LMFDB - Embedded newform 2240.2.bd.b.561.1

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			561.1
Character	$\chi$	$=$	2240.561
Dual form			2240.2.bd.b.1681.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.37790 + 2.37790i) q^{3} +(-0.707107 - 0.707107i) q^{5} +1.00000i q^{7} -8.30879i q^{9} +O(q^{10})$	\(q+(-2.37790 + 2.37790i) q^{3} +(-0.707107 - 0.707107i) q^{5} +1.00000i q^{7} -8.30879i q^{9} +(1.25501 + 1.25501i) q^{11} +(-4.11673 + 4.11673i) q^{13} +3.36285 q^{15} -2.87289 q^{17} +(-3.28189 + 3.28189i) q^{19} +(-2.37790 - 2.37790i) q^{21} -1.75198i q^{23} +1.00000i q^{25} +(12.6238 + 12.6238i) q^{27} +(4.43338 - 4.43338i) q^{29} -6.75204 q^{31} -5.96859 q^{33} +(0.707107 - 0.707107i) q^{35} +(0.623971 + 0.623971i) q^{37} -19.5783i q^{39} -6.40635i q^{41} +(-3.86088 - 3.86088i) q^{43} +(-5.87520 + 5.87520i) q^{45} -0.320755 q^{47} -1.00000 q^{49} +(6.83145 - 6.83145i) q^{51} +(0.669364 + 0.669364i) q^{53} -1.77486i q^{55} -15.6080i q^{57} +(-8.60128 - 8.60128i) q^{59} +(0.746751 - 0.746751i) q^{61} +8.30879 q^{63} +5.82193 q^{65} +(-2.91748 + 2.91748i) q^{67} +(4.16602 + 4.16602i) q^{69} +12.4076i q^{71} +6.12483i q^{73} +(-2.37790 - 2.37790i) q^{75} +(-1.25501 + 1.25501i) q^{77} +13.1093 q^{79} -35.1096 q^{81} +(2.87023 - 2.87023i) q^{83} +(2.03144 + 2.03144i) q^{85} +21.0842i q^{87} -16.6114i q^{89} +(-4.11673 - 4.11673i) q^{91} +(16.0556 - 16.0556i) q^{93} +4.64129 q^{95} +12.2240 q^{97} +(10.4277 - 10.4277i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.37790	+	2.37790i	−1.37288	+	1.37288i	−0.516733	+	0.856147i	$0.672852\pi$
$3$	−2.37790	+	2.37790i	−1.37288	+	1.37288i	−0.856147	+	0.516733i	$0.827148\pi$
$4$		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
$9$		−	8.30879i		−	2.76960i
$10$		0			0
$11$	1.25501	+	1.25501i	0.378401	+	0.378401i	0.870525	−	0.492124i	$-0.163779\pi$
$11$	1.25501	+	1.25501i	0.378401	+	0.378401i	−0.492124	+	0.870525i	$0.663779\pi$
$12$		0			0
$13$	−4.11673	+	4.11673i	−1.14178	+	1.14178i	−0.153650	+	0.988125i	$0.549103\pi$
$13$	−4.11673	+	4.11673i	−1.14178	+	1.14178i	−0.988125	+	0.153650i	$0.950897\pi$
$14$		0			0
$15$	3.36285			0.868285
$16$		0			0
$17$	−2.87289			−0.696779			−0.348390	−	0.937350i	$-0.613271\pi$
$17$	−2.87289			−0.696779			−0.348390	+	0.937350i	$0.613271\pi$
$18$		0			0
$19$	−3.28189	+	3.28189i	−0.752917	+	0.752917i	−0.975023	−	0.222105i	$-0.928707\pi$
$19$	−3.28189	+	3.28189i	−0.752917	+	0.752917i	0.222105	+	0.975023i	$0.428707\pi$
$20$		0			0
$21$	−2.37790	−	2.37790i	−0.518900	−	0.518900i
$22$		0			0
$23$		−	1.75198i		−	0.365312i	−0.983177	−	0.182656i	$-0.941530\pi$
$23$		−	1.75198i		−	0.365312i	0.983177	−	0.182656i	$-0.0584695\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$		0			0
$27$	12.6238	+	12.6238i	2.42944	+	2.42944i
$28$		0			0
$29$	4.43338	−	4.43338i	0.823258	−	0.823258i	−0.163316	−	0.986574i	$-0.552219\pi$
$29$	4.43338	−	4.43338i	0.823258	−	0.823258i	0.986574	+	0.163316i	$0.0522190\pi$
$30$		0			0
$31$	−6.75204			−1.21270			−0.606351	−	0.795197i	$-0.707367\pi$
$31$	−6.75204			−1.21270			−0.606351	+	0.795197i	$0.707367\pi$
$32$		0			0
$33$	−5.96859			−1.03900
$34$		0			0
$35$	0.707107	−	0.707107i	0.119523	−	0.119523i
$36$		0			0
$37$	0.623971	+	0.623971i	0.102580	+	0.102580i	0.756534	−	0.653954i	$-0.226891\pi$
$37$	0.623971	+	0.623971i	0.102580	+	0.102580i	−0.653954	+	0.756534i	$0.726891\pi$
$38$		0			0
$39$		−	19.5783i		−	3.13504i
$40$		0			0
$41$		−	6.40635i		−	1.00050i	−0.865880	−	0.500252i	$-0.833241\pi$
$41$		−	6.40635i		−	1.00050i	0.865880	−	0.500252i	$-0.166759\pi$
$42$		0			0
$43$	−3.86088	−	3.86088i	−0.588778	−	0.588778i	0.348522	−	0.937301i	$-0.386684\pi$
$43$	−3.86088	−	3.86088i	−0.588778	−	0.588778i	−0.937301	+	0.348522i	$0.886684\pi$
$44$		0			0
$45$	−5.87520	+	5.87520i	−0.875823	+	0.875823i
$46$		0			0
$47$	−0.320755			−0.0467869			−0.0233935	−	0.999726i	$-0.507447\pi$
$47$	−0.320755			−0.0467869			−0.0233935	+	0.999726i	$0.507447\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	6.83145	−	6.83145i	0.956594	−	0.956594i
$52$		0			0
$53$	0.669364	+	0.669364i	0.0919442	+	0.0919442i	0.751583	−	0.659639i	$-0.229291\pi$
$53$	0.669364	+	0.669364i	0.0919442	+	0.0919442i	−0.659639	+	0.751583i	$0.729291\pi$
$54$		0			0
$55$		−	1.77486i		−	0.239322i
$56$		0			0
$57$		−	15.6080i		−	2.06733i
$58$		0			0
$59$	−8.60128	−	8.60128i	−1.11979	−	1.11979i	−0.991772	−	0.128020i	$-0.959138\pi$
$59$	−8.60128	−	8.60128i	−1.11979	−	1.11979i	−0.128020	−	0.991772i	$-0.540862\pi$
$60$		0			0
$61$	0.746751	−	0.746751i	0.0956116	−	0.0956116i	−0.657683	−	0.753295i	$-0.728463\pi$
$61$	0.746751	−	0.746751i	0.0956116	−	0.0956116i	0.753295	+	0.657683i	$0.228463\pi$
$62$		0			0
$63$	8.30879			1.04681
$64$		0			0
$65$	5.82193			0.722122
$66$		0			0
$67$	−2.91748	+	2.91748i	−0.356427	+	0.356427i	−0.862494	−	0.506067i	$-0.831099\pi$
$67$	−2.91748	+	2.91748i	−0.356427	+	0.356427i	0.506067	+	0.862494i	$0.331099\pi$
$68$		0			0
$69$	4.16602	+	4.16602i	0.501530	+	0.501530i
$70$		0			0
$71$			12.4076i			1.47251i	0.676705	+	0.736254i	$0.263407\pi$
$71$			12.4076i			1.47251i	−0.676705	+	0.736254i	$0.736593\pi$
$72$		0			0
$73$			6.12483i			0.716858i	0.933557	+	0.358429i	$0.116687\pi$
$73$			6.12483i			0.716858i	−0.933557	+	0.358429i	$0.883313\pi$
$74$		0			0
$75$	−2.37790	−	2.37790i	−0.274576	−	0.274576i
$76$		0			0
$77$	−1.25501	+	1.25501i	−0.143022	+	0.143022i
$78$		0			0
$79$	13.1093			1.47491			0.737454	−	0.675397i	$-0.236028\pi$
$79$	13.1093			1.47491			0.737454	+	0.675397i	$0.236028\pi$
$80$		0			0
$81$	−35.1096			−3.90107
$82$		0			0
$83$	2.87023	−	2.87023i	0.315049	−	0.315049i	−0.531813	−	0.846862i	$-0.678489\pi$
$83$	2.87023	−	2.87023i	0.315049	−	0.315049i	0.846862	+	0.531813i	$0.178489\pi$
$84$		0			0
$85$	2.03144	+	2.03144i	0.220341	+	0.220341i
$86$		0			0
$87$			21.0842i			2.26047i
$88$		0			0
$89$		−	16.6114i		−	1.76080i	−0.474228	−	0.880402i	$-0.657273\pi$
