LMFDB - Embedded newform 2240.2.bd.a.561.11

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:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 560)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			561.11
Character	$\chi$	$=$	2240.561
Dual form			2240.2.bd.a.1681.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.257753 + 0.257753i) q^{3} +(-0.707107 - 0.707107i) q^{5} -1.00000i q^{7} +2.86713i q^{9} +O(q^{10})$	\(q+(-0.257753 + 0.257753i) q^{3} +(-0.707107 - 0.707107i) q^{5} -1.00000i q^{7} +2.86713i q^{9} +(1.38194 + 1.38194i) q^{11} +(-1.57738 + 1.57738i) q^{13} +0.364518 q^{15} -5.96316 q^{17} +(1.21624 - 1.21624i) q^{19} +(0.257753 + 0.257753i) q^{21} -5.13213i q^{23} +1.00000i q^{25} +(-1.51227 - 1.51227i) q^{27} +(2.01670 - 2.01670i) q^{29} +0.281404 q^{31} -0.712398 q^{33} +(-0.707107 + 0.707107i) q^{35} +(-2.94960 - 2.94960i) q^{37} -0.813148i q^{39} +7.72404i q^{41} +(-7.82272 - 7.82272i) q^{43} +(2.02736 - 2.02736i) q^{45} +9.99428 q^{47} -1.00000 q^{49} +(1.53703 - 1.53703i) q^{51} +(-8.16967 - 8.16967i) q^{53} -1.95435i q^{55} +0.626981i q^{57} +(-4.52459 - 4.52459i) q^{59} +(-6.03179 + 6.03179i) q^{61} +2.86713 q^{63} +2.23075 q^{65} +(7.46295 - 7.46295i) q^{67} +(1.32282 + 1.32282i) q^{69} -4.27771i q^{71} +13.6272i q^{73} +(-0.257753 - 0.257753i) q^{75} +(1.38194 - 1.38194i) q^{77} -11.0714 q^{79} -7.82179 q^{81} +(-8.88257 + 8.88257i) q^{83} +(4.21659 + 4.21659i) q^{85} +1.03962i q^{87} -7.06029i q^{89} +(1.57738 + 1.57738i) q^{91} +(-0.0725329 + 0.0725329i) q^{93} -1.72003 q^{95} -16.4580 q^{97} +(-3.96219 + 3.96219i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q+O(q^{10}) $ 44 * q	$ 44 q - 12 q^{11} - 8 q^{15} - 8 q^{19} + 24 q^{27} + 12 q^{29} + 28 q^{37} + 44 q^{43} - 44 q^{49} + 8 q^{51} - 12 q^{53} - 24 q^{59} - 16 q^{61} - 28 q^{63} - 40 q^{65} + 28 q^{67} + 40 q^{69} - 12 q^{77} + 16 q^{79} + 20 q^{81} + 16 q^{85} + 88 q^{93} + 32 q^{95} - 28 q^{99}+O(q^{100}) $ 44 * q - 12 * q^11 - 8 * q^15 - 8 * q^19 + 24 * q^27 + 12 * q^29 + 28 * q^37 + 44 * q^43 - 44 * q^49 + 8 * q^51 - 12 * q^53 - 24 * q^59 - 16 * q^61 - 28 * q^63 - 40 * q^65 + 28 * q^67 + 40 * q^69 - 12 * q^77 + 16 * q^79 + 20 * q^81 + 16 * q^85 + 88 * q^93 + 32 * q^95 - 28 * 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
$3$	−0.257753	+	0.257753i	−0.148814	+	0.148814i	−0.777588	−	0.628774i	$-0.783557\pi$
$3$	−0.257753	+	0.257753i	−0.148814	+	0.148814i	0.628774	+	0.777588i	$0.283557\pi$
$4$		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
$9$			2.86713i			0.955709i
$10$		0			0
$11$	1.38194	+	1.38194i	0.416670	+	0.416670i	0.884054	−	0.467385i	$-0.154804\pi$
$11$	1.38194	+	1.38194i	0.416670	+	0.416670i	−0.467385	+	0.884054i	$0.654804\pi$
$12$		0			0
$13$	−1.57738	+	1.57738i	−0.437485	+	0.437485i	−0.891165	−	0.453679i	$-0.850111\pi$
$13$	−1.57738	+	1.57738i	−0.437485	+	0.437485i	0.453679	+	0.891165i	$0.350111\pi$
$14$		0			0
$15$	0.364518			0.0941182
$16$		0			0
$17$	−5.96316			−1.44628			−0.723140	−	0.690702i	$-0.757302\pi$
$17$	−5.96316			−1.44628			−0.723140	+	0.690702i	$0.757302\pi$
$18$		0			0
$19$	1.21624	−	1.21624i	0.279025	−	0.279025i	−0.553695	−	0.832720i	$-0.686783\pi$
$19$	1.21624	−	1.21624i	0.279025	−	0.279025i	0.832720	+	0.553695i	$0.186783\pi$
$20$		0			0
$21$	0.257753	+	0.257753i	0.0562464	+	0.0562464i
$22$		0			0
$23$		−	5.13213i		−	1.07012i	−0.844813	−	0.535062i	$-0.820288\pi$
$23$		−	5.13213i		−	1.07012i	0.844813	−	0.535062i	$-0.179712\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$		0			0
$27$	−1.51227	−	1.51227i	−0.291037	−	0.291037i
$28$		0			0
$29$	2.01670	−	2.01670i	0.374492	−	0.374492i	−0.494618	−	0.869110i	$-0.664692\pi$
$29$	2.01670	−	2.01670i	0.374492	−	0.374492i	0.869110	+	0.494618i	$0.164692\pi$
$30$		0			0
$31$	0.281404			0.0505417			0.0252708	−	0.999681i	$-0.491955\pi$
$31$	0.281404			0.0505417			0.0252708	+	0.999681i	$0.491955\pi$
$32$		0			0
$33$	−0.712398			−0.124013
$34$		0			0
$35$	−0.707107	+	0.707107i	−0.119523	+	0.119523i
$36$		0			0
$37$	−2.94960	−	2.94960i	−0.484912	−	0.484912i	0.421784	−	0.906696i	$-0.361404\pi$
$37$	−2.94960	−	2.94960i	−0.484912	−	0.484912i	−0.906696	+	0.421784i	$0.861404\pi$
$38$		0			0
$39$		−	0.813148i		−	0.130208i
$40$		0			0
$41$			7.72404i			1.20629i	0.797631	+	0.603146i	$0.206086\pi$
$41$			7.72404i			1.20629i	−0.797631	+	0.603146i	$0.793914\pi$
$42$		0			0
$43$	−7.82272	−	7.82272i	−1.19295	−	1.19295i	−0.976234	−	0.216720i	$-0.930464\pi$
$43$	−7.82272	−	7.82272i	−1.19295	−	1.19295i	−0.216720	−	0.976234i	$-0.569536\pi$
$44$		0			0
$45$	2.02736	−	2.02736i	0.302222	−	0.302222i
$46$		0			0
$47$	9.99428			1.45782			0.728908	−	0.684612i	$-0.240028\pi$
$47$	9.99428			1.45782			0.728908	+	0.684612i	$0.240028\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	1.53703	−	1.53703i	0.215227	−	0.215227i
$52$		0			0
$53$	−8.16967	−	8.16967i	−1.12219	−	1.12219i	−0.991412	−	0.130779i	$-0.958252\pi$
$53$	−8.16967	−	8.16967i	−1.12219	−	1.12219i	−0.130779	−	0.991412i	$-0.541748\pi$
$54$		0			0
$55$		−	1.95435i		−	0.263525i
$56$		0			0
$57$			0.626981i			0.0830457i
$58$		0			0
$59$	−4.52459	−	4.52459i	−0.589051	−	0.589051i	0.348323	−	0.937374i	$-0.386751\pi$
$59$	−4.52459	−	4.52459i	−0.589051	−	0.589051i	−0.937374	+	0.348323i	$0.886751\pi$
$60$		0			0
$61$	−6.03179	+	6.03179i	−0.772292	+	0.772292i	−0.978507	−	0.206215i	$-0.933885\pi$
$61$	−6.03179	+	6.03179i	−0.772292	+	0.772292i	0.206215	+	0.978507i	$0.433885\pi$
$62$		0			0
$63$	2.86713			0.361224
$64$		0			0
$65$	2.23075			0.276690
$66$		0			0
$67$	7.46295	−	7.46295i	0.911744	−	0.911744i	−0.0846651	−	0.996409i	$-0.526982\pi$
$67$	7.46295	−	7.46295i	0.911744	−	0.911744i	0.996409	+	0.0846651i	$0.0269820\pi$
$68$		0			0
$69$	1.32282	+	1.32282i	0.159249	+	0.159249i
$70$		0			0
$71$		−	4.27771i		−	0.507671i	−0.967247	−	0.253835i	$-0.918308\pi$
$71$		−	4.27771i		−	0.507671i	0.967247	−	0.253835i	$-0.0816921\pi$
$72$		0			0
$73$			13.6272i			1.59494i	0.603360	+	0.797469i	$0.293828\pi$
$73$			13.6272i			1.59494i	−0.603360	+	0.797469i	$0.706172\pi$
$74$		0			0
$75$	−0.257753	−	0.257753i	−0.0297628	−	0.0297628i
