LMFDB - Embedded newform 1050.2.d.e.1049.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(1049,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1050.1049");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.d (of order $2$, degree $1$, 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:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1049.4
Root			$-1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1050.1049
Dual form			1050.2.d.e.1049.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(1.22474 + 1.22474i) q^{3} +1.00000 q^{4} +(1.22474 + 1.22474i) q^{6} +(2.44949 + 1.00000i) q^{7} +1.00000 q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(1.22474 + 1.22474i) q^{3} +1.00000 q^{4} +(1.22474 + 1.22474i) q^{6} +(2.44949 + 1.00000i) q^{7} +1.00000 q^{8} +3.00000i q^{9} +(1.22474 + 1.22474i) q^{12} +2.44949 q^{13} +(2.44949 + 1.00000i) q^{14} +1.00000 q^{16} -4.89898i q^{17} +3.00000i q^{18} -2.44949i q^{19} +(1.77526 + 4.22474i) q^{21} -6.00000 q^{23} +(1.22474 + 1.22474i) q^{24} +2.44949 q^{26} +(-3.67423 + 3.67423i) q^{27} +(2.44949 + 1.00000i) q^{28} +6.00000i q^{29} +1.00000 q^{32} -4.89898i q^{34} +3.00000i q^{36} +2.00000i q^{37} -2.44949i q^{38} +(3.00000 + 3.00000i) q^{39} -4.89898 q^{41} +(1.77526 + 4.22474i) q^{42} +4.00000i q^{43} -6.00000 q^{46} -4.89898i q^{47} +(1.22474 + 1.22474i) q^{48} +(5.00000 + 4.89898i) q^{49} +(6.00000 - 6.00000i) q^{51} +2.44949 q^{52} -6.00000 q^{53} +(-3.67423 + 3.67423i) q^{54} +(2.44949 + 1.00000i) q^{56} +(3.00000 - 3.00000i) q^{57} +6.00000i q^{58} +12.2474 q^{59} -12.2474i q^{61} +(-3.00000 + 7.34847i) q^{63} +1.00000 q^{64} -8.00000i q^{67} -4.89898i q^{68} +(-7.34847 - 7.34847i) q^{69} +3.00000i q^{72} -9.79796 q^{73} +2.00000i q^{74} -2.44949i q^{76} +(3.00000 + 3.00000i) q^{78} +10.0000 q^{79} -9.00000 q^{81} -4.89898 q^{82} +2.44949i q^{83} +(1.77526 + 4.22474i) q^{84} +4.00000i q^{86} +(-7.34847 + 7.34847i) q^{87} +(6.00000 + 2.44949i) q^{91} -6.00000 q^{92} -4.89898i q^{94} +(1.22474 + 1.22474i) q^{96} +4.89898 q^{97} +(5.00000 + 4.89898i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{4} + 4 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^4 + 4 * q^8	$ 4 q + 4 q^{2} + 4 q^{4} + 4 q^{8} + 4 q^{16} + 12 q^{21} - 24 q^{23} + 4 q^{32} + 12 q^{39} + 12 q^{42} - 24 q^{46} + 20 q^{49} + 24 q^{51} - 24 q^{53} + 12 q^{57} - 12 q^{63} + 4 q^{64} + 12 q^{78} + 40 q^{79} - 36 q^{81} + 12 q^{84} + 24 q^{91} - 24 q^{92} + 20 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^4 + 4 * q^8 + 4 * q^16 + 12 * q^21 - 24 * q^23 + 4 * q^32 + 12 * q^39 + 12 * q^42 - 24 * q^46 + 20 * q^49 + 24 * q^51 - 24 * q^53 + 12 * q^57 - 12 * q^63 + 4 * q^64 + 12 * q^78 + 40 * q^79 - 36 * q^81 + 12 * q^84 + 24 * q^91 - 24 * q^92 + 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	1.22474	+	1.22474i	0.707107	+	0.707107i
$3$	1.22474	+	1.22474i	0.707107	+	0.707107i
$4$	1.00000			0.500000
$5$		0			0
$5$		0			0
$6$	1.22474	+	1.22474i	0.500000	+	0.500000i
$7$	2.44949	+	1.00000i	0.925820	+	0.377964i
$7$	2.44949	+	1.00000i	0.925820	+	0.377964i
$8$	1.00000			0.353553
$9$			3.00000i			1.00000i
$10$		0			0
$11$		0			0		1.00000			$0$
$11$		0			0		−1.00000			$\pi$
$12$	1.22474	+	1.22474i	0.353553	+	0.353553i
$13$	2.44949			0.679366			0.339683	−	0.940540i	$-0.389680\pi$
$13$	2.44949			0.679366			0.339683	+	0.940540i	$0.389680\pi$
$14$	2.44949	+	1.00000i	0.654654	+	0.267261i
$15$		0			0
$16$	1.00000			0.250000
$17$		−	4.89898i		−	1.18818i	−0.804400	−	0.594089i	$-0.797513\pi$
$17$		−	4.89898i		−	1.18818i	0.804400	−	0.594089i	$-0.202487\pi$
$18$			3.00000i			0.707107i
$19$		−	2.44949i		−	0.561951i	−0.959715	−	0.280976i	$-0.909342\pi$
$19$		−	2.44949i		−	0.561951i	0.959715	−	0.280976i	$-0.0906580\pi$
$20$		0			0
$21$	1.77526	+	4.22474i	0.387392	+	0.921915i
$22$		0			0
$23$	−6.00000			−1.25109			−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000			−1.25109			−0.625543	+	0.780189i	$0.715123\pi$
$24$	1.22474	+	1.22474i	0.250000	+	0.250000i
$25$		0			0
$26$	2.44949			0.480384
$27$	−3.67423	+	3.67423i	−0.707107	+	0.707107i
$28$	2.44949	+	1.00000i	0.462910	+	0.188982i
$29$			6.00000i			1.11417i	0.830455	+	0.557086i	$0.188081\pi$
$29$			6.00000i			1.11417i	−0.830455	+	0.557086i	$0.811919\pi$
$30$		0			0
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$		−	4.89898i		−	0.840168i
$35$		0			0
$36$			3.00000i			0.500000i
$37$			2.00000i			0.328798i	0.986394	+	0.164399i	$0.0525685\pi$
$37$			2.00000i			0.328798i	−0.986394	+	0.164399i	$0.947432\pi$
$38$		−	2.44949i		−	0.397360i
$39$	3.00000	+	3.00000i	0.480384	+	0.480384i
$40$		0			0
$41$	−4.89898			−0.765092			−0.382546	−	0.923936i	$-0.624953\pi$
$41$	−4.89898			−0.765092			−0.382546	+	0.923936i	$0.624953\pi$
$42$	1.77526	+	4.22474i	0.273928	+	0.651892i
$43$			4.00000i			0.609994i	0.952353	+	0.304997i	$0.0986555\pi$
$43$			4.00000i			0.609994i	−0.952353	+	0.304997i	$0.901344\pi$
$44$		0			0
$45$		0			0
$46$	−6.00000			−0.884652
$47$		−	4.89898i		−	0.714590i	−0.933992	−	0.357295i	$-0.883699\pi$
$47$		−	4.89898i		−	0.714590i	0.933992	−	0.357295i	$-0.116301\pi$
$48$	1.22474	+	1.22474i	0.176777	+	0.176777i
$49$	5.00000	+	4.89898i	0.714286	+	0.699854i
$50$		0			0
$51$	6.00000	−	6.00000i	0.840168	−	0.840168i
$52$	2.44949			0.339683
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$	−3.67423	+	3.67423i	−0.500000	+	0.500000i
$55$		0			0
$56$	2.44949	+	1.00000i	0.327327	+	0.133631i
$57$	3.00000	−	3.00000i	0.397360	−	0.397360i
$58$			6.00000i			0.787839i
$59$	12.2474			1.59448			0.797241	−	0.603661i	$-0.206292\pi$
$59$	12.2474			1.59448			0.797241	+	0.603661i	$0.206292\pi$
$60$		0			0
$61$		−	12.2474i		−	1.56813i	−0.620682	−	0.784063i	$-0.713144\pi$
$61$		−	12.2474i		−	1.56813i	0.620682	−	0.784063i	$-0.286856\pi$
$62$		0			0
$63$	−3.00000	+	7.34847i	−0.377964	+	0.925820i
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$		−	8.00000i		−	0.977356i	−0.872464	−	0.488678i	$-0.837479\pi$
$67$		−	8.00000i		−	0.977356i	0.872464	−	0.488678i	$-0.162521\pi$
$68$		−	4.89898i		−	0.594089i
$69$	−7.34847	−	7.34847i	−0.884652	−	0.884652i
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$			3.00000i			0.353553i
$73$	−9.79796			−1.14676			−0.573382	−	0.819288i	$-0.694369\pi$
$73$	−9.79796			−1.14676			−0.573382	+	0.819288i	$0.694369\pi$
$74$			2.00000i			0.232495i
$75$		0			0
$76$		−	2.44949i		−	0.280976i
$77$		0			0
$78$	3.00000	+	3.00000i	0.339683	+	0.339683i
$79$	10.0000			1.12509			0.562544	−	0.826767i	$-0.309823\pi$
$79$	10.0000			1.12509			0.562544	+	0.826767i	$0.309823\pi$
$80$		0			0