$89$		−	16.6114i		−	1.76080i	0.474228	−	0.880402i	$-0.342727\pi$
$90$		0			0
$91$	−4.11673	−	4.11673i	−0.431550	−	0.431550i
$92$		0			0
$93$	16.0556	−	16.0556i	1.66489	−	1.66489i
$94$		0			0
$95$	4.64129			0.476187
$96$		0			0
$97$	12.2240			1.24116			0.620579	−	0.784144i	$-0.286898\pi$
$97$	12.2240			1.24116			0.620579	+	0.784144i	$0.286898\pi$
$98$		0			0
$99$	10.4277	−	10.4277i	1.04802	−	1.04802i
$100$		0			0
$101$	10.4022	+	10.4022i	1.03506	+	1.03506i	0.999363	+	0.0356954i	$0.0113646\pi$
$101$	10.4022	+	10.4022i	1.03506	+	1.03506i	0.0356954	+	0.999363i	$0.488635\pi$
$102$		0			0
$103$		−	13.1762i		−	1.29829i	−0.760663	−	0.649147i	$-0.775126\pi$
$103$		−	13.1762i		−	1.29829i	0.760663	−	0.649147i	$-0.224874\pi$
$104$		0			0
$105$			3.36285i			0.328181i
$106$		0			0
$107$	3.71846	+	3.71846i	0.359477	+	0.359477i	0.863620	−	0.504143i	$-0.168192\pi$
$107$	3.71846	+	3.71846i	0.359477	+	0.359477i	−0.504143	+	0.863620i	$0.668192\pi$
$108$		0			0
$109$	−2.01248	+	2.01248i	−0.192761	+	0.192761i	−0.796888	−	0.604127i	$-0.793522\pi$
$109$	−2.01248	+	2.01248i	−0.192761	+	0.192761i	0.604127	+	0.796888i	$0.293522\pi$
$110$		0			0
$111$	−2.96748			−0.281661
$112$		0			0
$113$	5.61909			0.528599			0.264300	−	0.964441i	$-0.414859\pi$
$113$	5.61909			0.528599			0.264300	+	0.964441i	$0.414859\pi$
$114$		0			0
$115$	−1.23883	+	1.23883i	−0.115522	+	0.115522i
$116$		0			0
$117$	34.2050	+	34.2050i	3.16226	+	3.16226i
$118$		0			0
$119$		−	2.87289i		−	0.263358i
$120$		0			0
$121$		−	7.84988i		−	0.713625i
$122$		0			0
$123$	15.2336	+	15.2336i	1.37357	+	1.37357i
$124$		0			0
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$		0			0
$127$	2.91626			0.258776			0.129388	−	0.991594i	$-0.458699\pi$
$127$	2.91626			0.258776			0.129388	+	0.991594i	$0.458699\pi$
$128$		0			0
$129$	18.3615			1.61664
$130$		0			0
$131$	10.9855	−	10.9855i	0.959804	−	0.959804i	−0.0394192	−	0.999223i	$-0.512551\pi$
$131$	10.9855	−	10.9855i	0.959804	−	0.959804i	0.999223	+	0.0394192i	$0.0125508\pi$
$132$		0			0
$133$	−3.28189	−	3.28189i	−0.284576	−	0.284576i
$134$		0			0
$135$		−	17.8527i		−	1.53651i
$136$		0			0
$137$			3.76211i			0.321419i	0.987002	+	0.160709i	$0.0513782\pi$
$137$			3.76211i			0.321419i	−0.987002	+	0.160709i	$0.948622\pi$
$138$		0			0
$139$	−3.48738	−	3.48738i	−0.295796	−	0.295796i	0.543569	−	0.839365i	$-0.317073\pi$
$139$	−3.48738	−	3.48738i	−0.295796	−	0.295796i	−0.839365	+	0.543569i	$0.817073\pi$
$140$		0			0
$141$	0.762722	−	0.762722i	0.0642328	−	0.0642328i
$142$		0			0
$143$	−10.3331			−0.864098
$144$		0			0
$145$	−6.26974			−0.520674
$146$		0			0
$147$	2.37790	−	2.37790i	0.196126	−	0.196126i
$148$		0			0
$149$	13.5536	+	13.5536i	1.11036	+	1.11036i	0.993102	+	0.117255i	$0.0374094\pi$
$149$	13.5536	+	13.5536i	1.11036	+	1.11036i	0.117255	+	0.993102i	$0.462591\pi$
$150$		0			0
$151$		−	8.59389i		−	0.699361i	−0.936869	−	0.349680i	$-0.886290\pi$
$151$		−	8.59389i		−	0.699361i	0.936869	−	0.349680i	$-0.113710\pi$
$152$		0			0
$153$			23.8703i			1.92980i
$154$		0			0
$155$	4.77441	+	4.77441i	0.383490	+	0.383490i
$156$		0			0
$157$	10.6575	−	10.6575i	0.850559	−	0.850559i	−0.139643	−	0.990202i	$-0.544596\pi$
$157$	10.6575	−	10.6575i	0.850559	−	0.850559i	0.990202	+	0.139643i	$0.0445956\pi$
$158$		0			0
$159$	−3.18336			−0.252457
$160$		0			0
$161$	1.75198			0.138075
$162$		0			0
$163$	−13.1625	+	13.1625i	−1.03096	+	1.03096i	−0.0314587	+	0.999505i	$0.510015\pi$
$163$	−13.1625	+	13.1625i	−1.03096	+	1.03096i	−0.999505	+	0.0314587i	$0.989985\pi$
$164$		0			0
$165$	4.22043	+	4.22043i	0.328560	+	0.328560i
$166$		0			0
$167$			22.5106i			1.74192i	0.491353	+	0.870961i	$0.336502\pi$
$167$			22.5106i			1.74192i	−0.491353	+	0.870961i	$0.663498\pi$
$168$		0			0
$169$		−	20.8949i		−	1.60730i
$170$		0			0
$171$	27.2685	+	27.2685i	2.08528	+	2.08528i
$172$		0			0
$173$	−2.86596	+	2.86596i	−0.217895	+	0.217895i	−0.807611	−	0.589716i	$-0.799240\pi$
$173$	−2.86596	+	2.86596i	−0.217895	+	0.217895i	0.589716	+	0.807611i	$0.299240\pi$
$174$		0			0
$175$	−1.00000			−0.0755929
$176$		0			0
$177$	40.9059			3.07468
$178$		0			0
$179$	−10.5882	+	10.5882i	−0.791402	+	0.791402i	−0.981722	−	0.190320i	$-0.939048\pi$
$179$	−10.5882	+	10.5882i	−0.791402	+	0.791402i	0.190320	+	0.981722i	$0.439048\pi$
$180$		0			0
$181$	9.40320	+	9.40320i	0.698934	+	0.698934i	0.964181	−	0.265246i	$-0.0854533\pi$
$181$	9.40320	+	9.40320i	0.698934	+	0.698934i	−0.265246	+	0.964181i	$0.585453\pi$
$182$		0			0
$183$			3.55139i			0.262526i
$184$		0			0
$185$		−	0.882429i		−	0.0648775i
$186$		0			0
$187$	−3.60552	−	3.60552i	−0.263662	−	0.263662i
$188$		0			0
$189$	−12.6238	+	12.6238i	−0.918243	+	0.918243i
$190$		0			0
$191$	−3.59651			−0.260234			−0.130117	−	0.991499i	$-0.541535\pi$
$191$	−3.59651			−0.260234			−0.130117	+	0.991499i	$0.541535\pi$
$192$		0			0
$193$	9.49758			0.683651			0.341825	−	0.939763i	$-0.388955\pi$
$193$	9.49758			0.683651			0.341825	+	0.939763i	$0.388955\pi$
$194$		0			0
$195$	−13.8440	+	13.8440i	−0.991386	+	0.991386i
$196$		0			0
$197$	−12.1400	−	12.1400i	−0.864942	−	0.864942i	0.126965	−	0.991907i	$-0.459476\pi$
$197$	−12.1400	−	12.1400i	−0.864942	−	0.864942i	−0.991907	+	0.126965i	$0.959476\pi$
$198$		0			0
$199$		−	0.496226i		−	0.0351766i	−0.999845	−	0.0175883i	$-0.994401\pi$
$199$		−	0.496226i		−	0.0351766i	0.999845	−	0.0175883i	$-0.00559881\pi$
$200$		0			0
$201$		−	13.8749i		−	0.978663i
$202$		0			0
$203$	4.43338	+	4.43338i	0.311162	+	0.311162i
$204$		0			0
$205$	−4.52997	+	4.52997i	−0.316387	+	0.316387i
$206$		0			0
$207$	−14.5568			−1.01177
$208$		0			0
$209$	−8.23764			−0.569810
$210$		0			0
$211$	11.9930	−	11.9930i	0.825635	−	0.825635i	−0.161275	−	0.986910i	$-0.551560\pi$
$211$	11.9930	−	11.9930i	0.825635	−	0.825635i	0.986910	+	0.161275i	$0.0515605\pi$
$212$		0			0
$213$	−29.5039	−	29.5039i	−2.02158	−	2.02158i
$214$		0			0
$215$			5.46011i			0.372376i
$216$		0			0
$217$		−	6.75204i		−	0.458358i
