LMFDB - Embedded newform 120.9.c.a.89.44

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [120,9,Mod(89,120)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(120, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 1, 1])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("120.89"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	120.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$48.8854332073$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			89.44
Character	$\chi$	$=$	120.89
Dual form			120.9.c.a.89.43

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(76.6243 + 26.2625i) q^{3} +(-461.945 - 420.989i) q^{5} +982.121i q^{7} +(5181.56 + 4024.69i) q^{9} +8653.99i q^{11} -18173.3i q^{13} +(-24340.0 - 44389.8i) q^{15} -4881.66 q^{17} -73530.2 q^{19} +(-25793.0 + 75254.3i) q^{21} +11644.6 q^{23} +(36161.6 + 388948. i) q^{25} +(291335. + 444470. i) q^{27} +981664. i q^{29} -853304. q^{31} +(-227276. + 663106. i) q^{33} +(413462. - 453686. i) q^{35} +712787. i q^{37} +(477276. - 1.39251e6i) q^{39} +4.65194e6i q^{41} -2.20493e6i q^{43} +(-699245. - 4.04057e6i) q^{45} -3.60712e6 q^{47} +4.80024e6 q^{49} +(-374053. - 128205. i) q^{51} -1.28038e7 q^{53} +(3.64323e6 - 3.99767e6i) q^{55} +(-5.63420e6 - 1.93109e6i) q^{57} +1.13258e7i q^{59} +8.48249e6 q^{61} +(-3.95273e6 + 5.08892e6i) q^{63} +(-7.65074e6 + 8.39505e6i) q^{65} +9.68738e6i q^{67} +(892256. + 305815. i) q^{69} +1.68485e7i q^{71} +4.32871e7i q^{73} +(-7.44389e6 + 3.07525e7i) q^{75} -8.49926e6 q^{77} -1.15899e7 q^{79} +(1.06504e7 + 4.17084e7i) q^{81} -7.18688e7 q^{83} +(2.25506e6 + 2.05512e6i) q^{85} +(-2.57810e7 + 7.52193e7i) q^{87} +7.55168e7i q^{89} +1.78483e7 q^{91} +(-6.53838e7 - 2.24099e7i) q^{93} +(3.39669e7 + 3.09554e7i) q^{95} -1.21749e8i q^{97} +(-3.48297e7 + 4.48412e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2528 q^{9} + 132352 q^{15} + 116176 q^{21} + 56976 q^{25} + 1395648 q^{31} + 6888832 q^{39} - 4287056 q^{45} - 30813552 q^{49} - 22815168 q^{51} - 6062784 q^{55} + 14031936 q^{61} + 2522608 q^{69}+ \cdots - 21719360 q^{99}+O(q^{100}) $ 48 * q + 2528 * q^9 + 132352 * q^15 + 116176 * q^21 + 56976 * q^25 + 1395648 * q^31 + 6888832 * q^39 - 4287056 * q^45 - 30813552 * q^49 - 22815168 * q^51 - 6062784 * q^55 + 14031936 * q^61 + 2522608 * q^69 + 41684416 * q^75 + 19866432 * q^79 - 93539312 * q^81 - 116297664 * q^85 + 16826880 * q^91 - 21719360 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$1$	$-1$	$1$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	76.6243	+	26.2625i	0.945979	+	0.324229i
$3$	76.6243	+	26.2625i	0.945979	+	0.324229i
$4$		0			0
$5$	−461.945	−	420.989i	−0.739112	−	0.673582i
$5$	−461.945	−	420.989i	−0.739112	−	0.673582i
$6$		0			0
$7$			982.121i			0.409047i	0.978862	+	0.204523i	$0.0655644\pi$
$7$			982.121i			0.409047i	−0.978862	+	0.204523i	$0.934436\pi$
$8$		0			0
$9$	5181.56	+	4024.69i	0.789752	+	0.613427i
$10$		0			0
$11$			8653.99i			0.591079i	0.955330	+	0.295540i	$0.0954994\pi$
$11$			8653.99i			0.591079i	−0.955330	+	0.295540i	$0.904501\pi$
$12$		0			0
$13$		−	18173.3i		−	0.636296i	−0.948041	−	0.318148i	$-0.896939\pi$
$13$		−	18173.3i		−	0.636296i	0.948041	−	0.318148i	$-0.103061\pi$
$14$		0			0
$15$	−24340.0	−	44389.8i	−0.480790	−	0.876836i
$16$		0			0
$17$	−4881.66			−0.0584483			−0.0292241	−	0.999573i	$-0.509304\pi$
$17$	−4881.66			−0.0584483			−0.0292241	+	0.999573i	$0.509304\pi$
$18$		0			0
$19$	−73530.2			−0.564224			−0.282112	−	0.959381i	$-0.591035\pi$
$19$	−73530.2			−0.564224			−0.282112	+	0.959381i	$0.591035\pi$
$20$		0			0
$21$	−25793.0	+	75254.3i	−0.132625	+	0.386949i
$22$		0			0
$23$	11644.6			0.0416113			0.0208057	−	0.999784i	$-0.493377\pi$
$23$	11644.6			0.0416113			0.0208057	+	0.999784i	$0.493377\pi$
$24$		0			0
$25$	36161.6	+	388948.i	0.0925737	+	0.995706i
$26$		0			0
$27$	291335.	+	444470.i	0.548198	+	0.836349i
$28$		0			0
$29$			981664.i			1.38794i	0.720003	+	0.693971i	$0.244140\pi$
$29$			981664.i			1.38794i	−0.720003	+	0.693971i	$0.755860\pi$
$30$		0			0
$31$	−853304.			−0.923968			−0.461984	−	0.886888i	$-0.652862\pi$
$31$	−853304.			−0.923968			−0.461984	+	0.886888i	$0.652862\pi$
$32$		0			0
$33$	−227276.	+	663106.i	−0.191645	+	0.559148i
$34$		0			0
$35$	413462.	−	453686.i	0.275526	−	0.302331i
$36$		0			0
$37$			712787.i			0.380323i	0.981753	+	0.190162i	$0.0609012\pi$
$37$			712787.i			0.380323i	−0.981753	+	0.190162i	$0.939099\pi$
$38$		0			0
$39$	477276.	−	1.39251e6i	0.206305	−	0.601923i
$40$		0			0
$41$			4.65194e6i			1.64626i	0.567852	+	0.823130i	$0.307774\pi$
$41$			4.65194e6i			1.64626i	−0.567852	+	0.823130i	$0.692226\pi$
$42$		0			0
$43$		−	2.20493e6i		−	0.644942i	−0.946579	−	0.322471i	$-0.895487\pi$
$43$		−	2.20493e6i		−	0.644942i	0.946579	−	0.322471i	$-0.104513\pi$
$44$		0			0
$45$	−699245.	−	4.04057e6i	−0.170522	−	0.985354i
$46$		0			0
$47$	−3.60712e6			−0.739212			−0.369606	−	0.929188i	$-0.620507\pi$
$47$	−3.60712e6			−0.739212			−0.369606	+	0.929188i	$0.620507\pi$
$48$		0			0
$49$	4.80024e6			0.832681
$50$		0			0
$51$	−374053.	−	128205.i	−0.0552908	−	0.0189506i
$52$		0			0
$53$	−1.28038e7			−1.62269			−0.811344	−	0.584569i	$-0.801264\pi$
$53$	−1.28038e7			−1.62269			−0.811344	+	0.584569i	$0.801264\pi$
$54$		0			0
$55$	3.64323e6	−	3.99767e6i	0.398141	−	0.436874i
$56$		0			0
$57$	−5.63420e6	−	1.93109e6i	−0.533744	−	0.182938i
$58$		0			0
$59$			1.13258e7i			0.934679i	0.884078	+	0.467339i	$0.154787\pi$
$59$			1.13258e7i			0.934679i	−0.884078	+	0.467339i	$0.845213\pi$
$60$		0			0
$61$	8.48249e6			0.612638			0.306319	−	0.951929i	$-0.400903\pi$
$61$	8.48249e6			0.612638			0.306319	+	0.951929i	$0.400903\pi$
$62$		0			0
$63$	−3.95273e6	+	5.08892e6i	−0.250920	+	0.323045i
$64$		0			0
$65$	−7.65074e6	+	8.39505e6i	−0.428598	+	0.470294i
$66$		0			0
$67$			9.68738e6i			0.480737i	0.970682	+	0.240368i	$0.0772682\pi$
$67$			9.68738e6i			0.480737i	−0.970682	+	0.240368i	$0.922732\pi$
$68$		0			0
$69$	892256.	+	305815.i	0.0393634	+	0.0134916i
$70$		0			0
$71$			1.68485e7i			0.663021i	0.943452	+	0.331510i	$0.107558\pi$
$71$			1.68485e7i			0.663021i	−0.943452	+	0.331510i	$0.892442\pi$
$72$		0			0
$73$			4.32871e7i			1.52429i	0.647407	+	0.762145i	$0.275853\pi$
