LMFDB - Embedded newform 100.9.f.c.57.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [100,9,Mod(57,100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("100.57"); S:= CuspForms(chi, 9); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(100, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 9, names="a")

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	100.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$40.7378610061$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 8 x^{10} + 1412 x^{9} + 550393 x^{8} - 1456736 x^{7} + 2420672 x^{6} + \cdots + 547748010000 $ x^12 - 4x^11 + 8x^10 + 1412x^9 + 550393x^8 - 1456736x^7 + 2420672x^6 + 375321568x^5 + 69558134536x^4 - 89027503680x^3 + 58317955200x^2 + 252758952000*x + 547748010000
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{22}\cdot 3^{6}\cdot 5^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			57.2
Root			$17.6536 - 17.6536i$ of defining polynomial
Character	$\chi$	$=$	100.57
Dual form			100.9.f.c.93.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-67.0124 + 67.0124i) q^{3} +(-1824.09 - 1824.09i) q^{7} -2420.33i q^{9} +14869.3 q^{11} +(16679.4 - 16679.4i) q^{13} +(2066.91 + 2066.91i) q^{17} +216344. i q^{19} +244473. q^{21} +(249231. - 249231. i) q^{23} +(-277476. - 277476. i) q^{27} -8533.70i q^{29} +630373. q^{31} +(-996427. + 996427. i) q^{33} +(-321392. - 321392. i) q^{37} +2.23545e6i q^{39} -3.93448e6 q^{41} +(-3.86409e6 + 3.86409e6i) q^{43} +(-87194.7 - 87194.7i) q^{47} +889788. i q^{49} -277017. q^{51} +(-1.05557e7 + 1.05557e7i) q^{53} +(-1.44977e7 - 1.44977e7i) q^{57} +2.14935e7i q^{59} +2.36025e7 q^{61} +(-4.41489e6 + 4.41489e6i) q^{63} +(738442. + 738442. i) q^{67} +3.34032e7i q^{69} -5.59110e6 q^{71} +(-893363. + 893363. i) q^{73} +(-2.71229e7 - 2.71229e7i) q^{77} +6.96271e7i q^{79} +5.30685e7 q^{81} +(-4.47947e7 + 4.47947e7i) q^{83} +(571864. + 571864. i) q^{87} -8.60305e7i q^{89} -6.08494e7 q^{91} +(-4.22428e7 + 4.22428e7i) q^{93} +(-2.99939e7 - 2.99939e7i) q^{97} -3.59886e7i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 420 q^{11} - 921168 q^{21} + 3833112 q^{31} + 3587532 q^{41} + 46092564 q^{51} + 31354704 q^{61} - 29589384 q^{71} + 104018868 q^{81} + 433229088 q^{91}+O(q^{100}) $ 12 * q - 420 * q^11 - 921168 * q^21 + 3833112 * q^31 + 3587532 * q^41 + 46092564 * q^51 + 31354704 * q^61 - 29589384 * q^71 + 104018868 * q^81 + 433229088 * q^91

Character values

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

$n$	$51$	$77$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−67.0124	+	67.0124i	−0.827314	+	0.827314i	−0.987144	−	0.159831i	$-0.948905\pi$
$3$	−67.0124	+	67.0124i	−0.827314	+	0.827314i	0.159831	+	0.987144i	$0.448905\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1824.09	−	1824.09i	−0.759720	−	0.759720i	0.216551	−	0.976271i	$-0.430519\pi$
$7$	−1824.09	−	1824.09i	−0.759720	−	0.759720i	−0.976271	+	0.216551i	$0.930519\pi$
$8$		0			0
$9$		−	2420.33i		−	0.368896i
$10$		0			0
$11$	14869.3			1.01559			0.507796	−	0.861477i	$-0.330460\pi$
$11$	14869.3			1.01559			0.507796	+	0.861477i	$0.330460\pi$
$12$		0			0
$13$	16679.4	−	16679.4i	0.583992	−	0.583992i	−0.352006	−	0.935998i	$-0.614500\pi$
$13$	16679.4	−	16679.4i	0.583992	−	0.583992i	0.935998	+	0.352006i	$0.114500\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2066.91	+	2066.91i	0.0247472	+	0.0247472i	0.719372	−	0.694625i	$-0.244430\pi$
$17$	2066.91	+	2066.91i	0.0247472	+	0.0247472i	−0.694625	+	0.719372i	$0.744430\pi$
$18$		0			0
$19$			216344.i			1.66008i	0.557701	+	0.830042i	$0.311684\pi$
$19$			216344.i			1.66008i	−0.557701	+	0.830042i	$0.688316\pi$
$20$		0			0
$21$	244473.			1.25705
$22$		0			0
$23$	249231.	−	249231.i	0.890618	−	0.890618i	−0.103963	−	0.994581i	$-0.533152\pi$
$23$	249231.	−	249231.i	0.890618	−	0.890618i	0.994581	+	0.103963i	$0.0331524\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−277476.	−	277476.i	−0.522121	−	0.522121i
$28$		0			0
$29$		−	8533.70i		−	0.0120655i	−0.999982	−	0.00603275i	$-0.998080\pi$
$29$		−	8533.70i		−	0.0120655i	0.999982	−	0.00603275i	$-0.00192030\pi$
$30$		0			0
$31$	630373.			0.682576			0.341288	−	0.939959i	$-0.389137\pi$
$31$	630373.			0.682576			0.341288	+	0.939959i	$0.389137\pi$
$32$		0			0
$33$	−996427.	+	996427.i	−0.840214	+	0.840214i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−321392.	−	321392.i	−0.171486	−	0.171486i	0.616146	−	0.787632i	$-0.288693\pi$
$37$	−321392.	−	321392.i	−0.171486	−	0.171486i	−0.787632	+	0.616146i	$0.788693\pi$
$38$		0			0
$39$			2.23545e6i			0.966290i
$40$		0			0
$41$	−3.93448e6			−1.39236			−0.696181	−	0.717866i	$-0.745119\pi$
$41$	−3.93448e6			−1.39236			−0.696181	+	0.717866i	$0.745119\pi$
$42$		0			0
$43$	−3.86409e6	+	3.86409e6i	−1.13025	+	1.13025i	−0.140110	+	0.990136i	$0.544746\pi$
$43$	−3.86409e6	+	3.86409e6i	−1.13025	+	1.13025i	−0.990136	+	0.140110i	$0.955254\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−87194.7	−	87194.7i	−0.0178689	−	0.0178689i	0.698116	−	0.715985i	$-0.254022\pi$
$47$	−87194.7	−	87194.7i	−0.0178689	−	0.0178689i	−0.715985	+	0.698116i	$0.754022\pi$
$48$		0			0
$49$			889788.i			0.154348i
$50$		0			0
$51$	−277017.			−0.0409473
$52$		0			0
$53$	−1.05557e7	+	1.05557e7i	−1.33777	+	1.33777i	−0.439555	+	0.898216i	$0.644864\pi$
$53$	−1.05557e7	+	1.05557e7i	−1.33777	+	1.33777i	−0.898216	+	0.439555i	$0.855136\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−1.44977e7	−	1.44977e7i	−1.37341	−	1.37341i
$58$		0			0
$59$			2.14935e7i			1.77378i	0.461979	+	0.886891i	$0.347139\pi$
$59$			2.14935e7i			1.77378i	−0.461979	+	0.886891i	$0.652861\pi$
$60$		0			0
$61$	2.36025e7			1.70467			0.852334	−	0.522999i	$-0.175187\pi$
$61$	2.36025e7			1.70467			0.852334	+	0.522999i	$0.175187\pi$
$62$		0			0
$63$	−4.41489e6	+	4.41489e6i	−0.280258	+	0.280258i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	738442.	+	738442.i	0.0366452	+	0.0366452i	0.725192	−	0.688547i	$-0.241751\pi$
$67$	738442.	+	738442.i	0.0366452	+	0.0366452i	−0.688547	+	0.725192i	$0.741751\pi$
$68$		0			0
$69$			3.34032e7i			1.47364i
$70$		0			0