$218$		0			0
$219$	−14.5642	−	14.5642i	−0.984159	−	0.984159i
$220$		0			0
$221$	11.8269	−	11.8269i	0.795565	−	0.795565i
$222$		0			0
$223$	−2.45569			−0.164445			−0.0822225	−	0.996614i	$-0.526202\pi$
$223$	−2.45569			−0.164445			−0.0822225	+	0.996614i	$0.526202\pi$
$224$		0			0
$225$	8.30879			0.553919
$226$		0			0
$227$	18.9413	−	18.9413i	1.25718	−	1.25718i	0.304748	−	0.952433i	$-0.401428\pi$
$227$	18.9413	−	18.9413i	1.25718	−	1.25718i	0.952433	−	0.304748i	$-0.0985723\pi$
$228$		0			0
$229$	−6.27061	−	6.27061i	−0.414374	−	0.414374i	0.468885	−	0.883259i	$-0.344656\pi$
$229$	−6.27061	−	6.27061i	−0.414374	−	0.414374i	−0.883259	+	0.468885i	$0.844656\pi$
$230$		0			0
$231$		−	5.96859i		−	0.392704i
$232$		0			0
$233$		−	5.69418i		−	0.373038i	−0.982451	−	0.186519i	$-0.940279\pi$
$233$		−	5.69418i		−	0.373038i	0.982451	−	0.186519i	$-0.0597206\pi$
$234$		0			0
$235$	0.226808	+	0.226808i	0.0147953	+	0.0147953i
$236$		0			0
$237$	−31.1725	+	31.1725i	−2.02487	+	2.02487i
$238$		0			0
$239$	10.4310			0.674724			0.337362	−	0.941375i	$-0.390465\pi$
$239$	10.4310			0.674724			0.337362	+	0.941375i	$0.390465\pi$
$240$		0			0
$241$	21.3882			1.37774			0.688869	−	0.724886i	$-0.258107\pi$
$241$	21.3882			1.37774			0.688869	+	0.724886i	$0.258107\pi$
$242$		0			0
$243$	45.6158	−	45.6158i	2.92625	−	2.92625i
$244$		0			0
$245$	0.707107	+	0.707107i	0.0451754	+	0.0451754i
$246$		0			0
$247$		−	27.0213i		−	1.71932i
$248$		0			0
$249$			13.6502i			0.865049i
$250$		0			0
$251$	−17.9204	−	17.9204i	−1.13113	−	1.13113i	−0.989990	−	0.141138i	$-0.954924\pi$
$251$	−17.9204	−	17.9204i	−1.13113	−	1.13113i	−0.141138	−	0.989990i	$-0.545076\pi$
$252$		0			0
$253$	2.19876	−	2.19876i	0.138235	−	0.138235i
$254$		0			0
$255$	−9.66112			−0.605003
$256$		0			0
$257$	−3.22928			−0.201437			−0.100718	−	0.994915i	$-0.532114\pi$
$257$	−3.22928			−0.201437			−0.100718	+	0.994915i	$0.532114\pi$
$258$		0			0
$259$	−0.623971	+	0.623971i	−0.0387717	+	0.0387717i
$260$		0			0
$261$	−36.8360	−	36.8360i	−2.28009	−	2.28009i
$262$		0			0
$263$		−	20.3905i		−	1.25733i	−0.777674	−	0.628667i	$-0.783601\pi$
$263$		−	20.3905i		−	1.25733i	0.777674	−	0.628667i	$-0.216399\pi$
$264$		0			0
$265$		−	0.946624i		−	0.0581506i
$266$		0			0
$267$	39.5002	+	39.5002i	2.41737	+	2.41737i
$268$		0			0
$269$	−10.1704	+	10.1704i	−0.620098	+	0.620098i	−0.945556	−	0.325459i	$-0.894481\pi$
$269$	−10.1704	+	10.1704i	−0.620098	+	0.620098i	0.325459	+	0.945556i	$0.394481\pi$
$270$		0			0
$271$	−9.49943			−0.577049			−0.288525	−	0.957472i	$-0.593165\pi$
$271$	−9.49943			−0.577049			−0.288525	+	0.957472i	$0.593165\pi$
$272$		0			0
$273$	19.5783			1.18493
$274$		0			0
$275$	−1.25501	+	1.25501i	−0.0756802	+	0.0756802i
$276$		0			0
$277$	−9.55772	−	9.55772i	−0.574268	−	0.574268i	0.359050	−	0.933318i	$-0.383101\pi$
$277$	−9.55772	−	9.55772i	−0.574268	−	0.574268i	−0.933318	+	0.359050i	$0.883101\pi$
$278$		0			0
$279$			56.1012i			3.35869i
$280$		0			0
$281$			0.724850i			0.0432409i	0.999766	+	0.0216205i	$0.00688255\pi$
$281$			0.724850i			0.0432409i	−0.999766	+	0.0216205i	$0.993117\pi$
$282$		0			0
$283$	−23.0331	−	23.0331i	−1.36917	−	1.36917i	−0.861619	−	0.507555i	$-0.830549\pi$
$283$	−23.0331	−	23.0331i	−1.36917	−	1.36917i	−0.507555	−	0.861619i	$-0.669451\pi$
$284$		0			0
$285$	−11.0365	+	11.0365i	−0.653747	+	0.653747i
$286$		0			0
$287$	6.40635			0.378155
$288$		0			0
$289$	−8.74648			−0.514499
$290$		0			0
$291$	−29.0674	+	29.0674i	−1.70396	+	1.70396i
$292$		0			0
$293$	5.80663	+	5.80663i	0.339227	+	0.339227i	0.856076	−	0.516849i	$-0.172895\pi$
$293$	5.80663	+	5.80663i	0.339227	+	0.339227i	−0.516849	+	0.856076i	$0.672895\pi$
$294$		0			0
$295$			12.1641i			0.708218i
$296$		0			0
$297$			31.6860i			1.83861i
$298$		0			0
$299$	7.21241	+	7.21241i	0.417105	+	0.417105i
$300$		0			0
$301$	3.86088	−	3.86088i	0.222537	−	0.222537i
$302$		0			0
$303$	−49.4707			−2.84202
$304$		0			0
$305$	−1.05606			−0.0604701
$306$		0			0
$307$	7.93304	−	7.93304i	0.452763	−	0.452763i	−0.443508	−	0.896271i	$-0.646266\pi$
$307$	7.93304	−	7.93304i	0.452763	−	0.452763i	0.896271	+	0.443508i	$0.146266\pi$
$308$		0			0
$309$	31.3317	+	31.3317i	1.78240	+	1.78240i
$310$		0			0
$311$		−	13.2327i		−	0.750356i	−0.926953	−	0.375178i	$-0.877582\pi$
$311$		−	13.2327i		−	0.750356i	0.926953	−	0.375178i	$-0.122418\pi$
$312$		0			0
$313$		−	14.2651i		−	0.806311i	−0.915131	−	0.403156i	$-0.867913\pi$
$313$		−	14.2651i		−	0.806311i	0.915131	−	0.403156i	$-0.132087\pi$
$314$		0			0
$315$	−5.87520	−	5.87520i	−0.331030	−	0.331030i
$316$		0			0
$317$	−15.1063	+	15.1063i	−0.848456	+	0.848456i	−0.989940	−	0.141485i	$-0.954812\pi$
$317$	−15.1063	+	15.1063i	−0.848456	+	0.848456i	0.141485	+	0.989940i	$0.454812\pi$
$318$		0			0
$319$	11.1279			0.623043
$320$		0			0
$321$	−17.6842			−0.987038
$322$		0			0
$323$	9.42852	−	9.42852i	0.524617	−	0.524617i
$324$		0			0
$325$	−4.11673	−	4.11673i	−0.228355	−	0.228355i
$326$		0			0
$327$		−	9.57096i		−	0.529275i
$328$		0			0
$329$		−	0.320755i		−	0.0176838i
$330$		0			0
$331$	3.74712	+	3.74712i	0.205960	+	0.205960i	0.802548	−	0.596588i	$-0.203477\pi$
$331$	3.74712	+	3.74712i	0.205960	+	0.205960i	−0.596588	+	0.802548i	$0.703477\pi$
$332$		0			0
$333$	5.18445	−	5.18445i	0.284106	−	0.284106i
$334$		0			0
$335$	4.12594			0.225424
$336$		0			0
$337$	−19.7990			−1.07852			−0.539260	−	0.842140i	$-0.681296\pi$
$337$	−19.7990			−1.07852			−0.539260	+	0.842140i	$0.681296\pi$
$338$		0			0
$339$	−13.3616	+	13.3616i	−0.725703	+	0.725703i
$340$		0			0
$341$	−8.47390	−	8.47390i	−0.458888	−	0.458888i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$		0			0
$345$		−	5.89164i		−	0.317195i
$346$		0			0
$347$	−3.10476	−	3.10476i	−0.166672	−	0.166672i	0.618843	−	0.785515i	$-0.287602\pi$
$347$	−3.10476	−	3.10476i	−0.166672	−	0.166672i	−0.785515	+	0.618843i	$0.787602\pi$
$348$		0			0
$349$	−2.23119	+	2.23119i	−0.119433	+	0.119433i	−0.764297	−	0.644864i	$-0.776914\pi$
