LMFDB - Embedded newform 120.9.c.a.89.12

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			89.12
Character	$\chi$	$=$	120.89
Dual form			120.9.c.a.89.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-58.3695 + 56.1605i) q^{3} +(-617.515 + 96.4387i) q^{5} +3509.51i q^{7} +(252.988 - 6556.12i) q^{9} -20700.8i q^{11} -21216.0i q^{13} +(30628.0 - 40309.0i) q^{15} +140324. q^{17} -182928. q^{19} +(-197096. - 204848. i) q^{21} -406324. q^{23} +(372024. - 119105. i) q^{25} +(353429. + 396885. i) q^{27} -85814.2i q^{29} +469925. q^{31} +(1.16257e6 + 1.20830e6i) q^{33} +(-338453. - 2.16717e6i) q^{35} -2.30493e6i q^{37} +(1.19150e6 + 1.23837e6i) q^{39} +1.66350e6i q^{41} +1.85333e6i q^{43} +(476040. + 4.07290e6i) q^{45} +5.76843e6 q^{47} -6.55186e6 q^{49} +(-8.19062e6 + 7.88066e6i) q^{51} -5.45851e6 q^{53} +(1.99636e6 + 1.27831e7i) q^{55} +(1.06774e7 - 1.02733e7i) q^{57} +9.28283e6i q^{59} +7.59067e6 q^{61} +(2.30088e7 + 887863. i) q^{63} +(2.04604e6 + 1.31012e7i) q^{65} +3.94772e7i q^{67} +(2.37169e7 - 2.28194e7i) q^{69} -1.39205e7i q^{71} +1.62493e7i q^{73} +(-1.50259e7 + 2.78452e7i) q^{75} +7.26498e7 q^{77} +9.06004e6 q^{79} +(-4.29187e7 - 3.31724e6i) q^{81} +4.45484e7 q^{83} +(-8.66520e7 + 1.35326e7i) q^{85} +(4.81937e6 + 5.00893e6i) q^{87} -6.34613e6i q^{89} +7.44578e7 q^{91} +(-2.74293e7 + 2.63913e7i) q^{93} +(1.12961e8 - 1.76413e7i) q^{95} +1.45115e8i q^{97} +(-1.35717e8 - 5.23706e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−58.3695	+	56.1605i	−0.720611	+	0.693340i
$3$	−58.3695	+	56.1605i	−0.720611	+	0.693340i
$4$		0			0
$5$	−617.515	+	96.4387i	−0.988024	+	0.154302i
$5$	−617.515	+	96.4387i	−0.988024	+	0.154302i
$6$		0			0
$7$			3509.51i			1.46169i	0.682545	+	0.730843i	$0.260873\pi$
$7$			3509.51i			1.46169i	−0.682545	+	0.730843i	$0.739127\pi$
$8$		0			0
$9$	252.988	−	6556.12i	0.0385593	−	0.999256i
$10$		0			0
$11$		−	20700.8i		−	1.41389i	−0.707266	−	0.706947i	$-0.750072\pi$
$11$		−	20700.8i		−	1.41389i	0.707266	−	0.706947i	$-0.249928\pi$
$12$		0			0
$13$		−	21216.0i		−	0.742831i	−0.928467	−	0.371416i	$-0.878872\pi$
$13$		−	21216.0i		−	0.742831i	0.928467	−	0.371416i	$-0.121128\pi$
$14$		0			0
$15$	30628.0	−	40309.0i	0.604997	−	0.796228i
$16$		0			0
$17$	140324.			1.68010			0.840051	−	0.542508i	$-0.182525\pi$
$17$	140324.			1.68010			0.840051	+	0.542508i	$0.182525\pi$
$18$		0			0
$19$	−182928.			−1.40367			−0.701837	−	0.712338i	$-0.747636\pi$
$19$	−182928.			−1.40367			−0.701837	+	0.712338i	$0.747636\pi$
$20$		0			0
$21$	−197096.	−	204848.i	−1.01345	−	1.05331i
$22$		0			0
$23$	−406324.			−1.45198			−0.725991	−	0.687704i	$-0.758619\pi$
$23$	−406324.			−1.45198			−0.725991	+	0.687704i	$0.758619\pi$
$24$		0			0
$25$	372024.	−	119105.i	0.952382	−	0.304908i
$26$		0			0
$27$	353429.	+	396885.i	0.665038	+	0.746809i
$28$		0			0
$29$		−	85814.2i		−	0.121330i	−0.998158	−	0.0606649i	$-0.980678\pi$
$29$		−	85814.2i		−	0.121330i	0.998158	−	0.0606649i	$-0.0193221\pi$
$30$		0			0
$31$	469925.			0.508841			0.254420	−	0.967094i	$-0.418115\pi$
$31$	469925.			0.508841			0.254420	+	0.967094i	$0.418115\pi$
$32$		0			0
$33$	1.16257e6	+	1.20830e6i	0.980309	+	1.01887i
$34$		0			0
$35$	−338453.	−	2.16717e6i	−0.225541	−	1.44418i
$36$		0			0
$37$		−	2.30493e6i		−	1.22985i	−0.788586	−	0.614924i	$-0.789187\pi$
$37$		−	2.30493e6i		−	1.22985i	0.788586	−	0.614924i	$-0.210813\pi$
$38$		0			0
$39$	1.19150e6	+	1.23837e6i	0.515035	+	0.535292i
$40$		0			0
$41$			1.66350e6i			0.588692i	0.955699	+	0.294346i	$0.0951018\pi$
$41$			1.66350e6i			0.588692i	−0.955699	+	0.294346i	$0.904898\pi$
$42$		0			0
$43$			1.85333e6i			0.542098i	0.962565	+	0.271049i	$0.0873706\pi$
$43$			1.85333e6i			0.542098i	−0.962565	+	0.271049i	$0.912629\pi$
$44$		0			0
$45$	476040.	+	4.07290e6i	0.116090	+	0.993239i
$46$		0			0
$47$	5.76843e6			1.18213			0.591066	−	0.806623i	$-0.298707\pi$
$47$	5.76843e6			1.18213			0.591066	+	0.806623i	$0.298707\pi$
$48$		0			0
$49$	−6.55186e6			−1.13653
$50$		0			0
$51$	−8.19062e6	+	7.88066e6i	−1.21070	+	1.16488i
$52$		0			0
$53$	−5.45851e6			−0.691784			−0.345892	−	0.938274i	$-0.612424\pi$
$53$	−5.45851e6			−0.691784			−0.345892	+	0.938274i	$0.612424\pi$
$54$		0			0
$55$	1.99636e6	+	1.27831e7i	0.218167	+	1.39696i
$56$		0			0
$57$	1.06774e7	−	1.02733e7i	1.01150	−	0.973223i
$58$		0			0
$59$			9.28283e6i			0.766077i	0.923732	+	0.383038i	$0.125122\pi$
$59$			9.28283e6i			0.766077i	−0.923732	+	0.383038i	$0.874878\pi$
$60$		0			0
$61$	7.59067e6			0.548228			0.274114	−	0.961697i	$-0.411615\pi$
$61$	7.59067e6			0.548228			0.274114	+	0.961697i	$0.411615\pi$
$62$		0			0
$63$	2.30088e7	+	887863.i	1.46060	+	0.0563617i
$64$		0			0
$65$	2.04604e6	+	1.31012e7i	0.114620	+	0.733935i
$66$		0			0
$67$			3.94772e7i			1.95906i	0.201306	+	0.979528i	$0.435482\pi$
$67$			3.94772e7i			1.95906i	−0.201306	+	0.979528i	$0.564518\pi$
$68$		0			0
$69$	2.37169e7	−	2.28194e7i	1.04631	−	1.00672i
$70$		0			0
$71$		−	1.39205e7i		−	0.547800i	−0.961758	−	0.273900i	$-0.911686\pi$
$71$		−	1.39205e7i		−	0.547800i	0.961758	−	0.273900i	$-0.0883137\pi$
$72$		0			0
$73$			1.62493e7i			0.572194i	0.958201	+	0.286097i	$0.0923579\pi$
$73$			1.62493e7i			0.572194i	−0.958201	+	0.286097i	$0.907642\pi$
$74$		0			0
$75$	−1.50259e7	+	2.78452e7i	−0.474892	+	0.880044i
$76$		0			0
$77$	7.26498e7			2.06667
$78$		0			0
$79$	9.06004e6			0.232607			0.116303	−	0.993214i	$-0.462896\pi$
$79$	9.06004e6			0.232607			0.116303	+	0.993214i	$0.462896\pi$
$80$		0			0
$81$	−4.29187e7	−	3.31724e6i	−0.997026	−	0.0770613i
$82$		0			0
$83$	4.45484e7			0.938685			0.469342	−	0.883016i	$-0.344491\pi$
$83$	4.45484e7			0.938685			0.469342	+	0.883016i	$0.344491\pi$
$84$		0			0
$85$	−8.66520e7	+	1.35326e7i	−1.65998	+	0.259243i
$86$		0			0
$87$	4.81937e6	+	5.00893e6i	0.0841228	+	0.0874315i
$88$		0			0
$89$		−	6.34613e6i		−	0.101146i	−0.998720	−	0.0505731i	$-0.983895\pi$
$89$		−	6.34613e6i		−	0.101146i	0.998720	−	0.0505731i	$-0.0161048\pi$
$90$		0			0
$91$	7.44578e7			1.08579
$92$		0			0
$93$	−2.74293e7	+	2.63913e7i	−0.366676	+	0.352800i
$94$		0			0