$73$			4.32871e7i			1.52429i	−0.647407	+	0.762145i	$0.724147\pi$
$74$		0			0
$75$	−7.44389e6	+	3.07525e7i	−0.235264	+	0.971932i
$76$		0			0
$77$	−8.49926e6			−0.241779
$78$		0			0
$79$	−1.15899e7			−0.297559			−0.148780	−	0.988870i	$-0.547534\pi$
$79$	−1.15899e7			−0.297559			−0.148780	+	0.988870i	$0.547534\pi$
$80$		0			0
$81$	1.06504e7	+	4.17084e7i	0.247415	+	0.968910i
$82$		0			0
$83$	−7.18688e7			−1.51436			−0.757178	−	0.653208i	$-0.773423\pi$
$83$	−7.18688e7			−1.51436			−0.757178	+	0.653208i	$0.773423\pi$
$84$		0			0
$85$	2.25506e6	+	2.05512e6i	0.0431998	+	0.0393697i
$86$		0			0
$87$	−2.57810e7	+	7.52193e7i	−0.450010	+	1.31296i
$88$		0			0
$89$			7.55168e7i			1.20360i	0.798645	+	0.601802i	$0.205550\pi$
$89$			7.55168e7i			1.20360i	−0.798645	+	0.601802i	$0.794450\pi$
$90$		0			0
$91$	1.78483e7			0.260275
$92$		0			0
$93$	−6.53838e7	−	2.24099e7i	−0.874054	−	0.299577i
$94$		0			0
$95$	3.39669e7	+	3.09554e7i	0.417025	+	0.380051i
$96$		0			0
$97$		−	1.21749e8i		−	1.37524i	−0.726073	−	0.687618i	$-0.758657\pi$
$97$		−	1.21749e8i		−	1.37524i	0.726073	−	0.687618i	$-0.241343\pi$
$98$		0			0
$99$	−3.48297e7	+	4.48412e7i	−0.362584	+	0.466806i
$100$		0			0
$101$		−	1.01046e8i		−	0.971033i	−0.874228	−	0.485516i	$-0.838632\pi$
$101$		−	1.01046e8i		−	0.971033i	0.874228	−	0.485516i	$-0.161368\pi$
$102$		0			0
$103$			7.00996e7i			0.622826i	0.950275	+	0.311413i	$0.100802\pi$
$103$			7.00996e7i			0.622826i	−0.950275	+	0.311413i	$0.899198\pi$
$104$		0			0
$105$	4.35962e7	−	2.39048e7i	0.358667	−	0.196665i
$106$		0			0
$107$	−3.07384e7			−0.234502			−0.117251	−	0.993102i	$-0.537408\pi$
$107$	−3.07384e7			−0.234502			−0.117251	+	0.993102i	$0.537408\pi$
$108$		0			0
$109$	1.12561e8			0.797409			0.398705	−	0.917079i	$-0.369460\pi$
$109$	1.12561e8			0.797409			0.398705	+	0.917079i	$0.369460\pi$
$110$		0			0
$111$	−1.87196e7	+	5.46168e7i	−0.123312	+	0.359778i
$112$		0			0
$113$	−1.58169e8			−0.970082			−0.485041	−	0.874491i	$-0.661195\pi$
$113$	−1.58169e8			−0.970082			−0.485041	+	0.874491i	$0.661195\pi$
$114$		0			0
$115$	−5.37915e6	−	4.90223e6i	−0.0307554	−	0.0280287i
$116$		0			0
$117$	7.31418e7	−	9.41658e7i	0.390321	−	0.502516i
$118$		0			0
$119$		−	4.79438e6i		−	0.0239081i
$120$		0			0
$121$	1.39467e8			0.650625
$122$		0			0
$123$	−1.22172e8	+	3.56451e8i	−0.533765	+	1.55733i
$124$		0			0
$125$	1.47038e8	−	1.94896e8i	0.602267	−	0.798294i
$126$		0			0
$127$		−	1.14202e8i		−	0.438993i	−0.975613	−	0.219496i	$-0.929559\pi$
$127$		−	1.14202e8i		−	0.438993i	0.975613	−	0.219496i	$-0.0704414\pi$
$128$		0			0
$129$	5.79070e7	−	1.68951e8i	0.209109	−	0.610101i
$130$		0			0
$131$			5.08690e7i			0.172730i	0.996264	+	0.0863650i	$0.0275251\pi$
$131$			5.08690e7i			0.172730i	−0.996264	+	0.0863650i	$0.972475\pi$
$132$		0			0
$133$		−	7.22156e7i		−	0.230794i
$134$		0			0
$135$	5.25363e7	−	3.27969e8i	0.158170	−	0.987412i
$136$		0			0
$137$	1.70775e8			0.484776			0.242388	−	0.970179i	$-0.422069\pi$
$137$	1.70775e8			0.484776			0.242388	+	0.970179i	$0.422069\pi$
$138$		0			0
$139$	−2.48000e8			−0.664344			−0.332172	−	0.943219i	$-0.607781\pi$
$139$	−2.48000e8			−0.664344			−0.332172	+	0.943219i	$0.607781\pi$
$140$		0			0
$141$	−2.76393e8	−	9.47321e7i	−0.699279	−	0.239674i
$142$		0			0
$143$	1.57271e8			0.376102
$144$		0			0
$145$	4.13270e8	−	4.53475e8i	0.934893	−	1.02584i
$146$		0			0
$147$	3.67815e8	+	1.26066e8i	0.787698	+	0.269979i
$148$		0			0
$149$		−	3.04126e8i		−	0.617034i	−0.951219	−	0.308517i	$-0.900167\pi$
$149$		−	3.04126e8i		−	0.617034i	0.951219	−	0.308517i	$-0.0998326\pi$
$150$		0			0
$151$	−2.94615e8			−0.566692			−0.283346	−	0.959018i	$-0.591445\pi$
$151$	−2.94615e8			−0.566692			−0.283346	+	0.959018i	$0.591445\pi$
$152$		0			0
$153$	−2.52946e7	−	1.96472e7i	−0.0461596	−	0.0358537i
$154$		0			0
$155$	3.94180e8	+	3.59231e8i	0.682916	+	0.622369i
$156$		0			0
$157$		−	5.91610e8i		−	0.973727i	−0.873478	−	0.486864i	$-0.838141\pi$
$157$		−	5.91610e8i		−	0.973727i	0.873478	−	0.486864i	$-0.161859\pi$
$158$		0			0
$159$	−9.81081e8	−	3.36260e8i	−1.53503	−	0.526122i
$160$		0			0
$161$			1.14364e7i			0.0170210i
$162$		0			0
$163$			4.81315e8i			0.681835i	0.940093	+	0.340918i	$0.110738\pi$
$163$			4.81315e8i			0.681835i	−0.940093	+	0.340918i	$0.889262\pi$
$164$		0			0
$165$	3.84149e8	−	2.10638e8i	0.518280	−	0.284185i
$166$		0			0
$167$	1.29753e9			1.66821			0.834104	−	0.551607i	$-0.185985\pi$
$167$	1.29753e9			1.66821			0.834104	+	0.551607i	$0.185985\pi$
$168$		0			0
$169$	4.85463e8			0.595127
$170$		0			0
$171$	−3.81001e8	−	2.95937e8i	−0.445597	−	0.346110i
$172$		0			0
$173$	−1.42317e8			−0.158881			−0.0794403	−	0.996840i	$-0.525313\pi$
$173$	−1.42317e8			−0.158881			−0.0794403	+	0.996840i	$0.525313\pi$
$174$		0			0
$175$	−3.81993e8	+	3.55151e7i	−0.407290	+	0.0378670i
$176$		0			0
$177$	−2.97445e8	+	8.67834e8i	−0.303050	+	0.884186i
$178$		0			0
$179$			2.71626e7i			0.0264582i	0.999912	+	0.0132291i	$0.00421107\pi$
$179$			2.71626e7i			0.0264582i	−0.999912	+	0.0132291i	$0.995789\pi$
$180$		0			0
$181$	1.10557e9			1.03008			0.515039	−	0.857167i	$-0.327777\pi$
$181$	1.10557e9			1.03008			0.515039	+	0.857167i	$0.327777\pi$
$182$		0			0
$183$	6.49965e8	+	2.22772e8i	0.579543	+	0.198635i
$184$		0			0
$185$	3.00075e8	−	3.29268e8i	0.256179	−	0.281101i
$186$		0			0
$187$		−	4.22458e7i		−	0.0345476i
$188$		0			0
$189$	−4.36523e8	+	2.86126e8i	−0.342106	+	0.224238i
$190$		0			0
$191$		−	2.33274e9i		−	1.75280i	−0.481585	−	0.876399i	$-0.659939\pi$
$191$		−	2.33274e9i		−	1.75280i	0.481585	−	0.876399i	$-0.340061\pi$
$192$		0			0
$193$		−	1.94812e9i		−	1.40406i	−0.712146	−	0.702031i	$-0.752277\pi$
$193$		−	1.94812e9i		−	1.40406i	0.712146	−	0.702031i	$-0.247723\pi$
$194$		0			0
$195$	−8.06708e8	+	4.42337e8i	−0.557927	+	0.305925i
$196$		0			0
$197$	−3.91016e8			−0.259615			−0.129807	−	0.991539i	$-0.541436\pi$
$197$	−3.91016e8			−0.259615			−0.129807	+	0.991539i	$0.541436\pi$
$198$		0			0
$199$	−1.05716e9			−0.674104			−0.337052	−	0.941486i	$-0.609430\pi$
$199$	−1.05716e9			−0.674104			−0.337052	+	0.941486i	$0.609430\pi$
$200$		0			0
$201$	−2.54415e8	+	7.42289e8i	−0.155869	+	0.454767i
$202$		0			0
$203$	−9.64113e8			−0.567733
$204$		0			0
$205$	1.95842e9	−	2.14894e9i	1.10889	−	1.21677i
$206$		0			0
