LMFDB - Embedded newform 2240.2.bd.b.561.14

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			561.14
Character	$\chi$	$=$	2240.561
Dual form			2240.2.bd.b.1681.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0811559 + 0.0811559i) q^{3} +(0.707107 + 0.707107i) q^{5} +1.00000i q^{7} +2.98683i q^{9} +O(q^{10})$	\(q+(-0.0811559 + 0.0811559i) q^{3} +(0.707107 + 0.707107i) q^{5} +1.00000i q^{7} +2.98683i q^{9} +(-2.06246 - 2.06246i) q^{11} +(-1.06124 + 1.06124i) q^{13} -0.114772 q^{15} -0.656960 q^{17} +(-1.58200 + 1.58200i) q^{19} +(-0.0811559 - 0.0811559i) q^{21} -2.96516i q^{23} +1.00000i q^{25} +(-0.485866 - 0.485866i) q^{27} +(-5.25418 + 5.25418i) q^{29} -1.51364 q^{31} +0.334762 q^{33} +(-0.707107 + 0.707107i) q^{35} +(-0.139266 - 0.139266i) q^{37} -0.172251i q^{39} +2.90904i q^{41} +(-4.84532 - 4.84532i) q^{43} +(-2.11201 + 2.11201i) q^{45} -3.17063 q^{47} -1.00000 q^{49} +(0.0533162 - 0.0533162i) q^{51} +(1.95069 + 1.95069i) q^{53} -2.91677i q^{55} -0.256777i q^{57} +(-9.71066 - 9.71066i) q^{59} +(8.38610 - 8.38610i) q^{61} -2.98683 q^{63} -1.50081 q^{65} +(-9.72620 + 9.72620i) q^{67} +(0.240641 + 0.240641i) q^{69} -5.04299i q^{71} +4.76680i q^{73} +(-0.0811559 - 0.0811559i) q^{75} +(2.06246 - 2.06246i) q^{77} +1.71346 q^{79} -8.88162 q^{81} +(4.82996 - 4.82996i) q^{83} +(-0.464541 - 0.464541i) q^{85} -0.852816i q^{87} +12.1581i q^{89} +(-1.06124 - 1.06124i) q^{91} +(0.122841 - 0.122841i) q^{93} -2.23728 q^{95} +1.15806 q^{97} +(6.16023 - 6.16023i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.0811559	+	0.0811559i	−0.0468554	+	0.0468554i	−0.730146	−	0.683291i	$-0.760548\pi$
$3$	−0.0811559	+	0.0811559i	−0.0468554	+	0.0468554i	0.683291	+	0.730146i	$0.260548\pi$
$4$		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
$9$			2.98683i			0.995609i
$10$		0			0
$11$	−2.06246	−	2.06246i	−0.621857	−	0.621857i	0.324149	−	0.946006i	$-0.394922\pi$
$11$	−2.06246	−	2.06246i	−0.621857	−	0.621857i	−0.946006	+	0.324149i	$0.894922\pi$
$12$		0			0
$13$	−1.06124	+	1.06124i	−0.294334	+	0.294334i	−0.838790	−	0.544456i	$-0.816736\pi$
$13$	−1.06124	+	1.06124i	−0.294334	+	0.294334i	0.544456	+	0.838790i	$0.316736\pi$
$14$		0			0
$15$	−0.114772			−0.0296340
$16$		0			0
$17$	−0.656960			−0.159336			−0.0796681	−	0.996821i	$-0.525386\pi$
$17$	−0.656960			−0.159336			−0.0796681	+	0.996821i	$0.525386\pi$
$18$		0			0
$19$	−1.58200	+	1.58200i	−0.362935	+	0.362935i	−0.864892	−	0.501957i	$-0.832613\pi$
$19$	−1.58200	+	1.58200i	−0.362935	+	0.362935i	0.501957	+	0.864892i	$0.332613\pi$
$20$		0			0
$21$	−0.0811559	−	0.0811559i	−0.0177097	−	0.0177097i
$22$		0			0
$23$		−	2.96516i		−	0.618280i	−0.951017	−	0.309140i	$-0.899959\pi$
$23$		−	2.96516i		−	0.618280i	0.951017	−	0.309140i	$-0.100041\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$		0			0
$27$	−0.485866	−	0.485866i	−0.0935050	−	0.0935050i
$28$		0			0
$29$	−5.25418	+	5.25418i	−0.975677	+	0.975677i	−0.999711	−	0.0240341i	$-0.992349\pi$
$29$	−5.25418	+	5.25418i	−0.975677	+	0.975677i	0.0240341	+	0.999711i	$0.492349\pi$
$30$		0			0
$31$	−1.51364			−0.271859			−0.135929	−	0.990719i	$-0.543402\pi$
$31$	−1.51364			−0.271859			−0.135929	+	0.990719i	$0.543402\pi$
$32$		0			0
$33$	0.334762			0.0582747
$34$		0			0
$35$	−0.707107	+	0.707107i	−0.119523	+	0.119523i
$36$		0			0
$37$	−0.139266	−	0.139266i	−0.0228952	−	0.0228952i	0.695567	−	0.718462i	$-0.255153\pi$
$37$	−0.139266	−	0.139266i	−0.0228952	−	0.0228952i	−0.718462	+	0.695567i	$0.755153\pi$
$38$		0			0
$39$		−	0.172251i		−	0.0275823i
$40$		0			0
$41$			2.90904i			0.454315i	0.973858	+	0.227158i	$0.0729433\pi$
$41$			2.90904i			0.454315i	−0.973858	+	0.227158i	$0.927057\pi$
$42$		0			0
$43$	−4.84532	−	4.84532i	−0.738904	−	0.738904i	0.233462	−	0.972366i	$-0.424995\pi$
$43$	−4.84532	−	4.84532i	−0.738904	−	0.738904i	−0.972366	+	0.233462i	$0.924995\pi$
$44$		0			0
$45$	−2.11201	+	2.11201i	−0.314839	+	0.314839i
$46$		0			0
$47$	−3.17063			−0.462483			−0.231242	−	0.972896i	$-0.574279\pi$
$47$	−3.17063			−0.462483			−0.231242	+	0.972896i	$0.574279\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	0.0533162	−	0.0533162i	0.00746576	−	0.00746576i
$52$		0			0
$53$	1.95069	+	1.95069i	0.267948	+	0.267948i	0.828273	−	0.560325i	$-0.189324\pi$
$53$	1.95069	+	1.95069i	0.267948	+	0.267948i	−0.560325	+	0.828273i	$0.689324\pi$
$54$		0			0
$55$		−	2.91677i		−	0.393297i
$56$		0			0
$57$		−	0.256777i		−	0.0340109i
$58$		0			0
$59$	−9.71066	−	9.71066i	−1.26422	−	1.26422i	−0.949028	−	0.315193i	$-0.897931\pi$
$59$	−9.71066	−	9.71066i	−1.26422	−	1.26422i	−0.315193	−	0.949028i	$-0.602069\pi$
$60$		0			0
$61$	8.38610	−	8.38610i	1.07373	−	1.07373i	0.0766733	−	0.997056i	$-0.475570\pi$
$61$	8.38610	−	8.38610i	1.07373	−	1.07373i	0.997056	−	0.0766733i	$-0.0244298\pi$
$62$		0			0
$63$	−2.98683			−0.376305
$64$		0			0
$65$	−1.50081			−0.186153
$66$		0			0
$67$	−9.72620	+	9.72620i	−1.18824	+	1.18824i	−0.210691	+	0.977553i	$0.567572\pi$
$67$	−9.72620	+	9.72620i	−1.18824	+	1.18824i	−0.977553	+	0.210691i	$0.932428\pi$
$68$		0			0
$69$	0.240641	+	0.240641i	0.0289697	+	0.0289697i
$70$		0			0
$71$		−	5.04299i		−	0.598492i	−0.954176	−	0.299246i	$-0.903265\pi$
$71$		−	5.04299i		−	0.598492i	0.954176	−	0.299246i	$-0.0967352\pi$
$72$		0			0
$73$			4.76680i			0.557911i	0.960304	+	0.278956i	$0.0899883\pi$
$73$			4.76680i			0.557911i	−0.960304	+	0.278956i	$0.910012\pi$
$74$		0			0
$75$	−0.0811559	−	0.0811559i	−0.00937108	−	0.00937108i
$76$		0			0
$77$	2.06246	−	2.06246i	0.235040	−	0.235040i
$78$		0			0
$79$	1.71346			0.192779			0.0963895	−	0.995344i	$-0.469271\pi$
$79$	1.71346			0.192779			0.0963895	+	0.995344i	$0.469271\pi$
$80$		0			0
$81$	−8.88162			−0.986847
$82$		0			0
$83$	4.82996	−	4.82996i	0.530157	−	0.530157i	−0.390462	−	0.920619i	$-0.627685\pi$
$83$	4.82996	−	4.82996i	0.530157	−	0.530157i	0.920619	+	0.390462i	$0.127685\pi$
$84$		0			0
$85$	−0.464541	−	0.464541i	−0.0503865	−	0.0503865i
$86$		0			0
$87$		−	0.852816i		−	0.0914315i
$88$		0			0