$349$	−2.23119	+	2.23119i	−0.119433	+	0.119433i	0.644864	+	0.764297i	$0.276914\pi$
$350$		0			0
$351$	−103.937			−5.54775
$352$		0			0
$353$	7.29254			0.388143			0.194071	−	0.980987i	$-0.437831\pi$
$353$	7.29254			0.388143			0.194071	+	0.980987i	$0.437831\pi$
$354$		0			0
$355$	8.77348	−	8.77348i	0.465648	−	0.465648i
$356$		0			0
$357$	6.83145	+	6.83145i	0.361558	+	0.361558i
$358$		0			0
$359$			2.53240i			0.133655i	0.997765	+	0.0668276i	$0.0212877\pi$
$359$			2.53240i			0.133655i	−0.997765	+	0.0668276i	$0.978712\pi$
$360$		0			0
$361$		−	2.54162i		−	0.133769i
$362$		0			0
$363$	18.6662	+	18.6662i	0.979721	+	0.979721i
$364$		0			0
$365$	4.33091	−	4.33091i	0.226690	−	0.226690i
$366$		0			0
$367$	29.5810			1.54412			0.772059	−	0.635551i	$-0.219227\pi$
$367$	29.5810			1.54412			0.772059	+	0.635551i	$0.219227\pi$
$368$		0			0
$369$	−53.2290			−2.77099
$370$		0			0
$371$	−0.669364	+	0.669364i	−0.0347517	+	0.0347517i
$372$		0			0
$373$	−8.82536	−	8.82536i	−0.456960	−	0.456960i	0.440696	−	0.897656i	$-0.354732\pi$
$373$	−8.82536	−	8.82536i	−0.456960	−	0.456960i	−0.897656	+	0.440696i	$0.854732\pi$
$374$		0			0
$375$			3.36285i			0.173657i
$376$		0			0
$377$			36.5020i			1.87995i
$378$		0			0
$379$	−19.7712	−	19.7712i	−1.01558	−	1.01558i	−0.999877	−	0.0157014i	$-0.995002\pi$
$379$	−19.7712	−	19.7712i	−1.01558	−	1.01558i	−0.0157014	−	0.999877i	$-0.504998\pi$
$380$		0			0
$381$	−6.93456	+	6.93456i	−0.355268	+	0.355268i
$382$		0			0
$383$	5.10399			0.260802			0.130401	−	0.991461i	$-0.458374\pi$
$383$	5.10399			0.260802			0.130401	+	0.991461i	$0.458374\pi$
$384$		0			0
$385$	1.77486			0.0904552
$386$		0			0
$387$	−32.0792	+	32.0792i	−1.63068	+	1.63068i
$388$		0			0
$389$	−13.6391	−	13.6391i	−0.691529	−	0.691529i	0.271039	−	0.962568i	$-0.412633\pi$
$389$	−13.6391	−	13.6391i	−0.691529	−	0.691529i	−0.962568	+	0.271039i	$0.912633\pi$
$390$		0			0
$391$			5.03324i			0.254542i
$392$		0			0
$393$			52.2446i			2.63539i
$394$		0			0
$395$	−9.26966	−	9.26966i	−0.466407	−	0.466407i
$396$		0			0
$397$	14.0868	−	14.0868i	0.706996	−	0.706996i	−0.258907	−	0.965902i	$-0.583362\pi$
$397$	14.0868	−	14.0868i	0.706996	−	0.706996i	0.965902	+	0.258907i	$0.0833622\pi$
$398$		0			0
$399$	15.6080			0.781377
$400$		0			0
$401$	23.2024			1.15867			0.579336	−	0.815089i	$-0.303312\pi$
$401$	23.2024			1.15867			0.579336	+	0.815089i	$0.303312\pi$
$402$		0			0
$403$	27.7963	−	27.7963i	1.38463	−	1.38463i
$404$		0			0
$405$	24.8262	+	24.8262i	1.23363	+	1.23363i
$406$		0			0
$407$			1.56619i			0.0776330i
$408$		0			0
$409$			21.8189i			1.07887i	0.842026	+	0.539437i	$0.181363\pi$
$409$			21.8189i			1.07887i	−0.842026	+	0.539437i	$0.818637\pi$
$410$		0			0
$411$	−8.94591	−	8.94591i	−0.441269	−	0.441269i
$412$		0			0
$413$	8.60128	−	8.60128i	0.423241	−	0.423241i
$414$		0			0
$415$	−4.05912			−0.199255
$416$		0			0
$417$	16.5853			0.812183
$418$		0			0
$419$	11.8739	−	11.8739i	0.580078	−	0.580078i	−0.354846	−	0.934925i	$-0.615467\pi$
$419$	11.8739	−	11.8739i	0.580078	−	0.580078i	0.934925	+	0.354846i	$0.115467\pi$
$420$		0			0
$421$	−24.0765	−	24.0765i	−1.17342	−	1.17342i	−0.981389	−	0.192030i	$-0.938493\pi$
$421$	−24.0765	−	24.0765i	−1.17342	−	1.17342i	−0.192030	−	0.981389i	$-0.561507\pi$
$422$		0			0
$423$			2.66509i			0.129581i
$424$		0			0
$425$		−	2.87289i		−	0.139356i
$426$		0			0
$427$	0.746751	+	0.746751i	0.0361378	+	0.0361378i
$428$		0			0
$429$	24.5711	−	24.5711i	1.18630	−	1.18630i
$430$		0			0
$431$	21.2683			1.02446			0.512230	−	0.858848i	$-0.328819\pi$
$431$	21.2683			1.02446			0.512230	+	0.858848i	$0.328819\pi$
$432$		0			0
$433$	−20.2717			−0.974197			−0.487098	−	0.873347i	$-0.661945\pi$
$433$	−20.2717			−0.974197			−0.487098	+	0.873347i	$0.661945\pi$
$434$		0			0
$435$	14.9088	−	14.9088i	0.714823	−	0.714823i
$436$		0			0
$437$	5.74980	+	5.74980i	0.275050	+	0.275050i
$438$		0			0
$439$			2.45267i			0.117059i	0.998286	+	0.0585297i	$0.0186412\pi$
$439$			2.45267i			0.117059i	−0.998286	+	0.0585297i	$0.981359\pi$
$440$		0			0
$441$			8.30879i			0.395657i
$442$		0			0
$443$	−9.64422	−	9.64422i	−0.458211	−	0.458211i	0.439857	−	0.898068i	$-0.355029\pi$
$443$	−9.64422	−	9.64422i	−0.458211	−	0.458211i	−0.898068	+	0.439857i	$0.855029\pi$
$444$		0			0
$445$	−11.7460	+	11.7460i	−0.556815	+	0.556815i
$446$		0			0
$447$	−64.4583			−3.04877
$448$		0			0
$449$	2.57381			0.121466			0.0607328	−	0.998154i	$-0.480656\pi$
$449$	2.57381			0.121466			0.0607328	+	0.998154i	$0.480656\pi$
$450$		0			0
$451$	8.04006	−	8.04006i	0.378592	−	0.378592i
$452$		0			0
$453$	20.4354	+	20.4354i	0.960138	+	0.960138i
$454$		0			0
$455$			5.82193i			0.272936i
$456$		0			0
$457$		−	24.4301i		−	1.14279i	−0.820675	−	0.571395i	$-0.806402\pi$
$457$		−	24.4301i		−	1.14279i	0.820675	−	0.571395i	$-0.193598\pi$
$458$		0			0
$459$	−36.2667	−	36.2667i	−1.69278	−	1.69278i
$460$		0			0
$461$	−18.6632	+	18.6632i	−0.869232	+	0.869232i	−0.992387	−	0.123155i	$-0.960699\pi$
$461$	−18.6632	+	18.6632i	−0.869232	+	0.869232i	0.123155	+	0.992387i	$0.460699\pi$
$462$		0			0
$463$	−15.3925			−0.715349			−0.357674	−	0.933846i	$-0.616430\pi$
$463$	−15.3925			−0.715349			−0.357674	+	0.933846i	$0.616430\pi$
$464$		0			0
$465$	−22.7061			−1.05297
$466$		0			0
$467$	22.3987	−	22.3987i	1.03649	−	1.03649i	0.0371781	−	0.999309i	$-0.488163\pi$
$467$	22.3987	−	22.3987i	1.03649	−	1.03649i	0.999309	−	0.0371781i	$-0.0118369\pi$
$468$		0			0
$469$	−2.91748	−	2.91748i	−0.134717	−	0.134717i
$470$		0			0
$471$			50.6847i			2.33543i
$472$		0			0
$473$		−	9.69092i		−	0.445589i
$474$		0			0
$475$	−3.28189	−	3.28189i	−0.150583	−	0.150583i
$476$		0			0
$477$	5.56160	−	5.56160i	0.254648	−	0.254648i
$478$		0			0
$479$	8.51824			0.389208			0.194604	−	0.980882i	$-0.437658\pi$
$479$	8.51824			0.389208			0.194604	+	0.980882i	$0.437658\pi$
$480$		0			0
$481$	−5.13744			−0.234247
$482$		0			0
$483$	−4.16602	+	4.16602i	−0.189561	+	0.189561i