$207$	6.03370e7	+	4.68658e7i	0.0328626	+	0.0255255i
$208$		0			0
$209$		−	6.36330e8i		−	0.333501i
$210$		0			0
$211$	3.51802e9			1.77488			0.887440	−	0.460924i	$-0.152482\pi$
$211$	3.51802e9			1.77488			0.887440	+	0.460924i	$0.152482\pi$
$212$		0			0
$213$	−4.42483e8	+	1.29100e9i	−0.214970	+	0.627203i
$214$		0			0
$215$	−9.28250e8	+	1.01856e9i	−0.434421	+	0.476684i
$216$		0			0
$217$		−	8.38047e8i		−	0.377946i
$218$		0			0
$219$	−1.13683e9	+	3.31684e9i	−0.494218	+	1.44194i
$220$		0			0
$221$			8.87156e7i			0.0371904i
$222$		0			0
$223$		−	2.16380e9i		−	0.874981i	−0.899223	−	0.437491i	$-0.855867\pi$
$223$		−	2.16380e9i		−	0.874981i	0.899223	−	0.437491i	$-0.144133\pi$
$224$		0			0
$225$	−1.37802e9	+	2.16089e9i	−0.537682	+	0.843147i
$226$		0			0
$227$	−3.66824e9			−1.38151			−0.690755	−	0.723089i	$-0.742722\pi$
$227$	−3.66824e9			−1.38151			−0.690755	+	0.723089i	$0.742722\pi$
$228$		0			0
$229$	1.22572e9			0.445707			0.222853	−	0.974852i	$-0.428463\pi$
$229$	1.22572e9			0.445707			0.222853	+	0.974852i	$0.428463\pi$
$230$		0			0
$231$	−6.51250e8	−	2.23212e8i	−0.228718	−	0.0783916i
$232$		0			0
$233$	2.59519e9			0.880531			0.440266	−	0.897868i	$-0.354884\pi$
$233$	2.59519e9			0.880531			0.440266	+	0.897868i	$0.354884\pi$
$234$		0			0
$235$	1.66629e9	+	1.51856e9i	0.546361	+	0.497920i
$236$		0			0
$237$	−8.88071e8	−	3.04381e8i	−0.281484	−	0.0964772i
$238$		0			0
$239$			4.00336e9i			1.22697i	0.789707	+	0.613484i	$0.210233\pi$
$239$			4.00336e9i			1.22697i	−0.789707	+	0.613484i	$0.789767\pi$
$240$		0			0
$241$	−2.29228e9			−0.679515			−0.339758	−	0.940513i	$-0.610345\pi$
$241$	−2.29228e9			−0.679515			−0.339758	+	0.940513i	$0.610345\pi$
$242$		0			0
$243$	−2.79287e8	+	3.47558e9i	−0.0800988	+	0.996787i
$244$		0			0
$245$	−2.21745e9	−	2.02085e9i	−0.615445	−	0.560879i
$246$		0			0
$247$			1.33628e9i			0.359014i
$248$		0			0
$249$	−5.50690e9	−	1.88746e9i	−1.43255	−	0.490998i
$250$		0			0
$251$			6.02678e9i			1.51842i	0.650849	+	0.759208i	$0.274413\pi$
$251$			6.02678e9i			1.51842i	−0.650849	+	0.759208i	$0.725587\pi$
$252$		0			0
$253$			1.00772e8i			0.0245956i
$254$		0			0
$255$	1.18819e8	+	2.16696e8i	0.0281013	+	0.0512495i
$256$		0			0
$257$	−5.11464e8			−0.117242			−0.0586209	−	0.998280i	$-0.518670\pi$
$257$	−5.11464e8			−0.117242			−0.0586209	+	0.998280i	$0.518670\pi$
$258$		0			0
$259$	−7.00043e8			−0.155570
$260$		0			0
$261$	−3.95090e9	+	5.08655e9i	−0.851400	+	1.09613i
$262$		0			0
$263$	5.43681e8			0.113637			0.0568186	−	0.998385i	$-0.481904\pi$
$263$	5.43681e8			0.113637			0.0568186	+	0.998385i	$0.481904\pi$
$264$		0			0
$265$	5.91465e9	+	5.39025e9i	1.19935	+	1.09301i
$266$		0			0
$267$	−1.98326e9	+	5.78642e9i	−0.390243	+	1.13858i
$268$		0			0
$269$			6.14651e9i			1.17387i	0.809635	+	0.586934i	$0.199665\pi$
$269$			6.14651e9i			1.17387i	−0.809635	+	0.586934i	$0.800335\pi$
$270$		0			0
$271$	9.86706e9			1.82941			0.914704	−	0.404125i	$-0.132424\pi$
$271$	9.86706e9			1.82941			0.914704	+	0.404125i	$0.132424\pi$
$272$		0			0
$273$	1.36762e9	+	4.68742e8i	0.246214	+	0.0843885i
$274$		0			0
$275$	−3.36595e9	+	3.12942e8i	−0.588541	+	0.0547184i
$276$		0			0
$277$			8.51275e8i			0.144594i	0.997383	+	0.0722971i	$0.0230330\pi$
$277$			8.51275e8i			0.144594i	−0.997383	+	0.0722971i	$0.976967\pi$
$278$		0			0
$279$	−4.42145e9	−	3.43429e9i	−0.729705	−	0.566787i
$280$		0			0
$281$			3.47324e9i			0.557070i	0.960426	+	0.278535i	$0.0898488\pi$
$281$			3.47324e9i			0.557070i	−0.960426	+	0.278535i	$0.910151\pi$
$282$		0			0
$283$		−	9.60563e9i		−	1.49755i	−0.662826	−	0.748773i	$-0.730643\pi$
$283$		−	9.60563e9i		−	1.49755i	0.662826	−	0.748773i	$-0.269357\pi$
$284$		0			0
$285$	1.78972e9	+	3.26399e9i	0.271273	+	0.494732i
$286$		0			0
$287$	−4.56877e9			−0.673397
$288$		0			0
$289$	−6.95193e9			−0.996584
$290$		0			0
$291$	3.19742e9	−	9.32890e9i	0.445891	−	1.30094i
$292$		0			0
$293$	1.51538e9			0.205613			0.102807	−	0.994701i	$-0.467218\pi$
$293$	1.51538e9			0.205613			0.102807	+	0.994701i	$0.467218\pi$
$294$		0			0
$295$	4.76805e9	−	5.23192e9i	0.629583	−	0.690832i
$296$		0			0
$297$	−3.84644e9	+	2.52121e9i	−0.494348	+	0.324028i
$298$		0			0
$299$		−	2.11620e8i		−	0.0264771i
$300$		0			0
$301$	2.16551e9			0.263811
$302$		0			0
$303$	2.65372e9	−	7.74258e9i	0.314837	−	0.918576i
$304$		0			0
$305$	−3.91845e9	−	3.57104e9i	−0.452808	−	0.412662i
$306$		0			0
$307$		−	1.76009e10i		−	1.98144i	−0.135927	−	0.990719i	$-0.543401\pi$
$307$		−	1.76009e10i		−	1.98144i	0.135927	−	0.990719i	$-0.456599\pi$
$308$		0			0
$309$	−1.84099e9	+	5.37133e9i	−0.201938	+	0.589180i
$310$		0			0
$311$		−	1.18673e10i		−	1.26856i	−0.773104	−	0.634280i	$-0.781297\pi$
$311$		−	1.18673e10i		−	1.26856i	0.773104	−	0.634280i	$-0.218703\pi$
$312$		0			0
$313$		−	2.01409e9i		−	0.209846i	−0.994480	−	0.104923i	$-0.966540\pi$
$313$		−	2.01409e9i		−	0.209846i	0.994480	−	0.104923i	$-0.0334596\pi$
$314$		0			0
$315$	3.96832e9	−	6.86743e8i	0.403056	−	0.0697513i
$316$		0			0
$317$	5.91329e9			0.585588			0.292794	−	0.956176i	$-0.405415\pi$
$317$	5.91329e9			0.585588			0.292794	+	0.956176i	$0.405415\pi$
$318$		0			0
$319$	−8.49532e9			−0.820383
$320$		0			0
$321$	−2.35531e9	−	8.07268e8i	−0.221834	−	0.0760322i
$322$		0			0
$323$	3.58949e8			0.0329779
$324$		0			0
$325$	7.06844e9	−	6.57174e8i	0.633564	−	0.0589043i
$326$		0			0
$327$	8.62489e9	+	2.95613e9i	0.754332	+	0.258543i
$328$		0			0
$329$		−	3.54263e9i		−	0.302372i
$330$		0			0
$331$	1.31827e10			1.09822			0.549112	−	0.835749i	$-0.314966\pi$
$331$	1.31827e10			1.09822			0.549112	+	0.835749i	$0.314966\pi$
$332$		0			0
$333$	−2.86875e9	+	3.69335e9i	−0.233300	+	0.300361i
$334$		0			0
$335$	4.07828e9	−	4.47504e9i	0.323816	−	0.355318i
$336$		0			0
$337$			1.66709e10i			1.29253i	0.763114	+	0.646264i	$0.223669\pi$
$337$			1.66709e10i			1.29253i	−0.763114	+	0.646264i	$0.776331\pi$
$338$		0			0
$339$	−1.21196e10	−	4.15393e9i	−0.917677	−	0.314528i
$340$		0			0
$341$		−	7.38448e9i		−	0.546138i
$342$		0			0
$343$			1.03761e10i			0.749652i
$344$		0			0
$345$	−2.83428e8	−	5.16900e8i	−0.0200063	−	0.0364863i
$346$		0			0
$347$	1.10956e10			0.765302			0.382651	−	0.923893i	$-0.375011\pi$
$347$	1.10956e10			0.765302			0.382651	+	0.923893i	$0.375011\pi$
$348$		0			0