$76$		0			0
$77$	1.38194	−	1.38194i	0.157486	−	0.157486i
$78$		0			0
$79$	−11.0714			−1.24563			−0.622814	−	0.782370i	$-0.714011\pi$
$79$	−11.0714			−1.24563			−0.622814	+	0.782370i	$0.714011\pi$
$80$		0			0
$81$	−7.82179			−0.869088
$82$		0			0
$83$	−8.88257	+	8.88257i	−0.974989	+	0.974989i	−0.999695	−	0.0247058i	$-0.992135\pi$
$83$	−8.88257	+	8.88257i	−0.974989	+	0.974989i	0.0247058	+	0.999695i	$0.492135\pi$
$84$		0			0
$85$	4.21659	+	4.21659i	0.457354	+	0.457354i
$86$		0			0
$87$			1.03962i			0.111459i
$88$		0			0
$89$		−	7.06029i		−	0.748389i	−0.927350	−	0.374195i	$-0.877919\pi$
$89$		−	7.06029i		−	0.748389i	0.927350	−	0.374195i	$-0.122081\pi$
$90$		0			0
$91$	1.57738	+	1.57738i	0.165354	+	0.165354i
$92$		0			0
$93$	−0.0725329	+	0.0725329i	−0.00752131	+	0.00752131i
$94$		0			0
$95$	−1.72003			−0.176471
$96$		0			0
$97$	−16.4580			−1.67105			−0.835527	−	0.549449i	$-0.814838\pi$
$97$	−16.4580			−1.67105			−0.835527	+	0.549449i	$0.814838\pi$
$98$		0			0
$99$	−3.96219	+	3.96219i	−0.398215	+	0.398215i
$100$		0			0
$101$	−3.91060	−	3.91060i	−0.389120	−	0.389120i	0.485254	−	0.874373i	$-0.338727\pi$
$101$	−3.91060	−	3.91060i	−0.389120	−	0.389120i	−0.874373	+	0.485254i	$0.838727\pi$
$102$		0			0
$103$			14.4201i			1.42085i	0.703770	+	0.710427i	$0.251498\pi$
$103$			14.4201i			1.42085i	−0.703770	+	0.710427i	$0.748502\pi$
$104$		0			0
$105$		−	0.364518i		−	0.0355734i
$106$		0			0
$107$	−11.4699	−	11.4699i	−1.10884	−	1.10884i	−0.993303	−	0.115538i	$-0.963141\pi$
$107$	−11.4699	−	11.4699i	−1.10884	−	1.10884i	−0.115538	−	0.993303i	$-0.536859\pi$
$108$		0			0
$109$	7.14502	−	7.14502i	0.684369	−	0.684369i	−0.276612	−	0.960982i	$-0.589212\pi$
$109$	7.14502	−	7.14502i	0.684369	−	0.684369i	0.960982	+	0.276612i	$0.0892118\pi$
$110$		0			0
$111$	1.52054			0.144323
$112$		0			0
$113$	0.797627			0.0750344			0.0375172	−	0.999296i	$-0.488055\pi$
$113$	0.797627			0.0750344			0.0375172	+	0.999296i	$0.488055\pi$
$114$		0			0
$115$	−3.62896	+	3.62896i	−0.338403	+	0.338403i
$116$		0			0
$117$	−4.52254	−	4.52254i	−0.418109	−	0.418109i
$118$		0			0
$119$			5.96316i			0.546642i
$120$		0			0
$121$		−	7.18050i		−	0.652773i
$122$		0			0
$123$	−1.99090	−	1.99090i	−0.179513	−	0.179513i
$124$		0			0
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$		0			0
$127$	−11.4382			−1.01498			−0.507489	−	0.861658i	$-0.669426\pi$
$127$	−11.4382			−1.01498			−0.507489	+	0.861658i	$0.669426\pi$
$128$		0			0
$129$	4.03267			0.355056
$130$		0			0
$131$	0.670252	−	0.670252i	0.0585602	−	0.0585602i	−0.677220	−	0.735780i	$-0.736816\pi$
$131$	0.670252	−	0.670252i	0.0585602	−	0.0585602i	0.735780	+	0.677220i	$0.236816\pi$
$132$		0			0
$133$	−1.21624	−	1.21624i	−0.105462	−	0.105462i
$134$		0			0
$135$			2.13868i			0.184068i
$136$		0			0
$137$		−	6.21865i		−	0.531295i	−0.964070	−	0.265648i	$-0.914414\pi$
$137$		−	6.21865i		−	0.531295i	0.964070	−	0.265648i	$-0.0855858\pi$
$138$		0			0
$139$	−6.26453	−	6.26453i	−0.531350	−	0.531350i	0.389624	−	0.920974i	$-0.372605\pi$
$139$	−6.26453	−	6.26453i	−0.531350	−	0.531350i	−0.920974	+	0.389624i	$0.872605\pi$
$140$		0			0
$141$	−2.57606	+	2.57606i	−0.216943	+	0.216943i
$142$		0			0
$143$	−4.35967			−0.364574
$144$		0			0
$145$	−2.85205			−0.236850
$146$		0			0
$147$	0.257753	−	0.257753i	0.0212591	−	0.0212591i
$148$		0			0
$149$	−8.46225	−	8.46225i	−0.693255	−	0.693255i	0.269692	−	0.962947i	$-0.413078\pi$
$149$	−8.46225	−	8.46225i	−0.693255	−	0.693255i	−0.962947	+	0.269692i	$0.913078\pi$
$150$		0			0
$151$			8.10659i			0.659705i	0.944033	+	0.329852i	$0.106999\pi$
$151$			8.10659i			0.659705i	−0.944033	+	0.329852i	$0.893001\pi$
$152$		0			0
$153$		−	17.0971i		−	1.38222i
$154$		0			0
$155$	−0.198983	−	0.198983i	−0.0159827	−	0.0159827i
$156$		0			0
$157$	10.0691	−	10.0691i	0.803603	−	0.803603i	−0.180054	−	0.983657i	$-0.557627\pi$
$157$	10.0691	−	10.0691i	0.803603	−	0.803603i	0.983657	+	0.180054i	$0.0576271\pi$
$158$		0			0
$159$	4.21152			0.333995
$160$		0			0
$161$	−5.13213			−0.404469
$162$		0			0
$163$	−5.22762	+	5.22762i	−0.409459	+	0.409459i	−0.881550	−	0.472091i	$-0.843499\pi$
$163$	−5.22762	+	5.22762i	−0.409459	+	0.409459i	0.472091	+	0.881550i	$0.343499\pi$
$164$		0			0
$165$	0.503741	+	0.503741i	0.0392162	+	0.0392162i
$166$		0			0
$167$			0.0647600i			0.00501128i	0.999997	+	0.00250564i	$0.000797570\pi$
$167$			0.0647600i			0.00501128i	−0.999997	+	0.00250564i	$0.999202\pi$
$168$		0			0
$169$			8.02377i			0.617213i
$170$		0			0
$171$	3.48712	+	3.48712i	0.266667	+	0.266667i
$172$		0			0
$173$	9.17106	−	9.17106i	0.697263	−	0.697263i	−0.266557	−	0.963819i	$-0.585886\pi$
$173$	9.17106	−	9.17106i	0.697263	−	0.697263i	0.963819	+	0.266557i	$0.0858860\pi$
$174$		0			0
$175$	1.00000			0.0755929
$176$		0			0
$177$	2.33245			0.175318
$178$		0			0
$179$	−1.41773	+	1.41773i	−0.105966	+	0.105966i	−0.758102	−	0.652136i	$-0.773873\pi$
$179$	−1.41773	+	1.41773i	−0.105966	+	0.105966i	0.652136	+	0.758102i	$0.273873\pi$
$180$		0			0
$181$	3.71468	+	3.71468i	0.276110	+	0.276110i	0.831554	−	0.555444i	$-0.187452\pi$
$181$	3.71468	+	3.71468i	0.276110	+	0.276110i	−0.555444	+	0.831554i	$0.687452\pi$
$182$		0			0
$183$		−	3.10943i		−	0.229856i
$184$		0			0
$185$			4.17137i			0.306685i
$186$		0			0
$187$	−8.24071	−	8.24071i	−0.602621	−	0.602621i
$188$		0			0
$189$	−1.51227	+	1.51227i	−0.110002	+	0.110002i
$190$		0			0
$191$	13.0454			0.943936			0.471968	−	0.881616i	$-0.343544\pi$
$191$	13.0454			0.943936			0.471968	+	0.881616i	$0.343544\pi$
$192$		0			0
$193$	7.34722			0.528864			0.264432	−	0.964404i	$-0.414816\pi$
$193$	7.34722			0.528864			0.264432	+	0.964404i	$0.414816\pi$
$194$		0			0
$195$	−0.574983	+	0.574983i	−0.0411754	+	0.0411754i
$196$		0			0
$197$	6.58204	+	6.58204i	0.468951	+	0.468951i	0.901575	−	0.432624i	$-0.142412\pi$
$197$	6.58204	+	6.58204i	0.468951	+	0.468951i	−0.432624	+	0.901575i	$0.642412\pi$
$198$		0			0
$199$		−	11.4790i		−	0.813722i	−0.913490	−	0.406861i	$-0.866623\pi$
$199$		−	11.4790i		−	0.813722i	0.913490	−	0.406861i	$-0.133377\pi$
$200$		0			0
$201$			3.84720i			0.271361i
$202$		0			0
$203$	−2.01670	−	2.01670i	−0.141545	−	0.141545i