$484$		0			0
$485$	−8.64366	−	8.64366i	−0.392488	−	0.392488i
$486$		0			0
$487$		−	1.15656i		−	0.0524086i	−0.999657	−	0.0262043i	$-0.991658\pi$
$487$		−	1.15656i		−	0.0524086i	0.999657	−	0.0262043i	$-0.00834204\pi$
$488$		0			0
$489$		−	62.5980i		−	2.83078i
$490$		0			0
$491$	−20.8462	−	20.8462i	−0.940777	−	0.940777i	0.0575650	−	0.998342i	$-0.481666\pi$
$491$	−20.8462	−	20.8462i	−0.940777	−	0.940777i	−0.998342	+	0.0575650i	$0.981666\pi$
$492$		0			0
$493$	−12.7366	+	12.7366i	−0.573629	+	0.573629i
$494$		0			0
$495$	−14.7469			−0.662825
$496$		0			0
$497$	−12.4076			−0.556556
$498$		0			0
$499$	7.69505	−	7.69505i	0.344478	−	0.344478i	−0.513570	−	0.858048i	$-0.671677\pi$
$499$	7.69505	−	7.69505i	0.344478	−	0.344478i	0.858048	+	0.513570i	$0.171677\pi$
$500$		0			0
$501$	−53.5278	−	53.5278i	−2.39145	−	2.39145i
$502$		0			0
$503$			14.7741i			0.658747i	0.944200	+	0.329373i	$0.106837\pi$
$503$			14.7741i			0.658747i	−0.944200	+	0.329373i	$0.893163\pi$
$504$		0			0
$505$		−	14.7109i		−	0.654628i
$506$		0			0
$507$	49.6859	+	49.6859i	2.20663	+	2.20663i
$508$		0			0
$509$	−15.8694	+	15.8694i	−0.703399	+	0.703399i	−0.965139	−	0.261740i	$-0.915704\pi$
$509$	−15.8694	+	15.8694i	−0.703399	+	0.703399i	0.261740	+	0.965139i	$0.415704\pi$
$510$		0			0
$511$	−6.12483			−0.270947
$512$		0			0
$513$	−82.8596			−3.65834
$514$		0			0
$515$	−9.31701	+	9.31701i	−0.410557	+	0.410557i
$516$		0			0
$517$	−0.402552	−	0.402552i	−0.0177042	−	0.0177042i
$518$		0			0
$519$		−	13.6299i		−	0.598287i
$520$		0			0
$521$			13.0157i			0.570229i	0.958493	+	0.285115i	$0.0920317\pi$
$521$			13.0157i			0.570229i	−0.958493	+	0.285115i	$0.907968\pi$
$522$		0			0
$523$	−7.19417	−	7.19417i	−0.314579	−	0.314579i	0.532102	−	0.846681i	$-0.321402\pi$
$523$	−7.19417	−	7.19417i	−0.314579	−	0.314579i	−0.846681	+	0.532102i	$0.821402\pi$
$524$		0			0
$525$	2.37790	−	2.37790i	0.103780	−	0.103780i
$526$		0			0
$527$	19.3979			0.844985
$528$		0			0
$529$	19.9306			0.866547
$530$		0			0
$531$	−71.4662	+	71.4662i	−3.10137	+	3.10137i
$532$		0			0
$533$	26.3732	+	26.3732i	1.14235	+	1.14235i
$534$		0			0
$535$		−	5.25870i		−	0.227353i
$536$		0			0
$537$		−	50.3555i		−	2.17300i
$538$		0			0
$539$	−1.25501	−	1.25501i	−0.0540573	−	0.0540573i
$540$		0			0
$541$	2.11432	−	2.11432i	0.0909018	−	0.0909018i	−0.660194	−	0.751095i	$-0.729526\pi$
$541$	2.11432	−	2.11432i	0.0909018	−	0.0909018i	0.751095	+	0.660194i	$0.229526\pi$
$542$		0			0
$543$	−44.7197			−1.91911
$544$		0			0
$545$	2.84608			0.121913
$546$		0			0
$547$	−18.0722	+	18.0722i	−0.772710	+	0.772710i	−0.978579	−	0.205870i	$-0.933998\pi$
$547$	−18.0722	+	18.0722i	−0.772710	+	0.772710i	0.205870	+	0.978579i	$0.433998\pi$
$548$		0			0
$549$	−6.20459	−	6.20459i	−0.264806	−	0.264806i
$550$		0			0
$551$			29.0997i			1.23969i
$552$		0			0
$553$			13.1093i			0.557463i
$554$		0			0
$555$	2.09833	+	2.09833i	0.0890689	+	0.0890689i
$556$		0			0
$557$	−14.2207	+	14.2207i	−0.602550	+	0.602550i	−0.940989	−	0.338438i	$-0.890101\pi$
$557$	−14.2207	+	14.2207i	−0.602550	+	0.602550i	0.338438	+	0.940989i	$0.390101\pi$
$558$		0			0
$559$	31.7884			1.34450
$560$		0			0
$561$	17.1471			0.723952
$562$		0			0
$563$	12.1888	−	12.1888i	0.513695	−	0.513695i	−0.401961	−	0.915657i	$-0.631671\pi$
$563$	12.1888	−	12.1888i	0.513695	−	0.513695i	0.915657	+	0.401961i	$0.131671\pi$
$564$		0			0
$565$	−3.97329	−	3.97329i	−0.167158	−	0.167158i
$566$		0			0
$567$		−	35.1096i		−	1.47446i
$568$		0			0
$569$		−	5.82007i		−	0.243990i	−0.992531	−	0.121995i	$-0.961071\pi$
$569$		−	5.82007i		−	0.243990i	0.992531	−	0.121995i	$-0.0389292\pi$
$570$		0			0
$571$	−14.6824	−	14.6824i	−0.614439	−	0.614439i	0.329660	−	0.944100i	$-0.393066\pi$
$571$	−14.6824	−	14.6824i	−0.614439	−	0.614439i	−0.944100	+	0.329660i	$0.893066\pi$
$572$		0			0
$573$	8.55213	−	8.55213i	0.357270	−	0.357270i
$574$		0			0
$575$	1.75198			0.0730625
$576$		0			0
$577$	17.8747			0.744131			0.372066	−	0.928206i	$-0.378650\pi$
$577$	17.8747			0.744131			0.372066	+	0.928206i	$0.378650\pi$
$578$		0			0
$579$	−22.5843	+	22.5843i	−0.938570	+	0.938570i
$580$		0			0
$581$	2.87023	+	2.87023i	0.119077	+	0.119077i
$582$		0			0
$583$			1.68012i			0.0695836i
$584$		0			0
$585$		−	48.3732i		−	1.99999i
$586$		0			0
$587$	1.33735	+	1.33735i	0.0551985	+	0.0551985i	0.734167	−	0.678969i	$-0.237573\pi$
$587$	1.33735	+	1.33735i	0.0551985	+	0.0551985i	−0.678969	+	0.734167i	$0.737573\pi$
$588$		0			0
$589$	22.1594	−	22.1594i	0.913064	−	0.913064i
$590$		0			0
$591$	57.7356			2.37492
$592$		0			0
$593$	−7.99404			−0.328276			−0.164138	−	0.986437i	$-0.552484\pi$
$593$	−7.99404			−0.328276			−0.164138	+	0.986437i	$0.552484\pi$
$594$		0			0
$595$	−2.03144	+	2.03144i	−0.0832810	+	0.0832810i
$596$		0			0
$597$	1.17998	+	1.17998i	0.0482932	+	0.0482932i
$598$		0			0
$599$			38.0110i			1.55309i	0.630063	+	0.776544i	$0.283029\pi$
$599$			38.0110i			1.55309i	−0.630063	+	0.776544i	$0.716971\pi$
$600$		0			0
$601$		−	39.4659i		−	1.60985i	−0.593377	−	0.804925i	$-0.702206\pi$
$601$		−	39.4659i		−	1.60985i	0.593377	−	0.804925i	$-0.297794\pi$
$602$		0			0
$603$	24.2407	+	24.2407i	0.987159	+	0.987159i
$604$		0			0
$605$	−5.55070	+	5.55070i	−0.225668	+	0.225668i
$606$		0			0
$607$	−34.6505			−1.40642			−0.703210	−	0.710983i	$-0.748250\pi$
$607$	−34.6505			−1.40642			−0.703210	+	0.710983i	$0.748250\pi$
$608$		0			0
$609$	−21.0842			−0.854376
$610$		0			0
$611$	1.32046	−	1.32046i	0.0534202	−	0.0534202i
$612$		0			0
$613$	11.4856	+	11.4856i	0.463898	+	0.463898i	0.899931	−	0.436033i	$-0.143617\pi$
$613$	11.4856	+	11.4856i	0.463898	+	0.463898i	−0.436033	+	0.899931i	$0.643617\pi$
$614$		0			0
$615$		−	21.5436i		−	0.868722i
$616$		0			0
$617$		−	19.0156i		−	0.765540i	−0.923844	−	0.382770i	$-0.874970\pi$
$617$		−	19.0156i		−	0.765540i	0.923844	−	0.382770i	$-0.125030\pi$
$618$		0			0
$619$	29.4885	+	29.4885i	1.18524	+	1.18524i	0.978367	+	0.206878i	$0.0663302\pi$
