85150e11			2.79380
$170$		0			0
$171$			3.13764e11i			2.14597i
$172$	−3.21393e10	−	6.74514e10i	−0.213498	−	0.448073i
$173$	−5.70570e10			−0.368195			−0.184098	−	0.982908i	$-0.558936\pi$
$173$	−5.70570e10			−0.368195			−0.184098	+	0.982908i	$0.558936\pi$
$174$	−1.34309e11	+	3.03626e10i	−0.842091	+	0.190367i
$175$		0			0
$176$	5.48758e10	+	4.45108e10i	0.324951	+	0.263574i
$177$	4.19436e11			2.41434
$178$	−1.58685e10	−	7.01943e10i	−0.0888046	−	0.392827i
$179$		−	8.94302e10i		−	0.486653i	−0.969944	−	0.243326i	$-0.921761\pi$
$179$		−	8.94302e10i		−	0.486653i	0.969944	−	0.243326i	$-0.0782386\pi$
$180$		0			0
$181$	−4.62386e10			−0.238019			−0.119010	−	0.992893i	$-0.537972\pi$
$181$	−4.62386e10			−0.238019			−0.119010	+	0.992893i	$0.537972\pi$
$182$	−5.54373e10	+	1.25324e10i	−0.277616	+	0.0627594i
$183$		−	4.11631e10i		−	0.200564i
$184$	1.77029e11	−	1.39385e11i	0.839373	−	0.660887i
$185$		0			0
$186$	−9.61652e10	−	4.25387e11i	−0.431970	−	1.91082i
$187$			5.51094e10i			0.241000i
$188$	−5.89809e10	−	1.23784e11i	−0.251144	−	0.527080i
$189$	−8.43611e10			−0.349811
$190$		0			0
$191$			3.33137e11i			1.31056i	0.755387	+	0.655279i	$0.227449\pi$
$191$			3.33137e11i			1.31056i	−0.755387	+	0.655279i	$0.772551\pi$
$192$	−4.61788e11	−	1.11456e11i	−1.76985	−	0.427166i
$193$	−2.22226e11			−0.829867			−0.414934	−	0.909852i	$-0.636195\pi$
$193$	−2.22226e11			−0.829867			−0.414934	+	0.909852i	$0.636195\pi$
$194$	−4.30481e10	−	1.90423e11i	−0.156655	−	0.692966i
$195$		0			0
$196$	−2.55551e11	+	1.21765e11i	−0.883482	+	0.420962i
$197$	−1.72455e11			−0.581225			−0.290612	−	0.956841i	$-0.593859\pi$
$197$	−1.72455e11			−0.581225			−0.290612	+	0.956841i	$0.593859\pi$
$198$	−2.87489e11	+	6.49913e10i	−0.944703	+	0.213564i
$199$		−	9.81051e10i		−	0.314359i	−0.987570	−	0.157180i	$-0.949760\pi$
$199$		−	9.81051e10i		−	0.314359i	0.987570	−	0.157180i	$-0.0502402\pi$
$200$		0			0
$201$	−8.31282e11			−2.53378
$202$	4.63637e10	+	2.05090e11i	0.137855	+	0.609800i
$203$			2.38870e10i			0.0692918i
$204$	−1.59374e11	−	3.34482e11i	−0.451095	−	0.946721i
$205$		0			0
$206$	−5.81629e11	+	1.31486e11i	−1.56787	+	0.354441i
$207$			9.39887e11i			2.47300i
$208$	4.77703e11	−	5.88943e11i	1.22699	−	1.51271i
$209$	1.54679e11			0.387883
$210$		0			0
$211$			6.46299e11i			1.54533i	0.634815	+	0.772664i	$0.281076\pi$
$211$			6.46299e11i			1.54533i	−0.634815	+	0.772664i	$0.718924\pi$
$212$	2.00716e11	−	9.56376e10i	0.468709	−	0.223331i
$213$	−2.64747e11			−0.603856
$214$	−5.19337e10	+	1.17404e10i	−0.115713	+	0.0261586i
$215$		0			0
$216$	8.84348e11	−	6.96298e11i	1.88085	−	1.48090i
$217$	−7.56556e10			−0.157233
$218$	1.22924e11	+	5.43757e11i	0.249664	+	1.10439i
$219$			1.62269e11i			0.322119i
$220$		0			0
$221$	5.91450e11			1.12191
$222$	1.42923e12	−	3.23099e11i	2.65056	−	0.599198i
$223$		−	7.49637e10i		−	0.135934i	−0.997688	−	0.0679668i	$-0.978349\pi$
$223$		−	7.49637e10i		−	0.135934i	0.997688	−	0.0679668i	$-0.0216512\pi$
$224$	−3.65227e10	+	7.38730e10i	−0.0647623	+	0.130992i
$225$		0			0
$226$	−1.46892e11	−	6.49776e11i	−0.249147	−	1.10210i
$227$			3.46148e11i			0.574292i	0.957887	+	0.287146i	$0.0927064\pi$
$227$			3.46148e11i			0.574292i	−0.957887	+	0.287146i	$0.907294\pi$
$228$	−9.38815e11	+	4.47327e11i	−1.52372	+	0.726024i
$229$	−2.98283e11			−0.473643			−0.236821	−	0.971553i	$-0.576106\pi$
$229$	−2.98283e11			−0.473643			−0.236821	+	0.971553i	$0.576106\pi$
$230$		0			0
$231$			7.32183e10i			0.111317i
$232$	−1.97158e11	−	2.50405e11i	−0.293342	−	0.372566i
$233$	9.68362e11			1.41013			0.705064	−	0.709144i	$-0.250918\pi$
$233$	9.68362e11			1.41013			0.705064	+	0.709144i	$0.250918\pi$
$234$	6.97505e11	+	3.08542e12i	0.994187	+	4.39779i
$235$		0			0
$236$	4.17585e11	+	8.76395e11i	0.570408	+	1.19713i
$237$	−1.08987e12			−1.45758
$238$	−6.26919e10	+	1.41725e10i	−0.0820969	+	0.0185593i
$239$		−	1.04679e12i		−	1.34237i	−0.741291	−	0.671184i	$-0.765786\pi$
$239$		−	1.04679e12i		−	1.34237i	0.741291	−	0.671184i	$-0.234214\pi$
$240$		0			0
$241$	3.50983e11			0.431719			0.215859	−	0.976424i	$-0.430745\pi$
$241$	3.50983e11			0.431719			0.215859	+	0.976424i	$0.430745\pi$
$242$	−1.50976e11	−	6.67842e11i	−0.181899	−	0.804632i
$243$			1.12426e12i			1.32689i
$244$	8.60086e10	−	4.09815e10i	0.0994473	−	0.0473847i
$245$		0			0
$246$	1.77020e12	−	4.00180e11i	1.96493	−	0.444201i
$247$		−	1.66006e12i		−	1.80568i
$248$	7.93089e11	−	6.24444e11i	0.845402	−	0.665634i
$249$	−2.05192e12			−2.14370
$250$		0			0
$251$		−	9.17781e11i		−	0.921235i	−0.887599	−	0.460617i	$-0.847628\pi$
$251$		−	9.17781e11i		−	0.921235i	0.887599	−	0.460617i	$-0.152372\pi$
$252$	−1.47867e11	−	3.10331e11i	−0.145502	−	0.305367i
$253$	4.63345e11			0.446994
$254$	6.60623e11	−	1.49344e11i	0.624864	−	0.141260i
$255$		0			0
$256$	−2.26868e11	−	1.07585e12i	−0.206335	−	0.978481i
$257$	−1.98515e12			−1.77063			−0.885313	−	0.464996i	$-0.846056\pi$
$257$	−1.98515e12			−1.77063			−0.885313	+	0.464996i	$0.846056\pi$
$258$	2.27781e11	+	1.00759e12i	0.199259	+	0.881424i
$259$		−	2.54190e11i		−	0.218102i
$260$		0			0
$261$	1.32946e12			1.09767
$262$	6.46824e11	−	1.46224e11i	0.523938	−	0.118444i
$263$			1.18872e12i			0.944715i	0.881407	+	0.472357i	$0.156597\pi$
$263$			1.18872e12i			0.944715i	−0.881407	+	0.472357i	$0.843403\pi$
$264$	−6.04328e11	−	7.67539e11i	−0.471251	−	0.598523i
$265$		0			0
$266$	3.97789e10	+	1.75962e11i	0.0298706	+	0.132133i
$267$			9.94975e11i			0.733257i
$268$	−8.27615e11	−	1.73693e12i	−0.598625	−	1.25634i
$269$	1.26671e12			0.899326			0.449663	−	0.893198i	$-0.351544\pi$
$269$	1.26671e12			0.899326			0.449663	+	0.893198i	$0.351544\pi$
$270$		0			0
$271$			3.12969e11i			0.214119i	0.994253	+	0.107060i	$0.0341435\pi$
$271$			3.12969e11i			0.214119i	−0.994253	+	0.107060i	$0.965856\pi$
$272$	5.40216e11	−	6.66013e11i	0.362846	−	0.447341i
$273$	7.85801e11			0.518202
$274$	−4.72637e11	−	2.09071e12i	−0.306038	−	1.35376i
$275$		0			0
$276$	−2.81223e12	+	1.33998e12i	−1.75593	+	0.836665i
$277$	7.07051e11			0.433563			0.216781	−	0.976220i	$-0.430444\pi$
$277$	7.07051e11			0.433563			0.216781	+	0.976220i	$0.430444\pi$
$278$	2.17480e11	−	4.91645e10i	0.130977	−	0.0296093i
$279$			4.21069e12i			2.49076i
$280$		0			0
$281$	−1.10018e12			−0.627958			−0.313979	−	0.949430i	$-0.601662\pi$