$89$			12.1581i			1.28875i	0.764708	+	0.644377i	$0.222883\pi$
$89$			12.1581i			1.28875i	−0.764708	+	0.644377i	$0.777117\pi$
$90$		0			0
$91$	−1.06124	−	1.06124i	−0.111248	−	0.111248i
$92$		0			0
$93$	0.122841	−	0.122841i	0.0127380	−	0.0127380i
$94$		0			0
$95$	−2.23728			−0.229540
$96$		0			0
$97$	1.15806			0.117583			0.0587916	−	0.998270i	$-0.481275\pi$
$97$	1.15806			0.117583			0.0587916	+	0.998270i	$0.481275\pi$
$98$		0			0
$99$	6.16023	−	6.16023i	0.619126	−	0.619126i
$100$		0			0
$101$	−11.4709	−	11.4709i	−1.14140	−	1.14140i	−0.988194	−	0.153206i	$-0.951040\pi$
$101$	−11.4709	−	11.4709i	−1.14140	−	1.14140i	−0.153206	−	0.988194i	$-0.548960\pi$
$102$		0			0
$103$			14.2790i			1.40695i	0.710721	+	0.703474i	$0.248369\pi$
$103$			14.2790i			1.40695i	−0.710721	+	0.703474i	$0.751631\pi$
$104$		0			0
$105$		−	0.114772i		−	0.0112006i
$106$		0			0
$107$	7.19515	+	7.19515i	0.695582	+	0.695582i	0.963454	−	0.267873i	$-0.0863206\pi$
$107$	7.19515	+	7.19515i	0.695582	+	0.695582i	−0.267873	+	0.963454i	$0.586321\pi$
$108$		0			0
$109$	3.40747	−	3.40747i	0.326376	−	0.326376i	−0.524830	−	0.851207i	$-0.675871\pi$
$109$	3.40747	−	3.40747i	0.326376	−	0.326376i	0.851207	+	0.524830i	$0.175871\pi$
$110$		0			0
$111$	0.0226045			0.00214553
$112$		0			0
$113$	−15.2718			−1.43665			−0.718323	−	0.695710i	$-0.755090\pi$
$113$	−15.2718			−1.43665			−0.718323	+	0.695710i	$0.755090\pi$
$114$		0			0
$115$	2.09669	−	2.09669i	0.195517	−	0.195517i
$116$		0			0
$117$	−3.16973	−	3.16973i	−0.293041	−	0.293041i
$118$		0			0
$119$		−	0.656960i		−	0.0602234i
$120$		0			0
$121$		−	2.49248i		−	0.226589i
$122$		0			0
$123$	−0.236086	−	0.236086i	−0.0212871	−	0.0212871i
$124$		0			0
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$		0			0
$127$	11.5810			1.02765			0.513823	−	0.857896i	$-0.328229\pi$
$127$	11.5810			1.02765			0.513823	+	0.857896i	$0.328229\pi$
$128$		0			0
$129$	0.786453			0.0692433
$130$		0			0
$131$	−15.9773	+	15.9773i	−1.39595	+	1.39595i	−0.584691	+	0.811256i	$0.698784\pi$
$131$	−15.9773	+	15.9773i	−1.39595	+	1.39595i	−0.811256	+	0.584691i	$0.801216\pi$
$132$		0			0
$133$	−1.58200	−	1.58200i	−0.137177	−	0.137177i
$134$		0			0
$135$		−	0.687119i		−	0.0591378i
$136$		0			0
$137$			4.97965i			0.425440i	0.977113	+	0.212720i	$0.0682322\pi$
$137$			4.97965i			0.425440i	−0.977113	+	0.212720i	$0.931768\pi$
$138$		0			0
$139$	−3.51390	−	3.51390i	−0.298045	−	0.298045i	0.542203	−	0.840248i	$-0.317590\pi$
$139$	−3.51390	−	3.51390i	−0.298045	−	0.298045i	−0.840248	+	0.542203i	$0.817590\pi$
$140$		0			0
$141$	0.257315	−	0.257315i	0.0216698	−	0.0216698i
$142$		0			0
$143$	4.37752			0.366067
$144$		0			0
$145$	−7.43054			−0.617072
$146$		0			0
$147$	0.0811559	−	0.0811559i	0.00669363	−	0.00669363i
$148$		0			0
$149$	−4.94065	−	4.94065i	−0.404754	−	0.404754i	0.475151	−	0.879904i	$-0.342394\pi$
$149$	−4.94065	−	4.94065i	−0.404754	−	0.404754i	−0.879904	+	0.475151i	$0.842394\pi$
$150$		0			0
$151$			11.2380i			0.914537i	0.889329	+	0.457268i	$0.151172\pi$
$151$			11.2380i			0.914537i	−0.889329	+	0.457268i	$0.848828\pi$
$152$		0			0
$153$		−	1.96222i		−	0.158636i
$154$		0			0
$155$	−1.07031	−	1.07031i	−0.0859692	−	0.0859692i
$156$		0			0
$157$	−0.918436	+	0.918436i	−0.0732992	+	0.0732992i	−0.742806	−	0.669507i	$-0.766506\pi$
$157$	−0.918436	+	0.918436i	−0.0732992	+	0.0732992i	0.669507	+	0.742806i	$0.266506\pi$
$158$		0			0
$159$	−0.316620			−0.0251096
$160$		0			0
$161$	2.96516			0.233688
$162$		0			0
$163$	−2.64719	+	2.64719i	−0.207344	+	0.207344i	−0.803138	−	0.595794i	$-0.796838\pi$
$163$	−2.64719	+	2.64719i	−0.207344	+	0.207344i	0.595794	+	0.803138i	$0.296838\pi$
$164$		0			0
$165$	0.236713	+	0.236713i	0.0184281	+	0.0184281i
$166$		0			0
$167$			3.29547i			0.255011i	0.991838	+	0.127506i	$0.0406971\pi$
$167$			3.29547i			0.255011i	−0.991838	+	0.127506i	$0.959303\pi$
$168$		0			0
$169$			10.7476i			0.826735i
$170$		0			0
$171$	−4.72515	−	4.72515i	−0.361342	−	0.361342i
$172$		0			0
$173$	5.01328	−	5.01328i	0.381153	−	0.381153i	−0.490365	−	0.871517i	$-0.663136\pi$
$173$	5.01328	−	5.01328i	0.381153	−	0.381153i	0.871517	+	0.490365i	$0.163136\pi$
$174$		0			0
$175$	−1.00000			−0.0755929
$176$		0			0
$177$	1.57616			0.118471
$178$		0			0
$179$	−9.94074	+	9.94074i	−0.743006	+	0.743006i	−0.973155	−	0.230149i	$-0.926079\pi$
$179$	−9.94074	+	9.94074i	−0.743006	+	0.743006i	0.230149	+	0.973155i	$0.426079\pi$
$180$		0			0
$181$	−13.2317	−	13.2317i	−0.983505	−	0.983505i	0.0163608	−	0.999866i	$-0.494792\pi$
$181$	−13.2317	−	13.2317i	−0.983505	−	0.983505i	−0.999866	+	0.0163608i	$0.994792\pi$
$182$		0			0
$183$			1.36116i			0.100620i
$184$		0			0
$185$		−	0.196952i		−	0.0144802i
$186$		0			0
$187$	1.35496	+	1.35496i	0.0990842	+	0.0990842i
$188$		0			0
$189$	0.485866	−	0.485866i	0.0353416	−	0.0353416i
$190$		0			0
$191$	1.40059			0.101343			0.0506715	−	0.998715i	$-0.483864\pi$
$191$	1.40059			0.101343			0.0506715	+	0.998715i	$0.483864\pi$
$192$		0			0
$193$	−5.86767			−0.422364			−0.211182	−	0.977447i	$-0.567731\pi$
$193$	−5.86767			−0.422364			−0.211182	+	0.977447i	$0.567731\pi$
$194$		0			0
$195$	0.121800	−	0.121800i	0.00872227	−	0.00872227i
$196$		0			0
$197$	−5.55336	−	5.55336i	−0.395660	−	0.395660i	0.481039	−	0.876699i	$-0.340260\pi$
$197$	−5.55336	−	5.55336i	−0.395660	−	0.395660i	−0.876699	+	0.481039i	$0.840260\pi$
$198$		0			0
$199$			11.4131i			0.809056i	0.914526	+	0.404528i	$0.132564\pi$
$199$			11.4131i			0.809056i	−0.914526	+	0.404528i	$0.867436\pi$
$200$		0			0
$201$		−	1.57868i		−	0.111351i
$202$		0			0
$203$	−5.25418	−	5.25418i	−0.368771	−	0.368771i
$204$		0			0
$205$	−2.05700	+	2.05700i	−0.143667	+	0.143667i
$206$		0			0
$207$	8.85644			0.615565
$208$		0			0
$209$	6.52563			0.451387
$210$		0			0
$211$	−11.0870	+	11.0870i	−0.763258	+	0.763258i	−0.976910	−	0.213652i	$-0.931464\pi$
$211$	−11.0870	+	11.0870i	−0.763258	+	0.763258i	0.213652	+	0.976910i	$0.431464\pi$
$212$		0			0
$213$	0.409268	+	0.409268i	0.0280426	+	0.0280426i
$214$		0			0