$95$	1.12961e8	−	1.76413e7i	1.38686	−	0.216589i
$96$		0			0
$97$			1.45115e8i			1.63917i	0.572957	+	0.819585i	$0.305796\pi$
$97$			1.45115e8i			1.63917i	−0.572957	+	0.819585i	$0.694204\pi$
$98$		0			0
$99$	−1.35717e8	−	5.23706e6i	−1.41284	−	0.0545188i
$100$		0			0
$101$		−	9.84342e7i		−	0.945934i	−0.881080	−	0.472967i	$-0.843183\pi$
$101$		−	9.84342e7i		−	0.945934i	0.881080	−	0.472967i	$-0.156817\pi$
$102$		0			0
$103$		−	1.80770e8i		−	1.60612i	−0.595897	−	0.803061i	$-0.703203\pi$
$103$		−	1.80770e8i		−	1.60612i	0.595897	−	0.803061i	$-0.296797\pi$
$104$		0			0
$105$	1.41465e8	+	1.07489e8i	1.16384	+	0.884316i
$106$		0			0
$107$	−1.33705e8			−1.02003			−0.510015	−	0.860165i	$-0.670360\pi$
$107$	−1.33705e8			−1.02003			−0.510015	+	0.860165i	$0.670360\pi$
$108$		0			0
$109$	3.31448e7			0.234806			0.117403	−	0.993084i	$-0.462543\pi$
$109$	3.31448e7			0.234806			0.117403	+	0.993084i	$0.462543\pi$
$110$		0			0
$111$	1.29446e8	+	1.34538e8i	0.852703	+	0.886242i
$112$		0			0
$113$	1.83998e8			1.12850			0.564248	−	0.825605i	$-0.309166\pi$
$113$	1.83998e8			1.12850			0.564248	+	0.825605i	$0.309166\pi$
$114$		0			0
$115$	2.50911e8	−	3.91854e7i	1.43459	−	0.224044i
$116$		0			0
$117$	−1.39095e8	−	5.36739e6i	−0.742279	−	0.0286431i
$118$		0			0
$119$			4.92468e8i			2.45578i
$120$		0			0
$121$	−2.14165e8			−0.999097
$122$		0			0
$123$	−9.34232e7	−	9.70978e7i	−0.408164	−	0.424218i
$124$		0			0
$125$	−2.18244e8	+	1.09426e8i	−0.893928	+	0.448211i
$126$		0			0
$127$			4.21390e8i			1.61983i	0.586546	+	0.809916i	$0.300487\pi$
$127$			4.21390e8i			1.61983i	−0.586546	+	0.809916i	$0.699513\pi$
$128$		0			0
$129$	−1.04084e8	−	1.08178e8i	−0.375858	−	0.390642i
$130$		0			0
$131$		−	1.64525e7i		−	0.0558659i	−0.999610	−	0.0279330i	$-0.991108\pi$
$131$		−	1.64525e7i		−	0.0558659i	0.999610	−	0.0279330i	$-0.00889250\pi$
$132$		0			0
$133$		−	6.41988e8i		−	2.05173i
$134$		0			0
$135$	−2.56522e8	−	2.10998e8i	−0.772308	−	0.635249i
$136$		0			0
$137$	−1.92453e8			−0.546315			−0.273157	−	0.961969i	$-0.588068\pi$
$137$	−1.92453e8			−0.546315			−0.273157	+	0.961969i	$0.588068\pi$
$138$		0			0
$139$	4.98620e8			1.33570			0.667852	−	0.744294i	$-0.267214\pi$
$139$	4.98620e8			1.33570			0.667852	+	0.744294i	$0.267214\pi$
$140$		0			0
$141$	−3.36700e8	+	3.23958e8i	−0.851857	+	0.819620i
$142$		0			0
$143$	−4.39189e8			−1.05029
$144$		0			0
$145$	8.27581e6	+	5.29915e7i	0.0187214	+	0.119877i
$146$		0			0
$147$	3.82429e8	−	3.67956e8i	0.818995	−	0.788001i
$148$		0			0
$149$		−	9.81881e8i		−	1.99211i	−0.0887242	−	0.996056i	$-0.528279\pi$
$149$		−	9.81881e8i		−	1.99211i	0.0887242	−	0.996056i	$-0.471721\pi$
$150$		0			0
$151$	1.48501e8			0.285642			0.142821	−	0.989749i	$-0.454383\pi$
$151$	1.48501e8			0.285642			0.142821	+	0.989749i	$0.454383\pi$
$152$		0			0
$153$	3.55002e7	−	9.19980e8i	0.0647836	−	1.67885i
$154$		0			0
$155$	−2.90186e8	+	4.53190e7i	−0.502747	+	0.0785151i
$156$		0			0
$157$		−	2.61216e8i		−	0.429933i	−0.976621	−	0.214966i	$-0.931036\pi$
$157$		−	2.61216e8i		−	0.429933i	0.976621	−	0.214966i	$-0.0689642\pi$
$158$		0			0
$159$	3.18610e8	−	3.06553e8i	0.498507	−	0.479642i
$160$		0			0
$161$		−	1.42600e9i		−	2.12234i
$162$		0			0
$163$		−	2.48329e8i		−	0.351785i	−0.984409	−	0.175892i	$-0.943719\pi$
$163$		−	2.48329e8i		−	0.351785i	0.984409	−	0.175892i	$-0.0562811\pi$
$164$		0			0
$165$	−8.34430e8	−	6.34024e8i	−1.12578	−	0.855401i
$166$		0			0
$167$	−5.23684e8			−0.673293			−0.336646	−	0.941631i	$-0.609293\pi$
$167$	−5.23684e8			−0.673293			−0.336646	+	0.941631i	$0.609293\pi$
$168$		0			0
$169$	3.65612e8			0.448201
$170$		0			0
$171$	−4.62786e7	+	1.19930e9i	−0.0541247	+	1.40263i
$172$		0			0
$173$	−1.08588e9			−1.21227			−0.606133	−	0.795364i	$-0.707280\pi$
$173$	−1.08588e9			−1.21227			−0.606133	+	0.795364i	$0.707280\pi$
$174$		0			0
$175$	4.17999e8	+	1.30562e9i	0.445680	+	1.39208i
$176$		0			0
$177$	−5.21329e8	−	5.41834e8i	−0.531152	−	0.552043i
$178$		0			0
$179$			7.43014e8i			0.723744i	0.932228	+	0.361872i	$0.117862\pi$
$179$			7.43014e8i			0.723744i	−0.932228	+	0.361872i	$0.882138\pi$
$180$		0			0
$181$	9.26876e8			0.863590			0.431795	−	0.901972i	$-0.357880\pi$
$181$	9.26876e8			0.863590			0.431795	+	0.901972i	$0.357880\pi$
$182$		0			0
$183$	−4.43064e8	+	4.26296e8i	−0.395059	+	0.380108i
$184$		0			0
$185$	2.22285e8	+	1.42333e9i	0.189768	+	1.21512i
$186$		0			0
$187$		−	2.90482e9i		−	2.37549i
$188$		0			0
$189$	−1.39287e9	+	1.24036e9i	−1.09160	+	0.972077i
$190$		0			0
$191$			5.32671e8i			0.400245i	0.979771	+	0.200122i	$0.0641340\pi$
$191$			5.32671e8i			0.400245i	−0.979771	+	0.200122i	$0.935866\pi$
$192$		0			0
$193$			5.57602e8i			0.401879i	0.979604	+	0.200939i	$0.0643994\pi$
$193$			5.57602e8i			0.401879i	−0.979604	+	0.200939i	$0.935601\pi$
$194$		0			0
$195$	−8.55197e8	−	6.49803e8i	−0.591463	−	0.449411i
$196$		0			0
$197$	1.77555e9			1.17887			0.589436	−	0.807815i	$-0.299350\pi$
$197$	1.77555e9			1.17887			0.589436	+	0.807815i	$0.299350\pi$
$198$		0			0
$199$	1.86342e9			1.18822			0.594112	−	0.804382i	$-0.297504\pi$
$199$	1.86342e9			1.18822			0.594112	+	0.804382i	$0.297504\pi$
$200$		0			0
$201$	−2.21706e9	−	2.30426e9i	−1.35829	−	1.41172i
$202$		0			0
$203$	3.01166e8			0.177346
$204$		0			0
$205$	−1.60426e8	−	1.02724e9i	−0.0908363	−	0.581642i
$206$		0			0
$207$	−1.02795e8	+	2.66391e9i	−0.0559875	+	1.45090i
$208$		0			0
$209$			3.78676e9i			1.98465i
$210$		0			0
$211$	2.90130e9			1.46374			0.731869	−	0.681445i	$-0.238648\pi$
$211$	2.90130e9			1.46374			0.731869	+	0.681445i	$0.238648\pi$
$212$		0			0
$213$	7.81783e8	+	8.12533e8i	0.379811	+	0.394750i
$214$		0			0
$215$	−1.78732e8	−	1.14446e9i	−0.0836468	−	0.535606i
$216$		0			0
$217$			1.64921e9i			0.743766i
$218$		0			0
$219$	−9.12569e8	−	9.48463e8i	−0.396725	−	0.412329i
$220$		0			0
$221$		−	2.97711e9i		−	1.24803i
$222$		0			0
$223$			1.33056e9i			0.538041i	0.963134	+	0.269020i	$0.0866999\pi$
$223$			1.33056e9i			0.538041i	−0.963134	+	0.269020i	$0.913300\pi$
$224$		0			0
$225$	−6.86747e8	−	2.46917e9i	−0.267958	−	0.963431i
