LMFDB - Embedded newform 240.2.w.a.223.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(127,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 0, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("240.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.w (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			223.2
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	240.223
Dual form			240.2.w.a.127.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{3} +(-2.00000 - 1.00000i) q^{5} +(-2.82843 - 2.82843i) q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{3} +(-2.00000 - 1.00000i) q^{5} +(-2.82843 - 2.82843i) q^{7} -1.00000i q^{9} -5.65685i q^{11} +(3.00000 + 3.00000i) q^{13} +(-2.12132 + 0.707107i) q^{15} +(-1.00000 + 1.00000i) q^{17} +5.65685 q^{19} -4.00000 q^{21} +(-2.82843 + 2.82843i) q^{23} +(3.00000 + 4.00000i) q^{25} +(-0.707107 - 0.707107i) q^{27} -4.00000i q^{29} +(-4.00000 - 4.00000i) q^{33} +(2.82843 + 8.48528i) q^{35} +(5.00000 - 5.00000i) q^{37} +4.24264 q^{39} +(-2.82843 + 2.82843i) q^{43} +(-1.00000 + 2.00000i) q^{45} +(-2.82843 - 2.82843i) q^{47} +9.00000i q^{49} +1.41421i q^{51} +(1.00000 + 1.00000i) q^{53} +(-5.65685 + 11.3137i) q^{55} +(4.00000 - 4.00000i) q^{57} +11.3137 q^{59} +4.00000 q^{61} +(-2.82843 + 2.82843i) q^{63} +(-3.00000 - 9.00000i) q^{65} +(2.82843 + 2.82843i) q^{67} +4.00000i q^{69} +5.65685i q^{71} +(-3.00000 - 3.00000i) q^{73} +(4.94975 + 0.707107i) q^{75} +(-16.0000 + 16.0000i) q^{77} +5.65685 q^{79} -1.00000 q^{81} +(-2.82843 + 2.82843i) q^{83} +(3.00000 - 1.00000i) q^{85} +(-2.82843 - 2.82843i) q^{87} -8.00000i q^{89} -16.9706i q^{91} +(-11.3137 - 5.65685i) q^{95} +(-3.00000 + 3.00000i) q^{97} -5.65685 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{5}+O(q^{10}) $ 4 * q - 8 * q^5	$ 4 q - 8 q^{5} + 12 q^{13} - 4 q^{17} - 16 q^{21} + 12 q^{25} - 16 q^{33} + 20 q^{37} - 4 q^{45} + 4 q^{53} + 16 q^{57} + 16 q^{61} - 12 q^{65} - 12 q^{73} - 64 q^{77} - 4 q^{81} + 12 q^{85} - 12 q^{97}+O(q^{100}) $ 4 * q - 8 * q^5 + 12 * q^13 - 4 * q^17 - 16 * q^21 + 12 * q^25 - 16 * q^33 + 20 * q^37 - 4 * q^45 + 4 * q^53 + 16 * q^57 + 16 * q^61 - 12 * q^65 - 12 * q^73 - 64 * q^77 - 4 * q^81 + 12 * q^85 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		0			0
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$6$		0			0
$7$	−2.82843	−	2.82843i	−1.06904	−	1.06904i	−0.997433	−	0.0716124i	$-0.977186\pi$
$7$	−2.82843	−	2.82843i	−1.06904	−	1.06904i	−0.0716124	−	0.997433i	$-0.522814\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$		−	5.65685i		−	1.70561i	−0.522233	−	0.852803i	$-0.674901\pi$
$11$		−	5.65685i		−	1.70561i	0.522233	−	0.852803i	$-0.325099\pi$
$12$		0			0
$13$	3.00000	+	3.00000i	0.832050	+	0.832050i	0.987797	−	0.155747i	$-0.0497784\pi$
$13$	3.00000	+	3.00000i	0.832050	+	0.832050i	−0.155747	+	0.987797i	$0.549778\pi$
$14$		0			0
$15$	−2.12132	+	0.707107i	−0.547723	+	0.182574i
$16$		0			0
$17$	−1.00000	+	1.00000i	−0.242536	+	0.242536i	−0.817898	−	0.575363i	$-0.804861\pi$
$17$	−1.00000	+	1.00000i	−0.242536	+	0.242536i	0.575363	+	0.817898i	$0.304861\pi$
$18$		0			0
$19$	5.65685			1.29777			0.648886	−	0.760886i	$-0.275235\pi$
$19$	5.65685			1.29777			0.648886	+	0.760886i	$0.275235\pi$
$20$		0			0
$21$	−4.00000			−0.872872
$22$		0			0
$23$	−2.82843	+	2.82843i	−0.589768	+	0.589768i	−0.937568	−	0.347801i	$-0.886929\pi$
$23$	−2.82843	+	2.82843i	−0.589768	+	0.589768i	0.347801	+	0.937568i	$0.386929\pi$
$24$		0			0
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$		−	4.00000i		−	0.742781i	−0.928477	−	0.371391i	$-0.878881\pi$
$29$		−	4.00000i		−	0.742781i	0.928477	−	0.371391i	$-0.121119\pi$
$30$		0			0
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$		0			0
$33$	−4.00000	−	4.00000i	−0.696311	−	0.696311i
$34$		0			0
$35$	2.82843	+	8.48528i	0.478091	+	1.43427i
$36$		0			0
$37$	5.00000	−	5.00000i	0.821995	−	0.821995i	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	5.00000	−	5.00000i	0.821995	−	0.821995i	0.986394	+	0.164399i	$0.0525685\pi$
$38$		0			0
$39$	4.24264			0.679366
$40$		0			0
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		0			0
$43$	−2.82843	+	2.82843i	−0.431331	+	0.431331i	−0.889081	−	0.457750i	$-0.848656\pi$
$43$	−2.82843	+	2.82843i	−0.431331	+	0.431331i	0.457750	+	0.889081i	$0.348656\pi$
$44$		0			0
$45$	−1.00000	+	2.00000i	−0.149071	+	0.298142i
$46$		0			0
$47$	−2.82843	−	2.82843i	−0.412568	−	0.412568i	0.470064	−	0.882632i	$-0.344231\pi$
$47$	−2.82843	−	2.82843i	−0.412568	−	0.412568i	−0.882632	+	0.470064i	$0.844231\pi$
$48$		0			0
$49$			9.00000i			1.28571i
$50$		0			0
$51$			1.41421i			0.198030i
$52$		0			0
$53$	1.00000	+	1.00000i	0.137361	+	0.137361i	0.772444	−	0.635083i	$-0.219034\pi$
$53$	1.00000	+	1.00000i	0.137361	+	0.137361i	−0.635083	+	0.772444i	$0.719034\pi$
$54$		0			0
$55$	−5.65685	+	11.3137i	−0.762770	+	1.52554i
$56$		0			0
$57$	4.00000	−	4.00000i	0.529813	−	0.529813i
$58$		0			0
$59$	11.3137			1.47292			0.736460	−	0.676481i	$-0.236496\pi$
$59$	11.3137			1.47292			0.736460	+	0.676481i	$0.236496\pi$
$60$		0			0
$61$	4.00000			0.512148			0.256074	−	0.966657i	$-0.417571\pi$
$61$	4.00000			0.512148			0.256074	+	0.966657i	$0.417571\pi$
$62$		0			0
$63$	−2.82843	+	2.82843i	−0.356348	+	0.356348i
$64$		0			0
$65$	−3.00000	−	9.00000i	−0.372104	−	1.11631i
$66$		0			0
$67$	2.82843	+	2.82843i	0.345547	+	0.345547i	0.858448	−	0.512901i	$-0.171429\pi$
$67$	2.82843	+	2.82843i	0.345547	+	0.345547i	−0.512901	+	0.858448i	$0.671429\pi$
$68$		0			0
$69$			4.00000i			0.481543i
$70$		0			0
$71$			5.65685i			0.671345i	0.941979	+	0.335673i	$0.108964\pi$
$71$			5.65685i			0.671345i	−0.941979	+	0.335673i	$0.891036\pi$
$72$		0			0
$73$	−3.00000	−	3.00000i	−0.351123	−	0.351123i	0.509404	−	0.860527i	$-0.329866\pi$
$73$	−3.00000	−	3.00000i	−0.351123	−	0.351123i	−0.860527	+	0.509404i	$0.829866\pi$
$74$		0			0
$75$	4.94975	+	0.707107i	0.571548	+	0.0816497i
$76$		0			0
$77$	−16.0000	+	16.0000i	−1.82337	+	1.82337i
$78$		0			0
$79$	5.65685			0.636446			0.318223	−	0.948016i	$-0.396914\pi$
$79$	5.65685			0.636446			0.318223	+	0.948016i	$0.396914\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−2.82843	+	2.82843i	−0.310460	+	0.310460i	−0.845088	−	0.534628i	$-0.820452\pi$