$215$		−	6.85232i		−	0.467324i
$216$		0			0
$217$		−	1.51364i		−	0.102753i
$218$		0			0
$219$	−0.386854	−	0.386854i	−0.0261412	−	0.0261412i
$220$		0			0
$221$	0.697189	−	0.697189i	0.0468980	−	0.0468980i
$222$		0			0
$223$	11.1852			0.749016			0.374508	−	0.927224i	$-0.377812\pi$
$223$	11.1852			0.749016			0.374508	+	0.927224i	$0.377812\pi$
$224$		0			0
$225$	−2.98683			−0.199122
$226$		0			0
$227$	−3.36782	+	3.36782i	−0.223530	+	0.223530i	−0.809983	−	0.586453i	$-0.800524\pi$
$227$	−3.36782	+	3.36782i	−0.223530	+	0.223530i	0.586453	+	0.809983i	$0.300524\pi$
$228$		0			0
$229$	4.58632	+	4.58632i	0.303072	+	0.303072i	0.842215	−	0.539142i	$-0.181252\pi$
$229$	4.58632	+	4.58632i	0.303072	+	0.303072i	−0.539142	+	0.842215i	$0.681252\pi$
$230$		0			0
$231$			0.334762i			0.0220258i
$232$		0			0
$233$			17.9023i			1.17282i	0.810015	+	0.586409i	$0.199459\pi$
$233$			17.9023i			1.17282i	−0.810015	+	0.586409i	$0.800541\pi$
$234$		0			0
$235$	−2.24197	−	2.24197i	−0.146250	−	0.146250i
$236$		0			0
$237$	−0.139057	+	0.139057i	−0.00903274	+	0.00903274i
$238$		0			0
$239$	27.5973			1.78512			0.892560	−	0.450929i	$-0.148907\pi$
$239$	27.5973			1.78512			0.892560	+	0.450929i	$0.148907\pi$
$240$		0			0
$241$	−9.84301			−0.634044			−0.317022	−	0.948418i	$-0.602683\pi$
$241$	−9.84301			−0.634044			−0.317022	+	0.948418i	$0.602683\pi$
$242$		0			0
$243$	2.17840	−	2.17840i	0.139744	−	0.139744i
$244$		0			0
$245$	−0.707107	−	0.707107i	−0.0451754	−	0.0451754i
$246$		0			0
$247$		−	3.35774i		−	0.213648i
$248$		0			0
$249$			0.783960i			0.0496815i
$250$		0			0
$251$	−6.75676	−	6.75676i	−0.426483	−	0.426483i	0.460945	−	0.887428i	$-0.347510\pi$
$251$	−6.75676	−	6.75676i	−0.426483	−	0.426483i	−0.887428	+	0.460945i	$0.847510\pi$
$252$		0			0
$253$	−6.11555	+	6.11555i	−0.384481	+	0.384481i
$254$		0			0
$255$	0.0754004			0.00472176
$256$		0			0
$257$	29.2377			1.82380			0.911899	−	0.410414i	$-0.134616\pi$
$257$	29.2377			1.82380			0.911899	+	0.410414i	$0.134616\pi$
$258$		0			0
$259$	0.139266	−	0.139266i	0.00865357	−	0.00865357i
$260$		0			0
$261$	−15.6933	−	15.6933i	−0.971393	−	0.971393i
$262$		0			0
$263$		−	7.51899i		−	0.463641i	−0.972759	−	0.231820i	$-0.925532\pi$
$263$		−	7.51899i		−	0.463641i	0.972759	−	0.231820i	$-0.0744681\pi$
$264$		0			0
$265$			2.75869i			0.169465i
$266$		0			0
$267$	−0.986700	−	0.986700i	−0.0603851	−	0.0603851i
$268$		0			0
$269$	20.1309	−	20.1309i	1.22740	−	1.22740i	0.262457	−	0.964944i	$-0.415467\pi$
$269$	20.1309	−	20.1309i	1.22740	−	1.22740i	0.964944	−	0.262457i	$-0.0845326\pi$
$270$		0			0
$271$	−15.9894			−0.971288			−0.485644	−	0.874157i	$-0.661415\pi$
$271$	−15.9894			−0.971288			−0.485644	+	0.874157i	$0.661415\pi$
$272$		0			0
$273$	0.172251			0.0104251
$274$		0			0
$275$	2.06246	−	2.06246i	0.124371	−	0.124371i
$276$		0			0
$277$	16.2840	+	16.2840i	0.978409	+	0.978409i	0.999772	−	0.0213630i	$-0.00680059\pi$
$277$	16.2840	+	16.2840i	0.978409	+	0.978409i	−0.0213630	+	0.999772i	$0.506801\pi$
$278$		0			0
$279$		−	4.52099i		−	0.270665i
$280$		0			0
$281$		−	20.6501i		−	1.23188i	−0.787793	−	0.615939i	$-0.788777\pi$
$281$		−	20.6501i		−	1.23188i	0.787793	−	0.615939i	$-0.211223\pi$
$282$		0			0
$283$	−3.50085	−	3.50085i	−0.208104	−	0.208104i	0.595357	−	0.803461i	$-0.297010\pi$
$283$	−3.50085	−	3.50085i	−0.208104	−	0.208104i	−0.803461	+	0.595357i	$0.797010\pi$
$284$		0			0
$285$	0.181569	−	0.181569i	0.0107552	−	0.0107552i
$286$		0			0
$287$	−2.90904			−0.171715
$288$		0			0
$289$	−16.5684			−0.974612
$290$		0			0
$291$	−0.0939834	+	0.0939834i	−0.00550940	+	0.00550940i
$292$		0			0
$293$	−10.4128	−	10.4128i	−0.608324	−	0.608324i	0.334184	−	0.942508i	$-0.391539\pi$
$293$	−10.4128	−	10.4128i	−0.608324	−	0.608324i	−0.942508	+	0.334184i	$0.891539\pi$
$294$		0			0
$295$		−	13.7329i		−	0.799563i
$296$		0			0
$297$			2.00416i			0.116293i
$298$		0			0
$299$	3.14674	+	3.14674i	0.181981	+	0.181981i
$300$		0			0
$301$	4.84532	−	4.84532i	0.279280	−	0.279280i
$302$		0			0
$303$	1.86187			0.106961
$304$		0			0
$305$	11.8597			0.679086
$306$		0			0
$307$	−6.77081	+	6.77081i	−0.386430	+	0.386430i	−0.873412	−	0.486982i	$-0.838098\pi$
$307$	−6.77081	+	6.77081i	−0.386430	+	0.386430i	0.486982	+	0.873412i	$0.338098\pi$
$308$		0			0
$309$	−1.15882	−	1.15882i	−0.0659231	−	0.0659231i
$310$		0			0
$311$		−	2.52750i		−	0.143321i	−0.997429	−	0.0716606i	$-0.977170\pi$
$311$		−	2.52750i		−	0.143321i	0.997429	−	0.0716606i	$-0.0228298\pi$
$312$		0			0
$313$			16.8556i			0.952735i	0.879246	+	0.476367i	$0.158047\pi$
$313$			16.8556i			0.952735i	−0.879246	+	0.476367i	$0.841953\pi$
$314$		0			0
$315$	−2.11201	−	2.11201i	−0.118998	−	0.118998i
$316$		0			0
$317$	−9.68834	+	9.68834i	−0.544151	+	0.544151i	−0.924743	−	0.380592i	$-0.875720\pi$
$317$	−9.68834	+	9.68834i	−0.544151	+	0.544151i	0.380592	+	0.924743i	$0.375720\pi$
$318$		0			0
$319$	21.6731			1.21346
$320$		0			0
$321$	−1.16786			−0.0651835
$322$		0			0
$323$	1.03931	−	1.03931i	0.0578287	−	0.0578287i
$324$		0			0
$325$	−1.06124	−	1.06124i	−0.0588668	−	0.0588668i
$326$		0			0
$327$			0.553073i			0.0305850i
$328$		0			0
$329$		−	3.17063i		−	0.174802i
$330$		0			0
$331$	−2.01488	−	2.01488i	−0.110748	−	0.110748i	0.649561	−	0.760309i	$-0.274953\pi$
$331$	−2.01488	−	2.01488i	−0.110748	−	0.110748i	−0.760309	+	0.649561i	$0.774953\pi$
$332$		0			0
$333$	0.415963	−	0.415963i	0.0227947	−	0.0227947i
$334$		0			0
$335$	−13.7549			−0.751512
$336$		0			0
$337$	22.0606			1.20172			0.600859	−	0.799355i	$-0.294825\pi$
$337$	22.0606			1.20172			0.600859	+	0.799355i	$0.294825\pi$
$338$		0			0
$339$	1.23939	−	1.23939i	0.0673146	−	0.0673146i
$340$		0			0
$341$	3.12184	+	3.12184i	0.169057	+	0.169057i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$		0			0
$345$			0.340317i			0.0183221i
$346$		0			0
$347$	21.4382	+	21.4382i	1.15086	+	1.15086i	0.986380	+	0.164483i	$0.0525956\pi$
$347$	21.4382	+	21.4382i	1.15086	+	1.15086i	0.164483	+	0.986380i	$0.447404\pi$
$348$		0			0