$226$		0			0
$227$	1.46689e9			0.552450			0.276225	−	0.961093i	$-0.410917\pi$
$227$	1.46689e9			0.552450			0.276225	+	0.961093i	$0.410917\pi$
$228$		0			0
$229$	1.94772e9			0.708247			0.354124	−	0.935199i	$-0.384779\pi$
$229$	1.94772e9			0.708247			0.354124	+	0.935199i	$0.384779\pi$
$230$		0			0
$231$	−4.24053e9	+	4.08005e9i	−1.48926	+	1.43291i
$232$		0			0
$233$	2.15115e9			0.729872			0.364936	−	0.931033i	$-0.381091\pi$
$233$	2.15115e9			0.729872			0.364936	+	0.931033i	$0.381091\pi$
$234$		0			0
$235$	−3.56209e9	+	5.56300e8i	−1.16797	+	0.182405i
$236$		0			0
$237$	−5.28830e8	+	5.08817e8i	−0.167619	+	0.161275i
$238$		0			0
$239$		−	5.99211e8i		−	0.183649i	−0.995775	−	0.0918244i	$-0.970730\pi$
$239$		−	5.99211e8i		−	0.183649i	0.995775	−	0.0918244i	$-0.0292698\pi$
$240$		0			0
$241$	1.64227e9			0.486829			0.243414	−	0.969922i	$-0.421732\pi$
$241$	1.64227e9			0.486829			0.243414	+	0.969922i	$0.421732\pi$
$242$		0			0
$243$	2.69144e9	−	2.21671e9i	0.771897	−	0.635747i
$244$		0			0
$245$	4.04587e9	−	6.31853e8i	1.12292	−	0.175369i
$246$		0			0
$247$			3.88100e9i			1.04269i
$248$		0			0
$249$	−2.60027e9	+	2.50186e9i	−0.676426	+	0.650828i
$250$		0			0
$251$		−	3.70168e6i		−	0.000932619i	−1.00000		0.000466309i	$-0.999852\pi$
$251$		−	3.70168e6i		−	0.000932619i	1.00000		0.000466309i	$-0.000148431\pi$
$252$		0			0
$253$			8.41124e9i			2.05295i
$254$		0			0
$255$	4.29783e9	−	5.65632e9i	1.01646	−	1.33774i
$256$		0			0
$257$	−2.04324e9			−0.468368			−0.234184	−	0.972192i	$-0.575242\pi$
$257$	−2.04324e9			−0.468368			−0.234184	+	0.972192i	$0.575242\pi$
$258$		0			0
$259$	8.08919e9			1.79765
$260$		0			0
$261$	−5.62608e8	−	2.17099e7i	−0.121239	−	0.00467839i
$262$		0			0
$263$	5.35938e9			1.12019			0.560095	−	0.828428i	$-0.310765\pi$
$263$	5.35938e9			1.12019			0.560095	+	0.828428i	$0.310765\pi$
$264$		0			0
$265$	3.37071e9	−	5.26412e8i	0.683499	−	0.106744i
$266$		0			0
$267$	3.56402e8	+	3.70420e8i	0.0701287	+	0.0728870i
$268$		0			0
$269$			5.28824e8i			0.100995i	0.998724	+	0.0504977i	$0.0160808\pi$
$269$			5.28824e8i			0.100995i	−0.998724	+	0.0504977i	$0.983919\pi$
$270$		0			0
$271$	−3.00472e9			−0.557093			−0.278546	−	0.960423i	$-0.589853\pi$
$271$	−3.00472e9			−0.557093			−0.278546	+	0.960423i	$0.589853\pi$
$272$		0			0
$273$	−4.34606e9	+	4.18159e9i	−0.782430	+	0.752820i
$274$		0			0
$275$	−2.46556e9	−	7.70121e9i	−0.431108	−	1.34657i
$276$		0			0
$277$			9.13777e8i			0.155210i	0.996984	+	0.0776052i	$0.0247274\pi$
$277$			9.13777e8i			0.155210i	−0.996984	+	0.0776052i	$0.975273\pi$
$278$		0			0
$279$	1.18885e8	−	3.08089e9i	0.0196206	−	0.508462i
$280$		0			0
$281$			2.60476e9i			0.417775i	0.977940	+	0.208888i	$0.0669843\pi$
$281$			2.60476e9i			0.417775i	−0.977940	+	0.208888i	$0.933016\pi$
$282$		0			0
$283$			1.09050e10i			1.70012i	0.526686	+	0.850060i	$0.323434\pi$
$283$			1.09050e10i			1.70012i	−0.526686	+	0.850060i	$0.676566\pi$
$284$		0			0
$285$	−5.60271e9	+	7.37366e9i	−0.849218	+	1.11764i
$286$		0			0
$287$	−5.83808e9			−0.860483
$288$		0			0
$289$	1.27150e10			1.82274
$290$		0			0
$291$	−8.14971e9	−	8.47026e9i	−1.13650	−	1.18120i
$292$		0			0
$293$	3.92694e9			0.532824			0.266412	−	0.963859i	$-0.414162\pi$
$293$	3.92694e9			0.532824			0.266412	+	0.963859i	$0.414162\pi$
$294$		0			0
$295$	−8.95224e8	−	5.73228e9i	−0.118207	−	0.756902i
$296$		0			0
$297$	8.21585e9	−	7.31626e9i	1.05591	−	0.940294i
$298$		0			0
$299$			8.62058e9i			1.07858i
$300$		0			0
$301$	−6.50427e9			−0.792378
$302$		0			0
$303$	5.52812e9	+	5.74555e9i	0.655854	+	0.681650i
$304$		0			0
$305$	−4.68735e9	+	7.32035e8i	−0.541662	+	0.0845926i
$306$		0			0
$307$		−	9.28577e9i		−	1.04536i	−0.852530	−	0.522678i	$-0.824933\pi$
$307$		−	9.28577e9i		−	1.04536i	0.852530	−	0.522678i	$-0.175067\pi$
$308$		0			0
$309$	1.01522e10	+	1.05515e10i	1.11359	+	1.15739i
$310$		0			0
$311$			7.90380e9i			0.844879i	0.906391	+	0.422439i	$0.138826\pi$
$311$			7.90380e9i			0.844879i	−0.906391	+	0.422439i	$0.861174\pi$
$312$		0			0
$313$		−	1.76807e10i		−	1.84214i	−0.389398	−	0.921070i	$-0.627317\pi$
$313$		−	1.76807e10i		−	1.84214i	0.389398	−	0.921070i	$-0.372683\pi$
$314$		0			0
$315$	−1.42939e10	+	1.67067e9i	−1.45180	+	0.169687i
$316$		0			0
$317$	5.47282e9			0.541968			0.270984	−	0.962584i	$-0.412651\pi$
$317$	5.47282e9			0.541968			0.270984	+	0.962584i	$0.412651\pi$
$318$		0			0
$319$	−1.77643e9			−0.171547
$320$		0			0
$321$	7.80430e9	−	7.50896e9i	0.735045	−	0.707228i
$322$		0			0
$323$	−2.56692e10			−2.35831
$324$		0			0
$325$	−2.52693e9	−	7.89287e9i	−0.226495	−	0.707459i
$326$		0			0
$327$	−1.93465e9	+	1.86143e9i	−0.169204	+	0.162801i
$328$		0			0
$329$			2.02444e10i			1.72791i
$330$		0			0
$331$	5.54260e9			0.461744			0.230872	−	0.972984i	$-0.425842\pi$
$331$	5.54260e9			0.461744			0.230872	+	0.972984i	$0.425842\pi$
$332$		0			0
$333$	−1.51114e10	−	5.83120e8i	−1.22893	−	0.0474221i
$334$		0			0
$335$	−3.80713e9	−	2.43778e10i	−0.302286	−	1.93559i
$336$		0			0
$337$			1.09681e10i			0.850380i	0.905104	+	0.425190i	$0.139793\pi$
$337$			1.09681e10i			0.850380i	−0.905104	+	0.425190i	$0.860207\pi$
$338$		0			0
$339$	−1.07399e10	+	1.03334e10i	−0.813206	+	0.782431i
$340$		0			0
$341$		−	9.72784e9i		−	0.719447i
$342$		0			0
$343$		−	2.76220e9i		−	0.199562i
$344$		0			0
$345$	−1.24449e10	+	1.63785e10i	−0.878444	+	1.15611i
$346$		0			0
$347$	1.26798e10			0.874571			0.437285	−	0.899323i	$-0.355940\pi$
$347$	1.26798e10			0.874571			0.437285	+	0.899323i	$0.355940\pi$
$348$		0			0
$349$	1.82021e10			1.22693			0.613465	−	0.789722i	$-0.289775\pi$
$349$	1.82021e10			1.22693			0.613465	+	0.789722i	$0.289775\pi$
$350$		0			0
$351$	8.42032e9	−	7.49834e9i	0.554754	−	0.494011i
$352$		0			0
$353$	6.70323e9			0.431703			0.215852	−	0.976426i	$-0.430747\pi$
$353$	6.70323e9			0.431703			0.215852	+	0.976426i	$0.430747\pi$
$354$		0			0
$355$	1.34248e9	+	8.59612e9i	0.0845266	+	0.541239i
$356$		0			0
$357$	−2.76573e10	−	2.87451e10i	−1.70269	−	1.76966i
$358$		0			0
$359$		−	6.58783e9i		−	0.396611i	−0.980140	−	0.198305i	$-0.936456\pi$