$349$	−2.56004e10			−1.72562			−0.862808	−	0.505531i	$-0.831296\pi$
$349$	−2.56004e10			−1.72562			−0.862808	+	0.505531i	$0.831296\pi$
$350$		0			0
$351$	8.07747e9	−	5.29450e9i	0.532166	−	0.348816i
$352$		0			0
$353$	2.46652e10			1.58850			0.794249	−	0.607593i	$-0.207865\pi$
$353$	2.46652e10			1.58850			0.794249	+	0.607593i	$0.207865\pi$
$354$		0			0
$355$	7.09302e9	−	7.78307e9i	0.446599	−	0.490047i
$356$		0			0
$357$	1.25912e8	−	3.67366e8i	0.00775168	−	0.0226165i
$358$		0			0
$359$			1.65018e10i			0.993467i	0.867903	+	0.496734i	$0.165467\pi$
$359$			1.65018e10i			0.993467i	−0.867903	+	0.496734i	$0.834533\pi$
$360$		0			0
$361$	−1.15769e10			−0.681651
$362$		0			0
$363$	1.06866e10	+	3.66276e9i	0.615478	+	0.210951i
$364$		0			0
$365$	1.82234e10	−	1.99963e10i	1.02673	−	1.12662i
$366$		0			0
$367$		−	3.02033e9i		−	0.166491i	−0.996529	−	0.0832455i	$-0.973471\pi$
$367$		−	3.02033e9i		−	0.166491i	0.996529	−	0.0832455i	$-0.0265286\pi$
$368$		0			0
$369$	−1.87226e10	+	2.41043e10i	−1.00986	+	1.30014i
$370$		0			0
$371$		−	1.25749e10i		−	0.663755i
$372$		0			0
$373$		−	6.87055e8i		−	0.0354941i	−0.999843	−	0.0177471i	$-0.994351\pi$
$373$		−	6.87055e8i		−	0.0354941i	0.999843	−	0.0177471i	$-0.00564936\pi$
$374$		0			0
$375$	1.63851e10	−	1.10722e10i	0.828562	−	0.559897i
$376$		0			0
$377$	1.78400e10			0.883142
$378$		0			0
$379$	−2.27101e10			−1.10068			−0.550342	−	0.834939i	$-0.685503\pi$
$379$	−2.27101e10			−1.10068			−0.550342	+	0.834939i	$0.685503\pi$
$380$		0			0
$381$	2.99922e9	−	8.75061e9i	0.142334	−	0.415278i
$382$		0			0
$383$	−3.67251e10			−1.70674			−0.853370	−	0.521305i	$-0.825445\pi$
$383$	−3.67251e10			−1.70674			−0.853370	+	0.521305i	$0.825445\pi$
$384$		0			0
$385$	3.92619e9	+	3.57810e9i	0.178702	+	0.162858i
$386$		0			0
$387$	8.87416e9	−	1.14250e10i	0.395625	−	0.509344i
$388$		0			0
$389$		−	2.81535e10i		−	1.22951i	−0.788716	−	0.614757i	$-0.789254\pi$
$389$		−	2.81535e10i		−	1.22951i	0.788716	−	0.614757i	$-0.210746\pi$
$390$		0			0
$391$	−5.68447e7			−0.00243211
$392$		0			0
$393$	−1.33595e9	+	3.89780e9i	−0.0560040	+	0.163399i
$394$		0			0
$395$	5.35392e9	+	4.87924e9i	0.219929	+	0.200430i
$396$		0			0
$397$		−	2.03348e10i		−	0.818611i	−0.912397	−	0.409305i	$-0.865771\pi$
$397$		−	2.03348e10i		−	0.818611i	0.912397	−	0.409305i	$-0.134229\pi$
$398$		0			0
$399$	1.89656e9	−	5.53346e9i	0.0748300	−	0.218326i
$400$		0			0
$401$			1.72949e9i			0.0668870i	0.999441	+	0.0334435i	$0.0106474\pi$
$401$			1.72949e9i			0.0668870i	−0.999441	+	0.0334435i	$0.989353\pi$
$402$		0			0
$403$			1.55073e10i			0.587917i
$404$		0			0
$405$	1.26389e10	−	2.37507e10i	0.469773	−	0.882787i
$406$		0			0
$407$	−6.16845e9			−0.224801
$408$		0			0
$409$	−3.80233e10			−1.35880			−0.679401	−	0.733767i	$-0.737761\pi$
$409$	−3.80233e10			−1.35880			−0.679401	+	0.733767i	$0.737761\pi$
$410$		0			0
$411$	1.30855e10	+	4.48498e9i	0.458588	+	0.157178i
$412$		0			0
$413$	−1.11233e10			−0.382327
$414$		0			0
$415$	3.31995e10	+	3.02560e10i	1.11928	+	1.02004i
$416$		0			0
$417$	−1.90028e10	−	6.51311e9i	−0.628455	−	0.215399i
$418$		0			0
$419$		−	2.94257e9i		−	0.0954708i	−0.998860	−	0.0477354i	$-0.984800\pi$
$419$		−	2.94257e9i		−	0.0954708i	0.998860	−	0.0477354i	$-0.0152004\pi$
$420$		0			0
$421$	3.68482e10			1.17297			0.586487	−	0.809959i	$-0.300511\pi$
$421$	3.68482e10			1.17297			0.586487	+	0.809959i	$0.300511\pi$
$422$		0			0
$423$	−1.86905e10	−	1.45176e10i	−0.583794	−	0.453453i
$424$		0			0
$425$	−1.76529e8	−	1.89871e9i	−0.00541077	−	0.0581973i
$426$		0			0
$427$			8.33083e9i			0.250598i
$428$		0			0
$429$	1.20508e10	+	4.13034e9i	0.355784	+	0.121943i
$430$		0			0
$431$			6.01364e10i			1.74272i	0.490641	+	0.871362i	$0.336763\pi$
$431$			6.01364e10i			1.74272i	−0.490641	+	0.871362i	$0.663237\pi$
$432$		0			0
$433$			9.53893e9i			0.271362i	0.990753	+	0.135681i	$0.0433221\pi$
$433$			9.53893e9i			0.271362i	−0.990753	+	0.135681i	$0.956678\pi$
$434$		0			0
$435$	4.35759e10	−	2.38937e10i	1.21700	−	0.667308i
$436$		0			0
$437$	−8.56227e8			−0.0234781
$438$		0			0
$439$	−5.74956e10			−1.54802			−0.774010	−	0.633173i	$-0.781752\pi$
$439$	−5.74956e10			−1.54802			−0.774010	+	0.633173i	$0.781752\pi$
$440$		0			0
$441$	2.48727e10	+	1.93195e10i	0.657611	+	0.510789i
$442$		0			0
$443$	−5.41194e10			−1.40520			−0.702600	−	0.711585i	$-0.747978\pi$
$443$	−5.41194e10			−1.40520			−0.702600	+	0.711585i	$0.747978\pi$
$444$		0			0
$445$	3.17917e10	−	3.48846e10i	0.810726	−	0.889598i
$446$		0			0
$447$	7.98712e9	−	2.33035e10i	0.200060	−	0.583701i
$448$		0			0
$449$			4.91595e10i			1.20954i	0.796399	+	0.604772i	$0.206736\pi$
$449$			4.91595e10i			1.20954i	−0.796399	+	0.604772i	$0.793264\pi$
$450$		0			0
$451$	−4.02578e10			−0.973071
$452$		0			0
$453$	−2.25747e10	−	7.73734e9i	−0.536079	−	0.183738i
$454$		0			0
$455$	−8.24495e9	−	7.51395e9i	−0.192372	−	0.175316i
$456$		0			0
$457$			3.97700e10i			0.911781i	0.890036	+	0.455891i	$0.150679\pi$
$457$			3.97700e10i			0.911781i	−0.890036	+	0.455891i	$0.849321\pi$
$458$		0			0
$459$	−1.42220e9	−	2.16975e9i	−0.0320412	−	0.0488831i
$460$		0			0
$461$		−	4.29664e10i		−	0.951317i	−0.879630	−	0.475658i	$-0.842210\pi$
$461$		−	4.29664e10i		−	0.951317i	0.879630	−	0.475658i	$-0.157790\pi$
$462$		0			0
$463$			8.71101e10i			1.89559i	0.318879	+	0.947795i	$0.396694\pi$
$463$			8.71101e10i			1.89559i	−0.318879	+	0.947795i	$0.603306\pi$
$464$		0			0
$465$	2.07694e10	+	3.78780e10i	0.444234	+	0.810168i
$466$		0			0
$467$	−8.13998e9			−0.171142			−0.0855708	−	0.996332i	$-0.527271\pi$
$467$	−8.13998e9			−0.171142			−0.0855708	+	0.996332i	$0.527271\pi$
$468$		0			0
$469$	−9.51418e9			−0.196644
$470$		0			0
$471$	1.55372e10	−	4.53317e10i	0.315710	−	0.921125i
$472$		0			0
$473$	1.90814e10			0.381212
$474$		0			0
$475$	−2.65897e9	−	2.85994e10i	−0.0522323	−	0.561801i
$476$		0			0
$477$	−6.63436e10	−	5.15313e10i	−1.28152	−	0.995400i
$478$		0			0
$479$			9.99358e10i			1.89836i	0.314729	+	0.949181i	$0.398086\pi$
$479$			9.99358e10i			1.89836i	−0.314729	+	0.949181i	$0.601914\pi$
$480$		0			0
$481$	1.29537e10			0.241998
$482$		0			0
$483$	−3.00348e8	+	8.76303e8i	−0.00551869	+	0.0161015i
$484$		0			0
$485$	−5.12548e10	+	5.62412e10i	−0.926334	+	1.01645i
$486$		0			0
