LMFDB - Embedded newform 2240.2.bd.b.561.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2240,2,Mod(561,2240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2240, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("2240.561");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2240 = 2^{6} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2240.bd (of order $4$, degree $2$, not 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:	$17.8864900528$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 560)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			561.16
Character	$\chi$	$=$	2240.561
Dual form			2240.2.bd.b.1681.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.367823 - 0.367823i) q^{3} +(-0.707107 - 0.707107i) q^{5} +1.00000i q^{7} +2.72941i q^{9} +O(q^{10})$	\(q+(0.367823 - 0.367823i) q^{3} +(-0.707107 - 0.707107i) q^{5} +1.00000i q^{7} +2.72941i q^{9} +(-0.909915 - 0.909915i) q^{11} +(3.20243 - 3.20243i) q^{13} -0.520180 q^{15} +3.62720 q^{17} +(-5.14288 + 5.14288i) q^{19} +(0.367823 + 0.367823i) q^{21} -0.827446i q^{23} +1.00000i q^{25} +(2.10741 + 2.10741i) q^{27} +(-7.41609 + 7.41609i) q^{29} +9.95425 q^{31} -0.669374 q^{33} +(0.707107 - 0.707107i) q^{35} +(-1.86914 - 1.86914i) q^{37} -2.35585i q^{39} -0.542242i q^{41} +(-3.21558 - 3.21558i) q^{43} +(1.92999 - 1.92999i) q^{45} +7.60995 q^{47} -1.00000 q^{49} +(1.33417 - 1.33417i) q^{51} +(9.56900 + 9.56900i) q^{53} +1.28681i q^{55} +3.78333i q^{57} +(-1.23721 - 1.23721i) q^{59} +(-0.710725 + 0.710725i) q^{61} -2.72941 q^{63} -4.52892 q^{65} +(5.53911 - 5.53911i) q^{67} +(-0.304353 - 0.304353i) q^{69} +13.2835i q^{71} +15.6824i q^{73} +(0.367823 + 0.367823i) q^{75} +(0.909915 - 0.909915i) q^{77} +14.2958 q^{79} -6.63794 q^{81} +(-3.42296 + 3.42296i) q^{83} +(-2.56482 - 2.56482i) q^{85} +5.45561i q^{87} +7.62322i q^{89} +(3.20243 + 3.20243i) q^{91} +(3.66140 - 3.66140i) q^{93} +7.27313 q^{95} -13.8958 q^{97} +(2.48353 - 2.48353i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q+O(q^{10}) $ 52 * q	$ 52 q + 4 q^{11} - 8 q^{15} - 8 q^{19} + 24 q^{27} + 4 q^{29} - 12 q^{37} - 36 q^{43} - 52 q^{49} + 8 q^{51} - 4 q^{53} - 24 q^{59} - 16 q^{61} + 68 q^{63} + 40 q^{65} + 12 q^{67} - 72 q^{69} - 4 q^{77} + 16 q^{79} - 116 q^{81} + 16 q^{85} + 8 q^{93} + 32 q^{95} + 52 q^{99}+O(q^{100}) $ 52 * q + 4 * q^11 - 8 * q^15 - 8 * q^19 + 24 * q^27 + 4 * q^29 - 12 * q^37 - 36 * q^43 - 52 * q^49 + 8 * q^51 - 4 * q^53 - 24 * q^59 - 16 * q^61 + 68 * q^63 + 40 * q^65 + 12 * q^67 - 72 * q^69 - 4 * q^77 + 16 * q^79 - 116 * q^81 + 16 * q^85 + 8 * q^93 + 32 * q^95 + 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times$.

$n$	$897$	$1471$	$1541$	$1921$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$	$1$

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
$3$	0.367823	−	0.367823i	0.212362	−	0.212362i	−0.592908	−	0.805270i	$-0.702020\pi$
$3$	0.367823	−	0.367823i	0.212362	−	0.212362i	0.805270	+	0.592908i	$0.202020\pi$
$4$		0			0
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$6$		0			0
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$		0			0
$9$			2.72941i			0.909804i
$10$		0			0
$11$	−0.909915	−	0.909915i	−0.274350	−	0.274350i	0.556499	−	0.830848i	$-0.312144\pi$
$11$	−0.909915	−	0.909915i	−0.274350	−	0.274350i	−0.830848	+	0.556499i	$0.812144\pi$
$12$		0			0
$13$	3.20243	−	3.20243i	0.888194	−	0.888194i	−0.106156	−	0.994350i	$-0.533854\pi$
$13$	3.20243	−	3.20243i	0.888194	−	0.888194i	0.994350	+	0.106156i	$0.0338543\pi$
$14$		0			0
$15$	−0.520180			−0.134310
$16$		0			0
$17$	3.62720			0.879725			0.439863	−	0.898065i	$-0.355027\pi$
$17$	3.62720			0.879725			0.439863	+	0.898065i	$0.355027\pi$
$18$		0			0
$19$	−5.14288	+	5.14288i	−1.17986	+	1.17986i	−0.200077	+	0.979780i	$0.564119\pi$
$19$	−5.14288	+	5.14288i	−1.17986	+	1.17986i	−0.979780	+	0.200077i	$0.935881\pi$
$20$		0			0
$21$	0.367823	+	0.367823i	0.0802655	+	0.0802655i
$22$		0			0
$23$		−	0.827446i		−	0.172534i	−0.996272	−	0.0862672i	$-0.972506\pi$
$23$		−	0.827446i		−	0.172534i	0.996272	−	0.0862672i	$-0.0274939\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$		0			0
$27$	2.10741	+	2.10741i	0.405571	+	0.405571i
$28$		0			0
$29$	−7.41609	+	7.41609i	−1.37713	+	1.37713i	−0.527706	+	0.849427i	$0.676948\pi$
$29$	−7.41609	+	7.41609i	−1.37713	+	1.37713i	−0.849427	+	0.527706i	$0.823052\pi$
$30$		0			0
$31$	9.95425			1.78784			0.893918	−	0.448230i	$-0.147946\pi$
$31$	9.95425			1.78784			0.893918	+	0.448230i	$0.147946\pi$
$32$		0			0
$33$	−0.669374			−0.116523
$34$		0			0
$35$	0.707107	−	0.707107i	0.119523	−	0.119523i
$36$		0			0
$37$	−1.86914	−	1.86914i	−0.307285	−	0.307285i	0.536570	−	0.843856i	$-0.319720\pi$
$37$	−1.86914	−	1.86914i	−0.307285	−	0.307285i	−0.843856	+	0.536570i	$0.819720\pi$
$38$		0			0
$39$		−	2.35585i		−	0.377238i
$40$		0			0
$41$		−	0.542242i		−	0.0846840i	−0.999103	−	0.0423420i	$-0.986518\pi$
$41$		−	0.542242i		−	0.0846840i	0.999103	−	0.0423420i	$-0.0134819\pi$
$42$		0			0
$43$	−3.21558	−	3.21558i	−0.490372	−	0.490372i	0.418051	−	0.908423i	$-0.362713\pi$
$43$	−3.21558	−	3.21558i	−0.490372	−	0.490372i	−0.908423	+	0.418051i	$0.862713\pi$
$44$		0			0
$45$	1.92999	−	1.92999i	0.287705	−	0.287705i
$46$		0			0
$47$	7.60995			1.11003			0.555013	−	0.831842i	$-0.312713\pi$
$47$	7.60995			1.11003			0.555013	+	0.831842i	$0.312713\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	1.33417	−	1.33417i	0.186821	−	0.186821i
$52$		0			0
$53$	9.56900	+	9.56900i	1.31440	+	1.31440i	0.918135	+	0.396268i	$0.129695\pi$
$53$	9.56900	+	9.56900i	1.31440	+	1.31440i	0.396268	+	0.918135i	$0.370305\pi$
$54$		0			0
$55$			1.28681i			0.173514i
$56$		0			0
$57$			3.78333i			0.501115i
$58$		0			0
$59$	−1.23721	−	1.23721i	−0.161070	−	0.161070i	0.621970	−	0.783041i	$-0.286332\pi$
$59$	−1.23721	−	1.23721i	−0.161070	−	0.161070i	−0.783041	+	0.621970i	$0.786332\pi$
$60$		0			0
$61$	−0.710725	+	0.710725i	−0.0909990	+	0.0909990i	−0.751141	−	0.660142i	$-0.770496\pi$
$61$	−0.710725	+	0.710725i	−0.0909990	+	0.0909990i	0.660142	+	0.751141i	$0.270496\pi$
$62$		0			0
$63$	−2.72941			−0.343874
$64$		0			0
$65$	−4.52892			−0.561743
$66$		0			0
$67$	5.53911	−	5.53911i	0.676710	−	0.676710i	−0.282544	−	0.959254i	$-0.591178\pi$