$359$		−	6.58783e9i		−	0.396611i	0.980140	−	0.198305i	$-0.0635438\pi$
$360$		0			0
$361$	1.64791e10			0.970299
$362$		0			0
$363$	1.25007e10	−	1.20276e10i	0.719960	−	0.692714i
$364$		0			0
$365$	−1.56706e9	−	1.00342e10i	−0.0882906	−	0.565341i
$366$		0			0
$367$		−	2.80712e10i		−	1.54738i	−0.633565	−	0.773689i	$-0.718409\pi$
$367$		−	2.80712e10i		−	1.54738i	0.633565	−	0.773689i	$-0.281591\pi$
$368$		0			0
$369$	1.09061e10	+	4.20846e8i	0.588254	+	0.0226996i
$370$		0			0
$371$		−	1.91567e10i		−	1.01117i
$372$		0			0
$373$		−	2.11306e10i		−	1.09163i	−0.837904	−	0.545817i	$-0.816219\pi$
$373$		−	2.11306e10i		−	1.09163i	0.837904	−	0.545817i	$-0.183781\pi$
$374$		0			0
$375$	6.59335e9	−	1.86439e10i	0.333412	−	0.942781i
$376$		0			0
$377$	−1.82064e9			−0.0901275
$378$		0			0
$379$	1.44678e9			0.0701206			0.0350603	−	0.999385i	$-0.488838\pi$
$379$	1.44678e9			0.0701206			0.0350603	+	0.999385i	$0.488838\pi$
$380$		0			0
$381$	−2.36655e10	−	2.45963e10i	−1.12309	−	1.16727i
$382$		0			0
$383$	9.44888e8			0.0439122			0.0219561	−	0.999759i	$-0.493011\pi$
$383$	9.44888e8			0.0439122			0.0219561	+	0.999759i	$0.493011\pi$
$384$		0			0
$385$	−4.48623e10	+	7.00625e9i	−2.04192	+	0.318891i
$386$		0			0
$387$	1.21506e10	+	4.68869e8i	0.541695	+	0.0209030i
$388$		0			0
$389$			9.47314e9i			0.413709i	0.978372	+	0.206855i	$0.0663227\pi$
$389$			9.47314e9i			0.413709i	−0.978372	+	0.206855i	$0.933677\pi$
$390$		0			0
$391$	−5.70169e10			−2.43948
$392$		0			0
$393$	9.23982e8	+	9.60325e8i	0.0387341	+	0.0402576i
$394$		0			0
$395$	−5.59471e9	+	8.73739e8i	−0.229821	+	0.0358916i
$396$		0			0
$397$			3.43909e10i			1.38446i	0.721675	+	0.692232i	$0.243372\pi$
$397$			3.43909e10i			1.38446i	−0.721675	+	0.692232i	$0.756628\pi$
$398$		0			0
$399$	3.60544e10	+	3.74725e10i	1.42255	+	1.47850i
$400$		0			0
$401$			3.57004e10i			1.38069i	0.723481	+	0.690344i	$0.242541\pi$
$401$			3.57004e10i			1.38069i	−0.723481	+	0.690344i	$0.757459\pi$
$402$		0			0
$403$		−	9.96994e9i		−	0.377983i
$404$		0			0
$405$	2.68229e10	−	2.09058e9i	0.996976	−	0.0777047i
$406$		0			0
$407$	−4.77140e10			−1.73888
$408$		0			0
$409$	4.36805e10			1.56097			0.780484	−	0.625176i	$-0.214973\pi$
$409$	4.36805e10			1.56097			0.780484	+	0.625176i	$0.214973\pi$
$410$		0			0
$411$	1.12334e10	−	1.08083e10i	0.393680	−	0.378782i
$412$		0			0
$413$	−3.25782e10			−1.11976
$414$		0			0
$415$	−2.75093e10	+	4.29619e9i	−0.927443	+	0.144841i
$416$		0			0
$417$	−2.91042e10	+	2.80028e10i	−0.962523	+	0.926098i
$418$		0			0
$419$			1.22779e10i			0.398353i	0.979964	+	0.199176i	$0.0638267\pi$
$419$			1.22779e10i			0.398353i	−0.979964	+	0.199176i	$0.936173\pi$
$420$		0			0
$421$	−2.98167e10			−0.949142			−0.474571	−	0.880217i	$-0.657397\pi$
$421$	−2.98167e10			−0.949142			−0.474571	+	0.880217i	$0.657397\pi$
$422$		0			0
$423$	1.45934e9	−	3.78185e10i	0.0455822	−	1.18125i
$424$		0			0
$425$	5.22038e10	−	1.67132e10i	1.60010	−	0.512276i
$426$		0			0
$427$			2.66395e10i			0.801337i
$428$		0			0
$429$	2.56352e10	−	2.46651e10i	0.756847	−	0.728205i
$430$		0			0
$431$			2.57496e10i			0.746211i	0.927789	+	0.373105i	$0.121707\pi$
$431$			2.57496e10i			0.746211i	−0.927789	+	0.373105i	$0.878293\pi$
$432$		0			0
$433$		−	1.99914e10i		−	0.568710i	−0.958719	−	0.284355i	$-0.908221\pi$
$433$		−	1.99914e10i		−	0.568710i	0.958719	−	0.284355i	$-0.0917794\pi$
$434$		0			0
$435$	−3.45909e9	−	2.62831e9i	−0.0966061	−	0.0734041i
$436$		0			0
$437$	7.43281e10			2.03811
$438$		0			0
$439$	4.78153e10			1.28739			0.643693	−	0.765283i	$-0.277401\pi$
$439$	4.78153e10			1.28739			0.643693	+	0.765283i	$0.277401\pi$
$440$		0			0
$441$	−1.65754e9	+	4.29548e10i	−0.0438238	+	1.13568i
$442$		0			0
$443$	3.71876e10			0.965569			0.482784	−	0.875739i	$-0.339625\pi$
$443$	3.71876e10			0.965569			0.482784	+	0.875739i	$0.339625\pi$
$444$		0			0
$445$	6.12013e8	+	3.91883e9i	0.0156070	+	0.0999348i
$446$		0			0
$447$	5.51430e10	+	5.73119e10i	1.38121	+	1.43554i
$448$		0			0
$449$			3.65198e10i			0.898552i	0.893393	+	0.449276i	$0.148318\pi$
$449$			3.65198e10i			0.898552i	−0.893393	+	0.449276i	$0.851682\pi$
$450$		0			0
$451$	3.44359e10			0.832348
$452$		0			0
$453$	−8.66792e9	+	8.33989e9i	−0.205836	+	0.198047i
$454$		0			0
$455$	−4.59788e10	+	7.18061e9i	−1.07278	+	0.167539i
$456$		0			0
$457$			2.53334e10i			0.580803i	0.956905	+	0.290401i	$0.0937888\pi$
$457$			2.53334e10i			0.580803i	−0.956905	+	0.290401i	$0.906211\pi$
$458$		0			0
$459$	4.95944e10	+	5.56924e10i	1.11733	+	1.25472i
$460$		0			0
$461$		−	3.97638e10i		−	0.880409i	−0.897897	−	0.440205i	$-0.854906\pi$
$461$		−	3.97638e10i		−	0.880409i	0.897897	−	0.440205i	$-0.145094\pi$
$462$		0			0
$463$			5.96733e9i			0.129854i	0.997890	+	0.0649271i	$0.0206815\pi$
$463$			5.96733e9i			0.129854i	−0.997890	+	0.0649271i	$0.979319\pi$
$464$		0			0
$465$	1.43929e10	−	1.89422e10i	0.307847	−	0.405153i
$466$		0			0
$467$	−5.93145e10			−1.24708			−0.623539	−	0.781792i	$-0.714306\pi$
$467$	−5.93145e10			−1.24708			−0.623539	+	0.781792i	$0.714306\pi$
$468$		0			0
$469$	−1.38546e11			−2.86353
$470$		0			0
$471$	1.46700e10	+	1.52470e10i	0.298090	+	0.309814i
$472$		0			0
$473$	3.83654e10			0.766470
$474$		0			0
$475$	−6.80537e10	+	2.17876e10i	−1.33683	+	0.427991i
$476$		0			0
$477$	−1.38094e9	+	3.57867e10i	−0.0266747	+	0.691270i
$478$		0			0
$479$			3.15355e10i			0.599042i	0.954090	+	0.299521i	$0.0968269\pi$
$479$			3.15355e10i			0.599042i	−0.954090	+	0.299521i	$0.903173\pi$
$480$		0			0
$481$	−4.89015e10			−0.913570
$482$		0			0
$483$	8.00849e10	+	8.32348e10i	1.47151	+	1.52938i
$484$		0			0
$485$	−1.39947e10	−	8.96104e10i	−0.252927	−	1.61954i
$486$		0			0
$487$		−	4.91361e10i		−	0.873544i	−0.899572	−	0.436772i	$-0.856122\pi$
$487$		−	4.91361e10i		−	0.873544i	0.899572	−	0.436772i	$-0.143878\pi$
$488$		0			0
$489$	1.39463e10	+	1.44948e10i	0.243906	+	0.253500i
$490$		0			0
$491$		−	1.06396e11i		−	1.83062i	−0.402748	−	0.915311i	$-0.631945\pi$
$491$		−	1.06396e11i		−	1.83062i	0.402748	−	0.915311i	$-0.368055\pi$
$492$		0			0
$493$		−	1.20418e10i		−	0.203846i