$281$	−1.10018e12			−0.627958			−0.313979	+	0.949430i	$0.601662\pi$
$282$	4.18015e11	+	1.84909e12i	0.234394	+	1.03684i
$283$		−	7.89753e11i		−	0.435070i	−0.976053	−	0.217535i	$-0.930198\pi$
$283$		−	7.89753e11i		−	0.435070i	0.976053	−	0.217535i	$-0.0698016\pi$
$284$	−2.63580e11	−	5.53179e11i	−0.142666	−	0.299415i
$285$		0			0
$286$	1.52105e12	−	3.43856e11i	0.794900	−	0.179699i
$287$		−	3.14832e11i		−	0.161685i
$288$	4.11147e12	+	2.03271e12i	2.07508	+	1.02592i
$289$	−1.34715e12			−0.668229
$290$		0			0
$291$			2.69917e12i			1.29350i
$292$	−3.39056e11	+	1.61554e11i	−0.159719	+	0.0761031i
$293$	7.43317e11			0.344220			0.172110	−	0.985078i	$-0.444942\pi$
$293$	7.43317e11			0.344220			0.172110	+	0.985078i	$0.444942\pi$
$294$	3.81743e12	−	8.62987e11i	1.73794	−	0.392887i
$295$		0			0
$296$	2.09803e12	+	2.66464e12i	0.923321	+	1.17268i
$297$	2.31464e12			1.00162
$298$	2.87658e11	+	1.27246e12i	0.122404	+	0.541454i
$299$		−	4.97275e12i		−	2.08085i
$300$		0			0
$301$	1.79201e11			0.0725283
$302$	−2.40087e12	+	5.42752e11i	−0.955726	+	0.216056i
$303$		−	2.90707e12i		−	1.13826i
$304$	−1.86935e12	−	1.51626e12i	−0.719982	−	0.583991i
$305$		0			0
$306$	7.88782e11	+	3.48918e12i	0.294002	+	1.30052i
$307$			3.92405e11i			0.143894i	0.997408	+	0.0719469i	$0.0229212\pi$
$307$			3.92405e11i			0.143894i	−0.997408	+	0.0719469i	$0.977079\pi$
$308$	−1.52987e11	+	7.28954e10i	−0.0551951	+	0.0262994i
$309$	8.24435e12			2.92660
$310$		0			0
$311$			7.88687e11i			0.271083i	0.990772	+	0.135542i	$0.0432774\pi$
$311$			7.88687e11i			0.271083i	−0.990772	+	0.135542i	$0.956723\pi$
$312$	−8.23746e12	+	6.48582e12i	−2.78625	+	2.19377i
$313$	3.93508e12			1.30988			0.654940	−	0.755681i	$-0.272694\pi$
$313$	3.93508e12			1.30988			0.654940	+	0.755681i	$0.272694\pi$
$314$	1.31733e11	+	5.82720e11i	0.0431564	+	0.190903i
$315$		0			0
$316$	−1.08506e12	−	2.27723e12i	−0.344364	−	0.722723i
$317$	2.67589e12			0.835933			0.417966	−	0.908463i	$-0.362743\pi$
$317$	2.67589e12			0.835933			0.417966	+	0.908463i	$0.362743\pi$
$318$	−2.99830e12	+	6.77812e11i	−0.922019	+	0.208436i
$319$		−	6.55394e11i		−	0.198403i
$320$		0			0
$321$	7.36139e11			0.215990
$322$	1.19158e11	+	5.27097e11i	0.0344227	+	0.152269i
$323$		−	1.87730e12i		−	0.533977i
$324$	−6.58717e12	+	3.13866e12i	−1.84491	+	0.879063i
$325$		0			0
$326$	−6.25964e12	+	1.41509e12i	−1.70005	+	0.384322i
$327$		−	7.70753e12i		−	2.06147i
$328$	2.59855e12	+	3.30034e12i	0.684481	+	0.869340i
$329$	3.28863e11			0.0853170
$330$		0			0
$331$		−	3.89209e12i		−	0.979587i	−0.871838	−	0.489794i	$-0.837072\pi$
$331$		−	3.89209e12i		−	0.979587i	0.871838	−	0.489794i	$-0.162928\pi$
$332$	−2.04287e12	−	4.28741e12i	−0.506466	−	1.06293i
$333$	−1.41472e13			−3.45501
$334$	2.61921e12	−	5.92111e11i	0.630140	−	0.142453i
$335$		0			0
$336$	7.17731e11	−	8.84865e11i	0.167597	−	0.206624i
$337$	6.65644e12			1.53141			0.765707	−	0.643189i	$-0.222389\pi$
$337$	6.65644e12			1.53141			0.765707	+	0.643189i	$0.222389\pi$
$338$	−2.71763e12	−	1.20214e13i	−0.616036	−	2.72504i
$339$			9.21031e12i			2.05720i
$340$		0			0
$341$	2.07578e12			0.450205
$342$	9.79333e12	−	2.21393e12i	2.09315	−	0.473188i
$343$		−	1.37268e12i		−	0.289134i
$344$	−1.87854e12	+	1.47908e12i	−0.389968	+	0.307044i
$345$		0			0
$346$	4.02596e11	+	1.78088e12i	0.0811874	+	0.359133i
$347$			5.14000e12i			1.02168i	0.859675	+	0.510841i	$0.170666\pi$
$347$			5.14000e12i			1.02168i	−0.859675	+	0.510841i	$0.829334\pi$
$348$	1.89538e12	+	3.97786e12i	0.371364	+	0.779388i
$349$	−1.31726e12			−0.254416			−0.127208	−	0.991876i	$-0.540602\pi$
$349$	−1.31726e12			−0.254416			−0.127208	+	0.991876i	$0.540602\pi$
$350$		0			0
$351$		−	2.48414e13i		−	4.66273i
$352$	1.00208e12	−	2.02687e12i	0.185434	−	0.375071i
$353$	1.36891e12			0.249747			0.124873	−	0.992173i	$-0.460148\pi$
$353$	1.36891e12			0.249747			0.124873	+	0.992173i	$0.460148\pi$
$354$	−2.95955e12	−	1.30916e13i	−0.532365	−	2.35492i
$355$		0			0
$356$	−2.07896e12	+	9.90586e11i	−0.363577	+	0.173238i
$357$	8.88632e11			0.153243
$358$	−2.79133e12	+	6.31022e11i	−0.474675	+	0.107307i
$359$			1.54669e12i			0.259377i	0.991555	+	0.129688i	$0.0413977\pi$
$359$			1.54669e12i			0.259377i	−0.991555	+	0.129688i	$0.958602\pi$
$360$		0			0
$361$	8.61901e11			0.140579
$362$	3.26261e11	+	1.44322e12i	0.0524834	+	0.232161i
$363$			9.46639e12i			1.50194i
$364$	7.82334e11	+	1.64190e12i	0.122429	+	0.256945i
$365$		0			0
$366$	−1.28480e12	+	2.90448e11i	−0.195627	+	0.0442245i
$367$		−	7.72418e12i		−	1.16017i	−0.814556	−	0.580085i	$-0.803019\pi$
$367$		−	7.72418e12i		−	1.16017i	0.814556	−	0.580085i	$-0.196981\pi$
$368$	−5.59966e12	−	4.54199e12i	−0.829703	−	0.672988i
$369$	−1.75223e13			−2.56129
$370$		0			0
$371$			5.33252e11i			0.0758687i
$372$	−1.25988e13	+	6.00309e12i	−1.76854	+	0.842675i
$373$	4.93744e12			0.683844			0.341922	−	0.939728i	$-0.388922\pi$
$373$	4.93744e12			0.683844			0.341922	+	0.939728i	$0.388922\pi$
$374$	1.72009e12	−	3.88854e11i	0.235068	−	0.0531408i
$375$		0			0
$376$	−3.44743e12	+	2.71436e12i	−0.458729	+	0.361184i
$377$	−7.03388e12			−0.923609
$378$	5.95255e11	+	2.63311e12i	0.0771337	+	0.341201i
$379$			5.74967e11i			0.0735270i	0.999324	+	0.0367635i	$0.0117048\pi$
$379$			5.74967e11i			0.0735270i	−0.999324	+	0.0367635i	$0.988295\pi$
$380$		0			0
$381$	−9.36406e12			−1.16638
$382$	1.03980e13	−	2.35063e12i	1.27830	−	0.288979i
$383$			5.07086e12i			0.615302i	0.951499	+	0.307651i	$0.0995428\pi$
$383$			5.07086e12i			0.615302i	−0.951499	+	0.307651i	$0.900457\pi$
$384$	−2.20415e11	+	1.51999e13i	−0.0263988	+	1.82048i
$385$		0			0
$386$	1.56803e12	+	6.93620e12i	0.182986	+	0.809441i
$387$		−	9.97360e12i		−	1.14894i
$388$	−5.63982e12	+	2.68727e12i	−0.641367	+	0.305599i
$389$	1.76599e12			0.198262			0.0991312	−	0.995074i	$-0.468394\pi$
$389$	1.76599e12			0.198262			0.0991312	+	0.995074i	$0.468394\pi$
$390$		0			0
$391$		−	5.62350e12i		−	0.615351i
$392$	5.60376e12	+	7.11718e12i	0.605410	+	0.768914i
$393$	−9.16846e12			−0.977989
$394$	1.21685e12	+	5.38272e12i	0.128161	+	0.566919i
$395$		0			0
$396$	4.05706e12	+	8.51464e12i	0.416616	+	0.874360i
$397$	−8.19026e12			−0.830510			−0.415255	−	0.909705i	$-0.636308\pi$
$397$	−8.19026e12			−0.830510			−0.415255	+	0.909705i	$0.636308\pi$