$487$			6.38070e10i			1.13436i	0.823592	+	0.567182i	$0.191967\pi$
$487$			6.38070e10i			1.13436i	−0.823592	+	0.567182i	$0.808033\pi$
$488$		0			0
$489$	−1.26406e10	+	3.68805e10i	−0.221071	+	0.645002i
$490$		0			0
$491$			5.68113e10i			0.977482i	0.872429	+	0.488741i	$0.162544\pi$
$491$			5.68113e10i			0.977482i	−0.872429	+	0.488741i	$0.837456\pi$
$492$		0			0
$493$		−	4.79215e9i		−	0.0811228i
$494$		0			0
$495$	3.49670e10	−	6.05126e9i	0.582422	−	0.100792i
$496$		0			0
$497$	−1.65472e10			−0.271206
$498$		0			0
$499$	−6.67795e10			−1.07706			−0.538531	−	0.842606i	$-0.681021\pi$
$499$	−6.67795e10			−1.07706			−0.538531	+	0.842606i	$0.681021\pi$
$500$		0			0
$501$	9.94220e10	+	3.40763e10i	1.57809	+	0.540881i
$502$		0			0
$503$	−4.26338e10			−0.666011			−0.333006	−	0.942925i	$-0.608063\pi$
$503$	−4.26338e10			−0.666011			−0.333006	+	0.942925i	$0.608063\pi$
$504$		0			0
$505$	−4.25393e10	+	4.66777e10i	−0.654070	+	0.717702i
$506$		0			0
$507$	3.71983e10	+	1.27495e10i	0.562978	+	0.192957i
$508$		0			0
$509$		−	6.75807e9i		−	0.100682i	−0.998732	−	0.0503410i	$-0.983969\pi$
$509$		−	6.75807e9i		−	0.100682i	0.998732	−	0.0503410i	$-0.0160308\pi$
$510$		0			0
$511$	−4.25132e10			−0.623505
$512$		0			0
$513$	−2.14219e10	−	3.26820e10i	−0.309306	−	0.471888i
$514$		0			0
$515$	2.95112e10	−	3.23822e10i	0.419524	−	0.460338i
$516$		0			0
$517$		−	3.12160e10i		−	0.436933i
$518$		0			0
$519$	−1.09049e10	−	3.73759e9i	−0.150298	−	0.0515137i
$520$		0			0
$521$		−	9.33239e10i		−	1.26661i	−0.773903	−	0.633304i	$-0.781698\pi$
$521$		−	9.33239e10i		−	1.26661i	0.773903	−	0.633304i	$-0.218302\pi$
$522$		0			0
$523$		−	1.23745e10i		−	0.165394i	−0.996575	−	0.0826969i	$-0.973647\pi$
$523$		−	1.23745e10i		−	0.165394i	0.996575	−	0.0826969i	$-0.0263533\pi$
$524$		0			0
$525$	−3.02027e10	−	7.31079e9i	−0.397565	−	0.0962337i
$526$		0			0
$527$	4.16554e9			0.0540043
$528$		0			0
$529$	−7.81754e10			−0.998268
$530$		0			0
$531$	−4.55830e10	+	5.86855e10i	−0.573357	+	0.738164i
$532$		0			0
$533$	8.45409e10			1.04751
$534$		0			0
$535$	1.41994e10	+	1.29405e10i	0.173323	+	0.157956i
$536$		0			0
$537$	−7.13359e8	+	2.08132e9i	−0.00857850	+	0.0250289i
$538$		0			0
$539$			4.15412e10i			0.492180i
$540$		0			0
$541$	1.16854e11			1.36413			0.682066	−	0.731291i	$-0.261082\pi$
$541$	1.16854e11			1.36413			0.682066	+	0.731291i	$0.261082\pi$
$542$		0			0
$543$	8.47132e10	+	2.90349e10i	0.974432	+	0.333981i
$544$		0			0
$545$	−5.19969e10	−	4.73868e10i	−0.589375	−	0.537121i
$546$		0			0
$547$			7.76902e10i			0.867795i	0.900962	+	0.433897i	$0.142862\pi$
$547$			7.76902e10i			0.867795i	−0.900962	+	0.433897i	$0.857138\pi$
$548$		0			0
$549$	4.39525e10	+	3.41394e10i	0.483832	+	0.375809i
$550$		0			0
$551$		−	7.21820e10i		−	0.783110i
$552$		0			0
$553$		−	1.13827e10i		−	0.121715i
$554$		0			0
$555$	3.16405e10	−	1.73492e10i	0.333481	−	0.182855i
$556$		0			0
$557$	3.10264e10			0.322338			0.161169	−	0.986927i	$-0.448474\pi$
$557$	3.10264e10			0.322338			0.161169	+	0.986927i	$0.448474\pi$
$558$		0			0
$559$	−4.00707e10			−0.410374
$560$		0			0
$561$	1.10948e9	−	3.23706e9i	0.0112013	−	0.0326813i
$562$		0			0
$563$	−2.20379e10			−0.219349			−0.109675	−	0.993968i	$-0.534981\pi$
$563$	−2.20379e10			−0.219349			−0.109675	+	0.993968i	$0.534981\pi$
$564$		0			0
$565$	7.30656e10	+	6.65875e10i	0.717000	+	0.653430i
$566$		0			0
$567$	−4.09627e10	+	1.04600e10i	−0.396329	+	0.101204i
$568$		0			0
$569$		−	1.19586e11i		−	1.14086i	−0.821346	−	0.570431i	$-0.806776\pi$
$569$		−	1.19586e11i		−	1.14086i	0.821346	−	0.570431i	$-0.193224\pi$
$570$		0			0
$571$	−4.63953e10			−0.436445			−0.218223	−	0.975899i	$-0.570026\pi$
$571$	−4.63953e10			−0.436445			−0.218223	+	0.975899i	$0.570026\pi$
$572$		0			0
$573$	6.12635e10	−	1.78744e11i	0.568308	−	1.65811i
$574$		0			0
$575$	4.21086e8	+	4.52912e9i	0.00385212	+	0.0414326i
$576$		0			0
$577$			6.88056e10i			0.620755i	0.950613	+	0.310378i	$0.100456\pi$
$577$			6.88056e10i			0.620755i	−0.950613	+	0.310378i	$0.899544\pi$
$578$		0			0
$579$	5.11625e10	−	1.49273e11i	0.455237	−	1.32821i
$580$		0			0
$581$		−	7.05839e10i		−	0.619442i
$582$		0			0
$583$		−	1.10804e11i		−	0.959137i
$584$		0			0
$585$	−7.34303e10	+	1.27076e10i	−0.626977	+	0.108502i
$586$		0			0
$587$	4.11725e10			0.346780			0.173390	−	0.984853i	$-0.444528\pi$
$587$	4.11725e10			0.346780			0.173390	+	0.984853i	$0.444528\pi$
$588$		0			0
$589$	6.27436e10			0.521325
$590$		0			0
$591$	−2.99613e10	−	1.02691e10i	−0.245590	−	0.0841745i
$592$		0			0
$593$	1.89369e11			1.53140			0.765701	−	0.643197i	$-0.222392\pi$
$593$	1.89369e11			1.53140			0.765701	+	0.643197i	$0.222392\pi$
$594$		0			0
$595$	−2.01838e9	+	2.21474e9i	−0.0161040	+	0.0176707i
$596$		0			0
$597$	−8.10038e10	−	2.77636e10i	−0.637688	−	0.218564i
$598$		0			0
$599$		−	1.15097e11i		−	0.894040i	−0.894524	−	0.447020i	$-0.852485\pi$
$599$		−	1.15097e11i		−	0.894040i	0.894524	−	0.447020i	$-0.147515\pi$
$600$		0			0
$601$	−1.43025e11			−1.09626			−0.548131	−	0.836393i	$-0.684660\pi$
$601$	−1.43025e11			−1.09626			−0.548131	+	0.836393i	$0.684660\pi$
$602$		0			0
$603$	−3.89887e10	+	5.01957e10i	−0.294897	+	0.379662i
$604$		0			0
$605$	−6.44262e10	−	5.87142e10i	−0.480885	−	0.438250i
$606$		0			0
$607$		−	1.61784e11i		−	1.19174i	−0.803081	−	0.595870i	$-0.796807\pi$
$607$		−	1.61784e11i		−	1.19174i	0.803081	−	0.595870i	$-0.203193\pi$
$608$		0			0
$609$	−7.38745e10	−	2.53200e10i	−0.537063	−	0.184075i
$610$		0			0
$611$			6.55531e10i			0.470358i
$612$		0			0
$613$		−	2.20878e11i		−	1.56427i	−0.623112	−	0.782133i	$-0.714132\pi$
$613$		−	2.20878e11i		−	1.56427i	0.623112	−	0.782133i	$-0.285868\pi$
$614$		0			0
$615$	2.06499e11	−	1.13228e11i	1.44350	−	0.791505i
$616$		0			0
$617$	1.71444e11			1.18299			0.591495	−	0.806309i	$-0.298538\pi$
$617$	1.71444e11			1.18299			0.591495	+	0.806309i	$0.298538\pi$
$618$		0			0
$619$	1.87051e11			1.27408			0.637042	−	0.770829i	$-0.280158\pi$
$619$	1.87051e11			1.27408			0.637042	+	0.770829i	$0.280158\pi$
$620$		0			0
$621$	3.39246e9	+	5.17566e9i	0.0228112	+	0.0348016i
$622$		0			0
$623$	−7.41666e10			−0.492330
$624$		0			0
$625$	−1.49973e11	+	2.81299e10i	−0.982860	+	0.184352i
$626$		0			0
$627$	1.67116e10	−	4.87583e10i	0.108131	−	0.315485i
$628$		0			0