$83$	−2.82843	+	2.82843i	−0.310460	+	0.310460i	0.534628	+	0.845088i	$0.320452\pi$
$84$		0			0
$85$	3.00000	−	1.00000i	0.325396	−	0.108465i
$86$		0			0
$87$	−2.82843	−	2.82843i	−0.303239	−	0.303239i
$88$		0			0
$89$		−	8.00000i		−	0.847998i	−0.905663	−	0.423999i	$-0.860626\pi$
$89$		−	8.00000i		−	0.847998i	0.905663	−	0.423999i	$-0.139374\pi$
$90$		0			0
$91$		−	16.9706i		−	1.77900i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−11.3137	−	5.65685i	−1.16076	−	0.580381i
$96$		0			0
$97$	−3.00000	+	3.00000i	−0.304604	+	0.304604i	−0.842812	−	0.538208i	$-0.819101\pi$
$97$	−3.00000	+	3.00000i	−0.304604	+	0.304604i	0.538208	+	0.842812i	$0.319101\pi$
$98$		0			0
$99$	−5.65685			−0.568535
$100$		0			0
$101$	18.0000			1.79107			0.895533	−	0.444994i	$-0.146794\pi$
$101$	18.0000			1.79107			0.895533	+	0.444994i	$0.146794\pi$
$102$		0			0
$103$	2.82843	−	2.82843i	0.278693	−	0.278693i	−0.553894	−	0.832587i	$-0.686859\pi$
$103$	2.82843	−	2.82843i	0.278693	−	0.278693i	0.832587	+	0.553894i	$0.186859\pi$
$104$		0			0
$105$	8.00000	+	4.00000i	0.780720	+	0.390360i
$106$		0			0
$107$	−8.48528	−	8.48528i	−0.820303	−	0.820303i	0.165848	−	0.986151i	$-0.446964\pi$
$107$	−8.48528	−	8.48528i	−0.820303	−	0.820303i	−0.986151	+	0.165848i	$0.946964\pi$
$108$		0			0
$109$		−	10.0000i		−	0.957826i	−0.877862	−	0.478913i	$-0.841031\pi$
$109$		−	10.0000i		−	0.957826i	0.877862	−	0.478913i	$-0.158969\pi$
$110$		0			0
$111$		−	7.07107i		−	0.671156i
$112$		0			0
$113$	11.0000	+	11.0000i	1.03479	+	1.03479i	0.999372	+	0.0354205i	$0.0112770\pi$
$113$	11.0000	+	11.0000i	1.03479	+	1.03479i	0.0354205	+	0.999372i	$0.488723\pi$
$114$		0			0
$115$	8.48528	−	2.82843i	0.791257	−	0.263752i
$116$		0			0
$117$	3.00000	−	3.00000i	0.277350	−	0.277350i
$118$		0			0
$119$	5.65685			0.518563
$120$		0			0
$121$	−21.0000			−1.90909
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$		0			0
$127$	−8.48528	−	8.48528i	−0.752947	−	0.752947i	0.222081	−	0.975028i	$-0.428715\pi$
$127$	−8.48528	−	8.48528i	−0.752947	−	0.752947i	−0.975028	+	0.222081i	$0.928715\pi$
$128$		0			0
$129$			4.00000i			0.352180i
$130$		0			0
$131$		−	5.65685i		−	0.494242i	−0.968985	−	0.247121i	$-0.920516\pi$
$131$		−	5.65685i		−	0.494242i	0.968985	−	0.247121i	$-0.0794845\pi$
$132$		0			0
$133$	−16.0000	−	16.0000i	−1.38738	−	1.38738i
$134$		0			0
$135$	0.707107	+	2.12132i	0.0608581	+	0.182574i
$136$		0			0
$137$	5.00000	−	5.00000i	0.427179	−	0.427179i	−0.460487	−	0.887666i	$-0.652325\pi$
$137$	5.00000	−	5.00000i	0.427179	−	0.427179i	0.887666	+	0.460487i	$0.152325\pi$
$138$		0			0
$139$	−16.9706			−1.43942			−0.719712	−	0.694273i	$-0.755726\pi$
$139$	−16.9706			−1.43942			−0.719712	+	0.694273i	$0.755726\pi$
$140$		0			0
$141$	−4.00000			−0.336861
$142$		0			0
$143$	16.9706	−	16.9706i	1.41915	−	1.41915i
$144$		0			0
$145$	−4.00000	+	8.00000i	−0.332182	+	0.664364i
$146$		0			0
$147$	6.36396	+	6.36396i	0.524891	+	0.524891i
$148$		0			0
$149$			18.0000i			1.47462i	0.675556	+	0.737309i	$0.263904\pi$
$149$			18.0000i			1.47462i	−0.675556	+	0.737309i	$0.736096\pi$
$150$		0			0
$151$			11.3137i			0.920697i	0.887738	+	0.460348i	$0.152275\pi$
$151$			11.3137i			0.920697i	−0.887738	+	0.460348i	$0.847725\pi$
$152$		0			0
$153$	1.00000	+	1.00000i	0.0808452	+	0.0808452i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	11.0000	−	11.0000i	0.877896	−	0.877896i	−0.115421	−	0.993317i	$-0.536822\pi$
$157$	11.0000	−	11.0000i	0.877896	−	0.877896i	0.993317	+	0.115421i	$0.0368217\pi$
$158$		0			0
$159$	1.41421			0.112154
$160$		0			0
$161$	16.0000			1.26098
$162$		0			0
$163$	−8.48528	+	8.48528i	−0.664619	+	0.664619i	−0.956465	−	0.291847i	$-0.905730\pi$
$163$	−8.48528	+	8.48528i	−0.664619	+	0.664619i	0.291847	+	0.956465i	$0.405730\pi$
$164$		0			0
$165$	4.00000	+	12.0000i	0.311400	+	0.934199i
$166$		0			0
$167$	8.48528	+	8.48528i	0.656611	+	0.656611i	0.954577	−	0.297966i	$-0.0963081\pi$
$167$	8.48528	+	8.48528i	0.656611	+	0.656611i	−0.297966	+	0.954577i	$0.596308\pi$
$168$		0			0
$169$			5.00000i			0.384615i
$170$		0			0
$171$		−	5.65685i		−	0.432590i
$172$		0			0
$173$	5.00000	+	5.00000i	0.380143	+	0.380143i	0.871154	−	0.491011i	$-0.163372\pi$
$173$	5.00000	+	5.00000i	0.380143	+	0.380143i	−0.491011	+	0.871154i	$0.663372\pi$
$174$		0			0
$175$	2.82843	−	19.7990i	0.213809	−	1.49666i
$176$		0			0
$177$	8.00000	−	8.00000i	0.601317	−	0.601317i
$178$		0			0
$179$	−22.6274			−1.69125			−0.845626	−	0.533775i	$-0.820773\pi$
$179$	−22.6274			−1.69125			−0.845626	+	0.533775i	$0.820773\pi$
$180$		0			0
$181$	−18.0000			−1.33793			−0.668965	−	0.743294i	$-0.733262\pi$
$181$	−18.0000			−1.33793			−0.668965	+	0.743294i	$0.733262\pi$
$182$		0			0
$183$	2.82843	−	2.82843i	0.209083	−	0.209083i
$184$		0			0
$185$	−15.0000	+	5.00000i	−1.10282	+	0.367607i
$186$		0			0
$187$	5.65685	+	5.65685i	0.413670	+	0.413670i
$188$		0			0
$189$			4.00000i			0.290957i
$190$		0			0
$191$			16.9706i			1.22795i	0.789327	+	0.613973i	$0.210430\pi$
$191$			16.9706i			1.22795i	−0.789327	+	0.613973i	$0.789570\pi$
$192$		0			0
$193$	−5.00000	−	5.00000i	−0.359908	−	0.359908i	0.503871	−	0.863779i	$-0.331909\pi$
$193$	−5.00000	−	5.00000i	−0.359908	−	0.359908i	−0.863779	+	0.503871i	$0.831909\pi$
$194$		0			0
$195$	−8.48528	−	4.24264i	−0.607644	−	0.303822i
$196$		0			0
$197$	−11.0000	+	11.0000i	−0.783718	+	0.783718i	−0.980456	−	0.196738i	$-0.936965\pi$
$197$	−11.0000	+	11.0000i	−0.783718	+	0.783718i	0.196738	+	0.980456i	$0.436965\pi$
$198$		0			0
$199$	16.9706			1.20301			0.601506	−	0.798869i	$-0.294568\pi$
$199$	16.9706			1.20301			0.601506	+	0.798869i	$0.294568\pi$
$200$		0			0
$201$	4.00000			0.282138
$202$		0			0
$203$	−11.3137	+	11.3137i	−0.794067	+	0.794067i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	2.82843	+	2.82843i	0.196589	+	0.196589i
$208$		0			0
$209$		−	32.0000i		−	2.21349i
$210$		0			0
$211$			22.6274i			1.55774i	0.627188	+	0.778868i	$0.284206\pi$
$211$			22.6274i			1.55774i	−0.627188	+	0.778868i	$0.715794\pi$
$212$		0			0
$213$	4.00000	+	4.00000i	0.274075	+	0.274075i
$214$		0			0
$215$	8.48528	−	2.82843i	0.578691	−	0.192897i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−4.24264			−0.286691