$81$	−9.00000			−1.00000
$82$	−4.89898			−0.541002
$83$			2.44949i			0.268866i	0.990923	+	0.134433i	$0.0429214\pi$
$83$			2.44949i			0.268866i	−0.990923	+	0.134433i	$0.957079\pi$
$84$	1.77526	+	4.22474i	0.193696	+	0.460957i
$85$		0			0
$86$			4.00000i			0.431331i
$87$	−7.34847	+	7.34847i	−0.787839	+	0.787839i
$88$		0			0
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$		0			0
$91$	6.00000	+	2.44949i	0.628971	+	0.256776i
$92$	−6.00000			−0.625543
$93$		0			0
$94$		−	4.89898i		−	0.505291i
$95$		0			0
$96$	1.22474	+	1.22474i	0.125000	+	0.125000i
$97$	4.89898			0.497416			0.248708	−	0.968579i	$-0.419994\pi$
$97$	4.89898			0.497416			0.248708	+	0.968579i	$0.419994\pi$
$98$	5.00000	+	4.89898i	0.505076	+	0.494872i
$99$		0			0
$100$		0			0
$101$	7.34847			0.731200			0.365600	−	0.930772i	$-0.380864\pi$
$101$	7.34847			0.731200			0.365600	+	0.930772i	$0.380864\pi$
$102$	6.00000	−	6.00000i	0.594089	−	0.594089i
$103$	−9.79796			−0.965422			−0.482711	−	0.875780i	$-0.660348\pi$
$103$	−9.79796			−0.965422			−0.482711	+	0.875780i	$0.660348\pi$
$104$	2.44949			0.240192
$105$		0			0
$106$	−6.00000			−0.582772
$107$	−12.0000			−1.16008			−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000			−1.16008			−0.580042	+	0.814587i	$0.696964\pi$
$108$	−3.67423	+	3.67423i	−0.353553	+	0.353553i
$109$	−10.0000			−0.957826			−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000			−0.957826			−0.478913	+	0.877862i	$0.658969\pi$
$110$		0			0
$111$	−2.44949	+	2.44949i	−0.232495	+	0.232495i
$112$	2.44949	+	1.00000i	0.231455	+	0.0944911i
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$	3.00000	−	3.00000i	0.280976	−	0.280976i
$115$		0			0
$116$			6.00000i			0.557086i
$117$			7.34847i			0.679366i
$118$	12.2474			1.12747
$119$	4.89898	−	12.0000i	0.449089	−	1.10004i
$120$		0			0
$121$	11.0000			1.00000
$122$		−	12.2474i		−	1.10883i
$123$	−6.00000	−	6.00000i	−0.541002	−	0.541002i
$124$		0			0
$125$		0			0
$126$	−3.00000	+	7.34847i	−0.267261	+	0.654654i
$127$		−	8.00000i		−	0.709885i	−0.934888	−	0.354943i	$-0.884500\pi$
$127$		−	8.00000i		−	0.709885i	0.934888	−	0.354943i	$-0.115500\pi$
$128$	1.00000			0.0883883
$129$	−4.89898	+	4.89898i	−0.431331	+	0.431331i
$130$		0			0
$131$	7.34847			0.642039			0.321019	−	0.947073i	$-0.395975\pi$
$131$	7.34847			0.642039			0.321019	+	0.947073i	$0.395975\pi$
$132$		0			0
$133$	2.44949	−	6.00000i	0.212398	−	0.520266i
$134$		−	8.00000i		−	0.691095i
$135$		0			0
$136$		−	4.89898i		−	0.420084i
$137$	−12.0000			−1.02523			−0.512615	−	0.858619i	$-0.671323\pi$
$137$	−12.0000			−1.02523			−0.512615	+	0.858619i	$0.671323\pi$
$138$	−7.34847	−	7.34847i	−0.625543	−	0.625543i
$139$		−	2.44949i		−	0.207763i	−0.994590	−	0.103882i	$-0.966874\pi$
$139$		−	2.44949i		−	0.207763i	0.994590	−	0.103882i	$-0.0331263\pi$
$140$		0			0
$141$	6.00000	−	6.00000i	0.505291	−	0.505291i
$142$		0			0
$143$		0			0
$144$			3.00000i			0.250000i
$145$		0			0
$146$	−9.79796			−0.810885
$147$	0.123724	+	12.1237i	0.0102046	+	0.999948i
$148$			2.00000i			0.164399i
$149$			6.00000i			0.491539i	0.969328	+	0.245770i	$0.0790407\pi$
$149$			6.00000i			0.491539i	−0.969328	+	0.245770i	$0.920959\pi$
$150$		0			0
$151$	−8.00000			−0.651031			−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000			−0.651031			−0.325515	+	0.945537i	$0.605538\pi$
$152$		−	2.44949i		−	0.198680i
$153$	14.6969			1.18818
$154$		0			0
$155$		0			0
$156$	3.00000	+	3.00000i	0.240192	+	0.240192i
$157$	−7.34847			−0.586472			−0.293236	−	0.956040i	$-0.594732\pi$
$157$	−7.34847			−0.586472			−0.293236	+	0.956040i	$0.594732\pi$
$158$	10.0000			0.795557
$159$	−7.34847	−	7.34847i	−0.582772	−	0.582772i
$160$		0			0
$161$	−14.6969	−	6.00000i	−1.15828	−	0.472866i
$162$	−9.00000			−0.707107
$163$		−	16.0000i		−	1.25322i	−0.779334	−	0.626608i	$-0.784443\pi$
$163$		−	16.0000i		−	1.25322i	0.779334	−	0.626608i	$-0.215557\pi$
$164$	−4.89898			−0.382546
$165$		0			0
$166$			2.44949i			0.190117i
$167$		−	4.89898i		−	0.379094i	−0.981872	−	0.189547i	$-0.939298\pi$
$167$		−	4.89898i		−	0.379094i	0.981872	−	0.189547i	$-0.0607020\pi$
$168$	1.77526	+	4.22474i	0.136964	+	0.325946i
$169$	−7.00000			−0.538462
$170$		0			0
$171$	7.34847			0.561951
$172$			4.00000i			0.304997i
$173$		−	22.0454i		−	1.67608i	−0.545608	−	0.838041i	$-0.683701\pi$
$173$		−	22.0454i		−	1.67608i	0.545608	−	0.838041i	$-0.316299\pi$
$174$	−7.34847	+	7.34847i	−0.557086	+	0.557086i
$175$		0			0
$176$		0			0
$177$	15.0000	+	15.0000i	1.12747	+	1.12747i
$178$		0			0
$179$		−	24.0000i		−	1.79384i	−0.442189	−	0.896922i	$-0.645798\pi$
$179$		−	24.0000i		−	1.79384i	0.442189	−	0.896922i	$-0.354202\pi$
$180$		0			0
$181$			12.2474i			0.910346i	0.890403	+	0.455173i	$0.150423\pi$
$181$			12.2474i			0.910346i	−0.890403	+	0.455173i	$0.849577\pi$
$182$	6.00000	+	2.44949i	0.444750	+	0.181568i
$183$	15.0000	−	15.0000i	1.10883	−	1.10883i
$184$	−6.00000			−0.442326
$185$		0			0
$186$		0			0
$187$		0			0
$188$		−	4.89898i		−	0.357295i
$189$	−12.6742	+	5.32577i	−0.921915	+	0.387392i
$190$		0			0
$191$		0			0		1.00000			$0$
$191$		0			0		−1.00000			$\pi$
$192$	1.22474	+	1.22474i	0.0883883	+	0.0883883i
$193$			4.00000i			0.287926i	0.989583	+	0.143963i	$0.0459847\pi$
$193$			4.00000i			0.287926i	−0.989583	+	0.143963i	$0.954015\pi$
$194$	4.89898			0.351726
$195$		0			0
$196$	5.00000	+	4.89898i	0.357143	+	0.349927i
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$		0			0
$199$			9.79796i			0.694559i	0.937762	+	0.347279i	$0.112894\pi$
$199$			9.79796i			0.694559i	−0.937762	+	0.347279i	$0.887106\pi$
$200$		0			0
$201$	9.79796	−	9.79796i	0.691095	−	0.691095i
$202$	7.34847			0.517036
$203$	−6.00000	+	14.6969i	−0.421117	+	1.03152i
$204$	6.00000	−	6.00000i	0.420084	−	0.420084i
$205$		0			0
$206$	−9.79796			−0.682656
$207$		−	18.0000i		−	1.25109i
$208$	2.44949			0.169842
$209$		0			0
$210$		0			0
$211$	−8.00000			−0.550743			−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000			−0.550743			−0.275371	+	0.961338i	$0.588801\pi$
$212$	−6.00000			−0.412082
$213$		0			0
$214$	−12.0000			−0.820303
$215$		0			0
$216$	−3.67423	+	3.67423i	−0.250000	+	0.250000i
$217$		0			0
$218$	−10.0000			−0.677285
$219$	−12.0000	−	12.0000i	−0.810885	−	0.810885i
$220$		0			0
$221$		−	12.0000i		−	0.807207i
$222$	−2.44949	+	2.44949i	−0.164399	+	0.164399i
$223$	14.6969			0.984180			0.492090	−	0.870544i	$-0.336233\pi$
$223$	14.6969			0.984180			0.492090	+	0.870544i	$0.336233\pi$
$224$	2.44949	+	1.00000i	0.163663	+	0.0668153i
$225$		0			0
$226$	−6.00000			−0.399114
$227$			7.34847i			0.487735i	0.969809	+	0.243868i	$0.0784162\pi$