$71$	−5.59110e6			−0.220021			−0.110011	−	0.993930i	$-0.535088\pi$
$71$	−5.59110e6			−0.220021			−0.110011	+	0.993930i	$0.535088\pi$
$72$		0			0
$73$	−893363.	+	893363.i	−0.0314584	+	0.0314584i	−0.722661	−	0.691203i	$-0.757081\pi$
$73$	−893363.	+	893363.i	−0.0314584	+	0.0314584i	0.691203	+	0.722661i	$0.257081\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.71229e7	−	2.71229e7i	−0.771566	−	0.771566i
$78$		0			0
$79$			6.96271e7i			1.78760i	0.448467	+	0.893799i	$0.351970\pi$
$79$			6.96271e7i			1.78760i	−0.448467	+	0.893799i	$0.648030\pi$
$80$		0			0
$81$	5.30685e7			1.23281
$82$		0			0
$83$	−4.47947e7	+	4.47947e7i	−0.943874	+	0.943874i	−0.998507	−	0.0546330i	$-0.982601\pi$
$83$	−4.47947e7	+	4.47947e7i	−0.943874	+	0.943874i	0.0546330	+	0.998507i	$0.482601\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	571864.	+	571864.i	0.00998196	+	0.00998196i
$88$		0			0
$89$		−	8.60305e7i		−	1.37117i	−0.727991	−	0.685587i	$-0.759546\pi$
$89$		−	8.60305e7i		−	1.37117i	0.727991	−	0.685587i	$-0.240454\pi$
$90$		0			0
$91$	−6.08494e7			−0.887341
$92$		0			0
$93$	−4.22428e7	+	4.22428e7i	−0.564704	+	0.564704i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−2.99939e7	−	2.99939e7i	−0.338802	−	0.338802i	0.517114	−	0.855916i	$-0.327006\pi$
$97$	−2.99939e7	−	2.99939e7i	−0.338802	−	0.338802i	−0.855916	+	0.517114i	$0.827006\pi$
$98$		0			0
$99$		−	3.59886e7i		−	0.374648i
$100$		0			0
$101$	−1.35552e8			−1.30262			−0.651312	−	0.758810i	$-0.725781\pi$
$101$	−1.35552e8			−1.30262			−0.651312	+	0.758810i	$0.725781\pi$
$102$		0			0
$103$	2.16076e7	−	2.16076e7i	0.191981	−	0.191981i	−0.604571	−	0.796552i	$-0.706655\pi$
$103$	2.16076e7	−	2.16076e7i	0.191981	−	0.191981i	0.796552	+	0.604571i	$0.206655\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.57285e8	+	1.57285e8i	1.19992	+	1.19992i	0.974190	+	0.225728i	$0.0724759\pi$
$107$	1.57285e8	+	1.57285e8i	1.19992	+	1.19992i	0.225728	+	0.974190i	$0.427524\pi$
$108$		0			0
$109$		−	3.57585e7i		−	0.253322i	−0.991946	−	0.126661i	$-0.959574\pi$
$109$		−	3.57585e7i		−	0.253322i	0.991946	−	0.126661i	$-0.0404261\pi$
$110$		0			0
$111$	4.30745e7			0.283745
$112$		0			0
$113$	5.85136e7	−	5.85136e7i	0.358875	−	0.358875i	−0.504523	−	0.863398i	$-0.668332\pi$
$113$	5.85136e7	−	5.85136e7i	0.358875	−	0.358875i	0.863398	+	0.504523i	$0.168332\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−4.03696e7	−	4.03696e7i	−0.215433	−	0.215433i
$118$		0			0
$119$		−	7.54044e6i		−	0.0376018i
$120$		0			0
$121$	6.73708e6			0.0314290
$122$		0			0
$123$	2.63659e8	−	2.63659e8i	1.15192	−	1.15192i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	1.03379e8	+	1.03379e8i	0.397391	+	0.397391i	0.877312	−	0.479921i	$-0.159335\pi$
$127$	1.03379e8	+	1.03379e8i	0.397391	+	0.397391i	−0.479921	+	0.877312i	$0.659335\pi$
$128$		0			0
$129$		−	5.17884e8i		−	1.87014i
$130$		0			0
$131$	3.14032e8			1.06632			0.533161	−	0.846014i	$-0.321004\pi$
$131$	3.14032e8			1.06632			0.533161	+	0.846014i	$0.321004\pi$
$132$		0			0
$133$	3.94630e8	−	3.94630e8i	1.26120	−	1.26120i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	7.98429e7	+	7.98429e7i	0.226649	+	0.226649i	0.811291	−	0.584642i	$-0.198765\pi$
$137$	7.98429e7	+	7.98429e7i	0.226649	+	0.226649i	−0.584642	+	0.811291i	$0.698765\pi$
$138$		0			0
$139$		−	1.74531e8i		−	0.467533i	−0.972293	−	0.233767i	$-0.924895\pi$
$139$		−	1.74531e8i		−	0.467533i	0.972293	−	0.233767i	$-0.0751052\pi$
$140$		0			0
$141$	1.16863e7			0.0295664
$142$		0			0
$143$	2.48011e8	−	2.48011e8i	0.593098	−	0.593098i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−5.96269e7	−	5.96269e7i	−0.127695	−	0.127695i
$148$		0			0
$149$			6.75364e8i			1.37023i	0.728436	+	0.685114i	$0.240247\pi$
$149$			6.75364e8i			1.37023i	−0.728436	+	0.685114i	$0.759753\pi$
$150$		0			0
$151$	−3.00444e8			−0.577905			−0.288952	−	0.957344i	$-0.593307\pi$
$151$	−3.00444e8			−0.577905			−0.288952	+	0.957344i	$0.593307\pi$
$152$		0			0
$153$	5.00260e6	−	5.00260e6i	0.00912914	−	0.00912914i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	6.14477e8	+	6.14477e8i	1.01136	+	1.01136i	0.999935	+	0.0114287i	$0.00363793\pi$
$157$	6.14477e8	+	6.14477e8i	1.01136	+	1.01136i	0.0114287	+	0.999935i	$0.496362\pi$
$158$		0			0
$159$		−	1.41472e9i		−	2.21351i
$160$		0			0
$161$	−9.09240e8			−1.35324
$162$		0			0
$163$	−7.22020e8	+	7.22020e8i	−1.02282	+	1.02282i	−0.0230852	+	0.999734i	$0.507349\pi$
$163$	−7.22020e8	+	7.22020e8i	−1.02282	+	1.02282i	−0.999734	+	0.0230852i	$0.992651\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.41221e8	+	2.41221e8i	0.310134	+	0.310134i	0.844961	−	0.534827i	$-0.179623\pi$
$167$	2.41221e8	+	2.41221e8i	0.310134	+	0.310134i	−0.534827	+	0.844961i	$0.679623\pi$
$168$		0			0
$169$			2.59326e8i			0.317906i
$170$		0			0
$171$	5.23623e8			0.612399
$172$		0			0
$173$	4.30005e8	−	4.30005e8i	0.480053	−	0.480053i	−0.425096	−	0.905148i	$-0.639759\pi$
$173$	4.30005e8	−	4.30005e8i	0.480053	−	0.480053i	0.905148	+	0.425096i	$0.139759\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1.44033e9	−	1.44033e9i	−1.46747	−	1.46747i
$178$		0			0
$179$		−	7.13896e7i		−	0.0695381i	−0.999395	−	0.0347691i	$-0.988930\pi$
$179$		−	7.13896e7i		−	0.0695381i	0.999395	−	0.0347691i	$-0.0110696\pi$
$180$		0			0
$181$	−9.52190e8			−0.887175			−0.443588	−	0.896231i	$-0.646295\pi$
$181$	−9.52190e8			−0.887175			−0.443588	+	0.896231i	$0.646295\pi$
$182$		0			0
$183$	−1.58166e9	+	1.58166e9i	−1.41029	+	1.41029i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	3.07335e7	+	3.07335e7i	0.0251330	+	0.0251330i
$188$		0			0
$189$			1.01228e9i			0.793331i
$190$		0			0
$191$	1.77574e9			1.33428			0.667138	−	0.744935i	$-0.267519\pi$
$191$	1.77574e9			1.33428			0.667138	+	0.744935i	$0.267519\pi$
$192$		0			0
$193$	−2.85453e8	+	2.85453e8i	−0.205734	+	0.205734i	−0.802451	−	0.596717i	$-0.796471\pi$
$193$	−2.85453e8	+	2.85453e8i	−0.205734	+	0.205734i	0.596717	+	0.802451i	$0.296471\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	2.45741e7	+	2.45741e7i	0.0163159	+	0.0163159i	0.715218	−	0.698902i	$-0.246328\pi$
$197$	2.45741e7	+	2.45741e7i	0.0163159	+	0.0163159i	−0.698902	+	0.715218i	$0.746328\pi$