$398$	−3.06209e12	+	6.92233e11i	−0.306622	+	0.0693165i
$399$		−	2.49419e12i		−	0.246641i
$400$		0			0
$401$	−3.61138e12			−0.348298			−0.174149	−	0.984719i	$-0.555717\pi$
$401$	−3.61138e12			−0.348298			−0.174149	+	0.984719i	$0.555717\pi$
$402$	5.86555e12	+	2.59463e13i	0.558700	+	2.47141i
$403$		−	2.22779e13i		−	2.09580i
$404$	6.07420e12	−	2.89424e12i	0.564394	−	0.268923i
$405$		0			0
$406$	7.45571e11	−	1.68548e11i	0.0675863	−	0.0152789i
$407$			6.97428e12i			0.624493i
$408$	−9.31543e12	+	7.33457e12i	−0.823952	+	0.648745i
$409$	9.03524e12			0.789447			0.394724	−	0.918800i	$-0.370840\pi$
$409$	9.03524e12			0.789447			0.394724	+	0.918800i	$0.370840\pi$
$410$		0			0
$411$			2.96350e13i			2.52694i
$412$	8.20798e12	+	1.72262e13i	0.691433	+	1.45112i
$413$	−2.32835e12			−0.193775
$414$	2.93361e13	−	6.63187e12i	2.41213	−	0.545298i
$415$		0			0
$416$	−2.17530e13	−	1.07546e13i	−1.74603	−	0.863235i
$417$	−3.08268e12			−0.244483
$418$	−1.09142e12	−	4.82791e12i	−0.0855287	−	0.378336i
$419$		−	1.23736e13i		−	0.958134i	−0.877778	−	0.479067i	$-0.840975\pi$
$419$		−	1.23736e13i		−	0.958134i	0.877778	−	0.479067i	$-0.159025\pi$
$420$		0			0
$421$	1.89253e13			1.43098			0.715488	−	0.698625i	$-0.246204\pi$
$421$	1.89253e13			1.43098			0.715488	+	0.698625i	$0.246204\pi$
$422$	2.01725e13	−	4.56030e12i	1.50729	−	0.340746i
$423$		−	1.83032e13i		−	1.35153i
$424$	−4.40134e12	−	5.59002e12i	−0.321185	−	0.407928i
$425$		0			0
$426$	1.86807e12	+	8.26339e12i	0.133151	+	0.588994i
$427$			2.28503e11i			0.0160973i
$428$	7.32891e11	+	1.53813e12i	0.0510294	+	0.107096i
$429$	−2.15602e13			−1.48377
$430$		0			0
$431$		−	1.86920e13i		−	1.25681i	−0.777887	−	0.628405i	$-0.783708\pi$
$431$		−	1.86920e13i		−	1.25681i	0.777887	−	0.628405i	$-0.216292\pi$
$432$	−2.79731e13	−	2.26895e13i	−1.85918	−	1.50802i
$433$	1.44652e13			0.950353			0.475177	−	0.879890i	$-0.342384\pi$
$433$	1.44652e13			0.950353			0.475177	+	0.879890i	$0.342384\pi$
$434$	5.33828e11	+	2.36139e12i	0.0346699	+	0.153363i
$435$		0			0
$436$	1.61046e13	−	7.67353e12i	1.02216	−	0.487038i
$437$	−1.57839e13			−0.990390
$438$	5.06481e12	−	1.14498e12i	0.314190	−	0.0710275i
$439$			2.86878e13i			1.75944i	0.475490	+	0.879721i	$0.342271\pi$
$439$			2.86878e13i			1.75944i	−0.475490	+	0.879721i	$0.657729\pi$
$440$		0			0
$441$	−3.77867e13			−2.26541
$442$	−4.17329e12	−	1.84606e13i	−0.247381	−	1.09429i
$443$			2.02275e13i			1.18556i	0.805363	+	0.592781i	$0.201970\pi$
$443$			2.02275e13i			1.18556i	−0.805363	+	0.592781i	$0.798030\pi$
$444$	−2.01694e13	−	4.23298e13i	−1.16890	−	2.45319i
$445$		0			0
$446$	−2.33979e12	+	5.28946e11i	−0.132588	+	0.0299735i
$447$		−	1.80366e13i		−	1.01069i
$448$	2.56346e12	+	6.18709e11i	0.142048	+	0.0342844i
$449$	6.40638e12			0.351060			0.175530	−	0.984474i	$-0.443836\pi$
$449$	6.40638e12			0.351060			0.175530	+	0.984474i	$0.443836\pi$
$450$		0			0
$451$			8.63812e12i			0.462952i
$452$	−1.92446e13	+	9.16968e12i	−1.02004	+	0.486029i
$453$	3.40313e13			1.78397
$454$	1.08041e13	−	2.44243e12i	0.560157	−	0.126632i
$455$		0			0
$456$	2.05865e13	+	2.61463e13i	1.04414	+	1.32613i
$457$	1.69605e13			0.850860			0.425430	−	0.904991i	$-0.360123\pi$
$457$	1.69605e13			0.850860			0.425430	+	0.904991i	$0.360123\pi$
$458$	2.10469e12	+	9.31011e12i	0.104439	+	0.461985i
$459$		−	2.80922e13i		−	1.37887i
$460$		0			0
$461$	2.32003e13			1.11427			0.557133	−	0.830423i	$-0.311901\pi$
$461$	2.32003e13			1.11427			0.557133	+	0.830423i	$0.311901\pi$
$462$	2.28532e12	−	5.16631e11i	0.108577	−	0.0245454i
$463$			4.03905e13i			1.89834i	0.314759	+	0.949171i	$0.398076\pi$
$463$			4.03905e13i			1.89834i	−0.314759	+	0.949171i	$0.601924\pi$
$464$	−6.42458e12	+	7.92063e12i	−0.298713	+	0.368273i
$465$		0			0
$466$	−6.83279e12	−	3.02249e13i	−0.310934	−	1.37542i
$467$			1.71681e13i			0.772928i	0.922304	+	0.386464i	$0.126304\pi$
$467$			1.71681e13i			0.772928i	−0.922304	+	0.386464i	$0.873696\pi$
$468$	9.13816e13	−	4.35416e13i	4.07033	−	1.93943i
$469$	4.61458e12			0.203361
$470$		0			0
$471$		−	8.25982e12i		−	0.356341i
$472$	2.44079e13	−	1.92177e13i	1.04188	−	0.820335i
$473$	−4.91678e12			−0.207671
$474$	7.69012e12	+	3.40173e13i	0.321397	+	1.42170i
$475$		0			0
$476$	8.84712e11	+	1.85676e12i	0.0362049	+	0.0759839i
$477$	2.96787e13			1.20186
$478$	−3.26729e13	+	7.38621e12i	−1.30933	+	0.295993i
$479$			4.04548e12i			0.160433i	0.996777	+	0.0802163i	$0.0255611\pi$
$479$			4.04548e12i			0.160433i	−0.996777	+	0.0802163i	$0.974439\pi$
$480$		0			0
$481$	7.48500e13			2.90714
$482$	−2.47655e12	−	1.09550e13i	−0.0951944	−	0.421093i
$483$		−	7.47138e12i		−	0.284227i
$484$	−1.97797e13	+	9.42463e12i	−0.744718	+	0.354844i
$485$		0			0
$486$	3.50909e13	−	7.93283e12i	1.29423	−	0.292581i
$487$		−	4.76129e13i		−	1.73812i	−0.494707	−	0.869060i	$-0.664725\pi$
$487$		−	4.76129e13i		−	1.73812i	0.494707	−	0.869060i	$-0.335275\pi$
$488$	−1.88601e12	−	2.39537e12i	−0.0681467	−	0.0865512i
$489$	8.87278e13			3.17333
$490$		0			0
$491$			2.54680e13i			0.892458i	0.894919	+	0.446229i	$0.147233\pi$
$491$			2.54680e13i			0.892458i	−0.894919	+	0.446229i	$0.852767\pi$
$492$	−2.49811e13	−	5.24284e13i	−0.866536	−	1.81862i
$493$	−7.95435e12			−0.273131
$494$	−5.18146e13	+	1.17135e13i	−1.76123	+	0.398154i
$495$		0			0
$496$	−2.50864e13	−	2.03481e13i	−0.835662	−	0.677822i
$497$	1.46965e12			0.0484656
$498$	1.44784e13	+	6.40454e13i	0.472688	+	2.09094i
$499$		−	5.20274e12i		−	0.168163i	−0.996459	−	0.0840813i	$-0.973204\pi$
$499$		−	5.20274e12i		−	0.168163i	0.996459	−	0.0840813i	$-0.0267956\pi$
$500$		0			0
$501$	−3.71262e13			−1.17623
$502$	−2.86461e13	+	6.47589e12i	−0.898560	+	0.203133i
$503$		−	3.74483e13i		−	1.16303i	−0.813535	−	0.581516i	$-0.802460\pi$
$503$		−	3.74483e13i		−	1.16303i	0.813535	−	0.581516i	$-0.197540\pi$
$504$	−8.64282e12	+	6.80498e12i	−0.265768	+	0.209254i
$505$		0			0
$506$	−3.26938e12	−	1.44621e13i	−0.0985626	−	0.435992i
$507$			1.70399e14i			5.08659i
$508$	−9.32276e12	−	1.95658e13i	−0.275566	−	0.578336i
$509$	−3.41894e13			−1.00070			−0.500348	−	0.865825i	$-0.666795\pi$
$509$	−3.41894e13			−1.00070			−0.500348	+	0.865825i	$0.666795\pi$
$510$		0			0
$511$		−	9.00783e11i		−	0.0258533i
$512$	−3.19791e13	+	1.46723e13i	−0.908901	+	0.417013i
$513$	−7.88483e13			−2.21925