$349$	16.2472	−	16.2472i	0.869695	−	0.869695i	−0.122744	−	0.992438i	$-0.539169\pi$
$349$	16.2472	−	16.2472i	0.869695	−	0.869695i	0.992438	+	0.122744i	$0.0391693\pi$
$350$		0			0
$351$	1.03124			0.0550434
$352$		0			0
$353$	33.7678			1.79728			0.898639	−	0.438689i	$-0.144557\pi$
$353$	33.7678			1.79728			0.898639	+	0.438689i	$0.144557\pi$
$354$		0			0
$355$	3.56593	−	3.56593i	0.189260	−	0.189260i
$356$		0			0
$357$	0.0533162	+	0.0533162i	0.00282179	+	0.00282179i
$358$		0			0
$359$			14.6070i			0.770927i	0.922723	+	0.385463i	$0.125958\pi$
$359$			14.6070i			0.770927i	−0.922723	+	0.385463i	$0.874042\pi$
$360$		0			0
$361$			13.9946i			0.736556i
$362$		0			0
$363$	0.202279	+	0.202279i	0.0106169	+	0.0106169i
$364$		0			0
$365$	−3.37063	+	3.37063i	−0.176427	+	0.176427i
$366$		0			0
$367$	1.38966			0.0725399			0.0362699	−	0.999342i	$-0.488452\pi$
$367$	1.38966			0.0725399			0.0362699	+	0.999342i	$0.488452\pi$
$368$		0			0
$369$	−8.68879			−0.452320
$370$		0			0
$371$	−1.95069	+	1.95069i	−0.101275	+	0.101275i
$372$		0			0
$373$	11.3139	+	11.3139i	0.585812	+	0.585812i	0.936495	−	0.350682i	$-0.114050\pi$
$373$	11.3139	+	11.3139i	0.585812	+	0.585812i	−0.350682	+	0.936495i	$0.614050\pi$
$374$		0			0
$375$		−	0.114772i		−	0.00592679i
$376$		0			0
$377$		−	11.1519i		−	0.574350i
$378$		0			0
$379$	−0.742178	−	0.742178i	−0.0381231	−	0.0381231i	0.687788	−	0.725911i	$-0.258582\pi$
$379$	−0.742178	−	0.742178i	−0.0381231	−	0.0381231i	−0.725911	+	0.687788i	$0.758582\pi$
$380$		0			0
$381$	−0.939865	+	0.939865i	−0.0481507	+	0.0481507i
$382$		0			0
$383$	13.9584			0.713243			0.356621	−	0.934249i	$-0.383929\pi$
$383$	13.9584			0.713243			0.356621	+	0.934249i	$0.383929\pi$
$384$		0			0
$385$	2.91677			0.148652
$386$		0			0
$387$	14.4721	−	14.4721i	0.735660	−	0.735660i
$388$		0			0
$389$	10.8118	+	10.8118i	0.548181	+	0.548181i	0.925914	−	0.377734i	$-0.123296\pi$
$389$	10.8118	+	10.8118i	0.548181	+	0.548181i	−0.377734	+	0.925914i	$0.623296\pi$
$390$		0			0
$391$			1.94799i			0.0985143i
$392$		0			0
$393$		−	2.59331i		−	0.130815i
$394$		0			0
$395$	1.21160	+	1.21160i	0.0609621	+	0.0609621i
$396$		0			0
$397$	5.83752	−	5.83752i	0.292977	−	0.292977i	−0.545278	−	0.838255i	$-0.683576\pi$
$397$	5.83752	−	5.83752i	0.292977	−	0.292977i	0.838255	+	0.545278i	$0.183576\pi$
$398$		0			0
$399$	0.256777			0.0128549
$400$		0			0
$401$	−22.9490			−1.14602			−0.573009	−	0.819549i	$-0.694224\pi$
$401$	−22.9490			−1.14602			−0.573009	+	0.819549i	$0.694224\pi$
$402$		0			0
$403$	1.60633	−	1.60633i	0.0800172	−	0.0800172i
$404$		0			0
$405$	−6.28025	−	6.28025i	−0.312068	−	0.312068i
$406$		0			0
$407$			0.574462i			0.0284750i
$408$		0			0
$409$		−	19.0722i		−	0.943058i	−0.881851	−	0.471529i	$-0.843702\pi$
$409$		−	19.0722i		−	0.943058i	0.881851	−	0.471529i	$-0.156298\pi$
$410$		0			0
$411$	−0.404128	−	0.404128i	−0.0199342	−	0.0199342i
$412$		0			0
$413$	9.71066	−	9.71066i	0.477830	−	0.477830i
$414$		0			0
$415$	6.83060			0.335301
$416$		0			0
$417$	0.570347			0.0279300
$418$		0			0
$419$	−1.15203	+	1.15203i	−0.0562802	+	0.0562802i	−0.734687	−	0.678407i	$-0.762671\pi$
$419$	−1.15203	+	1.15203i	−0.0562802	+	0.0562802i	0.678407	+	0.734687i	$0.262671\pi$
$420$		0			0
$421$	22.5495	+	22.5495i	1.09900	+	1.09900i	0.994528	+	0.104468i	$0.0333139\pi$
$421$	22.5495	+	22.5495i	1.09900	+	1.09900i	0.104468	+	0.994528i	$0.466686\pi$
$422$		0			0
$423$		−	9.47012i		−	0.460453i
$424$		0			0
$425$		−	0.656960i		−	0.0318672i
$426$		0			0
$427$	8.38610	+	8.38610i	0.405832	+	0.405832i
$428$		0			0
$429$	−0.355262	+	0.355262i	−0.0171522	+	0.0171522i
$430$		0			0
$431$	−3.63005			−0.174854			−0.0874268	−	0.996171i	$-0.527864\pi$
$431$	−3.63005			−0.174854			−0.0874268	+	0.996171i	$0.527864\pi$
$432$		0			0
$433$	−31.9828			−1.53699			−0.768497	−	0.639854i	$-0.778995\pi$
$433$	−31.9828			−1.53699			−0.768497	+	0.639854i	$0.778995\pi$
$434$		0			0
$435$	0.603032	−	0.603032i	0.0289132	−	0.0289132i
$436$		0			0
$437$	4.69088	+	4.69088i	0.224395	+	0.224395i
$438$		0			0
$439$			27.0604i			1.29152i	0.763540	+	0.645761i	$0.223460\pi$
$439$			27.0604i			1.29152i	−0.763540	+	0.645761i	$0.776540\pi$
$440$		0			0
$441$		−	2.98683i		−	0.142230i
$442$		0			0
$443$	4.64915	+	4.64915i	0.220888	+	0.220888i	0.808872	−	0.587984i	$-0.200078\pi$
$443$	4.64915	+	4.64915i	0.220888	+	0.220888i	−0.587984	+	0.808872i	$0.700078\pi$
$444$		0			0
$445$	−8.59706	+	8.59706i	−0.407540	+	0.407540i
$446$		0			0
$447$	0.801926			0.0379298
$448$		0			0
$449$	−9.41394			−0.444271			−0.222136	−	0.975016i	$-0.571303\pi$
$449$	−9.41394			−0.444271			−0.222136	+	0.975016i	$0.571303\pi$
$450$		0			0
$451$	5.99979	−	5.99979i	0.282519	−	0.282519i
$452$		0			0
$453$	−0.912031	−	0.912031i	−0.0428510	−	0.0428510i
$454$		0			0
$455$		−	1.50081i		−	0.0703592i
$456$		0			0
$457$			25.4435i			1.19020i	0.803653	+	0.595098i	$0.202887\pi$
$457$			25.4435i			1.19020i	−0.803653	+	0.595098i	$0.797113\pi$
$458$		0			0
$459$	0.319195	+	0.319195i	0.0148987	+	0.0148987i
$460$		0			0
$461$	24.0957	−	24.0957i	1.12225	−	1.12225i	0.130847	−	0.991403i	$-0.458230\pi$
$461$	24.0957	−	24.0957i	1.12225	−	1.12225i	0.991403	−	0.130847i	$-0.0417697\pi$
$462$		0			0
$463$	28.6286			1.33048			0.665241	−	0.746629i	$-0.268329\pi$
$463$	28.6286			1.33048			0.665241	+	0.746629i	$0.268329\pi$
$464$		0			0
$465$	0.173724			0.00805624
$466$		0			0
$467$	7.52704	−	7.52704i	0.348310	−	0.348310i	−0.511170	−	0.859480i	$-0.670788\pi$
$467$	7.52704	−	7.52704i	0.348310	−	0.348310i	0.859480	+	0.511170i	$0.170788\pi$
$468$		0			0
$469$	−9.72620	−	9.72620i	−0.449114	−	0.449114i
$470$		0			0
$471$		−	0.149073i		−	0.00686892i
$472$		0			0
$473$			19.9866i			0.918985i
$474$		0			0
$475$	−1.58200	−	1.58200i	−0.0725870	−	0.0725870i
$476$		0			0
$477$	−5.82637	+	5.82637i	−0.266771	+	0.266771i
$478$		0			0
$479$	−5.61593			−0.256598			−0.128299	−	0.991736i	$-0.540952\pi$
$479$	−5.61593			−0.256598			−0.128299	+	0.991736i	$0.540952\pi$
$480$		0			0
$481$	0.295588			0.0134777
$482$		0			0