$198$		0			0
$199$			2.42299e9i			1.54504i	0.634991	+	0.772520i	$0.281004\pi$
$199$			2.42299e9i			1.54504i	−0.634991	+	0.772520i	$0.718996\pi$
$200$		0			0
$201$	−9.89695e7			−0.0606342
$202$		0			0
$203$	−1.55662e7	+	1.55662e7i	−0.00916640	+	0.00916640i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−6.03222e8	−	6.03222e8i	−0.328546	−	0.328546i
$208$		0			0
$209$			3.21688e9i			1.68597i
$210$		0			0
$211$	2.16866e9			1.09411			0.547056	−	0.837096i	$-0.315748\pi$
$211$	2.16866e9			1.09411			0.547056	+	0.837096i	$0.315748\pi$
$212$		0			0
$213$	3.74673e8	−	3.74673e8i	0.182026	−	0.182026i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−1.14986e9	−	1.14986e9i	−0.518566	−	0.518566i
$218$		0			0
$219$		−	1.19733e8i		−	0.0520519i
$220$		0			0
$221$	6.89496e7			0.0289043
$222$		0			0
$223$	−1.67197e8	+	1.67197e8i	−0.0676097	+	0.0676097i	−0.740103	−	0.672493i	$-0.765223\pi$
$223$	−1.67197e8	+	1.67197e8i	−0.0676097	+	0.0676097i	0.672493	+	0.740103i	$0.265223\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	4.34285e8	+	4.34285e8i	0.163558	+	0.163558i	0.784141	−	0.620583i	$-0.213104\pi$
$227$	4.34285e8	+	4.34285e8i	0.163558	+	0.163558i	−0.620583	+	0.784141i	$0.713104\pi$
$228$		0			0
$229$			1.56042e9i			0.567415i	0.958911	+	0.283707i	$0.0915644\pi$
$229$			1.56042e9i			0.567415i	−0.958911	+	0.283707i	$0.908436\pi$
$230$		0			0
$231$	3.63514e9			1.27665
$232$		0			0
$233$	−3.48617e9	+	3.48617e9i	−1.18284	+	1.18284i	−0.203833	+	0.979006i	$0.565340\pi$
$233$	−3.48617e9	+	3.48617e9i	−1.18284	+	1.18284i	−0.979006	+	0.203833i	$0.934660\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−4.66588e9	−	4.66588e9i	−1.47890	−	1.47890i
$238$		0			0
$239$		−	4.20339e8i		−	0.128827i	−0.997923	−	0.0644136i	$-0.979482\pi$
$239$		−	4.20339e8i		−	0.128827i	0.997923	−	0.0644136i	$-0.0205177\pi$
$240$		0			0
$241$	−6.09300e9			−1.80619			−0.903094	−	0.429443i	$-0.858710\pi$
$241$	−6.09300e9			−1.80619			−0.903094	+	0.429443i	$0.858710\pi$
$242$		0			0
$243$	−1.73573e9	+	1.73573e9i	−0.497801	+	0.497801i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	3.60849e9	+	3.60849e9i	0.969476	+	0.969476i
$248$		0			0
$249$		−	6.00360e9i		−	1.56176i
$250$		0			0
$251$	−2.47458e9			−0.623458			−0.311729	−	0.950171i	$-0.600908\pi$
$251$	−2.47458e9			−0.623458			−0.311729	+	0.950171i	$0.600908\pi$
$252$		0			0
$253$	3.70590e9	−	3.70590e9i	0.904505	−	0.904505i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	2.95891e9	+	2.95891e9i	0.678264	+	0.678264i	0.959607	−	0.281343i	$-0.0907798\pi$
$257$	2.95891e9	+	2.95891e9i	0.678264	+	0.678264i	−0.281343	+	0.959607i	$0.590780\pi$
$258$		0			0
$259$			1.17249e9i			0.260562i
$260$		0			0
$261$	−2.06544e7			−0.00445092
$262$		0			0
$263$	−2.57619e9	+	2.57619e9i	−0.538461	+	0.538461i	−0.923077	−	0.384616i	$-0.874334\pi$
$263$	−2.57619e9	+	2.57619e9i	−0.538461	+	0.538461i	0.384616	+	0.923077i	$0.374334\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	5.76511e9	+	5.76511e9i	1.13439	+	1.13439i
$268$		0			0
$269$		−	2.69186e9i		−	0.514095i	−0.966399	−	0.257047i	$-0.917250\pi$
$269$		−	2.69186e9i		−	0.514095i	0.966399	−	0.257047i	$-0.0827497\pi$
$270$		0			0
$271$	−1.90218e9			−0.352674			−0.176337	−	0.984330i	$-0.556425\pi$
$271$	−1.90218e9			−0.352674			−0.176337	+	0.984330i	$0.556425\pi$
$272$		0			0
$273$	4.07766e9	−	4.07766e9i	0.734110	−	0.734110i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−7.96974e9	−	7.96974e9i	−1.35371	−	1.35371i	−0.881473	−	0.472235i	$-0.843448\pi$
$277$	−7.96974e9	−	7.96974e9i	−1.35371	−	1.35371i	−0.472235	−	0.881473i	$-0.656552\pi$
$278$		0			0
$279$		−	1.52571e9i		−	0.251800i
$280$		0			0
$281$	−5.45597e9			−0.875078			−0.437539	−	0.899199i	$-0.644150\pi$
$281$	−5.45597e9			−0.875078			−0.437539	+	0.899199i	$0.644150\pi$
$282$		0			0
$283$	5.55105e8	−	5.55105e8i	0.0865425	−	0.0865425i	−0.662510	−	0.749053i	$-0.730509\pi$
$283$	5.55105e8	−	5.55105e8i	0.0865425	−	0.0865425i	0.749053	+	0.662510i	$0.230509\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	7.17684e9	+	7.17684e9i	1.05780	+	1.05780i
$288$		0			0
$289$		−	6.96721e9i		−	0.998775i
$290$		0			0
$291$	4.01993e9			0.560592
$292$		0			0
$293$	9.04039e9	−	9.04039e9i	1.22664	−	1.22664i	0.261412	−	0.965227i	$-0.415812\pi$
$293$	9.04039e9	−	9.04039e9i	1.22664	−	1.22664i	0.965227	−	0.261412i	$-0.0841880\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−4.12588e9	−	4.12588e9i	−0.530262	−	0.530262i
$298$		0			0
$299$		−	8.31407e9i		−	1.04023i
$300$		0			0
$301$	1.40969e10			1.71734
$302$		0			0
$303$	9.08365e9	−	9.08365e9i	1.07768	−	1.07768i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	6.50352e9	+	6.50352e9i	0.732142	+	0.732142i	0.971044	−	0.238902i	$-0.0767875\pi$
$307$	6.50352e9	+	6.50352e9i	0.732142	+	0.732142i	−0.238902	+	0.971044i	$0.576788\pi$
$308$		0			0
$309$			2.89596e9i			0.317657i
$310$		0			0
$311$	9.19933e9			0.983365			0.491682	−	0.870775i	$-0.336382\pi$
$311$	9.19933e9			0.983365			0.491682	+	0.870775i	$0.336382\pi$
$312$		0			0
$313$	5.99222e9	−	5.99222e9i	0.624324	−	0.624324i	−0.322310	−	0.946634i	$-0.604459\pi$
$313$	5.99222e9	−	5.99222e9i	0.624324	−	0.624324i	0.946634	+	0.322310i	$0.104459\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.88098e8	+	2.88098e8i	0.0285301	+	0.0285301i	0.721228	−	0.692698i	$-0.243578\pi$
$317$	2.88098e8	+	2.88098e8i	0.0285301	+	0.0285301i	−0.692698	+	0.721228i	$0.743578\pi$
$318$		0			0
$319$		−	1.26890e8i		−	0.0122536i
$320$		0			0
$321$	−2.10801e10			−1.98542
$322$		0			0
$323$	−4.47163e8	+	4.47163e8i	−0.0410824	+	0.0410824i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	2.39626e9	+	2.39626e9i	0.209577	+	0.209577i
$328$		0			0
$329$			3.18102e8i			0.0271508i
$330$		0			0
$331$	−2.81201e9			−0.234264			−0.117132	−	0.993116i	$-0.537370\pi$
$331$	−2.81201e9			−0.234264			−0.117132	+	0.993116i	$0.537370\pi$
$332$		0			0
$333$	−7.77874e8	+	7.77874e8i	−0.0632604	+	0.0632604i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	4.41879e9	+	4.41879e9i	0.342597	+	0.342597i	0.857343	−	0.514746i	$-0.172114\pi$
$337$	4.41879e9	+	4.41879e9i	0.342597	+	0.342597i	−0.514746	+	0.857343i	$0.672114\pi$