$227$			7.34847i			0.487735i	−0.969809	+	0.243868i	$0.921584\pi$
$228$	3.00000	−	3.00000i	0.198680	−	0.198680i
$229$			22.0454i			1.45680i	0.685151	+	0.728401i	$0.259736\pi$
$229$			22.0454i			1.45680i	−0.685151	+	0.728401i	$0.740264\pi$
$230$		0			0
$231$		0			0
$232$			6.00000i			0.393919i
$233$	24.0000			1.57229			0.786146	−	0.618041i	$-0.212073\pi$
$233$	24.0000			1.57229			0.786146	+	0.618041i	$0.212073\pi$
$234$			7.34847i			0.480384i
$235$		0			0
$236$	12.2474			0.797241
$237$	12.2474	+	12.2474i	0.795557	+	0.795557i
$238$	4.89898	−	12.0000i	0.317554	−	0.777844i
$239$			6.00000i			0.388108i	0.980991	+	0.194054i	$0.0621637\pi$
$239$			6.00000i			0.388108i	−0.980991	+	0.194054i	$0.937836\pi$
$240$		0			0
$241$			24.4949i			1.57786i	0.614486	+	0.788928i	$0.289363\pi$
$241$			24.4949i			1.57786i	−0.614486	+	0.788928i	$0.710637\pi$
$242$	11.0000			0.707107
$243$	−11.0227	−	11.0227i	−0.707107	−	0.707107i
$244$		−	12.2474i		−	0.784063i
$245$		0			0
$246$	−6.00000	−	6.00000i	−0.382546	−	0.382546i
$247$		−	6.00000i		−	0.381771i
$248$		0			0
$249$	−3.00000	+	3.00000i	−0.190117	+	0.190117i
$250$		0			0
$251$	−17.1464			−1.08227			−0.541136	−	0.840935i	$-0.682006\pi$
$251$	−17.1464			−1.08227			−0.541136	+	0.840935i	$0.682006\pi$
$252$	−3.00000	+	7.34847i	−0.188982	+	0.462910i
$253$		0			0
$254$		−	8.00000i		−	0.501965i
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	29.3939i		−	1.83354i	−0.399416	−	0.916770i	$-0.630787\pi$
$257$		−	29.3939i		−	1.83354i	0.399416	−	0.916770i	$-0.369213\pi$
$258$	−4.89898	+	4.89898i	−0.304997	+	0.304997i
$259$	−2.00000	+	4.89898i	−0.124274	+	0.304408i
$260$		0			0
$261$	−18.0000			−1.11417
$262$	7.34847			0.453990
$263$	24.0000			1.47990			0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000			1.47990			0.739952	+	0.672660i	$0.234848\pi$
$264$		0			0
$265$		0			0
$266$	2.44949	−	6.00000i	0.150188	−	0.367884i
$267$		0			0
$268$		−	8.00000i		−	0.488678i
$269$	12.2474			0.746740			0.373370	−	0.927682i	$-0.378202\pi$
$269$	12.2474			0.746740			0.373370	+	0.927682i	$0.378202\pi$
$270$		0			0
$271$		−	24.4949i		−	1.48796i	−0.668202	−	0.743980i	$-0.732936\pi$
$271$		−	24.4949i		−	1.48796i	0.668202	−	0.743980i	$-0.267064\pi$
$272$		−	4.89898i		−	0.297044i
$273$	4.34847	+	10.3485i	0.263181	+	0.626318i
$274$	−12.0000			−0.724947
$275$		0			0
$276$	−7.34847	−	7.34847i	−0.442326	−	0.442326i
$277$			22.0000i			1.32185i	0.750451	+	0.660926i	$0.229836\pi$
$277$			22.0000i			1.32185i	−0.750451	+	0.660926i	$0.770164\pi$
$278$		−	2.44949i		−	0.146911i
$279$		0			0
$280$		0			0
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$	6.00000	−	6.00000i	0.357295	−	0.357295i
$283$	−22.0454			−1.31046			−0.655232	−	0.755428i	$-0.727429\pi$
$283$	−22.0454			−1.31046			−0.655232	+	0.755428i	$0.727429\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−12.0000	−	4.89898i	−0.708338	−	0.289178i
$288$			3.00000i			0.176777i
$289$	−7.00000			−0.411765
$290$		0			0
$291$	6.00000	+	6.00000i	0.351726	+	0.351726i
$292$	−9.79796			−0.573382
$293$			2.44949i			0.143101i	0.997437	+	0.0715504i	$0.0227947\pi$
$293$			2.44949i			0.143101i	−0.997437	+	0.0715504i	$0.977205\pi$
$294$	0.123724	+	12.1237i	0.00721575	+	0.707070i
$295$		0			0
$296$			2.00000i			0.116248i
$297$		0			0
$298$			6.00000i			0.347571i
$299$	−14.6969			−0.849946
$300$		0			0
$301$	−4.00000	+	9.79796i	−0.230556	+	0.564745i
$302$	−8.00000			−0.460348
$303$	9.00000	+	9.00000i	0.517036	+	0.517036i
$304$		−	2.44949i		−	0.140488i
$305$		0			0
$306$	14.6969			0.840168
$307$	−7.34847			−0.419399			−0.209700	−	0.977766i	$-0.567249\pi$
$307$	−7.34847			−0.419399			−0.209700	+	0.977766i	$0.567249\pi$
$308$		0			0
$309$	−12.0000	−	12.0000i	−0.682656	−	0.682656i
$310$		0			0
$311$	19.5959			1.11118			0.555591	−	0.831456i	$-0.312492\pi$
$311$	19.5959			1.11118			0.555591	+	0.831456i	$0.312492\pi$
$312$	3.00000	+	3.00000i	0.169842	+	0.169842i
$313$	−34.2929			−1.93835			−0.969173	−	0.246380i	$-0.920759\pi$
$313$	−34.2929			−1.93835			−0.969173	+	0.246380i	$0.920759\pi$
$314$	−7.34847			−0.414698
$315$		0			0
$316$	10.0000			0.562544
$317$	18.0000			1.01098			0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000			1.01098			0.505490	+	0.862832i	$0.331312\pi$
$318$	−7.34847	−	7.34847i	−0.412082	−	0.412082i
$319$		0			0
$320$		0			0
$321$	−14.6969	−	14.6969i	−0.820303	−	0.820303i
$322$	−14.6969	−	6.00000i	−0.819028	−	0.334367i
$323$	−12.0000			−0.667698
$324$	−9.00000			−0.500000
$325$		0			0
$326$		−	16.0000i		−	0.886158i
$327$	−12.2474	−	12.2474i	−0.677285	−	0.677285i
$328$	−4.89898			−0.270501
$329$	4.89898	−	12.0000i	0.270089	−	0.661581i
$330$		0			0
$331$	−8.00000			−0.439720			−0.219860	−	0.975531i	$-0.570560\pi$
$331$	−8.00000			−0.439720			−0.219860	+	0.975531i	$0.570560\pi$
$332$			2.44949i			0.134433i
$333$	−6.00000			−0.328798
$334$		−	4.89898i		−	0.268060i
$335$		0			0
$336$	1.77526	+	4.22474i	0.0968481	+	0.230479i
$337$			32.0000i			1.74315i	0.490261	+	0.871576i	$0.336901\pi$
$337$			32.0000i			1.74315i	−0.490261	+	0.871576i	$0.663099\pi$
$338$	−7.00000			−0.380750
$339$	−7.34847	−	7.34847i	−0.399114	−	0.399114i
$340$		0			0
$341$		0			0
$342$	7.34847			0.397360
$343$	7.34847	+	17.0000i	0.396780	+	0.917914i
$344$			4.00000i			0.215666i
$345$		0			0
$346$		−	22.0454i		−	1.18517i
$347$	−12.0000			−0.644194			−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−12.0000			−0.644194			−0.322097	+	0.946707i	$0.604388\pi$
$348$	−7.34847	+	7.34847i	−0.393919	+	0.393919i
$349$		−	2.44949i		−	0.131118i	−0.997849	−	0.0655591i	$-0.979117\pi$
$349$		−	2.44949i		−	0.131118i	0.997849	−	0.0655591i	$-0.0208831\pi$
$350$		0			0
$351$	−9.00000	+	9.00000i	−0.480384	+	0.480384i
$352$		0			0
$353$		−	9.79796i		−	0.521493i	−0.965407	−	0.260746i	$-0.916031\pi$
$353$		−	9.79796i		−	0.521493i	0.965407	−	0.260746i	$-0.0839686\pi$
$354$	15.0000	+	15.0000i	0.797241	+	0.797241i
$355$		0			0
$356$		0			0
$357$	20.6969	−	8.69694i	1.09540	−	0.460291i
$358$		−	24.0000i		−	1.26844i
$359$			6.00000i			0.316668i	0.987386	+	0.158334i	$0.0506123\pi$
$359$			6.00000i			0.316668i	−0.987386	+	0.158334i	$0.949388\pi$
$360$		0			0
$361$	13.0000			0.684211
$362$			12.2474i			0.643712i
$363$	13.4722	+	13.4722i	0.707107	+	0.707107i
$364$	6.00000	+	2.44949i	0.314485	+	0.128388i
$365$		0			0
$366$	15.0000	−	15.0000i	0.784063	−	0.784063i
$367$	4.89898			0.255725			0.127862	−	0.991792i	$-0.459188\pi$
$367$	4.89898			0.255725			0.127862	+	0.991792i	$0.459188\pi$
$368$	−6.00000			−0.312772
$369$		−	14.6969i		−	0.765092i
$370$		0			0