$619$	29.4885	+	29.4885i	1.18524	+	1.18524i	0.206878	+	0.978367i	$0.433670\pi$
$620$		0			0
$621$	22.1165	−	22.1165i	0.887506	−	0.887506i
$622$		0			0
$623$	16.6114			0.665521
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$	19.5883	−	19.5883i	0.782280	−	0.782280i
$628$		0			0
$629$	−1.79260	−	1.79260i	−0.0714758	−	0.0714758i
$630$		0			0
$631$		−	2.51839i		−	0.100256i	−0.998743	−	0.0501278i	$-0.984037\pi$
$631$		−	2.51839i		−	0.100256i	0.998743	−	0.0501278i	$-0.0159629\pi$
$632$		0			0
$633$			57.0364i			2.26699i
$634$		0			0
$635$	−2.06210	−	2.06210i	−0.0818321	−	0.0818321i
$636$		0			0
$637$	4.11673	−	4.11673i	0.163111	−	0.163111i
$638$		0			0
$639$	103.092			4.07825
$640$		0			0
$641$	1.59788			0.0631125			0.0315562	−	0.999502i	$-0.489954\pi$
$641$	1.59788			0.0631125			0.0315562	+	0.999502i	$0.489954\pi$
$642$		0			0
$643$	−4.63689	+	4.63689i	−0.182861	+	0.182861i	−0.792601	−	0.609740i	$-0.791274\pi$
$643$	−4.63689	+	4.63689i	−0.182861	+	0.182861i	0.609740	+	0.792601i	$0.291274\pi$
$644$		0			0
$645$	−12.9836	−	12.9836i	−0.511228	−	0.511228i
$646$		0			0
$647$		−	27.2170i		−	1.07001i	−0.844849	−	0.535004i	$-0.820310\pi$
$647$		−	27.2170i		−	1.07001i	0.844849	−	0.535004i	$-0.179690\pi$
$648$		0			0
$649$		−	21.5895i		−	0.847461i
$650$		0			0
$651$	16.0556	+	16.0556i	0.629270	+	0.629270i
$652$		0			0
$653$	−13.7192	+	13.7192i	−0.536874	+	0.536874i	−0.922610	−	0.385735i	$-0.873948\pi$
$653$	−13.7192	+	13.7192i	−0.536874	+	0.536874i	0.385735	+	0.922610i	$0.373948\pi$
$654$		0			0
$655$	−15.5358			−0.607033
$656$		0			0
$657$	50.8899			1.98541
$658$		0			0
$659$	−1.26700	+	1.26700i	−0.0493555	+	0.0493555i	−0.731354	−	0.681998i	$-0.761111\pi$
$659$	−1.26700	+	1.26700i	−0.0493555	+	0.0493555i	0.681998	+	0.731354i	$0.261111\pi$
$660$		0			0
$661$	10.0662	+	10.0662i	0.391530	+	0.391530i	0.875232	−	0.483703i	$-0.160708\pi$
$661$	10.0662	+	10.0662i	0.391530	+	0.391530i	−0.483703	+	0.875232i	$0.660708\pi$
$662$		0			0
$663$			56.2464i			2.18443i
$664$		0			0
$665$			4.64129i			0.179982i
$666$		0			0
$667$	−7.76718	−	7.76718i	−0.300746	−	0.300746i
$668$		0			0
$669$	5.83937	−	5.83937i	0.225763	−	0.225763i
$670$		0			0
$671$	1.87437			0.0723591
$672$		0			0
$673$	−30.8918			−1.19079			−0.595396	−	0.803432i	$-0.703005\pi$
$673$	−30.8918			−1.19079			−0.595396	+	0.803432i	$0.703005\pi$
$674$		0			0
$675$	−12.6238	+	12.6238i	−0.485888	+	0.485888i
$676$		0			0
$677$	−0.534249	−	0.534249i	−0.0205328	−	0.0205328i	0.696766	−	0.717299i	$-0.254622\pi$
$677$	−0.534249	−	0.534249i	−0.0205328	−	0.0205328i	−0.717299	+	0.696766i	$0.754622\pi$
$678$		0			0
$679$			12.2240i			0.469113i
$680$		0			0
$681$			90.0811i			3.45192i
$682$		0			0
$683$	−5.92660	−	5.92660i	−0.226775	−	0.226775i	0.584569	−	0.811344i	$-0.301264\pi$
$683$	−5.92660	−	5.92660i	−0.226775	−	0.226775i	−0.811344	+	0.584569i	$0.801264\pi$
$684$		0			0
$685$	2.66021	−	2.66021i	0.101642	−	0.101642i
$686$		0			0
$687$	29.8217			1.13777
$688$		0			0
$689$	−5.51118			−0.209959
$690$		0			0
$691$	1.14085	−	1.14085i	0.0433998	−	0.0433998i	−0.685074	−	0.728474i	$-0.740230\pi$
$691$	1.14085	−	1.14085i	0.0433998	−	0.0433998i	0.728474	+	0.685074i	$0.240230\pi$
$692$		0			0
$693$	10.4277	+	10.4277i	0.396114	+	0.396114i
$694$		0			0
$695$			4.93190i			0.187078i
$696$		0			0
$697$			18.4048i			0.697130i
$698$		0			0
$699$	13.5402	+	13.5402i	0.512136	+	0.512136i
$700$		0			0
$701$	9.14716	−	9.14716i	0.345483	−	0.345483i	−0.512941	−	0.858424i	$-0.671444\pi$
$701$	9.14716	−	9.14716i	0.345483	−	0.345483i	0.858424	+	0.512941i	$0.171444\pi$
$702$		0			0
$703$	−4.09561			−0.154469
$704$		0			0
$705$	−1.07865			−0.0406244
$706$		0			0
$707$	−10.4022	+	10.4022i	−0.391215	+	0.391215i
$708$		0			0
$709$	−4.35240	−	4.35240i	−0.163458	−	0.163458i	0.620639	−	0.784097i	$-0.286873\pi$
$709$	−4.35240	−	4.35240i	−0.163458	−	0.163458i	−0.784097	+	0.620639i	$0.786873\pi$
$710$		0			0
$711$		−	108.922i		−	4.08490i
$712$		0			0
$713$			11.8294i			0.443015i
$714$		0			0
$715$	7.30661	+	7.30661i	0.273252	+	0.273252i
$716$		0			0
$717$	−24.8038	+	24.8038i	−0.926314	+	0.926314i
$718$		0			0
$719$	−2.21572			−0.0826325			−0.0413162	−	0.999146i	$-0.513155\pi$
$719$	−2.21572			−0.0826325			−0.0413162	+	0.999146i	$0.513155\pi$
$720$		0			0
$721$	13.1762			0.490709
$722$		0			0
$723$	−50.8591	+	50.8591i	−1.89147	+	1.89147i
$724$		0			0
$725$	4.43338	+	4.43338i	0.164652	+	0.164652i
$726$		0			0
$727$		−	1.86211i		−	0.0690618i	−0.999404	−	0.0345309i	$-0.989006\pi$
$727$		−	1.86211i		−	0.0690618i	0.999404	−	0.0345309i	$-0.0109937\pi$
$728$		0			0
$729$			111.610i			4.13372i
$730$		0			0
$731$	11.0919	+	11.0919i	0.410248	+	0.410248i
$732$		0			0
$733$	−22.4099	+	22.4099i	−0.827730	+	0.827730i	−0.987202	−	0.159473i	$-0.949021\pi$
$733$	−22.4099	+	22.4099i	−0.827730	+	0.827730i	0.159473	+	0.987202i	$0.449021\pi$
$734$		0			0
$735$	−3.36285			−0.124041
$736$		0			0
$737$	−7.32296			−0.269745
$738$		0			0
$739$	0.402304	−	0.402304i	0.0147990	−	0.0147990i	−0.699669	−	0.714468i	$-0.746669\pi$
$739$	0.402304	−	0.402304i	0.0147990	−	0.0147990i	0.714468	+	0.699669i	$0.246669\pi$
$740$		0			0
$741$	64.2539	+	64.2539i	2.36043	+	2.36043i
$742$		0			0
$743$			15.3190i			0.562000i	0.959708	+	0.281000i	$0.0906660\pi$
$743$			15.3190i			0.562000i	−0.959708	+	0.281000i	$0.909334\pi$
$744$		0			0
$745$		−	19.1677i		−	0.702251i
$746$		0			0
$747$	−23.8482	−	23.8482i	−0.872559	−	0.872559i
$748$		0			0
$749$	−3.71846	+	3.71846i	−0.135870	+	0.135870i
$750$		0			0
$751$	9.17303			0.334729			0.167364	−	0.985895i	$-0.446474\pi$
$751$	9.17303			0.334729			0.167364	+	0.985895i	$0.446474\pi$
$752$		0			0
$753$	85.2259			3.10580
$754$		0			0
$755$	−6.07680	+	6.07680i	−0.221157	+	0.221157i
$756$		0			0
$757$	3.84533	+	3.84533i	0.139761	+	0.139761i	0.773526	−	0.633765i	$-0.218491\pi$
$757$	3.84533	+	3.84533i	0.139761	+	0.139761i	−0.633765	+	0.773526i	$0.718491\pi$
$758$		0			0