$338$		0			0
$339$			7.84228e9i			0.593804i
$340$		0			0
$341$	9.37320e9			0.693219
$342$		0			0
$343$	−8.89245e9	+	8.89245e9i	−0.642458	+	0.642458i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−6.62298e9	−	6.62298e9i	−0.456810	−	0.456810i	0.440797	−	0.897607i	$-0.354696\pi$
$347$	−6.62298e9	−	6.62298e9i	−0.456810	−	0.456810i	−0.897607	+	0.440797i	$0.854696\pi$
$348$		0			0
$349$		−	3.39723e9i		−	0.228993i	−0.993424	−	0.114497i	$-0.963474\pi$
$349$		−	3.39723e9i		−	0.228993i	0.993424	−	0.114497i	$-0.0365255\pi$
$350$		0			0
$351$	−9.25628e9			−0.609829
$352$		0			0
$353$	−1.45235e10	+	1.45235e10i	−0.935348	+	0.935348i	−0.998033	−	0.0626857i	$-0.980033\pi$
$353$	−1.45235e10	+	1.45235e10i	−0.935348	+	0.935348i	0.0626857	+	0.998033i	$0.480033\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	5.05303e8	+	5.05303e8i	0.0311085	+	0.0311085i
$358$		0			0
$359$		−	1.66475e10i		−	1.00224i	−0.865379	−	0.501119i	$-0.832922\pi$
$359$		−	1.66475e10i		−	1.00224i	0.865379	−	0.501119i	$-0.167078\pi$
$360$		0			0
$361$	−2.98211e10			−1.75588
$362$		0			0
$363$	−4.51468e8	+	4.51468e8i	−0.0260016	+	0.0260016i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−1.61073e10	−	1.61073e10i	−0.887890	−	0.887890i	0.106430	−	0.994320i	$-0.466058\pi$
$367$	−1.61073e10	−	1.61073e10i	−0.887890	−	0.887890i	−0.994320	+	0.106430i	$0.966058\pi$
$368$		0			0
$369$			9.52274e9i			0.513637i
$370$		0			0
$371$	3.85089e10			2.03266
$372$		0			0
$373$	−6.53374e9	+	6.53374e9i	−0.337541	+	0.337541i	−0.855441	−	0.517900i	$-0.826714\pi$
$373$	−6.53374e9	+	6.53374e9i	−0.337541	+	0.337541i	0.517900	+	0.855441i	$0.326714\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−1.42337e8	−	1.42337e8i	−0.00704616	−	0.00704616i
$378$		0			0
$379$		−	3.94682e9i		−	0.191289i	−0.995416	−	0.0956445i	$-0.969509\pi$
$379$		−	3.94682e9i		−	0.191289i	0.995416	−	0.0956445i	$-0.0304912\pi$
$380$		0			0
$381$	−1.38554e10			−0.657534
$382$		0			0
$383$	−2.67274e10	+	2.67274e10i	−1.24212	+	1.24212i	−0.282993	+	0.959122i	$0.591327\pi$
$383$	−2.67274e10	+	2.67274e10i	−1.24212	+	1.24212i	−0.959122	+	0.282993i	$0.908673\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	9.35236e9	+	9.35236e9i	0.416944	+	0.416944i
$388$		0			0
$389$			3.96726e10i			1.73258i	0.499544	+	0.866288i	$0.333501\pi$
$389$			3.96726e10i			1.73258i	−0.499544	+	0.866288i	$0.666499\pi$
$390$		0			0
$391$	1.03028e9			0.0440805
$392$		0			0
$393$	−2.10440e10	+	2.10440e10i	−0.882183	+	0.882183i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−2.49047e10	−	2.49047e10i	−1.00258	−	1.00258i	−0.999997	−	0.00258332i	$-0.999178\pi$
$397$	−2.49047e10	−	2.49047e10i	−1.00258	−	1.00258i	−0.00258332	−	0.999997i	$-0.500822\pi$
$398$		0			0
$399$			5.28902e10i			2.08681i
$400$		0			0
$401$	2.59767e10			1.00463			0.502316	−	0.864684i	$-0.332481\pi$
$401$	2.59767e10			1.00463			0.502316	+	0.864684i	$0.332481\pi$
$402$		0			0
$403$	1.05142e10	−	1.05142e10i	0.398619	−	0.398619i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−4.77887e9	−	4.77887e9i	−0.174160	−	0.174160i
$408$		0			0
$409$			1.80246e10i			0.644129i	0.946718	+	0.322065i	$0.104377\pi$
$409$			1.80246e10i			0.644129i	−0.946718	+	0.322065i	$0.895623\pi$
$410$		0			0
$411$	−1.07009e10			−0.375020
$412$		0			0
$413$	3.92061e10	−	3.92061e10i	1.34758	−	1.34758i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	1.16957e10	+	1.16957e10i	0.386797	+	0.386797i
$418$		0			0
$419$		−	1.70728e10i		−	0.553923i	−0.960881	−	0.276961i	$-0.910673\pi$
$419$		−	1.70728e10i		−	0.553923i	0.960881	−	0.276961i	$-0.0893274\pi$
$420$		0			0
$421$	3.26742e10			1.04010			0.520052	−	0.854135i	$-0.325913\pi$
$421$	3.26742e10			1.04010			0.520052	+	0.854135i	$0.325913\pi$
$422$		0			0
$423$	−2.11040e8	+	2.11040e8i	−0.00659179	+	0.00659179i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−4.30531e10	−	4.30531e10i	−1.29507	−	1.29507i
$428$		0			0
$429$			3.32396e10i			0.981357i
$430$		0			0
$431$	3.58171e10			1.03796			0.518980	−	0.854786i	$-0.326312\pi$
$431$	3.58171e10			1.03796			0.518980	+	0.854786i	$0.326312\pi$
$432$		0			0
$433$	−2.16854e10	+	2.16854e10i	−0.616901	+	0.616901i	−0.944735	−	0.327834i	$-0.893681\pi$
$433$	−2.16854e10	+	2.16854e10i	−0.616901	+	0.616901i	0.327834	+	0.944735i	$0.393681\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	5.39197e10	+	5.39197e10i	1.47850	+	1.47850i
$438$		0			0
$439$		−	2.38656e10i		−	0.642560i	−0.946984	−	0.321280i	$-0.895887\pi$
$439$		−	2.38656e10i		−	0.642560i	0.946984	−	0.321280i	$-0.104113\pi$
$440$		0			0
$441$	2.15358e9			0.0569386
$442$		0			0
$443$	−3.52746e10	+	3.52746e10i	−0.915899	+	0.915899i	−0.996728	−	0.0808289i	$-0.974243\pi$
$443$	−3.52746e10	+	3.52746e10i	−0.915899	+	0.915899i	0.0808289	+	0.996728i	$0.474243\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−4.52577e10	−	4.52577e10i	−1.13361	−	1.13361i
$448$		0			0
$449$		−	4.32717e10i		−	1.06468i	−0.846531	−	0.532339i	$-0.821313\pi$
$449$		−	4.32717e10i		−	1.06468i	0.846531	−	0.532339i	$-0.178687\pi$
$450$		0			0
$451$	−5.85030e10			−1.41407
$452$		0			0
$453$	2.01335e10	−	2.01335e10i	0.478108	−	0.478108i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.18804e10	−	1.18804e10i	−0.272374	−	0.272374i	0.557681	−	0.830055i	$-0.311691\pi$
$457$	−1.18804e10	−	1.18804e10i	−0.272374	−	0.272374i	−0.830055	+	0.557681i	$0.811691\pi$
$458$		0			0
$459$		−	1.14704e9i		−	0.0258420i
$460$		0			0
$461$	3.51539e10			0.778340			0.389170	−	0.921166i	$-0.372762\pi$
$461$	3.51539e10			0.778340			0.389170	+	0.921166i	$0.372762\pi$
$462$		0			0
$463$	4.57448e10	−	4.57448e10i	0.995447	−	0.995447i	−0.00454260	−	0.999990i	$-0.501446\pi$
$463$	4.57448e10	−	4.57448e10i	0.995447	−	0.995447i	0.999990	+	0.00454260i	$0.00144596\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	4.50208e10	+	4.50208e10i	0.946555	+	0.946555i	0.998643	−	0.0520875i	$-0.0165875\pi$
$467$	4.50208e10	+	4.50208e10i	0.946555	+	0.946555i	−0.0520875	+	0.998643i	$0.516587\pi$
$468$		0			0
$469$		−	2.69396e9i		−	0.0556802i
$470$		0			0
$471$	−8.23552e10			−1.67343
$472$		0			0