$67$	5.53911	−	5.53911i	0.676710	−	0.676710i	0.959254	+	0.282544i	$0.0911784\pi$
$68$		0			0
$69$	−0.304353	−	0.304353i	−0.0366398	−	0.0366398i
$70$		0			0
$71$			13.2835i			1.57646i	0.615383	+	0.788228i	$0.289001\pi$
$71$			13.2835i			1.57646i	−0.615383	+	0.788228i	$0.710999\pi$
$72$		0			0
$73$			15.6824i			1.83548i	0.397176	+	0.917742i	$0.369990\pi$
$73$			15.6824i			1.83548i	−0.397176	+	0.917742i	$0.630010\pi$
$74$		0			0
$75$	0.367823	+	0.367823i	0.0424725	+	0.0424725i
$76$		0			0
$77$	0.909915	−	0.909915i	0.103694	−	0.103694i
$78$		0			0
$79$	14.2958			1.60841			0.804203	−	0.594355i	$-0.202593\pi$
$79$	14.2958			1.60841			0.804203	+	0.594355i	$0.202593\pi$
$80$		0			0
$81$	−6.63794			−0.737548
$82$		0			0
$83$	−3.42296	+	3.42296i	−0.375718	+	0.375718i	−0.869555	−	0.493837i	$-0.835594\pi$
$83$	−3.42296	+	3.42296i	−0.375718	+	0.375718i	0.493837	+	0.869555i	$0.335594\pi$
$84$		0			0
$85$	−2.56482	−	2.56482i	−0.278194	−	0.278194i
$86$		0			0
$87$			5.45561i			0.584903i
$88$		0			0
$89$			7.62322i			0.808060i	0.914746	+	0.404030i	$0.132391\pi$
$89$			7.62322i			0.808060i	−0.914746	+	0.404030i	$0.867609\pi$
$90$		0			0
$91$	3.20243	+	3.20243i	0.335706	+	0.335706i
$92$		0			0
$93$	3.66140	−	3.66140i	0.379669	−	0.379669i
$94$		0			0
$95$	7.27313			0.746207
$96$		0			0
$97$	−13.8958			−1.41091			−0.705453	−	0.708756i	$-0.749257\pi$
$97$	−13.8958			−1.41091			−0.705453	+	0.708756i	$0.749257\pi$
$98$		0			0
$99$	2.48353	−	2.48353i	0.249605	−	0.249605i
$100$		0			0
$101$	5.57741	+	5.57741i	0.554973	+	0.554973i	0.927872	−	0.372899i	$-0.121636\pi$
$101$	5.57741	+	5.57741i	0.554973	+	0.554973i	−0.372899	+	0.927872i	$0.621636\pi$
$102$		0			0
$103$			3.63477i			0.358145i	0.983836	+	0.179072i	$0.0573097\pi$
$103$			3.63477i			0.358145i	−0.983836	+	0.179072i	$0.942690\pi$
$104$		0			0
$105$		−	0.520180i		−	0.0507643i
$106$		0			0
$107$	0.177470	+	0.177470i	0.0171566	+	0.0171566i	0.715633	−	0.698476i	$-0.246138\pi$
$107$	0.177470	+	0.177470i	0.0171566	+	0.0171566i	−0.698476	+	0.715633i	$0.746138\pi$
$108$		0			0
$109$	9.77336	−	9.77336i	0.936118	−	0.936118i	−0.0619609	−	0.998079i	$-0.519735\pi$
$109$	9.77336	−	9.77336i	0.936118	−	0.936118i	0.998079	+	0.0619609i	$0.0197354\pi$
$110$		0			0
$111$	−1.37503			−0.130512
$112$		0			0
$113$	6.24055			0.587062			0.293531	−	0.955950i	$-0.405170\pi$
$113$	6.24055			0.587062			0.293531	+	0.955950i	$0.405170\pi$
$114$		0			0
$115$	−0.585092	+	0.585092i	−0.0545602	+	0.0545602i
$116$		0			0
$117$	8.74075	+	8.74075i	0.808082	+	0.808082i
$118$		0			0
$119$			3.62720i			0.332505i
$120$		0			0
$121$		−	9.34411i		−	0.849465i
$122$		0			0
$123$	−0.199449	−	0.199449i	−0.0179837	−	0.0179837i
$124$		0			0
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$		0			0
$127$	5.82038			0.516475			0.258237	−	0.966081i	$-0.416858\pi$
$127$	5.82038			0.516475			0.258237	+	0.966081i	$0.416858\pi$
$128$		0			0
$129$	−2.36553			−0.208273
$130$		0			0
$131$	14.1865	−	14.1865i	1.23948	−	1.23948i	0.279261	−	0.960215i	$-0.409910\pi$
$131$	14.1865	−	14.1865i	1.23948	−	1.23948i	0.960215	−	0.279261i	$-0.0900896\pi$
$132$		0			0
$133$	−5.14288	−	5.14288i	−0.445944	−	0.445944i
$134$		0			0
$135$		−	2.98032i		−	0.256505i
$136$		0			0
$137$			7.93696i			0.678100i	0.940768	+	0.339050i	$0.110106\pi$
$137$			7.93696i			0.678100i	−0.940768	+	0.339050i	$0.889894\pi$
$138$		0			0
$139$	11.3482	+	11.3482i	0.962544	+	0.962544i	0.999323	−	0.0367797i	$-0.0117100\pi$
$139$	11.3482	+	11.3482i	0.962544	+	0.962544i	−0.0367797	+	0.999323i	$0.511710\pi$
$140$		0			0
$141$	2.79911	−	2.79911i	0.235728	−	0.235728i
$142$		0			0
$143$	−5.82787			−0.487351
$144$		0			0
$145$	10.4879			0.870975
$146$		0			0
$147$	−0.367823	+	0.367823i	−0.0303375	+	0.0303375i
$148$		0			0
$149$	−8.36702	−	8.36702i	−0.685453	−	0.685453i	0.275771	−	0.961223i	$-0.411067\pi$
$149$	−8.36702	−	8.36702i	−0.685453	−	0.685453i	−0.961223	+	0.275771i	$0.911067\pi$
$150$		0			0
$151$		−	15.5413i		−	1.26473i	−0.774669	−	0.632367i	$-0.782084\pi$
$151$		−	15.5413i		−	1.26473i	0.774669	−	0.632367i	$-0.217916\pi$
$152$		0			0
$153$			9.90013i			0.800378i
$154$		0			0
$155$	−7.03872	−	7.03872i	−0.565363	−	0.565363i
$156$		0			0
$157$	2.29237	−	2.29237i	0.182951	−	0.182951i	−0.609689	−	0.792640i	$-0.708706\pi$
$157$	2.29237	−	2.29237i	0.182951	−	0.182951i	0.792640	+	0.609689i	$0.208706\pi$
$158$		0			0
$159$	7.03939			0.558260
$160$		0			0
$161$	0.827446			0.0652119
$162$		0			0
$163$	−9.47255	+	9.47255i	−0.741947	+	0.741947i	−0.972953	−	0.231005i	$-0.925799\pi$
$163$	−9.47255	+	9.47255i	−0.741947	+	0.741947i	0.231005	+	0.972953i	$0.425799\pi$
$164$		0			0
$165$	0.473319	+	0.473319i	0.0368479	+	0.0368479i
$166$		0			0
$167$			10.7711i			0.833496i	0.909022	+	0.416748i	$0.136830\pi$
$167$			10.7711i			0.833496i	−0.909022	+	0.416748i	$0.863170\pi$
$168$		0			0
$169$		−	7.51109i		−	0.577776i
$170$		0			0
$171$	−14.0370	−	14.0370i	−1.07344	−	1.07344i
$172$		0			0
$173$	7.48450	−	7.48450i	0.569036	−	0.569036i	−0.362822	−	0.931858i	$-0.618187\pi$
$173$	7.48450	−	7.48450i	0.569036	−	0.569036i	0.931858	+	0.362822i	$0.118187\pi$
$174$		0			0
$175$	−1.00000			−0.0755929
$176$		0			0
$177$	−0.910144			−0.0684106
$178$		0			0
$179$	−6.42057	+	6.42057i	−0.479896	+	0.479896i	−0.905098	−	0.425202i	$-0.860203\pi$
$179$	−6.42057	+	6.42057i	−0.479896	+	0.479896i	0.425202	+	0.905098i	$0.360203\pi$
$180$		0			0
$181$	−7.14624	−	7.14624i	−0.531176	−	0.531176i	0.389747	−	0.920922i	$-0.372563\pi$
$181$	−7.14624	−	7.14624i	−0.531176	−	0.531176i	−0.920922	+	0.389747i	$0.872563\pi$
$182$		0			0
$183$			0.522841i			0.0386495i
$184$		0			0
$185$			2.64337i			0.194344i
$186$		0			0
$187$	−3.30044	−	3.30044i	−0.241352	−	0.241352i
$188$		0			0
$189$	−2.10741	+	2.10741i	−0.153291	+	0.153291i
$190$		0			0
$191$	−3.00780			−0.217637			−0.108818	−	0.994062i	$-0.534707\pi$
$191$	−3.00780			−0.217637			−0.108818	+	0.994062i	$0.534707\pi$
$192$		0			0
$193$	17.9507			1.29212			0.646061	−	0.763285i	$-0.276415\pi$
$193$	17.9507			1.29212			0.646061	+	0.763285i	$0.276415\pi$
$194$		0			0
$195$	−1.66584	+	1.66584i	−0.119293	+	0.119293i
$196$		0			0