$514$	1.40072e13	+	6.19611e13i	0.390425	+	1.72704i
$515$		0			0
$516$	2.98420e13	−	1.42192e13i	0.815792	−	0.388710i
$517$	−9.02310e12			−0.244288
$518$	−7.93388e12	+	1.79357e12i	−0.212734	+	0.0480917i
$519$		−	2.52433e13i		−	0.670362i
$520$		0			0
$521$	−9.44738e12			−0.246106			−0.123053	−	0.992400i	$-0.539269\pi$
$521$	−9.44738e12			−0.246106			−0.123053	+	0.992400i	$0.539269\pi$
$522$	−9.38068e12	−	4.14955e13i	−0.242037	−	1.07065i
$523$			4.44677e13i			1.13641i	0.822886	+	0.568207i	$0.192363\pi$
$523$			4.44677e13i			1.13641i	−0.822886	+	0.568207i	$0.807637\pi$
$524$	−9.12802e12	−	1.91572e13i	−0.231058	−	0.484925i
$525$		0			0
$526$	3.71028e13	−	8.38764e12i	0.921462	−	0.208311i
$527$		−	2.51932e13i		−	0.619771i
$528$	−1.96926e13	+	2.42783e13i	−0.479880	+	0.591627i
$529$	−5.85434e12			−0.141319
$530$		0			0
$531$			1.29587e14i			3.06965i
$532$	5.21151e12	−	2.48319e12i	0.122294	−	0.0582708i
$533$	9.27068e13			2.15514
$534$	3.10555e13	−	7.02058e12i	0.715209	−	0.161684i
$535$		0			0
$536$	−4.83741e13	+	3.80877e13i	−1.09342	+	0.860916i
$537$	3.95660e13			0.886034
$538$	−8.93797e12	−	3.95371e13i	−0.198302	−	0.877190i
$539$			1.86281e13i			0.409472i
$540$		0			0
$541$	−4.20395e13			−0.907133			−0.453566	−	0.891223i	$-0.649848\pi$
$541$	−4.20395e13			−0.907133			−0.453566	+	0.891223i	$0.649848\pi$
$542$	9.76851e12	−	2.20832e12i	0.208849	−	0.0472134i
$543$		−	2.04570e13i		−	0.433354i
$544$	−2.45996e13	−	1.21620e13i	−0.516338	−	0.255277i
$545$		0			0
$546$	−5.54463e12	−	2.45267e13i	−0.114264	−	0.505447i
$547$			3.24090e13i			0.661803i	0.943665	+	0.330902i	$0.107353\pi$
$547$			3.24090e13i			0.661803i	−0.943665	+	0.330902i	$0.892647\pi$
$548$	−6.19212e13	+	2.95043e13i	−1.25296	+	0.597011i
$549$	1.27175e13			0.255001
$550$		0			0
$551$			2.23260e13i			0.439596i
$552$	6.16671e13	+	7.83216e13i	1.20326	+	1.52822i
$553$	6.05002e12			0.116985
$554$	−4.98898e12	−	2.20688e13i	−0.0956011	−	0.422892i
$555$		0			0
$556$	−3.06908e12	−	6.44115e12i	−0.0577610	−	0.121224i
$557$	−7.91773e13			−1.47681			−0.738405	−	0.674357i	$-0.764421\pi$
$557$	−7.91773e13			−1.47681			−0.738405	+	0.674357i	$0.764421\pi$
$558$	1.31426e14	−	2.97107e13i	2.42946	−	0.549215i
$559$			5.27683e13i			0.966750i
$560$		0			0
$561$	−2.43816e13			−0.438782
$562$	7.76288e12	+	3.43391e13i	0.138465	+	0.612502i
$563$			1.00550e14i			1.77763i	0.458271	+	0.888813i	$0.348469\pi$
$563$			1.00550e14i			1.77763i	−0.458271	+	0.888813i	$0.651531\pi$
$564$	5.47650e13	−	2.60945e13i	0.959638	−	0.457249i
$565$		0			0
$566$	−2.46501e13	+	5.57252e12i	−0.424361	+	0.0959333i
$567$		−	1.75004e13i		−	0.298630i
$568$	−1.54062e13	+	1.21302e13i	−0.260588	+	0.205176i
$569$	−8.45480e13			−1.41756			−0.708781	−	0.705429i	$-0.750754\pi$
$569$	−8.45480e13			−1.41756			−0.708781	+	0.705429i	$0.750754\pi$
$570$		0			0
$571$		−	1.94028e12i		−	0.0319657i	−0.999872	−	0.0159828i	$-0.994912\pi$
$571$		−	1.94028e12i		−	0.0319657i	0.999872	−	0.0159828i	$-0.00508771\pi$
$572$	−2.14651e13	−	4.50492e13i	−0.350552	−	0.735711i
$573$	−1.47387e14			−2.38609
$574$	−9.82664e12	+	2.22146e12i	−0.157705	+	0.0356516i
$575$		0			0
$576$	3.44349e13	−	1.42672e14i	0.543108	−	2.25022i
$577$	−9.54895e13			−1.49306			−0.746528	−	0.665354i	$-0.768281\pi$
$577$	−9.54895e13			−1.49306			−0.746528	+	0.665354i	$0.768281\pi$
$578$	9.50550e12	+	4.20476e13i	0.147345	+	0.651782i
$579$		−	9.83178e13i		−	1.51091i
$580$		0			0
$581$	1.13905e13			0.172054
$582$	8.42476e13	−	1.90455e13i	1.26166	−	0.285218i
$583$		−	1.46310e13i		−	0.217235i
$584$	7.43486e12	+	9.44281e12i	0.109448	+	0.139007i
$585$		0			0
$586$	−5.24487e12	−	2.32007e13i	−0.0759009	−	0.335748i
$587$		−	1.05546e14i		−	1.51444i	−0.653159	−	0.757221i	$-0.726557\pi$
$587$		−	1.05546e14i		−	1.51444i	0.653159	−	0.757221i	$-0.273443\pi$
$588$	−5.38717e13	−	1.13062e14i	−0.766433	−	1.60853i
$589$	−7.07117e13			−0.997504
$590$		0			0
$591$		−	7.62979e13i		−	1.05822i
$592$	6.83662e13	−	8.42862e13i	0.940227	−	1.15917i
$593$	1.42515e14			1.94351			0.971754	−	0.235995i	$-0.0758349\pi$
$593$	1.42515e14			1.94351			0.971754	+	0.235995i	$0.0758349\pi$
$594$	−1.63322e13	−	7.22454e13i	−0.220857	−	0.976962i
$595$		0			0
$596$	3.76867e13	−	1.79570e13i	0.501137	−	0.238782i
$597$	4.34039e13			0.572344
$598$	−1.55211e14	+	3.50879e13i	−2.02963	+	0.458830i
$599$			2.87230e13i			0.372474i	0.982505	+	0.186237i	$0.0596293\pi$
$599$			2.87230e13i			0.372474i	−0.982505	+	0.186237i	$0.940371\pi$
$600$		0			0
$601$	−6.80904e11			−0.00868387			−0.00434194	−	0.999991i	$-0.501382\pi$
$601$	−6.80904e11			−0.00868387			−0.00434194	+	0.999991i	$0.501382\pi$
$602$	−1.26445e12	−	5.59329e12i	−0.0159926	−	0.0707432i
$603$		−	2.56829e14i		−	3.22150i
$604$	3.38812e13	+	7.11071e13i	0.421477	+	0.884562i
$605$		0			0
$606$	−9.07365e13	+	2.05124e13i	−1.11024	+	0.250988i
$607$			7.17005e13i			0.870119i	0.900402	+	0.435059i	$0.143273\pi$
$607$			7.17005e13i			0.870119i	−0.900402	+	0.435059i	$0.856727\pi$
$608$	−3.41360e13	+	6.90455e13i	−0.410861	+	0.831032i
$609$	−1.05682e13			−0.126157
$610$		0			0
$611$			9.68385e13i			1.13721i
$612$	1.03340e14	−	4.92395e13i	1.20368	−	0.573531i
$613$	6.89627e13			0.796732			0.398366	−	0.917227i	$-0.369577\pi$
$613$	6.89627e13			0.796732			0.398366	+	0.917227i	$0.369577\pi$
$614$	1.22479e13	−	2.76882e12i	0.140352	−	0.0317287i
$615$		0			0
$616$	3.35472e12	+	4.26073e12i	0.0378227	+	0.0480375i
$617$	−8.96742e13			−1.00286			−0.501432	−	0.865197i	$-0.667193\pi$
$617$	−8.96742e13			−1.00286			−0.501432	+	0.865197i	$0.667193\pi$
$618$	−5.81724e13	−	2.57326e14i	−0.645319	−	2.85457i
$619$		−	1.00887e14i		−	1.11015i	−0.831801	−	0.555074i	$-0.812690\pi$
$619$		−	1.00887e14i		−	1.11015i	0.831801	−	0.555074i	$-0.187310\pi$
$620$		0			0
$621$	−2.36191e14			−2.55744
$622$	2.46168e13	−	5.56500e12i	0.264411	−	0.0597741i
$623$		−	5.52326e12i		−	0.0588512i
$624$	2.60562e14	+	2.11346e14i	2.75415	+	2.23394i
$625$		0			0
$626$	−2.77660e13	−	1.22823e14i	−0.288830	−	1.27764i
$627$			6.84337e13i			0.706207i
$628$	1.72586e13	−	8.22339e12i	0.176688	−	0.0841884i
$629$	8.46451e13			0.859703
$630$		0			0
$631$		−	1.65548e14i		−	1.65492i	−0.561526	−	0.827459i	$-0.689785\pi$
$631$		−	1.65548e14i		−	1.65492i	0.561526	−	0.827459i	$-0.310215\pi$