$494$		0			0
$495$	8.43124e10	−	9.85442e9i	1.40433	−	0.164138i
$496$		0			0
$497$	4.88542e10			0.800712
$498$		0			0
$499$	−1.07193e10			−0.172887			−0.0864435	−	0.996257i	$-0.527550\pi$
$499$	−1.07193e10			−0.172887			−0.0864435	+	0.996257i	$0.527550\pi$
$500$		0			0
$501$	3.05672e10	−	2.94104e10i	0.485182	−	0.466821i
$502$		0			0
$503$	3.64842e10			0.569945			0.284973	−	0.958536i	$-0.408015\pi$
$503$	3.64842e10			0.569945			0.284973	+	0.958536i	$0.408015\pi$
$504$		0			0
$505$	9.49287e9	+	6.07846e10i	0.145959	+	0.934605i
$506$		0			0
$507$	−2.13406e10	+	2.05330e10i	−0.322979	+	0.310756i
$508$		0			0
$509$			4.39714e10i			0.655088i	0.944836	+	0.327544i	$0.106221\pi$
$509$			4.39714e10i			0.655088i	−0.944836	+	0.327544i	$0.893779\pi$
$510$		0			0
$511$	−5.70271e10			−0.836368
$512$		0			0
$513$	−6.46520e10	−	7.26015e10i	−0.933496	−	1.04828i
$514$		0			0
$515$	1.74333e10	+	1.11628e11i	0.247828	+	1.58689i
$516$		0			0
$517$		−	1.19411e11i		−	1.67141i
$518$		0			0
$519$	6.33823e10	−	6.09836e10i	0.873571	−	0.840512i
$520$		0			0
$521$		−	1.18460e11i		−	1.60776i	−0.594790	−	0.803881i	$-0.702765\pi$
$521$		−	1.18460e11i		−	1.60776i	0.594790	−	0.803881i	$-0.297235\pi$
$522$		0			0
$523$			1.10658e11i			1.47903i	0.673143	+	0.739513i	$0.264944\pi$
$523$			1.10658e11i			1.47903i	−0.673143	+	0.739513i	$0.735056\pi$
$524$		0			0
$525$	−9.77228e10	−	5.27334e10i	−1.28635	−	0.694143i
$526$		0			0
$527$	6.59417e10			0.854904
$528$		0			0
$529$	8.67883e10			1.10825
$530$		0			0
$531$	6.08593e10	+	2.34844e9i	0.765507	+	0.0295394i
$532$		0			0
$533$	3.52929e10			0.437299
$534$		0			0
$535$	8.25650e10	−	1.28944e10i	1.00781	−	0.157393i
$536$		0			0
$537$	−4.17281e10	−	4.33693e10i	−0.501801	−	0.521538i
$538$		0			0
$539$			1.35629e11i			1.60693i
$540$		0			0
$541$	−1.06194e11			−1.23968			−0.619842	−	0.784727i	$-0.712803\pi$
$541$	−1.06194e11			−1.23968			−0.619842	+	0.784727i	$0.712803\pi$
$542$		0			0
$543$	−5.41013e10	+	5.20539e10i	−0.622312	+	0.598761i
$544$		0			0
$545$	−2.04674e10	+	3.19644e9i	−0.231994	+	0.0362311i
$546$		0			0
$547$			5.49364e10i			0.613636i	0.951768	+	0.306818i	$0.0992643\pi$
$547$			5.49364e10i			0.613636i	−0.951768	+	0.306818i	$0.900736\pi$
$548$		0			0
$549$	1.92035e9	−	4.97654e10i	0.0211393	−	0.547820i
$550$		0			0
$551$			1.56978e10i			0.170307i
$552$		0			0
$553$			3.17963e10i			0.339998i
$554$		0			0
$555$	−9.29097e10	−	7.05954e10i	−0.979240	−	0.744054i
$556$		0			0
$557$	1.41683e11			1.47196			0.735981	−	0.677002i	$-0.236721\pi$
$557$	1.41683e11			1.47196			0.735981	+	0.677002i	$0.236721\pi$
$558$		0			0
$559$	3.93202e10			0.402688
$560$		0			0
$561$	1.63136e11	+	1.69553e11i	1.64702	+	1.71180i
$562$		0			0
$563$	−1.79075e11			−1.78239			−0.891193	−	0.453624i	$-0.850131\pi$
$563$	−1.79075e11			−1.78239			−0.891193	+	0.453624i	$0.850131\pi$
$564$		0			0
$565$	−1.13622e11	+	1.77446e10i	−1.11498	+	0.174129i
$566$		0			0
$567$	1.16419e10	−	1.50624e11i	0.112640	−	1.45734i
$568$		0			0
$569$			3.57832e10i			0.341374i	0.985325	+	0.170687i	$0.0545987\pi$
$569$			3.57832e10i			0.341374i	−0.985325	+	0.170687i	$0.945401\pi$
$570$		0			0
$571$	1.81409e10			0.170653			0.0853264	−	0.996353i	$-0.472807\pi$
$571$	1.81409e10			0.170653			0.0853264	+	0.996353i	$0.472807\pi$
$572$		0			0
$573$	−2.99151e10	−	3.10917e10i	−0.277506	−	0.288421i
$574$		0			0
$575$	−1.51162e11	+	4.83951e10i	−1.38284	+	0.442721i
$576$		0			0
$577$		−	6.74004e10i		−	0.608078i	−0.952660	−	0.304039i	$-0.901665\pi$
$577$		−	6.74004e10i		−	0.608078i	0.952660	−	0.304039i	$-0.0983353\pi$
$578$		0			0
$579$	−3.13152e10	−	3.25469e10i	−0.278638	−	0.289598i
$580$		0			0
$581$			1.56343e11i			1.37206i
$582$		0			0
$583$			1.12996e11i			0.978110i
$584$		0			0
$585$	8.64107e10	−	1.00997e10i	0.737809	−	0.0862350i
$586$		0			0
$587$	−5.75368e10			−0.484611			−0.242306	−	0.970200i	$-0.577904\pi$
$587$	−5.75368e10			−0.484611			−0.242306	+	0.970200i	$0.577904\pi$
$588$		0			0
$589$	−8.59625e10			−0.714246
$590$		0			0
$591$	−1.03638e11	+	9.97156e10i	−0.849508	+	0.817360i
$592$		0			0
$593$	−1.57134e11			−1.27072			−0.635362	−	0.772214i	$-0.719149\pi$
$593$	−1.57134e11			−1.27072			−0.635362	+	0.772214i	$0.719149\pi$
$594$		0			0
$595$	−4.74930e10	−	3.04106e11i	−0.378932	−	2.42637i
$596$		0			0
$597$	−1.08767e11	+	1.04651e11i	−0.856247	+	0.823843i
$598$		0			0
$599$		−	1.28179e11i		−	0.995657i	−0.867275	−	0.497829i	$-0.834131\pi$
$599$		−	1.28179e11i		−	0.995657i	0.867275	−	0.497829i	$-0.165869\pi$
$600$		0			0
$601$	−3.62465e10			−0.277823			−0.138912	−	0.990305i	$-0.544360\pi$
$601$	−3.62465e10			−0.277823			−0.138912	+	0.990305i	$0.544360\pi$
$602$		0			0
$603$	2.58817e11	+	9.98725e9i	1.95760	+	0.0755399i
$604$		0			0
$605$	1.32250e11	−	2.06538e10i	0.987131	−	0.154163i
$606$		0			0
$607$		−	9.54787e10i		−	0.703318i	−0.936128	−	0.351659i	$-0.885618\pi$
$607$		−	9.54787e10i		−	0.703318i	0.936128	−	0.351659i	$-0.114382\pi$
$608$		0			0
$609$	−1.75789e10	+	1.69136e10i	−0.127797	+	0.122961i
$610$		0			0
$611$		−	1.22383e11i		−	0.878125i
$612$		0			0
$613$		−	5.97421e10i		−	0.423096i	−0.977368	−	0.211548i	$-0.932150\pi$
$613$		−	5.97421e10i		−	0.423096i	0.977368	−	0.211548i	$-0.0678504\pi$
$614$		0			0
$615$	6.70542e10	+	5.09497e10i	0.468733	+	0.356157i
$616$		0			0
$617$	−8.94979e10			−0.617550			−0.308775	−	0.951135i	$-0.599919\pi$
$617$	−8.94979e10			−0.617550			−0.308775	+	0.951135i	$0.599919\pi$
$618$		0			0
$619$	1.08762e11			0.740825			0.370413	−	0.928867i	$-0.379216\pi$
$619$	1.08762e11			0.740825			0.370413	+	0.928867i	$0.379216\pi$
$620$		0			0
$621$	−1.43607e11	−	1.61264e11i	−0.965623	−	1.08435i
$622$		0			0
$623$	2.22718e10			0.147844
$624$		0			0
$625$	1.24216e11	−	8.86196e10i	0.814062	−	0.580778i
$626$		0			0
$627$	−2.12667e11	−	2.21031e11i	−1.37603	−	1.43016i
$628$		0			0
$629$		−	3.23437e11i		−	2.06627i
$630$		0			0
$631$	1.11998e11			0.706468			0.353234	−	0.935535i	$-0.385082\pi$
$631$	1.11998e11			0.706468			0.353234	+	0.935535i	$0.385082\pi$
$632$		0			0