$204$		0			0
$205$	5.46172	−	5.46172i	0.381463	−	0.381463i
$206$		0			0
$207$	14.7145			1.02273
$208$		0			0
$209$	3.36154			0.232523
$210$		0			0
$211$	−2.97800	+	2.97800i	−0.205014	+	0.205014i	−0.802144	−	0.597130i	$-0.796308\pi$
$211$	−2.97800	+	2.97800i	−0.205014	+	0.205014i	0.597130	+	0.802144i	$0.296308\pi$
$212$		0			0
$213$	1.10259	+	1.10259i	0.0755485	+	0.0755485i
$214$		0			0
$215$			11.0630i			0.754490i
$216$		0			0
$217$		−	0.281404i		−	0.0191030i
$218$		0			0
$219$	−3.51245	−	3.51245i	−0.237349	−	0.237349i
$220$		0			0
$221$	9.40615	−	9.40615i	0.632726	−	0.632726i
$222$		0			0
$223$	6.33449			0.424189			0.212094	−	0.977249i	$-0.431972\pi$
$223$	6.33449			0.424189			0.212094	+	0.977249i	$0.431972\pi$
$224$		0			0
$225$	−2.86713			−0.191142
$226$		0			0
$227$	2.96460	−	2.96460i	0.196767	−	0.196767i	−0.601845	−	0.798613i	$-0.705568\pi$
$227$	2.96460	−	2.96460i	0.196767	−	0.196767i	0.798613	+	0.601845i	$0.205568\pi$
$228$		0			0
$229$	−7.91983	−	7.91983i	−0.523357	−	0.523357i	0.395226	−	0.918584i	$-0.370666\pi$
$229$	−7.91983	−	7.91983i	−0.523357	−	0.523357i	−0.918584	+	0.395226i	$0.870666\pi$
$230$		0			0
$231$			0.712398i			0.0468723i
$232$		0			0
$233$			16.4309i			1.07643i	0.842809	+	0.538213i	$0.180900\pi$
$233$			16.4309i			1.07643i	−0.842809	+	0.538213i	$0.819100\pi$
$234$		0			0
$235$	−7.06702	−	7.06702i	−0.461002	−	0.461002i
$236$		0			0
$237$	2.85369	−	2.85369i	0.185367	−	0.185367i
$238$		0			0
$239$	−4.99610			−0.323171			−0.161585	−	0.986859i	$-0.551661\pi$
$239$	−4.99610			−0.323171			−0.161585	+	0.986859i	$0.551661\pi$
$240$		0			0
$241$	−25.0372			−1.61279			−0.806395	−	0.591377i	$-0.798584\pi$
$241$	−25.0372			−1.61279			−0.806395	+	0.591377i	$0.798584\pi$
$242$		0			0
$243$	6.55291	−	6.55291i	0.420369	−	0.420369i
$244$		0			0
$245$	0.707107	+	0.707107i	0.0451754	+	0.0451754i
$246$		0			0
$247$			3.83694i			0.244139i
$248$		0			0
$249$		−	4.57903i		−	0.290184i
$250$		0			0
$251$	1.70718	+	1.70718i	0.107757	+	0.107757i	0.758929	−	0.651173i	$-0.225723\pi$
$251$	1.70718	+	1.70718i	0.107757	+	0.107757i	−0.651173	+	0.758929i	$0.725723\pi$
$252$		0			0
$253$	7.09228	−	7.09228i	0.445888	−	0.445888i
$254$		0			0
$255$	−2.17368			−0.136121
$256$		0			0
$257$	3.81388			0.237904			0.118952	−	0.992900i	$-0.462047\pi$
$257$	3.81388			0.237904			0.118952	+	0.992900i	$0.462047\pi$
$258$		0			0
$259$	−2.94960	+	2.94960i	−0.183280	+	0.183280i
$260$		0			0
$261$	5.78214	+	5.78214i	0.357906	+	0.357906i
$262$		0			0
$263$		−	25.1430i		−	1.55039i	−0.631725	−	0.775193i	$-0.717653\pi$
$263$		−	25.1430i		−	1.55039i	0.631725	−	0.775193i	$-0.282347\pi$
$264$		0			0
$265$			11.5537i			0.709736i
$266$		0			0
$267$	1.81981	+	1.81981i	0.111371	+	0.111371i
$268$		0			0
$269$	−7.69282	+	7.69282i	−0.469040	+	0.469040i	−0.901603	−	0.432564i	$-0.857609\pi$
$269$	−7.69282	+	7.69282i	−0.469040	+	0.469040i	0.432564	+	0.901603i	$0.357609\pi$
$270$		0			0
$271$	13.5774			0.824768			0.412384	−	0.911010i	$-0.364696\pi$
$271$	13.5774			0.824768			0.412384	+	0.911010i	$0.364696\pi$
$272$		0			0
$273$	−0.813148			−0.0492140
$274$		0			0
$275$	−1.38194	+	1.38194i	−0.0833339	+	0.0833339i
$276$		0			0
$277$	−12.7584	−	12.7584i	−0.766577	−	0.766577i	0.210925	−	0.977502i	$-0.432352\pi$
$277$	−12.7584	−	12.7584i	−0.766577	−	0.766577i	−0.977502	+	0.210925i	$0.932352\pi$
$278$		0			0
$279$			0.806821i			0.0483031i
$280$		0			0
$281$			31.8610i			1.90067i	0.311228	+	0.950335i	$0.399260\pi$
$281$			31.8610i			1.90067i	−0.311228	+	0.950335i	$0.600740\pi$
$282$		0			0
$283$	8.91622	+	8.91622i	0.530014	+	0.530014i	0.920576	−	0.390562i	$-0.127719\pi$
$283$	8.91622	+	8.91622i	0.530014	+	0.530014i	−0.390562	+	0.920576i	$0.627719\pi$
$284$		0			0
$285$	0.443343	−	0.443343i	0.0262613	−	0.0262613i
$286$		0			0
$287$	7.72404			0.455936
$288$		0			0
$289$	18.5593			1.09172
$290$		0			0
$291$	4.24210	−	4.24210i	0.248676	−	0.248676i
$292$		0			0
$293$	−1.92076	−	1.92076i	−0.112212	−	0.112212i	0.648771	−	0.760983i	$-0.275283\pi$
$293$	−1.92076	−	1.92076i	−0.112212	−	0.112212i	−0.760983	+	0.648771i	$0.775283\pi$
$294$		0			0
$295$			6.39873i			0.372549i
$296$		0			0
$297$		−	4.17973i		−	0.242532i
$298$		0			0
$299$	8.09530	+	8.09530i	0.468163	+	0.468163i
$300$		0			0
$301$	−7.82272	+	7.82272i	−0.450894	+	0.450894i
$302$		0			0
$303$	2.01594			0.115813
$304$		0			0
$305$	8.53025			0.488440
$306$		0			0
$307$	−18.2687	+	18.2687i	−1.04265	+	1.04265i	−0.0436014	+	0.999049i	$0.513883\pi$
$307$	−18.2687	+	18.2687i	−1.04265	+	1.04265i	−0.999049	+	0.0436014i	$0.986117\pi$
$308$		0			0
$309$	−3.71683	−	3.71683i	−0.211443	−	0.211443i
$310$		0			0
$311$			20.4200i			1.15791i	0.815360	+	0.578955i	$0.196539\pi$
$311$			20.4200i			1.15791i	−0.815360	+	0.578955i	$0.803461\pi$
$312$		0			0
$313$		−	17.6594i		−	0.998170i	−0.866553	−	0.499085i	$-0.833669\pi$
$313$		−	17.6594i		−	0.998170i	0.866553	−	0.499085i	$-0.166331\pi$
$314$		0			0
$315$	−2.02736	−	2.02736i	−0.114229	−	0.114229i
$316$		0			0
$317$	7.03099	−	7.03099i	0.394900	−	0.394900i	−0.481530	−	0.876430i	$-0.659919\pi$
$317$	7.03099	−	7.03099i	0.394900	−	0.394900i	0.876430	+	0.481530i	$0.159919\pi$
$318$		0			0
$319$	5.57391			0.312079
$320$		0			0
$321$	5.91283			0.330022
$322$		0			0
$323$	−7.25265	+	7.25265i	−0.403548	+	0.403548i
$324$		0			0
$325$	−1.57738	−	1.57738i	−0.0874971	−	0.0874971i
$326$		0			0
$327$			3.68331i			0.203687i
$328$		0			0
$329$		−	9.99428i		−	0.551003i
$330$		0			0
$331$	4.85584	+	4.85584i	0.266901	+	0.266901i	0.827850	−	0.560949i	$-0.189564\pi$
$331$	4.85584	+	4.85584i	0.266901	+	0.266901i	−0.560949	+	0.827850i	$0.689564\pi$
$332$		0			0
$333$	8.45689	−	8.45689i	0.463435	−	0.463435i
$334$		0			0
$335$	−10.5542			−0.576638
$336$		0			0
$337$	−13.0779			−0.712397			−0.356199	−	0.934410i	$-0.615927\pi$
$337$	−13.0779			−0.712397			−0.356199	+	0.934410i	$0.615927\pi$
$338$		0			0
$339$	−0.205591	+	0.205591i	−0.0111662	+	0.0111662i
$340$		0			0
$341$	0.388883	+	0.388883i	0.0210592	+	0.0210592i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$		−	1.87076i		−	0.100718i
$346$		0			0