$473$	−5.74563e10	+	5.74563e10i	−1.14787	+	1.14787i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	2.55481e10	+	2.55481e10i	0.493499	+	0.493499i
$478$		0			0
$479$		−	2.53738e10i		−	0.481995i	−0.970526	−	0.240998i	$-0.922525\pi$
$479$		−	2.53738e10i		−	0.481995i	0.970526	−	0.240998i	$-0.0774746\pi$
$480$		0			0
$481$	−1.07212e10			−0.200293
$482$		0			0
$483$	6.09304e10	−	6.09304e10i	1.11955	−	1.11955i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	5.71816e10	+	5.71816e10i	1.01658	+	1.01658i	0.999860	+	0.0167166i	$0.00532132\pi$
$487$	5.71816e10	+	5.71816e10i	1.01658	+	1.01658i	0.0167166	+	0.999860i	$0.494679\pi$
$488$		0			0
$489$		−	9.67686e10i		−	1.69238i
$490$		0			0
$491$	−6.49461e10			−1.11745			−0.558723	−	0.829354i	$-0.688709\pi$
$491$	−6.49461e10			−1.11745			−0.558723	+	0.829354i	$0.688709\pi$
$492$		0			0
$493$	1.76384e7	−	1.76384e7i	0.000298587	−	0.000298587i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.01987e10	+	1.01987e10i	0.167154	+	0.167154i
$498$		0			0
$499$		−	1.18849e10i		−	0.191688i	−0.995396	−	0.0958438i	$-0.969445\pi$
$499$		−	1.18849e10i		−	0.191688i	0.995396	−	0.0958438i	$-0.0305549\pi$
$500$		0			0
$501$	−3.23296e10			−0.513156
$502$		0			0
$503$	5.44276e9	−	5.44276e9i	0.0850252	−	0.0850252i	−0.663315	−	0.748340i	$-0.730851\pi$
$503$	5.44276e9	−	5.44276e9i	0.0850252	−	0.0850252i	0.748340	+	0.663315i	$0.230851\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−1.73780e10	−	1.73780e10i	−0.263008	−	0.263008i
$508$		0			0
$509$		−	9.40470e10i		−	1.40112i	−0.713596	−	0.700558i	$-0.752935\pi$
$509$		−	9.40470e10i		−	1.40112i	0.713596	−	0.700558i	$-0.247065\pi$
$510$		0			0
$511$	3.25914e9			0.0477991
$512$		0			0
$513$	6.00303e10	−	6.00303e10i	0.866765	−	0.866765i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−1.29652e9	−	1.29652e9i	−0.0181476	−	0.0181476i
$518$		0			0
$519$			5.76314e10i			0.794309i
$520$		0			0
$521$	1.18614e11			1.60985			0.804923	−	0.593380i	$-0.202207\pi$
$521$	1.18614e11			1.60985			0.804923	+	0.593380i	$0.202207\pi$
$522$		0			0
$523$	6.34549e10	−	6.34549e10i	0.848122	−	0.848122i	−0.141776	−	0.989899i	$-0.545281\pi$
$523$	6.34549e10	−	6.34549e10i	0.848122	−	0.848122i	0.989899	+	0.141776i	$0.0452814\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.30292e9	+	1.30292e9i	0.0168918	+	0.0168918i
$528$		0			0
$529$		−	4.59217e10i		−	0.586401i
$530$		0			0
$531$	5.20214e10			0.654341
$532$		0			0
$533$	−6.56248e10	+	6.56248e10i	−0.813129	+	0.813129i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	4.78399e9	+	4.78399e9i	0.0575298	+	0.0575298i
$538$		0			0
$539$			1.32305e10i			0.156755i
$540$		0			0
$541$	3.81183e10			0.444984			0.222492	−	0.974935i	$-0.428581\pi$
$541$	3.81183e10			0.444984			0.222492	+	0.974935i	$0.428581\pi$
$542$		0			0
$543$	6.38086e10	−	6.38086e10i	0.733973	−	0.733973i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−4.70178e10	−	4.70178e10i	−0.525186	−	0.525186i	0.393947	−	0.919133i	$-0.371109\pi$
$547$	−4.70178e10	−	4.70178e10i	−0.525186	−	0.525186i	−0.919133	+	0.393947i	$0.871109\pi$
$548$		0			0
$549$		−	5.71259e10i		−	0.628845i
$550$		0			0
$551$	1.84621e9			0.0200298
$552$		0			0
$553$	1.27006e11	−	1.27006e11i	1.35807	−	1.35807i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	1.22536e11	+	1.22536e11i	1.27304	+	1.27304i	0.944486	+	0.328552i	$0.106561\pi$
$557$	1.22536e11	+	1.22536e11i	1.27304	+	1.27304i	0.328552	+	0.944486i	$0.393439\pi$
$558$		0			0
$559$			1.28901e11i			1.32011i
$560$		0			0
$561$	−4.11905e9			−0.0415858
$562$		0			0
$563$	7.79452e10	−	7.79452e10i	0.775811	−	0.775811i	−0.203304	−	0.979116i	$-0.565168\pi$
$563$	7.79452e10	−	7.79452e10i	0.775811	−	0.775811i	0.979116	+	0.203304i	$0.0651681\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−9.68016e10	−	9.68016e10i	−0.936592	−	0.936592i
$568$		0			0
$569$			5.27046e10i			0.502805i	0.967883	+	0.251402i	$0.0808917\pi$
$569$			5.27046e10i			0.502805i	−0.967883	+	0.251402i	$0.919108\pi$
$570$		0			0
$571$	−1.89693e11			−1.78446			−0.892231	−	0.451579i	$-0.850861\pi$
$571$	−1.89693e11			−1.78446			−0.892231	+	0.451579i	$0.850861\pi$
$572$		0			0
$573$	−1.18996e11	+	1.18996e11i	−1.10386	+	1.10386i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−8.62244e9	−	8.62244e9i	−0.0777906	−	0.0777906i	0.667141	−	0.744932i	$-0.267518\pi$
$577$	−8.62244e9	−	8.62244e9i	−0.0777906	−	0.0777906i	−0.744932	+	0.667141i	$0.767518\pi$
$578$		0			0
$579$		−	3.82578e10i		−	0.340413i
$580$		0			0
$581$	1.63419e11			1.43416
$582$		0			0
$583$	−1.56955e11	+	1.56955e11i	−1.35863	+	1.35863i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.39784e11	+	1.39784e11i	1.17735	+	1.17735i	0.980417	+	0.196934i	$0.0630986\pi$
$587$	1.39784e11	+	1.39784e11i	1.17735	+	1.17735i	0.196934	+	0.980417i	$0.436901\pi$
$588$		0			0
$589$			1.36377e11i			1.13313i
$590$		0			0
$591$	−3.29353e9			−0.0269968
$592$		0			0
$593$	−1.05062e11	+	1.05062e11i	−0.849623	+	0.849623i	−0.990086	−	0.140463i	$-0.955141\pi$
$593$	−1.05062e11	+	1.05062e11i	−0.849623	+	0.849623i	0.140463	+	0.990086i	$0.455141\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−1.62370e11	−	1.62370e11i	−1.27823	−	1.27823i
$598$		0			0
$599$			4.24466e10i			0.329713i	0.986318	+	0.164856i	$0.0527160\pi$
$599$			4.24466e10i			0.329713i	−0.986318	+	0.164856i	$0.947284\pi$
$600$		0			0
$601$	2.47731e10			0.189881			0.0949407	−	0.995483i	$-0.469734\pi$
$601$	2.47731e10			0.189881			0.0949407	+	0.995483i	$0.469734\pi$
$602$		0			0
$603$	1.78727e9	−	1.78727e9i	0.0135183	−	0.0135183i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−1.36799e11	−	1.36799e11i	−1.00769	−	1.00769i	−0.999970	−	0.00772443i	$-0.997541\pi$
$607$	−1.36799e11	−	1.36799e11i	−1.00769	−	1.00769i	−0.00772443	−	0.999970i	$-0.502459\pi$
$608$		0			0
$609$		−	2.08626e9i		−	0.0151670i
$610$		0			0
$611$	−2.90871e9			−0.0208706
$612$		0			0
$613$	−3.31585e10	+	3.31585e10i	−0.234830	+	0.234830i	−0.814705	−	0.579875i	$-0.803101\pi$
$613$	−3.31585e10	+	3.31585e10i	−0.234830	+	0.234830i	0.579875	+	0.814705i	$0.303101\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.46615e11	+	1.46615e11i	1.01167	+	1.01167i	0.999931	+	0.0117352i	$0.00373553\pi$