$197$	13.1549	+	13.1549i	0.937248	+	0.937248i	0.998144	−	0.0608959i	$-0.0193958\pi$
$197$	13.1549	+	13.1549i	0.937248	+	0.937248i	−0.0608959	+	0.998144i	$0.519396\pi$
$198$		0			0
$199$		−	1.01118i		−	0.0716808i	−0.999358	−	0.0358404i	$-0.988589\pi$
$199$		−	1.01118i		−	0.0716808i	0.999358	−	0.0358404i	$-0.0114108\pi$
$200$		0			0
$201$		−	4.07482i		−	0.287416i
$202$		0			0
$203$	−7.41609	−	7.41609i	−0.520507	−	0.520507i
$204$		0			0
$205$	−0.383423	+	0.383423i	−0.0267794	+	0.0267794i
$206$		0			0
$207$	2.25844			0.156973
$208$		0			0
$209$	9.35916			0.647387
$210$		0			0
$211$	2.89279	−	2.89279i	0.199148	−	0.199148i	−0.600487	−	0.799635i	$-0.705026\pi$
$211$	2.89279	−	2.89279i	0.199148	−	0.199148i	0.799635	+	0.600487i	$0.205026\pi$
$212$		0			0
$213$	4.88596	+	4.88596i	0.334780	+	0.334780i
$214$		0			0
$215$			4.54752i			0.310138i
$216$		0			0
$217$			9.95425i			0.675739i
$218$		0			0
$219$	5.76834	+	5.76834i	0.389788	+	0.389788i
$220$		0			0
$221$	11.6158	−	11.6158i	0.781366	−	0.781366i
$222$		0			0
$223$	7.17199			0.480272			0.240136	−	0.970739i	$-0.422808\pi$
$223$	7.17199			0.480272			0.240136	+	0.970739i	$0.422808\pi$
$224$		0			0
$225$	−2.72941			−0.181961
$226$		0			0
$227$	−13.1517	+	13.1517i	−0.872912	+	0.872912i	−0.992789	−	0.119877i	$-0.961750\pi$
$227$	−13.1517	+	13.1517i	−0.872912	+	0.872912i	0.119877	+	0.992789i	$0.461750\pi$
$228$		0			0
$229$	7.11076	+	7.11076i	0.469892	+	0.469892i	0.901880	−	0.431988i	$-0.142188\pi$
$229$	7.11076	+	7.11076i	0.469892	+	0.469892i	−0.431988	+	0.901880i	$0.642188\pi$
$230$		0			0
$231$		−	0.669374i		−	0.0440416i
$232$		0			0
$233$		−	5.86714i		−	0.384369i	−0.981359	−	0.192185i	$-0.938443\pi$
$233$		−	5.86714i		−	0.384369i	0.981359	−	0.192185i	$-0.0615573\pi$
$234$		0			0
$235$	−5.38105	−	5.38105i	−0.351021	−	0.351021i
$236$		0			0
$237$	5.25833	−	5.25833i	0.341565	−	0.341565i
$238$		0			0
$239$	−11.2368			−0.726849			−0.363424	−	0.931624i	$-0.618393\pi$
$239$	−11.2368			−0.726849			−0.363424	+	0.931624i	$0.618393\pi$
$240$		0			0
$241$	−6.14799			−0.396027			−0.198013	−	0.980199i	$-0.563449\pi$
$241$	−6.14799			−0.396027			−0.198013	+	0.980199i	$0.563449\pi$
$242$		0			0
$243$	−8.76380	+	8.76380i	−0.562198	+	0.562198i
$244$		0			0
$245$	0.707107	+	0.707107i	0.0451754	+	0.0451754i
$246$		0			0
$247$			32.9394i			2.09588i
$248$		0			0
$249$			2.51808i			0.159577i
$250$		0			0
$251$	6.46628	+	6.46628i	0.408148	+	0.408148i	0.881092	−	0.472944i	$-0.156809\pi$
$251$	6.46628	+	6.46628i	0.408148	+	0.408148i	−0.472944	+	0.881092i	$0.656809\pi$
$252$		0			0
$253$	−0.752905	+	0.752905i	−0.0473347	+	0.0473347i
$254$		0			0
$255$	−1.88680			−0.118156
$256$		0			0
$257$	−23.6174			−1.47321			−0.736607	−	0.676321i	$-0.763573\pi$
$257$	−23.6174			−1.47321			−0.736607	+	0.676321i	$0.763573\pi$
$258$		0			0
$259$	1.86914	−	1.86914i	0.116143	−	0.116143i
$260$		0			0
$261$	−20.2416	−	20.2416i	−1.25292	−	1.25292i
$262$		0			0
$263$		−	11.1159i		−	0.685438i	−0.939438	−	0.342719i	$-0.888652\pi$
$263$		−	11.1159i		−	0.685438i	0.939438	−	0.342719i	$-0.111348\pi$
$264$		0			0
$265$		−	13.5326i		−	0.831301i
$266$		0			0
$267$	2.80399	+	2.80399i	0.171602	+	0.171602i
$268$		0			0
$269$	−19.0074	+	19.0074i	−1.15890	+	1.15890i	−0.174193	+	0.984712i	$0.555732\pi$
$269$	−19.0074	+	19.0074i	−1.15890	+	1.15890i	−0.984712	+	0.174193i	$0.944268\pi$
$270$		0			0
$271$	−13.2706			−0.806131			−0.403066	−	0.915171i	$-0.632055\pi$
$271$	−13.2706			−0.806131			−0.403066	+	0.915171i	$0.632055\pi$
$272$		0			0
$273$	2.35585			0.142583
$274$		0			0
$275$	0.909915	−	0.909915i	0.0548699	−	0.0548699i
$276$		0			0
$277$	−5.66484	−	5.66484i	−0.340367	−	0.340367i	0.516138	−	0.856505i	$-0.327369\pi$
$277$	−5.66484	−	5.66484i	−0.340367	−	0.340367i	−0.856505	+	0.516138i	$0.827369\pi$
$278$		0			0
$279$			27.1693i			1.62658i
$280$		0			0
$281$			26.8757i			1.60327i	0.597812	+	0.801636i	$0.296037\pi$
$281$			26.8757i			1.60327i	−0.597812	+	0.801636i	$0.703963\pi$
$282$		0			0
$283$	−12.7142	−	12.7142i	−0.755783	−	0.755783i	0.219769	−	0.975552i	$-0.429470\pi$
$283$	−12.7142	−	12.7142i	−0.755783	−	0.755783i	−0.975552	+	0.219769i	$0.929470\pi$
$284$		0			0
$285$	2.67522	−	2.67522i	0.158466	−	0.158466i
$286$		0			0
$287$	0.542242			0.0320076
$288$		0			0
$289$	−3.84342			−0.226084
$290$		0			0
$291$	−5.11120	+	5.11120i	−0.299624	+	0.299624i
$292$		0			0
$293$	−9.98542	−	9.98542i	−0.583354	−	0.583354i	0.352469	−	0.935823i	$-0.385342\pi$
$293$	−9.98542	−	9.98542i	−0.583354	−	0.583354i	−0.935823	+	0.352469i	$0.885342\pi$
$294$		0			0
$295$			1.74967i			0.101870i
$296$		0			0
$297$		−	3.83512i		−	0.222536i
$298$		0			0
$299$	−2.64984	−	2.64984i	−0.153244	−	0.153244i
$300$		0			0
$301$	3.21558	−	3.21558i	0.185343	−	0.185343i
$302$		0			0
$303$	4.10299			0.235711
$304$		0			0
$305$	1.00512			0.0575528
$306$		0			0
$307$	4.51931	−	4.51931i	0.257931	−	0.257931i	−0.566281	−	0.824212i	$-0.691618\pi$
$307$	4.51931	−	4.51931i	0.257931	−	0.257931i	0.824212	+	0.566281i	$0.191618\pi$
$308$		0			0
$309$	1.33695	+	1.33695i	0.0760565	+	0.0760565i
$310$		0			0
$311$		−	19.8775i		−	1.12715i	−0.826065	−	0.563575i	$-0.809426\pi$
$311$		−	19.8775i		−	1.12715i	0.826065	−	0.563575i	$-0.190574\pi$
$312$		0			0
$313$		−	5.31023i		−	0.300152i	−0.988674	−	0.150076i	$-0.952048\pi$
$313$		−	5.31023i		−	0.300152i	0.988674	−	0.150076i	$-0.0479519\pi$
$314$		0			0
$315$	1.92999	+	1.92999i	0.108742	+	0.108742i
$316$		0			0
$317$	15.8576	−	15.8576i	0.890654	−	0.890654i	−0.103930	−	0.994585i	$-0.533142\pi$
$317$	15.8576	−	15.8576i	0.890654	−	0.890654i	0.994585	+	0.103930i	$0.0331420\pi$
$318$		0			0
$319$	13.4960			0.755632
$320$		0			0
$321$	0.130555			0.00728685
$322$		0			0
$323$	−18.6542	+	18.6542i	−1.03795	+	1.03795i
$324$		0			0
$325$	3.20243	+	3.20243i	0.177639	+	0.177639i
$326$		0			0
$327$		−	7.18972i		−	0.397592i
$328$		0			0
$329$			7.60995i			0.419550i
$330$		0			0
$331$	3.54040	+	3.54040i	0.194598	+	0.194598i	0.797679	−	0.603082i	$-0.206061\pi$
$331$	3.54040	+	3.54040i	0.194598	+	0.194598i	−0.603082	+	0.797679i	$0.706061\pi$
$332$		0			0
$333$	5.10167	−	5.10167i	0.279570	−	0.279570i
$334$		0			0
$335$	−7.83348			−0.427989
$336$		0			0