$347$	−22.9346	−	22.9346i	−1.23119	−	1.23119i	−0.963506	−	0.267685i	$-0.913741\pi$
$347$	−22.9346	−	22.9346i	−1.23119	−	1.23119i	−0.267685	−	0.963506i	$-0.586259\pi$
$348$		0			0
$349$	−17.4280	+	17.4280i	−0.932902	+	0.932902i	−0.997886	−	0.0649843i	$-0.979300\pi$
$349$	−17.4280	+	17.4280i	−0.932902	+	0.932902i	0.0649843	+	0.997886i	$0.479300\pi$
$350$		0			0
$351$	4.77084			0.254649
$352$		0			0
$353$	8.19586			0.436222			0.218111	−	0.975924i	$-0.430011\pi$
$353$	8.19586			0.436222			0.218111	+	0.975924i	$0.430011\pi$
$354$		0			0
$355$	−3.02480	+	3.02480i	−0.160540	+	0.160540i
$356$		0			0
$357$	−1.53703	−	1.53703i	−0.0813480	−	0.0813480i
$358$		0			0
$359$		−	10.2803i		−	0.542572i	−0.962499	−	0.271286i	$-0.912551\pi$
$359$		−	10.2803i		−	0.542572i	0.962499	−	0.271286i	$-0.0874490\pi$
$360$		0			0
$361$			16.0415i			0.844290i
$362$		0			0
$363$	1.85080	+	1.85080i	0.0971418	+	0.0971418i
$364$		0			0
$365$	9.63586	−	9.63586i	0.504364	−	0.504364i
$366$		0			0
$367$	−1.95256			−0.101923			−0.0509614	−	0.998701i	$-0.516229\pi$
$367$	−1.95256			−0.101923			−0.0509614	+	0.998701i	$0.516229\pi$
$368$		0			0
$369$	−22.1458			−1.15286
$370$		0			0
$371$	−8.16967	+	8.16967i	−0.424148	+	0.424148i
$372$		0			0
$373$	26.5872	+	26.5872i	1.37663	+	1.37663i	0.850244	+	0.526389i	$0.176454\pi$
$373$	26.5872	+	26.5872i	1.37663	+	1.37663i	0.526389	+	0.850244i	$0.323546\pi$
$374$		0			0
$375$			0.364518i			0.0188236i
$376$		0			0
$377$			6.36220i			0.327670i
$378$		0			0
$379$	20.9913	+	20.9913i	1.07825	+	1.07825i	0.996667	+	0.0815821i	$0.0259973\pi$
$379$	20.9913	+	20.9913i	1.07825	+	1.07825i	0.0815821	+	0.996667i	$0.474003\pi$
$380$		0			0
$381$	2.94824	−	2.94824i	0.151043	−	0.151043i
$382$		0			0
$383$	1.49852			0.0765708			0.0382854	−	0.999267i	$-0.487810\pi$
$383$	1.49852			0.0765708			0.0382854	+	0.999267i	$0.487810\pi$
$384$		0			0
$385$	−1.95435			−0.0996031
$386$		0			0
$387$	22.4287	−	22.4287i	1.14012	−	1.14012i
$388$		0			0
$389$	3.86346	+	3.86346i	0.195885	+	0.195885i	0.798233	−	0.602348i	$-0.205768\pi$
$389$	3.86346	+	3.86346i	0.195885	+	0.195885i	−0.602348	+	0.798233i	$0.705768\pi$
$390$		0			0
$391$			30.6037i			1.54770i
$392$		0			0
$393$			0.345519i			0.0174291i
$394$		0			0
$395$	7.82866	+	7.82866i	0.393902	+	0.393902i
$396$		0			0
$397$	0.326356	−	0.326356i	0.0163793	−	0.0163793i	−0.698870	−	0.715249i	$-0.746313\pi$
$397$	0.326356	−	0.326356i	0.0163793	−	0.0163793i	0.715249	+	0.698870i	$0.246313\pi$
$398$		0			0
$399$	0.626981			0.0313883
$400$		0			0
$401$	20.4461			1.02103			0.510516	−	0.859868i	$-0.329454\pi$
$401$	20.4461			1.02103			0.510516	+	0.859868i	$0.329454\pi$
$402$		0			0
$403$	−0.443880	+	0.443880i	−0.0221112	+	0.0221112i
$404$		0			0
$405$	5.53084	+	5.53084i	0.274830	+	0.274830i
$406$		0			0
$407$		−	8.15233i		−	0.404096i
$408$		0			0
$409$			19.5611i			0.967236i	0.875279	+	0.483618i	$0.160678\pi$
$409$			19.5611i			0.967236i	−0.875279	+	0.483618i	$0.839322\pi$
$410$		0			0
$411$	1.60288	+	1.60288i	0.0790642	+	0.0790642i
$412$		0			0
$413$	−4.52459	+	4.52459i	−0.222640	+	0.222640i
$414$		0			0
$415$	12.5619			0.616637
$416$		0			0
$417$	3.22941			0.158145
$418$		0			0
$419$	−1.57711	+	1.57711i	−0.0770467	+	0.0770467i	−0.744580	−	0.667533i	$-0.767350\pi$
$419$	−1.57711	+	1.57711i	−0.0770467	+	0.0770467i	0.667533	+	0.744580i	$0.267350\pi$
$420$		0			0
$421$	17.6868	+	17.6868i	0.862001	+	0.862001i	0.991570	−	0.129569i	$-0.0413595\pi$
$421$	17.6868	+	17.6868i	0.862001	+	0.862001i	−0.129569	+	0.991570i	$0.541360\pi$
$422$		0			0
$423$			28.6549i			1.39325i
$424$		0			0
$425$		−	5.96316i		−	0.289256i
$426$		0			0
$427$	6.03179	+	6.03179i	0.291899	+	0.291899i
$428$		0			0
$429$	1.12372	−	1.12372i	0.0542537	−	0.0542537i
$430$		0			0
$431$	19.5218			0.940331			0.470166	−	0.882578i	$-0.344194\pi$
$431$	19.5218			0.940331			0.470166	+	0.882578i	$0.344194\pi$
$432$		0			0
$433$	27.5661			1.32474			0.662371	−	0.749176i	$-0.269550\pi$
$433$	27.5661			1.32474			0.662371	+	0.749176i	$0.269550\pi$
$434$		0			0
$435$	0.735125	−	0.735125i	0.0352466	−	0.0352466i
$436$		0			0
$437$	−6.24191	−	6.24191i	−0.298591	−	0.298591i
$438$		0			0
$439$		−	41.1009i		−	1.96164i	−0.194912	−	0.980821i	$-0.562442\pi$
$439$		−	41.1009i		−	1.96164i	0.194912	−	0.980821i	$-0.437558\pi$
$440$		0			0
$441$		−	2.86713i		−	0.136530i
$442$		0			0
$443$	−24.1574	−	24.1574i	−1.14775	−	1.14775i	−0.986994	−	0.160758i	$-0.948606\pi$
$443$	−24.1574	−	24.1574i	−1.14775	−	1.14775i	−0.160758	−	0.986994i	$-0.551394\pi$
$444$		0			0
$445$	−4.99238	+	4.99238i	−0.236662	+	0.236662i
$446$		0			0
$447$	4.36235			0.206332
$448$		0			0
$449$	1.57581			0.0743671			0.0371836	−	0.999308i	$-0.488161\pi$
$449$	1.57581			0.0743671			0.0371836	+	0.999308i	$0.488161\pi$
$450$		0			0
$451$	−10.6741	+	10.6741i	−0.502625	+	0.502625i
$452$		0			0
$453$	−2.08950	−	2.08950i	−0.0981733	−	0.0981733i
$454$		0			0
$455$		−	2.23075i		−	0.104579i
$456$		0			0
$457$			0.401436i			0.0187784i	0.999956	+	0.00938918i	$0.00298871\pi$
$457$			0.401436i			0.0187784i	−0.999956	+	0.00938918i	$0.997011\pi$
$458$		0			0
$459$	9.01792	+	9.01792i	0.420921	+	0.420921i
$460$		0			0
$461$	−12.7001	+	12.7001i	−0.591504	+	0.591504i	−0.938038	−	0.346533i	$-0.887359\pi$
$461$	−12.7001	+	12.7001i	−0.591504	+	0.591504i	0.346533	+	0.938038i	$0.387359\pi$
$462$		0			0
$463$	−26.8151			−1.24620			−0.623101	−	0.782142i	$-0.714127\pi$
$463$	−26.8151			−1.24620			−0.623101	+	0.782142i	$0.714127\pi$
$464$		0			0
$465$	0.102577			0.00475689
$466$		0			0
$467$	22.5425	−	22.5425i	1.04314	−	1.04314i	0.0441137	−	0.999027i	$-0.485954\pi$
$467$	22.5425	−	22.5425i	1.04314	−	1.04314i	0.999027	−	0.0441137i	$-0.0140464\pi$
$468$		0			0
$469$	−7.46295	−	7.46295i	−0.344607	−	0.344607i
$470$		0			0
$471$			5.19070i			0.239175i
$472$		0			0
$473$		−	21.6210i		−	0.994135i
$474$		0			0
$475$	1.21624	+	1.21624i	0.0558050	+	0.0558050i
$476$		0			0
$477$	23.4235	−	23.4235i	1.07249	−	1.07249i
$478$		0			0
$479$	5.87740			0.268545			0.134273	−	0.990944i	$-0.457130\pi$
$479$	5.87740			0.268545			0.134273	+	0.990944i	$0.457130\pi$