$371$	−14.6969	−	6.00000i	−0.763027	−	0.311504i
$372$		0			0
$373$			14.0000i			0.724893i	0.932005	+	0.362446i	$0.118058\pi$
$373$			14.0000i			0.724893i	−0.932005	+	0.362446i	$0.881942\pi$
$374$		0			0
$375$		0			0
$376$		−	4.89898i		−	0.252646i
$377$			14.6969i			0.756931i
$378$	−12.6742	+	5.32577i	−0.651892	+	0.273928i
$379$	20.0000			1.02733			0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000			1.02733			0.513665	+	0.857991i	$0.328287\pi$
$380$		0			0
$381$	9.79796	−	9.79796i	0.501965	−	0.501965i
$382$		0			0
$383$		−	34.2929i		−	1.75228i	−0.482054	−	0.876142i	$-0.660109\pi$
$383$		−	34.2929i		−	1.75228i	0.482054	−	0.876142i	$-0.339891\pi$
$384$	1.22474	+	1.22474i	0.0625000	+	0.0625000i
$385$		0			0
$386$			4.00000i			0.203595i
$387$	−12.0000			−0.609994
$388$	4.89898			0.248708
$389$			6.00000i			0.304212i	0.988364	+	0.152106i	$0.0486055\pi$
$389$			6.00000i			0.304212i	−0.988364	+	0.152106i	$0.951394\pi$
$390$		0			0
$391$			29.3939i			1.48651i
$392$	5.00000	+	4.89898i	0.252538	+	0.247436i
$393$	9.00000	+	9.00000i	0.453990	+	0.453990i
$394$	18.0000			0.906827
$395$		0			0
$396$		0			0
$397$	−7.34847			−0.368809			−0.184405	−	0.982850i	$-0.559036\pi$
$397$	−7.34847			−0.368809			−0.184405	+	0.982850i	$0.559036\pi$
$398$			9.79796i			0.491127i
$399$	10.3485	−	4.34847i	0.518071	−	0.217696i
$400$		0			0
$401$			30.0000i			1.49813i	0.662497	+	0.749064i	$0.269497\pi$
$401$			30.0000i			1.49813i	−0.662497	+	0.749064i	$0.730503\pi$
$402$	9.79796	−	9.79796i	0.488678	−	0.488678i
$403$		0			0
$404$	7.34847			0.365600
$405$		0			0
$406$	−6.00000	+	14.6969i	−0.297775	+	0.729397i
$407$		0			0
$408$	6.00000	−	6.00000i	0.297044	−	0.297044i
$409$			34.2929i			1.69567i	0.530258	+	0.847836i	$0.322095\pi$
$409$			34.2929i			1.69567i	−0.530258	+	0.847836i	$0.677905\pi$
$410$		0			0
$411$	−14.6969	−	14.6969i	−0.724947	−	0.724947i
$412$	−9.79796			−0.482711
$413$	30.0000	+	12.2474i	1.47620	+	0.602658i
$414$		−	18.0000i		−	0.884652i
$415$		0			0
$416$	2.44949			0.120096
$417$	3.00000	−	3.00000i	0.146911	−	0.146911i
$418$		0			0
$419$	−12.2474			−0.598327			−0.299164	−	0.954202i	$-0.596708\pi$
$419$	−12.2474			−0.598327			−0.299164	+	0.954202i	$0.596708\pi$
$420$		0			0
$421$	2.00000			0.0974740			0.0487370	−	0.998812i	$-0.484480\pi$
$421$	2.00000			0.0974740			0.0487370	+	0.998812i	$0.484480\pi$
$422$	−8.00000			−0.389434
$423$	14.6969			0.714590
$424$	−6.00000			−0.291386
$425$		0			0
$426$		0			0
$427$	12.2474	−	30.0000i	0.592696	−	1.45180i
$428$	−12.0000			−0.580042
$429$		0			0
$430$		0			0
$431$			30.0000i			1.44505i	0.691345	+	0.722525i	$0.257018\pi$
$431$			30.0000i			1.44505i	−0.691345	+	0.722525i	$0.742982\pi$
$432$	−3.67423	+	3.67423i	−0.176777	+	0.176777i
$433$	14.6969			0.706290			0.353145	−	0.935569i	$-0.385112\pi$
$433$	14.6969			0.706290			0.353145	+	0.935569i	$0.385112\pi$
$434$		0			0
$435$		0			0
$436$	−10.0000			−0.478913
$437$			14.6969i			0.703050i
$438$	−12.0000	−	12.0000i	−0.573382	−	0.573382i
$439$		−	14.6969i		−	0.701447i	−0.936479	−	0.350723i	$-0.885936\pi$
$439$		−	14.6969i		−	0.701447i	0.936479	−	0.350723i	$-0.114064\pi$
$440$		0			0
$441$	−14.6969	+	15.0000i	−0.699854	+	0.714286i
$442$		−	12.0000i		−	0.570782i
$443$	−36.0000			−1.71041			−0.855206	−	0.518289i	$-0.826569\pi$
$443$	−36.0000			−1.71041			−0.855206	+	0.518289i	$0.826569\pi$
$444$	−2.44949	+	2.44949i	−0.116248	+	0.116248i
$445$		0			0
$446$	14.6969			0.695920
$447$	−7.34847	+	7.34847i	−0.347571	+	0.347571i
$448$	2.44949	+	1.00000i	0.115728	+	0.0472456i
$449$			36.0000i			1.69895i	0.527633	+	0.849473i	$0.323080\pi$
$449$			36.0000i			1.69895i	−0.527633	+	0.849473i	$0.676920\pi$
$450$		0			0
$451$		0			0
$452$	−6.00000			−0.282216
$453$	−9.79796	−	9.79796i	−0.460348	−	0.460348i
$454$			7.34847i			0.344881i
$455$		0			0
$456$	3.00000	−	3.00000i	0.140488	−	0.140488i
$457$		−	28.0000i		−	1.30978i	−0.755722	−	0.654892i	$-0.772714\pi$
$457$		−	28.0000i		−	1.30978i	0.755722	−	0.654892i	$-0.227286\pi$
$458$			22.0454i			1.03011i
$459$	18.0000	+	18.0000i	0.840168	+	0.840168i
$460$		0			0
$461$	31.8434			1.48309			0.741547	−	0.670901i	$-0.234093\pi$
$461$	31.8434			1.48309			0.741547	+	0.670901i	$0.234093\pi$
$462$		0			0
$463$			14.0000i			0.650635i	0.945605	+	0.325318i	$0.105471\pi$
$463$			14.0000i			0.650635i	−0.945605	+	0.325318i	$0.894529\pi$
$464$			6.00000i			0.278543i
$465$		0			0
$466$	24.0000			1.11178
$467$			7.34847i			0.340047i	0.985440	+	0.170023i	$0.0543843\pi$
$467$			7.34847i			0.340047i	−0.985440	+	0.170023i	$0.945616\pi$
$468$			7.34847i			0.339683i
$469$	8.00000	−	19.5959i	0.369406	−	0.904855i
$470$		0			0
$471$	−9.00000	−	9.00000i	−0.414698	−	0.414698i
$472$	12.2474			0.563735
$473$		0			0
$474$	12.2474	+	12.2474i	0.562544	+	0.562544i
$475$		0			0
$476$	4.89898	−	12.0000i	0.224544	−	0.550019i
$477$		−	18.0000i		−	0.824163i
$478$			6.00000i			0.274434i
$479$	−24.4949			−1.11920			−0.559600	−	0.828763i	$-0.689045\pi$
$479$	−24.4949			−1.11920			−0.559600	+	0.828763i	$0.689045\pi$
$480$		0			0
$481$			4.89898i			0.223374i
$482$			24.4949i			1.11571i
$483$	−10.6515	−	25.3485i	−0.484661	−	1.15340i
$484$	11.0000			0.500000
$485$		0			0
$486$	−11.0227	−	11.0227i	−0.500000	−	0.500000i
$487$			32.0000i			1.45006i	0.688718	+	0.725029i	$0.258174\pi$
$487$			32.0000i			1.45006i	−0.688718	+	0.725029i	$0.741826\pi$
$488$		−	12.2474i		−	0.554416i
$489$	19.5959	−	19.5959i	0.886158	−	0.886158i
$490$		0			0
$491$		0			0		1.00000			$0$
$491$		0			0		−1.00000			$\pi$
$492$	−6.00000	−	6.00000i	−0.270501	−	0.270501i
$493$	29.3939			1.32383
$494$		−	6.00000i		−	0.269953i
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−3.00000	+	3.00000i	−0.134433	+	0.134433i
$499$	20.0000			0.895323			0.447661	−	0.894203i	$-0.352257\pi$
$499$	20.0000			0.895323			0.447661	+	0.894203i	$0.352257\pi$
$500$		0			0
$501$	6.00000	−	6.00000i	0.268060	−	0.268060i
$502$	−17.1464			−0.765283
$503$			39.1918i			1.74748i	0.486395	+	0.873739i	$0.338311\pi$
$503$			39.1918i			1.74748i	−0.486395	+	0.873739i	$0.661689\pi$
$504$	−3.00000	+	7.34847i	−0.133631	+	0.327327i
$505$		0			0
$506$		0			0
$507$	−8.57321	−	8.57321i	−0.380750	−	0.380750i
$508$		−	8.00000i		−	0.354943i
$509$	12.2474			0.542859			0.271429	−	0.962458i	$-0.412504\pi$
$509$	12.2474			0.542859			0.271429	+	0.962458i	$0.412504\pi$
$510$		0			0
$511$	−24.0000	−	9.79796i	−1.06170	−	0.433436i
$512$	1.00000			0.0441942
$513$	9.00000	+	9.00000i	0.397360	+	0.397360i
$514$		−	29.3939i		−	1.29651i
$515$		0			0
$516$	−4.89898	+	4.89898i	−0.215666	+	0.215666i
$517$		0			0