$632$	−6.34216e13	+	4.99354e13i	−0.629002	+	0.495249i
$633$	−2.85937e14			−2.81353
$634$	−1.88811e13	−	8.35208e13i	−0.184324	−	0.815358i
$635$		0			0
$636$	4.23122e13	+	8.88015e13i	0.406612	+	0.853365i
$637$	1.99922e14			1.90618
$638$	−2.04564e13	+	4.62448e12i	−0.193520	+	0.0437482i
$639$		−	8.17951e13i		−	0.767755i
$640$		0			0
$641$	1.56158e14			1.44302			0.721511	−	0.692403i	$-0.243448\pi$
$641$	1.56158e14			1.44302			0.721511	+	0.692403i	$0.243448\pi$
$642$	−5.19422e12	−	2.29766e13i	−0.0476261	−	0.210674i
$643$			1.97408e13i			0.179601i	0.995960	+	0.0898007i	$0.0286230\pi$
$643$			1.97408e13i			0.179601i	−0.995960	+	0.0898007i	$0.971377\pi$
$644$	1.56112e13	−	7.43842e12i	0.140931	−	0.0671509i
$645$		0			0
$646$	−5.85951e13	+	1.32463e13i	−0.520834	+	0.117742i
$647$		−	5.79053e13i		−	0.510737i	−0.966844	−	0.255368i	$-0.917803\pi$
$647$		−	5.79053e13i		−	0.510737i	0.966844	−	0.255368i	$-0.0821967\pi$
$648$	1.44444e14	+	1.83455e14i	1.26423	+	1.60566i
$649$	6.38837e13			0.554838
$650$		0			0
$651$		−	3.34718e13i		−	0.286268i
$652$	8.83364e13	+	1.85393e14i	0.749725	+	1.57346i
$653$	4.59311e13			0.386848			0.193424	−	0.981115i	$-0.438041\pi$
$653$	4.59311e13			0.386848			0.193424	+	0.981115i	$0.438041\pi$
$654$	−2.40570e14	+	5.43845e13i	−2.01073	+	0.454555i
$655$		0			0
$656$	8.46761e13	−	1.04394e14i	0.697014	−	0.859324i
$657$	−5.01340e13			−0.409549
$658$	−2.32047e12	−	1.02646e13i	−0.0188125	−	0.0832170i
$659$			8.04209e13i			0.647056i	0.946219	+	0.323528i	$0.104869\pi$
$659$			8.04209e13i			0.647056i	−0.946219	+	0.323528i	$0.895131\pi$
$660$		0			0
$661$	1.56940e14			1.24373			0.621867	−	0.783123i	$-0.286375\pi$
$661$	1.56940e14			1.24373			0.621867	+	0.783123i	$0.286375\pi$
$662$	−1.21481e14	+	2.74627e13i	−0.955477	+	0.216000i
$663$			2.61671e14i			2.04262i
$664$	−1.19406e14	+	9.40150e13i	−0.925092	+	0.728378i
$665$		0			0
$666$	9.98231e13	+	4.41568e14i	0.761833	+	3.36997i
$667$			6.68780e13i			0.506587i
$668$	−3.69624e13	−	7.75737e13i	−0.277893	−	0.583219i
$669$	3.31656e13			0.247490
$670$		0			0
$671$		−	6.26949e12i		−	0.0460914i
$672$	−3.26831e13	−	1.61585e13i	−0.238494	−	0.117911i
$673$	1.41141e14			1.02230			0.511151	−	0.859491i	$-0.329219\pi$
$673$	1.41141e14			1.02230			0.511151	+	0.859491i	$0.329219\pi$
$674$	−4.69681e13	−	2.07763e14i	−0.337678	−	1.49372i
$675$		0			0
$676$	−3.56042e14	+	1.69647e14i	−2.52213	+	1.20175i
$677$	−4.70702e13			−0.330981			−0.165490	−	0.986211i	$-0.552921\pi$
$677$	−4.70702e13			−0.330981			−0.165490	+	0.986211i	$0.552921\pi$
$678$	2.87476e14	−	6.49882e13i	2.00656	−	0.453614i
$679$		−	1.49835e13i		−	0.103816i
$680$		0			0
$681$	−1.53144e14			−1.04560
$682$	−1.46468e13	−	6.47901e13i	−0.0992706	−	0.439124i
$683$			1.10351e14i			0.742462i	0.928541	+	0.371231i	$0.121064\pi$
$683$			1.10351e14i			0.742462i	−0.928541	+	0.371231i	$0.878936\pi$
$684$	−1.38204e14	−	2.90052e14i	−0.923082	−	1.93729i
$685$		0			0
$686$	−4.28446e13	+	9.68568e12i	−0.282017	+	0.0637543i
$687$		−	1.31967e14i		−	0.862347i
$688$	5.94207e13	+	4.81973e13i	0.385475	+	0.312666i
$689$	−1.57024e14			−1.01128
$690$		0			0
$691$			8.72354e13i			0.553736i	0.960908	+	0.276868i	$0.0892965\pi$
$691$			8.72354e13i			0.553736i	−0.960908	+	0.276868i	$0.910704\pi$
$692$	5.27449e13	−	2.51319e13i	0.332391	−	0.158378i
$693$	−2.26212e13			−0.141530
$694$	1.60432e14	−	3.62680e13i	0.996536	−	0.225282i
$695$		0			0
$696$	1.10785e14	−	8.72271e13i	0.678319	−	0.534079i
$697$	1.04839e14			0.637320
$698$	9.29461e12	+	4.11148e13i	0.0560989	+	0.248154i
$699$			4.28425e14i			2.56737i
$700$		0			0
$701$	3.45702e13			0.204227			0.102113	−	0.994773i	$-0.467440\pi$
$701$	3.45702e13			0.204227			0.102113	+	0.994773i	$0.467440\pi$
$702$	−7.75358e14	+	1.75282e14i	−4.54796	+	1.02814i
$703$		−	2.37579e14i		−	1.38367i
$704$	−7.03342e13	−	1.69757e13i	−0.406727	−	0.0981667i
$705$		0			0
$706$	−9.65904e12	−	4.27268e13i	−0.0550694	−	0.243600i
$707$			1.61376e13i			0.0913569i
$708$	−3.87737e14	+	1.84749e14i	−2.17957	+	1.03852i
$709$	2.76369e14			1.54262			0.771310	−	0.636460i	$-0.219602\pi$
$709$	2.76369e14			1.54262			0.771310	+	0.636460i	$0.219602\pi$
$710$		0			0
$711$		−	3.36720e14i		−	1.85319i
$712$	4.55878e13	+	5.78997e13i	0.249143	+	0.316429i
$713$	−2.11818e14			−1.14952
$714$	−6.27022e12	−	2.77363e13i	−0.0337903	−	0.149471i
$715$		0			0
$716$	3.93914e13	+	8.26715e13i	0.209332	+	0.439330i
$717$	4.63125e14			2.44401
$718$	4.82759e13	−	1.09135e13i	0.252993	−	0.0571928i
$719$			1.19415e14i			0.621462i	0.950498	+	0.310731i	$0.100574\pi$
$719$			1.19415e14i			0.621462i	−0.950498	+	0.310731i	$0.899426\pi$
$720$		0			0
$721$	−4.57657e13			−0.234890
$722$	−6.08160e12	−	2.69020e13i	−0.0309979	−	0.137119i
$723$			1.55283e14i			0.786017i
$724$	4.27441e13	−	2.03668e13i	0.214874	−	0.102383i
$725$		0			0
$726$	2.95469e14	−	6.67952e13i	1.46497	−	0.331178i
$727$			7.58961e13i			0.373721i	0.982386	+	0.186861i	$0.0598312\pi$
$727$			7.58961e13i			0.373721i	−0.982386	+	0.186861i	$0.940169\pi$
$728$	4.57274e13	−	3.60038e13i	0.223625	−	0.176073i
$729$	−7.66334e13			−0.372204
$730$		0			0
$731$			5.96737e13i			0.285888i
$732$	1.81311e13	+	3.80522e13i	0.0862719	+	0.181061i
$733$	−7.26675e12			−0.0343416			−0.0171708	−	0.999853i	$-0.505466\pi$
$733$	−7.26675e12			−0.0343416			−0.0171708	+	0.999853i	$0.505466\pi$
$734$	−2.41090e14	+	5.45020e13i	−1.13161	+	0.255819i
$735$		0			0
$736$	−1.02255e14	+	2.06827e14i	−0.473473	+	0.957675i
$737$	−1.26611e14			−0.582285
$738$	1.23638e14	+	5.46912e14i	0.564766	+	2.49825i
$739$		−	1.55132e14i		−	0.703848i	−0.936029	−	0.351924i	$-0.885528\pi$
$739$		−	1.55132e14i		−	0.703848i	0.936029	−	0.351924i	$-0.114472\pi$
$740$		0			0
$741$	7.34450e14			3.28754
$742$	1.66441e13	−	3.76264e12i	0.0740014	−	0.0167291i
$743$		−	4.24317e14i		−	1.87390i	−0.349463	−	0.936950i	$-0.613636\pi$
$743$		−	4.24317e14i		−	1.87390i	0.349463	−	0.936950i	$-0.386364\pi$
$744$	2.76268e14	+	3.50880e14i	1.21190	+	1.53920i
$745$		0			0
$746$	−3.48387e13	−	1.54109e14i	−0.150788	−	0.667013i
$747$		−	6.33952e14i		−	2.72555i
$748$	−2.42741e13	−	5.09445e13i	−0.103666	−	0.217565i
$749$	−4.08642e12			−0.0173354
$750$		0			0
$751$			2.86262e14i			1.19830i	0.800638	+	0.599148i	$0.204494\pi$