$220$		0			0
$221$	−6.00000			−0.403604
$222$		0			0
$223$	8.48528	−	8.48528i	0.568216	−	0.568216i	−0.363412	−	0.931629i	$-0.618388\pi$
$223$	8.48528	−	8.48528i	0.568216	−	0.568216i	0.931629	+	0.363412i	$0.118388\pi$
$224$		0			0
$225$	4.00000	−	3.00000i	0.266667	−	0.200000i
$226$		0			0
$227$	19.7990	+	19.7990i	1.31411	+	1.31411i	0.918361	+	0.395744i	$0.129513\pi$
$227$	19.7990	+	19.7990i	1.31411	+	1.31411i	0.395744	+	0.918361i	$0.370487\pi$
$228$		0			0
$229$		−	12.0000i		−	0.792982i	−0.918039	−	0.396491i	$-0.870228\pi$
$229$		−	12.0000i		−	0.792982i	0.918039	−	0.396491i	$-0.129772\pi$
$230$		0			0
$231$			22.6274i			1.48877i
$232$		0			0
$233$	15.0000	+	15.0000i	0.982683	+	0.982683i	0.999853	−	0.0171699i	$-0.00546562\pi$
$233$	15.0000	+	15.0000i	0.982683	+	0.982683i	−0.0171699	+	0.999853i	$0.505466\pi$
$234$		0			0
$235$	2.82843	+	8.48528i	0.184506	+	0.553519i
$236$		0			0
$237$	4.00000	−	4.00000i	0.259828	−	0.259828i
$238$		0			0
$239$	−11.3137			−0.731823			−0.365911	−	0.930650i	$-0.619243\pi$
$239$	−11.3137			−0.731823			−0.365911	+	0.930650i	$0.619243\pi$
$240$		0			0
$241$	8.00000			0.515325			0.257663	−	0.966235i	$-0.417048\pi$
$241$	8.00000			0.515325			0.257663	+	0.966235i	$0.417048\pi$
$242$		0			0
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	9.00000	−	18.0000i	0.574989	−	1.14998i
$246$		0			0
$247$	16.9706	+	16.9706i	1.07981	+	1.07981i
$248$		0			0
$249$			4.00000i			0.253490i
$250$		0			0
$251$		−	5.65685i		−	0.357057i	−0.983935	−	0.178529i	$-0.942866\pi$
$251$		−	5.65685i		−	0.357057i	0.983935	−	0.178529i	$-0.0571337\pi$
$252$		0			0
$253$	16.0000	+	16.0000i	1.00591	+	1.00591i
$254$		0			0
$255$	1.41421	−	2.82843i	0.0885615	−	0.177123i
$256$		0			0
$257$	−21.0000	+	21.0000i	−1.30994	+	1.30994i	−0.388492	+	0.921452i	$0.627004\pi$
$257$	−21.0000	+	21.0000i	−1.30994	+	1.30994i	−0.921452	+	0.388492i	$0.872996\pi$
$258$		0			0
$259$	−28.2843			−1.75750
$260$		0			0
$261$	−4.00000			−0.247594
$262$		0			0
$263$	−2.82843	+	2.82843i	−0.174408	+	0.174408i	−0.788913	−	0.614505i	$-0.789356\pi$
$263$	−2.82843	+	2.82843i	−0.174408	+	0.174408i	0.614505	+	0.788913i	$0.289356\pi$
$264$		0			0
$265$	−1.00000	−	3.00000i	−0.0614295	−	0.184289i
$266$		0			0
$267$	−5.65685	−	5.65685i	−0.346194	−	0.346194i
$268$		0			0
$269$		−	6.00000i		−	0.365826i	−0.983129	−	0.182913i	$-0.941447\pi$
$269$		−	6.00000i		−	0.365826i	0.983129	−	0.182913i	$-0.0585527\pi$
$270$		0			0
$271$			11.3137i			0.687259i	0.939105	+	0.343629i	$0.111656\pi$
$271$			11.3137i			0.687259i	−0.939105	+	0.343629i	$0.888344\pi$
$272$		0			0
$273$	−12.0000	−	12.0000i	−0.726273	−	0.726273i
$274$		0			0
$275$	22.6274	−	16.9706i	1.36448	−	1.02336i
$276$		0			0
$277$	3.00000	−	3.00000i	0.180253	−	0.180253i	−0.611213	−	0.791466i	$-0.709318\pi$
$277$	3.00000	−	3.00000i	0.180253	−	0.180253i	0.791466	+	0.611213i	$0.209318\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	8.00000			0.477240			0.238620	−	0.971113i	$-0.423305\pi$
$281$	8.00000			0.477240			0.238620	+	0.971113i	$0.423305\pi$
$282$		0			0
$283$	14.1421	−	14.1421i	0.840663	−	0.840663i	−0.148282	−	0.988945i	$-0.547374\pi$
$283$	14.1421	−	14.1421i	0.840663	−	0.840663i	0.988945	+	0.148282i	$0.0473744\pi$
$284$		0			0
$285$	−12.0000	+	4.00000i	−0.710819	+	0.236940i
$286$		0			0
$287$		0			0
$288$		0			0
$289$			15.0000i			0.882353i
$290$		0			0
$291$			4.24264i			0.248708i
$292$		0			0
$293$	−5.00000	−	5.00000i	−0.292103	−	0.292103i	0.545807	−	0.837911i	$-0.316223\pi$
$293$	−5.00000	−	5.00000i	−0.292103	−	0.292103i	−0.837911	+	0.545807i	$0.816223\pi$
$294$		0			0
$295$	−22.6274	−	11.3137i	−1.31742	−	0.658710i
$296$		0			0
$297$	−4.00000	+	4.00000i	−0.232104	+	0.232104i
$298$		0			0
$299$	−16.9706			−0.981433
$300$		0			0
$301$	16.0000			0.922225
$302$		0			0
$303$	12.7279	−	12.7279i	0.731200	−	0.731200i
$304$		0			0
$305$	−8.00000	−	4.00000i	−0.458079	−	0.229039i
$306$		0			0
$307$	−2.82843	−	2.82843i	−0.161427	−	0.161427i	0.621772	−	0.783199i	$-0.286413\pi$
$307$	−2.82843	−	2.82843i	−0.161427	−	0.161427i	−0.783199	+	0.621772i	$0.786413\pi$
$308$		0			0
$309$		−	4.00000i		−	0.227552i
$310$		0			0
$311$		−	5.65685i		−	0.320771i	−0.987054	−	0.160385i	$-0.948726\pi$
$311$		−	5.65685i		−	0.320771i	0.987054	−	0.160385i	$-0.0512737\pi$
$312$		0			0
$313$	−9.00000	−	9.00000i	−0.508710	−	0.508710i	0.405420	−	0.914130i	$-0.367125\pi$
$313$	−9.00000	−	9.00000i	−0.508710	−	0.508710i	−0.914130	+	0.405420i	$0.867125\pi$
$314$		0			0
$315$	8.48528	−	2.82843i	0.478091	−	0.159364i
$316$		0			0
$317$	11.0000	−	11.0000i	0.617822	−	0.617822i	−0.327151	−	0.944972i	$-0.606088\pi$
$317$	11.0000	−	11.0000i	0.617822	−	0.617822i	0.944972	+	0.327151i	$0.106088\pi$
$318$		0			0
$319$	−22.6274			−1.26689
$320$		0			0
$321$	−12.0000			−0.669775
$322$		0			0
$323$	−5.65685	+	5.65685i	−0.314756	+	0.314756i
$324$		0			0
$325$	−3.00000	+	21.0000i	−0.166410	+	1.16487i
$326$		0			0
$327$	−7.07107	−	7.07107i	−0.391031	−	0.391031i
$328$		0			0
$329$			16.0000i			0.882109i
$330$		0			0
$331$		−	22.6274i		−	1.24372i	−0.783130	−	0.621858i	$-0.786378\pi$
$331$		−	22.6274i		−	1.24372i	0.783130	−	0.621858i	$-0.213622\pi$
$332$		0			0
$333$	−5.00000	−	5.00000i	−0.273998	−	0.273998i
$334$		0			0
$335$	−2.82843	−	8.48528i	−0.154533	−	0.463600i
$336$		0			0
$337$	1.00000	−	1.00000i	0.0544735	−	0.0544735i	−0.679345	−	0.733819i	$-0.737736\pi$
$337$	1.00000	−	1.00000i	0.0544735	−	0.0544735i	0.733819	+	0.679345i	$0.237736\pi$
$338$		0			0
$339$	15.5563			0.844905
$340$		0			0
$341$		0			0
$342$		0			0
$343$	5.65685	−	5.65685i	0.305441	−	0.305441i
$344$		0			0
$345$	4.00000	−	8.00000i	0.215353	−	0.430706i
$346$		0			0
$347$	−2.82843	−	2.82843i	−0.151838	−	0.151838i	0.627100	−	0.778938i	$-0.284242\pi$
$347$	−2.82843	−	2.82843i	−0.151838	−	0.151838i	−0.778938	+	0.627100i	$0.784242\pi$
$348$		0			0
$349$			28.0000i			1.49881i	0.662114	+	0.749403i	$0.269659\pi$
$349$			28.0000i			1.49881i	−0.662114	+	0.749403i	$0.730341\pi$
$350$		0			0
$351$		−	4.24264i		−	0.226455i
$352$		0			0
$353$	−11.0000	−	11.0000i	−0.585471	−	0.585471i	0.350931	−	0.936401i	$-0.385865\pi$