$633$	−1.69348e11	+	1.62939e11i	−1.05479	+	1.01487i
$634$		0			0
$635$	−4.06384e10	−	2.60215e11i	−0.249943	−	1.60043i
$636$		0			0
$637$			1.39004e11i			0.844249i
$638$		0			0
$639$	−9.12646e10	−	3.52172e9i	−0.547392	−	0.0211228i
$640$		0			0
$641$			1.05818e11i			0.626797i	0.949622	+	0.313399i	$0.101468\pi$
$641$			1.05818e11i			0.626797i	−0.949622	+	0.313399i	$0.898532\pi$
$642$		0			0
$643$		−	2.65610e11i		−	1.55382i	−0.629610	−	0.776911i	$-0.716785\pi$
$643$		−	2.65610e11i		−	1.55382i	0.629610	−	0.776911i	$-0.283215\pi$
$644$		0			0
$645$	7.47058e10	+	5.67636e10i	0.431634	+	0.327968i
$646$		0			0
$647$	−9.85146e10			−0.562190			−0.281095	−	0.959680i	$-0.590698\pi$
$647$	−9.85146e10			−0.562190			−0.281095	+	0.959680i	$0.590698\pi$
$648$		0			0
$649$	1.92162e11			1.08315
$650$		0			0
$651$	−9.26204e10	−	9.62634e10i	−0.515683	−	0.535966i
$652$		0			0
$653$	−5.60145e10			−0.308069			−0.154034	−	0.988065i	$-0.549227\pi$
$653$	−5.60145e10			−0.308069			−0.154034	+	0.988065i	$0.549227\pi$
$654$		0			0
$655$	1.58666e9	+	1.01597e10i	0.00862022	+	0.0551969i
$656$		0			0
$657$	1.06532e11	+	4.11087e9i	0.571768	+	0.0220634i
$658$		0			0
$659$			1.00957e11i			0.535294i	0.963517	+	0.267647i	$0.0862462\pi$
$659$			1.00957e11i			0.535294i	−0.963517	+	0.267647i	$0.913754\pi$
$660$		0			0
$661$	2.51585e11			1.31789			0.658945	−	0.752191i	$-0.271003\pi$
$661$	2.51585e11			1.31789			0.658945	+	0.752191i	$0.271003\pi$
$662$		0			0
$663$	1.67196e11	+	1.73772e11i	0.865311	+	0.899345i
$664$		0			0
$665$	6.19125e10	+	3.96437e11i	0.316586	+	2.02716i
$666$		0			0
$667$			3.48684e10i			0.176169i
$668$		0			0
$669$	−7.47250e10	−	7.76641e10i	−0.373045	−	0.387718i
$670$		0			0
$671$		−	1.57133e11i		−	0.775136i
$672$		0			0
$673$		−	1.51950e11i		−	0.740698i	−0.928893	−	0.370349i	$-0.879238\pi$
$673$		−	1.51950e11i		−	0.740698i	0.928893	−	0.370349i	$-0.120762\pi$
$674$		0			0
$675$	1.78755e11	+	1.05556e11i	0.861078	+	0.508472i
$676$		0			0
$677$	−2.68132e11			−1.27642			−0.638211	−	0.769862i	$-0.720325\pi$
$677$	−2.68132e11			−1.27642			−0.638211	+	0.769862i	$0.720325\pi$
$678$		0			0
$679$	−5.09281e11			−2.39595
$680$		0			0
$681$	−8.56213e10	+	8.23811e10i	−0.398101	+	0.383036i
$682$		0			0
$683$	2.30446e11			1.05897			0.529487	−	0.848318i	$-0.322384\pi$
$683$	2.30446e11			1.05897			0.529487	+	0.848318i	$0.322384\pi$
$684$		0			0
$685$	1.18843e11	−	1.85599e10i	0.539772	−	0.0842974i
$686$		0			0
$687$	−1.13687e11	+	1.09385e11i	−0.510370	+	0.491056i
$688$		0			0
$689$			1.15808e11i			0.513879i
$690$		0			0
$691$	4.52320e10			0.198397			0.0991983	−	0.995068i	$-0.468372\pi$
$691$	4.52320e10			0.198397			0.0991983	+	0.995068i	$0.468372\pi$
$692$		0			0
$693$	1.83795e10	−	4.76301e11i	0.0796894	−	2.06513i
$694$		0			0
$695$	−3.07905e11	+	4.80863e10i	−1.31971	+	0.206102i
$696$		0			0
$697$			2.33429e11i			0.989062i
$698$		0			0
$699$	−1.25561e11	+	1.20810e11i	−0.525954	+	0.506050i
$700$		0			0
$701$			1.85644e11i			0.768793i	0.923168	+	0.384397i	$0.125591\pi$
$701$			1.85644e11i			0.768793i	−0.923168	+	0.384397i	$0.874409\pi$
$702$		0			0
$703$			4.21637e11i			1.72631i
$704$		0			0
$705$	1.76675e11	−	2.32520e11i	0.715186	−	0.941247i
$706$		0			0
$707$	3.45456e11			1.38266
$708$		0			0
$709$	−6.54534e10			−0.259028			−0.129514	−	0.991578i	$-0.541342\pi$
$709$	−6.54534e10			−0.259028			−0.129514	+	0.991578i	$0.541342\pi$
$710$		0			0
$711$	2.29208e9	−	5.93987e10i	0.00896915	−	0.232434i
$712$		0			0
$713$	−1.90942e11			−0.738828
$714$		0			0
$715$	2.71206e11	−	4.23548e10i	1.03771	−	0.162061i
$716$		0			0
$717$	3.36520e10	+	3.49756e10i	0.127331	+	0.132339i
$718$		0			0
$719$		−	3.18152e11i		−	1.19047i	−0.803551	−	0.595236i	$-0.797059\pi$
$719$		−	3.18152e11i		−	1.19047i	0.803551	−	0.595236i	$-0.202941\pi$
$720$		0			0
$721$	6.34416e11			2.34765
$722$		0			0
$723$	−9.58584e10	+	9.22308e10i	−0.350814	+	0.337538i
$724$		0			0
$725$	−1.02209e10	−	3.19250e10i	−0.0369944	−	0.115552i
$726$		0			0
$727$			4.08035e11i			1.46070i	0.683075	+	0.730348i	$0.260642\pi$
$727$			4.08035e11i			1.46070i	−0.683075	+	0.730348i	$0.739358\pi$
$728$		0			0
$729$	−3.26061e10	+	2.80541e11i	−0.115449	+	0.993313i
$730$		0			0
$731$			2.60066e11i			0.910780i
$732$		0			0
$733$			2.10940e10i			0.0730705i	0.999332	+	0.0365353i	$0.0116321\pi$
$733$			2.10940e10i			0.0730705i	−0.999332	+	0.0365353i	$0.988368\pi$
$734$		0			0
$735$	−2.00670e11	+	2.64099e11i	−0.687596	+	0.904936i
$736$		0			0
$737$	8.17210e11			2.76990
$738$		0			0
$739$	−4.66579e11			−1.56440			−0.782199	−	0.623029i	$-0.785902\pi$
$739$	−4.66579e11			−1.56440			−0.782199	+	0.623029i	$0.785902\pi$
$740$		0			0
$741$	−2.17959e11	−	2.26532e11i	−0.722940	−	0.751375i
$742$		0			0
$743$	3.85387e11			1.26457			0.632284	−	0.774737i	$-0.282118\pi$
$743$	3.85387e11			1.26457			0.632284	+	0.774737i	$0.282118\pi$
$744$		0			0
$745$	9.46913e10	+	6.06326e11i	0.307387	+	1.96825i
$746$		0			0
$747$	1.12702e10	−	2.92065e11i	0.0361951	−	0.937987i
$748$		0			0
$749$		−	4.69240e11i		−	1.49097i
$750$		0			0
$751$	2.05812e11			0.647011			0.323505	−	0.946226i	$-0.395139\pi$
$751$	2.05812e11			0.647011			0.323505	+	0.946226i	$0.395139\pi$
$752$		0			0
$753$	2.07888e8	+	2.16065e8i	0.000646622	+	0.000672055i
$754$		0			0
$755$	−9.17015e10	+	1.43212e10i	−0.282221	+	0.0440750i
$756$		0			0
$757$		−	2.39601e11i		−	0.729634i	−0.931079	−	0.364817i	$-0.881132\pi$
$757$		−	2.39601e11i		−	0.729634i	0.931079	−	0.364817i	$-0.118868\pi$
$758$		0			0
$759$	−4.72380e11	−	4.90960e11i	−1.42339	−	1.47938i
$760$		0			0
$761$			4.48955e11i			1.33864i	0.742974	+	0.669321i	$0.233415\pi$
$761$			4.48955e11i			1.33864i	−0.742974	+	0.669321i	$0.766585\pi$
$762$		0			0
$763$			1.16322e11i			0.343213i
$764$		0			0
$765$	6.67997e10	+	5.71525e11i	0.195042	+	1.66874i
$766$		0			0
$767$	1.96945e11			0.569066
$768$		0			0
$769$	2.47916e11			0.708922			0.354461	−	0.935071i	$-0.384664\pi$
$769$	2.47916e11			0.708922			0.354461	+	0.935071i	$0.384664\pi$
$770$		0			0
$771$	1.19263e11	−	1.14749e11i	0.337511	−	0.324738i
$772$		0			0