$617$	1.46615e11	+	1.46615e11i	1.01167	+	1.01167i	0.0117352	+	0.999931i	$0.496264\pi$
$618$		0			0
$619$		−	1.37744e11i		−	0.938229i	−0.883137	−	0.469114i	$-0.844573\pi$
$619$		−	1.37744e11i		−	0.938229i	0.883137	−	0.469114i	$-0.155427\pi$
$620$		0			0
$621$	−1.38312e11			−0.930021
$622$		0			0
$623$	−1.56927e11	+	1.56927e11i	−1.04171	+	1.04171i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−2.15571e11	−	2.15571e11i	−1.39483	−	1.39483i
$628$		0			0
$629$		−	1.32857e9i		−	0.00848757i
$630$		0			0
$631$	−2.71052e11			−1.70976			−0.854881	−	0.518824i	$-0.826370\pi$
$631$	−2.71052e11			−1.70976			−0.854881	+	0.518824i	$0.826370\pi$
$632$		0			0
$633$	−1.45327e11	+	1.45327e11i	−0.905174	+	0.905174i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	1.48411e10	+	1.48411e10i	0.0901383	+	0.0901383i
$638$		0			0
$639$			1.35323e10i			0.0811649i
$640$		0			0
$641$	2.60272e11			1.54169			0.770843	−	0.637025i	$-0.219835\pi$
$641$	2.60272e11			1.54169			0.770843	+	0.637025i	$0.219835\pi$
$642$		0			0
$643$	−4.79903e10	+	4.79903e10i	−0.280743	+	0.280743i	−0.833405	−	0.552662i	$-0.813612\pi$
$643$	−4.79903e10	+	4.79903e10i	−0.280743	+	0.280743i	0.552662	+	0.833405i	$0.313612\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	5.65569e10	+	5.65569e10i	0.322751	+	0.322751i	0.849822	−	0.527070i	$-0.176710\pi$
$647$	5.65569e10	+	5.65569e10i	0.322751	+	0.322751i	−0.527070	+	0.849822i	$0.676710\pi$
$648$		0			0
$649$			3.19594e11i			1.80144i
$650$		0			0
$651$	1.54109e11			0.858034
$652$		0			0
$653$	−3.80349e9	+	3.80349e9i	−0.0209184	+	0.0209184i	−0.717489	−	0.696570i	$-0.754708\pi$
$653$	−3.80349e9	+	3.80349e9i	−0.0209184	+	0.0209184i	0.696570	+	0.717489i	$0.254708\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	2.16223e9	+	2.16223e9i	0.0116049	+	0.0116049i
$658$		0			0
$659$			2.52199e11i			1.33721i	0.743616	+	0.668607i	$0.233109\pi$
$659$			2.52199e11i			1.33721i	−0.743616	+	0.668607i	$0.766891\pi$
$660$		0			0
$661$	−2.49889e11			−1.30900			−0.654502	−	0.756060i	$-0.727122\pi$
$661$	−2.49889e11			−1.30900			−0.654502	+	0.756060i	$0.727122\pi$
$662$		0			0
$663$	−4.62048e9	+	4.62048e9i	−0.0239129	+	0.0239129i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−2.12687e9	−	2.12687e9i	−0.0107458	−	0.0107458i
$668$		0			0
$669$		−	2.24085e10i		−	0.111869i
$670$		0			0
$671$	3.50953e11			1.73125
$672$		0			0
$673$	2.33984e11	−	2.33984e11i	1.14058	−	1.14058i	0.152235	−	0.988344i	$-0.451353\pi$
$673$	2.33984e11	−	2.33984e11i	1.14058	−	1.14058i	0.988344	−	0.152235i	$-0.0486471\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−6.08027e10	−	6.08027e10i	−0.289447	−	0.289447i	0.547415	−	0.836861i	$-0.315612\pi$
$677$	−6.08027e10	−	6.08027e10i	−0.289447	−	0.289447i	−0.836861	+	0.547415i	$0.815612\pi$
$678$		0			0
$679$			1.09423e11i			0.514790i
$680$		0			0
$681$	−5.82050e10			−0.270627
$682$		0			0
$683$	−2.63408e10	+	2.63408e10i	−0.121045	+	0.121045i	−0.765034	−	0.643990i	$-0.777278\pi$
$683$	−2.63408e10	+	2.63408e10i	−0.121045	+	0.121045i	0.643990	+	0.765034i	$0.277278\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−1.04568e11	−	1.04568e11i	−0.469430	−	0.469430i
$688$		0			0
$689$			3.52124e11i			1.56250i
$690$		0			0
$691$	2.23440e11			0.980052			0.490026	−	0.871708i	$-0.336987\pi$
$691$	2.23440e11			0.980052			0.490026	+	0.871708i	$0.336987\pi$
$692$		0			0
$693$	−6.56463e10	+	6.56463e10i	−0.284628	+	0.284628i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−8.13221e9	−	8.13221e9i	−0.0344570	−	0.0344570i
$698$		0			0
$699$		−	4.67234e11i		−	1.95716i
$700$		0			0
$701$	−6.51821e9			−0.0269933			−0.0134967	−	0.999909i	$-0.504296\pi$
$701$	−6.51821e9			−0.0269933			−0.0134967	+	0.999909i	$0.504296\pi$
$702$		0			0
$703$	6.95311e10	−	6.95311e10i	0.284681	−	0.284681i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	2.47258e11	+	2.47258e11i	0.989630	+	0.989630i
$708$		0			0
$709$		−	2.72652e11i		−	1.07901i	−0.841983	−	0.539503i	$-0.818612\pi$
$709$		−	2.72652e11i		−	1.07901i	0.841983	−	0.539503i	$-0.181388\pi$
$710$		0			0
$711$	1.68520e11			0.659438
$712$		0			0
$713$	1.57109e11	−	1.57109e11i	0.607914	−	0.607914i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	2.81679e10	+	2.81679e10i	0.106581	+	0.106581i
$718$		0			0
$719$		−	2.21796e11i		−	0.829925i	−0.909839	−	0.414962i	$-0.863795\pi$
$719$		−	2.21796e11i		−	0.829925i	0.909839	−	0.414962i	$-0.136205\pi$
$720$		0			0
$721$	−7.88285e10			−0.291704
$722$		0			0
$723$	4.08307e11	−	4.08307e11i	1.49428	−	1.49428i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−2.44521e11	−	2.44521e11i	−0.875344	−	0.875344i	0.117704	−	0.993049i	$-0.462446\pi$
$727$	−2.44521e11	−	2.44521e11i	−0.875344	−	0.875344i	−0.993049	+	0.117704i	$0.962446\pi$
$728$		0			0
$729$			1.15552e11i			0.409136i
$730$		0			0
$731$	−1.59734e10			−0.0559408
$732$		0			0
$733$	−7.98615e10	+	7.98615e10i	−0.276644	+	0.276644i	−0.831768	−	0.555124i	$-0.812671\pi$
$733$	−7.98615e10	+	7.98615e10i	−0.276644	+	0.276644i	0.555124	+	0.831768i	$0.312671\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.09801e10	+	1.09801e10i	0.0372166	+	0.0372166i
$738$		0			0
$739$		−	8.32618e10i		−	0.279170i	−0.990210	−	0.139585i	$-0.955423\pi$
$739$		−	8.32618e10i		−	0.279170i	0.990210	−	0.139585i	$-0.0445768\pi$
$740$		0			0
$741$	−4.83627e11			−1.60412
$742$		0			0
$743$	−2.21829e11	+	2.21829e11i	−0.727885	+	0.727885i	−0.970198	−	0.242313i	$-0.922094\pi$
$743$	−2.21829e11	+	2.21829e11i	−0.727885	+	0.727885i	0.242313	+	0.970198i	$0.422094\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1.08418e11	+	1.08418e11i	0.348191	+	0.348191i
$748$		0			0
$749$		−	5.73802e11i		−	1.82320i
$750$		0			0
$751$	−2.12972e10			−0.0669519			−0.0334759	−	0.999440i	$-0.510658\pi$
$751$	−2.12972e10			−0.0669519			−0.0334759	+	0.999440i	$0.510658\pi$
$752$		0			0
$753$	1.65828e11	−	1.65828e11i	0.515795	−	0.515795i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	3.61373e11	+	3.61373e11i	1.10045	+	1.10045i	0.994356	+	0.106098i	$0.0338359\pi$