$353$	−11.0000	−	11.0000i	−0.585471	−	0.585471i	−0.936401	+	0.350931i	$0.885865\pi$
$354$		0			0
$355$	5.65685	−	11.3137i	0.300235	−	0.600469i
$356$		0			0
$357$	4.00000	−	4.00000i	0.211702	−	0.211702i
$358$		0			0
$359$	11.3137			0.597115			0.298557	−	0.954392i	$-0.403495\pi$
$359$	11.3137			0.597115			0.298557	+	0.954392i	$0.403495\pi$
$360$		0			0
$361$	13.0000			0.684211
$362$		0			0
$363$	−14.8492	+	14.8492i	−0.779383	+	0.779383i
$364$		0			0
$365$	3.00000	+	9.00000i	0.157027	+	0.471082i
$366$		0			0
$367$	8.48528	+	8.48528i	0.442928	+	0.442928i	0.892995	−	0.450067i	$-0.148600\pi$
$367$	8.48528	+	8.48528i	0.442928	+	0.442928i	−0.450067	+	0.892995i	$0.648600\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		−	5.65685i		−	0.293689i
$372$		0			0
$373$	9.00000	+	9.00000i	0.466002	+	0.466002i	0.900617	−	0.434614i	$-0.143115\pi$
$373$	9.00000	+	9.00000i	0.466002	+	0.466002i	−0.434614	+	0.900617i	$0.643115\pi$
$374$		0			0
$375$	−9.19239	−	6.36396i	−0.474693	−	0.328634i
$376$		0			0
$377$	12.0000	−	12.0000i	0.618031	−	0.618031i
$378$		0			0
$379$	16.9706			0.871719			0.435860	−	0.900015i	$-0.356444\pi$
$379$	16.9706			0.871719			0.435860	+	0.900015i	$0.356444\pi$
$380$		0			0
$381$	−12.0000			−0.614779
$382$		0			0
$383$	14.1421	−	14.1421i	0.722629	−	0.722629i	−0.246511	−	0.969140i	$-0.579284\pi$
$383$	14.1421	−	14.1421i	0.722629	−	0.722629i	0.969140	+	0.246511i	$0.0792840\pi$
$384$		0			0
$385$	48.0000	−	16.0000i	2.44631	−	0.815436i
$386$		0			0
$387$	2.82843	+	2.82843i	0.143777	+	0.143777i
$388$		0			0
$389$		−	2.00000i		−	0.101404i	−0.998714	−	0.0507020i	$-0.983854\pi$
$389$		−	2.00000i		−	0.101404i	0.998714	−	0.0507020i	$-0.0161459\pi$
$390$		0			0
$391$		−	5.65685i		−	0.286079i
$392$		0			0
$393$	−4.00000	−	4.00000i	−0.201773	−	0.201773i
$394$		0			0
$395$	−11.3137	−	5.65685i	−0.569254	−	0.284627i
$396$		0			0
$397$	9.00000	−	9.00000i	0.451697	−	0.451697i	−0.444220	−	0.895918i	$-0.646519\pi$
$397$	9.00000	−	9.00000i	0.451697	−	0.451697i	0.895918	+	0.444220i	$0.146519\pi$
$398$		0			0
$399$	−22.6274			−1.13279
$400$		0			0
$401$	−30.0000			−1.49813			−0.749064	−	0.662497i	$-0.769497\pi$
$401$	−30.0000			−1.49813			−0.749064	+	0.662497i	$0.769497\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	2.00000	+	1.00000i	0.0993808	+	0.0496904i
$406$		0			0
$407$	−28.2843	−	28.2843i	−1.40200	−	1.40200i
$408$		0			0
$409$		−	10.0000i		−	0.494468i	−0.968956	−	0.247234i	$-0.920478\pi$
$409$		−	10.0000i		−	0.494468i	0.968956	−	0.247234i	$-0.0795217\pi$
$410$		0			0
$411$		−	7.07107i		−	0.348790i
$412$		0			0
$413$	−32.0000	−	32.0000i	−1.57462	−	1.57462i
$414$		0			0
$415$	8.48528	−	2.82843i	0.416526	−	0.138842i
$416$		0			0
$417$	−12.0000	+	12.0000i	−0.587643	+	0.587643i
$418$		0			0
$419$	−11.3137			−0.552711			−0.276355	−	0.961056i	$-0.589127\pi$
$419$	−11.3137			−0.552711			−0.276355	+	0.961056i	$0.589127\pi$
$420$		0			0
$421$	−4.00000			−0.194948			−0.0974740	−	0.995238i	$-0.531076\pi$
$421$	−4.00000			−0.194948			−0.0974740	+	0.995238i	$0.531076\pi$
$422$		0			0
$423$	−2.82843	+	2.82843i	−0.137523	+	0.137523i
$424$		0			0
$425$	−7.00000	−	1.00000i	−0.339550	−	0.0485071i
$426$		0			0
$427$	−11.3137	−	11.3137i	−0.547509	−	0.547509i
$428$		0			0
$429$		−	24.0000i		−	1.15873i
$430$		0			0
$431$			16.9706i			0.817443i	0.912659	+	0.408722i	$0.134025\pi$
$431$			16.9706i			0.817443i	−0.912659	+	0.408722i	$0.865975\pi$
$432$		0			0
$433$	21.0000	+	21.0000i	1.00920	+	1.00920i	0.999957	+	0.00923827i	$0.00294067\pi$
$433$	21.0000	+	21.0000i	1.00920	+	1.00920i	0.00923827	+	0.999957i	$0.497059\pi$
$434$		0			0
$435$	2.82843	+	8.48528i	0.135613	+	0.406838i
$436$		0			0
$437$	−16.0000	+	16.0000i	−0.765384	+	0.765384i
$438$		0			0
$439$	5.65685			0.269987			0.134993	−	0.990846i	$-0.456899\pi$
$439$	5.65685			0.269987			0.134993	+	0.990846i	$0.456899\pi$
$440$		0			0
$441$	9.00000			0.428571
$442$		0			0
$443$	25.4558	−	25.4558i	1.20944	−	1.20944i	0.238236	−	0.971207i	$-0.423431\pi$
$443$	25.4558	−	25.4558i	1.20944	−	1.20944i	0.971207	−	0.238236i	$-0.0765693\pi$
$444$		0			0
$445$	−8.00000	+	16.0000i	−0.379236	+	0.758473i
$446$		0			0
$447$	12.7279	+	12.7279i	0.602010	+	0.602010i
$448$		0			0
$449$			2.00000i			0.0943858i	0.998886	+	0.0471929i	$0.0150276\pi$
$449$			2.00000i			0.0943858i	−0.998886	+	0.0471929i	$0.984972\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	8.00000	+	8.00000i	0.375873	+	0.375873i
$454$		0			0
$455$	−16.9706	+	33.9411i	−0.795592	+	1.59118i
$456$		0			0
$457$	−17.0000	+	17.0000i	−0.795226	+	0.795226i	−0.982339	−	0.187112i	$-0.940087\pi$
$457$	−17.0000	+	17.0000i	−0.795226	+	0.795226i	0.187112	+	0.982339i	$0.440087\pi$
$458$		0			0
$459$	1.41421			0.0660098
$460$		0			0
$461$	10.0000			0.465746			0.232873	−	0.972507i	$-0.425187\pi$
$461$	10.0000			0.465746			0.232873	+	0.972507i	$0.425187\pi$
$462$		0			0
$463$	−25.4558	+	25.4558i	−1.18303	+	1.18303i	−0.204079	+	0.978954i	$0.565420\pi$
$463$	−25.4558	+	25.4558i	−1.18303	+	1.18303i	−0.978954	+	0.204079i	$0.934580\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	25.4558	+	25.4558i	1.17796	+	1.17796i	0.980264	+	0.197692i	$0.0633445\pi$
$467$	25.4558	+	25.4558i	1.17796	+	1.17796i	0.197692	+	0.980264i	$0.436655\pi$
$468$		0			0
$469$		−	16.0000i		−	0.738811i
$470$		0			0
$471$		−	15.5563i		−	0.716799i
$472$		0			0
$473$	16.0000	+	16.0000i	0.735681	+	0.735681i
$474$		0			0
$475$	16.9706	+	22.6274i	0.778663	+	1.03822i
$476$		0			0
$477$	1.00000	−	1.00000i	0.0457869	−	0.0457869i
$478$		0			0
$479$	22.6274			1.03387			0.516937	−	0.856024i	$-0.327072\pi$
$479$	22.6274			1.03387			0.516937	+	0.856024i	$0.327072\pi$
$480$		0			0
$481$	30.0000			1.36788
$482$		0			0
$483$	11.3137	−	11.3137i	0.514792	−	0.514792i
$484$		0			0
$485$	9.00000	−	3.00000i	0.408669	−	0.136223i
$486$		0			0
$487$	−19.7990	−	19.7990i	−0.897178	−	0.897178i	0.0980078	−	0.995186i	$-0.468753\pi$
$487$	−19.7990	−	19.7990i	−0.897178	−	0.897178i	−0.995186	+	0.0980078i	$0.968753\pi$
$488$		0			0
$489$			12.0000i			0.542659i
$490$		0			0
$491$			28.2843i			1.27645i	0.769849	+	0.638226i	$0.220331\pi$
$491$			28.2843i			1.27645i	−0.769849	+	0.638226i	$0.779669\pi$