$337$	−1.50920			−0.0822114			−0.0411057	−	0.999155i	$-0.513088\pi$
$337$	−1.50920			−0.0822114			−0.0411057	+	0.999155i	$0.513088\pi$
$338$		0			0
$339$	2.29542	−	2.29542i	0.124670	−	0.124670i
$340$		0			0
$341$	−9.05752	−	9.05752i	−0.490492	−	0.490492i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$		0			0
$345$			0.430420i			0.0231731i
$346$		0			0
$347$	−17.1439	−	17.1439i	−0.920333	−	0.920333i	0.0767195	−	0.997053i	$-0.475555\pi$
$347$	−17.1439	−	17.1439i	−0.920333	−	0.920333i	−0.997053	+	0.0767195i	$0.975555\pi$
$348$		0			0
$349$	8.14558	−	8.14558i	0.436023	−	0.436023i	−0.454648	−	0.890671i	$-0.650235\pi$
$349$	8.14558	−	8.14558i	0.436023	−	0.436023i	0.890671	+	0.454648i	$0.150235\pi$
$350$		0			0
$351$	13.4976			0.720451
$352$		0			0
$353$	12.7208			0.677059			0.338529	−	0.940956i	$-0.390071\pi$
$353$	12.7208			0.677059			0.338529	+	0.940956i	$0.390071\pi$
$354$		0			0
$355$	9.39282	−	9.39282i	0.498519	−	0.498519i
$356$		0			0
$357$	1.33417	+	1.33417i	0.0706115	+	0.0706115i
$358$		0			0
$359$		−	7.59869i		−	0.401043i	−0.979689	−	0.200522i	$-0.935736\pi$
$359$		−	7.59869i		−	0.401043i	0.979689	−	0.200522i	$-0.0642637\pi$
$360$		0			0
$361$		−	33.8984i		−	1.78413i
$362$		0			0
$363$	−3.43697	−	3.43697i	−0.180394	−	0.180394i
$364$		0			0
$365$	11.0891	−	11.0891i	0.580431	−	0.580431i
$366$		0			0
$367$	−11.0634			−0.577505			−0.288753	−	0.957404i	$-0.593241\pi$
$367$	−11.0634			−0.577505			−0.288753	+	0.957404i	$0.593241\pi$
$368$		0			0
$369$	1.48000			0.0770459
$370$		0			0
$371$	−9.56900	+	9.56900i	−0.496798	+	0.496798i
$372$		0			0
$373$	12.7185	+	12.7185i	0.658541	+	0.658541i	0.955035	−	0.296494i	$-0.0958173\pi$
$373$	12.7185	+	12.7185i	0.658541	+	0.658541i	−0.296494	+	0.955035i	$0.595817\pi$
$374$		0			0
$375$		−	0.520180i		−	0.0268620i
$376$		0			0
$377$			47.4990i			2.44632i
$378$		0			0
$379$	−16.0951	−	16.0951i	−0.826750	−	0.826750i	0.160316	−	0.987066i	$-0.448749\pi$
$379$	−16.0951	−	16.0951i	−0.826750	−	0.826750i	−0.987066	+	0.160316i	$0.948749\pi$
$380$		0			0
$381$	2.14087	−	2.14087i	0.109680	−	0.109680i
$382$		0			0
$383$	−37.0012			−1.89067			−0.945337	−	0.326096i	$-0.894267\pi$
$383$	−37.0012			−1.89067			−0.945337	+	0.326096i	$0.894267\pi$
$384$		0			0
$385$	−1.28681			−0.0655821
$386$		0			0
$387$	8.77666	−	8.77666i	0.446143	−	0.446143i
$388$		0			0
$389$	−6.94215	−	6.94215i	−0.351981	−	0.351981i	0.508865	−	0.860846i	$-0.330065\pi$
$389$	−6.94215	−	6.94215i	−0.351981	−	0.351981i	−0.860846	+	0.508865i	$0.830065\pi$
$390$		0			0
$391$		−	3.00131i		−	0.151783i
$392$		0			0
$393$		−	10.4362i		−	0.526437i
$394$		0			0
$395$	−10.1087	−	10.1087i	−0.508622	−	0.508622i
$396$		0			0
$397$	19.5605	−	19.5605i	0.981712	−	0.981712i	−0.0181236	−	0.999836i	$-0.505769\pi$
$397$	19.5605	−	19.5605i	0.981712	−	0.981712i	0.999836	+	0.0181236i	$0.00576923\pi$
$398$		0			0
$399$	−3.78333			−0.189404
$400$		0			0
$401$	−9.53838			−0.476324			−0.238162	−	0.971225i	$-0.576545\pi$
$401$	−9.53838			−0.476324			−0.238162	+	0.971225i	$0.576545\pi$
$402$		0			0
$403$	31.8778	−	31.8778i	1.58794	−	1.58794i
$404$		0			0
$405$	4.69373	+	4.69373i	0.233233	+	0.233233i
$406$		0			0
$407$			3.40152i			0.168607i
$408$		0			0
$409$		−	10.4539i		−	0.516910i	−0.966023	−	0.258455i	$-0.916787\pi$
$409$		−	10.4539i		−	0.516910i	0.966023	−	0.258455i	$-0.0832134\pi$
$410$		0			0
$411$	2.91939	+	2.91939i	0.144003	+	0.144003i
$412$		0			0
$413$	1.23721	−	1.23721i	0.0608789	−	0.0608789i
$414$		0			0
$415$	4.84079			0.237625
$416$		0			0
$417$	8.34827			0.408816
$418$		0			0
$419$	−5.95749	+	5.95749i	−0.291043	+	0.291043i	−0.837492	−	0.546449i	$-0.815979\pi$
$419$	−5.95749	+	5.95749i	−0.291043	+	0.291043i	0.546449	+	0.837492i	$0.315979\pi$
$420$		0			0
$421$	−25.7744	−	25.7744i	−1.25617	−	1.25617i	−0.952907	−	0.303262i	$-0.901924\pi$
$421$	−25.7744	−	25.7744i	−1.25617	−	1.25617i	−0.303262	−	0.952907i	$-0.598076\pi$
$422$		0			0
$423$			20.7707i			1.00991i
$424$		0			0
$425$			3.62720i			0.175945i
$426$		0			0
$427$	−0.710725	−	0.710725i	−0.0343944	−	0.0343944i
$428$		0			0
$429$	−2.14362	+	2.14362i	−0.103495	+	0.103495i
$430$		0			0
$431$	39.3950			1.89759			0.948795	−	0.315891i	$-0.102303\pi$
$431$	39.3950			1.89759			0.948795	+	0.315891i	$0.102303\pi$
$432$		0			0
$433$	−16.5612			−0.795879			−0.397939	−	0.917412i	$-0.630275\pi$
$433$	−16.5612			−0.795879			−0.397939	+	0.917412i	$0.630275\pi$
$434$		0			0
$435$	3.85770	−	3.85770i	0.184962	−	0.184962i
$436$		0			0
$437$	4.25545	+	4.25545i	0.203566	+	0.203566i
$438$		0			0
$439$		−	9.15988i		−	0.437177i	−0.975817	−	0.218589i	$-0.929855\pi$
$439$		−	9.15988i		−	0.437177i	0.975817	−	0.218589i	$-0.0701453\pi$
$440$		0			0
$441$		−	2.72941i		−	0.129972i
$442$		0			0
$443$	14.9856	+	14.9856i	0.711986	+	0.711986i	0.966951	−	0.254964i	$-0.0820636\pi$
$443$	14.9856	+	14.9856i	0.711986	+	0.711986i	−0.254964	+	0.966951i	$0.582064\pi$
$444$		0			0
$445$	5.39043	−	5.39043i	0.255531	−	0.255531i
$446$		0			0
$447$	−6.15515			−0.291129
$448$		0			0
$449$	−5.55953			−0.262371			−0.131185	−	0.991358i	$-0.541878\pi$
$449$	−5.55953			−0.262371			−0.131185	+	0.991358i	$0.541878\pi$
$450$		0			0
$451$	−0.493394	+	0.493394i	−0.0232330	+	0.0232330i
$452$		0			0
$453$	−5.71644	−	5.71644i	−0.268582	−	0.268582i
$454$		0			0
$455$		−	4.52892i		−	0.212319i
$456$		0			0
$457$		−	7.88592i		−	0.368888i	−0.982843	−	0.184444i	$-0.940952\pi$
$457$		−	7.88592i		−	0.368888i	0.982843	−	0.184444i	$-0.0590484\pi$
$458$		0			0
$459$	7.64399	+	7.64399i	0.356791	+	0.356791i
$460$		0			0
$461$	−20.0887	+	20.0887i	−0.935622	+	0.935622i	−0.998050	−	0.0624275i	$-0.980116\pi$
$461$	−20.0887	+	20.0887i	−0.935622	+	0.935622i	0.0624275	+	0.998050i	$0.480116\pi$
$462$		0			0
$463$	8.01693			0.372578			0.186289	−	0.982495i	$-0.440354\pi$
$463$	8.01693			0.372578			0.186289	+	0.982495i	$0.440354\pi$
$464$		0			0
$465$	−5.17800			−0.240124
$466$		0			0
$467$	−1.81325	+	1.81325i	−0.0839071	+	0.0839071i	−0.747815	−	0.663908i	$-0.768897\pi$
$467$	−1.81325	+	1.81325i	−0.0839071	+	0.0839071i	0.663908	+	0.747815i	$0.268897\pi$
$468$		0			0
$469$	5.53911	+	5.53911i	0.255772	+	0.255772i
$470$		0			0
$471$		−	1.68637i		−	0.0777038i