$483$	−0.240641	+	0.240641i	−0.0109495	+	0.0109495i
$484$		0			0
$485$	0.818872	+	0.818872i	0.0371831	+	0.0371831i
$486$		0			0
$487$			27.2776i			1.23607i	0.786152	+	0.618033i	$0.212070\pi$
$487$			27.2776i			1.23607i	−0.786152	+	0.618033i	$0.787930\pi$
$488$		0			0
$489$		−	0.429670i		−	0.0194304i
$490$		0			0
$491$	−26.3573	−	26.3573i	−1.18949	−	1.18949i	−0.977209	−	0.212278i	$-0.931912\pi$
$491$	−26.3573	−	26.3573i	−1.18949	−	1.18949i	−0.212278	−	0.977209i	$-0.568088\pi$
$492$		0			0
$493$	3.45179	−	3.45179i	0.155461	−	0.155461i
$494$		0			0
$495$	8.71188			0.391570
$496$		0			0
$497$	5.04299			0.226209
$498$		0			0
$499$	18.5897	−	18.5897i	0.832191	−	0.832191i	−0.155625	−	0.987816i	$-0.549739\pi$
$499$	18.5897	−	18.5897i	0.832191	−	0.832191i	0.987816	+	0.155625i	$0.0497393\pi$
$500$		0			0
$501$	−0.267447	−	0.267447i	−0.0119486	−	0.0119486i
$502$		0			0
$503$		−	34.7657i		−	1.55013i	−0.631884	−	0.775063i	$-0.717718\pi$
$503$		−	34.7657i		−	1.55013i	0.631884	−	0.775063i	$-0.282282\pi$
$504$		0			0
$505$		−	16.2223i		−	0.721885i
$506$		0			0
$507$	−0.872228	−	0.872228i	−0.0387370	−	0.0387370i
$508$		0			0
$509$	15.3663	−	15.3663i	0.681101	−	0.681101i	−0.279147	−	0.960248i	$-0.590052\pi$
$509$	15.3663	−	15.3663i	0.681101	−	0.681101i	0.960248	+	0.279147i	$0.0900518\pi$
$510$		0			0
$511$	−4.76680			−0.210871
$512$		0			0
$513$	1.53728			0.0678725
$514$		0			0
$515$	−10.0967	+	10.0967i	−0.444916	+	0.444916i
$516$		0			0
$517$	6.53931	+	6.53931i	0.287598	+	0.287598i
$518$		0			0
$519$			0.813715i			0.0357181i
$520$		0			0
$521$		−	44.6783i		−	1.95739i	−0.205315	−	0.978696i	$-0.565822\pi$
$521$		−	44.6783i		−	1.95739i	0.205315	−	0.978696i	$-0.434178\pi$
$522$		0			0
$523$	13.8199	+	13.8199i	0.604303	+	0.604303i	0.941451	−	0.337149i	$-0.109463\pi$
$523$	13.8199	+	13.8199i	0.604303	+	0.604303i	−0.337149	+	0.941451i	$0.609463\pi$
$524$		0			0
$525$	0.0811559	−	0.0811559i	0.00354193	−	0.00354193i
$526$		0			0
$527$	0.994403			0.0433169
$528$		0			0
$529$	14.2078			0.617730
$530$		0			0
$531$	29.0041	−	29.0041i	1.25867	−	1.25867i
$532$		0			0
$533$	−3.08717	−	3.08717i	−0.133720	−	0.133720i
$534$		0			0
$535$			10.1755i			0.439925i
$536$		0			0
$537$		−	1.61350i		−	0.0696277i
$538$		0			0
$539$	2.06246	+	2.06246i	0.0888366	+	0.0888366i
$540$		0			0
$541$	−15.6776	+	15.6776i	−0.674033	+	0.674033i	−0.958643	−	0.284611i	$-0.908136\pi$
$541$	−15.6776	+	15.6776i	−0.674033	+	0.674033i	0.284611	+	0.958643i	$0.408136\pi$
$542$		0			0
$543$	2.14766			0.0921651
$544$		0			0
$545$	4.81889			0.206419
$546$		0			0
$547$	9.03840	−	9.03840i	0.386454	−	0.386454i	−0.486967	−	0.873421i	$-0.661897\pi$
$547$	9.03840	−	9.03840i	0.386454	−	0.386454i	0.873421	+	0.486967i	$0.161897\pi$
$548$		0			0
$549$	25.0478	+	25.0478i	1.06901	+	1.06901i
$550$		0			0
$551$		−	16.6242i		−	0.708215i
$552$		0			0
$553$			1.71346i			0.0728636i
$554$		0			0
$555$	0.0159838	+	0.0159838i	0.000678475	+	0.000678475i
$556$		0			0
$557$	−24.0013	+	24.0013i	−1.01697	+	1.01697i	−0.0171146	+	0.999854i	$0.505448\pi$
$557$	−24.0013	+	24.0013i	−1.01697	+	1.01697i	−0.999854	+	0.0171146i	$0.994552\pi$
$558$		0			0
$559$	10.2841			0.434969
$560$		0			0
$561$	−0.219925			−0.00928526
$562$		0			0
$563$	−4.70978	+	4.70978i	−0.198493	+	0.198493i	−0.799354	−	0.600861i	$-0.794825\pi$
$563$	−4.70978	+	4.70978i	−0.198493	+	0.198493i	0.600861	+	0.799354i	$0.294825\pi$
$564$		0			0
$565$	−10.7988	−	10.7988i	−0.454307	−	0.454307i
$566$		0			0
$567$		−	8.88162i		−	0.372993i
$568$		0			0
$569$			21.7770i			0.912940i	0.889739	+	0.456470i	$0.150886\pi$
$569$			21.7770i			0.912940i	−0.889739	+	0.456470i	$0.849114\pi$
$570$		0			0
$571$	7.59764	+	7.59764i	0.317951	+	0.317951i	0.847980	−	0.530028i	$-0.177819\pi$
$571$	7.59764	+	7.59764i	0.317951	+	0.317951i	−0.530028	+	0.847980i	$0.677819\pi$
$572$		0			0
$573$	−0.113666	+	0.113666i	−0.00474847	+	0.00474847i
$574$		0			0
$575$	2.96516			0.123656
$576$		0			0
$577$	34.5687			1.43911			0.719557	−	0.694433i	$-0.244345\pi$
$577$	34.5687			1.43911			0.719557	+	0.694433i	$0.244345\pi$
$578$		0			0
$579$	0.476196	−	0.476196i	0.0197900	−	0.0197900i
$580$		0			0
$581$	4.82996	+	4.82996i	0.200381	+	0.200381i
$582$		0			0
$583$		−	8.04645i		−	0.333250i
$584$		0			0
$585$		−	4.48267i		−	0.185336i
$586$		0			0
$587$	30.6759	+	30.6759i	1.26613	+	1.26613i	0.948070	+	0.318060i	$0.103032\pi$
$587$	30.6759	+	30.6759i	1.26613	+	1.26613i	0.318060	+	0.948070i	$0.396968\pi$
$588$		0			0
$589$	2.39458	−	2.39458i	0.0986670	−	0.0986670i
$590$		0			0
$591$	0.901376			0.0370776
$592$		0			0
$593$	12.5863			0.516857			0.258429	−	0.966030i	$-0.416795\pi$
$593$	12.5863			0.516857			0.258429	+	0.966030i	$0.416795\pi$
$594$		0			0
$595$	0.464541	−	0.464541i	0.0190443	−	0.0190443i
$596$		0			0
$597$	−0.926244	−	0.926244i	−0.0379086	−	0.0379086i
$598$		0			0
$599$			19.3254i			0.789613i	0.918764	+	0.394806i	$0.129188\pi$
$599$			19.3254i			0.789613i	−0.918764	+	0.394806i	$0.870812\pi$
$600$		0			0
$601$			16.8221i			0.686190i	0.939301	+	0.343095i	$0.111475\pi$
$601$			16.8221i			0.686190i	−0.939301	+	0.343095i	$0.888525\pi$
$602$		0			0
$603$	−29.0505	−	29.0505i	−1.18303	−	1.18303i
$604$		0			0
$605$	1.76245	−	1.76245i	0.0716537	−	0.0716537i
$606$		0			0
$607$	−38.0319			−1.54367			−0.771834	−	0.635824i	$-0.780660\pi$
$607$	−38.0319			−1.54367			−0.771834	+	0.635824i	$0.780660\pi$
$608$		0			0
$609$	0.852816			0.0345578
$610$		0			0
$611$	3.36478	−	3.36478i	0.136125	−	0.136125i
$612$		0			0
$613$	21.7445	+	21.7445i	0.878252	+	0.878252i	0.993354	−	0.115102i	$-0.0367195\pi$
$613$	21.7445	+	21.7445i	0.878252	+	0.878252i	−0.115102	+	0.993354i	$0.536720\pi$
$614$		0			0
$615$		−	0.333875i		−	0.0134632i
$616$		0			0
$617$		−	41.6843i		−	1.67815i	−0.544019	−	0.839073i	$-0.683098\pi$
$617$		−	41.6843i		−	1.67815i	0.544019	−	0.839073i	$-0.316902\pi$
$618$		0			0
$619$	−15.3894	−	15.3894i	−0.618551	−	0.618551i	0.326609	−	0.945160i	$-0.394094\pi$