$492$		0			0
$493$	4.00000	+	4.00000i	0.180151	+	0.180151i
$494$		0			0
$495$	11.3137	+	5.65685i	0.508513	+	0.254257i
$496$		0			0
$497$	16.0000	−	16.0000i	0.717698	−	0.717698i
$498$		0			0
$499$	28.2843			1.26618			0.633089	−	0.774079i	$-0.281787\pi$
$499$	28.2843			1.26618			0.633089	+	0.774079i	$0.281787\pi$
$500$		0			0
$501$	12.0000			0.536120
$502$		0			0
$503$	−31.1127	+	31.1127i	−1.38725	+	1.38725i	−0.556195	+	0.831052i	$0.687739\pi$
$503$	−31.1127	+	31.1127i	−1.38725	+	1.38725i	−0.831052	+	0.556195i	$0.812261\pi$
$504$		0			0
$505$	−36.0000	−	18.0000i	−1.60198	−	0.800989i
$506$		0			0
$507$	3.53553	+	3.53553i	0.157019	+	0.157019i
$508$		0			0
$509$			20.0000i			0.886484i	0.896402	+	0.443242i	$0.146172\pi$
$509$			20.0000i			0.886484i	−0.896402	+	0.443242i	$0.853828\pi$
$510$		0			0
$511$			16.9706i			0.750733i
$512$		0			0
$513$	−4.00000	−	4.00000i	−0.176604	−	0.176604i
$514$		0			0
$515$	−8.48528	+	2.82843i	−0.373906	+	0.124635i
$516$		0			0
$517$	−16.0000	+	16.0000i	−0.703679	+	0.703679i
$518$		0			0
$519$	7.07107			0.310385
$520$		0			0
$521$	−10.0000			−0.438108			−0.219054	−	0.975713i	$-0.570297\pi$
$521$	−10.0000			−0.438108			−0.219054	+	0.975713i	$0.570297\pi$
$522$		0			0
$523$	−25.4558	+	25.4558i	−1.11311	+	1.11311i	−0.120378	+	0.992728i	$0.538411\pi$
$523$	−25.4558	+	25.4558i	−1.11311	+	1.11311i	−0.992728	+	0.120378i	$0.961589\pi$
$524$		0			0
$525$	−12.0000	−	16.0000i	−0.523723	−	0.698297i
$526$		0			0
$527$		0			0
$528$		0			0
$529$			7.00000i			0.304348i
$530$		0			0
$531$		−	11.3137i		−	0.490973i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	8.48528	+	25.4558i	0.366851	+	1.10055i
$536$		0			0
$537$	−16.0000	+	16.0000i	−0.690451	+	0.690451i
$538$		0			0
$539$	50.9117			2.19292
$540$		0			0
$541$	−22.0000			−0.945854			−0.472927	−	0.881102i	$-0.656803\pi$
$541$	−22.0000			−0.945854			−0.472927	+	0.881102i	$0.656803\pi$
$542$		0			0
$543$	−12.7279	+	12.7279i	−0.546207	+	0.546207i
$544$		0			0
$545$	−10.0000	+	20.0000i	−0.428353	+	0.856706i
$546$		0			0
$547$	8.48528	+	8.48528i	0.362804	+	0.362804i	0.864844	−	0.502040i	$-0.167417\pi$
$547$	8.48528	+	8.48528i	0.362804	+	0.362804i	−0.502040	+	0.864844i	$0.667417\pi$
$548$		0			0
$549$		−	4.00000i		−	0.170716i
$550$		0			0
$551$		−	22.6274i		−	0.963960i
$552$		0			0
$553$	−16.0000	−	16.0000i	−0.680389	−	0.680389i
$554$		0			0
$555$	−7.07107	+	14.1421i	−0.300150	+	0.600300i
$556$		0			0
$557$	17.0000	−	17.0000i	0.720313	−	0.720313i	−0.248356	−	0.968669i	$-0.579890\pi$
$557$	17.0000	−	17.0000i	0.720313	−	0.720313i	0.968669	+	0.248356i	$0.0798902\pi$
$558$		0			0
$559$	−16.9706			−0.717778
$560$		0			0
$561$	8.00000			0.337760
$562$		0			0
$563$	8.48528	−	8.48528i	0.357612	−	0.357612i	−0.505320	−	0.862932i	$-0.668626\pi$
$563$	8.48528	−	8.48528i	0.357612	−	0.357612i	0.862932	+	0.505320i	$0.168626\pi$
$564$		0			0
$565$	−11.0000	−	33.0000i	−0.462773	−	1.38832i
$566$		0			0
$567$	2.82843	+	2.82843i	0.118783	+	0.118783i
$568$		0			0
$569$		−	22.0000i		−	0.922288i	−0.887325	−	0.461144i	$-0.847439\pi$
$569$		−	22.0000i		−	0.922288i	0.887325	−	0.461144i	$-0.152561\pi$
$570$		0			0
$571$		−	11.3137i		−	0.473464i	−0.971575	−	0.236732i	$-0.923924\pi$
$571$		−	11.3137i		−	0.473464i	0.971575	−	0.236732i	$-0.0760763\pi$
$572$		0			0
$573$	12.0000	+	12.0000i	0.501307	+	0.501307i
$574$		0			0
$575$	−19.7990	−	2.82843i	−0.825675	−	0.117954i
$576$		0			0
$577$	23.0000	−	23.0000i	0.957503	−	0.957503i	−0.0416305	−	0.999133i	$-0.513255\pi$
$577$	23.0000	−	23.0000i	0.957503	−	0.957503i	0.999133	+	0.0416305i	$0.0132552\pi$
$578$		0			0
$579$	−7.07107			−0.293864
$580$		0			0
$581$	16.0000			0.663792
$582$		0			0
$583$	5.65685	−	5.65685i	0.234283	−	0.234283i
$584$		0			0
$585$	−9.00000	+	3.00000i	−0.372104	+	0.124035i
$586$		0			0
$587$	−14.1421	−	14.1421i	−0.583708	−	0.583708i	0.352212	−	0.935920i	$-0.385430\pi$
$587$	−14.1421	−	14.1421i	−0.583708	−	0.583708i	−0.935920	+	0.352212i	$0.885430\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$			15.5563i			0.639903i
$592$		0			0
$593$	21.0000	+	21.0000i	0.862367	+	0.862367i	0.991613	−	0.129246i	$-0.0412557\pi$
$593$	21.0000	+	21.0000i	0.862367	+	0.862367i	−0.129246	+	0.991613i	$0.541256\pi$
$594$		0			0
$595$	−11.3137	−	5.65685i	−0.463817	−	0.231908i
$596$		0			0
$597$	12.0000	−	12.0000i	0.491127	−	0.491127i
$598$		0			0
$599$	11.3137			0.462266			0.231133	−	0.972922i	$-0.425757\pi$
$599$	11.3137			0.462266			0.231133	+	0.972922i	$0.425757\pi$
$600$		0			0
$601$		0			0			−	1.00000i	$-0.5\pi$
$601$		0			0				1.00000i	$0.5\pi$
$602$		0			0
$603$	2.82843	−	2.82843i	0.115182	−	0.115182i
$604$		0			0
$605$	42.0000	+	21.0000i	1.70754	+	0.853771i
$606$		0			0
$607$	−8.48528	−	8.48528i	−0.344407	−	0.344407i	0.513614	−	0.858021i	$-0.328306\pi$
$607$	−8.48528	−	8.48528i	−0.344407	−	0.344407i	−0.858021	+	0.513614i	$0.828306\pi$
$608$		0			0
$609$			16.0000i			0.648353i
$610$		0			0
$611$		−	16.9706i		−	0.686555i
$612$		0			0
$613$	3.00000	+	3.00000i	0.121169	+	0.121169i	0.765091	−	0.643922i	$-0.222694\pi$
$613$	3.00000	+	3.00000i	0.121169	+	0.121169i	−0.643922	+	0.765091i	$0.722694\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	23.0000	−	23.0000i	0.925945	−	0.925945i	−0.0714958	−	0.997441i	$-0.522777\pi$
$617$	23.0000	−	23.0000i	0.925945	−	0.925945i	0.997441	+	0.0714958i	$0.0227772\pi$
$618$		0			0
$619$	39.5980			1.59158			0.795789	−	0.605575i	$-0.207057\pi$
$619$	39.5980			1.59158			0.795789	+	0.605575i	$0.207057\pi$
$620$		0			0
$621$	4.00000			0.160514
$622$		0			0
$623$	−22.6274	+	22.6274i	−0.906548	+	0.906548i
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$		0			0
$627$	−22.6274	−	22.6274i	−0.903652	−	0.903652i
$628$		0			0
$629$			10.0000i			0.398726i
$630$		0			0
$631$		−	22.6274i		−	0.900783i	−0.892831	−	0.450392i	$-0.851284\pi$
$631$		−	22.6274i		−	0.900783i	0.892831	−	0.450392i	$-0.148716\pi$
$632$		0			0
$633$	16.0000	+	16.0000i	0.635943	+	0.635943i
$634$		0			0
$635$	8.48528	+	25.4558i	0.336728	+	1.01018i
$636$		0			0
$637$	−27.0000	+	27.0000i	−1.06978	+	1.06978i
$638$		0			0
$639$	5.65685			0.223782
$640$		0			0
$641$	−48.0000			−1.89589			−0.947943	−	0.318440i	$-0.896841\pi$