$773$	−1.74374e11			−0.488386			−0.244193	−	0.969727i	$-0.578523\pi$
$773$	−1.74374e11			−0.488386			−0.244193	+	0.969727i	$0.578523\pi$
$774$		0			0
$775$	1.74824e11	−	5.59703e10i	0.484611	−	0.155150i
$776$		0			0
$777$	−4.72162e11	+	4.54293e11i	−1.29541	+	1.24639i
$778$		0			0
$779$		−	3.04301e11i		−	0.826331i
$780$		0			0
$781$	−2.88166e11			−0.774531
$782$		0			0
$783$	3.40584e10	−	3.03292e10i	0.0906102	−	0.0806889i
$784$		0			0
$785$	2.51913e10	+	1.61305e11i	0.0663395	+	0.424784i
$786$		0			0
$787$			1.09992e10i			0.0286724i	0.999897	+	0.0143362i	$0.00456351\pi$
$787$			1.09992e10i			0.0286724i	−0.999897	+	0.0143362i	$0.995436\pi$
$788$		0			0
$789$	−3.12824e11	+	3.00986e11i	−0.807221	+	0.776673i
$790$		0			0
$791$			6.45744e11i			1.64951i
$792$		0			0
$793$		−	1.61044e11i		−	0.407241i
$794$		0			0
$795$	−1.67183e11	+	2.20027e11i	−0.418527	+	0.550818i
$796$		0			0
$797$	5.12456e11			1.27006			0.635028	−	0.772489i	$-0.280988\pi$
$797$	5.12456e11			1.27006			0.635028	+	0.772489i	$0.280988\pi$
$798$		0			0
$799$	8.09448e11			1.98610
$800$		0			0
$801$	−4.16060e10	−	1.60549e9i	−0.101071	−	0.00390013i
$802$		0			0
$803$	3.36374e11			0.809022
$804$		0			0
$805$	1.37521e11	+	8.80575e11i	0.327482	+	2.09693i
$806$		0			0
$807$	−2.96990e10	−	3.08672e10i	−0.0700242	−	0.0727784i
$808$		0			0
$809$		−	3.89639e10i		−	0.0909637i	−0.998965	−	0.0454819i	$-0.985518\pi$
$809$		−	3.89639e10i		−	0.0909637i	0.998965	−	0.0454819i	$-0.0144823\pi$
$810$		0			0
$811$	−7.29160e11			−1.68554			−0.842771	−	0.538273i	$-0.819077\pi$
$811$	−7.29160e11			−1.68554			−0.842771	+	0.538273i	$0.819077\pi$
$812$		0			0
$813$	1.75384e11	−	1.68747e11i	0.401447	−	0.386255i
$814$		0			0
$815$	2.39485e10	+	1.53347e11i	0.0542811	+	0.347572i
$816$		0			0
$817$		−	3.39026e11i		−	0.760929i
$818$		0			0
$819$	1.88369e10	−	4.88154e11i	0.0418672	−	1.08498i
$820$		0			0
$821$		−	7.07145e11i		−	1.55645i	−0.627985	−	0.778226i	$-0.716120\pi$
$821$		−	7.07145e11i		−	1.55645i	0.627985	−	0.778226i	$-0.283880\pi$
$822$		0			0
$823$		−	7.55818e10i		−	0.164747i	−0.996602	−	0.0823735i	$-0.973750\pi$
$823$		−	7.55818e10i		−	0.164747i	0.996602	−	0.0823735i	$-0.0262501\pi$
$824$		0			0
$825$	5.76418e11	+	3.11048e11i	1.24429	+	0.671446i
$826$		0			0
$827$	7.05475e10			0.150820			0.0754102	−	0.997153i	$-0.475973\pi$
$827$	7.05475e10			0.150820			0.0754102	+	0.997153i	$0.475973\pi$
$828$		0			0
$829$	−2.09032e11			−0.442584			−0.221292	−	0.975208i	$-0.571027\pi$
$829$	−2.09032e11			−0.442584			−0.221292	+	0.975208i	$0.571027\pi$
$830$		0			0
$831$	−5.13182e10	−	5.33367e10i	−0.107614	−	0.111846i
$832$		0			0
$833$	−9.19382e11			−1.90948
$834$		0			0
$835$	3.23383e11	−	5.05035e10i	0.665229	−	0.103890i
$836$		0			0
$837$	1.66085e11	+	1.86506e11i	0.338399	+	0.380007i
$838$		0			0
$839$		−	4.83411e11i		−	0.975593i	−0.872957	−	0.487796i	$-0.837801\pi$
$839$		−	4.83411e11i		−	0.975593i	0.872957	−	0.487796i	$-0.162199\pi$
$840$		0			0
$841$	4.92882e11			0.985279
$842$		0			0
$843$	−1.46285e11	−	1.52038e11i	−0.289660	−	0.301053i
$844$		0			0
$845$	−2.25771e11	+	3.52591e10i	−0.442834	+	0.0691584i
$846$		0			0
$847$		−	7.51615e11i		−	1.46037i
$848$		0			0
$849$	−6.12430e11	−	6.36518e11i	−1.17876	−	1.22512i
$850$		0			0
$851$			9.36550e11i			1.78572i
$852$		0			0
$853$		−	1.04488e12i		−	1.97365i	−0.161782	−	0.986826i	$-0.551724\pi$
$853$		−	1.04488e12i		−	1.97365i	0.161782	−	0.986826i	$-0.448276\pi$
$854$		0			0
$855$	−8.70811e10	−	7.45048e11i	−0.162952	−	1.39418i
$856$		0			0
$857$	3.05438e10			0.0566238			0.0283119	−	0.999599i	$-0.490987\pi$
$857$	3.05438e10			0.0566238			0.0283119	+	0.999599i	$0.490987\pi$
$858$		0			0
$859$	−1.22316e11			−0.224651			−0.112326	−	0.993671i	$-0.535830\pi$
$859$	−1.22316e11			−0.224651			−0.112326	+	0.993671i	$0.535830\pi$
$860$		0			0
$861$	3.40766e11	−	3.27870e11i	0.620074	−	0.596608i
$862$		0			0
$863$	3.75525e11			0.677010			0.338505	−	0.940965i	$-0.390079\pi$
$863$	3.75525e11			0.677010			0.338505	+	0.940965i	$0.390079\pi$
$864$		0			0
$865$	6.70547e11	−	1.04721e11i	1.19775	−	0.187055i
$866$		0			0
$867$	−7.42168e11	+	7.14081e11i	−1.31349	+	1.26378i
$868$		0			0
$869$		−	1.87550e11i		−	0.328881i
$870$		0			0
$871$	8.37548e11			1.45525
$872$		0			0
$873$	9.51389e11	+	3.67122e10i	1.63795	+	0.0632053i
$874$		0			0
$875$	−3.84033e11	−	7.65930e11i	−0.655144	−	1.30664i
$876$		0			0
$877$			6.52303e11i			1.10268i	0.834280	+	0.551342i	$0.185884\pi$
$877$			6.52303e11i			1.10268i	−0.834280	+	0.551342i	$0.814116\pi$
$878$		0			0
$879$	−2.29213e11	+	2.20539e11i	−0.383958	+	0.369428i
$880$		0			0
$881$		−	6.12964e11i		−	1.01749i	−0.860917	−	0.508746i	$-0.830109\pi$
$881$		−	6.12964e11i		−	1.01749i	0.860917	−	0.508746i	$-0.169891\pi$
$882$		0			0
$883$			1.05327e12i			1.73259i	0.499535	+	0.866294i	$0.333504\pi$
$883$			1.05327e12i			1.73259i	−0.499535	+	0.866294i	$0.666496\pi$
$884$		0			0
$885$	3.74182e11	+	2.84314e11i	0.609972	+	0.463474i
$886$		0			0
$887$	−5.34671e11			−0.863759			−0.431879	−	0.901931i	$-0.642149\pi$
$887$	−5.34671e11			−0.863759			−0.431879	+	0.901931i	$0.642149\pi$
$888$		0			0
$889$	−1.47887e12			−2.36769
$890$		0			0
$891$	−6.86695e10	+	8.88453e11i	−0.108957	+	1.40969i
$892$		0			0
$893$	−1.05521e12			−1.65933
$894$		0			0
$895$	−7.16553e10	−	4.58822e11i	−0.111675	−	0.715076i
$896$		0			0
$897$	−4.84136e11	−	5.03178e11i	−0.747821	−	0.777235i
$898$		0			0
$899$		−	4.03263e10i		−	0.0617375i
$900$		0			0
$901$	−7.65959e11			−1.16227
$902$		0			0
$903$	3.79651e11	−	3.65283e11i	0.570996	−	0.549387i
$904$		0			0
$905$	−5.72360e11	+	8.93867e10i	−0.853247	+	0.133254i
$906$		0			0
$907$		−	3.80383e11i		−	0.562072i	−0.959697	−	0.281036i	$-0.909322\pi$
$907$		−	3.80383e11i		−	0.562072i	0.959697	−	0.281036i	$-0.0906781\pi$
$908$		0			0
$909$	−6.45347e11	−	2.49027e10i	−0.945230	−	0.0364746i
$910$		0			0
$911$		−	3.03154e11i		−	0.440139i	−0.975484	−	0.220069i	$-0.929372\pi$
$911$		−	3.03154e11i		−	0.440139i	0.975484	−	0.220069i	$-0.0706284\pi$
$912$		0			0
$913$		−	9.22189e11i		−	1.32720i