$480$		0			0
$481$	9.30527			0.424284
$482$		0			0
$483$	1.32282	−	1.32282i	0.0601906	−	0.0601906i
$484$		0			0
$485$	11.6375	+	11.6375i	0.528434	+	0.528434i
$486$		0			0
$487$			23.4101i			1.06081i	0.847744	+	0.530406i	$0.177960\pi$
$487$			23.4101i			1.06081i	−0.847744	+	0.530406i	$0.822040\pi$
$488$		0			0
$489$		−	2.69488i		−	0.121866i
$490$		0			0
$491$	2.04092	+	2.04092i	0.0921054	+	0.0921054i	0.751658	−	0.659553i	$-0.229254\pi$
$491$	2.04092	+	2.04092i	0.0921054	+	0.0921054i	−0.659553	+	0.751658i	$0.729254\pi$
$492$		0			0
$493$	−12.0259	+	12.0259i	−0.541621	+	0.541621i
$494$		0			0
$495$	5.60338			0.251853
$496$		0			0
$497$	−4.27771			−0.191881
$498$		0			0
$499$	−13.9574	+	13.9574i	−0.624819	+	0.624819i	−0.946760	−	0.321941i	$-0.895665\pi$
$499$	−13.9574	+	13.9574i	−0.624819	+	0.624819i	0.321941	+	0.946760i	$0.395665\pi$
$500$		0			0
$501$	−0.0166921	−	0.0166921i	−0.000745748	−	0.000745748i
$502$		0			0
$503$			9.88683i			0.440832i	0.975406	+	0.220416i	$0.0707415\pi$
$503$			9.88683i			0.440832i	−0.975406	+	0.220416i	$0.929259\pi$
$504$		0			0
$505$			5.53043i			0.246101i
$506$		0			0
$507$	−2.06815	−	2.06815i	−0.0918499	−	0.0918499i
$508$		0			0
$509$	13.3980	−	13.3980i	0.593854	−	0.593854i	−0.344816	−	0.938670i	$-0.612059\pi$
$509$	13.3980	−	13.3980i	0.593854	−	0.593854i	0.938670	+	0.344816i	$0.112059\pi$
$510$		0			0
$511$	13.6272			0.602830
$512$		0			0
$513$	−3.67858			−0.162413
$514$		0			0
$515$	10.1966	−	10.1966i	0.449314	−	0.449314i
$516$		0			0
$517$	13.8115	+	13.8115i	0.607427	+	0.607427i
$518$		0			0
$519$			4.72774i			0.207525i
$520$		0			0
$521$			2.34283i			0.102641i	0.998682	+	0.0513205i	$0.0163430\pi$
$521$			2.34283i			0.102641i	−0.998682	+	0.0513205i	$0.983657\pi$
$522$		0			0
$523$	1.51830	+	1.51830i	0.0663906	+	0.0663906i	0.739522	−	0.673132i	$-0.235051\pi$
$523$	1.51830	+	1.51830i	0.0663906	+	0.0663906i	−0.673132	+	0.739522i	$0.735051\pi$
$524$		0			0
$525$	−0.257753	+	0.257753i	−0.0112493	+	0.0112493i
$526$		0			0
$527$	−1.67806			−0.0730974
$528$		0			0
$529$	−3.33876			−0.145164
$530$		0			0
$531$	12.9726	−	12.9726i	0.562961	−	0.562961i
$532$		0			0
$533$	−12.1837	−	12.1837i	−0.527735	−	0.527735i
$534$		0			0
$535$			16.2209i			0.701293i
$536$		0			0
$537$		−	0.730850i		−	0.0315385i
$538$		0			0
$539$	−1.38194	−	1.38194i	−0.0595242	−	0.0595242i
$540$		0			0
$541$	−3.16195	+	3.16195i	−0.135943	+	0.135943i	−0.771804	−	0.635861i	$-0.780645\pi$
$541$	−3.16195	+	3.16195i	−0.135943	+	0.135943i	0.635861	+	0.771804i	$0.280645\pi$
$542$		0			0
$543$	−1.91494			−0.0821781
$544$		0			0
$545$	−10.1046			−0.432833
$546$		0			0
$547$	9.93939	−	9.93939i	0.424978	−	0.424978i	−0.461936	−	0.886913i	$-0.652845\pi$
$547$	9.93939	−	9.93939i	0.424978	−	0.424978i	0.886913	+	0.461936i	$0.152845\pi$
$548$		0			0
$549$	−17.2939	−	17.2939i	−0.738086	−	0.738086i
$550$		0			0
$551$		−	4.90560i		−	0.208986i
$552$		0			0
$553$			11.0714i			0.470803i
$554$		0			0
$555$	−1.07519	−	1.07519i	−0.0456391	−	0.0456391i
$556$		0			0
$557$	17.3193	−	17.3193i	0.733844	−	0.733844i	−0.237535	−	0.971379i	$-0.576339\pi$
$557$	17.3193	−	17.3193i	0.733844	−	0.733844i	0.971379	+	0.237535i	$0.0763394\pi$
$558$		0			0
$559$	24.6787			1.04380
$560$		0			0
$561$	4.24814			0.179357
$562$		0			0
$563$	5.74177	−	5.74177i	0.241987	−	0.241987i	−0.575685	−	0.817672i	$-0.695265\pi$
$563$	5.74177	−	5.74177i	0.241987	−	0.241987i	0.817672	+	0.575685i	$0.195265\pi$
$564$		0			0
$565$	−0.564007	−	0.564007i	−0.0237280	−	0.0237280i
$566$		0			0
$567$			7.82179i			0.328484i
$568$		0			0
$569$		−	1.59834i		−	0.0670057i	−0.999439	−	0.0335029i	$-0.989334\pi$
$569$		−	1.59834i		−	0.0670057i	0.999439	−	0.0335029i	$-0.0106663\pi$
$570$		0			0
$571$	17.0244	+	17.0244i	0.712447	+	0.712447i	0.967047	−	0.254599i	$-0.0819436\pi$
$571$	17.0244	+	17.0244i	0.712447	+	0.712447i	−0.254599	+	0.967047i	$0.581944\pi$
$572$		0			0
$573$	−3.36251	+	3.36251i	−0.140471	+	0.140471i
$574$		0			0
$575$	5.13213			0.214025
$576$		0			0
$577$	−34.0239			−1.41643			−0.708216	−	0.705996i	$-0.750500\pi$
$577$	−34.0239			−1.41643			−0.708216	+	0.705996i	$0.750500\pi$
$578$		0			0
$579$	−1.89377	+	1.89377i	−0.0787024	+	0.0787024i
$580$		0			0
$581$	8.88257	+	8.88257i	0.368511	+	0.368511i
$582$		0			0
$583$		−	22.5799i		−	0.935165i
$584$		0			0
$585$			6.39583i			0.264435i
$586$		0			0
$587$	−31.8543	−	31.8543i	−1.31477	−	1.31477i	−0.917858	−	0.396908i	$-0.870083\pi$
$587$	−31.8543	−	31.8543i	−1.31477	−	1.31477i	−0.396908	−	0.917858i	$-0.629917\pi$
$588$		0			0
$589$	0.342256	−	0.342256i	0.0141024	−	0.0141024i
$590$		0			0
$591$	−3.39309			−0.139573
$592$		0			0
$593$	30.6744			1.25965			0.629823	−	0.776739i	$-0.283128\pi$
$593$	30.6744			1.25965			0.629823	+	0.776739i	$0.283128\pi$
$594$		0			0
$595$	4.21659	−	4.21659i	0.172863	−	0.172863i
$596$		0			0
$597$	2.95874	+	2.95874i	0.121093	+	0.121093i
$598$		0			0
$599$		−	48.0568i		−	1.96355i	−0.190058	−	0.981773i	$-0.560868\pi$
$599$		−	48.0568i		−	1.96355i	0.190058	−	0.981773i	$-0.439132\pi$
$600$		0			0
$601$			26.9547i			1.09950i	0.835328	+	0.549752i	$0.185278\pi$
$601$			26.9547i			1.09950i	−0.835328	+	0.549752i	$0.814722\pi$
$602$		0			0
$603$	21.3972	+	21.3972i	0.871362	+	0.871362i
$604$		0			0
$605$	−5.07738	+	5.07738i	−0.206425	+	0.206425i
$606$		0			0
$607$	6.16549			0.250250			0.125125	−	0.992141i	$-0.460067\pi$
$607$	6.16549			0.250250			0.125125	+	0.992141i	$0.460067\pi$
$608$		0			0
$609$	1.03962			0.0421277
$610$		0			0
$611$	−15.7647	+	15.7647i	−0.637773	+	0.637773i
$612$		0			0
$613$	16.8259	+	16.8259i	0.679591	+	0.679591i	0.959908	−	0.280316i	$-0.0904394\pi$
$613$	16.8259	+	16.8259i	0.679591	+	0.679591i	−0.280316	+	0.959908i	$0.590439\pi$
$614$		0			0
$615$			2.81555i			0.113534i
$616$		0			0
$617$			32.0148i			1.28887i	0.764661	+	0.644433i	$0.222907\pi$
$617$			32.0148i			1.28887i	−0.764661	+	0.644433i	$0.777093\pi$
$618$		0			0
$619$	19.4054	+	19.4054i	0.779968	+	0.779968i	0.979825	−	0.199857i	$-0.0640477\pi$
$619$	19.4054	+	19.4054i	0.779968	+	0.779968i	−0.199857	+	0.979825i	$0.564048\pi$
$620$		0			0