$641$	−48.0000			−1.89589			−0.947943	+	0.318440i	$0.896841\pi$
$642$		0			0
$643$	19.7990	−	19.7990i	0.780796	−	0.780796i	−0.199169	−	0.979965i	$-0.563824\pi$
$643$	19.7990	−	19.7990i	0.780796	−	0.780796i	0.979965	+	0.199169i	$0.0638243\pi$
$644$		0			0
$645$	4.00000	−	8.00000i	0.157500	−	0.315000i
$646$		0			0
$647$	−8.48528	−	8.48528i	−0.333591	−	0.333591i	0.520358	−	0.853948i	$-0.325799\pi$
$647$	−8.48528	−	8.48528i	−0.333591	−	0.333591i	−0.853948	+	0.520358i	$0.825799\pi$
$648$		0			0
$649$		−	64.0000i		−	2.51222i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−23.0000	−	23.0000i	−0.900060	−	0.900060i	0.0953813	−	0.995441i	$-0.469593\pi$
$653$	−23.0000	−	23.0000i	−0.900060	−	0.900060i	−0.995441	+	0.0953813i	$0.969593\pi$
$654$		0			0
$655$	−5.65685	+	11.3137i	−0.221032	+	0.442063i
$656$		0			0
$657$	−3.00000	+	3.00000i	−0.117041	+	0.117041i
$658$		0			0
$659$	−11.3137			−0.440720			−0.220360	−	0.975419i	$-0.570723\pi$
$659$	−11.3137			−0.440720			−0.220360	+	0.975419i	$0.570723\pi$
$660$		0			0
$661$	−28.0000			−1.08907			−0.544537	−	0.838737i	$-0.683295\pi$
$661$	−28.0000			−1.08907			−0.544537	+	0.838737i	$0.683295\pi$
$662$		0			0
$663$	−4.24264	+	4.24264i	−0.164771	+	0.164771i
$664$		0			0
$665$	16.0000	+	48.0000i	0.620453	+	1.86136i
$666$		0			0
$667$	11.3137	+	11.3137i	0.438069	+	0.438069i
$668$		0			0
$669$		−	12.0000i		−	0.463947i
$670$		0			0
$671$		−	22.6274i		−	0.873522i
$672$		0			0
$673$	−35.0000	−	35.0000i	−1.34915	−	1.34915i	−0.886585	−	0.462566i	$-0.846929\pi$
$673$	−35.0000	−	35.0000i	−1.34915	−	1.34915i	−0.462566	−	0.886585i	$-0.653071\pi$
$674$		0			0
$675$	0.707107	−	4.94975i	0.0272166	−	0.190516i
$676$		0			0
$677$	5.00000	−	5.00000i	0.192166	−	0.192166i	−0.604466	−	0.796631i	$-0.706613\pi$
$677$	5.00000	−	5.00000i	0.192166	−	0.192166i	0.796631	+	0.604466i	$0.206613\pi$
$678$		0			0
$679$	16.9706			0.651270
$680$		0			0
$681$	28.0000			1.07296
$682$		0			0
$683$	−8.48528	+	8.48528i	−0.324680	+	0.324680i	−0.850559	−	0.525879i	$-0.823736\pi$
$683$	−8.48528	+	8.48528i	−0.324680	+	0.324680i	0.525879	+	0.850559i	$0.323736\pi$
$684$		0			0
$685$	−15.0000	+	5.00000i	−0.573121	+	0.191040i
$686$		0			0
$687$	−8.48528	−	8.48528i	−0.323734	−	0.323734i
$688$		0			0
$689$			6.00000i			0.228582i
$690$		0			0
$691$		−	22.6274i		−	0.860788i	−0.902641	−	0.430394i	$-0.858375\pi$
$691$		−	22.6274i		−	0.860788i	0.902641	−	0.430394i	$-0.141625\pi$
$692$		0			0
$693$	16.0000	+	16.0000i	0.607790	+	0.607790i
$694$		0			0
$695$	33.9411	+	16.9706i	1.28746	+	0.643730i
$696$		0			0
$697$		0			0
$698$		0			0
$699$	21.2132			0.802357
$700$		0			0
$701$	−28.0000			−1.05755			−0.528773	−	0.848763i	$-0.677348\pi$
$701$	−28.0000			−1.05755			−0.528773	+	0.848763i	$0.677348\pi$
$702$		0			0
$703$	28.2843	−	28.2843i	1.06676	−	1.06676i
$704$		0			0
$705$	8.00000	+	4.00000i	0.301297	+	0.150649i
$706$		0			0
$707$	−50.9117	−	50.9117i	−1.91473	−	1.91473i
$708$		0			0
$709$			28.0000i			1.05156i	0.850620	+	0.525781i	$0.176227\pi$
$709$			28.0000i			1.05156i	−0.850620	+	0.525781i	$0.823773\pi$
$710$		0			0
$711$		−	5.65685i		−	0.212149i
$712$		0			0
$713$		0			0
$714$		0			0
$715$	−50.9117	+	16.9706i	−1.90399	+	0.634663i
$716$		0			0
$717$	−8.00000	+	8.00000i	−0.298765	+	0.298765i
$718$		0			0
$719$	−11.3137			−0.421930			−0.210965	−	0.977494i	$-0.567661\pi$
$719$	−11.3137			−0.421930			−0.210965	+	0.977494i	$0.567661\pi$
$720$		0			0
$721$	−16.0000			−0.595871
$722$		0			0
$723$	5.65685	−	5.65685i	0.210381	−	0.210381i
$724$		0			0
$725$	16.0000	−	12.0000i	0.594225	−	0.445669i
$726$		0			0
$727$	−31.1127	−	31.1127i	−1.15391	−	1.15391i	−0.985763	−	0.168144i	$-0.946223\pi$
$727$	−31.1127	−	31.1127i	−1.15391	−	1.15391i	−0.168144	−	0.985763i	$-0.553777\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$		−	5.65685i		−	0.209226i
$732$		0			0
$733$	17.0000	+	17.0000i	0.627909	+	0.627909i	0.947542	−	0.319632i	$-0.103559\pi$
$733$	17.0000	+	17.0000i	0.627909	+	0.627909i	−0.319632	+	0.947542i	$0.603559\pi$
$734$		0			0
$735$	−6.36396	−	19.0919i	−0.234738	−	0.704215i
$736$		0			0
$737$	16.0000	−	16.0000i	0.589368	−	0.589368i
$738$		0			0
$739$	−28.2843			−1.04045			−0.520227	−	0.854028i	$-0.674153\pi$
$739$	−28.2843			−1.04045			−0.520227	+	0.854028i	$0.674153\pi$
$740$		0			0
$741$	24.0000			0.881662
$742$		0			0
$743$	25.4558	−	25.4558i	0.933884	−	0.933884i	−0.0640616	−	0.997946i	$-0.520405\pi$
$743$	25.4558	−	25.4558i	0.933884	−	0.933884i	0.997946	+	0.0640616i	$0.0204054\pi$
$744$		0			0
$745$	18.0000	−	36.0000i	0.659469	−	1.31894i
$746$		0			0
$747$	2.82843	+	2.82843i	0.103487	+	0.103487i
$748$		0			0
$749$			48.0000i			1.75388i
$750$		0			0
$751$		−	33.9411i		−	1.23853i	−0.785182	−	0.619265i	$-0.787431\pi$
$751$		−	33.9411i		−	1.23853i	0.785182	−	0.619265i	$-0.212569\pi$
$752$		0			0
$753$	−4.00000	−	4.00000i	−0.145768	−	0.145768i
$754$		0			0
$755$	11.3137	−	22.6274i	0.411748	−	0.823496i
$756$		0			0
$757$	−5.00000	+	5.00000i	−0.181728	+	0.181728i	−0.792108	−	0.610380i	$-0.791017\pi$
$757$	−5.00000	+	5.00000i	−0.181728	+	0.181728i	0.610380	+	0.792108i	$0.291017\pi$
$758$		0			0
$759$	22.6274			0.821323
$760$		0			0
$761$	−6.00000			−0.217500			−0.108750	−	0.994069i	$-0.534685\pi$
$761$	−6.00000			−0.217500			−0.108750	+	0.994069i	$0.534685\pi$
$762$		0			0
$763$	−28.2843	+	28.2843i	−1.02396	+	1.02396i
$764$		0			0
$765$	−1.00000	−	3.00000i	−0.0361551	−	0.108465i
$766$		0			0
$767$	33.9411	+	33.9411i	1.22554	+	1.22554i
$768$		0			0
$769$		−	8.00000i		−	0.288487i	−0.989542	−	0.144244i	$-0.953925\pi$
$769$		−	8.00000i		−	0.288487i	0.989542	−	0.144244i	$-0.0460749\pi$
$770$		0			0
$771$			29.6985i			1.06956i
$772$		0			0
$773$	−17.0000	−	17.0000i	−0.611448	−	0.611448i	0.331876	−	0.943323i	$-0.392319\pi$
$773$	−17.0000	−	17.0000i	−0.611448	−	0.611448i	−0.943323	+	0.331876i	$0.892319\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−20.0000	+	20.0000i	−0.717496	+	0.717496i
$778$		0			0
$779$		0			0
$780$		0			0
$781$	32.0000			1.14505
$782$		0			0
$783$	−2.82843	+	2.82843i	−0.101080	+	0.101080i
$784$		0			0
$785$	−33.0000	+	11.0000i	−1.17782	+	0.392607i
$786$		0			0