$518$	−2.00000	+	4.89898i	−0.0878750	+	0.215249i
$519$	27.0000	−	27.0000i	1.18517	−	1.18517i
$520$		0			0
$521$	−4.89898			−0.214628			−0.107314	−	0.994225i	$-0.534225\pi$
$521$	−4.89898			−0.214628			−0.107314	+	0.994225i	$0.534225\pi$
$522$	−18.0000			−0.787839
$523$	2.44949			0.107109			0.0535544	−	0.998565i	$-0.482945\pi$
$523$	2.44949			0.107109			0.0535544	+	0.998565i	$0.482945\pi$
$524$	7.34847			0.321019
$525$		0			0
$526$	24.0000			1.04645
$527$		0			0
$528$		0			0
$529$	13.0000			0.565217
$530$		0			0
$531$			36.7423i			1.59448i
$532$	2.44949	−	6.00000i	0.106199	−	0.260133i
$533$	−12.0000			−0.519778
$534$		0			0
$535$		0			0
$536$		−	8.00000i		−	0.345547i
$537$	29.3939	−	29.3939i	1.26844	−	1.26844i
$538$	12.2474			0.528025
$539$		0			0
$540$		0			0
$541$	2.00000			0.0859867			0.0429934	−	0.999075i	$-0.486311\pi$
$541$	2.00000			0.0859867			0.0429934	+	0.999075i	$0.486311\pi$
$542$		−	24.4949i		−	1.05215i
$543$	−15.0000	+	15.0000i	−0.643712	+	0.643712i
$544$		−	4.89898i		−	0.210042i
$545$		0			0
$546$	4.34847	+	10.3485i	0.186097	+	0.442874i
$547$		−	8.00000i		−	0.342055i	−0.985266	−	0.171028i	$-0.945291\pi$
$547$		−	8.00000i		−	0.342055i	0.985266	−	0.171028i	$-0.0547087\pi$
$548$	−12.0000			−0.512615
$549$	36.7423			1.56813
$550$		0			0
$551$	14.6969			0.626111
$552$	−7.34847	−	7.34847i	−0.312772	−	0.312772i
$553$	24.4949	+	10.0000i	1.04163	+	0.425243i
$554$			22.0000i			0.934690i
$555$		0			0
$556$		−	2.44949i		−	0.103882i
$557$	18.0000			0.762684			0.381342	−	0.924434i	$-0.375462\pi$
$557$	18.0000			0.762684			0.381342	+	0.924434i	$0.375462\pi$
$558$		0			0
$559$			9.79796i			0.414410i
$560$		0			0
$561$		0			0
$562$		0			0
$563$		−	22.0454i		−	0.929103i	−0.885546	−	0.464552i	$-0.846216\pi$
$563$		−	22.0454i		−	0.929103i	0.885546	−	0.464552i	$-0.153784\pi$
$564$	6.00000	−	6.00000i	0.252646	−	0.252646i
$565$		0			0
$566$	−22.0454			−0.926638
$567$	−22.0454	−	9.00000i	−0.925820	−	0.377964i
$568$		0			0
$569$			6.00000i			0.251533i	0.992060	+	0.125767i	$0.0401390\pi$
$569$			6.00000i			0.251533i	−0.992060	+	0.125767i	$0.959861\pi$
$570$		0			0
$571$	32.0000			1.33916			0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000			1.33916			0.669579	+	0.742741i	$0.266474\pi$
$572$		0			0
$573$		0			0
$574$	−12.0000	−	4.89898i	−0.500870	−	0.204479i
$575$		0			0
$576$			3.00000i			0.125000i
$577$	−19.5959			−0.815789			−0.407894	−	0.913029i	$-0.633737\pi$
$577$	−19.5959			−0.815789			−0.407894	+	0.913029i	$0.633737\pi$
$578$	−7.00000			−0.291162
$579$	−4.89898	+	4.89898i	−0.203595	+	0.203595i
$580$		0			0
$581$	−2.44949	+	6.00000i	−0.101622	+	0.248922i
$582$	6.00000	+	6.00000i	0.248708	+	0.248708i
$583$		0			0
$584$	−9.79796			−0.405442
$585$		0			0
$586$			2.44949i			0.101187i
$587$			7.34847i			0.303304i	0.988434	+	0.151652i	$0.0484593\pi$
$587$			7.34847i			0.303304i	−0.988434	+	0.151652i	$0.951541\pi$
$588$	0.123724	+	12.1237i	0.00510231	+	0.499974i
$589$		0			0
$590$		0			0
$591$	22.0454	+	22.0454i	0.906827	+	0.906827i
$592$			2.00000i			0.0821995i
$593$			39.1918i			1.60942i	0.593671	+	0.804708i	$0.297678\pi$
$593$			39.1918i			1.60942i	−0.593671	+	0.804708i	$0.702322\pi$
$594$		0			0
$595$		0			0
$596$			6.00000i			0.245770i
$597$	−12.0000	+	12.0000i	−0.491127	+	0.491127i
$598$	−14.6969			−0.601003
$599$		−	24.0000i		−	0.980613i	−0.871550	−	0.490307i	$-0.836885\pi$
$599$		−	24.0000i		−	0.980613i	0.871550	−	0.490307i	$-0.163115\pi$
$600$		0			0
$601$		0			0		1.00000			$0$
$601$		0			0		−1.00000			$\pi$
$602$	−4.00000	+	9.79796i	−0.163028	+	0.399335i
$603$	24.0000			0.977356
$604$	−8.00000			−0.325515
$605$		0			0
$606$	9.00000	+	9.00000i	0.365600	+	0.365600i
$607$	4.89898			0.198843			0.0994217	−	0.995045i	$-0.468301\pi$
$607$	4.89898			0.198843			0.0994217	+	0.995045i	$0.468301\pi$
$608$		−	2.44949i		−	0.0993399i
$609$	−25.3485	+	10.6515i	−1.02717	+	0.431622i
$610$		0			0
$611$		−	12.0000i		−	0.485468i
$612$	14.6969			0.594089
$613$			14.0000i			0.565455i	0.959200	+	0.282727i	$0.0912392\pi$
$613$			14.0000i			0.565455i	−0.959200	+	0.282727i	$0.908761\pi$
$614$	−7.34847			−0.296560
$615$		0			0
$616$		0			0
$617$	18.0000			0.724653			0.362326	−	0.932051i	$-0.381983\pi$
$617$	18.0000			0.724653			0.362326	+	0.932051i	$0.381983\pi$
$618$	−12.0000	−	12.0000i	−0.482711	−	0.482711i
$619$		−	26.9444i		−	1.08299i	−0.840705	−	0.541493i	$-0.817859\pi$
$619$		−	26.9444i		−	1.08299i	0.840705	−	0.541493i	$-0.182141\pi$
$620$		0			0
$621$	22.0454	−	22.0454i	0.884652	−	0.884652i
$622$	19.5959			0.785725
$623$		0			0
$624$	3.00000	+	3.00000i	0.120096	+	0.120096i
$625$		0			0
$626$	−34.2929			−1.37062
$627$		0			0
$628$	−7.34847			−0.293236
$629$	9.79796			0.390670
$630$		0			0
$631$	2.00000			0.0796187			0.0398094	−	0.999207i	$-0.487325\pi$
$631$	2.00000			0.0796187			0.0398094	+	0.999207i	$0.487325\pi$
$632$	10.0000			0.397779
$633$	−9.79796	−	9.79796i	−0.389434	−	0.389434i
$634$	18.0000			0.714871
$635$		0			0
$636$	−7.34847	−	7.34847i	−0.291386	−	0.291386i
$637$	12.2474	+	12.0000i	0.485262	+	0.475457i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	30.0000i		−	1.18493i	−0.805597	−	0.592464i	$-0.798155\pi$
$641$		−	30.0000i		−	1.18493i	0.805597	−	0.592464i	$-0.201845\pi$
$642$	−14.6969	−	14.6969i	−0.580042	−	0.580042i
$643$	−22.0454			−0.869386			−0.434693	−	0.900579i	$-0.643143\pi$
$643$	−22.0454			−0.869386			−0.434693	+	0.900579i	$0.643143\pi$
$644$	−14.6969	−	6.00000i	−0.579141	−	0.236433i
$645$		0			0
$646$	−12.0000			−0.472134
$647$			44.0908i			1.73339i	0.498839	+	0.866694i	$0.333760\pi$
$647$			44.0908i			1.73339i	−0.498839	+	0.866694i	$0.666240\pi$
$648$	−9.00000			−0.353553
$649$		0			0
$650$		0			0
$651$		0			0
$652$		−	16.0000i		−	0.626608i
$653$	−6.00000			−0.234798			−0.117399	−	0.993085i	$-0.537456\pi$
$653$	−6.00000			−0.234798			−0.117399	+	0.993085i	$0.537456\pi$
$654$	−12.2474	−	12.2474i	−0.478913	−	0.478913i
$655$		0			0
$656$	−4.89898			−0.191273
$657$		−	29.3939i		−	1.14676i
$658$	4.89898	−	12.0000i	0.190982	−	0.467809i
$659$			36.0000i			1.40236i	0.712984	+	0.701180i	$0.247343\pi$
$659$			36.0000i			1.40236i	−0.712984	+	0.701180i	$0.752657\pi$
$660$		0			0
$661$			12.2474i			0.476371i	0.971220	+	0.238185i	$0.0765525\pi$
$661$			12.2474i			0.476371i	−0.971220	+	0.238185i	$0.923447\pi$
$662$	−8.00000			−0.310929
$663$	14.6969	−	14.6969i	0.570782	−	0.570782i
$664$			2.44949i			0.0950586i
$665$		0			0
$666$	−6.00000			−0.232495
$667$		−	36.0000i		−	1.39393i
$668$		−	4.89898i		−	0.189547i
$669$	18.0000	+	18.0000i	0.695920	+	0.695920i
$670$		0			0