$759$			10.4568i			0.379559i
$760$		0			0
$761$			28.0121i			1.01544i	0.861522	+	0.507720i	$0.169511\pi$
$761$			28.0121i			1.01544i	−0.861522	+	0.507720i	$0.830489\pi$
$762$		0			0
$763$	−2.01248	−	2.01248i	−0.0728568	−	0.0728568i
$764$		0			0
$765$	16.8788	−	16.8788i	0.610255	−	0.610255i
$766$		0			0
$767$	70.8183			2.55710
$768$		0			0
$769$	46.1009			1.66244			0.831221	−	0.555942i	$-0.187642\pi$
$769$	46.1009			1.66244			0.831221	+	0.555942i	$0.187642\pi$
$770$		0			0
$771$	7.67889	−	7.67889i	0.276549	−	0.276549i
$772$		0			0
$773$	14.9964	+	14.9964i	0.539382	+	0.539382i	0.923347	−	0.383966i	$-0.125442\pi$
$773$	14.9964	+	14.9964i	0.539382	+	0.539382i	−0.383966	+	0.923347i	$0.625442\pi$
$774$		0			0
$775$		−	6.75204i		−	0.242540i
$776$		0			0
$777$		−	2.96748i		−	0.106458i
$778$		0			0
$779$	21.0249	+	21.0249i	0.753296	+	0.753296i
$780$		0			0
$781$	−15.5717	+	15.5717i	−0.557199	+	0.557199i
$782$		0			0
$783$	111.932			4.00011
$784$		0			0
$785$	−15.0719			−0.537941
$786$		0			0
$787$	−31.0487	+	31.0487i	−1.10677	+	1.10677i	−0.113195	+	0.993573i	$0.536108\pi$
$787$	−31.0487	+	31.0487i	−1.10677	+	1.10677i	−0.993573	+	0.113195i	$0.963892\pi$
$788$		0			0
$789$	48.4866	+	48.4866i	1.72617	+	1.72617i
$790$		0			0
$791$			5.61909i			0.199792i
$792$		0			0
$793$			6.14834i			0.218334i
$794$		0			0
$795$	2.25097	+	2.25097i	0.0798338	+	0.0798338i
$796$		0			0
$797$	8.69660	−	8.69660i	0.308049	−	0.308049i	−0.536103	−	0.844153i	$-0.680104\pi$
$797$	8.69660	−	8.69660i	0.308049	−	0.308049i	0.844153	+	0.536103i	$0.180104\pi$
$798$		0			0
$799$	0.921495			0.0326002
$800$		0			0
$801$	−138.021			−4.87672
$802$		0			0
$803$	−7.68676	+	7.68676i	−0.271260	+	0.271260i
$804$		0			0
$805$	−1.23883	−	1.23883i	−0.0436632	−	0.0436632i
$806$		0			0
$807$		−	48.3681i		−	1.70264i
$808$		0			0
$809$			8.91959i			0.313596i	0.987631	+	0.156798i	$0.0501172\pi$
$809$			8.91959i			0.313596i	−0.987631	+	0.156798i	$0.949883\pi$
$810$		0			0
$811$	0.578400	+	0.578400i	0.0203104	+	0.0203104i	0.717189	−	0.696879i	$-0.245428\pi$
$811$	0.578400	+	0.578400i	0.0203104	+	0.0203104i	−0.696879	+	0.717189i	$0.745428\pi$
$812$		0			0
$813$	22.5887	−	22.5887i	0.792219	−	0.792219i
$814$		0			0
$815$	18.6145			0.652039
$816$		0			0
$817$	25.3420			0.886603
$818$		0			0
$819$	−34.2050	+	34.2050i	−1.19522	+	1.19522i
$820$		0			0
$821$	−26.2064	−	26.2064i	−0.914610	−	0.914610i	0.0820211	−	0.996631i	$-0.473863\pi$
$821$	−26.2064	−	26.2064i	−0.914610	−	0.914610i	−0.996631	+	0.0820211i	$0.973863\pi$
$822$		0			0
$823$			26.7591i			0.932762i	0.884584	+	0.466381i	$0.154442\pi$
$823$			26.7591i			0.932762i	−0.884584	+	0.466381i	$0.845558\pi$
$824$		0			0
$825$		−	5.96859i		−	0.207800i
$826$		0			0
$827$	13.4175	+	13.4175i	0.466571	+	0.466571i	0.900802	−	0.434231i	$-0.142980\pi$
$827$	13.4175	+	13.4175i	0.466571	+	0.466571i	−0.434231	+	0.900802i	$0.642980\pi$
$828$		0			0
$829$	−18.0315	+	18.0315i	−0.626260	+	0.626260i	−0.947125	−	0.320865i	$-0.896026\pi$
$829$	−18.0315	+	18.0315i	−0.626260	+	0.626260i	0.320865	+	0.947125i	$0.396026\pi$
$830$		0			0
$831$	45.4546			1.57680
$832$		0			0
$833$	2.87289			0.0995399
$834$		0			0
$835$	15.9174	−	15.9174i	0.550844	−	0.550844i
$836$		0			0
$837$	−85.2360	−	85.2360i	−2.94619	−	2.94619i
$838$		0			0
$839$		−	32.5735i		−	1.12456i	−0.826947	−	0.562280i	$-0.809924\pi$
$839$		−	32.5735i		−	1.12456i	0.826947	−	0.562280i	$-0.190076\pi$
$840$		0			0
$841$		−	10.3097i		−	0.355507i
$842$		0			0
$843$	−1.72362	−	1.72362i	−0.0593646	−	0.0593646i
$844$		0			0
$845$	−14.7749	+	14.7749i	−0.508273	+	0.508273i
$846$		0			0
$847$	7.84988			0.269725
$848$		0			0
$849$	109.541			3.75942
$850$		0			0
$851$	1.09318	−	1.09318i	0.0374739	−	0.0374739i
$852$		0			0
$853$	−8.44932	−	8.44932i	−0.289299	−	0.289299i	0.547504	−	0.836803i	$-0.315578\pi$
$853$	−8.44932	−	8.44932i	−0.289299	−	0.289299i	−0.836803	+	0.547504i	$0.815578\pi$
$854$		0			0
$855$		−	38.5635i		−	1.31885i
$856$		0			0
$857$		−	36.7236i		−	1.25445i	−0.778836	−	0.627227i	$-0.784190\pi$
$857$		−	36.7236i		−	1.25445i	0.778836	−	0.627227i	$-0.215810\pi$
$858$		0			0
$859$	−32.1071	−	32.1071i	−1.09548	−	1.09548i	−0.994932	−	0.100549i	$-0.967940\pi$
$859$	−32.1071	−	32.1071i	−1.09548	−	1.09548i	−0.100549	−	0.994932i	$-0.532060\pi$
$860$		0			0
$861$	−15.2336	+	15.2336i	−0.519161	+	0.519161i
$862$		0			0
$863$	−4.71972			−0.160661			−0.0803306	−	0.996768i	$-0.525598\pi$
$863$	−4.71972			−0.160661			−0.0803306	+	0.996768i	$0.525598\pi$
$864$		0			0
$865$	4.05308			0.137809
$866$		0			0
$867$	20.7982	−	20.7982i	0.706345	−	0.706345i
$868$		0			0
$869$	16.4523	+	16.4523i	0.558107	+	0.558107i
$870$		0			0
$871$		−	24.0210i		−	0.813919i
$872$		0			0
$873$		−	101.566i		−	3.43750i
$874$		0			0
$875$	0.707107	+	0.707107i	0.0239046	+	0.0239046i
$876$		0			0
$877$	33.1265	−	33.1265i	1.11860	−	1.11860i	0.126657	−	0.991947i	$-0.459575\pi$
$877$	33.1265	−	33.1265i	1.11860	−	1.11860i	0.991947	−	0.126657i	$-0.0404249\pi$
$878$		0			0
$879$	−27.6151			−0.931435
$880$		0			0
$881$	−52.8233			−1.77966			−0.889831	−	0.456290i	$-0.849178\pi$
$881$	−52.8233			−1.77966			−0.889831	+	0.456290i	$0.849178\pi$
$882$		0			0
$883$	−30.4844	+	30.4844i	−1.02588	+	1.02588i	−0.0262253	+	0.999656i	$0.508349\pi$
$883$	−30.4844	+	30.4844i	−1.02588	+	1.02588i	−0.999656	+	0.0262253i	$0.991651\pi$
$884$		0			0
$885$	−28.9249	−	28.9249i	−0.972299	−	0.972299i
$886$		0			0
$887$		−	24.6022i		−	0.826060i	−0.910717	−	0.413030i	$-0.864471\pi$
$887$		−	24.6022i		−	0.826060i	0.910717	−	0.413030i	$-0.135529\pi$
$888$		0			0
$889$			2.91626i			0.0978081i
$890$		0			0
$891$	−44.0631	−	44.0631i	−1.47617	−	1.47617i
$892$		0			0
$893$	1.05268	−	1.05268i	0.0352267	−	0.0352267i
$894$		0			0
$895$	14.9740			0.500527
$896$		0			0
$897$	−34.3008			−1.14527
$898$		0			0
$899$	−29.9343	+	29.9343i	−0.998366	+	0.998366i
$900$		0			0
$901$	−1.92301	−	1.92301i	−0.0640648	−	0.0640648i