$787$	−14.1421	−	14.1421i	−0.504113	−	0.504113i	0.408601	−	0.912713i	$-0.366017\pi$
$787$	−14.1421	−	14.1421i	−0.504113	−	0.504113i	−0.912713	+	0.408601i	$0.866017\pi$
$788$		0			0
$789$			4.00000i			0.142404i
$790$		0			0
$791$		−	62.2254i		−	2.21248i
$792$		0			0
$793$	12.0000	+	12.0000i	0.426132	+	0.426132i
$794$		0			0
$795$	−2.82843	−	1.41421i	−0.100314	−	0.0501570i
$796$		0			0
$797$	27.0000	−	27.0000i	0.956389	−	0.956389i	−0.0426989	−	0.999088i	$-0.513596\pi$
$797$	27.0000	−	27.0000i	0.956389	−	0.956389i	0.999088	+	0.0426989i	$0.0135956\pi$
$798$		0			0
$799$	5.65685			0.200125
$800$		0			0
$801$	−8.00000			−0.282666
$802$		0			0
$803$	−16.9706	+	16.9706i	−0.598878	+	0.598878i
$804$		0			0
$805$	−32.0000	−	16.0000i	−1.12785	−	0.563926i
$806$		0			0
$807$	−4.24264	−	4.24264i	−0.149348	−	0.149348i
$808$		0			0
$809$			32.0000i			1.12506i	0.826777	+	0.562530i	$0.190172\pi$
$809$			32.0000i			1.12506i	−0.826777	+	0.562530i	$0.809828\pi$
$810$		0			0
$811$			33.9411i			1.19183i	0.803046	+	0.595917i	$0.203211\pi$
$811$			33.9411i			1.19183i	−0.803046	+	0.595917i	$0.796789\pi$
$812$		0			0
$813$	8.00000	+	8.00000i	0.280572	+	0.280572i
$814$		0			0
$815$	25.4558	−	8.48528i	0.891679	−	0.297226i
$816$		0			0
$817$	−16.0000	+	16.0000i	−0.559769	+	0.559769i
$818$		0			0
$819$	−16.9706			−0.592999
$820$		0			0
$821$	52.0000			1.81481			0.907406	−	0.420255i	$-0.138059\pi$
$821$	52.0000			1.81481			0.907406	+	0.420255i	$0.138059\pi$
$822$		0			0
$823$	−19.7990	+	19.7990i	−0.690149	+	0.690149i	−0.962265	−	0.272115i	$-0.912277\pi$
$823$	−19.7990	+	19.7990i	−0.690149	+	0.690149i	0.272115	+	0.962265i	$0.412277\pi$
$824$		0			0
$825$	4.00000	−	28.0000i	0.139262	−	0.974835i
$826$		0			0
$827$	2.82843	+	2.82843i	0.0983540	+	0.0983540i	0.754572	−	0.656218i	$-0.227845\pi$
$827$	2.82843	+	2.82843i	0.0983540	+	0.0983540i	−0.656218	+	0.754572i	$0.727845\pi$
$828$		0			0
$829$		−	38.0000i		−	1.31979i	−0.751356	−	0.659897i	$-0.770600\pi$
$829$		−	38.0000i		−	1.31979i	0.751356	−	0.659897i	$-0.229400\pi$
$830$		0			0
$831$		−	4.24264i		−	0.147176i
$832$		0			0
$833$	−9.00000	−	9.00000i	−0.311832	−	0.311832i
$834$		0			0
$835$	−8.48528	−	25.4558i	−0.293645	−	0.880936i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−11.3137			−0.390593			−0.195296	−	0.980744i	$-0.562567\pi$
$839$	−11.3137			−0.390593			−0.195296	+	0.980744i	$0.562567\pi$
$840$		0			0
$841$	13.0000			0.448276
$842$		0			0
$843$	5.65685	−	5.65685i	0.194832	−	0.194832i
$844$		0			0
$845$	5.00000	−	10.0000i	0.172005	−	0.344010i
$846$		0			0
$847$	59.3970	+	59.3970i	2.04090	+	2.04090i
$848$		0			0
$849$		−	20.0000i		−	0.686398i
$850$		0			0
$851$			28.2843i			0.969572i
$852$		0			0
$853$	−21.0000	−	21.0000i	−0.719026	−	0.719026i	0.249380	−	0.968406i	$-0.419773\pi$
$853$	−21.0000	−	21.0000i	−0.719026	−	0.719026i	−0.968406	+	0.249380i	$0.919773\pi$
$854$		0			0
$855$	−5.65685	+	11.3137i	−0.193460	+	0.386921i
$856$		0			0
$857$	5.00000	−	5.00000i	0.170797	−	0.170797i	−0.616533	−	0.787329i	$-0.711463\pi$
$857$	5.00000	−	5.00000i	0.170797	−	0.170797i	0.787329	+	0.616533i	$0.211463\pi$
$858$		0			0
$859$	39.5980			1.35107			0.675533	−	0.737330i	$-0.263914\pi$
$859$	39.5980			1.35107			0.675533	+	0.737330i	$0.263914\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−19.7990	+	19.7990i	−0.673965	+	0.673965i	−0.958628	−	0.284662i	$-0.908119\pi$
$863$	−19.7990	+	19.7990i	−0.673965	+	0.673965i	0.284662	+	0.958628i	$0.408119\pi$
$864$		0			0
$865$	−5.00000	−	15.0000i	−0.170005	−	0.510015i
$866$		0			0
$867$	10.6066	+	10.6066i	0.360219	+	0.360219i
$868$		0			0
$869$		−	32.0000i		−	1.08553i
$870$		0			0
$871$			16.9706i			0.575026i
$872$		0			0
$873$	3.00000	+	3.00000i	0.101535	+	0.101535i
$874$		0			0
$875$	−25.4558	+	36.7696i	−0.860565	+	1.24304i
$876$		0			0
$877$	−29.0000	+	29.0000i	−0.979260	+	0.979260i	−0.999789	−	0.0205288i	$-0.993465\pi$
$877$	−29.0000	+	29.0000i	−0.979260	+	0.979260i	0.0205288	+	0.999789i	$0.493465\pi$
$878$		0			0
$879$	−7.07107			−0.238501
$880$		0			0
$881$	24.0000			0.808581			0.404290	−	0.914631i	$-0.367519\pi$
$881$	24.0000			0.808581			0.404290	+	0.914631i	$0.367519\pi$
$882$		0			0
$883$	36.7696	−	36.7696i	1.23739	−	1.23739i	0.276332	−	0.961062i	$-0.410881\pi$
$883$	36.7696	−	36.7696i	1.23739	−	1.23739i	0.961062	−	0.276332i	$-0.0891188\pi$
$884$		0			0
$885$	−24.0000	+	8.00000i	−0.806751	+	0.268917i
$886$		0			0
$887$	25.4558	+	25.4558i	0.854724	+	0.854724i	0.990711	−	0.135987i	$-0.0434205\pi$
$887$	25.4558	+	25.4558i	0.854724	+	0.854724i	−0.135987	+	0.990711i	$0.543421\pi$
$888$		0			0
$889$			48.0000i			1.60987i
$890$		0			0
$891$			5.65685i			0.189512i
$892$		0			0
$893$	−16.0000	−	16.0000i	−0.535420	−	0.535420i
$894$		0			0
$895$	45.2548	+	22.6274i	1.51270	+	0.756351i
$896$		0			0
$897$	−12.0000	+	12.0000i	−0.400668	+	0.400668i
$898$		0			0
$899$		0			0
$900$		0			0
$901$	−2.00000			−0.0666297
$902$		0			0
$903$	11.3137	−	11.3137i	0.376497	−	0.376497i
$904$		0			0
$905$	36.0000	+	18.0000i	1.19668	+	0.598340i
$906$		0			0
$907$	−31.1127	−	31.1127i	−1.03308	−	1.03308i	−0.999434	−	0.0336464i	$-0.989288\pi$
$907$	−31.1127	−	31.1127i	−1.03308	−	1.03308i	−0.0336464	−	0.999434i	$-0.510712\pi$
$908$		0			0
$909$		−	18.0000i		−	0.597022i
$910$		0			0
$911$			39.5980i			1.31194i	0.754787	+	0.655970i	$0.227740\pi$
$911$			39.5980i			1.31194i	−0.754787	+	0.655970i	$0.772260\pi$
$912$		0			0
$913$	16.0000	+	16.0000i	0.529523	+	0.529523i
$914$		0			0
$915$	−8.48528	+	2.82843i	−0.280515	+	0.0935049i
$916$		0			0
$917$	−16.0000	+	16.0000i	−0.528367	+	0.528367i
$918$		0			0
$919$	−16.9706			−0.559807			−0.279904	−	0.960028i	$-0.590303\pi$
$919$	−16.9706			−0.559807			−0.279904	+	0.960028i	$0.590303\pi$
$920$		0			0
$921$	−4.00000			−0.131804
$922$		0			0
$923$	−16.9706	+	16.9706i	−0.558593	+	0.558593i
$924$		0			0
$925$	35.0000	+	5.00000i	1.15079	+	0.164399i
$926$		0			0
$927$	−2.82843	−	2.82843i	−0.0928977	−	0.0928977i
$928$		0			0
$929$			30.0000i			0.984268i	0.870519	+	0.492134i	$0.163783\pi$
$929$			30.0000i			0.984268i	−0.870519	+	0.492134i	$0.836217\pi$
$930$		0			0
$931$			50.9117i			1.66856i
$932$		0			0
$933$	−4.00000	−	4.00000i	−0.130954	−	0.130954i