$621$	−7.76118	+	7.76118i	−0.311445	+	0.311445i
$622$		0			0
$623$	−7.06029			−0.282865
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$	−0.866448	+	0.866448i	−0.0346026	+	0.0346026i
$628$		0			0
$629$	17.5890	+	17.5890i	0.701318	+	0.701318i
$630$		0			0
$631$		−	11.8136i		−	0.470293i	−0.971960	−	0.235147i	$-0.924443\pi$
$631$		−	11.8136i		−	0.470293i	0.971960	−	0.235147i	$-0.0755570\pi$
$632$		0			0
$633$		−	1.53518i		−	0.0610179i
$634$		0			0
$635$	8.08805	+	8.08805i	0.320964	+	0.320964i
$636$		0			0
$637$	1.57738	−	1.57738i	0.0624979	−	0.0624979i
$638$		0			0
$639$	12.2647			0.485185
$640$		0			0
$641$	26.1343			1.03224			0.516120	−	0.856516i	$-0.327376\pi$
$641$	26.1343			1.03224			0.516120	+	0.856516i	$0.327376\pi$
$642$		0			0
$643$	−9.95856	+	9.95856i	−0.392727	+	0.392727i	−0.875658	−	0.482931i	$-0.839572\pi$
$643$	−9.95856	+	9.95856i	−0.392727	+	0.392727i	0.482931	+	0.875658i	$0.339572\pi$
$644$		0			0
$645$	−2.85153	−	2.85153i	−0.112279	−	0.112279i
$646$		0			0
$647$		−	32.9890i		−	1.29693i	−0.761244	−	0.648465i	$-0.775411\pi$
$647$		−	32.9890i		−	1.29693i	0.761244	−	0.648465i	$-0.224589\pi$
$648$		0			0
$649$		−	12.5054i		−	0.490879i
$650$		0			0
$651$	0.0725329	+	0.0725329i	0.00284279	+	0.00284279i
$652$		0			0
$653$	−0.218647	+	0.218647i	−0.00855631	+	0.00855631i	−0.711372	−	0.702816i	$-0.751926\pi$
$653$	−0.218647	+	0.218647i	−0.00855631	+	0.00855631i	0.702816	+	0.711372i	$0.251926\pi$
$654$		0			0
$655$	−0.947879			−0.0370367
$656$		0			0
$657$	−39.0708			−1.52430
$658$		0			0
$659$	20.5978	−	20.5978i	0.802376	−	0.802376i	−0.181090	−	0.983467i	$-0.557963\pi$
$659$	20.5978	−	20.5978i	0.802376	−	0.802376i	0.983467	+	0.181090i	$0.0579625\pi$
$660$		0			0
$661$	−20.0510	−	20.0510i	−0.779894	−	0.779894i	0.199919	−	0.979812i	$-0.435932\pi$
$661$	−20.0510	−	20.0510i	−0.779894	−	0.779894i	−0.979812	+	0.199919i	$0.935932\pi$
$662$		0			0
$663$			4.84893i			0.188317i
$664$		0			0
$665$			1.72003i			0.0666998i
$666$		0			0
$667$	−10.3500	−	10.3500i	−0.400753	−	0.400753i
$668$		0			0
$669$	−1.63274	+	1.63274i	−0.0631252	+	0.0631252i
$670$		0			0
$671$	−16.6711			−0.643581
$672$		0			0
$673$	−15.8838			−0.612276			−0.306138	−	0.951987i	$-0.599037\pi$
$673$	−15.8838			−0.612276			−0.306138	+	0.951987i	$0.599037\pi$
$674$		0			0
$675$	1.51227	−	1.51227i	0.0582074	−	0.0582074i
$676$		0			0
$677$	19.4466	+	19.4466i	0.747392	+	0.747392i	0.973989	−	0.226596i	$-0.0727598\pi$
$677$	19.4466	+	19.4466i	0.747392	+	0.747392i	−0.226596	+	0.973989i	$0.572760\pi$
$678$		0			0
$679$			16.4580i			0.631599i
$680$		0			0
$681$			1.52827i			0.0585635i
$682$		0			0
$683$	24.6237	+	24.6237i	0.942201	+	0.942201i	0.998419	−	0.0562176i	$-0.0179041\pi$
$683$	24.6237	+	24.6237i	0.942201	+	0.942201i	−0.0562176	+	0.998419i	$0.517904\pi$
$684$		0			0
$685$	−4.39725	+	4.39725i	−0.168010	+	0.168010i
$686$		0			0
$687$	4.08273			0.155766
$688$		0			0
$689$	25.7733			0.981884
$690$		0			0
$691$	0.0258183	−	0.0258183i	0.000982175	−	0.000982175i	−0.706616	−	0.707598i	$-0.749779\pi$
$691$	0.0258183	−	0.0258183i	0.000982175	−	0.000982175i	0.707598	+	0.706616i	$0.249779\pi$
$692$		0			0
$693$	3.96219	+	3.96219i	0.150511	+	0.150511i
$694$		0			0
$695$			8.85938i			0.336055i
$696$		0			0
$697$		−	46.0597i		−	1.74464i
$698$		0			0
$699$	−4.23513	−	4.23513i	−0.160187	−	0.160187i
$700$		0			0
$701$	−27.2969	+	27.2969i	−1.03099	+	1.03099i	−0.0314855	+	0.999504i	$0.510024\pi$
$701$	−27.2969	+	27.2969i	−1.03099	+	1.03099i	−0.999504	+	0.0314855i	$0.989976\pi$
$702$		0			0
$703$	−7.17487			−0.270605
$704$		0			0
$705$	3.64310			0.137207
$706$		0			0
$707$	−3.91060	+	3.91060i	−0.147073	+	0.147073i
$708$		0			0
$709$	2.14435	+	2.14435i	0.0805327	+	0.0805327i	0.746226	−	0.665693i	$-0.231864\pi$
$709$	2.14435	+	2.14435i	0.0805327	+	0.0805327i	−0.665693	+	0.746226i	$0.731864\pi$
$710$		0			0
$711$		−	31.7431i		−	1.19046i
$712$		0			0
$713$		−	1.44420i		−	0.0540858i
$714$		0			0
$715$	3.08275	+	3.08275i	0.115288	+	0.115288i
$716$		0			0
$717$	1.28776	−	1.28776i	0.0480923	−	0.0480923i
$718$		0			0
$719$	−14.6890			−0.547806			−0.273903	−	0.961757i	$-0.588315\pi$
$719$	−14.6890			−0.547806			−0.273903	+	0.961757i	$0.588315\pi$
$720$		0			0
$721$	14.4201			0.537033
$722$		0			0
$723$	6.45343	−	6.45343i	0.240006	−	0.240006i
$724$		0			0
$725$	2.01670	+	2.01670i	0.0748985	+	0.0748985i
$726$		0			0
$727$			36.9028i			1.36865i	0.729177	+	0.684325i	$0.239903\pi$
$727$			36.9028i			1.36865i	−0.729177	+	0.684325i	$0.760097\pi$
$728$		0			0
$729$		−	20.0873i		−	0.743974i
$730$		0			0
$731$	46.6481	+	46.6481i	1.72534	+	1.72534i
$732$		0			0
$733$	−34.7724	+	34.7724i	−1.28435	+	1.28435i	−0.346179	+	0.938169i	$0.612521\pi$
$733$	−34.7724	+	34.7724i	−1.28435	+	1.28435i	−0.938169	+	0.346179i	$0.887479\pi$
$734$		0			0
$735$	−0.364518			−0.0134455
$736$		0			0
$737$	20.6266			0.759792
$738$		0			0
$739$	31.5578	−	31.5578i	1.16087	−	1.16087i	0.176589	−	0.984285i	$-0.443494\pi$
$739$	31.5578	−	31.5578i	1.16087	−	1.16087i	0.984285	−	0.176589i	$-0.0565062\pi$
$740$		0			0
$741$	−0.988985	−	0.988985i	−0.0363313	−	0.0363313i
$742$		0			0
$743$		−	6.36321i		−	0.233443i	−0.993165	−	0.116722i	$-0.962761\pi$
$743$		−	6.36321i		−	0.233443i	0.993165	−	0.116722i	$-0.0372386\pi$
$744$		0			0
$745$			11.9674i			0.438453i
$746$		0			0
$747$	−25.4675	−	25.4675i	−0.931806	−	0.931806i
$748$		0			0
$749$	−11.4699	+	11.4699i	−0.419102	+	0.419102i
$750$		0			0
$751$	−16.1353			−0.588785			−0.294392	−	0.955685i	$-0.595117\pi$
$751$	−16.1353			−0.588785			−0.294392	+	0.955685i	$0.595117\pi$
$752$		0			0
$753$	−0.880065			−0.0320714
$754$		0			0
$755$	5.73222	−	5.73222i	0.208617	−	0.208617i
$756$		0			0
$757$	−31.9755	−	31.9755i	−1.16217	−	1.16217i	−0.984000	−	0.178171i	$-0.942982\pi$
$757$	−31.9755	−	31.9755i	−1.16217	−	1.16217i	−0.178171	−	0.984000i	$-0.557018\pi$
$758$		0			0
$759$			3.65612i			0.132709i
$760$		0			0
$761$		−	37.3773i		−	1.35493i	−0.735557	−	0.677463i	$-0.763079\pi$
$761$		−	37.3773i		−	1.35493i	0.735557	−	0.677463i	$-0.236921\pi$
$762$		0			0
$763$	−7.14502	−	7.14502i	−0.258667	−	0.258667i