$671$		0			0
$672$	1.77526	+	4.22474i	0.0684820	+	0.162973i
$673$			34.0000i			1.31060i	0.755367	+	0.655302i	$0.227459\pi$
$673$			34.0000i			1.31060i	−0.755367	+	0.655302i	$0.772541\pi$
$674$			32.0000i			1.23259i
$675$		0			0
$676$	−7.00000			−0.269231
$677$			7.34847i			0.282425i	0.989979	+	0.141212i	$0.0451000\pi$
$677$			7.34847i			0.282425i	−0.989979	+	0.141212i	$0.954900\pi$
$678$	−7.34847	−	7.34847i	−0.282216	−	0.282216i
$679$	12.0000	+	4.89898i	0.460518	+	0.188006i
$680$		0			0
$681$	−9.00000	+	9.00000i	−0.344881	+	0.344881i
$682$		0			0
$683$	24.0000			0.918334			0.459167	−	0.888350i	$-0.348148\pi$
$683$	24.0000			0.918334			0.459167	+	0.888350i	$0.348148\pi$
$684$	7.34847			0.280976
$685$		0			0
$686$	7.34847	+	17.0000i	0.280566	+	0.649063i
$687$	−27.0000	+	27.0000i	−1.03011	+	1.03011i
$688$			4.00000i			0.152499i
$689$	−14.6969			−0.559909
$690$		0			0
$691$		−	36.7423i		−	1.39774i	−0.715246	−	0.698872i	$-0.753686\pi$
$691$		−	36.7423i		−	1.39774i	0.715246	−	0.698872i	$-0.246314\pi$
$692$		−	22.0454i		−	0.838041i
$693$		0			0
$694$	−12.0000			−0.455514
$695$		0			0
$696$	−7.34847	+	7.34847i	−0.278543	+	0.278543i
$697$			24.0000i			0.909065i
$698$		−	2.44949i		−	0.0927146i
$699$	29.3939	+	29.3939i	1.11178	+	1.11178i
$700$		0			0
$701$			30.0000i			1.13308i	0.824033	+	0.566542i	$0.191719\pi$
$701$			30.0000i			1.13308i	−0.824033	+	0.566542i	$0.808281\pi$
$702$	−9.00000	+	9.00000i	−0.339683	+	0.339683i
$703$	4.89898			0.184769
$704$		0			0
$705$		0			0
$706$		−	9.79796i		−	0.368751i
$707$	18.0000	+	7.34847i	0.676960	+	0.276368i
$708$	15.0000	+	15.0000i	0.563735	+	0.563735i
$709$	−10.0000			−0.375558			−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000			−0.375558			−0.187779	+	0.982211i	$0.560129\pi$
$710$		0			0
$711$			30.0000i			1.12509i
$712$		0			0
$713$		0			0
$714$	20.6969	−	8.69694i	0.774563	−	0.325475i
$715$		0			0
$716$		−	24.0000i		−	0.896922i
$717$	−7.34847	+	7.34847i	−0.274434	+	0.274434i
$718$			6.00000i			0.223918i
$719$	−24.4949			−0.913506			−0.456753	−	0.889594i	$-0.650988\pi$
$719$	−24.4949			−0.913506			−0.456753	+	0.889594i	$0.650988\pi$
$720$		0			0
$721$	−24.0000	−	9.79796i	−0.893807	−	0.364895i
$722$	13.0000			0.483810
$723$	−30.0000	+	30.0000i	−1.11571	+	1.11571i
$724$			12.2474i			0.455173i
$725$		0			0
$726$	13.4722	+	13.4722i	0.500000	+	0.500000i
$727$	29.3939			1.09016			0.545079	−	0.838385i	$-0.316500\pi$
$727$	29.3939			1.09016			0.545079	+	0.838385i	$0.316500\pi$
$728$	6.00000	+	2.44949i	0.222375	+	0.0907841i
$729$		−	27.0000i		−	1.00000i
$730$		0			0
$731$	19.5959			0.724781
$732$	15.0000	−	15.0000i	0.554416	−	0.554416i
$733$	−22.0454			−0.814266			−0.407133	−	0.913369i	$-0.633471\pi$
$733$	−22.0454			−0.814266			−0.407133	+	0.913369i	$0.633471\pi$
$734$	4.89898			0.180825
$735$		0			0
$736$	−6.00000			−0.221163
$737$		0			0
$738$		−	14.6969i		−	0.541002i
$739$	−20.0000			−0.735712			−0.367856	−	0.929883i	$-0.619908\pi$
$739$	−20.0000			−0.735712			−0.367856	+	0.929883i	$0.619908\pi$
$740$		0			0
$741$	7.34847	−	7.34847i	0.269953	−	0.269953i
$742$	−14.6969	−	6.00000i	−0.539542	−	0.220267i
$743$	−6.00000			−0.220119			−0.110059	−	0.993925i	$-0.535104\pi$
$743$	−6.00000			−0.220119			−0.110059	+	0.993925i	$0.535104\pi$
$744$		0			0
$745$		0			0
$746$			14.0000i			0.512576i
$747$	−7.34847			−0.268866
$748$		0			0
$749$	−29.3939	−	12.0000i	−1.07403	−	0.438470i
$750$		0			0
$751$	−8.00000			−0.291924			−0.145962	−	0.989290i	$-0.546628\pi$
$751$	−8.00000			−0.291924			−0.145962	+	0.989290i	$0.546628\pi$
$752$		−	4.89898i		−	0.178647i
$753$	−21.0000	−	21.0000i	−0.765283	−	0.765283i
$754$			14.6969i			0.535231i
$755$		0			0
$756$	−12.6742	+	5.32577i	−0.460957	+	0.193696i
$757$			2.00000i			0.0726912i	0.999339	+	0.0363456i	$0.0115717\pi$
$757$			2.00000i			0.0726912i	−0.999339	+	0.0363456i	$0.988428\pi$
$758$	20.0000			0.726433
$759$		0			0
$760$		0			0
$761$	−4.89898			−0.177588			−0.0887939	−	0.996050i	$-0.528301\pi$
$761$	−4.89898			−0.177588			−0.0887939	+	0.996050i	$0.528301\pi$
$762$	9.79796	−	9.79796i	0.354943	−	0.354943i
$763$	−24.4949	−	10.0000i	−0.886775	−	0.362024i
$764$		0			0
$765$		0			0
$766$		−	34.2929i		−	1.23905i
$767$	30.0000			1.08324
$768$	1.22474	+	1.22474i	0.0441942	+	0.0441942i
$769$			34.2929i			1.23663i	0.785930	+	0.618316i	$0.212185\pi$
$769$			34.2929i			1.23663i	−0.785930	+	0.618316i	$0.787815\pi$
$770$		0			0
$771$	36.0000	−	36.0000i	1.29651	−	1.29651i
$772$			4.00000i			0.143963i
$773$			26.9444i			0.969122i	0.874757	+	0.484561i	$0.161021\pi$
$773$			26.9444i			0.969122i	−0.874757	+	0.484561i	$0.838979\pi$
$774$	−12.0000			−0.431331
$775$		0			0
$776$	4.89898			0.175863
$777$	−8.44949	+	3.55051i	−0.303124	+	0.127374i
$778$			6.00000i			0.215110i
$779$			12.0000i			0.429945i
$780$		0			0
$781$		0			0
$782$			29.3939i			1.05112i
$783$	−22.0454	−	22.0454i	−0.787839	−	0.787839i
$784$	5.00000	+	4.89898i	0.178571	+	0.174964i
$785$		0			0
$786$	9.00000	+	9.00000i	0.321019	+	0.321019i
$787$	−31.8434			−1.13509			−0.567547	−	0.823341i	$-0.692107\pi$
$787$	−31.8434			−1.13509			−0.567547	+	0.823341i	$0.692107\pi$
$788$	18.0000			0.641223
$789$	29.3939	+	29.3939i	1.04645	+	1.04645i
$790$		0			0
$791$	−14.6969	−	6.00000i	−0.522563	−	0.213335i
$792$		0			0
$793$		−	30.0000i		−	1.06533i
$794$	−7.34847			−0.260787
$795$		0			0
$796$			9.79796i			0.347279i
$797$			7.34847i			0.260296i	0.991495	+	0.130148i	$0.0415453\pi$
$797$			7.34847i			0.260296i	−0.991495	+	0.130148i	$0.958455\pi$
$798$	10.3485	−	4.34847i	0.366332	−	0.153934i
$799$	−24.0000			−0.849059
$800$		0			0
$801$		0			0
$802$			30.0000i			1.05934i
$803$		0			0
$804$	9.79796	−	9.79796i	0.345547	−	0.345547i
$805$		0			0
$806$		0			0
$807$	15.0000	+	15.0000i	0.528025	+	0.528025i
$808$	7.34847			0.258518
$809$			6.00000i			0.210949i	0.994422	+	0.105474i	$0.0336361\pi$
$809$			6.00000i			0.210949i	−0.994422	+	0.105474i	$0.966364\pi$
$810$		0			0
$811$		−	36.7423i		−	1.29020i	−0.764099	−	0.645099i	$-0.776816\pi$
$811$		−	36.7423i		−	1.29020i	0.764099	−	0.645099i	$-0.223184\pi$
$812$	−6.00000	+	14.6969i	−0.210559	+	0.515761i
$813$	30.0000	−	30.0000i	1.05215	−	1.05215i
$814$		0			0
$815$		0			0
$816$	6.00000	−	6.00000i	0.210042	−	0.210042i
$817$	9.79796			0.342787
$818$			34.2929i			1.19902i
$819$	−7.34847	+	18.0000i	−0.256776	+	0.628971i
$820$		0			0
$821$		−	30.0000i		−	1.04701i	−0.852023	−	0.523504i	$-0.824625\pi$
$821$		−	30.0000i		−	1.04701i	0.852023	−	0.523504i	$-0.175375\pi$
$822$	−14.6969	−	14.6969i	−0.512615	−	0.512615i
$823$			14.0000i			0.488009i	0.969774	+	0.244005i	$0.0784612\pi$