$472$		0			0
$473$			5.85182i			0.269067i
$474$		0			0
$475$	−5.14288	−	5.14288i	−0.235971	−	0.235971i
$476$		0			0
$477$	−26.1177	+	26.1177i	−1.19585	+	1.19585i
$478$		0			0
$479$	−2.59834			−0.118721			−0.0593606	−	0.998237i	$-0.518906\pi$
$479$	−2.59834			−0.118721			−0.0593606	+	0.998237i	$0.518906\pi$
$480$		0			0
$481$	−11.9716			−0.545858
$482$		0			0
$483$	0.304353	−	0.304353i	0.0138486	−	0.0138486i
$484$		0			0
$485$	9.82583	+	9.82583i	0.446168	+	0.446168i
$486$		0			0
$487$			28.3185i			1.28323i	0.767025	+	0.641617i	$0.221736\pi$
$487$			28.3185i			1.28323i	−0.767025	+	0.641617i	$0.778264\pi$
$488$		0			0
$489$			6.96843i			0.315123i
$490$		0			0
$491$	−22.5469	−	22.5469i	−1.01753	−	1.01753i	−0.999844	−	0.0176843i	$-0.994371\pi$
$491$	−22.5469	−	22.5469i	−1.01753	−	1.01753i	−0.0176843	−	0.999844i	$-0.505629\pi$
$492$		0			0
$493$	−26.8996	+	26.8996i	−1.21150	+	1.21150i
$494$		0			0
$495$	−3.51225			−0.157864
$496$		0			0
$497$	−13.2835			−0.595845
$498$		0			0
$499$	−17.9604	+	17.9604i	−0.804020	+	0.804020i	−0.983721	−	0.179701i	$-0.942487\pi$
$499$	−17.9604	+	17.9604i	−0.804020	+	0.804020i	0.179701	+	0.983721i	$0.442487\pi$
$500$		0			0
$501$	3.96187	+	3.96187i	0.177003	+	0.177003i
$502$		0			0
$503$		−	25.7225i		−	1.14691i	−0.819238	−	0.573454i	$-0.805603\pi$
$503$		−	25.7225i		−	1.14691i	0.819238	−	0.573454i	$-0.194397\pi$
$504$		0			0
$505$		−	7.88764i		−	0.350996i
$506$		0			0
$507$	−2.76275	−	2.76275i	−0.122698	−	0.122698i
$508$		0			0
$509$	0.359115	−	0.359115i	0.0159175	−	0.0159175i	−0.699103	−	0.715021i	$-0.746417\pi$
$509$	0.359115	−	0.359115i	0.0159175	−	0.0159175i	0.715021	+	0.699103i	$0.246417\pi$
$510$		0			0
$511$	−15.6824			−0.693748
$512$		0			0
$513$	−21.6763			−0.957031
$514$		0			0
$515$	2.57017	−	2.57017i	0.113255	−	0.113255i
$516$		0			0
$517$	−6.92441	−	6.92441i	−0.304535	−	0.304535i
$518$		0			0
$519$		−	5.50594i		−	0.241684i
$520$		0			0
$521$		−	6.64929i		−	0.291311i	−0.989335	−	0.145655i	$-0.953471\pi$
$521$		−	6.64929i		−	0.291311i	0.989335	−	0.145655i	$-0.0465291\pi$
$522$		0			0
$523$	25.6417	+	25.6417i	1.12123	+	1.12123i	0.991556	+	0.129679i	$0.0413946\pi$
$523$	25.6417	+	25.6417i	1.12123	+	1.12123i	0.129679	+	0.991556i	$0.458605\pi$
$524$		0			0
$525$	−0.367823	+	0.367823i	−0.0160531	+	0.0160531i
$526$		0			0
$527$	36.1061			1.57280
$528$		0			0
$529$	22.3153			0.970232
$530$		0			0
$531$	3.37685	−	3.37685i	0.146543	−	0.146543i
$532$		0			0
$533$	−1.73649	−	1.73649i	−0.0752158	−	0.0752158i
$534$		0			0
$535$		−	0.250980i		−	0.0108508i
$536$		0			0
$537$			4.72326i			0.203824i
$538$		0			0
$539$	0.909915	+	0.909915i	0.0391928	+	0.0391928i
$540$		0			0
$541$	18.3994	−	18.3994i	0.791054	−	0.791054i	−0.190612	−	0.981666i	$-0.561047\pi$
$541$	18.3994	−	18.3994i	0.791054	−	0.791054i	0.981666	+	0.190612i	$0.0610471\pi$
$542$		0			0
$543$	−5.25709			−0.225604
$544$		0			0
$545$	−13.8216			−0.592053
$546$		0			0
$547$	2.89390	−	2.89390i	0.123734	−	0.123734i	−0.642528	−	0.766262i	$-0.722114\pi$
$547$	2.89390	−	2.89390i	0.123734	−	0.123734i	0.766262	+	0.642528i	$0.222114\pi$
$548$		0			0
$549$	−1.93986	−	1.93986i	−0.0827913	−	0.0827913i
$550$		0			0
$551$		−	76.2801i		−	3.24964i
$552$		0			0
$553$			14.2958i			0.607920i
$554$		0			0
$555$	0.972291	+	0.972291i	0.0412714	+	0.0412714i
$556$		0			0
$557$	−9.26240	+	9.26240i	−0.392460	+	0.392460i	−0.875564	−	0.483103i	$-0.839510\pi$
$557$	−9.26240	+	9.26240i	−0.392460	+	0.392460i	0.483103	+	0.875564i	$0.339510\pi$
$558$		0			0
$559$	−20.5954			−0.871091
$560$		0			0
$561$	−2.42795			−0.102508
$562$		0			0
$563$	1.74841	−	1.74841i	0.0736868	−	0.0736868i	−0.669303	−	0.742990i	$-0.733407\pi$
$563$	1.74841	−	1.74841i	0.0736868	−	0.0736868i	0.742990	+	0.669303i	$0.233407\pi$
$564$		0			0
$565$	−4.41274	−	4.41274i	−0.185645	−	0.185645i
$566$		0			0
$567$		−	6.63794i		−	0.278767i
$568$		0			0
$569$		−	3.45459i		−	0.144824i	−0.997375	−	0.0724119i	$-0.976930\pi$
$569$		−	3.45459i		−	0.144824i	0.997375	−	0.0724119i	$-0.0230696\pi$
$570$		0			0
$571$	−10.0604	−	10.0604i	−0.421015	−	0.421015i	0.464538	−	0.885553i	$-0.346220\pi$
$571$	−10.0604	−	10.0604i	−0.421015	−	0.421015i	−0.885553	+	0.464538i	$0.846220\pi$
$572$		0			0
$573$	−1.10634	+	1.10634i	−0.0462179	+	0.0462179i
$574$		0			0
$575$	0.827446			0.0345069
$576$		0			0
$577$	−31.2503			−1.30097			−0.650484	−	0.759520i	$-0.725434\pi$
$577$	−31.2503			−1.30097			−0.650484	+	0.759520i	$0.725434\pi$
$578$		0			0
$579$	6.60269	−	6.60269i	0.274398	−	0.274398i
$580$		0			0
$581$	−3.42296	−	3.42296i	−0.142008	−	0.142008i
$582$		0			0
$583$		−	17.4139i		−	0.721212i
$584$		0			0
$585$		−	12.3613i		−	0.511076i
$586$		0			0
$587$	−1.42377	−	1.42377i	−0.0587651	−	0.0587651i	0.677113	−	0.735879i	$-0.263231\pi$
$587$	−1.42377	−	1.42377i	−0.0587651	−	0.0587651i	−0.735879	+	0.677113i	$0.763231\pi$
$588$		0			0
$589$	−51.1935	+	51.1935i	−2.10939	+	2.10939i
$590$		0			0
$591$	9.67734			0.398073
$592$		0			0
$593$	14.5566			0.597766			0.298883	−	0.954290i	$-0.403386\pi$
$593$	14.5566			0.597766			0.298883	+	0.954290i	$0.403386\pi$
$594$		0			0
$595$	2.56482	−	2.56482i	0.105147	−	0.105147i
$596$		0			0
$597$	−0.371936	−	0.371936i	−0.0152223	−	0.0152223i
$598$		0			0
$599$		−	33.5709i		−	1.37167i	−0.727757	−	0.685835i	$-0.759437\pi$
$599$		−	33.5709i		−	1.37167i	0.727757	−	0.685835i	$-0.240563\pi$
$600$		0			0
$601$		−	19.3517i		−	0.789374i	−0.918816	−	0.394687i	$-0.870853\pi$
$601$		−	19.3517i		−	0.789374i	0.918816	−	0.394687i	$-0.129147\pi$
$602$		0			0
$603$	15.1185	+	15.1185i	0.615674	+	0.615674i
$604$		0			0
$605$	−6.60728	+	6.60728i	−0.268624	+	0.268624i
$606$		0			0
$607$	14.4997			0.588525			0.294263	−	0.955725i	$-0.404926\pi$
$607$	14.4997			0.588525			0.294263	+	0.955725i	$0.404926\pi$
$608$		0			0
$609$	−5.45561			−0.221072
$610$		0			0
$611$	24.3703	−	24.3703i	0.985918	−	0.985918i
$612$		0			0
$613$	−30.8505	−	30.8505i	−1.24604	−	1.24604i	−0.957455	−	0.288583i	$-0.906816\pi$
$613$	−30.8505	−	30.8505i	−1.24604	−	1.24604i	−0.288583	−	0.957455i	$-0.593184\pi$
$614$		0			0
$615$			0.282064i			0.0113739i
$616$		0			0
$617$		−	23.8852i		−	0.961582i	−0.876835	−	0.480791i	$-0.840350\pi$