$619$	−15.3894	−	15.3894i	−0.618551	−	0.618551i	−0.945160	+	0.326609i	$0.894094\pi$
$620$		0			0
$621$	−1.44067	+	1.44067i	−0.0578123	+	0.0578123i
$622$		0			0
$623$	−12.1581			−0.487103
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$	−0.529593	+	0.529593i	−0.0211499	+	0.0211499i
$628$		0			0
$629$	0.0914921	+	0.0914921i	0.00364803	+	0.00364803i
$630$		0			0
$631$		−	3.04991i		−	0.121415i	−0.998156	−	0.0607074i	$-0.980664\pi$
$631$		−	3.04991i		−	0.121415i	0.998156	−	0.0607074i	$-0.0193357\pi$
$632$		0			0
$633$		−	1.79955i		−	0.0715255i
$634$		0			0
$635$	8.18899	+	8.18899i	0.324970	+	0.324970i
$636$		0			0
$637$	1.06124	−	1.06124i	0.0420477	−	0.0420477i
$638$		0			0
$639$	15.0625			0.595865
$640$		0			0
$641$	35.3719			1.39710			0.698552	−	0.715559i	$-0.253828\pi$
$641$	35.3719			1.39710			0.698552	+	0.715559i	$0.253828\pi$
$642$		0			0
$643$	22.3427	−	22.3427i	0.881110	−	0.881110i	−0.112537	−	0.993647i	$-0.535898\pi$
$643$	22.3427	−	22.3427i	0.881110	−	0.881110i	0.993647	+	0.112537i	$0.0358978\pi$
$644$		0			0
$645$	0.556106	+	0.556106i	0.0218967	+	0.0218967i
$646$		0			0
$647$		−	33.6596i		−	1.32330i	−0.749814	−	0.661649i	$-0.769857\pi$
$647$		−	33.6596i		−	1.32330i	0.749814	−	0.661649i	$-0.230143\pi$
$648$		0			0
$649$			40.0558i			1.57233i
$650$		0			0
$651$	0.122841	+	0.122841i	0.00481453	+	0.00481453i
$652$		0			0
$653$	24.1695	−	24.1695i	0.945827	−	0.945827i	−0.0527787	−	0.998606i	$-0.516808\pi$
$653$	24.1695	−	24.1695i	0.945827	−	0.945827i	0.998606	+	0.0527787i	$0.0168078\pi$
$654$		0			0
$655$	−22.5954			−0.882874
$656$		0			0
$657$	−14.2376			−0.555462
$658$		0			0
$659$	−33.0400	+	33.0400i	−1.28705	+	1.28705i	−0.350486	+	0.936568i	$0.613983\pi$
$659$	−33.0400	+	33.0400i	−1.28705	+	1.28705i	−0.936568	+	0.350486i	$0.886017\pi$
$660$		0			0
$661$	−27.4237	−	27.4237i	−1.06666	−	1.06666i	−0.997614	−	0.0690455i	$-0.978005\pi$
$661$	−27.4237	−	27.4237i	−1.06666	−	1.06666i	−0.0690455	−	0.997614i	$-0.521995\pi$
$662$		0			0
$663$			0.113162i			0.00439485i
$664$		0			0
$665$		−	2.23728i		−	0.0867581i
$666$		0			0
$667$	15.5795	+	15.5795i	0.603241	+	0.603241i
$668$		0			0
$669$	−0.907744	+	0.907744i	−0.0350954	+	0.0350954i
$670$		0			0
$671$	−34.5921			−1.33541
$672$		0			0
$673$	5.89947			0.227408			0.113704	−	0.993515i	$-0.463728\pi$
$673$	5.89947			0.227408			0.113704	+	0.993515i	$0.463728\pi$
$674$		0			0
$675$	0.485866	−	0.485866i	0.0187010	−	0.0187010i
$676$		0			0
$677$	8.87438	+	8.87438i	0.341070	+	0.341070i	0.856770	−	0.515699i	$-0.172468\pi$
$677$	8.87438	+	8.87438i	0.341070	+	0.341070i	−0.515699	+	0.856770i	$0.672468\pi$
$678$		0			0
$679$			1.15806i			0.0444422i
$680$		0			0
$681$		−	0.546638i		−	0.0209472i
$682$		0			0
$683$	−13.8990	−	13.8990i	−0.531829	−	0.531829i	0.389287	−	0.921116i	$-0.372721\pi$
$683$	−13.8990	−	13.8990i	−0.531829	−	0.531829i	−0.921116	+	0.389287i	$0.872721\pi$
$684$		0			0
$685$	−3.52114	+	3.52114i	−0.134536	+	0.134536i
$686$		0			0
$687$	−0.744414			−0.0284011
$688$		0			0
$689$	−4.14028			−0.157732
$690$		0			0
$691$	5.29499	−	5.29499i	0.201431	−	0.201431i	−0.599182	−	0.800613i	$-0.704507\pi$
$691$	5.29499	−	5.29499i	0.201431	−	0.201431i	0.800613	+	0.599182i	$0.204507\pi$
$692$		0			0
$693$	6.16023	+	6.16023i	0.234008	+	0.234008i
$694$		0			0
$695$		−	4.96940i		−	0.188500i
$696$		0			0
$697$		−	1.91112i		−	0.0723888i
$698$		0			0
$699$	−1.45288	−	1.45288i	−0.0549529	−	0.0549529i
$700$		0			0
$701$	−9.78883	+	9.78883i	−0.369719	+	0.369719i	−0.867375	−	0.497656i	$-0.834194\pi$
$701$	−9.78883	+	9.78883i	−0.369719	+	0.369719i	0.497656	+	0.867375i	$0.334194\pi$
$702$		0			0
$703$	0.440637			0.0166189
$704$		0			0
$705$	0.363899			0.0137052
$706$		0			0
$707$	11.4709	−	11.4709i	0.431409	−	0.431409i
$708$		0			0
$709$	12.1812	+	12.1812i	0.457475	+	0.457475i	0.897826	−	0.440351i	$-0.145146\pi$
$709$	12.1812	+	12.1812i	0.457475	+	0.457475i	−0.440351	+	0.897826i	$0.645146\pi$
$710$		0			0
$711$			5.11780i			0.191933i
$712$		0			0
$713$			4.48820i			0.168085i
$714$		0			0
$715$	3.09538	+	3.09538i	0.115760	+	0.115760i
$716$		0			0
$717$	−2.23968	+	2.23968i	−0.0836425	+	0.0836425i
$718$		0			0
$719$	−34.5970			−1.29025			−0.645125	−	0.764077i	$-0.723195\pi$
$719$	−34.5970			−1.29025			−0.645125	+	0.764077i	$0.723195\pi$
$720$		0			0
$721$	−14.2790			−0.531776
$722$		0			0
$723$	0.798819	−	0.798819i	0.0297084	−	0.0297084i
$724$		0			0
$725$	−5.25418	−	5.25418i	−0.195135	−	0.195135i
$726$		0			0
$727$		−	33.7941i		−	1.25335i	−0.779280	−	0.626676i	$-0.784415\pi$
$727$		−	33.7941i		−	1.25335i	0.779280	−	0.626676i	$-0.215585\pi$
$728$		0			0
$729$		−	26.2913i		−	0.973751i
$730$		0			0
$731$	3.18318	+	3.18318i	0.117734	+	0.117734i
$732$		0			0
$733$	−35.7917	+	35.7917i	−1.32200	+	1.32200i	−0.409840	+	0.912157i	$0.634415\pi$
$733$	−35.7917	+	35.7917i	−1.32200	+	1.32200i	−0.912157	+	0.409840i	$0.865585\pi$
$734$		0			0
$735$	0.114772			0.00423342
$736$		0			0
$737$	40.1199			1.47783
$738$		0			0
$739$	4.77490	−	4.77490i	0.175648	−	0.175648i	−0.613808	−	0.789455i	$-0.710363\pi$
$739$	4.77490	−	4.77490i	0.175648	−	0.175648i	0.789455	+	0.613808i	$0.210363\pi$
$740$		0			0
$741$	0.272501	+	0.272501i	0.0100106	+	0.0100106i
$742$		0			0
$743$			18.5013i			0.678745i	0.940652	+	0.339373i	$0.110215\pi$
$743$			18.5013i			0.678745i	−0.940652	+	0.339373i	$0.889785\pi$
$744$		0			0
$745$		−	6.98714i		−	0.255989i
$746$		0			0
$747$	14.4263	+	14.4263i	0.527830	+	0.527830i
$748$		0			0
$749$	−7.19515	+	7.19515i	−0.262905	+	0.262905i
$750$		0			0
$751$	19.5064			0.711800			0.355900	−	0.934524i	$-0.384174\pi$
$751$	19.5064			0.711800			0.355900	+	0.934524i	$0.384174\pi$
$752$		0			0
$753$	1.09670			0.0399661
$754$		0			0
$755$	−7.94648	+	7.94648i	−0.289202	+	0.289202i
$756$		0			0
$757$	7.43520	+	7.43520i	0.270237	+	0.270237i	0.829196	−	0.558959i	$-0.188799\pi$
$757$	7.43520	+	7.43520i	0.270237	+	0.270237i	−0.558959	+	0.829196i	$0.688799\pi$
$758$		0			0
$759$		−	0.992626i		−	0.0360300i
$760$		0			0