$902$		0			0
$903$			18.3615i			0.611034i
$904$		0			0
$905$		−	13.2981i		−	0.442045i
$906$		0			0
$907$	−17.4262	−	17.4262i	−0.578629	−	0.578629i	0.355897	−	0.934525i	$-0.384175\pi$
$907$	−17.4262	−	17.4262i	−0.578629	−	0.578629i	−0.934525	+	0.355897i	$0.884175\pi$
$908$		0			0
$909$	86.4297	−	86.4297i	2.86669	−	2.86669i
$910$		0			0
$911$	−37.0743			−1.22833			−0.614164	−	0.789179i	$-0.710507\pi$
$911$	−37.0743			−1.22833			−0.614164	+	0.789179i	$0.710507\pi$
$912$		0			0
$913$	7.20437			0.238430
$914$		0			0
$915$	2.51121	−	2.51121i	0.0830182	−	0.0830182i
$916$		0			0
$917$	10.9855	+	10.9855i	0.362772	+	0.362772i
$918$		0			0
$919$			8.82519i			0.291116i	0.989350	+	0.145558i	$0.0464978\pi$
$919$			8.82519i			0.291116i	−0.989350	+	0.145558i	$0.953502\pi$
$920$		0			0
$921$			37.7279i			1.24318i
$922$		0			0
$923$	−51.0786	−	51.0786i	−1.68127	−	1.68127i
$924$		0			0
$925$	−0.623971	+	0.623971i	−0.0205161	+	0.0205161i
$926$		0			0
$927$	−109.479			−3.59575
$928$		0			0
$929$	−42.5840			−1.39713			−0.698567	−	0.715544i	$-0.746179\pi$
$929$	−42.5840			−1.39713			−0.698567	+	0.715544i	$0.746179\pi$
$930$		0			0
$931$	3.28189	−	3.28189i	0.107560	−	0.107560i
$932$		0			0
$933$	31.4659	+	31.4659i	1.03015	+	1.03015i
$934$		0			0
$935$			5.09898i			0.166754i
$936$		0			0
$937$		−	10.8663i		−	0.354987i	−0.984122	−	0.177493i	$-0.943201\pi$
$937$		−	10.8663i		−	0.354987i	0.984122	−	0.177493i	$-0.0567988\pi$
$938$		0			0
$939$	33.9209	+	33.9209i	1.10697	+	1.10697i
$940$		0			0
$941$	19.2518	−	19.2518i	0.627590	−	0.627590i	−0.319871	−	0.947461i	$-0.603640\pi$
$941$	19.2518	−	19.2518i	0.627590	−	0.627590i	0.947461	+	0.319871i	$0.103640\pi$
$942$		0			0
$943$	−11.2238			−0.365496
$944$		0			0
$945$	17.8527			0.580748
$946$		0			0
$947$	20.5171	−	20.5171i	0.666715	−	0.666715i	−0.290239	−	0.956954i	$-0.593735\pi$
$947$	20.5171	−	20.5171i	0.666715	−	0.666715i	0.956954	+	0.290239i	$0.0937347\pi$
$948$		0			0
$949$	−25.2143	−	25.2143i	−0.818490	−	0.818490i
$950$		0			0
$951$		−	71.8426i		−	2.32965i
$952$		0			0
$953$			13.5864i			0.440105i	0.975488	+	0.220053i	$0.0706229\pi$
$953$			13.5864i			0.440105i	−0.975488	+	0.220053i	$0.929377\pi$
$954$		0			0
$955$	2.54312	+	2.54312i	0.0822933	+	0.0822933i
$956$		0			0
$957$	−26.4610	+	26.4610i	−0.855363	+	0.855363i
$958$		0			0
$959$	−3.76211			−0.121485
$960$		0			0
$961$	14.5900			0.470645
$962$		0			0
$963$	30.8959	−	30.8959i	0.995607	−	0.995607i
$964$		0			0
$965$	−6.71580	−	6.71580i	−0.216189	−	0.216189i
$966$		0			0
$967$			12.1857i			0.391865i	0.980617	+	0.195932i	$0.0627733\pi$
$967$			12.1857i			0.391865i	−0.980617	+	0.195932i	$0.937227\pi$
$968$		0			0
$969$			44.8401i			1.44047i
$970$		0			0
$971$	−17.0874	−	17.0874i	−0.548360	−	0.548360i	0.377606	−	0.925966i	$-0.376747\pi$
$971$	−17.0874	−	17.0874i	−0.548360	−	0.548360i	−0.925966	+	0.377606i	$0.876747\pi$
$972$		0			0
$973$	3.48738	−	3.48738i	0.111800	−	0.111800i
$974$		0			0
$975$	19.5783			0.627008
$976$		0			0
$977$	−18.8136			−0.601902			−0.300951	−	0.953640i	$-0.597304\pi$
$977$	−18.8136			−0.601902			−0.300951	+	0.953640i	$0.597304\pi$
$978$		0			0
$979$	20.8475	−	20.8475i	0.666290	−	0.666290i
$980$		0			0
$981$	16.7213	+	16.7213i	0.533870	+	0.533870i
$982$		0			0
$983$		−	5.95522i		−	0.189942i	−0.995480	−	0.0949710i	$-0.969724\pi$
$983$		−	5.95522i		−	0.189942i	0.995480	−	0.0949710i	$-0.0302758\pi$
$984$		0			0
$985$			17.1686i			0.547038i
$986$		0			0
$987$	0.762722	+	0.762722i	0.0242777	+	0.0242777i
$988$		0			0
$989$	−6.76417	+	6.76417i	−0.215088	+	0.215088i
$990$		0			0
$991$	55.2961			1.75654			0.878269	−	0.478167i	$-0.158699\pi$
$991$	55.2961			1.75654			0.878269	+	0.478167i	$0.158699\pi$
$992$		0			0
$993$	−17.8205			−0.565517
$994$		0			0
$995$	−0.350885	+	0.350885i	−0.0111238	+	0.0111238i
$996$		0			0
$997$	−10.8008	−	10.8008i	−0.342064	−	0.342064i	0.515079	−	0.857143i	$-0.327763\pi$
$997$	−10.8008	−	10.8008i	−0.342064	−	0.342064i	−0.857143	+	0.515079i	$0.827763\pi$
$998$		0			0
$999$			15.7537i			0.498426i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2240.2.bd.b.561.1		52
4.3	odd	2		560.2.bd.b.421.3	yes	52
16.3	odd	4		560.2.bd.b.141.3	✓	52
16.13	even	4	inner	2240.2.bd.b.1681.1		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bd.b.141.3	✓	52	16.3	odd	4
560.2.bd.b.421.3	yes	52	4.3	odd	2
2240.2.bd.b.561.1		52	1.1	even	1	trivial
2240.2.bd.b.1681.1		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)

\(f(q)\)	\(=\)	\(q+(-2.37790 + 2.37790i) q^{3} +(-0.707107 - 0.707107i) q^{5} +1.00000i q^{7} -8.30879i q^{9} +O(q^{10})\)	\(q+(-2.37790 + 2.37790i) q^{3} +(-0.707107 - 0.707107i) q^{5} +1.00000i q^{7} -8.30879i q^{9} +(1.25501 + 1.25501i) q^{11} +(-4.11673 + 4.11673i) q^{13} +3.36285 q^{15} -2.87289 q^{17} +(-3.28189 + 3.28189i) q^{19} +(-2.37790 - 2.37790i) q^{21} -1.75198i q^{23} +1.00000i q^{25} +(12.6238 + 12.6238i) q^{27} +(4.43338 - 4.43338i) q^{29} -6.75204 q^{31} -5.96859 q^{33} +(0.707107 - 0.707107i) q^{35} +(0.623971 + 0.623971i) q^{37} -19.5783i q^{39} -6.40635i q^{41} +(-3.86088 - 3.86088i) q^{43} +(-5.87520 + 5.87520i) q^{45} -0.320755 q^{47} -1.00000 q^{49} +(6.83145 - 6.83145i) q^{51} +(0.669364 + 0.669364i) q^{53} -1.77486i q^{55} -15.6080i q^{57} +(-8.60128 - 8.60128i) q^{59} +(0.746751 - 0.746751i) q^{61} +8.30879 q^{63} +5.82193 q^{65} +(-2.91748 + 2.91748i) q^{67} +(4.16602 + 4.16602i) q^{69} +12.4076i q^{71} +6.12483i q^{73} +(-2.37790 - 2.37790i) q^{75} +(-1.25501 + 1.25501i) q^{77} +13.1093 q^{79} -35.1096 q^{81} +(2.87023 - 2.87023i) q^{83} +(2.03144 + 2.03144i) q^{85} +21.0842i q^{87} -16.6114i q^{89} +(-4.11673 - 4.11673i) q^{91} +(16.0556 - 16.0556i) q^{93} +4.64129 q^{95} +12.2240 q^{97} +(10.4277 - 10.4277i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q+O(q^{10}) \) 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

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