$823$			14.0000i			0.488009i	−0.969774	+	0.244005i	$0.921539\pi$
$824$	−9.79796			−0.341328
$825$		0			0
$826$	30.0000	+	12.2474i	1.04383	+	0.426143i
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$		−	18.0000i		−	0.625543i
$829$		−	26.9444i		−	0.935817i	−0.883777	−	0.467909i	$-0.845008\pi$
$829$		−	26.9444i		−	0.935817i	0.883777	−	0.467909i	$-0.154992\pi$
$830$		0			0
$831$	−26.9444	+	26.9444i	−0.934690	+	0.934690i
$832$	2.44949			0.0849208
$833$	24.0000	−	24.4949i	0.831551	−	0.848698i
$834$	3.00000	−	3.00000i	0.103882	−	0.103882i
$835$		0			0
$836$		0			0
$837$		0			0
$838$	−12.2474			−0.423081
$839$	24.4949			0.845658			0.422829	−	0.906210i	$-0.361037\pi$
$839$	24.4949			0.845658			0.422829	+	0.906210i	$0.361037\pi$
$840$		0			0
$841$	−7.00000			−0.241379
$842$	2.00000			0.0689246
$843$		0			0
$844$	−8.00000			−0.275371
$845$		0			0
$846$	14.6969			0.505291
$847$	26.9444	+	11.0000i	0.925820	+	0.377964i
$848$	−6.00000			−0.206041
$849$	−27.0000	−	27.0000i	−0.926638	−	0.926638i
$850$		0			0
$851$		−	12.0000i		−	0.411355i
$852$		0			0
$853$	2.44949			0.0838689			0.0419345	−	0.999120i	$-0.486648\pi$
$853$	2.44949			0.0838689			0.0419345	+	0.999120i	$0.486648\pi$
$854$	12.2474	−	30.0000i	0.419099	−	1.02658i
$855$		0			0
$856$	−12.0000			−0.410152
$857$		−	4.89898i		−	0.167346i	−0.996493	−	0.0836730i	$-0.973335\pi$
$857$		−	4.89898i		−	0.167346i	0.996493	−	0.0836730i	$-0.0266651\pi$
$858$		0			0
$859$		−	26.9444i		−	0.919331i	−0.888092	−	0.459665i	$-0.847969\pi$
$859$		−	26.9444i		−	0.919331i	0.888092	−	0.459665i	$-0.152031\pi$
$860$		0			0
$861$	−8.69694	−	20.6969i	−0.296391	−	0.705350i
$862$			30.0000i			1.02180i
$863$	24.0000			0.816970			0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000			0.816970			0.408485	+	0.912765i	$0.366057\pi$
$864$	−3.67423	+	3.67423i	−0.125000	+	0.125000i
$865$		0			0
$866$	14.6969			0.499422
$867$	−8.57321	−	8.57321i	−0.291162	−	0.291162i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		−	19.5959i		−	0.663982i
$872$	−10.0000			−0.338643
$873$			14.6969i			0.497416i
$874$			14.6969i			0.497131i
$875$		0			0
$876$	−12.0000	−	12.0000i	−0.405442	−	0.405442i
$877$			22.0000i			0.742887i	0.928456	+	0.371444i	$0.121137\pi$
$877$			22.0000i			0.742887i	−0.928456	+	0.371444i	$0.878863\pi$
$878$		−	14.6969i		−	0.495998i
$879$	−3.00000	+	3.00000i	−0.101187	+	0.101187i
$880$		0			0
$881$	−29.3939			−0.990305			−0.495152	−	0.868806i	$-0.664888\pi$
$881$	−29.3939			−0.990305			−0.495152	+	0.868806i	$0.664888\pi$
$882$	−14.6969	+	15.0000i	−0.494872	+	0.505076i
$883$		−	56.0000i		−	1.88455i	−0.334840	−	0.942275i	$-0.608682\pi$
$883$		−	56.0000i		−	1.88455i	0.334840	−	0.942275i	$-0.391318\pi$
$884$		−	12.0000i		−	0.403604i
$885$		0			0
$886$	−36.0000			−1.20944
$887$		−	4.89898i		−	0.164492i	−0.996612	−	0.0822458i	$-0.973791\pi$
$887$		−	4.89898i		−	0.164492i	0.996612	−	0.0822458i	$-0.0262093\pi$
$888$	−2.44949	+	2.44949i	−0.0821995	+	0.0821995i
$889$	8.00000	−	19.5959i	0.268311	−	0.657226i
$890$		0			0
$891$		0			0
$892$	14.6969			0.492090
$893$	−12.0000			−0.401565
$894$	−7.34847	+	7.34847i	−0.245770	+	0.245770i
$895$		0			0
$896$	2.44949	+	1.00000i	0.0818317	+	0.0334077i
$897$	−18.0000	−	18.0000i	−0.601003	−	0.601003i
$898$			36.0000i			1.20134i
$899$		0			0
$900$		0			0
$901$			29.3939i			0.979252i
$902$		0			0
$903$	−16.8990	+	7.10102i	−0.562363	+	0.236307i
$904$	−6.00000			−0.199557
$905$		0			0
$906$	−9.79796	−	9.79796i	−0.325515	−	0.325515i
$907$		−	28.0000i		−	0.929725i	−0.885383	−	0.464862i	$-0.846104\pi$
$907$		−	28.0000i		−	0.929725i	0.885383	−	0.464862i	$-0.153896\pi$
$908$			7.34847i			0.243868i
$909$			22.0454i			0.731200i
$910$		0			0
$911$			30.0000i			0.993944i	0.867766	+	0.496972i	$0.165555\pi$
$911$			30.0000i			0.993944i	−0.867766	+	0.496972i	$0.834445\pi$
$912$	3.00000	−	3.00000i	0.0993399	−	0.0993399i
$913$		0			0
$914$		−	28.0000i		−	0.926158i
$915$		0			0
$916$			22.0454i			0.728401i
$917$	18.0000	+	7.34847i	0.594412	+	0.242668i
$918$	18.0000	+	18.0000i	0.594089	+	0.594089i
$919$	−10.0000			−0.329870			−0.164935	−	0.986304i	$-0.552741\pi$
$919$	−10.0000			−0.329870			−0.164935	+	0.986304i	$0.552741\pi$
$920$		0			0
$921$	−9.00000	−	9.00000i	−0.296560	−	0.296560i
$922$	31.8434			1.04871
$923$		0			0
$924$		0			0
$925$		0			0
$926$			14.0000i			0.460069i
$927$		−	29.3939i		−	0.965422i
$928$			6.00000i			0.196960i
$929$	24.4949			0.803652			0.401826	−	0.915716i	$-0.368376\pi$
$929$	24.4949			0.803652			0.401826	+	0.915716i	$0.368376\pi$
$930$		0			0
$931$	12.0000	−	12.2474i	0.393284	−	0.401394i
$932$	24.0000			0.786146
$933$	24.0000	+	24.0000i	0.785725	+	0.785725i
$934$			7.34847i			0.240449i
$935$		0			0
$936$			7.34847i			0.240192i
$937$	−19.5959			−0.640171			−0.320085	−	0.947389i	$-0.603712\pi$
$937$	−19.5959			−0.640171			−0.320085	+	0.947389i	$0.603712\pi$
$938$	8.00000	−	19.5959i	0.261209	−	0.639829i
$939$	−42.0000	−	42.0000i	−1.37062	−	1.37062i
$940$		0			0
$941$	31.8434			1.03806			0.519032	−	0.854755i	$-0.326293\pi$
$941$	31.8434			1.03806			0.519032	+	0.854755i	$0.326293\pi$
$942$	−9.00000	−	9.00000i	−0.293236	−	0.293236i
$943$	29.3939			0.957196
$944$	12.2474			0.398621
$945$		0			0
$946$		0			0
$947$	−12.0000			−0.389948			−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000			−0.389948			−0.194974	+	0.980808i	$0.562462\pi$
$948$	12.2474	+	12.2474i	0.397779	+	0.397779i
$949$	−24.0000			−0.779073
$950$		0			0
$951$	22.0454	+	22.0454i	0.714871	+	0.714871i
$952$	4.89898	−	12.0000i	0.158777	−	0.388922i
$953$	−36.0000			−1.16615			−0.583077	−	0.812417i	$-0.698151\pi$
$953$	−36.0000			−1.16615			−0.583077	+	0.812417i	$0.698151\pi$
$954$		−	18.0000i		−	0.582772i
$955$		0			0
$956$			6.00000i			0.194054i
$957$		0			0
$958$	−24.4949			−0.791394
$959$	−29.3939	−	12.0000i	−0.949178	−	0.387500i
$960$		0			0
$961$	31.0000			1.00000
$962$			4.89898i			0.157949i
$963$		−	36.0000i		−	1.16008i
$964$			24.4949i			0.788928i
$965$		0			0
$966$	−10.6515	−	25.3485i	−0.342707	−	0.815574i
$967$		−	8.00000i		−	0.257263i	−0.991692	−	0.128631i	$-0.958942\pi$
$967$		−	8.00000i		−	0.257263i	0.991692	−	0.128631i	$-0.0410584\pi$
$968$	11.0000			0.353553
$969$	−14.6969	−	14.6969i	−0.472134	−	0.472134i
$970$		0			0
$971$	−41.6413			−1.33633			−0.668167	−	0.744011i	$-0.732921\pi$
$971$	−41.6413			−1.33633			−0.668167	+	0.744011i	$0.732921\pi$
$972$	−11.0227	−	11.0227i	−0.353553	−	0.353553i
$973$	2.44949	−	6.00000i	0.0785270	−	0.192351i
$974$			32.0000i			1.02535i
$975$		0			0
$976$		−	12.2474i		−	0.392031i