$764$		0			0
$765$	−12.0895	+	12.0895i	−0.437097	+	0.437097i
$766$		0			0
$767$	14.2739			0.515402
$768$		0			0
$769$	42.8490			1.54517			0.772587	−	0.634909i	$-0.218962\pi$
$769$	42.8490			1.54517			0.772587	+	0.634909i	$0.218962\pi$
$770$		0			0
$771$	−0.983042	+	0.983042i	−0.0354034	+	0.0354034i
$772$		0			0
$773$	14.4423	+	14.4423i	0.519452	+	0.519452i	0.917406	−	0.397953i	$-0.130279\pi$
$773$	14.4423	+	14.4423i	0.519452	+	0.519452i	−0.397953	+	0.917406i	$0.630279\pi$
$774$		0			0
$775$			0.281404i			0.0101083i
$776$		0			0
$777$		−	1.52054i		−	0.0545491i
$778$		0			0
$779$	9.39430	+	9.39430i	0.336586	+	0.336586i
$780$		0			0
$781$	5.91152	−	5.91152i	0.211531	−	0.211531i
$782$		0			0
$783$	−6.09961			−0.217982
$784$		0			0
$785$	−14.2399			−0.508243
$786$		0			0
$787$	−4.53967	+	4.53967i	−0.161822	+	0.161822i	−0.783373	−	0.621551i	$-0.786503\pi$
$787$	−4.53967	+	4.53967i	−0.161822	+	0.161822i	0.621551	+	0.783373i	$0.286503\pi$
$788$		0			0
$789$	6.48070	+	6.48070i	0.230719	+	0.230719i
$790$		0			0
$791$		−	0.797627i		−	0.0283604i
$792$		0			0
$793$		−	19.0288i		−	0.675733i
$794$		0			0
$795$	−2.97799	−	2.97799i	−0.105619	−	0.105619i
$796$		0			0
$797$	−27.7921	+	27.7921i	−0.984448	+	0.984448i	−0.999881	−	0.0154331i	$-0.995087\pi$
$797$	−27.7921	+	27.7921i	−0.984448	+	0.984448i	0.0154331	+	0.999881i	$0.495087\pi$
$798$		0			0
$799$	−59.5975			−2.10841
$800$		0			0
$801$	20.2427			0.715242
$802$		0			0
$803$	−18.8319	+	18.8319i	−0.664562	+	0.664562i
$804$		0			0
$805$	3.62896	+	3.62896i	0.127904	+	0.127904i
$806$		0			0
$807$		−	3.96570i		−	0.139599i
$808$		0			0
$809$		−	30.8775i		−	1.08559i	−0.839864	−	0.542797i	$-0.817365\pi$
$809$		−	30.8775i		−	1.08559i	0.839864	−	0.542797i	$-0.182635\pi$
$810$		0			0
$811$	−3.81141	−	3.81141i	−0.133837	−	0.133837i	0.637015	−	0.770852i	$-0.280169\pi$
$811$	−3.81141	−	3.81141i	−0.133837	−	0.133837i	−0.770852	+	0.637015i	$0.780169\pi$
$812$		0			0
$813$	−3.49962	+	3.49962i	−0.122737	+	0.122737i
$814$		0			0
$815$	7.39297			0.258965
$816$		0			0
$817$	−19.0286			−0.665728
$818$		0			0
$819$	−4.52254	+	4.52254i	−0.158030	+	0.158030i
$820$		0			0
$821$	−16.3264	−	16.3264i	−0.569795	−	0.569795i	0.362276	−	0.932071i	$-0.382000\pi$
$821$	−16.3264	−	16.3264i	−0.569795	−	0.569795i	−0.932071	+	0.362276i	$0.882000\pi$
$822$		0			0
$823$		−	39.7008i		−	1.38388i	−0.721953	−	0.691942i	$-0.756756\pi$
$823$		−	39.7008i		−	1.38388i	0.721953	−	0.691942i	$-0.243244\pi$
$824$		0			0
$825$		−	0.712398i		−	0.0248025i
$826$		0			0
$827$	27.8107	+	27.8107i	0.967071	+	0.967071i	0.999475	−	0.0324034i	$-0.0103161\pi$
$827$	27.8107	+	27.8107i	0.967071	+	0.967071i	−0.0324034	+	0.999475i	$0.510316\pi$
$828$		0			0
$829$	−27.1435	+	27.1435i	−0.942733	+	0.942733i	−0.998447	−	0.0557134i	$-0.982257\pi$
$829$	−27.1435	+	27.1435i	−0.942733	+	0.942733i	0.0557134	+	0.998447i	$0.482257\pi$
$830$		0			0
$831$	6.57703			0.228155
$832$		0			0
$833$	5.96316			0.206611
$834$		0			0
$835$	0.0457922	−	0.0457922i	0.00158470	−	0.00158470i
$836$		0			0
$837$	−0.425560	−	0.425560i	−0.0147095	−	0.0147095i
$838$		0			0
$839$		−	37.1623i		−	1.28299i	−0.767129	−	0.641493i	$-0.778315\pi$
$839$		−	37.1623i		−	1.28299i	0.767129	−	0.641493i	$-0.221685\pi$
$840$		0			0
$841$			20.8658i			0.719511i
$842$		0			0
$843$	−8.21229	−	8.21229i	−0.282846	−	0.282846i
$844$		0			0
$845$	5.67366	−	5.67366i	0.195180	−	0.195180i
$846$		0			0
$847$	−7.18050			−0.246725
$848$		0			0
$849$	−4.59637			−0.157747
$850$		0			0
$851$	−15.1378	+	15.1378i	−0.518916	+	0.518916i
$852$		0			0
$853$	−16.4723	−	16.4723i	−0.564001	−	0.564001i	0.366441	−	0.930441i	$-0.380576\pi$
$853$	−16.4723	−	16.4723i	−0.564001	−	0.564001i	−0.930441	+	0.366441i	$0.880576\pi$
$854$		0			0
$855$		−	4.93153i		−	0.168655i
$856$		0			0
$857$			53.8480i			1.83941i	0.392606	+	0.919707i	$0.371573\pi$
$857$			53.8480i			1.83941i	−0.392606	+	0.919707i	$0.628427\pi$
$858$		0			0
$859$	−2.27467	−	2.27467i	−0.0776108	−	0.0776108i	0.667236	−	0.744847i	$-0.267477\pi$
$859$	−2.27467	−	2.27467i	−0.0776108	−	0.0776108i	−0.744847	+	0.667236i	$0.767477\pi$
$860$		0			0
$861$	−1.99090	+	1.99090i	−0.0678496	+	0.0678496i
$862$		0			0
$863$	−44.3977			−1.51131			−0.755657	−	0.654967i	$-0.772682\pi$
$863$	−44.3977			−1.51131			−0.755657	+	0.654967i	$0.772682\pi$
$864$		0			0
$865$	−12.9698			−0.440988
$866$		0			0
$867$	−4.78372	+	4.78372i	−0.162464	+	0.162464i
$868$		0			0
$869$	−15.3000	−	15.3000i	−0.519016	−	0.519016i
$870$		0			0
$871$			23.5438i			0.797750i
$872$		0			0
$873$		−	47.1871i		−	1.59704i
$874$		0			0
$875$	−0.707107	−	0.707107i	−0.0239046	−	0.0239046i
$876$		0			0
$877$	27.6441	−	27.6441i	0.933475	−	0.933475i	−0.0644466	−	0.997921i	$-0.520528\pi$
$877$	27.6441	−	27.6441i	0.933475	−	0.933475i	0.997921	+	0.0644466i	$0.0205282\pi$
$878$		0			0
$879$	0.990166			0.0333975
$880$		0			0
$881$	35.4403			1.19401			0.597007	−	0.802236i	$-0.296356\pi$
$881$	35.4403			1.19401			0.597007	+	0.802236i	$0.296356\pi$
$882$		0			0
$883$	8.17225	−	8.17225i	0.275018	−	0.275018i	−0.556098	−	0.831116i	$-0.687702\pi$
$883$	8.17225	−	8.17225i	0.275018	−	0.275018i	0.831116	+	0.556098i	$0.187702\pi$
$884$		0			0
$885$	−1.64929	−	1.64929i	−0.0554404	−	0.0554404i
$886$		0			0
$887$		−	9.88891i		−	0.332037i	−0.986123	−	0.166019i	$-0.946909\pi$
$887$		−	9.88891i		−	0.332037i	0.986123	−	0.166019i	$-0.0530912\pi$
$888$		0			0
$889$			11.4382i			0.383626i
$890$		0			0
$891$	−10.8092	−	10.8092i	−0.362123	−	0.362123i
$892$		0			0
$893$	12.1555	−	12.1555i	0.406767	−	0.406767i
$894$		0			0
$895$	2.00497			0.0670189
$896$		0			0
$897$	−4.17318			−0.139339
$898$		0			0
$899$	0.567509	−	0.567509i	0.0189275	−	0.0189275i
$900$		0			0
$901$	48.7171	+	48.7171i	1.62300	+	1.62300i
$902$		0			0
$903$		−	4.03267i		−	0.134199i
$904$		0			0
$905$		−	5.25335i		−	0.174627i
$906$		0			0
$907$	20.1663	+	20.1663i	0.669610	+	0.669610i	0.957626	−	0.288016i	$-0.0929956\pi$
$907$	20.1663	+	20.1663i	0.669610	+	0.669610i	−0.288016	+	0.957626i	$0.592996\pi$
$908$		0			0
$909$	11.2122	−	11.2122i	0.371885	−	0.371885i
$910$		0			0