$761$			8.95694i			0.324689i	0.986734	+	0.162344i	$0.0519056\pi$
$761$			8.95694i			0.324689i	−0.986734	+	0.162344i	$0.948094\pi$
$762$		0			0
$763$	3.40747	+	3.40747i	0.123359	+	0.123359i
$764$		0			0
$765$	1.38750	−	1.38750i	0.0501653	−	0.0501653i
$766$		0			0
$767$	20.6106			0.744206
$768$		0			0
$769$	−7.47870			−0.269689			−0.134844	−	0.990867i	$-0.543053\pi$
$769$	−7.47870			−0.269689			−0.134844	+	0.990867i	$0.543053\pi$
$770$		0			0
$771$	−2.37281	+	2.37281i	−0.0854548	+	0.0854548i
$772$		0			0
$773$	3.34237	+	3.34237i	0.120217	+	0.120217i	0.764656	−	0.644439i	$-0.222909\pi$
$773$	3.34237	+	3.34237i	0.120217	+	0.120217i	−0.644439	+	0.764656i	$0.722909\pi$
$774$		0			0
$775$		−	1.51364i		−	0.0543717i
$776$		0			0
$777$			0.0226045i			0.000810932i
$778$		0			0
$779$	−4.60209	−	4.60209i	−0.164887	−	0.164887i
$780$		0			0
$781$	−10.4010	+	10.4010i	−0.372176	+	0.372176i
$782$		0			0
$783$	5.10566			0.182461
$784$		0			0
$785$	−1.29886			−0.0463585
$786$		0			0
$787$	−26.3129	+	26.3129i	−0.937952	+	0.937952i	−0.998184	−	0.0602319i	$-0.980816\pi$
$787$	−26.3129	+	26.3129i	−0.937952	+	0.937952i	0.0602319	+	0.998184i	$0.480816\pi$
$788$		0			0
$789$	0.610210	+	0.610210i	0.0217241	+	0.0217241i
$790$		0			0
$791$		−	15.2718i		−	0.543001i
$792$		0			0
$793$			17.7992i			0.632070i
$794$		0			0
$795$	−0.223884	−	0.223884i	−0.00794035	−	0.00794035i
$796$		0			0
$797$	−31.3870	+	31.3870i	−1.11179	+	1.11179i	−0.118877	+	0.992909i	$0.537929\pi$
$797$	−31.3870	+	31.3870i	−1.11179	+	1.11179i	−0.992909	+	0.118877i	$0.962071\pi$
$798$		0			0
$799$	2.08297			0.0736903
$800$		0			0
$801$	−36.3141			−1.28310
$802$		0			0
$803$	9.83135	−	9.83135i	0.346941	−	0.346941i
$804$		0			0
$805$	2.09669	+	2.09669i	0.0738986	+	0.0738986i
$806$		0			0
$807$			3.26748i			0.115021i
$808$		0			0
$809$			11.3626i			0.399487i	0.979848	+	0.199743i	$0.0640108\pi$
$809$			11.3626i			0.399487i	−0.979848	+	0.199743i	$0.935989\pi$
$810$		0			0
$811$	−13.4922	−	13.4922i	−0.473775	−	0.473775i	0.429359	−	0.903134i	$-0.358740\pi$
$811$	−13.4922	−	13.4922i	−0.473775	−	0.473775i	−0.903134	+	0.429359i	$0.858740\pi$
$812$		0			0
$813$	1.29764	−	1.29764i	0.0455101	−	0.0455101i
$814$		0			0
$815$	−3.74369			−0.131136
$816$		0			0
$817$	15.3306			0.536349
$818$		0			0
$819$	3.16973	−	3.16973i	0.110759	−	0.110759i
$820$		0			0
$821$	−4.18365	−	4.18365i	−0.146010	−	0.146010i	0.630323	−	0.776333i	$-0.282923\pi$
$821$	−4.18365	−	4.18365i	−0.146010	−	0.146010i	−0.776333	+	0.630323i	$0.782923\pi$
$822$		0			0
$823$			53.4812i			1.86424i	0.362151	+	0.932119i	$0.382043\pi$
$823$			53.4812i			1.86424i	−0.362151	+	0.932119i	$0.617957\pi$
$824$		0			0
$825$			0.334762i			0.0116549i
$826$		0			0
$827$	15.5164	+	15.5164i	0.539557	+	0.539557i	0.923399	−	0.383842i	$-0.125399\pi$
$827$	15.5164	+	15.5164i	0.539557	+	0.539557i	−0.383842	+	0.923399i	$0.625399\pi$
$828$		0			0
$829$	−8.48820	+	8.48820i	−0.294807	+	0.294807i	−0.838976	−	0.544169i	$-0.816845\pi$
$829$	−8.48820	+	8.48820i	−0.294807	+	0.294807i	0.544169	+	0.838976i	$0.316845\pi$
$830$		0			0
$831$	−2.64308			−0.0916874
$832$		0			0
$833$	0.656960			0.0227623
$834$		0			0
$835$	−2.33025	+	2.33025i	−0.0806416	+	0.0806416i
$836$		0			0
$837$	0.735429	+	0.735429i	0.0254201	+	0.0254201i
$838$		0			0
$839$		−	27.5214i		−	0.950144i	−0.879947	−	0.475072i	$-0.842422\pi$
$839$		−	27.5214i		−	0.950144i	0.879947	−	0.475072i	$-0.157578\pi$
$840$		0			0
$841$		−	26.2129i		−	0.903891i
$842$		0			0
$843$	1.67587	+	1.67587i	0.0577202	+	0.0577202i
$844$		0			0
$845$	−7.59967	+	7.59967i	−0.261437	+	0.261437i
$846$		0			0
$847$	2.49248			0.0856426
$848$		0			0
$849$	0.568229			0.0195016
$850$		0			0
$851$	−0.412947	+	0.412947i	−0.0141556	+	0.0141556i
$852$		0			0
$853$	−3.40599	−	3.40599i	−0.116619	−	0.116619i	0.646389	−	0.763008i	$-0.276278\pi$
$853$	−3.40599	−	3.40599i	−0.116619	−	0.116619i	−0.763008	+	0.646389i	$0.776278\pi$
$854$		0			0
$855$		−	6.68238i		−	0.228532i
$856$		0			0
$857$		−	39.9062i		−	1.36317i	−0.731740	−	0.681584i	$-0.761291\pi$
$857$		−	39.9062i		−	1.36317i	0.731740	−	0.681584i	$-0.238709\pi$
$858$		0			0
$859$	27.5359	+	27.5359i	0.939512	+	0.939512i	0.998272	−	0.0587606i	$-0.0187148\pi$
$859$	27.5359	+	27.5359i	0.939512	+	0.939512i	−0.0587606	+	0.998272i	$0.518715\pi$
$860$		0			0
$861$	0.236086	−	0.236086i	0.00804577	−	0.00804577i
$862$		0			0
$863$	−31.1231			−1.05944			−0.529722	−	0.848171i	$-0.677704\pi$
$863$	−31.1231			−1.05944			−0.529722	+	0.848171i	$0.677704\pi$
$864$		0			0
$865$	7.08985			0.241062
$866$		0			0
$867$	1.34462	−	1.34462i	0.0456658	−	0.0456658i
$868$		0			0
$869$	−3.53395	−	3.53395i	−0.119881	−	0.119881i
$870$		0			0
$871$		−	20.6436i		−	0.699481i
$872$		0			0
$873$			3.45892i			0.117067i
$874$		0			0
$875$	−0.707107	−	0.707107i	−0.0239046	−	0.0239046i
$876$		0			0
$877$	16.6945	−	16.6945i	0.563735	−	0.563735i	−0.366631	−	0.930366i	$-0.619489\pi$
$877$	16.6945	−	16.6945i	0.563735	−	0.563735i	0.930366	+	0.366631i	$0.119489\pi$
$878$		0			0
$879$	1.69013			0.0570065
$880$		0			0
$881$	8.24269			0.277703			0.138852	−	0.990313i	$-0.455659\pi$
$881$	8.24269			0.277703			0.138852	+	0.990313i	$0.455659\pi$
$882$		0			0
$883$	−8.56428	+	8.56428i	−0.288211	+	0.288211i	−0.836372	−	0.548162i	$-0.815328\pi$
$883$	−8.56428	+	8.56428i	−0.288211	+	0.288211i	0.548162	+	0.836372i	$0.315328\pi$
$884$		0			0
$885$	1.11451	+	1.11451i	0.0374638	+	0.0374638i
$886$		0			0
$887$		−	15.8630i		−	0.532628i	−0.963886	−	0.266314i	$-0.914194\pi$
$887$		−	15.8630i		−	0.532628i	0.963886	−	0.266314i	$-0.0858058\pi$
$888$		0			0
$889$			11.5810i			0.388414i
$890$		0			0
$891$	18.3180	+	18.3180i	0.613677	+	0.613677i
$892$		0			0
$893$	5.01592	−	5.01592i	0.167852	−	0.167852i
$894$		0			0
$895$	−14.0583			−0.469918
$896$		0			0
$897$	−0.510753			−0.0170535
$898$		0			0
$899$	7.95296	−	7.95296i	0.265246	−	0.265246i
$900$		0			0
$901$	−1.28152	−	1.28152i	−0.0426937	−	0.0426937i
$902$		0			0