$934$		0			0
$935$	−5.65685	−	16.9706i	−0.184999	−	0.554997i
$936$		0			0
$937$	−5.00000	+	5.00000i	−0.163343	+	0.163343i	−0.784046	−	0.620703i	$-0.786847\pi$
$937$	−5.00000	+	5.00000i	−0.163343	+	0.163343i	0.620703	+	0.784046i	$0.286847\pi$
$938$		0			0
$939$	−12.7279			−0.415360
$940$		0			0
$941$	−42.0000			−1.36916			−0.684580	−	0.728937i	$-0.740015\pi$
$941$	−42.0000			−1.36916			−0.684580	+	0.728937i	$0.740015\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	4.00000	−	8.00000i	0.130120	−	0.260240i
$946$		0			0
$947$	19.7990	+	19.7990i	0.643381	+	0.643381i	0.951385	−	0.308004i	$-0.0996611\pi$
$947$	19.7990	+	19.7990i	0.643381	+	0.643381i	−0.308004	+	0.951385i	$0.599661\pi$
$948$		0			0
$949$		−	18.0000i		−	0.584305i
$950$		0			0
$951$		−	15.5563i		−	0.504449i
$952$		0			0
$953$	−5.00000	−	5.00000i	−0.161966	−	0.161966i	0.621471	−	0.783437i	$-0.286535\pi$
$953$	−5.00000	−	5.00000i	−0.161966	−	0.161966i	−0.783437	+	0.621471i	$0.786535\pi$
$954$		0			0
$955$	16.9706	−	33.9411i	0.549155	−	1.09831i
$956$		0			0
$957$	−16.0000	+	16.0000i	−0.517207	+	0.517207i
$958$		0			0
$959$	−28.2843			−0.913347
$960$		0			0
$961$	31.0000			1.00000
$962$		0			0
$963$	−8.48528	+	8.48528i	−0.273434	+	0.273434i
$964$		0			0
$965$	5.00000	+	15.0000i	0.160956	+	0.482867i
$966$		0			0
$967$	−2.82843	−	2.82843i	−0.0909561	−	0.0909561i	0.660165	−	0.751121i	$-0.270486\pi$
$967$	−2.82843	−	2.82843i	−0.0909561	−	0.0909561i	−0.751121	+	0.660165i	$0.770486\pi$
$968$		0			0
$969$			8.00000i			0.256997i
$970$		0			0
$971$			16.9706i			0.544611i	0.962211	+	0.272306i	$0.0877862\pi$
$971$			16.9706i			0.544611i	−0.962211	+	0.272306i	$0.912214\pi$
$972$		0			0
$973$	48.0000	+	48.0000i	1.53881	+	1.53881i
$974$		0			0
$975$	12.7279	+	16.9706i	0.407620	+	0.543493i
$976$		0			0
$977$	25.0000	−	25.0000i	0.799821	−	0.799821i	−0.183246	−	0.983067i	$-0.558661\pi$
$977$	25.0000	−	25.0000i	0.799821	−	0.799821i	0.983067	+	0.183246i	$0.0586605\pi$
$978$		0			0
$979$	−45.2548			−1.44635
$980$		0			0
$981$	−10.0000			−0.319275
$982$		0			0
$983$	25.4558	−	25.4558i	0.811915	−	0.811915i	−0.173006	−	0.984921i	$-0.555348\pi$
$983$	25.4558	−	25.4558i	0.811915	−	0.811915i	0.984921	+	0.173006i	$0.0553478\pi$
$984$		0			0
$985$	33.0000	−	11.0000i	1.05147	−	0.350489i
$986$		0			0
$987$	11.3137	+	11.3137i	0.360119	+	0.360119i
$988$		0			0
$989$		−	16.0000i		−	0.508770i
$990$		0			0
$991$			33.9411i			1.07818i	0.842250	+	0.539088i	$0.181231\pi$
$991$			33.9411i			1.07818i	−0.842250	+	0.539088i	$0.818769\pi$
$992$		0			0
$993$	−16.0000	−	16.0000i	−0.507745	−	0.507745i
$994$		0			0
$995$	−33.9411	−	16.9706i	−1.07601	−	0.538003i
$996$		0			0
$997$	7.00000	−	7.00000i	0.221692	−	0.221692i	−0.587519	−	0.809211i	$-0.699895\pi$
$997$	7.00000	−	7.00000i	0.221692	−	0.221692i	0.809211	+	0.587519i	$0.199895\pi$
$998$		0			0
$999$	−7.07107			−0.223719

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.w.a.223.2	yes	4
3.2	odd	2		720.2.x.e.703.1		4
4.3	odd	2	inner	240.2.w.a.223.1	yes	4
5.2	odd	4	inner	240.2.w.a.127.1	✓	4
5.3	odd	4		1200.2.w.a.607.2		4
5.4	even	2		1200.2.w.a.943.1		4
8.3	odd	2		960.2.w.c.703.2		4
8.5	even	2		960.2.w.c.703.1		4
12.11	even	2		720.2.x.e.703.2		4
15.2	even	4		720.2.x.e.127.2		4
15.8	even	4		3600.2.x.d.3007.1		4
15.14	odd	2		3600.2.x.d.2143.2		4
20.3	even	4		1200.2.w.a.607.1		4
20.7	even	4	inner	240.2.w.a.127.2	yes	4
20.19	odd	2		1200.2.w.a.943.2		4
40.27	even	4		960.2.w.c.127.1		4
40.37	odd	4		960.2.w.c.127.2		4
60.23	odd	4		3600.2.x.d.3007.2		4
60.47	odd	4		720.2.x.e.127.1		4
60.59	even	2		3600.2.x.d.2143.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.w.a.127.1	✓	4	5.2	odd	4	inner
240.2.w.a.127.2	yes	4	20.7	even	4	inner
240.2.w.a.223.1	yes	4	4.3	odd	2	inner
240.2.w.a.223.2	yes	4	1.1	even	1	trivial
720.2.x.e.127.1		4	60.47	odd	4
720.2.x.e.127.2		4	15.2	even	4
720.2.x.e.703.1		4	3.2	odd	2
720.2.x.e.703.2		4	12.11	even	2
960.2.w.c.127.1		4	40.27	even	4
960.2.w.c.127.2		4	40.37	odd	4
960.2.w.c.703.1		4	8.5	even	2
960.2.w.c.703.2		4	8.3	odd	2
1200.2.w.a.607.1		4	20.3	even	4
1200.2.w.a.607.2		4	5.3	odd	4
1200.2.w.a.943.1		4	5.4	even	2
1200.2.w.a.943.2		4	20.19	odd	2
3600.2.x.d.2143.1		4	60.59	even	2
3600.2.x.d.2143.2		4	15.14	odd	2
3600.2.x.d.3007.1		4	15.8	even	4
3600.2.x.d.3007.2		4	60.23	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{3} +(-2.00000 - 1.00000i) q^{5} +(-2.82843 - 2.82843i) q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{3} +(-2.00000 - 1.00000i) q^{5} +(-2.82843 - 2.82843i) q^{7} -1.00000i q^{9} -5.65685i q^{11} +(3.00000 + 3.00000i) q^{13} +(-2.12132 + 0.707107i) q^{15} +(-1.00000 + 1.00000i) q^{17} +5.65685 q^{19} -4.00000 q^{21} +(-2.82843 + 2.82843i) q^{23} +(3.00000 + 4.00000i) q^{25} +(-0.707107 - 0.707107i) q^{27} -4.00000i q^{29} +(-4.00000 - 4.00000i) q^{33} +(2.82843 + 8.48528i) q^{35} +(5.00000 - 5.00000i) q^{37} +4.24264 q^{39} +(-2.82843 + 2.82843i) q^{43} +(-1.00000 + 2.00000i) q^{45} +(-2.82843 - 2.82843i) q^{47} +9.00000i q^{49} +1.41421i q^{51} +(1.00000 + 1.00000i) q^{53} +(-5.65685 + 11.3137i) q^{55} +(4.00000 - 4.00000i) q^{57} +11.3137 q^{59} +4.00000 q^{61} +(-2.82843 + 2.82843i) q^{63} +(-3.00000 - 9.00000i) q^{65} +(2.82843 + 2.82843i) q^{67} +4.00000i q^{69} +5.65685i q^{71} +(-3.00000 - 3.00000i) q^{73} +(4.94975 + 0.707107i) q^{75} +(-16.0000 + 16.0000i) q^{77} +5.65685 q^{79} -1.00000 q^{81} +(-2.82843 + 2.82843i) q^{83} +(3.00000 - 1.00000i) q^{85} +(-2.82843 - 2.82843i) q^{87} -8.00000i q^{89} -16.9706i q^{91} +(-11.3137 - 5.65685i) q^{95} +(-3.00000 + 3.00000i) q^{97} -5.65685 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{5}+O(q^{10}) \) 4 * q - 8 * q^5	\( 4 q - 8 q^{5} + 12 q^{13} - 4 q^{17} - 16 q^{21} + 12 q^{25} - 16 q^{33} + 20 q^{37} - 4 q^{45} + 4 q^{53} + 16 q^{57} + 16 q^{61} - 12 q^{65} - 12 q^{73} - 64 q^{77} - 4 q^{81} + 12 q^{85} - 12 q^{97}+O(q^{100}) \) 4 * q - 8 * q^5 + 12 * q^13 - 4 * q^17 - 16 * q^21 + 12 * q^25 - 16 * q^33 + 20 * q^37 - 4 * q^45 + 4 * q^53 + 16 * q^57 + 16 * q^61 - 12 * q^65 - 12 * q^73 - 64 * q^77 - 4 * q^81 + 12 * q^85 - 12 * q^97

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