$757$	3.61373e11	+	3.61373e11i	1.10045	+	1.10045i	0.106098	+	0.994356i	$0.466164\pi$
$758$		0			0
$759$			4.96682e11i			1.49662i
$760$		0			0
$761$	−2.37570e10			−0.0708360			−0.0354180	−	0.999373i	$-0.511276\pi$
$761$	−2.37570e10			−0.0708360			−0.0354180	+	0.999373i	$0.511276\pi$
$762$		0			0
$763$	−6.52266e10	+	6.52266e10i	−0.192454	+	0.192454i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	3.58500e11	+	3.58500e11i	1.03587	+	1.03587i
$768$		0			0
$769$		−	1.62927e11i		−	0.465894i	−0.972489	−	0.232947i	$-0.925163\pi$
$769$		−	1.62927e11i		−	0.465894i	0.972489	−	0.232947i	$-0.0748368\pi$
$770$		0			0
$771$	−3.96567e11			−1.12228
$772$		0			0
$773$	4.39446e10	−	4.39446e10i	0.123080	−	0.123080i	−0.642884	−	0.765964i	$-0.722262\pi$
$773$	4.39446e10	−	4.39446e10i	0.123080	−	0.123080i	0.765964	+	0.642884i	$0.222262\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−7.85716e10	−	7.85716e10i	−0.215567	−	0.215567i
$778$		0			0
$779$		−	8.51201e11i		−	2.31144i
$780$		0			0
$781$	−8.31358e10			−0.223452
$782$		0			0
$783$	−2.36790e9	+	2.36790e9i	−0.00629965	+	0.00629965i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	4.00167e11	+	4.00167e11i	1.04314	+	1.04314i	0.999027	+	0.0441121i	$0.0140459\pi$
$787$	4.00167e11	+	4.00167e11i	1.04314	+	1.04314i	0.0441121	+	0.999027i	$0.485954\pi$
$788$		0			0
$789$		−	3.45273e11i		−	0.890952i
$790$		0			0
$791$	−2.13468e11			−0.545289
$792$		0			0
$793$	3.93676e11	−	3.93676e11i	0.995512	−	0.995512i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−3.15419e11	−	3.15419e11i	−0.781726	−	0.781726i	0.198396	−	0.980122i	$-0.436427\pi$
$797$	−3.15419e11	−	3.15419e11i	−0.781726	−	0.781726i	−0.980122	+	0.198396i	$0.936427\pi$
$798$		0			0
$799$		−	3.60447e8i		−	0.000884411i
$800$		0			0
$801$	−2.08222e11			−0.505821
$802$		0			0
$803$	−1.32837e10	+	1.32837e10i	−0.0319489	+	0.0319489i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1.80388e11	+	1.80388e11i	0.425318	+	0.425318i
$808$		0			0
$809$		−	1.46517e11i		−	0.342055i	−0.985266	−	0.171027i	$-0.945291\pi$
$809$		−	1.46517e11i		−	0.342055i	0.985266	−	0.171027i	$-0.0547086\pi$
$810$		0			0
$811$	2.95022e10			0.0681979			0.0340989	−	0.999418i	$-0.489144\pi$
$811$	2.95022e10			0.0681979			0.0340989	+	0.999418i	$0.489144\pi$
$812$		0			0
$813$	1.27469e11	−	1.27469e11i	0.291772	−	0.291772i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−8.35971e11	−	8.35971e11i	−1.87630	−	1.87630i
$818$		0			0
$819$			1.47275e11i			0.327337i
$820$		0			0
$821$	3.27089e11			0.719935			0.359968	−	0.932965i	$-0.382788\pi$
$821$	3.27089e11			0.719935			0.359968	+	0.932965i	$0.382788\pi$
$822$		0			0
$823$	−1.62737e11	+	1.62737e11i	−0.354720	+	0.354720i	−0.861862	−	0.507142i	$-0.830702\pi$
$823$	−1.62737e11	+	1.62737e11i	−0.354720	+	0.354720i	0.507142	+	0.861862i	$0.330702\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	4.65014e11	+	4.65014e11i	0.994131	+	0.994131i	0.999983	−	0.00585168i	$-0.00186266\pi$
$827$	4.65014e11	+	4.65014e11i	0.994131	+	0.994131i	−0.00585168	+	0.999983i	$0.501863\pi$
$828$		0			0
$829$			3.70693e11i			0.784867i	0.919780	+	0.392433i	$0.128367\pi$
$829$			3.70693e11i			0.784867i	−0.919780	+	0.392433i	$0.871633\pi$
$830$		0			0
$831$	1.06814e12			2.23988
$832$		0			0
$833$	−1.83911e9	+	1.83911e9i	−0.00381969	+	0.00381969i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−1.74914e11	−	1.74914e11i	−0.356387	−	0.356387i
$838$		0			0
$839$			3.78408e11i			0.763682i	0.924228	+	0.381841i	$0.124710\pi$
$839$			3.78408e11i			0.763682i	−0.924228	+	0.381841i	$0.875290\pi$
$840$		0			0
$841$	5.00174e11			0.999854
$842$		0			0
$843$	3.65618e11	−	3.65618e11i	0.723964	−	0.723964i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−1.22890e10	−	1.22890e10i	−0.0238772	−	0.0238772i
$848$		0			0
$849$			7.43979e10i			0.143196i
$850$		0			0
$851$	−1.60202e11			−0.305457
$852$		0			0
$853$	1.83957e11	−	1.83957e11i	0.347472	−	0.347472i	−0.511695	−	0.859167i	$-0.670982\pi$
$853$	1.83957e11	−	1.83957e11i	0.347472	−	0.347472i	0.859167	+	0.511695i	$0.170982\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−2.29371e11	−	2.29371e11i	−0.425222	−	0.425222i	0.461775	−	0.886997i	$-0.347213\pi$
$857$	−2.29371e11	−	2.29371e11i	−0.425222	−	0.425222i	−0.886997	+	0.461775i	$0.847213\pi$
$858$		0			0
$859$		−	3.79888e11i		−	0.697723i	−0.937174	−	0.348861i	$-0.886568\pi$
$859$		−	3.79888e11i		−	0.697723i	0.937174	−	0.348861i	$-0.113432\pi$
$860$		0			0
$861$	−9.61874e11			−1.75027
$862$		0			0
$863$	−6.48008e11	+	6.48008e11i	−1.16825	+	1.16825i	−0.185635	+	0.982619i	$0.559434\pi$
$863$	−6.48008e11	+	6.48008e11i	−1.16825	+	1.16825i	−0.982619	+	0.185635i	$0.940566\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	4.66890e11	+	4.66890e11i	0.826300	+	0.826300i
$868$		0			0
$869$			1.03531e12i			1.81547i
$870$		0			0
$871$	2.46335e10			0.0428010
$872$		0			0
$873$	−7.25952e10	+	7.25952e10i	−0.124983	+	0.124983i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−2.29437e11	−	2.29437e11i	−0.387852	−	0.387852i	0.486069	−	0.873920i	$-0.338430\pi$
$877$	−2.29437e11	−	2.29437e11i	−0.387852	−	0.387852i	−0.873920	+	0.486069i	$0.838430\pi$
$878$		0			0
$879$			1.21164e12i			2.02963i
$880$		0			0
$881$	5.51671e11			0.915750			0.457875	−	0.889017i	$-0.348611\pi$
$881$	5.51671e11			0.915750			0.457875	+	0.889017i	$0.348611\pi$
$882$		0			0
$883$	3.85317e11	−	3.85317e11i	0.633833	−	0.633833i	−0.315194	−	0.949027i	$-0.602070\pi$
$883$	3.85317e11	−	3.85317e11i	0.633833	−	0.633833i	0.949027	+	0.315194i	$0.102070\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−4.55043e11	−	4.55043e11i	−0.735120	−	0.735120i	0.236509	−	0.971629i	$-0.423997\pi$
$887$	−4.55043e11	−	4.55043e11i	−0.735120	−	0.735120i	−0.971629	+	0.236509i	$0.923997\pi$
$888$		0			0
$889$		−	3.77145e11i		−	0.603811i
$890$		0			0
$891$	7.89091e11			1.25203
$892$		0			0
$893$	1.88640e10	−	1.88640e10i	0.0296639	−	0.0296639i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	5.57146e11	+	5.57146e11i	0.860595	+	0.860595i
$898$		0			0
$899$		−	5.37941e9i		−	0.00823562i
$900$		0			0
$901$	−4.36351e10			−0.0662121
$902$		0			0