$903$			0.786453i			0.0261715i
$904$		0			0
$905$		−	18.7125i		−	0.622023i
$906$		0			0
$907$	28.8485	+	28.8485i	0.957898	+	0.957898i	0.999149	−	0.0412504i	$-0.0131341\pi$
$907$	28.8485	+	28.8485i	0.957898	+	0.957898i	−0.0412504	+	0.999149i	$0.513134\pi$
$908$		0			0
$909$	34.2617	−	34.2617i	1.13639	−	1.13639i
$910$		0			0
$911$	−25.5557			−0.846698			−0.423349	−	0.905967i	$-0.639146\pi$
$911$	−25.5557			−0.846698			−0.423349	+	0.905967i	$0.639146\pi$
$912$		0			0
$913$	−19.9233			−0.659364
$914$		0			0
$915$	−0.962487	+	0.962487i	−0.0318188	+	0.0318188i
$916$		0			0
$917$	−15.9773	−	15.9773i	−0.527618	−	0.527618i
$918$		0			0
$919$			45.9935i			1.51719i	0.651565	+	0.758593i	$0.274113\pi$
$919$			45.9935i			1.51719i	−0.651565	+	0.758593i	$0.725887\pi$
$920$		0			0
$921$		−	1.09898i		−	0.0362127i
$922$		0			0
$923$	5.35180	+	5.35180i	0.176157	+	0.176157i
$924$		0			0
$925$	0.139266	−	0.139266i	0.00457904	−	0.00457904i
$926$		0			0
$927$	−42.6488			−1.40077
$928$		0			0
$929$	−17.8101			−0.584331			−0.292165	−	0.956368i	$-0.594376\pi$
$929$	−17.8101			−0.584331			−0.292165	+	0.956368i	$0.594376\pi$
$930$		0			0
$931$	1.58200	−	1.58200i	0.0518479	−	0.0518479i
$932$		0			0
$933$	0.205121	+	0.205121i	0.00671537	+	0.00671537i
$934$		0			0
$935$			1.91620i			0.0626663i
$936$		0			0
$937$			25.1994i			0.823229i	0.911358	+	0.411615i	$0.135035\pi$
$937$			25.1994i			0.823229i	−0.911358	+	0.411615i	$0.864965\pi$
$938$		0			0
$939$	−1.36793	−	1.36793i	−0.0446408	−	0.0446408i
$940$		0			0
$941$	−21.7888	+	21.7888i	−0.710294	+	0.710294i	−0.966597	−	0.256303i	$-0.917496\pi$
$941$	−21.7888	+	21.7888i	−0.710294	+	0.710294i	0.256303	+	0.966597i	$0.417496\pi$
$942$		0			0
$943$	8.62577			0.280894
$944$		0			0
$945$	0.687119			0.0223520
$946$		0			0
$947$	10.7626	−	10.7626i	0.349738	−	0.349738i	−0.510274	−	0.860012i	$-0.670456\pi$
$947$	10.7626	−	10.7626i	0.349738	−	0.349738i	0.860012	+	0.510274i	$0.170456\pi$
$948$		0			0
$949$	−5.05870	−	5.05870i	−0.164212	−	0.164212i
$950$		0			0
$951$		−	1.57253i		−	0.0509928i
$952$		0			0
$953$		−	52.9498i		−	1.71521i	−0.514306	−	0.857607i	$-0.671950\pi$
$953$		−	52.9498i		−	1.71521i	0.514306	−	0.857607i	$-0.328050\pi$
$954$		0			0
$955$	0.990366	+	0.990366i	0.0320475	+	0.0320475i
$956$		0			0
$957$	−1.75890	+	1.75890i	−0.0568572	+	0.0568572i
$958$		0			0
$959$	−4.97965			−0.160801
$960$		0			0
$961$	−28.7089			−0.926093
$962$		0			0
$963$	−21.4907	+	21.4907i	−0.692528	+	0.692528i
$964$		0			0
$965$	−4.14907	−	4.14907i	−0.133563	−	0.133563i
$966$		0			0
$967$		−	25.1341i		−	0.808259i	−0.914702	−	0.404129i	$-0.867575\pi$
$967$		−	25.1341i		−	0.808259i	0.914702	−	0.404129i	$-0.132425\pi$
$968$		0			0
$969$			0.168692i			0.00541917i
$970$		0			0
$971$	−32.3599	−	32.3599i	−1.03848	−	1.03848i	−0.999229	−	0.0392481i	$-0.987504\pi$
$971$	−32.3599	−	32.3599i	−1.03848	−	1.03848i	−0.0392481	−	0.999229i	$-0.512496\pi$
$972$		0			0
$973$	3.51390	−	3.51390i	0.112650	−	0.112650i
$974$		0			0
$975$	0.172251			0.00551645
$976$		0			0
$977$	−4.87345			−0.155915			−0.0779577	−	0.996957i	$-0.524840\pi$
$977$	−4.87345			−0.155915			−0.0779577	+	0.996957i	$0.524840\pi$
$978$		0			0
$979$	25.0756	−	25.0756i	0.801420	−	0.801420i
$980$		0			0
$981$	10.1775	+	10.1775i	0.324943	+	0.324943i
$982$		0			0
$983$		−	13.8364i		−	0.441314i	−0.975351	−	0.220657i	$-0.929180\pi$
$983$		−	13.8364i		−	0.441314i	0.975351	−	0.220657i	$-0.0708202\pi$
$984$		0			0
$985$		−	7.85363i		−	0.250238i
$986$		0			0
$987$	0.257315	+	0.257315i	0.00819043	+	0.00819043i
$988$		0			0
$989$	−14.3672	+	14.3672i	−0.456850	+	0.456850i
$990$		0			0
$991$	−7.07383			−0.224708			−0.112354	−	0.993668i	$-0.535839\pi$
$991$	−7.07383			−0.224708			−0.112354	+	0.993668i	$0.535839\pi$
$992$		0			0
$993$	0.327039			0.0103783
$994$		0			0
$995$	−8.07031	+	8.07031i	−0.255846	+	0.255846i
$996$		0			0
$997$	30.6771	+	30.6771i	0.971553	+	0.971553i	0.999606	−	0.0280536i	$-0.00893091\pi$
$997$	30.6771	+	30.6771i	0.971553	+	0.971553i	−0.0280536	+	0.999606i	$0.508931\pi$
$998$		0			0
$999$			0.135329i			0.00428163i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2240.2.bd.b.561.14		52
4.3	odd	2		560.2.bd.b.421.1	yes	52
16.3	odd	4		560.2.bd.b.141.1	✓	52
16.13	even	4	inner	2240.2.bd.b.1681.14		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bd.b.141.1	✓	52	16.3	odd	4
560.2.bd.b.421.1	yes	52	4.3	odd	2
2240.2.bd.b.561.14		52	1.1	even	1	trivial
2240.2.bd.b.1681.14		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)

\(f(q)\)	\(=\)	\(q+(-0.0811559 + 0.0811559i) q^{3} +(0.707107 + 0.707107i) q^{5} +1.00000i q^{7} +2.98683i q^{9} +O(q^{10})\)	\(q+(-0.0811559 + 0.0811559i) q^{3} +(0.707107 + 0.707107i) q^{5} +1.00000i q^{7} +2.98683i q^{9} +(-2.06246 - 2.06246i) q^{11} +(-1.06124 + 1.06124i) q^{13} -0.114772 q^{15} -0.656960 q^{17} +(-1.58200 + 1.58200i) q^{19} +(-0.0811559 - 0.0811559i) q^{21} -2.96516i q^{23} +1.00000i q^{25} +(-0.485866 - 0.485866i) q^{27} +(-5.25418 + 5.25418i) q^{29} -1.51364 q^{31} +0.334762 q^{33} +(-0.707107 + 0.707107i) q^{35} +(-0.139266 - 0.139266i) q^{37} -0.172251i q^{39} +2.90904i q^{41} +(-4.84532 - 4.84532i) q^{43} +(-2.11201 + 2.11201i) q^{45} -3.17063 q^{47} -1.00000 q^{49} +(0.0533162 - 0.0533162i) q^{51} +(1.95069 + 1.95069i) q^{53} -2.91677i q^{55} -0.256777i q^{57} +(-9.71066 - 9.71066i) q^{59} +(8.38610 - 8.38610i) q^{61} -2.98683 q^{63} -1.50081 q^{65} +(-9.72620 + 9.72620i) q^{67} +(0.240641 + 0.240641i) q^{69} -5.04299i q^{71} +4.76680i q^{73} +(-0.0811559 - 0.0811559i) q^{75} +(2.06246 - 2.06246i) q^{77} +1.71346 q^{79} -8.88162 q^{81} +(4.82996 - 4.82996i) q^{83} +(-0.464541 - 0.464541i) q^{85} -0.852816i q^{87} +12.1581i q^{89} +(-1.06124 - 1.06124i) q^{91} +(0.122841 - 0.122841i) q^{93} -2.23728 q^{95} +1.15806 q^{97} +(6.16023 - 6.16023i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q+O(q^{10}) \) 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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