$629$		−	3.47958e9i		−	0.0222292i
$630$		0			0
$631$	−4.85806e10			−0.306440			−0.153220	−	0.988192i	$-0.548964\pi$
$631$	−4.85806e10			−0.306440			−0.153220	+	0.988192i	$0.548964\pi$
$632$		0			0
$633$	2.69566e11	+	9.23921e10i	1.67900	+	0.575467i
$634$		0			0
$635$	−4.80776e10	+	5.27549e10i	−0.295698	+	0.324465i
$636$		0			0
$637$		−	8.72360e10i		−	0.529832i
$638$		0			0
$639$	−6.78099e10	+	8.73013e10i	−0.406715	+	0.523622i
$640$		0			0
$641$			1.11927e11i			0.662984i	0.943458	+	0.331492i	$0.107552\pi$
$641$			1.11927e11i			0.662984i	−0.943458	+	0.331492i	$0.892448\pi$
$642$		0			0
$643$			4.88967e10i			0.286046i	0.989719	+	0.143023i	$0.0456822\pi$
$643$			4.88967e10i			0.286046i	−0.989719	+	0.143023i	$0.954318\pi$
$644$		0			0
$645$	−9.78764e10	+	5.36679e10i	−0.565508	+	0.310081i
$646$		0			0
$647$	1.53100e11			0.873694			0.436847	−	0.899536i	$-0.356095\pi$
$647$	1.53100e11			0.873694			0.436847	+	0.899536i	$0.356095\pi$
$648$		0			0
$649$	−9.80137e10			−0.552469
$650$		0			0
$651$	2.20092e10	−	6.42148e10i	0.122541	−	0.357529i
$652$		0			0
$653$	2.87587e11			1.58167			0.790836	−	0.612028i	$-0.209646\pi$
$653$	2.87587e11			1.58167			0.790836	+	0.612028i	$0.209646\pi$
$654$		0			0
$655$	2.14153e10	−	2.34987e10i	0.116348	−	0.127667i
$656$		0			0
$657$	−1.74217e11	+	2.24295e11i	−0.935040	+	1.20381i
$658$		0			0
$659$		−	3.92994e10i		−	0.208374i	−0.994558	−	0.104187i	$-0.966776\pi$
$659$		−	3.92994e10i		−	0.208374i	0.994558	−	0.104187i	$-0.0332241\pi$
$660$		0			0
$661$	5.99838e9			0.0314216			0.0157108	−	0.999877i	$-0.494999\pi$
$661$	5.99838e9			0.0314216			0.0157108	+	0.999877i	$0.494999\pi$
$662$		0			0
$663$	−2.32990e9	+	6.79777e9i	−0.0120582	+	0.0351813i
$664$		0			0
$665$	−3.04020e10	+	3.33596e10i	−0.155459	+	0.170583i
$666$		0			0
$667$			1.14310e10i			0.0577541i
$668$		0			0
$669$	5.68270e10	−	1.65800e11i	0.283694	−	0.827713i
$670$		0			0
$671$			7.34074e10i			0.362118i
$672$		0			0
$673$			3.78758e11i			1.84630i	0.384442	+	0.923149i	$0.374394\pi$
$673$			3.78758e11i			1.84630i	−0.384442	+	0.923149i	$0.625606\pi$
$674$		0			0
$675$	−1.62340e11	+	1.29387e11i	−0.782009	+	0.623268i
$676$		0			0
$677$	−1.64834e11			−0.784681			−0.392340	−	0.919820i	$-0.628334\pi$
$677$	−1.64834e11			−0.784681			−0.392340	+	0.919820i	$0.628334\pi$
$678$		0			0
$679$	1.19572e11			0.562535
$680$		0			0
$681$	−2.81076e11	−	9.63371e10i	−1.30688	−	0.447925i
$682$		0			0
$683$	−3.32594e11			−1.52838			−0.764189	−	0.644992i	$-0.776861\pi$
$683$	−3.32594e11			−1.52838			−0.764189	+	0.644992i	$0.776861\pi$
$684$		0			0
$685$	−7.88886e10	−	7.18943e10i	−0.358304	−	0.326537i
$686$		0			0
$687$	9.39199e10	+	3.21905e10i	0.421629	+	0.144511i
$688$		0			0
$689$			2.32687e11i			1.03251i
$690$		0			0
$691$	1.93057e11			0.846787			0.423394	−	0.905946i	$-0.360839\pi$
$691$	1.93057e11			0.846787			0.423394	+	0.905946i	$0.360839\pi$
$692$		0			0
$693$	−4.40394e10	−	3.42069e10i	−0.190945	−	0.148314i
$694$		0			0
$695$	1.14563e11	+	1.04405e11i	0.491025	+	0.447490i
$696$		0			0
$697$		−	2.27092e10i		−	0.0962211i
$698$		0			0
$699$	1.98854e11	+	6.81561e10i	0.832964	+	0.285493i
$700$		0			0
$701$		−	1.43333e11i		−	0.593572i	−0.954944	−	0.296786i	$-0.904085\pi$
$701$		−	1.43333e11i		−	0.593572i	0.954944	−	0.296786i	$-0.0959148\pi$
$702$		0			0
$703$		−	5.24114e10i		−	0.214587i
$704$		0			0
$705$	8.77973e10	+	1.60119e11i	0.355406	+	0.648168i
$706$		0			0
$707$	9.92394e10			0.397197
$708$		0			0
$709$	4.78173e11			1.89235			0.946173	−	0.323662i	$-0.104914\pi$
$709$	4.78173e11			1.89235			0.946173	+	0.323662i	$0.104914\pi$
$710$		0			0
$711$	−6.00540e10	−	4.66460e10i	−0.234998	−	0.182531i
$712$		0			0
$713$	−9.93635e9			−0.0384475
$714$		0			0
$715$	−7.26507e10	−	6.62094e10i	−0.277981	−	0.253335i
$716$		0			0
$717$	−1.05138e11	+	3.06755e11i	−0.397818	+	1.16069i
$718$		0			0
$719$		−	2.12668e11i		−	0.795769i	−0.917436	−	0.397885i	$-0.869744\pi$
$719$		−	2.12668e11i		−	0.795769i	0.917436	−	0.397885i	$-0.130256\pi$
$720$		0			0
$721$	−6.88463e10			−0.254765
$722$		0			0
$723$	−1.75644e11	−	6.02010e10i	−0.642807	−	0.220318i
$724$		0			0
$725$	−3.81816e11	+	3.54986e10i	−1.38198	+	0.128487i
$726$		0			0
$727$		−	4.90130e11i		−	1.75458i	−0.479959	−	0.877291i	$-0.659349\pi$
$727$		−	4.90130e11i		−	1.75458i	0.479959	−	0.877291i	$-0.340651\pi$
$728$		0			0
$729$	−1.12678e11	+	2.58979e11i	−0.398959	+	0.916969i
$730$		0			0
$731$			1.07637e10i			0.0376957i
$732$		0			0
$733$		−	4.32453e11i		−	1.49804i	−0.662548	−	0.749020i	$-0.730525\pi$
$733$		−	4.32453e11i		−	1.49804i	0.662548	−	0.749020i	$-0.269475\pi$
$734$		0			0
$735$	−1.16838e11	−	2.13082e11i	−0.400344	−	0.730125i
$736$		0			0
$737$	−8.38345e10			−0.284153
$738$		0			0
$739$	5.43589e11			1.82261			0.911304	−	0.411734i	$-0.135077\pi$
$739$	5.43589e11			1.82261			0.911304	+	0.411734i	$0.135077\pi$
$740$		0			0
$741$	−3.50942e10	+	1.02392e11i	−0.116402	+	0.339619i
$742$		0			0
$743$	−5.04564e11			−1.65562			−0.827811	−	0.561007i	$-0.810414\pi$
$743$	−5.04564e11			−1.65562			−0.827811	+	0.561007i	$0.810414\pi$
$744$		0			0
$745$	−1.28034e11	+	1.40490e11i	−0.415623	+	0.456057i
$746$		0			0
$747$	−3.72393e11	−	2.89250e11i	−1.19597	−	0.928947i
$748$		0			0
$749$		−	3.01888e10i		−	0.0959221i
$750$		0			0
$751$	4.04292e11			1.27097			0.635485	−	0.772113i	$-0.280800\pi$
$751$	4.04292e11			1.27097			0.635485	+	0.772113i	$0.280800\pi$
$752$		0			0
$753$	−1.58278e11	+	4.61798e11i	−0.492314	+	1.43639i
$754$		0			0
$755$	1.36096e11	+	1.24030e11i	0.418849	+	0.381714i
$756$		0			0
$757$			1.17725e11i			0.358497i	0.983804	+	0.179248i	$0.0573666\pi$
$757$			1.17725e11i			0.358497i	−0.983804	+	0.179248i	$0.942633\pi$
$758$		0			0
$759$	−2.64652e9	+	7.72157e9i	−0.00797460	+	0.0232669i
$760$		0			0
$761$			5.94214e11i			1.77176i	0.463917	+	0.885879i	$0.346443\pi$
$761$			5.94214e11i			1.77176i	−0.463917	+	0.885879i	$0.653557\pi$
$762$		0			0
$763$			1.10548e11i			0.326177i
$764$		0			0
$765$	3.41347e9	+	1.97247e10i	0.00996669	+	0.0575922i
$766$		0			0
$767$	2.05827e11			0.594733
$768$		0			0
$769$	4.55193e11			1.30164			0.650820	−	0.759232i	$-0.274425\pi$
$769$	4.55193e11			1.30164			0.650820	+	0.759232i	$0.274425\pi$
$770$		0			0