$617$		−	23.8852i		−	0.961582i	0.876835	−	0.480791i	$-0.159650\pi$
$618$		0			0
$619$	9.88367	+	9.88367i	0.397258	+	0.397258i	0.877265	−	0.480007i	$-0.159366\pi$
$619$	9.88367	+	9.88367i	0.397258	+	0.397258i	−0.480007	+	0.877265i	$0.659366\pi$
$620$		0			0
$621$	1.74377	−	1.74377i	0.0699749	−	0.0699749i
$622$		0			0
$623$	−7.62322			−0.305418
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$	3.44251	−	3.44251i	0.137481	−	0.137481i
$628$		0			0
$629$	−6.77976	−	6.77976i	−0.270327	−	0.270327i
$630$		0			0
$631$			13.0946i			0.521288i	0.965435	+	0.260644i	$0.0839350\pi$
$631$			13.0946i			0.521288i	−0.965435	+	0.260644i	$0.916065\pi$
$632$		0			0
$633$		−	2.12807i		−	0.0845831i
$634$		0			0
$635$	−4.11563	−	4.11563i	−0.163324	−	0.163324i
$636$		0			0
$637$	−3.20243	+	3.20243i	−0.126885	+	0.126885i
$638$		0			0
$639$	−36.2560			−1.43427
$640$		0			0
$641$	23.5030			0.928314			0.464157	−	0.885753i	$-0.346357\pi$
$641$	23.5030			0.928314			0.464157	+	0.885753i	$0.346357\pi$
$642$		0			0
$643$	−1.26548	+	1.26548i	−0.0499057	+	0.0499057i	−0.731619	−	0.681714i	$-0.761235\pi$
$643$	−1.26548	+	1.26548i	−0.0499057	+	0.0499057i	0.681714	+	0.731619i	$0.261235\pi$
$644$		0			0
$645$	1.67268	+	1.67268i	0.0658618	+	0.0658618i
$646$		0			0
$647$			32.7858i			1.28894i	0.764628	+	0.644472i	$0.222923\pi$
$647$			32.7858i			1.28894i	−0.764628	+	0.644472i	$0.777077\pi$
$648$		0			0
$649$			2.25150i			0.0883792i
$650$		0			0
$651$	3.66140	+	3.66140i	0.143501	+	0.143501i
$652$		0			0
$653$	−11.3777	+	11.3777i	−0.445243	+	0.445243i	−0.893770	−	0.448526i	$-0.851949\pi$
$653$	−11.3777	+	11.3777i	−0.445243	+	0.445243i	0.448526	+	0.893770i	$0.351949\pi$
$654$		0			0
$655$	−20.0627			−0.783914
$656$		0			0
$657$	−42.8037			−1.66993
$658$		0			0
$659$	−12.6508	+	12.6508i	−0.492806	+	0.492806i	−0.909189	−	0.416383i	$-0.863297\pi$
$659$	−12.6508	+	12.6508i	−0.492806	+	0.492806i	0.416383	+	0.909189i	$0.363297\pi$
$660$		0			0
$661$	3.44470	+	3.44470i	0.133983	+	0.133983i	0.770918	−	0.636934i	$-0.219798\pi$
$661$	3.44470	+	3.44470i	0.133983	+	0.133983i	−0.636934	+	0.770918i	$0.719798\pi$
$662$		0			0
$663$		−	8.54514i		−	0.331866i
$664$		0			0
$665$			7.27313i			0.282040i
$666$		0			0
$667$	6.13641	+	6.13641i	0.237603	+	0.237603i
$668$		0			0
$669$	2.63802	−	2.63802i	0.101992	−	0.101992i
$670$		0			0
$671$	1.29340			0.0499311
$672$		0			0
$673$	2.93416			0.113103			0.0565517	−	0.998400i	$-0.481989\pi$
$673$	2.93416			0.113103			0.0565517	+	0.998400i	$0.481989\pi$
$674$		0			0
$675$	−2.10741	+	2.10741i	−0.0811142	+	0.0811142i
$676$		0			0
$677$	2.60791	+	2.60791i	0.100230	+	0.100230i	0.755444	−	0.655214i	$-0.227421\pi$
$677$	2.60791	+	2.60791i	0.100230	+	0.100230i	−0.655214	+	0.755444i	$0.727421\pi$
$678$		0			0
$679$		−	13.8958i		−	0.533273i
$680$		0			0
$681$			9.67502i			0.370747i
$682$		0			0
$683$	−7.42381	−	7.42381i	−0.284064	−	0.284064i	0.550663	−	0.834728i	$-0.314375\pi$
$683$	−7.42381	−	7.42381i	−0.284064	−	0.284064i	−0.834728	+	0.550663i	$0.814375\pi$
$684$		0			0
$685$	5.61228	−	5.61228i	0.214434	−	0.214434i
$686$		0			0
$687$	5.23099			0.199575
$688$		0			0
$689$	61.2880			2.33489
$690$		0			0
$691$	16.7063	−	16.7063i	0.635536	−	0.635536i	−0.313915	−	0.949451i	$-0.601641\pi$
$691$	16.7063	−	16.7063i	0.635536	−	0.635536i	0.949451	+	0.313915i	$0.101641\pi$
$692$		0			0
$693$	2.48353	+	2.48353i	0.0943416	+	0.0943416i
$694$		0			0
$695$		−	16.0488i		−	0.608766i
$696$		0			0
$697$		−	1.96682i		−	0.0744987i
$698$		0			0
$699$	−2.15807	−	2.15807i	−0.0816256	−	0.0816256i
$700$		0			0
$701$	5.43694	−	5.43694i	0.205350	−	0.205350i	−0.596937	−	0.802288i	$-0.703616\pi$
$701$	5.43694	−	5.43694i	0.205350	−	0.205350i	0.802288	+	0.596937i	$0.203616\pi$
$702$		0			0
$703$	19.2256			0.725106
$704$		0			0
$705$	−3.95854			−0.149087
$706$		0			0
$707$	−5.57741	+	5.57741i	−0.209760	+	0.209760i
$708$		0			0
$709$	−12.5624	−	12.5624i	−0.471792	−	0.471792i	0.430702	−	0.902494i	$-0.358266\pi$
$709$	−12.5624	−	12.5624i	−0.471792	−	0.471792i	−0.902494	+	0.430702i	$0.858266\pi$
$710$		0			0
$711$			39.0192i			1.46333i
$712$		0			0
$713$		−	8.23660i		−	0.308463i
$714$		0			0
$715$	4.12093	+	4.12093i	0.154114	+	0.154114i
$716$		0			0
$717$	−4.13315	+	4.13315i	−0.154355	+	0.154355i
$718$		0			0
$719$	−17.7738			−0.662851			−0.331426	−	0.943481i	$-0.607530\pi$
$719$	−17.7738			−0.662851			−0.331426	+	0.943481i	$0.607530\pi$
$720$		0			0
$721$	−3.63477			−0.135366
$722$		0			0
$723$	−2.26137	+	2.26137i	−0.0841012	+	0.0841012i
$724$		0			0
$725$	−7.41609	−	7.41609i	−0.275427	−	0.275427i
$726$		0			0
$727$			6.78730i			0.251727i	0.992048	+	0.125864i	$0.0401701\pi$
$727$			6.78730i			0.251727i	−0.992048	+	0.125864i	$0.959830\pi$
$728$		0			0
$729$		−	13.4668i		−	0.498769i
$730$		0			0
$731$	−11.6636	−	11.6636i	−0.431393	−	0.431393i
$732$		0			0
$733$	25.5886	−	25.5886i	0.945136	−	0.945136i	−0.0534349	−	0.998571i	$-0.517017\pi$
$733$	25.5886	−	25.5886i	0.945136	−	0.945136i	0.998571	+	0.0534349i	$0.0170170\pi$
$734$		0			0
$735$	0.520180			0.0191871
$736$		0			0
$737$	−10.0802			−0.371310
$738$		0			0
$739$	26.3444	−	26.3444i	0.969095	−	0.969095i	−0.0304414	−	0.999537i	$-0.509691\pi$
$739$	26.3444	−	26.3444i	0.969095	−	0.969095i	0.999537	+	0.0304414i	$0.00969129\pi$
$740$		0			0
$741$	12.1159	+	12.1159i	0.445087	+	0.445087i
$742$		0			0
$743$			19.2708i			0.706976i	0.935439	+	0.353488i	$0.115005\pi$
$743$			19.2708i			0.706976i	−0.935439	+	0.353488i	$0.884995\pi$
$744$		0			0
$745$			11.8327i			0.433518i
$746$		0			0
$747$	−9.34266	−	9.34266i	−0.341830	−	0.341830i
$748$		0			0
$749$	−0.177470	+	0.177470i	−0.00648459	+	0.00648459i
$750$		0			0
$751$	−36.7732			−1.34187			−0.670937	−	0.741515i	$-0.734108\pi$
$751$	−36.7732			−1.34187			−0.670937	+	0.741515i	$0.734108\pi$
$752$		0			0
$753$	4.75689			0.173351
$754$		0			0
$755$	−10.9894	+	10.9894i	−0.399944	+	0.399944i
$756$		0			0
$757$	26.0764	+	26.0764i	0.947762	+	0.947762i	0.998702	−	0.0509401i	$-0.0162218\pi$
$757$	26.0764	+	26.0764i	0.947762	+	0.947762i	−0.0509401	+	0.998702i	$0.516222\pi$
$758$		0			0
$759$			0.553871i			0.0201042i
$760$		0			0
$761$			20.7995i			0.753981i	0.926217	+	0.376991i	$0.123041\pi$