$751$			2.86262e14i			1.19830i	−0.800638	+	0.599148i	$0.795506\pi$
$752$	1.09047e14	+	8.84499e13i	0.453444	+	0.367797i
$753$	4.06047e14			1.67726
$754$	4.96313e13	+	2.19544e14i	0.203657	+	0.900876i
$755$		0			0
$756$	7.79855e13	−	3.71586e13i	0.315795	−	0.150470i
$757$	−2.62906e14			−1.05760			−0.528799	−	0.848747i	$-0.677357\pi$
$757$	−2.62906e14			−1.05760			−0.528799	+	0.848747i	$0.677357\pi$
$758$	1.79461e13	−	4.05698e12i	0.0717172	−	0.0162128i
$759$			2.04994e14i			0.813828i
$760$		0			0
$761$	1.06875e13			0.0418749			0.0209375	−	0.999781i	$-0.493335\pi$
$761$	1.06875e13			0.0418749			0.0209375	+	0.999781i	$0.493335\pi$
$762$	6.60731e13	+	2.92275e14i	0.257188	+	1.13767i
$763$			4.27857e13i			0.165453i
$764$	−1.46737e14	−	3.07960e14i	−0.563733	−	1.18312i
$765$		0			0
$766$	1.58274e14	−	3.57802e13i	0.600157	−	0.135675i
$767$		−	6.85618e14i		−	2.58289i
$768$	4.75981e14	−	1.00371e14i	1.78149	−	0.375668i
$769$	3.63890e14			1.35313			0.676563	−	0.736385i	$-0.263469\pi$
$769$	3.63890e14			1.35313			0.676563	+	0.736385i	$0.263469\pi$
$770$		0			0
$771$		−	8.78273e14i		−	3.22372i
$772$	2.05431e14	−	9.78841e13i	0.749170	−	0.356965i
$773$	4.08388e14			1.47971			0.739853	−	0.672768i	$-0.234895\pi$
$773$	4.08388e14			1.47971			0.739853	+	0.672768i	$0.234895\pi$
$774$	−3.11300e14	+	7.03740e13i	−1.12066	+	0.253342i
$775$		0			0
$776$	1.23671e14	+	1.57071e14i	0.439499	+	0.558196i
$777$	1.12459e14			0.397092
$778$	−1.24609e13	−	5.51208e13i	−0.0437171	−	0.193383i
$779$		−	2.94258e14i		−	1.02575i
$780$		0			0
$781$	−4.03233e13			−0.138772
$782$	−1.75523e14	+	3.96796e13i	−0.600205	+	0.135685i
$783$			3.34089e14i			1.13515i
$784$	1.82604e14	−	2.25126e14i	0.616495	−	0.760055i
$785$		0			0
$786$	6.46930e13	+	2.86170e14i	0.215647	+	0.953917i
$787$			2.71187e14i			0.898244i	0.893470	+	0.449122i	$0.148263\pi$
$787$			2.71187e14i			0.898244i	−0.893470	+	0.449122i	$0.851737\pi$
$788$	1.59421e14	−	7.59613e13i	0.524706	−	0.250012i
$789$	−5.25917e14			−1.72001
$790$		0			0
$791$		−	5.11279e13i		−	0.165111i
$792$	2.37135e14	−	1.86710e14i	0.760975	−	0.599159i
$793$	−6.72860e13			−0.214565
$794$	5.77907e13	+	2.55637e14i	0.183128	+	0.810069i
$795$		0			0
$796$	4.32124e13	+	9.06908e13i	0.135221	+	0.283790i
$797$	−3.01683e14			−0.938122			−0.469061	−	0.883166i	$-0.655408\pi$
$797$	−3.01683e14			−0.938122			−0.469061	+	0.883166i	$0.655408\pi$
$798$	−7.78495e13	+	1.75991e13i	−0.240570	+	0.0543845i
$799$			1.09511e14i			0.336298i
$800$		0			0
$801$	−3.07403e14			−0.932277
$802$	2.54820e13	+	1.12720e14i	0.0768001	+	0.339725i
$803$			2.47150e13i			0.0740258i
$804$	7.68458e14	−	3.66156e14i	2.28739	−	1.08990i
$805$		0			0
$806$	−6.95346e14	+	1.57194e14i	−2.04421	+	0.462125i
$807$			5.60423e14i			1.63737i
$808$	−1.33196e14	−	1.69168e14i	−0.386754	−	0.491205i
$809$	−4.23399e14			−1.22182			−0.610910	−	0.791700i	$-0.709196\pi$
$809$	−4.23399e14			−1.22182			−0.610910	+	0.791700i	$0.709196\pi$
$810$		0			0
$811$			8.35423e13i			0.238124i	0.992887	+	0.119062i	$0.0379887\pi$
$811$			8.35423e13i			0.238124i	−0.992887	+	0.119062i	$0.962011\pi$
$812$	−1.05215e13	−	2.20818e13i	−0.0298057	−	0.0625538i
$813$	−1.38465e14			−0.389840
$814$	2.17684e14	−	4.92107e13i	0.609122	−	0.137701i
$815$		0			0
$816$	2.94659e14	+	2.39004e14i	0.814459	+	0.660623i
$817$	1.67490e14			0.460129
$818$	−6.37529e13	−	2.82011e14i	−0.174074	−	0.770016i
$819$			2.42777e14i			0.658853i
$820$		0			0
$821$	−1.84804e14			−0.495444			−0.247722	−	0.968831i	$-0.579682\pi$
$821$	−1.84804e14			−0.495444			−0.247722	+	0.968831i	$0.579682\pi$
$822$	9.24978e14	−	2.09105e14i	2.46475	−	0.557194i
$823$			3.70851e14i			0.982201i	0.871103	+	0.491101i	$0.163405\pi$
$823$			3.70851e14i			0.982201i	−0.871103	+	0.491101i	$0.836595\pi$
$824$	4.79756e14	−	3.77740e14i	1.26295	−	0.994389i
$825$		0			0
$826$	1.64289e13	+	7.26735e13i	0.0427277	+	0.189006i
$827$			2.92690e14i			0.756623i	0.925678	+	0.378312i	$0.123495\pi$
$827$			2.92690e14i			0.756623i	−0.925678	+	0.378312i	$0.876505\pi$
$828$	−4.13993e14	−	8.68855e14i	−1.06375	−	2.23252i
$829$	−1.25030e14			−0.319331			−0.159665	−	0.987171i	$-0.551042\pi$
$829$	−1.25030e14			−0.319331			−0.159665	+	0.987171i	$0.551042\pi$
$830$		0			0
$831$			3.12816e14i			0.789375i
$832$	−1.82188e14	+	7.54847e14i	−0.456986	+	1.89340i
$833$	2.26084e14			0.563696
$834$	2.17515e13	+	9.62179e13i	0.0539087	+	0.238465i
$835$		0			0
$836$	−1.42990e14	+	6.81318e13i	−0.350165	+	0.166847i
$837$	−1.05814e15			−2.57581
$838$	−3.86210e14	+	8.73086e13i	−0.934551	+	0.211270i
$839$		−	7.94005e14i		−	1.90991i	−0.296746	−	0.954956i	$-0.595902\pi$
$839$		−	7.94005e14i		−	1.90991i	0.296746	−	0.954956i	$-0.404098\pi$
$840$		0			0
$841$	−3.26109e14			−0.775145
$842$	−1.33538e14	−	5.90704e14i	−0.315532	−	1.39576i
$843$		−	4.86743e14i		−	1.14330i
$844$	−2.84676e14	−	5.97454e14i	−0.664719	−	1.39506i
$845$		0			0
$846$	−5.71286e14	+	1.29148e14i	−1.31826	+	0.298013i
$847$		−	5.25494e13i		−	0.120546i
$848$	−1.43422e14	+	1.76820e14i	−0.327066	+	0.403228i
$849$	3.49405e14			0.792118
$850$		0			0
$851$		−	7.11673e14i		−	1.59453i
$852$	2.44739e14	−	1.16614e14i	0.545137	−	0.259747i
$853$	−2.57449e14			−0.570092			−0.285046	−	0.958514i	$-0.592009\pi$
$853$	−2.57449e14			−0.570092			−0.285046	+	0.958514i	$0.592009\pi$
$854$	7.13211e12	−	1.61232e12i	0.0157011	−	0.00354946i
$855$		0			0
$856$	4.28375e13	−	3.37284e13i	0.0932084	−	0.0733883i
$857$	−9.32214e12			−0.0201656			−0.0100828	−	0.999949i	$-0.503210\pi$
$857$	−9.32214e12			−0.0201656			−0.0100828	+	0.999949i	$0.503210\pi$
$858$	1.52130e14	+	6.72946e14i	0.327173	+	1.44725i
$859$		−	5.64544e14i		−	1.20707i	−0.797337	−	0.603534i	$-0.793759\pi$
$859$		−	5.64544e14i		−	1.20707i	0.797337	−	0.603534i	$-0.206241\pi$
$860$		0			0
$861$	1.39289e14			0.294374
$862$	−5.83422e14	+	1.31891e14i	−1.22588	+	0.277128i
$863$		−	7.05605e13i		−	0.147403i	−0.997280	−	0.0737017i	$-0.976519\pi$
$863$		−	7.05605e13i		−	0.147403i	0.997280	−	0.0737017i	$-0.0234813\pi$
$864$	−5.10814e14	+	1.03320e15i	−1.06095	+	2.14594i
$865$		0			0
$866$	−1.02067e14	−	4.51493e14i	−0.209554	−	0.926962i
$867$		−	5.96008e14i		−	1.21662i
$868$	6.99379e13	−	3.33241e13i	0.141943	−	0.0676332i
$869$	−1.65996e14			−0.334964
$870$		0			0
$871$			1.35883e15i			2.71066i