$911$	−36.2376			−1.20060			−0.600302	−	0.799773i	$-0.704953\pi$
$911$	−36.2376			−1.20060			−0.600302	+	0.799773i	$0.704953\pi$
$912$		0			0
$913$	−24.5503			−0.812496
$914$		0			0
$915$	−2.19870	+	2.19870i	−0.0726868	+	0.0726868i
$916$		0			0
$917$	−0.670252	−	0.670252i	−0.0221337	−	0.0221337i
$918$		0			0
$919$			11.5146i			0.379832i	0.981800	+	0.189916i	$0.0608215\pi$
$919$			11.5146i			0.379832i	−0.981800	+	0.189916i	$0.939178\pi$
$920$		0			0
$921$		−	9.41764i		−	0.310322i
$922$		0			0
$923$	6.74756	+	6.74756i	0.222099	+	0.222099i
$924$		0			0
$925$	2.94960	−	2.94960i	0.0969824	−	0.0969824i
$926$		0			0
$927$	−41.3443			−1.35792
$928$		0			0
$929$	47.9515			1.57324			0.786620	−	0.617438i	$-0.211829\pi$
$929$	47.9515			1.57324			0.786620	+	0.617438i	$0.211829\pi$
$930$		0			0
$931$	−1.21624	+	1.21624i	−0.0398607	+	0.0398607i
$932$		0			0
$933$	−5.26331	−	5.26331i	−0.172313	−	0.172313i
$934$		0			0
$935$			11.6541i			0.381131i
$936$		0			0
$937$		−	46.0710i		−	1.50507i	−0.658550	−	0.752537i	$-0.728830\pi$
$937$		−	46.0710i		−	1.50507i	0.658550	−	0.752537i	$-0.271170\pi$
$938$		0			0
$939$	4.55178	+	4.55178i	0.148542	+	0.148542i
$940$		0			0
$941$	34.0409	−	34.0409i	1.10970	−	1.10970i	0.116514	−	0.993189i	$-0.462828\pi$
$941$	34.0409	−	34.0409i	1.10970	−	1.10970i	0.993189	−	0.116514i	$-0.0371719\pi$
$942$		0			0
$943$	39.6408			1.29088
$944$		0			0
$945$	2.13868			0.0695711
$946$		0			0
$947$	14.8358	−	14.8358i	0.482098	−	0.482098i	−0.423703	−	0.905801i	$-0.639270\pi$
$947$	14.8358	−	14.8358i	0.482098	−	0.482098i	0.905801	+	0.423703i	$0.139270\pi$
$948$		0			0
$949$	−21.4952	−	21.4952i	−0.697762	−	0.697762i
$950$		0			0
$951$			3.62452i			0.117533i
$952$		0			0
$953$			12.8981i			0.417812i	0.977936	+	0.208906i	$0.0669902\pi$
$953$			12.8981i			0.417812i	−0.977936	+	0.208906i	$0.933010\pi$
$954$		0			0
$955$	−9.22453	−	9.22453i	−0.298499	−	0.298499i
$956$		0			0
$957$	−1.43669	+	1.43669i	−0.0464417	+	0.0464417i
$958$		0			0
$959$	−6.21865			−0.200811
$960$		0			0
$961$	−30.9208			−0.997446
$962$		0			0
$963$	32.8858	−	32.8858i	1.05973	−	1.05973i
$964$		0			0
$965$	−5.19527	−	5.19527i	−0.167242	−	0.167242i
$966$		0			0
$967$			47.4885i			1.52713i	0.645733	+	0.763563i	$0.276552\pi$
$967$			47.4885i			1.52713i	−0.645733	+	0.763563i	$0.723448\pi$
$968$		0			0
$969$		−	3.73879i		−	0.120107i
$970$		0			0
$971$	−33.8039	−	33.8039i	−1.08482	−	1.08482i	−0.996053	−	0.0887650i	$-0.971708\pi$
$971$	−33.8039	−	33.8039i	−1.08482	−	1.08482i	−0.0887650	−	0.996053i	$-0.528292\pi$
$972$		0			0
$973$	−6.26453	+	6.26453i	−0.200831	+	0.200831i
$974$		0			0
$975$	0.813148			0.0260416
$976$		0			0
$977$	−43.8336			−1.40236			−0.701181	−	0.712983i	$-0.747344\pi$
$977$	−43.8336			−1.40236			−0.701181	+	0.712983i	$0.747344\pi$
$978$		0			0
$979$	9.75688	−	9.75688i	0.311831	−	0.311831i
$980$		0			0
$981$	20.4857	+	20.4857i	0.654058	+	0.654058i
$982$		0			0
$983$		−	36.8813i		−	1.17633i	−0.808741	−	0.588165i	$-0.799850\pi$
$983$		−	36.8813i		−	1.17633i	0.808741	−	0.588165i	$-0.200150\pi$
$984$		0			0
$985$		−	9.30841i		−	0.296591i
$986$		0			0
$987$	2.57606	+	2.57606i	0.0819969	+	0.0819969i
$988$		0			0
$989$	−40.1472	+	40.1472i	−1.27661	+	1.27661i
$990$		0			0
$991$	−24.8982			−0.790916			−0.395458	−	0.918484i	$-0.629414\pi$
$991$	−24.8982			−0.790916			−0.395458	+	0.918484i	$0.629414\pi$
$992$		0			0
$993$	−2.50322			−0.0794373
$994$		0			0
$995$	−8.11685	+	8.11685i	−0.257322	+	0.257322i
$996$		0			0
$997$	35.1804	+	35.1804i	1.11417	+	1.11417i	0.992580	+	0.121594i	$0.0388006\pi$
$997$	35.1804	+	35.1804i	1.11417	+	1.11417i	0.121594	+	0.992580i	$0.461199\pi$
$998$		0			0
$999$			8.92121i			0.282255i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2240.2.bd.a.561.11		44
4.3	odd	2		560.2.bd.a.421.1	yes	44
16.3	odd	4		560.2.bd.a.141.1	✓	44
16.13	even	4	inner	2240.2.bd.a.1681.11		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bd.a.141.1	✓	44	16.3	odd	4
560.2.bd.a.421.1	yes	44	4.3	odd	2
2240.2.bd.a.561.11		44	1.1	even	1	trivial
2240.2.bd.a.1681.11		44	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)

\(f(q)\)	\(=\)	\(q+(-0.257753 + 0.257753i) q^{3} +(-0.707107 - 0.707107i) q^{5} -1.00000i q^{7} +2.86713i q^{9} +O(q^{10})\)	\(q+(-0.257753 + 0.257753i) q^{3} +(-0.707107 - 0.707107i) q^{5} -1.00000i q^{7} +2.86713i q^{9} +(1.38194 + 1.38194i) q^{11} +(-1.57738 + 1.57738i) q^{13} +0.364518 q^{15} -5.96316 q^{17} +(1.21624 - 1.21624i) q^{19} +(0.257753 + 0.257753i) q^{21} -5.13213i q^{23} +1.00000i q^{25} +(-1.51227 - 1.51227i) q^{27} +(2.01670 - 2.01670i) q^{29} +0.281404 q^{31} -0.712398 q^{33} +(-0.707107 + 0.707107i) q^{35} +(-2.94960 - 2.94960i) q^{37} -0.813148i q^{39} +7.72404i q^{41} +(-7.82272 - 7.82272i) q^{43} +(2.02736 - 2.02736i) q^{45} +9.99428 q^{47} -1.00000 q^{49} +(1.53703 - 1.53703i) q^{51} +(-8.16967 - 8.16967i) q^{53} -1.95435i q^{55} +0.626981i q^{57} +(-4.52459 - 4.52459i) q^{59} +(-6.03179 + 6.03179i) q^{61} +2.86713 q^{63} +2.23075 q^{65} +(7.46295 - 7.46295i) q^{67} +(1.32282 + 1.32282i) q^{69} -4.27771i q^{71} +13.6272i q^{73} +(-0.257753 - 0.257753i) q^{75} +(1.38194 - 1.38194i) q^{77} -11.0714 q^{79} -7.82179 q^{81} +(-8.88257 + 8.88257i) q^{83} +(4.21659 + 4.21659i) q^{85} +1.03962i q^{87} -7.06029i q^{89} +(1.57738 + 1.57738i) q^{91} +(-0.0725329 + 0.0725329i) q^{93} -1.72003 q^{95} -16.4580 q^{97} +(-3.96219 + 3.96219i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q+O(q^{10}) \) 44 * q	\( 44 q - 12 q^{11} - 8 q^{15} - 8 q^{19} + 24 q^{27} + 12 q^{29} + 28 q^{37} + 44 q^{43} - 44 q^{49} + 8 q^{51} - 12 q^{53} - 24 q^{59} - 16 q^{61} - 28 q^{63} - 40 q^{65} + 28 q^{67} + 40 q^{69} - 12 q^{77} + 16 q^{79} + 20 q^{81} + 16 q^{85} + 88 q^{93} + 32 q^{95} - 28 q^{99}+O(q^{100}) \) 44 * q - 12 * q^11 - 8 * q^15 - 8 * q^19 + 24 * q^27 + 12 * q^29 + 28 * q^37 + 44 * q^43 - 44 * q^49 + 8 * q^51 - 12 * q^53 - 24 * q^59 - 16 * q^61 - 28 * q^63 - 40 * q^65 + 28 * q^67 + 40 * q^69 - 12 * q^77 + 16 * q^79 + 20 * q^81 + 16 * q^85 + 88 * q^93 + 32 * q^95 - 28 * q^99

Introduction

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