$761$			20.7995i			0.753981i	−0.926217	+	0.376991i	$0.876959\pi$
$762$		0			0
$763$	9.77336	+	9.77336i	0.353819	+	0.353819i
$764$		0			0
$765$	7.00045	−	7.00045i	0.253102	−	0.253102i
$766$		0			0
$767$	−7.92412			−0.286123
$768$		0			0
$769$	30.4135			1.09674			0.548369	−	0.836237i	$-0.315249\pi$
$769$	30.4135			1.09674			0.548369	+	0.836237i	$0.315249\pi$
$770$		0			0
$771$	−8.68702	+	8.68702i	−0.312855	+	0.312855i
$772$		0			0
$773$	−2.61065	−	2.61065i	−0.0938987	−	0.0938987i	0.658597	−	0.752496i	$-0.271150\pi$
$773$	−2.61065	−	2.61065i	−0.0938987	−	0.0938987i	−0.752496	+	0.658597i	$0.771150\pi$
$774$		0			0
$775$			9.95425i			0.357567i
$776$		0			0
$777$		−	1.37503i		−	0.0493288i
$778$		0			0
$779$	2.78869	+	2.78869i	0.0999151	+	0.0999151i
$780$		0			0
$781$	12.0868	−	12.0868i	0.432500	−	0.432500i
$782$		0			0
$783$	−31.2574			−1.11705
$784$		0			0
$785$	−3.24190			−0.115708
$786$		0			0
$787$	−9.79302	+	9.79302i	−0.349084	+	0.349084i	−0.859768	−	0.510685i	$-0.829392\pi$
$787$	−9.79302	+	9.79302i	−0.349084	+	0.349084i	0.510685	+	0.859768i	$0.329392\pi$
$788$		0			0
$789$	−4.08869	−	4.08869i	−0.145561	−	0.145561i
$790$		0			0
$791$			6.24055i			0.221888i
$792$		0			0
$793$			4.55209i			0.161649i
$794$		0			0
$795$	−4.97760	−	4.97760i	−0.176537	−	0.176537i
$796$		0			0
$797$	−16.4080	+	16.4080i	−0.581201	+	0.581201i	−0.935233	−	0.354032i	$-0.884810\pi$
$797$	−16.4080	+	16.4080i	−0.581201	+	0.581201i	0.354032	+	0.935233i	$0.384810\pi$
$798$		0			0
$799$	27.6028			0.976517
$800$		0			0
$801$	−20.8069			−0.735176
$802$		0			0
$803$	14.2696	−	14.2696i	0.503565	−	0.503565i
$804$		0			0
$805$	−0.585092	−	0.585092i	−0.0206218	−	0.0206218i
$806$		0			0
$807$			13.9827i			0.492216i
$808$		0			0
$809$		−	10.3599i		−	0.364235i	−0.983277	−	0.182118i	$-0.941705\pi$
$809$		−	10.3599i		−	0.364235i	0.983277	−	0.182118i	$-0.0582951\pi$
$810$		0			0
$811$	6.71492	+	6.71492i	0.235793	+	0.235793i	0.815105	−	0.579313i	$-0.196679\pi$
$811$	6.71492	+	6.71492i	0.235793	+	0.235793i	−0.579313	+	0.815105i	$0.696679\pi$
$812$		0			0
$813$	−4.88122	+	4.88122i	−0.171192	+	0.171192i
$814$		0			0
$815$	13.3962			0.469249
$816$		0			0
$817$	33.0747			1.15714
$818$		0			0
$819$	−8.74075	+	8.74075i	−0.305426	+	0.305426i
$820$		0			0
$821$	−15.5104	−	15.5104i	−0.541318	−	0.541318i	0.382598	−	0.923915i	$-0.375030\pi$
$821$	−15.5104	−	15.5104i	−0.541318	−	0.541318i	−0.923915	+	0.382598i	$0.875030\pi$
$822$		0			0
$823$		−	53.6845i		−	1.87133i	−0.352896	−	0.935663i	$-0.614803\pi$
$823$		−	53.6845i		−	1.87133i	0.352896	−	0.935663i	$-0.385197\pi$
$824$		0			0
$825$		−	0.669374i		−	0.0233046i
$826$		0			0
$827$	−4.53375	−	4.53375i	−0.157654	−	0.157654i	0.623872	−	0.781526i	$-0.285559\pi$
$827$	−4.53375	−	4.53375i	−0.157654	−	0.157654i	−0.781526	+	0.623872i	$0.785559\pi$
$828$		0			0
$829$	20.4958	−	20.4958i	0.711848	−	0.711848i	−0.255074	−	0.966922i	$-0.582100\pi$
$829$	20.4958	−	20.4958i	0.711848	−	0.711848i	0.966922	+	0.255074i	$0.0820998\pi$
$830$		0			0
$831$	−4.16731			−0.144562
$832$		0			0
$833$	−3.62720			−0.125675
$834$		0			0
$835$	7.61634	−	7.61634i	0.263574	−	0.263574i
$836$		0			0
$837$	20.9777	+	20.9777i	0.725094	+	0.725094i
$838$		0			0
$839$		−	20.5679i		−	0.710084i	−0.934850	−	0.355042i	$-0.884467\pi$
$839$		−	20.5679i		−	0.710084i	0.934850	−	0.355042i	$-0.115533\pi$
$840$		0			0
$841$		−	80.9967i		−	2.79299i
$842$		0			0
$843$	9.88550	+	9.88550i	0.340475	+	0.340475i
$844$		0			0
$845$	−5.31114	+	5.31114i	−0.182709	+	0.182709i
$846$		0			0
$847$	9.34411			0.321067
$848$		0			0
$849$	−9.35317			−0.321000
$850$		0			0
$851$	−1.54661	+	1.54661i	−0.0530173	+	0.0530173i
$852$		0			0
$853$	33.0185	+	33.0185i	1.13053	+	1.13053i	0.990089	+	0.140443i	$0.0448526\pi$
$853$	33.0185	+	33.0185i	1.13053	+	1.13053i	0.140443	+	0.990089i	$0.455147\pi$
$854$		0			0
$855$			19.8514i			0.678903i
$856$		0			0
$857$		−	11.9197i		−	0.407168i	−0.979057	−	0.203584i	$-0.934741\pi$
$857$		−	11.9197i		−	0.407168i	0.979057	−	0.203584i	$-0.0652590\pi$
$858$		0			0
$859$	18.5793	+	18.5793i	0.633917	+	0.633917i	0.949048	−	0.315131i	$-0.102049\pi$
$859$	18.5793	+	18.5793i	0.633917	+	0.633917i	−0.315131	+	0.949048i	$0.602049\pi$
$860$		0			0
$861$	0.199449	−	0.199449i	0.00679720	−	0.00679720i
$862$		0			0
$863$	18.9014			0.643412			0.321706	−	0.946840i	$-0.395744\pi$
$863$	18.9014			0.643412			0.321706	+	0.946840i	$0.395744\pi$
$864$		0			0
$865$	−10.5847			−0.359890
$866$		0			0
$867$	−1.41370	+	1.41370i	−0.0480117	+	0.0480117i
$868$		0			0
$869$	−13.0080	−	13.0080i	−0.441266	−	0.441266i
$870$		0			0
$871$		−	35.4772i		−	1.20210i
$872$		0			0
$873$		−	37.9274i		−	1.28365i
$874$		0			0
$875$	0.707107	+	0.707107i	0.0239046	+	0.0239046i
$876$		0			0
$877$	14.6582	−	14.6582i	0.494971	−	0.494971i	−0.414898	−	0.909868i	$-0.636183\pi$
$877$	14.6582	−	14.6582i	0.494971	−	0.494971i	0.909868	+	0.414898i	$0.136183\pi$
$878$		0			0
$879$	−7.34572			−0.247765
$880$		0			0
$881$	−1.84335			−0.0621042			−0.0310521	−	0.999518i	$-0.509886\pi$
$881$	−1.84335			−0.0621042			−0.0310521	+	0.999518i	$0.509886\pi$
$882$		0			0
$883$	−8.10084	+	8.10084i	−0.272615	+	0.272615i	−0.830152	−	0.557537i	$-0.811746\pi$
$883$	−8.10084	+	8.10084i	−0.272615	+	0.272615i	0.557537	+	0.830152i	$0.311746\pi$
$884$		0			0
$885$	0.643569	+	0.643569i	0.0216333	+	0.0216333i
$886$		0			0
$887$			26.6580i			0.895090i	0.894262	+	0.447545i	$0.147701\pi$
$887$			26.6580i			0.895090i	−0.894262	+	0.447545i	$0.852299\pi$
$888$		0			0
$889$			5.82038i			0.195209i
$890$		0			0
$891$	6.03996	+	6.03996i	0.202346	+	0.202346i
$892$		0			0
$893$	−39.1371	+	39.1371i	−1.30967	+	1.30967i
$894$		0			0
$895$	9.08006			0.303513
$896$		0			0
$897$	−1.94934			−0.0650865
$898$		0			0
$899$	−73.8216	+	73.8216i	−2.46209	+	2.46209i
$900$		0			0
$901$	34.7087	+	34.7087i	1.15631	+	1.15631i
$902$		0			0
$903$		−	2.36553i		−	0.0787199i
$904$		0			0
$905$			10.1063i			0.335945i
$906$		0			0
$907$	4.53397	+	4.53397i	0.150548	+	0.150548i	0.778363	−	0.627815i	$-0.216050\pi$
$907$	4.53397	+	4.53397i	0.150548	+	0.150548i	−0.627815	+	0.778363i	$0.716050\pi$
$908$		0			0
$909$	−15.2230	+	15.2230i	−0.504917	+	0.504917i
$910$		0			0