$903$	−9.44665e11	+	9.44665e11i	−1.42078	+	1.42078i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−4.42629e11	−	4.42629e11i	−0.654049	−	0.654049i	0.299916	−	0.953965i	$-0.403041\pi$
$907$	−4.42629e11	−	4.42629e11i	−0.654049	−	0.654049i	−0.953965	+	0.299916i	$0.903041\pi$
$908$		0			0
$909$			3.28080e11i			0.480533i
$910$		0			0
$911$	−2.98653e11			−0.433604			−0.216802	−	0.976216i	$-0.569563\pi$
$911$	−2.98653e11			−0.433604			−0.216802	+	0.976216i	$0.569563\pi$
$912$		0			0
$913$	−6.66065e11	+	6.66065e11i	−0.958591	+	0.958591i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−5.72822e11	−	5.72822e11i	−0.810107	−	0.810107i
$918$		0			0
$919$			3.41448e11i			0.478699i	0.970933	+	0.239350i	$0.0769342\pi$
$919$			3.41448e11i			0.478699i	−0.970933	+	0.239350i	$0.923066\pi$
$920$		0			0
$921$	−8.71633e11			−1.21142
$922$		0			0
$923$	−9.32563e10	+	9.32563e10i	−0.128491	+	0.128491i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−5.22976e10	−	5.22976e10i	−0.0708211	−	0.0708211i
$928$		0			0
$929$		−	9.58950e11i		−	1.28746i	−0.765254	−	0.643729i	$-0.777386\pi$
$929$		−	9.58950e11i		−	1.28746i	0.765254	−	0.643729i	$-0.222614\pi$
$930$		0			0
$931$	−1.92500e11			−0.256231
$932$		0			0
$933$	−6.16469e11	+	6.16469e11i	−0.813551	+	0.813551i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−6.99661e11	−	6.99661e11i	−0.907673	−	0.907673i	0.0884113	−	0.996084i	$-0.471821\pi$
$937$	−6.99661e11	−	6.99661e11i	−0.907673	−	0.907673i	−0.996084	+	0.0884113i	$0.971821\pi$
$938$		0			0
$939$			8.03106e11i			1.03302i
$940$		0			0
$941$	1.00859e10			0.0128634			0.00643170	−	0.999979i	$-0.497953\pi$
$941$	1.00859e10			0.0128634			0.00643170	+	0.999979i	$0.497953\pi$
$942$		0			0
$943$	−9.80597e11	+	9.80597e11i	−1.24006	+	1.24006i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−6.73871e10	−	6.73871e10i	−0.0837870	−	0.0837870i	0.663971	−	0.747758i	$-0.268870\pi$
$947$	−6.73871e10	−	6.73871e10i	−0.0837870	−	0.0837870i	−0.747758	+	0.663971i	$0.768870\pi$
$948$		0			0
$949$			2.98015e10i			0.0367429i
$950$		0			0
$951$	−3.86123e10			−0.0472067
$952$		0			0
$953$	−1.82422e11	+	1.82422e11i	−0.221159	+	0.221159i	−0.808986	−	0.587827i	$-0.799983\pi$
$953$	−1.82422e11	+	1.82422e11i	−0.221159	+	0.221159i	0.587827	+	0.808986i	$0.299983\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	8.50322e9	+	8.50322e9i	0.0101376	+	0.0101376i
$958$		0			0
$959$		−	2.91281e11i		−	0.344380i
$960$		0			0
$961$	−4.55521e11			−0.534091
$962$		0			0
$963$	3.80681e11	−	3.80681e11i	0.442645	−	0.442645i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	8.06230e11	+	8.06230e11i	0.922047	+	0.922047i	0.997174	−	0.0751265i	$-0.0239361\pi$
$967$	8.06230e11	+	8.06230e11i	0.922047	+	0.922047i	−0.0751265	+	0.997174i	$0.523936\pi$
$968$		0			0
$969$		−	5.99309e10i		−	0.0679760i
$970$		0			0
$971$	4.58944e11			0.516277			0.258138	−	0.966108i	$-0.416891\pi$
$971$	4.58944e11			0.516277			0.258138	+	0.966108i	$0.416891\pi$
$972$		0			0
$973$	−3.18359e11	+	3.18359e11i	−0.355194	+	0.355194i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	6.48952e11	+	6.48952e11i	0.712253	+	0.712253i	0.967006	−	0.254753i	$-0.0819942\pi$
$977$	6.48952e11	+	6.48952e11i	0.712253	+	0.712253i	−0.254753	+	0.967006i	$0.581994\pi$
$978$		0			0
$979$		−	1.27921e12i		−	1.39255i
$980$		0			0
$981$	−8.65473e10			−0.0934496
$982$		0			0
$983$	1.04063e12	−	1.04063e12i	1.11451	−	1.11451i	0.121977	−	0.992533i	$-0.461077\pi$
$983$	1.04063e12	−	1.04063e12i	1.11451	−	1.11451i	0.992533	−	0.121977i	$-0.0389234\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−2.13168e10	−	2.13168e10i	−0.0224622	−	0.0224622i
$988$		0			0
$989$			1.92610e12i			2.01324i
$990$		0			0
$991$	8.09242e11			0.839042			0.419521	−	0.907746i	$-0.362198\pi$
$991$	8.09242e11			0.839042			0.419521	+	0.907746i	$0.362198\pi$
$992$		0			0
$993$	1.88440e11	−	1.88440e11i	0.193810	−	0.193810i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	9.33394e11	+	9.33394e11i	0.944679	+	0.944679i	0.998548	−	0.0538691i	$-0.0171554\pi$
$997$	9.33394e11	+	9.33394e11i	0.944679	+	0.944679i	−0.0538691	+	0.998548i	$0.517155\pi$
$998$		0			0
$999$			1.78357e11i			0.179072i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.f.c.57.2	✓	12
5.2	odd	4	inner	100.9.f.c.93.5	yes	12
5.3	odd	4	inner	100.9.f.c.93.2	yes	12
5.4	even	2	inner	100.9.f.c.57.5	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.9.f.c.57.2	✓	12	1.1	even	1	trivial
100.9.f.c.57.5	yes	12	5.4	even	2	inner
100.9.f.c.93.2	yes	12	5.3	odd	4	inner
100.9.f.c.93.5	yes	12	5.2	odd	4	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	100.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-67.0124 + 67.0124i) q^{3} +(-1824.09 - 1824.09i) q^{7} -2420.33i q^{9} +14869.3 q^{11} +(16679.4 - 16679.4i) q^{13} +(2066.91 + 2066.91i) q^{17} +216344. i q^{19} +244473. q^{21} +(249231. - 249231. i) q^{23} +(-277476. - 277476. i) q^{27} -8533.70i q^{29} +630373. q^{31} +(-996427. + 996427. i) q^{33} +(-321392. - 321392. i) q^{37} +2.23545e6i q^{39} -3.93448e6 q^{41} +(-3.86409e6 + 3.86409e6i) q^{43} +(-87194.7 - 87194.7i) q^{47} +889788. i q^{49} -277017. q^{51} +(-1.05557e7 + 1.05557e7i) q^{53} +(-1.44977e7 - 1.44977e7i) q^{57} +2.14935e7i q^{59} +2.36025e7 q^{61} +(-4.41489e6 + 4.41489e6i) q^{63} +(738442. + 738442. i) q^{67} +3.34032e7i q^{69} -5.59110e6 q^{71} +(-893363. + 893363. i) q^{73} +(-2.71229e7 - 2.71229e7i) q^{77} +6.96271e7i q^{79} +5.30685e7 q^{81} +(-4.47947e7 + 4.47947e7i) q^{83} +(571864. + 571864. i) q^{87} -8.60305e7i q^{89} -6.08494e7 q^{91} +(-4.22428e7 + 4.22428e7i) q^{93} +(-2.99939e7 - 2.99939e7i) q^{97} -3.59886e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 420 q^{11} - 921168 q^{21} + 3833112 q^{31} + 3587532 q^{41} + 46092564 q^{51} + 31354704 q^{61} - 29589384 q^{71} + 104018868 q^{81} + 433229088 q^{91}+O(q^{100}) \) 12 * q - 420 * q^11 - 921168 * q^21 + 3833112 * q^31 + 3587532 * q^41 + 46092564 * q^51 + 31354704 * q^61 - 29589384 * q^71 + 104018868 * q^81 + 433229088 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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