$872$	−3.53143e14	−	4.48517e14i	−0.700436	−	0.889604i
$873$	−8.33924e14			−1.64458
$874$	1.11371e14	+	4.92652e14i	0.218382	+	0.966013i
$875$		0			0
$876$	−7.14750e13	−	1.50006e14i	−0.138559	−	0.290796i
$877$	−6.20358e14			−1.19576			−0.597880	−	0.801585i	$-0.703990\pi$
$877$	−6.20358e14			−1.19576			−0.597880	+	0.801585i	$0.703990\pi$
$878$	8.95415e14	−	2.02422e14i	1.71614	−	0.387959i
$879$			3.28860e14i			0.626711i
$880$		0			0
$881$	−6.83835e12			−0.0128846			−0.00644231	−	0.999979i	$-0.502051\pi$
$881$	−6.83835e12			−0.0128846			−0.00644231	+	0.999979i	$0.502051\pi$
$882$	2.66624e14	+	1.17941e15i	0.499524	+	2.20965i
$883$		−	4.19788e14i		−	0.782036i	−0.920383	−	0.391018i	$-0.872123\pi$
$883$		−	4.19788e14i		−	0.782036i	0.920383	−	0.391018i	$-0.127877\pi$
$884$	−5.46751e14	+	2.60517e14i	−1.01281	+	0.482585i
$885$		0			0
$886$	6.31350e14	−	1.42726e14i	1.15638	−	0.261418i
$887$			6.11379e14i			1.11351i	0.830678	+	0.556753i	$0.187953\pi$
$887$			6.11379e14i			1.11351i	−0.830678	+	0.556753i	$0.812047\pi$
$888$	−1.17890e15	+	9.28215e14i	−2.13507	+	1.68106i
$889$	5.19814e13			0.0936136
$890$		0			0
$891$			4.80164e14i			0.855068i
$892$	3.30193e13	+	6.92983e13i	0.0584715	+	0.122715i
$893$	3.07372e14			0.541262
$894$	−5.62964e14	+	1.27267e14i	−0.985809	+	0.222857i
$895$		0			0
$896$	1.22356e12	−	8.43772e13i	0.00211877	−	0.146112i
$897$	2.20006e15			3.78854
$898$	−4.52036e13	−	1.99958e14i	−0.0774090	−	0.342419i
$899$			2.99613e14i			0.510226i
$900$		0			0
$901$	−1.77572e14			−0.299055
$902$	2.69616e14	−	6.09508e13i	0.451558	−	0.102081i
$903$			7.92825e13i			0.132050i
$904$	4.21998e14	+	5.35968e14i	0.698986	+	0.887762i
$905$		0			0
$906$	−2.40126e14	−	1.06220e15i	−0.393367	−	1.74006i
$907$		−	6.79963e14i		−	1.10777i	−0.832594	−	0.553884i	$-0.813145\pi$
$907$		−	6.79963e14i		−	1.10777i	0.832594	−	0.553884i	$-0.186855\pi$
$908$	−1.52468e14	−	3.19988e14i	−0.247030	−	0.518447i
$909$	8.98153e14			1.44721
$910$		0			0
$911$		−	5.12899e14i		−	0.817410i	−0.912666	−	0.408705i	$-0.865980\pi$
$911$		−	5.12899e14i		−	0.817410i	0.912666	−	0.408705i	$-0.134020\pi$
$912$	6.70829e14	−	8.27041e14i	1.06326	−	1.31085i
$913$	−3.12525e14			−0.492642
$914$	−1.19674e14	−	5.29378e14i	−0.187615	−	0.829917i
$915$		0			0
$916$	2.75740e14	−	1.31385e14i	0.427585	−	0.203736i
$917$	5.08956e13			0.0784935
$918$	−8.76824e14	+	1.98219e14i	−1.34493	+	0.304041i
$919$			1.75216e14i			0.267298i	0.991029	+	0.133649i	$0.0426695\pi$
$919$			1.75216e14i			0.267298i	−0.991029	+	0.133649i	$0.957330\pi$
$920$		0			0
$921$	−1.73609e14			−0.261983
$922$	−1.63702e14	−	7.24137e14i	−0.245697	−	1.08684i
$923$			4.32761e14i			0.646011i
$924$	−3.22506e13	−	6.76849e13i	−0.0478826	−	0.100492i
$925$		0			0
$926$	1.26068e15	−	2.84997e14i	1.85162	−	0.418586i
$927$			2.54713e15i			3.72094i
$928$	2.92554e14	+	1.44638e14i	0.425075	+	0.210156i
$929$	−9.69508e14			−1.40111			−0.700556	−	0.713598i	$-0.747064\pi$
$929$	−9.69508e14			−1.40111			−0.700556	+	0.713598i	$0.747064\pi$
$930$		0			0
$931$		−	6.34567e14i		−	0.907254i
$932$	−8.95178e14	+	4.26535e14i	−1.27300	+	0.606563i
$933$	−3.48933e14			−0.493553
$934$	5.35859e14	−	1.21139e14i	0.753904	−	0.170431i
$935$		0			0
$936$	−2.00383e15	−	2.54501e15i	−2.78921	−	3.54250i
$937$	1.25131e15			1.73248			0.866239	−	0.499629i	$-0.166530\pi$
$937$	1.25131e15			1.73248			0.866239	+	0.499629i	$0.166530\pi$
$938$	−3.25606e13	−	1.44032e14i	−0.0448413	−	0.198356i
$939$			1.74097e15i			2.38486i
$940$		0			0
$941$	−9.98221e14			−1.35294			−0.676470	−	0.736470i	$-0.736491\pi$
$941$	−9.98221e14			−1.35294			−0.676470	+	0.736470i	$0.736491\pi$
$942$	−2.57809e14	+	5.82816e13i	−0.347571	+	0.0785736i
$943$		−	8.81455e14i		−	1.18207i
$944$	−7.72053e14	−	6.26227e14i	−1.02988	−	0.835356i
$945$		0			0
$946$	3.46930e13	+	1.53464e14i	0.0457916	+	0.202559i
$947$		−	7.66086e14i		−	1.00584i	−0.864334	−	0.502919i	$-0.832259\pi$
$947$		−	7.66086e14i		−	1.00584i	0.864334	−	0.502919i	$-0.167741\pi$
$948$	1.00750e15	−	4.80054e14i	1.31584	−	0.626972i
$949$	2.65249e14			0.344606
$950$		0			0
$951$			1.18387e15i			1.52196i
$952$	5.17114e13	−	4.07154e13i	0.0661305	−	0.0520683i
$953$	−1.40347e15			−1.78541			−0.892707	−	0.450638i	$-0.851196\pi$
$953$	−1.40347e15			−1.78541			−0.892707	+	0.450638i	$0.851196\pi$
$954$	−2.09414e14	−	9.26341e14i	−0.265010	−	1.17227i
$955$		0			0
$956$	4.61082e14	+	9.67682e14i	0.577416	+	1.21183i
$957$	2.89961e14			0.361227
$958$	1.26269e14	−	2.85450e13i	0.156484	−	0.0353755i
$959$		−	1.64509e14i		−	0.202813i
$960$		0			0
$961$	−1.29316e14			−0.157773
$962$	−5.28144e14	−	2.33625e15i	−0.641028	−	2.83559i
$963$			2.27434e14i			0.274615i
$964$	−3.24457e14	+	1.54598e14i	−0.389738	+	0.185703i
$965$		0			0
$966$	−2.33200e14	+	5.27183e13i	−0.277231	+	0.0626723i
$967$			8.64693e13i			0.102266i	0.998692	+	0.0511328i	$0.0162832\pi$
$967$			8.64693e13i			0.102266i	−0.998692	+	0.0511328i	$0.983717\pi$
$968$	4.33731e14	+	5.50870e14i	0.510321	+	0.648145i
$969$	8.30562e14			0.972195
$970$		0			0
$971$		−	7.03867e14i		−	0.815445i	−0.913106	−	0.407722i	$-0.866323\pi$
$971$		−	7.03867e14i		−	0.815445i	0.913106	−	0.407722i	$-0.133677\pi$
$972$	−4.95205e14	−	1.03930e15i	−0.570760	−	1.19786i
$973$	1.71125e13			0.0196222
$974$	−1.48611e15	+	3.35958e14i	−1.69534	+	0.383257i
$975$		0			0
$976$	−6.14574e13	+	7.57686e13i	−0.0693945	+	0.0855540i
$977$	−1.20639e15			−1.35524			−0.677620	−	0.735412i	$-0.736989\pi$
$977$	−1.20639e15			−1.35524			−0.677620	+	0.735412i	$0.736989\pi$
$978$	−6.26066e14	−	2.76941e15i	−0.699723	−	3.09523i
$979$			1.51543e14i			0.168509i
$980$		0			0
$981$	2.38128e15			2.62099
$982$	7.94917e14	−	1.79703e14i	0.870491	−	0.196788i
$983$			1.52661e15i			1.66326i	0.555328	+	0.831631i	$0.312593\pi$
$983$			1.52661e15i			1.66326i	−0.555328	+	0.831631i	$0.687407\pi$
$984$	−1.46015e15	+	1.14966e15i	−1.58278	+	1.24621i
$985$		0			0
$986$	5.61262e13	+	2.48274e14i	0.0602255	+	0.266408i
$987$			1.45496e14i			0.155334i
$988$	7.31210e14	+	1.53461e15i	0.776708	+	1.63009i
$989$	5.01720e14			0.530250
$990$		0			0
$991$			6.22983e14i			0.651791i	0.945406	+	0.325895i	$0.105666\pi$
$991$			6.22983e14i			0.651791i	−0.945406	+	0.325895i	$0.894334\pi$
$992$	−4.58102e14	+	9.26584e14i	−0.476874	+	0.964554i