$914$		0			0
$915$	2.32487e11	−	3.05973e11i	0.331676	−	0.436514i
$916$		0			0
$917$	5.77403e10			0.0816585
$918$		0			0
$919$	−3.33331e11			−0.467320			−0.233660	−	0.972318i	$-0.575070\pi$
$919$	−3.33331e11			−0.467320			−0.233660	+	0.972318i	$0.575070\pi$
$920$		0			0
$921$	5.21494e11	+	5.42006e11i	0.724788	+	0.753295i
$922$		0			0
$923$	−2.95338e11			−0.406923
$924$		0			0
$925$	−2.74528e11	−	8.57491e11i	−0.374991	−	1.17129i
$926$		0			0
$927$	−1.18515e12	−	4.57327e10i	−1.60493	−	0.0619310i
$928$		0			0
$929$			1.24660e12i			1.67365i	0.547472	+	0.836824i	$0.315590\pi$
$929$			1.24660e12i			1.67365i	−0.547472	+	0.836824i	$0.684410\pi$
$930$		0			0
$931$	1.19852e12			1.59532
$932$		0			0
$933$	−4.43882e11	−	4.61340e11i	−0.585788	−	0.608828i
$934$		0			0
$935$	2.80137e11	+	1.79377e12i	0.366542	+	2.34704i
$936$		0			0
$937$			6.54853e11i			0.849543i	0.905301	+	0.424772i	$0.139646\pi$
$937$			6.54853e11i			0.849543i	−0.905301	+	0.424772i	$0.860354\pi$
$938$		0			0
$939$	9.92958e11	+	1.03201e12i	1.27723	+	1.32746i
$940$		0			0
$941$		−	9.83748e10i		−	0.125466i	−0.998030	−	0.0627329i	$-0.980018\pi$
$941$		−	9.83748e10i		−	0.125466i	0.998030	−	0.0627329i	$-0.0199816\pi$
$942$		0			0
$943$		−	6.75921e11i		−	0.854770i
$944$		0			0
$945$	7.40501e11	−	9.00268e11i	0.928535	−	1.12887i
$946$		0			0
$947$	1.04818e12			1.30327			0.651637	−	0.758531i	$-0.274083\pi$
$947$	1.04818e12			1.30327			0.651637	+	0.758531i	$0.274083\pi$
$948$		0			0
$949$	3.44745e11			0.425044
$950$		0			0
$951$	−3.19445e11	+	3.07356e11i	−0.390548	+	0.375768i
$952$		0			0
$953$	−7.95476e11			−0.964396			−0.482198	−	0.876062i	$-0.660161\pi$
$953$	−7.95476e11			−0.964396			−0.482198	+	0.876062i	$0.660161\pi$
$954$		0			0
$955$	−5.13701e10	−	3.28932e11i	−0.0617586	−	0.395451i
$956$		0			0
$957$	1.03689e11	−	9.97650e10i	0.123619	−	0.118941i
$958$		0			0
$959$		−	6.75417e11i		−	0.798541i
$960$		0			0
$961$	−6.32061e11			−0.741081
$962$		0			0
$963$	−3.38258e10	+	8.76588e11i	−0.0393317	+	1.01927i
$964$		0			0
$965$	−5.37744e10	−	3.44327e11i	−0.0620106	−	0.397066i
$966$		0			0
$967$			1.22123e11i			0.139666i	0.997559	+	0.0698332i	$0.0222467\pi$
$967$			1.22123e11i			0.139666i	−0.997559	+	0.0698332i	$0.977753\pi$
$968$		0			0
$969$	1.49830e12	−	1.44159e12i	1.69943	−	1.63511i
$970$		0			0
$971$		−	5.74843e11i		−	0.646654i	−0.946287	−	0.323327i	$-0.895199\pi$
$971$		−	5.74843e11i		−	0.646654i	0.946287	−	0.323327i	$-0.104801\pi$
$972$		0			0
$973$			1.74991e12i			1.95238i
$974$		0			0
$975$	5.90763e11	+	3.18789e11i	0.653725	+	0.352764i
$976$		0			0
$977$	−8.41722e11			−0.923827			−0.461913	−	0.886925i	$-0.652837\pi$
$977$	−8.41722e11			−0.923827			−0.461913	+	0.886925i	$0.652837\pi$
$978$		0			0
$979$	−1.31370e11			−0.143010
$980$		0			0
$981$	8.38523e9	−	2.17301e11i	0.00905397	−	0.234632i
$982$		0			0
$983$	−5.79056e11			−0.620164			−0.310082	−	0.950710i	$-0.600356\pi$
$983$	−5.79056e11			−0.620164			−0.310082	+	0.950710i	$0.600356\pi$
$984$		0			0
$985$	−1.09643e12	+	1.71231e11i	−1.16475	+	0.181902i
$986$		0			0
$987$	−1.13693e12	−	1.18165e12i	−1.19803	−	1.24515i
$988$		0			0
$989$		−	7.53051e11i		−	0.787117i
$990$		0			0
$991$	5.05654e11			0.524274			0.262137	−	0.965031i	$-0.415573\pi$
$991$	5.05654e11			0.524274			0.262137	+	0.965031i	$0.415573\pi$
$992$		0			0
$993$	−3.23518e11	+	3.11275e11i	−0.332738	+	0.320146i
$994$		0			0
$995$	−1.15069e12	+	1.79706e11i	−1.17399	+	0.183345i
$996$		0			0
$997$		−	8.47251e11i		−	0.857495i	−0.903424	−	0.428747i	$-0.858955\pi$
$997$		−	8.47251e11i		−	0.857495i	0.903424	−	0.428747i	$-0.141045\pi$
$998$		0			0
$999$	9.14794e11	−	8.14630e11i	0.918463	−	0.817896i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.9.c.a.89.12	yes	48
3.2	odd	2	inner	120.9.c.a.89.38	yes	48
4.3	odd	2		240.9.c.f.209.37		48
5.4	even	2	inner	120.9.c.a.89.37	yes	48
12.11	even	2		240.9.c.f.209.11		48
15.14	odd	2	inner	120.9.c.a.89.11	✓	48
20.19	odd	2		240.9.c.f.209.12		48
60.59	even	2		240.9.c.f.209.38		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.9.c.a.89.11	✓	48	15.14	odd	2	inner
120.9.c.a.89.12	yes	48	1.1	even	1	trivial
120.9.c.a.89.37	yes	48	5.4	even	2	inner
120.9.c.a.89.38	yes	48	3.2	odd	2	inner
240.9.c.f.209.11		48	12.11	even	2
240.9.c.f.209.12		48	20.19	odd	2
240.9.c.f.209.37		48	4.3	odd	2
240.9.c.f.209.38		48	60.59	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

\(f(q)\)	\(=\)	\(q+(-58.3695 + 56.1605i) q^{3} +(-617.515 + 96.4387i) q^{5} +3509.51i q^{7} +(252.988 - 6556.12i) q^{9} -20700.8i q^{11} -21216.0i q^{13} +(30628.0 - 40309.0i) q^{15} +140324. q^{17} -182928. q^{19} +(-197096. - 204848. i) q^{21} -406324. q^{23} +(372024. - 119105. i) q^{25} +(353429. + 396885. i) q^{27} -85814.2i q^{29} +469925. q^{31} +(1.16257e6 + 1.20830e6i) q^{33} +(-338453. - 2.16717e6i) q^{35} -2.30493e6i q^{37} +(1.19150e6 + 1.23837e6i) q^{39} +1.66350e6i q^{41} +1.85333e6i q^{43} +(476040. + 4.07290e6i) q^{45} +5.76843e6 q^{47} -6.55186e6 q^{49} +(-8.19062e6 + 7.88066e6i) q^{51} -5.45851e6 q^{53} +(1.99636e6 + 1.27831e7i) q^{55} +(1.06774e7 - 1.02733e7i) q^{57} +9.28283e6i q^{59} +7.59067e6 q^{61} +(2.30088e7 + 887863. i) q^{63} +(2.04604e6 + 1.31012e7i) q^{65} +3.94772e7i q^{67} +(2.37169e7 - 2.28194e7i) q^{69} -1.39205e7i q^{71} +1.62493e7i q^{73} +(-1.50259e7 + 2.78452e7i) q^{75} +7.26498e7 q^{77} +9.06004e6 q^{79} +(-4.29187e7 - 3.31724e6i) q^{81} +4.45484e7 q^{83} +(-8.66520e7 + 1.35326e7i) q^{85} +(4.81937e6 + 5.00893e6i) q^{87} -6.34613e6i q^{89} +7.44578e7 q^{91} +(-2.74293e7 + 2.63913e7i) q^{93} +(1.12961e8 - 1.76413e7i) q^{95} +1.45115e8i q^{97} +(-1.35717e8 - 5.23706e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2528 q^{9} + 132352 q^{15} + 116176 q^{21} + 56976 q^{25} + 1395648 q^{31} + 6888832 q^{39} - 4287056 q^{45} - 30813552 q^{49} - 22815168 q^{51} - 6062784 q^{55} + 14031936 q^{61} + 2522608 q^{69}+ \cdots - 21719360 q^{99}+O(q^{100}) \) 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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