$771$	−3.91906e10	−	1.34323e10i	−0.110908	−	0.0380132i
$772$		0			0
$773$	−1.90114e11			−0.532470			−0.266235	−	0.963908i	$-0.585780\pi$
$773$	−1.90114e11			−0.532470			−0.266235	+	0.963908i	$0.585780\pi$
$774$		0			0
$775$	−3.08568e10	−	3.31890e11i	−0.0855352	−	0.920000i
$776$		0			0
$777$	−5.36403e10	−	1.83849e10i	−0.147166	−	0.0504402i
$778$		0			0
$779$		−	3.42058e11i		−	0.928860i
$780$		0			0
$781$	−1.45806e11			−0.391898
$782$		0			0
$783$	−4.36320e11	+	2.85993e11i	−1.16080	+	0.760866i
$784$		0			0
$785$	−2.49061e11	+	2.73292e11i	−0.655885	+	0.719694i
$786$		0			0
$787$			3.73829e11i			0.974483i	0.873267	+	0.487241i	$0.161997\pi$
$787$			3.73829e11i			0.974483i	−0.873267	+	0.487241i	$0.838003\pi$
$788$		0			0
$789$	4.16591e10	+	1.42784e10i	0.107498	+	0.0368445i
$790$		0			0
$791$		−	1.55341e11i		−	0.396809i
$792$		0			0
$793$		−	1.54155e11i		−	0.389819i
$794$		0			0
$795$	3.11644e11	+	5.68358e11i	0.780172	+	1.42283i
$796$		0			0
$797$	9.22241e10			0.228566			0.114283	−	0.993448i	$-0.463543\pi$
$797$	9.22241e10			0.228566			0.114283	+	0.993448i	$0.463543\pi$
$798$		0			0
$799$	1.76087e10			0.0432057
$800$		0			0
$801$	−3.03932e11	+	3.91295e11i	−0.738323	+	0.950548i
$802$		0			0
$803$	−3.74606e11			−0.900976
$804$		0			0
$805$	4.81458e9	−	5.28297e9i	0.0114650	−	0.0125804i
$806$		0			0
$807$	−1.61423e11	+	4.70972e11i	−0.380602	+	1.11045i
$808$		0			0
$809$		−	4.59130e11i		−	1.07187i	−0.844260	−	0.535934i	$-0.819960\pi$
$809$		−	4.59130e11i		−	1.07187i	0.844260	−	0.535934i	$-0.180040\pi$
$810$		0			0
$811$	−3.20148e11			−0.740060			−0.370030	−	0.929020i	$-0.620653\pi$
$811$	−3.20148e11			−0.740060			−0.370030	+	0.929020i	$0.620653\pi$
$812$		0			0
$813$	7.56056e11	+	2.59134e11i	1.73058	+	0.593146i
$814$		0			0
$815$	2.02629e11	−	2.22341e11i	0.459272	−	0.503953i
$816$		0			0
$817$			1.62129e11i			0.363892i
$818$		0			0
$819$	9.24822e10	+	7.18341e10i	0.205552	+	0.159660i
$820$		0			0
$821$			2.06997e11i			0.455608i	0.973707	+	0.227804i	$0.0731545\pi$
$821$			2.06997e11i			0.455608i	−0.973707	+	0.227804i	$0.926846\pi$
$822$		0			0
$823$			3.04522e11i			0.663774i	0.943319	+	0.331887i	$0.107685\pi$
$823$			3.04522e11i			0.663774i	−0.943319	+	0.331887i	$0.892315\pi$
$824$		0			0
$825$	−2.66132e11	−	6.44193e10i	−0.574489	−	0.139059i
$826$		0			0
$827$	7.16880e11			1.53258			0.766292	−	0.642493i	$-0.222100\pi$
$827$	7.16880e11			1.53258			0.766292	+	0.642493i	$0.222100\pi$
$828$		0			0
$829$	4.07865e11			0.863572			0.431786	−	0.901976i	$-0.357884\pi$
$829$	4.07865e11			0.863572			0.431786	+	0.901976i	$0.357884\pi$
$830$		0			0
$831$	−2.23566e10	+	6.52284e10i	−0.0468816	+	0.136783i
$832$		0			0
$833$	−2.34331e10			−0.0486688
$834$		0			0
$835$	−5.99386e11	−	5.46244e11i	−1.23299	−	1.12368i
$836$		0			0
$837$	−2.48597e11	−	3.79268e11i	−0.506517	−	0.772760i
$838$		0			0
$839$			8.70596e11i			1.75699i	0.477753	+	0.878494i	$0.341452\pi$
$839$			8.70596e11i			1.75699i	−0.477753	+	0.878494i	$0.658548\pi$
$840$		0			0
$841$	−4.63419e11			−0.926381
$842$		0			0
$843$	−9.12160e10	+	2.66134e11i	−0.180618	+	0.526976i
$844$		0			0
$845$	−2.24257e11	−	2.04375e11i	−0.439866	−	0.400867i
$846$		0			0
$847$			1.36974e11i			0.266136i
$848$		0			0
$849$	2.52268e11	−	7.36025e11i	0.485547	−	1.41665i
$850$		0			0
$851$			8.30009e9i			0.0158258i
$852$		0			0
$853$			1.49120e11i			0.281670i	0.990033	+	0.140835i	$0.0449788\pi$
$853$			1.49120e11i			0.281670i	−0.990033	+	0.140835i	$0.955021\pi$
$854$		0			0
$855$	5.14156e10	+	2.97104e11i	0.0962124	+	0.555960i
$856$		0			0
$857$	5.02032e11			0.930697			0.465348	−	0.885128i	$-0.345929\pi$
$857$	5.02032e11			0.930697			0.465348	+	0.885128i	$0.345929\pi$
$858$		0			0
$859$	6.42420e11			1.17990			0.589952	−	0.807438i	$-0.299147\pi$
$859$	6.42420e11			1.17990			0.589952	+	0.807438i	$0.299147\pi$
$860$		0			0
$861$	−3.50078e11	−	1.19987e11i	−0.637019	−	0.218335i
$862$		0			0
$863$	−4.15471e11			−0.749028			−0.374514	−	0.927221i	$-0.622190\pi$
$863$	−4.15471e11			−0.749028			−0.374514	+	0.927221i	$0.622190\pi$
$864$		0			0
$865$	6.57424e10	+	5.99137e10i	0.117431	+	0.107019i
$866$		0			0
$867$	−5.32686e11	−	1.82575e11i	−0.942747	−	0.323121i
$868$		0			0
$869$		−	1.00299e11i		−	0.175881i
$870$		0			0
$871$	1.76051e11			0.305891
$872$		0			0
$873$	4.90001e11	−	6.30848e11i	0.843606	−	1.08609i
$874$		0			0
$875$	1.91411e11	+	1.44409e11i	0.326540	+	0.246355i
$876$		0			0
$877$		−	9.26709e11i		−	1.56655i	−0.621673	−	0.783277i	$-0.713547\pi$
$877$		−	9.26709e11i		−	1.56655i	0.621673	−	0.783277i	$-0.286453\pi$
$878$		0			0
$879$	1.16115e11	+	3.97977e10i	0.194506	+	0.0666657i
$880$		0			0
$881$			1.15034e11i			0.190952i	0.995432	+	0.0954758i	$0.0304373\pi$
$881$			1.15034e11i			0.190952i	−0.995432	+	0.0954758i	$0.969563\pi$
$882$		0			0
$883$			2.46808e11i			0.405990i	0.979180	+	0.202995i	$0.0650676\pi$
$883$			2.46808e11i			0.405990i	−0.979180	+	0.202995i	$0.934932\pi$
$884$		0			0
$885$	5.02752e11	−	2.75671e11i	0.819560	−	0.449384i
$886$		0			0
$887$	4.76996e11			0.770585			0.385292	−	0.922795i	$-0.374101\pi$
$887$	4.76996e11			0.770585			0.385292	+	0.922795i	$0.374101\pi$
$888$		0			0
$889$	1.12160e11			0.179568
$890$		0			0
$891$	−3.60944e11	+	9.21685e10i	−0.572702	+	0.146242i
$892$		0			0
$893$	2.65232e11			0.417081
$894$		0			0
$895$	1.14352e10	−	1.25476e10i	0.0178218	−	0.0195556i
$896$		0			0
$897$	5.55766e9	−	1.62152e10i	0.00858465	−	0.0250468i
$898$		0			0
$899$		−	8.37658e11i		−	1.28241i
$900$		0			0
$901$	6.25037e10			0.0948433
$902$		0			0
$903$	1.65930e11	+	5.68716e10i	0.249560	+	0.0855352i
$904$		0			0
$905$	−5.10711e11	−	4.65431e11i	−0.761344	−	0.693843i
$906$		0			0
$907$		−	6.78246e11i		−	1.00221i	−0.865387	−	0.501104i	$-0.832927\pi$
$907$		−	6.78246e11i		−	1.00221i	0.865387	−	0.501104i	$-0.167073\pi$
$908$		0			0
$909$	4.06679e11	−	5.23576e11i	0.595657	−	0.766874i
$910$		0			0
$911$		−	4.37255e11i		−	0.634835i	−0.948286	−	0.317418i	$-0.897184\pi$
$911$		−	4.37255e11i		−	0.634835i	0.948286	−	0.317418i	$-0.102816\pi$
$912$		0			0
$913$		−	6.21952e11i		−	0.895105i
$914$		0			0
$915$	−2.06464e11	−	3.76536e11i	−0.294550	−	0.537183i
$916$		0			0
$917$	−4.99595e10			−0.0706546
$918$		0			0
$919$	−4.60392e11			−0.645455			−0.322728	−	0.946492i	$-0.604600\pi$