$993$	1.72195e15			1.78350
$994$	−1.03699e13	−	4.58714e13i	−0.0106867	−	0.0472727i
$995$		0			0
$996$	1.89685e15	−	9.03812e14i	1.93525	−	0.922108i
$997$	5.06209e14			0.513871			0.256936	−	0.966428i	$-0.417287\pi$
$997$	5.06209e14			0.513871			0.256936	+	0.966428i	$0.417287\pi$
$998$	−1.62390e14	+	3.67107e13i	−0.164024	+	0.0370800i
$999$		−	3.55516e15i		−	3.57299i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.11.b.e.51.9		20
4.3	odd	2	inner	100.11.b.e.51.10		20
5.2	odd	4		100.11.d.c.99.37		40
5.3	odd	4		100.11.d.c.99.4		40
5.4	even	2		20.11.b.a.11.12	yes	20
15.14	odd	2		180.11.c.a.91.9		20
20.3	even	4		100.11.d.c.99.38		40
20.7	even	4		100.11.d.c.99.3		40
20.19	odd	2		20.11.b.a.11.11	✓	20
40.19	odd	2		320.11.b.d.191.2		20
40.29	even	2		320.11.b.d.191.19		20
60.59	even	2		180.11.c.a.91.10		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.11.b.a.11.11	✓	20	20.19	odd	2
20.11.b.a.11.12	yes	20	5.4	even	2
100.11.b.e.51.9		20	1.1	even	1	trivial
100.11.b.e.51.10		20	4.3	odd	2	inner
100.11.d.c.99.3		40	20.7	even	4
100.11.d.c.99.4		40	5.3	odd	4
100.11.d.c.99.37		40	5.2	odd	4
100.11.d.c.99.38		40	20.3	even	4
180.11.c.a.91.9		20	15.14	odd	2
180.11.c.a.91.10		20	60.59	even	2
320.11.b.d.191.2		20	40.19	odd	2
320.11.b.d.191.19		20	40.29	even	2

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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	100.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.05603 - 31.2124i) q^{2} +442.423i q^{3} +(-924.425 + 440.471i) q^{4} +(13809.1 - 3121.75i) q^{6} -2455.96i q^{7} +(20270.9 + 25745.5i) q^{8} -136689. q^{9} +O(q^{10})\)	\(q+(-7.05603 - 31.2124i) q^{2} +442.423i q^{3} +(-924.425 + 440.471i) q^{4} +(13809.1 - 3121.75i) q^{6} -2455.96i q^{7} +(20270.9 + 25745.5i) q^{8} -136689. q^{9} +67384.8i q^{11} +(-194874. - 408986. i) q^{12} +723193. q^{13} +(-76656.3 + 17329.3i) q^{14} +(660547. - 814365. i) q^{16} +817832. q^{17} +(964480. + 4.26638e6i) q^{18} -2.29547e6i q^{19} +1.08657e6 q^{21} +(2.10324e6 - 475469. i) q^{22} -6.87611e6i q^{23} +(-1.13904e7 + 8.96831e6i) q^{24} +(-5.10287e6 - 2.25726e7i) q^{26} -3.43496e7i q^{27} +(1.08178e6 + 2.27035e6i) q^{28} -9.72615e6 q^{29} -3.08049e7i q^{31} +(-3.00791e7 - 1.48710e7i) q^{32} -2.98125e7 q^{33} +(-5.77065e6 - 2.55265e7i) q^{34} +(1.26358e8 - 6.02074e7i) q^{36} +1.03499e8 q^{37} +(-7.16470e7 + 1.61969e7i) q^{38} +3.19957e8i q^{39} +1.28191e8 q^{41} +(-7.66688e6 - 3.39145e7i) q^{42} +7.29658e7i q^{43} +(-2.96810e7 - 6.22921e7i) q^{44} +(-2.14620e8 + 4.85180e7i) q^{46} +1.33904e8i q^{47} +(3.60293e8 + 2.92241e8i) q^{48} +2.76444e8 q^{49} +3.61827e8i q^{51} +(-6.68538e8 + 3.18545e8i) q^{52} -2.17126e8 q^{53} +(-1.07213e9 + 2.42372e8i) q^{54} +(6.32299e7 - 4.97845e7i) q^{56} +1.01557e9 q^{57} +(6.86280e7 + 3.03576e8i) q^{58} -9.48043e8i q^{59} -9.30401e7 q^{61} +(-9.61495e8 + 2.17361e8i) q^{62} +3.35702e8i q^{63} +(-2.51922e8 + 1.04377e9i) q^{64} +(2.10358e8 + 9.30520e8i) q^{66} +1.87893e9i q^{67} +(-7.56024e8 + 3.60231e8i) q^{68} +3.04215e9 q^{69} +5.98404e8i q^{71} +(-2.77081e9 - 3.51912e9i) q^{72} +3.66775e8 q^{73} +(-7.30295e8 - 3.23046e9i) q^{74} +(1.01109e9 + 2.12199e9i) q^{76} +1.65494e8 q^{77} +(9.98662e9 - 2.25763e9i) q^{78} +2.46340e9i q^{79} +7.12570e9 q^{81} +(-9.04519e8 - 4.00114e9i) q^{82} +4.63792e9i q^{83} +(-1.00445e9 + 4.78603e8i) q^{84} +(2.27744e9 - 5.14849e8i) q^{86} -4.30307e9i q^{87} +(-1.73486e9 + 1.36595e9i) q^{88} +2.24892e9 q^{89} -1.77613e9i q^{91} +(3.02873e9 + 6.35644e9i) q^{92} +1.36288e10 q^{93} +(4.17947e9 - 9.44832e8i) q^{94} +(6.57929e9 - 1.33077e10i) q^{96} +6.10089e9 q^{97} +(-1.95059e9 - 8.62846e9i) q^{98} -9.21074e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 22 q^{2} - 644 q^{4} - 14784 q^{6} - 3448 q^{8} - 414868 q^{9}+O(q^{10}) \) 20 * q - 22 * q^2 - 644 * q^4 - 14784 * q^6 - 3448 * q^8 - 414868 * q^9	\( 20 q - 22 q^{2} - 644 q^{4} - 14784 q^{6} - 3448 q^{8} - 414868 q^{9} - 1329640 q^{12} + 278864 q^{13} - 2240504 q^{14} + 4261360 q^{16} + 1921656 q^{17} + 3556082 q^{18} + 4157512 q^{21} + 5811280 q^{22} - 19112144 q^{24} + 25066884 q^{26} + 87415400 q^{28} - 66014888 q^{29} + 33171328 q^{32} - 85980560 q^{33} - 27236084 q^{34} + 355456476 q^{36} + 153620656 q^{37} - 250352720 q^{38} + 477406160 q^{41} + 570662040 q^{42} + 339141040 q^{44} - 897549304 q^{46} + 479727360 q^{48} + 333772012 q^{49} + 110465096 q^{52} + 1669491824 q^{53} + 706139792 q^{54} - 1362290224 q^{56} - 3973032960 q^{57} - 2075027916 q^{58} - 4283166080 q^{61} - 1664032240 q^{62} + 340459456 q^{64} + 1884031760 q^{66} - 3042411896 q^{68} - 5321669928 q^{69} - 1632326712 q^{72} - 2474287656 q^{73} + 188682276 q^{74} + 2323171200 q^{76} - 410885040 q^{77} + 19914223760 q^{78} + 9939722652 q^{81} + 3197757116 q^{82} + 2383099552 q^{84} + 19648321456 q^{86} - 2774318240 q^{88} + 3011851592 q^{89} + 27349072440 q^{92} + 11861394640 q^{93} + 15684681576 q^{94} - 1990377984 q^{96} + 39984502056 q^{97} - 38416891998 q^{98}+O(q^{100}) \) 20 * q - 22 * q^2 - 644 * q^4 - 14784 * q^6 - 3448 * q^8 - 414868 * q^9 - 1329640 * q^12 + 278864 * q^13 - 2240504 * q^14 + 4261360 * q^16 + 1921656 * q^17 + 3556082 * q^18 + 4157512 * q^21 + 5811280 * q^22 - 19112144 * q^24 + 25066884 * q^26 + 87415400 * q^28 - 66014888 * q^29 + 33171328 * q^32 - 85980560 * q^33 - 27236084 * q^34 + 355456476 * q^36 + 153620656 * q^37 - 250352720 * q^38 + 477406160 * q^41 + 570662040 * q^42 + 339141040 * q^44 - 897549304 * q^46 + 479727360 * q^48 + 333772012 * q^49 + 110465096 * q^52 + 1669491824 * q^53 + 706139792 * q^54 - 1362290224 * q^56 - 3973032960 * q^57 - 2075027916 * q^58 - 4283166080 * q^61 - 1664032240 * q^62 + 340459456 * q^64 + 1884031760 * q^66 - 3042411896 * q^68 - 5321669928 * q^69 - 1632326712 * q^72 - 2474287656 * q^73 + 188682276 * q^74 + 2323171200 * q^76 - 410885040 * q^77 + 19914223760 * q^78 + 9939722652 * q^81 + 3197757116 * q^82 + 2383099552 * q^84 + 19648321456 * q^86 - 2774318240 * q^88 + 3011851592 * q^89 + 27349072440 * q^92 + 11861394640 * q^93 + 15684681576 * q^94 - 1990377984 * q^96 + 39984502056 * q^97 - 38416891998 * q^98

Introduction

L-functions

Modular forms

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