$911$	−2.90883			−0.0963739			−0.0481870	−	0.998838i	$-0.515344\pi$
$911$	−2.90883			−0.0963739			−0.0481870	+	0.998838i	$0.515344\pi$
$912$		0			0
$913$	6.22920			0.206156
$914$		0			0
$915$	0.369705	−	0.369705i	0.0122221	−	0.0122221i
$916$		0			0
$917$	14.1865	+	14.1865i	0.468478	+	0.468478i
$918$		0			0
$919$		−	49.9320i		−	1.64710i	−0.567241	−	0.823552i	$-0.691989\pi$
$919$		−	49.9320i		−	1.64710i	0.567241	−	0.823552i	$-0.308011\pi$
$920$		0			0
$921$		−	3.32461i		−	0.109550i
$922$		0			0
$923$	42.5393	+	42.5393i	1.40020	+	1.40020i
$924$		0			0
$925$	1.86914	−	1.86914i	0.0614571	−	0.0614571i
$926$		0			0
$927$	−9.92080			−0.325842
$928$		0			0
$929$	45.0363			1.47759			0.738796	−	0.673929i	$-0.235395\pi$
$929$	45.0363			1.47759			0.738796	+	0.673929i	$0.235395\pi$
$930$		0			0
$931$	5.14288	−	5.14288i	0.168551	−	0.168551i
$932$		0			0
$933$	−7.31139	−	7.31139i	−0.239364	−	0.239364i
$934$		0			0
$935$			4.66753i			0.152645i
$936$		0			0
$937$			23.2062i			0.758115i	0.925373	+	0.379058i	$0.123752\pi$
$937$			23.2062i			0.758115i	−0.925373	+	0.379058i	$0.876248\pi$
$938$		0			0
$939$	−1.95322	−	1.95322i	−0.0637411	−	0.0637411i
$940$		0			0
$941$	−26.8072	+	26.8072i	−0.873891	+	0.873891i	−0.992894	−	0.119003i	$-0.962030\pi$
$941$	−26.8072	+	26.8072i	−0.873891	+	0.873891i	0.119003	+	0.992894i	$0.462030\pi$
$942$		0			0
$943$	−0.448676			−0.0146109
$944$		0			0
$945$	2.98032			0.0969500
$946$		0			0
$947$	−11.8597	+	11.8597i	−0.385390	+	0.385390i	−0.873039	−	0.487650i	$-0.837854\pi$
$947$	−11.8597	+	11.8597i	−0.385390	+	0.385390i	0.487650	+	0.873039i	$0.337854\pi$
$948$		0			0
$949$	50.2217	+	50.2217i	1.63027	+	1.63027i
$950$		0			0
$951$		−	11.6656i		−	0.378283i
$952$		0			0
$953$		−	48.4780i		−	1.57036i	−0.619270	−	0.785178i	$-0.712571\pi$
$953$		−	48.4780i		−	1.57036i	0.619270	−	0.785178i	$-0.287429\pi$
$954$		0			0
$955$	2.12683	+	2.12683i	0.0688227	+	0.0688227i
$956$		0			0
$957$	4.96414	−	4.96414i	0.160468	−	0.160468i
$958$		0			0
$959$	−7.93696			−0.256298
$960$		0			0
$961$	68.0871			2.19636
$962$		0			0
$963$	−0.484388	+	0.484388i	−0.0156092	+	0.0156092i
$964$		0			0
$965$	−12.6931	−	12.6931i	−0.408605	−	0.408605i
$966$		0			0
$967$			43.5111i			1.39922i	0.714524	+	0.699611i	$0.246643\pi$
$967$			43.5111i			1.39922i	−0.714524	+	0.699611i	$0.753357\pi$
$968$		0			0
$969$			13.7229i			0.440843i
$970$		0			0
$971$	5.06858	+	5.06858i	0.162658	+	0.162658i	0.783743	−	0.621085i	$-0.213308\pi$
$971$	5.06858	+	5.06858i	0.162658	+	0.162658i	−0.621085	+	0.783743i	$0.713308\pi$
$972$		0			0
$973$	−11.3482	+	11.3482i	−0.363807	+	0.363807i
$974$		0			0
$975$	2.35585			0.0754476
$976$		0			0
$977$	20.0446			0.641282			0.320641	−	0.947201i	$-0.396102\pi$
$977$	20.0446			0.641282			0.320641	+	0.947201i	$0.396102\pi$
$978$		0			0
$979$	6.93648	−	6.93648i	0.221691	−	0.221691i
$980$		0			0
$981$	26.6755	+	26.6755i	0.851684	+	0.851684i
$982$		0			0
$983$			24.9679i			0.796351i	0.917309	+	0.398176i	$0.130357\pi$
$983$			24.9679i			0.796351i	−0.917309	+	0.398176i	$0.869643\pi$
$984$		0			0
$985$		−	18.6038i		−	0.592768i
$986$		0			0
$987$	2.79911	+	2.79911i	0.0890967	+	0.0890967i
$988$		0			0
$989$	−2.66072	+	2.66072i	−0.0846060	+	0.0846060i
$990$		0			0
$991$	−10.3429			−0.328552			−0.164276	−	0.986414i	$-0.552529\pi$
$991$	−10.3429			−0.328552			−0.164276	+	0.986414i	$0.552529\pi$
$992$		0			0
$993$	2.60448			0.0826506
$994$		0			0
$995$	−0.715014	+	0.715014i	−0.0226675	+	0.0226675i
$996$		0			0
$997$	−4.60935	−	4.60935i	−0.145980	−	0.145980i	0.630340	−	0.776319i	$-0.282916\pi$
$997$	−4.60935	−	4.60935i	−0.145980	−	0.145980i	−0.776319	+	0.630340i	$0.782916\pi$
$998$		0			0
$999$		−	7.87809i		−	0.249252i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2240.2.bd.b.561.16		52
4.3	odd	2		560.2.bd.b.421.25	yes	52
16.3	odd	4		560.2.bd.b.141.25	✓	52
16.13	even	4	inner	2240.2.bd.b.1681.16		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bd.b.141.25	✓	52	16.3	odd	4
560.2.bd.b.421.25	yes	52	4.3	odd	2
2240.2.bd.b.561.16		52	1.1	even	1	trivial
2240.2.bd.b.1681.16		52	16.13	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2240.bd (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.367823 - 0.367823i) q^{3} +(-0.707107 - 0.707107i) q^{5} +1.00000i q^{7} +2.72941i q^{9} +O(q^{10})\)	\(q+(0.367823 - 0.367823i) q^{3} +(-0.707107 - 0.707107i) q^{5} +1.00000i q^{7} +2.72941i q^{9} +(-0.909915 - 0.909915i) q^{11} +(3.20243 - 3.20243i) q^{13} -0.520180 q^{15} +3.62720 q^{17} +(-5.14288 + 5.14288i) q^{19} +(0.367823 + 0.367823i) q^{21} -0.827446i q^{23} +1.00000i q^{25} +(2.10741 + 2.10741i) q^{27} +(-7.41609 + 7.41609i) q^{29} +9.95425 q^{31} -0.669374 q^{33} +(0.707107 - 0.707107i) q^{35} +(-1.86914 - 1.86914i) q^{37} -2.35585i q^{39} -0.542242i q^{41} +(-3.21558 - 3.21558i) q^{43} +(1.92999 - 1.92999i) q^{45} +7.60995 q^{47} -1.00000 q^{49} +(1.33417 - 1.33417i) q^{51} +(9.56900 + 9.56900i) q^{53} +1.28681i q^{55} +3.78333i q^{57} +(-1.23721 - 1.23721i) q^{59} +(-0.710725 + 0.710725i) q^{61} -2.72941 q^{63} -4.52892 q^{65} +(5.53911 - 5.53911i) q^{67} +(-0.304353 - 0.304353i) q^{69} +13.2835i q^{71} +15.6824i q^{73} +(0.367823 + 0.367823i) q^{75} +(0.909915 - 0.909915i) q^{77} +14.2958 q^{79} -6.63794 q^{81} +(-3.42296 + 3.42296i) q^{83} +(-2.56482 - 2.56482i) q^{85} +5.45561i q^{87} +7.62322i q^{89} +(3.20243 + 3.20243i) q^{91} +(3.66140 - 3.66140i) q^{93} +7.27313 q^{95} -13.8958 q^{97} +(2.48353 - 2.48353i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q+O(q^{10}) \) 52 * q	\( 52 q + 4 q^{11} - 8 q^{15} - 8 q^{19} + 24 q^{27} + 4 q^{29} - 12 q^{37} - 36 q^{43} - 52 q^{49} + 8 q^{51} - 4 q^{53} - 24 q^{59} - 16 q^{61} + 68 q^{63} + 40 q^{65} + 12 q^{67} - 72 q^{69} - 4 q^{77} + 16 q^{79} - 116 q^{81} + 16 q^{85} + 8 q^{93} + 32 q^{95} + 52 q^{99}+O(q^{100}) \) 52 * q + 4 * q^11 - 8 * q^15 - 8 * q^19 + 24 * q^27 + 4 * q^29 - 12 * q^37 - 36 * q^43 - 52 * q^49 + 8 * q^51 - 4 * q^53 - 24 * q^59 - 16 * q^61 + 68 * q^63 + 40 * q^65 + 12 * q^67 - 72 * q^69 - 4 * q^77 + 16 * q^79 - 116 * q^81 + 16 * q^85 + 8 * q^93 + 32 * q^95 + 52 * q^99

Introduction

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