$977$	−12.0000			−0.383914			−0.191957	−	0.981403i	$-0.561483\pi$
$977$	−12.0000			−0.383914			−0.191957	+	0.981403i	$0.561483\pi$
$978$	19.5959	−	19.5959i	0.626608	−	0.626608i
$979$		0			0
$980$		0			0
$981$		−	30.0000i		−	0.957826i
$982$		0			0
$983$		−	34.2929i		−	1.09377i	−0.837207	−	0.546886i	$-0.815813\pi$
$983$		−	34.2929i		−	1.09377i	0.837207	−	0.546886i	$-0.184187\pi$
$984$	−6.00000	−	6.00000i	−0.191273	−	0.191273i
$985$		0			0
$986$	29.3939			0.936092
$987$	20.6969	−	8.69694i	0.658791	−	0.276827i
$988$		−	6.00000i		−	0.190885i
$989$		−	24.0000i		−	0.763156i
$990$		0			0
$991$	−38.0000			−1.20711			−0.603555	−	0.797321i	$-0.706250\pi$
$991$	−38.0000			−1.20711			−0.603555	+	0.797321i	$0.706250\pi$
$992$		0			0
$993$	−9.79796	−	9.79796i	−0.310929	−	0.310929i
$994$		0			0
$995$		0			0
$996$	−3.00000	+	3.00000i	−0.0950586	+	0.0950586i
$997$	−7.34847			−0.232728			−0.116364	−	0.993207i	$-0.537124\pi$
$997$	−7.34847			−0.232728			−0.116364	+	0.993207i	$0.537124\pi$
$998$	20.0000			0.633089
$999$	−7.34847	−	7.34847i	−0.232495	−	0.232495i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.d.e.1049.4		4
3.2	odd	2		1050.2.d.b.1049.3		4
5.2	odd	4		42.2.d.a.41.4	yes	4
5.3	odd	4		1050.2.b.b.251.1		4
5.4	even	2		1050.2.d.b.1049.1		4
7.6	odd	2	inner	1050.2.d.e.1049.1		4
15.2	even	4		42.2.d.a.41.1	✓	4
15.8	even	4		1050.2.b.b.251.4		4
15.14	odd	2	inner	1050.2.d.e.1049.2		4
20.7	even	4		336.2.k.b.209.2		4
21.20	even	2		1050.2.d.b.1049.2		4
35.2	odd	12		294.2.f.b.227.4		8
35.12	even	12		294.2.f.b.227.3		8
35.13	even	4		1050.2.b.b.251.2		4
35.17	even	12		294.2.f.b.215.2		8
35.27	even	4		42.2.d.a.41.3	yes	4
35.32	odd	12		294.2.f.b.215.1		8
35.34	odd	2		1050.2.d.b.1049.4		4
40.27	even	4		1344.2.k.d.1217.3		4
40.37	odd	4		1344.2.k.c.1217.2		4
45.2	even	12		1134.2.m.g.377.1		8
45.7	odd	12		1134.2.m.g.377.4		8
45.22	odd	12		1134.2.m.g.755.2		8
45.32	even	12		1134.2.m.g.755.3		8
60.47	odd	4		336.2.k.b.209.4		4
105.2	even	12		294.2.f.b.227.2		8
105.17	odd	12		294.2.f.b.215.4		8
105.32	even	12		294.2.f.b.215.3		8
105.47	odd	12		294.2.f.b.227.1		8
105.62	odd	4		42.2.d.a.41.2	yes	4
105.83	odd	4		1050.2.b.b.251.3		4
105.104	even	2	inner	1050.2.d.e.1049.3		4
120.77	even	4		1344.2.k.c.1217.4		4
120.107	odd	4		1344.2.k.d.1217.1		4
140.27	odd	4		336.2.k.b.209.3		4
280.27	odd	4		1344.2.k.d.1217.2		4
280.237	even	4		1344.2.k.c.1217.3		4
315.97	even	12		1134.2.m.g.377.3		8
315.167	odd	12		1134.2.m.g.755.4		8
315.202	even	12		1134.2.m.g.755.1		8
315.272	odd	12		1134.2.m.g.377.2		8
420.167	even	4		336.2.k.b.209.1		4
840.587	even	4		1344.2.k.d.1217.4		4
840.797	odd	4		1344.2.k.c.1217.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.2.d.a.41.1	✓	4	15.2	even	4
42.2.d.a.41.2	yes	4	105.62	odd	4
42.2.d.a.41.3	yes	4	35.27	even	4
42.2.d.a.41.4	yes	4	5.2	odd	4
294.2.f.b.215.1		8	35.32	odd	12
294.2.f.b.215.2		8	35.17	even	12
294.2.f.b.215.3		8	105.32	even	12
294.2.f.b.215.4		8	105.17	odd	12
294.2.f.b.227.1		8	105.47	odd	12
294.2.f.b.227.2		8	105.2	even	12
294.2.f.b.227.3		8	35.12	even	12
294.2.f.b.227.4		8	35.2	odd	12
336.2.k.b.209.1		4	420.167	even	4
336.2.k.b.209.2		4	20.7	even	4
336.2.k.b.209.3		4	140.27	odd	4
336.2.k.b.209.4		4	60.47	odd	4
1050.2.b.b.251.1		4	5.3	odd	4
1050.2.b.b.251.2		4	35.13	even	4
1050.2.b.b.251.3		4	105.83	odd	4
1050.2.b.b.251.4		4	15.8	even	4
1050.2.d.b.1049.1		4	5.4	even	2
1050.2.d.b.1049.2		4	21.20	even	2
1050.2.d.b.1049.3		4	3.2	odd	2
1050.2.d.b.1049.4		4	35.34	odd	2
1050.2.d.e.1049.1		4	7.6	odd	2	inner
1050.2.d.e.1049.2		4	15.14	odd	2	inner
1050.2.d.e.1049.3		4	105.104	even	2	inner
1050.2.d.e.1049.4		4	1.1	even	1	trivial
1134.2.m.g.377.1		8	45.2	even	12
1134.2.m.g.377.2		8	315.272	odd	12
1134.2.m.g.377.3		8	315.97	even	12
1134.2.m.g.377.4		8	45.7	odd	12
1134.2.m.g.755.1		8	315.202	even	12
1134.2.m.g.755.2		8	45.22	odd	12
1134.2.m.g.755.3		8	45.32	even	12
1134.2.m.g.755.4		8	315.167	odd	12
1344.2.k.c.1217.1		4	840.797	odd	4
1344.2.k.c.1217.2		4	40.37	odd	4
1344.2.k.c.1217.3		4	280.237	even	4
1344.2.k.c.1217.4		4	120.77	even	4
1344.2.k.d.1217.1		4	120.107	odd	4
1344.2.k.d.1217.2		4	280.27	odd	4
1344.2.k.d.1217.3		4	40.27	even	4
1344.2.k.d.1217.4		4	840.587	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.22474 + 1.22474i) q^{3} +1.00000 q^{4} +(1.22474 + 1.22474i) q^{6} +(2.44949 + 1.00000i) q^{7} +1.00000 q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(1.22474 + 1.22474i) q^{3} +1.00000 q^{4} +(1.22474 + 1.22474i) q^{6} +(2.44949 + 1.00000i) q^{7} +1.00000 q^{8} +3.00000i q^{9} +(1.22474 + 1.22474i) q^{12} +2.44949 q^{13} +(2.44949 + 1.00000i) q^{14} +1.00000 q^{16} -4.89898i q^{17} +3.00000i q^{18} -2.44949i q^{19} +(1.77526 + 4.22474i) q^{21} -6.00000 q^{23} +(1.22474 + 1.22474i) q^{24} +2.44949 q^{26} +(-3.67423 + 3.67423i) q^{27} +(2.44949 + 1.00000i) q^{28} +6.00000i q^{29} +1.00000 q^{32} -4.89898i q^{34} +3.00000i q^{36} +2.00000i q^{37} -2.44949i q^{38} +(3.00000 + 3.00000i) q^{39} -4.89898 q^{41} +(1.77526 + 4.22474i) q^{42} +4.00000i q^{43} -6.00000 q^{46} -4.89898i q^{47} +(1.22474 + 1.22474i) q^{48} +(5.00000 + 4.89898i) q^{49} +(6.00000 - 6.00000i) q^{51} +2.44949 q^{52} -6.00000 q^{53} +(-3.67423 + 3.67423i) q^{54} +(2.44949 + 1.00000i) q^{56} +(3.00000 - 3.00000i) q^{57} +6.00000i q^{58} +12.2474 q^{59} -12.2474i q^{61} +(-3.00000 + 7.34847i) q^{63} +1.00000 q^{64} -8.00000i q^{67} -4.89898i q^{68} +(-7.34847 - 7.34847i) q^{69} +3.00000i q^{72} -9.79796 q^{73} +2.00000i q^{74} -2.44949i q^{76} +(3.00000 + 3.00000i) q^{78} +10.0000 q^{79} -9.00000 q^{81} -4.89898 q^{82} +2.44949i q^{83} +(1.77526 + 4.22474i) q^{84} +4.00000i q^{86} +(-7.34847 + 7.34847i) q^{87} +(6.00000 + 2.44949i) q^{91} -6.00000 q^{92} -4.89898i q^{94} +(1.22474 + 1.22474i) q^{96} +4.89898 q^{97} +(5.00000 + 4.89898i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{4} + 4 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^4 + 4 * q^8	\( 4 q + 4 q^{2} + 4 q^{4} + 4 q^{8} + 4 q^{16} + 12 q^{21} - 24 q^{23} + 4 q^{32} + 12 q^{39} + 12 q^{42} - 24 q^{46} + 20 q^{49} + 24 q^{51} - 24 q^{53} + 12 q^{57} - 12 q^{63} + 4 q^{64} + 12 q^{78} + 40 q^{79} - 36 q^{81} + 12 q^{84} + 24 q^{91} - 24 q^{92} + 20 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^4 + 4 * q^8 + 4 * q^16 + 12 * q^21 - 24 * q^23 + 4 * q^32 + 12 * q^39 + 12 * q^42 - 24 * q^46 + 20 * q^49 + 24 * q^51 - 24 * q^53 + 12 * q^57 - 12 * q^63 + 4 * q^64 + 12 * q^78 + 40 * q^79 - 36 * q^81 + 12 * q^84 + 24 * q^91 - 24 * q^92 + 20 * q^98

Introduction

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