$919$	−4.60392e11			−0.645455			−0.322728	+	0.946492i	$0.604600\pi$
$920$		0			0
$921$	4.62243e11	−	1.34865e12i	0.642439	−	1.87440i
$922$		0			0
$923$	3.06192e11			0.421877
$924$		0			0
$925$	−2.77237e11	+	2.57755e10i	−0.378690	+	0.0352079i
$926$		0			0
$927$	−2.82129e11	+	3.63225e11i	−0.382058	+	0.491878i
$928$		0			0
$929$			1.25173e11i			0.168054i	0.996463	+	0.0840270i	$0.0267782\pi$
$929$			1.25173e11i			0.168054i	−0.996463	+	0.0840270i	$0.973222\pi$
$930$		0			0
$931$	−3.52963e11			−0.469819
$932$		0			0
$933$	3.11665e11	−	9.09324e11i	0.411303	−	1.20003i
$934$		0			0
$935$	−1.77850e10	+	1.95153e10i	−0.0232706	+	0.0255345i
$936$		0			0
$937$			3.77571e11i			0.489824i	0.969545	+	0.244912i	$0.0787590\pi$
$937$			3.77571e11i			0.489824i	−0.969545	+	0.244912i	$0.921241\pi$
$938$		0			0
$939$	5.28950e10	−	1.54328e11i	0.0680381	−	0.198510i
$940$		0			0
$941$		−	6.06020e10i		−	0.0772910i	−0.999253	−	0.0386455i	$-0.987696\pi$
$941$		−	6.06020e10i		−	0.0772910i	0.999253	−	0.0386455i	$-0.0123043\pi$
$942$		0			0
$943$			5.41698e10i			0.0685031i
$944$		0			0
$945$	3.22106e11	+	5.15970e10i	0.403897	+	0.0646990i
$946$		0			0
$947$	1.28296e12			1.59520			0.797598	−	0.603189i	$-0.206104\pi$
$947$	1.28296e12			1.59520			0.797598	+	0.603189i	$0.206104\pi$
$948$		0			0
$949$	7.86668e11			0.969899
$950$		0			0
$951$	4.53102e11	+	1.55298e11i	0.553954	+	0.189864i
$952$		0			0
$953$	9.26120e11			1.12278			0.561391	−	0.827551i	$-0.310266\pi$
$953$	9.26120e11			1.12278			0.561391	+	0.827551i	$0.310266\pi$
$954$		0			0
$955$	−9.82056e11	+	1.07760e12i	−1.18065	+	1.29551i
$956$		0			0
$957$	−6.50947e11	−	2.23108e11i	−0.776065	−	0.265992i
$958$		0			0
$959$			1.67721e11i			0.198296i
$960$		0			0
$961$	−1.24764e11			−0.146283
$962$		0			0
$963$	−1.59273e11	−	1.23713e11i	−0.185198	−	0.143850i
$964$		0			0
$965$	−8.20137e11	+	8.99925e11i	−0.945752	+	1.03776i
$966$		0			0
$967$			5.95759e11i			0.681341i	0.940183	+	0.340671i	$0.110654\pi$
$967$			5.95759e11i			0.681341i	−0.940183	+	0.340671i	$0.889346\pi$
$968$		0			0
$969$	2.75042e10	+	9.42692e9i	0.0311964	+	0.0106924i
$970$		0			0
$971$		−	1.75041e12i		−	1.96908i	−0.175162	−	0.984540i	$-0.556045\pi$
$971$		−	1.75041e12i		−	1.96908i	0.175162	−	0.984540i	$-0.443955\pi$
$972$		0			0
$973$		−	2.43566e11i		−	0.271748i
$974$		0			0
$975$	5.58874e11	+	1.35280e11i	0.618436	+	0.149697i
$976$		0			0
$977$	−4.97635e11			−0.546176			−0.273088	−	0.961989i	$-0.588045\pi$
$977$	−4.97635e11			−0.546176			−0.273088	+	0.961989i	$0.588045\pi$
$978$		0			0
$979$	−6.53522e11			−0.711425
$980$		0			0
$981$	5.83240e11	+	4.53023e11i	0.629755	+	0.489152i
$982$		0			0
$983$	2.41169e10			0.0258289			0.0129145	−	0.999917i	$-0.495889\pi$
$983$	2.41169e10			0.0258289			0.0129145	+	0.999917i	$0.495889\pi$
$984$		0			0
$985$	1.80628e11	+	1.64613e11i	0.191884	+	0.174872i
$986$		0			0
$987$	9.30383e10	−	2.71451e11i	0.0980377	−	0.286038i
$988$		0			0
$989$		−	2.56754e10i		−	0.0268369i
$990$		0			0
$991$	−3.00351e11			−0.311411			−0.155705	−	0.987804i	$-0.549765\pi$
$991$	−3.00351e11			−0.311411			−0.155705	+	0.987804i	$0.549765\pi$
$992$		0			0
$993$	1.01011e12	+	3.46210e11i	1.03890	+	0.356076i
$994$		0			0
$995$	4.88348e11	+	4.45051e11i	0.498238	+	0.454064i
$996$		0			0
$997$			1.33535e12i			1.35149i	0.737134	+	0.675746i	$0.236178\pi$
$997$			1.33535e12i			1.35149i	−0.737134	+	0.675746i	$0.763822\pi$
$998$		0			0
$999$	−3.16812e11	+	2.07660e11i	−0.318083	+	0.208492i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.9.c.a.89.44	yes	48
3.2	odd	2	inner	120.9.c.a.89.6	yes	48
4.3	odd	2		240.9.c.f.209.5		48
5.4	even	2	inner	120.9.c.a.89.5	✓	48
12.11	even	2		240.9.c.f.209.43		48
15.14	odd	2	inner	120.9.c.a.89.43	yes	48
20.19	odd	2		240.9.c.f.209.44		48
60.59	even	2		240.9.c.f.209.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.9.c.a.89.5	✓	48	5.4	even	2	inner
120.9.c.a.89.6	yes	48	3.2	odd	2	inner
120.9.c.a.89.43	yes	48	15.14	odd	2	inner
120.9.c.a.89.44	yes	48	1.1	even	1	trivial
240.9.c.f.209.5		48	4.3	odd	2
240.9.c.f.209.6		48	60.59	even	2
240.9.c.f.209.43		48	12.11	even	2
240.9.c.f.209.44		48	20.19	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	120.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(76.6243 + 26.2625i) q^{3} +(-461.945 - 420.989i) q^{5} +982.121i q^{7} +(5181.56 + 4024.69i) q^{9} +8653.99i q^{11} -18173.3i q^{13} +(-24340.0 - 44389.8i) q^{15} -4881.66 q^{17} -73530.2 q^{19} +(-25793.0 + 75254.3i) q^{21} +11644.6 q^{23} +(36161.6 + 388948. i) q^{25} +(291335. + 444470. i) q^{27} +981664. i q^{29} -853304. q^{31} +(-227276. + 663106. i) q^{33} +(413462. - 453686. i) q^{35} +712787. i q^{37} +(477276. - 1.39251e6i) q^{39} +4.65194e6i q^{41} -2.20493e6i q^{43} +(-699245. - 4.04057e6i) q^{45} -3.60712e6 q^{47} +4.80024e6 q^{49} +(-374053. - 128205. i) q^{51} -1.28038e7 q^{53} +(3.64323e6 - 3.99767e6i) q^{55} +(-5.63420e6 - 1.93109e6i) q^{57} +1.13258e7i q^{59} +8.48249e6 q^{61} +(-3.95273e6 + 5.08892e6i) q^{63} +(-7.65074e6 + 8.39505e6i) q^{65} +9.68738e6i q^{67} +(892256. + 305815. i) q^{69} +1.68485e7i q^{71} +4.32871e7i q^{73} +(-7.44389e6 + 3.07525e7i) q^{75} -8.49926e6 q^{77} -1.15899e7 q^{79} +(1.06504e7 + 4.17084e7i) q^{81} -7.18688e7 q^{83} +(2.25506e6 + 2.05512e6i) q^{85} +(-2.57810e7 + 7.52193e7i) q^{87} +7.55168e7i q^{89} +1.78483e7 q^{91} +(-6.53838e7 - 2.24099e7i) q^{93} +(3.39669e7 + 3.09554e7i) q^{95} -1.21749e8i q^{97} +(-3.48297e7 + 4.48412e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2528 q^{9} + 132352 q^{15} + 116176 q^{21} + 56976 q^{25} + 1395648 q^{31} + 6888832 q^{39} - 4287056 q^{45} - 30813552 q^{49} - 22815168 q^{51} - 6062784 q^{55} + 14031936 q^{61} + 2522608 q^{69}+ \cdots - 21719360 q^{99}+O(q^{100}) \) 48 * q + 2528 * q^9 + 132352 * q^15 + 116176 * q^21 + 56976 * q^25 + 1395648 * q^31 + 6888832 * q^39 - 4287056 * q^45 - 30813552 * q^49 - 22815168 * q^51 - 6062784 * q^55 + 14031936 * q^61 + 2522608 * q^69 + 41684416 * q^75 + 19866432 * q^79 - 93539312 * q^81 - 116297664 * q^85 + 16826880 * q^91 - 21719360 * q^99

Introduction

L-functions

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Database

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